LMFDB - Embedded newform 300.2.e.e.251.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [300,2,Mod(251,300)]

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, 0]))

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

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

chi := DirichletCharacter("300.251");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 300 = 2^{2} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	300.e (of order $2$, degree $1$, 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:	$8$
Coefficient field:	8.0.4521217600.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + x^{6} - 2x^{4} + 4x^{2} + 16 $ x^8 + x^6 - 2x^4 + 4x^2 + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			251.8
Root			$-1.29437 + 0.569745i$ of defining polynomial
Character	$\chi$	$=$	300.251
Dual form			300.2.e.e.251.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.29437 + 0.569745i) q^{2} +(0.908080 - 1.47492i) q^{3} +(1.35078 + 1.47492i) q^{4} +(2.01572 - 1.39172i) q^{6} +2.50967i q^{7} +(0.908080 + 2.67869i) q^{8} +(-1.35078 - 2.67869i) q^{9} +O(q^{10})$	\(q+(1.29437 + 0.569745i) q^{2} +(0.908080 - 1.47492i) q^{3} +(1.35078 + 1.47492i) q^{4} +(2.01572 - 1.39172i) q^{6} +2.50967i q^{7} +(0.908080 + 2.67869i) q^{8} +(-1.35078 - 2.67869i) q^{9} +3.36131 q^{11} +(3.40201 - 0.652949i) q^{12} -3.70156 q^{13} +(-1.42987 + 3.24844i) q^{14} +(-0.350781 + 3.98459i) q^{16} -7.63636i q^{17} +(-0.222237 - 4.23682i) q^{18} -0.440172i q^{19} +(3.70156 + 2.27898i) q^{21} +(4.35078 + 1.91509i) q^{22} -5.17748 q^{23} +(4.77547 + 1.09312i) q^{24} +(-4.79119 - 2.10895i) q^{26} +(-5.17748 - 0.440172i) q^{27} +(-3.70156 + 3.39001i) q^{28} -2.27898i q^{29} +3.39001i q^{31} +(-2.72424 + 4.95767i) q^{32} +(3.05234 - 4.95767i) q^{33} +(4.35078 - 9.88427i) q^{34} +(2.12625 - 5.61062i) q^{36} -7.40312 q^{37} +(0.250786 - 0.569745i) q^{38} +(-3.36131 + 5.45951i) q^{39} +3.07840i q^{41} +(3.49275 + 5.05879i) q^{42} +8.40935i q^{43} +(4.54040 + 4.95767i) q^{44} +(-6.70156 - 2.94984i) q^{46} +3.63232 q^{47} +(5.55842 + 4.13570i) q^{48} +0.701562 q^{49} +(-11.2630 - 6.93443i) q^{51} +(-5.00000 - 5.45951i) q^{52} +2.27898i q^{53} +(-6.45078 - 3.51959i) q^{54} +(-6.72263 + 2.27898i) q^{56} +(-0.649219 - 0.399712i) q^{57} +(1.29844 - 2.94984i) q^{58} -5.70156 q^{61} +(-1.93144 + 4.38793i) q^{62} +(6.72263 - 3.39001i) q^{63} +(-6.35078 + 4.86493i) q^{64} +(6.77547 - 4.67800i) q^{66} -5.45951i q^{67} +(11.2630 - 10.3151i) q^{68} +(-4.70156 + 7.63636i) q^{69} +12.4421 q^{71} +(5.94877 - 6.05079i) q^{72} +1.29844 q^{73} +(-9.58237 - 4.21789i) q^{74} +(0.649219 - 0.594576i) q^{76} +8.43579i q^{77} +(-7.46131 + 5.15153i) q^{78} -5.01934i q^{79} +(-5.35078 + 7.23665i) q^{81} +(-1.75391 + 3.98459i) q^{82} +1.81616 q^{83} +(1.63869 + 8.53791i) q^{84} +(-4.79119 + 10.8848i) q^{86} +(-3.36131 - 2.06950i) q^{87} +(3.05234 + 9.00393i) q^{88} -5.35738i q^{89} -9.28970i q^{91} +(-6.99364 - 7.63636i) q^{92} +(5.00000 + 3.07840i) q^{93} +(4.70156 + 2.06950i) q^{94} +(4.83834 + 8.52000i) q^{96} +11.1047 q^{97} +(0.908080 + 0.399712i) q^{98} +(-4.54040 - 9.00393i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{4} + 3 q^{6} + 2 q^{9}+O(q^{10}) $ 8 * q - 2 * q^4 + 3 * q^6 + 2 * q^9	$ 8 q - 2 q^{4} + 3 q^{6} + 2 q^{9} + 11 q^{12} - 4 q^{13} + 10 q^{16} - 7 q^{18} + 4 q^{21} + 22 q^{22} + 13 q^{24} - 4 q^{28} - 14 q^{33} + 22 q^{34} - 21 q^{36} - 8 q^{37} - 36 q^{42} - 28 q^{46} + 15 q^{48} - 20 q^{49} - 40 q^{52} - 28 q^{54} - 18 q^{57} + 36 q^{58} - 20 q^{61} - 38 q^{64} + 29 q^{66} - 12 q^{69} + 51 q^{72} + 36 q^{73} + 18 q^{76} - 22 q^{78} - 30 q^{81} + 50 q^{82} + 40 q^{84} - 14 q^{88} + 40 q^{93} + 12 q^{94} - 39 q^{96} + 12 q^{97}+O(q^{100}) $ 8 * q - 2 * q^4 + 3 * q^6 + 2 * q^9 + 11 * q^12 - 4 * q^13 + 10 * q^16 - 7 * q^18 + 4 * q^21 + 22 * q^22 + 13 * q^24 - 4 * q^28 - 14 * q^33 + 22 * q^34 - 21 * q^36 - 8 * q^37 - 36 * q^42 - 28 * q^46 + 15 * q^48 - 20 * q^49 - 40 * q^52 - 28 * q^54 - 18 * q^57 + 36 * q^58 - 20 * q^61 - 38 * q^64 + 29 * q^66 - 12 * q^69 + 51 * q^72 + 36 * q^73 + 18 * q^76 - 22 * q^78 - 30 * q^81 + 50 * q^82 + 40 * q^84 - 14 * q^88 + 40 * q^93 + 12 * q^94 - 39 * q^96 + 12 * q^97

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 $

$2$	1.29437	+	0.569745i	0.915257	+	0.402871i
$2$	1.29437	+	0.569745i	0.915257	+	0.402871i
$3$	0.908080	−	1.47492i	0.524280	−	0.851546i
$3$	0.908080	−	1.47492i	0.524280	−	0.851546i
$4$	1.35078	+	1.47492i	0.675391	+	0.737460i
$5$		0			0
$5$		0			0
$6$	2.01572	−	1.39172i	0.822914	−	0.568166i
$7$			2.50967i			0.948566i	0.880373	+	0.474283i	$0.157293\pi$
$7$			2.50967i			0.948566i	−0.880373	+	0.474283i	$0.842707\pi$
$8$	0.908080	+	2.67869i	0.321055	+	0.947061i
$9$	−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	$0.330851\pi$
$12$	3.40201	−	0.652949i	0.982075	−	0.188490i
$13$	−3.70156			−1.02663			−0.513314	−	0.858201i	$-0.671582\pi$
$13$	−3.70156			−1.02663			−0.513314	+	0.858201i	$0.671582\pi$
$14$	−1.42987	+	3.24844i	−0.382149	+	0.868181i
$15$		0			0
$16$	−0.350781	+	3.98459i	−0.0876953	+	0.996147i
$17$		−	7.63636i		−	1.85209i	−0.377413	−	0.926045i	$-0.623186\pi$
$17$		−	7.63636i		−	1.85209i	0.377413	−	0.926045i	$-0.376814\pi$
$18$	−0.222237	−	4.23682i	−0.0523818	−	0.998627i
$19$		−	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
$22$	4.35078	+	1.91509i	0.927590	+	0.408299i
$23$	−5.17748			−1.07958			−0.539789	−	0.841800i	$-0.681496\pi$
$23$	−5.17748			−1.07958			−0.539789	+	0.841800i	$0.681496\pi$
$24$	4.77547	+	1.09312i	0.974788	+	0.223132i
$25$		0			0
$26$	−4.79119	−	2.10895i	−0.939629	−	0.413599i
$27$	−5.17748	−	0.440172i	−0.996406	−	0.0847112i
$28$	−3.70156	+	3.39001i	−0.699529	+	0.640652i
$29$		−	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	$0.0984667\pi$
$31$			3.39001i			0.608864i	−0.952534	+	0.304432i	$0.901533\pi$
$32$	−2.72424	+	4.95767i	−0.481582	+	0.876401i
$33$	3.05234	−	4.95767i	0.531345	−	0.863020i
$34$	4.35078	−	9.88427i	0.746153	−	1.69514i
$35$		0			0
$36$	2.12625	−	5.61062i	0.354375	−	0.935104i
$37$	−7.40312			−1.21707			−0.608533	−	0.793529i	$-0.708242\pi$
$37$	−7.40312			−1.21707			−0.608533	+	0.793529i	$0.708242\pi$
$38$	0.250786	−	0.569745i	0.0406828	−	0.0924249i
$39$	−3.36131	+	5.45951i	−0.538241	+	0.874221i
$40$		0			0
$41$			3.07840i			0.480766i	0.970678	+	0.240383i	$0.0772730\pi$
$41$			3.07840i			0.480766i	−0.970678	+	0.240383i	$0.922727\pi$
$42$	3.49275	+	5.05879i	0.538943	+	0.780588i
$43$			8.40935i			1.28241i	0.767368	+	0.641207i	$0.221566\pi$
$43$			8.40935i			1.28241i	−0.767368	+	0.641207i	$0.778434\pi$
$44$	4.54040	+	4.95767i	0.684491	+	0.747397i
$45$		0			0
$46$	−6.70156	−	2.94984i	−0.988091	−	0.434930i
$47$	3.63232			0.529828			0.264914	−	0.964272i	$-0.414656\pi$
$47$	3.63232			0.529828			0.264914	+	0.964272i	$0.414656\pi$
$48$	5.55842	+	4.13570i	0.802288	+	0.596937i
$49$	0.701562			0.100223
$50$		0			0
$51$	−11.2630	−	6.93443i	−1.57714	−	0.971014i
$52$	−5.00000	−	5.45951i	−0.693375	−	0.757098i
$53$			2.27898i			0.313042i	0.987675	+	0.156521i	$0.0500279\pi$
$53$			2.27898i			0.313042i	−0.987675	+	0.156521i	$0.949972\pi$
$54$	−6.45078	−	3.51959i	−0.877839	−	0.478955i
$55$		0			0
$56$	−6.72263	+	2.27898i	−0.898349	+	0.304542i
$57$	−0.649219	−	0.399712i	−0.0859911	−	0.0529431i
$58$	1.29844	−	2.94984i	0.170493	−	0.387333i
$59$		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	$0.618933\pi$
$62$	−1.93144	+	4.38793i	−0.245294	+	0.557267i
$63$	6.72263	−	3.39001i	0.846972	−	0.427102i
$64$	−6.35078	+	4.86493i	−0.793848	+	0.608117i
$65$		0			0
$66$	6.77547	−	4.67800i	0.834002	−	0.575822i
$67$		−	5.45951i		−	0.666985i	−0.942753	−	0.333493i	$-0.891773\pi$
$67$		−	5.45951i		−	0.666985i	0.942753	−	0.333493i	$-0.108227\pi$
$68$	11.2630	−	10.3151i	1.36584	−	1.25088i
$69$	−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	$0.235627\pi$
$72$	5.94877	−	6.05079i	0.701070	−	0.713093i
$73$	1.29844			0.151971			0.0759853	−	0.997109i	$-0.475790\pi$
$73$	1.29844			0.151971			0.0759853	+	0.997109i	$0.475790\pi$
$74$	−9.58237	−	4.21789i	−1.11393	−	0.490320i
$75$		0			0
$76$	0.649219	−	0.594576i	0.0744705	−	0.0682026i
$77$			8.43579i			0.961347i
$78$	−7.46131	+	5.15153i	−0.844827	+	0.583296i
$79$		−	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
$82$	−1.75391	+	3.98459i	−0.193686	+	0.440024i
$83$	1.81616			0.199349			0.0996747	−	0.995020i	$-0.468220\pi$
$83$	1.81616			0.199349			0.0996747	+	0.995020i	$0.468220\pi$
$84$	1.63869	+	8.53791i	0.178795	+	0.931563i
$85$		0			0
$86$	−4.79119	+	10.8848i	−0.516647	+	1.17374i
$87$	−3.36131	−	2.06950i	−0.360371	−	0.221873i
$88$	3.05234	+	9.00393i	0.325381	+	0.959822i
$89$		−	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
$92$	−6.99364	−	7.63636i	−0.729137	−	0.796146i
$93$	5.00000	+	3.07840i	0.518476	+	0.319216i
$94$	4.70156	+	2.06950i	0.484929	+	0.213452i
$95$		0			0
$96$	4.83834	+	8.52000i	0.493811	+	0.869569i
$97$	11.1047			1.12751			0.563755	−	0.825942i	$-0.309356\pi$
$97$	11.1047			1.12751			0.563755	+	0.825942i	$0.309356\pi$
$98$	0.908080	+	0.399712i	0.0917299	+	0.0403770i
$99$	−4.54040	−	9.00393i	−0.456327	−	0.904929i
$100$		0			0
$101$		−	17.5517i		−	1.74646i	−0.487308	−	0.873230i	$-0.662021\pi$
$101$		−	17.5517i		−	1.74646i	0.487308	−	0.873230i	$-0.337979\pi$
$102$	−10.6277	−	15.3928i	−1.05229	−	1.52411i
$103$		−	10.9190i		−	1.07588i	−0.842982	−	0.537941i	$-0.819202\pi$
$103$		−	10.9190i		−	1.07588i	0.842982	−	0.537941i	$-0.180798\pi$
$104$	−3.36131	−	9.91534i	−0.329604	−	0.972280i
$105$		0			0
$106$	−1.29844	+	2.94984i	−0.126115	+	0.286514i
$107$	6.45162			0.623702			0.311851	−	0.950131i	$-0.399051\pi$
$107$	6.45162			0.623702			0.311851	+	0.950131i	$0.399051\pi$
$108$	−6.34442	−	8.23094i	−0.610492	−	0.792023i
$109$	2.29844			0.220150			0.110075	−	0.993923i	$-0.464891\pi$
$109$	2.29844			0.220150			0.110075	+	0.993923i	$0.464891\pi$
$110$		0			0
$111$	−6.72263	+	10.9190i	−0.638084	+	1.03639i
$112$	−10.0000	−	0.880344i	−0.944911	−	0.0831847i
$113$		−	0.799423i		−	0.0752034i	−0.999293	−	0.0376017i	$-0.988028\pi$
$113$		−	0.799423i		−	0.0752034i	0.999293	−	0.0376017i	$-0.0119718\pi$
$114$	−0.612595	−	0.887263i	−0.0573748	−	0.0830998i
$115$		0			0
$116$	3.36131	−	3.07840i	0.312090	−	0.285823i
$117$	5.00000	+	9.91534i	0.462250	+	0.916674i
$118$		0			0
$119$	19.1647			1.75683
$120$		0			0
$121$	0.298438			0.0271307
$122$	−7.37992	−	3.24844i	−0.668147	−	0.294100i
$123$	4.54040	+	2.79544i	0.409394	+	0.252056i
$124$	−5.00000	+	4.57917i	−0.449013	+	0.411221i
$125$		0			0
$126$	10.6330	−	0.557742i	0.947263	−	0.0496876i
$127$			12.6797i			1.12514i	0.826749	+	0.562571i	$0.190188\pi$
$127$			12.6797i			1.12514i	−0.826749	+	0.562571i	$0.809812\pi$
$128$	−10.9920	+	2.67869i	−0.971567	+	0.236765i
$129$	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	$0.580384\pi$
$132$	11.4352	−	2.19477i	0.995308	−	0.191030i
$133$	1.10469			0.0957885
$134$	3.11053	−	7.06662i	0.268709	−	0.610463i
$135$		0			0
$136$	20.4555	−	6.93443i	1.75404	−	0.594623i
$137$			9.91534i			0.847125i	0.905867	+	0.423563i	$0.139221\pi$
$137$			9.91534i			0.847125i	−0.905867	+	0.423563i	$0.860779\pi$
$138$	−10.4363	+	7.20558i	−0.888400	+	0.613380i
$139$			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
$142$	16.1047	+	7.08883i	1.35148	+	0.594882i
$143$	−12.4421			−1.04046
$144$	11.1473	−	4.44267i	0.928943	−	0.370223i
$145$		0			0
$146$	1.68066	+	0.739779i	0.139092	+	0.0612245i
$147$	0.637075	−	1.03475i	0.0525450	−	0.0853446i
$148$	−10.0000	−	10.9190i	−0.821995	−	0.897538i
$149$			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	$0.288089\pi$
$151$			19.3284i			1.57292i	−0.617641	+	0.786460i	$0.711911\pi$
$152$	1.17909	−	0.399712i	0.0956365	−	0.0324209i
$153$	−20.4555	+	10.3151i	−1.65373	+	0.833923i
$154$	−4.80625	+	10.9190i	−0.387299	+	0.879880i
$155$		0			0
$156$	−12.5927	+	2.41693i	−1.00823	+	0.193509i
$157$	11.1047			0.886250			0.443125	−	0.896460i	$-0.353870\pi$
$157$	11.1047			0.886250			0.443125	+	0.896460i	$0.353870\pi$
$158$	2.85974	−	6.49687i	0.227509	−	0.516864i
$159$	3.36131	+	2.06950i	0.266570	+	0.164122i
$160$		0			0
$161$		−	12.9937i		−	1.02405i
$162$	−11.0489	+	6.31832i	−0.868086	+	0.496414i
$163$			0.440172i			0.0344769i	0.999851	+	0.0172385i	$0.00548745\pi$
$163$			0.440172i			0.0344769i	−0.999851	+	0.0172385i	$0.994513\pi$
$164$	−4.54040	+	4.15825i	−0.354546	+	0.324705i
$165$		0			0
$166$	2.35078	+	1.03475i	0.182456	+	0.0803120i
$167$	15.5324			1.20194			0.600968	−	0.799273i	$-0.294782\pi$
$167$	15.5324			1.20194			0.600968	+	0.799273i	$0.294782\pi$
$168$	−2.74337	+	11.9848i	−0.211656	+	0.924651i
$169$	0.701562			0.0539663
$170$		0			0
$171$	−1.17909	+	0.594576i	−0.0901669	+	0.0454684i
$172$	−12.4031	+	11.3592i	−0.945729	+	0.866130i
$173$			8.43579i			0.641361i	0.947187	+	0.320681i	$0.103912\pi$
$173$			8.43579i			0.641361i	−0.947187	+	0.320681i	$0.896088\pi$
$174$	−3.17170	−	4.59378i	−0.240446	−	0.348254i
$175$		0			0
$176$	−1.17909	+	13.3935i	−0.0888769	+	1.00957i
$177$		0			0
$178$	3.05234	−	6.93443i	0.228783	−	0.519758i
$179$	−9.08080			−0.678731			−0.339365	−	0.940655i	$-0.610212\pi$
$179$	−9.08080			−0.678731			−0.339365	+	0.940655i	$0.610212\pi$
$180$		0			0
$181$	10.5078			0.781039			0.390520	−	0.920595i	$-0.372295\pi$
$181$	10.5078			0.781039			0.390520	+	0.920595i	$0.372295\pi$
$182$	5.29276	−	12.0243i	0.392325	−	0.891300i
$183$	−5.17748	+	8.40935i	−0.382730	+	0.621637i
$184$	−4.70156	−	13.8689i	−0.346604	−	1.02243i
$185$		0			0
$186$	4.71794	+	6.83331i	0.345936	+	0.501043i
$187$		−	25.6682i		−	1.87705i
$188$	4.90647	+	5.35738i	0.357841	+	0.390727i
$189$	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	$0.351374\pi$
$192$	1.40837	+	13.7846i	0.101641	+	0.994821i
$193$	19.8062			1.42568			0.712842	−	0.701324i	$-0.247407\pi$
$193$	19.8062			1.42568			0.712842	+	0.701324i	$0.247407\pi$
$194$	14.3736	+	6.32684i	1.03196	+	0.454241i
$195$		0			0
$196$	0.947657	+	1.03475i	0.0676898	+	0.0739106i
$197$		−	10.7148i		−	0.763396i	−0.924287	−	0.381698i	$-0.875340\pi$
$197$		−	10.7148i		−	0.763396i	0.924287	−	0.381698i	$-0.124660\pi$
$198$	−0.747009	−	14.2413i	−0.0530876	−	1.01208i
$199$			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
$202$	10.0000	−	22.7184i	0.703598	−	1.59846i
$203$	5.71949			0.401429
$204$	−4.98615	−	25.9790i	−0.349101	−	1.81889i
$205$		0			0
$206$	6.22106	−	14.1332i	0.433442	−	0.984709i
$207$	6.99364	+	13.8689i	0.486091	+	0.963952i
$208$	1.29844	−	14.7492i	0.0900305	−	1.02267i
$209$		−	1.47956i		−	0.102343i
$210$		0			0
$211$		−	18.1392i		−	1.24876i	−0.781123	−	0.624378i	$-0.785353\pi$
$211$		−	18.1392i		−	1.24876i	0.781123	−	0.624378i	$-0.214647\pi$
$212$	−3.36131	+	3.07840i	−0.230856	+	0.211426i
$213$	11.2984	−	18.3511i	0.774156	−	1.25740i
$214$	8.35078	+	3.67578i	0.570848	+	0.251271i
$215$		0			0
$216$	−3.52248	−	14.2686i	−0.239674	−	0.970853i
$217$	−8.50781			−0.577548
$218$	2.97503	+	1.30952i	0.201494	+	0.0886921i
$219$	1.17909	−	1.91509i	0.0796752	−	0.129410i
$220$		0			0
$221$			28.2665i			1.90141i
$222$	−14.9226	+	10.3031i	−1.00154	+	0.691496i
$223$		−	21.0891i		−	1.41223i	−0.708098	−	0.706114i	$-0.750447\pi$
$223$		−	21.0891i		−	1.41223i	0.708098	−	0.706114i	$-0.249553\pi$
$224$	−12.4421	−	6.83694i	−0.831324	−	0.456812i
$225$		0			0
$226$	0.455467	−	1.03475i	0.0302972	−	0.0688304i
$227$	−22.2551			−1.47712			−0.738560	−	0.674188i	$-0.764494\pi$
$227$	−22.2551			−1.47712			−0.738560	+	0.674188i	$0.764494\pi$
$228$	−0.287410	−	1.49747i	−0.0190342	−	0.0991723i
$229$	2.29844			0.151885			0.0759425	−	0.997112i	$-0.475803\pi$
$229$	2.29844			0.151885			0.0759425	+	0.997112i	$0.475803\pi$
$230$		0			0
$231$	12.4421	+	7.66037i	0.818631	+	0.504015i
$232$	6.10469	−	2.06950i	0.400792	−	0.135869i
$233$			8.43579i			0.552647i	0.961065	+	0.276323i	$0.0891161\pi$
$233$			8.43579i			0.552647i	−0.961065	+	0.276323i	$0.910884\pi$
$234$	0.822625	+	15.6828i	0.0537767	+	1.02522i
$235$		0			0
$236$		0			0
$237$	−7.40312	−	4.55796i	−0.480885	−	0.296071i
$238$	24.8062	+	10.9190i	1.60795	+	0.707775i
$239$	−25.8874			−1.67452			−0.837258	−	0.546809i	$-0.815842\pi$
$239$	−25.8874			−1.67452			−0.837258	+	0.546809i	$0.815842\pi$
$240$		0			0
$241$	7.00000			0.450910			0.225455	−	0.974254i	$-0.427613\pi$
$241$	7.00000			0.450910			0.225455	+	0.974254i	$0.427613\pi$
$242$	0.386289	+	0.170034i	0.0248316	+	0.0109302i
$243$	5.81455	+	14.4634i	0.373004	+	0.927830i
$244$	−7.70156	−	8.40935i	−0.493042	−	0.538354i
$245$		0			0
$246$	4.28427	+	6.20520i	0.273155	+	0.395629i
$247$			1.62932i			0.103671i
$248$	−9.08080	+	3.07840i	−0.576631	+	0.195479i
$249$	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	$0.751719\pi$
$252$	14.0808	+	5.33618i	0.887007	+	0.336148i
$253$	−17.4031			−1.09413
$254$	−7.22420	+	16.4122i	−0.453287	+	1.02979i
$255$		0			0
$256$	−15.7539	−	2.79544i	−0.984619	−	0.174715i
$257$		−	4.55796i		−	0.284318i	−0.989844	−	0.142159i	$-0.954596\pi$
$257$		−	4.55796i		−	0.284318i	0.989844	−	0.142159i	$-0.0454044\pi$
$258$	11.7034	+	16.9509i	0.728624	+	1.05532i
$259$		−	18.5794i		−	1.15447i
$260$		0			0
$261$	−6.10469	+	3.07840i	−0.377871	+	0.190548i
$262$	−7.40312	−	3.25865i	−0.457367	−	0.201320i
$263$	18.6227			1.14833			0.574164	−	0.818741i	$-0.305327\pi$
$263$	18.6227			1.14833			0.574164	+	0.818741i	$0.305327\pi$
$264$	16.0518	+	3.67432i	0.987923	+	0.226139i
$265$		0			0
$266$	1.42987	+	0.629390i	0.0876710	+	0.0385904i
$267$	−7.90172	−	4.86493i	−0.483577	−	0.297729i
$268$	8.05234	−	7.37460i	0.491875	−	0.450476i
$269$		−	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	$-0.910274\pi$
$271$		−	9.15833i		−	0.556329i	0.960533	−	0.278165i	$-0.0897260\pi$
$272$	30.4278	+	2.67869i	1.84495	+	0.162420i
$273$	−13.7016	−	8.43579i	−0.829256	−	0.510557i
$274$	−5.64922	+	12.8341i	−0.341282	+	0.775337i
$275$		0			0
$276$	−17.6138	+	3.38063i	−1.06023	+	0.203490i
$277$	−8.89531			−0.534468			−0.267234	−	0.963632i	$-0.586110\pi$
$277$	−8.89531			−0.534468			−0.267234	+	0.963632i	$0.586110\pi$
$278$	−1.68066	+	3.81818i	−0.100799	+	0.228999i
$279$	9.08080	−	4.57917i	0.543653	−	0.274147i
$280$		0			0
$281$			17.5517i			1.04705i	0.852011	+	0.523524i	$0.175383\pi$
$281$			17.5517i			1.04705i	−0.852011	+	0.523524i	$0.824617\pi$
$282$	7.32174	−	5.05516i	0.436003	−	0.301030i
$283$			16.3785i			0.973603i	0.873513	+	0.486801i	$0.161836\pi$
$283$			16.3785i			0.973603i	−0.873513	+	0.486801i	$0.838164\pi$
$284$	16.8066	+	18.3511i	0.997287	+	1.08894i
$285$		0			0
$286$	−16.1047	−	7.08883i	−0.952290	−	0.419172i
$287$	−7.72577			−0.456038
$288$	16.9599	+	0.600671i	0.999373	+	0.0353949i
$289$	−41.3141			−2.43024
$290$		0			0
$291$	10.0839	−	16.3785i	0.591131	−	0.960126i
$292$	1.75391	+	1.91509i	0.102640	+	0.112072i
$293$		−	21.4295i		−	1.25193i	−0.779852	−	0.625963i	$-0.784706\pi$
$293$		−	21.4295i		−	1.25193i	0.779852	−	0.625963i	$-0.215294\pi$
$294$	1.41415	−	0.976376i	0.0824750	−	0.0569434i
$295$		0			0
$296$	−6.72263	−	19.8307i	−0.390745	−	1.15264i
$297$	−17.4031	−	1.47956i	−1.00983	−	0.0858526i
$298$	−8.70156	+	19.7685i	−0.504068	+	1.14516i
$299$	19.1647			1.10833
$300$		0			0
$301$	−21.1047			−1.21645
$302$	−11.0122	+	25.0180i	−0.633683	+	1.43963i
$303$	−25.8874	−	15.9384i	−1.48719	−	0.915635i
$304$	1.75391	+	0.154404i	0.100593	+	0.00885568i
$305$		0			0
$306$	−32.3539	+	1.69708i	−1.84955	+	0.0970159i
$307$			26.4172i			1.50771i	0.657041	+	0.753855i	$0.271808\pi$
$307$			26.4172i			1.50771i	−0.657041	+	0.753855i	$0.728192\pi$
$308$	−12.4421	+	11.3949i	−0.708955	+	0.649285i
$309$	−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	$0.624491\pi$
$312$	−17.6767	−	4.04625i	−1.00075	−	0.229074i
$313$	16.2984			0.921242			0.460621	−	0.887597i	$-0.347627\pi$
$313$	16.2984			0.921242			0.460621	+	0.887597i	$0.347627\pi$
$314$	14.3736	+	6.32684i	0.811147	+	0.357044i
$315$		0			0
$316$	7.40312	−	6.78003i	0.416458	−	0.381406i
$317$		−	16.8716i		−	0.947602i	−0.880632	−	0.473801i	$-0.842882\pi$
$317$		−	16.8716i		−	0.947602i	0.880632	−	0.473801i	$-0.157118\pi$
$318$	3.17170	+	4.59378i	0.177860	+	0.257607i
$319$		−	7.66037i		−	0.428898i
$320$		0			0
$321$	5.85859	−	9.51563i	0.326995	−	0.531111i
$322$	7.40312	−	16.8187i	0.412560	−	0.937270i
$323$	−3.36131			−0.187029
$324$	−17.9012	+	1.88316i	−0.994512	+	0.104620i
$325$		0			0
$326$	−0.250786	+	0.569745i	−0.0138897	+	0.0315553i
$327$	2.08717	−	3.39001i	0.115421	−	0.187468i
$328$	−8.24609	+	2.79544i	−0.455314	+	0.154352i
$329$			9.11592i			0.502577i
$330$		0			0
$331$		−	17.1275i		−	0.941413i	−0.882290	−	0.470707i	$-0.843999\pi$
$331$		−	17.1275i		−	0.941413i	0.882290	−	0.470707i	$-0.156001\pi$
$332$	2.45323	+	2.67869i	0.134639	+	0.147012i
$333$	10.0000	+	19.8307i	0.547997	+	1.08672i
$334$	20.1047	+	8.84952i	1.10008	+	0.484224i
$335$		0			0
$336$	−10.3792	+	13.9498i	−0.566234	+	0.761023i
$337$	−12.4031			−0.675641			−0.337821	−	0.941211i	$-0.609690\pi$
$337$	−12.4031			−0.675641			−0.337821	+	0.941211i	$0.609690\pi$
$338$	0.908080	+	0.399712i	0.0493930	+	0.0217414i
$339$	−1.17909	−	0.725940i	−0.0640391	−	0.0394277i
$340$		0			0
$341$			11.3949i			0.617069i
$342$	−1.86493	+	0.0978226i	−0.100844	+	0.00528964i
$343$			19.3284i			1.04363i
$344$	−22.5261	+	7.63636i	−1.21452	+	0.411725i
$345$		0			0
$346$	−4.80625	+	10.9190i	−0.258386	+	0.587010i
$347$	−19.4358			−1.04337			−0.521683	−	0.853139i	$-0.674696\pi$
$347$	−19.4358			−1.04337			−0.521683	+	0.853139i	$0.674696\pi$
$348$	−1.48806	−	7.75311i	−0.0797682	−	0.415610i
$349$	26.2094			1.40296			0.701478	−	0.712691i	$-0.252524\pi$
$349$	26.2094			1.40296			0.701478	+	0.712691i	$0.252524\pi$
$350$		0			0
$351$	19.1647	+	1.62932i	1.02294	+	0.0869669i
$352$	−9.15703	+	16.6643i	−0.488071	+	0.888210i
$353$		−	26.6676i		−	1.41937i	−0.704517	−	0.709687i	$-0.748836\pi$
$353$		−	26.6676i		−	1.41937i	0.704517	−	0.709687i	$-0.251164\pi$
$354$		0			0
$355$		0			0
$356$	7.90172	−	7.23665i	0.418790	−	0.383542i
$357$	17.4031	−	28.2665i	0.921071	−	1.49602i
$358$	−11.7539	−	5.17374i	−0.621213	−	0.273441i
$359$	−7.72577			−0.407751			−0.203875	−	0.978997i	$-0.565354\pi$
$359$	−7.72577			−0.407751			−0.203875	+	0.978997i	$0.565354\pi$
$360$		0			0
$361$	18.8062			0.989803
$362$	13.6010	+	5.98677i	0.714852	+	0.314658i
$363$	0.271006	−	0.440172i	0.0142241	−	0.0231030i
$364$	13.7016	−	12.5483i	0.718157	−	0.657712i
$365$		0			0
$366$	−11.4927	+	7.93496i	−0.600736	+	0.414767i
$367$			2.50967i			0.131004i	0.997852	+	0.0655018i	$0.0208648\pi$
$367$			2.50967i			0.131004i	−0.997852	+	0.0655018i	$0.979135\pi$
$368$	1.81616	−	20.6301i	0.0946739	−	1.07542i
$369$	8.24609	−	4.15825i	0.429275	−	0.216470i
$370$		0			0
$371$	−5.71949			−0.296941
$372$	2.21350	+	11.5329i	0.114765	+	0.597951i
$373$	−23.7016			−1.22722			−0.613610	−	0.789609i	$-0.710283\pi$
$373$	−23.7016			−1.22722			−0.613610	+	0.789609i	$0.710283\pi$
$374$	14.6243	−	33.2241i	0.756207	−	1.71798i
$375$		0			0
$376$	3.29844	+	9.72987i	0.170104	+	0.501780i
$377$			8.43579i			0.434465i
$378$	8.83300	−	16.1893i	0.454320	−	0.832688i
$379$			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
$382$	16.1047	+	7.08883i	0.823987	+	0.362696i
$383$	−7.26464			−0.371206			−0.185603	−	0.982625i	$-0.559424\pi$
$383$	−7.26464			−0.371206			−0.185603	+	0.982625i	$0.559424\pi$
$384$	−6.03078	+	18.6448i	−0.307757	+	0.951465i
$385$		0			0
$386$	25.6366	+	11.2845i	1.30487	+	0.574367i
$387$	22.5261	−	11.3592i	1.14506	−	0.577420i
$388$	15.0000	+	16.3785i	0.761510	+	0.831494i
$389$		−	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
$392$	0.637075	+	1.87927i	0.0321771	+	0.0949174i
$393$	−5.19375	+	8.43579i	−0.261990	+	0.425529i
$394$	6.10469	−	13.8689i	0.307550	−	0.698703i
$395$		0			0
$396$	7.14699	−	18.8591i	0.359150	−	0.947704i
$397$	−15.9109			−0.798547			−0.399273	−	0.916832i	$-0.630738\pi$
$397$	−15.9109			−0.798547			−0.399273	+	0.916832i	$0.630738\pi$
$398$	−12.0154	+	27.2970i	−0.602277	+	1.36828i
$399$	1.00314	−	1.62932i	0.0502200	−	0.0815683i
$400$		0			0
$401$		−	9.23521i		−	0.461184i	−0.973050	−	0.230592i	$-0.925934\pi$
$401$		−	9.23521i		−	0.461184i	0.973050	−	0.230592i	$-0.0740663\pi$
$402$	−7.59809	−	11.0048i	−0.378958	−	0.548871i
$403$		−	12.5483i		−	0.625078i
$404$	25.8874	−	23.7085i	1.28795	−	1.17954i
$405$		0			0
$406$	7.40312	+	3.25865i	0.367411	+	0.161724i
$407$	−24.8842			−1.23347
$408$	8.34747	−	36.4672i	0.413261	−	1.80540i
$409$	11.2094			0.554268			0.277134	−	0.960831i	$-0.410615\pi$
$409$	11.2094			0.554268			0.277134	+	0.960831i	$0.410615\pi$
$410$		0			0
$411$	14.6243	+	9.00393i	0.721366	+	0.444131i
$412$	16.1047	−	14.7492i	0.793421	−	0.726641i
$413$		0			0
$414$	1.15063	+	21.9360i	0.0565503	+	1.07810i
$415$		0			0
$416$	10.0839	−	18.3511i	0.494406	−	0.899738i
$417$	4.35078	+	2.67869i	0.213059	+	0.131176i
$418$	0.842970	−	1.91509i	0.0412310	−	0.0936702i
$419$	−34.9682			−1.70831			−0.854154	−	0.520021i	$-0.825924\pi$
$419$	−34.9682			−1.70831			−0.854154	+	0.520021i	$0.825924\pi$
$420$		0			0
$421$	−14.2094			−0.692522			−0.346261	−	0.938138i	$-0.612549\pi$
$421$	−14.2094			−0.692522			−0.346261	+	0.938138i	$0.612549\pi$
$422$	10.3347	−	23.4788i	0.503087	−	1.14293i
$423$	−4.90647	−	9.72987i	−0.238561	−	0.473082i
$424$	−6.10469	+	2.06950i	−0.296470	+	0.100504i
$425$		0			0
$426$	25.0798	−	17.3159i	1.21512	−	0.838958i
$427$		−	14.3090i		−	0.692463i
$428$	8.71473	+	9.51563i	0.421242	+	0.459955i
$429$	−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	$0.543987\pi$
$432$	3.57007	−	20.4757i	0.171765	−	0.985138i
$433$	−7.20937			−0.346460			−0.173230	−	0.984881i	$-0.555420\pi$
$433$	−7.20937			−0.346460			−0.173230	+	0.984881i	$0.555420\pi$
$434$	−11.0122	−	4.84728i	−0.528605	−	0.232677i
$435$		0			0
$436$	3.10469	+	3.39001i	0.148688	+	0.162352i
$437$			2.27898i			0.109018i
$438$	2.61729	−	1.80706i	0.125059	−	0.0863446i
$439$			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
$442$	−16.1047	+	36.5872i	−0.766022	+	1.74028i
$443$	29.7907			1.41540			0.707699	−	0.706514i	$-0.249733\pi$
$443$	29.7907			1.41540			0.707699	+	0.706514i	$0.249733\pi$
$444$	−25.1855	+	4.83386i	−1.19525	+	0.229405i
$445$		0			0
$446$	12.0154	−	27.2970i	0.568945	−	1.29255i
$447$	22.5261	+	13.8689i	1.06545	+	0.655975i
$448$	−12.2094	−	15.9384i	−0.576839	−	0.753017i
$449$			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
$452$	1.17909	−	1.07985i	0.0554595	−	0.0507917i
$453$	28.5078	+	17.5517i	1.33941	+	0.824651i
$454$	−28.8062	−	12.6797i	−1.35194	−	0.595088i
$455$		0			0
$456$	0.481161	−	2.10203i	0.0225324	−	0.0984365i
$457$	36.1047			1.68891			0.844453	−	0.535630i	$-0.179926\pi$
$457$	36.1047			1.68891			0.844453	+	0.535630i	$0.179926\pi$
$458$	2.97503	+	1.30952i	0.139014	+	0.0611900i
$459$	−3.36131	+	39.5371i	−0.156893	+	1.84543i
$460$		0			0
$461$		−	17.5517i		−	0.817465i	−0.912654	−	0.408732i	$-0.865971\pi$
$461$		−	17.5517i		−	0.817465i	0.912654	−	0.408732i	$-0.134029\pi$
$462$	11.7402	+	17.0042i	0.546205	+	0.791106i
$463$			5.01934i			0.233268i	0.993175	+	0.116634i	$0.0372105\pi$
$463$			5.01934i			0.233268i	−0.993175	+	0.116634i	$0.962789\pi$
$464$	9.08080	+	0.799423i	0.421566	+	0.0371123i
$465$		0			0
$466$	−4.80625	+	10.9190i	−0.222645	+	0.505814i
$467$	29.5197			1.36601			0.683004	−	0.730414i	$-0.260673\pi$
$467$	29.5197			1.36601			0.683004	+	0.730414i	$0.260673\pi$
$468$	−7.87044	+	20.7681i	−0.363811	+	0.960004i
$469$	13.7016			0.632679
$470$		0			0
$471$	10.0839	−	16.3785i	0.464644	−	0.754683i
$472$		0			0
$473$			28.2665i			1.29969i
$474$	−6.98550	−	10.1176i	−0.320855	−	0.464716i
$475$		0			0
$476$	25.8874	+	28.2665i	1.18655	+	1.29559i
$477$	6.10469	−	3.07840i	0.279514	−	0.140950i
$478$	−33.5078	−	14.7492i	−1.53261	−	0.674613i
$479$	33.6131			1.53582			0.767912	−	0.640555i	$-0.221296\pi$
$479$	33.6131			1.53582			0.767912	+	0.640555i	$0.221296\pi$
$480$		0			0
$481$	27.4031			1.24947
$482$	9.06058	+	3.98822i	0.412698	+	0.181658i
$483$	−19.1647	−	11.7994i	−0.872026	−	0.536890i
$484$	0.403124	+	0.440172i	0.0183238	+	0.0200078i
$485$		0			0
$486$	−0.714301	+	22.0338i	−0.0324013	+	0.999475i
$487$			0.131364i			0.00595267i	0.999996	+	0.00297634i	$0.000947399\pi$
$487$			0.131364i			0.00595267i	−0.999996	+	0.00297634i	$0.999053\pi$
$488$	−5.17748	−	15.2727i	−0.234373	−	0.691364i
$489$	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	$0.598118\pi$
$492$	2.01004	+	10.4728i	0.0906196	+	0.472148i
$493$	−17.4031			−0.783797
$494$	−0.928300	+	2.10895i	−0.0417662	+	0.0948860i
$495$		0			0
$496$	−13.5078	−	1.18915i	−0.606519	−	0.0533945i
$497$			31.2256i			1.40066i
$498$	3.66087	−	2.52758i	0.164047	−	0.113264i
$499$		−	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
$502$	−29.1570	−	12.8341i	−1.30134	−	0.572814i
$503$	12.9841			0.578934			0.289467	−	0.957188i	$-0.406522\pi$
$503$	12.9841			0.578934			0.289467	+	0.957188i	$0.406522\pi$
$504$	15.1855	+	14.9295i	0.676415	+	0.665011i
$505$		0			0
$506$	−22.5261	−	9.91534i	−1.00141	−	0.440791i
$507$	0.637075	−	1.03475i	0.0282935	−	0.0459548i
$508$	−18.7016	+	17.1275i	−0.829748	+	0.759910i
$509$			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
$512$	−18.7987	−	12.5940i	−0.830792	−	0.556583i
$513$	−0.193752	+	2.27898i	−0.00855434	+	0.100619i
$514$	2.59688	−	5.89968i	0.114543	−	0.260224i
$515$		0			0
$516$	5.49087	+	28.6087i	0.241722	+	1.25943i
$517$	12.2094			0.536968
$518$	10.5855	−	24.0486i	0.465101	−	1.05663i
$519$	12.4421	+	7.66037i	0.546148	+	0.336253i
$520$		0			0
$521$		−	3.07840i		−	0.134867i	−0.997724	−	0.0674337i	$-0.978519\pi$
$521$		−	3.07840i		−	0.134867i	0.997724	−	0.0674337i	$-0.0214811\pi$
$522$	−9.65562	+	0.506474i	−0.422615	+	0.0221678i
$523$			14.0002i			0.612187i	0.952001	+	0.306094i	$0.0990220\pi$
$523$			14.0002i			0.612187i	−0.952001	+	0.306094i	$0.900978\pi$
$524$	−7.72577	−	8.43579i	−0.337502	−	0.368519i
$525$		0			0
$526$	24.1047	+	10.6102i	1.05101	+	0.462627i
$527$	25.8874			1.12767
$528$	18.6836	+	13.9014i	0.813099	+	0.604980i
$529$	3.80625			0.165489
$530$		0			0
$531$		0			0
$532$	1.49219	+	1.62932i	0.0646946	+	0.0706402i
$533$		−	11.3949i		−	0.493568i
$534$	−7.45596	−	10.7990i	−0.322651	−	0.467318i
$535$		0			0
$536$	14.6243	−	4.95767i	0.631676	−	0.214139i
$537$	−8.24609	+	13.3935i	−0.355845	+	0.577970i
$538$	4.80625	−	10.9190i	0.207212	−	0.470752i
$539$	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	$0.686325\pi$
$542$	5.21791	−	11.8543i	0.224129	−	0.509184i
$543$	9.54193	−	15.4982i	0.409484	−	0.665091i
$544$	37.8586	+	20.8033i	1.62317	+	0.891934i
$545$		0			0
$546$	−12.9286	−	18.7254i	−0.553294	−	0.801374i
$547$			4.71053i			0.201408i	0.994916	+	0.100704i	$0.0321095\pi$
$547$			4.71053i			0.201408i	−0.994916	+	0.100704i	$0.967891\pi$
$548$	−14.6243	+	13.3935i	−0.624721	+	0.572140i
$549$	7.70156	+	15.2727i	0.328695	+	0.651824i
$550$		0			0
$551$	−1.00314			−0.0427354
$552$	−24.7249	−	5.65961i	−1.05236	−	0.240889i
$553$	12.5969			0.535674
$554$	−11.5138	−	5.06806i	−0.489175	−	0.215321i
$555$		0			0
$556$	−4.35078	+	3.98459i	−0.184514	+	0.168984i
$557$			36.7023i			1.55512i	0.628806	+	0.777562i	$0.283544\pi$
$557$			36.7023i			1.55512i	−0.628806	+	0.777562i	$0.716456\pi$
$558$	14.3629	−	0.753387i	0.608028	−	0.0318934i
$559$		−	31.1277i		−	1.31656i
$560$		0			0
$561$	−37.8586	−	23.3088i	−1.59839	−	0.984098i
$562$	−10.0000	+	22.7184i	−0.421825	+	0.958317i
$563$	−23.3391			−0.983625			−0.491812	−	0.870701i	$-0.663665\pi$
$563$	−23.3391			−0.983625			−0.491812	+	0.870701i	$0.663665\pi$
$564$	12.3572	−	2.37172i	0.520331	−	0.0998674i
$565$		0			0
$566$	−9.33159	+	21.1999i	−0.392236	+	0.891096i
$567$	−18.1616	−	13.4287i	−0.762716	−	0.563952i
$568$	11.2984	+	33.3286i	0.474072	+	1.39844i
$569$		−	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	$0.115406\pi$
$571$			16.9501i			0.709338i	−0.934992	+	0.354669i	$0.884594\pi$
$572$	−16.8066	−	18.3511i	−0.702718	−	0.767299i
$573$	11.2984	−	18.3511i	0.471999	−	0.766630i
$574$	−10.0000	−	4.40172i	−0.417392	−	0.183724i
$575$		0			0
$576$	21.6102	+	10.4403i	0.900424	+	0.435014i
$577$	−12.4031			−0.516349			−0.258174	−	0.966098i	$-0.583121\pi$
$577$	−12.4031			−0.516349			−0.258174	+	0.966098i	$0.583121\pi$
$578$	−53.4756	−	23.5385i	−2.22429	−	0.979072i
$579$	17.9857	−	29.2126i	0.747459	−	1.21404i
$580$		0			0
$581$			4.55796i			0.189096i
$582$	22.3839	−	15.4546i	0.927844	−	0.640613i
$583$			7.66037i			0.317260i
$584$	1.17909	+	3.47812i	0.0487909	+	0.143925i
$585$		0			0
$586$	12.2094	−	27.7377i	0.504365	−	1.14583i
$587$	−31.3359			−1.29337			−0.646685	−	0.762758i	$-0.723845\pi$
$587$	−31.3359			−1.29337			−0.646685	+	0.762758i	$0.723845\pi$
$588$	2.38672	−	0.458084i	0.0984267	−	0.0188911i
$589$	1.49219			0.0614846
$590$		0			0
$591$	−15.8034	−	9.72987i	−0.650066	−	0.400233i
$592$	2.59688	−	29.4984i	0.106731	−	1.21238i
$593$			10.5955i			0.435104i	0.976049	+	0.217552i	$0.0698072\pi$
$593$			10.5955i			0.435104i	−0.976049	+	0.217552i	$0.930193\pi$
$594$	−21.6831	−	11.8304i	−0.889668	−	0.485409i
$595$		0			0
$596$	−22.5261	+	20.6301i	−0.922703	+	0.845042i
$597$	31.1047	+	19.1506i	1.27303	+	0.783780i
$598$	24.8062	+	10.9190i	1.01440	+	0.446512i
$599$		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	$0.803888\pi$
$602$	−27.3172	−	12.0243i	−1.11337	−	0.490074i
$603$	−14.6243	+	7.37460i	−0.595549	+	0.300317i
$604$	−28.5078	+	26.1084i	−1.15997	+	1.06234i
$605$		0			0
$606$	−24.4270	−	35.3793i	−0.992279	−	1.43719i
$607$		−	3.25865i		−	0.132264i	−0.997811	−	0.0661322i	$-0.978934\pi$
$607$		−	3.25865i		−	0.132264i	0.997811	−	0.0661322i	$-0.0210659\pi$
$608$	2.18223	+	1.19913i	0.0885011	+	0.0486313i
$609$	5.19375	−	8.43579i	0.210461	−	0.341835i
$610$		0			0
$611$	−13.4453			−0.543937
$612$	−42.8447	−	16.2368i	−1.73190	−	0.656334i
$613$	4.80625			0.194123			0.0970613	−	0.995278i	$-0.469056\pi$
$613$	4.80625			0.194123			0.0970613	+	0.995278i	$0.469056\pi$
$614$	−15.0511	+	34.1936i	−0.607412	+	1.37994i
$615$		0			0
$616$	−22.5969	+	7.66037i	−0.910454	+	0.308645i
$617$		−	22.1097i		−	0.890102i	−0.895505	−	0.445051i	$-0.853186\pi$
$617$		−	22.1097i		−	0.890102i	0.895505	−	0.445051i	$-0.146814\pi$
$618$	−15.1962	−	22.0097i	−0.611280	−	0.885359i
$619$			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
$622$	−17.4031	−	7.66037i	−0.697802	−	0.307153i
$623$	13.4453			0.538673
$624$	−20.5748	−	15.3086i	−0.823652	−	0.612833i
$625$		0			0
$626$	21.0962	+	9.28595i	0.843173	+	0.371141i
$627$	−2.18223	−	1.34356i	−0.0871498	−	0.0536565i
$628$	15.0000	+	16.3785i	0.598565	+	0.653574i
$629$			56.5330i			2.25412i
$630$		0			0
$631$		−	42.0468i		−	1.67385i	−0.547314	−	0.836927i	$-0.684350\pi$
$631$		−	42.0468i		−	1.67385i	0.547314	−	0.836927i	$-0.315650\pi$
$632$	13.4453	−	4.55796i	0.534824	−	0.181306i
$633$	−26.7539	−	16.4719i	−1.06337	−	0.654698i
$634$	9.61250	−	21.8380i	0.381761	−	0.867299i
$635$		0			0
$636$	1.48806	+	7.75311i	0.0590053	+	0.307431i
$637$	−2.59688			−0.102892
$638$	4.36446	−	9.91534i	0.172791	−	0.392552i
$639$	−16.8066	−	33.3286i	−0.664858	−	1.31846i
$640$		0			0
$641$			12.3136i			0.486359i	0.969981	+	0.243179i	$0.0781903\pi$
$641$			12.3136i			0.486359i	−0.969981	+	0.243179i	$0.921810\pi$
$642$	13.0047	−	8.97883i	0.513253	−	0.354366i
$643$		−	24.4791i		−	0.965360i	−0.875797	−	0.482680i	$-0.839663\pi$
$643$		−	24.4791i		−	0.965360i	0.875797	−	0.482680i	$-0.160337\pi$
$644$	19.1647	−	17.5517i	0.755197	−	0.691634i
$645$		0			0
$646$	−4.35078	−	1.91509i	−0.171179	−	0.0753483i
$647$	−10.3550			−0.407095			−0.203548	−	0.979065i	$-0.565247\pi$
$647$	−10.3550			−0.407095			−0.203548	+	0.979065i	$0.565247\pi$
$648$	−24.2437	−	7.76163i	−0.952383	−	0.304906i
$649$		0			0
$650$		0			0
$651$	−7.72577	+	12.5483i	−0.302797	+	0.491808i
$652$	−0.649219	+	0.594576i	−0.0254254	+	0.0232854i
$653$			25.9875i			1.01697i	0.861071	+	0.508485i	$0.169794\pi$
$653$			25.9875i			1.01697i	−0.861071	+	0.508485i	$0.830206\pi$
$654$	4.63301	−	3.19877i	0.181165	−	0.125082i
$655$		0			0
$656$	−12.2662	−	1.07985i	−0.478914	−	0.0421609i
$657$	−1.75391	−	3.47812i	−0.0684264	−	0.135694i
$658$	−5.19375	+	11.7994i	−0.202474	+	0.459987i
$659$	16.8066			0.654691			0.327346	−	0.944905i	$-0.393846\pi$
$659$	16.8066			0.654691			0.327346	+	0.944905i	$0.393846\pi$
$660$		0			0
$661$	−18.0000			−0.700119			−0.350059	−	0.936727i	$-0.613839\pi$
$661$	−18.0000			−0.700119			−0.350059	+	0.936727i	$0.613839\pi$
$662$	9.75831	−	22.1693i	0.379268	−	0.861635i
$663$	41.6908	+	25.6682i	1.61914	+	0.996871i
$664$	1.64922	+	4.86493i	0.0640021	+	0.188796i
$665$		0			0
$666$	1.64525	+	31.3657i	0.0637521	+	1.21540i
$667$			11.7994i			0.456873i
$668$	20.9809	+	22.9091i	0.811776	+	0.886379i
$669$	−31.1047	−	19.1506i	−1.20258	−	0.740403i
$670$		0			0
$671$	−19.1647			−0.739847
$672$	−21.3824	+	12.1426i	−0.824843	+	0.468413i
$673$	24.8062			0.956211			0.478105	−	0.878303i	$-0.341324\pi$
$673$	24.8062			0.956211			0.478105	+	0.878303i	$0.341324\pi$
$674$	−16.0542	−	7.06662i	−0.618385	−	0.272196i
$675$		0			0
$676$	0.947657	+	1.03475i	0.0364483	+	0.0397980i
$677$			12.9937i			0.499390i	0.968324	+	0.249695i	$0.0803304\pi$
$677$			12.9937i			0.499390i	−0.968324	+	0.249695i	$0.919670\pi$
$678$	−1.11257	−	1.61141i	−0.0427280	−	0.0618859i
$679$			27.8691i			1.06952i
$680$		0			0
$681$	−20.2094	+	32.8244i	−0.774425	+	1.25784i
$682$	−6.49219	+	14.7492i	−0.248599	+	0.564776i
$683$	11.6291			0.444975			0.222488	−	0.974936i	$-0.428582\pi$
$683$	11.6291			0.444975			0.222488	+	0.974936i	$0.428582\pi$
$684$	−2.46964	−	0.935915i	−0.0944290	−	0.0357856i
$685$		0			0
$686$	−11.0122	+	25.0180i	−0.420449	+	0.955193i
$687$	2.08717	−	3.39001i	0.0796303	−	0.129337i
$688$	−33.5078	−	2.94984i	−1.27747	−	0.112462i
$689$		−	8.43579i		−	0.321378i
$690$		0			0
$691$		−	1.18915i		−	0.0452375i	−0.999744	−	0.0226187i	$-0.992800\pi$
$691$		−	1.18915i		−	0.0452375i	0.999744	−	0.0226187i	$-0.00720038\pi$
$692$	−12.4421	+	11.3949i	−0.472978	+	0.433169i
$693$	22.5969	−	11.3949i	0.858384	−	0.432857i
$694$	−25.1570	−	11.0734i	−0.954948	−	0.420341i
$695$		0			0
$696$	2.49120	−	10.8832i	0.0944287	−	0.412526i
$697$	23.5078			0.890422
$698$	33.9246	+	14.9327i	1.28406	+	0.565210i
$699$	12.4421	+	7.66037i	0.470604	+	0.289742i
$700$		0			0
$701$		−	11.3949i		−	0.430380i	−0.976572	−	0.215190i	$-0.930963\pi$
$701$		−	11.3949i		−	0.430380i	0.976572	−	0.215190i	$-0.0690370\pi$
$702$	23.8779	+	13.0280i	0.901215	+	0.491709i
$703$			3.25865i			0.122902i
$704$	−21.3470	+	16.3526i	−0.804544	+	0.616311i
$705$		0			0
$706$	15.1938	−	34.5177i	0.571824	−	1.29909i
$707$	44.0490			1.65663
$708$		0			0
$709$	−17.7016			−0.664796			−0.332398	−	0.943139i	$-0.607858\pi$
$709$	−17.7016			−0.664796			−0.332398	+	0.943139i	$0.607858\pi$
$710$		0			0
$711$	−13.4453	+	6.78003i	−0.504237	+	0.254271i
$712$	14.3508	−	4.86493i	0.537818	−	0.182321i
$713$		−	17.5517i		−	0.657317i
$714$	38.6307	−	26.6719i	1.44572	−	0.998171i
$715$		0			0
$716$	−12.2662	−	13.3935i	−0.458408	−	0.500537i
$717$	−23.5078	+	38.1818i	−0.877915	+	1.42593i
$718$	−10.0000	−	4.40172i	−0.373197	−	0.164271i
$719$	−44.0490			−1.64275			−0.821375	−	0.570389i	$-0.806793\pi$
$719$	−44.0490			−1.64275			−0.821375	+	0.570389i	$0.806793\pi$
$720$		0			0
$721$	27.4031			1.02055
$722$	24.3422	+	10.7148i	0.905924	+	0.398762i
$723$	6.35656	−	10.3244i	0.236403	−	0.383970i
$724$	14.1938	+	15.4982i	0.527507	+	0.575986i
$725$		0			0
$726$	0.601567	−	0.415341i	0.0223262	−	0.0154148i
$727$		−	40.5488i		−	1.50387i	−0.659236	−	0.751936i	$-0.729120\pi$
$727$		−	40.5488i		−	1.50387i	0.659236	−	0.751936i	$-0.270880\pi$
$728$	24.8842	−	8.43579i	0.922271	−	0.312651i
$729$	26.6125	+	4.55796i	0.985648	+	0.168813i
$730$		0			0
$731$	64.2169			2.37515
$732$	−19.3968	+	3.72283i	−0.716925	+	0.137600i
$733$	4.80625			0.177523			0.0887614	−	0.996053i	$-0.471709\pi$
$733$	4.80625			0.177523			0.0887614	+	0.996053i	$0.471709\pi$
$734$	−1.42987	+	3.24844i	−0.0527775	+	0.119902i
$735$		0			0
$736$	14.1047	−	25.6682i	0.519906	−	0.946143i
$737$		−	18.3511i		−	0.675973i
$738$	13.0426	−	0.684136i	0.480106	−	0.0251834i
$739$			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
$742$	−7.40312	−	3.25865i	−0.271777	−	0.119629i
$743$	−40.8778			−1.49966			−0.749830	−	0.661630i	$-0.769865\pi$
$743$	−40.8778			−1.49966			−0.749830	+	0.661630i	$0.769865\pi$
$744$	−3.70569	+	16.1889i	−0.135857	+	0.593514i
$745$		0			0
$746$	−30.6786	−	13.5038i	−1.12322	−	0.494411i
$747$	−2.45323	−	4.86493i	−0.0897592	−	0.177999i
$748$	37.8586	−	34.6722i	1.38425	−	1.26774i
$749$			16.1914i			0.591622i
$750$		0			0
$751$		−	36.2784i		−	1.32382i	−0.749584	−	0.661909i	$-0.769746\pi$
$751$		−	36.2784i		−	1.32382i	0.749584	−	0.661909i	$-0.230254\pi$
$752$	−1.27415	+	14.4733i	−0.0464634	+	0.527787i
$753$	−20.4555	+	33.2241i	−0.745439	+	1.21076i
$754$	−4.80625	+	10.9190i	−0.175033	+	0.397647i
$755$		0			0
$756$	20.6569	−	15.9224i	0.751285	−	0.579092i
$757$	−35.9109			−1.30521			−0.652603	−	0.757700i	$-0.726323\pi$
$757$	−35.9109			−1.30521			−0.652603	+	0.757700i	$0.726323\pi$
$758$	−7.47499	+	16.9820i	−0.271504	+	0.616813i
$759$	−15.8034	+	25.6682i	−0.573628	+	0.931698i
$760$		0			0
$761$		−	20.6301i		−	0.747841i	−0.927461	−	0.373920i	$-0.878013\pi$
$761$		−	20.6301i		−	0.747841i	0.927461	−	0.373920i	$-0.121987\pi$
$762$	17.6466	+	25.5587i	0.639268	+	0.925895i
$763$			5.76832i			0.208827i
$764$	16.8066	+	18.3511i	0.608041	+	0.663921i
$765$		0			0
$766$	−9.40312	−	4.13899i	−0.339749	−	0.149548i
$767$		0			0
$768$	−18.4289	+	20.6973i	−0.664994	+	0.746849i
$769$	−14.1938			−0.511840			−0.255920	−	0.966698i	$-0.582378\pi$
$769$	−14.1938			−0.511840			−0.255920	+	0.966698i	$0.582378\pi$
$770$		0			0
$771$	−6.72263	−	4.13899i	−0.242110	−	0.149062i
$772$	26.7539	+	29.2126i	0.962894	+	1.05139i
$773$			2.27898i			0.0819692i	0.999160	+	0.0409846i	$0.0130495\pi$
$773$			2.27898i			0.0819692i	−0.999160	+	0.0409846i	$0.986951\pi$
$774$	35.6289	−	1.86887i	1.28065	−	0.0671752i
$775$		0			0
$776$	10.0839	+	29.7460i	0.361993	+	1.06782i
$777$	−27.4031	−	16.8716i	−0.983082	−	0.605264i
$778$	21.2984	−	48.3866i	0.763586	−	1.73474i
$779$	1.35503			0.0485489
$780$		0			0
$781$	41.8219			1.49650
$782$	−22.5261	+	51.1756i	−0.805530	+	1.83003i
$783$	−1.00314	+	11.7994i	−0.0358494	+	0.421675i
$784$	−0.246095	+	2.79544i	−0.00878910	+	0.0998370i
$785$		0			0
$786$	−11.5289	+	7.95991i	−0.411221	+	0.283920i
$787$			18.4480i			0.657601i	0.944399	+	0.328801i	$0.106644\pi$
$787$			18.4480i			0.657601i	−0.944399	+	0.328801i	$0.893356\pi$
$788$	15.8034	−	14.4733i	0.562974	−	0.515590i
$789$	16.9109	−	27.4671i	0.602045	−	0.977853i
$790$		0			0
$791$	2.00629			0.0713354
$792$	19.9957	−	20.3386i	0.710516	−	0.722701i
$793$	21.1047			0.749449
$794$	−20.5946	−	9.06518i	−0.730876	−	0.321711i
$795$		0			0
$796$	−31.1047	+	28.4867i	−1.10248	+	1.00968i
$797$		−	45.8182i		−	1.62296i	−0.584378	−	0.811482i	$-0.698661\pi$
$797$		−	45.8182i		−	1.62296i	0.584378	−	0.811482i	$-0.301339\pi$
$798$	2.22674	−	1.53741i	0.0788257	−	0.0544237i
$799$		−	27.7377i		−	0.981290i
$800$		0			0
$801$	−14.3508	+	7.23665i	−0.507060	+	0.255695i
$802$	5.26172	−	11.9538i	0.185798	−	0.422102i
$803$	4.36446			0.154018
$804$	−3.56478	−	18.5733i	−0.125720	−	0.655030i
$805$		0			0
$806$	7.14936	−	16.2422i	0.251825	−	0.572107i
$807$	−12.4421	−	7.66037i	−0.437983	−	0.269658i
$808$	47.0156	−	15.9384i	1.65400	−	0.560709i
$809$		−	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	$0.212539\pi$
$811$			35.2667i			1.23838i	−0.785240	+	0.619191i	$0.787461\pi$
$812$	7.72577	+	8.43579i	0.271121	+	0.296038i
$813$	−13.5078	−	8.31650i	−0.473740	−	0.291672i
$814$	−32.2094	−	14.1777i	−1.12894	−	0.496927i
$815$		0			0
$816$	31.5817	−	42.4461i	1.10558	−	1.48591i
$817$	3.70156			0.129501
$818$	14.5091	+	6.38649i	0.507297	+	0.223298i
$819$	−24.8842	+	12.5483i	−0.869525	+	0.438475i
$820$		0			0
$821$			6.15681i			0.214874i	0.994212	+	0.107437i	$0.0342644\pi$
$821$			6.15681i			0.214874i	−0.994212	+	0.107437i	$0.965736\pi$
$822$	13.7994	+	19.9866i	0.481308	+	0.697111i
$823$			6.03105i			0.210229i	0.994460	+	0.105115i	$0.0335209\pi$
$823$			6.03105i			0.210229i	−0.994460	+	0.105115i	$0.966479\pi$
$824$	29.2487	−	9.91534i	1.01893	−	0.345417i
$825$		0			0
$826$		0			0
$827$	20.4389			0.710730			0.355365	−	0.934728i	$-0.384357\pi$
$827$	20.4389			0.710730			0.355365	+	0.934728i	$0.384357\pi$
$828$	−11.0086	+	29.0489i	−0.382575	+	1.00952i
$829$	19.1938			0.666627			0.333313	−	0.942816i	$-0.391833\pi$
$829$	19.1938			0.666627			0.333313	+	0.942816i	$0.391833\pi$
$830$		0			0
$831$	−8.07766	+	13.1199i	−0.280211	+	0.455124i
$832$	23.5078	−	18.0079i	0.814987	−	0.624310i
$833$		−	5.35738i		−	0.185622i
$834$	4.10534	+	5.94605i	0.142156	+	0.205895i
$835$		0			0
$836$	2.18223	−	1.99856i	0.0754740	−	0.0691216i
$837$	1.49219	−	17.5517i	0.0515776	−	0.606676i
$838$	−45.2617	−	19.9229i	−1.56354	−	0.688227i
$839$	44.0490			1.52074			0.760370	−	0.649490i	$-0.225018\pi$
$839$	44.0490			1.52074			0.760370	+	0.649490i	$0.225018\pi$
$840$		0			0
$841$	23.8062			0.820905
$842$	−18.3922	−	8.09572i	−0.633836	−	0.278997i
$843$	25.8874	+	15.9384i	0.891609	+	0.548946i
$844$	26.7539	−	24.5021i	0.920907	−	0.843397i
$845$		0			0
$846$	−0.807237	−	15.3895i	−0.0277534	−	0.529101i
$847$			0.748980i			0.0257353i
$848$	−9.08080	−	0.799423i	−0.311836	−	0.0274523i
$849$	24.1570	+	14.8730i	0.829067	+	0.510441i
$850$		0			0
$851$	38.3295			1.31392
$852$	42.3282	−	8.12406i	1.45014	−	0.278326i
$853$	−43.7016			−1.49631			−0.748156	−	0.663522i	$-0.769061\pi$
$853$	−43.7016			−1.49631			−0.748156	+	0.663522i	$0.769061\pi$
$854$	8.15250	−	18.5212i	0.278973	−	0.633781i
$855$		0			0
$856$	5.85859	+	17.2819i	0.200243	+	0.590684i
$857$		−	31.3449i		−	1.07072i	−0.844624	−	0.535360i	$-0.820176\pi$
$857$		−	31.3449i		−	1.07072i	0.844624	−	0.535360i	$-0.179824\pi$
$858$	−25.0798	+	17.3159i	−0.856211	+	0.591155i
$859$			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
$862$	−7.40312	−	3.25865i	−0.252151	−	0.110990i
$863$	−40.8778			−1.39150			−0.695748	−	0.718286i	$-0.744927\pi$
$863$	−40.8778			−1.39150			−0.695748	+	0.718286i	$0.744927\pi$
$864$	16.2869	−	24.4691i	0.554092	−	0.832455i
$865$		0			0
$866$	−9.33159	−	4.10750i	−0.317100	−	0.139579i
$867$	−37.5165	+	60.9350i	−1.27413	+	2.06946i
$868$	−11.4922	−	12.5483i	−0.390070	−	0.425919i
$869$		−	16.8716i		−	0.572329i
$870$		0			0
$871$			20.2087i			0.684746i
$872$	2.08717	+	6.15681i	0.0706803	+	0.208496i
$873$	−15.0000	−	29.7460i	−0.507673	−	1.00675i
$874$	−1.29844	+	2.94984i	−0.0439203	+	0.0997799i
$875$		0			0
$876$	4.41730	−	0.847813i	0.149247	−	0.0286450i
$877$	4.08907			0.138078			0.0690390	−	0.997614i	$-0.478007\pi$
$877$	4.08907			0.138078			0.0690390	+	0.997614i	$0.478007\pi$
$878$	−13.3704	+	30.3754i	−0.451230	+	1.02512i
$879$	−31.6069	−	19.4597i	−1.06607	−	0.656361i
$880$		0			0
$881$			47.4170i			1.59752i	0.601650	+	0.798760i	$0.294510\pi$
$881$			47.4170i			1.59752i	−0.601650	+	0.798760i	$0.705490\pi$
$882$	−0.155913	−	2.97239i	−0.00524987	−	0.100086i
$883$		−	58.5566i		−	1.97059i	−0.170867	−	0.985294i	$-0.554657\pi$
$883$		−	58.5566i		−	1.97059i	0.170867	−	0.985294i	$-0.445343\pi$
$884$	−41.6908	+	38.1818i	−1.40221	+	1.28419i
$885$		0			0
$886$	38.5602	+	16.9731i	1.29545	+	0.570223i
$887$	−14.5293			−0.487846			−0.243923	−	0.969795i	$-0.578434\pi$
$887$	−14.5293			−0.487846			−0.243923	+	0.969795i	$0.578434\pi$
$888$	−35.3534	−	8.09251i	−1.18638	−	0.271567i
$889$	−31.8219			−1.06727
$890$		0			0
$891$	−17.9857	+	24.3247i	−0.602542	+	0.814907i
$892$	31.1047	−	28.4867i	1.04146	−	0.953805i
$893$		−	1.59885i		−	0.0535034i
$894$	21.2553	+	30.7855i	0.710884	+	1.02962i
$895$		0			0
$896$	−6.72263	−	27.5863i	−0.224587	−	0.921595i
$897$	17.4031	−	28.2665i	0.581073	−	0.943790i
$898$	−16.9477	+	38.5023i	−0.565551	+	1.28484i
$899$	7.72577			0.257669
$900$		0			0
$901$	17.4031			0.579782
$902$	−5.89543	+	13.3935i	−0.196296	+	0.445953i
$903$	−19.1647	+	31.1277i	−0.637763	+	1.03587i
$904$	2.14141	−	0.725940i	0.0712222	−	0.0241444i
$905$		0			0
$906$	26.8996	+	38.9606i	0.893680	+	1.29438i
$907$		−	0.880344i		−	0.0292314i	−0.999893	−	0.0146157i	$-0.995348\pi$
$907$		−	0.880344i		−	0.0292314i	0.999893	−	0.0146157i	$-0.00465248\pi$
$908$	−30.0617	−	32.8244i	−0.997633	−	1.08932i
$909$	−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	$0.489419\pi$
$912$	1.82042	−	2.44666i	0.0602801	−	0.0810170i
$913$	6.10469			0.202036
$914$	46.7328	+	20.5705i	1.54578	+	0.680411i
$915$		0			0
$916$	3.10469	+	3.39001i	0.102582	+	0.112009i
$917$		−	14.3540i		−	0.474011i
$918$	−26.8768	+	49.2605i	−0.887068	+	1.62584i
$919$		−	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
$922$	10.0000	−	22.7184i	0.329332	−	0.748190i
$923$	−46.0553			−1.51593
$924$	5.50814	+	28.6986i	0.181204	+	0.944115i
$925$		0			0
$926$	−2.85974	+	6.49687i	−0.0939770	+	0.213501i
$927$	−29.2487	+	14.7492i	−0.960653	+	0.484427i
$928$	11.2984	+	6.20849i	0.370889	+	0.203804i
$929$		−	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
$932$	−12.4421	+	11.3949i	−0.407555	+	0.373252i
$933$	−12.2094	+	19.8307i	−0.399717	+	0.649228i
$934$	38.2094	+	16.8187i	1.25025	+	0.550325i
$935$		0			0
$936$	−22.0198	+	22.3974i	−0.719738	+	0.732081i
$937$	34.6125			1.13074			0.565370	−	0.824837i	$-0.308733\pi$
$937$	34.6125			1.13074			0.565370	+	0.824837i	$0.308733\pi$
$938$	17.7349	+	7.80640i	0.579064	+	0.254888i
$939$	14.8003	−	24.0389i	0.482989	−	0.784480i
$940$		0			0
$941$		−	53.5738i		−	1.74646i	−0.487311	−	0.873229i	$-0.662022\pi$
$941$		−	53.5738i		−	1.74646i	0.487311	−	0.873229i	$-0.337978\pi$
$942$	22.3839	−	15.4546i	0.729308	−	0.503537i
$943$		−	15.9384i		−	0.519024i
$944$		0			0
$945$		0			0
$946$	−16.1047	+	36.5872i	−0.523609	+	1.18955i
$947$	−18.0807			−0.587545			−0.293772	−	0.955875i	$-0.594911\pi$
$947$	−18.0807			−0.587545			−0.293772	+	0.955875i	$0.594911\pi$
$948$	−3.27737	−	17.0758i	−0.106444	−	0.554597i
$949$	−4.80625			−0.156017
$950$		0			0
$951$	−24.8842	−	15.3207i	−0.806927	−	0.496809i
$952$	17.4031	+	51.3364i	0.564038	+	1.66382i
$953$		−	42.0596i		−	1.36245i	−0.732076	−	0.681223i	$-0.761448\pi$
$953$		−	42.0596i		−	1.36245i	0.732076	−	0.681223i	$-0.238552\pi$
$954$	9.65562	−	0.506474i	0.312612	−	0.0163977i
$955$		0			0
$956$	−34.9682	−	38.1818i	−1.13095	−	1.23489i
$957$	−11.2984	−	6.95623i	−0.365227	−	0.224863i
$958$	43.5078	+	19.1509i	1.40567	+	0.618738i
$959$	−24.8842			−0.803554
$960$		0			0
$961$	19.5078			0.629284
$962$	35.4697	+	15.6128i	1.14359	+	0.503377i
$963$	−8.71473	−	17.2819i	−0.280828	−	0.556902i
$964$	9.45547	+	10.3244i	0.304540	+	0.332528i
$965$		0			0
$966$	−18.0836	−	26.1917i	−0.581831	−	0.842706i
$967$			1.49796i			0.0481712i	0.999710	+	0.0240856i	$0.00766742\pi$
$967$			1.49796i			0.0481712i	−0.999710	+	0.0240856i	$0.992333\pi$
$968$	0.271006	+	0.799423i	0.00871045	+	0.0256944i
$969$	−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	$0.224839\pi$
$972$	−13.4782	+	28.1129i	−0.432315	+	0.901723i
$973$	−7.40312			−0.237333
$974$	−0.0748440	+	0.170034i	−0.00239816	+	0.00544823i
$975$		0			0
$976$	2.00000	−	22.7184i	0.0640184	−	0.727198i
$977$		−	19.0313i		−	0.608864i	−0.952534	−	0.304432i	$-0.901533\pi$
$977$		−	19.0313i		−	0.608864i	0.952534	−	0.304432i	$-0.0984667\pi$
$978$	0.612595	+	0.887263i	0.0195886	+	0.0283716i
$979$		−	18.0079i		−	0.575534i
$980$		0			0
$981$	−3.10469	−	6.15681i	−0.0991250	−	0.196572i
$982$	−17.4031	−	7.66037i	−0.555356	−	0.244452i
$983$	57.0331			1.81907			0.909537	−	0.415623i	$-0.136437\pi$
$983$	57.0331			1.81907			0.909537	+	0.415623i	$0.136437\pi$
$984$	−3.36507	+	14.7008i	−0.107274	+	0.468645i
$985$		0			0
$986$	−22.5261	−	9.91534i	−0.717376	−	0.315769i
$987$	13.4453	+	8.27799i	0.427967	+	0.263491i
$988$	−2.40312	+	2.20086i	−0.0764536	+	0.0700187i
$989$		−	43.5392i		−	1.38447i
$990$		0			0
$991$		−	44.4251i		−	1.41121i	−0.708606	−	0.705604i	$-0.750676\pi$
$991$		−	44.4251i		−	1.41121i	0.708606	−	0.705604i	$-0.249324\pi$
$992$	−16.8066	−	9.23521i	−0.533609	−	0.293218i
$993$	−25.2617	−	15.5532i	−0.801656	−	0.493564i
$994$	−17.7906	+	40.4174i	−0.564284	+	1.28196i
$995$		0			0
$996$	6.17859	−	1.18586i	0.195776	−	0.0375754i
$997$	−47.4031			−1.50127			−0.750636	−	0.660716i	$-0.770253\pi$
$997$	−47.4031			−1.50127			−0.750636	+	0.660716i	$0.770253\pi$
$998$	22.9528	−	52.1450i	0.726558	−	1.65062i
$999$	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.e.e.251.8	yes	8
3.2	odd	2	inner	300.2.e.e.251.1	yes	8
4.3	odd	2	inner	300.2.e.e.251.2	yes	8
5.2	odd	4		300.2.h.c.299.7		16
5.3	odd	4		300.2.h.c.299.10		16
5.4	even	2		300.2.e.d.251.1	✓	8
12.11	even	2	inner	300.2.e.e.251.7	yes	8
15.2	even	4		300.2.h.c.299.9		16
15.8	even	4		300.2.h.c.299.8		16
15.14	odd	2		300.2.e.d.251.8	yes	8
20.3	even	4		300.2.h.c.299.11		16
20.7	even	4		300.2.h.c.299.6		16
20.19	odd	2		300.2.e.d.251.7	yes	8
60.23	odd	4		300.2.h.c.299.5		16
60.47	odd	4		300.2.h.c.299.12		16
60.59	even	2		300.2.e.d.251.2	yes	8

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

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.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.29437 + 0.569745i) q^{2} +(0.908080 - 1.47492i) q^{3} +(1.35078 + 1.47492i) q^{4} +(2.01572 - 1.39172i) q^{6} +2.50967i q^{7} +(0.908080 + 2.67869i) q^{8} +(-1.35078 - 2.67869i) q^{9} +O(q^{10})\)	\(q+(1.29437 + 0.569745i) q^{2} +(0.908080 - 1.47492i) q^{3} +(1.35078 + 1.47492i) q^{4} +(2.01572 - 1.39172i) q^{6} +2.50967i q^{7} +(0.908080 + 2.67869i) q^{8} +(-1.35078 - 2.67869i) q^{9} +3.36131 q^{11} +(3.40201 - 0.652949i) q^{12} -3.70156 q^{13} +(-1.42987 + 3.24844i) q^{14} +(-0.350781 + 3.98459i) q^{16} -7.63636i q^{17} +(-0.222237 - 4.23682i) q^{18} -0.440172i q^{19} +(3.70156 + 2.27898i) q^{21} +(4.35078 + 1.91509i) q^{22} -5.17748 q^{23} +(4.77547 + 1.09312i) q^{24} +(-4.79119 - 2.10895i) q^{26} +(-5.17748 - 0.440172i) q^{27} +(-3.70156 + 3.39001i) q^{28} -2.27898i q^{29} +3.39001i q^{31} +(-2.72424 + 4.95767i) q^{32} +(3.05234 - 4.95767i) q^{33} +(4.35078 - 9.88427i) q^{34} +(2.12625 - 5.61062i) q^{36} -7.40312 q^{37} +(0.250786 - 0.569745i) q^{38} +(-3.36131 + 5.45951i) q^{39} +3.07840i q^{41} +(3.49275 + 5.05879i) q^{42} +8.40935i q^{43} +(4.54040 + 4.95767i) q^{44} +(-6.70156 - 2.94984i) q^{46} +3.63232 q^{47} +(5.55842 + 4.13570i) q^{48} +0.701562 q^{49} +(-11.2630 - 6.93443i) q^{51} +(-5.00000 - 5.45951i) q^{52} +2.27898i q^{53} +(-6.45078 - 3.51959i) q^{54} +(-6.72263 + 2.27898i) q^{56} +(-0.649219 - 0.399712i) q^{57} +(1.29844 - 2.94984i) q^{58} -5.70156 q^{61} +(-1.93144 + 4.38793i) q^{62} +(6.72263 - 3.39001i) q^{63} +(-6.35078 + 4.86493i) q^{64} +(6.77547 - 4.67800i) q^{66} -5.45951i q^{67} +(11.2630 - 10.3151i) q^{68} +(-4.70156 + 7.63636i) q^{69} +12.4421 q^{71} +(5.94877 - 6.05079i) q^{72} +1.29844 q^{73} +(-9.58237 - 4.21789i) q^{74} +(0.649219 - 0.594576i) q^{76} +8.43579i q^{77} +(-7.46131 + 5.15153i) q^{78} -5.01934i q^{79} +(-5.35078 + 7.23665i) q^{81} +(-1.75391 + 3.98459i) q^{82} +1.81616 q^{83} +(1.63869 + 8.53791i) q^{84} +(-4.79119 + 10.8848i) q^{86} +(-3.36131 - 2.06950i) q^{87} +(3.05234 + 9.00393i) q^{88} -5.35738i q^{89} -9.28970i q^{91} +(-6.99364 - 7.63636i) q^{92} +(5.00000 + 3.07840i) q^{93} +(4.70156 + 2.06950i) q^{94} +(4.83834 + 8.52000i) q^{96} +11.1047 q^{97} +(0.908080 + 0.399712i) q^{98} +(-4.54040 - 9.00393i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{4} + 3 q^{6} + 2 q^{9}+O(q^{10}) \) 8 * q - 2 * q^4 + 3 * q^6 + 2 * q^9	\( 8 q - 2 q^{4} + 3 q^{6} + 2 q^{9} + 11 q^{12} - 4 q^{13} + 10 q^{16} - 7 q^{18} + 4 q^{21} + 22 q^{22} + 13 q^{24} - 4 q^{28} - 14 q^{33} + 22 q^{34} - 21 q^{36} - 8 q^{37} - 36 q^{42} - 28 q^{46} + 15 q^{48} - 20 q^{49} - 40 q^{52} - 28 q^{54} - 18 q^{57} + 36 q^{58} - 20 q^{61} - 38 q^{64} + 29 q^{66} - 12 q^{69} + 51 q^{72} + 36 q^{73} + 18 q^{76} - 22 q^{78} - 30 q^{81} + 50 q^{82} + 40 q^{84} - 14 q^{88} + 40 q^{93} + 12 q^{94} - 39 q^{96} + 12 q^{97}+O(q^{100}) \) 8 * q - 2 * q^4 + 3 * q^6 + 2 * q^9 + 11 * q^12 - 4 * q^13 + 10 * q^16 - 7 * q^18 + 4 * q^21 + 22 * q^22 + 13 * q^24 - 4 * q^28 - 14 * q^33 + 22 * q^34 - 21 * q^36 - 8 * q^37 - 36 * q^42 - 28 * q^46 + 15 * q^48 - 20 * q^49 - 40 * q^52 - 28 * q^54 - 18 * q^57 + 36 * q^58 - 20 * q^61 - 38 * q^64 + 29 * q^66 - 12 * q^69 + 51 * q^72 + 36 * q^73 + 18 * q^76 - 22 * q^78 - 30 * q^81 + 50 * q^82 + 40 * q^84 - 14 * q^88 + 40 * q^93 + 12 * q^94 - 39 * q^96 + 12 * q^97

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