LMFDB - Embedded newform 429.2.bd.b.76.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(76,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 6, 7]))

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

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

chi := DirichletCharacter("429.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.bd (of order $12$, degree $4$, 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:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			76.9
Character	$\chi$	$=$	429.76
Dual form			429.2.bd.b.175.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.391582 + 0.104924i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.58972 - 0.917827i) q^{4} +(2.00961 + 2.00961i) q^{5} +(0.104924 + 0.391582i) q^{6} +(3.95482 - 1.05969i) q^{7} +(-1.09952 - 1.09952i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.391582 + 0.104924i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.58972 - 0.917827i) q^{4} +(2.00961 + 2.00961i) q^{5} +(0.104924 + 0.391582i) q^{6} +(3.95482 - 1.05969i) q^{7} +(-1.09952 - 1.09952i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.576070 + 0.997782i) q^{10} +(-3.19384 + 0.894092i) q^{11} -1.83565i q^{12} +(3.35978 - 1.30837i) q^{13} +1.65982 q^{14} +(-0.735567 + 2.74517i) q^{15} +(1.52047 + 2.63353i) q^{16} +(0.407381 - 0.705605i) q^{17} +(-0.286658 + 0.286658i) q^{18} +(0.953793 + 3.55960i) q^{19} +(-1.35025 - 5.03919i) q^{20} +(2.89513 + 2.89513i) q^{21} +(-1.34446 + 0.0149999i) q^{22} +(-3.35891 + 1.93927i) q^{23} +(0.402453 - 1.50197i) q^{24} +3.07703i q^{25} +(1.45291 - 0.159814i) q^{26} -1.00000 q^{27} +(-7.25968 - 1.94523i) q^{28} +(4.70672 - 2.71742i) q^{29} +(-0.576070 + 0.997782i) q^{30} +(4.88323 + 4.88323i) q^{31} +(1.12397 + 4.19472i) q^{32} +(-2.37123 - 2.31890i) q^{33} +(0.233558 - 0.233558i) q^{34} +(10.0772 + 5.81807i) q^{35} +(1.58972 - 0.917827i) q^{36} +(-2.24755 - 0.602228i) q^{37} +1.49395i q^{38} +(2.81298 + 2.25547i) q^{39} -4.41921i q^{40} +(-6.89125 - 1.84650i) q^{41} +(0.829912 + 1.43745i) q^{42} +(4.75179 - 8.23034i) q^{43} +(5.89794 + 1.51003i) q^{44} +(-2.74517 + 0.735567i) q^{45} +(-1.51877 + 0.406952i) q^{46} +(-5.58658 + 5.58658i) q^{47} +(-1.52047 + 2.63353i) q^{48} +(8.45547 - 4.88177i) q^{49} +(-0.322855 + 1.20491i) q^{50} +0.814762 q^{51} +(-6.54199 - 1.00375i) q^{52} -3.97736 q^{53} +(-0.391582 - 0.104924i) q^{54} +(-8.21513 - 4.62158i) q^{55} +(-5.51356 - 3.18326i) q^{56} +(-2.60581 + 2.60581i) q^{57} +(2.12819 - 0.570247i) q^{58} +(-2.78917 - 10.4093i) q^{59} +(3.68894 - 3.68894i) q^{60} +(-9.30427 - 5.37182i) q^{61} +(1.39982 + 2.42455i) q^{62} +(-1.05969 + 3.95482i) q^{63} -4.32136i q^{64} +(9.38116 + 4.12253i) q^{65} +(-0.685221 - 1.15684i) q^{66} +(1.10134 - 4.11026i) q^{67} +(-1.29525 + 0.747811i) q^{68} +(-3.35891 - 1.93927i) q^{69} +(3.33559 + 3.33559i) q^{70} +(-0.994820 + 0.266561i) q^{71} +(1.50197 - 0.402453i) q^{72} +(-9.57876 - 9.57876i) q^{73} +(-0.816911 - 0.471644i) q^{74} +(-2.66479 + 1.53852i) q^{75} +(1.75083 - 6.53420i) q^{76} +(-11.6836 + 6.92045i) q^{77} +(0.864859 + 1.17835i) q^{78} -4.76856i q^{79} +(-2.23681 + 8.34789i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.50475 - 1.44612i) q^{82} +(-5.63465 + 5.63465i) q^{83} +(-1.94523 - 7.25968i) q^{84} +(2.23666 - 0.599312i) q^{85} +(2.72428 - 2.72428i) q^{86} +(4.70672 + 2.71742i) q^{87} +(4.49477 + 2.52862i) q^{88} +(14.1263 + 3.78514i) q^{89} -1.15214 q^{90} +(11.9009 - 8.73472i) q^{91} +7.11965 q^{92} +(-1.78738 + 6.67061i) q^{93} +(-2.77377 + 1.60144i) q^{94} +(-5.23665 + 9.07015i) q^{95} +(-3.07075 + 3.07075i) q^{96} +(-8.44167 + 2.26194i) q^{97} +(3.82323 - 1.02443i) q^{98} +(0.822612 - 3.21299i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9}+O(q^{10}) $ 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9	$ 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9} - 4 q^{11} - 24 q^{14} - 8 q^{15} + 4 q^{16} + 80 q^{20} - 10 q^{22} - 12 q^{23} + 40 q^{26} - 56 q^{27} - 12 q^{31} - 8 q^{33} - 16 q^{34} - 12 q^{37} - 12 q^{42} + 24 q^{44} - 4 q^{45} - 40 q^{47} - 4 q^{48} + 24 q^{49} - 88 q^{53} - 18 q^{55} + 72 q^{56} + 40 q^{58} + 8 q^{59} + 52 q^{60} - 20 q^{66} - 4 q^{67} - 12 q^{69} + 40 q^{70} - 24 q^{71} + 12 q^{75} - 4 q^{78} - 188 q^{80} - 28 q^{81} - 12 q^{82} + 32 q^{86} + 18 q^{88} - 16 q^{89} + 28 q^{91} - 96 q^{92} - 12 q^{93} - 28 q^{97} - 4 q^{99}+O(q^{100}) $ 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9 - 4 * q^11 - 24 * q^14 - 8 * q^15 + 4 * q^16 + 80 * q^20 - 10 * q^22 - 12 * q^23 + 40 * q^26 - 56 * q^27 - 12 * q^31 - 8 * q^33 - 16 * q^34 - 12 * q^37 - 12 * q^42 + 24 * q^44 - 4 * q^45 - 40 * q^47 - 4 * q^48 + 24 * q^49 - 88 * q^53 - 18 * q^55 + 72 * q^56 + 40 * q^58 + 8 * q^59 + 52 * q^60 - 20 * q^66 - 4 * q^67 - 12 * q^69 + 40 * q^70 - 24 * q^71 + 12 * q^75 - 4 * q^78 - 188 * q^80 - 28 * q^81 - 12 * q^82 + 32 * q^86 + 18 * q^88 - 16 * q^89 + 28 * q^91 - 96 * q^92 - 12 * q^93 - 28 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{7}{12}\right)$	$-1$	$1$

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 $

$2$	0.391582	+	0.104924i	0.276890	+	0.0741926i	0.394592	−	0.918856i	$-0.370886\pi$
$2$	0.391582	+	0.104924i	0.276890	+	0.0741926i	−0.117702	+	0.993049i	$0.537553\pi$
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−1.58972	−	0.917827i	−0.794862	−	0.458914i
$5$	2.00961	+	2.00961i	0.898723	+	0.898723i	0.995323	−	0.0966002i	$-0.0307968\pi$
$5$	2.00961	+	2.00961i	0.898723	+	0.898723i	−0.0966002	+	0.995323i	$0.530797\pi$
$6$	0.104924	+	0.391582i	0.0428351	+	0.159863i
$7$	3.95482	−	1.05969i	1.49478	−	0.400525i	0.583433	−	0.812162i	$-0.301709\pi$
$7$	3.95482	−	1.05969i	1.49478	−	0.400525i	0.911348	+	0.411636i	$0.135043\pi$
$8$	−1.09952	−	1.09952i	−0.388739	−	0.388739i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.576070	+	0.997782i	0.182169	+	0.315526i
$11$	−3.19384	+	0.894092i	−0.962978	+	0.269579i
$11$	−3.19384	+	0.894092i	−0.962978	+	0.269579i
$12$		−	1.83565i		−	0.529908i
$13$	3.35978	−	1.30837i	0.931837	−	0.362878i
$13$	3.35978	−	1.30837i	0.931837	−	0.362878i
$14$	1.65982			0.443607
$15$	−0.735567	+	2.74517i	−0.189923	+	0.708801i
$16$	1.52047	+	2.63353i	0.380117	+	0.658382i
$17$	0.407381	−	0.705605i	0.0988044	−	0.171134i	−0.812386	−	0.583121i	$-0.801832\pi$
$17$	0.407381	−	0.705605i	0.0988044	−	0.171134i	0.911190	+	0.411986i	$0.135165\pi$
$18$	−0.286658	+	0.286658i	−0.0675660	+	0.0675660i
$19$	0.953793	+	3.55960i	0.218815	+	0.816629i	0.984789	+	0.173757i	$0.0555907\pi$
$19$	0.953793	+	3.55960i	0.218815	+	0.816629i	−0.765973	+	0.642872i	$0.777743\pi$
$20$	−1.35025	−	5.03919i	−0.301924	−	1.12680i
$21$	2.89513	+	2.89513i	0.631769	+	0.631769i
$22$	−1.34446	+	0.0149999i	−0.286640	+	0.00319798i
$23$	−3.35891	+	1.93927i	−0.700381	+	0.404365i	−0.807489	−	0.589882i	$-0.799174\pi$
$23$	−3.35891	+	1.93927i	−0.700381	+	0.404365i	0.107108	+	0.994247i	$0.465841\pi$
$24$	0.402453	−	1.50197i	0.0821503	−	0.306589i
$25$			3.07703i			0.615406i
$26$	1.45291	−	0.159814i	0.284940	−	0.0313421i
$27$	−1.00000			−0.192450
$28$	−7.25968	−	1.94523i	−1.37195	−	0.367613i
$29$	4.70672	−	2.71742i	0.874015	−	0.504613i	0.00533471	−	0.999986i	$-0.498302\pi$
$29$	4.70672	−	2.71742i	0.874015	−	0.504613i	0.868680	+	0.495373i	$0.164969\pi$
$30$	−0.576070	+	0.997782i	−0.105175	+	0.182169i
$31$	4.88323	+	4.88323i	0.877053	+	0.877053i	0.993229	−	0.116176i	$-0.0370635\pi$
$31$	4.88323	+	4.88323i	0.877053	+	0.877053i	−0.116176	+	0.993229i	$0.537064\pi$
$32$	1.12397	+	4.19472i	0.198692	+	0.741530i
$33$	−2.37123	−	2.31890i	−0.412777	−	0.403668i
$34$	0.233558	−	0.233558i	0.0400549	−	0.0400549i
$35$	10.0772	+	5.81807i	1.70336	+	0.983433i
$36$	1.58972	−	0.917827i	0.264954	−	0.152971i
$37$	−2.24755	−	0.602228i	−0.369494	−	0.0990057i	0.0692938	−	0.997596i	$-0.477925\pi$
$37$	−2.24755	−	0.602228i	−0.369494	−	0.0990057i	−0.438788	+	0.898591i	$0.644592\pi$
$38$			1.49395i			0.242351i
$39$	2.81298	+	2.25547i	0.450437	+	0.361165i
$40$		−	4.41921i		−	0.698738i
$41$	−6.89125	−	1.84650i	−1.07623	−	0.288375i	−0.323181	−	0.946337i	$-0.604752\pi$
$41$	−6.89125	−	1.84650i	−1.07623	−	0.288375i	−0.753051	+	0.657962i	$0.771419\pi$
$42$	0.829912	+	1.43745i	0.128058	+	0.221803i
$43$	4.75179	−	8.23034i	0.724641	−	1.25511i	−0.234481	−	0.972121i	$-0.575339\pi$
$43$	4.75179	−	8.23034i	0.724641	−	1.25511i	0.959122	−	0.282994i	$-0.0913276\pi$
$44$	5.89794	+	1.51003i	0.889148	+	0.227646i
$45$	−2.74517	+	0.735567i	−0.409226	+	0.109652i
$46$	−1.51877	+	0.406952i	−0.223930	+	0.0600018i
$47$	−5.58658	+	5.58658i	−0.814886	+	0.814886i	−0.985362	−	0.170476i	$-0.945469\pi$
$47$	−5.58658	+	5.58658i	−0.814886	+	0.814886i	0.170476	+	0.985362i	$0.445469\pi$
$48$	−1.52047	+	2.63353i	−0.219461	+	0.380117i
$49$	8.45547	−	4.88177i	1.20792	−	0.697395i
$50$	−0.322855	+	1.20491i	−0.0456586	+	0.170400i
$51$	0.814762			0.114090
$52$	−6.54199	−	1.00375i	−0.907211	−	0.139195i
$53$	−3.97736			−0.546333			−0.273166	−	0.961967i	$-0.588071\pi$
$53$	−3.97736			−0.546333			−0.273166	+	0.961967i	$0.588071\pi$
$54$	−0.391582	−	0.104924i	−0.0532876	−	0.0142784i
$55$	−8.21513	−	4.62158i	−1.10773	−	0.623174i
$56$	−5.51356	−	3.18326i	−0.736780	−	0.425380i
$57$	−2.60581	+	2.60581i	−0.345148	+	0.345148i
$58$	2.12819	−	0.570247i	0.279445	−	0.0748771i
$59$	−2.78917	−	10.4093i	−0.363120	−	1.35518i	−0.869952	−	0.493136i	$-0.835850\pi$
$59$	−2.78917	−	10.4093i	−0.363120	−	1.35518i	0.506832	−	0.862045i	$-0.330816\pi$
$60$	3.68894	−	3.68894i	0.476240	−	0.476240i
$61$	−9.30427	−	5.37182i	−1.19129	−	0.687791i	−0.232691	−	0.972551i	$-0.574753\pi$
$61$	−9.30427	−	5.37182i	−1.19129	−	0.687791i	−0.958599	+	0.284759i	$0.908086\pi$
$62$	1.39982	+	2.42455i	0.177777	+	0.307918i
$63$	−1.05969	+	3.95482i	−0.133508	+	0.498260i
$64$		−	4.32136i		−	0.540170i
$65$	9.38116	+	4.12253i	1.16359	+	0.511336i
$66$	−0.685221	−	1.15684i	−0.0843449	−	0.142397i
$67$	1.10134	−	4.11026i	0.134550	−	0.502148i	−0.865449	−	0.500997i	$-0.832967\pi$
$67$	1.10134	−	4.11026i	0.134550	−	0.502148i	0.999999	−	0.00115109i	$-0.000366402\pi$
$68$	−1.29525	+	0.747811i	−0.157072	+	0.0906854i
$69$	−3.35891	−	1.93927i	−0.404365	−	0.233460i
$70$	3.33559	+	3.33559i	0.398679	+	0.398679i
$71$	−0.994820	+	0.266561i	−0.118063	+	0.0316350i	−0.317367	−	0.948303i	$-0.602799\pi$
$71$	−0.994820	+	0.266561i	−0.118063	+	0.0316350i	0.199304	+	0.979938i	$0.436132\pi$
$72$	1.50197	−	0.402453i	0.177009	−	0.0474295i
$73$	−9.57876	−	9.57876i	−1.12111	−	1.12111i	−0.991575	−	0.129534i	$-0.958652\pi$
$73$	−9.57876	−	9.57876i	−1.12111	−	1.12111i	−0.129534	−	0.991575i	$-0.541348\pi$
$74$	−0.816911	−	0.471644i	−0.0949639	−	0.0548274i
$75$	−2.66479	+	1.53852i	−0.307703	+	0.177653i
$76$	1.75083	−	6.53420i	0.200834	−	0.749525i
$77$	−11.6836	+	6.92045i	−1.33147	+	0.788659i
$78$	0.864859	+	1.17835i	0.0979260	+	0.133422i
$79$		−	4.76856i		−	0.536505i	−0.963349	−	0.268252i	$-0.913554\pi$
$79$		−	4.76856i		−	0.536505i	0.963349	−	0.268252i	$-0.0864461\pi$
$80$	−2.23681	+	8.34789i	−0.250083	+	0.933323i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.50475	−	1.44612i	−0.276603	−	0.159697i
$83$	−5.63465	+	5.63465i	−0.618484	+	0.618484i	−0.945142	−	0.326659i	$-0.894077\pi$
$83$	−5.63465	+	5.63465i	−0.618484	+	0.618484i	0.326659	+	0.945142i	$0.394077\pi$
$84$	−1.94523	−	7.25968i	−0.212241	−	0.792096i
$85$	2.23666	−	0.599312i	0.242600	−	0.0650045i
$86$	2.72428	−	2.72428i	0.293766	−	0.293766i
$87$	4.70672	+	2.71742i	0.504613	+	0.291338i
$88$	4.49477	+	2.52862i	0.479144	+	0.269552i
$89$	14.1263	+	3.78514i	1.49739	+	0.401224i	0.912225	−	0.409690i	$-0.134363\pi$
$89$	14.1263	+	3.78514i	1.49739	+	0.401224i	0.585165	+	0.810914i	$0.301030\pi$
$90$	−1.15214			−0.121446
$91$	11.9009	−	8.73472i	1.24755	−	0.915647i
$92$	7.11965			0.742275
$93$	−1.78738	+	6.67061i	−0.185343	+	0.691710i
$94$	−2.77377	+	1.60144i	−0.286093	+	0.165176i
$95$	−5.23665	+	9.07015i	−0.537269	+	0.930578i
$96$	−3.07075	+	3.07075i	−0.313407	+	0.313407i
$97$	−8.44167	+	2.26194i	−0.857122	+	0.229665i	−0.660511	−	0.750816i	$-0.729660\pi$
$97$	−8.44167	+	2.26194i	−0.857122	+	0.229665i	−0.196611	+	0.980482i	$0.562994\pi$
$98$	3.82323	−	1.02443i	0.386204	−	0.103483i
$99$	0.822612	−	3.21299i	0.0826757	−	0.322918i
$100$	2.82418	−	4.89163i	0.282418	−	0.489163i
$101$	−2.03636	−	3.52707i	−0.202625	−	0.350957i	0.746748	−	0.665107i	$-0.231614\pi$
$101$	−2.03636	−	3.52707i	−0.202625	−	0.350957i	−0.949373	+	0.314150i	$0.898281\pi$
$102$	0.319046	+	0.0854882i	0.0315903	+	0.00846459i
$103$			2.51492i			0.247802i	0.992295	+	0.123901i	$0.0395405\pi$
$103$			2.51492i			0.247802i	−0.992295	+	0.123901i	$0.960459\pi$
$104$	−5.13274	−	2.25557i	−0.503307	−	0.221177i
$105$			11.6361i			1.13557i
$106$	−1.55746	−	0.417321i	−0.151274	−	0.0405338i
$107$	4.69636	−	2.71144i	0.454014	−	0.262125i	−0.255510	−	0.966806i	$-0.582243\pi$
$107$	4.69636	−	2.71144i	0.454014	−	0.262125i	0.709524	+	0.704681i	$0.248910\pi$
$108$	1.58972	+	0.917827i	0.152971	+	0.0883180i
$109$	−6.02896	+	6.02896i	−0.577470	+	0.577470i	−0.934205	−	0.356736i	$-0.883890\pi$
$109$	−6.02896	+	6.02896i	−0.577470	+	0.577470i	0.356736	+	0.934205i	$0.383890\pi$
$110$	−2.73198	−	2.67169i	−0.260484	−	0.254736i
$111$	−0.602228	−	2.24755i	−0.0571609	−	0.213328i
$112$	8.80390	+	8.80390i	0.831890	+	0.831890i
$113$	4.45504	−	7.71635i	0.419095	−	0.725893i	−0.576754	−	0.816918i	$-0.695681\pi$
$113$	4.45504	−	7.71635i	0.419095	−	0.725893i	0.995849	+	0.0910247i	$0.0290142\pi$
$114$	−1.29380	+	0.746977i	−0.121176	+	0.0699608i
$115$	−10.6472	−	2.85292i	−0.992861	−	0.266036i
$116$	−9.97650			−0.926295
$117$	−0.546807	+	3.56385i	−0.0505523	+	0.329478i
$118$		−	4.36877i		−	0.402177i
$119$	0.863396	−	3.22224i	0.0791474	−	0.295382i
$120$	3.82715	−	2.20960i	0.349369	−	0.201708i
$121$	9.40120	−	5.71117i	0.854654	−	0.519197i
$122$	−3.07975	−	3.07975i	−0.278828	−	0.278828i
$123$	−1.84650	−	6.89125i	−0.166494	−	0.621363i
$124$	−3.28102	−	12.2449i	−0.294644	−	1.09963i
$125$	3.86441	−	3.86441i	0.345643	−	0.345643i
$126$	−0.829912	+	1.43745i	−0.0739344	+	0.128058i
$127$	−1.79483	−	3.10873i	−0.159265	−	0.275855i	0.775339	−	0.631546i	$-0.217579\pi$
$127$	−1.79483	−	3.10873i	−0.159265	−	0.275855i	−0.934604	+	0.355690i	$0.884246\pi$
$128$	2.70136	−	10.0816i	0.238769	−	0.891097i
$129$	9.50357			0.836743
$130$	3.24094	+	2.59862i	0.284250	+	0.227914i
$131$			7.05407i			0.616317i	0.951335	+	0.308159i	$0.0997128\pi$
$131$			7.05407i			0.616317i	−0.951335	+	0.308159i	$0.900287\pi$
$132$	1.64124	+	5.86278i	0.142852	+	0.510290i
$133$	7.54416	+	13.0669i	0.654161	+	1.13304i
$134$	0.862530	−	1.49395i	0.0745112	−	0.129057i
$135$	−2.00961	−	2.00961i	−0.172959	−	0.172959i
$136$	−1.22375	+	0.327903i	−0.104936	+	0.0281175i
$137$	−2.81361	−	10.5005i	−0.240383	−	0.897120i	−0.975648	−	0.219341i	$-0.929609\pi$
$137$	−2.81361	−	10.5005i	−0.240383	−	0.897120i	0.735266	−	0.677779i	$-0.237057\pi$
$138$	−1.11181	−	1.11181i	−0.0946438	−	0.0946438i
$139$	−6.60159	−	3.81143i	−0.559940	−	0.323281i	0.193182	−	0.981163i	$-0.438119\pi$
$139$	−6.60159	−	3.81143i	−0.559940	−	0.323281i	−0.753121	+	0.657882i	$0.771453\pi$
$140$	−10.6800	−	18.4982i	−0.902621	−	1.56339i
$141$	−7.63141	−	2.04483i	−0.642680	−	0.172206i
$142$	−0.417523			−0.0350377
$143$	−9.56080	+	7.18269i	−0.799514	+	0.600647i
$144$	−3.04094			−0.253411
$145$	14.9196	+	3.99769i	1.23900	+	0.331990i
$146$	−2.74583	−	4.75592i	−0.227246	−	0.393602i
$147$	8.45547	+	4.88177i	0.697395	+	0.402641i
$148$	3.02023	+	3.02023i	0.248262	+	0.248262i
$149$	−2.59701	−	9.69215i	−0.212755	−	0.794012i	−0.986945	−	0.161059i	$-0.948509\pi$
$149$	−2.59701	−	9.69215i	−0.212755	−	0.794012i	0.774190	−	0.632953i	$-0.218158\pi$
$150$	−1.20491	+	0.322855i	−0.0983806	+	0.0263610i
$151$	14.9563	+	14.9563i	1.21713	+	1.21713i	0.968634	+	0.248492i	$0.0799349\pi$
$151$	14.9563	+	14.9563i	1.21713	+	1.21713i	0.248492	+	0.968634i	$0.420065\pi$
$152$	2.86515	−	4.96258i	0.232394	−	0.402518i
$153$	0.407381	+	0.705605i	0.0329348	+	0.0570448i
$154$	−5.30121	+	1.48404i	−0.427184	+	0.119587i
$155$			19.6267i			1.57646i
$156$	−2.40172	−	6.16740i	−0.192292	−	0.493787i
$157$	−22.2134			−1.77282			−0.886411	−	0.462899i	$-0.846809\pi$
$157$	−22.2134			−1.77282			−0.886411	+	0.462899i	$0.846809\pi$
$158$	0.500337	−	1.86728i	0.0398047	−	0.148553i
$159$	−1.98868	−	3.44450i	−0.157713	−	0.273166i
$160$	−6.17100	+	10.6885i	−0.487860	+	0.844999i
$161$	−11.2289	+	11.2289i	−0.884958	+	0.884958i
$162$	−0.104924	−	0.391582i	−0.00824362	−	0.0307656i
$163$	3.45186	+	12.8825i	0.270370	+	1.00904i	0.958881	+	0.283810i	$0.0915983\pi$
$163$	3.45186	+	12.8825i	0.270370	+	1.00904i	−0.688510	+	0.725227i	$0.741735\pi$
$164$	9.26040	+	9.26040i	0.723116	+	0.723116i
$165$	−0.105156	−	9.42530i	−0.00818638	−	0.733759i
$166$	−2.79764	+	1.61522i	−0.217139	+	0.125365i
$167$	−4.51531	+	16.8514i	−0.349405	+	1.30400i	0.537976	+	0.842960i	$0.319189\pi$
$167$	−4.51531	+	16.8514i	−0.349405	+	1.30400i	−0.887381	+	0.461037i	$0.847478\pi$
$168$		−	6.36651i		−	0.491187i
$169$	9.57631	−	8.79172i	0.736639	−	0.676286i
$170$	0.938720			0.0719965
$171$	−3.55960	−	0.953793i	−0.272210	−	0.0729384i
$172$	−15.1081	+	8.72264i	−1.15198	+	0.665095i
$173$	6.42530	−	11.1289i	0.488507	−	0.846118i	−0.511406	−	0.859339i	$-0.670875\pi$
$173$	6.42530	−	11.1289i	0.488507	−	0.846118i	0.999913	+	0.0132209i	$0.00420848\pi$
$174$	1.55794	+	1.55794i	0.118107	+	0.118107i
$175$	3.26070	+	12.1691i	0.246486	+	0.919898i
$176$	−7.21074	−	7.05162i	−0.543530	−	0.531536i
$177$	7.62017	−	7.62017i	0.572767	−	0.572767i
$178$	5.13447	+	2.96439i	0.384845	+	0.222190i
$179$	−16.8258	+	9.71437i	−1.25762	+	0.726086i	−0.972611	−	0.232439i	$-0.925329\pi$
$179$	−16.8258	+	9.71437i	−1.25762	+	0.726086i	−0.285007	+	0.958525i	$0.591996\pi$
$180$	5.03919	+	1.35025i	0.375599	+	0.100641i
$181$			20.6946i			1.53822i	0.639117	+	0.769109i	$0.279300\pi$
$181$			20.6946i			1.53822i	−0.639117	+	0.769109i	$0.720700\pi$
$182$	5.57665	−	2.17167i	0.413369	−	0.160975i
$183$		−	10.7436i		−	0.794193i
$184$	5.82546	+	1.56093i	0.429458	+	0.115073i
$185$	−3.30644	−	5.72692i	−0.243094	−	0.421052i
$186$	−1.39982	+	2.42455i	−0.102639	+	0.177777i
$187$	−0.670233	+	2.61782i	−0.0490123	+	0.191434i
$188$	14.0086	−	3.75360i	1.02168	−	0.273759i
$189$	−3.95482	+	1.05969i	−0.287671	+	0.0770811i
$190$	−3.00226	+	3.00226i	−0.217807	+	0.217807i
$191$	−8.11011	+	14.0471i	−0.586827	+	1.01641i	0.407818	+	0.913063i	$0.366290\pi$
$191$	−8.11011	+	14.0471i	−0.586827	+	1.01641i	−0.994645	+	0.103351i	$0.967044\pi$
$192$	3.74241	−	2.16068i	0.270085	−	0.155934i
$193$	6.28919	−	23.4716i	0.452706	−	1.68952i	−0.242041	−	0.970266i	$-0.577817\pi$
$193$	6.28919	−	23.4716i	0.452706	−	1.68952i	0.694747	−	0.719254i	$-0.255516\pi$
$194$	−3.54294			−0.254368
$195$	1.12037	+	10.1856i	0.0802313	+	0.729405i
$196$	−17.9225			−1.28018
$197$	20.9622	+	5.61680i	1.49349	+	0.400180i	0.910915	−	0.412594i	$-0.135377\pi$
$197$	20.9622	+	5.61680i	1.49349	+	0.400180i	0.582578	+	0.812775i	$0.302044\pi$
$198$	0.659241	−	1.17184i	0.0468502	−	0.0832789i
$199$	5.75748	+	3.32408i	0.408137	+	0.235638i	0.689989	−	0.723820i	$-0.257615\pi$
$199$	5.75748	+	3.32408i	0.408137	+	0.235638i	−0.281852	+	0.959458i	$0.590949\pi$
$200$	3.38326	−	3.38326i	0.239233	−	0.239233i
$201$	4.11026	−	1.10134i	0.289915	−	0.0776825i
$202$	−0.427326	−	1.59480i	−0.0300665	−	0.112210i
$203$	15.7346	−	15.7346i	1.10435	−	1.10435i
$204$	−1.29525	−	0.747811i	−0.0906854	−	0.0523572i
$205$	−10.1379	−	17.5594i	−0.708065	−	1.22640i
$206$	−0.263876	+	0.984797i	−0.0183851	+	0.0686141i
$207$		−	3.87853i		−	0.269577i
$208$	8.55409	+	6.85874i	0.593119	+	0.475568i
$209$	−6.22887	−	10.5160i	−0.430860	−	0.727408i
$210$	−1.22091	+	4.55650i	−0.0842509	+	0.314429i
$211$	−16.9556	+	9.78932i	−1.16727	+	0.673925i	−0.953036	−	0.302857i	$-0.902059\pi$
$211$	−16.9556	+	9.78932i	−1.16727	+	0.673925i	−0.214236	+	0.976782i	$0.568726\pi$
$212$	6.32291	+	3.65053i	0.434259	+	0.250720i
$213$	−0.728259	−	0.728259i	−0.0498995	−	0.0498995i
$214$	2.12351	−	0.568992i	0.145160	−	0.0388955i
$215$	26.0890	−	6.99051i	1.77925	−	0.476749i
$216$	1.09952	+	1.09952i	0.0748130	+	0.0748130i
$217$	24.4870	+	14.1376i	1.66228	+	0.959720i
$218$	−2.99342	+	1.72825i	−0.202740	+	0.117052i
$219$	3.50607	−	13.0848i	0.236918	−	0.884191i
$220$	8.81797	+	14.8871i	0.594507	+	1.00369i
$221$	0.445517	−	2.90369i	0.0299687	−	0.195323i
$222$		−	0.943287i		−	0.0633093i
$223$	1.56442	−	5.83849i	0.104761	−	0.390974i	−0.893557	−	0.448950i	$-0.851798\pi$
$223$	1.56442	−	5.83849i	0.104761	−	0.390974i	0.998318	+	0.0579759i	$0.0184647\pi$
$224$	8.89022	+	15.3983i	0.594003	+	1.02884i
$225$	−2.66479	−	1.53852i	−0.177653	−	0.102568i
$226$	2.55414	−	2.55414i	0.169899	−	0.169899i
$227$	3.79339	+	14.1571i	0.251776	+	0.939641i	0.969856	+	0.243680i	$0.0783546\pi$
$227$	3.79339	+	14.1571i	0.251776	+	0.939641i	−0.718080	+	0.695961i	$0.754979\pi$
$228$	6.53420	−	1.75083i	0.432738	−	0.115952i
$229$	2.63621	−	2.63621i	0.174206	−	0.174206i	−0.614619	−	0.788824i	$-0.710690\pi$
$229$	2.63621	−	2.63621i	0.174206	−	0.174206i	0.788824	+	0.614619i	$0.210690\pi$
$230$	−3.86993	−	2.23431i	−0.255176	−	0.147326i
$231$	−11.8351	−	6.65806i	−0.778691	−	0.438068i
$232$	−8.16300	−	2.18727i	−0.535927	−	0.143601i
$233$	12.6584			0.829277			0.414639	−	0.909986i	$-0.363908\pi$
$233$	12.6584			0.829277			0.414639	+	0.909986i	$0.363908\pi$
$234$	−0.588053	+	1.33817i	−0.0384422	+	0.0874786i
$235$	−22.4536			−1.46471
$236$	−5.11996	+	19.1080i	−0.333281	+	1.24382i
$237$	4.12969	−	2.38428i	0.268252	−	0.154876i
$238$	0.676181	−	1.17118i	0.0438303	−	0.0759163i
$239$	15.5478	−	15.5478i	1.00570	−	1.00570i	0.00571889	−	0.999984i	$-0.498180\pi$
$239$	15.5478	−	15.5478i	1.00570	−	1.00570i	0.999984	−	0.00571889i	$-0.00182039\pi$
$240$	−8.34789	+	2.23681i	−0.538854	+	0.144386i
$241$	22.6969	−	6.08161i	1.46203	−	0.391751i	0.561843	−	0.827244i	$-0.310093\pi$
$241$	22.6969	−	6.08161i	1.46203	−	0.391751i	0.900192	+	0.435493i	$0.143426\pi$
$242$	4.28058	−	1.24998i	0.275166	−	0.0803517i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	9.86081	+	17.0794i	0.631274	+	1.09340i
$245$	26.8026	+	7.18173i	1.71235	+	0.458824i
$246$		−	2.89223i		−	0.184402i
$247$	7.86184	+	10.7116i	0.500237	+	0.681562i
$248$		−	10.7384i		−	0.681890i
$249$	−7.69708	−	2.06243i	−0.487783	−	0.130701i
$250$	1.91870	−	1.10776i	0.121349	−	0.0700611i
$251$	−1.66319	−	0.960242i	−0.104980	−	0.0606099i	0.446591	−	0.894738i	$-0.352638\pi$
$251$	−1.66319	−	0.960242i	−0.104980	−	0.0606099i	−0.551571	+	0.834128i	$0.685971\pi$
$252$	5.31445	−	5.31445i	0.334779	−	0.334779i
$253$	8.99393	−	9.19688i	0.565443	−	0.578203i
$254$	−0.376641	−	1.40564i	−0.0236326	−	0.0881980i
$255$	1.63735	+	1.63735i	0.102535	+	0.102535i
$256$	−2.20575	+	3.82047i	−0.137859	+	0.238779i
$257$	−17.6940	+	10.2156i	−1.10372	+	0.637234i	−0.937196	−	0.348803i	$-0.886588\pi$
$257$	−17.6940	+	10.2156i	−1.10372	+	0.637234i	−0.166526	+	0.986037i	$0.553255\pi$
$258$	3.72143	+	0.997154i	0.231686	+	0.0620801i
$259$	−9.52681			−0.591967
$260$	−11.1297	−	15.1640i	−0.690234	−	0.940429i
$261$			5.43485i			0.336409i
$262$	−0.740143	+	2.76225i	−0.0457262	+	0.170652i
$263$	−3.90007	+	2.25171i	−0.240489	+	0.138846i	−0.615401	−	0.788214i	$-0.711006\pi$
$263$	−3.90007	+	2.25171i	−0.240489	+	0.138846i	0.374913	+	0.927060i	$0.377673\pi$
$264$	0.0575343	+	5.15689i	0.00354099	+	0.317385i
$265$	−7.99293	−	7.99293i	−0.491002	−	0.491002i
$266$	1.58313	+	5.90832i	0.0970678	+	0.362262i
$267$	3.78514	+	14.1263i	0.231647	+	0.864518i
$268$	−5.52333	+	5.52333i	−0.337391	+	0.337391i
$269$	−1.50710	+	2.61037i	−0.0918894	+	0.159157i	−0.908306	−	0.418306i	$-0.862624\pi$
$269$	−1.50710	+	2.61037i	−0.0918894	+	0.159157i	0.816417	+	0.577463i	$0.195957\pi$
$270$	−0.576070	−	0.997782i	−0.0350585	−	0.0607231i
$271$	−1.20307	+	4.48992i	−0.0730814	+	0.272743i	−0.992791	−	0.119855i	$-0.961757\pi$
$271$	−1.20307	+	4.48992i	−0.0730814	+	0.272743i	0.919710	+	0.392598i	$0.128424\pi$
$272$	2.47764			0.150229
$273$	13.5149	+	5.93910i	0.817960	+	0.359450i
$274$		−	4.40703i		−	0.266238i
$275$	−2.75115	−	9.82754i	−0.165901	−	0.592623i
$276$	3.55982	+	6.16580i	0.214276	+	0.371137i
$277$	4.04445	−	7.00520i	0.243008	−	0.420902i	−0.718562	−	0.695463i	$-0.755199\pi$
$277$	4.04445	−	7.00520i	0.243008	−	0.420902i	0.961570	+	0.274561i	$0.0885327\pi$
$278$	−2.18515	−	2.18515i	−0.131057	−	0.131057i
$279$	−6.67061	+	1.78738i	−0.399359	+	0.107008i
$280$	−4.68299	−	17.4772i	−0.279862	−	1.04446i
$281$	11.7836	+	11.7836i	0.702952	+	0.702952i	0.965043	−	0.262091i	$-0.0844122\pi$
$281$	11.7836	+	11.7836i	0.702952	+	0.702952i	−0.262091	+	0.965043i	$0.584412\pi$
$282$	−2.77377	−	1.60144i	−0.165176	−	0.0953642i
$283$	5.79787	+	10.0422i	0.344648	+	0.596947i	0.985290	−	0.170892i	$-0.0546651\pi$
$283$	5.79787	+	10.0422i	0.344648	+	0.596947i	−0.640642	+	0.767840i	$0.721332\pi$
$284$	1.82615	+	0.489314i	0.108362	+	0.0290355i
$285$	−10.4733			−0.620385
$286$	−4.49748	+	1.80946i	−0.265941	+	0.106995i
$287$	−29.2103			−1.72423
$288$	−4.19472	−	1.12397i	−0.247177	−	0.0662307i
$289$	8.16808	+	14.1475i	0.480475	+	0.832208i
$290$	5.42279	+	3.13085i	0.318437	+	0.183850i
$291$	−6.17973	−	6.17973i	−0.362262	−	0.362262i
$292$	6.43593	+	24.0192i	0.376634	+	1.40562i
$293$	−23.4225	+	6.27605i	−1.36836	+	0.366651i	−0.866879	−	0.498519i	$-0.833877\pi$
$293$	−23.4225	+	6.27605i	−1.36836	+	0.366651i	−0.501480	+	0.865169i	$0.667211\pi$
$294$	2.79880	+	2.79880i	0.163229	+	0.163229i
$295$	15.3135	−	26.5238i	0.891588	−	1.54428i
$296$	1.80906	+	3.13339i	0.105150	+	0.182124i
$297$	3.19384	−	0.894092i	0.185325	−	0.0518805i
$298$		−	4.06776i		−	0.235639i
$299$	−8.74793	+	10.9102i	−0.505906	+	0.630955i
$300$	5.64837			0.326109
$301$	10.0708	−	37.5849i	0.580474	−	2.16636i
$302$	4.28734	+	7.42589i	0.246709	+	0.427312i
$303$	2.03636	−	3.52707i	0.116986	−	0.202625i
$304$	−7.92410	+	7.92410i	−0.454479	+	0.454479i
$305$	−7.90267	−	29.4932i	−0.452506	−	1.68877i
$306$	0.0854882	+	0.319046i	0.00488704	+	0.0182387i
$307$	−11.3350	−	11.3350i	−0.646920	−	0.646920i	0.305327	−	0.952247i	$-0.401234\pi$
$307$	−11.3350	−	11.3350i	−0.646920	−	0.646920i	−0.952247	+	0.305327i	$0.901234\pi$
$308$	24.9254	−	0.278088i	1.42026	−	0.0158455i
$309$	−2.17798	+	1.25746i	−0.123901	+	0.0715343i
$310$	−2.05932	+	7.68547i	−0.116961	+	0.436506i
$311$		−	7.64419i		−	0.433462i	−0.976231	−	0.216731i	$-0.930461\pi$
$311$		−	7.64419i		−	0.433462i	0.976231	−	0.216731i	$-0.0695395\pi$
$312$	−0.612991	−	5.57287i	−0.0347038	−	0.315502i
$313$	−10.6415			−0.601494			−0.300747	−	0.953704i	$-0.597236\pi$
$313$	−10.6415			−0.601494			−0.300747	+	0.953704i	$0.597236\pi$
$314$	−8.69837	−	2.33072i	−0.490878	−	0.131530i
$315$	−10.0772	+	5.81807i	−0.567785	+	0.327811i
$316$	−4.37671	+	7.58069i	−0.246209	+	0.426447i
$317$	15.4997	+	15.4997i	0.870552	+	0.870552i	0.992532	−	0.121981i	$-0.0389246\pi$
$317$	15.4997	+	15.4997i	0.870552	+	0.870552i	−0.121981	+	0.992532i	$0.538925\pi$
$318$	−0.417321	−	1.55746i	−0.0234022	−	0.0873383i
$319$	−12.6029	+	12.8872i	−0.705625	+	0.721547i
$320$	8.68423	−	8.68423i	0.485463	−	0.485463i
$321$	4.69636	+	2.71144i	0.262125	+	0.151338i
$322$	−5.57520	+	3.21884i	−0.310694	+	0.179379i
$323$	2.90023	+	0.777115i	0.161373	+	0.0432398i
$324$			1.83565i			0.101981i
$325$	4.02591	+	10.3382i	0.223317	+	0.573458i
$326$			5.40675i			0.299452i
$327$	−8.23571	−	2.20675i	−0.455436	−	0.122034i
$328$	5.54680	+	9.60734i	0.306271	+	0.530477i
$329$	−16.1739	+	28.0139i	−0.891693	+	1.54446i
$330$	0.947764	−	3.70181i	0.0521727	−	0.203778i
$331$	−1.50410	+	0.403023i	−0.0826729	+	0.0221521i	−0.299918	−	0.953965i	$-0.596959\pi$
$331$	−1.50410	+	0.403023i	−0.0826729	+	0.0221521i	0.217245	+	0.976117i	$0.430293\pi$
$332$	14.1292	−	3.78590i	0.775439	−	0.207778i
$333$	1.64532	−	1.64532i	0.0901628	−	0.0901628i
$334$	−3.53623	+	6.12493i	−0.193494	+	0.335141i
$335$	10.4733	−	6.04674i	0.572215	−	0.330368i
$336$	−3.22245	+	12.0263i	−0.175799	+	0.656091i
$337$	−21.6012			−1.17669			−0.588347	−	0.808609i	$-0.700221\pi$
$337$	−21.6012			−1.17669			−0.588347	+	0.808609i	$0.700221\pi$
$338$	4.67238	−	2.43789i	0.254144	−	0.132604i
$339$	8.91007			0.483929
$340$	−4.10574	−	1.10013i	−0.222665	−	0.0596629i
$341$	−19.9623	−	11.2302i	−1.08102	−	0.608148i
$342$	−1.29380	−	0.746977i	−0.0699608	−	0.0403919i
$343$	8.00079	−	8.00079i	0.432002	−	0.432002i
$344$	−14.2741	+	3.82474i	−0.769609	+	0.206216i
$345$	−2.85292	−	10.6472i	−0.153596	−	0.573229i
$346$	3.68373	−	3.68373i	0.198039	−	0.198039i
$347$	−30.5530	−	17.6398i	−1.64017	−	0.946953i	−0.980772	−	0.195159i	$-0.937478\pi$
$347$	−30.5530	−	17.6398i	−1.64017	−	0.946953i	−0.659398	−	0.751794i	$-0.729189\pi$
$348$	−4.98825	−	8.63990i	−0.267398	−	0.463147i
$349$	−6.28137	+	23.4424i	−0.336234	+	1.25484i	0.566291	+	0.824206i	$0.308378\pi$
$349$	−6.28137	+	23.4424i	−0.336234	+	1.25484i	−0.902525	+	0.430638i	$0.858289\pi$
$350$			5.10733i			0.272998i
$351$	−3.35978	+	1.30837i	−0.179332	+	0.0698359i
$352$	−7.34026	−	12.3923i	−0.391237	−	0.660514i
$353$	3.68953	−	13.7695i	0.196374	−	0.732878i	−0.795533	−	0.605910i	$-0.792809\pi$
$353$	3.68953	−	13.7695i	0.196374	−	0.732878i	0.991907	−	0.126967i	$-0.0405243\pi$
$354$	3.78346	−	2.18438i	0.201089	−	0.116099i
$355$	−2.53488	−	1.46351i	−0.134537	−	0.0776752i
$356$	−18.9829	−	18.9829i	−1.00609	−	1.00609i
$357$	3.22224	−	0.863396i	0.170539	−	0.0456957i
$358$	−7.60795	+	2.03854i	−0.402093	+	0.107740i
$359$	6.70912	+	6.70912i	0.354094	+	0.354094i	0.861630	−	0.507536i	$-0.169444\pi$
$359$	6.70912	+	6.70912i	0.354094	+	0.354094i	−0.507536	+	0.861630i	$0.669444\pi$
$360$	3.82715	+	2.20960i	0.201708	+	0.116456i
$361$	4.69342	−	2.70975i	0.247022	−	0.142618i
$362$	−2.17137	+	8.10364i	−0.114124	+	0.425918i
$363$	9.64662	+	5.28609i	0.506316	+	0.277448i
$364$	−26.9360	+	2.96284i	−1.41183	+	0.155295i
$365$		−	38.4991i		−	2.01513i
$366$	1.12727	−	4.20702i	0.0589232	−	0.219905i
$367$	16.3714	+	28.3560i	0.854579	+	1.48017i	0.877035	+	0.480426i	$0.159518\pi$
$367$	16.3714	+	28.3560i	0.854579	+	1.48017i	−0.0224568	+	0.999748i	$0.507149\pi$
$368$	−10.2142	−	5.89719i	−0.532453	−	0.307412i
$369$	5.04474	−	5.04474i	0.262619	−	0.262619i
$370$	−0.693851	−	2.58949i	−0.0360716	−	0.134621i
$371$	−15.7297	+	4.21477i	−0.816648	+	0.218820i
$372$	8.96391	−	8.96391i	0.464757	−	0.464757i
$373$	2.60807	+	1.50577i	0.135041	+	0.0779660i	0.565999	−	0.824406i	$-0.308491\pi$
$373$	2.60807	+	1.50577i	0.135041	+	0.0779660i	−0.430958	+	0.902372i	$0.641824\pi$
$374$	−0.537124	+	0.954769i	−0.0277740	+	0.0493699i
$375$	5.27888	+	1.41447i	0.272600	+	0.0730430i
$376$	12.2851			0.633557
$377$	12.2581	−	15.2881i	0.631327	−	0.787378i
$378$	−1.65982			−0.0853721
$379$	−0.105875	+	0.395132i	−0.00543844	+	0.0202965i	−0.968592	−	0.248656i	$-0.920011\pi$
$379$	−0.105875	+	0.395132i	−0.00543844	+	0.0202965i	0.963153	+	0.268953i	$0.0866776\pi$
$380$	16.6497	−	9.61269i	0.854110	−	0.493120i
$381$	1.79483	−	3.10873i	0.0919518	−	0.159265i
$382$	−4.64965	+	4.64965i	−0.237897	+	0.237897i
$383$	−17.2452	+	4.62084i	−0.881189	+	0.236114i	−0.670920	−	0.741530i	$-0.734101\pi$
$383$	−17.2452	+	4.62084i	−0.881189	+	0.236114i	−0.210269	+	0.977644i	$0.567434\pi$
$384$	10.0816	−	2.70136i	0.514475	−	0.137853i
$385$	−37.3868	−	9.57203i	−1.90541	−	0.487836i
$386$	4.92547	−	8.53116i	0.250700	−	0.434225i
$387$	4.75179	+	8.23034i	0.241547	+	0.418372i
$388$	15.4960	+	4.15214i	0.786690	+	0.210793i
$389$		−	17.4218i		−	0.883322i	−0.897182	−	0.441661i	$-0.854389\pi$
$389$		−	17.4218i		−	0.883322i	0.897182	−	0.441661i	$-0.145611\pi$
$390$	−0.629997	+	4.10605i	−0.0319012	+	0.207918i
$391$			3.16008i			0.159812i
$392$	−14.6646	−	3.92936i	−0.740673	−	0.198463i
$393$	−6.10901	+	3.52704i	−0.308159	+	0.177915i
$394$	7.61908	+	4.39888i	0.383844	+	0.221612i
$395$	9.58292	−	9.58292i	0.482169	−	0.482169i
$396$	−4.25670	+	4.35275i	−0.213907	+	0.218734i
$397$	−4.49773	−	16.7858i	−0.225735	−	0.842453i	−0.982109	−	0.188314i	$-0.939698\pi$
$397$	−4.49773	−	16.7858i	−0.225735	−	0.842453i	0.756374	−	0.654139i	$-0.226969\pi$
$398$	1.90575	+	1.90575i	0.0955267	+	0.0955267i
$399$	−7.54416	+	13.0669i	−0.377680	+	0.654161i
$400$	−8.10345	+	4.67853i	−0.405172	+	0.233926i
$401$	1.03360	+	0.276953i	0.0516157	+	0.0138304i	0.284534	−	0.958666i	$-0.408161\pi$
$401$	1.03360	+	0.276953i	0.0516157	+	0.0138304i	−0.232919	+	0.972496i	$0.574828\pi$
$402$	1.72506			0.0860382
$403$	22.7957	+	10.0175i	1.13553	+	0.499007i
$404$			7.47609i			0.371950i
$405$	0.735567	−	2.74517i	0.0365506	−	0.136409i
$406$	7.81232	−	4.51044i	0.387719	−	0.223850i
$407$	7.71674	−	0.0860939i	0.382505	−	0.00426752i
$408$	−0.895848	−	0.895848i	−0.0443511	−	0.0443511i
$409$	−6.44859	−	24.0665i	−0.318862	−	1.19001i	−0.920340	−	0.391120i	$-0.872088\pi$
$409$	−6.44859	−	24.0665i	−0.318862	−	1.19001i	0.601478	−	0.798890i	$-0.294579\pi$
$410$	−2.12743	−	7.93968i	−0.105066	−	0.392113i
$411$	7.68691	−	7.68691i	0.379167	−	0.379167i
$412$	2.30826	−	3.99802i	0.113720	−	0.196968i
$413$	−22.0614	−	38.2114i	−1.08557	−	1.88026i
$414$	0.406952	−	1.51877i	0.0200006	−	0.0746432i
$415$	−22.6469			−1.11169
$416$	9.26458	+	12.6228i	0.454233	+	0.618883i
$417$		−	7.62286i		−	0.373293i
$418$	−1.33573	−	4.77145i	−0.0653328	−	0.233379i
$419$	−3.42080	−	5.92500i	−0.167117	−	0.289455i	0.770288	−	0.637696i	$-0.220112\pi$
$419$	−3.42080	−	5.92500i	−0.167117	−	0.289455i	−0.937405	+	0.348241i	$0.886779\pi$
$420$	10.6800	−	18.4982i	0.521129	−	0.902621i
$421$	11.7634	+	11.7634i	0.573313	+	0.573313i	0.933053	−	0.359739i	$-0.117134\pi$
$421$	11.7634	+	11.7634i	0.573313	+	0.573313i	−0.359739	+	0.933053i	$0.617134\pi$
$422$	−7.66665	+	2.05427i	−0.373207	+	0.100000i
$423$	−2.04483	−	7.63141i	−0.0994230	−	0.371052i
$424$	4.37320	+	4.37320i	0.212381	+	0.212381i
$425$	2.17117	+	1.25352i	0.105317	+	0.0608049i
$426$	−0.208761	−	0.361585i	−0.0101145	−	0.0175189i
$427$	−42.4892	−	11.3849i	−2.05620	−	0.550956i
$428$	−9.95455			−0.481171
$429$	−11.0008	−	4.68855i	−0.531123	−	0.226365i
$430$	10.9494			0.528029
$431$	14.9754	+	4.01264i	0.721338	+	0.193282i	0.600768	−	0.799423i	$-0.294861\pi$
$431$	14.9754	+	4.01264i	0.721338	+	0.193282i	0.120569	+	0.992705i	$0.461528\pi$
$432$	−1.52047	−	2.63353i	−0.0731535	−	0.126706i
$433$	8.34486	+	4.81791i	0.401029	+	0.231534i	0.686928	−	0.726726i	$-0.258959\pi$
$433$	8.34486	+	4.81791i	0.401029	+	0.231534i	−0.285899	+	0.958260i	$0.592292\pi$
$434$	8.10529	+	8.10529i	0.389067	+	0.389067i
$435$	3.99769	+	14.9196i	0.191675	+	0.715340i
$436$	15.1179	−	4.05083i	0.724017	−	0.194000i
$437$	−10.1067	−	10.1067i	−0.483470	−	0.483470i
$438$	2.74583	−	4.75592i	0.131201	−	0.227246i
$439$	10.6942	+	18.5228i	0.510404	+	0.884046i	0.999927	+	0.0120558i	$0.00383758\pi$
$439$	10.6942	+	18.5228i	0.510404	+	0.884046i	−0.489523	+	0.871990i	$0.662829\pi$
$440$	3.95118	+	14.1142i	0.188365	+	0.672870i
$441$			9.76353i			0.464930i
$442$	0.479124	−	1.09029i	0.0227896	−	0.0518597i
$443$	25.5779			1.21524			0.607622	−	0.794226i	$-0.292123\pi$
$443$	25.5779			1.21524			0.607622	+	0.794226i	$0.292123\pi$
$444$	−1.10548	+	4.12572i	−0.0524639	+	0.195798i
$445$	20.7817	+	35.9950i	0.985149	+	1.70633i
$446$	1.22520	−	2.12211i	0.0580148	−	0.100485i
$447$	7.09515	−	7.09515i	0.335589	−	0.335589i
$448$	−4.57930	−	17.0902i	−0.216352	−	0.807436i
$449$	0.642646	+	2.39839i	0.0303283	+	0.113187i	0.979431	−	0.201781i	$-0.0646729\pi$
$449$	0.642646	+	2.39839i	0.0303283	+	0.113187i	−0.949102	+	0.314968i	$0.898006\pi$
$450$	−0.882056	−	0.882056i	−0.0415805	−	0.0415805i
$451$	23.6605	−	0.263974i	1.11413	−	0.0124301i
$452$	−14.1646	+	8.17791i	−0.666245	+	0.384656i
$453$	−5.47438	+	20.4307i	−0.257209	+	0.959917i
$454$			5.94169i			0.278857i
$455$	41.4694	+	6.36271i	1.94412	+	0.298289i
$456$	5.73029			0.268345
$457$	12.5267	+	3.35652i	0.585974	+	0.157011i	0.539612	−	0.841914i	$-0.318571\pi$
$457$	12.5267	+	3.35652i	0.585974	+	0.157011i	0.0463613	+	0.998925i	$0.485237\pi$
$458$	1.30889	−	0.755691i	0.0611606	−	0.0353111i
$459$	−0.407381	+	0.705605i	−0.0190149	+	0.0329348i
$460$	14.3077	+	14.3077i	0.667099	+	0.667099i
$461$	2.71188	+	10.1209i	0.126305	+	0.471376i	0.999883	−	0.0153081i	$-0.00487291\pi$
$461$	2.71188	+	10.1209i	0.126305	+	0.471376i	−0.873578	+	0.486684i	$0.838206\pi$
$462$	−3.93582	−	3.84896i	−0.183111	−	0.179070i
$463$	4.73643	−	4.73643i	0.220121	−	0.220121i	−0.588429	−	0.808549i	$-0.700253\pi$
$463$	4.73643	−	4.73643i	0.220121	−	0.220121i	0.808549	+	0.588429i	$0.200253\pi$
$464$	14.3128	+	8.26351i	0.664456	+	0.383624i
$465$	−16.9972	+	9.81336i	−0.788228	+	0.455084i
$466$	4.95679	+	1.32817i	0.229619	+	0.0615262i
$467$		−	22.1757i		−	1.02617i	−0.858338	−	0.513085i	$-0.828503\pi$
$467$		−	22.1757i		−	1.02617i	0.858338	−	0.513085i	$-0.171497\pi$
$468$	4.14027	−	5.16366i	0.191384	−	0.238690i
$469$		−	17.4224i		−	0.804491i
$470$	−8.79244	−	2.35593i	−0.405565	−	0.108671i
$471$	−11.1067	−	19.2374i	−0.511770	−	0.886411i
$472$	−8.37854	+	14.5121i	−0.385653	+	0.667971i
$473$	−7.81776	+	30.5349i	−0.359461	+	1.40400i
$474$	1.86728	−	0.500337i	0.0857671	−	0.0229812i
$475$	−10.9530	+	2.93485i	−0.502559	+	0.134660i
$476$	−4.33002	+	4.33002i	−0.198466	+	0.198466i
$477$	1.98868	−	3.44450i	0.0910555	−	0.157713i
$478$	7.71957	−	4.45690i	0.353085	−	0.203854i
$479$	8.47302	−	31.6217i	0.387142	−	1.44483i	−0.447620	−	0.894224i	$-0.647728\pi$
$479$	8.47302	−	31.6217i	0.387142	−	1.44483i	0.834762	−	0.550610i	$-0.185605\pi$
$480$	−12.3420			−0.563333
$481$	−8.33921	+	0.917276i	−0.380235	+	0.0418242i
$482$	9.52580			0.433889
$483$	−15.3389	−	4.11005i	−0.697944	−	0.187014i
$484$	−20.1872	+	0.450503i	−0.917599	+	0.0204774i
$485$	−21.5100	−	12.4188i	−0.976721	−	0.563910i
$486$	0.286658	−	0.286658i	0.0130031	−	0.0130031i
$487$	−2.40652	+	0.644825i	−0.109050	+	0.0292198i	−0.312931	−	0.949776i	$-0.601311\pi$
$487$	−2.40652	+	0.644825i	−0.109050	+	0.0292198i	0.203881	+	0.978996i	$0.434644\pi$
$488$	4.32381	+	16.1367i	0.195730	+	0.730473i
$489$	−9.43065	+	9.43065i	−0.426469	+	0.426469i
$490$	9.74188	+	5.62448i	0.440093	+	0.254088i
$491$	8.28373	+	14.3478i	0.373839	+	0.647509i	0.990153	−	0.139992i	$-0.0447078\pi$
$491$	8.28373	+	14.3478i	0.373839	+	0.647509i	−0.616313	+	0.787501i	$0.711374\pi$
$492$	−3.38954	+	12.6499i	−0.152812	+	0.570304i
$493$		−	4.42811i		−	0.199432i
$494$	1.95465	+	5.01936i	0.0879439	+	0.225832i
$495$	8.10997	−	4.80372i	0.364516	−	0.215911i
$496$	−5.43532	+	20.2849i	−0.244053	+	0.910819i
$497$	−3.65186	+	2.10840i	−0.163808	+	0.0945748i
$498$	−2.79764	−	1.61522i	−0.125365	−	0.0723797i
$499$	−30.2590	−	30.2590i	−1.35458	−	1.35458i	−0.880462	−	0.474116i	$-0.842768\pi$
$499$	−30.2590	−	30.2590i	−1.35458	−	1.35458i	−0.474116	−	0.880462i	$-0.657232\pi$
$500$	−9.69020	+	2.59648i	−0.433359	+	0.116118i
$501$	−16.8514	+	4.51531i	−0.752863	+	0.201729i
$502$	−0.550522	−	0.550522i	−0.0245710	−	0.0245710i
$503$	−14.8715	−	8.58605i	−0.663087	−	0.382833i	0.130365	−	0.991466i	$-0.458385\pi$
$503$	−14.8715	−	8.58605i	−0.663087	−	0.382833i	−0.793452	+	0.608633i	$0.791718\pi$
$504$	5.51356	−	3.18326i	0.245593	−	0.141793i
$505$	2.99575	−	11.1803i	0.133309	−	0.497517i
$506$	4.48684	−	2.65765i	0.199464	−	0.118147i
$507$	12.4020	+	3.89747i	0.550792	+	0.173093i
$508$			6.58937i			0.292356i
$509$	6.27542	−	23.4202i	0.278153	−	1.03808i	−0.675545	−	0.737318i	$-0.736092\pi$
$509$	6.27542	−	23.4202i	0.278153	−	1.03808i	0.953699	−	0.300764i	$-0.0972416\pi$
$510$	0.469360	+	0.812955i	0.0207836	+	0.0359983i
$511$	−48.0328	−	27.7317i	−2.12484	−	1.22678i
$512$	−16.0251	+	16.0251i	−0.708216	+	0.708216i
$513$	−0.953793	−	3.55960i	−0.0421110	−	0.157160i
$514$	−8.00053	+	2.14373i	−0.352888	+	0.0945561i
$515$	−5.05399	+	5.05399i	−0.222706	+	0.222706i
$516$	−15.1081	−	8.72264i	−0.665095	−	0.383993i
$517$	12.8477	−	22.8375i	0.565041	−	1.00439i
$518$	−3.73053	−	0.999592i	−0.163910	−	0.0439196i
$519$	12.8506			0.564079
$520$	−5.78198	−	14.8476i	−0.253557	−	0.651110i
$521$	−20.9463			−0.917672			−0.458836	−	0.888521i	$-0.651733\pi$
$521$	−20.9463			−0.917672			−0.458836	+	0.888521i	$0.651733\pi$
$522$	−0.570247	+	2.12819i	−0.0249590	+	0.0931483i
$523$	23.3421	−	13.4766i	1.02068	−	0.589290i	0.106379	−	0.994326i	$-0.466074\pi$
$523$	23.3421	−	13.4766i	1.02068	−	0.589290i	0.914301	+	0.405035i	$0.132741\pi$
$524$	6.47442	−	11.2140i	0.282836	−	0.489887i
$525$	−8.90840	+	8.90840i	−0.388795	+	0.388795i
$526$	−1.76346	+	0.472517i	−0.0768903	+	0.0206027i
$527$	5.43496	−	1.45629i	0.236751	−	0.0634371i
$528$	2.50151	−	9.77050i	0.108864	−	0.425206i
$529$	−3.97848	+	6.89094i	−0.172978	+	0.299606i
$530$	−2.29124	−	3.96854i	−0.0995250	−	0.172382i
$531$	10.4093	+	2.78917i	0.451727	+	0.121040i
$532$		−	27.6969i		−	1.20081i
$533$	−25.5690	+	2.81248i	−1.10752	+	0.121822i
$534$			5.92878i			0.256563i
$535$	14.8868	+	3.98890i	0.643611	+	0.172455i
$536$	−5.73026	+	3.30837i	−0.247510	+	0.142900i
$537$	−16.8258	−	9.71437i	−0.726086	−	0.419206i
$538$	−0.864044	+	0.864044i	−0.0372516	+	0.0372516i
$539$	−22.6406	+	23.1515i	−0.975202	+	0.997207i
$540$	1.35025	+	5.03919i	0.0581054	+	0.216852i
$541$	−16.8496	−	16.8496i	−0.724420	−	0.724420i	0.245082	−	0.969502i	$-0.421185\pi$
$541$	−16.8496	−	16.8496i	−0.724420	−	0.724420i	−0.969502	+	0.245082i	$0.921185\pi$
$542$	−0.942203	+	1.63194i	−0.0404711	+	0.0700980i
$543$	−17.9221	+	10.3473i	−0.769109	+	0.444046i
$544$	3.41770	+	0.915771i	0.146533	+	0.0392633i
$545$	−24.2317			−1.03797
$546$	4.66905	+	3.74369i	0.199817	+	0.160215i
$547$		−	4.70387i		−	0.201123i	−0.994931	−	0.100561i	$-0.967936\pi$
$547$		−	4.70387i		−	0.201123i	0.994931	−	0.100561i	$-0.0320639\pi$
$548$	−5.16481	+	19.2753i	−0.220630	+	0.823401i
$549$	9.30427	−	5.37182i	0.397097	−	0.229264i
$550$	−0.0461550	−	4.13695i	−0.00196806	−	0.176400i
$551$	14.1622	+	14.1622i	0.603329	+	0.603329i
$552$	1.56093	+	5.82546i	0.0664375	+	0.247948i
$553$	−5.05319	−	18.8588i	−0.214884	−	0.801957i
$554$	2.31875	−	2.31875i	0.0985143	−	0.0985143i
$555$	3.30644	−	5.72692i	0.140351	−	0.243094i
$556$	6.99647	+	12.1182i	0.296716	+	0.513928i
$557$	−4.09358	+	15.2774i	−0.173450	+	0.647325i	0.823360	+	0.567519i	$0.192097\pi$
$557$	−4.09358	+	15.2774i	−0.173450	+	0.647325i	−0.996810	+	0.0798061i	$0.974570\pi$
$558$	−2.79963			−0.118518
$559$	5.19662	−	33.8693i	0.219793	−	1.43252i
$560$			35.3847i			1.49528i
$561$	−2.60222	+	0.728472i	−0.109866	+	0.0307561i
$562$	3.37787	+	5.85064i	0.142487	+	0.246794i
$563$	11.1080	−	19.2397i	0.468148	−	0.810856i	−0.531190	−	0.847253i	$-0.678255\pi$
$563$	11.1080	−	19.2397i	0.468148	−	0.810856i	0.999337	+	0.0363972i	$0.0115881\pi$
$564$	10.2550	+	10.2550i	0.431814	+	0.431814i
$565$	24.4597	−	6.55396i	1.02903	−	0.275727i
$566$	1.21667	+	4.54069i	0.0511406	+	0.190859i
$567$	−2.89513	−	2.89513i	−0.121584	−	0.121584i
$568$	1.38692	+	0.800736i	0.0581937	+	0.0335982i
$569$	18.7671	+	32.5056i	0.786759	+	1.36271i	0.927943	+	0.372723i	$0.121576\pi$
$569$	18.7671	+	32.5056i	0.786759	+	1.36271i	−0.141184	+	0.989983i	$0.545091\pi$
$570$	−4.10116	−	1.09890i	−0.171779	−	0.0460280i
$571$	−4.41199			−0.184636			−0.0923181	−	0.995730i	$-0.529428\pi$
$571$	−4.41199			−0.184636			−0.0923181	+	0.995730i	$0.529428\pi$
$572$	21.7915	−	2.64333i	0.911148	−	0.110523i
$573$	−16.2202			−0.677609
$574$	−11.4383	−	3.06487i	−0.477423	−	0.127925i
$575$	−5.96719	−	10.3355i	−0.248849	−	0.431019i
$576$	3.74241	+	2.16068i	0.155934	+	0.0900283i
$577$	25.6639	+	25.6639i	1.06840	+	1.06840i	0.997482	+	0.0709204i	$0.0225936\pi$
$577$	25.6639	+	25.6639i	1.06840	+	1.06840i	0.0709204	+	0.997482i	$0.477406\pi$
$578$	1.71406	+	6.39695i	0.0712954	+	0.266078i
$579$	23.4716	−	6.28919i	0.975445	−	0.261370i
$580$	−20.0488	−	20.0488i	−0.832483	−	0.832483i
$581$	−16.3130	+	28.2550i	−0.676779	+	1.17222i
$582$	−1.77147	−	3.06828i	−0.0734298	−	0.127184i
$583$	12.7031	−	3.55613i	0.526107	−	0.147280i
$584$			21.0641i			0.871639i
$585$	−8.26079	+	6.06306i	−0.341542	+	0.250677i
$586$	−9.83035			−0.406088
$587$	−11.3887	+	42.5032i	−0.470061	+	1.75429i	0.169477	+	0.985534i	$0.445792\pi$
$587$	−11.3887	+	42.5032i	−0.470061	+	1.75429i	−0.639538	+	0.768759i	$0.720874\pi$
$588$	−8.96124	−	15.5213i	−0.369555	−	0.640088i
$589$	−12.7248	+	22.0399i	−0.524315	+	0.908140i
$590$	8.77950	−	8.77950i	0.361446	−	0.361446i
$591$	5.61680	+	20.9622i	0.231044	+	0.862269i
$592$	−1.83134	−	6.83464i	−0.0752675	−	0.280902i
$593$	20.3525	+	20.3525i	0.835778	+	0.835778i	0.988300	−	0.152522i	$-0.0487394\pi$
$593$	20.3525	+	20.3525i	0.835778	+	0.835778i	−0.152522	+	0.988300i	$0.548739\pi$
$594$	1.34446	−	0.0149999i	0.0551639	−	0.000615451i
$595$	8.21051	−	4.74034i	0.336598	−	0.194335i
$596$	−4.76720	+	17.7914i	−0.195272	+	0.728766i
$597$			6.64817i			0.272091i
$598$	−4.57028	+	3.35439i	−0.186893	+	0.137171i
$599$	−7.10192			−0.290177			−0.145088	−	0.989419i	$-0.546347\pi$
$599$	−7.10192			−0.290177			−0.145088	+	0.989419i	$0.546347\pi$
$600$	4.62162	+	1.23836i	0.188677	+	0.0505558i
$601$	15.5542	−	8.98021i	0.634468	−	0.366310i	−0.148012	−	0.988986i	$-0.547288\pi$
$601$	15.5542	−	8.98021i	0.634468	−	0.366310i	0.782480	+	0.622675i	$0.213954\pi$
$602$	7.88713	−	13.6609i	0.321455	−	0.556777i
$603$	3.00892	+	3.00892i	0.122533	+	0.122533i
$604$	−10.0491	−	37.5037i	−0.408891	−	1.52600i
$605$	30.3699	+	7.41551i	1.23471	+	0.301483i
$606$	1.16748	−	1.16748i	0.0474255	−	0.0474255i
$607$	−7.54902	−	4.35843i	−0.306405	−	0.176903i	0.338912	−	0.940818i	$-0.389941\pi$
$607$	−7.54902	−	4.35843i	−0.306405	−	0.176903i	−0.645317	+	0.763915i	$0.723275\pi$
$608$	−13.8595	+	8.00180i	−0.562078	+	0.324516i
$609$	21.4938	+	5.75926i	0.870974	+	0.233377i
$610$		−	12.3782i		−	0.501178i
$611$	−11.4604	+	26.0790i	−0.463637	+	1.05504i
$612$		−	1.49562i		−	0.0604569i
$613$	4.81573	+	1.29037i	0.194506	+	0.0521176i	0.354757	−	0.934959i	$-0.384564\pi$
$613$	4.81573	+	1.29037i	0.194506	+	0.0521176i	−0.160251	+	0.987076i	$0.551230\pi$
$614$	−3.24926	−	5.62788i	−0.131129	−	0.227123i
$615$	10.1379	−	17.5594i	0.408801	−	0.708065i
$616$	20.4555	+	5.23717i	0.824177	+	0.211012i
$617$	32.7446	−	8.77389i	1.31825	−	0.353223i	0.469926	−	0.882706i	$-0.344280\pi$
$617$	32.7446	−	8.77389i	1.31825	−	0.353223i	0.848321	+	0.529482i	$0.177614\pi$
$618$	−0.984797	+	0.263876i	−0.0396143	+	0.0106146i
$619$	−30.6722	+	30.6722i	−1.23282	+	1.23282i	−0.269942	+	0.962877i	$0.587004\pi$
$619$	−30.6722	+	30.6722i	−1.23282	+	1.23282i	−0.962877	+	0.269942i	$0.912996\pi$
$620$	18.0139	−	31.2010i	0.723457	−	1.25306i
$621$	3.35891	−	1.93927i	0.134788	−	0.0778201i
$622$	0.802060	−	2.99333i	0.0321597	−	0.120022i
$623$	59.8782			2.39897
$624$	−1.66280	+	10.8374i	−0.0665654	+	0.433844i
$625$	30.9170			1.23668
$626$	−4.16703	−	1.11655i	−0.166548	−	0.0446264i
$627$	5.99270	−	10.6524i	0.239326	−	0.425415i
$628$	35.3132	+	20.3881i	1.40915	+	0.813572i
$629$	−1.34054	+	1.34054i	−0.0534509	+	0.0534509i
$630$	−4.55650	+	1.22091i	−0.181535	+	0.0486423i
$631$	10.2920	+	38.4104i	0.409720	+	1.52909i	0.795182	+	0.606371i	$0.207375\pi$
$631$	10.2920	+	38.4104i	0.409720	+	1.52909i	−0.385463	+	0.922723i	$0.625958\pi$
$632$	−5.24313	+	5.24313i	−0.208561	+	0.208561i
$633$	−16.9556	−	9.78932i	−0.673925	−	0.389091i
$634$	4.44312	+	7.69572i	0.176459	+	0.305636i
$635$	2.64043	−	9.85422i	0.104782	−	0.391053i
$636$			7.30106i			0.289506i
$637$	22.0214	−	27.4646i	0.872519	−	1.08819i
$638$	−6.28724	+	3.72407i	−0.248914	+	0.147437i
$639$	0.266561	−	0.994820i	0.0105450	−	0.0393545i
$640$	25.6887	−	14.8314i	1.01544	−	0.586263i
$641$	−18.5437	−	10.7062i	−0.732433	−	0.422870i	0.0868788	−	0.996219i	$-0.472311\pi$
$641$	−18.5437	−	10.7062i	−0.732433	−	0.422870i	−0.819311	+	0.573349i	$0.805644\pi$
$642$	1.55451	+	1.55451i	0.0613518	+	0.0613518i
$643$	23.1088	−	6.19199i	0.911324	−	0.244188i	0.227451	−	0.973790i	$-0.426961\pi$
$643$	23.1088	−	6.19199i	0.911324	−	0.244188i	0.683873	+	0.729601i	$0.260294\pi$
$644$	28.1569	−	7.54462i	1.10954	−	0.297300i
$645$	19.0984	+	19.0984i	0.752000	+	0.752000i
$646$	1.05414	+	0.608608i	0.0414746	+	0.0239454i
$647$	40.4881	−	23.3758i	1.59175	−	0.918998i	0.598745	−	0.800940i	$-0.295666\pi$
$647$	40.4881	−	23.3758i	1.59175	−	0.918998i	0.993007	−	0.118059i	$-0.0376672\pi$
$648$	−0.402453	+	1.50197i	−0.0158098	+	0.0590031i
$649$	18.2151	+	30.7520i	0.715004	+	1.20712i
$650$	0.491752	+	4.47066i	0.0192881	+	0.175354i
$651$			28.2751i			1.10819i
$652$	6.33642	−	23.6478i	0.248153	−	0.926121i
$653$	13.1820	+	22.8319i	0.515851	+	0.893480i	0.999831	+	0.0184010i	$0.00585755\pi$
$653$	13.1820	+	22.8319i	0.515851	+	0.893480i	−0.483980	+	0.875079i	$0.660809\pi$
$654$	−2.99342	−	1.72825i	−0.117052	−	0.0675799i
$655$	−14.1759	+	14.1759i	−0.553899	+	0.553899i
$656$	−5.61510	−	20.9558i	−0.219233	−	0.818188i
$657$	13.0848	−	3.50607i	0.510488	−	0.136785i
$658$	−9.27273	+	9.27273i	−0.361489	+	0.361489i
$659$	−1.77308	−	1.02369i	−0.0690695	−	0.0398773i	0.465068	−	0.885275i	$-0.346030\pi$
$659$	−1.77308	−	1.02369i	−0.0690695	−	0.0398773i	−0.534137	+	0.845398i	$0.679363\pi$
$660$	−8.48363	+	15.0801i	−0.330225	+	0.586993i
$661$	10.2379	+	2.74324i	0.398209	+	0.106700i	0.452365	−	0.891833i	$-0.350580\pi$
$661$	10.2379	+	2.74324i	0.398209	+	0.106700i	−0.0541564	+	0.998532i	$0.517247\pi$
$662$	−0.631267			−0.0245349
$663$	2.73743	−	1.06601i	0.106313	−	0.0414006i
$664$	12.3908			0.480858
$665$	−11.0985	+	41.4200i	−0.430380	+	1.60620i
$666$	0.816911	−	0.471644i	0.0316546	−	0.0182758i
$667$	−10.5396	+	18.2552i	−0.408096	+	0.706843i
$668$	22.6447	−	22.6447i	0.876151	−	0.876151i
$669$	5.83849	−	1.56442i	0.225729	−	0.0604840i
$670$	4.73559	−	1.26890i	0.182952	−	0.0490218i
$671$	34.5192	+	8.83786i	1.33260	+	0.341182i
$672$	−8.89022	+	15.3983i	−0.342948	+	0.594003i
$673$	−4.53777	−	7.85965i	−0.174918	−	0.302967i	0.765215	−	0.643775i	$-0.222633\pi$
$673$	−4.53777	−	7.85965i	−0.174918	−	0.302967i	−0.940133	+	0.340808i	$0.889299\pi$
$674$	−8.45866	−	2.26649i	−0.325815	−	0.0873020i
$675$		−	3.07703i		−	0.118435i
$676$	−23.2930	+	5.18700i	−0.895883	+	0.199500i
$677$		−	24.9170i		−	0.957636i	−0.877914	−	0.478818i	$-0.841065\pi$
$677$		−	24.9170i		−	0.957636i	0.877914	−	0.478818i	$-0.158935\pi$
$678$	3.48903	+	0.934882i	0.133995	+	0.0359039i
$679$	−30.9883	+	17.8911i	−1.18922	+	0.686598i
$680$	−3.11821	−	1.80030i	−0.119578	−	0.0690384i
$681$	−10.3637	+	10.3637i	−0.397139	+	0.397139i
$682$	−6.63856	−	6.49206i	−0.254204	−	0.248594i
$683$	1.31828	+	4.91990i	0.0504427	+	0.188255i	0.986550	−	0.163460i	$-0.0522654\pi$
$683$	1.31828	+	4.91990i	0.0504427	+	0.188255i	−0.936107	+	0.351715i	$0.885599\pi$
$684$	4.78337	+	4.78337i	0.182897	+	0.182897i
$685$	15.4477	−	26.7561i	0.590225	−	1.02230i
$686$	3.97244	−	2.29349i	0.151669	−	0.0875659i
$687$	3.60113	+	0.964920i	0.137392	+	0.0368140i
$688$	28.8998			1.10179
$689$	−13.3631	+	5.20388i	−0.509093	+	0.198252i
$690$		−	4.46861i		−	0.170117i
$691$	−12.9353	+	48.2753i	−0.492083	+	1.83648i	0.0537042	+	0.998557i	$0.482897\pi$
$691$	−12.9353	+	48.2753i	−0.492083	+	1.83648i	−0.545788	+	0.837924i	$0.683769\pi$
$692$	−20.4289	+	11.7946i	−0.776590	+	0.448365i
$693$	−0.151492	−	13.5785i	−0.00575472	−	0.515805i
$694$	−10.1132	−	10.1132i	−0.383891	−	0.383891i
$695$	−5.60712	−	20.9261i	−0.212690	−	0.793771i
$696$	−2.18727	−	8.16300i	−0.0829082	−	0.309418i
$697$	−4.11026	+	4.11026i	−0.155687	+	0.155687i
$698$	−4.91935	+	8.52056i	−0.186200	+	0.322508i
$699$	6.32918	+	10.9625i	0.239392	+	0.414639i
$700$	5.98552	−	22.3383i	0.226231	−	0.844307i
$701$	8.59749			0.324723			0.162361	−	0.986731i	$-0.448089\pi$
$701$	8.59749			0.324723			0.162361	+	0.986731i	$0.448089\pi$
$702$	−1.45291	+	0.159814i	−0.0548366	+	0.00603178i
$703$		−	8.57477i		−	0.323404i
$704$	3.86369	+	13.8017i	0.145618	+	0.520172i
$705$	−11.2268	−	19.4454i	−0.422826	−	0.732357i
$706$	2.88951	−	5.00478i	0.108748	−	0.188357i
$707$	−11.7910	−	11.7910i	−0.443447	−	0.443447i
$708$	−19.1080	+	5.11996i	−0.718121	+	0.192420i
$709$	−10.5778	−	39.4768i	−0.397257	−	1.48258i	−0.817902	−	0.575358i	$-0.804863\pi$
$709$	−10.5778	−	39.4768i	−0.397257	−	1.48258i	0.420645	−	0.907225i	$-0.361804\pi$
$710$	−0.839056	−	0.839056i	−0.0314892	−	0.0314892i
$711$	4.12969	+	2.38428i	0.154876	+	0.0894174i
$712$	−11.3704	−	19.6941i	−0.426123	−	0.738066i
$713$	−25.8722	−	6.93243i	−0.968921	−	0.259622i
$714$	1.35236			0.0506109
$715$	−33.6478	−	4.77906i	−1.25836	−	0.178727i
$716$	35.6645			1.33284
$717$	21.2387	+	5.69088i	0.793173	+	0.212530i
$718$	1.92322	+	3.33112i	0.0717741	+	0.124316i
$719$	9.22484	+	5.32596i	0.344028	+	0.198625i	0.662052	−	0.749458i	$-0.269686\pi$
$719$	9.22484	+	5.32596i	0.344028	+	0.198625i	−0.318024	+	0.948083i	$0.603019\pi$
$720$	−6.11108	−	6.11108i	−0.227747	−	0.227747i
$721$	2.66503	+	9.94604i	0.0992510	+	0.370410i
$722$	2.12218	−	0.568636i	0.0789793	−	0.0211624i
$723$	16.6153	+	16.6153i	0.617929	+	0.617929i
$724$	18.9941	−	32.8987i	0.705910	−	1.22267i
$725$	8.36160	+	14.4827i	0.310542	+	0.537874i
$726$	3.22281	+	3.08210i	0.119610	+	0.114388i
$727$		−	9.87894i		−	0.366390i	−0.983077	−	0.183195i	$-0.941356\pi$
$727$		−	9.87894i		−	0.366390i	0.983077	−	0.183195i	$-0.0586439\pi$
$728$	−22.6893	−	3.48125i	−0.840920	−	0.129024i
$729$	1.00000			0.0370370
$730$	4.03948	−	15.0755i	0.149508	−	0.557971i
$731$	−3.87158	−	6.70577i	−0.143195	−	0.248022i
$732$	−9.86081	+	17.0794i	−0.364466	+	0.631274i
$733$	7.78756	−	7.78756i	0.287640	−	0.287640i	−0.548506	−	0.836146i	$-0.684803\pi$
$733$	7.78756	−	7.78756i	0.287640	−	0.287640i	0.836146	+	0.548506i	$0.184803\pi$
$734$	3.43550	+	12.8215i	0.126807	+	0.473249i
$735$	7.18173	+	26.8026i	0.264902	+	0.988628i
$736$	−11.9100	−	11.9100i	−0.439009	−	0.439009i
$737$	0.157446	+	14.1122i	0.00579961	+	0.519829i
$738$	2.50475	−	1.44612i	0.0922010	−	0.0532323i
$739$	1.41605	−	5.28476i	0.0520902	−	0.194403i	−0.934978	−	0.354707i	$-0.884581\pi$
$739$	1.41605	−	5.28476i	0.0520902	−	0.194403i	0.987068	+	0.160304i	$0.0512474\pi$
$740$			12.1390i			0.446237i
$741$	−5.34559	+	12.1643i	−0.196375	+	0.446868i
$742$	−6.60172			−0.242357
$743$	−19.8362	−	5.31509i	−0.727719	−	0.194992i	−0.124106	−	0.992269i	$-0.539606\pi$
$743$	−19.8362	−	5.31509i	−0.727719	−	0.194992i	−0.603613	+	0.797277i	$0.706273\pi$
$744$	9.29975	−	5.36921i	0.340945	−	0.196845i
$745$	14.2585	−	24.6964i	0.522389	−	0.904805i
$746$	0.863284	+	0.863284i	0.0316071	+	0.0316071i
$747$	−2.06243	−	7.69708i	−0.0754602	−	0.281621i
$748$	3.46819	−	3.54646i	0.126810	−	0.129671i
$749$	15.7000	−	15.7000i	0.573664	−	0.573664i
$750$	1.91870	+	1.10776i	0.0700611	+	0.0404498i
$751$	−11.4288	+	6.59844i	−0.417044	+	0.240780i	−0.693812	−	0.720156i	$-0.744070\pi$
$751$	−11.4288	+	6.59844i	−0.417044	+	0.240780i	0.276768	+	0.960937i	$0.410737\pi$
$752$	−23.2066	−	6.21819i	−0.846258	−	0.226754i
$753$		−	1.92048i		−	0.0699863i
$754$	6.40416	−	4.70038i	0.233226	−	0.171178i
$755$			60.1125i			2.18772i
$756$	7.25968	+	1.94523i	0.264032	+	0.0707472i
$757$	1.43465	+	2.48488i	0.0521431	+	0.0903144i	0.890919	−	0.454163i	$-0.150061\pi$
$757$	1.43465	+	2.48488i	0.0521431	+	0.0903144i	−0.838776	+	0.544477i	$0.816728\pi$
$758$	−0.0829177	+	0.143618i	−0.00301171	+	0.00521643i
$759$	12.4617	+	3.19053i	0.452331	+	0.115809i
$760$	15.7306	−	4.21501i	0.570610	−	0.152895i
$761$	−43.9456	+	11.7752i	−1.59303	+	0.426850i	−0.942927	−	0.332999i	$-0.891939\pi$
$761$	−43.9456	+	11.7752i	−1.59303	+	0.426850i	−0.650099	+	0.759850i	$0.725273\pi$
$762$	1.02900	−	1.02900i	0.0372769	−	0.0372769i
$763$	−17.4546	+	30.2323i	−0.631899	+	1.09448i
$764$	25.7856	−	14.8874i	0.932892	−	0.538605i
$765$	−0.599312	+	2.23666i	−0.0216682	+	0.0808667i
$766$	−7.23775			−0.261511
$767$	−22.9903	−	31.3239i	−0.830133	−	1.13104i
$768$	−4.41150			−0.159186
$769$	9.50710	+	2.54742i	0.342835	+	0.0918623i	0.426128	−	0.904663i	$-0.359877\pi$
$769$	9.50710	+	2.54742i	0.342835	+	0.0918623i	−0.0832935	+	0.996525i	$0.526544\pi$
$770$	−13.6357	−	7.67101i	−0.491395	−	0.276444i
$771$	−17.6940	−	10.2156i	−0.637234	−	0.367907i
$772$	−31.5409	+	31.5409i	−1.13518	+	1.13518i
$773$	27.5842	−	7.39115i	0.992133	−	0.265841i	0.273987	−	0.961733i	$-0.411658\pi$
$773$	27.5842	−	7.39115i	0.992133	−	0.265841i	0.718146	+	0.695892i	$0.244991\pi$
$774$	0.997154	+	3.72143i	0.0358420	+	0.133764i
$775$	−15.0258	+	15.0258i	−0.539744	+	0.539744i
$776$	11.7688	+	6.79475i	0.422477	+	0.243917i
$777$	−4.76340	−	8.25046i	−0.170886	−	0.295984i
$778$	1.82797	−	6.82208i	0.0655360	−	0.244584i
$779$		−	26.2913i		−	0.941983i
$780$	7.56753	−	17.2206i	0.270961	−	0.616595i
$781$	2.93896	−	1.74081i	0.105164	−	0.0622912i
$782$	−0.331569	+	1.23743i	−0.0118569	+	0.0442505i
$783$	−4.70672	+	2.71742i	−0.168204	+	0.0971128i
$784$	25.7125	+	14.8451i	0.918305	+	0.530183i
$785$	−44.6402	−	44.6402i	−1.59328	−	1.59328i
$786$	−2.76225	+	0.740143i	−0.0985262	+	0.0264000i
$787$	9.31415	−	2.49572i	0.332014	−	0.0889628i	−0.0889612	−	0.996035i	$-0.528355\pi$
$787$	9.31415	−	2.49572i	0.332014	−	0.0889628i	0.420975	+	0.907072i	$0.361688\pi$
$788$	−28.1688	−	28.1688i	−1.00347	−	1.00347i
$789$	−3.90007	−	2.25171i	−0.138846	−	0.0801629i
$790$	4.75798	−	2.74702i	0.169281	−	0.0977346i
$791$	9.44192	−	35.2377i	0.335716	−	1.25291i
$792$	−4.43723	+	2.62827i	−0.157670	+	0.0933916i
$793$	−38.2887	−	5.87470i	−1.35967	−	0.208617i
$794$		−	7.04493i		−	0.250015i
$795$	2.92562	−	10.9185i	0.103761	−	0.387241i
$796$	−6.10187	−	10.5687i	−0.216275	−	0.374599i
$797$	−43.0405	−	24.8495i	−1.52457	−	0.880213i	−0.999576	−	0.0291101i	$-0.990733\pi$
$797$	−43.0405	−	24.8495i	−1.52457	−	0.880213i	−0.524998	−	0.851103i	$-0.675934\pi$
$798$	−4.32519	+	4.32519i	−0.153110	+	0.153110i
$799$	1.66605	+	6.21778i	0.0589406	+	0.219969i
$800$	−12.9073	+	3.45850i	−0.456342	+	0.122276i
$801$	−10.3412	+	10.3412i	−0.365388	+	0.365388i
$802$	0.375682	+	0.216900i	0.0132658	+	0.00765900i
$803$	39.1573	+	22.0287i	1.38183	+	0.777376i
$804$	−7.54501	−	2.02168i	−0.266092	−	0.0712991i
$805$	−45.1311			−1.59066
$806$	7.87530	+	6.31449i	0.277396	+	0.222418i
$807$	−3.01420			−0.106105
$808$	−1.63907	+	6.11711i	−0.0576624	+	0.215199i
$809$	−21.1719	+	12.2236i	−0.744366	+	0.429760i	−0.823655	−	0.567092i	$-0.808068\pi$
$809$	−21.1719	+	12.2236i	−0.744366	+	0.429760i	0.0792887	+	0.996852i	$0.474735\pi$
$810$	0.576070	−	0.997782i	0.0202410	−	0.0350585i
$811$	−24.8203	+	24.8203i	−0.871559	+	0.871559i	−0.992642	−	0.121083i	$-0.961363\pi$
$811$	−24.8203	+	24.8203i	−0.871559	+	0.871559i	0.121083	+	0.992642i	$0.461363\pi$
$812$	−39.4552	+	10.5720i	−1.38461	+	0.371005i
$813$	−4.48992	+	1.20307i	−0.157469	+	0.0421936i
$814$	3.03077	+	0.775960i	0.106229	+	0.0271974i
$815$	−18.9519	+	32.8256i	−0.663856	+	1.14983i
$816$	1.23882	+	2.14570i	0.0433674	+	0.0751145i
$817$	33.8290	+	9.06444i	1.18353	+	0.317125i
$818$		−	10.1006i		−	0.353159i
$819$	1.61405	+	14.6738i	0.0563996	+	0.512745i
$820$			37.2195i			1.29976i
$821$	25.6077	+	6.86157i	0.893716	+	0.239471i	0.676316	−	0.736612i	$-0.263576\pi$
$821$	25.6077	+	6.86157i	0.893716	+	0.239471i	0.217401	+	0.976082i	$0.430242\pi$
$822$	3.81660	−	2.20352i	0.133119	−	0.0768564i
$823$	32.9786	+	19.0402i	1.14956	+	0.663700i	0.948781	−	0.315936i	$-0.102318\pi$
$823$	32.9786	+	19.0402i	1.14956	+	0.663700i	0.200782	+	0.979636i	$0.435652\pi$
$824$	2.76521	−	2.76521i	0.0963305	−	0.0963305i
$825$	7.13533	−	7.29634i	0.248420	−	0.254026i
$826$	−4.62954	−	17.2777i	−0.161082	−	0.601167i
$827$	7.09916	+	7.09916i	0.246862	+	0.246862i	0.819681	−	0.572820i	$-0.194150\pi$
$827$	7.09916	+	7.09916i	0.246862	+	0.246862i	−0.572820	+	0.819681i	$0.694150\pi$
$828$	−3.55982	+	6.16580i	−0.123712	+	0.214276i
$829$	30.4168	−	17.5612i	1.05642	−	0.609924i	0.131980	−	0.991252i	$-0.457866\pi$
$829$	30.4168	−	17.5612i	1.05642	−	0.609924i	0.924440	+	0.381328i	$0.124533\pi$
$830$	−8.86811	−	2.37620i	−0.307817	−	0.0824792i
$831$	8.08891			0.280601
$832$	−5.65396	−	14.5188i	−0.196016	−	0.503350i
$833$		−	7.95496i		−	0.275623i
$834$	0.799822	−	2.98498i	0.0276956	−	0.103361i
$835$	−42.9386	+	24.7906i	−1.48595	+	0.857914i
$836$	0.250298	+	22.4346i	0.00865672	+	0.775917i
$837$	−4.88323	−	4.88323i	−0.168789	−	0.168789i
$838$	−0.717849	−	2.67905i	−0.0247977	−	0.0925462i
$839$	2.59301	+	9.67723i	0.0895205	+	0.334095i	0.996132	−	0.0878716i	$-0.0280065\pi$
$839$	2.59301	+	9.67723i	0.0895205	+	0.334095i	−0.906611	+	0.421967i	$0.861340\pi$
$840$	12.7942	−	12.7942i	0.441441	−	0.441441i
$841$	0.268781	−	0.465542i	0.00926831	−	0.0160532i
$842$	3.37208	+	5.84061i	0.116209	+	0.201281i
$843$	−4.31310	+	16.0967i	−0.148551	+	0.554401i
$844$	35.9396			1.23709
$845$	36.9125	+	1.57672i	1.26983	+	0.0542409i
$846$		−	3.20287i		−	0.110117i
$847$	31.1280	−	32.5490i	1.06957	−	1.11840i
$848$	−6.04745	−	10.4745i	−0.207670	−	0.359696i
$849$	−5.79787	+	10.0422i	−0.198982	+	0.344648i
$850$	0.718666	+	0.718666i	0.0246500	+	0.0246500i
$851$	8.71718	−	2.33576i	0.298821	−	0.0800689i
$852$	0.489314	+	1.82615i	0.0167636	+	0.0625627i
$853$	−20.4127	−	20.4127i	−0.698919	−	0.698919i	0.265258	−	0.964177i	$-0.414543\pi$
$853$	−20.4127	−	20.4127i	−0.698919	−	0.698919i	−0.964177	+	0.265258i	$0.914543\pi$
$854$	−15.4435	−	8.91628i	−0.528464	−	0.305109i
$855$	−5.23665	−	9.07015i	−0.179090	−	0.310193i
$856$	−8.14504	−	2.18246i	−0.278392	−	0.0745948i
$857$	−20.7248			−0.707947			−0.353973	−	0.935255i	$-0.615170\pi$
$857$	−20.7248			−0.707947			−0.353973	+	0.935255i	$0.615170\pi$
$858$	−3.81577	−	2.99020i	−0.130268	−	0.102084i
$859$	−17.2940			−0.590065			−0.295033	−	0.955487i	$-0.595331\pi$
$859$	−17.2940			−0.590065			−0.295033	+	0.955487i	$0.595331\pi$
$860$	−47.8903	−	12.8322i	−1.63305	−	0.437573i
$861$	−14.6052	−	25.2969i	−0.497743	−	0.862116i
$862$	5.44306	+	3.14255i	0.185391	+	0.107036i
$863$	30.2785	+	30.2785i	1.03069	+	1.03069i	0.999514	+	0.0311793i	$0.00992630\pi$
$863$	30.2785	+	30.2785i	1.03069	+	1.03069i	0.0311793	+	0.999514i	$0.490074\pi$
$864$	−1.12397	−	4.19472i	−0.0382383	−	0.142707i
$865$	35.2771	−	9.45248i	1.19946	−	0.321394i
$866$	2.76219	+	2.76219i	0.0938629	+	0.0938629i
$867$	−8.16808	+	14.1475i	−0.277403	+	0.480475i
$868$	−25.9517	−	44.9496i	−0.880857	−	1.52569i
$869$	4.26353	+	15.2300i	0.144630	+	0.516642i
$870$			6.26170i			0.212292i
$871$	−1.67749	−	15.2505i	−0.0568396	−	0.516745i
$872$	13.2579			0.448970
$873$	2.26194	−	8.44167i	0.0765550	−	0.285707i
$874$	−2.89718	−	5.01806i	−0.0979984	−	0.169738i
$875$	11.1880	−	19.3781i	0.378222	−	0.655100i
$876$	−17.5833	+	17.5833i	−0.594084	+	0.594084i
$877$	7.48595	+	27.9379i	0.252782	+	0.943397i	0.969311	+	0.245839i	$0.0790634\pi$
$877$	7.48595	+	27.9379i	0.252782	+	0.943397i	−0.716528	+	0.697558i	$0.754270\pi$
$878$	2.24415	+	8.37528i	0.0757364	+	0.282652i
$879$	−17.1465	−	17.1465i	−0.578336	−	0.578336i
$880$	−0.319772	−	28.6617i	−0.0107795	−	0.966187i
$881$	−24.5680	+	14.1843i	−0.827716	+	0.477882i	−0.853070	−	0.521797i	$-0.825262\pi$
$881$	−24.5680	+	14.1843i	−0.827716	+	0.477882i	0.0253541	+	0.999679i	$0.491929\pi$
$882$	−1.02443	+	3.82323i	−0.0344944	+	0.128735i
$883$			12.9290i			0.435096i	0.976050	+	0.217548i	$0.0698059\pi$
$883$			12.9290i			0.435096i	−0.976050	+	0.217548i	$0.930194\pi$
$884$	−3.37333	+	4.20715i	−0.113457	+	0.141502i
$885$	30.6271			1.02952
$886$	10.0159	+	2.68374i	0.336490	+	0.0901621i
$887$	27.8036	−	16.0524i	0.933555	−	0.538988i	0.0456208	−	0.998959i	$-0.485473\pi$
$887$	27.8036	−	16.0524i	0.933555	−	0.538988i	0.887934	+	0.459971i	$0.152140\pi$
$888$	−1.80906	+	3.13339i	−0.0607081	+	0.105150i
$889$	−10.3925	−	10.3925i	−0.348554	−	0.348554i
$890$	4.36101	+	16.2755i	0.146182	+	0.545557i
$891$	2.37123	+	2.31890i	0.0794390	+	0.0776860i
$892$	−7.84572	+	7.84572i	−0.262694	+	0.262694i
$893$	−25.2144	−	14.5576i	−0.843769	−	0.487150i
$894$	3.52279	−	2.03388i	0.117820	−	0.0680232i
$895$	−53.3352	−	14.2911i	−1.78280	−	0.477700i
$896$		−	42.7336i		−	1.42763i
$897$	−13.8225	−	2.12081i	−0.461520	−	0.0708117i
$898$			1.00659i			0.0335905i
$899$	36.2537	+	9.71416i	1.20913	+	0.323985i
$900$	2.82418	+	4.89163i	0.0941394	+	0.163054i
$901$	−1.62030	+	2.80645i	−0.0539801	+	0.0934963i
$902$	9.29271	+	2.37919i	0.309414	+	0.0792182i
$903$	37.5849	−	10.0708i	1.25075	−	0.335137i
$904$	−13.3827	+	3.58588i	−0.445102	+	0.119265i
$905$	−41.5880	+	41.5880i	−1.38243	+	1.38243i
$906$	−4.28734	+	7.42589i	−0.142437	+	0.246709i
$907$	33.9994	−	19.6295i	1.12893	−	0.651788i	0.185264	−	0.982689i	$-0.440686\pi$
$907$	33.9994	−	19.6295i	1.12893	−	0.651788i	0.943666	+	0.330901i	$0.107353\pi$
$908$	6.96335	−	25.9876i	0.231087	−	0.862428i
$909$	4.07271			0.135083
$910$	15.5711	+	6.84267i	0.516176	+	0.226832i
$911$	−8.71548			−0.288757			−0.144378	−	0.989523i	$-0.546118\pi$
$911$	−8.71548			−0.288757			−0.144378	+	0.989523i	$0.546118\pi$
$912$	−10.8245	−	2.90042i	−0.358436	−	0.0960426i
$913$	12.9583	−	23.0341i	0.428856	−	0.762316i
$914$	4.55305	+	2.62870i	0.150601	+	0.0869498i
$915$	21.5905	−	21.5905i	0.713760	−	0.713760i
$916$	−6.61043	+	1.77126i	−0.218415	+	0.0585240i
$917$	7.47513	+	27.8976i	0.246851	+	0.921259i
$918$	−0.233558	+	0.233558i	−0.00770857	+	0.00770857i
$919$	−35.1630	−	20.3014i	−1.15992	−	0.669681i	−0.208636	−	0.977993i	$-0.566902\pi$
$919$	−35.1630	−	20.3014i	−1.15992	−	0.669681i	−0.951285	+	0.308312i	$0.900236\pi$
$920$	8.57003	+	14.8437i	0.282545	+	0.489383i
$921$	4.14888	−	15.4838i	0.136710	−	0.510210i
$922$			4.24770i			0.139890i
$923$	−2.99362	+	2.19719i	−0.0985362	+	0.0723213i
$924$	12.7036	+	21.4470i	0.417916	+	0.705555i
$925$	1.85307	−	6.91577i	0.0609287	−	0.227389i
$926$	2.35167	−	1.35774i	0.0772806	−	0.0446180i
$927$	−2.17798	−	1.25746i	−0.0715343	−	0.0413004i
$928$	16.6891	+	16.6891i	0.547845	+	0.547845i
$929$	51.7369	−	13.8629i	1.69743	−	0.454825i	0.725141	−	0.688600i	$-0.241775\pi$
$929$	51.7369	−	13.8629i	1.69743	−	0.454825i	0.972291	+	0.233775i	$0.0751079\pi$
$930$	−7.68547	+	2.05932i	−0.252017	+	0.0675276i
$931$	25.4419	+	25.4419i	0.833826	+	0.833826i
$932$	−20.1233	−	11.6182i	−0.659161	−	0.380567i
$933$	6.62006	−	3.82209i	0.216731	−	0.125130i
$934$	2.32677	−	8.68361i	0.0761341	−	0.284136i
$935$	−6.60770	+	3.91389i	−0.216095	+	0.127998i
$936$	4.51975	−	3.31730i	0.147733	−	0.108429i
$937$			38.4606i			1.25645i	0.778030	+	0.628227i	$0.216219\pi$
$937$			38.4606i			1.25645i	−0.778030	+	0.628227i	$0.783781\pi$
$938$	1.82803	−	6.82230i	0.0596873	−	0.222756i
$939$	−5.32075	−	9.21582i	−0.173636	−	0.300747i
$940$	35.6951	+	20.6086i	1.16424	+	0.672177i
$941$	26.2401	−	26.2401i	0.855402	−	0.855402i	−0.135391	−	0.990792i	$-0.543229\pi$
$941$	26.2401	−	26.2401i	0.855402	−	0.855402i	0.990792	+	0.135391i	$0.0432289\pi$
$942$	−2.33072	−	8.69837i	−0.0759390	−	0.283408i
$943$	26.7279	−	7.16173i	0.870381	−	0.233218i
$944$	23.1724	−	23.1724i	0.754199	−	0.754199i
$945$	−10.0772	−	5.81807i	−0.327811	−	0.189262i
$946$	−6.26514	+	11.1367i	−0.203697	+	0.362084i
$947$	−32.7023	−	8.76255i	−1.06268	−	0.284745i	−0.315199	−	0.949026i	$-0.602071\pi$
$947$	−32.7023	−	8.76255i	−1.06268	−	0.284745i	−0.747483	+	0.664281i	$0.768738\pi$
$948$	−8.75342			−0.284298
$949$	−44.7152	−	19.6500i	−1.45152	−	0.637865i
$950$	−4.59694			−0.149145
$951$	−5.67330	+	21.1730i	−0.183969	+	0.686582i
$952$	−4.49224	+	2.59360i	−0.145594	+	0.0840589i
$953$	−18.0820	+	31.3190i	−0.585734	+	1.01452i	0.409049	+	0.912512i	$0.365860\pi$
$953$	−18.0820	+	31.3190i	−0.585734	+	1.01452i	−0.994783	+	0.102009i	$0.967473\pi$
$954$	1.14014	−	1.14014i	0.0369135	−	0.0369135i
$955$	−44.5273	+	11.9310i	−1.44087	+	0.386080i
$956$	−38.9869	+	10.4465i	−1.26092	+	0.337864i
$957$	−17.4621	−	4.47077i	−0.564470	−	0.144520i
$958$	6.63577	−	11.4935i	0.214392	−	0.371338i
$959$	−22.2546	−	38.5461i	−0.718638	−	1.24472i
$960$	11.8629	+	3.17865i	0.382873	+	0.102590i
$961$			16.6918i			0.538445i
$962$	−3.36173	−	0.515796i	−0.108387	−	0.0166299i
$963$			5.42289i			0.174750i
$964$	−41.6636	−	11.1637i	−1.34190	−	0.359560i
$965$	59.8074	−	34.5298i	1.92527	−	1.11155i
$966$	−5.57520	−	3.21884i	−0.179379	−	0.103565i
$967$	18.5937	−	18.5937i	0.597934	−	0.597934i	−0.341829	−	0.939762i	$-0.611046\pi$
$967$	18.5937	−	18.5937i	0.597934	−	0.597934i	0.939762	+	0.341829i	$0.111046\pi$
$968$	−16.6164	−	4.05727i	−0.534070	−	0.130405i
$969$	0.777115	+	2.90023i	0.0249645	+	0.0931688i
$970$	−7.11991	−	7.11991i	−0.228607	−	0.228607i
$971$	−15.4973	+	26.8422i	−0.497333	+	0.861406i	−0.999995	−	0.00307706i	$-0.999021\pi$
$971$	−15.4973	+	26.8422i	−0.497333	+	0.861406i	0.502662	+	0.864483i	$0.332354\pi$
$972$	−1.58972	+	0.917827i	−0.0509904	+	0.0294393i
$973$	−30.1470	−	8.07787i	−0.966469	−	0.258965i
$974$	−1.01001			−0.0323628
$975$	−6.94016	+	8.65562i	−0.222263	+	0.277202i
$976$		−	32.6707i		−	1.04576i
$977$	12.5294	−	46.7603i	0.400851	−	1.49600i	−0.410731	−	0.911757i	$-0.634726\pi$
$977$	12.5294	−	46.7603i	0.400851	−	1.49600i	0.811582	−	0.584239i	$-0.198607\pi$
$978$	−4.68238	+	2.70337i	−0.149726	+	0.0864443i
$979$	−48.5015	+	0.541120i	−1.55012	+	0.0172943i
$980$	−36.0171	−	36.0171i	−1.15052	−	1.15052i
$981$	−2.20675	−	8.23571i	−0.0704562	−	0.262946i
$982$	1.73833	+	6.48752i	0.0554722	+	0.207025i
$983$	21.4410	−	21.4410i	0.683860	−	0.683860i	−0.277007	−	0.960868i	$-0.589343\pi$
$983$	21.4410	−	21.4410i	0.683860	−	0.683860i	0.960868	+	0.277007i	$0.0893427\pi$
$984$	−5.54680	+	9.60734i	−0.176826	+	0.306271i
$985$	30.8382	+	53.4133i	0.982585	+	1.70189i
$986$	0.464615	−	1.73397i	0.0147964	−	0.0552208i
$987$	−32.3477			−1.02964
$988$	−2.66676	−	24.2443i	−0.0848410	−	0.771313i
$989$			36.8599i			1.17208i
$990$	3.67975	−	1.03012i	0.116950	−	0.0327393i
$991$	6.76841	+	11.7232i	0.215006	+	0.372401i	0.953274	−	0.302106i	$-0.0976897\pi$
$991$	6.76841	+	11.7232i	0.215006	+	0.372401i	−0.738269	+	0.674507i	$0.764356\pi$
$992$	−14.9952	+	25.9724i	−0.476097	+	0.824624i
$993$	−1.10108	−	1.10108i	−0.0349417	−	0.0349417i
$994$	−1.65123	+	0.442445i	−0.0523737	+	0.0140335i
$995$	4.89017	+	18.2504i	0.155029	+	0.578575i
$996$	10.3433	+	10.3433i	0.327739	+	0.327739i
$997$	45.1556	+	26.0706i	1.43009	+	0.825665i	0.997127	−	0.0757452i	$-0.0241336\pi$
$997$	45.1556	+	26.0706i	1.43009	+	0.825665i	0.432966	+	0.901410i	$0.357467\pi$
$998$	−8.67398	−	15.0238i	−0.274570	−	0.475570i
$999$	2.24755	+	0.602228i	0.0711092	+	0.0190536i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.bd.b.76.9	yes	56
11.10	odd	2	inner	429.2.bd.b.76.6	✓	56
13.6	odd	12	inner	429.2.bd.b.175.6	yes	56
143.32	even	12	inner	429.2.bd.b.175.9	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.bd.b.76.6	✓	56	11.10	odd	2	inner
429.2.bd.b.76.9	yes	56	1.1	even	1	trivial
429.2.bd.b.175.6	yes	56	13.6	odd	12	inner
429.2.bd.b.175.9	yes	56	143.32	even	12	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.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.391582 + 0.104924i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.58972 - 0.917827i) q^{4} +(2.00961 + 2.00961i) q^{5} +(0.104924 + 0.391582i) q^{6} +(3.95482 - 1.05969i) q^{7} +(-1.09952 - 1.09952i) q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.391582 + 0.104924i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-1.58972 - 0.917827i) q^{4} +(2.00961 + 2.00961i) q^{5} +(0.104924 + 0.391582i) q^{6} +(3.95482 - 1.05969i) q^{7} +(-1.09952 - 1.09952i) q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.576070 + 0.997782i) q^{10} +(-3.19384 + 0.894092i) q^{11} -1.83565i q^{12} +(3.35978 - 1.30837i) q^{13} +1.65982 q^{14} +(-0.735567 + 2.74517i) q^{15} +(1.52047 + 2.63353i) q^{16} +(0.407381 - 0.705605i) q^{17} +(-0.286658 + 0.286658i) q^{18} +(0.953793 + 3.55960i) q^{19} +(-1.35025 - 5.03919i) q^{20} +(2.89513 + 2.89513i) q^{21} +(-1.34446 + 0.0149999i) q^{22} +(-3.35891 + 1.93927i) q^{23} +(0.402453 - 1.50197i) q^{24} +3.07703i q^{25} +(1.45291 - 0.159814i) q^{26} -1.00000 q^{27} +(-7.25968 - 1.94523i) q^{28} +(4.70672 - 2.71742i) q^{29} +(-0.576070 + 0.997782i) q^{30} +(4.88323 + 4.88323i) q^{31} +(1.12397 + 4.19472i) q^{32} +(-2.37123 - 2.31890i) q^{33} +(0.233558 - 0.233558i) q^{34} +(10.0772 + 5.81807i) q^{35} +(1.58972 - 0.917827i) q^{36} +(-2.24755 - 0.602228i) q^{37} +1.49395i q^{38} +(2.81298 + 2.25547i) q^{39} -4.41921i q^{40} +(-6.89125 - 1.84650i) q^{41} +(0.829912 + 1.43745i) q^{42} +(4.75179 - 8.23034i) q^{43} +(5.89794 + 1.51003i) q^{44} +(-2.74517 + 0.735567i) q^{45} +(-1.51877 + 0.406952i) q^{46} +(-5.58658 + 5.58658i) q^{47} +(-1.52047 + 2.63353i) q^{48} +(8.45547 - 4.88177i) q^{49} +(-0.322855 + 1.20491i) q^{50} +0.814762 q^{51} +(-6.54199 - 1.00375i) q^{52} -3.97736 q^{53} +(-0.391582 - 0.104924i) q^{54} +(-8.21513 - 4.62158i) q^{55} +(-5.51356 - 3.18326i) q^{56} +(-2.60581 + 2.60581i) q^{57} +(2.12819 - 0.570247i) q^{58} +(-2.78917 - 10.4093i) q^{59} +(3.68894 - 3.68894i) q^{60} +(-9.30427 - 5.37182i) q^{61} +(1.39982 + 2.42455i) q^{62} +(-1.05969 + 3.95482i) q^{63} -4.32136i q^{64} +(9.38116 + 4.12253i) q^{65} +(-0.685221 - 1.15684i) q^{66} +(1.10134 - 4.11026i) q^{67} +(-1.29525 + 0.747811i) q^{68} +(-3.35891 - 1.93927i) q^{69} +(3.33559 + 3.33559i) q^{70} +(-0.994820 + 0.266561i) q^{71} +(1.50197 - 0.402453i) q^{72} +(-9.57876 - 9.57876i) q^{73} +(-0.816911 - 0.471644i) q^{74} +(-2.66479 + 1.53852i) q^{75} +(1.75083 - 6.53420i) q^{76} +(-11.6836 + 6.92045i) q^{77} +(0.864859 + 1.17835i) q^{78} -4.76856i q^{79} +(-2.23681 + 8.34789i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.50475 - 1.44612i) q^{82} +(-5.63465 + 5.63465i) q^{83} +(-1.94523 - 7.25968i) q^{84} +(2.23666 - 0.599312i) q^{85} +(2.72428 - 2.72428i) q^{86} +(4.70672 + 2.71742i) q^{87} +(4.49477 + 2.52862i) q^{88} +(14.1263 + 3.78514i) q^{89} -1.15214 q^{90} +(11.9009 - 8.73472i) q^{91} +7.11965 q^{92} +(-1.78738 + 6.67061i) q^{93} +(-2.77377 + 1.60144i) q^{94} +(-5.23665 + 9.07015i) q^{95} +(-3.07075 + 3.07075i) q^{96} +(-8.44167 + 2.26194i) q^{97} +(3.82323 - 1.02443i) q^{98} +(0.822612 - 3.21299i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9}+O(q^{10}) \) 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9	\( 56 q + 28 q^{3} - 4 q^{5} - 28 q^{9} - 4 q^{11} - 24 q^{14} - 8 q^{15} + 4 q^{16} + 80 q^{20} - 10 q^{22} - 12 q^{23} + 40 q^{26} - 56 q^{27} - 12 q^{31} - 8 q^{33} - 16 q^{34} - 12 q^{37} - 12 q^{42} + 24 q^{44} - 4 q^{45} - 40 q^{47} - 4 q^{48} + 24 q^{49} - 88 q^{53} - 18 q^{55} + 72 q^{56} + 40 q^{58} + 8 q^{59} + 52 q^{60} - 20 q^{66} - 4 q^{67} - 12 q^{69} + 40 q^{70} - 24 q^{71} + 12 q^{75} - 4 q^{78} - 188 q^{80} - 28 q^{81} - 12 q^{82} + 32 q^{86} + 18 q^{88} - 16 q^{89} + 28 q^{91} - 96 q^{92} - 12 q^{93} - 28 q^{97} - 4 q^{99}+O(q^{100}) \) 56 * q + 28 * q^3 - 4 * q^5 - 28 * q^9 - 4 * q^11 - 24 * q^14 - 8 * q^15 + 4 * q^16 + 80 * q^20 - 10 * q^22 - 12 * q^23 + 40 * q^26 - 56 * q^27 - 12 * q^31 - 8 * q^33 - 16 * q^34 - 12 * q^37 - 12 * q^42 + 24 * q^44 - 4 * q^45 - 40 * q^47 - 4 * q^48 + 24 * q^49 - 88 * q^53 - 18 * q^55 + 72 * q^56 + 40 * q^58 + 8 * q^59 + 52 * q^60 - 20 * q^66 - 4 * q^67 - 12 * q^69 + 40 * q^70 - 24 * q^71 + 12 * q^75 - 4 * q^78 - 188 * q^80 - 28 * q^81 - 12 * q^82 + 32 * q^86 + 18 * q^88 - 16 * q^89 + 28 * q^91 - 96 * q^92 - 12 * q^93 - 28 * q^97 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more