LMFDB - Embedded newform 370.2.r.d.23.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [370,2,Mod(23,370)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("370.23"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(370, base_ring=CyclotomicField(12)) chi = DirichletCharacter(H, H._module([9, 5])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 370 = 2 \cdot 5 \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	370.r (of order $12$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$2.95446487479$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{12})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} - 4x^{10} + 6x^{8} + 44x^{7} + 56x^{6} + 32x^{5} + 92x^{4} - 16x^{3} + 36x^{2} - 24x + 4 $ x^12 - 2x^11 - 4x^10 + 6x^8 + 44x^7 + 56x^6 + 32x^5 + 92x^4 - 16x^3 + 36x^2 - 24x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			23.1
Root			$0.270517 - 0.0724848i$ of defining polynomial
Character	$\chi$	$=$	370.23
Dual form			370.2.r.d.177.1

$q$-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} +(-0.658815 - 0.176529i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.32150 + 1.80379i) q^{5} +(-0.482286 - 0.482286i) q^{6} +(-4.10264 - 1.09930i) q^{7} +1.00000i q^{8} +(-2.19520 - 1.26740i) q^{9} +(-2.04634 + 0.901374i) q^{10} +2.14497i q^{11} +(-0.176529 - 0.658815i) q^{12} +(-4.46146 + 2.57582i) q^{13} +(-3.00334 - 3.00334i) q^{14} +(1.18904 - 0.955079i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.60783 - 2.78485i) q^{17} +(-1.26740 - 2.19520i) q^{18} +(6.69996 + 1.79525i) q^{19} +(-2.22287 - 0.242559i) q^{20} +(2.50882 + 1.44847i) q^{21} +(-1.07248 + 1.85760i) q^{22} +2.23008i q^{23} +(0.176529 - 0.658815i) q^{24} +(-1.50728 - 4.76740i) q^{25} -5.15165 q^{26} +(2.66936 + 2.66936i) q^{27} +(-1.09930 - 4.10264i) q^{28} +(-0.485118 - 0.485118i) q^{29} +(1.50728 - 0.232600i) q^{30} +(-5.21767 + 5.21767i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.378650 - 1.41314i) q^{33} +(2.78485 - 1.60783i) q^{34} +(7.40453 - 5.94755i) q^{35} -2.53480i q^{36} +(-5.38642 - 2.82604i) q^{37} +(4.90471 + 4.90471i) q^{38} +(3.39398 - 0.909415i) q^{39} +(-1.80379 - 1.32150i) q^{40} +(0.247679 - 0.142998i) q^{41} +(1.44847 + 2.50882i) q^{42} +12.4261i q^{43} +(-1.85760 + 1.07248i) q^{44} +(5.18707 - 2.28480i) q^{45} +(-1.11504 + 1.93130i) q^{46} +(2.42838 - 2.42838i) q^{47} +(0.482286 - 0.482286i) q^{48} +(9.56099 + 5.52004i) q^{49} +(1.07836 - 4.88233i) q^{50} +(-1.55087 + 1.55087i) q^{51} +(-4.46146 - 2.57582i) q^{52} +(-7.23790 + 1.93939i) q^{53} +(0.977053 + 3.64641i) q^{54} +(-3.86906 - 2.83457i) q^{55} +(1.09930 - 4.10264i) q^{56} +(-4.09712 - 2.36548i) q^{57} +(-0.177565 - 0.662683i) q^{58} +(1.59354 + 5.94716i) q^{59} +(1.42164 + 0.552203i) q^{60} +(6.45558 + 1.72977i) q^{61} +(-7.12748 + 1.90980i) q^{62} +(7.61286 + 7.61286i) q^{63} -1.00000 q^{64} +(1.24958 - 11.4515i) q^{65} +(1.03449 - 1.03449i) q^{66} +(0.635595 - 2.37207i) q^{67} +3.21567 q^{68} +(0.393674 - 1.46921i) q^{69} +(9.38628 - 1.44847i) q^{70} +(-6.41760 - 11.1156i) q^{71} +(1.26740 - 2.19520i) q^{72} +(9.49086 - 9.49086i) q^{73} +(-3.25176 - 5.14063i) q^{74} +(0.151436 + 3.40692i) q^{75} +(1.79525 + 6.69996i) q^{76} +(2.35796 - 8.80003i) q^{77} +(3.39398 + 0.909415i) q^{78} +(-0.585692 - 0.156936i) q^{79} +(-0.901374 - 2.04634i) q^{80} +(2.51480 + 4.35577i) q^{81} +0.285995 q^{82} +(3.55006 - 0.951235i) q^{83} +2.89694i q^{84} +(2.89852 + 6.58036i) q^{85} +(-6.21303 + 10.7613i) q^{86} +(0.233966 + 0.405241i) q^{87} -2.14497 q^{88} +(-5.82591 + 1.56105i) q^{89} +(5.63454 + 0.614838i) q^{90} +(21.1353 - 5.66319i) q^{91} +(-1.93130 + 1.11504i) q^{92} +(4.35856 - 2.51641i) q^{93} +(3.31722 - 0.888848i) q^{94} +(-12.0922 + 9.71287i) q^{95} +(0.658815 - 0.176529i) q^{96} -14.2602 q^{97} +(5.52004 + 9.56099i) q^{98} +(2.71853 - 4.70864i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 6 q^{4} - 8 q^{5} + 6 q^{6} - 4 q^{7} - 18 q^{9} - 4 q^{10} - 6 q^{13} - 8 q^{14} - 14 q^{15} - 6 q^{16} + 12 q^{17} + 10 q^{18} + 8 q^{19} - 4 q^{20} + 54 q^{21} - 10 q^{22} - 10 q^{25}+ \cdots - 28 q^{99}+O(q^{100}) $ 12 * q + 6 * q^3 + 6 * q^4 - 8 * q^5 + 6 * q^6 - 4 * q^7 - 18 * q^9 - 4 * q^10 - 6 * q^13 - 8 * q^14 - 14 * q^15 - 6 * q^16 + 12 * q^17 + 10 * q^18 + 8 * q^19 - 4 * q^20 + 54 * q^21 - 10 * q^22 - 10 * q^25 - 18 * q^27 + 4 * q^28 - 4 * q^29 + 10 * q^30 - 2 * q^31 - 28 * q^33 - 12 * q^34 + 14 * q^35 + 12 * q^37 + 16 * q^38 + 30 * q^39 - 2 * q^40 + 12 * q^41 - 22 * q^42 - 6 * q^44 + 24 * q^45 + 2 * q^46 - 28 * q^47 - 6 * q^48 - 24 * q^49 + 16 * q^50 - 8 * q^51 - 6 * q^52 + 14 * q^53 + 18 * q^54 - 32 * q^55 - 4 * q^56 - 72 * q^57 - 10 * q^58 + 14 * q^60 + 24 * q^61 - 16 * q^62 + 8 * q^63 - 12 * q^64 - 26 * q^65 + 8 * q^66 + 18 * q^67 + 24 * q^68 + 40 * q^69 + 6 * q^70 - 10 * q^72 + 28 * q^73 - 38 * q^74 - 30 * q^75 - 8 * q^76 + 26 * q^77 + 30 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^81 - 28 * q^82 + 14 * q^83 + 28 * q^85 - 22 * q^86 - 10 * q^87 - 20 * q^88 + 2 * q^89 + 42 * q^90 + 38 * q^91 - 18 * q^92 + 18 * q^93 + 16 * q^94 - 56 * q^95 - 6 * q^96 - 44 * q^97 + 22 * q^98 - 28 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/370\mathbb{Z}\right)^\times$.

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$	−0.658815	−	0.176529i	−0.380367	−	0.101919i	0.0635690	−	0.997977i	$-0.479752\pi$
$3$	−0.658815	−	0.176529i	−0.380367	−	0.101919i	−0.443936	+	0.896058i	$0.646418\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.32150	+	1.80379i	−0.590992	+	0.806677i
$5$	−1.32150	+	1.80379i	−0.590992	+	0.806677i
$6$	−0.482286	−	0.482286i	−0.196893	−	0.196893i
$7$	−4.10264	−	1.09930i	−1.55065	−	0.415496i	−0.620962	−	0.783841i	$-0.713258\pi$
$7$	−4.10264	−	1.09930i	−1.55065	−	0.415496i	−0.929689	+	0.368345i	$0.879924\pi$
$8$			1.00000i			0.353553i
$9$	−2.19520	−	1.26740i	−0.731734	−	0.422467i
$10$	−2.04634	+	0.901374i	−0.647111	+	0.285040i
$11$			2.14497i			0.646733i	0.946274	+	0.323366i	$0.104815\pi$
$11$			2.14497i			0.646733i	−0.946274	+	0.323366i	$0.895185\pi$
$12$	−0.176529	−	0.658815i	−0.0509596	−	0.190184i
$13$	−4.46146	+	2.57582i	−1.23739	+	0.714405i	−0.968559	−	0.248784i	$-0.919969\pi$
$13$	−4.46146	+	2.57582i	−1.23739	+	0.714405i	−0.268826	+	0.963189i	$0.586636\pi$
$14$	−3.00334	−	3.00334i	−0.802676	−	0.802676i
$15$	1.18904	−	0.955079i	0.307010	−	0.246600i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.60783	−	2.78485i	0.389957	−	0.675425i	−0.602486	−	0.798129i	$-0.705823\pi$
$17$	1.60783	−	2.78485i	0.389957	−	0.675425i	0.992443	+	0.122704i	$0.0391565\pi$
$18$	−1.26740	−	2.19520i	−0.298729	−	0.517414i
$19$	6.69996	+	1.79525i	1.53708	+	0.411858i	0.925320	−	0.379188i	$-0.123796\pi$
$19$	6.69996	+	1.79525i	1.53708	+	0.411858i	0.611757	+	0.791046i	$0.290463\pi$
$20$	−2.22287	−	0.242559i	−0.497050	−	0.0542378i
$21$	2.50882	+	1.44847i	0.547470	+	0.316082i
$22$	−1.07248	+	1.85760i	−0.228655	+	0.396041i
$23$			2.23008i			0.465004i	0.972596	+	0.232502i	$0.0746911\pi$
$23$			2.23008i			0.465004i	−0.972596	+	0.232502i	$0.925309\pi$
$24$	0.176529	−	0.658815i	0.0360338	−	0.134480i
$25$	−1.50728	−	4.76740i	−0.301456	−	0.953480i
$26$	−5.15165			−1.01032
$27$	2.66936	+	2.66936i	0.513718	+	0.513718i
$28$	−1.09930	−	4.10264i	−0.207748	−	0.775325i
$29$	−0.485118	−	0.485118i	−0.0900841	−	0.0900841i	0.660629	−	0.750713i	$-0.270290\pi$
$29$	−0.485118	−	0.485118i	−0.0900841	−	0.0900841i	−0.750713	+	0.660629i	$0.770290\pi$
$30$	1.50728	−	0.232600i	0.275191	−	0.0424668i
$31$	−5.21767	+	5.21767i	−0.937122	+	0.937122i	−0.998137	−	0.0610148i	$-0.980566\pi$
$31$	−5.21767	+	5.21767i	−0.937122	+	0.937122i	0.0610148	+	0.998137i	$0.480566\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$	0.378650	−	1.41314i	0.0659144	−	0.245996i
$34$	2.78485	−	1.60783i	0.477598	−	0.275741i
$35$	7.40453	−	5.94755i	1.25159	−	1.00532i
$36$		−	2.53480i		−	0.422467i
$37$	−5.38642	−	2.82604i	−0.885522	−	0.464598i
$37$	−5.38642	−	2.82604i	−0.885522	−	0.464598i
$38$	4.90471	+	4.90471i	0.795649	+	0.795649i
$39$	3.39398	−	0.909415i	0.543472	−	0.145623i
$40$	−1.80379	−	1.32150i	−0.285203	−	0.208947i
$41$	0.247679	−	0.142998i	0.0386810	−	0.0223325i	−0.480535	−	0.876976i	$-0.659557\pi$
$41$	0.247679	−	0.142998i	0.0386810	−	0.0223325i	0.519216	+	0.854643i	$0.326224\pi$
$42$	1.44847	+	2.50882i	0.223504	+	0.387120i
$43$			12.4261i			1.89496i	0.319822	+	0.947478i	$0.396377\pi$
$43$			12.4261i			1.89496i	−0.319822	+	0.947478i	$0.603623\pi$
$44$	−1.85760	+	1.07248i	−0.280043	+	0.161683i
$45$	5.18707	−	2.28480i	0.773243	−	0.340598i
$46$	−1.11504	+	1.93130i	−0.164404	+	0.284755i
$47$	2.42838	−	2.42838i	0.354215	−	0.354215i	−0.507460	−	0.861675i	$-0.669416\pi$
$47$	2.42838	−	2.42838i	0.354215	−	0.354215i	0.861675	+	0.507460i	$0.169416\pi$
$48$	0.482286	−	0.482286i	0.0696120	−	0.0696120i
$49$	9.56099	+	5.52004i	1.36586	+	0.788577i
$50$	1.07836	−	4.88233i	0.152502	−	0.690466i
$51$	−1.55087	+	1.55087i	−0.217166	+	0.217166i
$52$	−4.46146	−	2.57582i	−0.618693	−	0.357202i
$53$	−7.23790	+	1.93939i	−0.994202	+	0.266396i	−0.719014	−	0.694995i	$-0.755407\pi$
$53$	−7.23790	+	1.93939i	−0.994202	+	0.266396i	−0.275187	+	0.961391i	$0.588740\pi$
$54$	0.977053	+	3.64641i	0.132960	+	0.496214i
$55$	−3.86906	−	2.83457i	−0.521705	−	0.382214i
$56$	1.09930	−	4.10264i	0.146900	−	0.548238i
$57$	−4.09712	−	2.36548i	−0.542677	−	0.313315i
$58$	−0.177565	−	0.662683i	−0.0233155	−	0.0870146i
$59$	1.59354	+	5.94716i	0.207461	+	0.774254i	0.988685	+	0.150004i	$0.0479287\pi$
$59$	1.59354	+	5.94716i	0.207461	+	0.774254i	−0.781225	+	0.624250i	$0.785405\pi$
$60$	1.42164	+	0.552203i	0.183534	+	0.0712891i
$61$	6.45558	+	1.72977i	0.826553	+	0.221474i	0.647209	−	0.762312i	$-0.275936\pi$
$61$	6.45558	+	1.72977i	0.826553	+	0.221474i	0.179344	+	0.983786i	$0.442603\pi$
$62$	−7.12748	+	1.90980i	−0.905190	+	0.242545i
$63$	7.61286	+	7.61286i	0.959130	+	0.959130i
$64$	−1.00000			−0.125000
$65$	1.24958	−	11.4515i	0.154991	−	1.42038i
$66$	1.03449	−	1.03449i	0.127337	−	0.127337i
$67$	0.635595	−	2.37207i	0.0776503	−	0.289795i	−0.916171	−	0.400788i	$-0.868736\pi$
$67$	0.635595	−	2.37207i	0.0776503	−	0.289795i	0.993821	+	0.110993i	$0.0354031\pi$
$68$	3.21567			0.389957
$69$	0.393674	−	1.46921i	0.0473927	−	0.176872i
$70$	9.38628	−	1.44847i	1.12188	−	0.173125i
$71$	−6.41760	−	11.1156i	−0.761629	−	1.31918i	−0.942010	−	0.335584i	$-0.891066\pi$
$71$	−6.41760	−	11.1156i	−0.761629	−	1.31918i	0.180381	−	0.983597i	$-0.442267\pi$
$72$	1.26740	−	2.19520i	0.149365	−	0.258707i
$73$	9.49086	−	9.49086i	1.11082	−	1.11082i	0.117781	−	0.993040i	$-0.462422\pi$
$73$	9.49086	−	9.49086i	1.11082	−	1.11082i	0.993040	−	0.117781i	$-0.0375781\pi$
$74$	−3.25176	−	5.14063i	−0.378009	−	0.597586i
$75$	0.151436	+	3.40692i	0.0174863	+	0.393397i
$76$	1.79525	+	6.69996i	0.205929	+	0.768538i
$77$	2.35796	−	8.80003i	0.268715	−	1.00286i
$78$	3.39398	+	0.909415i	0.384293	+	0.102971i
$79$	−0.585692	−	0.156936i	−0.0658955	−	0.0176566i	0.225721	−	0.974192i	$-0.427526\pi$
$79$	−0.585692	−	0.156936i	−0.0658955	−	0.0176566i	−0.291616	+	0.956535i	$0.594193\pi$
$80$	−0.901374	−	2.04634i	−0.100777	−	0.228788i
$81$	2.51480	+	4.35577i	0.279423	+	0.483974i
$82$	0.285995			0.0315829
$83$	3.55006	−	0.951235i	0.389669	−	0.104412i	−0.0586645	−	0.998278i	$-0.518684\pi$
$83$	3.55006	−	0.951235i	0.389669	−	0.104412i	0.448334	+	0.893866i	$0.352018\pi$
$84$			2.89694i			0.316082i
$85$	2.89852	+	6.58036i	0.314389	+	0.713741i
$86$	−6.21303	+	10.7613i	−0.669968	+	1.16042i
$87$	0.233966	+	0.405241i	0.0250838	+	0.0434463i
$88$	−2.14497			−0.228655
$89$	−5.82591	+	1.56105i	−0.617546	+	0.165471i	−0.554012	−	0.832509i	$-0.686904\pi$
$89$	−5.82591	+	1.56105i	−0.617546	+	0.165471i	−0.0635339	+	0.997980i	$0.520237\pi$
$90$	5.63454	+	0.614838i	0.593932	+	0.0648096i
$91$	21.1353	−	5.66319i	2.21558	−	0.593664i
$92$	−1.93130	+	1.11504i	−0.201352	+	0.116251i
$93$	4.35856	−	2.51641i	0.451961	−	0.260940i
$94$	3.31722	−	0.888848i	0.342146	−	0.0916776i
$95$	−12.0922	+	9.71287i	−1.24064	+	0.996520i
$96$	0.658815	−	0.176529i	0.0672401	−	0.0180169i
$97$	−14.2602			−1.44791			−0.723954	−	0.689848i	$-0.757677\pi$
$97$	−14.2602			−1.44791			−0.723954	+	0.689848i	$0.757677\pi$
$98$	5.52004	+	9.56099i	0.557608	+	0.965805i
$99$	2.71853	−	4.70864i	0.273223	−	0.473236i
$100$	3.37505	−	3.68904i	0.337505	−	0.368904i
$101$			0.276126i			0.0274755i	0.999906	+	0.0137378i	$0.00437300\pi$
$101$			0.276126i			0.0274755i	−0.999906	+	0.0137378i	$0.995627\pi$
$102$	−2.11853	+	0.567659i	−0.209766	+	0.0562066i
$103$	3.59072			0.353804			0.176902	−	0.984228i	$-0.443392\pi$
$103$	3.59072			0.353804			0.176902	+	0.984228i	$0.443392\pi$
$104$	−2.57582	−	4.46146i	−0.252580	−	0.437482i
$105$	−5.92813	+	2.61123i	−0.578526	+	0.254830i
$106$	−7.23790	−	1.93939i	−0.703007	−	0.188370i
$107$	−15.4330	−	4.13526i	−1.49197	−	0.399771i	−0.581565	−	0.813500i	$-0.697560\pi$
$107$	−15.4330	−	4.13526i	−1.49197	−	0.399771i	−0.910400	+	0.413729i	$0.864226\pi$
$108$	−0.977053	+	3.64641i	−0.0940170	+	0.350876i
$109$	2.04066	+	7.61584i	0.195460	+	0.729465i	0.992147	+	0.125074i	$0.0399169\pi$
$109$	2.04066	+	7.61584i	0.195460	+	0.729465i	−0.796688	+	0.604391i	$0.793416\pi$
$110$	−1.93342	−	4.38935i	−0.184344	−	0.418508i
$111$	3.04978	+	2.81270i	0.289472	+	0.266969i
$112$	3.00334	−	3.00334i	0.283789	−	0.283789i
$113$	−0.347841	+	0.602478i	−0.0327221	+	0.0566763i	−0.881923	−	0.471394i	$-0.843751\pi$
$113$	−0.347841	+	0.602478i	−0.0327221	+	0.0566763i	0.849201	+	0.528070i	$0.177084\pi$
$114$	−2.36548	−	4.09712i	−0.221547	−	0.383731i
$115$	−4.02258	−	2.94705i	−0.375108	−	0.274813i
$116$	0.177565	−	0.662683i	0.0164865	−	0.0615286i
$117$	13.0584			1.20725
$118$	−1.59354	+	5.94716i	−0.146697	+	0.547480i
$119$	−9.65774	+	9.65774i	−0.885323	+	0.885323i
$120$	0.955079	+	1.18904i	0.0871864	+	0.108544i
$121$	6.39911			0.581737
$122$	4.72582	+	4.72582i	0.427855	+	0.427855i
$123$	−0.188418	+	0.0504864i	−0.0169891	+	0.00455221i
$124$	−7.12748	−	1.90980i	−0.640066	−	0.171505i
$125$	10.5912	+	3.58130i	0.947309	+	0.320321i
$126$	2.78650	+	10.3994i	0.248241	+	0.926449i
$127$	1.97047	+	7.35388i	0.174851	+	0.652552i	0.996577	+	0.0826694i	$0.0263446\pi$
$127$	1.97047	+	7.35388i	0.174851	+	0.652552i	−0.821726	+	0.569882i	$0.806989\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$	2.19356	−	8.18648i	0.193132	−	0.720779i
$130$	6.80789	−	9.29246i	0.597092	−	0.815003i
$131$	4.05890	+	15.1480i	0.354628	+	1.32349i	0.880952	+	0.473205i	$0.156903\pi$
$131$	4.05890	+	15.1480i	0.354628	+	1.32349i	−0.526324	+	0.850284i	$0.676430\pi$
$132$	1.41314	−	0.378650i	0.122998	−	0.0329572i
$133$	−25.5140	−	14.7305i	−2.21234	−	1.27730i
$134$	1.73648	−	1.73648i	0.150009	−	0.150009i
$135$	−8.34250	+	1.28740i	−0.718008	+	0.110801i
$136$	2.78485	+	1.60783i	0.238799	+	0.137871i
$137$	−13.4346	+	13.4346i	−1.14779	+	1.14779i	−0.160807	+	0.986986i	$0.551410\pi$
$137$	−13.4346	+	13.4346i	−1.14779	+	1.14779i	−0.986986	+	0.160807i	$0.948590\pi$
$138$	1.07554	−	1.07554i	0.0915558	−	0.0915558i
$139$	−0.119885	+	0.207646i	−0.0101685	+	0.0176123i	−0.871065	−	0.491168i	$-0.836570\pi$
$139$	−0.119885	+	0.207646i	−0.0101685	+	0.0176123i	0.860896	+	0.508780i	$0.169903\pi$
$140$	8.85299	+	3.43873i	0.748215	+	0.290626i
$141$	−2.02853	+	1.17117i	−0.170833	+	0.0986306i
$142$		−	12.8352i		−	1.07711i
$143$	−5.52506	−	9.56969i	−0.462029	−	0.800257i
$144$	2.19520	−	1.26740i	0.182933	−	0.105617i
$145$	1.51613	−	0.233966i	0.125908	−	0.0194298i
$146$	12.9648	−	3.47389i	1.07297	−	0.287502i
$147$	−5.32448	−	5.32448i	−0.439156	−	0.439156i
$148$	−0.245788	−	6.07779i	−0.0202036	−	0.499592i
$149$		−	6.48140i		−	0.530977i	−0.964114	−	0.265488i	$-0.914467\pi$
$149$		−	6.48140i		−	0.530977i	0.964114	−	0.265488i	$-0.0855332\pi$
$150$	−1.57231	+	3.02619i	−0.128379	+	0.247088i
$151$	−9.69607	+	5.59803i	−0.789055	+	0.455561i	−0.839630	−	0.543159i	$-0.817228\pi$
$151$	−9.69607	+	5.59803i	−0.789055	+	0.455561i	0.0505748	+	0.998720i	$0.483895\pi$
$152$	−1.79525	+	6.69996i	−0.145614	+	0.543439i
$153$	−7.05904	+	4.07554i	−0.570689	+	0.329488i
$154$	6.44207	−	6.44207i	0.519117	−	0.519117i
$155$	−2.51641	−	16.3067i	−0.202123	−	1.30979i
$156$	2.48457	+	2.48457i	0.198925	+	0.198925i
$157$	3.76715	+	14.0592i	0.300651	+	1.12205i	0.936624	+	0.350335i	$0.113932\pi$
$157$	3.76715	+	14.0592i	0.300651	+	1.12205i	−0.635973	+	0.771711i	$0.719401\pi$
$158$	−0.428756	−	0.428756i	−0.0341100	−	0.0341100i
$159$	5.11080			0.405313
$160$	0.242559	−	2.22287i	0.0191760	−	0.175734i
$161$	2.45152	−	9.14920i	0.193207	−	0.721058i
$162$			5.02961i			0.395163i
$163$	−5.81158	+	10.0660i	−0.455198	+	0.788426i	−0.998700	−	0.0509818i	$-0.983765\pi$
$163$	−5.81158	+	10.0660i	−0.455198	+	0.788426i	0.543501	+	0.839408i	$0.317098\pi$
$164$	0.247679	+	0.142998i	0.0193405	+	0.0111662i
$165$	2.04861	+	2.55046i	0.159484	+	0.198553i
$166$	3.55006	+	0.951235i	0.275538	+	0.0738302i
$167$	−0.711584	−	1.23250i	−0.0550640	−	0.0953737i	0.837179	−	0.546928i	$-0.184203\pi$
$167$	−0.711584	−	1.23250i	−0.0550640	−	0.0953737i	−0.892244	+	0.451555i	$0.850870\pi$
$168$	−1.44847	+	2.50882i	−0.111752	+	0.193560i
$169$	6.76972	−	11.7255i	0.520748	−	0.901962i
$170$	−0.779989	+	7.14802i	−0.0598224	+	0.548228i
$171$	−12.4325	−	12.4325i	−0.950734	−	0.950734i
$172$	−10.7613	+	6.21303i	−0.820540	+	0.473739i
$173$	−4.51757	−	16.8598i	−0.343465	−	1.28183i	−0.894396	−	0.447277i	$-0.852394\pi$
$173$	−4.51757	−	16.8598i	−0.343465	−	1.28183i	0.550931	−	0.834551i	$-0.314273\pi$
$174$			0.467931i			0.0354738i
$175$	0.943036	+	21.2159i	0.0712868	+	1.60377i
$176$	−1.85760	−	1.07248i	−0.140022	−	0.0808416i
$177$		−	4.19939i		−	0.315645i
$178$	−5.82591	−	1.56105i	−0.436671	−	0.117006i
$179$	−2.52136	−	2.52136i	−0.188455	−	0.188455i	0.606573	−	0.795028i	$-0.292544\pi$
$179$	−2.52136	−	2.52136i	−0.188455	−	0.188455i	−0.795028	+	0.606573i	$0.792544\pi$
$180$	4.57223	+	3.34973i	0.340794	+	0.249674i
$181$	−12.1826	−	21.1009i	−0.905525	−	1.56841i	−0.820211	−	0.572061i	$-0.806144\pi$
$181$	−12.1826	−	21.1009i	−0.905525	−	1.56841i	−0.0853132	−	0.996354i	$-0.527189\pi$
$182$	21.1353	+	5.66319i	1.56665	+	0.419784i
$183$	−3.94768	−	2.27920i	−0.291821	−	0.168483i
$184$	−2.23008			−0.164404
$185$	12.2157	−	5.98134i	0.898117	−	0.439756i
$186$	5.03283			0.369025
$187$	5.97342	+	3.44875i	0.436820	+	0.252198i
$188$	3.31722	+	0.888848i	0.241933	+	0.0648259i
$189$	−8.01699	−	13.8858i	−0.583150	−	1.01005i
$190$	−15.3286	+	2.36548i	−1.11205	+	0.171610i
$191$	1.45174	+	1.45174i	0.105044	+	0.105044i	0.757676	−	0.652631i	$-0.226335\pi$
$191$	1.45174	+	1.45174i	0.105044	+	0.105044i	−0.652631	+	0.757676i	$0.726335\pi$
$192$	0.658815	+	0.176529i	0.0475459	+	0.0127399i
$193$			5.87874i			0.423161i	0.977361	+	0.211580i	$0.0678610\pi$
$193$			5.87874i			0.423161i	−0.977361	+	0.211580i	$0.932139\pi$
$194$	−12.3497	−	7.13012i	−0.886659	−	0.511913i
$195$	−2.84476	+	7.32381i	−0.203717	+	0.524469i
$196$			11.0401i			0.788577i
$197$	−6.45581	−	24.0934i	−0.459957	−	1.71658i	−0.673090	−	0.739561i	$-0.735033\pi$
$197$	−6.45581	−	24.0934i	−0.459957	−	1.71658i	0.213133	−	0.977023i	$-0.431633\pi$
$198$	4.70864	−	2.71853i	0.334628	−	0.193198i
$199$	17.8265	+	17.8265i	1.26369	+	1.26369i	0.949293	+	0.314393i	$0.101801\pi$
$199$	17.8265	+	17.8265i	1.26369	+	1.26369i	0.314393	+	0.949293i	$0.398199\pi$
$200$	4.76740	−	1.50728i	0.337106	−	0.106581i
$201$	−0.837480	+	1.45056i	−0.0590713	+	0.102314i
$202$	−0.138063	+	0.239132i	−0.00971406	+	0.0168252i
$203$	1.45697	+	2.52355i	0.102259	+	0.177119i
$204$	−2.11853	−	0.567659i	−0.148327	−	0.0397441i
$205$	−0.0693707	+	0.635731i	−0.00484506	+	0.0444014i
$206$	3.10965	+	1.79536i	0.216660	+	0.125089i
$207$	2.82640	−	4.89547i	0.196448	−	0.340259i
$208$		−	5.15165i		−	0.357202i
$209$	−3.85076	+	14.3712i	−0.266362	+	0.994078i
$210$	−6.43953	−	0.702678i	−0.444369	−	0.0484894i
$211$	6.03261			0.415302			0.207651	−	0.978203i	$-0.433418\pi$
$211$	6.03261			0.415302			0.207651	+	0.978203i	$0.433418\pi$
$212$	−5.29851	−	5.29851i	−0.363903	−	0.363903i
$213$	2.26579	+	8.45603i	0.155249	+	0.579398i
$214$	−11.2978	−	11.2978i	−0.772298	−	0.772298i
$215$	−22.4139	−	16.4210i	−1.52862	−	1.11990i
$216$	−2.66936	+	2.66936i	−0.181627	+	0.181627i
$217$	27.1420	−	15.6704i	1.84252	−	1.06378i
$218$	−2.04066	+	7.61584i	−0.138211	+	0.515810i
$219$	−7.92813	+	4.57731i	−0.535734	+	0.309306i
$220$	0.520282	−	4.76800i	0.0350774	−	0.321458i
$221$			16.5660i			1.11435i
$222$	1.23484	+	3.96076i	0.0828768	+	0.265829i
$223$	5.22436	+	5.22436i	0.349849	+	0.349849i	0.860053	−	0.510204i	$-0.170430\pi$
$223$	5.22436	+	5.22436i	0.349849	+	0.349849i	−0.510204	+	0.860053i	$0.670430\pi$
$224$	4.10264	−	1.09930i	0.274119	−	0.0734499i
$225$	−2.73341	+	12.3757i	−0.182228	+	0.825049i
$226$	−0.602478	+	0.347841i	−0.0400762	+	0.0231380i
$227$	4.56757	+	7.91126i	0.303160	+	0.525089i	0.976850	−	0.213925i	$-0.0686249\pi$
$227$	4.56757	+	7.91126i	0.303160	+	0.525089i	−0.673690	+	0.739014i	$0.735292\pi$
$228$		−	4.73095i		−	0.313315i
$229$	−3.08729	+	1.78245i	−0.204014	+	0.117787i	−0.598526	−	0.801103i	$-0.704247\pi$
$229$	−3.08729	+	1.78245i	−0.204014	+	0.117787i	0.394512	+	0.918891i	$0.370913\pi$
$230$	−2.01014	−	4.56351i	−0.132544	−	0.300909i
$231$	−3.10692	+	5.38135i	−0.204420	+	0.354067i
$232$	0.485118	−	0.485118i	0.0318495	−	0.0318495i
$233$	−12.9851	+	12.9851i	−0.850683	+	0.850683i	−0.990217	−	0.139534i	$-0.955440\pi$
$233$	−12.9851	+	12.9851i	−0.850683	+	0.850683i	0.139534	+	0.990217i	$0.455440\pi$
$234$	11.3089	+	6.52919i	0.739286	+	0.426827i
$235$	1.17117	+	7.58937i	0.0763989	+	0.495076i
$236$	−4.35362	+	4.35362i	−0.283397	+	0.283397i
$237$	0.358159	+	0.206783i	0.0232649	+	0.0134320i
$238$	−13.1927	+	3.53498i	−0.855157	+	0.229139i
$239$	−3.67854	−	13.7285i	−0.237945	−	0.888022i	−0.976799	−	0.214157i	$-0.931300\pi$
$239$	−3.67854	−	13.7285i	−0.237945	−	0.888022i	0.738855	−	0.673865i	$-0.235367\pi$
$240$	0.232600	+	1.50728i	0.0150143	+	0.0972946i
$241$	1.66171	−	6.20157i	0.107040	−	0.399478i	−0.891529	−	0.452964i	$-0.850367\pi$
$241$	1.66171	−	6.20157i	0.107040	−	0.399478i	0.998569	+	0.0534859i	$0.0170332\pi$
$242$	5.54179	+	3.19955i	0.356240	+	0.205675i
$243$	−3.81903	−	14.2528i	−0.244991	−	0.914319i
$244$	1.72977	+	6.45558i	0.110737	+	0.413276i
$245$	−22.5918	+	9.95124i	−1.44334	+	0.635761i
$246$	−0.188418	−	0.0504864i	−0.0120131	−	0.00321890i
$247$	−34.5158	+	9.24849i	−2.19619	+	0.588467i
$248$	−5.21767	−	5.21767i	−0.331323	−	0.331323i
$249$	−2.50675			−0.158859
$250$	7.38163	+	8.39712i	0.466855	+	0.531080i
$251$	14.5938	−	14.5938i	0.921154	−	0.921154i	−0.0759571	−	0.997111i	$-0.524201\pi$
$251$	14.5938	−	14.5938i	0.921154	−	0.921154i	0.997111	+	0.0759571i	$0.0242012\pi$
$252$	−2.78650	+	10.3994i	−0.175533	+	0.655098i
$253$	−4.78345			−0.300733
$254$	−1.97047	+	7.35388i	−0.123638	+	0.461424i
$255$	−0.747965	−	4.84692i	−0.0468394	−	0.303526i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.151158	−	0.261814i	0.00942900	−	0.0163315i	−0.861272	−	0.508144i	$-0.830332\pi$
$257$	0.151158	−	0.261814i	0.00942900	−	0.0163315i	0.870701	+	0.491812i	$0.163665\pi$
$258$	5.99292	−	5.99292i	0.373103	−	0.373103i
$259$	18.9919	+	17.5155i	1.18010	+	1.08836i
$260$	10.5420	−	4.64356i	0.653789	−	0.287981i
$261$	0.450093	+	1.67977i	0.0278600	+	0.103975i
$262$	−4.05890	+	15.1480i	−0.250760	+	0.935848i
$263$	28.7392	+	7.70063i	1.77213	+	0.474841i	0.989113	−	0.147156i	$-0.0470120\pi$
$263$	28.7392	+	7.70063i	1.77213	+	0.474841i	0.783019	+	0.621998i	$0.213679\pi$
$264$	1.41314	+	0.378650i	0.0869727	+	0.0233043i
$265$	6.06663	−	15.6185i	0.372670	−	0.959438i
$266$	−14.7305	−	25.5140i	−0.903185	−	1.56436i
$267$	4.11377			0.251759
$268$	2.37207	−	0.635595i	0.144898	−	0.0388252i
$269$		−	2.24109i		−	0.136642i	−0.997663	−	0.0683209i	$-0.978236\pi$
$269$		−	2.24109i		−	0.136642i	0.997663	−	0.0683209i	$-0.0217642\pi$
$270$	−7.86852	−	3.05633i	−0.478863	−	0.186003i
$271$	−3.83082	+	6.63517i	−0.232706	+	0.403058i	−0.958603	−	0.284745i	$-0.908091\pi$
$271$	−3.83082	+	6.63517i	−0.232706	+	0.403058i	0.725898	+	0.687803i	$0.241425\pi$
$272$	1.60783	+	2.78485i	0.0974892	+	0.168856i
$273$	−14.9240			−0.903241
$274$	−18.3520	+	4.91739i	−1.10868	+	0.297071i
$275$	10.2259	−	3.23307i	0.616647	−	0.194962i
$276$	1.46921	−	0.393674i	0.0884361	−	0.0236964i
$277$	6.57774	−	3.79766i	0.395218	−	0.228179i	−0.289201	−	0.957269i	$-0.593389\pi$
$277$	6.57774	−	3.79766i	0.395218	−	0.228179i	0.684419	+	0.729089i	$0.260056\pi$
$278$	−0.207646	+	0.119885i	−0.0124538	+	0.00719020i
$279$	18.0667	−	4.84096i	1.08163	−	0.289821i
$280$	5.94755	+	7.40453i	0.355434	+	0.442505i
$281$	−29.7397	+	7.96873i	−1.77412	+	0.475374i	−0.989492	−	0.144590i	$-0.953814\pi$
$281$	−29.7397	+	7.96873i	−1.77412	+	0.475374i	−0.784630	+	0.619964i	$0.787147\pi$
$282$	−2.34235			−0.139485
$283$	−0.455722	−	0.789334i	−0.0270899	−	0.0469210i	0.852163	−	0.523277i	$-0.175291\pi$
$283$	−0.455722	−	0.789334i	−0.0270899	−	0.0469210i	−0.879253	+	0.476356i	$0.841957\pi$
$284$	6.41760	−	11.1156i	0.380815	−	0.659590i
$285$	9.68116	−	4.26436i	0.573462	−	0.252599i
$286$		−	11.0501i		−	0.653407i
$287$	−1.17333	+	0.314394i	−0.0692597	+	0.0185581i
$288$	2.53480			0.149365
$289$	3.32974	+	5.76728i	0.195867	+	0.339252i
$290$	1.42999	+	0.555445i	0.0839720	+	0.0326169i
$291$	9.39487	+	2.51735i	0.550737	+	0.147570i
$292$	12.9648	+	3.47389i	0.758705	+	0.203294i
$293$	−5.14775	+	19.2117i	−0.300735	+	1.12236i	0.635820	+	0.771837i	$0.280662\pi$
$293$	−5.14775	+	19.2117i	−0.300735	+	1.12236i	−0.936555	+	0.350520i	$0.886005\pi$
$294$	−1.94889	−	7.27337i	−0.113662	−	0.424192i
$295$	−12.8333	−	4.98476i	−0.747181	−	0.290224i
$296$	2.82604	−	5.38642i	0.164260	−	0.313079i
$297$	−5.72569	+	5.72569i	−0.332238	+	0.332238i
$298$	3.24070	−	5.61305i	0.187729	−	0.325155i
$299$	−5.74429	−	9.94940i	−0.332201	−	0.575388i
$300$	−2.87476	+	1.83461i	−0.165974	+	0.105921i
$301$	13.6599	−	50.9796i	0.787345	−	2.93841i
$302$	−11.1961			−0.644261
$303$	0.0487442	−	0.181916i	0.00280028	−	0.0104508i
$304$	−4.90471	+	4.90471i	−0.281305	+	0.281305i
$305$	−11.6512	+	9.35860i	−0.667145	+	0.535872i
$306$	−8.15107			−0.465966
$307$	9.95227	+	9.95227i	0.568006	+	0.568006i	0.931570	−	0.363563i	$-0.118440\pi$
$307$	9.95227	+	9.95227i	0.568006	+	0.568006i	−0.363563	+	0.931570i	$0.618440\pi$
$308$	8.80003	−	2.35796i	0.501428	−	0.134357i
$309$	−2.36562	−	0.633866i	−0.134575	−	0.0360594i
$310$	5.97408	−	15.3802i	0.339305	−	0.873539i
$311$	6.10141	+	22.7708i	0.345979	+	1.29121i	0.891464	+	0.453092i	$0.149679\pi$
$311$	6.10141	+	22.7708i	0.345979	+	1.29121i	−0.545484	+	0.838121i	$0.683654\pi$
$312$	0.909415	+	3.39398i	0.0514855	+	0.192146i
$313$	10.8376	+	6.25706i	0.612575	+	0.353670i	0.773972	−	0.633219i	$-0.218267\pi$
$313$	10.8376	+	6.25706i	0.612575	+	0.353670i	−0.161398	+	0.986889i	$0.551600\pi$
$314$	−3.76715	+	14.0592i	−0.212593	+	0.793407i
$315$	−23.7923	+	3.67158i	−1.34055	+	0.206870i
$316$	−0.156936	−	0.585692i	−0.00882832	−	0.0329477i
$317$	15.1469	−	4.05859i	0.850734	−	0.227953i	0.192995	−	0.981200i	$-0.438180\pi$
$317$	15.1469	−	4.05859i	0.850734	−	0.227953i	0.657739	+	0.753246i	$0.271513\pi$
$318$	4.42608	+	2.55540i	0.248202	+	0.143300i
$319$	1.04056	−	1.04056i	0.0582603	−	0.0582603i
$320$	1.32150	−	1.80379i	0.0738740	−	0.100835i
$321$	9.43751	+	5.44875i	0.526751	+	0.304120i
$322$	6.69768	−	6.69768i	0.373247	−	0.373247i
$323$	15.7719	−	15.7719i	0.877573	−	0.877573i
$324$	−2.51480	+	4.35577i	−0.139711	+	0.241987i
$325$	19.0046	+	17.3871i	1.05419	+	0.964460i
$326$	−10.0660	+	5.81158i	−0.557502	+	0.321874i
$327$		−	5.37767i		−	0.297386i
$328$	0.142998	+	0.247679i	0.00789572	+	0.0136758i
$329$	−12.6323	+	7.29324i	−0.696439	+	0.402089i
$330$	0.498920	+	3.23307i	0.0274647	+	0.177975i
$331$	−1.35226	+	0.362336i	−0.0743268	+	0.0199158i	−0.295791	−	0.955253i	$-0.595583\pi$
$331$	−1.35226	+	0.362336i	−0.0743268	+	0.0199158i	0.221464	+	0.975169i	$0.428916\pi$
$332$	2.59882	+	2.59882i	0.142629	+	0.142629i
$333$	8.24255	+	13.0305i	0.451689	+	0.714065i
$334$		−	1.42317i		−	0.0778723i
$335$	3.43877	+	4.28117i	0.187880	+	0.233905i
$336$	−2.50882	+	1.44847i	−0.136867	+	0.0790205i
$337$	−1.79593	+	6.70249i	−0.0978303	+	0.365108i	−0.997433	−	0.0716008i	$-0.977189\pi$
$337$	−1.79593	+	6.70249i	−0.0978303	+	0.365108i	0.899603	+	0.436709i	$0.143856\pi$
$338$	11.7255	−	6.76972i	0.637783	−	0.368224i
$339$	0.335518	−	0.335518i	0.0182228	−	0.0182228i
$340$	−4.24950	+	5.80037i	−0.230462	+	0.314569i
$341$	−11.1918	−	11.1918i	−0.606067	−	0.606067i
$342$	−4.55060	−	16.9831i	−0.246068	−	0.918339i
$343$	−12.1337	−	12.1337i	−0.655159	−	0.655159i
$344$	−12.4261			−0.669968
$345$	2.12990	+	2.65166i	0.114670	+	0.142761i
$346$	4.51757	−	16.8598i	0.242866	−	0.906389i
$347$		−	10.3061i		−	0.553259i	−0.960977	−	0.276629i	$-0.910783\pi$
$347$		−	10.3061i		−	0.553259i	0.960977	−	0.276629i	$-0.0892174\pi$
$348$	−0.233966	+	0.405241i	−0.0125419	+	0.0217232i
$349$	−7.88832	−	4.55432i	−0.422252	−	0.243787i	0.273788	−	0.961790i	$-0.411723\pi$
$349$	−7.88832	−	4.55432i	−0.422252	−	0.243787i	−0.696040	+	0.718003i	$0.745057\pi$
$350$	−9.79123	+	18.8450i	−0.523364	+	1.00731i
$351$	−18.7850	−	5.03343i	−1.00267	−	0.268665i
$352$	−1.07248	−	1.85760i	−0.0571636	−	0.0990103i
$353$	1.57873	−	2.73444i	0.0840274	−	0.145540i	−0.820949	−	0.571002i	$-0.806555\pi$
$353$	1.57873	−	2.73444i	0.0840274	−	0.145540i	0.904976	+	0.425462i	$0.139888\pi$
$354$	2.09969	−	3.63677i	0.111597	−	0.193292i
$355$	28.5310	+	3.11329i	1.51427	+	0.165236i
$356$	−4.26487	−	4.26487i	−0.226037	−	0.226037i
$357$	8.06754	−	4.65779i	0.426979	−	0.246517i
$358$	−0.922883	−	3.44425i	−0.0487759	−	0.182034i
$359$		−	0.295823i		−	0.0156129i	−0.999970	−	0.00780646i	$-0.997515\pi$
$359$		−	0.295823i		−	0.0156129i	0.999970	−	0.00780646i	$-0.00248490\pi$
$360$	2.28480	+	5.18707i	0.120420	+	0.273383i
$361$	25.2121	+	14.5562i	1.32695	+	0.766116i
$362$		−	24.3652i		−	1.28061i
$363$	−4.21583	−	1.12963i	−0.221274	−	0.0592901i
$364$	15.4721	+	15.4721i	0.810960	+	0.810960i
$365$	4.57731	+	29.6616i	0.239587	+	1.55256i
$366$	−2.27920	−	3.94768i	−0.119136	−	0.206349i
$367$	21.7015	+	5.81490i	1.13281	+	0.303535i	0.776056	−	0.630663i	$-0.217217\pi$
$367$	21.7015	+	5.81490i	1.13281	+	0.303535i	0.356753	+	0.934199i	$0.383884\pi$
$368$	−1.93130	−	1.11504i	−0.100676	−	0.0581254i
$369$	−0.724940			−0.0377389
$370$	13.5698	+	0.927868i	0.705460	+	0.0482376i
$371$	31.8264			1.65235
$372$	4.35856	+	2.51641i	0.225981	+	0.130470i
$373$	21.3637	+	5.72439i	1.10617	+	0.296398i	0.765275	−	0.643703i	$-0.222603\pi$
$373$	21.3637	+	5.72439i	1.10617	+	0.296398i	0.340896	+	0.940101i	$0.389270\pi$
$374$	3.44875	+	5.97342i	0.178331	+	0.308878i
$375$	−6.34547	−	4.22908i	−0.327679	−	0.218389i
$376$	2.42838	+	2.42838i	0.125234	+	0.125234i
$377$	3.41391	+	0.914754i	0.175825	+	0.0471122i
$378$		−	16.0340i		−	0.824698i
$379$	−8.58408	−	4.95602i	−0.440935	−	0.254574i	0.263059	−	0.964780i	$-0.415269\pi$
$379$	−8.58408	−	4.95602i	−0.440935	−	0.254574i	−0.703994	+	0.710206i	$0.748602\pi$
$380$	−14.4577	−	5.61575i	−0.741665	−	0.288082i
$381$		−	5.19270i		−	0.266030i
$382$	0.531374	+	1.98312i	0.0271875	+	0.101465i
$383$	27.4315	−	15.8376i	1.40168	−	0.809262i	0.407118	−	0.913376i	$-0.366534\pi$
$383$	27.4315	−	15.8376i	1.40168	−	0.809262i	0.994565	+	0.104114i	$0.0332006\pi$
$384$	0.482286	+	0.482286i	0.0246116	+	0.0246116i
$385$	12.7573	+	15.8825i	0.650173	+	0.809446i
$386$	−2.93937	+	5.09114i	−0.149610	+	0.259132i
$387$	15.7488	−	27.2777i	0.800555	−	1.38660i
$388$	−7.13012	−	12.3497i	−0.361977	−	0.626963i
$389$	32.1209	+	8.60677i	1.62859	+	0.436380i	0.953510	−	0.301360i	$-0.0974408\pi$
$389$	32.1209	+	8.60677i	1.62859	+	0.436380i	0.675084	+	0.737741i	$0.264107\pi$
$390$	−6.12553	+	4.92023i	−0.310179	+	0.249145i
$391$	6.21043	+	3.58560i	0.314075	+	0.181331i
$392$	−5.52004	+	9.56099i	−0.278804	+	0.482903i
$393$		−	10.6963i		−	0.539555i
$394$	6.45581	−	24.0934i	0.325239	−	1.21381i
$395$	1.05707	−	0.849072i	0.0531869	−	0.0427214i
$396$	5.43707			0.273223
$397$	25.5772	+	25.5772i	1.28368	+	1.28368i	0.938557	+	0.345124i	$0.112163\pi$
$397$	25.5772	+	25.5772i	1.28368	+	1.28368i	0.345124	+	0.938557i	$0.387837\pi$
$398$	6.52495	+	24.3514i	0.327066	+	1.22063i
$399$	14.2086	+	14.2086i	0.711322	+	0.711322i
$400$	4.88233	+	1.07836i	0.244117	+	0.0539178i
$401$	12.4307	−	12.4307i	0.620759	−	0.620759i	−0.324966	−	0.945726i	$-0.605353\pi$
$401$	12.4307	−	12.4307i	0.620759	−	0.620759i	0.945726	+	0.324966i	$0.105353\pi$
$402$	−1.45056	+	0.837480i	−0.0723473	+	0.0417697i
$403$	9.83862	−	36.7182i	0.490097	−	1.82907i
$404$	−0.239132	+	0.138063i	−0.0118972	+	0.00686888i
$405$	−11.1802	−	1.21998i	−0.555548	−	0.0606211i
$406$			2.91395i			0.144617i
$407$	6.06177	−	11.5537i	0.300471	−	0.572696i
$408$	−1.55087	−	1.55087i	−0.0767796	−	0.0767796i
$409$	−22.5508	+	6.04247i	−1.11507	+	0.298781i	−0.768885	−	0.639387i	$-0.779188\pi$
$409$	−22.5508	+	6.04247i	−1.11507	+	0.298781i	−0.346181	+	0.938168i	$0.612522\pi$
$410$	−0.377942	+	0.515874i	−0.0186652	+	0.0254772i
$411$	11.2225	−	6.47931i	0.553565	−	0.319601i
$412$	1.79536	+	3.10965i	0.0884509	+	0.153202i
$413$		−	26.1508i		−	1.28680i
$414$	4.89547	−	2.82640i	0.240599	−	0.138910i
$415$	−2.97557	+	7.66060i	−0.146065	+	0.376044i
$416$	2.57582	−	4.46146i	0.126290	−	0.218741i
$417$	0.115637	−	0.115637i	0.00566279	−	0.00566279i
$418$	−10.5205	+	10.5205i	−0.514572	+	0.514572i
$419$	−23.5500	−	13.5966i	−1.15049	−	0.664238i	−0.201487	−	0.979491i	$-0.564577\pi$
$419$	−23.5500	−	13.5966i	−1.15049	−	0.664238i	−0.949008	+	0.315253i	$0.897911\pi$
$420$	−5.22545	−	3.82830i	−0.254976	−	0.186802i
$421$	−7.60610	+	7.60610i	−0.370699	+	0.370699i	−0.867732	−	0.497033i	$-0.834423\pi$
$421$	−7.60610	+	7.60610i	−0.370699	+	0.370699i	0.497033	+	0.867732i	$0.334423\pi$
$422$	5.22439	+	3.01630i	0.254319	+	0.146831i
$423$	−8.40850	+	2.25305i	−0.408835	+	0.109547i
$424$	−1.93939	−	7.23790i	−0.0941850	−	0.351503i
$425$	−15.7000	−	3.46763i	−0.761560	−	0.168205i
$426$	−2.26579	+	8.45603i	−0.109778	+	0.409696i
$427$	−24.5834	−	14.1932i	−1.18967	−	0.686858i
$428$	−4.13526	−	15.4330i	−0.199886	−	0.745983i
$429$	1.95067	+	7.27999i	0.0941791	+	0.351481i
$430$	−11.2005	−	25.4280i	−0.540137	−	1.22625i
$431$	−12.1918	−	3.26679i	−0.587259	−	0.157355i	−0.0470587	−	0.998892i	$-0.514985\pi$
$431$	−12.1918	−	3.26679i	−0.587259	−	0.157355i	−0.540200	+	0.841537i	$0.681651\pi$
$432$	−3.64641	+	0.977053i	−0.175438	+	0.0470085i
$433$	11.1419	+	11.1419i	0.535445	+	0.535445i	0.922188	−	0.386743i	$-0.126400\pi$
$433$	11.1419	+	11.1419i	0.535445	+	0.535445i	−0.386743	+	0.922188i	$0.626400\pi$
$434$	31.3409			1.50441
$435$	−1.04015	−	0.113501i	−0.0498715	−	0.00544195i
$436$	−5.57518	+	5.57518i	−0.267003	+	0.267003i
$437$	−4.00355	+	14.9414i	−0.191516	+	0.714746i
$438$	−9.15462			−0.437425
$439$	−6.68433	+	24.9462i	−0.319025	+	1.19062i	0.601157	+	0.799131i	$0.294706\pi$
$439$	−6.68433	+	24.9462i	−0.319025	+	1.19062i	−0.920183	+	0.391489i	$0.871960\pi$
$440$	2.83457	−	3.86906i	0.135133	−	0.184450i
$441$	−13.9922	−	24.2352i	−0.666295	−	1.15406i
$442$	−8.28299	+	14.3466i	−0.393982	+	0.682396i
$443$	4.30555	−	4.30555i	0.204563	−	0.204563i	−0.597389	−	0.801952i	$-0.703795\pi$
$443$	4.30555	−	4.30555i	0.204563	−	0.204563i	0.801952	+	0.597389i	$0.203795\pi$
$444$	−0.910979	+	4.04753i	−0.0432331	+	0.192087i
$445$	4.88314	−	12.5716i	0.231483	−	0.595952i
$446$	1.91225	+	7.13661i	0.0905476	+	0.337928i
$447$	−1.14415	+	4.27004i	−0.0541167	+	0.201966i
$448$	4.10264	+	1.09930i	0.193831	+	0.0519369i
$449$	−5.71034	−	1.53008i	−0.269488	−	0.0722090i	0.121545	−	0.992586i	$-0.461215\pi$
$449$	−5.71034	−	1.53008i	−0.269488	−	0.0722090i	−0.391032	+	0.920377i	$0.627882\pi$
$450$	−8.55507	+	9.35099i	−0.403290	+	0.440810i
$451$	0.306725	+	0.531264i	0.0144431	+	0.0250162i
$452$	−0.695681			−0.0327221
$453$	7.37614	−	1.97643i	0.346561	−	0.0928608i
$454$			9.13514i			0.428733i
$455$	−17.7151	+	45.6075i	−0.830498	+	2.13811i
$456$	2.36548	−	4.09712i	0.110774	−	0.191865i
$457$	−14.6778	−	25.4227i	−0.686598	−	1.18922i	−0.972932	−	0.231093i	$-0.925770\pi$
$457$	−14.6778	−	25.4227i	−0.686598	−	1.18922i	0.286333	−	0.958130i	$-0.407564\pi$
$458$	−3.56490			−0.166577
$459$	11.7256	−	3.14188i	0.547306	−	0.146650i
$460$	0.540925	−	4.95718i	0.0252208	−	0.231130i
$461$	−34.1306	+	9.14527i	−1.58962	+	0.425938i	−0.941887	−	0.335929i	$-0.890950\pi$
$461$	−34.1306	+	9.14527i	−1.58962	+	0.425938i	−0.647734	+	0.761866i	$0.724283\pi$
$462$	−5.38135	+	3.10692i	−0.250363	+	0.144547i
$463$	−22.5200	+	13.0019i	−1.04659	+	0.604251i	−0.921693	−	0.387919i	$-0.873194\pi$
$463$	−22.5200	+	13.0019i	−1.04659	+	0.604251i	−0.124899	+	0.992169i	$0.539861\pi$
$464$	0.662683	−	0.177565i	0.0307643	−	0.00824327i
$465$	−1.22076	+	11.1873i	−0.0566113	+	0.518800i
$466$	−17.7380	+	4.75288i	−0.821697	+	0.220173i
$467$	25.1172			1.16229			0.581143	−	0.813802i	$-0.302606\pi$
$467$	25.1172			1.16229			0.581143	+	0.813802i	$0.302606\pi$
$468$	6.52919	+	11.3089i	0.301812	+	0.522754i
$469$	−5.21523	+	9.03305i	−0.240817	+	0.417107i
$470$	−2.78042	+	7.15817i	−0.128251	+	0.330182i
$471$		−	9.92743i		−	0.457432i
$472$	−5.94716	+	1.59354i	−0.273740	+	0.0733484i
$473$	−26.6535			−1.22553
$474$	0.206783	+	0.358159i	0.00949787	+	0.0164508i
$475$	−1.54006	−	34.6473i	−0.0706628	−	1.58973i
$476$	−13.1927	−	3.53498i	−0.604687	−	0.162025i
$477$	18.3466	+	4.91596i	0.840034	+	0.225086i
$478$	3.67854	−	13.7285i	0.168252	−	0.627926i
$479$	−7.38625	−	27.5659i	−0.337486	−	1.25952i	−0.901148	−	0.433511i	$-0.857275\pi$
$479$	−7.38625	−	27.5659i	−0.337486	−	1.25952i	0.563662	−	0.826005i	$-0.309392\pi$
$480$	−0.552203	+	1.42164i	−0.0252045	+	0.0648889i
$481$	31.3106	−	1.26621i	1.42764	−	0.0577343i
$482$	4.53987	−	4.53987i	0.206785	−	0.206785i
$483$	−3.23020	+	5.59487i	−0.146979	+	0.254575i
$484$	3.19955	+	5.54179i	0.145434	+	0.251899i
$485$	18.8449	−	25.7224i	0.855703	−	1.16799i
$486$	3.81903	−	14.2528i	0.173235	−	0.646521i
$487$	−14.0181			−0.635222			−0.317611	−	0.948221i	$-0.602881\pi$
$487$	−14.0181			−0.635222			−0.317611	+	0.948221i	$0.602881\pi$
$488$	−1.72977	+	6.45558i	−0.0783030	+	0.292231i
$489$	5.60569	−	5.60569i	0.253498	−	0.253498i
$490$	−24.5407	−	2.67787i	−1.10864	−	0.120974i
$491$	−18.9862			−0.856836			−0.428418	−	0.903581i	$-0.640929\pi$
$491$	−18.9862			−0.856836			−0.428418	+	0.903581i	$0.640929\pi$
$492$	−0.137932	−	0.137932i	−0.00621843	−	0.00621843i
$493$	−2.13097	+	0.570991i	−0.0959740	+	0.0257162i
$494$	−34.5158	−	9.24849i	−1.55294	−	0.416109i
$495$	4.90083	+	11.1261i	0.220276	+	0.500082i
$496$	−1.90980	−	7.12748i	−0.0857526	−	0.320033i
$497$	14.1097	+	52.6582i	0.632907	+	2.36204i
$498$	−2.17091	−	1.25338i	−0.0972809	−	0.0561652i
$499$	−8.46237	+	31.5820i	−0.378828	+	1.41380i	0.468843	+	0.883281i	$0.344671\pi$
$499$	−8.46237	+	31.5820i	−0.378828	+	1.41380i	−0.847671	+	0.530522i	$0.821996\pi$
$500$	2.19412	+	10.9629i	0.0981241	+	0.490277i
$501$	0.251231	+	0.937605i	0.0112242	+	0.0418891i
$502$	19.9355	−	5.34171i	0.889766	−	0.238412i
$503$	−27.2503	−	15.7329i	−1.21503	−	0.701497i	−0.251178	−	0.967941i	$-0.580818\pi$
$503$	−27.2503	−	15.7329i	−1.21503	−	0.701497i	−0.963851	+	0.266444i	$0.914151\pi$
$504$	−7.61286	+	7.61286i	−0.339104	+	0.339104i
$505$	−0.498071	−	0.364900i	−0.0221639	−	0.0162378i
$506$	−4.14259	−	2.39173i	−0.184161	−	0.106325i
$507$	−6.52989	+	6.52989i	−0.290003	+	0.290003i
$508$	−5.38342	+	5.38342i	−0.238851	+	0.238851i
$509$	8.50407	−	14.7295i	0.376936	−	0.652872i	−0.613679	−	0.789556i	$-0.710311\pi$
$509$	8.50407	−	14.7295i	0.376936	−	0.652872i	0.990615	+	0.136683i	$0.0436443\pi$
$510$	1.77570	−	4.57154i	0.0786294	−	0.202431i
$511$	−49.3708	+	28.5042i	−2.18404	+	1.26095i
$512$		−	1.00000i		−	0.0441942i
$513$	13.0924	+	22.6768i	0.578045	+	1.00120i
$514$	0.261814	−	0.151158i	0.0115481	−	0.00666731i
$515$	−4.74513	+	6.47688i	−0.209095	+	0.285405i
$516$	8.18648	−	2.19356i	0.360389	−	0.0965661i
$517$	5.20880	+	5.20880i	0.229083	+	0.229083i
$518$	7.68968	+	24.6648i	0.337865	+	1.08371i
$519$			11.9050i			0.522571i
$520$	11.4515	+	1.24958i	0.502179	+	0.0547976i
$521$	−22.7709	+	13.1468i	−0.997609	+	0.575970i	−0.907540	−	0.419966i	$-0.862042\pi$
$521$	−22.7709	+	13.1468i	−0.997609	+	0.575970i	−0.0900692	+	0.995936i	$0.528709\pi$
$522$	−0.450093	+	1.67977i	−0.0197000	+	0.0735215i
$523$	8.88721	−	5.13103i	0.388611	−	0.224364i	−0.292947	−	0.956129i	$-0.594636\pi$
$523$	8.88721	−	5.13103i	0.388611	−	0.224364i	0.681558	+	0.731764i	$0.261303\pi$
$524$	−11.0891	+	11.0891i	−0.484431	+	0.484431i
$525$	3.12393	−	14.1438i	0.136339	−	0.617286i
$526$	21.0385	+	21.0385i	0.917323	+	0.917323i
$527$	6.14129	+	22.9196i	0.267519	+	0.998393i
$528$	1.03449	+	1.03449i	0.0450204	+	0.0450204i
$529$	18.0267			0.783772
$530$	13.0631	−	10.4927i	0.567425	−	0.455774i
$531$	4.03929	−	15.0749i	0.175290	−	0.654193i
$532$		−	29.4610i		−	1.27730i
$533$	−0.736673	+	1.27595i	−0.0319088	+	0.0552677i
$534$	3.56263	+	2.05689i	0.154170	+	0.0890102i
$535$	27.8538	−	22.3731i	1.20423	−	0.967273i
$536$	2.37207	+	0.635595i	0.102458	+	0.0274535i
$537$	1.21602	+	2.10621i	0.0524751	+	0.0908895i
$538$	1.12055	−	1.94084i	0.0483102	−	0.0836756i
$539$	−11.8403	+	20.5080i	−0.509998	+	0.883343i
$540$	−5.28617	−	6.58112i	−0.227480	−	0.283206i
$541$	−16.3259	−	16.3259i	−0.701907	−	0.701907i	0.262913	−	0.964820i	$-0.415317\pi$
$541$	−16.3259	−	16.3259i	−0.701907	−	0.701907i	−0.964820	+	0.262913i	$0.915317\pi$
$542$	−6.63517	+	3.83082i	−0.285005	+	0.164548i
$543$	4.30116	+	16.0522i	0.184581	+	0.688864i
$544$			3.21567i			0.137871i
$545$	−16.4341	−	6.38342i	−0.703958	−	0.273436i
$546$	−12.9246	−	7.46200i	−0.553120	−	0.319344i
$547$			18.0278i			0.770814i	0.922747	+	0.385407i	$0.125939\pi$
$547$			18.0278i			0.770814i	−0.922747	+	0.385407i	$0.874061\pi$
$548$	−18.3520	−	4.91739i	−0.783957	−	0.210061i
$549$	−11.9790	−	11.9790i	−0.511251	−	0.511251i
$550$	10.4725	+	2.31304i	0.446547	+	0.0986283i
$551$	−2.37936	−	4.12118i	−0.101364	−	0.175568i
$552$	1.46921	+	0.393674i	0.0625337	+	0.0167559i
$553$	2.23036	+	1.28770i	0.0948446	+	0.0547586i
$554$	7.59532			0.322694
$555$	−9.10378	+	1.78417i	−0.386434	+	0.0757337i
$556$	−0.239769			−0.0101685
$557$	26.7567	+	15.4480i	1.13372	+	0.654552i	0.944867	−	0.327454i	$-0.106191\pi$
$557$	26.7567	+	15.4480i	1.13372	+	0.654552i	0.188850	+	0.982006i	$0.439524\pi$
$558$	18.0667	+	4.84096i	0.764825	+	0.204934i
$559$	−32.0073	−	55.4383i	−1.35376	−	2.34479i
$560$	1.44847	+	9.38628i	0.0612090	+	0.396643i
$561$	−3.32658	−	3.32658i	−0.140448	−	0.140448i
$562$	−29.7397	−	7.96873i	−1.25449	−	0.336141i
$563$		−	3.58859i		−	0.151241i	−0.997137	−	0.0756205i	$-0.975906\pi$
$563$		−	3.58859i		−	0.151241i	0.997137	−	0.0756205i	$-0.0240938\pi$
$564$	−2.02853	−	1.17117i	−0.0854166	−	0.0493153i
$565$	−0.627069	−	1.42360i	−0.0263810	−	0.0598914i
$566$		−	0.911444i		−	0.0383108i
$567$	−5.52904	−	20.6346i	−0.232198	−	0.866574i
$568$	11.1156	−	6.41760i	0.466401	−	0.269277i
$569$	−18.3582	−	18.3582i	−0.769616	−	0.769616i	0.208423	−	0.978039i	$-0.433167\pi$
$569$	−18.3582	−	18.3582i	−0.769616	−	0.769616i	−0.978039	+	0.208423i	$0.933167\pi$
$570$	10.5163	+	1.14753i	0.440480	+	0.0480649i
$571$	−18.7879	+	32.5416i	−0.786248	+	1.36182i	0.142002	+	0.989866i	$0.454646\pi$
$571$	−18.7879	+	32.5416i	−0.786248	+	1.36182i	−0.928250	+	0.371956i	$0.878687\pi$
$572$	5.52506	−	9.56969i	0.231014	−	0.400129i
$573$	−0.700155	−	1.21270i	−0.0292494	−	0.0506614i
$574$	−1.17333	−	0.314394i	−0.0489740	−	0.0131225i
$575$	10.6317	−	3.36136i	0.443372	−	0.140178i
$576$	2.19520	+	1.26740i	0.0914667	+	0.0528083i
$577$	14.4475	−	25.0238i	0.601456	−	1.04175i	−0.391145	−	0.920329i	$-0.627921\pi$
$577$	14.4475	−	25.0238i	0.601456	−	1.04175i	0.992601	−	0.121423i	$-0.0387459\pi$
$578$			6.65948i			0.276998i
$579$	1.03777	−	3.87300i	0.0431282	−	0.160957i
$580$	0.960686	+	1.19603i	0.0398903	+	0.0496622i
$581$	−15.6103			−0.647624
$582$	6.87752	+	6.87752i	0.285082	+	0.285082i
$583$	−4.15993	−	15.5251i	−0.172287	−	0.642983i
$584$	9.49086	+	9.49086i	0.392734	+	0.392734i
$585$	−17.2566	+	23.5545i	−0.713474	+	0.973860i
$586$	−14.0639	+	14.0639i	−0.580975	+	0.580975i
$587$	30.3542	−	17.5250i	1.25285	−	0.723335i	0.281178	−	0.959656i	$-0.409275\pi$
$587$	30.3542	−	17.5250i	1.25285	−	0.723335i	0.971675	+	0.236321i	$0.0759416\pi$
$588$	1.94889	−	7.27337i	0.0803710	−	0.299949i
$589$	−44.3252	+	25.5912i	−1.82639	+	1.05447i
$590$	−8.62154	−	10.7336i	−0.354943	−	0.441894i
$591$			17.0127i			0.699811i
$592$	5.14063	−	3.25176i	0.211279	−	0.133646i
$593$	30.2234	+	30.2234i	1.24113	+	1.24113i	0.959534	+	0.281593i	$0.0908627\pi$
$593$	30.2234	+	30.2234i	1.24113	+	1.24113i	0.281593	+	0.959534i	$0.409137\pi$
$594$	−7.82144	+	2.09575i	−0.320918	+	0.0859896i
$595$	−4.65779	−	30.1832i	−0.190951	−	1.23739i
$596$	5.61305	−	3.24070i	0.229920	−	0.132744i
$597$	−8.59747	−	14.8913i	−0.351871	−	0.609459i
$598$		−	11.4886i		−	0.469803i
$599$	20.7282	−	11.9674i	0.846932	−	0.488976i	−0.0126828	−	0.999920i	$-0.504037\pi$
$599$	20.7282	−	11.9674i	0.846932	−	0.488976i	0.859614	+	0.510943i	$0.170704\pi$
$600$	−3.40692	+	0.151436i	−0.139087	+	0.00618235i
$601$	3.89797	−	6.75147i	0.159001	−	0.275398i	−0.775507	−	0.631338i	$-0.782506\pi$
$601$	3.89797	−	6.75147i	0.159001	−	0.275398i	0.934509	+	0.355940i	$0.115839\pi$
$602$	37.3196	−	37.3196i	1.52103	−	1.52103i
$603$	−4.40163	+	4.40163i	−0.179248	+	0.179248i
$604$	−9.69607	−	5.59803i	−0.394527	−	0.227781i
$605$	−8.45641	+	11.5426i	−0.343802	+	0.469274i
$606$	0.133172	−	0.133172i	0.00540973	−	0.00540973i
$607$	14.6752	+	8.47275i	0.595649	+	0.343898i	0.767328	−	0.641255i	$-0.221586\pi$
$607$	14.6752	+	8.47275i	0.595649	+	0.343898i	−0.171679	+	0.985153i	$0.554919\pi$
$608$	−6.69996	+	1.79525i	−0.271719	+	0.0728070i
$609$	−0.514396	−	1.91975i	−0.0208444	−	0.0777923i
$610$	−14.7695	+	2.27920i	−0.598000	+	0.0922820i
$611$	−4.57903	+	17.0892i	−0.185248	+	0.691354i
$612$	−7.05904	−	4.07554i	−0.285345	−	0.164744i
$613$	0.00877176	+	0.0327367i	0.000354288	+	0.00132222i	0.966103	−	0.258158i	$-0.0831155\pi$
$613$	0.00877176	+	0.0327367i	0.000354288	+	0.00132222i	−0.965748	+	0.259480i	$0.916449\pi$
$614$	3.64279	+	13.5951i	0.147011	+	0.548652i
$615$	0.157927	−	0.406583i	0.00636825	−	0.0163950i
$616$	8.80003	+	2.35796i	0.354563	+	0.0950049i
$617$	−20.6233	+	5.52599i	−0.830262	+	0.222468i	−0.648828	−	0.760935i	$-0.724741\pi$
$617$	−20.6233	+	5.52599i	−0.830262	+	0.222468i	−0.181434	+	0.983403i	$0.558074\pi$
$618$	−1.73175	−	1.73175i	−0.0696613	−	0.0696613i
$619$	−0.953588			−0.0383279			−0.0191640	−	0.999816i	$-0.506100\pi$
$619$	−0.953588			−0.0383279			−0.0191640	+	0.999816i	$0.506100\pi$
$620$	12.8638	−	10.3326i	0.516624	−	0.414969i
$621$	−5.95288	+	5.95288i	−0.238881	+	0.238881i
$622$	−6.10141	+	22.7708i	−0.244644	+	0.913025i
$623$	25.6177			1.02635
$624$	−0.909415	+	3.39398i	−0.0364057	+	0.135868i
$625$	−20.4562	+	14.3716i	−0.818248	+	0.574865i
$626$	6.25706	+	10.8376i	0.250083	+	0.433156i
$627$	5.07387	−	8.78821i	0.202631	−	0.350967i
$628$	−10.2921	+	10.2921i	−0.410698	+	0.410698i
$629$	−16.5306	+	10.4566i	−0.659117	+	0.416931i
$630$	−22.4406	−	8.71649i	−0.894054	−	0.347273i
$631$	6.58035	+	24.5582i	0.261960	+	0.977646i	0.964085	+	0.265593i	$0.0855678\pi$
$631$	6.58035	+	24.5582i	0.261960	+	0.977646i	−0.702126	+	0.712053i	$0.747766\pi$
$632$	0.156936	−	0.585692i	0.00624256	−	0.0232976i
$633$	−3.97438	−	1.06493i	−0.157967	−	0.0423272i
$634$	15.1469	+	4.05859i	0.601559	+	0.161187i
$635$	−15.8688	−	6.16385i	−0.629734	−	0.244605i
$636$	2.55540	+	4.42608i	0.101328	+	0.175506i
$637$	−56.8745			−2.25345
$638$	1.42144	−	0.380873i	0.0562752	−	0.0150789i
$639$			32.5347i			1.28705i
$640$	2.04634	−	0.901374i	0.0808889	−	0.0356300i
$641$	21.4385	−	37.1326i	0.846770	−	1.46665i	−0.0373050	−	0.999304i	$-0.511877\pi$
$641$	21.4385	−	37.1326i	0.846770	−	1.46665i	0.884075	−	0.467345i	$-0.154789\pi$
$642$	5.44875	+	9.43751i	0.215045	+	0.372469i
$643$	17.9644			0.708447			0.354224	−	0.935161i	$-0.384745\pi$
$643$	17.9644			0.708447			0.354224	+	0.935161i	$0.384745\pi$
$644$	9.14920	−	2.45152i	0.360529	−	0.0966035i
$645$	11.8679	+	14.7751i	0.467296	+	0.581770i
$646$	21.5448	−	5.77292i	0.847671	−	0.227133i
$647$	−18.2580	+	10.5413i	−0.717797	+	0.414420i	−0.813941	−	0.580947i	$-0.802682\pi$
$647$	−18.2580	+	10.5413i	−0.717797	+	0.414420i	0.0961443	+	0.995367i	$0.469349\pi$
$648$	−4.35577	+	2.51480i	−0.171111	+	0.0987908i
$649$	−12.7565	+	3.41809i	−0.500735	+	0.134172i
$650$	7.76498	+	24.5600i	0.304568	+	0.963321i
$651$	−20.6479	+	5.53258i	−0.809253	+	0.216839i
$652$	−11.6232			−0.455198
$653$	−0.954568	−	1.65336i	−0.0373551	−	0.0647010i	0.846743	−	0.532002i	$-0.178560\pi$
$653$	−0.954568	−	1.65336i	−0.0373551	−	0.0647010i	−0.884099	+	0.467301i	$0.845227\pi$
$654$	2.68884	−	4.65720i	0.105142	−	0.182111i
$655$	−32.6876	−	12.6967i	−1.27721	−	0.496102i
$656$			0.285995i			0.0111662i
$657$	−32.8630	+	8.80563i	−1.28211	+	0.343540i
$658$	−14.5865			−0.568640
$659$	−11.0325	−	19.1088i	−0.429763	−	0.744372i	0.567089	−	0.823657i	$-0.308070\pi$
$659$	−11.0325	−	19.1088i	−0.429763	−	0.744372i	−0.996852	+	0.0792848i	$0.974736\pi$
$660$	−1.18446	+	3.04938i	−0.0461050	+	0.118697i
$661$	2.67149	+	0.715823i	0.103909	+	0.0278423i	0.310399	−	0.950606i	$-0.399537\pi$
$661$	2.67149	+	0.715823i	0.103909	+	0.0278423i	−0.206490	+	0.978449i	$0.566204\pi$
$662$	−1.35226	−	0.362336i	−0.0525570	−	0.0140826i
$663$	2.92438	−	10.9139i	0.113573	−	0.423862i
$664$	0.951235	+	3.55006i	0.0369151	+	0.137769i
$665$	60.2874	−	26.5554i	2.33784	−	1.02977i
$666$	0.623023	+	15.4060i	0.0241416	+	0.596970i
$667$	1.08185	−	1.08185i	0.0418894	−	0.0418894i
$668$	0.711584	−	1.23250i	0.0275320	−	0.0476868i
$669$	−2.51964	−	4.36414i	−0.0974148	−	0.168727i
$670$	0.837480	+	5.42699i	0.0323547	+	0.209663i
$671$	−3.71030	+	13.8470i	−0.143235	+	0.534559i
$672$	−2.89694			−0.111752
$673$	4.38545	−	16.3667i	0.169047	−	0.630891i	−0.828443	−	0.560074i	$-0.810773\pi$
$673$	4.38545	−	16.3667i	0.169047	−	0.630891i	0.997489	−	0.0708171i	$-0.0225607\pi$
$674$	−4.90656	+	4.90656i	−0.188994	+	0.188994i
$675$	8.70242	−	16.7494i	0.334956	−	0.644684i
$676$	13.5394			0.520748
$677$	18.3803	+	18.3803i	0.706413	+	0.706413i	0.965779	−	0.259366i	$-0.0835137\pi$
$677$	18.3803	+	18.3803i	0.706413	+	0.706413i	−0.259366	+	0.965779i	$0.583514\pi$
$678$	0.458326	−	0.122808i	0.0176019	−	0.00471641i
$679$	58.5046	+	15.6763i	2.24520	+	0.601600i
$680$	−6.58036	+	2.89852i	−0.252345	+	0.111153i
$681$	−1.61262	−	6.01837i	−0.0617956	−	0.230624i
$682$	−4.09647	−	15.2882i	−0.156862	−	0.585416i
$683$	18.4860	+	10.6729i	0.707349	+	0.408388i	0.810079	−	0.586321i	$-0.199424\pi$
$683$	18.4860	+	10.6729i	0.707349	+	0.408388i	−0.102730	+	0.994709i	$0.532758\pi$
$684$	4.55060	−	16.9831i	0.173996	−	0.649364i
$685$	−6.47931	−	41.9868i	−0.247562	−	1.60423i
$686$	−4.44125	−	16.5750i	−0.169568	−	0.632835i
$687$	2.34861	−	0.629308i	0.0896050	−	0.0240096i
$688$	−10.7613	−	6.21303i	−0.410270	−	0.236869i
$689$	27.2960	−	27.2960i	1.03990	−	1.03990i
$690$	0.518717	+	3.36136i	0.0197472	+	0.127965i
$691$	−36.1687	−	20.8820i	−1.37592	−	0.794388i	−0.384256	−	0.923227i	$-0.625542\pi$
$691$	−36.1687	−	20.8820i	−1.37592	−	0.794388i	−0.991666	+	0.128838i	$0.958875\pi$
$692$	12.3422	−	12.3422i	0.469182	−	0.469182i
$693$	−16.3294	+	16.3294i	−0.620301	+	0.620301i
$694$	5.15303	−	8.92532i	0.195607	−	0.338800i
$695$	−0.216122	−	0.490650i	−0.00819797	−	0.0186114i
$696$	−0.405241	+	0.233966i	−0.0153606	+	0.00886845i
$697$		−	0.919665i		−	0.0348348i
$698$	−4.55432	−	7.88832i	−0.172384	−	0.298577i
$699$	10.8470	−	6.26255i	0.410273	−	0.236871i
$700$	−17.9020	+	11.4246i	−0.676630	+	0.431810i
$701$	31.8107	−	8.52365i	1.20147	−	0.321934i	0.398062	−	0.917358i	$-0.369683\pi$
$701$	31.8107	−	8.52365i	1.20147	−	0.321934i	0.803411	+	0.595424i	$0.203016\pi$
$702$	−13.7516	−	13.7516i	−0.519020	−	0.519020i
$703$	−31.0154	−	28.6043i	−1.16977	−	1.07883i
$704$		−	2.14497i		−	0.0808416i
$705$	0.568157	−	5.20674i	0.0213980	−	0.196097i
$706$	2.73444	−	1.57873i	0.102912	−	0.0594164i
$707$	0.303544	−	1.13284i	0.0114160	−	0.0426049i
$708$	3.63677	−	2.09969i	0.136678	−	0.0789113i
$709$	−6.36597	+	6.36597i	−0.239079	+	0.239079i	−0.816469	−	0.577390i	$-0.804071\pi$
$709$	−6.36597	+	6.36597i	−0.239079	+	0.239079i	0.577390	+	0.816469i	$0.304071\pi$
$710$	23.1519	+	16.9617i	0.868877	+	0.636561i
$711$	1.08681	+	1.08681i	0.0407586	+	0.0407586i
$712$	−1.56105	−	5.82591i	−0.0585028	−	0.218335i
$713$	−11.6358	−	11.6358i	−0.435765	−	0.435765i
$714$	9.31559			0.348627
$715$	24.5630	+	2.68031i	0.918605	+	0.100238i
$716$	0.922883	−	3.44425i	0.0344897	−	0.128717i
$717$			9.69391i			0.362026i
$718$	0.147911	−	0.256190i	0.00552000	−	0.00956093i
$719$	6.88749	+	3.97650i	0.256860	+	0.148298i	0.622901	−	0.782300i	$-0.285954\pi$
$719$	6.88749	+	3.97650i	0.256860	+	0.148298i	−0.366041	+	0.930599i	$0.619287\pi$
$720$	−0.614838	+	5.63454i	−0.0229137	+	0.209987i
$721$	−14.7314	−	3.94727i	−0.548626	−	0.147004i
$722$	14.5562	+	25.2121i	0.541726	+	0.938296i
$723$	−2.18952	+	3.79235i	−0.0814290	+	0.141039i
$724$	12.1826	−	21.1009i	0.452762	−	0.784207i
$725$	−1.58154	+	3.04396i	−0.0587370	+	0.113050i
$726$	−3.08620	−	3.08620i	−0.114540	−	0.114540i
$727$	10.0177	−	5.78371i	0.371535	−	0.214506i	−0.302594	−	0.953120i	$-0.597853\pi$
$727$	10.0177	−	5.78371i	0.371535	−	0.214506i	0.674129	+	0.738614i	$0.264519\pi$
$728$	5.66319	+	21.1353i	0.209892	+	0.783327i
$729$		−	5.02468i		−	0.186099i
$730$	−10.8667	+	27.9764i	−0.402196	+	1.03545i
$731$	34.6047	+	19.9790i	1.27990	+	0.738951i
$732$		−	4.55839i		−	0.168483i
$733$	−12.7924	−	3.42772i	−0.472499	−	0.126606i	0.0147088	−	0.999892i	$-0.495318\pi$
$733$	−12.7924	−	3.42772i	−0.472499	−	0.126606i	−0.487208	+	0.873286i	$0.661985\pi$
$734$	15.8866	+	15.8866i	0.586385	+	0.586385i
$735$	16.6405	−	2.56792i	0.613794	−	0.0947193i
$736$	−1.11504	−	1.93130i	−0.0411009	−	0.0711888i
$737$	5.08803	+	1.36333i	0.187420	+	0.0502190i
$738$	−0.627817	−	0.362470i	−0.0231103	−	0.0133427i
$739$	−15.3469			−0.564544			−0.282272	−	0.959334i	$-0.591088\pi$
$739$	−15.3469			−0.564544			−0.282272	+	0.959334i	$0.591088\pi$
$740$	11.2878	+	7.58845i	0.414949	+	0.278957i
$741$	24.3722			0.895335
$742$	27.5625	+	15.9132i	1.01185	+	0.584192i
$743$	−9.46639	−	2.53651i	−0.347288	−	0.0930555i	0.0809586	−	0.996717i	$-0.474202\pi$
$743$	−9.46639	−	2.53651i	−0.347288	−	0.0930555i	−0.428247	+	0.903662i	$0.640869\pi$
$744$	2.51641	+	4.35856i	0.0922562	+	0.159792i
$745$	11.6910	+	8.56516i	0.428327	+	0.313803i
$746$	15.6393	+	15.6393i	0.572596	+	0.572596i
$747$	−8.99868	−	2.41119i	−0.329245	−	0.0882208i
$748$			6.89751i			0.252198i
$749$	58.7701	+	33.9310i	2.14741	+	1.23981i
$750$	−3.38080	−	6.83522i	−0.123449	−	0.249587i
$751$		−	46.1172i		−	1.68284i	−0.540381	−	0.841421i	$-0.681720\pi$
$751$		−	46.1172i		−	1.68284i	0.540381	−	0.841421i	$-0.318280\pi$
$752$	0.888848	+	3.31722i	0.0324129	+	0.120967i
$753$	−12.1909	+	7.03840i	−0.444260	+	0.256494i
$754$	2.49915	+	2.49915i	0.0910139	+	0.0910139i
$755$	2.71570	−	24.8874i	0.0988346	−	0.905746i
$756$	8.01699	−	13.8858i	0.291575	−	0.505023i
$757$	−10.0423	+	17.3937i	−0.364992	+	0.632185i	−0.988775	−	0.149413i	$-0.952262\pi$
$757$	−10.0423	+	17.3937i	−0.364992	+	0.632185i	0.623783	+	0.781598i	$0.285595\pi$
$758$	−4.95602	−	8.58408i	−0.180011	−	0.311788i
$759$	3.15141	+	0.844418i	0.114389	+	0.0306504i
$760$	−9.71287	−	12.0922i	−0.352323	−	0.438631i
$761$	24.6417	+	14.2269i	0.893260	+	0.515724i	0.875007	−	0.484110i	$-0.160856\pi$
$761$	24.6417	+	14.2269i	0.893260	+	0.515724i	0.0182525	+	0.999833i	$0.494190\pi$
$762$	2.59635	−	4.49701i	0.0940558	−	0.162909i
$763$		−	33.4883i		−	1.21236i
$764$	−0.531374	+	1.98312i	−0.0192244	+	0.0717466i
$765$	1.97712	−	18.1188i	0.0714828	−	0.655087i
$766$	31.6751			1.14447
$767$	−22.4283	−	22.4283i	−0.809839	−	0.809839i
$768$	0.176529	+	0.658815i	0.00636994	+	0.0237730i
$769$	−10.6047	−	10.6047i	−0.382417	−	0.382417i	0.489555	−	0.871972i	$-0.337159\pi$
$769$	−10.6047	−	10.6047i	−0.382417	−	0.382417i	−0.871972	+	0.489555i	$0.837159\pi$
$770$	3.10692	+	20.1333i	0.111966	+	0.725554i
$771$	−0.145803	+	0.145803i	−0.00525098	+	0.00525098i
$772$	−5.09114	+	2.93937i	−0.183234	+	0.105790i
$773$	−12.0973	+	45.1478i	−0.435110	+	1.62385i	0.305691	+	0.952131i	$0.401112\pi$
$773$	−12.0973	+	45.1478i	−0.435110	+	1.62385i	−0.740802	+	0.671724i	$0.765554\pi$
$774$	27.2777	−	15.7488i	0.980476	−	0.566078i
$775$	32.7392	+	17.0102i	1.17603	+	0.611026i
$776$		−	14.2602i		−	0.511913i
$777$	−9.42013	−	14.8921i	−0.337945	−	0.534251i
$778$	23.5141	+	23.5141i	0.843022	+	0.843022i
$779$	1.91616	−	0.513432i	0.0686534	−	0.0183956i
$780$	−7.76498	+	1.19827i	−0.278031	+	0.0429051i
$781$	23.8426	−	13.7656i	0.853157	−	0.492570i
$782$	3.58560	+	6.21043i	0.128221	+	0.222085i
$783$		−	2.58991i		−	0.0925557i
$784$	−9.56099	+	5.52004i	−0.341464	+	0.197144i
$785$	−30.3381	−	11.7841i	−1.08281	−	0.420592i
$786$	5.34813	−	9.26324i	0.190762	−	0.330409i
$787$	−7.48984	+	7.48984i	−0.266984	+	0.266984i	−0.827884	−	0.560900i	$-0.810455\pi$
$787$	−7.48984	+	7.48984i	−0.266984	+	0.266984i	0.560900	+	0.827884i	$0.310455\pi$
$788$	17.6376	−	17.6376i	0.628313	−	0.628313i
$789$	−17.5744	−	10.1466i	−0.625666	−	0.361228i
$790$	1.33998	−	0.206783i	0.0476745	−	0.00735702i
$791$	2.08937	−	2.08937i	0.0742893	−	0.0742893i
$792$	4.70864	+	2.71853i	0.167314	+	0.0965989i
$793$	−33.2569	+	8.91115i	−1.18099	+	0.316444i
$794$	9.36189	+	34.9391i	0.332241	+	1.23994i
$795$	−6.75391	+	9.21878i	−0.239537	+	0.326956i
$796$	−6.52495	+	24.3514i	−0.231271	+	0.863114i
$797$	−17.4401	−	10.0690i	−0.617759	−	0.356663i	0.158237	−	0.987401i	$-0.449419\pi$
$797$	−17.4401	−	10.0690i	−0.617759	−	0.356663i	−0.775996	+	0.630738i	$0.782752\pi$
$798$	5.20073	+	19.4094i	0.184104	+	0.687084i
$799$	−2.85824	−	10.6671i	−0.101117	−	0.377375i
$800$	3.68904	+	3.37505i	0.130427	+	0.119326i
$801$	14.7675	+	3.95695i	0.521785	+	0.139812i
$802$	16.9806	−	4.54995i	0.599608	−	0.160664i
$803$	20.3576	+	20.3576i	0.718404	+	0.718404i
$804$	−1.67496			−0.0590713
$805$	13.2635	+	16.5127i	0.467477	+	0.581995i
$806$	26.8796	−	26.8796i	0.946794	−	0.946794i
$807$	−0.395618	+	1.47647i	−0.0139264	+	0.0519741i
$808$	−0.276126			−0.00971406
$809$	3.51422	−	13.1152i	0.123553	−	0.461107i	−0.876231	−	0.481892i	$-0.839950\pi$
$809$	3.51422	−	13.1152i	0.123553	−	0.461107i	0.999784	+	0.0207847i	$0.00661646\pi$
$810$	−9.07233	−	6.64662i	−0.318769	−	0.233538i
$811$	6.41738	+	11.1152i	0.225345	+	0.390308i	0.956423	−	0.291985i	$-0.0943159\pi$
$811$	6.41738	+	11.1152i	0.225345	+	0.390308i	−0.731078	+	0.682294i	$0.760983\pi$
$812$	−1.45697	+	2.52355i	−0.0511297	+	0.0885593i
$813$	3.69510	−	3.69510i	0.129593	−	0.129593i
$814$	11.0265	−	6.97492i	0.386479	−	0.244471i
$815$	−10.4768	−	23.7850i	−0.366987	−	0.833152i
$816$	−0.567659	−	2.11853i	−0.0198720	−	0.0741634i
$817$	−22.3079	+	83.2541i	−0.780453	+	2.91269i
$818$	−22.5508	−	6.04247i	−0.788471	−	0.211270i
$819$	−53.5738	−	14.3551i	−1.87202	−	0.501606i
$820$	−0.585244	+	0.257789i	−0.0204376	+	0.00900237i
$821$	23.0468	+	39.9183i	0.804340	+	1.39316i	0.916735	+	0.399495i	$0.130815\pi$
$821$	23.0468	+	39.9183i	0.804340	+	1.39316i	−0.112395	+	0.993664i	$0.535852\pi$
$822$	12.9586			0.451984
$823$	−23.4782	+	6.29097i	−0.818399	+	0.219289i	−0.643646	−	0.765323i	$-0.722579\pi$
$823$	−23.4782	+	6.29097i	−0.818399	+	0.219289i	−0.174753	+	0.984612i	$0.555913\pi$
$824$			3.59072i			0.125089i
$825$	−7.30773	+	0.324826i	−0.254423	+	0.0113090i
$826$	13.0754	−	22.6473i	0.454951	−	0.787999i
$827$	−4.61146	−	7.98729i	−0.160356	−	0.277745i	0.774640	−	0.632402i	$-0.217931\pi$
$827$	−4.61146	−	7.98729i	−0.160356	−	0.277745i	−0.934996	+	0.354657i	$0.884598\pi$
$828$	5.65280			0.196448
$829$	5.94419	−	1.59274i	0.206450	−	0.0553182i	−0.154112	−	0.988053i	$-0.549252\pi$
$829$	5.94419	−	1.59274i	0.206450	−	0.0553182i	0.360562	+	0.932735i	$0.382585\pi$
$830$	−6.40722	+	5.14648i	−0.222398	+	0.178637i
$831$	−5.00391	+	1.34079i	−0.173584	+	0.0465117i
$832$	4.46146	−	2.57582i	0.154673	−	0.0893006i
$833$	30.7450	−	17.7506i	1.06525	−	0.615022i
$834$	0.157964	−	0.0423262i	0.00546983	−	0.00146564i
$835$	3.16352	+	0.345202i	0.109478	+	0.0119462i
$836$	−14.3712	+	3.85076i	−0.497039	+	0.133181i
$837$	−27.8557			−0.962834
$838$	−13.5966	−	23.5500i	−0.469688	−	0.813523i
$839$	19.1957	−	33.2480i	0.662710	−	1.14785i	−0.317191	−	0.948362i	$-0.602740\pi$
$839$	19.1957	−	33.2480i	0.662710	−	1.14785i	0.979901	−	0.199485i	$-0.0639270\pi$
$840$	−2.61123	−	5.92813i	−0.0900958	−	0.204540i
$841$		−	28.5293i		−	0.983770i
$842$	−10.3901	+	2.78403i	−0.358068	+	0.0959439i
$843$	20.9997			0.723268
$844$	3.01630	+	5.22439i	0.103825	+	0.179831i
$845$	12.2041	+	27.7064i	0.419834	+	0.953128i
$846$	−8.40850	−	2.25305i	−0.289090	−	0.0774615i
$847$	−26.2532	−	7.03452i	−0.902070	−	0.241709i
$848$	1.93939	−	7.23790i	0.0665989	−	0.248550i
$849$	0.160896	+	0.600473i	0.00552195	+	0.0206082i
$850$	−11.8627	−	10.8530i	−0.406889	−	0.372256i
$851$	6.30229	−	12.0121i	0.216040	−	0.411771i
$852$	−6.19024	+	6.19024i	−0.212074	+	0.212074i
$853$	−6.22252	+	10.7777i	−0.213055	+	0.369022i	−0.952669	−	0.304009i	$-0.901675\pi$
$853$	−6.22252	+	10.7777i	−0.213055	+	0.369022i	0.739614	+	0.673031i	$0.235008\pi$
$854$	−14.1932	−	24.5834i	−0.485682	−	0.841226i
$855$	38.8550	−	5.99601i	1.32881	−	0.205059i
$856$	4.13526	−	15.4330i	0.141340	−	0.527490i
$857$	3.80939			0.130126			0.0650631	−	0.997881i	$-0.479275\pi$
$857$	3.80939			0.130126			0.0650631	+	0.997881i	$0.479275\pi$
$858$	−1.95067	+	7.27999i	−0.0665947	+	0.248535i
$859$	−0.520431	+	0.520431i	−0.0177569	+	0.0177569i	−0.715929	−	0.698173i	$-0.753997\pi$
$859$	−0.520431	+	0.520431i	−0.0177569	+	0.0177569i	0.698173	+	0.715929i	$0.253997\pi$
$860$	3.01405	−	27.6215i	0.102778	−	0.941887i
$861$	0.828510			0.0282355
$862$	−8.92502	−	8.92502i	−0.303987	−	0.303987i
$863$	−22.6680	+	6.07386i	−0.771626	+	0.206757i	−0.623090	−	0.782150i	$-0.714123\pi$
$863$	−22.6680	+	6.07386i	−0.771626	+	0.206757i	−0.148536	+	0.988907i	$0.547456\pi$
$864$	−3.64641	−	0.977053i	−0.124053	−	0.0332400i
$865$	36.3814	+	14.1315i	1.23701	+	0.480485i
$866$	4.07821	+	15.2201i	0.138583	+	0.517200i
$867$	−1.17559	−	4.38737i	−0.0399252	−	0.149003i
$868$	27.1420	+	15.6704i	0.921259	+	0.531889i
$869$	0.336622	−	1.25629i	0.0114191	−	0.0426168i
$870$	−0.844048	−	0.618371i	−0.0286159	−	0.0209647i
$871$	3.27436	+	12.2201i	0.110948	+	0.414062i
$872$	−7.61584	+	2.04066i	−0.257905	+	0.0691054i
$873$	31.3041	+	18.0734i	1.05948	+	0.611693i
$874$	−10.9379	+	10.9379i	−0.369980	+	0.369980i
$875$	−39.5151	−	26.3357i	−1.33585	−	0.890309i
$876$	−7.92813	−	4.57731i	−0.267867	−	0.154653i
$877$	−28.8202	+	28.8202i	−0.973187	+	0.973187i	−0.999650	−	0.0264624i	$-0.991576\pi$
$877$	−28.8202	+	28.8202i	−0.973187	+	0.973187i	0.0264624	+	0.999650i	$0.491576\pi$
$878$	−18.2619	+	18.2619i	−0.616310	+	0.616310i
$879$	6.78284	−	11.7482i	0.228779	−	0.396257i
$880$	4.38935	−	1.93342i	0.147965	−	0.0651756i
$881$	12.2138	−	7.05162i	0.411492	−	0.237575i	−0.279938	−	0.960018i	$-0.590314\pi$
$881$	12.2138	−	7.05162i	0.411492	−	0.237575i	0.691431	+	0.722443i	$0.256981\pi$
$882$		−	27.9844i		−	0.942283i
$883$	−27.9483	−	48.4079i	−0.940536	−	1.62906i	−0.764451	−	0.644682i	$-0.776990\pi$
$883$	−27.9483	−	48.4079i	−0.940536	−	1.62906i	−0.176085	−	0.984375i	$-0.556343\pi$
$884$	−14.3466	+	8.28299i	−0.482527	+	0.278587i
$885$	7.57479	+	5.54948i	0.254624	+	0.186544i
$886$	5.88150	−	1.57594i	0.197593	−	0.0529448i
$887$	10.5153	+	10.5153i	0.353069	+	0.353069i	0.861250	−	0.508181i	$-0.169682\pi$
$887$	10.5153	+	10.5153i	0.353069	+	0.353069i	−0.508181	+	0.861250i	$0.669682\pi$
$888$	−2.81270	+	3.04978i	−0.0943880	+	0.102344i
$889$		−	32.3364i		−	1.08453i
$890$	10.5147	−	8.44577i	0.352455	−	0.283103i
$891$	−9.34299	+	5.39418i	−0.313002	+	0.180712i
$892$	−1.91225	+	7.13661i	−0.0640268	+	0.238951i
$893$	20.6296	−	11.9105i	0.690342	−	0.398569i
$894$	−3.12589	+	3.12589i	−0.104545	+	0.104545i
$895$	7.87997	−	1.21602i	0.263398	−	0.0406470i
$896$	3.00334	+	3.00334i	0.100334	+	0.100334i
$897$	2.02807	+	7.56885i	0.0677152	+	0.252717i
$898$	−4.18026	−	4.18026i	−0.139497	−	0.139497i
$899$	5.06237			0.168840
$900$	−12.0844	+	3.82066i	−0.402813	+	0.127355i
$901$	−6.23643	+	23.2747i	−0.207766	+	0.775392i
$902$			0.613451i			0.0204257i
$903$	−17.9988	+	31.1748i	−0.598961	+	1.03743i
$904$	−0.602478	−	0.347841i	−0.0200381	−	0.0115690i
$905$	54.1607	+	5.90999i	1.80036	+	0.196455i
$906$	7.37614	+	1.97643i	0.245056	+	0.0656625i
$907$	−16.7787	−	29.0616i	−0.557128	−	0.964974i	−0.997735	−	0.0672736i	$-0.978570\pi$
$907$	−16.7787	−	29.0616i	−0.557128	−	0.964974i	0.440607	−	0.897700i	$-0.354763\pi$
$908$	−4.56757	+	7.91126i	−0.151580	+	0.262544i
$909$	0.349961	−	0.606151i	0.0116075	−	0.0201048i
$910$	−38.1455	+	30.6397i	−1.26451	+	1.01570i
$911$	12.1730	+	12.1730i	0.403310	+	0.403310i	0.879398	−	0.476088i	$-0.157946\pi$
$911$	12.1730	+	12.1730i	0.403310	+	0.403310i	−0.476088	+	0.879398i	$0.657946\pi$
$912$	4.09712	−	2.36548i	0.135669	−	0.0783287i
$913$	2.04037	+	7.61477i	0.0675264	+	0.252012i
$914$		−	29.3556i		−	0.970997i
$915$	9.32804	−	4.10882i	0.308376	−	0.135833i
$916$	−3.08729	−	1.78245i	−0.102007	−	0.0588937i
$917$		−	66.6088i		−	2.19962i
$918$	11.7256	+	3.14188i	0.387004	+	0.103697i
$919$	7.15066	+	7.15066i	0.235879	+	0.235879i	0.815141	−	0.579262i	$-0.196659\pi$
$919$	7.15066	+	7.15066i	0.235879	+	0.235879i	−0.579262	+	0.815141i	$0.696659\pi$
$920$	2.94705	−	4.02258i	0.0971612	−	0.132621i
$921$	−4.79985	−	8.31358i	−0.158160	−	0.273942i
$922$	−34.1306	−	9.14527i	−1.12403	−	0.301184i
$923$	57.2637	+	33.0612i	1.88486	+	1.08822i
$924$	−6.21384			−0.204420
$925$	−5.35401	+	29.9388i	−0.176039	+	0.984383i
$926$	−26.0038			−0.854539
$927$	−7.88234	−	4.55087i	−0.258890	−	0.149470i
$928$	0.662683	+	0.177565i	0.0217536	+	0.00582887i
$929$	−7.00582	−	12.1344i	−0.229854	−	0.398118i	0.727911	−	0.685672i	$-0.240491\pi$
$929$	−7.00582	−	12.1344i	−0.229854	−	0.398118i	−0.957765	+	0.287554i	$0.907158\pi$
$930$	−6.65088	+	9.07814i	−0.218091	+	0.297684i
$931$	54.1484	+	54.1484i	1.77464	+	1.77464i
$932$	−17.7380	−	4.75288i	−0.581028	−	0.155686i
$933$		−	16.0788i		−	0.526397i
$934$	21.7521	+	12.5586i	0.711752	+	0.410930i
$935$	−14.1147	+	6.21724i	−0.461599	+	0.203325i
$936$			13.0584i			0.426827i
$937$	−1.93111	−	7.20700i	−0.0630866	−	0.235443i	0.927182	−	0.374611i	$-0.122224\pi$
$937$	−1.93111	−	7.20700i	−0.0630866	−	0.235443i	−0.990269	+	0.139168i	$0.955557\pi$
$938$	−9.03305	+	5.21523i	−0.294939	+	0.170283i
$939$	−6.03539	−	6.03539i	−0.196958	−	0.196958i
$940$	−5.98700	+	4.80895i	−0.195274	+	0.156851i
$941$	−26.3830	+	45.6967i	−0.860062	+	1.48967i	0.0118063	+	0.999930i	$0.496242\pi$
$941$	−26.3830	+	45.6967i	−0.860062	+	1.48967i	−0.871868	+	0.489741i	$0.837091\pi$
$942$	4.96372	−	8.59741i	0.161727	−	0.280119i
$943$	0.318896	+	0.552344i	0.0103847	+	0.0179868i
$944$	−5.94716	−	1.59354i	−0.193563	−	0.0518652i
$945$	35.6415	+	3.88918i	1.15942	+	0.126515i
$946$	−23.0826	−	13.3268i	−0.750480	−	0.433290i
$947$	−8.69529	+	15.0607i	−0.282559	+	0.489406i	−0.972014	−	0.234922i	$-0.924517\pi$
$947$	−8.69529	+	15.0607i	−0.282559	+	0.489406i	0.689455	+	0.724328i	$0.257850\pi$
$948$			0.413567i			0.0134320i
$949$	−17.8963	+	66.7898i	−0.580938	+	2.16809i
$950$	15.9899	−	30.7755i	0.518782	−	0.998489i
$951$	−10.6955			−0.346824
$952$	−9.65774	−	9.65774i	−0.313009	−	0.313009i
$953$	−4.97127	−	18.5530i	−0.161035	−	0.600992i	−0.998513	−	0.0545200i	$-0.982637\pi$
$953$	−4.97127	−	18.5530i	−0.161035	−	0.600992i	0.837477	−	0.546472i	$-0.184030\pi$
$954$	13.4307	+	13.4307i	0.434834	+	0.434834i
$955$	−4.53710	+	0.700155i	−0.146817	+	0.0226565i
$956$	10.0499	−	10.0499i	0.325039	−	0.325039i
$957$	−0.869229	+	0.501849i	−0.0280982	+	0.0162225i
$958$	7.38625	−	27.5659i	0.238639	−	0.890612i
$959$	69.8857	−	40.3485i	2.25673	−	1.30292i
$960$	−1.18904	+	0.955079i	−0.0383762	+	0.0308250i
$961$		−	23.4483i		−	0.756396i
$962$	27.7489	+	14.5587i	0.894661	+	0.469393i
$963$	28.6375	+	28.6375i	0.922832	+	0.922832i
$964$	6.20157	−	1.66171i	0.199739	−	0.0535199i
$965$	−10.6040	−	7.76875i	−0.341354	−	0.250085i
$966$	−5.59487	+	3.23020i	−0.180012	+	0.103930i
$967$	−1.16960	−	2.02581i	−0.0376119	−	0.0651457i	0.846607	−	0.532219i	$-0.178642\pi$
$967$	−1.16960	−	2.02581i	−0.0376119	−	0.0651457i	−0.884219	+	0.467073i	$0.845308\pi$
$968$			6.39911i			0.205675i
$969$	−13.1750	+	7.60658i	−0.423242	+	0.244359i
$970$	29.1814	−	12.8538i	0.936957	−	0.412711i
$971$	−7.81050	+	13.5282i	−0.250651	+	0.434140i	−0.963705	−	0.266969i	$-0.913978\pi$
$971$	−7.81050	+	13.5282i	−0.250651	+	0.434140i	0.713054	+	0.701109i	$0.247311\pi$
$972$	10.4338	−	10.4338i	0.334664	−	0.334664i
$973$	0.720108	−	0.720108i	0.0230856	−	0.0230856i
$974$	−12.1401	−	7.00906i	−0.388992	−	0.224585i
$975$	−9.45124	−	14.8097i	−0.302682	−	0.474291i
$976$	−4.72582	+	4.72582i	−0.151270	+	0.151270i
$977$	15.0345	+	8.68016i	0.480996	+	0.277703i	0.720831	−	0.693111i	$-0.243760\pi$
$977$	15.0345	+	8.68016i	0.480996	+	0.277703i	−0.239836	+	0.970814i	$0.577094\pi$
$978$	7.65752	−	2.05183i	0.244861	−	0.0656102i
$979$	−3.34840	−	12.4964i	−0.107015	−	0.399387i
$980$	−19.9139	−	14.5894i	−0.636127	−	0.466043i
$981$	5.17266	−	19.3046i	0.165150	−	0.616350i
$982$	−16.4425	−	9.49311i	−0.524703	−	0.302937i
$983$	−5.26670	−	19.6556i	−0.167982	−	0.626916i	−0.997641	−	0.0686461i	$-0.978132\pi$
$983$	−5.26670	−	19.6556i	−0.167982	−	0.626916i	0.829659	−	0.558270i	$-0.188535\pi$
$984$	−0.0504864	−	0.188418i	−0.00160945	−	0.00600655i
$985$	51.9907	+	20.1945i	1.65656	+	0.643451i
$986$	−2.13097	−	0.570991i	−0.0678639	−	0.0181841i
$987$	9.60979	−	2.57494i	0.305883	−	0.0819611i
$988$	−25.2673	−	25.2673i	−0.803861	−	0.803861i
$989$	−27.7111			−0.881161
$990$	−1.31881	+	12.0859i	−0.0419145	+	0.384116i
$991$	−15.7357	+	15.7357i	−0.499860	+	0.499860i	−0.911394	−	0.411534i	$-0.864993\pi$
$991$	−15.7357	+	15.7357i	−0.499860	+	0.499860i	0.411534	+	0.911394i	$0.364993\pi$
$992$	1.90980	−	7.12748i	0.0606363	−	0.226298i
$993$	0.954851			0.0303013
$994$	−14.1097	+	52.6582i	−0.447533	+	1.67022i
$995$	−55.7128	+	8.59747i	−1.76622	+	0.272558i
$996$	−1.25338	−	2.17091i	−0.0397148	−	0.0687880i
$997$	2.05203	−	3.55422i	0.0649884	−	0.112563i	−0.831700	−	0.555225i	$-0.812632\pi$
$997$	2.05203	−	3.55422i	0.0649884	−	0.112563i	0.896689	+	0.442661i	$0.145966\pi$
$998$	−23.1196	+	23.1196i	−0.731839	+	0.731839i
$999$	−6.83457	−	21.9220i	−0.216236	−	0.693581i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	370.2.r.d.23.1	yes	12
5.2	odd	4		370.2.q.d.97.1	✓	12
37.29	odd	12		370.2.q.d.103.1	yes	12
185.177	even	12	inner	370.2.r.d.177.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.d.97.1	✓	12	5.2	odd	4
370.2.q.d.103.1	yes	12	37.29	odd	12
370.2.r.d.23.1	yes	12	1.1	even	1	trivial
370.2.r.d.177.1	yes	12	185.177	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 370 = 2 \cdot 5 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	370.r (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(-0.658815 - 0.176529i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.32150 + 1.80379i) q^{5} +(-0.482286 - 0.482286i) q^{6} +(-4.10264 - 1.09930i) q^{7} +1.00000i q^{8} +(-2.19520 - 1.26740i) q^{9} +(-2.04634 + 0.901374i) q^{10} +2.14497i q^{11} +(-0.176529 - 0.658815i) q^{12} +(-4.46146 + 2.57582i) q^{13} +(-3.00334 - 3.00334i) q^{14} +(1.18904 - 0.955079i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.60783 - 2.78485i) q^{17} +(-1.26740 - 2.19520i) q^{18} +(6.69996 + 1.79525i) q^{19} +(-2.22287 - 0.242559i) q^{20} +(2.50882 + 1.44847i) q^{21} +(-1.07248 + 1.85760i) q^{22} +2.23008i q^{23} +(0.176529 - 0.658815i) q^{24} +(-1.50728 - 4.76740i) q^{25} -5.15165 q^{26} +(2.66936 + 2.66936i) q^{27} +(-1.09930 - 4.10264i) q^{28} +(-0.485118 - 0.485118i) q^{29} +(1.50728 - 0.232600i) q^{30} +(-5.21767 + 5.21767i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(0.378650 - 1.41314i) q^{33} +(2.78485 - 1.60783i) q^{34} +(7.40453 - 5.94755i) q^{35} -2.53480i q^{36} +(-5.38642 - 2.82604i) q^{37} +(4.90471 + 4.90471i) q^{38} +(3.39398 - 0.909415i) q^{39} +(-1.80379 - 1.32150i) q^{40} +(0.247679 - 0.142998i) q^{41} +(1.44847 + 2.50882i) q^{42} +12.4261i q^{43} +(-1.85760 + 1.07248i) q^{44} +(5.18707 - 2.28480i) q^{45} +(-1.11504 + 1.93130i) q^{46} +(2.42838 - 2.42838i) q^{47} +(0.482286 - 0.482286i) q^{48} +(9.56099 + 5.52004i) q^{49} +(1.07836 - 4.88233i) q^{50} +(-1.55087 + 1.55087i) q^{51} +(-4.46146 - 2.57582i) q^{52} +(-7.23790 + 1.93939i) q^{53} +(0.977053 + 3.64641i) q^{54} +(-3.86906 - 2.83457i) q^{55} +(1.09930 - 4.10264i) q^{56} +(-4.09712 - 2.36548i) q^{57} +(-0.177565 - 0.662683i) q^{58} +(1.59354 + 5.94716i) q^{59} +(1.42164 + 0.552203i) q^{60} +(6.45558 + 1.72977i) q^{61} +(-7.12748 + 1.90980i) q^{62} +(7.61286 + 7.61286i) q^{63} -1.00000 q^{64} +(1.24958 - 11.4515i) q^{65} +(1.03449 - 1.03449i) q^{66} +(0.635595 - 2.37207i) q^{67} +3.21567 q^{68} +(0.393674 - 1.46921i) q^{69} +(9.38628 - 1.44847i) q^{70} +(-6.41760 - 11.1156i) q^{71} +(1.26740 - 2.19520i) q^{72} +(9.49086 - 9.49086i) q^{73} +(-3.25176 - 5.14063i) q^{74} +(0.151436 + 3.40692i) q^{75} +(1.79525 + 6.69996i) q^{76} +(2.35796 - 8.80003i) q^{77} +(3.39398 + 0.909415i) q^{78} +(-0.585692 - 0.156936i) q^{79} +(-0.901374 - 2.04634i) q^{80} +(2.51480 + 4.35577i) q^{81} +0.285995 q^{82} +(3.55006 - 0.951235i) q^{83} +2.89694i q^{84} +(2.89852 + 6.58036i) q^{85} +(-6.21303 + 10.7613i) q^{86} +(0.233966 + 0.405241i) q^{87} -2.14497 q^{88} +(-5.82591 + 1.56105i) q^{89} +(5.63454 + 0.614838i) q^{90} +(21.1353 - 5.66319i) q^{91} +(-1.93130 + 1.11504i) q^{92} +(4.35856 - 2.51641i) q^{93} +(3.31722 - 0.888848i) q^{94} +(-12.0922 + 9.71287i) q^{95} +(0.658815 - 0.176529i) q^{96} -14.2602 q^{97} +(5.52004 + 9.56099i) q^{98} +(2.71853 - 4.70864i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 6 q^{4} - 8 q^{5} + 6 q^{6} - 4 q^{7} - 18 q^{9} - 4 q^{10} - 6 q^{13} - 8 q^{14} - 14 q^{15} - 6 q^{16} + 12 q^{17} + 10 q^{18} + 8 q^{19} - 4 q^{20} + 54 q^{21} - 10 q^{22} - 10 q^{25}+ \cdots - 28 q^{99}+O(q^{100}) \) 12 * q + 6 * q^3 + 6 * q^4 - 8 * q^5 + 6 * q^6 - 4 * q^7 - 18 * q^9 - 4 * q^10 - 6 * q^13 - 8 * q^14 - 14 * q^15 - 6 * q^16 + 12 * q^17 + 10 * q^18 + 8 * q^19 - 4 * q^20 + 54 * q^21 - 10 * q^22 - 10 * q^25 - 18 * q^27 + 4 * q^28 - 4 * q^29 + 10 * q^30 - 2 * q^31 - 28 * q^33 - 12 * q^34 + 14 * q^35 + 12 * q^37 + 16 * q^38 + 30 * q^39 - 2 * q^40 + 12 * q^41 - 22 * q^42 - 6 * q^44 + 24 * q^45 + 2 * q^46 - 28 * q^47 - 6 * q^48 - 24 * q^49 + 16 * q^50 - 8 * q^51 - 6 * q^52 + 14 * q^53 + 18 * q^54 - 32 * q^55 - 4 * q^56 - 72 * q^57 - 10 * q^58 + 14 * q^60 + 24 * q^61 - 16 * q^62 + 8 * q^63 - 12 * q^64 - 26 * q^65 + 8 * q^66 + 18 * q^67 + 24 * q^68 + 40 * q^69 + 6 * q^70 - 10 * q^72 + 28 * q^73 - 38 * q^74 - 30 * q^75 - 8 * q^76 + 26 * q^77 + 30 * q^78 + 56 * q^79 + 4 * q^80 + 4 * q^81 - 28 * q^82 + 14 * q^83 + 28 * q^85 - 22 * q^86 - 10 * q^87 - 20 * q^88 + 2 * q^89 + 42 * q^90 + 38 * q^91 - 18 * q^92 + 18 * q^93 + 16 * q^94 - 56 * q^95 - 6 * q^96 - 44 * q^97 + 22 * q^98 - 28 * q^99

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