LMFDB - Embedded newform 370.2.q.d.97.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [370,2,Mod(97,370)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(370, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("370.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.95446487479$
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			97.1
Root			$0.270517 + 0.0724848i$ of defining polynomial
Character	$\chi$	$=$	370.97
Dual form			370.2.q.d.103.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.176529 + 0.658815i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.242559 + 2.22287i) q^{5} +(-0.482286 - 0.482286i) q^{6} +(1.09930 - 4.10264i) q^{7} +1.00000 q^{8} +(2.19520 + 1.26740i) q^{9} +(-2.04634 - 0.901374i) q^{10} +2.14497i q^{11} +(0.658815 - 0.176529i) q^{12} +(2.57582 + 4.46146i) q^{13} +(3.00334 + 3.00334i) q^{14} +(-1.50728 - 0.232600i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.78485 + 1.60783i) q^{17} +(-2.19520 + 1.26740i) q^{18} +(-6.69996 - 1.79525i) q^{19} +(1.80379 - 1.32150i) q^{20} +(2.50882 + 1.44847i) q^{21} +(-1.85760 - 1.07248i) q^{22} +2.23008 q^{23} +(-0.176529 + 0.658815i) q^{24} +(-4.88233 + 1.07836i) q^{25} -5.15165 q^{26} +(-2.66936 + 2.66936i) q^{27} +(-4.10264 + 1.09930i) q^{28} +(0.485118 + 0.485118i) q^{29} +(0.955079 - 1.18904i) q^{30} +(-5.21767 + 5.21767i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.41314 - 0.378650i) q^{33} +(-2.78485 + 1.60783i) q^{34} +(9.38628 + 1.44847i) q^{35} -2.53480i q^{36} +(2.82604 - 5.38642i) q^{37} +(4.90471 - 4.90471i) q^{38} +(-3.39398 + 0.909415i) q^{39} +(0.242559 + 2.22287i) q^{40} +(0.247679 - 0.142998i) q^{41} +(-2.50882 + 1.44847i) q^{42} +12.4261 q^{43} +(1.85760 - 1.07248i) q^{44} +(-2.28480 + 5.18707i) 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} +(1.50728 - 4.76740i) q^{50} +(-1.55087 + 1.55087i) q^{51} +(2.57582 - 4.46146i) q^{52} +(1.93939 + 7.23790i) q^{53} +(-0.977053 - 3.64641i) q^{54} +(-4.76800 + 0.520282i) q^{55} +(1.09930 - 4.10264i) q^{56} +(2.36548 - 4.09712i) q^{57} +(-0.662683 + 0.177565i) q^{58} +(-1.59354 - 5.94716i) q^{59} +(0.552203 + 1.42164i) q^{60} +(6.45558 + 1.72977i) q^{61} +(-1.90980 - 7.12748i) q^{62} +(7.61286 - 7.61286i) q^{63} +1.00000 q^{64} +(-9.29246 + 6.80789i) q^{65} +(1.03449 - 1.03449i) q^{66} +(2.37207 + 0.635595i) q^{67} -3.21567i q^{68} +(-0.393674 + 1.46921i) q^{69} +(-5.94755 + 7.40453i) q^{70} +(-6.41760 - 11.1156i) q^{71} +(2.19520 + 1.26740i) 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} +(8.80003 + 2.35796i) q^{77} +(0.909415 - 3.39398i) q^{78} +(0.585692 + 0.156936i) q^{79} +(-2.04634 - 0.901374i) q^{80} +(2.51480 + 4.35577i) q^{81} +0.285995i q^{82} +(-0.951235 - 3.55006i) q^{83} -2.89694i q^{84} +(-2.89852 + 6.58036i) q^{85} +(-6.21303 + 10.7613i) q^{86} +(-0.405241 + 0.233966i) q^{87} +2.14497i q^{88} +(5.82591 - 1.56105i) q^{89} +(-3.34973 - 4.57223i) q^{90} +(21.1353 - 5.66319i) q^{91} +(-1.11504 - 1.93130i) q^{92} +(-2.51641 - 4.35856i) q^{93} +(-3.31722 + 0.888848i) q^{94} +(2.36548 - 15.3286i) q^{95} +(0.658815 - 0.176529i) q^{96} -14.2602i q^{97} +(9.56099 - 5.52004i) q^{98} +(-2.71853 + 4.70864i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{4} + 2 q^{5} + 6 q^{6} - 4 q^{7} + 12 q^{8} + 18 q^{9} - 4 q^{10} - 6 q^{12} + 8 q^{14} - 10 q^{15} - 6 q^{16} - 12 q^{17} - 18 q^{18} - 8 q^{19} + 2 q^{20} + 54 q^{21} - 6 q^{22}+ \cdots + 28 q^{99}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^4 + 2 * q^5 + 6 * q^6 - 4 * q^7 + 12 * q^8 + 18 * q^9 - 4 * q^10 - 6 * q^12 + 8 * q^14 - 10 * q^15 - 6 * q^16 - 12 * q^17 - 18 * q^18 - 8 * q^19 + 2 * q^20 + 54 * q^21 - 6 * q^22 - 4 * q^23 - 14 * q^25 + 18 * q^27 - 4 * q^28 + 4 * q^29 - 4 * q^30 - 2 * q^31 - 6 * q^32 + 20 * q^33 + 12 * q^34 + 6 * q^35 + 14 * q^37 + 16 * q^38 - 30 * q^39 + 2 * q^40 + 12 * q^41 - 54 * q^42 + 44 * q^43 + 6 * q^44 - 60 * q^45 + 2 * q^46 - 28 * q^47 + 6 * q^48 + 24 * q^49 + 10 * q^50 - 8 * q^51 + 8 * q^53 - 18 * q^54 - 4 * q^56 - 28 * q^57 - 14 * q^58 + 14 * q^60 + 24 * q^61 - 14 * q^62 + 8 * q^63 + 12 * q^64 - 10 * q^65 + 8 * q^66 + 18 * q^67 - 40 * q^69 - 30 * q^70 + 18 * q^72 - 28 * q^73 + 38 * q^74 - 30 * q^75 - 8 * q^76 + 10 * q^77 + 48 * q^78 - 56 * q^79 - 4 * q^80 + 4 * q^81 + 14 * q^83 - 28 * q^85 - 22 * q^86 + 18 * q^87 - 2 * q^89 + 18 * q^90 + 38 * q^91 + 2 * q^92 - 16 * q^94 - 28 * q^95 - 6 * q^96 - 24 * q^98 + 28 * q^99

Character values

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

$n$	$261$	$297$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{4}\right)$

Coefficient data

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

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

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

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	−0.176529	+	0.658815i	−0.101919	+	0.380367i	−0.997977	−	0.0635690i	$-0.979752\pi$
$3$	−0.176529	+	0.658815i	−0.101919	+	0.380367i	0.896058	+	0.443936i	$0.146418\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	0.242559	+	2.22287i	0.108476	+	0.994099i
$5$	0.242559	+	2.22287i	0.108476	+	0.994099i
$6$	−0.482286	−	0.482286i	−0.196893	−	0.196893i
$7$	1.09930	−	4.10264i	0.415496	−	1.55065i	−0.368345	−	0.929689i	$-0.620076\pi$
$7$	1.09930	−	4.10264i	0.415496	−	1.55065i	0.783841	−	0.620962i	$-0.213258\pi$
$8$	1.00000			0.353553
$9$	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	$0.895185\pi$
$12$	0.658815	−	0.176529i	0.190184	−	0.0509596i
$13$	2.57582	+	4.46146i	0.714405	+	1.23739i	0.963189	+	0.268826i	$0.0866357\pi$
$13$	2.57582	+	4.46146i	0.714405	+	1.23739i	−0.248784	+	0.968559i	$0.580031\pi$
$14$	3.00334	+	3.00334i	0.802676	+	0.802676i
$15$	−1.50728	−	0.232600i	−0.389179	−	0.0600571i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	2.78485	+	1.60783i	0.675425	+	0.389957i	0.798129	−	0.602486i	$-0.205823\pi$
$17$	2.78485	+	1.60783i	0.675425	+	0.389957i	−0.122704	+	0.992443i	$0.539157\pi$
$18$	−2.19520	+	1.26740i	−0.517414	+	0.298729i
$19$	−6.69996	−	1.79525i	−1.53708	−	0.411858i	−0.611757	−	0.791046i	$-0.709537\pi$
$19$	−6.69996	−	1.79525i	−1.53708	−	0.411858i	−0.925320	+	0.379188i	$0.876204\pi$
$20$	1.80379	−	1.32150i	0.403339	−	0.295496i
$21$	2.50882	+	1.44847i	0.547470	+	0.316082i
$22$	−1.85760	−	1.07248i	−0.396041	−	0.228655i
$23$	2.23008			0.465004			0.232502	−	0.972596i	$-0.425309\pi$
$23$	2.23008			0.465004			0.232502	+	0.972596i	$0.425309\pi$
$24$	−0.176529	+	0.658815i	−0.0360338	+	0.134480i
$25$	−4.88233	+	1.07836i	−0.976466	+	0.215671i
$26$	−5.15165			−1.01032
$27$	−2.66936	+	2.66936i	−0.513718	+	0.513718i
$28$	−4.10264	+	1.09930i	−0.775325	+	0.207748i
$29$	0.485118	+	0.485118i	0.0900841	+	0.0900841i	0.750713	−	0.660629i	$-0.229710\pi$
$29$	0.485118	+	0.485118i	0.0900841	+	0.0900841i	−0.660629	+	0.750713i	$0.729710\pi$
$30$	0.955079	−	1.18904i	0.174373	−	0.217089i
$31$	−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	$0.480566\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.41314	−	0.378650i	−0.245996	−	0.0659144i
$34$	−2.78485	+	1.60783i	−0.477598	+	0.275741i
$35$	9.38628	+	1.44847i	1.58657	+	0.244836i
$36$		−	2.53480i		−	0.422467i
$37$	2.82604	−	5.38642i	0.464598	−	0.885522i
$37$	2.82604	−	5.38642i	0.464598	−	0.885522i
$38$	4.90471	−	4.90471i	0.795649	−	0.795649i
$39$	−3.39398	+	0.909415i	−0.543472	+	0.145623i
$40$	0.242559	+	2.22287i	0.0383519	+	0.351467i
$41$	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	$0.326224\pi$
$42$	−2.50882	+	1.44847i	−0.387120	+	0.223504i
$43$	12.4261			1.89496			0.947478	−	0.319822i	$-0.103623\pi$
$43$	12.4261			1.89496			0.947478	+	0.319822i	$0.103623\pi$
$44$	1.85760	−	1.07248i	0.280043	−	0.161683i
$45$	−2.28480	+	5.18707i	−0.340598	+	0.773243i
$46$	−1.11504	+	1.93130i	−0.164404	+	0.284755i
$47$	2.42838	+	2.42838i	0.354215	+	0.354215i	0.861675	−	0.507460i	$-0.169416\pi$
$47$	2.42838	+	2.42838i	0.354215	+	0.354215i	−0.507460	+	0.861675i	$0.669416\pi$
$48$	−0.482286	−	0.482286i	−0.0696120	−	0.0696120i
$49$	−9.56099	−	5.52004i	−1.36586	−	0.788577i
$50$	1.50728	−	4.76740i	0.213162	−	0.674212i
$51$	−1.55087	+	1.55087i	−0.217166	+	0.217166i
$52$	2.57582	−	4.46146i	0.357202	−	0.618693i
$53$	1.93939	+	7.23790i	0.266396	+	0.994202i	0.961391	+	0.275187i	$0.0887398\pi$
$53$	1.93939	+	7.23790i	0.266396	+	0.994202i	−0.694995	+	0.719014i	$0.744593\pi$
$54$	−0.977053	−	3.64641i	−0.132960	−	0.496214i
$55$	−4.76800	+	0.520282i	−0.642916	+	0.0701547i
$56$	1.09930	−	4.10264i	0.146900	−	0.548238i
$57$	2.36548	−	4.09712i	0.313315	−	0.542677i
$58$	−0.662683	+	0.177565i	−0.0870146	+	0.0233155i
$59$	−1.59354	−	5.94716i	−0.207461	−	0.774254i	−0.988685	−	0.150004i	$-0.952071\pi$
$59$	−1.59354	−	5.94716i	−0.207461	−	0.774254i	0.781225	−	0.624250i	$-0.214595\pi$
$60$	0.552203	+	1.42164i	0.0712891	+	0.183534i
$61$	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	$0.442603\pi$
$62$	−1.90980	−	7.12748i	−0.242545	−	0.905190i
$63$	7.61286	−	7.61286i	0.959130	−	0.959130i
$64$	1.00000			0.125000
$65$	−9.29246	+	6.80789i	−1.15259	+	0.844415i
$66$	1.03449	−	1.03449i	0.127337	−	0.127337i
$67$	2.37207	+	0.635595i	0.289795	+	0.0776503i	0.400788	−	0.916171i	$-0.368736\pi$
$67$	2.37207	+	0.635595i	0.289795	+	0.0776503i	−0.110993	+	0.993821i	$0.535403\pi$
$68$		−	3.21567i		−	0.389957i
$69$	−0.393674	+	1.46921i	−0.0473927	+	0.176872i
$70$	−5.94755	+	7.40453i	−0.710868	+	0.885010i
$71$	−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	$-0.442267\pi$
$72$	2.19520	+	1.26740i	0.258707	+	0.149365i
$73$	−9.49086	−	9.49086i	−1.11082	−	1.11082i	−0.993040	−	0.117781i	$-0.962422\pi$
$73$	−9.49086	−	9.49086i	−1.11082	−	1.11082i	−0.117781	−	0.993040i	$-0.537578\pi$
$74$	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
$77$	8.80003	+	2.35796i	1.00286	+	0.268715i
$78$	0.909415	−	3.39398i	0.102971	−	0.384293i
$79$	0.585692	+	0.156936i	0.0658955	+	0.0176566i	0.291616	−	0.956535i	$-0.405807\pi$
$79$	0.585692	+	0.156936i	0.0658955	+	0.0176566i	−0.225721	+	0.974192i	$0.572474\pi$
$80$	−2.04634	−	0.901374i	−0.228788	−	0.100777i
$81$	2.51480	+	4.35577i	0.279423	+	0.483974i
$82$			0.285995i			0.0315829i
$83$	−0.951235	−	3.55006i	−0.104412	−	0.389669i	0.893866	−	0.448334i	$-0.147982\pi$
$83$	−0.951235	−	3.55006i	−0.104412	−	0.389669i	−0.998278	+	0.0586645i	$0.981316\pi$
$84$		−	2.89694i		−	0.316082i
$85$	−2.89852	+	6.58036i	−0.314389	+	0.713741i
$86$	−6.21303	+	10.7613i	−0.669968	+	1.16042i
$87$	−0.405241	+	0.233966i	−0.0434463	+	0.0250838i
$88$			2.14497i			0.228655i
$89$	5.82591	−	1.56105i	0.617546	−	0.165471i	0.0635339	−	0.997980i	$-0.479763\pi$
$89$	5.82591	−	1.56105i	0.617546	−	0.165471i	0.554012	+	0.832509i	$0.313096\pi$
$90$	−3.34973	−	4.57223i	−0.353093	−	0.481956i
$91$	21.1353	−	5.66319i	2.21558	−	0.593664i
$92$	−1.11504	−	1.93130i	−0.116251	−	0.201352i
$93$	−2.51641	−	4.35856i	−0.260940	−	0.451961i
$94$	−3.31722	+	0.888848i	−0.342146	+	0.0916776i
$95$	2.36548	−	15.3286i	0.242693	−	1.57268i
$96$	0.658815	−	0.176529i	0.0672401	−	0.0180169i
$97$		−	14.2602i		−	1.44791i	−0.689848	−	0.723954i	$-0.742323\pi$
$97$		−	14.2602i		−	1.44791i	0.689848	−	0.723954i	$-0.257677\pi$
$98$	9.56099	−	5.52004i	0.965805	−	0.557608i
$99$	−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	$0.995627\pi$
$102$	−0.567659	−	2.11853i	−0.0562066	−	0.209766i
$103$		−	3.59072i		−	0.353804i	−0.984228	−	0.176902i	$-0.943392\pi$
$103$		−	3.59072i		−	0.353804i	0.984228	−	0.176902i	$-0.0566075\pi$
$104$	2.57582	+	4.46146i	0.252580	+	0.437482i
$105$	−2.61123	+	5.92813i	−0.254830	+	0.578526i
$106$	−7.23790	−	1.93939i	−0.703007	−	0.188370i
$107$	4.13526	−	15.4330i	0.399771	−	1.49197i	−0.413729	−	0.910400i	$-0.635774\pi$
$107$	4.13526	−	15.4330i	0.399771	−	1.49197i	0.813500	−	0.581565i	$-0.197560\pi$
$108$	3.64641	+	0.977053i	0.350876	+	0.0940170i
$109$	−2.04066	−	7.61584i	−0.195460	−	0.729465i	−0.992147	−	0.125074i	$-0.960083\pi$
$109$	−2.04066	−	7.61584i	−0.195460	−	0.729465i	0.796688	−	0.604391i	$-0.206584\pi$
$110$	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
$113$	0.602478	+	0.347841i	0.0566763	+	0.0327221i	0.528070	−	0.849201i	$-0.322916\pi$
$113$	0.602478	+	0.347841i	0.0566763	+	0.0327221i	−0.471394	+	0.881923i	$0.656249\pi$
$114$	2.36548	+	4.09712i	0.221547	+	0.383731i
$115$	0.540925	+	4.95718i	0.0504416	+	0.462260i
$116$	0.177565	−	0.662683i	0.0164865	−	0.0615286i
$117$			13.0584i			1.20725i
$118$	5.94716	+	1.59354i	0.547480	+	0.146697i
$119$	9.65774	−	9.65774i	0.885323	−	0.885323i
$120$	−1.50728	−	0.232600i	−0.137595	−	0.0212334i
$121$	6.39911			0.581737
$122$	−4.72582	+	4.72582i	−0.427855	+	0.427855i
$123$	0.0504864	+	0.188418i	0.00455221	+	0.0169891i
$124$	7.12748	+	1.90980i	0.640066	+	0.171505i
$125$	−3.58130	−	10.5912i	−0.320321	−	0.947309i
$126$	2.78650	+	10.3994i	0.248241	+	0.926449i
$127$	−7.35388	+	1.97047i	−0.652552	+	0.174851i	−0.569882	−	0.821726i	$-0.693011\pi$
$127$	−7.35388	+	1.97047i	−0.652552	+	0.174851i	−0.0826694	+	0.996577i	$0.526345\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−2.19356	+	8.18648i	−0.193132	+	0.720779i
$130$	−1.24958	−	11.4515i	−0.109595	−	1.00436i
$131$	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	$0.676430\pi$
$132$	0.378650	+	1.41314i	0.0329572	+	0.122998i
$133$	−14.7305	+	25.5140i	−1.27730	+	2.21234i
$134$	−1.73648	+	1.73648i	−0.150009	+	0.150009i
$135$	−6.58112	−	5.28617i	−0.566413	−	0.454961i
$136$	2.78485	+	1.60783i	0.238799	+	0.137871i
$137$	−13.4346	−	13.4346i	−1.14779	−	1.14779i	−0.986986	−	0.160807i	$-0.948590\pi$
$137$	−13.4346	−	13.4346i	−1.14779	−	1.14779i	−0.160807	−	0.986986i	$-0.551410\pi$
$138$	−1.07554	−	1.07554i	−0.0915558	−	0.0915558i
$139$	0.119885	−	0.207646i	0.0101685	−	0.0176123i	−0.860896	−	0.508780i	$-0.830097\pi$
$139$	0.119885	−	0.207646i	0.0101685	−	0.0176123i	0.871065	+	0.491168i	$0.163430\pi$
$140$	−3.43873	−	8.85299i	−0.290626	−	0.748215i
$141$	−2.02853	+	1.17117i	−0.170833	+	0.0986306i
$142$	12.8352			1.07711
$143$	−9.56969	+	5.52506i	−0.800257	+	0.462029i
$144$	−2.19520	+	1.26740i	−0.182933	+	0.105617i
$145$	−0.960686	+	1.19603i	−0.0797806	+	0.0993245i
$146$	12.9648	−	3.47389i	1.07297	−	0.287502i
$147$	5.32448	−	5.32448i	0.439156	−	0.439156i
$148$	−6.07779	+	0.245788i	−0.499592	+	0.0202036i
$149$			6.48140i			0.530977i	0.964114	+	0.265488i	$0.0855332\pi$
$149$			6.48140i			0.530977i	−0.964114	+	0.265488i	$0.914467\pi$
$150$	2.87476	+	1.83461i	0.234723	+	0.149795i
$151$	−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	$0.483895\pi$
$152$	−6.69996	−	1.79525i	−0.543439	−	0.145614i
$153$	4.07554	+	7.05904i	0.329488	+	0.570689i
$154$	−6.44207	+	6.44207i	−0.519117	+	0.519117i
$155$	−12.8638	−	10.3326i	−1.03325	−	0.829937i
$156$	2.48457	+	2.48457i	0.198925	+	0.198925i
$157$	−14.0592	+	3.76715i	−1.12205	+	0.300651i	−0.771711	−	0.635973i	$-0.780599\pi$
$157$	−14.0592	+	3.76715i	−1.12205	+	0.300651i	−0.350335	+	0.936624i	$0.613932\pi$
$158$	−0.428756	+	0.428756i	−0.0341100	+	0.0341100i
$159$	−5.11080			−0.405313
$160$	1.80379	−	1.32150i	0.142602	−	0.104474i
$161$	2.45152	−	9.14920i	0.193207	−	0.721058i
$162$	−5.02961			−0.395163
$163$	10.0660	+	5.81158i	0.788426	+	0.455198i	0.839408	−	0.543501i	$-0.182902\pi$
$163$	10.0660	+	5.81158i	0.788426	+	0.455198i	−0.0509818	+	0.998700i	$0.516235\pi$
$164$	−0.247679	−	0.142998i	−0.0193405	−	0.0111662i
$165$	0.498920	−	3.23307i	0.0388409	−	0.251694i
$166$	3.55006	+	0.951235i	0.275538	+	0.0738302i
$167$	1.23250	−	0.711584i	0.0953737	−	0.0550640i	−0.451555	−	0.892244i	$-0.649130\pi$
$167$	1.23250	−	0.711584i	0.0953737	−	0.0550640i	0.546928	+	0.837179i	$0.315797\pi$
$168$	2.50882	+	1.44847i	0.193560	+	0.111752i
$169$	−6.76972	+	11.7255i	−0.520748	+	0.901962i
$170$	−4.24950	−	5.80037i	−0.325922	−	0.444868i
$171$	−12.4325	−	12.4325i	−0.950734	−	0.950734i
$172$	−6.21303	−	10.7613i	−0.473739	−	0.820540i
$173$	−16.8598	+	4.51757i	−1.28183	+	0.343465i	−0.834551	−	0.550931i	$-0.814273\pi$
$173$	−16.8598	+	4.51757i	−1.28183	+	0.343465i	−0.447277	+	0.894396i	$0.647606\pi$
$174$		−	0.467931i		−	0.0354738i
$175$	−0.943036	+	21.2159i	−0.0712868	+	1.60377i
$176$	−1.85760	−	1.07248i	−0.140022	−	0.0808416i
$177$	4.19939			0.315645
$178$	−1.56105	+	5.82591i	−0.117006	+	0.436671i
$179$	2.52136	+	2.52136i	0.188455	+	0.188455i	0.795028	−	0.606573i	$-0.207456\pi$
$179$	2.52136	+	2.52136i	0.188455	+	0.188455i	−0.606573	+	0.795028i	$0.707456\pi$
$180$	5.63454	−	0.614838i	0.419974	−	0.0458273i
$181$	−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	$-0.527189\pi$
$182$	−5.66319	+	21.1353i	−0.419784	+	1.56665i
$183$	−2.27920	+	3.94768i	−0.168483	+	0.291821i
$184$	2.23008			0.164404
$185$	12.6588	+	4.97540i	0.930694	+	0.365799i
$186$	5.03283			0.369025
$187$	−3.44875	+	5.97342i	−0.252198	+	0.436820i
$188$	0.888848	−	3.31722i	0.0648259	−	0.241933i
$189$	8.01699	+	13.8858i	0.583150	+	1.01005i
$190$	12.0922	+	9.71287i	0.877263	+	0.704646i
$191$	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	$0.726335\pi$
$192$	−0.176529	+	0.658815i	−0.0127399	+	0.0475459i
$193$	5.87874			0.423161			0.211580	−	0.977361i	$-0.432139\pi$
$193$	5.87874			0.423161			0.211580	+	0.977361i	$0.432139\pi$
$194$	12.3497	+	7.13012i	0.886659	+	0.511913i
$195$	−2.84476	−	7.32381i	−0.203717	−	0.524469i
$196$			11.0401i			0.788577i
$197$	24.0934	−	6.45581i	1.71658	−	0.459957i	0.739561	−	0.673090i	$-0.235033\pi$
$197$	24.0934	−	6.45581i	1.71658	−	0.459957i	0.977023	+	0.213133i	$0.0683666\pi$
$198$	−2.71853	−	4.70864i	−0.193198	−	0.334628i
$199$	−17.8265	−	17.8265i	−1.26369	−	1.26369i	−0.949293	−	0.314393i	$-0.898199\pi$
$199$	−17.8265	−	17.8265i	−1.26369	−	1.26369i	−0.314393	−	0.949293i	$-0.601801\pi$
$200$	−4.88233	+	1.07836i	−0.345233	+	0.0762512i
$201$	−0.837480	+	1.45056i	−0.0590713	+	0.102314i
$202$	−0.239132	−	0.138063i	−0.0168252	−	0.00971406i
$203$	2.52355	−	1.45697i	0.177119	−	0.102259i
$204$	2.11853	+	0.567659i	0.148327	+	0.0397441i
$205$	0.377942	+	0.515874i	0.0263966	+	0.0360302i
$206$	3.10965	+	1.79536i	0.216660	+	0.125089i
$207$	4.89547	+	2.82640i	0.340259	+	0.196448i
$208$	−5.15165			−0.357202
$209$	3.85076	−	14.3712i	0.266362	−	0.994078i
$210$	−3.82830	−	5.22545i	−0.264178	−	0.360591i
$211$	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
$213$	8.45603	−	2.26579i	0.579398	−	0.155249i
$214$	11.2978	+	11.2978i	0.772298	+	0.772298i
$215$	3.01405	+	27.6215i	0.205556	+	1.88377i
$216$	−2.66936	+	2.66936i	−0.181627	+	0.181627i
$217$	15.6704	+	27.1420i	1.06378	+	1.84252i
$218$	7.61584	+	2.04066i	0.515810	+	0.138211i
$219$	7.92813	−	4.57731i	0.535734	−	0.309306i
$220$	2.83457	+	3.86906i	0.191107	+	0.260852i
$221$			16.5660i			1.11435i
$222$	−3.96076	+	1.23484i	−0.265829	+	0.0828768i
$223$	5.22436	−	5.22436i	0.349849	−	0.349849i	−0.510204	−	0.860053i	$-0.670430\pi$
$223$	5.22436	−	5.22436i	0.349849	−	0.349849i	0.860053	+	0.510204i	$0.170430\pi$
$224$	−4.10264	+	1.09930i	−0.274119	+	0.0734499i
$225$	−12.0844	−	3.82066i	−0.805627	−	0.254711i
$226$	−0.602478	+	0.347841i	−0.0400762	+	0.0231380i
$227$	−7.91126	+	4.56757i	−0.525089	+	0.303160i	−0.739014	−	0.673690i	$-0.764708\pi$
$227$	−7.91126	+	4.56757i	−0.525089	+	0.303160i	0.213925	+	0.976850i	$0.431375\pi$
$228$	−4.73095			−0.313315
$229$	3.08729	−	1.78245i	0.204014	−	0.117787i	−0.394512	−	0.918891i	$-0.629087\pi$
$229$	3.08729	−	1.78245i	0.204014	−	0.117787i	0.598526	+	0.801103i	$0.295753\pi$
$230$	−4.56351	−	2.01014i	−0.300909	−	0.132544i
$231$	−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	$-0.0445604\pi$
$233$	12.9851	+	12.9851i	0.850683	+	0.850683i	−0.139534	+	0.990217i	$0.544560\pi$
$234$	−11.3089	−	6.52919i	−0.739286	−	0.426827i
$235$	−4.80895	+	5.98700i	−0.313701	+	0.390549i
$236$	−4.35362	+	4.35362i	−0.283397	+	0.283397i
$237$	−0.206783	+	0.358159i	−0.0134320	+	0.0232649i
$238$	3.53498	+	13.1927i	0.229139	+	0.855157i
$239$	3.67854	+	13.7285i	0.237945	+	0.888022i	0.976799	+	0.214157i	$0.0687004\pi$
$239$	3.67854	+	13.7285i	0.237945	+	0.888022i	−0.738855	+	0.673865i	$0.764633\pi$
$240$	0.955079	−	1.18904i	0.0616501	−	0.0767525i
$241$	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	$0.0170332\pi$
$242$	−3.19955	+	5.54179i	−0.205675	+	0.356240i
$243$	−14.2528	+	3.81903i	−0.914319	+	0.244991i
$244$	−1.72977	−	6.45558i	−0.110737	−	0.413276i
$245$	9.95124	−	22.5918i	0.635761	−	1.44334i
$246$	−0.188418	−	0.0504864i	−0.0120131	−	0.00321890i
$247$	−9.24849	−	34.5158i	−0.588467	−	2.19619i
$248$	−5.21767	+	5.21767i	−0.331323	+	0.331323i
$249$	2.50675			0.158859
$250$	10.9629	+	2.19412i	0.693357	+	0.138768i
$251$	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	$0.0242012\pi$
$252$	−10.3994	−	2.78650i	−0.655098	−	0.175533i
$253$			4.78345i			0.300733i
$254$	1.97047	−	7.35388i	0.123638	−	0.461424i
$255$	−3.82357	−	3.07122i	−0.239441	−	0.192327i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.261814	+	0.151158i	0.0163315	+	0.00942900i	0.508144	−	0.861272i	$-0.330332\pi$
$257$	0.261814	+	0.151158i	0.0163315	+	0.00942900i	−0.491812	+	0.870701i	$0.663665\pi$
$258$	−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
$262$	−15.1480	−	4.05890i	−0.935848	−	0.250760i
$263$	7.70063	−	28.7392i	0.474841	−	1.77213i	−0.147156	−	0.989113i	$-0.547012\pi$
$263$	7.70063	−	28.7392i	0.474841	−	1.77213i	0.621998	−	0.783019i	$-0.286321\pi$
$264$	−1.41314	−	0.378650i	−0.0869727	−	0.0233043i
$265$	−15.6185	+	6.06663i	−0.959438	+	0.372670i
$266$	−14.7305	−	25.5140i	−0.903185	−	1.56436i
$267$			4.11377i			0.251759i
$268$	−0.635595	−	2.37207i	−0.0388252	−	0.144898i
$269$			2.24109i			0.136642i	0.997663	+	0.0683209i	$0.0217642\pi$
$269$			2.24109i			0.136642i	−0.997663	+	0.0683209i	$0.978236\pi$
$270$	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	$0.241425\pi$
$272$	−2.78485	+	1.60783i	−0.168856	+	0.0974892i
$273$			14.9240i			0.903241i
$274$	18.3520	−	4.91739i	1.10868	−	0.297071i
$275$	−2.31304	−	10.4725i	−0.139482	−	0.631513i
$276$	1.46921	−	0.393674i	0.0884361	−	0.0236964i
$277$	3.79766	+	6.57774i	0.228179	+	0.395218i	0.957269	−	0.289201i	$-0.0933894\pi$
$277$	3.79766	+	6.57774i	0.228179	+	0.395218i	−0.729089	+	0.684419i	$0.760056\pi$
$278$	0.119885	+	0.207646i	0.00719020	+	0.0124538i
$279$	−18.0667	+	4.84096i	−1.08163	+	0.289821i
$280$	9.38628	+	1.44847i	0.560938	+	0.0865626i
$281$	−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	$0.787147\pi$
$282$		−	2.34235i		−	0.139485i
$283$	−0.789334	+	0.455722i	−0.0469210	+	0.0270899i	−0.523277	−	0.852163i	$-0.675291\pi$
$283$	−0.789334	+	0.455722i	−0.0469210	+	0.0270899i	0.476356	+	0.879253i	$0.341957\pi$
$284$	−6.41760	+	11.1156i	−0.380815	+	0.659590i
$285$	9.68116	+	4.26436i	0.573462	+	0.252599i
$286$		−	11.0501i		−	0.653407i
$287$	−0.314394	−	1.17333i	−0.0185581	−	0.0692597i
$288$		−	2.53480i		−	0.149365i
$289$	−3.32974	−	5.76728i	−0.195867	−	0.339252i
$290$	−0.555445	−	1.42999i	−0.0326169	−	0.0839720i
$291$	9.39487	+	2.51735i	0.550737	+	0.147570i
$292$	−3.47389	+	12.9648i	−0.203294	+	0.758705i
$293$	19.2117	+	5.14775i	1.12236	+	0.300735i	0.771837	−	0.635820i	$-0.219338\pi$
$293$	19.2117	+	5.14775i	1.12236	+	0.300735i	0.350520	+	0.936555i	$0.386005\pi$
$294$	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
$298$	−5.61305	−	3.24070i	−0.325155	−	0.187729i
$299$	5.74429	+	9.94940i	0.332201	+	0.575388i
$300$	−3.02619	+	1.57231i	−0.174717	+	0.0907774i
$301$	13.6599	−	50.9796i	0.787345	−	2.93841i
$302$		−	11.1961i		−	0.644261i
$303$	−0.181916	−	0.0487442i	−0.0104508	−	0.00280028i
$304$	4.90471	−	4.90471i	0.281305	−	0.281305i
$305$	−2.27920	+	14.7695i	−0.130506	+	0.845700i
$306$	−8.15107			−0.465966
$307$	−9.95227	+	9.95227i	−0.568006	+	0.568006i	−0.931570	−	0.363563i	$-0.881560\pi$
$307$	−9.95227	+	9.95227i	−0.568006	+	0.568006i	0.363563	+	0.931570i	$0.381560\pi$
$308$	−2.35796	−	8.80003i	−0.134357	−	0.501428i
$309$	2.36562	+	0.633866i	0.134575	+	0.0360594i
$310$	15.3802	−	5.97408i	0.873539	−	0.339305i
$311$	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	$0.683654\pi$
$312$	−3.39398	+	0.909415i	−0.192146	+	0.0514855i
$313$	6.25706	−	10.8376i	0.353670	−	0.612575i	−0.633219	−	0.773972i	$-0.718267\pi$
$313$	6.25706	−	10.8376i	0.353670	−	0.612575i	0.986889	+	0.161398i	$0.0516002\pi$
$314$	3.76715	−	14.0592i	0.212593	−	0.793407i
$315$	18.7690	+	15.0759i	1.05751	+	0.849428i
$316$	−0.156936	−	0.585692i	−0.00882832	−	0.0329477i
$317$	4.05859	+	15.1469i	0.227953	+	0.850734i	0.981200	+	0.192995i	$0.0618201\pi$
$317$	4.05859	+	15.1469i	0.227953	+	0.850734i	−0.753246	+	0.657739i	$0.771513\pi$
$318$	2.55540	−	4.42608i	0.143300	−	0.248202i
$319$	−1.04056	+	1.04056i	−0.0582603	+	0.0582603i
$320$	0.242559	+	2.22287i	0.0135595	+	0.124262i
$321$	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
$325$	−17.3871	−	19.0046i	−0.964460	−	1.05419i
$326$	−10.0660	+	5.81158i	−0.557502	+	0.321874i
$327$	5.37767			0.297386
$328$	0.247679	−	0.142998i	0.0136758	−	0.00789572i
$329$	12.6323	−	7.29324i	0.696439	−	0.402089i
$330$	2.55046	+	2.04861i	0.140398	+	0.112773i
$331$	−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
$333$	13.0305	−	8.24255i	0.714065	−	0.451689i
$334$			1.42317i			0.0778723i
$335$	−0.837480	+	5.42699i	−0.0457564	+	0.296508i
$336$	−2.50882	+	1.44847i	−0.136867	+	0.0790205i
$337$	−6.70249	−	1.79593i	−0.365108	−	0.0978303i	0.0716008	−	0.997433i	$-0.477189\pi$
$337$	−6.70249	−	1.79593i	−0.365108	−	0.0978303i	−0.436709	+	0.899603i	$0.643856\pi$
$338$	−6.76972	−	11.7255i	−0.368224	−	0.637783i
$339$	−0.335518	+	0.335518i	−0.0182228	+	0.0182228i
$340$	7.14802	−	0.779989i	0.387656	−	0.0423008i
$341$	−11.1918	−	11.1918i	−0.606067	−	0.606067i
$342$	16.9831	−	4.55060i	0.918339	−	0.246068i
$343$	−12.1337	+	12.1337i	−0.655159	+	0.655159i
$344$	12.4261			0.669968
$345$	−3.36136	−	0.518717i	−0.180969	−	0.0279268i
$346$	4.51757	−	16.8598i	0.242866	−	0.906389i
$347$	10.3061			0.553259			0.276629	−	0.960977i	$-0.410783\pi$
$347$	10.3061			0.553259			0.276629	+	0.960977i	$0.410783\pi$
$348$	0.405241	+	0.233966i	0.0217232	+	0.0125419i
$349$	7.88832	+	4.55432i	0.422252	+	0.243787i	0.696040	−	0.718003i	$-0.254943\pi$
$349$	7.88832	+	4.55432i	0.422252	+	0.243787i	−0.273788	+	0.961790i	$0.588277\pi$
$350$	−17.9020	−	11.4246i	−0.956900	−	0.610672i
$351$	−18.7850	−	5.03343i	−1.00267	−	0.268665i
$352$	1.85760	−	1.07248i	0.0990103	−	0.0571636i
$353$	−2.73444	−	1.57873i	−0.145540	−	0.0840274i	0.425462	−	0.904976i	$-0.360112\pi$
$353$	−2.73444	−	1.57873i	−0.145540	−	0.0840274i	−0.571002	+	0.820949i	$0.693445\pi$
$354$	−2.09969	+	3.63677i	−0.111597	+	0.193292i
$355$	23.1519	−	16.9617i	1.22878	−	0.900234i
$356$	−4.26487	−	4.26487i	−0.226037	−	0.226037i
$357$	4.65779	+	8.06754i	0.246517	+	0.426979i
$358$	−3.44425	+	0.922883i	−0.182034	+	0.0487759i
$359$			0.295823i			0.0156129i	0.999970	+	0.00780646i	$0.00248490\pi$
$359$			0.295823i			0.0156129i	−0.999970	+	0.00780646i	$0.997515\pi$
$360$	−2.28480	+	5.18707i	−0.120420	+	0.273383i
$361$	25.2121	+	14.5562i	1.32695	+	0.766116i
$362$	24.3652			1.28061
$363$	−1.12963	+	4.21583i	−0.0592901	+	0.221274i
$364$	−15.4721	−	15.4721i	−0.810960	−	0.810960i
$365$	18.7949	−	23.3991i	0.983769	−	1.22476i
$366$	−2.27920	−	3.94768i	−0.119136	−	0.206349i
$367$	−5.81490	+	21.7015i	−0.303535	+	1.13281i	0.630663	+	0.776056i	$0.282783\pi$
$367$	−5.81490	+	21.7015i	−0.303535	+	1.13281i	−0.934199	+	0.356753i	$0.883884\pi$
$368$	−1.11504	+	1.93130i	−0.0581254	+	0.100676i
$369$	0.724940			0.0377389
$370$	−10.6382	+	8.47515i	−0.553055	+	0.440602i
$371$	31.8264			1.65235
$372$	−2.51641	+	4.35856i	−0.130470	+	0.225981i
$373$	5.72439	−	21.3637i	0.296398	−	1.10617i	−0.643703	−	0.765275i	$-0.722603\pi$
$373$	5.72439	−	21.3637i	0.296398	−	1.10617i	0.940101	−	0.340896i	$-0.110730\pi$
$374$	−3.44875	−	5.97342i	−0.178331	−	0.308878i
$375$	7.60987	−	0.489755i	0.392972	−	0.0252908i
$376$	2.42838	+	2.42838i	0.125234	+	0.125234i
$377$	−0.914754	+	3.41391i	−0.0471122	+	0.175825i
$378$	−16.0340			−0.824698
$379$	8.58408	+	4.95602i	0.440935	+	0.254574i	0.703994	−	0.710206i	$-0.251398\pi$
$379$	8.58408	+	4.95602i	0.440935	+	0.254574i	−0.263059	+	0.964780i	$0.584731\pi$
$380$	−14.4577	+	5.61575i	−0.741665	+	0.288082i
$381$		−	5.19270i		−	0.266030i
$382$	−1.98312	+	0.531374i	−0.101465	+	0.0271875i
$383$	−15.8376	−	27.4315i	−0.809262	−	1.40168i	−0.913376	−	0.407118i	$-0.866534\pi$
$383$	−15.8376	−	27.4315i	−0.809262	−	1.40168i	0.104114	−	0.994565i	$-0.466799\pi$
$384$	−0.482286	−	0.482286i	−0.0246116	−	0.0246116i
$385$	−3.10692	+	20.1333i	−0.158343	+	1.02609i
$386$	−2.93937	+	5.09114i	−0.149610	+	0.259132i
$387$	27.2777	+	15.7488i	1.38660	+	0.800555i
$388$	−12.3497	+	7.13012i	−0.626963	+	0.361977i
$389$	−32.1209	−	8.60677i	−1.62859	−	0.436380i	−0.675084	−	0.737741i	$-0.735893\pi$
$389$	−32.1209	−	8.60677i	−1.62859	−	0.436380i	−0.953510	+	0.301360i	$0.902559\pi$
$390$	7.76498	+	1.19827i	0.393195	+	0.0606769i
$391$	6.21043	+	3.58560i	0.314075	+	0.181331i
$392$	−9.56099	−	5.52004i	−0.482903	−	0.278804i
$393$	−10.6963			−0.539555
$394$	−6.45581	+	24.0934i	−0.325239	+	1.21381i
$395$	−0.206783	+	1.33998i	−0.0104044	+	0.0674219i
$396$	5.43707			0.273223
$397$	−25.5772	+	25.5772i	−1.28368	+	1.28368i	−0.345124	+	0.938557i	$0.612163\pi$
$397$	−25.5772	+	25.5772i	−1.28368	+	1.28368i	−0.938557	+	0.345124i	$0.887837\pi$
$398$	24.3514	−	6.52495i	1.22063	−	0.327066i
$399$	−14.2086	−	14.2086i	−0.711322	−	0.711322i
$400$	1.50728	−	4.76740i	0.0753641	−	0.238370i
$401$	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	$0.105353\pi$
$402$	−0.837480	−	1.45056i	−0.0417697	−	0.0723473i
$403$	−36.7182	−	9.83862i	−1.82907	−	0.490097i
$404$	0.239132	−	0.138063i	0.0118972	−	0.00686888i
$405$	−9.07233	+	6.64662i	−0.450808	+	0.330273i
$406$			2.91395i			0.144617i
$407$	11.5537	+	6.06177i	0.572696	+	0.300471i
$408$	−1.55087	+	1.55087i	−0.0767796	+	0.0767796i
$409$	22.5508	−	6.04247i	1.11507	−	0.298781i	0.346181	−	0.938168i	$-0.387478\pi$
$409$	22.5508	−	6.04247i	1.11507	−	0.298781i	0.768885	+	0.639387i	$0.220812\pi$
$410$	−0.635731	+	0.0693707i	−0.0313965	+	0.00342597i
$411$	11.2225	−	6.47931i	0.553565	−	0.319601i
$412$	−3.10965	+	1.79536i	−0.153202	+	0.0884509i
$413$	−26.1508			−1.28680
$414$	−4.89547	+	2.82640i	−0.240599	+	0.138910i
$415$	7.66060	−	2.97557i	0.376044	−	0.146065i
$416$	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	0.949008	−	0.315253i	$-0.102089\pi$
$419$	23.5500	+	13.5966i	1.15049	+	0.664238i	0.201487	+	0.979491i	$0.435423\pi$
$420$	6.43953	−	0.702678i	0.314217	−	0.0342872i
$421$	−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	$0.334423\pi$
$422$	−3.01630	+	5.22439i	−0.146831	+	0.254319i
$423$	2.25305	+	8.40850i	0.109547	+	0.408835i
$424$	1.93939	+	7.23790i	0.0941850	+	0.351503i
$425$	−15.3304	−	4.84692i	−0.743632	−	0.235110i
$426$	−2.26579	+	8.45603i	−0.109778	+	0.409696i
$427$	14.1932	−	24.5834i	0.686858	−	1.18967i
$428$	−15.4330	+	4.13526i	−0.745983	+	0.199886i
$429$	−1.95067	−	7.27999i	−0.0941791	−	0.351481i
$430$	−25.4280	−	11.2005i	−1.22625	−	0.540137i
$431$	−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	$0.681651\pi$
$432$	−0.977053	−	3.64641i	−0.0470085	−	0.175438i
$433$	11.1419	−	11.1419i	0.535445	−	0.535445i	−0.386743	−	0.922188i	$-0.626400\pi$
$433$	11.1419	−	11.1419i	0.535445	−	0.535445i	0.922188	+	0.386743i	$0.126400\pi$
$434$	−31.3409			−1.50441
$435$	−0.618371	−	0.844048i	−0.0296486	−	0.0404690i
$436$	−5.57518	+	5.57518i	−0.267003	+	0.267003i
$437$	−14.9414	−	4.00355i	−0.714746	−	0.191516i
$438$			9.15462i			0.437425i
$439$	6.68433	−	24.9462i	0.319025	−	1.19062i	−0.601157	−	0.799131i	$-0.705294\pi$
$439$	6.68433	−	24.9462i	0.319025	−	1.19062i	0.920183	−	0.391489i	$-0.128040\pi$
$440$	−4.76800	+	0.520282i	−0.227305	+	0.0248034i
$441$	−13.9922	−	24.2352i	−0.666295	−	1.15406i
$442$	−14.3466	−	8.28299i	−0.682396	−	0.393982i
$443$	−4.30555	−	4.30555i	−0.204563	−	0.204563i	0.597389	−	0.801952i	$-0.296205\pi$
$443$	−4.30555	−	4.30555i	−0.204563	−	0.204563i	−0.801952	+	0.597389i	$0.796205\pi$
$444$	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
$447$	−4.27004	−	1.14415i	−0.201966	−	0.0541167i
$448$	1.09930	−	4.10264i	0.0519369	−	0.193831i
$449$	5.71034	+	1.53008i	0.269488	+	0.0722090i	0.391032	−	0.920377i	$-0.372118\pi$
$449$	5.71034	+	1.53008i	0.269488	+	0.0722090i	−0.121545	+	0.992586i	$0.538785\pi$
$450$	9.35099	−	8.55507i	0.440810	−	0.403290i
$451$	0.306725	+	0.531264i	0.0144431	+	0.0250162i
$452$		−	0.695681i		−	0.0327221i
$453$	−1.97643	−	7.37614i	−0.0928608	−	0.346561i
$454$		−	9.13514i		−	0.428733i
$455$	17.7151	+	45.6075i	0.830498	+	2.13811i
$456$	2.36548	−	4.09712i	0.110774	−	0.191865i
$457$	25.4227	−	14.6778i	1.18922	−	0.686598i	0.231093	−	0.972932i	$-0.425770\pi$
$457$	25.4227	−	14.6778i	1.18922	−	0.686598i	0.958130	+	0.286333i	$0.0924365\pi$
$458$			3.56490i			0.166577i
$459$	−11.7256	+	3.14188i	−0.547306	+	0.146650i
$460$	4.02258	−	2.94705i	0.187554	−	0.137407i
$461$	−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	$0.724283\pi$
$462$	−3.10692	−	5.38135i	−0.144547	−	0.250363i
$463$	13.0019	+	22.5200i	0.604251	+	1.04659i	0.992169	+	0.124899i	$0.0398607\pi$
$463$	13.0019	+	22.5200i	0.604251	+	1.04659i	−0.387919	+	0.921693i	$0.626806\pi$
$464$	−0.662683	+	0.177565i	−0.0307643	+	0.00824327i
$465$	9.07814	−	6.65088i	0.420989	−	0.308427i
$466$	−17.7380	+	4.75288i	−0.821697	+	0.220173i
$467$			25.1172i			1.16229i	0.813802	+	0.581143i	$0.197394\pi$
$467$			25.1172i			1.16229i	−0.813802	+	0.581143i	$0.802606\pi$
$468$	11.3089	−	6.52919i	0.522754	−	0.301812i
$469$	5.21523	−	9.03305i	0.240817	−	0.417107i
$470$	−2.78042	−	7.15817i	−0.128251	−	0.330182i
$471$		−	9.92743i		−	0.457432i
$472$	−1.59354	−	5.94716i	−0.0733484	−	0.273740i
$473$			26.6535i			1.22553i
$474$	−0.206783	−	0.358159i	−0.00949787	−	0.0164508i
$475$	34.6473	+	1.54006i	1.58973	+	0.0706628i
$476$	−13.1927	−	3.53498i	−0.604687	−	0.162025i
$477$	−4.91596	+	18.3466i	−0.225086	+	0.840034i
$478$	−13.7285	−	3.67854i	−0.627926	−	0.168252i
$479$	7.38625	+	27.5659i	0.337486	+	1.25952i	0.901148	+	0.433511i	$0.142725\pi$
$479$	7.38625	+	27.5659i	0.337486	+	1.25952i	−0.563662	+	0.826005i	$0.690608\pi$
$480$	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
$483$	5.59487	+	3.23020i	0.254575	+	0.146979i
$484$	−3.19955	−	5.54179i	−0.145434	−	0.251899i
$485$	31.6987	−	3.45895i	1.43936	−	0.157063i
$486$	3.81903	−	14.2528i	0.173235	−	0.646521i
$487$		−	14.0181i		−	0.635222i	−0.948221	−	0.317611i	$-0.897119\pi$
$487$		−	14.0181i		−	0.635222i	0.948221	−	0.317611i	$-0.102881\pi$
$488$	6.45558	+	1.72977i	0.292231	+	0.0783030i
$489$	−5.60569	+	5.60569i	−0.253498	+	0.253498i
$490$	14.5894	+	19.9139i	0.659084	+	0.899619i
$491$	−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
$493$	0.570991	+	2.13097i	0.0257162	+	0.0959740i
$494$	34.5158	+	9.24849i	1.55294	+	0.416109i
$495$	−11.1261	−	4.90083i	−0.500082	−	0.220276i
$496$	−1.90980	−	7.12748i	−0.0857526	−	0.320033i
$497$	−52.6582	+	14.1097i	−2.36204	+	0.632907i
$498$	−1.25338	+	2.17091i	−0.0561652	+	0.0972809i
$499$	8.46237	−	31.5820i	0.378828	−	1.41380i	−0.468843	−	0.883281i	$-0.655329\pi$
$499$	8.46237	−	31.5820i	0.378828	−	1.41380i	0.847671	−	0.530522i	$-0.178004\pi$
$500$	−7.38163	+	8.39712i	−0.330117	+	0.375530i
$501$	0.251231	+	0.937605i	0.0112242	+	0.0418891i
$502$	5.34171	+	19.9355i	0.238412	+	0.889766i
$503$	−15.7329	+	27.2503i	−0.701497	+	1.21503i	0.266444	+	0.963851i	$0.414151\pi$
$503$	−15.7329	+	27.2503i	−0.701497	+	1.21503i	−0.967941	+	0.251178i	$0.919182\pi$
$504$	7.61286	−	7.61286i	0.339104	−	0.339104i
$505$	−0.613792	+	0.0669767i	−0.0273134	+	0.00298042i
$506$	−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	−0.990615	−	0.136683i	$-0.956356\pi$
$509$	−8.50407	+	14.7295i	−0.376936	+	0.652872i	0.613679	+	0.789556i	$0.289689\pi$
$510$	4.57154	−	1.77570i	0.202431	−	0.0786294i
$511$	−49.3708	+	28.5042i	−2.18404	+	1.26095i
$512$	1.00000			0.0441942
$513$	22.6768	−	13.0924i	1.00120	−	0.578045i
$514$	−0.261814	+	0.151158i	−0.0115481	+	0.00666731i
$515$	7.98171	−	0.870960i	0.351716	−	0.0383791i
$516$	8.18648	−	2.19356i	0.360389	−	0.0965661i
$517$	−5.20880	+	5.20880i	−0.229083	+	0.229083i
$518$	24.6648	−	7.68968i	1.08371	−	0.337865i
$519$		−	11.9050i		−	0.522571i
$520$	−9.29246	+	6.80789i	−0.407501	+	0.298546i
$521$	−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	$0.528709\pi$
$522$	−1.67977	−	0.450093i	−0.0735215	−	0.0197000i
$523$	−5.13103	−	8.88721i	−0.224364	−	0.388611i	0.731764	−	0.681558i	$-0.238697\pi$
$523$	−5.13103	−	8.88721i	−0.224364	−	0.388611i	−0.956129	+	0.292947i	$0.905364\pi$
$524$	11.0891	−	11.0891i	0.484431	−	0.484431i
$525$	−13.8109	−	4.36650i	−0.602755	−	0.190570i
$526$	21.0385	+	21.0385i	0.917323	+	0.917323i
$527$	−22.9196	+	6.14129i	−0.998393	+	0.267519i
$528$	1.03449	−	1.03449i	0.0450204	−	0.0450204i
$529$	−18.0267			−0.783772
$530$	2.55540	−	16.5593i	0.110999	−	0.719292i
$531$	4.03929	−	15.0749i	0.175290	−	0.654193i
$532$	29.4610			1.27730
$533$	1.27595	+	0.736673i	0.0552677	+	0.0319088i
$534$	−3.56263	−	2.05689i	−0.154170	−	0.0890102i
$535$	35.3087	+	5.44875i	1.52653	+	0.235570i
$536$	2.37207	+	0.635595i	0.102458	+	0.0274535i
$537$	−2.10621	+	1.21602i	−0.0908895	+	0.0524751i
$538$	−1.94084	−	1.12055i	−0.0836756	−	0.0483102i
$539$	11.8403	−	20.5080i	0.509998	−	0.883343i
$540$	−1.28740	+	8.34250i	−0.0554007	+	0.359004i
$541$	−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	$0.915317\pi$
$542$	−3.83082	−	6.63517i	−0.164548	−	0.285005i
$543$	16.0522	−	4.30116i	0.688864	−	0.184581i
$544$		−	3.21567i		−	0.137871i
$545$	16.4341	−	6.38342i	0.703958	−	0.273436i
$546$	−12.9246	−	7.46200i	−0.553120	−	0.319344i
$547$	−18.0278			−0.770814			−0.385407	−	0.922747i	$-0.625939\pi$
$547$	−18.0278			−0.770814			−0.385407	+	0.922747i	$0.625939\pi$
$548$	−4.91739	+	18.3520i	−0.210061	+	0.783957i
$549$	11.9790	+	11.9790i	0.511251	+	0.511251i
$550$	10.2259	+	3.23307i	0.436035	+	0.137859i
$551$	−2.37936	−	4.12118i	−0.101364	−	0.175568i
$552$	−0.393674	+	1.46921i	−0.0167559	+	0.0625337i
$553$	1.28770	−	2.23036i	0.0547586	−	0.0948446i
$554$	−7.59532			−0.322694
$555$	−5.51252	+	7.46151i	−0.233993	+	0.316724i
$556$	−0.239769			−0.0101685
$557$	−15.4480	+	26.7567i	−0.654552	+	1.13372i	0.327454	+	0.944867i	$0.393809\pi$
$557$	−15.4480	+	26.7567i	−0.654552	+	1.13372i	−0.982006	+	0.188850i	$0.939524\pi$
$558$	4.84096	−	18.0667i	0.204934	−	0.764825i
$559$	32.0073	+	55.4383i	1.35376	+	2.34479i
$560$	−5.94755	+	7.40453i	−0.251330	+	0.312898i
$561$	−3.32658	−	3.32658i	−0.140448	−	0.140448i
$562$	7.96873	−	29.7397i	0.336141	−	1.25449i
$563$	−3.58859			−0.151241			−0.0756205	−	0.997137i	$-0.524094\pi$
$563$	−3.58859			−0.151241			−0.0756205	+	0.997137i	$0.524094\pi$
$564$	2.02853	+	1.17117i	0.0854166	+	0.0493153i
$565$	−0.627069	+	1.42360i	−0.0263810	+	0.0598914i
$566$		−	0.911444i		−	0.0383108i
$567$	20.6346	−	5.52904i	0.866574	−	0.232198i
$568$	−6.41760	−	11.1156i	−0.269277	−	0.466401i
$569$	18.3582	+	18.3582i	0.769616	+	0.769616i	0.978039	−	0.208423i	$-0.0668330\pi$
$569$	18.3582	+	18.3582i	0.769616	+	0.769616i	−0.208423	+	0.978039i	$0.566833\pi$
$570$	−8.53362	+	6.25195i	−0.357434	+	0.261865i
$571$	−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	$0.878687\pi$
$572$	9.56969	+	5.52506i	0.400129	+	0.231014i
$573$	−1.21270	+	0.700155i	−0.0506614	+	0.0292494i
$574$	1.17333	+	0.314394i	0.0489740	+	0.0131225i
$575$	−10.8880	+	2.40482i	−0.454060	+	0.100288i
$576$	2.19520	+	1.26740i	0.0914667	+	0.0528083i
$577$	25.0238	+	14.4475i	1.04175	+	0.601456i	0.920329	−	0.391145i	$-0.127921\pi$
$577$	25.0238	+	14.4475i	1.04175	+	0.601456i	0.121423	+	0.992601i	$0.461254\pi$
$578$	6.65948			0.276998
$579$	−1.03777	+	3.87300i	−0.0431282	+	0.160957i
$580$	1.51613	+	0.233966i	0.0629539	+	0.00971490i
$581$	−15.6103			−0.647624
$582$	−6.87752	+	6.87752i	−0.285082	+	0.285082i
$583$	−15.5251	+	4.15993i	−0.642983	+	0.172287i
$584$	−9.49086	−	9.49086i	−0.392734	−	0.392734i
$585$	−29.0271	+	3.16743i	−1.20012	+	0.130957i
$586$	−14.0639	+	14.0639i	−0.580975	+	0.580975i
$587$	17.5250	+	30.3542i	0.723335	+	1.25285i	0.959656	+	0.281178i	$0.0907250\pi$
$587$	17.5250	+	30.3542i	0.723335	+	1.25285i	−0.236321	+	0.971675i	$0.575942\pi$
$588$	−7.27337	−	1.94889i	−0.299949	−	0.0803710i
$589$	44.3252	−	25.5912i	1.82639	−	1.05447i
$590$	−2.09969	+	13.6063i	−0.0864430	+	0.560163i
$591$			17.0127i			0.699811i
$592$	3.25176	+	5.14063i	0.133646	+	0.211279i
$593$	30.2234	−	30.2234i	1.24113	−	1.24113i	0.281593	−	0.959534i	$-0.409137\pi$
$593$	30.2234	−	30.2234i	1.24113	−	1.24113i	0.959534	−	0.281593i	$-0.0908627\pi$
$594$	7.82144	−	2.09575i	0.320918	−	0.0859896i
$595$	23.8105	+	19.1254i	0.976135	+	0.784063i
$596$	5.61305	−	3.24070i	0.229920	−	0.132744i
$597$	14.8913	−	8.59747i	0.609459	−	0.351871i
$598$	−11.4886			−0.469803
$599$	−20.7282	+	11.9674i	−0.846932	+	0.488976i	−0.859614	−	0.510943i	$-0.829296\pi$
$599$	−20.7282	+	11.9674i	−0.846932	+	0.488976i	0.0126828	+	0.999920i	$0.495963\pi$
$600$	0.151436	−	3.40692i	0.00618235	−	0.139087i
$601$	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
$605$	1.55216	+	14.2244i	0.0631043	+	0.578304i
$606$	0.133172	−	0.133172i	0.00540973	−	0.00540973i
$607$	−8.47275	+	14.6752i	−0.343898	+	0.595649i	−0.985153	−	0.171679i	$-0.945081\pi$
$607$	−8.47275	+	14.6752i	−0.343898	+	0.595649i	0.641255	+	0.767328i	$0.278414\pi$
$608$	1.79525	+	6.69996i	0.0728070	+	0.271719i
$609$	0.514396	+	1.91975i	0.0208444	+	0.0777923i
$610$	−11.6512	−	9.35860i	−0.471742	−	0.378919i
$611$	−4.57903	+	17.0892i	−0.185248	+	0.691354i
$612$	4.07554	−	7.05904i	0.164744	−	0.285345i
$613$	0.0327367	−	0.00877176i	0.00132222	−	0.000354288i	−0.258158	−	0.966103i	$-0.583115\pi$
$613$	0.0327367	−	0.00877176i	0.00132222	−	0.000354288i	0.259480	+	0.965748i	$0.416449\pi$
$614$	−3.64279	−	13.5951i	−0.147011	−	0.548652i
$615$	−0.406583	+	0.157927i	−0.0163950	+	0.00636825i
$616$	8.80003	+	2.35796i	0.354563	+	0.0950049i
$617$	−5.52599	−	20.6233i	−0.222468	−	0.830262i	−0.983403	−	0.181434i	$-0.941926\pi$
$617$	−5.52599	−	20.6233i	−0.222468	−	0.830262i	0.760935	−	0.648828i	$-0.224741\pi$
$618$	−1.73175	+	1.73175i	−0.0696613	+	0.0696613i
$619$	0.953588			0.0383279			0.0191640	−	0.999816i	$-0.493900\pi$
$619$	0.953588			0.0383279			0.0191640	+	0.999816i	$0.493900\pi$
$620$	−2.51641	+	16.3067i	−0.101062	+	0.654893i
$621$	−5.95288	+	5.95288i	−0.238881	+	0.238881i
$622$	−22.7708	−	6.10141i	−0.913025	−	0.244644i
$623$		−	25.6177i		−	1.02635i
$624$	0.909415	−	3.39398i	0.0364057	−	0.135868i
$625$	22.6743	−	10.5298i	0.906972	−	0.421191i
$626$	6.25706	+	10.8376i	0.250083	+	0.433156i
$627$	8.78821	+	5.07387i	0.350967	+	0.202631i
$628$	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	$0.747766\pi$
$632$	0.585692	+	0.156936i	0.0232976	+	0.00624256i
$633$	−1.06493	+	3.97438i	−0.0423272	+	0.157967i
$634$	−15.1469	−	4.05859i	−0.601559	−	0.161187i
$635$	−6.16385	−	15.8688i	−0.244605	−	0.629734i
$636$	2.55540	+	4.42608i	0.101328	+	0.175506i
$637$		−	56.8745i		−	2.25345i
$638$	−0.380873	−	1.42144i	−0.0150789	−	0.0562752i
$639$		−	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	$-0.154789\pi$
$642$	−9.43751	+	5.44875i	−0.372469	+	0.215045i
$643$		−	17.9644i		−	0.708447i	−0.935161	−	0.354224i	$-0.884745\pi$
$643$		−	17.9644i		−	0.708447i	0.935161	−	0.354224i	$-0.115255\pi$
$644$	−9.14920	+	2.45152i	−0.360529	+	0.0966035i
$645$	−18.7296	−	2.89030i	−0.737476	−	0.113806i
$646$	21.5448	−	5.77292i	0.847671	−	0.227133i
$647$	−10.5413	−	18.2580i	−0.414420	−	0.717797i	0.580947	−	0.813941i	$-0.302682\pi$
$647$	−10.5413	−	18.2580i	−0.414420	−	0.717797i	−0.995367	+	0.0961443i	$0.969349\pi$
$648$	2.51480	+	4.35577i	0.0987908	+	0.171111i
$649$	12.7565	−	3.41809i	0.500735	−	0.134172i
$650$	25.1520	−	5.55530i	0.986544	−	0.217897i
$651$	−20.6479	+	5.53258i	−0.809253	+	0.216839i
$652$		−	11.6232i		−	0.455198i
$653$	−1.65336	+	0.954568i	−0.0647010	+	0.0373551i	−0.532002	−	0.846743i	$-0.678560\pi$
$653$	−1.65336	+	0.954568i	−0.0647010	+	0.0373551i	0.467301	+	0.884099i	$0.345227\pi$
$654$	−2.68884	+	4.65720i	−0.105142	+	0.182111i
$655$	−32.6876	+	12.6967i	−1.27721	+	0.496102i
$656$			0.285995i			0.0111662i
$657$	−8.80563	−	32.8630i	−0.343540	−	1.28211i
$658$			14.5865i			0.568640i
$659$	11.0325	+	19.1088i	0.429763	+	0.744372i	0.996852	−	0.0792848i	$-0.0252636\pi$
$659$	11.0325	+	19.1088i	0.429763	+	0.744372i	−0.567089	+	0.823657i	$0.691930\pi$
$660$	−3.04938	+	1.18446i	−0.118697	+	0.0461050i
$661$	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	$0.566204\pi$
$662$	0.362336	−	1.35226i	0.0140826	−	0.0525570i
$663$	−10.9139	−	2.92438i	−0.423862	−	0.113573i
$664$	−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
$668$	−1.23250	−	0.711584i	−0.0476868	−	0.0275320i
$669$	2.51964	+	4.36414i	0.0974148	+	0.168727i
$670$	−4.28117	−	3.43877i	−0.165396	−	0.132851i
$671$	−3.71030	+	13.8470i	−0.143235	+	0.534559i
$672$		−	2.89694i		−	0.111752i
$673$	−16.3667	−	4.38545i	−0.630891	−	0.169047i	−0.0708171	−	0.997489i	$-0.522561\pi$
$673$	−16.3667	−	4.38545i	−0.630891	−	0.169047i	−0.560074	+	0.828443i	$0.689227\pi$
$674$	4.90656	−	4.90656i	0.188994	−	0.188994i
$675$	10.1542	−	15.9112i	0.390834	−	0.612423i
$676$	13.5394			0.520748
$677$	−18.3803	+	18.3803i	−0.706413	+	0.706413i	−0.965779	−	0.259366i	$-0.916486\pi$
$677$	−18.3803	+	18.3803i	−0.706413	+	0.706413i	0.259366	+	0.965779i	$0.416486\pi$
$678$	−0.122808	−	0.458326i	−0.00471641	−	0.0176019i
$679$	−58.5046	−	15.6763i	−2.24520	−	0.601600i
$680$	−2.89852	+	6.58036i	−0.111153	+	0.252345i
$681$	−1.61262	−	6.01837i	−0.0617956	−	0.230624i
$682$	15.2882	−	4.09647i	0.585416	−	0.156862i
$683$	10.6729	−	18.4860i	0.408388	−	0.707349i	−0.586321	−	0.810079i	$-0.699424\pi$
$683$	10.6729	−	18.4860i	0.408388	−	0.707349i	0.994709	+	0.102730i	$0.0327577\pi$
$684$	−4.55060	+	16.9831i	−0.173996	+	0.649364i
$685$	26.6047	−	33.1220i	1.01651	−	1.26553i
$686$	−4.44125	−	16.5750i	−0.169568	−	0.632835i
$687$	0.629308	+	2.34861i	0.0240096	+	0.0896050i
$688$	−6.21303	+	10.7613i	−0.236869	+	0.410270i
$689$	−27.2960	+	27.2960i	−1.03990	+	1.03990i
$690$	2.12990	−	2.65166i	0.0810839	−	0.100947i
$691$	−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
$695$	0.490650	+	0.216122i	0.0186114	+	0.00819797i
$696$	−0.405241	+	0.233966i	−0.0153606	+	0.00886845i
$697$	0.919665			0.0348348
$698$	−7.88832	+	4.55432i	−0.298577	+	0.172384i
$699$	−10.8470	+	6.26255i	−0.410273	+	0.236871i
$700$	18.8450	−	9.79123i	0.712274	−	0.370074i
$701$	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
$703$	−28.6043	+	31.0154i	−1.07883	+	1.16977i
$704$			2.14497i			0.0808416i
$705$	−3.09541	−	4.22509i	−0.116580	−	0.159126i
$706$	2.73444	−	1.57873i	0.102912	−	0.0594164i
$707$	1.13284	+	0.303544i	0.0426049	+	0.0114160i
$708$	−2.09969	−	3.63677i	−0.0789113	−	0.136678i
$709$	6.36597	−	6.36597i	0.239079	−	0.239079i	−0.577390	−	0.816469i	$-0.695929\pi$
$709$	6.36597	−	6.36597i	0.239079	−	0.239079i	0.816469	+	0.577390i	$0.195929\pi$
$710$	3.11329	+	28.5310i	0.116840	+	1.07075i
$711$	1.08681	+	1.08681i	0.0407586	+	0.0407586i
$712$	5.82591	−	1.56105i	0.218335	−	0.0585028i
$713$	−11.6358	+	11.6358i	−0.435765	+	0.435765i
$714$	−9.31559			−0.348627
$715$	−14.6027	−	19.9320i	−0.546111	−	0.745416i
$716$	0.922883	−	3.44425i	0.0344897	−	0.128717i
$717$	−9.69391			−0.362026
$718$	−0.256190	−	0.147911i	−0.00956093	−	0.00552000i
$719$	−6.88749	−	3.97650i	−0.256860	−	0.148298i	0.366041	−	0.930599i	$-0.380713\pi$
$719$	−6.88749	−	3.97650i	−0.256860	−	0.148298i	−0.622901	+	0.782300i	$0.714046\pi$
$720$	−3.34973	−	4.57223i	−0.124837	−	0.170397i
$721$	−14.7314	−	3.94727i	−0.548626	−	0.147004i
$722$	−25.2121	+	14.5562i	−0.938296	+	0.541726i
$723$	3.79235	+	2.18952i	0.141039	+	0.0814290i
$724$	−12.1826	+	21.1009i	−0.452762	+	0.784207i
$725$	−2.89163	−	1.84538i	−0.107393	−	0.0685355i
$726$	−3.08620	−	3.08620i	−0.114540	−	0.114540i
$727$	5.78371	+	10.0177i	0.214506	+	0.371535i	0.953120	−	0.302594i	$-0.0978526\pi$
$727$	5.78371	+	10.0177i	0.214506	+	0.371535i	−0.738614	+	0.674129i	$0.764519\pi$
$728$	21.1353	−	5.66319i	0.783327	−	0.209892i
$729$			5.02468i			0.186099i
$730$	10.8667	+	27.9764i	0.402196	+	1.03545i
$731$	34.6047	+	19.9790i	1.27990	+	0.738951i
$732$	4.55839			0.168483
$733$	−3.42772	+	12.7924i	−0.126606	+	0.472499i	−0.999892	−	0.0147088i	$-0.995318\pi$
$733$	−3.42772	+	12.7924i	−0.126606	+	0.472499i	0.873286	+	0.487208i	$0.161985\pi$
$734$	−15.8866	−	15.8866i	−0.586385	−	0.586385i
$735$	13.1271	+	10.5441i	0.484202	+	0.388926i
$736$	−1.11504	−	1.93130i	−0.0411009	−	0.0711888i
$737$	−1.36333	+	5.08803i	−0.0502190	+	0.187420i
$738$	−0.362470	+	0.627817i	−0.0133427	+	0.0231103i
$739$	15.3469			0.564544			0.282272	−	0.959334i	$-0.408912\pi$
$739$	15.3469			0.564544			0.282272	+	0.959334i	$0.408912\pi$
$740$	−2.02058	−	13.4505i	−0.0742779	−	0.494452i
$741$	24.3722			0.895335
$742$	−15.9132	+	27.5625i	−0.584192	+	1.01185i
$743$	−2.53651	+	9.46639i	−0.0930555	+	0.347288i	−0.996717	−	0.0809586i	$-0.974202\pi$
$743$	−2.53651	+	9.46639i	−0.0930555	+	0.347288i	0.903662	+	0.428247i	$0.140869\pi$
$744$	−2.51641	−	4.35856i	−0.0922562	−	0.159792i
$745$	−14.4073	+	1.57212i	−0.527843	+	0.0575980i
$746$	15.6393	+	15.6393i	0.572596	+	0.572596i
$747$	2.41119	−	8.99868i	0.0882208	−	0.329245i
$748$	6.89751			0.252198
$749$	−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	$-0.318280\pi$
$752$	−3.31722	+	0.888848i	−0.120967	+	0.0324129i
$753$	7.03840	+	12.1909i	0.256494	+	0.444260i
$754$	−2.49915	−	2.49915i	−0.0910139	−	0.0910139i
$755$	−14.7956	−	20.1953i	−0.538466	−	0.734982i
$756$	8.01699	−	13.8858i	0.291575	−	0.505023i
$757$	−17.3937	−	10.0423i	−0.632185	−	0.364992i	0.149413	−	0.988775i	$-0.452262\pi$
$757$	−17.3937	−	10.0423i	−0.632185	−	0.364992i	−0.781598	+	0.623783i	$0.785595\pi$
$758$	−8.58408	+	4.95602i	−0.311788	+	0.180011i
$759$	−3.15141	−	0.844418i	−0.114389	−	0.0306504i
$760$	2.36548	−	15.3286i	0.0858048	−	0.556027i
$761$	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	$0.494190\pi$
$762$	4.49701	+	2.59635i	0.162909	+	0.0940558i
$763$	−33.4883			−1.21236
$764$	0.531374	−	1.98312i	0.0192244	−	0.0717466i
$765$	−14.7028	+	10.7716i	−0.531580	+	0.389449i
$766$	31.6751			1.14447
$767$	22.4283	−	22.4283i	0.809839	−	0.809839i
$768$	0.658815	−	0.176529i	0.0237730	−	0.00636994i
$769$	10.6047	+	10.6047i	0.382417	+	0.382417i	0.871972	−	0.489555i	$-0.162841\pi$
$769$	10.6047	+	10.6047i	0.382417	+	0.382417i	−0.489555	+	0.871972i	$0.662841\pi$
$770$	−15.8825	−	12.7573i	−0.572365	−	0.459742i
$771$	−0.145803	+	0.145803i	−0.00525098	+	0.00525098i
$772$	−2.93937	−	5.09114i	−0.105790	−	0.183234i
$773$	45.1478	+	12.0973i	1.62385	+	0.435110i	0.952131	−	0.305691i	$-0.0988876\pi$
$773$	45.1478	+	12.0973i	1.62385	+	0.435110i	0.671724	+	0.740802i	$0.265554\pi$
$774$	−27.2777	+	15.7488i	−0.980476	+	0.566078i
$775$	19.8479	−	31.1009i	0.712958	−	1.11718i
$776$		−	14.2602i		−	0.511913i
$777$	14.8921	−	9.42013i	0.534251	−	0.337945i
$778$	23.5141	−	23.5141i	0.843022	−	0.843022i
$779$	−1.91616	+	0.513432i	−0.0686534	+	0.0183956i
$780$	−4.92023	+	6.12553i	−0.176172	+	0.219329i
$781$	23.8426	−	13.7656i	0.853157	−	0.492570i
$782$	−6.21043	+	3.58560i	−0.222085	+	0.128221i
$783$	−2.58991			−0.0925557
$784$	9.56099	−	5.52004i	0.341464	−	0.197144i
$785$	−11.7841	−	30.3381i	−0.420592	−	1.08281i
$786$	5.34813	−	9.26324i	0.190762	−	0.330409i
$787$	−7.48984	−	7.48984i	−0.266984	−	0.266984i	0.560900	−	0.827884i	$-0.310455\pi$
$787$	−7.48984	−	7.48984i	−0.266984	−	0.266984i	−0.827884	+	0.560900i	$0.810455\pi$
$788$	−17.6376	−	17.6376i	−0.628313	−	0.628313i
$789$	17.5744	+	10.1466i	0.625666	+	0.361228i
$790$	−1.05707	−	0.849072i	−0.0376088	−	0.0302086i
$791$	2.08937	−	2.08937i	0.0742893	−	0.0742893i
$792$	−2.71853	+	4.70864i	−0.0965989	+	0.167314i
$793$	8.91115	+	33.2569i	0.316444	+	1.18099i
$794$	−9.36189	−	34.9391i	−0.332241	−	1.23994i
$795$	−1.23967	−	11.3607i	−0.0439665	−	0.402921i
$796$	−6.52495	+	24.3514i	−0.231271	+	0.863114i
$797$	10.0690	−	17.4401i	0.356663	−	0.617759i	−0.630738	−	0.775996i	$-0.717248\pi$
$797$	10.0690	−	17.4401i	0.356663	−	0.617759i	0.987401	+	0.158237i	$0.0505811\pi$
$798$	19.4094	−	5.20073i	0.687084	−	0.184104i
$799$	2.85824	+	10.6671i	0.101117	+	0.377375i
$800$	3.37505	+	3.68904i	0.119326	+	0.130427i
$801$	14.7675	+	3.95695i	0.521785	+	0.139812i
$802$	4.54995	+	16.9806i	0.160664	+	0.599608i
$803$	20.3576	−	20.3576i	0.718404	−	0.718404i
$804$	1.67496			0.0590713
$805$	20.9321	+	3.23020i	0.737761	+	0.113850i
$806$	26.8796	−	26.8796i	0.946794	−	0.946794i
$807$	−1.47647	−	0.395618i	−0.0519741	−	0.0139264i
$808$			0.276126i			0.00971406i
$809$	−3.51422	+	13.1152i	−0.123553	+	0.461107i	−0.999784	−	0.0207847i	$-0.993384\pi$
$809$	−3.51422	+	13.1152i	−0.123553	+	0.461107i	0.876231	+	0.481892i	$0.160050\pi$
$810$	−1.21998	−	11.1802i	−0.0428656	−	0.392832i
$811$	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	$0.760983\pi$
$812$	−2.52355	−	1.45697i	−0.0885593	−	0.0511297i
$813$	−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
$817$	−83.2541	−	22.3079i	−2.91269	−	0.780453i
$818$	−6.04247	+	22.5508i	−0.211270	+	0.788471i
$819$	53.5738	+	14.3551i	1.87202	+	0.501606i
$820$	0.257789	−	0.585244i	0.00900237	−	0.0204376i
$821$	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	$0.535852\pi$
$822$			12.9586i			0.451984i
$823$	6.29097	+	23.4782i	0.219289	+	0.818399i	0.984612	+	0.174753i	$0.0559126\pi$
$823$	6.29097	+	23.4782i	0.219289	+	0.818399i	−0.765323	+	0.643646i	$0.777421\pi$
$824$		−	3.59072i		−	0.125089i
$825$	7.30773	+	0.324826i	0.254423	+	0.0113090i
$826$	13.0754	−	22.6473i	0.454951	−	0.787999i
$827$	7.98729	−	4.61146i	0.277745	−	0.160356i	−0.354657	−	0.934996i	$-0.615402\pi$
$827$	7.98729	−	4.61146i	0.277745	−	0.160356i	0.632402	+	0.774640i	$0.282069\pi$
$828$		−	5.65280i		−	0.196448i
$829$	−5.94419	+	1.59274i	−0.206450	+	0.0553182i	−0.360562	−	0.932735i	$-0.617415\pi$
$829$	−5.94419	+	1.59274i	−0.206450	+	0.0553182i	0.154112	+	0.988053i	$0.450748\pi$
$830$	−1.25338	+	8.12206i	−0.0435053	+	0.281921i
$831$	−5.00391	+	1.34079i	−0.173584	+	0.0465117i
$832$	2.57582	+	4.46146i	0.0893006	+	0.154673i
$833$	−17.7506	−	30.7450i	−0.615022	−	1.06525i
$834$	−0.157964	+	0.0423262i	−0.00546983	+	0.00146564i
$835$	1.88071	+	2.56709i	0.0650848	+	0.0888378i
$836$	−14.3712	+	3.85076i	−0.497039	+	0.133181i
$837$		−	27.8557i		−	0.962834i
$838$	−23.5500	+	13.5966i	−0.813523	+	0.469688i
$839$	−19.1957	+	33.2480i	−0.662710	+	1.14785i	0.317191	+	0.948362i	$0.397260\pi$
$839$	−19.1957	+	33.2480i	−0.662710	+	1.14785i	−0.979901	+	0.199485i	$0.936073\pi$
$840$	−2.61123	+	5.92813i	−0.0900958	+	0.204540i
$841$		−	28.5293i		−	0.983770i
$842$	−2.78403	−	10.3901i	−0.0959439	−	0.358068i
$843$		−	20.9997i		−	0.723268i
$844$	−3.01630	−	5.22439i	−0.103825	−	0.179831i
$845$	−27.7064	−	12.2041i	−0.953128	−	0.419834i
$846$	−8.40850	−	2.25305i	−0.289090	−	0.0774615i
$847$	7.03452	−	26.2532i	0.241709	−	0.902070i
$848$	−7.23790	−	1.93939i	−0.248550	−	0.0665989i
$849$	−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
$853$	10.7777	+	6.22252i	0.369022	+	0.213055i	0.673031	−	0.739614i	$-0.264992\pi$
$853$	10.7777	+	6.22252i	0.369022	+	0.213055i	−0.304009	+	0.952669i	$0.598325\pi$
$854$	14.1932	+	24.5834i	0.485682	+	0.841226i
$855$	24.6202	−	30.6514i	0.841992	−	1.04826i
$856$	4.13526	−	15.4330i	0.141340	−	0.527490i
$857$			3.80939i			0.130126i	0.997881	+	0.0650631i	$0.0207249\pi$
$857$			3.80939i			0.130126i	−0.997881	+	0.0650631i	$0.979275\pi$
$858$	7.27999	+	1.95067i	0.248535	+	0.0665947i
$859$	0.520431	−	0.520431i	0.0177569	−	0.0177569i	−0.698173	−	0.715929i	$-0.746003\pi$
$859$	0.520431	−	0.520431i	0.0177569	−	0.0177569i	0.715929	+	0.698173i	$0.246003\pi$
$860$	22.4139	−	16.4210i	0.764309	−	0.559952i
$861$	0.828510			0.0282355
$862$	8.92502	−	8.92502i	0.303987	−	0.303987i
$863$	6.07386	+	22.6680i	0.206757	+	0.771626i	0.988907	+	0.148536i	$0.0474562\pi$
$863$	6.07386	+	22.6680i	0.206757	+	0.771626i	−0.782150	+	0.623090i	$0.785877\pi$
$864$	3.64641	+	0.977053i	0.124053	+	0.0332400i
$865$	−14.1315	−	36.3814i	−0.480485	−	1.23701i
$866$	4.07821	+	15.2201i	0.138583	+	0.517200i
$867$	4.38737	−	1.17559i	0.149003	−	0.0399252i
$868$	15.6704	−	27.1420i	0.531889	−	0.921259i
$869$	−0.336622	+	1.25629i	−0.0114191	+	0.0426168i
$870$	1.04015	−	0.113501i	0.0352645	−	0.00384804i
$871$	3.27436	+	12.2201i	0.110948	+	0.414062i
$872$	−2.04066	−	7.61584i	−0.0691054	−	0.257905i
$873$	18.0734	−	31.3041i	0.611693	−	1.05948i
$874$	10.9379	−	10.9379i	0.369980	−	0.369980i
$875$	−47.3889	+	3.04985i	−1.60204	+	0.103104i
$876$	−7.92813	−	4.57731i	−0.267867	−	0.154653i
$877$	−28.8202	−	28.8202i	−0.973187	−	0.973187i	0.0264624	−	0.999650i	$-0.491576\pi$
$877$	−28.8202	−	28.8202i	−0.973187	−	0.973187i	−0.999650	+	0.0264624i	$0.991576\pi$
$878$	18.2619	+	18.2619i	0.616310	+	0.616310i
$879$	−6.78284	+	11.7482i	−0.228779	+	0.396257i
$880$	1.93342	−	4.38935i	0.0651756	−	0.147965i
$881$	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	$0.256981\pi$
$882$	27.9844			0.942283
$883$	−48.4079	+	27.9483i	−1.62906	+	0.940536i	−0.644682	+	0.764451i	$0.723010\pi$
$883$	−48.4079	+	27.9483i	−1.62906	+	0.940536i	−0.984375	+	0.176085i	$0.943657\pi$
$884$	14.3466	−	8.28299i	0.482527	−	0.278587i
$885$	1.01860	+	9.33470i	0.0342398	+	0.313783i
$886$	5.88150	−	1.57594i	0.197593	−	0.0529448i
$887$	−10.5153	+	10.5153i	−0.353069	+	0.353069i	−0.861250	−	0.508181i	$-0.830318\pi$
$887$	−10.5153	+	10.5153i	−0.353069	+	0.353069i	0.508181	+	0.861250i	$0.330318\pi$
$888$	3.04978	+	2.81270i	0.102344	+	0.0943880i
$889$			32.3364i			1.08453i
$890$	−13.3289	−	2.05689i	−0.446786	−	0.0689470i
$891$	−9.34299	+	5.39418i	−0.313002	+	0.180712i
$892$	−7.13661	−	1.91225i	−0.238951	−	0.0640268i
$893$	−11.9105	−	20.6296i	−0.398569	−	0.690342i
$894$	3.12589	−	3.12589i	0.104545	−	0.104545i
$895$	−4.99309	+	6.21625i	−0.166901	+	0.207786i
$896$	3.00334	+	3.00334i	0.100334	+	0.100334i
$897$	−7.56885	+	2.02807i	−0.252717	+	0.0677152i
$898$	−4.18026	+	4.18026i	−0.139497	+	0.139497i
$899$	−5.06237			−0.168840
$900$	2.73341	+	12.3757i	0.0911138	+	0.412524i
$901$	−6.23643	+	23.2747i	−0.207766	+	0.775392i
$902$	−0.613451			−0.0204257
$903$	31.1748	+	17.9988i	1.03743	+	0.598961i
$904$	0.602478	+	0.347841i	0.0200381	+	0.0115690i
$905$	43.9495	−	32.1986i	1.46093	−	1.07032i
$906$	7.37614	+	1.97643i	0.245056	+	0.0656625i
$907$	29.0616	−	16.7787i	0.964974	−	0.557128i	0.0672736	−	0.997735i	$-0.478570\pi$
$907$	29.0616	−	16.7787i	0.964974	−	0.557128i	0.897700	+	0.440607i	$0.145237\pi$
$908$	7.91126	+	4.56757i	0.262544	+	0.151580i
$909$	−0.349961	+	0.606151i	−0.0116075	+	0.0201048i
$910$	−48.3548	−	7.46200i	−1.60295	−	0.247363i
$911$	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	$0.657946\pi$
$912$	2.36548	+	4.09712i	0.0783287	+	0.135669i
$913$	7.61477	−	2.04037i	0.252012	−	0.0675264i
$914$			29.3556i			0.970997i
$915$	−9.32804	−	4.10882i	−0.308376	−	0.135833i
$916$	−3.08729	−	1.78245i	−0.102007	−	0.0588937i
$917$	66.6088			2.19962
$918$	3.14188	−	11.7256i	0.103697	−	0.387004i
$919$	−7.15066	−	7.15066i	−0.235879	−	0.235879i	0.579262	−	0.815141i	$-0.303341\pi$
$919$	−7.15066	−	7.15066i	−0.235879	−	0.235879i	−0.815141	+	0.579262i	$0.803341\pi$
$920$	0.540925	+	4.95718i	0.0178338	+	0.163433i
$921$	−4.79985	−	8.31358i	−0.158160	−	0.273942i
$922$	9.14527	−	34.1306i	0.301184	−	1.12403i
$923$	33.0612	−	57.2637i	1.08822	−	1.88486i
$924$	6.21384			0.204420
$925$	−7.98918	+	29.3457i	−0.262683	+	0.964882i
$926$	−26.0038			−0.854539
$927$	4.55087	−	7.88234i	0.149470	−	0.258890i
$928$	0.177565	−	0.662683i	0.00582887	−	0.0217536i
$929$	7.00582	+	12.1344i	0.229854	+	0.398118i	0.957765	−	0.287554i	$-0.0928420\pi$
$929$	7.00582	+	12.1344i	0.229854	+	0.398118i	−0.727911	+	0.685672i	$0.759509\pi$
$930$	1.22076	+	11.1873i	0.0400302	+	0.366847i
$931$	54.1484	+	54.1484i	1.77464	+	1.77464i
$932$	4.75288	−	17.7380i	0.155686	−	0.581028i
$933$	−16.0788			−0.526397
$934$	−21.7521	−	12.5586i	−0.711752	−	0.410930i
$935$	−14.1147	−	6.21724i	−0.461599	−	0.203325i
$936$			13.0584i			0.426827i
$937$	7.20700	−	1.93111i	0.235443	−	0.0630866i	−0.139168	−	0.990269i	$-0.544443\pi$
$937$	7.20700	−	1.93111i	0.235443	−	0.0630866i	0.374611	+	0.927182i	$0.377776\pi$
$938$	5.21523	+	9.03305i	0.170283	+	0.294939i
$939$	6.03539	+	6.03539i	0.196958	+	0.196958i
$940$	7.58937	+	1.17117i	0.247538	+	0.0381995i
$941$	−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	$0.837091\pi$
$942$	8.59741	+	4.96372i	0.280119	+	0.161727i
$943$	0.552344	−	0.318896i	0.0179868	−	0.0103847i
$944$	5.94716	+	1.59354i	0.193563	+	0.0518652i
$945$	−28.9218	+	21.1889i	−0.940828	+	0.689274i
$946$	−23.0826	−	13.3268i	−0.750480	−	0.433290i
$947$	−15.0607	−	8.69529i	−0.489406	−	0.282559i	0.234922	−	0.972014i	$-0.424517\pi$
$947$	−15.0607	−	8.69529i	−0.489406	−	0.282559i	−0.724328	+	0.689455i	$0.757850\pi$
$948$	0.413567			0.0134320
$949$	17.8963	−	66.7898i	0.580938	−	2.16809i
$950$	−18.6574	+	29.2354i	−0.605326	+	0.948523i
$951$	−10.6955			−0.346824
$952$	9.65774	−	9.65774i	0.313009	−	0.313009i
$953$	−18.5530	+	4.97127i	−0.600992	+	0.161035i	−0.546472	−	0.837477i	$-0.684030\pi$
$953$	−18.5530	+	4.97127i	−0.600992	+	0.161035i	−0.0545200	+	0.998513i	$0.517363\pi$
$954$	−13.4307	−	13.4307i	−0.434834	−	0.434834i
$955$	−2.87490	+	3.57917i	−0.0930297	+	0.115819i
$956$	10.0499	−	10.0499i	0.325039	−	0.325039i
$957$	−0.501849	−	0.869229i	−0.0162225	−	0.0280982i
$958$	−27.5659	−	7.38625i	−0.890612	−	0.238639i
$959$	−69.8857	+	40.3485i	−2.25673	+	1.30292i
$960$	−1.50728	−	0.232600i	−0.0486473	−	0.00750714i
$961$		−	23.4483i		−	0.756396i
$962$	−14.5587	+	27.7489i	−0.469393	+	0.894661i
$963$	28.6375	−	28.6375i	0.922832	−	0.922832i
$964$	−6.20157	+	1.66171i	−0.199739	+	0.0535199i
$965$	1.42594	+	13.0677i	0.0459027	+	0.420664i
$966$	−5.59487	+	3.23020i	−0.180012	+	0.103930i
$967$	2.02581	−	1.16960i	0.0651457	−	0.0376119i	−0.467073	−	0.884219i	$-0.654692\pi$
$967$	2.02581	−	1.16960i	0.0651457	−	0.0376119i	0.532219	+	0.846607i	$0.321358\pi$
$968$	6.39911			0.205675
$969$	13.1750	−	7.60658i	0.423242	−	0.244359i
$970$	−12.8538	+	29.1814i	−0.412711	+	0.936957i
$971$	−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
$975$	15.5899	−	8.09999i	0.499276	−	0.259407i
$976$	−4.72582	+	4.72582i	−0.151270	+	0.151270i
$977$	−8.68016	+	15.0345i	−0.277703	+	0.480996i	−0.970814	−	0.239836i	$-0.922906\pi$
$977$	−8.68016	+	15.0345i	−0.277703	+	0.480996i	0.693111	+	0.720831i	$0.256240\pi$
$978$	−2.05183	−	7.65752i	−0.0656102	−	0.244861i
$979$	3.34840	+	12.4964i	0.107015	+	0.399387i
$980$	−24.5407	+	2.67787i	−0.783923	+	0.0855414i
$981$	5.17266	−	19.3046i	0.165150	−	0.616350i
$982$	9.49311	−	16.4425i	0.302937	−	0.524703i
$983$	−19.6556	+	5.26670i	−0.626916	+	0.167982i	−0.558270	−	0.829659i	$-0.688535\pi$
$983$	−19.6556	+	5.26670i	−0.626916	+	0.167982i	−0.0686461	+	0.997641i	$0.521868\pi$
$984$	0.0504864	+	0.188418i	0.00160945	+	0.00600655i
$985$	20.1945	+	51.9907i	0.643451	+	1.65656i
$986$	−2.13097	−	0.570991i	−0.0678639	−	0.0181841i
$987$	2.57494	+	9.60979i	0.0819611	+	0.305883i
$988$	−25.2673	+	25.2673i	−0.803861	+	0.803861i
$989$	27.7111			0.881161
$990$	9.80730	−	7.18508i	0.311697	−	0.228357i
$991$	−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	$0.364993\pi$
$992$	7.12748	+	1.90980i	0.226298	+	0.0606363i
$993$		−	0.954851i		−	0.0303013i
$994$	14.1097	−	52.6582i	0.447533	−	1.67022i
$995$	35.3020	−	43.9500i	1.11915	−	1.39331i
$996$	−1.25338	−	2.17091i	−0.0397148	−	0.0687880i
$997$	3.55422	+	2.05203i	0.112563	+	0.0649884i	0.555225	−	0.831700i	$-0.312632\pi$
$997$	3.55422	+	2.05203i	0.112563	+	0.0649884i	−0.442661	+	0.896689i	$0.645966\pi$
$998$	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.q.d.97.1	✓	12
5.3	odd	4		370.2.r.d.23.1	yes	12
37.29	odd	12		370.2.r.d.177.1	yes	12
185.103	even	12	inner	370.2.q.d.103.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
370.2.q.d.97.1	✓	12	1.1	even	1	trivial
370.2.q.d.103.1	yes	12	185.103	even	12	inner
370.2.r.d.23.1	yes	12	5.3	odd	4
370.2.r.d.177.1	yes	12	37.29	odd	12

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

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.176529 + 0.658815i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.242559 + 2.22287i) q^{5} +(-0.482286 - 0.482286i) q^{6} +(1.09930 - 4.10264i) q^{7} +1.00000 q^{8} +(2.19520 + 1.26740i) q^{9} +(-2.04634 - 0.901374i) q^{10} +2.14497i q^{11} +(0.658815 - 0.176529i) q^{12} +(2.57582 + 4.46146i) q^{13} +(3.00334 + 3.00334i) q^{14} +(-1.50728 - 0.232600i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(2.78485 + 1.60783i) q^{17} +(-2.19520 + 1.26740i) q^{18} +(-6.69996 - 1.79525i) q^{19} +(1.80379 - 1.32150i) q^{20} +(2.50882 + 1.44847i) q^{21} +(-1.85760 - 1.07248i) q^{22} +2.23008 q^{23} +(-0.176529 + 0.658815i) q^{24} +(-4.88233 + 1.07836i) q^{25} -5.15165 q^{26} +(-2.66936 + 2.66936i) q^{27} +(-4.10264 + 1.09930i) q^{28} +(0.485118 + 0.485118i) q^{29} +(0.955079 - 1.18904i) q^{30} +(-5.21767 + 5.21767i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.41314 - 0.378650i) q^{33} +(-2.78485 + 1.60783i) q^{34} +(9.38628 + 1.44847i) q^{35} -2.53480i q^{36} +(2.82604 - 5.38642i) q^{37} +(4.90471 - 4.90471i) q^{38} +(-3.39398 + 0.909415i) q^{39} +(0.242559 + 2.22287i) q^{40} +(0.247679 - 0.142998i) q^{41} +(-2.50882 + 1.44847i) q^{42} +12.4261 q^{43} +(1.85760 - 1.07248i) q^{44} +(-2.28480 + 5.18707i) 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} +(1.50728 - 4.76740i) q^{50} +(-1.55087 + 1.55087i) q^{51} +(2.57582 - 4.46146i) q^{52} +(1.93939 + 7.23790i) q^{53} +(-0.977053 - 3.64641i) q^{54} +(-4.76800 + 0.520282i) q^{55} +(1.09930 - 4.10264i) q^{56} +(2.36548 - 4.09712i) q^{57} +(-0.662683 + 0.177565i) q^{58} +(-1.59354 - 5.94716i) q^{59} +(0.552203 + 1.42164i) q^{60} +(6.45558 + 1.72977i) q^{61} +(-1.90980 - 7.12748i) q^{62} +(7.61286 - 7.61286i) q^{63} +1.00000 q^{64} +(-9.29246 + 6.80789i) q^{65} +(1.03449 - 1.03449i) q^{66} +(2.37207 + 0.635595i) q^{67} -3.21567i q^{68} +(-0.393674 + 1.46921i) q^{69} +(-5.94755 + 7.40453i) q^{70} +(-6.41760 - 11.1156i) q^{71} +(2.19520 + 1.26740i) 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} +(8.80003 + 2.35796i) q^{77} +(0.909415 - 3.39398i) q^{78} +(0.585692 + 0.156936i) q^{79} +(-2.04634 - 0.901374i) q^{80} +(2.51480 + 4.35577i) q^{81} +0.285995i q^{82} +(-0.951235 - 3.55006i) q^{83} -2.89694i q^{84} +(-2.89852 + 6.58036i) q^{85} +(-6.21303 + 10.7613i) q^{86} +(-0.405241 + 0.233966i) q^{87} +2.14497i q^{88} +(5.82591 - 1.56105i) q^{89} +(-3.34973 - 4.57223i) q^{90} +(21.1353 - 5.66319i) q^{91} +(-1.11504 - 1.93130i) q^{92} +(-2.51641 - 4.35856i) q^{93} +(-3.31722 + 0.888848i) q^{94} +(2.36548 - 15.3286i) q^{95} +(0.658815 - 0.176529i) q^{96} -14.2602i q^{97} +(9.56099 - 5.52004i) q^{98} +(-2.71853 + 4.70864i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} + 2 q^{5} + 6 q^{6} - 4 q^{7} + 12 q^{8} + 18 q^{9} - 4 q^{10} - 6 q^{12} + 8 q^{14} - 10 q^{15} - 6 q^{16} - 12 q^{17} - 18 q^{18} - 8 q^{19} + 2 q^{20} + 54 q^{21} - 6 q^{22}+ \cdots + 28 q^{99}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 + 2 * q^5 + 6 * q^6 - 4 * q^7 + 12 * q^8 + 18 * q^9 - 4 * q^10 - 6 * q^12 + 8 * q^14 - 10 * q^15 - 6 * q^16 - 12 * q^17 - 18 * q^18 - 8 * q^19 + 2 * q^20 + 54 * q^21 - 6 * q^22 - 4 * q^23 - 14 * q^25 + 18 * q^27 - 4 * q^28 + 4 * q^29 - 4 * q^30 - 2 * q^31 - 6 * q^32 + 20 * q^33 + 12 * q^34 + 6 * q^35 + 14 * q^37 + 16 * q^38 - 30 * q^39 + 2 * q^40 + 12 * q^41 - 54 * q^42 + 44 * q^43 + 6 * q^44 - 60 * q^45 + 2 * q^46 - 28 * q^47 + 6 * q^48 + 24 * q^49 + 10 * q^50 - 8 * q^51 + 8 * q^53 - 18 * q^54 - 4 * q^56 - 28 * q^57 - 14 * q^58 + 14 * q^60 + 24 * q^61 - 14 * q^62 + 8 * q^63 + 12 * q^64 - 10 * q^65 + 8 * q^66 + 18 * q^67 - 40 * q^69 - 30 * q^70 + 18 * q^72 - 28 * q^73 + 38 * q^74 - 30 * q^75 - 8 * q^76 + 10 * q^77 + 48 * q^78 - 56 * q^79 - 4 * q^80 + 4 * q^81 + 14 * q^83 - 28 * q^85 - 22 * q^86 + 18 * q^87 - 2 * q^89 + 18 * q^90 + 38 * q^91 + 2 * q^92 - 16 * q^94 - 28 * q^95 - 6 * q^96 - 24 * q^98 + 28 * q^99

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