LMFDB - Embedded newform 429.2.bi.a.5.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(5,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 8, 15]))

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

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

chi := DirichletCharacter("429.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bi (of order $20$, 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:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$416$
Relative dimension:	$52$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			5.13
Character	$\chi$	$=$	429.5
Dual form			429.2.bi.a.86.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.698951 + 1.37177i) q^{2} +(-1.70131 + 0.324864i) q^{3} +(-0.217646 - 0.299564i) q^{4} +(-0.540754 + 0.275528i) q^{5} +(0.743496 - 2.56087i) q^{6} +(4.34543 + 0.688249i) q^{7} +(-2.47818 + 0.392505i) q^{8} +(2.78893 - 1.10539i) q^{9} +O(q^{10})$	\(q+(-0.698951 + 1.37177i) q^{2} +(-1.70131 + 0.324864i) q^{3} +(-0.217646 - 0.299564i) q^{4} +(-0.540754 + 0.275528i) q^{5} +(0.743496 - 2.56087i) q^{6} +(4.34543 + 0.688249i) q^{7} +(-2.47818 + 0.392505i) q^{8} +(2.78893 - 1.10539i) q^{9} -0.934371i q^{10} +(1.00815 + 3.15969i) q^{11} +(0.467601 + 0.438946i) q^{12} +(1.75992 + 3.14685i) q^{13} +(-3.98136 + 5.47988i) q^{14} +(0.830483 - 0.644431i) q^{15} +(1.42255 - 4.37815i) q^{16} +(-0.0194099 + 0.0597374i) q^{17} +(-0.432984 + 4.59838i) q^{18} +(-3.84043 + 0.608265i) q^{19} +(0.200231 + 0.102023i) q^{20} +(-7.61653 + 0.240748i) q^{21} +(-5.03901 - 0.825526i) q^{22} +6.84720 q^{23} +(4.08864 - 1.47284i) q^{24} +(-2.72243 + 3.74710i) q^{25} +(-5.54685 + 0.214711i) q^{26} +(-4.38573 + 2.78664i) q^{27} +(-0.739592 - 1.45153i) q^{28} +(-4.40043 - 6.05667i) q^{29} +(0.303543 + 1.58966i) q^{30} +(-3.39908 - 1.73192i) q^{31} +(1.46315 + 1.46315i) q^{32} +(-2.74164 - 5.04811i) q^{33} +(-0.0683794 - 0.0683794i) q^{34} +(-2.53945 + 0.825116i) q^{35} +(-0.938133 - 0.594878i) q^{36} +(-5.32933 - 0.844083i) q^{37} +(1.84988 - 5.69333i) q^{38} +(-4.01648 - 4.78204i) q^{39} +(1.23194 - 0.895057i) q^{40} +(1.29204 + 8.15764i) q^{41} +(4.99333 - 10.6164i) q^{42} +0.354193i q^{43} +(0.727110 - 0.989698i) q^{44} +(-1.20356 + 1.36617i) q^{45} +(-4.78586 + 9.39278i) q^{46} +(-0.797407 + 0.126297i) q^{47} +(-0.997893 + 7.91073i) q^{48} +(11.7517 + 3.81837i) q^{49} +(-3.23731 - 6.35358i) q^{50} +(0.0136157 - 0.107938i) q^{51} +(0.559643 - 1.21211i) q^{52} +(2.08760 - 0.678302i) q^{53} +(-0.757205 - 7.96393i) q^{54} +(-1.41574 - 1.43084i) q^{55} -11.0389 q^{56} +(6.33617 - 2.28247i) q^{57} +(11.3840 - 1.80306i) q^{58} +(0.00765109 - 0.0483071i) q^{59} +(-0.373799 - 0.108525i) q^{60} +(-3.57398 + 10.9996i) q^{61} +(4.75158 - 3.45222i) q^{62} +(12.8799 - 2.88392i) q^{63} +(5.72651 - 1.86066i) q^{64} +(-1.81873 - 1.21677i) q^{65} +(8.84111 - 0.232515i) q^{66} +(2.57557 - 2.57557i) q^{67} +(0.0221196 - 0.00718711i) q^{68} +(-11.6492 + 2.22441i) q^{69} +(0.643080 - 4.06025i) q^{70} +(-3.32548 + 1.69442i) q^{71} +(-6.47759 + 3.83402i) q^{72} +(9.09191 + 1.44002i) q^{73} +(4.88283 - 6.72064i) q^{74} +(3.41440 - 7.25940i) q^{75} +(1.01807 + 1.01807i) q^{76} +(2.20618 + 14.4241i) q^{77} +(9.36717 - 2.16726i) q^{78} +(-3.21667 - 9.89990i) q^{79} +(0.437054 + 2.75945i) q^{80} +(6.55623 - 6.16570i) q^{81} +(-12.0935 - 3.92941i) q^{82} +(-0.431593 + 0.219908i) q^{83} +(1.72983 + 2.22924i) q^{84} +(-0.00596337 - 0.0376512i) q^{85} +(-0.485870 - 0.247563i) q^{86} +(9.45410 + 8.87475i) q^{87} +(-3.73856 - 7.43457i) q^{88} +(-1.52851 + 1.52851i) q^{89} +(-1.03284 - 2.60589i) q^{90} +(5.48181 + 14.8857i) q^{91} +(-1.49027 - 2.05117i) q^{92} +(6.34553 + 1.84229i) q^{93} +(0.384099 - 1.18213i) q^{94} +(1.90914 - 1.38707i) q^{95} +(-2.96461 - 2.01395i) q^{96} +(12.2769 + 6.25539i) q^{97} +(-13.4518 + 13.4518i) q^{98} +(6.30433 + 7.69775i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	$ 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) $ 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{2}{5}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.698951	+	1.37177i	−0.494233	+	0.969987i	0.500329	+	0.865836i	$0.333213\pi$
$2$	−0.698951	+	1.37177i	−0.494233	+	0.969987i	−0.994561	+	0.104151i	$0.966787\pi$
$3$	−1.70131	+	0.324864i	−0.982253	+	0.187560i
$3$	−1.70131	+	0.324864i	−0.982253	+	0.187560i
$4$	−0.217646	−	0.299564i	−0.108823	−	0.149782i
$5$	−0.540754	+	0.275528i	−0.241833	+	0.123220i	−0.570707	−	0.821154i	$-0.693331\pi$
$5$	−0.540754	+	0.275528i	−0.241833	+	0.123220i	0.328874	+	0.944374i	$0.393331\pi$
$6$	0.743496	−	2.56087i	0.303531	−	1.04547i
$7$	4.34543	+	0.688249i	1.64242	+	0.260134i	0.908126	−	0.418698i	$-0.137513\pi$
$7$	4.34543	+	0.688249i	1.64242	+	0.260134i	0.734294	+	0.678831i	$0.237513\pi$
$8$	−2.47818	+	0.392505i	−0.876168	+	0.138771i
$9$	2.78893	−	1.10539i	0.929642	−	0.368463i
$10$		−	0.934371i		−	0.295474i
$11$	1.00815	+	3.15969i	0.303967	+	0.952682i
$11$	1.00815	+	3.15969i	0.303967	+	0.952682i
$12$	0.467601	+	0.438946i	0.134985	+	0.126713i
$13$	1.75992	+	3.14685i	0.488115	+	0.872780i
$13$	1.75992	+	3.14685i	0.488115	+	0.872780i
$14$	−3.98136	+	5.47988i	−1.06406	+	1.46456i
$15$	0.830483	−	0.644431i	0.214430	−	0.166391i
$16$	1.42255	−	4.37815i	0.355636	−	1.09454i
$17$	−0.0194099	+	0.0597374i	−0.00470758	+	0.0144884i	−0.953383	−	0.301764i	$-0.902425\pi$
$17$	−0.0194099	+	0.0597374i	−0.00470758	+	0.0144884i	0.948675	+	0.316252i	$0.102425\pi$
$18$	−0.432984	+	4.59838i	−0.102055	+	1.08385i
$19$	−3.84043	+	0.608265i	−0.881056	+	0.139545i	−0.580540	−	0.814232i	$-0.697159\pi$
$19$	−3.84043	+	0.608265i	−0.881056	+	0.139545i	−0.300515	+	0.953777i	$0.597159\pi$
$20$	0.200231	+	0.102023i	0.0447731	+	0.0228130i
$21$	−7.61653	+	0.240748i	−1.66206	+	0.0525355i
$22$	−5.03901	−	0.825526i	−1.07432	−	0.176003i
$23$	6.84720			1.42774			0.713870	−	0.700278i	$-0.246941\pi$
$23$	6.84720			1.42774			0.713870	+	0.700278i	$0.246941\pi$
$24$	4.08864	−	1.47284i	0.834591	−	0.300643i
$25$	−2.72243	+	3.74710i	−0.544485	+	0.749420i
$26$	−5.54685	+	0.214711i	−1.08783	+	0.0421083i
$27$	−4.38573	+	2.78664i	−0.844035	+	0.536288i
$28$	−0.739592	−	1.45153i	−0.139770	−	0.274313i
$29$	−4.40043	−	6.05667i	−0.817140	−	1.12470i	−0.990182	−	0.139782i	$-0.955360\pi$
$29$	−4.40043	−	6.05667i	−0.817140	−	1.12470i	0.173043	−	0.984914i	$-0.444640\pi$
$30$	0.303543	+	1.58966i	0.0554192	+	0.290230i
$31$	−3.39908	−	1.73192i	−0.610492	−	0.311061i	0.121272	−	0.992619i	$-0.461303\pi$
$31$	−3.39908	−	1.73192i	−0.610492	−	0.311061i	−0.731764	+	0.681558i	$0.761303\pi$
$32$	1.46315	+	1.46315i	0.258651	+	0.258651i
$33$	−2.74164	−	5.04811i	−0.477258	−	0.878763i
$34$	−0.0683794	−	0.0683794i	−0.0117270	−	0.0117270i
$35$	−2.53945	+	0.825116i	−0.429245	+	0.139470i
$36$	−0.938133	−	0.594878i	−0.156356	−	0.0991464i
$37$	−5.32933	−	0.844083i	−0.876137	−	0.138766i	−0.297863	−	0.954609i	$-0.596274\pi$
$37$	−5.32933	−	0.844083i	−0.876137	−	0.138766i	−0.578274	+	0.815842i	$0.696274\pi$
$38$	1.84988	−	5.69333i	0.300089	−	0.923580i
$39$	−4.01648	−	4.78204i	−0.643151	−	0.765739i
$40$	1.23194	−	0.895057i	0.194787	−	0.141521i
$41$	1.29204	+	8.15764i	0.201783	+	1.27401i	0.855712	+	0.517453i	$0.173120\pi$
$41$	1.29204	+	8.15764i	0.201783	+	1.27401i	−0.653929	+	0.756556i	$0.726880\pi$
$42$	4.99333	−	10.6164i	0.770488	−	1.63814i
$43$			0.354193i			0.0540139i	0.999635	+	0.0270069i	$0.00859762\pi$
$43$			0.354193i			0.0540139i	−0.999635	+	0.0270069i	$0.991402\pi$
$44$	0.727110	−	0.989698i	0.109616	−	0.149203i
$45$	−1.20356	+	1.36617i	−0.179416	+	0.203657i
$46$	−4.78586	+	9.39278i	−0.705636	+	1.38489i
$47$	−0.797407	+	0.126297i	−0.116314	+	0.0184223i	−0.214320	−	0.976764i	$-0.568754\pi$
$47$	−0.797407	+	0.126297i	−0.116314	+	0.0184223i	0.0980061	+	0.995186i	$0.468754\pi$
$48$	−0.997893	+	7.91073i	−0.144033	+	1.14181i
$49$	11.7517	+	3.81837i	1.67882	+	0.545481i
$50$	−3.23731	−	6.35358i	−0.457825	−	0.898532i
$51$	0.0136157	−	0.107938i	0.00190658	−	0.0151143i
$52$	0.559643	−	1.21211i	0.0776085	−	0.168089i
$53$	2.08760	−	0.678302i	0.286754	−	0.0931720i	−0.162108	−	0.986773i	$-0.551829\pi$
$53$	2.08760	−	0.678302i	0.286754	−	0.0931720i	0.448862	+	0.893601i	$0.351829\pi$
$54$	−0.757205	−	7.96393i	−0.103043	−	1.08375i
$55$	−1.41574	−	1.43084i	−0.190899	−	0.192935i
$56$	−11.0389			−1.47514
$57$	6.33617	−	2.28247i	0.839246	−	0.302320i
$58$	11.3840	−	1.80306i	1.49480	−	0.236753i
$59$	0.00765109	−	0.0483071i	0.000996087	−	0.00628904i	−0.987185	−	0.159578i	$-0.948987\pi$
$59$	0.00765109	−	0.0483071i	0.000996087	−	0.00628904i	0.988181	+	0.153289i	$0.0489866\pi$
$60$	−0.373799	−	0.108525i	−0.0482573	−	0.0140105i
$61$	−3.57398	+	10.9996i	−0.457601	+	1.40835i	0.410454	+	0.911881i	$0.365370\pi$
$61$	−3.57398	+	10.9996i	−0.457601	+	1.40835i	−0.868055	+	0.496469i	$0.834630\pi$
$62$	4.75158	−	3.45222i	0.603451	−	0.438433i
$63$	12.8799	−	2.88392i	1.62271	−	0.363340i
$64$	5.72651	−	1.86066i	0.715814	−	0.232582i
$65$	−1.81873	−	1.21677i	−0.225586	−	0.150921i
$66$	8.84111	−	0.232515i	1.08827	−	0.0286206i
$67$	2.57557	−	2.57557i	0.314657	−	0.314657i	−0.532054	−	0.846710i	$-0.678580\pi$
$67$	2.57557	−	2.57557i	0.314657	−	0.314657i	0.846710	+	0.532054i	$0.178580\pi$
$68$	0.0221196	−	0.00718711i	0.00268240	−	0.000871565i
$69$	−11.6492	+	2.22441i	−1.40240	+	0.267787i
$70$	0.643080	−	4.06025i	0.0768627	−	0.485292i
$71$	−3.32548	+	1.69442i	−0.394662	+	0.201090i	−0.640048	−	0.768335i	$-0.721085\pi$
$71$	−3.32548	+	1.69442i	−0.394662	+	0.201090i	0.245386	+	0.969426i	$0.421085\pi$
$72$	−6.47759	+	3.83402i	−0.763391	+	0.451844i
$73$	9.09191	+	1.44002i	1.06413	+	0.168541i	0.663860	−	0.747857i	$-0.268917\pi$
$73$	9.09191	+	1.44002i	1.06413	+	0.168541i	0.400268	+	0.916398i	$0.368917\pi$
$74$	4.88283	−	6.72064i	0.567617	−	0.781258i
$75$	3.41440	−	7.25940i	0.394261	−	0.838244i
$76$	1.01807	+	1.01807i	0.116780	+	0.116780i
$77$	2.20618	+	14.4241i	0.251417	+	1.64378i
$78$	9.36717	−	2.16726i	1.06062	−	0.245394i
$79$	−3.21667	−	9.89990i	−0.361904	−	1.11383i	−0.951897	−	0.306417i	$-0.900870\pi$
$79$	−3.21667	−	9.89990i	−0.361904	−	1.11383i	0.589993	−	0.807408i	$-0.299130\pi$
$80$	0.437054	+	2.75945i	0.0488642	+	0.308516i
$81$	6.55623	−	6.16570i	0.728470	−	0.685078i
$82$	−12.0935	−	3.92941i	−1.33550	−	0.433930i
$83$	−0.431593	+	0.219908i	−0.0473735	+	0.0241380i	−0.477517	−	0.878623i	$-0.658463\pi$
$83$	−0.431593	+	0.219908i	−0.0473735	+	0.0241380i	0.430143	+	0.902761i	$0.358463\pi$
$84$	1.72983	+	2.22924i	0.188739	+	0.243230i
$85$	−0.00596337	−	0.0376512i	−0.000646818	−	0.00408385i
$86$	−0.485870	−	0.247563i	−0.0523928	−	0.0266954i
$87$	9.45410	+	8.87475i	1.01359	+	0.951473i
$88$	−3.73856	−	7.43457i	−0.398532	−	0.792528i
$89$	−1.52851	+	1.52851i	−0.162022	+	0.162022i	−0.783462	−	0.621440i	$-0.786548\pi$
$89$	−1.52851	+	1.52851i	−0.162022	+	0.162022i	0.621440	+	0.783462i	$0.286548\pi$
$90$	−1.03284	−	2.60589i	−0.108871	−	0.274685i
$91$	5.48181	+	14.8857i	0.574650	+	1.56045i
$92$	−1.49027	−	2.05117i	−0.155371	−	0.213850i
$93$	6.34553	+	1.84229i	0.658001	+	0.191037i
$94$	0.384099	−	1.18213i	0.0396167	−	0.121928i
$95$	1.90914	−	1.38707i	0.195873	−	0.142310i
$96$	−2.96461	−	2.01395i	−0.302574	−	0.205548i
$97$	12.2769	+	6.25539i	1.24653	+	0.635139i	0.947698	−	0.319167i	$-0.103403\pi$
$97$	12.2769	+	6.25539i	1.24653	+	0.635139i	0.298831	+	0.954306i	$0.403403\pi$
$98$	−13.4518	+	13.4518i	−1.35884	+	1.35884i
$99$	6.30433	+	7.69775i	0.633609	+	0.773653i
$100$	1.71502			0.171502
$101$	3.14285	+	9.67270i	0.312725	+	0.962470i	0.976681	+	0.214697i	$0.0688766\pi$
$101$	3.14285	+	9.67270i	0.312725	+	0.962470i	−0.663955	+	0.747772i	$0.731123\pi$
$102$	0.138549	+	0.0941206i	0.0137184	+	0.00931933i
$103$	−4.41747	−	6.08013i	−0.435266	−	0.599093i	0.533886	−	0.845557i	$-0.320731\pi$
$103$	−4.41747	−	6.08013i	−0.435266	−	0.599093i	−0.969152	+	0.246464i	$0.920731\pi$
$104$	−5.59656	−	7.10768i	−0.548787	−	0.696965i
$105$	4.05234	−	2.22875i	0.395468	−	0.217504i
$106$	−0.528656	+	3.33780i	−0.0513476	+	0.324196i
$107$	9.14463	−	12.5865i	0.884045	−	1.21678i	−0.0912396	−	0.995829i	$-0.529083\pi$
$107$	9.14463	−	12.5865i	0.884045	−	1.21678i	0.975284	−	0.220954i	$-0.0709171\pi$
$108$	1.78931	+	0.707308i	0.172177	+	0.0680607i
$109$	−3.20072	+	3.20072i	−0.306574	+	0.306574i	−0.843579	−	0.537005i	$-0.819556\pi$
$109$	−3.20072	+	3.20072i	−0.306574	+	0.306574i	0.537005	+	0.843579i	$0.319556\pi$
$110$	2.95232	−	0.941982i	0.281493	−	0.0898144i
$111$	9.34107	−	0.295258i	0.886615	−	0.0280247i
$112$	9.19483	−	18.0459i	0.868830	−	1.70518i
$113$	1.70252	−	2.34332i	0.160160	−	0.220441i	−0.721394	−	0.692525i	$-0.756498\pi$
$113$	1.70252	−	2.34332i	0.160160	−	0.220441i	0.881553	+	0.472084i	$0.156498\pi$
$114$	−1.29766	+	10.2871i	−0.121537	+	0.963474i
$115$	−3.70266	+	1.88660i	−0.345274	+	0.175926i
$116$	−0.856625	+	2.63642i	−0.0795356	+	0.244786i
$117$	8.38679	+	6.83094i	0.775359	+	0.631520i
$118$	0.0609184	+	0.0442598i	0.00560799	+	0.00407444i
$119$	−0.125459	+	0.246226i	−0.0115008	+	0.0225715i
$120$	−1.80514	+	1.92298i	−0.164786	+	0.175544i
$121$	−8.96728	+	6.37086i	−0.815208	+	0.579169i
$122$	−12.5908	−	12.5908i	−1.13992	−	1.13992i
$123$	−4.84829	−	13.4590i	−0.437156	−	1.21355i
$124$	0.220976	+	1.39519i	0.0198442	+	0.125291i
$125$	0.914436	−	5.77352i	0.0817896	−	0.516399i
$126$	−5.04633	+	19.6839i	−0.449563	+	1.75358i
$127$	15.5384	+	5.04874i	1.37881	+	0.448003i	0.902279	−	0.431154i	$-0.141893\pi$
$127$	15.5384	+	5.04874i	1.37881	+	0.448003i	0.476533	+	0.879157i	$0.341893\pi$
$128$	−2.09755	+	13.2434i	−0.185399	+	1.17056i
$129$	−0.115064	−	0.602592i	−0.0101309	−	0.0530553i
$130$	2.94033	−	1.64442i	0.257884	−	0.144225i
$131$		−	0.393472i		−	0.0343778i	−0.999852	−	0.0171889i	$-0.994528\pi$
$131$		−	0.393472i		−	0.0343778i	0.999852	−	0.0171889i	$-0.00547167\pi$
$132$	−0.915525	+	1.92000i	−0.0796862	+	0.167114i
$133$	−17.1070			−1.48336
$134$	1.73289	+	5.33329i	0.149699	+	0.460726i
$135$	1.60381	−	2.71528i	0.138034	−	0.233694i
$136$	0.0246539	−	0.155658i	0.00211405	−	0.0133476i
$137$	−7.13220	−	13.9977i	−0.609345	−	1.19591i	−0.965236	−	0.261380i	$-0.915823\pi$
$137$	−7.13220	−	13.9977i	−0.609345	−	1.19591i	0.355891	−	0.934527i	$-0.384177\pi$
$138$	5.09087	−	17.5348i	0.433363	−	1.49266i
$139$	13.9372	−	10.1260i	1.18214	−	0.858874i	0.189727	−	0.981837i	$-0.439240\pi$
$139$	13.9372	−	10.1260i	1.18214	−	0.858874i	0.992411	+	0.122963i	$0.0392397\pi$
$140$	0.799875	+	0.581143i	0.0676018	+	0.0491156i
$141$	1.31561	−	0.473919i	0.110794	−	0.0399112i
$142$		−	5.74610i		−	0.482202i
$143$	−8.16882	+	8.73329i	−0.683111	+	0.730315i
$144$	−0.872182	−	13.7828i	−0.0726818	−	1.14857i
$145$	4.04834	+	2.06273i	0.336196	+	0.171300i
$146$	−8.33017	+	11.4655i	−0.689410	+	0.948891i
$147$	−21.2338	−	2.67852i	−1.75133	−	0.220921i
$148$	0.907051	+	1.78019i	0.0745591	+	0.146330i
$149$	10.7184	−	5.46130i	0.878086	−	0.447407i	0.0439932	−	0.999032i	$-0.485992\pi$
$149$	10.7184	−	5.46130i	0.878086	−	0.447407i	0.834092	+	0.551625i	$0.185992\pi$
$150$	7.57172	+	9.75773i	0.618229	+	0.796716i
$151$	1.91672	+	12.1017i	0.155981	+	0.984824i	0.934179	+	0.356805i	$0.116134\pi$
$151$	1.91672	+	12.1017i	0.155981	+	0.984824i	−0.778198	+	0.628019i	$0.783866\pi$
$152$	9.27853	−	3.01478i	0.752588	−	0.244531i
$153$	0.0119004	+	0.188059i	0.000962094	+	0.0152036i
$154$	−21.3285	−	7.05536i	−1.71870	−	0.568537i
$155$	2.31526			0.185966
$156$	−0.558357	+	2.24398i	−0.0447044	+	0.179662i
$157$	−9.30067	−	6.75733i	−0.742274	−	0.539294i	0.151148	−	0.988511i	$-0.451703\pi$
$157$	−9.30067	−	6.75733i	−0.742274	−	0.539294i	−0.893423	+	0.449217i	$0.851703\pi$
$158$	15.8287	+	2.50701i	1.25926	+	0.199447i
$159$	−3.33130	+	1.83219i	−0.264189	+	0.145302i
$160$	−1.19435	−	0.388067i	−0.0944214	−	0.0306794i
$161$	29.7541	+	4.71258i	2.34495	+	0.371404i
$162$	3.87544	+	13.3031i	0.304483	+	1.04519i
$163$	0.111252	−	0.218344i	0.00871391	−	0.0171020i	−0.886609	−	0.462521i	$-0.846945\pi$
$163$	0.111252	−	0.218344i	0.00871391	−	0.0171020i	0.895322	+	0.445419i	$0.146945\pi$
$164$	2.16253	−	2.16253i	0.168865	−	0.168865i
$165$	2.87345	+	1.97439i	0.223698	+	0.153706i
$166$		−	0.745750i		−	0.0578815i
$167$	11.6353	+	5.92849i	0.900367	+	0.458760i	0.841964	−	0.539533i	$-0.181399\pi$
$167$	11.6353	+	5.92849i	0.900367	+	0.458760i	0.0584030	+	0.998293i	$0.481399\pi$
$168$	18.7806	−	3.58614i	1.44896	−	0.276677i
$169$	−6.80535	+	11.0764i	−0.523488	+	0.852033i
$170$	0.0558169	+	0.0181360i	0.00428096	+	0.00139097i
$171$	−10.0383	+	5.94158i	−0.767649	+	0.454364i
$172$	0.106103	−	0.0770886i	0.00809030	−	0.00587795i
$173$	3.93022	+	2.85547i	0.298809	+	0.217098i	0.727080	−	0.686553i	$-0.240877\pi$
$173$	3.93022	+	2.85547i	0.298809	+	0.217098i	−0.428271	+	0.903651i	$0.640877\pi$
$174$	−18.7821	+	6.76582i	−1.42386	+	0.512916i
$175$	−14.4091	+	14.4091i	−1.08922	+	1.08922i
$176$	15.2677	+	0.0809942i	1.15085	+	0.00610517i
$177$	0.00267633	+	0.0846709i	0.000201165	+	0.00636426i
$178$	−1.02841	−	3.16512i	−0.0770825	−	0.237236i
$179$	−20.0667	−	14.5793i	−1.49986	−	1.08971i	−0.970439	−	0.241347i	$-0.922411\pi$
$179$	−20.0667	−	14.5793i	−1.49986	−	1.08971i	−0.529417	−	0.848362i	$-0.677589\pi$
$180$	0.671206	+	0.0632009i	0.0500287	+	0.00471071i
$181$	−20.3218	−	6.60294i	−1.51051	−	0.490793i	−0.567444	−	0.823412i	$-0.692068\pi$
$181$	−20.3218	−	6.60294i	−1.51051	−	0.490793i	−0.943061	+	0.332619i	$0.892068\pi$
$182$	−24.2513	−	2.88460i	−1.79762	−	0.213821i
$183$	2.50709	−	19.8748i	0.185329	−	1.46918i
$184$	−16.9686	+	2.68756i	−1.25094	+	0.198130i
$185$	3.11443	−	1.01194i	0.228977	−	0.0743993i
$186$	−6.96241	+	7.41692i	−0.510509	+	0.543835i
$187$	−0.208320	−	0.00110512i	−0.0152338	−	8.08145e-5i
$188$	0.211386	+	0.211386i	0.0154169	+	0.0154169i
$189$	−20.9758	+	9.09066i	−1.52577	+	0.661248i
$190$	0.568345	+	3.58839i	0.0412321	+	0.260329i
$191$	−8.31950	−	11.4508i	−0.601978	−	0.828552i	0.393909	−	0.919149i	$-0.371122\pi$
$191$	−8.31950	−	11.4508i	−0.601978	−	0.828552i	−0.995888	+	0.0905974i	$0.971122\pi$
$192$	−9.13812	+	5.02589i	−0.659487	+	0.362713i
$193$	11.3847	−	5.80079i	0.819488	−	0.417550i	0.00660573	−	0.999978i	$-0.497897\pi$
$193$	11.3847	−	5.80079i	0.819488	−	0.417550i	0.812882	+	0.582428i	$0.197897\pi$
$194$	−17.1619	+	12.4688i	−1.23215	+	0.895211i
$195$	3.48951	+	1.47926i	0.249889	+	0.105932i
$196$	−1.41387	−	4.35144i	−0.100991	−	0.310817i
$197$	16.3980	+	16.3980i	1.16831	+	1.16831i	0.982606	+	0.185701i	$0.0594557\pi$
$197$	16.3980	+	16.3980i	1.16831	+	1.16831i	0.185701	+	0.982606i	$0.440544\pi$
$198$	−14.9660	+	3.26774i	−1.06358	+	0.232228i
$199$		−	13.8617i		−	0.982633i	−0.870981	−	0.491317i	$-0.836516\pi$
$199$		−	13.8617i		−	0.982633i	0.870981	−	0.491317i	$-0.163484\pi$
$200$	5.27590	−	10.3545i	0.373063	−	0.732177i
$201$	−3.54515	+	5.21857i	−0.250055	+	0.368089i
$202$	−15.4654	−	2.44948i	−1.08814	−	0.172345i
$203$	−14.9533	−	29.3475i	−1.04952	−	2.05979i
$204$	−0.0352976	+	0.0194134i	−0.00247133	+	0.00135921i
$205$	−2.94634	−	4.05529i	−0.205781	−	0.283233i
$206$	11.4281	−	1.81004i	0.796235	−	0.126111i
$207$	19.0963	−	7.56883i	1.32729	−	0.526070i
$208$	16.2809	−	3.22866i	1.12888	−	0.223867i
$209$	−5.79364	−	11.5214i	−0.400755	−	0.796949i
$210$	0.224948	+	7.11666i	0.0155229	+	0.491096i
$211$	−8.76558	−	26.9777i	−0.603448	−	1.85722i	−0.507129	−	0.861870i	$-0.669293\pi$
$211$	−8.76558	−	26.9777i	−0.603448	−	1.85722i	−0.0963184	−	0.995351i	$-0.530707\pi$
$212$	−0.657552	−	0.477740i	−0.0451609	−	0.0328113i
$213$	5.10723	−	3.96306i	0.349941	−	0.271544i
$214$	10.8741	+	21.3417i	0.743339	+	1.45889i
$215$	−0.0975901	−	0.191531i	−0.00665559	−	0.0130623i
$216$	9.77486	−	8.62720i	0.665095	−	0.587007i
$217$	−13.5785	−	9.86534i	−0.921767	−	0.669703i
$218$	−2.15350	−	6.62780i	−0.145854	−	0.448891i
$219$	−15.9360	+	0.503715i	−1.07685	+	0.0340379i
$220$	−0.120499	+	0.735523i	−0.00812401	+	0.0495889i
$221$	−0.222145	+	0.0440533i	−0.0149431	+	0.00296334i
$222$	−6.12392	+	13.0202i	−0.411011	+	0.873856i
$223$	23.9717	−	3.79674i	1.60526	−	0.254248i	0.711465	−	0.702721i	$-0.248032\pi$
$223$	23.9717	−	3.79674i	1.60526	−	0.254248i	0.893796	+	0.448473i	$0.148032\pi$
$224$	5.35102	+	7.36505i	0.357530	+	0.492098i
$225$	−3.45064	+	13.4597i	−0.230043	+	0.897315i
$226$	2.02451	+	3.97333i	0.134669	+	0.264302i
$227$	5.46618	+	0.865758i	0.362803	+	0.0574624i	0.335175	−	0.942156i	$-0.391205\pi$
$227$	5.46618	+	0.865758i	0.362803	+	0.0574624i	0.0276282	+	0.999618i	$0.491205\pi$
$228$	−2.06279	−	1.40132i	−0.136611	−	0.0928046i
$229$	−1.29656	+	2.54464i	−0.0856790	+	0.168155i	−0.929870	−	0.367888i	$-0.880081\pi$
$229$	−1.29656	+	2.54464i	−0.0856790	+	0.168155i	0.844191	+	0.536042i	$0.180081\pi$
$230$		−	6.39783i		−	0.421860i
$231$	−8.43926	−	23.8232i	−0.555263	−	1.56745i
$232$	13.2823	+	13.2823i	0.872028	+	0.872028i
$233$	3.58099	+	11.0211i	0.234598	+	0.722019i	0.997174	+	0.0751209i	$0.0239343\pi$
$233$	3.58099	+	11.0211i	0.234598	+	0.722019i	−0.762576	+	0.646898i	$0.776066\pi$
$234$	−15.2324	+	6.73025i	−0.995775	+	0.439970i
$235$	0.396403	−	0.288004i	0.0258585	−	0.0187873i
$236$	−0.0161363	+	0.00822184i	−0.00105038	+	0.000535196i
$237$	8.68868	+	15.7978i	0.564391	+	1.02618i
$238$	−0.250076	−	0.344200i	−0.0162100	−	0.0223112i
$239$	−0.198526	−	1.25344i	−0.0128416	−	0.0810786i	0.980435	−	0.196842i	$-0.0630686\pi$
$239$	−0.198526	−	1.25344i	−0.0128416	−	0.0810786i	−0.993277	+	0.115763i	$0.963069\pi$
$240$	−1.64001	−	4.55271i	−0.105862	−	0.293876i
$241$	−2.13041	−	2.13041i	−0.137232	−	0.137232i	0.635154	−	0.772386i	$-0.280937\pi$
$241$	−2.13041	−	2.13041i	−0.137232	−	0.137232i	−0.772386	+	0.635154i	$0.780937\pi$
$242$	−2.47165	−	16.7540i	−0.158884	−	1.07698i
$243$	−9.15117	+	12.6197i	−0.587048	+	0.809552i
$244$	4.07293	−	1.32338i	0.260743	−	0.0847205i
$245$	−7.40686	+	1.17313i	−0.473207	+	0.0749486i
$246$	21.8513	+	2.75641i	1.39319	+	0.175743i
$247$	−8.67298	−	11.0148i	−0.551849	−	0.700853i
$248$	9.10330	+	2.95784i	0.578060	+	0.187823i
$249$	0.662835	−	0.514341i	0.0420054	−	0.0325950i
$250$	7.28079	+	5.28980i	0.460477	+	0.334556i
$251$	7.78265	+	23.9525i	0.491236	+	1.51187i	0.822741	+	0.568416i	$0.192444\pi$
$251$	7.78265	+	23.9525i	0.491236	+	1.51187i	−0.331505	+	0.943453i	$0.607556\pi$
$252$	−3.66717	−	3.23067i	−0.231010	−	0.203513i
$253$	6.90298	+	21.6350i	0.433987	+	1.36018i
$254$	−17.7863	+	17.7863i	−1.11601	+	1.11601i
$255$	0.0223771	+	0.0621192i	0.00140131	+	0.00389006i
$256$	−6.95831	−	5.05551i	−0.434894	−	0.315969i
$257$	−7.79276	+	5.66177i	−0.486099	+	0.353172i	−0.803682	−	0.595059i	$-0.797129\pi$
$257$	−7.79276	+	5.66177i	−0.486099	+	0.353172i	0.317583	+	0.948230i	$0.397129\pi$
$258$	0.907042	+	0.263341i	0.0564700	+	0.0163949i
$259$	−22.5773	−	7.33582i	−1.40289	−	0.455826i
$260$	0.0313405	+	0.809651i	0.00194365	+	0.0502124i
$261$	−18.9675	−	12.0274i	−1.17406	−	0.744479i
$262$	0.539753	+	0.275018i	0.0333461	+	0.0169907i
$263$		−	21.9387i		−	1.35280i	−0.736535	−	0.676399i	$-0.763540\pi$
$263$		−	21.9387i		−	1.35280i	0.736535	−	0.676399i	$-0.236460\pi$
$264$	8.77568	+	11.4340i	0.540106	+	0.703714i
$265$	−0.941987	+	0.941987i	−0.0578658	+	0.0578658i
$266$	11.9569	−	23.4668i	0.733127	−	1.43884i
$267$	2.10392	−	3.09703i	0.128758	−	0.189535i
$268$	−1.33211	−	0.210986i	−0.0813717	−	0.0128880i
$269$	22.2385	+	7.22571i	1.35590	+	0.440560i	0.894673	−	0.446721i	$-0.147408\pi$
$269$	22.2385	+	7.22571i	1.35590	+	0.440560i	0.461230	+	0.887281i	$0.347408\pi$
$270$	2.60375	+	4.09790i	0.158459	+	0.249390i
$271$	−3.76924	−	0.596989i	−0.228965	−	0.0362645i	0.0408975	−	0.999163i	$-0.486978\pi$
$271$	−3.76924	−	0.596989i	−0.228965	−	0.0362645i	−0.269863	+	0.962899i	$0.586978\pi$
$272$	0.233928	+	0.169958i	0.0141839	+	0.0103052i
$273$	−14.1621	−	23.5444i	−0.857129	−	1.42497i
$274$	24.1867			1.46117
$275$	−14.5843	−	4.82440i	−0.879465	−	0.290922i
$276$	3.20176	+	3.00556i	0.192723	+	0.180913i
$277$	−7.00566	+	2.27628i	−0.420929	+	0.136768i	−0.511820	−	0.859093i	$-0.671029\pi$
$277$	−7.00566	+	2.27628i	−0.420929	+	0.136768i	0.0908908	+	0.995861i	$0.471029\pi$
$278$	4.14907	+	26.1962i	0.248844	+	1.57114i
$279$	−11.3942	−	1.07288i	−0.682154	−	0.0642318i
$280$	5.96934	−	3.04153i	0.356736	−	0.181766i
$281$	8.89365	+	17.4548i	0.530551	+	1.04126i	0.988348	+	0.152208i	$0.0486384\pi$
$281$	8.89365	+	17.4548i	0.530551	+	1.04126i	−0.457798	+	0.889056i	$0.651362\pi$
$282$	−0.269439	+	2.13596i	−0.0160449	+	0.127194i
$283$	10.7190	−	14.7534i	0.637179	−	0.877001i	−0.361283	−	0.932456i	$-0.617661\pi$
$283$	10.7190	−	14.7534i	0.637179	−	0.877001i	0.998461	+	0.0554554i	$0.0176611\pi$
$284$	1.23136	+	0.627411i	0.0730680	+	0.0372300i
$285$	−2.79743	+	2.98005i	−0.165705	+	0.176523i
$286$	−6.27046	−	17.3099i	−0.370780	−	1.02355i
$287$			36.3377i			2.14495i
$288$	5.69798	+	2.46327i	0.335757	+	0.145150i
$289$	13.7501	+	9.99003i	0.808829	+	0.587649i
$290$	−5.65918	+	4.11163i	−0.332318	+	0.241443i
$291$	−22.9190	−	6.65405i	−1.34353	−	0.390067i
$292$	−1.54744	−	3.03702i	−0.0905571	−	0.177728i
$293$	−2.54217	+	16.0506i	−0.148515	+	0.937689i	0.795060	+	0.606531i	$0.207439\pi$
$293$	−2.54217	+	16.0506i	−0.148515	+	0.937689i	−0.943575	+	0.331158i	$0.892561\pi$
$294$	18.5157	−	27.2557i	1.07986	−	1.58958i
$295$	0.00917259	+	0.0282303i	0.000534049	+	0.00164363i
$296$	13.5383			0.786900
$297$	−13.2264	−	11.0482i	−0.767471	−	0.641083i
$298$			18.5203i			1.07285i
$299$	12.0505	+	21.5471i	0.696901	+	1.24610i
$300$	−2.91779	+	0.557148i	−0.168458	+	0.0321670i
$301$	−0.243773	+	1.53912i	−0.0140508	+	0.0887135i
$302$	−17.9404	−	5.82921i	−1.03236	−	0.335433i
$303$	−8.48928	−	15.4353i	−0.487697	−	0.886734i
$304$	−2.80012	+	17.6793i	−0.160598	+	1.01397i
$305$	−1.09805	−	6.93280i	−0.0628740	−	0.396971i
$306$	−0.266291	−	0.115119i	−0.0152228	−	0.00658092i
$307$	17.6953	+	17.6953i	1.00992	+	1.00992i	0.999950	+	0.00997166i	$0.00317413\pi$
$307$	17.6953	+	17.6953i	1.00992	+	1.00992i	0.00997166	+	0.999950i	$0.496826\pi$
$308$	3.84077	−	3.80023i	0.218848	−	0.216538i
$309$	9.49071	+	8.90912i	0.539908	+	0.506822i
$310$	−1.61825	+	3.17600i	−0.0919105	+	0.180385i
$311$	−5.90292	−	4.28872i	−0.334724	−	0.243191i	0.407709	−	0.913112i	$-0.366328\pi$
$311$	−5.90292	−	4.28872i	−0.334724	−	0.243191i	−0.742432	+	0.669921i	$0.766328\pi$
$312$	11.8305	+	10.2743i	0.669771	+	0.581666i
$313$	0.423118	−	1.30222i	0.0239160	−	0.0736060i	−0.938386	−	0.345589i	$-0.887679\pi$
$313$	0.423118	−	1.30222i	0.0239160	−	0.0736060i	0.962302	+	0.271983i	$0.0876793\pi$
$314$	15.7702	−	8.03532i	0.889964	−	0.453459i
$315$	−6.17025	+	5.10826i	−0.347654	+	0.287818i
$316$	−2.26556	+	3.11827i	−0.127447	+	0.175416i
$317$	4.39572	−	8.62709i	0.246888	−	0.484546i	−0.733992	−	0.679158i	$-0.762345\pi$
$317$	4.39572	−	8.62709i	0.246888	−	0.484546i	0.980880	+	0.194613i	$0.0623450\pi$
$318$	−0.184923	−	5.85039i	−0.0103699	−	0.328073i
$319$	14.7009	−	20.0100i	0.823094	−	1.12035i
$320$	−2.58397	+	2.58397i	−0.144448	+	0.144448i
$321$	−11.4690	+	24.3843i	−0.640135	+	1.36100i
$322$	−27.2612	+	37.5218i	−1.51921	+	2.09101i
$323$	0.0382061	−	0.241224i	0.00212584	−	0.0134221i
$324$	−3.27396	−	0.622069i	−0.181887	−	0.0345594i
$325$	−16.5828	−	1.97247i	−0.919849	−	0.109413i
$326$	0.221758	+	0.305223i	0.0122820	+	0.0169047i
$327$	4.40563	−	6.48523i	0.243632	−	0.358634i
$328$	−6.40383	−	19.7089i	−0.353592	−	1.08824i
$329$	−3.55201			−0.195828
$330$	−4.71680	+	2.56171i	−0.259652	+	0.141017i
$331$	17.3716	−	17.3716i	0.954829	−	0.954829i	−0.0441940	−	0.999023i	$-0.514072\pi$
$331$	17.3716	−	17.3716i	0.954829	−	0.954829i	0.999023	+	0.0441940i	$0.0140720\pi$
$332$	0.159811	+	0.0814277i	0.00877076	+	0.00446893i
$333$	−15.7962	+	3.53690i	−0.865624	+	0.193821i
$334$	−16.2650	+	11.8172i	−0.889983	+	0.646610i
$335$	−0.683110	+	2.10240i	−0.0373223	+	0.114866i
$336$	−9.78083	+	33.6887i	−0.533588	+	1.83787i
$337$	8.99992	+	12.3873i	0.490257	+	0.674781i	0.980435	−	0.196841i	$-0.0630684\pi$
$337$	8.99992	+	12.3873i	0.490257	+	0.674781i	−0.490178	+	0.871622i	$0.663068\pi$
$338$	−10.4377	−	17.0772i	−0.567736	−	0.928879i
$339$	−2.13526	+	4.53980i	−0.115971	+	0.246568i
$340$	−0.00998105	+	0.00998105i	−0.000541298	+	0.000541298i
$341$	2.04555	−	12.4861i	0.110773	−	0.676158i
$342$	−1.13418	−	17.9231i	−0.0613296	−	0.969171i
$343$	20.9978	+	10.6989i	1.13378	+	0.577688i
$344$	−0.139022	−	0.877753i	−0.00749558	−	0.0473253i
$345$	5.68649	−	4.41255i	0.306150	−	0.237564i
$346$	−6.66408	+	3.39552i	−0.358263	+	0.182544i
$347$	20.9168	+	6.79627i	1.12287	+	0.364843i	0.810862	−	0.585237i	$-0.198998\pi$
$347$	20.9168	+	6.79627i	1.12287	+	0.364843i	0.312008	+	0.950079i	$0.398998\pi$
$348$	0.600909	−	4.76366i	0.0322121	−	0.255359i
$349$	0.911036	+	5.75206i	0.0487667	+	0.307901i	1.00000		0.000572182i	$-0.000182131\pi$
$349$	0.911036	+	5.75206i	0.0487667	+	0.307901i	−0.951233	+	0.308473i	$0.900182\pi$
$350$	−9.69467	−	29.8371i	−0.518202	−	1.59486i
$351$	−16.4877	−	8.89699i	−0.880047	−	0.474886i
$352$	−3.14804	+	6.09818i	−0.167791	+	0.325034i
$353$	−8.05230	−	8.05230i	−0.428581	−	0.428581i	0.459564	−	0.888145i	$-0.348006\pi$
$353$	−8.05230	−	8.05230i	−0.428581	−	0.428581i	−0.888145	+	0.459564i	$0.848006\pi$
$354$	−0.118020	−	0.0555095i	−0.00627267	−	0.00295030i
$355$	1.33141	−	1.83253i	0.0706638	−	0.0972604i
$356$	0.790561	+	0.125213i	0.0418997	+	0.00663625i
$357$	0.133454	−	0.459665i	0.00706314	−	0.0243280i
$358$	34.0251	−	17.3366i	1.79828	−	0.916270i
$359$	−1.00480	+	6.34405i	−0.0530313	+	0.334826i	0.946881	+	0.321584i	$0.104215\pi$
$359$	−1.00480	+	6.34405i	−0.0530313	+	0.334826i	−0.999912	+	0.0132422i	$0.995785\pi$
$360$	2.44640	−	3.85802i	0.128937	−	0.203336i
$361$	−3.69114	+	1.19932i	−0.194271	+	0.0631224i
$362$	23.2616	−	23.2616i	1.22260	−	1.22260i
$363$	13.1865	−	13.7520i	0.692111	−	0.721791i
$364$	3.26613	−	4.88196i	0.171192	−	0.255884i
$365$	−5.31326	+	1.72638i	−0.278109	+	0.0903629i
$366$	25.5112	+	17.3306i	1.33349	+	0.905886i
$367$	4.63915	−	3.37054i	0.242162	−	0.175941i	−0.460084	−	0.887875i	$-0.652181\pi$
$367$	4.63915	−	3.37054i	0.242162	−	0.175941i	0.702246	+	0.711935i	$0.252181\pi$
$368$	9.74046	−	29.9780i	0.507757	−	1.56271i
$369$	12.6208	+	21.3228i	0.657012	+	1.11002i
$370$	−0.788687	+	4.97957i	−0.0410019	+	0.258876i
$371$	9.53837	−	1.51073i	0.495207	−	0.0784331i
$372$	−0.829194	−	2.30186i	−0.0429917	−	0.119346i
$373$	8.66816			0.448820			0.224410	−	0.974495i	$-0.427954\pi$
$373$	8.66816			0.448820			0.224410	+	0.974495i	$0.427954\pi$
$374$	0.147121	−	0.284994i	0.00760746	−	0.0147367i
$375$	0.319868	+	10.1196i	0.0165179	+	0.522575i
$376$	1.92655	−	0.625973i	0.0993540	−	0.0322821i
$377$	11.3150	−	24.5068i	0.582754	−	1.26216i
$378$	2.19079	−	35.1279i	0.112682	−	1.80678i
$379$	8.08507	+	15.8679i	0.415302	+	0.815077i	0.999993	+	0.00382020i	$0.00121601\pi$
$379$	8.08507	+	15.8679i	0.415302	+	0.815077i	−0.584690	+	0.811257i	$0.698784\pi$
$380$	−0.831032	−	0.270019i	−0.0426310	−	0.0138517i
$381$	−28.0758	−	3.54161i	−1.43837	−	0.181442i
$382$	21.5228	−	3.40888i	1.10120	−	0.174413i
$383$	−5.66764	+	11.1234i	−0.289603	+	0.568378i	−0.989271	−	0.146090i	$-0.953331\pi$
$383$	−5.66764	+	11.1234i	−0.289603	+	0.568378i	0.699668	+	0.714468i	$0.253331\pi$
$384$	−0.733719	−	23.2126i	−0.0374425	−	1.18456i
$385$	−5.16724	−	7.19202i	−0.263347	−	0.366539i
$386$			19.6716i			1.00126i
$387$	0.391521	+	0.987818i	0.0199021	+	0.0502136i
$388$	−0.798127	−	5.03917i	−0.0405187	−	0.255825i
$389$	4.24418	−	3.08358i	0.215189	−	0.156344i	−0.474970	−	0.880002i	$-0.657541\pi$
$389$	4.24418	−	3.08358i	0.215189	−	0.156344i	0.690158	+	0.723659i	$0.257541\pi$
$390$	−4.46820	+	3.75288i	−0.226256	+	0.190034i
$391$	−0.132903	+	0.409034i	−0.00672121	+	0.0206857i
$392$	−30.6216	−	4.84998i	−1.54662	−	0.244961i
$393$	0.127825	+	0.669419i	0.00644792	+	0.0337677i
$394$	−33.9556	+	11.0328i	−1.71066	+	0.555827i
$395$	4.46713	+	4.46713i	0.224766	+	0.224766i
$396$	0.933855	−	3.56394i	0.0469280	−	0.179094i
$397$	2.52276	+	2.52276i	0.126614	+	0.126614i	0.767574	−	0.640960i	$-0.221464\pi$
$397$	2.52276	+	2.52276i	0.126614	+	0.126614i	−0.640960	+	0.767574i	$0.721464\pi$
$398$	19.0151	+	9.68868i	0.953141	+	0.485650i
$399$	29.1043	−	5.55744i	1.45704	−	0.278220i
$400$	12.5326	+	17.2496i	0.626628	+	0.862480i
$401$	−5.30529	−	10.4122i	−0.264934	−	0.519962i	0.719767	−	0.694216i	$-0.244249\pi$
$401$	−5.30529	−	10.4122i	−0.264934	−	0.519962i	−0.984701	+	0.174254i	$0.944249\pi$
$402$	−4.68078	−	8.51064i	−0.233456	−	0.424472i
$403$	−0.532029	−	13.7444i	−0.0265022	−	0.684659i
$404$	2.21356	−	3.04671i	0.110129	−	0.151579i
$405$	−1.84648	+	5.14056i	−0.0917525	+	0.255436i
$406$	50.7096			2.51667
$407$	−2.70570	−	17.6900i	−0.134117	−	0.876861i
$408$	0.00862387	+	0.272833i	0.000426945	+	0.0135072i
$409$	9.30304	+	4.74013i	0.460006	+	0.234385i	0.668607	−	0.743616i	$-0.266891\pi$
$409$	9.30304	+	4.74013i	0.460006	+	0.234385i	−0.208601	+	0.978001i	$0.566891\pi$
$410$	7.62226	−	1.20725i	0.376436	−	0.0596217i
$411$	16.6815	+	21.4975i	0.822836	+	1.06039i
$412$	−0.859942	+	2.64663i	−0.0423663	+	0.130390i
$413$	0.0664946	−	0.204649i	0.00327199	−	0.0100701i
$414$	−2.96473	+	31.4860i	−0.145709	+	1.54745i
$415$	0.172795	−	0.237832i	0.00848218	−	0.0116747i
$416$	−2.02929	+	7.17936i	−0.0994941	+	0.351997i
$417$	−20.4220	+	21.7551i	−1.00007	+	1.06535i
$418$	19.8541	+	0.105325i	0.971096	+	0.00515160i
$419$		−	18.0627i		−	0.882420i	−0.897404	−	0.441210i	$-0.854549\pi$
$419$		−	18.0627i		−	0.882420i	0.897404	−	0.441210i	$-0.145451\pi$
$420$	−1.54963	−	0.728855i	−0.0756142	−	0.0355645i
$421$	22.2400	−	3.52247i	1.08391	−	0.171675i	0.411175	−	0.911556i	$-0.365118\pi$
$421$	22.2400	−	3.52247i	1.08391	−	0.171675i	0.672737	+	0.739881i	$0.265118\pi$
$422$	43.1339	+	6.83173i	2.09972	+	0.332563i
$423$	−2.08430	+	1.23368i	−0.101342	+	0.0599835i
$424$	−4.90721	+	2.50035i	−0.238315	+	0.121428i
$425$	−0.171000	−	0.235361i	−0.00829472	−	0.0114167i
$426$	1.86670	+	9.77592i	0.0904420	+	0.473645i
$427$	−23.1009	+	45.3381i	−1.11793	+	2.19407i
$428$	−5.76075			−0.278456
$429$	11.0606	−	17.5118i	0.534010	−	0.845478i
$430$	0.330947			0.0159597
$431$	10.8118	−	21.2194i	0.520787	−	1.02210i	−0.469483	−	0.882941i	$-0.655560\pi$
$431$	10.8118	−	21.2194i	0.520787	−	1.02210i	0.990270	−	0.139160i	$-0.0444402\pi$
$432$	5.96139	+	23.1655i	0.286817	+	1.11455i
$433$	−7.25006	−	9.97885i	−0.348416	−	0.479553i	0.598460	−	0.801153i	$-0.295779\pi$
$433$	−7.25006	−	9.97885i	−0.348416	−	0.479553i	−0.946876	+	0.321600i	$0.895779\pi$
$434$	23.0237	−	11.7311i	1.10517	−	0.563113i
$435$	−7.55759	−	2.19419i	−0.362359	−	0.105203i
$436$	1.65545	+	0.262197i	0.0792815	+	0.0125570i
$437$	−26.2962	+	4.16491i	−1.25792	+	0.199235i
$438$	10.4475	−	22.2126i	0.499201	−	1.06136i
$439$		−	27.6742i		−	1.32082i	−0.750906	−	0.660409i	$-0.770383\pi$
$439$		−	27.6742i		−	1.32082i	0.750906	−	0.660409i	$-0.229617\pi$
$440$	4.07008	+	2.99020i	0.194033	+	0.142552i
$441$	36.9955	−	2.34109i	1.76169	−	0.111481i
$442$	0.0948373	−	0.335522i	0.00451095	−	0.0159592i
$443$	12.1696	−	16.7500i	0.578195	−	0.795817i	−0.415301	−	0.909684i	$-0.636324\pi$
$443$	12.1696	−	16.7500i	0.578195	−	0.795817i	0.993496	+	0.113867i	$0.0363237\pi$
$444$	−2.12149	−	2.73399i	−0.100682	−	0.129749i
$445$	0.405401	−	1.24770i	0.0192179	−	0.0591465i
$446$	−11.5468	+	35.5373i	−0.546755	+	1.68274i
$447$	−16.4612	+	12.7734i	−0.778586	+	0.604161i
$448$	26.1648	−	4.14409i	1.23617	−	0.195790i
$449$	21.4410	+	10.9248i	1.01187	+	0.515571i	0.879636	−	0.475648i	$-0.157786\pi$
$449$	21.4410	+	10.9248i	1.01187	+	0.515571i	0.132230	+	0.991219i	$0.457786\pi$
$450$	−16.0518	−	14.1412i	−0.756689	−	0.666621i
$451$	−24.4730	+	12.3065i	−1.15239	+	0.579493i
$452$	−1.07252			−0.0504471
$453$	−7.19236	−	19.9661i	−0.337926	−	0.938090i
$454$	−5.00821	+	6.89321i	−0.235047	+	0.323514i
$455$	−7.06574	−	6.53912i	−0.331247	−	0.306559i
$456$	−14.8063	+	8.14333i	−0.693368	+	0.381347i
$457$	−13.5633	−	26.6195i	−0.634464	−	1.24521i	−0.954616	−	0.297839i	$-0.903734\pi$
$457$	−13.5633	−	26.6195i	−0.634464	−	1.24521i	0.320152	−	0.947366i	$-0.396266\pi$
$458$	−2.58443	−	3.55716i	−0.120762	−	0.166215i
$459$	−0.0813399	−	0.316081i	−0.00379662	−	0.0147534i
$460$	1.37102	+	0.698572i	0.0639243	+	0.0325711i
$461$	3.56623	+	3.56623i	0.166096	+	0.166096i	0.785261	−	0.619165i	$-0.212529\pi$
$461$	3.56623	+	3.56623i	0.166096	+	0.166096i	−0.619165	+	0.785261i	$0.712529\pi$
$462$	38.5785	+	5.07451i	1.79483	+	0.236088i
$463$	−6.91076	−	6.91076i	−0.321170	−	0.321170i	0.528046	−	0.849216i	$-0.322925\pi$
$463$	−6.91076	−	6.91076i	−0.321170	−	0.321170i	−0.849216	+	0.528046i	$0.822925\pi$
$464$	−32.7768	+	10.6498i	−1.52163	+	0.494406i
$465$	−3.93898	+	0.752144i	−0.182666	+	0.0348798i
$466$	−17.6214	−	2.79096i	−0.816296	−	0.129289i
$467$	−11.1432	+	34.2952i	−0.515646	+	1.58699i	0.266458	+	0.963846i	$0.414147\pi$
$467$	−11.1432	+	34.2952i	−0.515646	+	1.58699i	−0.782104	+	0.623148i	$0.785853\pi$
$468$	0.220951	−	3.99911i	0.0102135	−	0.184859i
$469$	12.9646	−	9.41935i	0.598651	−	0.434945i
$470$	0.118008	+	0.745074i	0.00544331	+	0.0343677i
$471$	18.0186	+	8.47488i	0.830251	+	0.390502i
$472$			0.122717i			0.00564849i
$473$	−1.11914	+	0.357078i	−0.0514581	+	0.0164185i
$474$	−27.7439	+	0.876948i	−1.27432	+	0.0402795i
$475$	8.17607	−	16.0464i	0.375144	−	0.736261i
$476$	0.101066	−	0.0160073i	0.00463235	−	0.000733693i
$477$	5.07237	−	4.19935i	0.232248	−	0.192275i
$478$	1.85820	+	0.603764i	0.0849919	+	0.0276155i
$479$	−13.0328	−	25.5784i	−0.595486	−	1.16871i	−0.970367	−	0.241634i	$-0.922317\pi$
$479$	−13.0328	−	25.5784i	−0.595486	−	1.16871i	0.374882	−	0.927073i	$-0.377683\pi$
$480$	2.15802	+	0.272223i	0.0984999	+	0.0124252i
$481$	−6.72301	−	18.2561i	−0.306543	−	0.832408i
$482$	4.41148	−	1.43338i	0.200937	−	0.0652885i
$483$	−52.1519	+	1.64845i	−2.37299	+	0.0750071i
$484$	3.86017	+	1.29968i	0.175462	+	0.0590765i
$485$	−8.36232			−0.379713
$486$	−10.9150	−	21.3738i	−0.495116	−	0.969536i
$487$	−38.2905	+	6.06462i	−1.73511	+	0.274814i	−0.942327	−	0.334693i	$-0.891367\pi$
$487$	−38.2905	+	6.06462i	−1.73511	+	0.274814i	−0.792781	+	0.609507i	$0.791367\pi$
$488$	4.53957	−	28.6617i	0.205496	−	1.29745i
$489$	−0.118342	+	0.407613i	−0.00535160	+	0.0184329i
$490$	3.56777	−	10.9805i	0.161175	−	0.496047i
$491$	14.1544	−	10.2838i	0.638780	−	0.464101i	−0.220651	−	0.975353i	$-0.570818\pi$
$491$	14.1544	−	10.2838i	0.638780	−	0.464101i	0.859431	+	0.511252i	$0.170818\pi$
$492$	−2.97661	+	4.38166i	−0.134196	+	0.197540i
$493$	0.447222	−	0.145311i	0.0201419	−	0.00654449i
$494$	21.1717	−	4.19854i	0.952560	−	0.188901i
$495$	−5.53004	−	2.42557i	−0.248557	−	0.109021i
$496$	−12.4179	+	12.4179i	−0.557581	+	0.557581i
$497$	−15.6168	+	5.07422i	−0.700511	+	0.227610i
$498$	0.242267	+	1.26875i	0.0108563	+	0.0568542i
$499$	−2.32751	+	14.6953i	−0.104194	+	0.657852i	0.879212	+	0.476431i	$0.158070\pi$
$499$	−2.32751	+	14.6953i	−0.104194	+	0.657852i	−0.983405	+	0.181421i	$0.941930\pi$
$500$	−1.92856	+	0.982651i	−0.0862479	+	0.0439455i
$501$	−21.7213	−	6.30632i	−0.970434	−	0.281745i
$502$	−38.2970	−	6.06565i	−1.70928	−	0.270723i
$503$	−25.5310	+	35.1405i	−1.13837	+	1.56684i	−0.367284	+	0.930109i	$0.619712\pi$
$503$	−25.5310	+	35.1405i	−1.13837	+	1.56684i	−0.771089	+	0.636727i	$0.780288\pi$
$504$	−30.7867	+	12.2023i	−1.37135	+	0.543533i
$505$	−4.36461	−	4.36461i	−0.194223	−	0.194223i
$506$	−34.5031	−	5.65254i	−1.53385	−	0.251286i
$507$	7.97969	−	21.0553i	0.354390	−	0.935098i
$508$	−1.86945	−	5.75359i	−0.0829436	−	0.255274i
$509$	−5.16007	−	32.5794i	−0.228716	−	1.44406i	−0.788304	−	0.615286i	$-0.789040\pi$
$509$	−5.16007	−	32.5794i	−0.228716	−	1.44406i	0.559587	−	0.828771i	$-0.310960\pi$
$510$	−0.100854	−	0.0127221i	−0.00446588	−	0.000563345i
$511$	38.5172	+	12.5150i	1.70390	+	0.553631i
$512$	−12.0956	+	6.16303i	−0.534557	+	0.272370i
$513$	15.1481	−	13.3696i	0.668805	−	0.590281i
$514$	−2.31988	−	14.6472i	−0.102326	−	0.646059i
$515$	4.06401	+	2.07072i	0.179082	+	0.0912468i
$516$	−0.155472	+	0.165621i	−0.00684426	+	0.00729105i
$517$	−1.20296	−	2.39223i	−0.0529062	−	0.105210i
$518$	25.8435	−	25.8435i	1.13550	−	1.13550i
$519$	−7.61418	−	3.58127i	−0.334225	−	0.157200i
$520$	4.98473	+	2.30150i	0.218595	+	0.100927i
$521$	−5.84014	−	8.03826i	−0.255861	−	0.352163i	0.661692	−	0.749776i	$-0.269839\pi$
$521$	−5.84014	−	8.03826i	−0.255861	−	0.352163i	−0.917553	+	0.397613i	$0.869839\pi$
$522$	29.7562	−	17.6124i	1.30239	−	0.770874i
$523$	−7.18830	+	22.1233i	−0.314323	+	0.967385i	0.661710	+	0.749760i	$0.269831\pi$
$523$	−7.18830	+	22.1233i	−0.314323	+	0.967385i	−0.976032	+	0.217625i	$0.930169\pi$
$524$	−0.117870	+	0.0856376i	−0.00514918	+	0.00374110i
$525$	19.8333	−	29.1953i	0.865598	−	1.27419i
$526$	30.0948	+	15.3341i	1.31220	+	0.668597i
$527$	0.169436	−	0.169436i	0.00738074	−	0.00738074i
$528$	−26.0015	+	4.82213i	−1.13157	+	0.209856i
$529$	23.8842			1.03844
$530$	−0.633786	−	1.95059i	−0.0275299	−	0.0847283i
$531$	−0.0320598	−	0.143182i	−0.00139128	−	0.00621358i
$532$	3.72327	+	5.12464i	0.161424	+	0.222181i
$533$	−23.3970	+	18.4227i	−1.01344	+	0.797975i
$534$	2.77788	+	5.05076i	0.120211	+	0.218568i
$535$	−1.47706	+	9.32581i	−0.0638590	+	0.403190i
$536$	−5.37181	+	7.39366i	−0.232027	+	0.319357i
$537$	38.8760	+	18.2850i	1.67762	+	0.789057i
$538$	−25.4556	+	25.4556i	−1.09747	+	1.09747i
$539$	−0.217403	+	40.9813i	−0.00936421	+	1.76519i
$540$	−1.16246	+	0.110526i	−0.0500244	+	0.00475628i
$541$	−7.06301	+	13.8619i	−0.303662	+	0.595971i	−0.991532	−	0.129863i	$-0.958546\pi$
$541$	−7.06301	+	13.8619i	−0.303662	+	0.595971i	0.687869	+	0.725834i	$0.258546\pi$
$542$	3.45345	−	4.75326i	0.148338	−	0.204170i
$543$	36.7187	+	4.63186i	1.57575	+	0.198772i
$544$	−0.115805	+	0.0590054i	−0.00496508	+	0.00252983i
$545$	0.848916	−	2.61270i	0.0363636	−	0.111916i
$546$	42.1961	−	2.97075i	1.80582	−	0.127136i
$547$	−9.17663	−	6.66721i	−0.392364	−	0.285069i	0.374059	−	0.927405i	$-0.377966\pi$
$547$	−9.17663	−	6.66721i	−0.392364	−	0.285069i	−0.766424	+	0.642335i	$0.777966\pi$
$548$	−2.64092	+	5.18310i	−0.112815	+	0.221411i
$549$	2.19125	+	34.6276i	0.0935204	+	1.47787i
$550$	16.8117	−	16.6342i	0.716851	−	0.709286i
$551$	20.5836	+	20.5836i	0.876892	+	0.876892i
$552$	27.9958	−	10.0849i	1.19158	−	0.429240i
$553$	−7.16424	−	45.2332i	−0.304654	−	1.92351i
$554$	1.77409	−	11.2011i	0.0753738	−	0.475891i
$555$	−4.96987	+	2.73339i	−0.210959	+	0.116026i
$556$	−6.06675	−	1.97121i	−0.257288	−	0.0835978i
$557$	0.648088	−	4.09187i	0.0274604	−	0.173378i	−0.970146	−	0.242520i	$-0.922026\pi$
$557$	0.648088	−	4.09187i	0.0274604	−	0.173378i	0.997607	+	0.0691418i	$0.0220261\pi$
$558$	9.43575	−	14.8803i	0.399447	−	0.629935i
$559$	−1.11459	+	0.623352i	−0.0471422	+	0.0263650i
$560$			12.2918i			0.519424i
$561$	0.354776	−	0.0657954i	0.0149786	−	0.00277788i
$562$	−30.1601			−1.27223
$563$	7.07627	+	21.7785i	0.298229	+	0.917856i	0.982118	+	0.188269i	$0.0602876\pi$
$563$	7.07627	+	21.7785i	0.298229	+	0.917856i	−0.683888	+	0.729587i	$0.739712\pi$
$564$	−0.428306	−	0.290963i	−0.0180349	−	0.0122517i
$565$	−0.274995	+	1.73625i	−0.0115691	+	0.0730447i
$566$	12.7462	+	25.0159i	0.535765	+	1.05150i
$567$	32.7332	−	22.2803i	1.37466	−	0.935687i
$568$	7.57607	−	5.50433i	0.317885	−	0.230957i
$569$	−32.8201	−	23.8452i	−1.37589	−	0.999644i	−0.997251	−	0.0741005i	$-0.976391\pi$
$569$	−32.8201	−	23.8452i	−1.37589	−	0.999644i	−0.378641	−	0.925544i	$-0.623609\pi$
$570$	−2.13267	−	5.92033i	−0.0893277	−	0.247975i
$571$			20.2743i			0.848454i	0.905556	+	0.424227i	$0.139454\pi$
$571$			20.2743i			0.848454i	−0.905556	+	0.424227i	$0.860546\pi$
$572$	4.39409	+	0.546317i	0.183726	+	0.0228427i
$573$	17.8740	+	16.7787i	0.746698	+	0.700940i
$574$	−49.8470	−	25.3983i	−2.08057	−	1.06010i
$575$	−18.6410	+	25.6571i	−0.777384	+	1.06998i
$576$	13.9141	−	11.5193i	0.579753	−	0.479969i
$577$	−14.8189	−	29.0837i	−0.616918	−	1.21077i	−0.962219	−	0.272277i	$-0.912223\pi$
$577$	−14.8189	−	29.0837i	−0.616918	−	1.21077i	0.345301	−	0.938492i	$-0.387777\pi$
$578$	−23.3147	+	11.8794i	−0.969762	+	0.494118i
$579$	−17.4844	+	13.5674i	−0.726629	+	0.563843i
$580$	−0.263184	−	1.66168i	−0.0109281	−	0.0689975i
$581$	−2.02681	+	0.658551i	−0.0840863	+	0.0273213i
$582$	25.1471	−	26.7887i	1.04238	−	1.11043i
$583$	4.24783	+	5.91234i	0.175927	+	0.244864i
$584$	−23.0966			−0.955744
$585$	−6.41731	−	1.38306i	−0.265323	−	0.0571826i
$586$	−20.2409	−	14.7059i	−0.836144	−	0.607494i
$587$	11.6128	+	1.83929i	0.479312	+	0.0759156i	0.391416	−	0.920214i	$-0.371985\pi$
$587$	11.6128	+	1.83929i	0.479312	+	0.0759156i	0.0878967	+	0.996130i	$0.471985\pi$
$588$	3.81906	+	6.94385i	0.157495	+	0.286359i
$589$	14.1074	+	4.58377i	0.581285	+	0.188871i
$590$	−0.0451367	−	0.00714895i	−0.00185825	−	0.000294318i
$591$	−33.2252	−	22.5710i	−1.36670	−	0.928446i
$592$	−11.2767	+	22.1318i	−0.463471	+	0.909613i
$593$	−10.5383	+	10.5383i	−0.432757	+	0.432757i	−0.889565	−	0.456808i	$-0.848993\pi$
$593$	−10.5383	+	10.5383i	−0.432757	+	0.432757i	0.456808	+	0.889565i	$0.348993\pi$
$594$	24.4002	−	10.4213i	1.00115	−	0.427593i
$595$		−	0.167715i		−	0.00687566i
$596$	−3.96882	−	2.02222i	−0.162569	−	0.0828332i
$597$	4.50318	+	23.5832i	0.184303	+	0.965195i
$598$	−37.9804	+	1.47017i	−1.55313	+	0.0601198i
$599$	−4.58154	−	1.48863i	−0.187197	−	0.0608239i	0.213918	−	0.976852i	$-0.431377\pi$
$599$	−4.58154	−	1.48863i	−0.187197	−	0.0608239i	−0.401115	+	0.916028i	$0.631377\pi$
$600$	−5.61214	+	19.3303i	−0.229115	+	0.789155i
$601$	−32.2540	+	23.4339i	−1.31567	+	0.955890i	−0.315694	+	0.948861i	$0.602237\pi$
$601$	−32.2540	+	23.4339i	−1.31567	+	0.955890i	−0.999975	+	0.00702917i	$0.997763\pi$
$602$	−1.94093	−	1.41017i	−0.0791065	−	0.0574743i
$603$	4.33608	−	10.0301i	0.176579	−	0.408457i
$604$	3.20807	−	3.20807i	0.130535	−	0.130535i
$605$	3.09375	−	5.91581i	0.125779	−	0.240512i
$606$	27.1072	−	0.856823i	1.10116	−	0.0348060i
$607$	−10.7984	−	33.2340i	−0.438292	−	1.34892i	−0.889675	−	0.456594i	$-0.849069\pi$
$607$	−10.7984	−	33.2340i	−0.438292	−	1.34892i	0.451383	−	0.892330i	$-0.350931\pi$
$608$	−6.50912	−	4.72916i	−0.263980	−	0.191793i
$609$	34.9741	+	45.0714i	1.41722	+	1.82639i
$610$	10.2777	+	3.33942i	0.416131	+	0.135209i
$611$	−1.80081	−	2.28705i	−0.0728531	−	0.0925241i
$612$	0.0537455	−	0.0444952i	0.00217253	−	0.00179861i
$613$	−25.5213	+	4.04218i	−1.03080	+	0.163262i	−0.648845	−	0.760921i	$-0.724748\pi$
$613$	−25.5213	+	4.04218i	−1.03080	+	0.163262i	−0.381951	+	0.924183i	$0.624748\pi$
$614$	−36.6419	+	11.9057i	−1.47875	+	0.480474i
$615$	6.33006	+	5.94215i	0.255252	+	0.239611i
$616$	−11.1288	−	34.8795i	−0.448393	−	1.40534i
$617$	−18.2566	−	18.2566i	−0.734985	−	0.734985i	0.236618	−	0.971603i	$-0.423961\pi$
$617$	−18.2566	−	18.2566i	−0.734985	−	0.734985i	−0.971603	+	0.236618i	$0.923961\pi$
$618$	−18.8548	+	6.79202i	−0.758451	+	0.273215i
$619$	1.25535	+	7.92597i	0.0504568	+	0.318572i	0.999988	+	0.00489911i	$0.00155944\pi$
$619$	1.25535	+	7.92597i	0.0504568	+	0.318572i	−0.949531	+	0.313673i	$0.898441\pi$
$620$	−0.503906	−	0.693568i	−0.0202374	−	0.0278543i
$621$	−30.0300	+	19.0807i	−1.20506	+	0.765680i
$622$	10.0090	−	5.09983i	0.401324	−	0.204485i
$623$	−7.69404	+	5.59005i	−0.308255	+	0.223961i
$624$	−26.6501	+	10.7820i	−1.06686	+	0.431627i
$625$	−6.06004	−	18.6509i	−0.242402	−	0.746035i
$626$	1.49061	+	1.49061i	0.0595768	+	0.0595768i
$627$	13.5997	+	17.7193i	0.543118	+	0.707640i
$628$			4.25685i			0.169867i
$629$	0.153865	−	0.301977i	0.00613500	−	0.0120406i
$630$	−2.69465	−	12.0346i	−0.107358	−	0.479469i
$631$	14.7376	+	2.33421i	0.586695	+	0.0929234i	0.442723	−	0.896658i	$-0.354012\pi$
$631$	14.7376	+	2.33421i	0.586695	+	0.0929234i	0.143972	+	0.989582i	$0.454012\pi$
$632$	11.8572	+	23.2711i	0.471656	+	0.925677i
$633$	23.6771	+	43.0499i	0.941079	+	1.71108i
$634$	8.76198	+	12.0598i	0.347983	+	0.478957i
$635$	−9.79354	+	1.55114i	−0.388645	+	0.0615553i
$636$	1.27390	+	0.599169i	0.0505135	+	0.0237586i
$637$	8.66629	+	43.7009i	0.343371	+	1.73149i
$638$	17.1739	+	34.1523i	0.679920	+	1.35210i
$639$	−7.40153	+	8.40156i	−0.292800	+	0.332360i
$640$	−2.51468	−	7.73938i	−0.0994013	−	0.305926i
$641$	29.9042	+	21.7267i	1.18114	+	0.858152i	0.992300	−	0.123855i	$-0.0395258\pi$
$641$	29.9042	+	21.7267i	1.18114	+	0.858152i	0.188844	+	0.982007i	$0.439526\pi$
$642$	−25.4334	−	32.7762i	−1.00378	−	1.29357i
$643$	−11.1252	−	21.8345i	−0.438737	−	0.861070i	−0.999453	−	0.0330618i	$-0.989474\pi$
$643$	−11.1252	−	21.8345i	−0.438737	−	0.861070i	0.560716	−	0.828008i	$-0.310526\pi$
$644$	−5.06413	−	9.93892i	−0.199555	−	0.391648i
$645$	0.228253	+	0.294151i	0.00898744	+	0.0115822i
$646$	0.304199	+	0.221014i	0.0119685	+	0.00869566i
$647$	9.03190	+	27.7973i	0.355081	+	1.09283i	0.955963	+	0.293488i	$0.0948162\pi$
$647$	9.03190	+	27.7973i	0.355081	+	1.09283i	−0.600882	+	0.799338i	$0.705184\pi$
$648$	−13.8274	+	17.8531i	−0.543193	+	0.701334i
$649$	0.160349	−	0.0245255i	0.00629424	−	0.000962710i
$650$	14.2964	−	21.3691i	0.560749	−	0.838166i
$651$	26.3061	+	12.3729i	1.03102	+	0.484931i
$652$	−0.0896214	+	0.0141946i	−0.00350984	+	0.000555905i
$653$	4.30476	+	5.92499i	0.168458	+	0.231863i	0.884897	−	0.465788i	$-0.154229\pi$
$653$	4.30476	+	5.92499i	0.168458	+	0.231863i	−0.716438	+	0.697650i	$0.754229\pi$
$654$	5.81692	+	10.5764i	0.227459	+	0.413569i
$655$	0.108413	+	0.212772i	0.00423604	+	0.00831369i
$656$	37.5533	+	5.94786i	1.46621	+	0.232225i
$657$	26.9485	−	6.03400i	1.05136	−	0.235409i
$658$	2.48268	−	4.87253i	0.0967849	−	0.189951i
$659$		−	19.3753i		−	0.754754i	−0.926060	−	0.377377i	$-0.876826\pi$
$659$		−	19.3753i		−	0.754754i	0.926060	−	0.377377i	$-0.123174\pi$
$660$	−0.0339392	−	1.29050i	−0.00132108	−	0.0502326i
$661$	−1.02129	−	1.02129i	−0.0397238	−	0.0397238i	0.686966	−	0.726690i	$-0.258942\pi$
$661$	−1.02129	−	1.02129i	−0.0397238	−	0.0397238i	−0.726690	+	0.686966i	$0.758942\pi$
$662$	11.6879	+	35.9717i	0.454264	+	1.39808i
$663$	0.363626	−	0.147115i	0.0141221	−	0.00571348i
$664$	0.983250	−	0.714373i	0.0381575	−	0.0277230i
$665$	9.25068	−	4.71346i	0.358726	−	0.182780i
$666$	6.18893	−	24.1408i	0.239816	−	0.935437i
$667$	−30.1306	−	41.4713i	−1.16666	−	1.60577i
$668$	−0.756417	−	4.77583i	−0.0292667	−	0.184782i
$669$	−39.5499	+	14.2470i	−1.52909	+	0.550820i
$670$	−2.40654	−	2.40654i	−0.0929728	−	0.0929728i
$671$	−38.3583	−	0.203488i	−1.48081	−	0.00785558i
$672$	−11.4964	−	10.7919i	−0.443483	−	0.416306i
$673$	40.2489	−	13.0777i	1.55148	−	0.504106i	0.596964	−	0.802268i	$-0.296373\pi$
$673$	40.2489	−	13.0777i	1.55148	−	0.504106i	0.954515	+	0.298161i	$0.0963733\pi$
$674$	−23.2830	+	3.68767i	−0.896829	+	0.142044i
$675$	1.49804	−	24.0202i	0.0576597	−	0.924538i
$676$	4.79925	−	0.372103i	0.184587	−	0.0143117i
$677$	−19.3017	−	6.27149i	−0.741823	−	0.241033i	−0.0863641	−	0.996264i	$-0.527525\pi$
$677$	−19.3017	−	6.27149i	−0.741823	−	0.241033i	−0.655459	+	0.755231i	$0.727525\pi$
$678$	−4.73512	−	6.10218i	−0.181851	−	0.234353i
$679$	49.0432	+	35.6320i	1.88210	+	1.36743i
$680$	0.0295566	+	0.0909658i	0.00113344	+	0.00348838i
$681$	−9.58093	+	0.302840i	−0.367142	+	0.0116049i
$682$	15.6982	+	11.5332i	0.601117	+	0.441628i
$683$	−23.9039	+	23.9039i	−0.914656	+	0.914656i	−0.996634	−	0.0819778i	$-0.973876\pi$
$683$	−23.9039	+	23.9039i	−0.914656	+	0.914656i	0.0819778	+	0.996634i	$0.473876\pi$
$684$	3.96468	+	1.71396i	0.151593	+	0.0655347i
$685$	7.71354	+	5.60421i	0.294719	+	0.214126i
$686$	−29.3529	+	21.3261i	−1.12070	+	0.814236i
$687$	1.37919	−	4.75043i	0.0526194	−	0.181240i
$688$	1.55071	+	0.503855i	0.0591202	+	0.0192093i
$689$	5.80853	+	5.37561i	0.221287	+	0.204794i
$690$	2.07842	+	10.8847i	0.0791242	+	0.414373i
$691$	10.2242	+	5.20949i	0.388947	+	0.198178i	0.637518	−	0.770435i	$-0.279961\pi$
$691$	10.2242	+	5.20949i	0.388947	+	0.198178i	−0.248571	+	0.968614i	$0.579961\pi$
$692$		−	1.79884i		−	0.0683814i
$693$	22.0971	+	37.7890i	0.839400	+	1.43549i
$694$	−23.9427	+	23.9427i	−0.908852	+	0.908852i
$695$	−4.74661	+	9.31575i	−0.180049	+	0.353367i
$696$	−26.9123	−	18.2824i	−1.02011	−	0.692994i
$697$	−0.512395	−	0.0811553i	−0.0194083	−	0.00307398i
$698$	−8.52726	−	2.77068i	−0.322762	−	0.104872i
$699$	−9.67275	−	17.5871i	−0.365857	−	0.665204i
$700$	7.45251	+	1.18036i	0.281678	+	0.0446135i
$701$	−3.53683	−	2.56966i	−0.133584	−	0.0970545i	0.518987	−	0.854782i	$-0.326309\pi$
$701$	−3.53683	−	2.56966i	−0.133584	−	0.0970545i	−0.652571	+	0.757728i	$0.726309\pi$
$702$	23.7287	−	16.3987i	0.895582	−	0.618930i
$703$	20.9804			0.791290
$704$	11.6523	+	16.2182i	0.439161	+	0.611246i
$705$	−0.580844	+	0.618762i	−0.0218758	+	0.0233039i
$706$	16.6741	−	5.41773i	0.627536	−	0.203899i
$707$	6.99983	+	44.1952i	0.263256	+	1.66213i
$708$	0.0247819	−	0.0192300i	0.000931360	−	0.000722708i
$709$	0.327316	−	0.166776i	0.0122926	−	0.00626339i	−0.447833	−	0.894117i	$-0.647804\pi$
$709$	0.327316	−	0.166776i	0.0122926	−	0.00626339i	0.460126	+	0.887854i	$0.347804\pi$
$710$	1.58321	+	3.10723i	0.0594169	+	0.116612i
$711$	−19.9143	−	24.0544i	−0.746845	−	0.902111i
$712$	3.18798	−	4.38787i	0.119474	−	0.164442i
$713$	−23.2742	−	11.8588i	−0.871625	−	0.444115i
$714$	0.537276	+	0.504351i	0.0201070	+	0.0188749i
$715$	2.01106	−	6.97331i	0.0752092	−	0.260787i
$716$			9.18439i			0.343237i
$717$	0.744954	+	2.06801i	0.0278208	+	0.0772311i
$718$	−8.00027	−	5.81253i	−0.298567	−	0.216922i
$719$	17.7792	−	12.9174i	0.663054	−	0.481737i	−0.204639	−	0.978838i	$-0.565602\pi$
$719$	17.7792	−	12.9174i	0.663054	−	0.481737i	0.867693	+	0.497101i	$0.165602\pi$
$720$	4.26918	+	7.21280i	0.159103	+	0.268805i
$721$	−15.0112	−	29.4611i	−0.559046	−	1.09719i
$722$	0.934731	−	5.90166i	0.0347871	−	0.219637i
$723$	4.31658	+	2.93240i	0.160536	+	0.109057i
$724$	2.44495	+	7.52477i	0.0908657	+	0.279656i
$725$	34.6748			1.28779
$726$	9.64780	+	27.7008i	0.358064	+	1.02807i
$727$		−	21.8054i		−	0.808717i	−0.914601	−	0.404359i	$-0.867495\pi$
$727$		−	21.8054i		−	0.808717i	0.914601	−	0.404359i	$-0.132505\pi$
$728$	−19.4276	−	34.7378i	−0.720035	−	1.28747i
$729$	11.4693	−	24.4429i	0.424790	−	0.905292i
$730$	1.34551	−	8.49521i	0.0497995	−	0.314422i
$731$	−0.0211586	−	0.00687483i	−0.000782577	−	0.000254275i
$732$	−6.49942	+	3.57463i	−0.240225	+	0.132122i
$733$	5.92639	−	37.4177i	0.218896	−	1.38206i	−0.596249	−	0.802799i	$-0.703343\pi$
$733$	5.92639	−	37.4177i	0.218896	−	1.38206i	0.815145	−	0.579256i	$-0.196657\pi$
$734$	1.38106	+	8.71968i	0.0509759	+	0.321849i
$735$	12.2203	−	4.40209i	0.450752	−	0.162373i
$736$	10.0185	+	10.0185i	0.369287	+	0.369287i
$737$	10.7346	+	5.54146i	0.395413	+	0.204122i
$738$	−38.0713	+	2.40917i	−1.40142	+	0.0886828i
$739$	−0.0248321	+	0.0487358i	−0.000913464	+	0.00179277i	−0.891463	−	0.453094i	$-0.850320\pi$
$739$	−0.0248321	+	0.0487358i	−0.000913464	+	0.00179277i	0.890549	+	0.454887i	$0.150320\pi$
$740$	−0.980983	−	0.712726i	−0.0360617	−	0.0262003i
$741$	18.3337	+	15.9220i	0.673507	+	0.584910i
$742$	−4.59448	+	14.1404i	−0.168669	+	0.519109i
$743$	35.9782	−	18.3318i	1.31991	−	0.672529i	0.354943	−	0.934888i	$-0.384500\pi$
$743$	35.9782	−	18.3318i	1.31991	−	0.672529i	0.964970	+	0.262359i	$0.0845004\pi$
$744$	−16.4485	−	2.07488i	−0.603030	−	0.0760688i
$745$	−4.29128	+	5.90644i	−0.157220	+	0.216395i
$746$	−6.05862	+	11.8907i	−0.221822	+	0.435350i
$747$	−0.960598	+	1.09039i	−0.0351464	+	0.0398951i
$748$	0.0450089	+	0.0626456i	0.00164569	+	0.00229055i
$749$	48.4000	−	48.4000i	1.76850	−	1.76850i
$750$	−14.1054	−	6.63434i	−0.515055	−	0.242252i
$751$	5.52354	−	7.60250i	0.201557	−	0.277419i	−0.696259	−	0.717791i	$-0.745153\pi$
$751$	5.52354	−	7.60250i	0.201557	−	0.277419i	0.897816	+	0.440372i	$0.145153\pi$
$752$	−0.581402	+	3.67083i	−0.0212016	+	0.133861i
$753$	−21.0220	−	38.2224i	−0.766085	−	1.39290i
$754$	25.7090	+	32.6506i	0.936266	+	1.18907i
$755$	−4.37084	−	6.01595i	−0.159071	−	0.218943i
$756$	7.28854	+	4.30505i	0.265082	+	0.156573i
$757$	1.56487	+	4.81618i	0.0568763	+	0.175047i	0.975459	−	0.220182i	$-0.0706651\pi$
$757$	1.56487	+	4.81618i	0.0568763	+	0.175047i	−0.918583	+	0.395229i	$0.870665\pi$
$758$	−27.4181			−0.995870
$759$	−18.7726	−	34.5654i	−0.681401	−	1.25465i
$760$	−4.18675	+	4.18675i	−0.151869	+	0.151869i
$761$	−3.80341	−	1.93794i	−0.137874	−	0.0702501i	0.383693	−	0.923461i	$-0.374652\pi$
$761$	−3.80341	−	1.93794i	−0.137874	−	0.0702501i	−0.521566	+	0.853211i	$0.674652\pi$
$762$	24.4819	−	36.0382i	0.886886	−	1.30552i
$763$	−16.1114	+	11.7056i	−0.583273	+	0.423773i
$764$	−1.61954	+	4.98445i	−0.0585931	+	0.180331i
$765$	−0.0582507	−	0.0984147i	−0.00210606	−	0.00355819i
$766$	−11.2973	−	15.5494i	−0.408188	−	0.561822i
$767$	0.165480	−	0.0609398i	0.00597515	−	0.00220041i
$768$	13.4806	+	6.34049i	0.486439	+	0.228793i
$769$	1.53585	−	1.53585i	0.0553841	−	0.0553841i	−0.678872	−	0.734256i	$-0.737531\pi$
$769$	1.53585	−	1.53585i	0.0553841	−	0.0553841i	0.734256	+	0.678872i	$0.237531\pi$
$770$	13.4774	−	2.06139i	0.485693	−	0.0742873i
$771$	11.4186	−	12.1640i	0.411231	−	0.438077i
$772$	−4.21554	−	2.14792i	−0.151721	−	0.0773055i
$773$	−5.34023	−	33.7169i	−0.192075	−	1.21271i	−0.875691	−	0.482871i	$-0.839594\pi$
$773$	−5.34023	−	33.7169i	−0.192075	−	1.21271i	0.683617	−	0.729841i	$-0.260406\pi$
$774$	−1.62871	−	0.153360i	−0.0585428	−	0.00551240i
$775$	15.7434	−	8.02166i	0.565520	−	0.288147i
$776$	−32.8796	−	10.6832i	−1.18031	−	0.383506i
$777$	40.7942	+	5.14596i	1.46348	+	0.184610i
$778$	1.26348	+	7.97731i	0.0452980	+	0.286000i
$779$	−9.92401	−	30.5430i	−0.355564	−	1.09431i
$780$	−0.316346	−	1.36729i	−0.0113270	−	0.0489567i
$781$	−8.70640	−	8.79927i	−0.311540	−	0.314863i
$782$	−0.468207	−	0.468207i	−0.0167431	−	0.0167431i
$783$	36.1769	+	14.3006i	1.29286	+	0.511061i
$784$	33.4347	−	46.0189i	1.19410	−	1.64353i
$785$	6.89121	+	1.09146i	0.245958	+	0.0389559i
$786$	−1.00763	−	0.292545i	−0.0359410	−	0.0104347i
$787$	−34.9854	+	17.8260i	−1.24710	+	0.635427i	−0.947840	−	0.318746i	$-0.896738\pi$
$787$	−34.9854	+	17.8260i	−1.24710	+	0.635427i	−0.299255	+	0.954173i	$0.596738\pi$
$788$	1.34329	−	8.48120i	0.0478527	−	0.302130i
$789$	7.12709	+	37.3246i	0.253731	+	1.32879i
$790$	−9.25017	+	3.00556i	−0.329106	+	0.106933i
$791$	9.01098	−	9.01098i	0.320394	−	0.320394i
$792$	−18.6447	−	16.6019i	−0.662509	−	0.589923i
$793$	−40.9039	+	8.11161i	−1.45254	+	0.288052i
$794$	−5.22394	+	1.69736i	−0.185391	+	0.0602371i
$795$	1.29660	−	1.90863i	0.0459855	−	0.0676922i
$796$	−4.15248	+	3.01695i	−0.147181	+	0.106933i
$797$	15.4955	−	47.6903i	0.548879	−	1.68928i	−0.162705	−	0.986675i	$-0.552022\pi$
$797$	15.4955	−	47.6903i	0.548879	−	1.68928i	0.711584	−	0.702601i	$-0.247978\pi$
$798$	−12.7190	+	43.8088i	−0.450247	+	1.55081i
$799$	0.00793292	−	0.0500865i	0.000280646	−	0.00177193i
$800$	−9.46591	+	1.49925i	−0.334670	+	0.0530066i
$801$	−2.57331	+	5.95251i	−0.0909233	+	0.210322i
$802$	17.9913			0.635295
$803$	4.61596	+	30.1794i	0.162894	+	1.06501i
$804$	2.33488	−	0.0738024i	0.0823449	−	0.00260281i
$805$	−17.3881	+	5.64974i	−0.612850	+	0.199127i
$806$	19.2260	+	8.87686i	0.677208	+	0.312674i
$807$	−40.1819	−	5.06872i	−1.41447	−	0.178427i
$808$	−11.5851	−	22.7371i	−0.407563	−	0.799888i
$809$	18.9483	+	6.15667i	0.666186	+	0.216457i	0.622538	−	0.782590i	$-0.286102\pi$
$809$	18.9483	+	6.15667i	0.666186	+	0.216457i	0.0436486	+	0.999047i	$0.486102\pi$
$810$	−5.76105	−	6.12594i	−0.202423	−	0.215244i
$811$	−8.60176	+	1.36239i	−0.302049	+	0.0478398i	−0.305619	−	0.952154i	$-0.598863\pi$
$811$	−8.60176	+	1.36239i	−0.302049	+	0.0478398i	0.00357055	+	0.999994i	$0.498863\pi$
$812$	−5.53692	+	10.8668i	−0.194308	+	0.381351i
$813$	6.60660	−	0.208825i	0.231703	−	0.00732383i
$814$	26.1577	+	8.65284i	0.916828	+	0.303282i
$815$			0.148723i			0.00520955i
$816$	−0.453197	−	0.213158i	−0.0158651	−	0.00746201i
$817$	−0.215443	−	1.36025i	−0.00753739	−	0.0475892i
$818$	−13.0047	+	9.44849i	−0.454700	+	0.330359i
$819$	31.7429	+	35.4556i	1.10919	+	1.23892i
$820$	−0.573559	+	1.76523i	−0.0200295	+	0.0616446i
$821$	−49.9208	−	7.90667i	−1.74225	−	0.275945i	−0.797399	−	0.603453i	$-0.793791\pi$
$821$	−49.9208	−	7.90667i	−1.74225	−	0.275945i	−0.944848	+	0.327508i	$0.893791\pi$
$822$	−41.1491	+	7.85739i	−1.43524	+	0.274058i
$823$	−19.3371	+	6.28301i	−0.674049	+	0.219012i	−0.625988	−	0.779833i	$-0.715304\pi$
$823$	−19.3371	+	6.28301i	−0.674049	+	0.219012i	−0.0480610	+	0.998844i	$0.515304\pi$
$824$	13.3338	+	13.3338i	0.464504	+	0.464504i
$825$	26.3797	+	3.46991i	0.918423	+	0.120807i
$826$	0.234255	+	0.234255i	0.00815077	+	0.00815077i
$827$	26.5661	+	13.5361i	0.923794	+	0.470697i	0.850122	−	0.526586i	$-0.176528\pi$
$827$	26.5661	+	13.5361i	0.923794	+	0.470697i	0.0736724	+	0.997282i	$0.476528\pi$
$828$	−6.42359	−	4.07325i	−0.223235	−	0.141555i
$829$	−18.8476	−	25.9415i	−0.654605	−	0.900987i	0.344683	−	0.938719i	$-0.387987\pi$
$829$	−18.8476	−	25.9415i	−0.654605	−	0.900987i	−0.999288	+	0.0377324i	$0.987987\pi$
$830$	0.205475	+	0.403268i	0.00713215	+	0.0139976i
$831$	11.1793	−	6.14854i	0.387807	−	0.213291i
$832$	15.9334	+	14.7459i	0.552392	+	0.511221i
$833$	−0.456199	+	0.627903i	−0.0158063	+	0.0217556i
$834$	−15.5690	−	43.2200i	−0.539112	−	1.49659i
$835$	−7.92531			−0.274267
$836$	−2.19042	+	4.24314i	−0.0757572	+	0.146752i
$837$	19.7337	−	1.87626i	0.682095	−	0.0648532i
$838$	24.7778	+	12.6249i	0.855936	+	0.436121i
$839$	−47.8599	+	7.58026i	−1.65231	+	0.261700i	−0.911886	−	0.410444i	$-0.865374\pi$
$839$	−47.8599	+	7.58026i	−1.65231	+	0.261700i	−0.740421	+	0.672144i	$0.765374\pi$
$840$	−9.16762	+	7.11381i	−0.316313	+	0.245450i
$841$	−8.35801	+	25.7233i	−0.288207	+	0.887011i
$842$	−10.7127	+	32.9702i	−0.369183	+	1.13623i
$843$	−20.8013	−	26.8068i	−0.716435	−	0.923275i
$844$	−6.17375	+	8.49744i	−0.212509	+	0.292494i
$845$	0.628154	−	7.86469i	0.0216092	−	0.270554i
$846$	−0.235496	−	3.72146i	−0.00809652	−	0.127947i
$847$	−43.3515	+	21.5124i	−1.48957	+	0.739175i
$848$		−	10.1047i		−	0.346998i
$849$	−13.4435	+	28.5824i	−0.461380	+	0.980946i
$850$	0.442382	−	0.0700664i	0.0151736	−	0.00240326i
$851$	−36.4910	−	5.77961i	−1.25090	−	0.198122i
$852$	−2.29876	−	0.667396i	−0.0787541	−	0.0228646i
$853$	25.5158	−	13.0009i	0.873643	−	0.445144i	0.0411335	−	0.999154i	$-0.486903\pi$
$853$	25.5158	−	13.0009i	0.873643	−	0.445144i	0.832510	+	0.554010i	$0.186903\pi$
$854$	−46.0470	−	63.3782i	−1.57570	−	2.16876i
$855$	3.79119	−	5.97877i	0.129656	−	0.204470i
$856$	−17.7218	+	34.7809i	−0.605717	+	1.18879i
$857$	−48.6895			−1.66320			−0.831600	−	0.555375i	$-0.812575\pi$
$857$	−48.6895			−1.66320			−0.831600	+	0.555375i	$0.812575\pi$
$858$	16.2914	+	27.4125i	0.556178	+	0.935846i
$859$	22.0098			0.750964			0.375482	−	0.926830i	$-0.377477\pi$
$859$	22.0098			0.750964			0.375482	+	0.926830i	$0.377477\pi$
$860$	−0.0361358	+	0.0709205i	−0.00123222	+	0.00241837i
$861$	−11.8048	−	61.8218i	−0.402307	−	2.10688i
$862$	21.5511	+	29.6626i	0.734035	+	1.01031i
$863$	5.42662	−	2.76500i	0.184724	−	0.0941217i	−0.359183	−	0.933267i	$-0.616944\pi$
$863$	5.42662	−	2.76500i	0.184724	−	0.0941217i	0.543907	+	0.839146i	$0.316944\pi$
$864$	−10.4943	−	2.33973i	−0.357022	−	0.0795991i
$865$	−2.91205	−	0.461223i	−0.0990126	−	0.0156821i
$866$	18.7561	−	2.97068i	0.637359	−	0.100948i
$867$	−26.6386	−	12.5293i	−0.904695	−	0.425516i
$868$			6.21477i			0.210943i
$869$	28.0377	−	20.1442i	0.951115	−	0.683346i
$870$	8.29231	−	8.83364i	0.281136	−	0.299488i
$871$	12.6378	+	3.57214i	0.428214	+	0.121037i
$872$	6.67567	−	9.18827i	0.226067	−	0.311154i
$873$	41.1540	+	3.87507i	1.39285	+	0.131151i
$874$	12.6665	−	38.9834i	0.428450	−	1.31863i
$875$	7.94724	−	24.4591i	0.268666	−	0.826868i
$876$	3.61930	+	4.66422i	0.122285	+	0.157589i
$877$	−33.0307	+	5.23155i	−1.11537	+	0.176657i	−0.686795	−	0.726851i	$-0.740983\pi$
$877$	−33.0307	+	5.23155i	−1.11537	+	0.176657i	−0.428572	+	0.903508i	$0.640983\pi$
$878$	37.9626	+	19.3429i	1.28118	+	0.652792i
$879$	−0.889246	−	28.1330i	−0.0299935	−	0.948903i
$880$	−8.27840	+	4.16289i	−0.279065	+	0.140331i
$881$	−16.6789			−0.561926			−0.280963	−	0.959719i	$-0.590654\pi$
$881$	−16.6789			−0.561926			−0.280963	+	0.959719i	$0.590654\pi$
$882$	−22.6466	+	52.3855i	−0.762550	+	1.76391i
$883$	−1.79956	+	2.47688i	−0.0605600	+	0.0833537i	−0.838223	−	0.545328i	$-0.816405\pi$
$883$	−1.79956	+	2.47688i	−0.0605600	+	0.0833537i	0.777663	+	0.628682i	$0.216405\pi$
$884$	0.0615456	+	0.0569585i	0.00207000	+	0.00191572i
$885$	−0.0247765	−	0.0450488i	−0.000832852	−	0.00151430i
$886$	14.4712	+	28.4013i	0.486169	+	0.954161i
$887$	1.07782	+	1.48349i	0.0361897	+	0.0498108i	0.826728	−	0.562601i	$-0.190199\pi$
$887$	1.07782	+	1.48349i	0.0361897	+	0.0498108i	−0.790539	+	0.612412i	$0.790199\pi$
$888$	−23.0329	+	4.39812i	−0.772935	+	0.147591i
$889$	64.0464	+	32.6333i	2.14805	+	1.09448i
$890$	1.42820	+	1.42820i	0.0478732	+	0.0478732i
$891$	26.0913	+	14.4997i	0.874093	+	0.485759i
$892$	−6.35470	−	6.35470i	−0.212771	−	0.212771i
$893$	2.98557	−	0.970070i	0.0999082	−	0.0324621i
$894$	−6.01659	−	31.5089i	−0.201225	−	1.05381i
$895$	14.8682	+	2.35489i	0.496988	+	0.0787152i
$896$	−18.2296	+	56.1048i	−0.609007	+	1.87433i
$897$	−27.5016	−	32.7436i	−0.918253	−	1.09328i
$898$	−29.9725	+	21.7763i	−1.00019	+	0.726684i
$899$	4.46775	+	28.2083i	0.149008	+	0.940799i
$900$	4.78307	−	1.89577i	0.159436	−	0.0631922i
$901$			0.137874i			0.00459323i
$902$	0.223725	−	42.1730i	0.00744923	−	1.40421i
$903$	−0.0852712	−	2.69772i	−0.00283765	−	0.0897745i
$904$	−3.29938	+	6.47541i	−0.109736	+	0.215369i
$905$	12.8084	−	2.02865i	0.425765	−	0.0674346i
$906$	32.4160	+	4.08909i	1.07695	+	0.135851i
$907$	19.3585	+	6.28997i	0.642790	+	0.208855i	0.612232	−	0.790678i	$-0.290272\pi$
$907$	19.3585	+	6.28997i	0.642790	+	0.208855i	0.0305576	+	0.999533i	$0.490272\pi$
$908$	−0.930342	−	1.82590i	−0.0308745	−	0.0605946i
$909$	19.4573	+	23.5024i	0.645358	+	0.779525i
$910$	13.9088	−	5.12204i	0.461071	−	0.169794i
$911$	27.9770	−	9.09027i	0.926919	−	0.301174i	0.193617	−	0.981077i	$-0.437978\pi$
$911$	27.9770	−	9.09027i	0.926919	−	0.301174i	0.733302	+	0.679903i	$0.237978\pi$
$912$	−0.979475	−	30.9876i	−0.0324337	−	1.02610i
$913$	−1.12995	−	1.14200i	−0.0373958	−	0.0377947i
$914$	45.9958			1.52141
$915$	4.12034	+	11.4381i	0.136214	+	0.378133i
$916$	1.04447	−	0.165428i	0.0345104	−	0.00546590i
$917$	0.270807	−	1.70981i	0.00894284	−	0.0564629i
$918$	0.490442	+	0.109345i	0.0161870	+	0.00360893i
$919$	13.9695	−	42.9938i	0.460812	−	1.41823i	−0.403361	−	0.915041i	$-0.632158\pi$
$919$	13.9695	−	42.9938i	0.460812	−	1.41823i	0.864174	−	0.503194i	$-0.167842\pi$
$920$	8.43534	−	6.12863i	0.278105	−	0.202055i
$921$	−35.8537	−	24.3566i	−1.18142	−	0.802578i
$922$	−7.38466	+	2.39942i	−0.243201	+	0.0790207i
$923$	−11.1847	−	7.48275i	−0.368148	−	0.246298i
$924$	−5.29979	+	7.71311i	−0.174350	+	0.253743i
$925$	17.6716	−	17.6716i	0.581038	−	0.581038i
$926$	14.3103	−	4.64968i	0.470264	−	0.152798i
$927$	−19.0409	−	12.0740i	−0.625386	−	0.396562i
$928$	2.42334	−	15.3003i	0.0795499	−	0.502258i
$929$	−9.80918	+	4.99803i	−0.321829	+	0.163980i	−0.607440	−	0.794366i	$-0.707803\pi$
$929$	−9.80918	+	4.99803i	−0.321829	+	0.163980i	0.285611	+	0.958346i	$0.407803\pi$
$930$	1.72138	−	5.92908i	0.0564464	−	0.194422i
$931$	−47.4543	−	7.51602i	−1.55525	−	0.246328i
$932$	2.52215	−	3.47144i	0.0826158	−	0.113711i
$933$	11.4360	+	5.37881i	0.374396	+	0.176094i
$934$	−39.2566	−	39.2566i	−1.28451	−	1.28451i
$935$	0.112954	−	0.0568003i	0.00369400	−	0.00185757i
$936$	−23.4651	−	13.6364i	−0.766982	−	0.445720i
$937$	15.9525	+	49.0968i	0.521146	+	1.60392i	0.771813	+	0.635849i	$0.219350\pi$
$937$	15.9525	+	49.0968i	0.521146	+	1.60392i	−0.250667	+	0.968073i	$0.580650\pi$
$938$	3.85953	+	24.3681i	0.126018	+	0.795648i
$939$	−0.296811	+	2.35294i	−0.00968605	+	0.0767855i
$940$	−0.172551	−	0.0560652i	−0.00562800	−	0.00182865i
$941$	3.33147	−	1.69747i	0.108603	−	0.0553359i	−0.398845	−	0.917018i	$-0.630589\pi$
$941$	3.33147	−	1.69747i	0.108603	−	0.0553359i	0.507448	+	0.861682i	$0.330589\pi$
$942$	−24.2197	+	18.7938i	−0.789119	+	0.612334i
$943$	8.84688	+	55.8570i	0.288094	+	1.81895i
$944$	−0.200611	−	0.102217i	−0.00652934	−	0.00332687i
$945$	8.83804	−	10.6952i	0.287501	−	0.347916i
$946$	0.292395	−	1.78478i	0.00950659	−	0.0580282i
$947$	−0.229049	+	0.229049i	−0.00744310	+	0.00744310i	−0.710819	−	0.703375i	$-0.751675\pi$
$947$	−0.229049	+	0.229049i	−0.00744310	+	0.00744310i	0.703375	+	0.710819i	$0.251675\pi$
$948$	2.84140	−	6.04115i	0.0922845	−	0.196207i
$949$	11.4695	+	31.1452i	0.372317	+	1.01102i
$950$	16.2973	+	22.4313i	0.528755	+	0.727769i
$951$	−4.67587	+	16.1054i	−0.151625	+	0.522253i
$952$	0.214264	−	0.659435i	0.00694432	−	0.0213724i
$953$	20.0972	−	14.6015i	0.651014	−	0.472989i	−0.212603	−	0.977139i	$-0.568194\pi$
$953$	20.0972	−	14.6015i	0.651014	−	0.472989i	0.863616	+	0.504150i	$0.168194\pi$
$954$	2.21519	+	9.89326i	0.0717194	+	0.320306i
$955$	7.65383	+	3.89982i	0.247672	+	0.126195i
$956$	−0.332278	+	0.332278i	−0.0107466	+	0.0107466i
$957$	−18.5104	+	38.8191i	−0.598355	+	1.25484i
$958$	44.1970			1.42794
$959$	−21.3586	−	65.7350i	−0.689705	−	2.12269i
$960$	3.55671	−	5.23558i	0.114792	−	0.168978i
$961$	−9.66715	−	13.3057i	−0.311844	−	0.429216i
$962$	29.7423	+	3.53774i	0.958929	+	0.114061i
$963$	11.5907	−	45.2112i	0.373505	−	1.45691i
$964$	−0.174519	+	1.10187i	−0.00562087	+	0.0354888i
$965$	−4.55804	+	6.27360i	−0.146729	+	0.201954i
$966$	34.1903	−	72.6925i	1.10006	−	2.33884i
$967$	−6.86279	+	6.86279i	−0.220692	+	0.220692i	−0.808790	−	0.588098i	$-0.799877\pi$
$967$	−6.86279	+	6.86279i	−0.220692	+	0.220692i	0.588098	+	0.808790i	$0.299877\pi$
$968$	19.7219	−	19.3078i	0.633887	−	0.620577i
$969$	0.0133644	+	0.422809i	0.000429327	+	0.0135826i
$970$	5.84485	−	11.4712i	0.187667	−	0.368317i
$971$	7.02139	−	9.66412i	0.225327	−	0.310136i	−0.681353	−	0.731955i	$-0.738608\pi$
$971$	7.02139	−	9.66412i	0.225327	−	0.310136i	0.906680	+	0.421819i	$0.138608\pi$
$972$	5.77211	−	0.00525794i	0.185141	−	0.000168649i
$973$	67.5324	−	34.4095i	2.16499	−	1.10312i
$974$	18.4439	−	56.7646i	0.590981	−	1.81885i
$975$	28.8533	−	2.03137i	0.924047	−	0.0650561i
$976$	43.0736	+	31.2948i	1.37875	+	1.00172i
$977$	−2.80085	+	5.49697i	−0.0896071	+	0.175864i	−0.931461	−	0.363842i	$-0.881465\pi$
$977$	−2.80085	+	5.49697i	−0.0896071	+	0.175864i	0.841853	+	0.539706i	$0.181465\pi$
$978$	−0.476435	−	0.447239i	−0.0152347	−	0.0143011i
$979$	−6.37059	−	3.28866i	−0.203605	−	0.105106i
$980$	1.96350	+	1.96350i	0.0627218	+	0.0627218i
$981$	−5.38854	+	12.4646i	−0.172043	+	0.397965i
$982$	4.21373	+	26.6045i	0.134466	+	0.848983i
$983$	−3.06489	+	19.3509i	−0.0977548	+	0.617199i	0.889363	+	0.457202i	$0.151148\pi$
$983$	−3.06489	+	19.3509i	−0.0977548	+	0.617199i	−0.987118	+	0.159997i	$0.948852\pi$
$984$	17.2976	+	31.4507i	0.551428	+	1.00261i
$985$	−13.3854	−	4.34917i	−0.426494	−	0.138576i
$986$	−0.113253	+	0.715050i	−0.00360670	+	0.0227718i
$987$	6.04307	−	1.15392i	0.192353	−	0.0367296i
$988$	−1.41199	+	4.99543i	−0.0449213	+	0.158926i
$989$			2.42523i			0.0771178i
$990$	7.19255	−	5.89058i	0.228594	−	0.187215i
$991$	13.6370			0.433192			0.216596	−	0.976261i	$-0.430505\pi$
$991$	13.6370			0.433192			0.216596	+	0.976261i	$0.430505\pi$
$992$	−2.43931	−	7.50743i	−0.0774482	−	0.238361i
$993$	−23.9111	+	35.1979i	−0.758796	+	1.11697i
$994$	3.95475	−	24.9693i	0.125437	−	0.791979i
$995$	3.81930	+	7.49580i	0.121080	+	0.237633i
$996$	−0.298341	−	0.0866172i	−0.00945330	−	0.00274457i
$997$	22.6626	−	16.4654i	0.717733	−	0.521464i	−0.167926	−	0.985800i	$-0.553707\pi$
$997$	22.6626	−	16.4654i	0.717733	−	0.521464i	0.885659	+	0.464336i	$0.153707\pi$
$998$	−18.5317	−	13.4641i	−0.586612	−	0.426199i
$999$	25.7252	−	11.1490i	0.813909	−	0.352738i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bi.a.5.13	✓	416
3.2	odd	2	inner	429.2.bi.a.5.40	yes	416
11.9	even	5	inner	429.2.bi.a.317.40	yes	416
13.8	odd	4	inner	429.2.bi.a.203.13	yes	416
33.20	odd	10	inner	429.2.bi.a.317.13	yes	416
39.8	even	4	inner	429.2.bi.a.203.40	yes	416
143.86	odd	20	inner	429.2.bi.a.86.40	yes	416
429.86	even	20	inner	429.2.bi.a.86.13	yes	416

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bi.a.5.13	✓	416	1.1	even	1	trivial
429.2.bi.a.5.40	yes	416	3.2	odd	2	inner
429.2.bi.a.86.13	yes	416	429.86	even	20	inner
429.2.bi.a.86.40	yes	416	143.86	odd	20	inner
429.2.bi.a.203.13	yes	416	13.8	odd	4	inner
429.2.bi.a.203.40	yes	416	39.8	even	4	inner
429.2.bi.a.317.13	yes	416	33.20	odd	10	inner
429.2.bi.a.317.40	yes	416	11.9	even	5	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.bi (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.698951 + 1.37177i) q^{2} +(-1.70131 + 0.324864i) q^{3} +(-0.217646 - 0.299564i) q^{4} +(-0.540754 + 0.275528i) q^{5} +(0.743496 - 2.56087i) q^{6} +(4.34543 + 0.688249i) q^{7} +(-2.47818 + 0.392505i) q^{8} +(2.78893 - 1.10539i) q^{9} +O(q^{10})\)	\(q+(-0.698951 + 1.37177i) q^{2} +(-1.70131 + 0.324864i) q^{3} +(-0.217646 - 0.299564i) q^{4} +(-0.540754 + 0.275528i) q^{5} +(0.743496 - 2.56087i) q^{6} +(4.34543 + 0.688249i) q^{7} +(-2.47818 + 0.392505i) q^{8} +(2.78893 - 1.10539i) q^{9} -0.934371i q^{10} +(1.00815 + 3.15969i) q^{11} +(0.467601 + 0.438946i) q^{12} +(1.75992 + 3.14685i) q^{13} +(-3.98136 + 5.47988i) q^{14} +(0.830483 - 0.644431i) q^{15} +(1.42255 - 4.37815i) q^{16} +(-0.0194099 + 0.0597374i) q^{17} +(-0.432984 + 4.59838i) q^{18} +(-3.84043 + 0.608265i) q^{19} +(0.200231 + 0.102023i) q^{20} +(-7.61653 + 0.240748i) q^{21} +(-5.03901 - 0.825526i) q^{22} +6.84720 q^{23} +(4.08864 - 1.47284i) q^{24} +(-2.72243 + 3.74710i) q^{25} +(-5.54685 + 0.214711i) q^{26} +(-4.38573 + 2.78664i) q^{27} +(-0.739592 - 1.45153i) q^{28} +(-4.40043 - 6.05667i) q^{29} +(0.303543 + 1.58966i) q^{30} +(-3.39908 - 1.73192i) q^{31} +(1.46315 + 1.46315i) q^{32} +(-2.74164 - 5.04811i) q^{33} +(-0.0683794 - 0.0683794i) q^{34} +(-2.53945 + 0.825116i) q^{35} +(-0.938133 - 0.594878i) q^{36} +(-5.32933 - 0.844083i) q^{37} +(1.84988 - 5.69333i) q^{38} +(-4.01648 - 4.78204i) q^{39} +(1.23194 - 0.895057i) q^{40} +(1.29204 + 8.15764i) q^{41} +(4.99333 - 10.6164i) q^{42} +0.354193i q^{43} +(0.727110 - 0.989698i) q^{44} +(-1.20356 + 1.36617i) q^{45} +(-4.78586 + 9.39278i) q^{46} +(-0.797407 + 0.126297i) q^{47} +(-0.997893 + 7.91073i) q^{48} +(11.7517 + 3.81837i) q^{49} +(-3.23731 - 6.35358i) q^{50} +(0.0136157 - 0.107938i) q^{51} +(0.559643 - 1.21211i) q^{52} +(2.08760 - 0.678302i) q^{53} +(-0.757205 - 7.96393i) q^{54} +(-1.41574 - 1.43084i) q^{55} -11.0389 q^{56} +(6.33617 - 2.28247i) q^{57} +(11.3840 - 1.80306i) q^{58} +(0.00765109 - 0.0483071i) q^{59} +(-0.373799 - 0.108525i) q^{60} +(-3.57398 + 10.9996i) q^{61} +(4.75158 - 3.45222i) q^{62} +(12.8799 - 2.88392i) q^{63} +(5.72651 - 1.86066i) q^{64} +(-1.81873 - 1.21677i) q^{65} +(8.84111 - 0.232515i) q^{66} +(2.57557 - 2.57557i) q^{67} +(0.0221196 - 0.00718711i) q^{68} +(-11.6492 + 2.22441i) q^{69} +(0.643080 - 4.06025i) q^{70} +(-3.32548 + 1.69442i) q^{71} +(-6.47759 + 3.83402i) q^{72} +(9.09191 + 1.44002i) q^{73} +(4.88283 - 6.72064i) q^{74} +(3.41440 - 7.25940i) q^{75} +(1.01807 + 1.01807i) q^{76} +(2.20618 + 14.4241i) q^{77} +(9.36717 - 2.16726i) q^{78} +(-3.21667 - 9.89990i) q^{79} +(0.437054 + 2.75945i) q^{80} +(6.55623 - 6.16570i) q^{81} +(-12.0935 - 3.92941i) q^{82} +(-0.431593 + 0.219908i) q^{83} +(1.72983 + 2.22924i) q^{84} +(-0.00596337 - 0.0376512i) q^{85} +(-0.485870 - 0.247563i) q^{86} +(9.45410 + 8.87475i) q^{87} +(-3.73856 - 7.43457i) q^{88} +(-1.52851 + 1.52851i) q^{89} +(-1.03284 - 2.60589i) q^{90} +(5.48181 + 14.8857i) q^{91} +(-1.49027 - 2.05117i) q^{92} +(6.34553 + 1.84229i) q^{93} +(0.384099 - 1.18213i) q^{94} +(1.90914 - 1.38707i) q^{95} +(-2.96461 - 2.01395i) q^{96} +(12.2769 + 6.25539i) q^{97} +(-13.4518 + 13.4518i) q^{98} +(6.30433 + 7.69775i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9}+O(q^{10}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9	\( 416 q - 12 q^{3} - 14 q^{6} - 12 q^{7} - 12 q^{9} - 20 q^{13} - 30 q^{15} + 32 q^{16} + 2 q^{18} - 4 q^{19} - 12 q^{21} - 24 q^{22} - 78 q^{24} - 36 q^{27} - 84 q^{28} - 28 q^{31} - 44 q^{33} - 24 q^{34} - 12 q^{37} + 54 q^{39} + 88 q^{40} - 56 q^{42} + 8 q^{45} - 92 q^{46} + 40 q^{48} - 44 q^{52} - 176 q^{54} - 72 q^{55} - 6 q^{57} - 4 q^{58} + 12 q^{60} - 48 q^{61} - 46 q^{63} + 204 q^{66} - 64 q^{67} + 56 q^{70} - 66 q^{72} - 12 q^{73} - 104 q^{76} - 92 q^{78} + 104 q^{79} + 124 q^{81} + 16 q^{84} - 12 q^{85} - 24 q^{87} - 84 q^{91} - 124 q^{93} + 328 q^{94} - 152 q^{96} + 52 q^{97} - 142 q^{99}+O(q^{100}) \) 416 * q - 12 * q^3 - 14 * q^6 - 12 * q^7 - 12 * q^9 - 20 * q^13 - 30 * q^15 + 32 * q^16 + 2 * q^18 - 4 * q^19 - 12 * q^21 - 24 * q^22 - 78 * q^24 - 36 * q^27 - 84 * q^28 - 28 * q^31 - 44 * q^33 - 24 * q^34 - 12 * q^37 + 54 * q^39 + 88 * q^40 - 56 * q^42 + 8 * q^45 - 92 * q^46 + 40 * q^48 - 44 * q^52 - 176 * q^54 - 72 * q^55 - 6 * q^57 - 4 * q^58 + 12 * q^60 - 48 * q^61 - 46 * q^63 + 204 * q^66 - 64 * q^67 + 56 * q^70 - 66 * q^72 - 12 * q^73 - 104 * q^76 - 92 * q^78 + 104 * q^79 + 124 * q^81 + 16 * q^84 - 12 * q^85 - 24 * q^87 - 84 * q^91 - 124 * q^93 + 328 * q^94 - 152 * q^96 + 52 * q^97 - 142 * q^99

Introduction

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