LMFDB - Embedded newform 99.2.p.a.29.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [99,2,Mod(2,99)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(99, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([5, 3]))

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

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

chi := DirichletCharacter("99.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 99 = 3^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	99.p (of order $30$, degree $8$, 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:	$0.790518980011$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			29.4
Character	$\chi$	$=$	99.29
Dual form			99.2.p.a.41.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31398 + 0.585020i) q^{2} +(1.60559 - 0.649686i) q^{3} +(0.0460231 - 0.0511138i) q^{4} +(1.45099 - 3.25897i) q^{5} +(-1.72962 + 1.79297i) q^{6} +(-0.449955 + 2.11687i) q^{7} +(0.858363 - 2.64177i) q^{8} +(2.15582 - 2.08625i) q^{9} +O(q^{10})$	\(q+(-1.31398 + 0.585020i) q^{2} +(1.60559 - 0.649686i) q^{3} +(0.0460231 - 0.0511138i) q^{4} +(1.45099 - 3.25897i) q^{5} +(-1.72962 + 1.79297i) q^{6} +(-0.449955 + 2.11687i) q^{7} +(0.858363 - 2.64177i) q^{8} +(2.15582 - 2.08625i) q^{9} +5.13106i q^{10} +(-0.670091 + 3.24823i) q^{11} +(0.0406861 - 0.111968i) q^{12} +(2.80353 + 0.294663i) q^{13} +(-0.647182 - 3.04475i) q^{14} +(0.212377 - 6.17525i) q^{15} +(0.431998 + 4.11019i) q^{16} +(-0.345974 + 0.251365i) q^{17} +(-1.61219 + 4.00248i) q^{18} +(-3.47799 - 1.13007i) q^{19} +(-0.0997996 - 0.224153i) q^{20} +(0.652861 + 3.69115i) q^{21} +(-1.01979 - 4.66011i) q^{22} +(-6.93913 + 4.00631i) q^{23} +(-0.338145 - 4.79926i) q^{24} +(-5.16987 - 5.74172i) q^{25} +(-3.85615 + 1.25294i) q^{26} +(2.10594 - 4.75027i) q^{27} +(0.0874932 + 0.120424i) q^{28} +(-6.59765 - 1.40237i) q^{29} +(3.33358 + 8.23837i) q^{30} +(0.0132129 - 0.125713i) q^{31} +(-0.194455 - 0.336806i) q^{32} +(1.03444 + 5.65066i) q^{33} +(0.307548 - 0.532688i) q^{34} +(6.24595 + 4.53795i) q^{35} +(-0.00741914 - 0.206208i) q^{36} +(1.89382 + 5.82859i) q^{37} +(5.23111 - 0.549812i) q^{38} +(4.69274 - 1.34831i) q^{39} +(-7.36398 - 6.63056i) q^{40} +(2.15199 - 0.457420i) q^{41} +(-3.01724 - 4.46815i) q^{42} +(2.48738 + 1.43609i) q^{43} +(0.135190 + 0.183744i) q^{44} +(-3.67098 - 10.0529i) q^{45} +(6.77408 - 9.32372i) q^{46} +(2.50344 - 2.25411i) q^{47} +(3.36394 + 6.31860i) q^{48} +(2.11612 + 0.942159i) q^{49} +(10.1521 + 4.52001i) q^{50} +(-0.392182 + 0.628362i) q^{51} +(0.144088 - 0.129738i) q^{52} +(-1.52002 + 2.09212i) q^{53} +(0.0118478 + 7.47375i) q^{54} +(9.61358 + 6.89694i) q^{55} +(5.20607 + 3.00573i) q^{56} +(-6.31841 + 0.445181i) q^{57} +(9.48957 - 2.01707i) q^{58} +(3.41571 + 3.07552i) q^{59} +(-0.305866 - 0.295059i) q^{60} +(-7.97621 + 0.838333i) q^{61} +(0.0561830 + 0.172913i) q^{62} +(3.44632 + 5.50231i) q^{63} +(-6.23451 - 4.52964i) q^{64} +(5.02818 - 8.70906i) q^{65} +(-4.66497 - 6.81966i) q^{66} +(2.75806 + 4.77710i) q^{67} +(-0.00307457 + 0.0292526i) q^{68} +(-8.53853 + 10.9407i) q^{69} +(-10.8618 - 2.30875i) q^{70} +(-5.13082 - 7.06197i) q^{71} +(-3.66093 - 7.48594i) q^{72} +(4.81457 - 1.56435i) q^{73} +(-5.89828 - 6.55070i) q^{74} +(-12.0310 - 5.86004i) q^{75} +(-0.217830 + 0.125764i) q^{76} +(-6.57457 - 2.88006i) q^{77} +(-5.37737 + 4.51699i) q^{78} +(-5.58618 - 12.5468i) q^{79} +(14.0218 + 4.55596i) q^{80} +(0.295083 - 8.99516i) q^{81} +(-2.56007 + 1.86000i) q^{82} +(1.52351 + 14.4952i) q^{83} +(0.218716 + 0.136508i) q^{84} +(0.317186 + 1.49224i) q^{85} +(-4.10849 - 0.431820i) q^{86} +(-11.5042 + 2.03477i) q^{87} +(8.00589 + 4.55839i) q^{88} -5.40631i q^{89} +(10.7047 + 11.0616i) q^{90} +(-1.88523 + 5.80213i) q^{91} +(-0.114583 + 0.539069i) q^{92} +(-0.0604593 - 0.210427i) q^{93} +(-1.97076 + 4.42640i) q^{94} +(-8.72938 + 9.69496i) q^{95} +(-0.531033 - 0.414437i) q^{96} +(6.49965 - 2.89383i) q^{97} -3.33172 q^{98} +(5.33204 + 8.40056i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9}+O(q^{10}) $ 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9	$ 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9} - 3 q^{11} - 54 q^{12} - 5 q^{13} - 9 q^{14} + 5 q^{16} - 50 q^{19} - 3 q^{20} - 11 q^{22} - 42 q^{23} - 5 q^{24} - 2 q^{25} + 3 q^{27} - 20 q^{28} + 30 q^{29} + 50 q^{30} - 6 q^{31} + 4 q^{33} - 10 q^{34} - 17 q^{36} - 6 q^{37} + 9 q^{38} + 85 q^{39} + 15 q^{40} - 15 q^{41} + 19 q^{42} - 12 q^{45} - 40 q^{46} - 21 q^{47} + 70 q^{48} - q^{49} + 60 q^{50} - 45 q^{51} - 5 q^{52} - 18 q^{55} + 90 q^{56} + 60 q^{57} - 29 q^{58} + 81 q^{59} + 43 q^{60} - 5 q^{61} + 15 q^{63} - 8 q^{64} - 39 q^{66} + 10 q^{67} + 180 q^{68} - 20 q^{69} + 30 q^{70} + 5 q^{72} - 20 q^{73} - 15 q^{74} - 30 q^{75} + 33 q^{77} + 152 q^{78} - 5 q^{79} - 73 q^{81} - 2 q^{82} - 60 q^{83} - 135 q^{84} - 5 q^{85} - 48 q^{86} - 59 q^{88} - 70 q^{90} + 52 q^{91} - 213 q^{92} - 34 q^{93} - 5 q^{94} - 135 q^{95} - 145 q^{96} + 27 q^{97} + 35 q^{99}+O(q^{100}) $ 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9 - 3 * q^11 - 54 * q^12 - 5 * q^13 - 9 * q^14 + 5 * q^16 - 50 * q^19 - 3 * q^20 - 11 * q^22 - 42 * q^23 - 5 * q^24 - 2 * q^25 + 3 * q^27 - 20 * q^28 + 30 * q^29 + 50 * q^30 - 6 * q^31 + 4 * q^33 - 10 * q^34 - 17 * q^36 - 6 * q^37 + 9 * q^38 + 85 * q^39 + 15 * q^40 - 15 * q^41 + 19 * q^42 - 12 * q^45 - 40 * q^46 - 21 * q^47 + 70 * q^48 - q^49 + 60 * q^50 - 45 * q^51 - 5 * q^52 - 18 * q^55 + 90 * q^56 + 60 * q^57 - 29 * q^58 + 81 * q^59 + 43 * q^60 - 5 * q^61 + 15 * q^63 - 8 * q^64 - 39 * q^66 + 10 * q^67 + 180 * q^68 - 20 * q^69 + 30 * q^70 + 5 * q^72 - 20 * q^73 - 15 * q^74 - 30 * q^75 + 33 * q^77 + 152 * q^78 - 5 * q^79 - 73 * q^81 - 2 * q^82 - 60 * q^83 - 135 * q^84 - 5 * q^85 - 48 * q^86 - 59 * q^88 - 70 * q^90 + 52 * q^91 - 213 * q^92 - 34 * q^93 - 5 * q^94 - 135 * q^95 - 145 * q^96 + 27 * q^97 + 35 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/99\mathbb{Z}\right)^\times$.

$n$	$46$	$56$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.31398	+	0.585020i	−0.929121	+	0.413671i	−0.814780	−	0.579770i	$-0.803142\pi$
$2$	−1.31398	+	0.585020i	−0.929121	+	0.413671i	−0.114341	+	0.993442i	$0.536476\pi$
$3$	1.60559	−	0.649686i	0.926986	−	0.375096i
$3$	1.60559	−	0.649686i	0.926986	−	0.375096i
$4$	0.0460231	−	0.0511138i	0.0230116	−	0.0255569i
$5$	1.45099	−	3.25897i	0.648901	−	1.45746i	−0.226477	−	0.974017i	$-0.572721\pi$
$5$	1.45099	−	3.25897i	0.648901	−	1.45746i	0.875378	−	0.483439i	$-0.160613\pi$
$6$	−1.72962	+	1.79297i	−0.706115	+	0.731978i
$7$	−0.449955	+	2.11687i	−0.170067	+	0.800103i	0.807565	+	0.589779i	$0.200785\pi$
$7$	−0.449955	+	2.11687i	−0.170067	+	0.800103i	−0.977632	+	0.210324i	$0.932548\pi$
$8$	0.858363	−	2.64177i	0.303477	−	0.934007i
$9$	2.15582	−	2.08625i	0.718605	−	0.695418i
$10$			5.13106i			1.62259i
$11$	−0.670091	+	3.24823i	−0.202040	+	0.979377i
$11$	−0.670091	+	3.24823i	−0.202040	+	0.979377i
$12$	0.0406861	−	0.111968i	0.0117451	−	0.0323225i
$13$	2.80353	+	0.294663i	0.777559	+	0.0817247i	0.484990	−	0.874520i	$-0.338823\pi$
$13$	2.80353	+	0.294663i	0.777559	+	0.0817247i	0.292569	+	0.956244i	$0.405490\pi$
$14$	−0.647182	−	3.04475i	−0.172967	−	0.813745i
$15$	0.212377	−	6.17525i	0.0548356	−	1.59444i
$16$	0.431998	+	4.11019i	0.108000	+	1.02755i
$17$	−0.345974	+	0.251365i	−0.0839109	+	0.0609648i	−0.628950	−	0.777446i	$-0.716515\pi$
$17$	−0.345974	+	0.251365i	−0.0839109	+	0.0609648i	0.545039	+	0.838411i	$0.316515\pi$
$18$	−1.61219	+	4.00248i	−0.379997	+	0.943394i
$19$	−3.47799	−	1.13007i	−0.797906	−	0.259255i	−0.118439	−	0.992961i	$-0.537789\pi$
$19$	−3.47799	−	1.13007i	−0.797906	−	0.259255i	−0.679467	+	0.733706i	$0.737789\pi$
$20$	−0.0997996	−	0.224153i	−0.0223159	−	0.0501222i
$21$	0.652861	+	3.69115i	0.142466	+	0.805476i
$22$	−1.01979	−	4.66011i	−0.217421	−	0.993538i
$23$	−6.93913	+	4.00631i	−1.44691	+	0.835373i	−0.998296	−	0.0583527i	$-0.981415\pi$
$23$	−6.93913	+	4.00631i	−1.44691	+	0.835373i	−0.448613	+	0.893726i	$0.648082\pi$
$24$	−0.338145	−	4.79926i	−0.0690236	−	0.979645i
$25$	−5.16987	−	5.74172i	−1.03397	−	1.14834i
$26$	−3.85615	+	1.25294i	−0.756253	+	0.245722i
$27$	2.10594	−	4.75027i	0.405288	−	0.914189i
$28$	0.0874932	+	0.120424i	0.0165347	+	0.0227580i
$29$	−6.59765	−	1.40237i	−1.22515	−	0.260414i	−0.450486	−	0.892784i	$-0.648749\pi$
$29$	−6.59765	−	1.40237i	−1.22515	−	0.260414i	−0.774667	+	0.632369i	$0.782083\pi$
$30$	3.33358	+	8.23837i	0.608626	+	1.50411i
$31$	0.0132129	−	0.125713i	0.00237312	−	0.0225787i	−0.993271	−	0.115811i	$-0.963053\pi$
$31$	0.0132129	−	0.125713i	0.00237312	−	0.0225787i	0.995644	+	0.0932324i	$0.0297200\pi$
$32$	−0.194455	−	0.336806i	−0.0343751	−	0.0595395i
$33$	1.03444	+	5.65066i	0.180073	+	0.983653i
$34$	0.307548	−	0.532688i	0.0527440	−	0.0913553i
$35$	6.24595	+	4.53795i	1.05576	+	0.767053i
$36$	−0.00741914	−	0.206208i	−0.00123652	−	0.0343680i
$37$	1.89382	+	5.82859i	0.311343	+	0.958214i	0.977234	+	0.212165i	$0.0680515\pi$
$37$	1.89382	+	5.82859i	0.311343	+	0.958214i	−0.665891	+	0.746049i	$0.731949\pi$
$38$	5.23111	−	0.549812i	0.848598	−	0.0891913i
$39$	4.69274	−	1.34831i	0.751440	−	0.215902i
$40$	−7.36398	−	6.63056i	−1.16435	−	1.04838i
$41$	2.15199	−	0.457420i	0.336085	−	0.0714371i	−0.0367780	−	0.999323i	$-0.511709\pi$
$41$	2.15199	−	0.457420i	0.336085	−	0.0714371i	0.372863	+	0.927886i	$0.378376\pi$
$42$	−3.01724	−	4.46815i	−0.465570	−	0.689450i
$43$	2.48738	+	1.43609i	0.379321	+	0.219001i	0.677523	−	0.735502i	$-0.263053\pi$
$43$	2.48738	+	1.43609i	0.379321	+	0.219001i	−0.298202	+	0.954503i	$0.596387\pi$
$44$	0.135190	+	0.183744i	0.0203806	+	0.0277005i
$45$	−3.67098	−	10.0529i	−0.547238	−	1.49859i
$46$	6.77408	−	9.32372i	0.998784	−	1.37471i
$47$	2.50344	−	2.25411i	0.365164	−	0.328795i	−0.466039	−	0.884764i	$-0.654319\pi$
$47$	2.50344	−	2.25411i	0.365164	−	0.328795i	0.831203	+	0.555969i	$0.187653\pi$
$48$	3.36394	+	6.31860i	0.485544	+	0.912012i
$49$	2.11612	+	0.942159i	0.302304	+	0.134594i
$50$	10.1521	+	4.52001i	1.43573	+	0.639226i
$51$	−0.392182	+	0.628362i	−0.0549165	+	0.0879882i
$52$	0.144088	−	0.129738i	0.0199815	−	0.0179914i
$53$	−1.52002	+	2.09212i	−0.208790	+	0.287375i	−0.900550	−	0.434753i	$-0.856836\pi$
$53$	−1.52002	+	2.09212i	−0.208790	+	0.287375i	0.691760	+	0.722128i	$0.256836\pi$
$54$	0.0118478	+	7.47375i	0.00161228	+	1.01705i
$55$	9.61358	+	6.89694i	1.29630	+	0.929984i
$56$	5.20607	+	3.00573i	0.695690	+	0.401657i
$57$	−6.31841	+	0.445181i	−0.836894	+	0.0589657i
$58$	9.48957	−	2.01707i	1.24604	−	0.264854i
$59$	3.41571	+	3.07552i	0.444688	+	0.400399i	0.860823	−	0.508904i	$-0.169949\pi$
$59$	3.41571	+	3.07552i	0.444688	+	0.400399i	−0.416136	+	0.909303i	$0.636616\pi$
$60$	−0.305866	−	0.295059i	−0.0394872	−	0.0380920i
$61$	−7.97621	+	0.838333i	−1.02125	+	0.107338i	−0.600323	−	0.799758i	$-0.704961\pi$
$61$	−7.97621	+	0.838333i	−1.02125	+	0.107338i	−0.420926	+	0.907095i	$0.638295\pi$
$62$	0.0561830	+	0.172913i	0.00713524	+	0.0219600i
$63$	3.44632	+	5.50231i	0.434195	+	0.693226i
$64$	−6.23451	−	4.52964i	−0.779314	−	0.566205i
$65$	5.02818	−	8.70906i	0.623669	−	1.08023i
$66$	−4.66497	−	6.81966i	−0.574219	−	0.839442i
$67$	2.75806	+	4.77710i	0.336951	+	0.583615i	0.983858	−	0.178953i	$-0.0572712\pi$
$67$	2.75806	+	4.77710i	0.336951	+	0.583615i	−0.646907	+	0.762569i	$0.723938\pi$
$68$	−0.00307457	+	0.0292526i	−0.000372847	+	0.00354740i
$69$	−8.53853	+	10.9407i	−1.02792	+	1.31711i
$70$	−10.8618	−	2.30875i	−1.29824	−	0.275948i
$71$	−5.13082	−	7.06197i	−0.608916	−	0.838101i	0.387572	−	0.921840i	$-0.373314\pi$
$71$	−5.13082	−	7.06197i	−0.608916	−	0.838101i	−0.996488	+	0.0837384i	$0.973314\pi$
$72$	−3.66093	−	7.48594i	−0.431445	−	0.882226i
$73$	4.81457	−	1.56435i	0.563503	−	0.183093i	−0.0133940	−	0.999910i	$-0.504264\pi$
$73$	4.81457	−	1.56435i	0.563503	−	0.183093i	0.576897	+	0.816817i	$0.304264\pi$
$74$	−5.89828	−	6.55070i	−0.685661	−	0.761503i
$75$	−12.0310	−	5.86004i	−1.38922	−	0.676659i
$76$	−0.217830	+	0.125764i	−0.0249868	+	0.0144262i
$77$	−6.57457	−	2.88006i	−0.749242	−	0.328213i
$78$	−5.37737	+	4.51699i	−0.608867	+	0.511448i
$79$	−5.58618	−	12.5468i	−0.628494	−	1.41162i	−0.894245	−	0.447578i	$-0.852287\pi$
$79$	−5.58618	−	12.5468i	−0.628494	−	1.41162i	0.265751	−	0.964042i	$-0.414380\pi$
$80$	14.0218	+	4.55596i	1.56769	+	0.509372i
$81$	0.295083	−	8.99516i	0.0327870	−	0.999462i
$82$	−2.56007	+	1.86000i	−0.282712	+	0.205402i
$83$	1.52351	+	14.4952i	0.167227	+	1.59106i	0.680446	+	0.732798i	$0.261786\pi$
$83$	1.52351	+	14.4952i	0.167227	+	1.59106i	−0.513220	+	0.858257i	$0.671547\pi$
$84$	0.218716	+	0.136508i	0.0238638	+	0.0148943i
$85$	0.317186	+	1.49224i	0.0344037	+	0.161857i
$86$	−4.10849	−	0.431820i	−0.443030	−	0.0465643i
$87$	−11.5042	+	2.03477i	−1.23338	+	0.218150i
$88$	8.00589	+	4.55839i	0.853431	+	0.485926i
$89$		−	5.40631i		−	0.573068i	−0.958070	−	0.286534i	$-0.907497\pi$
$89$		−	5.40631i		−	0.573068i	0.958070	−	0.286534i	$-0.0925031\pi$
$90$	10.7047	+	11.0616i	1.12838	+	1.16600i
$91$	−1.88523	+	5.80213i	−0.197625	+	0.608228i
$92$	−0.114583	+	0.539069i	−0.0119461	+	0.0562018i
$93$	−0.0604593	−	0.210427i	−0.00626934	−	0.0218203i
$94$	−1.97076	+	4.42640i	−0.203269	+	0.456549i
$95$	−8.72938	+	9.69496i	−0.895616	+	0.994682i
$96$	−0.531033	−	0.414437i	−0.0541983	−	0.0422983i
$97$	6.49965	−	2.89383i	0.659940	−	0.293824i	−0.0493077	−	0.998784i	$-0.515702\pi$
$97$	6.49965	−	2.89383i	0.659940	−	0.293824i	0.709248	+	0.704959i	$0.249035\pi$
$98$	−3.33172			−0.336554
$99$	5.33204	+	8.40056i	0.535890	+	0.844288i
$100$	−0.531415			−0.0531415
$101$	5.99492	−	2.66911i	0.596517	−	0.265586i	−0.0861901	−	0.996279i	$-0.527469\pi$
$101$	5.99492	−	2.66911i	0.596517	−	0.265586i	0.682707	+	0.730692i	$0.260803\pi$
$102$	0.147714	−	1.05509i	0.0146259	−	0.104469i
$103$	6.10385	−	6.77901i	0.601430	−	0.667956i	−0.363155	−	0.931729i	$-0.618300\pi$
$103$	6.10385	−	6.77901i	0.601430	−	0.667956i	0.964585	+	0.263773i	$0.0849671\pi$
$104$	3.18488	−	7.15335i	0.312303	−	0.701444i
$105$	12.9767	+	3.22816i	1.26639	+	0.315036i
$106$	0.773331	−	3.63824i	0.0751125	−	0.353377i
$107$	0.506436	−	1.55865i	0.0489590	−	0.150680i	−0.923588	−	0.383386i	$-0.874758\pi$
$107$	0.506436	−	1.55865i	0.0489590	−	0.150680i	0.972547	+	0.232706i	$0.0747579\pi$
$108$	−0.145883	−	0.326265i	−0.0140376	−	0.0313948i
$109$		−	13.4796i		−	1.29111i	−0.763714	−	0.645555i	$-0.776626\pi$
$109$		−	13.4796i		−	1.29111i	0.763714	−	0.645555i	$-0.223374\pi$
$110$	−16.6669	−	3.43828i	−1.58912	−	0.327827i
$111$	6.82745	+	8.12791i	0.648033	+	0.771467i
$112$	−8.89513	−	0.934916i	−0.840511	−	0.0883413i
$113$	1.54842	+	7.28475i	0.145663	+	0.685292i	0.989001	+	0.147908i	$0.0472540\pi$
$113$	1.54842	+	7.28475i	0.145663	+	0.685292i	−0.843338	+	0.537384i	$0.819413\pi$
$114$	8.04180	−	4.28135i	0.753183	−	0.400985i
$115$	2.98785	+	28.4275i	0.278619	+	2.65088i
$116$	−0.375325	+	0.272690i	−0.0348481	+	0.0253186i
$117$	6.65863	−	5.21363i	0.615590	−	0.482001i
$118$	−6.28740	−	2.04290i	−0.578802	−	0.188064i
$119$	−0.376434	−	0.845485i	−0.0345077	−	0.0775055i
$120$	−16.1313	−	5.86166i	−1.47258	−	0.535094i
$121$	−10.1020	−	4.35322i	−0.918360	−	0.395747i
$122$	9.99010	−	5.76779i	0.904461	−	0.522191i
$123$	3.15803	−	2.13255i	0.284750	−	0.192285i
$124$	−0.00581756	−	0.00646106i	−0.000522433	−	0.000580220i
$125$	−9.24960	+	3.00538i	−0.827309	+	0.268809i
$126$	−7.74734	−	5.21374i	−0.690188	−	0.464477i
$127$	−1.80470	−	2.48395i	−0.160141	−	0.220415i	0.721405	−	0.692514i	$-0.243497\pi$
$127$	−1.80470	−	2.48395i	−0.160141	−	0.220415i	−0.881546	+	0.472098i	$0.843497\pi$
$128$	11.6027	+	2.46624i	1.02555	+	0.217987i
$129$	4.92670	+	0.689748i	0.433772	+	0.0607289i
$130$	−1.51193	+	14.3851i	−0.132605	+	1.26165i
$131$	−1.72969	−	2.99591i	−0.151124	−	0.261754i	0.780517	−	0.625134i	$-0.214956\pi$
$131$	−1.72969	−	2.99591i	−0.151124	−	0.261754i	−0.931641	+	0.363381i	$0.881622\pi$
$132$	0.336435	+	0.207187i	0.0292829	+	0.0180333i
$133$	3.95715	−	6.85399i	0.343129	−	0.594316i
$134$	−6.41872	−	4.66347i	−0.554493	−	0.402863i
$135$	−12.4253	−	13.7558i	−1.06940	−	1.18391i
$136$	0.367076	+	1.12975i	0.0314765	+	0.0968748i
$137$	10.0336	−	1.05458i	0.857230	−	0.0900985i	0.334292	−	0.942469i	$-0.391503\pi$
$137$	10.0336	−	1.05458i	0.857230	−	0.0900985i	0.522938	+	0.852371i	$0.324836\pi$
$138$	4.81888	−	19.3711i	0.410210	−	1.64898i
$139$	4.94017	+	4.44815i	0.419020	+	0.377287i	0.851498	−	0.524357i	$-0.175694\pi$
$139$	4.94017	+	4.44815i	0.419020	+	0.377287i	−0.432479	+	0.901644i	$0.642361\pi$
$140$	0.519410	−	0.110404i	0.0438981	−	0.00933084i
$141$	2.55503	−	5.24561i	0.215172	−	0.441760i
$142$	10.8732	+	6.27762i	0.912455	+	0.526806i
$143$	−2.83575	+	8.90904i	−0.237137	+	0.745011i
$144$	9.50621	+	7.95955i	0.792184	+	0.663296i
$145$	−14.1434	+	19.4667i	−1.17455	+	1.61662i
$146$	−5.41105	+	4.87213i	−0.447822	+	0.403221i
$147$	4.00973	+	0.137901i	0.330717	+	0.0113739i
$148$	0.385081	+	0.171449i	0.0316535	+	0.0140930i
$149$	−12.5827	−	5.60217i	−1.03081	−	0.458948i	−0.179585	−	0.983742i	$-0.557475\pi$
$149$	−12.5827	−	5.60217i	−1.03081	−	0.458948i	−0.851229	+	0.524795i	$0.824142\pi$
$150$	19.2367	+	0.661582i	1.57067	+	0.0540180i
$151$	15.2763	−	13.7548i	1.24317	−	1.11935i	0.254843	−	0.966982i	$-0.417976\pi$
$151$	15.2763	−	13.7548i	1.24317	−	1.11935i	0.988324	−	0.152370i	$-0.0486904\pi$
$152$	−5.97076	+	8.21805i	−0.484293	+	0.666572i
$153$	−0.221445	+	1.26368i	−0.0179028	+	0.102163i
$154$	10.3237	−	0.0619326i	0.831909	−	0.00499067i
$155$	−0.390522	−	0.225468i	−0.0313675	−	0.0181100i
$156$	0.147058	−	0.301917i	0.0117740	−	0.0241727i
$157$	−7.48182	+	1.59031i	−0.597114	+	0.126921i	−0.496547	−	0.868010i	$-0.665399\pi$
$157$	−7.48182	+	1.59031i	−0.597114	+	0.126921i	−0.100567	+	0.994930i	$0.532066\pi$
$158$	14.6802	+	13.2181i	1.16789	+	1.05158i
$159$	−1.08129	+	4.34661i	−0.0857521	+	0.344709i
$160$	−1.37979	+	0.145022i	−0.109082	+	0.0114650i
$161$	−5.35855	−	16.4919i	−0.422313	−	1.29975i
$162$	4.87461	+	11.9921i	0.382986	+	0.942185i
$163$	−7.23192	−	5.25430i	−0.566448	−	0.411548i	0.267365	−	0.963595i	$-0.413847\pi$
$163$	−7.23192	−	5.25430i	−0.566448	−	0.411548i	−0.833813	+	0.552047i	$0.813847\pi$
$164$	0.0756609	−	0.131049i	0.00590813	−	0.0102332i
$165$	19.9163	+	4.82783i	1.55048	+	0.375846i
$166$	−10.4818	−	18.1551i	−0.813548	−	1.40911i
$167$	0.274382	−	2.61057i	0.0212323	−	0.202012i	−0.978763	−	0.204994i	$-0.934283\pi$
$167$	0.274382	−	2.61057i	0.0212323	−	0.202012i	0.999996	+	0.00298200i	$0.000949200\pi$
$168$	10.3116	+	1.44364i	0.795555	+	0.111379i
$169$	−4.94298	−	1.05066i	−0.380229	−	0.0808202i
$170$	−1.28977	−	1.77521i	−0.0989206	−	0.136153i
$171$	−9.85552	+	4.81976i	−0.753671	+	0.368576i
$172$	0.187881	−	0.0610461i	0.0143258	−	0.00465472i
$173$	−11.1594	−	12.3938i	−0.848435	−	0.942283i	0.150491	−	0.988611i	$-0.451915\pi$
$173$	−11.1594	−	12.3938i	−0.848435	−	0.942283i	−0.998926	+	0.0463287i	$0.985248\pi$
$174$	13.9259	−	9.40382i	1.05572	−	0.712902i
$175$	14.4807	−	8.36045i	1.09464	−	0.631990i
$176$	−13.6403	−	1.35097i	−1.02818	−	0.101833i
$177$	7.48234	+	2.71887i	0.562407	+	0.204363i
$178$	3.16280	+	7.10376i	0.237062	+	0.532449i
$179$	−15.2409	−	4.95208i	−1.13916	−	0.370136i	−0.322110	−	0.946702i	$-0.604392\pi$
$179$	−15.2409	−	4.95208i	−1.13916	−	0.370136i	−0.817050	+	0.576567i	$0.804392\pi$
$180$	−0.682791	−	0.275026i	−0.0508922	−	0.0204993i
$181$	−10.6647	+	7.74833i	−0.792698	+	0.575929i	−0.908763	−	0.417313i	$-0.862972\pi$
$181$	−10.6647	+	7.74833i	−0.792698	+	0.575929i	0.116065	+	0.993242i	$0.462972\pi$
$182$	−0.917218	−	8.72675i	−0.0679887	−	0.646870i
$183$	−12.2618	+	6.52805i	−0.906421	+	0.482567i
$184$	4.62746	+	21.7705i	0.341141	+	1.60494i
$185$	21.7431	+	2.28529i	1.59859	+	0.168018i
$186$	0.202546	+	0.241126i	0.0148514	+	0.0176802i
$187$	−0.584655	−	1.29224i	−0.0427542	−	0.0944978i
$188$		−	0.231701i		−	0.0168986i
$189$	9.10813	+	6.59541i	0.662519	+	0.479746i
$190$	5.79845	−	17.8458i	0.420664	−	1.29467i
$191$	−2.24874	+	10.5795i	−0.162713	+	0.765505i	0.818795	+	0.574086i	$0.194642\pi$
$191$	−2.24874	+	10.5795i	−0.162713	+	0.765505i	−0.981508	+	0.191419i	$0.938691\pi$
$192$	−12.9529	−	3.22225i	−0.934794	−	0.232546i
$193$	−3.76061	+	8.44646i	−0.270694	+	0.607990i	−0.996830	−	0.0795620i	$-0.974648\pi$
$193$	−3.76061	+	8.44646i	−0.270694	+	0.607990i	0.726136	+	0.687552i	$0.241314\pi$
$194$	−6.84744	+	7.60485i	−0.491617	+	0.545996i
$195$	2.41502	−	17.2499i	0.172943	−	1.23529i
$196$	0.145548	−	0.0648022i	0.0103963	−	0.00462873i
$197$	22.2431			1.58475			0.792377	−	0.610032i	$-0.208843\pi$
$197$	22.2431			1.58475			0.792377	+	0.610032i	$0.208843\pi$
$198$	−11.9207	−	7.91879i	−0.847164	−	0.562764i
$199$	−2.40521			−0.170500			−0.0852502	−	0.996360i	$-0.527169\pi$
$199$	−2.40521			−0.170500			−0.0852502	+	0.996360i	$0.527169\pi$
$200$	−19.6060	+	8.72913i	−1.38635	+	0.617243i
$201$	7.53192	+	5.87817i	0.531260	+	0.414614i
$202$	−6.31570	+	7.01429i	−0.444371	+	0.493524i
$203$	5.93730	−	13.3354i	0.416717	−	0.935961i
$204$	0.0140685	+	0.0489651i	0.000984994	+	0.00342824i
$205$	1.63180	−	7.67700i	0.113970	−	0.536185i
$206$	−4.05445	+	12.4783i	−0.282487	+	0.869406i
$207$	−6.60131	+	23.1137i	−0.458823	+	1.60651i
$208$			11.6503i			0.807805i
$209$	6.00129	−	10.5401i	0.415118	−	0.729071i
$210$	−18.9395	+	3.34987i	−1.30695	+	0.231163i
$211$	17.5916	+	1.84895i	1.21106	+	0.127287i	0.688449	−	0.725285i	$-0.258292\pi$
$211$	17.5916	+	1.84895i	1.21106	+	0.127287i	0.522609	+	0.852572i	$0.324959\pi$
$212$	0.0369805	+	0.173980i	0.00253983	+	0.0119490i
$213$	−12.8260	−	8.00517i	−0.878825	−	0.548506i
$214$	0.246396	+	2.34430i	0.0168433	+	0.160253i
$215$	8.28931	−	6.02254i	0.565327	−	0.410734i
$216$	−10.7415	−	9.64086i	−0.730863	−	0.655977i
$217$	0.260173	+	0.0845353i	0.0176617	+	0.00573863i
$218$	7.88582	+	17.7118i	0.534095	+	1.19960i
$219$	6.71387	−	5.63965i	0.453681	−	0.381093i
$220$	0.794976	−	0.173968i	0.0535973	−	0.0117289i
$221$	−1.04401	+	0.602762i	−0.0702280	+	0.0405461i
$222$	−13.7261	−	6.68569i	−0.921235	−	0.448714i
$223$	4.21351	+	4.67958i	0.282158	+	0.313368i	0.867518	−	0.497405i	$-0.165714\pi$
$223$	4.21351	+	4.67958i	0.282158	+	0.313368i	−0.585361	+	0.810773i	$0.699047\pi$
$224$	0.800472	−	0.260089i	0.0534838	−	0.0173779i
$225$	−23.1240	−	1.59243i	−1.54160	−	0.106162i
$226$	−6.29631	−	8.66613i	−0.418824	−	0.576462i
$227$	2.88982	+	0.614250i	0.191804	+	0.0407692i	0.302812	−	0.953050i	$-0.402075\pi$
$227$	2.88982	+	0.614250i	0.191804	+	0.0407692i	−0.111008	+	0.993820i	$0.535408\pi$
$228$	−0.268038	+	0.343447i	−0.0177512	+	0.0227453i
$229$	−2.00088	+	19.0371i	−0.132222	+	1.25801i	0.704231	+	0.709971i	$0.251292\pi$
$229$	−2.00088	+	19.0371i	−0.132222	+	1.25801i	−0.836453	+	0.548038i	$0.815375\pi$
$230$	−20.5566	−	35.6051i	−1.35546	−	2.34773i
$231$	−12.4272	−	0.352768i	−0.817648	−	0.0232104i
$232$	−9.36793	+	16.2257i	−0.615035	+	1.06527i
$233$	7.96945	+	5.79015i	0.522096	+	0.379325i	0.817393	−	0.576080i	$-0.195419\pi$
$233$	7.96945	+	5.79015i	0.522096	+	0.379325i	−0.295297	+	0.955406i	$0.595419\pi$
$234$	−5.69920	+	10.7460i	−0.372568	+	0.702489i
$235$	−3.71361	−	11.4293i	−0.242249	−	0.745566i
$236$	0.314403	−	0.0330451i	0.0204659	−	0.00215105i
$237$	−17.1205	−	16.5156i	−1.11210	−	1.07281i
$238$	0.989251	+	0.890725i	0.0641236	+	0.0577372i
$239$	−5.73578	+	1.21918i	−0.371017	+	0.0788621i	−0.389647	−	0.920964i	$-0.627403\pi$
$239$	−5.73578	+	1.21918i	−0.371017	+	0.0788621i	0.0186298	+	0.999826i	$0.494070\pi$
$240$	25.4732	−	1.79478i	1.64429	−	0.115853i
$241$	5.65553	+	3.26522i	0.364305	+	0.210332i	0.670968	−	0.741487i	$-0.265879\pi$
$241$	5.65553	+	3.26522i	0.364305	+	0.210332i	−0.306663	+	0.951818i	$0.599212\pi$
$242$	15.8204	−	0.189822i	1.01698	−	0.0122022i
$243$	−5.37025	−	14.6342i	−0.344502	−	0.938786i
$244$	−0.324239	+	0.446277i	−0.0207573	+	0.0285700i
$245$	6.14094	−	5.52933i	0.392330	−	0.353256i
$246$	−2.90200	+	4.64963i	−0.185024	+	0.296450i
$247$	−9.41766	−	4.19301i	−0.599231	−	0.266795i
$248$	−0.320763	−	0.142813i	−0.0203685	−	0.00906862i
$249$	11.8635	+	22.2835i	0.751816	+	1.41216i
$250$	10.3955	−	9.36019i	0.657472	−	0.591990i
$251$	14.9833	−	20.6228i	0.945739	−	1.30170i	−0.00765590	−	0.999971i	$-0.502437\pi$
$251$	14.9833	−	20.6228i	0.945739	−	1.30170i	0.953394	−	0.301727i	$-0.0975630\pi$
$252$	0.439854	+	0.0770790i	0.0277082	+	0.00485552i
$253$	−8.36355	−	25.2245i	−0.525812	−	1.58585i
$254$	3.82449	+	2.20807i	0.239970	+	0.138547i
$255$	1.47876	+	2.18986i	0.0926036	+	0.137134i
$256$	−1.61277	+	0.342805i	−0.100798	+	0.0214253i
$257$	2.76608	+	2.49059i	0.172543	+	0.155359i	0.750878	−	0.660441i	$-0.229631\pi$
$257$	2.76608	+	2.49059i	0.172543	+	0.155359i	−0.578335	+	0.815800i	$0.696297\pi$
$258$	−6.87708	+	1.97591i	−0.428149	+	0.123014i
$259$	−13.1905	+	1.38638i	−0.819619	+	0.0861454i
$260$	−0.213741	−	0.657828i	−0.0132557	−	0.0407967i
$261$	−17.1490	+	10.7411i	−1.06150	+	0.664859i
$262$	4.02543	+	2.92465i	0.248692	+	0.180685i
$263$	−10.8550	+	18.8014i	−0.669347	+	1.15934i	0.308740	+	0.951146i	$0.400093\pi$
$263$	−10.8550	+	18.8014i	−0.669347	+	1.15934i	−0.978087	+	0.208196i	$0.933241\pi$
$264$	15.8157	+	2.11757i	0.973387	+	0.130327i
$265$	4.61264	+	7.98933i	0.283352	+	0.490780i
$266$	−1.18988	+	11.3210i	−0.0729565	+	0.694135i
$267$	−3.51240	−	8.68030i	−0.214956	−	0.531226i
$268$	0.371110	+	0.0788819i	0.0226692	+	0.00481848i
$269$	15.9480	+	21.9505i	0.972365	+	1.33835i	0.940843	+	0.338843i	$0.110035\pi$
$269$	15.9480	+	21.9505i	0.972365	+	1.33835i	0.0315222	+	0.999503i	$0.489965\pi$
$270$	24.3739	+	10.8057i	1.48335	+	0.657614i
$271$	19.9213	−	6.47282i	1.21013	−	0.393196i	0.366654	−	0.930358i	$-0.380503\pi$
$271$	19.9213	−	6.47282i	1.21013	−	0.393196i	0.843479	+	0.537162i	$0.180503\pi$
$272$	−1.18262	−	1.31343i	−0.0717066	−	0.0796383i
$273$	0.742669	+	10.5406i	0.0449484	+	0.637947i
$274$	−12.5670	+	7.25555i	−0.759199	+	0.438324i
$275$	22.1147	−	12.9454i	1.33357	−	0.780639i
$276$	0.166253	+	0.939964i	0.0100073	+	0.0565792i
$277$	−8.66016	−	19.4510i	−0.520339	−	1.16870i	−0.962380	−	0.271706i	$-0.912412\pi$
$277$	−8.66016	−	19.4510i	−0.520339	−	1.16870i	0.442042	−	0.896995i	$-0.354254\pi$
$278$	−9.09352	−	2.95466i	−0.545393	−	0.177209i
$279$	−0.233784	−	0.298579i	−0.0139963	−	0.0178755i
$280$	17.3495	−	12.6052i	1.03683	−	0.753302i
$281$	2.49297	+	23.7190i	0.148718	+	1.41496i	0.773320	+	0.634016i	$0.218595\pi$
$281$	2.49297	+	23.7190i	0.148718	+	1.41496i	−0.624602	+	0.780944i	$0.714739\pi$
$282$	−0.288455	+	8.38735i	−0.0171773	+	0.499459i
$283$	−6.81879	−	32.0799i	−0.405335	−	1.90695i	−0.420971	−	0.907074i	$-0.638311\pi$
$283$	−6.81879	−	32.0799i	−0.405335	−	1.90695i	0.0156363	−	0.999878i	$-0.495023\pi$
$284$	−0.597100	−	0.0627578i	−0.0354314	−	0.00372399i
$285$	−7.71710	+	21.2375i	−0.457121	+	1.25800i
$286$	−1.48586	−	13.3652i	−0.0878607	−	0.790303i
$287$			4.76132i			0.281052i
$288$	−1.12187	−	0.320409i	−0.0661070	−	0.0188803i
$289$	−5.19678	+	15.9940i	−0.305693	+	0.940825i
$290$	7.19567	−	33.8530i	0.422544	−	1.98792i
$291$	8.55567	−	8.86903i	0.501542	−	0.519912i
$292$	0.141622	−	0.318087i	0.00828778	−	0.0186146i
$293$	−2.94291	+	3.26844i	−0.171927	+	0.190944i	−0.822950	−	0.568114i	$-0.807673\pi$
$293$	−2.94291	+	3.26844i	−0.171927	+	0.190944i	0.651023	+	0.759058i	$0.274340\pi$
$294$	−5.34936	+	2.16457i	−0.311981	+	0.126240i
$295$	14.9792	−	6.66916i	0.872122	−	0.388294i
$296$	17.0234			0.989464
$297$	14.0188	+	10.0237i	0.813452	+	0.581633i
$298$	19.8107			1.14760
$299$	−20.6346	+	9.18710i	−1.19333	+	0.531303i
$300$	−0.853233	+	0.345253i	−0.0492614	+	0.0199332i
$301$	−4.15922	+	4.61928i	−0.239734	+	0.266251i
$302$	−12.0258	+	27.0104i	−0.692008	+	1.55428i
$303$	7.89128	−	8.18030i	0.453342	−	0.469946i
$304$	3.14231	−	14.7834i	0.180224	−	0.847886i
$305$	−8.84127	+	27.2106i	−0.506250	+	1.55808i
$306$	−0.448307	−	1.79000i	−0.0256280	−	0.102328i
$307$			10.1101i			0.577013i	0.957478	+	0.288507i	$0.0931587\pi$
$307$			10.1101i			0.577013i	−0.957478	+	0.288507i	$0.906841\pi$
$308$	−0.449793	+	0.203503i	−0.0256293	+	0.0115956i
$309$	5.39603	−	14.8499i	0.306969	−	0.844780i
$310$	0.645040	+	0.0677965i	0.0366358	+	0.00385058i
$311$	−1.55212	−	7.30217i	−0.0880128	−	0.414068i	−0.999993	−	0.00383280i	$-0.998780\pi$
$311$	−1.55212	−	7.30217i	−0.0880128	−	0.414068i	0.911980	−	0.410235i	$-0.134553\pi$
$312$	0.466162	−	13.5545i	0.0263912	−	0.767372i
$313$	−3.10427	−	29.5352i	−0.175464	−	1.66943i	−0.628405	−	0.777887i	$-0.716292\pi$
$313$	−3.10427	−	29.5352i	−0.175464	−	1.66943i	0.452941	−	0.891541i	$-0.350375\pi$
$314$	8.90057	−	6.46664i	0.502288	−	0.364934i
$315$	22.9324	−	3.24766i	1.29210	−	0.182985i
$316$	−0.898406	−	0.291910i	−0.0505393	−	0.0164212i
$317$	−2.13218	−	4.78895i	−0.119755	−	0.268974i	0.843715	−	0.536792i	$-0.180364\pi$
$317$	−2.13218	−	4.78895i	−0.119755	−	0.268974i	−0.963470	+	0.267818i	$0.913697\pi$
$318$	−1.12206	−	6.34392i	−0.0629221	−	0.355750i
$319$	8.97626	−	20.4909i	0.502574	−	1.14727i
$320$	−23.8082	+	13.7456i	−1.33092	+	0.768405i
$321$	−0.199506	−	2.83157i	−0.0111354	−	0.158043i
$322$	16.6891	+	18.5351i	0.930048	+	1.03292i
$323$	1.48735	−	0.483270i	0.0827585	−	0.0268899i
$324$	−0.446197	−	0.429068i	−0.0247887	−	0.0238371i
$325$	−12.8020	−	17.6204i	−0.710128	−	0.977407i
$326$	12.5764	+	2.67320i	0.696544	+	0.148055i
$327$	−8.75750	−	21.6426i	−0.484291	−	1.19684i
$328$	0.638793	−	6.07771i	0.0352714	−	0.335585i
$329$	3.64522	+	6.31371i	0.200968	+	0.348086i
$330$	−28.9939	+	5.30777i	−1.59606	+	0.292183i
$331$	−7.63109	+	13.2174i	−0.419442	+	0.726496i	−0.995883	−	0.0906432i	$-0.971108\pi$
$331$	−7.63109	+	13.2174i	−0.419442	+	0.726496i	0.576441	+	0.817139i	$0.304441\pi$
$332$	0.811022	+	0.589242i	0.0445106	+	0.0323389i
$333$	16.2427	+	8.61437i	0.890092	+	0.472064i
$334$	1.16670	+	3.59074i	0.0638392	+	0.196477i
$335$	19.5703	−	2.05692i	1.06924	−	0.112382i
$336$	−14.8893	+	4.27796i	−0.812278	+	0.233382i
$337$	4.96306	+	4.46876i	0.270355	+	0.243429i	0.793145	−	0.609033i	$-0.208442\pi$
$337$	4.96306	+	4.46876i	0.270355	+	0.243429i	−0.522790	+	0.852462i	$0.675109\pi$
$338$	7.10961	−	1.51120i	0.386712	−	0.0821982i
$339$	7.21893	+	10.6903i	0.392078	+	0.580618i
$340$	0.0908722	+	0.0524651i	0.00492824	+	0.00284532i
$341$	0.399490	+	0.127158i	0.0216336	+	0.00688597i
$342$	10.1303	−	12.0987i	0.547782	−	0.654224i
$343$	−11.8510	+	16.3116i	−0.639896	+	0.880742i
$344$	5.92888	−	5.33839i	0.319664	−	0.287827i
$345$	23.2662	+	43.7017i	1.25261	+	2.35282i
$346$	21.9138	+	9.75666i	1.17809	+	0.524521i
$347$	21.5076	+	9.57579i	1.15459	+	0.514055i	0.892526	−	0.450996i	$-0.148931\pi$
$347$	21.5076	+	9.57579i	1.15459	+	0.514055i	0.262061	+	0.965051i	$0.415598\pi$
$348$	−0.425454	+	0.681670i	−0.0228067	+	0.0365414i
$349$	−25.3551	+	22.8298i	−1.35723	+	1.22205i	−0.405881	+	0.913926i	$0.633035\pi$
$349$	−25.3551	+	22.8298i	−1.35723	+	1.22205i	−0.951345	+	0.308126i	$0.900298\pi$
$350$	−14.1363	+	19.4569i	−0.755616	+	1.04002i
$351$	7.30378	−	12.6970i	0.389847	−	0.677713i
$352$	1.22433	−	0.405944i	0.0652568	−	0.0216369i
$353$	−5.17243	−	2.98630i	−0.275301	−	0.158945i	0.355993	−	0.934488i	$-0.384143\pi$
$353$	−5.17243	−	2.98630i	−0.275301	−	0.158945i	−0.631294	+	0.775544i	$0.717476\pi$
$354$	−11.4222	+	0.804784i	−0.607084	+	0.0427738i
$355$	−30.4595	+	6.47436i	−1.61662	+	0.343624i
$356$	−0.276337	−	0.248815i	−0.0146458	−	0.0131872i
$357$	−1.15370	−	1.11294i	−0.0610602	−	0.0589028i
$358$	22.9233	−	2.40933i	1.21153	−	0.127337i
$359$	1.78228	+	5.48528i	0.0940649	+	0.289502i	0.987009	−	0.160666i	$-0.0513641\pi$
$359$	1.78228	+	5.48528i	0.0940649	+	0.289502i	−0.892944	+	0.450168i	$0.851364\pi$
$360$	−29.7084	+	1.06888i	−1.56577	+	0.0563348i
$361$	−4.55194	−	3.30718i	−0.239576	−	0.174062i
$362$	9.48018	−	16.4201i	0.498267	−	0.863024i
$363$	−19.0478	−	0.426364i	−0.999750	−	0.0223783i
$364$	0.209805	+	0.363393i	0.0109968	+	0.0190470i
$365$	1.88771	−	17.9604i	0.0988074	−	0.940090i
$366$	12.2927	−	15.7511i	0.642551	−	0.823324i
$367$	−18.1772	−	3.86368i	−0.948842	−	0.201683i	−0.292602	−	0.956234i	$-0.594521\pi$
$367$	−18.1772	−	3.86368i	−0.948842	−	0.201683i	−0.656241	+	0.754552i	$0.727854\pi$
$368$	−19.4644	−	26.7904i	−1.01465	−	1.39655i
$369$	3.68501	−	5.47572i	0.191834	−	0.285055i
$370$	−29.9069	+	9.71733i	−1.55478	+	0.505180i
$371$	−3.74482	−	4.15904i	−0.194421	−	0.215927i
$372$	−0.0135383	−	0.00659420i	−0.000701926	−	0.000341893i
$373$	0.528176	−	0.304942i	0.0273479	−	0.0157893i	−0.486264	−	0.873812i	$-0.661641\pi$
$373$	0.528176	−	0.304942i	0.0273479	−	0.0157893i	0.513612	+	0.858023i	$0.328307\pi$
$374$	1.52421	+	1.35593i	0.0788149	+	0.0701137i
$375$	−12.8985	+	10.8347i	−0.666074	+	0.559503i
$376$	−3.80597	−	8.54836i	−0.196278	−	0.440848i
$377$	−18.0835	−	5.87567i	−0.931346	−	0.302613i
$378$	−15.8263	−	3.33777i	−0.814018	−	0.171677i
$379$	−3.40205	+	2.47174i	−0.174752	+	0.126965i	−0.671723	−	0.740802i	$-0.734445\pi$
$379$	−3.40205	+	2.47174i	−0.174752	+	0.126965i	0.496971	+	0.867767i	$0.334445\pi$
$380$	0.0937934	+	0.892385i	0.00481150	+	0.0457784i
$381$	−4.51139	−	2.81571i	−0.231125	−	0.144253i
$382$	−3.23442	−	15.2168i	−0.165487	−	0.778557i
$383$	−2.47026	−	0.259635i	−0.126224	−	0.0132667i	0.0412056	−	0.999151i	$-0.486880\pi$
$383$	−2.47026	−	0.259635i	−0.126224	−	0.0132667i	−0.167430	+	0.985884i	$0.553547\pi$
$384$	20.2315	−	3.57838i	1.03243	−	0.182609i
$385$	−18.9256	+	17.2474i	−0.964540	+	0.879010i
$386$		−	13.2985i		−	0.676875i
$387$	8.35837	−	2.09336i	0.424880	−	0.106411i
$388$	0.151219	−	0.465405i	0.00767700	−	0.0236274i
$389$	4.68563	−	22.0442i	0.237571	−	1.11768i	−0.684002	−	0.729480i	$-0.739762\pi$
$389$	4.68563	−	22.0442i	0.237571	−	1.11768i	0.921573	−	0.388204i	$-0.126904\pi$
$390$	6.91825	+	24.0788i	0.350319	+	1.21928i
$391$	1.39371	−	3.13033i	0.0704831	−	0.158308i
$392$	4.30537	−	4.78160i	0.217454	−	0.241507i
$393$	−4.72356	−	3.68644i	−0.238272	−	0.185956i
$394$	−29.2269	+	13.0126i	−1.47243	+	0.655567i
$395$	−48.9950			−2.46520
$396$	0.674782	+	0.114079i	0.0339091	+	0.00573269i
$397$	5.07245			0.254579			0.127289	−	0.991866i	$-0.459372\pi$
$397$	5.07245			0.254579			0.127289	+	0.991866i	$0.459372\pi$
$398$	3.16038	−	1.40709i	0.158416	−	0.0705312i
$399$	1.90061	−	13.5756i	0.0951495	−	0.679629i
$400$	21.3662	−	23.7296i	1.06831	−	1.18648i
$401$	−7.67997	+	17.2495i	−0.383519	+	0.861398i	0.613885	+	0.789395i	$0.289606\pi$
$401$	−7.67997	+	17.2495i	−0.383519	+	0.861398i	−0.997404	+	0.0720029i	$0.977061\pi$
$402$	−13.3356	−	3.31746i	−0.665119	−	0.165460i
$403$	0.0740857	−	0.348546i	0.00369047	−	0.0173623i
$404$	0.139476	−	0.429264i	0.00693921	−	0.0213567i
$405$	−28.8868	−	14.0135i	−1.43540	−	0.696338i
$406$			20.9958i			1.04200i
$407$	−20.2016	+	2.24588i	−1.00136	+	0.111324i
$408$	1.32335	+	1.57542i	0.0655157	+	0.0779949i
$409$	24.7201	+	2.59819i	1.22233	+	0.128472i	0.693627	−	0.720335i	$-0.256012\pi$
$409$	24.7201	+	2.59819i	1.22233	+	0.128472i	0.528703	+	0.848807i	$0.322678\pi$
$410$	2.34705	+	11.0420i	0.115913	+	0.545327i
$411$	15.4247	−	8.21192i	0.760844	−	0.405064i
$412$	−0.0655832	−	0.623982i	−0.00323105	−	0.0307414i
$413$	−8.04740	+	5.84678i	−0.395987	+	0.287701i
$414$	−4.84799	−	34.2327i	−0.238266	−	1.68244i
$415$	49.4500	+	16.0673i	2.42741	+	0.788712i
$416$	−0.445916	−	1.00154i	−0.0218628	−	0.0491047i
$417$	10.8218	+	3.93233i	0.529944	+	0.192567i
$418$	−1.71941	+	17.3603i	−0.0840990	+	0.849118i
$419$	−9.82661	+	5.67340i	−0.480062	+	0.277164i	−0.720442	−	0.693515i	$-0.756061\pi$
$419$	−9.82661	+	5.67340i	−0.480062	+	0.277164i	0.240381	+	0.970679i	$0.422728\pi$
$420$	0.762230	−	0.514717i	0.0371930	−	0.0251156i
$421$	21.5140	+	23.8937i	1.04853	+	1.16451i	0.986048	+	0.166460i	$0.0532336\pi$
$421$	21.5140	+	23.8937i	1.04853	+	1.16451i	0.0624778	+	0.998046i	$0.480100\pi$
$422$	−24.1966	+	7.86197i	−1.17787	+	0.382715i
$423$	0.694313	−	10.0823i	0.0337587	−	0.490216i
$424$	4.22218	+	5.81133i	0.205047	+	0.282223i
$425$	3.23190	+	0.686963i	0.156770	+	0.0333226i
$426$	21.5363	+	3.01512i	1.04344	+	0.146083i
$427$	1.81429	−	17.2618i	0.0877997	−	0.835359i
$428$	−0.0563608	−	0.0976198i	−0.00272430	−	0.00471863i
$429$	1.23504	+	16.1466i	0.0596283	+	0.779564i
$430$	−7.36865	+	12.7629i	−0.355348	+	0.615481i
$431$	9.91948	+	7.20693i	0.477805	+	0.347145i	0.800475	−	0.599366i	$-0.204581\pi$
$431$	9.91948	+	7.20693i	0.477805	+	0.347145i	−0.322670	+	0.946511i	$0.604581\pi$
$432$	20.4343	+	6.60370i	0.983144	+	0.317721i
$433$	6.07293	+	18.6905i	0.291846	+	0.898210i	0.984263	+	0.176712i	$0.0565462\pi$
$433$	6.07293	+	18.6905i	0.291846	+	0.898210i	−0.692416	+	0.721498i	$0.743454\pi$
$434$	−0.391316	+	0.0411289i	−0.0187837	+	0.00197425i
$435$	−10.0612	+	40.4443i	−0.482397	+	1.93915i
$436$	−0.688993	−	0.620372i	−0.0329968	−	0.0297104i
$437$	28.6617	−	6.09222i	1.37107	−	0.291431i
$438$	−5.52255	+	11.3381i	−0.263878	+	0.541756i
$439$	−14.3191	−	8.26712i	−0.683412	−	0.394568i	0.117727	−	0.993046i	$-0.462439\pi$
$439$	−14.3191	−	8.26712i	−0.683412	−	0.394568i	−0.801140	+	0.598478i	$0.795773\pi$
$440$	26.4721	−	19.4768i	1.26201	−	0.928520i
$441$	6.52756	−	2.38365i	0.310836	−	0.113507i
$442$	1.01918	−	1.40278i	0.0484775	−	0.0667236i
$443$	−8.11908	+	7.31045i	−0.385749	+	0.347330i	−0.839076	−	0.544014i	$-0.816904\pi$
$443$	−8.11908	+	7.31045i	−0.385749	+	0.347330i	0.453327	+	0.891344i	$0.350237\pi$
$444$	0.729669	+	0.0250946i	0.0346286	+	0.00119094i
$445$	−17.6190	−	7.84449i	−0.835221	−	0.371864i
$446$	−8.27410	−	3.68387i	−0.391790	−	0.174436i
$447$	−23.8422	−	0.819976i	−1.12770	−	0.0387835i
$448$	12.3939	−	11.1595i	0.585558	−	0.527239i
$449$	19.5758	−	26.9438i	0.923840	−	1.27156i	−0.0383749	−	0.999263i	$-0.512218\pi$
$449$	19.5758	−	26.9438i	0.923840	−	1.27156i	0.962214	−	0.272293i	$-0.0877819\pi$
$450$	31.3160	−	11.4356i	1.47625	−	0.539078i
$451$	0.0437732	+	7.29668i	0.00206120	+	0.343587i
$452$	0.443615	+	0.256121i	0.0208659	+	0.0120469i
$453$	15.5911	−	32.0094i	0.732533	−	1.50393i
$454$	−4.15650	+	0.883492i	−0.195074	+	0.0414643i
$455$	16.1735	+	14.5627i	0.758227	+	0.682710i
$456$	−4.24742	+	17.0739i	−0.198904	+	0.799559i
$457$	31.4646	−	3.30706i	1.47185	−	0.154698i	0.665616	−	0.746295i	$-0.268169\pi$
$457$	31.4646	−	3.30706i	1.47185	−	0.154698i	0.806234	+	0.591597i	$0.201502\pi$
$458$	−8.50799	−	26.1849i	−0.397552	−	1.22354i
$459$	0.465449	+	2.17282i	0.0217253	+	0.101419i
$460$	1.59055	+	1.15560i	0.0741598	+	0.0538803i
$461$	−12.6435	+	21.8992i	−0.588868	+	1.01995i	0.405513	+	0.914089i	$0.367093\pi$
$461$	−12.6435	+	21.8992i	−0.588868	+	1.01995i	−0.994381	+	0.105860i	$0.966241\pi$
$462$	16.5354	−	6.80662i	0.769296	−	0.316672i
$463$	−0.467506	−	0.809744i	−0.0217269	−	0.0376320i	0.854958	−	0.518698i	$-0.173583\pi$
$463$	−0.467506	−	0.809744i	−0.0217269	−	0.0376320i	−0.876684	+	0.481066i	$0.840250\pi$
$464$	2.91385	−	27.7234i	0.135272	−	1.28703i
$465$	−0.773501	−	0.108292i	−0.0358703	−	0.00502191i
$466$	−13.8590	−	2.94583i	−0.642007	−	0.136463i
$467$	−7.72052	−	10.6264i	−0.357263	−	0.491731i	0.592120	−	0.805850i	$-0.298291\pi$
$467$	−7.72052	−	10.6264i	−0.357263	−	0.491731i	−0.949384	+	0.314119i	$0.898291\pi$
$468$	0.0399620	−	0.580296i	0.00184724	−	0.0268242i
$469$	−11.3535	+	3.68898i	−0.524257	+	0.170341i
$470$	11.5660	+	12.8453i	0.533498	+	0.592510i
$471$	−10.9795	+	7.41421i	−0.505909	+	0.341629i
$472$	11.0567	−	6.38361i	0.508928	−	0.293830i
$473$	−6.33150	+	7.11725i	−0.291123	+	0.327252i
$474$	32.1579	+	11.6853i	1.47706	+	0.536723i
$475$	11.4922	+	25.8120i	0.527300	+	1.18434i
$476$	−0.0605407	−	0.0196709i	−0.00277488	−	0.000901612i
$477$	1.08783	+	7.68137i	0.0498081	+	0.351706i
$478$	6.82344	−	4.95752i	0.312097	−	0.226752i
$479$	−3.00353	−	28.5767i	−0.137235	−	1.30570i	−0.818856	−	0.573999i	$-0.805391\pi$
$479$	−3.00353	−	28.5767i	−0.137235	−	1.30570i	0.681621	−	0.731705i	$-0.261275\pi$
$480$	−2.12116	+	1.12928i	−0.0968172	+	0.0515443i
$481$	3.59192	+	16.8986i	0.163777	+	0.770512i
$482$	−9.34145	−	0.981826i	−0.425492	−	0.0447210i
$483$	−19.3182	−	22.9978i	−0.879008	−	1.04644i
$484$	−0.687433	+	0.316001i	−0.0312470	+	0.0143637i
$485$		−	25.3811i		−	1.15250i
$486$	15.6177	+	16.0873i	0.708433	+	0.729735i
$487$	2.91324	−	8.96603i	0.132011	−	0.406289i	−0.863102	−	0.505030i	$-0.831481\pi$
$487$	2.91324	−	8.96603i	0.132011	−	0.406289i	0.995113	+	0.0987406i	$0.0314814\pi$
$488$	−4.63180	+	21.7909i	−0.209672	+	0.986428i
$489$	−15.0251	−	3.73775i	−0.679459	−	0.169027i
$490$	−4.83428	+	10.8580i	−0.218391	+	0.490513i
$491$	2.69576	−	2.99394i	0.121658	−	0.135115i	−0.679239	−	0.733917i	$-0.737690\pi$
$491$	2.69576	−	2.99394i	0.121658	−	0.135115i	0.800897	+	0.598803i	$0.204357\pi$
$492$	0.0363397	−	0.259566i	0.00163832	−	0.0117021i
$493$	2.63512	−	1.17323i	0.118680	−	0.0528397i
$494$	14.8276			0.667124
$495$	35.1139	−	5.18784i	1.57825	−	0.233176i
$496$	0.522411			0.0234570
$497$	17.2579	−	7.68372i	0.774124	−	0.344662i
$498$	−28.6246	−	22.3396i	−1.28270	−	1.00106i
$499$	−15.5170	+	17.2334i	−0.694636	+	0.771471i	−0.982513	−	0.186196i	$-0.940384\pi$
$499$	−15.5170	+	17.2334i	−0.694636	+	0.771471i	0.287877	+	0.957667i	$0.407051\pi$
$500$	−0.272079	+	0.611099i	−0.0121677	+	0.0273292i
$501$	−1.25551	−	4.36976i	−0.0560919	−	0.195226i
$502$	−7.62299	+	35.8634i	−0.340231	+	1.60066i
$503$	−10.5281	+	32.4020i	−0.469423	+	1.44473i	0.383911	+	0.923370i	$0.374577\pi$
$503$	−10.5281	+	32.4020i	−0.469423	+	1.44473i	−0.853334	+	0.521365i	$0.825423\pi$
$504$	17.4940	−	4.38140i	0.779246	−	0.195163i
$505$		−	23.4101i		−	1.04174i
$506$	25.7463	+	28.2515i	1.14456	+	1.25593i
$507$	−8.61898	+	1.52446i	−0.382782	+	0.0677035i
$508$	−0.210022	−	0.0220742i	−0.00931823	−	0.000979385i
$509$	−6.71643	−	31.5983i	−0.297700	−	1.40057i	−0.831765	−	0.555127i	$-0.812670\pi$
$509$	−6.71643	−	31.5983i	−0.297700	−	1.40057i	0.534065	−	0.845443i	$-0.320664\pi$
$510$	−3.22416	−	2.01231i	−0.142768	−	0.0891067i
$511$	1.14519	+	10.8957i	0.0506601	+	0.481998i
$512$	−17.2745	+	12.5506i	−0.763431	+	0.554665i
$513$	−12.6926	+	14.1415i	−0.560390	+	0.624364i
$514$	−5.09161	−	1.65436i	−0.224581	−	0.0729709i
$515$	−13.2360	−	29.7285i	−0.583247	−	1.30999i
$516$	0.261998	−	0.220078i	0.0115338	−	0.00968841i
$517$	5.64432	+	9.64220i	0.248237	+	0.424063i
$518$	16.5210	−	9.53838i	0.725890	−	0.419093i
$519$	−25.9695	−	12.6492i	−1.13993	−	0.555238i
$520$	−18.6913	−	20.7588i	−0.819669	−	0.910335i
$521$	−13.9354	+	4.52790i	−0.610523	+	0.198371i	−0.597928	−	0.801550i	$-0.704009\pi$
$521$	−13.9354	+	4.52790i	−0.610523	+	0.198371i	−0.0125949	+	0.999921i	$0.504009\pi$
$522$	16.2496	−	24.1461i	0.711228	−	1.05685i
$523$	8.72743	+	12.0123i	0.381624	+	0.525260i	0.956014	−	0.293322i	$-0.0947607\pi$
$523$	8.72743	+	12.0123i	0.381624	+	0.525260i	−0.574390	+	0.818582i	$0.694761\pi$
$524$	−0.232738	−	0.0494700i	−0.0101672	−	0.00216111i
$525$	17.8184	−	22.8313i	0.777658	−	0.996441i
$526$	3.26401	−	31.0549i	0.142317	−	1.35406i
$527$	0.0270284	+	0.0468146i	0.00117738	+	0.00203927i
$528$	−22.7784	+	6.69281i	−0.991303	+	0.291267i
$529$	20.6010	−	35.6820i	0.895697	−	1.55139i
$530$	−10.7348	−	7.79930i	−0.466290	−	0.338780i
$531$	13.7800	−	0.495788i	0.597999	−	0.0215154i
$532$	−0.168213	−	0.517707i	−0.00729297	−	0.0224455i
$533$	6.16796	−	0.648279i	0.267164	−	0.0280801i
$534$	9.69336	+	9.35088i	0.419473	+	0.404652i
$535$	−4.34476	−	3.91204i	−0.187840	−	0.169132i
$536$	14.9874	−	3.18567i	0.647358	−	0.137600i
$537$	−27.6879	+	1.95083i	−1.19482	+	0.0841846i
$538$	−33.7967	−	19.5126i	−1.45708	−	0.841246i
$539$	−4.47834	+	6.24232i	−0.192896	+	0.268876i
$540$	−1.27496	+	0.00202113i	−0.0548656	+	8.69757e-5i
$541$	−9.38031	+	12.9109i	−0.403291	+	0.555082i	−0.961566	−	0.274574i	$-0.911463\pi$
$541$	−9.38031	+	12.9109i	−0.403291	+	0.555082i	0.558275	+	0.829656i	$0.311463\pi$
$542$	−22.3894	+	20.1595i	−0.961706	+	0.865924i
$543$	−12.0890	+	19.3693i	−0.518791	+	0.831216i
$544$	0.151937	+	0.0676469i	0.00651427	+	0.00290034i
$545$	−43.9296	−	19.5587i	−1.88174	−	0.837803i
$546$	−7.14232	−	13.4156i	−0.305663	−	0.574137i
$547$	−10.4204	+	9.38255i	−0.445543	+	0.401169i	−0.861130	−	0.508385i	$-0.830243\pi$
$547$	−10.4204	+	9.38255i	−0.445543	+	0.401169i	0.415587	+	0.909553i	$0.363576\pi$
$548$	0.407875	−	0.561392i	0.0174236	−	0.0239815i
$549$	−15.4463	+	18.4477i	−0.659230	+	0.787328i
$550$	−21.4849	+	29.9475i	−0.916117	+	1.27697i
$551$	21.3618	+	12.3332i	0.910044	+	0.525414i
$552$	21.5738	+	31.9480i	0.918240	+	1.35980i
$553$	29.0734	−	6.17975i	1.23633	−	0.262790i
$554$	22.7585	+	20.4918i	0.966916	+	0.870615i
$555$	36.3952	−	10.4570i	1.54489	−	0.443873i
$556$	0.454724	−	0.0477934i	0.0192846	−	0.00202689i
$557$	6.60761	+	20.3361i	0.279974	+	0.861670i	0.987860	+	0.155344i	$0.0496487\pi$
$557$	6.60761	+	20.3361i	0.279974	+	0.861670i	−0.707887	+	0.706326i	$0.750351\pi$
$558$	0.481861	+	0.255557i	0.0203988	+	0.0108186i
$559$	6.55026	+	4.75904i	0.277047	+	0.201286i
$560$	−15.9536	+	27.6324i	−0.674162	+	1.16768i
$561$	−1.77826	−	1.69496i	−0.0750783	−	0.0715611i
$562$	−17.1518	−	29.7078i	−0.723506	−	1.25315i
$563$	−0.503255	+	4.78815i	−0.0212097	+	0.201796i	−0.999995	−	0.00309091i	$-0.999016\pi$
$563$	−0.503255	+	4.78815i	−0.0212097	+	0.201796i	0.978786	+	0.204887i	$0.0656828\pi$
$564$	−0.150533	−	0.372017i	−0.00633859	−	0.0156647i
$565$	25.9875	+	5.52382i	1.09330	+	0.232389i
$566$	27.7271	+	38.1631i	1.16546	+	1.60411i
$567$	18.9088	+	4.67208i	0.794097	+	0.196209i
$568$	−23.0602	+	7.49271i	−0.967585	+	0.314387i
$569$	−10.5545	−	11.7220i	−0.442469	−	0.491411i	0.480116	−	0.877205i	$-0.340594\pi$
$569$	−10.5545	−	11.7220i	−0.442469	−	0.491411i	−0.922585	+	0.385794i	$0.873928\pi$
$570$	−2.28425	−	32.4202i	−0.0956769	−	1.35793i
$571$	8.55788	−	4.94089i	0.358136	−	0.206770i	−0.310127	−	0.950695i	$-0.600371\pi$
$571$	8.55788	−	4.94089i	0.358136	−	0.206770i	0.668263	+	0.743925i	$0.267038\pi$
$572$	0.324865	+	0.554968i	0.0135833	+	0.0232044i
$573$	3.26280	+	18.4473i	0.136306	+	0.770646i
$574$	−2.78546	−	6.25626i	−0.116263	−	0.261131i
$575$	58.8776	+	19.1305i	2.45536	+	0.797796i
$576$	−22.8904	+	3.24171i	−0.953768	+	0.135071i
$577$	29.2977	−	21.2860i	1.21968	−	0.886147i	0.223604	−	0.974680i	$-0.428218\pi$
$577$	29.2977	−	21.2860i	1.21968	−	0.886147i	0.996073	+	0.0885327i	$0.0282178\pi$
$578$	−2.52839	−	24.0560i	−0.105167	−	1.00060i
$579$	−0.550430	+	16.0047i	−0.0228751	+	0.665134i
$580$	0.344096	+	1.61884i	0.0142878	+	0.0672188i
$581$	−31.3700	−	3.29712i	−1.30145	−	0.136788i
$582$	−6.05339	+	16.6589i	−0.250921	+	0.690535i
$583$	−5.77714	−	6.33927i	−0.239265	−	0.262546i
$584$		−	14.0618i		−	0.581880i
$585$	−7.32949	−	29.2652i	−0.303037	−	1.20997i
$586$	1.95482	−	6.01631i	0.0807527	−	0.248531i
$587$	9.81362	−	46.1695i	0.405052	−	1.90562i	−0.0186701	−	0.999826i	$-0.505943\pi$
$587$	9.81362	−	46.1695i	0.405052	−	1.90562i	0.423722	−	0.905792i	$-0.360723\pi$
$588$	0.191589	−	0.198606i	0.00790099	−	0.00819037i
$589$	−0.188019	+	0.422297i	−0.00774717	+	0.0174004i
$590$	−15.7807	+	17.5262i	−0.649681	+	0.721544i
$591$	35.7132	−	14.4510i	1.46904	−	0.594436i
$592$	−23.1385	+	10.3019i	−0.950986	+	0.423406i
$593$	34.2927			1.40823			0.704117	−	0.710084i	$-0.251343\pi$
$593$	34.2927			1.40823			0.704117	+	0.710084i	$0.251343\pi$
$594$	−24.2844	−	4.96961i	−0.996400	−	0.203906i
$595$	−3.30161			−0.135353
$596$	−0.865443	+	0.385320i	−0.0354499	+	0.0157833i
$597$	−3.86176	+	1.56263i	−0.158052	+	0.0639541i
$598$	21.7387	−	24.1432i	0.888961	−	0.987291i
$599$	−14.9487	+	33.5752i	−0.610786	+	1.37185i	0.297993	+	0.954568i	$0.403683\pi$
$599$	−14.9487	+	33.5752i	−0.610786	+	1.37185i	−0.908778	+	0.417279i	$0.862984\pi$
$600$	−25.8079	+	26.7531i	−1.05360	+	1.09219i
$601$	0.566213	−	2.66383i	0.0230963	−	0.108660i	−0.965089	−	0.261921i	$-0.915644\pi$
$601$	0.566213	−	2.66383i	0.0230963	−	0.108660i	0.988186	+	0.153261i	$0.0489775\pi$
$602$	2.76274	−	8.50285i	0.112601	−	0.346550i
$603$	15.9121	+	4.54453i	0.647991	+	0.185068i
$604$		−	1.41387i		−	0.0575295i
$605$	−28.8448	+	26.6055i	−1.17271	+	1.08167i
$606$	−5.58331	+	15.3653i	−0.226806	+	0.624172i
$607$	−11.7417	−	1.23410i	−0.476582	−	0.0500908i	−0.136807	−	0.990598i	$-0.543684\pi$
$607$	−11.7417	−	1.23410i	−0.476582	−	0.0500908i	−0.339775	+	0.940507i	$0.610351\pi$
$608$	0.295700	+	1.39116i	0.0119922	+	0.0564189i
$609$	0.869027	−	25.2685i	0.0352148	−	1.02393i
$610$	−4.30154	−	40.9264i	−0.174164	−	1.65706i
$611$	7.68266	−	5.58178i	0.310807	−	0.225815i
$612$	0.0544002	+	0.0694776i	0.00219900	+	0.00280846i
$613$	−8.06638	−	2.62093i	−0.325798	−	0.105858i	0.141551	−	0.989931i	$-0.454791\pi$
$613$	−8.06638	−	2.62093i	−0.325798	−	0.105858i	−0.467349	+	0.884073i	$0.654791\pi$
$614$	−5.91460	−	13.2844i	−0.238694	−	0.536115i
$615$	−2.36765	−	13.3862i	−0.0954728	−	0.539785i
$616$	−13.2518	+	14.8964i	−0.533931	+	0.600192i
$617$	7.87941	−	4.54918i	0.317213	−	0.183143i	−0.332937	−	0.942949i	$-0.608040\pi$
$617$	7.87941	−	4.54918i	0.317213	−	0.183143i	0.650150	+	0.759806i	$0.274706\pi$
$618$	1.59722	+	22.6691i	0.0642496	+	0.911887i
$619$	−14.5118	−	16.1170i	−0.583280	−	0.647798i	0.377205	−	0.926130i	$-0.376885\pi$
$619$	−14.5118	−	16.1170i	−0.583280	−	0.647798i	−0.960485	+	0.278331i	$0.910219\pi$
$620$	−0.0294976	+	0.00958435i	−0.00118465	+	0.000384917i
$621$	4.41766	+	41.3998i	0.177274	+	1.66132i
$622$	6.31136	+	8.68685i	0.253063	+	0.348311i
$623$	11.4445	+	2.43260i	0.458513	+	0.0974600i
$624$	7.56905	+	18.7056i	0.303005	+	0.748823i
$625$	0.411453	−	3.91472i	0.0164581	−	0.156589i
$626$	21.3576	+	36.9925i	0.853622	+	1.47852i
$627$	2.78786	−	20.8219i	0.111336	−	0.831548i
$628$	−0.263050	+	0.455616i	−0.0104968	+	0.0181810i
$629$	−2.12031	−	1.54050i	−0.0845424	−	0.0614237i
$630$	−28.2327	+	17.6833i	−1.12482	+	0.704518i
$631$	−6.35103	−	19.5465i	−0.252831	−	0.778133i	−0.994249	−	0.107090i	$-0.965847\pi$
$631$	−6.35103	−	19.5465i	−0.252831	−	0.778133i	0.741419	−	0.671043i	$-0.234153\pi$
$632$	−37.9406	+	3.98772i	−1.50920	+	0.158623i
$633$	29.4461	−	8.46038i	1.17038	−	0.336270i
$634$	5.60326	+	5.04520i	0.222534	+	0.200370i
$635$	−10.7137	+	2.27727i	−0.425161	+	0.0903708i
$636$	0.172408	+	0.255314i	0.00683641	+	0.0101238i
$637$	5.65499	+	3.26491i	0.224059	+	0.129361i
$638$	0.193025	+	32.1759i	0.00764194	+	1.27386i
$639$	−25.7942	−	4.52010i	−1.02040	−	0.178813i
$640$	24.8728	−	34.2345i	0.983186	−	1.35324i
$641$	7.35399	−	6.62156i	0.290465	−	0.261536i	−0.510996	−	0.859583i	$-0.670723\pi$
$641$	7.35399	−	6.62156i	0.290465	−	0.261536i	0.801461	+	0.598047i	$0.204056\pi$
$642$	1.91867	+	3.60390i	0.0757240	+	0.142235i
$643$	−37.0199	−	16.4823i	−1.45992	−	0.649999i	−0.485401	−	0.874292i	$-0.661326\pi$
$643$	−37.0199	−	16.4823i	−1.45992	−	0.649999i	−0.974522	+	0.224292i	$0.927993\pi$
$644$	−1.08958	−	0.485114i	−0.0429356	−	0.0191162i
$645$	9.39645	−	15.0552i	0.369985	−	0.592796i
$646$	−1.67162	+	1.50514i	−0.0657691	+	0.0592188i
$647$	−17.5380	+	24.1390i	−0.689490	+	0.949001i	−0.999999	−	0.00156921i	$-0.999501\pi$
$647$	−17.5380	+	24.1390i	−0.689490	+	0.949001i	0.310509	+	0.950570i	$0.399501\pi$
$648$	−23.5099	−	8.50066i	−0.923555	−	0.333937i
$649$	−12.2788	+	9.03412i	−0.481986	+	0.354620i
$650$	27.1298	+	15.6634i	1.06412	+	0.614370i
$651$	0.472651	−	0.0333020i	0.0185247	−	0.00130521i
$652$	−0.601403	+	0.127832i	−0.0235527	+	0.00500629i
$653$	−25.7409	−	23.1772i	−1.00732	−	0.906995i	−0.0116480	−	0.999932i	$-0.503708\pi$
$653$	−25.7409	−	23.1772i	−1.00732	−	0.906995i	−0.995672	+	0.0929372i	$0.970374\pi$
$654$	24.1685	+	23.3146i	0.945063	+	0.911673i
$655$	−12.2733	+	1.28998i	−0.479559	+	0.0504037i
$656$	2.80974	+	8.64750i	0.109702	+	0.337628i
$657$	7.11569	−	13.4169i	0.277610	−	0.523442i
$658$	−8.48338	−	6.16354i	−0.330717	−	0.240280i
$659$	−1.59381	+	2.76056i	−0.0620860	+	0.107536i	−0.895398	−	0.445267i	$-0.853109\pi$
$659$	−1.59381	+	2.76056i	−0.0620860	+	0.107536i	0.833312	+	0.552803i	$0.186442\pi$
$660$	1.16338	−	0.795806i	0.0452844	−	0.0309767i
$661$	4.84495	+	8.39171i	0.188447	+	0.326400i	0.944733	−	0.327842i	$-0.106321\pi$
$661$	4.84495	+	8.39171i	0.188447	+	0.326400i	−0.756286	+	0.654241i	$0.772988\pi$
$662$	2.29461	−	21.8317i	0.0891824	−	0.848514i
$663$	−1.28465	+	1.64607i	−0.0498916	+	0.0639280i
$664$	39.6007	+	8.41739i	1.53681	+	0.326658i
$665$	−16.5952	−	22.8413i	−0.643533	−	0.885748i
$666$	−26.3820	−	1.81680i	−1.02228	−	0.0703994i
$667$	51.4003	−	16.7010i	1.99023	−	0.646664i
$668$	−0.120808	−	0.134171i	−0.00467421	−	0.00519124i
$669$	9.80542	+	4.77601i	0.379099	+	0.184651i
$670$	−24.5116	+	14.1518i	−0.946966	+	0.546731i
$671$	2.62169	−	26.4703i	0.101209	−	1.02187i
$672$	1.11625	−	0.937652i	0.0430603	−	0.0361707i
$673$	1.85510	+	4.16661i	0.0715087	+	0.160611i	0.945763	−	0.324857i	$-0.105316\pi$
$673$	1.85510	+	4.16661i	0.0715087	+	0.160611i	−0.874255	+	0.485468i	$0.838649\pi$
$674$	−9.13566	−	2.96836i	−0.351892	−	0.114337i
$675$	−38.1621	+	12.4666i	−1.46886	+	0.479838i
$676$	−0.281195	+	0.204300i	−0.0108152	+	0.00785769i
$677$	4.96186	+	47.2089i	0.190700	+	1.81439i	0.502872	+	0.864361i	$0.332277\pi$
$677$	4.96186	+	47.2089i	0.190700	+	1.81439i	−0.312172	+	0.950025i	$0.601057\pi$
$678$	−15.7395	−	9.82359i	−0.604473	−	0.377273i
$679$	3.20132	+	15.0610i	0.122855	+	0.577990i
$680$	4.21443	+	0.442954i	0.161616	+	0.0169865i
$681$	5.03893	−	0.891245i	0.193092	−	0.0341526i
$682$	−0.599310	+	0.0666273i	−0.0229488	+	0.00255129i
$683$			19.9649i			0.763936i	0.924175	+	0.381968i	$0.124754\pi$
$683$			19.9649i			0.763936i	−0.924175	+	0.381968i	$0.875246\pi$
$684$	−0.207225	+	0.725574i	−0.00792346	+	0.0277430i
$685$	11.1218	−	34.2294i	0.424943	−	1.30784i
$686$	6.02940	−	28.3661i	0.230204	−	1.08302i
$687$	9.15557	+	31.8657i	0.349307	+	1.21575i
$688$	−4.82805	+	10.8440i	−0.184068	+	0.413423i
$689$	−4.87787	+	5.41743i	−0.185832	+	0.206388i
$690$	−56.1376	−	43.8118i	−2.13712	−	1.66789i
$691$	4.78568	−	2.13072i	0.182056	−	0.0810565i	−0.313685	−	0.949527i	$-0.601563\pi$
$691$	4.78568	−	2.13072i	0.182056	−	0.0810565i	0.495740	+	0.868471i	$0.334897\pi$
$692$	−1.14709			−0.0436057
$693$	−20.1821	+	7.50737i	−0.766655	+	0.285181i
$694$	−33.8625			−1.28540
$695$	21.6645	−	9.64566i	0.821782	−	0.365881i
$696$	−4.49939	+	32.1380i	−0.170549	+	1.21819i
$697$	−0.629554	+	0.699190i	−0.0238460	+	0.0264837i
$698$	19.9601	−	44.8311i	0.755500	−	1.69688i
$699$	16.5574	+	4.11894i	0.626259	+	0.155793i
$700$	0.239113	−	1.12494i	0.00903763	−	0.0425187i
$701$	10.9266	−	33.6287i	0.412694	−	1.27014i	−0.501604	−	0.865097i	$-0.667257\pi$
$701$	10.9266	−	33.6287i	0.412694	−	1.27014i	0.914298	−	0.405043i	$-0.132743\pi$
$702$	−2.16902	+	20.9564i	−0.0818643	+	0.790946i
$703$		−	22.4119i		−	0.845282i
$704$	18.8910	−	17.2158i	0.711981	−	0.648846i
$705$	−13.3880	−	15.9381i	−0.504221	−	0.600263i
$706$	8.54349	+	0.897957i	0.321539	+	0.0337951i
$707$	2.95272	+	13.8915i	0.111049	+	0.522442i
$708$	0.483333	−	0.257320i	0.0181648	−	0.00967069i
$709$	−0.588413	−	5.59838i	−0.0220983	−	0.210251i	−0.999999	−	0.00118287i	$-0.999623\pi$
$709$	−0.588413	−	5.59838i	−0.0220983	−	0.210251i	0.977901	−	0.209069i	$-0.0670432\pi$
$710$	36.2354	−	26.3266i	1.35989	−	0.988018i
$711$	−38.2185	−	15.3943i	−1.43331	−	0.577332i
$712$	−14.2822	−	4.64058i	−0.535249	−	0.173913i
$713$	0.411958	+	0.925273i	0.0154279	+	0.0346517i
$714$	2.16702	+	0.787434i	0.0810987	+	0.0294690i
$715$	24.9197	+	22.1685i	0.931943	+	0.829056i
$716$	−0.954554	+	0.551112i	−0.0356734	+	0.0205960i
$717$	−8.41721	+	5.68396i	−0.314347	+	0.212271i
$718$	−5.55087	−	6.16486i	−0.207156	−	0.230071i
$719$	7.99933	−	2.59914i	0.298325	−	0.0969316i	−0.156030	−	0.987752i	$-0.549870\pi$
$719$	7.99933	−	2.59914i	0.298325	−	0.0969316i	0.454355	+	0.890821i	$0.349870\pi$
$720$	39.7333	−	19.4313i	1.48077	−	0.724160i
$721$	11.6038	+	15.9713i	0.432150	+	0.594803i
$722$	7.91591	+	1.68258i	0.294599	+	0.0626191i
$723$	11.2018	+	1.56828i	0.416600	+	0.0583249i
$724$	−0.0947739	+	0.901714i	−0.00352225	+	0.0335119i
$725$	26.0570	+	45.1320i	0.967732	+	1.67616i
$726$	25.2778	−	10.5831i	0.938146	−	0.392776i
$727$	−12.2768	+	21.2640i	−0.455321	+	0.788638i	−0.998707	−	0.0508446i	$-0.983809\pi$
$727$	−12.2768	+	21.2640i	−0.455321	+	0.788638i	0.543386	+	0.839483i	$0.317142\pi$
$728$	13.7097	+	9.96067i	0.508115	+	0.369167i
$729$	−18.1301	−	20.0075i	−0.671483	−	0.741020i
$730$	8.02677	+	24.7039i	0.297084	+	0.914331i
$731$	−1.22155	+	0.128390i	−0.0451806	+	0.00474867i
$732$	−0.230654	+	0.927191i	−0.00852523	+	0.0342700i
$733$	11.9656	+	10.7739i	0.441961	+	0.397943i	0.859844	−	0.510558i	$-0.170561\pi$
$733$	11.9656	+	10.7739i	0.441961	+	0.397943i	−0.417883	+	0.908501i	$0.637228\pi$
$734$	26.1447	−	5.55724i	0.965020	−	0.205121i
$735$	6.26748	−	12.8675i	0.231180	−	0.474625i
$736$	2.69870	+	1.55810i	0.0994754	+	0.0574322i
$737$	−17.3652	+	5.75771i	−0.639657	+	0.212088i
$738$	−1.63861	+	9.35077i	−0.0603179	+	0.344207i
$739$	−6.18559	+	8.51373i	−0.227540	+	0.313183i	−0.907488	−	0.420078i	$-0.862003\pi$
$739$	−6.18559	+	8.51373i	−0.227540	+	0.313183i	0.679947	+	0.733261i	$0.262003\pi$
$740$	1.11750	−	1.00620i	0.0410800	−	0.0369886i
$741$	−17.8450	−	0.613721i	−0.655553	−	0.0225456i
$742$	7.35372	+	3.27409i	0.269964	+	0.120196i
$743$	17.1724	+	7.64563i	0.629993	+	0.280491i	0.696790	−	0.717276i	$-0.254611\pi$
$743$	17.1724	+	7.64563i	0.629993	+	0.280491i	−0.0667965	+	0.997767i	$0.521278\pi$
$744$	−0.607796	−	0.0209032i	−0.0222829	−	0.000766347i
$745$	−36.5146	+	32.8779i	−1.33779	+	1.20455i
$746$	−0.515613	+	0.709680i	−0.0188779	+	0.0259832i
$747$	33.5251	+	28.0706i	1.22662	+	1.02705i
$748$	−0.0929589	−	0.0295888i	−0.00339891	−	0.00108187i
$749$	3.07159	+	1.77338i	0.112234	+	0.0647981i
$750$	10.6098	−	21.7824i	0.387413	−	0.795382i
$751$	13.2201	−	2.81002i	0.482409	−	0.102539i	0.0397133	−	0.999211i	$-0.487356\pi$
$751$	13.2201	−	2.81002i	0.482409	−	0.102539i	0.442696	+	0.896672i	$0.354022\pi$
$752$	10.3463	+	9.31584i	0.377290	+	0.339714i
$753$	10.6587	−	42.8461i	0.388424	−	1.56140i
$754$	27.1986	−	2.85869i	0.990515	−	0.104107i
$755$	−22.6609	−	69.7430i	−0.824714	−	2.53821i
$756$	0.756301	−	0.162010i	0.0275064	−	0.00589226i
$757$	24.2204	+	17.5972i	0.880307	+	0.639581i	0.933333	−	0.359013i	$-0.116887\pi$
$757$	24.2204	+	17.5972i	0.880307	+	0.639581i	−0.0530256	+	0.998593i	$0.516887\pi$
$758$	3.02420	−	5.23807i	0.109844	−	0.190255i
$759$	−29.8164	−	35.0664i	−1.08227	−	1.27283i
$760$	18.1189	+	31.3828i	0.657241	+	1.13838i
$761$	0.142360	−	1.35447i	0.00516056	−	0.0490995i	−0.991639	−	0.129046i	$-0.958808\pi$
$761$	0.142360	−	1.35447i	0.00516056	−	0.0490995i	0.996799	+	0.0799469i	$0.0254751\pi$
$762$	7.57510	+	1.06053i	0.274417	+	0.0384189i
$763$	28.5346	+	6.06521i	1.03302	+	0.219575i
$764$	0.437264	+	0.601843i	0.0158197	+	0.0217739i
$765$	3.79700	+	2.55527i	0.137281	+	0.0923861i
$766$	3.39775	−	1.10400i	0.122766	−	0.0398890i
$767$	8.66980	+	9.62878i	0.313048	+	0.347675i
$768$	−2.36673	+	1.59820i	−0.0854019	+	0.0576700i
$769$	−26.1294	+	15.0858i	−0.942250	+	0.544008i	−0.890665	−	0.454660i	$-0.849761\pi$
$769$	−26.1294	+	15.0858i	−0.942250	+	0.544008i	−0.0515851	+	0.998669i	$0.516427\pi$
$770$	14.7777	−	33.7346i	0.532553	−	1.21571i
$771$	6.05929	+	2.20177i	0.218220	+	0.0792950i
$772$	0.258656	+	0.580951i	0.00930924	+	0.0209089i
$773$	14.7588	+	4.79543i	0.530837	+	0.172479i	0.562158	−	0.827030i	$-0.309971\pi$
$773$	14.7588	+	4.79543i	0.530837	+	0.172479i	−0.0313207	+	0.999509i	$0.509971\pi$
$774$	−9.75803	+	7.64043i	−0.350745	+	0.274630i
$775$	−0.790117	+	0.574054i	−0.0283819	+	0.0206206i
$776$	−2.06578	−	19.6546i	−0.0741571	−	0.705557i
$777$	−20.2778	+	10.7957i	−0.727462	+	0.387292i
$778$	6.73947	+	31.7067i	0.241622	+	1.13674i
$779$	−8.00154	−	0.840995i	−0.286685	−	0.0301318i
$780$	−0.770561	−	0.917334i	−0.0275905	−	0.0328458i
$781$	26.3770	−	11.9339i	0.943843	−	0.427029i
$782$			4.92853i			0.176244i
$783$	−20.5559	+	28.3873i	−0.734608	+	1.01448i
$784$	−2.95829	+	9.10469i	−0.105653	+	0.325167i
$785$	−5.67325	+	26.6905i	−0.202487	+	0.952627i
$786$	8.36329	+	2.08051i	0.298309	+	0.0742093i
$787$	9.29786	−	20.8833i	0.331433	−	0.744410i	−0.668567	−	0.743652i	$-0.733092\pi$
$787$	9.29786	−	20.8833i	0.331433	−	0.744410i	1.00000		0.000758240i	$-0.000241355\pi$
$788$	1.02370	−	1.13693i	0.0364677	−	0.0405014i
$789$	−5.21362	+	37.2396i	−0.185610	+	1.32576i
$790$	64.3782	−	28.6630i	2.29047	−	1.01978i
$791$	−16.1176			−0.573076
$792$	26.7692	−	6.87528i	0.951201	−	0.244303i
$793$	−22.6085			−0.802853
$794$	−6.66507	+	2.96748i	−0.236535	+	0.105312i
$795$	12.5965	+	9.83079i	0.446753	+	0.348662i
$796$	−0.110695	+	0.122939i	−0.00392348	+	0.00435747i
$797$	−9.17384	+	20.6048i	−0.324954	+	0.729858i	−0.999968	−	0.00794601i	$-0.997471\pi$
$797$	−9.17384	+	20.6048i	−0.324954	+	0.729858i	0.675015	+	0.737804i	$0.264137\pi$
$798$	5.44463	+	18.9499i	0.192738	+	0.670819i
$799$	−0.299521	+	1.40914i	−0.0105963	+	0.0498517i
$800$	−0.928540	+	2.85775i	−0.0328289	+	0.101037i
$801$	−11.2789	−	11.6550i	−0.398522	−	0.411809i
$802$		−	27.1583i		−	0.958994i
$803$	1.85516	+	16.6871i	0.0654671	+	0.588874i
$804$	0.647098	−	0.114453i	0.0228214	−	0.00403646i
$805$	−61.5219	−	6.46621i	−2.16836	−	0.227904i
$806$	0.106559	+	0.501322i	0.00375339	+	0.0176583i
$807$	39.8668	+	24.8823i	1.40338	+	0.875897i
$808$	−1.90536	−	18.1283i	−0.0670303	−	0.637750i
$809$	−17.0062	+	12.3557i	−0.597905	+	0.434404i	−0.845135	−	0.534553i	$-0.820480\pi$
$809$	−17.0062	+	12.3557i	−0.597905	+	0.434404i	0.247229	+	0.968957i	$0.420480\pi$
$810$	46.1548	+	1.51409i	1.62171	+	0.0531998i
$811$	−52.0358	−	16.9075i	−1.82722	−	0.593701i	−0.999468	−	0.0326137i	$-0.989617\pi$
$811$	−52.0358	−	16.9075i	−1.82722	−	0.593701i	−0.827756	−	0.561088i	$-0.810383\pi$
$812$	−0.408370	−	0.917214i	−0.0143310	−	0.0321879i
$813$	27.7801	−	23.3353i	0.974290	−	0.818404i
$814$	25.2305	−	14.7694i	0.884330	−	0.517666i
$815$	−27.6170	+	15.9447i	−0.967382	+	0.558518i
$816$	−2.75211	−	1.34049i	−0.0963431	−	0.0469266i
$817$	−7.02820	−	7.80560i	−0.245886	−	0.273084i
$818$	−34.0016	+	11.0478i	−1.18884	+	0.386277i
$819$	8.04052	+	16.4414i	0.280958	+	0.574508i
$820$	−0.317300	−	0.436727i	−0.0110806	−	0.0152512i
$821$	−28.7336	−	6.10751i	−1.00281	−	0.213154i	−0.322887	−	0.946438i	$-0.604653\pi$
$821$	−28.7336	−	6.10751i	−1.00281	−	0.213154i	−0.679923	+	0.733284i	$0.737987\pi$
$822$	−15.4635	+	19.8140i	−0.539353	+	0.691093i
$823$	−2.50224	+	23.8072i	−0.0872227	+	0.829868i	0.860216	+	0.509930i	$0.170329\pi$
$823$	−2.50224	+	23.8072i	−0.0872227	+	0.829868i	−0.947438	+	0.319938i	$0.896338\pi$
$824$	−12.6693	−	21.9438i	−0.441355	−	0.764449i
$825$	27.0966	−	35.1526i	0.943383	−	1.22386i
$826$	7.15361	−	12.3904i	0.248906	−	0.431118i
$827$	26.5521	+	19.2912i	0.923308	+	0.670822i	0.944345	−	0.328956i	$-0.106697\pi$
$827$	26.5521	+	19.2912i	0.923308	+	0.670822i	−0.0210374	+	0.999779i	$0.506697\pi$
$828$	0.877615	+	1.40118i	0.0304992	+	0.0486944i
$829$	1.05596	+	3.24990i	0.0366749	+	0.112874i	0.967718	−	0.252036i	$-0.0811000\pi$
$829$	1.05596	+	3.24990i	0.0366749	+	0.112874i	−0.931043	+	0.364909i	$0.881100\pi$
$830$	−74.3758	+	7.81721i	−2.58162	+	0.271339i
$831$	−26.5417	−	25.6039i	−0.920722	−	0.888191i
$832$	−16.1439	−	14.5360i	−0.559689	−	0.503947i
$833$	−0.968949	+	0.205956i	−0.0335721	+	0.00713597i
$834$	−16.5200	+	1.16397i	−0.572042	+	0.0403048i
$835$	−8.10964	−	4.68211i	−0.280646	−	0.162031i
$836$	−0.262545	−	0.791835i	−0.00908031	−	0.0273862i
$837$	−0.569344	−	0.327508i	−0.0196794	−	0.0113203i
$838$	9.59288	−	13.2035i	0.331381	−	0.456106i
$839$	16.7494	−	15.0812i	0.578252	−	0.520661i	−0.327286	−	0.944925i	$-0.606134\pi$
$839$	16.7494	−	15.0812i	0.578252	−	0.520661i	0.905538	+	0.424265i	$0.139467\pi$
$840$	19.6667	−	31.5104i	0.678567	−	1.08721i
$841$	15.0695	+	6.70939i	0.519639	+	0.231358i
$842$	−42.2471	−	18.8096i	−1.45593	−	0.648222i
$843$	19.4126	+	36.4633i	0.668606	+	1.25586i
$844$	0.904128	−	0.814081i	0.0311214	−	0.0280218i
$845$	−10.5963	+	14.5845i	−0.364523	+	0.501723i
$846$	4.98601	+	13.6540i	0.171422	+	0.469435i
$847$	13.7606	−	19.4258i	0.472821	−	0.667479i
$848$	−9.25566	−	5.34376i	−0.317841	−	0.183505i
$849$	−31.7900	−	47.0770i	−1.09103	−	1.61568i
$850$	−4.64853	+	0.988076i	−0.159443	+	0.0338907i
$851$	−36.4926	−	32.8581i	−1.25095	−	1.12636i
$852$	−0.999469	+	0.287165i	−0.0342413	+	0.00983810i
$853$	20.4388	−	2.14821i	0.699811	−	0.0735531i	0.252061	−	0.967711i	$-0.418892\pi$
$853$	20.4388	−	2.14821i	0.699811	−	0.0735531i	0.447751	+	0.894158i	$0.352225\pi$
$854$	7.71458	+	23.7430i	0.263987	+	0.812470i
$855$	1.40722	+	39.1123i	0.0481258	+	1.33761i
$856$	−3.68289	−	2.67578i	−0.125879	−	0.0914562i
$857$	−12.8350	+	22.2308i	−0.438435	+	0.759391i	−0.997569	−	0.0696859i	$-0.977800\pi$
$857$	−12.8350	+	22.2308i	−0.438435	+	0.759391i	0.559134	+	0.829077i	$0.311134\pi$
$858$	−11.0689	−	20.4937i	−0.377885	−	0.699643i
$859$	−1.43676	−	2.48855i	−0.0490218	−	0.0849082i	0.840473	−	0.541853i	$-0.182277\pi$
$859$	−1.43676	−	2.48855i	−0.0490218	−	0.0849082i	−0.889495	+	0.456945i	$0.848944\pi$
$860$	0.0736649	−	0.700875i	0.00251195	−	0.0238996i
$861$	3.09336	+	7.64471i	0.105422	+	0.260531i
$862$	−17.2502	−	3.66663i	−0.587543	−	0.124886i
$863$	−17.7481	−	24.4282i	−0.604153	−	0.831546i	0.391927	−	0.919996i	$-0.371808\pi$
$863$	−17.7481	−	24.4282i	−0.604153	−	0.831546i	−0.996081	+	0.0884505i	$0.971808\pi$
$864$	−2.00943	+	0.214421i	−0.0683622	+	0.00729474i
$865$	−56.5832	+	18.3850i	−1.92389	+	0.625108i
$866$	−18.9140	−	21.0061i	−0.642724	−	0.713818i
$867$	2.04723	+	29.0561i	0.0695275	+	0.986796i
$868$	0.0162949	−	0.00940786i	0.000553084	−	0.000319323i
$869$	44.4980	−	9.73769i	1.50949	−	0.330329i
$870$	−10.4405	−	59.0288i	−0.353967	−	2.00126i
$871$	6.32466	+	14.2054i	0.214303	+	0.481332i
$872$	−35.6100	−	11.5704i	−1.20591	−	0.391823i
$873$	7.97478	−	19.7985i	0.269906	−	0.670078i
$874$	−34.0967	+	24.7727i	−1.15334	+	0.837948i
$875$	−2.20010	−	20.9325i	−0.0743768	−	0.707648i
$876$	0.0207288	−	0.602726i	0.000700361	−	0.0203642i
$877$	−3.08170	−	14.4983i	−0.104062	−	0.489571i	−0.999054	−	0.0434898i	$-0.986152\pi$
$877$	−3.08170	−	14.4983i	−0.104062	−	0.489571i	0.894992	−	0.446082i	$-0.147181\pi$
$878$	23.6514	+	2.48586i	0.798195	+	0.0838936i
$879$	−2.60164	+	7.15973i	−0.0877513	+	0.241492i
$880$	−24.1947	+	42.4931i	−0.815603	+	1.43244i
$881$		−	7.29612i		−	0.245813i	−0.992418	−	0.122906i	$-0.960779\pi$
$881$		−	7.29612i		−	0.245813i	0.992418	−	0.122906i	$-0.0392215\pi$
$882$	−7.18257	+	6.95081i	−0.241850	+	0.234046i
$883$	−13.3053	+	40.9496i	−0.447760	+	1.37806i	0.431668	+	0.902032i	$0.357925\pi$
$883$	−13.3053	+	40.9496i	−0.447760	+	1.37806i	−0.879428	+	0.476031i	$0.842075\pi$
$884$	−0.0172393	+	0.0811045i	−0.000579820	+	0.00272784i
$885$	19.7175	−	20.4397i	0.662797	−	0.687072i
$886$	6.39151	−	14.3556i	0.214727	−	0.482285i
$887$	24.3625	−	27.0573i	0.818014	−	0.908497i	−0.179145	−	0.983823i	$-0.557333\pi$
$887$	24.3625	−	27.0573i	0.818014	−	0.908497i	0.997159	+	0.0753261i	$0.0239998\pi$
$888$	27.3325	−	11.0599i	0.917219	−	0.371145i
$889$	6.07025	−	2.70265i	0.203590	−	0.0906439i
$890$	27.7401			0.929851
$891$	29.0206	+	6.98608i	0.972226	+	0.234042i
$892$	0.433110			0.0145016
$893$	−11.2542	+	5.01071i	−0.376609	+	0.167677i
$894$	31.8078	−	12.8708i	1.06381	−	0.430462i
$895$	−38.2531	+	42.4843i	−1.27866	+	1.42009i
$896$	−10.4414	+	23.4519i	−0.348824	+	0.783471i
$897$	−27.1618	+	28.1567i	−0.906907	+	0.940124i
$898$	−9.95949	+	46.8557i	−0.332353	+	1.56360i
$899$	−0.263471	+	0.810880i	−0.00878724	+	0.0270443i
$900$	−1.14563	+	1.10867i	−0.0381878	+	0.0369556i
$901$		−	1.10590i		−	0.0368428i
$902$	−4.32622	−	9.56205i	−0.144047	−	0.318381i
$903$	−3.67691	+	10.1188i	−0.122360	+	0.336734i
$904$	20.5738	+	2.16239i	0.684273	+	0.0719200i
$905$	9.77729	+	45.9985i	0.325008	+	1.52904i
$906$	−1.76019	+	51.1806i	−0.0584784	+	1.70036i
$907$	4.77914	+	45.4705i	0.158689	+	1.50982i	0.726788	+	0.686862i	$0.241012\pi$
$907$	4.77914	+	45.4705i	0.158689	+	1.50982i	−0.568099	+	0.822960i	$0.692321\pi$
$908$	0.164395	−	0.119440i	0.00545565	−	0.00396376i
$909$	7.35550	−	18.2610i	0.243966	−	0.605680i
$910$	−29.7711	−	9.67321i	−0.986902	−	0.320664i
$911$	11.6960	+	26.2697i	0.387507	+	0.870356i	0.996988	+	0.0775547i	$0.0247113\pi$
$911$	11.6960	+	26.2697i	0.387507	+	0.870356i	−0.609481	+	0.792801i	$0.708622\pi$
$912$	−4.55932	−	25.7775i	−0.150974	−	0.853580i
$913$	−48.1046	−	4.76441i	−1.59203	−	0.157679i
$914$	−39.4090	+	22.7528i	−1.30353	+	0.752595i
$915$	3.48295	+	49.4331i	0.115143	+	1.63421i
$916$	0.880974	+	0.978421i	0.0291082	+	0.0323279i
$917$	7.12024	−	2.31351i	0.235131	−	0.0763987i
$918$	−1.88273	−	2.58274i	−0.0621395	−	0.0852432i
$919$	−4.49558	−	6.18764i	−0.148296	−	0.204111i	0.728406	−	0.685145i	$-0.240261\pi$
$919$	−4.49558	−	6.18764i	−0.148296	−	0.204111i	−0.876702	+	0.481034i	$0.840261\pi$
$920$	77.6637	+	16.5079i	2.56050	+	0.544250i
$921$	6.56838	+	16.2326i	0.216436	+	0.534883i
$922$	3.80181	−	36.1718i	0.125206	−	1.19125i
$923$	−12.3035	−	21.3103i	−0.404974	−	0.701436i
$924$	−0.589969	+	0.618965i	−0.0194085	+	0.0203625i
$925$	23.6753	−	41.0069i	0.778440	−	1.34830i
$926$	1.08801	+	0.790484i	0.0357542	+	0.0259769i
$927$	−0.983969	−	27.3485i	−0.0323178	−	0.898242i
$928$	0.810619	+	2.49483i	0.0266099	+	0.0818968i
$929$	34.7455	−	3.65190i	1.13996	−	0.119815i	0.484324	−	0.874889i	$-0.339066\pi$
$929$	34.7455	−	3.65190i	1.13996	−	0.119815i	0.655640	+	0.755074i	$0.272399\pi$
$930$	1.07971	−	0.310221i	0.0354052	−	0.0101725i
$931$	−6.29516	−	5.66819i	−0.206316	−	0.185767i
$932$	0.662736	−	0.140869i	0.0217086	−	0.00461431i
$933$	−7.23619	−	10.7159i	−0.236902	−	0.350822i
$934$	16.3612	+	9.44616i	0.535356	+	0.309088i
$935$	−5.05969	+	0.0303534i	−0.165470	+	0.000992662i
$936$	−8.05770	−	22.0658i	−0.263374	−	0.721242i
$937$	33.5209	−	46.1375i	1.09508	−	1.50725i	0.253328	−	0.967381i	$-0.418475\pi$
$937$	33.5209	−	46.1375i	1.09508	−	1.50725i	0.841751	−	0.539866i	$-0.181525\pi$
$938$	12.7601	−	11.4893i	0.416633	−	0.375138i
$939$	−24.1728	−	45.4045i	−0.788849	−	1.48172i
$940$	−0.755108	−	0.336196i	−0.0246289	−	0.0109655i
$941$	−15.3686	−	6.84253i	−0.501001	−	0.223060i	0.140646	−	0.990060i	$-0.455082\pi$
$941$	−15.3686	−	6.84253i	−0.501001	−	0.223060i	−0.641647	+	0.767000i	$0.721749\pi$
$942$	10.0893	−	16.1653i	0.328729	−	0.526695i
$943$	−13.1004	+	11.7957i	−0.426608	+	0.384119i
$944$	−11.1654	+	15.3678i	−0.363402	+	0.500181i
$945$	34.7100	−	20.1133i	1.12912	−	0.654285i
$946$	4.15571	−	13.0559i	0.135114	−	0.424486i
$947$	−46.6899	−	26.9564i	−1.51722	−	0.875966i	−0.999795	−	0.0202354i	$-0.993558\pi$
$947$	−46.6899	−	26.9564i	−1.51722	−	0.875966i	−0.517422	−	0.855730i	$-0.673108\pi$
$948$	−1.63212	+	0.114996i	−0.0530087	+	0.00373488i
$949$	13.9587	−	2.96702i	0.453119	−	0.0963135i
$950$	−30.2010	−	27.1931i	−0.979851	−	0.882262i
$951$	−6.53471	−	6.30383i	−0.211902	−	0.204416i
$952$	−2.55670	+	0.268720i	−0.0828630	+	0.00870925i
$953$	1.34167	+	4.12923i	0.0434609	+	0.133759i	0.970433	−	0.241372i	$-0.0775976\pi$
$953$	1.34167	+	4.12923i	0.0434609	+	0.133759i	−0.926972	+	0.375131i	$0.877598\pi$
$954$	−5.92313	−	9.45673i	−0.191768	−	0.306173i
$955$	31.2154	+	22.6793i	1.01011	+	0.733884i
$956$	−0.201662	+	0.349288i	−0.00652221	+	0.0112968i
$957$	1.09947	−	38.7317i	0.0355408	−	1.25202i
$958$	20.6645	+	35.7920i	0.667640	+	1.15639i
$959$	−2.28228	+	21.7144i	−0.0736986	+	0.701195i
$960$	−29.2957	+	37.5376i	−0.945514	+	1.21152i
$961$	30.3069	+	6.44194i	0.977643	+	0.207805i
$962$	−14.6057	−	20.1031i	−0.470908	−	0.648149i
$963$	−2.15996	−	4.41672i	−0.0696037	−	0.142327i
$964$	0.427183	−	0.138800i	0.0137586	−	0.00447046i
$965$	22.0702	+	24.5114i	0.710464	+	0.789050i
$966$	38.8378	+	18.9171i	1.24959	+	0.608647i
$967$	−15.9721	+	9.22147i	−0.513627	+	0.296542i	−0.734323	−	0.678800i	$-0.762500\pi$
$967$	−15.9721	+	9.22147i	−0.513627	+	0.296542i	0.220697	+	0.975343i	$0.429167\pi$
$968$	−20.1714	+	22.9504i	−0.648332	+	0.737654i
$969$	2.07410	−	1.74224i	0.0666297	−	0.0559690i
$970$	14.8484	+	33.3501i	0.476755	+	1.07081i
$971$	−11.5909	−	3.76611i	−0.371970	−	0.120860i	0.117066	−	0.993124i	$-0.462651\pi$
$971$	−11.5909	−	3.76611i	−0.371970	−	0.120860i	−0.489036	+	0.872264i	$0.662651\pi$
$972$	−0.995167	−	0.399018i	−0.0319200	−	0.0127985i
$973$	−11.6390	+	8.45625i	−0.373130	+	0.271095i
$974$	1.41738	+	13.4854i	0.0454157	+	0.432101i
$975$	−32.0025	−	19.9739i	−1.02490	−	0.639676i
$976$	−6.89142	−	32.4216i	−0.220589	−	1.03779i
$977$	30.4904	+	3.20467i	0.975475	+	0.102527i	0.578832	−	0.815447i	$-0.303509\pi$
$977$	30.4904	+	3.20467i	0.975475	+	0.102527i	0.396643	+	0.917973i	$0.370175\pi$
$978$	21.9293	−	3.87867i	0.701221	−	0.124026i
$979$	17.5609	+	3.62272i	0.561250	+	0.115783i
$980$		−	0.568364i		−	0.0181557i
$981$	−28.1218	−	29.0595i	−0.897861	−	0.927798i
$982$	−1.79065	+	5.51104i	−0.0571418	+	0.175864i
$983$	−2.66212	+	12.5243i	−0.0849085	+	0.399463i	−0.999993	−	0.00379955i	$-0.998791\pi$
$983$	−2.66212	+	12.5243i	−0.0849085	+	0.399463i	0.915084	+	0.403263i	$0.132124\pi$
$984$	−2.92297	−	10.1733i	−0.0931808	−	0.324313i
$985$	32.2744	−	72.4896i	1.02835	−	2.30971i
$986$	−2.77612	+	3.08319i	−0.0884097	+	0.0981889i
$987$	9.95465	+	7.76896i	0.316860	+	0.247289i
$988$	−0.647751	+	0.288397i	−0.0206077	+	0.00917514i
$989$	−23.0136			−0.731791
$990$	−43.1038	+	27.3590i	−1.36993	+	0.869527i
$991$	13.7769			0.437638			0.218819	−	0.975765i	$-0.429780\pi$
$991$	13.7769			0.437638			0.218819	+	0.975765i	$0.429780\pi$
$992$	−0.0449102	+	0.0199953i	−0.00142590	+	0.000634851i
$993$	−3.66519	+	26.1795i	−0.116311	+	0.830782i
$994$	−18.1814	+	20.1925i	−0.576678	+	0.640466i
$995$	−3.48992	+	7.83849i	−0.110638	+	0.248497i
$996$	1.68499	+	0.419169i	0.0533909	+	0.0132819i
$997$	1.36452	−	6.41958i	0.0432149	−	0.203310i	−0.951244	−	0.308441i	$-0.900193\pi$
$997$	1.36452	−	6.41958i	0.0432149	−	0.203310i	0.994458	+	0.105131i	$0.0335261\pi$
$998$	10.3071	−	31.7220i	0.326265	−	1.00414i
$999$	31.6756	+	3.27848i	1.00217	+	0.103727i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	99.2.p.a.29.4	✓	80
3.2	odd	2		297.2.t.a.62.7		80
9.2	odd	6		891.2.k.a.161.6		80
9.4	even	3		297.2.t.a.260.7		80
9.5	odd	6	inner	99.2.p.a.95.4	yes	80
9.7	even	3		891.2.k.a.161.15		80
11.8	odd	10	inner	99.2.p.a.74.4	yes	80
33.8	even	10		297.2.t.a.8.7		80
99.41	even	30	inner	99.2.p.a.41.4	yes	80
99.52	odd	30		891.2.k.a.404.6		80
99.74	even	30		891.2.k.a.404.15		80
99.85	odd	30		297.2.t.a.206.7		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.4	✓	80	1.1	even	1	trivial
99.2.p.a.41.4	yes	80	99.41	even	30	inner
99.2.p.a.74.4	yes	80	11.8	odd	10	inner
99.2.p.a.95.4	yes	80	9.5	odd	6	inner
297.2.t.a.8.7		80	33.8	even	10
297.2.t.a.62.7		80	3.2	odd	2
297.2.t.a.206.7		80	99.85	odd	30
297.2.t.a.260.7		80	9.4	even	3
891.2.k.a.161.6		80	9.2	odd	6
891.2.k.a.161.15		80	9.7	even	3
891.2.k.a.404.6		80	99.52	odd	30
891.2.k.a.404.15		80	99.74	even	30

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:	\( N \)	\(=\)	\( 99 = 3^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	99.p (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.31398 + 0.585020i) q^{2} +(1.60559 - 0.649686i) q^{3} +(0.0460231 - 0.0511138i) q^{4} +(1.45099 - 3.25897i) q^{5} +(-1.72962 + 1.79297i) q^{6} +(-0.449955 + 2.11687i) q^{7} +(0.858363 - 2.64177i) q^{8} +(2.15582 - 2.08625i) q^{9} +O(q^{10})\)	\(q+(-1.31398 + 0.585020i) q^{2} +(1.60559 - 0.649686i) q^{3} +(0.0460231 - 0.0511138i) q^{4} +(1.45099 - 3.25897i) q^{5} +(-1.72962 + 1.79297i) q^{6} +(-0.449955 + 2.11687i) q^{7} +(0.858363 - 2.64177i) q^{8} +(2.15582 - 2.08625i) q^{9} +5.13106i q^{10} +(-0.670091 + 3.24823i) q^{11} +(0.0406861 - 0.111968i) q^{12} +(2.80353 + 0.294663i) q^{13} +(-0.647182 - 3.04475i) q^{14} +(0.212377 - 6.17525i) q^{15} +(0.431998 + 4.11019i) q^{16} +(-0.345974 + 0.251365i) q^{17} +(-1.61219 + 4.00248i) q^{18} +(-3.47799 - 1.13007i) q^{19} +(-0.0997996 - 0.224153i) q^{20} +(0.652861 + 3.69115i) q^{21} +(-1.01979 - 4.66011i) q^{22} +(-6.93913 + 4.00631i) q^{23} +(-0.338145 - 4.79926i) q^{24} +(-5.16987 - 5.74172i) q^{25} +(-3.85615 + 1.25294i) q^{26} +(2.10594 - 4.75027i) q^{27} +(0.0874932 + 0.120424i) q^{28} +(-6.59765 - 1.40237i) q^{29} +(3.33358 + 8.23837i) q^{30} +(0.0132129 - 0.125713i) q^{31} +(-0.194455 - 0.336806i) q^{32} +(1.03444 + 5.65066i) q^{33} +(0.307548 - 0.532688i) q^{34} +(6.24595 + 4.53795i) q^{35} +(-0.00741914 - 0.206208i) q^{36} +(1.89382 + 5.82859i) q^{37} +(5.23111 - 0.549812i) q^{38} +(4.69274 - 1.34831i) q^{39} +(-7.36398 - 6.63056i) q^{40} +(2.15199 - 0.457420i) q^{41} +(-3.01724 - 4.46815i) q^{42} +(2.48738 + 1.43609i) q^{43} +(0.135190 + 0.183744i) q^{44} +(-3.67098 - 10.0529i) q^{45} +(6.77408 - 9.32372i) q^{46} +(2.50344 - 2.25411i) q^{47} +(3.36394 + 6.31860i) q^{48} +(2.11612 + 0.942159i) q^{49} +(10.1521 + 4.52001i) q^{50} +(-0.392182 + 0.628362i) q^{51} +(0.144088 - 0.129738i) q^{52} +(-1.52002 + 2.09212i) q^{53} +(0.0118478 + 7.47375i) q^{54} +(9.61358 + 6.89694i) q^{55} +(5.20607 + 3.00573i) q^{56} +(-6.31841 + 0.445181i) q^{57} +(9.48957 - 2.01707i) q^{58} +(3.41571 + 3.07552i) q^{59} +(-0.305866 - 0.295059i) q^{60} +(-7.97621 + 0.838333i) q^{61} +(0.0561830 + 0.172913i) q^{62} +(3.44632 + 5.50231i) q^{63} +(-6.23451 - 4.52964i) q^{64} +(5.02818 - 8.70906i) q^{65} +(-4.66497 - 6.81966i) q^{66} +(2.75806 + 4.77710i) q^{67} +(-0.00307457 + 0.0292526i) q^{68} +(-8.53853 + 10.9407i) q^{69} +(-10.8618 - 2.30875i) q^{70} +(-5.13082 - 7.06197i) q^{71} +(-3.66093 - 7.48594i) q^{72} +(4.81457 - 1.56435i) q^{73} +(-5.89828 - 6.55070i) q^{74} +(-12.0310 - 5.86004i) q^{75} +(-0.217830 + 0.125764i) q^{76} +(-6.57457 - 2.88006i) q^{77} +(-5.37737 + 4.51699i) q^{78} +(-5.58618 - 12.5468i) q^{79} +(14.0218 + 4.55596i) q^{80} +(0.295083 - 8.99516i) q^{81} +(-2.56007 + 1.86000i) q^{82} +(1.52351 + 14.4952i) q^{83} +(0.218716 + 0.136508i) q^{84} +(0.317186 + 1.49224i) q^{85} +(-4.10849 - 0.431820i) q^{86} +(-11.5042 + 2.03477i) q^{87} +(8.00589 + 4.55839i) q^{88} -5.40631i q^{89} +(10.7047 + 11.0616i) q^{90} +(-1.88523 + 5.80213i) q^{91} +(-0.114583 + 0.539069i) q^{92} +(-0.0604593 - 0.210427i) q^{93} +(-1.97076 + 4.42640i) q^{94} +(-8.72938 + 9.69496i) q^{95} +(-0.531033 - 0.414437i) q^{96} +(6.49965 - 2.89383i) q^{97} -3.33172 q^{98} +(5.33204 + 8.40056i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9}+O(q^{10}) \) 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9	\( 80 q - 15 q^{2} - 3 q^{3} + 5 q^{4} - 6 q^{5} - 15 q^{6} - 5 q^{7} - q^{9} - 3 q^{11} - 54 q^{12} - 5 q^{13} - 9 q^{14} + 5 q^{16} - 50 q^{19} - 3 q^{20} - 11 q^{22} - 42 q^{23} - 5 q^{24} - 2 q^{25} + 3 q^{27} - 20 q^{28} + 30 q^{29} + 50 q^{30} - 6 q^{31} + 4 q^{33} - 10 q^{34} - 17 q^{36} - 6 q^{37} + 9 q^{38} + 85 q^{39} + 15 q^{40} - 15 q^{41} + 19 q^{42} - 12 q^{45} - 40 q^{46} - 21 q^{47} + 70 q^{48} - q^{49} + 60 q^{50} - 45 q^{51} - 5 q^{52} - 18 q^{55} + 90 q^{56} + 60 q^{57} - 29 q^{58} + 81 q^{59} + 43 q^{60} - 5 q^{61} + 15 q^{63} - 8 q^{64} - 39 q^{66} + 10 q^{67} + 180 q^{68} - 20 q^{69} + 30 q^{70} + 5 q^{72} - 20 q^{73} - 15 q^{74} - 30 q^{75} + 33 q^{77} + 152 q^{78} - 5 q^{79} - 73 q^{81} - 2 q^{82} - 60 q^{83} - 135 q^{84} - 5 q^{85} - 48 q^{86} - 59 q^{88} - 70 q^{90} + 52 q^{91} - 213 q^{92} - 34 q^{93} - 5 q^{94} - 135 q^{95} - 145 q^{96} + 27 q^{97} + 35 q^{99}+O(q^{100}) \) 80 * q - 15 * q^2 - 3 * q^3 + 5 * q^4 - 6 * q^5 - 15 * q^6 - 5 * q^7 - q^9 - 3 * q^11 - 54 * q^12 - 5 * q^13 - 9 * q^14 + 5 * q^16 - 50 * q^19 - 3 * q^20 - 11 * q^22 - 42 * q^23 - 5 * q^24 - 2 * q^25 + 3 * q^27 - 20 * q^28 + 30 * q^29 + 50 * q^30 - 6 * q^31 + 4 * q^33 - 10 * q^34 - 17 * q^36 - 6 * q^37 + 9 * q^38 + 85 * q^39 + 15 * q^40 - 15 * q^41 + 19 * q^42 - 12 * q^45 - 40 * q^46 - 21 * q^47 + 70 * q^48 - q^49 + 60 * q^50 - 45 * q^51 - 5 * q^52 - 18 * q^55 + 90 * q^56 + 60 * q^57 - 29 * q^58 + 81 * q^59 + 43 * q^60 - 5 * q^61 + 15 * q^63 - 8 * q^64 - 39 * q^66 + 10 * q^67 + 180 * q^68 - 20 * q^69 + 30 * q^70 + 5 * q^72 - 20 * q^73 - 15 * q^74 - 30 * q^75 + 33 * q^77 + 152 * q^78 - 5 * q^79 - 73 * q^81 - 2 * q^82 - 60 * q^83 - 135 * q^84 - 5 * q^85 - 48 * q^86 - 59 * q^88 - 70 * q^90 + 52 * q^91 - 213 * q^92 - 34 * q^93 - 5 * q^94 - 135 * q^95 - 145 * q^96 + 27 * q^97 + 35 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more