LMFDB - Embedded newform 891.2.n.h.757.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [891,2,Mod(136,891)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(891, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([20, 6]))

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

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

chi := DirichletCharacter("891.136");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 891 = 3^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	891.n (of order $15$, degree $8$, 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:	$7.11467082010$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 297)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			757.3
Character	$\chi$	$=$	891.757
Dual form			891.2.n.h.379.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.22359 - 0.260081i) q^{2} +(-0.397568 + 0.177009i) q^{4} +(-1.60550 - 0.341260i) q^{5} +(0.307337 - 2.92412i) q^{7} +(-2.46446 + 1.79053i) q^{8} -2.05323 q^{10} +(-2.70129 + 1.92433i) q^{11} +(2.42094 + 2.68872i) q^{13} +(-0.384455 - 3.65784i) q^{14} +(-1.96739 + 2.18501i) q^{16} +(1.98276 + 6.10230i) q^{17} +(-5.02334 + 3.64967i) q^{19} +(0.698701 - 0.148514i) q^{20} +(-2.80478 + 3.05714i) q^{22} +(-0.195223 + 0.338136i) q^{23} +(-2.10655 - 0.937897i) q^{25} +(3.66151 + 2.66025i) q^{26} +(0.395406 + 1.21694i) q^{28} +(-0.553896 + 5.26997i) q^{29} +(-2.27658 - 2.52840i) q^{31} +(1.20724 - 2.09100i) q^{32} +(4.01317 + 6.95102i) q^{34} +(-1.49131 + 4.58979i) q^{35} +(-2.61803 - 1.90211i) q^{37} +(-5.19728 + 5.77216i) q^{38} +(4.56773 - 2.03368i) q^{40} +(0.818041 + 7.78314i) q^{41} +(-0.325465 - 0.563722i) q^{43} +(0.733321 - 1.24320i) q^{44} +(-0.150930 + 0.464513i) q^{46} +(-12.2557 - 5.45658i) q^{47} +(-1.60897 - 0.341997i) q^{49} +(-2.82148 - 0.599724i) q^{50} +(-1.43841 - 0.640423i) q^{52} +(1.48983 - 4.58522i) q^{53} +(4.99362 - 2.16768i) q^{55} +(4.47831 + 7.75666i) q^{56} +(0.692881 + 6.59232i) q^{58} +(-1.79533 + 0.799333i) q^{59} +(7.64725 - 8.49314i) q^{61} +(-3.44318 - 2.50162i) q^{62} +(2.75049 - 8.46514i) q^{64} +(-2.96926 - 5.14292i) q^{65} +(-0.427051 + 0.739674i) q^{67} +(-1.86844 - 2.07511i) q^{68} +(-0.631032 + 6.00387i) q^{70} +(0.340470 + 1.04786i) q^{71} +(2.52131 + 1.83184i) q^{73} +(-3.69810 - 1.64650i) q^{74} +(1.35109 - 2.34016i) q^{76} +(4.79677 + 8.49029i) q^{77} +(-1.61881 + 0.344089i) q^{79} +(3.90431 - 2.83665i) q^{80} +(3.02520 + 9.31060i) q^{82} +(-8.65701 + 9.61458i) q^{83} +(-1.10085 - 10.4739i) q^{85} +(-0.544848 - 0.605115i) q^{86} +(3.21162 - 9.57918i) q^{88} +5.92297 q^{89} +(8.60618 - 6.25276i) q^{91} +(0.0177614 - 0.168988i) q^{92} +(-16.4150 - 3.48912i) q^{94} +(9.31046 - 4.14528i) q^{95} +(-18.2345 + 3.87586i) q^{97} -2.05766 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 10 q^{4} + 24 q^{10} + 10 q^{16} - 4 q^{19} + 36 q^{22} - 32 q^{25} + 84 q^{28} + 26 q^{31} + 48 q^{34} - 48 q^{37} + 20 q^{40} - 24 q^{43} - 32 q^{46} - 24 q^{49} + 40 q^{52} - 32 q^{55} - 106 q^{58}+ \cdots - 72 q^{97}+O(q^{100}) $ 32 * q + 10 * q^4 + 24 * q^10 + 10 * q^16 - 4 * q^19 + 36 * q^22 - 32 * q^25 + 84 * q^28 + 26 * q^31 + 48 * q^34 - 48 * q^37 + 20 * q^40 - 24 * q^43 - 32 * q^46 - 24 * q^49 + 40 * q^52 - 32 * q^55 - 106 * q^58 + 6 * q^61 + 124 * q^64 + 40 * q^67 + 58 * q^70 - 60 * q^76 - 64 * q^79 - 168 * q^82 + 18 * q^85 - 80 * q^88 - 20 * q^91 - 90 * q^94 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/891\mathbb{Z}\right)^\times$.

$n$	$244$	$650$
$\chi(n)$	$e\left(\frac{3}{5}\right)$	$e\left(\frac{1}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	1.22359	−	0.260081i	0.865207	−	0.183905i	0.246131	−	0.969237i	$-0.420841\pi$
$2$	1.22359	−	0.260081i	0.865207	−	0.183905i	0.619076	+	0.785331i	$0.287507\pi$
$3$		0			0
$3$		0			0
$4$	−0.397568	+	0.177009i	−0.198784	+	0.0885043i
$5$	−1.60550	−	0.341260i	−0.718002	−	0.152616i	−0.165599	−	0.986193i	$-0.552956\pi$
$5$	−1.60550	−	0.341260i	−0.718002	−	0.152616i	−0.552403	+	0.833577i	$0.686289\pi$
$6$		0			0
$7$	0.307337	−	2.92412i	0.116162	−	1.10521i	−0.768780	−	0.639513i	$-0.779136\pi$
$7$	0.307337	−	2.92412i	0.116162	−	1.10521i	0.884943	−	0.465699i	$-0.154197\pi$
$8$	−2.46446	+	1.79053i	−0.871317	+	0.633049i
$9$		0			0
$10$	−2.05323			−0.649287
$11$	−2.70129	+	1.92433i	−0.814468	+	0.580208i
$11$	−2.70129	+	1.92433i	−0.814468	+	0.580208i
$12$		0			0
$13$	2.42094	+	2.68872i	0.671447	+	0.745718i	0.978561	−	0.205955i	$-0.0660301\pi$
$13$	2.42094	+	2.68872i	0.671447	+	0.745718i	−0.307114	+	0.951673i	$0.599363\pi$
$14$	−0.384455	−	3.65784i	−0.102750	−	0.977600i
$15$		0			0
$16$	−1.96739	+	2.18501i	−0.491848	+	0.546253i
$17$	1.98276	+	6.10230i	0.480889	+	1.48003i	0.837847	+	0.545905i	$0.183814\pi$
$17$	1.98276	+	6.10230i	0.480889	+	1.48003i	−0.356958	+	0.934121i	$0.616186\pi$
$18$		0			0
$19$	−5.02334	+	3.64967i	−1.15243	+	0.837291i	−0.988802	−	0.149230i	$-0.952320\pi$
$19$	−5.02334	+	3.64967i	−1.15243	+	0.837291i	−0.163630	+	0.986522i	$0.552320\pi$
$20$	0.698701	−	0.148514i	0.156234	−	0.0332086i
$21$		0			0
$22$	−2.80478	+	3.05714i	−0.597980	+	0.651785i
$23$	−0.195223	+	0.338136i	−0.0407068	+	0.0705063i	−0.885661	−	0.464332i	$-0.846294\pi$
$23$	−0.195223	+	0.338136i	−0.0407068	+	0.0705063i	0.844954	+	0.534839i	$0.179628\pi$
$24$		0			0
$25$	−2.10655	−	0.937897i	−0.421310	−	0.187579i
$26$	3.66151	+	2.66025i	0.718082	+	0.521717i
$27$		0			0
$28$	0.395406	+	1.21694i	0.0747248	+	0.229979i
$29$	−0.553896	+	5.26997i	−0.102856	+	0.978608i	0.814398	+	0.580306i	$0.197067\pi$
$29$	−0.553896	+	5.26997i	−0.102856	+	0.978608i	−0.917254	+	0.398302i	$0.869600\pi$
$30$		0			0
$31$	−2.27658	−	2.52840i	−0.408886	−	0.454114i	0.503165	−	0.864190i	$-0.332169\pi$
$31$	−2.27658	−	2.52840i	−0.408886	−	0.454114i	−0.912051	+	0.410076i	$0.865502\pi$
$32$	1.20724	−	2.09100i	0.213412	−	0.369641i
$33$		0			0
$34$	4.01317	+	6.95102i	0.688253	+	1.19209i
$35$	−1.49131	+	4.58979i	−0.252078	+	0.775816i
$36$		0			0
$37$	−2.61803	−	1.90211i	−0.430402	−	0.312705i	0.351408	−	0.936223i	$-0.385703\pi$
$37$	−2.61803	−	1.90211i	−0.430402	−	0.312705i	−0.781810	+	0.623517i	$0.785703\pi$
$38$	−5.19728	+	5.77216i	−0.843110	+	0.936369i
$39$		0			0
$40$	4.56773	−	2.03368i	0.722221	−	0.321554i
$41$	0.818041	+	7.78314i	0.127757	+	1.21552i	0.851088	+	0.525022i	$0.175943\pi$
$41$	0.818041	+	7.78314i	0.127757	+	1.21552i	−0.723332	+	0.690501i	$0.757390\pi$
$42$		0			0
$43$	−0.325465	−	0.563722i	−0.0496329	−	0.0859667i	0.840142	−	0.542367i	$-0.182472\pi$
$43$	−0.325465	−	0.563722i	−0.0496329	−	0.0859667i	−0.889775	+	0.456400i	$0.849138\pi$
$44$	0.733321	−	1.24320i	0.110552	−	0.187420i
$45$		0			0
$46$	−0.150930	+	0.464513i	−0.0222533	+	0.0684888i
$47$	−12.2557	−	5.45658i	−1.78767	−	0.795924i	−0.977867	−	0.209226i	$-0.932905\pi$
$47$	−12.2557	−	5.45658i	−1.78767	−	0.795924i	−0.809806	−	0.586697i	$-0.800428\pi$
$48$		0			0
$49$	−1.60897	−	0.341997i	−0.229853	−	0.0488567i
$50$	−2.82148	−	0.599724i	−0.399017	−	0.0848138i
$51$		0			0
$52$	−1.43841	−	0.640423i	−0.199472	−	0.0888107i
$53$	1.48983	−	4.58522i	0.204644	−	0.629828i	−0.795084	−	0.606499i	$-0.792573\pi$
$53$	1.48983	−	4.58522i	0.204644	−	0.629828i	0.999728	−	0.0233292i	$-0.00742659\pi$
$54$		0			0
$55$	4.99362	−	2.16768i	0.673339	−	0.292290i
$56$	4.47831	+	7.75666i	0.598439	+	1.03653i
$57$		0			0
$58$	0.692881	+	6.59232i	0.0909797	+	0.865614i
$59$	−1.79533	+	0.799333i	−0.233732	+	0.104064i	−0.520261	−	0.854007i	$-0.674165\pi$
$59$	−1.79533	+	0.799333i	−0.233732	+	0.104064i	0.286529	+	0.958072i	$0.407499\pi$
$60$		0			0
$61$	7.64725	−	8.49314i	0.979131	−	1.08743i	−0.0170270	−	0.999855i	$-0.505420\pi$
$61$	7.64725	−	8.49314i	0.979131	−	1.08743i	0.996158	−	0.0875796i	$-0.0279132\pi$
$62$	−3.44318	−	2.50162i	−0.437285	−	0.317706i
$63$		0			0
$64$	2.75049	−	8.46514i	0.343811	−	1.05814i
$65$	−2.96926	−	5.14292i	−0.368292	−	0.637900i
$66$		0			0
$67$	−0.427051	+	0.739674i	−0.0521726	+	0.0903656i	−0.890932	−	0.454136i	$-0.849948\pi$
$67$	−0.427051	+	0.739674i	−0.0521726	+	0.0903656i	0.838760	+	0.544502i	$0.183281\pi$
$68$	−1.86844	−	2.07511i	−0.226582	−	0.251644i
$69$		0			0
$70$	−0.631032	+	6.00387i	−0.0754228	+	0.717600i
$71$	0.340470	+	1.04786i	0.0404064	+	0.124358i	0.969225	−	0.246177i	$-0.0791744\pi$
$71$	0.340470	+	1.04786i	0.0404064	+	0.124358i	−0.928819	+	0.370535i	$0.879174\pi$
$72$		0			0
$73$	2.52131	+	1.83184i	0.295097	+	0.214401i	0.725476	−	0.688248i	$-0.241620\pi$
$73$	2.52131	+	1.83184i	0.295097	+	0.214401i	−0.430378	+	0.902649i	$0.641620\pi$
$74$	−3.69810	−	1.64650i	−0.429895	−	0.191402i
$75$		0			0
$76$	1.35109	−	2.34016i	0.154981	−	0.268435i
$77$	4.79677	+	8.49029i	0.546642	+	0.967559i
$78$		0			0
$79$	−1.61881	+	0.344089i	−0.182131	+	0.0387131i	−0.298074	−	0.954543i	$-0.596344\pi$
$79$	−1.61881	+	0.344089i	−0.182131	+	0.0387131i	0.115943	+	0.993256i	$0.463011\pi$
$80$	3.90431	−	2.83665i	0.436515	−	0.317147i
$81$		0			0
$82$	3.02520	+	9.31060i	0.334077	+	1.02818i
$83$	−8.65701	+	9.61458i	−0.950230	+	1.05534i	0.0481727	+	0.998839i	$0.484660\pi$
$83$	−8.65701	+	9.61458i	−0.950230	+	1.05534i	−0.998403	+	0.0564983i	$0.982006\pi$
$84$		0			0
$85$	−1.10085	−	10.4739i	−0.119404	−	1.13605i
$86$	−0.544848	−	0.605115i	−0.0587525	−	0.0652512i
$87$		0			0
$88$	3.21162	−	9.57918i	0.342360	−	1.02114i
$89$	5.92297			0.627834			0.313917	−	0.949451i	$-0.398359\pi$
$89$	5.92297			0.627834			0.313917	+	0.949451i	$0.398359\pi$
$90$		0			0
$91$	8.60618	−	6.25276i	0.902173	−	0.655467i
$92$	0.0177614	−	0.168988i	0.00185175	−	0.0176183i
$93$		0			0
$94$	−16.4150	−	3.48912i	−1.69308	−	0.359876i
$95$	9.31046	−	4.14528i	0.955233	−	0.425297i
$96$		0			0
$97$	−18.2345	+	3.87586i	−1.85143	+	0.393534i	−0.992873	−	0.119177i	$-0.961974\pi$
$97$	−18.2345	+	3.87586i	−1.85143	+	0.393534i	−0.858561	+	0.512712i	$0.828641\pi$
$98$	−2.05766			−0.207855
$99$		0			0
$100$	1.00351			0.100351
$101$	1.77171	−	0.376588i	0.176291	−	0.0374719i	−0.118920	−	0.992904i	$-0.537943\pi$
$101$	1.77171	−	0.376588i	0.176291	−	0.0374719i	0.295212	+	0.955432i	$0.404610\pi$
$102$		0			0
$103$	14.7867	−	6.58345i	1.45697	−	0.648686i	0.483056	−	0.875589i	$-0.339527\pi$
$103$	14.7867	−	6.58345i	1.45697	−	0.648686i	0.973917	+	0.226903i	$0.0728600\pi$
$104$	−10.7805	−	2.29148i	−1.05712	−	0.224698i
$105$		0			0
$106$	0.630404	−	5.99789i	0.0612302	−	0.582567i
$107$	−8.63171	+	6.27130i	−0.834459	+	0.606270i	−0.920817	−	0.389994i	$-0.872477\pi$
$107$	−8.63171	+	6.27130i	−0.834459	+	0.606270i	0.0863585	+	0.996264i	$0.472477\pi$
$108$		0			0
$109$	3.37595			0.323357			0.161679	−	0.986843i	$-0.448309\pi$
$109$	3.37595			0.323357			0.161679	+	0.986843i	$0.448309\pi$
$110$	5.54635	−	3.95109i	0.528824	−	0.376722i
$111$		0			0
$112$	5.78458	+	6.42442i	0.546591	+	0.607051i
$113$	1.44311	+	13.7303i	0.135757	+	1.29164i	0.824179	+	0.566330i	$0.191637\pi$
$113$	1.44311	+	13.7303i	0.135757	+	1.29164i	−0.688422	+	0.725310i	$0.741696\pi$
$114$		0			0
$115$	0.428823	−	0.476257i	0.0399880	−	0.0444112i
$116$	−0.712618	−	2.19321i	−0.0661649	−	0.203635i
$117$		0			0
$118$	−1.98885	+	1.44499i	−0.183089	+	0.133022i
$119$	18.4532	−	3.92235i	1.69160	−	0.359561i
$120$		0			0
$121$	3.59389	−	10.3963i	0.326717	−	0.945122i
$122$	7.14817	−	12.3810i	0.647165	−	1.12092i
$123$		0			0
$124$	1.35264	+	0.602236i	0.121471	+	0.0540824i
$125$	9.70148	+	7.04854i	0.867727	+	0.630440i
$126$		0			0
$127$	0.297703	+	0.916236i	0.0264169	+	0.0813028i	0.963396	−	0.268083i	$-0.0863902\pi$
$127$	0.297703	+	0.916236i	0.0264169	+	0.0813028i	−0.936979	+	0.349386i	$0.886390\pi$
$128$	0.659075	−	6.27068i	0.0582546	−	0.554255i
$129$		0			0
$130$	−4.97073	−	5.52056i	−0.435962	−	0.484185i
$131$	5.14336	−	8.90855i	0.449377	−	0.778344i	−0.548968	−	0.835843i	$-0.684979\pi$
$131$	5.14336	−	8.90855i	0.449377	−	0.778344i	0.998346	+	0.0574991i	$0.0183126\pi$
$132$		0			0
$133$	9.12820	+	15.8105i	0.791515	+	1.37094i
$134$	−0.330159	+	1.01612i	−0.0285214	+	0.0877797i
$135$		0			0
$136$	−15.8128	−	11.4887i	−1.35594	−	0.985145i
$137$	12.8899	−	14.3157i	1.10126	−	1.22307i	0.128391	−	0.991724i	$-0.459019\pi$
$137$	12.8899	−	14.3157i	1.10126	−	1.22307i	0.972870	−	0.231351i	$-0.0743145\pi$
$138$		0			0
$139$	5.17127	−	2.30240i	0.438622	−	0.195287i	−0.175532	−	0.984474i	$-0.556164\pi$
$139$	5.17127	−	2.30240i	0.438622	−	0.195287i	0.614153	+	0.789187i	$0.289498\pi$
$140$	−0.219534	−	2.08873i	−0.0185540	−	0.176530i
$141$		0			0
$142$	0.689124	+	1.19360i	0.0578300	+	0.100165i
$143$	−11.7136	−	2.60432i	−0.979544	−	0.217784i
$144$		0			0
$145$	2.68771	−	8.27191i	0.223202	−	0.686945i
$146$	3.56148	+	1.58567i	0.294750	+	0.131231i
$147$		0			0
$148$	1.37754	+	0.292804i	0.113233	+	0.0240684i
$149$	−7.74806	−	1.64690i	−0.634746	−	0.134919i	−0.120710	−	0.992688i	$-0.538517\pi$
$149$	−7.74806	−	1.64690i	−0.634746	−	0.134919i	−0.514036	+	0.857768i	$0.671850\pi$
$150$		0			0
$151$	15.2972	+	6.81073i	1.24486	+	0.554249i	0.920151	−	0.391563i	$-0.128066\pi$
$151$	15.2972	+	6.81073i	1.24486	+	0.554249i	0.324713	+	0.945813i	$0.394732\pi$
$152$	5.84495	−	17.9889i	0.474088	−	1.45909i
$153$		0			0
$154$	8.07743	+	9.14106i	0.650898	+	0.736608i
$155$	2.79221	+	4.83625i	0.224276	+	0.388457i
$156$		0			0
$157$	1.38456	+	13.1732i	0.110500	+	1.05134i	0.899493	+	0.436936i	$0.143936\pi$
$157$	1.38456	+	13.1732i	0.110500	+	1.05134i	−0.788992	+	0.614403i	$0.789397\pi$
$158$	−1.89127	+	0.842046i	−0.150461	+	0.0669896i
$159$		0			0
$160$	−2.65180	+	2.94512i	−0.209643	+	0.232833i
$161$	0.928751	+	0.674777i	0.0731958	+	0.0531799i
$162$		0			0
$163$	−4.12803	+	12.7048i	−0.323333	+	0.995115i	0.648855	+	0.760912i	$0.275248\pi$
$163$	−4.12803	+	12.7048i	−0.323333	+	0.995115i	−0.972188	+	0.234203i	$0.924752\pi$
$164$	−1.70291	−	2.94953i	−0.132975	−	0.230319i
$165$		0			0
$166$	−8.09203	+	14.0158i	−0.628063	+	1.08784i
$167$	−3.60938	−	4.00863i	−0.279302	−	0.310197i	0.587128	−	0.809494i	$-0.300258\pi$
$167$	−3.60938	−	4.00863i	−0.279302	−	0.310197i	−0.866431	+	0.499297i	$0.833592\pi$
$168$		0			0
$169$	−0.00942533	+	0.0896760i	−0.000725025	+	0.00689815i
$170$	−4.07105	−	12.5294i	−0.312235	−	0.960961i
$171$		0			0
$172$	0.229178	+	0.166507i	0.0174746	+	0.0126961i
$173$	5.86601	+	2.61172i	0.445984	+	0.198565i	0.617426	−	0.786629i	$-0.288176\pi$
$173$	5.86601	+	2.61172i	0.445984	+	0.198565i	−0.171441	+	0.985194i	$0.554842\pi$
$174$		0			0
$175$	−3.38994	+	5.87155i	−0.256255	+	0.443848i
$176$	1.10980	−	9.68826i	0.0836546	−	0.730280i
$177$		0			0
$178$	7.24727	−	1.54045i	0.543206	−	0.115462i
$179$	−16.0419	+	11.6551i	−1.19903	+	0.871144i	−0.994189	−	0.107651i	$-0.965667\pi$
$179$	−16.0419	+	11.6551i	−1.19903	+	0.871144i	−0.204839	+	0.978796i	$0.565667\pi$
$180$		0			0
$181$	−2.22263	−	6.84054i	−0.165207	−	0.508454i	0.833845	−	0.551999i	$-0.186135\pi$
$181$	−2.22263	−	6.84054i	−0.165207	−	0.508454i	−0.999051	+	0.0435452i	$0.986135\pi$
$182$	8.90419	−	9.88910i	0.660022	−	0.733029i
$183$		0			0
$184$	−0.124325	−	1.18288i	−0.00916539	−	0.0872028i
$185$	3.55414	+	3.94727i	0.261306	+	0.290209i
$186$		0			0
$187$	−17.0989	−	12.6686i	−1.25039	−	0.926418i
$188$	5.83832			0.425803
$189$		0			0
$190$	10.3140	−	7.49359i	0.748260	−	0.543643i
$191$	−0.271989	+	2.58780i	−0.0196804	+	0.187247i	−0.999945	−	0.0104410i	$-0.996676\pi$
$191$	−0.271989	+	2.58780i	−0.0196804	+	0.187247i	0.980265	+	0.197688i	$0.0633431\pi$
$192$		0			0
$193$	−24.6614	−	5.24195i	−1.77517	−	0.377324i	−0.800211	−	0.599718i	$-0.795279\pi$
$193$	−24.6614	−	5.24195i	−1.77517	−	0.377324i	−0.974957	+	0.222395i	$0.928613\pi$
$194$	−21.3035	+	9.48492i	−1.52950	+	0.680977i
$195$		0			0
$196$	0.700211	−	0.148834i	0.0500151	−	0.0106310i
$197$	−21.2052			−1.51081			−0.755403	−	0.655260i	$-0.772559\pi$
$197$	−21.2052			−1.51081			−0.755403	+	0.655260i	$0.772559\pi$
$198$		0			0
$199$	−23.5761			−1.67126			−0.835632	−	0.549289i	$-0.814898\pi$
$199$	−23.5761			−1.67126			−0.835632	+	0.549289i	$0.814898\pi$
$200$	6.87084	−	1.46044i	0.485842	−	0.103269i
$201$		0			0
$202$	2.06989	−	0.921577i	0.145637	−	0.0648419i
$203$	15.2398	+	3.23931i	1.06962	+	0.227355i
$204$		0			0
$205$	1.34271	−	12.7750i	0.0937788	−	0.892246i
$206$	16.3805	−	11.9012i	1.14129	−	0.829193i
$207$		0			0
$208$	−10.6378			−0.737601
$209$	6.54630	−	19.5254i	0.452817	−	1.35060i
$210$		0			0
$211$	18.1650	+	20.1742i	1.25053	+	1.38885i	0.889909	+	0.456138i	$0.150768\pi$
$211$	18.1650	+	20.1742i	1.25053	+	1.38885i	0.360619	+	0.932713i	$0.382565\pi$
$212$	0.219315	+	2.08665i	0.0150626	+	0.143312i
$213$		0			0
$214$	−8.93060	+	9.91843i	−0.610483	+	0.678010i
$215$	0.330159	+	1.01612i	0.0225166	+	0.0692991i
$216$		0			0
$217$	−8.09301	+	5.87992i	−0.549389	+	0.399155i
$218$	4.13077	−	0.878022i	0.279771	−	0.0594672i
$219$		0			0
$220$	−1.60160	+	1.74571i	−0.107980	+	0.117696i
$221$	−11.6073	+	20.1044i	−0.780789	+	1.35237i
$222$		0			0
$223$	−6.07364	−	2.70416i	−0.406721	−	0.181084i	0.193170	−	0.981165i	$-0.438123\pi$
$223$	−6.07364	−	2.70416i	−0.406721	−	0.181084i	−0.599892	+	0.800081i	$0.704790\pi$
$224$	−5.74331	−	4.17276i	−0.383741	−	0.278804i
$225$		0			0
$226$	5.33678	+	16.4249i	0.354997	+	1.09257i
$227$	−1.11093	+	10.5698i	−0.0737347	+	0.701539i	0.893742	+	0.448581i	$0.148070\pi$
$227$	−1.11093	+	10.5698i	−0.0737347	+	0.701539i	−0.967477	+	0.252958i	$0.918596\pi$
$228$		0			0
$229$	2.83864	+	3.15263i	0.187583	+	0.208332i	0.829600	−	0.558359i	$-0.188569\pi$
$229$	2.83864	+	3.15263i	0.187583	+	0.208332i	−0.642017	+	0.766691i	$0.721902\pi$
$230$	0.400837	−	0.694271i	0.0264304	−	0.0457788i
$231$		0			0
$232$	−8.07100	−	13.9794i	−0.529887	−	0.917791i
$233$	5.26466	−	16.2029i	0.344899	−	1.06149i	−0.616739	−	0.787168i	$-0.711546\pi$
$233$	5.26466	−	16.2029i	0.344899	−	1.06149i	0.961638	−	0.274322i	$-0.0884535\pi$
$234$		0			0
$235$	17.8144	+	12.9429i	1.16208	+	0.844302i
$236$	0.572277	−	0.635578i	0.0372520	−	0.0413726i
$237$		0			0
$238$	21.5590	−	9.59868i	1.39746	−	0.622190i
$239$	−1.71837	−	16.3492i	−0.111152	−	1.05754i	−0.897879	−	0.440242i	$-0.854893\pi$
$239$	−1.71837	−	16.3492i	−0.111152	−	1.05754i	0.786727	−	0.617301i	$-0.211774\pi$
$240$		0			0
$241$	1.56137	+	2.70437i	0.100577	+	0.174204i	0.911922	−	0.410363i	$-0.134598\pi$
$241$	1.56137	+	2.70437i	0.100577	+	0.174204i	−0.811346	+	0.584566i	$0.801265\pi$
$242$	1.69354	−	13.6555i	0.108865	−	0.877811i
$243$		0			0
$244$	−1.53694	+	4.73023i	−0.0983927	+	0.302822i
$245$	2.46649	+	1.09815i	0.157578	+	0.0701584i
$246$		0			0
$247$	−21.9741	−	4.67075i	−1.39818	−	0.297192i
$248$	10.1377	+	2.15484i	0.643746	+	0.136832i
$249$		0			0
$250$	13.7038	+	6.10133i	0.866705	+	0.385882i
$251$	3.20271	−	9.85694i	0.202154	−	0.622165i	−0.797665	−	0.603101i	$-0.793932\pi$
$251$	3.20271	−	9.85694i	0.202154	−	0.622165i	0.999818	−	0.0190635i	$-0.00606848\pi$
$252$		0			0
$253$	−0.123333	−	1.28908i	−0.00775390	−	0.0810436i
$254$	0.602562	+	1.04367i	0.0378081	+	0.0654855i
$255$		0			0
$256$	1.03632	+	9.85990i	0.0647698	+	0.616244i
$257$	15.5478	−	6.92231i	0.969842	−	0.431802i	0.140216	−	0.990121i	$-0.455220\pi$
$257$	15.5478	−	6.92231i	0.969842	−	0.431802i	0.829626	+	0.558319i	$0.188554\pi$
$258$		0			0
$259$	−6.36662	+	7.07085i	−0.395602	+	0.439361i
$260$	2.09082	+	1.51907i	0.129667	+	0.0942089i
$261$		0			0
$262$	3.97639	−	12.2381i	0.245662	−	0.756071i
$263$	−6.58321	−	11.4025i	−0.405938	−	0.703105i	0.588492	−	0.808503i	$-0.299722\pi$
$263$	−6.58321	−	11.4025i	−0.405938	−	0.703105i	−0.994430	+	0.105398i	$0.966388\pi$
$264$		0			0
$265$	−3.95667	+	6.85316i	−0.243056	+	0.420986i
$266$	15.2812	+	16.9715i	0.936948	+	1.04059i
$267$		0			0
$268$	0.0388531	−	0.369662i	0.00237333	−	0.0225807i
$269$	2.84018	+	8.74119i	0.173169	+	0.532960i	0.999545	−	0.0301591i	$-0.00960140\pi$
$269$	2.84018	+	8.74119i	0.173169	+	0.532960i	−0.826376	+	0.563119i	$0.809601\pi$
$270$		0			0
$271$	6.17656	+	4.48753i	0.375199	+	0.272598i	0.759364	−	0.650667i	$-0.225510\pi$
$271$	6.17656	+	4.48753i	0.375199	+	0.272598i	−0.384164	+	0.923265i	$0.625510\pi$
$272$	−17.2345	−	7.67328i	−1.04499	−	0.465261i
$273$		0			0
$274$	12.0487	−	20.8690i	0.727889	−	1.26074i
$275$	7.49522	−	1.52018i	0.451979	−	0.0916701i
$276$		0			0
$277$	−0.727352	+	0.154603i	−0.0437023	+	0.00928922i	−0.229711	−	0.973259i	$-0.573778\pi$
$277$	−0.727352	+	0.154603i	−0.0437023	+	0.00928922i	0.186009	+	0.982548i	$0.440445\pi$
$278$	5.72869	−	4.16214i	0.343584	−	0.249628i
$279$		0			0
$280$	−4.54290	−	13.9816i	−0.271490	−	0.835560i
$281$	−16.6130	+	18.4506i	−0.991049	+	1.10067i	0.00386981	+	0.999993i	$0.498768\pi$
$281$	−16.6130	+	18.4506i	−0.991049	+	1.10067i	−0.994919	+	0.100679i	$0.967898\pi$
$282$		0			0
$283$	1.70519	+	16.2238i	0.101363	+	0.964403i	0.920483	+	0.390782i	$0.127795\pi$
$283$	1.70519	+	16.2238i	0.101363	+	0.964403i	−0.819121	+	0.573621i	$0.805538\pi$
$284$	−0.320840	−	0.356329i	−0.0190384	−	0.0211443i
$285$		0			0
$286$	−15.0100	−	0.140114i	−0.887560	−	0.00828514i
$287$	23.0102			1.35825
$288$		0			0
$289$	−19.5535	+	14.2064i	−1.15020	+	0.835672i
$290$	1.13727	−	10.8204i	0.0667830	−	0.635398i
$291$		0			0
$292$	−1.32664	−	0.281987i	−0.0776360	−	0.0165020i
$293$	−5.21785	+	2.32314i	−0.304830	+	0.135719i	−0.553451	−	0.832882i	$-0.686689\pi$
$293$	−5.21785	+	2.32314i	−0.304830	+	0.135719i	0.248621	+	0.968601i	$0.420023\pi$
$294$		0			0
$295$	3.15519	−	0.670655i	0.183702	−	0.0390471i
$296$	9.85783			0.572975
$297$		0			0
$298$	−9.90876			−0.573999
$299$	−1.38178	+	0.293706i	−0.0799103	+	0.0169855i
$300$		0			0
$301$	−1.74841	+	0.778444i	−0.100777	+	0.0448688i
$302$	20.4887	+	4.35502i	1.17899	+	0.250603i
$303$		0			0
$304$	1.90831	−	18.1564i	0.109449	−	1.04134i
$305$	−15.1760	+	11.0260i	−0.868978	+	0.631349i
$306$		0			0
$307$	−1.48842			−0.0849485			−0.0424743	−	0.999098i	$-0.513524\pi$
$307$	−1.48842			−0.0849485			−0.0424743	+	0.999098i	$0.513524\pi$
$308$	−3.40989	−	2.52640i	−0.194297	−	0.143955i
$309$		0			0
$310$	4.67434	+	5.19138i	0.265484	+	0.294850i
$311$	−3.10076	−	29.5017i	−0.175828	−	1.67289i	−0.625904	−	0.779900i	$-0.715270\pi$
$311$	−3.10076	−	29.5017i	−0.175828	−	1.67289i	0.450076	−	0.892990i	$-0.351397\pi$
$312$		0			0
$313$	12.4559	−	13.8336i	0.704047	−	0.781923i	−0.279968	−	0.960009i	$-0.590324\pi$
$313$	12.4559	−	13.8336i	0.704047	−	0.781923i	0.984015	+	0.178086i	$0.0569905\pi$
$314$	5.12025	+	15.7585i	0.288952	+	0.889304i
$315$		0			0
$316$	0.582681	−	0.423343i	0.0327784	−	0.0238149i
$317$	4.56815	−	0.970991i	0.256573	−	0.0545363i	−0.0778292	−	0.996967i	$-0.524799\pi$
$317$	4.56815	−	0.970991i	0.256573	−	0.0545363i	0.334402	+	0.942430i	$0.391466\pi$
$318$		0			0
$319$	−8.64493	−	15.3016i	−0.484023	−	0.856723i
$320$	−7.30473	+	12.6522i	−0.408347	+	0.707278i
$321$		0			0
$322$	1.31190	+	0.584098i	0.0731096	+	0.0325505i
$323$	−32.2314	−	23.4175i	−1.79341	−	1.30299i
$324$		0			0
$325$	−2.57808	−	7.93452i	−0.143006	−	0.440128i
$326$	−1.74673	+	16.6190i	−0.0967425	+	0.920443i
$327$		0			0
$328$	−15.9520	−	17.7165i	−0.880802	−	0.978230i
$329$	−19.7223	+	34.1600i	−1.08733	+	1.88330i
$330$		0			0
$331$	12.7376	+	22.0621i	0.700119	+	1.21264i	0.968424	+	0.249308i	$0.0802033\pi$
$331$	12.7376	+	22.0621i	0.700119	+	1.21264i	−0.268305	+	0.963334i	$0.586463\pi$
$332$	1.73988	−	5.35481i	0.0954885	−	0.293883i
$333$		0			0
$334$	−5.45896	−	3.96617i	−0.298701	−	0.217019i
$335$	0.938052	−	1.04181i	0.0512513	−	0.0569203i
$336$		0			0
$337$	24.0202	−	10.6945i	1.30846	−	0.582565i	0.370348	−	0.928893i	$-0.379238\pi$
$337$	24.0202	−	10.6945i	1.30846	−	0.582565i	0.938113	+	0.346328i	$0.112572\pi$
$338$	0.0117904	+	0.112178i	0.000641311	+	0.00610166i
$339$		0			0
$340$	2.29163	+	3.96922i	0.124281	+	0.215261i
$341$	11.0152	+	2.44903i	0.596505	+	0.132622i
$342$		0			0
$343$	4.86552	−	14.9745i	0.262713	−	0.808548i
$344$	1.81146	+	0.806512i	0.0976672	+	0.0434842i
$345$		0			0
$346$	7.85683	+	1.67002i	0.422386	+	0.0897809i
$347$	10.9282	+	2.32287i	0.586658	+	0.124698i	0.491672	−	0.870781i	$-0.336386\pi$
$347$	10.9282	+	2.32287i	0.586658	+	0.124698i	0.0949860	+	0.995479i	$0.469719\pi$
$348$		0			0
$349$	6.67458	+	2.97171i	0.357282	+	0.159072i	0.577525	−	0.816373i	$-0.304018\pi$
$349$	6.67458	+	2.97171i	0.357282	+	0.159072i	−0.220243	+	0.975445i	$0.570685\pi$
$350$	−2.62081	+	8.06602i	−0.140088	+	0.431147i
$351$		0			0
$352$	0.762681	+	7.97153i	0.0406510	+	0.424884i
$353$	10.0286	+	17.3700i	0.533768	+	0.924513i	0.999222	+	0.0394411i	$0.0125578\pi$
$353$	10.0286	+	17.3700i	0.533768	+	0.924513i	−0.465454	+	0.885072i	$0.654109\pi$
$354$		0			0
$355$	−0.189033	−	1.79853i	−0.0100328	−	0.0954561i
$356$	−2.35478	+	1.04842i	−0.124803	+	0.0555660i
$357$		0			0
$358$	−16.5974	+	18.4333i	−0.877199	+	0.974228i
$359$	22.4760	+	16.3297i	1.18624	+	0.861851i	0.992861	−	0.119274i	$-0.0380567\pi$
$359$	22.4760	+	16.3297i	1.18624	+	0.861851i	0.193375	+	0.981125i	$0.438057\pi$
$360$		0			0
$361$	6.04252	−	18.5970i	0.318027	−	0.978788i
$362$	−4.49868	−	7.79194i	−0.236445	−	0.409535i
$363$		0			0
$364$	−2.31475	+	4.00926i	−0.121326	+	0.210143i
$365$	−3.42284	−	3.80145i	−0.179160	−	0.198977i
$366$		0			0
$367$	−2.93908	+	27.9635i	−0.153419	+	1.45968i	0.598868	+	0.800847i	$0.295617\pi$
$367$	−2.93908	+	27.9635i	−0.153419	+	1.45968i	−0.752287	+	0.658835i	$0.771049\pi$
$368$	−0.354751	−	1.09181i	−0.0184927	−	0.0569147i
$369$		0			0
$370$	5.37542	+	3.90547i	0.279455	+	0.203036i
$371$	−12.9498	−	5.76564i	−0.672322	−	0.299337i
$372$		0			0
$373$	−13.1644	+	22.8014i	−0.681625	+	1.18061i	0.292859	+	0.956156i	$0.405393\pi$
$373$	−13.1644	+	22.8014i	−0.681625	+	1.18061i	−0.974485	+	0.224454i	$0.927940\pi$
$374$	−24.2168	−	11.0540i	−1.25222	−	0.571589i
$375$		0			0
$376$	39.9738	−	8.49669i	2.06149	−	0.438183i
$377$	−15.5104	+	11.2690i	−0.798828	+	0.580382i
$378$		0			0
$379$	1.83772	+	5.65591i	0.0943972	+	0.290525i	0.987096	−	0.160129i	$-0.0511910\pi$
$379$	1.83772	+	5.65591i	0.0943972	+	0.290525i	−0.892699	+	0.450654i	$0.851191\pi$
$380$	−2.96779	+	3.29606i	−0.152244	+	0.169084i
$381$		0			0
$382$	0.340237	+	3.23714i	0.0174080	+	0.165626i
$383$	−8.95621	−	9.94688i	−0.457641	−	0.508262i	0.469522	−	0.882921i	$-0.344426\pi$
$383$	−8.95621	−	9.94688i	−0.457641	−	0.508262i	−0.927163	+	0.374659i	$0.877760\pi$
$384$		0			0
$385$	−4.80382	−	15.2681i	−0.244825	−	0.778136i
$386$	−31.5387			−1.60528
$387$		0			0
$388$	6.56339	−	4.76858i	0.333206	−	0.242088i
$389$	−2.03350	+	19.3474i	−0.103102	+	0.980953i	0.813612	+	0.581409i	$0.197498\pi$
$389$	−2.03350	+	19.3474i	−0.103102	+	0.980953i	−0.916714	+	0.399544i	$0.869168\pi$
$390$		0			0
$391$	−2.45049	−	0.520868i	−0.123927	−	0.0263414i
$392$	4.57759	−	2.03808i	0.231203	−	0.102938i
$393$		0			0
$394$	−25.9464	+	5.51507i	−1.30716	+	0.277845i
$395$	2.71643			0.136678
$396$		0			0
$397$	22.4919			1.12884			0.564419	−	0.825489i	$-0.309100\pi$
$397$	22.4919			1.12884			0.564419	+	0.825489i	$0.309100\pi$
$398$	−28.8474	+	6.13170i	−1.44599	+	0.307355i
$399$		0			0
$400$	6.19373	−	2.75763i	0.309687	−	0.137881i
$401$	−5.15321	−	1.09535i	−0.257339	−	0.0546991i	0.0774354	−	0.996997i	$-0.475327\pi$
$401$	−5.15321	−	1.09535i	−0.257339	−	0.0546991i	−0.334775	+	0.942298i	$0.608660\pi$
$402$		0			0
$403$	1.28671	−	12.2422i	0.0640954	−	0.609827i
$404$	−0.637714	+	0.463327i	−0.0317275	+	0.0230514i
$405$		0			0
$406$	19.4897			0.967256
$407$	10.7324	+	0.100184i	0.531983	+	0.00496592i
$408$		0			0
$409$	7.62569	+	8.46918i	0.377066	+	0.418774i	0.901570	−	0.432634i	$-0.142416\pi$
$409$	7.62569	+	8.46918i	0.377066	+	0.418774i	−0.524504	+	0.851408i	$0.675749\pi$
$410$	−1.67962	−	15.9806i	−0.0829507	−	0.789223i
$411$		0			0
$412$	−4.71338	+	5.23473i	−0.232211	+	0.257897i
$413$	1.78557	+	5.49542i	0.0878622	+	0.270412i
$414$		0			0
$415$	17.1799	−	12.4819i	0.843328	−	0.612714i
$416$	8.54478	−	1.81625i	0.418942	−	0.0890490i
$417$		0			0
$418$	2.93178	−	25.5936i	0.143398	−	1.25182i
$419$	7.82991	−	13.5618i	0.382516	−	0.662537i	−0.608905	−	0.793243i	$-0.708391\pi$
$419$	7.82991	−	13.5618i	0.382516	−	0.662537i	0.991421	+	0.130706i	$0.0417244\pi$
$420$		0			0
$421$	23.5913	+	10.5035i	1.14977	+	0.511910i	0.890988	−	0.454027i	$-0.150013\pi$
$421$	23.5913	+	10.5035i	1.14977	+	0.511910i	0.258780	+	0.965936i	$0.416680\pi$
$422$	27.4734	+	19.9606i	1.33738	+	0.971665i
$423$		0			0
$424$	4.53837	+	13.9677i	0.220403	+	0.678330i
$425$	1.54655	−	14.7144i	0.0750187	−	0.713755i
$426$		0			0
$427$	−22.4846	−	24.9717i	−1.08811	−	1.20847i
$428$	2.32161	−	4.02115i	0.112219	−	0.194370i
$429$		0			0
$430$	0.668253	+	1.15745i	0.0322260	+	0.0558171i
$431$	−2.82734	+	8.70166i	−0.136188	+	0.419144i	−0.995773	−	0.0918491i	$-0.970722\pi$
$431$	−2.82734	+	8.70166i	−0.136188	+	0.419144i	0.859585	+	0.510993i	$0.170722\pi$
$432$		0			0
$433$	10.9105	+	7.92694i	0.524325	+	0.380945i	0.818231	−	0.574890i	$-0.194955\pi$
$433$	10.9105	+	7.92694i	0.524325	+	0.380945i	−0.293906	+	0.955834i	$0.594955\pi$
$434$	−8.37325	+	9.29943i	−0.401929	+	0.446387i
$435$		0			0
$436$	−1.34217	+	0.597572i	−0.0642783	+	0.0286185i
$437$	−0.253414	−	2.41107i	−0.0121224	−	0.115337i
$438$		0			0
$439$	−15.0834	−	26.1251i	−0.719889	−	1.24688i	−0.961043	−	0.276398i	$-0.910859\pi$
$439$	−15.0834	−	26.1251i	−0.719889	−	1.24688i	0.241154	−	0.970487i	$-0.422474\pi$
$440$	−8.42525	+	14.2834i	−0.401658	+	0.680934i
$441$		0			0
$442$	−8.97373	+	27.6183i	−0.426837	+	1.31367i
$443$	−0.0474141	−	0.0211101i	−0.00225271	−	0.00100297i	0.405610	−	0.914046i	$-0.367059\pi$
$443$	−0.0474141	−	0.0211101i	−0.00225271	−	0.00100297i	−0.407863	+	0.913043i	$0.633726\pi$
$444$		0			0
$445$	−9.50934	−	2.02127i	−0.450786	−	0.0958175i
$446$	−8.13493	−	1.72913i	−0.385200	−	0.0818768i
$447$		0			0
$448$	−23.9077	−	10.6444i	−1.12953	−	0.502901i
$449$	−9.77373	+	30.0804i	−0.461251	+	1.41958i	0.402387	+	0.915470i	$0.368181\pi$
$449$	−9.77373	+	30.0804i	−0.461251	+	1.41958i	−0.863637	+	0.504114i	$0.831819\pi$
$450$		0			0
$451$	−17.1871	−	19.4503i	−0.809310	−	0.915879i
$452$	−3.00412	−	5.20329i	−0.141302	−	0.244742i
$453$		0			0
$454$	1.38968	+	13.2219i	0.0652210	+	0.620537i
$455$	−15.9511	+	7.10187i	−0.747797	+	0.332941i
$456$		0			0
$457$	−9.94395	+	11.0439i	−0.465158	+	0.516611i	−0.929388	−	0.369104i	$-0.879665\pi$
$457$	−9.94395	+	11.0439i	−0.465158	+	0.516611i	0.464230	+	0.885715i	$0.346331\pi$
$458$	4.29327	+	3.11924i	0.200611	+	0.145753i
$459$		0			0
$460$	−0.0861849	+	0.265250i	−0.00401839	+	0.0123673i
$461$	3.20407	+	5.54962i	0.149229	+	0.258471i	0.930943	−	0.365166i	$-0.118988\pi$
$461$	3.20407	+	5.54962i	0.149229	+	0.258471i	−0.781714	+	0.623637i	$0.785654\pi$
$462$		0			0
$463$	−6.57285	+	11.3845i	−0.305466	+	0.529083i	−0.977365	−	0.211560i	$-0.932146\pi$
$463$	−6.57285	+	11.3845i	−0.305466	+	0.529083i	0.671899	+	0.740643i	$0.265479\pi$
$464$	−10.4252	−	11.5784i	−0.483978	−	0.537512i
$465$		0			0
$466$	2.22768	−	21.1950i	0.103195	−	0.981838i
$467$	3.71967	+	11.4480i	0.172126	+	0.529749i	0.999491	−	0.0319163i	$-0.0101610\pi$
$467$	3.71967	+	11.4480i	0.172126	+	0.529749i	−0.827365	+	0.561665i	$0.810161\pi$
$468$		0			0
$469$	2.03164	+	1.47608i	0.0938126	+	0.0681589i
$470$	25.1637	+	11.2036i	1.16071	+	0.516783i
$471$		0			0
$472$	2.99328	−	5.18452i	0.137777	−	0.238637i
$473$	1.96396	+	0.896471i	0.0903030	+	0.0412198i
$474$		0			0
$475$	14.0049	−	2.97684i	0.642590	−	0.136587i
$476$	−6.64211	+	4.82578i	−0.304441	+	0.221189i
$477$		0			0
$478$	−6.35471	−	19.5578i	−0.290658	−	0.894552i
$479$	−6.96610	+	7.73664i	−0.318289	+	0.353496i	−0.880965	−	0.473182i	$-0.843105\pi$
$479$	−6.96610	+	7.73664i	−0.318289	+	0.353496i	0.562676	+	0.826678i	$0.309772\pi$
$480$		0			0
$481$	−1.22384	−	11.6441i	−0.0558023	−	0.530924i
$482$	2.61382	+	2.90295i	0.119056	+	0.132226i
$483$		0			0
$484$	0.411427	+	4.76940i	0.0187012	+	0.216791i
$485$	30.5982			1.38939
$486$		0			0
$487$	−13.3271	+	9.68267i	−0.603907	+	0.438764i	−0.847263	−	0.531173i	$-0.821751\pi$
$487$	−13.3271	+	9.68267i	−0.603907	+	0.438764i	0.243357	+	0.969937i	$0.421751\pi$
$488$	−3.63909	+	34.6236i	−0.164734	+	1.56734i
$489$		0			0
$490$	3.30358	+	0.702197i	0.149240	+	0.0317220i
$491$	15.0358	−	6.69438i	0.678558	−	0.302113i	−0.0383672	−	0.999264i	$-0.512216\pi$
$491$	15.0358	−	6.69438i	0.678558	−	0.302113i	0.716925	+	0.697150i	$0.245549\pi$
$492$		0			0
$493$	−33.2572	+	7.06903i	−1.49783	+	0.318373i
$494$	−28.1020			−1.26437
$495$		0			0
$496$	10.0035			0.449171
$497$	3.16871	−	0.673529i	0.142136	−	0.0302119i
$498$		0			0
$499$	−18.4649	+	8.22111i	−0.826603	+	0.368027i	−0.776032	−	0.630693i	$-0.782771\pi$
$499$	−18.4649	+	8.22111i	−0.826603	+	0.368027i	−0.0505708	+	0.998720i	$0.516104\pi$
$500$	−5.10465	−	1.08503i	−0.228287	−	0.0485239i
$501$		0			0
$502$	1.35519	−	12.8938i	0.0604852	−	0.575478i
$503$	19.6309	−	14.2627i	0.875299	−	0.635942i	−0.0567046	−	0.998391i	$-0.518059\pi$
$503$	19.6309	−	14.2627i	0.875299	−	0.635942i	0.932004	+	0.362449i	$0.118059\pi$
$504$		0			0
$505$	−2.97299			−0.132296
$506$	−0.486174	−	1.54522i	−0.0216131	−	0.0686935i
$507$		0			0
$508$	−0.280539	−	0.311570i	−0.0124469	−	0.0138237i
$509$	2.67540	+	25.4547i	0.118585	+	1.12826i	0.878335	+	0.478045i	$0.158655\pi$
$509$	2.67540	+	25.4547i	0.118585	+	1.12826i	−0.759750	+	0.650215i	$0.774679\pi$
$510$		0			0
$511$	6.13141	−	6.80962i	0.271238	−	0.301240i
$512$	7.72924	+	23.7882i	0.341587	+	1.05130i
$513$		0			0
$514$	17.2237	−	12.5137i	0.759703	−	0.551957i
$515$	−25.9867	+	5.52364i	−1.14511	+	0.243401i
$516$		0			0
$517$	43.6063	−	8.84421i	1.91780	−	0.388968i
$518$	−5.95112	+	10.3076i	−0.261477	+	0.452892i
$519$		0			0
$520$	16.5262	+	7.35793i	0.724721	+	0.322667i
$521$	−19.4725	−	14.1476i	−0.853105	−	0.619817i	0.0728952	−	0.997340i	$-0.476776\pi$
$521$	−19.4725	−	14.1476i	−0.853105	−	0.619817i	−0.926000	+	0.377522i	$0.876776\pi$
$522$		0			0
$523$	−4.79382	−	14.7539i	−0.209619	−	0.645141i	−0.999492	−	0.0318707i	$-0.989854\pi$
$523$	−4.79382	−	14.7539i	−0.209619	−	0.645141i	0.789873	−	0.613271i	$-0.210146\pi$
$524$	−0.467942	+	4.45217i	−0.0204421	+	0.194494i
$525$		0			0
$526$	−11.0207	−	12.2397i	−0.480525	−	0.533677i
$527$	10.9151	−	18.9056i	0.475471	−	0.823540i
$528$		0			0
$529$	11.4238	+	19.7866i	0.496686	+	0.860285i
$530$	−3.05895	+	9.41449i	−0.132872	+	0.408939i
$531$		0			0
$532$	−6.42767	−	4.66998i	−0.278675	−	0.202469i
$533$	−18.9463	+	21.0420i	−0.820655	+	0.911430i
$534$		0			0
$535$	15.9984	−	7.12293i	0.691670	−	0.307951i
$536$	−0.271962	−	2.58754i	−0.0117470	−	0.111765i
$537$		0			0
$538$	5.74863	+	9.95692i	0.247841	+	0.429273i
$539$	5.00440	−	2.17236i	0.215555	−	0.0935702i
$540$		0			0
$541$	−3.39223	+	10.4402i	−0.145844	+	0.448860i	−0.997119	−	0.0758596i	$-0.975830\pi$
$541$	−3.39223	+	10.4402i	−0.145844	+	0.448860i	0.851275	+	0.524720i	$0.175830\pi$
$542$	8.72468	+	3.88448i	0.374757	+	0.166853i
$543$		0			0
$544$	15.1536	+	3.22100i	0.649705	+	0.138099i
$545$	−5.42009	−	1.15208i	−0.232171	−	0.0493495i
$546$		0			0
$547$	7.69685	+	3.42686i	0.329094	+	0.146522i	0.564631	−	0.825343i	$-0.309018\pi$
$547$	7.69685	+	3.42686i	0.329094	+	0.146522i	−0.235538	+	0.971865i	$0.575685\pi$
$548$	−2.59062	+	7.97310i	−0.110666	+	0.340594i
$549$		0			0
$550$	8.77569	−	3.80944i	0.374197	−	0.162435i
$551$	−16.4512	−	28.4944i	−0.700846	−	1.21390i
$552$		0			0
$553$	0.508636	+	4.83935i	0.0216294	+	0.205790i
$554$	−0.849769	+	0.378342i	−0.0361032	+	0.0160742i
$555$		0			0
$556$	−1.64839	+	1.83072i	−0.0699072	+	0.0776398i
$557$	19.9867	+	14.5212i	0.846864	+	0.615283i	0.924280	−	0.381716i	$-0.124667\pi$
$557$	19.9867	+	14.5212i	0.846864	+	0.615283i	−0.0774156	+	0.996999i	$0.524667\pi$
$558$		0			0
$559$	0.727761	−	2.23982i	0.0307810	−	0.0947343i
$560$	−7.09475	−	12.2885i	−0.299808	−	0.519282i
$561$		0			0
$562$	−15.5288	+	26.8967i	−0.655043	+	1.13457i
$563$	−2.87763	−	3.19593i	−0.121278	−	0.134692i	0.679448	−	0.733723i	$-0.262219\pi$
$563$	−2.87763	−	3.19593i	−0.121278	−	0.134692i	−0.800726	+	0.599031i	$0.795553\pi$
$564$		0			0
$565$	2.36868	−	22.5365i	0.0996513	−	0.948119i
$566$	6.30595	+	19.4077i	0.265059	+	0.815767i
$567$		0			0
$568$	−2.71530	−	1.97278i	−0.113932	−	0.0827762i
$569$	7.20042	+	3.20584i	0.301858	+	0.134396i	0.552076	−	0.833794i	$-0.313836\pi$
$569$	7.20042	+	3.20584i	0.301858	+	0.134396i	−0.250219	+	0.968189i	$0.580502\pi$
$570$		0			0
$571$	11.5035	−	19.9247i	0.481407	−	0.833821i	−0.518365	−	0.855159i	$-0.673459\pi$
$571$	11.5035	−	19.9247i	0.481407	−	0.833821i	0.999772	+	0.0213379i	$0.00679257\pi$
$572$	5.11795	−	1.03802i	0.213992	−	0.0434018i
$573$		0			0
$574$	28.1550	−	5.98454i	1.17517	−	0.249790i
$575$	0.728385	−	0.529202i	0.0303757	−	0.0220693i
$576$		0			0
$577$	7.80507	+	24.0215i	0.324929	+	1.00003i	0.971472	+	0.237152i	$0.0762140\pi$
$577$	7.80507	+	24.0215i	0.324929	+	1.00003i	−0.646543	+	0.762877i	$0.723786\pi$
$578$	−20.2305	+	22.4683i	−0.841480	+	0.934558i
$579$		0			0
$580$	0.395654	+	3.76439i	0.0164286	+	0.156308i
$581$	25.4535	+	28.2690i	1.05599	+	1.17280i
$582$		0			0
$583$	4.79903	+	15.2529i	0.198756	+	0.631711i
$584$	−9.49365			−0.392850
$585$		0			0
$586$	−5.78029	+	4.19962i	−0.238781	+	0.173485i
$587$	2.43294	−	23.1479i	0.100418	−	0.955417i	−0.822069	−	0.569389i	$-0.807180\pi$
$587$	2.43294	−	23.1479i	0.100418	−	0.955417i	0.922487	−	0.386028i	$-0.126153\pi$
$588$		0			0
$589$	20.6639	+	4.39224i	0.851439	+	0.180979i
$590$	3.68622	−	1.64121i	0.151759	−	0.0675676i
$591$		0			0
$592$	9.30684	−	1.97823i	0.382509	−	0.0813048i
$593$	17.1253			0.703251			0.351626	−	0.936141i	$-0.385629\pi$
$593$	17.1253			0.703251			0.351626	+	0.936141i	$0.385629\pi$
$594$		0			0
$595$	−30.9652			−1.26945
$596$	3.37190	−	0.716719i	0.138118	−	0.0293579i
$597$		0			0
$598$	−1.61434	+	0.718750i	−0.0660152	+	0.0293919i
$599$	−41.8000	−	8.88486i	−1.70790	−	0.363025i	−0.752558	−	0.658526i	$-0.771180\pi$
$599$	−41.8000	−	8.88486i	−1.70790	−	0.363025i	−0.955343	+	0.295501i	$0.904514\pi$
$600$		0			0
$601$	−1.33865	+	12.7364i	−0.0546047	+	0.519529i	0.932696	+	0.360664i	$0.117450\pi$
$601$	−1.33865	+	12.7364i	−0.0546047	+	0.519529i	−0.987300	+	0.158865i	$0.949217\pi$
$602$	−1.93688	+	1.40722i	−0.0789413	+	0.0573542i
$603$		0			0
$604$	−7.28721			−0.296512
$605$	−9.31785	+	15.4649i	−0.378824	+	0.628737i
$606$		0			0
$607$	7.65508	+	8.50183i	0.310710	+	0.345079i	0.878193	−	0.478307i	$-0.158749\pi$
$607$	7.65508	+	8.50183i	0.310710	+	0.345079i	−0.567483	+	0.823385i	$0.692083\pi$
$608$	1.56709	+	14.9098i	0.0635538	+	0.604674i
$609$		0			0
$610$	−15.7015	+	17.4383i	−0.635737	+	0.706057i
$611$	−14.9990	−	46.1621i	−0.606794	−	1.86752i
$612$		0			0
$613$	−15.2464	+	11.0772i	−0.615796	+	0.447402i	−0.851451	−	0.524435i	$-0.824277\pi$
$613$	−15.2464	+	11.0772i	−0.615796	+	0.447402i	0.235654	+	0.971837i	$0.424277\pi$
$614$	−1.82121	+	0.387110i	−0.0734980	+	0.0156225i
$615$		0			0
$616$	−27.0236	−	12.3352i	−1.08881	−	0.496999i
$617$	7.65992	−	13.2674i	0.308377	−	0.534124i	−0.669631	−	0.742694i	$-0.733548\pi$
$617$	7.65992	−	13.2674i	0.308377	−	0.534124i	0.978007	+	0.208570i	$0.0668809\pi$
$618$		0			0
$619$	−2.02690	−	0.902432i	−0.0814679	−	0.0362718i	0.365598	−	0.930773i	$-0.380864\pi$
$619$	−2.02690	−	0.902432i	−0.0814679	−	0.0362718i	−0.447066	+	0.894501i	$0.647531\pi$
$620$	−1.96615	−	1.42849i	−0.0789626	−	0.0573697i
$621$		0			0
$622$	−11.4669	−	35.2915i	−0.459781	−	1.41506i
$623$	1.82035	−	17.3195i	0.0729307	−	0.693889i
$624$		0			0
$625$	−5.45559	−	6.05905i	−0.218224	−	0.242362i
$626$	11.6430	−	20.1662i	0.465346	−	0.806004i
$627$		0			0
$628$	−2.88223	−	4.99218i	−0.115014	−	0.199209i
$629$	6.41634	−	19.7475i	0.255836	−	0.787383i
$630$		0			0
$631$	10.0626	+	7.31089i	0.400585	+	0.291042i	0.769779	−	0.638310i	$-0.220366\pi$
$631$	10.0626	+	7.31089i	0.400585	+	0.291042i	−0.369194	+	0.929352i	$0.620366\pi$
$632$	3.37339	−	3.74653i	0.134186	−	0.149029i
$633$		0			0
$634$	5.33700	−	2.37618i	0.211959	−	0.0943704i
$635$	−0.165288	−	1.57261i	−0.00655926	−	0.0624072i
$636$		0			0
$637$	−2.97568	−	5.15403i	−0.117901	−	0.204210i
$638$	−14.5575	−	16.4744i	−0.576336	−	0.652228i
$639$		0			0
$640$	−3.19808	+	9.84267i	−0.126415	+	0.389066i
$641$	−22.5348	−	10.0332i	−0.890073	−	0.396286i	−0.0898264	−	0.995957i	$-0.528631\pi$
$641$	−22.5348	−	10.0332i	−0.890073	−	0.396286i	−0.800246	+	0.599672i	$0.795298\pi$
$642$		0			0
$643$	−16.7162	−	3.55313i	−0.659222	−	0.140122i	−0.133859	−	0.991000i	$-0.542737\pi$
$643$	−16.7162	−	3.55313i	−0.659222	−	0.140122i	−0.525363	+	0.850878i	$0.676070\pi$
$644$	−0.488683	−	0.103873i	−0.0192568	−	0.00409316i
$645$		0			0
$646$	−45.5284	−	20.2706i	−1.79129	−	0.797535i
$647$	12.2195	−	37.6077i	0.480398	−	1.47851i	−0.358139	−	0.933668i	$-0.616589\pi$
$647$	12.2195	−	37.6077i	0.480398	−	1.47851i	0.838537	−	0.544844i	$-0.183411\pi$
$648$		0			0
$649$	3.31152	−	5.61404i	0.129988	−	0.220370i
$650$	−5.21813	−	9.03807i	−0.204672	−	0.354502i
$651$		0			0
$652$	−0.607682	−	5.78171i	−0.0237987	−	0.226429i
$653$	−26.4170	+	11.7616i	−1.03378	+	0.460267i	−0.852258	−	0.523121i	$-0.824768\pi$
$653$	−26.4170	+	11.7616i	−1.03378	+	0.460267i	−0.181518	+	0.983388i	$0.558101\pi$
$654$		0			0
$655$	−11.2978	+	12.5475i	−0.441441	+	0.490270i
$656$	−18.6157	−	13.5251i	−0.726820	−	0.528066i
$657$		0			0
$658$	−15.2476	+	46.9272i	−0.594412	+	1.82941i
$659$	12.2344	+	21.1906i	0.476585	+	0.825470i	0.999640	−	0.0268290i	$-0.00854098\pi$
$659$	12.2344	+	21.1906i	0.476585	+	0.825470i	−0.523055	+	0.852299i	$0.675208\pi$
$660$		0			0
$661$	−14.9366	+	25.8710i	−0.580967	+	1.00626i	0.414398	+	0.910096i	$0.363992\pi$
$661$	−14.9366	+	25.8710i	−0.580967	+	1.00626i	−0.995365	+	0.0961687i	$0.969341\pi$
$662$	21.3235	+	23.6821i	0.828760	+	0.920431i
$663$		0			0
$664$	4.11960	−	39.1954i	0.159872	−	1.52108i
$665$	−9.25985	−	28.4989i	−0.359081	−	1.10514i
$666$		0			0
$667$	−1.67383	−	1.21611i	−0.0648111	−	0.0470880i
$668$	2.14454	+	0.954809i	0.0829746	+	0.0369427i
$669$		0			0
$670$	0.876832	−	1.51872i	0.0338750	−	0.0586732i
$671$	−4.31380	+	37.6582i	−0.166533	+	1.45378i
$672$		0			0
$673$	−25.7168	+	5.46628i	−0.991312	+	0.210710i	−0.674898	−	0.737911i	$-0.735812\pi$
$673$	−25.7168	+	5.46628i	−0.991312	+	0.210710i	−0.316414	+	0.948621i	$0.602479\pi$
$674$	26.6093	−	19.3328i	1.02495	−	0.744672i
$675$		0			0
$676$	−0.0121262	−	0.0373206i	−0.000466393	−	0.00143541i
$677$	29.2654	−	32.5025i	1.12476	−	1.24917i	0.159695	−	0.987166i	$-0.448949\pi$
$677$	29.2654	−	32.5025i	1.12476	−	1.24917i	0.965066	−	0.262007i	$-0.0843845\pi$
$678$		0			0
$679$	5.72934	+	54.5110i	0.219872	+	2.09194i
$680$	21.4668	+	23.8413i	0.823216	+	0.914274i
$681$		0			0
$682$	14.1150	+	0.131760i	0.540490	+	0.00504534i
$683$	−14.0939			−0.539288			−0.269644	−	0.962960i	$-0.586906\pi$
$683$	−14.0939			−0.539288			−0.269644	+	0.962960i	$0.586906\pi$
$684$		0			0
$685$	−25.5802	+	18.5851i	−0.977368	+	0.710100i
$686$	2.05879	−	19.5881i	0.0786049	−	0.747876i
$687$		0			0
$688$	1.87206	+	0.397918i	0.0713714	+	0.0151705i
$689$	15.9352	−	7.09479i	0.607081	−	0.270290i
$690$		0			0
$691$	5.74534	−	1.22121i	0.218563	−	0.0464570i	−0.0973286	−	0.995252i	$-0.531030\pi$
$691$	5.74534	−	1.22121i	0.218563	−	0.0464570i	0.315892	+	0.948795i	$0.397696\pi$
$692$	−2.79443			−0.106228
$693$		0			0
$694$	13.9758			0.530513
$695$	−9.08820	+	1.93176i	−0.344735	+	0.0732757i
$696$		0			0
$697$	−45.8731	+	20.4240i	−1.73757	+	0.773615i
$698$	8.93982	+	1.90022i	0.338377	+	0.0719243i
$699$		0			0
$700$	0.308417	−	2.93439i	0.0116571	−	0.110909i
$701$	0.165822	−	0.120477i	0.00626302	−	0.00455035i	−0.584649	−	0.811286i	$-0.698768\pi$
$701$	0.165822	−	0.120477i	0.00626302	−	0.00455035i	0.590912	+	0.806736i	$0.298768\pi$
$702$		0			0
$703$	20.0934			0.757835
$704$	8.85988	+	28.1596i	0.333919	+	1.06131i
$705$		0			0
$706$	16.7885	+	18.6455i	0.631843	+	0.701732i
$707$	−0.556676	−	5.29642i	−0.0209360	−	0.199192i
$708$		0			0
$709$	−25.6436	+	28.4801i	−0.963065	+	1.06959i	0.0344689	+	0.999406i	$0.489026\pi$
$709$	−25.6436	+	28.4801i	−0.963065	+	1.06959i	−0.997534	+	0.0701863i	$0.977641\pi$
$710$	−0.699063	−	2.15149i	−0.0262354	−	0.0807441i
$711$		0			0
$712$	−14.5969	+	10.6053i	−0.547042	+	0.397449i
$713$	1.29939	−	0.276193i	0.0486624	−	0.0103435i
$714$		0			0
$715$	17.9175	+	8.17864i	0.670077	+	0.305864i
$716$	4.31468	−	7.47325i	0.161247	−	0.279289i
$717$		0			0
$718$	31.7484	+	14.1353i	1.18484	+	0.527524i
$719$	32.0818	+	23.3088i	1.19645	+	0.869270i	0.993931	−	0.110009i	$-0.0350878\pi$
$719$	32.0818	+	23.3088i	1.19645	+	0.869270i	0.202517	+	0.979279i	$0.435088\pi$
$720$		0			0
$721$	−14.7063	−	45.2613i	−0.547691	−	1.68562i
$722$	2.55682	−	24.3266i	0.0951551	−	0.905341i
$723$		0			0
$724$	2.09448	+	2.32616i	0.0778407	+	0.0864509i
$725$	6.10949	−	10.5820i	0.226901	−	0.393004i
$726$		0			0
$727$	6.09749	+	10.5612i	0.226144	+	0.391692i	0.956662	−	0.291201i	$-0.0940548\pi$
$727$	6.09749	+	10.5612i	0.226144	+	0.391692i	−0.730518	+	0.682893i	$0.760722\pi$
$728$	−10.0138	+	30.8193i	−0.371136	+	1.14224i
$729$		0			0
$730$	−5.17683	−	3.76119i	−0.191603	−	0.139208i
$731$	2.79468	−	3.10381i	0.103365	−	0.114798i
$732$		0			0
$733$	13.7947	−	6.14182i	0.509521	−	0.226853i	−0.135841	−	0.990731i	$-0.543374\pi$
$733$	13.7947	−	6.14182i	0.509521	−	0.226853i	0.645361	+	0.763877i	$0.276707\pi$
$734$	3.67656	+	34.9802i	0.135704	+	1.29114i
$735$		0			0
$736$	0.471363	+	0.816424i	0.0173747	+	0.0300938i
$737$	−0.269792	−	2.81986i	−0.00993791	−	0.103871i
$738$		0			0
$739$	−5.34127	+	16.4387i	−0.196482	+	0.604709i	0.803474	+	0.595339i	$0.202982\pi$
$739$	−5.34127	+	16.4387i	−0.196482	+	0.604709i	−0.999956	+	0.00936931i	$0.997018\pi$
$740$	−2.11171	−	0.940196i	−0.0776281	−	0.0345623i
$741$		0			0
$742$	−17.3448	−	3.68675i	−0.636747	−	0.135345i
$743$	−19.0991	−	4.05964i	−0.700678	−	0.148934i	−0.156221	−	0.987722i	$-0.549931\pi$
$743$	−19.0991	−	4.05964i	−0.700678	−	0.148934i	−0.544457	+	0.838788i	$0.683264\pi$
$744$		0			0
$745$	11.8775	+	5.28821i	0.435158	+	0.193745i
$746$	−10.1775	+	31.3233i	−0.372626	+	1.14683i
$747$		0			0
$748$	9.04040	+	2.00997i	0.330550	+	0.0734919i
$749$	15.6852	+	27.1675i	0.573124	+	0.992680i
$750$		0			0
$751$	−3.78252	−	35.9883i	−0.138026	−	1.31323i	−0.815960	−	0.578108i	$-0.803791\pi$
$751$	−3.78252	−	35.9883i	−0.138026	−	1.31323i	0.677934	−	0.735123i	$-0.262875\pi$
$752$	36.0344	−	16.0436i	1.31404	−	0.585048i
$753$		0			0
$754$	−16.0475	+	17.8226i	−0.584416	+	0.649059i
$755$	−22.2354	−	16.1549i	−0.809228	−	0.587938i
$756$		0			0
$757$	−8.14836	+	25.0781i	−0.296157	+	0.911479i	0.686673	+	0.726967i	$0.259070\pi$
$757$	−8.14836	+	25.0781i	−0.296157	+	0.911479i	−0.982830	+	0.184512i	$0.940930\pi$
$758$	3.71961	+	6.44255i	0.135102	+	0.234004i
$759$		0			0
$760$	−15.5230	+	26.8866i	−0.563077	+	0.975278i
$761$	−5.65857	−	6.28448i	−0.205123	−	0.227812i	0.631802	−	0.775130i	$-0.282316\pi$
$761$	−5.65857	−	6.28448i	−0.205123	−	0.227812i	−0.836925	+	0.547318i	$0.815649\pi$
$762$		0			0
$763$	1.03755	−	9.87168i	0.0375620	−	0.357379i
$764$	−0.349929	−	1.07697i	−0.0126600	−	0.0389634i
$765$		0			0
$766$	−13.5457	−	9.84153i	−0.489426	−	0.355589i
$767$	−6.49557	−	2.89201i	−0.234541	−	0.104425i
$768$		0			0
$769$	−2.53050	+	4.38295i	−0.0912520	+	0.158053i	−0.908038	−	0.418887i	$-0.862420\pi$
$769$	−2.53050	+	4.38295i	−0.0912520	+	0.158053i	0.816786	+	0.576940i	$0.195754\pi$
$770$	−9.84885	−	17.4325i	−0.354928	−	0.628223i
$771$		0			0
$772$	10.7325	−	2.28125i	0.386269	−	0.0821041i
$773$	21.8296	−	15.8601i	0.785156	−	0.570449i	−0.121366	−	0.992608i	$-0.538727\pi$
$773$	21.8296	−	15.8601i	0.785156	−	0.570449i	0.906522	+	0.422159i	$0.138727\pi$
$774$		0			0
$775$	2.42436	+	7.46140i	0.0870854	+	0.268021i
$776$	37.9983	−	42.2014i	1.36406	−	1.51494i
$777$		0			0
$778$	2.54375	+	24.2021i	0.0911977	+	0.867688i
$779$	−32.5152	−	36.1118i	−1.16498	−	1.29384i
$780$		0			0
$781$	−2.93614	−	2.17539i	−0.105063	−	0.0778416i
$782$	−3.13386			−0.112066
$783$		0			0
$784$	3.91274	−	2.84277i	0.139741	−	0.101528i
$785$	2.27258	−	21.6221i	0.0811118	−	0.771727i
$786$		0			0
$787$	−14.9044	−	3.16804i	−0.531286	−	0.112928i	−0.0655452	−	0.997850i	$-0.520879\pi$
$787$	−14.9044	−	3.16804i	−0.531286	−	0.112928i	−0.465741	+	0.884921i	$0.654212\pi$
$788$	8.43050	−	3.75350i	0.300324	−	0.133713i
$789$		0			0
$790$	3.32379	−	0.706493i	0.118255	−	0.0251359i
$791$	40.5926			1.44331
$792$		0			0
$793$	41.3492			1.46835
$794$	27.5208	−	5.84973i	0.976678	−	0.207599i
$795$		0			0
$796$	9.37309	−	4.17317i	0.332220	−	0.147914i
$797$	9.71899	+	2.06584i	0.344264	+	0.0731757i	0.376799	−	0.926295i	$-0.377025\pi$
$797$	9.71899	+	2.06584i	0.344264	+	0.0731757i	−0.0325348	+	0.999471i	$0.510358\pi$
$798$		0			0
$799$	8.99765	−	85.6069i	0.318314	−	3.02855i
$800$	−4.50426	+	3.27254i	−0.159250	+	0.115702i
$801$		0			0
$802$	−6.59029			−0.232711
$803$	−10.3359	−	0.0964826i	−0.364745	−	0.00340480i
$804$		0			0
$805$	−1.26084	−	1.40030i	−0.0444387	−	0.0493541i
$806$	−1.60957	−	15.3140i	−0.0566947	−	0.539414i
$807$		0			0
$808$	−3.69200	+	4.10039i	−0.129884	+	0.144251i
$809$	−11.4547	−	35.2540i	−0.402727	−	1.23947i	−0.922778	−	0.385331i	$-0.874087\pi$
$809$	−11.4547	−	35.2540i	−0.402727	−	1.23947i	0.520052	−	0.854135i	$-0.325913\pi$
$810$		0			0
$811$	34.3539	−	24.9596i	1.20633	−	0.876449i	0.211436	−	0.977392i	$-0.432186\pi$
$811$	34.3539	−	24.9596i	1.20633	−	0.876449i	0.994892	+	0.100943i	$0.0321860\pi$
$812$	−6.63222	+	1.40972i	−0.232745	+	0.0494716i
$813$		0			0
$814$	13.1580	−	2.66870i	0.461189	−	0.0935380i
$815$	10.9632	−	18.9888i	0.384024	−	0.665149i
$816$		0			0
$817$	3.69232	+	1.64393i	0.129178	+	0.0575137i
$818$	11.5334	+	8.37948i	0.403255	+	0.292982i
$819$		0			0
$820$	1.72747	+	5.31660i	0.0603258	+	0.185664i
$821$	−0.800958	+	7.62061i	−0.0279536	+	0.265961i	0.971614	+	0.236570i	$0.0760234\pi$
$821$	−0.800958	+	7.62061i	−0.0279536	+	0.265961i	−0.999568	+	0.0293907i	$0.990643\pi$
$822$		0			0
$823$	2.48273	+	2.75735i	0.0865424	+	0.0961150i	0.784860	−	0.619672i	$-0.212735\pi$
$823$	2.48273	+	2.75735i	0.0865424	+	0.0961150i	−0.698318	+	0.715788i	$0.746068\pi$
$824$	−24.6532	+	42.7007i	−0.858836	+	1.48755i
$825$		0			0
$826$	3.61406	+	6.25973i	0.125749	+	0.217804i
$827$	1.30500	−	4.01636i	0.0453791	−	0.139663i	−0.925800	−	0.378014i	$-0.876607\pi$
$827$	1.30500	−	4.01636i	0.0453791	−	0.139663i	0.971179	+	0.238352i	$0.0766070\pi$
$828$		0			0
$829$	21.2154	+	15.4139i	0.736840	+	0.535346i	0.891720	−	0.452588i	$-0.149499\pi$
$829$	21.2154	+	15.4139i	0.736840	+	0.535346i	−0.154880	+	0.987933i	$0.549499\pi$
$830$	17.7748	−	19.7409i	0.616972	−	0.685217i
$831$		0			0
$832$	29.4192	−	13.0983i	1.01993	−	0.454101i
$833$	−1.10323	−	10.4965i	−0.0382246	−	0.363683i
$834$		0			0
$835$	4.42689	+	7.66759i	0.153199	+	0.265348i
$836$	0.853561	+	8.92141i	0.0295210	+	0.308553i
$837$		0			0
$838$	6.05340	−	18.6305i	0.209111	−	0.643578i
$839$	−14.9574	−	6.65948i	−0.516388	−	0.229911i	0.131960	−	0.991255i	$-0.457873\pi$
$839$	−14.9574	−	6.65948i	−0.516388	−	0.229911i	−0.648348	+	0.761344i	$0.724540\pi$
$840$		0			0
$841$	0.900543	+	0.191416i	0.0310532	+	0.00660056i
$842$	31.5977	+	6.71631i	1.08893	+	0.231459i
$843$		0			0
$844$	−10.7928	−	4.80527i	−0.371504	−	0.165404i
$845$	0.0457352	−	0.140758i	0.00157334	−	0.00484224i
$846$		0			0
$847$	−29.2956	−	13.7041i	−1.00661	−	0.470880i
$848$	7.08768	+	12.2762i	0.243392	+	0.421567i
$849$		0			0
$850$	−1.93461	−	18.4066i	−0.0663567	−	0.631342i
$851$	1.15427	−	0.513916i	0.0395680	−	0.0176168i
$852$		0			0
$853$	27.9237	−	31.0125i	0.956091	−	1.06185i	−0.0419399	−	0.999120i	$-0.513354\pi$
$853$	27.9237	−	31.0125i	0.956091	−	1.06185i	0.998031	−	0.0627264i	$-0.0199795\pi$
$854$	−34.0066	−	24.7072i	−1.16368	−	0.845464i
$855$		0			0
$856$	10.0435	−	30.9107i	0.343280	−	1.05651i
$857$	22.1267	+	38.3246i	0.755834	+	1.30914i	0.944959	+	0.327190i	$0.106102\pi$
$857$	22.1267	+	38.3246i	0.755834	+	1.30914i	−0.189124	+	0.981953i	$0.560565\pi$
$858$		0			0
$859$	11.2862	−	19.5482i	0.385080	−	0.666978i	−0.606701	−	0.794930i	$-0.707507\pi$
$859$	11.2862	−	19.5482i	0.385080	−	0.666978i	0.991780	+	0.127953i	$0.0408406\pi$
$860$	−0.311123	−	0.345537i	−0.0106092	−	0.0117827i
$861$		0			0
$862$	−1.19636	+	11.3826i	−0.0407481	+	0.387692i
$863$	−0.793169	−	2.44112i	−0.0269998	−	0.0830968i	0.936649	−	0.350270i	$-0.113910\pi$
$863$	−0.793169	−	2.44112i	−0.0269998	−	0.0830968i	−0.963648	+	0.267174i	$0.913910\pi$
$864$		0			0
$865$	−8.52661	−	6.19495i	−0.289914	−	0.210635i
$866$	15.4116	+	6.86169i	0.523707	+	0.233170i
$867$		0			0
$868$	2.17672	−	3.77020i	0.0738829	−	0.127969i
$869$	3.71073	−	4.04462i	0.125878	−	0.137204i
$870$		0			0
$871$	−3.02264	+	0.642482i	−0.102418	+	0.0217697i
$872$	−8.31989	+	6.04475i	−0.281747	+	0.204701i
$873$		0			0
$874$	−0.937150	−	2.88425i	−0.0316996	−	0.0975612i
$875$	23.5924	−	26.2020i	0.797568	−	0.885789i
$876$		0			0
$877$	−5.62263	−	53.4958i	−0.189863	−	1.80642i	−0.511204	−	0.859460i	$-0.670800\pi$
$877$	−5.62263	−	53.4958i	−0.189863	−	1.80642i	0.321341	−	0.946964i	$-0.395866\pi$
$878$	−25.2505	−	28.0435i	−0.852162	−	0.946421i
$879$		0			0
$880$	−5.08801	+	15.1758i	−0.171517	+	0.511576i
$881$	−42.7815			−1.44134			−0.720672	−	0.693276i	$-0.756167\pi$
$881$	−42.7815			−1.44134			−0.720672	+	0.693276i	$0.756167\pi$
$882$		0			0
$883$	−2.00195	+	1.45450i	−0.0673711	+	0.0489479i	−0.620961	−	0.783841i	$-0.713257\pi$
$883$	−2.00195	+	1.45450i	−0.0673711	+	0.0489479i	0.553590	+	0.832789i	$0.313257\pi$
$884$	1.05603	−	10.0474i	0.0355181	−	0.337932i
$885$		0			0
$886$	−0.0635057	−	0.0134985i	−0.00213352	−	0.000453493i
$887$	−1.92343	+	0.856366i	−0.0645825	+	0.0287540i	−0.438774	−	0.898598i	$-0.644587\pi$
$887$	−1.92343	+	0.856366i	−0.0645825	+	0.0287540i	0.374191	+	0.927352i	$0.377920\pi$
$888$		0			0
$889$	2.77068	−	0.588925i	0.0929255	−	0.0197519i
$890$	−12.1612			−0.407644
$891$		0			0
$892$	2.89334			0.0968763
$893$	81.4791	−	17.3189i	2.72659	−	0.579555i
$894$		0			0
$895$	29.7327	−	13.2379i	0.993855	−	0.442493i
$896$	−18.1336	−	3.85443i	−0.605803	−	0.128767i
$897$		0			0
$898$	−4.13564	+	39.3480i	−0.138008	+	1.31306i
$899$	14.5856	−	10.5970i	0.486456	−	0.353431i
$900$		0			0
$901$	30.9344			1.03057
$902$	−26.0886	−	19.3291i	−0.868655	−	0.643589i
$903$		0			0
$904$	−28.1411	−	31.2538i	−0.935959	−	1.03949i
$905$	1.23403	+	11.7410i	0.0410205	+	0.390284i
$906$		0			0
$907$	−9.13214	+	10.1423i	−0.303228	+	0.336768i	−0.875431	−	0.483344i	$-0.839422\pi$
$907$	−9.13214	+	10.1423i	−0.303228	+	0.336768i	0.572203	+	0.820112i	$0.306089\pi$
$908$	−1.42927	−	4.39884i	−0.0474319	−	0.145980i
$909$		0			0
$910$	−17.6704	+	12.8383i	−0.585769	+	0.425586i
$911$	7.40931	−	1.57490i	0.245481	−	0.0521787i	−0.0835277	−	0.996505i	$-0.526619\pi$
$911$	7.40931	−	1.57490i	0.245481	−	0.0521787i	0.329009	+	0.944327i	$0.393285\pi$
$912$		0			0
$913$	4.88340	−	42.6307i	0.161617	−	1.41087i
$914$	−9.29498	+	16.0994i	−0.307451	+	0.532520i
$915$		0			0
$916$	−1.68660	−	0.750921i	−0.0557267	−	0.0248111i
$917$	−24.4689	−	17.7777i	−0.808034	−	0.587071i
$918$		0			0
$919$	−5.16917	−	15.9091i	−0.170515	−	0.524792i	0.828885	−	0.559419i	$-0.188976\pi$
$919$	−5.16917	−	15.9091i	−0.170515	−	0.524792i	−0.999400	+	0.0346269i	$0.988976\pi$
$920$	−0.204064	+	1.94154i	−0.00672778	+	0.0640106i
$921$		0			0
$922$	5.36381	+	5.95712i	0.176648	+	0.196187i
$923$	−1.99315	+	3.45224i	−0.0656053	+	0.113632i
$924$		0			0
$925$	3.73104	+	6.46234i	0.122676	+	0.212481i
$926$	−5.08155	+	15.6394i	−0.166990	+	0.513943i
$927$		0			0
$928$	10.3508	+	7.52032i	0.339783	+	0.246866i
$929$	13.8030	−	15.3298i	0.452863	−	0.502955i	−0.472871	−	0.881132i	$-0.656782\pi$
$929$	13.8030	−	15.3298i	0.452863	−	0.502955i	0.925733	+	0.378177i	$0.123449\pi$
$930$		0			0
$931$	9.33057	−	4.15424i	0.305797	−	0.136150i
$932$	0.775003	+	7.37366i	0.0253861	+	0.241532i
$933$		0			0
$934$	7.52874	+	13.0402i	0.246348	+	0.426687i
$935$	23.1290	+	26.1746i	0.756398	+	0.856000i
$936$		0			0
$937$	−9.60247	+	29.5534i	−0.313699	+	0.965466i	0.662588	+	0.748984i	$0.269458\pi$
$937$	−9.60247	+	29.5534i	−0.313699	+	0.965466i	−0.976287	+	0.216482i	$0.930542\pi$
$938$	2.86979	+	1.27771i	0.0937021	+	0.0417189i
$939$		0			0
$940$	−9.37343	−	1.99238i	−0.305728	−	0.0649844i
$941$	−15.4487	−	3.28372i	−0.503612	−	0.107046i	−0.0509018	−	0.998704i	$-0.516210\pi$
$941$	−15.4487	−	3.28372i	−0.503612	−	0.107046i	−0.452710	+	0.891658i	$0.649543\pi$
$942$		0			0
$943$	−2.79147	−	1.24284i	−0.0909026	−	0.0404725i
$944$	1.78557	−	5.49542i	0.0581154	−	0.178861i
$945$		0			0
$946$	2.63623	+	0.586120i	0.0857113	+	0.0190564i
$947$	−26.3537	−	45.6460i	−0.856381	−	1.48329i	−0.875358	−	0.483475i	$-0.839374\pi$
$947$	−26.3537	−	45.6460i	−0.856381	−	1.48329i	0.0189774	−	0.999820i	$-0.493959\pi$
$948$		0			0
$949$	1.17863	+	11.2139i	0.0382599	+	0.364018i
$950$	16.3620	−	7.28485i	0.530854	−	0.236352i
$951$		0			0
$952$	−38.4541	+	42.7076i	−1.24630	+	1.38416i
$953$	−38.4078	−	27.9049i	−1.24415	−	0.903928i	−0.246282	−	0.969198i	$-0.579209\pi$
$953$	−38.4078	−	27.9049i	−1.24415	−	0.903928i	−0.997868	+	0.0652707i	$0.979209\pi$
$954$		0			0
$955$	1.31979	−	4.06190i	0.0427074	−	0.131440i
$956$	3.57712	+	6.19576i	0.115692	+	0.200385i
$957$		0			0
$958$	−6.51147	+	11.2782i	−0.210376	+	0.364382i
$959$	−37.8993	−	42.0914i	−1.22383	−	1.35920i
$960$		0			0
$961$	2.03040	−	19.3180i	0.0654968	−	0.623160i
$962$	−4.52588	−	13.9292i	−0.145920	−	0.449096i
$963$		0			0
$964$	−1.09945	−	0.798794i	−0.0354108	−	0.0257274i
$965$	37.8051	+	16.8319i	1.21699	+	0.541838i
$966$		0			0
$967$	−6.56700	+	11.3744i	−0.211180	+	0.365775i	−0.952084	−	0.305836i	$-0.901064\pi$
$967$	−6.56700	+	11.3744i	−0.211180	+	0.365775i	0.740904	+	0.671611i	$0.234397\pi$
$968$	9.75801	+	32.0563i	0.313634	+	1.03033i
$969$		0			0
$970$	37.4396	−	7.95803i	1.20211	−	0.255517i
$971$	26.8860	−	19.5338i	0.862814	−	0.626871i	−0.0658353	−	0.997831i	$-0.520971\pi$
$971$	26.8860	−	19.5338i	0.862814	−	0.626871i	0.928649	+	0.370960i	$0.120971\pi$
$972$		0			0
$973$	−5.14316	−	15.8290i	−0.164882	−	0.507455i
$974$	−13.7885	+	15.3137i	−0.441813	+	0.490683i
$975$		0			0
$976$	3.51245	+	33.4187i	0.112431	+	1.06971i
$977$	−10.2957	−	11.4346i	−0.329389	−	0.365824i	0.555588	−	0.831458i	$-0.312493\pi$
$977$	−10.2957	−	11.4346i	−0.329389	−	0.365824i	−0.884978	+	0.465634i	$0.845826\pi$
$978$		0			0
$979$	−15.9996	+	11.3978i	−0.511351	+	0.364274i
$980$	−1.17498			−0.0375334
$981$		0			0
$982$	16.6566	−	12.1017i	0.531532	−	0.386181i
$983$	4.02969	−	38.3400i	0.128527	−	1.22285i	−0.720103	−	0.693868i	$-0.755905\pi$
$983$	4.02969	−	38.3400i	0.128527	−	1.22285i	0.848630	−	0.528987i	$-0.177428\pi$
$984$		0			0
$985$	34.0449	+	7.23648i	1.08476	+	0.230573i
$986$	−38.8545	+	17.2991i	−1.23738	+	0.550917i
$987$		0			0
$988$	9.56297	−	2.03267i	0.304239	−	0.0646679i
$989$	0.254153			0.00808160
$990$		0			0
$991$	10.3606			0.329114			0.164557	−	0.986368i	$-0.447381\pi$
$991$	10.3606			0.329114			0.164557	+	0.986368i	$0.447381\pi$
$992$	−8.03527	+	1.70795i	−0.255120	+	0.0542275i
$993$		0			0
$994$	3.70201	−	1.64824i	0.117421	−	0.0522791i
$995$	37.8514	+	8.04557i	1.19997	+	0.255062i
$996$		0			0
$997$	0.477189	−	4.54015i	0.0151127	−	0.143788i	−0.984364	−	0.176149i	$-0.943636\pi$
$997$	0.477189	−	4.54015i	0.0151127	−	0.143788i	0.999476	+	0.0323610i	$0.0103026\pi$
$998$	−20.4553	+	14.8616i	−0.647500	+	0.470437i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	891.2.n.h.757.3		32
3.2	odd	2	inner	891.2.n.h.757.2		32
9.2	odd	6	inner	891.2.n.h.460.3		32
9.4	even	3		297.2.f.b.163.2	yes	16
9.5	odd	6		297.2.f.b.163.3	yes	16
9.7	even	3	inner	891.2.n.h.460.2		32
11.5	even	5	inner	891.2.n.h.676.2		32
33.5	odd	10	inner	891.2.n.h.676.3		32
99.4	even	15		3267.2.a.bj.1.3		8
99.5	odd	30		297.2.f.b.82.3	yes	16
99.16	even	15	inner	891.2.n.h.379.3		32
99.38	odd	30	inner	891.2.n.h.379.2		32
99.40	odd	30		3267.2.a.bi.1.6		8
99.49	even	15		297.2.f.b.82.2	✓	16
99.59	odd	30		3267.2.a.bj.1.6		8
99.95	even	30		3267.2.a.bi.1.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
297.2.f.b.82.2	✓	16	99.49	even	15
297.2.f.b.82.3	yes	16	99.5	odd	30
297.2.f.b.163.2	yes	16	9.4	even	3
297.2.f.b.163.3	yes	16	9.5	odd	6
891.2.n.h.379.2		32	99.38	odd	30	inner
891.2.n.h.379.3		32	99.16	even	15	inner
891.2.n.h.460.2		32	9.7	even	3	inner
891.2.n.h.460.3		32	9.2	odd	6	inner
891.2.n.h.676.2		32	11.5	even	5	inner
891.2.n.h.676.3		32	33.5	odd	10	inner
891.2.n.h.757.2		32	3.2	odd	2	inner
891.2.n.h.757.3		32	1.1	even	1	trivial
3267.2.a.bi.1.3		8	99.95	even	30
3267.2.a.bi.1.6		8	99.40	odd	30
3267.2.a.bj.1.3		8	99.4	even	15
3267.2.a.bj.1.6		8	99.59	odd	30

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:	\( N \)	\(=\)	\( 891 = 3^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	891.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22359 - 0.260081i) q^{2} +(-0.397568 + 0.177009i) q^{4} +(-1.60550 - 0.341260i) q^{5} +(0.307337 - 2.92412i) q^{7} +(-2.46446 + 1.79053i) q^{8} -2.05323 q^{10} +(-2.70129 + 1.92433i) q^{11} +(2.42094 + 2.68872i) q^{13} +(-0.384455 - 3.65784i) q^{14} +(-1.96739 + 2.18501i) q^{16} +(1.98276 + 6.10230i) q^{17} +(-5.02334 + 3.64967i) q^{19} +(0.698701 - 0.148514i) q^{20} +(-2.80478 + 3.05714i) q^{22} +(-0.195223 + 0.338136i) q^{23} +(-2.10655 - 0.937897i) q^{25} +(3.66151 + 2.66025i) q^{26} +(0.395406 + 1.21694i) q^{28} +(-0.553896 + 5.26997i) q^{29} +(-2.27658 - 2.52840i) q^{31} +(1.20724 - 2.09100i) q^{32} +(4.01317 + 6.95102i) q^{34} +(-1.49131 + 4.58979i) q^{35} +(-2.61803 - 1.90211i) q^{37} +(-5.19728 + 5.77216i) q^{38} +(4.56773 - 2.03368i) q^{40} +(0.818041 + 7.78314i) q^{41} +(-0.325465 - 0.563722i) q^{43} +(0.733321 - 1.24320i) q^{44} +(-0.150930 + 0.464513i) q^{46} +(-12.2557 - 5.45658i) q^{47} +(-1.60897 - 0.341997i) q^{49} +(-2.82148 - 0.599724i) q^{50} +(-1.43841 - 0.640423i) q^{52} +(1.48983 - 4.58522i) q^{53} +(4.99362 - 2.16768i) q^{55} +(4.47831 + 7.75666i) q^{56} +(0.692881 + 6.59232i) q^{58} +(-1.79533 + 0.799333i) q^{59} +(7.64725 - 8.49314i) q^{61} +(-3.44318 - 2.50162i) q^{62} +(2.75049 - 8.46514i) q^{64} +(-2.96926 - 5.14292i) q^{65} +(-0.427051 + 0.739674i) q^{67} +(-1.86844 - 2.07511i) q^{68} +(-0.631032 + 6.00387i) q^{70} +(0.340470 + 1.04786i) q^{71} +(2.52131 + 1.83184i) q^{73} +(-3.69810 - 1.64650i) q^{74} +(1.35109 - 2.34016i) q^{76} +(4.79677 + 8.49029i) q^{77} +(-1.61881 + 0.344089i) q^{79} +(3.90431 - 2.83665i) q^{80} +(3.02520 + 9.31060i) q^{82} +(-8.65701 + 9.61458i) q^{83} +(-1.10085 - 10.4739i) q^{85} +(-0.544848 - 0.605115i) q^{86} +(3.21162 - 9.57918i) q^{88} +5.92297 q^{89} +(8.60618 - 6.25276i) q^{91} +(0.0177614 - 0.168988i) q^{92} +(-16.4150 - 3.48912i) q^{94} +(9.31046 - 4.14528i) q^{95} +(-18.2345 + 3.87586i) q^{97} -2.05766 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 10 q^{4} + 24 q^{10} + 10 q^{16} - 4 q^{19} + 36 q^{22} - 32 q^{25} + 84 q^{28} + 26 q^{31} + 48 q^{34} - 48 q^{37} + 20 q^{40} - 24 q^{43} - 32 q^{46} - 24 q^{49} + 40 q^{52} - 32 q^{55} - 106 q^{58}+ \cdots - 72 q^{97}+O(q^{100}) \) 32 * q + 10 * q^4 + 24 * q^10 + 10 * q^16 - 4 * q^19 + 36 * q^22 - 32 * q^25 + 84 * q^28 + 26 * q^31 + 48 * q^34 - 48 * q^37 + 20 * q^40 - 24 * q^43 - 32 * q^46 - 24 * q^49 + 40 * q^52 - 32 * q^55 - 106 * q^58 + 6 * q^61 + 124 * q^64 + 40 * q^67 + 58 * q^70 - 60 * q^76 - 64 * q^79 - 168 * q^82 + 18 * q^85 - 80 * q^88 - 20 * q^91 - 90 * q^94 - 72 * q^97

Introduction

L-functions

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