LMFDB - Embedded newform 1183.2.e.l.508.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1183,2,Mod(170,1183)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1183, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 0]))

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

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

chi := DirichletCharacter("1183.170");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, degree $2$, 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:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			508.3
Character	$\chi$	$=$	1183.508
Dual form			1183.2.e.l.170.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.19245 - 2.06538i) q^{2} +(-0.352721 + 0.610931i) q^{3} +(-1.84386 + 3.19366i) q^{4} +(0.384905 + 0.666675i) q^{5} +1.68241 q^{6} +(-2.49409 - 0.882891i) q^{7} +4.02505 q^{8} +(1.25118 + 2.16710i) q^{9} +O(q^{10})$	\(q+(-1.19245 - 2.06538i) q^{2} +(-0.352721 + 0.610931i) q^{3} +(-1.84386 + 3.19366i) q^{4} +(0.384905 + 0.666675i) q^{5} +1.68241 q^{6} +(-2.49409 - 0.882891i) q^{7} +4.02505 q^{8} +(1.25118 + 2.16710i) q^{9} +(0.917958 - 1.58995i) q^{10} +(-0.556434 + 0.963772i) q^{11} +(-1.30074 - 2.25294i) q^{12} +(1.15057 + 6.20405i) q^{14} -0.543056 q^{15} +(-1.11193 - 1.92592i) q^{16} +(-3.52812 + 6.11088i) q^{17} +(2.98392 - 5.16831i) q^{18} +(-1.86064 - 3.22273i) q^{19} -2.83885 q^{20} +(1.41910 - 1.21230i) q^{21} +2.65407 q^{22} +(-3.01206 - 5.21703i) q^{23} +(-1.41972 + 2.45902i) q^{24} +(2.20370 - 3.81691i) q^{25} -3.88159 q^{27} +(7.41842 - 6.33737i) q^{28} +4.31164 q^{29} +(0.647566 + 1.12162i) q^{30} +(1.26887 - 2.19775i) q^{31} +(1.37320 - 2.37846i) q^{32} +(-0.392532 - 0.679886i) q^{33} +16.8284 q^{34} +(-0.371388 - 2.00258i) q^{35} -9.22798 q^{36} +(0.0519393 + 0.0899614i) q^{37} +(-4.43744 + 7.68587i) q^{38} +(1.54926 + 2.68340i) q^{40} +8.12661 q^{41} +(-4.19608 - 1.48538i) q^{42} -2.53454 q^{43} +(-2.05198 - 3.55413i) q^{44} +(-0.963167 + 1.66825i) q^{45} +(-7.18344 + 12.4421i) q^{46} +(-4.69122 - 8.12544i) q^{47} +1.56881 q^{48} +(5.44101 + 4.40402i) q^{49} -10.5112 q^{50} +(-2.48888 - 4.31087i) q^{51} +(5.73721 - 9.93714i) q^{53} +(4.62859 + 8.01696i) q^{54} -0.856697 q^{55} +(-10.0388 - 3.55368i) q^{56} +2.62515 q^{57} +(-5.14140 - 8.90517i) q^{58} +(4.54100 - 7.86524i) q^{59} +(1.00132 - 1.73434i) q^{60} +(-7.69656 - 13.3308i) q^{61} -6.05226 q^{62} +(-1.20724 - 6.50960i) q^{63} -10.9976 q^{64} +(-0.936148 + 1.62146i) q^{66} +(-6.79763 + 11.7738i) q^{67} +(-13.0107 - 22.5353i) q^{68} +4.24966 q^{69} +(-3.69322 + 3.15503i) q^{70} +1.13421 q^{71} +(5.03604 + 8.72268i) q^{72} +(-3.83796 + 6.64755i) q^{73} +(0.123870 - 0.214549i) q^{74} +(1.55458 + 2.69261i) q^{75} +13.7231 q^{76} +(2.23870 - 1.91247i) q^{77} +(-2.75598 - 4.77350i) q^{79} +(0.855977 - 1.48259i) q^{80} +(-2.38441 + 4.12992i) q^{81} +(-9.69056 - 16.7845i) q^{82} -5.42111 q^{83} +(1.25506 + 6.76746i) q^{84} -5.43196 q^{85} +(3.02230 + 5.23478i) q^{86} +(-1.52081 + 2.63411i) q^{87} +(-2.23967 + 3.87923i) q^{88} +(-7.64141 - 13.2353i) q^{89} +4.59411 q^{90} +22.2153 q^{92} +(0.895116 + 1.55039i) q^{93} +(-11.1881 + 19.3783i) q^{94} +(1.43234 - 2.48089i) q^{95} +(0.968716 + 1.67786i) q^{96} -12.1661 q^{97} +(2.60787 - 16.4893i) q^{98} -2.78479 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9}+O(q^{10}) $ 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9	\( 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9} - 5 q^{10} + q^{11} - 5 q^{12} - 2 q^{14} + 10 q^{15} - 17 q^{16} + 5 q^{17} - 24 q^{19} + 68 q^{20} - q^{21} - 28 q^{22} - 11 q^{23} - 32 q^{24} - 33 q^{25} - 42 q^{27} - 15 q^{28} + 8 q^{29} + 22 q^{30} - 40 q^{31} + 6 q^{32} - 24 q^{33} + 72 q^{34} + 44 q^{35} - 30 q^{36} + 4 q^{37} + 29 q^{38} + 4 q^{40} + 98 q^{41} - 9 q^{42} + 26 q^{43} - 10 q^{44} - 58 q^{45} + 10 q^{46} - 62 q^{47} + 178 q^{48} + 31 q^{49} - 46 q^{50} + 21 q^{51} + 18 q^{53} - 12 q^{54} - 28 q^{55} - 56 q^{56} - 26 q^{57} - 56 q^{58} - 79 q^{59} - 22 q^{60} - 13 q^{61} + 24 q^{62} + 22 q^{63} + 36 q^{64} + 38 q^{66} + 2 q^{67} + 12 q^{68} - 56 q^{69} + 85 q^{70} - 38 q^{71} - 81 q^{72} - 17 q^{73} - 17 q^{74} - 24 q^{75} + 116 q^{76} - 30 q^{77} + 9 q^{79} - 63 q^{80} - 16 q^{81} + 22 q^{82} + 162 q^{83} + 203 q^{84} - 68 q^{85} - 22 q^{86} - 70 q^{87} + 33 q^{88} - 72 q^{89} + 2 q^{90} - 8 q^{92} - 19 q^{93} + 30 q^{94} - 13 q^{95} - 11 q^{96} + 90 q^{97} + 81 q^{98} - 78 q^{99}+O(q^{100}) \) 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9 - 5 * q^10 + q^11 - 5 * q^12 - 2 * q^14 + 10 * q^15 - 17 * q^16 + 5 * q^17 - 24 * q^19 + 68 * q^20 - q^21 - 28 * q^22 - 11 * q^23 - 32 * q^24 - 33 * q^25 - 42 * q^27 - 15 * q^28 + 8 * q^29 + 22 * q^30 - 40 * q^31 + 6 * q^32 - 24 * q^33 + 72 * q^34 + 44 * q^35 - 30 * q^36 + 4 * q^37 + 29 * q^38 + 4 * q^40 + 98 * q^41 - 9 * q^42 + 26 * q^43 - 10 * q^44 - 58 * q^45 + 10 * q^46 - 62 * q^47 + 178 * q^48 + 31 * q^49 - 46 * q^50 + 21 * q^51 + 18 * q^53 - 12 * q^54 - 28 * q^55 - 56 * q^56 - 26 * q^57 - 56 * q^58 - 79 * q^59 - 22 * q^60 - 13 * q^61 + 24 * q^62 + 22 * q^63 + 36 * q^64 + 38 * q^66 + 2 * q^67 + 12 * q^68 - 56 * q^69 + 85 * q^70 - 38 * q^71 - 81 * q^72 - 17 * q^73 - 17 * q^74 - 24 * q^75 + 116 * q^76 - 30 * q^77 + 9 * q^79 - 63 * q^80 - 16 * q^81 + 22 * q^82 + 162 * q^83 + 203 * q^84 - 68 * q^85 - 22 * q^86 - 70 * q^87 + 33 * q^88 - 72 * q^89 + 2 * q^90 - 8 * q^92 - 19 * q^93 + 30 * q^94 - 13 * q^95 - 11 * q^96 + 90 * q^97 + 81 * q^98 - 78 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−1.19245	−	2.06538i	−0.843188	−	1.46044i	−0.887186	−	0.461412i	$-0.847343\pi$
$2$	−1.19245	−	2.06538i	−0.843188	−	1.46044i	0.0439980	−	0.999032i	$-0.485990\pi$
$3$	−0.352721	+	0.610931i	−0.203644	+	0.352721i	−0.949700	−	0.313162i	$-0.898612\pi$
$3$	−0.352721	+	0.610931i	−0.203644	+	0.352721i	0.746056	+	0.665883i	$0.231945\pi$
$4$	−1.84386	+	3.19366i	−0.921931	+	1.59683i
$5$	0.384905	+	0.666675i	0.172135	+	0.298146i	0.939166	−	0.343464i	$-0.111600\pi$
$5$	0.384905	+	0.666675i	0.172135	+	0.298146i	−0.767031	+	0.641610i	$0.778267\pi$
$6$	1.68241			0.686839
$7$	−2.49409	−	0.882891i	−0.942679	−	0.333701i
$7$	−2.49409	−	0.882891i	−0.942679	−	0.333701i
$8$	4.02505			1.42307
$9$	1.25118	+	2.16710i	0.417059	+	0.722367i
$10$	0.917958	−	1.58995i	0.290284	−	0.502786i
$11$	−0.556434	+	0.963772i	−0.167771	+	0.290588i	−0.937636	−	0.347619i	$-0.886990\pi$
$11$	−0.556434	+	0.963772i	−0.167771	+	0.290588i	0.769865	+	0.638207i	$0.220324\pi$
$12$	−1.30074	−	2.25294i	−0.375491	−	0.650369i
$13$		0			0
$13$		0			0
$14$	1.15057	+	6.20405i	0.307503	+	1.65810i
$15$	−0.543056			−0.140216
$16$	−1.11193	−	1.92592i	−0.277983	−	0.481481i
$17$	−3.52812	+	6.11088i	−0.855695	+	1.48211i	0.0203041	+	0.999794i	$0.493537\pi$
$17$	−3.52812	+	6.11088i	−0.855695	+	1.48211i	−0.875999	+	0.482313i	$0.839797\pi$
$18$	2.98392	−	5.16831i	0.703317	−	1.21818i
$19$	−1.86064	−	3.22273i	−0.426861	−	0.739344i	0.569731	−	0.821831i	$-0.307047\pi$
$19$	−1.86064	−	3.22273i	−0.426861	−	0.739344i	−0.996592	+	0.0824865i	$0.973714\pi$
$20$	−2.83885			−0.634785
$21$	1.41910	−	1.21230i	0.309674	−	0.264546i
$22$	2.65407			0.565851
$23$	−3.01206	−	5.21703i	−0.628057	−	1.08783i	−0.987941	−	0.154830i	$-0.950517\pi$
$23$	−3.01206	−	5.21703i	−0.628057	−	1.08783i	0.359884	−	0.932997i	$-0.382816\pi$
$24$	−1.41972	+	2.45902i	−0.289799	+	0.501946i
$25$	2.20370	−	3.81691i	0.440739	−	0.763383i
$26$		0			0
$27$	−3.88159			−0.747012
$28$	7.41842	−	6.33737i	1.40195	−	1.19765i
$29$	4.31164			0.800651			0.400326	−	0.916373i	$-0.368897\pi$
$29$	4.31164			0.800651			0.400326	+	0.916373i	$0.368897\pi$
$30$	0.647566	+	1.12162i	0.118229	+	0.204778i
$31$	1.26887	−	2.19775i	0.227896	−	0.394728i	−0.729288	−	0.684207i	$-0.760149\pi$
$31$	1.26887	−	2.19775i	0.227896	−	0.394728i	0.957184	+	0.289479i	$0.0934820\pi$
$32$	1.37320	−	2.37846i	0.242750	−	0.420456i
$33$	−0.392532	−	0.679886i	−0.0683311	−	0.118353i
$34$	16.8284			2.88605
$35$	−0.371388	−	2.00258i	−0.0627760	−	0.338497i
$36$	−9.22798			−1.53800
$37$	0.0519393	+	0.0899614i	0.00853876	+	0.0147896i	0.870263	−	0.492587i	$-0.163949\pi$
$37$	0.0519393	+	0.0899614i	0.00853876	+	0.0147896i	−0.861724	+	0.507377i	$0.830615\pi$
$38$	−4.43744	+	7.68587i	−0.719847	+	1.24681i
$39$		0			0
$40$	1.54926	+	2.68340i	0.244960	+	0.424282i
$41$	8.12661			1.26916			0.634582	−	0.772856i	$-0.281172\pi$
$41$	8.12661			1.26916			0.634582	+	0.772856i	$0.281172\pi$
$42$	−4.19608	−	1.48538i	−0.647469	−	0.229199i
$43$	−2.53454			−0.386513			−0.193257	−	0.981148i	$-0.561905\pi$
$43$	−2.53454			−0.386513			−0.193257	+	0.981148i	$0.561905\pi$
$44$	−2.05198	−	3.55413i	−0.309347	−	0.535805i
$45$	−0.963167	+	1.66825i	−0.143580	+	0.248689i
$46$	−7.18344	+	12.4421i	−1.05914	+	1.83448i
$47$	−4.69122	−	8.12544i	−0.684285	−	1.18522i	−0.973661	−	0.228001i	$-0.926781\pi$
$47$	−4.69122	−	8.12544i	−0.684285	−	1.18522i	0.289376	−	0.957216i	$-0.406552\pi$
$48$	1.56881			0.226438
$49$	5.44101	+	4.40402i	0.777287	+	0.629146i
$50$	−10.5112			−1.48650
$51$	−2.48888	−	4.31087i	−0.348513	−	0.603643i
$52$		0			0
$53$	5.73721	−	9.93714i	0.788067	−	1.36497i	−0.139083	−	0.990281i	$-0.544415\pi$
$53$	5.73721	−	9.93714i	0.788067	−	1.36497i	0.927150	−	0.374691i	$-0.122251\pi$
$54$	4.62859	+	8.01696i	0.629872	+	1.09097i
$55$	−0.856697			−0.115517
$56$	−10.0388	−	3.55368i	−1.34150	−	0.474880i
$57$	2.62515			0.347710
$58$	−5.14140	−	8.90517i	−0.675100	−	1.16931i
$59$	4.54100	−	7.86524i	0.591187	−	1.02397i	−0.402885	−	0.915250i	$-0.631993\pi$
$59$	4.54100	−	7.86524i	0.591187	−	1.02397i	0.994073	−	0.108716i	$-0.0346740\pi$
$60$	1.00132	−	1.73434i	0.129270	−	0.223902i
$61$	−7.69656	−	13.3308i	−0.985443	−	1.70684i	−0.639950	−	0.768417i	$-0.721045\pi$
$61$	−7.69656	−	13.3308i	−0.985443	−	1.70684i	−0.345494	−	0.938421i	$-0.612289\pi$
$62$	−6.05226			−0.768637
$63$	−1.20724	−	6.50960i	−0.152098	−	0.820133i
$64$	−10.9976			−1.37470
$65$		0			0
$66$	−0.936148	+	1.62146i	−0.115232	+	0.199587i
$67$	−6.79763	+	11.7738i	−0.830463	+	1.43840i	0.0672083	+	0.997739i	$0.478591\pi$
$67$	−6.79763	+	11.7738i	−0.830463	+	1.43840i	−0.897671	+	0.440665i	$0.854743\pi$
$68$	−13.0107	−	22.5353i	−1.57778	−	2.73280i
$69$	4.24966			0.511599
$70$	−3.69322	+	3.15503i	−0.441425	+	0.377098i
$71$	1.13421			0.134606			0.0673028	−	0.997733i	$-0.478561\pi$
$71$	1.13421			0.134606			0.0673028	+	0.997733i	$0.478561\pi$
$72$	5.03604	+	8.72268i	0.593503	+	1.02798i
$73$	−3.83796	+	6.64755i	−0.449200	+	0.778037i	−0.998334	−	0.0576973i	$-0.981624\pi$
$73$	−3.83796	+	6.64755i	−0.449200	+	0.778037i	0.549134	+	0.835734i	$0.314958\pi$
$74$	0.123870	−	0.214549i	0.0143996	−	0.0249408i
$75$	1.55458	+	2.69261i	0.179507	+	0.310916i
$76$	13.7231			1.57414
$77$	2.23870	−	1.91247i	0.255124	−	0.217946i
$78$		0			0
$79$	−2.75598	−	4.77350i	−0.310072	−	0.537061i	0.668306	−	0.743887i	$-0.267020\pi$
$79$	−2.75598	−	4.77350i	−0.310072	−	0.537061i	−0.978378	+	0.206826i	$0.933687\pi$
$80$	0.855977	−	1.48259i	0.0957011	−	0.165759i
$81$	−2.38441	+	4.12992i	−0.264934	+	0.458880i
$82$	−9.69056	−	16.7845i	−1.07014	−	1.85354i
$83$	−5.42111			−0.595044			−0.297522	−	0.954715i	$-0.596160\pi$
$83$	−5.42111			−0.595044			−0.297522	+	0.954715i	$0.596160\pi$
$84$	1.25506	+	6.76746i	0.136938	+	0.738391i
$85$	−5.43196			−0.589179
$86$	3.02230	+	5.23478i	0.325903	+	0.564481i
$87$	−1.52081	+	2.63411i	−0.163048	+	0.282407i
$88$	−2.23967	+	3.87923i	−0.238750	+	0.413527i
$89$	−7.64141	−	13.2353i	−0.809988	−	1.40294i	−0.912872	−	0.408247i	$-0.866140\pi$
$89$	−7.64141	−	13.2353i	−0.809988	−	1.40294i	0.102884	−	0.994693i	$-0.467193\pi$
$90$	4.59411			0.484261
$91$		0			0
$92$	22.2153			2.31610
$93$	0.895116	+	1.55039i	0.0928192	+	0.160768i
$94$	−11.1881	+	19.3783i	−1.15396	+	1.99872i
$95$	1.43234	−	2.48089i	0.146955	−	0.254534i
$96$	0.968716	+	1.67786i	0.0988691	+	0.171246i
$97$	−12.1661			−1.23528			−0.617641	−	0.786460i	$-0.711912\pi$
$97$	−12.1661			−1.23528			−0.617641	+	0.786460i	$0.711912\pi$
$98$	2.60787	−	16.4893i	0.263434	−	1.66567i
$99$	−2.78479			−0.279882
$100$	8.12663	+	14.0757i	0.812663	+	1.40757i
$101$	−0.201680	+	0.349320i	−0.0200679	+	0.0347586i	−0.875885	−	0.482520i	$-0.839722\pi$
$101$	−0.201680	+	0.349320i	−0.0200679	+	0.0347586i	0.855817	+	0.517279i	$0.173055\pi$
$102$	−5.93573	+	10.2810i	−0.587725	+	1.01797i
$103$	−1.90020	−	3.29124i	−0.187232	−	0.324296i	0.757094	−	0.653306i	$-0.226618\pi$
$103$	−1.90020	−	3.29124i	−0.187232	−	0.324296i	−0.944326	+	0.329010i	$0.893285\pi$
$104$		0			0
$105$	1.35443	+	0.479459i	0.132179	+	0.0467904i
$106$	−27.3653			−2.65795
$107$	4.32973	+	7.49932i	0.418571	+	0.724986i	0.995796	−	0.0915988i	$-0.0291977\pi$
$107$	4.32973	+	7.49932i	0.418571	+	0.724986i	−0.577225	+	0.816585i	$0.695864\pi$
$108$	7.15712	−	12.3965i	0.688694	−	1.19285i
$109$	2.00744	−	3.47699i	0.192278	−	0.333036i	−0.753727	−	0.657188i	$-0.771746\pi$
$109$	2.00744	−	3.47699i	0.192278	−	0.333036i	0.946005	+	0.324152i	$0.105079\pi$
$110$	1.02157	+	1.76940i	0.0974025	+	0.168706i
$111$	−0.0732803			−0.00695546
$112$	1.07288	+	5.78515i	0.101378	+	0.546645i
$113$	4.01288			0.377500			0.188750	−	0.982025i	$-0.439556\pi$
$113$	4.01288			0.377500			0.188750	+	0.982025i	$0.439556\pi$
$114$	−3.13036	−	5.42193i	−0.293185	−	0.507811i
$115$	2.31871	−	4.01612i	0.216221	−	0.374505i
$116$	−7.95007	+	13.7699i	−0.738146	+	1.27851i
$117$		0			0
$118$	−21.6596			−1.99393
$119$	14.1947	−	12.1262i	1.30123	−	1.11160i
$120$	−2.18583			−0.199538
$121$	4.88076	+	8.45373i	0.443706	+	0.768521i
$122$	−18.3555	+	31.7926i	−1.66183	+	2.87837i
$123$	−2.86643	+	4.96480i	−0.258457	+	0.447661i
$124$	4.67925	+	8.10471i	0.420209	+	0.727824i
$125$	7.24190			0.647735
$126$	−12.0052	+	10.2558i	−1.06951	+	0.913656i
$127$	−3.95166			−0.350654			−0.175327	−	0.984510i	$-0.556098\pi$
$127$	−3.95166			−0.350654			−0.175327	+	0.984510i	$0.556098\pi$
$128$	10.3677	+	17.9574i	0.916383	+	1.58722i
$129$	0.893984	−	1.54843i	0.0787109	−	0.136331i
$130$		0			0
$131$	−1.62906	−	2.82161i	−0.142331	−	0.246525i	0.786043	−	0.618172i	$-0.212127\pi$
$131$	−1.62906	−	2.82161i	−0.142331	−	0.246525i	−0.928374	+	0.371647i	$0.878793\pi$
$132$	2.89510			0.251986
$133$	1.79530	+	9.68053i	0.155672	+	0.839408i
$134$	32.4233			2.80095
$135$	−1.49404	−	2.58776i	−0.128587	−	0.222719i
$136$	−14.2008	+	24.5966i	−1.21771	+	2.10914i
$137$	4.42794	−	7.66941i	0.378304	−	0.655242i	−0.612511	−	0.790462i	$-0.709841\pi$
$137$	4.42794	−	7.66941i	0.378304	−	0.655242i	0.990816	+	0.135220i	$0.0431740\pi$
$138$	−5.06750	−	8.77716i	−0.431374	−	0.747162i
$139$	21.8559			1.85379			0.926895	−	0.375321i	$-0.122467\pi$
$139$	21.8559			1.85379			0.926895	+	0.375321i	$0.122467\pi$
$140$	7.08035	+	2.50639i	0.598399	+	0.211829i
$141$	6.61877			0.557401
$142$	−1.35248	−	2.34257i	−0.113498	−	0.196584i
$143$		0			0
$144$	2.78245	−	4.81934i	0.231871	−	0.401612i
$145$	1.65957	+	2.87446i	0.137820	+	0.238711i
$146$	18.3063			1.51504
$147$	−4.60971	+	1.77069i	−0.380203	+	0.146044i
$148$	−0.383075			−0.0314886
$149$	−1.18111	−	2.04574i	−0.0967601	−	0.167593i	0.813582	−	0.581451i	$-0.197515\pi$
$149$	−1.18111	−	2.04574i	−0.0967601	−	0.167593i	−0.910342	+	0.413857i	$0.864181\pi$
$150$	3.70751	−	6.42160i	0.302717	−	0.524321i
$151$	−6.01843	+	10.4242i	−0.489773	+	0.848312i	−0.999931	−	0.0117692i	$-0.996254\pi$
$151$	−6.01843	+	10.4242i	−0.489773	+	0.848312i	0.510158	+	0.860081i	$0.329587\pi$
$152$	−7.48917	−	12.9716i	−0.607452	−	1.05214i
$153$	−17.6572			−1.42750
$154$	−6.61951	−	2.34326i	−0.533415	−	0.188825i
$155$	1.95358			0.156915
$156$		0			0
$157$	1.22684	−	2.12494i	0.0979121	−	0.169589i	−0.812908	−	0.582392i	$-0.802117\pi$
$157$	1.22684	−	2.12494i	0.0979121	−	0.169589i	0.910820	+	0.412803i	$0.135450\pi$
$158$	−6.57273	+	11.3843i	−0.522898	+	0.905686i
$159$	4.04727	+	7.01008i	0.320969	+	0.555935i
$160$	2.11421			0.167143
$161$	2.90628	+	15.6711i	0.229047	+	1.23505i
$162$	11.3731			0.893558
$163$	−8.95038	−	15.5025i	−0.701048	−	1.21425i	−0.968099	−	0.250569i	$-0.919382\pi$
$163$	−8.95038	−	15.5025i	−0.701048	−	1.21425i	0.267051	−	0.963682i	$-0.413951\pi$
$164$	−14.9844	+	25.9537i	−1.17008	+	2.02664i
$165$	0.302175	−	0.523382i	0.0235243	−	0.0407453i
$166$	6.46439	+	11.1966i	0.501734	+	0.869029i
$167$	0.741807			0.0574028			0.0287014	−	0.999588i	$-0.490863\pi$
$167$	0.741807			0.0574028			0.0287014	+	0.999588i	$0.490863\pi$
$168$	5.71196	−	4.87958i	0.440687	−	0.376468i
$169$		0			0
$170$	6.47733	+	11.2191i	0.496789	+	0.860463i
$171$	4.65598	−	8.06440i	0.356052	−	0.616700i
$172$	4.67334	−	8.09446i	0.356339	−	0.617197i
$173$	−0.807878	−	1.39929i	−0.0614219	−	0.106386i	0.833679	−	0.552249i	$-0.186230\pi$
$173$	−0.807878	−	1.39929i	−0.0614219	−	0.106386i	−0.895101	+	0.445863i	$0.852897\pi$
$174$	7.25393			0.549919
$175$	−8.86614	+	7.57412i	−0.670218	+	0.572550i
$176$	2.47487			0.186550
$177$	3.20341	+	5.54847i	0.240783	+	0.417048i
$178$	−18.2240	+	31.5648i	−1.36594	+	2.36588i
$179$	6.77841	−	11.7406i	0.506642	−	0.877530i	−0.493328	−	0.869843i	$-0.664220\pi$
$179$	6.77841	−	11.7406i	0.506642	−	0.877530i	0.999970	−	0.00768695i	$-0.00244686\pi$
$180$	−3.55190	−	6.15206i	−0.264743	−	0.458548i
$181$	−7.15326			−0.531698			−0.265849	−	0.964015i	$-0.585652\pi$
$181$	−7.15326			−0.531698			−0.265849	+	0.964015i	$0.585652\pi$
$182$		0			0
$183$	10.8590			0.802717
$184$	−12.1237	−	20.9988i	−0.893769	−	1.54805i
$185$	−0.0399833	+	0.0692532i	−0.00293963	+	0.00509160i
$186$	2.13476	−	3.69751i	0.156528	−	0.271115i
$187$	−3.92633	−	6.80061i	−0.287122	−	0.497310i
$188$	34.5999			2.52346
$189$	9.68105	+	3.42702i	0.704193	+	0.249279i
$190$	−6.83197			−0.495643
$191$	−8.13226	−	14.0855i	−0.588430	−	1.01919i	−0.994438	−	0.105321i	$-0.966413\pi$
$191$	−8.13226	−	14.0855i	−0.588430	−	1.01919i	0.406009	−	0.913869i	$-0.366920\pi$
$192$	3.87909	−	6.71879i	0.279949	−	0.484887i
$193$	6.85969	−	11.8813i	0.493771	−	0.855237i	−0.506203	−	0.862414i	$-0.668951\pi$
$193$	6.85969	−	11.8813i	0.493771	−	0.855237i	0.999974	+	0.00717736i	$0.00228464\pi$
$194$	14.5075	+	25.1277i	1.04157	+	1.80406i
$195$		0			0
$196$	−24.0974	+	9.25633i	−1.72125	+	0.661167i
$197$	−8.00113			−0.570057			−0.285028	−	0.958519i	$-0.592003\pi$
$197$	−8.00113			−0.570057			−0.285028	+	0.958519i	$0.592003\pi$
$198$	3.32071	+	5.75165i	0.235993	+	0.408752i
$199$	2.31688	−	4.01295i	0.164239	−	0.284470i	−0.772146	−	0.635445i	$-0.780817\pi$
$199$	2.31688	−	4.01295i	0.164239	−	0.284470i	0.936385	+	0.350975i	$0.114150\pi$
$200$	8.86998	−	15.3633i	0.627202	−	1.08635i
$201$	−4.79534	−	8.30577i	−0.338237	−	0.585844i
$202$	0.961970			0.0676840
$203$	−10.7536	−	3.80671i	−0.754757	−	0.267178i
$204$	18.3566			1.28522
$205$	3.12797	+	5.41781i	0.218467	+	0.378396i
$206$	−4.53177	+	7.84926i	−0.315744	+	0.546884i
$207$	7.53722	−	13.0549i	0.523873	−	0.907375i
$208$		0			0
$209$	4.14130			0.286460
$210$	−0.624825	−	3.36915i	−0.0431170	−	0.232493i
$211$	6.47571			0.445806			0.222903	−	0.974841i	$-0.428447\pi$
$211$	6.47571			0.445806			0.222903	+	0.974841i	$0.428447\pi$
$212$	21.1573	+	36.6455i	1.45309	+	2.51682i
$213$	−0.400058	+	0.692922i	−0.0274116	+	0.0474782i
$214$	10.3260	−	17.8851i	0.705868	−	1.22260i
$215$	−0.975556	−	1.68971i	−0.0665323	−	0.115237i
$216$	−15.6236			−1.06305
$217$	−5.10506	+	4.36112i	−0.346554	+	0.296052i
$218$	−9.57508			−0.648506
$219$	−2.70746	−	4.68946i	−0.182953	−	0.316884i
$220$	1.57963	−	2.73600i	0.106499	−	0.184461i
$221$		0			0
$222$	0.0873829	+	0.151352i	0.00586476	+	0.0101581i
$223$	−10.7063			−0.716948			−0.358474	−	0.933540i	$-0.616703\pi$
$223$	−10.7063			−0.716948			−0.358474	+	0.933540i	$0.616703\pi$
$224$	−5.52482	+	4.71971i	−0.369142	+	0.315349i
$225$	11.0288			0.735256
$226$	−4.78515	−	8.28813i	−0.318304	−	0.551318i
$227$	−5.67410	+	9.82784i	−0.376604	+	0.652296i	−0.990566	−	0.137039i	$-0.956241\pi$
$227$	−5.67410	+	9.82784i	−0.376604	+	0.652296i	0.613962	+	0.789335i	$0.289575\pi$
$228$	−4.84042	+	8.38385i	−0.320564	+	0.555234i
$229$	−7.32801	−	12.6925i	−0.484248	−	0.838743i	0.515588	−	0.856837i	$-0.327574\pi$
$229$	−7.32801	−	12.6925i	−0.484248	−	0.838743i	−0.999836	+	0.0180939i	$0.994240\pi$
$230$	−11.0598			−0.729259
$231$	0.378747	+	2.04226i	0.0249197	+	0.134371i
$232$	17.3546			1.13938
$233$	4.31684	+	7.47698i	0.282805	+	0.489833i	0.972075	−	0.234672i	$-0.0754016\pi$
$233$	4.31684	+	7.47698i	0.282805	+	0.489833i	−0.689269	+	0.724505i	$0.742068\pi$
$234$		0			0
$235$	3.61135	−	6.25504i	0.235578	−	0.408034i
$236$	16.7459	+	29.0048i	1.09007	+	1.88805i
$237$	3.88837			0.252577
$238$	−41.9716	−	14.8576i	−2.72061	−	0.963077i
$239$	12.7158			0.822514			0.411257	−	0.911519i	$-0.365090\pi$
$239$	12.7158			0.822514			0.411257	+	0.911519i	$0.365090\pi$
$240$	0.603842	+	1.04588i	0.0389778	+	0.0675116i
$241$	−8.00758	+	13.8695i	−0.515814	+	0.893415i	0.484018	+	0.875058i	$0.339177\pi$
$241$	−8.00758	+	13.8695i	−0.515814	+	0.893415i	−0.999831	+	0.0183573i	$0.994156\pi$
$242$	11.6401	−	20.1613i	0.748254	−	1.29601i
$243$	−7.50445	−	12.9981i	−0.481411	−	0.833827i
$244$	56.7656			3.63404
$245$	−0.841781	+	5.32251i	−0.0537794	+	0.340043i
$246$	13.6723			0.871711
$247$		0			0
$248$	5.10727	−	8.84606i	0.324312	−	0.561725i
$249$	1.91214	−	3.31192i	0.121177	−	0.209885i
$250$	−8.63559	−	14.9573i	−0.546163	−	0.945981i
$251$	−22.9647			−1.44952			−0.724758	−	0.689003i	$-0.758049\pi$
$251$	−22.9647			−1.44952			−0.724758	+	0.689003i	$0.758049\pi$
$252$	23.0155	+	8.14730i	1.44984	+	0.513232i
$253$	6.70404			0.421480
$254$	4.71215	+	8.16169i	0.295667	+	0.512110i
$255$	1.91597	−	3.31855i	0.119983	−	0.207816i
$256$	13.7282	−	23.7780i	0.858013	−	1.48612i
$257$	10.1200	+	17.5283i	0.631268	+	1.09339i	0.987293	+	0.158911i	$0.0507984\pi$
$257$	10.1200	+	17.5283i	0.631268	+	1.09339i	−0.356025	+	0.934476i	$0.615868\pi$
$258$	−4.26412			−0.265472
$259$	−0.0501153	−	0.270229i	−0.00311401	−	0.0167912i
$260$		0			0
$261$	5.39462	+	9.34376i	0.333919	+	0.578364i
$262$	−3.88513	+	6.72924i	−0.240024	+	0.415734i
$263$	13.3147	−	23.0618i	0.821021	−	1.42205i	−0.0839024	−	0.996474i	$-0.526738\pi$
$263$	13.3147	−	23.0618i	0.821021	−	1.42205i	0.904923	−	0.425575i	$-0.139928\pi$
$264$	−1.57996	−	2.73657i	−0.0972398	−	0.168424i
$265$	8.83312			0.542614
$266$	17.8532	−	15.2515i	1.09465	−	0.935130i
$267$	10.7811			0.659795
$268$	−25.0678	−	43.4187i	−1.53126	−	2.65222i
$269$	6.25774	−	10.8387i	0.381541	−	0.660849i	−0.609741	−	0.792600i	$-0.708727\pi$
$269$	6.25774	−	10.8387i	0.381541	−	0.660849i	0.991283	+	0.131751i	$0.0420600\pi$
$270$	−3.56314	+	6.17153i	−0.216845	+	0.375587i
$271$	8.50396	+	14.7293i	0.516579	+	0.894741i	0.999815	+	0.0192505i	$0.00612799\pi$
$271$	8.50396	+	14.7293i	0.516579	+	0.894741i	−0.483236	+	0.875490i	$0.660539\pi$
$272$	15.6921			0.951475
$273$		0			0
$274$	−21.1203			−1.27593
$275$	2.45242	+	4.24772i	0.147887	+	0.256147i
$276$	−7.83579	+	13.5720i	−0.471659	+	0.816938i
$277$	−6.58600	+	11.4073i	−0.395715	+	0.685398i	−0.993192	−	0.116488i	$-0.962836\pi$
$277$	−6.58600	+	11.4073i	−0.395715	+	0.685398i	0.597478	+	0.801886i	$0.296170\pi$
$278$	−26.0620	−	45.1407i	−1.56309	−	2.70736i
$279$	6.35033			0.380184
$280$	−1.49485	−	8.06047i	−0.0893346	−	0.481705i
$281$	8.92658			0.532515			0.266258	−	0.963902i	$-0.414213\pi$
$281$	8.92658			0.532515			0.266258	+	0.963902i	$0.414213\pi$
$282$	−7.89254	−	13.6703i	−0.469994	−	0.814053i
$283$	5.77071	−	9.99516i	0.343033	−	0.594151i	−0.641961	−	0.766737i	$-0.721879\pi$
$283$	5.77071	−	9.99516i	0.343033	−	0.594151i	0.984994	+	0.172586i	$0.0552124\pi$
$284$	−2.09132	+	3.62227i	−0.124097	+	0.214942i
$285$	1.01043	+	1.75012i	0.0598529	+	0.103668i
$286$		0			0
$287$	−20.2685	−	7.17491i	−1.19641	−	0.423521i
$288$	6.87248			0.404965
$289$	−16.3953	−	28.3974i	−0.964427	−	1.67044i
$290$	3.95790	−	6.85529i	0.232416	−	0.402556i
$291$	4.29125	−	7.43265i	0.251557	−	0.435710i
$292$	−14.1534	−	24.5143i	−0.828263	−	1.43459i
$293$	−0.750227			−0.0438287			−0.0219144	−	0.999760i	$-0.506976\pi$
$293$	−0.750227			−0.0438287			−0.0219144	+	0.999760i	$0.506976\pi$
$294$	9.15398	+	7.40935i	0.533871	+	0.432122i
$295$	6.99141			0.407055
$296$	0.209058	+	0.362099i	0.0121512	+	0.0210466i
$297$	2.15985	−	3.74097i	0.125327	−	0.217073i
$298$	−2.81682	+	4.87887i	−0.163174	+	0.282626i
$299$		0			0
$300$	−11.4657			−0.661974
$301$	6.32137	+	2.23772i	0.364358	+	0.128980i
$302$	28.7067			1.65188
$303$	−0.142273	−	0.246425i	−0.00817339	−	0.0141567i
$304$	−4.13782	+	7.16691i	−0.237320	+	0.411051i
$305$	5.92489	−	10.2622i	0.339258	−	0.587612i
$306$	21.0553	+	36.4688i	1.20365	+	2.08478i
$307$	8.68971			0.495948			0.247974	−	0.968767i	$-0.420235\pi$
$307$	8.68971			0.495948			0.247974	+	0.968767i	$0.420235\pi$
$308$	1.97992	+	10.6760i	0.112816	+	0.608321i
$309$	2.68096			0.152514
$310$	−2.32954	−	4.03489i	−0.132309	−	0.229166i
$311$	11.8543	−	20.5323i	0.672198	−	1.16428i	−0.305082	−	0.952326i	$-0.598684\pi$
$311$	11.8543	−	20.5323i	0.672198	−	1.16428i	0.977279	−	0.211955i	$-0.0679829\pi$
$312$		0			0
$313$	−11.7850	−	20.4122i	−0.666125	−	1.15376i	−0.978979	−	0.203962i	$-0.934618\pi$
$313$	−11.7850	−	20.4122i	−0.666125	−	1.15376i	0.312854	−	0.949801i	$-0.398715\pi$
$314$	−5.85175			−0.330233
$315$	3.87512	−	3.31041i	0.218338	−	0.186521i
$316$	20.3266			1.14346
$317$	−6.08017	−	10.5312i	−0.341497	−	0.591489i	0.643214	−	0.765686i	$-0.277600\pi$
$317$	−6.08017	−	10.5312i	−0.341497	−	0.591489i	−0.984711	+	0.174197i	$0.944267\pi$
$318$	9.65232	−	16.7183i	0.541275	−	0.937516i
$319$	−2.39914	+	4.15544i	−0.134326	+	0.232660i
$320$	−4.23304	−	7.33184i	−0.236634	−	0.409862i
$321$	−6.10875			−0.340957
$322$	28.9012	−	24.6895i	1.61060	−	1.37589i
$323$	26.2583			1.46105
$324$	−8.79305	−	15.2300i	−0.488503	−	0.846111i
$325$		0			0
$326$	−21.3457	+	36.9719i	−1.18223	+	2.04768i
$327$	1.41613	+	2.45282i	0.0783124	+	0.135641i
$328$	32.7100			1.80611
$329$	4.52648	+	24.4074i	0.249553	+	1.34563i
$330$	−1.44131			−0.0793416
$331$	0.716230	+	1.24055i	0.0393676	+	0.0681866i	0.885038	−	0.465519i	$-0.154132\pi$
$331$	0.716230	+	1.24055i	0.0393676	+	0.0681866i	−0.845670	+	0.533706i	$0.820799\pi$
$332$	9.99578	−	17.3132i	0.548590	−	0.950185i
$333$	−0.129970	+	0.225115i	−0.00712233	+	0.0123362i
$334$	−0.884566	−	1.53211i	−0.0484013	−	0.0838335i
$335$	−10.4658			−0.571806
$336$	−3.91275	−	1.38509i	−0.213458	−	0.0755626i
$337$	9.39905			0.511999			0.255999	−	0.966677i	$-0.417595\pi$
$337$	9.39905			0.511999			0.255999	+	0.966677i	$0.417595\pi$
$338$		0			0
$339$	−1.41543	+	2.45159i	−0.0768755	+	0.133152i
$340$	10.0158	−	17.3479i	0.543183	−	0.940820i
$341$	1.41209	+	2.44581i	0.0764689	+	0.132448i
$342$	−22.2081			−1.20087
$343$	−9.68211	−	15.7879i	−0.522785	−	0.852465i
$344$	−10.2016			−0.550035
$345$	1.63572	+	2.83314i	0.0880639	+	0.152531i
$346$	−1.92671	+	3.33715i	−0.103580	+	0.179406i
$347$	4.91015	−	8.50463i	0.263591	−	0.456552i	−0.703603	−	0.710593i	$-0.748427\pi$
$347$	4.91015	−	8.50463i	0.263591	−	0.456552i	0.967193	+	0.254041i	$0.0817599\pi$
$348$	−5.60831	−	9.71389i	−0.300637	−	0.520719i
$349$	−34.1355			−1.82723			−0.913616	−	0.406578i	$-0.866722\pi$
$349$	−34.1355			−1.82723			−0.913616	+	0.406578i	$0.866722\pi$
$350$	26.2158	+	9.28021i	1.40130	+	0.496048i
$351$		0			0
$352$	1.52820	+	2.64691i	0.0814531	+	0.141081i
$353$	5.92702	−	10.2659i	0.315463	−	0.546399i	−0.664073	−	0.747668i	$-0.731173\pi$
$353$	5.92702	−	10.2659i	0.315463	−	0.546399i	0.979536	+	0.201270i	$0.0645067\pi$
$354$	7.63980	−	13.2325i	0.406051	−	0.703300i
$355$	0.436562	+	0.756147i	0.0231703	+	0.0401321i
$356$	56.3588			2.98701
$357$	2.40148	+	12.9491i	0.127100	+	0.685341i
$358$	−32.3316			−1.70878
$359$	6.51543	+	11.2851i	0.343871	+	0.595603i	0.985148	−	0.171707i	$-0.0549283\pi$
$359$	6.51543	+	11.2851i	0.343871	+	0.595603i	−0.641277	+	0.767310i	$0.721595\pi$
$360$	−3.87679	+	6.71480i	−0.204325	+	0.353901i
$361$	2.57602	−	4.46179i	0.135580	−	0.234831i
$362$	8.52989	+	14.7742i	0.448321	+	0.776515i
$363$	−6.88619			−0.361431
$364$		0			0
$365$	−5.90900			−0.309291
$366$	−12.9487	−	22.4279i	−0.676841	−	1.17232i
$367$	0.425803	−	0.737512i	0.0222267	−	0.0384978i	−0.854698	−	0.519125i	$-0.826258\pi$
$367$	0.425803	−	0.737512i	0.0222267	−	0.0384978i	0.876925	+	0.480628i	$0.159591\pi$
$368$	−6.69841	+	11.6020i	−0.349179	+	0.604795i
$369$	10.1678	+	17.6112i	0.529316	+	0.916801i
$370$	0.190712			0.00991465
$371$	−23.0826	+	19.7188i	−1.19839	+	1.02375i
$372$	−6.60188			−0.342292
$373$	16.2998	+	28.2320i	0.843970	+	1.46180i	0.886513	+	0.462704i	$0.153121\pi$
$373$	16.2998	+	28.2320i	0.843970	+	1.46180i	−0.0425432	+	0.999095i	$0.513546\pi$
$374$	−9.36389	+	16.2187i	−0.484195	+	0.838651i
$375$	−2.55437	+	4.42430i	−0.131907	+	0.228470i
$376$	−18.8824	−	32.7053i	−0.973785	−	1.68665i
$377$		0			0
$378$	−4.46605	−	24.0816i	−0.229709	−	1.23862i
$379$	−19.1587			−0.984116			−0.492058	−	0.870562i	$-0.663755\pi$
$379$	−19.1587			−0.984116			−0.492058	+	0.870562i	$0.663755\pi$
$380$	5.28208	+	9.14883i	0.270965	+	0.469325i
$381$	1.39384	−	2.41419i	0.0714083	−	0.123683i
$382$	−19.3946	+	33.5924i	−0.992313	+	1.71874i
$383$	14.0203	+	24.2839i	0.716404	+	1.24085i	0.962416	+	0.271581i	$0.0875465\pi$
$383$	14.0203	+	24.2839i	0.716404	+	1.24085i	−0.246012	+	0.969267i	$0.579120\pi$
$384$	−14.6276			−0.746462
$385$	2.13668	+	0.756370i	0.108895	+	0.0385482i
$386$	−32.7193			−1.66537
$387$	−3.17115	−	5.49260i	−0.161199	−	0.279204i
$388$	22.4326	−	38.8545i	1.13885	−	1.97254i
$389$	3.79850	−	6.57919i	0.192591	−	0.333578i	−0.753517	−	0.657429i	$-0.771644\pi$
$389$	3.79850	−	6.57919i	0.192591	−	0.333578i	0.946108	+	0.323850i	$0.104977\pi$
$390$		0			0
$391$	42.5076			2.14970
$392$	21.9003	+	17.7264i	1.10613	+	0.895319i
$393$	2.29841			0.115939
$394$	9.54093	+	16.5254i	0.480665	+	0.832536i
$395$	2.12158	−	3.67469i	0.106748	−	0.184894i
$396$	5.13477	−	8.89368i	0.258032	−	0.446924i
$397$	5.74428	+	9.94938i	0.288297	+	0.499345i	0.973403	−	0.229098i	$-0.0735776\pi$
$397$	5.74428	+	9.94938i	0.288297	+	0.499345i	−0.685106	+	0.728443i	$0.740244\pi$
$398$	−11.0510			−0.553937
$399$	−6.54737	−	2.31772i	−0.327779	−	0.116031i
$400$	−9.80145			−0.490073
$401$	−2.82547	−	4.89385i	−0.141097	−	0.244387i	0.786813	−	0.617192i	$-0.211730\pi$
$401$	−2.82547	−	4.89385i	−0.141097	−	0.244387i	−0.927910	+	0.372804i	$0.878396\pi$
$402$	−11.4364	+	19.8084i	−0.570395	+	0.987952i
$403$		0			0
$404$	−0.743740	−	1.28819i	−0.0370024	−	0.0640901i
$405$	−3.67108			−0.182418
$406$	4.96085	+	26.7496i	0.246203	+	1.32756i
$407$	−0.115603			−0.00573024
$408$	−10.0179	−	17.3515i	−0.495959	−	0.859026i
$409$	−14.3539	+	24.8616i	−0.709752	+	1.22933i	0.255197	+	0.966889i	$0.417860\pi$
$409$	−14.3539	+	24.8616i	−0.709752	+	1.22933i	−0.964949	+	0.262438i	$0.915474\pi$
$410$	7.45988	−	12.9209i	0.368417	−	0.638118i
$411$	3.12365	+	5.41033i	0.154078	+	0.266872i
$412$	14.0148			0.690461
$413$	−18.2698	+	15.6074i	−0.898999	+	0.767992i
$414$	−35.9510			−1.76689
$415$	−2.08661	−	3.61412i	−0.102428	−	0.177410i
$416$		0			0
$417$	−7.70902	+	13.3524i	−0.377512	+	0.653871i
$418$	−4.93829	−	8.55336i	−0.241539	−	0.418359i
$419$	−31.0913			−1.51891			−0.759454	−	0.650561i	$-0.774534\pi$
$419$	−31.0913			−1.51891			−0.759454	+	0.650561i	$0.774534\pi$
$420$	−4.02862	+	3.44155i	−0.196576	+	0.167930i
$421$	−11.7143			−0.570922			−0.285461	−	0.958390i	$-0.592147\pi$
$421$	−11.7143			−0.570922			−0.285461	+	0.958390i	$0.592147\pi$
$422$	−7.72195	−	13.3748i	−0.375898	−	0.651075i
$423$	11.7391	−	20.3327i	0.570774	−	0.988610i
$424$	23.0926	−	39.9975i	1.12147	−	1.94245i
$425$	15.5498	+	26.9331i	0.754277	+	1.30645i
$426$	1.90819			0.0924523
$427$	7.42627	+	40.0436i	0.359383	+	1.93784i
$428$	−31.9337			−1.54358
$429$		0			0
$430$	−2.32660	+	4.02979i	−0.112199	+	0.194334i
$431$	3.86105	−	6.68753i	0.185980	−	0.322127i	−0.757926	−	0.652340i	$-0.773787\pi$
$431$	3.86105	−	6.68753i	0.185980	−	0.322127i	0.943906	+	0.330213i	$0.107121\pi$
$432$	4.31607	+	7.47565i	0.207657	+	0.359672i
$433$	−22.7946			−1.09544			−0.547718	−	0.836663i	$-0.684503\pi$
$433$	−22.7946			−1.09544			−0.547718	+	0.836663i	$0.684503\pi$
$434$	15.0949	+	5.34348i	0.724578	+	0.256495i
$435$	−2.34146			−0.112265
$436$	7.40290	+	12.8222i	0.354535	+	0.614072i
$437$	−11.2087	+	19.4141i	−0.536186	+	0.928701i
$438$	−6.45701	+	11.1839i	−0.308528	+	0.534386i
$439$	−7.19363	−	12.4597i	−0.343333	−	0.594670i	0.641716	−	0.766942i	$-0.278223\pi$
$439$	−7.19363	−	12.4597i	−0.343333	−	0.594670i	−0.985049	+	0.172272i	$0.944889\pi$
$440$	−3.44825			−0.164389
$441$	−2.73630	+	17.3014i	−0.130300	+	0.823877i
$442$		0			0
$443$	17.1347	+	29.6782i	0.814094	+	1.41005i	0.909977	+	0.414659i	$0.136099\pi$
$443$	17.1347	+	29.6782i	0.814094	+	1.41005i	−0.0958830	+	0.995393i	$0.530567\pi$
$444$	0.135119	−	0.234033i	0.00641245	−	0.0111067i
$445$	5.88243	−	10.1887i	0.278854	−	0.482989i
$446$	12.7667	+	22.1126i	0.604522	+	1.04706i
$447$	1.66641			0.0788183
$448$	27.4291	+	9.70970i	1.29590	+	0.458740i
$449$	25.5552			1.20602			0.603012	−	0.797732i	$-0.293967\pi$
$449$	25.5552			1.20602			0.603012	+	0.797732i	$0.293967\pi$
$450$	−13.1513	−	22.7788i	−0.619959	−	1.07380i
$451$	−4.52192	+	7.83220i	−0.212929	+	0.368804i
$452$	−7.39921	+	12.8158i	−0.348029	+	0.602805i
$453$	−4.24565	−	7.35369i	−0.199478	−	0.345506i
$454$	27.0643			1.27019
$455$		0			0
$456$	10.5664			0.494815
$457$	−13.7310	−	23.7828i	−0.642309	−	1.11251i	−0.984916	−	0.173033i	$-0.944643\pi$
$457$	−13.7310	−	23.7828i	−0.642309	−	1.11251i	0.342607	−	0.939479i	$-0.388690\pi$
$458$	−17.4765	+	30.2702i	−0.816625	+	1.41444i
$459$	13.6947	−	23.7199i	0.639215	−	1.10715i
$460$	8.55076	+	14.8104i	0.398681	+	0.690536i
$461$	−5.85152			−0.272533			−0.136266	−	0.990672i	$-0.543510\pi$
$461$	−5.85152			−0.272533			−0.136266	+	0.990672i	$0.543510\pi$
$462$	3.76641	−	3.21755i	0.175229	−	0.149694i
$463$	−18.9046			−0.878570			−0.439285	−	0.898348i	$-0.644768\pi$
$463$	−18.9046			−0.878570			−0.439285	+	0.898348i	$0.644768\pi$
$464$	−4.79425	−	8.30389i	−0.222568	−	0.385498i
$465$	−0.689069	+	1.19350i	−0.0319548	+	0.0553474i
$466$	10.2952	−	17.8318i	0.476916	−	0.826043i
$467$	5.13106	+	8.88725i	0.237437	+	0.411253i	0.959978	−	0.280075i	$-0.0903593\pi$
$467$	5.13106	+	8.88725i	0.237437	+	0.411253i	−0.722541	+	0.691328i	$0.757026\pi$
$468$		0			0
$469$	27.3490	−	23.3635i	1.26286	−	1.07883i
$470$	−17.2254			−0.794547
$471$	0.865461	+	1.49902i	0.0398783	+	0.0690713i
$472$	18.2777	−	31.6580i	0.841301	−	1.45718i
$473$	1.41030	−	2.44272i	0.0648458	−	0.112316i
$474$	−4.63668	−	8.03096i	−0.212970	−	0.368874i
$475$	−16.4012			−0.752537
$476$	12.5538	+	67.6921i	0.575404	+	3.10266i
$477$	28.7130			1.31468
$478$	−15.1629	−	26.2629i	−0.693534	−	1.20124i
$479$	−14.7056	+	25.4709i	−0.671918	+	1.16380i	0.305442	+	0.952211i	$0.401196\pi$
$479$	−14.7056	+	25.4709i	−0.671918	+	1.16380i	−0.977360	+	0.211585i	$0.932137\pi$
$480$	−0.745727	+	1.29164i	−0.0340376	+	0.0589549i
$481$		0			0
$482$	38.1945			1.73971
$483$	−10.5991	−	3.75199i	−0.482274	−	0.170721i
$484$	−35.9978			−1.63626
$485$	−4.68280	−	8.11084i	−0.212635	−	0.368294i
$486$	−17.8973	+	30.9991i	−0.811839	+	1.40615i
$487$	8.29480	−	14.3670i	0.375873	−	0.651031i	−0.614584	−	0.788851i	$-0.710676\pi$
$487$	8.29480	−	14.3670i	0.375873	−	0.651031i	0.990457	+	0.137820i	$0.0440095\pi$
$488$	−30.9790	−	53.6572i	−1.40235	−	2.42895i
$489$	12.6280			0.571056
$490$	11.9968	−	4.60822i	0.541960	−	0.208178i
$491$	6.25288			0.282189			0.141094	−	0.989996i	$-0.454938\pi$
$491$	6.25288			0.282189			0.141094	+	0.989996i	$0.454938\pi$
$492$	−10.5706	−	18.3088i	−0.476559	−	0.825425i
$493$	−15.2120	+	26.3479i	−0.685113	+	1.18665i
$494$		0			0
$495$	−1.07188	−	1.85655i	−0.0481774	−	0.0834456i
$496$	−5.64361			−0.253405
$497$	−2.82882	−	1.00138i	−0.126890	−	0.0449180i
$498$	−9.12050			−0.408699
$499$	13.0888	+	22.6705i	0.585935	+	1.01487i	0.994758	+	0.102256i	$0.0326061\pi$
$499$	13.0888	+	22.6705i	0.585935	+	1.01487i	−0.408823	+	0.912614i	$0.634061\pi$
$500$	−13.3531	+	23.1282i	−0.597168	+	1.03432i
$501$	−0.261651	+	0.453193i	−0.0116897	+	0.0202472i
$502$	27.3842	+	47.4307i	1.22221	+	2.11694i
$503$	−20.5184			−0.914870			−0.457435	−	0.889243i	$-0.651232\pi$
$503$	−20.5184			−0.914870			−0.457435	+	0.889243i	$0.651232\pi$
$504$	−4.85919	−	26.2015i	−0.216445	−	1.16711i
$505$	−0.310510			−0.0138175
$506$	−7.99422	−	13.8464i	−0.355386	−	0.615547i
$507$		0			0
$508$	7.28633	−	12.6203i	0.323278	−	0.559935i
$509$	6.76903	+	11.7243i	0.300032	+	0.519670i	0.976143	−	0.217129i	$-0.0696694\pi$
$509$	6.76903	+	11.7243i	0.300032	+	0.519670i	−0.676111	+	0.736800i	$0.736336\pi$
$510$	−9.13876			−0.404671
$511$	15.4413	−	13.1911i	0.683083	−	0.583540i
$512$	−24.0100			−1.06110
$513$	7.22225	+	12.5093i	0.318870	+	0.552299i
$514$	24.1351	−	41.8032i	1.06455	−	1.84386i
$515$	1.46279	−	2.53363i	0.0644583	−	0.111645i
$516$	3.29677	+	5.71017i	0.145132	+	0.251376i
$517$	10.4414			0.459214
$518$	−0.498366	+	0.425741i	−0.0218969	+	0.0187060i
$519$	1.13982			0.0500327
$520$		0			0
$521$	−12.0622	+	20.8924i	−0.528457	+	0.915314i	0.470993	+	0.882137i	$0.343896\pi$
$521$	−12.0622	+	20.8924i	−0.528457	+	0.915314i	−0.999449	+	0.0331769i	$0.989438\pi$
$522$	12.8656	−	22.2839i	0.563112	−	0.975339i
$523$	12.6491	+	21.9090i	0.553109	+	0.958012i	0.998048	+	0.0624515i	$0.0198919\pi$
$523$	12.6491	+	21.9090i	0.553109	+	0.958012i	−0.444939	+	0.895561i	$0.646775\pi$
$524$	12.0150			0.524879
$525$	−1.49999	−	8.08815i	−0.0654648	−	0.352996i
$526$	−63.5084			−2.76910
$527$	8.95347	+	15.5079i	0.390019	+	0.675533i
$528$	−0.872939	+	1.51197i	−0.0379898	+	0.0658002i
$529$	−6.64496	+	11.5094i	−0.288911	+	0.500409i
$530$	−10.5330	−	18.2438i	−0.457526	−	0.792458i
$531$	22.7263			0.986239
$532$	−34.2266	−	12.1160i	−1.48391	−	0.525294i
$533$		0			0
$534$	−12.8559	−	22.2672i	−0.556331	−	0.963594i
$535$	−3.33307	+	5.77305i	−0.144101	+	0.249591i
$536$	−27.3608	+	47.3903i	−1.18181	+	2.04695i
$537$	4.78178	+	8.28228i	0.206349	+	0.357407i
$538$	−29.8481			−1.28684
$539$	−7.27204	+	2.79334i	−0.313229	+	0.120318i
$540$	11.0192			0.474192
$541$	13.1582	+	22.7907i	0.565716	+	0.979848i	0.996983	+	0.0776240i	$0.0247334\pi$
$541$	13.1582	+	22.7907i	0.565716	+	0.979848i	−0.431267	+	0.902224i	$0.641933\pi$
$542$	20.2811	−	35.1278i	0.871146	−	1.50887i
$543$	2.52310	−	4.37015i	0.108277	−	0.187541i
$544$	9.68966	+	16.7830i	0.415441	+	0.719564i
$545$	3.09070			0.132391
$546$		0			0
$547$	−19.4439			−0.831362			−0.415681	−	0.909510i	$-0.636457\pi$
$547$	−19.4439			−0.831362			−0.415681	+	0.909510i	$0.636457\pi$
$548$	16.3290	+	28.2827i	0.697541	+	1.20818i
$549$	19.2595	−	33.3584i	0.821975	−	1.42370i
$550$	5.84878	−	10.1304i	0.249393	−	0.431961i
$551$	−8.02242	−	13.8952i	−0.341767	−	0.591957i
$552$	17.1051			0.728041
$553$	2.65920	+	14.3388i	0.113081	+	0.609747i
$554$	31.4138			1.33465
$555$	−0.0282059	−	0.0488541i	−0.00119728	−	0.00207374i
$556$	−40.2992	+	69.8003i	−1.70907	+	2.96019i
$557$	20.5119	−	35.5276i	0.869117	−	1.50535i	0.00621596	−	0.999981i	$-0.498021\pi$
$557$	20.5119	−	35.5276i	0.869117	−	1.50535i	0.862901	−	0.505374i	$-0.168645\pi$
$558$	−7.57244	−	13.1158i	−0.320567	−	0.555238i
$559$		0			0
$560$	−3.44386	+	2.94200i	−0.145529	+	0.124322i
$561$	5.53960			0.233882
$562$	−10.6445	−	18.4368i	−0.449010	−	0.777709i
$563$	15.1356	−	26.2156i	0.637888	−	1.10485i	−0.348007	−	0.937492i	$-0.613141\pi$
$563$	15.1356	−	26.2156i	0.637888	−	1.10485i	0.985895	−	0.167363i	$-0.0535252\pi$
$564$	−12.2041	+	21.1381i	−0.513886	+	0.890076i
$565$	1.54458	+	2.67529i	0.0649809	+	0.112550i
$566$	−27.5251			−1.15697
$567$	9.59321	−	8.19523i	0.402877	−	0.344167i
$568$	4.56523			0.191553
$569$	6.54938	+	11.3439i	0.274564	+	0.475559i	0.970025	−	0.243005i	$-0.0781331\pi$
$569$	6.54938	+	11.3439i	0.274564	+	0.475559i	−0.695461	+	0.718564i	$0.744800\pi$
$570$	2.40978	−	4.17386i	0.100934	−	0.174824i
$571$	5.98580	−	10.3677i	0.250498	−	0.433875i	−0.713165	−	0.700996i	$-0.752739\pi$
$571$	5.98580	−	10.3677i	0.250498	−	0.433875i	0.963663	+	0.267121i	$0.0860723\pi$
$572$		0			0
$573$	11.4737			0.479320
$574$	9.35025	+	50.4179i	0.390272	+	2.10440i
$575$	−26.5506			−1.10724
$576$	−13.7600	−	23.8330i	−0.573332	−	0.993040i
$577$	1.00752	−	1.74507i	0.0419435	−	0.0726483i	−0.844292	−	0.535884i	$-0.819978\pi$
$577$	1.00752	−	1.74507i	0.0419435	−	0.0726483i	0.886235	+	0.463236i	$0.153312\pi$
$578$	−39.1010	+	67.7249i	−1.62639	+	2.81698i
$579$	4.83911	+	8.38159i	0.201107	+	0.348327i
$580$	−12.2401			−0.508242
$581$	13.5208	+	4.78625i	0.560935	+	0.198567i
$582$	−20.4683			−0.848440
$583$	6.38476	+	11.0587i	0.264430	+	0.458006i
$584$	−15.4480	+	26.7567i	−0.639242	+	1.10720i
$585$		0			0
$586$	0.894606	+	1.54950i	0.0369558	+	0.0640094i
$587$	17.7652			0.733247			0.366624	−	0.930369i	$-0.380514\pi$
$587$	17.7652			0.733247			0.366624	+	0.930369i	$0.380514\pi$
$588$	2.84470	−	17.9868i	0.117313	−	0.741762i
$589$	−9.44368			−0.389120
$590$	−8.33689	−	14.4399i	−0.343224	−	0.594482i
$591$	2.82217	−	4.88814i	0.116088	−	0.201071i
$592$	0.115506	−	0.200062i	0.00474727	−	0.00822250i
$593$	−14.5652	−	25.2277i	−0.598121	−	1.03598i	−0.993098	−	0.117285i	$-0.962581\pi$
$593$	−14.5652	−	25.2277i	−0.598121	−	1.03598i	0.394978	−	0.918691i	$-0.370752\pi$
$594$	−10.3020			−0.422697
$595$	13.5478	+	4.79583i	0.555407	+	0.196610i
$596$	8.71120			0.356825
$597$	1.63442	+	2.83090i	0.0668924	+	0.115861i
$598$		0			0
$599$	−12.7659	+	22.1111i	−0.521600	+	0.903437i	0.478085	+	0.878314i	$0.341331\pi$
$599$	−12.7659	+	22.1111i	−0.521600	+	0.903437i	−0.999684	+	0.0251232i	$0.992002\pi$
$600$	6.25726	+	10.8379i	0.255451	+	0.442455i
$601$	−34.4411			−1.40488			−0.702441	−	0.711742i	$-0.747907\pi$
$601$	−34.4411			−1.40488			−0.702441	+	0.711742i	$0.747907\pi$
$602$	−2.91617	−	15.7244i	−0.118854	−	0.640879i
$603$	−34.0201			−1.38541
$604$	−22.1943	−	38.4417i	−0.903074	−	1.56417i
$605$	−3.75726	+	6.50776i	−0.152754	+	0.264578i
$606$	−0.339307	+	0.587697i	−0.0137834	+	0.0238736i
$607$	−10.4819	−	18.1552i	−0.425449	−	0.736898i	0.571014	−	0.820941i	$-0.306550\pi$
$607$	−10.4819	−	18.1552i	−0.425449	−	0.736898i	−0.996462	+	0.0840421i	$0.973217\pi$
$608$	−10.2202			−0.414483
$609$	6.11867	−	5.22702i	0.247941	−	0.211810i
$610$	−28.2605			−1.14423
$611$		0			0
$612$	32.5574	−	56.3911i	1.31606	−	2.27948i
$613$	−6.06480	+	10.5045i	−0.244955	+	0.424275i	−0.962119	−	0.272630i	$-0.912107\pi$
$613$	−6.06480	+	10.5045i	−0.244955	+	0.424275i	0.717164	+	0.696904i	$0.245440\pi$
$614$	−10.3620	−	17.9475i	−0.418177	−	0.724304i
$615$	−4.41321			−0.177958
$616$	9.01089	−	7.69777i	0.363059	−	0.310152i
$617$	−5.46234			−0.219906			−0.109953	−	0.993937i	$-0.535070\pi$
$617$	−5.46234			−0.219906			−0.109953	+	0.993937i	$0.535070\pi$
$618$	−3.19690	−	5.53720i	−0.128598	−	0.222739i
$619$	−6.63530	+	11.4927i	−0.266695	+	0.461930i	−0.968006	−	0.250926i	$-0.919265\pi$
$619$	−6.63530	+	11.4927i	−0.266695	+	0.461930i	0.701311	+	0.712855i	$0.252598\pi$
$620$	−3.60213	+	6.23908i	−0.144665	+	0.250568i
$621$	11.6916	+	20.2504i	0.469166	+	0.812620i
$622$	−56.5427			−2.26716
$623$	7.37306	+	39.7566i	0.295395	+	1.59282i
$624$		0			0
$625$	−8.23104	−	14.2566i	−0.329242	−	0.570263i
$626$	−28.1059	+	48.6808i	−1.12334	+	1.94568i
$627$	−1.46072	+	2.53005i	−0.0583357	+	0.101040i
$628$	4.52423	+	7.83620i	0.180536	+	0.312698i
$629$	−0.732992			−0.0292263
$630$	−11.4581	−	4.05609i	−0.456503	−	0.161599i
$631$	27.6525			1.10083			0.550414	−	0.834892i	$-0.314470\pi$
$631$	27.6525			1.10083			0.550414	+	0.834892i	$0.314470\pi$
$632$	−11.0930	−	19.2136i	−0.441254	−	0.764274i
$633$	−2.28412	+	3.95621i	−0.0907856	+	0.157245i
$634$	−14.5006	+	25.1157i	−0.575891	+	0.997473i
$635$	−1.52101	−	2.63447i	−0.0603596	−	0.104546i
$636$	−29.8504			−1.18365
$637$		0			0
$638$	11.4434			0.453049
$639$	1.41909	+	2.45794i	0.0561384	+	0.0972346i
$640$	−7.98114	+	13.8237i	−0.315482	+	0.546432i
$641$	7.27920	−	12.6079i	0.287511	−	0.497984i	−0.685704	−	0.727881i	$-0.740506\pi$
$641$	7.27920	−	12.6079i	0.287511	−	0.497984i	0.973215	+	0.229897i	$0.0738388\pi$
$642$	7.28437	+	12.6169i	0.287491	+	0.497949i
$643$	−5.35888			−0.211334			−0.105667	−	0.994402i	$-0.533698\pi$
$643$	−5.35888			−0.211334			−0.105667	+	0.994402i	$0.533698\pi$
$644$	−55.4070	−	19.6137i	−2.18334	−	0.772886i
$645$	1.37640			0.0541955
$646$	−31.3116	−	54.2333i	−1.23194	−	2.13378i
$647$	−9.04617	+	15.6684i	−0.355641	+	0.615989i	−0.987228	−	0.159317i	$-0.949071\pi$
$647$	−9.04617	+	15.6684i	−0.355641	+	0.615989i	0.631586	+	0.775306i	$0.282404\pi$
$648$	−9.59736	+	16.6231i	−0.377020	+	0.653018i
$649$	5.05353	+	8.75298i	0.198369	+	0.343584i
$650$		0			0
$651$	−0.863682	−	4.65710i	−0.0338504	−	0.182526i
$652$	66.0131			2.58527
$653$	−19.9819	−	34.6096i	−0.781951	−	1.35438i	−0.930804	−	0.365519i	$-0.880891\pi$
$653$	−19.9819	−	34.6096i	−0.781951	−	1.35438i	0.148853	−	0.988859i	$-0.452442\pi$
$654$	3.37733	−	5.84971i	0.132064	−	0.228742i
$655$	1.25406	−	2.17210i	0.0490003	−	0.0848710i
$656$	−9.03625	−	15.6512i	−0.352806	−	0.611078i
$657$	−19.2079			−0.749370
$658$	45.0130	−	38.4535i	1.75479	−	1.49907i
$659$	−40.8081			−1.58966			−0.794828	−	0.606834i	$-0.792439\pi$
$659$	−40.8081			−1.58966			−0.794828	+	0.606834i	$0.792439\pi$
$660$	1.11434	+	1.93009i	0.0433756	+	0.0751287i
$661$	−4.74488	+	8.21837i	−0.184554	+	0.319658i	−0.943426	−	0.331582i	$-0.892418\pi$
$661$	−4.74488	+	8.21837i	−0.184554	+	0.319658i	0.758872	+	0.651240i	$0.225751\pi$
$662$	1.70813	−	2.95858i	0.0663885	−	0.114988i
$663$		0			0
$664$	−21.8202			−0.846789
$665$	−5.76274	+	4.92296i	−0.223470	+	0.190904i
$666$	0.619931			0.0240218
$667$	−12.9869	−	22.4940i	−0.502855	−	0.870970i
$668$	−1.36779	+	2.36908i	−0.0529214	+	0.0916626i
$669$	3.77634	−	6.54082i	0.146002	−	0.252883i
$670$	12.4799	+	21.6158i	0.482140	+	0.835091i
$671$	17.1305			0.661316
$672$	−0.934697	−	5.04002i	−0.0360567	−	0.194423i
$673$	−5.64510			−0.217603			−0.108801	−	0.994064i	$-0.534701\pi$
$673$	−5.64510			−0.217603			−0.108801	+	0.994064i	$0.534701\pi$
$674$	−11.2079	−	19.4126i	−0.431711	−	0.747746i
$675$	−8.55385	+	14.8157i	−0.329238	+	0.570256i
$676$		0			0
$677$	−4.71924	−	8.17396i	−0.181375	−	0.314151i	0.760974	−	0.648782i	$-0.224721\pi$
$677$	−4.71924	−	8.17396i	−0.181375	−	0.314151i	−0.942349	+	0.334632i	$0.891388\pi$
$678$	6.75130			0.259282
$679$	30.3434	+	10.7414i	1.16447	+	0.412215i
$680$	−21.8639			−0.838442
$681$	−4.00275	−	6.93297i	−0.153386	−	0.265672i
$682$	3.36768	−	5.83300i	0.128955	−	0.223357i
$683$	8.30765	−	14.3893i	0.317883	−	0.550590i	−0.662163	−	0.749360i	$-0.730361\pi$
$683$	8.30765	−	14.3893i	0.317883	−	0.550590i	0.980046	+	0.198770i	$0.0636946\pi$
$684$	17.1700	+	29.7393i	0.656511	+	1.13711i
$685$	6.81734			0.260477
$686$	−21.0625	+	38.8234i	−0.804171	+	1.48229i
$687$	10.3390			0.394456
$688$	2.81823	+	4.88133i	0.107444	+	0.186099i
$689$		0			0
$690$	3.90101	−	6.75675i	0.148509	−	0.257225i
$691$	−18.1380	−	31.4160i	−0.690003	−	1.19512i	−0.971836	−	0.235657i	$-0.924276\pi$
$691$	−18.1380	−	31.4160i	−0.690003	−	1.19512i	0.281833	−	0.959463i	$-0.409058\pi$
$692$	5.95847			0.226507
$693$	6.94552	+	2.45866i	0.263839	+	0.0933969i
$694$	−23.4204			−0.889025
$695$	8.41243	+	14.5707i	0.319102	+	0.552700i
$696$	−6.12132	+	10.6024i	−0.232028	+	0.401884i
$697$	−28.6717	+	49.6608i	−1.08602	+	1.88104i
$698$	40.7048	+	70.5028i	1.54070	+	2.66857i
$699$	−6.09056			−0.230366
$700$	−7.84124	−	42.2811i	−0.296371	−	1.59808i
$701$	14.8413			0.560547			0.280273	−	0.959920i	$-0.409575\pi$
$701$	14.8413			0.560547			0.280273	+	0.959920i	$0.409575\pi$
$702$		0			0
$703$	0.193281	−	0.334772i	0.00728973	−	0.0126262i
$704$	6.11946	−	10.5992i	0.230636	−	0.399473i
$705$	2.54760	+	4.41257i	0.0959481	+	0.166187i
$706$	−28.2706			−1.06398
$707$	0.811419	−	0.693175i	0.0305166	−	0.0260695i
$708$	−23.6266			−0.887942
$709$	11.2020	+	19.4025i	0.420701	+	0.728676i	0.996008	−	0.0892614i	$-0.0284507\pi$
$709$	11.2020	+	19.4025i	0.420701	+	0.728676i	−0.575307	+	0.817938i	$0.695117\pi$
$710$	1.04115	−	1.80333i	0.0390738	−	0.0676778i
$711$	6.89643	−	11.9450i	0.258636	−	0.447972i
$712$	−30.7570	−	53.2728i	−1.15267	−	1.99648i
$713$	−15.2877			−0.572527
$714$	23.8812	−	20.4011i	0.893733	−	0.763493i
$715$		0			0
$716$	24.9969	+	43.2959i	0.934179	+	1.61805i
$717$	−4.48512	+	7.76845i	−0.167500	+	0.290118i
$718$	15.5386	−	26.9137i	0.579896	−	1.00441i
$719$	−3.96850	−	6.87365i	−0.148000	−	0.256344i	0.782488	−	0.622666i	$-0.213950\pi$
$719$	−3.96850	−	6.87365i	−0.148000	−	0.256344i	−0.930488	+	0.366322i	$0.880617\pi$
$720$	4.28391			0.159652
$721$	1.83347	+	9.88633i	0.0682819	+	0.368186i
$722$	−12.2871			−0.457277
$723$	−5.64888	−	9.78415i	−0.210084	−	0.363877i
$724$	13.1896	−	22.8451i	0.490189	−	0.849032i
$725$	9.50155	−	16.4572i	0.352879	−	0.611204i
$726$	8.21142	+	14.2226i	0.304754	+	0.527850i
$727$	−52.6516			−1.95274			−0.976370	−	0.216106i	$-0.930664\pi$
$727$	−52.6516			−1.95274			−0.976370	+	0.216106i	$0.930664\pi$
$728$		0			0
$729$	−3.71855			−0.137724
$730$	7.04618	+	12.2043i	0.260791	+	0.451703i
$731$	8.94215	−	15.4883i	0.330737	−	0.572854i
$732$	−20.0224	+	34.6798i	−0.740050	+	1.28180i
$733$	12.1309	+	21.0113i	0.448065	+	0.776071i	0.998260	−	0.0589649i	$-0.0187800\pi$
$733$	12.1309	+	21.0113i	0.448065	+	0.776071i	−0.550195	+	0.835036i	$0.685447\pi$
$734$	−2.03099			−0.0749652
$735$	−2.95477	−	2.39163i	−0.108988	−	0.0882167i
$736$	−16.5447			−0.609845
$737$	−7.56487	−	13.1027i	−0.278656	−	0.482646i
$738$	24.2492	−	42.0008i	0.892625	−	1.54607i
$739$	−15.1742	+	26.2826i	−0.558193	+	0.966819i	0.439454	+	0.898265i	$0.355172\pi$
$739$	−15.1742	+	26.2826i	−0.558193	+	0.966819i	−0.997647	+	0.0685542i	$0.978161\pi$
$740$	−0.147448	−	0.255387i	−0.00542028	−	0.00938820i
$741$		0			0
$742$	68.2516	+	24.1606i	2.50560	+	0.886962i
$743$	22.0992			0.810743			0.405371	−	0.914152i	$-0.367142\pi$
$743$	22.0992			0.810743			0.405371	+	0.914152i	$0.367142\pi$
$744$	3.60288	+	6.24038i	0.132088	+	0.228783i
$745$	0.909228	−	1.57483i	0.0333115	−	0.0576973i
$746$	38.8732	−	67.3304i	1.42325	−	2.46514i
$747$	−6.78276	−	11.7481i	−0.248168	−	0.429840i
$748$	28.9585			1.05883
$749$	−4.17768	−	22.5267i	−0.152649	−	0.823107i
$750$	12.1838			0.444890
$751$	−17.5833	−	30.4552i	−0.641624	−	1.11132i	−0.985070	−	0.172153i	$-0.944928\pi$
$751$	−17.5833	−	30.4552i	−0.641624	−	1.11132i	0.343447	−	0.939172i	$-0.388406\pi$
$752$	−10.4327	+	18.0699i	−0.380440	+	0.658941i
$753$	8.10012	−	14.0298i	0.295185	−	0.511275i
$754$		0			0
$755$	−9.26609			−0.337228
$756$	−28.7953	+	24.5991i	−1.04727	+	0.894659i
$757$	−23.3691			−0.849365			−0.424682	−	0.905342i	$-0.639614\pi$
$757$	−23.3691			−0.849365			−0.424682	+	0.905342i	$0.639614\pi$
$758$	22.8457	+	39.5700i	0.829795	+	1.43725i
$759$	−2.36466	+	4.09571i	−0.0858316	+	0.148665i
$760$	5.76524	−	9.98569i	0.209127	−	0.362219i
$761$	−19.8951	−	34.4593i	−0.721196	−	1.24915i	−0.960521	−	0.278209i	$-0.910259\pi$
$761$	−19.8951	−	34.4593i	−0.721196	−	1.24915i	0.239324	−	0.970940i	$-0.423074\pi$
$762$	−6.64830			−0.240843
$763$	−8.07656	+	6.89960i	−0.292391	+	0.249782i
$764$	59.9791			2.16997
$765$	−6.79634	−	11.7716i	−0.245722	−	0.425603i
$766$	33.4369	−	57.9145i	1.20813	−	2.09254i
$767$		0			0
$768$	9.68446	+	16.7740i	0.349458	+	0.605279i
$769$	12.2562			0.441968			0.220984	−	0.975277i	$-0.429073\pi$
$769$	12.2562			0.441968			0.220984	+	0.975277i	$0.429073\pi$
$770$	−0.985691	−	5.31499i	−0.0355218	−	0.191539i
$771$	−14.2781			−0.514214
$772$	25.2967	+	43.8151i	0.910446	+	1.57694i
$773$	18.9964	−	32.9027i	0.683252	−	1.18343i	−0.290731	−	0.956805i	$-0.593898\pi$
$773$	18.9964	−	32.9027i	0.683252	−	1.18343i	0.973983	−	0.226622i	$-0.0727682\pi$
$774$	−7.56286	+	13.0993i	−0.271842	+	0.470843i
$775$	−5.59242	−	9.68636i	−0.200886	−	0.347944i
$776$	−48.9692			−1.75789
$777$	0.182768	+	0.0646985i	0.00655676	+	0.00232104i
$778$	−18.1180			−0.649563
$779$	−15.1207	−	26.1899i	−0.541756	−	0.938349i
$780$		0			0
$781$	−0.631111	+	1.09312i	−0.0225829	+	0.0391148i
$782$	−50.6881	−	87.7943i	−1.81260	−	3.13952i
$783$	−16.7360			−0.598097
$784$	2.43178	−	15.3759i	0.0868493	−	0.549141i
$785$	1.88886			0.0674163
$786$	−2.74073	−	4.74709i	−0.0977587	−	0.169323i
$787$	−18.8911	+	32.7203i	−0.673393	+	1.16635i	0.303543	+	0.952818i	$0.401831\pi$
$787$	−18.8911	+	32.7203i	−0.673393	+	1.16635i	−0.976936	+	0.213533i	$0.931503\pi$
$788$	14.7530	−	25.5529i	0.525553	−	0.910285i
$789$	9.39276	+	16.2687i	0.334391	+	0.579182i
$790$	−10.1195			−0.360035
$791$	−10.0085	−	3.54294i	−0.355862	−	0.125972i
$792$	−11.2089			−0.398291
$793$		0			0
$794$	13.6995	−	23.7282i	0.486177	−	0.842083i
$795$	−3.11563	+	5.39643i	−0.110500	+	0.191392i
$796$	8.54400	+	14.7986i	0.302834	+	0.524524i
$797$	4.55614			0.161387			0.0806935	−	0.996739i	$-0.474287\pi$
$797$	4.55614			0.161387			0.0806935	+	0.996739i	$0.474287\pi$
$798$	3.02042	+	16.2866i	0.106922	+	0.576538i
$799$	66.2048			2.34216
$800$	−6.05225	−	10.4828i	−0.213979	−	0.370623i
$801$	19.1215	−	33.1194i	0.675625	−	1.17022i
$802$	−6.73845	+	11.6713i	−0.237943	+	0.412129i
$803$	−4.27115	−	7.39785i	−0.150726	−	0.261064i
$804$	35.3678			1.24732
$805$	−9.32888	+	7.96942i	−0.328800	+	0.280885i
$806$		0			0
$807$	4.41448	+	7.64610i	0.155397	+	0.269155i
$808$	−0.811771	+	1.40603i	−0.0285580	+	0.0494639i
$809$	−13.3555	+	23.1325i	−0.469556	+	0.813295i	−0.999394	−	0.0348040i	$-0.988919\pi$
$809$	−13.3555	+	23.1325i	−0.469556	+	0.813295i	0.529838	+	0.848099i	$0.322253\pi$
$810$	4.37757	+	7.58218i	0.153812	+	0.266411i
$811$	5.89688			0.207068			0.103534	−	0.994626i	$-0.466985\pi$
$811$	5.89688			0.207068			0.103534	+	0.994626i	$0.466985\pi$
$812$	31.9856	−	27.3244i	1.12247	−	0.958900i
$813$	−11.9981			−0.420792
$814$	0.137851	+	0.238764i	0.00483166	+	0.00836869i
$815$	6.89009	−	11.9340i	0.241349	−	0.418029i
$816$	−5.53494	+	9.58680i	−0.193762	+	0.335605i
$817$	4.71587	+	8.16812i	0.164987	+	0.285766i
$818$	68.4649			2.39382
$819$		0			0
$820$	−23.0702			−0.805646
$821$	8.12138	+	14.0666i	0.283438	+	0.490929i	0.972229	−	0.234031i	$-0.0751916\pi$
$821$	8.12138	+	14.0666i	0.283438	+	0.490929i	−0.688791	+	0.724960i	$0.741858\pi$
$822$	7.44959	−	12.9031i	0.259834	−	0.450046i
$823$	−19.2590	+	33.3576i	−0.671328	+	1.16277i	0.306199	+	0.951967i	$0.400943\pi$
$823$	−19.2590	+	33.3576i	−0.671328	+	1.16277i	−0.977528	+	0.210807i	$0.932391\pi$
$824$	−7.64839	−	13.2474i	−0.266444	−	0.461495i
$825$	−3.46009			−0.120465
$826$	54.0211	+	19.1231i	1.87963	+	0.665376i
$827$	23.5064			0.817398			0.408699	−	0.912669i	$-0.365983\pi$
$827$	23.5064			0.817398			0.408699	+	0.912669i	$0.365983\pi$
$828$	27.7952	+	48.1427i	0.965950	+	1.67307i
$829$	−0.306676	+	0.531178i	−0.0106513	+	0.0184486i	−0.871302	−	0.490747i	$-0.836724\pi$
$829$	−0.306676	+	0.531178i	−0.0106513	+	0.0184486i	0.860651	+	0.509196i	$0.170057\pi$
$830$	−4.97635	+	8.61929i	−0.172732	+	0.299180i
$831$	−4.64604	−	8.04718i	−0.161169	−	0.279154i
$832$		0			0
$833$	−46.1090	+	17.7114i	−1.59758	+	0.613665i
$834$	36.7704			1.27326
$835$	0.285525	+	0.494544i	0.00988101	+	0.0171144i
$836$	−7.63599	+	13.2259i	−0.264096	+	0.457428i
$837$	−4.92524	+	8.53077i	−0.170241	+	0.294867i
$838$	37.0747	+	64.2153i	1.28072	+	2.21828i
$839$	18.0433			0.622924			0.311462	−	0.950259i	$-0.399181\pi$
$839$	18.0433			0.622924			0.311462	+	0.950259i	$0.399181\pi$
$840$	5.45166	+	1.92985i	0.188100	+	0.0665860i
$841$	−10.4098			−0.358957
$842$	13.9687	+	24.1945i	0.481394	+	0.833799i
$843$	−3.14859	+	5.45352i	−0.108443	+	0.187829i
$844$	−11.9403	+	20.6812i	−0.411003	+	0.711878i
$845$		0			0
$846$	−55.9930			−1.92508
$847$	−4.70936	−	25.3936i	−0.161816	−	0.872533i
$848$	−25.5176			−0.876277
$849$	4.07090	+	7.05101i	0.139713	+	0.241990i
$850$	37.0847	−	64.2325i	1.27199	−	2.20316i
$851$	0.312888	−	0.541938i	0.0107257	−	0.0185774i
$852$	−1.47531	−	2.55530i	−0.0505431	−	0.0875433i
$853$	50.0142			1.71245			0.856227	−	0.516599i	$-0.172802\pi$
$853$	50.0142			1.71245			0.856227	+	0.516599i	$0.172802\pi$
$854$	73.8497	−	63.0879i	2.52709	−	2.15882i
$855$	7.16844			0.245155
$856$	17.4274	+	30.1851i	0.595656	+	1.03171i
$857$	−6.20769	+	10.7520i	−0.212051	+	0.367283i	−0.952356	−	0.304988i	$-0.901348\pi$
$857$	−6.20769	+	10.7520i	−0.212051	+	0.367283i	0.740305	+	0.672271i	$0.234681\pi$
$858$		0			0
$859$	18.5798	+	32.1811i	0.633934	+	1.09801i	0.986740	+	0.162309i	$0.0518942\pi$
$859$	18.5798	+	32.1811i	0.633934	+	1.09801i	−0.352806	+	0.935696i	$0.614772\pi$
$860$	7.19516			0.245353
$861$	11.5325	−	9.85193i	0.393027	−	0.335753i
$862$	−18.4164			−0.627265
$863$	−13.0818	−	22.6584i	−0.445310	−	0.771300i	0.552764	−	0.833338i	$-0.313573\pi$
$863$	−13.0818	−	22.6584i	−0.445310	−	0.771300i	−0.998074	+	0.0620384i	$0.980240\pi$
$864$	−5.33021	+	9.23220i	−0.181338	+	0.314086i
$865$	0.621913	−	1.07718i	0.0211457	−	0.0366254i
$866$	27.1813	+	47.0794i	0.923659	+	1.59982i
$867$	23.1318			0.785598
$868$	−4.51493	−	24.3452i	−0.153247	−	0.826329i
$869$	6.13409			0.208085
$870$	2.79207	+	4.83601i	0.0946601	+	0.163956i
$871$		0			0
$872$	8.08005	−	13.9951i	0.273625	−	0.473933i
$873$	−15.2220	−	26.3652i	−0.515185	−	0.892327i
$874$	53.4632			1.80842
$875$	−18.0620	−	6.39381i	−0.610606	−	0.216150i
$876$	19.9687			0.674681
$877$	−27.7749	−	48.1075i	−0.937892	−	1.62448i	−0.769394	−	0.638774i	$-0.779442\pi$
$877$	−27.7749	−	48.1075i	−0.937892	−	1.62448i	−0.168497	−	0.985702i	$-0.553891\pi$
$878$	−17.1560	+	29.7151i	−0.578989	+	1.00284i
$879$	0.264621	−	0.458337i	0.00892544	−	0.0154593i
$880$	0.952589	+	1.64993i	0.0321118	+	0.0556192i
$881$	−35.1270			−1.18346			−0.591730	−	0.806136i	$-0.701555\pi$
$881$	−35.1270			−1.18346			−0.591730	+	0.806136i	$0.701555\pi$
$882$	38.9969	−	14.9795i	1.31309	−	0.504387i
$883$	43.7616			1.47270			0.736348	−	0.676603i	$-0.236549\pi$
$883$	43.7616			1.47270			0.736348	+	0.676603i	$0.236549\pi$
$884$		0			0
$885$	−2.46602	+	4.27126i	−0.0828942	+	0.143577i
$886$	40.8644	−	70.7793i	1.37287	−	2.37788i
$887$	19.8530	+	34.3865i	0.666600	+	1.15458i	0.978849	+	0.204584i	$0.0655843\pi$
$887$	19.8530	+	34.3865i	0.666600	+	1.15458i	−0.312249	+	0.950000i	$0.601082\pi$
$888$	−0.294957			−0.00989809
$889$	9.85582	+	3.48889i	0.330554	+	0.117014i
$890$	−28.0580			−0.940505
$891$	−2.65353	−	4.59606i	−0.0888967	−	0.153974i
$892$	19.7410	−	34.1924i	0.660977	−	1.14485i
$893$	−17.4574	+	30.2371i	−0.584189	+	1.01185i
$894$	−1.98710	−	3.44176i	−0.0664586	−	0.115110i
$895$	10.4362			0.348843
$896$	−10.0036	−	53.9409i	−0.334197	−	1.80204i
$897$		0			0
$898$	−30.4732	−	52.7811i	−1.01690	−	1.76133i
$899$	5.47092	−	9.47592i	0.182465	−	0.316040i
$900$	−20.3357	+	35.2224i	−0.677856	+	1.17408i
$901$	40.4832	+	70.1189i	1.34869	+	2.33600i
$902$	21.5686			0.718157
$903$	−3.59677	+	3.07263i	−0.119693	+	0.102251i
$904$	16.1520			0.537209
$905$	−2.75332	−	4.76890i	−0.0915236	−	0.158523i
$906$	−10.1254	+	17.5378i	−0.336395	+	0.582654i
$907$	23.8863	−	41.3722i	0.793131	−	1.37374i	−0.130889	−	0.991397i	$-0.541783\pi$
$907$	23.8863	−	41.3722i	0.793131	−	1.37374i	0.924020	−	0.382345i	$-0.124884\pi$
$908$	−20.9245	−	36.2424i	−0.694405	−	1.20274i
$909$	−1.00935			−0.0334779
$910$		0			0
$911$	−3.43817			−0.113912			−0.0569559	−	0.998377i	$-0.518139\pi$
$911$	−3.43817			−0.113912			−0.0569559	+	0.998377i	$0.518139\pi$
$912$	−2.91899	−	5.05584i	−0.0966575	−	0.167416i
$913$	3.01649	−	5.22472i	0.0998313	−	0.172913i
$914$	−32.7470	+	56.7194i	−1.08317	+	1.87611i
$915$	4.17966	+	7.23939i	0.138175	+	0.239327i
$916$	54.0473			1.78577
$917$	1.57185	+	8.47564i	0.0519070	+	0.279890i
$918$	−65.3209			−2.15591
$919$	−3.62345	−	6.27599i	−0.119526	−	0.207026i	0.800054	−	0.599928i	$-0.204804\pi$
$919$	−3.62345	−	6.27599i	−0.119526	−	0.207026i	−0.919580	+	0.392903i	$0.871471\pi$
$920$	9.33292	−	16.1651i	0.307697	−	0.532947i
$921$	−3.06504	+	5.30881i	−0.100997	+	0.174931i
$922$	6.97763	+	12.0856i	0.229796	+	0.398019i
$923$		0			0
$924$	−7.22065	−	2.55606i	−0.237542	−	0.0840881i
$925$	0.457834			0.0150535
$926$	22.5427	+	39.0451i	0.740799	+	1.28310i
$927$	4.75497	−	8.23584i	0.156174	−	0.270501i
$928$	5.92076	−	10.2551i	0.194359	−	0.336639i
$929$	−11.4989	−	19.9167i	−0.377267	−	0.653445i	0.613397	−	0.789775i	$-0.289803\pi$
$929$	−11.4989	−	19.9167i	−0.377267	−	0.653445i	−0.990664	+	0.136330i	$0.956469\pi$
$930$	3.28671			0.107776
$931$	4.06920	−	25.7292i	0.133363	−	0.843241i
$932$	−31.8386			−1.04291
$933$	8.36255	+	14.4844i	0.273778	+	0.474197i
$934$	12.2370	−	21.1952i	0.400408	−	0.693527i
$935$	3.02253	−	5.23517i	0.0988473	−	0.171209i
$936$		0			0
$937$	−10.9823			−0.358775			−0.179387	−	0.983779i	$-0.557412\pi$
$937$	−10.9823			−0.358775			−0.179387	+	0.983779i	$0.557412\pi$
$938$	−80.8667	−	28.6262i	−2.64039	−	0.934679i
$939$	16.6272			0.542609
$940$	13.3177	+	23.0669i	0.434374	+	0.752358i
$941$	−16.0847	+	27.8596i	−0.524347	+	0.908196i	0.475251	+	0.879850i	$0.342357\pi$
$941$	−16.0847	+	27.8596i	−0.524347	+	0.908196i	−0.999598	+	0.0283458i	$0.990976\pi$
$942$	2.06403	−	3.57501i	0.0672499	−	0.116480i
$943$	−24.4778	−	42.3968i	−0.797107	−	1.38063i
$944$	−20.1971			−0.657361
$945$	1.44158	+	7.77319i	0.0468944	+	0.252862i
$946$	−6.72685			−0.218709
$947$	21.9413	+	38.0035i	0.712998	+	1.23495i	0.963727	+	0.266891i	$0.0859964\pi$
$947$	21.9413	+	38.0035i	0.712998	+	1.23495i	−0.250729	+	0.968057i	$0.580670\pi$
$948$	−7.16962	+	12.4181i	−0.232858	+	0.403323i
$949$		0			0
$950$	19.5575	+	33.8746i	0.634530	+	1.09904i
$951$	8.57842			0.278174
$952$	57.1344	−	48.8084i	1.85174	−	1.58189i
$953$	−5.23257			−0.169500			−0.0847499	−	0.996402i	$-0.527009\pi$
$953$	−5.23257			−0.169500			−0.0847499	+	0.996402i	$0.527009\pi$
$954$	−34.2388	−	59.3033i	−1.10852	−	1.92002i
$955$	6.26029	−	10.8431i	0.202578	−	0.350876i
$956$	−23.4461	+	40.6099i	−0.758301	+	1.31342i
$957$	−1.69246	−	2.93142i	−0.0547094	−	0.0947594i
$958$	70.1428			2.26621
$959$	−17.8149	+	15.2189i	−0.575275	+	0.491442i
$960$	5.97233			0.192756
$961$	12.2799	+	21.2695i	0.396127	+	0.686111i
$962$		0			0
$963$	−10.8345	+	18.7659i	−0.349137	+	0.604724i
$964$	−29.5298	−	51.1470i	−0.951089	−	1.64734i
$965$	10.5613			0.339981
$966$	4.88954	+	26.3651i	0.157318	+	0.848284i
$967$	14.5514			0.467942			0.233971	−	0.972244i	$-0.424828\pi$
$967$	14.5514			0.467942			0.233971	+	0.972244i	$0.424828\pi$
$968$	19.6453	+	34.0267i	0.631424	+	1.09366i
$969$	−9.26185	+	16.0420i	−0.297533	+	0.515343i
$970$	−11.1680	+	19.3435i	−0.358582	+	0.621083i
$971$	−4.62540	−	8.01143i	−0.148436	−	0.257099i	0.782213	−	0.623011i	$-0.214091\pi$
$971$	−4.62540	−	8.01143i	−0.148436	−	0.257099i	−0.930650	+	0.365911i	$0.880757\pi$
$972$	55.3487			1.77531
$973$	−54.5106	−	19.2963i	−1.74753	−	0.618612i
$974$	−39.5644			−1.26773
$975$		0			0
$976$	−17.1161	+	29.6460i	−0.547873	+	0.948945i
$977$	−10.9022	+	18.8831i	−0.348791	+	0.604124i	−0.986035	−	0.166538i	$-0.946741\pi$
$977$	−10.9022	+	18.8831i	−0.348791	+	0.604124i	0.637244	+	0.770662i	$0.280074\pi$
$978$	−15.0582	−	26.0815i	−0.481507	−	0.833995i
$979$	17.0078			0.543571
$980$	−15.4462	−	12.5023i	−0.493410	−	0.399373i
$981$	10.0467			0.320765
$982$	−7.45624	−	12.9146i	−0.237938	−	0.412121i
$983$	−2.16580	+	3.75128i	−0.0690783	+	0.119647i	−0.898496	−	0.438982i	$-0.855339\pi$
$983$	−2.16580	+	3.75128i	−0.0690783	+	0.119647i	0.829418	+	0.558629i	$0.188673\pi$
$984$	−11.5375	+	19.9835i	−0.367802	+	0.637052i
$985$	−3.07967	−	5.33415i	−0.0981266	−	0.169960i
$986$	72.5580			2.31072
$987$	−16.5078	−	5.84365i	−0.525450	−	0.186006i
$988$		0			0
$989$	7.63417	+	13.2228i	0.242752	+	0.420459i
$990$	−2.55632	+	4.42767i	−0.0812451	+	0.140721i
$991$	−13.5810	+	23.5230i	−0.431415	+	0.747233i	−0.996995	−	0.0774601i	$-0.975319\pi$
$991$	−13.5810	+	23.5230i	−0.431415	+	0.747233i	0.565580	+	0.824693i	$0.308652\pi$
$992$	−3.48484	−	6.03592i	−0.110644	−	0.191641i
$993$	−1.01052			−0.0320678
$994$	1.30499	+	7.03668i	0.0413916	+	0.223190i
$995$	3.56711			0.113085
$996$	7.05144	+	12.2135i	0.223434	+	0.386998i
$997$	−26.3294	+	45.6038i	−0.833860	+	1.44429i	0.0610957	+	0.998132i	$0.480541\pi$
$997$	−26.3294	+	45.6038i	−0.833860	+	1.44429i	−0.894955	+	0.446156i	$0.852793\pi$
$998$	31.2154	−	54.0667i	0.988107	−	1.71145i
$999$	−0.201607	−	0.349193i	−0.00637856	−	0.0110480i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.l.508.3	yes	48
7.2	even	3	inner	1183.2.e.l.170.3	yes	48
7.3	odd	6		8281.2.a.ct.1.22		24
7.4	even	3		8281.2.a.cu.1.22		24
13.12	even	2		1183.2.e.k.508.22	yes	48
91.25	even	6		8281.2.a.cv.1.3		24
91.38	odd	6		8281.2.a.cw.1.3		24
91.51	even	6		1183.2.e.k.170.22	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.e.k.170.22	✓	48	91.51	even	6
1183.2.e.k.508.22	yes	48	13.12	even	2
1183.2.e.l.170.3	yes	48	7.2	even	3	inner
1183.2.e.l.508.3	yes	48	1.1	even	1	trivial
8281.2.a.ct.1.22		24	7.3	odd	6
8281.2.a.cu.1.22		24	7.4	even	3
8281.2.a.cv.1.3		24	91.25	even	6
8281.2.a.cw.1.3		24	91.38	odd	6

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:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19245 - 2.06538i) q^{2} +(-0.352721 + 0.610931i) q^{3} +(-1.84386 + 3.19366i) q^{4} +(0.384905 + 0.666675i) q^{5} +1.68241 q^{6} +(-2.49409 - 0.882891i) q^{7} +4.02505 q^{8} +(1.25118 + 2.16710i) q^{9} +O(q^{10})\)	\(q+(-1.19245 - 2.06538i) q^{2} +(-0.352721 + 0.610931i) q^{3} +(-1.84386 + 3.19366i) q^{4} +(0.384905 + 0.666675i) q^{5} +1.68241 q^{6} +(-2.49409 - 0.882891i) q^{7} +4.02505 q^{8} +(1.25118 + 2.16710i) q^{9} +(0.917958 - 1.58995i) q^{10} +(-0.556434 + 0.963772i) q^{11} +(-1.30074 - 2.25294i) q^{12} +(1.15057 + 6.20405i) q^{14} -0.543056 q^{15} +(-1.11193 - 1.92592i) q^{16} +(-3.52812 + 6.11088i) q^{17} +(2.98392 - 5.16831i) q^{18} +(-1.86064 - 3.22273i) q^{19} -2.83885 q^{20} +(1.41910 - 1.21230i) q^{21} +2.65407 q^{22} +(-3.01206 - 5.21703i) q^{23} +(-1.41972 + 2.45902i) q^{24} +(2.20370 - 3.81691i) q^{25} -3.88159 q^{27} +(7.41842 - 6.33737i) q^{28} +4.31164 q^{29} +(0.647566 + 1.12162i) q^{30} +(1.26887 - 2.19775i) q^{31} +(1.37320 - 2.37846i) q^{32} +(-0.392532 - 0.679886i) q^{33} +16.8284 q^{34} +(-0.371388 - 2.00258i) q^{35} -9.22798 q^{36} +(0.0519393 + 0.0899614i) q^{37} +(-4.43744 + 7.68587i) q^{38} +(1.54926 + 2.68340i) q^{40} +8.12661 q^{41} +(-4.19608 - 1.48538i) q^{42} -2.53454 q^{43} +(-2.05198 - 3.55413i) q^{44} +(-0.963167 + 1.66825i) q^{45} +(-7.18344 + 12.4421i) q^{46} +(-4.69122 - 8.12544i) q^{47} +1.56881 q^{48} +(5.44101 + 4.40402i) q^{49} -10.5112 q^{50} +(-2.48888 - 4.31087i) q^{51} +(5.73721 - 9.93714i) q^{53} +(4.62859 + 8.01696i) q^{54} -0.856697 q^{55} +(-10.0388 - 3.55368i) q^{56} +2.62515 q^{57} +(-5.14140 - 8.90517i) q^{58} +(4.54100 - 7.86524i) q^{59} +(1.00132 - 1.73434i) q^{60} +(-7.69656 - 13.3308i) q^{61} -6.05226 q^{62} +(-1.20724 - 6.50960i) q^{63} -10.9976 q^{64} +(-0.936148 + 1.62146i) q^{66} +(-6.79763 + 11.7738i) q^{67} +(-13.0107 - 22.5353i) q^{68} +4.24966 q^{69} +(-3.69322 + 3.15503i) q^{70} +1.13421 q^{71} +(5.03604 + 8.72268i) q^{72} +(-3.83796 + 6.64755i) q^{73} +(0.123870 - 0.214549i) q^{74} +(1.55458 + 2.69261i) q^{75} +13.7231 q^{76} +(2.23870 - 1.91247i) q^{77} +(-2.75598 - 4.77350i) q^{79} +(0.855977 - 1.48259i) q^{80} +(-2.38441 + 4.12992i) q^{81} +(-9.69056 - 16.7845i) q^{82} -5.42111 q^{83} +(1.25506 + 6.76746i) q^{84} -5.43196 q^{85} +(3.02230 + 5.23478i) q^{86} +(-1.52081 + 2.63411i) q^{87} +(-2.23967 + 3.87923i) q^{88} +(-7.64141 - 13.2353i) q^{89} +4.59411 q^{90} +22.2153 q^{92} +(0.895116 + 1.55039i) q^{93} +(-11.1881 + 19.3783i) q^{94} +(1.43234 - 2.48089i) q^{95} +(0.968716 + 1.67786i) q^{96} -12.1661 q^{97} +(2.60787 - 16.4893i) q^{98} -2.78479 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9}+O(q^{10}) \) 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9	\( 48 q + q^{2} - 23 q^{4} - 13 q^{5} + 28 q^{6} + 3 q^{7} - 26 q^{9} - 5 q^{10} + q^{11} - 5 q^{12} - 2 q^{14} + 10 q^{15} - 17 q^{16} + 5 q^{17} - 24 q^{19} + 68 q^{20} - q^{21} - 28 q^{22} - 11 q^{23} - 32 q^{24} - 33 q^{25} - 42 q^{27} - 15 q^{28} + 8 q^{29} + 22 q^{30} - 40 q^{31} + 6 q^{32} - 24 q^{33} + 72 q^{34} + 44 q^{35} - 30 q^{36} + 4 q^{37} + 29 q^{38} + 4 q^{40} + 98 q^{41} - 9 q^{42} + 26 q^{43} - 10 q^{44} - 58 q^{45} + 10 q^{46} - 62 q^{47} + 178 q^{48} + 31 q^{49} - 46 q^{50} + 21 q^{51} + 18 q^{53} - 12 q^{54} - 28 q^{55} - 56 q^{56} - 26 q^{57} - 56 q^{58} - 79 q^{59} - 22 q^{60} - 13 q^{61} + 24 q^{62} + 22 q^{63} + 36 q^{64} + 38 q^{66} + 2 q^{67} + 12 q^{68} - 56 q^{69} + 85 q^{70} - 38 q^{71} - 81 q^{72} - 17 q^{73} - 17 q^{74} - 24 q^{75} + 116 q^{76} - 30 q^{77} + 9 q^{79} - 63 q^{80} - 16 q^{81} + 22 q^{82} + 162 q^{83} + 203 q^{84} - 68 q^{85} - 22 q^{86} - 70 q^{87} + 33 q^{88} - 72 q^{89} + 2 q^{90} - 8 q^{92} - 19 q^{93} + 30 q^{94} - 13 q^{95} - 11 q^{96} + 90 q^{97} + 81 q^{98} - 78 q^{99}+O(q^{100}) \) 48 * q + q^2 - 23 * q^4 - 13 * q^5 + 28 * q^6 + 3 * q^7 - 26 * q^9 - 5 * q^10 + q^11 - 5 * q^12 - 2 * q^14 + 10 * q^15 - 17 * q^16 + 5 * q^17 - 24 * q^19 + 68 * q^20 - q^21 - 28 * q^22 - 11 * q^23 - 32 * q^24 - 33 * q^25 - 42 * q^27 - 15 * q^28 + 8 * q^29 + 22 * q^30 - 40 * q^31 + 6 * q^32 - 24 * q^33 + 72 * q^34 + 44 * q^35 - 30 * q^36 + 4 * q^37 + 29 * q^38 + 4 * q^40 + 98 * q^41 - 9 * q^42 + 26 * q^43 - 10 * q^44 - 58 * q^45 + 10 * q^46 - 62 * q^47 + 178 * q^48 + 31 * q^49 - 46 * q^50 + 21 * q^51 + 18 * q^53 - 12 * q^54 - 28 * q^55 - 56 * q^56 - 26 * q^57 - 56 * q^58 - 79 * q^59 - 22 * q^60 - 13 * q^61 + 24 * q^62 + 22 * q^63 + 36 * q^64 + 38 * q^66 + 2 * q^67 + 12 * q^68 - 56 * q^69 + 85 * q^70 - 38 * q^71 - 81 * q^72 - 17 * q^73 - 17 * q^74 - 24 * q^75 + 116 * q^76 - 30 * q^77 + 9 * q^79 - 63 * q^80 - 16 * q^81 + 22 * q^82 + 162 * q^83 + 203 * q^84 - 68 * q^85 - 22 * q^86 - 70 * q^87 + 33 * q^88 - 72 * q^89 + 2 * q^90 - 8 * q^92 - 19 * q^93 + 30 * q^94 - 13 * q^95 - 11 * q^96 + 90 * q^97 + 81 * q^98 - 78 * q^99

Introduction

L-functions

Modular forms

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