LMFDB - Embedded newform 71.2.g.a.12.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [71,2,Mod(2,71)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(71, base_ring=CyclotomicField(70))

chi = DirichletCharacter(H, H._module([6]))

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

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

chi := DirichletCharacter("71.2");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	71.g (of order $35$, degree $24$, 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:	$0.566937854351$
Analytic rank:	$0$
Dimension:	$120$
Relative dimension:	$5$ over $\Q(\zeta_{35})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{35}]$

Embedding invariants

Embedding label			12.2
Character	$\chi$	$=$	71.12
Dual form			71.2.g.a.6.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18839 - 1.24296i) q^{2} +(1.54029 + 0.578081i) q^{3} +(-0.0429451 + 0.956246i) q^{4} +(1.33583 + 0.970538i) q^{5} +(-1.11193 - 2.60150i) q^{6} +(0.313169 - 2.31191i) q^{7} +(-1.35044 + 1.17984i) q^{8} +(-0.220897 - 0.192992i) q^{9} +O(q^{10})$	\(q+(-1.18839 - 1.24296i) q^{2} +(1.54029 + 0.578081i) q^{3} +(-0.0429451 + 0.956246i) q^{4} +(1.33583 + 0.970538i) q^{5} +(-1.11193 - 2.60150i) q^{6} +(0.313169 - 2.31191i) q^{7} +(-1.35044 + 1.17984i) q^{8} +(-0.220897 - 0.192992i) q^{9} +(-0.381149 - 2.81376i) q^{10} +(-0.481884 + 0.287912i) q^{11} +(-0.618935 + 1.44807i) q^{12} +(-0.253369 - 0.151381i) q^{13} +(-3.24577 + 2.35819i) q^{14} +(1.49652 + 2.26713i) q^{15} +(4.97805 + 0.448032i) q^{16} +(-2.23337 + 6.87360i) q^{17} +(0.0226308 + 0.503915i) q^{18} +(-2.14710 + 3.25272i) q^{19} +(-0.985440 + 1.23570i) q^{20} +(1.81884 - 3.37997i) q^{21} +(0.930528 + 0.256809i) q^{22} +(-0.570677 - 0.274824i) q^{23} +(-2.76211 + 1.03664i) q^{24} +(-0.702585 - 2.16233i) q^{25} +(0.112941 + 0.494825i) q^{26} +(-2.56750 - 4.77122i) q^{27} +(2.19730 + 0.398751i) q^{28} +(-4.57803 + 1.26346i) q^{29} +(1.03950 - 4.55434i) q^{30} +(9.28502 - 0.835667i) q^{31} +(-3.12284 - 3.91592i) q^{32} +(-0.908678 + 0.164901i) q^{33} +(11.1977 - 5.39252i) q^{34} +(2.66213 - 2.78437i) q^{35} +(0.194034 - 0.202944i) q^{36} +(-6.32017 + 3.04363i) q^{37} +(6.59459 - 1.19674i) q^{38} +(-0.302751 - 0.379638i) q^{39} +(-2.94904 + 0.265418i) q^{40} +(2.45921 - 10.7745i) q^{41} +(-6.36264 + 1.75598i) q^{42} +(-2.38217 - 0.432301i) q^{43} +(-0.254620 - 0.473164i) q^{44} +(-0.107775 - 0.472194i) q^{45} +(0.336592 + 1.03592i) q^{46} +(2.68029 - 1.00593i) q^{47} +(7.40864 + 3.56781i) q^{48} +(1.50091 + 0.414224i) q^{49} +(-1.85274 + 3.44298i) q^{50} +(-7.41353 + 9.29627i) q^{51} +(0.155638 - 0.235782i) q^{52} +(0.297013 + 6.61350i) q^{53} +(-2.87923 + 8.86136i) q^{54} +(-0.923145 - 0.0830846i) q^{55} +(2.30477 + 3.49157i) q^{56} +(-5.18750 + 3.76894i) q^{57} +(7.01090 + 4.18882i) q^{58} +(3.82454 - 8.94795i) q^{59} +(-2.23220 + 1.33368i) q^{60} +(1.44618 + 10.6761i) q^{61} +(-12.0729 - 10.5478i) q^{62} +(-0.515357 + 0.450254i) q^{63} +(0.185672 - 1.37069i) q^{64} +(-0.191537 - 0.448123i) q^{65} +(1.28483 + 0.933481i) q^{66} +(0.189349 - 4.21618i) q^{67} +(-6.47694 - 2.43083i) q^{68} +(-0.720138 - 0.753205i) q^{69} -6.62450 q^{70} +(8.42610 + 0.0275788i) q^{71} +0.526007 q^{72} +(-8.16593 - 8.54089i) q^{73} +(11.2939 + 4.23868i) q^{74} +(0.167819 - 3.73677i) q^{75} +(-3.01819 - 2.19285i) q^{76} +(0.514715 + 1.20424i) q^{77} +(-0.112088 + 0.827464i) q^{78} +(9.22622 - 8.06070i) q^{79} +(6.21500 + 5.42988i) q^{80} +(-1.07843 - 7.96126i) q^{81} +(-16.3147 + 9.74761i) q^{82} +(4.88253 - 11.4232i) q^{83} +(3.15397 + 1.88441i) q^{84} +(-9.65449 + 7.01439i) q^{85} +(2.29362 + 3.47468i) q^{86} +(-7.78188 - 0.700382i) q^{87} +(0.311063 - 0.957354i) q^{88} +(0.286358 + 6.37626i) q^{89} +(-0.458838 + 0.695109i) q^{90} +(-0.429325 + 0.538357i) q^{91} +(0.287307 - 0.533905i) q^{92} +(14.7847 + 4.08032i) q^{93} +(-4.43555 - 2.13605i) q^{94} +(-6.02506 + 2.26124i) q^{95} +(-2.54636 - 7.83690i) q^{96} +(2.94476 + 12.9018i) q^{97} +(-1.26880 - 2.35782i) q^{98} +(0.162011 + 0.0294007i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) $ 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/71\mathbb{Z}\right)^\times$.

$n$	$7$
$\chi(n)$	$e\left(\frac{19}{35}\right)$

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 $

$2$	−1.18839	−	1.24296i	−0.840318	−	0.878903i	0.153701	−	0.988117i	$-0.450881\pi$
$2$	−1.18839	−	1.24296i	−0.840318	−	0.878903i	−0.994018	+	0.109214i	$0.965167\pi$
$3$	1.54029	+	0.578081i	0.889287	+	0.333755i	0.753862	−	0.657033i	$-0.228189\pi$
$3$	1.54029	+	0.578081i	0.889287	+	0.333755i	0.135425	+	0.990788i	$0.456760\pi$
$4$	−0.0429451	+	0.956246i	−0.0214725	+	0.478123i
$5$	1.33583	+	0.970538i	0.597402	+	0.434038i	0.844956	−	0.534836i	$-0.179627\pi$
$5$	1.33583	+	0.970538i	0.597402	+	0.434038i	−0.247554	+	0.968874i	$0.579627\pi$
$6$	−1.11193	−	2.60150i	−0.453945	−	1.06206i
$7$	0.313169	−	2.31191i	0.118367	−	0.873818i	−0.830250	−	0.557391i	$-0.811802\pi$
$7$	0.313169	−	2.31191i	0.118367	−	0.873818i	0.948617	−	0.316427i	$-0.102483\pi$
$8$	−1.35044	+	1.17984i	−0.477451	+	0.417137i
$9$	−0.220897	−	0.192992i	−0.0736323	−	0.0643306i
$10$	−0.381149	−	2.81376i	−0.120530	−	0.889788i
$11$	−0.481884	+	0.287912i	−0.145293	+	0.0868088i	−0.583706	−	0.811965i	$-0.698398\pi$
$11$	−0.481884	+	0.287912i	−0.145293	+	0.0868088i	0.438413	+	0.898774i	$0.355541\pi$
$12$	−0.618935	+	1.44807i	−0.178671	+	0.418022i
$13$	−0.253369	−	0.151381i	−0.0702718	−	0.0419855i	0.477334	−	0.878722i	$-0.341603\pi$
$13$	−0.253369	−	0.151381i	−0.0702718	−	0.0419855i	−0.547605	+	0.836737i	$0.684460\pi$
$14$	−3.24577	+	2.35819i	−0.867467	+	0.630252i
$15$	1.49652	+	2.26713i	0.386399	+	0.585370i
$16$	4.97805	+	0.448032i	1.24451	+	0.112008i
$17$	−2.23337	+	6.87360i	−0.541671	+	1.66709i	0.187105	+	0.982340i	$0.440090\pi$
$17$	−2.23337	+	6.87360i	−0.541671	+	1.66709i	−0.728776	+	0.684752i	$0.759910\pi$
$18$	0.0226308	+	0.503915i	0.00533414	+	0.118774i
$19$	−2.14710	+	3.25272i	−0.492579	+	0.746225i	−0.992814	−	0.119664i	$-0.961818\pi$
$19$	−2.14710	+	3.25272i	−0.492579	+	0.746225i	0.500235	+	0.865889i	$0.333247\pi$
$20$	−0.985440	+	1.23570i	−0.220351	+	0.276312i
$21$	1.81884	−	3.37997i	0.396903	−	0.737570i
$22$	0.930528	+	0.256809i	0.198389	+	0.0547519i
$23$	−0.570677	−	0.274824i	−0.118994	−	0.0573047i	0.373439	−	0.927655i	$-0.378178\pi$
$23$	−0.570677	−	0.274824i	−0.118994	−	0.0573047i	−0.492434	+	0.870350i	$0.663893\pi$
$24$	−2.76211	+	1.03664i	−0.563813	+	0.211603i
$25$	−0.702585	−	2.16233i	−0.140517	−	0.432467i
$26$	0.112941	+	0.494825i	0.0221495	+	0.0970432i
$27$	−2.56750	−	4.77122i	−0.494116	−	0.918221i
$28$	2.19730	+	0.398751i	0.415251	+	0.0753569i
$29$	−4.57803	+	1.26346i	−0.850119	+	0.234618i	−0.663836	−	0.747878i	$-0.731073\pi$
$29$	−4.57803	+	1.26346i	−0.850119	+	0.234618i	−0.186283	+	0.982496i	$0.559644\pi$
$30$	1.03950	−	4.55434i	0.189785	−	0.831504i
$31$	9.28502	−	0.835667i	1.66764	−	0.150090i	0.784794	−	0.619757i	$-0.212769\pi$
$31$	9.28502	−	0.835667i	1.66764	−	0.150090i	0.882844	+	0.469666i	$0.155626\pi$
$32$	−3.12284	−	3.91592i	−0.552045	−	0.692243i
$33$	−0.908678	+	0.164901i	−0.158180	+	0.0287055i
$34$	11.1977	−	5.39252i	1.92039	−	0.924810i
$35$	2.66213	−	2.78437i	0.449983	−	0.470645i
$36$	0.194034	−	0.202944i	0.0323390	−	0.0338240i
$37$	−6.32017	+	3.04363i	−1.03903	+	0.500370i	−0.874004	−	0.485919i	$-0.838485\pi$
$37$	−6.32017	+	3.04363i	−1.03903	+	0.500370i	−0.165025	+	0.986289i	$0.552771\pi$
$38$	6.59459	−	1.19674i	1.06978	−	0.194137i
$39$	−0.302751	−	0.379638i	−0.0484790	−	0.0607907i
$40$	−2.94904	+	0.265418i	−0.466283	+	0.0419663i
$41$	2.45921	−	10.7745i	0.384064	−	1.68270i	−0.300531	−	0.953772i	$-0.597164\pi$
$41$	2.45921	−	10.7745i	0.384064	−	1.68270i	0.684595	−	0.728923i	$-0.259979\pi$
$42$	−6.36264	+	1.75598i	−0.981777	+	0.270953i
$43$	−2.38217	−	0.432301i	−0.363278	−	0.0659253i	−0.00615106	−	0.999981i	$-0.501958\pi$
$43$	−2.38217	−	0.432301i	−0.363278	−	0.0659253i	−0.357127	+	0.934056i	$0.616244\pi$
$44$	−0.254620	−	0.473164i	−0.0383855	−	0.0713321i
$45$	−0.107775	−	0.472194i	−0.0160662	−	0.0703905i
$46$	0.336592	+	1.03592i	0.0496278	+	0.152739i
$47$	2.68029	−	1.00593i	0.390960	−	0.146730i	−0.148150	−	0.988965i	$-0.547332\pi$
$47$	2.68029	−	1.00593i	0.390960	−	0.146730i	0.539111	+	0.842235i	$0.318760\pi$
$48$	7.40864	+	3.56781i	1.06935	+	0.514969i
$49$	1.50091	+	0.414224i	0.214415	+	0.0591749i
$50$	−1.85274	+	3.44298i	−0.262018	+	0.486910i
$51$	−7.41353	+	9.29627i	−1.03810	+	1.30174i
$52$	0.155638	−	0.235782i	0.0215831	−	0.0326970i
$53$	0.297013	+	6.61350i	0.0407978	+	0.908434i	0.910159	+	0.414258i	$0.135959\pi$
$53$	0.297013	+	6.61350i	0.0407978	+	0.908434i	−0.869362	+	0.494176i	$0.835470\pi$
$54$	−2.87923	+	8.86136i	−0.391813	+	1.20588i
$55$	−0.923145	−	0.0830846i	−0.124477	−	0.0112031i
$56$	2.30477	+	3.49157i	0.307987	+	0.466581i
$57$	−5.18750	+	3.76894i	−0.687101	+	0.499208i
$58$	7.01090	+	4.18882i	0.920577	+	0.550019i
$59$	3.82454	−	8.94795i	0.497912	−	1.16492i	−0.462570	−	0.886583i	$-0.653073\pi$
$59$	3.82454	−	8.94795i	0.497912	−	1.16492i	0.960482	−	0.278341i	$-0.0897846\pi$
$60$	−2.23220	+	1.33368i	−0.288176	+	0.172177i
$61$	1.44618	+	10.6761i	0.185165	+	1.36694i	0.810113	+	0.586274i	$0.199406\pi$
$61$	1.44618	+	10.6761i	0.185165	+	1.36694i	−0.624948	+	0.780666i	$0.714880\pi$
$62$	−12.0729	−	10.5478i	−1.53326	−	1.33957i
$63$	−0.515357	+	0.450254i	−0.0649289	+	0.0567267i
$64$	0.185672	−	1.37069i	0.0232090	−	0.171336i
$65$	−0.191537	−	0.448123i	−0.0237572	−	0.0555828i
$66$	1.28483	+	0.933481i	0.158151	+	0.114904i
$67$	0.189349	−	4.21618i	0.0231326	−	0.515088i	−0.953658	−	0.300892i	$-0.902715\pi$
$67$	0.189349	−	4.21618i	0.0231326	−	0.515088i	0.976791	−	0.214196i	$-0.0687131\pi$
$68$	−6.47694	−	2.43083i	−0.785444	−	0.294782i
$69$	−0.720138	−	0.753205i	−0.0866944	−	0.0906753i
$70$	−6.62450			−0.791780
$71$	8.42610	+	0.0275788i	0.999995	+	0.00327300i
$71$	8.42610	+	0.0275788i	0.999995	+	0.00327300i
$72$	0.526007			0.0619905
$73$	−8.16593	−	8.54089i	−0.955749	−	0.999635i	−1.00000		0.000614933i	$-0.999804\pi$
$73$	−8.16593	−	8.54089i	−0.955749	−	0.999635i	0.0442505	−	0.999020i	$-0.485910\pi$
$74$	11.2939	+	4.23868i	1.31289	+	0.492736i
$75$	0.167819	−	3.73677i	0.0193780	−	0.431485i
$76$	−3.01819	−	2.19285i	−0.346211	−	0.251537i
$77$	0.514715	+	1.20424i	0.0586572	+	0.137235i
$78$	−0.112088	+	0.827464i	−0.0126914	+	0.0936918i
$79$	9.22622	−	8.06070i	1.03803	−	0.906900i	0.0422907	−	0.999105i	$-0.486534\pi$
$79$	9.22622	−	8.06070i	1.03803	−	0.906900i	0.995740	+	0.0922052i	$0.0293916\pi$
$80$	6.21500	+	5.42988i	0.694858	+	0.607079i
$81$	−1.07843	−	7.96126i	−0.119825	−	0.884585i
$82$	−16.3147	+	9.74761i	−1.80166	+	1.07644i
$83$	4.88253	−	11.4232i	0.535927	−	1.25386i	−0.404709	−	0.914446i	$-0.632627\pi$
$83$	4.88253	−	11.4232i	0.535927	−	1.25386i	0.940636	−	0.339418i	$-0.110230\pi$
$84$	3.15397	+	1.88441i	0.344126	+	0.205606i
$85$	−9.65449	+	7.01439i	−1.04718	+	0.760818i
$86$	2.29362	+	3.47468i	0.247327	+	0.374684i
$87$	−7.78188	−	0.700382i	−0.834305	−	0.0750888i
$88$	0.311063	−	0.957354i	0.0331594	−	0.102054i
$89$	0.286358	+	6.37626i	0.0303539	+	0.675882i	0.955274	+	0.295721i	$0.0955599\pi$
$89$	0.286358	+	6.37626i	0.0303539	+	0.675882i	−0.924920	+	0.380161i	$0.875869\pi$
$90$	−0.458838	+	0.695109i	−0.0483657	+	0.0732709i
$91$	−0.429325	+	0.538357i	−0.0450055	+	0.0564351i
$92$	0.287307	−	0.533905i	0.0299538	−	0.0556635i
$93$	14.7847	+	4.08032i	1.53310	+	0.423109i
$94$	−4.43555	−	2.13605i	−0.457492	−	0.220317i
$95$	−6.02506	+	2.26124i	−0.618158	+	0.231998i
$96$	−2.54636	−	7.83690i	−0.259887	−	0.799850i
$97$	2.94476	+	12.9018i	0.298995	+	1.30998i	0.871627	+	0.490169i	$0.163065\pi$
$97$	2.94476	+	12.9018i	0.298995	+	1.30998i	−0.572632	+	0.819812i	$0.694078\pi$
$98$	−1.26880	−	2.35782i	−0.128168	−	0.238176i
$99$	0.162011	+	0.0294007i	0.0162828	+	0.00295489i
$100$	2.09789	−	0.578982i	0.209789	−	0.0578982i
$101$	0.916768	−	4.01662i	0.0912218	−	0.399669i	−0.908617	−	0.417631i	$-0.862861\pi$
$101$	0.916768	−	4.01662i	0.0912218	−	0.399669i	0.999839	+	0.0179619i	$0.00571775\pi$
$102$	20.3650	−	1.83288i	2.01644	−	0.181483i
$103$	−1.50573	−	1.88812i	−0.148364	−	0.186042i	0.702096	−	0.712082i	$-0.252248\pi$
$103$	−1.50573	−	1.88812i	−0.148364	−	0.186042i	−0.850460	+	0.526040i	$0.823676\pi$
$104$	0.520763	−	0.0945046i	0.0510651	−	0.00926694i
$105$	5.71005	−	2.74982i	0.557244	−	0.268354i
$106$	7.86733	−	8.22858i	0.764143	−	0.799231i
$107$	−5.80080	+	6.06716i	−0.560784	+	0.586534i	−0.941018	−	0.338356i	$-0.890129\pi$
$107$	−5.80080	+	6.06716i	−0.560784	+	0.586534i	0.380234	+	0.924890i	$0.375844\pi$
$108$	4.67272	−	2.25026i	0.449633	−	0.216532i
$109$	3.37099	−	0.611745i	0.322883	−	0.0585946i	−0.0146956	−	0.999892i	$-0.504678\pi$
$109$	3.37099	−	0.611745i	0.322883	−	0.0585946i	0.337578	+	0.941297i	$0.390392\pi$
$110$	0.993785	+	1.24617i	0.0947537	+	0.118817i
$111$	−11.4944	+	1.03451i	−1.09100	+	0.0981914i
$112$	2.59478	−	11.3685i	0.245184	−	1.07422i
$113$	−10.8148	+	2.98469i	−1.01737	+	0.280776i	−0.734665	−	0.678430i	$-0.762661\pi$
$113$	−10.8148	+	2.98469i	−1.01737	+	0.280776i	−0.282706	+	0.959207i	$0.591232\pi$
$114$	10.8494	+	1.96887i	1.01614	+	0.184402i
$115$	−0.495601	−	0.920981i	−0.0462150	−	0.0858820i
$116$	−1.01157	−	4.43198i	−0.0939220	−	0.411499i
$117$	0.0267531	+	0.0823376i	0.00247333	+	0.00761212i
$118$	−15.6670	+	5.87991i	−1.44226	+	0.541289i
$119$	15.1917	+	7.31593i	1.39262	+	0.670650i
$120$	−4.69580	−	1.29596i	−0.428666	−	0.118304i
$121$	−5.06324	+	9.40907i	−0.460294	+	0.855370i
$122$	11.5514	−	14.4849i	1.04581	−	1.31141i
$123$	10.0164	−	15.1742i	0.903151	−	1.36822i
$124$	0.400357	+	8.91465i	0.0359531	+	0.800559i
$125$	3.71130	−	11.4222i	0.331949	−	1.02163i
$126$	1.17209	+	0.105490i	0.104418	+	0.00939781i
$127$	2.37069	+	3.59145i	0.210365	+	0.318689i	0.924403	−	0.381418i	$-0.124564\pi$
$127$	2.37069	+	3.59145i	0.210365	+	0.318689i	−0.714038	+	0.700107i	$0.753135\pi$
$128$	−10.0285	+	7.28614i	−0.886403	+	0.644010i
$129$	−3.41933	−	2.04296i	−0.301056	−	0.179872i
$130$	−0.329377	+	0.770616i	−0.0288883	+	0.0675875i
$131$	−15.2967	+	9.13937i	−1.33648	+	0.798511i	−0.990205	−	0.139621i	$-0.955411\pi$
$131$	−15.2967	+	9.13937i	−1.33648	+	0.798511i	−0.346277	+	0.938132i	$0.612554\pi$
$132$	−0.118662	−	0.876001i	−0.0103282	−	0.0762461i
$133$	6.84758	+	5.98255i	0.593760	+	0.518753i
$134$	−5.46555	+	4.77511i	−0.472152	+	0.412506i
$135$	1.20090	−	8.86540i	0.103357	−	0.763012i
$136$	−5.09373	−	11.9174i	−0.436784	−	1.02191i
$137$	−7.44125	−	5.40638i	−0.635749	−	0.461899i	0.222638	−	0.974901i	$-0.428533\pi$
$137$	−7.44125	−	5.40638i	−0.635749	−	0.461899i	−0.858387	+	0.513003i	$0.828533\pi$
$138$	−0.0803980	+	1.79020i	−0.00684393	+	0.152392i
$139$	2.04244	+	0.766540i	0.173237	+	0.0650171i	0.436486	−	0.899711i	$-0.356223\pi$
$139$	2.04244	+	0.766540i	0.173237	+	0.0650171i	−0.263249	+	0.964728i	$0.584794\pi$
$140$	2.54822	+	2.66523i	0.215364	+	0.225253i
$141$	4.70993			0.396648
$142$	−9.97921	−	10.5061i	−0.837436	−	0.881649i
$143$	0.165679			0.0138547
$144$	−1.01317	−	1.05969i	−0.0844308	−	0.0883077i
$145$	−7.34171	−	2.75539i	−0.609696	−	0.228823i
$146$	−0.911665	+	20.2998i	−0.0754499	+	1.68002i
$147$	2.07238	+	1.50567i	0.170927	+	0.124186i
$148$	−2.63904	−	6.17434i	−0.216928	−	0.507528i
$149$	0.0710306	−	0.524369i	0.00581905	−	0.0429580i	−0.987807	−	0.155681i	$-0.950243\pi$
$149$	0.0710306	−	0.524369i	0.00581905	−	0.0429580i	0.993626	+	0.112723i	$0.0359572\pi$
$150$	−4.84408	+	4.23215i	−0.395518	+	0.345553i
$151$	9.61818	+	8.40315i	0.782716	+	0.683839i	0.953474	−	0.301474i	$-0.0974787\pi$
$151$	9.61818	+	8.40315i	0.782716	+	0.683839i	−0.170758	+	0.985313i	$0.554622\pi$
$152$	−0.938168	−	6.92583i	−0.0760955	−	0.561759i
$153$	1.81989	−	1.08734i	0.147130	−	0.0879058i
$154$	0.885131	−	2.07087i	0.0713259	−	0.166875i
$155$	13.2143	+	7.89515i	1.06139	+	0.634154i
$156$	0.376029	−	0.273201i	0.0301064	−	0.0218736i
$157$	5.39745	+	8.17679i	0.430764	+	0.652579i	0.983527	−	0.180759i	$-0.0578554\pi$
$157$	5.39745	+	8.17679i	0.430764	+	0.652579i	−0.552764	+	0.833338i	$0.686427\pi$
$158$	−20.9834	−	1.88854i	−1.66935	−	0.150245i
$159$	−3.36565	+	10.3584i	−0.266914	+	0.821475i
$160$	−0.371039	−	8.26183i	−0.0293332	−	0.653155i
$161$	−0.814084	+	1.23328i	−0.0641588	+	0.0971965i
$162$	−8.61392	+	10.8015i	−0.676773	+	0.848647i
$163$	−7.99256	+	14.8527i	−0.626026	+	1.16335i	0.348124	+	0.937448i	$0.386819\pi$
$163$	−7.99256	+	14.8527i	−0.626026	+	1.16335i	−0.974150	+	0.225902i	$0.927467\pi$
$164$	10.1975	+	2.81432i	0.796288	+	0.219762i
$165$	−1.37388	−	0.661627i	−0.106957	−	0.0515076i
$166$	−20.0009	+	7.50648i	−1.55237	+	0.582616i
$167$	0.106853	+	0.328861i	0.00826856	+	0.0254480i	0.955106	−	0.296265i	$-0.0957413\pi$
$167$	0.106853	+	0.328861i	0.00826856	+	0.0254480i	−0.946837	+	0.321713i	$0.895741\pi$
$168$	1.53160	+	6.71038i	0.118165	+	0.517717i
$169$	−6.11901	−	11.3710i	−0.470693	−	0.874695i
$170$	20.1919	+	3.66428i	1.54865	+	0.281038i
$171$	1.10204	−	0.304143i	0.0842749	−	0.0232584i
$172$	0.515688	−	2.25938i	0.0393209	−	0.172276i
$173$	12.1160	−	1.09046i	0.921163	−	0.0829062i	0.381103	−	0.924533i	$-0.375544\pi$
$173$	12.1160	−	1.09046i	0.921163	−	0.0829062i	0.540060	+	0.841627i	$0.318402\pi$
$174$	8.37735	+	10.5049i	0.635085	+	0.796372i
$175$	−5.21914	+	0.947134i	−0.394530	+	0.0715966i
$176$	−2.52784	+	1.21734i	−0.190543	+	0.0917606i
$177$	11.0635	−	11.5716i	0.831586	−	0.869771i
$178$	7.58511	−	7.93340i	0.568528	−	0.594634i
$179$	5.31643	−	2.56026i	0.397369	−	0.191363i	−0.224518	−	0.974470i	$-0.572081\pi$
$179$	5.31643	−	2.56026i	0.397369	−	0.191363i	0.621887	+	0.783107i	$0.286366\pi$
$180$	0.456161	−	0.0827811i	0.0340003	−	0.00617014i
$181$	5.05265	+	6.33582i	0.375561	+	0.470938i	0.933310	−	0.359071i	$-0.116906\pi$
$181$	5.05265	+	6.33582i	0.375561	+	0.470938i	−0.557750	+	0.830009i	$0.688335\pi$
$182$	1.17936	−	0.106144i	0.0874199	−	0.00786793i
$183$	−3.94413	+	17.2804i	−0.291559	+	1.27740i
$184$	1.09491	−	0.302176i	0.0807179	−	0.0222767i
$185$	−11.3966	−	2.06818i	−0.837897	−	0.152056i
$186$	−12.4983	−	23.2258i	−0.916421	−	1.70300i
$187$	−0.902769	−	3.95529i	−0.0660170	−	0.289239i
$188$	0.846811	+	2.60622i	0.0617600	+	0.190078i
$189$	−11.8347	+	4.44163i	−0.860845	+	0.323081i
$190$	9.97073	+	4.80165i	0.723353	+	0.348348i
$191$	−25.2885	−	6.97919i	−1.82981	−	0.504997i	−0.831121	−	0.556092i	$-0.812300\pi$
$191$	−25.2885	−	6.97919i	−1.82981	−	0.504997i	−0.998694	+	0.0510948i	$0.983729\pi$
$192$	1.07836	−	2.00392i	0.0778236	−	0.144620i
$193$	8.10483	−	10.1631i	0.583398	−	0.731558i	−0.399290	−	0.916825i	$-0.630743\pi$
$193$	8.10483	−	10.1631i	0.583398	−	0.731558i	0.982688	+	0.185266i	$0.0593148\pi$
$194$	12.5369	−	18.9926i	0.900097	−	1.36359i
$195$	−0.0359713	−	0.800963i	−0.00257596	−	0.0573582i
$196$	−0.460557	+	1.41745i	−0.0328969	+	0.101246i
$197$	19.3574	+	1.74220i	1.37916	+	0.124127i	0.754258	−	0.656578i	$-0.227997\pi$
$197$	19.3574	+	1.74220i	1.37916	+	0.124127i	0.624901	+	0.780704i	$0.285139\pi$
$198$	−0.155989	−	0.236313i	−0.0110856	−	0.0167940i
$199$	−5.30552	+	3.85469i	−0.376099	+	0.273252i	−0.759735	−	0.650232i	$-0.774671\pi$
$199$	−5.30552	+	3.85469i	−0.376099	+	0.273252i	0.383637	+	0.923484i	$0.374671\pi$
$200$	3.50001	+	2.09116i	0.247488	+	0.147867i
$201$	2.72894	−	6.38468i	0.192485	−	0.450341i
$202$	−6.08196	+	3.63380i	−0.427925	+	0.255674i
$203$	1.48730	+	10.9797i	0.104388	+	0.770621i
$204$	−8.57114	−	7.48838i	−0.600100	−	0.524292i
$205$	13.7422	−	12.0062i	0.959794	−	0.838547i
$206$	−0.557466	+	4.11538i	−0.0388405	+	0.286732i
$207$	0.0730221	+	0.170844i	0.00507539	+	0.0118745i
$208$	−1.19346	−	0.867098i	−0.0827514	−	0.0601224i
$209$	0.0981559	−	2.18561i	0.00678959	−	0.151182i
$210$	−10.2037	−	3.82950i	−0.704119	−	0.264260i
$211$	3.55227	+	3.71538i	0.244548	+	0.255777i	0.833665	−	0.552271i	$-0.186238\pi$
$211$	3.55227	+	3.71538i	0.244548	+	0.255777i	−0.589117	+	0.808048i	$0.700524\pi$
$212$	−6.33689			−0.435219
$213$	12.9627	+	4.91345i	0.888190	+	0.336664i
$214$	14.4348			0.986744
$215$	−2.76262	−	2.88947i	−0.188409	−	0.197060i
$216$	9.09653	+	3.41398i	0.618940	+	0.232292i
$217$	0.975796	−	21.7278i	0.0662413	−	1.47498i
$218$	−4.76642	−	3.46301i	−0.322823	−	0.234545i
$219$	−7.64057	−	17.8760i	−0.516302	−	1.20795i
$220$	0.119094	−	0.879186i	0.00802930	−	0.0592747i
$221$	1.60639	−	1.40346i	0.108058	−	0.0944073i
$222$	14.9456	+	13.0576i	1.00308	+	0.876368i
$223$	0.778072	+	5.74396i	0.0521035	+	0.384644i	0.998160	+	0.0606409i	$0.0193144\pi$
$223$	0.778072	+	5.74396i	0.0521035	+	0.384644i	−0.946056	+	0.324003i	$0.894971\pi$
$224$	−10.0312	+	5.99336i	−0.670238	+	0.400449i
$225$	−0.262114	+	0.613246i	−0.0174743	+	0.0408831i
$226$	16.5620	+	9.89535i	1.10169	+	0.658229i
$227$	−3.42842	+	2.49089i	−0.227552	+	0.165326i	−0.695720	−	0.718314i	$-0.744914\pi$
$227$	−3.42842	+	2.49089i	−0.227552	+	0.165326i	0.468168	+	0.883640i	$0.344914\pi$
$228$	−3.38125	−	5.12238i	−0.223929	−	0.339238i
$229$	−21.7088	−	1.95383i	−1.43456	−	0.129113i	−0.655088	−	0.755552i	$-0.727369\pi$
$229$	−21.7088	−	1.95383i	−1.43456	−	0.129113i	−0.779470	+	0.626440i	$0.784511\pi$
$230$	−0.555773	+	1.71049i	−0.0366466	+	0.112787i
$231$	0.0966652	+	2.15242i	0.00636011	+	0.141619i
$232$	4.69166	−	7.10757i	0.308023	−	0.466635i
$233$	6.60053	−	8.27681i	0.432415	−	0.542232i	−0.517111	−	0.855918i	$-0.672993\pi$
$233$	6.60053	−	8.27681i	0.432415	−	0.542232i	0.949527	+	0.313686i	$0.101564\pi$
$234$	0.0705490	−	0.131102i	0.00461194	−	0.00857041i
$235$	4.55671	+	1.25757i	0.297247	+	0.0820349i
$236$	8.39220	+	4.04147i	0.546285	+	0.263077i
$237$	18.8708	−	7.08233i	1.22579	−	0.460047i
$238$	−8.96024	−	27.5768i	−0.580806	−	1.78754i
$239$	−2.86959	−	12.5725i	−0.185619	−	0.813248i	−0.978891	−	0.204382i	$-0.934482\pi$
$239$	−2.86959	−	12.5725i	−0.185619	−	0.813248i	0.793273	−	0.608867i	$-0.208376\pi$
$240$	6.43399	+	11.9564i	0.415312	+	0.771780i
$241$	−19.2827	−	3.49929i	−1.24211	−	0.225409i	−0.482561	−	0.875863i	$-0.660293\pi$
$241$	−19.2827	−	3.49929i	−1.24211	−	0.225409i	−0.759546	+	0.650453i	$0.774579\pi$
$242$	17.7122	−	4.88825i	1.13858	−	0.314228i
$243$	−0.675807	+	2.96090i	−0.0433530	+	0.189942i
$244$	−10.2711	+	0.924418i	−0.657541	+	0.0591798i
$245$	1.60294	+	2.01002i	0.102408	+	0.128416i
$246$	−30.7644	+	5.58291i	−1.96146	+	0.355953i
$247$	1.03641	−	0.499108i	0.0659450	−	0.0317575i
$248$	−11.5529	+	12.0834i	−0.733608	+	0.767294i
$249$	14.1241	−	14.7726i	0.895076	−	0.936176i
$250$	−18.6078	+	8.96104i	−1.17686	+	0.566746i
$251$	−10.8285	+	1.96508i	−0.683489	+	0.124035i	−0.509185	−	0.860657i	$-0.670053\pi$
$251$	−10.8285	+	1.96508i	−0.683489	+	0.124035i	−0.174304	+	0.984692i	$0.555767\pi$
$252$	−0.408421	−	0.512144i	−0.0257281	−	0.0322621i
$253$	0.354125	−	0.0318718i	0.0222637	−	0.00200377i
$254$	1.64671	−	7.21471i	0.103324	−	0.452691i
$255$	−18.9256	+	5.22313i	−1.18517	+	0.327085i
$256$	18.2522	+	3.31228i	1.14076	+	0.207018i
$257$	1.35999	+	2.52728i	0.0848338	+	0.157648i	0.919477	−	0.393143i	$-0.128612\pi$
$257$	1.35999	+	2.52728i	0.0848338	+	0.157648i	−0.834644	+	0.550790i	$0.814326\pi$
$258$	1.52419	+	6.67791i	0.0948919	+	0.415749i
$259$	5.05731	+	15.5648i	0.314246	+	0.967150i
$260$	0.436741	−	0.163912i	0.0270855	−	0.0101654i
$261$	1.25511	+	0.604429i	0.0776894	+	0.0374132i
$262$	29.5383	+	8.15206i	1.82488	+	0.503636i
$263$	−0.738325	+	1.37204i	−0.0455271	+	0.0846034i	−0.902342	−	0.431020i	$-0.858154\pi$
$263$	−0.738325	+	1.37204i	−0.0455271	+	0.0846034i	0.856815	+	0.515623i	$0.172440\pi$
$264$	1.03256	−	1.29478i	0.0635494	−	0.0796884i
$265$	−6.02190	+	9.12278i	−0.369922	+	0.560408i
$266$	−0.701533	−	15.6208i	−0.0430137	−	0.957775i
$267$	−3.24492	+	9.98683i	−0.198586	+	0.611184i
$268$	4.02357	+	0.362128i	0.245779	+	0.0221205i
$269$	3.82874	+	5.80029i	0.233442	+	0.353650i	0.932347	−	0.361565i	$-0.117757\pi$
$269$	3.82874	+	5.80029i	0.233442	+	0.353650i	−0.698905	+	0.715215i	$0.746329\pi$
$270$	−12.4464	+	9.04287i	−0.757467	+	0.550332i
$271$	14.6330	+	8.74282i	0.888892	+	0.531088i	0.883254	−	0.468896i	$-0.155348\pi$
$271$	14.6330	+	8.74282i	0.888892	+	0.531088i	0.00563881	+	0.999984i	$0.498205\pi$
$272$	−14.1974	+	33.2165i	−0.860844	+	2.01404i
$273$	−0.972499	+	0.581041i	−0.0588583	+	0.0351662i
$274$	2.12319	+	15.6740i	0.128267	+	0.946903i
$275$	0.961127	+	0.839711i	0.0579581	+	0.0506365i
$276$	0.751176	−	0.656283i	0.0452155	−	0.0395036i
$277$	−2.93764	+	21.6865i	−0.176506	+	1.30302i	0.658418	+	0.752652i	$0.271226\pi$
$277$	−2.93764	+	21.6865i	−0.176506	+	1.30302i	−0.834924	+	0.550365i	$0.814489\pi$
$278$	−1.47443	−	3.44961i	−0.0884307	−	0.206894i
$279$	−2.21231	−	1.60734i	−0.132447	−	0.0962287i
$280$	−0.309925	+	6.90101i	−0.0185216	+	0.412414i
$281$	10.2537	+	3.84827i	0.611683	+	0.229568i	0.637939	−	0.770087i	$-0.279787\pi$
$281$	10.2537	+	3.84827i	0.611683	+	0.229568i	−0.0262563	+	0.999655i	$0.508359\pi$
$282$	−5.59723	−	5.85424i	−0.333310	−	0.348615i
$283$	11.1629			0.663567			0.331784	−	0.943356i	$-0.392350\pi$
$283$	11.1629			0.663567			0.331784	+	0.943356i	$0.392350\pi$
$284$	−0.388232	+	8.05624i	−0.0230373	+	0.478050i
$285$	−10.5875			−0.627150
$286$	−0.196891	−	0.205931i	−0.0116424	−	0.0121770i
$287$	−24.1395	−	9.05970i	−1.42491	−	0.534777i
$288$	−0.0659143	+	1.46770i	−0.00388404	+	0.0864849i
$289$	−28.5051	−	20.7102i	−1.67677	−	1.21825i
$290$	5.29997	+	12.3999i	0.311225	+	0.728147i
$291$	−2.92251	+	21.5749i	−0.171321	+	1.26474i
$292$	8.51788	−	7.44184i	0.498471	−	0.435501i
$293$	−7.35210	−	6.42333i	−0.429514	−	0.375255i	0.415861	−	0.909428i	$-0.363480\pi$
$293$	−7.35210	−	6.42333i	−0.429514	−	0.375255i	−0.845375	+	0.534173i	$0.820623\pi$
$294$	−0.591306	−	4.36520i	−0.0344857	−	0.254584i
$295$	13.7933	−	8.24109i	0.803075	−	0.479815i
$296$	4.94398	−	11.5670i	0.287363	−	0.672320i
$297$	2.61093	+	1.55996i	0.151502	+	0.0905180i
$298$	−0.736180	+	0.534866i	−0.0426458	+	0.0309840i
$299$	0.102989	+	0.156021i	0.00595599	+	0.00902293i
$300$	3.56607	+	0.320952i	0.205887	+	0.0185302i
$301$	−1.74546	+	5.37198i	−0.100607	+	0.309636i
$302$	−0.985380	−	21.9412i	−0.0567023	−	1.26257i
$303$	3.73402	−	5.65680i	0.214514	−	0.324975i
$304$	−12.1457	+	15.2302i	−0.696604	+	0.873514i
$305$	−8.42975	+	15.6651i	−0.482686	+	0.896981i
$306$	−3.51425	−	0.969872i	−0.200896	−	0.0554439i
$307$	−15.3940	−	7.41338i	−0.878585	−	0.423104i	−0.0604773	−	0.998170i	$-0.519262\pi$
$307$	−15.3940	−	7.41338i	−0.878585	−	0.423104i	−0.818107	+	0.575065i	$0.804977\pi$
$308$	−1.17365	+	0.440478i	−0.0668749	+	0.0250986i
$309$	−1.22777	−	3.77869i	−0.0698455	−	0.214962i
$310$	−5.89034	−	25.8073i	−0.334549	−	1.46575i
$311$	−13.7585	−	25.5675i	−0.780171	−	1.44980i	−0.890053	−	0.455857i	$-0.849333\pi$
$311$	−13.7585	−	25.5675i	−0.780171	−	1.44980i	0.109882	−	0.993945i	$-0.464953\pi$
$312$	0.856758	+	0.155479i	0.0485044	+	0.00880225i
$313$	22.3167	−	6.15902i	1.26142	−	0.348128i	0.429518	−	0.903058i	$-0.358683\pi$
$313$	22.3167	−	6.15902i	1.26142	−	0.348128i	0.831897	+	0.554930i	$0.187255\pi$
$314$	3.74913	−	16.4260i	0.211576	−	0.926973i
$315$	−1.12542	+	0.101290i	−0.0634102	+	0.00570702i
$316$	7.31180	+	9.16870i	0.411321	+	0.515780i
$317$	7.43441	−	1.34915i	0.417558	−	0.0757756i	0.0342881	−	0.999412i	$-0.489084\pi$
$317$	7.43441	−	1.34915i	0.417558	−	0.0757756i	0.383270	+	0.923636i	$0.374798\pi$
$318$	16.8748	−	8.12646i	0.946290	−	0.455709i
$319$	1.84232	−	1.92691i	0.103150	−	0.107886i
$320$	1.57833	−	1.65080i	0.0882312	−	0.0922826i
$321$	−12.4422	+	5.99186i	−0.694457	+	0.334433i
$322$	2.50037	−	0.453750i	0.139340	−	0.0252865i
$323$	−17.5626	−	22.0228i	−0.977211	−	1.22538i
$324$	7.65924	−	0.689344i	0.425513	−	0.0382969i
$325$	−0.149323	+	0.654225i	−0.00828293	+	0.0362899i
$326$	27.9595	−	7.71633i	1.54853	−	0.427368i
$327$	5.54595	+	1.00644i	0.306692	+	0.0556563i
$328$	9.39120	+	17.4518i	0.518542	+	0.963613i
$329$	−1.48623	−	6.51160i	−0.0819386	−	0.358996i
$330$	0.810332	+	2.49395i	0.0446073	+	0.137287i
$331$	14.5645	−	5.46615i	0.800537	−	0.300447i	0.0826253	−	0.996581i	$-0.473670\pi$
$331$	14.5645	−	5.46615i	0.800537	−	0.300447i	0.717912	+	0.696134i	$0.245098\pi$
$332$	10.7137	+	5.15947i	0.587993	+	0.283163i
$333$	1.98350	+	0.547412i	0.108695	+	0.0299980i
$334$	0.281777	−	0.523629i	0.0154181	−	0.0286517i
$335$	4.34490	−	5.44833i	0.237387	−	0.297674i
$336$	10.5686	−	16.0107i	0.576565	−	0.873458i
$337$	0.265712	+	5.91654i	0.0144743	+	0.322295i	0.993147	+	0.116870i	$0.0372861\pi$
$337$	0.265712	+	5.91654i	0.0144743	+	0.322295i	−0.978673	+	0.205425i	$0.934142\pi$
$338$	−6.86194	+	21.1189i	−0.373240	+	1.14872i
$339$	−18.3833	−	1.65453i	−0.998445	−	0.0898617i
$340$	−6.29287	−	9.53330i	−0.341279	−	0.517016i
$341$	−4.23370	+	3.07596i	−0.229268	+	0.166573i
$342$	−1.68769	−	1.00835i	−0.0912596	−	0.0545251i
$343$	7.84623	−	18.3572i	0.423657	−	0.991194i
$344$	3.72702	−	2.22679i	0.200948	−	0.120061i
$345$	−0.230968	−	1.70508i	−0.0124349	−	0.0917982i
$346$	−15.7539	−	13.7638i	−0.846936	−	0.739946i
$347$	1.55808	−	1.36126i	0.0836424	−	0.0730761i	−0.615102	−	0.788447i	$-0.710885\pi$
$347$	1.55808	−	1.36126i	0.0836424	−	0.0730761i	0.698745	+	0.715371i	$0.253742\pi$
$348$	1.00393	−	7.41131i	0.0538163	−	0.397288i
$349$	−1.35251	−	3.16436i	−0.0723983	−	0.169384i	0.879420	−	0.476047i	$-0.157931\pi$
$349$	−1.35251	−	3.16436i	−0.0723983	−	0.169384i	−0.951818	+	0.306662i	$0.900788\pi$
$350$	7.37961	+	5.36160i	0.394457	+	0.286590i
$351$	−0.0717459	+	1.59755i	−0.00382951	+	0.0852708i
$352$	2.63229	+	0.987913i	0.140301	+	0.0526560i
$353$	8.62385	+	9.01984i	0.459001	+	0.480078i	0.911273	−	0.411802i	$-0.135101\pi$
$353$	8.62385	+	9.01984i	0.459001	+	0.480078i	−0.452272	+	0.891880i	$0.649386\pi$
$354$	−27.5307			−1.46324
$355$	11.2291	+	8.21469i	0.595978	+	0.435991i
$356$	−6.10957			−0.323806
$357$	19.1704	+	20.0507i	1.01461	+	1.06119i
$358$	−9.50028	−	3.56551i	−0.502105	−	0.188443i
$359$	−1.21020	+	26.9471i	−0.0638717	+	1.42221i	0.669715	+	0.742618i	$0.266416\pi$
$359$	−1.21020	+	26.9471i	−0.0638717	+	1.42221i	−0.733587	+	0.679596i	$0.762155\pi$
$360$	0.702657	+	0.510510i	0.0370333	+	0.0269062i
$361$	1.49733	+	3.50318i	0.0788068	+	0.184378i
$362$	1.87064	−	13.8097i	0.0983189	−	0.725819i
$363$	−13.2381	+	11.5657i	−0.694818	+	0.607044i
$364$	−0.496364	−	0.433660i	−0.0260165	−	0.0227300i
$365$	−2.61904	−	19.3345i	−0.137087	−	1.01202i
$366$	26.1659	−	15.6334i	1.36771	−	0.817171i
$367$	−8.14436	+	19.0547i	−0.425132	+	0.994646i	0.560869	+	0.827905i	$0.310467\pi$
$367$	−8.14436	+	19.0547i	−0.425132	+	0.994646i	−0.986001	+	0.166741i	$0.946676\pi$
$368$	−2.71773	−	1.62377i	−0.141671	−	0.0846447i
$369$	−2.62263	+	1.90545i	−0.136528	+	0.0991937i
$370$	10.9730	+	16.6233i	0.570457	+	0.864206i
$371$	15.3828	+	1.38448i	0.798636	+	0.0718785i
$372$	−4.53672	+	13.9626i	−0.235218	+	0.723926i
$373$	−0.758863	−	16.8974i	−0.0392924	−	0.874914i	−0.917766	−	0.397122i	$-0.870009\pi$
$373$	−0.758863	−	16.8974i	−0.0392924	−	0.874914i	0.878473	−	0.477791i	$-0.158563\pi$
$374$	−3.84341	+	5.82252i	−0.198738	+	0.301076i
$375$	12.3194	−	15.4481i	0.636173	−	0.797736i
$376$	−2.43272	+	4.52076i	−0.125458	+	0.233140i
$377$	1.35119	+	0.372905i	0.0695900	+	0.0192056i
$378$	19.5849	+	9.43161i	1.00734	+	0.485110i
$379$	23.1051	−	8.67150i	1.18683	−	0.445425i	0.321637	−	0.946863i	$-0.395767\pi$
$379$	23.1051	−	8.67150i	1.18683	−	0.445425i	0.865194	+	0.501438i	$0.167195\pi$
$380$	−1.90356	−	5.85854i	−0.0976504	−	0.300537i
$381$	1.57541	+	6.90233i	0.0807107	+	0.353617i
$382$	21.3778	+	39.7266i	1.09378	+	2.03259i
$383$	−0.421453	−	0.0764825i	−0.0215353	−	0.00390807i	0.167779	−	0.985825i	$-0.446341\pi$
$383$	−0.421453	−	0.0764825i	−0.0215353	−	0.00390807i	−0.189314	+	0.981917i	$0.560626\pi$
$384$	−19.6588	+	5.42548i	−1.00321	+	0.276868i
$385$	−0.481184	+	2.10821i	−0.0245234	+	0.107444i
$386$	−22.2640	+	2.00380i	−1.13321	+	0.101991i
$387$	0.442785	+	0.555234i	0.0225080	+	0.0282241i
$388$	−12.4638	+	2.26184i	−0.632752	+	0.114828i
$389$	−11.1394	+	5.36445i	−0.564790	+	0.271988i	−0.694415	−	0.719575i	$-0.744337\pi$
$389$	−11.1394	+	5.36445i	−0.564790	+	0.271988i	0.129625	+	0.991563i	$0.458623\pi$
$390$	−0.952815	+	0.996566i	−0.0482477	+	0.0504631i
$391$	3.16356	−	3.30882i	0.159988	−	0.167334i
$392$	−2.51560	+	1.21145i	−0.127057	+	0.0611874i
$393$	−28.8447	+	5.23454i	−1.45502	+	0.264048i
$394$	−20.8387	−	26.1309i	−1.04984	−	1.31645i
$395$	20.1479	−	1.81334i	1.01375	−	0.0912392i
$396$	−0.0350719	+	0.153660i	−0.00176243	+	0.00772171i
$397$	−4.47413	+	1.23478i	−0.224550	+	0.0619719i	−0.376501	−	0.926416i	$-0.622873\pi$
$397$	−4.47413	+	1.23478i	−0.224550	+	0.0619719i	0.151951	+	0.988388i	$0.451444\pi$
$398$	11.0962	+	2.01367i	0.556204	+	0.100936i
$399$	7.08886	+	13.1733i	0.354887	+	0.659491i
$400$	−2.52870	−	11.0790i	−0.126435	−	0.553949i
$401$	1.28078	+	3.94185i	0.0639593	+	0.196847i	0.977930	−	0.208935i	$-0.0669996\pi$
$401$	1.28078	+	3.94185i	0.0639593	+	0.196847i	−0.913970	+	0.405781i	$0.867000\pi$
$402$	−11.1789	+	4.19552i	−0.557554	+	0.209254i
$403$	−2.47904	−	1.19384i	−0.123490	−	0.0594694i
$404$	3.80151	+	1.04915i	0.189132	+	0.0521971i
$405$	6.28611	−	11.6816i	0.312360	−	0.580461i
$406$	11.8798	−	14.8967i	0.589582	−	0.739313i
$407$	2.16929	−	3.28633i	0.107528	−	0.162897i
$408$	−0.956620	−	21.3008i	−0.0473598	−	1.05455i
$409$	−3.20018	+	9.84914i	−0.158239	+	0.487009i	−0.998475	−	0.0552123i	$-0.982416\pi$
$409$	−3.20018	+	9.84914i	−0.158239	+	0.487009i	0.840236	+	0.542221i	$0.182416\pi$
$410$	−31.2542	−	2.81293i	−1.54353	−	0.138921i
$411$	−8.33636	−	12.6290i	−0.411202	−	0.622945i
$412$	1.87017	−	1.35876i	0.0921369	−	0.0669413i
$413$	−19.4891	−	11.6442i	−0.958995	−	0.572973i
$414$	0.125573	−	0.293792i	0.00617156	−	0.0144391i
$415$	17.6089	−	10.5208i	0.864388	−	0.516448i
$416$	0.198435	+	1.46491i	0.00972909	+	0.0718230i
$417$	2.70283	+	2.36139i	0.132358	+	0.115638i
$418$	−2.83327	+	2.47535i	−0.138580	+	0.121073i
$419$	−4.69852	+	34.6859i	−0.229538	+	1.69452i	0.399171	+	0.916876i	$0.369298\pi$
$419$	−4.69852	+	34.6859i	−0.229538	+	1.69452i	−0.628709	+	0.777641i	$0.716416\pi$
$420$	2.38428	+	5.57830i	0.116341	+	0.272193i
$421$	28.6868	+	20.8422i	1.39811	+	1.01579i	0.994920	+	0.100672i	$0.0320991\pi$
$421$	28.6868	+	20.8422i	1.39811	+	1.01579i	0.403192	+	0.915116i	$0.367901\pi$
$422$	0.396584	−	8.83063i	0.0193054	−	0.429868i
$423$	−0.786204	−	0.295067i	−0.0382266	−	0.0143467i
$424$	−8.20398	−	8.58069i	−0.398420	−	0.416715i
$425$	16.4321			0.797076
$426$	−9.29753	−	21.9512i	−0.450467	−	1.06354i
$427$	25.1351			1.21637
$428$	−5.55258	−	5.80754i	−0.268394	−	0.280718i
$429$	0.255193	+	0.0957756i	0.0123208	+	0.00462409i
$430$	−0.308426	+	6.86763i	−0.0148736	+	0.331186i
$431$	−11.0098	−	7.99908i	−0.530323	−	0.385302i	0.290156	−	0.956979i	$-0.406293\pi$
$431$	−11.0098	−	7.99908i	−0.530323	−	0.385302i	−0.820478	+	0.571677i	$0.806293\pi$
$432$	−10.6435	−	24.9017i	−0.512085	−	1.19808i
$433$	1.54692	−	11.4198i	0.0743404	−	0.548803i	−0.915030	−	0.403386i	$-0.867833\pi$
$433$	1.54692	−	11.4198i	0.0743404	−	0.548803i	0.989370	−	0.145417i	$-0.0464524\pi$
$434$	−28.1663	+	24.6082i	−1.35203	+	1.18123i
$435$	−9.71553	−	8.48820i	−0.465824	−	0.406978i
$436$	0.440211	+	3.24977i	0.0210823	+	0.155636i
$437$	2.11923	−	1.26618i	0.101376	−	0.0605695i
$438$	−13.1391	+	30.7406i	−0.627813	+	1.46884i
$439$	−27.0118	−	16.1388i	−1.28920	−	0.770263i	−0.305870	−	0.952073i	$-0.598947\pi$
$439$	−27.0118	−	16.1388i	−1.28920	−	0.770263i	−0.983334	+	0.181810i	$0.941804\pi$
$440$	1.34468	−	0.976964i	0.0641049	−	0.0465749i
$441$	−0.251604	−	0.381164i	−0.0119811	−	0.0181507i
$442$	−3.65347	−	0.328818i	−0.173778	−	0.0156403i
$443$	−4.87006	+	14.9885i	−0.231384	+	0.712126i	0.766197	+	0.642606i	$0.222147\pi$
$443$	−4.87006	+	14.9885i	−0.231384	+	0.712126i	−0.997581	+	0.0695199i	$0.977853\pi$
$444$	−0.495621	−	11.0359i	−0.0235211	−	0.523739i
$445$	−5.80587	+	8.79552i	−0.275225	+	0.416948i
$446$	6.21484	−	7.79316i	0.294281	−	0.369017i
$447$	0.412535	−	0.766619i	0.0195122	−	0.0362598i
$448$	−3.11075	−	0.858512i	−0.146969	−	0.0405609i
$449$	28.6752	+	13.8092i	1.35327	+	0.651699i	0.963125	−	0.269056i	$-0.0867117\pi$
$449$	28.6752	+	13.8092i	1.35327	+	0.651699i	0.390142	+	0.920755i	$0.372426\pi$
$450$	1.07373	−	0.402978i	0.0506162	−	0.0189966i
$451$	1.91706	+	5.90010i	0.0902707	+	0.277825i
$452$	−2.38966	−	10.4698i	−0.112400	−	0.492457i
$453$	9.95709	+	18.5034i	0.467825	+	0.869365i
$454$	7.17036	+	1.30123i	0.336522	+	0.0610697i
$455$	−1.09600	+	0.302477i	−0.0513813	+	0.0141803i
$456$	2.55864	−	11.2101i	0.119819	−	0.524963i
$457$	−21.6227	+	1.94608i	−1.01147	+	0.0910336i	−0.582956	−	0.812503i	$-0.698104\pi$
$457$	−21.6227	+	1.94608i	−1.01147	+	0.0910336i	−0.428510	+	0.903537i	$0.640961\pi$
$458$	23.3700	+	29.3050i	1.09201	+	1.36933i
$459$	38.5296	−	6.99209i	1.79841	−	0.326363i
$460$	0.901968	−	0.434365i	0.0420545	−	0.0202524i
$461$	0.295009	−	0.308556i	0.0137400	−	0.0143709i	−0.715889	−	0.698214i	$-0.753978\pi$
$461$	0.295009	−	0.308556i	0.0137400	−	0.0143709i	0.729629	+	0.683843i	$0.239693\pi$
$462$	2.56049	−	2.67806i	0.119125	−	0.124595i
$463$	4.29960	−	2.07058i	0.199819	−	0.0962279i	−0.331298	−	0.943526i	$-0.607487\pi$
$463$	4.29960	−	2.07058i	0.199819	−	0.0962279i	0.531117	+	0.847298i	$0.321772\pi$
$464$	−23.3557	+	4.23844i	−1.08426	+	0.196765i
$465$	15.7898	+	19.7997i	0.732233	+	0.918191i
$466$	−18.1317	+	1.63188i	−0.839935	+	0.0755956i
$467$	−1.88907	+	8.27656i	−0.0874158	+	0.382993i	−0.999644	−	0.0266894i	$-0.991503\pi$
$467$	−1.88907	+	8.27656i	−0.0874158	+	0.382993i	0.912228	+	0.409683i	$0.134361\pi$
$468$	−0.0798839	+	0.0220466i	−0.00369264	+	0.00101910i
$469$	−9.68811	−	1.75813i	−0.447355	−	0.0811830i
$470$	−3.85203	−	7.15827i	−0.177681	−	0.330187i
$471$	3.58680	+	15.7148i	0.165271	+	0.724100i
$472$	5.39236	+	16.5960i	0.248204	+	0.763892i
$473$	1.27240	−	0.477538i	0.0585048	−	0.0219572i
$474$	−31.2289	−	15.0390i	−1.43439	−	0.690765i
$475$	8.54199	+	2.35744i	0.391933	+	0.108167i
$476$	−7.64823	+	14.2128i	−0.350556	+	0.651443i
$477$	1.21074	−	1.51822i	0.0554361	−	0.0695147i
$478$	−12.2169	+	18.5078i	−0.558788	+	0.846528i
$479$	−0.880024	−	19.5953i	−0.0402093	−	0.895331i	−0.913180	−	0.407557i	$-0.866381\pi$
$479$	−0.880024	−	19.5953i	−0.0402093	−	0.895331i	0.872970	−	0.487773i	$-0.162191\pi$
$480$	4.20450	−	12.9401i	0.191908	−	0.590633i
$481$	2.06208	+	0.185590i	0.0940227	+	0.00846220i
$482$	18.5659	+	28.1261i	0.845651	+	1.28111i
$483$	−1.96686	+	1.42901i	−0.0894954	+	0.0650222i
$484$	−8.77994	−	5.24577i	−0.399088	−	0.238444i
$485$	−8.58801	+	20.0927i	−0.389961	+	0.912360i
$486$	4.48340	−	2.67871i	0.203371	−	0.121509i
$487$	−2.52924	−	18.6716i	−0.114611	−	0.846091i	−0.953416	−	0.301659i	$-0.902460\pi$
$487$	−2.52924	−	18.6716i	−0.114611	−	0.846091i	0.838805	−	0.544432i	$-0.183255\pi$
$488$	−14.5491	−	12.7112i	−0.658608	−	0.575409i
$489$	−20.8969	+	18.2571i	−0.944991	+	0.825614i
$490$	0.593456	−	4.38107i	0.0268096	−	0.197917i
$491$	6.97705	+	16.3236i	0.314870	+	0.736674i	0.999966	+	0.00822205i	$0.00261719\pi$
$491$	6.97705	+	16.3236i	0.314870	+	0.736674i	−0.685096	+	0.728452i	$0.740240\pi$
$492$	14.0802	+	10.2298i	0.634782	+	0.461196i
$493$	1.53993	−	34.2893i	0.0693552	−	1.54431i
$494$	−1.85202	−	0.695076i	−0.0833265	−	0.0312730i
$495$	0.187885	+	0.196513i	0.00844482	+	0.00883259i
$496$	46.5957			2.09221
$497$	2.70255	−	19.4717i	0.121226	−	0.873426i
$498$	−35.1466			−1.57496
$499$	−2.88112	−	3.01341i	−0.128977	−	0.134899i	0.655153	−	0.755497i	$-0.272604\pi$
$499$	−2.88112	−	3.01341i	−0.128977	−	0.134899i	−0.784129	+	0.620598i	$0.786890\pi$
$500$	10.7631	+	4.03944i	0.481339	+	0.180649i
$501$	−0.0255229	+	0.568311i	−0.00114028	+	0.0253903i
$502$	15.3110	+	11.1241i	0.683363	+	0.496492i
$503$	−2.65090	−	6.20210i	−0.118198	−	0.276538i	0.849974	−	0.526825i	$-0.176618\pi$
$503$	−2.65090	−	6.20210i	−0.118198	−	0.276538i	−0.968172	+	0.250287i	$0.919475\pi$
$504$	0.164729	−	1.21608i	0.00733762	−	0.0541685i
$505$	5.12293	−	4.47577i	0.227967	−	0.199169i
$506$	−0.460454	−	0.402286i	−0.0204697	−	0.0178838i
$507$	−2.85168	−	21.0520i	−0.126648	−	0.934951i
$508$	−3.53612	+	2.11273i	−0.156890	+	0.0937373i
$509$	4.21552	−	9.86270i	0.186850	−	0.437157i	−0.799746	−	0.600338i	$-0.795033\pi$
$509$	4.21552	−	9.86270i	0.186850	−	0.437157i	0.986596	+	0.163181i	$0.0521756\pi$
$510$	28.9831	+	17.3166i	1.28339	+	0.766792i
$511$	−22.3030	+	16.2041i	−0.986628	+	0.716828i
$512$	−3.91590	−	5.93234i	−0.173060	−	0.262175i
$513$	21.0321	+	1.89293i	0.928591	+	0.0835747i
$514$	1.52511	−	4.69380i	0.0672697	−	0.207035i
$515$	−0.178903	−	3.98358i	−0.00788340	−	0.175538i
$516$	2.10041	−	3.18199i	0.0924655	−	0.140079i
$517$	−1.00197	+	1.25643i	−0.0440666	+	0.0552577i
$518$	13.3363	−	24.7831i	0.585965	−	1.08890i
$519$	19.2925	+	5.32440i	0.846849	+	0.233715i
$520$	0.787372	+	0.379178i	0.0345286	+	0.0166281i
$521$	19.0593	−	7.15306i	0.835001	−	0.313381i	0.102997	−	0.994682i	$-0.467157\pi$
$521$	19.0593	−	7.15306i	0.835001	−	0.313381i	0.732004	+	0.681300i	$0.238585\pi$
$522$	−0.740279	−	2.27835i	−0.0324011	−	0.0997205i
$523$	−7.70159	−	33.7429i	−0.336767	−	1.47547i	−0.805744	−	0.592263i	$-0.798235\pi$
$523$	−7.70159	−	33.7429i	−0.336767	−	1.47547i	0.468977	−	0.883210i	$-0.344623\pi$
$524$	−8.08257	−	15.0199i	−0.353089	−	0.656149i
$525$	−8.58651	−	1.55822i	−0.374746	−	0.0680064i
$526$	2.58280	−	0.712807i	0.112615	−	0.0310799i
$527$	−14.9928	+	65.6878i	−0.653097	+	2.86141i
$528$	−4.59732	+	0.413766i	−0.200073	+	0.0180069i
$529$	−14.0901	−	17.6685i	−0.612614	−	0.768194i
$530$	18.4956	−	3.35645i	0.803397	−	0.145795i
$531$	−2.57171	+	1.23847i	−0.111603	+	0.0537451i
$532$	−6.01486	+	6.29105i	−0.260777	+	0.272752i
$533$	−2.25414	+	2.35764i	−0.0976376	+	0.102121i
$534$	16.2694	−	7.83494i	0.704047	−	0.339051i
$535$	−13.6373	+	2.47480i	−0.589592	+	0.106995i
$536$	4.71872	+	5.91709i	0.203818	+	0.255579i
$537$	9.66888	−	0.870215i	0.417243	−	0.0375526i
$538$	2.65948	−	11.6519i	0.114658	−	0.502351i
$539$	−0.842523	+	0.232522i	−0.0362900	+	0.0100154i
$540$	8.42593	+	1.52908i	0.362594	+	0.0658011i
$541$	13.4890	+	25.0667i	0.579937	+	1.07770i	0.986451	+	0.164058i	$0.0524586\pi$
$541$	13.4890	+	25.0667i	0.579937	+	1.07770i	−0.406514	+	0.913645i	$0.633256\pi$
$542$	−6.52276	−	28.5781i	−0.280177	−	1.22753i
$543$	4.11993	+	12.6799i	0.176803	+	0.544144i
$544$	33.8909	−	12.7195i	1.45306	−	0.545342i
$545$	5.09680	+	2.45449i	0.218323	+	0.105139i
$546$	1.87792	+	0.518272i	0.0803674	+	0.0221800i
$547$	18.3444	−	34.0897i	0.784351	−	1.45757i	−0.102113	−	0.994773i	$-0.532560\pi$
$547$	18.3444	−	34.0897i	0.784351	−	1.45757i	0.886465	−	0.462796i	$-0.153154\pi$
$548$	5.48940	−	6.88349i	0.234495	−	0.294048i
$549$	1.74095	−	2.63743i	0.0743020	−	0.112563i
$550$	−0.0984672	−	2.19254i	−0.00419865	−	0.0934903i
$551$	5.71983	−	17.6038i	0.243673	−	0.749949i
$552$	1.86116	+	0.167508i	0.0792164	+	0.00712960i
$553$	−15.7462	−	23.8545i	−0.669598	−	1.01440i
$554$	30.4465	−	22.1207i	1.29355	−	0.939817i
$555$	−16.3586	−	9.77378i	−0.694382	−	0.414874i
$556$	−0.820714	+	1.92015i	−0.0348060	+	0.0814327i
$557$	−29.8992	+	17.8640i	−1.26687	+	0.756921i	−0.979606	−	0.200930i	$-0.935604\pi$
$557$	−29.8992	+	17.8640i	−1.26687	+	0.756921i	−0.287266	+	0.957851i	$0.592746\pi$
$558$	0.631233	+	4.65995i	0.0267222	+	0.197271i
$559$	0.538126	+	0.470147i	0.0227603	+	0.0198851i
$560$	14.4997	−	12.6680i	0.612725	−	0.535321i
$561$	0.895950	−	6.61417i	0.0378270	−	0.279250i
$562$	−7.40211	−	17.3181i	−0.312239	−	0.730520i
$563$	−12.8314	−	9.32254i	−0.540778	−	0.392898i	0.283596	−	0.958944i	$-0.408473\pi$
$563$	−12.8314	−	9.32254i	−0.540778	−	0.392898i	−0.824374	+	0.566046i	$0.808473\pi$
$564$	−0.202268	+	4.50385i	−0.00851703	+	0.189646i
$565$	−17.3435	−	6.50912i	−0.729647	−	0.273841i
$566$	−13.2659	−	13.8750i	−0.557607	−	0.583211i
$567$	−18.7434			−0.787150
$568$	−11.4115	+	9.90422i	−0.478814	+	0.415572i
$569$	13.2828			0.556845			0.278423	−	0.960459i	$-0.410188\pi$
$569$	13.2828			0.556845			0.278423	+	0.960459i	$0.410188\pi$
$570$	12.5821	+	13.1598i	0.527005	+	0.551204i
$571$	−36.3974	−	13.6602i	−1.52318	−	0.571661i	−0.557226	−	0.830361i	$-0.688134\pi$
$571$	−36.3974	−	13.6602i	−1.52318	−	0.571661i	−0.965958	+	0.258700i	$0.916706\pi$
$572$	−0.00711508	+	0.158429i	−0.000297496	+	0.00662427i
$573$	−34.9172	−	25.3688i	−1.45869	−	1.05980i
$574$	17.4263	+	40.7708i	0.727359	+	1.70174i
$575$	−0.193311	+	1.42708i	−0.00806163	+	0.0595134i
$576$	−0.305546	+	0.266947i	−0.0127311	+	0.0111228i
$577$	−34.7152	−	30.3297i	−1.44521	−	1.26264i	−0.907852	−	0.419291i	$-0.862279\pi$
$577$	−34.7152	−	30.3297i	−1.44521	−	1.26264i	−0.537360	−	0.843353i	$-0.680578\pi$
$578$	8.13329	+	60.0424i	0.338300	+	2.49743i
$579$	18.3589	−	10.9689i	0.762970	−	0.455853i
$580$	2.95012	−	6.90215i	0.122497	−	0.286596i
$581$	−24.8804	−	14.8653i	−1.03221	−	0.616719i
$582$	30.2897	−	22.0068i	1.25555	−	0.912210i
$583$	−2.04723	−	3.10143i	−0.0847878	−	0.128448i
$584$	21.1045	+	1.89944i	0.873309	+	0.0785992i
$585$	−0.0441742	+	0.135954i	−0.00182638	+	0.00562101i
$586$	0.753221	+	16.7718i	0.0311153	+	0.692835i
$587$	−1.74543	+	2.64421i	−0.0720414	+	0.109138i	−0.868808	−	0.495149i	$-0.835113\pi$
$587$	−1.74543	+	2.64421i	−0.0720414	+	0.109138i	0.796767	+	0.604287i	$0.206542\pi$
$588$	−1.52879	+	1.91704i	−0.0630462	+	0.0790575i
$589$	−17.2177	+	31.9958i	−0.709443	+	1.31837i
$590$	−26.6351	−	7.35081i	−1.09655	−	0.302628i
$591$	28.8089	+	13.8736i	1.18504	+	0.570685i
$592$	−32.8257	+	12.3197i	−1.34913	+	0.506337i
$593$	8.42362	+	25.9252i	0.345917	+	1.06462i	0.961091	+	0.276231i	$0.0890855\pi$
$593$	8.42362	+	25.9252i	0.345917	+	1.06462i	−0.615175	+	0.788391i	$0.710914\pi$
$594$	−1.16384	−	5.09911i	−0.0477529	−	0.209219i
$595$	13.1931	+	24.5170i	0.540866	+	1.00510i
$596$	0.498375	+	0.0904418i	0.0204142	+	0.00370464i
$597$	−10.4004	+	2.87032i	−0.425659	+	0.117474i
$598$	0.0715370	−	0.313424i	0.00292537	−	0.0128169i
$599$	17.2911	−	1.55623i	0.706496	−	0.0635857i	0.269436	−	0.963018i	$-0.413163\pi$
$599$	17.2911	−	1.55623i	0.706496	−	0.0635857i	0.437060	+	0.899433i	$0.356020\pi$
$600$	4.18217	+	5.24427i	0.170736	+	0.214097i
$601$	−21.5438	+	3.90962i	−0.878788	+	0.159477i	−0.599158	−	0.800631i	$-0.704498\pi$
$601$	−21.5438	+	3.90962i	−0.878788	+	0.159477i	−0.279631	+	0.960108i	$0.590212\pi$
$602$	8.75142	−	4.21446i	0.356681	−	0.171769i
$603$	−0.855515	+	0.894799i	−0.0348393	+	0.0364390i
$604$	−8.44853	+	8.83647i	−0.343766	+	0.359551i
$605$	−15.8955	+	7.65486i	−0.646243	+	0.311214i
$606$	−11.4686	+	2.08125i	−0.465881	+	0.0845449i
$607$	4.53568	+	5.68757i	0.184098	+	0.230851i	0.865313	−	0.501232i	$-0.167120\pi$
$607$	4.53568	+	5.68757i	0.184098	+	0.230851i	−0.681215	+	0.732083i	$0.738548\pi$
$608$	19.4424	−	1.74985i	0.788495	−	0.0709658i
$609$	−4.05626	+	17.7716i	−0.164368	+	0.720143i
$610$	29.4889	−	8.13841i	1.19397	−	0.329514i
$611$	−0.831380	−	0.150873i	−0.0336340	−	0.00610367i
$612$	0.961604	+	1.78696i	0.0388706	+	0.0722336i
$613$	4.96799	+	21.7662i	0.200655	+	0.879129i	0.970539	+	0.240944i	$0.0774571\pi$
$613$	4.96799	+	21.7662i	0.200655	+	0.879129i	−0.769884	+	0.638184i	$0.779686\pi$
$614$	9.07959	+	27.9441i	0.366423	+	1.12773i
$615$	28.1074	−	10.5489i	1.13340	−	0.425373i
$616$	−2.11590	−	1.01896i	−0.0852519	−	0.0410551i
$617$	9.34586	+	2.57929i	0.376250	+	0.103838i	0.449046	−	0.893508i	$-0.351764\pi$
$617$	9.34586	+	2.57929i	0.376250	+	0.103838i	−0.0727964	+	0.997347i	$0.523192\pi$
$618$	−3.23768	+	6.01662i	−0.130239	+	0.242024i
$619$	−24.1302	+	30.2583i	−0.969875	+	1.21618i	0.00647334	+	0.999979i	$0.497939\pi$
$619$	−24.1302	+	30.2583i	−0.969875	+	1.21618i	−0.976348	+	0.216205i	$0.930632\pi$
$620$	−8.11719	+	12.2970i	−0.325994	+	0.493860i
$621$	0.153971	+	3.42843i	0.00617865	+	0.137578i
$622$	−15.4289	+	47.4853i	−0.618644	+	1.90399i
$623$	14.8310	+	1.33481i	0.594191	+	0.0534781i
$624$	−1.33702	−	2.02550i	−0.0535236	−	0.0810848i
$625$	6.84641	−	4.97421i	0.273856	−	0.198968i
$626$	−34.1763	−	20.4194i	−1.36596	−	0.816123i
$627$	1.41465	−	3.30973i	0.0564956	−	0.132178i
$628$	−8.05082	+	4.81014i	−0.321263	+	0.191945i
$629$	−6.80545	−	50.2398i	−0.271351	−	2.00319i
$630$	1.46333	+	1.27848i	0.0583006	+	0.0509357i
$631$	26.6092	−	23.2478i	1.05930	−	0.925480i	0.0619355	−	0.998080i	$-0.480273\pi$
$631$	26.6092	−	23.2478i	1.05930	−	0.925480i	0.997361	+	0.0726006i	$0.0231298\pi$
$632$	−2.94907	+	21.7709i	−0.117308	+	0.866002i
$633$	3.32373	+	7.77626i	0.132107	+	0.309079i
$634$	−10.5119	−	7.63734i	−0.417481	−	0.303318i
$635$	−0.318790	+	7.09842i	−0.0126508	+	0.281692i
$636$	−9.76065	−	3.66323i	−0.387035	−	0.145257i
$637$	−0.317577	−	0.332160i	−0.0125829	−	0.0131606i
$638$	−4.58445			−0.181500
$639$	−1.85598	−	1.63226i	−0.0734214	−	0.0645713i
$640$	−20.4679			−0.809063
$641$	1.05651	+	1.10502i	0.0417295	+	0.0436456i	0.743330	−	0.668925i	$-0.233245\pi$
$641$	1.05651	+	1.10502i	0.0417295	+	0.0436456i	−0.701601	+	0.712570i	$0.747531\pi$
$642$	22.2338	+	8.34449i	0.877499	+	0.329331i
$643$	−0.489994	+	10.9106i	−0.0193235	+	0.430271i	0.965891	+	0.258948i	$0.0833757\pi$
$643$	−0.489994	+	10.9106i	−0.0193235	+	0.430271i	−0.985215	+	0.171323i	$0.945196\pi$
$644$	−1.14436	−	0.831428i	−0.0450942	−	0.0327629i
$645$	−2.58489	−	6.04764i	−0.101780	−	0.238126i
$646$	−6.50221	+	48.0013i	−0.255826	+	1.88858i
$647$	−14.6567	+	12.8052i	−0.576216	+	0.503425i	−0.895993	−	0.444068i	$-0.853535\pi$
$647$	−14.6567	+	12.8052i	−0.576216	+	0.503425i	0.319777	+	0.947493i	$0.396392\pi$
$648$	10.8494	+	9.47881i	0.426204	+	0.372363i
$649$	0.733241	+	5.41300i	0.0287822	+	0.212479i
$650$	0.990627	−	0.591872i	0.0388556	−	0.0232151i
$651$	14.0634	−	32.9030i	0.551189	−	1.28957i
$652$	−13.8596	−	8.28070i	−0.542782	−	0.324297i
$653$	37.5893	−	27.3102i	1.47098	−	1.06873i	0.490657	−	0.871353i	$-0.336757\pi$
$653$	37.5893	−	27.3102i	1.47098	−	1.06873i	0.980327	−	0.197379i	$-0.0632430\pi$
$654$	−5.33978	−	8.08942i	−0.208802	−	0.316321i
$655$	−29.3040	−	2.63740i	−1.14500	−	0.103052i
$656$	17.0694	−	52.5342i	0.666448	−	2.05112i
$657$	0.155506	+	3.46261i	0.00606687	+	0.135089i
$658$	−6.32742	+	9.58564i	−0.246669	+	0.373687i
$659$	15.8985	−	19.9361i	0.619318	−	0.776600i	−0.368930	−	0.929457i	$-0.620276\pi$
$659$	15.8985	−	19.9361i	0.619318	−	0.776600i	0.988248	+	0.152857i	$0.0488473\pi$
$660$	0.691679	−	1.28536i	0.0269236	−	0.0500324i
$661$	3.60872	+	0.995945i	0.140363	+	0.0387378i	0.335512	−	0.942036i	$-0.391091\pi$
$661$	3.60872	+	0.995945i	0.140363	+	0.0387378i	−0.195149	+	0.980774i	$0.562519\pi$
$662$	−24.1025	−	11.6071i	−0.936769	−	0.451124i
$663$	3.28563	−	1.23312i	0.127603	−	0.0478903i
$664$	6.88406	+	21.1870i	0.267154	+	0.822214i
$665$	3.34092	+	14.6375i	0.129555	+	0.567618i
$666$	−1.67676	−	3.11595i	−0.0649732	−	0.120740i
$667$	2.95980	+	0.537125i	0.114604	+	0.0207976i
$668$	−0.319061	+	0.0880552i	−0.0123448	+	0.00340696i
$669$	−2.12201	+	9.29715i	−0.0820418	+	0.359449i
$670$	−11.9355	+	1.07421i	−0.461108	+	0.0415004i
$671$	−3.77068	−	4.72829i	−0.145566	−	0.182534i
$672$	−18.9156	+	3.43268i	−0.729686	+	0.132418i
$673$	−39.8333	+	19.1827i	−1.53546	+	0.739438i	−0.994804	−	0.101806i	$-0.967538\pi$
$673$	−39.8333	+	19.1827i	−1.53546	+	0.739438i	−0.540655	+	0.841244i	$0.681824\pi$
$674$	7.03824	−	7.36142i	0.271103	−	0.283551i
$675$	−8.51308	+	8.90398i	−0.327668	+	0.342714i
$676$	11.1363	−	5.36295i	0.428319	−	0.206267i
$677$	38.4002	−	6.96861i	1.47584	−	0.267826i	0.619810	−	0.784752i	$-0.287210\pi$
$677$	38.4002	−	6.96861i	1.47584	−	0.267826i	0.856030	+	0.516926i	$0.172924\pi$
$678$	19.7900	+	24.8159i	0.760031	+	0.953049i
$679$	30.7500	−	2.76755i	1.18008	−	0.106209i
$680$	4.76190	−	20.8633i	0.182611	−	0.800069i
$681$	−6.72069	+	1.85479i	−0.257537	+	0.0710758i
$682$	8.85457	+	1.60687i	0.339059	+	0.0615302i
$683$	−14.4319	−	26.8190i	−0.552221	−	1.02620i	−0.991776	−	0.127983i	$-0.959150\pi$
$683$	−14.4319	−	26.8190i	−0.552221	−	1.02620i	0.439555	−	0.898216i	$-0.355136\pi$
$684$	0.243508	+	1.06688i	0.00931078	+	0.0407932i
$685$	−4.69315	−	14.4440i	−0.179316	−	0.551878i
$686$	−32.1415	+	12.0629i	−1.22717	+	0.460565i
$687$	−32.3084	−	15.5589i	−1.23264	−	0.593609i
$688$	−11.6649	−	3.21930i	−0.444720	−	0.122735i
$689$	0.925903	−	1.72062i	0.0352741	−	0.0655502i
$690$	−1.84486	+	2.31338i	−0.0702325	+	0.0880687i
$691$	−25.9956	+	39.3816i	−0.988918	+	1.49815i	−0.126490	+	0.991968i	$0.540371\pi$
$691$	−25.9956	+	39.3816i	−0.988918	+	1.49815i	−0.862428	+	0.506179i	$0.831058\pi$
$692$	0.522426	+	11.6327i	0.0198596	+	0.442209i
$693$	0.118709	−	0.365348i	0.00450937	−	0.0138784i
$694$	−3.54359	−	0.318929i	−0.134513	−	0.0121064i
$695$	1.98440	+	3.00623i	0.0752725	+	0.114033i
$696$	11.3353	−	8.23556i	0.429662	−	0.312168i
$697$	68.5673	+	40.9670i	2.59717	+	1.55174i
$698$	−2.32585	+	5.44160i	−0.0880348	+	0.205968i
$699$	14.9514	−	8.93305i	0.565514	−	0.337879i
$700$	−0.681557	−	5.03145i	−0.0257604	−	0.190171i
$701$	17.7958	+	15.5477i	0.672138	+	0.587229i	0.924859	−	0.380310i	$-0.124183\pi$
$701$	17.7958	+	15.5477i	0.672138	+	0.587229i	−0.252721	+	0.967539i	$0.581325\pi$
$702$	2.07094	−	1.80933i	0.0781628	−	0.0682888i
$703$	3.66996	−	27.0927i	0.138415	−	1.02182i
$704$	0.305165	+	0.713968i	0.0115013	+	0.0269087i
$705$	6.29167	+	4.57117i	0.236958	+	0.172160i
$706$	0.962788	−	21.4381i	0.0362350	−	0.806835i
$707$	−8.99895	−	3.37736i	−0.338440	−	0.127019i
$708$	10.5901	+	11.0764i	0.398001	+	0.416277i
$709$	−40.7976			−1.53218			−0.766092	−	0.642731i	$-0.777801\pi$
$709$	−40.7976			−1.53218			−0.766092	+	0.642731i	$0.777801\pi$
$710$	−3.13400	−	23.7195i	−0.117617	−	0.890178i
$711$	−3.59370			−0.134774
$712$	−7.90968	−	8.27288i	−0.296428	−	0.310039i
$713$	−5.52840	−	2.07485i	−0.207040	−	0.0777036i
$714$	2.14023	−	47.6560i	0.0800962	−	1.78348i
$715$	0.221319	+	0.160797i	0.00827685	+	0.00601348i
$716$	2.21992	+	5.19376i	0.0829624	+	0.194100i
$717$	2.84792	−	21.0242i	0.106357	−	0.785162i
$718$	34.9323	−	30.5194i	1.30366	−	1.13897i
$719$	21.3872	+	18.6854i	0.797607	+	0.696848i	0.956911	−	0.290382i	$-0.0937823\pi$
$719$	21.3872	+	18.6854i	0.797607	+	0.696848i	−0.159304	+	0.987230i	$0.550925\pi$
$720$	−0.324952	−	2.39889i	−0.0121102	−	0.0894013i
$721$	−4.83671	+	2.88980i	−0.180129	+	0.107622i
$722$	2.57489	−	6.02425i	0.0958274	−	0.224199i
$723$	−27.6781	−	16.5369i	−1.02936	−	0.615013i
$724$	−6.27559	+	4.55948i	−0.233231	+	0.169452i
$725$	5.94847	+	9.01155i	0.220921	+	0.334680i
$726$	30.1077	+	2.70974i	1.11740	+	0.100568i
$727$	13.3463	−	41.0758i	0.494988	−	1.52342i	−0.321987	−	0.946744i	$-0.604351\pi$
$727$	13.3463	−	41.0758i	0.494988	−	1.52342i	0.816975	−	0.576673i	$-0.195649\pi$
$728$	−0.0553989	−	1.23355i	−0.00205322	−	0.0457185i
$729$	−16.0303	+	24.2848i	−0.593713	+	0.899437i
$730$	−20.9195	+	26.2323i	−0.774267	+	0.970900i
$731$	8.29173	−	15.4086i	0.306681	−	0.569908i
$732$	−16.3549	−	4.51367i	−0.604495	−	0.166830i
$733$	−12.3009	−	5.92378i	−0.454343	−	0.218800i	0.192694	−	0.981259i	$-0.438278\pi$
$733$	−12.3009	−	5.92378i	−0.454343	−	0.218800i	−0.647037	+	0.762459i	$0.723992\pi$
$734$	33.3628	−	12.5213i	1.23144	−	0.462168i
$735$	1.30704	+	4.02264i	0.0482107	+	0.148377i
$736$	0.705946	+	3.09295i	0.0260215	+	0.114008i
$737$	1.12265	+	2.08623i	0.0413532	+	0.0768471i
$738$	5.48509	+	0.995397i	0.201909	+	0.0366411i
$739$	41.6053	−	11.4823i	1.53048	−	0.422385i	0.603457	−	0.797396i	$-0.293790\pi$
$739$	41.6053	−	11.4823i	1.53048	−	0.422385i	0.927020	+	0.375011i	$0.122361\pi$
$740$	2.46712	−	10.8092i	0.0906932	−	0.397353i
$741$	1.88489	−	0.169643i	0.0692433	−	0.00623201i
$742$	−16.5599	−	20.7655i	−0.607933	−	0.762324i
$743$	34.4429	−	6.25046i	1.26359	−	0.229307i	0.494909	−	0.868945i	$-0.335201\pi$
$743$	34.4429	−	6.25046i	1.26359	−	0.229307i	0.768677	+	0.639637i	$0.220916\pi$
$744$	−24.7799	+	11.9334i	−0.908477	+	0.437499i
$745$	0.603805	−	0.631530i	0.0221217	−	0.0231375i
$746$	−20.1009	+	21.0239i	−0.735946	+	0.769740i
$747$	−3.28313	+	1.58107i	−0.120123	+	0.0578484i
$748$	3.82100	−	0.693409i	0.139710	−	0.0253535i
$749$	12.2101	+	15.3109i	0.446146	+	0.559450i
$750$	−33.8416	+	3.04580i	−1.23572	+	0.111217i
$751$	3.03349	−	13.2906i	0.110694	−	0.484980i	−0.888943	−	0.458018i	$-0.848560\pi$
$751$	3.03349	−	13.2906i	0.110694	−	0.484980i	0.999636	−	0.0269621i	$-0.00858334\pi$
$752$	13.7933	−	3.80671i	0.502990	−	0.138816i
$753$	−17.8150	−	3.23295i	−0.649215	−	0.117815i
$754$	−1.14224	−	2.12263i	−0.0415978	−	0.0773017i
$755$	4.69269	+	20.5600i	0.170784	+	0.748255i
$756$	−3.73905	−	11.5076i	−0.135988	−	0.418527i
$757$	15.6990	−	5.89192i	0.570589	−	0.214146i	−0.0493691	−	0.998781i	$-0.515721\pi$
$757$	15.6990	−	5.89192i	0.570589	−	0.214146i	0.619958	+	0.784635i	$0.287150\pi$
$758$	−38.2362	−	18.4136i	−1.38880	−	0.668811i
$759$	0.563880	+	0.155621i	0.0204675	+	0.00564868i
$760$	5.46855	−	10.1623i	0.198365	−	0.368624i
$761$	9.36059	−	11.7378i	0.339321	−	0.425495i	−0.582668	−	0.812710i	$-0.697991\pi$
$761$	9.36059	−	11.7378i	0.339321	−	0.425495i	0.921990	+	0.387215i	$0.126563\pi$
$762$	6.70709	−	10.1608i	0.242972	−	0.368087i
$763$	−0.358607	−	7.98500i	−0.0129824	−	0.289076i
$764$	7.75984	−	23.8823i	0.280741	−	0.864033i
$765$	3.48637	+	0.313779i	0.126050	+	0.0113447i
$766$	0.405786	+	0.614739i	0.0146616	+	0.0222114i
$767$	−2.32356	+	1.68817i	−0.0838991	+	0.0609562i
$768$	26.1989	+	15.6531i	0.945371	+	0.564833i
$769$	8.32189	−	19.4700i	0.300095	−	0.702107i	−0.699831	−	0.714309i	$-0.746741\pi$
$769$	8.32189	−	19.4700i	0.300095	−	0.702107i	0.999926	+	0.0122017i	$0.00388403\pi$
$770$	3.19224	−	1.90728i	0.115040	−	0.0687335i
$771$	0.633805	+	4.67893i	0.0228259	+	0.168508i
$772$	9.37039	+	8.18666i	0.337248	+	0.294644i
$773$	−8.92196	+	7.79488i	−0.320901	+	0.280362i	−0.803282	−	0.595599i	$-0.796915\pi$
$773$	−8.92196	+	7.79488i	−0.320901	+	0.280362i	0.482381	+	0.875961i	$0.339772\pi$
$774$	0.163932	−	1.21020i	0.00589242	−	0.0434996i
$775$	−8.33050	−	19.4902i	−0.299240	−	0.700108i
$776$	−19.1988	−	13.9487i	−0.689197	−	0.500731i
$777$	−1.20798	+	26.8978i	−0.0433362	+	0.964955i
$778$	19.9057	+	7.47074i	0.713654	+	0.267839i
$779$	29.7663	+	31.1331i	1.06649	+	1.11546i
$780$	0.767462			0.0274796
$781$	−4.06834	+	2.41269i	−0.145577	+	0.0863328i
$782$	−7.87226			−0.281511
$783$	17.7823	+	18.5989i	0.635489	+	0.664669i
$784$	7.28600	+	2.73448i	0.260214	+	0.0976601i
$785$	−0.725802	+	16.1612i	−0.0259050	+	0.576820i
$786$	40.7850	+	29.6321i	1.45475	+	1.05694i
$787$	−12.3856	−	28.9775i	−0.441498	−	1.03293i	−0.981533	−	0.191293i	$-0.938732\pi$
$787$	−12.3856	−	28.9775i	−0.441498	−	1.03293i	0.540035	−	0.841642i	$-0.318411\pi$
$788$	−2.49728	+	18.4356i	−0.0889618	+	0.656742i
$789$	−1.93038	+	1.68652i	−0.0687234	+	0.0600419i
$790$	−26.1974	−	22.8880i	−0.932063	−	0.814319i
$791$	3.51347	+	25.9375i	0.124925	+	0.922232i
$792$	−0.253474	+	0.151444i	−0.00900682	+	0.00538133i
$793$	1.24974	−	2.92392i	0.0443797	−	0.103832i
$794$	6.85179	+	4.09375i	0.243161	+	0.145282i
$795$	−14.5492	+	10.5706i	−0.516006	+	0.374900i
$796$	−3.45818	−	5.23892i	−0.122572	−	0.185689i
$797$	−2.32493	−	0.209247i	−0.0823532	−	0.00741192i	0.0483861	−	0.998829i	$-0.484592\pi$
$797$	−2.32493	−	0.209247i	−0.0823532	−	0.00741192i	−0.130739	+	0.991417i	$0.541735\pi$
$798$	7.94954	−	24.4662i	0.281411	−	0.866093i
$799$	0.928284	+	20.6698i	0.0328403	+	0.731246i
$800$	−6.27346	+	9.50388i	−0.221800	+	0.336013i
$801$	1.16731	−	1.46376i	0.0412449	−	0.0517195i
$802$	3.37748	−	6.27641i	0.119263	−	0.221628i
$803$	6.39405	+	1.76465i	0.225641	+	0.0622730i
$804$	5.98813	+	2.88373i	0.211185	+	0.101701i
$805$	−2.28443	+	0.857360i	−0.0805155	+	0.0302180i
$806$	1.46216	+	4.50008i	0.0515026	+	0.158509i
$807$	2.54433	+	11.1474i	0.0895647	+	0.392409i
$808$	3.50094	+	6.50583i	0.123163	+	0.228874i
$809$	−13.3485	−	2.42240i	−0.469308	−	0.0851669i	−0.0612494	−	0.998122i	$-0.519509\pi$
$809$	−13.3485	−	2.42240i	−0.469308	−	0.0851669i	−0.408059	+	0.912956i	$0.633794\pi$
$810$	−21.9900	+	6.06886i	−0.772651	+	0.213238i
$811$	0.515978	−	2.26065i	0.0181184	−	0.0793820i	−0.965060	−	0.262027i	$-0.915609\pi$
$811$	0.515978	−	2.26065i	0.0181184	−	0.0793820i	0.983179	+	0.182645i	$0.0584660\pi$
$812$	−10.5631	+	0.950698i	−0.370693	+	0.0333630i
$813$	17.4850	+	21.9255i	0.613227	+	0.768962i
$814$	−6.66273	+	1.20911i	−0.233528	+	0.0423792i
$815$	−25.0918	+	12.0836i	−0.878927	+	0.423269i
$816$	−41.0699	+	42.9558i	−1.43773	+	1.50375i
$817$	6.52092	−	6.82035i	0.228138	−	0.238614i
$818$	16.0451	−	7.72692i	0.561004	−	0.270165i
$819$	0.198735	−	0.0360651i	0.00694437	−	0.00126022i
$820$	10.8907	+	13.6565i	0.380319	+	0.476905i
$821$	−21.2471	+	1.91227i	−0.741529	+	0.0667388i	−0.453961	−	0.891021i	$-0.649990\pi$
$821$	−21.2471	+	1.91227i	−0.741529	+	0.0667388i	−0.287568	+	0.957760i	$0.592847\pi$
$822$	−5.79053	+	25.3700i	−0.201968	+	0.884879i
$823$	4.37795	−	1.20824i	0.152606	−	0.0421165i	−0.188899	−	0.981996i	$-0.560492\pi$
$823$	4.37795	−	1.20824i	0.152606	−	0.0421165i	0.341505	+	0.939880i	$0.389063\pi$
$824$	4.26108	+	0.773271i	0.148442	+	0.0269382i
$825$	0.994993	+	1.84901i	0.0346412	+	0.0643742i
$826$	8.68739	+	38.0619i	0.302273	+	1.32434i
$827$	−7.27067	−	22.3768i	−0.252826	−	0.778119i	−0.994250	−	0.107082i	$-0.965849\pi$
$827$	−7.27067	−	22.3768i	−0.252826	−	0.778119i	0.741424	−	0.671037i	$-0.234151\pi$
$828$	−0.166505	+	0.0624902i	−0.00578643	+	0.00217168i
$829$	2.97026	+	1.43040i	0.103161	+	0.0496799i	0.484753	−	0.874651i	$-0.338910\pi$
$829$	2.97026	+	1.43040i	0.103161	+	0.0496799i	−0.381591	+	0.924331i	$0.624624\pi$
$830$	−34.0032	−	9.38429i	−1.18027	−	0.325733i
$831$	−17.0614	+	31.7054i	−0.591853	+	1.09985i
$832$	−0.254539	+	0.319181i	−0.00882454	+	0.0110656i
$833$	−6.19929	+	9.39152i	−0.214793	+	0.325397i
$834$	−0.276904	−	6.16575i	−0.00958840	−	0.213502i
$835$	−0.176434	+	0.543008i	−0.00610575	+	0.0187916i
$836$	2.08577	+	0.187722i	0.0721377	+	0.00649251i
$837$	−27.8264	−	42.1553i	−0.961823	−	1.45710i
$838$	48.6968	−	35.3803i	1.68220	−	1.22219i
$839$	−28.7254	−	17.1626i	−0.991710	−	0.592519i	−0.0771717	−	0.997018i	$-0.524589\pi$
$839$	−28.7254	−	17.1626i	−0.991710	−	0.592519i	−0.914539	+	0.404498i	$0.867446\pi$
$840$	−4.46672	+	10.4504i	−0.154116	+	0.360573i
$841$	−5.53296	+	3.30579i	−0.190792	+	0.113993i
$842$	−8.18514	−	60.4252i	−0.282079	−	2.08239i
$843$	13.5690	+	11.8549i	0.467342	+	0.408304i
$844$	−3.70537	+	3.23728i	−0.127544	+	0.111432i
$845$	2.86205	−	21.1285i	0.0984576	−	0.726843i
$846$	0.567560	+	1.32787i	0.0195131	+	0.0456532i
$847$	20.1672	+	14.6524i	0.692954	+	0.503461i
$848$	−1.48452	+	33.0554i	−0.0509786	+	1.13513i
$849$	17.1942	+	6.45307i	0.590102	+	0.221469i
$850$	−19.5278	−	20.4244i	−0.669797	−	0.700552i
$851$	4.44324			0.152312
$852$	−5.25515	+	12.1845i	−0.180038	+	0.417435i
$853$	22.6398			0.775173			0.387587	−	0.921833i	$-0.373309\pi$
$853$	22.6398			0.775173			0.387587	+	0.921833i	$0.373309\pi$
$854$	−29.8703	−	31.2419i	−1.02214	−	1.06908i
$855$	1.76732	+	0.663286i	0.0604410	+	0.0226839i
$856$	0.675327	−	15.0373i	0.0230822	−	0.513966i
$857$	23.2091	+	16.8624i	0.792809	+	0.576009i	0.908796	−	0.417242i	$-0.137003\pi$
$857$	23.2091	+	16.8624i	0.792809	+	0.576009i	−0.115987	+	0.993251i	$0.537003\pi$
$858$	−0.184224	−	0.431013i	−0.00628929	−	0.0147145i
$859$	−4.14641	+	30.6100i	−0.141474	+	1.04440i	0.771456	+	0.636283i	$0.219529\pi$
$859$	−4.14641	+	30.6100i	−0.141474	+	1.04440i	−0.912930	+	0.408117i	$0.866186\pi$
$860$	2.88168	−	2.51765i	0.0982646	−	0.0858512i
$861$	−31.9446	−	27.9091i	−1.08867	−	0.951141i
$862$	3.14139	+	23.1907i	0.106996	+	0.789879i
$863$	−20.0344	+	11.9700i	−0.681980	+	0.407464i	−0.811691	−	0.584088i	$-0.801452\pi$
$863$	−20.0344	+	11.9700i	−0.681980	+	0.407464i	0.129710	+	0.991552i	$0.458595\pi$
$864$	−10.6658	+	24.9539i	−0.362858	+	0.848948i
$865$	17.2433	+	10.3024i	0.586289	+	0.350291i
$866$	−16.0327	+	11.6485i	−0.544814	+	0.395831i
$867$	−31.9340	−	48.3779i	−1.08454	−	1.64300i
$868$	20.7352	+	1.86620i	0.703799	+	0.0633430i
$869$	−2.12519	+	6.54067i	−0.0720922	+	0.221877i
$870$	0.995353	+	22.1633i	0.0337456	+	0.751405i
$871$	−0.686223	+	1.03958i	−0.0232518	+	0.0352250i
$872$	−3.83055	+	4.80336i	−0.129719	+	0.162662i
$873$	1.83946	−	3.41829i	0.0622563	−	0.115692i
$874$	−4.09227	−	1.12939i	−0.138423	−	0.0382023i
$875$	−25.2448	−	12.1573i	−0.853431	−	0.410990i
$876$	17.4220	−	6.53858i	0.588634	−	0.220918i
$877$	2.94023	+	9.04910i	0.0992845	+	0.305566i	0.988347	−	0.152220i	$-0.0486423\pi$
$877$	2.94023	+	9.04910i	0.0992845	+	0.305566i	−0.889062	+	0.457787i	$0.848642\pi$
$878$	12.0407	+	52.7537i	0.406354	+	1.78035i
$879$	−7.61116	−	14.1439i	−0.256718	−	0.477062i
$880$	−4.55824	−	0.827198i	−0.153658	−	0.0278848i
$881$	−15.9743	+	4.40863i	−0.538188	+	0.148531i	−0.524555	−	0.851377i	$-0.675768\pi$
$881$	−15.9743	+	4.40863i	−0.538188	+	0.148531i	−0.0136332	+	0.999907i	$0.504340\pi$
$882$	−0.174767	+	0.765704i	−0.00588471	+	0.0257826i
$883$	−6.18049	+	0.556254i	−0.207990	+	0.0187194i	−0.193144	−	0.981170i	$-0.561869\pi$
$883$	−6.18049	+	0.556254i	−0.207990	+	0.0187194i	−0.0148456	+	0.999890i	$0.504726\pi$
$884$	1.27307	+	1.59638i	0.0428180	+	0.0536921i
$885$	26.0096	−	4.72005i	0.874305	−	0.158663i
$886$	24.4176	−	11.7589i	0.820326	−	0.395048i
$887$	31.9507	−	33.4178i	1.07280	−	1.12206i	0.0806831	−	0.996740i	$-0.474290\pi$
$887$	31.9507	−	33.4178i	1.07280	−	1.12206i	0.992116	−	0.125320i	$-0.0399959\pi$
$888$	14.3018	−	14.9586i	0.479939	−	0.501976i
$889$	9.04552	−	4.35609i	0.303377	−	0.146099i
$890$	17.8321	−	3.23605i	0.597733	−	0.108473i
$891$	2.81182	+	3.52591i	0.0941996	+	0.118123i
$892$	−5.52605	+	0.497353i	−0.185026	+	0.0166526i
$893$	−2.48285	+	10.8781i	−0.0830854	+	0.364021i
$894$	−1.44313	+	0.398278i	−0.0482654	+	0.0133204i
$895$	9.58668	+	1.73973i	0.320447	+	0.0581526i
$896$	13.7042	+	25.4668i	0.457827	+	0.850785i
$897$	0.0684396	+	0.299854i	0.00228513	+	0.0100118i
$898$	−16.9130	−	52.0528i	−0.564393	−	1.73702i
$899$	−41.4513	+	15.5569i	−1.38248	+	0.518852i
$900$	−0.575158	−	0.276981i	−0.0191719	−	0.00923271i
$901$	−46.1219	−	12.7288i	−1.53654	−	0.424059i
$902$	5.05536	−	9.39443i	0.168325	−	0.312800i
$903$	−5.79395	+	7.26539i	−0.192811	+	0.241777i
$904$	11.0832	−	16.7904i	0.368623	−	0.558440i
$905$	0.600330	+	13.3674i	0.0199556	+	0.444347i
$906$	11.1660	−	34.3654i	0.370966	−	1.14172i
$907$	18.1176	+	1.63061i	0.601585	+	0.0541436i	0.386246	−	0.922396i	$-0.373772\pi$
$907$	18.1176	+	1.63061i	0.601585	+	0.0541436i	0.215339	+	0.976539i	$0.430914\pi$
$908$	−2.23467	−	3.38538i	−0.0741601	−	0.112348i
$909$	−0.977687	+	0.710331i	−0.0324278	+	0.0235602i
$910$	1.67844	+	1.00282i	0.0556398	+	0.0332432i
$911$	6.74939	−	15.7910i	0.223617	−	0.523179i	−0.769725	−	0.638375i	$-0.779607\pi$
$911$	6.74939	−	15.7910i	0.223617	−	0.523179i	0.993343	+	0.115196i	$0.0367497\pi$
$912$	−27.5122	+	16.4378i	−0.911020	+	0.544309i
$913$	0.936080	+	6.91042i	0.0309797	+	0.228701i
$914$	28.1150	+	24.5634i	0.929963	+	0.812484i
$915$	−22.0399	+	19.2557i	−0.728618	+	0.636575i
$916$	2.80063	−	20.6750i	0.0925353	−	0.683123i
$917$	16.3389	+	38.2268i	0.539558	+	1.26236i
$918$	−54.4790	−	39.5813i	−1.79808	−	1.30638i
$919$	−2.01246	+	44.8109i	−0.0663850	+	1.47818i	0.638921	+	0.769273i	$0.279381\pi$
$919$	−2.01246	+	44.8109i	−0.0663850	+	1.47818i	−0.705306	+	0.708903i	$0.749190\pi$
$920$	1.75589	+	0.658996i	0.0578900	+	0.0217265i
$921$	−19.4258	−	20.3178i	−0.640101	−	0.669493i
$922$	−0.734107			−0.0241765
$923$	−2.13074	−	1.28254i	−0.0701340	−	0.0422152i
$924$	−2.06239			−0.0678477
$925$	11.0218	+	11.5279i	0.362395	+	0.379035i
$926$	−7.68323	−	2.88356i	−0.252487	−	0.0947598i
$927$	−0.0317817	+	0.707674i	−0.00104385	+	0.0232431i
$928$	19.2440	+	13.9816i	0.631717	+	0.458969i
$929$	−2.43180	−	5.68948i	−0.0797848	−	0.186666i	0.874886	−	0.484328i	$-0.160936\pi$
$929$	−2.43180	−	5.68948i	−0.0797848	−	0.186666i	−0.954671	+	0.297662i	$0.903793\pi$
$930$	5.84585	−	43.1558i	0.191693	−	1.41513i
$931$	−4.56996	+	3.99265i	−0.149774	+	0.130854i
$932$	7.63120	+	6.66718i	0.249968	+	0.218391i
$933$	−6.41195	−	47.3349i	−0.209918	−	1.54968i
$934$	12.5324	−	7.48774i	0.410071	−	0.245006i
$935$	2.63281	−	6.15977i	0.0861021	−	0.201446i
$936$	−0.133274	−	0.0796273i	−0.00435619	−	0.00260270i
$937$	36.4622	−	26.4913i	1.19117	−	0.865433i	0.197780	−	0.980246i	$-0.436627\pi$
$937$	36.4622	−	26.4913i	1.19117	−	0.865433i	0.993387	+	0.114813i	$0.0366269\pi$
$938$	9.32796	+	14.1313i	0.304569	+	0.461402i
$939$	37.9346	+	3.41418i	1.23795	+	0.111418i
$940$	−1.39824	+	4.30333i	−0.0456054	+	0.140359i
$941$	1.00315	+	22.3369i	0.0327018	+	0.728161i	0.946637	+	0.322301i	$0.104456\pi$
$941$	1.00315	+	22.3369i	0.0327018	+	0.728161i	−0.913935	+	0.405860i	$0.866972\pi$
$942$	15.2703	−	23.1335i	0.497534	−	0.753731i
$943$	−4.36450	+	5.47291i	−0.142128	+	0.178223i
$944$	23.0477	−	42.8298i	0.750139	−	1.39399i
$945$	−20.1199	−	5.55273i	−0.654500	−	0.180630i
$946$	−2.10566	−	1.01403i	−0.0684609	−	0.0329690i
$947$	−43.7974	+	16.4375i	−1.42323	+	0.534146i	−0.939947	−	0.341321i	$-0.889126\pi$
$947$	−43.7974	+	16.4375i	−1.42323	+	0.534146i	−0.483279	+	0.875466i	$0.660554\pi$
$948$	5.96204	+	18.3493i	0.193638	+	0.595957i
$949$	0.776064	+	3.40016i	0.0251921	+	0.110374i
$950$	−7.22101	−	13.4189i	−0.234280	−	0.435366i
$951$	12.2311	+	2.21961i	0.396619	+	0.0719758i
$952$	−29.1470	+	8.04407i	−0.944661	+	0.260710i
$953$	−7.92843	+	34.7367i	−0.256827	+	1.12523i	0.667795	+	0.744346i	$0.267238\pi$
$953$	−7.92843	+	34.7367i	−0.256827	+	1.12523i	−0.924622	+	0.380887i	$0.875619\pi$
$954$	−3.32592	+	0.299338i	−0.107681	+	0.00969143i
$955$	−27.0076	−	33.8665i	−0.873947	−	1.09589i
$956$	12.1456	−	2.20411i	0.392818	−	0.0712860i
$957$	3.95161	−	1.90300i	0.127737	−	0.0615151i
$958$	−23.3103	+	24.3806i	−0.753120	+	0.787702i
$959$	−14.8294	+	15.5104i	−0.478867	+	0.500856i
$960$	3.38538	−	1.63031i	0.109263	−	0.0526181i
$961$	55.0114	−	9.98309i	1.77456	−	0.322035i
$962$	−2.21987	−	2.78363i	−0.0715715	−	0.0897478i
$963$	2.45229	−	0.220710i	0.0790240	−	0.00711229i
$964$	4.17428	−	18.2887i	0.134444	−	0.589040i
$965$	20.6904	−	5.71018i	0.666047	−	0.183817i
$966$	4.11360	+	0.746508i	0.132353	+	0.0240185i
$967$	10.7773	+	20.0276i	0.346574	+	0.644043i	0.992891	−	0.119026i	$-0.0379772\pi$
$967$	10.7773	+	20.0276i	0.346574	+	0.644043i	−0.646317	+	0.763069i	$0.723691\pi$
$968$	−4.26363	−	18.6802i	−0.137038	−	0.600403i
$969$	−14.3206	−	44.0742i	−0.460043	−	1.41587i
$970$	35.1802	−	13.2033i	1.12957	−	0.423934i
$971$	20.0618	+	9.66127i	0.643815	+	0.310045i	0.727152	−	0.686476i	$-0.240844\pi$
$971$	20.0618	+	9.66127i	0.643815	+	0.310045i	−0.0833370	+	0.996521i	$0.526558\pi$
$972$	−2.80233	−	0.773394i	−0.0898848	−	0.0248066i
$973$	2.41180	−	4.48187i	0.0773187	−	0.143682i
$974$	−20.2023	+	25.3329i	−0.647323	+	0.811717i
$975$	−0.608195	+	0.921376i	−0.0194778	+	0.0295077i
$976$	2.41590	+	53.7943i	0.0773312	+	1.72191i
$977$	−3.86877	+	11.9068i	−0.123773	+	0.380933i	−0.993675	−	0.112290i	$-0.964181\pi$
$977$	−3.86877	+	11.9068i	−0.123773	+	0.380933i	0.869903	+	0.493223i	$0.164181\pi$
$978$	47.5264	+	4.27745i	1.51973	+	0.136778i
$979$	−1.97379	−	2.99017i	−0.0630827	−	0.0955663i
$980$	−1.99091	+	1.44648i	−0.0635974	+	0.0462062i
$981$	−0.862705	−	0.515442i	−0.0275440	−	0.0164568i
$982$	11.9981	−	28.0710i	0.382875	−	0.895781i
$983$	29.8753	−	17.8497i	0.952874	−	0.569316i	0.0497809	−	0.998760i	$-0.484148\pi$
$983$	29.8753	−	17.8497i	0.952874	−	0.569316i	0.903093	+	0.429444i	$0.141291\pi$
$984$	4.37664	+	32.3097i	0.139522	+	1.02999i
$985$	24.1674	+	21.1144i	0.770036	+	0.672761i
$986$	−44.4502	+	38.8349i	−1.41558	+	1.23676i
$987$	1.47500	−	10.8889i	0.0469499	−	0.346598i
$988$	0.432761	+	1.01249i	0.0137680	+	0.0322117i
$989$	1.24065	+	0.901381i	0.0394502	+	0.0286623i
$990$	0.0209760	−	0.467067i	0.000666661	−	0.0148444i
$991$	−18.8558	−	7.07671i	−0.598975	−	0.224799i	0.0334247	−	0.999441i	$-0.489359\pi$
$991$	−18.8558	−	7.07671i	−0.598975	−	0.224799i	−0.632400	+	0.774642i	$0.717930\pi$
$992$	−32.2680	−	33.7497i	−1.02451	−	1.07155i
$993$	25.5934			0.812183
$994$	−27.4142	+	19.7808i	−0.869526	+	0.627409i
$995$	−10.8284			−0.343283
$996$	13.5197	+	14.1405i	0.428388	+	0.448059i
$997$	23.6045	+	8.85890i	0.747561	+	0.280564i	0.695938	−	0.718102i	$-0.254989\pi$
$997$	23.6045	+	8.85890i	0.747561	+	0.280564i	0.0516234	+	0.998667i	$0.483560\pi$
$998$	−0.321655	+	7.16221i	−0.0101818	+	0.226716i
$999$	30.7489	+	22.3404i	0.972851	+	0.706818i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	71.2.g.a.12.2	yes	120
3.2	odd	2		639.2.v.a.154.4		120
71.6	even	35	inner	71.2.g.a.6.2	✓	120
71.19	even	35		5041.2.a.s.1.50		60
71.52	odd	70		5041.2.a.t.1.50		60
213.77	odd	70		639.2.v.a.361.4		120

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
71.2.g.a.6.2	✓	120	71.6	even	35	inner
71.2.g.a.12.2	yes	120	1.1	even	1	trivial
639.2.v.a.154.4		120	3.2	odd	2
639.2.v.a.361.4		120	213.77	odd	70
5041.2.a.s.1.50		60	71.19	even	35
5041.2.a.t.1.50		60	71.52	odd	70

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:	\( N \)	\(=\)	\( 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	71.g (of order \(35\), degree \(24\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18839 - 1.24296i) q^{2} +(1.54029 + 0.578081i) q^{3} +(-0.0429451 + 0.956246i) q^{4} +(1.33583 + 0.970538i) q^{5} +(-1.11193 - 2.60150i) q^{6} +(0.313169 - 2.31191i) q^{7} +(-1.35044 + 1.17984i) q^{8} +(-0.220897 - 0.192992i) q^{9} +O(q^{10})\)	\(q+(-1.18839 - 1.24296i) q^{2} +(1.54029 + 0.578081i) q^{3} +(-0.0429451 + 0.956246i) q^{4} +(1.33583 + 0.970538i) q^{5} +(-1.11193 - 2.60150i) q^{6} +(0.313169 - 2.31191i) q^{7} +(-1.35044 + 1.17984i) q^{8} +(-0.220897 - 0.192992i) q^{9} +(-0.381149 - 2.81376i) q^{10} +(-0.481884 + 0.287912i) q^{11} +(-0.618935 + 1.44807i) q^{12} +(-0.253369 - 0.151381i) q^{13} +(-3.24577 + 2.35819i) q^{14} +(1.49652 + 2.26713i) q^{15} +(4.97805 + 0.448032i) q^{16} +(-2.23337 + 6.87360i) q^{17} +(0.0226308 + 0.503915i) q^{18} +(-2.14710 + 3.25272i) q^{19} +(-0.985440 + 1.23570i) q^{20} +(1.81884 - 3.37997i) q^{21} +(0.930528 + 0.256809i) q^{22} +(-0.570677 - 0.274824i) q^{23} +(-2.76211 + 1.03664i) q^{24} +(-0.702585 - 2.16233i) q^{25} +(0.112941 + 0.494825i) q^{26} +(-2.56750 - 4.77122i) q^{27} +(2.19730 + 0.398751i) q^{28} +(-4.57803 + 1.26346i) q^{29} +(1.03950 - 4.55434i) q^{30} +(9.28502 - 0.835667i) q^{31} +(-3.12284 - 3.91592i) q^{32} +(-0.908678 + 0.164901i) q^{33} +(11.1977 - 5.39252i) q^{34} +(2.66213 - 2.78437i) q^{35} +(0.194034 - 0.202944i) q^{36} +(-6.32017 + 3.04363i) q^{37} +(6.59459 - 1.19674i) q^{38} +(-0.302751 - 0.379638i) q^{39} +(-2.94904 + 0.265418i) q^{40} +(2.45921 - 10.7745i) q^{41} +(-6.36264 + 1.75598i) q^{42} +(-2.38217 - 0.432301i) q^{43} +(-0.254620 - 0.473164i) q^{44} +(-0.107775 - 0.472194i) q^{45} +(0.336592 + 1.03592i) q^{46} +(2.68029 - 1.00593i) q^{47} +(7.40864 + 3.56781i) q^{48} +(1.50091 + 0.414224i) q^{49} +(-1.85274 + 3.44298i) q^{50} +(-7.41353 + 9.29627i) q^{51} +(0.155638 - 0.235782i) q^{52} +(0.297013 + 6.61350i) q^{53} +(-2.87923 + 8.86136i) q^{54} +(-0.923145 - 0.0830846i) q^{55} +(2.30477 + 3.49157i) q^{56} +(-5.18750 + 3.76894i) q^{57} +(7.01090 + 4.18882i) q^{58} +(3.82454 - 8.94795i) q^{59} +(-2.23220 + 1.33368i) q^{60} +(1.44618 + 10.6761i) q^{61} +(-12.0729 - 10.5478i) q^{62} +(-0.515357 + 0.450254i) q^{63} +(0.185672 - 1.37069i) q^{64} +(-0.191537 - 0.448123i) q^{65} +(1.28483 + 0.933481i) q^{66} +(0.189349 - 4.21618i) q^{67} +(-6.47694 - 2.43083i) q^{68} +(-0.720138 - 0.753205i) q^{69} -6.62450 q^{70} +(8.42610 + 0.0275788i) q^{71} +0.526007 q^{72} +(-8.16593 - 8.54089i) q^{73} +(11.2939 + 4.23868i) q^{74} +(0.167819 - 3.73677i) q^{75} +(-3.01819 - 2.19285i) q^{76} +(0.514715 + 1.20424i) q^{77} +(-0.112088 + 0.827464i) q^{78} +(9.22622 - 8.06070i) q^{79} +(6.21500 + 5.42988i) q^{80} +(-1.07843 - 7.96126i) q^{81} +(-16.3147 + 9.74761i) q^{82} +(4.88253 - 11.4232i) q^{83} +(3.15397 + 1.88441i) q^{84} +(-9.65449 + 7.01439i) q^{85} +(2.29362 + 3.47468i) q^{86} +(-7.78188 - 0.700382i) q^{87} +(0.311063 - 0.957354i) q^{88} +(0.286358 + 6.37626i) q^{89} +(-0.458838 + 0.695109i) q^{90} +(-0.429325 + 0.538357i) q^{91} +(0.287307 - 0.533905i) q^{92} +(14.7847 + 4.08032i) q^{93} +(-4.43555 - 2.13605i) q^{94} +(-6.02506 + 2.26124i) q^{95} +(-2.54636 - 7.83690i) q^{96} +(2.94476 + 12.9018i) q^{97} +(-1.26880 - 2.35782i) q^{98} +(0.162011 + 0.0294007i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9}+O(q^{10}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9	\( 120 q - 22 q^{2} - 20 q^{3} - 18 q^{4} - 20 q^{5} - 20 q^{6} - 27 q^{7} - 27 q^{8} - 11 q^{9} - 8 q^{10} - 27 q^{11} + 3 q^{12} - 31 q^{13} + 2 q^{14} + 12 q^{15} + 30 q^{16} + 9 q^{17} + 27 q^{18} - 31 q^{19} + 72 q^{20} - 32 q^{21} - 24 q^{22} - 6 q^{23} - 47 q^{24} - 42 q^{25} + 77 q^{26} - 2 q^{27} - 18 q^{28} + q^{29} + 15 q^{30} + 15 q^{31} - 10 q^{32} - 24 q^{33} + 20 q^{34} + 74 q^{35} + 8 q^{36} - 22 q^{37} - 39 q^{38} + 86 q^{39} - 30 q^{40} + 39 q^{41} - 34 q^{42} + 33 q^{43} - 23 q^{44} + 121 q^{45} + 124 q^{46} + 6 q^{47} + 131 q^{48} - 22 q^{49} - 15 q^{50} + 29 q^{51} + 83 q^{52} - 30 q^{53} - 25 q^{54} + 32 q^{55} + 11 q^{56} - 10 q^{57} + 12 q^{58} - 80 q^{59} + 80 q^{60} - 12 q^{61} - 68 q^{62} - 79 q^{63} - 117 q^{64} - 89 q^{65} - 39 q^{66} - 74 q^{67} - 67 q^{68} - 95 q^{69} - 64 q^{70} - 115 q^{71} - 144 q^{72} - 14 q^{73} - 70 q^{74} - 13 q^{75} + 8 q^{76} + 47 q^{77} - 218 q^{78} - 25 q^{79} - 103 q^{80} - 28 q^{81} - 88 q^{82} - 20 q^{83} - 142 q^{84} + 22 q^{85} + 159 q^{86} - 105 q^{87} + 43 q^{88} + 33 q^{89} + 33 q^{90} + 60 q^{91} - 2 q^{92} + 63 q^{93} + 174 q^{94} + 20 q^{95} - 30 q^{96} + 121 q^{97} + 128 q^{98} - 2 q^{99}+O(q^{100}) \) 120 * q - 22 * q^2 - 20 * q^3 - 18 * q^4 - 20 * q^5 - 20 * q^6 - 27 * q^7 - 27 * q^8 - 11 * q^9 - 8 * q^10 - 27 * q^11 + 3 * q^12 - 31 * q^13 + 2 * q^14 + 12 * q^15 + 30 * q^16 + 9 * q^17 + 27 * q^18 - 31 * q^19 + 72 * q^20 - 32 * q^21 - 24 * q^22 - 6 * q^23 - 47 * q^24 - 42 * q^25 + 77 * q^26 - 2 * q^27 - 18 * q^28 + q^29 + 15 * q^30 + 15 * q^31 - 10 * q^32 - 24 * q^33 + 20 * q^34 + 74 * q^35 + 8 * q^36 - 22 * q^37 - 39 * q^38 + 86 * q^39 - 30 * q^40 + 39 * q^41 - 34 * q^42 + 33 * q^43 - 23 * q^44 + 121 * q^45 + 124 * q^46 + 6 * q^47 + 131 * q^48 - 22 * q^49 - 15 * q^50 + 29 * q^51 + 83 * q^52 - 30 * q^53 - 25 * q^54 + 32 * q^55 + 11 * q^56 - 10 * q^57 + 12 * q^58 - 80 * q^59 + 80 * q^60 - 12 * q^61 - 68 * q^62 - 79 * q^63 - 117 * q^64 - 89 * q^65 - 39 * q^66 - 74 * q^67 - 67 * q^68 - 95 * q^69 - 64 * q^70 - 115 * q^71 - 144 * q^72 - 14 * q^73 - 70 * q^74 - 13 * q^75 + 8 * q^76 + 47 * q^77 - 218 * q^78 - 25 * q^79 - 103 * q^80 - 28 * q^81 - 88 * q^82 - 20 * q^83 - 142 * q^84 + 22 * q^85 + 159 * q^86 - 105 * q^87 + 43 * q^88 + 33 * q^89 + 33 * q^90 + 60 * q^91 - 2 * q^92 + 63 * q^93 + 174 * q^94 + 20 * q^95 - 30 * q^96 + 121 * q^97 + 128 * q^98 - 2 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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