LMFDB - Embedded newform 354.2.e.c.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,2,Mod(7,354)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(58))

chi = DirichletCharacter(H, H._module([0, 18]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("354.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	354.e (of order $29$, degree $28$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.82670423155$
Analytic rank:	$0$
Dimension:	$84$
Relative dimension:	$3$ over $\Q(\zeta_{29})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{29}]$

Embedding invariants

Embedding label			7.2
Character	$\chi$	$=$	354.7
Dual form			354.2.e.c.253.2

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.561187 - 0.827689i) q^{2} +(-0.0541389 + 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(-0.0493609 + 0.0228368i) q^{5} +(0.856857 - 0.515554i) q^{6} +(-0.676801 + 2.43762i) q^{7} +(0.976621 - 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +O(q^{10})$	\(q+(-0.561187 - 0.827689i) q^{2} +(-0.0541389 + 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(-0.0493609 + 0.0228368i) q^{5} +(0.856857 - 0.515554i) q^{6} +(-0.676801 + 2.43762i) q^{7} +(0.976621 - 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +(0.0466025 + 0.0280398i) q^{10} +(0.0375051 - 0.0355267i) q^{11} +(-0.907575 - 0.419889i) q^{12} +(-4.97780 + 0.541368i) q^{13} +(2.39740 - 0.807778i) q^{14} +(-0.0201310 - 0.0505249i) q^{15} +(-0.725995 - 0.687699i) q^{16} +(1.56763 + 5.64608i) q^{17} +(0.468408 + 0.883512i) q^{18} +(-3.72737 + 2.83347i) q^{19} +(-0.00294449 - 0.0543079i) q^{20} +(-2.39740 - 0.807778i) q^{21} +(-0.0504525 - 0.0111054i) q^{22} +(3.48218 - 6.56809i) q^{23} +(0.161782 + 0.986827i) q^{24} +(-3.23502 + 3.80856i) q^{25} +(3.24156 + 3.81626i) q^{26} +(0.161782 - 0.986827i) q^{27} +(-2.01398 - 1.53099i) q^{28} +(-4.33702 + 6.39663i) q^{29} +(-0.0305217 + 0.0450161i) q^{30} +(8.10725 + 6.16297i) q^{31} +(-0.161782 + 0.986827i) q^{32} +(0.0334442 + 0.0393735i) q^{33} +(3.79347 - 4.46602i) q^{34} +(-0.0222598 - 0.135779i) q^{35} +(0.468408 - 0.883512i) q^{36} +(0.292782 + 0.0644462i) q^{37} +(4.43698 + 1.49499i) q^{38} +(-0.271082 - 4.99981i) q^{39} +(-0.0432977 + 0.0329140i) q^{40} +(0.0856414 + 0.161537i) q^{41} +(0.676801 + 2.43762i) q^{42} +(-7.33873 - 6.95161i) q^{43} +(0.0191214 + 0.0479912i) q^{44} +(0.0515407 - 0.0173661i) q^{45} +(-7.39050 + 0.803765i) q^{46} +(1.94471 + 0.899718i) q^{47} +(0.725995 - 0.687699i) q^{48} +(0.514084 + 0.309314i) q^{49} +(4.96775 + 0.540275i) q^{50} +(-5.72267 + 1.25966i) q^{51} +(1.33955 - 4.82464i) q^{52} +(9.27118 - 5.57828i) q^{53} +(-0.907575 + 0.419889i) q^{54} +(-0.00103997 + 0.00261013i) q^{55} +(-0.136962 + 2.52612i) q^{56} +(-2.62752 - 3.87530i) q^{57} +7.72830 q^{58} +(7.00645 + 3.14795i) q^{59} +0.0543877 q^{60} +(1.89559 + 2.79578i) q^{61} +(0.551340 - 10.1689i) q^{62} +(0.936386 - 2.35015i) q^{63} +(0.907575 - 0.419889i) q^{64} +(0.233346 - 0.140399i) q^{65} +(0.0138206 - 0.0497773i) q^{66} +(2.89152 - 0.636471i) q^{67} +(-5.82532 - 0.633542i) q^{68} +(6.36994 + 3.83267i) q^{69} +(-0.0998908 + 0.0946216i) q^{70} +(-3.69390 - 1.70898i) q^{71} +(-0.994138 + 0.108119i) q^{72} +(-9.37093 + 3.15743i) q^{73} +(-0.110964 - 0.278499i) q^{74} +(-3.62783 - 3.43646i) q^{75} +(-1.25259 - 4.51141i) q^{76} +(0.0612171 + 0.115468i) q^{77} +(-3.98616 + 3.03020i) q^{78} +(-0.382833 - 7.06093i) q^{79} +(0.0515407 + 0.0173661i) q^{80} +(0.976621 + 0.214970i) q^{81} +(0.0856414 - 0.161537i) q^{82} +(-2.48735 - 15.1722i) q^{83} +(1.63778 - 1.92814i) q^{84} +(-0.206318 - 0.242896i) q^{85} +(-1.63537 + 9.97534i) q^{86} +(-6.15244 - 4.67697i) q^{87} +(0.0289911 - 0.0427586i) q^{88} +(8.24122 - 12.1549i) q^{89} +(-0.0432977 - 0.0329140i) q^{90} +(2.04933 - 12.5004i) q^{91} +(4.81272 + 5.66597i) q^{92} +(-6.59285 + 7.76171i) q^{93} +(-0.346659 - 2.11452i) q^{94} +(0.119279 - 0.224984i) q^{95} +(-0.976621 - 0.214970i) q^{96} +(-1.43577 - 0.483766i) q^{97} +(-0.0324814 - 0.599085i) q^{98} +(-0.0411264 + 0.0312635i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	$ 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) $ 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$e\left(\frac{9}{29}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.561187	−	0.827689i	−0.396819	−	0.585265i
$2$	−0.561187	−	0.827689i	−0.396819	−	0.585265i
$3$	−0.0541389	+	0.998533i	−0.0312571	+	0.576504i
$3$	−0.0541389	+	0.998533i	−0.0312571	+	0.576504i
$4$	−0.370138	+	0.928977i	−0.185069	+	0.464488i
$5$	−0.0493609	+	0.0228368i	−0.0220749	+	0.0102129i	−0.430895	−	0.902402i	$-0.641802\pi$
$5$	−0.0493609	+	0.0228368i	−0.0220749	+	0.0102129i	0.408821	+	0.912615i	$0.365940\pi$
$6$	0.856857	−	0.515554i	0.349810	−	0.210474i
$7$	−0.676801	+	2.43762i	−0.255807	+	0.921333i	0.718392	+	0.695639i	$0.244879\pi$
$7$	−0.676801	+	2.43762i	−0.255807	+	0.921333i	−0.974198	+	0.225694i	$0.927535\pi$
$8$	0.976621	−	0.214970i	0.345288	−	0.0760035i
$9$	−0.994138	−	0.108119i	−0.331379	−	0.0360397i
$10$	0.0466025	+	0.0280398i	0.0147370	+	0.00886696i
$11$	0.0375051	−	0.0355267i	0.0113082	−	0.0107117i	−0.682024	−	0.731329i	$-0.738900\pi$
$11$	0.0375051	−	0.0355267i	0.0113082	−	0.0107117i	0.693333	+	0.720618i	$0.256142\pi$
$12$	−0.907575	−	0.419889i	−0.261994	−	0.121212i
$13$	−4.97780	+	0.541368i	−1.38059	+	0.150148i	−0.768101	−	0.640329i	$-0.778798\pi$
$13$	−4.97780	+	0.541368i	−1.38059	+	0.150148i	−0.612492	+	0.790477i	$0.709833\pi$
$14$	2.39740	−	0.807778i	0.640732	−	0.215888i
$15$	−0.0201310	−	0.0505249i	−0.00519779	−	0.0130455i
$16$	−0.725995	−	0.687699i	−0.181499	−	0.171925i
$17$	1.56763	+	5.64608i	0.380205	+	1.36938i	0.868063	+	0.496453i	$0.165365\pi$
$17$	1.56763	+	5.64608i	0.380205	+	1.36938i	−0.487858	+	0.872923i	$0.662222\pi$
$18$	0.468408	+	0.883512i	0.110405	+	0.208246i
$19$	−3.72737	+	2.83347i	−0.855116	+	0.650042i	−0.938045	−	0.346513i	$-0.887366\pi$
$19$	−3.72737	+	2.83347i	−0.855116	+	0.650042i	0.0829289	+	0.996555i	$0.473573\pi$
$20$	−0.00294449	−	0.0543079i	−0.000658408	−	0.0121436i
$21$	−2.39740	−	0.807778i	−0.523156	−	0.176272i
$22$	−0.0504525	−	0.0111054i	−0.0107565	−	0.00236769i
$23$	3.48218	−	6.56809i	0.726085	−	1.36954i	−0.195242	−	0.980755i	$-0.562549\pi$
$23$	3.48218	−	6.56809i	0.726085	−	1.36954i	0.921328	−	0.388787i	$-0.127106\pi$
$24$	0.161782	+	0.986827i	0.0330236	+	0.201435i
$25$	−3.23502	+	3.80856i	−0.647003	+	0.761711i
$26$	3.24156	+	3.81626i	0.635722	+	0.748430i
$27$	0.161782	−	0.986827i	0.0311350	−	0.189915i
$28$	−2.01398	−	1.53099i	−0.380606	−	0.289329i
$29$	−4.33702	+	6.39663i	−0.805364	+	1.18782i	0.173805	+	0.984780i	$0.444394\pi$
$29$	−4.33702	+	6.39663i	−0.805364	+	1.18782i	−0.979170	+	0.203044i	$0.934917\pi$
$30$	−0.0305217	+	0.0450161i	−0.00557247	+	0.00821878i
$31$	8.10725	+	6.16297i	1.45611	+	1.10690i	0.972854	+	0.231421i	$0.0743376\pi$
$31$	8.10725	+	6.16297i	1.45611	+	1.10690i	0.483252	+	0.875481i	$0.339456\pi$
$32$	−0.161782	+	0.986827i	−0.0285993	+	0.174448i
$33$	0.0334442	+	0.0393735i	0.00582188	+	0.00685405i
$34$	3.79347	−	4.46602i	0.650575	−	0.765916i
$35$	−0.0222598	−	0.135779i	−0.00376260	−	0.0229508i
$36$	0.468408	−	0.883512i	0.0780681	−	0.147252i
$37$	0.292782	+	0.0644462i	0.0481330	+	0.0105949i	0.238972	−	0.971027i	$-0.423190\pi$
$37$	0.292782	+	0.0644462i	0.0481330	+	0.0105949i	−0.190839	+	0.981621i	$0.561121\pi$
$38$	4.43698	+	1.49499i	0.719773	+	0.242520i
$39$	−0.271082	−	4.99981i	−0.0434078	−	0.800610i
$40$	−0.0432977	+	0.0329140i	−0.00684596	+	0.00520416i
$41$	0.0856414	+	0.161537i	0.0133749	+	0.0252278i	0.890109	−	0.455747i	$-0.150628\pi$
$41$	0.0856414	+	0.161537i	0.0133749	+	0.0252278i	−0.876735	+	0.480975i	$0.840283\pi$
$42$	0.676801	+	2.43762i	0.104433	+	0.376132i
$43$	−7.33873	−	6.95161i	−1.11915	−	1.06011i	−0.997719	−	0.0675108i	$-0.978494\pi$
$43$	−7.33873	−	6.95161i	−1.11915	−	1.06011i	−0.121427	−	0.992600i	$-0.538747\pi$
$44$	0.0191214	+	0.0479912i	0.00288267	+	0.00723495i
$45$	0.0515407	−	0.0173661i	0.00768323	−	0.00258878i
$46$	−7.39050	+	0.803765i	−1.08967	+	0.118509i
$47$	1.94471	+	0.899718i	0.283665	+	0.131237i	0.556563	−	0.830806i	$-0.312120\pi$
$47$	1.94471	+	0.899718i	0.283665	+	0.131237i	−0.272898	+	0.962043i	$0.587982\pi$
$48$	0.725995	−	0.687699i	0.104788	−	0.0992609i
$49$	0.514084	+	0.309314i	0.0734406	+	0.0441877i
$50$	4.96775	+	0.540275i	0.702546	+	0.0764065i
$51$	−5.72267	+	1.25966i	−0.801334	+	0.176387i
$52$	1.33955	−	4.82464i	0.185763	−	0.669057i
$53$	9.27118	−	5.57828i	1.27349	−	0.766236i	0.291760	−	0.956492i	$-0.405759\pi$
$53$	9.27118	−	5.57828i	1.27349	−	0.766236i	0.981735	+	0.190256i	$0.0609317\pi$
$54$	−0.907575	+	0.419889i	−0.123505	+	0.0571397i
$55$	−0.00103997	+	0.00261013i	−0.000140230	+	0.000351950i
$56$	−0.136962	+	2.52612i	−0.0183023	+	0.337567i
$57$	−2.62752	−	3.87530i	−0.348023	−	0.513296i
$58$	7.72830			1.01477
$59$	7.00645	+	3.14795i	0.912163	+	0.409828i
$59$	7.00645	+	3.14795i	0.912163	+	0.409828i
$60$	0.0543877			0.00702142
$61$	1.89559	+	2.79578i	0.242705	+	0.357963i	0.929458	−	0.368928i	$-0.120275\pi$
$61$	1.89559	+	2.79578i	0.242705	+	0.357963i	−0.686753	+	0.726891i	$0.740965\pi$
$62$	0.551340	−	10.1689i	0.0700202	−	1.29145i
$63$	0.936386	−	2.35015i	0.117974	−	0.296091i
$64$	0.907575	−	0.419889i	0.113447	−	0.0524861i
$65$	0.233346	−	0.140399i	0.0289430	−	0.0174144i
$66$	0.0138206	−	0.0497773i	0.00170120	−	0.00612716i
$67$	2.89152	−	0.636471i	0.353255	−	0.0777573i	−0.0347980	−	0.999394i	$-0.511079\pi$
$67$	2.89152	−	0.636471i	0.353255	−	0.0777573i	0.388053	+	0.921637i	$0.373148\pi$
$68$	−5.82532	−	0.633542i	−0.706424	−	0.0768282i
$69$	6.36994	+	3.83267i	0.766851	+	0.461399i
$70$	−0.0998908	+	0.0946216i	−0.0119392	+	0.0113094i
$71$	−3.69390	−	1.70898i	−0.438385	−	0.202819i	0.188266	−	0.982118i	$-0.439713\pi$
$71$	−3.69390	−	1.70898i	−0.438385	−	0.202819i	−0.626652	+	0.779299i	$0.715575\pi$
$72$	−0.994138	+	0.108119i	−0.117160	+	0.0127419i
$73$	−9.37093	+	3.15743i	−1.09678	+	0.369550i	−0.808799	−	0.588085i	$-0.799882\pi$
$73$	−9.37093	+	3.15743i	−1.09678	+	0.369550i	−0.287985	+	0.957635i	$0.592985\pi$
$74$	−0.110964	−	0.278499i	−0.0128993	−	0.0323748i
$75$	−3.62783	−	3.43646i	−0.418906	−	0.396809i
$76$	−1.25259	−	4.51141i	−0.143682	−	0.517494i
$77$	0.0612171	+	0.115468i	0.00697633	+	0.0131588i
$78$	−3.98616	+	3.03020i	−0.451343	+	0.343102i
$79$	−0.382833	−	7.06093i	−0.0430720	−	0.794417i	−0.937666	−	0.347537i	$-0.887018\pi$
$79$	−0.382833	−	7.06093i	−0.0430720	−	0.794417i	0.894594	−	0.446880i	$-0.147465\pi$
$80$	0.0515407	+	0.0173661i	0.00576242	+	0.00194159i
$81$	0.976621	+	0.214970i	0.108513	+	0.0238856i
$82$	0.0856414	−	0.161537i	0.00945751	−	0.0178388i
$83$	−2.48735	−	15.1722i	−0.273022	−	1.66536i	−0.666105	−	0.745858i	$-0.732040\pi$
$83$	−2.48735	−	15.1722i	−0.273022	−	1.66536i	0.393083	−	0.919503i	$-0.371408\pi$
$84$	1.63778	−	1.92814i	0.178696	−	0.210377i
$85$	−0.206318	−	0.242896i	−0.0223783	−	0.0263458i
$86$	−1.63537	+	9.97534i	−0.176347	+	1.07567i
$87$	−6.15244	−	4.67697i	−0.659611	−	0.501423i
$88$	0.0289911	−	0.0427586i	0.00309046	−	0.00455809i
$89$	8.24122	−	12.1549i	0.873568	−	1.28842i	−0.0828943	−	0.996558i	$-0.526416\pi$
$89$	8.24122	−	12.1549i	0.873568	−	1.28842i	0.956462	−	0.291857i	$-0.0942733\pi$
$90$	−0.0432977	−	0.0329140i	−0.00456397	−	0.00346944i
$91$	2.04933	−	12.5004i	0.214828	−	1.31039i
$92$	4.81272	+	5.66597i	0.501761	+	0.590718i
$93$	−6.59285	+	7.76171i	−0.683647	+	0.804851i
$94$	−0.346659	−	2.11452i	−0.0357551	−	0.218097i
$95$	0.119279	−	0.224984i	0.0122378	−	0.0230828i
$96$	−0.976621	−	0.214970i	−0.0996759	−	0.0219403i
$97$	−1.43577	−	0.483766i	−0.145780	−	0.0491190i	0.245466	−	0.969405i	$-0.421059\pi$
$97$	−1.43577	−	0.483766i	−0.145780	−	0.0491190i	−0.391246	+	0.920286i	$0.627956\pi$
$98$	−0.0324814	−	0.599085i	−0.00328112	−	0.0605167i
$99$	−0.0411264	+	0.0312635i	−0.00413336	+	0.00314210i
$100$	−2.34066	−	4.41495i	−0.234066	−	0.441495i
$101$	0.269281	+	0.969863i	0.0267945	+	0.0965050i	0.975738	−	0.218940i	$-0.0702600\pi$
$101$	0.269281	+	0.969863i	0.0267945	+	0.0965050i	−0.948944	+	0.315445i	$0.897846\pi$
$102$	4.25409	+	4.02969i	0.421218	+	0.398999i
$103$	0.0346054	+	0.0868530i	0.00340977	+	0.00855788i	0.930672	−	0.365855i	$-0.119223\pi$
$103$	0.0346054	+	0.0868530i	0.00340977	+	0.00855788i	−0.927262	+	0.374413i	$0.877844\pi$
$104$	−4.74504	+	1.59879i	−0.465290	+	0.156774i
$105$	0.136785	−	0.0148763i	0.0133488	−	0.00145177i
$106$	−9.81995	−	4.54319i	−0.953798	−	0.441274i
$107$	−7.98102	+	7.56002i	−0.771554	+	0.730855i	−0.968352	−	0.249589i	$-0.919704\pi$
$107$	−7.98102	+	7.56002i	−0.771554	+	0.730855i	0.196798	+	0.980444i	$0.436946\pi$
$108$	0.856857	+	0.515554i	0.0824511	+	0.0496092i
$109$	10.8573	+	1.18080i	1.03994	+	0.113100i	0.612120	−	0.790765i	$-0.290317\pi$
$109$	10.8573	+	1.18080i	1.03994	+	0.113100i	0.427818	+	0.903865i	$0.359282\pi$
$110$	0.00274399		0.000603999i	0.000261630		5.75890e-5i
$111$	−0.0802025	+	0.288863i	−0.00761249	+	0.0274177i
$112$	2.16770	−	1.30426i	0.204829	−	0.123241i
$113$	−9.16498	+	4.24017i	−0.862169	+	0.398882i	−0.800584	−	0.599220i	$-0.795477\pi$
$113$	−9.16498	+	4.24017i	−0.862169	+	0.398882i	−0.0615845	+	0.998102i	$0.519615\pi$
$114$	−1.73301	+	4.34954i	−0.162312	+	0.407371i
$115$	−0.0218896	+	0.403729i	−0.00204121	+	0.0376479i
$116$	−4.33702	−	6.39663i	−0.402682	−	0.593912i
$117$	5.00715			0.462911
$118$	−1.32641	−	7.56575i	−0.122106	−	0.696484i
$119$	−14.8240			−1.35891
$120$	−0.0305217	−	0.0450161i	−0.00278623	−	0.00410939i
$121$	−0.595384	+	10.9812i	−0.0541258	+	0.998291i
$122$	1.25026	−	3.13791i	0.113193	−	0.284093i
$123$	−0.165936	+	0.0767704i	−0.0149620	+	0.00692215i
$124$	−8.72606	+	5.25030i	−0.783624	+	0.471491i
$125$	0.145459	−	0.523898i	0.0130103	−	0.0468588i
$126$	−2.47068	+	0.543838i	−0.220106	+	0.0484490i
$127$	16.1561	+	1.75708i	1.43362	+	0.155916i	0.791727	−	0.610875i	$-0.209182\pi$
$127$	16.1561	+	1.75708i	1.43362	+	0.155916i	0.641897	+	0.766791i	$0.278148\pi$
$128$	−0.856857	−	0.515554i	−0.0757362	−	0.0455690i
$129$	7.33873	−	6.95161i	0.646139	−	0.612055i
$130$	−0.247158	−	0.114347i	−0.0216771	−	0.0100289i
$131$	7.11351	−	0.773640i	0.621510	−	0.0675933i	0.208054	−	0.978117i	$-0.433287\pi$
$131$	7.11351	−	0.773640i	0.621510	−	0.0675933i	0.413456	+	0.910524i	$0.364322\pi$
$132$	−0.0489560	+	0.0164952i	−0.00426108	+	0.00143572i
$133$	−4.38423	−	11.0036i	−0.380161	−	0.954132i
$134$	−2.14948	−	2.03610i	−0.185687	−	0.175892i
$135$	0.0145502	+	0.0524053i	0.00125229	+	0.00451033i
$136$	2.74472	+	5.17709i	0.235358	+	0.443932i
$137$	2.94557	−	2.23916i	0.251657	−	0.191304i	−0.471739	−	0.881738i	$-0.656373\pi$
$137$	2.94557	−	2.23916i	0.251657	−	0.191304i	0.723395	+	0.690434i	$0.242580\pi$
$138$	−0.402473	−	7.42317i	−0.0342607	−	0.631902i
$139$	20.7315	+	6.98526i	1.75842	+	0.592482i	0.998354	−	0.0573596i	$-0.0182682\pi$
$139$	20.7315	+	6.98526i	1.75842	+	0.592482i	0.760070	+	0.649841i	$0.225165\pi$
$140$	0.134375	+	0.0295781i	0.0113567	+	0.00249981i
$141$	−1.00368	+	1.89315i	−0.0845254	+	0.159432i
$142$	0.658465	+	4.01646i	0.0552572	+	0.337054i
$143$	−0.167460	+	0.197149i	−0.0140037	+	0.0164864i
$144$	0.647386	+	0.762162i	0.0539489	+	0.0635135i
$145$	0.0680009	−	0.414787i	0.00564717	−	0.0344462i
$146$	7.87222	+	5.98431i	0.651509	+	0.495265i
$147$	−0.336692	+	0.496584i	−0.0277699	+	0.0409576i
$148$	−0.168239	+	0.248134i	−0.0138291	+	0.0203965i
$149$	3.07820	+	2.33999i	0.252176	+	0.191699i	0.723623	−	0.690195i	$-0.242475\pi$
$149$	3.07820	+	2.33999i	0.252176	+	0.191699i	−0.471448	+	0.881894i	$0.656268\pi$
$150$	−0.808431	+	4.93121i	−0.0660081	+	0.402632i
$151$	7.01021	+	8.25306i	0.570483	+	0.671625i	0.969435	−	0.245347i	$-0.0789019\pi$
$151$	7.01021	+	8.25306i	0.570483	+	0.671625i	−0.398952	+	0.916972i	$0.630626\pi$
$152$	−3.03111	+	3.56850i	−0.245855	+	0.289443i
$153$	−0.947989	−	5.78248i	−0.0766404	−	0.467485i
$154$	0.0612171	−	0.115468i	0.00493301	−	0.00930465i
$155$	−0.540924	−	0.119066i	−0.0434481	−	0.00956364i
$156$	4.74504	+	1.59879i	0.379907	+	0.128006i
$157$	0.537099	+	9.90621i	0.0428652	+	0.790601i	0.938388	+	0.345585i	$0.112319\pi$
$157$	0.537099	+	9.90621i	0.0428652	+	0.790601i	−0.895522	+	0.445016i	$0.853198\pi$
$158$	−5.62942	+	4.27937i	−0.447852	+	0.340448i
$159$	5.06817	+	9.55958i	0.401932	+	0.758124i
$160$	−0.0145502	−	0.0524053i	−0.00115030	−	0.00414300i
$161$	13.6538	+	12.9335i	1.07607	+	1.01930i
$162$	−0.370138	−	0.928977i	−0.0290808	−	0.0729873i
$163$	−10.7534	+	3.62325i	−0.842273	+	0.283795i	−0.707176	−	0.707038i	$-0.750031\pi$
$163$	−10.7534	+	3.62325i	−0.842273	+	0.283795i	−0.135097	+	0.990832i	$0.543135\pi$
$164$	−0.181763	+	0.0197679i	−0.0141933	+	0.00154362i
$165$	−0.00255000	−	0.00117976i	−0.000198517	−	9.18438e-5i
$166$	−11.1620	+	10.5732i	−0.866336	+	0.820637i
$167$	8.95150	+	5.38594i	0.692688	+	0.416776i	0.817905	−	0.575353i	$-0.195135\pi$
$167$	8.95150	+	5.38594i	0.692688	+	0.416776i	−0.125218	+	0.992129i	$0.539963\pi$
$168$	−2.51500	−	0.273523i	−0.194036	−	0.0211027i
$169$	11.7893	−	2.59503i	0.906871	−	0.199617i
$170$	−0.0852596	+	0.307077i	−0.00653911	+	0.0235518i
$171$	4.01187	−	2.41386i	0.306795	−	0.184593i
$172$	9.17423	−	4.24445i	0.699529	−	0.323636i
$173$	−5.35868	+	13.4493i	−0.407413	+	1.02253i	0.571926	+	0.820305i	$0.306196\pi$
$173$	−5.35868	+	13.4493i	−0.407413	+	1.02253i	−0.979339	+	0.202224i	$0.935183\pi$
$174$	−0.418402	+	7.71696i	−0.0317189	+	0.585021i
$175$	−7.09434	−	10.4634i	−0.536281	−	0.790956i
$176$	−0.0516603			−0.00389404
$177$	−3.52266	+	6.82575i	−0.264779	+	0.513055i
$178$	−14.6853			−1.10071
$179$	−9.27630	−	13.6815i	−0.693343	−	1.02260i	−0.997547	−	0.0699979i	$-0.977701\pi$
$179$	−9.27630	−	13.6815i	−0.693343	−	1.02260i	0.304204	−	0.952607i	$-0.401610\pi$
$180$	−0.00294449	+	0.0543079i	−0.000219469	+	0.00404787i
$181$	−0.187405	+	0.470351i	−0.0139297	+	0.0349609i	−0.935777	−	0.352592i	$-0.885300\pi$
$181$	−0.187405	+	0.470351i	−0.0139297	+	0.0349609i	0.921847	+	0.387553i	$0.126680\pi$
$182$	−11.4965	+	5.31883i	−0.852175	+	0.394258i
$183$	−2.89430	+	1.74145i	−0.213953	+	0.128731i
$184$	1.98883	−	7.16310i	0.146618	−	0.528071i
$185$	−0.0159237	+	0.00350508i	−0.00117074	+	0.000257698i
$186$	10.1241	+	1.10106i	0.742335	+	0.0807338i
$187$	0.259381	+	0.156064i	0.0189678	+	0.0114126i
$188$	−1.55563	+	1.47357i	−0.113456	+	0.107471i
$189$	2.29601	+	1.06225i	0.167010	+	0.0772671i
$190$	−0.253154	+	0.0275322i	−0.0183657	+	0.00199740i
$191$	−7.26326	+	2.44728i	−0.525551	+	0.177079i	−0.569556	−	0.821953i	$-0.692885\pi$
$191$	−7.26326	+	2.44728i	−0.525551	+	0.177079i	0.0440049	+	0.999031i	$0.485988\pi$
$192$	0.370138	+	0.928977i	0.0267124	+	0.0670431i
$193$	10.5832	+	10.0250i	0.761798	+	0.721613i	0.966347	−	0.257243i	$-0.0828142\pi$
$193$	10.5832	+	10.0250i	0.761798	+	0.721613i	−0.204549	+	0.978856i	$0.565573\pi$
$194$	0.405326	+	1.45985i	0.0291007	+	0.104811i
$195$	0.127560	+	0.240604i	0.00913479	+	0.0172300i
$196$	−0.477628	+	0.363083i	−0.0341163	+	0.0259345i
$197$	0.825110	+	15.2183i	0.0587867	+	1.08426i	0.867943	+	0.496663i	$0.165442\pi$
$197$	0.825110	+	15.2183i	0.0587867	+	1.08426i	−0.809157	+	0.587593i	$0.800076\pi$
$198$	0.0489560	+	0.0164952i	0.00347915	+	0.00117226i
$199$	19.6447	+	4.32412i	1.39257	+	0.306529i	0.847026	−	0.531551i	$-0.178391\pi$
$199$	19.6447	+	4.32412i	1.39257	+	0.306529i	0.545548	+	0.838080i	$0.316322\pi$
$200$	−2.34066	+	4.41495i	−0.165509	+	0.312184i
$201$	0.478994	+	2.92173i	0.0337856	+	0.206083i
$202$	0.651628	−	0.767156i	0.0458484	−	0.0539769i
$203$	−12.6572	−	14.9012i	−0.888363	−	1.04586i
$204$	0.947989	−	5.78248i	0.0663725	−	0.404854i
$205$	−0.00791632	−	0.00601783i	−0.000552900	−	0.000420303i
$206$	0.0524672	−	0.0773833i	0.00365556	−	0.00539155i
$207$	−4.17191	+	6.15310i	−0.289968	+	0.427670i
$208$	3.98616	+	3.03020i	0.276390	+	0.210106i
$209$	−0.0391314	+	0.238691i	−0.00270677	+	0.0165106i
$210$	−0.0890749	−	0.104867i	−0.00614675	−	0.00723651i
$211$	1.39867	−	1.64664i	0.0962885	−	0.113360i	−0.711907	−	0.702273i	$-0.752168\pi$
$211$	1.39867	−	1.64664i	0.0962885	−	0.113360i	0.808196	+	0.588914i	$0.200444\pi$
$212$	1.75048	+	10.6774i	0.120223	+	0.733330i
$213$	1.90646	−	3.59596i	0.130628	−	0.246391i
$214$	10.7362	+	2.36321i	0.733911	+	0.161546i
$215$	0.520999	+	0.175545i	0.0355318	+	0.0119721i
$216$	−0.0541389	−	0.998533i	−0.00368369	−	0.0679416i
$217$	−20.5100	+	15.5913i	−1.39231	+	1.05840i
$218$	−5.11563	−	9.64910i	−0.346474	−	0.653520i
$219$	−2.64547	−	9.52813i	−0.178764	−	0.643851i
$220$	−0.00203982	−	0.00193222i	−0.000137524	−	0.000130270i
$221$	−10.8599	−	27.2564i	−0.730519	−	1.83346i
$222$	0.284098	−	0.0957237i	0.0190674	−	0.00642455i
$223$	−4.16142	+	0.452582i	−0.278669	+	0.0303071i	−0.246386	−	0.969172i	$-0.579243\pi$
$223$	−4.16142	+	0.452582i	−0.278669	+	0.0303071i	−0.0322828	+	0.999479i	$0.510278\pi$
$224$	−2.29601	−	1.06225i	−0.153409	−	0.0709744i
$225$	3.62783	−	3.43646i	0.241855	−	0.229098i
$226$	8.65281	+	5.20622i	0.575576	+	0.346313i
$227$	−12.6563	−	1.37646i	−0.840028	−	0.0913585i	−0.322018	−	0.946733i	$-0.604361\pi$
$227$	−12.6563	−	1.37646i	−0.840028	−	0.0913585i	−0.518010	+	0.855375i	$0.673327\pi$
$228$	4.57261	−	1.00651i	0.302828	−	0.0666576i
$229$	−1.49299	+	5.37726i	−0.0986595	+	0.355339i	−0.996358	−	0.0852713i	$-0.972824\pi$
$229$	−1.49299	+	5.37726i	−0.0986595	+	0.355339i	0.897698	+	0.440611i	$0.145238\pi$
$230$	0.346446	−	0.208450i	0.0228440	−	0.0137448i
$231$	−0.118613	+	0.0548760i	−0.00780413	+	0.00361058i
$232$	−2.86054	+	7.17941i	−0.187803	+	0.471351i
$233$	−0.388057	+	7.15729i	−0.0254225	+	0.468890i	0.957909	+	0.287070i	$0.0926814\pi$
$233$	−0.388057	+	7.15729i	−0.0254225	+	0.468890i	−0.983332	+	0.181819i	$0.941801\pi$
$234$	−2.80995	−	4.14436i	−0.183692	−	0.270925i
$235$	−0.116539			−0.00760219
$236$	−5.51773	+	5.34366i	−0.359174	+	0.347842i
$237$	7.07130			0.459331
$238$	8.31901	+	12.2696i	0.539242	+	0.795322i
$239$	0.828543	−	15.2816i	0.0535940	−	0.988483i	−0.840840	−	0.541283i	$-0.817939\pi$
$239$	0.828543	−	15.2816i	0.0535940	−	0.988483i	0.894434	−	0.447199i	$-0.147579\pi$
$240$	−0.0201310	+	0.0505249i	−0.00129945	+	0.00326137i
$241$	−25.0313	+	11.5807i	−1.61241	+	0.745979i	−0.999039	−	0.0438189i	$-0.986048\pi$
$241$	−25.0313	+	11.5807i	−1.61241	+	0.745979i	−0.613367	+	0.789798i	$0.710185\pi$
$242$	9.42314	−	5.66972i	0.605743	−	0.364463i
$243$	−0.267528	+	0.963550i	−0.0171620	+	0.0618118i
$244$	−3.29884	+	0.726130i	−0.211187	+	0.0464857i
$245$	−0.0324394	−	0.00352800i	−0.00207248	−	0.000225396i
$246$	0.156663	+	0.0942612i	0.00998849	+	0.00600987i
$247$	17.0201	−	16.1223i	1.08296	−	1.02584i
$248$	9.24257	+	4.27607i	0.586904	+	0.271531i
$249$	15.2846	−	1.66230i	0.968620	−	0.105344i
$250$	−0.515254	+	0.173609i	−0.0325875	+	0.0109800i
$251$	−0.298557	−	0.749321i	−0.0188447	−	0.0472967i	0.919253	−	0.393667i	$-0.128794\pi$
$251$	−0.298557	−	0.749321i	−0.0188447	−	0.0472967i	−0.938098	+	0.346370i	$0.887414\pi$
$252$	1.83664	+	1.73976i	0.115698	+	0.109595i
$253$	−0.102743	−	0.370048i	−0.00645942	−	0.0232647i
$254$	−7.61229	−	14.3583i	−0.477637	−	0.900920i
$255$	0.253710	−	0.192865i	0.0158879	−	0.0120777i
$256$	0.0541389	+	0.998533i	0.00338368	+	0.0624083i
$257$	−7.77321	−	2.61910i	−0.484879	−	0.163375i	0.0662360	−	0.997804i	$-0.478901\pi$
$257$	−7.77321	−	2.61910i	−0.484879	−	0.163375i	−0.551115	+	0.834429i	$0.685798\pi$
$258$	−9.87217	−	2.17303i	−0.614615	−	0.135287i
$259$	−0.355250	+	0.670073i	−0.0220742	+	0.0416363i
$260$	0.0440576	+	0.268740i	0.00273234	+	0.0166665i
$261$	5.00319	−	5.89021i	0.309690	−	0.364595i
$262$	−4.63234	−	5.45361i	−0.286187	−	0.336925i
$263$	−0.373678	+	2.27933i	−0.0230419	+	0.140550i	−0.995842	−	0.0910964i	$-0.970963\pi$
$263$	−0.373678	+	2.27933i	−0.0230419	+	0.140550i	0.972800	+	0.231646i	$0.0744111\pi$
$264$	0.0411264	+	0.0312635i	0.00253115	+	0.00192413i
$265$	−0.330244	+	0.487073i	−0.0202867	+	0.0299207i
$266$	−6.64717	+	9.80385i	−0.407564	+	0.601112i
$267$	11.6909	+	8.88719i	0.715471	+	0.543887i
$268$	−0.478994	+	2.92173i	−0.0292592	+	0.178473i
$269$	5.91513	+	6.96382i	0.360652	+	0.424592i	0.912324	−	0.409469i	$-0.134286\pi$
$269$	5.91513	+	6.96382i	0.360652	+	0.424592i	−0.551672	+	0.834061i	$0.686010\pi$
$270$	0.0352098	−	0.0414522i	0.00214280	−	0.00252270i
$271$	−3.39929	−	20.7347i	−0.206492	−	1.25955i	−0.862991	−	0.505219i	$-0.831412\pi$
$271$	−3.39929	−	20.7347i	−0.206492	−	1.25955i	0.656499	−	0.754327i	$-0.272037\pi$
$272$	2.74472	−	5.17709i	0.166423	−	0.313907i
$273$	12.3711	+	2.72308i	0.748732	+	0.164808i
$274$	−3.50634	−	1.18142i	−0.211826	−	0.0713724i
$275$	0.0139759	+	0.257770i	0.000842777	+	0.0155441i
$276$	−5.91822	+	4.49891i	−0.356235	+	0.270803i
$277$	−14.4001	−	27.1615i	−0.865218	−	1.63197i	−0.771369	−	0.636388i	$-0.780428\pi$
$277$	−14.4001	−	27.1615i	−0.865218	−	1.63197i	−0.0938485	−	0.995586i	$-0.529917\pi$
$278$	−5.85263	−	21.0793i	−0.351018	−	1.26425i
$279$	−7.39339	−	7.00339i	−0.442631	−	0.419282i
$280$	−0.0509279	−	0.127819i	−0.00304352	−	0.00763867i
$281$	−0.793420	+	0.267334i	−0.0473315	+	0.0159478i	−0.342868	−	0.939384i	$-0.611398\pi$
$281$	−0.793420	+	0.267334i	−0.0473315	+	0.0159478i	0.295536	+	0.955332i	$0.404502\pi$
$282$	2.13019	−	0.231672i	0.126851	−	0.0137959i
$283$	7.94546	+	3.67596i	0.472308	+	0.218513i	0.641580	−	0.767056i	$-0.278279\pi$
$283$	7.94546	+	3.67596i	0.472308	+	0.218513i	−0.169271	+	0.985569i	$0.554141\pi$
$284$	2.95486	−	2.79899i	0.175339	−	0.166089i
$285$	0.218196	+	0.131284i	0.0129248	+	0.00777661i
$286$	0.257154	+	0.0279672i	0.0152059	+	0.00165374i
$287$	−0.451727	+	0.0994326i	−0.0266646	+	0.00586932i
$288$	0.267528	−	0.963550i	0.0157643	−	0.0567777i
$289$	−14.8542	+	8.93749i	−0.873778	+	0.525735i
$290$	−0.381476	+	0.176490i	−0.0224010	+	0.0103638i
$291$	0.560788	−	1.40747i	0.0328740	−	0.0825074i
$292$	0.535356	−	9.87406i	0.0313294	−	0.577836i
$293$	−14.6597	−	21.6214i	−0.856428	−	1.26314i	−0.963182	−	0.268851i	$-0.913356\pi$
$293$	−14.6597	−	21.6214i	−0.856428	−	1.26314i	0.106754	−	0.994285i	$-0.465954\pi$
$294$	0.599965			0.0349907
$295$	−0.417734	+	0.00461913i	−0.0243214	+	0.000268936i
$296$	0.299791			0.0174250
$297$	−0.0289911	−	0.0427586i	−0.00168223	−	0.00248111i
$298$	0.209335	−	3.86096i	0.0121265	−	0.223659i
$299$	−13.7778	+	34.5798i	−0.796793	+	1.99980i
$300$	4.53519	−	2.09820i	0.261839	−	0.121140i
$301$	21.9122	−	13.1842i	1.26300	−	0.759922i
$302$	2.89693	−	10.4338i	0.166699	−	0.600397i
$303$	−0.983019	+	0.216379i	−0.0564730	+	0.0124306i
$304$	4.65463	+	0.506221i	0.266961	+	0.0290338i
$305$	−0.157415	−	0.0947132i	−0.00901353	−	0.00542326i
$306$	−4.25409	+	4.02969i	−0.243190	+	0.230362i
$307$	−28.6530	−	13.2563i	−1.63531	−	0.756577i	−0.635436	−	0.772154i	$-0.719180\pi$
$307$	−28.6530	−	13.2563i	−1.63531	−	0.756577i	−0.999879	+	0.0155764i	$0.995042\pi$
$308$	−0.129926	+	0.0141303i	−0.00740320	+	0.000805146i
$309$	−0.0885991	+	0.0298525i	−0.00504023	+	0.00169825i
$310$	0.205010	+	0.514535i	0.0116438	+	0.0292236i
$311$	17.2724	+	16.3613i	0.979427	+	0.927763i	0.997399	−	0.0720758i	$-0.0229624\pi$
$311$	17.2724	+	16.3613i	0.979427	+	0.927763i	−0.0179720	+	0.999838i	$0.505721\pi$
$312$	−1.33955	−	4.82464i	−0.0758373	−	0.273141i
$313$	9.20439	+	17.3613i	0.520263	+	0.981320i	0.994874	+	0.101124i	$0.0322440\pi$
$313$	9.20439	+	17.3613i	0.520263	+	0.981320i	−0.474611	+	0.880196i	$0.657411\pi$
$314$	7.89784	−	6.00379i	0.445701	−	0.338813i
$315$	0.00744906	+	0.137390i	0.000419707	+	0.00774104i
$316$	6.70114	+	2.25788i	0.376969	+	0.127016i
$317$	3.49290	+	0.768845i	0.196181	+	0.0431826i	0.311974	−	0.950091i	$-0.399010\pi$
$317$	3.49290	+	0.768845i	0.196181	+	0.0431826i	−0.115793	+	0.993273i	$0.536941\pi$
$318$	5.06817	−	9.55958i	0.284209	−	0.536075i
$319$	0.0645908	+	0.393986i	0.00361639	+	0.0220590i
$320$	−0.0352098	+	0.0414522i	−0.00196829	+	0.00231725i
$321$	−7.11685	−	8.37860i	−0.397224	−	0.467648i
$322$	3.04262	−	18.5592i	0.169559	−	1.03426i
$323$	−21.8411	−	16.6032i	−1.21527	−	0.923826i
$324$	−0.561187	+	0.827689i	−0.0311771	+	0.0459827i
$325$	14.0414	−	20.7096i	0.778878	−	1.14876i
$326$	9.03361	+	6.86717i	0.500325	+	0.380337i
$327$	−1.76687	+	10.7774i	−0.0977081	+	0.595993i
$328$	0.118365	+	0.139350i	0.00653560	+	0.00769430i
$329$	−3.50935	+	4.13152i	−0.193477	+	0.227778i
$330$	0.000454556		0.00277267i	2.50225e−5		0.000152630i
$331$	−16.5127	+	31.1463i	−0.907623	+	1.71196i	−0.234966	+	0.972004i	$0.575498\pi$
$331$	−16.5127	+	31.1463i	−0.907623	+	1.71196i	−0.672657	+	0.739954i	$0.734847\pi$
$332$	15.0152	+	3.30511i	0.824069	+	0.181391i
$333$	−0.284098	−	0.0957237i	−0.0155685	−	0.00524562i
$334$	−0.565584	−	10.4316i	−0.0309474	−	0.570790i
$335$	−0.128193	+	0.0974498i	−0.00700393	+	0.00532425i
$336$	1.18499	+	2.23513i	0.0646467	+	0.121937i
$337$	−0.656506	−	2.36452i	−0.0357622	−	0.128804i	0.943514	−	0.331332i	$-0.107498\pi$
$337$	−0.656506	−	2.36452i	−0.0357622	−	0.128804i	−0.979276	+	0.202528i	$0.935084\pi$
$338$	−8.76389	−	8.30159i	−0.476693	−	0.451547i
$339$	−3.73777	−	9.38110i	−0.203008	−	0.509511i
$340$	0.302011	−	0.101759i	0.0163789	−	0.00551868i
$341$	0.523014	−	0.0568812i	0.0283228	−	0.00308029i
$342$	−4.24933	−	1.96595i	−0.229778	−	0.106306i
$343$	−13.9584	+	13.2221i	−0.753685	+	0.713928i
$344$	−8.66155	−	5.21148i	−0.466999	−	0.280984i
$345$	−0.401952	−	0.0437149i	−0.0216404	−	0.00235353i
$346$	14.1390	−	3.11224i	0.760119	−	0.167315i
$347$	3.13864	−	11.3044i	0.168491	−	0.606850i	−0.830283	−	0.557343i	$-0.811821\pi$
$347$	3.13864	−	11.3044i	0.168491	−	0.606850i	0.998774	−	0.0495077i	$-0.0157652\pi$
$348$	6.62205	−	3.98435i	0.354979	−	0.213584i
$349$	−26.2901	+	12.1631i	−1.40728	+	0.651077i	−0.968841	−	0.247685i	$-0.920330\pi$
$349$	−26.2901	+	12.1631i	−1.40728	+	0.651077i	−0.438438	+	0.898761i	$0.644468\pi$
$350$	−4.67916	+	11.7438i	−0.250112	+	0.627733i
$351$	−0.271082	+	4.99981i	−0.0144693	+	0.266870i
$352$	0.0289911	+	0.0427586i	0.00154523	+	0.00227904i
$353$	31.7765			1.69129			0.845646	−	0.533744i	$-0.179215\pi$
$353$	31.7765			1.69129			0.845646	+	0.533744i	$0.179215\pi$
$354$	7.62647	−	0.914859i	0.405342	−	0.0486242i
$355$	0.221362			0.0117487
$356$	8.24122	+	12.1549i	0.436784	+	0.644208i
$357$	0.802553	−	14.8022i	0.0424756	−	0.783416i
$358$	−6.11830	+	15.3558i	−0.323362	+	0.811578i
$359$	16.6406	−	7.69874i	0.878255	−	0.406324i	0.0716605	−	0.997429i	$-0.477170\pi$
$359$	16.6406	−	7.69874i	0.878255	−	0.406324i	0.806595	+	0.591105i	$0.201308\pi$
$360$	0.0466025	−	0.0280398i	0.00245617	−	0.00147783i
$361$	0.781665	−	2.81530i	0.0411403	−	0.148174i
$362$	0.494474	−	0.108842i	0.0259890	−	0.00572061i
$363$	−10.9329	−	1.18902i	−0.573827	−	0.0624074i
$364$	10.8540	+	6.53064i	0.568905	+	0.342299i
$365$	0.390452	−	0.369856i	0.0204372	−	0.0193591i
$366$	3.06562	+	1.41831i	0.160243	+	0.0741361i
$367$	22.4129	−	2.43755i	1.16994	−	0.127239i	0.497551	−	0.867435i	$-0.334233\pi$
$367$	22.4129	−	2.43755i	1.16994	−	0.127239i	0.672391	+	0.740196i	$0.265267\pi$
$368$	−7.04492	+	2.37371i	−0.367242	+	0.123738i
$369$	−0.0676741	−	0.169849i	−0.00352298	−	0.00884200i
$370$	0.0118373	+	0.0112129i	0.000615392	+	0.000582930i
$371$	7.32297	+	26.3750i	0.380190	+	1.36932i
$372$	−4.77018	−	8.99751i	−0.247322	−	0.466499i
$373$	12.5892	−	9.57009i	0.651846	−	0.495521i	−0.226210	−	0.974079i	$-0.572633\pi$
$373$	12.5892	−	9.57009i	0.651846	−	0.495521i	0.878056	+	0.478558i	$0.158840\pi$
$374$	−0.0163885	−	0.302268i	−0.000847429	−	0.0156299i
$375$	0.515254	+	0.173609i	0.0266076	+	0.00896515i
$376$	2.09266	+	0.460628i	0.107920	+	0.0237551i
$377$	18.1259	−	34.1890i	0.933530	−	1.76082i
$378$	−0.409281	−	2.49650i	−0.0210511	−	0.128406i
$379$	10.9703	−	12.9152i	0.563504	−	0.663409i	−0.404443	−	0.914563i	$-0.632534\pi$
$379$	10.9703	−	12.9152i	0.563504	−	0.663409i	0.967947	+	0.251155i	$0.0808103\pi$
$380$	0.164855	+	0.194082i	0.00845688	+	0.00995621i
$381$	−2.62918	+	16.0373i	−0.134697	+	0.821616i
$382$	6.10163	+	4.63834i	0.312187	+	0.237318i
$383$	4.16049	−	6.13626i	0.212591	−	0.313548i	−0.706410	−	0.707802i	$-0.749687\pi$
$383$	4.16049	−	6.13626i	0.212591	−	0.313548i	0.919001	+	0.394254i	$0.128997\pi$
$384$	0.561187	−	0.827689i	0.0286380	−	0.0422378i
$385$	−0.00565864	−	0.00430159i	−0.000288391	−	0.000219229i
$386$	2.35838	−	14.3855i	0.120039	−	0.732203i
$387$	6.54411	+	7.70432i	0.332656	+	0.391633i
$388$	0.980840	−	1.15473i	0.0497946	−	0.0586227i
$389$	−1.29858	−	7.92101i	−0.0658408	−	0.401611i	−0.999100	−	0.0424083i	$-0.986497\pi$
$389$	−1.29858	−	7.92101i	−0.0658408	−	0.401611i	0.933260	−	0.359203i	$-0.116951\pi$
$390$	0.127560	−	0.240604i	0.00645927	−	0.0121835i
$391$	42.5428	+	9.36437i	2.15148	+	0.473577i
$392$	0.568558	+	0.191570i	0.0287165	+	0.00967573i
$393$	0.387388	+	7.14496i	0.0195412	+	0.360415i
$394$	12.1329	−	9.22322i	0.611249	−	0.464659i
$395$	0.180146	+	0.339792i	0.00906413	+	0.0170968i
$396$	−0.0138206	−	0.0497773i	−0.000694511	−	0.00250140i
$397$	−9.50182	−	9.00060i	−0.476883	−	0.451727i	0.411109	−	0.911586i	$-0.365141\pi$
$397$	−9.50182	−	9.00060i	−0.476883	−	0.451727i	−0.887992	+	0.459859i	$0.847900\pi$
$398$	−7.44531	−	18.6863i	−0.373200	−	0.936661i
$399$	11.2248	−	3.78208i	0.561943	−	0.189341i
$400$	4.96775	−	0.540275i	0.248387	−	0.0270138i
$401$	−15.6320	−	7.23211i	−0.780623	−	0.361154i	−0.0112352	−	0.999937i	$-0.503576\pi$
$401$	−15.6320	−	7.23211i	−0.780623	−	0.361154i	−0.769387	+	0.638782i	$0.779438\pi$
$402$	2.14948	−	2.03610i	0.107206	−	0.101551i
$403$	−43.6927	−	26.2890i	−2.17649	−	1.30955i
$404$	−1.00065	−	0.108827i	−0.0497843	−	0.00541437i
$405$	−0.0531161	+	0.0116917i	−0.00263936	+	0.000580967i
$406$	−5.23052	+	18.8386i	−0.259586	+	0.934945i
$407$	0.0132704	−	0.00798453i	0.000657789	−	0.000395778i
$408$	−5.31809	+	2.46041i	−0.263285	+	0.121808i
$409$	−2.03787	+	5.11466i	−0.100766	+	0.252904i	−0.970713	−	0.240241i	$-0.922773\pi$
$409$	−2.03787	+	5.11466i	−0.100766	+	0.252904i	0.869947	+	0.493145i	$0.164153\pi$
$410$	−0.000538355		0.00992938i	−2.65875e−5		0.000490377i
$411$	2.07641	+	3.06247i	0.102422	+	0.151061i
$412$	−0.0934932			−0.00460608
$413$	−12.4155	+	14.9485i	−0.610926	+	0.735568i
$414$	7.43407			0.365365
$415$	0.469261	+	0.692109i	0.0230351	+	0.0339743i
$416$	0.271082	−	4.99981i	0.0132909	−	0.245136i
$417$	−8.09739	+	20.3229i	−0.396531	+	0.995218i
$418$	0.219522	−	0.101562i	0.0107372	−	0.00496754i
$419$	−12.1203	+	7.29253i	−0.592115	+	0.356264i	−0.779860	−	0.625954i	$-0.784710\pi$
$419$	−12.1203	+	7.29253i	−0.592115	+	0.356264i	0.187745	+	0.982218i	$0.439882\pi$
$420$	−0.0368096	+	0.132576i	−0.00179613	+	0.00646906i
$421$	−1.39251	+	0.306514i	−0.0678666	+	0.0149386i	−0.248774	−	0.968562i	$-0.580028\pi$
$421$	−1.39251	+	0.306514i	−0.0678666	+	0.0149386i	0.180907	+	0.983500i	$0.442097\pi$
$422$	−2.14782	−	0.233590i	−0.104554	−	0.0113710i
$423$	−1.83603	−	1.10470i	−0.0892709	−	0.0537125i
$424$	7.85526	−	7.44090i	0.381485	−	0.361362i
$425$	−26.5747	−	12.2948i	−1.28906	−	0.596384i
$426$	−4.04622	+	0.440053i	−0.196040	+	0.0213206i
$427$	−8.09798	+	2.72853i	−0.391888	+	0.132043i
$428$	−4.06900	−	10.2124i	−0.196683	−	0.493636i
$429$	−0.187794	−	0.177888i	−0.00906677	−	0.00858850i
$430$	−0.147081	−	0.529739i	−0.00709289	−	0.0255463i
$431$	4.30862	+	8.12692i	0.207539	+	0.391460i	0.965328	−	0.261040i	$-0.0840653\pi$
$431$	4.30862	+	8.12692i	0.207539	+	0.391460i	−0.757789	+	0.652499i	$0.773720\pi$
$432$	−0.796093	+	0.605174i	−0.0383020	+	0.0291165i
$433$	−1.14507	−	21.1196i	−0.0550286	−	1.01494i	−0.887481	−	0.460845i	$-0.847546\pi$
$433$	−1.14507	−	21.1196i	−0.0550286	−	1.01494i	0.832452	−	0.554097i	$-0.186936\pi$
$434$	24.4146	+	8.22625i	1.17194	+	0.394873i
$435$	0.410497	+	0.0903573i	0.0196818	+	0.00433230i
$436$	−5.11563	+	9.64910i	−0.244994	+	0.462108i
$437$	5.63113	+	34.3483i	0.269373	+	1.64310i
$438$	−6.40172	+	7.53669i	−0.305886	+	0.360117i
$439$	21.8654	+	25.7419i	1.04358	+	1.22859i	0.972932	+	0.231092i	$0.0742299\pi$
$439$	21.8654	+	25.7419i	1.04358	+	1.22859i	0.0706451	+	0.997502i	$0.477494\pi$
$440$	−0.000454556		0.00277267i	−2.16701e−5		0.000132182i
$441$	−0.477628	−	0.363083i	−0.0227442	−	0.0172897i
$442$	−16.4654	+	24.2846i	−0.783177	+	1.15510i
$443$	−8.56531	+	12.6329i	−0.406950	+	0.600206i	−0.974842	−	0.222897i	$-0.928449\pi$
$443$	−8.56531	+	12.6329i	−0.406950	+	0.600206i	0.567892	+	0.823103i	$0.307759\pi$
$444$	−0.238661	−	0.181426i	−0.0113264	−	0.00861008i
$445$	−0.129215	+	0.788180i	−0.00612540	+	0.0373633i
$446$	2.70993	+	3.19038i	0.128319	+	0.151069i
$447$	−2.50320	+	2.94700i	−0.118398	+	0.139388i
$448$	0.409281	+	2.49650i	0.0193367	+	0.117949i
$449$	−15.1151	+	28.5102i	−0.713327	+	1.34548i	0.216063	+	0.976379i	$0.430678\pi$
$449$	−15.1151	+	28.5102i	−0.713327	+	1.34548i	−0.929390	+	0.369099i	$0.879666\pi$
$450$	−4.88021	−	1.07422i	−0.230055	−	0.0506390i
$451$	0.00895087	+	0.00301590i	0.000421480	+	0.000142013i
$452$	−0.546712	−	10.0835i	−0.0257152	−	0.474288i
$453$	−8.62048	+	6.55312i	−0.405026	+	0.307893i
$454$	5.96327	+	11.2479i	0.279870	+	0.527891i
$455$	0.184311	+	0.663829i	0.00864065	+	0.0311208i
$456$	−3.39916	−	3.21986i	−0.159180	−	0.150784i
$457$	−1.51154	−	3.79368i	−0.0707068	−	0.177461i	0.889376	−	0.457176i	$-0.151139\pi$
$457$	−1.51154	−	3.79368i	−0.0707068	−	0.177461i	−0.960083	+	0.279716i	$0.909760\pi$
$458$	5.28855	−	1.78192i	0.247118	−	0.0832636i
$459$	5.82532	−	0.633542i	0.271903	−	0.0295712i
$460$	−0.366953	−	0.169770i	−0.0171093	−	0.00791559i
$461$	22.9524	−	21.7417i	1.06900	−	1.01261i	0.0691137	−	0.997609i	$-0.477983\pi$
$461$	22.9524	−	21.7417i	1.06900	−	1.01261i	0.999887	−	0.0150028i	$-0.00477573\pi$
$462$	0.111984	+	0.0673786i	0.00520997	+	0.00313474i
$463$	−15.2672	−	1.66041i	−0.709526	−	0.0771656i	−0.253763	−	0.967267i	$-0.581668\pi$
$463$	−15.2672	−	1.66041i	−0.709526	−	0.0771656i	−0.455764	+	0.890101i	$0.650634\pi$
$464$	7.54761	−	1.66136i	0.350389	−	0.0771265i
$465$	0.148177	−	0.533685i	0.00687153	−	0.0247490i
$466$	6.14178	−	3.69539i	0.284513	−	0.171186i
$467$	7.97138	−	3.68795i	0.368872	−	0.170658i	−0.226692	−	0.973967i	$-0.572791\pi$
$467$	7.97138	−	3.68795i	0.368872	−	0.170658i	0.595563	+	0.803308i	$0.296929\pi$
$468$	−1.85334	+	4.65153i	−0.0856705	+	0.215017i
$469$	−0.405509	+	7.47917i	−0.0187247	+	0.345356i
$470$	0.0654003	+	0.0964583i	0.00301669	+	0.00444929i
$471$	−9.92075			−0.457124
$472$	7.51936	+	1.56817i	0.346107	+	0.0721811i
$473$	−0.522208			−0.0240112
$474$	−3.96832	−	5.85284i	−0.182271	−	0.268830i
$475$	1.26666	−	23.3622i	0.0581184	−	1.07193i
$476$	5.48691	−	13.7711i	0.251492	−	0.631198i
$477$	−9.81995	+	4.54319i	−0.449625	+	0.208018i
$478$	−13.1134	+	7.89004i	−0.599791	+	0.360882i
$479$	−1.00570	+	3.62222i	−0.0459518	+	0.165503i	−0.982966	−	0.183788i	$-0.941164\pi$
$479$	−1.00570	+	3.62222i	−0.0459518	+	0.165503i	0.937014	+	0.349292i	$0.113578\pi$
$480$	0.0531161	−	0.0116917i	0.00242441	−	0.000533653i
$481$	−1.49230	−	0.162297i	−0.0680429	−	0.00740011i
$482$	23.6325	+	14.2192i	1.07643	+	0.647666i
$483$	−13.6538	+	12.9335i	−0.621267	+	0.588496i
$484$	−9.98091	−	4.61766i	−0.453678	−	0.209894i
$485$	0.0819185	−	0.00890917i	0.00371973	−	0.000404545i
$486$	0.947653	−	0.319302i	0.0429864	−	0.0144838i
$487$	0.410499	+	1.03027i	0.0186015	+	0.0466862i	0.937984	−	0.346678i	$-0.112690\pi$
$487$	0.410499	+	1.03027i	0.0186015	+	0.0466862i	−0.919383	+	0.393364i	$0.871311\pi$
$488$	2.45228	+	2.32292i	0.111009	+	0.105154i
$489$	−3.03576	−	10.9338i	−0.137282	−	0.494444i
$490$	0.0152845	+	0.0288296i	0.000690483	+	0.00130239i
$491$	0.359122	−	0.272997i	0.0162070	−	0.0123202i	−0.597039	−	0.802212i	$-0.703656\pi$
$491$	0.359122	−	0.272997i	0.0162070	−	0.0123202i	0.613246	+	0.789892i	$0.289863\pi$
$492$	−0.00989848	−	0.182567i	−0.000446258	−	0.00823074i
$493$	−42.9147	−	14.4596i	−1.93278	−	0.651230i
$494$	−22.8957	−	5.03973i	−1.03013	−	0.226748i
$495$	0.00131608	−	0.00248239i	5.91534e−5	−	0.000111575i
$496$	−1.64756	−	10.0496i	−0.0739774	−	0.451242i
$497$	6.66588	−	7.84768i	0.299005	−	0.352016i
$498$	−9.95337	−	11.7180i	−0.446021	−	0.525097i
$499$	−0.475769	+	2.90207i	−0.0212984	+	0.129914i	−0.995336	−	0.0964740i	$-0.969244\pi$
$499$	−0.475769	+	2.90207i	−0.0212984	+	0.129914i	0.974037	+	0.226388i	$0.0726918\pi$
$500$	0.432849	+	0.329043i	0.0193576	+	0.0147152i
$501$	−5.86266	+	8.64678i	−0.261924	+	0.386310i
$502$	−0.452658	+	0.667621i	−0.0202031	+	0.0297974i
$503$	21.5706	+	16.3976i	0.961788	+	0.731132i	0.963177	−	0.268867i	$-0.0866492\pi$
$503$	21.5706	+	16.3976i	0.961788	+	0.731132i	−0.00138960	+	0.999999i	$0.500442\pi$
$504$	0.409281	−	2.49650i	0.0182308	−	0.111203i
$505$	−0.0354405	−	0.0417238i	−0.00157708	−	0.00185669i
$506$	−0.248626	+	0.292706i	−0.0110528	+	0.0130124i
$507$	1.95296	+	11.9125i	0.0867339	+	0.529054i
$508$	−7.61229	+	14.3583i	−0.337741	+	0.637046i
$509$	20.0668	+	4.41704i	0.889446	+	0.195782i	0.636112	−	0.771597i	$-0.280542\pi$
$509$	20.0668	+	4.41704i	0.889446	+	0.195782i	0.253334	+	0.967379i	$0.418473\pi$
$510$	−0.302011	−	0.101759i	−0.0133733	−	0.00450598i
$511$	−1.35436	−	24.9797i	−0.0599133	−	1.10504i
$512$	0.796093	−	0.605174i	0.0351827	−	0.0267452i
$513$	2.19312	+	4.13667i	0.0968287	+	0.182638i
$514$	2.19442	+	7.90360i	0.0967919	+	0.348613i
$515$	−0.00369160	−	0.00349687i	−0.000162671	−	0.000154090i
$516$	3.74154	+	9.39057i	0.164712	+	0.413397i
$517$	0.104901	−	0.0353451i	0.00461352	−	0.00155448i
$518$	0.753974	−	0.0819996i	0.0331277	−	0.00360285i
$519$	−13.1394	−	6.07895i	−0.576757	−	0.266836i
$520$	0.197708	−	0.187279i	0.00867009	−	0.00821274i
$521$	25.9805	+	15.6319i	1.13823	+	0.684848i	0.954524	−	0.298134i	$-0.0963644\pi$
$521$	25.9805	+	15.6319i	1.13823	+	0.684848i	0.183702	+	0.982982i	$0.441192\pi$
$522$	−7.68299	−	0.835576i	−0.336275	−	0.0365722i
$523$	−0.0690194	+	0.0151923i	−0.00301801	+	0.000664314i	−0.216479	−	0.976287i	$-0.569457\pi$
$523$	−0.0690194	+	0.0151923i	−0.00301801	+	0.000664314i	0.213461	+	0.976952i	$0.431526\pi$
$524$	−1.91429	+	6.89464i	−0.0836260	+	0.301194i
$525$	10.8321	−	6.51746i	0.472752	−	0.284445i
$526$	2.09628	−	0.969843i	0.0914022	−	0.0422872i
$527$	−22.0875	+	55.4355i	−0.962147	+	2.41481i
$528$	0.00279683	−	0.0515845i	0.000121716	−	0.00224493i
$529$	−18.1070	−	26.7058i	−0.787259	−	1.16112i
$530$	0.588474			0.0255617
$531$	−6.62503	−	3.88703i	−0.287502	−	0.168683i
$532$	11.8448			0.513539
$533$	−0.513756	−	0.757734i	−0.0222533	−	0.0328211i
$534$	0.795048	−	14.6638i	0.0344051	−	0.634565i
$535$	0.221304	−	0.555430i	0.00956779	−	0.0240133i
$536$	2.68709	−	1.24318i	0.116065	−	0.0536972i
$537$	14.1637	−	8.52199i	0.611207	−	0.367751i
$538$	2.44439	−	8.80389i	0.105385	−	0.379563i
$539$	0.0302697	−	0.00666287i	0.00130381	−	0.000286990i
$540$	−0.0540689	−	0.00588034i	−0.00232675	−	0.000253050i
$541$	3.73002	+	2.24428i	0.160366	+	0.0964892i	0.593475	−	0.804853i	$-0.297756\pi$
$541$	3.73002	+	2.24428i	0.160366	+	0.0964892i	−0.433108	+	0.901342i	$0.642583\pi$
$542$	−15.2543	+	14.4496i	−0.655228	+	0.620665i
$543$	−0.459516	−	0.212595i	−0.0197197	−	0.00912331i
$544$	−5.82532	+	0.633542i	−0.249758	+	0.0271629i
$545$	−0.562891	+	0.189660i	−0.0241116	+	0.00812415i
$546$	−4.68863	−	11.7676i	−0.200655	−	0.503605i
$547$	−0.624683	−	0.591731i	−0.0267095	−	0.0253006i	0.674228	−	0.738523i	$-0.264476\pi$
$547$	−0.624683	−	0.591731i	−0.0267095	−	0.0253006i	−0.700938	+	0.713222i	$0.747235\pi$
$548$	0.989862	+	3.56516i	0.0422848	+	0.152296i
$549$	−1.58220	−	2.98434i	−0.0675265	−	0.127369i
$550$	0.205510	−	0.156225i	0.00876299	−	0.00666145i
$551$	−1.95899	−	36.1314i	−0.0834556	−	1.53925i
$552$	7.04492	+	2.37371i	0.299852	+	0.101032i
$553$	17.4710	+	3.84565i	0.742940	+	0.163534i
$554$	−14.4001	+	27.1615i	−0.611801	+	1.15398i
$555$	−0.00263784	−	0.0160901i	−0.000111970	−	0.000682988i
$556$	−14.1627	+	16.6736i	−0.600631	+	0.707117i
$557$	24.7298	+	29.1142i	1.04784	+	1.23361i	0.971627	+	0.236516i	$0.0760057\pi$
$557$	24.7298	+	29.1142i	1.04784	+	1.23361i	0.0762088	+	0.997092i	$0.475718\pi$
$558$	−1.64756	+	10.0496i	−0.0697466	+	0.425435i
$559$	40.2941	+	30.6308i	1.70426	+	1.29554i
$560$	−0.0772146	+	0.113883i	−0.00326291	+	0.00481244i
$561$	−0.169878	+	0.250551i	−0.00717226	+	0.0105783i
$562$	0.666527	+	0.506680i	0.0281157	+	0.0213730i
$563$	4.51316	−	27.5290i	0.190207	−	1.16021i	−0.703210	−	0.710982i	$-0.748251\pi$
$563$	4.51316	−	27.5290i	0.190207	−	1.16021i	0.893417	−	0.449228i	$-0.148301\pi$
$564$	−1.38719	−	1.63312i	−0.0584112	−	0.0687669i
$565$	0.355560	−	0.418598i	0.0149585	−	0.0176105i
$566$	−1.41634	−	8.63927i	−0.0595331	−	0.363136i
$567$	−1.18499	+	2.23513i	−0.0497650	+	0.0938668i
$568$	−3.97492	−	0.874946i	−0.166784	−	0.0367119i
$569$	−36.4768	−	12.2905i	−1.52919	−	0.515243i	−0.575955	−	0.817481i	$-0.695370\pi$
$569$	−36.4768	−	12.2905i	−1.52919	−	0.515243i	−0.953232	+	0.302238i	$0.902266\pi$
$570$	−0.0137863	−	0.254274i	−0.000577445	−	0.0106503i
$571$	19.9817	−	15.1897i	0.836210	−	0.635670i	−0.0968868	−	0.995295i	$-0.530888\pi$
$571$	19.9817	−	15.1897i	0.836210	−	0.635670i	0.933097	+	0.359625i	$0.117095\pi$
$572$	−0.121164	−	0.228539i	−0.00506610	−	0.00955568i
$573$	−2.05046	−	7.38510i	−0.0856593	−	0.308517i
$574$	0.335803	+	0.318089i	0.0140161	+	0.0132768i
$575$	13.7500	+	34.5100i	0.573416	+	1.43917i
$576$	−0.947653	+	0.319302i	−0.0394855	+	0.0133042i
$577$	−39.4719	+	4.29283i	−1.64324	+	0.178713i	−0.882488	−	0.470335i	$-0.844133\pi$
$577$	−39.4719	+	4.29283i	−1.64324	+	0.178713i	−0.760748	+	0.649047i	$0.775168\pi$
$578$	15.7335	+	7.27908i	0.654426	+	0.302770i
$579$	−10.5832	+	10.0250i	−0.439824	+	0.416624i
$580$	0.360158	+	0.216700i	0.0149547	+	0.00899797i
$581$	38.6673	+	4.20533i	1.60419	+	0.174466i
$582$	−1.47966	+	0.325697i	−0.0613337	+	0.0135006i
$583$	0.149539	−	0.538589i	0.00619325	−	0.0223061i
$584$	−8.47309	+	5.09809i	−0.350619	+	0.210960i
$585$	−0.247158	+	0.114347i	−0.0102187	+	0.00472768i
$586$	−9.66898	+	24.2673i	−0.399422	+	1.00247i
$587$	0.130411	−	2.40529i	0.00538263	−	0.0992768i	−0.994608	−	0.103710i	$-0.966928\pi$
$587$	0.130411	−	2.40529i	0.00538263	−	0.0992768i	0.999990	+	0.00443356i	$0.00141125\pi$
$588$	−0.336692	−	0.496584i	−0.0138850	−	0.0204788i
$589$	−47.6813			−1.96467
$590$	0.238250	+	0.343162i	0.00980861	+	0.0141277i
$591$	−15.2406			−0.626915
$592$	−0.168239	−	0.248134i	−0.00691457	−	0.0101982i
$593$	0.702635	−	12.9593i	0.0288538	−	0.532176i	−0.948000	−	0.318269i	$-0.896898\pi$
$593$	0.702635	−	12.9593i	0.0288538	−	0.532176i	0.976854	−	0.213907i	$-0.0686189\pi$
$594$	−0.0191214	+	0.0479912i	−0.000784562	+	0.00196910i
$595$	0.731724	−	0.338532i	0.0299978	−	0.0138784i
$596$	−3.31315	+	1.99346i	−0.135712	+	0.0816552i
$597$	−5.38132	+	19.3818i	−0.220243	+	0.793243i
$598$	36.3533	−	8.00196i	1.48660	−	0.327224i
$599$	1.10478	+	0.120152i	0.0451399	+	0.00490926i	0.130661	−	0.991427i	$-0.458290\pi$
$599$	1.10478	+	0.120152i	0.0451399	+	0.00490926i	−0.0855212	+	0.996336i	$0.527256\pi$
$600$	−4.28175	−	2.57624i	−0.174802	−	0.105175i
$601$	13.5660	−	12.8504i	0.553370	−	0.524180i	−0.359113	−	0.933294i	$-0.616921\pi$
$601$	13.5660	−	12.8504i	0.553370	−	0.524180i	0.912483	+	0.409114i	$0.134162\pi$
$602$	−23.2092	−	10.7377i	−0.945938	−	0.437637i
$603$	−2.94338	+	0.320112i	−0.119864	+	0.0130360i
$604$	−10.2617	+	3.45755i	−0.417541	+	0.140686i
$605$	−0.221387	−	0.555639i	−0.00900065	−	0.0225899i
$606$	0.730752	+	0.692205i	0.0296848	+	0.0281189i
$607$	8.51772	+	30.6781i	0.345724	+	1.24518i	0.908258	+	0.418411i	$0.137413\pi$
$607$	8.51772	+	30.6781i	0.345724	+	1.24518i	−0.562534	+	0.826774i	$0.690174\pi$
$608$	−2.19312	−	4.13667i	−0.0889429	−	0.167764i
$609$	15.5646	−	11.8319i	0.630711	−	0.479454i
$610$	0.00994594	+	0.183442i	0.000402699	+	0.00742735i
$611$	−10.1674	−	3.42581i	−0.411331	−	0.138593i
$612$	5.72267	+	1.25966i	0.231325	+	0.0509186i
$613$	2.14851	−	4.05253i	0.0867777	−	0.163680i	−0.836325	−	0.548235i	$-0.815300\pi$
$613$	2.14851	−	4.05253i	0.0867777	−	0.163680i	0.923102	+	0.384555i	$0.125645\pi$
$614$	5.10761	+	31.1551i	0.206126	+	1.25732i
$615$	0.00643759	−	0.00757891i	0.000259588	−	0.000305611i
$616$	0.0846080	+	0.0996082i	0.00340895	+	0.00401333i
$617$	1.76185	−	10.7468i	0.0709294	−	0.432650i	−0.927359	−	0.374172i	$-0.877927\pi$
$617$	1.76185	−	10.7468i	0.0709294	−	0.432650i	0.998289	−	0.0584783i	$-0.0186248\pi$
$618$	0.0744293	+	0.0565797i	0.00299399	+	0.00227597i
$619$	−3.16277	+	4.66474i	−0.127122	+	0.187492i	−0.885924	−	0.463830i	$-0.846475\pi$
$619$	−3.16277	+	4.66474i	−0.127122	+	0.187492i	0.758802	+	0.651322i	$0.225785\pi$
$620$	0.310827	−	0.458435i	0.0124831	−	0.0184112i
$621$	−5.91822	−	4.49891i	−0.237490	−	0.180535i
$622$	3.84901	−	23.4779i	0.154331	−	0.941378i
$623$	24.0513	+	28.3154i	0.963595	+	1.13443i
$624$	−3.24156	+	3.81626i	−0.129766	+	0.152773i
$625$	−4.03737	−	24.6269i	−0.161495	−	0.985075i
$626$	9.20439	−	17.3613i	0.367882	−	0.693898i
$627$	−0.236222	−	0.0519964i	−0.00943381	−	0.00207654i
$628$	−9.40143	−	3.16771i	−0.375158	−	0.126405i
$629$	0.0951044	+	1.75410i	0.00379206	+	0.0699405i
$630$	0.109536	−	0.0832669i	0.00436401	−	0.00331743i
$631$	6.06763	+	11.4448i	0.241549	+	0.455609i	0.974413	−	0.224766i	$-0.0721618\pi$
$631$	6.06763	+	11.4448i	0.241549	+	0.455609i	−0.732864	+	0.680375i	$0.761817\pi$
$632$	−1.89177	−	6.81355i	−0.0752507	−	0.271029i
$633$	1.56851	+	1.48577i	0.0623425	+	0.0590539i
$634$	−1.32380	−	3.32250i	−0.0525750	−	0.131953i
$635$	−0.837607	+	0.282223i	−0.0332394	+	0.0111997i
$636$	−10.7566	+	1.16985i	−0.426525	+	0.0463874i
$637$	−2.72646	−	1.26139i	−0.108026	−	0.0499783i
$638$	0.289851	−	0.274561i	0.0114753	−	0.0108700i
$639$	3.48747	+	2.09834i	0.137962	+	0.0830092i
$640$	0.0540689	+	0.00588034i	0.00213726	+	0.000232441i
$641$	17.2423	−	3.79531i	0.681029	−	0.149906i	0.139034	−	0.990288i	$-0.455600\pi$
$641$	17.2423	−	3.79531i	0.681029	−	0.149906i	0.541995	+	0.840382i	$0.317669\pi$
$642$	−2.94099	+	10.5925i	−0.116072	+	0.418053i
$643$	23.3169	−	14.0293i	0.919530	−	0.553263i	0.0247122	−	0.999695i	$-0.492133\pi$
$643$	23.3169	−	14.0293i	0.919530	−	0.553263i	0.894818	+	0.446432i	$0.147305\pi$
$644$	−17.0687	+	7.89683i	−0.672602	+	0.311179i
$645$	−0.203494	+	0.510731i	−0.00801256	+	0.0201100i
$646$	−1.48532	+	27.3952i	−0.0584392	+	1.07785i
$647$	−5.37316	−	7.92482i	−0.211241	−	0.311557i	0.707277	−	0.706936i	$-0.249923\pi$
$647$	−5.37316	−	7.92482i	−0.211241	−	0.311557i	−0.918518	+	0.395380i	$0.870613\pi$
$648$	1.00000			0.0392837
$649$	0.374614	−	0.130852i	0.0147049	−	0.00513640i
$650$	−25.0209			−0.981402
$651$	−14.4580	−	21.3240i	−0.566654	−	0.835753i
$652$	0.614337	−	11.3308i	0.0240593	−	0.443748i
$653$	16.0736	−	40.3416i	0.629007	−	1.57869i	−0.175326	−	0.984510i	$-0.556098\pi$
$653$	16.0736	−	40.3416i	0.629007	−	1.57869i	0.804333	−	0.594179i	$-0.202523\pi$
$654$	9.91190	−	4.58574i	0.387586	−	0.179316i
$655$	−0.333462	+	0.200637i	−0.0130294	+	0.00783955i
$656$	0.0489135	−	0.176171i	0.00190975	−	0.00687830i
$657$	9.65738	−	2.12575i	0.376770	−	0.0829334i
$658$	5.38902	+	0.586091i	0.210086	+	0.0228482i
$659$	41.6489	+	25.0593i	1.62241	+	0.976171i	0.977242	+	0.212130i	$0.0680399\pi$
$659$	41.6489	+	25.0593i	1.62241	+	0.976171i	0.645167	+	0.764041i	$0.276788\pi$
$660$	0.00203982	−	0.00193222i	7.93998e−5	−	7.52115e-5i
$661$	−18.4115	−	8.51808i	−0.716126	−	0.331315i	0.0277668	−	0.999614i	$-0.491160\pi$
$661$	−18.4115	−	8.51808i	−0.716126	−	0.331315i	−0.743892	+	0.668299i	$0.767022\pi$
$662$	35.0462	−	3.81151i	1.36211	−	0.148138i
$663$	27.8044	−	9.36838i	1.07983	−	0.363838i
$664$	−5.69076	−	14.2827i	−0.220844	−	0.554278i
$665$	0.467696	+	0.443025i	0.0181365	+	0.0171798i
$666$	0.0802025	+	0.288863i	0.00310779	+	0.0111932i
$667$	26.9113	+	50.7602i	1.04201	+	1.96544i
$668$	−8.31670	+	6.32219i	−0.321783	+	0.244613i
$669$	−0.226623	−	4.17982i	−0.00876176	−	0.161601i
$670$	0.152598	+	0.0514164i	0.00589539	+	0.00198639i
$671$	0.170419	+	0.0375121i	0.00657896	+	0.00144814i
$672$	1.18499	−	2.23513i	0.0457121	−	0.0862222i
$673$	−5.68459	−	34.6745i	−0.219125	−	1.33660i	−0.835648	−	0.549266i	$-0.814908\pi$
$673$	−5.68459	−	34.6745i	−0.219125	−	1.33660i	0.616523	−	0.787337i	$-0.288541\pi$
$674$	−1.58867	+	1.87032i	−0.0611931	+	0.0720421i
$675$	3.23502	+	3.80856i	0.124516	+	0.146591i
$676$	−1.95296	+	11.9125i	−0.0751138	+	0.458174i
$677$	7.12415	+	5.41563i	0.273803	+	0.208140i	0.733060	−	0.680164i	$-0.238091\pi$
$677$	7.12415	+	5.41563i	0.273803	+	0.208140i	−0.459257	+	0.888303i	$0.651884\pi$
$678$	−5.66704	+	8.35826i	−0.217641	+	0.320997i
$679$	2.15097	−	3.17244i	0.0825465	−	0.121747i
$680$	−0.253710	−	0.192865i	−0.00972933	−	0.00739604i
$681$	2.05963	−	12.5632i	0.0789254	−	0.481423i
$682$	−0.340589	−	0.400972i	−0.0130418	−	0.0153540i
$683$	−23.7106	+	27.9143i	−0.907260	+	1.06811i	0.0901313	+	0.995930i	$0.471271\pi$
$683$	−23.7106	+	27.9143i	−0.907260	+	1.06811i	−0.997392	+	0.0721795i	$0.977005\pi$
$684$	0.757475	+	4.62039i	0.0289628	+	0.176665i
$685$	−0.0942606	+	0.177794i	−0.00360151	+	0.00679317i
$686$	18.7771	+	4.13315i	0.716913	+	0.157805i
$687$	−5.28855	−	1.78192i	−0.201771	−	0.0679844i
$688$	0.547263	+	10.0937i	0.0208642	+	0.384818i
$689$	−43.1301	+	32.7867i	−1.64313	+	1.24907i
$690$	0.189388	+	0.357223i	0.00720987	+	0.0135993i
$691$	−0.280763	−	1.01122i	−0.0106807	−	0.0384685i	0.958018	−	0.286709i	$-0.0925614\pi$
$691$	−0.280763	−	1.01122i	−0.0106807	−	0.0384685i	−0.968698	+	0.248241i	$0.920148\pi$
$692$	−10.5106	−	9.95618i	−0.399553	−	0.378477i
$693$	−0.0483740	−	0.121410i	−0.00183758	−	0.00461197i
$694$	−11.1179	+	3.74605i	−0.422028	+	0.142198i
$695$	−1.18285	+	0.128642i	−0.0448680	+	0.00487968i
$696$	−7.01401	−	3.24503i	−0.265865	−	0.123002i
$697$	−0.777796	+	0.736768i	−0.0294611	+	0.0279071i
$698$	24.8210	+	14.9343i	0.939487	+	0.565271i
$699$	−7.12579	−	0.774976i	−0.269522	−	0.0293123i
$700$	12.3461	−	2.71758i	0.466639	−	0.102715i
$701$	−9.18697	+	33.0885i	−0.346987	+	1.24974i	0.559970	+	0.828513i	$0.310813\pi$
$701$	−9.18697	+	33.0885i	−0.346987	+	1.24974i	−0.906957	+	0.421222i	$0.861601\pi$
$702$	4.29041	−	2.58146i	0.161931	−	0.0974307i
$703$	−1.27391	+	0.589374i	−0.0480465	+	0.0222287i
$704$	0.0191214	−	0.0479912i	0.000720666	−	0.00180874i
$705$	0.00630931	−	0.116368i	0.000237622	−	0.00438269i
$706$	−17.8326	−	26.3011i	−0.671137	−	0.989853i
$707$	−2.54640			−0.0957674
$708$	−5.03709	−	5.79894i	−0.189306	−	0.217937i
$709$	−20.4338			−0.767407			−0.383703	−	0.923456i	$-0.625351\pi$
$709$	−20.4338			−0.767407			−0.383703	+	0.923456i	$0.625351\pi$
$710$	−0.124226	−	0.183219i	−0.00466210	−	0.00687608i
$711$	−0.382833	+	7.06093i	−0.0143573	+	0.264806i
$712$	5.43560	−	13.6423i	0.203708	−	0.511268i
$713$	68.7099	−	31.7886i	2.57321	−	1.19049i
$714$	−12.7020	+	7.64255i	−0.475361	+	0.286015i
$715$	0.00376372	−	0.0135557i	0.000140755	−	0.000506955i
$716$	16.1433	−	3.55342i	0.603304	−	0.132797i
$717$	15.2143	+	1.65466i	0.568189	+	0.0617942i
$718$	−15.7106	−	9.45277i	−0.586316	−	0.352774i
$719$	34.3544	−	32.5422i	1.28120	−	1.21362i	0.317007	−	0.948423i	$-0.397322\pi$
$719$	34.3544	−	32.5422i	1.28120	−	1.21362i	0.964195	−	0.265196i	$-0.0854366\pi$
$720$	−0.0493609	−	0.0228368i	−0.00183957	−	0.000851077i
$721$	−0.235135	+	0.0255725i	−0.00875690	+	0.000952370i
$722$	−2.76886	+	0.932936i	−0.103046	+	0.0347203i
$723$	−10.2086	−	25.6215i	−0.379660	−	0.952875i
$724$	−0.367580	−	0.348190i	−0.0136610	−	0.0129404i
$725$	−10.3316	−	37.2110i	−0.383705	−	1.38198i
$726$	5.15124	+	9.71627i	0.191181	+	0.360605i
$727$	21.7054	−	16.5000i	0.805007	−	0.611950i	−0.119622	−	0.992820i	$-0.538168\pi$
$727$	21.7054	−	16.5000i	0.805007	−	0.611950i	0.924629	+	0.380869i	$0.124375\pi$
$728$	−0.685790	−	12.6487i	−0.0254171	−	0.468790i
$729$	−0.947653	−	0.319302i	−0.0350983	−	0.0118260i
$730$	−0.525242	−	0.115615i	−0.0194401	−	0.00427909i
$731$	27.7450	−	52.3326i	1.02619	−	1.93559i
$732$	−0.546470	−	3.33332i	−0.0201981	−	0.123203i
$733$	2.42257	−	2.85207i	0.0894795	−	0.105343i	−0.715600	−	0.698510i	$-0.753847\pi$
$733$	2.42257	−	2.85207i	0.0894795	−	0.105343i	0.805080	+	0.593167i	$0.202123\pi$
$734$	−14.5953	−	17.1830i	−0.538724	−	0.634235i
$735$	0.00527906	−	0.0322008i	0.000194721	−	0.00118775i
$736$	5.91822	+	4.49891i	0.218148	+	0.165832i
$737$	0.0858350	−	0.126597i	0.00316177	−	0.00466326i
$738$	−0.102605	+	0.151330i	−0.00377693	+	0.00557055i
$739$	20.8832	+	15.8750i	0.768200	+	0.583970i	0.914176	−	0.405318i	$-0.132839\pi$
$739$	20.8832	+	15.8750i	0.768200	+	0.583970i	−0.145976	+	0.989288i	$0.546632\pi$
$740$	0.00263784	−	0.0160901i	9.69691e−5	−	0.000591485i
$741$	15.1772	+	17.8680i	0.557549	+	0.656397i
$742$	17.7207	−	20.8624i	0.650548	−	0.765884i
$743$	−5.07859	−	30.9780i	−0.186315	−	1.13647i	−0.899962	−	0.435968i	$-0.856406\pi$
$743$	−5.07859	−	30.9780i	−0.186315	−	1.13647i	0.713647	−	0.700505i	$-0.247042\pi$
$744$	−4.77018	+	8.99751i	−0.174883	+	0.329865i
$745$	−0.205381	−	0.0452077i	−0.00752456	−	0.00165628i
$746$	−14.9860	−	5.04936i	−0.548676	−	0.184870i
$747$	0.832369	+	15.3521i	0.0304548	+	0.561706i
$748$	−0.240987	+	0.183194i	−0.00881136	+	0.00669822i
$749$	−13.0269	−	24.5713i	−0.475992	−	0.897815i
$750$	−0.145459	−	0.523898i	−0.00531143	−	0.0191300i
$751$	−18.4325	−	17.4602i	−0.672612	−	0.637132i	0.273158	−	0.961969i	$-0.411932\pi$
$751$	−18.4325	−	17.4602i	−0.672612	−	0.637132i	−0.945770	+	0.324837i	$0.894691\pi$
$752$	−0.793114	−	1.99057i	−0.0289219	−	0.0725885i
$753$	0.764385	−	0.257551i	0.0278557	−	0.00938569i
$754$	−38.4699	+	4.18385i	−1.40099	+	0.152367i
$755$	−0.534504	−	0.247288i	−0.0194526	−	0.00899973i
$756$	−1.83664	+	1.73976i	−0.0667981	+	0.0632745i
$757$	26.7323	+	16.0843i	0.971601	+	0.584593i	0.910487	−	0.413538i	$-0.135707\pi$
$757$	26.7323	+	16.0843i	0.971601	+	0.584593i	0.0611140	+	0.998131i	$0.480535\pi$
$758$	−16.8461	−	1.83213i	−0.611879	−	0.0665458i
$759$	0.375068	−	0.0825586i	0.0136141	−	0.00299669i
$760$	0.0681253	−	0.245365i	0.00247116	−	0.00890033i
$761$	10.0584	−	6.05196i	0.364618	−	0.219384i	−0.321440	−	0.946930i	$-0.604167\pi$
$761$	10.0584	−	6.05196i	0.364618	−	0.219384i	0.686059	+	0.727546i	$0.259339\pi$
$762$	14.7494	−	6.82378i	0.534313	−	0.247199i
$763$	−10.2266	+	25.6667i	−0.370226	+	0.929198i
$764$	0.414946	−	7.65323i	0.0150122	−	0.276884i
$765$	0.178847	+	0.263779i	0.00646622	+	0.00953696i
$766$	−7.41373			−0.267869
$767$	−36.5809	−	11.8768i	−1.32086	−	0.428846i
$768$	−1.00000			−0.0360844
$769$	28.1826	+	41.5662i	1.01629	+	1.49891i	0.859404	+	0.511298i	$0.170835\pi$
$769$	28.1826	+	41.5662i	1.01629	+	1.49891i	0.156885	+	0.987617i	$0.449855\pi$
$770$	−0.000384820		0.00709759i	−1.38680e−5		0.000255780i
$771$	3.03609	−	7.62001i	0.109342	−	0.274428i
$772$	−13.2302	+	6.12095i	−0.476166	+	0.220298i
$773$	−8.50467	+	5.11709i	−0.305892	+	0.184049i	−0.660220	−	0.751072i	$-0.729537\pi$
$773$	−8.50467	+	5.11709i	−0.305892	+	0.184049i	0.354328	+	0.935121i	$0.384709\pi$
$774$	2.70431	−	9.74005i	0.0972045	−	0.350099i
$775$	−49.6991	+	10.9396i	−1.78525	+	0.392962i
$776$	−1.50620	−	0.163809i	−0.0540693	−	0.00588039i
$777$	−0.649857	−	0.391006i	−0.0233135	−	0.0140273i
$778$	−5.82738	+	5.51999i	−0.208922	+	0.197901i
$779$	−0.776926	−	0.359444i	−0.0278363	−	0.0128784i
$780$	−0.270731	+	0.0294438i	−0.00969372	+	0.00105426i
$781$	−0.199255	+	0.0671368i	−0.00712990	+	0.00240234i
$782$	−16.1237	−	40.4673i	−0.576581	−	1.44711i
$783$	5.61071	+	5.31474i	0.200510	+	0.189933i
$784$	−0.160508	−	0.578096i	−0.00573241	−	0.0206463i
$785$	−0.252738	−	0.476714i	−0.00902059	−	0.0170146i
$786$	5.69641	−	4.33029i	0.203184	−	0.154457i
$787$	1.55309	+	28.6450i	0.0553616	+	1.02108i	0.885827	+	0.464015i	$0.153592\pi$
$787$	1.55309	+	28.6450i	0.0553616	+	1.02108i	−0.830466	+	0.557070i	$0.811926\pi$
$788$	−14.4428	−	4.86635i	−0.514504	−	0.173357i
$789$	−2.25576	−	0.496530i	−0.0803071	−	0.0176769i
$790$	0.180146	−	0.339792i	0.00640931	−	0.0120892i
$791$	−4.13305	−	25.2105i	−0.146954	−	0.896381i
$792$	−0.0334442	+	0.0393735i	−0.00118839	+	0.00139908i
$793$	−10.9494	−	12.8906i	−0.388824	−	0.457759i
$794$	−2.11740	+	12.9156i	−0.0751437	+	0.458357i
$795$	−0.468480	−	0.356129i	−0.0166153	−	0.0126306i
$796$	−11.2883	+	16.6489i	−0.400102	+	0.590106i
$797$	−15.4738	+	22.8221i	−0.548110	+	0.808402i	−0.996337	−	0.0855183i	$-0.972745\pi$
$797$	−15.4738	+	22.8221i	−0.548110	+	0.808402i	0.448227	+	0.893920i	$0.352056\pi$
$798$	−9.42960	−	7.16819i	−0.333804	−	0.253751i
$799$	−2.03130	+	12.3904i	−0.0718624	+	0.438341i
$800$	−3.23502	−	3.80856i	−0.114375	−	0.134653i
$801$	−9.50708	+	11.1926i	−0.335916	+	0.395471i
$802$	2.78651	+	16.9970i	0.0983951	+	0.600184i
$803$	−0.239285	+	0.451339i	−0.00844417	+	0.0159274i
$804$	−2.89152	−	0.636471i	−0.101976	−	0.0224466i
$805$	−0.969322	−	0.326603i	−0.0341641	−	0.0115112i
$806$	2.76064	+	50.9170i	0.0972394	+	1.79348i
$807$	−7.27385	+	5.52944i	−0.256052	+	0.194645i
$808$	0.471477	+	0.889301i	0.0165865	+	0.0312855i
$809$	−3.04957	−	10.9836i	−0.107217	−	0.386161i	0.890398	−	0.455183i	$-0.150426\pi$
$809$	−3.04957	−	10.9836i	−0.107217	−	0.386161i	−0.997615	+	0.0690216i	$0.978012\pi$
$810$	0.0394852	+	0.0374024i	0.00138737	+	0.00131419i
$811$	−13.8884	−	34.8572i	−0.487687	−	1.22400i	−0.942737	−	0.333537i	$-0.891758\pi$
$811$	−13.8884	−	34.8572i	−0.487687	−	1.22400i	0.455050	−	0.890466i	$-0.349621\pi$
$812$	18.5278	−	6.24275i	0.650199	−	0.219078i
$813$	20.8884	−	2.27175i	0.732587	−	0.0796737i
$814$	−0.0140559	−	0.00650294i	−0.000492658	−	0.000227928i
$815$	0.448055	−	0.424421i	0.0156947	−	0.0148668i
$816$	5.02090	+	3.02097i	0.175767	+	0.105755i
$817$	47.0513	+	5.11714i	1.64612	+	0.179026i
$818$	5.37697	−	1.18356i	0.188001	−	0.0413822i
$819$	−3.38884	+	12.2055i	−0.118416	+	0.426495i
$820$	0.00852056	−	0.00512665i	0.000297551	−	0.000179030i
$821$	1.36806	−	0.632933i	0.0477457	−	0.0220895i	−0.395871	−	0.918306i	$-0.629557\pi$
$821$	1.36806	−	0.632933i	0.0477457	−	0.0220895i	0.443617	+	0.896217i	$0.353695\pi$
$822$	1.36952	−	3.43724i	0.0477675	−	0.119887i
$823$	−0.835834	+	15.4161i	−0.0291353	+	0.537370i	0.947138	+	0.320827i	$0.103961\pi$
$823$	−0.835834	+	15.4161i	−0.0291353	+	0.537370i	−0.976273	+	0.216543i	$0.930522\pi$
$824$	0.0524672	+	0.0773833i	0.00182778	+	0.00269577i
$825$	−0.258149			−0.00898758
$826$	19.3401	+	1.88724i	0.672929	+	0.0656655i
$827$	−17.8511			−0.620745			−0.310372	−	0.950615i	$-0.600454\pi$
$827$	−17.8511			−0.620745			−0.310372	+	0.950615i	$0.600454\pi$
$828$	−4.17191	−	6.15310i	−0.144984	−	0.213835i
$829$	2.12970	−	39.2800i	0.0739676	−	1.36425i	−0.692244	−	0.721663i	$-0.743378\pi$
$829$	2.12970	−	39.2800i	0.0739676	−	1.36425i	0.766212	−	0.642588i	$-0.222139\pi$
$830$	0.309507	−	0.776805i	0.0107432	−	0.0269633i
$831$	27.9012	−	12.9085i	0.967883	−	0.447790i
$832$	−4.29041	+	2.58146i	−0.148743	+	0.0894959i
$833$	−0.940521	+	3.38745i	−0.0325871	+	0.117368i
$834$	21.3652	−	4.70284i	0.739817	−	0.162846i
$835$	−0.564852	−	0.0614313i	−0.0195475	−	0.00212592i
$836$	−0.207254	−	0.124701i	−0.00716804	−	0.00431286i
$837$	7.39339	−	7.00339i	0.255553	−	0.242073i
$838$	12.8377	+	5.93935i	0.443471	+	0.205171i
$839$	−37.8891	+	4.12069i	−1.30808	+	0.142262i	−0.735464	−	0.677564i	$-0.763036\pi$
$839$	−37.8891	+	4.12069i	−1.30808	+	0.142262i	−0.572613	+	0.819826i	$0.694070\pi$
$840$	0.130389	−	0.0439332i	0.00449885	−	0.00151584i
$841$	−11.3731	−	28.5443i	−0.392175	−	0.984285i
$842$	1.03516	+	0.980551i	0.0356738	+	0.0337920i
$843$	−0.223987	−	0.806730i	−0.00771453	−	0.0277852i
$844$	1.01199	+	1.90882i	0.0348342	+	0.0657042i
$845$	−0.522670	+	0.397323i	−0.0179804	+	0.0136683i
$846$	0.116006	+	2.13961i	0.00398838	+	0.0735613i
$847$	−26.3650	−	8.88341i	−0.905912	−	0.305237i
$848$	−10.5670	−	2.32598i	−0.362873	−	0.0798743i
$849$	−4.10073	+	7.73479i	−0.140737	+	0.265457i
$850$	4.73714	+	28.8953i	0.162483	+	0.991100i
$851$	1.44281	−	1.69861i	0.0494588	−	0.0582274i
$852$	2.63491	+	3.10206i	0.0902706	+	0.106275i
$853$	8.38433	−	51.1422i	0.287074	−	1.75107i	−0.311722	−	0.950173i	$-0.600906\pi$
$853$	8.38433	−	51.1422i	0.287074	−	1.75107i	0.598796	−	0.800901i	$-0.295646\pi$
$854$	6.80285	+	5.17139i	0.232789	+	0.176961i
$855$	−0.142905	+	0.210769i	−0.00488724	+	0.00720813i
$856$	−6.16924	+	9.09895i	−0.210860	+	0.310996i
$857$	−25.9135	−	19.6989i	−0.885187	−	0.672902i	0.0604341	−	0.998172i	$-0.480752\pi$
$857$	−25.9135	−	19.6989i	−0.885187	−	0.672902i	−0.945621	+	0.325271i	$0.894545\pi$
$858$	−0.0418483	+	0.255263i	−0.00142868	+	0.00871454i
$859$	−21.4930	−	25.3035i	−0.733330	−	0.863343i	0.261467	−	0.965212i	$-0.415794\pi$
$859$	−21.4930	−	25.3035i	−0.733330	−	0.863343i	−0.994798	+	0.101869i	$0.967518\pi$
$860$	−0.355919	+	0.419020i	−0.0121367	+	0.0142885i
$861$	−0.0748308	−	0.456448i	−0.00255023	−	0.0155557i
$862$	4.30862	−	8.12692i	0.146752	−	0.276804i
$863$	22.8008	+	5.01883i	0.776147	+	0.170843i	0.585343	−	0.810785i	$-0.300960\pi$
$863$	22.8008	+	5.01883i	0.776147	+	0.170843i	0.190803	+	0.981628i	$0.438891\pi$
$864$	0.947653	+	0.319302i	0.0322398	+	0.0108629i
$865$	−0.0426289	−	0.786243i	−0.00144943	−	0.0267331i
$866$	−16.8378	+	12.7998i	−0.572173	+	0.434955i
$867$	−8.12019	−	15.3163i	−0.275776	−	0.520169i
$868$	−6.89241	−	24.8242i	−0.233944	−	0.842588i
$869$	−0.265210	−	0.251220i	−0.00899664	−	0.00852207i
$870$	−0.155578	−	0.390471i	−0.00527459	−	0.0132382i
$871$	−14.0488	+	4.73360i	−0.476026	+	0.160392i
$872$	10.8573	−	1.18080i	0.367674	−	0.0399869i
$873$	1.37505	+	0.636164i	0.0465383	+	0.0215309i
$874$	25.2696	−	23.9367i	0.854758	−	0.809670i
$875$	1.17861	+	0.709149i	0.0398444	+	0.0239736i
$876$	9.83060	+	1.06914i	0.332145	+	0.0361230i
$877$	30.8126	−	6.78237i	1.04047	−	0.229024i	0.338302	−	0.941038i	$-0.390148\pi$
$877$	30.8126	−	6.78237i	1.04047	−	0.229024i	0.702166	+	0.712013i	$0.252216\pi$
$878$	9.03573	−	32.5437i	0.304941	−	1.09830i
$879$	22.3834	−	13.4676i	0.754972	−	0.454252i
$880$	0.00255000	−	0.00117976i	8.59605e−5	−	3.97695e-5i
$881$	5.45948	−	13.7023i	0.183935	−	0.461641i	−0.807877	−	0.589351i	$-0.799383\pi$
$881$	5.45948	−	13.7023i	0.183935	−	0.461641i	0.991812	+	0.127710i	$0.0407627\pi$
$882$	−0.0324814	+	0.599085i	−0.00109371	+	0.0201722i
$883$	2.12091	+	3.12810i	0.0713742	+	0.105269i	0.861701	−	0.507417i	$-0.169399\pi$
$883$	2.12091	+	3.12810i	0.0713742	+	0.105269i	−0.790327	+	0.612686i	$0.790089\pi$
$884$	29.3402			0.986819
$885$	0.0180033	−	0.417372i	0.000605175	−	0.0140298i
$886$	15.2628			0.512765
$887$	−12.7904	−	18.8644i	−0.429459	−	0.633405i	0.549972	−	0.835183i	$-0.314638\pi$
$887$	−12.7904	−	18.8644i	−0.429459	−	0.633405i	−0.979431	+	0.201778i	$0.935328\pi$
$888$	−0.0162303	+	0.299351i	−0.000544655	+	0.0100456i
$889$	−15.2176	+	38.1932i	−0.510381	+	1.28096i
$890$	0.724882	−	0.335366i	0.0242981	−	0.0112415i
$891$	0.0442655	−	0.0266337i	0.00148295	−	0.000892261i
$892$	1.11986	−	4.03338i	0.0374958	−	0.135047i
$893$	−9.79796	+	2.15669i	−0.327876	+	0.0721710i
$894$	3.84397	+	0.418056i	0.128561	+	0.0139819i
$895$	0.770329	+	0.463492i	0.0257493	+	0.0154928i
$896$	1.83664	−	1.73976i	0.0613580	−	0.0581214i
$897$	−33.7832	−	15.6298i	−1.12799	−	0.521862i
$898$	32.0800	−	3.48891i	1.07052	−	0.116426i
$899$	−74.5835	+	25.1301i	−2.48750	+	0.838137i
$900$	1.84960	+	4.64214i	0.0616532	+	0.154738i
$901$	46.0292	+	43.6012i	1.53346	+	1.45257i
$902$	−0.00252689	−	0.00910102i	−8.41361e−5	−	0.000303031i
$903$	11.9785	+	22.5939i	0.398620	+	0.751877i
$904$	−8.03920	+	6.11124i	−0.267380	+	0.203257i
$905$	−0.00149083	−	0.0274967i	−4.95568e−5	−	0.000914021i
$906$	10.2617	+	3.45755i	0.340921	+	0.114870i
$907$	−9.15812	−	2.01586i	−0.304090	−	0.0669354i	0.0603040	−	0.998180i	$-0.480793\pi$
$907$	−9.15812	−	2.01586i	−0.304090	−	0.0669354i	−0.364394	+	0.931245i	$0.618724\pi$
$908$	5.96327	−	11.2479i	0.197898	−	0.373276i
$909$	−0.162842	−	0.993292i	−0.00540113	−	0.0329454i
$910$	0.446011	−	0.525085i	0.0147851	−	0.0174064i
$911$	19.6427	+	23.1252i	0.650791	+	0.766171i	0.984286	−	0.176581i	$-0.0565038\pi$
$911$	19.6427	+	23.1252i	0.650791	+	0.766171i	−0.333495	+	0.942752i	$0.608228\pi$
$912$	−0.757475	+	4.62039i	−0.0250825	+	0.152997i
$913$	−0.632306	−	0.480666i	−0.0209263	−	0.0159077i
$914$	−2.29173	+	3.38005i	−0.0758036	+	0.111802i
$915$	0.103097	−	0.152056i	0.00340827	−	0.00502682i
$916$	−4.44274	−	3.37728i	−0.146792	−	0.111589i
$917$	−2.92859	+	17.8636i	−0.0967105	+	0.589908i
$918$	−3.79347	−	4.46602i	−0.125203	−	0.147401i
$919$	30.7883	−	36.2467i	1.01561	−	1.19567i	0.0350636	−	0.999385i	$-0.488837\pi$
$919$	30.7883	−	36.2467i	1.01561	−	1.19567i	0.980547	−	0.196284i	$-0.0628875\pi$
$920$	0.0654120	+	0.398996i	0.00215657	+	0.0131545i
$921$	14.7881	−	27.8933i	0.487285	−	0.919116i
$922$	−30.8760	−	6.79631i	−1.01685	−	0.223825i
$923$	19.3127	+	6.50720i	0.635685	+	0.214187i
$924$	−0.00707551	−	0.130500i	−0.000232767	−	0.00429314i
$925$	−1.19260	+	0.906592i	−0.0392125	+	0.0298086i
$926$	7.19345	+	13.5683i	0.236391	+	0.445881i
$927$	−0.0250121	−	0.0900854i	−0.000821505	−	0.00295879i
$928$	−5.61071	−	5.31474i	−0.184181	−	0.174465i
$929$	−5.65090	−	14.1827i	−0.185400	−	0.465319i	0.806671	−	0.591001i	$-0.201267\pi$
$929$	−5.65090	−	14.1827i	−0.185400	−	0.465319i	−0.992071	+	0.125683i	$0.959888\pi$
$930$	−0.524880	+	0.176853i	−0.0172115	+	0.00579923i
$931$	−2.79261	+	0.303715i	−0.0915241	+	0.00995385i
$932$	−6.50532	−	3.00968i	−0.213089	−	0.0985854i
$933$	−17.2724	+	16.3613i	−0.565473	+	0.535644i
$934$	−7.52592	−	4.52819i	−0.246256	−	0.148167i
$935$	−0.0163673	−	0.00178005i	−0.000535268	−	5.82139e-5i
$936$	4.89008	−	1.07639i	0.159837	−	0.0351829i
$937$	9.26270	−	33.3612i	0.302599	−	1.08986i	−0.643356	−	0.765567i	$-0.722459\pi$
$937$	9.26270	−	33.3612i	0.302599	−	1.08986i	0.945955	−	0.324297i	$-0.105128\pi$
$938$	6.41800	−	3.86158i	0.209555	−	0.126085i
$939$	−17.8342	+	8.25097i	−0.581997	+	0.269260i
$940$	0.0431356	−	0.108262i	0.00140693	−	0.00353113i
$941$	−0.399758	+	7.37309i	−0.0130317	+	0.240356i	0.984759	+	0.173923i	$0.0556445\pi$
$941$	−0.399758	+	7.37309i	−0.0130317	+	0.240356i	−0.997791	+	0.0664326i	$0.978838\pi$
$942$	5.56740	+	8.21130i	0.181396	+	0.267539i
$943$	1.35921			0.0442619
$944$	−2.92181	−	7.10373i	−0.0950968	−	0.231207i
$945$	−0.137592			−0.00447585
$946$	0.293057	+	0.432226i	0.00952809	+	0.0140529i
$947$	0.144147	−	2.65864i	0.00468416	−	0.0863942i	−0.995257	−	0.0972853i	$-0.968984\pi$
$947$	0.144147	−	2.65864i	0.00468416	−	0.0863942i	0.999941	+	0.0108911i	$0.00346682\pi$
$948$	−2.61736	+	6.56908i	−0.0850079	+	0.213354i
$949$	44.9373	−	20.7902i	1.45873	−	0.674878i
$950$	−20.0475	+	12.0622i	−0.650426	+	0.391348i
$951$	−0.956819	+	3.44615i	−0.0310270	+	0.111749i
$952$	−14.4774	+	3.18671i	−0.469215	+	0.103282i
$953$	54.6782	+	5.94662i	1.77120	+	0.192630i	0.934725	−	0.355373i	$-0.115646\pi$
$953$	54.6782	+	5.94662i	1.77120	+	0.192630i	0.836477	+	0.548002i	$0.184612\pi$
$954$	9.27118	+	5.57828i	0.300165	+	0.180604i
$955$	0.302633	−	0.286670i	0.00979298	−	0.00927641i
$956$	13.8895	+	6.42599i	0.449220	+	0.207831i
$957$	−0.396906	+	0.0431661i	−0.0128301	+	0.00139536i
$958$	3.56246	−	1.20033i	0.115098	−	0.0387810i
$959$	3.46465	+	8.69563i	0.111880	+	0.280796i
$960$	−0.0394852	−	0.0374024i	−0.00127438	−	0.00120716i
$961$	19.4519	+	70.0595i	0.627482	+	2.25998i
$962$	0.703127	+	1.32624i	0.0226697	+	0.0427596i
$963$	8.75161	−	6.65280i	0.282017	−	0.214384i
$964$	−1.49317	−	27.5399i	−0.0480918	−	0.887002i
$965$	−0.751336	−	0.253155i	−0.0241864	−	0.00814934i
$966$	18.3672	+	4.04294i	0.590956	+	0.130079i
$967$	−20.8669	+	39.3592i	−0.671034	+	1.26571i	0.280998	+	0.959708i	$0.409335\pi$
$967$	−20.8669	+	39.3592i	−0.671034	+	1.26571i	−0.952033	+	0.305997i	$0.901010\pi$
$968$	1.77917	+	10.8525i	0.0571847	+	0.348811i
$969$	17.7613	−	20.9102i	0.570575	−	0.671733i
$970$	−0.0533456	−	0.0628033i	−0.00171282	−	0.00201649i
$971$	−3.19707	+	19.5013i	−0.102599	+	0.625826i	0.884602	+	0.466346i	$0.154430\pi$
$971$	−3.19707	+	19.5013i	−0.102599	+	0.625826i	−0.987201	+	0.159480i	$0.949018\pi$
$972$	−0.796093	−	0.605174i	−0.0255347	−	0.0194110i
$973$	−31.0585	+	45.8078i	−0.995689	+	1.46853i
$974$	0.622380	−	0.917942i	0.0199423	−	0.0294128i
$975$	19.9190	+	15.1420i	0.637918	+	0.484933i
$976$	0.546470	−	3.33332i	0.0174921	−	0.106697i
$977$	−37.7678	−	44.4637i	−1.20830	−	1.42252i	−0.878013	−	0.478638i	$-0.841131\pi$
$977$	−37.7678	−	44.4637i	−1.20830	−	1.42252i	−0.330286	−	0.943881i	$-0.607145\pi$
$978$	−7.34617	+	8.64858i	−0.234905	+	0.276551i
$979$	−0.122736	−	0.748654i	−0.00392265	−	0.0239271i
$980$	0.0152845	−	0.0288296i	0.000488245	−	0.000920928i
$981$	−10.6660	−	2.34776i	−0.340538	−	0.0749581i
$982$	−0.427492	−	0.144039i	−0.0136418	−	0.00459646i
$983$	0.338990	+	6.25230i	0.0108121	+	0.199417i	0.998949	+	0.0458404i	$0.0145966\pi$
$983$	0.338990	+	6.25230i	0.0108121	+	0.199417i	−0.988137	+	0.153577i	$0.950921\pi$
$984$	−0.145554	+	0.110647i	−0.00464008	+	0.00352730i
$985$	−0.388264	−	0.732344i	−0.0123711	−	0.0233344i
$986$	12.1151	+	43.6346i	0.385823	+	1.38961i
$987$	−3.93547	−	3.72788i	−0.125267	−	0.118660i
$988$	8.67746	+	21.7788i	0.276067	+	0.692875i
$989$	−71.2137	+	23.9947i	−2.26446	+	0.762986i
$990$	−0.00279321		0.000303780i	−8.87741e−5		9.65477e-6i
$991$	−21.7388	−	10.0575i	−0.690557	−	0.319485i	0.0430375	−	0.999073i	$-0.486297\pi$
$991$	−21.7388	−	10.0575i	−0.690557	−	0.319485i	−0.733594	+	0.679588i	$0.762159\pi$
$992$	−7.39339	+	7.00339i	−0.234740	+	0.222358i
$993$	−30.2067	−	18.1748i	−0.958580	−	0.576759i
$994$	−10.2362	−	1.11326i	−0.324674	−	0.0353104i
$995$	−1.06843	+	0.235179i	−0.0338715	+	0.00745567i
$996$	−4.11317	+	14.8143i	−0.130331	+	0.469409i
$997$	21.2486	−	12.7848i	0.672949	−	0.404900i	−0.137667	−	0.990479i	$-0.543960\pi$
$997$	21.2486	−	12.7848i	0.672949	−	0.404900i	0.810616	+	0.585579i	$0.199133\pi$
$998$	2.66900	−	1.23481i	0.0844858	−	0.0390873i
$999$	0.110964	−	0.278499i	0.00351075	−	0.00881131i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.2.e.c.7.2	✓	84
59.17	even	29	inner	354.2.e.c.253.2	yes	84

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.2.e.c.7.2	✓	84	1.1	even	1	trivial
354.2.e.c.253.2	yes	84	59.17	even	29	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	354.e (of order \(29\), degree \(28\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.561187 - 0.827689i) q^{2} +(-0.0541389 + 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(-0.0493609 + 0.0228368i) q^{5} +(0.856857 - 0.515554i) q^{6} +(-0.676801 + 2.43762i) q^{7} +(0.976621 - 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +O(q^{10})\)	\(q+(-0.561187 - 0.827689i) q^{2} +(-0.0541389 + 0.998533i) q^{3} +(-0.370138 + 0.928977i) q^{4} +(-0.0493609 + 0.0228368i) q^{5} +(0.856857 - 0.515554i) q^{6} +(-0.676801 + 2.43762i) q^{7} +(0.976621 - 0.214970i) q^{8} +(-0.994138 - 0.108119i) q^{9} +(0.0466025 + 0.0280398i) q^{10} +(0.0375051 - 0.0355267i) q^{11} +(-0.907575 - 0.419889i) q^{12} +(-4.97780 + 0.541368i) q^{13} +(2.39740 - 0.807778i) q^{14} +(-0.0201310 - 0.0505249i) q^{15} +(-0.725995 - 0.687699i) q^{16} +(1.56763 + 5.64608i) q^{17} +(0.468408 + 0.883512i) q^{18} +(-3.72737 + 2.83347i) q^{19} +(-0.00294449 - 0.0543079i) q^{20} +(-2.39740 - 0.807778i) q^{21} +(-0.0504525 - 0.0111054i) q^{22} +(3.48218 - 6.56809i) q^{23} +(0.161782 + 0.986827i) q^{24} +(-3.23502 + 3.80856i) q^{25} +(3.24156 + 3.81626i) q^{26} +(0.161782 - 0.986827i) q^{27} +(-2.01398 - 1.53099i) q^{28} +(-4.33702 + 6.39663i) q^{29} +(-0.0305217 + 0.0450161i) q^{30} +(8.10725 + 6.16297i) q^{31} +(-0.161782 + 0.986827i) q^{32} +(0.0334442 + 0.0393735i) q^{33} +(3.79347 - 4.46602i) q^{34} +(-0.0222598 - 0.135779i) q^{35} +(0.468408 - 0.883512i) q^{36} +(0.292782 + 0.0644462i) q^{37} +(4.43698 + 1.49499i) q^{38} +(-0.271082 - 4.99981i) q^{39} +(-0.0432977 + 0.0329140i) q^{40} +(0.0856414 + 0.161537i) q^{41} +(0.676801 + 2.43762i) q^{42} +(-7.33873 - 6.95161i) q^{43} +(0.0191214 + 0.0479912i) q^{44} +(0.0515407 - 0.0173661i) q^{45} +(-7.39050 + 0.803765i) q^{46} +(1.94471 + 0.899718i) q^{47} +(0.725995 - 0.687699i) q^{48} +(0.514084 + 0.309314i) q^{49} +(4.96775 + 0.540275i) q^{50} +(-5.72267 + 1.25966i) q^{51} +(1.33955 - 4.82464i) q^{52} +(9.27118 - 5.57828i) q^{53} +(-0.907575 + 0.419889i) q^{54} +(-0.00103997 + 0.00261013i) q^{55} +(-0.136962 + 2.52612i) q^{56} +(-2.62752 - 3.87530i) q^{57} +7.72830 q^{58} +(7.00645 + 3.14795i) q^{59} +0.0543877 q^{60} +(1.89559 + 2.79578i) q^{61} +(0.551340 - 10.1689i) q^{62} +(0.936386 - 2.35015i) q^{63} +(0.907575 - 0.419889i) q^{64} +(0.233346 - 0.140399i) q^{65} +(0.0138206 - 0.0497773i) q^{66} +(2.89152 - 0.636471i) q^{67} +(-5.82532 - 0.633542i) q^{68} +(6.36994 + 3.83267i) q^{69} +(-0.0998908 + 0.0946216i) q^{70} +(-3.69390 - 1.70898i) q^{71} +(-0.994138 + 0.108119i) q^{72} +(-9.37093 + 3.15743i) q^{73} +(-0.110964 - 0.278499i) q^{74} +(-3.62783 - 3.43646i) q^{75} +(-1.25259 - 4.51141i) q^{76} +(0.0612171 + 0.115468i) q^{77} +(-3.98616 + 3.03020i) q^{78} +(-0.382833 - 7.06093i) q^{79} +(0.0515407 + 0.0173661i) q^{80} +(0.976621 + 0.214970i) q^{81} +(0.0856414 - 0.161537i) q^{82} +(-2.48735 - 15.1722i) q^{83} +(1.63778 - 1.92814i) q^{84} +(-0.206318 - 0.242896i) q^{85} +(-1.63537 + 9.97534i) q^{86} +(-6.15244 - 4.67697i) q^{87} +(0.0289911 - 0.0427586i) q^{88} +(8.24122 - 12.1549i) q^{89} +(-0.0432977 - 0.0329140i) q^{90} +(2.04933 - 12.5004i) q^{91} +(4.81272 + 5.66597i) q^{92} +(-6.59285 + 7.76171i) q^{93} +(-0.346659 - 2.11452i) q^{94} +(0.119279 - 0.224984i) q^{95} +(-0.976621 - 0.214970i) q^{96} +(-1.43577 - 0.483766i) q^{97} +(-0.0324814 - 0.599085i) q^{98} +(-0.0411264 + 0.0312635i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9}+O(q^{10}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9	\( 84 q - 3 q^{2} + 3 q^{3} - 3 q^{4} + 3 q^{6} + q^{7} - 3 q^{8} - 3 q^{9} - 26 q^{11} + 3 q^{12} - 3 q^{13} + q^{14} - 3 q^{16} + 3 q^{17} - 3 q^{18} + 4 q^{19} - q^{21} + 3 q^{22} - 2 q^{23} + 3 q^{24} + 41 q^{25} + 26 q^{26} + 3 q^{27} + q^{28} - 2 q^{29} + 8 q^{31} - 3 q^{32} - 3 q^{33} - 26 q^{34} + 83 q^{35} - 3 q^{36} - 53 q^{37} + 4 q^{38} + 3 q^{39} - 7 q^{41} - q^{42} + 119 q^{43} + 3 q^{44} - 31 q^{46} - 12 q^{47} + 3 q^{48} - 38 q^{49} - 133 q^{50} - 3 q^{51} - 32 q^{52} - 83 q^{53} + 3 q^{54} - 83 q^{55} + q^{56} - 4 q^{57} + 56 q^{58} - 57 q^{59} - 48 q^{61} - 21 q^{62} + q^{63} - 3 q^{64} - 33 q^{65} - 3 q^{66} - 88 q^{67} - 26 q^{68} + 89 q^{69} - 62 q^{70} - 35 q^{71} - 3 q^{72} - 71 q^{73} - 24 q^{74} + 17 q^{75} + 33 q^{76} + 113 q^{77} + 3 q^{78} - 5 q^{79} - 3 q^{81} - 7 q^{82} - 51 q^{83} - q^{84} + 125 q^{85} + 61 q^{86} + 31 q^{87} + 32 q^{88} - 58 q^{89} + 173 q^{91} - 2 q^{92} + 21 q^{93} + 17 q^{94} + 26 q^{95} + 3 q^{96} + 20 q^{98} + 3 q^{99}+O(q^{100}) \) 84 * q - 3 * q^2 + 3 * q^3 - 3 * q^4 + 3 * q^6 + q^7 - 3 * q^8 - 3 * q^9 - 26 * q^11 + 3 * q^12 - 3 * q^13 + q^14 - 3 * q^16 + 3 * q^17 - 3 * q^18 + 4 * q^19 - q^21 + 3 * q^22 - 2 * q^23 + 3 * q^24 + 41 * q^25 + 26 * q^26 + 3 * q^27 + q^28 - 2 * q^29 + 8 * q^31 - 3 * q^32 - 3 * q^33 - 26 * q^34 + 83 * q^35 - 3 * q^36 - 53 * q^37 + 4 * q^38 + 3 * q^39 - 7 * q^41 - q^42 + 119 * q^43 + 3 * q^44 - 31 * q^46 - 12 * q^47 + 3 * q^48 - 38 * q^49 - 133 * q^50 - 3 * q^51 - 32 * q^52 - 83 * q^53 + 3 * q^54 - 83 * q^55 + q^56 - 4 * q^57 + 56 * q^58 - 57 * q^59 - 48 * q^61 - 21 * q^62 + q^63 - 3 * q^64 - 33 * q^65 - 3 * q^66 - 88 * q^67 - 26 * q^68 + 89 * q^69 - 62 * q^70 - 35 * q^71 - 3 * q^72 - 71 * q^73 - 24 * q^74 + 17 * q^75 + 33 * q^76 + 113 * q^77 + 3 * q^78 - 5 * q^79 - 3 * q^81 - 7 * q^82 - 51 * q^83 - q^84 + 125 * q^85 + 61 * q^86 + 31 * q^87 + 32 * q^88 - 58 * q^89 + 173 * q^91 - 2 * q^92 + 21 * q^93 + 17 * q^94 + 26 * q^95 + 3 * q^96 + 20 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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