LMFDB - Embedded newform 966.2.j.a.137.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(137,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4, 3]))

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

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

chi := DirichletCharacter("966.137");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.j (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$64$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			137.11
Character	$\chi$	$=$	966.137
Dual form			966.2.j.a.275.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(-0.608468 + 1.62166i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.435291 - 0.753947i) q^{5} +(-0.283879 - 1.70863i) q^{6} +(-2.60300 - 0.473676i) q^{7} +1.00000i q^{8} +(-2.25953 - 1.97345i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.608468 + 1.62166i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.435291 - 0.753947i) q^{5} +(-0.283879 - 1.70863i) q^{6} +(-2.60300 - 0.473676i) q^{7} +1.00000i q^{8} +(-2.25953 - 1.97345i) q^{9} +(0.753947 + 0.435291i) q^{10} +(-2.32829 + 4.03272i) q^{11} +(1.10016 + 1.33778i) q^{12} +2.50822 q^{13} +(2.49111 - 0.891287i) q^{14} +(1.48750 - 0.247140i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.428155 + 0.741587i) q^{17} +(2.94354 + 0.579292i) q^{18} +(-3.91551 + 2.26062i) q^{19} -0.870583 q^{20} +(2.35198 - 3.93296i) q^{21} -4.65658i q^{22} +(-0.383923 + 4.78044i) q^{23} +(-1.62166 - 0.608468i) q^{24} +(2.12104 - 3.67375i) q^{25} +(-2.17218 + 1.25411i) q^{26} +(4.57511 - 2.46340i) q^{27} +(-1.71172 + 2.01743i) q^{28} -8.08792i q^{29} +(-1.16465 + 0.957781i) q^{30} +(5.09424 - 8.82348i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-5.12299 - 6.22947i) q^{33} -0.856311i q^{34} +(0.775939 + 2.16871i) q^{35} +(-2.83883 + 0.970088i) q^{36} +(4.90568 - 2.83230i) q^{37} +(2.26062 - 3.91551i) q^{38} +(-1.52617 + 4.06747i) q^{39} +(0.753947 - 0.435291i) q^{40} -2.07230i q^{41} +(-0.0703971 + 4.58203i) q^{42} -10.5370i q^{43} +(2.32829 + 4.03272i) q^{44} +(-0.504321 + 2.56259i) q^{45} +(-2.05773 - 4.33194i) q^{46} +(-3.17464 + 1.83288i) q^{47} +(1.70863 - 0.283879i) q^{48} +(6.55126 + 2.46596i) q^{49} +4.24209i q^{50} +(-0.942080 - 1.14555i) q^{51} +(1.25411 - 2.17218i) q^{52} +(1.00780 - 1.74556i) q^{53} +(-2.73046 + 4.42093i) q^{54} +4.05394 q^{55} +(0.473676 - 2.60300i) q^{56} +(-1.28349 - 7.72512i) q^{57} +(4.04396 + 7.00434i) q^{58} +(-5.96739 - 3.44527i) q^{59} +(0.529722 - 1.41179i) q^{60} +(-3.00192 + 1.73316i) q^{61} +10.1885i q^{62} +(4.94680 + 6.20719i) q^{63} -1.00000 q^{64} +(-1.09181 - 1.89106i) q^{65} +(7.55137 + 2.83338i) q^{66} +(-1.60030 - 0.923931i) q^{67} +(0.428155 + 0.741587i) q^{68} +(-7.51862 - 3.53133i) q^{69} +(-1.75634 - 1.49019i) q^{70} +5.65946i q^{71} +(1.97345 - 2.25953i) q^{72} +(0.383621 - 0.664451i) q^{73} +(-2.83230 + 4.90568i) q^{74} +(4.66698 + 5.67496i) q^{75} +4.52124i q^{76} +(7.97075 - 9.39433i) q^{77} +(-0.712031 - 4.28562i) q^{78} +(-2.12444 + 1.22655i) q^{79} +(-0.435291 + 0.753947i) q^{80} +(1.21098 + 8.91816i) q^{81} +(1.03615 + 1.79467i) q^{82} +12.9529 q^{83} +(-2.23005 - 4.00336i) q^{84} +0.745489 q^{85} +(5.26848 + 9.12528i) q^{86} +(13.1158 + 4.92124i) q^{87} +(-4.03272 - 2.32829i) q^{88} +(-4.13880 - 7.16861i) q^{89} +(-0.844542 - 2.47143i) q^{90} +(-6.52891 - 1.18808i) q^{91} +(3.94802 + 2.72271i) q^{92} +(11.2090 + 13.6299i) q^{93} +(1.83288 - 3.17464i) q^{94} +(3.40877 + 1.96806i) q^{95} +(-1.33778 + 1.10016i) q^{96} -6.85811i q^{97} +(-6.90654 + 1.14005i) q^{98} +(13.2192 - 4.51730i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) $ 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9	$ 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9} - 64 q^{16} + 4 q^{24} - 72 q^{25} + 24 q^{27} - 8 q^{36} + 4 q^{39} + 12 q^{46} + 72 q^{49} + 4 q^{54} - 96 q^{55} - 128 q^{64} - 56 q^{69} + 32 q^{70} - 40 q^{73} - 40 q^{75} - 16 q^{78} + 36 q^{81} - 32 q^{82} - 64 q^{85} - 24 q^{87} + 32 q^{93} - 8 q^{94} - 4 q^{96}+O(q^{100}) $ 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9 - 64 * q^16 + 4 * q^24 - 72 * q^25 + 24 * q^27 - 8 * q^36 + 4 * q^39 + 12 * q^46 + 72 * q^49 + 4 * q^54 - 96 * q^55 - 128 * q^64 - 56 * q^69 + 32 * q^70 - 40 * q^73 - 40 * q^75 - 16 * q^78 + 36 * q^81 - 32 * q^82 - 64 * q^85 - 24 * q^87 + 32 * q^93 - 8 * q^94 - 4 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$	$-1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	−0.608468	+	1.62166i	−0.351299	+	0.936263i
$3$	−0.608468	+	1.62166i	−0.351299	+	0.936263i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.435291	−	0.753947i	−0.194668	−	0.337175i	0.752123	−	0.659022i	$-0.229030\pi$
$5$	−0.435291	−	0.753947i	−0.194668	−	0.337175i	−0.946792	+	0.321847i	$0.895696\pi$
$6$	−0.283879	−	1.70863i	−0.115893	−	0.697545i
$7$	−2.60300	−	0.473676i	−0.983843	−	0.179033i
$7$	−2.60300	−	0.473676i	−0.983843	−	0.179033i
$8$			1.00000i			0.353553i
$9$	−2.25953	−	1.97345i	−0.753178	−	0.657817i
$10$	0.753947	+	0.435291i	0.238419	+	0.137651i
$11$	−2.32829	+	4.03272i	−0.702006	+	1.21591i	0.265755	+	0.964041i	$0.414379\pi$
$11$	−2.32829	+	4.03272i	−0.702006	+	1.21591i	−0.967761	+	0.251870i	$0.918955\pi$
$12$	1.10016	+	1.33778i	0.317589	+	0.386183i
$13$	2.50822			0.695655			0.347828	−	0.937559i	$-0.386919\pi$
$13$	2.50822			0.695655			0.347828	+	0.937559i	$0.386919\pi$
$14$	2.49111	−	0.891287i	0.665776	−	0.238206i
$15$	1.48750	−	0.247140i	0.384072	−	0.0638113i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.428155	+	0.741587i	−0.103843	+	0.179861i	−0.913265	−	0.407366i	$-0.866447\pi$
$17$	−0.428155	+	0.741587i	−0.103843	+	0.179861i	0.809422	+	0.587227i	$0.199781\pi$
$18$	2.94354	+	0.579292i	0.693799	+	0.136540i
$19$	−3.91551	+	2.26062i	−0.898279	+	0.518622i	−0.876642	−	0.481144i	$-0.840221\pi$
$19$	−3.91551	+	2.26062i	−0.898279	+	0.518622i	−0.0216377	+	0.999766i	$0.506888\pi$
$20$	−0.870583			−0.194668
$21$	2.35198	−	3.93296i	0.513245	−	0.858242i
$22$		−	4.65658i		−	0.992787i
$23$	−0.383923	+	4.78044i	−0.0800534	+	0.996791i
$23$	−0.383923	+	4.78044i	−0.0800534	+	0.996791i
$24$	−1.62166	−	0.608468i	−0.331019	−	0.124203i
$25$	2.12104	−	3.67375i	0.424209	−	0.734751i
$26$	−2.17218	+	1.25411i	−0.426000	+	0.245951i
$27$	4.57511	−	2.46340i	0.880481	−	0.474082i
$28$	−1.71172	+	2.01743i	−0.323484	+	0.381258i
$29$		−	8.08792i		−	1.50189i	−0.660365	−	0.750945i	$-0.729599\pi$
$29$		−	8.08792i		−	1.50189i	0.660365	−	0.750945i	$-0.270401\pi$
$30$	−1.16465	+	0.957781i	−0.212634	+	0.174866i
$31$	5.09424	−	8.82348i	0.914952	−	1.58474i	0.107981	−	0.994153i	$-0.465561\pi$
$31$	5.09424	−	8.82348i	0.914952	−	1.58474i	0.806971	−	0.590591i	$-0.201105\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−5.12299	−	6.22947i	−0.891798	−	1.08441i
$34$		−	0.856311i		−	0.146856i
$35$	0.775939	+	2.16871i	0.131158	+	0.366579i
$36$	−2.83883	+	0.970088i	−0.473138	+	0.161681i
$37$	4.90568	−	2.83230i	0.806489	−	0.465627i	−0.0392458	−	0.999230i	$-0.512496\pi$
$37$	4.90568	−	2.83230i	0.806489	−	0.465627i	0.845735	+	0.533603i	$0.179162\pi$
$38$	2.26062	−	3.91551i	0.366721	−	0.635179i
$39$	−1.52617	+	4.06747i	−0.244383	+	0.651316i
$40$	0.753947	−	0.435291i	0.119209	−	0.0688256i
$41$		−	2.07230i		−	0.323640i	−0.986820	−	0.161820i	$-0.948264\pi$
$41$		−	2.07230i		−	0.323640i	0.986820	−	0.161820i	$-0.0517363\pi$
$42$	−0.0703971	+	4.58203i	−0.0108625	+	0.707023i
$43$		−	10.5370i		−	1.60687i	−0.595391	−	0.803436i	$-0.703003\pi$
$43$		−	10.5370i		−	1.60687i	0.595391	−	0.803436i	$-0.296997\pi$
$44$	2.32829	+	4.03272i	0.351003	+	0.607955i
$45$	−0.504321	+	2.56259i	−0.0751798	+	0.382009i
$46$	−2.05773	−	4.33194i	−0.303396	−	0.638710i
$47$	−3.17464	+	1.83288i	−0.463069	+	0.267353i	−0.713334	−	0.700824i	$-0.752816\pi$
$47$	−3.17464	+	1.83288i	−0.463069	+	0.267353i	0.250265	+	0.968177i	$0.419482\pi$
$48$	1.70863	−	0.283879i	0.246619	−	0.0409744i
$49$	6.55126	+	2.46596i	0.935895	+	0.352280i
$50$			4.24209i			0.599922i
$51$	−0.942080	−	1.14555i	−0.131918	−	0.160409i
$52$	1.25411	−	2.17218i	0.173914	−	0.301227i
$53$	1.00780	−	1.74556i	0.138432	−	0.239771i	−0.788471	−	0.615071i	$-0.789127\pi$
$53$	1.00780	−	1.74556i	0.138432	−	0.239771i	0.926903	+	0.375301i	$0.122460\pi$
$54$	−2.73046	+	4.42093i	−0.371569	+	0.601612i
$55$	4.05394			0.546633
$56$	0.473676	−	2.60300i	0.0632976	−	0.347841i
$57$	−1.28349	−	7.72512i	−0.170002	−	1.02322i
$58$	4.04396	+	7.00434i	0.530998	+	0.919715i
$59$	−5.96739	−	3.44527i	−0.776888	−	0.448537i	0.0584382	−	0.998291i	$-0.481388\pi$
$59$	−5.96739	−	3.44527i	−0.776888	−	0.448537i	−0.835326	+	0.549755i	$0.814721\pi$
$60$	0.529722	−	1.41179i	0.0683868	−	0.182261i
$61$	−3.00192	+	1.73316i	−0.384356	+	0.221908i	−0.679712	−	0.733479i	$-0.737895\pi$
$61$	−3.00192	+	1.73316i	−0.384356	+	0.221908i	0.295356	+	0.955387i	$0.404562\pi$
$62$			10.1885i			1.29394i
$63$	4.94680	+	6.20719i	0.623238	+	0.782032i
$64$	−1.00000			−0.125000
$65$	−1.09181	−	1.89106i	−0.135422	−	0.234558i
$66$	7.55137	+	2.83338i	0.929510	+	0.348765i
$67$	−1.60030	−	0.923931i	−0.195507	−	0.112876i	0.399051	−	0.916929i	$-0.369340\pi$
$67$	−1.60030	−	0.923931i	−0.195507	−	0.112876i	−0.594558	+	0.804053i	$0.702673\pi$
$68$	0.428155	+	0.741587i	0.0519215	+	0.0899306i
$69$	−7.51862	−	3.53133i	−0.905136	−	0.425123i
$70$	−1.75634	−	1.49019i	−0.209923	−	0.178112i
$71$			5.65946i			0.671655i	0.941924	+	0.335827i	$0.109016\pi$
$71$			5.65946i			0.671655i	−0.941924	+	0.335827i	$0.890984\pi$
$72$	1.97345	−	2.25953i	0.232573	−	0.266289i
$73$	0.383621	−	0.664451i	0.0448994	−	0.0777681i	−0.842702	−	0.538380i	$-0.819037\pi$
$73$	0.383621	−	0.664451i	0.0448994	−	0.0777681i	0.887602	+	0.460612i	$0.152370\pi$
$74$	−2.83230	+	4.90568i	−0.329248	+	0.570274i
$75$	4.66698	+	5.67496i	0.538896	+	0.655288i
$76$			4.52124i			0.518622i
$77$	7.97075	−	9.39433i	0.908351	−	1.07058i
$78$	−0.712031	−	4.28562i	−0.0806217	−	0.485251i
$79$	−2.12444	+	1.22655i	−0.239018	+	0.137997i	−0.614726	−	0.788741i	$-0.710733\pi$
$79$	−2.12444	+	1.22655i	−0.239018	+	0.137997i	0.375707	+	0.926738i	$0.377400\pi$
$80$	−0.435291	+	0.753947i	−0.0486671	+	0.0842938i
$81$	1.21098	+	8.91816i	0.134554	+	0.990906i
$82$	1.03615	+	1.79467i	0.114424	+	0.198188i
$83$	12.9529			1.42177			0.710885	−	0.703309i	$-0.248295\pi$
$83$	12.9529			1.42177			0.710885	+	0.703309i	$0.248295\pi$
$84$	−2.23005	−	4.00336i	−0.243319	−	0.436802i
$85$	0.745489			0.0808597
$86$	5.26848	+	9.12528i	0.568115	+	0.984004i
$87$	13.1158	+	4.92124i	1.40616	+	0.527612i
$88$	−4.03272	−	2.32829i	−0.429889	−	0.248197i
$89$	−4.13880	−	7.16861i	−0.438712	−	0.759871i	0.558878	−	0.829250i	$-0.311232\pi$
$89$	−4.13880	−	7.16861i	−0.438712	−	0.759871i	−0.997590	+	0.0693781i	$0.977899\pi$
$90$	−0.844542	−	2.47143i	−0.0890225	−	0.260512i
$91$	−6.52891	−	1.18808i	−0.684415	−	0.124545i
$92$	3.94802	+	2.72271i	0.411610	+	0.283862i
$93$	11.2090	+	13.6299i	1.16232	+	1.41336i
$94$	1.83288	−	3.17464i	0.189047	−	0.327440i
$95$	3.40877	+	1.96806i	0.349733	+	0.201918i
$96$	−1.33778	+	1.10016i	−0.136536	+	0.112285i
$97$		−	6.85811i		−	0.696336i	−0.937432	−	0.348168i	$-0.886804\pi$
$97$		−	6.85811i		−	0.696336i	0.937432	−	0.348168i	$-0.113196\pi$
$98$	−6.90654	+	1.14005i	−0.697666	+	0.115162i
$99$	13.2192	−	4.51730i	1.32858	−	0.454005i
$100$	−2.12104	−	3.67375i	−0.212104	−	0.367375i
$101$	14.9225	+	8.61551i	1.48484	+	0.857275i	0.999851	−	0.0172426i	$-0.00548878\pi$
$101$	14.9225	+	8.61551i	1.48484	+	0.857275i	0.484993	+	0.874518i	$0.338822\pi$
$102$	1.38864	+	0.521038i	0.137496	+	0.0515904i
$103$	10.9830	−	6.34104i	1.08219	−	0.624801i	0.150701	−	0.988579i	$-0.451847\pi$
$103$	10.9830	−	6.34104i	1.08219	−	0.624801i	0.931485	+	0.363779i	$0.118514\pi$
$104$			2.50822i			0.245951i
$105$	−3.98904	−	0.0612865i	−0.389290	−	0.00598095i
$106$			2.01560i			0.195772i
$107$	−9.57407	−	16.5828i	−0.925561	−	1.60312i	−0.790657	−	0.612259i	$-0.790261\pi$
$107$	−9.57407	−	16.5828i	−0.925561	−	1.60312i	−0.134904	−	0.990859i	$-0.543072\pi$
$108$	0.154185	−	5.19386i	0.0148365	−	0.499780i
$109$	−5.68036	−	3.27956i	−0.544080	−	0.314125i	0.202651	−	0.979251i	$-0.435044\pi$
$109$	−5.68036	−	3.27956i	−0.544080	−	0.314125i	−0.746731	+	0.665126i	$0.768378\pi$
$110$	−3.51081	+	2.02697i	−0.334743	+	0.193264i
$111$	1.60806	+	9.67869i	0.152630	+	0.918661i
$112$	0.891287	+	2.49111i	0.0842187	+	0.235387i
$113$	7.81671			0.735334			0.367667	−	0.929958i	$-0.380157\pi$
$113$	7.81671			0.735334			0.367667	+	0.929958i	$0.380157\pi$
$114$	4.97409	+	6.04841i	0.465866	+	0.566485i
$115$	3.77132	−	1.79143i	0.351677	−	0.167051i
$116$	−7.00434	−	4.04396i	−0.650337	−	0.375472i
$117$	−5.66741	−	4.94985i	−0.523952	−	0.457614i
$118$	6.89055			0.634326
$119$	1.46576	−	1.72755i	0.134366	−	0.158364i
$120$	0.247140	+	1.48750i	0.0225607	+	0.135790i
$121$	−5.34188	−	9.25240i	−0.485625	−	0.841127i
$122$	1.73316	−	3.00192i	0.156913	−	0.271781i
$123$	3.36056	+	1.26093i	0.303012	+	0.113694i
$124$	−5.09424	−	8.82348i	−0.457476	−	0.792372i
$125$	−8.04600			−0.719656
$126$	−7.38765	−	2.90218i	−0.658144	−	0.258547i
$127$	−15.9716			−1.41725			−0.708625	−	0.705586i	$-0.750684\pi$
$127$	−15.9716			−1.41725			−0.708625	+	0.705586i	$0.750684\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	17.0873	+	6.41141i	1.50446	+	0.564493i
$130$	1.89106	+	1.09181i	0.165857	+	0.0957578i
$131$	6.00998	−	3.46986i	0.525094	−	0.303163i	−0.213922	−	0.976851i	$-0.568624\pi$
$131$	6.00998	−	3.46986i	0.525094	−	0.303163i	0.739016	+	0.673687i	$0.235291\pi$
$132$	−7.95637	+	1.32191i	−0.692513	+	0.115057i
$133$	11.2629	−	4.02972i	0.976616	−	0.349421i
$134$	1.84786			0.159631
$135$	−3.84878	−	2.37709i	−0.331250	−	0.204587i
$136$	−0.741587	−	0.428155i	−0.0635906	−	0.0367140i
$137$	−9.63555	+	16.6893i	−0.823220	+	1.42586i	0.0800517	+	0.996791i	$0.474491\pi$
$137$	−9.63555	+	16.6893i	−0.823220	+	1.42586i	−0.903272	+	0.429069i	$0.858842\pi$
$138$	8.27698	−	0.701086i	0.704584	−	0.0596804i
$139$	−9.97039			−0.845677			−0.422839	−	0.906205i	$-0.638966\pi$
$139$	−9.97039			−0.845677			−0.422839	+	0.906205i	$0.638966\pi$
$140$	2.26613	+	0.412374i	0.191523	+	0.0348519i
$141$	−1.04063	−	6.26343i	−0.0876372	−	0.527476i
$142$	−2.82973	−	4.90124i	−0.237466	−	0.411303i
$143$	−5.83987	+	10.1149i	−0.488354	+	0.845854i
$144$	−0.579292	+	2.94354i	−0.0482743	+	0.245295i
$145$	−6.09786	+	3.52060i	−0.506400	+	0.292370i
$146$			0.767242i			0.0634974i
$147$	−7.98517	+	9.12344i	−0.658606	+	0.752488i
$148$		−	5.66460i		−	0.465627i
$149$	−9.76577	−	16.9148i	−0.800043	−	1.38572i	−0.919587	−	0.392886i	$-0.871477\pi$
$149$	−9.76577	−	16.9148i	−0.800043	−	1.38572i	0.119544	−	0.992829i	$-0.461857\pi$
$150$	−6.87920	−	2.58117i	−0.561684	−	0.210752i
$151$	−4.71947	+	8.17435i	−0.384065	+	0.665220i	−0.991639	−	0.129043i	$-0.958809\pi$
$151$	−4.71947	+	8.17435i	−0.384065	+	0.665220i	0.607574	+	0.794263i	$0.292143\pi$
$152$	−2.26062	−	3.91551i	−0.183360	−	0.317590i
$153$	2.43092	−	0.830697i	0.196528	−	0.0671579i
$154$	−2.20571	+	12.1211i	−0.177741	+	0.976746i
$155$	−8.86991			−0.712448
$156$	2.75945	+	3.35544i	0.220932	+	0.268650i
$157$	6.77166	+	3.90962i	0.540437	+	0.312021i	0.745256	−	0.666778i	$-0.232327\pi$
$157$	6.77166	+	3.90962i	0.540437	+	0.312021i	−0.204819	+	0.978800i	$0.565661\pi$
$158$	1.22655	−	2.12444i	0.0975789	−	0.169012i
$159$	2.21748	+	2.69642i	0.175858	+	0.213840i
$160$		−	0.870583i		−	0.0688256i
$161$	3.26373	−	12.2617i	0.257218	−	0.966353i
$162$	−5.50782	−	7.11786i	−0.432735	−	0.559232i
$163$	−4.40131	−	7.62329i	−0.344737	−	0.597102i	0.640569	−	0.767901i	$-0.278699\pi$
$163$	−4.40131	−	7.62329i	−0.344737	−	0.597102i	−0.985306	+	0.170799i	$0.945365\pi$
$164$	−1.79467	−	1.03615i	−0.140140	−	0.0809099i
$165$	−2.46669	+	6.57409i	−0.192032	+	0.511792i
$166$	−11.2176	+	6.47647i	−0.870652	+	0.502671i
$167$			14.3252i			1.10852i	0.832345	+	0.554258i	$0.186998\pi$
$167$			14.3252i			1.10852i	−0.832345	+	0.554258i	$0.813002\pi$
$168$	3.93296	+	2.35198i	0.303434	+	0.181459i
$169$	−6.70883			−0.516064
$170$	−0.645613	+	0.372745i	−0.0495162	+	0.0285882i
$171$	13.3084	+	2.61912i	1.01772	+	0.200289i
$172$	−9.12528	−	5.26848i	−0.695796	−	0.401718i
$173$	2.79426	−	1.61326i	0.212443	−	0.122654i	−0.390003	−	0.920814i	$-0.627526\pi$
$173$	2.79426	−	1.61326i	0.212443	−	0.122654i	0.602446	+	0.798159i	$0.294193\pi$
$174$	−13.8193	+	2.29599i	−1.04763	+	0.174059i
$175$	−7.26125	+	8.55811i	−0.548899	+	0.646932i
$176$	4.65658			0.351003
$177$	9.21801	−	7.58071i	0.692868	−	0.569801i
$178$	7.16861	+	4.13880i	0.537310	+	0.310216i
$179$	−7.29994	−	4.21462i	−0.545623	−	0.315015i	0.201732	−	0.979441i	$-0.435343\pi$
$179$	−7.29994	−	4.21462i	−0.545623	−	0.315015i	−0.747355	+	0.664425i	$0.768676\pi$
$180$	1.96711	+	1.71805i	0.146620	+	0.128056i
$181$			20.0189i			1.48800i	0.668182	+	0.743998i	$0.267073\pi$
$181$			20.0189i			1.48800i	−0.668182	+	0.743998i	$0.732927\pi$
$182$	6.24824	−	2.23554i	0.463150	−	0.165710i
$183$	−0.984014	−	5.92264i	−0.0727404	−	0.437814i
$184$	−4.78044	−	0.383923i	−0.352419	−	0.0283031i
$185$	−4.27080	−	2.46575i	−0.313996	−	0.181286i
$186$	−16.5222	−	6.19936i	−1.21147	−	0.454559i
$187$	−1.99374	−	3.45326i	−0.145797	−	0.252527i
$188$			3.66576i			0.267353i
$189$	−13.0759	+	4.24513i	−0.951131	+	0.308788i
$190$	−3.93611			−0.285556
$191$	−2.60077	−	4.50467i	−0.188185	−	0.325946i	0.756460	−	0.654040i	$-0.226927\pi$
$191$	−2.60077	−	4.50467i	−0.188185	−	0.325946i	−0.944645	+	0.328094i	$0.893594\pi$
$192$	0.608468	−	1.62166i	0.0439124	−	0.117033i
$193$	0.0533758	−	0.0924496i	0.00384207	−	0.00665466i	−0.864098	−	0.503324i	$-0.832110\pi$
$193$	0.0533758	−	0.0924496i	0.00384207	−	0.00665466i	0.867940	+	0.496669i	$0.165444\pi$
$194$	3.42906	+	5.93930i	0.246192	+	0.426417i
$195$	3.73098	−	0.619882i	0.267181	−	0.0443907i
$196$	5.41121	−	4.44058i	0.386515	−	0.317184i
$197$		−	22.4464i		−	1.59924i	−0.600507	−	0.799619i	$-0.705035\pi$
$197$		−	22.4464i		−	1.59924i	0.600507	−	0.799619i	$-0.294965\pi$
$198$	−9.18953	+	10.5217i	−0.653072	+	0.747745i
$199$	13.5074	+	7.79851i	0.957516	+	0.552822i	0.895408	−	0.445247i	$-0.146884\pi$
$199$	13.5074	+	7.79851i	0.957516	+	0.552822i	0.0621082	+	0.998069i	$0.480218\pi$
$200$	3.67375	+	2.12104i	0.259774	+	0.149980i
$201$	2.47203	−	2.03295i	0.174363	−	0.143393i
$202$	−17.2310			−1.21237
$203$	−3.83105	+	21.0529i	−0.268887	+	1.47762i
$204$	−1.46312	+	0.243089i	−0.102439	+	0.0170196i
$205$	−1.56241	+	0.902056i	−0.109123	+	0.0630023i
$206$	−6.34104	+	10.9830i	−0.441801	+	0.765222i
$207$	10.3014	−	10.0439i	0.716000	−	0.698100i
$208$	−1.25411	−	2.17218i	−0.0869569	−	0.150614i
$209$		−	21.0535i		−	1.45630i
$210$	3.48525	−	1.94144i	0.240505	−	0.133972i
$211$	−9.77273			−0.672783			−0.336391	−	0.941722i	$-0.609206\pi$
$211$	−9.77273			−0.672783			−0.336391	+	0.941722i	$0.609206\pi$
$212$	−1.00780	−	1.74556i	−0.0692159	−	0.119885i
$213$	−9.17770	−	3.44360i	−0.628845	−	0.235952i
$214$	16.5828	+	9.57407i	1.13358	+	0.654470i
$215$	−7.94431	+	4.58665i	−0.541798	+	0.312807i
$216$	2.46340	+	4.57511i	0.167613	+	0.311297i
$217$	−17.4398	+	20.5545i	−1.18389	+	1.39533i
$218$	6.55912			0.444239
$219$	0.844090	+	1.02640i	0.0570383	+	0.0693576i
$220$	2.02697	−	3.51081i	0.136658	−	0.236699i
$221$	−1.07391	+	1.86006i	−0.0722389	+	0.125121i
$222$	−6.23197	−	7.57796i	−0.418262	−	0.508600i
$223$	14.7371			0.986868			0.493434	−	0.869783i	$-0.335741\pi$
$223$	14.7371			0.986868			0.493434	+	0.869783i	$0.335741\pi$
$224$	−2.01743	−	1.71172i	−0.134795	−	0.114369i
$225$	−12.0425	+	4.11520i	−0.802836	+	0.274346i
$226$	−6.76947	+	3.90835i	−0.450298	+	0.259980i
$227$	7.73416	−	13.3960i	0.513334	−	0.889121i	−0.486546	−	0.873655i	$-0.661744\pi$
$227$	7.73416	−	13.3960i	0.513334	−	0.889121i	0.999880	−	0.0154658i	$-0.00492313\pi$
$228$	−7.33189	−	2.75103i	−0.485567	−	0.182191i
$229$	−4.04934	+	2.33789i	−0.267588	+	0.154492i	−0.627791	−	0.778382i	$-0.716041\pi$
$229$	−4.04934	+	2.33789i	−0.267588	+	0.154492i	0.360203	+	0.932874i	$0.382707\pi$
$230$	−2.37034	+	3.43708i	−0.156296	+	0.226634i
$231$	10.3844	+	18.6420i	0.683245	+	1.22655i
$232$	8.08792			0.530998
$233$	−15.3145	+	8.84185i	−1.00329	+	0.579249i	−0.909220	−	0.416317i	$-0.863321\pi$
$233$	−15.3145	+	8.84185i	−1.00329	+	0.579249i	−0.0940687	+	0.995566i	$0.529987\pi$
$234$	7.38304	+	1.45299i	0.482645	+	0.0949850i
$235$	2.76379	+	1.59567i	0.180290	+	0.104090i
$236$	−5.96739	+	3.44527i	−0.388444	+	0.224268i
$237$	−0.696383	−	4.19143i	−0.0452349	−	0.272263i
$238$	−0.405614	+	2.22898i	−0.0262920	+	0.144483i
$239$			5.12861i			0.331742i	0.986147	+	0.165871i	$0.0530436\pi$
$239$			5.12861i			0.331742i	−0.986147	+	0.165871i	$0.946956\pi$
$240$	−0.957781	−	1.16465i	−0.0618245	−	0.0751775i
$241$	−7.32713	−	4.23032i	−0.471982	−	0.272499i	0.245087	−	0.969501i	$-0.421183\pi$
$241$	−7.32713	−	4.23032i	−0.471982	−	0.272499i	−0.717069	+	0.697002i	$0.754517\pi$
$242$	9.25240	+	5.34188i	0.594767	+	0.343389i
$243$	−15.1990	−	3.46261i	−0.975018	−	0.222127i
$244$			3.46631i			0.221908i
$245$	−0.992506	−	6.01271i	−0.0634089	−	0.384138i
$246$	−3.54080	+	0.588284i	−0.225753	+	0.0375076i
$247$	−9.82096	+	5.67013i	−0.624893	+	0.360782i
$248$	8.82348	+	5.09424i	0.560291	+	0.323484i
$249$	−7.88144	+	21.0052i	−0.499466	+	1.33115i
$250$	6.96804	−	4.02300i	0.440698	−	0.254437i
$251$	4.03820			0.254889			0.127445	−	0.991846i	$-0.459323\pi$
$251$	4.03820			0.254889			0.127445	+	0.991846i	$0.459323\pi$
$252$	7.84898	−	1.18046i	0.494439	−	0.0743621i
$253$	−18.3843	−	12.6785i	−1.15581	−	0.797091i
$254$	13.8318	−	7.98579i	0.867884	−	0.501073i
$255$	−0.453606	+	1.20893i	−0.0284059	+	0.0757060i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	22.1306	−	12.7771i	1.38047	−	0.797015i	0.388256	−	0.921552i	$-0.373078\pi$
$257$	22.1306	−	12.7771i	1.38047	−	0.797015i	0.992215	+	0.124536i	$0.0397443\pi$
$258$	−18.0038	+	2.99122i	−1.12087	+	0.186226i
$259$	−14.1111	+	5.04878i	−0.876821	+	0.313716i
$260$	−2.18361			−0.135422
$261$	−15.9611	+	18.2749i	−0.987968	+	1.13119i
$262$	−3.46986	+	6.00998i	−0.214369	+	0.371298i
$263$	9.77985	−	16.9392i	0.603051	−	1.04452i	−0.389305	−	0.921109i	$-0.627285\pi$
$263$	9.77985	−	16.9392i	0.603051	−	1.04452i	0.992356	−	0.123407i	$-0.0393820\pi$
$264$	6.22947	−	5.12299i	0.383397	−	0.315298i
$265$	−1.75474			−0.107793
$266$	−7.73908	+	9.12128i	−0.474514	+	0.559262i
$267$	14.1433	−	2.34984i	0.865559	−	0.143808i
$268$	−1.60030	+	0.923931i	−0.0977536	+	0.0564381i
$269$	−27.0421	−	15.6128i	−1.64878	−	0.951926i	−0.977556	−	0.210676i	$-0.932433\pi$
$269$	−27.0421	−	15.6128i	−1.64878	−	0.951926i	−0.671229	−	0.741250i	$-0.734233\pi$
$270$	4.52169	+	0.134231i	0.275181	+	0.00816902i
$271$	1.31173	+	2.27199i	0.0796822	+	0.138014i	0.903113	−	0.429403i	$-0.141276\pi$
$271$	1.31173	+	2.27199i	0.0796822	+	0.138014i	−0.823431	+	0.567417i	$0.807943\pi$
$272$	0.856311			0.0519215
$273$	5.89929	−	9.86473i	0.357041	−	0.597041i
$274$		−	19.2711i		−	1.16421i
$275$	9.87681	+	17.1071i	0.595594	+	1.03160i
$276$	−6.81754	+	4.74565i	−0.410367	+	0.285655i
$277$	14.0907	−	24.4058i	0.846627	−	1.46640i	−0.0375735	−	0.999294i	$-0.511963\pi$
$277$	14.0907	−	24.4058i	0.846627	−	1.46640i	0.884201	−	0.467107i	$-0.154704\pi$
$278$	8.63461	−	4.98520i	0.517870	−	0.298992i
$279$	−28.9233	+	9.88372i	−1.73159	+	0.591723i
$280$	−2.16871	+	0.775939i	−0.129605	+	0.0463712i
$281$	−15.9712			−0.952763			−0.476381	−	0.879239i	$-0.658052\pi$
$281$	−15.9712			−0.952763			−0.476381	+	0.879239i	$0.658052\pi$
$282$	4.03293	+	4.90397i	0.240157	+	0.292027i
$283$	−13.5206	−	7.80615i	−0.803719	−	0.464027i	0.0410511	−	0.999157i	$-0.486929\pi$
$283$	−13.5206	−	7.80615i	−0.803719	−	0.464027i	−0.844770	+	0.535130i	$0.820263\pi$
$284$	4.90124	+	2.82973i	0.290835	+	0.167914i
$285$	−5.26564	+	4.33036i	−0.311910	+	0.256508i
$286$		−	11.6797i		−	0.690637i
$287$	−0.981600	+	5.39422i	−0.0579420	+	0.318411i
$288$	−0.970088	−	2.83883i	−0.0571630	−	0.167279i
$289$	8.13337	+	14.0874i	0.478433	+	0.828671i
$290$	3.52060	−	6.09786i	0.206737	−	0.358079i
$291$	11.1215	+	4.17294i	0.651954	+	0.244622i
$292$	−0.383621	−	0.664451i	−0.0224497	−	0.0388840i
$293$	−23.8809			−1.39514			−0.697568	−	0.716518i	$-0.745735\pi$
$293$	−23.8809			−1.39514			−0.697568	+	0.716518i	$0.745735\pi$
$294$	2.35364	−	11.8937i	0.137267	−	0.693655i
$295$			5.99879i			0.349263i
$296$	2.83230	+	4.90568i	0.164624	+	0.285137i
$297$	−0.717975	+	24.1857i	−0.0416611	+	1.40339i
$298$	16.9148	+	9.76577i	0.979849	+	0.565716i
$299$	−0.962962	+	11.9904i	−0.0556895	+	0.693422i
$300$	7.24815	−	1.20424i	0.418472	−	0.0695268i
$301$	−4.99110	+	27.4278i	−0.287682	+	1.58091i
$302$		−	9.43893i		−	0.543149i
$303$	−23.0513	+	18.9569i	−1.32426	+	1.08905i
$304$	3.91551	+	2.26062i	0.224570	+	0.129655i
$305$	2.61342	+	1.50886i	0.149644	+	0.0863969i
$306$	−1.68989	+	1.93486i	−0.0966044	+	0.110609i
$307$	24.1378			1.37762			0.688809	−	0.724943i	$-0.258134\pi$
$307$	24.1378			1.37762			0.688809	+	0.724943i	$0.258134\pi$
$308$	−4.15035	−	11.6000i	−0.236488	−	0.660973i
$309$	3.60018	+	21.6690i	0.204807	+	1.23270i
$310$	7.68157	−	4.43496i	0.436284	−	0.251889i
$311$	−3.80785	−	2.19846i	−0.215923	−	0.124663i	0.388138	−	0.921601i	$-0.373118\pi$
$311$	−3.80785	−	2.19846i	−0.215923	−	0.124663i	−0.604061	+	0.796938i	$0.706452\pi$
$312$	−4.06747	−	1.52617i	−0.230275	−	0.0864024i
$313$	26.2540	−	15.1578i	1.48396	−	0.856767i	0.484130	−	0.874996i	$-0.339136\pi$
$313$	26.2540	−	15.1578i	1.48396	−	0.856767i	0.999834	+	0.0182294i	$0.00580292\pi$
$314$	−7.81924			−0.441265
$315$	2.52659	−	6.43156i	0.142357	−	0.362377i
$316$			2.45309i			0.137997i
$317$	−7.55330	+	4.36090i	−0.424236	+	0.244933i	−0.696888	−	0.717180i	$-0.745433\pi$
$317$	−7.55330	+	4.36090i	−0.424236	+	0.244933i	0.272652	+	0.962113i	$0.412099\pi$
$318$	−3.26860	−	1.22643i	−0.183294	−	0.0687746i
$319$	32.6163	+	18.8310i	1.82616	+	1.05434i
$320$	0.435291	+	0.753947i	0.0243335	+	0.0421469i
$321$	32.7171	−	5.43576i	1.82609	−	0.303395i
$322$	3.30435	+	12.2508i	0.184144	+	0.682708i
$323$		−	3.87159i		−	0.215421i
$324$	8.32884	+	3.41033i	0.462713	+	0.189463i
$325$	5.32004	−	9.21458i	0.295103	−	0.511133i
$326$	7.62329	+	4.40131i	0.422215	+	0.243766i
$327$	8.77463	−	7.21608i	0.485238	−	0.399050i
$328$	2.07230			0.114424
$329$	9.13180	−	3.26725i	0.503453	−	0.180129i
$330$	−1.15083	−	6.92668i	−0.0633510	−	0.381301i
$331$	4.32059	+	7.48347i	0.237481	+	0.411329i	0.959991	−	0.280032i	$-0.0903450\pi$
$331$	4.32059	+	7.48347i	0.237481	+	0.411329i	−0.722510	+	0.691361i	$0.757012\pi$
$332$	6.47647	−	11.2176i	0.355442	−	0.615644i
$333$	−16.6740	−	3.28145i	−0.913727	−	0.179822i
$334$	−7.16259	−	12.4060i	−0.391919	−	0.678824i
$335$			1.60872i			0.0878936i
$336$	−4.58203	−	0.0703971i	−0.249970	−	0.00384047i
$337$		−	24.5894i		−	1.33947i	−0.742600	−	0.669735i	$-0.766408\pi$
$337$		−	24.5894i		−	1.33947i	0.742600	−	0.669735i	$-0.233592\pi$
$338$	5.81002	−	3.35442i	0.316023	−	0.182456i
$339$	−4.75622	+	12.6760i	−0.258322	+	0.688466i
$340$	0.372745	−	0.645613i	0.0202149	−	0.0350133i
$341$	23.7217	+	41.0873i	1.28460	+	2.22500i
$342$	−12.8350	+	4.38600i	−0.694038	+	0.237168i
$343$	−15.8849	−	9.52207i	−0.857704	−	0.514144i
$344$	10.5370			0.568115
$345$	0.610353	+	7.20580i	0.0328603	+	0.387947i
$346$	−1.61326	+	2.79426i	−0.0867297	+	0.150220i
$347$	−1.45033	−	0.837348i	−0.0778577	−	0.0449512i	0.460566	−	0.887626i	$-0.347647\pi$
$347$	−1.45033	−	0.837348i	−0.0778577	−	0.0449512i	−0.538423	+	0.842674i	$0.680980\pi$
$348$	10.8198	−	8.89801i	0.580004	−	0.476984i
$349$	−3.63761			−0.194717			−0.0973584	−	0.995249i	$-0.531039\pi$
$349$	−3.63761			−0.194717			−0.0973584	+	0.995249i	$0.531039\pi$
$350$	2.00937	−	11.0422i	0.107405	−	0.590229i
$351$	11.4754	−	6.17876i	0.612511	−	0.329798i
$352$	−4.03272	+	2.32829i	−0.214945	+	0.124098i
$353$	11.3126	+	6.53136i	0.602111	+	0.347629i	0.769872	−	0.638199i	$-0.220320\pi$
$353$	11.3126	+	6.53136i	0.602111	+	0.347629i	−0.167761	+	0.985828i	$0.553654\pi$
$354$	−4.19268	+	11.1741i	−0.222838	+	0.593897i
$355$	4.26693	−	2.46351i	0.226465	−	0.130750i
$356$	−8.27760			−0.438712
$357$	1.90962	+	3.42812i	0.101068	+	0.181435i
$358$	8.42924			0.445499
$359$	−2.62739	−	4.55077i	−0.138668	−	0.240181i	0.788324	−	0.615260i	$-0.210949\pi$
$359$	−2.62739	−	4.55077i	−0.138668	−	0.240181i	−0.926993	+	0.375079i	$0.877616\pi$
$360$	−2.56259	−	0.504321i	−0.135061	−	0.0265801i
$361$	0.720804	−	1.24847i	0.0379371	−	0.0657089i
$362$	−10.0095	−	17.3369i	−0.526086	−	0.911207i
$363$	18.2546	−	3.03289i	0.958116	−	0.159186i
$364$	−4.29336	+	5.06016i	−0.225033	+	0.265224i
$365$	−0.667947			−0.0349620
$366$	3.81350	+	4.63715i	0.199335	+	0.242388i
$367$	−16.0463	−	9.26434i	−0.837611	−	0.483595i	0.0188406	−	0.999823i	$-0.494002\pi$
$367$	−16.0463	−	9.26434i	−0.837611	−	0.483595i	−0.856451	+	0.516228i	$0.827336\pi$
$368$	4.33194	−	2.05773i	0.225818	−	0.107267i
$369$	−4.08959	+	4.68244i	−0.212896	+	0.243758i
$370$	4.93150			0.256376
$371$	−3.45013	+	4.06633i	−0.179122	+	0.211113i
$372$	17.4083	−	2.89230i	0.902580	−	0.149959i
$373$	8.60425	−	4.96767i	0.445511	−	0.257216i	−0.260421	−	0.965495i	$-0.583861\pi$
$373$	8.60425	−	4.96767i	0.445511	−	0.257216i	0.705933	+	0.708279i	$0.250528\pi$
$374$	3.45326	+	1.99374i	0.178564	+	0.103094i
$375$	4.89573	−	13.0478i	0.252815	−	0.673788i
$376$	−1.83288	−	3.17464i	−0.0945236	−	0.163720i
$377$		−	20.2863i		−	1.04480i
$378$	9.20148	−	10.2143i	0.473273	−	0.525369i
$379$		−	7.55660i		−	0.388156i	−0.980986	−	0.194078i	$-0.937828\pi$
$379$		−	7.55660i		−	0.388156i	0.980986	−	0.194078i	$-0.0621715\pi$
$380$	3.40877	−	1.96806i	0.174866	−	0.100959i
$381$	9.71820	−	25.9004i	0.497878	−	1.32692i
$382$	4.50467	+	2.60077i	0.230479	+	0.133067i
$383$	−10.4947	−	18.1773i	−0.536253	−	0.928817i	−0.999102	−	0.0423797i	$-0.986506\pi$
$383$	−10.4947	−	18.1773i	−0.536253	−	0.928817i	0.462849	−	0.886437i	$-0.346827\pi$
$384$	0.283879	+	1.70863i	0.0144866	+	0.0871931i
$385$	−10.5524	−	1.92025i	−0.537801	−	0.0978651i
$386$			0.106752i			0.00543351i
$387$	−20.7942	+	23.8086i	−1.05703	+	1.21026i
$388$	−5.93930	−	3.42906i	−0.301522	−	0.174084i
$389$	−15.4376	+	26.7388i	−0.782719	+	1.35571i	0.147634	+	0.989042i	$0.452834\pi$
$389$	−15.4376	+	26.7388i	−0.782719	+	1.35571i	−0.930352	+	0.366667i	$0.880499\pi$
$390$	−2.92119	+	2.40233i	−0.147920	+	0.121646i
$391$	−3.38073	−	2.33148i	−0.170971	−	0.117908i
$392$	−2.46596	+	6.55126i	−0.124550	+	0.330889i
$393$	1.97004	+	11.8574i	0.0993755	+	0.598127i
$394$	11.2232	+	19.4391i	0.565416	+	0.979330i
$395$	1.84950	+	1.06781i	0.0930586	+	0.0537274i
$396$	2.69752	−	13.7068i	0.135555	−	0.688794i
$397$	−4.08183	−	7.06993i	−0.204861	−	0.354830i	0.745227	−	0.666810i	$-0.232341\pi$
$397$	−4.08183	−	7.06993i	−0.204861	−	0.354830i	−0.950088	+	0.311981i	$0.899008\pi$
$398$	−15.5970			−0.781808
$399$	−0.318282	+	20.7165i	−0.0159340	+	1.03712i
$400$	−4.24209			−0.212104
$401$	−17.1375	−	29.6830i	−0.855804	−	1.48230i	−0.875897	−	0.482498i	$-0.839729\pi$
$401$	−17.1375	−	29.6830i	−0.855804	−	1.48230i	0.0200927	−	0.999798i	$-0.493604\pi$
$402$	−1.12436	+	2.99660i	−0.0560782	+	0.149457i
$403$	12.7775	−	22.1312i	0.636491	−	1.10243i
$404$	14.9225	−	8.61551i	0.742422	−	0.428638i
$405$	6.19668	−	4.79501i	0.307916	−	0.238266i
$406$	−7.20866	−	20.1479i	−0.357760	−	0.999922i
$407$			26.3777i			1.30749i
$408$	1.14555	−	0.942080i	0.0567133	−	0.0466399i
$409$	−11.4227	+	19.7846i	−0.564814	+	0.978287i	0.432253	+	0.901753i	$0.357719\pi$
$409$	−11.4227	+	19.7846i	−0.564814	+	0.978287i	−0.997067	+	0.0765344i	$0.975614\pi$
$410$	0.902056	−	1.56241i	0.0445494	−	0.0771618i
$411$	−21.2013	−	25.7804i	−1.04578	−	1.27165i
$412$		−	12.6821i		−	0.624801i
$413$	13.9012	+	11.7947i	0.684033	+	0.580378i
$414$	−3.89936	+	13.8490i	−0.191643	+	0.680642i
$415$	−5.63830	−	9.76582i	−0.276773	−	0.479385i
$416$	2.17218	+	1.25411i	0.106500	+	0.0614878i
$417$	6.06666	−	16.1685i	0.297086	−	0.791777i
$418$	10.5268	+	18.2329i	0.514881	+	0.891800i
$419$	−2.49320			−0.121801			−0.0609003	−	0.998144i	$-0.519397\pi$
$419$	−2.49320			−0.121801			−0.0609003	+	0.998144i	$0.519397\pi$
$420$	−2.04760	+	3.42397i	−0.0999124	+	0.167072i
$421$		−	35.2121i		−	1.71613i	−0.513540	−	0.858066i	$-0.671666\pi$
$421$		−	35.2121i		−	1.71613i	0.513540	−	0.858066i	$-0.328334\pi$
$422$	8.46343	−	4.88637i	0.411994	−	0.237865i
$423$	10.7903	+	2.12355i	0.524643	+	0.103250i
$424$	1.74556	+	1.00780i	0.0847718	+	0.0489430i
$425$	1.81627	+	3.14588i	0.0881021	+	0.152597i
$426$	9.66992	−	1.60660i	0.468509	−	0.0778402i
$427$	8.63495	−	3.08948i	0.417875	−	0.149510i
$428$	−19.1481			−0.925561
$429$	−12.8496	−	15.6249i	−0.620384	−	0.754376i
$430$	4.58665	−	7.94431i	0.221188	−	0.383109i
$431$	−2.32795	+	4.03212i	−0.112133	+	0.194221i	−0.916630	−	0.399736i	$-0.869102\pi$
$431$	−2.32795	+	4.03212i	−0.112133	+	0.194221i	0.804497	+	0.593957i	$0.202435\pi$
$432$	−4.42093	−	2.73046i	−0.212702	−	0.131369i
$433$			39.7953i			1.91244i	0.292652	+	0.956219i	$0.405462\pi$
$433$			39.7953i			1.91244i	−0.292652	+	0.956219i	$0.594538\pi$
$434$	4.82603	−	26.5206i	0.231657	−	1.27303i
$435$	−1.99885	−	12.0308i	−0.0958376	−	0.576833i
$436$	−5.68036	+	3.27956i	−0.272040	+	0.157062i
$437$	−9.30350	−	19.5858i	−0.445047	−	0.936914i
$438$	−1.24420	−	0.466842i	−0.0594503	−	0.0223066i
$439$	2.44069	+	4.22740i	0.116488	+	0.201763i	0.918373	−	0.395715i	$-0.129503\pi$
$439$	2.44069	+	4.22740i	0.116488	+	0.201763i	−0.801886	+	0.597477i	$0.796170\pi$
$440$			4.05394i			0.193264i
$441$	−9.93635	−	18.5005i	−0.473160	−	0.880977i
$442$		−	2.14782i		−	0.102161i
$443$	14.7527	−	8.51749i	0.700923	−	0.404678i	−0.106768	−	0.994284i	$-0.534050\pi$
$443$	14.7527	−	8.51749i	0.700923	−	0.404678i	0.807691	+	0.589606i	$0.200717\pi$
$444$	9.18602	+	3.44672i	0.435949	+	0.163574i
$445$	−3.60317	+	6.24087i	−0.170807	+	0.295846i
$446$	−12.7627	+	7.36854i	−0.604331	+	0.348910i
$447$	33.3722	−	5.54460i	1.57845	−	0.262250i
$448$	2.60300	+	0.473676i	0.122980	+	0.0223791i
$449$			19.7554i			0.932315i	0.884702	+	0.466157i	$0.154362\pi$
$449$			19.7554i			0.932315i	−0.884702	+	0.466157i	$0.845638\pi$
$450$	8.37155	−	9.58514i	0.394639	−	0.451848i
$451$	8.35702	+	4.82493i	0.393517	+	0.227197i
$452$	3.90835	−	6.76947i	0.183833	−	0.318409i
$453$	−10.3843	−	12.6272i	−0.487899	−	0.593277i
$454$			15.4683i			0.725964i
$455$	1.94623	+	5.43961i	0.0912405	+	0.255013i
$456$	7.72512	−	1.28349i	0.361762	−	0.0601047i
$457$	−11.7276	+	6.77093i	−0.548594	+	0.316731i	−0.748555	−	0.663073i	$-0.769252\pi$
$457$	−11.7276	+	6.77093i	−0.548594	+	0.316731i	0.199961	+	0.979804i	$0.435918\pi$
$458$	2.33789	−	4.04934i	0.109242	−	0.189213i
$459$	−0.132030	+	4.44756i	−0.00616265	+	0.207594i
$460$	0.334236	−	4.16177i	0.0155839	−	0.194043i
$461$			18.4580i			0.859676i	0.902906	+	0.429838i	$0.141429\pi$
$461$			18.4580i			0.859676i	−0.902906	+	0.429838i	$0.858571\pi$
$462$	−18.3142	−	10.9522i	−0.852051	−	0.509543i
$463$	0.757863			0.0352209			0.0176104	−	0.999845i	$-0.494394\pi$
$463$	0.757863			0.0352209			0.0176104	+	0.999845i	$0.494394\pi$
$464$	−7.00434	+	4.04396i	−0.325169	+	0.187736i
$465$	5.39706	−	14.3839i	0.250282	−	0.667039i
$466$	8.84185	−	15.3145i	0.409591	−	0.709432i
$467$	4.04169	+	7.00041i	0.187027	+	0.323940i	0.944258	−	0.329207i	$-0.106781\pi$
$467$	4.04169	+	7.00041i	0.187027	+	0.323940i	−0.757231	+	0.653148i	$0.773448\pi$
$468$	−7.12040	+	2.43319i	−0.329141	+	0.112474i
$469$	3.72793	+	3.16302i	0.172140	+	0.146055i
$470$	−3.19135			−0.147206
$471$	−10.4604	+	8.60242i	−0.481989	+	0.396378i
$472$	3.44527	−	5.96739i	0.158582	−	0.274671i
$473$	42.4926	+	24.5331i	1.95381	+	1.12803i
$474$	2.69880	+	3.28169i	0.123960	+	0.150733i
$475$			19.1795i			0.880015i
$476$	−0.763219	−	2.13316i	−0.0349821	−	0.0977733i
$477$	−5.72193	+	1.95531i	−0.261989	+	0.0895274i
$478$	−2.56431	−	4.44151i	−0.117289	−	0.203150i
$479$	−1.39065	+	2.40867i	−0.0635404	+	0.110055i	−0.896046	−	0.443962i	$-0.853572\pi$
$479$	−1.39065	+	2.40867i	−0.0635404	+	0.110055i	0.832505	+	0.554017i	$0.186906\pi$
$480$	1.41179	+	0.529722i	0.0644389	+	0.0241784i
$481$	12.3045	−	7.10403i	0.561038	−	0.323916i
$482$	8.46064			0.385372
$483$	17.8983	+	12.7535i	0.814401	+	0.580303i
$484$	−10.6838			−0.485625
$485$	−5.17065	+	2.98528i	−0.234787	+	0.135554i
$486$	14.8940	−	4.60080i	0.675608	−	0.208697i
$487$	2.33434	−	4.04320i	0.105779	−	0.183215i	−0.808277	−	0.588802i	$-0.799600\pi$
$487$	2.33434	−	4.04320i	0.105779	−	0.183215i	0.914056	+	0.405587i	$0.132933\pi$
$488$	−1.73316	−	3.00192i	−0.0784563	−	0.135890i
$489$	15.0404	−	2.49888i	0.680150	−	0.113003i
$490$	3.86589	+	4.71091i	0.174643	+	0.212817i
$491$		−	12.4523i		−	0.561963i	−0.959713	−	0.280981i	$-0.909340\pi$
$491$		−	12.4523i		−	0.561963i	0.959713	−	0.280981i	$-0.0906599\pi$
$492$	2.77228	−	2.27987i	0.124984	−	0.102784i
$493$	5.99790	+	3.46289i	0.270132	+	0.155961i
$494$	5.67013	−	9.82096i	0.255111	−	0.441866i
$495$	−9.16001	−	8.00025i	−0.411712	−	0.359584i
$496$	−10.1885			−0.457476
$497$	2.68075	−	14.7316i	0.120248	−	0.660803i
$498$	−3.67707	−	22.1318i	−0.164773	−	0.991748i
$499$	5.37744	+	9.31399i	0.240727	+	0.416952i	0.960922	−	0.276821i	$-0.0892808\pi$
$499$	5.37744	+	9.31399i	0.240727	+	0.416952i	−0.720194	+	0.693772i	$0.755947\pi$
$500$	−4.02300	+	6.96804i	−0.179914	+	0.311620i
$501$	−23.2305	−	8.71641i	−1.03786	−	0.389420i
$502$	−3.49718	+	2.01910i	−0.156087	+	0.0901169i
$503$	22.2533			0.992227			0.496114	−	0.868258i	$-0.334760\pi$
$503$	22.2533			0.992227			0.496114	+	0.868258i	$0.334760\pi$
$504$	−6.20719	+	4.94680i	−0.276490	+	0.220348i
$505$		−	15.0010i		−	0.667537i
$506$	22.2605	+	1.78777i	0.989600	+	0.0794759i
$507$	4.08211	−	10.8794i	0.181293	−	0.483172i
$508$	−7.98579	+	13.8318i	−0.354312	+	0.613687i
$509$	20.8752	−	12.0523i	0.925277	−	0.534209i	0.0399623	−	0.999201i	$-0.487276\pi$
$509$	20.8752	−	12.0523i	0.925277	−	0.534209i	0.885315	+	0.464992i	$0.153943\pi$
$510$	−0.211629	−	1.27376i	−0.00937109	−	0.0564033i
$511$	−1.31330	+	1.54786i	−0.0580970	+	0.0684732i
$512$		−	1.00000i		−	0.0441942i
$513$	−12.3451	+	19.9881i	−0.545048	+	0.882495i
$514$	−12.7771	+	22.1306i	−0.563575	+	0.976140i
$515$	−9.56161	−	5.52040i	−0.421335	−	0.243258i
$516$	14.0961	−	11.5924i	0.620546	−	0.510325i
$517$		−	17.0699i		−	0.750734i
$518$	9.69619	−	11.4279i	0.426026	−	0.502114i
$519$	0.915945	+	5.51294i	0.0402055	+	0.241991i
$520$	1.89106	−	1.09181i	0.0829287	−	0.0478789i
$521$	4.68896	−	8.12151i	0.205427	−	0.355810i	−0.744842	−	0.667241i	$-0.767475\pi$
$521$	4.68896	−	8.12151i	0.205427	−	0.355810i	0.950269	+	0.311431i	$0.100808\pi$
$522$	4.68526	−	23.8071i	0.205068	−	1.04201i
$523$	16.5039	−	9.52851i	0.721664	−	0.416653i	−0.0937009	−	0.995600i	$-0.529870\pi$
$523$	16.5039	−	9.52851i	0.721664	−	0.416653i	0.815365	+	0.578948i	$0.196536\pi$
$524$		−	6.93972i		−	0.303163i
$525$	−9.46007	−	16.9826i	−0.412871	−	0.741181i
$526$			19.5597i			0.852844i
$527$	4.36225	+	7.55564i	0.190023	+	0.329129i
$528$	−2.83338	+	7.55137i	−0.123307	+	0.328631i
$529$	−22.7052	−	3.67064i	−0.987183	−	0.159593i
$530$	1.51965	−	0.877372i	0.0660095	−	0.0381106i
$531$	6.68444	+	19.5611i	0.290080	+	0.848878i
$532$	2.14160	−	11.7688i	0.0928502	−	0.510242i
$533$		−	5.19779i		−	0.225141i
$534$	−11.0736	+	9.10669i	−0.479201	+	0.394085i
$535$	−8.33502	+	14.4367i	−0.360354	+	0.624152i
$536$	0.923931	−	1.60030i	0.0399077	−	0.0691222i
$537$	11.2764	−	9.27352i	0.486614	−	0.400182i
$538$	31.2255			1.34623
$539$	−25.1978	+	20.6779i	−1.08534	+	0.890661i
$540$	−3.98301	+	2.14460i	−0.171402	+	0.0922888i
$541$	0.878151	+	1.52100i	0.0377547	+	0.0653930i	0.884285	−	0.466947i	$-0.154646\pi$
$541$	0.878151	+	1.52100i	0.0377547	+	0.0653930i	−0.846531	+	0.532340i	$0.821313\pi$
$542$	−2.27199	−	1.31173i	−0.0975904	−	0.0563438i
$543$	−32.4638	−	12.1809i	−1.39316	−	0.522731i
$544$	−0.741587	+	0.428155i	−0.0317953	+	0.0183570i
$545$			5.71025i			0.244600i
$546$	−0.176571	+	11.4928i	−0.00755655	+	0.491844i
$547$	9.80124			0.419071			0.209535	−	0.977801i	$-0.432805\pi$
$547$	9.80124			0.419071			0.209535	+	0.977801i	$0.432805\pi$
$548$	9.63555	+	16.6893i	0.411610	+	0.712930i
$549$	10.2032	+	2.00801i	0.435463	+	0.0856996i
$550$	−17.1071	−	9.87681i	−0.729451	−	0.421149i
$551$	18.2837	+	31.6683i	0.778912	+	1.34912i
$552$	3.53133	−	7.51862i	0.150304	−	0.320014i
$553$	6.11092	−	2.18641i	0.259863	−	0.0929757i
$554$			28.1814i			1.19731i
$555$	6.59724	−	5.42544i	0.280037	−	0.230297i
$556$	−4.98520	+	8.63461i	−0.211419	+	0.366189i
$557$	−4.41094	+	7.63998i	−0.186898	+	0.323716i	−0.944214	−	0.329332i	$-0.893177\pi$
$557$	−4.41094	+	7.63998i	−0.186898	+	0.323716i	0.757317	+	0.653048i	$0.226510\pi$
$558$	20.1065	−	23.0212i	0.851174	−	0.974565i
$559$		−	26.4290i		−	1.11783i
$560$	1.49019	−	1.75634i	0.0629721	−	0.0742189i
$561$	6.81313	−	1.13196i	0.287650	−	0.0477915i
$562$	13.8315	−	7.98561i	0.583446	−	0.336852i
$563$	18.2301	−	31.5755i	0.768309	−	1.33075i	−0.170170	−	0.985415i	$-0.554432\pi$
$563$	18.2301	−	31.5755i	0.768309	−	1.33075i	0.938479	−	0.345335i	$-0.112235\pi$
$564$	−5.94460	−	2.23050i	−0.250313	−	0.0939209i
$565$	−3.40255	−	5.89338i	−0.143146	−	0.247936i
$566$	15.6123			0.656234
$567$	1.07211	−	23.7876i	0.0450245	−	0.998986i
$568$	−5.65946			−0.237466
$569$	−23.1558	−	40.1071i	−0.970743	−	1.68138i	−0.693324	−	0.720626i	$-0.743854\pi$
$569$	−23.1558	−	40.1071i	−0.970743	−	1.68138i	−0.277419	−	0.960749i	$-0.589479\pi$
$570$	2.39500	−	6.38302i	0.100315	−	0.267355i
$571$	28.6203	+	16.5239i	1.19772	+	0.691505i	0.960047	−	0.279840i	$-0.0902814\pi$
$571$	28.6203	+	16.5239i	1.19772	+	0.691505i	0.237675	+	0.971345i	$0.423615\pi$
$572$	5.83987	+	10.1149i	0.244177	+	0.422927i
$573$	8.88751	−	1.47661i	0.371281	−	0.0616863i
$574$	−1.84702	−	5.16233i	−0.0770930	−	0.215471i
$575$	16.7478	+	11.5500i	0.698433	+	0.481666i
$576$	2.25953	+	1.97345i	0.0941472	+	0.0822271i
$577$	1.97147	−	3.41469i	0.0820734	−	0.142155i	−0.822067	−	0.569391i	$-0.807179\pi$
$577$	1.97147	−	3.41469i	0.0820734	−	0.142155i	0.904140	+	0.427236i	$0.140512\pi$
$578$	−14.0874	−	8.13337i	−0.585959	−	0.338303i
$579$	0.117444	+	0.142810i	0.00488080	+	0.00593497i
$580$			7.04120i			0.292370i
$581$	−33.7165	−	6.13549i	−1.39880	−	0.254543i
$582$	−11.7180	+	1.94687i	−0.485725	+	0.0807006i
$583$	4.69290	+	8.12833i	0.194360	+	0.336641i
$584$	0.664451	+	0.383621i	0.0274952	+	0.0158743i
$585$	−1.26495	+	6.42755i	−0.0522992	+	0.265746i
$586$	20.6815	−	11.9404i	0.854343	−	0.493255i
$587$		−	38.4015i		−	1.58500i	−0.609871	−	0.792500i	$-0.708779\pi$
$587$		−	38.4015i		−	1.58500i	0.609871	−	0.792500i	$-0.291221\pi$
$588$	3.90854	+	11.4771i	0.161186	+	0.473307i
$589$			46.0645i			1.89806i
$590$	−2.99940	−	5.19511i	−0.123483	−	0.213879i
$591$	36.4003	+	13.6579i	1.49731	+	0.561811i
$592$	−4.90568	−	2.83230i	−0.201622	−	0.116407i
$593$	−17.9716	+	10.3759i	−0.738004	+	0.426087i	−0.821343	−	0.570434i	$-0.806775\pi$
$593$	−17.9716	+	10.3759i	−0.738004	+	0.426087i	0.0833392	+	0.996521i	$0.473442\pi$
$594$	−11.4710	−	21.3044i	−0.470663	−	0.874129i
$595$	−1.94051	−	0.353120i	−0.0795532	−	0.0144765i
$596$	−19.5315			−0.800043
$597$	−20.8653	+	17.1592i	−0.853961	+	0.702281i
$598$	−5.16125	−	10.8655i	−0.211059	−	0.444322i
$599$	−11.2685	−	6.50585i	−0.460417	−	0.265822i	0.251802	−	0.967779i	$-0.418977\pi$
$599$	−11.2685	−	6.50585i	−0.460417	−	0.265822i	−0.712220	+	0.701957i	$0.752310\pi$
$600$	−5.67496	+	4.66698i	−0.231679	+	0.190529i
$601$	7.51273			0.306451			0.153225	−	0.988191i	$-0.451034\pi$
$601$	7.51273			0.306451			0.153225	+	0.988191i	$0.451034\pi$
$602$	−9.39146	−	26.2487i	−0.382767	−	1.06982i
$603$	1.79259	+	5.24576i	0.0729999	+	0.213624i
$604$	4.71947	+	8.17435i	0.192032	+	0.332610i
$605$	−4.65055	+	8.05498i	−0.189072	+	0.327482i
$606$	10.4845	−	27.9428i	0.425905	−	1.13510i
$607$	−12.2520	−	21.2210i	−0.497292	−	0.861334i	0.502703	−	0.864459i	$-0.332339\pi$
$607$	−12.2520	−	21.2210i	−0.497292	−	0.861334i	−0.999995	+	0.00312446i	$0.999005\pi$
$608$	−4.52124			−0.183360
$609$	−31.8095	−	19.0227i	−1.28898	−	0.770837i
$610$	−3.01771			−0.122184
$611$	−7.96270	+	4.59727i	−0.322137	+	0.185986i
$612$	0.496054	−	2.52058i	0.0200518	−	0.101889i
$613$	25.8058	+	14.8990i	1.04229	+	0.601764i	0.920480	−	0.390790i	$-0.127798\pi$
$613$	25.8058	+	14.8990i	1.04229	+	0.601764i	0.121806	+	0.992554i	$0.461131\pi$
$614$	−20.9040	+	12.0689i	−0.843615	+	0.487061i
$615$	−0.512150	−	3.08256i	−0.0206519	−	0.124301i
$616$	9.39433	+	7.97075i	0.378508	+	0.321151i
$617$	21.5124			0.866056			0.433028	−	0.901381i	$-0.357445\pi$
$617$	21.5124			0.866056			0.433028	+	0.901381i	$0.357445\pi$
$618$	−13.9523	−	16.9658i	−0.561245	−	0.682464i
$619$	−22.0454	−	12.7279i	−0.886078	−	0.511577i	−0.0134205	−	0.999910i	$-0.504272\pi$
$619$	−22.0454	−	12.7279i	−0.886078	−	0.511577i	−0.872658	+	0.488332i	$0.837605\pi$
$620$	−4.43496	+	7.68157i	−0.178112	+	0.308499i
$621$	10.0197	+	22.8168i	0.402075	+	0.915607i
$622$	4.39693			0.176301
$623$	7.37772	+	20.6204i	0.295582	+	0.826138i
$624$	4.28562	−	0.712031i	0.171562	−	0.0285041i
$625$	−7.10286	−	12.3025i	−0.284114	−	0.492101i
$626$	−15.1578	+	26.2540i	−0.605826	+	1.04932i
$627$	34.1416	+	12.8104i	1.36348	+	0.511598i
$628$	6.77166	−	3.90962i	0.270219	−	0.156011i
$629$			4.85065i			0.193408i
$630$	1.02769	+	6.83319i	0.0409441	+	0.272241i
$631$			0.722137i			0.0287478i	0.999897	+	0.0143739i	$0.00457551\pi$
$631$			0.722137i			0.0287478i	−0.999897	+	0.0143739i	$0.995424\pi$
$632$	−1.22655	−	2.12444i	−0.0487894	−	0.0845058i
$633$	5.94639	−	15.8480i	0.236348	−	0.629902i
$634$	4.36090	−	7.55330i	0.173194	−	0.299980i
$635$	6.95229	+	12.0417i	0.275893	+	0.477861i
$636$	3.44391	−	0.572186i	0.136560	−	0.0226887i
$637$	16.4320	+	6.18517i	0.651060	+	0.245065i
$638$	−37.6621			−1.49106
$639$	11.1687	−	12.7877i	0.441826	−	0.505875i
$640$	−0.753947	−	0.435291i	−0.0298024	−	0.0172064i
$641$	14.3866	−	24.9184i	0.568237	−	0.984216i	−0.428503	−	0.903540i	$-0.640959\pi$
$641$	14.3866	−	24.9184i	0.568237	−	0.984216i	0.996740	−	0.0806757i	$-0.0257078\pi$
$642$	−25.6159	+	21.0660i	−1.01098	+	0.831410i
$643$			43.3220i			1.70845i	0.519900	+	0.854227i	$0.325969\pi$
$643$			43.3220i			1.70845i	−0.519900	+	0.854227i	$0.674031\pi$
$644$	−8.98704	−	8.95730i	−0.354139	−	0.352967i
$645$	−2.60411	−	15.6738i	−0.102537	−	0.617154i
$646$	1.93579	+	3.35289i	0.0761628	+	0.131918i
$647$	13.9666	+	8.06363i	0.549085	+	0.317014i	0.748753	−	0.662849i	$-0.230653\pi$
$647$	13.9666	+	8.06363i	0.549085	+	0.317014i	−0.199668	+	0.979864i	$0.563986\pi$
$648$	−8.91816	+	1.21098i	−0.350338	+	0.0475720i
$649$	27.7876	−	16.0432i	1.09076	−	0.629751i
$650$			10.6401i			0.417338i
$651$	−22.7208	−	40.7881i	−0.890500	−	1.59861i
$652$	−8.80261			−0.344737
$653$	−30.4292	+	17.5683i	−1.19079	+	0.687501i	−0.958485	−	0.285143i	$-0.907959\pi$
$653$	−30.4292	+	17.5683i	−1.19079	+	0.687501i	−0.232302	+	0.972644i	$0.574626\pi$
$654$	−3.99101	+	10.6366i	−0.156061	+	0.415925i
$655$	−5.23218	−	3.02080i	−0.204438	−	0.118033i
$656$	−1.79467	+	1.03615i	−0.0700700	+	0.0404549i
$657$	−2.17807	+	0.744292i	−0.0849744	+	0.0290376i
$658$	−6.27475	+	7.39542i	−0.244615	+	0.288303i
$659$	−33.8882			−1.32010			−0.660048	−	0.751224i	$-0.729464\pi$
$659$	−33.8882			−1.32010			−0.660048	+	0.751224i	$0.729464\pi$
$660$	4.45999	+	5.42326i	0.173605	+	0.211100i
$661$	−4.69538	−	2.71088i	−0.182629	−	0.105441i	0.405898	−	0.913918i	$-0.366959\pi$
$661$	−4.69538	−	2.71088i	−0.182629	−	0.105441i	−0.588527	+	0.808477i	$0.700292\pi$
$662$	−7.48347	−	4.32059i	−0.290853	−	0.167924i
$663$	−2.36294	−	2.87330i	−0.0917691	−	0.111590i
$664$			12.9529i			0.502671i
$665$	−7.94083	−	6.73751i	−0.307932	−	0.261270i
$666$	16.0808	−	5.49516i	0.623118	−	0.212933i
$667$	38.6638	+	3.10514i	1.49707	+	0.120231i
$668$	12.4060	+	7.16259i	0.480001	+	0.277129i
$669$	−8.96704	+	23.8985i	−0.346686	+	0.923968i
$670$	−0.804358	−	1.39319i	−0.0310751	−	0.0538236i
$671$		−	16.1412i		−	0.623123i
$672$	4.00336	−	2.23005i	0.154433	−	0.0860261i
$673$	32.8792			1.26740			0.633701	−	0.773578i	$-0.281535\pi$
$673$	32.8792			1.26740			0.633701	+	0.773578i	$0.281535\pi$
$674$	12.2947	+	21.2950i	0.473574	+	0.820254i
$675$	0.654066	−	22.0328i	0.0251750	−	0.848044i
$676$	−3.35442	+	5.81002i	−0.129016	+	0.223462i
$677$	12.4773	+	21.6114i	0.479543	+	0.830593i	0.999725	−	0.0234626i	$-0.00746906\pi$
$677$	12.4773	+	21.6114i	0.479543	+	0.830593i	−0.520182	+	0.854056i	$0.674136\pi$
$678$	−2.21900	−	13.3559i	−0.0852202	−	0.512928i
$679$	−3.24852	+	17.8517i	−0.124667	+	0.685085i
$680$			0.745489i			0.0285882i
$681$	17.0176	+	20.6931i	0.652117	+	0.792963i
$682$	−41.0873	−	23.7217i	−1.57331	−	0.908352i
$683$	−13.4354	−	7.75691i	−0.514090	−	0.296810i	0.220423	−	0.975404i	$-0.429256\pi$
$683$	−13.4354	−	7.75691i	−0.514090	−	0.296810i	−0.734513	+	0.678594i	$0.762589\pi$
$684$	8.92244	−	10.2159i	0.341158	−	0.390614i
$685$	16.7771			0.641019
$686$	18.5178	+	0.303908i	0.707012	+	0.0116033i
$687$	−1.32735	−	7.98916i	−0.0506417	−	0.304806i
$688$	−9.12528	+	5.26848i	−0.347898	+	0.200859i
$689$	2.52778	−	4.37824i	0.0963008	−	0.166798i
$690$	−4.13148	−	5.93523i	−0.157283	−	0.225950i
$691$	13.3120	+	23.0571i	0.506413	+	0.877133i	0.999972	+	0.00742066i	$0.00236209\pi$
$691$	13.3120	+	23.0571i	0.506413	+	0.877133i	−0.493560	+	0.869712i	$0.664305\pi$
$692$		−	3.22653i		−	0.122654i
$693$	−36.5494	+	5.49692i	−1.38840	+	0.208811i
$694$	1.67470			0.0635706
$695$	4.34002	+	7.51714i	0.164627	+	0.285141i
$696$	−4.92124	+	13.1158i	−0.186539	+	0.497154i
$697$	1.53679	+	0.887268i	0.0582102	+	0.0336077i
$698$	3.15026	−	1.81880i	0.119239	−	0.0688428i
$699$	−5.02003	−	30.2149i	−0.189875	−	1.14283i
$700$	3.78092	+	10.5675i	0.142905	+	0.399413i
$701$	−9.60992			−0.362962			−0.181481	−	0.983394i	$-0.558089\pi$
$701$	−9.60992			−0.362962			−0.181481	+	0.983394i	$0.558089\pi$
$702$	−6.84860	+	11.0887i	−0.258484	+	0.418514i
$703$	−12.8055	+	22.1798i	−0.482968	+	0.836526i
$704$	2.32829	−	4.03272i	0.0877508	−	0.151989i
$705$	−4.26931	+	3.51100i	−0.160792	+	0.132232i
$706$	−13.0627			−0.491622
$707$	−34.7624	−	29.4946i	−1.30737	−	1.10926i
$708$	−1.95608	−	11.7734i	−0.0735141	−	0.442471i
$709$	27.2348	−	15.7240i	1.02283	−	0.590529i	0.107904	−	0.994161i	$-0.465586\pi$
$709$	27.2348	−	15.7240i	1.02283	−	0.590529i	0.914921	+	0.403633i	$0.132253\pi$
$710$	−2.46351	+	4.26693i	−0.0924541	+	0.160135i
$711$	7.22078	+	1.42106i	0.270800	+	0.0532938i
$712$	7.16861	−	4.13880i	0.268655	−	0.155108i
$713$	40.2243	+	27.7402i	1.50641	+	1.03888i
$714$	−3.36784	−	2.01403i	−0.126038	−	0.0753731i
$715$	10.1682			0.380268
$716$	−7.29994	+	4.21462i	−0.272811	+	0.157508i
$717$	−8.31685	−	3.12060i	−0.310598	−	0.116541i
$718$	4.55077	+	2.62739i	0.169833	+	0.0980533i
$719$	8.70543	−	5.02608i	0.324658	−	0.187441i	−0.328809	−	0.944396i	$-0.606647\pi$
$719$	8.70543	−	5.02608i	0.324658	−	0.187441i	0.653467	+	0.756955i	$0.273314\pi$
$720$	2.47143	−	0.844542i	0.0921048	−	0.0314742i
$721$	−31.5924	+	11.3034i	−1.17656	+	0.420959i
$722$			1.44161i			0.0536511i
$723$	11.3185	−	9.30807i	0.420938	−	0.346171i
$724$	17.3369	+	10.0095i	0.644321	+	0.371999i
$725$	−29.7130	−	17.1548i	−1.10351	−	0.637114i
$726$	−14.2925	+	11.7538i	−0.530443	+	0.436226i
$727$			15.8188i			0.586686i	0.956007	+	0.293343i	$0.0947679\pi$
$727$			15.8188i			0.586686i	−0.956007	+	0.293343i	$0.905232\pi$
$728$	1.18808	−	6.52891i	0.0440333	−	0.241977i
$729$	14.8633	−	22.5407i	0.550492	−	0.834841i
$730$	0.578459	−	0.333974i	0.0214097	−	0.0123609i
$731$	7.81408	+	4.51146i	0.289014	+	0.166862i
$732$	−5.62117	−	2.10914i	−0.207764	−	0.0779561i
$733$	−43.1727	+	24.9258i	−1.59462	+	0.920655i	−0.602122	+	0.798404i	$0.705678\pi$
$733$	−43.1727	+	24.9258i	−1.59462	+	0.920655i	−0.992499	+	0.122250i	$0.960989\pi$
$734$	18.5287			0.683906
$735$	10.3545	+	2.04904i	0.381930	+	0.0755800i
$736$	−2.72271	+	3.94802i	−0.100360	+	0.145526i
$737$	7.45190	−	4.30236i	0.274494	−	0.158479i
$738$	1.20047	−	6.09991i	0.0441898	−	0.224541i
$739$	−20.3811	+	35.3011i	−0.749730	+	1.29857i	0.198222	+	0.980157i	$0.436483\pi$
$739$	−20.3811	+	35.3011i	−0.749730	+	1.29857i	−0.947952	+	0.318414i	$0.896850\pi$
$740$	−4.27080	+	2.46575i	−0.156998	+	0.0906428i
$741$	−3.21926	−	19.3763i	−0.118263	−	0.711806i
$742$	0.954739	−	5.24661i	0.0350496	−	0.192609i
$743$	29.2601			1.07345			0.536725	−	0.843757i	$-0.319661\pi$
$743$	29.2601			1.07345			0.536725	+	0.843757i	$0.319661\pi$
$744$	−13.6299	+	11.2090i	−0.499696	+	0.410941i
$745$	−8.50191	+	14.7257i	−0.311486	+	0.539509i
$746$	−4.96767	+	8.60425i	−0.181879	+	0.315024i
$747$	−29.2676	−	25.5620i	−1.07085	−	0.935264i
$748$	−3.98748			−0.145797
$749$	17.0665	+	47.7001i	0.623596	+	1.74292i
$750$	2.28409	+	13.7476i	0.0834032	+	0.501992i
$751$	28.4035	−	16.3988i	1.03646	−	0.598400i	0.117631	−	0.993057i	$-0.462470\pi$
$751$	28.4035	−	16.3988i	1.03646	−	0.598400i	0.918828	+	0.394658i	$0.129137\pi$
$752$	3.17464	+	1.83288i	0.115767	+	0.0668383i
$753$	−2.45712	+	6.54857i	−0.0895423	+	0.238643i
$754$	10.1431	+	17.5684i	0.369391	+	0.639805i
$755$	8.21737			0.299061
$756$	−2.86155	+	13.4466i	−0.104074	+	0.489049i
$757$			29.9257i			1.08767i	0.839193	+	0.543834i	$0.183028\pi$
$757$			29.9257i			1.08767i	−0.839193	+	0.543834i	$0.816972\pi$
$758$	3.77830	+	6.54420i	0.137234	+	0.237696i
$759$	31.7464	−	22.0985i	1.15232	−	0.802125i
$760$	−1.96806	+	3.40877i	−0.0713889	+	0.123649i
$761$	33.6135	−	19.4068i	1.21849	−	0.703495i	0.253894	−	0.967232i	$-0.418289\pi$
$761$	33.6135	−	19.4068i	1.21849	−	0.703495i	0.964595	+	0.263737i	$0.0849552\pi$
$762$	4.53400	+	27.2895i	0.164250	+	0.988595i
$763$	13.2326	+	11.2274i	0.479051	+	0.406457i
$764$	−5.20154			−0.188185
$765$	−1.68446	−	1.47119i	−0.0609017	−	0.0531909i
$766$	18.1773	+	10.4947i	0.656773	+	0.379188i
$767$	−14.9675	−	8.64151i	−0.540446	−	0.312027i
$768$	−1.10016	−	1.33778i	−0.0396986	−	0.0482728i
$769$		−	3.97640i		−	0.143393i	−0.997427	−	0.0716963i	$-0.977159\pi$
$769$		−	3.97640i		−	0.143393i	0.997427	−	0.0716963i	$-0.0228412\pi$
$770$	10.0988	−	3.61322i	0.363935	−	0.130212i
$771$	7.25432	+	43.6627i	0.261258	+	1.57248i
$772$	−0.0533758	−	0.0924496i	−0.00192104	−	0.00332733i
$773$	−22.1893	+	38.4331i	−0.798095	+	1.38234i	0.122760	+	0.992436i	$0.460825\pi$
$773$	−22.1893	+	38.4331i	−0.798095	+	1.38234i	−0.920855	+	0.389905i	$0.872508\pi$
$774$	6.10398	−	31.0160i	0.219403	−	1.11485i
$775$	−21.6102	−	37.4300i	−0.776261	−	1.34452i
$776$	6.85811			0.246192
$777$	0.398771	−	25.9554i	0.0143058	−	0.931144i
$778$		−	30.8753i		−	1.10693i
$779$	4.68469	+	8.11412i	0.167847	+	0.290719i
$780$	1.32866	−	3.54107i	0.0475736	−	0.126791i
$781$	−22.8230	−	13.1769i	−0.816672	−	0.471506i
$782$	4.09354	+	0.328757i	0.146385	+	0.0117563i
$783$	−19.9238	−	37.0031i	−0.712019	−	1.32238i
$784$	−1.14005	−	6.90654i	−0.0407160	−	0.246662i
$785$		−	6.80729i		−	0.242963i
$786$	−7.63481	−	9.28380i	−0.272325	−	0.331142i
$787$	8.63706	+	4.98661i	0.307878	+	0.177753i	0.645976	−	0.763357i	$-0.276450\pi$
$787$	8.63706	+	4.98661i	0.307878	+	0.177753i	−0.338099	+	0.941111i	$0.609784\pi$
$788$	−19.4391	−	11.2232i	−0.692491	−	0.399810i
$789$	21.5188	+	26.1665i	0.766090	+	0.931552i
$790$	−2.13562			−0.0759820
$791$	−20.3469	−	3.70258i	−0.723453	−	0.131649i
$792$	4.51730	+	13.2192i	0.160515	+	0.469725i
$793$	−7.52947	+	4.34714i	−0.267379	+	0.154371i
$794$	7.06993	+	4.08183i	0.250902	+	0.144859i
$795$	1.06771	−	2.84559i	0.0378676	−	0.100923i
$796$	13.5074	−	7.79851i	0.478758	−	0.276411i
$797$	−47.5806			−1.68539			−0.842695	−	0.538391i	$-0.819032\pi$
$797$	−47.5806			−1.68539			−0.842695	+	0.538391i	$0.819032\pi$
$798$	−10.0826	−	18.1001i	−0.356920	−	0.640738i
$799$		−	3.13903i		−	0.111051i
$800$	3.67375	−	2.12104i	0.129887	−	0.0749902i
$801$	−4.79514	+	24.3654i	−0.169428	+	0.860911i
$802$	29.6830	+	17.1375i	1.04814	+	0.605145i
$803$	1.78636	+	3.09407i	0.0630394	+	0.109187i
$804$	−0.524569	−	3.15731i	−0.0185001	−	0.111350i
$805$	−10.6653	+	2.87671i	−0.375903	+	0.101391i
$806$			25.5549i			0.900134i
$807$	41.7727	−	34.3531i	1.47047	−	1.20929i
$808$	−8.61551	+	14.9225i	−0.303093	+	0.524972i
$809$	26.3154	+	15.1932i	0.925200	+	0.534164i	0.885290	−	0.465039i	$-0.153960\pi$
$809$	26.3154	+	15.1932i	0.925200	+	0.534164i	0.0399095	+	0.999203i	$0.487293\pi$
$810$	−2.96898	+	7.25095i	−0.104319	+	0.254772i
$811$	−31.0050			−1.08873			−0.544367	−	0.838847i	$-0.683230\pi$
$811$	−31.0050			−1.08873			−0.544367	+	0.838847i	$0.683230\pi$
$812$	16.3168	+	13.8442i	0.572608	+	0.485837i
$813$	−4.48254	+	0.744748i	−0.157209	+	0.0261195i
$814$	−13.1888	−	22.8437i	−0.462268	−	0.800672i
$815$	−3.83170	+	6.63670i	−0.134219	+	0.232474i
$816$	−0.521038	+	1.38864i	−0.0182400	+	0.0486122i
$817$	23.8201	+	41.2576i	0.833359	+	1.44342i
$818$		−	22.8453i		−	0.798768i
$819$	12.4077	+	15.5690i	0.433559	+	0.544025i
$820$			1.80411i			0.0630023i
$821$	−26.8413	+	15.4968i	−0.936768	+	0.540843i	−0.888946	−	0.458013i	$-0.848561\pi$
$821$	−26.8413	+	15.4968i	−0.936768	+	0.540843i	−0.0478223	+	0.998856i	$0.515228\pi$
$822$	31.2511	+	11.7258i	1.09001	+	0.408986i
$823$	−16.5316	+	28.6336i	−0.576256	+	0.998105i	0.419648	+	0.907687i	$0.362154\pi$
$823$	−16.5316	+	28.6336i	−0.576256	+	0.998105i	−0.995904	+	0.0904176i	$0.971180\pi$
$824$	6.34104	+	10.9830i	0.220900	+	0.382611i
$825$	−33.7516	+	5.60764i	−1.17508	+	0.195233i
$826$	−17.9361	−	3.26388i	−0.624078	−	0.113565i
$827$	−6.68573			−0.232486			−0.116243	−	0.993221i	$-0.537085\pi$
$827$	−6.68573			−0.232486			−0.116243	+	0.993221i	$0.537085\pi$
$828$	−3.54756	−	13.9433i	−0.123286	−	0.484562i
$829$	−2.36774	+	4.10104i	−0.0822349	+	0.142435i	−0.904210	−	0.427089i	$-0.859539\pi$
$829$	−2.36774	+	4.10104i	−0.0822349	+	0.142435i	0.821975	+	0.569524i	$0.192872\pi$
$830$	9.76582	+	5.63830i	0.338977	+	0.195708i
$831$	31.0040	+	37.7004i	1.07552	+	1.30781i
$832$	−2.50822			−0.0869569
$833$	−4.63368	+	3.80252i	−0.160548	+	0.131749i
$834$	2.83039	+	17.0357i	0.0980082	+	0.589898i
$835$	10.8004	−	6.23562i	0.373764	−	0.215793i
$836$	−18.2329	−	10.5268i	−0.630598	−	0.364076i
$837$	1.57091	−	52.9176i	0.0542986	−	1.82910i
$838$	2.15917	−	1.24660i	0.0745874	−	0.0430630i
$839$	−13.2911			−0.458859			−0.229430	−	0.973325i	$-0.573686\pi$
$839$	−13.2911			−0.458859			−0.229430	+	0.973325i	$0.573686\pi$
$840$	0.0612865	−	3.98904i	0.00211458	−	0.137635i
$841$	−36.4144			−1.25567
$842$	17.6060	+	30.4946i	0.606744	+	1.05091i
$843$	9.71797	−	25.8998i	0.334705	−	0.892037i
$844$	−4.88637	+	8.46343i	−0.168196	+	0.291323i
$845$	2.92030	+	5.05810i	0.100461	+	0.174004i
$846$	−10.4065	+	3.55611i	−0.357781	+	0.122262i
$847$	9.52229	+	26.6144i	0.327190	+	0.914480i
$848$	−2.01560			−0.0692159
$849$	20.8858	−	17.1760i	0.716797	−	0.589480i
$850$	−3.14588	−	1.81627i	−0.107903	−	0.0622976i
$851$	11.6562	+	24.5387i	0.399570	+	0.841176i
$852$	−7.57109	+	6.22632i	−0.259381	+	0.213310i
$853$	−16.2250			−0.555535			−0.277768	−	0.960648i	$-0.589594\pi$
$853$	−16.2250			−0.555535			−0.277768	+	0.960648i	$0.589594\pi$
$854$	−5.93335	+	6.99305i	−0.203035	+	0.239297i
$855$	−3.81838	−	11.1739i	−0.130586	−	0.382141i
$856$	16.5828	−	9.57407i	0.566788	−	0.327235i
$857$	15.8788	+	9.16762i	0.542409	+	0.313160i	0.746055	−	0.665885i	$-0.231946\pi$
$857$	15.8788	+	9.16762i	0.542409	+	0.313160i	−0.203646	+	0.979045i	$0.565279\pi$
$858$	18.9405	+	7.10674i	0.646618	+	0.242620i
$859$	−14.1922	−	24.5815i	−0.484230	−	0.838712i	0.515606	−	0.856826i	$-0.327567\pi$
$859$	−14.1922	−	24.5815i	−0.484230	−	0.838712i	−0.999836	+	0.0181144i	$0.994234\pi$
$860$			9.17330i			0.312807i
$861$	−8.15029	−	4.87402i	−0.277761	−	0.166106i
$862$		−	4.65589i		−	0.158580i
$863$	−27.7133	+	16.0003i	−0.943371	+	0.544656i	−0.891016	−	0.453973i	$-0.850006\pi$
$863$	−27.7133	+	16.0003i	−0.943371	+	0.544656i	−0.0523558	+	0.998628i	$0.516673\pi$
$864$	5.19386	+	0.154185i	0.176699	+	0.00524548i
$865$	−2.43263	−	1.40448i	−0.0827120	−	0.0477538i
$866$	−19.8976	−	34.4637i	−0.676149	−	1.17112i
$867$	−27.7938	+	4.61779i	−0.943927	+	0.156828i
$868$	9.08086	+	25.3806i	0.308224	+	0.861473i
$869$		−	11.4230i		−	0.387500i
$870$	7.74646	+	9.41956i	0.262629	+	0.319353i
$871$	−4.01389	−	2.31742i	−0.136006	−	0.0785228i
$872$	3.27956	−	5.68036i	0.111060	−	0.192361i
$873$	−13.5341	+	15.4961i	−0.458061	+	0.524465i
$874$	17.8499	+	12.3100i	0.603784	+	0.416392i
$875$	20.9438	+	3.81119i	0.708029	+	0.128842i
$876$	1.31093	−	0.217804i	0.0442923	−	0.00735891i
$877$	−27.1196	−	46.9725i	−0.915763	−	1.58615i	−0.805780	−	0.592215i	$-0.798254\pi$
$877$	−27.1196	−	46.9725i	−0.915763	−	1.58615i	−0.109983	−	0.993933i	$-0.535080\pi$
$878$	−4.22740	−	2.44069i	−0.142668	−	0.0823692i
$879$	14.5308	−	38.7266i	0.490110	−	1.30621i
$880$	−2.02697	−	3.51081i	−0.0683291	−	0.118350i
$881$	2.59487			0.0874234			0.0437117	−	0.999044i	$-0.486082\pi$
$881$	2.59487			0.0874234			0.0437117	+	0.999044i	$0.486082\pi$
$882$	17.8554	+	11.0537i	0.601222	+	0.372199i
$883$	−18.5876			−0.625522			−0.312761	−	0.949832i	$-0.601254\pi$
$883$	−18.5876			−0.625522			−0.312761	+	0.949832i	$0.601254\pi$
$884$	1.07391	+	1.86006i	0.0361194	+	0.0625607i
$885$	−9.72798	−	3.65007i	−0.327002	−	0.122696i
$886$	−8.51749	+	14.7527i	−0.286151	+	0.495628i
$887$	3.61132	−	2.08500i	0.121256	−	0.0700074i	−0.438145	−	0.898904i	$-0.644364\pi$
$887$	3.61132	−	2.08500i	0.121256	−	0.0700074i	0.559401	+	0.828897i	$0.311031\pi$
$888$	−9.67869	+	1.60806i	−0.324796	+	0.0539630i
$889$	41.5741	+	7.56535i	1.39435	+	0.253734i
$890$		−	7.20634i		−	0.241557i
$891$	−38.7839	−	15.8805i	−1.29931	−	0.532017i
$892$	7.36854	−	12.7627i	0.246717	−	0.427326i
$893$	8.28690	−	14.3533i	0.277310	−	0.480316i
$894$	−26.1288	+	21.4878i	−0.873879	+	0.718661i
$895$			7.33835i			0.245294i
$896$	−2.49111	+	0.891287i	−0.0832220	+	0.0297758i
$897$	−18.8584	−	8.85736i	−0.629662	−	0.295739i
$898$	−9.87770	−	17.1087i	−0.329623	−	0.570924i
$899$	−71.3636	−	41.2018i	−2.38011	−	1.37416i
$900$	−2.45740	+	12.4867i	−0.0819135	+	0.416225i
$901$	0.862989	+	1.49474i	0.0287503	+	0.0497970i
$902$	−9.64985			−0.321305
$903$	−41.4415	−	24.7828i	−1.37909	−	0.824719i
$904$			7.81671i			0.259980i
$905$	15.0932	−	8.71407i	0.501715	−	0.289665i
$906$	15.3067	+	5.74329i	0.508531	+	0.190808i
$907$	−37.4067	−	21.5967i	−1.24207	−	0.717108i	−0.272553	−	0.962141i	$-0.587868\pi$
$907$	−37.4067	−	21.5967i	−1.24207	−	0.717108i	−0.969515	+	0.245033i	$0.921201\pi$
$908$	−7.73416	−	13.3960i	−0.256667	−	0.444560i
$909$	−16.7156	−	48.9159i	−0.554422	−	1.62244i
$910$	−4.40529	−	3.73773i	−0.146034	−	0.123904i
$911$	9.89616			0.327874			0.163937	−	0.986471i	$-0.447581\pi$
$911$	9.89616			0.327874			0.163937	+	0.986471i	$0.447581\pi$
$912$	−6.04841	+	4.97409i	−0.200283	+	0.164709i
$913$	−30.1582	+	52.2355i	−0.998091	+	1.72874i
$914$	6.77093	−	11.7276i	0.223962	−	0.387914i
$915$	−4.03703	+	3.31997i	−0.133460	+	0.109755i
$916$			4.67577i			0.154492i
$917$	−17.2876	+	6.18529i	−0.570886	+	0.204256i
$918$	−2.10944	−	3.91772i	−0.0696219	−	0.129304i
$919$	−11.1433	+	6.43359i	−0.367584	+	0.212225i	−0.672402	−	0.740186i	$-0.734738\pi$
$919$	−11.1433	+	6.43359i	−0.367584	+	0.212225i	0.304819	+	0.952410i	$0.401404\pi$
$920$	1.79143	+	3.77132i	0.0590616	+	0.124337i
$921$	−14.6871	+	39.1432i	−0.483956	+	1.28981i
$922$	−9.22902	−	15.9851i	−0.303941	−	0.526442i
$923$			14.1952i			0.467240i
$924$	21.3366	+	0.327810i	0.701923	+	0.0107841i
$925$		−	24.0297i		−	0.790092i
$926$	−0.656328	+	0.378931i	−0.0215683	+	0.0124525i
$927$	−37.3302	−	7.34662i	−1.22608	−	0.241295i
$928$	4.04396	−	7.00434i	0.132749	−	0.229929i
$929$	41.4374	−	23.9239i	1.35952	−	0.784918i	0.369959	−	0.929048i	$-0.379372\pi$
$929$	41.4374	−	23.9239i	1.35952	−	0.784918i	0.989559	+	0.144131i	$0.0460385\pi$
$930$	2.51798	+	15.1554i	0.0825679	+	0.496965i
$931$	−31.2261	+	5.15443i	−1.02339	+	0.168930i
$932$			17.6837i			0.579249i
$933$	5.88211	−	4.83733i	0.192572	−	0.158367i
$934$	−7.00041	−	4.04169i	−0.229060	−	0.132248i
$935$	−1.73572	+	3.00635i	−0.0567640	+	0.0983181i
$936$	4.94985	−	5.66741i	0.161791	−	0.185245i
$937$		−	5.61680i		−	0.183493i	−0.995782	−	0.0917464i	$-0.970755\pi$
$937$		−	5.61680i		−	0.183493i	0.995782	−	0.0917464i	$-0.0292449\pi$
$938$	−4.80999	−	0.875287i	−0.157052	−	0.0285791i
$939$	8.60594	+	51.7979i	0.280844	+	1.69036i
$940$	2.76379	−	1.59567i	0.0901449	−	0.0520452i
$941$	10.1394	−	17.5619i	0.330535	−	0.572503i	−0.652082	−	0.758148i	$-0.726104\pi$
$941$	10.1394	−	17.5619i	0.330535	−	0.572503i	0.982617	+	0.185645i	$0.0594376\pi$
$942$	4.75775	−	12.6801i	0.155016	−	0.413140i
$943$	9.90652	+	0.795604i	0.322601	+	0.0259084i
$944$			6.89055i			0.224268i
$945$	8.89243	+	8.01065i	0.289271	+	0.260587i
$946$	−49.0662			−1.59528
$947$	−37.9709	+	21.9225i	−1.23389	+	0.712387i	−0.967838	−	0.251572i	$-0.919052\pi$
$947$	−37.9709	+	21.9225i	−1.23389	+	0.712387i	−0.266051	+	0.963959i	$0.585719\pi$
$948$	−3.97808	−	1.49263i	−0.129202	−	0.0484784i
$949$	0.962206	−	1.66659i	0.0312345	−	0.0540998i
$950$	−9.58974	−	16.6099i	−0.311132	−	0.538897i
$951$	−2.47594	−	14.9023i	−0.0802878	−	0.483241i
$952$	1.72755	+	1.46576i	0.0559901	+	0.0475056i
$953$	−7.83379			−0.253761			−0.126881	−	0.991918i	$-0.540497\pi$
$953$	−7.83379			−0.253761			−0.126881	+	0.991918i	$0.540497\pi$
$954$	3.97768	−	4.55431i	0.128782	−	0.147451i
$955$	−2.26419	+	3.92169i	−0.0732674	+	0.126903i
$956$	4.44151	+	2.56431i	0.143649	+	0.0829356i
$957$	−50.3834	+	41.4343i	−1.62866	+	1.33938i
$958$		−	2.78130i		−	0.0898596i
$959$	32.9867	−	38.8781i	1.06519	−	1.25544i
$960$	−1.48750	+	0.247140i	−0.0480089	+	0.00797642i
$961$	−36.4025	−	63.0510i	−1.17427	−	2.03390i
$962$	−7.10403	+	12.3045i	−0.229043	+	0.396714i
$963$	−11.0924	+	56.3633i	−0.357446	+	1.81628i
$964$	−7.32713	+	4.23032i	−0.235991	+	0.136250i
$965$	−0.0929361			−0.00299172
$966$	−21.8771	−	2.09568i	−0.703885	−	0.0674273i
$967$	−7.24133			−0.232866			−0.116433	−	0.993199i	$-0.537146\pi$
$967$	−7.24133			−0.232866			−0.116433	+	0.993199i	$0.537146\pi$
$968$	9.25240	−	5.34188i	0.297383	−	0.171694i
$969$	6.27838	+	2.35574i	0.201691	+	0.0756771i
$970$	2.98528	−	5.17065i	0.0958515	−	0.166020i
$971$	−15.2000	−	26.3272i	−0.487792	−	0.844881i	0.512109	−	0.858920i	$-0.328864\pi$
$971$	−15.2000	−	26.3272i	−0.487792	−	0.844881i	−0.999901	+	0.0140397i	$0.995531\pi$
$972$	−10.5982	+	11.4314i	−0.339938	+	0.366663i
$973$	25.9530	+	4.72273i	0.832014	+	0.151404i
$974$			4.66868i			0.149594i
$975$	11.7058	+	14.2341i	0.374886	+	0.455855i
$976$	3.00192	+	1.73316i	0.0960890	+	0.0554770i
$977$	20.4237	−	35.3748i	0.653411	−	1.13174i	−0.328879	−	0.944372i	$-0.606671\pi$
$977$	20.4237	−	35.3748i	0.653411	−	1.13174i	0.982290	−	0.187369i	$-0.0599960\pi$
$978$	−11.7759	+	9.68429i	−0.376553	+	0.309669i
$979$	38.5453			1.23191
$980$	−5.70342	−	2.14682i	−0.182189	−	0.0685777i
$981$	6.36292	+	18.6202i	0.203152	+	0.594497i
$982$	6.22613	+	10.7840i	0.198684	+	0.344131i
$983$	21.1571	−	36.6452i	0.674807	−	1.16880i	−0.301718	−	0.953397i	$-0.597560\pi$
$983$	21.1571	−	36.6452i	0.674807	−	1.16880i	0.976525	−	0.215403i	$-0.0691066\pi$
$984$	−1.26093	+	3.36056i	−0.0401970	+	0.107131i
$985$	−16.9234	+	9.77072i	−0.539224	+	0.311321i
$986$	−6.92577			−0.220562
$987$	−0.258059	+	16.7967i	−0.00821411	+	0.534643i
$988$			11.3403i			0.360782i
$989$	50.3713	+	4.04538i	1.60172	+	0.128636i
$990$	11.9329	+	2.34841i	0.379253	+	0.0746375i
$991$	26.2315	−	45.4343i	0.833271	−	1.44327i	−0.0621599	−	0.998066i	$-0.519799\pi$
$991$	26.2315	−	45.4343i	0.833271	−	1.44327i	0.895431	−	0.445201i	$-0.146868\pi$
$992$	8.82348	−	5.09424i	0.280146	−	0.161742i
$993$	−14.7646	+	2.45305i	−0.468539	+	0.0778451i
$994$	5.04421	+	14.0983i	0.159992	+	0.447171i
$995$		−	13.5785i		−	0.430467i
$996$	14.2503	+	17.3281i	0.451538	+	0.549063i
$997$	23.7636	−	41.1598i	0.752601	−	1.30354i	−0.193957	−	0.981010i	$-0.562132\pi$
$997$	23.7636	−	41.1598i	0.752601	−	1.30354i	0.946558	−	0.322533i	$-0.104534\pi$
$998$	−9.31399	−	5.37744i	−0.294829	−	0.170220i
$999$	15.4670	−	25.0428i	0.489353	−	0.792318i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.j.a.137.11	✓	128
3.2	odd	2	inner	966.2.j.a.137.42	yes	128
7.2	even	3	inner	966.2.j.a.275.41	yes	128
21.2	odd	6	inner	966.2.j.a.275.12	yes	128
23.22	odd	2	inner	966.2.j.a.137.12	yes	128
69.68	even	2	inner	966.2.j.a.137.41	yes	128
161.114	odd	6	inner	966.2.j.a.275.42	yes	128
483.275	even	6	inner	966.2.j.a.275.11	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.j.a.137.11	✓	128	1.1	even	1	trivial
966.2.j.a.137.12	yes	128	23.22	odd	2	inner
966.2.j.a.137.41	yes	128	69.68	even	2	inner
966.2.j.a.137.42	yes	128	3.2	odd	2	inner
966.2.j.a.275.11	yes	128	483.275	even	6	inner
966.2.j.a.275.12	yes	128	21.2	odd	6	inner
966.2.j.a.275.41	yes	128	7.2	even	3	inner
966.2.j.a.275.42	yes	128	161.114	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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.j (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.608468 + 1.62166i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.435291 - 0.753947i) q^{5} +(-0.283879 - 1.70863i) q^{6} +(-2.60300 - 0.473676i) q^{7} +1.00000i q^{8} +(-2.25953 - 1.97345i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(-0.608468 + 1.62166i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.435291 - 0.753947i) q^{5} +(-0.283879 - 1.70863i) q^{6} +(-2.60300 - 0.473676i) q^{7} +1.00000i q^{8} +(-2.25953 - 1.97345i) q^{9} +(0.753947 + 0.435291i) q^{10} +(-2.32829 + 4.03272i) q^{11} +(1.10016 + 1.33778i) q^{12} +2.50822 q^{13} +(2.49111 - 0.891287i) q^{14} +(1.48750 - 0.247140i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-0.428155 + 0.741587i) q^{17} +(2.94354 + 0.579292i) q^{18} +(-3.91551 + 2.26062i) q^{19} -0.870583 q^{20} +(2.35198 - 3.93296i) q^{21} -4.65658i q^{22} +(-0.383923 + 4.78044i) q^{23} +(-1.62166 - 0.608468i) q^{24} +(2.12104 - 3.67375i) q^{25} +(-2.17218 + 1.25411i) q^{26} +(4.57511 - 2.46340i) q^{27} +(-1.71172 + 2.01743i) q^{28} -8.08792i q^{29} +(-1.16465 + 0.957781i) q^{30} +(5.09424 - 8.82348i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-5.12299 - 6.22947i) q^{33} -0.856311i q^{34} +(0.775939 + 2.16871i) q^{35} +(-2.83883 + 0.970088i) q^{36} +(4.90568 - 2.83230i) q^{37} +(2.26062 - 3.91551i) q^{38} +(-1.52617 + 4.06747i) q^{39} +(0.753947 - 0.435291i) q^{40} -2.07230i q^{41} +(-0.0703971 + 4.58203i) q^{42} -10.5370i q^{43} +(2.32829 + 4.03272i) q^{44} +(-0.504321 + 2.56259i) q^{45} +(-2.05773 - 4.33194i) q^{46} +(-3.17464 + 1.83288i) q^{47} +(1.70863 - 0.283879i) q^{48} +(6.55126 + 2.46596i) q^{49} +4.24209i q^{50} +(-0.942080 - 1.14555i) q^{51} +(1.25411 - 2.17218i) q^{52} +(1.00780 - 1.74556i) q^{53} +(-2.73046 + 4.42093i) q^{54} +4.05394 q^{55} +(0.473676 - 2.60300i) q^{56} +(-1.28349 - 7.72512i) q^{57} +(4.04396 + 7.00434i) q^{58} +(-5.96739 - 3.44527i) q^{59} +(0.529722 - 1.41179i) q^{60} +(-3.00192 + 1.73316i) q^{61} +10.1885i q^{62} +(4.94680 + 6.20719i) q^{63} -1.00000 q^{64} +(-1.09181 - 1.89106i) q^{65} +(7.55137 + 2.83338i) q^{66} +(-1.60030 - 0.923931i) q^{67} +(0.428155 + 0.741587i) q^{68} +(-7.51862 - 3.53133i) q^{69} +(-1.75634 - 1.49019i) q^{70} +5.65946i q^{71} +(1.97345 - 2.25953i) q^{72} +(0.383621 - 0.664451i) q^{73} +(-2.83230 + 4.90568i) q^{74} +(4.66698 + 5.67496i) q^{75} +4.52124i q^{76} +(7.97075 - 9.39433i) q^{77} +(-0.712031 - 4.28562i) q^{78} +(-2.12444 + 1.22655i) q^{79} +(-0.435291 + 0.753947i) q^{80} +(1.21098 + 8.91816i) q^{81} +(1.03615 + 1.79467i) q^{82} +12.9529 q^{83} +(-2.23005 - 4.00336i) q^{84} +0.745489 q^{85} +(5.26848 + 9.12528i) q^{86} +(13.1158 + 4.92124i) q^{87} +(-4.03272 - 2.32829i) q^{88} +(-4.13880 - 7.16861i) q^{89} +(-0.844542 - 2.47143i) q^{90} +(-6.52891 - 1.18808i) q^{91} +(3.94802 + 2.72271i) q^{92} +(11.2090 + 13.6299i) q^{93} +(1.83288 - 3.17464i) q^{94} +(3.40877 + 1.96806i) q^{95} +(-1.33778 + 1.10016i) q^{96} -6.85811i q^{97} +(-6.90654 + 1.14005i) q^{98} +(13.2192 - 4.51730i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9}+O(q^{10}) \) 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9	\( 128 q + 64 q^{4} + 8 q^{6} - 4 q^{9} - 64 q^{16} + 4 q^{24} - 72 q^{25} + 24 q^{27} - 8 q^{36} + 4 q^{39} + 12 q^{46} + 72 q^{49} + 4 q^{54} - 96 q^{55} - 128 q^{64} - 56 q^{69} + 32 q^{70} - 40 q^{73} - 40 q^{75} - 16 q^{78} + 36 q^{81} - 32 q^{82} - 64 q^{85} - 24 q^{87} + 32 q^{93} - 8 q^{94} - 4 q^{96}+O(q^{100}) \) 128 * q + 64 * q^4 + 8 * q^6 - 4 * q^9 - 64 * q^16 + 4 * q^24 - 72 * q^25 + 24 * q^27 - 8 * q^36 + 4 * q^39 + 12 * q^46 + 72 * q^49 + 4 * q^54 - 96 * q^55 - 128 * q^64 - 56 * q^69 + 32 * q^70 - 40 * q^73 - 40 * q^75 - 16 * q^78 + 36 * q^81 - 32 * q^82 - 64 * q^85 - 24 * q^87 + 32 * q^93 - 8 * q^94 - 4 * q^96

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