LMFDB - Embedded newform 260.2.bg.c.23.35

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [260,2,Mod(23,260)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(260, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 10]))

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

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

chi := DirichletCharacter("260.23");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 260 = 2^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	260.bg (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:	$2.07611045255$
Analytic rank:	$0$
Dimension:	$144$
Relative dimension:	$36$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.35
Character	$\chi$	$=$	260.23
Dual form			260.2.bg.c.147.35

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.39887 + 0.207750i) q^{2} +(-3.04677 - 0.816378i) q^{3} +(1.91368 + 0.581230i) q^{4} +(-0.215330 + 2.22568i) q^{5} +(-4.09243 - 1.77497i) q^{6} +(0.0424015 + 0.158244i) q^{7} +(2.55624 + 1.21063i) q^{8} +(6.01823 + 3.47463i) q^{9} +(-0.763602 + 3.06870i) q^{10} +(1.67952 + 2.90902i) q^{11} +(-5.35603 - 3.33316i) q^{12} +(-0.302905 + 3.59281i) q^{13} +(0.0264389 + 0.230172i) q^{14} +(2.47305 - 6.60532i) q^{15} +(3.32434 + 2.22458i) q^{16} +(-1.11891 - 4.17582i) q^{17} +(7.69687 + 6.11084i) q^{18} +(1.77930 + 1.02728i) q^{19} +(-1.70570 + 4.13408i) q^{20} -0.516749i q^{21} +(1.74509 + 4.41826i) q^{22} +(1.12010 + 0.300129i) q^{23} +(-6.79993 - 5.77537i) q^{24} +(-4.90727 - 0.958509i) q^{25} +(-1.17013 + 4.96294i) q^{26} +(-8.80836 - 8.80836i) q^{27} +(-0.0108336 + 0.327474i) q^{28} +(0.663797 - 0.383243i) q^{29} +(4.83174 - 8.72622i) q^{30} -9.22182 q^{31} +(4.18817 + 3.80253i) q^{32} +(-2.74225 - 10.2342i) q^{33} +(-0.697682 - 6.07389i) q^{34} +(-0.361331 + 0.0602971i) q^{35} +(9.49741 + 10.1473i) q^{36} +(0.405598 - 1.51371i) q^{37} +(2.27559 + 1.80668i) q^{38} +(3.85597 - 10.6991i) q^{39} +(-3.24491 + 5.42868i) q^{40} +(7.36261 - 4.25081i) q^{41} +(0.107355 - 0.722865i) q^{42} +(0.817373 + 3.05048i) q^{43} +(1.52326 + 6.54312i) q^{44} +(-9.02930 + 12.6464i) q^{45} +(1.50452 + 0.652541i) q^{46} +(4.21757 - 4.21757i) q^{47} +(-8.31240 - 9.49169i) q^{48} +(6.03893 - 3.48658i) q^{49} +(-6.66550 - 2.36031i) q^{50} +13.6362i q^{51} +(-2.66791 + 6.69942i) q^{52} +(-8.62782 - 8.62782i) q^{53} +(-10.4918 - 14.1517i) q^{54} +(-6.83618 + 3.11167i) q^{55} +(-0.0831875 + 0.455843i) q^{56} +(-4.58246 - 4.58246i) q^{57} +(1.00819 - 0.398204i) q^{58} +(1.72021 + 0.993165i) q^{59} +(8.57185 - 11.2031i) q^{60} +(0.793873 - 1.37503i) q^{61} +(-12.9001 - 1.91583i) q^{62} +(-0.294658 + 1.09968i) q^{63} +(5.06874 + 6.18934i) q^{64} +(-7.93119 - 1.44781i) q^{65} +(-1.70990 - 14.8861i) q^{66} +(5.45208 + 1.46088i) q^{67} +(0.285882 - 8.64153i) q^{68} +(-3.16765 - 1.82884i) q^{69} +(-0.517982 + 0.00928149i) q^{70} +(4.47121 - 7.74436i) q^{71} +(11.1775 + 16.1678i) q^{72} +(-9.06992 + 9.06992i) q^{73} +(0.881852 - 2.03322i) q^{74} +(14.1688 + 6.92654i) q^{75} +(2.80792 + 3.00007i) q^{76} +(-0.389122 + 0.389122i) q^{77} +(7.61675 - 14.1657i) q^{78} -6.33294 q^{79} +(-5.66702 + 6.91989i) q^{80} +(9.22218 + 15.9733i) q^{81} +(11.1824 - 4.41675i) q^{82} +(6.74106 + 6.74106i) q^{83} +(0.300350 - 0.988893i) q^{84} +(9.53496 - 1.59115i) q^{85} +(0.509663 + 4.43703i) q^{86} +(-2.33531 + 0.625743i) q^{87} +(0.771512 + 9.46944i) q^{88} +(3.93581 + 6.81702i) q^{89} +(-15.2581 + 15.8149i) q^{90} +(-0.581385 + 0.104407i) q^{91} +(1.96906 + 1.22538i) q^{92} +(28.0967 + 7.52850i) q^{93} +(6.77604 - 5.02364i) q^{94} +(-2.66953 + 3.73894i) q^{95} +(-9.65607 - 15.0045i) q^{96} +(14.4151 - 3.86251i) q^{97} +(9.17203 - 3.62269i) q^{98} +23.3429i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 144 q - 6 q^{2} - 12 q^{6} + 12 q^{10} - 12 q^{12} + 4 q^{13} - 12 q^{16} - 24 q^{17} - 42 q^{20} - 12 q^{22} - 24 q^{25} - 36 q^{26} - 6 q^{28} - 36 q^{32} - 12 q^{33} - 76 q^{36} + 48 q^{37} - 16 q^{38}+ \cdots - 162 q^{98}+O(q^{100}) $ 144 * q - 6 * q^2 - 12 * q^6 + 12 * q^10 - 12 * q^12 + 4 * q^13 - 12 * q^16 - 24 * q^17 - 42 * q^20 - 12 * q^22 - 24 * q^25 - 36 * q^26 - 6 * q^28 - 36 * q^32 - 12 * q^33 - 76 * q^36 + 48 * q^37 - 16 * q^38 + 76 * q^40 - 72 * q^41 + 40 * q^42 - 120 * q^45 - 12 * q^46 - 40 * q^48 + 120 * q^50 - 10 * q^52 + 8 * q^53 - 20 * q^56 + 126 * q^58 + 16 * q^61 - 44 * q^62 + 32 * q^65 + 96 * q^66 - 64 * q^68 - 54 * q^72 - 12 * q^76 + 40 * q^77 - 100 * q^78 - 24 * q^80 - 32 * q^81 - 78 * q^82 - 24 * q^85 - 10 * q^88 - 8 * q^90 + 100 * q^92 - 48 * q^93 - 12 * q^97 - 162 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

$n$	$41$	$131$	$157$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	1.39887	+	0.207750i	0.989151	+	0.146901i
$2$	1.39887	+	0.207750i	0.989151	+	0.146901i
$3$	−3.04677	−	0.816378i	−1.75905	−	0.471336i	−0.772531	−	0.634977i	$-0.781009\pi$
$3$	−3.04677	−	0.816378i	−1.75905	−	0.471336i	−0.986520	+	0.163641i	$0.947676\pi$
$4$	1.91368	+	0.581230i	0.956840	+	0.290615i
$5$	−0.215330	+	2.22568i	−0.0962985	+	0.995353i
$5$	−0.215330	+	2.22568i	−0.0962985	+	0.995353i
$6$	−4.09243	−	1.77497i	−1.67073	−	0.724630i
$7$	0.0424015	+	0.158244i	0.0160262	+	0.0598108i	0.973476	−	0.228790i	$-0.0734768\pi$
$7$	0.0424015	+	0.158244i	0.0160262	+	0.0598108i	−0.957450	+	0.288600i	$0.906810\pi$
$8$	2.55624	+	1.21063i	0.903768	+	0.428023i
$9$	6.01823	+	3.47463i	2.00608	+	1.15821i
$10$	−0.763602	+	3.06870i	−0.241472	+	0.970408i
$11$	1.67952	+	2.90902i	0.506395	+	0.877102i	0.999973	+	0.00740021i	$0.00235558\pi$
$11$	1.67952	+	2.90902i	0.506395	+	0.877102i	−0.493578	+	0.869702i	$0.664311\pi$
$12$	−5.35603	−	3.33316i	−1.54615	−	0.962200i
$13$	−0.302905	+	3.59281i	−0.0840109	+	0.996465i
$13$	−0.302905	+	3.59281i	−0.0840109	+	0.996465i
$14$	0.0264389	+	0.230172i	0.00706610	+	0.0615162i
$15$	2.47305	−	6.60532i	0.638540	−	1.70549i
$16$	3.32434	+	2.22458i	0.831086	+	0.556144i
$17$	−1.11891	−	4.17582i	−0.271375	−	1.01279i	−0.958232	−	0.285993i	$-0.907677\pi$
$17$	−1.11891	−	4.17582i	−0.271375	−	1.01279i	0.686857	−	0.726793i	$-0.258990\pi$
$18$	7.69687	+	6.11084i	1.81417	+	1.44034i
$19$	1.77930	+	1.02728i	0.408199	+	0.235674i	0.690016	−	0.723794i	$-0.257604\pi$
$19$	1.77930	+	1.02728i	0.408199	+	0.235674i	−0.281816	+	0.959468i	$0.590937\pi$
$20$	−1.70570	+	4.13408i	−0.381407	+	0.924407i
$21$		−	0.516749i		−	0.112764i
$22$	1.74509	+	4.41826i	0.372054	+	0.941977i
$23$	1.12010	+	0.300129i	0.233556	+	0.0625812i	0.373699	−	0.927550i	$-0.378089\pi$
$23$	1.12010	+	0.300129i	0.233556	+	0.0625812i	−0.140143	+	0.990131i	$0.544756\pi$
$24$	−6.79993	−	5.77537i	−1.38803	−	1.17889i
$25$	−4.90727	−	0.958509i	−0.981453	−	0.191702i
$26$	−1.17013	+	4.96294i	−0.229481	+	0.973313i
$27$	−8.80836	−	8.80836i	−1.69517	−	1.69517i
$28$	−0.0108336	+	0.327474i	−0.00204736	+	0.0618868i
$29$	0.663797	−	0.383243i	0.123264	−	0.0711665i	−0.437100	−	0.899413i	$-0.643994\pi$
$29$	0.663797	−	0.383243i	0.123264	−	0.0711665i	0.560364	+	0.828246i	$0.310661\pi$
$30$	4.83174	−	8.72622i	0.882150	−	1.59318i
$31$	−9.22182			−1.65629			−0.828144	−	0.560515i	$-0.810603\pi$
$31$	−9.22182			−1.65629			−0.828144	+	0.560515i	$0.810603\pi$
$32$	4.18817	+	3.80253i	0.740371	+	0.672198i
$33$	−2.74225	−	10.2342i	−0.477365	−	1.78155i
$34$	−0.697682	−	6.07389i	−0.119652	−	1.04166i
$35$	−0.361331	+	0.0602971i	−0.0610761	+	0.0101921i
$36$	9.49741	+	10.1473i	1.58290	+	1.69122i
$37$	0.405598	−	1.51371i	0.0666799	−	0.248853i	−0.924538	−	0.381089i	$-0.875549\pi$
$37$	0.405598	−	1.51371i	0.0666799	−	0.248853i	0.991218	+	0.132236i	$0.0422158\pi$
$38$	2.27559	+	1.80668i	0.369150	+	0.293082i
$39$	3.85597	−	10.6991i	0.617449	−	1.71323i
$40$	−3.24491	+	5.42868i	−0.513066	+	0.858349i
$41$	7.36261	−	4.25081i	1.14985	−	0.663864i	0.200997	−	0.979592i	$-0.435582\pi$
$41$	7.36261	−	4.25081i	1.14985	−	0.663864i	0.948850	+	0.315727i	$0.102249\pi$
$42$	0.107355	−	0.722865i	0.0165652	−	0.111541i
$43$	0.817373	+	3.05048i	0.124648	+	0.465193i	0.999827	−	0.0186065i	$-0.00592297\pi$
$43$	0.817373	+	3.05048i	0.124648	+	0.465193i	−0.875179	+	0.483800i	$0.839256\pi$
$44$	1.52326	+	6.54312i	0.229640	+	0.986412i
$45$	−9.02930	+	12.6464i	−1.34601	+	1.88522i
$46$	1.50452	+	0.652541i	0.221829	+	0.0962120i
$47$	4.21757	−	4.21757i	0.615196	−	0.615196i	−0.329099	−	0.944295i	$-0.606745\pi$
$47$	4.21757	−	4.21757i	0.615196	−	0.615196i	0.944295	+	0.329099i	$0.106745\pi$
$48$	−8.31240	−	9.49169i	−1.19979	−	1.37001i
$49$	6.03893	−	3.48658i	0.862705	−	0.498083i
$50$	−6.66550	−	2.36031i	−0.942644	−	0.333799i
$51$			13.6362i			1.90945i
$52$	−2.66791	+	6.69942i	−0.369973	+	0.929043i
$53$	−8.62782	−	8.62782i	−1.18512	−	1.18512i	−0.978400	−	0.206723i	$-0.933720\pi$
$53$	−8.62782	−	8.62782i	−1.18512	−	1.18512i	−0.206723	−	0.978400i	$-0.566280\pi$
$54$	−10.4918	−	14.1517i	−1.42776	−	1.92580i
$55$	−6.83618	+	3.11167i	−0.921791	+	0.419578i
$56$	−0.0831875	+	0.455843i	−0.0111164	+	0.0609146i
$57$	−4.58246	−	4.58246i	−0.606962	−	0.606962i
$58$	1.00819	−	0.398204i	0.132381	−	0.0522868i
$59$	1.72021	+	0.993165i	0.223953	+	0.129299i	0.607779	−	0.794106i	$-0.292061\pi$
$59$	1.72021	+	0.993165i	0.223953	+	0.129299i	−0.383827	+	0.923405i	$0.625394\pi$
$60$	8.57185	−	11.2031i	1.10662	−	1.44631i
$61$	0.793873	−	1.37503i	0.101645	−	0.176054i	−0.810718	−	0.585438i	$-0.800923\pi$
$61$	0.793873	−	1.37503i	0.101645	−	0.176054i	0.912363	+	0.409383i	$0.134256\pi$
$62$	−12.9001	−	1.91583i	−1.63832	−	0.243311i
$63$	−0.294658	+	1.09968i	−0.0371235	+	0.138547i
$64$	5.06874	+	6.18934i	0.633592	+	0.773667i
$65$	−7.93119	−	1.44781i	−0.983744	−	0.179578i
$66$	−1.70990	−	14.8861i	−0.210474	−	1.83235i
$67$	5.45208	+	1.46088i	0.666077	+	0.178475i	0.575987	−	0.817459i	$-0.304618\pi$
$67$	5.45208	+	1.46088i	0.666077	+	0.178475i	0.0900900	+	0.995934i	$0.471285\pi$
$68$	0.285882	−	8.64153i	0.0346683	−	1.04794i
$69$	−3.16765	−	1.82884i	−0.381340	−	0.220167i
$70$	−0.517982	+	0.00928149i	−0.0619107	+	0.00110935i
$71$	4.47121	−	7.74436i	0.530635	−	0.919086i	−0.468726	−	0.883343i	$-0.655287\pi$
$71$	4.47121	−	7.74436i	0.530635	−	0.919086i	0.999361	−	0.0357428i	$-0.0113797\pi$
$72$	11.1775	+	16.1678i	1.31729	+	1.90540i
$73$	−9.06992	+	9.06992i	−1.06155	+	1.06155i	−0.0635775	+	0.997977i	$0.520251\pi$
$73$	−9.06992	+	9.06992i	−1.06155	+	1.06155i	−0.997977	+	0.0635775i	$0.979749\pi$
$74$	0.881852	−	2.03322i	0.102513	−	0.236358i
$75$	14.1688	+	6.92654i	1.63607	+	0.799808i
$76$	2.80792	+	3.00007i	0.322091	+	0.344131i
$77$	−0.389122	+	0.389122i	−0.0443445	+	0.0443445i
$78$	7.61675	−	14.1657i	0.862427	−	1.60394i
$79$	−6.33294			−0.712512			−0.356256	−	0.934388i	$-0.615947\pi$
$79$	−6.33294			−0.712512			−0.356256	+	0.934388i	$0.615947\pi$
$80$	−5.66702	+	6.91989i	−0.633592	+	0.773667i
$81$	9.22218	+	15.9733i	1.02469	+	1.77481i
$82$	11.1824	−	4.41675i	1.23489	−	0.487748i
$83$	6.74106	+	6.74106i	0.739928	+	0.739928i	0.972564	−	0.232636i	$-0.0747351\pi$
$83$	6.74106	+	6.74106i	0.739928	+	0.739928i	−0.232636	+	0.972564i	$0.574735\pi$
$84$	0.300350	−	0.988893i	0.0327709	−	0.107897i
$85$	9.53496	−	1.59115i	1.03421	−	0.172584i
$86$	0.509663	+	4.43703i	0.0549584	+	0.478457i
$87$	−2.33531	+	0.625743i	−0.250371	+	0.0670867i
$88$	0.771512	+	9.46944i	0.0822434	+	1.00945i
$89$	3.93581	+	6.81702i	0.417195	+	0.722603i	0.995656	−	0.0931070i	$-0.0296799\pi$
$89$	3.93581	+	6.81702i	0.417195	+	0.722603i	−0.578461	+	0.815710i	$0.696347\pi$
$90$	−15.2581	+	15.8149i	−1.60835	+	1.66704i
$91$	−0.581385	+	0.104407i	−0.0609457	+	0.0109448i
$92$	1.96906	+	1.22538i	0.205289	+	0.127755i
$93$	28.0967	+	7.52850i	2.91350	+	0.780669i
$94$	6.77604	−	5.02364i	0.698895	−	0.518149i
$95$	−2.66953	+	3.73894i	−0.273888	+	0.383607i
$96$	−9.65607	−	15.0045i	−0.985519	−	1.53139i
$97$	14.4151	−	3.86251i	1.46363	−	0.392179i	0.562889	−	0.826533i	$-0.309690\pi$
$97$	14.4151	−	3.86251i	1.46363	−	0.392179i	0.900742	+	0.434354i	$0.143023\pi$
$98$	9.17203	−	3.62269i	0.926515	−	0.365947i
$99$			23.3429i			2.34604i
$100$	−8.83382	−	4.68653i	−0.883382	−	0.468653i
$101$	−3.12177	−	5.40707i	−0.310628	−	0.538024i	0.667870	−	0.744278i	$-0.267206\pi$
$101$	−3.12177	−	5.40707i	−0.310628	−	0.538024i	−0.978499	+	0.206254i	$0.933873\pi$
$102$	−2.83292	+	19.0753i	−0.280501	+	1.88874i
$103$	9.83374	−	9.83374i	0.968947	−	0.968947i	−0.0305847	−	0.999532i	$-0.509737\pi$
$103$	9.83374	−	9.83374i	0.968947	−	0.968947i	0.999532	+	0.0305847i	$0.00973693\pi$
$104$	−5.12387	+	8.81737i	−0.502436	+	0.864614i
$105$	1.15012	+	0.111272i	0.112240	+	0.0108590i
$106$	−10.2768	−	13.8616i	−0.998169	−	1.34636i
$107$	4.00736	−	14.9557i	0.387406	−	1.44582i	−0.446933	−	0.894568i	$-0.647484\pi$
$107$	4.00736	−	14.9557i	0.387406	−	1.44582i	0.834339	−	0.551252i	$-0.185850\pi$
$108$	−11.7367	−	21.9761i	−1.12936	−	2.11465i
$109$	−10.1909			−0.976116			−0.488058	−	0.872811i	$-0.662294\pi$
$109$	−10.1909			−0.976116			−0.488058	+	0.872811i	$0.662294\pi$
$110$	−10.2094	+	2.93261i	−0.973427	+	0.279614i
$111$	−2.47152	+	4.28080i	−0.234587	+	0.406316i
$112$	−0.211070	+	0.620384i	−0.0199442	+	0.0586208i
$113$	−6.35536	+	1.70291i	−0.597862	+	0.160197i	−0.545044	−	0.838408i	$-0.683487\pi$
$113$	−6.35536	+	1.70291i	−0.597862	+	0.160197i	−0.0528180	+	0.998604i	$0.516820\pi$
$114$	−5.45827	−	7.36228i	−0.511213	−	0.689540i
$115$	−0.909180	+	2.42834i	−0.0847815	+	0.226444i
$116$	1.49305	−	0.347586i	0.138626	−	0.0322726i
$117$	−14.3066	+	20.5698i	−1.32265	+	1.90168i
$118$	2.20003	+	1.74668i	0.202529	+	0.160795i
$119$	0.613357	−	0.354122i	0.0562264	−	0.0324623i
$120$	14.3183	−	13.8908i	1.30708	−	1.26805i
$121$	−0.141592	+	0.245244i	−0.0128720	+	0.0222949i
$122$	1.39619	−	1.75856i	0.126405	−	0.159213i
$123$	−25.9024	+	6.94053i	−2.33554	+	0.625807i
$124$	−17.6476	−	5.36000i	−1.58480	−	0.481342i
$125$	3.19001	−	10.7156i	0.285323	−	0.958431i
$126$	−0.640647	+	1.47710i	−0.0570734	+	0.131590i
$127$	−3.88958	+	14.5161i	−0.345144	+	1.28810i	0.547299	+	0.836937i	$0.315656\pi$
$127$	−3.88958	+	14.5161i	−0.345144	+	1.28810i	−0.892444	+	0.451159i	$0.851011\pi$
$128$	5.80468	+	9.71111i	0.513066	+	0.858349i
$129$		−	9.96137i		−	0.877050i
$130$	−10.7939	−	3.67300i	−0.946691	−	0.322143i
$131$		−	2.19741i		−	0.191988i	−0.995382	−	0.0959942i	$-0.969397\pi$
$131$		−	2.19741i		−	0.191988i	0.995382	−	0.0959942i	$-0.0306030\pi$
$132$	0.700647	−	21.1789i	0.0609835	−	1.84339i
$133$	−0.0871163	+	0.325122i	−0.00755394	+	0.0281917i
$134$	7.32325	+	3.17625i	0.632633	+	0.274386i
$135$	21.5013	−	17.7079i	1.85053	−	1.52405i
$136$	2.19519	−	12.0290i	0.188236	−	1.03148i
$137$	5.05134	−	1.35350i	0.431565	−	0.115637i	−0.0364958	−	0.999334i	$-0.511620\pi$
$137$	5.05134	−	1.35350i	0.431565	−	0.115637i	0.468061	+	0.883696i	$0.344953\pi$
$138$	−4.05119	−	3.21640i	−0.344861	−	0.273798i
$139$	2.09826	−	3.63429i	0.177972	−	0.308257i	−0.763214	−	0.646146i	$-0.776380\pi$
$139$	2.09826	−	3.63429i	0.177972	−	0.308257i	0.941186	+	0.337890i	$0.109713\pi$
$140$	−0.726519	−	0.0946271i	−0.0614020	−	0.00799745i
$141$	−16.2931	+	9.40682i	−1.37213	+	0.792197i
$142$	7.86353	−	9.90447i	0.659893	−	0.831164i
$143$	−10.9603	+	5.15304i	−0.916544	+	0.430919i
$144$	12.2771	+	24.9389i	1.02309	+	2.07824i
$145$	0.710040	+	1.55992i	0.0589656	+	0.129544i
$146$	−14.5719	+	10.8034i	−1.20598	+	0.894094i
$147$	−21.2456	+	5.69274i	−1.75231	+	0.469529i
$148$	1.65600	−	2.66101i	0.136122	−	0.218734i
$149$	−0.0288765	+	0.0500155i	−0.00236565	+	0.00409743i	−0.867206	−	0.497950i	$-0.834086\pi$
$149$	−0.0288765	+	0.0500155i	−0.00236565	+	0.00409743i	0.864840	+	0.502047i	$0.167420\pi$
$150$	18.3813	+	12.6329i	1.50083	+	1.03147i
$151$	15.6443			1.27311			0.636557	−	0.771230i	$-0.280358\pi$
$151$	15.6443			1.27311			0.636557	+	0.771230i	$0.280358\pi$
$152$	3.30466	+	4.78005i	0.268043	+	0.387713i
$153$	7.77558	−	29.0189i	0.628618	−	2.34604i
$154$	−0.625171	+	0.463491i	−0.0503777	+	0.0373492i
$155$	1.98573	−	20.5248i	0.159498	−	1.64859i
$156$	13.5978	−	18.2335i	1.08869	−	1.45985i
$157$	−7.76316	+	7.76316i	−0.619568	+	0.619568i	−0.945420	−	0.325853i	$-0.894349\pi$
$157$	−7.76316	+	7.76316i	−0.619568	+	0.619568i	0.325853	+	0.945420i	$0.394349\pi$
$158$	−8.85897	−	1.31567i	−0.704782	−	0.104669i
$159$	19.2434	+	33.3305i	1.52610	+	2.64328i
$160$	−9.36503	+	8.50271i	−0.740371	+	0.672199i
$161$			0.189975i			0.0149721i
$162$	9.58219	+	24.2605i	0.752848	+	1.90608i
$163$	−6.34860	+	1.70110i	−0.497261	+	0.133241i	−0.498729	−	0.866758i	$-0.666200\pi$
$163$	−6.34860	+	1.70110i	−0.497261	+	0.133241i	0.00146753	+	0.999999i	$0.499533\pi$
$164$	16.5604	−	3.85531i	1.29315	−	0.301049i
$165$	23.3685	−	3.89963i	1.81924	−	0.303586i
$166$	8.02942	+	10.8303i	0.623204	+	0.840597i
$167$	−17.0827	−	4.57729i	−1.32190	−	0.354201i	−0.472209	−	0.881487i	$-0.656543\pi$
$167$	−17.0827	−	4.57729i	−1.32190	−	0.354201i	−0.849688	+	0.527285i	$0.823210\pi$
$168$	0.625593	−	1.32094i	0.0482656	−	0.101912i
$169$	−12.8165	−	2.17656i	−0.985884	−	0.167428i
$170$	13.6687	−	0.244924i	1.04834	−	0.0187848i
$171$	7.13882	+	12.3648i	0.545919	+	0.945560i
$172$	−0.208839	+	6.31272i	−0.0159238	+	0.481340i
$173$	−2.61845	+	0.701612i	−0.199077	+	0.0533426i	−0.356980	−	0.934112i	$-0.616193\pi$
$173$	−2.61845	+	0.701612i	−0.199077	+	0.0533426i	0.157903	+	0.987455i	$0.449527\pi$
$174$	−3.39679	+	0.390175i	−0.257510	+	0.0295791i
$175$	−0.0563965	−	0.817190i	−0.00426318	−	0.0617737i
$176$	−0.888028	+	13.4068i	−0.0669376	+	1.01058i
$177$	−4.43028	−	4.43028i	−0.333001	−	0.333001i
$178$	4.08946	+	10.3538i	0.306518	+	0.776050i
$179$	−9.55658	−	16.5525i	−0.714292	−	1.23719i	−0.963232	−	0.268671i	$-0.913416\pi$
$179$	−9.55658	−	16.5525i	−0.714292	−	1.23719i	0.248940	−	0.968519i	$-0.419918\pi$
$180$	−24.6297	+	18.9531i	−1.83579	+	1.41268i
$181$	−9.00568			−0.669387			−0.334693	−	0.942327i	$-0.608633\pi$
$181$	−9.00568			−0.669387			−0.334693	+	0.942327i	$0.608633\pi$
$182$	−0.834973	+	0.0252695i	−0.0618923	+	0.00187310i
$183$	−3.54129	+	3.54129i	−0.261780	+	0.261780i
$184$	2.49989	+	2.12323i	0.184294	+	0.156526i
$185$	3.28169	+	1.22868i	0.241275	+	0.0903341i
$186$	37.7397	+	16.3685i	2.76721	+	1.20020i
$187$	10.2683	−	10.2683i	0.750894	−	0.750894i
$188$	10.5225	−	5.61970i	0.767430	−	0.409859i
$189$	1.02039	−	1.76736i	0.0742222	−	0.128557i
$190$	−4.51109	+	4.67570i	−0.327269	+	0.339211i
$191$	0.478629	+	0.276336i	0.0346323	+	0.0199950i	0.517216	−	0.855855i	$-0.326968\pi$
$191$	0.478629	+	0.276336i	0.0346323	+	0.0199950i	−0.482584	+	0.875850i	$0.660302\pi$
$192$	−10.3904	−	22.9955i	−0.749863	−	1.65955i
$193$	10.7568	+	2.88227i	0.774289	+	0.207470i	0.624265	−	0.781212i	$-0.285398\pi$
$193$	10.7568	+	2.88227i	0.774289	+	0.207470i	0.150023	+	0.988682i	$0.452065\pi$
$194$	20.9673	−	2.40842i	1.50536	−	0.172915i
$195$	22.9825	+	10.8860i	1.64581	+	0.779562i
$196$	13.5831	−	3.16219i	0.970221	−	0.225871i
$197$	1.03819	−	3.87460i	0.0739683	−	0.276054i	−0.919029	−	0.394190i	$-0.871025\pi$
$197$	1.03819	−	3.87460i	0.0739683	−	0.276054i	0.992997	+	0.118136i	$0.0376920\pi$
$198$	−4.84947	+	32.6536i	−0.344637	+	2.32059i
$199$	−1.12144	+	1.94240i	−0.0794970	+	0.137693i	−0.903033	−	0.429571i	$-0.858665\pi$
$199$	−1.12144	+	1.94240i	−0.0794970	+	0.137693i	0.823536	+	0.567264i	$0.191998\pi$
$200$	−11.3838	−	8.39108i	−0.804953	−	0.593339i
$201$	−15.4186	−	8.90191i	−1.08754	−	0.627893i
$202$	−3.24364	−	8.21234i	−0.228222	−	0.577819i
$203$	0.0887921	+	0.0887921i	0.00623198	+	0.00623198i
$204$	−7.92578	+	26.0953i	−0.554915	+	1.82704i
$205$	7.87553	+	17.3021i	0.550051	+	1.20843i
$206$	15.7991	−	11.7132i	1.10078	−	0.816096i
$207$	5.69816	+	5.69816i	0.396049	+	0.396049i
$208$	−8.99943	+	11.2699i	−0.623999	+	0.781426i
$209$			6.90135i			0.477377i
$210$	1.58575	+	0.394591i	0.109427	+	0.0272294i
$211$	−12.8705	+	7.43079i	−0.886042	+	0.511557i	−0.872646	−	0.488354i	$-0.837598\pi$
$211$	−12.8705	+	7.43079i	−0.886042	+	0.511557i	−0.0133964	+	0.999910i	$0.504264\pi$
$212$	−11.4961	−	21.5256i	−0.789558	−	1.47839i
$213$	−19.9450	+	19.9450i	−1.36661	+	1.36661i
$214$	8.71282	−	20.0885i	0.595596	−	1.37322i
$215$	−6.96538	+	1.16235i	−0.475035	+	0.0792715i
$216$	−11.8526	−	33.1800i	−0.806468	−	2.25761i
$217$	−0.391019	−	1.45930i	−0.0265441	−	0.0990639i
$218$	−14.2558	−	2.11717i	−0.965526	−	0.143393i
$219$	35.0384	−	20.2294i	2.36768	−	1.36698i
$220$	−14.8909	+	1.98135i	−1.00394	+	0.133583i
$221$	15.3418	−	2.75514i	1.03200	−	0.185331i
$222$	−4.34668	+	5.47483i	−0.291730	+	0.367447i
$223$	−0.369164	+	1.37774i	−0.0247210	+	0.0922602i	−0.977184	−	0.212394i	$-0.931874\pi$
$223$	−0.369164	+	1.37774i	−0.0247210	+	0.0922602i	0.952463	+	0.304654i	$0.0985408\pi$
$224$	−0.424144	+	0.823987i	−0.0283393	+	0.0550550i
$225$	−26.2026	−	22.8194i	−1.74684	−	1.52130i
$226$	−9.24411	+	1.06183i	−0.614909	+	0.0706320i
$227$	−5.00768	−	18.6889i	−0.332371	−	1.24043i	−0.906691	−	0.421796i	$-0.861400\pi$
$227$	−5.00768	−	18.6889i	−0.332371	−	1.24043i	0.574320	−	0.818631i	$-0.305267\pi$
$228$	−6.10590	−	11.4328i	−0.404373	−	0.757158i
$229$	−7.01559			−0.463603			−0.231802	−	0.972763i	$-0.574462\pi$
$229$	−7.01559			−0.463603			−0.231802	+	0.972763i	$0.574462\pi$
$230$	−1.77631	+	3.20806i	−0.117127	+	0.211533i
$231$	1.50323	−	0.867892i	0.0989055	−	0.0571031i
$232$	2.16079	−	0.176048i	0.141863	−	0.0115581i
$233$	2.28199	+	2.28199i	0.149498	+	0.149498i	0.777894	−	0.628396i	$-0.216288\pi$
$233$	2.28199	+	2.28199i	0.149498	+	0.149498i	−0.628396	+	0.777894i	$0.716288\pi$
$234$	−24.2865	+	25.8024i	−1.58766	+	1.68675i
$235$	8.47878	+	10.2951i	0.553095	+	0.671579i
$236$	2.71468	+	2.90044i	0.176711	+	0.188803i
$237$	19.2950	+	5.17008i	1.25334	+	0.335832i
$238$	0.931577	−	0.367946i	0.0603851	−	0.0238504i
$239$		−	21.3250i		−	1.37940i	−0.724095	−	0.689700i	$-0.757742\pi$
$239$		−	21.3250i		−	1.37940i	0.724095	−	0.689700i	$-0.242258\pi$
$240$	22.9153	−	16.4569i	1.47918	−	1.06229i
$241$	−6.14607	−	3.54844i	−0.395903	−	0.228575i	0.288812	−	0.957386i	$-0.406740\pi$
$241$	−6.14607	−	3.54844i	−0.395903	−	0.228575i	−0.684715	+	0.728811i	$0.740073\pi$
$242$	−0.249018	+	0.313649i	−0.0160075	+	0.0201621i
$243$	−5.38532	−	20.0983i	−0.345468	−	1.28930i
$244$	2.31843	−	2.16994i	0.148422	−	0.138916i
$245$	6.45963	+	14.1915i	0.412691	+	0.906660i
$246$	−37.6760	+	4.32769i	−2.40214	+	0.275923i
$247$	−4.22977	+	6.08151i	−0.269134	+	0.386957i
$248$	−23.5732	−	11.1642i	−1.49690	−	0.708930i
$249$	−15.0352	−	26.0417i	−0.952816	−	1.65032i
$250$	6.68858	−	14.3270i	0.423023	−	0.906119i
$251$	−5.22758	−	3.01814i	−0.329962	−	0.190504i	0.325862	−	0.945417i	$-0.394345\pi$
$251$	−5.22758	−	3.01814i	−0.329962	−	0.190504i	−0.655824	+	0.754914i	$0.727679\pi$
$252$	−1.20305	+	1.93317i	−0.0757850	+	0.121778i
$253$	1.00815	+	3.76245i	0.0633816	+	0.236543i
$254$	−8.45674	+	19.4981i	−0.530623	+	1.22342i
$255$	−30.3498	−	2.93628i	−1.90058	−	0.183877i
$256$	6.10251	+	14.7905i	0.381407	+	0.924407i
$257$	19.3375	+	5.18147i	1.20624	+	0.323211i	0.805286	−	0.592886i	$-0.202012\pi$
$257$	19.3375	+	5.18147i	1.20624	+	0.323211i	0.400955	+	0.916098i	$0.368678\pi$
$258$	2.06947	−	13.9347i	0.128840	−	0.867535i
$259$	0.256734			0.0159527
$260$	−14.3363	−	7.38049i	−0.889097	−	0.457719i
$261$	5.32651			0.329703
$262$	0.456511	−	3.07389i	0.0282033	−	0.189906i
$263$	16.9714	+	4.54747i	1.04650	+	0.280409i	0.740805	−	0.671720i	$-0.234444\pi$
$263$	16.9714	+	4.54747i	1.04650	+	0.280409i	0.305696	+	0.952129i	$0.401111\pi$
$264$	5.38003	−	29.4810i	0.331118	−	1.81443i
$265$	21.0606	−	17.3449i	1.29374	−	1.06549i
$266$	−0.189409	+	0.436706i	−0.0116134	+	0.0267762i
$267$	−6.42622	−	23.9830i	−0.393278	−	1.46773i
$268$	9.58442	+	5.96457i	0.585462	+	0.364344i
$269$	5.65892	+	3.26718i	0.345031	+	0.199204i	0.662494	−	0.749067i	$-0.269498\pi$
$269$	5.65892	+	3.26718i	0.345031	+	0.199204i	−0.317464	+	0.948270i	$0.602831\pi$
$270$	33.7563	−	20.3041i	2.05434	−	1.23567i
$271$	1.38207	+	2.39382i	0.0839550	+	0.145414i	0.904945	−	0.425528i	$-0.139911\pi$
$271$	1.38207	+	2.39382i	0.0839550	+	0.145414i	−0.820990	+	0.570942i	$0.806578\pi$
$272$	5.56981	−	16.3710i	0.337719	−	0.992636i
$273$	1.85658	+	0.156526i	0.112365	+	0.00947339i
$274$	7.34736	−	0.843960i	0.443870	−	0.0509855i
$275$	−5.45354	−	15.8852i	−0.328861	−	0.957911i
$276$	−4.99889	−	5.34096i	−0.300898	−	0.321488i
$277$	5.26392	+	19.6452i	0.316278	+	1.18037i	0.922794	+	0.385295i	$0.125900\pi$
$277$	5.26392	+	19.6452i	0.316278	+	1.18037i	−0.606515	+	0.795072i	$0.707433\pi$
$278$	3.69022	−	4.64799i	0.221324	−	0.278768i
$279$	−55.4990	−	32.0424i	−3.32264	−	1.91833i
$280$	−0.996647	−	0.283305i	−0.0595610	−	0.0169307i
$281$		−	2.39574i		−	0.142918i	−0.997444	−	0.0714588i	$-0.977235\pi$
$281$		−	2.39574i		−	0.142918i	0.997444	−	0.0714588i	$-0.0227654\pi$
$282$	−24.7462	+	9.77404i	−1.47361	+	0.582036i
$283$	1.46412	+	0.392310i	0.0870329	+	0.0233204i	0.302073	−	0.953285i	$-0.402321\pi$
$283$	1.46412	+	0.392310i	0.0870329	+	0.0233204i	−0.215040	+	0.976605i	$0.568988\pi$
$284$	13.0577	−	12.2214i	0.774833	−	0.725208i
$285$	11.1858	−	9.21233i	0.662590	−	0.545691i
$286$	−16.4025	+	4.93144i	−0.969903	+	0.291602i
$287$	0.984852	+	0.984852i	0.0581340	+	0.0581340i
$288$	11.9930	+	37.4368i	0.706695	+	2.20599i
$289$	−1.46312	+	0.844730i	−0.0860656	+	0.0496900i
$290$	0.669181	+	2.32964i	0.0392957	+	0.136801i
$291$	−47.0727			−2.75945
$292$	−22.6286	+	12.0852i	−1.32424	+	0.707234i
$293$	3.72018	+	13.8839i	0.217335	+	0.811106i	0.985331	+	0.170652i	$0.0545873\pi$
$293$	3.72018	+	13.8839i	0.217335	+	0.811106i	−0.767996	+	0.640455i	$0.778746\pi$
$294$	−30.9025	+	3.54964i	−1.80227	+	0.207019i
$295$	−2.58088	+	3.61478i	−0.150264	+	0.210460i
$296$	2.86935	−	3.37838i	0.166778	−	0.196364i
$297$	10.8298	−	40.4175i	0.628411	−	2.34526i
$298$	−0.0507852	+	0.0639662i	−0.00294191	+	0.00370546i
$299$	−1.41759	+	3.93338i	−0.0819812	+	0.227473i
$300$	23.0886	+	21.4905i	1.33302	+	1.24075i
$301$	−0.448063	+	0.258689i	−0.0258259	+	0.0149106i
$302$	21.8843	+	3.25010i	1.25930	+	0.187022i
$303$	5.09710	+	19.0226i	0.292821	+	1.09282i
$304$	3.62974	+	7.37322i	0.208180	+	0.422883i
$305$	2.88942	+	2.06299i	0.165448	+	0.118126i
$306$	16.9057	−	38.9783i	0.966434	−	2.22824i
$307$	−7.62821	+	7.62821i	−0.435365	+	0.435365i	−0.890449	−	0.455084i	$-0.849609\pi$
$307$	−7.62821	+	7.62821i	−0.435365	+	0.435365i	0.455084	+	0.890449i	$0.349609\pi$
$308$	−0.970824	+	0.518485i	−0.0553178	+	0.0295434i
$309$	−37.9892	+	21.9331i	−2.16113	+	1.24773i
$310$	7.04181	−	28.2990i	0.399948	−	1.60727i
$311$			16.0897i			0.912363i	0.889887	+	0.456181i	$0.150783\pi$
$311$			16.0897i			0.912363i	−0.889887	+	0.456181i	$0.849217\pi$
$312$	22.8095	−	22.6814i	1.29134	−	1.28408i
$313$	11.6193	+	11.6193i	0.656759	+	0.656759i	0.954612	−	0.297853i	$-0.0962704\pi$
$313$	11.6193	+	11.6193i	0.656759	+	0.656759i	−0.297853	+	0.954612i	$0.596270\pi$
$314$	−12.4725	+	9.24686i	−0.703861	+	0.521831i
$315$	−2.38408	−	0.892608i	−0.134328	−	0.0502928i
$316$	−12.1192	−	3.68090i	−0.681760	−	0.207067i
$317$	−5.28001	−	5.28001i	−0.296555	−	0.296555i	0.543108	−	0.839663i	$-0.317247\pi$
$317$	−5.28001	−	5.28001i	−0.296555	−	0.296555i	−0.839663	+	0.543108i	$0.817247\pi$
$318$	19.9946	+	50.6229i	1.12124	+	2.83879i
$319$	2.22972	+	1.28733i	0.124841	+	0.0720767i
$320$	−14.8669	+	9.94862i	−0.831086	+	0.556145i
$321$	−24.4190	+	42.2949i	−1.36293	+	2.36067i
$322$	−0.0394672	+	0.265750i	−0.00219942	+	0.0148097i
$323$	2.29886	−	8.57947i	0.127912	−	0.477375i
$324$	8.36414	+	35.9279i	0.464675	+	1.99600i
$325$	4.93017	−	17.3405i	0.273477	−	0.961879i
$326$	−9.23428	+	1.06070i	−0.511440	+	0.0587469i
$327$	31.0494	+	8.31967i	1.71704	+	0.460079i
$328$	23.9668	−	1.95267i	1.32334	−	0.107818i
$329$	0.846238	+	0.488576i	0.0466546	+	0.0269361i
$330$	33.4997	−	0.600266i	1.84410	−	0.0330436i
$331$	10.3898	−	17.9957i	0.571078	−	0.989136i	−0.425378	−	0.905016i	$-0.639859\pi$
$331$	10.3898	−	17.9957i	0.571078	−	0.989136i	0.996456	−	0.0841198i	$-0.0268078\pi$
$332$	8.98213	+	16.8183i	0.492958	+	0.923027i
$333$	7.70056	−	7.70056i	0.421988	−	0.421988i
$334$	−22.9455	−	9.95196i	−1.25552	−	0.544547i
$335$	−4.42544	+	11.8200i	−0.241788	+	0.645795i
$336$	1.14955	−	1.71785i	0.0627130	−	0.0937165i
$337$	−21.7455	+	21.7455i	−1.18455	+	1.18455i	−0.206004	+	0.978551i	$0.566046\pi$
$337$	−21.7455	+	21.7455i	−1.18455	+	1.18455i	−0.978551	+	0.206004i	$0.933954\pi$
$338$	−17.4764	−	5.70735i	−0.950593	−	0.310439i
$339$	20.7535			1.12718
$340$	19.1717	+	2.49706i	1.03973	+	0.135422i
$341$	−15.4883	−	26.8265i	−0.838736	−	1.45273i
$342$	7.41751	+	18.7799i	0.401093	+	1.01550i
$343$	1.61869	+	1.61869i	0.0874012	+	0.0874012i
$344$	−1.60360	+	8.78729i	−0.0864606	+	0.473779i
$345$	4.75251	−	6.65636i	0.255866	−	0.358366i
$346$	−3.80863	+	0.437482i	−0.204753	+	0.0235192i
$347$	33.8608	−	9.07296i	1.81774	−	0.487062i	0.821235	−	0.570590i	$-0.193285\pi$
$347$	33.8608	−	9.07296i	1.81774	−	0.487062i	0.996505	+	0.0835278i	$0.0266187\pi$
$348$	−4.83273	−	0.159878i	−0.259061	−	0.00857035i
$349$	8.33710	+	14.4403i	0.446275	+	0.772971i	0.998140	−	0.0609628i	$-0.0194171\pi$
$349$	8.33710	+	14.4403i	0.446275	+	0.772971i	−0.551865	+	0.833933i	$0.686084\pi$
$350$	0.0908795	−	1.15486i	0.00485771	−	0.0617298i
$351$	34.3148	−	28.9786i	1.83159	−	1.54676i
$352$	−4.02750	+	18.5699i	−0.214666	+	0.989779i
$353$	−6.02155	−	1.61347i	−0.320495	−	0.0858762i	0.0949852	−	0.995479i	$-0.469720\pi$
$353$	−6.02155	−	1.61347i	−0.320495	−	0.0858762i	−0.415480	+	0.909602i	$0.636386\pi$
$354$	−5.27701	−	7.11779i	−0.280470	−	0.378306i
$355$	16.2736	+	11.6191i	0.863715	+	0.616675i
$356$	3.56962	+	15.3332i	0.189190	+	0.812659i
$357$	−2.15785	+	0.578195i	−0.114206	+	0.0306013i
$358$	−9.92964	−	25.1402i	−0.524798	−	1.32870i
$359$			15.1568i			0.799944i	0.916527	+	0.399972i	$0.130980\pi$
$359$			15.1568i			0.799944i	−0.916527	+	0.399972i	$0.869020\pi$
$360$	−38.3912	+	21.3962i	−2.02340	+	1.12768i
$361$	−7.38939	−	12.7988i	−0.388916	−	0.673621i
$362$	−12.5978	−	1.87093i	−0.662125	−	0.0983338i
$363$	0.631608	−	0.631608i	0.0331508	−	0.0331508i
$364$	−1.17327	−	0.138117i	−0.0614960	−	0.00723928i
$365$	−18.2337	−	22.1397i	−0.954395	−	1.15885i
$366$	−5.68951	+	4.21810i	−0.297395	+	0.220484i
$367$	−7.93725	+	29.6222i	−0.414321	+	1.54627i	0.371871	+	0.928284i	$0.378716\pi$
$367$	−7.93725	+	29.6222i	−0.414321	+	1.54627i	−0.786192	+	0.617982i	$0.787950\pi$
$368$	3.05592	+	3.48947i	0.159301	+	0.181901i
$369$	59.0799			3.07557
$370$	4.33541	+	2.40053i	0.225387	+	0.124798i
$371$	0.999472	−	1.73114i	0.0518900	−	0.0898761i
$372$	49.3924	+	30.7378i	2.56087	+	1.59368i
$373$	−13.9598	+	3.74051i	−0.722810	+	0.193676i	−0.601425	−	0.798929i	$-0.705400\pi$
$373$	−13.9598	+	3.74051i	−0.722810	+	0.193676i	−0.121385	+	0.992606i	$0.538734\pi$
$374$	16.4973	−	12.2308i	0.853054	−	0.632440i
$375$	−18.4672	+	30.0436i	−0.953642	+	1.55145i
$376$	15.8871	−	5.67520i	0.819313	−	0.292676i
$377$	1.17585	+	2.50098i	0.0605594	+	0.128807i
$378$	1.79456	−	2.26033i	0.0923021	−	0.116259i
$379$	−13.2319	+	7.63943i	−0.679676	+	0.392411i	−0.799733	−	0.600356i	$-0.795026\pi$
$379$	−13.2319	+	7.63943i	−0.679676	+	0.392411i	0.120057	+	0.992767i	$0.461692\pi$
$380$	−7.28181	+	5.60353i	−0.373549	+	0.287455i
$381$	23.7013	−	41.0518i	1.21425	−	2.10315i
$382$	0.612131	+	0.485994i	0.0313193	+	0.0248656i
$383$	1.98917	−	0.532995i	0.101642	−	0.0272348i	−0.207640	−	0.978205i	$-0.566578\pi$
$383$	1.98917	−	0.532995i	0.101642	−	0.0272348i	0.309281	+	0.950971i	$0.399912\pi$
$384$	−9.75754	−	34.3263i	−0.497937	−	1.75171i
$385$	−0.782269	−	0.949848i	−0.0398681	−	0.0484087i
$386$	14.4485	+	6.26663i	0.735411	+	0.318963i
$387$	−5.68013	+	21.1985i	−0.288737	+	1.07758i
$388$	29.8309	+	0.986875i	1.51443	+	0.0501010i
$389$			30.7357i			1.55836i	0.626799	+	0.779181i	$0.284365\pi$
$389$			30.7357i			1.55836i	−0.626799	+	0.779181i	$0.715635\pi$
$390$	29.8880	+	20.0027i	1.51344	+	1.01288i
$391$		−	5.01314i		−	0.253525i
$392$	19.6579	−	1.60161i	0.992876	−	0.0808934i
$393$	−1.79392	+	6.69498i	−0.0904911	+	0.337717i
$394$	2.25725	−	5.20437i	0.113718	−	0.262193i
$395$	1.36367	−	14.0951i	0.0686138	−	0.709200i
$396$	−13.5676	+	44.6707i	−0.681796	+	2.24479i
$397$	−8.35399	+	2.23844i	−0.419275	+	0.112344i	−0.462287	−	0.886730i	$-0.652971\pi$
$397$	−8.35399	+	2.23844i	−0.419275	+	0.112344i	0.0430126	+	0.999075i	$0.486304\pi$
$398$	−1.97229	+	2.48418i	−0.0988618	+	0.124521i
$399$	0.530846	−	0.919452i	0.0265755	−	0.0460302i
$400$	−14.1812	−	14.1030i	−0.709058	−	0.705150i
$401$	−14.1843	+	8.18931i	−0.708330	+	0.408955i	−0.810442	−	0.585818i	$-0.800773\pi$
$401$	−14.1843	+	8.18931i	−0.708330	+	0.408955i	0.102112	+	0.994773i	$0.467440\pi$
$402$	−19.7192	−	15.6558i	−0.983505	−	0.780842i
$403$	2.79334	−	33.1322i	0.139146	−	1.65043i
$404$	−2.83132	−	12.1619i	−0.140864	−	0.605076i
$405$	−37.5371	+	17.0860i	−1.86524	+	0.849013i
$406$	0.105762	+	0.142655i	0.00524889	+	0.00707986i
$407$	5.08463	−	1.36242i	0.252036	−	0.0675327i
$408$	−16.5084	+	34.8574i	−0.817290	+	1.72570i
$409$	8.64649	−	14.9762i	0.427541	−	0.740523i	−0.569113	−	0.822260i	$-0.692713\pi$
$409$	8.64649	−	14.9762i	0.427541	−	0.740523i	0.996654	+	0.0817363i	$0.0260465\pi$
$410$	7.42233	+	25.8396i	0.366563	+	1.27613i
$411$	−16.4952			−0.813648
$412$	24.5343	−	13.1030i	1.20872	−	0.645537i
$413$	−0.0842233	+	0.314326i	−0.00414436	+	0.0154670i
$414$	6.78720	+	9.15478i	0.333573	+	0.449933i
$415$	−16.4550	+	13.5519i	−0.807743	+	0.665235i
$416$	−14.9304	+	13.8955i	−0.732021	+	0.681282i
$417$	−9.35986	+	9.35986i	−0.458354	+	0.458354i
$418$	−1.43375	+	9.65410i	−0.0701272	+	0.472198i
$419$	−7.42077	−	12.8531i	−0.362528	−	0.627917i	0.625848	−	0.779945i	$-0.284753\pi$
$419$	−7.42077	−	12.8531i	−0.362528	−	0.627917i	−0.988376	+	0.152028i	$0.951420\pi$
$420$	2.13628	+	0.881421i	0.104240	+	0.0430089i
$421$		−	23.5194i		−	1.14627i	−0.819462	−	0.573134i	$-0.805728\pi$
$421$		−	23.5194i		−	1.14627i	0.819462	−	0.573134i	$-0.194272\pi$
$422$	−19.5479	+	7.72087i	−0.951578	+	0.375846i
$423$	40.0368	−	10.7278i	1.94666	−	0.521605i
$424$	−11.6097	−	32.4999i	−0.563815	−	1.57834i
$425$	1.48822	+	21.5644i	0.0721891	+	1.04603i
$426$	−32.0441	+	23.7570i	−1.55254	+	1.15103i
$427$	0.251252	+	0.0673227i	0.0121589	+	0.00325798i
$428$	16.3615	−	26.2912i	0.790863	−	1.27083i
$429$	37.6002	−	6.75237i	1.81536	−	0.326008i
$430$	−9.98514	+	0.178919i	−0.481526	+	0.00862825i
$431$	−13.4711	−	23.3326i	−0.648879	−	1.12389i	−0.983391	−	0.181500i	$-0.941905\pi$
$431$	−13.4711	−	23.3326i	−0.648879	−	1.12389i	0.334512	−	0.942391i	$-0.391428\pi$
$432$	−9.68713	−	48.8769i	−0.466072	−	2.35159i
$433$	23.7791	−	6.37160i	1.14275	−	0.306200i	0.362695	−	0.931908i	$-0.381857\pi$
$433$	23.7791	−	6.37160i	1.14275	−	0.306200i	0.780057	+	0.625708i	$0.215190\pi$
$434$	−0.243815	−	2.12261i	−0.0117035	−	0.101888i
$435$	−0.889840	−	5.33237i	−0.0426646	−	0.255668i
$436$	−19.5022	−	5.92329i	−0.933987	−	0.283674i
$437$	1.68467	+	1.68467i	0.0805887	+	0.0805887i
$438$	53.2169	−	21.0192i	2.54280	−	1.00433i
$439$	0.831387	+	1.44000i	0.0396799	+	0.0687276i	0.885183	−	0.465242i	$-0.154033\pi$
$439$	0.831387	+	1.44000i	0.0396799	+	0.0687276i	−0.845503	+	0.533970i	$0.820700\pi$
$440$	−21.2420	−	0.321918i	−1.01267	−	0.0153469i
$441$	48.4583			2.30754
$442$	22.0336	−	0.666822i	1.04803	−	0.0317175i
$443$	−18.5752	+	18.5752i	−0.882532	+	0.882532i	−0.993791	−	0.111259i	$-0.964512\pi$
$443$	−18.5752	+	18.5752i	−0.882532	+	0.882532i	0.111259	+	0.993791i	$0.464512\pi$
$444$	−7.21784	+	6.75556i	−0.342543	+	0.320605i
$445$	−16.0200	+	7.29193i	−0.759420	+	0.345671i
$446$	−0.802637	+	1.85058i	−0.0380060	+	0.0876277i
$447$	0.128812	−	0.128812i	0.00609257	−	0.00609257i
$448$	−0.764506	+	1.06454i	−0.0361195	+	0.0502946i
$449$	−11.2483	+	19.4826i	−0.530838	+	0.919439i	0.468514	+	0.883456i	$0.344790\pi$
$449$	−11.2483	+	19.4826i	−0.530838	+	0.919439i	−0.999352	+	0.0359829i	$0.988544\pi$
$450$	−31.9133	−	37.3650i	−1.50441	−	1.76140i
$451$	24.7313	+	14.2787i	1.16455	+	0.672355i
$452$	−13.1519	−	0.435096i	−0.618614	−	0.0204652i
$453$	−47.6645	−	12.7717i	−2.23947	−	0.600065i
$454$	−3.12248	−	27.1837i	−0.146545	−	1.27580i
$455$	−0.107187	−	1.31646i	−0.00502499	−	0.0617164i
$456$	−6.16620	−	17.2616i	−0.288759	−	0.808346i
$457$	3.04489	−	11.3637i	0.142434	−	0.531571i	−0.857422	−	0.514614i	$-0.827935\pi$
$457$	3.04489	−	11.3637i	0.142434	−	0.531571i	0.999856	−	0.0169575i	$-0.00539801\pi$
$458$	−9.81390	−	1.45749i	−0.458574	−	0.0681039i
$459$	−26.9264	+	46.6379i	−1.25682	+	2.17687i
$460$	−3.15131	+	4.11863i	−0.146930	+	0.192032i
$461$	−0.245659	−	0.141831i	−0.0114415	−	0.00660574i	0.494268	−	0.869309i	$-0.335436\pi$
$461$	−0.245659	−	0.141831i	−0.0114415	−	0.00660574i	−0.505710	+	0.862704i	$0.668769\pi$
$462$	2.28313	−	0.901772i	0.106221	−	0.0419543i
$463$	−9.78891	−	9.78891i	−0.454929	−	0.454929i	0.442058	−	0.896987i	$-0.354249\pi$
$463$	−9.78891	−	9.78891i	−0.454929	−	0.454929i	−0.896987	+	0.442058i	$0.854249\pi$
$464$	3.05924	+	0.202636i	0.142022	+	0.00940712i
$465$	−22.8061	+	60.9131i	−1.05761	+	2.82478i
$466$	2.71813	+	3.66630i	0.125915	+	0.169838i
$467$	7.98810	+	7.98810i	0.369645	+	0.369645i	0.867348	−	0.497703i	$-0.165823\pi$
$467$	7.98810	+	7.98810i	0.369645	+	0.369645i	−0.497703	+	0.867348i	$0.665823\pi$
$468$	−39.3341	+	31.0487i	−1.81822	+	1.43522i
$469$			0.924704i			0.0426989i
$470$	9.72191	+	16.1630i	0.448438	+	0.745544i
$471$	29.9902	−	17.3148i	1.38188	−	0.797826i
$472$	3.19492	+	4.62131i	0.147058	+	0.212713i
$473$	−7.50110	+	7.50110i	−0.344901	+	0.344901i
$474$	25.9171	+	11.2408i	1.19041	+	0.516307i
$475$	−7.74684	−	6.74661i	−0.355449	−	0.309556i
$476$	1.37960	−	0.321174i	0.0632337	−	0.0147210i
$477$	−21.9457	−	81.9027i	−1.00483	−	3.75006i
$478$	4.43026	−	29.8309i	0.202636	−	1.36443i
$479$	−2.34517	+	1.35398i	−0.107154	+	0.0618651i	−0.552619	−	0.833434i	$-0.686372\pi$
$479$	−2.34517	+	1.35398i	−0.107154	+	0.0618651i	0.445466	+	0.895299i	$0.353038\pi$
$480$	35.4745	−	18.2604i	1.61918	−	0.833468i
$481$	5.31561	+	1.91575i	0.242371	+	0.0873505i
$482$	−7.86037	−	6.24065i	−0.358030	−	0.284254i
$483$	0.155091	−	0.578809i	0.00705690	−	0.0263367i
$484$	−0.413504	+	0.387021i	−0.0187956	+	0.0175918i
$485$	5.49270	+	32.9150i	0.249411	+	1.49459i
$486$	−3.35795	−	29.2337i	−0.152320	−	1.32607i
$487$	2.51813	+	9.39781i	0.114108	+	0.425855i	0.999219	−	0.0395247i	$-0.0125844\pi$
$487$	2.51813	+	9.39781i	0.114108	+	0.425855i	−0.885111	+	0.465380i	$0.845918\pi$
$488$	3.69398	−	2.55382i	0.167219	−	0.115606i
$489$	20.7314			0.937509
$490$	6.08792	+	21.1940i	0.275024	+	0.957449i
$491$	1.40495	−	0.811148i	0.0634045	−	0.0366066i	−0.467963	−	0.883748i	$-0.655012\pi$
$491$	1.40495	−	0.811148i	0.0634045	−	0.0366066i	0.531367	+	0.847142i	$0.321678\pi$
$492$	−53.6030	−	1.77331i	−2.41661	−	0.0799470i
$493$	−2.34309	−	2.34309i	−0.105527	−	0.105527i
$494$	−7.18034	+	7.62851i	−0.323059	+	0.343223i
$495$	−51.9536	−	5.02641i	−2.33514	−	0.225921i
$496$	−30.6565	−	20.5147i	−1.37652	−	0.921135i
$497$	1.41509	+	0.379171i	0.0634753	+	0.0170082i
$498$	−15.6221	−	39.5525i	−0.700044	−	1.77239i
$499$			31.4652i			1.40858i	0.709914	+	0.704289i	$0.248734\pi$
$499$			31.4652i			1.40858i	−0.709914	+	0.704289i	$0.751266\pi$
$500$	12.3329	−	18.6521i	0.551543	−	0.834146i
$501$	48.3101	+	27.8919i	2.15834	+	1.24612i
$502$	−6.68569	−	5.30802i	−0.298397	−	0.236909i
$503$	1.56391	+	5.83660i	0.0697314	+	0.260241i	0.991987	−	0.126339i	$-0.0403228\pi$
$503$	1.56391	+	5.83660i	0.0697314	+	0.260241i	−0.922256	+	0.386580i	$0.873656\pi$
$504$	−2.08453	+	2.45432i	−0.0928522	+	0.109324i
$505$	12.7066	−	5.78375i	0.565436	−	0.257374i
$506$	0.628618	+	5.47263i	0.0279455	+	0.243288i
$507$	37.2720	+	17.0946i	1.65531	+	0.759197i
$508$	−15.8806	+	25.5184i	−0.704588	+	1.13220i
$509$	−6.49123	−	11.2431i	−0.287719	−	0.498344i	0.685546	−	0.728029i	$-0.259564\pi$
$509$	−6.49123	−	11.2431i	−0.287719	−	0.498344i	−0.973265	+	0.229686i	$0.926230\pi$
$510$	−41.8454	−	10.4126i	−1.85295	−	0.461080i
$511$	−1.81984	−	1.05069i	−0.0805051	−	0.0464796i
$512$	5.46390	+	21.9578i	0.241472	+	0.970408i
$513$	−6.62407	−	24.7214i	−0.292460	−	1.09147i
$514$	25.9743	+	11.2656i	1.14568	+	0.496903i
$515$	19.7692	+	24.0042i	0.871136	+	1.05775i
$516$	5.78985	−	19.0629i	0.254884	−	0.839196i
$517$	19.3525	+	5.18549i	0.851122	+	0.228057i
$518$	0.359138	+	0.0533365i	0.0157796	+	0.00234347i
$519$	8.55059			0.375329
$520$	−18.5213	−	13.3027i	−0.812212	−	0.583362i
$521$	25.1504			1.10186			0.550929	−	0.834552i	$-0.314274\pi$
$521$	25.1504			1.10186			0.550929	+	0.834552i	$0.314274\pi$
$522$	7.45110	+	1.10658i	0.326126	+	0.0484337i
$523$	−14.8595	−	3.98160i	−0.649761	−	0.174103i	−0.0811405	−	0.996703i	$-0.525856\pi$
$523$	−14.8595	−	3.98160i	−0.649761	−	0.174103i	−0.568621	+	0.822600i	$0.692523\pi$
$524$	1.27720	−	4.20513i	0.0557947	−	0.183702i
$525$	−0.495309	+	2.53583i	−0.0216171	+	0.110673i
$526$	22.7960	+	9.88712i	0.993955	+	0.431099i
$527$	10.3184	+	38.5087i	0.449476	+	1.67747i
$528$	13.6506	−	40.1224i	0.594068	−	1.74610i
$529$	−18.7540	−	10.8277i	−0.815393	−	0.470768i
$530$	33.0644	−	19.8880i	1.43623	−	0.863878i
$531$	6.90175	+	11.9542i	0.299511	+	0.518768i
$532$	−0.355684	+	0.571546i	−0.0154208	+	0.0247796i
$533$	13.0421	+	27.7400i	0.564918	+	1.20155i
$534$	−4.00699	−	34.8841i	−0.173400	−	1.50958i
$535$	32.4236	+	12.1395i	1.40179	+	0.524836i
$536$	12.1682	+	10.3348i	0.525588	+	0.446396i
$537$	15.6036	+	58.2333i	0.673343	+	2.51295i
$538$	7.23735	+	5.74601i	0.312024	+	0.247728i
$539$	20.2851	+	11.7116i	0.873739	+	0.504453i
$540$	51.4389	−	21.3900i	2.21358	−	0.920478i
$541$			12.5555i			0.539804i	0.962888	+	0.269902i	$0.0869913\pi$
$541$			12.5555i			0.539804i	−0.962888	+	0.269902i	$0.913009\pi$
$542$	1.43603	+	3.63577i	0.0616826	+	0.156170i
$543$	27.4382	+	7.35204i	1.17749	+	0.315506i
$544$	11.1925	−	21.7437i	0.479875	−	0.932255i
$545$	2.19442	−	22.6817i	0.0939985	−	0.971579i
$546$	2.56460	+	0.604664i	0.109755	+	0.0258772i
$547$	−20.8999	−	20.8999i	−0.893617	−	0.893617i	0.101244	−	0.994862i	$-0.467718\pi$
$547$	−20.8999	−	20.8999i	−0.893617	−	0.893617i	−0.994862	+	0.101244i	$0.967718\pi$
$548$	10.4533	+	0.345821i	0.446544	+	0.0147727i
$549$	9.55542	−	5.51682i	0.407815	−	0.235452i
$550$	−4.32866	−	23.3543i	−0.184575	−	0.995829i
$551$	1.57479			0.0670884
$552$	−5.88322	−	8.50983i	−0.250407	−	0.362202i
$553$	−0.268526	−	1.00215i	−0.0114189	−	0.0426159i
$554$	3.28225	+	28.5747i	0.139450	+	1.21402i
$555$	−8.99549	−	6.42259i	−0.381837	−	0.272624i
$556$	6.12776	−	5.73530i	0.259875	−	0.243231i
$557$	4.74177	−	17.6965i	0.200915	−	0.749826i	−0.789741	−	0.613441i	$-0.789785\pi$
$557$	4.74177	−	17.6965i	0.200915	−	0.749826i	0.990656	−	0.136385i	$-0.0435484\pi$
$558$	−70.9792	−	56.3531i	−3.00479	−	2.38562i
$559$	−11.2074	+	2.01265i	−0.474021	+	0.0851262i
$560$	−1.33532	−	0.603361i	−0.0564277	−	0.0254966i
$561$	−39.6680	+	22.9023i	−1.67478	+	0.966937i
$562$	0.497714	−	3.35133i	0.0209948	−	0.141367i
$563$	7.29035	+	27.2080i	0.307252	+	1.14668i	0.930990	+	0.365045i	$0.118947\pi$
$563$	7.29035	+	27.2080i	0.307252	+	1.14668i	−0.623738	+	0.781633i	$0.714387\pi$
$564$	−36.6473	+	8.53161i	−1.54313	+	0.359245i
$565$	−2.42163	−	14.5117i	−0.101879	−	0.610510i
$566$	1.96661	+	0.852961i	0.0826629	+	0.0358526i
$567$	−2.13665	+	2.13665i	−0.0897308	+	0.0897308i
$568$	20.8051	−	14.3835i	0.872961	−	0.603516i
$569$	−23.7981	+	13.7398i	−0.997668	+	0.576004i	−0.907557	−	0.419928i	$-0.862055\pi$
$569$	−23.7981	+	13.7398i	−0.997668	+	0.576004i	−0.0901103	+	0.995932i	$0.528722\pi$
$570$	17.5614	−	10.5630i	0.735565	−	0.442436i
$571$		−	47.3246i		−	1.98047i	−0.139401	−	0.990236i	$-0.544518\pi$
$571$		−	47.3246i		−	1.98047i	0.139401	−	0.990236i	$-0.455482\pi$
$572$	−23.9696	+	3.49083i	−1.00222	+	0.145959i
$573$	−1.23267	−	1.23267i	−0.0514957	−	0.0514957i
$574$	1.17308	+	1.58228i	0.0489633	+	0.0660432i
$575$	−5.20893	−	2.54643i	−0.217228	−	0.106194i
$576$	8.99918	+	54.8608i	0.374966	+	2.28587i
$577$	−28.3643	−	28.3643i	−1.18082	−	1.18082i	−0.979532	−	0.201287i	$-0.935488\pi$
$577$	−28.3643	−	28.3643i	−1.18082	−	1.18082i	−0.201287	−	0.979532i	$-0.564512\pi$
$578$	−2.22220	+	0.877707i	−0.0924314	+	0.0365078i
$579$	−30.4203	−	17.5632i	−1.26423	−	0.729901i
$580$	0.452117	+	3.39789i	0.0187731	+	0.141090i
$581$	−0.780904	+	1.35257i	−0.0323974	+	0.0561139i
$582$	−65.8486	−	9.77934i	−2.72951	−	0.405367i
$583$	10.6079	−	39.5891i	0.439333	−	1.63961i
$584$	−34.1653	+	12.2046i	−1.41377	+	0.505029i
$585$	−42.7012	−	36.2712i	−1.76548	−	1.49963i
$586$	2.31968	+	20.1947i	0.0958249	+	0.834234i
$587$	−22.2127	−	5.95187i	−0.916816	−	0.245660i	−0.230592	−	0.973050i	$-0.574066\pi$
$587$	−22.2127	−	5.95187i	−0.916816	−	0.245660i	−0.686224	+	0.727390i	$0.740733\pi$
$588$	−43.9660	−	1.45450i	−1.81313	−	0.0599825i
$589$	−16.4084	−	9.47339i	−0.676096	−	0.390344i
$590$	−4.36128	+	4.52043i	−0.179551	+	0.186103i
$591$	−6.32627	+	10.9574i	−0.260228	+	0.450728i
$592$	4.71571	−	4.12981i	0.193815	−	0.169734i
$593$	−5.59820	+	5.59820i	−0.229891	+	0.229891i	−0.812647	−	0.582756i	$-0.801974\pi$
$593$	−5.59820	+	5.59820i	−0.229891	+	0.229891i	0.582756	+	0.812647i	$0.301974\pi$
$594$	23.5463	−	54.2890i	0.966116	−	2.22750i
$595$	0.656087	+	1.44139i	0.0268969	+	0.0590911i
$596$	−0.0843309	+	0.0789299i	−0.00345433	+	0.00323309i
$597$	5.00250	−	5.00250i	0.204739	−	0.204739i
$598$	−2.80018	+	5.20778i	−0.114508	+	0.212962i
$599$	−13.9664			−0.570653			−0.285326	−	0.958430i	$-0.592102\pi$
$599$	−13.9664			−0.570653			−0.285326	+	0.958430i	$0.592102\pi$
$600$	27.8333	+	34.8591i	1.13629	+	1.42312i
$601$	−17.0086	−	29.4598i	−0.693797	−	1.20169i	−0.970585	−	0.240760i	$-0.922603\pi$
$601$	−17.0086	−	29.4598i	−0.693797	−	1.20169i	0.276788	−	0.960931i	$-0.410730\pi$
$602$	−0.680525	+	0.268788i	−0.0277361	+	0.0109550i
$603$	27.7358	+	27.7358i	1.12949	+	1.12949i
$604$	29.9382	+	9.09293i	1.21817	+	0.369986i
$605$	−0.515344	−	0.367945i	−0.0209517	−	0.0149591i
$606$	3.17824	+	27.6691i	0.129107	+	1.12398i
$607$	−7.35319	+	1.97028i	−0.298457	+	0.0799712i	−0.404940	−	0.914343i	$-0.632708\pi$
$607$	−7.35319	+	1.97028i	−0.298457	+	0.0799712i	0.106483	+	0.994314i	$0.466041\pi$
$608$	3.54575	+	11.0683i	0.143799	+	0.448877i
$609$	−0.198041	−	0.343017i	−0.00802501	−	0.0138997i
$610$	3.61334	+	3.48613i	0.146300	+	0.141149i
$611$	13.8754	+	16.4304i	0.561338	+	0.664704i
$612$	31.7466	−	51.0134i	1.28328	−	2.06209i
$613$	−26.7684	−	7.17258i	−1.08117	−	0.289698i	−0.326093	−	0.945338i	$-0.605732\pi$
$613$	−26.7684	−	7.17258i	−1.08117	−	0.289698i	−0.755074	+	0.655640i	$0.772399\pi$
$614$	−12.2556	+	9.08612i	−0.494597	+	0.366686i
$615$	−9.86981	−	59.1449i	−0.397989	−	2.38495i
$616$	−1.46577	+	0.523605i	−0.0590576	+	0.0210967i
$617$	32.5157	−	8.71256i	1.30903	−	0.350754i	0.464175	−	0.885744i	$-0.346351\pi$
$617$	32.5157	−	8.71256i	1.30903	−	0.350754i	0.844859	+	0.534989i	$0.179684\pi$
$618$	−57.6985	+	22.7893i	−2.32097	+	0.916719i
$619$		−	26.6411i		−	1.07080i	−0.844599	−	0.535399i	$-0.820161\pi$
$619$		−	26.6411i		−	1.07080i	0.844599	−	0.535399i	$-0.179839\pi$
$620$	15.7297	−	38.1237i	0.631720	−	1.53109i
$621$	−7.22257	−	12.5099i	−0.289832	−	0.502003i
$622$	−3.34263	+	22.5074i	−0.134027	+	0.902465i
$623$	−0.911872	+	0.911872i	−0.0365334	+	0.0365334i
$624$	36.6197	−	26.9897i	1.46596	−	1.08045i
$625$	23.1625	+	9.40732i	0.926501	+	0.376293i
$626$	13.8399	+	18.6677i	0.553155	+	0.746113i
$627$	5.63412	−	21.0268i	0.225005	−	0.839730i
$628$	−19.3684	+	10.3440i	−0.772883	+	0.412771i
$629$	−6.77482			−0.270130
$630$	−3.14959	−	1.74394i	−0.125482	−	0.0694801i
$631$	−18.1187	+	31.3825i	−0.721295	+	1.24932i	0.239186	+	0.970974i	$0.423119\pi$
$631$	−18.1187	+	31.3825i	−0.721295	+	1.24932i	−0.960481	+	0.278345i	$0.910214\pi$
$632$	−16.1885	−	7.66687i	−0.643945	−	0.304972i
$633$	45.2798	−	12.1327i	1.79971	−	0.482230i
$634$	−6.28913	−	8.48297i	−0.249773	−	0.336902i
$635$	−31.4706	−	11.7827i	−1.24887	−	0.467582i
$636$	17.4530	+	74.9688i	0.692055	+	2.97270i
$637$	10.6974	+	22.7528i	0.423846	+	0.901499i
$638$	2.85165	+	2.26404i	0.112898	+	0.0896340i
$639$	53.8175	−	31.0715i	2.12899	−	1.22917i
$640$	−22.8637	+	10.8282i	−0.903768	+	0.428023i
$641$	−0.857438	+	1.48513i	−0.0338668	+	0.0586589i	−0.882462	−	0.470384i	$-0.844116\pi$
$641$	−0.857438	+	1.48513i	−0.0338668	+	0.0586589i	0.848595	+	0.529043i	$0.177449\pi$
$642$	−42.9458	+	54.0921i	−1.69493	+	2.13484i
$643$	13.2883	−	3.56058i	0.524039	−	0.140416i	0.0129046	−	0.999917i	$-0.495892\pi$
$643$	13.2883	−	3.56058i	0.524039	−	0.140416i	0.511134	+	0.859501i	$0.329226\pi$
$644$	−0.110419	+	0.363551i	−0.00435112	+	0.0143259i
$645$	22.1708	+	2.14498i	0.872974	+	0.0844586i
$646$	4.99820	−	11.5240i	0.196651	−	0.453405i
$647$	−1.11465	+	4.15992i	−0.0438213	+	0.163543i	−0.984369	−	0.176118i	$-0.943646\pi$
$647$	−1.11465	+	4.15992i	−0.0438213	+	0.163543i	0.940548	+	0.339662i	$0.110313\pi$
$648$	4.23633	+	51.9962i	0.166419	+	2.04260i
$649$			6.67217i			0.261906i
$650$	10.4992	−	23.2329i	0.411811	−	0.911269i
$651$			4.76537i			0.186770i
$652$	−13.1379	−	0.434633i	−0.514521	−	0.0170215i
$653$	2.65151	−	9.89557i	0.103762	−	0.387243i	−0.894440	−	0.447188i	$-0.852426\pi$
$653$	2.65151	−	9.89557i	0.103762	−	0.387243i	0.998202	+	0.0599442i	$0.0190923\pi$
$654$	41.7057	+	18.0887i	1.63082	+	0.707322i
$655$	4.89072	+	0.473168i	0.191096	+	0.0184882i
$656$	33.9321	+	2.24756i	1.32483	+	0.0877527i
$657$	−86.0995	+	23.0703i	−3.35906	+	0.900058i
$658$	1.08228	+	0.859261i	0.0421915	+	0.0334975i
$659$	5.49476	−	9.51720i	0.214045	−	0.370737i	−0.738932	−	0.673781i	$-0.764669\pi$
$659$	5.49476	−	9.51720i	0.214045	−	0.370737i	0.952977	+	0.303043i	$0.0980026\pi$
$660$	46.9865	+	6.11987i	1.82895	+	0.238215i
$661$	−7.87543	+	4.54688i	−0.306319	+	0.176853i	−0.645278	−	0.763948i	$-0.723258\pi$
$661$	−7.87543	+	4.54688i	−0.306319	+	0.176853i	0.338959	+	0.940801i	$0.389925\pi$
$662$	18.2727	−	23.0152i	0.710187	−	0.894513i
$663$	−48.9922	−	4.13048i	−1.90270	−	0.160415i
$664$	9.07083	+	25.3927i	0.352016	+	0.985429i
$665$	−0.704858	−	0.263901i	−0.0273332	−	0.0102336i
$666$	12.3719	−	9.17230i	0.479401	−	0.355420i
$667$	0.858539	−	0.230045i	0.0332428	−	0.00890737i
$668$	−30.0303	−	18.6884i	−1.16191	−	0.723078i
$669$	2.24951	−	3.89627i	0.0869711	−	0.150638i
$670$	−8.64622	+	15.6152i	−0.334033	+	0.603270i
$671$	5.33331			0.205890
$672$	1.96495	−	2.16423i	0.0757997	−	0.0834871i
$673$	8.78429	−	32.7834i	0.338609	−	1.26371i	−0.561293	−	0.827617i	$-0.689696\pi$
$673$	8.78429	−	32.7834i	0.338609	−	1.26371i	0.899903	−	0.436091i	$-0.143637\pi$
$674$	−34.9368	+	25.9016i	−1.34572	+	0.997691i
$675$	34.7821	+	51.6679i	1.33876	+	1.98870i
$676$	−23.2616	−	11.6146i	−0.894677	−	0.446714i
$677$	16.8240	−	16.8240i	0.646600	−	0.646600i	−0.305570	−	0.952170i	$-0.598847\pi$
$677$	16.8240	−	16.8240i	0.646600	−	0.646600i	0.952170	+	0.305570i	$0.0988469\pi$
$678$	29.0315	+	4.31154i	1.11495	+	0.165584i
$679$	1.22244	+	2.11733i	0.0469130	+	0.0812557i
$680$	26.3000	+	7.47598i	1.00856	+	0.286691i
$681$			61.0289i			2.33863i
$682$	−16.0929	−	40.7444i	−0.616229	−	1.56018i
$683$	−1.44830	+	0.388072i	−0.0554178	+	0.0148492i	−0.286421	−	0.958104i	$-0.592466\pi$
$683$	−1.44830	+	0.388072i	−0.0554178	+	0.0148492i	0.231004	+	0.972953i	$0.425799\pi$
$684$	6.47462	+	27.8116i	0.247563	+	1.06340i
$685$	1.92475	+	11.5341i	0.0735410	+	0.440695i
$686$	1.92806	+	2.60062i	0.0736136	+	0.0992923i
$687$	21.3749	+	5.72737i	0.815502	+	0.218513i
$688$	−4.06879	+	11.9591i	−0.155121	+	0.455938i
$689$	33.6115	−	28.3847i	1.28050	−	1.08137i
$690$	8.03100	−	8.32406i	0.305735	−	0.316891i
$691$	10.9649	+	18.9917i	0.417124	+	0.722480i	0.995649	−	0.0931851i	$-0.0297048\pi$
$691$	10.9649	+	18.9917i	0.417124	+	0.722480i	−0.578525	+	0.815665i	$0.696372\pi$
$692$	−5.41868	−	0.179262i	−0.205987	−	0.00681453i
$693$	−3.69388	+	0.989771i	−0.140319	+	0.0375983i
$694$	49.2517	−	5.65734i	1.86957	−	0.214750i
$695$	7.63693	+	5.45262i	0.289685	+	0.206829i
$696$	−6.72715	−	1.22765i	−0.254992	−	0.0465338i
$697$	−25.9887	−	25.9887i	−0.984393	−	0.984393i
$698$	8.66256	+	21.9321i	0.327883	+	0.830143i
$699$	−5.08973	−	8.81567i	−0.192511	−	0.333439i
$700$	0.367050	−	1.59662i	0.0138732	−	0.0603465i
$701$	−10.0746			−0.380511			−0.190256	−	0.981735i	$-0.560932\pi$
$701$	−10.0746			−0.380511			−0.190256	+	0.981735i	$0.560932\pi$
$702$	54.0223	−	33.4085i	2.03894	−	1.26092i
$703$	2.27668	−	2.27668i	0.0858668	−	0.0858668i
$704$	−9.49184	+	25.1402i	−0.357737	+	0.947506i
$705$	−17.4281	−	38.2887i	−0.656382	−	1.44204i
$706$	−8.08817	−	3.50801i	−0.304402	−	0.132026i
$707$	0.723271	−	0.723271i	0.0272014	−	0.0272014i
$708$	−5.90313	−	11.0532i	−0.221853	−	0.415403i
$709$	11.8760	−	20.5697i	0.446011	−	0.772513i	−0.552111	−	0.833770i	$-0.686178\pi$
$709$	11.8760	−	20.5697i	0.446011	−	0.772513i	0.998122	+	0.0612572i	$0.0195110\pi$
$710$	20.3509	+	19.6344i	0.763755	+	0.736866i
$711$	−38.1131	−	22.0046i	−1.42935	−	0.825237i
$712$	1.80797	+	22.1908i	0.0677565	+	0.831634i
$713$	−10.3293	−	2.76774i	−0.386836	−	0.103653i
$714$	−3.13868	+	0.360527i	−0.117462	+	0.0134924i
$715$	−9.10892	−	25.5036i	−0.340654	−	0.953781i
$716$	−8.66743	−	37.2307i	−0.323917	−	1.39138i
$717$	−17.4093	+	64.9723i	−0.650161	+	2.42643i
$718$	−3.14881	+	21.2024i	−0.117513	+	0.791265i
$719$	−6.07419	+	10.5208i	−0.226529	+	0.392360i	−0.956777	−	0.290822i	$-0.906071\pi$
$719$	−6.07419	+	10.5208i	−0.226529	+	0.392360i	0.730248	+	0.683182i	$0.239404\pi$
$720$	−58.1495	+	21.9547i	−2.16710	+	0.818204i
$721$	1.97310	+	1.13917i	0.0734821	+	0.0424249i
$722$	−7.67786	−	19.4390i	−0.285740	−	0.723446i
$723$	15.8288	+	15.8288i	0.588678	+	0.588678i
$724$	−17.2340	−	5.23437i	−0.640496	−	0.194534i
$725$	−3.62477	+	1.24442i	−0.134621	+	0.0462167i
$726$	1.01475	−	0.752321i	0.0376611	−	0.0279213i
$727$	−27.0352	−	27.0352i	−1.00268	−	1.00268i	−0.999996	−	0.00268440i	$-0.999146\pi$
$727$	−27.0352	−	27.0352i	−1.00268	−	1.00268i	−0.00268440	−	0.999996i	$-0.500854\pi$
$728$	−1.61256	−	0.436954i	−0.0597654	−	0.0161946i
$729$			10.2981i			0.381412i
$730$	−20.9070	−	34.7587i	−0.773805	−	1.28648i
$731$	11.8237	−	6.82641i	0.437315	−	0.252484i
$732$	−8.83520	+	4.71859i	−0.326558	+	0.174404i
$733$	18.5471	−	18.5471i	0.685053	−	0.685053i	−0.276082	−	0.961134i	$-0.589036\pi$
$733$	18.5471	−	18.5471i	0.685053	−	0.685053i	0.961134	+	0.276082i	$0.0890360\pi$
$734$	−17.2572	+	39.7887i	−0.636975	+	1.46863i
$735$	−8.09538	−	48.5116i	−0.298602	−	1.78938i
$736$	3.54991	+	5.51619i	0.130851	+	0.203329i
$737$	4.90716	+	18.3138i	0.180758	+	0.674596i
$738$	82.6451	+	12.2738i	3.04221	+	0.451806i
$739$	−23.6085	+	13.6304i	−0.868451	+	0.501401i	−0.866833	−	0.498598i	$-0.833848\pi$
$739$	−23.6085	+	13.6304i	−0.868451	+	0.501401i	−0.00161807	+	0.999999i	$0.500515\pi$
$740$	5.56597	+	4.25871i	0.204609	+	0.156553i
$741$	17.8519	−	15.0758i	0.655807	−	0.553825i
$742$	1.75778	−	2.21400i	0.0645300	−	0.0812784i
$743$	8.94853	−	33.3964i	0.328290	−	1.22519i	−0.582674	−	0.812706i	$-0.697993\pi$
$743$	8.94853	−	33.3964i	0.328290	−	1.22519i	0.910963	−	0.412487i	$-0.135340\pi$
$744$	62.7078	+	53.2595i	2.29898	+	1.95259i
$745$	−0.105100	−	0.0750396i	−0.00385058	−	0.00274924i
$746$	−20.3050	+	2.33235i	−0.743420	+	0.0853935i
$747$	17.1466	+	63.9919i	0.627361	+	2.34134i
$748$	25.6185	−	13.6820i	0.936706	−	0.500264i
$749$	2.53657			0.0926842
$750$	−32.0748	+	38.1906i	−1.17121	+	1.39452i
$751$	9.18463	−	5.30275i	0.335152	−	0.193500i	−0.322974	−	0.946408i	$-0.604683\pi$
$751$	9.18463	−	5.30275i	0.335152	−	0.193500i	0.658126	+	0.752908i	$0.271349\pi$
$752$	23.4030	−	4.63834i	0.853419	−	0.169143i
$753$	13.4633	+	13.4633i	0.490628	+	0.490628i
$754$	1.12529	+	3.74283i	0.0409805	+	0.136306i
$755$	−3.36868	+	34.8191i	−0.122599	+	1.26720i
$756$	2.97994	−	2.78908i	0.108379	−	0.101438i
$757$	16.7429	+	4.48624i	0.608530	+	0.163055i	0.549908	−	0.835225i	$-0.314663\pi$
$757$	16.7429	+	4.48624i	0.608530	+	0.163055i	0.0586216	+	0.998280i	$0.481329\pi$
$758$	−20.0968	+	7.93765i	−0.729948	+	0.288309i
$759$		−	12.2863i		−	0.445966i
$760$	−11.3504	+	6.32582i	−0.411724	+	0.229461i
$761$	−4.45299	−	2.57093i	−0.161421	−	0.0931963i	0.417114	−	0.908854i	$-0.363042\pi$
$761$	−4.45299	−	2.57093i	−0.161421	−	0.0931963i	−0.578534	+	0.815658i	$0.696375\pi$
$762$	41.6835	−	52.5022i	1.51003	−	1.90196i
$763$	−0.432111	−	1.61266i	−0.0156435	−	0.0583822i
$764$	0.755327	+	0.807013i	0.0273268	+	0.0291967i
$765$	62.9122	+	23.5545i	2.27460	+	0.851616i
$766$	2.89332	−	0.332343i	0.104540	−	0.0120080i
$767$	−4.08931	+	5.87955i	−0.147656	+	0.212298i
$768$	−6.51826	−	50.0452i	−0.235207	−	1.80585i
$769$	−2.73010	−	4.72867i	−0.0984498	−	0.170520i	0.812593	−	0.582831i	$-0.198055\pi$
$769$	−2.73010	−	4.72867i	−0.0984498	−	0.170520i	−0.911043	+	0.412311i	$0.864722\pi$
$770$	−0.896963	−	1.49123i	−0.0323243	−	0.0537402i
$771$	−54.6869	−	31.5735i	−1.96950	−	1.13709i
$772$	18.9097	+	11.7679i	0.680577	+	0.423536i
$773$	1.64450	+	6.13736i	0.0591486	+	0.220745i	0.989173	−	0.146751i	$-0.0468816\pi$
$773$	1.64450	+	6.13736i	0.0591486	+	0.220745i	−0.930025	+	0.367497i	$0.880215\pi$
$774$	−12.3498	+	28.4740i	−0.443903	+	1.02348i
$775$	45.2539	+	8.83920i	1.62557	+	0.317514i
$776$	41.5245	+	7.57787i	1.49064	+	0.272030i
$777$	−0.782209	−	0.209592i	−0.0280616	−	0.00751908i
$778$	−6.38533	+	42.9953i	−0.228925	+	1.54146i
$779$	17.4671			0.625822
$780$	37.6539	+	34.1904i	1.34823	+	1.22421i
$781$	30.0380			1.07484
$782$	1.04148	−	7.01274i	0.0372432	−	0.250775i
$783$	−9.22271	−	2.47122i	−0.329593	−	0.0883141i
$784$	27.8317	+	1.84349i	0.993988	+	0.0658389i
$785$	−15.6066	−	18.9499i	−0.557025	−	0.676351i
$786$	−3.90034	+	8.99273i	−0.139120	+	0.320760i
$787$	−6.31029	−	23.5503i	−0.224938	−	0.839479i	−0.982429	−	0.186634i	$-0.940242\pi$
$787$	−6.31029	−	23.5503i	−0.224938	−	0.839479i	0.757492	−	0.652845i	$-0.226425\pi$
$788$	4.23880	−	6.81131i	0.151001	−	0.242643i
$789$	−47.9954	−	27.7101i	−1.70868	−	0.986507i
$790$	4.83585	−	19.4339i	0.172052	−	0.691427i
$791$	−0.538953	−	0.933494i	−0.0191630	−	0.0331912i
$792$	−28.2596	+	59.6700i	−1.00416	+	2.12028i
$793$	4.69974	+	3.26873i	0.166893	+	0.116076i
$794$	−12.1512	+	1.39576i	−0.431230	+	0.0495335i
$795$	−78.3266	+	35.6525i	−2.77796	+	1.26446i
$796$	−3.27506	+	3.06531i	−0.116081	+	0.108647i
$797$	−8.06689	−	30.1060i	−0.285744	−	1.06641i	−0.948294	−	0.317393i	$-0.897193\pi$
$797$	−8.06689	−	30.1060i	−0.285744	−	1.06641i	0.662550	−	0.749017i	$-0.269474\pi$
$798$	0.933601	−	1.17591i	0.0330491	−	0.0416268i
$799$	−22.3309	−	12.8928i	−0.790011	−	0.456113i
$800$	−16.9077	−	22.6744i	−0.597778	−	0.801662i
$801$			54.7019i			1.93280i
$802$	−21.5433	+	8.50900i	−0.760722	+	0.300463i
$803$	−41.6177	−	11.1514i	−1.46866	−	0.393526i
$804$	−24.3321	−	25.9972i	−0.858128	−	0.916849i
$805$	−0.422822	−	0.0409073i	−0.0149025	−	0.00144179i
$806$	10.7907	−	45.7674i	0.380087	−	1.61209i
$807$	−14.5742	−	14.5742i	−0.513035	−	0.513035i
$808$	−1.43403	−	17.6011i	−0.0504490	−	0.619205i
$809$	−15.0899	+	8.71214i	−0.530531	+	0.306302i	−0.741233	−	0.671248i	$-0.765759\pi$
$809$	−15.0899	+	8.71214i	−0.530531	+	0.306302i	0.210701	+	0.977550i	$0.432425\pi$
$810$	−56.0592	+	16.1028i	−1.96972	+	0.565796i
$811$	29.7766			1.04560			0.522798	−	0.852457i	$-0.324888\pi$
$811$	29.7766			1.04560			0.522798	+	0.852457i	$0.324888\pi$
$812$	0.118311	+	0.221528i	0.00415190	+	0.00777412i
$813$	−2.25659	−	8.42171i	−0.0791420	−	0.295362i
$814$	7.39578	−	0.849522i	0.259222	−	0.0297757i
$815$	−2.41906	−	14.4962i	−0.0847360	−	0.507781i
$816$	−30.3348	+	45.3314i	−1.06193	+	1.58692i
$817$	−1.67934	+	6.26738i	−0.0587527	+	0.219268i
$818$	15.2066	−	19.1534i	0.531687	−	0.669683i
$819$	−3.86168	−	1.39175i	−0.134938	−	0.0486317i
$820$	5.01473	+	37.6882i	0.175122	+	1.31613i
$821$	22.7382	−	13.1279i	0.793569	−	0.458168i	−0.0476482	−	0.998864i	$-0.515173\pi$
$821$	22.7382	−	13.1279i	0.793569	−	0.458168i	0.841218	+	0.540697i	$0.181839\pi$
$822$	−23.0747	−	3.42687i	−0.804821	−	0.119526i
$823$	−9.76939	−	36.4599i	−0.340540	−	1.27091i	−0.897737	−	0.440531i	$-0.854790\pi$
$823$	−9.76939	−	36.4599i	−0.340540	−	1.27091i	0.557198	−	0.830380i	$-0.311877\pi$
$824$	37.0425	−	13.2324i	1.29044	−	0.460971i
$825$	3.64736	+	52.8505i	0.126985	+	1.84002i
$826$	−0.183119	+	0.422204i	−0.00637151	+	0.0146903i
$827$	−22.3365	+	22.3365i	−0.776715	+	0.776715i	−0.979271	−	0.202556i	$-0.935075\pi$
$827$	−22.3365	+	22.3365i	−0.776715	+	0.776715i	0.202556	+	0.979271i	$0.435075\pi$
$828$	7.59251	+	14.2164i	0.263858	+	0.494054i
$829$	5.14191	−	2.96868i	0.178586	−	0.103107i	−0.408042	−	0.912963i	$-0.633788\pi$
$829$	5.14191	−	2.96868i	0.178586	−	0.103107i	0.586628	+	0.809856i	$0.300455\pi$
$830$	−25.8338	+	15.5388i	−0.896703	+	0.539359i
$831$		−	64.1517i		−	2.22540i
$832$	−23.7724	+	16.3362i	−0.824161	+	0.566356i
$833$	−21.3164	−	21.3164i	−0.738568	−	0.738568i
$834$	−15.0377	+	11.1487i	−0.520714	+	0.386049i
$835$	13.8660	−	37.0349i	0.479852	−	1.28165i
$836$	−4.01128	+	13.2070i	−0.138733	+	0.456773i
$837$	81.2291	+	81.2291i	2.80769	+	2.80769i
$838$	−7.71046	−	19.5216i	−0.266353	−	0.674361i
$839$	36.2372	+	20.9215i	1.25105	+	0.722292i	0.971317	−	0.237787i	$-0.0764220\pi$
$839$	36.2372	+	20.9215i	1.25105	+	0.722292i	0.279729	+	0.960079i	$0.409755\pi$
$840$	2.80527	+	1.67681i	0.0967908	+	0.0578553i
$841$	−14.2062	+	24.6059i	−0.489871	+	0.848481i
$842$	4.88616	−	32.9007i	0.168388	−	1.13383i
$843$	−1.95583	+	7.29924i	−0.0673622	+	0.251399i
$844$	−28.9490	+	6.73943i	−0.996467	+	0.231981i
$845$	7.60409	−	28.0567i	0.261589	−	0.965179i
$846$	58.2350	−	6.68921i	2.00216	−	0.229980i
$847$	−0.0448121	−	0.0120074i	−0.00153976	−	0.000412578i
$848$	−9.48858	−	47.8751i	−0.325839	−	1.64404i
$849$	−4.14055	−	2.39055i	−0.142103	−	0.0820435i
$850$	−2.39817	+	30.4749i	−0.0822565	+	1.04528i
$851$	0.908617	−	1.57377i	0.0311470	−	0.0539482i
$852$	−49.7611	+	26.5758i	−1.70479	+	0.910471i
$853$	−12.3949	+	12.3949i	−0.424395	+	0.424395i	−0.886714	−	0.462319i	$-0.847018\pi$
$853$	−12.3949	+	12.3949i	−0.424395	+	0.424395i	0.462319	+	0.886714i	$0.347018\pi$
$854$	0.337483	+	0.146373i	0.0115484	+	0.00500879i
$855$	−29.0572	+	13.2262i	−0.993737	+	0.452326i
$856$	28.3496	−	33.3789i	0.968970	−	1.14087i
$857$	−37.7415	+	37.7415i	−1.28923	+	1.28923i	−0.353969	+	0.935257i	$0.615168\pi$
$857$	−37.7415	+	37.7415i	−1.28923	+	1.28923i	−0.935257	+	0.353969i	$0.884832\pi$
$858$	54.0006	−	1.63426i	1.84355	−	0.0557929i
$859$	44.0614			1.50335			0.751677	−	0.659531i	$-0.229245\pi$
$859$	44.0614			1.50335			0.751677	+	0.659531i	$0.229245\pi$
$860$	−14.0051	−	1.82413i	−0.477570	−	0.0622022i
$861$	−2.19660	−	3.80462i	−0.0748600	−	0.129661i
$862$	−13.9970	−	35.4379i	−0.476738	−	1.20702i
$863$	−27.0922	−	27.0922i	−0.922229	−	0.922229i	0.0749581	−	0.997187i	$-0.476118\pi$
$863$	−27.0922	−	27.0922i	−0.922229	−	0.922229i	−0.997187	+	0.0749581i	$0.976118\pi$
$864$	−3.39688	−	70.3850i	−0.115564	−	2.39455i
$865$	−0.997730	−	5.97890i	−0.0339238	−	0.203289i
$866$	34.5876	−	3.97294i	1.17534	−	0.135006i
$867$	5.14739	−	1.37924i	0.174815	−	0.0468414i
$868$	0.0999056	−	3.01991i	0.00339102	−	0.102502i
$869$	−10.6363	−	18.4226i	−0.360812	−	0.624945i
$870$	−0.136972	−	7.64417i	−0.00464380	−	0.259162i
$871$	−6.90012	+	19.1457i	−0.233802	+	0.648729i
$872$	−26.0505	−	12.3375i	−0.882182	−	0.417800i
$873$	100.174	+	26.8416i	3.39038	+	0.908450i
$874$	2.00665	+	2.70663i	0.0678759	+	0.0915530i
$875$	1.83094	+	0.0504450i	0.0618972	+	0.00170535i
$876$	78.8103	−	18.3473i	2.66275	−	0.619897i
$877$	11.0734	−	2.96711i	0.373922	−	0.100192i	−0.0669636	−	0.997755i	$-0.521331\pi$
$877$	11.0734	−	2.96711i	0.373922	−	0.100192i	0.440885	+	0.897563i	$0.354664\pi$
$878$	0.863842	+	2.18710i	0.0291533	+	0.0738111i
$879$		−	45.3381i		−	1.52922i
$880$	−29.6480	−	4.86335i	−0.999433	−	0.163943i
$881$	9.11153	+	15.7816i	0.306975	+	0.531696i	0.977699	−	0.210011i	$-0.0673498\pi$
$881$	9.11153	+	15.7816i	0.306975	+	0.531696i	−0.670724	+	0.741707i	$0.734016\pi$
$882$	67.7868	+	10.0672i	2.28250	+	0.338980i
$883$	−22.5334	+	22.5334i	−0.758309	+	0.758309i	−0.976014	−	0.217706i	$-0.930143\pi$
$883$	−22.5334	+	22.5334i	−0.758309	+	0.758309i	0.217706	+	0.976014i	$0.430143\pi$
$884$	30.9608	+	3.64469i	1.04132	+	0.122584i
$885$	10.8143	−	8.90640i	0.363520	−	0.299385i
$886$	−29.8432	+	22.1253i	−1.00260	+	0.743313i
$887$	−9.29347	+	34.6837i	−0.312044	+	1.16457i	0.614666	+	0.788788i	$0.289291\pi$
$887$	−9.29347	+	34.6837i	−0.312044	+	1.16457i	−0.926710	+	0.375777i	$0.877376\pi$
$888$	−11.5003	+	7.95066i	−0.385924	+	0.266807i
$889$	−2.46202			−0.0825734
$890$	−23.9248	+	6.87232i	−0.801961	+	0.230361i
$891$	−30.9777	+	53.6550i	−1.03779	+	1.79751i
$892$	−1.50724	+	2.42198i	−0.0504663	+	0.0810939i
$893$	11.8369	−	3.17170i	0.396108	−	0.106137i
$894$	0.206951	−	0.153430i	0.00692148	−	0.00513147i
$895$	38.8983	−	17.7056i	1.30023	−	0.591833i
$896$	−1.29060	+	1.33032i	−0.0431160	+	0.0444430i
$897$	7.53018	−	10.8268i	0.251425	−	0.361496i
$898$	−19.7824	+	24.9168i	−0.660146	+	0.831483i
$899$	−6.12142	+	3.53420i	−0.204161	+	0.117872i
$900$	−36.8800	−	58.8989i	−1.22933	−	1.96330i
$901$	−26.3745	+	45.6820i	−0.878662	+	1.52189i
$902$	31.6296	+	25.1119i	1.05315	+	0.836136i
$903$	1.57633	−	0.422377i	0.0524570	−	0.0140558i
$904$	−18.3074	−	3.34095i	−0.608896	−	0.111118i
$905$	1.93919	−	20.0437i	0.0644609	−	0.666276i
$906$	−64.0231	−	27.7682i	−2.12703	−	0.922536i
$907$	1.12659	−	4.20448i	0.0374077	−	0.139607i	−0.944696	−	0.327946i	$-0.893644\pi$
$907$	1.12659	−	4.20448i	0.0374077	−	0.139607i	0.982104	+	0.188339i	$0.0603102\pi$
$908$	1.27947	−	38.6752i	0.0424606	−	1.28348i
$909$		−	43.3880i		−	1.43909i
$910$	0.123553	−	1.86382i	0.00409574	−	0.0617851i
$911$			5.66695i			0.187754i	0.995584	+	0.0938772i	$0.0299261\pi$
$911$			5.66695i			0.187754i	−0.995584	+	0.0938772i	$0.970074\pi$
$912$	−5.03963	−	25.4277i	−0.166879	−	0.841996i
$913$	−8.28811	+	30.9316i	−0.274296	+	1.02369i
$914$	6.62022	−	15.2638i	0.218977	−	0.504881i
$915$	−7.11921	−	8.64430i	−0.235354	−	0.285772i
$916$	−13.4256	−	4.07767i	−0.443594	−	0.134730i
$917$	0.347727	−	0.0931733i	0.0114830	−	0.00307685i
$918$	−47.3556	+	59.6465i	−1.56297	+	1.96863i
$919$	−29.0439	+	50.3054i	−0.958069	+	1.65942i	−0.230884	+	0.972981i	$0.574162\pi$
$919$	−29.0439	+	50.3054i	−0.958069	+	1.65942i	−0.727184	+	0.686442i	$0.759171\pi$
$920$	−5.26392	+	5.10675i	−0.173546	+	0.168365i
$921$	29.4689	−	17.0139i	0.971032	−	0.560626i
$922$	−0.314180	−	0.249439i	−0.0103470	−	0.00821485i
$923$	26.4696	+	18.4100i	0.871258	+	0.605972i
$924$	3.38115	−	0.787143i	0.111232	−	0.0258951i
$925$	−3.44128	+	7.03942i	−0.113149	+	0.231455i
$926$	−11.6598	−	15.7271i	−0.383164	−	0.516823i
$927$	93.3503	−	25.0131i	3.06603	−	0.821539i
$928$	4.23739	+	0.919018i	0.139099	+	0.0301682i
$929$	−18.9298	+	32.7874i	−0.621068	+	1.07572i	0.368219	+	0.929739i	$0.379968\pi$
$929$	−18.9298	+	32.7874i	−0.621068	+	1.07572i	−0.989287	+	0.145982i	$0.953366\pi$
$930$	−44.5574	+	80.4716i	−1.46110	+	2.63877i
$931$	14.3268			0.469541
$932$	3.04064	+	5.69337i	0.0995996	+	0.186493i
$933$	13.1353	−	49.0215i	0.430030	−	1.60489i
$934$	9.51480	+	12.8338i	0.311334	+	0.419936i
$935$	20.6429	+	25.0650i	0.675094	+	0.819714i
$936$	−61.4737	+	35.2614i	−2.00933	+	1.15256i
$937$	15.3936	−	15.3936i	0.502888	−	0.502888i	−0.409446	−	0.912334i	$-0.634278\pi$
$937$	15.3936	−	15.3936i	0.502888	−	0.502888i	0.912334	+	0.409446i	$0.134278\pi$
$938$	−0.192107	+	1.29354i	−0.00627252	+	0.0422356i
$939$	−25.9154	−	44.8869i	−0.845718	−	1.46483i
$940$	10.2418	+	24.6297i	0.334052	+	0.803332i
$941$		−	45.4266i		−	1.48087i	−0.672131	−	0.740433i	$-0.734621\pi$
$941$		−	45.4266i		−	1.48087i	0.672131	−	0.740433i	$-0.265379\pi$
$942$	45.5496	−	17.9908i	1.48409	−	0.586171i
$943$	9.52262	−	2.55158i	0.310099	−	0.0830909i
$944$	3.50920	+	7.12837i	0.114215	+	0.232009i
$945$	3.71385	+	2.65162i	0.120812	+	0.0862571i
$946$	−12.0514	+	8.93471i	−0.391825	+	0.290493i
$947$	37.2065	+	9.96946i	1.20905	+	0.323964i	0.806389	−	0.591385i	$-0.201419\pi$
$947$	37.2065	+	9.96946i	1.20905	+	0.323964i	0.402661	+	0.915349i	$0.368085\pi$
$948$	33.9194	+	21.1087i	1.10165	+	0.685579i
$949$	−29.8391	−	35.3338i	−0.968620	−	1.14698i
$950$	−9.43522	−	11.0470i	−0.306119	−	0.358413i
$951$	11.7765	+	20.3974i	0.381878	+	0.661432i
$952$	1.99660	−	0.162671i	0.0647102	−	0.00527219i
$953$	−28.8611	+	7.73331i	−0.934903	+	0.250506i	−0.693944	−	0.720029i	$-0.744128\pi$
$953$	−28.8611	+	7.73331i	−0.934903	+	0.250506i	−0.240959	+	0.970535i	$0.577462\pi$
$954$	−13.6840	−	119.130i	−0.443036	−	3.85699i
$955$	−0.718098	+	1.00577i	−0.0232371	+	0.0325459i
$956$	12.3947	−	40.8092i	0.400874	−	1.31986i
$957$	−5.74250	−	5.74250i	−0.185629	−	0.185629i
$958$	−3.56188	+	1.40684i	−0.115079	+	0.0454530i
$959$	0.428368	+	0.741955i	0.0138327	+	0.0239590i
$960$	53.4178	−	18.1741i	1.72405	−	0.586566i
$961$	54.0420			1.74329
$962$	7.03786	+	3.78420i	0.226910	+	0.122007i
$963$	76.0826	−	76.0826i	2.45173	−	2.45173i
$964$	−9.69916	−	10.3629i	−0.312389	−	0.333765i
$965$	−8.73124	+	23.3204i	−0.281069	+	0.750711i
$966$	0.337200	−	0.777459i	0.0108492	−	0.0250143i
$967$	−2.15476	+	2.15476i	−0.0692926	+	0.0692926i	−0.740904	−	0.671611i	$-0.765603\pi$
$967$	−2.15476	+	2.15476i	−0.0692926	+	0.0692926i	0.671611	+	0.740904i	$0.265603\pi$
$968$	−0.658842	+	0.455487i	−0.0211760	+	0.0146399i
$969$	−14.0082	+	24.2629i	−0.450008	+	0.779437i
$970$	0.845486	+	47.1850i	0.0271469	+	1.51502i
$971$	−32.1864	−	18.5828i	−1.03291	−	0.596352i	−0.115094	−	0.993355i	$-0.536717\pi$
$971$	−32.1864	−	18.5828i	−1.03291	−	0.596352i	−0.917818	+	0.397003i	$0.870050\pi$
$972$	1.37595	−	41.5918i	0.0441337	−	1.33406i
$973$	0.664075	+	0.177938i	0.0212893	+	0.00570445i
$974$	1.57015	+	13.6695i	0.0503110	+	0.437998i
$975$	−29.1775	+	48.8076i	−0.934428	+	1.56309i
$976$	5.69796	−	2.80503i	0.182387	−	0.0897869i
$977$	9.05993	−	33.8121i	0.289853	−	1.08175i	−0.655367	−	0.755311i	$-0.727486\pi$
$977$	9.05993	−	33.8121i	0.289853	−	1.08175i	0.945220	−	0.326435i	$-0.105847\pi$
$978$	29.0006	+	4.30695i	0.927338	+	0.137721i
$979$	−13.2206	+	22.8987i	−0.422531	+	0.731845i
$980$	4.11316	+	30.9125i	0.131390	+	0.987463i
$981$	−61.3315	−	35.4097i	−1.95816	−	1.13055i
$982$	2.13386	−	0.842814i	0.0680942	−	0.0268953i
$983$	0.544366	+	0.544366i	0.0173626	+	0.0173626i	0.715735	−	0.698372i	$-0.246092\pi$
$983$	0.544366	+	0.544366i	0.0173626	+	0.0173626i	−0.698372	+	0.715735i	$0.746092\pi$
$984$	−74.6153	−	13.6166i	−2.37865	−	0.434083i
$985$	8.40004	+	3.14500i	0.267648	+	0.100208i
$986$	−2.79090	−	3.76445i	−0.0888803	−	0.119884i
$987$	−2.17943	−	2.17943i	−0.0693719	−	0.0693719i
$988$	−11.6292	+	9.17959i	−0.369974	+	0.292042i
$989$			3.66214i			0.116449i
$990$	−71.6322	−	17.8247i	−2.27662	−	0.566505i
$991$	−36.3606	+	20.9928i	−1.15503	+	0.666858i	−0.950108	−	0.311920i	$-0.899028\pi$
$991$	−36.3606	+	20.9928i	−1.15503	+	0.666858i	−0.204923	+	0.978778i	$0.565694\pi$
$992$	−38.6226	−	35.0662i	−1.22627	−	1.11335i
$993$	−46.3468	+	46.3468i	−1.47077	+	1.47077i
$994$	1.90075	+	0.824396i	0.0602882	+	0.0261483i
$995$	−4.08166	−	2.91422i	−0.129397	−	0.0923871i
$996$	−13.6363	−	58.5744i	−0.432083	−	1.85600i
$997$	0.338676	+	1.26396i	0.0107260	+	0.0400299i	0.971081	−	0.238749i	$-0.0767372\pi$
$997$	0.338676	+	1.26396i	0.0107260	+	0.0400299i	−0.960355	+	0.278778i	$0.910070\pi$
$998$	−6.53690	+	44.0158i	−0.206922	+	1.39330i
$999$	−16.9060	+	9.76067i	−0.534881	+	0.308814i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	260.2.bg.c.23.35	yes	144
4.3	odd	2	inner	260.2.bg.c.23.6	✓	144
5.2	odd	4	inner	260.2.bg.c.127.19	yes	144
13.4	even	6	inner	260.2.bg.c.43.24	yes	144
20.7	even	4	inner	260.2.bg.c.127.24	yes	144
52.43	odd	6	inner	260.2.bg.c.43.19	yes	144
65.17	odd	12	inner	260.2.bg.c.147.6	yes	144
260.147	even	12	inner	260.2.bg.c.147.35	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bg.c.23.6	✓	144	4.3	odd	2	inner
260.2.bg.c.23.35	yes	144	1.1	even	1	trivial
260.2.bg.c.43.19	yes	144	52.43	odd	6	inner
260.2.bg.c.43.24	yes	144	13.4	even	6	inner
260.2.bg.c.127.19	yes	144	5.2	odd	4	inner
260.2.bg.c.127.24	yes	144	20.7	even	4	inner
260.2.bg.c.147.6	yes	144	65.17	odd	12	inner
260.2.bg.c.147.35	yes	144	260.147	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:	\( N \)	\(=\)	\( 260 = 2^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	260.bg (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.39887 + 0.207750i) q^{2} +(-3.04677 - 0.816378i) q^{3} +(1.91368 + 0.581230i) q^{4} +(-0.215330 + 2.22568i) q^{5} +(-4.09243 - 1.77497i) q^{6} +(0.0424015 + 0.158244i) q^{7} +(2.55624 + 1.21063i) q^{8} +(6.01823 + 3.47463i) q^{9} +(-0.763602 + 3.06870i) q^{10} +(1.67952 + 2.90902i) q^{11} +(-5.35603 - 3.33316i) q^{12} +(-0.302905 + 3.59281i) q^{13} +(0.0264389 + 0.230172i) q^{14} +(2.47305 - 6.60532i) q^{15} +(3.32434 + 2.22458i) q^{16} +(-1.11891 - 4.17582i) q^{17} +(7.69687 + 6.11084i) q^{18} +(1.77930 + 1.02728i) q^{19} +(-1.70570 + 4.13408i) q^{20} -0.516749i q^{21} +(1.74509 + 4.41826i) q^{22} +(1.12010 + 0.300129i) q^{23} +(-6.79993 - 5.77537i) q^{24} +(-4.90727 - 0.958509i) q^{25} +(-1.17013 + 4.96294i) q^{26} +(-8.80836 - 8.80836i) q^{27} +(-0.0108336 + 0.327474i) q^{28} +(0.663797 - 0.383243i) q^{29} +(4.83174 - 8.72622i) q^{30} -9.22182 q^{31} +(4.18817 + 3.80253i) q^{32} +(-2.74225 - 10.2342i) q^{33} +(-0.697682 - 6.07389i) q^{34} +(-0.361331 + 0.0602971i) q^{35} +(9.49741 + 10.1473i) q^{36} +(0.405598 - 1.51371i) q^{37} +(2.27559 + 1.80668i) q^{38} +(3.85597 - 10.6991i) q^{39} +(-3.24491 + 5.42868i) q^{40} +(7.36261 - 4.25081i) q^{41} +(0.107355 - 0.722865i) q^{42} +(0.817373 + 3.05048i) q^{43} +(1.52326 + 6.54312i) q^{44} +(-9.02930 + 12.6464i) q^{45} +(1.50452 + 0.652541i) q^{46} +(4.21757 - 4.21757i) q^{47} +(-8.31240 - 9.49169i) q^{48} +(6.03893 - 3.48658i) q^{49} +(-6.66550 - 2.36031i) q^{50} +13.6362i q^{51} +(-2.66791 + 6.69942i) q^{52} +(-8.62782 - 8.62782i) q^{53} +(-10.4918 - 14.1517i) q^{54} +(-6.83618 + 3.11167i) q^{55} +(-0.0831875 + 0.455843i) q^{56} +(-4.58246 - 4.58246i) q^{57} +(1.00819 - 0.398204i) q^{58} +(1.72021 + 0.993165i) q^{59} +(8.57185 - 11.2031i) q^{60} +(0.793873 - 1.37503i) q^{61} +(-12.9001 - 1.91583i) q^{62} +(-0.294658 + 1.09968i) q^{63} +(5.06874 + 6.18934i) q^{64} +(-7.93119 - 1.44781i) q^{65} +(-1.70990 - 14.8861i) q^{66} +(5.45208 + 1.46088i) q^{67} +(0.285882 - 8.64153i) q^{68} +(-3.16765 - 1.82884i) q^{69} +(-0.517982 + 0.00928149i) q^{70} +(4.47121 - 7.74436i) q^{71} +(11.1775 + 16.1678i) q^{72} +(-9.06992 + 9.06992i) q^{73} +(0.881852 - 2.03322i) q^{74} +(14.1688 + 6.92654i) q^{75} +(2.80792 + 3.00007i) q^{76} +(-0.389122 + 0.389122i) q^{77} +(7.61675 - 14.1657i) q^{78} -6.33294 q^{79} +(-5.66702 + 6.91989i) q^{80} +(9.22218 + 15.9733i) q^{81} +(11.1824 - 4.41675i) q^{82} +(6.74106 + 6.74106i) q^{83} +(0.300350 - 0.988893i) q^{84} +(9.53496 - 1.59115i) q^{85} +(0.509663 + 4.43703i) q^{86} +(-2.33531 + 0.625743i) q^{87} +(0.771512 + 9.46944i) q^{88} +(3.93581 + 6.81702i) q^{89} +(-15.2581 + 15.8149i) q^{90} +(-0.581385 + 0.104407i) q^{91} +(1.96906 + 1.22538i) q^{92} +(28.0967 + 7.52850i) q^{93} +(6.77604 - 5.02364i) q^{94} +(-2.66953 + 3.73894i) q^{95} +(-9.65607 - 15.0045i) q^{96} +(14.4151 - 3.86251i) q^{97} +(9.17203 - 3.62269i) q^{98} +23.3429i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 144 q - 6 q^{2} - 12 q^{6} + 12 q^{10} - 12 q^{12} + 4 q^{13} - 12 q^{16} - 24 q^{17} - 42 q^{20} - 12 q^{22} - 24 q^{25} - 36 q^{26} - 6 q^{28} - 36 q^{32} - 12 q^{33} - 76 q^{36} + 48 q^{37} - 16 q^{38}+ \cdots - 162 q^{98}+O(q^{100}) \) 144 * q - 6 * q^2 - 12 * q^6 + 12 * q^10 - 12 * q^12 + 4 * q^13 - 12 * q^16 - 24 * q^17 - 42 * q^20 - 12 * q^22 - 24 * q^25 - 36 * q^26 - 6 * q^28 - 36 * q^32 - 12 * q^33 - 76 * q^36 + 48 * q^37 - 16 * q^38 + 76 * q^40 - 72 * q^41 + 40 * q^42 - 120 * q^45 - 12 * q^46 - 40 * q^48 + 120 * q^50 - 10 * q^52 + 8 * q^53 - 20 * q^56 + 126 * q^58 + 16 * q^61 - 44 * q^62 + 32 * q^65 + 96 * q^66 - 64 * q^68 - 54 * q^72 - 12 * q^76 + 40 * q^77 - 100 * q^78 - 24 * q^80 - 32 * q^81 - 78 * q^82 - 24 * q^85 - 10 * q^88 - 8 * q^90 + 100 * q^92 - 48 * q^93 - 12 * q^97 - 162 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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