LMFDB - Embedded newform 300.2.h.c.299.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(299,300)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(300, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("300.299");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.h (of order $2$, degree $1$, 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:	$2.39551206064$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} + 2 x^{14} + 10 x^{13} - 42 x^{11} + 134 x^{10} + 110 x^{9} + 92 x^{8} + 142 x^{7} + \cdots + 100 $ x^16 - 2x^15 + 2x^14 + 10x^13 - 42x^11 + 134x^10 + 110x^9 + 92x^8 + 142x^7 + 1514x^6 + 1102x^5 + 249x^4 - 1056x^3 + 392x^2 - 280x + 100
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{6}\cdot 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			299.12
Root			$-1.05054 - 0.869987i$ of defining polynomial
Character	$\chi$	$=$	300.299
Dual form			300.2.h.c.299.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.569745 + 1.29437i) q^{2} +(1.47492 - 0.908080i) q^{3} +(-1.35078 + 1.47492i) q^{4} +(2.01572 + 1.39172i) q^{6} +2.50967 q^{7} +(-2.67869 - 0.908080i) q^{8} +(1.35078 - 2.67869i) q^{9} +O(q^{10})$	\(q+(0.569745 + 1.29437i) q^{2} +(1.47492 - 0.908080i) q^{3} +(-1.35078 + 1.47492i) q^{4} +(2.01572 + 1.39172i) q^{6} +2.50967 q^{7} +(-2.67869 - 0.908080i) q^{8} +(1.35078 - 2.67869i) q^{9} +3.36131 q^{11} +(-0.652949 + 3.40201i) q^{12} +3.70156i q^{13} +(1.42987 + 3.24844i) q^{14} +(-0.350781 - 3.98459i) q^{16} -7.63636 q^{17} +(4.23682 + 0.222237i) q^{18} -0.440172i q^{19} +(3.70156 - 2.27898i) q^{21} +(1.91509 + 4.35078i) q^{22} +5.17748i q^{23} +(-4.77547 + 1.09312i) q^{24} +(-4.79119 + 2.10895i) q^{26} +(-0.440172 - 5.17748i) q^{27} +(-3.39001 + 3.70156i) q^{28} -2.27898i q^{29} -3.39001i q^{31} +(4.95767 - 2.72424i) q^{32} +(4.95767 - 3.05234i) q^{33} +(-4.35078 - 9.88427i) q^{34} +(2.12625 + 5.61062i) q^{36} -7.40312i q^{37} +(0.569745 - 0.250786i) q^{38} +(3.36131 + 5.45951i) q^{39} -3.07840i q^{41} +(5.05879 + 3.49275i) q^{42} -8.40935 q^{43} +(-4.54040 + 4.95767i) q^{44} +(-6.70156 + 2.94984i) q^{46} +3.63232i q^{47} +(-4.13570 - 5.55842i) q^{48} -0.701562 q^{49} +(-11.2630 + 6.93443i) q^{51} +(-5.45951 - 5.00000i) q^{52} -2.27898 q^{53} +(6.45078 - 3.51959i) q^{54} +(-6.72263 - 2.27898i) q^{56} +(-0.399712 - 0.649219i) q^{57} +(2.94984 - 1.29844i) q^{58} -5.70156 q^{61} +(4.38793 - 1.93144i) q^{62} +(3.39001 - 6.72263i) q^{63} +(6.35078 + 4.86493i) q^{64} +(6.77547 + 4.67800i) q^{66} -5.45951 q^{67} +(10.3151 - 11.2630i) q^{68} +(4.70156 + 7.63636i) q^{69} +12.4421 q^{71} +(-6.05079 + 5.94877i) q^{72} -1.29844i q^{73} +(9.58237 - 4.21789i) q^{74} +(0.649219 + 0.594576i) q^{76} +8.43579 q^{77} +(-5.15153 + 7.46131i) q^{78} -5.01934i q^{79} +(-5.35078 - 7.23665i) q^{81} +(3.98459 - 1.75391i) q^{82} -1.81616i q^{83} +(-1.63869 + 8.53791i) q^{84} +(-4.79119 - 10.8848i) q^{86} +(-2.06950 - 3.36131i) q^{87} +(-9.00393 - 3.05234i) q^{88} -5.35738i q^{89} +9.28970i q^{91} +(-7.63636 - 6.99364i) q^{92} +(-3.07840 - 5.00000i) q^{93} +(-4.70156 + 2.06950i) q^{94} +(4.83834 - 8.52000i) q^{96} +11.1047i q^{97} +(-0.399712 - 0.908080i) q^{98} +(4.54040 - 9.00393i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{4} + 6 q^{6} - 4 q^{9}+O(q^{10}) $ 16 * q + 4 * q^4 + 6 * q^6 - 4 * q^9	$ 16 q + 4 q^{4} + 6 q^{6} - 4 q^{9} + 20 q^{16} + 8 q^{21} - 26 q^{24} - 44 q^{34} - 42 q^{36} - 56 q^{46} + 40 q^{49} + 56 q^{54} - 40 q^{61} + 76 q^{64} + 58 q^{66} + 24 q^{69} + 36 q^{76} - 60 q^{81} - 80 q^{84} - 24 q^{94} - 78 q^{96}+O(q^{100}) $ 16 * q + 4 * q^4 + 6 * q^6 - 4 * q^9 + 20 * q^16 + 8 * q^21 - 26 * q^24 - 44 * q^34 - 42 * q^36 - 56 * q^46 + 40 * q^49 + 56 * q^54 - 40 * q^61 + 76 * q^64 + 58 * q^66 + 24 * q^69 + 36 * q^76 - 60 * q^81 - 80 * q^84 - 24 * q^94 - 78 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/300\mathbb{Z}\right)^\times$.

$n$	$101$	$151$	$277$
$\chi(n)$	$-1$	$-1$	$-1$

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 $

$2$	0.569745	+	1.29437i	0.402871	+	0.915257i
$2$	0.569745	+	1.29437i	0.402871	+	0.915257i
$3$	1.47492	−	0.908080i	0.851546	−	0.524280i
$3$	1.47492	−	0.908080i	0.851546	−	0.524280i
$4$	−1.35078	+	1.47492i	−0.675391	+	0.737460i
$5$		0			0
$5$		0			0
$6$	2.01572	+	1.39172i	0.822914	+	0.568166i
$7$	2.50967			0.948566			0.474283	−	0.880373i	$-0.342707\pi$
$7$	2.50967			0.948566			0.474283	+	0.880373i	$0.342707\pi$
$8$	−2.67869	−	0.908080i	−0.947061	−	0.321055i
$9$	1.35078	−	2.67869i	0.450260	−	0.892897i
$10$		0			0
$11$	3.36131			1.01347			0.506737	−	0.862101i	$-0.330851\pi$
$11$	3.36131			1.01347			0.506737	+	0.862101i	$0.330851\pi$
$12$	−0.652949	+	3.40201i	−0.188490	+	0.982075i
$13$			3.70156i			1.02663i	0.858201	+	0.513314i	$0.171582\pi$
$13$			3.70156i			1.02663i	−0.858201	+	0.513314i	$0.828418\pi$
$14$	1.42987	+	3.24844i	0.382149	+	0.868181i
$15$		0			0
$16$	−0.350781	−	3.98459i	−0.0876953	−	0.996147i
$17$	−7.63636			−1.85209			−0.926045	−	0.377413i	$-0.876814\pi$
$17$	−7.63636			−1.85209			−0.926045	+	0.377413i	$0.876814\pi$
$18$	4.23682	+	0.222237i	0.998627	+	0.0523818i
$19$		−	0.440172i		−	0.100982i	−0.998725	−	0.0504912i	$-0.983921\pi$
$19$		−	0.440172i		−	0.100982i	0.998725	−	0.0504912i	$-0.0160787\pi$
$20$		0			0
$21$	3.70156	−	2.27898i	0.807747	−	0.497314i
$22$	1.91509	+	4.35078i	0.408299	+	0.927590i
$23$			5.17748i			1.07958i	0.841800	+	0.539789i	$0.181496\pi$
$23$			5.17748i			1.07958i	−0.841800	+	0.539789i	$0.818504\pi$
$24$	−4.77547	+	1.09312i	−0.974788	+	0.223132i
$25$		0			0
$26$	−4.79119	+	2.10895i	−0.939629	+	0.413599i
$27$	−0.440172	−	5.17748i	−0.0847112	−	0.996406i
$28$	−3.39001	+	3.70156i	−0.640652	+	0.699529i
$29$		−	2.27898i		−	0.423196i	−0.977357	−	0.211598i	$-0.932133\pi$
$29$		−	2.27898i		−	0.423196i	0.977357	−	0.211598i	$-0.0678668\pi$
$30$		0			0
$31$		−	3.39001i		−	0.608864i	−0.952534	−	0.304432i	$-0.901533\pi$
$31$		−	3.39001i		−	0.608864i	0.952534	−	0.304432i	$-0.0984667\pi$
$32$	4.95767	−	2.72424i	0.876401	−	0.481582i
$33$	4.95767	−	3.05234i	0.863020	−	0.531345i
$34$	−4.35078	−	9.88427i	−0.746153	−	1.69514i
$35$		0			0
$36$	2.12625	+	5.61062i	0.354375	+	0.935104i
$37$		−	7.40312i		−	1.21707i	−0.793529	−	0.608533i	$-0.791758\pi$
$37$		−	7.40312i		−	1.21707i	0.793529	−	0.608533i	$-0.208242\pi$
$38$	0.569745	−	0.250786i	0.0924249	−	0.0406828i
$39$	3.36131	+	5.45951i	0.538241	+	0.874221i
$40$		0			0
$41$		−	3.07840i		−	0.480766i	−0.970678	−	0.240383i	$-0.922727\pi$
$41$		−	3.07840i		−	0.480766i	0.970678	−	0.240383i	$-0.0772730\pi$
$42$	5.05879	+	3.49275i	0.780588	+	0.538943i
$43$	−8.40935			−1.28241			−0.641207	−	0.767368i	$-0.721566\pi$
$43$	−8.40935			−1.28241			−0.641207	+	0.767368i	$0.721566\pi$
$44$	−4.54040	+	4.95767i	−0.684491	+	0.747397i
$45$		0			0
$46$	−6.70156	+	2.94984i	−0.988091	+	0.434930i
$47$			3.63232i			0.529828i	0.964272	+	0.264914i	$0.0853436\pi$
$47$			3.63232i			0.529828i	−0.964272	+	0.264914i	$0.914656\pi$
$48$	−4.13570	−	5.55842i	−0.596937	−	0.802288i
$49$	−0.701562			−0.100223
$50$		0			0
$51$	−11.2630	+	6.93443i	−1.57714	+	0.971014i
$52$	−5.45951	−	5.00000i	−0.757098	−	0.693375i
$53$	−2.27898			−0.313042			−0.156521	−	0.987675i	$-0.550028\pi$
$53$	−2.27898			−0.313042			−0.156521	+	0.987675i	$0.550028\pi$
$54$	6.45078	−	3.51959i	0.877839	−	0.478955i
$55$		0			0
$56$	−6.72263	−	2.27898i	−0.898349	−	0.304542i
$57$	−0.399712	−	0.649219i	−0.0529431	−	0.0859911i
$58$	2.94984	−	1.29844i	0.387333	−	0.170493i
$59$		0			0			−	1.00000i	$-0.5\pi$
$59$		0			0				1.00000i	$0.5\pi$
$60$		0			0
$61$	−5.70156			−0.730010			−0.365005	−	0.931006i	$-0.618933\pi$
$61$	−5.70156			−0.730010			−0.365005	+	0.931006i	$0.618933\pi$
$62$	4.38793	−	1.93144i	0.557267	−	0.245294i
$63$	3.39001	−	6.72263i	0.427102	−	0.846972i
$64$	6.35078	+	4.86493i	0.793848	+	0.608117i
$65$		0			0
$66$	6.77547	+	4.67800i	0.834002	+	0.575822i
$67$	−5.45951			−0.666985			−0.333493	−	0.942753i	$-0.608227\pi$
$67$	−5.45951			−0.666985			−0.333493	+	0.942753i	$0.608227\pi$
$68$	10.3151	−	11.2630i	1.25088	−	1.36584i
$69$	4.70156	+	7.63636i	0.566002	+	0.919310i
$70$		0			0
$71$	12.4421			1.47661			0.738304	−	0.674468i	$-0.235627\pi$
$71$	12.4421			1.47661			0.738304	+	0.674468i	$0.235627\pi$
$72$	−6.05079	+	5.94877i	−0.713093	+	0.701070i
$73$		−	1.29844i		−	0.151971i	−0.997109	−	0.0759853i	$-0.975790\pi$
$73$		−	1.29844i		−	0.151971i	0.997109	−	0.0759853i	$-0.0242102\pi$
$74$	9.58237	−	4.21789i	1.11393	−	0.490320i
$75$		0			0
$76$	0.649219	+	0.594576i	0.0744705	+	0.0682026i
$77$	8.43579			0.961347
$78$	−5.15153	+	7.46131i	−0.583296	+	0.844827i
$79$		−	5.01934i		−	0.564720i	−0.959309	−	0.282360i	$-0.908883\pi$
$79$		−	5.01934i		−	0.564720i	0.959309	−	0.282360i	$-0.0911172\pi$
$80$		0			0
$81$	−5.35078	−	7.23665i	−0.594531	−	0.804073i
$82$	3.98459	−	1.75391i	0.440024	−	0.193686i
$83$		−	1.81616i		−	0.199349i	−0.995020	−	0.0996747i	$-0.968220\pi$
$83$		−	1.81616i		−	0.199349i	0.995020	−	0.0996747i	$-0.0317802\pi$
$84$	−1.63869	+	8.53791i	−0.178795	+	0.931563i
$85$		0			0
$86$	−4.79119	−	10.8848i	−0.516647	−	1.17374i
$87$	−2.06950	−	3.36131i	−0.221873	−	0.360371i
$88$	−9.00393	−	3.05234i	−0.959822	−	0.325381i
$89$		−	5.35738i		−	0.567882i	−0.958842	−	0.283941i	$-0.908358\pi$
$89$		−	5.35738i		−	0.567882i	0.958842	−	0.283941i	$-0.0916419\pi$
$90$		0			0
$91$			9.28970i			0.973825i
$92$	−7.63636	−	6.99364i	−0.796146	−	0.729137i
$93$	−3.07840	−	5.00000i	−0.319216	−	0.518476i
$94$	−4.70156	+	2.06950i	−0.484929	+	0.213452i
$95$		0			0
$96$	4.83834	−	8.52000i	0.493811	−	0.869569i
$97$			11.1047i			1.12751i	0.825942	+	0.563755i	$0.190644\pi$
$97$			11.1047i			1.12751i	−0.825942	+	0.563755i	$0.809356\pi$
$98$	−0.399712	−	0.908080i	−0.0403770	−	0.0917299i
$99$	4.54040	−	9.00393i	0.456327	−	0.904929i
$100$		0			0
$101$			17.5517i			1.74646i	0.487308	+	0.873230i	$0.337979\pi$
$101$			17.5517i			1.74646i	−0.487308	+	0.873230i	$0.662021\pi$
$102$	−15.3928	−	10.6277i	−1.52411	−	1.05229i
$103$	10.9190			1.07588			0.537941	−	0.842982i	$-0.319202\pi$
$103$	10.9190			1.07588			0.537941	+	0.842982i	$0.319202\pi$
$104$	3.36131	−	9.91534i	0.329604	−	0.972280i
$105$		0			0
$106$	−1.29844	−	2.94984i	−0.126115	−	0.286514i
$107$			6.45162i			0.623702i	0.950131	+	0.311851i	$0.100949\pi$
$107$			6.45162i			0.623702i	−0.950131	+	0.311851i	$0.899051\pi$
$108$	8.23094	+	6.34442i	0.792023	+	0.610492i
$109$	−2.29844			−0.220150			−0.110075	−	0.993923i	$-0.535109\pi$
$109$	−2.29844			−0.220150			−0.110075	+	0.993923i	$0.535109\pi$
$110$		0			0
$111$	−6.72263	−	10.9190i	−0.638084	−	1.03639i
$112$	−0.880344	−	10.0000i	−0.0831847	−	0.944911i
$113$	0.799423			0.0752034			0.0376017	−	0.999293i	$-0.488028\pi$
$113$	0.799423			0.0752034			0.0376017	+	0.999293i	$0.488028\pi$
$114$	0.612595	−	0.887263i	0.0573748	−	0.0830998i
$115$		0			0
$116$	3.36131	+	3.07840i	0.312090	+	0.285823i
$117$	9.91534	+	5.00000i	0.916674	+	0.462250i
$118$		0			0
$119$	−19.1647			−1.75683
$120$		0			0
$121$	0.298438			0.0271307
$122$	−3.24844	−	7.37992i	−0.294100	−	0.668147i
$123$	−2.79544	−	4.54040i	−0.252056	−	0.409394i
$124$	5.00000	+	4.57917i	0.449013	+	0.411221i
$125$		0			0
$126$	10.6330	+	0.557742i	0.947263	+	0.0496876i
$127$	12.6797			1.12514			0.562571	−	0.826749i	$-0.309812\pi$
$127$	12.6797			1.12514			0.562571	+	0.826749i	$0.309812\pi$
$128$	−2.67869	+	10.9920i	−0.236765	+	0.971567i
$129$	−12.4031	+	7.63636i	−1.09203	+	0.672344i
$130$		0			0
$131$	−5.71949			−0.499714			−0.249857	−	0.968283i	$-0.580384\pi$
$131$	−5.71949			−0.499714			−0.249857	+	0.968283i	$0.580384\pi$
$132$	−2.19477	+	11.4352i	−0.191030	+	0.995308i
$133$		−	1.10469i		−	0.0957885i
$134$	−3.11053	−	7.06662i	−0.268709	−	0.610463i
$135$		0			0
$136$	20.4555	+	6.93443i	1.75404	+	0.594623i
$137$	9.91534			0.847125			0.423563	−	0.905867i	$-0.360779\pi$
$137$	9.91534			0.847125			0.423563	+	0.905867i	$0.360779\pi$
$138$	−7.20558	+	10.4363i	−0.613380	+	0.888400i
$139$			2.94984i			0.250202i	0.992144	+	0.125101i	$0.0399255\pi$
$139$			2.94984i			0.250202i	−0.992144	+	0.125101i	$0.960074\pi$
$140$		0			0
$141$	3.29844	+	5.35738i	0.277779	+	0.451173i
$142$	7.08883	+	16.1047i	0.594882	+	1.35148i
$143$			12.4421i			1.04046i
$144$	−11.1473	−	4.44267i	−0.928943	−	0.370223i
$145$		0			0
$146$	1.68066	−	0.739779i	0.139092	−	0.0612245i
$147$	−1.03475	+	0.637075i	−0.0853446	+	0.0525450i
$148$	10.9190	+	10.0000i	0.897538	+	0.821995i
$149$			15.2727i			1.25119i	0.780148	+	0.625595i	$0.215144\pi$
$149$			15.2727i			1.25119i	−0.780148	+	0.625595i	$0.784856\pi$
$150$		0			0
$151$		−	19.3284i		−	1.57292i	−0.617641	−	0.786460i	$-0.711911\pi$
$151$		−	19.3284i		−	1.57292i	0.617641	−	0.786460i	$-0.288089\pi$
$152$	−0.399712	+	1.17909i	−0.0324209	+	0.0956365i
$153$	−10.3151	+	20.4555i	−0.833923	+	1.65373i
$154$	4.80625	+	10.9190i	0.387299	+	0.879880i
$155$		0			0
$156$	−12.5927	−	2.41693i	−1.00823	−	0.193509i
$157$			11.1047i			0.886250i	0.896460	+	0.443125i	$0.146130\pi$
$157$			11.1047i			0.886250i	−0.896460	+	0.443125i	$0.853870\pi$
$158$	6.49687	−	2.85974i	0.516864	−	0.227509i
$159$	−3.36131	+	2.06950i	−0.266570	+	0.164122i
$160$		0			0
$161$			12.9937i			1.02405i
$162$	6.31832	−	11.0489i	0.496414	−	0.868086i
$163$	−0.440172			−0.0344769			−0.0172385	−	0.999851i	$-0.505487\pi$
$163$	−0.440172			−0.0344769			−0.0172385	+	0.999851i	$0.505487\pi$
$164$	4.54040	+	4.15825i	0.354546	+	0.324705i
$165$		0			0
$166$	2.35078	−	1.03475i	0.182456	−	0.0803120i
$167$			15.5324i			1.20194i	0.799273	+	0.600968i	$0.205218\pi$
$167$			15.5324i			1.20194i	−0.799273	+	0.600968i	$0.794782\pi$
$168$	−11.9848	+	2.74337i	−0.924651	+	0.211656i
$169$	−0.701562			−0.0539663
$170$		0			0
$171$	−1.17909	−	0.594576i	−0.0901669	−	0.0454684i
$172$	11.3592	−	12.4031i	0.866130	−	0.945729i
$173$	−8.43579			−0.641361			−0.320681	−	0.947187i	$-0.603912\pi$
$173$	−8.43579			−0.641361			−0.320681	+	0.947187i	$0.603912\pi$
$174$	3.17170	−	4.59378i	0.240446	−	0.348254i
$175$		0			0
$176$	−1.17909	−	13.3935i	−0.0888769	−	1.00957i
$177$		0			0
$178$	6.93443	−	3.05234i	0.519758	−	0.228783i
$179$	9.08080			0.678731			0.339365	−	0.940655i	$-0.389788\pi$
$179$	9.08080			0.678731			0.339365	+	0.940655i	$0.389788\pi$
$180$		0			0
$181$	10.5078			0.781039			0.390520	−	0.920595i	$-0.372295\pi$
$181$	10.5078			0.781039			0.390520	+	0.920595i	$0.372295\pi$
$182$	−12.0243	+	5.29276i	−0.891300	+	0.392325i
$183$	−8.40935	+	5.17748i	−0.621637	+	0.382730i
$184$	4.70156	−	13.8689i	0.346604	−	1.02243i
$185$		0			0
$186$	4.71794	−	6.83331i	0.345936	−	0.501043i
$187$	−25.6682			−1.87705
$188$	−5.35738	−	4.90647i	−0.390727	−	0.357841i
$189$	−1.10469	−	12.9937i	−0.0803541	−	0.945156i
$190$		0			0
$191$	12.4421			0.900280			0.450140	−	0.892958i	$-0.351374\pi$
$191$	12.4421			0.900280			0.450140	+	0.892958i	$0.351374\pi$
$192$	13.7846	+	1.40837i	0.994821	+	0.101641i
$193$		−	19.8062i		−	1.42568i	−0.701324	−	0.712842i	$-0.747407\pi$
$193$		−	19.8062i		−	1.42568i	0.701324	−	0.712842i	$-0.252593\pi$
$194$	−14.3736	+	6.32684i	−1.03196	+	0.454241i
$195$		0			0
$196$	0.947657	−	1.03475i	0.0676898	−	0.0739106i
$197$	−10.7148			−0.763396			−0.381698	−	0.924287i	$-0.624660\pi$
$197$	−10.7148			−0.763396			−0.381698	+	0.924287i	$0.624660\pi$
$198$	14.2413	+	0.747009i	1.01208	+	0.0530876i
$199$			21.0891i			1.49496i	0.664282	+	0.747482i	$0.268737\pi$
$199$			21.0891i			1.49496i	−0.664282	+	0.747482i	$0.731263\pi$
$200$		0			0
$201$	−8.05234	+	4.95767i	−0.567968	+	0.349687i
$202$	−22.7184	+	10.0000i	−1.59846	+	0.703598i
$203$		−	5.71949i		−	0.401429i
$204$	4.98615	−	25.9790i	0.349101	−	1.81889i
$205$		0			0
$206$	6.22106	+	14.1332i	0.433442	+	0.984709i
$207$	13.8689	+	6.99364i	0.963952	+	0.486091i
$208$	14.7492	−	1.29844i	1.02267	−	0.0900305i
$209$		−	1.47956i		−	0.102343i
$210$		0			0
$211$			18.1392i			1.24876i	0.781123	+	0.624378i	$0.214647\pi$
$211$			18.1392i			1.24876i	−0.781123	+	0.624378i	$0.785353\pi$
$212$	3.07840	−	3.36131i	0.211426	−	0.230856i
$213$	18.3511	−	11.2984i	1.25740	−	0.774156i
$214$	−8.35078	+	3.67578i	−0.570848	+	0.251271i
$215$		0			0
$216$	−3.52248	+	14.2686i	−0.239674	+	0.970853i
$217$		−	8.50781i		−	0.577548i
$218$	−1.30952	−	2.97503i	−0.0886921	−	0.201494i
$219$	−1.17909	−	1.91509i	−0.0796752	−	0.129410i
$220$		0			0
$221$		−	28.2665i		−	1.90141i
$222$	10.3031	−	14.9226i	0.691496	−	1.00154i
$223$	21.0891			1.41223			0.706114	−	0.708098i	$-0.250447\pi$
$223$	21.0891			1.41223			0.706114	+	0.708098i	$0.250447\pi$
$224$	12.4421	−	6.83694i	0.831324	−	0.456812i
$225$		0			0
$226$	0.455467	+	1.03475i	0.0302972	+	0.0688304i
$227$		−	22.2551i		−	1.47712i	−0.674188	−	0.738560i	$-0.735506\pi$
$227$		−	22.2551i		−	1.47712i	0.674188	−	0.738560i	$-0.264494\pi$
$228$	1.49747	+	0.287410i	0.0991723	+	0.0190342i
$229$	−2.29844			−0.151885			−0.0759425	−	0.997112i	$-0.524197\pi$
$229$	−2.29844			−0.151885			−0.0759425	+	0.997112i	$0.524197\pi$
$230$		0			0
$231$	12.4421	−	7.66037i	0.818631	−	0.504015i
$232$	−2.06950	+	6.10469i	−0.135869	+	0.400792i
$233$	−8.43579			−0.552647			−0.276323	−	0.961065i	$-0.589116\pi$
$233$	−8.43579			−0.552647			−0.276323	+	0.961065i	$0.589116\pi$
$234$	−0.822625	+	15.6828i	−0.0537767	+	1.02522i
$235$		0			0
$236$		0			0
$237$	−4.55796	−	7.40312i	−0.296071	−	0.480885i
$238$	−10.9190	−	24.8062i	−0.707775	−	1.60795i
$239$	25.8874			1.67452			0.837258	−	0.546809i	$-0.184158\pi$
$239$	25.8874			1.67452			0.837258	+	0.546809i	$0.184158\pi$
$240$		0			0
$241$	7.00000			0.450910			0.225455	−	0.974254i	$-0.427613\pi$
$241$	7.00000			0.450910			0.225455	+	0.974254i	$0.427613\pi$
$242$	0.170034	+	0.386289i	0.0109302	+	0.0248316i
$243$	−14.4634	−	5.81455i	−0.927830	−	0.373004i
$244$	7.70156	−	8.40935i	0.493042	−	0.538354i
$245$		0			0
$246$	4.28427	−	6.20520i	0.273155	−	0.395629i
$247$	1.62932			0.103671
$248$	−3.07840	+	9.08080i	−0.195479	+	0.576631i
$249$	−1.64922	−	2.67869i	−0.104515	−	0.169755i
$250$		0			0
$251$	−22.5261			−1.42183			−0.710916	−	0.703277i	$-0.751719\pi$
$251$	−22.5261			−1.42183			−0.710916	+	0.703277i	$0.751719\pi$
$252$	5.33618	+	14.0808i	0.336148	+	0.887007i
$253$			17.4031i			1.09413i
$254$	7.22420	+	16.4122i	0.453287	+	1.02979i
$255$		0			0
$256$	−15.7539	+	2.79544i	−0.984619	+	0.174715i
$257$	−4.55796			−0.284318			−0.142159	−	0.989844i	$-0.545404\pi$
$257$	−4.55796			−0.284318			−0.142159	+	0.989844i	$0.545404\pi$
$258$	−16.9509	−	11.7034i	−1.05532	−	0.728624i
$259$		−	18.5794i		−	1.15447i
$260$		0			0
$261$	−6.10469	−	3.07840i	−0.377871	−	0.190548i
$262$	−3.25865	−	7.40312i	−0.201320	−	0.457367i
$263$		−	18.6227i		−	1.14833i	−0.818741	−	0.574164i	$-0.805327\pi$
$263$		−	18.6227i		−	1.14833i	0.818741	−	0.574164i	$-0.194673\pi$
$264$	−16.0518	+	3.67432i	−0.987923	+	0.226139i
$265$		0			0
$266$	1.42987	−	0.629390i	0.0876710	−	0.0385904i
$267$	−4.86493	−	7.90172i	−0.297729	−	0.483577i
$268$	7.37460	−	8.05234i	0.450476	−	0.491875i
$269$		−	8.43579i		−	0.514339i	−0.966366	−	0.257170i	$-0.917210\pi$
$269$		−	8.43579i		−	0.514339i	0.966366	−	0.257170i	$-0.0827899\pi$
$270$		0			0
$271$			9.15833i			0.556329i	0.960533	+	0.278165i	$0.0897260\pi$
$271$			9.15833i			0.556329i	−0.960533	+	0.278165i	$0.910274\pi$
$272$	2.67869	+	30.4278i	0.162420	+	1.84495i
$273$	8.43579	+	13.7016i	0.510557	+	0.829256i
$274$	5.64922	+	12.8341i	0.341282	+	0.775337i
$275$		0			0
$276$	−17.6138	−	3.38063i	−1.06023	−	0.203490i
$277$		−	8.89531i		−	0.534468i	−0.963632	−	0.267234i	$-0.913890\pi$
$277$		−	8.89531i		−	0.534468i	0.963632	−	0.267234i	$-0.0861096\pi$
$278$	−3.81818	+	1.68066i	−0.228999	+	0.100799i
$279$	−9.08080	−	4.57917i	−0.543653	−	0.274147i
$280$		0			0
$281$		−	17.5517i		−	1.04705i	−0.852011	−	0.523524i	$-0.824617\pi$
$281$		−	17.5517i		−	1.04705i	0.852011	−	0.523524i	$-0.175383\pi$
$282$	−5.05516	+	7.32174i	−0.301030	+	0.436003i
$283$	−16.3785			−0.973603			−0.486801	−	0.873513i	$-0.661836\pi$
$283$	−16.3785			−0.973603			−0.486801	+	0.873513i	$0.661836\pi$
$284$	−16.8066	+	18.3511i	−0.997287	+	1.08894i
$285$		0			0
$286$	−16.1047	+	7.08883i	−0.952290	+	0.419172i
$287$		−	7.72577i		−	0.456038i
$288$	−0.600671	−	16.9599i	−0.0353949	−	0.999373i
$289$	41.3141			2.43024
$290$		0			0
$291$	10.0839	+	16.3785i	0.591131	+	0.960126i
$292$	1.91509	+	1.75391i	0.112072	+	0.102640i
$293$	21.4295			1.25193			0.625963	−	0.779852i	$-0.284706\pi$
$293$	21.4295			1.25193			0.625963	+	0.779852i	$0.284706\pi$
$294$	−1.41415	−	0.976376i	−0.0824750	−	0.0569434i
$295$		0			0
$296$	−6.72263	+	19.8307i	−0.390745	+	1.15264i
$297$	−1.47956	−	17.4031i	−0.0858526	−	1.00983i
$298$	−19.7685	+	8.70156i	−1.14516	+	0.504068i
$299$	−19.1647			−1.10833
$300$		0			0
$301$	−21.1047			−1.21645
$302$	25.0180	−	11.0122i	1.43963	−	0.633683i
$303$	15.9384	+	25.8874i	0.915635	+	1.48719i
$304$	−1.75391	+	0.154404i	−0.100593	+	0.00885568i
$305$		0			0
$306$	−32.3539	−	1.69708i	−1.84955	−	0.0970159i
$307$	26.4172			1.50771			0.753855	−	0.657041i	$-0.228192\pi$
$307$	26.4172			1.50771			0.753855	+	0.657041i	$0.228192\pi$
$308$	−11.3949	+	12.4421i	−0.649285	+	0.708955i
$309$	16.1047	−	9.91534i	0.916164	−	0.564064i
$310$		0			0
$311$	−13.4453			−0.762411			−0.381205	−	0.924490i	$-0.624491\pi$
$311$	−13.4453			−0.762411			−0.381205	+	0.924490i	$0.624491\pi$
$312$	−4.04625	−	17.6767i	−0.229074	−	1.00075i
$313$		−	16.2984i		−	0.921242i	−0.887597	−	0.460621i	$-0.847627\pi$
$313$		−	16.2984i		−	0.921242i	0.887597	−	0.460621i	$-0.152373\pi$
$314$	−14.3736	+	6.32684i	−0.811147	+	0.357044i
$315$		0			0
$316$	7.40312	+	6.78003i	0.416458	+	0.381406i
$317$	−16.8716			−0.947602			−0.473801	−	0.880632i	$-0.657118\pi$
$317$	−16.8716			−0.947602			−0.473801	+	0.880632i	$0.657118\pi$
$318$	−4.59378	−	3.17170i	−0.257607	−	0.177860i
$319$		−	7.66037i		−	0.428898i
$320$		0			0
$321$	5.85859	+	9.51563i	0.326995	+	0.531111i
$322$	−16.8187	+	7.40312i	−0.937270	+	0.412560i
$323$			3.36131i			0.187029i
$324$	17.9012	+	1.88316i	0.994512	+	0.104620i
$325$		0			0
$326$	−0.250786	−	0.569745i	−0.0138897	−	0.0315553i
$327$	−3.39001	+	2.08717i	−0.187468	+	0.115421i
$328$	−2.79544	+	8.24609i	−0.154352	+	0.455314i
$329$			9.11592i			0.502577i
$330$		0			0
$331$			17.1275i			0.941413i	0.882290	+	0.470707i	$0.156001\pi$
$331$			17.1275i			0.941413i	−0.882290	+	0.470707i	$0.843999\pi$
$332$	2.67869	+	2.45323i	0.147012	+	0.134639i
$333$	−19.8307	−	10.0000i	−1.08672	−	0.547997i
$334$	−20.1047	+	8.84952i	−1.10008	+	0.484224i
$335$		0			0
$336$	−10.3792	−	13.9498i	−0.566234	−	0.761023i
$337$		−	12.4031i		−	0.675641i	−0.941211	−	0.337821i	$-0.890310\pi$
$337$		−	12.4031i		−	0.675641i	0.941211	−	0.337821i	$-0.109690\pi$
$338$	−0.399712	−	0.908080i	−0.0217414	−	0.0493930i
$339$	1.17909	−	0.725940i	0.0640391	−	0.0394277i
$340$		0			0
$341$		−	11.3949i		−	0.617069i
$342$	0.0978226	−	1.86493i	0.00528964	−	0.100844i
$343$	−19.3284			−1.04363
$344$	22.5261	+	7.63636i	1.21452	+	0.411725i
$345$		0			0
$346$	−4.80625	−	10.9190i	−0.258386	−	0.587010i
$347$		−	19.4358i		−	1.04337i	−0.853139	−	0.521683i	$-0.825304\pi$
$347$		−	19.4358i		−	1.04337i	0.853139	−	0.521683i	$-0.174696\pi$
$348$	7.75311	+	1.48806i	0.415610	+	0.0797682i
$349$	−26.2094			−1.40296			−0.701478	−	0.712691i	$-0.747476\pi$
$349$	−26.2094			−1.40296			−0.701478	+	0.712691i	$0.747476\pi$
$350$		0			0
$351$	19.1647	−	1.62932i	1.02294	−	0.0869669i
$352$	16.6643	−	9.15703i	0.888210	−	0.488071i
$353$	26.6676			1.41937			0.709687	−	0.704517i	$-0.248836\pi$
$353$	26.6676			1.41937			0.709687	+	0.704517i	$0.248836\pi$
$354$		0			0
$355$		0			0
$356$	7.90172	+	7.23665i	0.418790	+	0.383542i
$357$	−28.2665	+	17.4031i	−1.49602	+	0.921071i
$358$	5.17374	+	11.7539i	0.273441	+	0.621213i
$359$	7.72577			0.407751			0.203875	−	0.978997i	$-0.434646\pi$
$359$	7.72577			0.407751			0.203875	+	0.978997i	$0.434646\pi$
$360$		0			0
$361$	18.8062			0.989803
$362$	5.98677	+	13.6010i	0.314658	+	0.714852i
$363$	0.440172	−	0.271006i	0.0231030	−	0.0142241i
$364$	−13.7016	−	12.5483i	−0.718157	−	0.657712i
$365$		0			0
$366$	−11.4927	−	7.93496i	−0.600736	−	0.414767i
$367$	2.50967			0.131004			0.0655018	−	0.997852i	$-0.479135\pi$
$367$	2.50967			0.131004			0.0655018	+	0.997852i	$0.479135\pi$
$368$	20.6301	−	1.81616i	1.07542	−	0.0946739i
$369$	−8.24609	−	4.15825i	−0.429275	−	0.216470i
$370$		0			0
$371$	−5.71949			−0.296941
$372$	11.5329	+	2.21350i	0.597951	+	0.114765i
$373$			23.7016i			1.22722i	0.789609	+	0.613610i	$0.210283\pi$
$373$			23.7016i			1.22722i	−0.789609	+	0.613610i	$0.789717\pi$
$374$	−14.6243	−	33.2241i	−0.756207	−	1.71798i
$375$		0			0
$376$	3.29844	−	9.72987i	0.170104	−	0.501780i
$377$	8.43579			0.434465
$378$	16.1893	−	8.83300i	0.832688	−	0.454320i
$379$			13.1199i			0.673923i	0.941518	+	0.336961i	$0.109399\pi$
$379$			13.1199i			0.673923i	−0.941518	+	0.336961i	$0.890601\pi$
$380$		0			0
$381$	18.7016	−	11.5142i	0.958110	−	0.589890i
$382$	7.08883	+	16.1047i	0.362696	+	0.823987i
$383$			7.26464i			0.371206i	0.982625	+	0.185603i	$0.0594238\pi$
$383$			7.26464i			0.371206i	−0.982625	+	0.185603i	$0.940576\pi$
$384$	6.03078	+	18.6448i	0.307757	+	0.951465i
$385$		0			0
$386$	25.6366	−	11.2845i	1.30487	−	0.574367i
$387$	−11.3592	+	22.5261i	−0.577420	+	1.14506i
$388$	−16.3785	−	15.0000i	−0.831494	−	0.761510i
$389$		−	37.3824i		−	1.89536i	−0.319218	−	0.947681i	$-0.603420\pi$
$389$		−	37.3824i		−	1.89536i	0.319218	−	0.947681i	$-0.396580\pi$
$390$		0			0
$391$		−	39.5371i		−	1.99948i
$392$	1.87927	+	0.637075i	0.0949174	+	0.0321771i
$393$	−8.43579	+	5.19375i	−0.425529	+	0.261990i
$394$	−6.10469	−	13.8689i	−0.307550	−	0.698703i
$395$		0			0
$396$	7.14699	+	18.8591i	0.359150	+	0.947704i
$397$		−	15.9109i		−	0.798547i	−0.916832	−	0.399273i	$-0.869262\pi$
$397$		−	15.9109i		−	0.798547i	0.916832	−	0.399273i	$-0.130738\pi$
$398$	−27.2970	+	12.0154i	−1.36828	+	0.602277i
$399$	−1.00314	−	1.62932i	−0.0502200	−	0.0815683i
$400$		0			0
$401$			9.23521i			0.461184i	0.973050	+	0.230592i	$0.0740663\pi$
$401$			9.23521i			0.461184i	−0.973050	+	0.230592i	$0.925934\pi$
$402$	−11.0048	−	7.59809i	−0.548871	−	0.378958i
$403$	12.5483			0.625078
$404$	−25.8874	−	23.7085i	−1.28795	−	1.17954i
$405$		0			0
$406$	7.40312	−	3.25865i	0.367411	−	0.161724i
$407$		−	24.8842i		−	1.23347i
$408$	36.4672	−	8.34747i	1.80540	−	0.413261i
$409$	−11.2094			−0.554268			−0.277134	−	0.960831i	$-0.589385\pi$
$409$	−11.2094			−0.554268			−0.277134	+	0.960831i	$0.589385\pi$
$410$		0			0
$411$	14.6243	−	9.00393i	0.721366	−	0.444131i
$412$	−14.7492	+	16.1047i	−0.726641	+	0.793421i
$413$		0			0
$414$	−1.15063	+	21.9360i	−0.0565503	+	1.07810i
$415$		0			0
$416$	10.0839	+	18.3511i	0.494406	+	0.899738i
$417$	2.67869	+	4.35078i	0.131176	+	0.213059i
$418$	1.91509	−	0.842970i	0.0936702	−	0.0412310i
$419$	34.9682			1.70831			0.854154	−	0.520021i	$-0.174076\pi$
$419$	34.9682			1.70831			0.854154	+	0.520021i	$0.174076\pi$
$420$		0			0
$421$	−14.2094			−0.692522			−0.346261	−	0.938138i	$-0.612549\pi$
$421$	−14.2094			−0.692522			−0.346261	+	0.938138i	$0.612549\pi$
$422$	−23.4788	+	10.3347i	−1.14293	+	0.503087i
$423$	9.72987	+	4.90647i	0.473082	+	0.238561i
$424$	6.10469	+	2.06950i	0.296470	+	0.100504i
$425$		0			0
$426$	25.0798	+	17.3159i	1.21512	+	0.838958i
$427$	−14.3090			−0.692463
$428$	−9.51563	−	8.71473i	−0.459955	−	0.421242i
$429$	11.2984	+	18.3511i	0.545494	+	0.886001i
$430$		0			0
$431$	−5.71949			−0.275498			−0.137749	−	0.990467i	$-0.543987\pi$
$431$	−5.71949			−0.275498			−0.137749	+	0.990467i	$0.543987\pi$
$432$	−20.4757	+	3.57007i	−0.985138	+	0.171765i
$433$			7.20937i			0.346460i	0.984881	+	0.173230i	$0.0554205\pi$
$433$			7.20937i			0.346460i	−0.984881	+	0.173230i	$0.944580\pi$
$434$	11.0122	−	4.84728i	0.528605	−	0.232677i
$435$		0			0
$436$	3.10469	−	3.39001i	0.148688	−	0.162352i
$437$	2.27898			0.109018
$438$	1.80706	−	2.61729i	0.0863446	−	0.125059i
$439$			23.4674i			1.12004i	0.828480	+	0.560018i	$0.189206\pi$
$439$			23.4674i			1.12004i	−0.828480	+	0.560018i	$0.810794\pi$
$440$		0			0
$441$	−0.947657	+	1.87927i	−0.0451265	+	0.0894890i
$442$	36.5872	−	16.1047i	1.74028	−	0.766022i
$443$		−	29.7907i		−	1.41540i	−0.706514	−	0.707699i	$-0.749733\pi$
$443$		−	29.7907i		−	1.41540i	0.706514	−	0.707699i	$-0.250267\pi$
$444$	25.1855	+	4.83386i	1.19525	+	0.229405i
$445$		0			0
$446$	12.0154	+	27.2970i	0.568945	+	1.29255i
$447$	13.8689	+	22.5261i	0.655975	+	1.06545i
$448$	15.9384	+	12.2094i	0.753017	+	0.576839i
$449$			29.7460i			1.40380i	0.712274	+	0.701901i	$0.247665\pi$
$449$			29.7460i			1.40380i	−0.712274	+	0.701901i	$0.752335\pi$
$450$		0			0
$451$		−	10.3475i		−	0.487244i
$452$	−1.07985	+	1.17909i	−0.0507917	+	0.0554595i
$453$	−17.5517	−	28.5078i	−0.824651	−	1.33941i
$454$	28.8062	−	12.6797i	1.35194	−	0.595088i
$455$		0			0
$456$	0.481161	+	2.10203i	0.0225324	+	0.0984365i
$457$			36.1047i			1.68891i	0.535630	+	0.844453i	$0.320074\pi$
$457$			36.1047i			1.68891i	−0.535630	+	0.844453i	$0.679926\pi$
$458$	−1.30952	−	2.97503i	−0.0611900	−	0.139014i
$459$	3.36131	+	39.5371i	0.156893	+	1.84543i
$460$		0			0
$461$			17.5517i			0.817465i	0.912654	+	0.408732i	$0.134029\pi$
$461$			17.5517i			0.817465i	−0.912654	+	0.408732i	$0.865971\pi$
$462$	17.0042	+	11.7402i	0.791106	+	0.546205i
$463$	−5.01934			−0.233268			−0.116634	−	0.993175i	$-0.537211\pi$
$463$	−5.01934			−0.233268			−0.116634	+	0.993175i	$0.537211\pi$
$464$	−9.08080	+	0.799423i	−0.421566	+	0.0371123i
$465$		0			0
$466$	−4.80625	−	10.9190i	−0.222645	−	0.505814i
$467$			29.5197i			1.36601i	0.730414	+	0.683004i	$0.239327\pi$
$467$			29.5197i			1.36601i	−0.730414	+	0.683004i	$0.760673\pi$
$468$	−20.7681	+	7.87044i	−0.960004	+	0.363811i
$469$	−13.7016			−0.632679
$470$		0			0
$471$	10.0839	+	16.3785i	0.464644	+	0.754683i
$472$		0			0
$473$	−28.2665			−1.29969
$474$	6.98550	−	10.1176i	0.320855	−	0.464716i
$475$		0			0
$476$	25.8874	−	28.2665i	1.18655	−	1.29559i
$477$	−3.07840	+	6.10469i	−0.140950	+	0.279514i
$478$	14.7492	+	33.5078i	0.674613	+	1.53261i
$479$	−33.6131			−1.53582			−0.767912	−	0.640555i	$-0.778704\pi$
$479$	−33.6131			−1.53582			−0.767912	+	0.640555i	$0.778704\pi$
$480$		0			0
$481$	27.4031			1.24947
$482$	3.98822	+	9.06058i	0.181658	+	0.412698i
$483$	11.7994	+	19.1647i	0.536890	+	0.872026i
$484$	−0.403124	+	0.440172i	−0.0183238	+	0.0200078i
$485$		0			0
$486$	−0.714301	−	22.0338i	−0.0324013	−	0.999475i
$487$	0.131364			0.00595267			0.00297634	−	0.999996i	$-0.499053\pi$
$487$	0.131364			0.00595267			0.00297634	+	0.999996i	$0.499053\pi$
$488$	15.2727	+	5.17748i	0.691364	+	0.234373i
$489$	−0.649219	+	0.399712i	−0.0293587	+	0.0180756i
$490$		0			0
$491$	−13.4453			−0.606776			−0.303388	−	0.952867i	$-0.598118\pi$
$491$	−13.4453			−0.606776			−0.303388	+	0.952867i	$0.598118\pi$
$492$	10.4728	+	2.01004i	0.472148	+	0.0906196i
$493$			17.4031i			0.783797i
$494$	0.928300	+	2.10895i	0.0417662	+	0.0948860i
$495$		0			0
$496$	−13.5078	+	1.18915i	−0.606519	+	0.0533945i
$497$	31.2256			1.40066
$498$	2.52758	−	3.66087i	0.113264	−	0.164047i
$499$		−	40.2861i		−	1.80345i	−0.432308	−	0.901726i	$-0.642301\pi$
$499$		−	40.2861i		−	1.80345i	0.432308	−	0.901726i	$-0.357699\pi$
$500$		0			0
$501$	14.1047	+	22.9091i	0.630151	+	1.02350i
$502$	−12.8341	−	29.1570i	−0.572814	−	1.30134i
$503$		−	12.9841i		−	0.578934i	−0.957188	−	0.289467i	$-0.906522\pi$
$503$		−	12.9841i		−	0.578934i	0.957188	−	0.289467i	$-0.0934780\pi$
$504$	−15.1855	+	14.9295i	−0.676415	+	0.665011i
$505$		0			0
$506$	−22.5261	+	9.91534i	−1.00141	+	0.440791i
$507$	−1.03475	+	0.637075i	−0.0459548	+	0.0282935i
$508$	−17.1275	+	18.7016i	−0.759910	+	0.829748i
$509$			2.95911i			0.131160i	0.997847	+	0.0655802i	$0.0208898\pi$
$509$			2.95911i			0.131160i	−0.997847	+	0.0655802i	$0.979110\pi$
$510$		0			0
$511$		−	3.25865i		−	0.144154i
$512$	−12.5940	−	18.7987i	−0.556583	−	0.830792i
$513$	−2.27898	+	0.193752i	−0.100619	+	0.00855434i
$514$	−2.59688	−	5.89968i	−0.114543	−	0.260224i
$515$		0			0
$516$	5.49087	−	28.6087i	0.241722	−	1.25943i
$517$			12.2094i			0.536968i
$518$	24.0486	−	10.5855i	1.05663	−	0.465101i
$519$	−12.4421	+	7.66037i	−0.546148	+	0.336253i
$520$		0			0
$521$			3.07840i			0.134867i	0.997724	+	0.0674337i	$0.0214811\pi$
$521$			3.07840i			0.134867i	−0.997724	+	0.0674337i	$0.978519\pi$
$522$	0.506474	−	9.65562i	0.0221678	−	0.422615i
$523$	−14.0002			−0.612187			−0.306094	−	0.952001i	$-0.599022\pi$
$523$	−14.0002			−0.612187			−0.306094	+	0.952001i	$0.599022\pi$
$524$	7.72577	−	8.43579i	0.337502	−	0.368519i
$525$		0			0
$526$	24.1047	−	10.6102i	1.05101	−	0.462627i
$527$			25.8874i			1.12767i
$528$	−13.9014	−	18.6836i	−0.604980	−	0.813099i
$529$	−3.80625			−0.165489
$530$		0			0
$531$		0			0
$532$	1.62932	+	1.49219i	0.0706402	+	0.0646946i
$533$	11.3949			0.493568
$534$	7.45596	−	10.7990i	0.322651	−	0.467318i
$535$		0			0
$536$	14.6243	+	4.95767i	0.631676	+	0.214139i
$537$	13.3935	−	8.24609i	0.577970	−	0.355845i
$538$	10.9190	−	4.80625i	0.470752	−	0.207212i
$539$	−2.35817			−0.101574
$540$		0			0
$541$	−25.7016			−1.10500			−0.552498	−	0.833514i	$-0.686325\pi$
$541$	−25.7016			−1.10500			−0.552498	+	0.833514i	$0.686325\pi$
$542$	−11.8543	+	5.21791i	−0.509184	+	0.224129i
$543$	15.4982	−	9.54193i	0.665091	−	0.409484i
$544$	−37.8586	+	20.8033i	−1.62317	+	0.891934i
$545$		0			0
$546$	−12.9286	+	18.7254i	−0.553294	+	0.801374i
$547$	4.71053			0.201408			0.100704	−	0.994916i	$-0.467891\pi$
$547$	4.71053			0.201408			0.100704	+	0.994916i	$0.467891\pi$
$548$	−13.3935	+	14.6243i	−0.572140	+	0.624721i
$549$	−7.70156	+	15.2727i	−0.328695	+	0.651824i
$550$		0			0
$551$	−1.00314			−0.0427354
$552$	−5.65961	−	24.7249i	−0.240889	−	1.05236i
$553$		−	12.5969i		−	0.535674i
$554$	11.5138	−	5.06806i	0.489175	−	0.215321i
$555$		0			0
$556$	−4.35078	−	3.98459i	−0.184514	−	0.168984i
$557$	36.7023			1.55512			0.777562	−	0.628806i	$-0.216456\pi$
$557$	36.7023			1.55512			0.777562	+	0.628806i	$0.216456\pi$
$558$	0.753387	−	14.3629i	0.0318934	−	0.608028i
$559$		−	31.1277i		−	1.31656i
$560$		0			0
$561$	−37.8586	+	23.3088i	−1.59839	+	0.984098i
$562$	22.7184	−	10.0000i	0.958317	−	0.421825i
$563$			23.3391i			0.983625i	0.870701	+	0.491812i	$0.163665\pi$
$563$			23.3391i			0.983625i	−0.870701	+	0.491812i	$0.836335\pi$
$564$	−12.3572	−	2.37172i	−0.520331	−	0.0998674i
$565$		0			0
$566$	−9.33159	−	21.1999i	−0.392236	−	0.891096i
$567$	−13.4287	−	18.1616i	−0.563952	−	0.762716i
$568$	−33.3286	−	11.2984i	−1.39844	−	0.474072i
$569$		−	10.5955i		−	0.444186i	−0.975026	−	0.222093i	$-0.928711\pi$
$569$		−	10.5955i		−	0.444186i	0.975026	−	0.222093i	$-0.0712888\pi$
$570$		0			0
$571$		−	16.9501i		−	0.709338i	−0.934992	−	0.354669i	$-0.884594\pi$
$571$		−	16.9501i		−	0.709338i	0.934992	−	0.354669i	$-0.115406\pi$
$572$	−18.3511	−	16.8066i	−0.767299	−	0.702718i
$573$	18.3511	−	11.2984i	0.766630	−	0.471999i
$574$	10.0000	−	4.40172i	0.417392	−	0.183724i
$575$		0			0
$576$	21.6102	−	10.4403i	0.900424	−	0.435014i
$577$		−	12.4031i		−	0.516349i	−0.966098	−	0.258174i	$-0.916879\pi$
$577$		−	12.4031i		−	0.516349i	0.966098	−	0.258174i	$-0.0831209\pi$
$578$	23.5385	+	53.4756i	0.979072	+	2.22429i
$579$	−17.9857	−	29.2126i	−0.747459	−	1.21404i
$580$		0			0
$581$		−	4.55796i		−	0.189096i
$582$	−15.4546	+	22.3839i	−0.640613	+	0.927844i
$583$	−7.66037			−0.317260
$584$	−1.17909	+	3.47812i	−0.0487909	+	0.143925i
$585$		0			0
$586$	12.2094	+	27.7377i	0.504365	+	1.14583i
$587$		−	31.3359i		−	1.29337i	−0.762758	−	0.646685i	$-0.776155\pi$
$587$		−	31.3359i		−	1.29337i	0.762758	−	0.646685i	$-0.223845\pi$
$588$	0.458084	−	2.38672i	0.0188911	−	0.0984267i
$589$	−1.49219			−0.0614846
$590$		0			0
$591$	−15.8034	+	9.72987i	−0.650066	+	0.400233i
$592$	−29.4984	+	2.59688i	−1.21238	+	0.106731i
$593$	−10.5955			−0.435104			−0.217552	−	0.976049i	$-0.569807\pi$
$593$	−10.5955			−0.435104			−0.217552	+	0.976049i	$0.569807\pi$
$594$	21.6831	−	11.8304i	0.889668	−	0.485409i
$595$		0			0
$596$	−22.5261	−	20.6301i	−0.922703	−	0.845042i
$597$	19.1506	+	31.1047i	0.783780	+	1.27303i
$598$	−10.9190	−	24.8062i	−0.446512	−	1.01440i
$599$		0			0			−	1.00000i	$-0.5\pi$
$599$		0			0				1.00000i	$0.5\pi$
$600$		0			0
$601$	−40.0156			−1.63227			−0.816136	−	0.577860i	$-0.803888\pi$
$601$	−40.0156			−1.63227			−0.816136	+	0.577860i	$0.803888\pi$
$602$	−12.0243	−	27.3172i	−0.490074	−	1.11337i
$603$	−7.37460	+	14.6243i	−0.300317	+	0.595549i
$604$	28.5078	+	26.1084i	1.15997	+	1.06234i
$605$		0			0
$606$	−24.4270	+	35.3793i	−0.992279	+	1.43719i
$607$	−3.25865			−0.132264			−0.0661322	−	0.997811i	$-0.521066\pi$
$607$	−3.25865			−0.132264			−0.0661322	+	0.997811i	$0.521066\pi$
$608$	−1.19913	−	2.18223i	−0.0486313	−	0.0885011i
$609$	−5.19375	−	8.43579i	−0.210461	−	0.341835i
$610$		0			0
$611$	−13.4453			−0.543937
$612$	−16.2368	−	42.8447i	−0.656334	−	1.73190i
$613$		−	4.80625i		−	0.194123i	−0.995278	−	0.0970613i	$-0.969056\pi$
$613$		−	4.80625i		−	0.194123i	0.995278	−	0.0970613i	$-0.0309443\pi$
$614$	15.0511	+	34.1936i	0.607412	+	1.37994i
$615$		0			0
$616$	−22.5969	−	7.66037i	−0.910454	−	0.308645i
$617$	−22.1097			−0.890102			−0.445051	−	0.895505i	$-0.646814\pi$
$617$	−22.1097			−0.890102			−0.445051	+	0.895505i	$0.646814\pi$
$618$	22.0097	+	15.1962i	0.885359	+	0.611280i
$619$			5.15070i			0.207024i	0.994628	+	0.103512i	$0.0330080\pi$
$619$			5.15070i			0.207024i	−0.994628	+	0.103512i	$0.966992\pi$
$620$		0			0
$621$	26.8062	−	2.27898i	1.07570	−	0.0914523i
$622$	−7.66037	−	17.4031i	−0.307153	−	0.697802i
$623$		−	13.4453i		−	0.538673i
$624$	20.5748	−	15.3086i	0.823652	−	0.612833i
$625$		0			0
$626$	21.0962	−	9.28595i	0.843173	−	0.371141i
$627$	−1.34356	−	2.18223i	−0.0536565	−	0.0871498i
$628$	−16.3785	−	15.0000i	−0.653574	−	0.598565i
$629$			56.5330i			2.25412i
$630$		0			0
$631$			42.0468i			1.67385i	0.547314	+	0.836927i	$0.315650\pi$
$631$			42.0468i			1.67385i	−0.547314	+	0.836927i	$0.684350\pi$
$632$	−4.55796	+	13.4453i	−0.181306	+	0.534824i
$633$	16.4719	+	26.7539i	0.654698	+	1.06337i
$634$	−9.61250	−	21.8380i	−0.381761	−	0.867299i
$635$		0			0
$636$	1.48806	−	7.75311i	0.0590053	−	0.307431i
$637$		−	2.59688i		−	0.102892i
$638$	9.91534	−	4.36446i	0.392552	−	0.172791i
$639$	16.8066	−	33.3286i	0.664858	−	1.31846i
$640$		0			0
$641$		−	12.3136i		−	0.486359i	−0.969981	−	0.243179i	$-0.921810\pi$
$641$		−	12.3136i		−	0.486359i	0.969981	−	0.243179i	$-0.0781903\pi$
$642$	−8.97883	+	13.0047i	−0.354366	+	0.513253i
$643$	24.4791			0.965360			0.482680	−	0.875797i	$-0.339663\pi$
$643$	24.4791			0.965360			0.482680	+	0.875797i	$0.339663\pi$
$644$	−19.1647	−	17.5517i	−0.755197	−	0.691634i
$645$		0			0
$646$	−4.35078	+	1.91509i	−0.171179	+	0.0753483i
$647$		−	10.3550i		−	0.407095i	−0.979065	−	0.203548i	$-0.934753\pi$
$647$		−	10.3550i		−	0.407095i	0.979065	−	0.203548i	$-0.0652472\pi$
$648$	7.76163	+	24.2437i	0.304906	+	0.952383i
$649$		0			0
$650$		0			0
$651$	−7.72577	−	12.5483i	−0.302797	−	0.491808i
$652$	0.594576	−	0.649219i	0.0232854	−	0.0254254i
$653$	−25.9875			−1.01697			−0.508485	−	0.861071i	$-0.669794\pi$
$653$	−25.9875			−1.01697			−0.508485	+	0.861071i	$0.669794\pi$
$654$	−4.63301	−	3.19877i	−0.181165	−	0.125082i
$655$		0			0
$656$	−12.2662	+	1.07985i	−0.478914	+	0.0421609i
$657$	−3.47812	−	1.75391i	−0.135694	−	0.0684264i
$658$	−11.7994	+	5.19375i	−0.459987	+	0.202474i
$659$	−16.8066			−0.654691			−0.327346	−	0.944905i	$-0.606154\pi$
$659$	−16.8066			−0.654691			−0.327346	+	0.944905i	$0.606154\pi$
$660$		0			0
$661$	−18.0000			−0.700119			−0.350059	−	0.936727i	$-0.613839\pi$
$661$	−18.0000			−0.700119			−0.350059	+	0.936727i	$0.613839\pi$
$662$	−22.1693	+	9.75831i	−0.861635	+	0.379268i
$663$	−25.6682	−	41.6908i	−0.996871	−	1.61914i
$664$	−1.64922	+	4.86493i	−0.0640021	+	0.188796i
$665$		0			0
$666$	1.64525	−	31.3657i	0.0637521	−	1.21540i
$667$	11.7994			0.456873
$668$	−22.9091	−	20.9809i	−0.886379	−	0.811776i
$669$	31.1047	−	19.1506i	1.20258	−	0.740403i
$670$		0			0
$671$	−19.1647			−0.739847
$672$	12.1426	−	21.3824i	0.468413	−	0.824843i
$673$		−	24.8062i		−	0.956211i	−0.878303	−	0.478105i	$-0.841324\pi$
$673$		−	24.8062i		−	0.956211i	0.878303	−	0.478105i	$-0.158676\pi$
$674$	16.0542	−	7.06662i	0.618385	−	0.272196i
$675$		0			0
$676$	0.947657	−	1.03475i	0.0364483	−	0.0397980i
$677$	12.9937			0.499390			0.249695	−	0.968324i	$-0.419670\pi$
$677$	12.9937			0.499390			0.249695	+	0.968324i	$0.419670\pi$
$678$	1.61141	+	1.11257i	0.0618859	+	0.0427280i
$679$			27.8691i			1.06952i
$680$		0			0
$681$	−20.2094	−	32.8244i	−0.774425	−	1.25784i
$682$	14.7492	−	6.49219i	0.564776	−	0.248599i
$683$		−	11.6291i		−	0.444975i	−0.974936	−	0.222488i	$-0.928582\pi$
$683$		−	11.6291i		−	0.444975i	0.974936	−	0.222488i	$-0.0714177\pi$
$684$	2.46964	−	0.935915i	0.0944290	−	0.0357856i
$685$		0			0
$686$	−11.0122	−	25.0180i	−0.420449	−	0.955193i
$687$	−3.39001	+	2.08717i	−0.129337	+	0.0796303i
$688$	2.94984	+	33.5078i	0.112462	+	1.27747i
$689$		−	8.43579i		−	0.321378i
$690$		0			0
$691$			1.18915i			0.0452375i	0.999744	+	0.0226187i	$0.00720038\pi$
$691$			1.18915i			0.0452375i	−0.999744	+	0.0226187i	$0.992800\pi$
$692$	11.3949	−	12.4421i	0.433169	−	0.472978i
$693$	11.3949	−	22.5969i	0.432857	−	0.858384i
$694$	25.1570	−	11.0734i	0.954948	−	0.420341i
$695$		0			0
$696$	2.49120	+	10.8832i	0.0944287	+	0.412526i
$697$			23.5078i			0.890422i
$698$	−14.9327	−	33.9246i	−0.565210	−	1.28406i
$699$	−12.4421	+	7.66037i	−0.470604	+	0.289742i
$700$		0			0
$701$			11.3949i			0.430380i	0.976572	+	0.215190i	$0.0690370\pi$
$701$			11.3949i			0.430380i	−0.976572	+	0.215190i	$0.930963\pi$
$702$	13.0280	+	23.8779i	0.491709	+	0.901215i
$703$	−3.25865			−0.122902
$704$	21.3470	+	16.3526i	0.804544	+	0.616311i
$705$		0			0
$706$	15.1938	+	34.5177i	0.571824	+	1.29909i
$707$			44.0490i			1.65663i
$708$		0			0
$709$	17.7016			0.664796			0.332398	−	0.943139i	$-0.392142\pi$
$709$	17.7016			0.664796			0.332398	+	0.943139i	$0.392142\pi$
$710$		0			0
$711$	−13.4453	−	6.78003i	−0.504237	−	0.254271i
$712$	−4.86493	+	14.3508i	−0.182321	+	0.537818i
$713$	17.5517			0.657317
$714$	−38.6307	−	26.6719i	−1.44572	−	0.998171i
$715$		0			0
$716$	−12.2662	+	13.3935i	−0.458408	+	0.500537i
$717$	38.1818	−	23.5078i	1.42593	−	0.877915i
$718$	4.40172	+	10.0000i	0.164271	+	0.373197i
$719$	44.0490			1.64275			0.821375	−	0.570389i	$-0.193207\pi$
$719$	44.0490			1.64275			0.821375	+	0.570389i	$0.193207\pi$
$720$		0			0
$721$	27.4031			1.02055
$722$	10.7148	+	24.3422i	0.398762	+	0.905924i
$723$	10.3244	−	6.35656i	0.383970	−	0.236403i
$724$	−14.1938	+	15.4982i	−0.527507	+	0.575986i
$725$		0			0
$726$	0.601567	+	0.415341i	0.0223262	+	0.0154148i
$727$	−40.5488			−1.50387			−0.751936	−	0.659236i	$-0.770880\pi$
$727$	−40.5488			−1.50387			−0.751936	+	0.659236i	$0.770880\pi$
$728$	8.43579	−	24.8842i	0.312651	−	0.922271i
$729$	−26.6125	+	4.55796i	−0.985648	+	0.168813i
$730$		0			0
$731$	64.2169			2.37515
$732$	3.72283	−	19.3968i	0.137600	−	0.716925i
$733$		−	4.80625i		−	0.177523i	−0.996053	−	0.0887614i	$-0.971709\pi$
$733$		−	4.80625i		−	0.177523i	0.996053	−	0.0887614i	$-0.0282909\pi$
$734$	1.42987	+	3.24844i	0.0527775	+	0.119902i
$735$		0			0
$736$	14.1047	+	25.6682i	0.519906	+	0.946143i
$737$	−18.3511			−0.675973
$738$	0.684136	−	13.0426i	0.0251834	−	0.480106i
$739$			29.2357i			1.07545i	0.843120	+	0.537726i	$0.180717\pi$
$739$			29.2357i			1.07545i	−0.843120	+	0.537726i	$0.819283\pi$
$740$		0			0
$741$	2.40312	−	1.47956i	0.0882810	−	0.0543529i
$742$	−3.25865	−	7.40312i	−0.119629	−	0.271777i
$743$			40.8778i			1.49966i	0.661630	+	0.749830i	$0.269865\pi$
$743$			40.8778i			1.49966i	−0.661630	+	0.749830i	$0.730135\pi$
$744$	3.70569	+	16.1889i	0.135857	+	0.593514i
$745$		0			0
$746$	−30.6786	+	13.5038i	−1.12322	+	0.494411i
$747$	−4.86493	−	2.45323i	−0.177999	−	0.0897592i
$748$	34.6722	−	37.8586i	1.26774	−	1.38425i
$749$			16.1914i			0.591622i
$750$		0			0
$751$			36.2784i			1.32382i	0.749584	+	0.661909i	$0.230254\pi$
$751$			36.2784i			1.32382i	−0.749584	+	0.661909i	$0.769746\pi$
$752$	14.4733	−	1.27415i	0.527787	−	0.0464634i
$753$	−33.2241	+	20.4555i	−1.21076	+	0.745439i
$754$	4.80625	+	10.9190i	0.175033	+	0.397647i
$755$		0			0
$756$	20.6569	+	15.9224i	0.751285	+	0.579092i
$757$		−	35.9109i		−	1.30521i	−0.757700	−	0.652603i	$-0.773677\pi$
$757$		−	35.9109i		−	1.30521i	0.757700	−	0.652603i	$-0.226323\pi$
$758$	−16.9820	+	7.47499i	−0.616813	+	0.271504i
$759$	15.8034	+	25.6682i	0.573628	+	0.931698i
$760$		0			0
$761$			20.6301i			0.747841i	0.927461	+	0.373920i	$0.121987\pi$
$761$			20.6301i			0.747841i	−0.927461	+	0.373920i	$0.878013\pi$
$762$	25.5587	+	17.6466i	0.925895	+	0.639268i
$763$	−5.76832			−0.208827
$764$	−16.8066	+	18.3511i	−0.608041	+	0.663921i
$765$		0			0
$766$	−9.40312	+	4.13899i	−0.339749	+	0.149548i
$767$		0			0
$768$	−20.6973	+	18.4289i	−0.746849	+	0.664994i
$769$	14.1938			0.511840			0.255920	−	0.966698i	$-0.417622\pi$
$769$	14.1938			0.511840			0.255920	+	0.966698i	$0.417622\pi$
$770$		0			0
$771$	−6.72263	+	4.13899i	−0.242110	+	0.149062i
$772$	29.2126	+	26.7539i	1.05139	+	0.962894i
$773$	−2.27898			−0.0819692			−0.0409846	−	0.999160i	$-0.513049\pi$
$773$	−2.27898			−0.0819692			−0.0409846	+	0.999160i	$0.513049\pi$
$774$	−35.6289	−	1.86887i	−1.28065	−	0.0671752i
$775$		0			0
$776$	10.0839	−	29.7460i	0.361993	−	1.06782i
$777$	−16.8716	−	27.4031i	−0.605264	−	0.983082i
$778$	48.3866	−	21.2984i	1.73474	−	0.763586i
$779$	−1.35503			−0.0485489
$780$		0			0
$781$	41.8219			1.49650
$782$	51.1756	−	22.5261i	1.83003	−	0.805530i
$783$	−11.7994	+	1.00314i	−0.421675	+	0.0358494i
$784$	0.246095	+	2.79544i	0.00878910	+	0.0998370i
$785$		0			0
$786$	−11.5289	−	7.95991i	−0.411221	−	0.283920i
$787$	18.4480			0.657601			0.328801	−	0.944399i	$-0.393356\pi$
$787$	18.4480			0.657601			0.328801	+	0.944399i	$0.393356\pi$
$788$	14.4733	−	15.8034i	0.515590	−	0.562974i
$789$	−16.9109	−	27.4671i	−0.602045	−	0.977853i
$790$		0			0
$791$	2.00629			0.0713354
$792$	−20.3386	+	19.9957i	−0.722701	+	0.710516i
$793$		−	21.1047i		−	0.749449i
$794$	20.5946	−	9.06518i	0.730876	−	0.321711i
$795$		0			0
$796$	−31.1047	−	28.4867i	−1.10248	−	1.00968i
$797$	−45.8182			−1.62296			−0.811482	−	0.584378i	$-0.801339\pi$
$797$	−45.8182			−1.62296			−0.811482	+	0.584378i	$0.801339\pi$
$798$	1.53741	−	2.22674i	0.0544237	−	0.0788257i
$799$		−	27.7377i		−	0.981290i
$800$		0			0
$801$	−14.3508	−	7.23665i	−0.507060	−	0.255695i
$802$	−11.9538	+	5.26172i	−0.422102	+	0.185798i
$803$		−	4.36446i		−	0.154018i
$804$	3.56478	−	18.5733i	0.125720	−	0.655030i
$805$		0			0
$806$	7.14936	+	16.2422i	0.251825	+	0.572107i
$807$	−7.66037	−	12.4421i	−0.269658	−	0.437983i
$808$	15.9384	−	47.0156i	0.560709	−	1.65400i
$809$		−	43.5392i		−	1.53076i	−0.643580	−	0.765378i	$-0.722552\pi$
$809$		−	43.5392i		−	1.53076i	0.643580	−	0.765378i	$-0.277448\pi$
$810$		0			0
$811$		−	35.2667i		−	1.23838i	−0.785240	−	0.619191i	$-0.787461\pi$
$811$		−	35.2667i		−	1.23838i	0.785240	−	0.619191i	$-0.212539\pi$
$812$	8.43579	+	7.72577i	0.296038	+	0.271121i
$813$	8.31650	+	13.5078i	0.291672	+	0.473740i
$814$	32.2094	−	14.1777i	1.12894	−	0.496927i
$815$		0			0
$816$	31.5817	+	42.4461i	1.10558	+	1.48591i
$817$			3.70156i			0.129501i
$818$	−6.38649	−	14.5091i	−0.223298	−	0.507297i
$819$	24.8842	+	12.5483i	0.869525	+	0.438475i
$820$		0			0
$821$		−	6.15681i		−	0.214874i	−0.994212	−	0.107437i	$-0.965736\pi$
$821$		−	6.15681i		−	0.214874i	0.994212	−	0.107437i	$-0.0342644\pi$
$822$	19.9866	+	13.7994i	0.697111	+	0.481308i
$823$	−6.03105			−0.210229			−0.105115	−	0.994460i	$-0.533521\pi$
$823$	−6.03105			−0.210229			−0.105115	+	0.994460i	$0.533521\pi$
$824$	−29.2487	−	9.91534i	−1.01893	−	0.345417i
$825$		0			0
$826$		0			0
$827$			20.4389i			0.710730i	0.934728	+	0.355365i	$0.115643\pi$
$827$			20.4389i			0.710730i	−0.934728	+	0.355365i	$0.884357\pi$
$828$	−29.0489	+	11.0086i	−1.00952	+	0.382575i
$829$	−19.1938			−0.666627			−0.333313	−	0.942816i	$-0.608167\pi$
$829$	−19.1938			−0.666627			−0.333313	+	0.942816i	$0.608167\pi$
$830$		0			0
$831$	−8.07766	−	13.1199i	−0.280211	−	0.455124i
$832$	−18.0079	+	23.5078i	−0.624310	+	0.814987i
$833$	5.35738			0.185622
$834$	−4.10534	+	5.94605i	−0.142156	+	0.205895i
$835$		0			0
$836$	2.18223	+	1.99856i	0.0754740	+	0.0691216i
$837$	−17.5517	+	1.49219i	−0.606676	+	0.0515776i
$838$	19.9229	+	45.2617i	0.688227	+	1.56354i
$839$	−44.0490			−1.52074			−0.760370	−	0.649490i	$-0.774982\pi$
$839$	−44.0490			−1.52074			−0.760370	+	0.649490i	$0.774982\pi$
$840$		0			0
$841$	23.8062			0.820905
$842$	−8.09572	−	18.3922i	−0.278997	−	0.633836i
$843$	−15.9384	−	25.8874i	−0.548946	−	0.891609i
$844$	−26.7539	−	24.5021i	−0.920907	−	0.843397i
$845$		0			0
$846$	−0.807237	+	15.3895i	−0.0277534	+	0.529101i
$847$	0.748980			0.0257353
$848$	0.799423	+	9.08080i	0.0274523	+	0.311836i
$849$	−24.1570	+	14.8730i	−0.829067	+	0.510441i
$850$		0			0
$851$	38.3295			1.31392
$852$	−8.12406	+	42.3282i	−0.278326	+	1.45014i
$853$			43.7016i			1.49631i	0.663522	+	0.748156i	$0.269061\pi$
$853$			43.7016i			1.49631i	−0.663522	+	0.748156i	$0.730939\pi$
$854$	−8.15250	−	18.5212i	−0.278973	−	0.633781i
$855$		0			0
$856$	5.85859	−	17.2819i	0.200243	−	0.590684i
$857$	−31.3449			−1.07072			−0.535360	−	0.844624i	$-0.679824\pi$
$857$	−31.3449			−1.07072			−0.535360	+	0.844624i	$0.679824\pi$
$858$	−17.3159	+	25.0798i	−0.591155	+	0.856211i
$859$			50.7649i			1.73208i	0.499978	+	0.866038i	$0.333342\pi$
$859$			50.7649i			1.73208i	−0.499978	+	0.866038i	$0.666658\pi$
$860$		0			0
$861$	−7.01562	−	11.3949i	−0.239092	−	0.388337i
$862$	−3.25865	−	7.40312i	−0.110990	−	0.252151i
$863$			40.8778i			1.39150i	0.718286	+	0.695748i	$0.244927\pi$
$863$			40.8778i			1.39150i	−0.718286	+	0.695748i	$0.755073\pi$
$864$	−16.2869	−	24.4691i	−0.554092	−	0.832455i
$865$		0			0
$866$	−9.33159	+	4.10750i	−0.317100	+	0.139579i
$867$	60.9350	−	37.5165i	2.06946	−	1.27413i
$868$	12.5483	+	11.4922i	0.425919	+	0.390070i
$869$		−	16.8716i		−	0.572329i
$870$		0			0
$871$		−	20.2087i		−	0.684746i
$872$	6.15681	+	2.08717i	0.208496	+	0.0706803i
$873$	29.7460	+	15.0000i	1.00675	+	0.507673i
$874$	1.29844	+	2.94984i	0.0439203	+	0.0997799i
$875$		0			0
$876$	4.41730	+	0.847813i	0.149247	+	0.0286450i
$877$			4.08907i			0.138078i	0.997614	+	0.0690390i	$0.0219933\pi$
$877$			4.08907i			0.138078i	−0.997614	+	0.0690390i	$0.978007\pi$
$878$	−30.3754	+	13.3704i	−1.02512	+	0.451230i
$879$	31.6069	−	19.4597i	1.06607	−	0.656361i
$880$		0			0
$881$		−	47.4170i		−	1.59752i	−0.601650	−	0.798760i	$-0.705490\pi$
$881$		−	47.4170i		−	1.59752i	0.601650	−	0.798760i	$-0.294510\pi$
$882$	−2.97239	−	0.155913i	−0.100086	−	0.00524987i
$883$	58.5566			1.97059			0.985294	−	0.170867i	$-0.0546569\pi$
$883$	58.5566			1.97059			0.985294	+	0.170867i	$0.0546569\pi$
$884$	41.6908	+	38.1818i	1.40221	+	1.28419i
$885$		0			0
$886$	38.5602	−	16.9731i	1.29545	−	0.570223i
$887$		−	14.5293i		−	0.487846i	−0.969795	−	0.243923i	$-0.921566\pi$
$887$		−	14.5293i		−	0.487846i	0.969795	−	0.243923i	$-0.0784343\pi$
$888$	8.09251	+	35.3534i	0.271567	+	1.18638i
$889$	31.8219			1.06727
$890$		0			0
$891$	−17.9857	−	24.3247i	−0.602542	−	0.814907i
$892$	−28.4867	+	31.1047i	−0.953805	+	1.04146i
$893$	1.59885			0.0535034
$894$	−21.2553	+	30.7855i	−0.710884	+	1.02962i
$895$		0			0
$896$	−6.72263	+	27.5863i	−0.224587	+	0.921595i
$897$	−28.2665	+	17.4031i	−0.943790	+	0.581073i
$898$	−38.5023	+	16.9477i	−1.28484	+	0.565551i
$899$	−7.72577			−0.257669
$900$		0			0
$901$	17.4031			0.579782
$902$	13.3935	−	5.89543i	0.445953	−	0.196296i
$903$	−31.1277	+	19.1647i	−1.03587	+	0.637763i
$904$	−2.14141	−	0.725940i	−0.0712222	−	0.0241444i
$905$		0			0
$906$	26.8996	−	38.9606i	0.893680	−	1.29438i
$907$	−0.880344			−0.0292314			−0.0146157	−	0.999893i	$-0.504652\pi$
$907$	−0.880344			−0.0292314			−0.0146157	+	0.999893i	$0.504652\pi$
$908$	32.8244	+	30.0617i	1.08932	+	0.997633i
$909$	47.0156	+	23.7085i	1.55941	+	0.786362i
$910$		0			0
$911$	2.00629			0.0664713			0.0332356	−	0.999448i	$-0.489419\pi$
$911$	2.00629			0.0664713			0.0332356	+	0.999448i	$0.489419\pi$
$912$	−2.44666	+	1.82042i	−0.0810170	+	0.0602801i
$913$		−	6.10469i		−	0.202036i
$914$	−46.7328	+	20.5705i	−1.54578	+	0.680411i
$915$		0			0
$916$	3.10469	−	3.39001i	0.102582	−	0.112009i
$917$	−14.3540			−0.474011
$918$	−49.2605	+	26.8768i	−1.62584	+	0.887068i
$919$		−	8.40935i		−	0.277399i	−0.990335	−	0.138699i	$-0.955708\pi$
$919$		−	8.40935i		−	0.277399i	0.990335	−	0.138699i	$-0.0442922\pi$
$920$		0			0
$921$	38.9633	−	23.9889i	1.28388	−	0.790462i
$922$	−22.7184	+	10.0000i	−0.748190	+	0.329332i
$923$			46.0553i			1.51593i
$924$	−5.50814	+	28.6986i	−0.181204	+	0.944115i
$925$		0			0
$926$	−2.85974	−	6.49687i	−0.0939770	−	0.213501i
$927$	14.7492	−	29.2487i	0.484427	−	0.960653i
$928$	−6.20849	−	11.2984i	−0.203804	−	0.370889i
$929$		−	43.5392i		−	1.42847i	−0.699903	−	0.714237i	$-0.746774\pi$
$929$		−	43.5392i		−	1.42847i	0.699903	−	0.714237i	$-0.253226\pi$
$930$		0			0
$931$			0.308808i			0.0101208i
$932$	11.3949	−	12.4421i	0.373252	−	0.407555i
$933$	−19.8307	+	12.2094i	−0.649228	+	0.399717i
$934$	−38.2094	+	16.8187i	−1.25025	+	0.550325i
$935$		0			0
$936$	−22.0198	−	22.3974i	−0.719738	−	0.732081i
$937$			34.6125i			1.13074i	0.824837	+	0.565370i	$0.191267\pi$
$937$			34.6125i			1.13074i	−0.824837	+	0.565370i	$0.808733\pi$
$938$	−7.80640	−	17.7349i	−0.254888	−	0.579064i
$939$	−14.8003	−	24.0389i	−0.482989	−	0.784480i
$940$		0			0
$941$			53.5738i			1.74646i	0.487311	+	0.873229i	$0.337978\pi$
$941$			53.5738i			1.74646i	−0.487311	+	0.873229i	$0.662022\pi$
$942$	−15.4546	+	22.3839i	−0.503537	+	0.729308i
$943$	15.9384			0.519024
$944$		0			0
$945$		0			0
$946$	−16.1047	−	36.5872i	−0.523609	−	1.18955i
$947$		−	18.0807i		−	0.587545i	−0.955875	−	0.293772i	$-0.905089\pi$
$947$		−	18.0807i		−	0.587545i	0.955875	−	0.293772i	$-0.0949107\pi$
$948$	17.0758	+	3.27737i	0.554597	+	0.106444i
$949$	4.80625			0.156017
$950$		0			0
$951$	−24.8842	+	15.3207i	−0.806927	+	0.496809i
$952$	51.3364	+	17.4031i	1.66382	+	0.564038i
$953$	42.0596			1.36245			0.681223	−	0.732076i	$-0.261448\pi$
$953$	42.0596			1.36245			0.681223	+	0.732076i	$0.261448\pi$
$954$	−9.65562	−	0.506474i	−0.312612	−	0.0163977i
$955$		0			0
$956$	−34.9682	+	38.1818i	−1.13095	+	1.23489i
$957$	−6.95623	−	11.2984i	−0.224863	−	0.365227i
$958$	−19.1509	−	43.5078i	−0.618738	−	1.40567i
$959$	24.8842			0.803554
$960$		0			0
$961$	19.5078			0.629284
$962$	15.6128	+	35.4697i	0.503377	+	1.14359i
$963$	17.2819	+	8.71473i	0.556902	+	0.280828i
$964$	−9.45547	+	10.3244i	−0.304540	+	0.332528i
$965$		0			0
$966$	−18.0836	+	26.1917i	−0.581831	+	0.842706i
$967$	1.49796			0.0481712			0.0240856	−	0.999710i	$-0.492333\pi$
$967$	1.49796			0.0481712			0.0240856	+	0.999710i	$0.492333\pi$
$968$	−0.799423	−	0.271006i	−0.0256944	−	0.00871045i
$969$	3.05234	+	4.95767i	0.0980554	+	0.159263i
$970$		0			0
$971$	47.4103			1.52147			0.760734	−	0.649063i	$-0.224839\pi$
$971$	47.4103			1.52147			0.760734	+	0.649063i	$0.224839\pi$
$972$	28.1129	−	13.4782i	0.901723	−	0.432315i
$973$			7.40312i			0.237333i
$974$	0.0748440	+	0.170034i	0.00239816	+	0.00544823i
$975$		0			0
$976$	2.00000	+	22.7184i	0.0640184	+	0.727198i
$977$	−19.0313			−0.608864			−0.304432	−	0.952534i	$-0.598467\pi$
$977$	−19.0313			−0.608864			−0.304432	+	0.952534i	$0.598467\pi$
$978$	−0.887263	−	0.612595i	−0.0283716	−	0.0195886i
$979$		−	18.0079i		−	0.575534i
$980$		0			0
$981$	−3.10469	+	6.15681i	−0.0991250	+	0.196572i
$982$	−7.66037	−	17.4031i	−0.244452	−	0.555356i
$983$		−	57.0331i		−	1.81907i	−0.415623	−	0.909537i	$-0.636437\pi$
$983$		−	57.0331i		−	1.81907i	0.415623	−	0.909537i	$-0.363563\pi$
$984$	3.36507	+	14.7008i	0.107274	+	0.468645i
$985$		0			0
$986$	−22.5261	+	9.91534i	−0.717376	+	0.315769i
$987$	8.27799	+	13.4453i	0.263491	+	0.427967i
$988$	−2.20086	+	2.40312i	−0.0700187	+	0.0764536i
$989$		−	43.5392i		−	1.38447i
$990$		0			0
$991$			44.4251i			1.41121i	0.708606	+	0.705604i	$0.249324\pi$
$991$			44.4251i			1.41121i	−0.708606	+	0.705604i	$0.750676\pi$
$992$	−9.23521	−	16.8066i	−0.293218	−	0.533609i
$993$	15.5532	+	25.2617i	0.493564	+	0.801656i
$994$	17.7906	+	40.4174i	0.564284	+	1.28196i
$995$		0			0
$996$	6.17859	+	1.18586i	0.195776	+	0.0375754i
$997$		−	47.4031i		−	1.50127i	−0.660716	−	0.750636i	$-0.729747\pi$
$997$		−	47.4031i		−	1.50127i	0.660716	−	0.750636i	$-0.270253\pi$
$998$	52.1450	−	22.9528i	1.65062	−	0.726558i
$999$	−38.3295	+	3.25865i	−1.21269	+	0.103099i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	300.2.h.c.299.12		16
3.2	odd	2	inner	300.2.h.c.299.6		16
4.3	odd	2	inner	300.2.h.c.299.9		16
5.2	odd	4		300.2.e.d.251.2	yes	8
5.3	odd	4		300.2.e.e.251.7	yes	8
5.4	even	2	inner	300.2.h.c.299.5		16
12.11	even	2	inner	300.2.h.c.299.7		16
15.2	even	4		300.2.e.d.251.7	yes	8
15.8	even	4		300.2.e.e.251.2	yes	8
15.14	odd	2	inner	300.2.h.c.299.11		16
20.3	even	4		300.2.e.e.251.1	yes	8
20.7	even	4		300.2.e.d.251.8	yes	8
20.19	odd	2	inner	300.2.h.c.299.8		16
60.23	odd	4		300.2.e.e.251.8	yes	8
60.47	odd	4		300.2.e.d.251.1	✓	8
60.59	even	2	inner	300.2.h.c.299.10		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.e.d.251.1	✓	8	60.47	odd	4
300.2.e.d.251.2	yes	8	5.2	odd	4
300.2.e.d.251.7	yes	8	15.2	even	4
300.2.e.d.251.8	yes	8	20.7	even	4
300.2.e.e.251.1	yes	8	20.3	even	4
300.2.e.e.251.2	yes	8	15.8	even	4
300.2.e.e.251.7	yes	8	5.3	odd	4
300.2.e.e.251.8	yes	8	60.23	odd	4
300.2.h.c.299.5		16	5.4	even	2	inner
300.2.h.c.299.6		16	3.2	odd	2	inner
300.2.h.c.299.7		16	12.11	even	2	inner
300.2.h.c.299.8		16	20.19	odd	2	inner
300.2.h.c.299.9		16	4.3	odd	2	inner
300.2.h.c.299.10		16	60.59	even	2	inner
300.2.h.c.299.11		16	15.14	odd	2	inner
300.2.h.c.299.12		16	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 300 = 2^{2} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	300.h (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.569745 + 1.29437i) q^{2} +(1.47492 - 0.908080i) q^{3} +(-1.35078 + 1.47492i) q^{4} +(2.01572 + 1.39172i) q^{6} +2.50967 q^{7} +(-2.67869 - 0.908080i) q^{8} +(1.35078 - 2.67869i) q^{9} +O(q^{10})\)	\(q+(0.569745 + 1.29437i) q^{2} +(1.47492 - 0.908080i) q^{3} +(-1.35078 + 1.47492i) q^{4} +(2.01572 + 1.39172i) q^{6} +2.50967 q^{7} +(-2.67869 - 0.908080i) q^{8} +(1.35078 - 2.67869i) q^{9} +3.36131 q^{11} +(-0.652949 + 3.40201i) q^{12} +3.70156i q^{13} +(1.42987 + 3.24844i) q^{14} +(-0.350781 - 3.98459i) q^{16} -7.63636 q^{17} +(4.23682 + 0.222237i) q^{18} -0.440172i q^{19} +(3.70156 - 2.27898i) q^{21} +(1.91509 + 4.35078i) q^{22} +5.17748i q^{23} +(-4.77547 + 1.09312i) q^{24} +(-4.79119 + 2.10895i) q^{26} +(-0.440172 - 5.17748i) q^{27} +(-3.39001 + 3.70156i) q^{28} -2.27898i q^{29} -3.39001i q^{31} +(4.95767 - 2.72424i) q^{32} +(4.95767 - 3.05234i) q^{33} +(-4.35078 - 9.88427i) q^{34} +(2.12625 + 5.61062i) q^{36} -7.40312i q^{37} +(0.569745 - 0.250786i) q^{38} +(3.36131 + 5.45951i) q^{39} -3.07840i q^{41} +(5.05879 + 3.49275i) q^{42} -8.40935 q^{43} +(-4.54040 + 4.95767i) q^{44} +(-6.70156 + 2.94984i) q^{46} +3.63232i q^{47} +(-4.13570 - 5.55842i) q^{48} -0.701562 q^{49} +(-11.2630 + 6.93443i) q^{51} +(-5.45951 - 5.00000i) q^{52} -2.27898 q^{53} +(6.45078 - 3.51959i) q^{54} +(-6.72263 - 2.27898i) q^{56} +(-0.399712 - 0.649219i) q^{57} +(2.94984 - 1.29844i) q^{58} -5.70156 q^{61} +(4.38793 - 1.93144i) q^{62} +(3.39001 - 6.72263i) q^{63} +(6.35078 + 4.86493i) q^{64} +(6.77547 + 4.67800i) q^{66} -5.45951 q^{67} +(10.3151 - 11.2630i) q^{68} +(4.70156 + 7.63636i) q^{69} +12.4421 q^{71} +(-6.05079 + 5.94877i) q^{72} -1.29844i q^{73} +(9.58237 - 4.21789i) q^{74} +(0.649219 + 0.594576i) q^{76} +8.43579 q^{77} +(-5.15153 + 7.46131i) q^{78} -5.01934i q^{79} +(-5.35078 - 7.23665i) q^{81} +(3.98459 - 1.75391i) q^{82} -1.81616i q^{83} +(-1.63869 + 8.53791i) q^{84} +(-4.79119 - 10.8848i) q^{86} +(-2.06950 - 3.36131i) q^{87} +(-9.00393 - 3.05234i) q^{88} -5.35738i q^{89} +9.28970i q^{91} +(-7.63636 - 6.99364i) q^{92} +(-3.07840 - 5.00000i) q^{93} +(-4.70156 + 2.06950i) q^{94} +(4.83834 - 8.52000i) q^{96} +11.1047i q^{97} +(-0.399712 - 0.908080i) q^{98} +(4.54040 - 9.00393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{4} + 6 q^{6} - 4 q^{9}+O(q^{10}) \) 16 * q + 4 * q^4 + 6 * q^6 - 4 * q^9	\( 16 q + 4 q^{4} + 6 q^{6} - 4 q^{9} + 20 q^{16} + 8 q^{21} - 26 q^{24} - 44 q^{34} - 42 q^{36} - 56 q^{46} + 40 q^{49} + 56 q^{54} - 40 q^{61} + 76 q^{64} + 58 q^{66} + 24 q^{69} + 36 q^{76} - 60 q^{81} - 80 q^{84} - 24 q^{94} - 78 q^{96}+O(q^{100}) \) 16 * q + 4 * q^4 + 6 * q^6 - 4 * q^9 + 20 * q^16 + 8 * q^21 - 26 * q^24 - 44 * q^34 - 42 * q^36 - 56 * q^46 + 40 * q^49 + 56 * q^54 - 40 * q^61 + 76 * q^64 + 58 * q^66 + 24 * q^69 + 36 * q^76 - 60 * q^81 - 80 * q^84 - 24 * q^94 - 78 * q^96

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