LMFDB - Embedded newform 300.2.e.e.251.1

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			251.1
Root			$1.29437 - 0.569745i$ of defining polynomial
Character	$\chi$	$=$	300.251
Dual form			300.2.e.e.251.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.29437 - 0.569745i) q^{2} +(-0.908080 - 1.47492i) q^{3} +(1.35078 + 1.47492i) q^{4} +(0.335062 + 2.42647i) q^{6} +2.50967i q^{7} +(-0.908080 - 2.67869i) q^{8} +(-1.35078 + 2.67869i) q^{9} +O(q^{10})$	\(q+(-1.29437 - 0.569745i) q^{2} +(-0.908080 - 1.47492i) q^{3} +(1.35078 + 1.47492i) q^{4} +(0.335062 + 2.42647i) q^{6} +2.50967i q^{7} +(-0.908080 - 2.67869i) q^{8} +(-1.35078 + 2.67869i) q^{9} -3.36131 q^{11} +(0.948773 - 3.33164i) q^{12} -3.70156 q^{13} +(1.42987 - 3.24844i) q^{14} +(-0.350781 + 3.98459i) q^{16} +7.63636i q^{17} +(3.27458 - 2.69761i) q^{18} -0.440172i q^{19} +(3.70156 - 2.27898i) q^{21} +(4.35078 + 1.91509i) q^{22} +5.17748 q^{23} +(-3.12625 + 3.77181i) 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} +(-5.77547 + 1.62603i) q^{36} -7.40312 q^{37} +(-0.250786 + 0.569745i) q^{38} +(3.36131 + 5.45951i) q^{39} -3.07840i q^{41} +(-6.08962 + 0.840894i) q^{42} +8.40935i q^{43} +(-4.54040 - 4.95767i) q^{44} +(-6.70156 - 2.94984i) q^{46} -3.63232 q^{47} +(6.19549 - 3.10095i) q^{48} +0.701562 q^{49} +(11.2630 - 6.93443i) q^{51} +(-5.00000 - 5.45951i) q^{52} -2.27898i q^{53} +(-6.95235 - 2.38010i) 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} +(-1.12625 - 8.15611i) q^{66} -5.45951i q^{67} +(-11.2630 + 10.3151i) q^{68} +(-4.70156 - 7.63636i) q^{69} -12.4421 q^{71} +(8.40201 + 1.18586i) q^{72} +1.29844 q^{73} +(9.58237 + 4.21789i) q^{74} +(0.649219 - 0.594576i) q^{76} -8.43579i q^{77} +(-1.24025 - 8.98171i) q^{78} -5.01934i q^{79} +(-5.35078 - 7.23665i) q^{81} +(-1.75391 + 3.98459i) q^{82} -1.81616 q^{83} +(8.36131 + 2.38111i) 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} +(-9.78600 + 0.483926i) 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
$6$	0.335062	+	2.42647i	0.136788	+	0.990600i
$7$			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	$-0.669149\pi$
$11$	−3.36131			−1.01347			−0.506737	+	0.862101i	$0.669149\pi$
$12$	0.948773	−	3.33164i	0.273887	−	0.961762i
$13$	−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	$0.376814\pi$
$17$			7.63636i			1.85209i	−0.377413	+	0.926045i	$0.623186\pi$
$18$	3.27458	−	2.69761i	0.771826	−	0.635834i
$19$		−	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	$-0.318504\pi$
$23$	5.17748			1.07958			0.539789	+	0.841800i	$0.318504\pi$
$24$	−3.12625	+	3.77181i	−0.638143	+	0.769918i
$25$		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	$0.0678668\pi$
$29$			2.27898i			0.423196i	−0.977357	+	0.211598i	$0.932133\pi$
$30$		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
$36$	−5.77547	+	1.62603i	−0.962578	+	0.271005i
$37$	−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	$-0.922727\pi$
$41$		−	3.07840i		−	0.480766i	0.970678	−	0.240383i	$-0.0772730\pi$
$42$	−6.08962	+	0.840894i	−0.939649	+	0.129753i
$43$			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	$-0.585344\pi$
$47$	−3.63232			−0.529828			−0.264914	+	0.964272i	$0.585344\pi$
$48$	6.19549	−	3.10095i	0.894242	−	0.447584i
$49$	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	$-0.949972\pi$
$53$		−	2.27898i		−	0.313042i	0.987675	−	0.156521i	$-0.0500279\pi$
$54$	−6.95235	−	2.38010i	−0.946095	−	0.323890i
$55$		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
$66$	−1.12625	−	8.15611i	−0.138632	−	1.00395i
$67$		−	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	$-0.764373\pi$
$71$	−12.4421			−1.47661			−0.738304	+	0.674468i	$0.764373\pi$
$72$	8.40201	+	1.18586i	0.990186	+	0.139755i
$73$	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
$78$	−1.24025	−	8.98171i	−0.140431	−	1.01698i
$79$		−	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	$-0.531780\pi$
$83$	−1.81616			−0.199349			−0.0996747	+	0.995020i	$0.531780\pi$
$84$	8.36131	+	2.38111i	0.912294	+	0.259800i
$85$		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	$0.0916419\pi$
$89$			5.35738i			0.567882i	−0.958842	+	0.283941i	$0.908358\pi$
$90$		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
$96$	−9.78600	+	0.483926i	−0.998780	+	0.0493905i
$97$	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	$0.337979\pi$
$101$			17.5517i			1.74646i	−0.487308	+	0.873230i	$0.662021\pi$
$102$	−18.5294	+	2.55865i	−1.83468	+	0.253344i
$103$		−	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	$-0.600949\pi$
$107$	−6.45162			−0.623702			−0.311851	+	0.950131i	$0.600949\pi$
$108$	7.64285	+	7.04179i	0.735434	+	0.677596i
$109$	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	$0.0119718\pi$
$113$			0.799423i			0.0752034i	−0.999293	+	0.0376017i	$0.988028\pi$
$114$	1.06806	−	0.147485i	0.100033	−	0.0138132i
$115$		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
$126$	6.77012	+	8.21811i	0.603130	+	0.732128i
$127$			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	$-0.419616\pi$
$131$	5.71949			0.499714			0.249857	+	0.968283i	$0.419616\pi$
$132$	−3.18913	+	11.1987i	−0.277578	+	0.974721i
$133$	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	$-0.860779\pi$
$137$		−	9.91534i		−	0.847125i	0.905867	−	0.423563i	$-0.139221\pi$
$138$	1.73477	+	12.5630i	0.147674	+	1.06943i
$139$			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
$144$	−10.1997	−	6.32194i	−0.849972	−	0.526829i
$145$		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	$-0.784856\pi$
$149$		−	15.2727i		−	1.25119i	0.780148	−	0.625595i	$-0.215144\pi$
$150$		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
$156$	−3.51194	+	12.3323i	−0.281180	+	0.987372i
$157$	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
$162$	2.80284	+	12.4155i	0.220212	+	0.975452i
$163$			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	$-0.705218\pi$
$167$	−15.5324			−1.20194			−0.600968	+	0.799273i	$0.705218\pi$
$168$	−9.46600	−	7.84585i	−0.730318	−	0.605320i
$169$	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	$-0.896088\pi$
$173$		−	8.43579i		−	0.641361i	0.947187	−	0.320681i	$-0.103912\pi$
$174$	−5.52987	+	0.763599i	−0.419218	+	0.0578883i
$175$		0			0
$176$	1.17909	−	13.3935i	0.0888769	−	1.00957i
$177$		0			0
$178$	3.05234	−	6.93443i	0.228783	−	0.519758i
$179$	9.08080			0.678731			0.339365	−	0.940655i	$-0.389788\pi$
$179$	9.08080			0.678731			0.339365	+	0.940655i	$0.389788\pi$
$180$		0			0
$181$	10.5078			0.781039			0.390520	−	0.920595i	$-0.372295\pi$
$181$	10.5078			0.781039			0.390520	+	0.920595i	$0.372295\pi$
$182$	−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
$186$	−8.22575	+	1.13586i	−0.603141	+	0.0832856i
$187$		−	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	$-0.648626\pi$
$191$	−12.4421			−0.900280			−0.450140	+	0.892958i	$0.648626\pi$
$192$	12.9424	+	4.94915i	0.934038	+	0.357174i
$193$	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	$0.124660\pi$
$197$			10.7148i			0.763396i	−0.924287	+	0.381698i	$0.875340\pi$
$198$	−11.0069	+	9.06753i	−0.782226	+	0.644401i
$199$			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
$204$	25.4416	+	7.24518i	1.78127	+	0.507264i
$205$		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
$216$	−5.88065	−	13.4691i	−0.400127	−	0.916460i
$217$	−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
$222$	−2.48050	−	17.9634i	−0.166481	−	1.20563i
$223$		−	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	$-0.235506\pi$
$227$	22.2551			1.47712			0.738560	+	0.674188i	$0.235506\pi$
$228$	−1.46650	−	0.417624i	−0.0971210	−	0.0276578i
$229$	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	$-0.910884\pi$
$233$		−	8.43579i		−	0.552647i	0.961065	−	0.276323i	$-0.0891161\pi$
$234$	−12.1211	+	9.98539i	−0.792379	+	0.652765i
$235$		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	$-0.184158\pi$
$239$	25.8874			1.67452			0.837258	+	0.546809i	$0.184158\pi$
$240$		0			0
$241$	7.00000			0.450910			0.225455	−	0.974254i	$-0.427613\pi$
$241$	7.00000			0.450910			0.225455	+	0.974254i	$0.427613\pi$
$242$	−0.386289	−	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
$246$	7.46964	−	1.03146i	0.476247	−	0.0657632i
$247$			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	$-0.248281\pi$
$251$	22.5261			1.42183			0.710916	+	0.703277i	$0.248281\pi$
$252$	−4.08080	−	14.4945i	−0.257066	−	0.913068i
$253$	−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	$0.0454044\pi$
$257$			4.55796i			0.284318i	−0.989844	+	0.142159i	$0.954596\pi$
$258$	−20.4050	+	2.81765i	−1.27036	+	0.175419i
$259$		−	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	$-0.694673\pi$
$263$	−18.6227			−1.14833			−0.574164	+	0.818741i	$0.694673\pi$
$264$	10.5083	−	12.6783i	0.646741	−	0.780292i
$265$		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	$0.0827899\pi$
$269$			8.43579i			0.514339i	−0.966366	+	0.257170i	$0.917210\pi$
$270$		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
$276$	4.91225	−	17.2495i	0.295683	−	1.03830i
$277$	−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	$-0.824617\pi$
$281$		−	17.5517i		−	1.04705i	0.852011	−	0.523524i	$-0.175383\pi$
$282$	−1.21705	−	8.81370i	−0.0724744	−	0.524848i
$283$			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
$288$	9.60022	+	13.9941i	0.565699	+	0.824612i
$289$	−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	$0.215294\pi$
$293$			21.4295i			1.25193i	−0.779852	+	0.625963i	$0.784706\pi$
$294$	0.235067	+	1.70232i	0.0137094	+	0.0992811i
$295$		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
$306$	20.6000	+	25.0059i	1.17762	+	1.42949i
$307$			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	$-0.375509\pi$
$311$	13.4453			0.762411			0.381205	+	0.924490i	$0.375509\pi$
$312$	11.5720	−	13.9616i	0.655136	−	0.790420i
$313$	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	$0.157118\pi$
$317$			16.8716i			0.947602i	−0.880632	+	0.473801i	$0.842882\pi$
$318$	5.52987	−	0.763599i	0.310100	−	0.0428205i
$319$		−	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
$324$	3.44575	−	17.6671i	0.191431	−	0.981506i
$325$		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
$336$	7.78236	+	15.5486i	0.424563	+	0.848247i
$337$	−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
$342$	−1.18741	−	1.44138i	−0.0642080	−	0.0779409i
$343$			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	$-0.325304\pi$
$347$	19.4358			1.04337			0.521683	+	0.853139i	$0.325304\pi$
$348$	7.59274	+	2.16224i	0.407014	+	0.115908i
$349$	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	$0.251164\pi$
$353$			26.6676i			1.41937i	−0.704517	+	0.709687i	$0.748836\pi$
$354$		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	$-0.434646\pi$
$359$	7.72577			0.407751			0.203875	+	0.978997i	$0.434646\pi$
$360$		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
$366$	−1.91038	−	13.8346i	−0.0998569	−	0.723148i
$367$			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
$372$	11.2943	+	3.21635i	0.585582	+	0.166760i
$373$	−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
$378$	5.97325	−	17.4481i	0.307231	−	0.897433i
$379$			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	$-0.440576\pi$
$383$	7.26464			0.371206			0.185603	+	0.982625i	$0.440576\pi$
$384$	−13.9325	−	13.7799i	−0.710990	−	0.703202i
$385$		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	$0.396580\pi$
$389$			37.3824i			1.89536i	−0.319218	+	0.947681i	$0.603420\pi$
$390$		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
$396$	19.4132	−	5.46560i	0.975548	−	0.274657i
$397$	−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	$0.0740663\pi$
$401$			9.23521i			0.461184i	−0.973050	+	0.230592i	$0.925934\pi$
$402$	13.2473	−	1.82927i	0.660716	−	0.0912359i
$403$		−	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
$408$	−28.8029	−	23.8732i	−1.42596	−	1.18190i
$409$	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
$414$	16.9541	−	13.9668i	0.833247	−	0.686432i
$415$		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	$-0.174076\pi$
$419$	34.9682			1.70831			0.854154	+	0.520021i	$0.174076\pi$
$420$		0			0
$421$	−14.2094			−0.692522			−0.346261	−	0.938138i	$-0.612549\pi$
$421$	−14.2094			−0.692522			−0.346261	+	0.938138i	$0.612549\pi$
$422$	−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
$426$	−4.16888	−	30.1904i	−0.201983	−	1.46273i
$427$		−	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	$-0.456013\pi$
$431$	5.71949			0.275498			0.137749	+	0.990467i	$0.456013\pi$
$432$	−0.0622549	+	20.7845i	−0.00299524	+	0.999996i
$433$	−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
$438$	0.435057	+	3.15061i	0.0207878	+	0.150542i
$439$			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	$-0.750267\pi$
$443$	−29.7907			−1.41540			−0.707699	+	0.706514i	$0.750267\pi$
$444$	−7.02389	+	24.6645i	−0.333339	+	1.17053i
$445$		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	$-0.752335\pi$
$449$		−	29.7460i		−	1.40380i	0.712274	−	0.701901i	$-0.247665\pi$
$450$		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
$456$	1.66025	+	1.37609i	0.0777482	+	0.0644412i
$457$	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	$0.134029\pi$
$461$			17.5517i			0.817465i	−0.912654	+	0.408732i	$0.865971\pi$
$462$	20.4691	−	2.82651i	0.952311	−	0.131501i
$463$			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	$-0.739327\pi$
$467$	−29.5197			−1.36601			−0.683004	+	0.730414i	$0.739327\pi$
$468$	21.3783	−	6.01886i	0.988210	−	0.278222i
$469$	13.7016			0.632679
$470$		0			0
$471$	−10.0839	−	16.3785i	−0.464644	−	0.754683i
$472$		0			0
$473$		−	28.2665i		−	1.29969i
$474$	12.1792	−	1.68179i	0.559411	−	0.0772471i
$475$		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	$-0.778704\pi$
$479$	−33.6131			−1.53582			−0.767912	+	0.640555i	$0.778704\pi$
$480$		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
$486$	15.7666	−	15.4082i	0.715189	−	0.698931i
$487$			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	$-0.401882\pi$
$491$	13.4453			0.606776			0.303388	+	0.952867i	$0.401882\pi$
$492$	−10.2561	−	2.92071i	−0.462382	−	0.131676i
$493$	−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
$498$	−0.608526	−	4.40685i	−0.0272687	−	0.197476i
$499$		−	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	$-0.593478\pi$
$503$	−12.9841			−0.578934			−0.289467	+	0.957188i	$0.593478\pi$
$504$	−2.97611	+	21.0863i	−0.132567	+	0.939257i
$505$		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	$-0.979110\pi$
$509$		−	2.95911i		−	0.131160i	0.997847	−	0.0655802i	$-0.0208898\pi$
$510$		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
$516$	28.0169	+	7.97857i	1.23338	+	0.351237i
$517$	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	$0.0214811\pi$
$521$			3.07840i			0.134867i	−0.997724	+	0.0674337i	$0.978519\pi$
$522$	6.14781	+	7.46270i	0.269082	+	0.326634i
$523$			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
$528$	−20.8250	+	10.4233i	−0.906291	+	0.453615i
$529$	3.80625			0.165489
$530$		0			0
$531$		0			0
$532$	1.49219	+	1.62932i	0.0646946	+	0.0706402i
$533$			11.3949i			0.493568i
$534$	−12.9995	+	1.79505i	−0.562544	+	0.0776796i
$535$		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
$546$	22.5411	−	3.11262i	0.964671	−	0.133208i
$547$			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
$552$	−16.1861	+	19.5285i	−0.688925	+	0.831187i
$553$	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	$-0.716456\pi$
$557$		−	36.7023i		−	1.55512i	0.628806	−	0.777562i	$-0.283544\pi$
$558$	9.14495	+	11.1009i	0.387137	+	0.469937i
$559$		−	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	$-0.336335\pi$
$563$	23.3391			0.983625			0.491812	+	0.870701i	$0.336335\pi$
$564$	−3.44625	+	12.1016i	−0.145113	+	0.509569i
$565$		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	$0.0712888\pi$
$569$			10.5955i			0.444186i	−0.975026	+	0.222093i	$0.928711\pi$
$570$		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
$576$	−4.45314	−	23.5832i	−0.185548	−	0.982635i
$577$	−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
$582$	3.72076	+	26.9451i	0.154230	+	1.11691i
$583$			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	$-0.276155\pi$
$587$	31.3359			1.29337			0.646685	+	0.762758i	$0.276155\pi$
$588$	0.665623	−	2.33735i	0.0274498	−	0.0963908i
$589$	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	$-0.930193\pi$
$593$		−	10.5955i		−	0.435104i	0.976049	−	0.217552i	$-0.0698072\pi$
$594$	23.3690	+	8.00025i	0.958843	+	0.328254i
$595$		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
$606$	−42.5886	+	5.88091i	−1.73004	+	0.238896i
$607$		−	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
$612$	−12.4170	−	44.1036i	−0.501926	−	1.78278i
$613$	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	$0.146814\pi$
$617$			22.1097i			0.890102i	−0.895505	+	0.445051i	$0.853186\pi$
$618$	26.4946	−	3.65855i	1.06577	−	0.147168i
$619$			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
$624$	−22.9330	+	11.4784i	−0.918054	+	0.459502i
$625$		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
$636$	−7.59274	−	2.16224i	−0.301072	−	0.0857382i
$637$	−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	$-0.921810\pi$
$641$		−	12.3136i		−	0.486359i	0.969981	−	0.243179i	$-0.0781903\pi$
$642$	−2.16169	−	15.6546i	−0.0853152	−	0.617839i
$643$		−	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	$-0.434753\pi$
$647$	10.3550			0.407095			0.203548	+	0.979065i	$0.434753\pi$
$648$	−14.5258	+	20.9046i	−0.570628	+	0.821208i
$649$		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	$-0.830206\pi$
$653$		−	25.9875i		−	1.01697i	0.861071	−	0.508485i	$-0.169794\pi$
$654$	0.770119	+	5.57708i	0.0301140	+	0.218081i
$655$		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	$-0.606154\pi$
$659$	−16.8066			−0.654691			−0.327346	+	0.944905i	$0.606154\pi$
$660$		0			0
$661$	−18.0000			−0.700119			−0.350059	−	0.936727i	$-0.613839\pi$
$661$	−18.0000			−0.700119			−0.350059	+	0.936727i	$0.613839\pi$
$662$	−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
$666$	−24.2421	+	19.9708i	−0.939363	+	0.773852i
$667$			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
$672$	−1.21449	−	24.5596i	−0.0468501	−	0.947408i
$673$	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	$-0.919670\pi$
$677$		−	12.9937i		−	0.499390i	0.968324	−	0.249695i	$-0.0803304\pi$
$678$	−1.93977	+	0.267856i	−0.0744965	+	0.0102870i
$679$			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	$-0.571418\pi$
$683$	−11.6291			−0.444975			−0.222488	+	0.974936i	$0.571418\pi$
$684$	0.715734	+	2.54220i	0.0273668	+	0.0972034i
$685$		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
$696$	−8.59589	−	7.12466i	−0.325826	−	0.270059i
$697$	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	$0.0690370\pi$
$701$			11.3949i			0.430380i	−0.976572	+	0.215190i	$0.930963\pi$
$702$	25.7345	+	8.81007i	0.971288	+	0.332515i
$703$			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
$714$	−6.42137	−	46.5026i	−0.240314	−	1.74032i
$715$		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	$-0.193207\pi$
$719$	44.0490			1.64275			0.821375	+	0.570389i	$0.193207\pi$
$720$		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
$726$	0.0999951	+	0.724149i	0.00371117	+	0.0268757i
$727$		−	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
$732$	−5.40949	+	18.9956i	−0.199940	+	0.702096i
$733$	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
$738$	−8.30435	−	10.0805i	−0.305687	−	0.371068i
$739$			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	$-0.230135\pi$
$743$	40.8778			1.49966			0.749830	+	0.661630i	$0.230135\pi$
$744$	−12.7865	−	10.5980i	−0.468776	−	0.388542i
$745$		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
$756$	−17.6726	+	19.1810i	−0.642745	+	0.697607i
$757$	−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	$0.121987\pi$
$761$			20.6301i			0.747841i	−0.927461	+	0.373920i	$0.878013\pi$
$762$	−30.7669	+	4.24849i	−1.11457	+	0.153906i
$763$			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
$768$	10.1828	+	25.7742i	0.367439	+	0.930048i
$769$	−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	$-0.986951\pi$
$773$		−	2.27898i		−	0.0819692i	0.999160	−	0.0409846i	$-0.0130495\pi$
$774$	22.6852	+	27.5371i	0.815402	+	0.989800i
$775$		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
$786$	1.91638	+	13.8781i	0.0683551	+	0.495017i
$787$			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
$792$	−28.2418	−	3.98605i	−1.00353	−	0.141638i
$793$	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	$0.301339\pi$
$797$			45.8182i			1.62296i	−0.584378	+	0.811482i	$0.698661\pi$
$798$	0.370138	+	2.68048i	0.0131028	+	0.0948881i
$799$		−	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
$804$	−18.1891	−	5.17984i	−0.641481	−	0.182679i
$805$		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	$0.277448\pi$
$809$			43.5392i			1.53076i	−0.643580	+	0.765378i	$0.722552\pi$
$810$		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
$816$	23.6800	+	47.3110i	0.828966	+	1.65622i
$817$	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	$-0.965736\pi$
$821$		−	6.15681i		−	0.214874i	0.994212	−	0.107437i	$-0.0342644\pi$
$822$	24.0592	−	3.32225i	0.839162	−	0.115877i
$823$			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	$-0.615643\pi$
$827$	−20.4389			−0.710730			−0.355365	+	0.934728i	$0.615643\pi$
$828$	−29.9023	+	8.41874i	−1.03918	+	0.292571i
$829$	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
$834$	−7.15769	+	0.988379i	−0.247850	+	0.0342248i
$835$		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	$-0.774982\pi$
$839$	−44.0490			−1.52074			−0.760370	+	0.649490i	$0.774982\pi$
$840$		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
$846$	−11.8943	+	9.79860i	−0.408935	+	0.336883i
$847$			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
$852$	−11.8047	+	41.4527i	−0.404424	+	1.42014i
$853$	−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	$0.179824\pi$
$857$			31.3449i			1.07072i	−0.844624	+	0.535360i	$0.820176\pi$
$858$	4.16888	+	30.1904i	0.142323	+	1.03068i
$859$			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	$-0.255073\pi$
$863$	40.8778			1.39150			0.695748	+	0.718286i	$0.255073\pi$
$864$	11.9225	−	26.8674i	0.405610	−	0.914046i
$865$		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
$876$	1.23192	−	4.32593i	0.0416228	−	0.146160i
$877$	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	$-0.705490\pi$
$881$		−	47.4170i		−	1.59752i	0.601650	−	0.798760i	$-0.294510\pi$
$882$	2.29732	−	1.89254i	0.0773548	−	0.0637253i
$883$		−	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	$-0.421566\pi$
$887$	14.5293			0.487846			0.243923	+	0.969795i	$0.421566\pi$
$888$	23.1440	−	27.9232i	0.776662	−	0.937041i
$889$	−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
$894$	37.0587	−	5.11731i	1.23943	−	0.171148i
$895$		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
$906$	−46.8996	+	6.47620i	−1.55814	+	0.215157i
$907$		−	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	$-0.510581\pi$
$911$	−2.00629			−0.0664713			−0.0332356	+	0.999448i	$0.510581\pi$
$912$	−1.36495	−	2.72708i	−0.0451981	−	0.0903027i
$913$	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
$918$	18.1753	−	53.0907i	0.599874	−	1.75225i
$919$		−	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
$924$	−28.1050	−	8.00365i	−0.924587	−	0.263301i
$925$		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	$0.253226\pi$
$929$			43.5392i			1.42847i	−0.699903	+	0.714237i	$0.746774\pi$
$930$		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
$936$	−31.1006	−	4.38953i	−1.01655	−	0.143476i
$937$	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	$0.337978\pi$
$941$			53.5738i			1.74646i	−0.487311	+	0.873229i	$0.662022\pi$
$942$	3.72076	+	26.9451i	0.121229	+	0.877920i
$943$		−	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	$-0.405089\pi$
$947$	18.0807			0.587545			0.293772	+	0.955875i	$0.405089\pi$
$948$	−16.7226	−	4.76221i	−0.543126	−	0.154669i
$949$	−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	$0.238552\pi$
$953$			42.0596i			1.36245i	−0.732076	+	0.681223i	$0.761448\pi$
$954$	−6.14781	−	7.46270i	−0.199043	−	0.241614i
$955$		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
$966$	−31.5289	+	4.35371i	−1.01443	+	0.140078i
$967$			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	$-0.775161\pi$
$971$	−47.4103			−1.52147			−0.760734	+	0.649063i	$0.775161\pi$
$972$	−29.1866	+	10.9609i	−0.936161	+	0.351572i
$973$	−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	$0.0984667\pi$
$977$			19.0313i			0.608864i	−0.952534	+	0.304432i	$0.901533\pi$
$978$	−1.06806	+	0.147485i	−0.0341529	+	0.00471605i
$979$		−	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	$-0.863563\pi$
$983$	−57.0331			−1.81907			−0.909537	+	0.415623i	$0.863563\pi$
$984$	11.6112	+	9.62385i	0.370150	+	0.306797i
$985$		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
$996$	−1.72312	+	6.05079i	−0.0545993	+	0.191727i
$997$	−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.251.1	yes	8
3.2	odd	2	inner	300.2.e.e.251.8	yes	8
4.3	odd	2	inner	300.2.e.e.251.7	yes	8
5.2	odd	4		300.2.h.c.299.9		16
5.3	odd	4		300.2.h.c.299.8		16
5.4	even	2		300.2.e.d.251.8	yes	8
12.11	even	2	inner	300.2.e.e.251.2	yes	8
15.2	even	4		300.2.h.c.299.7		16
15.8	even	4		300.2.h.c.299.10		16
15.14	odd	2		300.2.e.d.251.1	✓	8
20.3	even	4		300.2.h.c.299.5		16
20.7	even	4		300.2.h.c.299.12		16
20.19	odd	2		300.2.e.d.251.2	yes	8
60.23	odd	4		300.2.h.c.299.11		16
60.47	odd	4		300.2.h.c.299.6		16
60.59	even	2		300.2.e.d.251.7	yes	8

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

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