LMFDB - Embedded newform 300.2.h.c.299.9

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			299.9
Root			$-0.869987 - 1.05054i$ of defining polynomial
Character	$\chi$	$=$	300.299
Dual form			300.2.h.c.299.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.569745 - 1.29437i) q^{2} +(-1.47492 + 0.908080i) q^{3} +(-1.35078 - 1.47492i) q^{4} +(0.335062 + 2.42647i) q^{6} -2.50967 q^{7} +(-2.67869 + 0.908080i) q^{8} +(1.35078 - 2.67869i) q^{9} +O(q^{10})$	\(q+(0.569745 - 1.29437i) q^{2} +(-1.47492 + 0.908080i) q^{3} +(-1.35078 - 1.47492i) q^{4} +(0.335062 + 2.42647i) q^{6} -2.50967 q^{7} +(-2.67869 + 0.908080i) q^{8} +(1.35078 - 2.67869i) q^{9} -3.36131 q^{11} +(3.33164 + 0.948773i) q^{12} +3.70156i q^{13} +(-1.42987 + 3.24844i) q^{14} +(-0.350781 + 3.98459i) q^{16} -7.63636 q^{17} +(-2.69761 - 3.27458i) q^{18} +0.440172i q^{19} +(3.70156 - 2.27898i) q^{21} +(-1.91509 + 4.35078i) q^{22} -5.17748i q^{23} +(3.12625 - 3.77181i) 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} +(-5.77547 + 1.62603i) q^{36} -7.40312i q^{37} +(0.569745 + 0.250786i) q^{38} +(-3.36131 - 5.45951i) q^{39} -3.07840i q^{41} +(-0.840894 - 6.08962i) q^{42} +8.40935 q^{43} +(4.54040 + 4.95767i) q^{44} +(-6.70156 - 2.94984i) q^{46} -3.63232i q^{47} +(-3.10095 - 6.19549i) q^{48} -0.701562 q^{49} +(11.2630 - 6.93443i) q^{51} +(5.45951 - 5.00000i) q^{52} -2.27898 q^{53} +(6.95235 + 2.38010i) 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} +(-1.12625 - 8.15611i) q^{66} +5.45951 q^{67} +(10.3151 + 11.2630i) q^{68} +(4.70156 + 7.63636i) q^{69} -12.4421 q^{71} +(-1.18586 + 8.40201i) q^{72} -1.29844i q^{73} +(-9.58237 - 4.21789i) q^{74} +(0.649219 - 0.594576i) q^{76} +8.43579 q^{77} +(-8.98171 + 1.24025i) q^{78} +5.01934i q^{79} +(-5.35078 - 7.23665i) q^{81} +(-3.98459 - 1.75391i) q^{82} +1.81616i q^{83} +(-8.36131 - 2.38111i) 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} +(-9.78600 + 0.483926i) 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
$6$	0.335062	+	2.42647i	0.136788	+	0.990600i
$7$	−2.50967			−0.948566			−0.474283	−	0.880373i	$-0.657293\pi$
$7$	−2.50967			−0.948566			−0.474283	+	0.880373i	$0.657293\pi$
$8$	−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	$-0.669149\pi$
$11$	−3.36131			−1.01347			−0.506737	+	0.862101i	$0.669149\pi$
$12$	3.33164	+	0.948773i	0.961762	+	0.273887i
$13$			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	$0.876814\pi$
$18$	−2.69761	−	3.27458i	−0.635834	−	0.771826i
$19$			0.440172i			0.100982i	0.998725	+	0.0504912i	$0.0160787\pi$
$19$			0.440172i			0.100982i	−0.998725	+	0.0504912i	$0.983921\pi$
$20$		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	$-0.818504\pi$
$23$		−	5.17748i		−	1.07958i	0.841800	−	0.539789i	$-0.181496\pi$
$24$	3.12625	−	3.77181i	0.638143	−	0.769918i
$25$		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	$0.0984667\pi$
$31$			3.39001i			0.608864i	−0.952534	+	0.304432i	$0.901533\pi$
$32$	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
$36$	−5.77547	+	1.62603i	−0.962578	+	0.271005i
$37$		−	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	$-0.0772730\pi$
$42$	−0.840894	−	6.08962i	−0.129753	−	0.939649i
$43$	8.40935			1.28241			0.641207	−	0.767368i	$-0.278434\pi$
$43$	8.40935			1.28241			0.641207	+	0.767368i	$0.278434\pi$
$44$	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	$-0.914656\pi$
$47$		−	3.63232i		−	0.529828i	0.964272	−	0.264914i	$-0.0853436\pi$
$48$	−3.10095	−	6.19549i	−0.447584	−	0.894242i
$49$	−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	$0.550028\pi$
$54$	6.95235	+	2.38010i	0.946095	+	0.323890i
$55$		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
$66$	−1.12625	−	8.15611i	−0.138632	−	1.00395i
$67$	5.45951			0.666985			0.333493	−	0.942753i	$-0.391773\pi$
$67$	5.45951			0.666985			0.333493	+	0.942753i	$0.391773\pi$
$68$	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	$-0.764373\pi$
$71$	−12.4421			−1.47661			−0.738304	+	0.674468i	$0.764373\pi$
$72$	−1.18586	+	8.40201i	−0.139755	+	0.990186i
$73$		−	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
$78$	−8.98171	+	1.24025i	−1.01698	+	0.140431i
$79$			5.01934i			0.564720i	0.959309	+	0.282360i	$0.0911172\pi$
$79$			5.01934i			0.564720i	−0.959309	+	0.282360i	$0.908883\pi$
$80$		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	$0.0317802\pi$
$83$			1.81616i			0.199349i	−0.995020	+	0.0996747i	$0.968220\pi$
$84$	−8.36131	−	2.38111i	−0.912294	−	0.259800i
$85$		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
$96$	−9.78600	+	0.483926i	−0.998780	+	0.0493905i
$97$			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	$0.662021\pi$
$102$	−2.55865	−	18.5294i	−0.253344	−	1.83468i
$103$	−10.9190			−1.07588			−0.537941	−	0.842982i	$-0.680798\pi$
$103$	−10.9190			−1.07588			−0.537941	+	0.842982i	$0.680798\pi$
$104$	−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	$-0.899051\pi$
$107$		−	6.45162i		−	0.623702i	0.950131	−	0.311851i	$-0.100949\pi$
$108$	7.04179	−	7.64285i	0.677596	−	0.735434i
$109$	−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	$0.488028\pi$
$114$	−1.06806	+	0.147485i	−0.100033	+	0.0138132i
$115$		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
$126$	6.77012	+	8.21811i	0.603130	+	0.732128i
$127$	−12.6797			−1.12514			−0.562571	−	0.826749i	$-0.690188\pi$
$127$	−12.6797			−1.12514			−0.562571	+	0.826749i	$0.690188\pi$
$128$	−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	$-0.419616\pi$
$131$	5.71949			0.499714			0.249857	+	0.968283i	$0.419616\pi$
$132$	−11.1987	−	3.18913i	−0.974721	−	0.277578i
$133$		−	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	$0.360779\pi$
$138$	12.5630	−	1.73477i	1.06943	−	0.147674i
$139$		−	2.94984i		−	0.250202i	−0.992144	−	0.125101i	$-0.960074\pi$
$139$		−	2.94984i		−	0.250202i	0.992144	−	0.125101i	$-0.0399255\pi$
$140$		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
$144$	10.1997	+	6.32194i	0.849972	+	0.526829i
$145$		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	$0.288089\pi$
$151$			19.3284i			1.57292i	−0.617641	+	0.786460i	$0.711911\pi$
$152$	−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
$156$	−3.51194	+	12.3323i	−0.281180	+	0.987372i
$157$			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
$162$	−12.4155	+	2.80284i	−0.975452	+	0.220212i
$163$	0.440172			0.0344769			0.0172385	−	0.999851i	$-0.494513\pi$
$163$	0.440172			0.0344769			0.0172385	+	0.999851i	$0.494513\pi$
$164$	−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	$-0.794782\pi$
$167$		−	15.5324i		−	1.20194i	0.799273	−	0.600968i	$-0.205218\pi$
$168$	−7.84585	+	9.46600i	−0.605320	+	0.730318i
$169$	−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	$0.603912\pi$
$174$	5.52987	−	0.763599i	0.419218	−	0.0578883i
$175$		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	$-0.610212\pi$
$179$	−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	$0.372295\pi$
$182$	−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
$186$	−8.22575	+	1.13586i	−0.603141	+	0.0832856i
$187$	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	$-0.648626\pi$
$191$	−12.4421			−0.900280			−0.450140	+	0.892958i	$0.648626\pi$
$192$	−4.94915	+	12.9424i	−0.357174	+	0.934038i
$193$		−	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	$0.624660\pi$
$198$	9.06753	+	11.0069i	0.644401	+	0.782226i
$199$		−	21.0891i		−	1.49496i	−0.664282	−	0.747482i	$-0.731263\pi$
$199$		−	21.0891i		−	1.49496i	0.664282	−	0.747482i	$-0.268737\pi$
$200$		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
$204$	−25.4416	−	7.24518i	−1.78127	−	0.507264i
$205$		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	$-0.785353\pi$
$211$		−	18.1392i		−	1.24876i	0.781123	−	0.624378i	$-0.214647\pi$
$212$	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
$216$	−5.88065	−	13.4691i	−0.400127	−	0.916460i
$217$		−	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
$222$	17.9634	−	2.48050i	1.20563	−	0.166481i
$223$	−21.0891			−1.41223			−0.706114	−	0.708098i	$-0.749553\pi$
$223$	−21.0891			−1.41223			−0.706114	+	0.708098i	$0.749553\pi$
$224$	−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	$0.264494\pi$
$227$			22.2551i			1.47712i	−0.674188	+	0.738560i	$0.735506\pi$
$228$	−0.417624	+	1.46650i	−0.0276578	+	0.0971210i
$229$	−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	$0.589116\pi$
$234$	12.1211	−	9.98539i	0.792379	−	0.652765i
$235$		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	$-0.815842\pi$
$239$	−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	$0.427613\pi$
$242$	0.170034	−	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
$246$	7.46964	−	1.03146i	0.476247	−	0.0657632i
$247$	−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	$-0.248281\pi$
$251$	22.5261			1.42183			0.710916	+	0.703277i	$0.248281\pi$
$252$	14.4945	−	4.08080i	0.913068	−	0.257066i
$253$			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	$0.545404\pi$
$258$	2.81765	+	20.4050i	0.175419	+	1.27036i
$259$			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	$0.194673\pi$
$263$			18.6227i			1.14833i	−0.818741	+	0.574164i	$0.805327\pi$
$264$	−10.5083	+	12.6783i	−0.646741	+	0.780292i
$265$		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	$-0.910274\pi$
$271$		−	9.15833i		−	0.556329i	0.960533	−	0.278165i	$-0.0897260\pi$
$272$	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
$276$	4.91225	−	17.2495i	0.295683	−	1.03830i
$277$		−	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	$-0.175383\pi$
$282$	8.81370	−	1.21705i	0.524848	−	0.0724744i
$283$	16.3785			0.973603			0.486801	−	0.873513i	$-0.338164\pi$
$283$	16.3785			0.973603			0.486801	+	0.873513i	$0.338164\pi$
$284$	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
$288$	13.9941	−	9.60022i	0.824612	−	0.565699i
$289$	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	$0.284706\pi$
$294$	−0.235067	−	1.70232i	−0.0137094	−	0.0992811i
$295$		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
$306$	20.6000	+	25.0059i	1.17762	+	1.42949i
$307$	−26.4172			−1.50771			−0.753855	−	0.657041i	$-0.771808\pi$
$307$	−26.4172			−1.50771			−0.753855	+	0.657041i	$0.771808\pi$
$308$	−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	$-0.375509\pi$
$311$	13.4453			0.762411			0.381205	+	0.924490i	$0.375509\pi$
$312$	13.9616	+	11.5720i	0.790420	+	0.655136i
$313$		−	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	$0.657118\pi$
$318$	−0.763599	−	5.52987i	−0.0428205	−	0.310100i
$319$			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
$324$	−3.44575	+	17.6671i	−0.191431	+	0.981506i
$325$		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	$-0.843999\pi$
$331$		−	17.1275i		−	0.941413i	0.882290	−	0.470707i	$-0.156001\pi$
$332$	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
$336$	7.78236	+	15.5486i	0.424563	+	0.848247i
$337$		−	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
$342$	1.44138	−	1.18741i	0.0779409	−	0.0642080i
$343$	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	$0.174696\pi$
$347$			19.4358i			1.04337i	−0.853139	+	0.521683i	$0.825304\pi$
$348$	2.16224	−	7.59274i	0.115908	−	0.407014i
$349$	−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	$-0.565354\pi$
$359$	−7.72577			−0.407751			−0.203875	+	0.978997i	$0.565354\pi$
$360$		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
$366$	−1.91038	−	13.8346i	−0.0998569	−	0.723148i
$367$	−2.50967			−0.131004			−0.0655018	−	0.997852i	$-0.520865\pi$
$367$	−2.50967			−0.131004			−0.0655018	+	0.997852i	$0.520865\pi$
$368$	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
$372$	−3.21635	+	11.2943i	−0.166760	+	0.585582i
$373$			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
$378$	−17.4481	−	5.97325i	−0.897433	−	0.307231i
$379$		−	13.1199i		−	0.673923i	−0.941518	−	0.336961i	$-0.890601\pi$
$379$		−	13.1199i		−	0.673923i	0.941518	−	0.336961i	$-0.109399\pi$
$380$		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	$-0.940576\pi$
$383$		−	7.26464i		−	0.371206i	0.982625	−	0.185603i	$-0.0594238\pi$
$384$	13.9325	+	13.7799i	0.710990	+	0.703202i
$385$		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
$396$	19.4132	−	5.46560i	0.975548	−	0.274657i
$397$		−	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	$0.925934\pi$
$402$	1.82927	+	13.2473i	0.0912359	+	0.660716i
$403$	−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
$408$	−23.8732	+	28.8029i	−1.18190	+	1.42596i
$409$	−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
$414$	−16.9541	+	13.9668i	−0.833247	+	0.686432i
$415$		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	$-0.825924\pi$
$419$	−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	$0.612549\pi$
$422$	−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
$426$	−4.16888	−	30.1904i	−0.201983	−	1.46273i
$427$	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	$-0.456013\pi$
$431$	5.71949			0.275498			0.137749	+	0.990467i	$0.456013\pi$
$432$	−20.7845	−	0.0622549i	−0.999996	−	0.00299524i
$433$			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
$438$	3.15061	−	0.435057i	0.150542	−	0.0207878i
$439$		−	23.4674i		−	1.12004i	−0.828480	−	0.560018i	$-0.810794\pi$
$439$		−	23.4674i		−	1.12004i	0.828480	−	0.560018i	$-0.189206\pi$
$440$		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	$0.250267\pi$
$443$			29.7907i			1.41540i	−0.706514	+	0.707699i	$0.749733\pi$
$444$	7.02389	−	24.6645i	0.333339	−	1.17053i
$445$		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
$456$	1.66025	+	1.37609i	0.0777482	+	0.0644412i
$457$			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	$0.865971\pi$
$462$	2.82651	+	20.4691i	0.131501	+	0.952311i
$463$	5.01934			0.233268			0.116634	−	0.993175i	$-0.462789\pi$
$463$	5.01934			0.233268			0.116634	+	0.993175i	$0.462789\pi$
$464$	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	$-0.760673\pi$
$467$		−	29.5197i		−	1.36601i	0.730414	−	0.683004i	$-0.239327\pi$
$468$	−6.01886	−	21.3783i	−0.278222	−	0.988210i
$469$	−13.7016			−0.632679
$470$		0			0
$471$	−10.0839	−	16.3785i	−0.464644	−	0.754683i
$472$		0			0
$473$	−28.2665			−1.29969
$474$	−12.1792	+	1.68179i	−0.559411	+	0.0772471i
$475$		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	$-0.221296\pi$
$479$	33.6131			1.53582			0.767912	+	0.640555i	$0.221296\pi$
$480$		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
$486$	15.7666	−	15.4082i	0.715189	−	0.698931i
$487$	−0.131364			−0.00595267			−0.00297634	−	0.999996i	$-0.500947\pi$
$487$	−0.131364			−0.00595267			−0.00297634	+	0.999996i	$0.500947\pi$
$488$	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	$-0.401882\pi$
$491$	13.4453			0.606776			0.303388	+	0.952867i	$0.401882\pi$
$492$	2.92071	−	10.2561i	0.131676	−	0.462382i
$493$			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
$498$	−4.40685	+	0.608526i	−0.197476	+	0.0272687i
$499$			40.2861i			1.80345i	0.432308	+	0.901726i	$0.357699\pi$
$499$			40.2861i			1.80345i	−0.432308	+	0.901726i	$0.642301\pi$
$500$		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	$0.0934780\pi$
$503$			12.9841i			0.578934i	−0.957188	+	0.289467i	$0.906522\pi$
$504$	2.97611	−	21.0863i	0.132567	−	0.939257i
$505$		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
$516$	28.0169	+	7.97857i	1.23338	+	0.351237i
$517$			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	$0.978519\pi$
$522$	−7.46270	+	6.14781i	−0.326634	+	0.269082i
$523$	14.0002			0.612187			0.306094	−	0.952001i	$-0.400978\pi$
$523$	14.0002			0.612187			0.306094	+	0.952001i	$0.400978\pi$
$524$	−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
$528$	10.4233	+	20.8250i	0.453615	+	0.906291i
$529$	−3.80625			−0.165489
$530$		0			0
$531$		0			0
$532$	−1.62932	+	1.49219i	−0.0706402	+	0.0646946i
$533$	11.3949			0.493568
$534$	12.9995	−	1.79505i	0.562544	−	0.0776796i
$535$		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
$546$	22.5411	−	3.11262i	0.964671	−	0.133208i
$547$	−4.71053			−0.201408			−0.100704	−	0.994916i	$-0.532109\pi$
$547$	−4.71053			−0.201408			−0.100704	+	0.994916i	$0.532109\pi$
$548$	−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
$552$	−19.5285	−	16.1861i	−0.831187	−	0.688925i
$553$		−	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	$0.216456\pi$
$558$	11.1009	−	9.14495i	0.469937	−	0.387137i
$559$			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	$-0.836335\pi$
$563$		−	23.3391i		−	0.983625i	0.870701	−	0.491812i	$-0.163665\pi$
$564$	3.44625	−	12.1016i	0.145113	−	0.509569i
$565$		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	$0.115406\pi$
$571$			16.9501i			0.709338i	−0.934992	+	0.354669i	$0.884594\pi$
$572$	−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
$576$	−4.45314	−	23.5832i	−0.185548	−	0.982635i
$577$		−	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
$582$	−26.9451	+	3.72076i	−1.11691	+	0.154230i
$583$	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	$0.223845\pi$
$587$			31.3359i			1.29337i	−0.762758	+	0.646685i	$0.776155\pi$
$588$	−2.33735	−	0.665623i	−0.0963908	−	0.0274498i
$589$	−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	$0.569807\pi$
$594$	−23.3690	−	8.00025i	−0.958843	−	0.328254i
$595$		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
$606$	−42.5886	+	5.88091i	−1.73004	+	0.238896i
$607$	3.25865			0.132264			0.0661322	−	0.997811i	$-0.478934\pi$
$607$	3.25865			0.132264			0.0661322	+	0.997811i	$0.478934\pi$
$608$	−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
$612$	44.1036	−	12.4170i	1.78278	−	0.501926i
$613$		−	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	$0.646814\pi$
$618$	−3.65855	−	26.4946i	−0.147168	−	1.06577i
$619$		−	5.15070i		−	0.207024i	−0.994628	−	0.103512i	$-0.966992\pi$
$619$		−	5.15070i		−	0.207024i	0.994628	−	0.103512i	$-0.0330080\pi$
$620$		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
$624$	22.9330	−	11.4784i	0.918054	−	0.459502i
$625$		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	$-0.684350\pi$
$631$		−	42.0468i		−	1.67385i	0.547314	−	0.836927i	$-0.315650\pi$
$632$	−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
$636$	−7.59274	−	2.16224i	−0.301072	−	0.0857382i
$637$		−	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	$-0.0781903\pi$
$642$	15.6546	−	2.16169i	0.617839	−	0.0853152i
$643$	−24.4791			−0.965360			−0.482680	−	0.875797i	$-0.660337\pi$
$643$	−24.4791			−0.965360			−0.482680	+	0.875797i	$0.660337\pi$
$644$	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	$0.0652472\pi$
$647$			10.3550i			0.407095i	−0.979065	+	0.203548i	$0.934753\pi$
$648$	20.9046	+	14.5258i	0.821208	+	0.570628i
$649$		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	$0.669794\pi$
$654$	−0.770119	−	5.57708i	−0.0301140	−	0.218081i
$655$		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	$-0.393846\pi$
$659$	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	$0.613839\pi$
$662$	−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
$666$	−24.2421	+	19.9708i	−0.939363	+	0.773852i
$667$	−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
$672$	24.5596	−	1.21449i	0.947408	−	0.0468501i
$673$		−	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	$0.419670\pi$
$678$	0.267856	+	1.93977i	0.0102870	+	0.0744965i
$679$		−	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	$0.0714177\pi$
$683$			11.6291i			0.444975i	−0.974936	+	0.222488i	$0.928582\pi$
$684$	−0.715734	−	2.54220i	−0.0273668	−	0.0972034i
$685$		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	$-0.992800\pi$
$691$		−	1.18915i		−	0.0452375i	0.999744	−	0.0226187i	$-0.00720038\pi$
$692$	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
$696$	−8.59589	−	7.12466i	−0.325826	−	0.270059i
$697$			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	$0.930963\pi$
$702$	−8.81007	+	25.7345i	−0.332515	+	0.971288i
$703$	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
$714$	6.42137	+	46.5026i	0.240314	+	1.74032i
$715$		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	$-0.806793\pi$
$719$	−44.0490			−1.64275			−0.821375	+	0.570389i	$0.806793\pi$
$720$		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
$726$	0.0999951	+	0.724149i	0.00371117	+	0.0268757i
$727$	40.5488			1.50387			0.751936	−	0.659236i	$-0.229120\pi$
$727$	40.5488			1.50387			0.751936	+	0.659236i	$0.229120\pi$
$728$	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
$732$	−18.9956	−	5.40949i	−0.702096	−	0.199940i
$733$		−	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
$738$	−10.0805	+	8.30435i	−0.371068	+	0.305687i
$739$		−	29.2357i		−	1.07545i	−0.843120	−	0.537726i	$-0.819283\pi$
$739$		−	29.2357i		−	1.07545i	0.843120	−	0.537726i	$-0.180717\pi$
$740$		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	$-0.730135\pi$
$743$		−	40.8778i		−	1.49966i	0.661630	−	0.749830i	$-0.269865\pi$
$744$	12.7865	+	10.5980i	0.468776	+	0.388542i
$745$		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	$-0.769746\pi$
$751$		−	36.2784i		−	1.32382i	0.749584	−	0.661909i	$-0.230254\pi$
$752$	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
$756$	−17.6726	+	19.1810i	−0.642745	+	0.697607i
$757$		−	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	$0.878013\pi$
$762$	−4.24849	−	30.7669i	−0.153906	−	1.11457i
$763$	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
$768$	25.7742	−	10.1828i	0.930048	−	0.367439i
$769$	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	$0.513049\pi$
$774$	−22.6852	−	27.5371i	−0.815402	−	0.989800i
$775$		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
$786$	1.91638	+	13.8781i	0.0683551	+	0.495017i
$787$	−18.4480			−0.657601			−0.328801	−	0.944399i	$-0.606644\pi$
$787$	−18.4480			−0.657601			−0.328801	+	0.944399i	$0.606644\pi$
$788$	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
$792$	3.98605	−	28.2418i	0.141638	−	1.00353i
$793$		−	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	$0.801339\pi$
$798$	2.68048	−	0.370138i	0.0948881	−	0.0131028i
$799$			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
$804$	18.1891	+	5.17984i	0.641481	+	0.182679i
$805$		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	$0.212539\pi$
$811$			35.2667i			1.23838i	−0.785240	+	0.619191i	$0.787461\pi$
$812$	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
$816$	23.6800	+	47.3110i	0.828966	+	1.65622i
$817$			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	$-0.0342644\pi$
$822$	3.32225	+	24.0592i	0.115877	+	0.839162i
$823$	6.03105			0.210229			0.105115	−	0.994460i	$-0.466479\pi$
$823$	6.03105			0.210229			0.105115	+	0.994460i	$0.466479\pi$
$824$	29.2487	−	9.91534i	1.01893	−	0.345417i
$825$		0			0
$826$		0			0
$827$		−	20.4389i		−	0.710730i	−0.934728	−	0.355365i	$-0.884357\pi$
$827$		−	20.4389i		−	0.710730i	0.934728	−	0.355365i	$-0.115643\pi$
$828$	8.41874	+	29.9023i	0.292571	+	1.03918i
$829$	−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
$834$	7.15769	−	0.988379i	0.247850	−	0.0342248i
$835$		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	$-0.225018\pi$
$839$	44.0490			1.52074			0.760370	+	0.649490i	$0.225018\pi$
$840$		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
$846$	−11.8943	+	9.79860i	−0.408935	+	0.336883i
$847$	−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
$852$	−41.4527	−	11.8047i	−1.42014	−	0.404424i
$853$			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	$0.679824\pi$
$858$	30.1904	−	4.16888i	1.03068	−	0.142323i
$859$		−	50.7649i		−	1.73208i	−0.499978	−	0.866038i	$-0.666658\pi$
$859$		−	50.7649i		−	1.73208i	0.499978	−	0.866038i	$-0.333342\pi$
$860$		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	$-0.755073\pi$
$863$		−	40.8778i		−	1.39150i	0.718286	−	0.695748i	$-0.244927\pi$
$864$	−11.9225	+	26.8674i	−0.405610	+	0.914046i
$865$		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
$876$	1.23192	−	4.32593i	0.0416228	−	0.146160i
$877$			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	$-0.294510\pi$
$882$	1.89254	+	2.29732i	0.0637253	+	0.0773548i
$883$	−58.5566			−1.97059			−0.985294	−	0.170867i	$-0.945343\pi$
$883$	−58.5566			−1.97059			−0.985294	+	0.170867i	$0.945343\pi$
$884$	−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	$0.0784343\pi$
$887$			14.5293i			0.487846i	−0.969795	+	0.243923i	$0.921566\pi$
$888$	−27.9232	−	23.1440i	−0.937041	−	0.776662i
$889$	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
$894$	−37.0587	+	5.11731i	−1.23943	+	0.171148i
$895$		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
$906$	−46.8996	+	6.47620i	−1.55814	+	0.215157i
$907$	0.880344			0.0292314			0.0146157	−	0.999893i	$-0.495348\pi$
$907$	0.880344			0.0292314			0.0146157	+	0.999893i	$0.495348\pi$
$908$	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	$-0.510581\pi$
$911$	−2.00629			−0.0664713			−0.0332356	+	0.999448i	$0.510581\pi$
$912$	2.72708	−	1.36495i	0.0903027	−	0.0451981i
$913$		−	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
$918$	−53.0907	−	18.1753i	−1.75225	−	0.599874i
$919$			8.40935i			0.277399i	0.990335	+	0.138699i	$0.0442922\pi$
$919$			8.40935i			0.277399i	−0.990335	+	0.138699i	$0.955708\pi$
$920$		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
$924$	28.1050	+	8.00365i	0.924587	+	0.263301i
$925$		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
$936$	−31.1006	−	4.38953i	−1.01655	−	0.143476i
$937$			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	$0.662022\pi$
$942$	−26.9451	+	3.72076i	−0.877920	+	0.121229i
$943$	−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	$0.0949107\pi$
$947$			18.0807i			0.587545i	−0.955875	+	0.293772i	$0.905089\pi$
$948$	−4.76221	+	16.7226i	−0.154669	+	0.543126i
$949$	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	$0.261448\pi$
$954$	6.14781	+	7.46270i	0.199043	+	0.241614i
$955$		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
$966$	−31.5289	+	4.35371i	−1.01443	+	0.140078i
$967$	−1.49796			−0.0481712			−0.0240856	−	0.999710i	$-0.507667\pi$
$967$	−1.49796			−0.0481712			−0.0240856	+	0.999710i	$0.507667\pi$
$968$	−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	$-0.775161\pi$
$971$	−47.4103			−1.52147			−0.760734	+	0.649063i	$0.775161\pi$
$972$	−10.9609	−	29.1866i	−0.351572	−	0.936161i
$973$			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	$0.598467\pi$
$978$	0.147485	+	1.06806i	0.00471605	+	0.0341529i
$979$			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	$0.363563\pi$
$983$			57.0331i			1.81907i	−0.415623	+	0.909537i	$0.636437\pi$
$984$	−11.6112	−	9.62385i	−0.370150	−	0.306797i
$985$		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	$-0.750676\pi$
$991$		−	44.4251i		−	1.41121i	0.708606	−	0.705604i	$-0.249324\pi$
$992$	−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
$996$	−1.72312	+	6.05079i	−0.0545993	+	0.191727i
$997$		−	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.299.9		16
3.2	odd	2	inner	300.2.h.c.299.7		16
4.3	odd	2	inner	300.2.h.c.299.12		16
5.2	odd	4		300.2.e.d.251.8	yes	8
5.3	odd	4		300.2.e.e.251.1	yes	8
5.4	even	2	inner	300.2.h.c.299.8		16
12.11	even	2	inner	300.2.h.c.299.6		16
15.2	even	4		300.2.e.d.251.1	✓	8
15.8	even	4		300.2.e.e.251.8	yes	8
15.14	odd	2	inner	300.2.h.c.299.10		16
20.3	even	4		300.2.e.e.251.7	yes	8
20.7	even	4		300.2.e.d.251.2	yes	8
20.19	odd	2	inner	300.2.h.c.299.5		16
60.23	odd	4		300.2.e.e.251.2	yes	8
60.47	odd	4		300.2.e.d.251.7	yes	8
60.59	even	2	inner	300.2.h.c.299.11		16

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.569745 - 1.29437i) q^{2} +(-1.47492 + 0.908080i) q^{3} +(-1.35078 - 1.47492i) q^{4} +(0.335062 + 2.42647i) q^{6} -2.50967 q^{7} +(-2.67869 + 0.908080i) q^{8} +(1.35078 - 2.67869i) q^{9} +O(q^{10})\)	\(q+(0.569745 - 1.29437i) q^{2} +(-1.47492 + 0.908080i) q^{3} +(-1.35078 - 1.47492i) q^{4} +(0.335062 + 2.42647i) q^{6} -2.50967 q^{7} +(-2.67869 + 0.908080i) q^{8} +(1.35078 - 2.67869i) q^{9} -3.36131 q^{11} +(3.33164 + 0.948773i) q^{12} +3.70156i q^{13} +(-1.42987 + 3.24844i) q^{14} +(-0.350781 + 3.98459i) q^{16} -7.63636 q^{17} +(-2.69761 - 3.27458i) q^{18} +0.440172i q^{19} +(3.70156 - 2.27898i) q^{21} +(-1.91509 + 4.35078i) q^{22} -5.17748i q^{23} +(3.12625 - 3.77181i) 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} +(-5.77547 + 1.62603i) q^{36} -7.40312i q^{37} +(0.569745 + 0.250786i) q^{38} +(-3.36131 - 5.45951i) q^{39} -3.07840i q^{41} +(-0.840894 - 6.08962i) q^{42} +8.40935 q^{43} +(4.54040 + 4.95767i) q^{44} +(-6.70156 - 2.94984i) q^{46} -3.63232i q^{47} +(-3.10095 - 6.19549i) q^{48} -0.701562 q^{49} +(11.2630 - 6.93443i) q^{51} +(5.45951 - 5.00000i) q^{52} -2.27898 q^{53} +(6.95235 + 2.38010i) 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} +(-1.12625 - 8.15611i) q^{66} +5.45951 q^{67} +(10.3151 + 11.2630i) q^{68} +(4.70156 + 7.63636i) q^{69} -12.4421 q^{71} +(-1.18586 + 8.40201i) q^{72} -1.29844i q^{73} +(-9.58237 - 4.21789i) q^{74} +(0.649219 - 0.594576i) q^{76} +8.43579 q^{77} +(-8.98171 + 1.24025i) q^{78} +5.01934i q^{79} +(-5.35078 - 7.23665i) q^{81} +(-3.98459 - 1.75391i) q^{82} +1.81616i q^{83} +(-8.36131 - 2.38111i) 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} +(-9.78600 + 0.483926i) 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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