LMFDB - Embedded newform 925.2.bc.e.49.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [925,2,Mod(49,925)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(925, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 14]))

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

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

chi := DirichletCharacter("925.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 925 = 5^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	925.bc (of order $18$, degree $6$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.38616218697$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			49.17
Character	$\chi$	$=$	925.49
Dual form			925.2.bc.e.774.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.671547 + 0.800319i) q^{2} +(1.71214 - 2.04045i) q^{3} +(0.157762 - 0.894712i) q^{4} +2.78280 q^{6} +(1.70393 + 4.68151i) q^{7} +(2.63155 - 1.51932i) q^{8} +(-0.711068 - 4.03267i) q^{9} +O(q^{10})$	\(q+(0.671547 + 0.800319i) q^{2} +(1.71214 - 2.04045i) q^{3} +(0.157762 - 0.894712i) q^{4} +2.78280 q^{6} +(1.70393 + 4.68151i) q^{7} +(2.63155 - 1.51932i) q^{8} +(-0.711068 - 4.03267i) q^{9} +(-1.59308 - 2.75930i) q^{11} +(-1.55551 - 1.85378i) q^{12} +(2.83077 + 0.499141i) q^{13} +(-2.60243 + 4.50754i) q^{14} +(1.27570 + 0.464318i) q^{16} +(-0.0791936 + 0.0139640i) q^{17} +(2.74990 - 3.27721i) q^{18} +(4.80732 + 4.03382i) q^{19} +(12.4698 + 4.53863i) q^{21} +(1.13849 - 3.12798i) q^{22} +(-5.41516 - 3.12644i) q^{23} +(1.40547 - 7.97084i) q^{24} +(1.50152 + 2.60072i) q^{26} +(-2.52563 - 1.45817i) q^{27} +(4.45742 - 0.785963i) q^{28} +(-1.27956 - 2.21626i) q^{29} -7.35330 q^{31} +(-1.59346 - 4.37801i) q^{32} +(-8.35781 - 1.47371i) q^{33} +(-0.0643579 - 0.0540027i) q^{34} -3.72025 q^{36} +(5.30473 - 2.97656i) q^{37} +6.55629i q^{38} +(5.86516 - 4.92145i) q^{39} +(-0.755580 + 4.28511i) q^{41} +(4.74169 + 13.0277i) q^{42} +8.44694i q^{43} +(-2.72011 + 0.990038i) q^{44} +(-1.13438 - 6.43341i) q^{46} +(-9.57440 - 5.52778i) q^{47} +(3.13160 - 1.80803i) q^{48} +(-13.6509 + 11.4544i) q^{49} +(-0.107098 + 0.185499i) q^{51} +(0.893175 - 2.45398i) q^{52} +(0.755838 - 2.07665i) q^{53} +(-0.529075 - 3.00054i) q^{54} +(11.5967 + 9.73079i) q^{56} +(16.4616 - 2.90263i) q^{57} +(0.914431 - 2.51238i) q^{58} +(-5.99512 - 2.18205i) q^{59} +(-0.335898 + 1.90497i) q^{61} +(-4.93809 - 5.88498i) q^{62} +(17.6674 - 10.2003i) q^{63} +(3.79129 - 6.56671i) q^{64} +(-4.43323 - 7.67858i) q^{66} +(-1.16788 - 3.20872i) q^{67} +0.0730584i q^{68} +(-15.6509 + 5.69646i) q^{69} +(4.05666 + 3.40394i) q^{71} +(-7.99813 - 9.53181i) q^{72} -9.33421i q^{73} +(5.94457 + 2.24657i) q^{74} +(4.36752 - 3.66478i) q^{76} +(10.2032 - 12.1597i) q^{77} +(7.87746 + 1.38901i) q^{78} +(1.77405 - 0.645703i) q^{79} +(4.24422 - 1.54477i) q^{81} +(-3.93686 + 2.27295i) q^{82} +(-4.03212 + 0.710972i) q^{83} +(6.02802 - 10.4408i) q^{84} +(-6.76024 + 5.67252i) q^{86} +(-6.71296 - 1.18368i) q^{87} +(-8.38455 - 4.84082i) q^{88} +(2.57418 + 0.936926i) q^{89} +(2.48670 + 14.1028i) q^{91} +(-3.65157 + 4.35177i) q^{92} +(-12.5899 + 15.0041i) q^{93} +(-2.00567 - 11.3747i) q^{94} +(-11.6614 - 4.24439i) q^{96} +(2.87410 + 1.65936i) q^{97} +(-18.3344 - 3.23285i) q^{98} +(-9.99456 + 8.38643i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 6 q^{4}+O(q^{10}) $ 156 * q - 6 * q^4	$ 156 q - 6 q^{4} - 12 q^{14} + 42 q^{16} + 24 q^{19} + 30 q^{21} - 30 q^{24} + 6 q^{29} - 72 q^{31} + 42 q^{34} + 216 q^{36} - 18 q^{39} - 6 q^{41} + 30 q^{44} - 72 q^{46} + 60 q^{49} - 60 q^{51} - 54 q^{54} + 240 q^{56} - 30 q^{59} - 12 q^{61} + 108 q^{64} - 12 q^{66} - 90 q^{69} + 144 q^{71} - 192 q^{74} + 42 q^{76} - 96 q^{79} + 96 q^{81} - 54 q^{84} + 216 q^{86} + 42 q^{89} - 54 q^{91} + 156 q^{94} - 252 q^{96} - 282 q^{99}+O(q^{100}) $ 156 * q - 6 * q^4 - 12 * q^14 + 42 * q^16 + 24 * q^19 + 30 * q^21 - 30 * q^24 + 6 * q^29 - 72 * q^31 + 42 * q^34 + 216 * q^36 - 18 * q^39 - 6 * q^41 + 30 * q^44 - 72 * q^46 + 60 * q^49 - 60 * q^51 - 54 * q^54 + 240 * q^56 - 30 * q^59 - 12 * q^61 + 108 * q^64 - 12 * q^66 - 90 * q^69 + 144 * q^71 - 192 * q^74 + 42 * q^76 - 96 * q^79 + 96 * q^81 - 54 * q^84 + 216 * q^86 + 42 * q^89 - 54 * q^91 + 156 * q^94 - 252 * q^96 - 282 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/925\mathbb{Z}\right)^\times$.

$n$	$76$	$852$
$\chi(n)$	$e\left(\frac{7}{9}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.671547	+	0.800319i	0.474856	+	0.565911i	0.949299	−	0.314375i	$-0.101795\pi$
$2$	0.671547	+	0.800319i	0.474856	+	0.565911i	−0.474443	+	0.880286i	$0.657351\pi$
$3$	1.71214	−	2.04045i	0.988506	−	1.17806i	0.00448748	−	0.999990i	$-0.498572\pi$
$3$	1.71214	−	2.04045i	0.988506	−	1.17806i	0.984019	−	0.178066i	$-0.0569840\pi$
$4$	0.157762	−	0.894712i	0.0788809	−	0.447356i
$5$		0			0
$5$		0			0
$6$	2.78280			1.13607
$7$	1.70393	+	4.68151i	0.644025	+	1.76944i	0.638696	+	0.769459i	$0.279474\pi$
$7$	1.70393	+	4.68151i	0.644025	+	1.76944i	0.00532890	+	0.999986i	$0.498304\pi$
$8$	2.63155	−	1.51932i	0.930392	−	0.537162i
$9$	−0.711068	−	4.03267i	−0.237023	−	1.34422i
$10$		0			0
$11$	−1.59308	−	2.75930i	−0.480333	−	0.831961i	0.519413	−	0.854524i	$-0.326151\pi$
$11$	−1.59308	−	2.75930i	−0.480333	−	0.831961i	−0.999745	+	0.0225627i	$0.992817\pi$
$12$	−1.55551	−	1.85378i	−0.449036	−	0.535140i
$13$	2.83077	+	0.499141i	0.785115	+	0.138437i	0.551813	−	0.833968i	$-0.313936\pi$
$13$	2.83077	+	0.499141i	0.785115	+	0.138437i	0.233301	+	0.972404i	$0.425047\pi$
$14$	−2.60243	+	4.50754i	−0.695529	+	1.20469i
$15$		0			0
$16$	1.27570	+	0.464318i	0.318926	+	0.116079i
$17$	−0.0791936	+	0.0139640i	−0.0192073	+	0.00338676i	−0.183244	−	0.983068i	$-0.558660\pi$
$17$	−0.0791936	+	0.0139640i	−0.0192073	+	0.00338676i	0.164036	+	0.986454i	$0.447549\pi$
$18$	2.74990	−	3.27721i	0.648159	−	0.772445i
$19$	4.80732	+	4.03382i	1.10288	+	0.925422i	0.997615	−	0.0690226i	$-0.0219881\pi$
$19$	4.80732	+	4.03382i	1.10288	+	0.925422i	0.105260	+	0.994445i	$0.466433\pi$
$20$		0			0
$21$	12.4698	+	4.53863i	2.72113	+	0.990409i
$22$	1.13849	−	3.12798i	0.242727	−	0.666887i
$23$	−5.41516	−	3.12644i	−1.12914	−	0.651909i	−0.185421	−	0.982659i	$-0.559365\pi$
$23$	−5.41516	−	3.12644i	−1.12914	−	0.651909i	−0.943718	+	0.330750i	$0.892698\pi$
$24$	1.40547	−	7.97084i	0.286891	−	1.62704i
$25$		0			0
$26$	1.50152	+	2.60072i	0.294473	+	0.510043i
$27$	−2.52563	−	1.45817i	−0.486057	−	0.280625i
$28$	4.45742	−	0.785963i	0.842373	−	0.148533i
$29$	−1.27956	−	2.21626i	−0.237608	−	0.411549i	0.722419	−	0.691455i	$-0.243030\pi$
$29$	−1.27956	−	2.21626i	−0.237608	−	0.411549i	−0.960027	+	0.279906i	$0.909697\pi$
$30$		0			0
$31$	−7.35330			−1.32069			−0.660346	−	0.750962i	$-0.729590\pi$
$31$	−7.35330			−1.32069			−0.660346	+	0.750962i	$0.729590\pi$
$32$	−1.59346	−	4.37801i	−0.281687	−	0.773930i
$33$	−8.35781	−	1.47371i	−1.45491	−	0.256540i
$34$	−0.0643579	−	0.0540027i	−0.0110373	−	0.00926138i
$35$		0			0
$36$	−3.72025			−0.620042
$37$	5.30473	−	2.97656i	0.872092	−	0.489343i
$37$	5.30473	−	2.97656i	0.872092	−	0.489343i
$38$			6.55629i			1.06357i
$39$	5.86516	−	4.92145i	0.939177	−	0.788063i
$40$		0			0
$41$	−0.755580	+	4.28511i	−0.118002	+	0.669222i	0.867218	+	0.497928i	$0.165906\pi$
$41$	−0.755580	+	4.28511i	−0.118002	+	0.669222i	−0.985220	+	0.171293i	$0.945205\pi$
$42$	4.74169	+	13.0277i	0.731659	+	2.01022i
$43$			8.44694i			1.28815i	0.764964	+	0.644073i	$0.222757\pi$
$43$			8.44694i			1.28815i	−0.764964	+	0.644073i	$0.777243\pi$
$44$	−2.72011	+	0.990038i	−0.410072	+	0.149254i
$45$		0			0
$46$	−1.13438	−	6.43341i	−0.167256	−	0.948555i
$47$	−9.57440	−	5.52778i	−1.39657	−	0.806310i	−0.402538	−	0.915403i	$-0.631872\pi$
$47$	−9.57440	−	5.52778i	−1.39657	−	0.806310i	−0.994031	+	0.109094i	$0.965205\pi$
$48$	3.13160	−	1.80803i	0.452008	−	0.260967i
$49$	−13.6509	+	11.4544i	−1.95012	+	1.63635i
$50$		0			0
$51$	−0.107098	+	0.185499i	−0.0149967	+	0.0259751i
$52$	0.893175	−	2.45398i	0.123861	−	0.340306i
$53$	0.755838	−	2.07665i	0.103822	−	0.285249i	−0.876895	−	0.480682i	$-0.840389\pi$
$53$	0.755838	−	2.07665i	0.103822	−	0.285249i	0.980717	+	0.195433i	$0.0626112\pi$
$54$	−0.529075	−	3.00054i	−0.0719980	−	0.408321i
$55$		0			0
$56$	11.5967	+	9.73079i	1.54967	+	1.30033i
$57$	16.4616	−	2.90263i	2.18040	−	0.384463i
$58$	0.914431	−	2.51238i	0.120071	−	0.329891i
$59$	−5.99512	−	2.18205i	−0.780498	−	0.284078i	−0.0791179	−	0.996865i	$-0.525210\pi$
$59$	−5.99512	−	2.18205i	−0.780498	−	0.284078i	−0.701380	+	0.712787i	$0.747433\pi$
$60$		0			0
$61$	−0.335898	+	1.90497i	−0.0430073	+	0.243907i	−0.998731	−	0.0503582i	$-0.983964\pi$
$61$	−0.335898	+	1.90497i	−0.0430073	+	0.243907i	0.955724	+	0.294265i	$0.0950748\pi$
$62$	−4.93809	−	5.88498i	−0.627138	−	0.747394i
$63$	17.6674	−	10.2003i	2.22588	−	1.28511i
$64$	3.79129	−	6.56671i	0.473911	−	0.820838i
$65$		0			0
$66$	−4.43323	−	7.67858i	−0.545693	−	0.945168i
$67$	−1.16788	−	3.20872i	−0.142679	−	0.392007i	0.847684	−	0.530501i	$-0.177996\pi$
$67$	−1.16788	−	3.20872i	−0.142679	−	0.392007i	−0.990363	+	0.138494i	$0.955774\pi$
$68$			0.0730584i			0.00885963i
$69$	−15.6509	+	5.69646i	−1.88415	+	0.685773i
$70$		0			0
$71$	4.05666	+	3.40394i	0.481437	+	0.403974i	0.850946	−	0.525253i	$-0.176029\pi$
$71$	4.05666	+	3.40394i	0.481437	+	0.403974i	−0.369508	+	0.929227i	$0.620474\pi$
$72$	−7.99813	−	9.53181i	−0.942589	−	1.12333i
$73$		−	9.33421i		−	1.09249i	−0.837626	−	0.546244i	$-0.816057\pi$
$73$		−	9.33421i		−	1.09249i	0.837626	−	0.546244i	$-0.183943\pi$
$74$	5.94457	+	2.24657i	0.691042	+	0.261159i
$75$		0			0
$76$	4.36752	−	3.66478i	0.500989	−	0.420380i
$77$	10.2032	−	12.1597i	1.16276	−	1.38573i
$78$	7.87746	+	1.38901i	0.891947	+	0.157274i
$79$	1.77405	−	0.645703i	0.199597	−	0.0726473i	−0.240287	−	0.970702i	$-0.577242\pi$
$79$	1.77405	−	0.645703i	0.199597	−	0.0726473i	0.439884	+	0.898055i	$0.355019\pi$
$80$		0			0
$81$	4.24422	−	1.54477i	0.471580	−	0.171641i
$82$	−3.93686	+	2.27295i	−0.434754	+	0.251005i
$83$	−4.03212	+	0.710972i	−0.442583	+	0.0780393i	−0.390499	−	0.920603i	$-0.627697\pi$
$83$	−4.03212	+	0.710972i	−0.442583	+	0.0780393i	−0.0520839	+	0.998643i	$0.516586\pi$
$84$	6.02802	−	10.4408i	0.657710	−	1.13919i
$85$		0			0
$86$	−6.76024	+	5.67252i	−0.728976	+	0.611683i
$87$	−6.71296	−	1.18368i	−0.719705	−	0.126903i
$88$	−8.38455	−	4.84082i	−0.893796	−	0.516033i
$89$	2.57418	+	0.936926i	0.272863	+	0.0993140i	0.474828	−	0.880079i	$-0.342510\pi$
$89$	2.57418	+	0.936926i	0.272863	+	0.0993140i	−0.201965	+	0.979393i	$0.564733\pi$
$90$		0			0
$91$	2.48670	+	14.1028i	0.260677	+	1.47837i
$92$	−3.65157	+	4.35177i	−0.380703	+	0.453704i
$93$	−12.5899	+	15.0041i	−1.30551	+	1.55585i
$94$	−2.00567	−	11.3747i	−0.206869	−	1.17321i
$95$		0			0
$96$	−11.6614	−	4.24439i	−1.19018	−	0.433191i
$97$	2.87410	+	1.65936i	0.291821	+	0.168483i	0.638763	−	0.769404i	$-0.279447\pi$
$97$	2.87410	+	1.65936i	0.291821	+	0.168483i	−0.346942	+	0.937887i	$0.612780\pi$
$98$	−18.3344	−	3.23285i	−1.85205	−	0.326567i
$99$	−9.99456	+	8.38643i	−1.00449	+	0.842868i
$100$		0			0
$101$	−6.80834	+	11.7924i	−0.677456	+	1.17339i	0.298289	+	0.954476i	$0.403584\pi$
$101$	−6.80834	+	11.7924i	−0.677456	+	1.17339i	−0.975745	+	0.218912i	$0.929749\pi$
$102$	−0.220380	+	0.0388589i	−0.0218208	+	0.00384760i
$103$	−2.26649	+	1.30856i	−0.223324	+	0.128936i	−0.607489	−	0.794328i	$-0.707823\pi$
$103$	−2.26649	+	1.30856i	−0.223324	+	0.128936i	0.384164	+	0.923265i	$0.374490\pi$
$104$	8.20766	−	2.98734i	0.804827	−	0.292933i
$105$		0			0
$106$	2.16956	−	0.789656i	0.210726	−	0.0766981i
$107$	16.6821	+	2.94150i	1.61272	+	0.284366i	0.906047	−	0.423177i	$-0.139085\pi$
$107$	16.6821	+	2.94150i	1.61272	+	0.284366i	0.706670	+	0.707543i	$0.250196\pi$
$108$	−1.70309	+	2.02966i	−0.163880	+	0.195304i
$109$	−14.0594	+	11.7973i	−1.34665	+	1.12997i	−0.366784	+	0.930306i	$0.619541\pi$
$109$	−14.0594	+	11.7973i	−1.34665	+	1.12997i	−0.979864	+	0.199666i	$0.936014\pi$
$110$		0			0
$111$	3.00893	−	15.9203i	0.285595	−	1.51109i
$112$			6.76338i			0.639079i
$113$	10.3594	+	12.3459i	0.974532	+	1.16140i	0.986876	+	0.161478i	$0.0516262\pi$
$113$	10.3594	+	12.3459i	0.974532	+	1.16140i	−0.0123441	+	0.999924i	$0.503929\pi$
$114$	13.3778	+	11.2253i	1.25295	+	1.05135i
$115$		0			0
$116$	−2.18478	+	0.795194i	−0.202852	+	0.0738320i
$117$		−	11.7705i		−	1.08818i
$118$	−2.27968	−	6.26336i	−0.209861	−	0.576589i
$119$	−0.200313	−	0.346952i	−0.0183626	−	0.0318050i
$120$		0			0
$121$	0.424168	−	0.734680i	0.0385607	−	0.0667891i
$122$	−1.75016	+	1.01045i	−0.158452	+	0.0914821i
$123$	7.44990	+	8.87844i	0.671735	+	0.800542i
$124$	−1.16007	+	6.57908i	−0.104177	+	0.590819i
$125$		0			0
$126$	20.0279	+	7.28957i	1.78423	+	0.649407i
$127$	4.04192	−	11.1051i	0.358662	−	0.985416i	−0.620832	−	0.783944i	$-0.713205\pi$
$127$	4.04192	−	11.1051i	0.358662	−	0.985416i	0.979494	−	0.201473i	$-0.0645727\pi$
$128$	−1.37491	+	0.242434i	−0.121526	+	0.0214283i
$129$	17.2356	+	14.4624i	1.51751	+	1.27334i
$130$		0			0
$131$	1.03298	+	5.85830i	0.0902515	+	0.511842i	0.996099	+	0.0882386i	$0.0281238\pi$
$131$	1.03298	+	5.85830i	0.0902515	+	0.511842i	−0.905848	+	0.423603i	$0.860765\pi$
$132$	−2.63709	+	7.24534i	−0.229529	+	0.630626i
$133$	−10.6930	+	29.3789i	−0.927204	+	2.54747i
$134$	1.78371	−	3.08948i	0.154089	−	0.266890i
$135$		0			0
$136$	−0.187186	+	0.157067i	−0.0160510	+	0.0134684i
$137$	−12.4518	+	7.18905i	−1.06383	+	0.614202i	−0.926489	−	0.376322i	$-0.877189\pi$
$137$	−12.4518	+	7.18905i	−1.06383	+	0.614202i	−0.137340	+	0.990524i	$0.543855\pi$
$138$	−15.0693	−	8.70026i	−1.28278	−	0.740615i
$139$	2.80733	+	15.9212i	0.238115	+	1.35041i	0.835954	+	0.548799i	$0.184915\pi$
$139$	2.80733	+	15.9212i	0.238115	+	1.35041i	−0.597840	+	0.801616i	$0.703974\pi$
$140$		0			0
$141$	−27.6719	+	10.0717i	−2.33039	+	0.848194i
$142$			5.53253i			0.464280i
$143$	−3.13237	−	8.60613i	−0.261942	−	0.719681i
$144$	0.965328	−	5.47464i	0.0804440	−	0.456220i
$145$		0			0
$146$	7.47035	−	6.26837i	0.618250	−	0.518774i
$147$			47.4655i			3.91489i
$148$	−1.82628	−	5.21579i	−0.150119	−	0.428735i
$149$	4.96931			0.407102			0.203551	−	0.979064i	$-0.434752\pi$
$149$	4.96931			0.407102			0.203551	+	0.979064i	$0.434752\pi$
$150$		0			0
$151$	−6.84988	−	5.74773i	−0.557435	−	0.467744i	0.320014	−	0.947413i	$-0.396312\pi$
$151$	−6.84988	−	5.74773i	−0.557435	−	0.467744i	−0.877450	+	0.479669i	$0.840757\pi$
$152$	18.7794	+	3.31131i	1.52321	+	0.268583i
$153$	0.112624	+	0.309432i	0.00910512	+	0.0250161i
$154$	16.5836			1.33634
$155$		0			0
$156$	−3.47798	−	6.02404i	−0.278462	−	0.482310i
$157$	−3.24551	+	0.572270i	−0.259020	+	0.0456721i	−0.301650	−	0.953419i	$-0.597537\pi$
$157$	−3.24551	+	0.572270i	−0.259020	+	0.0456721i	0.0426303	+	0.999091i	$0.486426\pi$
$158$	1.70813	+	0.986189i	0.135891	+	0.0784570i
$159$	−2.94320	−	5.09777i	−0.233411	−	0.404279i
$160$		0			0
$161$	5.40943	−	30.6784i	0.426322	−	2.41779i
$162$	4.08650	+	2.35934i	0.321066	+	0.185368i
$163$	−2.34648	+	6.44690i	−0.183790	+	0.504960i	−0.997034	−	0.0769635i	$-0.975478\pi$
$163$	−2.34648	+	6.44690i	−0.183790	+	0.504960i	0.813243	+	0.581924i	$0.197700\pi$
$164$	3.71474	+	1.35205i	0.290072	+	0.105578i
$165$		0			0
$166$	−3.27676	−	2.74953i	−0.254326	−	0.213405i
$167$	−11.4953	+	13.6996i	−0.889533	+	1.06010i	0.108288	+	0.994120i	$0.465463\pi$
$167$	−11.4953	+	13.6996i	−0.889533	+	1.06010i	−0.997821	+	0.0659845i	$0.978981\pi$
$168$	39.7104	−	7.00202i	3.06372	−	0.540217i
$169$	−4.45188	−	1.62035i	−0.342452	−	0.124642i
$170$		0			0
$171$	12.8487	−	22.2547i	0.982567	−	1.70186i
$172$	7.55757	+	1.33260i	0.576260	+	0.101610i
$173$	−13.6766	−	16.2991i	−1.03981	−	1.23920i	−0.970372	−	0.241615i	$-0.922323\pi$
$173$	−13.6766	−	16.2991i	−1.03981	−	1.23920i	−0.0694408	−	0.997586i	$-0.522121\pi$
$174$	−3.56075	−	6.16740i	−0.269940	−	0.467549i
$175$		0			0
$176$	−0.751108	−	4.25974i	−0.0566169	−	0.321090i
$177$	−14.7169	+	8.49679i	−1.10619	+	0.638658i
$178$	0.978846	+	2.68936i	0.0733676	+	0.201576i
$179$	11.6085			0.867663			0.433832	−	0.900994i	$-0.357161\pi$
$179$	11.6085			0.867663			0.433832	+	0.900994i	$0.357161\pi$
$180$		0			0
$181$	0.106834	−	0.605885i	0.00794091	−	0.0450351i	−0.980580	−	0.196120i	$-0.937166\pi$
$181$	0.106834	−	0.605885i	0.00794091	−	0.0450351i	0.988521	+	0.151085i	$0.0482768\pi$
$182$	−9.61679	+	11.4608i	−0.712844	+	0.849534i
$183$	3.31190	+	3.94697i	0.244823	+	0.291768i
$184$	−19.0003			−1.40072
$185$		0			0
$186$	−20.4627			−1.50040
$187$	0.164693	+	0.196273i	0.0120435	+	0.0143529i
$188$	−6.45624	+	7.69425i	−0.470870	+	0.561161i
$189$	2.52295	−	14.3084i	0.183518	−	1.04078i
$190$		0			0
$191$	5.57413			0.403330			0.201665	−	0.979455i	$-0.435365\pi$
$191$	5.57413			0.403330			0.201665	+	0.979455i	$0.435365\pi$
$192$	−6.90782	−	18.9791i	−0.498529	−	1.36970i
$193$	4.59566	−	2.65330i	0.330803	−	0.190989i	−0.325395	−	0.945578i	$-0.605497\pi$
$193$	4.59566	−	2.65330i	0.330803	−	0.190989i	0.656197	+	0.754589i	$0.272164\pi$
$194$	0.602075	+	3.41454i	0.0432265	+	0.245150i
$195$		0			0
$196$	8.09483	+	14.0206i	0.578202	+	1.00147i
$197$	7.25433	+	8.64538i	0.516850	+	0.615958i	0.959833	−	0.280572i	$-0.0905243\pi$
$197$	7.25433	+	8.64538i	0.516850	+	0.615958i	−0.442983	+	0.896530i	$0.646080\pi$
$198$	−13.4236	−	2.36695i	−0.953976	−	0.168212i
$199$	4.98473	−	8.63381i	0.353358	−	0.612035i	−0.633477	−	0.773761i	$-0.718373\pi$
$199$	4.98473	−	8.63381i	0.353358	−	0.612035i	0.986836	+	0.161727i	$0.0517063\pi$
$200$		0			0
$201$	−8.54681	−	3.11078i	−0.602845	−	0.219418i
$202$	−14.0098	+	2.47031i	−0.985726	+	0.173810i
$203$	8.19516	−	9.76662i	0.575188	−	0.685482i
$204$	0.149072	+	0.125086i	0.0104371	+	0.00875780i
$205$		0			0
$206$	−2.56932	−	0.935157i	−0.179013	−	0.0651555i
$207$	−8.75736	+	24.0607i	−0.608679	+	1.67233i
$208$	3.37946	+	1.95113i	0.234323	+	0.135287i
$209$	3.47207	−	19.6911i	0.240168	−	1.36206i
$210$		0			0
$211$	4.17535	+	7.23192i	0.287443	+	0.497866i	0.973199	−	0.229966i	$-0.0738615\pi$
$211$	4.17535	+	7.23192i	0.287443	+	0.497866i	−0.685756	+	0.727832i	$0.740528\pi$
$212$	−1.73876	−	1.00387i	−0.119418	−	0.0689463i
$213$	13.8912	−	2.44939i	0.951808	−	0.167829i
$214$	8.84866	+	15.3263i	0.604882	+	1.04769i
$215$		0			0
$216$	−8.86173			−0.602964
$217$	−12.5295	−	34.4246i	−0.850559	−	2.33689i
$218$	−18.8831	−	3.32961i	−1.27893	−	0.225509i
$219$	−19.0460	−	15.9815i	−1.28701	−	1.07993i
$220$		0			0
$221$	−0.231149			−0.0155488
$222$	14.7620	−	8.28315i	0.990759	−	0.555929i
$223$			16.1616i			1.08226i	0.840938	+	0.541131i	$0.182004\pi$
$223$			16.1616i			1.08226i	−0.840938	+	0.541131i	$0.817996\pi$
$224$	17.7805	−	14.9196i	1.18801	−	0.996861i
$225$		0			0
$226$	−2.92380	+	16.5817i	−0.194488	+	1.10300i
$227$	−6.79757	−	18.6762i	−0.451171	−	1.23958i	−0.931901	−	0.362713i	$-0.881851\pi$
$227$	−6.79757	−	18.6762i	−0.451171	−	1.23958i	0.480730	−	0.876869i	$-0.340372\pi$
$228$		−	15.1863i		−	1.00574i
$229$	−16.0263	+	5.83308i	−1.05904	+	0.385461i	−0.812069	−	0.583561i	$-0.801659\pi$
$229$	−16.0263	+	5.83308i	−1.05904	+	0.385461i	−0.246975	+	0.969022i	$0.579437\pi$
$230$		0			0
$231$	−7.34195	−	41.6383i	−0.483065	−	2.73960i
$232$	−6.73443	−	3.88813i	−0.442137	−	0.255268i
$233$	22.9180	−	13.2317i	1.50141	−	0.866837i	0.501407	−	0.865212i	$-0.332816\pi$
$233$	22.9180	−	13.2317i	1.50141	−	0.866837i	0.999999	−	0.00162504i	$-0.000517266\pi$
$234$	9.42014	−	7.90444i	0.615814	−	0.516729i
$235$		0			0
$236$	−2.89810	+	5.01966i	−0.188650	+	0.326752i
$237$	1.71991	−	4.72541i	0.111720	−	0.306948i
$238$	0.143153	−	0.393309i	0.00927921	−	0.0254944i
$239$	−1.16640	−	6.61497i	−0.0754480	−	0.427887i	−0.999012	−	0.0444423i	$-0.985849\pi$
$239$	−1.16640	−	6.61497i	−0.0754480	−	0.427887i	0.923564	−	0.383444i	$-0.125262\pi$
$240$		0			0
$241$	−3.45982	−	2.90313i	−0.222867	−	0.187007i	0.524517	−	0.851400i	$-0.324246\pi$
$241$	−3.45982	−	2.90313i	−0.222867	−	0.187007i	−0.747384	+	0.664393i	$0.768690\pi$
$242$	0.872827	−	0.153903i	0.0561074	−	0.00989325i
$243$	7.10703	−	19.5264i	0.455916	−	1.25262i
$244$	1.65141	+	0.601064i	0.105721	+	0.0384792i
$245$		0			0
$246$	−2.10263	+	11.9246i	−0.134059	+	0.760284i
$247$	11.5950	+	13.8184i	0.737771	+	0.879241i
$248$	−19.3505	+	11.1720i	−1.22876	+	0.709425i
$249$	−5.45286	+	9.44463i	−0.345561	+	0.598529i
$250$		0			0
$251$	−3.86083	−	6.68715i	−0.243693	−	0.422089i	0.718070	−	0.695971i	$-0.245026\pi$
$251$	−3.86083	−	6.68715i	−0.243693	−	0.422089i	−0.961763	+	0.273882i	$0.911692\pi$
$252$	−6.33906	−	17.4164i	−0.399323	−	1.09713i
$253$			19.9228i			1.25253i
$254$	11.6019	−	4.22276i	0.727971	−	0.264960i
$255$		0			0
$256$	−12.7345	−	10.6855i	−0.795908	−	0.667846i
$257$	16.8589	+	20.0917i	1.05163	+	1.25328i	0.966433	+	0.256919i	$0.0827073\pi$
$257$	16.8589	+	20.0917i	1.05163	+	1.25328i	0.0851962	+	0.996364i	$0.472848\pi$
$258$			23.5061i			1.46343i
$259$	22.9737	+	19.7623i	1.42751	+	1.22797i
$260$		0			0
$261$	−8.02759	+	6.73594i	−0.496895	+	0.416944i
$262$	−3.99481	+	4.76083i	−0.246800	+	0.294125i
$263$	−24.2132	−	4.26944i	−1.49305	−	0.263265i	−0.633271	−	0.773931i	$-0.718288\pi$
$263$	−24.2132	−	4.26944i	−1.49305	−	0.263265i	−0.859779	+	0.510666i	$0.829399\pi$
$264$	−24.2330	+	8.82009i	−1.49144	+	0.542839i
$265$		0			0
$266$	−30.6933	+	11.1715i	−1.88193	+	0.684966i
$267$	6.31912	−	3.64835i	0.386724	−	0.223275i
$268$	−3.05512	+	0.538701i	−0.186621	+	0.0329064i
$269$	3.74436	−	6.48542i	0.228298	−	0.395423i	−0.729006	−	0.684507i	$-0.760017\pi$
$269$	3.74436	−	6.48542i	0.228298	−	0.395423i	0.957304	+	0.289084i	$0.0933507\pi$
$270$		0			0
$271$	0.352308	−	0.295622i	0.0214012	−	0.0179578i	−0.632024	−	0.774949i	$-0.717776\pi$
$271$	0.352308	−	0.295622i	0.0214012	−	0.0179578i	0.653426	+	0.756991i	$0.273331\pi$
$272$	−0.107511	−	0.0189571i	−0.00651882	−	0.00114944i
$273$	33.0337	+	19.0720i	1.99929	+	1.15429i
$274$	−14.1155	−	5.13762i	−0.852749	−	0.310375i
$275$		0			0
$276$	2.62757	+	14.9017i	0.158161	+	0.896978i
$277$	19.1447	−	22.8158i	1.15030	−	1.37087i	0.233090	−	0.972455i	$-0.425116\pi$
$277$	19.1447	−	22.8158i	1.15030	−	1.37087i	0.917206	−	0.398414i	$-0.130439\pi$
$278$	−10.8567	+	12.9386i	−0.651144	+	0.776004i
$279$	5.22870	+	29.6534i	0.313034	+	1.77530i
$280$		0			0
$281$	13.3544	+	4.86061i	0.796658	+	0.289960i	0.708101	−	0.706111i	$-0.249552\pi$
$281$	13.3544	+	4.86061i	0.796658	+	0.289960i	0.0885571	+	0.996071i	$0.471774\pi$
$282$	−26.6436	−	15.3827i	−1.58660	−	0.916026i
$283$	19.1513	+	3.37689i	1.13843	+	0.200735i	0.710918	−	0.703275i	$-0.248280\pi$
$283$	19.1513	+	3.37689i	1.13843	+	0.200735i	0.427510	+	0.904011i	$0.359391\pi$
$284$	3.68554	−	3.09253i	0.218696	−	0.183508i
$285$		0			0
$286$	4.78411	−	8.28632i	0.282890	−	0.489980i
$287$	−21.3482	+	3.76427i	−1.26015	+	0.222198i
$288$	−16.5220	+	9.53898i	−0.973568	+	0.562090i
$289$	−15.9687	+	5.81213i	−0.939335	+	0.341890i
$290$		0			0
$291$	8.30673	−	3.02340i	0.486949	−	0.177235i
$292$	−8.35143	−	1.47258i	−0.488731	−	0.0861764i
$293$	5.46938	−	6.51816i	0.319525	−	0.380795i	−0.582244	−	0.813014i	$-0.697825\pi$
$293$	5.46938	−	6.51816i	0.319525	−	0.380795i	0.901768	+	0.432220i	$0.142269\pi$
$294$	−37.9876	+	31.8753i	−2.21548	+	1.85901i
$295$		0			0
$296$	9.43728	−	15.8925i	0.548530	−	0.923735i
$297$			9.29195i			0.539174i
$298$	3.33713	+	3.97703i	0.193314	+	0.230383i
$299$	−13.7685	−	11.5532i	−0.796256	−	0.668138i
$300$		0			0
$301$	−39.5444	+	14.3930i	−2.27930	+	0.829598i
$302$		−	9.34196i		−	0.537569i
$303$	12.4050	+	34.0824i	0.712647	+	1.95798i
$304$	4.25974	+	7.37808i	0.244313	+	0.423162i
$305$		0			0
$306$	−0.172012	+	0.297933i	−0.00983327	+	0.0170317i
$307$	−16.9403	+	9.78051i	−0.966836	+	0.558203i	−0.898270	−	0.439444i	$-0.855176\pi$
$307$	−16.9403	+	9.78051i	−0.966836	+	0.558203i	−0.0685658	+	0.997647i	$0.521842\pi$
$308$	−9.26975	−	11.0473i	−0.528193	−	0.629476i
$309$	−1.21051	+	6.86512i	−0.0688632	+	0.390543i
$310$		0			0
$311$	−2.49881	−	0.909494i	−0.141695	−	0.0515727i	0.270199	−	0.962804i	$-0.412910\pi$
$311$	−2.49881	−	0.909494i	−0.141695	−	0.0515727i	−0.411894	+	0.911232i	$0.635133\pi$
$312$	7.95715	−	21.8621i	0.450485	−	1.23770i
$313$	5.46501	−	0.963629i	0.308901	−	0.0544676i	−0.0170489	−	0.999855i	$-0.505427\pi$
$313$	5.46501	−	0.963629i	0.308901	−	0.0544676i	0.325950	+	0.945387i	$0.394316\pi$
$314$	−2.63751	−	2.21313i	−0.148843	−	0.124894i
$315$		0			0
$316$	−0.297840	−	1.68913i	−0.0167548	−	0.0950212i
$317$	8.73896	−	24.0101i	0.490829	−	1.34854i	−0.409094	−	0.912492i	$-0.634155\pi$
$317$	8.73896	−	24.0101i	0.490829	−	1.34854i	0.899923	−	0.436049i	$-0.143623\pi$
$318$	2.10334	−	5.77889i	0.117950	−	0.324064i
$319$	−4.07689	+	7.06137i	−0.228262	+	0.395361i
$320$		0			0
$321$	34.5641	−	29.0027i	1.92918	−	1.61877i
$322$	28.1852	−	16.2727i	1.57070	−	0.906843i
$323$	−0.437037	−	0.252324i	−0.0243174	−	0.0140397i
$324$	−0.712548	−	4.04106i	−0.0395860	−	0.224503i
$325$		0			0
$326$	−6.73535	+	2.45147i	−0.373036	+	0.135774i
$327$			48.8862i			2.70341i
$328$	4.52212	+	12.4244i	0.249692	+	0.686024i
$329$	9.56426	−	54.2416i	0.527295	−	2.99044i
$330$		0			0
$331$	4.68985	−	3.93525i	0.257777	−	0.216301i	−0.504735	−	0.863274i	$-0.668410\pi$
$331$	4.68985	−	3.93525i	0.257777	−	0.216301i	0.762513	+	0.646973i	$0.223965\pi$
$332$			3.71975i			0.204148i
$333$	−15.7755	−	19.2757i	−0.864491	−	1.05630i
$334$	−18.6837			−1.02232
$335$		0			0
$336$	13.8004	+	11.5799i	0.752871	+	0.631734i
$337$	7.30961	+	1.28888i	0.398180	+	0.0702098i	0.369153	−	0.929369i	$-0.379648\pi$
$337$	7.30961	+	1.28888i	0.398180	+	0.0702098i	0.0290271	+	0.999579i	$0.490759\pi$
$338$	−1.69285	−	4.65106i	−0.0920788	−	0.252985i
$339$	42.9280			2.33153
$340$		0			0
$341$	11.7144	+	20.2900i	0.634372	+	1.09876i
$342$	26.4393	−	4.66197i	1.42968	−	0.252090i
$343$	−46.6826	−	26.9522i	−2.52062	−	1.45528i
$344$	12.8336	+	22.2285i	0.691943	+	1.19848i
$345$		0			0
$346$	3.86002	−	21.8913i	0.207516	−	1.17688i
$347$	−18.9388	−	10.9343i	−1.01669	−	0.586986i	−0.103546	−	0.994625i	$-0.533019\pi$
$347$	−18.9388	−	10.9343i	−1.01669	−	0.586986i	−0.913143	+	0.407638i	$0.866352\pi$
$348$	−2.11810	+	5.81942i	−0.113542	+	0.311954i
$349$	0.0544715	+	0.0198260i	0.00291579	+	0.00106126i	0.343478	−	0.939161i	$-0.388395\pi$
$349$	0.0544715	+	0.0198260i	0.00291579	+	0.00106126i	−0.340562	+	0.940222i	$0.610617\pi$
$350$		0			0
$351$	−6.42164	−	5.38839i	−0.342762	−	0.287611i
$352$	−9.54173	+	11.3714i	−0.508576	+	0.606097i
$353$	−1.69698	+	0.299224i	−0.0903213	+	0.0159261i	−0.218626	−	0.975809i	$-0.570158\pi$
$353$	−1.69698	+	0.299224i	−0.0903213	+	0.0159261i	0.128305	+	0.991735i	$0.459046\pi$
$354$	−16.6832	−	6.07219i	−0.886703	−	0.322733i
$355$		0			0
$356$	1.24439	−	2.15534i	0.0659523	−	0.114233i
$357$	−1.05090	−	0.185303i	−0.0556197	−	0.00980725i
$358$	7.79569	+	9.29054i	0.412015	+	0.491020i
$359$	−9.22498	−	15.9781i	−0.486876	−	0.843293i	0.513011	−	0.858382i	$-0.328530\pi$
$359$	−9.22498	−	15.9781i	−0.486876	−	0.843293i	−0.999886	+	0.0150890i	$0.995197\pi$
$360$		0			0
$361$	3.53931	+	20.0724i	0.186279	+	1.05644i
$362$	0.556646	−	0.321379i	0.0292566	−	0.0168913i
$363$	−0.772844	−	2.12337i	−0.0405638	−	0.111448i
$364$	13.0102			0.681922
$365$		0			0
$366$	−0.934736	+	5.30115i	−0.0488594	+	0.277096i
$367$	3.73524	−	4.45149i	0.194978	−	0.232366i	−0.659694	−	0.751535i	$-0.729314\pi$
$367$	3.73524	−	4.45149i	0.194978	−	0.232366i	0.854672	+	0.519169i	$0.173758\pi$
$368$	−5.45647	−	6.50277i	−0.284438	−	0.338980i
$369$	17.8177			0.927552
$370$		0			0
$371$	11.0097			0.571597
$372$	11.4381	+	13.6314i	0.593038	+	0.706755i
$373$	22.7543	−	27.1176i	1.17817	−	1.40409i	0.282568	−	0.959247i	$-0.408814\pi$
$373$	22.7543	−	27.1176i	1.17817	−	1.40409i	0.895607	−	0.444847i	$-0.146742\pi$
$374$	−0.0464822	+	0.263614i	−0.00240354	+	0.0136311i
$375$		0			0
$376$	−33.5939			−1.73248
$377$	−2.51591	−	6.91241i	−0.129576	−	0.356007i
$378$	13.1455	−	7.58958i	0.676133	−	0.390366i
$379$	−3.19414	−	18.1149i	−0.164072	−	0.930499i	−0.950016	−	0.312201i	$-0.898934\pi$
$379$	−3.19414	−	18.1149i	−0.164072	−	0.930499i	0.785944	−	0.618298i	$-0.212177\pi$
$380$		0			0
$381$	−15.7390	−	27.2608i	−0.806335	−	1.39661i
$382$	3.74329	+	4.46108i	0.191523	+	0.228249i
$383$	14.5960	+	2.57367i	0.745820	+	0.131508i	0.533627	−	0.845720i	$-0.320828\pi$
$383$	14.5960	+	2.57367i	0.745820	+	0.131508i	0.212193	+	0.977228i	$0.431940\pi$
$384$	−1.85937	+	3.22052i	−0.0948854	+	0.164346i
$385$		0			0
$386$	5.20969	+	1.89617i	0.265166	+	0.0965126i
$387$	34.0637	−	6.00635i	1.73155	−	0.305320i
$388$	1.93808	−	2.30971i	0.0983909	−	0.117258i
$389$	−26.9094	−	22.5796i	−1.36436	−	1.14483i	−0.974609	−	0.223912i	$-0.928117\pi$
$389$	−26.9094	−	22.5796i	−1.36436	−	1.14483i	−0.389749	−	0.920921i	$-0.627438\pi$
$390$		0			0
$391$	0.472504	+	0.171977i	0.0238955	+	0.00869726i
$392$	−18.5199	+	50.8829i	−0.935394	+	2.56997i
$393$	13.7222	+	7.92250i	0.692192	+	0.399637i
$394$	−2.04743	+	11.6116i	−0.103148	+	0.584982i
$395$		0			0
$396$	5.92668	+	10.2653i	0.297827	+	0.515851i
$397$	−21.6773	−	12.5154i	−1.08795	−	0.628131i	−0.154923	−	0.987927i	$-0.549513\pi$
$397$	−21.6773	−	12.5154i	−1.08795	−	0.628131i	−0.933031	+	0.359796i	$0.882846\pi$
$398$	10.2573	−	1.80864i	0.514151	−	0.0906588i
$399$	41.6382	+	72.1195i	2.08452	+	3.61049i
$400$		0			0
$401$	3.25793			0.162693			0.0813467	−	0.996686i	$-0.474078\pi$
$401$	3.25793			0.162693			0.0813467	+	0.996686i	$0.474078\pi$
$402$	−3.24997	−	8.92921i	−0.162094	−	0.445348i
$403$	−20.8155	−	3.67034i	−1.03689	−	0.182832i
$404$	9.47670	+	7.95190i	0.471483	+	0.395622i
$405$		0			0
$406$	13.3198			0.661053
$407$	−16.6641	−	9.89544i	−0.826008	−	0.490499i
$408$			0.650866i			0.0322226i
$409$	20.6592	−	17.3351i	1.02153	−	0.857166i	0.0317117	−	0.999497i	$-0.489904\pi$
$409$	20.6592	−	17.3351i	1.02153	−	0.857166i	0.989819	+	0.142331i	$0.0454597\pi$
$410$		0			0
$411$	−6.65035	+	37.7160i	−0.328037	+	1.86039i
$412$	0.813219	+	2.23430i	0.0400644	+	0.110076i
$413$		−	31.7843i		−	1.56400i
$414$	−25.1372	+	9.14919i	−1.23543	+	0.449658i
$415$		0			0
$416$	−2.32549	−	13.1885i	−0.114017	−	0.646620i
$417$	37.2929	+	21.5311i	1.82624	+	1.05438i
$418$	18.0908	−	10.4447i	0.884849	−	0.510868i
$419$	−9.61442	+	8.06746i	−0.469695	+	0.394121i	−0.846683	−	0.532097i	$-0.821404\pi$
$419$	−9.61442	+	8.06746i	−0.469695	+	0.394121i	0.376988	+	0.926218i	$0.376960\pi$
$420$		0			0
$421$	5.52635	−	9.57191i	0.269338	−	0.466506i	−0.699353	−	0.714776i	$-0.746529\pi$
$421$	5.52635	−	9.57191i	0.269338	−	0.466506i	0.968691	+	0.248270i	$0.0798619\pi$
$422$	−2.98390	+	8.19819i	−0.145254	+	0.399081i
$423$	−15.4837	+	42.5410i	−0.752841	+	2.06841i
$424$	−1.16608	−	6.61315i	−0.0566297	−	0.321163i
$425$		0			0
$426$	11.2889	+	9.47249i	0.546948	+	0.458944i
$427$	−9.49049	+	1.67343i	−0.459277	+	0.0809830i
$428$	5.26359	−	14.4616i	0.254425	−	0.699027i
$429$	−22.9235	−	8.34346i	−1.10676	−	0.402826i
$430$		0			0
$431$	−3.66521	+	20.7864i	−0.176547	+	1.00125i	0.759796	+	0.650161i	$0.225299\pi$
$431$	−3.66521	+	20.7864i	−0.176547	+	1.00125i	−0.936343	+	0.351086i	$0.885812\pi$
$432$	−2.54489	−	3.03288i	−0.122441	−	0.145920i
$433$	−5.95907	+	3.44047i	−0.286375	+	0.165339i	−0.636306	−	0.771437i	$-0.719538\pi$
$433$	−5.95907	+	3.44047i	−0.286375	+	0.165339i	0.349931	+	0.936775i	$0.386205\pi$
$434$	19.1365	−	33.1453i	0.918579	−	1.59103i
$435$		0			0
$436$	8.33710	+	14.4403i	0.399275	+	0.691564i
$437$	−13.4209	−	36.8736i	−0.642009	−	1.76390i
$438$		−	25.9752i		−	1.24114i
$439$	−19.7407	+	7.18502i	−0.942171	+	0.342922i	−0.767023	−	0.641620i	$-0.778263\pi$
$439$	−19.7407	+	7.18502i	−0.942171	+	0.342922i	−0.175148	+	0.984542i	$0.556040\pi$
$440$		0			0
$441$	55.8986	+	46.9045i	2.66184	+	2.23355i
$442$	−0.155227	−	0.184993i	−0.00738342	−	0.00879921i
$443$			28.8154i			1.36906i	0.728985	+	0.684530i	$0.239992\pi$
$443$			28.8154i			1.36906i	−0.728985	+	0.684530i	$0.760008\pi$
$444$	−13.7694	−	5.20374i	−0.653467	−	0.246959i
$445$		0			0
$446$	−12.9345	+	10.8533i	−0.612464	+	0.513919i
$447$	8.50817	−	10.1396i	0.402422	−	0.479588i
$448$	37.2022	+	6.55975i	1.75764	+	0.309919i
$449$	−3.69401	+	1.34451i	−0.174331	+	0.0634514i	−0.427711	−	0.903915i	$-0.640680\pi$
$449$	−3.69401	+	1.34451i	−0.174331	+	0.0634514i	0.253380	+	0.967367i	$0.418458\pi$
$450$		0			0
$451$	13.0276	−	4.74166i	0.613446	−	0.223276i
$452$	12.6803	−	7.32099i	0.596432	−	0.344350i
$453$	−23.4559	+	4.13592i	−1.10206	+	0.194322i
$454$	10.3820	−	17.9822i	0.487252	−	0.843945i
$455$		0			0
$456$	38.9095	−	32.6490i	1.82211	−	1.52893i
$457$	16.9152	+	2.98261i	0.791260	+	0.139521i	0.554650	−	0.832084i	$-0.312852\pi$
$457$	16.9152	+	2.98261i	0.791260	+	0.139521i	0.236611	+	0.971605i	$0.423963\pi$
$458$	−15.4307	−	8.90892i	−0.721030	−	0.416287i
$459$	0.220375	+	0.0802100i	0.0102862	+	0.00374388i
$460$		0			0
$461$	3.97914	+	22.5668i	0.185327	+	1.05104i	0.925534	+	0.378664i	$0.123616\pi$
$461$	3.97914	+	22.5668i	0.185327	+	1.05104i	−0.740207	+	0.672379i	$0.765273\pi$
$462$	28.3934	−	33.8380i	1.32098	−	1.57428i
$463$	18.2936	−	21.8014i	0.850174	−	1.01320i	−0.149528	−	0.988758i	$-0.547775\pi$
$463$	18.2936	−	21.8014i	0.850174	−	1.01320i	0.999701	−	0.0244399i	$-0.00778024\pi$
$464$	−0.603287	−	3.42141i	−0.0280069	−	0.158835i
$465$		0			0
$466$	25.9801	+	9.45597i	1.20350	+	0.438039i
$467$	14.8325	+	8.56355i	0.686366	+	0.396274i	0.802249	−	0.596989i	$-0.203636\pi$
$467$	14.8325	+	8.56355i	0.686366	+	0.396274i	−0.115883	+	0.993263i	$0.536970\pi$
$468$	−10.5312	−	1.85693i	−0.486804	−	0.0858368i
$469$	13.0317	−	10.9349i	0.601746	−	0.504925i
$470$		0			0
$471$	−4.38908	+	7.60211i	−0.202238	+	0.350287i
$472$	−19.0917	+	3.36638i	−0.878765	+	0.154950i
$473$	23.3077	−	13.4567i	1.07169	−	0.618739i
$474$	4.93683	−	1.79686i	0.226756	−	0.0825325i
$475$		0			0
$476$	−0.342024	+	0.124486i	−0.0156766	+	0.00570583i
$477$	−8.91188	−	1.57141i	−0.408047	−	0.0719497i
$478$	4.51079	−	5.37575i	0.206319	−	0.245881i
$479$	−5.06826	+	4.25278i	−0.231575	+	0.194314i	−0.751190	−	0.660086i	$-0.770520\pi$
$479$	−5.06826	+	4.25278i	−0.231575	+	0.194314i	0.519615	+	0.854400i	$0.326075\pi$
$480$		0			0
$481$	16.5022	−	5.77814i	0.752435	−	0.263461i
$482$		−	4.71855i		−	0.214924i
$483$	−53.3361	−	63.5634i	−2.42687	−	2.89224i
$484$	−0.590409	−	0.495412i	−0.0268368	−	0.0225187i
$485$		0			0
$486$	20.4000	−	7.42501i	0.925365	−	0.336805i
$487$		−	3.43300i		−	0.155564i	−0.996970	−	0.0777821i	$-0.975216\pi$
$487$		−	3.43300i		−	0.155564i	0.996970	−	0.0777821i	$-0.0247838\pi$
$488$	2.01034	+	5.52336i	0.0910037	+	0.250031i
$489$	9.13708	+	15.8259i	0.413193	+	0.715671i
$490$		0			0
$491$	−9.00979	+	15.6054i	−0.406606	+	0.704263i	−0.994507	−	0.104670i	$-0.966621\pi$
$491$	−9.00979	+	15.6054i	−0.406606	+	0.704263i	0.587901	+	0.808933i	$0.299955\pi$
$492$	9.11896	−	5.26483i	0.411114	−	0.237357i
$493$	0.132281	+	0.157646i	0.00595762	+	0.00710001i
$494$	−3.27252	+	18.5594i	−0.147237	+	0.835025i
$495$		0			0
$496$	−9.38062	−	3.41427i	−0.421202	−	0.153305i
$497$	−9.02333	+	24.7914i	−0.404752	+	1.11205i
$498$	−11.2206	+	1.97849i	−0.502806	+	0.0886582i
$499$	−6.16657	−	5.17436i	−0.276053	−	0.231636i	0.494241	−	0.869325i	$-0.335446\pi$
$499$	−6.16657	−	5.17436i	−0.276053	−	0.231636i	−0.770294	+	0.637689i	$0.779891\pi$
$500$		0			0
$501$	8.27171	+	46.9112i	0.369553	+	2.09584i
$502$	2.75912	−	7.58063i	0.123146	−	0.338340i
$503$	−8.15701	+	22.4112i	−0.363703	+	0.999266i	0.614006	+	0.789302i	$0.289557\pi$
$503$	−8.15701	+	22.4112i	−0.363703	+	0.999266i	−0.977709	+	0.209965i	$0.932665\pi$
$504$	30.9950	−	53.6849i	1.38063	−	2.39132i
$505$		0			0
$506$	−15.9446	+	13.3791i	−0.708822	+	0.594772i
$507$	−10.9285	+	6.30957i	−0.485352	+	0.280218i
$508$	−9.29818	−	5.36831i	−0.412540	−	0.238180i
$509$	1.08826	+	6.17183i	0.0482363	+	0.273562i	0.999381	−	0.0351844i	$-0.0112018\pi$
$509$	1.08826	+	6.17183i	0.0482363	+	0.273562i	−0.951145	+	0.308746i	$0.900091\pi$
$510$		0			0
$511$	43.6982	−	15.9049i	1.93310	−	0.703589i
$512$		−	14.5753i		−	0.644143i
$513$	−6.25949	−	17.1978i	−0.276363	−	0.759302i
$514$	−4.75818	+	26.9850i	−0.209874	+	1.19026i
$515$		0			0
$516$	15.6588	−	13.1393i	0.689339	−	0.578424i
$517$			35.2249i			1.54919i
$518$	−0.388229	+	31.6576i	−0.0170578	+	1.39095i
$519$	−56.6739			−2.48771
$520$		0			0
$521$	−14.0940	−	11.8263i	−0.617470	−	0.518118i	0.279537	−	0.960135i	$-0.409819\pi$
$521$	−14.0940	−	11.8263i	−0.617470	−	0.518118i	−0.897007	+	0.442016i	$0.854263\pi$
$522$	−10.7818	−	1.90112i	−0.471907	−	0.0832099i
$523$	5.07840	+	13.9528i	0.222063	+	0.610112i	0.999830	−	0.0184401i	$-0.00587000\pi$
$523$	5.07840	+	13.9528i	0.222063	+	0.610112i	−0.777767	+	0.628552i	$0.783648\pi$
$524$	5.40445			0.236095
$525$		0			0
$526$	−12.8434	−	22.2454i	−0.559999	−	0.969946i
$527$	0.582334	−	0.102681i	0.0253669	−	0.00447286i
$528$	−9.97781	−	5.76069i	−0.434228	−	0.250702i
$529$	8.04931	+	13.9418i	0.349970	+	0.606166i
$530$		0			0
$531$	−4.53653	+	25.7279i	−0.196868	+	1.11650i
$532$	24.5987	+	14.2021i	1.06649	+	0.615737i
$533$	−4.27775	+	11.7530i	−0.185290	+	0.509080i
$534$	7.16343	+	2.60727i	0.309992	+	0.112828i
$535$		0			0
$536$	−7.94840	−	6.66950i	−0.343319	−	0.288079i
$537$	19.8755	−	23.6867i	0.857690	−	1.02216i
$538$	7.70492	−	1.35859i	0.332183	−	0.0585728i
$539$	53.3532	+	19.4190i	2.29808	+	0.836434i
$540$		0			0
$541$	15.9985	−	27.7102i	0.687829	−	1.19135i	−0.284710	−	0.958614i	$-0.591897\pi$
$541$	15.9985	−	27.7102i	0.687829	−	1.19135i	0.972539	−	0.232741i	$-0.0747695\pi$
$542$	0.473184	+	0.0834350i	0.0203250	+	0.00358384i
$543$	−1.05337	−	1.25535i	−0.0452042	−	0.0538723i
$544$	0.187327	+	0.324459i	0.00803156	+	0.0139111i
$545$		0			0
$546$	6.91999	+	39.2452i	0.296148	+	1.67954i
$547$	38.1374	−	22.0187i	1.63064	−	0.941450i	0.646743	−	0.762708i	$-0.276131\pi$
$547$	38.1374	−	22.0187i	1.63064	−	0.941450i	0.983896	−	0.178742i	$-0.0572028\pi$
$548$	4.46771	+	12.2749i	0.190851	+	0.524359i
$549$	7.92097			0.338059
$550$		0			0
$551$	2.78875	−	15.8158i	0.118805	−	0.673775i
$552$	−32.5313	+	38.7693i	−1.38462	+	1.65013i
$553$	6.04573	+	7.20502i	0.257091	+	0.306389i
$554$	31.1165			1.32201
$555$		0			0
$556$	14.6877			0.622899
$557$	15.3473	+	18.2902i	0.650287	+	0.774981i	0.985957	−	0.166998i	$-0.0534074\pi$
$557$	15.3473	+	18.2902i	0.650287	+	0.774981i	−0.335671	+	0.941979i	$0.608963\pi$
$558$	−20.2209	+	24.0983i	−0.856018	+	1.02016i
$559$	−4.21622	+	23.9114i	−0.178327	+	1.01134i
$560$		0			0
$561$	0.682464			0.0288136
$562$	5.07808	+	13.9519i	0.214206	+	0.588526i
$563$	4.72936	−	2.73050i	0.199319	−	0.115077i	−0.397019	−	0.917810i	$-0.629955\pi$
$563$	4.72936	−	2.73050i	0.199319	−	0.115077i	0.596338	+	0.802734i	$0.296622\pi$
$564$	4.64574	+	26.3473i	0.195621	+	1.10942i
$565$		0			0
$566$	10.1584	+	17.5949i	0.426990	+	0.739569i
$567$	14.4637	+	17.2372i	0.607419	+	0.723894i
$568$	15.8470	+	2.79425i	0.664925	+	0.117244i
$569$	−7.72113	+	13.3734i	−0.323686	+	0.560641i	−0.981246	−	0.192762i	$-0.938256\pi$
$569$	−7.72113	+	13.3734i	−0.323686	+	0.560641i	0.657559	+	0.753403i	$0.271589\pi$
$570$		0			0
$571$	−27.3413	−	9.95143i	−1.14420	−	0.416454i	−0.300771	−	0.953696i	$-0.597244\pi$
$571$	−27.3413	−	9.95143i	−1.14420	−	0.416454i	−0.843428	+	0.537242i	$0.819466\pi$
$572$	−8.19417	+	1.44485i	−0.342616	+	0.0604124i
$573$	9.54370	−	11.3737i	0.398694	−	0.475145i
$574$	−17.3490	−	14.5575i	−0.724132	−	0.607619i
$575$		0			0
$576$	−29.1772	−	10.6196i	−1.21572	−	0.442485i
$577$	2.31136	−	6.35040i	0.0962231	−	0.264371i	−0.882237	−	0.470805i	$-0.843964\pi$
$577$	2.31136	−	6.35040i	0.0962231	−	0.264371i	0.978461	+	0.206434i	$0.0661859\pi$
$578$	−15.3753	−	8.87693i	−0.639528	−	0.369232i
$579$	2.45448	−	13.9201i	0.102005	−	0.578498i
$580$		0			0
$581$	−10.1989	−	17.6650i	−0.423121	−	0.732866i
$582$	7.99804	+	4.61767i	0.331530	+	0.191409i
$583$	−6.93421	+	1.22269i	−0.287186	+	0.0506386i
$584$	−14.1817	−	24.5634i	−0.586843	−	1.01644i
$585$		0			0
$586$	8.88955			0.367224
$587$	−4.49130	−	12.3397i	−0.185376	−	0.509316i	0.811841	−	0.583879i	$-0.198466\pi$
$587$	−4.49130	−	12.3397i	−0.185376	−	0.509316i	−0.997216	+	0.0745636i	$0.976244\pi$
$588$	42.4680	+	7.48825i	1.75135	+	0.308810i
$589$	−35.3497	−	29.6619i	−1.45656	−	1.22220i
$590$		0			0
$591$	30.0609			1.23654
$592$	8.14932	−	1.33412i	0.334935	−	0.0548321i
$593$		−	5.47880i		−	0.224987i	−0.993652	−	0.112494i	$-0.964116\pi$
$593$		−	5.47880i		−	0.224987i	0.993652	−	0.112494i	$-0.0358838\pi$
$594$	−7.43652	+	6.23998i	−0.305124	+	0.256030i
$595$		0			0
$596$	0.783967	−	4.44610i	0.0321125	−	0.182119i
$597$	−9.08231	−	24.9534i	−0.371714	−	1.02128i
$598$		−	18.7777i		−	0.767879i
$599$	−20.8876	+	7.60246i	−0.853443	+	0.310628i	−0.731443	−	0.681902i	$-0.761153\pi$
$599$	−20.8876	+	7.60246i	−0.853443	+	0.310628i	−0.122000	+	0.992530i	$0.538931\pi$
$600$		0			0
$601$	2.73822	+	15.5292i	0.111694	+	0.633449i	0.988334	+	0.152302i	$0.0486687\pi$
$601$	2.73822	+	15.5292i	0.111694	+	0.633449i	−0.876640	+	0.481147i	$0.840220\pi$
$602$	−38.0749	−	21.9826i	−1.55182	−	0.895943i
$603$	−12.1092	+	6.99128i	−0.493127	+	0.284707i
$604$	−6.22321	+	5.22190i	−0.253219	+	0.212476i
$605$		0			0
$606$	−18.9462	+	32.8159i	−0.769638	+	1.33305i
$607$	−0.815201	+	2.23975i	−0.0330880	+	0.0909085i	−0.955137	−	0.296166i	$-0.904292\pi$
$607$	−0.815201	+	2.23975i	−0.0330880	+	0.0909085i	0.922049	+	0.387074i	$0.126514\pi$
$608$	9.99981	−	27.4742i	0.405546	−	1.11423i
$609$	−5.89702	−	33.4437i	−0.238959	−	1.35521i
$610$		0			0
$611$	−24.3438	−	20.4269i	−0.984844	−	0.826382i
$612$	0.294620	−	0.0519495i	0.0119093	−	0.00209993i
$613$	6.45695	−	17.7403i	0.260794	−	0.716525i	−0.738321	−	0.674450i	$-0.764381\pi$
$613$	6.45695	−	17.7403i	0.260794	−	0.716525i	0.999114	−	0.0420753i	$-0.0133969\pi$
$614$	−19.2038	−	6.98960i	−0.775001	−	0.282077i
$615$		0			0
$616$	8.37567	−	47.5008i	0.337465	−	1.91386i
$617$	−29.0230	−	34.5882i	−1.16842	−	1.39247i	−0.903712	−	0.428142i	$-0.859168\pi$
$617$	−29.0230	−	34.5882i	−1.16842	−	1.39247i	−0.264710	−	0.964328i	$-0.585276\pi$
$618$	−6.30719	+	3.64146i	−0.253712	+	0.146481i
$619$	16.2799	−	28.1975i	0.654343	−	1.13335i	−0.327716	−	0.944776i	$-0.606279\pi$
$619$	16.2799	−	28.1975i	0.654343	−	1.13335i	0.982058	−	0.188578i	$-0.0603879\pi$
$620$		0			0
$621$	9.11778	+	15.7925i	0.365884	+	0.633729i
$622$	−0.950187	−	2.61062i	−0.0380990	−	0.104676i
$623$			13.6475i			0.546776i
$624$	9.76731	−	3.55501i	0.391006	−	0.142314i
$625$		0			0
$626$	4.44123	+	3.72663i	0.177507	+	0.148946i
$627$	−34.2340	−	40.7985i	−1.36717	−	1.62934i
$628$			2.99408i			0.119477i
$629$	−0.378536	+	0.309799i	−0.0150932	+	0.0123525i
$630$		0			0
$631$	−6.83746	+	5.73731i	−0.272195	+	0.228399i	−0.768659	−	0.639658i	$-0.779076\pi$
$631$	−6.83746	+	5.73731i	−0.272195	+	0.228399i	0.496464	+	0.868057i	$0.334631\pi$
$632$	3.68747	−	4.39456i	0.146680	−	0.174806i
$633$	21.9052	+	3.86247i	0.870653	+	0.153520i
$634$	25.0844	−	9.12996i	0.996227	−	0.362597i
$635$		0			0
$636$	−5.02536	+	1.82908i	−0.199268	+	0.0725278i
$637$	−44.3598	+	25.6112i	−1.75760	+	1.01475i
$638$	−8.38917	+	1.47924i	−0.332131	+	0.0585636i
$639$	10.8424	−	18.7796i	0.428919	−	0.742910i
$640$		0			0
$641$	−22.1766	+	18.6083i	−0.875922	+	0.734985i	−0.965336	−	0.261009i	$-0.915945\pi$
$641$	−22.1766	+	18.6083i	−0.875922	+	0.734985i	0.0894148	+	0.995994i	$0.471500\pi$
$642$	46.4228	+	8.18560i	1.83216	+	0.323060i
$643$	12.0874	+	6.97865i	0.476680	+	0.275211i	0.719032	−	0.694977i	$-0.244586\pi$
$643$	12.0874	+	6.97865i	0.476680	+	0.275211i	−0.242352	+	0.970188i	$0.577919\pi$
$644$	−26.5949	−	9.67975i	−1.04799	−	0.381436i
$645$		0			0
$646$	−0.0915518	−	0.519216i	−0.00360206	−	0.0204283i
$647$	25.5038	−	30.3942i	1.00266	−	1.19492i	0.0218847	−	0.999761i	$-0.493033\pi$
$647$	25.5038	−	30.3942i	1.00266	−	1.19492i	0.980772	−	0.195159i	$-0.0625222\pi$
$648$	8.82186	−	10.5135i	0.346555	−	0.413009i
$649$	3.52981	+	20.0185i	0.138557	+	0.785796i
$650$		0			0
$651$	−91.6940	−	33.3739i	−3.59377	−	1.30803i
$652$	5.39793	+	3.11650i	0.211399	+	0.122051i
$653$	−2.92209	−	0.515243i	−0.114350	−	0.0201630i	0.116180	−	0.993228i	$-0.462935\pi$
$653$	−2.92209	−	0.515243i	−0.114350	−	0.0201630i	−0.230530	+	0.973065i	$0.574046\pi$
$654$	−39.1245	+	32.8294i	−1.52989	+	1.28373i
$655$		0			0
$656$	−2.95355	+	5.11569i	−0.115317	+	0.199734i
$657$	−37.6418	+	6.63726i	−1.46855	+	0.258944i
$658$	49.8334	−	28.7713i	1.94271	−	1.12162i
$659$	9.57151	−	3.48375i	0.372853	−	0.135707i	−0.148795	−	0.988868i	$-0.547540\pi$
$659$	9.57151	−	3.48375i	0.372853	−	0.135707i	0.521648	+	0.853161i	$0.325317\pi$
$660$		0			0
$661$	−14.8577	+	5.40775i	−0.577897	+	0.210337i	−0.614398	−	0.788996i	$-0.710601\pi$
$661$	−14.8577	+	5.40775i	−0.577897	+	0.210337i	0.0365011	+	0.999334i	$0.488379\pi$
$662$	6.29891	+	1.11067i	0.244814	+	0.0431673i
$663$	−0.395760	+	0.471648i	−0.0153700	+	0.0183173i
$664$	−9.53051	+	7.99705i	−0.369856	+	0.310346i
$665$		0			0
$666$	4.83269	−	25.5699i	0.187263	−	0.990815i
$667$			16.0019i			0.619595i
$668$	10.4436	+	12.4462i	0.404077	+	0.481560i
$669$	32.9770	+	27.6710i	1.27497	+	1.06982i
$670$		0			0
$671$	5.79151	−	2.10794i	0.223579	−	0.0813760i
$672$		−	61.8249i		−	2.38495i
$673$	3.83578	+	10.5387i	0.147858	+	0.406238i	0.991407	−	0.130816i	$-0.0417596\pi$
$673$	3.83578	+	10.5387i	0.147858	+	0.406238i	−0.843548	+	0.537053i	$0.819537\pi$
$674$	3.87723	+	6.71556i	0.149345	+	0.258674i
$675$		0			0
$676$	−2.15208	+	3.72752i	−0.0827724	+	0.143366i
$677$	34.6388	−	19.9987i	1.33128	−	0.768614i	0.345783	−	0.938315i	$-0.387613\pi$
$677$	34.6388	−	19.9987i	1.33128	−	0.768614i	0.985496	+	0.169701i	$0.0542801\pi$
$678$	28.8282	+	34.3561i	1.10714	+	1.31944i
$679$	−2.87106	+	16.2826i	−0.110181	+	0.624868i
$680$		0			0
$681$	−49.7463	−	18.1062i	−1.90628	−	0.693830i
$682$	−8.37166	+	23.0009i	−0.320567	+	0.880752i
$683$	−19.1448	+	3.37574i	−0.732555	+	0.129169i	−0.527468	−	0.849575i	$-0.676859\pi$
$683$	−19.1448	+	3.37574i	−0.732555	+	0.129169i	−0.205087	+	0.978744i	$0.565748\pi$
$684$	−17.8845	−	15.0068i	−0.683829	−	0.573801i
$685$		0			0
$686$	−9.77921	−	55.4606i	−0.373372	−	2.11750i
$687$	−15.5371	+	42.6879i	−0.592778	+	1.62864i
$688$	−3.92206	+	10.7758i	−0.149527	+	0.410823i
$689$	3.17615	−	5.50125i	0.121002	−	0.209581i
$690$		0			0
$691$	−8.25740	+	6.92878i	−0.314126	+	0.263583i	−0.786195	−	0.617979i	$-0.787952\pi$
$691$	−8.25740	+	6.92878i	−0.314126	+	0.263583i	0.472069	+	0.881562i	$0.343507\pi$
$692$	−16.7407	+	9.66524i	−0.636385	+	0.367417i
$693$	−56.2912	−	32.4997i	−2.13833	−	1.23456i
$694$	−3.96736	−	22.5000i	−0.150599	−	0.854090i
$695$		0			0
$696$	−19.4638	+	7.08426i	−0.737775	+	0.268528i
$697$		−	0.349904i		−	0.0132536i
$698$	0.0207131	+	0.0569087i	0.000784001	+	0.00215403i
$699$	12.2402	−	69.4175i	0.462966	−	2.62561i
$700$		0			0
$701$	4.07453	−	3.41894i	0.153893	−	0.129132i	−0.562590	−	0.826736i	$-0.690195\pi$
$701$	4.07453	−	3.41894i	0.153893	−	0.129132i	0.716483	+	0.697604i	$0.245751\pi$
$702$		−	8.75792i		−	0.330546i
$703$	37.5084	+	7.08906i	1.41466	+	0.267369i
$704$	−24.1594			−0.910540
$705$		0			0
$706$	−1.37908	−	1.15718i	−0.0519023	−	0.0435512i
$707$	−66.8072	−	11.7799i	−2.51254	−	0.443029i
$708$	5.28041	+	14.5078i	0.198450	+	0.545237i
$709$	−6.11691			−0.229726			−0.114863	−	0.993381i	$-0.536643\pi$
$709$	−6.11691			−0.229726			−0.114863	+	0.993381i	$0.536643\pi$
$710$		0			0
$711$	−3.86538	−	6.69503i	−0.144963	−	0.251083i
$712$	8.19757	−	1.44545i	0.307217	−	0.0541707i
$713$	39.8193	+	22.9897i	1.49124	+	0.860970i
$714$	−0.557430	−	0.965497i	−0.0208613	−	0.0361328i
$715$		0			0
$716$	1.83139	−	10.3863i	0.0684421	−	0.388154i
$717$	−15.4946	−	8.94579i	−0.578655	−	0.334087i
$718$	6.59259	−	18.1130i	0.246033	−	0.675971i
$719$	−41.6005	−	15.1413i	−1.55144	−	0.564676i	−0.582682	−	0.812701i	$-0.697997\pi$
$719$	−41.6005	−	15.1413i	−1.55144	−	0.564676i	−0.968754	+	0.248024i	$0.920219\pi$
$720$		0			0
$721$	−9.98799	−	8.38092i	−0.371972	−	0.312122i
$722$	−13.6875	+	16.3121i	−0.509396	+	0.607075i
$723$	−11.8474	+	2.08902i	−0.440610	+	0.0776914i
$724$	−0.525239	−	0.191171i	−0.0195203	−	0.00710482i
$725$		0			0
$726$	1.18037	−	2.04446i	0.0438077	−	0.0758772i
$727$	19.3623	+	3.41410i	0.718110	+	0.126622i	0.520750	−	0.853709i	$-0.325652\pi$
$727$	19.3623	+	3.41410i	0.718110	+	0.126622i	0.197359	+	0.980331i	$0.436763\pi$
$728$	27.9706	+	33.3340i	1.03666	+	1.23544i
$729$	−20.8995	−	36.1990i	−0.774056	−	1.34070i
$730$		0			0
$731$	−0.117953	−	0.668943i	−0.00436264	−	0.0247418i
$732$	4.05389	−	2.34051i	0.149836	−	0.0865079i
$733$	2.56044	+	7.03474i	0.0945719	+	0.259834i	0.977954	−	0.208819i	$-0.0669618\pi$
$733$	2.56044	+	7.03474i	0.0945719	+	0.259834i	−0.883383	+	0.468653i	$0.844740\pi$
$734$	6.07101			0.224085
$735$		0			0
$736$	−5.05873	+	28.6895i	−0.186467	+	1.05751i
$737$	−6.99329	+	8.33428i	−0.257601	+	0.306997i
$738$	11.9654	+	14.2598i	0.440453	+	0.524912i
$739$	−7.65461			−0.281580			−0.140790	−	0.990040i	$-0.544964\pi$
$739$	−7.65461			−0.281580			−0.140790	+	0.990040i	$0.544964\pi$
$740$		0			0
$741$	48.0480			1.76509
$742$	7.39356	+	8.81131i	0.271426	+	0.323473i
$743$	13.7485	−	16.3848i	0.504383	−	0.601100i	−0.452432	−	0.891799i	$-0.649443\pi$
$743$	13.7485	−	16.3848i	0.504383	−	0.601100i	0.956815	+	0.290699i	$0.0938878\pi$
$744$	−10.3349	+	58.6120i	−0.378895	+	2.14882i
$745$		0			0
$746$	36.9833			1.35405
$747$	5.73422	+	15.7547i	0.209804	+	0.576433i
$748$	0.201590	−	0.116388i	0.00737087	−	0.00425557i
$749$	14.6544	+	83.1094i	0.535461	+	3.03675i
$750$		0			0
$751$	−8.99207	−	15.5747i	−0.328125	−	0.568330i	0.654015	−	0.756482i	$-0.273083\pi$
$751$	−8.99207	−	15.5747i	−0.328125	−	0.568330i	−0.982140	+	0.188152i	$0.939750\pi$
$752$	−9.64743	−	11.4974i	−0.351806	−	0.419266i
$753$	−20.2551	−	3.57152i	−0.738137	−	0.130153i
$754$	3.84258	−	6.65554i	0.139938	−	0.242380i
$755$		0			0
$756$	−12.4038	−	4.51463i	−0.451123	−	0.164195i
$757$	50.1988	−	8.85139i	1.82450	−	0.321709i	0.846835	−	0.531856i	$-0.178505\pi$
$757$	50.1988	−	8.85139i	1.82450	−	0.321709i	0.977670	+	0.210147i	$0.0673942\pi$
$758$	12.3527	−	14.7213i	0.448669	−	0.534703i
$759$	40.6514	+	34.1106i	1.47555	+	1.23814i
$760$		0			0
$761$	30.9833	+	11.2770i	1.12314	+	0.408790i	0.835798	−	0.549037i	$-0.185005\pi$
$761$	30.9833	+	11.2770i	1.12314	+	0.408790i	0.287344	+	0.957827i	$0.407228\pi$
$762$	11.2478	−	30.9032i	0.407466	−	1.11950i
$763$	−79.1852	−	45.7176i	−2.86670	−	1.65509i
$764$	0.879385	−	4.98724i	0.0318150	−	0.180432i
$765$		0			0
$766$	7.74214	+	13.4098i	0.279735	+	0.484515i
$767$	−15.8817	−	9.16929i	−0.573454	−	0.331084i
$768$	−43.6067	+	7.68903i	−1.57352	+	0.277454i
$769$	−15.5904	−	27.0033i	−0.562203	−	0.973765i	−0.997304	−	0.0733827i	$-0.976621\pi$
$769$	−15.5904	−	27.0033i	−0.562203	−	0.973765i	0.435101	−	0.900382i	$-0.356713\pi$
$770$		0			0
$771$	69.8609			2.51598
$772$	−1.64892	−	4.53038i	−0.0593460	−	0.163052i
$773$	16.8875	+	2.97772i	0.607402	+	0.107101i	0.468886	−	0.883259i	$-0.344656\pi$
$773$	16.8875	+	2.97772i	0.607402	+	0.107101i	0.138516	+	0.990360i	$0.455767\pi$
$774$	27.6824	+	23.2283i	0.995022	+	0.834923i
$775$		0			0
$776$	10.0844			0.362010
$777$	79.6582	−	13.0408i	2.85772	−	0.467836i
$778$		−	36.6994i		−	1.31574i
$779$	−20.9177	+	17.5520i	−0.749454	+	0.628866i
$780$		0			0
$781$	2.92991	−	16.6163i	0.104840	−	0.594579i
$782$	0.179672	+	0.493644i	0.00642505	+	0.0176527i
$783$			7.46325i			0.266715i
$784$	−22.7329	+	8.27410i	−0.811890	+	0.295504i
$785$		0			0
$786$	2.87456	+	16.3025i	0.102532	+	0.581489i
$787$	−6.37168	−	3.67869i	−0.227126	−	0.131131i	0.382120	−	0.924113i	$-0.375194\pi$
$787$	−6.37168	−	3.67869i	−0.227126	−	0.131131i	−0.609245	+	0.792982i	$0.708528\pi$
$788$	8.87958	−	5.12663i	0.316322	−	0.182628i
$789$	−50.1680	+	42.0960i	−1.78603	+	1.49866i
$790$		0			0
$791$	−40.1456	+	69.5342i	−1.42741	+	2.47235i
$792$	−13.5594	+	37.2542i	−0.481813	+	1.32377i
$793$	−1.90170	+	5.22488i	−0.0675314	+	0.185541i
$794$	−4.54103	−	25.7535i	−0.161155	−	0.913956i
$795$		0			0
$796$	−6.93837	−	5.82199i	−0.245924	−	0.206355i
$797$	38.3928	−	6.76969i	1.35994	−	0.239795i	0.554360	−	0.832277i	$-0.312963\pi$
$797$	38.3928	−	6.76969i	1.35994	−	0.239795i	0.805583	+	0.592482i	$0.201852\pi$
$798$	−29.7566	+	81.7555i	−1.05337	+	2.89411i
$799$	0.835421	+	0.304068i	0.0295551	+	0.0107572i
$800$		0			0
$801$	1.94789	−	11.0470i	0.0688254	−	0.390328i
$802$	2.18786	+	2.60738i	0.0772559	+	0.0920700i
$803$	−25.7559	+	14.8702i	−0.908907	+	0.524757i
$804$	−4.13161	+	7.15617i	−0.145711	+	0.252378i
$805$		0			0
$806$	−11.0412	−	19.1239i	−0.388908	−	0.673609i
$807$	−6.82231	−	18.7442i	−0.240157	−	0.659825i
$808$			41.3763i			1.45561i
$809$	44.8078	−	16.3087i	1.57536	−	0.573383i	0.601169	−	0.799122i	$-0.294702\pi$
$809$	44.8078	−	16.3087i	1.57536	−	0.573383i	0.974188	+	0.225739i	$0.0724795\pi$
$810$		0			0
$811$	17.0315	+	14.2911i	0.598057	+	0.501830i	0.890821	−	0.454355i	$-0.150130\pi$
$811$	17.0315	+	14.2911i	0.598057	+	0.501830i	−0.292763	+	0.956185i	$0.594575\pi$
$812$	−7.44542	−	8.87311i	−0.261283	−	0.311385i
$813$		−	1.22502i		−	0.0429632i
$814$	−3.27122	−	19.9818i	−0.114656	−	0.700363i
$815$		0			0
$816$	−0.222756	+	0.186914i	−0.00779800	+	0.00654330i
$817$	−34.0734	+	40.6071i	−1.19208	+	1.42066i
$818$	27.7472	+	4.89259i	0.970159	+	0.171065i
$819$	55.1037	−	20.0561i	1.92548	−	0.700816i
$820$		0			0
$821$	−21.5501	+	7.84360i	−0.752104	+	0.273743i	−0.689491	−	0.724294i	$-0.742166\pi$
$821$	−21.5501	+	7.84360i	−0.752104	+	0.273743i	−0.0626132	+	0.998038i	$0.519943\pi$
$822$	−34.6508	+	20.0057i	−1.20859	+	0.697778i
$823$	−36.6392	+	6.46049i	−1.27716	+	0.225198i	−0.770775	−	0.637107i	$-0.780131\pi$
$823$	−36.6392	+	6.46049i	−1.27716	+	0.225198i	−0.506389	+	0.862305i	$0.669020\pi$
$824$	−3.97625	+	6.88707i	−0.138519	+	0.239923i
$825$		0			0
$826$	25.4376	−	21.3446i	0.885086	−	0.742675i
$827$	11.0563	+	1.94952i	0.384465	+	0.0677916i	0.362540	−	0.931968i	$-0.381909\pi$
$827$	11.0563	+	1.94952i	0.384465	+	0.0677916i	0.0219247	+	0.999760i	$0.493021\pi$
$828$	20.1458	+	11.6312i	0.700114	+	0.404211i
$829$	13.1844	+	4.79873i	0.457914	+	0.166667i	0.560669	−	0.828040i	$-0.310544\pi$
$829$	13.1844	+	4.79873i	0.457914	+	0.166667i	−0.102756	+	0.994707i	$0.532766\pi$
$830$		0			0
$831$	−13.7760	−	78.1279i	−0.477886	−	2.71023i
$832$	14.0100	−	16.6965i	0.485709	−	0.578845i
$833$	0.921111	−	1.09774i	0.0319146	−	0.0380343i
$834$	7.81223	+	44.3053i	0.270515	+	1.53417i
$835$		0			0
$836$	−17.0701	−	6.21300i	−0.590381	−	0.214881i
$837$	18.5717	+	10.7224i	0.641931	+	0.370619i
$838$	−12.9131	−	2.27692i	−0.446075	−	0.0786550i
$839$	7.38006	−	6.19260i	0.254788	−	0.213792i	−0.506443	−	0.862274i	$-0.669040\pi$
$839$	7.38006	−	6.19260i	0.254788	−	0.213792i	0.761231	+	0.648481i	$0.224595\pi$
$840$		0			0
$841$	11.2255	−	19.4431i	0.387085	−	0.670451i
$842$	11.3718	−	2.00515i	0.391897	−	0.0691021i
$843$	32.7825	−	18.9270i	1.12909	−	0.651880i
$844$	7.12919	−	2.59481i	0.245397	−	0.0893172i
$845$		0			0
$846$	−44.4444	+	16.1764i	−1.52803	+	0.556157i
$847$	4.16216	+	0.733902i	0.143014	+	0.0252172i
$848$	1.92845	−	2.29824i	0.0662232	−	0.0789217i
$849$	39.6802	−	33.2956i	1.36182	−	1.14270i
$850$		0			0
$851$	−38.0320	−	0.466401i	−1.30372	−	0.0159880i
$852$		−	12.8150i		−	0.439035i
$853$	9.34650	+	11.1387i	0.320018	+	0.381382i	0.901939	−	0.431862i	$-0.142143\pi$
$853$	9.34650	+	11.1387i	0.320018	+	0.381382i	−0.581922	+	0.813245i	$0.697699\pi$
$854$	−7.71259	−	6.47163i	−0.263919	−	0.221455i
$855$		0			0
$856$	48.3687	−	17.6048i	1.65321	−	0.601719i
$857$			39.3109i			1.34284i	0.741079	+	0.671418i	$0.234314\pi$
$857$			39.3109i			1.34284i	−0.741079	+	0.671418i	$0.765686\pi$
$858$	−8.71676	−	23.9491i	−0.297585	−	0.817609i
$859$	13.8271	+	23.9493i	0.471776	+	0.817140i	0.999479	−	0.0322890i	$-0.0102797\pi$
$859$	13.8271	+	23.9493i	0.471776	+	0.817140i	−0.527702	+	0.849429i	$0.676946\pi$
$860$		0			0
$861$	−28.8704	+	50.0050i	−0.983901	+	1.70417i
$862$	−19.0971	+	11.0257i	−0.650451	+	0.375538i
$863$	−24.9643	−	29.7513i	−0.849796	−	1.01275i	−0.999711	−	0.0240482i	$-0.992344\pi$
$863$	−24.9643	−	29.7513i	−0.849796	−	1.01275i	0.149915	−	0.988699i	$-0.452100\pi$
$864$	−2.35939	+	13.3808i	−0.0802680	+	0.455222i
$865$		0			0
$866$	−6.75528	−	2.45872i	−0.229554	−	0.0835507i
$867$	−15.4813	+	42.5346i	−0.525773	+	1.44455i
$868$	−32.7767	+	5.77942i	−1.11251	+	0.196166i
$869$	−4.60791	−	3.86649i	−0.156313	−	0.131162i
$870$		0			0
$871$	−1.70439	−	9.66608i	−0.0577511	−	0.327523i
$872$	−19.0742	+	52.4058i	−0.645932	+	1.77468i
$873$	4.64798	−	12.7702i	0.157310	−	0.432206i
$874$	20.4979	−	35.5034i	0.693351	−	1.20092i
$875$		0			0
$876$	−17.3036	+	14.5194i	−0.584634	+	0.490566i
$877$	−23.4597	+	13.5445i	−0.792179	+	0.457365i	−0.840729	−	0.541456i	$-0.817873\pi$
$877$	−23.4597	+	13.5445i	−0.792179	+	0.457365i	0.0485499	+	0.998821i	$0.484540\pi$
$878$	−19.0071	−	10.9738i	−0.641459	−	0.370346i
$879$	−3.93562	−	22.3200i	−0.132745	−	0.752836i
$880$		0			0
$881$	37.0041	−	13.4684i	1.24670	−	0.453762i	0.367415	−	0.930057i	$-0.380243\pi$
$881$	37.0041	−	13.4684i	1.24670	−	0.453762i	0.879285	+	0.476295i	$0.158021\pi$
$882$			76.2353i			2.56697i
$883$	16.1070	+	44.2537i	0.542044	+	1.48925i	0.844217	+	0.536001i	$0.180066\pi$
$883$	16.1070	+	44.2537i	0.542044	+	1.48925i	−0.302173	+	0.953253i	$0.597712\pi$
$884$	−0.0364665	+	0.206812i	−0.00122650	+	0.00695583i
$885$		0			0
$886$	−23.0615	+	19.3509i	−0.774765	+	0.650105i
$887$		−	30.4180i		−	1.02134i	−0.859778	−	0.510668i	$-0.829398\pi$
$887$		−	30.4180i		−	1.02134i	0.859778	−	0.510668i	$-0.170602\pi$
$888$	−16.2700	−	46.4666i	−0.545985	−	1.55932i
$889$	58.8757			1.97463
$890$		0			0
$891$	−11.0239	−	9.25014i	−0.369314	−	0.309891i
$892$	14.4600	+	2.54969i	0.484157	+	0.0853699i
$893$	−23.7291	−	65.1952i	−0.794065	−	2.18167i
$894$	13.8286			0.462497
$895$		0			0
$896$	−3.47770	−	6.02356i	−0.116182	−	0.201233i
$897$	−47.1474	+	8.31336i	−1.57421	+	0.277575i
$898$	−3.55674	−	2.05349i	−0.118690	−	0.0685257i
$899$	9.40897	+	16.2968i	0.313807	+	0.543529i
$900$		0			0
$901$	−0.0308593	+	0.175012i	−0.00102807	+	0.00583048i
$902$	12.5435	+	7.24199i	0.417653	+	0.241132i
$903$	−38.3375	+	105.331i	−1.27579	+	3.50521i
$904$	46.0187	+	16.7494i	1.53056	+	0.557077i
$905$		0			0
$906$	−19.0618	−	15.9948i	−0.633287	−	0.531391i
$907$	−22.3359	+	26.6189i	−0.741652	+	0.883866i	−0.996541	−	0.0831043i	$-0.973517\pi$
$907$	−22.3359	+	26.6189i	−0.741652	+	0.883866i	0.254889	+	0.966970i	$0.417961\pi$
$908$	−17.7822	+	3.13548i	−0.590123	+	0.104055i
$909$	52.3960	+	19.0706i	1.73787	+	0.632532i
$910$		0			0
$911$	−6.29239	+	10.8987i	−0.208476	+	0.361092i	−0.951235	−	0.308468i	$-0.900184\pi$
$911$	−6.29239	+	10.8987i	−0.208476	+	0.361092i	0.742758	+	0.669559i	$0.233517\pi$
$912$	22.3479	+	3.94054i	0.740013	+	0.130484i
$913$	8.38529	+	9.99320i	0.277513	+	0.330727i
$914$	8.97233	+	15.5405i	0.296778	+	0.514035i
$915$		0			0
$916$	2.69059	+	15.2591i	0.0888997	+	0.504175i
$917$	−25.6656	+	14.8180i	−0.847551	+	0.489334i
$918$	0.0837988	+	0.230235i	0.00276577	+	0.00759889i
$919$	16.1213			0.531794			0.265897	−	0.964001i	$-0.414332\pi$
$919$	16.1213			0.531794			0.265897	+	0.964001i	$0.414332\pi$
$920$		0			0
$921$	−9.04761	+	51.3116i	−0.298129	+	1.69077i
$922$	−15.3885	+	18.3393i	−0.506793	+	0.603972i
$923$	9.78444	+	11.6606i	0.322059	+	0.383815i
$924$	−38.4125			−1.26368
$925$		0			0
$926$	29.7331			0.977089
$927$	6.88862	+	8.20954i	0.226252	+	0.269637i
$928$	−7.66387	+	9.13345i	−0.251579	+	0.299820i
$929$	8.36210	−	47.4238i	0.274352	−	1.55592i	−0.466663	−	0.884435i	$-0.654544\pi$
$929$	8.36210	−	47.4238i	0.274352	−	1.55592i	0.741014	−	0.671489i	$-0.234345\pi$
$930$		0			0
$931$	−111.829			−3.66505
$932$	−8.22297	−	22.5924i	−0.269352	−	0.740039i
$933$	−6.13411	+	3.54153i	−0.200822	+	0.115944i
$934$	3.10716	+	17.6216i	0.101669	+	0.576595i
$935$		0			0
$936$	−17.8832	−	30.9746i	−0.584530	−	1.01244i
$937$	0.848071	+	1.01069i	0.0277053	+	0.0330179i	0.779719	−	0.626129i	$-0.215362\pi$
$937$	0.848071	+	1.01069i	0.0277053	+	0.0330179i	−0.752014	+	0.659147i	$0.770917\pi$
$938$	17.5028	+	3.08621i	0.571485	+	0.100768i
$939$	7.39064	−	12.8010i	0.241185	−	0.417744i
$940$		0			0
$941$	51.8169	+	18.8598i	1.68918	+	0.614813i	0.994522	−	0.104524i	$-0.0333319\pi$
$941$	51.8169	+	18.8598i	1.68918	+	0.614813i	0.694662	+	0.719337i	$0.255554\pi$
$942$	−9.03159	+	1.59251i	−0.294265	+	0.0518869i
$943$	17.4887	−	20.8423i	0.569512	−	0.678718i
$944$	−6.63483	−	5.56728i	−0.215945	−	0.181200i
$945$		0			0
$946$	26.4218	+	9.61676i	0.859048	+	0.312668i
$947$	19.7591	−	54.2878i	0.642086	−	1.76412i	−0.00298728	−	0.999996i	$-0.500951\pi$
$947$	19.7591	−	54.2878i	0.642086	−	1.76412i	0.645073	−	0.764121i	$-0.276827\pi$
$948$	−3.95654	−	2.28431i	−0.128503	−	0.0741910i
$949$	4.65909	−	26.4230i	0.151241	−	0.857728i
$950$		0			0
$951$	−34.0291	−	58.9402i	−1.10347	−	1.91127i
$952$	−1.05426	−	0.608680i	−0.0341689	−	0.0197274i
$953$	11.4036	−	2.01076i	0.369399	−	0.0651350i	0.0141326	−	0.999900i	$-0.495501\pi$
$953$	11.4036	−	2.01076i	0.369399	−	0.0651350i	0.355266	+	0.934765i	$0.384390\pi$
$954$	−4.72712	−	8.18762i	−0.153046	−	0.265084i
$955$		0			0
$956$	−6.10250			−0.197369
$957$	7.42819	+	20.4088i	0.240119	+	0.659722i
$958$	−6.80715	−	1.20028i	−0.219929	−	0.0387794i
$959$	−54.8726	−	46.0436i	−1.77193	−	1.48683i
$960$		0			0
$961$	23.0710			0.744226
$962$	15.7064	+	9.32672i	0.506393	+	0.300705i
$963$		−	69.3649i		−	2.23525i
$964$	−3.14329	+	2.63754i	−0.101239	+	0.0849493i
$965$		0			0
$966$	15.0533	−	85.3717i	0.484333	−	2.74679i
$967$	2.46714	+	6.77841i	0.0793378	+	0.217979i	0.973020	−	0.230722i	$-0.0741089\pi$
$967$	2.46714	+	6.77841i	0.0793378	+	0.217979i	−0.893682	+	0.448701i	$0.851887\pi$
$968$		−	2.57779i		−	0.0828533i
$969$	−1.26312	+	0.459740i	−0.0405774	+	0.0147690i
$970$		0			0
$971$	−3.47399	−	19.7020i	−0.111486	−	0.632266i	−0.988430	−	0.151675i	$-0.951533\pi$
$971$	−3.47399	−	19.7020i	−0.111486	−	0.632266i	0.876945	−	0.480591i	$-0.159578\pi$
$972$	−16.3493	−	9.43926i	−0.524403	−	0.302764i
$973$	−69.7516	+	40.2711i	−2.23613	+	1.29103i
$974$	2.74750	−	2.30542i	0.0880355	−	0.0738705i
$975$		0			0
$976$	−1.31302	+	2.27421i	−0.0420287	+	0.0727958i
$977$	−14.9007	+	40.9394i	−0.476717	+	1.30977i	0.435548	+	0.900166i	$0.356555\pi$
$977$	−14.9007	+	40.9394i	−0.476717	+	1.30977i	−0.912264	+	0.409602i	$0.865667\pi$
$978$	−6.52978	+	17.9404i	−0.208799	+	0.573671i
$979$	−1.51563	−	8.59555i	−0.0484397	−	0.274715i
$980$		0			0
$981$	57.5716	+	48.3083i	1.83812	+	1.54237i
$982$	−18.5398	+	3.26907i	−0.591629	+	0.104320i
$983$	2.45926	−	6.75676i	0.0784382	−	0.215507i	−0.894275	−	0.447518i	$-0.852308\pi$
$983$	2.45926	−	6.75676i	0.0784382	−	0.215507i	0.972713	+	0.232010i	$0.0745304\pi$
$984$	33.0940	+	12.0452i	1.05500	+	0.383988i
$985$		0			0
$986$	−0.0373343	+	0.211733i	−0.00118897	+	0.00674296i
$987$	−94.3020	−	112.385i	−3.00167	−	3.57725i
$988$	14.1927	−	8.19416i	0.451530	−	0.260691i
$989$	26.4089	−	45.7415i	0.839754	−	1.45450i
$990$		0			0
$991$	−0.209269	−	0.362464i	−0.00664764	−	0.0115141i	0.862682	−	0.505746i	$-0.168783\pi$
$991$	−0.209269	−	0.362464i	−0.00664764	−	0.0115141i	−0.869330	+	0.494232i	$0.835449\pi$
$992$	11.7172	+	32.1928i	0.372022	+	1.02212i
$993$		−	16.3071i		−	0.517491i
$994$	−25.9006	+	9.42705i	−0.821518	+	0.299008i
$995$		0			0
$996$	7.58997	+	6.36874i	0.240497	+	0.201801i
$997$	37.1795	+	44.3088i	1.17749	+	1.40327i	0.896199	+	0.443652i	$0.146317\pi$
$997$	37.1795	+	44.3088i	1.17749	+	1.40327i	0.281288	+	0.959623i	$0.409238\pi$
$998$		−	8.41005i		−	0.266215i
$999$	−17.7381	−	0.217529i	−0.561208	−	0.00688231i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	925.2.bc.e.49.17		156
5.2	odd	4		925.2.p.e.826.5	yes	78
5.3	odd	4		925.2.p.f.826.9	yes	78
5.4	even	2	inner	925.2.bc.e.49.10		156
37.34	even	9	inner	925.2.bc.e.774.10		156
185.34	even	18	inner	925.2.bc.e.774.17		156
185.108	odd	36		925.2.p.f.626.9	yes	78
185.182	odd	36		925.2.p.e.626.5	✓	78

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
925.2.p.e.626.5	✓	78	185.182	odd	36
925.2.p.e.826.5	yes	78	5.2	odd	4
925.2.p.f.626.9	yes	78	185.108	odd	36
925.2.p.f.826.9	yes	78	5.3	odd	4
925.2.bc.e.49.10		156	5.4	even	2	inner
925.2.bc.e.49.17		156	1.1	even	1	trivial
925.2.bc.e.774.10		156	37.34	even	9	inner
925.2.bc.e.774.17		156	185.34	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 925 = 5^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	925.bc (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.671547 + 0.800319i) q^{2} +(1.71214 - 2.04045i) q^{3} +(0.157762 - 0.894712i) q^{4} +2.78280 q^{6} +(1.70393 + 4.68151i) q^{7} +(2.63155 - 1.51932i) q^{8} +(-0.711068 - 4.03267i) q^{9} +O(q^{10})\)	\(q+(0.671547 + 0.800319i) q^{2} +(1.71214 - 2.04045i) q^{3} +(0.157762 - 0.894712i) q^{4} +2.78280 q^{6} +(1.70393 + 4.68151i) q^{7} +(2.63155 - 1.51932i) q^{8} +(-0.711068 - 4.03267i) q^{9} +(-1.59308 - 2.75930i) q^{11} +(-1.55551 - 1.85378i) q^{12} +(2.83077 + 0.499141i) q^{13} +(-2.60243 + 4.50754i) q^{14} +(1.27570 + 0.464318i) q^{16} +(-0.0791936 + 0.0139640i) q^{17} +(2.74990 - 3.27721i) q^{18} +(4.80732 + 4.03382i) q^{19} +(12.4698 + 4.53863i) q^{21} +(1.13849 - 3.12798i) q^{22} +(-5.41516 - 3.12644i) q^{23} +(1.40547 - 7.97084i) q^{24} +(1.50152 + 2.60072i) q^{26} +(-2.52563 - 1.45817i) q^{27} +(4.45742 - 0.785963i) q^{28} +(-1.27956 - 2.21626i) q^{29} -7.35330 q^{31} +(-1.59346 - 4.37801i) q^{32} +(-8.35781 - 1.47371i) q^{33} +(-0.0643579 - 0.0540027i) q^{34} -3.72025 q^{36} +(5.30473 - 2.97656i) q^{37} +6.55629i q^{38} +(5.86516 - 4.92145i) q^{39} +(-0.755580 + 4.28511i) q^{41} +(4.74169 + 13.0277i) q^{42} +8.44694i q^{43} +(-2.72011 + 0.990038i) q^{44} +(-1.13438 - 6.43341i) q^{46} +(-9.57440 - 5.52778i) q^{47} +(3.13160 - 1.80803i) q^{48} +(-13.6509 + 11.4544i) q^{49} +(-0.107098 + 0.185499i) q^{51} +(0.893175 - 2.45398i) q^{52} +(0.755838 - 2.07665i) q^{53} +(-0.529075 - 3.00054i) q^{54} +(11.5967 + 9.73079i) q^{56} +(16.4616 - 2.90263i) q^{57} +(0.914431 - 2.51238i) q^{58} +(-5.99512 - 2.18205i) q^{59} +(-0.335898 + 1.90497i) q^{61} +(-4.93809 - 5.88498i) q^{62} +(17.6674 - 10.2003i) q^{63} +(3.79129 - 6.56671i) q^{64} +(-4.43323 - 7.67858i) q^{66} +(-1.16788 - 3.20872i) q^{67} +0.0730584i q^{68} +(-15.6509 + 5.69646i) q^{69} +(4.05666 + 3.40394i) q^{71} +(-7.99813 - 9.53181i) q^{72} -9.33421i q^{73} +(5.94457 + 2.24657i) q^{74} +(4.36752 - 3.66478i) q^{76} +(10.2032 - 12.1597i) q^{77} +(7.87746 + 1.38901i) q^{78} +(1.77405 - 0.645703i) q^{79} +(4.24422 - 1.54477i) q^{81} +(-3.93686 + 2.27295i) q^{82} +(-4.03212 + 0.710972i) q^{83} +(6.02802 - 10.4408i) q^{84} +(-6.76024 + 5.67252i) q^{86} +(-6.71296 - 1.18368i) q^{87} +(-8.38455 - 4.84082i) q^{88} +(2.57418 + 0.936926i) q^{89} +(2.48670 + 14.1028i) q^{91} +(-3.65157 + 4.35177i) q^{92} +(-12.5899 + 15.0041i) q^{93} +(-2.00567 - 11.3747i) q^{94} +(-11.6614 - 4.24439i) q^{96} +(2.87410 + 1.65936i) q^{97} +(-18.3344 - 3.23285i) q^{98} +(-9.99456 + 8.38643i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 6 q^{4}+O(q^{10}) \) 156 * q - 6 * q^4	\( 156 q - 6 q^{4} - 12 q^{14} + 42 q^{16} + 24 q^{19} + 30 q^{21} - 30 q^{24} + 6 q^{29} - 72 q^{31} + 42 q^{34} + 216 q^{36} - 18 q^{39} - 6 q^{41} + 30 q^{44} - 72 q^{46} + 60 q^{49} - 60 q^{51} - 54 q^{54} + 240 q^{56} - 30 q^{59} - 12 q^{61} + 108 q^{64} - 12 q^{66} - 90 q^{69} + 144 q^{71} - 192 q^{74} + 42 q^{76} - 96 q^{79} + 96 q^{81} - 54 q^{84} + 216 q^{86} + 42 q^{89} - 54 q^{91} + 156 q^{94} - 252 q^{96} - 282 q^{99}+O(q^{100}) \) 156 * q - 6 * q^4 - 12 * q^14 + 42 * q^16 + 24 * q^19 + 30 * q^21 - 30 * q^24 + 6 * q^29 - 72 * q^31 + 42 * q^34 + 216 * q^36 - 18 * q^39 - 6 * q^41 + 30 * q^44 - 72 * q^46 + 60 * q^49 - 60 * q^51 - 54 * q^54 + 240 * q^56 - 30 * q^59 - 12 * q^61 + 108 * q^64 - 12 * q^66 - 90 * q^69 + 144 * q^71 - 192 * q^74 + 42 * q^76 - 96 * q^79 + 96 * q^81 - 54 * q^84 + 216 * q^86 + 42 * q^89 - 54 * q^91 + 156 * q^94 - 252 * q^96 - 282 * q^99

Introduction

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