LMFDB - Embedded newform 441.2.bg.a.278.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,2,Mod(17,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(42))

chi = DirichletCharacter(H, H._module([21, 25]))

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

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

chi := DirichletCharacter("441.17");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	441.bg (of order $42$, degree $12$, 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:	$3.52140272914$
Analytic rank:	$0$
Dimension:	$216$
Relative dimension:	$18$ over $\Q(\zeta_{42})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{42}]$

Embedding invariants

Embedding label			278.10
Character	$\chi$	$=$	441.278
Dual form			441.2.bg.a.395.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.132489 - 0.0519980i) q^{2} +(-1.45125 + 1.34657i) q^{4} +(1.27700 - 0.870646i) q^{5} +(-1.61234 + 2.09770i) q^{7} +(-0.245763 + 0.510332i) q^{8} +O(q^{10})$	\(q+(0.132489 - 0.0519980i) q^{2} +(-1.45125 + 1.34657i) q^{4} +(1.27700 - 0.870646i) q^{5} +(-1.61234 + 2.09770i) q^{7} +(-0.245763 + 0.510332i) q^{8} +(0.123917 - 0.181752i) q^{10} +(-0.796043 + 5.28140i) q^{11} +(-4.42567 - 3.52936i) q^{13} +(-0.104541 + 0.361760i) q^{14} +(0.289868 - 3.86802i) q^{16} +(-2.27068 + 0.700411i) q^{17} +(2.04813 + 1.18249i) q^{19} +(-0.680873 + 2.98310i) q^{20} +(0.169155 + 0.741118i) q^{22} +(-1.72793 + 5.60180i) q^{23} +(-0.953993 + 2.43073i) q^{25} +(-0.769871 - 0.237474i) q^{26} +(-0.484776 - 5.21543i) q^{28} +(9.35903 + 2.13614i) q^{29} +(-6.48566 + 3.74450i) q^{31} +(-0.496639 - 1.61006i) q^{32} +(-0.264419 + 0.210867i) q^{34} +(-0.232612 + 4.08255i) q^{35} +(1.55935 + 1.44686i) q^{37} +(0.332840 + 0.0501676i) q^{38} +(0.130478 + 0.865668i) q^{40} +(-0.180363 - 0.0868585i) q^{41} +(-5.56553 + 2.68022i) q^{43} +(-5.95650 - 8.73658i) q^{44} +(0.0623516 + 0.832024i) q^{46} +(-4.15730 - 10.5926i) q^{47} +(-1.80070 - 6.76443i) q^{49} +0.371651i q^{50} +(11.1753 - 0.837473i) q^{52} +(2.89757 + 3.12284i) q^{53} +(3.58168 + 7.43743i) q^{55} +(-0.674270 - 1.33837i) q^{56} +(1.35104 - 0.203637i) q^{58} +(10.3645 + 7.06637i) q^{59} +(3.33764 - 3.59712i) q^{61} +(-0.664571 + 0.833345i) q^{62} +(4.68735 + 5.87775i) q^{64} +(-8.72442 - 0.653805i) q^{65} +(-4.48870 - 7.77466i) q^{67} +(2.35218 - 4.07409i) q^{68} +(0.181466 + 0.552987i) q^{70} +(12.2266 - 2.79063i) q^{71} +(5.02779 + 1.97326i) q^{73} +(0.281830 + 0.110610i) q^{74} +(-4.56465 + 1.04185i) q^{76} +(-9.79530 - 10.1853i) q^{77} +(1.88456 - 3.26415i) q^{79} +(-2.99751 - 5.19185i) q^{80} +(-0.0284126 - 0.00212923i) q^{82} +(5.58349 + 7.00147i) q^{83} +(-2.28985 + 2.87138i) q^{85} +(-0.598003 + 0.644494i) q^{86} +(-2.49963 - 1.70422i) q^{88} +(1.95325 - 0.294405i) q^{89} +(14.5392 - 3.59321i) q^{91} +(-5.03554 - 10.4564i) q^{92} +(-1.10159 - 1.18723i) q^{94} +(3.64499 - 0.273154i) q^{95} -8.13308i q^{97} +(-0.590309 - 0.802577i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) $ 216 * q - 16 * q^4 + 2 * q^7	$ 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) $ 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{41}{42}\right)$	$-1$

Coefficient data

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

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

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

$2$	0.132489	−	0.0519980i	0.0936836	−	0.0367681i	−0.318036	−	0.948079i	$-0.603023\pi$
$2$	0.132489	−	0.0519980i	0.0936836	−	0.0367681i	0.411720	+	0.911310i	$0.364928\pi$
$3$		0			0
$3$		0			0
$4$	−1.45125	+	1.34657i	−0.725627	+	0.673284i
$5$	1.27700	−	0.870646i	0.571093	−	0.389365i	−0.243063	−	0.970010i	$-0.578152\pi$
$5$	1.27700	−	0.870646i	0.571093	−	0.389365i	0.814156	+	0.580646i	$0.197200\pi$
$6$		0			0
$7$	−1.61234	+	2.09770i	−0.609408	+	0.792857i
$7$	−1.61234	+	2.09770i	−0.609408	+	0.792857i
$8$	−0.245763	+	0.510332i	−0.0868903	+	0.180430i
$9$		0			0
$10$	0.123917	−	0.181752i	0.0391859	−	0.0574751i
$11$	−0.796043	+	5.28140i	−0.240016	+	1.59240i	0.466380	+	0.884584i	$0.345558\pi$
$11$	−0.796043	+	5.28140i	−0.240016	+	1.59240i	−0.706396	+	0.707817i	$0.749680\pi$
$12$		0			0
$13$	−4.42567	−	3.52936i	−1.22746	−	0.978868i	−0.999987	−	0.00508348i	$-0.998382\pi$
$13$	−4.42567	−	3.52936i	−1.22746	−	0.978868i	−0.227474	−	0.973784i	$-0.573047\pi$
$14$	−0.104541	+	0.361760i	−0.0279398	+	0.0966845i
$15$		0			0
$16$	0.289868	−	3.86802i	0.0724670	−	0.967006i
$17$	−2.27068	+	0.700411i	−0.550720	+	0.169875i	−0.557612	−	0.830102i	$-0.688282\pi$
$17$	−2.27068	+	0.700411i	−0.550720	+	0.169875i	0.00689217	+	0.999976i	$0.497806\pi$
$18$		0			0
$19$	2.04813	+	1.18249i	0.469872	+	0.271281i	0.716186	−	0.697909i	$-0.245886\pi$
$19$	2.04813	+	1.18249i	0.469872	+	0.271281i	−0.246314	+	0.969190i	$0.579219\pi$
$20$	−0.680873	+	2.98310i	−0.152248	+	0.667041i
$21$		0			0
$22$	0.169155	+	0.741118i	0.0360640	+	0.158007i
$23$	−1.72793	+	5.60180i	−0.360298	+	1.16806i	0.576178	+	0.817324i	$0.304543\pi$
$23$	−1.72793	+	5.60180i	−0.360298	+	1.16806i	−0.936476	+	0.350732i	$0.885933\pi$
$24$		0			0
$25$	−0.953993	+	2.43073i	−0.190799	+	0.486147i
$26$	−0.769871	−	0.237474i	−0.150984	−	0.0465724i
$27$		0			0
$28$	−0.484776	−	5.21543i	−0.0916140	−	0.985623i
$29$	9.35903	+	2.13614i	1.73793	+	0.396671i	0.969854	−	0.243688i	$-0.0783574\pi$
$29$	9.35903	+	2.13614i	1.73793	+	0.396671i	0.768076	+	0.640359i	$0.221215\pi$
$30$		0			0
$31$	−6.48566	+	3.74450i	−1.16486	+	0.672532i	−0.952464	−	0.304652i	$-0.901460\pi$
$31$	−6.48566	+	3.74450i	−1.16486	+	0.672532i	−0.212396	+	0.977184i	$0.568127\pi$
$32$	−0.496639	−	1.61006i	−0.0877942	−	0.284622i
$33$		0			0
$34$	−0.264419	+	0.210867i	−0.0453475	+	0.0361634i
$35$	−0.232612	+	4.08255i	−0.0393186	+	0.690077i
$36$		0			0
$37$	1.55935	+	1.44686i	0.256355	+	0.237863i	0.797872	−	0.602827i	$-0.205959\pi$
$37$	1.55935	+	1.44686i	0.256355	+	0.237863i	−0.541517	+	0.840690i	$0.682150\pi$
$38$	0.332840	+	0.0501676i	0.0539938	+	0.00813826i
$39$		0			0
$40$	0.130478	+	0.865668i	0.0206305	+	0.136874i
$41$	−0.180363	−	0.0868585i	−0.0281680	−	0.0135650i	0.419747	−	0.907641i	$-0.362119\pi$
$41$	−0.180363	−	0.0868585i	−0.0281680	−	0.0135650i	−0.447915	+	0.894076i	$0.647833\pi$
$42$		0			0
$43$	−5.56553	+	2.68022i	−0.848735	+	0.408729i	−0.807108	−	0.590404i	$-0.798968\pi$
$43$	−5.56553	+	2.68022i	−0.848735	+	0.408729i	−0.0416270	+	0.999133i	$0.513254\pi$
$44$	−5.95650	−	8.73658i	−0.897976	−	1.31709i
$45$		0			0
$46$	0.0623516	+	0.832024i	0.00919323	+	0.122675i
$47$	−4.15730	−	10.5926i	−0.606405	−	1.54509i	−0.822526	−	0.568728i	$-0.807436\pi$
$47$	−4.15730	−	10.5926i	−0.606405	−	1.54509i	0.216121	−	0.976367i	$-0.430660\pi$
$48$		0			0
$49$	−1.80070	−	6.76443i	−0.257243	−	0.966347i
$50$			0.371651i			0.0525593i
$51$		0			0
$52$	11.1753	−	0.837473i	1.54973	−	0.116137i
$53$	2.89757	+	3.12284i	0.398012	+	0.428955i	0.899980	−	0.435931i	$-0.143581\pi$
$53$	2.89757	+	3.12284i	0.398012	+	0.428955i	−0.501968	+	0.864886i	$0.667390\pi$
$54$		0			0
$55$	3.58168	+	7.43743i	0.482953	+	1.00286i
$56$	−0.674270	−	1.33837i	−0.0901031	−	0.178847i
$57$		0			0
$58$	1.35104	−	0.203637i	0.177400	−	0.0267388i
$59$	10.3645	+	7.06637i	1.34934	+	0.919962i	0.999856	−	0.0169808i	$-0.00540543\pi$
$59$	10.3645	+	7.06637i	1.34934	+	0.919962i	0.349481	+	0.936943i	$0.386358\pi$
$60$		0			0
$61$	3.33764	−	3.59712i	0.427341	−	0.460564i	−0.482272	−	0.876022i	$-0.660188\pi$
$61$	3.33764	−	3.59712i	0.427341	−	0.460564i	0.909612	+	0.415458i	$0.136379\pi$
$62$	−0.664571	+	0.833345i	−0.0844005	+	0.105835i
$63$		0			0
$64$	4.68735	+	5.87775i	0.585919	+	0.734719i
$65$	−8.72442	−	0.653805i	−1.08213	−	0.0810945i
$66$		0			0
$67$	−4.48870	−	7.77466i	−0.548383	−	0.949826i	−0.998386	−	0.0567994i	$-0.981910\pi$
$67$	−4.48870	−	7.77466i	−0.548383	−	0.949826i	0.450003	−	0.893027i	$-0.351423\pi$
$68$	2.35218	−	4.07409i	0.285244	−	0.494056i
$69$		0			0
$70$	0.181466	+	0.552987i	0.0216893	+	0.0660946i
$71$	12.2266	−	2.79063i	1.45103	−	0.331187i	0.576871	−	0.816835i	$-0.304273\pi$
$71$	12.2266	−	2.79063i	1.45103	−	0.331187i	0.874154	+	0.485648i	$0.161416\pi$
$72$		0			0
$73$	5.02779	+	1.97326i	0.588458	+	0.230953i	0.640840	−	0.767674i	$-0.278586\pi$
$73$	5.02779	+	1.97326i	0.588458	+	0.230953i	−0.0523820	+	0.998627i	$0.516681\pi$
$74$	0.281830	+	0.110610i	0.0327621	+	0.0128582i
$75$		0			0
$76$	−4.56465	+	1.04185i	−0.523601	+	0.119509i
$77$	−9.79530	−	10.1853i	−1.11628	−	1.16072i
$78$		0			0
$79$	1.88456	−	3.26415i	0.212029	−	0.367245i	−0.740320	−	0.672254i	$-0.765326\pi$
$79$	1.88456	−	3.26415i	0.212029	−	0.367245i	0.952349	+	0.305009i	$0.0986595\pi$
$80$	−2.99751	−	5.19185i	−0.335132	−	0.580466i
$81$		0			0
$82$	−0.0284126	−	0.00212923i	−0.00313765	−	0.000235134i
$83$	5.58349	+	7.00147i	0.612867	+	0.768511i	0.987321	−	0.158734i	$-0.0507413\pi$
$83$	5.58349	+	7.00147i	0.612867	+	0.768511i	−0.374454	+	0.927245i	$0.622170\pi$
$84$		0			0
$85$	−2.28985	+	2.87138i	−0.248369	+	0.311445i
$86$	−0.598003	+	0.644494i	−0.0644844	+	0.0694976i
$87$		0			0
$88$	−2.49963	−	1.70422i	−0.266461	−	0.181670i
$89$	1.95325	−	0.294405i	0.207044	−	0.0312068i	−0.0447013	−	0.999000i	$-0.514234\pi$
$89$	1.95325	−	0.294405i	0.207044	−	0.0312068i	0.251745	+	0.967794i	$0.418996\pi$
$90$		0			0
$91$	14.5392	−	3.59321i	1.52413	−	0.376670i
$92$	−5.03554	−	10.4564i	−0.524991	−	1.09016i
$93$		0			0
$94$	−1.10159	−	1.18723i	−0.113620	−	0.122454i
$95$	3.64499	−	0.273154i	0.373968	−	0.0280250i
$96$		0			0
$97$		−	8.13308i		−	0.825789i	−0.910779	−	0.412894i	$-0.864518\pi$
$97$		−	8.13308i		−	0.825789i	0.910779	−	0.412894i	$-0.135482\pi$
$98$	−0.590309	−	0.802577i	−0.0596302	−	0.0810726i
$99$		0			0
$100$	−1.88866	−	4.81223i	−0.188866	−	0.481223i
$101$	−1.30963	−	17.4759i	−0.130313	−	1.73891i	−0.553482	−	0.832861i	$-0.686701\pi$
$101$	−1.30963	−	17.4759i	−0.130313	−	1.73891i	0.423168	−	0.906051i	$-0.360918\pi$
$102$		0			0
$103$	9.00447	+	13.2071i	0.887236	+	1.30134i	0.952834	+	0.303491i	$0.0981521\pi$
$103$	9.00447	+	13.2071i	0.887236	+	1.30134i	−0.0655981	+	0.997846i	$0.520896\pi$
$104$	2.88881	−	1.39118i	0.283271	−	0.136416i
$105$		0			0
$106$	0.546277	+	0.263073i	0.0530591	+	0.0255519i
$107$	0.349737	+	2.32035i	0.0338104	+	0.224317i	0.999355	−	0.0359219i	$-0.0114367\pi$
$107$	0.349737	+	2.32035i	0.0338104	+	0.224317i	−0.965544	+	0.260239i	$0.916199\pi$
$108$		0			0
$109$	−1.53500	−	0.231364i	−0.147027	−	0.0221607i	0.0751165	−	0.997175i	$-0.476067\pi$
$109$	−1.53500	−	0.231364i	−0.147027	−	0.0221607i	−0.222143	+	0.975014i	$0.571305\pi$
$110$	0.861263	+	0.799135i	0.0821182	+	0.0761946i
$111$		0			0
$112$	7.64659	+	6.84463i	0.722535	+	0.646757i
$113$	−5.99228	+	4.77868i	−0.563706	+	0.449541i	−0.863418	−	0.504489i	$-0.831681\pi$
$113$	−5.99228	+	4.77868i	−0.563706	+	0.449541i	0.299712	+	0.954030i	$0.403109\pi$
$114$		0			0
$115$	2.67062	+	8.65792i	0.249036	+	0.807356i
$116$	−16.4588	+	9.50249i	−1.52816	+	0.882284i
$117$		0			0
$118$	1.74061	+	0.397283i	0.160236	+	0.0365728i
$119$	2.19186	−	5.89250i	0.200927	−	0.540165i
$120$		0			0
$121$	−16.7482	−	5.16613i	−1.52256	−	0.469648i
$122$	0.255156	−	0.650128i	0.0231008	−	0.0588598i
$123$		0			0
$124$	4.37013	−	14.1676i	0.392449	−	1.27229i
$125$	2.61766	+	11.4687i	0.234130	+	1.02579i
$126$		0			0
$127$	0.921236	−	4.03620i	0.0817465	−	0.358155i	−0.917467	−	0.397812i	$-0.869770\pi$
$127$	0.921236	−	4.03620i	0.0817465	−	0.358155i	0.999213	+	0.0396575i	$0.0126267\pi$
$128$	3.84502	+	2.21992i	0.339855	+	0.196215i
$129$		0			0
$130$	−1.18988	+	0.367030i	−0.104360	+	0.0321907i
$131$	0.577413	−	7.70505i	0.0504488	−	0.673193i	−0.913455	−	0.406941i	$-0.866596\pi$
$131$	0.577413	−	7.70505i	0.0504488	−	0.673193i	0.963903	−	0.266252i	$-0.0857854\pi$
$132$		0			0
$133$	−5.78278	+	2.38978i	−0.501431	+	0.207220i
$134$	−0.998969	−	0.796651i	−0.0862978	−	0.0688202i
$135$		0			0
$136$	0.200606	−	1.33093i	0.0172018	−	0.114127i
$137$	−7.70966	+	11.3080i	−0.658681	+	0.966107i	0.340980	+	0.940071i	$0.389241\pi$
$137$	−7.70966	+	11.3080i	−0.658681	+	0.966107i	−0.999661	+	0.0260369i	$0.991711\pi$
$138$		0			0
$139$	−8.53176	+	17.7164i	−0.723654	+	1.50268i	0.135396	+	0.990792i	$0.456769\pi$
$139$	−8.53176	+	17.7164i	−0.723654	+	1.50268i	−0.859050	+	0.511892i	$0.828945\pi$
$140$	−5.15985	−	6.23805i	−0.436087	−	0.527211i
$141$		0			0
$142$	1.47477	−	1.00548i	0.123760	−	0.0843783i
$143$	22.1630	−	20.5642i	1.85336	−	1.71967i
$144$		0			0
$145$	13.8113	−	5.42055i	1.14697	−	0.450152i
$146$	0.768731			0.0636206
$147$		0			0
$148$	−4.21131			−0.346167
$149$	−7.28530	+	2.85927i	−0.596835	+	0.234241i	−0.644477	−	0.764624i	$-0.722925\pi$
$149$	−7.28530	+	2.85927i	−0.596835	+	0.234241i	0.0476415	+	0.998864i	$0.484829\pi$
$150$		0			0
$151$	0.0863492	−	0.0801204i	0.00702700	−	0.00652010i	−0.676651	−	0.736304i	$-0.736570\pi$
$151$	0.0863492	−	0.0801204i	0.00702700	−	0.00652010i	0.683678	+	0.729783i	$0.260379\pi$
$152$	−1.10681	+	0.754613i	−0.0897745	+	0.0612072i
$153$		0			0
$154$	−1.82738	−	0.840099i	−0.147255	−	0.0676971i
$155$	−5.02208	+	10.4285i	−0.403383	+	0.837633i
$156$		0			0
$157$	−4.14063	+	6.07318i	−0.330458	+	0.484693i	−0.955127	−	0.296197i	$-0.904282\pi$
$157$	−4.14063	+	6.07318i	−0.330458	+	0.484693i	0.624669	+	0.780890i	$0.285234\pi$
$158$	0.0799534	−	0.530456i	0.00636075	−	0.0422008i
$159$		0			0
$160$	−2.03600	−	1.62366i	−0.160960	−	0.128362i
$161$	−8.96489	−	12.6567i	−0.706532	−	0.997487i
$162$		0			0
$163$	−0.233664	+	3.11803i	−0.0183020	+	0.244223i	0.980548	+	0.196279i	$0.0628858\pi$
$163$	−0.233664	+	3.11803i	−0.0183020	+	0.244223i	−0.998850	+	0.0479437i	$0.984733\pi$
$164$	0.378714	−	0.116818i	0.0295726	−	0.00912194i
$165$		0			0
$166$	1.10381	+	0.637286i	0.0856724	+	0.0494630i
$167$	1.10358	−	4.83508i	0.0853972	−	0.374150i	−0.914112	−	0.405461i	$-0.867111\pi$
$167$	1.10358	−	4.83508i	0.0853972	−	0.374150i	0.999510	+	0.0313111i	$0.00996826\pi$
$168$		0			0
$169$	4.23746	+	18.5655i	0.325958	+	1.42812i
$170$	−0.154073	+	0.499493i	−0.0118169	+	0.0383094i
$171$		0			0
$172$	4.46790	−	11.3840i	0.340674	−	0.868024i
$173$	7.47647	+	2.30619i	0.568426	+	0.175336i	0.565629	−	0.824660i	$-0.308634\pi$
$173$	7.47647	+	2.30619i	0.568426	+	0.175336i	0.00279697	+	0.999996i	$0.499110\pi$
$174$		0			0
$175$	−3.56079	−	5.92037i	−0.269170	−	0.447538i
$176$	20.1978	+	4.61002i	1.52247	+	0.347493i
$177$		0			0
$178$	0.243475	−	0.140570i	0.0182492	−	0.0105362i
$179$	−1.84791	−	5.99077i	−0.138119	−	0.447771i	0.859915	−	0.510437i	$-0.170516\pi$
$179$	−1.84791	−	5.99077i	−0.138119	−	0.447771i	−0.998035	+	0.0626651i	$0.980040\pi$
$180$		0			0
$181$	2.27095	−	1.81102i	0.168798	−	0.134612i	−0.535447	−	0.844569i	$-0.679857\pi$
$181$	2.27095	−	1.81102i	0.168798	−	0.134612i	0.704246	+	0.709957i	$0.251285\pi$
$182$	1.73945	−	1.23207i	0.128936	−	0.0913271i
$183$		0			0
$184$	−2.43412	−	2.25853i	−0.179445	−	0.166501i
$185$	3.25100	+	0.490009i	0.239018	+	0.0360262i
$186$		0			0
$187$	−1.89159	−	12.5499i	−0.138327	−	0.917740i
$188$	20.2970	+	9.77452i	1.48031	+	0.712880i
$189$		0			0
$190$	0.468716	−	0.225722i	0.0340043	−	0.0163756i
$191$	7.16605	+	10.5107i	0.518518	+	0.760526i	0.992792	−	0.119852i	$-0.0382419\pi$
$191$	7.16605	+	10.5107i	0.518518	+	0.760526i	−0.474274	+	0.880377i	$0.657289\pi$
$192$		0			0
$193$	0.140668	+	1.87709i	0.0101255	+	0.135116i	0.999975	−	0.00700057i	$-0.00222837\pi$
$193$	0.140668	+	1.87709i	0.0101255	+	0.135116i	−0.989850	+	0.142116i	$0.954609\pi$
$194$	−0.422904	−	1.07754i	−0.0303627	−	0.0773629i
$195$		0			0
$196$	11.7220	+	7.39214i	0.837288	+	0.528010i
$197$			12.8075i			0.912499i	0.889852	+	0.456250i	$0.150808\pi$
$197$			12.8075i			0.912499i	−0.889852	+	0.456250i	$0.849192\pi$
$198$		0			0
$199$	8.90734	−	0.667513i	0.631425	−	0.0473187i	0.244826	−	0.969567i	$-0.421269\pi$
$199$	8.90734	−	0.667513i	0.631425	−	0.0473187i	0.386598	+	0.922248i	$0.373650\pi$
$200$	−1.00603	−	1.08424i	−0.0711367	−	0.0766672i
$201$		0			0
$202$	−1.08222	−	2.24725i	−0.0761448	−	0.158116i
$203$	−19.5710	+	16.1883i	−1.37361	+	1.13619i
$204$		0			0
$205$	−0.305948	+	0.0461142i	−0.0213683	+	0.00322075i
$206$	1.87973	+	1.28158i	0.130967	+	0.0892920i
$207$		0			0
$208$	−14.9345	+	16.0956i	−1.03552	+	1.11603i
$209$	−7.87557	+	9.87566i	−0.544765	+	0.683114i
$210$		0			0
$211$	−3.93423	−	4.93337i	−0.270844	−	0.339627i	0.627745	−	0.778419i	$-0.283978\pi$
$211$	−3.93423	−	4.93337i	−0.270844	−	0.339627i	−0.898589	+	0.438792i	$0.855407\pi$
$212$	−8.41023	−	0.630260i	−0.577617	−	0.0432864i
$213$		0			0
$214$	0.166990	+	0.289235i	0.0114152	+	0.0197717i
$215$	−4.77367	+	8.26825i	−0.325562	+	0.563890i
$216$		0			0
$217$	2.60227	−	19.6424i	0.176654	−	1.33341i
$218$	−0.215401	+	0.0491639i	−0.0145888	+	0.00332980i
$219$		0			0
$220$	−15.2129	−	5.97063i	−1.02566	−	0.402540i
$221$	12.5213	+	4.91424i	0.842272	+	0.330567i
$222$		0			0
$223$	−16.5223	+	3.77110i	−1.10641	+	0.252531i	−0.736434	−	0.676509i	$-0.763492\pi$
$223$	−16.5223	+	3.77110i	−1.10641	+	0.252531i	−0.369978	+	0.929041i	$0.620635\pi$
$224$	4.17819	+	1.55418i	0.279167	+	0.103843i
$225$		0			0
$226$	−0.545427	+	0.944708i	−0.0362813	+	0.0628410i
$227$	7.18229	+	12.4401i	0.476705	+	0.825678i	0.999644	−	0.0266927i	$-0.00849757\pi$
$227$	7.18229	+	12.4401i	0.476705	+	0.825678i	−0.522938	+	0.852370i	$0.675164\pi$
$228$		0			0
$229$	−11.9655	−	0.896691i	−0.790704	−	0.0592550i	−0.326746	−	0.945112i	$-0.605952\pi$
$229$	−11.9655	−	0.896691i	−0.790704	−	0.0592550i	−0.463958	+	0.885857i	$0.653571\pi$
$230$	0.804021	+	1.00821i	0.0530156	+	0.0664794i
$231$		0			0
$232$	−3.39024	+	4.25123i	−0.222580	+	0.279107i
$233$	−10.9139	+	11.7624i	−0.714995	+	0.770582i	−0.981129	−	0.193355i	$-0.938063\pi$
$233$	−10.9139	+	11.7624i	−0.714995	+	0.770582i	0.266134	+	0.963936i	$0.414254\pi$
$234$		0			0
$235$	−14.5313	−	9.90729i	−0.947919	−	0.646280i
$236$	−24.5568	+	3.70134i	−1.59851	+	0.240937i
$237$		0			0
$238$	−0.0160021	−	0.894662i	−0.00103726	−	0.0579923i
$239$	−0.383320	−	0.795973i	−0.0247949	−	0.0514872i	0.888204	−	0.459450i	$-0.151954\pi$
$239$	−0.383320	−	0.795973i	−0.0247949	−	0.0514872i	−0.912998	+	0.407963i	$0.866239\pi$
$240$		0			0
$241$	16.5585	+	17.8458i	1.06663	+	1.14955i	0.988284	+	0.152625i	$0.0487726\pi$
$241$	16.5585	+	17.8458i	1.06663	+	1.14955i	0.0783436	+	0.996926i	$0.475037\pi$
$242$	−2.48757	+	0.186418i	−0.159907	+	0.0119834i
$243$		0			0
$244$			9.71469i			0.621919i
$245$	−8.18892	−	7.07042i	−0.523171	−	0.451713i
$246$		0			0
$247$	−4.89092	−	12.4619i	−0.311202	−	0.792930i
$248$	−0.317002	−	4.23010i	−0.0201297	−	0.268612i
$249$		0			0
$250$	0.943159	+	1.38336i	0.0596506	+	0.0874914i
$251$	4.29738	−	2.06951i	0.271248	−	0.130626i	−0.293316	−	0.956016i	$-0.594759\pi$
$251$	4.29738	−	2.06951i	0.271248	−	0.130626i	0.564564	+	0.825389i	$0.309044\pi$
$252$		0			0
$253$	−28.2098	−	13.5851i	−1.77354	−	0.854090i
$254$	−0.0878208	−	0.582653i	−0.00551037	−	0.0365589i
$255$		0			0
$256$	−14.2431	−	2.14680i	−0.890191	−	0.134175i
$257$	−2.64481	−	2.45402i	−0.164979	−	0.153078i	0.593363	−	0.804935i	$-0.297800\pi$
$257$	−2.64481	−	2.45402i	−0.164979	−	0.153078i	−0.758342	+	0.651857i	$0.773990\pi$
$258$		0			0
$259$	−5.54929	+	0.938205i	−0.344816	+	0.0582973i
$260$	13.5417	−	10.7992i	0.839823	−	0.669737i
$261$		0			0
$262$	−0.324146	−	1.05086i	−0.0200258	−	0.0649221i
$263$	2.04056	−	1.17812i	0.125826	−	0.0726459i	−0.435766	−	0.900060i	$-0.643522\pi$
$263$	2.04056	−	1.17812i	0.125826	−	0.0726459i	0.561592	+	0.827414i	$0.310189\pi$
$264$		0			0
$265$	6.41910	+	1.46512i	0.394322	+	0.0900015i
$266$	−0.641890	+	0.617312i	−0.0393568	+	0.0378498i
$267$		0			0
$268$	16.9834	+	5.23867i	1.03742	+	0.320003i
$269$	−11.2079	+	28.5573i	−0.683358	+	1.74117i	−0.0121194	+	0.999927i	$0.503858\pi$
$269$	−11.2079	+	28.5573i	−0.683358	+	1.74117i	−0.671239	+	0.741241i	$0.734237\pi$
$270$		0			0
$271$	−1.90974	+	6.19121i	−0.116008	+	0.376089i	−0.994892	−	0.100947i	$-0.967813\pi$
$271$	−1.90974	+	6.19121i	−0.116008	+	0.376089i	0.878884	+	0.477036i	$0.158289\pi$
$272$	2.05101	+	8.98605i	0.124361	+	0.544860i
$273$		0			0
$274$	−0.433450	+	1.89907i	−0.0261857	+	0.114727i
$275$	−12.0783	−	6.97338i	−0.728346	−	0.420511i
$276$		0			0
$277$	17.8269	−	5.49888i	1.07112	−	0.330395i	0.291446	−	0.956587i	$-0.405863\pi$
$277$	17.8269	−	5.49888i	1.07112	−	0.330395i	0.779669	+	0.626192i	$0.215387\pi$
$278$	−0.209146	+	2.79085i	−0.0125437	+	0.167384i
$279$		0			0
$280$	−2.02629	−	1.12205i	−0.121094	−	0.0670552i
$281$	−2.93272	−	2.33877i	−0.174952	−	0.139519i	0.532099	−	0.846682i	$-0.321403\pi$
$281$	−2.93272	−	2.33877i	−0.174952	−	0.139519i	−0.707051	+	0.707163i	$0.749975\pi$
$282$		0			0
$283$	−0.700508	+	4.64757i	−0.0416409	+	0.276269i	−0.999955	−	0.00944618i	$-0.996993\pi$
$283$	−0.700508	+	4.64757i	−0.0416409	+	0.276269i	0.958314	+	0.285716i	$0.0922312\pi$
$284$	−13.9861	+	20.5138i	−0.829921	+	1.21727i
$285$		0			0
$286$	1.86704	−	3.87696i	0.110401	−	0.229249i
$287$	0.473011	−	0.238303i	0.0279210	−	0.0140666i
$288$		0			0
$289$	−9.38066	+	6.39563i	−0.551804	+	0.376213i
$290$	1.54799	−	1.43632i	0.0909010	−	0.0843438i
$291$		0			0
$292$	−9.95373	+	3.90655i	−0.582498	+	0.228614i
$293$	−0.798413			−0.0466438			−0.0233219	−	0.999728i	$-0.507424\pi$
$293$	−0.798413			−0.0466438			−0.0233219	+	0.999728i	$0.507424\pi$
$294$		0			0
$295$	19.3877			1.12880
$296$	−1.12161	+	0.440200i	−0.0651923	+	0.0255861i
$297$		0			0
$298$	−0.816544	+	0.757642i	−0.0473011	+	0.0438890i
$299$	27.4180	−	18.6933i	1.58562	−	1.08106i
$300$		0			0
$301$	3.35124	−	15.9962i	0.193163	−	0.922008i
$302$	0.00727420	−	0.0151050i	0.000418583	−	0.000869196i
$303$		0			0
$304$	5.16757	−	7.57943i	0.296380	−	0.434710i
$305$	1.13036	−	7.49943i	0.0647241	−	0.429416i
$306$		0			0
$307$	7.36091	+	5.87013i	0.420109	+	0.335026i	0.810620	−	0.585572i	$-0.199130\pi$
$307$	7.36091	+	5.87013i	0.420109	+	0.335026i	−0.390511	+	0.920598i	$0.627702\pi$
$308$	27.9306	+	1.59141i	1.59150	+	0.0906788i
$309$		0			0
$310$	−0.123110	+	1.64279i	−0.00699218	+	0.0933042i
$311$	15.9258	−	4.91246i	0.903069	−	0.278560i	0.191762	−	0.981441i	$-0.438580\pi$
$311$	15.9258	−	4.91246i	0.903069	−	0.278560i	0.711307	+	0.702881i	$0.248104\pi$
$312$		0			0
$313$	8.15020	+	4.70552i	0.460677	+	0.265972i	0.712329	−	0.701846i	$-0.247641\pi$
$313$	8.15020	+	4.70552i	0.460677	+	0.265972i	−0.251652	+	0.967818i	$0.580974\pi$
$314$	−0.232793	+	1.01993i	−0.0131373	+	0.0575581i
$315$		0			0
$316$	1.66042	+	7.27479i	0.0934061	+	0.409239i
$317$	4.32032	−	14.0061i	0.242653	−	0.786663i	−0.749540	−	0.661959i	$-0.769725\pi$
$317$	4.32032	−	14.0061i	0.242653	−	0.786663i	0.992194	−	0.124705i	$-0.0397983\pi$
$318$		0			0
$319$	−18.7320	+	47.7283i	−1.04879	+	2.67227i
$320$	11.1032	+	3.42488i	0.620688	+	0.191457i
$321$		0			0
$322$	−1.84587	−	1.21071i	−0.102866	−	0.0674704i
$323$	−5.47886	−	1.25051i	−0.304852	−	0.0695804i
$324$		0			0
$325$	12.8010	−	7.39066i	0.710071	−	0.409960i
$326$	0.131173	+	0.425253i	0.00726502	+	0.0235526i
$327$		0			0
$328$	0.0886533	−	0.0706987i	0.00489506	−	0.00390368i
$329$	28.9232	+	8.35818i	1.59459	+	0.460802i
$330$		0			0
$331$	3.16291	+	2.93475i	0.173849	+	0.161309i	0.762299	−	0.647226i	$-0.224071\pi$
$331$	3.16291	+	2.93475i	0.173849	+	0.161309i	−0.588449	+	0.808534i	$0.700261\pi$
$332$	−17.5310	−	2.64237i	−0.962139	−	0.145019i
$333$		0			0
$334$	−0.105203	−	0.697977i	−0.00575646	−	0.0381916i
$335$	−12.5011	−	6.02020i	−0.683006	−	0.328918i
$336$		0			0
$337$	21.3676	−	10.2901i	1.16397	−	0.560537i	0.250767	−	0.968047i	$-0.419317\pi$
$337$	21.3676	−	10.2901i	1.16397	−	0.560537i	0.913201	+	0.407510i	$0.133603\pi$
$338$	1.52678	+	2.23938i	0.0830461	+	0.121806i
$339$		0			0
$340$	−0.543353	−	7.25054i	−0.0294675	−	0.393216i
$341$	−14.6133	−	37.2341i	−0.791356	−	2.01634i
$342$		0			0
$343$	17.0931	+	7.12925i	0.922940	+	0.384943i
$344$		−	3.49896i		−	0.188652i
$345$		0			0
$346$	1.11047	−	0.0832179i	0.0596990	−	0.00447382i
$347$	−11.0072	−	11.8629i	−0.590895	−	0.636833i	0.364837	−	0.931071i	$-0.381125\pi$
$347$	−11.0072	−	11.8629i	−0.590895	−	0.636833i	−0.955732	+	0.294238i	$0.904934\pi$
$348$		0			0
$349$	−5.81027	−	12.0651i	−0.311016	−	0.645832i	0.685604	−	0.727974i	$-0.259538\pi$
$349$	−5.81027	−	12.0651i	−0.311016	−	0.645832i	−0.996621	+	0.0821423i	$0.973824\pi$
$350$	−0.779612	−	0.599228i	−0.0416720	−	0.0320301i
$351$		0			0
$352$	8.89873	−	1.34127i	0.474304	−	0.0714898i
$353$	−21.6850	−	14.7846i	−1.15417	−	0.786903i	−0.173943	−	0.984756i	$-0.555651\pi$
$353$	−21.6850	−	14.7846i	−1.15417	−	0.786903i	−0.980232	+	0.197853i	$0.936603\pi$
$354$		0			0
$355$	13.1837	−	14.2086i	0.699718	−	0.754117i
$356$	−2.43822	+	3.05744i	−0.129226	+	0.162044i
$357$		0			0
$358$	−0.556335	−	0.697622i	−0.0294032	−	0.0368705i
$359$	24.8015	+	1.85861i	1.30897	+	0.0980938i	0.710868	−	0.703325i	$-0.248302\pi$
$359$	24.8015	+	1.85861i	1.30897	+	0.0980938i	0.598103	+	0.801419i	$0.295921\pi$
$360$		0			0
$361$	−6.70345	−	11.6107i	−0.352813	−	0.611091i
$362$	0.206706	−	0.358025i	0.0108642	−	0.0188174i
$363$		0			0
$364$	−16.2616	+	24.7927i	−0.852342	+	1.29949i
$365$	8.13851	−	1.85756i	0.425989	−	0.0972293i
$366$		0			0
$367$	−31.0028	−	12.1677i	−1.61833	−	0.635149i	−0.628555	−	0.777765i	$-0.716353\pi$
$367$	−31.0028	−	12.1677i	−1.61833	−	0.635149i	−0.989778	+	0.142616i	$0.954449\pi$
$368$	21.1670	+	8.30744i	1.10341	+	0.433055i
$369$		0			0
$370$	0.456200	−	0.104125i	0.0237167	−	0.00541318i
$371$	−11.2227	+	1.04315i	−0.582652	+	0.0541577i
$372$		0			0
$373$	10.1986	−	17.6645i	0.528063	−	0.914631i	−0.471402	−	0.881918i	$-0.656252\pi$
$373$	10.1986	−	17.6645i	0.528063	−	0.914631i	0.999465	−	0.0327130i	$-0.0104147\pi$
$374$	−0.903184	−	1.56436i	−0.0467025	−	0.0808912i
$375$		0			0
$376$	6.42747	+	0.481672i	0.331472	+	0.0248404i
$377$	−33.8808	−	42.4852i	−1.74495	−	2.18810i
$378$		0			0
$379$	6.66886	−	8.36249i	0.342556	−	0.429552i	−0.580474	−	0.814279i	$-0.697133\pi$
$379$	6.66886	−	8.36249i	0.342556	−	0.429552i	0.923031	+	0.384726i	$0.125704\pi$
$380$	−4.92199	+	5.30464i	−0.252493	+	0.272122i
$381$		0			0
$382$	1.49595	+	1.01992i	0.0765397	+	0.0521839i
$383$	−11.7815	+	1.77578i	−0.602008	+	0.0907382i	−0.442973	−	0.896535i	$-0.646076\pi$
$383$	−11.7815	+	1.77578i	−0.602008	+	0.0907382i	−0.159035	+	0.987273i	$0.550838\pi$
$384$		0			0
$385$	−21.3764	−	4.47840i	−1.08944	−	0.228240i
$386$	0.116242	+	0.241378i	0.00591654	+	0.0122858i
$387$		0			0
$388$	10.9517	+	11.8032i	0.555990	+	0.599215i
$389$	13.0029	−	0.974431i	0.659272	−	0.0494056i	0.259107	−	0.965849i	$-0.416572\pi$
$389$	13.0029	−	0.974431i	0.659272	−	0.0494056i	0.400165	+	0.916443i	$0.368953\pi$
$390$		0			0
$391$		−	13.9301i		−	0.704477i
$392$	3.89465	+	0.743491i	0.196709	+	0.0375520i
$393$		0			0
$394$	0.665966	+	1.69685i	0.0335509	+	0.0854863i
$395$	−0.435333	−	5.80911i	−0.0219040	−	0.292288i
$396$		0			0
$397$	12.4223	+	18.2202i	0.623458	+	0.914445i	0.999928	−	0.0119840i	$-0.00381471\pi$
$397$	12.4223	+	18.2202i	0.623458	+	0.914445i	−0.376470	+	0.926429i	$0.622862\pi$
$398$	1.14541	−	0.551602i	0.0574143	−	0.0276493i
$399$		0			0
$400$	9.12560	+	4.39466i	0.456280	+	0.219733i
$401$	1.08944	+	7.22798i	0.0544042	+	0.360948i	0.999424	+	0.0339353i	$0.0108040\pi$
$401$	1.08944	+	7.22798i	0.0544042	+	0.360948i	−0.945020	+	0.327013i	$0.893958\pi$
$402$		0			0
$403$	41.9191	+	6.31829i	2.08814	+	0.314736i
$404$	25.4330	+	23.5984i	1.26534	+	1.17406i
$405$		0			0
$406$	−1.75117	+	3.16241i	−0.0869092	+	0.156948i
$407$	−8.88277	+	7.08377i	−0.440302	+	0.351129i
$408$		0			0
$409$	−4.43550	−	14.3795i	−0.219321	−	0.711022i	−0.996639	−	0.0819142i	$-0.973897\pi$
$409$	−4.43550	−	14.3795i	−0.219321	−	0.711022i	0.777318	−	0.629108i	$-0.216580\pi$
$410$	−0.0381368	+	0.0220183i	−0.00188344	+	0.00108740i
$411$		0			0
$412$	−30.8521	−	7.04178i	−1.51997	−	0.346924i
$413$	−31.5342	+	10.3481i	−1.55170	+	0.509198i
$414$		0			0
$415$	13.2259	+	4.07966i	0.649235	+	0.200263i
$416$	−3.48453	+	8.87843i	−0.170843	+	0.435301i
$417$		0			0
$418$	−0.529910	+	1.71793i	−0.0259188	+	0.0840266i
$419$	0.364788	+	1.59824i	0.0178210	+	0.0780791i	0.983056	−	0.183303i	$-0.0586789\pi$
$419$	0.364788	+	1.59824i	0.0178210	+	0.0780791i	−0.965235	+	0.261382i	$0.915822\pi$
$420$		0			0
$421$	−6.33211	+	27.7428i	−0.308608	+	1.35210i	0.548149	+	0.836381i	$0.315333\pi$
$421$	−6.33211	+	27.7428i	−0.308608	+	1.35210i	−0.856757	+	0.515720i	$0.827524\pi$
$422$	−0.777766	−	0.449043i	−0.0378611	−	0.0218591i
$423$		0			0
$424$	−2.30580	+	0.711246i	−0.111980	+	0.0345412i
$425$	0.463696	−	6.18760i	0.0224926	−	0.300143i
$426$		0			0
$427$	2.16426	+	12.8012i	0.104736	+	0.619492i
$428$	−3.63207	−	2.89648i	−0.175563	−	0.140007i
$429$		0			0
$430$	−0.202526	+	1.34367i	−0.00976666	+	0.0647975i
$431$	3.73526	−	5.47862i	0.179921	−	0.263896i	−0.725674	−	0.688038i	$-0.758472\pi$
$431$	3.73526	−	5.47862i	0.179921	−	0.263896i	0.905595	+	0.424143i	$0.139424\pi$
$432$		0			0
$433$	13.9812	−	29.0322i	0.671891	−	1.39520i	−0.234231	−	0.972181i	$-0.575257\pi$
$433$	13.9812	−	29.0322i	0.671891	−	1.39520i	0.906122	−	0.423016i	$-0.139029\pi$
$434$	−0.676593	−	2.73771i	−0.0324775	−	0.131414i
$435$		0			0
$436$	2.53923	−	1.73122i	0.121607	−	0.0829102i
$437$	−10.1631	+	9.42994i	−0.486165	+	0.451095i
$438$		0			0
$439$	14.5264	−	5.70118i	0.693305	−	0.272102i	0.00758904	−	0.999971i	$-0.497584\pi$
$439$	14.5264	−	5.70118i	0.693305	−	0.272102i	0.685716	+	0.727869i	$0.259489\pi$
$440$	−4.67580			−0.222910
$441$		0			0
$442$	1.91446			0.0910615
$443$	10.3309	−	4.05457i	0.490834	−	0.192638i	−0.106998	−	0.994259i	$-0.534124\pi$
$443$	10.3309	−	4.05457i	0.490834	−	0.192638i	0.597833	+	0.801621i	$0.296029\pi$
$444$		0			0
$445$	2.23798	−	2.07654i	0.106090	−	0.0984376i
$446$	−1.99292	+	1.35875i	−0.0943676	+	0.0643388i
$447$		0			0
$448$	−19.8874	+	0.355709i	−0.939590	+	0.0168057i
$449$	1.22019	−	2.53375i	0.0575843	−	0.119575i	−0.870191	−	0.492715i	$-0.836005\pi$
$449$	1.22019	−	2.53375i	0.0575843	−	0.119575i	0.927775	+	0.373140i	$0.121719\pi$
$450$		0			0
$451$	0.602311	−	0.883428i	0.0283617	−	0.0415990i
$452$	2.26150	−	15.0041i	0.106372	−	0.705733i
$453$		0			0
$454$	1.59843	+	1.27471i	0.0750181	+	0.0598249i
$455$	15.4382	−	17.2471i	0.723756	−	0.808555i
$456$		0			0
$457$	−0.164588	+	2.19628i	−0.00769911	+	0.102737i	−0.999729	−	0.0232621i	$-0.992595\pi$
$457$	−0.164588	+	2.19628i	−0.00769911	+	0.102737i	0.992030	+	0.126000i	$0.0402138\pi$
$458$	−1.63192	+	0.503381i	−0.0762547	+	0.0235215i
$459$		0			0
$460$	−15.5342	−	8.96869i	−0.724287	−	0.418167i
$461$	5.01510	−	21.9726i	0.233577	−	1.02337i	−0.713070	−	0.701093i	$-0.752696\pi$
$461$	5.01510	−	21.9726i	0.233577	−	1.02337i	0.946647	−	0.322273i	$-0.104447\pi$
$462$		0			0
$463$	0.0445324	+	0.195109i	0.00206960	+	0.00906749i	0.975952	−	0.217985i	$-0.0699483\pi$
$463$	0.0445324	+	0.195109i	0.00206960	+	0.00906749i	−0.973883	+	0.227052i	$0.927091\pi$
$464$	10.9755	−	35.5818i	0.509526	−	1.65184i
$465$		0			0
$466$	−0.834350	+	2.12589i	−0.0386505	+	0.0984799i
$467$	−14.6853	−	4.52982i	−0.679556	−	0.209615i	−0.0642857	−	0.997932i	$-0.520477\pi$
$467$	−14.6853	−	4.52982i	−0.679556	−	0.209615i	−0.615270	+	0.788316i	$0.710953\pi$
$468$		0			0
$469$	23.5463	+	3.11946i	1.08726	+	0.144044i
$470$	−2.44039	−	0.557004i	−0.112567	−	0.0256927i
$471$		0			0
$472$	−6.15339	+	3.55266i	−0.283233	+	0.163525i
$473$	−9.72489	−	31.5273i	−0.447151	−	1.44963i
$474$		0			0
$475$	−4.82821	+	3.85037i	−0.221533	+	0.176667i
$476$	4.75371	+	11.5030i	0.217886	+	0.527239i
$477$		0			0
$478$	−0.0921746	−	0.0855255i	−0.00421597	−	0.00391185i
$479$	15.8422	+	2.38783i	0.723850	+	0.109103i	0.500625	−	0.865664i	$-0.333104\pi$
$479$	15.8422	+	2.38783i	0.723850	+	0.109103i	0.223225	+	0.974767i	$0.428342\pi$
$480$		0			0
$481$	−1.79467	−	11.9068i	−0.0818298	−	0.542905i
$482$	3.12176	+	1.50336i	0.142192	+	0.0684763i
$483$		0			0
$484$	31.2624	−	15.0552i	1.42102	−	0.684326i
$485$	−7.08103	−	10.3860i	−0.321533	−	0.471602i
$486$		0			0
$487$	1.60891	+	21.4694i	0.0729065	+	0.972870i	0.906968	+	0.421199i	$0.138391\pi$
$487$	1.60891	+	21.4694i	0.0729065	+	0.972870i	−0.834062	+	0.551671i	$0.813990\pi$
$488$	1.01546	+	2.58734i	0.0459676	+	0.117124i
$489$		0			0
$490$	−1.45259	−	0.510944i	−0.0656212	−	0.0230821i
$491$		−	9.31223i		−	0.420255i	−0.977674	−	0.210127i	$-0.932612\pi$
$491$		−	9.31223i		−	0.420255i	0.977674	−	0.210127i	$-0.0673879\pi$
$492$		0			0
$493$	−22.7475	+	1.70469i	−1.02450	+	0.0767754i
$494$	−1.29598	−	1.39674i	−0.0583091	−	0.0628422i
$495$		0			0
$496$	12.6038	+	26.1721i	0.565928	+	1.17516i
$497$	−13.8595	+	30.1471i	−0.621683	+	1.35228i
$498$		0			0
$499$	−13.2189	+	1.99243i	−0.591761	+	0.0891936i	−0.438094	−	0.898929i	$-0.644346\pi$
$499$	−13.2189	+	1.99243i	−0.591761	+	0.0891936i	−0.153667	+	0.988123i	$0.549108\pi$
$500$	−19.2423	−	13.1192i	−0.860540	−	0.586706i
$501$		0			0
$502$	0.461743	−	0.497641i	0.0206086	−	0.0222108i
$503$	5.59198	−	7.01212i	0.249334	−	0.312655i	−0.641376	−	0.767227i	$-0.721636\pi$
$503$	5.59198	−	7.01212i	0.249334	−	0.312655i	0.890710	+	0.454572i	$0.150208\pi$
$504$		0			0
$505$	−16.8877	−	21.1765i	−0.751492	−	0.942341i
$506$	−4.44388	−	0.333023i	−0.197555	−	0.0148047i
$507$		0			0
$508$	4.09807	+	7.09806i	0.181822	+	0.314925i
$509$	−13.5956	+	23.5483i	−0.602614	+	1.04376i	0.389810	+	0.920895i	$0.372541\pi$
$509$	−13.5956	+	23.5483i	−0.602614	+	1.04376i	−0.992424	+	0.122862i	$0.960793\pi$
$510$		0			0
$511$	−12.2458	+	7.36522i	−0.541724	+	0.325818i
$512$	−10.6557	+	2.43210i	−0.470921	+	0.107485i
$513$		0			0
$514$	−0.478011	−	0.187606i	−0.0210842	−	0.00827493i
$515$	22.9975	+	9.02584i	1.01339	+	0.397726i
$516$		0			0
$517$	59.2533	−	13.5242i	2.60596	−	0.594793i
$518$	−0.686433	+	0.412853i	−0.0301601	+	0.0181397i
$519$		0			0
$520$	2.47780	−	4.29167i	0.108659	−	0.188202i
$521$	16.8688	+	29.2177i	0.739037	+	1.28005i	0.952929	+	0.303192i	$0.0980525\pi$
$521$	16.8688	+	29.2177i	0.739037	+	1.28005i	−0.213892	+	0.976857i	$0.568614\pi$
$522$		0			0
$523$	−32.0598	−	2.40255i	−1.40188	−	0.105056i	−0.647783	−	0.761825i	$-0.724304\pi$
$523$	−32.0598	−	2.40255i	−1.40188	−	0.105056i	−0.754092	+	0.656769i	$0.771923\pi$
$524$	9.53739	+	11.9595i	0.416643	+	0.522453i
$525$		0			0
$526$	0.209091	−	0.262192i	0.00911682	−	0.0114321i
$527$	12.1042	−	13.0452i	0.527265	−	0.568257i
$528$		0			0
$529$	−9.39093	−	6.40263i	−0.408301	−	0.278375i
$530$	0.926641	−	0.139669i	0.0402507	−	0.00606682i
$531$		0			0
$532$	5.17429	−	11.2551i	0.224334	−	0.487970i
$533$	0.491675	+	1.02097i	0.0212968	+	0.0442233i
$534$		0			0
$535$	2.46682	+	2.65860i	0.106650	+	0.114941i
$536$	5.07082	−	0.380005i	0.219026	−	0.0164137i
$537$		0			0
$538$			4.36630i			0.188245i
$539$	37.1591	−	4.12544i	1.60055	−	0.177695i
$540$		0			0
$541$	8.62785	+	21.9834i	0.370940	+	0.945140i	0.987470	+	0.157808i	$0.0504429\pi$
$541$	8.62785	+	21.9834i	0.370940	+	0.945140i	−0.616530	+	0.787332i	$0.711462\pi$
$542$	0.0689121	+	0.919568i	0.00296003	+	0.0394988i
$543$		0			0
$544$	2.25541	+	3.30808i	0.0967000	+	0.141833i
$545$	−2.16164	+	1.04099i	−0.0925944	+	0.0445911i
$546$		0			0
$547$	−16.6334	−	8.01025i	−0.711195	−	0.342493i	0.0430624	−	0.999072i	$-0.486289\pi$
$547$	−16.6334	−	8.01025i	−0.711195	−	0.342493i	−0.754257	+	0.656579i	$0.772003\pi$
$548$	−4.03830	−	26.7924i	−0.172508	−	1.14451i
$549$		0			0
$550$	−1.96283	−	0.295850i	−0.0836955	−	0.0126151i
$551$	16.6425	+	15.4420i	0.708996	+	0.657852i
$552$		0			0
$553$	3.80866	+	9.21617i	0.161961	+	0.391911i
$554$	2.07593	−	1.65550i	0.0881980	−	0.0703356i
$555$		0			0
$556$	−11.4745	−	37.1996i	−0.486629	−	1.57761i
$557$	−2.68708	+	1.55139i	−0.113855	+	0.0657344i	−0.555846	−	0.831285i	$-0.687606\pi$
$557$	−2.68708	+	1.55139i	−0.113855	+	0.0657344i	0.441991	+	0.897020i	$0.354272\pi$
$558$		0			0
$559$	34.0906	+	7.78097i	1.44188	+	0.329100i
$560$	15.7240	+	2.08315i	0.664459	+	0.0880291i
$561$		0			0
$562$	−0.510164	−	0.157365i	−0.0215200	−	0.00663803i
$563$	−10.2429	+	26.0984i	−0.431685	+	1.09992i	0.535205	+	0.844722i	$0.320234\pi$
$563$	−10.2429	+	26.0984i	−0.431685	+	1.09992i	−0.966890	+	0.255193i	$0.917861\pi$
$564$		0			0
$565$	−3.49162	+	11.3195i	−0.146893	+	0.476217i
$566$	0.148855	+	0.652175i	0.00625683	+	0.0274130i
$567$		0			0
$568$	−1.58069	+	6.92544i	−0.0663241	+	0.290585i
$569$	12.7564	+	7.36489i	0.534775	+	0.308752i	0.742959	−	0.669337i	$-0.233422\pi$
$569$	12.7564	+	7.36489i	0.534775	+	0.308752i	−0.208184	+	0.978090i	$0.566755\pi$
$570$		0			0
$571$	34.3341	−	10.5907i	1.43684	−	0.443205i	0.524066	−	0.851678i	$-0.324415\pi$
$571$	34.3341	−	10.5907i	1.43684	−	0.443205i	0.912771	+	0.408472i	$0.133938\pi$
$572$	−4.47299	+	59.6878i	−0.187025	+	2.49567i
$573$		0			0
$574$	0.0502773	−	0.0561681i	0.00209853	−	0.00234441i
$575$	−11.9681	−	9.54421i	−0.499102	−	0.398021i
$576$		0			0
$577$	2.23881	−	14.8535i	0.0932029	−	0.618361i	−0.892650	−	0.450750i	$-0.851157\pi$
$577$	2.23881	−	14.8535i	0.0932029	−	0.618361i	0.985853	−	0.167611i	$-0.0536053\pi$
$578$	−0.910272	+	1.33512i	−0.0378623	+	0.0555338i
$579$		0			0
$580$	−12.7446	+	26.4645i	−0.529192	+	1.09888i
$581$	−23.6895	+	0.423714i	−0.982806	+	0.0175786i
$582$		0			0
$583$	−18.7996	+	12.8173i	−0.778598	+	0.530839i
$584$	−2.24266	+	2.08089i	−0.0928021	+	0.0861077i
$585$		0			0
$586$	−0.105781	+	0.0415158i	−0.00436976	+	0.00171500i
$587$	−23.0393			−0.950936			−0.475468	−	0.879733i	$-0.657721\pi$
$587$	−23.0393			−0.950936			−0.475468	+	0.879733i	$0.657721\pi$
$588$		0			0
$589$	−17.7113			−0.729780
$590$	2.56866	−	1.00812i	0.105750	−	0.0415038i
$591$		0			0
$592$	6.04850	−	5.61219i	0.248592	−	0.230660i
$593$	23.1902	−	15.8108i	0.952308	−	0.649272i	0.0157835	−	0.999875i	$-0.494976\pi$
$593$	23.1902	−	15.8108i	0.952308	−	0.649272i	0.936524	+	0.350603i	$0.114023\pi$
$594$		0			0
$595$	−2.33128	−	9.43307i	−0.0955730	−	0.386718i
$596$	6.72263	−	13.9597i	0.275369	−	0.571811i
$597$		0			0
$598$	2.66056	−	3.90233i	0.108798	−	0.159578i
$599$	4.00751	−	26.5881i	0.163742	−	1.08636i	−0.744411	−	0.667722i	$-0.767269\pi$
$599$	4.00751	−	26.5881i	0.163742	−	1.08636i	0.908153	−	0.418638i	$-0.137492\pi$
$600$		0			0
$601$	−13.6496	−	10.8852i	−0.556780	−	0.444017i	0.304235	−	0.952597i	$-0.401599\pi$
$601$	−13.6496	−	10.8852i	−0.556780	−	0.444017i	−0.861015	+	0.508580i	$0.830171\pi$
$602$	−0.387770	−	2.29358i	−0.0158043	−	0.0934793i
$603$		0			0
$604$	−0.0174272	+	0.232550i	−0.000709103	+	0.00946233i
$605$	−25.8853	+	7.98457i	−1.05239	+	0.324619i
$606$		0			0
$607$	−16.2456	−	9.37939i	−0.659388	−	0.380698i	0.132656	−	0.991162i	$-0.457649\pi$
$607$	−16.2456	−	9.37939i	−0.659388	−	0.380698i	−0.792044	+	0.610464i	$0.790983\pi$
$608$	0.886699	−	3.88488i	0.0359604	−	0.157553i
$609$		0			0
$610$	−0.240196	−	1.05237i	−0.00972524	−	0.0426091i
$611$	−18.9863	+	61.5522i	−0.768105	+	2.49013i
$612$		0			0
$613$	5.60979	−	14.2935i	0.226577	−	0.577310i	−0.771700	−	0.635987i	$-0.780593\pi$
$613$	5.60979	−	14.2935i	0.226577	−	0.577310i	0.998277	+	0.0586776i	$0.0186884\pi$
$614$	1.28047	+	0.394973i	0.0516757	+	0.0159398i
$615$		0			0
$616$	7.60520	−	2.49569i	0.306422	−	0.100554i
$617$	−36.9315	−	8.42938i	−1.48681	−	0.339354i	−0.599441	−	0.800419i	$-0.704611\pi$
$617$	−36.9315	−	8.42938i	−1.48681	−	0.339354i	−0.887367	+	0.461065i	$0.847468\pi$
$618$		0			0
$619$	−9.93774	+	5.73756i	−0.399431	+	0.230612i	−0.686239	−	0.727376i	$-0.740739\pi$
$619$	−9.93774	+	5.73756i	−0.399431	+	0.230612i	0.286807	+	0.957988i	$0.407406\pi$
$620$	−6.75430	−	21.8969i	−0.271259	−	0.879401i
$621$		0			0
$622$	1.85455	−	1.47895i	0.0743607	−	0.0593007i
$623$	−2.53173	+	4.57201i	−0.101432	+	0.183174i
$624$		0			0
$625$	3.75706	+	3.48604i	0.150282	+	0.139442i
$626$	1.32449	+	0.199634i	0.0529371	+	0.00797899i
$627$		0			0
$628$	−2.16885	−	14.3894i	−0.0865464	−	0.574198i
$629$	−4.55417	−	2.19317i	−0.181587	−	0.0874476i
$630$		0			0
$631$	−37.9021	+	18.2527i	−1.50886	+	0.726628i	−0.991617	−	0.129211i	$-0.958756\pi$
$631$	−37.9021	+	18.2527i	−1.50886	+	0.726628i	−0.517242	+	0.855839i	$0.673041\pi$
$632$	1.20265	+	1.76396i	0.0478387	+	0.0701664i
$633$		0			0
$634$	−0.155897	−	2.08030i	−0.00619147	−	0.0826194i
$635$	−2.33768	−	5.95631i	−0.0927679	−	0.236369i
$636$		0			0
$637$	−15.9048	+	36.2925i	−0.630170	+	1.43796i
$638$			7.29749i			0.288910i
$639$		0			0
$640$	6.84287	−	0.512802i	0.270488	−	0.0202703i
$641$	21.6891	+	23.3753i	0.856669	+	0.923269i	0.997771	−	0.0667258i	$-0.0212553\pi$
$641$	21.6891	+	23.3753i	0.856669	+	0.923269i	−0.141103	+	0.989995i	$0.545065\pi$
$642$		0			0
$643$	−10.0844	−	20.9404i	−0.397689	−	0.825810i	−0.999628	−	0.0272678i	$-0.991319\pi$
$643$	−10.0844	−	20.9404i	−0.397689	−	0.825810i	0.601939	−	0.798542i	$-0.294395\pi$
$644$	30.0534	+	6.29625i	1.18427	+	0.248107i
$645$		0			0
$646$	−0.790911	+	0.119211i	−0.0311180	+	0.00469028i
$647$	−3.53050	−	2.40705i	−0.138798	−	0.0946310i	0.491930	−	0.870635i	$-0.336291\pi$
$647$	−3.53050	−	2.40705i	−0.138798	−	0.0946310i	−0.630729	+	0.776004i	$0.717244\pi$
$648$		0			0
$649$	−45.5708	+	49.1137i	−1.78881	+	1.92788i
$650$	1.31169	−	1.64480i	0.0514486	−	0.0645145i
$651$		0			0
$652$	−3.85953	−	4.83969i	−0.151151	−	0.189537i
$653$	30.8531	+	2.31212i	1.20737	+	0.0904801i	0.663167	−	0.748471i	$-0.269212\pi$
$653$	30.8531	+	2.31212i	1.20737	+	0.0904801i	0.544206	+	0.838951i	$0.316831\pi$
$654$		0			0
$655$	−5.97101	−	10.3421i	−0.233307	−	0.404099i
$656$	−0.388252	+	0.672472i	−0.0151587	+	0.0262556i
$657$		0			0
$658$	4.26660	−	0.396582i	0.166330	−	0.0154604i
$659$	−31.3870	+	7.16389i	−1.22267	+	0.279065i	−0.784671	−	0.619912i	$-0.787168\pi$
$659$	−31.3870	+	7.16389i	−1.22267	+	0.279065i	−0.437994	+	0.898978i	$0.644311\pi$
$660$		0			0
$661$	−0.246290	−	0.0966616i	−0.00957956	−	0.00375970i	0.360546	−	0.932741i	$-0.382590\pi$
$661$	−0.246290	−	0.0966616i	−0.00957956	−	0.00375970i	−0.370126	+	0.928982i	$0.620685\pi$
$662$	0.571651	+	0.224357i	0.0222179	+	0.00871986i
$663$		0			0
$664$	−4.94529	+	1.12873i	−0.191914	+	0.0438032i
$665$	−5.30398	+	8.08652i	−0.205679	+	0.313582i
$666$		0			0
$667$	−28.1379	+	48.7363i	−1.08951	+	1.88708i
$668$	4.90919	+	8.50297i	0.189942	+	0.328990i
$669$		0			0
$670$	−1.96929	−	0.147578i	−0.0760802	−	0.00570142i
$671$	16.3409	+	20.4909i	0.630834	+	0.791041i
$672$		0			0
$673$	16.2674	−	20.3986i	0.627060	−	0.786309i	−0.362258	−	0.932078i	$-0.617994\pi$
$673$	16.2674	−	20.3986i	0.627060	−	0.786309i	0.989319	+	0.145769i	$0.0465656\pi$
$674$	2.29590	−	2.47439i	0.0884348	−	0.0953101i
$675$		0			0
$676$	−31.1493	−	21.2373i	−1.19805	−	0.816817i
$677$	−28.9323	+	4.36084i	−1.11196	+	0.167601i	−0.679231	−	0.733925i	$-0.737687\pi$
$677$	−28.9323	+	4.36084i	−1.11196	+	0.167601i	−0.432727	+	0.901525i	$0.642448\pi$
$678$		0			0
$679$	17.0608	+	13.1133i	0.654732	+	0.503243i
$680$	−0.902598	−	1.87426i	−0.0346130	−	0.0718747i
$681$		0			0
$682$	−3.87220	−	4.17324i	−0.148274	−	0.159802i
$683$	32.5940	−	2.44258i	1.24717	−	0.0934627i	0.565270	−	0.824906i	$-0.308772\pi$
$683$	32.5940	−	2.44258i	1.24717	−	0.0934627i	0.681903	+	0.731443i	$0.261153\pi$
$684$		0			0
$685$			21.1527i			0.808204i
$686$	2.63535	+	0.0557382i	0.100618	+	0.00212810i
$687$		0			0
$688$	8.75387	+	22.3045i	0.333738	+	0.850351i
$689$	−1.80209	−	24.0473i	−0.0686543	−	0.916128i
$690$		0			0
$691$	−8.21280	−	12.0460i	−0.312430	−	0.458250i	0.637619	−	0.770352i	$-0.279919\pi$
$691$	−8.21280	−	12.0460i	−0.312430	−	0.458250i	−0.950049	+	0.312102i	$0.898967\pi$
$692$	−13.9557	+	6.72071i	−0.530516	+	0.255483i
$693$		0			0
$694$	−2.07517	−	0.999349i	−0.0787723	−	0.0379348i
$695$	4.52961	+	30.0520i	0.171818	+	1.13994i
$696$		0			0
$697$	0.470384	+	0.0708989i	0.0178171	+	0.00268549i
$698$	−1.39716	−	1.29637i	−0.0528832	−	0.0490684i
$699$		0			0
$700$	13.1398	+	3.79712i	0.496637	+	0.143518i
$701$	−29.6568	+	23.6505i	−1.12012	+	0.893268i	−0.995099	−	0.0988857i	$-0.968472\pi$
$701$	−29.6568	+	23.6505i	−1.12012	+	0.893268i	−0.125024	+	0.992154i	$0.539901\pi$
$702$		0			0
$703$	1.48284	+	4.80726i	0.0559265	+	0.181309i
$704$	−34.7741	+	20.0768i	−1.31060	+	0.756674i
$705$		0			0
$706$	−3.64178	−	0.831213i	−0.137060	−	0.0312831i
$707$	38.7707	+	25.4299i	1.45812	+	0.956388i
$708$		0			0
$709$	−5.37503	−	1.65798i	−0.201863	−	0.0622666i	0.192175	−	0.981361i	$-0.438446\pi$
$709$	−5.37503	−	1.65798i	−0.201863	−	0.0622666i	−0.394038	+	0.919094i	$0.628922\pi$
$710$	1.00787	−	2.56801i	0.0378247	−	0.0963757i
$711$		0			0
$712$	−0.329792	+	1.06916i	−0.0123595	+	0.0400684i
$713$	−9.76918	−	42.8016i	−0.365859	−	1.60293i
$714$		0			0
$715$	10.3980	−	45.5567i	0.388864	−	1.70372i
$716$	10.7488	+	6.20580i	0.401700	+	0.231922i
$717$		0			0
$718$	3.38256	−	1.04338i	0.126236	−	0.0389386i
$719$	−3.85528	+	51.4451i	−0.143778	+	1.91858i	0.200470	+	0.979700i	$0.435753\pi$
$719$	−3.85528	+	51.4451i	−0.143778	+	1.91858i	−0.344247	+	0.938879i	$0.611866\pi$
$720$		0			0
$721$	−42.2229	−	2.40574i	−1.57246	−	0.0895944i
$722$	−1.49187	−	1.18972i	−0.0555215	−	0.0442769i
$723$		0			0
$724$	−0.857063	+	5.68624i	−0.0318525	+	0.211328i
$725$	−14.1208	+	20.7115i	−0.524435	+	0.769205i
$726$		0			0
$727$	13.0750	−	27.1505i	0.484925	−	1.00696i	−0.504702	−	0.863294i	$-0.668397\pi$
$727$	13.0750	−	27.1505i	0.484925	−	1.00696i	0.989627	−	0.143663i	$-0.0458882\pi$
$728$	−1.73948	+	8.30292i	−0.0644694	+	0.307727i
$729$		0			0
$730$	0.981671	−	0.669292i	0.0363333	−	0.0247716i
$731$	10.7603	−	9.98406i	0.397982	−	0.369274i
$732$		0			0
$733$	47.3364	−	18.5782i	1.74841	−	0.686200i	0.748680	−	0.662932i	$-0.230688\pi$
$733$	47.3364	−	18.5782i	1.74841	−	0.686200i	0.999729	−	0.0232679i	$-0.00740708\pi$
$734$	−4.74022			−0.174965
$735$		0			0
$736$	9.87741			0.364086
$737$	44.6343	−	17.5177i	1.64413	−	0.645272i
$738$		0			0
$739$	20.5359	−	19.0545i	0.755424	−	0.700931i	−0.205219	−	0.978716i	$-0.565791\pi$
$739$	20.5359	−	19.0545i	0.755424	−	0.700931i	0.960643	+	0.277785i	$0.0896003\pi$
$740$	−5.37785	+	3.66656i	−0.197694	+	0.134785i
$741$		0			0
$742$	−1.43264	+	0.721762i	−0.0525937	+	0.0264967i
$743$	−8.02702	+	16.6683i	−0.294483	+	0.611500i	−0.994745	−	0.102386i	$-0.967352\pi$
$743$	−8.02702	+	16.6683i	−0.294483	+	0.611500i	0.700262	+	0.713886i	$0.253067\pi$
$744$		0			0
$745$	−6.81394	+	9.99421i	−0.249643	+	0.366160i
$746$	0.432681	−	2.87065i	0.0158416	−	0.105102i
$747$		0			0
$748$	19.6445	+	15.6659i	0.718273	+	0.572804i
$749$	−5.43131	−	3.00756i	−0.198456	−	0.109894i
$750$		0			0
$751$	0.447222	−	5.96776i	0.0163194	−	0.217767i	−0.983082	−	0.183167i	$-0.941365\pi$
$751$	0.447222	−	5.96776i	0.0163194	−	0.217767i	0.999401	−	0.0346001i	$-0.0110157\pi$
$752$	−42.1776	+	13.0101i	−1.53806	+	0.474429i
$753$		0			0
$754$	−6.69797	−	3.86708i	−0.243926	−	0.140831i
$755$	0.0405117	−	0.177493i	0.00147437	−	0.00645965i
$756$		0			0
$757$	−11.6835	−	51.1888i	−0.424645	−	1.86049i	−0.504091	−	0.863651i	$-0.668172\pi$
$757$	−11.6835	−	51.1888i	−0.424645	−	1.86049i	0.0794461	−	0.996839i	$-0.474685\pi$
$758$	0.448716	−	1.45470i	0.0162981	−	0.0528372i
$759$		0			0
$760$	−0.756404	+	1.92729i	−0.0274377	+	0.0699100i
$761$	26.2357	+	8.09263i	0.951042	+	0.293358i	0.731189	−	0.682175i	$-0.238966\pi$
$761$	26.2357	+	8.09263i	0.951042	+	0.293358i	0.219853	+	0.975533i	$0.429442\pi$
$762$		0			0
$763$	2.96028	−	2.84694i	0.107169	−	0.103066i
$764$	−24.5531	−	5.60408i	−0.888300	−	0.202749i
$765$		0			0
$766$	−1.46858	+	0.847887i	−0.0530621	+	0.0306354i
$767$	−20.9300	−	67.8533i	−0.755737	−	2.45004i
$768$		0			0
$769$	0.181697	−	0.144899i	0.00655217	−	0.00522518i	−0.620208	−	0.784437i	$-0.712952\pi$
$769$	0.181697	−	0.144899i	0.00655217	−	0.00522518i	0.626760	+	0.779212i	$0.284380\pi$
$770$	−3.06500	+	0.518192i	−0.110455	+	0.0186744i
$771$		0			0
$772$	−2.73177	−	2.53471i	−0.0983185	−	0.0912262i
$773$	42.5241	+	6.40948i	1.52949	+	0.230533i	0.859227	−	0.511594i	$-0.170945\pi$
$773$	42.5241	+	6.40948i	1.52949	+	0.230533i	0.670259	+	0.742127i	$0.266183\pi$
$774$		0			0
$775$	−2.91461	−	19.3371i	−0.104696	−	0.694611i
$776$	4.15057	+	1.99881i	0.148997	+	0.0717531i
$777$		0			0
$778$	1.67207	−	0.805224i	0.0599464	−	0.0288687i
$779$	−0.266698	−	0.391174i	−0.00955545	−	0.0140153i
$780$		0			0
$781$	5.00558	+	66.7948i	0.179114	+	2.39011i
$782$	−0.724339	−	1.84558i	−0.0259023	−	0.0659980i
$783$		0			0
$784$	−26.6869	+	5.00436i	−0.953104	+	0.178727i
$785$			11.3605i			0.405473i
$786$		0			0
$787$	25.2189	−	1.88990i	0.898957	−	0.0673675i	0.382770	−	0.923844i	$-0.374970\pi$
$787$	25.2189	−	1.88990i	0.898957	−	0.0673675i	0.516187	+	0.856476i	$0.327351\pi$
$788$	−17.2462	−	18.5870i	−0.614371	−	0.662134i
$789$		0			0
$790$	−0.359739	−	0.747005i	−0.0127989	−	0.0265772i
$791$	−0.362640	−	20.2749i	−0.0128940	−	0.720892i
$792$		0			0
$793$	−27.4668	+	4.13996i	−0.975375	+	0.147014i
$794$	2.59323	+	1.76803i	0.0920302	+	0.0627451i
$795$		0			0
$796$	−12.0280	+	12.9631i	−0.426320	+	0.459464i
$797$	−2.63783	+	3.30773i	−0.0934366	+	0.117166i	−0.826352	−	0.563154i	$-0.809588\pi$
$797$	−2.63783	+	3.30773i	−0.0934366	+	0.117166i	0.732915	+	0.680320i	$0.238159\pi$
$798$		0			0
$799$	16.8591	+	21.1406i	0.596432	+	0.747902i
$800$	4.38743	+	0.328792i	0.155119	+	0.0116246i
$801$		0			0
$802$	0.520179	+	0.900977i	0.0183682	+	0.0318146i
$803$	−14.4239	+	24.9830i	−0.509009	+	0.881629i
$804$		0			0
$805$	−22.4677	−	8.35739i	−0.791882	−	0.294559i
$806$	5.88235	−	1.34261i	0.207197	−	0.0472913i
$807$		0			0
$808$	9.24035	+	3.62657i	0.325074	+	0.127582i
$809$	17.1208	+	6.71942i	0.601935	+	0.236242i	0.646686	−	0.762756i	$-0.276154\pi$
$809$	17.1208	+	6.71942i	0.601935	+	0.236242i	−0.0447511	+	0.998998i	$0.514249\pi$
$810$		0			0
$811$	−27.0745	+	6.17958i	−0.950714	+	0.216994i	−0.669635	−	0.742690i	$-0.733550\pi$
$811$	−27.0745	+	6.17958i	−0.950714	+	0.216994i	−0.281079	+	0.959685i	$0.590692\pi$
$812$	6.60384	−	49.8469i	0.231749	−	1.74928i
$813$		0			0
$814$	−0.808524	+	1.40041i	−0.0283388	+	0.0490842i
$815$	2.41631	+	4.18517i	0.0846396	+	0.146600i
$816$		0			0
$817$	−14.5682	−	1.09174i	−0.509677	−	0.0381950i
$818$	−1.33536	−	1.67449i	−0.0466898	−	0.0585471i
$819$		0			0
$820$	0.381912	−	0.478902i	0.0133369	−	0.0167240i
$821$	34.0627	−	36.7108i	1.18880	−	1.28122i	0.238046	−	0.971254i	$-0.423493\pi$
$821$	34.0627	−	36.7108i	1.18880	−	1.28122i	0.950749	−	0.309963i	$-0.100317\pi$
$822$		0			0
$823$	41.5671	+	28.3400i	1.44894	+	0.987869i	0.995316	+	0.0966740i	$0.0308204\pi$
$823$	41.5671	+	28.3400i	1.44894	+	0.987869i	0.453621	+	0.891195i	$0.350132\pi$
$824$	−8.95298	+	1.34944i	−0.311892	+	0.0470101i
$825$		0			0
$826$	−3.63984	+	3.01072i	−0.126646	+	0.104756i
$827$	−3.46487	−	7.19487i	−0.120485	−	0.250190i	0.832000	−	0.554776i	$-0.187196\pi$
$827$	−3.46487	−	7.19487i	−0.120485	−	0.250190i	−0.952485	+	0.304586i	$0.901482\pi$
$828$		0			0
$829$	−20.9734	−	22.6039i	−0.728435	−	0.785066i	0.254881	−	0.966972i	$-0.417964\pi$
$829$	−20.9734	−	22.6039i	−0.728435	−	0.785066i	−0.983316	+	0.181906i	$0.941773\pi$
$830$	1.96442	−	0.147213i	0.0681860	−	0.00510983i
$831$		0			0
$832$		−	42.5563i		−	1.47538i
$833$	8.82669	+	14.0986i	0.305827	+	0.488487i
$834$		0			0
$835$	−2.80037	−	7.13523i	−0.0969109	−	0.246925i
$836$	−1.86878	−	24.9371i	−0.0646330	−	0.862467i
$837$		0			0
$838$	0.131435	+	0.192780i	0.00454036	+	0.00665948i
$839$	38.1667	−	18.3801i	1.31766	−	0.634552i	0.362872	−	0.931839i	$-0.381796\pi$
$839$	38.1667	−	18.3801i	1.31766	−	0.634552i	0.954788	+	0.297287i	$0.0960819\pi$
$840$		0			0
$841$	56.9003	+	27.4018i	1.96208	+	0.944888i
$842$	0.603636	+	4.00486i	0.0208027	+	0.138017i
$843$		0			0
$844$	12.3527	+	1.86187i	0.425197	+	0.0640881i
$845$	21.5752	+	20.0189i	0.742210	+	0.688671i
$846$		0			0
$847$	37.8408	−	26.8031i	1.30023	−	0.920965i
$848$	12.9191	−	10.3027i	0.443645	−	0.353795i
$849$		0			0
$850$	−0.260308	−	0.843898i	−0.00892849	−	0.0289455i
$851$	−10.7995	+	6.23508i	−0.370201	+	0.213736i
$852$		0			0
$853$	1.91444	+	0.436959i	0.0655492	+	0.0149612i	0.255170	−	0.966896i	$-0.417869\pi$
$853$	1.91444	+	0.436959i	0.0655492	+	0.0149612i	−0.189621	+	0.981857i	$0.560726\pi$
$854$	0.952375	+	1.58347i	0.0325896	+	0.0541853i
$855$		0			0
$856$	−1.27010	−	0.391775i	−0.0434112	−	0.0133906i
$857$	2.53923	−	6.46986i	0.0867385	−	0.221006i	−0.880922	−	0.473261i	$-0.843077\pi$
$857$	2.53923	−	6.46986i	0.0867385	−	0.221006i	0.967661	+	0.252255i	$0.0811721\pi$
$858$		0			0
$859$	−5.28966	+	17.1486i	−0.180481	+	0.585104i	0.819448	+	0.573154i	$0.194280\pi$
$859$	−5.28966	+	17.1486i	−0.180481	+	0.585104i	−0.999929	+	0.0119505i	$0.996196\pi$
$860$	−4.20593	−	18.4274i	−0.143421	−	0.628369i
$861$		0			0
$862$	0.210002	−	0.920080i	0.00715271	−	0.0313381i
$863$	12.2134	+	7.05140i	0.415748	+	0.240032i	0.693257	−	0.720691i	$-0.256175\pi$
$863$	12.2134	+	7.05140i	0.415748	+	0.240032i	−0.277508	+	0.960723i	$0.589509\pi$
$864$		0			0
$865$	11.5554	−	3.56435i	0.392894	−	0.121192i
$866$	0.342731	−	4.57343i	0.0116465	−	0.155411i
$867$		0			0
$868$	22.6732	+	32.0103i	0.769580	+	1.08650i
$869$	15.7391	+	12.5515i	0.533912	+	0.425780i
$870$		0			0
$871$	−7.57402	+	50.2504i	−0.256636	+	1.70267i
$872$	0.495319	−	0.726500i	0.0167736	−	0.0246024i
$873$		0			0
$874$	−0.856153	+	1.77782i	−0.0289598	+	0.0601356i
$875$	−28.2785	−	13.0004i	−0.955987	−	0.439494i
$876$		0			0
$877$	47.4767	−	32.3691i	1.60317	−	1.09303i	0.665011	−	0.746834i	$-0.268427\pi$
$877$	47.4767	−	32.3691i	1.60317	−	1.09303i	0.938164	−	0.346192i	$-0.112525\pi$
$878$	1.62813	−	1.51068i	0.0549467	−	0.0509831i
$879$		0			0
$880$	29.8064	−	11.6981i	1.00477	−	0.394344i
$881$	36.5243			1.23054			0.615268	−	0.788318i	$-0.289048\pi$
$881$	36.5243			1.23054			0.615268	+	0.788318i	$0.289048\pi$
$882$		0			0
$883$	−36.1524			−1.21663			−0.608313	−	0.793697i	$-0.708153\pi$
$883$	−36.1524			−1.21663			−0.608313	+	0.793697i	$0.708153\pi$
$884$	−24.7889	+	9.72893i	−0.833741	+	0.327219i
$885$		0			0
$886$	1.15789	−	1.07437i	0.0389002	−	0.0360941i
$887$	40.6621	−	27.7229i	1.36530	−	0.930845i	0.365299	−	0.930890i	$-0.380967\pi$
$887$	40.6621	−	27.7229i	1.36530	−	0.930845i	1.00000		4.55407e-5i	$1.44961e-5\pi$
$888$		0			0
$889$	6.98139	+	8.44022i	0.234148	+	0.283076i
$890$	0.188531	−	0.391489i	0.00631958	−	0.0131227i
$891$		0			0
$892$	18.9000	−	27.7212i	0.632818	−	0.928173i
$893$	4.01096	−	26.6110i	0.134222	−	0.890503i
$894$		0			0
$895$	−7.57563	−	6.04136i	−0.253225	−	0.201940i
$896$	−10.8562	+	4.48642i	−0.362681	+	0.149881i
$897$		0			0
$898$	0.0299115	−	0.399141i	0.000998158	−	0.0133195i
$899$	−68.6983	+	21.1906i	−2.29122	+	0.706747i
$900$		0			0
$901$	−8.76673	−	5.06147i	−0.292062	−	0.168622i
$902$	0.0338629	−	0.148363i	0.00112751	−	0.00493995i
$903$		0			0
$904$	−0.966035	−	4.23247i	−0.0321298	−	0.140770i
$905$	1.32325	−	4.28988i	0.0439864	−	0.142600i
$906$		0			0
$907$	−16.1318	+	41.1031i	−0.535647	+	1.36481i	0.365306	+	0.930887i	$0.380964\pi$
$907$	−16.1318	+	41.1031i	−0.535647	+	1.36481i	−0.900953	+	0.433918i	$0.857131\pi$
$908$	−27.1747	−	8.38230i	−0.901826	−	0.278176i
$909$		0			0
$910$	1.14858	−	3.08780i	0.0380751	−	0.102360i
$911$	−1.11899	−	0.255402i	−0.0370737	−	0.00846184i	0.203944	−	0.978983i	$-0.434624\pi$
$911$	−1.11899	−	0.255402i	−0.0370737	−	0.00846184i	−0.241018	+	0.970521i	$0.577481\pi$
$912$		0			0
$913$	−41.4222	+	23.9151i	−1.37088	+	0.791476i
$914$	0.0923959	+	0.299540i	0.00305618	+	0.00990790i
$915$		0			0
$916$	18.5725	−	14.8110i	0.613651	−	0.489371i
$917$	15.2319	+	13.6344i	0.503001	+	0.450248i
$918$		0			0
$919$	23.6413	+	21.9359i	0.779854	+	0.723599i	0.965892	−	0.258944i	$-0.0833745\pi$
$919$	23.6413	+	21.9359i	0.779854	+	0.723599i	−0.186039	+	0.982542i	$0.559565\pi$
$920$	−5.07475	−	0.764896i	−0.167310	−	0.0252179i
$921$		0			0
$922$	−0.478086	−	3.17190i	−0.0157449	−	0.104461i
$923$	−63.9599	−	30.8015i	−2.10527	−	1.01384i
$924$		0			0
$925$	−5.00455	+	2.41006i	−0.164548	+	0.0792424i
$926$	0.0160453	+	0.0235342i	0.000527282	+	0.000773380i
$927$		0			0
$928$	−1.20874	−	16.1295i	−0.0396789	−	0.529478i
$929$	4.10673	+	10.4638i	0.134737	+	0.343305i	0.982279	−	0.187423i	$-0.0600136\pi$
$929$	4.10673	+	10.4638i	0.134737	+	0.343305i	−0.847542	+	0.530729i	$0.821918\pi$
$930$		0			0
$931$	4.31078	−	15.9837i	0.141280	−	0.523845i
$932$		−	31.7666i		−	1.04055i
$933$		0			0
$934$	−2.18118	+	0.163457i	−0.0713704	+	0.00534848i
$935$	−13.3421	−	14.3794i	−0.436333	−	0.470255i
$936$		0			0
$937$	12.3161	+	25.5745i	0.402348	+	0.835484i	0.999445	+	0.0333149i	$0.0106064\pi$
$937$	12.3161	+	25.5745i	0.402348	+	0.835484i	−0.597097	+	0.802169i	$0.703679\pi$
$938$	3.28182	−	0.811064i	0.107155	−	0.0264822i
$939$		0			0
$940$	34.4295	−	5.18941i	1.12297	−	0.169260i
$941$	−2.19043	−	1.49341i	−0.0714061	−	0.0486839i	0.527091	−	0.849809i	$-0.323283\pi$
$941$	−2.19043	−	1.49341i	−0.0714061	−	0.0486839i	−0.598497	+	0.801125i	$0.704235\pi$
$942$		0			0
$943$	0.798218	−	0.860275i	0.0259936	−	0.0280144i
$944$	30.3372	−	38.0416i	0.987391	−	1.23815i
$945$		0			0
$946$	−2.92780	−	3.67134i	−0.0951908	−	0.119366i
$947$	−35.5917	−	2.66723i	−1.15657	−	0.0866732i	−0.517406	−	0.855740i	$-0.673102\pi$
$947$	−35.5917	−	2.66723i	−1.15657	−	0.0866732i	−0.639168	+	0.769067i	$0.720721\pi$
$948$		0			0
$949$	−15.2870	−	26.4779i	−0.496237	−	0.859508i
$950$	−0.439472	+	0.761187i	−0.0142583	+	0.0246962i
$951$		0			0
$952$	2.46846	+	2.56673i	0.0800031	+	0.0831883i
$953$	4.37063	−	0.997568i	0.141579	−	0.0323144i	−0.151144	−	0.988512i	$-0.548296\pi$
$953$	4.37063	−	0.997568i	0.141579	−	0.0323144i	0.292723	+	0.956197i	$0.405439\pi$
$954$		0			0
$955$	18.3021	+	7.18306i	0.592243	+	0.232438i
$956$	1.62813	+	0.638992i	0.0526574	+	0.0206665i
$957$		0			0
$958$	2.22308	−	0.507403i	0.0718244	−	0.0163934i
$959$	−11.2902	−	34.4049i	−0.364579	−	1.11099i
$960$		0			0
$961$	12.5425	−	21.7243i	0.404598	−	0.700785i
$962$	−0.856905	−	1.48420i	−0.0276277	−	0.0478526i
$963$		0			0
$964$	−48.0612	−	3.60169i	−1.54795	−	0.116003i
$965$	1.81391	+	2.27457i	0.0583919	+	0.0732211i
$966$		0			0
$967$	−3.75970	+	4.71451i	−0.120904	+	0.151608i	−0.838600	−	0.544748i	$-0.816625\pi$
$967$	−3.75970	+	4.71451i	−0.120904	+	0.151608i	0.717696	+	0.696356i	$0.245197\pi$
$968$	6.75252	−	7.27749i	0.217034	−	0.233907i
$969$		0			0
$970$	−1.47821	−	1.00782i	−0.0474623	−	0.0323593i
$971$	−49.6592	+	7.48492i	−1.59364	+	0.240202i	−0.885076	−	0.465446i	$-0.845894\pi$
$971$	−49.6592	+	7.48492i	−1.59364	+	0.240202i	−0.708562	+	0.705648i	$0.750656\pi$
$972$		0			0
$973$	−23.4075	−	46.4620i	−0.750412	−	1.48950i
$974$	1.32953	+	2.76079i	0.0426008	+	0.0884614i
$975$		0			0
$976$	−12.9463	−	13.9528i	−0.414400	−	0.446617i
$977$	23.9644	−	1.79588i	0.766689	−	0.0574554i	0.314357	−	0.949305i	$-0.398211\pi$
$977$	23.9644	−	1.79588i	0.766689	−	0.0574554i	0.452332	+	0.891849i	$0.350592\pi$
$978$		0			0
$979$			10.5502i			0.337187i
$980$	21.4050	−	0.765951i	0.683758	−	0.0244674i
$981$		0			0
$982$	−0.484217	−	1.23376i	−0.0154520	−	0.0393710i
$983$	3.12311	+	41.6749i	0.0996116	+	1.32922i	0.793248	+	0.608899i	$0.208388\pi$
$983$	3.12311	+	41.6749i	0.0996116	+	1.32922i	−0.693636	+	0.720325i	$0.743992\pi$
$984$		0			0
$985$	11.1508	+	16.3553i	0.355295	+	0.521122i
$986$	−2.92515	+	1.40868i	−0.0931557	+	0.0448614i
$987$		0			0
$988$	23.8787	+	11.4994i	0.759683	+	0.365844i
$989$	−5.39721	−	35.8082i	−0.171621	−	1.13863i
$990$		0			0
$991$	−2.55181	−	0.384623i	−0.0810608	−	0.0122180i	0.108387	−	0.994109i	$-0.465432\pi$
$991$	−2.55181	−	0.384623i	−0.0810608	−	0.0122180i	−0.189447	+	0.981891i	$0.560670\pi$
$992$	9.24992	+	8.58267i	0.293685	+	0.272500i
$993$		0			0
$994$	−0.268637	+	4.71482i	−0.00852064	+	0.149545i
$995$	10.7935	−	8.60755i	0.342178	−	0.272878i
$996$		0			0
$997$	−6.75188	−	21.8891i	−0.213834	−	0.693233i	−0.997409	−	0.0719362i	$-0.977082\pi$
$997$	−6.75188	−	21.8891i	−0.213834	−	0.693233i	0.783575	−	0.621297i	$-0.213394\pi$
$998$	−1.64776	+	0.951333i	−0.0521588	+	0.0301139i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.2.bg.a.278.10	yes	216
3.2	odd	2	inner	441.2.bg.a.278.9	✓	216
49.3	odd	42	inner	441.2.bg.a.395.9	yes	216
147.101	even	42	inner	441.2.bg.a.395.10	yes	216

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.2.bg.a.278.9	✓	216	3.2	odd	2	inner
441.2.bg.a.278.10	yes	216	1.1	even	1	trivial
441.2.bg.a.395.9	yes	216	49.3	odd	42	inner
441.2.bg.a.395.10	yes	216	147.101	even	42	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	441.bg (of order \(42\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(0.132489 - 0.0519980i) q^{2} +(-1.45125 + 1.34657i) q^{4} +(1.27700 - 0.870646i) q^{5} +(-1.61234 + 2.09770i) q^{7} +(-0.245763 + 0.510332i) q^{8} +O(q^{10})\)	\(q+(0.132489 - 0.0519980i) q^{2} +(-1.45125 + 1.34657i) q^{4} +(1.27700 - 0.870646i) q^{5} +(-1.61234 + 2.09770i) q^{7} +(-0.245763 + 0.510332i) q^{8} +(0.123917 - 0.181752i) q^{10} +(-0.796043 + 5.28140i) q^{11} +(-4.42567 - 3.52936i) q^{13} +(-0.104541 + 0.361760i) q^{14} +(0.289868 - 3.86802i) q^{16} +(-2.27068 + 0.700411i) q^{17} +(2.04813 + 1.18249i) q^{19} +(-0.680873 + 2.98310i) q^{20} +(0.169155 + 0.741118i) q^{22} +(-1.72793 + 5.60180i) q^{23} +(-0.953993 + 2.43073i) q^{25} +(-0.769871 - 0.237474i) q^{26} +(-0.484776 - 5.21543i) q^{28} +(9.35903 + 2.13614i) q^{29} +(-6.48566 + 3.74450i) q^{31} +(-0.496639 - 1.61006i) q^{32} +(-0.264419 + 0.210867i) q^{34} +(-0.232612 + 4.08255i) q^{35} +(1.55935 + 1.44686i) q^{37} +(0.332840 + 0.0501676i) q^{38} +(0.130478 + 0.865668i) q^{40} +(-0.180363 - 0.0868585i) q^{41} +(-5.56553 + 2.68022i) q^{43} +(-5.95650 - 8.73658i) q^{44} +(0.0623516 + 0.832024i) q^{46} +(-4.15730 - 10.5926i) q^{47} +(-1.80070 - 6.76443i) q^{49} +0.371651i q^{50} +(11.1753 - 0.837473i) q^{52} +(2.89757 + 3.12284i) q^{53} +(3.58168 + 7.43743i) q^{55} +(-0.674270 - 1.33837i) q^{56} +(1.35104 - 0.203637i) q^{58} +(10.3645 + 7.06637i) q^{59} +(3.33764 - 3.59712i) q^{61} +(-0.664571 + 0.833345i) q^{62} +(4.68735 + 5.87775i) q^{64} +(-8.72442 - 0.653805i) q^{65} +(-4.48870 - 7.77466i) q^{67} +(2.35218 - 4.07409i) q^{68} +(0.181466 + 0.552987i) q^{70} +(12.2266 - 2.79063i) q^{71} +(5.02779 + 1.97326i) q^{73} +(0.281830 + 0.110610i) q^{74} +(-4.56465 + 1.04185i) q^{76} +(-9.79530 - 10.1853i) q^{77} +(1.88456 - 3.26415i) q^{79} +(-2.99751 - 5.19185i) q^{80} +(-0.0284126 - 0.00212923i) q^{82} +(5.58349 + 7.00147i) q^{83} +(-2.28985 + 2.87138i) q^{85} +(-0.598003 + 0.644494i) q^{86} +(-2.49963 - 1.70422i) q^{88} +(1.95325 - 0.294405i) q^{89} +(14.5392 - 3.59321i) q^{91} +(-5.03554 - 10.4564i) q^{92} +(-1.10159 - 1.18723i) q^{94} +(3.64499 - 0.273154i) q^{95} -8.13308i q^{97} +(-0.590309 - 0.802577i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 216 q - 16 q^{4} + 2 q^{7}+O(q^{10}) \) 216 * q - 16 * q^4 + 2 * q^7	\( 216 q - 16 q^{4} + 2 q^{7} + 12 q^{10} + 12 q^{16} - 6 q^{19} + 44 q^{22} + 26 q^{25} + 84 q^{28} - 6 q^{31} - 112 q^{34} + 60 q^{37} - 304 q^{40} + 20 q^{43} - 20 q^{46} - 86 q^{49} - 168 q^{52} - 84 q^{55} - 120 q^{58} - 2 q^{61} + 32 q^{64} + 22 q^{67} - 136 q^{70} - 6 q^{73} + 84 q^{76} + 2 q^{79} - 104 q^{82} + 96 q^{85} - 12 q^{88} + 58 q^{91} + 52 q^{94}+O(q^{100}) \) 216 * q - 16 * q^4 + 2 * q^7 + 12 * q^10 + 12 * q^16 - 6 * q^19 + 44 * q^22 + 26 * q^25 + 84 * q^28 - 6 * q^31 - 112 * q^34 + 60 * q^37 - 304 * q^40 + 20 * q^43 - 20 * q^46 - 86 * q^49 - 168 * q^52 - 84 * q^55 - 120 * q^58 - 2 * q^61 + 32 * q^64 + 22 * q^67 - 136 * q^70 - 6 * q^73 + 84 * q^76 + 2 * q^79 - 104 * q^82 + 96 * q^85 - 12 * q^88 + 58 * q^91 + 52 * q^94

Introduction

L-functions

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