LMFDB - Embedded newform 260.2.bg.c.127.19

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			127.19
Character	$\chi$	$=$	260.127
Dual form			260.2.bg.c.43.19

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.207750 + 1.39887i) q^{2} +(-0.816378 + 3.04677i) q^{3} +(-1.91368 - 0.581230i) q^{4} +(0.215330 + 2.22568i) q^{5} +(-4.09243 - 1.77497i) q^{6} +(-0.158244 + 0.0424015i) q^{7} +(1.21063 - 2.55624i) q^{8} +(-6.01823 - 3.47463i) q^{9} +(-3.15817 - 0.161165i) q^{10} +(1.67952 + 2.90902i) q^{11} +(3.33316 - 5.35603i) q^{12} +(3.59281 + 0.302905i) q^{13} +(-0.0264389 - 0.230172i) q^{14} +(-6.95690 - 1.16093i) q^{15} +(3.32434 + 2.22458i) q^{16} +(4.17582 - 1.11891i) q^{17} +(6.11084 - 7.69687i) q^{18} +(-1.77930 - 1.02728i) q^{19} +(0.881558 - 4.38439i) q^{20} -0.516749i q^{21} +(-4.41826 + 1.74509i) q^{22} +(0.300129 - 1.12010i) 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} +(0.327474 + 0.0108336i) q^{28} +(-0.663797 + 0.383243i) q^{29} +(3.06929 - 9.49063i) q^{30} -9.22182 q^{31} +(-3.80253 + 4.18817i) q^{32} +(-10.2342 + 2.74225i) q^{33} +(0.697682 + 6.07389i) q^{34} +(-0.128447 - 0.343070i) q^{35} +(9.49741 + 10.1473i) q^{36} +(1.51371 + 0.405598i) q^{37} +(1.80668 - 2.27559i) q^{38} +(-3.85597 + 10.6991i) q^{39} +(5.95005 + 2.14404i) q^{40} +(7.36261 - 4.25081i) q^{41} +(0.722865 + 0.107355i) q^{42} +(3.05048 - 0.817373i) q^{43} +(-1.52326 - 6.54312i) q^{44} +(6.43749 - 14.1428i) q^{45} +(1.50452 + 0.652541i) q^{46} +(4.21757 + 4.21757i) q^{47} +(-9.49169 + 8.31240i) q^{48} +(-6.03893 + 3.48658i) q^{49} +(-0.321347 - 7.06376i) q^{50} +13.6362i q^{51} +(-6.69942 - 2.66791i) q^{52} +(-8.62782 + 8.62782i) q^{53} +(10.4918 + 14.1517i) q^{54} +(-6.11288 + 4.36447i) q^{55} +(-0.0831875 + 0.455843i) q^{56} +(4.58246 - 4.58246i) q^{57} +(-0.398204 - 1.00819i) q^{58} +(-1.72021 - 0.993165i) q^{59} +(12.6385 + 6.26522i) q^{60} +(0.793873 - 1.37503i) q^{61} +(1.91583 - 12.9001i) q^{62} +(1.09968 + 0.294658i) q^{63} +(-5.06874 - 6.18934i) q^{64} +(0.0994692 + 8.06164i) q^{65} +(-1.70990 - 14.8861i) q^{66} +(-1.46088 + 5.45208i) q^{67} +(-8.64153 - 0.285882i) q^{68} +(3.16765 + 1.82884i) q^{69} +(0.506596 - 0.108408i) q^{70} +(4.47121 - 7.74436i) q^{71} +(-16.1678 + 11.1775i) q^{72} +(9.06992 + 9.06992i) q^{73} +(-0.881852 + 2.03322i) q^{74} +(1.08583 - 15.7338i) q^{75} +(2.80792 + 3.00007i) q^{76} +(-0.389122 - 0.389122i) q^{77} +(-14.1657 - 7.61675i) q^{78} +6.33294 q^{79} +(-4.23536 + 7.87793i) q^{80} +(9.22218 + 15.9733i) q^{81} +(4.41675 + 11.1824i) q^{82} +(6.74106 - 6.74106i) q^{83} +(-0.300350 + 0.988893i) q^{84} +(3.38951 + 9.05310i) q^{85} +(0.509663 + 4.43703i) q^{86} +(-0.625743 - 2.33531i) q^{87} +(9.46944 - 0.771512i) q^{88} +(-3.93581 - 6.81702i) q^{89} +(18.4466 + 11.9434i) q^{90} +(-0.581385 + 0.104407i) q^{91} +(-1.22538 + 1.96906i) q^{92} +(7.52850 - 28.0967i) q^{93} +(-6.77604 + 5.02364i) q^{94} +(1.90325 - 4.18135i) q^{95} +(-9.65607 - 15.0045i) q^{96} +(3.86251 + 14.4151i) q^{97} +(-3.62269 - 9.17203i) 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 $\left(\mathbb{Z}/260\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.207750	+	1.39887i	−0.146901	+	0.989151i
$2$	−0.207750	+	1.39887i	−0.146901	+	0.989151i
$3$	−0.816378	+	3.04677i	−0.471336	+	1.75905i	0.163641	+	0.986520i	$0.447676\pi$
$3$	−0.816378	+	3.04677i	−0.471336	+	1.75905i	−0.634977	+	0.772531i	$0.718991\pi$
$4$	−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
$7$	−0.158244	+	0.0424015i	−0.0598108	+	0.0160262i	−0.288600	−	0.957450i	$-0.593190\pi$
$7$	−0.158244	+	0.0424015i	−0.0598108	+	0.0160262i	0.228790	+	0.973476i	$0.426523\pi$
$8$	1.21063	−	2.55624i	0.428023	−	0.903768i
$9$	−6.01823	−	3.47463i	−2.00608	−	1.15821i
$10$	−3.15817	−	0.161165i	−0.998700	−	0.0509648i
$11$	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	$0.664311\pi$
$12$	3.33316	−	5.35603i	0.962200	−	1.54615i
$13$	3.59281	+	0.302905i	0.996465	+	0.0840109i
$13$	3.59281	+	0.302905i	0.996465	+	0.0840109i
$14$	−0.0264389	−	0.230172i	−0.00706610	−	0.0615162i
$15$	−6.95690	−	1.16093i	−1.79626	−	0.299752i
$16$	3.32434	+	2.22458i	0.831086	+	0.556144i
$17$	4.17582	−	1.11891i	1.01279	−	0.271375i	0.285993	−	0.958232i	$-0.407677\pi$
$17$	4.17582	−	1.11891i	1.01279	−	0.271375i	0.726793	+	0.686857i	$0.241010\pi$
$18$	6.11084	−	7.69687i	1.44034	−	1.81417i
$19$	−1.77930	−	1.02728i	−0.408199	−	0.235674i	0.281816	−	0.959468i	$-0.409063\pi$
$19$	−1.77930	−	1.02728i	−0.408199	−	0.235674i	−0.690016	+	0.723794i	$0.742396\pi$
$20$	0.881558	−	4.38439i	0.197122	−	0.980379i
$21$		−	0.516749i		−	0.112764i
$22$	−4.41826	+	1.74509i	−0.941977	+	0.372054i
$23$	0.300129	−	1.12010i	0.0625812	−	0.233556i	−0.927550	−	0.373699i	$-0.878089\pi$
$23$	0.300129	−	1.12010i	0.0625812	−	0.233556i	0.990131	+	0.140143i	$0.0447561\pi$
$24$	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
$28$	0.327474	+	0.0108336i	0.0618868	+	0.00204736i
$29$	−0.663797	+	0.383243i	−0.123264	+	0.0711665i	−0.560364	−	0.828246i	$-0.689339\pi$
$29$	−0.663797	+	0.383243i	−0.123264	+	0.0711665i	0.437100	+	0.899413i	$0.356006\pi$
$30$	3.06929	−	9.49063i	0.560373	−	1.73274i
$31$	−9.22182			−1.65629			−0.828144	−	0.560515i	$-0.810603\pi$
$31$	−9.22182			−1.65629			−0.828144	+	0.560515i	$0.810603\pi$
$32$	−3.80253	+	4.18817i	−0.672198	+	0.740371i
$33$	−10.2342	+	2.74225i	−1.78155	+	0.477365i
$34$	0.697682	+	6.07389i	0.119652	+	1.04166i
$35$	−0.128447	−	0.343070i	−0.0217114	−	0.0579895i
$36$	9.49741	+	10.1473i	1.58290	+	1.69122i
$37$	1.51371	+	0.405598i	0.248853	+	0.0666799i	0.381089	−	0.924538i	$-0.375549\pi$
$37$	1.51371	+	0.405598i	0.248853	+	0.0666799i	−0.132236	+	0.991218i	$0.542216\pi$
$38$	1.80668	−	2.27559i	0.293082	−	0.369150i
$39$	−3.85597	+	10.6991i	−0.617449	+	1.71323i
$40$	5.95005	+	2.14404i	0.940785	+	0.339003i
$41$	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	$0.102249\pi$
$42$	0.722865	+	0.107355i	0.111541	+	0.0165652i
$43$	3.05048	−	0.817373i	0.465193	−	0.124648i	−0.0186065	−	0.999827i	$-0.505923\pi$
$43$	3.05048	−	0.817373i	0.465193	−	0.124648i	0.483800	+	0.875179i	$0.339256\pi$
$44$	−1.52326	−	6.54312i	−0.229640	−	0.986412i
$45$	6.43749	−	14.1428i	0.959644	−	2.10829i
$46$	1.50452	+	0.652541i	0.221829	+	0.0962120i
$47$	4.21757	+	4.21757i	0.615196	+	0.615196i	0.944295	−	0.329099i	$-0.106745\pi$
$47$	4.21757	+	4.21757i	0.615196	+	0.615196i	−0.329099	+	0.944295i	$0.606745\pi$
$48$	−9.49169	+	8.31240i	−1.37001	+	1.19979i
$49$	−6.03893	+	3.48658i	−0.862705	+	0.498083i
$50$	−0.321347	−	7.06376i	−0.0454454	−	0.998967i
$51$			13.6362i			1.90945i
$52$	−6.69942	−	2.66791i	−0.929043	−	0.369973i
$53$	−8.62782	+	8.62782i	−1.18512	+	1.18512i	−0.206723	+	0.978400i	$0.566280\pi$
$53$	−8.62782	+	8.62782i	−1.18512	+	1.18512i	−0.978400	+	0.206723i	$0.933720\pi$
$54$	10.4918	+	14.1517i	1.42776	+	1.92580i
$55$	−6.11288	+	4.36447i	−0.824261	+	0.588505i
$56$	−0.0831875	+	0.455843i	−0.0111164	+	0.0609146i
$57$	4.58246	−	4.58246i	0.606962	−	0.606962i
$58$	−0.398204	−	1.00819i	−0.0522868	−	0.132381i
$59$	−1.72021	−	0.993165i	−0.223953	−	0.129299i	0.383827	−	0.923405i	$-0.374606\pi$
$59$	−1.72021	−	0.993165i	−0.223953	−	0.129299i	−0.607779	+	0.794106i	$0.707939\pi$
$60$	12.6385	+	6.26522i	1.63163	+	0.808836i
$61$	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	$0.134256\pi$
$62$	1.91583	−	12.9001i	0.243311	−	1.63832i
$63$	1.09968	+	0.294658i	0.138547	+	0.0371235i
$64$	−5.06874	−	6.18934i	−0.633592	−	0.773667i
$65$	0.0994692	+	8.06164i	0.0123376	+	0.999924i
$66$	−1.70990	−	14.8861i	−0.210474	−	1.83235i
$67$	−1.46088	+	5.45208i	−0.178475	+	0.666077i	0.817459	+	0.575987i	$0.195382\pi$
$67$	−1.46088	+	5.45208i	−0.178475	+	0.666077i	−0.995934	+	0.0900900i	$0.971285\pi$
$68$	−8.64153	−	0.285882i	−1.04794	−	0.0346683i
$69$	3.16765	+	1.82884i	0.381340	+	0.220167i
$70$	0.506596	−	0.108408i	0.0605498	−	0.0129572i
$71$	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	$-0.0113797\pi$
$72$	−16.1678	+	11.1775i	−1.90540	+	1.31729i
$73$	9.06992	+	9.06992i	1.06155	+	1.06155i	0.997977	+	0.0635775i	$0.0202510\pi$
$73$	9.06992	+	9.06992i	1.06155	+	1.06155i	0.0635775	+	0.997977i	$0.479749\pi$
$74$	−0.881852	+	2.03322i	−0.102513	+	0.236358i
$75$	1.08583	−	15.7338i	0.125381	−	1.81678i
$76$	2.80792	+	3.00007i	0.322091	+	0.344131i
$77$	−0.389122	−	0.389122i	−0.0443445	−	0.0443445i
$78$	−14.1657	−	7.61675i	−1.60394	−	0.862427i
$79$	6.33294			0.712512			0.356256	−	0.934388i	$-0.384053\pi$
$79$	6.33294			0.712512			0.356256	+	0.934388i	$0.384053\pi$
$80$	−4.23536	+	7.87793i	−0.473527	+	0.880779i
$81$	9.22218	+	15.9733i	1.02469	+	1.77481i
$82$	4.41675	+	11.1824i	0.487748	+	1.23489i
$83$	6.74106	−	6.74106i	0.739928	−	0.739928i	−0.232636	−	0.972564i	$-0.574735\pi$
$83$	6.74106	−	6.74106i	0.739928	−	0.739928i	0.972564	+	0.232636i	$0.0747351\pi$
$84$	−0.300350	+	0.988893i	−0.0327709	+	0.107897i
$85$	3.38951	+	9.05310i	0.367644	+	0.981946i
$86$	0.509663	+	4.43703i	0.0549584	+	0.478457i
$87$	−0.625743	−	2.33531i	−0.0670867	−	0.250371i
$88$	9.46944	−	0.771512i	1.00945	−	0.0822434i
$89$	−3.93581	−	6.81702i	−0.417195	−	0.722603i	0.578461	−	0.815710i	$-0.303653\pi$
$89$	−3.93581	−	6.81702i	−0.417195	−	0.722603i	−0.995656	+	0.0931070i	$0.970320\pi$
$90$	18.4466	+	11.9434i	1.94444	+	1.25894i
$91$	−0.581385	+	0.104407i	−0.0609457	+	0.0109448i
$92$	−1.22538	+	1.96906i	−0.127755	+	0.205289i
$93$	7.52850	−	28.0967i	0.780669	−	2.91350i
$94$	−6.77604	+	5.02364i	−0.698895	+	0.518149i
$95$	1.90325	−	4.18135i	0.195270	−	0.428997i
$96$	−9.65607	−	15.0045i	−0.985519	−	1.53139i
$97$	3.86251	+	14.4151i	0.392179	+	1.46363i	0.826533	+	0.562889i	$0.190310\pi$
$97$	3.86251	+	14.4151i	0.392179	+	1.46363i	−0.434354	+	0.900742i	$0.643023\pi$
$98$	−3.62269	−	9.17203i	−0.365947	−	0.926515i
$99$		−	23.3429i		−	2.34604i
$100$	9.94805	+	1.01797i	0.994805	+	0.101797i
$101$	−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	$0.933873\pi$
$102$	−19.0753	−	2.83292i	−1.88874	−	0.280501i
$103$	−9.83374	−	9.83374i	−0.968947	−	0.968947i	0.0305847	−	0.999532i	$-0.490263\pi$
$103$	−9.83374	−	9.83374i	−0.968947	−	0.968947i	−0.999532	+	0.0305847i	$0.990263\pi$
$104$	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
$107$	14.9557	+	4.00736i	1.44582	+	0.387406i	0.894568	−	0.446933i	$-0.147484\pi$
$107$	14.9557	+	4.00736i	1.44582	+	0.387406i	0.551252	+	0.834339i	$0.314150\pi$
$108$	−21.9761	+	11.7367i	−2.11465	+	1.12936i
$109$	10.1909			0.976116			0.488058	−	0.872811i	$-0.337706\pi$
$109$	10.1909			0.976116			0.488058	+	0.872811i	$0.337706\pi$
$110$	−4.83538	−	9.45785i	−0.461036	−	0.901770i
$111$	−2.47152	+	4.28080i	−0.234587	+	0.406316i
$112$	−0.620384	−	0.211070i	−0.0586208	−	0.0199442i
$113$	1.70291	+	6.35536i	0.160197	+	0.597862i	0.998604	+	0.0528180i	$0.0168203\pi$
$113$	1.70291	+	6.35536i	0.160197	+	0.597862i	−0.838408	+	0.545044i	$0.816513\pi$
$114$	5.45827	+	7.36228i	0.511213	+	0.689540i
$115$	2.55760	+	0.426799i	0.238497	+	0.0397992i
$116$	1.49305	−	0.347586i	0.138626	−	0.0322726i
$117$	−20.5698	−	14.3066i	−1.90168	−	1.32265i
$118$	1.74668	−	2.20003i	0.160795	−	0.202529i
$119$	−0.613357	+	0.354122i	−0.0562264	+	0.0324623i
$120$	−11.3899	+	16.3781i	−1.03975	+	1.49511i
$121$	−0.141592	+	0.245244i	−0.0128720	+	0.0222949i
$122$	1.75856	+	1.39619i	0.159213	+	0.126405i
$123$	6.94053	+	25.9024i	0.625807	+	2.33554i
$124$	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
$127$	−14.5161	−	3.88958i	−1.28810	−	0.345144i	−0.451159	−	0.892444i	$-0.648989\pi$
$127$	−14.5161	−	3.88958i	−1.28810	−	0.345144i	−0.836937	+	0.547299i	$0.815656\pi$
$128$	9.71111	−	5.80468i	0.858349	−	0.513066i
$129$			9.96137i			0.877050i
$130$	−11.2979	−	1.53566i	−0.990888	−	0.134686i
$131$		−	2.19741i		−	0.191988i	−0.995382	−	0.0959942i	$-0.969397\pi$
$131$		−	2.19741i		−	0.191988i	0.995382	−	0.0959942i	$-0.0306030\pi$
$132$	21.1789	+	0.700647i	1.84339	+	0.0609835i
$133$	0.325122	+	0.0871163i	0.0281917	+	0.00755394i
$134$	−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
$137$	1.35350	+	5.05134i	0.115637	+	0.431565i	0.999334	−	0.0364958i	$-0.0116196\pi$
$137$	1.35350	+	5.05134i	0.115637	+	0.431565i	−0.883696	+	0.468061i	$0.844953\pi$
$138$	−3.21640	+	4.05119i	−0.273798	+	0.344861i
$139$	−2.09826	+	3.63429i	−0.177972	+	0.308257i	−0.941186	−	0.337890i	$-0.890287\pi$
$139$	−2.09826	+	3.63429i	−0.177972	+	0.308257i	0.763214	+	0.646146i	$0.223620\pi$
$140$	0.0464029	+	0.731184i	0.00392176	+	0.0617963i
$141$	−16.2931	+	9.40682i	−1.37213	+	0.792197i
$142$	9.90447	+	7.86353i	0.831164	+	0.659893i
$143$	5.15304	+	10.9603i	0.430919	+	0.916544i
$144$	−12.2771	−	24.9389i	−1.02309	−	2.07824i
$145$	−0.995911	−	1.39487i	−0.0827059	−	0.115838i
$146$	−14.5719	+	10.8034i	−1.20598	+	0.894094i
$147$	−5.69274	−	21.2456i	−0.469529	−	1.75231i
$148$	−2.66101	−	1.65600i	−0.218734	−	0.136122i
$149$	0.0288765	−	0.0500155i	0.00236565	−	0.00409743i	−0.864840	−	0.502047i	$-0.832580\pi$
$149$	0.0288765	−	0.0500155i	0.00236565	−	0.00409743i	0.867206	+	0.497950i	$0.165914\pi$
$150$	21.7840	+	4.78763i	1.77865	+	0.390908i
$151$	15.6443			1.27311			0.636557	−	0.771230i	$-0.280358\pi$
$151$	15.6443			1.27311			0.636557	+	0.771230i	$0.280358\pi$
$152$	−4.78005	+	3.30466i	−0.387713	+	0.268043i
$153$	−29.0189	−	7.77558i	−2.34604	−	0.628618i
$154$	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	0.325853	−	0.945420i	$-0.394349\pi$
$157$	−7.76316	−	7.76316i	−0.619568	−	0.619568i	−0.945420	+	0.325853i	$0.894349\pi$
$158$	−1.31567	+	8.85897i	−0.104669	+	0.704782i
$159$	−19.2434	−	33.3305i	−1.52610	−	2.64328i
$160$	−10.1403	−	7.56136i	−0.801662	−	0.597778i
$161$			0.189975i			0.0149721i
$162$	−24.2605	+	9.58219i	−1.90608	+	0.752848i
$163$	1.70110	+	6.34860i	0.133241	+	0.497261i	0.999999	−	0.00146753i	$-0.000467131\pi$
$163$	1.70110	+	6.34860i	0.133241	+	0.497261i	−0.866758	+	0.498729i	$0.833800\pi$
$164$	−16.5604	+	3.85531i	−1.29315	+	0.301049i
$165$	−8.30710	−	22.1876i	−0.646707	−	1.72730i
$166$	8.02942	+	10.8303i	0.623204	+	0.840597i
$167$	4.57729	−	17.0827i	0.354201	−	1.32190i	−0.527285	−	0.849688i	$-0.676790\pi$
$167$	4.57729	−	17.0827i	0.354201	−	1.32190i	0.881487	−	0.472209i	$-0.156543\pi$
$168$	−1.32094	−	0.625593i	−0.101912	−	0.0482656i
$169$	12.8165	+	2.17656i	0.985884	+	0.167428i
$170$	−13.3683	+	2.86071i	−1.02530	+	0.219406i
$171$	7.13882	+	12.3648i	0.545919	+	0.945560i
$172$	−6.31272	−	0.208839i	−0.481340	−	0.0159238i
$173$	0.701612	+	2.61845i	0.0533426	+	0.199077i	0.987455	−	0.157903i	$-0.0504732\pi$
$173$	0.701612	+	2.61845i	0.0533426	+	0.199077i	−0.934112	+	0.356980i	$0.883807\pi$
$174$	3.39679	−	0.390175i	0.257510	−	0.0295791i
$175$	0.735905	−	0.359754i	0.0556292	−	0.0271948i
$176$	−0.888028	+	13.4068i	−0.0669376	+	1.01058i
$177$	4.43028	−	4.43028i	0.333001	−	0.333001i
$178$	10.3538	−	4.08946i	0.776050	−	0.306518i
$179$	9.55658	+	16.5525i	0.714292	+	1.23719i	0.963232	+	0.268671i	$0.0865845\pi$
$179$	9.55658	+	16.5525i	0.714292	+	1.23719i	−0.248940	+	0.968519i	$0.580082\pi$
$180$	−20.5395	+	23.3232i	−1.53093	+	1.73841i
$181$	−9.00568			−0.669387			−0.334693	−	0.942327i	$-0.608633\pi$
$181$	−9.00568			−0.669387			−0.334693	+	0.942327i	$0.608633\pi$
$182$	−0.0252695	−	0.834973i	−0.00187310	−	0.0618923i
$183$	3.54129	+	3.54129i	0.261780	+	0.261780i
$184$	−2.49989	−	2.12323i	−0.184294	−	0.156526i
$185$	−0.576782	+	3.45637i	−0.0424058	+	0.254117i
$186$	37.7397	+	16.3685i	2.76721	+	1.20020i
$187$	10.2683	+	10.2683i	0.750894	+	0.750894i
$188$	−5.61970	−	10.5225i	−0.409859	−	0.767430i
$189$	−1.02039	+	1.76736i	−0.0742222	+	0.128557i
$190$	5.45377	+	3.53108i	0.395658	+	0.256172i
$191$	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	$0.660302\pi$
$192$	22.9955	−	10.3904i	1.65955	−	0.749863i
$193$	2.88227	−	10.7568i	0.207470	−	0.774289i	−0.781212	−	0.624265i	$-0.785398\pi$
$193$	2.88227	−	10.7568i	0.207470	−	0.774289i	0.988682	−	0.150023i	$-0.0479349\pi$
$194$	−20.9673	+	2.40842i	−1.50536	+	0.172915i
$195$	−24.6431	−	6.27829i	−1.76473	−	0.449598i
$196$	13.5831	−	3.16219i	0.970221	−	0.225871i
$197$	3.87460	+	1.03819i	0.276054	+	0.0739683i	0.394190	−	0.919029i	$-0.371025\pi$
$197$	3.87460	+	1.03819i	0.276054	+	0.0739683i	−0.118136	+	0.992997i	$0.537692\pi$
$198$	32.6536	+	4.84947i	2.32059	+	0.344637i
$199$	1.12144	−	1.94240i	0.0794970	−	0.137693i	−0.823536	−	0.567264i	$-0.808002\pi$
$199$	1.12144	−	1.94240i	0.0794970	−	0.137693i	0.903033	+	0.429571i	$0.141335\pi$
$200$	−3.49072	+	13.7046i	−0.246831	+	0.969059i
$201$	−15.4186	−	8.90191i	−1.08754	−	0.627893i
$202$	8.21234	−	3.24364i	0.577819	−	0.228222i
$203$	0.0887921	−	0.0887921i	0.00623198	−	0.00623198i
$204$	7.92578	−	26.0953i	0.554915	−	1.82704i
$205$	11.0463	+	15.4715i	0.771508	+	1.08057i
$206$	15.7991	−	11.7132i	1.10078	−	0.816096i
$207$	−5.69816	+	5.69816i	−0.396049	+	0.396049i
$208$	11.2699	+	8.99943i	0.781426	+	0.623999i
$209$		−	6.90135i		−	0.477377i
$210$	−0.0832818	+	1.63198i	−0.00574699	+	0.112617i
$211$	−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	$0.504264\pi$
$212$	21.5256	−	11.4961i	1.47839	−	0.789558i
$213$	19.9450	+	19.9450i	1.36661	+	1.36661i
$214$	−8.71282	+	20.0885i	−0.595596	+	1.37322i
$215$	2.47607	+	6.61337i	0.168866	+	0.451028i
$216$	−11.8526	−	33.1800i	−0.806468	−	2.25761i
$217$	1.45930	−	0.391019i	0.0990639	−	0.0265441i
$218$	−2.11717	+	14.2558i	−0.143393	+	0.965526i
$219$	−35.0384	+	20.2294i	−2.36768	+	1.36698i
$220$	14.2349	−	4.79921i	0.959714	−	0.323563i
$221$	15.3418	−	2.75514i	1.03200	−	0.185331i
$222$	−5.47483	−	4.34668i	−0.367447	−	0.291730i
$223$	1.37774	+	0.369164i	0.0922602	+	0.0247210i	0.304654	−	0.952463i	$-0.401459\pi$
$223$	1.37774	+	0.369164i	0.0922602	+	0.0247210i	−0.212394	+	0.977184i	$0.568126\pi$
$224$	0.424144	−	0.823987i	0.0283393	−	0.0550550i
$225$	32.8635	+	11.2824i	2.19090	+	0.752159i
$226$	−9.24411	+	1.06183i	−0.614909	+	0.0706320i
$227$	18.6889	−	5.00768i	1.24043	−	0.332371i	0.421796	−	0.906691i	$-0.361400\pi$
$227$	18.6889	−	5.00768i	1.24043	−	0.332371i	0.818631	+	0.574320i	$0.194733\pi$
$228$	−11.4328	+	6.10590i	−0.757158	+	0.404373i
$229$	7.01559			0.463603			0.231802	−	0.972763i	$-0.425538\pi$
$229$	7.01559			0.463603			0.231802	+	0.972763i	$0.425538\pi$
$230$	−1.12838	+	3.48908i	−0.0744030	+	0.230063i
$231$	1.50323	−	0.867892i	0.0989055	−	0.0571031i
$232$	0.176048	+	2.16079i	0.0115581	+	0.141863i
$233$	2.28199	−	2.28199i	0.149498	−	0.149498i	−0.628396	−	0.777894i	$-0.716288\pi$
$233$	2.28199	−	2.28199i	0.149498	−	0.149498i	0.777894	+	0.628396i	$0.216288\pi$
$234$	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
$237$	−5.17008	+	19.2950i	−0.335832	+	1.25334i
$238$	−0.367946	−	0.931577i	−0.0238504	−	0.0603851i
$239$			21.3250i			1.37940i	0.724095	+	0.689700i	$0.242258\pi$
$239$			21.3250i			1.37940i	−0.724095	+	0.689700i	$0.757742\pi$
$240$	−20.5445	−	19.3355i	−1.32614	−	1.24810i
$241$	−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	$0.740073\pi$
$242$	−0.313649	−	0.249018i	−0.0201621	−	0.0160075i
$243$	−20.0983	+	5.38532i	−1.28930	+	0.345468i
$244$	−2.31843	+	2.16994i	−0.148422	+	0.138916i
$245$	−9.06036	−	12.6899i	−0.578845	−	0.810731i
$246$	−37.6760	+	4.32769i	−2.40214	+	0.275923i
$247$	−6.08151	−	4.22977i	−0.386957	−	0.269134i
$248$	−11.1642	+	23.5732i	−0.708930	+	1.49690i
$249$	15.0352	+	26.0417i	0.952816	+	1.65032i
$250$	15.6524	−	2.23625i	0.989948	−	0.141433i
$251$	−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	$0.727679\pi$
$252$	−1.93317	−	1.20305i	−0.121778	−	0.0757850i
$253$	3.76245	−	1.00815i	0.236543	−	0.0633816i
$254$	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
$257$	−5.18147	+	19.3375i	−0.323211	+	1.20624i	0.592886	+	0.805286i	$0.297988\pi$
$257$	−5.18147	+	19.3375i	−0.323211	+	1.20624i	−0.916098	+	0.400955i	$0.868678\pi$
$258$	−13.9347	−	2.06947i	−0.867535	−	0.128840i
$259$	−0.256734			−0.0159527
$260$	4.49532	−	15.4852i	0.278788	−	0.960353i
$261$	5.32651			0.329703
$262$	3.07389	+	0.456511i	0.189906	+	0.0282033i
$263$	4.54747	−	16.9714i	0.280409	−	1.04650i	−0.671720	−	0.740805i	$-0.734444\pi$
$263$	4.54747	−	16.9714i	0.280409	−	1.04650i	0.952129	−	0.305696i	$-0.0988890\pi$
$264$	−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
$267$	23.9830	−	6.42622i	1.46773	−	0.393278i
$268$	5.96457	−	9.58442i	0.364344	−	0.585462i
$269$	−5.65892	−	3.26718i	−0.345031	−	0.199204i	0.317464	−	0.948270i	$-0.397169\pi$
$269$	−5.65892	−	3.26718i	−0.345031	−	0.199204i	−0.662494	+	0.749067i	$0.730502\pi$
$270$	−29.2379	+	26.3987i	−1.77936	+	1.60657i
$271$	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	$0.806578\pi$
$272$	16.3710	+	5.56981i	0.992636	+	0.337719i
$273$	0.156526	−	1.85658i	0.00947339	−	0.112365i
$274$	−7.34736	+	0.843960i	−0.443870	+	0.0509855i
$275$	−11.0302	−	12.6655i	−0.665145	−	0.763758i
$276$	−4.99889	−	5.34096i	−0.300898	−	0.321488i
$277$	−19.6452	+	5.26392i	−1.18037	+	0.316278i	−0.795072	−	0.606515i	$-0.792567\pi$
$277$	−19.6452	+	5.26392i	−1.18037	+	0.316278i	−0.385295	+	0.922794i	$0.625900\pi$
$278$	−4.64799	−	3.69022i	−0.278768	−	0.221324i
$279$	55.4990	+	32.0424i	3.32264	+	1.91833i
$280$	−1.03247	−	0.0869917i	−0.0617020	−	0.00519875i
$281$		−	2.39574i		−	0.142918i	−0.997444	−	0.0714588i	$-0.977235\pi$
$281$		−	2.39574i		−	0.142918i	0.997444	−	0.0714588i	$-0.0227654\pi$
$282$	−9.77404	−	24.7462i	−0.582036	−	1.47361i
$283$	0.392310	−	1.46412i	0.0233204	−	0.0870329i	−0.953285	−	0.302073i	$-0.902321\pi$
$283$	0.392310	−	1.46412i	0.0233204	−	0.0870329i	0.976605	+	0.215040i	$0.0689881\pi$
$284$	−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
$288$	37.4368	−	11.9930i	2.20599	−	0.706695i
$289$	1.46312	−	0.844730i	0.0860656	−	0.0496900i
$290$	2.15815	−	1.10337i	0.126731	−	0.0647919i
$291$	−47.0727			−2.75945
$292$	−12.0852	−	22.6286i	−0.707234	−	1.32424i
$293$	13.8839	−	3.72018i	0.811106	−	0.217335i	0.170652	−	0.985331i	$-0.445413\pi$
$293$	13.8839	−	3.72018i	0.811106	−	0.217335i	0.640455	+	0.767996i	$0.278746\pi$
$294$	30.9025	−	3.54964i	1.80227	−	0.207019i
$295$	1.84005	−	4.04249i	0.107132	−	0.235363i
$296$	2.86935	−	3.37838i	0.166778	−	0.196364i
$297$	40.4175	+	10.8298i	2.34526	+	0.628411i
$298$	0.0639662	+	0.0507852i	0.00370546	+	0.00294191i
$299$	1.41759	−	3.93338i	0.0819812	−	0.227473i
$300$	−11.2229	+	29.4783i	−0.647954	+	1.70193i
$301$	−0.448063	+	0.258689i	−0.0258259	+	0.0149106i
$302$	−3.25010	+	21.8843i	−0.187022	+	1.25930i
$303$	19.0226	−	5.09710i	1.09282	−	0.292821i
$304$	−3.62974	−	7.37322i	−0.208180	−	0.422883i
$305$	3.23131	+	1.47082i	0.185024	+	0.0842189i
$306$	16.9057	−	38.9783i	0.966434	−	2.22824i
$307$	−7.62821	−	7.62821i	−0.435365	−	0.435365i	0.455084	−	0.890449i	$-0.349609\pi$
$307$	−7.62821	−	7.62821i	−0.435365	−	0.435365i	−0.890449	+	0.455084i	$0.849609\pi$
$308$	0.518485	+	0.970824i	0.0295434	+	0.0553178i
$309$	37.9892	−	21.9331i	2.16113	−	1.24773i
$310$	29.1241	+	1.48623i	1.65414	+	0.0844124i
$311$			16.0897i			0.912363i	0.889887	+	0.456181i	$0.150783\pi$
$311$			16.0897i			0.912363i	−0.889887	+	0.456181i	$0.849217\pi$
$312$	22.6814	+	22.8095i	1.28408	+	1.29134i
$313$	11.6193	−	11.6193i	0.656759	−	0.656759i	−0.297853	−	0.954612i	$-0.596270\pi$
$313$	11.6193	−	11.6193i	0.656759	−	0.656759i	0.954612	+	0.297853i	$0.0962704\pi$
$314$	12.4725	−	9.24686i	0.703861	−	0.521831i
$315$	−0.419020	+	2.51098i	−0.0236091	+	0.141478i
$316$	−12.1192	−	3.68090i	−0.681760	−	0.207067i
$317$	5.28001	−	5.28001i	0.296555	−	0.296555i	−0.543108	−	0.839663i	$-0.682753\pi$
$317$	5.28001	−	5.28001i	0.296555	−	0.296555i	0.839663	+	0.543108i	$0.182753\pi$
$318$	50.6229	−	19.9946i	2.83879	−	1.12124i
$319$	−2.22972	−	1.28733i	−0.124841	−	0.0720767i
$320$	12.6840	−	12.6141i	0.709058	−	0.705150i
$321$	−24.4190	+	42.2949i	−1.36293	+	2.36067i
$322$	−0.265750	−	0.0394672i	−0.0148097	−	0.00219942i
$323$	−8.57947	−	2.29886i	−0.477375	−	0.127912i
$324$	−8.36414	−	35.9279i	−0.464675	−	1.99600i
$325$	−17.9212	+	1.95730i	−0.994089	+	0.108571i
$326$	−9.23428	+	1.06070i	−0.511440	+	0.0587469i
$327$	−8.31967	+	31.0494i	−0.460079	+	1.71704i
$328$	−1.95267	−	23.9668i	−0.107818	−	1.32334i
$329$	−0.846238	−	0.488576i	−0.0466546	−	0.0269361i
$330$	32.7633	−	7.01109i	1.80356	−	0.385948i
$331$	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	$-0.0268078\pi$
$332$	−16.8183	+	8.98213i	−0.923027	+	0.492958i
$333$	−7.70056	−	7.70056i	−0.421988	−	0.421988i
$334$	22.9455	+	9.95196i	1.25552	+	0.544547i
$335$	−12.4491	−	2.07745i	−0.680168	−	0.113503i
$336$	1.14955	−	1.71785i	0.0627130	−	0.0937165i
$337$	−21.7455	−	21.7455i	−1.18455	−	1.18455i	−0.978551	−	0.206004i	$-0.933954\pi$
$337$	−21.7455	−	21.7455i	−1.18455	−	1.18455i	−0.206004	−	0.978551i	$-0.566046\pi$
$338$	−5.70735	+	17.4764i	−0.310439	+	0.950593i
$339$	−20.7535			−1.12718
$340$	−1.22450	−	19.2948i	−0.0664079	−	1.04641i
$341$	−15.4883	−	26.8265i	−0.838736	−	1.45273i
$342$	−18.7799	+	7.41751i	−1.01550	+	0.401093i
$343$	1.61869	−	1.61869i	0.0874012	−	0.0874012i
$344$	1.60360	−	8.78729i	0.0864606	−	0.473779i
$345$	−3.38832	+	7.44397i	−0.182421	+	0.400770i
$346$	−3.80863	+	0.437482i	−0.204753	+	0.0235192i
$347$	9.07296	+	33.8608i	0.487062	+	1.81774i	0.570590	+	0.821235i	$0.306715\pi$
$347$	9.07296	+	33.8608i	0.487062	+	1.81774i	−0.0835278	+	0.996505i	$0.526619\pi$
$348$	−0.159878	+	4.83273i	−0.00857035	+	0.259061i
$349$	−8.33710	−	14.4403i	−0.446275	−	0.772971i	0.551865	−	0.833933i	$-0.313916\pi$
$349$	−8.33710	−	14.4403i	−0.446275	−	0.772971i	−0.998140	+	0.0609628i	$0.980583\pi$
$350$	0.350365	+	1.10418i	0.0187278	+	0.0590206i
$351$	34.3148	−	28.9786i	1.83159	−	1.54676i
$352$	−18.5699	−	4.02750i	−0.989779	−	0.214666i
$353$	−1.61347	+	6.02155i	−0.0858762	+	0.320495i	−0.995479	−	0.0949852i	$-0.969720\pi$
$353$	−1.61347	+	6.02155i	−0.0858762	+	0.320495i	0.909602	+	0.415480i	$0.136386\pi$
$354$	5.27701	+	7.11779i	0.280470	+	0.378306i
$355$	18.1992	+	8.28387i	0.965914	+	0.439662i
$356$	3.56962	+	15.3332i	0.189190	+	0.812659i
$357$	−0.578195	−	2.15785i	−0.0306013	−	0.114206i
$358$	−25.1402	+	9.92964i	−1.32870	+	0.524798i
$359$		−	15.1568i		−	0.799944i	−0.916527	−	0.399972i	$-0.869020\pi$
$359$		−	15.1568i		−	0.799944i	0.916527	−	0.399972i	$-0.130980\pi$
$360$	−28.3590	−	33.5775i	−1.49465	−	1.76969i
$361$	−7.38939	−	12.7988i	−0.388916	−	0.673621i
$362$	1.87093	−	12.5978i	0.0983338	−	0.662125i
$363$	−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
$367$	−29.6222	−	7.93725i	−1.54627	−	0.414321i	−0.617982	−	0.786192i	$-0.712050\pi$
$367$	−29.6222	−	7.93725i	−1.54627	−	0.414321i	−0.928284	+	0.371871i	$0.878716\pi$
$368$	3.48947	−	3.05592i	0.181901	−	0.159301i
$369$	−59.0799			−3.07557
$370$	−4.71519	−	1.52490i	−0.245131	−	0.0792759i
$371$	0.999472	−	1.73114i	0.0518900	−	0.0898761i
$372$	−30.7378	+	49.3924i	−1.59368	+	2.56087i
$373$	3.74051	+	13.9598i	0.193676	+	0.722810i	0.992606	+	0.121385i	$0.0387335\pi$
$373$	3.74051	+	13.9598i	0.193676	+	0.722810i	−0.798929	+	0.601425i	$0.794600\pi$
$374$	−16.4973	+	12.2308i	−0.853054	+	0.632440i
$375$	35.2521	−	0.971246i	1.82041	−	0.0501549i
$376$	15.8871	−	5.67520i	0.819313	−	0.292676i
$377$	−2.50098	+	1.17585i	−0.128807	+	0.0605594i
$378$	−2.26033	−	1.79456i	−0.116259	−	0.0923021i
$379$	13.2319	−	7.63943i	0.679676	−	0.392411i	−0.120057	−	0.992767i	$-0.538308\pi$
$379$	13.2319	−	7.63943i	0.679676	−	0.392411i	0.799733	+	0.600356i	$0.204974\pi$
$380$	−6.07255	+	6.89553i	−0.311515	+	0.353733i
$381$	23.7013	−	41.0518i	1.21425	−	2.10315i
$382$	−0.485994	+	0.612131i	−0.0248656	+	0.0313193i
$383$	−0.532995	−	1.98917i	−0.0272348	−	0.101642i	0.950971	−	0.309281i	$-0.100088\pi$
$383$	−0.532995	−	1.98917i	−0.0272348	−	0.101642i	−0.978205	+	0.207640i	$0.933422\pi$
$384$	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
$387$	−21.1985	−	5.68013i	−1.07758	−	0.288737i
$388$	0.986875	−	29.8309i	0.0501010	−	1.51443i
$389$		−	30.7357i		−	1.55836i	−0.626799	−	0.779181i	$-0.715635\pi$
$389$		−	30.7357i		−	1.55836i	0.626799	−	0.779181i	$-0.284365\pi$
$390$	13.9021	−	33.1683i	0.703962	−	1.67954i
$391$		−	5.01314i		−	0.253525i
$392$	1.60161	+	19.6579i	0.0808934	+	0.992876i
$393$	6.69498	+	1.79392i	0.337717	+	0.0904911i
$394$	−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
$397$	−2.23844	−	8.35399i	−0.112344	−	0.419275i	0.886730	−	0.462287i	$-0.152971\pi$
$397$	−2.23844	−	8.35399i	−0.112344	−	0.419275i	−0.999075	+	0.0430126i	$0.986304\pi$
$398$	2.48418	+	1.97229i	0.124521	+	0.0988618i
$399$	−0.530846	+	0.919452i	−0.0265755	+	0.0460302i
$400$	−18.4457	−	7.73018i	−0.922286	−	0.386509i
$401$	−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	$0.467440\pi$
$402$	15.6558	−	19.7192i	0.780842	−	0.983505i
$403$	−33.1322	−	2.79334i	−1.65043	−	0.139146i
$404$	2.83132	+	12.1619i	0.140864	+	0.605076i
$405$	−33.5655	+	23.9651i	−1.66788	+	1.19084i
$406$	0.105762	+	0.142655i	0.00524889	+	0.00707986i
$407$	1.36242	+	5.08463i	0.0675327	+	0.252036i
$408$	34.8574	+	16.5084i	1.72570	+	0.817290i
$409$	−8.64649	+	14.9762i	−0.427541	+	0.740523i	−0.996654	−	0.0817363i	$-0.973953\pi$
$409$	−8.64649	+	14.9762i	−0.427541	+	0.740523i	0.569113	+	0.822260i	$0.307287\pi$
$410$	−23.9375	+	12.2382i	−1.18219	+	0.604400i
$411$	−16.4952			−0.813648
$412$	13.1030	+	24.5343i	0.645537	+	1.20872i
$413$	0.314326	+	0.0842233i	0.0154670	+	0.00414436i
$414$	−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
$418$	9.65410	+	1.43375i	0.472198	+	0.0701272i
$419$	7.42077	+	12.8531i	0.362528	+	0.627917i	0.988376	−	0.152028i	$-0.0485803\pi$
$419$	7.42077	+	12.8531i	0.362528	+	0.627917i	−0.625848	+	0.779945i	$0.715247\pi$
$420$	−2.26563	−	0.455544i	−0.110551	−	0.0222283i
$421$		−	23.5194i		−	1.14627i	−0.819462	−	0.573134i	$-0.805728\pi$
$421$		−	23.5194i		−	1.14627i	0.819462	−	0.573134i	$-0.194272\pi$
$422$	−7.72087	−	19.5479i	−0.375846	−	0.951578i
$423$	−10.7278	−	40.0368i	−0.521605	−	1.94666i
$424$	11.6097	+	32.4999i	0.563815	+	1.57834i
$425$	−19.4194	+	9.49335i	−0.941979	+	0.460495i
$426$	−32.0441	+	23.7570i	−1.55254	+	1.15103i
$427$	−0.0673227	+	0.251252i	−0.00325798	+	0.0121589i
$428$	−26.2912	−	16.3615i	−1.27083	−	0.790863i
$429$	−37.6002	+	6.75237i	−1.81536	+	0.326008i
$430$	−9.76565	+	2.08977i	−0.470941	+	0.100778i
$431$	−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	$-0.391428\pi$
$432$	48.8769	−	9.68713i	2.35159	−	0.466072i
$433$	−6.37160	−	23.7791i	−0.306200	−	1.14275i	−0.931908	−	0.362695i	$-0.881857\pi$
$433$	−6.37160	−	23.7791i	−0.306200	−	1.14275i	0.625708	−	0.780057i	$-0.284810\pi$
$434$	0.243815	+	2.12261i	0.0117035	+	0.101888i
$435$	5.06289	−	1.89556i	0.242747	−	0.0908853i
$436$	−19.5022	−	5.92329i	−0.933987	−	0.283674i
$437$	−1.68467	+	1.68467i	−0.0805887	+	0.0805887i
$438$	−21.0192	−	53.2169i	−1.00433	−	2.54280i
$439$	−0.831387	−	1.44000i	−0.0396799	−	0.0687276i	0.845503	−	0.533970i	$-0.179300\pi$
$439$	−0.831387	−	1.44000i	−0.0396799	−	0.0687276i	−0.885183	+	0.465242i	$0.845967\pi$
$440$	3.75619	+	20.9098i	0.179069	+	0.996834i
$441$	48.4583			2.30754
$442$	0.666822	+	22.0336i	0.0317175	+	1.04803i
$443$	18.5752	+	18.5752i	0.882532	+	0.882532i	0.993791	−	0.111259i	$-0.0354884\pi$
$443$	18.5752	+	18.5752i	0.882532	+	0.882532i	−0.111259	+	0.993791i	$0.535488\pi$
$444$	7.21784	−	6.75556i	0.342543	−	0.320605i
$445$	14.3250	−	10.2277i	0.679069	−	0.484842i
$446$	−0.802637	+	1.85058i	−0.0380060	+	0.0876277i
$447$	0.128812	+	0.128812i	0.00609257	+	0.00609257i
$448$	1.06454	+	0.764506i	0.0502946	+	0.0361195i
$449$	11.2483	−	19.4826i	0.530838	−	0.919439i	−0.468514	−	0.883456i	$-0.655210\pi$
$449$	11.2483	−	19.4826i	0.530838	−	0.919439i	0.999352	−	0.0359829i	$-0.0114562\pi$
$450$	−22.6100	+	43.6279i	−1.06585	+	2.05664i
$451$	24.7313	+	14.2787i	1.16455	+	0.672355i
$452$	0.435096	−	13.1519i	0.0204652	−	0.618614i
$453$	−12.7717	+	47.6645i	−0.600065	+	2.23947i
$454$	3.12248	+	27.1837i	0.146545	+	1.27580i
$455$	−0.357566	−	1.27149i	−0.0167629	−	0.0596085i
$456$	−6.16620	−	17.2616i	−0.288759	−	0.808346i
$457$	11.3637	+	3.04489i	0.531571	+	0.142434i	0.514614	−	0.857422i	$-0.327935\pi$
$457$	11.3637	+	3.04489i	0.531571	+	0.142434i	0.0169575	+	0.999856i	$0.494602\pi$
$458$	−1.45749	+	9.81390i	−0.0681039	+	0.458574i
$459$	26.9264	−	46.6379i	1.25682	−	2.17687i
$460$	−4.64636	−	2.30331i	−0.216637	−	0.107392i
$461$	−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	$0.668769\pi$
$462$	0.901772	+	2.28313i	0.0419543	+	0.106221i
$463$	−9.78891	+	9.78891i	−0.454929	+	0.454929i	−0.896987	−	0.442058i	$-0.854249\pi$
$463$	−9.78891	+	9.78891i	−0.454929	+	0.454929i	0.442058	+	0.896987i	$0.354249\pi$
$464$	−3.05924	−	0.202636i	−0.142022	−	0.00940712i
$465$	64.1553	+	10.7059i	2.97513	+	0.496475i
$466$	2.71813	+	3.66630i	0.125915	+	0.169838i
$467$	−7.98810	+	7.98810i	−0.369645	+	0.369645i	−0.867348	−	0.497703i	$-0.834177\pi$
$467$	−7.98810	+	7.98810i	−0.369645	+	0.369645i	0.497703	+	0.867348i	$0.334177\pi$
$468$	31.0487	+	39.3341i	1.43522	+	1.81822i
$469$		−	0.924704i		−	0.0426989i
$470$	−12.6401	−	13.9995i	−0.583043	−	0.645750i
$471$	29.9902	−	17.3148i	1.38188	−	0.797826i
$472$	−4.62131	+	3.19492i	−0.212713	+	0.147058i
$473$	7.50110	+	7.50110i	0.344901	+	0.344901i
$474$	−25.9171	−	11.2408i	−1.19041	−	0.516307i
$475$	9.71615	+	3.33566i	0.445808	+	0.153050i
$476$	1.37960	−	0.321174i	0.0632337	−	0.0147210i
$477$	81.9027	−	21.9457i	3.75006	−	1.00483i
$478$	−29.8309	−	4.43026i	−1.36443	−	0.202636i
$479$	2.34517	−	1.35398i	0.107154	−	0.0618651i	−0.445466	−	0.895299i	$-0.646962\pi$
$479$	2.34517	−	1.35398i	0.107154	−	0.0618651i	0.552619	+	0.833434i	$0.313628\pi$
$480$	31.3160	−	24.7222i	1.42937	−	1.12841i
$481$	5.31561	+	1.91575i	0.242371	+	0.0873505i
$482$	6.24065	−	7.86037i	0.284254	−	0.358030i
$483$	−0.578809	−	0.155091i	−0.0263367	−	0.00705690i
$484$	0.413504	−	0.387021i	0.0187956	−	0.0175918i
$485$	−31.2516	+	11.7007i	−1.41906	+	0.531302i
$486$	−3.35795	−	29.2337i	−0.152320	−	1.32607i
$487$	−9.39781	+	2.51813i	−0.425855	+	0.114108i	−0.465380	−	0.885111i	$-0.654082\pi$
$487$	−9.39781	+	2.51813i	−0.425855	+	0.114108i	0.0395247	+	0.999219i	$0.487416\pi$
$488$	−2.55382	−	3.69398i	−0.115606	−	0.167219i
$489$	−20.7314			−0.937509
$490$	19.6339	−	10.0379i	0.886968	−	0.453468i
$491$	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	$0.321678\pi$
$492$	1.77331	−	53.6030i	0.0799470	−	2.41661i
$493$	−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
$497$	−0.379171	+	1.41509i	−0.0170082	+	0.0634753i
$498$	−39.5525	+	15.6221i	−1.77239	+	0.700044i
$499$		−	31.4652i		−	1.40858i	−0.709914	−	0.704289i	$-0.751266\pi$
$499$		−	31.4652i		−	1.40858i	0.709914	−	0.704289i	$-0.248734\pi$
$500$	−0.123561	+	22.3603i	−0.00552580	+	0.999985i
$501$	48.3101	+	27.8919i	2.15834	+	1.24612i
$502$	5.30802	−	6.68569i	0.236909	−	0.298397i
$503$	5.83660	−	1.56391i	0.260241	−	0.0697314i	−0.126339	−	0.991987i	$-0.540323\pi$
$503$	5.83660	−	1.56391i	0.260241	−	0.0697314i	0.386580	+	0.922256i	$0.373656\pi$
$504$	2.08453	−	2.45432i	0.0928522	−	0.109324i
$505$	11.3622	−	8.11236i	0.505610	−	0.360995i
$506$	0.628618	+	5.47263i	0.0279455	+	0.243288i
$507$	−17.0946	+	37.2720i	−0.759197	+	1.65531i
$508$	25.5184	+	15.8806i	1.13220	+	0.704588i
$509$	6.49123	+	11.2431i	0.287719	+	0.498344i	0.973265	−	0.229686i	$-0.0737698\pi$
$509$	6.49123	+	11.2431i	0.287719	+	0.498344i	−0.685546	+	0.728029i	$0.740436\pi$
$510$	2.19768	−	43.0654i	0.0973148	−	1.90697i
$511$	−1.81984	−	1.05069i	−0.0805051	−	0.0464796i
$512$	−21.9578	+	5.46390i	−0.970408	+	0.241472i
$513$	−24.7214	+	6.62407i	−1.09147	+	0.292460i
$514$	−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
$517$	−5.18549	+	19.3525i	−0.228057	+	0.851122i
$518$	0.0533365	−	0.359138i	0.00234347	−	0.0157796i
$519$	−8.55059			−0.375329
$520$	20.7279	+	9.50542i	0.908980	+	0.416840i
$521$	25.1504			1.10186			0.550929	−	0.834552i	$-0.314274\pi$
$521$	25.1504			1.10186			0.550929	+	0.834552i	$0.314274\pi$
$522$	−1.10658	+	7.45110i	−0.0484337	+	0.326126i
$523$	−3.98160	+	14.8595i	−0.174103	+	0.649761i	0.822600	+	0.568621i	$0.192523\pi$
$523$	−3.98160	+	14.8595i	−0.174103	+	0.649761i	−0.996703	+	0.0811405i	$0.974144\pi$
$524$	−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
$527$	−38.5087	+	10.3184i	−1.67747	+	0.449476i
$528$	−40.1224	−	13.6506i	−1.74610	−	0.594068i
$529$	18.7540	+	10.8277i	0.815393	+	0.470768i
$530$	28.6386	−	25.8576i	1.24398	−	1.12318i
$531$	6.90175	+	11.9542i	0.299511	+	0.518768i
$532$	−0.571546	−	0.355684i	−0.0247796	−	0.0154208i
$533$	27.7400	−	13.0421i	1.20155	−	0.564918i
$534$	4.00699	+	34.8841i	0.173400	+	1.50958i
$535$	−5.69868	+	34.1494i	−0.246376	+	1.47641i
$536$	12.1682	+	10.3348i	0.525588	+	0.446396i
$537$	−58.2333	+	15.6036i	−2.51295	+	0.673343i
$538$	5.74601	−	7.23735i	0.247728	−	0.312024i
$539$	−20.2851	−	11.7116i	−0.873739	−	0.504453i
$540$	−30.8542	−	46.3843i	−1.32775	−	1.99606i
$541$			12.5555i			0.539804i	0.962888	+	0.269902i	$0.0869913\pi$
$541$			12.5555i			0.539804i	−0.962888	+	0.269902i	$0.913009\pi$
$542$	−3.63577	+	1.43603i	−0.156170	+	0.0616826i
$543$	7.35204	−	27.4382i	0.315506	−	1.17749i
$544$	−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	$-0.532282\pi$
$547$	20.8999	−	20.8999i	0.893617	−	0.893617i	0.994862	+	0.101244i	$0.0322824\pi$
$548$	0.345821	−	10.4533i	0.0147727	−	0.446544i
$549$	−9.55542	+	5.51682i	−0.407815	+	0.235452i
$550$	20.0089	−	12.7986i	0.853182	−	0.545732i
$551$	1.57479			0.0670884
$552$	8.50983	−	5.88322i	0.362202	−	0.250407i
$553$	−1.00215	+	0.268526i	−0.0426159	+	0.0114189i
$554$	−3.28225	−	28.5747i	−0.139450	−	1.21402i
$555$	−10.0599	−	4.57902i	−0.427018	−	0.194369i
$556$	6.12776	−	5.73530i	0.259875	−	0.243231i
$557$	17.6965	+	4.74177i	0.749826	+	0.200915i	0.613441	−	0.789741i	$-0.289785\pi$
$557$	17.6965	+	4.74177i	0.749826	+	0.200915i	0.136385	+	0.990656i	$0.456452\pi$
$558$	−56.3531	+	70.9792i	−2.38562	+	3.00479i
$559$	11.2074	−	2.01265i	0.474021	−	0.0851262i
$560$	0.336186	−	1.42622i	0.0142065	−	0.0602689i
$561$	−39.6680	+	22.9023i	−1.67478	+	0.966937i
$562$	3.35133	+	0.497714i	0.141367	+	0.0209948i
$563$	27.2080	−	7.29035i	1.14668	−	0.307252i	0.365045	−	0.930990i	$-0.381053\pi$
$563$	27.2080	−	7.29035i	1.14668	−	0.307252i	0.781633	+	0.623738i	$0.214387\pi$
$564$	36.6473	−	8.53161i	1.54313	−	0.359245i
$565$	−13.7783	+	5.15863i	−0.579657	+	0.217025i
$566$	1.96661	+	0.852961i	0.0826629	+	0.0358526i
$567$	−2.13665	−	2.13665i	−0.0897308	−	0.0897308i
$568$	−14.3835	−	20.8051i	−0.603516	−	0.872961i
$569$	23.7981	−	13.7398i	0.997668	−	0.576004i	0.0901103	−	0.995932i	$-0.471278\pi$
$569$	23.7981	−	13.7398i	0.997668	−	0.576004i	0.907557	+	0.419928i	$0.137945\pi$
$570$	−15.2107	+	13.7336i	−0.637107	+	0.575239i
$571$		−	47.3246i		−	1.98047i	−0.139401	−	0.990236i	$-0.544518\pi$
$571$		−	47.3246i		−	1.98047i	0.139401	−	0.990236i	$-0.455482\pi$
$572$	−3.49083	−	23.9696i	−0.145959	−	1.00222i
$573$	−1.23267	+	1.23267i	−0.0514957	+	0.0514957i
$574$	−1.17308	−	1.58228i	−0.0489633	−	0.0660432i
$575$	−0.399190	+	5.78429i	−0.0166474	+	0.241221i
$576$	8.99918	+	54.8608i	0.374966	+	2.28587i
$577$	28.3643	−	28.3643i	1.18082	−	1.18082i	0.201287	−	0.979532i	$-0.435488\pi$
$577$	28.3643	−	28.3643i	1.18082	−	1.18082i	0.979532	−	0.201287i	$-0.0645125\pi$
$578$	0.877707	+	2.22220i	0.0365078	+	0.0924314i
$579$	30.4203	+	17.5632i	1.26423	+	0.729901i
$580$	1.09511	+	3.24819i	0.0454721	+	0.134874i
$581$	−0.780904	+	1.35257i	−0.0323974	+	0.0561139i
$582$	9.77934	−	65.8486i	0.405367	−	2.72951i
$583$	−39.5891	−	10.6079i	−1.63961	−	0.439333i
$584$	34.1653	−	12.2046i	1.41377	−	0.505029i
$585$	27.4126	−	48.8624i	1.13337	−	2.02021i
$586$	2.31968	+	20.1947i	0.0958249	+	0.834234i
$587$	5.95187	−	22.2127i	0.245660	−	0.916816i	−0.727390	−	0.686224i	$-0.759267\pi$
$587$	5.95187	−	22.2127i	0.245660	−	0.916816i	0.973050	−	0.230592i	$-0.0740663\pi$
$588$	−1.45450	+	43.9660i	−0.0599825	+	1.81313i
$589$	16.4084	+	9.47339i	0.676096	+	0.390344i
$590$	5.27266	+	3.41382i	0.217072	+	0.140545i
$591$	−6.32627	+	10.9574i	−0.260228	+	0.450728i
$592$	4.12981	+	4.71571i	0.169734	+	0.193815i
$593$	5.59820	+	5.59820i	0.229891	+	0.229891i	0.812647	−	0.582756i	$-0.198026\pi$
$593$	5.59820	+	5.59820i	0.229891	+	0.229891i	−0.582756	+	0.812647i	$0.698026\pi$
$594$	−23.5463	+	54.2890i	−0.966116	+	2.22750i
$595$	−0.920235	−	1.28888i	−0.0377260	−	0.0528390i
$596$	−0.0843309	+	0.0789299i	−0.00345433	+	0.00323309i
$597$	5.00250	+	5.00250i	0.204739	+	0.204739i
$598$	5.20778	+	2.80018i	0.212962	+	0.114508i
$599$	13.9664			0.570653			0.285326	−	0.958430i	$-0.407898\pi$
$599$	13.9664			0.570653			0.285326	+	0.958430i	$0.407898\pi$
$600$	−38.9048	−	21.8235i	−1.58828	−	0.890940i
$601$	−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	$-0.410730\pi$
$602$	−0.268788	−	0.680525i	−0.0109550	−	0.0277361i
$603$	27.7358	−	27.7358i	1.12949	−	1.12949i
$604$	−29.9382	−	9.09293i	−1.21817	−	0.369986i
$605$	−0.576322	−	0.262328i	−0.0234308	−	0.0106652i
$606$	3.17824	+	27.6691i	0.129107	+	1.12398i
$607$	−1.97028	−	7.35319i	−0.0799712	−	0.298457i	0.914343	−	0.404940i	$-0.132708\pi$
$607$	−1.97028	−	7.35319i	−0.0799712	−	0.298457i	−0.994314	+	0.106483i	$0.966041\pi$
$608$	11.0683	−	3.54575i	0.448877	−	0.143799i
$609$	0.198041	+	0.343017i	0.00802501	+	0.0138997i
$610$	−2.72879	+	4.21463i	−0.110485	+	0.170645i
$611$	13.8754	+	16.4304i	0.561338	+	0.664704i
$612$	51.0134	+	31.7466i	2.06209	+	1.28328i
$613$	−7.17258	+	26.7684i	−0.289698	+	1.08117i	0.655640	+	0.755074i	$0.272399\pi$
$613$	−7.17258	+	26.7684i	−0.289698	+	1.08117i	−0.945338	+	0.326093i	$0.894268\pi$
$614$	12.2556	−	9.08612i	0.494597	−	0.366686i
$615$	−56.1559	+	21.0249i	−2.26442	+	0.847808i
$616$	−1.46577	+	0.523605i	−0.0590576	+	0.0210967i
$617$	8.71256	+	32.5157i	0.350754	+	1.30903i	0.885744	+	0.464175i	$0.153649\pi$
$617$	8.71256	+	32.5157i	0.350754	+	1.30903i	−0.534989	+	0.844859i	$0.679684\pi$
$618$	22.7893	+	57.6985i	0.916719	+	2.32097i
$619$			26.6411i			1.07080i	0.844599	+	0.535399i	$0.179839\pi$
$619$			26.6411i			1.07080i	−0.844599	+	0.535399i	$0.820161\pi$
$620$	−8.12957	+	40.4320i	−0.326491	+	1.62379i
$621$	−7.22257	−	12.5099i	−0.289832	−	0.502003i
$622$	−22.5074	−	3.34263i	−0.902465	−	0.134027i
$623$	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
$627$	21.0268	+	5.63412i	0.839730	+	0.225005i
$628$	10.3440	+	19.3684i	0.412771	+	0.772883i
$629$	6.77482			0.270130
$630$	−3.42549	−	1.10781i	−0.136475	−	0.0441362i
$631$	−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	$0.910214\pi$
$632$	7.66687	−	16.1885i	0.304972	−	0.643945i
$633$	−12.1327	−	45.2798i	−0.482230	−	1.79971i
$634$	6.28913	+	8.48297i	0.249773	+	0.336902i
$635$	5.53119	−	33.1457i	0.219499	−	1.31535i
$636$	17.4530	+	74.9688i	0.692055	+	2.97270i
$637$	−22.7528	+	10.6974i	−0.901499	+	0.423846i
$638$	2.26404	−	2.85165i	0.0896340	−	0.112898i
$639$	−53.8175	+	31.0715i	−2.12899	+	1.22917i
$640$	15.0104	+	20.3639i	0.593339	+	0.804953i
$641$	−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	$0.177449\pi$
$642$	−54.0921	−	42.9458i	−2.13484	−	1.69493i
$643$	−3.56058	−	13.2883i	−0.140416	−	0.524039i	−0.999917	−	0.0129046i	$-0.995892\pi$
$643$	−3.56058	−	13.2883i	−0.140416	−	0.524039i	0.859501	−	0.511134i	$-0.170774\pi$
$644$	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
$647$	−4.15992	−	1.11465i	−0.163543	−	0.0438213i	0.176118	−	0.984369i	$-0.443646\pi$
$647$	−4.15992	−	1.11465i	−0.163543	−	0.0438213i	−0.339662	+	0.940548i	$0.610313\pi$
$648$	51.9962	−	4.23633i	2.04260	−	0.166419i
$649$		−	6.67217i		−	0.261906i
$650$	0.985113	−	25.4761i	0.0386393	−	0.999253i
$651$			4.76537i			0.186770i
$652$	0.434633	−	13.1379i	0.0170215	−	0.514521i
$653$	−9.89557	−	2.65151i	−0.387243	−	0.103762i	0.0599442	−	0.998202i	$-0.480908\pi$
$653$	−9.89557	−	2.65151i	−0.387243	−	0.103762i	−0.447188	+	0.894440i	$0.647574\pi$
$654$	−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
$657$	−23.0703	−	86.0995i	−0.900058	−	3.35906i
$658$	0.859261	−	1.08228i	0.0334975	−	0.0421915i
$659$	−5.49476	+	9.51720i	−0.214045	+	0.370737i	−0.952977	−	0.303043i	$-0.901997\pi$
$659$	−5.49476	+	9.51720i	−0.214045	+	0.370737i	0.738932	+	0.673781i	$0.235331\pi$
$660$	3.00104	+	47.2882i	0.116815	+	1.84069i
$661$	−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	$0.389925\pi$
$662$	23.0152	+	18.2727i	0.894513	+	0.710187i
$663$	−4.13048	+	48.9922i	−0.160415	+	1.90270i
$664$	−9.07083	−	25.3927i	−0.352016	−	0.985429i
$665$	−0.123884	+	0.742376i	−0.00480402	+	0.0287881i
$666$	12.3719	−	9.17230i	0.479401	−	0.355420i
$667$	0.230045	+	0.858539i	0.00890737	+	0.0332428i
$668$	−18.6884	+	30.0303i	−0.723078	+	1.16191i
$669$	−2.24951	+	3.89627i	−0.0869711	+	0.150638i
$670$	5.49239	−	16.9831i	0.212189	−	0.656116i
$671$	5.33331			0.205890
$672$	2.16423	+	1.96495i	0.0834871	+	0.0757997i
$673$	−32.7834	−	8.78429i	−1.26371	−	0.338609i	−0.436091	−	0.899903i	$-0.643637\pi$
$673$	−32.7834	−	8.78429i	−1.26371	−	0.338609i	−0.827617	+	0.561293i	$0.810304\pi$
$674$	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	0.952170	−	0.305570i	$-0.0988469\pi$
$677$	16.8240	+	16.8240i	0.646600	+	0.646600i	−0.305570	+	0.952170i	$0.598847\pi$
$678$	4.31154	−	29.0315i	0.165584	−	1.11495i
$679$	−1.22244	−	2.11733i	−0.0469130	−	0.0812557i
$680$	27.2453	+	2.29557i	1.04481	+	0.0880313i
$681$			61.0289i			2.33863i
$682$	40.7444	−	16.0929i	1.56018	−	0.616229i
$683$	0.388072	+	1.44830i	0.0148492	+	0.0554178i	0.972953	−	0.231004i	$-0.0742009\pi$
$683$	0.388072	+	1.44830i	0.0148492	+	0.0554178i	−0.958104	+	0.286421i	$0.907534\pi$
$684$	−6.47462	−	27.8116i	−0.247563	−	1.06340i
$685$	−10.9512	+	4.10016i	−0.418423	+	0.156659i
$686$	1.92806	+	2.60062i	0.0736136	+	0.0992923i
$687$	−5.72737	+	21.3749i	−0.218513	+	0.815502i
$688$	11.9591	+	4.06879i	0.455938	+	0.155121i
$689$	−33.6115	+	28.3847i	−1.28050	+	1.08137i
$690$	−9.70923	−	6.28631i	−0.369624	−	0.239316i
$691$	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	$0.696372\pi$
$692$	0.179262	−	5.41868i	0.00681453	−	0.205987i
$693$	0.989771	+	3.69388i	0.0375983	+	0.140319i
$694$	−49.2517	+	5.65734i	−1.86957	+	0.214750i
$695$	−8.54057	−	3.88747i	−0.323962	−	0.147460i
$696$	−6.72715	−	1.22765i	−0.254992	−	0.0465338i
$697$	25.9887	−	25.9887i	0.984393	−	0.984393i
$698$	21.9321	−	8.66256i	0.830143	−	0.327883i
$699$	5.08973	+	8.81567i	0.192511	+	0.333439i
$700$	−1.61739	+	0.260724i	−0.0611315	+	0.00985443i
$701$	−10.0746			−0.380511			−0.190256	−	0.981735i	$-0.560932\pi$
$701$	−10.0746			−0.380511			−0.190256	+	0.981735i	$0.560932\pi$
$702$	33.4085	+	54.0223i	1.26092	+	2.03894i
$703$	−2.27668	−	2.27668i	−0.0858668	−	0.0858668i
$704$	9.49184	−	25.1402i	0.357737	−	0.947506i
$705$	−24.4449	−	34.2376i	−0.920649	−	1.28946i
$706$	−8.08817	−	3.50801i	−0.304402	−	0.132026i
$707$	0.723271	+	0.723271i	0.0272014	+	0.0272014i
$708$	−11.0532	+	5.90313i	−0.415403	+	0.221853i
$709$	−11.8760	+	20.5697i	−0.446011	+	0.772513i	−0.998122	−	0.0612572i	$-0.980489\pi$
$709$	−11.8760	+	20.5697i	−0.446011	+	0.772513i	0.552111	+	0.833770i	$0.313822\pi$
$710$	−15.3689	+	23.7374i	−0.576786	+	0.890848i
$711$	−38.1131	−	22.0046i	−1.42935	−	0.825237i
$712$	−22.1908	+	1.80797i	−0.831634	+	0.0677565i
$713$	−2.76774	+	10.3293i	−0.103653	+	0.386836i
$714$	3.13868	−	0.360527i	0.117462	−	0.0134924i
$715$	−23.2844	+	13.8291i	−0.870788	+	0.517178i
$716$	−8.66743	−	37.2307i	−0.323917	−	1.39138i
$717$	−64.9723	−	17.4093i	−2.42643	−	0.650161i
$718$	21.2024	+	3.14881i	0.791265	+	0.117513i
$719$	6.07419	−	10.5208i	0.226529	−	0.392360i	−0.730248	−	0.683182i	$-0.760596\pi$
$719$	6.07419	−	10.5208i	0.226529	−	0.392360i	0.956777	+	0.290822i	$0.0939289\pi$
$720$	52.8622	−	32.6949i	1.97006	−	1.21847i
$721$	1.97310	+	1.13917i	0.0734821	+	0.0424249i
$722$	19.4390	−	7.67786i	0.723446	−	0.285740i
$723$	15.8288	−	15.8288i	0.588678	−	0.588678i
$724$	17.2340	+	5.23437i	0.640496	+	0.194534i
$725$	2.89009	−	2.51693i	0.107335	−	0.0934765i
$726$	1.01475	−	0.752321i	0.0376611	−	0.0279213i
$727$	27.0352	−	27.0352i	1.00268	−	1.00268i	0.00268440	−	0.999996i	$-0.499146\pi$
$727$	27.0352	−	27.0352i	1.00268	−	1.00268i	0.999996	−	0.00268440i	$-0.000854473\pi$
$728$	−0.436954	+	1.61256i	−0.0161946	+	0.0597654i
$729$		−	10.2981i		−	0.381412i
$730$	−27.1826	−	30.1061i	−1.00607	−	1.11428i
$731$	11.8237	−	6.82641i	0.437315	−	0.252484i
$732$	−4.71859	−	8.83520i	−0.174404	−	0.326558i
$733$	−18.5471	−	18.5471i	−0.685053	−	0.685053i	0.276082	−	0.961134i	$-0.410964\pi$
$733$	−18.5471	−	18.5471i	−0.685053	−	0.685053i	−0.961134	+	0.276082i	$0.910964\pi$
$734$	17.2572	−	39.7887i	0.636975	−	1.46863i
$735$	46.0600	−	17.2450i	1.69895	−	0.636091i
$736$	3.54991	+	5.51619i	0.130851	+	0.203329i
$737$	−18.3138	+	4.90716i	−0.674596	+	0.180758i
$738$	12.2738	−	82.6451i	0.451806	−	3.04221i
$739$	23.6085	−	13.6304i	0.868451	−	0.501401i	0.00161807	−	0.999999i	$-0.499485\pi$
$739$	23.6085	−	13.6304i	0.868451	−	0.501401i	0.866833	+	0.498598i	$0.166152\pi$
$740$	3.11272	−	6.27914i	0.114426	−	0.230826i
$741$	17.8519	−	15.0758i	0.655807	−	0.553825i
$742$	2.21400	+	1.75778i	0.0812784	+	0.0645300i
$743$	−33.3964	−	8.94853i	−1.22519	−	0.328290i	−0.412487	−	0.910963i	$-0.635340\pi$
$743$	−33.3964	−	8.94853i	−1.22519	−	0.328290i	−0.812706	+	0.582674i	$0.802007\pi$
$744$	−62.7078	−	53.2595i	−2.29898	−	1.95259i
$745$	0.117536	+	0.0534999i	0.00430620	+	0.00196008i
$746$	−20.3050	+	2.33235i	−0.743420	+	0.0853935i
$747$	−63.9919	+	17.1466i	−2.34134	+	0.627361i
$748$	−13.6820	−	25.6185i	−0.500264	−	0.936706i
$749$	−2.53657			−0.0926842
$750$	−5.96498	+	49.5150i	−0.217810	+	1.80803i
$751$	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	$0.271349\pi$
$752$	4.63834	+	23.4030i	0.169143	+	0.853419i
$753$	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
$757$	−4.48624	+	16.7429i	−0.163055	+	0.608530i	0.835225	+	0.549908i	$0.185337\pi$
$757$	−4.48624	+	16.7429i	−0.163055	+	0.608530i	−0.998280	+	0.0586216i	$0.981329\pi$
$758$	7.93765	+	20.0968i	0.288309	+	0.729948i
$759$			12.2863i			0.445966i
$760$	−8.38439	−	9.92725i	−0.304134	−	0.360099i
$761$	−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	$0.696375\pi$
$762$	52.5022	+	41.6835i	1.90196	+	1.51003i
$763$	−1.61266	+	0.432111i	−0.0583822	+	0.0156435i
$764$	−0.755327	−	0.807013i	−0.0273268	−	0.0291967i
$765$	11.0573	−	66.2609i	0.399777	−	2.39567i
$766$	2.89332	−	0.332343i	0.104540	−	0.0120080i
$767$	−5.87955	−	4.08931i	−0.212298	−	0.147656i
$768$	−50.0452	+	6.51826i	−1.80585	+	0.235207i
$769$	2.73010	+	4.72867i	0.0984498	+	0.170520i	0.911043	−	0.412311i	$-0.135278\pi$
$769$	2.73010	+	4.72867i	0.0984498	+	0.170520i	−0.812593	+	0.582831i	$0.801945\pi$
$770$	1.16620	+	1.29162i	0.0420269	+	0.0465469i
$771$	−54.6869	−	31.5735i	−1.96950	−	1.13709i
$772$	−11.7679	+	18.9097i	−0.423536	+	0.680577i
$773$	6.13736	−	1.64450i	0.220745	−	0.0591486i	−0.146751	−	0.989173i	$-0.546882\pi$
$773$	6.13736	−	1.64450i	0.220745	−	0.0591486i	0.367497	+	0.930025i	$0.380215\pi$
$774$	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
$777$	0.209592	−	0.782209i	0.00751908	−	0.0280616i
$778$	42.9953	+	6.38533i	1.54146	+	0.228925i
$779$	−17.4671			−0.625822
$780$	43.5100	+	26.3380i	1.55791	+	0.943051i
$781$	30.0380			1.07484
$782$	7.01274	+	1.04148i	0.250775	+	0.0372432i
$783$	−2.47122	+	9.22271i	−0.0883141	+	0.329593i
$784$	−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
$787$	23.5503	−	6.31029i	0.839479	−	0.224938i	0.186634	−	0.982429i	$-0.440242\pi$
$787$	23.5503	−	6.31029i	0.839479	−	0.224938i	0.652845	+	0.757492i	$0.273575\pi$
$788$	−6.81131	−	4.23880i	−0.242643	−	0.151001i
$789$	47.9954	+	27.7101i	1.70868	+	0.986507i
$790$	−20.0005	−	1.02065i	−0.711586	−	0.0363130i
$791$	−0.538953	−	0.933494i	−0.0191630	−	0.0331912i
$792$	−59.6700	−	28.2596i	−2.12028	−	1.00416i
$793$	3.26873	−	4.69974i	0.116076	−	0.166893i
$794$	12.1512	−	1.39576i	0.431230	−	0.0495335i
$795$	70.0392	−	50.0066i	2.48404	−	1.77355i
$796$	−3.27506	+	3.06531i	−0.116081	+	0.108647i
$797$	30.1060	−	8.06689i	1.06641	−	0.285744i	0.317393	−	0.948294i	$-0.397193\pi$
$797$	30.1060	−	8.06689i	1.06641	−	0.285744i	0.749017	+	0.662550i	$0.230526\pi$
$798$	−1.17591	−	0.933601i	−0.0416268	−	0.0330491i
$799$	22.3309	+	12.8928i	0.790011	+	0.456113i
$800$	14.6456	−	24.1972i	0.517801	−	0.855501i
$801$			54.7019i			1.93280i
$802$	−8.50900	−	21.5433i	−0.300463	−	0.760722i
$803$	−11.1514	+	41.6177i	−0.393526	+	1.46866i
$804$	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
$808$	−17.6011	+	1.43403i	−0.619205	+	0.0504490i
$809$	15.0899	−	8.71214i	0.530531	−	0.306302i	−0.210701	−	0.977550i	$-0.567575\pi$
$809$	15.0899	−	8.71214i	0.530531	−	0.306302i	0.741233	+	0.671248i	$0.234241\pi$
$810$	−26.5508	−	51.9326i	−0.932902	−	1.82472i
$811$	29.7766			1.04560			0.522798	−	0.852457i	$-0.324888\pi$
$811$	29.7766			1.04560			0.522798	+	0.852457i	$0.324888\pi$
$812$	−0.221528	+	0.118311i	−0.00777412	+	0.00415190i
$813$	−8.42171	+	2.25659i	−0.295362	+	0.0791420i
$814$	−7.39578	+	0.849522i	−0.259222	+	0.0297757i
$815$	−13.7636	+	5.15315i	−0.482119	+	0.180507i
$816$	−30.3348	+	45.3314i	−1.06193	+	1.58692i
$817$	−6.26738	−	1.67934i	−0.219268	−	0.0587527i
$818$	−19.1534	−	15.2066i	−0.669683	−	0.531687i
$819$	3.86168	+	1.39175i	0.134938	+	0.0486317i
$820$	−12.1466	−	36.0279i	−0.424178	−	1.25815i
$821$	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	$0.181839\pi$
$822$	3.42687	−	23.0747i	0.119526	−	0.804821i
$823$	−36.4599	+	9.76939i	−1.27091	+	0.340540i	−0.830380	−	0.557198i	$-0.811877\pi$
$823$	−36.4599	+	9.76939i	−1.27091	+	0.340540i	−0.440531	+	0.897737i	$0.645210\pi$
$824$	−37.0425	+	13.2324i	−1.29044	+	0.460971i
$825$	47.5936	−	23.2666i	1.65700	−	0.810037i
$826$	−0.183119	+	0.422204i	−0.00637151	+	0.0146903i
$827$	−22.3365	−	22.3365i	−0.776715	−	0.776715i	0.202556	−	0.979271i	$-0.435075\pi$
$827$	−22.3365	−	22.3365i	−0.776715	−	0.776715i	−0.979271	+	0.202556i	$0.935075\pi$
$828$	14.2164	−	7.59251i	0.494054	−	0.263858i
$829$	−5.14191	+	2.96868i	−0.178586	+	0.103107i	−0.586628	−	0.809856i	$-0.699545\pi$
$829$	−5.14191	+	2.96868i	−0.178586	+	0.103107i	0.408042	+	0.912963i	$0.366212\pi$
$830$	−22.3758	+	20.2030i	−0.776676	+	0.701256i
$831$		−	64.1517i		−	2.22540i
$832$	−16.3362	−	23.7724i	−0.566356	−	0.824161i
$833$	−21.3164	+	21.3164i	−0.738568	+	0.738568i
$834$	15.0377	−	11.1487i	0.520714	−	0.386049i
$835$	39.0061	+	6.50915i	1.34986	+	0.225259i
$836$	−4.01128	+	13.2070i	−0.138733	+	0.456773i
$837$	−81.2291	+	81.2291i	−2.80769	+	2.80769i
$838$	−19.5216	+	7.71046i	−0.674361	+	0.266353i
$839$	−36.2372	−	20.9215i	−1.25105	−	0.722292i	−0.279729	−	0.960079i	$-0.590245\pi$
$839$	−36.2372	−	20.9215i	−1.25105	−	0.722292i	−0.971317	+	0.237787i	$0.923578\pi$
$840$	1.10793	−	3.07468i	0.0382273	−	0.106087i
$841$	−14.2062	+	24.6059i	−0.489871	+	0.848481i
$842$	32.9007	+	4.88616i	1.13383	+	0.168388i
$843$	7.29924	+	1.95583i	0.251399	+	0.0673622i
$844$	28.9490	−	6.73943i	0.996467	−	0.231981i
$845$	−2.08454	+	28.9940i	−0.0717104	+	0.997425i
$846$	58.2350	−	6.68921i	2.00216	−	0.229980i
$847$	0.0120074	−	0.0448121i	0.000412578	−	0.00153976i
$848$	−47.8751	+	9.48858i	−1.64404	+	0.325839i
$849$	4.14055	+	2.39055i	0.142103	+	0.0820435i
$850$	−9.24559	−	29.1375i	−0.317121	−	0.999407i
$851$	0.908617	−	1.57377i	0.0311470	−	0.0539482i
$852$	−26.5758	−	49.7611i	−0.910471	−	1.70479i
$853$	12.3949	+	12.3949i	0.424395	+	0.424395i	0.886714	−	0.462319i	$-0.152982\pi$
$853$	12.3949	+	12.3949i	0.424395	+	0.424395i	−0.462319	+	0.886714i	$0.652982\pi$
$854$	−0.337483	−	0.146373i	−0.0115484	−	0.00500879i
$855$	−25.9828	+	18.5512i	−0.888594	+	0.634438i
$856$	28.3496	−	33.3789i	0.968970	−	1.14087i
$857$	−37.7415	−	37.7415i	−1.28923	−	1.28923i	−0.935257	−	0.353969i	$-0.884832\pi$
$857$	−37.7415	−	37.7415i	−1.28923	−	1.28923i	−0.353969	−	0.935257i	$-0.615168\pi$
$858$	−1.63426	−	54.0006i	−0.0557929	−	1.84355i
$859$	−44.0614			−1.50335			−0.751677	−	0.659531i	$-0.770755\pi$
$859$	−44.0614			−1.50335			−0.751677	+	0.659531i	$0.770755\pi$
$860$	−0.894508	−	14.0950i	−0.0305025	−	0.480637i
$861$	−2.19660	−	3.80462i	−0.0748600	−	0.129661i
$862$	35.4379	−	13.9970i	1.20702	−	0.476738i
$863$	−27.0922	+	27.0922i	−0.922229	+	0.922229i	−0.997187	−	0.0749581i	$-0.976118\pi$
$863$	−27.0922	+	27.0922i	−0.922229	+	0.922229i	0.0749581	+	0.997187i	$0.476118\pi$
$864$	3.39688	+	70.3850i	0.115564	+	2.39455i
$865$	−5.67674	+	2.12539i	−0.193015	+	0.0722655i
$866$	34.5876	−	3.97294i	1.17534	−	0.135006i
$867$	1.37924	+	5.14739i	0.0468414	+	0.174815i
$868$	−3.01991	−	0.0999056i	−0.102502	−	0.00339102i
$869$	10.6363	+	18.4226i	0.360812	+	0.624945i
$870$	1.59983	+	7.47614i	0.0542394	+	0.253465i
$871$	−6.90012	+	19.1457i	−0.233802	+	0.648729i
$872$	12.3375	−	26.0505i	0.417800	−	0.882182i
$873$	26.8416	−	100.174i	0.908450	−	3.39038i
$874$	−2.00665	−	2.70663i	−0.0678759	−	0.0915530i
$875$	0.959158	+	1.56042i	0.0324255	+	0.0527518i
$876$	78.8103	−	18.3473i	2.66275	−	0.619897i
$877$	2.96711	+	11.0734i	0.100192	+	0.373922i	0.997755	−	0.0669636i	$-0.0213312\pi$
$877$	2.96711	+	11.0734i	0.100192	+	0.373922i	−0.897563	+	0.440885i	$0.854664\pi$
$878$	2.18710	−	0.863842i	0.0738111	−	0.0291533i
$879$			45.3381i			1.52922i
$880$	−30.0304	+	0.910423i	−1.01233	+	0.0306904i
$881$	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	$0.734016\pi$
$882$	−10.0672	+	67.7868i	−0.338980	+	2.28250i
$883$	22.5334	+	22.5334i	0.758309	+	0.758309i	0.976014	−	0.217706i	$-0.0698573\pi$
$883$	22.5334	+	22.5334i	0.758309	+	0.758309i	−0.217706	+	0.976014i	$0.569857\pi$
$884$	−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
$887$	−34.6837	−	9.29347i	−1.16457	−	0.312044i	−0.375777	−	0.926710i	$-0.622624\pi$
$887$	−34.6837	−	9.29347i	−1.16457	−	0.312044i	−0.788788	+	0.614666i	$0.789291\pi$
$888$	7.95066	+	11.5003i	0.266807	+	0.385924i
$889$	2.46202			0.0825734
$890$	11.3313	+	22.1636i	0.379826	+	0.742926i
$891$	−30.9777	+	53.6550i	−1.03779	+	1.79751i
$892$	−2.42198	−	1.50724i	−0.0810939	−	0.0504663i
$893$	−3.17170	−	11.8369i	−0.106137	−	0.396108i
$894$	−0.206951	+	0.153430i	−0.00692148	+	0.00513147i
$895$	−34.7826	+	24.8341i	−1.16265	+	0.830112i
$896$	−1.29060	+	1.33032i	−0.0431160	+	0.0444430i
$897$	10.8268	+	7.53018i	0.361496	+	0.251425i
$898$	24.9168	+	19.7824i	0.831483	+	0.660146i
$899$	6.12142	−	3.53420i	0.204161	−	0.117872i
$900$	−56.3326	−	40.6921i	−1.87775	−	1.35640i
$901$	−26.3745	+	45.6820i	−0.878662	+	1.52189i
$902$	−25.1119	+	31.6296i	−0.836136	+	1.05315i
$903$	−0.422377	−	1.57633i	−0.0140558	−	0.0524570i
$904$	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
$907$	4.20448	+	1.12659i	0.139607	+	0.0374077i	0.327946	−	0.944696i	$-0.393644\pi$
$907$	4.20448	+	1.12659i	0.139607	+	0.0374077i	−0.188339	+	0.982104i	$0.560310\pi$
$908$	−38.6752	−	1.27947i	−1.28348	−	0.0424606i
$909$			43.3880i			1.43909i
$910$	1.85294	−	0.236036i	0.0614243	−	0.00782453i
$911$			5.66695i			0.187754i	0.995584	+	0.0938772i	$0.0299261\pi$
$911$			5.66695i			0.187754i	−0.995584	+	0.0938772i	$0.970074\pi$
$912$	25.4277	−	5.03963i	0.841996	−	0.166879i
$913$	30.9316	+	8.28811i	1.02369	+	0.274296i
$914$	−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
$917$	0.0931733	+	0.347727i	0.00307685	+	0.0114830i
$918$	59.6465	+	47.3556i	1.96863	+	1.56297i
$919$	29.0439	−	50.3054i	0.958069	−	1.65942i	0.230884	−	0.972981i	$-0.425838\pi$
$919$	29.0439	−	50.3054i	0.958069	−	1.65942i	0.727184	−	0.686442i	$-0.240829\pi$
$920$	4.18731	−	6.02114i	0.138052	−	0.198511i
$921$	29.4689	−	17.0139i	0.971032	−	0.560626i
$922$	0.249439	−	0.314180i	0.00821485	−	0.0103470i
$923$	18.4100	−	26.4696i	0.605972	−	0.871258i
$924$	−3.38115	+	0.787143i	−0.111232	+	0.0258951i
$925$	−7.81695	−	0.539470i	−0.257020	−	0.0177377i
$926$	−11.6598	−	15.7271i	−0.383164	−	0.516823i
$927$	25.0131	+	93.3503i	0.821539	+	3.06603i
$928$	0.919018	−	4.23739i	0.0301682	−	0.139099i
$929$	18.9298	−	32.7874i	0.621068	−	1.07572i	−0.368219	−	0.929739i	$-0.620032\pi$
$929$	18.9298	−	32.7874i	0.621068	−	1.07572i	0.989287	−	0.145982i	$-0.0466342\pi$
$930$	−28.3045	+	87.5209i	−0.928140	+	2.86992i
$931$	14.3268			0.469541
$932$	−5.69337	+	3.04064i	−0.186493	+	0.0995996i
$933$	−49.0215	−	13.1353i	−1.60489	−	0.430030i
$934$	−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	0.912334	−	0.409446i	$-0.134278\pi$
$937$	15.3936	+	15.3936i	0.502888	+	0.502888i	−0.409446	+	0.912334i	$0.634278\pi$
$938$	1.29354	+	0.192107i	0.0422356	+	0.00627252i
$939$	25.9154	+	44.8869i	0.845718	+	1.46483i
$940$	22.2095	−	14.7734i	0.724394	−	0.481856i
$941$		−	45.4266i		−	1.48087i	−0.672131	−	0.740433i	$-0.734621\pi$
$941$		−	45.4266i		−	1.48087i	0.672131	−	0.740433i	$-0.265379\pi$
$942$	17.9908	+	45.5496i	0.586171	+	1.48409i
$943$	−2.55158	−	9.52262i	−0.0830909	−	0.310099i
$944$	−3.50920	−	7.12837i	−0.114215	−	0.232009i
$945$	−4.15329	−	1.89048i	−0.135107	−	0.0614974i
$946$	−12.0514	+	8.93471i	−0.391825	+	0.290493i
$947$	−9.96946	+	37.2065i	−0.323964	+	1.20905i	0.591385	+	0.806389i	$0.298581\pi$
$947$	−9.96946	+	37.2065i	−0.323964	+	1.20905i	−0.915349	+	0.402661i	$0.868085\pi$
$948$	21.1087	−	33.9194i	0.685579	−	1.10165i
$949$	29.8391	+	35.3338i	0.968620	+	1.14698i
$950$	−6.68468	+	12.8987i	−0.216880	+	0.418488i
$951$	11.7765	+	20.3974i	0.381878	+	0.661432i
$952$	0.162671	+	1.99660i	0.00527219	+	0.0647102i
$953$	7.73331	+	28.8611i	0.250506	+	0.934903i	0.970535	+	0.240959i	$0.0774618\pi$
$953$	7.73331	+	28.8611i	0.250506	+	0.934903i	−0.720029	+	0.693944i	$0.755872\pi$
$954$	13.6840	+	119.130i	0.443036	+	3.85699i
$955$	−0.511972	+	1.12478i	−0.0165670	+	0.0363969i
$956$	12.3947	−	40.8092i	0.400874	−	1.31986i
$957$	5.74250	−	5.74250i	0.185629	−	0.185629i
$958$	1.40684	+	3.56188i	0.0454530	+	0.115079i
$959$	−0.428368	−	0.741955i	−0.0138327	−	0.0239590i
$960$	28.0773	+	48.9431i	0.906191	+	1.57963i
$961$	54.0420			1.74329
$962$	−3.78420	+	7.03786i	−0.122007	+	0.226910i
$963$	−76.0826	−	76.0826i	−2.45173	−	2.45173i
$964$	9.69916	+	10.3629i	0.312389	+	0.333765i
$965$	24.5617	+	4.09874i	0.790669	+	0.131943i
$966$	0.337200	−	0.777459i	0.0108492	−	0.0250143i
$967$	−2.15476	−	2.15476i	−0.0692926	−	0.0692926i	0.671611	−	0.740904i	$-0.265603\pi$
$967$	−2.15476	−	2.15476i	−0.0692926	−	0.0692926i	−0.740904	+	0.671611i	$0.765603\pi$
$968$	0.455487	+	0.658842i	0.0146399	+	0.0211760i
$969$	14.0082	−	24.2629i	0.450008	−	0.779437i
$970$	−9.87526	−	46.1478i	−0.317075	−	1.48172i
$971$	−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	$0.870050\pi$
$972$	41.5918	+	1.37595i	1.33406	+	0.0441337i
$973$	0.177938	−	0.664075i	0.00570445	−	0.0212893i
$974$	−1.57015	−	13.6695i	−0.0503110	−	0.437998i
$975$	8.66704	−	56.1996i	0.277567	−	1.79983i
$976$	5.69796	−	2.80503i	0.182387	−	0.0897869i
$977$	33.8121	+	9.05993i	1.08175	+	0.289853i	0.755311	−	0.655367i	$-0.227486\pi$
$977$	33.8121	+	9.05993i	1.08175	+	0.289853i	0.326435	+	0.945220i	$0.394153\pi$
$978$	4.30695	−	29.0006i	0.137721	−	0.927338i
$979$	13.2206	−	22.8987i	0.422531	−	0.731845i
$980$	9.96285	+	29.5507i	0.318252	+	0.943961i
$981$	−61.3315	−	35.4097i	−1.95816	−	1.13055i
$982$	0.842814	+	2.13386i	0.0268953	+	0.0680942i
$983$	0.544366	−	0.544366i	0.0173626	−	0.0173626i	−0.698372	−	0.715735i	$-0.746092\pi$
$983$	0.544366	−	0.544366i	0.0173626	−	0.0173626i	0.715735	+	0.698372i	$0.246092\pi$
$984$	74.6153	+	13.6166i	2.37865	+	0.434083i
$985$	−1.47637	+	8.84715i	−0.0470410	+	0.281894i
$986$	−2.79090	−	3.76445i	−0.0888803	−	0.119884i
$987$	2.17943	−	2.17943i	0.0693719	−	0.0693719i
$988$	9.17959	+	11.6292i	0.292042	+	0.369974i
$989$		−	3.66214i		−	0.116449i
$990$	−3.76205	+	73.7206i	−0.119566	+	2.34300i
$991$	−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	$0.565694\pi$
$992$	35.0662	−	38.6226i	1.11335	−	1.22627i
$993$	46.3468	+	46.3468i	1.47077	+	1.47077i
$994$	−1.90075	−	0.824396i	−0.0602882	−	0.0261483i
$995$	4.56462	+	2.07771i	0.144708	+	0.0658679i
$996$	−13.6363	−	58.5744i	−0.432083	−	1.85600i
$997$	−1.26396	+	0.338676i	−0.0400299	+	0.0107260i	−0.278778	−	0.960355i	$-0.589930\pi$
$997$	−1.26396	+	0.338676i	−0.0400299	+	0.0107260i	0.238749	+	0.971081i	$0.423263\pi$
$998$	44.0158	+	6.53690i	1.39330	+	0.206922i
$999$	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.127.19	yes	144
4.3	odd	2	inner	260.2.bg.c.127.24	yes	144
5.3	odd	4	inner	260.2.bg.c.23.35	yes	144
13.4	even	6	inner	260.2.bg.c.147.6	yes	144
20.3	even	4	inner	260.2.bg.c.23.6	✓	144
52.43	odd	6	inner	260.2.bg.c.147.35	yes	144
65.43	odd	12	inner	260.2.bg.c.43.24	yes	144
260.43	even	12	inner	260.2.bg.c.43.19	yes	144

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
260.2.bg.c.23.6	✓	144	20.3	even	4	inner
260.2.bg.c.23.35	yes	144	5.3	odd	4	inner
260.2.bg.c.43.19	yes	144	260.43	even	12	inner
260.2.bg.c.43.24	yes	144	65.43	odd	12	inner
260.2.bg.c.127.19	yes	144	1.1	even	1	trivial
260.2.bg.c.127.24	yes	144	4.3	odd	2	inner
260.2.bg.c.147.6	yes	144	13.4	even	6	inner
260.2.bg.c.147.35	yes	144	52.43	odd	6	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+(-0.207750 + 1.39887i) q^{2} +(-0.816378 + 3.04677i) q^{3} +(-1.91368 - 0.581230i) q^{4} +(0.215330 + 2.22568i) q^{5} +(-4.09243 - 1.77497i) q^{6} +(-0.158244 + 0.0424015i) q^{7} +(1.21063 - 2.55624i) q^{8} +(-6.01823 - 3.47463i) q^{9} +(-3.15817 - 0.161165i) q^{10} +(1.67952 + 2.90902i) q^{11} +(3.33316 - 5.35603i) q^{12} +(3.59281 + 0.302905i) q^{13} +(-0.0264389 - 0.230172i) q^{14} +(-6.95690 - 1.16093i) q^{15} +(3.32434 + 2.22458i) q^{16} +(4.17582 - 1.11891i) q^{17} +(6.11084 - 7.69687i) q^{18} +(-1.77930 - 1.02728i) q^{19} +(0.881558 - 4.38439i) q^{20} -0.516749i q^{21} +(-4.41826 + 1.74509i) q^{22} +(0.300129 - 1.12010i) 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} +(0.327474 + 0.0108336i) q^{28} +(-0.663797 + 0.383243i) q^{29} +(3.06929 - 9.49063i) q^{30} -9.22182 q^{31} +(-3.80253 + 4.18817i) q^{32} +(-10.2342 + 2.74225i) q^{33} +(0.697682 + 6.07389i) q^{34} +(-0.128447 - 0.343070i) q^{35} +(9.49741 + 10.1473i) q^{36} +(1.51371 + 0.405598i) q^{37} +(1.80668 - 2.27559i) q^{38} +(-3.85597 + 10.6991i) q^{39} +(5.95005 + 2.14404i) q^{40} +(7.36261 - 4.25081i) q^{41} +(0.722865 + 0.107355i) q^{42} +(3.05048 - 0.817373i) q^{43} +(-1.52326 - 6.54312i) q^{44} +(6.43749 - 14.1428i) q^{45} +(1.50452 + 0.652541i) q^{46} +(4.21757 + 4.21757i) q^{47} +(-9.49169 + 8.31240i) q^{48} +(-6.03893 + 3.48658i) q^{49} +(-0.321347 - 7.06376i) q^{50} +13.6362i q^{51} +(-6.69942 - 2.66791i) q^{52} +(-8.62782 + 8.62782i) q^{53} +(10.4918 + 14.1517i) q^{54} +(-6.11288 + 4.36447i) q^{55} +(-0.0831875 + 0.455843i) q^{56} +(4.58246 - 4.58246i) q^{57} +(-0.398204 - 1.00819i) q^{58} +(-1.72021 - 0.993165i) q^{59} +(12.6385 + 6.26522i) q^{60} +(0.793873 - 1.37503i) q^{61} +(1.91583 - 12.9001i) q^{62} +(1.09968 + 0.294658i) q^{63} +(-5.06874 - 6.18934i) q^{64} +(0.0994692 + 8.06164i) q^{65} +(-1.70990 - 14.8861i) q^{66} +(-1.46088 + 5.45208i) q^{67} +(-8.64153 - 0.285882i) q^{68} +(3.16765 + 1.82884i) q^{69} +(0.506596 - 0.108408i) q^{70} +(4.47121 - 7.74436i) q^{71} +(-16.1678 + 11.1775i) q^{72} +(9.06992 + 9.06992i) q^{73} +(-0.881852 + 2.03322i) q^{74} +(1.08583 - 15.7338i) q^{75} +(2.80792 + 3.00007i) q^{76} +(-0.389122 - 0.389122i) q^{77} +(-14.1657 - 7.61675i) q^{78} +6.33294 q^{79} +(-4.23536 + 7.87793i) q^{80} +(9.22218 + 15.9733i) q^{81} +(4.41675 + 11.1824i) q^{82} +(6.74106 - 6.74106i) q^{83} +(-0.300350 + 0.988893i) q^{84} +(3.38951 + 9.05310i) q^{85} +(0.509663 + 4.43703i) q^{86} +(-0.625743 - 2.33531i) q^{87} +(9.46944 - 0.771512i) q^{88} +(-3.93581 - 6.81702i) q^{89} +(18.4466 + 11.9434i) q^{90} +(-0.581385 + 0.104407i) q^{91} +(-1.22538 + 1.96906i) q^{92} +(7.52850 - 28.0967i) q^{93} +(-6.77604 + 5.02364i) q^{94} +(1.90325 - 4.18135i) q^{95} +(-9.65607 - 15.0045i) q^{96} +(3.86251 + 14.4151i) q^{97} +(-3.62269 - 9.17203i) 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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