LMFDB - Embedded newform 114.2.i.d.55.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,2,Mod(25,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([0, 14]))

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

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

chi := DirichletCharacter("114.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	114.i (of order $9$, degree $6$, 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:	$0.910294583043$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			55.1
Root			$-0.173648 + 0.984808i$ of defining polynomial
Character	$\chi$	$=$	114.55
Dual form			114.2.i.d.85.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(3.20574 - 1.16679i) q^{5} +(0.766044 - 0.642788i) q^{6} +(1.43969 + 2.49362i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(0.592396 + 3.35965i) q^{10} +(0.173648 - 0.300767i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-1.26604 + 1.06234i) q^{13} +(-2.70574 + 0.984808i) q^{14} +(-3.20574 - 1.16679i) q^{15} +(0.766044 + 0.642788i) q^{16} +(1.20574 - 6.83807i) q^{17} -1.00000 q^{18} +(-2.82635 + 3.31839i) q^{19} -3.41147 q^{20} +(0.500000 - 2.83564i) q^{21} +(0.266044 + 0.223238i) q^{22} +(-6.39053 - 2.32596i) q^{23} +(-0.939693 + 0.342020i) q^{24} +(5.08512 - 4.26692i) q^{25} +(-0.826352 - 1.43128i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-0.500000 - 2.83564i) q^{28} +(1.10354 + 6.25849i) q^{29} +(1.70574 - 2.95442i) q^{30} +(-0.798133 - 1.38241i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-0.326352 + 0.118782i) q^{33} +(6.52481 + 2.37484i) q^{34} +(7.52481 + 6.31407i) q^{35} +(0.173648 - 0.984808i) q^{36} -11.2121 q^{37} +(-2.77719 - 3.35965i) q^{38} +1.65270 q^{39} +(0.592396 - 3.35965i) q^{40} +(-2.67365 - 2.24346i) q^{41} +(2.70574 + 0.984808i) q^{42} +(-2.14543 + 0.780873i) q^{43} +(-0.266044 + 0.223238i) q^{44} +(1.70574 + 2.95442i) q^{45} +(3.40033 - 5.88954i) q^{46} +(0.971782 + 5.51125i) q^{47} +(-0.173648 - 0.984808i) q^{48} +(-0.645430 + 1.11792i) q^{49} +(3.31908 + 5.74881i) q^{50} +(-5.31908 + 4.46324i) q^{51} +(1.55303 - 0.565258i) q^{52} +(-1.86097 - 0.677337i) q^{53} +(0.766044 + 0.642788i) q^{54} +(0.205737 - 1.16679i) q^{55} +2.87939 q^{56} +(4.29813 - 0.725293i) q^{57} -6.35504 q^{58} +(0.0773815 - 0.438852i) q^{59} +(2.61334 + 2.19285i) q^{60} +(11.7763 + 4.28623i) q^{61} +(1.50000 - 0.545955i) q^{62} +(-2.20574 + 1.85083i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.81908 + 4.88279i) q^{65} +(-0.0603074 - 0.342020i) q^{66} +(-0.187319 - 1.06234i) q^{67} +(-3.47178 + 6.01330i) q^{68} +(3.40033 + 5.88954i) q^{69} +(-7.52481 + 6.31407i) q^{70} +(15.6211 - 5.68561i) q^{71} +(0.939693 + 0.342020i) q^{72} +(9.51367 + 7.98292i) q^{73} +(1.94697 - 11.0418i) q^{74} -6.63816 q^{75} +(3.79086 - 2.15160i) q^{76} +1.00000 q^{77} +(-0.286989 + 1.62760i) q^{78} +(-8.36824 - 7.02179i) q^{79} +(3.20574 + 1.16679i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(2.67365 - 2.24346i) q^{82} +(-5.85844 - 10.1471i) q^{83} +(-1.43969 + 2.49362i) q^{84} +(-4.11334 - 23.3279i) q^{85} +(-0.396459 - 2.24843i) q^{86} +(3.17752 - 5.50362i) q^{87} +(-0.173648 - 0.300767i) q^{88} +(1.37346 - 1.15247i) q^{89} +(-3.20574 + 1.16679i) q^{90} +(-4.47178 - 1.62760i) q^{91} +(5.20961 + 4.37138i) q^{92} +(-0.277189 + 1.57202i) q^{93} -5.59627 q^{94} +(-5.18866 + 13.9357i) q^{95} +1.00000 q^{96} +(0.634285 - 3.59721i) q^{97} +(-0.988856 - 0.829748i) q^{98} +(0.326352 + 0.118782i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{5} + 3 q^{7} + 3 q^{8} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 9 q^{15} - 3 q^{17} - 6 q^{18} - 18 q^{19} + 3 q^{21} - 3 q^{22} - 21 q^{23} + 9 q^{25} - 6 q^{26} + 3 q^{27} - 3 q^{28} - 3 q^{29} + 9 q^{31}+ \cdots + 3 q^{99}+O(q^{100}) $ 6 * q + 9 * q^5 + 3 * q^7 + 3 * q^8 + 3 * q^12 - 3 * q^13 - 6 * q^14 - 9 * q^15 - 3 * q^17 - 6 * q^18 - 18 * q^19 + 3 * q^21 - 3 * q^22 - 21 * q^23 + 9 * q^25 - 6 * q^26 + 3 * q^27 - 3 * q^28 - 3 * q^29 + 9 * q^31 - 3 * q^33 + 12 * q^34 + 18 * q^35 - 18 * q^37 - 6 * q^38 + 12 * q^39 - 15 * q^41 + 6 * q^42 + 3 * q^43 + 3 * q^44 + 6 * q^46 - 9 * q^47 + 12 * q^49 + 3 * q^50 - 15 * q^51 - 3 * q^52 + 12 * q^53 - 9 * q^55 + 6 * q^56 + 12 * q^57 + 12 * q^58 + 27 * q^59 + 9 * q^60 + 3 * q^61 + 9 * q^62 - 3 * q^63 - 3 * q^64 - 6 * q^66 + 21 * q^67 - 6 * q^68 + 6 * q^69 - 18 * q^70 + 39 * q^71 + 36 * q^73 + 24 * q^74 - 6 * q^75 - 9 * q^76 + 6 * q^77 + 6 * q^78 - 45 * q^79 + 9 * q^80 + 15 * q^82 - 27 * q^83 - 3 * q^84 - 18 * q^85 - 12 * q^86 - 6 * q^87 - 30 * q^89 - 9 * q^90 - 12 * q^91 - 3 * q^92 + 9 * q^93 - 6 * q^94 + 6 * q^96 - 6 * q^97 - 12 * q^98 + 3 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{5}{9}\right)$

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 $

$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$2$	−0.173648	+	0.984808i	−0.122788	+	0.696364i
$3$	−0.766044	−	0.642788i	−0.442276	−	0.371114i
$3$	−0.766044	−	0.642788i	−0.442276	−	0.371114i
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$	3.20574	−	1.16679i	1.43365	−	0.521806i	0.495674	−	0.868509i	$-0.334921\pi$
$5$	3.20574	−	1.16679i	1.43365	−	0.521806i	0.937975	+	0.346703i	$0.112699\pi$
$6$	0.766044	−	0.642788i	0.312736	−	0.262417i
$7$	1.43969	+	2.49362i	0.544153	+	0.942500i	0.998660	+	0.0517569i	$0.0164821\pi$
$7$	1.43969	+	2.49362i	0.544153	+	0.942500i	−0.454507	+	0.890743i	$0.650185\pi$
$8$	0.500000	−	0.866025i	0.176777	−	0.306186i
$9$	0.173648	+	0.984808i	0.0578827	+	0.328269i
$10$	0.592396	+	3.35965i	0.187332	+	1.06241i
$11$	0.173648	−	0.300767i	0.0523569	−	0.0906848i	−0.838659	−	0.544657i	$-0.816660\pi$
$11$	0.173648	−	0.300767i	0.0523569	−	0.0906848i	0.891016	+	0.453972i	$0.149993\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−1.26604	+	1.06234i	−0.351138	+	0.294639i	−0.801247	−	0.598334i	$-0.795830\pi$
$13$	−1.26604	+	1.06234i	−0.351138	+	0.294639i	0.450109	+	0.892974i	$0.351385\pi$
$14$	−2.70574	+	0.984808i	−0.723139	+	0.263201i
$15$	−3.20574	−	1.16679i	−0.827718	−	0.301265i
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	1.20574	−	6.83807i	0.292434	−	1.65848i	−0.385017	−	0.922909i	$-0.625805\pi$
$17$	1.20574	−	6.83807i	0.292434	−	1.65848i	0.677452	−	0.735567i	$-0.263084\pi$
$18$	−1.00000			−0.235702
$19$	−2.82635	+	3.31839i	−0.648410	+	0.761292i
$19$	−2.82635	+	3.31839i	−0.648410	+	0.761292i
$20$	−3.41147			−0.762829
$21$	0.500000	−	2.83564i	0.109109	−	0.618788i
$22$	0.266044	+	0.223238i	0.0567209	+	0.0475945i
$23$	−6.39053	−	2.32596i	−1.33252	−	0.484997i	−0.425069	−	0.905161i	$-0.639750\pi$
$23$	−6.39053	−	2.32596i	−1.33252	−	0.484997i	−0.907448	+	0.420164i	$0.861973\pi$
$24$	−0.939693	+	0.342020i	−0.191814	+	0.0698146i
$25$	5.08512	−	4.26692i	1.01702	−	0.853385i
$26$	−0.826352	−	1.43128i	−0.162061	−	0.280698i
$27$	0.500000	−	0.866025i	0.0962250	−	0.166667i
$28$	−0.500000	−	2.83564i	−0.0944911	−	0.535886i
$29$	1.10354	+	6.25849i	0.204922	+	1.16217i	0.897562	+	0.440888i	$0.145337\pi$
$29$	1.10354	+	6.25849i	0.204922	+	1.16217i	−0.692640	+	0.721284i	$0.743552\pi$
$30$	1.70574	−	2.95442i	0.311424	−	0.539401i
$31$	−0.798133	−	1.38241i	−0.143349	−	0.248288i	0.785407	−	0.618980i	$-0.212454\pi$
$31$	−0.798133	−	1.38241i	−0.143349	−	0.248288i	−0.928756	+	0.370692i	$0.879120\pi$
$32$	−0.766044	+	0.642788i	−0.135419	+	0.113630i
$33$	−0.326352	+	0.118782i	−0.0568106	+	0.0206774i
$34$	6.52481	+	2.37484i	1.11900	+	0.407281i
$35$	7.52481	+	6.31407i	1.27193	+	1.06727i
$36$	0.173648	−	0.984808i	0.0289414	−	0.164135i
$37$	−11.2121			−1.84326			−0.921632	−	0.388066i	$-0.873143\pi$
$37$	−11.2121			−1.84326			−0.921632	+	0.388066i	$0.873143\pi$
$38$	−2.77719	−	3.35965i	−0.450520	−	0.545007i
$39$	1.65270			0.264644
$40$	0.592396	−	3.35965i	0.0936661	−	0.531207i
$41$	−2.67365	−	2.24346i	−0.417554	−	0.350369i	0.409678	−	0.912230i	$-0.365641\pi$
$41$	−2.67365	−	2.24346i	−0.417554	−	0.350369i	−0.827232	+	0.561861i	$0.810086\pi$
$42$	2.70574	+	0.984808i	0.417504	+	0.151959i
$43$	−2.14543	+	0.780873i	−0.327175	+	0.119082i	−0.500385	−	0.865803i	$-0.666808\pi$
$43$	−2.14543	+	0.780873i	−0.327175	+	0.119082i	0.173210	+	0.984885i	$0.444586\pi$
$44$	−0.266044	+	0.223238i	−0.0401077	+	0.0336544i
$45$	1.70574	+	2.95442i	0.254276	+	0.440419i
$46$	3.40033	−	5.88954i	0.501351	−	0.868366i
$47$	0.971782	+	5.51125i	0.141749	+	0.803898i	0.969920	+	0.243423i	$0.0782703\pi$
$47$	0.971782	+	5.51125i	0.141749	+	0.803898i	−0.828171	+	0.560475i	$0.810619\pi$
$48$	−0.173648	−	0.984808i	−0.0250640	−	0.142145i
$49$	−0.645430	+	1.11792i	−0.0922042	+	0.159702i
$50$	3.31908	+	5.74881i	0.469388	+	0.813005i
$51$	−5.31908	+	4.46324i	−0.744820	+	0.624978i
$52$	1.55303	−	0.565258i	0.215367	−	0.0783872i
$53$	−1.86097	−	0.677337i	−0.255623	−	0.0930393i	0.211030	−	0.977480i	$-0.432318\pi$
$53$	−1.86097	−	0.677337i	−0.255623	−	0.0930393i	−0.466653	+	0.884440i	$0.654540\pi$
$54$	0.766044	+	0.642788i	0.104245	+	0.0874723i
$55$	0.205737	−	1.16679i	0.0277416	−	0.157330i
$56$	2.87939			0.384774
$57$	4.29813	−	0.725293i	0.569302	−	0.0960674i
$58$	−6.35504			−0.834457
$59$	0.0773815	−	0.438852i	0.0100742	−	0.0571337i	−0.979356	−	0.202142i	$-0.935210\pi$
$59$	0.0773815	−	0.438852i	0.0100742	−	0.0571337i	0.989430	+	0.145008i	$0.0463209\pi$
$60$	2.61334	+	2.19285i	0.337381	+	0.283096i
$61$	11.7763	+	4.28623i	1.50780	+	0.548795i	0.958067	−	0.286544i	$-0.0925064\pi$
$61$	11.7763	+	4.28623i	1.50780	+	0.548795i	0.549735	+	0.835339i	$0.314729\pi$
$62$	1.50000	−	0.545955i	0.190500	−	0.0693364i
$63$	−2.20574	+	1.85083i	−0.277897	+	0.233183i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$	−2.81908	+	4.88279i	−0.349664	+	0.605635i
$66$	−0.0603074	−	0.342020i	−0.00742333	−	0.0420998i
$67$	−0.187319	−	1.06234i	−0.0228846	−	0.129785i	0.971225	−	0.238163i	$-0.0765454\pi$
$67$	−0.187319	−	1.06234i	−0.0228846	−	0.129785i	−0.994110	+	0.108378i	$0.965434\pi$
$68$	−3.47178	+	6.01330i	−0.421015	+	0.729220i
$69$	3.40033	+	5.88954i	0.409352	+	0.709018i
$70$	−7.52481	+	6.31407i	−0.899387	+	0.754676i
$71$	15.6211	−	5.68561i	1.85388	−	0.674758i	0.870786	−	0.491662i	$-0.163610\pi$
$71$	15.6211	−	5.68561i	1.85388	−	0.674758i	0.983095	−	0.183096i	$-0.0586119\pi$
$72$	0.939693	+	0.342020i	0.110744	+	0.0403075i
$73$	9.51367	+	7.98292i	1.11349	+	0.934330i	0.998257	−	0.0590086i	$-0.0187939\pi$
$73$	9.51367	+	7.98292i	1.11349	+	0.934330i	0.115233	+	0.993338i	$0.463238\pi$
$74$	1.94697	−	11.0418i	0.226330	−	1.28358i
$75$	−6.63816			−0.766508
$76$	3.79086	−	2.15160i	0.434841	−	0.246806i
$77$	1.00000			0.113961
$78$	−0.286989	+	1.62760i	−0.0324951	+	0.184289i
$79$	−8.36824	−	7.02179i	−0.941501	−	0.790013i	0.0363452	−	0.999339i	$-0.488428\pi$
$79$	−8.36824	−	7.02179i	−0.941501	−	0.790013i	−0.977846	+	0.209326i	$0.932873\pi$
$80$	3.20574	+	1.16679i	0.358412	+	0.130451i
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	2.67365	−	2.24346i	0.295255	−	0.247748i
$83$	−5.85844	−	10.1471i	−0.643047	−	1.11379i	−0.984749	−	0.173982i	$-0.944336\pi$
$83$	−5.85844	−	10.1471i	−0.643047	−	1.11379i	0.341701	−	0.939809i	$-0.388997\pi$
$84$	−1.43969	+	2.49362i	−0.157083	+	0.272076i
$85$	−4.11334	−	23.3279i	−0.446154	−	2.53027i
$86$	−0.396459	−	2.24843i	−0.0427513	−	0.242455i
$87$	3.17752	−	5.50362i	0.340666	−	0.590050i
$88$	−0.173648	−	0.300767i	−0.0185110	−	0.0320619i
$89$	1.37346	−	1.15247i	0.145586	−	0.122161i	−0.567086	−	0.823659i	$-0.691929\pi$
$89$	1.37346	−	1.15247i	0.145586	−	0.122161i	0.712672	+	0.701497i	$0.247485\pi$
$90$	−3.20574	+	1.16679i	−0.337914	+	0.122991i
$91$	−4.47178	−	1.62760i	−0.468770	−	0.170618i
$92$	5.20961	+	4.37138i	0.543139	+	0.455748i
$93$	−0.277189	+	1.57202i	−0.0287431	+	0.163010i
$94$	−5.59627			−0.577211
$95$	−5.18866	+	13.9357i	−0.532346	+	1.42977i
$96$	1.00000			0.102062
$97$	0.634285	−	3.59721i	0.0644019	−	0.365241i	−0.935526	−	0.353257i	$-0.885074\pi$
$97$	0.634285	−	3.59721i	0.0644019	−	0.365241i	0.999928	−	0.0119843i	$-0.00381481\pi$
$98$	−0.988856	−	0.829748i	−0.0998895	−	0.0838172i
$99$	0.326352	+	0.118782i	0.0327996	+	0.0119381i
$100$	−6.23783	+	2.27038i	−0.623783	+	0.227038i
$101$	−7.58899	+	6.36792i	−0.755133	+	0.633632i	−0.936855	−	0.349718i	$-0.886277\pi$
$101$	−7.58899	+	6.36792i	−0.755133	+	0.633632i	0.181722	+	0.983350i	$0.441833\pi$
$102$	−3.47178	−	6.01330i	−0.343758	−	0.595406i
$103$	−3.92262	+	6.79417i	−0.386507	+	0.669450i	−0.991977	−	0.126418i	$-0.959652\pi$
$103$	−3.92262	+	6.79417i	−0.386507	+	0.669450i	0.605470	+	0.795868i	$0.292985\pi$
$104$	0.286989	+	1.62760i	0.0281416	+	0.159599i
$105$	−1.70574	−	9.67372i	−0.166463	−	0.944058i
$106$	0.990200	−	1.71508i	0.0961767	−	0.166583i
$107$	0.0136706	+	0.0236781i	0.00132158	+	0.00228905i	0.866685	−	0.498855i	$-0.166246\pi$
$107$	0.0136706	+	0.0236781i	0.00132158	+	0.00228905i	−0.865364	+	0.501144i	$0.832913\pi$
$108$	−0.766044	+	0.642788i	−0.0737127	+	0.0618523i
$109$	10.1236	−	3.68469i	0.969666	−	0.352929i	0.191852	−	0.981424i	$-0.438551\pi$
$109$	10.1236	−	3.68469i	0.969666	−	0.352929i	0.777814	+	0.628494i	$0.216329\pi$
$110$	1.11334	+	0.405223i	0.106153	+	0.0386365i
$111$	8.58899	+	7.20702i	0.815231	+	0.684060i
$112$	−0.500000	+	2.83564i	−0.0472456	+	0.267943i
$113$	−11.6604			−1.09692			−0.548461	−	0.836176i	$-0.684786\pi$
$113$	−11.6604			−1.09692			−0.548461	+	0.836176i	$0.684786\pi$
$114$	−0.0320889	+	4.35878i	−0.00300540	+	0.408237i
$115$	−23.2003			−2.16344
$116$	1.10354	−	6.25849i	0.102461	−	0.581086i
$117$	−1.26604	−	1.06234i	−0.117046	−	0.0982131i
$118$	0.418748	+	0.152412i	0.0385489	+	0.0140306i
$119$	18.7875	−	6.83807i	1.72224	−	0.626845i
$120$	−2.61334	+	2.19285i	−0.238564	+	0.200179i
$121$	5.43969	+	9.42182i	0.494518	+	0.856529i
$122$	−6.26604	+	10.8531i	−0.567301	+	0.982594i
$123$	0.606067	+	3.43718i	0.0546472	+	0.309920i
$124$	0.277189	+	1.57202i	0.0248923	+	0.141171i
$125$	2.79426	−	4.83981i	0.249926	−	0.432885i
$126$	−1.43969	−	2.49362i	−0.128258	−	0.222149i
$127$	12.4192	−	10.4210i	1.10203	−	0.924711i	0.104467	−	0.994528i	$-0.466686\pi$
$127$	12.4192	−	10.4210i	1.10203	−	0.924711i	0.997560	+	0.0698178i	$0.0222418\pi$
$128$	0.939693	−	0.342020i	0.0830579	−	0.0302306i
$129$	2.14543	+	0.780873i	0.188895	+	0.0687520i
$130$	−4.31908	−	3.62414i	−0.378808	−	0.317858i
$131$	−0.486329	+	2.75811i	−0.0424908	+	0.240977i	−0.998655	−	0.0518550i	$-0.983487\pi$
$131$	−0.486329	+	2.75811i	−0.0424908	+	0.240977i	0.956164	+	0.292832i	$0.0945978\pi$
$132$	0.347296			0.0302283
$133$	−12.3439	−	2.27038i	−1.07035	−	0.196867i
$134$	1.07873			0.0931877
$135$	0.592396	−	3.35965i	0.0509854	−	0.289152i
$136$	−5.31908	−	4.46324i	−0.456107	−	0.382719i
$137$	−15.0680	−	5.48432i	−1.28735	−	0.468557i	−0.394494	−	0.918899i	$-0.629080\pi$
$137$	−15.0680	−	5.48432i	−1.28735	−	0.468557i	−0.892856	+	0.450341i	$0.851302\pi$
$138$	−6.39053	+	2.32596i	−0.543998	+	0.197999i
$139$	−1.59240	+	1.33618i	−0.135065	+	0.113333i	−0.707818	−	0.706395i	$-0.750320\pi$
$139$	−1.59240	+	1.33618i	−0.135065	+	0.113333i	0.572752	+	0.819728i	$0.305876\pi$
$140$	−4.91147	−	8.50692i	−0.415095	−	0.718966i
$141$	2.79813	−	4.84651i	0.235645	−	0.408150i
$142$	2.88666	+	16.3711i	0.242243	+	1.37383i
$143$	0.0996702	+	0.565258i	0.00833484	+	0.0472692i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	10.8400	+	18.7755i	0.900215	+	1.55922i
$146$	−9.51367	+	7.98292i	−0.787357	+	0.660671i
$147$	1.21301	−	0.441500i	0.100047	−	0.0364143i
$148$	10.5360	+	3.83478i	0.866051	+	0.315217i
$149$	−1.27719	−	1.07169i	−0.104631	−	0.0877962i	0.588971	−	0.808154i	$-0.299533\pi$
$149$	−1.27719	−	1.07169i	−0.104631	−	0.0877962i	−0.693603	+	0.720358i	$0.743978\pi$
$150$	1.15270	−	6.53731i	0.0941179	−	0.533769i
$151$	20.0523			1.63183			0.815917	−	0.578169i	$-0.196232\pi$
$151$	20.0523			1.63183			0.815917	+	0.578169i	$0.196232\pi$
$152$	1.46064	+	4.10689i	0.118473	+	0.333113i
$153$	6.94356			0.561354
$154$	−0.173648	+	0.984808i	−0.0139930	+	0.0793581i
$155$	−4.17159	−	3.50038i	−0.335070	−	0.281157i
$156$	−1.55303	−	0.565258i	−0.124342	−	0.0452569i
$157$	3.85117	−	1.40171i	0.307357	−	0.111869i	−0.183737	−	0.982975i	$-0.558820\pi$
$157$	3.85117	−	1.40171i	0.307357	−	0.111869i	0.491094	+	0.871107i	$0.336597\pi$
$158$	8.36824	−	7.02179i	0.665741	−	0.558623i
$159$	0.990200	+	1.71508i	0.0785280	+	0.136014i
$160$	−1.70574	+	2.95442i	−0.134850	+	0.233568i
$161$	−3.40033	−	19.2842i	−0.267984	−	1.51981i
$162$	−0.173648	−	0.984808i	−0.0136431	−	0.0773738i
$163$	4.06758	−	7.04526i	0.318598	−	0.551827i	−0.661598	−	0.749859i	$-0.730121\pi$
$163$	4.06758	−	7.04526i	0.318598	−	0.551827i	0.980196	+	0.198031i	$0.0634548\pi$
$164$	1.74510	+	3.02260i	0.136269	+	0.236026i
$165$	−0.907604	+	0.761570i	−0.0706569	+	0.0592881i
$166$	11.0103	−	4.00741i	0.854562	−	0.311035i
$167$	12.5890	+	4.58202i	0.974166	+	0.354567i	0.779569	−	0.626316i	$-0.215438\pi$
$167$	12.5890	+	4.58202i	0.974166	+	0.354567i	0.194596	+	0.980883i	$0.437660\pi$
$168$	−2.20574	−	1.85083i	−0.170176	−	0.142795i
$169$	−1.78312	+	10.1126i	−0.137163	+	0.777890i
$170$	23.6878			1.81677
$171$	−3.75877	−	2.20718i	−0.287440	−	0.168787i
$172$	2.28312			0.174086
$173$	−0.177519	+	1.00676i	−0.0134965	+	0.0765424i	−0.990812	−	0.135246i	$-0.956818\pi$
$173$	−0.177519	+	1.00676i	−0.0134965	+	0.0765424i	0.977316	+	0.211788i	$0.0679287\pi$
$174$	4.86824	+	4.08494i	0.369060	+	0.309678i
$175$	17.9611	+	6.53731i	1.35773	+	0.494174i
$176$	0.326352	−	0.118782i	0.0245997	−	0.00895356i
$177$	−0.341367	+	0.286441i	−0.0256587	+	0.0215302i
$178$	0.896459	+	1.55271i	0.0671925	+	0.116381i
$179$	−1.01754	+	1.76243i	−0.0760546	+	0.131730i	−0.901544	−	0.432687i	$-0.857566\pi$
$179$	−1.01754	+	1.76243i	−0.0760546	+	0.131730i	0.825490	+	0.564417i	$0.190899\pi$
$180$	−0.592396	−	3.35965i	−0.0441546	−	0.250413i
$181$	3.87299	+	21.9648i	0.287877	+	1.63263i	0.694824	+	0.719180i	$0.255482\pi$
$181$	3.87299	+	21.9648i	0.287877	+	1.63263i	−0.406947	+	0.913452i	$0.633407\pi$
$182$	2.37939	−	4.12122i	0.176372	−	0.305485i
$183$	−6.26604	−	10.8531i	−0.463199	−	0.802285i
$184$	−5.20961	+	4.37138i	−0.384057	+	0.322262i
$185$	−35.9432	+	13.0822i	−2.64259	+	0.961825i
$186$	−1.50000	−	0.545955i	−0.109985	−	0.0400314i
$187$	−1.84730	−	1.55007i	−0.135088	−	0.113352i
$188$	0.971782	−	5.51125i	0.0708745	−	0.401949i
$189$	2.87939			0.209444
$190$	−12.8229	−	7.52974i	−0.930274	−	0.546265i
$191$	10.7861			0.780456			0.390228	−	0.920718i	$-0.372396\pi$
$191$	10.7861			0.780456			0.390228	+	0.920718i	$0.372396\pi$
$192$	−0.173648	+	0.984808i	−0.0125320	+	0.0710724i
$193$	−2.19459	−	1.84148i	−0.157970	−	0.132553i	0.560377	−	0.828238i	$-0.310656\pi$
$193$	−2.19459	−	1.84148i	−0.157970	−	0.132553i	−0.718347	+	0.695685i	$0.755101\pi$
$194$	3.43242	+	1.24930i	0.246433	+	0.0896944i
$195$	5.29813	−	1.92836i	0.379407	−	0.138093i
$196$	0.988856	−	0.829748i	0.0706325	−	0.0592677i
$197$	4.16772	+	7.21870i	0.296938	+	0.514311i	0.975434	−	0.220293i	$-0.0707013\pi$
$197$	4.16772	+	7.21870i	0.296938	+	0.514311i	−0.678496	+	0.734604i	$0.737368\pi$
$198$	−0.173648	+	0.300767i	−0.0123406	+	0.0213746i
$199$	−0.526874	−	2.98805i	−0.0373491	−	0.211817i	0.960422	−	0.278550i	$-0.0898537\pi$
$199$	−0.526874	−	2.98805i	−0.0373491	−	0.211817i	−0.997771	+	0.0667324i	$0.978743\pi$
$200$	−1.15270	−	6.53731i	−0.0815085	−	0.462257i
$201$	−0.539363	+	0.934204i	−0.0380437	+	0.0658937i
$202$	−4.95336	−	8.57948i	−0.348517	−	0.603650i
$203$	−14.0175	+	11.7621i	−0.983839	+	0.825539i
$204$	6.52481	−	2.37484i	0.456828	−	0.166272i
$205$	−11.1887	−	4.07234i	−0.781450	−	0.284425i
$206$	−6.00980	−	5.04282i	−0.418723	−	0.351350i
$207$	1.18092	−	6.69734i	0.0820798	−	0.465497i
$208$	−1.65270			−0.114594
$209$	0.507274	+	1.42631i	0.0350889	+	0.0986598i
$210$	9.82295			0.677848
$211$	−2.88919	+	16.3854i	−0.198900	+	1.12802i	0.707855	+	0.706358i	$0.249663\pi$
$211$	−2.88919	+	16.3854i	−0.198900	+	1.12802i	−0.906755	+	0.421659i	$0.861448\pi$
$212$	1.51707	+	1.27298i	0.104193	+	0.0874284i
$213$	−15.6211	−	5.68561i	−1.07034	−	0.389571i
$214$	−0.0256923	+	0.00935122i	−0.00175629	+	0.000639236i
$215$	−5.96657	+	5.00654i	−0.406916	+	0.341443i
$216$	−0.500000	−	0.866025i	−0.0340207	−	0.0589256i
$217$	2.29813	−	3.98048i	0.156007	−	0.270213i
$218$	1.87077	+	10.6096i	0.126704	+	0.718576i
$219$	−2.15657	−	12.2305i	−0.145728	−	0.826463i
$220$	−0.592396	+	1.02606i	−0.0399393	+	0.0691770i
$221$	5.73783	+	9.93821i	0.385968	+	0.668516i
$222$	−8.58899	+	7.20702i	−0.576455	+	0.483704i
$223$	7.67752	−	2.79439i	0.514125	−	0.187126i	−0.0719114	−	0.997411i	$-0.522910\pi$
$223$	7.67752	−	2.79439i	0.514125	−	0.187126i	0.586036	+	0.810285i	$0.300688\pi$
$224$	−2.70574	−	0.984808i	−0.180785	−	0.0658002i
$225$	5.08512	+	4.26692i	0.339008	+	0.284462i
$226$	2.02481	−	11.4833i	0.134689	−	0.763857i
$227$	1.80066			0.119514			0.0597570	−	0.998213i	$-0.480967\pi$
$227$	1.80066			0.119514			0.0597570	+	0.998213i	$0.480967\pi$
$228$	−4.28699	−	0.788496i	−0.283913	−	0.0522194i
$229$	−18.7392			−1.23832			−0.619160	−	0.785265i	$-0.712527\pi$
$229$	−18.7392			−1.23832			−0.619160	+	0.785265i	$0.712527\pi$
$230$	4.02869	−	22.8478i	0.265644	−	1.50654i
$231$	−0.766044	−	0.642788i	−0.0504020	−	0.0422923i
$232$	5.97178	+	2.17355i	0.392067	+	0.142701i
$233$	3.85117	−	1.40171i	0.252298	−	0.0918291i	−0.212775	−	0.977101i	$-0.568250\pi$
$233$	3.85117	−	1.40171i	0.252298	−	0.0918291i	0.465073	+	0.885272i	$0.346028\pi$
$234$	1.26604	−	1.06234i	0.0827639	−	0.0694472i
$235$	9.54576	+	16.5337i	0.622697	+	1.07854i
$236$	−0.222811	+	0.385920i	−0.0145038	+	0.0251213i
$237$	1.89693	+	10.7580i	0.123219	+	0.698807i
$238$	3.47178	+	19.6895i	0.225042	+	1.27628i
$239$	14.1138	−	24.4458i	0.912946	−	1.58127i	0.103066	−	0.994675i	$-0.467135\pi$
$239$	14.1138	−	24.4458i	0.912946	−	1.58127i	0.809881	−	0.586595i	$-0.199532\pi$
$240$	−1.70574	−	2.95442i	−0.110105	−	0.190707i
$241$	5.02687	−	4.21805i	0.323809	−	0.271708i	−0.466362	−	0.884594i	$-0.654436\pi$
$241$	5.02687	−	4.21805i	0.323809	−	0.271708i	0.790172	+	0.612885i	$0.209991\pi$
$242$	−10.2233	+	3.72097i	−0.657177	+	0.239193i
$243$	0.939693	+	0.342020i	0.0602813	+	0.0219406i
$244$	−9.60014	−	8.05547i	−0.614586	−	0.515699i
$245$	−0.764700	+	4.33683i	−0.0488549	+	0.277070i
$246$	−3.49020			−0.222527
$247$	0.0530334	−	7.20377i	0.00337444	−	0.458365i
$248$	−1.59627			−0.101363
$249$	−2.03462	+	11.5389i	−0.128938	+	0.731247i
$250$	4.28106	+	3.59224i	0.270758	+	0.227193i
$251$	−8.35756	−	3.04190i	−0.527525	−	0.192003i	0.0645080	−	0.997917i	$-0.479452\pi$
$251$	−8.35756	−	3.04190i	−0.527525	−	0.192003i	−0.592033	+	0.805914i	$0.701674\pi$
$252$	2.70574	−	0.984808i	0.170445	−	0.0620371i
$253$	−1.80928	+	1.51816i	−0.113748	+	0.0954462i
$254$	8.10607	+	14.0401i	0.508620	+	0.880955i
$255$	−11.8439	+	20.5142i	−0.741693	+	1.28465i
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−2.33837	−	13.2616i	−0.145864	−	0.827234i	−0.966670	−	0.256027i	$-0.917586\pi$
$257$	−2.33837	−	13.2616i	−0.145864	−	0.827234i	0.820806	−	0.571207i	$-0.193525\pi$
$258$	−1.14156	+	1.97724i	−0.0710704	+	0.123098i
$259$	−16.1420	−	27.9588i	−1.00302	−	1.73728i
$260$	4.31908	−	3.62414i	0.267858	−	0.224759i
$261$	−5.97178	+	2.17355i	−0.369644	+	0.134539i
$262$	−2.63176	−	0.957882i	−0.162591	−	0.0591781i
$263$	−12.8327	−	10.7680i	−0.791301	−	0.663981i	0.154766	−	0.987951i	$-0.450538\pi$
$263$	−12.8327	−	10.7680i	−0.791301	−	0.663981i	−0.946067	+	0.323971i	$0.894982\pi$
$264$	−0.0603074	+	0.342020i	−0.00371166	+	0.0210499i
$265$	−6.75608			−0.415023
$266$	4.37939	−	11.7621i	0.268517	−	0.721181i
$267$	−1.79292			−0.109725
$268$	−0.187319	+	1.06234i	−0.0114423	+	0.0648926i
$269$	2.74969	+	2.30726i	0.167651	+	0.140676i	0.722753	−	0.691106i	$-0.242876\pi$
$269$	2.74969	+	2.30726i	0.167651	+	0.140676i	−0.555102	+	0.831782i	$0.687321\pi$
$270$	3.20574	+	1.16679i	0.195095	+	0.0710088i
$271$	−22.5141	+	8.19448i	−1.36764	+	0.497779i	−0.918407	−	0.395637i	$-0.870524\pi$
$271$	−22.5141	+	8.19448i	−1.36764	+	0.497779i	−0.449230	+	0.893416i	$0.648301\pi$
$272$	5.31908	−	4.46324i	0.322516	−	0.270623i
$273$	2.37939	+	4.12122i	0.144007	+	0.249427i
$274$	8.01754	−	13.8868i	0.484357	−	0.838932i
$275$	−0.400330	−	2.27038i	−0.0241408	−	0.136909i
$276$	−1.18092	−	6.69734i	−0.0710832	−	0.403133i
$277$	9.36097	−	16.2137i	0.562446	−	0.974185i	−0.434836	−	0.900510i	$-0.643194\pi$
$277$	9.36097	−	16.2137i	0.562446	−	0.974185i	0.997282	−	0.0736755i	$-0.0234729\pi$
$278$	−1.03936	−	1.80023i	−0.0623368	−	0.107971i
$279$	1.22281	−	1.02606i	0.0732078	−	0.0614286i
$280$	9.23055	−	3.35965i	0.551631	−	0.200777i
$281$	9.99660	+	3.63846i	0.596347	+	0.217053i	0.622519	−	0.782605i	$-0.286109\pi$
$281$	9.99660	+	3.63846i	0.596347	+	0.217053i	−0.0261718	+	0.999657i	$0.508332\pi$
$282$	4.28699	+	3.59721i	0.255286	+	0.214211i
$283$	−2.43330	+	13.7999i	−0.144644	+	0.820319i	0.823008	+	0.568030i	$0.192294\pi$
$283$	−2.43330	+	13.7999i	−0.144644	+	0.820319i	−0.967652	+	0.252289i	$0.918817\pi$
$284$	−16.6236			−0.986430
$285$	12.9324	−	7.34013i	0.766050	−	0.434792i
$286$	−0.573978			−0.0339400
$287$	1.74510	−	9.89695i	0.103010	−	0.584199i
$288$	−0.766044	−	0.642788i	−0.0451396	−	0.0378766i
$289$	−29.3307	−	10.6755i	−1.72533	−	0.627970i
$290$	−20.3726	+	7.41501i	−1.19632	+	0.435424i
$291$	−2.79813	+	2.34791i	−0.164029	+	0.137637i
$292$	−6.20961	−	10.7554i	−0.363390	−	0.629410i
$293$	5.76011	−	9.97681i	0.336509	−	0.582852i	−0.647264	−	0.762266i	$-0.724087\pi$
$293$	5.76011	−	9.97681i	0.336509	−	0.582852i	0.983774	+	0.179414i	$0.0574202\pi$
$294$	0.224155	+	1.27125i	0.0130730	+	0.0741407i
$295$	−0.263985	−	1.49713i	−0.0153698	−	0.0871665i
$296$	−5.60607	+	9.70999i	−0.325846	+	0.564382i
$297$	−0.173648	−	0.300767i	−0.0100761	−	0.0174523i
$298$	1.27719	−	1.07169i	0.0739856	−	0.0620813i
$299$	10.5617	−	3.84413i	0.610796	−	0.222312i
$300$	6.23783	+	2.27038i	0.360141	+	0.131081i
$301$	−5.03596	−	4.22567i	−0.290268	−	0.243564i
$302$	−3.48205	+	19.7477i	−0.200369	+	1.13635i
$303$	9.90673			0.569127
$304$	−4.29813	+	0.725293i	−0.246515	+	0.0415984i
$305$	42.7529			2.44802
$306$	−1.20574	+	6.83807i	−0.0689274	+	0.390907i
$307$	3.29220	+	2.76249i	0.187896	+	0.157663i	0.731883	−	0.681430i	$-0.238642\pi$
$307$	3.29220	+	2.76249i	0.187896	+	0.157663i	−0.543987	+	0.839093i	$0.683086\pi$
$308$	−0.939693	−	0.342020i	−0.0535440	−	0.0194884i
$309$	7.37211	−	2.68323i	0.419385	−	0.152644i
$310$	4.17159	−	3.50038i	0.236930	−	0.198808i
$311$	11.4966	+	19.9127i	0.651912	+	1.12915i	0.982658	+	0.185425i	$0.0593663\pi$
$311$	11.4966	+	19.9127i	0.651912	+	1.12915i	−0.330746	+	0.943720i	$0.607300\pi$
$312$	0.826352	−	1.43128i	0.0467830	−	0.0810305i
$313$	−1.59926	−	9.06985i	−0.0903955	−	0.512658i	−0.996061	−	0.0886663i	$-0.971740\pi$
$313$	−1.59926	−	9.06985i	−0.0903955	−	0.512658i	0.905666	−	0.423992i	$-0.139372\pi$
$314$	0.711667	+	4.03606i	0.0401617	+	0.227768i
$315$	−4.91147	+	8.50692i	−0.276730	+	0.479311i
$316$	5.46198	+	9.46043i	0.307260	+	0.532191i
$317$	2.57011	−	2.15658i	0.144352	−	0.121125i	−0.567752	−	0.823199i	$-0.692187\pi$
$317$	2.57011	−	2.15658i	0.144352	−	0.121125i	0.712104	+	0.702074i	$0.247742\pi$
$318$	−1.86097	+	0.677337i	−0.104358	+	0.0379831i
$319$	2.07398	+	0.754866i	0.116120	+	0.0422644i
$320$	−2.61334	−	2.19285i	−0.146090	−	0.122584i
$321$	0.00474774	−	0.0269258i	0.000264993	−	0.00150285i
$322$	19.5817			1.09125
$323$	19.2836	+	23.3279i	1.07297	+	1.29800i
$324$	1.00000			0.0555556
$325$	−1.90508	+	10.8042i	−0.105675	+	0.599311i
$326$	6.23190	+	5.22918i	0.345153	+	0.289618i
$327$	−10.1236	−	3.68469i	−0.559837	−	0.203764i
$328$	−3.27972	+	1.19372i	−0.181092	+	0.0659121i
$329$	−12.3439	+	10.3578i	−0.680541	+	0.571042i
$330$	−0.592396	−	1.02606i	−0.0326103	−	0.0564828i
$331$	11.0371	−	19.1169i	0.606656	−	1.05076i	−0.385131	−	0.922862i	$-0.625844\pi$
$331$	11.0371	−	19.1169i	0.606656	−	1.05076i	0.991787	−	0.127897i	$-0.0408228\pi$
$332$	2.03462	+	11.5389i	0.111664	+	0.633278i
$333$	−1.94697	−	11.0418i	−0.106693	−	0.605087i
$334$	−6.69846	+	11.6021i	−0.366524	+	0.634837i
$335$	−1.84002	−	3.18701i	−0.100531	−	0.174125i
$336$	2.20574	−	1.85083i	0.120333	−	0.100971i
$337$	12.3255	−	4.48611i	0.671411	−	0.244374i	0.0162559	−	0.999868i	$-0.494825\pi$
$337$	12.3255	−	4.48611i	0.671411	−	0.244374i	0.655155	+	0.755494i	$0.272603\pi$
$338$	−9.64930	−	3.51206i	−0.524853	−	0.191031i
$339$	8.93242	+	7.49519i	0.485142	+	0.407083i
$340$	−4.11334	+	23.3279i	−0.223077	+	1.26513i
$341$	−0.554378			−0.0300212
$342$	2.82635	−	3.31839i	0.152832	−	0.179438i
$343$	16.4388			0.887613
$344$	−0.396459	+	2.24843i	−0.0213757	+	0.121227i
$345$	17.7724	+	14.9128i	0.956836	+	0.802881i
$346$	−0.960637	−	0.349643i	−0.0516442	−	0.0187969i
$347$	−8.23055	+	2.99568i	−0.441839	+	0.160816i	−0.553354	−	0.832947i	$-0.686652\pi$
$347$	−8.23055	+	2.99568i	−0.441839	+	0.160816i	0.111514	+	0.993763i	$0.464430\pi$
$348$	−4.86824	+	4.08494i	−0.260965	+	0.218976i
$349$	−1.63176	−	2.82629i	−0.0873461	−	0.151288i	0.819042	−	0.573733i	$-0.194505\pi$
$349$	−1.63176	−	2.82629i	−0.0873461	−	0.151288i	−0.906389	+	0.422445i	$0.861172\pi$
$350$	−9.55690	+	16.5530i	−0.510838	+	0.884797i
$351$	0.286989	+	1.62760i	0.0153183	+	0.0868746i
$352$	0.0603074	+	0.342020i	0.00321439	+	0.0182297i
$353$	−14.5419	+	25.1873i	−0.773987	+	1.34058i	0.161376	+	0.986893i	$0.448407\pi$
$353$	−14.5419	+	25.1873i	−0.773987	+	1.34058i	−0.935362	+	0.353691i	$0.884926\pi$
$354$	−0.222811	−	0.385920i	−0.0118423	−	0.0205114i
$355$	43.4432	−	36.4531i	2.30572	−	1.93473i
$356$	−1.68479	+	0.613214i	−0.0892938	+	0.0325003i
$357$	−18.7875	−	6.83807i	−0.994338	−	0.361909i
$358$	−1.55896	−	1.30813i	−0.0823938	−	0.0691366i
$359$	1.14796	−	6.51038i	0.0605868	−	0.343605i	−0.939413	−	0.342788i	$-0.888629\pi$
$359$	1.14796	−	6.51038i	0.0605868	−	0.343605i	1.00000		0.000817017i	$-0.000260065\pi$
$360$	3.41147			0.179800
$361$	−3.02347	−	18.7579i	−0.159130	−	0.987258i
$362$	−22.3037			−1.17225
$363$	1.88919	−	10.7141i	0.0991565	−	0.562345i
$364$	3.64543	+	3.05888i	0.191072	+	0.160329i
$365$	39.8127	+	14.4907i	2.08389	+	0.758475i
$366$	11.7763	−	4.28623i	0.615558	−	0.224045i
$367$	−4.43969	+	3.72534i	−0.231750	+	0.194461i	−0.751266	−	0.659999i	$-0.770557\pi$
$367$	−4.43969	+	3.72534i	−0.231750	+	0.194461i	0.519516	+	0.854461i	$0.326112\pi$
$368$	−3.40033	−	5.88954i	−0.177254	−	0.307014i
$369$	1.74510	−	3.02260i	0.0908463	−	0.157350i
$370$	−6.64203	−	37.6688i	−0.345302	−	1.95831i
$371$	−0.990200	−	5.61570i	−0.0514086	−	0.291553i
$372$	0.798133	−	1.38241i	0.0413813	−	0.0716745i
$373$	12.9449	+	22.4212i	0.670262	+	1.16093i	0.977830	+	0.209401i	$0.0671516\pi$
$373$	12.9449	+	22.4212i	0.670262	+	1.16093i	−0.307568	+	0.951526i	$0.599515\pi$
$374$	1.84730	−	1.55007i	0.0955214	−	0.0801520i
$375$	−5.25150	+	1.91139i	−0.271186	+	0.0987037i
$376$	5.25877	+	1.91404i	0.271200	+	0.0987089i
$377$	−8.04576	−	6.75119i	−0.414378	−	0.347704i
$378$	−0.500000	+	2.83564i	−0.0257172	+	0.145850i
$379$	−19.1557			−0.983962			−0.491981	−	0.870606i	$-0.663727\pi$
$379$	−19.1557			−0.983962			−0.491981	+	0.870606i	$0.663727\pi$
$380$	9.64203	−	11.3206i	0.494626	−	0.580735i
$381$	−16.2121			−0.830573
$382$	−1.87299	+	10.6222i	−0.0958304	+	0.543481i
$383$	−7.42649	−	6.23156i	−0.379476	−	0.318418i	0.433021	−	0.901384i	$-0.357448\pi$
$383$	−7.42649	−	6.23156i	−0.379476	−	0.318418i	−0.812497	+	0.582966i	$0.801892\pi$
$384$	−0.939693	−	0.342020i	−0.0479535	−	0.0174536i
$385$	3.20574	−	1.16679i	0.163379	−	0.0594653i
$386$	2.19459	−	1.84148i	0.111702	−	0.0937290i
$387$	−1.14156	−	1.97724i	−0.0580287	−	0.100509i
$388$	−1.82635	+	3.16333i	−0.0927190	+	0.160594i
$389$	−0.142026	−	0.805470i	−0.00720101	−	0.0408390i	0.980996	−	0.194030i	$-0.0621560\pi$
$389$	−0.142026	−	0.805470i	−0.00720101	−	0.0408390i	−0.988197	+	0.153191i	$0.951045\pi$
$390$	0.979055	+	5.55250i	0.0495764	+	0.281162i
$391$	−23.6104	+	40.8944i	−1.19403	+	2.06812i
$392$	0.645430	+	1.11792i	0.0325991	+	0.0564633i
$393$	2.14543	−	1.80023i	0.108223	−	0.0908096i
$394$	−7.83275	+	2.85089i	−0.394608	+	0.143626i
$395$	−35.0194	−	12.7460i	−1.76201	−	0.641321i
$396$	−0.266044	−	0.223238i	−0.0133692	−	0.0112181i
$397$	−0.642026	+	3.64111i	−0.0322224	+	0.182742i	−0.996671	−	0.0815281i	$-0.974020\pi$
$397$	−0.642026	+	3.64111i	−0.0322224	+	0.182742i	0.964449	+	0.264270i	$0.0851311\pi$
$398$	3.03415			0.152088
$399$	7.99660	+	9.67372i	0.400331	+	0.484292i
$400$	6.63816			0.331908
$401$	−3.77513	+	21.4098i	−0.188521	+	1.06916i	0.732827	+	0.680416i	$0.238201\pi$
$401$	−3.77513	+	21.4098i	−0.188521	+	1.06916i	−0.921347	+	0.388740i	$0.872910\pi$
$402$	−0.826352	−	0.693392i	−0.0412147	−	0.0345832i
$403$	2.47906	+	0.902302i	0.123491	+	0.0449469i
$404$	9.30928	−	3.38830i	0.463154	−	0.168574i
$405$	−2.61334	+	2.19285i	−0.129858	+	0.108964i
$406$	−9.14930	−	15.8471i	−0.454072	−	0.786476i
$407$	−1.94697	+	3.37225i	−0.0965076	+	0.167156i
$408$	1.20574	+	6.83807i	0.0596929	+	0.338535i
$409$	−0.704088	−	3.99308i	−0.0348149	−	0.197445i	0.962440	−	0.271496i	$-0.0875184\pi$
$409$	−0.704088	−	3.99308i	−0.0348149	−	0.197445i	−0.997254	+	0.0740509i	$0.976407\pi$
$410$	5.95336	−	10.3115i	0.294016	−	0.509250i
$411$	8.01754	+	13.8868i	0.395476	+	0.684985i
$412$	6.00980	−	5.04282i	0.296082	−	0.248442i
$413$	1.20574	−	0.438852i	0.0593304	−	0.0215945i
$414$	6.39053	+	2.32596i	0.314077	+	0.114315i
$415$	−30.6202	−	25.6934i	−1.50309	−	1.26124i
$416$	0.286989	−	1.62760i	0.0140708	−	0.0797994i
$417$	2.07873			0.101796
$418$	−1.49273	+	0.251892i	−0.0730116	+	0.0123204i
$419$	23.4989			1.14800			0.573998	−	0.818857i	$-0.305392\pi$
$419$	23.4989			1.14800			0.573998	+	0.818857i	$0.305392\pi$
$420$	−1.70574	+	9.67372i	−0.0832314	+	0.472029i
$421$	−17.6748	−	14.8309i	−0.861419	−	0.722816i	0.100855	−	0.994901i	$-0.467842\pi$
$421$	−17.6748	−	14.8309i	−0.861419	−	0.722816i	−0.962273	+	0.272085i	$0.912287\pi$
$422$	−15.6348	−	5.69058i	−0.761088	−	0.277013i
$423$	−5.25877	+	1.91404i	−0.255690	+	0.0930636i
$424$	−1.51707	+	1.27298i	−0.0736756	+	0.0618212i
$425$	−23.0462	−	39.9172i	−1.11791	−	1.93627i
$426$	8.31180	−	14.3965i	0.402708	−	0.697511i
$427$	6.26604	+	35.5365i	0.303235	+	1.71973i
$428$	−0.00474774	−	0.0269258i	−0.000229491	−	0.00130151i
$429$	0.286989	−	0.497079i	0.0138560	−	0.0239992i
$430$	−3.89440	−	6.74530i	−0.187805	−	0.325287i
$431$	−2.69253	+	2.25930i	−0.129695	+	0.108827i	−0.705328	−	0.708881i	$-0.749200\pi$
$431$	−2.69253	+	2.25930i	−0.129695	+	0.108827i	0.575633	+	0.817708i	$0.304756\pi$
$432$	0.939693	−	0.342020i	0.0452110	−	0.0164555i
$433$	32.0574	+	11.6679i	1.54058	+	0.560725i	0.966184	−	0.257853i	$-0.0830152\pi$
$433$	32.0574	+	11.6679i	1.54058	+	0.560725i	0.574395	+	0.818578i	$0.305237\pi$
$434$	3.52094	+	2.95442i	0.169011	+	0.141817i
$435$	3.76470	−	21.3507i	0.180504	−	1.02369i
$436$	−10.7733			−0.515948
$437$	25.7803	−	14.6323i	1.23324	−	0.699958i
$438$	12.4192			0.593413
$439$	1.68463	−	9.55401i	0.0804030	−	0.455988i	−0.917851	−	0.396925i	$-0.870077\pi$
$439$	1.68463	−	9.55401i	0.0804030	−	0.455988i	0.998254	−	0.0590636i	$-0.0188115\pi$
$440$	−0.907604	−	0.761570i	−0.0432683	−	0.0363064i
$441$	−1.21301	−	0.441500i	−0.0577624	−	0.0210238i
$442$	−10.7836	+	3.92490i	−0.512923	+	0.186689i
$443$	11.6302	−	9.75887i	0.552566	−	0.463658i	−0.323243	−	0.946316i	$-0.604773\pi$
$443$	11.6302	−	9.75887i	0.552566	−	0.463658i	0.875809	+	0.482658i	$0.160329\pi$
$444$	−5.60607	−	9.70999i	−0.266052	−	0.460816i
$445$	3.05825	−	5.29704i	0.144975	−	0.251104i
$446$	1.41875	+	8.04612i	0.0671797	+	0.380995i
$447$	0.289515	+	1.64192i	0.0136936	+	0.0776603i
$448$	1.43969	−	2.49362i	0.0680191	−	0.117813i
$449$	−17.4192	−	30.1710i	−0.822064	−	1.42386i	−0.904143	−	0.427230i	$-0.859489\pi$
$449$	−17.4192	−	30.1710i	−0.822064	−	1.42386i	0.0820794	−	0.996626i	$-0.473844\pi$
$450$	−5.08512	+	4.26692i	−0.239715	+	0.201145i
$451$	−1.13903	+	0.414574i	−0.0536350	+	0.0195215i
$452$	10.9572	+	3.98811i	0.515385	+	0.187585i
$453$	−15.3610	−	12.8894i	−0.721721	−	0.605596i
$454$	−0.312681	+	1.77330i	−0.0146749	+	0.0832253i
$455$	−16.2344			−0.761081
$456$	1.52094	−	4.08494i	0.0712248	−	0.191295i
$457$	−31.8749			−1.49105			−0.745523	−	0.666479i	$-0.767800\pi$
$457$	−31.8749			−1.49105			−0.745523	+	0.666479i	$0.767800\pi$
$458$	3.25402	−	18.4545i	0.152050	−	0.862321i
$459$	−5.31908	−	4.46324i	−0.248273	−	0.208326i
$460$	21.8011	+	7.93496i	1.01648	+	0.369969i
$461$	10.0449	−	3.65604i	0.467837	−	0.170279i	−0.0973354	−	0.995252i	$-0.531032\pi$
$461$	10.0449	−	3.65604i	0.467837	−	0.170279i	0.565172	+	0.824973i	$0.308810\pi$
$462$	0.766044	−	0.642788i	0.0356396	−	0.0299052i
$463$	−7.65910	−	13.2660i	−0.355949	−	0.616521i	0.631331	−	0.775513i	$-0.282509\pi$
$463$	−7.65910	−	13.2660i	−0.355949	−	0.616521i	−0.987280	+	0.158992i	$0.949176\pi$
$464$	−3.17752	+	5.50362i	−0.147513	+	0.255499i
$465$	0.945622	+	5.36289i	0.0438522	+	0.248698i
$466$	0.711667	+	4.03606i	0.0329673	+	0.186967i
$467$	−14.2562	+	24.6925i	−0.659700	+	1.14263i	0.320993	+	0.947082i	$0.395983\pi$
$467$	−14.2562	+	24.6925i	−0.659700	+	1.14263i	−0.980693	+	0.195553i	$0.937350\pi$
$468$	0.826352	+	1.43128i	0.0381981	+	0.0661611i
$469$	2.37939	−	1.99654i	0.109870	−	0.0921917i
$470$	−17.9402	+	6.52968i	−0.827518	+	0.301192i
$471$	−3.85117	−	1.40171i	−0.177452	−	0.0645874i
$472$	−0.341367	−	0.286441i	−0.0157127	−	0.0131845i
$473$	−0.137689	+	0.780873i	−0.00633094	+	0.0359046i
$474$	−10.9240			−0.501754
$475$	−0.213011	+	28.9343i	−0.00977362	+	1.32760i
$476$	−19.9932			−0.916386
$477$	0.343893	−	1.95031i	0.0157458	−	0.0892987i
$478$	21.6236	+	18.1444i	0.989041	+	0.829904i
$479$	−7.56583	−	2.75374i	−0.345691	−	0.125821i	0.163339	−	0.986570i	$-0.447774\pi$
$479$	−7.56583	−	2.75374i	−0.345691	−	0.125821i	−0.509030	+	0.860749i	$0.669996\pi$
$480$	3.20574	−	1.16679i	0.146321	−	0.0532566i
$481$	14.1951	−	11.9111i	0.647239	−	0.543098i
$482$	3.28106	+	5.68296i	0.149448	+	0.258852i
$483$	−9.79086	+	16.9583i	−0.445500	+	0.771628i
$484$	−1.88919	−	10.7141i	−0.0858721	−	0.487005i
$485$	−2.16385	−	12.2718i	−0.0982553	−	0.557233i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−3.05778	−	5.29623i	−0.138561	−	0.239995i	0.788391	−	0.615175i	$-0.210914\pi$
$487$	−3.05778	−	5.29623i	−0.138561	−	0.239995i	−0.926952	+	0.375179i	$0.877581\pi$
$488$	9.60014	−	8.05547i	0.434578	−	0.364654i
$489$	−7.64455	+	2.78239i	−0.345699	+	0.125824i
$490$	−4.13816	−	1.50617i	−0.186943	−	0.0680416i
$491$	−17.3778	−	14.5817i	−0.784249	−	0.658063i	0.160066	−	0.987106i	$-0.448829\pi$
$491$	−17.3778	−	14.5817i	−0.784249	−	0.658063i	−0.944315	+	0.329043i	$0.893274\pi$
$492$	0.606067	−	3.43718i	0.0273236	−	0.154960i
$493$	44.1266			1.98736
$494$	7.08512	+	1.30315i	0.318775	+	0.0586315i
$495$	1.18479			0.0532525
$496$	0.277189	−	1.57202i	0.0124461	−	0.0705856i
$497$	36.6673	+	30.7675i	1.64475	+	1.38011i
$498$	−11.0103	−	4.00741i	−0.493382	−	0.179576i
$499$	−23.3567	+	8.50114i	−1.04559	+	0.380563i	−0.806996	−	0.590557i	$-0.798908\pi$
$499$	−23.3567	+	8.50114i	−1.04559	+	0.380563i	−0.238593	+	0.971120i	$0.576686\pi$
$500$	−4.28106	+	3.59224i	−0.191455	+	0.160650i
$501$	−6.69846	−	11.6021i	−0.299265	−	0.518343i
$502$	4.44697	−	7.70237i	0.198478	−	0.343774i
$503$	4.34524	+	24.6431i	0.193745	+	1.09878i	0.914195	+	0.405274i	$0.132824\pi$
$503$	4.34524	+	24.6431i	0.193745	+	1.09878i	−0.720451	+	0.693506i	$0.756065\pi$
$504$	0.500000	+	2.83564i	0.0222718	+	0.126309i
$505$	−16.8983	+	29.2687i	−0.751963	+	1.30244i
$506$	−1.18092	−	2.04542i	−0.0524984	−	0.0909299i
$507$	7.86618	−	6.60051i	0.349349	−	0.293139i
$508$	−15.2344	+	5.54488i	−0.675918	+	0.246014i
$509$	−0.845075	−	0.307582i	−0.0374573	−	0.0136333i	0.323224	−	0.946323i	$-0.395233\pi$
$509$	−0.845075	−	0.307582i	−0.0374573	−	0.0136333i	−0.360681	+	0.932689i	$0.617456\pi$
$510$	−18.1459	−	15.2262i	−0.803514	−	0.674228i
$511$	−6.20961	+	35.2164i	−0.274697	+	1.55788i
$512$	−1.00000			−0.0441942
$513$	1.46064	+	4.10689i	0.0644887	+	0.181324i
$514$	13.4662			0.593967
$515$	−4.64749	+	26.3572i	−0.204793	+	1.16144i
$516$	−1.74897	−	1.46756i	−0.0769941	−	0.0646057i
$517$	1.82635	+	0.664738i	0.0803229	+	0.0292351i
$518$	30.3371	−	11.0418i	1.33294	−	0.485149i
$519$	0.783119	−	0.657115i	0.0343751	−	0.0288441i
$520$	2.81908	+	4.88279i	0.123625	+	0.214124i
$521$	3.31773	−	5.74648i	0.145353	−	0.251758i	−0.784152	−	0.620569i	$-0.786902\pi$
$521$	3.31773	−	5.74648i	0.145353	−	0.251758i	0.929504	+	0.368811i	$0.120235\pi$
$522$	−1.10354	−	6.25849i	−0.0483007	−	0.273927i
$523$	6.59034	+	37.3757i	0.288175	+	1.63432i	0.693718	+	0.720247i	$0.255972\pi$
$523$	6.59034	+	37.3757i	0.288175	+	1.63432i	−0.405542	+	0.914076i	$0.632917\pi$
$524$	1.40033	−	2.42544i	0.0611737	−	0.105956i
$525$	−9.55690	−	16.5530i	−0.417097	−	0.722434i
$526$	12.8327	−	10.7680i	0.559534	−	0.469505i
$527$	−10.4153	+	3.79088i	−0.453700	+	0.165133i
$528$	−0.326352	−	0.118782i	−0.0142026	−	0.00516934i
$529$	17.8097	+	14.9442i	0.774337	+	0.649746i
$530$	1.17318	−	6.65344i	0.0509597	−	0.289007i
$531$	0.445622			0.0193384
$532$	10.8229	+	6.35532i	0.469234	+	0.275538i
$533$	5.76827			0.249851
$534$	0.311337	−	1.76568i	0.0134729	−	0.0764085i
$535$	0.0714517	+	0.0599551i	0.00308913	+	0.00259209i
$536$	−1.01367	−	0.368946i	−0.0437839	−	0.0159360i
$537$	1.91235	−	0.696039i	0.0825241	−	0.0300363i
$538$	−2.74969	+	2.30726i	−0.118547	+	0.0994730i
$539$	0.224155	+	0.388249i	0.00965506	+	0.0167230i
$540$	−1.70574	+	2.95442i	−0.0734032	+	0.127138i
$541$	2.62742	+	14.9009i	0.112962	+	0.640638i	0.987739	+	0.156113i	$0.0498963\pi$
$541$	2.62742	+	14.9009i	0.112962	+	0.640638i	−0.874778	+	0.484525i	$0.838993\pi$
$542$	−4.16044	−	23.5951i	−0.178706	−	1.01349i
$543$	11.1518	−	19.3155i	0.478571	−	0.828909i
$544$	3.47178	+	6.01330i	0.148851	+	0.257818i
$545$	28.1544	−	23.6243i	1.20600	−	1.01195i
$546$	−4.47178	+	1.62760i	−0.191375	+	0.0696547i
$547$	−30.6215	−	11.1453i	−1.30928	−	0.476540i	−0.409274	−	0.912412i	$-0.634218\pi$
$547$	−30.6215	−	11.1453i	−1.30928	−	0.476540i	−0.900009	+	0.435872i	$0.856440\pi$
$548$	12.2836	+	10.3072i	0.524729	+	0.440300i
$549$	−2.17617	+	12.3417i	−0.0928769	+	0.526731i
$550$	2.30541			0.0983029
$551$	−23.8871	−	14.0267i	−1.01763	−	0.597558i
$552$	6.80066			0.289455
$553$	5.46198	−	30.9764i	0.232267	−	1.31725i
$554$	14.3418	+	12.0342i	0.609326	+	0.511285i
$555$	35.9432	+	13.0822i	1.52570	+	0.555310i
$556$	1.95336	−	0.710966i	0.0828411	−	0.0301517i
$557$	−15.2777	+	12.8195i	−0.647335	+	0.543179i	−0.906261	−	0.422719i	$-0.861076\pi$
$557$	−15.2777	+	12.8195i	−0.647335	+	0.543179i	0.258926	+	0.965897i	$0.416631\pi$
$558$	0.798133	+	1.38241i	0.0337877	+	0.0585220i
$559$	1.88666	−	3.26779i	0.0797972	−	0.138213i
$560$	1.70574	+	9.67372i	0.0720805	+	0.408789i
$561$	0.418748	+	2.37484i	0.0176796	+	0.100266i
$562$	−5.31908	+	9.21291i	−0.224372	+	0.388623i
$563$	−1.98411	−	3.43658i	−0.0836202	−	0.144834i	0.821182	−	0.570666i	$-0.193315\pi$
$563$	−1.98411	−	3.43658i	−0.0836202	−	0.144834i	−0.904802	+	0.425832i	$0.859982\pi$
$564$	−4.28699	+	3.59721i	−0.180515	+	0.151470i
$565$	−37.3803	+	13.6053i	−1.57260	+	0.572380i
$566$	−13.1677	−	4.79266i	−0.553480	−	0.201450i
$567$	−2.20574	−	1.85083i	−0.0926322	−	0.0777277i
$568$	2.88666	−	16.3711i	0.121122	−	0.686914i
$569$	14.8135			0.621012			0.310506	−	0.950571i	$-0.399501\pi$
$569$	14.8135			0.621012			0.310506	+	0.950571i	$0.399501\pi$
$570$	4.98293	+	14.0105i	0.208712	+	0.586837i
$571$	21.0615			0.881396			0.440698	−	0.897655i	$-0.354731\pi$
$571$	21.0615			0.881396			0.440698	+	0.897655i	$0.354731\pi$
$572$	0.0996702	−	0.565258i	0.00416742	−	0.0236346i
$573$	−8.26264	−	6.93318i	−0.345177	−	0.289638i
$574$	9.44356	+	3.43718i	0.394167	+	0.143465i
$575$	−42.4213	+	15.4401i	−1.76909	+	0.643897i
$576$	0.766044	−	0.642788i	0.0319185	−	0.0267828i
$577$	22.1211	+	38.3148i	0.920913	+	1.59507i	0.798006	+	0.602649i	$0.205888\pi$
$577$	22.1211	+	38.3148i	0.920913	+	1.59507i	0.122907	+	0.992418i	$0.460778\pi$
$578$	15.6065	−	27.0313i	0.649146	−	1.12435i
$579$	0.497474	+	2.82131i	0.0206743	+	0.117250i
$580$	−3.76470	−	21.3507i	−0.156321	−	0.886539i
$581$	16.8687	−	29.2175i	0.699832	−	1.21214i
$582$	−1.82635	−	3.16333i	−0.0757047	−	0.131124i
$583$	−0.526874	+	0.442100i	−0.0218209	+	0.0183099i
$584$	11.6702	−	4.24762i	0.482918	−	0.175768i
$585$	−5.29813	−	1.92836i	−0.219051	−	0.0797280i
$586$	8.82501	+	7.40506i	0.364558	+	0.305900i
$587$	1.73689	−	9.85041i	0.0716892	−	0.406570i	−0.927754	−	0.373193i	$-0.878263\pi$
$587$	1.73689	−	9.85041i	0.0716892	−	0.406570i	0.999443	−	0.0333765i	$-0.0106260\pi$
$588$	−1.29086			−0.0532341
$589$	6.84318	+	1.25865i	0.281968	+	0.0518617i
$590$	1.52023			0.0625869
$591$	1.44743	−	8.20880i	0.0595395	−	0.337665i
$592$	−8.58899	−	7.20702i	−0.353005	−	0.296207i
$593$	10.7981	+	3.93020i	0.443426	+	0.161394i	0.554077	−	0.832465i	$-0.313071\pi$
$593$	10.7981	+	3.93020i	0.443426	+	0.161394i	−0.110651	+	0.993859i	$0.535294\pi$
$594$	0.326352	−	0.118782i	0.0133904	−	0.00487370i
$595$	52.2490	−	43.8421i	2.14200	−	1.79735i
$596$	0.833626	+	1.44388i	0.0341466	+	0.0591437i
$597$	−1.51707	+	2.62765i	−0.0620897	+	0.107543i
$598$	1.95171	+	11.0687i	0.0798115	+	0.452634i
$599$	1.11422	+	6.31905i	0.0455257	+	0.258189i	0.999073	−	0.0430552i	$-0.0137091\pi$
$599$	1.11422	+	6.31905i	0.0455257	+	0.258189i	−0.953547	+	0.301244i	$0.902598\pi$
$600$	−3.31908	+	5.74881i	−0.135501	+	0.234694i
$601$	−15.7579	−	27.2935i	−0.642778	−	1.11332i	−0.984810	−	0.173636i	$-0.944448\pi$
$601$	−15.7579	−	27.2935i	−0.642778	−	1.11332i	0.342032	−	0.939688i	$-0.388885\pi$
$602$	5.03596	−	4.22567i	0.205250	−	0.172226i
$603$	1.01367	−	0.368946i	0.0412799	−	0.0150246i
$604$	−18.8430	−	6.85830i	−0.766711	−	0.279060i
$605$	28.4315	+	23.8569i	1.15591	+	0.969921i
$606$	−1.72028	+	9.75622i	−0.0698818	+	0.396319i
$607$	0.748341			0.0303742			0.0151871	−	0.999885i	$-0.495166\pi$
$607$	0.748341			0.0303742			0.0151871	+	0.999885i	$0.495166\pi$
$608$	0.0320889	−	4.35878i	0.00130138	−	0.176772i
$609$	18.2986			0.741497
$610$	−7.42396	+	42.1034i	−0.300587	+	1.70472i
$611$	−7.08512	−	5.94512i	−0.286633	−	0.240514i
$612$	−6.52481	−	2.37484i	−0.263750	−	0.0959972i
$613$	28.8371	−	10.4958i	1.16472	−	0.423923i	0.313938	−	0.949443i	$-0.398352\pi$
$613$	28.8371	−	10.4958i	1.16472	−	0.423923i	0.850781	+	0.525520i	$0.176129\pi$
$614$	−3.29220	+	2.76249i	−0.132863	+	0.111485i
$615$	5.95336	+	10.3115i	0.240063	+	0.415801i
$616$	0.500000	−	0.866025i	0.0201456	−	0.0348932i
$617$	−4.73917	−	26.8772i	−0.190792	−	1.08203i	−0.918285	−	0.395919i	$-0.870426\pi$
$617$	−4.73917	−	26.8772i	−0.190792	−	1.08203i	0.727493	−	0.686115i	$-0.240685\pi$
$618$	1.36231	+	7.72605i	0.0548002	+	0.310787i
$619$	6.61856	−	11.4637i	0.266022	−	0.460764i	−0.701809	−	0.712365i	$-0.747624\pi$
$619$	6.61856	−	11.4637i	0.266022	−	0.460764i	0.967831	+	0.251601i	$0.0809572\pi$
$620$	2.72281	+	4.71605i	0.109351	+	0.189401i
$621$	−5.20961	+	4.37138i	−0.209054	+	0.175417i
$622$	−21.6065	+	7.86414i	−0.866343	+	0.315323i
$623$	4.85117	+	1.76568i	0.194358	+	0.0707405i
$624$	1.26604	+	1.06234i	0.0506823	+	0.0425275i
$625$	−2.45290	+	13.9111i	−0.0981159	+	0.556443i
$626$	9.20977			0.368096
$627$	0.528218	−	1.41868i	0.0210950	−	0.0566568i
$628$	−4.09833			−0.163541
$629$	−13.5189	+	76.6694i	−0.539033	+	3.05701i
$630$	−7.52481	−	6.31407i	−0.299796	−	0.251559i
$631$	11.5013	+	4.18615i	0.457861	+	0.166648i	0.560646	−	0.828056i	$-0.310553\pi$
$631$	11.5013	+	4.18615i	0.457861	+	0.166648i	−0.102784	+	0.994704i	$0.532775\pi$
$632$	−10.2652	+	3.73622i	−0.408326	+	0.148619i
$633$	12.7456	−	10.6948i	0.506591	−	0.425080i
$634$	1.67752	+	2.90555i	0.0666228	+	0.115394i
$635$	27.6536	−	47.8975i	1.09740	−	1.90075i
$636$	−0.343893	−	1.95031i	−0.0136362	−	0.0773349i
$637$	−0.370462	−	2.10100i	−0.0146783	−	0.0832445i
$638$	−1.10354	+	1.91139i	−0.0436896	+	0.0756726i
$639$	8.31180	+	14.3965i	0.328810	+	0.569515i
$640$	2.61334	−	2.19285i	0.103301	−	0.0866801i
$641$	−8.41370	+	3.06233i	−0.332321	+	0.120955i	−0.502791	−	0.864408i	$-0.667694\pi$
$641$	−8.41370	+	3.06233i	−0.332321	+	0.120955i	0.170470	+	0.985363i	$0.445471\pi$
$642$	0.0256923	+	0.00935122i	0.00101399	+	0.000369063i
$643$	−24.0305	−	20.1640i	−0.947670	−	0.795190i	0.0312334	−	0.999512i	$-0.490056\pi$
$643$	−24.0305	−	20.1640i	−0.947670	−	0.795190i	−0.978904	+	0.204322i	$0.934501\pi$
$644$	−3.40033	+	19.2842i	−0.133992	+	0.759905i
$645$	7.78880			0.306684
$646$	−26.3221	+	14.9398i	−1.03563	+	0.587798i
$647$	−5.54933			−0.218166			−0.109083	−	0.994033i	$-0.534792\pi$
$647$	−5.54933			−0.218166			−0.109083	+	0.994033i	$0.534792\pi$
$648$	−0.173648	+	0.984808i	−0.00682154	+	0.0386869i
$649$	−0.118555	−	0.0994798i	−0.00465371	−	0.00390492i
$650$	−10.3093	−	3.75227i	−0.404363	−	0.147176i
$651$	−4.31908	+	1.57202i	−0.169278	+	0.0616122i
$652$	−6.23190	+	5.22918i	−0.244060	+	0.204791i
$653$	−19.4552	−	33.6974i	−0.761340	−	1.31868i	−0.942160	−	0.335163i	$-0.891209\pi$
$653$	−19.4552	−	33.6974i	−0.761340	−	1.31868i	0.180820	−	0.983516i	$-0.442125\pi$
$654$	5.38666	−	9.32997i	0.210635	−	0.364831i
$655$	1.65910	+	9.40923i	0.0648264	+	0.367649i
$656$	−0.606067	−	3.43718i	−0.0236629	−	0.134199i
$657$	−6.20961	+	10.7554i	−0.242260	+	0.419606i
$658$	−8.05690	−	13.9550i	−0.314091	−	0.544021i
$659$	−30.2708	+	25.4003i	−1.17918	+	0.989454i	−0.179201	+	0.983813i	$0.557351\pi$
$659$	−30.2708	+	25.4003i	−1.17918	+	0.989454i	−0.999984	+	0.00564104i	$0.998204\pi$
$660$	1.11334	−	0.405223i	0.0433367	−	0.0157733i
$661$	0.0859997	+	0.0313013i	0.00334500	+	0.00121748i	0.343692	−	0.939082i	$-0.388322\pi$
$661$	0.0859997	+	0.0313013i	0.00334500	+	0.00121748i	−0.340347	+	0.940300i	$0.610545\pi$
$662$	16.9099	+	14.1891i	0.657221	+	0.551474i
$663$	1.99273	−	11.3013i	0.0773911	−	0.438907i
$664$	−11.7169			−0.454703
$665$	−42.2203	+	7.12452i	−1.63723	+	0.276277i
$666$	11.2121			0.434461
$667$	7.50480	−	42.5619i	0.290587	−	1.64800i
$668$	−10.2626	−	8.61138i	−0.397073	−	0.333184i
$669$	−7.67752	−	2.79439i	−0.296830	−	0.108037i
$670$	3.45811	−	1.25865i	0.133598	−	0.0486259i
$671$	3.33409	−	2.79764i	0.128711	−	0.108002i
$672$	1.43969	+	2.49362i	0.0555373	+	0.0961935i
$673$	19.9281	−	34.5165i	0.768173	−	1.33052i	−0.170379	−	0.985379i	$-0.554499\pi$
$673$	19.9281	−	34.5165i	0.768173	−	1.33052i	0.938552	−	0.345137i	$-0.112167\pi$
$674$	2.27766	+	12.9172i	0.0877320	+	0.497553i
$675$	−1.15270	−	6.53731i	−0.0443676	−	0.251621i
$676$	5.13429	−	8.89284i	0.197473	−	0.342032i
$677$	−14.6912	−	25.4459i	−0.564628	−	0.977965i	−0.997084	−	0.0763098i	$-0.975686\pi$
$677$	−14.6912	−	25.4459i	−0.564628	−	0.977965i	0.432456	−	0.901655i	$-0.357647\pi$
$678$	−8.93242	+	7.49519i	−0.343047	+	0.287851i
$679$	9.88326	−	3.59721i	0.379285	−	0.138048i
$680$	−22.2592	−	8.10170i	−0.853603	−	0.310686i
$681$	−1.37939	−	1.15744i	−0.0528582	−	0.0443533i
$682$	0.0962667	−	0.545955i	0.00368624	−	0.0209057i
$683$	−21.0933			−0.807112			−0.403556	−	0.914955i	$-0.632226\pi$
$683$	−21.0933			−0.807112			−0.403556	+	0.914955i	$0.632226\pi$
$684$	2.77719	+	3.35965i	0.106188	+	0.128459i
$685$	−54.7033			−2.09010
$686$	−2.85457	+	16.1891i	−0.108988	+	0.618102i
$687$	14.3550	+	12.0453i	0.547679	+	0.459557i
$688$	−2.14543	−	0.780873i	−0.0817937	−	0.0297705i
$689$	3.07563	−	1.11944i	0.117172	−	0.0426471i
$690$	−17.7724	+	14.9128i	−0.676585	+	0.567722i
$691$	8.08172	+	13.9979i	0.307443	+	0.532507i	0.977802	−	0.209530i	$-0.0671933\pi$
$691$	8.08172	+	13.9979i	0.307443	+	0.532507i	−0.670359	+	0.742037i	$0.733860\pi$
$692$	0.511144	−	0.885328i	0.0194308	−	0.0336551i
$693$	0.173648	+	0.984808i	0.00659635	+	0.0374098i
$694$	−1.52094	−	8.62571i	−0.0577343	−	0.327427i
$695$	−3.54576	+	6.14144i	−0.134498	+	0.232958i
$696$	−3.17752	−	5.50362i	−0.120444	−	0.208614i
$697$	−18.5646	+	15.5776i	−0.703186	+	0.590043i
$698$	3.06670	−	1.11619i	0.116076	−	0.0422484i
$699$	−3.85117	−	1.40171i	−0.145665	−	0.0530175i
$700$	−14.6420	−	12.2861i	−0.553417	−	0.464372i
$701$	−3.48561	+	19.7679i	−0.131650	+	0.746623i	0.845484	+	0.534000i	$0.179312\pi$
$701$	−3.48561	+	19.7679i	−0.131650	+	0.746623i	−0.977134	+	0.212623i	$0.931799\pi$
$702$	−1.65270			−0.0623773
$703$	31.6894	−	37.2063i	1.19519	−	1.40326i
$704$	−0.347296			−0.0130892
$705$	3.31521	−	18.8015i	0.124858	−	0.708105i
$706$	−22.2795	−	18.6947i	−0.838499	−	0.703584i
$707$	−26.8050	−	9.75622i	−1.00811	−	0.366920i
$708$	0.418748	−	0.152412i	0.0157375	−	0.00572799i
$709$	−29.7998	+	25.0050i	−1.11915	+	0.939082i	−0.998561	−	0.0536201i	$-0.982924\pi$
$709$	−29.7998	+	25.0050i	−1.11915	+	0.939082i	−0.120593	+	0.992702i	$0.538480\pi$
$710$	28.3555	+	49.1132i	1.06416	+	1.84318i
$711$	5.46198	−	9.46043i	0.204840	−	0.354794i
$712$	−0.311337	−	1.76568i	−0.0116679	−	0.0661717i
$713$	1.88507	+	10.6907i	0.0705963	+	0.400372i
$714$	9.99660	−	17.3146i	0.374113	−	0.647983i
$715$	0.979055	+	1.69577i	0.0366146	+	0.0634183i
$716$	1.55896	−	1.30813i	0.0582612	−	0.0488869i
$717$	−26.5253	+	9.65441i	−0.990605	+	0.360551i
$718$	6.21213	+	2.26103i	0.231835	+	0.0843810i
$719$	2.34549	+	1.96810i	0.0874718	+	0.0733976i	0.685475	−	0.728096i	$-0.259595\pi$
$719$	2.34549	+	1.96810i	0.0874718	+	0.0733976i	−0.598003	+	0.801494i	$0.704039\pi$
$720$	−0.592396	+	3.35965i	−0.0220773	+	0.125207i
$721$	−22.5895			−0.841275
$722$	18.9979	+	0.279737i	0.707030	+	0.0104107i
$723$	−6.56212			−0.244048
$724$	3.87299	−	21.9648i	0.143938	−	0.816316i
$725$	32.3161	+	27.1165i	1.20019	+	1.00708i
$726$	10.2233	+	3.72097i	0.379421	+	0.138098i
$727$	16.4226	−	5.97734i	0.609081	−	0.221687i	−0.0190200	−	0.999819i	$-0.506055\pi$
$727$	16.4226	−	5.97734i	0.609081	−	0.221687i	0.628101	+	0.778132i	$0.283832\pi$
$728$	−3.64543	+	3.05888i	−0.135109	+	0.113370i
$729$	−0.500000	−	0.866025i	−0.0185185	−	0.0320750i
$730$	−21.1839	+	36.6916i	−0.784052	+	1.35802i
$731$	2.75284	+	15.6121i	0.101817	+	0.577436i
$732$	2.17617	+	12.3417i	0.0804337	+	0.456162i
$733$	20.7087	−	35.8686i	0.764894	−	1.32484i	−0.175408	−	0.984496i	$-0.556124\pi$
$733$	20.7087	−	35.8686i	0.764894	−	1.32484i	0.940302	−	0.340340i	$-0.110542\pi$
$734$	−2.89780	−	5.01914i	−0.106960	−	0.185260i
$735$	3.37346	−	2.83067i	0.124432	−	0.104411i
$736$	6.39053	−	2.32596i	0.235558	−	0.0857361i
$737$	−0.352044	−	0.128134i	−0.0129677	−	0.00471986i
$738$	2.67365	+	2.24346i	0.0984183	+	0.0825828i
$739$	4.59358	−	26.0515i	0.168978	−	0.958319i	−0.775890	−	0.630868i	$-0.782699\pi$
$739$	4.59358	−	26.0515i	0.168978	−	0.958319i	0.944868	−	0.327451i	$-0.106190\pi$
$740$	38.2499			1.40609
$741$	−4.67112	+	5.48432i	−0.171598	+	0.201472i
$742$	5.70233			0.209339
$743$	−2.61793	+	14.8470i	−0.0960424	+	0.544684i	0.898381	+	0.439218i	$0.144744\pi$
$743$	−2.61793	+	14.8470i	−0.0960424	+	0.544684i	−0.994423	+	0.105466i	$0.966367\pi$
$744$	1.22281	+	1.02606i	0.0448304	+	0.0376172i
$745$	−5.34477	−	1.94534i	−0.195817	−	0.0712716i
$746$	−24.3285	+	8.85484i	−0.890728	+	0.324199i
$747$	8.97565	−	7.53147i	0.328402	−	0.275562i
$748$	1.20574	+	2.08840i	0.0440861	+	0.0763594i
$749$	−0.0393628	+	0.0681784i	−0.00143829	+	0.00249119i
$750$	−0.970437	−	5.50362i	−0.0354354	−	0.200964i
$751$	−0.921274	−	5.22481i	−0.0336178	−	0.190656i	0.963374	−	0.268161i	$-0.0864158\pi$
$751$	−0.921274	−	5.22481i	−0.0336178	−	0.190656i	−0.996992	+	0.0775048i	$0.975305\pi$
$752$	−2.79813	+	4.84651i	−0.102037	+	0.176734i
$753$	4.44697	+	7.70237i	0.162056	+	0.280690i
$754$	8.04576	−	6.75119i	0.293009	−	0.245864i
$755$	64.2825	−	23.3969i	2.33948	−	0.851500i
$756$	−2.70574	−	0.984808i	−0.0984067	−	0.0358171i
$757$	6.23442	+	5.23130i	0.226594	+	0.190135i	0.749016	−	0.662552i	$-0.230527\pi$
$757$	6.23442	+	5.23130i	0.226594	+	0.190135i	−0.522422	+	0.852687i	$0.674971\pi$
$758$	3.32635	−	18.8647i	0.120819	−	0.685196i
$759$	2.36184			0.0857295
$760$	9.47431	+	11.4613i	0.343669	+	0.415747i
$761$	−46.2113			−1.67516			−0.837579	−	0.546316i	$-0.816030\pi$
$761$	−46.2113			−1.67516			−0.837579	+	0.546316i	$0.816030\pi$
$762$	2.81521	−	15.9658i	0.101984	−	0.578381i
$763$	23.7631	+	19.9396i	0.860282	+	0.721863i
$764$	−10.1356	−	3.68907i	−0.366694	−	0.133466i
$765$	22.2592	−	8.10170i	0.804784	−	0.292918i
$766$	7.42649	−	6.23156i	0.268330	−	0.225156i
$767$	0.368241	+	0.637812i	0.0132964	+	0.0230301i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−4.66132	−	26.4357i	−0.168092	−	0.953295i	−0.945819	−	0.324693i	$-0.894739\pi$
$769$	−4.66132	−	26.4357i	−0.168092	−	0.953295i	0.777728	−	0.628601i	$-0.216372\pi$
$770$	0.592396	+	3.35965i	0.0213485	+	0.121073i
$771$	−6.73308	+	11.6620i	−0.242486	+	0.419998i
$772$	1.43242	+	2.48102i	0.0515539	+	0.0892939i
$773$	−16.1065	+	13.5150i	−0.579312	+	0.486100i	−0.884721	−	0.466121i	$-0.845651\pi$
$773$	−16.1065	+	13.5150i	−0.579312	+	0.486100i	0.305409	+	0.952221i	$0.401207\pi$
$774$	2.14543	−	0.780873i	0.0771159	−	0.0280679i
$775$	−9.95723	−	3.62414i	−0.357674	−	0.130183i
$776$	−2.79813	−	2.34791i	−0.100447	−	0.0842852i
$777$	−5.60607	+	31.7936i	−0.201117	+	1.14059i
$778$	0.817896			0.0293230
$779$	15.0013	−	2.53142i	0.537479	−	0.0906974i
$780$	−5.63816			−0.201878
$781$	1.00253	−	5.68561i	0.0358732	−	0.203447i
$782$	−36.1732	−	30.3530i	−1.29355	−	1.08542i
$783$	5.97178	+	2.17355i	0.213414	+	0.0776764i
$784$	−1.21301	+	0.441500i	−0.0433218	+	0.0157679i
$785$	10.7103	−	8.98703i	0.382268	−	0.320761i
$786$	1.40033	+	2.42544i	0.0499481	+	0.0865127i
$787$	−22.7656	+	39.4312i	−0.811507	+	1.40557i	0.100302	+	0.994957i	$0.468019\pi$
$787$	−22.7656	+	39.4312i	−0.811507	+	1.40557i	−0.911809	+	0.410615i	$0.865314\pi$
$788$	−1.44743	−	8.20880i	−0.0515627	−	0.292426i
$789$	2.90895	+	16.4975i	0.103561	+	0.587325i
$790$	18.6334	−	32.2740i	0.662947	−	1.14826i
$791$	−16.7875	−	29.0767i	−0.596893	−	1.03385i
$792$	0.266044	−	0.223238i	0.00945348	−	0.00793241i
$793$	−19.4628	+	7.08386i	−0.691143	+	0.251555i
$794$	−3.47431	−	1.26454i	−0.123299	−	0.0448770i
$795$	5.17546	+	4.34273i	0.183555	+	0.154021i
$796$	−0.526874	+	2.98805i	−0.0186746	+	0.105909i
$797$	36.1780			1.28149			0.640745	−	0.767754i	$-0.278626\pi$
$797$	36.1780			1.28149			0.640745	+	0.767754i	$0.278626\pi$
$798$	−10.9153	+	6.19529i	−0.386399	+	0.219311i
$799$	38.8580			1.37470
$800$	−1.15270	+	6.53731i	−0.0407542	+	0.231129i
$801$	1.37346	+	1.15247i	0.0485287	+	0.0407204i
$802$	−20.4290	−	7.43555i	−0.721374	−	0.262559i
$803$	4.05303	−	1.47518i	0.143028	−	0.0520581i
$804$	0.826352	−	0.693392i	0.0291432	−	0.0244540i
$805$	−33.4013	−	57.8527i	−1.17724	−	2.03904i
$806$	−1.31908	+	2.28471i	−0.0464625	+	0.0804755i
$807$	−0.623303	−	3.53493i	−0.0219413	−	0.124435i
$808$	1.72028	+	9.75622i	0.0605194	+	0.343223i
$809$	−1.18938	+	2.06006i	−0.0418163	+	0.0724280i	−0.886176	−	0.463349i	$-0.846648\pi$
$809$	−1.18938	+	2.06006i	−0.0418163	+	0.0724280i	0.844360	+	0.535777i	$0.179981\pi$
$810$	−1.70574	−	2.95442i	−0.0599335	−	0.103808i
$811$	−28.3904	+	23.8223i	−0.996921	+	0.836516i	−0.986555	−	0.163431i	$-0.947744\pi$
$811$	−28.3904	+	23.8223i	−0.996921	+	0.836516i	−0.0103658	+	0.999946i	$0.503300\pi$
$812$	17.1951	−	6.25849i	0.603428	−	0.219630i
$813$	22.5141	+	8.19448i	0.789605	+	0.287393i
$814$	−2.98293	−	2.50297i	−0.104551	−	0.0877291i
$815$	4.81924	−	27.3313i	0.168811	−	0.957373i
$816$	−6.94356			−0.243073
$817$	3.47250	−	9.32640i	0.121487	−	0.326289i
$818$	4.05468			0.141769
$819$	0.826352	−	4.68647i	0.0288751	−	0.163759i
$820$	9.12108	+	7.65350i	0.318522	+	0.267272i
$821$	24.3949	+	8.87901i	0.851387	+	0.309879i	0.730606	−	0.682800i	$-0.239238\pi$
$821$	24.3949	+	8.87901i	0.851387	+	0.309879i	0.120781	+	0.992679i	$0.461460\pi$
$822$	−15.0680	+	5.48432i	−0.525559	+	0.191288i
$823$	−34.4805	+	28.9325i	−1.20191	+	1.00852i	−0.202340	+	0.979315i	$0.564855\pi$
$823$	−34.4805	+	28.9325i	−1.20191	+	1.00852i	−0.999573	+	0.0292095i	$0.990701\pi$
$824$	3.92262	+	6.79417i	0.136651	+	0.236686i
$825$	−1.15270	+	1.99654i	−0.0401320	+	0.0695106i
$826$	0.222811	+	1.26363i	0.00775259	+	0.0439671i
$827$	−2.92473	−	16.5870i	−0.101703	−	0.576786i	−0.992486	−	0.122358i	$-0.960955\pi$
$827$	−2.92473	−	16.5870i	−0.101703	−	0.576786i	0.890783	−	0.454429i	$-0.150157\pi$
$828$	−3.40033	+	5.88954i	−0.118170	+	0.204676i
$829$	6.50000	+	11.2583i	0.225754	+	0.391018i	0.956545	−	0.291583i	$-0.0941820\pi$
$829$	6.50000	+	11.2583i	0.225754	+	0.391018i	−0.730791	+	0.682601i	$0.760849\pi$
$830$	30.6202	−	25.6934i	1.06284	−	0.891831i
$831$	−17.5929	+	6.40328i	−0.610290	+	0.222127i
$832$	1.55303	+	0.565258i	0.0538417	+	0.0195968i
$833$	6.86618	+	5.76141i	0.237899	+	0.199621i
$834$	−0.360967	+	2.04715i	−0.0124993	+	0.0708868i
$835$	45.7033			1.58163
$836$	0.0111444	−	1.51379i	0.000385436	−	0.0523555i
$837$	−1.59627			−0.0551750
$838$	−4.08054	+	23.1419i	−0.140960	+	0.799423i
$839$	1.02687	+	0.861650i	0.0354516	+	0.0297475i	0.660341	−	0.750966i	$-0.270412\pi$
$839$	1.02687	+	0.861650i	0.0354516	+	0.0297475i	−0.624890	+	0.780713i	$0.714856\pi$
$840$	−9.23055	−	3.35965i	−0.318484	−	0.115919i
$841$	−10.6998	+	3.89441i	−0.368959	+	0.134290i
$842$	17.6748	−	14.8309i	0.609115	−	0.511108i
$843$	−5.31908	−	9.21291i	−0.183199	−	0.317310i
$844$	8.31908	−	14.4091i	0.286354	−	0.495980i
$845$	6.08306	+	34.4988i	0.209264	+	1.18679i
$846$	−0.971782	−	5.51125i	−0.0334105	−	0.189481i
$847$	−15.6630	+	27.1291i	−0.538186	+	0.932166i
$848$	−0.990200	−	1.71508i	−0.0340036	−	0.0588960i
$849$	10.7344	−	9.00725i	0.368404	−	0.309128i
$850$	43.3127	−	15.7645i	1.48561	−	0.540720i
$851$	71.6515	+	26.0790i	2.45618	+	0.893977i
$852$	12.7344	+	10.6854i	0.436274	+	0.366077i
$853$	−1.37969	+	7.82461i	−0.0472397	+	0.267910i	−0.999275	−	0.0380795i	$-0.987876\pi$
$853$	−1.37969	+	7.82461i	−0.0472397	+	0.267910i	0.952035	+	0.305989i	$0.0989871\pi$
$854$	−36.0847			−1.23479
$855$	−14.6250	−	2.68993i	−0.500163	−	0.0919938i
$856$	0.0273411			0.000934501
$857$	8.31356	−	47.1485i	0.283986	−	1.61056i	−0.424900	−	0.905240i	$-0.639691\pi$
$857$	8.31356	−	47.1485i	0.283986	−	1.61056i	0.708886	−	0.705323i	$-0.249198\pi$
$858$	0.439693	+	0.368946i	0.0150109	+	0.0125956i
$859$	−1.53849	−	0.559963i	−0.0524924	−	0.0191057i	0.315640	−	0.948879i	$-0.397781\pi$
$859$	−1.53849	−	0.559963i	−0.0524924	−	0.0191057i	−0.368133	+	0.929773i	$0.620003\pi$
$860$	7.31908	−	2.66393i	0.249578	−	0.0908391i
$861$	−7.69846	+	6.45978i	−0.262363	+	0.220149i
$862$	−1.75743	−	3.04395i	−0.0598582	−	0.103677i
$863$	−17.4616	+	30.2443i	−0.594399	+	1.02953i	0.399233	+	0.916850i	$0.369277\pi$
$863$	−17.4616	+	30.2443i	−0.594399	+	1.02953i	−0.993631	+	0.112679i	$0.964057\pi$
$864$	0.173648	+	0.984808i	0.00590763	+	0.0335038i
$865$	0.605600	+	3.43453i	0.0205910	+	0.116777i
$866$	−17.0574	+	29.5442i	−0.579633	+	1.00395i
$867$	15.6065	+	27.0313i	0.530026	+	0.918031i
$868$	−3.52094	+	2.95442i	−0.119509	+	0.100280i
$869$	−3.56506	+	1.29757i	−0.120936	+	0.0440172i
$870$	20.3726	+	7.41501i	0.690695	+	0.251392i
$871$	1.36571	+	1.14597i	0.0462755	+	0.0388297i
$872$	1.87077	−	10.6096i	0.0633522	−	0.359288i
$873$	3.65270			0.123625
$874$	9.93330	+	27.9296i	0.335999	+	0.944731i
$875$	16.0915			0.543993
$876$	−2.15657	+	12.2305i	−0.0728639	+	0.413232i
$877$	−4.88120	−	4.09581i	−0.164826	−	0.138306i	0.556644	−	0.830751i	$-0.312089\pi$
$877$	−4.88120	−	4.09581i	−0.164826	−	0.138306i	−0.721470	+	0.692446i	$0.756533\pi$
$878$	9.11633	+	3.31807i	0.307661	+	0.111980i
$879$	−10.8255	+	3.94015i	−0.365134	+	0.132898i
$880$	0.907604	−	0.761570i	0.0305953	−	0.0256725i
$881$	−2.63697	−	4.56737i	−0.0888419	−	0.153879i	0.818180	−	0.574962i	$-0.194983\pi$
$881$	−2.63697	−	4.56737i	−0.0888419	−	0.153879i	−0.907022	+	0.421084i	$0.861650\pi$
$882$	0.645430	−	1.11792i	0.0217327	−	0.0376422i
$883$	−0.564588	−	3.20194i	−0.0189999	−	0.107754i	0.973833	−	0.227265i	$-0.0729784\pi$
$883$	−0.564588	−	3.20194i	−0.0189999	−	0.107754i	−0.992833	+	0.119511i	$0.961867\pi$
$884$	−1.99273	−	11.3013i	−0.0670226	−	0.380104i
$885$	−0.760115	+	1.31656i	−0.0255510	+	0.0442556i
$886$	7.59105	+	13.1481i	0.255026	+	0.441719i
$887$	−17.1368	+	14.3795i	−0.575398	+	0.482816i	−0.883432	−	0.468559i	$-0.844773\pi$
$887$	−17.1368	+	14.3795i	−0.575398	+	0.482816i	0.308034	+	0.951375i	$0.400329\pi$
$888$	10.5360	−	3.83478i	0.353564	−	0.128687i
$889$	43.8658	+	15.9658i	1.47121	+	0.535477i
$890$	4.68551	+	3.93161i	0.157059	+	0.131788i
$891$	−0.0603074	+	0.342020i	−0.00202037	+	0.0114581i
$892$	−8.17024			−0.273560
$893$	−21.0351	−	12.3520i	−0.703912	−	0.413343i
$894$	−1.66725			−0.0557612
$895$	−1.20557	+	6.83716i	−0.0402979	+	0.228541i
$896$	2.20574	+	1.85083i	0.0736885	+	0.0618320i
$897$	−10.5617	−	3.84413i	−0.352643	−	0.128352i
$898$	32.7374	−	11.9154i	1.09246	−	0.397624i
$899$	7.77101	−	6.52065i	0.259178	−	0.217476i
$900$	−3.31908	−	5.74881i	−0.110636	−	0.191627i
$901$	−6.87551	+	11.9087i	−0.229057	+	0.396738i
$902$	−0.210485	−	1.19372i	−0.00700838	−	0.0397465i
$903$	1.14156	+	6.47410i	0.0379887	+	0.215445i
$904$	−5.83022	+	10.0982i	−0.193910	+	0.335863i
$905$	38.0442	+	65.8944i	1.26463	+	2.19040i
$906$	15.3610	−	12.8894i	0.510334	−	0.428221i
$907$	−2.96703	+	1.07991i	−0.0985187	+	0.0358579i	−0.390809	−	0.920472i	$-0.627805\pi$
$907$	−2.96703	+	1.07991i	−0.0985187	+	0.0358579i	0.292291	+	0.956330i	$0.405583\pi$
$908$	−1.69207	−	0.615862i	−0.0561532	−	0.0204381i
$909$	−7.58899	−	6.36792i	−0.251711	−	0.211211i
$910$	2.81908	−	15.9878i	0.0934515	−	0.529990i
$911$	−44.3387			−1.46901			−0.734504	−	0.678604i	$-0.762585\pi$
$911$	−44.3387			−1.46901			−0.734504	+	0.678604i	$0.762585\pi$
$912$	3.75877	+	2.20718i	0.124465	+	0.0730870i
$913$	−4.06923			−0.134672
$914$	5.53503	−	31.3907i	0.183082	−	1.03831i
$915$	−32.7506	−	27.4810i	−1.08270	−	0.908495i
$916$	17.6091	+	6.40917i	0.581820	+	0.211765i
$917$	−7.57785	+	2.75811i	−0.250243	+	0.0910809i
$918$	5.31908	−	4.46324i	0.175556	−	0.147309i
$919$	−7.10220	−	12.3014i	−0.234280	−	0.405785i	0.724783	−	0.688977i	$-0.241940\pi$
$919$	−7.10220	−	12.3014i	−0.234280	−	0.405785i	−0.959063	+	0.283192i	$0.908607\pi$
$920$	−11.6001	+	20.0920i	−0.382445	+	0.662415i
$921$	−0.746282	−	4.23238i	−0.0245908	−	0.139462i
$922$	1.85622	+	10.5271i	0.0611313	+	0.346693i
$923$	−13.7369	+	23.7931i	−0.452157	+	0.783159i
$924$	0.500000	+	0.866025i	0.0164488	+	0.0284901i
$925$	−57.0151	+	47.8413i	−1.87464	+	1.57301i
$926$	14.3944	−	5.23913i	0.473029	−	0.172169i
$927$	−7.37211	−	2.68323i	−0.242132	−	0.0881288i
$928$	−4.86824	−	4.08494i	−0.159808	−	0.134095i
$929$	−2.67881	+	15.1923i	−0.0878888	+	0.498442i	0.908807	+	0.417217i	$0.136994\pi$
$929$	−2.67881	+	15.1923i	−0.0878888	+	0.498442i	−0.996696	+	0.0812253i	$0.974117\pi$
$930$	−5.44562			−0.178569
$931$	−1.88548	−	5.30142i	−0.0617940	−	0.173747i
$932$	−4.09833			−0.134245
$933$	3.99273	−	22.6439i	0.130716	−	0.741327i
$934$	−21.8418	−	18.3275i	−0.714687	−	0.599693i
$935$	−7.73055	−	2.81369i	−0.252816	−	0.0920175i
$936$	−1.55303	+	0.565258i	−0.0507625	+	0.0184760i
$937$	−7.42830	+	6.23308i	−0.242672	+	0.203626i	−0.756009	−	0.654561i	$-0.772853\pi$
$937$	−7.42830	+	6.23308i	−0.242672	+	0.203626i	0.513337	+	0.858187i	$0.328409\pi$
$938$	1.55303	+	2.68993i	0.0507083	+	0.0878294i
$939$	−4.60488	+	7.97589i	−0.150275	+	0.260283i
$940$	−3.31521	−	18.8015i	−0.108130	−	0.613237i
$941$	−3.12314	−	17.7122i	−0.101811	−	0.577402i	−0.992446	−	0.122682i	$-0.960851\pi$
$941$	−3.12314	−	17.7122i	−0.101811	−	0.577402i	0.890635	−	0.454720i	$-0.150261\pi$
$942$	2.04916	−	3.54925i	0.0667653	−	0.115641i
$943$	11.8678	+	20.5557i	0.386470	+	0.669385i
$944$	0.341367	−	0.286441i	0.0111105	−	0.00932285i
$945$	9.23055	−	3.35965i	0.300270	−	0.109289i
$946$	−0.745100	−	0.271194i	−0.0242253	−	0.00881728i
$947$	1.68067	+	1.41025i	0.0546146	+	0.0458271i	0.669686	−	0.742644i	$-0.266429\pi$
$947$	1.68067	+	1.41025i	0.0546146	+	0.0458271i	−0.615072	+	0.788471i	$0.710873\pi$
$948$	1.89693	−	10.7580i	0.0616093	−	0.349404i
$949$	−20.5253			−0.666279
$950$	−28.4577	−	5.23416i	−0.923290	−	0.169818i
$951$	−3.35504			−0.108795
$952$	3.47178	−	19.6895i	0.112521	−	0.638139i
$953$	−8.66456	−	7.27043i	−0.280673	−	0.235512i	0.491573	−	0.870836i	$-0.336422\pi$
$953$	−8.66456	−	7.27043i	−0.280673	−	0.235512i	−0.772246	+	0.635324i	$0.780867\pi$
$954$	1.86097	+	0.677337i	0.0602510	+	0.0219296i
$955$	34.5774	−	12.5852i	1.11890	−	0.407246i
$956$	−21.6236	+	18.1444i	−0.699357	+	0.586831i
$957$	−1.10354	−	1.91139i	−0.0356724	−	0.0617864i
$958$	4.02569	−	6.97270i	0.130064	−	0.225278i
$959$	−8.01754	−	45.4697i	−0.258900	−	1.46829i
$960$	0.592396	+	3.35965i	0.0191195	+	0.108432i
$961$	14.2260	−	24.6401i	0.458902	−	0.794842i
$962$	9.26517	+	16.0477i	0.298721	+	0.517400i
$963$	−0.0209445	+	0.0175745i	−0.000674928	+	0.000566332i
$964$	−6.16637	+	2.24438i	−0.198606	+	0.0722865i
$965$	−9.18392	−	3.34267i	−0.295641	−	0.107604i
$966$	−15.0005	−	12.5869i	−0.482632	−	0.404976i
$967$	8.12402	−	46.0736i	0.261251	−	1.48163i	−0.518252	−	0.855228i	$-0.673417\pi$
$967$	8.12402	−	46.0736i	0.261251	−	1.48163i	0.779503	−	0.626399i	$-0.215472\pi$
$968$	10.8794			0.349677
$969$	0.222811	−	30.2655i	0.00715773	−	0.972267i
$970$	12.4611			0.400102
$971$	10.4834	−	59.4543i	0.336428	−	1.90798i	−0.0762258	−	0.997091i	$-0.524287\pi$
$971$	10.4834	−	59.4543i	0.336428	−	1.90798i	0.412654	−	0.910888i	$-0.364602\pi$
$972$	−0.766044	−	0.642788i	−0.0245709	−	0.0206174i
$973$	−5.62449	−	2.04715i	−0.180313	−	0.0656285i
$974$	5.74675	−	2.09165i	0.184138	−	0.0670206i
$975$	8.40420	−	7.05196i	0.269150	−	0.225844i
$976$	6.26604	+	10.8531i	0.200571	+	0.347400i
$977$	−11.3978	+	19.7416i	−0.364648	+	0.631589i	−0.988720	−	0.149778i	$-0.952144\pi$
$977$	−11.3978	+	19.7416i	−0.364648	+	0.631589i	0.624072	+	0.781367i	$0.285477\pi$
$978$	−1.41266	−	8.01157i	−0.0451718	−	0.256182i
$979$	−0.108126	−	0.613214i	−0.00345573	−	0.0195984i
$980$	2.20187	−	3.81374i	0.0703361	−	0.121826i
$981$	5.38666	+	9.32997i	0.171983	+	0.297883i
$982$	17.3778	−	14.5817i	0.554548	−	0.465321i
$983$	28.9359	−	10.5318i	0.922911	−	0.335912i	0.163515	−	0.986541i	$-0.447717\pi$
$983$	28.9359	−	10.5318i	0.922911	−	0.335912i	0.759396	+	0.650629i	$0.225495\pi$
$984$	3.27972	+	1.19372i	0.104553	+	0.0380544i
$985$	21.7833	+	18.2784i	0.694075	+	0.582398i
$986$	−7.66250	+	43.4562i	−0.244024	+	1.38393i
$987$	16.1138			0.512908
$988$	−2.51367	+	6.75119i	−0.0799705	+	0.214784i
$989$	15.5267			0.493721
$990$	−0.205737	+	1.16679i	−0.00653875	+	0.0370831i
$991$	−29.2467	−	24.5409i	−0.929054	−	0.779569i	0.0465937	−	0.998914i	$-0.485163\pi$
$991$	−29.2467	−	24.5409i	−0.929054	−	0.779569i	−0.975647	+	0.219345i	$0.929608\pi$
$992$	1.50000	+	0.545955i	0.0476250	+	0.0173341i
$993$	−20.7430	+	7.54985i	−0.658260	+	0.239587i
$994$	−36.6673	+	30.7675i	−1.16302	+	0.975887i
$995$	−5.17546	−	8.96416i	−0.164073	−	0.284183i
$996$	5.85844	−	10.1471i	0.185632	−	0.321524i
$997$	5.37423	+	30.4788i	0.170203	+	0.965272i	0.943536	+	0.331271i	$0.107477\pi$
$997$	5.37423	+	30.4788i	0.170203	+	0.965272i	−0.773332	+	0.634001i	$0.781411\pi$
$998$	−4.31614	−	24.4781i	−0.136625	−	0.774839i
$999$	−5.60607	+	9.70999i	−0.177368	+	0.307211i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.2.i.d.55.1	✓	6
3.2	odd	2		342.2.u.a.55.1		6
4.3	odd	2		912.2.bo.f.625.1		6
19.3	odd	18		2166.2.a.u.1.1		3
19.9	even	9	inner	114.2.i.d.85.1	yes	6
19.16	even	9		2166.2.a.o.1.1		3
57.35	odd	18		6498.2.a.bs.1.3		3
57.41	even	18		6498.2.a.bn.1.3		3
57.47	odd	18		342.2.u.a.199.1		6
76.47	odd	18		912.2.bo.f.769.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.i.d.55.1	✓	6	1.1	even	1	trivial
114.2.i.d.85.1	yes	6	19.9	even	9	inner
342.2.u.a.55.1		6	3.2	odd	2
342.2.u.a.199.1		6	57.47	odd	18
912.2.bo.f.625.1		6	4.3	odd	2
912.2.bo.f.769.1		6	76.47	odd	18
2166.2.a.o.1.1		3	19.16	even	9
2166.2.a.u.1.1		3	19.3	odd	18
6498.2.a.bn.1.3		3	57.41	even	18
6498.2.a.bs.1.3		3	57.35	odd	18

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	114.i (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 + 0.984808i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(3.20574 - 1.16679i) q^{5} +(0.766044 - 0.642788i) q^{6} +(1.43969 + 2.49362i) q^{7} +(0.500000 - 0.866025i) q^{8} +(0.173648 + 0.984808i) q^{9} +(0.592396 + 3.35965i) q^{10} +(0.173648 - 0.300767i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-1.26604 + 1.06234i) q^{13} +(-2.70574 + 0.984808i) q^{14} +(-3.20574 - 1.16679i) q^{15} +(0.766044 + 0.642788i) q^{16} +(1.20574 - 6.83807i) q^{17} -1.00000 q^{18} +(-2.82635 + 3.31839i) q^{19} -3.41147 q^{20} +(0.500000 - 2.83564i) q^{21} +(0.266044 + 0.223238i) q^{22} +(-6.39053 - 2.32596i) q^{23} +(-0.939693 + 0.342020i) q^{24} +(5.08512 - 4.26692i) q^{25} +(-0.826352 - 1.43128i) q^{26} +(0.500000 - 0.866025i) q^{27} +(-0.500000 - 2.83564i) q^{28} +(1.10354 + 6.25849i) q^{29} +(1.70574 - 2.95442i) q^{30} +(-0.798133 - 1.38241i) q^{31} +(-0.766044 + 0.642788i) q^{32} +(-0.326352 + 0.118782i) q^{33} +(6.52481 + 2.37484i) q^{34} +(7.52481 + 6.31407i) q^{35} +(0.173648 - 0.984808i) q^{36} -11.2121 q^{37} +(-2.77719 - 3.35965i) q^{38} +1.65270 q^{39} +(0.592396 - 3.35965i) q^{40} +(-2.67365 - 2.24346i) q^{41} +(2.70574 + 0.984808i) q^{42} +(-2.14543 + 0.780873i) q^{43} +(-0.266044 + 0.223238i) q^{44} +(1.70574 + 2.95442i) q^{45} +(3.40033 - 5.88954i) q^{46} +(0.971782 + 5.51125i) q^{47} +(-0.173648 - 0.984808i) q^{48} +(-0.645430 + 1.11792i) q^{49} +(3.31908 + 5.74881i) q^{50} +(-5.31908 + 4.46324i) q^{51} +(1.55303 - 0.565258i) q^{52} +(-1.86097 - 0.677337i) q^{53} +(0.766044 + 0.642788i) q^{54} +(0.205737 - 1.16679i) q^{55} +2.87939 q^{56} +(4.29813 - 0.725293i) q^{57} -6.35504 q^{58} +(0.0773815 - 0.438852i) q^{59} +(2.61334 + 2.19285i) q^{60} +(11.7763 + 4.28623i) q^{61} +(1.50000 - 0.545955i) q^{62} +(-2.20574 + 1.85083i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-2.81908 + 4.88279i) q^{65} +(-0.0603074 - 0.342020i) q^{66} +(-0.187319 - 1.06234i) q^{67} +(-3.47178 + 6.01330i) q^{68} +(3.40033 + 5.88954i) q^{69} +(-7.52481 + 6.31407i) q^{70} +(15.6211 - 5.68561i) q^{71} +(0.939693 + 0.342020i) q^{72} +(9.51367 + 7.98292i) q^{73} +(1.94697 - 11.0418i) q^{74} -6.63816 q^{75} +(3.79086 - 2.15160i) q^{76} +1.00000 q^{77} +(-0.286989 + 1.62760i) q^{78} +(-8.36824 - 7.02179i) q^{79} +(3.20574 + 1.16679i) q^{80} +(-0.939693 + 0.342020i) q^{81} +(2.67365 - 2.24346i) q^{82} +(-5.85844 - 10.1471i) q^{83} +(-1.43969 + 2.49362i) q^{84} +(-4.11334 - 23.3279i) q^{85} +(-0.396459 - 2.24843i) q^{86} +(3.17752 - 5.50362i) q^{87} +(-0.173648 - 0.300767i) q^{88} +(1.37346 - 1.15247i) q^{89} +(-3.20574 + 1.16679i) q^{90} +(-4.47178 - 1.62760i) q^{91} +(5.20961 + 4.37138i) q^{92} +(-0.277189 + 1.57202i) q^{93} -5.59627 q^{94} +(-5.18866 + 13.9357i) q^{95} +1.00000 q^{96} +(0.634285 - 3.59721i) q^{97} +(-0.988856 - 0.829748i) q^{98} +(0.326352 + 0.118782i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{5} + 3 q^{7} + 3 q^{8} + 3 q^{12} - 3 q^{13} - 6 q^{14} - 9 q^{15} - 3 q^{17} - 6 q^{18} - 18 q^{19} + 3 q^{21} - 3 q^{22} - 21 q^{23} + 9 q^{25} - 6 q^{26} + 3 q^{27} - 3 q^{28} - 3 q^{29} + 9 q^{31}+ \cdots + 3 q^{99}+O(q^{100}) \) 6 * q + 9 * q^5 + 3 * q^7 + 3 * q^8 + 3 * q^12 - 3 * q^13 - 6 * q^14 - 9 * q^15 - 3 * q^17 - 6 * q^18 - 18 * q^19 + 3 * q^21 - 3 * q^22 - 21 * q^23 + 9 * q^25 - 6 * q^26 + 3 * q^27 - 3 * q^28 - 3 * q^29 + 9 * q^31 - 3 * q^33 + 12 * q^34 + 18 * q^35 - 18 * q^37 - 6 * q^38 + 12 * q^39 - 15 * q^41 + 6 * q^42 + 3 * q^43 + 3 * q^44 + 6 * q^46 - 9 * q^47 + 12 * q^49 + 3 * q^50 - 15 * q^51 - 3 * q^52 + 12 * q^53 - 9 * q^55 + 6 * q^56 + 12 * q^57 + 12 * q^58 + 27 * q^59 + 9 * q^60 + 3 * q^61 + 9 * q^62 - 3 * q^63 - 3 * q^64 - 6 * q^66 + 21 * q^67 - 6 * q^68 + 6 * q^69 - 18 * q^70 + 39 * q^71 + 36 * q^73 + 24 * q^74 - 6 * q^75 - 9 * q^76 + 6 * q^77 + 6 * q^78 - 45 * q^79 + 9 * q^80 + 15 * q^82 - 27 * q^83 - 3 * q^84 - 18 * q^85 - 12 * q^86 - 6 * q^87 - 30 * q^89 - 9 * q^90 - 12 * q^91 - 3 * q^92 + 9 * q^93 - 6 * q^94 + 6 * q^96 - 6 * q^97 - 12 * q^98 + 3 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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