LMFDB - Embedded newform 1450.2.j.e.157.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1450,2,Mod(157,1450)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1450, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("1450.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1450 = 2 \cdot 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1450.j (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$11.5783082931$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.6420496384.3
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 22x^{6} + 155x^{4} + 406x^{2} + 289 $ x^8 + 22x^6 + 155x^4 + 406*x^2 + 289
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 290)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			157.2
Root			$-1.05614i$ of defining polynomial
Character	$\chi$	$=$	1450.157
Dual form			1450.2.j.e.1293.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} -1.05614 q^{3} -1.00000 q^{4} -1.05614i q^{6} +(3.51005 + 3.51005i) q^{7} -1.00000i q^{8} -1.88457 q^{9} +O(q^{10})$	\(q+1.00000i q^{2} -1.05614 q^{3} -1.00000 q^{4} -1.05614i q^{6} +(3.51005 + 3.51005i) q^{7} -1.00000i q^{8} -1.88457 q^{9} +(1.41421 + 1.41421i) q^{11} +1.05614 q^{12} +(0.746804 + 0.746804i) q^{13} +(-3.51005 + 3.51005i) q^{14} +1.00000 q^{16} +2.13553i q^{17} -1.88457i q^{18} +(2.35807 - 2.35807i) q^{19} +(-3.70711 - 3.70711i) q^{21} +(-1.41421 + 1.41421i) q^{22} +(-3.29655 + 3.29655i) q^{23} +1.05614i q^{24} +(-0.746804 + 0.746804i) q^{26} +5.15879 q^{27} +(-3.51005 - 3.51005i) q^{28} +(0.878680 - 5.31300i) q^{29} +(2.86812 + 2.86812i) q^{31} +1.00000i q^{32} +(-1.49361 - 1.49361i) q^{33} -2.13553 q^{34} +1.88457 q^{36} +1.01278 q^{37} +(2.35807 + 2.35807i) q^{38} +(-0.788730 - 0.788730i) q^{39} +(-1.92061 + 1.92061i) q^{41} +(3.70711 - 3.70711i) q^{42} +11.8718 q^{43} +(-1.41421 - 1.41421i) q^{44} +(-3.29655 - 3.29655i) q^{46} -6.90782 q^{47} -1.05614 q^{48} +17.6409i q^{49} -2.25542i q^{51} +(-0.746804 - 0.746804i) q^{52} +(-9.80883 + 9.80883i) q^{53} +5.15879i q^{54} +(3.51005 - 3.51005i) q^{56} +(-2.49046 + 2.49046i) q^{57} +(5.31300 + 0.878680i) q^{58} +6.54975i q^{59} +(-7.61859 - 7.61859i) q^{61} +(-2.86812 + 2.86812i) q^{62} +(-6.61493 - 6.61493i) q^{63} -1.00000 q^{64} +(1.49361 - 1.49361i) q^{66} +(-4.13553 + 4.13553i) q^{67} -2.13553i q^{68} +(3.48162 - 3.48162i) q^{69} -9.39310i q^{71} +1.88457i q^{72} +3.41939i q^{73} +1.01278i q^{74} +(-2.35807 + 2.35807i) q^{76} +9.92792i q^{77} +(0.788730 - 0.788730i) q^{78} +(-9.76691 + 9.76691i) q^{79} +0.205297 q^{81} +(-1.92061 - 1.92061i) q^{82} +(-0.887719 + 0.887719i) q^{83} +(3.70711 + 3.70711i) q^{84} +11.8718i q^{86} +(-0.928009 + 5.61127i) q^{87} +(1.41421 - 1.41421i) q^{88} +(4.79239 - 4.79239i) q^{89} +5.24264i q^{91} +(3.29655 - 3.29655i) q^{92} +(-3.02914 - 3.02914i) q^{93} -6.90782i q^{94} -1.05614i q^{96} -9.37818 q^{97} -17.6409 q^{98} +(-2.66518 - 2.66518i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{3} - 8 q^{4} + 4 q^{7} + 20 q^{9}+O(q^{10}) $ 8 * q + 4 * q^3 - 8 * q^4 + 4 * q^7 + 20 * q^9	$ 8 q + 4 q^{3} - 8 q^{4} + 4 q^{7} + 20 q^{9} - 4 q^{12} - 4 q^{14} + 8 q^{16} + 20 q^{19} - 24 q^{21} + 4 q^{23} + 40 q^{27} - 4 q^{28} + 24 q^{29} - 4 q^{34} - 20 q^{36} + 32 q^{37} + 20 q^{38} + 16 q^{39} - 16 q^{41} + 24 q^{42} + 36 q^{43} + 4 q^{46} - 32 q^{47} + 4 q^{48} - 8 q^{53} + 4 q^{56} + 52 q^{57} + 4 q^{61} - 24 q^{63} - 8 q^{64} - 20 q^{67} - 4 q^{69} - 20 q^{76} - 16 q^{78} - 24 q^{79} + 24 q^{81} - 16 q^{82} - 32 q^{83} + 24 q^{84} + 12 q^{87} - 20 q^{89} - 4 q^{92} + 16 q^{93} - 28 q^{97} - 12 q^{98} - 32 q^{99}+O(q^{100}) $ 8 * q + 4 * q^3 - 8 * q^4 + 4 * q^7 + 20 * q^9 - 4 * q^12 - 4 * q^14 + 8 * q^16 + 20 * q^19 - 24 * q^21 + 4 * q^23 + 40 * q^27 - 4 * q^28 + 24 * q^29 - 4 * q^34 - 20 * q^36 + 32 * q^37 + 20 * q^38 + 16 * q^39 - 16 * q^41 + 24 * q^42 + 36 * q^43 + 4 * q^46 - 32 * q^47 + 4 * q^48 - 8 * q^53 + 4 * q^56 + 52 * q^57 + 4 * q^61 - 24 * q^63 - 8 * q^64 - 20 * q^67 - 4 * q^69 - 20 * q^76 - 16 * q^78 - 24 * q^79 + 24 * q^81 - 16 * q^82 - 32 * q^83 + 24 * q^84 + 12 * q^87 - 20 * q^89 - 4 * q^92 + 16 * q^93 - 28 * q^97 - 12 * q^98 - 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1450\mathbb{Z}\right)^\times$.

$n$	$901$	$1277$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.05614			−0.609763			−0.304881	−	0.952390i	$-0.598617\pi$
$3$	−1.05614			−0.609763			−0.304881	+	0.952390i	$0.598617\pi$
$4$	−1.00000			−0.500000
$5$		0			0
$5$		0			0
$6$		−	1.05614i		−	0.431168i
$7$	3.51005	+	3.51005i	1.32667	+	1.32667i	0.908253	+	0.418422i	$0.137417\pi$
$7$	3.51005	+	3.51005i	1.32667	+	1.32667i	0.418422	+	0.908253i	$0.362583\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−1.88457			−0.628189
$10$		0			0
$11$	1.41421	+	1.41421i	0.426401	+	0.426401i	0.887401	−	0.460999i	$-0.152509\pi$
$11$	1.41421	+	1.41421i	0.426401	+	0.426401i	−0.460999	+	0.887401i	$0.652509\pi$
$12$	1.05614			0.304881
$13$	0.746804	+	0.746804i	0.207126	+	0.207126i	0.803045	−	0.595919i	$-0.203212\pi$
$13$	0.746804	+	0.746804i	0.207126	+	0.207126i	−0.595919	+	0.803045i	$0.703212\pi$
$14$	−3.51005	+	3.51005i	−0.938101	+	0.938101i
$15$		0			0
$16$	1.00000			0.250000
$17$			2.13553i			0.517943i	0.965885	+	0.258972i	$0.0833836\pi$
$17$			2.13553i			0.517943i	−0.965885	+	0.258972i	$0.916616\pi$
$18$		−	1.88457i		−	0.444197i
$19$	2.35807	−	2.35807i	0.540979	−	0.540979i	−0.382837	−	0.923816i	$-0.625053\pi$
$19$	2.35807	−	2.35807i	0.540979	−	0.540979i	0.923816	+	0.382837i	$0.125053\pi$
$20$		0			0
$21$	−3.70711	−	3.70711i	−0.808957	−	0.808957i
$22$	−1.41421	+	1.41421i	−0.301511	+	0.301511i
$23$	−3.29655	+	3.29655i	−0.687379	+	0.687379i	−0.961652	−	0.274273i	$-0.911563\pi$
$23$	−3.29655	+	3.29655i	−0.687379	+	0.687379i	0.274273	+	0.961652i	$0.411563\pi$
$24$			1.05614i			0.215584i
$25$		0			0
$26$	−0.746804	+	0.746804i	−0.146460	+	0.146460i
$27$	5.15879			0.992809
$28$	−3.51005	−	3.51005i	−0.663337	−	0.663337i
$29$	0.878680	−	5.31300i	0.163167	−	0.986599i
$29$	0.878680	−	5.31300i	0.163167	−	0.986599i
$30$		0			0
$31$	2.86812	+	2.86812i	0.515130	+	0.515130i	0.916094	−	0.400964i	$-0.131325\pi$
$31$	2.86812	+	2.86812i	0.515130	+	0.515130i	−0.400964	+	0.916094i	$0.631325\pi$
$32$			1.00000i			0.176777i
$33$	−1.49361	−	1.49361i	−0.260004	−	0.260004i
$34$	−2.13553			−0.366241
$35$		0			0
$36$	1.88457			0.314095
$37$	1.01278			0.166501			0.0832503	−	0.996529i	$-0.473470\pi$
$37$	1.01278			0.166501			0.0832503	+	0.996529i	$0.473470\pi$
$38$	2.35807	+	2.35807i	0.382530	+	0.382530i
$39$	−0.788730	−	0.788730i	−0.126298	−	0.126298i
$40$		0			0
$41$	−1.92061	+	1.92061i	−0.299948	+	0.299948i	−0.840993	−	0.541045i	$-0.818029\pi$
$41$	−1.92061	+	1.92061i	−0.299948	+	0.299948i	0.541045	+	0.840993i	$0.318029\pi$
$42$	3.70711	−	3.70711i	0.572019	−	0.572019i
$43$	11.8718			1.81043			0.905215	−	0.424954i	$-0.139710\pi$
$43$	11.8718			1.81043			0.905215	+	0.424954i	$0.139710\pi$
$44$	−1.41421	−	1.41421i	−0.213201	−	0.213201i
$45$		0			0
$46$	−3.29655	−	3.29655i	−0.486050	−	0.486050i
$47$	−6.90782			−1.00761			−0.503805	−	0.863818i	$-0.668067\pi$
$47$	−6.90782			−1.00761			−0.503805	+	0.863818i	$0.668067\pi$
$48$	−1.05614			−0.152441
$49$			17.6409i			2.52013i
$50$		0			0
$51$		−	2.25542i		−	0.315823i
$52$	−0.746804	−	0.746804i	−0.103563	−	0.103563i
$53$	−9.80883	+	9.80883i	−1.34735	+	1.34735i	−0.458815	+	0.888532i	$0.651726\pi$
$53$	−9.80883	+	9.80883i	−1.34735	+	1.34735i	−0.888532	+	0.458815i	$0.848274\pi$
$54$			5.15879i			0.702022i
$55$		0			0
$56$	3.51005	−	3.51005i	0.469050	−	0.469050i
$57$	−2.49046	+	2.49046i	−0.329869	+	0.329869i
$58$	5.31300	+	0.878680i	0.697630	+	0.115376i
$59$			6.54975i			0.852705i	0.904557	+	0.426352i	$0.140202\pi$
$59$			6.54975i			0.852705i	−0.904557	+	0.426352i	$0.859798\pi$
$60$		0			0
$61$	−7.61859	−	7.61859i	−0.975460	−	0.975460i	0.0242458	−	0.999706i	$-0.492282\pi$
$61$	−7.61859	−	7.61859i	−0.975460	−	0.975460i	−0.999706	+	0.0242458i	$0.992282\pi$
$62$	−2.86812	+	2.86812i	−0.364252	+	0.364252i
$63$	−6.61493	−	6.61493i	−0.833403	−	0.833403i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	1.49361	−	1.49361i	0.183850	−	0.183850i
$67$	−4.13553	+	4.13553i	−0.505236	+	0.505236i	−0.913060	−	0.407824i	$-0.866288\pi$
$67$	−4.13553	+	4.13553i	−0.505236	+	0.505236i	0.407824	+	0.913060i	$0.366288\pi$
$68$		−	2.13553i		−	0.258972i
$69$	3.48162	−	3.48162i	0.419138	−	0.419138i
$70$		0			0
$71$		−	9.39310i		−	1.11476i	−0.830259	−	0.557378i	$-0.811807\pi$
$71$		−	9.39310i		−	1.11476i	0.830259	−	0.557378i	$-0.188193\pi$
$72$			1.88457i			0.222098i
$73$			3.41939i			0.400209i	0.979775	+	0.200105i	$0.0641282\pi$
$73$			3.41939i			0.400209i	−0.979775	+	0.200105i	$0.935872\pi$
$74$			1.01278i			0.117734i
$75$		0			0
$76$	−2.35807	+	2.35807i	−0.270490	+	0.270490i
$77$			9.92792i			1.13139i
$78$	0.788730	−	0.788730i	0.0893061	−	0.0893061i
$79$	−9.76691	+	9.76691i	−1.09886	+	1.09886i	−0.104319	+	0.994544i	$0.533266\pi$
$79$	−9.76691	+	9.76691i	−1.09886	+	1.09886i	−0.994544	+	0.104319i	$0.966734\pi$
$80$		0			0
$81$	0.205297			0.0228108
$82$	−1.92061	−	1.92061i	−0.212095	−	0.212095i
$83$	−0.887719	+	0.887719i	−0.0974398	+	0.0974398i	−0.754146	−	0.656706i	$-0.771949\pi$
$83$	−0.887719	+	0.887719i	−0.0974398	+	0.0974398i	0.656706	+	0.754146i	$0.271949\pi$
$84$	3.70711	+	3.70711i	0.404479	+	0.404479i
$85$		0			0
$86$			11.8718i			1.28017i
$87$	−0.928009	+	5.61127i	−0.0994930	+	0.601591i
$88$	1.41421	−	1.41421i	0.150756	−	0.150756i
$89$	4.79239	−	4.79239i	0.507992	−	0.507992i	−0.405917	−	0.913910i	$-0.633048\pi$
$89$	4.79239	−	4.79239i	0.507992	−	0.507992i	0.913910	+	0.405917i	$0.133048\pi$
$90$		0			0
$91$			5.24264i			0.549578i
$92$	3.29655	−	3.29655i	0.343689	−	0.343689i
$93$	−3.02914	−	3.02914i	−0.314107	−	0.314107i
$94$		−	6.90782i		−	0.712487i
$95$		0			0
$96$		−	1.05614i		−	0.107792i
$97$	−9.37818			−0.952209			−0.476105	−	0.879389i	$-0.657952\pi$
$97$	−9.37818			−0.952209			−0.476105	+	0.879389i	$0.657952\pi$
$98$	−17.6409			−1.78200
$99$	−2.66518	−	2.66518i	−0.267861	−	0.267861i
$100$		0			0
$101$	4.81573	+	4.81573i	0.479183	+	0.479183i	0.904870	−	0.425687i	$-0.139968\pi$
$101$	4.81573	+	4.81573i	0.479183	+	0.479183i	−0.425687	+	0.904870i	$0.639968\pi$
$102$	2.25542			0.223320
$103$	1.49361	−	1.49361i	0.147170	−	0.147170i	−0.629683	−	0.776852i	$-0.716815\pi$
$103$	1.49361	−	1.49361i	0.147170	−	0.147170i	0.776852	+	0.629683i	$0.216815\pi$
$104$	0.746804	−	0.746804i	0.0732302	−	0.0732302i
$105$		0			0
$106$	−9.80883	−	9.80883i	−0.952718	−	0.952718i
$107$	−8.17372	−	8.17372i	−0.790183	−	0.790183i	0.191341	−	0.981524i	$-0.438716\pi$
$107$	−8.17372	−	8.17372i	−0.790183	−	0.790183i	−0.981524	+	0.191341i	$0.938716\pi$
$108$	−5.15879			−0.496405
$109$	−2.92590			−0.280250			−0.140125	−	0.990134i	$-0.544751\pi$
$109$	−2.92590			−0.280250			−0.140125	+	0.990134i	$0.544751\pi$
$110$		0			0
$111$	−1.06964			−0.101526
$112$	3.51005	+	3.51005i	0.331669	+	0.331669i
$113$			10.4312i			0.981281i	0.871362	+	0.490641i	$0.163237\pi$
$113$			10.4312i			0.981281i	−0.871362	+	0.490641i	$0.836763\pi$
$114$	−2.49046	−	2.49046i	−0.233253	−	0.233253i
$115$		0			0
$116$	−0.878680	+	5.31300i	−0.0815834	+	0.493299i
$117$	−1.40740	−	1.40740i	−0.130114	−	0.130114i
$118$	−6.54975			−0.602953
$119$	−7.49584	+	7.49584i	−0.687142	+	0.687142i
$120$		0			0
$121$		−	7.00000i		−	0.636364i
$122$	7.61859	−	7.61859i	0.689755	−	0.689755i
$123$	2.02843	−	2.02843i	0.182897	−	0.182897i
$124$	−2.86812	−	2.86812i	−0.257565	−	0.257565i
$125$		0			0
$126$	6.61493	−	6.61493i	0.589305	−	0.589305i
$127$			3.79025i			0.336330i	0.985759	+	0.168165i	$0.0537841\pi$
$127$			3.79025i			0.336330i	−0.985759	+	0.168165i	$0.946216\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−12.5383			−1.10393
$130$		0			0
$131$	−11.5571	+	11.5571i	−1.00975	+	1.00975i	−0.00979358	+	0.999952i	$0.503117\pi$
$131$	−11.5571	+	11.5571i	−1.00975	+	1.00975i	−0.999952	+	0.00979358i	$0.996883\pi$
$132$	1.49361	+	1.49361i	0.130002	+	0.130002i
$133$	16.5539			1.43541
$134$	−4.13553	−	4.13553i	−0.357256	−	0.357256i
$135$		0			0
$136$	2.13553			0.183121
$137$			17.1473i			1.46499i	0.680770	+	0.732497i	$0.261645\pi$
$137$			17.1473i			1.46499i	−0.680770	+	0.732497i	$0.738355\pi$
$138$	3.48162	+	3.48162i	0.296375	+	0.296375i
$139$			4.62082i			0.391933i	0.980611	+	0.195966i	$0.0627843\pi$
$139$			4.62082i			0.391933i	−0.980611	+	0.195966i	$0.937216\pi$
$140$		0			0
$141$	7.29563			0.614403
$142$	9.39310			0.788252
$143$			2.11228i			0.176638i
$144$	−1.88457			−0.157047
$145$		0			0
$146$	−3.41939			−0.282991
$147$		−	18.6313i		−	1.53668i
$148$	−1.01278			−0.0832503
$149$	3.31674			0.271718			0.135859	−	0.990728i	$-0.456621\pi$
$149$	3.31674			0.271718			0.135859	+	0.990728i	$0.456621\pi$
$150$		0			0
$151$			11.1685i			0.908883i	0.890777	+	0.454442i	$0.150161\pi$
$151$			11.1685i			0.908883i	−0.890777	+	0.454442i	$0.849839\pi$
$152$	−2.35807	−	2.35807i	−0.191265	−	0.191265i
$153$		−	4.02456i		−	0.325366i
$154$	−9.92792			−0.800015
$155$		0			0
$156$	0.788730	+	0.788730i	0.0631489	+	0.0631489i
$157$	13.2912			1.06075			0.530376	−	0.847763i	$-0.322051\pi$
$157$	13.2912			1.06075			0.530376	+	0.847763i	$0.322051\pi$
$158$	−9.76691	−	9.76691i	−0.777013	−	0.777013i
$159$	10.3595	−	10.3595i	0.821562	−	0.821562i
$160$		0			0
$161$	−23.1421			−1.82386
$162$			0.205297i			0.0161297i
$163$		−	20.2544i		−	1.58645i	−0.608930	−	0.793224i	$-0.708401\pi$
$163$		−	20.2544i		−	1.58645i	0.608930	−	0.793224i	$-0.291599\pi$
$164$	1.92061	−	1.92061i	0.149974	−	0.149974i
$165$		0			0
$166$	−0.887719	−	0.887719i	−0.0689004	−	0.0689004i
$167$	9.68062	−	9.68062i	0.749109	−	0.749109i	−0.225203	−	0.974312i	$-0.572305\pi$
$167$	9.68062	−	9.68062i	0.749109	−	0.749109i	0.974312	+	0.225203i	$0.0723046\pi$
$168$	−3.70711	+	3.70711i	−0.286009	+	0.286009i
$169$		−	11.8846i		−	0.914198i
$170$		0			0
$171$	−4.44395	+	4.44395i	−0.339837	+	0.339837i
$172$	−11.8718			−0.905215
$173$	15.8179	+	15.8179i	1.20261	+	1.20261i	0.973370	+	0.229241i	$0.0736243\pi$
$173$	15.8179	+	15.8179i	1.20261	+	1.20261i	0.229241	+	0.973370i	$0.426376\pi$
$174$	−5.61127	−	0.928009i	−0.425389	−	0.0703522i
$175$		0			0
$176$	1.41421	+	1.41421i	0.106600	+	0.106600i
$177$		−	6.91745i		−	0.519948i
$178$	4.79239	+	4.79239i	0.359205	+	0.359205i
$179$	10.8507			0.811017			0.405509	−	0.914091i	$-0.367094\pi$
$179$	10.8507			0.811017			0.405509	+	0.914091i	$0.367094\pi$
$180$		0			0
$181$	5.82313			0.432830			0.216415	−	0.976301i	$-0.430564\pi$
$181$	5.82313			0.432830			0.216415	+	0.976301i	$0.430564\pi$
$182$	−5.24264			−0.388610
$183$	8.04630	+	8.04630i	0.594799	+	0.594799i
$184$	3.29655	+	3.29655i	0.243025	+	0.243025i
$185$		0			0
$186$	3.02914	−	3.02914i	0.222107	−	0.222107i
$187$	−3.02010	+	3.02010i	−0.220852	+	0.220852i
$188$	6.90782			0.503805
$189$	18.1076	+	18.1076i	1.31714	+	1.31714i
$190$		0			0
$191$	7.53331	+	7.53331i	0.545091	+	0.545091i	0.925017	−	0.379926i	$-0.124051\pi$
$191$	7.53331	+	7.53331i	0.545091	+	0.545091i	−0.379926	+	0.925017i	$0.624051\pi$
$192$	1.05614			0.0762204
$193$	−4.81047			−0.346265			−0.173133	−	0.984899i	$-0.555389\pi$
$193$	−4.81047			−0.346265			−0.173133	+	0.984899i	$0.555389\pi$
$194$		−	9.37818i		−	0.673314i
$195$		0			0
$196$		−	17.6409i		−	1.26007i
$197$	−12.5024	−	12.5024i	−0.890762	−	0.890762i	0.103833	−	0.994595i	$-0.466889\pi$
$197$	−12.5024	−	12.5024i	−0.890762	−	0.890762i	−0.994595	+	0.103833i	$0.966889\pi$
$198$	2.66518	−	2.66518i	0.189406	−	0.189406i
$199$		−	19.5411i		−	1.38523i	−0.721306	−	0.692617i	$-0.756458\pi$
$199$		−	19.5411i		−	1.38523i	0.721306	−	0.692617i	$-0.243542\pi$
$200$		0			0
$201$	4.36771	−	4.36771i	0.308074	−	0.308074i
$202$	−4.81573	+	4.81573i	−0.338833	+	0.338833i
$203$	21.7331	−	15.5647i	1.52536	−	1.09243i
$204$			2.25542i			0.157911i
$205$		0			0
$206$	1.49361	+	1.49361i	0.104065	+	0.104065i
$207$	6.21258	−	6.21258i	0.431804	−	0.431804i
$208$	0.746804	+	0.746804i	0.0517815	+	0.0517815i
$209$	6.66964			0.461349
$210$		0			0
$211$	2.27107	−	2.27107i	0.156347	−	0.156347i	−0.624599	−	0.780946i	$-0.714738\pi$
$211$	2.27107	−	2.27107i	0.156347	−	0.156347i	0.780946	+	0.624599i	$0.214738\pi$
$212$	9.80883	−	9.80883i	0.673673	−	0.673673i
$213$			9.92044i			0.679737i
$214$	8.17372	−	8.17372i	0.558744	−	0.558744i
$215$		0			0
$216$		−	5.15879i		−	0.351011i
$217$			20.1345i			1.36682i
$218$		−	2.92590i		−	0.198167i
$219$		−	3.61135i		−	0.244033i
$220$		0			0
$221$	−1.59483	+	1.59483i	−0.107280	+	0.107280i
$222$		−	1.06964i		−	0.0717897i
$223$	2.38141	−	2.38141i	0.159471	−	0.159471i	−0.622861	−	0.782332i	$-0.714030\pi$
$223$	2.38141	−	2.38141i	0.159471	−	0.159471i	0.782332	+	0.622861i	$0.214030\pi$
$224$	−3.51005	+	3.51005i	−0.234525	+	0.234525i
$225$		0			0
$226$	−10.4312			−0.693871
$227$	−19.2880	−	19.2880i	−1.28019	−	1.28019i	−0.940558	−	0.339633i	$-0.889697\pi$
$227$	−19.2880	−	19.2880i	−1.28019	−	1.28019i	−0.339633	−	0.940558i	$-0.610303\pi$
$228$	2.49046	−	2.49046i	0.164934	−	0.164934i
$229$	16.2664	+	16.2664i	1.07491	+	1.07491i	0.996957	+	0.0779574i	$0.0248398\pi$
$229$	16.2664	+	16.2664i	1.07491	+	1.07491i	0.0779574	+	0.996957i	$0.475160\pi$
$230$		0			0
$231$		−	10.4853i		−	0.689881i
$232$	−5.31300	−	0.878680i	−0.348815	−	0.0576881i
$233$	−3.38133	+	3.38133i	−0.221518	+	0.221518i	−0.809137	−	0.587619i	$-0.800065\pi$
$233$	−3.38133	+	3.38133i	−0.221518	+	0.221518i	0.587619	+	0.809137i	$0.300065\pi$
$234$	1.40740	−	1.40740i	0.0920048	−	0.0920048i
$235$		0			0
$236$		−	6.54975i		−	0.426352i
$237$	10.3152	−	10.3152i	0.670046	−	0.670046i
$238$	−7.49584	−	7.49584i	−0.485883	−	0.485883i
$239$		−	26.3622i		−	1.70523i	−0.522538	−	0.852616i	$-0.675015\pi$
$239$		−	26.3622i		−	1.70523i	0.522538	−	0.852616i	$-0.324985\pi$
$240$		0			0
$241$		−	9.58793i		−	0.617613i	−0.951125	−	0.308806i	$-0.900070\pi$
$241$		−	9.58793i		−	0.617613i	0.951125	−	0.308806i	$-0.0999295\pi$
$242$	7.00000			0.449977
$243$	−15.6932			−1.00672
$244$	7.61859	+	7.61859i	0.487730	+	0.487730i
$245$		0			0
$246$	2.02843	+	2.02843i	0.129328	+	0.129328i
$247$	3.52204			0.224102
$248$	2.86812	−	2.86812i	0.182126	−	0.182126i
$249$	0.937556	−	0.937556i	0.0594152	−	0.0594152i
$250$		0			0
$251$	4.39411	+	4.39411i	0.277354	+	0.277354i	0.832052	−	0.554698i	$-0.187166\pi$
$251$	4.39411	+	4.39411i	0.277354	+	0.277354i	−0.554698	+	0.832052i	$0.687166\pi$
$252$	6.61493	+	6.61493i	0.416701	+	0.416701i
$253$	−9.32406			−0.586199
$254$	−3.79025			−0.237821
$255$		0			0
$256$	1.00000			0.0625000
$257$	6.38133	+	6.38133i	0.398056	+	0.398056i	0.877547	−	0.479491i	$-0.159179\pi$
$257$	6.38133	+	6.38133i	0.398056	+	0.398056i	−0.479491	+	0.877547i	$0.659179\pi$
$258$		−	12.5383i		−	0.780599i
$259$	3.55492	+	3.55492i	0.220892	+	0.220892i
$260$		0			0
$261$	−1.65593	+	10.0127i	−0.102500	+	0.619770i
$262$	−11.5571	−	11.5571i	−0.713998	−	0.713998i
$263$	4.67250			0.288119			0.144059	−	0.989569i	$-0.453984\pi$
$263$	4.67250			0.288119			0.144059	+	0.989569i	$0.453984\pi$
$264$	−1.49361	+	1.49361i	−0.0919252	+	0.0919252i
$265$		0			0
$266$			16.5539i			1.01499i
$267$	−5.06144	+	5.06144i	−0.309755	+	0.309755i
$268$	4.13553	−	4.13553i	0.252618	−	0.252618i
$269$	5.79920	+	5.79920i	0.353583	+	0.353583i	0.861441	−	0.507858i	$-0.169562\pi$
$269$	5.79920	+	5.79920i	0.353583	+	0.353583i	−0.507858	+	0.861441i	$0.669562\pi$
$270$		0			0
$271$	2.74903	−	2.74903i	0.166992	−	0.166992i	−0.618664	−	0.785656i	$-0.712326\pi$
$271$	2.74903	−	2.74903i	0.166992	−	0.166992i	0.785656	+	0.618664i	$0.212326\pi$
$272$			2.13553i			0.129486i
$273$		−	5.53696i		−	0.335112i
$274$	−17.1473			−1.03591
$275$		0			0
$276$	−3.48162	+	3.48162i	−0.209569	+	0.209569i
$277$	3.01278	+	3.01278i	0.181021	+	0.181021i	0.791800	−	0.610780i	$-0.209144\pi$
$277$	3.01278	+	3.01278i	0.181021	+	0.181021i	−0.610780	+	0.791800i	$0.709144\pi$
$278$	−4.62082			−0.277138
$279$	−5.40517	−	5.40517i	−0.323599	−	0.323599i
$280$		0			0
$281$	29.1958			1.74168			0.870839	−	0.491568i	$-0.163576\pi$
$281$	29.1958			1.74168			0.870839	+	0.491568i	$0.163576\pi$
$282$			7.29563i			0.434448i
$283$	19.8963	+	19.8963i	1.18271	+	1.18271i	0.979038	+	0.203677i	$0.0652891\pi$
$283$	19.8963	+	19.8963i	1.18271	+	1.18271i	0.203677	+	0.979038i	$0.434711\pi$
$284$			9.39310i			0.557378i
$285$		0			0
$286$	−2.11228			−0.124902
$287$	−13.4828			−0.795867
$288$		−	1.88457i		−	0.111049i
$289$	12.4395			0.731735
$290$		0			0
$291$	9.90467			0.580622
$292$		−	3.41939i		−	0.200105i
$293$	5.82640			0.340382			0.170191	−	0.985411i	$-0.445562\pi$
$293$	5.82640			0.340382			0.170191	+	0.985411i	$0.445562\pi$
$294$	18.6313			1.08660
$295$		0			0
$296$		−	1.01278i		−	0.0588669i
$297$	7.29563	+	7.29563i	0.423335	+	0.423335i
$298$			3.31674i			0.192134i
$299$	−4.92376			−0.284748
$300$		0			0
$301$	41.6706	+	41.6706i	2.40185	+	2.40185i
$302$	−11.1685			−0.642677
$303$	−5.08609	−	5.08609i	−0.292188	−	0.292188i
$304$	2.35807	−	2.35807i	0.135245	−	0.135245i
$305$		0			0
$306$	4.02456			0.230069
$307$			21.2672i			1.21378i	0.794785	+	0.606892i	$0.207584\pi$
$307$			21.2672i			1.21378i	−0.794785	+	0.606892i	$0.792416\pi$
$308$		−	9.92792i		−	0.565696i
$309$	−1.57746	+	1.57746i	−0.0897386	+	0.0897386i
$310$		0			0
$311$	−10.0276	−	10.0276i	−0.568615	−	0.568615i	0.363126	−	0.931740i	$-0.381710\pi$
$311$	−10.0276	−	10.0276i	−0.568615	−	0.568615i	−0.931740	+	0.363126i	$0.881710\pi$
$312$	−0.788730	+	0.788730i	−0.0446530	+	0.0446530i
$313$	8.08154	−	8.08154i	0.456796	−	0.456796i	−0.440807	−	0.897602i	$-0.645308\pi$
$313$	8.08154	−	8.08154i	0.456796	−	0.456796i	0.897602	+	0.440807i	$0.145308\pi$
$314$			13.2912i			0.750064i
$315$		0			0
$316$	9.76691	−	9.76691i	0.549431	−	0.549431i
$317$	4.71287			0.264701			0.132351	−	0.991203i	$-0.457747\pi$
$317$	4.71287			0.264701			0.132351	+	0.991203i	$0.457747\pi$
$318$	10.3595	+	10.3595i	0.580932	+	0.580932i
$319$	8.75635	−	6.27107i	0.490262	−	0.351112i
$320$		0			0
$321$	8.63259	+	8.63259i	0.481824	+	0.481824i
$322$		−	23.1421i		−	1.28966i
$323$	5.03575	+	5.03575i	0.280196	+	0.280196i
$324$	−0.205297			−0.0114054
$325$		0			0
$326$	20.2544			1.12179
$327$	3.09016			0.170886
$328$	1.92061	+	1.92061i	0.106048	+	0.106048i
$329$	−24.2468	−	24.2468i	−1.33677	−	1.33677i
$330$		0			0
$331$	4.14832	−	4.14832i	0.228012	−	0.228012i	−0.583850	−	0.811862i	$-0.698454\pi$
$331$	4.14832	−	4.14832i	0.228012	−	0.228012i	0.811862	+	0.583850i	$0.198454\pi$
$332$	0.887719	−	0.887719i	0.0487199	−	0.0487199i
$333$	−1.90866			−0.104594
$334$	9.68062	+	9.68062i	0.529700	+	0.529700i
$335$		0			0
$336$	−3.70711	−	3.70711i	−0.202239	−	0.202239i
$337$	13.1630			0.717032			0.358516	−	0.933524i	$-0.383283\pi$
$337$	13.1630			0.717032			0.358516	+	0.933524i	$0.383283\pi$
$338$	11.8846			0.646435
$339$		−	11.0168i		−	0.598349i
$340$		0			0
$341$			8.11228i			0.439305i
$342$	−4.44395	−	4.44395i	−0.240301	−	0.240301i
$343$	−37.3502	+	37.3502i	−2.01672	+	2.01672i
$344$		−	11.8718i		−	0.640084i
$345$		0			0
$346$	−15.8179	+	15.8179i	−0.850374	+	0.850374i
$347$	−12.3549	+	12.3549i	−0.663247	+	0.663247i	−0.956144	−	0.292897i	$-0.905381\pi$
$347$	−12.3549	+	12.3549i	−0.663247	+	0.663247i	0.292897	+	0.956144i	$0.405381\pi$
$348$	0.928009	−	5.61127i	0.0497465	−	0.300796i
$349$			13.9387i			0.746121i	0.927807	+	0.373060i	$0.121692\pi$
$349$			13.9387i			0.746121i	−0.927807	+	0.373060i	$0.878308\pi$
$350$		0			0
$351$	3.85260	+	3.85260i	0.205637	+	0.205637i
$352$	−1.41421	+	1.41421i	−0.0753778	+	0.0753778i
$353$	−24.5414	−	24.5414i	−1.30621	−	1.30621i	−0.924130	−	0.382078i	$-0.875209\pi$
$353$	−24.5414	−	24.5414i	−1.30621	−	1.30621i	−0.382078	−	0.924130i	$-0.624791\pi$
$354$	6.91745			0.367659
$355$		0			0
$356$	−4.79239	+	4.79239i	−0.253996	+	0.253996i
$357$	7.91666	−	7.91666i	0.418994	−	0.418994i
$358$			10.8507i			0.573476i
$359$	6.13991	−	6.13991i	0.324052	−	0.324052i	−0.526267	−	0.850319i	$-0.676409\pi$
$359$	6.13991	−	6.13991i	0.324052	−	0.324052i	0.850319	+	0.526267i	$0.176409\pi$
$360$		0			0
$361$			7.87898i			0.414683i
$362$			5.82313i			0.306057i
$363$			7.39298i			0.388031i
$364$		−	5.24264i		−	0.274789i
$365$		0			0
$366$	−8.04630	+	8.04630i	−0.420587	+	0.420587i
$367$		−	26.0118i		−	1.35780i	−0.734229	−	0.678902i	$-0.762456\pi$
$367$		−	26.0118i		−	1.35780i	0.734229	−	0.678902i	$-0.237544\pi$
$368$	−3.29655	+	3.29655i	−0.171845	+	0.171845i
$369$	3.61951	−	3.61951i	0.188424	−	0.188424i
$370$		0			0
$371$	−68.8590			−3.57498
$372$	3.02914	+	3.02914i	0.157054	+	0.157054i
$373$	12.1804	−	12.1804i	0.630678	−	0.630678i	−0.317560	−	0.948238i	$-0.602864\pi$
$373$	12.1804	−	12.1804i	0.630678	−	0.630678i	0.948238	+	0.317560i	$0.102864\pi$
$374$	−3.02010	−	3.02010i	−0.156166	−	0.156166i
$375$		0			0
$376$			6.90782i			0.356244i
$377$	4.62397	−	3.31156i	0.238146	−	0.170554i
$378$	−18.1076	+	18.1076i	−0.931355	+	0.931355i
$379$	0.757359	−	0.757359i	0.0389029	−	0.0389029i	−0.687388	−	0.726291i	$-0.741243\pi$
$379$	0.757359	−	0.757359i	0.0389029	−	0.0389029i	0.726291	+	0.687388i	$0.241243\pi$
$380$		0			0
$381$		−	4.00303i		−	0.205082i
$382$	−7.53331	+	7.53331i	−0.385437	+	0.385437i
$383$	−12.1257	−	12.1257i	−0.619594	−	0.619594i	0.325833	−	0.945427i	$-0.394355\pi$
$383$	−12.1257	−	12.1257i	−0.619594	−	0.619594i	−0.945427	+	0.325833i	$0.894355\pi$
$384$			1.05614i			0.0538959i
$385$		0			0
$386$		−	4.81047i		−	0.244846i
$387$	−22.3732			−1.13729
$388$	9.37818			0.476105
$389$	−7.45442	−	7.45442i	−0.377954	−	0.377954i	0.492410	−	0.870364i	$-0.336116\pi$
$389$	−7.45442	−	7.45442i	−0.377954	−	0.377954i	−0.870364	+	0.492410i	$0.836116\pi$
$390$		0			0
$391$	−7.03990	−	7.03990i	−0.356023	−	0.356023i
$392$	17.6409			0.891001
$393$	12.2059	−	12.2059i	0.615705	−	0.615705i
$394$	12.5024	−	12.5024i	0.629864	−	0.629864i
$395$		0			0
$396$	2.66518	+	2.66518i	0.133930	+	0.133930i
$397$	21.2123	+	21.2123i	1.06461	+	1.06461i	0.997763	+	0.0668511i	$0.0212953\pi$
$397$	21.2123	+	21.2123i	1.06461	+	1.06461i	0.0668511	+	0.997763i	$0.478705\pi$
$398$	19.5411			0.979508
$399$	−17.4833			−0.875258
$400$		0			0
$401$	12.7492			0.636662			0.318331	−	0.947980i	$-0.396878\pi$
$401$	12.7492			0.636662			0.318331	+	0.947980i	$0.396878\pi$
$402$	4.36771	+	4.36771i	0.217841	+	0.217841i
$403$			4.28385i			0.213394i
$404$	−4.81573	−	4.81573i	−0.239591	−	0.239591i
$405$		0			0
$406$	15.5647	+	21.7331i	0.772462	+	1.07860i
$407$	1.43229	+	1.43229i	0.0709961	+	0.0709961i
$408$	−2.25542			−0.111660
$409$	−1.02010	+	1.02010i	−0.0504408	+	0.0504408i	−0.731877	−	0.681436i	$-0.761356\pi$
$409$	−1.02010	+	1.02010i	−0.0504408	+	0.0504408i	0.681436	+	0.731877i	$0.261356\pi$
$410$		0			0
$411$		−	18.1100i		−	0.893299i
$412$	−1.49361	+	1.49361i	−0.0735848	+	0.0735848i
$413$	−22.9900	+	22.9900i	−1.13126	+	1.13126i
$414$	6.21258	+	6.21258i	0.305331	+	0.305331i
$415$		0			0
$416$	−0.746804	+	0.746804i	−0.0366151	+	0.0366151i
$417$		−	4.88023i		−	0.238986i
$418$			6.66964i			0.326223i
$419$	−10.6777			−0.521639			−0.260819	−	0.965388i	$-0.583993\pi$
$419$	−10.6777			−0.521639			−0.260819	+	0.965388i	$0.583993\pi$
$420$		0			0
$421$	23.5411	−	23.5411i	1.14732	−	1.14732i	0.160248	−	0.987077i	$-0.448771\pi$
$421$	23.5411	−	23.5411i	1.14732	−	1.14732i	0.987077	−	0.160248i	$-0.0512293\pi$
$422$	2.27107	+	2.27107i	0.110554	+	0.110554i
$423$	13.0183			0.632969
$424$	9.80883	+	9.80883i	0.476359	+	0.476359i
$425$		0			0
$426$	−9.92044			−0.480647
$427$		−	53.4833i		−	2.58824i
$428$	8.17372	+	8.17372i	0.395091	+	0.395091i
$429$		−	2.23086i		−	0.107707i
$430$		0			0
$431$	3.72447			0.179402			0.0897008	−	0.995969i	$-0.471409\pi$
$431$	3.72447			0.179402			0.0897008	+	0.995969i	$0.471409\pi$
$432$	5.15879			0.248202
$433$			29.8751i			1.43571i	0.696195	+	0.717853i	$0.254875\pi$
$433$			29.8751i			1.43571i	−0.696195	+	0.717853i	$0.745125\pi$
$434$	−20.1345			−0.966488
$435$		0			0
$436$	2.92590			0.140125
$437$			15.5470i			0.743715i
$438$	3.61135			0.172557
$439$	35.8678			1.71188			0.855938	−	0.517078i	$-0.172980\pi$
$439$	35.8678			1.71188			0.855938	+	0.517078i	$0.172980\pi$
$440$		0			0
$441$		−	33.2455i		−	1.58312i
$442$	−1.59483	−	1.59483i	−0.0758581	−	0.0758581i
$443$		−	6.07321i		−	0.288547i	−0.989538	−	0.144273i	$-0.953915\pi$
$443$		−	6.07321i		−	0.288547i	0.989538	−	0.144273i	$-0.0460845\pi$
$444$	1.06964			0.0507630
$445$		0			0
$446$	2.38141	+	2.38141i	0.112763	+	0.112763i
$447$	−3.50294			−0.165684
$448$	−3.51005	−	3.51005i	−0.165834	−	0.165834i
$449$	−7.28915	+	7.28915i	−0.343996	+	0.343996i	−0.857867	−	0.513871i	$-0.828211\pi$
$449$	−7.28915	+	7.28915i	−0.343996	+	0.343996i	0.513871	+	0.857867i	$0.328211\pi$
$450$		0			0
$451$	−5.43229			−0.255797
$452$		−	10.4312i		−	0.490641i
$453$		−	11.7955i		−	0.554203i
$454$	19.2880	−	19.2880i	0.905232	−	0.905232i
$455$		0			0
$456$	2.49046	+	2.49046i	0.116626	+	0.116626i
$457$	−5.96611	+	5.96611i	−0.279083	+	0.279083i	−0.832743	−	0.553660i	$-0.813231\pi$
$457$	−5.96611	+	5.96611i	−0.279083	+	0.279083i	0.553660	+	0.832743i	$0.313231\pi$
$458$	−16.2664	+	16.2664i	−0.760079	+	0.760079i
$459$			11.0168i			0.514219i
$460$		0			0
$461$	−22.7620	+	22.7620i	−1.06013	+	1.06013i	−0.0620612	+	0.998072i	$0.519767\pi$
$461$	−22.7620	+	22.7620i	−1.06013	+	1.06013i	−0.998072	+	0.0620612i	$0.980233\pi$
$462$	10.4853			0.487819
$463$	−15.5878	−	15.5878i	−0.724427	−	0.724427i	0.245077	−	0.969504i	$-0.421187\pi$
$463$	−15.5878	−	15.5878i	−0.724427	−	0.724427i	−0.969504	+	0.245077i	$0.921187\pi$
$464$	0.878680	−	5.31300i	0.0407917	−	0.246650i
$465$		0			0
$466$	−3.38133	−	3.38133i	−0.156637	−	0.156637i
$467$			7.54386i			0.349088i	0.984649	+	0.174544i	$0.0558451\pi$
$467$			7.54386i			0.349088i	−0.984649	+	0.174544i	$0.944155\pi$
$468$	1.40740	+	1.40740i	0.0650572	+	0.0650572i
$469$	−29.0319			−1.34057
$470$		0			0
$471$	−14.0373			−0.646807
$472$	6.54975			0.301477
$473$	16.7892	+	16.7892i	0.771970	+	0.771970i
$474$	10.3152	+	10.3152i	0.473794	+	0.473794i
$475$		0			0
$476$	7.49584	−	7.49584i	0.343571	−	0.343571i
$477$	18.4854	−	18.4854i	0.846389	−	0.846389i
$478$	26.3622			1.20578
$479$	−17.6064	−	17.6064i	−0.804457	−	0.804457i	0.179332	−	0.983789i	$-0.442606\pi$
$479$	−17.6064	−	17.6064i	−0.804457	−	0.804457i	−0.983789	+	0.179332i	$0.942606\pi$
$480$		0			0
$481$	0.756351	+	0.756351i	0.0344866	+	0.0344866i
$482$	9.58793			0.436718
$483$	24.4413			1.11212
$484$			7.00000i			0.318182i
$485$		0			0
$486$		−	15.6932i		−	0.711858i
$487$	14.5445	+	14.5445i	0.659074	+	0.659074i	0.955161	−	0.296087i	$-0.0956819\pi$
$487$	14.5445	+	14.5445i	0.659074	+	0.659074i	−0.296087	+	0.955161i	$0.595682\pi$
$488$	−7.61859	+	7.61859i	−0.344877	+	0.344877i
$489$			21.3915i			0.967357i
$490$		0			0
$491$	14.0656	−	14.0656i	0.634772	−	0.634772i	−0.314489	−	0.949261i	$-0.601833\pi$
$491$	14.0656	−	14.0656i	0.634772	−	0.634772i	0.949261	+	0.314489i	$0.101833\pi$
$492$	−2.02843	+	2.02843i	−0.0914486	+	0.0914486i
$493$	11.3461	+	1.87645i	0.511002	+	0.0845111i
$494$			3.52204i			0.158464i
$495$		0			0
$496$	2.86812	+	2.86812i	0.128783	+	0.128783i
$497$	32.9703	−	32.9703i	1.47892	−	1.47892i
$498$	0.937556	+	0.937556i	0.0420129	+	0.0420129i
$499$	38.1345			1.70714			0.853568	−	0.520982i	$-0.174434\pi$
$499$	38.1345			1.70714			0.853568	+	0.520982i	$0.174434\pi$
$500$		0			0
$501$	−10.2241	+	10.2241i	−0.456779	+	0.456779i
$502$	−4.39411	+	4.39411i	−0.196119	+	0.196119i
$503$		−	37.2847i		−	1.66244i	−0.555942	−	0.831221i	$-0.687642\pi$
$503$		−	37.2847i		−	1.66244i	0.555942	−	0.831221i	$-0.312358\pi$
$504$	−6.61493	+	6.61493i	−0.294652	+	0.294652i
$505$		0			0
$506$		−	9.32406i		−	0.414505i
$507$			12.5518i			0.557444i
$508$		−	3.79025i		−	0.168165i
$509$		−	6.59310i		−	0.292234i	−0.989267	−	0.146117i	$-0.953322\pi$
$509$		−	6.59310i		−	0.292234i	0.989267	−	0.146117i	$-0.0466776\pi$
$510$		0			0
$511$	−12.0022	+	12.0022i	−0.530947	+	0.530947i
$512$			1.00000i			0.0441942i
$513$	12.1648	−	12.1648i	0.537089	−	0.537089i
$514$	−6.38133	+	6.38133i	−0.281468	+	0.281468i
$515$		0			0
$516$	12.5383			0.551967
$517$	−9.76914	−	9.76914i	−0.429646	−	0.429646i
$518$	−3.55492	+	3.55492i	−0.156194	+	0.156194i
$519$	−16.7059	−	16.7059i	−0.733307	−	0.733307i
$520$		0			0
$521$		−	5.90794i		−	0.258832i	−0.991590	−	0.129416i	$-0.958690\pi$
$521$		−	5.90794i		−	0.258832i	0.991590	−	0.129416i	$-0.0413102\pi$
$522$	−10.0127	−	1.65593i	−0.438244	−	0.0724781i
$523$	14.3854	−	14.3854i	0.629028	−	0.629028i	−0.318795	−	0.947824i	$-0.603278\pi$
$523$	14.3854	−	14.3854i	0.629028	−	0.629028i	0.947824	+	0.318795i	$0.103278\pi$
$524$	11.5571	−	11.5571i	0.504873	−	0.504873i
$525$		0			0
$526$			4.67250i			0.203731i
$527$	−6.12498	+	6.12498i	−0.266808	+	0.266808i
$528$	−1.49361	−	1.49361i	−0.0650009	−	0.0650009i
$529$			1.26548i			0.0550210i
$530$		0			0
$531$		−	12.3434i		−	0.535660i
$532$	−16.5539			−0.717703
$533$	−2.86863			−0.124254
$534$	−5.06144	−	5.06144i	−0.219030	−	0.219030i
$535$		0			0
$536$	4.13553	+	4.13553i	0.178628	+	0.178628i
$537$	−11.4598			−0.494528
$538$	−5.79920	+	5.79920i	−0.250021	+	0.250021i
$539$	−24.9480	+	24.9480i	−1.07459	+	1.07459i
$540$		0			0
$541$	28.2526	+	28.2526i	1.21467	+	1.21467i	0.969472	+	0.245203i	$0.0788545\pi$
$541$	28.2526	+	28.2526i	1.21467	+	1.21467i	0.245203	+	0.969472i	$0.421145\pi$
$542$	2.74903	+	2.74903i	0.118081	+	0.118081i
$543$	−6.15004			−0.263924
$544$	−2.13553			−0.0915603
$545$		0			0
$546$	5.53696			0.236960
$547$	−17.5795	−	17.5795i	−0.751644	−	0.751644i	0.223142	−	0.974786i	$-0.428369\pi$
$547$	−17.5795	−	17.5795i	−0.751644	−	0.751644i	−0.974786	+	0.223142i	$0.928369\pi$
$548$		−	17.1473i		−	0.732497i
$549$	14.3577	+	14.3577i	0.612774	+	0.612774i
$550$		0			0
$551$	−10.4564	−	14.6004i	−0.445459	−	0.621999i
$552$	−3.48162	−	3.48162i	−0.148188	−	0.148188i
$553$	−68.5647			−2.91567
$554$	−3.01278	+	3.01278i	−0.128001	+	0.128001i
$555$		0			0
$556$		−	4.62082i		−	0.195966i
$557$	13.9841	−	13.9841i	0.592527	−	0.592527i	−0.345786	−	0.938313i	$-0.612388\pi$
$557$	13.9841	−	13.9841i	0.592527	−	0.592527i	0.938313	+	0.345786i	$0.112388\pi$
$558$	5.40517	−	5.40517i	0.228819	−	0.228819i
$559$	8.86590	+	8.86590i	0.374987	+	0.374987i
$560$		0			0
$561$	3.18965	−	3.18965i	0.134667	−	0.134667i
$562$			29.1958i			1.23155i
$563$			14.8718i			0.626771i	0.949626	+	0.313385i	$0.101463\pi$
$563$			14.8718i			0.626771i	−0.949626	+	0.313385i	$0.898537\pi$
$564$	−7.29563			−0.307201
$565$		0			0
$566$	−19.8963	+	19.8963i	−0.836306	+	0.836306i
$567$	0.720604	+	0.720604i	0.0302625	+	0.0302625i
$568$	−9.39310			−0.394126
$569$	6.51614	+	6.51614i	0.273171	+	0.273171i	0.830375	−	0.557204i	$-0.188126\pi$
$569$	6.51614	+	6.51614i	0.273171	+	0.273171i	−0.557204	+	0.830375i	$0.688126\pi$
$570$		0			0
$571$	17.6582			0.738971			0.369485	−	0.929236i	$-0.379534\pi$
$571$	17.6582			0.738971			0.369485	+	0.929236i	$0.379534\pi$
$572$		−	2.11228i		−	0.0883189i
$573$	−7.95623	−	7.95623i	−0.332376	−	0.332376i
$574$		−	13.4828i		−	0.562763i
$575$		0			0
$576$	1.88457			0.0785236
$577$	−17.6169			−0.733403			−0.366702	−	0.930339i	$-0.619513\pi$
$577$	−17.6169			−0.733403			−0.366702	+	0.930339i	$0.619513\pi$
$578$			12.4395i			0.517415i
$579$	5.08053			0.211140
$580$		0			0
$581$	−6.23188			−0.258542
$582$			9.90467i			0.410562i
$583$	−27.7436			−1.14902
$584$	3.41939			0.141495
$585$		0			0
$586$			5.82640i			0.240687i
$587$	−14.7404	−	14.7404i	−0.608402	−	0.608402i	0.334126	−	0.942528i	$-0.391559\pi$
$587$	−14.7404	−	14.7404i	−0.608402	−	0.608402i	−0.942528	+	0.334126i	$0.891559\pi$
$588$			18.6313i			0.768341i
$589$	13.5265			0.557349
$590$		0			0
$591$	13.2043	+	13.2043i	0.543154	+	0.543154i
$592$	1.01278			0.0416252
$593$	−18.4416	−	18.4416i	−0.757307	−	0.757307i	0.218524	−	0.975831i	$-0.429876\pi$
$593$	−18.4416	−	18.4416i	−0.757307	−	0.757307i	−0.975831	+	0.218524i	$0.929876\pi$
$594$	−7.29563	+	7.29563i	−0.299343	+	0.299343i
$595$		0			0
$596$	−3.31674			−0.135859
$597$			20.6382i			0.844664i
$598$		−	4.92376i		−	0.201347i
$599$	−7.69655	+	7.69655i	−0.314473	+	0.314473i	−0.846639	−	0.532167i	$-0.821378\pi$
$599$	−7.69655	+	7.69655i	−0.314473	+	0.314473i	0.532167	+	0.846639i	$0.321378\pi$
$600$		0			0
$601$	−30.9376	−	30.9376i	−1.26197	−	1.26197i	−0.950137	−	0.311832i	$-0.899057\pi$
$601$	−30.9376	−	30.9376i	−1.26197	−	1.26197i	−0.311832	−	0.950137i	$-0.600943\pi$
$602$	−41.6706	+	41.6706i	−1.69837	+	1.69837i
$603$	7.79369	−	7.79369i	0.317384	−	0.317384i
$604$		−	11.1685i		−	0.454442i
$605$		0			0
$606$	5.08609	−	5.08609i	0.206608	−	0.206608i
$607$	26.9492			1.09383			0.546917	−	0.837187i	$-0.315801\pi$
$607$	26.9492			1.09383			0.546917	+	0.837187i	$0.315801\pi$
$608$	2.35807	+	2.35807i	0.0956325	+	0.0956325i
$609$	−22.9532	+	16.4385i	−0.930111	+	0.666121i
$610$		0			0
$611$	−5.15879	−	5.15879i	−0.208702	−	0.208702i
$612$			4.02456i			0.162683i
$613$	−25.8342	−	25.8342i	−1.04343	−	1.04343i	−0.999013	−	0.0444219i	$-0.985855\pi$
$613$	−25.8342	−	25.8342i	−1.04343	−	1.04343i	−0.0444219	−	0.999013i	$-0.514145\pi$
$614$	−21.2672			−0.858274
$615$		0			0
$616$	9.92792			0.400007
$617$	−15.8180			−0.636807			−0.318403	−	0.947955i	$-0.603147\pi$
$617$	−15.8180			−0.636807			−0.318403	+	0.947955i	$0.603147\pi$
$618$	−1.57746	−	1.57746i	−0.0634547	−	0.0634547i
$619$	25.4469	+	25.4469i	1.02280	+	1.02280i	0.999734	+	0.0230645i	$0.00734230\pi$
$619$	25.4469	+	25.4469i	1.02280	+	1.02280i	0.0230645	+	0.999734i	$0.492658\pi$
$620$		0			0
$621$	−17.0062	+	17.0062i	−0.682436	+	0.682436i
$622$	10.0276	−	10.0276i	0.402071	−	0.402071i
$623$	33.6431			1.34788
$624$	−0.788730	−	0.788730i	−0.0315745	−	0.0315745i
$625$		0			0
$626$	8.08154	+	8.08154i	0.323003	+	0.323003i
$627$	−7.04407			−0.281313
$628$	−13.2912			−0.530376
$629$			2.16284i			0.0862379i
$630$		0			0
$631$			5.21522i			0.207615i	0.994597	+	0.103807i	$0.0331025\pi$
$631$			5.21522i			0.207615i	−0.994597	+	0.103807i	$0.966897\pi$
$632$	9.76691	+	9.76691i	0.388507	+	0.388507i
$633$	−2.39857	+	2.39857i	−0.0953345	+	0.0953345i
$634$			4.71287i			0.187172i
$635$		0			0
$636$	−10.3595	+	10.3595i	−0.410781	+	0.410781i
$637$	−13.1743	+	13.1743i	−0.521985	+	0.521985i
$638$	6.27107	+	8.75635i	0.248274	+	0.346667i
$639$			17.7019i			0.700278i
$640$		0			0
$641$	6.55808	+	6.55808i	0.259028	+	0.259028i	0.824659	−	0.565630i	$-0.191367\pi$
$641$	6.55808	+	6.55808i	0.259028	+	0.259028i	−0.565630	+	0.824659i	$0.691367\pi$
$642$	−8.63259	+	8.63259i	−0.340701	+	0.340701i
$643$	2.70050	+	2.70050i	0.106497	+	0.106497i	0.758348	−	0.651850i	$-0.226007\pi$
$643$	2.70050	+	2.70050i	0.106497	+	0.106497i	−0.651850	+	0.758348i	$0.726007\pi$
$644$	23.1421			0.911928
$645$		0			0
$646$	−5.03575	+	5.03575i	−0.198129	+	0.198129i
$647$	−14.3338	+	14.3338i	−0.563520	+	0.563520i	−0.930306	−	0.366785i	$-0.880458\pi$
$647$	−14.3338	+	14.3338i	−0.563520	+	0.563520i	0.366785	+	0.930306i	$0.380458\pi$
$648$		−	0.205297i		−	0.00806483i
$649$	−9.26274	+	9.26274i	−0.363594	+	0.363594i
$650$		0			0
$651$		−	21.2649i		−	0.833437i
$652$			20.2544i			0.793224i
$653$			17.2774i			0.676116i	0.941125	+	0.338058i	$0.109770\pi$
$653$			17.2774i			0.676116i	−0.941125	+	0.338058i	$0.890230\pi$
$654$			3.09016i			0.120835i
$655$		0			0
$656$	−1.92061	+	1.92061i	−0.0749870	+	0.0749870i
$657$		−	6.44407i		−	0.251407i
$658$	24.2468	−	24.2468i	0.945239	−	0.945239i
$659$	−2.87696	+	2.87696i	−0.112070	+	0.112070i	−0.760918	−	0.648848i	$-0.775251\pi$
$659$	−2.87696	+	2.87696i	−0.112070	+	0.112070i	0.648848	+	0.760918i	$0.275251\pi$
$660$		0			0
$661$	−17.0530			−0.663284			−0.331642	−	0.943405i	$-0.607603\pi$
$661$	−17.0530			−0.663284			−0.331642	+	0.943405i	$0.607603\pi$
$662$	4.14832	+	4.14832i	0.161229	+	0.161229i
$663$	1.68436	−	1.68436i	0.0654151	−	0.0654151i
$664$	0.887719	+	0.887719i	0.0344502	+	0.0344502i
$665$		0			0
$666$		−	1.90866i		−	0.0739591i
$667$	14.6180	+	20.4112i	0.566009	+	0.790324i
$668$	−9.68062	+	9.68062i	−0.374554	+	0.374554i
$669$	−2.51511	+	2.51511i	−0.0972396	+	0.0972396i
$670$		0			0
$671$		−	21.5486i		−	0.831875i
$672$	3.70711	−	3.70711i	0.143005	−	0.143005i
$673$	20.2043	+	20.2043i	0.778818	+	0.778818i	0.979630	−	0.200812i	$-0.0643580\pi$
$673$	20.2043	+	20.2043i	0.778818	+	0.778818i	−0.200812	+	0.979630i	$0.564358\pi$
$674$			13.1630i			0.507018i
$675$		0			0
$676$			11.8846i			0.457099i
$677$	19.4739			0.748444			0.374222	−	0.927339i	$-0.377910\pi$
$677$	19.4739			0.748444			0.374222	+	0.927339i	$0.377910\pi$
$678$	11.0168			0.423097
$679$	−32.9179	−	32.9179i	−1.26327	−	1.26327i
$680$		0			0
$681$	20.3709	+	20.3709i	0.780613	+	0.780613i
$682$	−8.11228			−0.310635
$683$	19.3294	−	19.3294i	0.739617	−	0.739617i	−0.232887	−	0.972504i	$-0.574817\pi$
$683$	19.3294	−	19.3294i	0.739617	−	0.739617i	0.972504	+	0.232887i	$0.0748171\pi$
$684$	4.44395	−	4.44395i	0.169919	−	0.169919i
$685$		0			0
$686$	−37.3502	−	37.3502i	−1.42604	−	1.42604i
$687$	−17.1796	−	17.1796i	−0.655443	−	0.655443i
$688$	11.8718			0.452608
$689$	−14.6506			−0.558142
$690$		0			0
$691$	−28.2671			−1.07533			−0.537665	−	0.843158i	$-0.680694\pi$
$691$	−28.2671			−1.07533			−0.537665	+	0.843158i	$0.680694\pi$
$692$	−15.8179	−	15.8179i	−0.601305	−	0.601305i
$693$		−	18.7098i		−	0.710728i
$694$	−12.3549	−	12.3549i	−0.468986	−	0.468986i
$695$		0			0
$696$	5.61127	+	0.928009i	0.212695	+	0.0351761i
$697$	−4.10152	−	4.10152i	−0.155356	−	0.155356i
$698$	−13.9387			−0.527587
$699$	3.57116	−	3.57116i	0.135074	−	0.135074i
$700$		0			0
$701$		−	42.5805i		−	1.60824i	−0.594465	−	0.804122i	$-0.702636\pi$
$701$		−	42.5805i		−	1.60824i	0.594465	−	0.804122i	$-0.297364\pi$
$702$	−3.85260	+	3.85260i	−0.145407	+	0.145407i
$703$	2.38822	−	2.38822i	0.0900734	−	0.0900734i
$704$	−1.41421	−	1.41421i	−0.0533002	−	0.0533002i
$705$		0			0
$706$	24.5414	−	24.5414i	0.923629	−	0.923629i
$707$			33.8069i			1.27144i
$708$			6.91745i			0.259974i
$709$	−18.8477			−0.707840			−0.353920	−	0.935276i	$-0.615151\pi$
$709$	−18.8477			−0.707840			−0.353920	+	0.935276i	$0.615151\pi$
$710$		0			0
$711$	18.4064	−	18.4064i	0.690294	−	0.690294i
$712$	−4.79239	−	4.79239i	−0.179602	−	0.179602i
$713$	−18.9098			−0.708179
$714$	7.91666	+	7.91666i	0.296273	+	0.296273i
$715$		0			0
$716$	−10.8507			−0.405509
$717$			27.8422i			1.03979i
$718$	6.13991	+	6.13991i	0.229139	+	0.229139i
$719$		−	7.88587i		−	0.294093i	−0.989130	−	0.147047i	$-0.953023\pi$
$719$		−	7.88587i		−	0.294093i	0.989130	−	0.147047i	$-0.0469768\pi$
$720$		0			0
$721$	10.4853			0.390492
$722$	−7.87898			−0.293225
$723$			10.1262i			0.376597i
$724$	−5.82313			−0.216415
$725$		0			0
$726$	−7.39298			−0.274379
$727$		−	16.2235i		−	0.601698i	−0.953672	−	0.300849i	$-0.902730\pi$
$727$		−	16.2235i		−	0.601698i	0.953672	−	0.300849i	$-0.0972700\pi$
$728$	5.24264			0.194305
$729$	15.9583			0.591049
$730$		0			0
$731$			25.3526i			0.937700i
$732$	−8.04630	−	8.04630i	−0.297400	−	0.297400i
$733$		−	34.7097i		−	1.28203i	−0.767528	−	0.641016i	$-0.778513\pi$
$733$		−	34.7097i		−	1.28203i	0.767528	−	0.641016i	$-0.221487\pi$
$734$	26.0118			0.960112
$735$		0			0
$736$	−3.29655	−	3.29655i	−0.121513	−	0.121513i
$737$	−11.6971			−0.430867
$738$	3.61951	+	3.61951i	0.133236	+	0.133236i
$739$	−34.4798	+	34.4798i	−1.26836	+	1.26836i	−0.321426	+	0.946935i	$0.604162\pi$
$739$	−34.4798	+	34.4798i	−1.26836	+	1.26836i	−0.946935	+	0.321426i	$0.895838\pi$
$740$		0			0
$741$	−3.71977			−0.136649
$742$		−	68.8590i		−	2.52789i
$743$			47.1621i			1.73021i	0.501592	+	0.865104i	$0.332748\pi$
$743$			47.1621i			1.73021i	−0.501592	+	0.865104i	$0.667252\pi$
$744$	−3.02914	+	3.02914i	−0.111054	+	0.111054i
$745$		0			0
$746$	12.1804	+	12.1804i	0.445956	+	0.445956i
$747$	1.67297	−	1.67297i	0.0612107	−	0.0612107i
$748$	3.02010	−	3.02010i	0.110426	−	0.110426i
$749$		−	57.3803i		−	2.09663i
$750$		0			0
$751$	29.2343	−	29.2343i	1.06678	−	1.06678i	0.0691704	−	0.997605i	$-0.477965\pi$
$751$	29.2343	−	29.2343i	1.06678	−	1.06678i	0.997605	−	0.0691704i	$-0.0220352\pi$
$752$	−6.90782			−0.251902
$753$	−4.64080	−	4.64080i	−0.169120	−	0.169120i
$754$	3.31156	+	4.62397i	0.120600	+	0.168395i
$755$		0			0
$756$	−18.1076	−	18.1076i	−0.658568	−	0.658568i
$757$			42.1746i			1.53286i	0.642326	+	0.766431i	$0.277969\pi$
$757$			42.1746i			1.53286i	−0.642326	+	0.766431i	$0.722031\pi$
$758$	0.757359	+	0.757359i	0.0275085	+	0.0275085i
$759$	9.84751			0.357442
$760$		0			0
$761$	−25.9944			−0.942297			−0.471148	−	0.882054i	$-0.656160\pi$
$761$	−25.9944			−0.942297			−0.471148	+	0.882054i	$0.656160\pi$
$762$	4.00303			0.145015
$763$	−10.2701	−	10.2701i	−0.371801	−	0.371801i
$764$	−7.53331	−	7.53331i	−0.272545	−	0.272545i
$765$		0			0
$766$	12.1257	−	12.1257i	0.438119	−	0.438119i
$767$	−4.89138	+	4.89138i	−0.176617	+	0.176617i
$768$	−1.05614			−0.0381102
$769$	−19.2299	−	19.2299i	−0.693446	−	0.693446i	0.269542	−	0.962989i	$-0.413128\pi$
$769$	−19.2299	−	19.2299i	−0.693446	−	0.693446i	−0.962989	+	0.269542i	$0.913128\pi$
$770$		0			0
$771$	−6.73958	−	6.73958i	−0.242720	−	0.242720i
$772$	4.81047			0.173133
$773$	29.1923			1.04997			0.524986	−	0.851111i	$-0.324070\pi$
$773$	29.1923			1.04997			0.524986	+	0.851111i	$0.324070\pi$
$774$		−	22.3732i		−	0.804187i
$775$		0			0
$776$			9.37818i			0.336657i
$777$	−3.75450	−	3.75450i	−0.134692	−	0.134692i
$778$	7.45442	−	7.45442i	0.267254	−	0.267254i
$779$			9.05786i			0.324531i
$780$		0			0
$781$	13.2839	−	13.2839i	0.475334	−	0.475334i
$782$	7.03990	−	7.03990i	0.251746	−	0.251746i
$783$	4.53292	−	27.4086i	0.161993	−	0.979504i
$784$			17.6409i			0.630033i
$785$		0			0
$786$	12.2059	+	12.2059i	0.435369	+	0.435369i
$787$	3.13553	−	3.13553i	0.111770	−	0.111770i	−0.649010	−	0.760780i	$-0.724817\pi$
$787$	3.13553	−	3.13553i	0.111770	−	0.111770i	0.760780	+	0.649010i	$0.224817\pi$
$788$	12.5024	+	12.5024i	0.445381	+	0.445381i
$789$	−4.93482			−0.175684
$790$		0			0
$791$	−36.6139	+	36.6139i	−1.30184	+	1.30184i
$792$	−2.66518	+	2.66518i	−0.0947031	+	0.0947031i
$793$		−	11.3792i		−	0.404087i
$794$	−21.2123	+	21.2123i	−0.752796	+	0.752796i
$795$		0			0
$796$			19.5411i			0.692617i
$797$		−	37.8146i		−	1.33946i	−0.742603	−	0.669732i	$-0.766409\pi$
$797$		−	37.8146i		−	1.33946i	0.742603	−	0.669732i	$-0.233591\pi$
$798$		−	17.4833i		−	0.618901i
$799$		−	14.7519i		−	0.521884i
$800$		0			0
$801$	−9.03158	+	9.03158i	−0.319115	+	0.319115i
$802$			12.7492i			0.450188i
$803$	−4.83575	+	4.83575i	−0.170650	+	0.170650i
$804$	−4.36771	+	4.36771i	−0.154037	+	0.154037i
$805$		0			0
$806$	−4.28385			−0.150892
$807$	−6.12477	−	6.12477i	−0.215602	−	0.215602i
$808$	4.81573	−	4.81573i	0.169417	−	0.169417i
$809$	14.5986	+	14.5986i	0.513258	+	0.513258i	0.915523	−	0.402265i	$-0.131777\pi$
$809$	14.5986	+	14.5986i	0.513258	+	0.513258i	−0.402265	+	0.915523i	$0.631777\pi$
$810$		0			0
$811$			10.1209i			0.355393i	0.984085	+	0.177696i	$0.0568645\pi$
$811$			10.1209i			0.355393i	−0.984085	+	0.177696i	$0.943135\pi$
$812$	−21.7331	+	15.5647i	−0.762682	+	0.546213i
$813$	−2.90336	+	2.90336i	−0.101825	+	0.101825i
$814$	−1.43229	+	1.43229i	−0.0502018	+	0.0502018i
$815$		0			0
$816$		−	2.25542i		−	0.0789557i
$817$	27.9945	−	27.9945i	0.979405	−	0.979405i
$818$	−1.02010	−	1.02010i	−0.0356670	−	0.0356670i
$819$		−	9.88011i		−	0.345239i
$820$		0			0
$821$			4.31758i			0.150685i	0.997158	+	0.0753423i	$0.0240049\pi$
$821$			4.31758i			0.150685i	−0.997158	+	0.0753423i	$0.975995\pi$
$822$	18.1100			0.631658
$823$	20.4569			0.713081			0.356541	−	0.934280i	$-0.383956\pi$
$823$	20.4569			0.713081			0.356541	+	0.934280i	$0.383956\pi$
$824$	−1.49361	−	1.49361i	−0.0520323	−	0.0520323i
$825$		0			0
$826$	−22.9900	−	22.9900i	−0.799923	−	0.799923i
$827$	31.9272			1.11022			0.555109	−	0.831778i	$-0.312677\pi$
$827$	31.9272			1.11022			0.555109	+	0.831778i	$0.312677\pi$
$828$	−6.21258	+	6.21258i	−0.215902	+	0.215902i
$829$	−8.34883	+	8.34883i	−0.289967	+	0.289967i	−0.837067	−	0.547100i	$-0.815732\pi$
$829$	−8.34883	+	8.34883i	−0.289967	+	0.289967i	0.547100	+	0.837067i	$0.315732\pi$
$830$		0			0
$831$	−3.18192	−	3.18192i	−0.110380	−	0.110380i
$832$	−0.746804	−	0.746804i	−0.0258908	−	0.0258908i
$833$	−37.6728			−1.30529
$834$	4.88023			0.168989
$835$		0			0
$836$	−6.66964			−0.230674
$837$	14.7960	+	14.7960i	0.511426	+	0.511426i
$838$		−	10.6777i		−	0.368854i
$839$	16.4162	+	16.4162i	0.566751	+	0.566751i	0.931217	−	0.364465i	$-0.118748\pi$
$839$	16.4162	+	16.4162i	0.566751	+	0.566751i	−0.364465	+	0.931217i	$0.618748\pi$
$840$		0			0
$841$	−27.4558	−	9.33684i	−0.946753	−	0.321960i
$842$	23.5411	+	23.5411i	0.811281	+	0.811281i
$843$	−30.8349			−1.06201
$844$	−2.27107	+	2.27107i	−0.0781734	+	0.0781734i
$845$		0			0
$846$			13.0183i			0.447577i
$847$	24.5704	−	24.5704i	0.844248	−	0.844248i
$848$	−9.80883	+	9.80883i	−0.336837	+	0.336837i
$849$	−21.0133	−	21.0133i	−0.721176	−	0.721176i
$850$		0			0
$851$	−3.33870	+	3.33870i	−0.114449	+	0.114449i
$852$		−	9.92044i		−	0.339869i
$853$			23.2299i			0.795375i	0.917521	+	0.397688i	$0.130187\pi$
$853$			23.2299i			0.795375i	−0.917521	+	0.397688i	$0.869813\pi$
$854$	53.4833			1.83016
$855$		0			0
$856$	−8.17372	+	8.17372i	−0.279372	+	0.279372i
$857$	15.3217	+	15.3217i	0.523381	+	0.523381i	0.918591	−	0.395210i	$-0.129328\pi$
$857$	15.3217	+	15.3217i	0.523381	+	0.523381i	−0.395210	+	0.918591i	$0.629328\pi$
$858$	2.23086			0.0761605
$859$	−23.9121	−	23.9121i	−0.815871	−	0.815871i	0.169636	−	0.985507i	$-0.445741\pi$
$859$	−23.9121	−	23.9121i	−0.815871	−	0.815871i	−0.985507	+	0.169636i	$0.945741\pi$
$860$		0			0
$861$	14.2398			0.485290
$862$			3.72447i			0.126856i
$863$	23.0074	+	23.0074i	0.783181	+	0.783181i	0.980366	−	0.197185i	$-0.0631800\pi$
$863$	23.0074	+	23.0074i	0.783181	+	0.783181i	−0.197185	+	0.980366i	$0.563180\pi$
$864$			5.15879i			0.175506i
$865$		0			0
$866$	−29.8751			−1.01520
$867$	−13.1378			−0.446185
$868$		−	20.1345i		−	0.683410i
$869$	−27.6250			−0.937113
$870$		0			0
$871$	−6.17687			−0.209295
$872$			2.92590i			0.0990835i
$873$	17.6738			0.598168
$874$	−15.5470			−0.525886
$875$		0			0
$876$			3.61135i			0.122016i
$877$	34.8390	+	34.8390i	1.17643	+	1.17643i	0.980648	+	0.195782i	$0.0627243\pi$
$877$	34.8390	+	34.8390i	1.17643	+	1.17643i	0.195782	+	0.980648i	$0.437276\pi$
$878$			35.8678i			1.21048i
$879$	−6.15350			−0.207552
$880$		0			0
$881$	−1.74701	−	1.74701i	−0.0588582	−	0.0588582i	0.677065	−	0.735923i	$-0.263252\pi$
$881$	−1.74701	−	1.74701i	−0.0588582	−	0.0588582i	−0.735923	+	0.677065i	$0.763252\pi$
$882$	33.2455			1.11943
$883$	−0.141000	−	0.141000i	−0.00474504	−	0.00474504i	0.704730	−	0.709475i	$-0.251068\pi$
$883$	−0.141000	−	0.141000i	−0.00474504	−	0.00474504i	−0.709475	+	0.704730i	$0.751068\pi$
$884$	1.59483	−	1.59483i	0.0536398	−	0.0536398i
$885$		0			0
$886$	6.07321			0.204034
$887$		−	3.17300i		−	0.106539i	−0.998580	−	0.0532694i	$-0.983036\pi$
$887$		−	3.17300i		−	0.106539i	0.998580	−	0.0532694i	$-0.0169642\pi$
$888$			1.06964i			0.0358948i
$889$	−13.3040	+	13.3040i	−0.446200	+	0.446200i
$890$		0			0
$891$	0.290334	+	0.290334i	0.00972656	+	0.00972656i
$892$	−2.38141	+	2.38141i	−0.0797356	+	0.0797356i
$893$	−16.2891	+	16.2891i	−0.545096	+	0.545096i
$894$		−	3.50294i		−	0.117156i
$895$		0			0
$896$	3.51005	−	3.51005i	0.117263	−	0.117263i
$897$	5.20018			0.173629
$898$	−7.28915	−	7.28915i	−0.243242	−	0.243242i
$899$	17.7585	−	12.7182i	0.592279	−	0.424175i
$900$		0			0
$901$	−20.9471	−	20.9471i	−0.697849	−	0.697849i
$902$		−	5.43229i		−	0.180876i
$903$	−44.0100	−	44.0100i	−1.46456	−	1.46456i
$904$	10.4312			0.346935
$905$		0			0
$906$	11.7955			0.391881
$907$	6.16842			0.204819			0.102410	−	0.994742i	$-0.467345\pi$
$907$	6.16842			0.204819			0.102410	+	0.994742i	$0.467345\pi$
$908$	19.2880	+	19.2880i	0.640095	+	0.640095i
$909$	−9.07557	−	9.07557i	−0.301017	−	0.301017i
$910$		0			0
$911$	−5.66842	+	5.66842i	−0.187803	+	0.187803i	−0.794746	−	0.606943i	$-0.792396\pi$
$911$	−5.66842	+	5.66842i	−0.187803	+	0.187803i	0.606943	+	0.794746i	$0.292396\pi$
$912$	−2.49046	+	2.49046i	−0.0824672	+	0.0824672i
$913$	−2.51085			−0.0830970
$914$	−5.96611	−	5.96611i	−0.197341	−	0.197341i
$915$		0			0
$916$	−16.2664	−	16.2664i	−0.537457	−	0.537457i
$917$	−81.1318			−2.67921
$918$	−11.0168			−0.363608
$919$		−	16.0098i		−	0.528113i	−0.964507	−	0.264057i	$-0.914939\pi$
$919$		−	16.0098i		−	0.528113i	0.964507	−	0.264057i	$-0.0850606\pi$
$920$		0			0
$921$		−	22.4611i		−	0.740120i
$922$	−22.7620	−	22.7620i	−0.749628	−	0.749628i
$923$	7.01481	−	7.01481i	0.230895	−	0.230895i
$924$			10.4853i			0.344940i
$925$		0			0
$926$	15.5878	−	15.5878i	0.512247	−	0.512247i
$927$	−2.81481	+	2.81481i	−0.0924503	+	0.0924503i
$928$	5.31300	+	0.878680i	0.174408	+	0.0288441i
$929$		−	14.6577i		−	0.480905i	−0.970661	−	0.240453i	$-0.922704\pi$
$929$		−	14.6577i		−	0.480905i	0.970661	−	0.240453i	$-0.0772958\pi$
$930$		0			0
$931$	41.5986	+	41.5986i	1.36334	+	1.36334i
$932$	3.38133	−	3.38133i	0.110759	−	0.110759i
$933$	10.5906	+	10.5906i	0.346720	+	0.346720i
$934$	−7.54386			−0.246843
$935$		0			0
$936$	−1.40740	+	1.40740i	−0.0460024	+	0.0460024i
$937$	−14.6152	+	14.6152i	−0.477459	+	0.477459i	−0.904318	−	0.426859i	$-0.859620\pi$
$937$	−14.6152	+	14.6152i	−0.477459	+	0.477459i	0.426859	+	0.904318i	$0.359620\pi$
$938$		−	29.0319i		−	0.947924i
$939$	−8.53524	+	8.53524i	−0.278537	+	0.278537i
$940$		0			0
$941$			1.22658i			0.0399855i	0.999800	+	0.0199928i	$0.00636432\pi$
$941$			1.22658i			0.0399855i	−0.999800	+	0.0199928i	$0.993636\pi$
$942$		−	14.0373i		−	0.457361i
$943$		−	12.6628i		−	0.412356i
$944$			6.54975i			0.213176i
$945$		0			0
$946$	−16.7892	+	16.7892i	−0.545865	+	0.545865i
$947$		−	12.7469i		−	0.414218i	−0.978318	−	0.207109i	$-0.933594\pi$
$947$		−	12.7469i		−	0.414218i	0.978318	−	0.207109i	$-0.0664056\pi$
$948$	−10.3152	+	10.3152i	−0.335023	+	0.335023i
$949$	−2.55361	+	2.55361i	−0.0828938	+	0.0828938i
$950$		0			0
$951$	−4.97746			−0.161405
$952$	7.49584	+	7.49584i	0.242941	+	0.242941i
$953$	−36.4204	+	36.4204i	−1.17977	+	1.17977i	−0.199971	+	0.979802i	$0.564085\pi$
$953$	−36.4204	+	36.4204i	−1.17977	+	1.17977i	−0.979802	+	0.199971i	$0.935915\pi$
$954$	18.4854	+	18.4854i	0.598487	+	0.598487i
$955$		0			0
$956$			26.3622i			0.852616i
$957$	−9.24794	+	6.62313i	−0.298943	+	0.214095i
$958$	17.6064	−	17.6064i	0.568837	−	0.568837i
$959$	−60.1879	+	60.1879i	−1.94357	+	1.94357i
$960$		0			0
$961$		−	14.5477i		−	0.469281i
$962$	−0.756351	+	0.756351i	−0.0243857	+	0.0243857i
$963$	15.4039	+	15.4039i	0.496384	+	0.496384i
$964$			9.58793i			0.308806i
$965$		0			0
$966$			24.4413i			0.786387i
$967$	27.0603			0.870201			0.435100	−	0.900382i	$-0.356713\pi$
$967$	27.0603			0.870201			0.435100	+	0.900382i	$0.356713\pi$
$968$	−7.00000			−0.224989
$969$	−5.31846	−	5.31846i	−0.170853	−	0.170853i
$970$		0			0
$971$	36.9526	+	36.9526i	1.18587	+	1.18587i	0.978200	+	0.207666i	$0.0665866\pi$
$971$	36.9526	+	36.9526i	1.18587	+	1.18587i	0.207666	+	0.978200i	$0.433413\pi$
$972$	15.6932			0.503359
$973$	−16.2193	+	16.2193i	−0.519967	+	0.519967i
$974$	−14.5445	+	14.5445i	−0.466035	+	0.466035i
$975$		0			0
$976$	−7.61859	−	7.61859i	−0.243865	−	0.243865i
$977$	25.2860	+	25.2860i	0.808971	+	0.808971i	0.984478	−	0.175507i	$-0.0561566\pi$
$977$	25.2860	+	25.2860i	0.808971	+	0.808971i	−0.175507	+	0.984478i	$0.556157\pi$
$978$	−21.3915			−0.684025
$979$	13.5549			0.433217
$980$		0			0
$981$	5.51406			0.176050
$982$	14.0656	+	14.0656i	0.448851	+	0.448851i
$983$		−	6.02843i		−	0.192277i	−0.995368	−	0.0961385i	$-0.969351\pi$
$983$		−	6.02843i		−	0.192277i	0.995368	−	0.0961385i	$-0.0306492\pi$
$984$	−2.02843	−	2.02843i	−0.0646640	−	0.0646640i
$985$		0			0
$986$	−1.87645	+	11.3461i	−0.0597584	+	0.361333i
$987$	25.6080	+	25.6080i	0.815113	+	0.815113i
$988$	−3.52204			−0.112051
$989$	−39.1360	+	39.1360i	−1.24445	+	1.24445i
$990$		0			0
$991$		−	32.6006i		−	1.03559i	−0.855504	−	0.517796i	$-0.826753\pi$
$991$		−	32.6006i		−	1.03559i	0.855504	−	0.517796i	$-0.173247\pi$
$992$	−2.86812	+	2.86812i	−0.0910630	+	0.0910630i
$993$	−4.38121	+	4.38121i	−0.139033	+	0.139033i
$994$	32.9703	+	32.9703i	1.04575	+	1.04575i
$995$		0			0
$996$	−0.937556	+	0.937556i	−0.0297076	+	0.0297076i
$997$			3.26560i			0.103423i	0.998662	+	0.0517114i	$0.0164676\pi$
$997$			3.26560i			0.103423i	−0.998662	+	0.0517114i	$0.983532\pi$
$998$			38.1345i			1.20713i
$999$	5.22474			0.165303

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1450.2.j.e.157.2		8
5.2	odd	4		290.2.e.e.273.3	yes	8
5.3	odd	4		1450.2.e.e.1143.2		8
5.4	even	2		290.2.j.e.157.3	yes	8
29.17	odd	4		1450.2.e.e.307.3		8
145.17	even	4		290.2.j.e.133.3	yes	8
145.104	odd	4		290.2.e.e.17.2	✓	8
145.133	even	4	inner	1450.2.j.e.1293.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
290.2.e.e.17.2	✓	8	145.104	odd	4
290.2.e.e.273.3	yes	8	5.2	odd	4
290.2.j.e.133.3	yes	8	145.17	even	4
290.2.j.e.157.3	yes	8	5.4	even	2
1450.2.e.e.307.3		8	29.17	odd	4
1450.2.e.e.1143.2		8	5.3	odd	4
1450.2.j.e.157.2		8	1.1	even	1	trivial
1450.2.j.e.1293.2		8	145.133	even	4	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:	\( N \)	\(=\)	\( 1450 = 2 \cdot 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1450.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} -1.05614 q^{3} -1.00000 q^{4} -1.05614i q^{6} +(3.51005 + 3.51005i) q^{7} -1.00000i q^{8} -1.88457 q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} -1.05614 q^{3} -1.00000 q^{4} -1.05614i q^{6} +(3.51005 + 3.51005i) q^{7} -1.00000i q^{8} -1.88457 q^{9} +(1.41421 + 1.41421i) q^{11} +1.05614 q^{12} +(0.746804 + 0.746804i) q^{13} +(-3.51005 + 3.51005i) q^{14} +1.00000 q^{16} +2.13553i q^{17} -1.88457i q^{18} +(2.35807 - 2.35807i) q^{19} +(-3.70711 - 3.70711i) q^{21} +(-1.41421 + 1.41421i) q^{22} +(-3.29655 + 3.29655i) q^{23} +1.05614i q^{24} +(-0.746804 + 0.746804i) q^{26} +5.15879 q^{27} +(-3.51005 - 3.51005i) q^{28} +(0.878680 - 5.31300i) q^{29} +(2.86812 + 2.86812i) q^{31} +1.00000i q^{32} +(-1.49361 - 1.49361i) q^{33} -2.13553 q^{34} +1.88457 q^{36} +1.01278 q^{37} +(2.35807 + 2.35807i) q^{38} +(-0.788730 - 0.788730i) q^{39} +(-1.92061 + 1.92061i) q^{41} +(3.70711 - 3.70711i) q^{42} +11.8718 q^{43} +(-1.41421 - 1.41421i) q^{44} +(-3.29655 - 3.29655i) q^{46} -6.90782 q^{47} -1.05614 q^{48} +17.6409i q^{49} -2.25542i q^{51} +(-0.746804 - 0.746804i) q^{52} +(-9.80883 + 9.80883i) q^{53} +5.15879i q^{54} +(3.51005 - 3.51005i) q^{56} +(-2.49046 + 2.49046i) q^{57} +(5.31300 + 0.878680i) q^{58} +6.54975i q^{59} +(-7.61859 - 7.61859i) q^{61} +(-2.86812 + 2.86812i) q^{62} +(-6.61493 - 6.61493i) q^{63} -1.00000 q^{64} +(1.49361 - 1.49361i) q^{66} +(-4.13553 + 4.13553i) q^{67} -2.13553i q^{68} +(3.48162 - 3.48162i) q^{69} -9.39310i q^{71} +1.88457i q^{72} +3.41939i q^{73} +1.01278i q^{74} +(-2.35807 + 2.35807i) q^{76} +9.92792i q^{77} +(0.788730 - 0.788730i) q^{78} +(-9.76691 + 9.76691i) q^{79} +0.205297 q^{81} +(-1.92061 - 1.92061i) q^{82} +(-0.887719 + 0.887719i) q^{83} +(3.70711 + 3.70711i) q^{84} +11.8718i q^{86} +(-0.928009 + 5.61127i) q^{87} +(1.41421 - 1.41421i) q^{88} +(4.79239 - 4.79239i) q^{89} +5.24264i q^{91} +(3.29655 - 3.29655i) q^{92} +(-3.02914 - 3.02914i) q^{93} -6.90782i q^{94} -1.05614i q^{96} -9.37818 q^{97} -17.6409 q^{98} +(-2.66518 - 2.66518i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{3} - 8 q^{4} + 4 q^{7} + 20 q^{9}+O(q^{10}) \) 8 * q + 4 * q^3 - 8 * q^4 + 4 * q^7 + 20 * q^9	\( 8 q + 4 q^{3} - 8 q^{4} + 4 q^{7} + 20 q^{9} - 4 q^{12} - 4 q^{14} + 8 q^{16} + 20 q^{19} - 24 q^{21} + 4 q^{23} + 40 q^{27} - 4 q^{28} + 24 q^{29} - 4 q^{34} - 20 q^{36} + 32 q^{37} + 20 q^{38} + 16 q^{39} - 16 q^{41} + 24 q^{42} + 36 q^{43} + 4 q^{46} - 32 q^{47} + 4 q^{48} - 8 q^{53} + 4 q^{56} + 52 q^{57} + 4 q^{61} - 24 q^{63} - 8 q^{64} - 20 q^{67} - 4 q^{69} - 20 q^{76} - 16 q^{78} - 24 q^{79} + 24 q^{81} - 16 q^{82} - 32 q^{83} + 24 q^{84} + 12 q^{87} - 20 q^{89} - 4 q^{92} + 16 q^{93} - 28 q^{97} - 12 q^{98} - 32 q^{99}+O(q^{100}) \) 8 * q + 4 * q^3 - 8 * q^4 + 4 * q^7 + 20 * q^9 - 4 * q^12 - 4 * q^14 + 8 * q^16 + 20 * q^19 - 24 * q^21 + 4 * q^23 + 40 * q^27 - 4 * q^28 + 24 * q^29 - 4 * q^34 - 20 * q^36 + 32 * q^37 + 20 * q^38 + 16 * q^39 - 16 * q^41 + 24 * q^42 + 36 * q^43 + 4 * q^46 - 32 * q^47 + 4 * q^48 - 8 * q^53 + 4 * q^56 + 52 * q^57 + 4 * q^61 - 24 * q^63 - 8 * q^64 - 20 * q^67 - 4 * q^69 - 20 * q^76 - 16 * q^78 - 24 * q^79 + 24 * q^81 - 16 * q^82 - 32 * q^83 + 24 * q^84 + 12 * q^87 - 20 * q^89 - 4 * q^92 + 16 * q^93 - 28 * q^97 - 12 * q^98 - 32 * q^99

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