LMFDB - Embedded newform 1950.2.bc.k.751.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(751,1950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 5]))

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

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

chi := DirichletCharacter("1950.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.bc (of order $6$, degree $2$, 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:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 87 x^{10} - 380 x^{9} + 2556 x^{8} - 8010 x^{7} + 29687 x^{6} - 62556 x^{5} + \cdots + 14089 $ x^12 - 6x^11 + 87x^10 - 380x^9 + 2556x^8 - 8010x^7 + 29687x^6 - 62556x^5 + 115386x^4 - 135130x^3 + 113253x^2 - 54888*x + 14089
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.1
Root			$0.500000 - 4.99624i$ of defining polynomial
Character	$\chi$	$=$	1950.751
Dual form			1950.2.bc.k.901.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-4.44290 - 2.56511i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-4.44290 - 2.56511i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.83209 + 2.78981i) q^{11} +1.00000 q^{12} +(3.19076 - 1.67900i) q^{13} +5.13022 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.641326 + 1.11081i) q^{17} -1.00000i q^{18} +(5.75861 + 3.32474i) q^{19} -5.13022i q^{21} +(2.78981 - 4.83209i) q^{22} +(-3.43113 - 5.94290i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-1.92378 + 3.04944i) q^{26} -1.00000 q^{27} +(-4.44290 + 2.56511i) q^{28} +(-1.75214 - 3.03479i) q^{29} +6.30618i q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.83209 - 2.78981i) q^{33} -1.28265i q^{34} +(0.500000 + 0.866025i) q^{36} +(7.25861 - 4.19076i) q^{37} -6.64947 q^{38} +(3.04944 + 1.92378i) q^{39} +(1.11081 - 0.641326i) q^{41} +(2.56511 + 4.44290i) q^{42} +(2.17900 - 3.77414i) q^{43} +5.57962i q^{44} +(5.94290 + 3.43113i) q^{46} +5.02353i q^{47} +(0.500000 - 0.866025i) q^{48} +(9.65957 + 16.7309i) q^{49} -1.28265 q^{51} +(0.141326 - 3.60278i) q^{52} +6.30618 q^{53} +(0.866025 - 0.500000i) q^{54} +(2.56511 - 4.44290i) q^{56} +6.64947i q^{57} +(3.03479 + 1.75214i) q^{58} +(1.31571 + 0.759628i) q^{59} +(5.19076 - 8.99066i) q^{61} +(-3.15309 - 5.46131i) q^{62} +(4.44290 - 2.56511i) q^{63} -1.00000 q^{64} +5.57962 q^{66} +(2.48644 - 1.43555i) q^{67} +(0.641326 + 1.11081i) q^{68} +(3.43113 - 5.94290i) q^{69} +(9.44775 + 5.45466i) q^{71} +(-0.866025 - 0.500000i) q^{72} -4.94644i q^{73} +(-4.19076 + 7.25861i) q^{74} +(5.75861 - 3.32474i) q^{76} +28.6246 q^{77} +(-3.60278 - 0.141326i) q^{78} +10.1485 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-0.641326 + 1.11081i) q^{82} +17.3887i q^{83} +(-4.44290 - 2.56511i) q^{84} +4.35800i q^{86} +(1.75214 - 3.03479i) q^{87} +(-2.78981 - 4.83209i) q^{88} +(5.57884 - 3.22094i) q^{89} +(-18.4830 - 0.725036i) q^{91} -6.86227 q^{92} +(-5.46131 + 3.15309i) q^{93} +(-2.51176 - 4.35050i) q^{94} +1.00000i q^{96} +(-6.20806 - 3.58423i) q^{97} +(-16.7309 - 9.65957i) q^{98} -5.57962i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 6 q^{4} + 6 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 + 6 * q^4 + 6 * q^7 - 6 * q^9	$ 12 q + 6 q^{3} + 6 q^{4} + 6 q^{7} - 6 q^{9} - 12 q^{11} + 12 q^{12} + 8 q^{14} - 6 q^{16} - 6 q^{19} + 4 q^{22} - 4 q^{23} - 4 q^{26} - 12 q^{27} + 6 q^{28} - 12 q^{33} + 6 q^{36} + 12 q^{37} - 24 q^{38} + 6 q^{39} + 4 q^{42} + 10 q^{43} + 12 q^{46} + 6 q^{48} + 32 q^{49} - 6 q^{52} + 16 q^{53} + 4 q^{56} + 24 q^{61} - 8 q^{62} - 6 q^{63} - 12 q^{64} + 8 q^{66} - 6 q^{67} + 4 q^{69} + 12 q^{71} - 12 q^{74} - 6 q^{76} + 48 q^{77} - 8 q^{78} + 52 q^{79} - 6 q^{81} + 6 q^{84} - 4 q^{88} + 24 q^{89} - 54 q^{91} - 8 q^{92} - 8 q^{94} - 12 q^{97} - 36 q^{98}+O(q^{100}) $ 12 * q + 6 * q^3 + 6 * q^4 + 6 * q^7 - 6 * q^9 - 12 * q^11 + 12 * q^12 + 8 * q^14 - 6 * q^16 - 6 * q^19 + 4 * q^22 - 4 * q^23 - 4 * q^26 - 12 * q^27 + 6 * q^28 - 12 * q^33 + 6 * q^36 + 12 * q^37 - 24 * q^38 + 6 * q^39 + 4 * q^42 + 10 * q^43 + 12 * q^46 + 6 * q^48 + 32 * q^49 - 6 * q^52 + 16 * q^53 + 4 * q^56 + 24 * q^61 - 8 * q^62 - 6 * q^63 - 12 * q^64 + 8 * q^66 - 6 * q^67 + 4 * q^69 + 12 * q^71 - 12 * q^74 - 6 * q^76 + 48 * q^77 - 8 * q^78 + 52 * q^79 - 6 * q^81 + 6 * q^84 - 4 * q^88 + 24 * q^89 - 54 * q^91 - 8 * q^92 - 8 * q^94 - 12 * q^97 - 36 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1950\mathbb{Z}\right)^\times$.

$n$	$301$	$1301$	$1327$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$2$	−0.866025	+	0.500000i	−0.612372	+	0.353553i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	−4.44290	−	2.56511i	−1.67926	−	0.969520i	−0.962135	−	0.272574i	$-0.912125\pi$
$7$	−4.44290	−	2.56511i	−1.67926	−	0.969520i	−0.717123	−	0.696947i	$-0.754541\pi$
$8$			1.00000i			0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−4.83209	+	2.78981i	−1.45693	+	0.841159i	−0.998859	−	0.0477570i	$-0.984793\pi$
$11$	−4.83209	+	2.78981i	−1.45693	+	0.841159i	−0.458071	+	0.888916i	$0.651459\pi$
$12$	1.00000			0.288675
$13$	3.19076	−	1.67900i	0.884958	−	0.465670i
$13$	3.19076	−	1.67900i	0.884958	−	0.465670i
$14$	5.13022			1.37111
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−0.641326	+	1.11081i	−0.155545	+	0.269411i	−0.933257	−	0.359209i	$-0.883047\pi$
$17$	−0.641326	+	1.11081i	−0.155545	+	0.269411i	0.777713	+	0.628620i	$0.216380\pi$
$18$		−	1.00000i		−	0.235702i
$19$	5.75861	+	3.32474i	1.32112	+	0.762747i	0.983907	−	0.178682i	$-0.0571835\pi$
$19$	5.75861	+	3.32474i	1.32112	+	0.762747i	0.337210	+	0.941430i	$0.390517\pi$
$20$		0			0
$21$		−	5.13022i		−	1.11951i
$22$	2.78981	−	4.83209i	0.594789	−	1.03020i
$23$	−3.43113	−	5.94290i	−0.715441	−	1.23918i	−0.962789	−	0.270253i	$-0.912892\pi$
$23$	−3.43113	−	5.94290i	−0.715441	−	1.23918i	0.247348	−	0.968927i	$-0.420441\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$		0			0
$26$	−1.92378	+	3.04944i	−0.377285	+	0.598044i
$27$	−1.00000			−0.192450
$28$	−4.44290	+	2.56511i	−0.839629	+	0.484760i
$29$	−1.75214	−	3.03479i	−0.325364	−	0.563546i	0.656222	−	0.754568i	$-0.272153\pi$
$29$	−1.75214	−	3.03479i	−0.325364	−	0.563546i	−0.981586	+	0.191021i	$0.938820\pi$
$30$		0			0
$31$			6.30618i			1.13262i	0.824191	+	0.566312i	$0.191630\pi$
$31$			6.30618i			1.13262i	−0.824191	+	0.566312i	$0.808370\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$	−4.83209	−	2.78981i	−0.841159	−	0.485643i
$34$		−	1.28265i		−	0.219973i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	7.25861	−	4.19076i	1.19331	−	0.688957i	0.234253	−	0.972176i	$-0.424735\pi$
$37$	7.25861	−	4.19076i	1.19331	−	0.688957i	0.959055	+	0.283218i	$0.0914021\pi$
$38$	−6.64947			−1.07869
$39$	3.04944	+	1.92378i	0.488301	+	0.308052i
$40$		0			0
$41$	1.11081	−	0.641326i	0.173479	−	0.100158i	−0.410746	−	0.911750i	$-0.634732\pi$
$41$	1.11081	−	0.641326i	0.173479	−	0.100158i	0.584225	+	0.811591i	$0.301398\pi$
$42$	2.56511	+	4.44290i	0.395805	+	0.685554i
$43$	2.17900	−	3.77414i	0.332294	−	0.575550i	−0.650667	−	0.759363i	$-0.725511\pi$
$43$	2.17900	−	3.77414i	0.332294	−	0.575550i	0.982961	+	0.183813i	$0.0588440\pi$
$44$			5.57962i			0.841159i
$45$		0			0
$46$	5.94290	+	3.43113i	0.876233	+	0.505893i
$47$			5.02353i			0.732757i	0.930466	+	0.366379i	$0.119402\pi$
$47$			5.02353i			0.732757i	−0.930466	+	0.366379i	$0.880598\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	9.65957	+	16.7309i	1.37994	+	2.39012i
$50$		0			0
$51$	−1.28265			−0.179607
$52$	0.141326	−	3.60278i	0.0195985	−	0.499616i
$53$	6.30618			0.866221			0.433110	−	0.901341i	$-0.357416\pi$
$53$	6.30618			0.866221			0.433110	+	0.901341i	$0.357416\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$		0			0
$56$	2.56511	−	4.44290i	0.342777	−	0.593707i
$57$			6.64947i			0.880744i
$58$	3.03479	+	1.75214i	0.398487	+	0.230067i
$59$	1.31571	+	0.759628i	0.171291	+	0.0988952i	0.583195	−	0.812332i	$-0.301802\pi$
$59$	1.31571	+	0.759628i	0.171291	+	0.0988952i	−0.411903	+	0.911228i	$0.635136\pi$
$60$		0			0
$61$	5.19076	−	8.99066i	0.664609	−	1.15114i	−0.314782	−	0.949164i	$-0.601931\pi$
$61$	5.19076	−	8.99066i	0.664609	−	1.15114i	0.979391	−	0.201973i	$-0.0647352\pi$
$62$	−3.15309	−	5.46131i	−0.400443	−	0.693588i
$63$	4.44290	−	2.56511i	0.559753	−	0.323173i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	5.57962			0.686803
$67$	2.48644	−	1.43555i	0.303767	−	0.175380i	−0.340367	−	0.940293i	$-0.610551\pi$
$67$	2.48644	−	1.43555i	0.303767	−	0.175380i	0.644134	+	0.764913i	$0.277218\pi$
$68$	0.641326	+	1.11081i	0.0777723	+	0.134706i
$69$	3.43113	−	5.94290i	0.413060	−	0.715441i
$70$		0			0
$71$	9.44775	+	5.45466i	1.12124	+	0.647350i	0.941718	−	0.336404i	$-0.109211\pi$
$71$	9.44775	+	5.45466i	1.12124	+	0.647350i	0.179524	+	0.983754i	$0.442544\pi$
$72$	−0.866025	−	0.500000i	−0.102062	−	0.0589256i
$73$		−	4.94644i		−	0.578937i	−0.957188	−	0.289468i	$-0.906522\pi$
$73$		−	4.94644i		−	0.578937i	0.957188	−	0.289468i	$-0.0934785\pi$
$74$	−4.19076	+	7.25861i	−0.487166	+	0.843797i
$75$		0			0
$76$	5.75861	−	3.32474i	0.660558	−	0.381374i
$77$	28.6246			3.26208
$78$	−3.60278	−	0.141326i	−0.407935	−	0.0160021i
$79$	10.1485			1.14179			0.570895	−	0.821023i	$-0.306596\pi$
$79$	10.1485			1.14179			0.570895	+	0.821023i	$0.306596\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.641326	+	1.11081i	−0.0708227	+	0.122668i
$83$			17.3887i			1.90866i	0.298755	+	0.954330i	$0.403429\pi$
$83$			17.3887i			1.90866i	−0.298755	+	0.954330i	$0.596571\pi$
$84$	−4.44290	−	2.56511i	−0.484760	−	0.279876i
$85$		0			0
$86$			4.35800i			0.469935i
$87$	1.75214	−	3.03479i	0.187849	−	0.325364i
$88$	−2.78981	−	4.83209i	−0.297395	−	0.515102i
$89$	5.57884	−	3.22094i	0.591355	−	0.341419i	−0.174278	−	0.984697i	$-0.555759\pi$
$89$	5.57884	−	3.22094i	0.591355	−	0.341419i	0.765633	+	0.643277i	$0.222426\pi$
$90$		0			0
$91$	−18.4830	−	0.725036i	−1.93755	−	0.0760044i
$92$	−6.86227			−0.715441
$93$	−5.46131	+	3.15309i	−0.566312	+	0.326960i
$94$	−2.51176	−	4.35050i	−0.259069	−	0.448720i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	−6.20806	−	3.58423i	−0.630333	−	0.363923i	0.150548	−	0.988603i	$-0.451896\pi$
$97$	−6.20806	−	3.58423i	−0.630333	−	0.363923i	−0.780881	+	0.624680i	$0.785230\pi$
$98$	−16.7309	−	9.65957i	−1.69007	−	0.975764i
$99$		−	5.57962i		−	0.560772i
$100$		0			0
$101$	−7.33175	−	12.6990i	−0.729537	−	1.26359i	−0.957079	−	0.289826i	$-0.906402\pi$
$101$	−7.33175	−	12.6990i	−0.729537	−	1.26359i	0.227543	−	0.973768i	$-0.426931\pi$
$102$	1.11081	−	0.641326i	0.109987	−	0.0635008i
$103$	4.04929			0.398989			0.199494	−	0.979899i	$-0.436070\pi$
$103$	4.04929			0.398989			0.199494	+	0.979899i	$0.436070\pi$
$104$	1.67900	+	3.19076i	0.164639	+	0.312880i
$105$		0			0
$106$	−5.46131	+	3.15309i	−0.530450	+	0.306255i
$107$	−3.88044	−	6.72112i	−0.375136	−	0.649755i	0.615211	−	0.788362i	$-0.289071\pi$
$107$	−3.88044	−	6.72112i	−0.375136	−	0.649755i	−0.990347	+	0.138608i	$0.955737\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$			0.792690i			0.0759259i	0.999279	+	0.0379630i	$0.0120869\pi$
$109$			0.792690i			0.0759259i	−0.999279	+	0.0379630i	$0.987913\pi$
$110$		0			0
$111$	7.25861	+	4.19076i	0.688957	+	0.397770i
$112$			5.13022i			0.484760i
$113$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$113$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$114$	−3.32474	−	5.75861i	−0.311390	−	0.539344i
$115$		0			0
$116$	−3.50427			−0.325364
$117$	−0.141326	+	3.60278i	−0.0130656	+	0.333077i
$118$	−1.51926			−0.139859
$119$	5.69870	−	3.29014i	0.522399	−	0.301607i
$120$		0			0
$121$	10.0661	−	17.4349i	0.915096	−	1.58499i
$122$			10.3815i			0.939899i
$123$	1.11081	+	0.641326i	0.100158	+	0.0578265i
$124$	5.46131	+	3.15309i	0.490440	+	0.283156i
$125$		0			0
$126$	−2.56511	+	4.44290i	−0.228518	+	0.395805i
$127$	8.12651	+	14.0755i	0.721111	+	1.24900i	0.960555	+	0.278090i	$0.0897015\pi$
$127$	8.12651	+	14.0755i	0.721111	+	1.24900i	−0.239444	+	0.970910i	$0.576965\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$	4.35800			0.383700
$130$		0			0
$131$	7.04605			0.615616			0.307808	−	0.951448i	$-0.400405\pi$
$131$	7.04605			0.615616			0.307808	+	0.951448i	$0.400405\pi$
$132$	−4.83209	+	2.78981i	−0.420579	+	0.242822i
$133$	−17.0566	−	29.5429i	−1.47900	−	2.56170i
$134$	−1.43555	+	2.48644i	−0.124012	+	0.214796i
$135$		0			0
$136$	−1.11081	−	0.641326i	−0.0952512	−	0.0549933i
$137$	0.769058	+	0.444016i	0.0657051	+	0.0379348i	0.532493	−	0.846435i	$-0.321255\pi$
$137$	0.769058	+	0.444016i	0.0657051	+	0.0379348i	−0.466788	+	0.884369i	$0.654589\pi$
$138$			6.86227i			0.584155i
$139$	−0.266279	+	0.461208i	−0.0225854	+	0.0391191i	−0.877097	−	0.480313i	$-0.840523\pi$
$139$	−0.266279	+	0.461208i	−0.0225854	+	0.0391191i	0.854512	+	0.519432i	$0.173856\pi$
$140$		0			0
$141$	−4.35050	+	2.51176i	−0.366379	+	0.211529i
$142$	−10.9093			−0.915490
$143$	−10.7340	+	17.0147i	−0.897619	+	1.42284i
$144$	1.00000			0.0833333
$145$		0			0
$146$	2.47322	+	4.28374i	0.204685	+	0.354525i
$147$	−9.65957	+	16.7309i	−0.796708	+	1.37994i
$148$		−	8.38153i		−	0.688957i
$149$	18.0113	+	10.3988i	1.47554	+	0.851905i	0.999620	−	0.0275822i	$-0.00878080\pi$
$149$	18.0113	+	10.3988i	1.47554	+	0.851905i	0.475923	+	0.879487i	$0.342114\pi$
$150$		0			0
$151$			2.15400i			0.175290i	0.996152	+	0.0876448i	$0.0279341\pi$
$151$			2.15400i			0.175290i	−0.996152	+	0.0876448i	$0.972066\pi$
$152$	−3.32474	+	5.75861i	−0.269672	+	0.467085i
$153$	−0.641326	−	1.11081i	−0.0518482	−	0.0898037i
$154$	−24.7897	+	14.3123i	−1.99761	+	1.15332i
$155$		0			0
$156$	3.19076	−	1.67900i	0.255465	−	0.134427i
$157$	−7.70236			−0.614716			−0.307358	−	0.951594i	$-0.599445\pi$
$157$	−7.70236			−0.614716			−0.307358	+	0.951594i	$0.599445\pi$
$158$	−8.78882	+	5.07423i	−0.699201	+	0.403684i
$159$	3.15309	+	5.46131i	0.250056	+	0.433110i
$160$		0			0
$161$			35.2049i			2.77454i
$162$	0.866025	+	0.500000i	0.0680414	+	0.0392837i
$163$	0.382683	+	0.220942i	0.0299741	+	0.0173055i	0.514912	−	0.857243i	$-0.327825\pi$
$163$	0.382683	+	0.220942i	0.0299741	+	0.0173055i	−0.484938	+	0.874548i	$0.661158\pi$
$164$		−	1.28265i		−	0.100158i
$165$		0			0
$166$	−8.69436	−	15.0591i	−0.674813	−	1.16881i
$167$	5.94290	−	3.43113i	0.459875	−	0.265509i	−0.252116	−	0.967697i	$-0.581127\pi$
$167$	5.94290	−	3.43113i	0.459875	−	0.265509i	0.711992	+	0.702188i	$0.247793\pi$
$168$	5.13022			0.395805
$169$	7.36193	−	10.7146i	0.566302	−	0.824197i
$170$		0			0
$171$	−5.75861	+	3.32474i	−0.440372	+	0.254249i
$172$	−2.17900	−	3.77414i	−0.166147	−	0.287775i
$173$	11.1449	−	19.3036i	0.847333	−	1.46762i	−0.0362472	−	0.999343i	$-0.511540\pi$
$173$	11.1449	−	19.3036i	0.847333	−	1.46762i	0.883580	−	0.468280i	$-0.155126\pi$
$174$			3.50427i			0.265658i
$175$		0			0
$176$	4.83209	+	2.78981i	0.364232	+	0.210290i
$177$			1.51926i			0.114194i
$178$	−3.22094	+	5.57884i	−0.241420	+	0.418151i
$179$	0.784447	+	1.35870i	0.0586324	+	0.101554i	0.893852	−	0.448363i	$-0.147993\pi$
$179$	0.784447	+	1.35870i	0.0586324	+	0.101554i	−0.835219	+	0.549917i	$0.814659\pi$
$180$		0			0
$181$	11.4419			0.850469			0.425234	−	0.905083i	$-0.360192\pi$
$181$	11.4419			0.850469			0.425234	+	0.905083i	$0.360192\pi$
$182$	16.3693	−	8.61363i	1.21337	−	0.638484i
$183$	10.3815			0.767424
$184$	5.94290	−	3.43113i	0.438116	−	0.252947i
$185$		0			0
$186$	3.15309	−	5.46131i	0.231196	−	0.400443i
$187$		−	7.15671i		−	0.523351i
$188$	4.35050	+	2.51176i	0.317293	+	0.183189i
$189$	4.44290	+	2.56511i	0.323173	+	0.186584i
$190$		0			0
$191$	−4.41092	+	7.63995i	−0.319163	+	0.552807i	−0.980314	−	0.197446i	$-0.936735\pi$
$191$	−4.41092	+	7.63995i	−0.319163	+	0.552807i	0.661150	+	0.750253i	$0.270069\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−9.68914	+	5.59403i	−0.697440	+	0.402667i	−0.806393	−	0.591380i	$-0.798583\pi$
$193$	−9.68914	+	5.59403i	−0.697440	+	0.402667i	0.108953	+	0.994047i	$0.465250\pi$
$194$	7.16845			0.514665
$195$		0			0
$196$	19.3191			1.37994
$197$	−19.8624	+	11.4675i	−1.41514	+	0.817029i	−0.995866	−	0.0908332i	$-0.971047\pi$
$197$	−19.8624	+	11.4675i	−1.41514	+	0.817029i	−0.419269	+	0.907862i	$0.637714\pi$
$198$	2.78981	+	4.83209i	0.198263	+	0.343402i
$199$	5.52892	−	9.57637i	0.391935	−	0.678851i	−0.600770	−	0.799422i	$-0.705139\pi$
$199$	5.52892	−	9.57637i	0.391935	−	0.678851i	0.992705	+	0.120571i	$0.0384726\pi$
$200$		0			0
$201$	2.48644	+	1.43555i	0.175380	+	0.101256i
$202$	12.6990	+	7.33175i	0.893496	+	0.515860i
$203$			17.9777i			1.26179i
$204$	−0.641326	+	1.11081i	−0.0449018	+	0.0777723i
$205$		0			0
$206$	−3.50679	+	2.02465i	−0.244330	+	0.141064i
$207$	6.86227			0.476961
$208$	−3.04944	−	1.92378i	−0.211440	−	0.133390i
$209$	−37.1015			−2.56637
$210$		0			0
$211$	−13.4171	−	23.2391i	−0.923671	−	1.59984i	−0.793685	−	0.608329i	$-0.791840\pi$
$211$	−13.4171	−	23.2391i	−0.923671	−	1.59984i	−0.129986	−	0.991516i	$-0.541493\pi$
$212$	3.15309	−	5.46131i	0.216555	−	0.375085i
$213$			10.9093i			0.747495i
$214$	6.72112	+	3.88044i	0.459446	+	0.265261i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	16.1760	−	28.0177i	1.09810	−	1.90197i
$218$	−0.396345	−	0.686490i	−0.0268439	−	0.0464949i
$219$	4.28374	−	2.47322i	0.289468	−	0.167125i
$220$		0			0
$221$	−0.181273	+	4.62112i	−0.0121937	+	0.310850i
$222$	−8.38153			−0.562531
$223$	0.0599161	−	0.0345926i	0.00401228	−	0.00231649i	−0.497993	−	0.867181i	$-0.665929\pi$
$223$	0.0599161	−	0.0345926i	0.00401228	−	0.00231649i	0.502005	+	0.864865i	$0.332596\pi$
$224$	−2.56511	−	4.44290i	−0.171389	−	0.296854i
$225$		0			0
$226$		0			0
$227$	−5.36241	−	3.09599i	−0.355916	−	0.205488i	0.311372	−	0.950288i	$-0.399212\pi$
$227$	−5.36241	−	3.09599i	−0.355916	−	0.205488i	−0.667288	+	0.744800i	$0.732545\pi$
$228$	5.75861	+	3.32474i	0.381374	+	0.220186i
$229$			17.3857i			1.14888i	0.818548	+	0.574438i	$0.194779\pi$
$229$			17.3857i			1.14888i	−0.818548	+	0.574438i	$0.805221\pi$
$230$		0			0
$231$	14.3123	+	24.7897i	0.941682	+	1.63104i
$232$	3.03479	−	1.75214i	0.199244	−	0.115033i
$233$	17.7716			1.16426			0.582128	−	0.813097i	$-0.302220\pi$
$233$	17.7716			1.16426			0.582128	+	0.813097i	$0.302220\pi$
$234$	−1.67900	−	3.19076i	−0.109760	−	0.208587i
$235$		0			0
$236$	1.31571	−	0.759628i	0.0856457	−	0.0494476i
$237$	5.07423	+	8.78882i	0.329606	+	0.570895i
$238$	−3.29014	+	5.69870i	−0.213268	+	0.369392i
$239$		−	17.1487i		−	1.10925i	−0.832099	−	0.554627i	$-0.812861\pi$
$239$		−	17.1487i		−	1.10925i	0.832099	−	0.554627i	$-0.187139\pi$
$240$		0			0
$241$	−15.1831	−	8.76597i	−0.978029	−	0.564665i	−0.0763547	−	0.997081i	$-0.524328\pi$
$241$	−15.1831	−	8.76597i	−0.978029	−	0.564665i	−0.901675	+	0.432415i	$0.857661\pi$
$242$			20.1321i			1.29414i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−5.19076	−	8.99066i	−0.332305	−	0.575568i
$245$		0			0
$246$	−1.28265			−0.0817790
$247$	23.9566	+	0.939747i	1.52432	+	0.0597947i
$248$	−6.30618			−0.400443
$249$	−15.0591	+	8.69436i	−0.954330	+	0.550983i
$250$		0			0
$251$	−9.10358	+	15.7679i	−0.574613	+	0.995259i	0.421470	+	0.906842i	$0.361514\pi$
$251$	−9.10358	+	15.7679i	−0.574613	+	0.995259i	−0.996084	+	0.0884170i	$0.971819\pi$
$252$		−	5.13022i		−	0.323173i
$253$	33.1591	+	19.1444i	2.08469	+	1.20360i
$254$	−14.0755	−	8.12651i	−0.883177	−	0.509902i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	8.80056	+	15.2430i	0.548964	+	0.950833i	0.998346	+	0.0574935i	$0.0183108\pi$
$257$	8.80056	+	15.2430i	0.548964	+	0.950833i	−0.449382	+	0.893340i	$0.648356\pi$
$258$	−3.77414	+	2.17900i	−0.234967	+	0.135658i
$259$	−42.9991			−2.67183
$260$		0			0
$261$	3.50427			0.216909
$262$	−6.10206	+	3.52302i	−0.376986	+	0.217653i
$263$	5.88051	+	10.1853i	0.362608	+	0.628055i	0.988389	−	0.151943i	$-0.0485531\pi$
$263$	5.88051	+	10.1853i	0.362608	+	0.628055i	−0.625781	+	0.779999i	$0.715220\pi$
$264$	2.78981	−	4.83209i	0.171701	−	0.297395i
$265$		0			0
$266$	29.5429	+	17.0566i	1.81139	+	1.04581i
$267$	5.57884	+	3.22094i	0.341419	+	0.197118i
$268$		−	2.87109i		−	0.175380i
$269$	3.20490	−	5.55106i	0.195406	−	0.338454i	−0.751627	−	0.659588i	$-0.770731\pi$
$269$	3.20490	−	5.55106i	0.195406	−	0.338454i	0.947034	+	0.321134i	$0.104064\pi$
$270$		0			0
$271$	13.6919	−	7.90503i	0.831725	−	0.480196i	−0.0227182	−	0.999742i	$-0.507232\pi$
$271$	13.6919	−	7.90503i	0.831725	−	0.480196i	0.854443	+	0.519545i	$0.173899\pi$
$272$	1.28265			0.0777723
$273$	−8.61363	−	16.3693i	−0.521320	−	0.990716i
$274$	−0.888032			−0.0536480
$275$		0			0
$276$	−3.43113	−	5.94290i	−0.206530	−	0.357720i
$277$	−2.49319	+	4.31832i	−0.149801	+	0.259463i	−0.931154	−	0.364627i	$-0.881197\pi$
$277$	−2.49319	+	4.31832i	−0.149801	+	0.259463i	0.781353	+	0.624090i	$0.214530\pi$
$278$		−	0.532557i		−	0.0319406i
$279$	−5.46131	−	3.15309i	−0.326960	−	0.188771i
$280$		0			0
$281$			0.515726i			0.0307656i	0.999882	+	0.0153828i	$0.00489670\pi$
$281$			0.515726i			0.0307656i	−0.999882	+	0.0153828i	$0.995103\pi$
$282$	2.51176	−	4.35050i	0.149573	−	0.259069i
$283$	8.97308	+	15.5418i	0.533394	+	0.923866i	0.999239	+	0.0389995i	$0.0124171\pi$
$283$	8.97308	+	15.5418i	0.533394	+	0.923866i	−0.465845	+	0.884866i	$0.654250\pi$
$284$	9.44775	−	5.45466i	0.560621	−	0.323675i
$285$		0			0
$286$	0.788547	−	20.1021i	0.0466278	−	1.18866i
$287$	−6.58029			−0.388422
$288$	−0.866025	+	0.500000i	−0.0510310	+	0.0294628i
$289$	7.67740	+	13.2976i	0.451612	+	0.782215i
$290$		0			0
$291$		−	7.16845i		−	0.420222i
$292$	−4.28374	−	2.47322i	−0.250687	−	0.144734i
$293$	14.9572	+	8.63553i	0.873808	+	0.504493i	0.868612	−	0.495493i	$-0.165013\pi$
$293$	14.9572	+	8.63553i	0.873808	+	0.504493i	0.00519587	+	0.999987i	$0.498346\pi$
$294$		−	19.3191i		−	1.12671i
$295$		0			0
$296$	4.19076	+	7.25861i	0.243583	+	0.421898i
$297$	4.83209	−	2.78981i	0.280386	−	0.161881i
$298$	−20.7976			−1.20478
$299$	−20.9261	−	13.2015i	−1.21018	−	0.763463i
$300$		0			0
$301$	−19.3621	+	11.1787i	−1.11601	+	0.644332i
$302$	−1.07700	−	1.86541i	−0.0619742	−	0.107343i
$303$	7.33175	−	12.6990i	0.421198	−	0.729537i
$304$		−	6.64947i		−	0.381374i
$305$		0			0
$306$	1.11081	+	0.641326i	0.0635008	+	0.0366622i
$307$		−	14.2673i		−	0.814279i	−0.913366	−	0.407140i	$-0.866526\pi$
$307$		−	14.2673i		−	0.814279i	0.913366	−	0.407140i	$-0.133474\pi$
$308$	14.3123	−	24.7897i	0.815520	−	1.41252i
$309$	2.02465	+	3.50679i	0.115178	+	0.199494i
$310$		0			0
$311$	−23.1487			−1.31264			−0.656320	−	0.754483i	$-0.727888\pi$
$311$	−23.1487			−1.31264			−0.656320	+	0.754483i	$0.727888\pi$
$312$	−1.92378	+	3.04944i	−0.108913	+	0.172640i
$313$	14.1122			0.797667			0.398834	−	0.917023i	$-0.369415\pi$
$313$	14.1122			0.797667			0.398834	+	0.917023i	$0.369415\pi$
$314$	6.67044	−	3.85118i	0.376435	−	0.217335i
$315$		0			0
$316$	5.07423	−	8.78882i	0.285448	−	0.494410i
$317$		−	12.1814i		−	0.684176i	−0.939668	−	0.342088i	$-0.888866\pi$
$317$		−	12.1814i		−	0.684176i	0.939668	−	0.342088i	$-0.111134\pi$
$318$	−5.46131	−	3.15309i	−0.306255	−	0.176817i
$319$	16.9330	+	9.77625i	0.948064	+	0.547365i
$320$		0			0
$321$	3.88044	−	6.72112i	0.216585	−	0.375136i
$322$	−17.6025	−	30.4884i	−0.980947	−	1.69905i
$323$	−7.38630	+	4.26448i	−0.410985	+	0.237282i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	−0.441885			−0.0244737
$327$	−0.686490	+	0.396345i	−0.0379630	+	0.0219179i
$328$	0.641326	+	1.11081i	0.0354113	+	0.0613342i
$329$	12.8859	−	22.3190i	0.710423	−	1.23049i
$330$		0			0
$331$	3.86463	+	2.23125i	0.212419	+	0.122640i	0.602435	−	0.798168i	$-0.294197\pi$
$331$	3.86463	+	2.23125i	0.212419	+	0.122640i	−0.390016	+	0.920808i	$0.627530\pi$
$332$	15.0591	+	8.69436i	0.826474	+	0.477165i
$333$			8.38153i			0.459305i
$334$	−3.43113	+	5.94290i	−0.187743	+	0.325181i
$335$		0			0
$336$	−4.44290	+	2.56511i	−0.242380	+	0.139938i
$337$	6.04773			0.329441			0.164720	−	0.986340i	$-0.447328\pi$
$337$	6.04773			0.329441			0.164720	+	0.986340i	$0.447328\pi$
$338$	−1.01834	+	12.9601i	−0.0553902	+	0.704934i
$339$		0			0
$340$		0			0
$341$	−17.5930	−	30.4720i	−0.952716	−	1.65015i
$342$	3.32474	−	5.75861i	0.179781	−	0.311390i
$343$		−	63.1999i		−	3.41247i
$344$	3.77414	+	2.17900i	0.203488	+	0.117484i
$345$		0			0
$346$			22.2898i			1.19831i
$347$	−3.17327	+	5.49627i	−0.170350	+	0.295055i	−0.938542	−	0.345164i	$-0.887823\pi$
$347$	−3.17327	+	5.49627i	−0.170350	+	0.295055i	0.768192	+	0.640219i	$0.221157\pi$
$348$	−1.75214	−	3.03479i	−0.0939244	−	0.162682i
$349$	−24.4438	+	14.1126i	−1.30844	+	0.755431i	−0.981836	−	0.189729i	$-0.939239\pi$
$349$	−24.4438	+	14.1126i	−1.30844	+	0.755431i	−0.326608	+	0.945160i	$0.605906\pi$
$350$		0			0
$351$	−3.19076	+	1.67900i	−0.170310	+	0.0896183i
$352$	−5.57962			−0.297395
$353$	13.9378	−	8.04696i	0.741832	−	0.428297i	−0.0809033	−	0.996722i	$-0.525780\pi$
$353$	13.9378	−	8.04696i	0.741832	−	0.428297i	0.822735	+	0.568425i	$0.192447\pi$
$354$	−0.759628	−	1.31571i	−0.0403738	−	0.0699294i
$355$		0			0
$356$		−	6.44188i		−	0.341419i
$357$	5.69870	+	3.29014i	0.301607	+	0.174133i
$358$	−1.35870	−	0.784447i	−0.0718097	−	0.0414593i
$359$		−	8.79689i		−	0.464282i	−0.972682	−	0.232141i	$-0.925427\pi$
$359$		−	8.79689i		−	0.464282i	0.972682	−	0.232141i	$-0.0745731\pi$
$360$		0			0
$361$	12.6078	+	21.8373i	0.663566	+	1.14933i
$362$	−9.90896	+	5.72094i	−0.520804	+	0.300686i
$363$	20.1321			1.05666
$364$	−9.86942	+	15.6443i	−0.517298	+	0.819983i
$365$		0			0
$366$	−8.99066	+	5.19076i	−0.469950	+	0.271326i
$367$	−19.0032	−	32.9145i	−0.991958	−	1.71812i	−0.605588	−	0.795779i	$-0.707062\pi$
$367$	−19.0032	−	32.9145i	−0.991958	−	1.71812i	−0.386371	−	0.922344i	$-0.626271\pi$
$368$	−3.43113	+	5.94290i	−0.178860	+	0.309795i
$369$			1.28265i			0.0667722i
$370$		0			0
$371$	−28.0177	−	16.1760i	−1.45461	−	0.839818i
$372$			6.30618i			0.326960i
$373$	−8.50787	+	14.7361i	−0.440521	+	0.763004i	−0.997728	−	0.0673691i	$-0.978540\pi$
$373$	−8.50787	+	14.7361i	−0.440521	+	0.763004i	0.557207	+	0.830373i	$0.311873\pi$
$374$	3.57836	+	6.19789i	0.185032	+	0.320485i
$375$		0			0
$376$	−5.02353			−0.259069
$377$	−10.6861	−	6.74146i	−0.550360	−	0.347203i
$378$	−5.13022			−0.263870
$379$	11.0257	−	6.36569i	0.566352	−	0.326983i	−0.189339	−	0.981912i	$-0.560635\pi$
$379$	11.0257	−	6.36569i	0.566352	−	0.326983i	0.755691	+	0.654928i	$0.227301\pi$
$380$		0			0
$381$	−8.12651	+	14.0755i	−0.416334	+	0.721111i
$382$		−	8.82185i		−	0.451365i
$383$	−19.5478	−	11.2859i	−0.998845	−	0.576683i	−0.0909383	−	0.995857i	$-0.528987\pi$
$383$	−19.5478	−	11.2859i	−0.998845	−	0.576683i	−0.907906	+	0.419173i	$0.862320\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$		0			0
$386$	5.59403	−	9.68914i	0.284729	−	0.493164i
$387$	2.17900	+	3.77414i	0.110765	+	0.191850i
$388$	−6.20806	+	3.58423i	−0.315167	+	0.181961i
$389$	3.50427			0.177674			0.0888368	−	0.996046i	$-0.471685\pi$
$389$	3.50427			0.177674			0.0888368	+	0.996046i	$0.471685\pi$
$390$		0			0
$391$	8.80191			0.445132
$392$	−16.7309	+	9.65957i	−0.845036	+	0.487882i
$393$	3.52302	+	6.10206i	0.177713	+	0.307808i
$394$	11.4675	−	19.8624i	0.577727	−	1.00065i
$395$		0			0
$396$	−4.83209	−	2.78981i	−0.242822	−	0.140193i
$397$	−25.8640	−	14.9326i	−1.29808	−	0.749445i	−0.318005	−	0.948089i	$-0.603013\pi$
$397$	−25.8640	−	14.9326i	−1.29808	−	0.749445i	−0.980072	+	0.198644i	$0.936346\pi$
$398$			11.0578i			0.554279i
$399$	17.0566	−	29.5429i	0.853899	−	1.47900i
$400$		0			0
$401$	−21.7592	+	12.5627i	−1.08660	+	0.627351i	−0.932670	−	0.360730i	$-0.882528\pi$
$401$	−21.7592	+	12.5627i	−1.08660	+	0.627351i	−0.153934	+	0.988081i	$0.549194\pi$
$402$	−2.87109			−0.143197
$403$	10.5881	+	20.1215i	0.527429	+	1.00232i
$404$	−14.6635			−0.729537
$405$		0			0
$406$	−8.98884	−	15.5691i	−0.446109	−	0.772683i
$407$	−23.3828	+	40.5003i	−1.15904	+	2.00752i
$408$		−	1.28265i		−	0.0635008i
$409$	4.54462	+	2.62384i	0.224717	+	0.129740i	0.608132	−	0.793836i	$-0.291919\pi$
$409$	4.54462	+	2.62384i	0.224717	+	0.129740i	−0.383416	+	0.923576i	$0.625252\pi$
$410$		0			0
$411$			0.888032i			0.0438034i
$412$	2.02465	−	3.50679i	0.0997472	−	0.172767i
$413$	−3.89706	−	6.74990i	−0.191762	−	0.332141i
$414$	−5.94290	+	3.43113i	−0.292078	+	0.168631i
$415$		0			0
$416$	3.60278	+	0.141326i	0.176641	+	0.00692910i
$417$	−0.532557			−0.0260794
$418$	32.1309	−	18.5508i	1.57157	−	0.907347i
$419$	9.01326	+	15.6114i	0.440326	+	0.762668i	0.997714	−	0.0675850i	$-0.0215294\pi$
$419$	9.01326	+	15.6114i	0.440326	+	0.762668i	−0.557387	+	0.830253i	$0.688196\pi$
$420$		0			0
$421$			7.92370i			0.386178i	0.981181	+	0.193089i	$0.0618506\pi$
$421$			7.92370i			0.386178i	−0.981181	+	0.193089i	$0.938149\pi$
$422$	23.2391	+	13.4171i	1.13126	+	0.653134i
$423$	−4.35050	−	2.51176i	−0.211529	−	0.122126i
$424$			6.30618i			0.306255i
$425$		0			0
$426$	−5.45466	−	9.44775i	−0.264279	−	0.457745i
$427$	−46.1241	+	26.6297i	−2.23210	+	1.28870i
$428$	−7.76088			−0.375136
$429$	−20.1021	−	0.788547i	−0.970540	−	0.0380714i
$430$		0			0
$431$	33.1752	−	19.1537i	1.59800	−	0.922603i	0.606122	−	0.795372i	$-0.292724\pi$
$431$	33.1752	−	19.1537i	1.59800	−	0.922603i	0.991873	−	0.127231i	$-0.0406090\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−10.0026	+	17.3250i	−0.480693	+	0.832585i	−0.999755	−	0.0221517i	$-0.992948\pi$
$433$	−10.0026	+	17.3250i	−0.480693	+	0.832585i	0.519061	+	0.854737i	$0.326282\pi$
$434$			32.3521i			1.55295i
$435$		0			0
$436$	0.686490	+	0.396345i	0.0328769	+	0.0189815i
$437$		−	45.6305i		−	2.18280i
$438$	−2.47322	+	4.28374i	−0.118175	+	0.204685i
$439$	5.96660	+	10.3345i	0.284770	+	0.493237i	0.972553	−	0.232680i	$-0.0747493\pi$
$439$	5.96660	+	10.3345i	0.284770	+	0.493237i	−0.687783	+	0.725916i	$0.741416\pi$
$440$		0			0
$441$	−19.3191			−0.919959
$442$	−2.15357	−	4.09264i	−0.102435	−	0.194667i
$443$	26.0565			1.23798			0.618990	−	0.785399i	$-0.287542\pi$
$443$	26.0565			1.23798			0.618990	+	0.785399i	$0.287542\pi$
$444$	7.25861	−	4.19076i	0.344479	−	0.198885i
$445$		0			0
$446$	−0.0345926	+	0.0599161i	−0.00163801	+	0.00283711i
$447$			20.7976i			0.983695i
$448$	4.44290	+	2.56511i	0.209907	+	0.121190i
$449$	−14.4966	−	8.36959i	−0.684135	−	0.394985i	0.117276	−	0.993099i	$-0.462584\pi$
$449$	−14.4966	−	8.36959i	−0.684135	−	0.394985i	−0.801411	+	0.598114i	$0.795917\pi$
$450$		0			0
$451$	−3.57836	+	6.19789i	−0.168498	+	0.291847i
$452$		0			0
$453$	−1.86541	+	1.07700i	−0.0876448	+	0.0506018i
$454$	6.19198			0.290604
$455$		0			0
$456$	−6.64947			−0.311390
$457$	6.15626	−	3.55432i	0.287977	−	0.166264i	−0.349052	−	0.937103i	$-0.613496\pi$
$457$	6.15626	−	3.55432i	0.287977	−	0.166264i	0.637029	+	0.770840i	$0.280163\pi$
$458$	−8.69283	−	15.0564i	−0.406189	−	0.703540i
$459$	0.641326	−	1.11081i	0.0299346	−	0.0518482i
$460$		0			0
$461$	−4.77730	−	2.75817i	−0.222501	−	0.128461i	0.384607	−	0.923081i	$-0.374337\pi$
$461$	−4.77730	−	2.75817i	−0.222501	−	0.128461i	−0.607108	+	0.794620i	$0.707670\pi$
$462$	−24.7897	−	14.3123i	−1.15332	−	0.665870i
$463$		−	4.98759i		−	0.231793i	−0.993261	−	0.115896i	$-0.963026\pi$
$463$		−	4.98759i		−	0.231793i	0.993261	−	0.115896i	$-0.0369741\pi$
$464$	−1.75214	+	3.03479i	−0.0813409	+	0.140887i
$465$		0			0
$466$	−15.3907	+	8.88580i	−0.712958	+	0.411627i
$467$	−19.7410			−0.913506			−0.456753	−	0.889594i	$-0.650988\pi$
$467$	−19.7410			−0.913506			−0.456753	+	0.889594i	$0.650988\pi$
$468$	3.04944	+	1.92378i	0.140960	+	0.0889269i
$469$	−14.7293			−0.680138
$470$		0			0
$471$	−3.85118	−	6.67044i	−0.177453	−	0.307358i
$472$	−0.759628	+	1.31571i	−0.0349647	+	0.0605607i
$473$			24.3159i			1.11805i
$474$	−8.78882	−	5.07423i	−0.403684	−	0.233067i
$475$		0			0
$476$		−	6.58029i		−	0.301607i
$477$	−3.15309	+	5.46131i	−0.144370	+	0.250056i
$478$	8.57433	+	14.8512i	0.392181	+	0.679277i
$479$	−7.46188	+	4.30812i	−0.340942	+	0.196843i	−0.660689	−	0.750660i	$-0.729736\pi$
$479$	−7.46188	+	4.30812i	−0.340942	+	0.196843i	0.319746	+	0.947503i	$0.396402\pi$
$480$		0			0
$481$	16.1242	−	25.5589i	0.735202	−	1.16539i
$482$	17.5319			0.798558
$483$	−30.4884	+	17.6025i	−1.38727	+	0.800940i
$484$	−10.0661	−	17.4349i	−0.457548	−	0.792496i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	16.9919	+	9.81026i	0.769975	+	0.444545i	0.832866	−	0.553475i	$-0.186699\pi$
$487$	16.9919	+	9.81026i	0.769975	+	0.444545i	−0.0628907	+	0.998020i	$0.520032\pi$
$488$	8.99066	+	5.19076i	0.406988	+	0.234975i
$489$			0.441885i			0.0199827i
$490$		0			0
$491$	−19.8921	−	34.4541i	−0.897718	−	1.55489i	−0.830404	−	0.557161i	$-0.811890\pi$
$491$	−19.8921	−	34.4541i	−0.897718	−	1.55489i	−0.0673138	−	0.997732i	$-0.521443\pi$
$492$	1.11081	−	0.641326i	0.0500792	−	0.0289132i
$493$	4.49477			0.202434
$494$	−21.2169	+	11.1645i	−0.954593	+	0.502313i
$495$		0			0
$496$	5.46131	−	3.15309i	0.245220	−	0.141578i
$497$	−27.9836	−	48.4690i	−1.25524	−	2.17413i
$498$	8.69436	−	15.0591i	0.389603	−	0.674813i
$499$		−	7.84082i		−	0.351004i	−0.984479	−	0.175502i	$-0.943845\pi$
$499$		−	7.84082i		−	0.351004i	0.984479	−	0.175502i	$-0.0561548\pi$
$500$		0			0
$501$	5.94290	+	3.43113i	0.265509	+	0.153292i
$502$		−	18.2072i		−	0.812626i
$503$	3.55194	−	6.15215i	0.158373	−	0.274311i	−0.775909	−	0.630845i	$-0.782708\pi$
$503$	3.55194	−	6.15215i	0.158373	−	0.274311i	0.934282	+	0.356534i	$0.116042\pi$
$504$	2.56511	+	4.44290i	0.114259	+	0.197902i
$505$		0			0
$506$	−38.2888			−1.70215
$507$	12.9601	+	1.01834i	0.575576	+	0.0452259i
$508$	16.2530			0.721111
$509$	34.0477	−	19.6575i	1.50914	−	0.871302i	0.509196	−	0.860651i	$-0.329943\pi$
$509$	34.0477	−	19.6575i	1.50914	−	0.871302i	0.999943	−	0.0106512i	$-0.00339045\pi$
$510$		0			0
$511$	−12.6882	+	21.9765i	−0.561291	+	0.972184i
$512$		−	1.00000i		−	0.0441942i
$513$	−5.75861	−	3.32474i	−0.254249	−	0.146791i
$514$	−15.2430	−	8.80056i	−0.672341	−	0.388176i
$515$		0			0
$516$	2.17900	−	3.77414i	0.0959250	−	0.166147i
$517$	−14.0147	−	24.2741i	−0.616365	−	1.06758i
$518$	37.2383	−	21.4995i	1.63616	−	0.944635i
$519$	22.2898			0.978416
$520$		0			0
$521$	39.1840			1.71668			0.858341	−	0.513080i	$-0.171496\pi$
$521$	39.1840			1.71668			0.858341	+	0.513080i	$0.171496\pi$
$522$	−3.03479	+	1.75214i	−0.132829	+	0.0766889i
$523$	4.23654	+	7.33790i	0.185251	+	0.320864i	0.943661	−	0.330914i	$-0.107357\pi$
$523$	4.23654	+	7.33790i	0.185251	+	0.320864i	−0.758410	+	0.651778i	$0.774024\pi$
$524$	3.52302	−	6.10206i	0.153904	−	0.266570i
$525$		0			0
$526$	−10.1853	−	5.88051i	−0.444102	−	0.256402i
$527$	−7.00497	−	4.04432i	−0.305141	−	0.176173i
$528$			5.57962i			0.242822i
$529$	−12.0454	+	20.8632i	−0.523712	+	0.907095i
$530$		0			0
$531$	−1.31571	+	0.759628i	−0.0570972	+	0.0329651i
$532$	−34.1133			−1.47900
$533$	2.46755	−	3.91137i	0.106881	−	0.169420i
$534$	−6.44188			−0.278768
$535$		0			0
$536$	1.43555	+	2.48644i	0.0620062	+	0.107398i
$537$	−0.784447	+	1.35870i	−0.0338514	+	0.0586324i
$538$			6.40981i			0.276346i
$539$	−93.3518	−	53.8967i	−4.02095	−	2.32149i
$540$		0			0
$541$			14.5899i			0.627269i	0.949544	+	0.313634i	$0.101547\pi$
$541$			14.5899i			0.627269i	−0.949544	+	0.313634i	$0.898453\pi$
$542$	−7.90503	+	13.6919i	−0.339550	+	0.588118i
$543$	5.72094	+	9.90896i	0.245509	+	0.425234i
$544$	−1.11081	+	0.641326i	−0.0476256	+	0.0274966i
$545$		0			0
$546$	15.6443	+	9.86942i	0.669513	+	0.422372i
$547$	14.2246			0.608200			0.304100	−	0.952640i	$-0.401644\pi$
$547$	14.2246			0.608200			0.304100	+	0.952640i	$0.401644\pi$
$548$	0.769058	−	0.444016i	0.0328525	−	0.0189674i
$549$	5.19076	+	8.99066i	0.221536	+	0.383712i
$550$		0			0
$551$		−	23.3016i		−	0.992680i
$552$	5.94290	+	3.43113i	0.252947	+	0.146039i
$553$	−45.0885	−	26.0319i	−1.91736	−	1.10699i
$554$		−	4.98637i		−	0.211851i
$555$		0			0
$556$	0.266279	+	0.461208i	0.0112927	+	0.0195596i
$557$	30.2289	−	17.4527i	1.28084	−	0.739493i	0.303838	−	0.952724i	$-0.401732\pi$
$557$	30.2289	−	17.4527i	1.28084	−	0.739493i	0.977002	+	0.213231i	$0.0683986\pi$
$558$	6.30618			0.266962
$559$	0.615900	−	15.7009i	0.0260498	−	0.664077i
$560$		0			0
$561$	6.19789	−	3.57836i	0.261675	−	0.151078i
$562$	−0.257863	−	0.446632i	−0.0108773	−	0.0188400i
$563$	7.90879	−	13.6984i	0.333316	−	0.577320i	−0.649844	−	0.760067i	$-0.725166\pi$
$563$	7.90879	−	13.6984i	0.333316	−	0.577320i	0.983160	+	0.182748i	$0.0584992\pi$
$564$			5.02353i			0.211529i
$565$		0			0
$566$	−15.5418	−	8.97308i	−0.653272	−	0.377167i
$567$			5.13022i			0.215449i
$568$	−5.45466	+	9.44775i	−0.228873	+	0.396419i
$569$	−0.234472	−	0.406118i	−0.00982959	−	0.0170253i	0.861069	−	0.508489i	$-0.169796\pi$
$569$	−0.234472	−	0.406118i	−0.00982959	−	0.0170253i	−0.870898	+	0.491463i	$0.836462\pi$
$570$		0			0
$571$	21.6325			0.905292			0.452646	−	0.891690i	$-0.350480\pi$
$571$	21.6325			0.905292			0.452646	+	0.891690i	$0.350480\pi$
$572$	9.36816	+	17.8032i	0.391703	+	0.744390i
$573$	−8.82185			−0.368538
$574$	5.69870	−	3.29014i	0.237859	−	0.137328i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	21.2140i		−	0.883149i	−0.897225	−	0.441574i	$-0.854420\pi$
$577$		−	21.2140i		−	0.883149i	0.897225	−	0.441574i	$-0.145580\pi$
$578$	−13.2976	−	7.67740i	−0.553109	−	0.319338i
$579$	−9.68914	−	5.59403i	−0.402667	−	0.232480i
$580$		0			0
$581$	44.6040	−	77.2563i	1.85048	−	3.20513i
$582$	3.58423	+	6.20806i	0.148571	+	0.257332i
$583$	−30.4720	+	17.5930i	−1.26202	+	0.728629i
$584$	4.94644			0.204685
$585$		0			0
$586$	−17.2711			−0.713461
$587$	−2.05536	+	1.18666i	−0.0848338	+	0.0489788i	−0.541817	−	0.840497i	$-0.682263\pi$
$587$	−2.05536	+	1.18666i	−0.0848338	+	0.0489788i	0.456983	+	0.889475i	$0.348930\pi$
$588$	9.65957	+	16.7309i	0.398354	+	0.689969i
$589$	−20.9664	+	36.3149i	−0.863905	+	1.49633i
$590$		0			0
$591$	−19.8624	−	11.4675i	−0.817029	−	0.471712i
$592$	−7.25861	−	4.19076i	−0.298327	−	0.172239i
$593$			2.26258i			0.0929130i	0.998920	+	0.0464565i	$0.0147929\pi$
$593$			2.26258i			0.0929130i	−0.998920	+	0.0464565i	$0.985207\pi$
$594$	−2.78981	+	4.83209i	−0.114467	+	0.198263i
$595$		0			0
$596$	18.0113	−	10.3988i	0.737771	−	0.425952i
$597$	11.0578			0.452567
$598$	24.7232	+	0.969820i	1.01101	+	0.0396589i
$599$	−8.04828			−0.328844			−0.164422	−	0.986390i	$-0.552576\pi$
$599$	−8.04828			−0.328844			−0.164422	+	0.986390i	$0.552576\pi$
$600$		0			0
$601$	−1.32625	−	2.29713i	−0.0540988	−	0.0937019i	0.837708	−	0.546119i	$-0.183895\pi$
$601$	−1.32625	−	2.29713i	−0.0540988	−	0.0937019i	−0.891807	+	0.452417i	$0.850562\pi$
$602$	11.1787	−	19.3621i	0.455611	−	0.789142i
$603$			2.87109i			0.116920i
$604$	1.86541	+	1.07700i	0.0759026	+	0.0438224i
$605$		0			0
$606$			14.6635i			0.595664i
$607$	1.09680	−	1.89971i	0.0445177	−	0.0771070i	−0.842908	−	0.538058i	$-0.819158\pi$
$607$	1.09680	−	1.89971i	0.0445177	−	0.0771070i	0.887426	+	0.460951i	$0.152492\pi$
$608$	3.32474	+	5.75861i	0.134836	+	0.233543i
$609$	−15.5691	+	8.98884i	−0.630893	+	0.364246i
$610$		0			0
$611$	8.43450	+	16.0289i	0.341223	+	0.648459i
$612$	−1.28265			−0.0518482
$613$	0.0840326	−	0.0485163i	0.00339405	−	0.00195955i	−0.498302	−	0.867004i	$-0.666043\pi$
$613$	0.0840326	−	0.0485163i	0.00339405	−	0.00195955i	0.501696	+	0.865044i	$0.332710\pi$
$614$	7.13366	+	12.3559i	0.287891	+	0.498642i
$615$		0			0
$616$			28.6246i			1.15332i
$617$	5.74580	+	3.31734i	0.231317	+	0.133551i	0.611180	−	0.791492i	$-0.290695\pi$
$617$	5.74580	+	3.31734i	0.231317	+	0.133551i	−0.379862	+	0.925043i	$0.624029\pi$
$618$	−3.50679	−	2.02465i	−0.141064	−	0.0814432i
$619$		−	14.0315i		−	0.563973i	−0.959418	−	0.281987i	$-0.909007\pi$
$619$		−	14.0315i		−	0.563973i	0.959418	−	0.281987i	$-0.0909934\pi$
$620$		0			0
$621$	3.43113	+	5.94290i	0.137687	+	0.238480i
$622$	20.0473	−	11.5743i	0.803824	−	0.464088i
$623$	−33.0483			−1.32405
$624$	0.141326	−	3.60278i	0.00565759	−	0.144227i
$625$		0			0
$626$	−12.2215	+	7.05609i	−0.488469	+	0.282018i
$627$	−18.5508	−	32.1309i	−0.740846	−	1.28318i
$628$	−3.85118	+	6.67044i	−0.153679	+	0.266180i
$629$			10.7506i			0.428654i
$630$		0			0
$631$	−36.1445	−	20.8680i	−1.43889	−	0.830743i	−0.441116	−	0.897450i	$-0.645417\pi$
$631$	−36.1445	−	20.8680i	−1.43889	−	0.830743i	−0.997773	+	0.0667070i	$0.978751\pi$
$632$			10.1485i			0.403684i
$633$	13.4171	−	23.2391i	0.533282	−	0.923671i
$634$	6.09070	+	10.5494i	0.241893	+	0.418970i
$635$		0			0
$636$	6.30618			0.250056
$637$	58.9125	+	37.1658i	2.33420	+	1.47256i
$638$	−19.5525			−0.774091
$639$	−9.44775	+	5.45466i	−0.373747	+	0.215783i
$640$		0			0
$641$	−18.4382	+	31.9358i	−0.728264	+	1.26139i	0.229353	+	0.973343i	$0.426339\pi$
$641$	−18.4382	+	31.9358i	−0.728264	+	1.26139i	−0.957617	+	0.288046i	$0.906994\pi$
$642$			7.76088i			0.306297i
$643$	−18.9996	−	10.9694i	−0.749271	−	0.432592i	0.0761597	−	0.997096i	$-0.475734\pi$
$643$	−18.9996	−	10.9694i	−0.749271	−	0.432592i	−0.825430	+	0.564504i	$0.809067\pi$
$644$	30.4884	+	17.6025i	1.20141	+	0.693634i
$645$		0			0
$646$	4.26448	−	7.38630i	0.167784	−	0.290610i
$647$	−0.971183	−	1.68214i	−0.0381811	−	0.0661317i	0.846303	−	0.532701i	$-0.178823\pi$
$647$	−0.971183	−	1.68214i	−0.0381811	−	0.0661317i	−0.884485	+	0.466570i	$0.845490\pi$
$648$	0.866025	−	0.500000i	0.0340207	−	0.0196419i
$649$	−8.47687			−0.332746
$650$		0			0
$651$	32.3521			1.26798
$652$	0.382683	−	0.220942i	0.0149870	−	0.00865277i
$653$	5.27812	+	9.14197i	0.206549	+	0.357753i	0.950625	−	0.310342i	$-0.100443\pi$
$653$	5.27812	+	9.14197i	0.206549	+	0.357753i	−0.744076	+	0.668095i	$0.767110\pi$
$654$	0.396345	−	0.686490i	0.0154983	−	0.0268439i
$655$		0			0
$656$	−1.11081	−	0.641326i	−0.0433698	−	0.0250396i
$657$	4.28374	+	2.47322i	0.167125	+	0.0964895i
$658$			25.7718i			1.00469i
$659$	0.191440	−	0.331584i	0.00745746	−	0.0129167i	−0.862273	−	0.506444i	$-0.830960\pi$
$659$	0.191440	−	0.331584i	0.00745746	−	0.0129167i	0.869730	+	0.493528i	$0.164293\pi$
$660$		0			0
$661$	22.5877	−	13.0410i	0.878560	−	0.507237i	0.00837690	−	0.999965i	$-0.497334\pi$
$661$	22.5877	−	13.0410i	0.878560	−	0.507237i	0.870183	+	0.492728i	$0.164000\pi$
$662$	−4.46249			−0.173440
$663$	−4.09264	+	2.15357i	−0.158945	+	0.0836378i
$664$	−17.3887			−0.674813
$665$		0			0
$666$	−4.19076	−	7.25861i	−0.162389	−	0.281266i
$667$	−12.0236	+	20.8255i	−0.465557	+	0.806368i
$668$		−	6.86227i		−	0.265509i
$669$	0.0599161	+	0.0345926i	0.00231649	+	0.00133743i
$670$		0			0
$671$			57.9249i			2.23617i
$672$	2.56511	−	4.44290i	0.0989512	−	0.171389i
$673$	6.41571	+	11.1123i	0.247307	+	0.428349i	0.962778	−	0.270294i	$-0.0871209\pi$
$673$	6.41571	+	11.1123i	0.247307	+	0.428349i	−0.715470	+	0.698643i	$0.753788\pi$
$674$	−5.23749	+	3.02387i	−0.201741	+	0.116475i
$675$		0			0
$676$	−5.59812	−	11.7329i	−0.215312	−	0.451266i
$677$	−22.3408			−0.858626			−0.429313	−	0.903156i	$-0.641244\pi$
$677$	−22.3408			−0.858626			−0.429313	+	0.903156i	$0.641244\pi$
$678$		0			0
$679$	18.3879	+	31.8487i	0.705661	+	1.22224i
$680$		0			0
$681$		−	6.19198i		−	0.237277i
$682$	30.4720	+	17.5930i	1.16683	+	0.673672i
$683$	−17.5060	−	10.1071i	−0.669850	−	0.386738i	0.126170	−	0.992009i	$-0.459732\pi$
$683$	−17.5060	−	10.1071i	−0.669850	−	0.386738i	−0.796020	+	0.605271i	$0.793065\pi$
$684$			6.64947i			0.254249i
$685$		0			0
$686$	31.5999	+	54.7327i	1.20649	+	2.08970i
$687$	−15.0564	+	8.69283i	−0.574438	+	0.331652i
$688$	−4.35800			−0.166147
$689$	20.1215	−	10.5881i	0.766569	−	0.403373i
$690$		0			0
$691$	21.3351	−	12.3178i	0.811625	−	0.468592i	−0.0358950	−	0.999356i	$-0.511428\pi$
$691$	21.3351	−	12.3178i	0.811625	−	0.468592i	0.847520	+	0.530764i	$0.178095\pi$
$692$	−11.1449	−	19.3036i	−0.423666	−	0.733812i
$693$	−14.3123	+	24.7897i	−0.543680	+	0.941682i
$694$		−	6.34654i		−	0.240911i
$695$		0			0
$696$	3.03479	+	1.75214i	0.115033	+	0.0664146i
$697$			1.64520i			0.0623163i
$698$	14.1126	−	24.4438i	0.534170	−	0.925210i
$699$	8.88580	+	15.3907i	0.336092	+	0.582128i
$700$		0			0
$701$	43.4688			1.64179			0.820897	−	0.571076i	$-0.193474\pi$
$701$	43.4688			1.64179			0.820897	+	0.571076i	$0.193474\pi$
$702$	1.92378	−	3.04944i	0.0726085	−	0.115094i
$703$	55.7327			2.10200
$704$	4.83209	−	2.78981i	0.182116	−	0.105145i
$705$		0			0
$706$	−8.04696	+	13.9378i	−0.302851	+	0.524554i
$707$			75.2270i			2.82920i
$708$	1.31571	+	0.759628i	0.0494476	+	0.0285486i
$709$	4.05937	+	2.34368i	0.152453	+	0.0880187i	0.574286	−	0.818655i	$-0.305280\pi$
$709$	4.05937	+	2.34368i	0.152453	+	0.0880187i	−0.421833	+	0.906674i	$0.638613\pi$
$710$		0			0
$711$	−5.07423	+	8.78882i	−0.190298	+	0.329606i
$712$	3.22094	+	5.57884i	0.120710	+	0.209076i
$713$	37.4770	−	21.6374i	1.40352	−	0.810325i
$714$	−6.58029			−0.246261
$715$		0			0
$716$	1.56889			0.0586324
$717$	14.8512	−	8.57433i	0.554627	−	0.320214i
$718$	4.39845	+	7.61833i	0.164149	+	0.284314i
$719$	13.6893	−	23.7106i	0.510526	−	0.884257i	−0.489400	−	0.872060i	$-0.662784\pi$
$719$	13.6893	−	23.7106i	0.510526	−	0.884257i	0.999926	−	0.0121971i	$-0.00388256\pi$
$720$		0			0
$721$	−17.9906	−	10.3869i	−0.670005	−	0.386827i
$722$	−21.8373	−	12.6078i	−0.812699	−	0.469212i
$723$		−	17.5319i		−	0.652020i
$724$	5.72094	−	9.90896i	0.212617	−	0.368264i
$725$		0			0
$726$	−17.4349	+	10.0661i	−0.647071	+	0.373586i
$727$	−12.4066			−0.460136			−0.230068	−	0.973175i	$-0.573895\pi$
$727$	−12.4066			−0.460136			−0.230068	+	0.973175i	$0.573895\pi$
$728$	0.725036	−	18.4830i	0.0268716	−	0.685027i
$729$	1.00000			0.0370370
$730$		0			0
$731$	2.79490	+	4.84091i	0.103373	+	0.179047i
$732$	5.19076	−	8.99066i	0.191856	−	0.332305i
$733$		−	18.7638i		−	0.693056i	−0.938040	−	0.346528i	$-0.887361\pi$
$733$		−	18.7638i		−	0.693056i	0.938040	−	0.346528i	$-0.112639\pi$
$734$	32.9145	+	19.0032i	1.21490	+	0.701420i
$735$		0			0
$736$		−	6.86227i		−	0.252947i
$737$	−8.00980	+	13.8734i	−0.295045	+	0.511033i
$738$	−0.641326	−	1.11081i	−0.0236076	−	0.0408895i
$739$	44.5751	−	25.7355i	1.63972	−	0.946694i	0.658794	−	0.752324i	$-0.271067\pi$
$739$	44.5751	−	25.7355i	1.63972	−	0.946694i	0.980928	−	0.194370i	$-0.0622663\pi$
$740$		0			0
$741$	11.1645	+	21.2169i	0.410136	+	0.779422i
$742$	32.3521			1.18768
$743$	−42.9547	+	24.7999i	−1.57585	+	0.909819i	−0.580424	+	0.814314i	$0.697113\pi$
$743$	−42.9547	+	24.7999i	−1.57585	+	0.909819i	−0.995429	+	0.0955053i	$0.969553\pi$
$744$	−3.15309	−	5.46131i	−0.115598	−	0.200221i
$745$		0			0
$746$		−	17.0157i		−	0.622990i
$747$	−15.0591	−	8.69436i	−0.550983	−	0.318110i
$748$	−6.19789	−	3.57836i	−0.226617	−	0.130838i
$749$			39.8150i			1.45481i
$750$		0			0
$751$	5.15058	+	8.92107i	0.187947	+	0.325535i	0.944566	−	0.328322i	$-0.106483\pi$
$751$	5.15058	+	8.92107i	0.187947	+	0.325535i	−0.756618	+	0.653857i	$0.773150\pi$
$752$	4.35050	−	2.51176i	0.158647	−	0.0915946i
$753$	−18.2072			−0.663506
$754$	12.6251	+	0.495247i	0.459780	+	0.0180358i
$755$		0			0
$756$	4.44290	−	2.56511i	0.161587	−	0.0932921i
$757$	−2.21571	−	3.83773i	−0.0805314	−	0.139485i	0.822947	−	0.568118i	$-0.192328\pi$
$757$	−2.21571	−	3.83773i	−0.0805314	−	0.139485i	−0.903478	+	0.428634i	$0.858995\pi$
$758$	−6.36569	+	11.0257i	−0.231212	+	0.400471i
$759$			38.2888i			1.38980i
$760$		0			0
$761$	9.89888	+	5.71512i	0.358834	+	0.207173i	0.668569	−	0.743650i	$-0.266907\pi$
$761$	9.89888	+	5.71512i	0.358834	+	0.207173i	−0.309735	+	0.950823i	$0.600240\pi$
$762$		−	16.2530i		−	0.588785i
$763$	2.03334	−	3.52184i	0.0736117	−	0.127499i
$764$	4.41092	+	7.63995i	0.159582	+	0.276404i
$765$		0			0
$766$	22.5718			0.815553
$767$	5.47355	+	0.214711i	0.197638	+	0.00775277i
$768$	−1.00000			−0.0360844
$769$	8.46766	−	4.88880i	0.305352	−	0.176295i	−0.339493	−	0.940609i	$-0.610255\pi$
$769$	8.46766	−	4.88880i	0.305352	−	0.176295i	0.644844	+	0.764314i	$0.276922\pi$
$770$		0			0
$771$	−8.80056	+	15.2430i	−0.316944	+	0.548964i
$772$			11.1881i			0.402667i
$773$	−5.88192	−	3.39593i	−0.211558	−	0.122143i	0.390477	−	0.920613i	$-0.372310\pi$
$773$	−5.88192	−	3.39593i	−0.211558	−	0.122143i	−0.602035	+	0.798470i	$0.705643\pi$
$774$	−3.77414	−	2.17900i	−0.135658	−	0.0783225i
$775$		0			0
$776$	3.58423	−	6.20806i	0.128666	−	0.222856i
$777$	−21.4995	−	37.2383i	−0.771291	−	1.33592i
$778$	−3.03479	+	1.75214i	−0.108802	+	0.0628171i
$779$	8.52897			0.305582
$780$		0			0
$781$	−60.8699			−2.17809
$782$	−7.62268	+	4.40095i	−0.272586	+	0.157378i
$783$	1.75214	+	3.03479i	0.0626163	+	0.108455i
$784$	9.65957	−	16.7309i	0.344985	−	0.597531i
$785$		0			0
$786$	−6.10206	−	3.52302i	−0.217653	−	0.125662i
$787$	4.34247	+	2.50713i	0.154792	+	0.0893694i	0.575395	−	0.817875i	$-0.304848\pi$
$787$	4.34247	+	2.50713i	0.154792	+	0.0893694i	−0.420603	+	0.907245i	$0.638182\pi$
$788$			22.9351i			0.817029i
$789$	−5.88051	+	10.1853i	−0.209352	+	0.362608i
$790$		0			0
$791$		0			0
$792$	5.57962			0.198263
$793$	1.46718	−	37.4024i	0.0521012	−	1.32820i
$794$	29.8652			1.05988
$795$		0			0
$796$	−5.52892	−	9.57637i	−0.195967	−	0.339425i
$797$	4.96356	−	8.59714i	0.175818	−	0.304526i	−0.764626	−	0.644474i	$-0.777076\pi$
$797$	4.96356	−	8.59714i	0.175818	−	0.304526i	0.940444	+	0.339948i	$0.110410\pi$
$798$			34.1133i			1.20760i
$799$	−5.58019	−	3.22172i	−0.197413	−	0.113976i
$800$		0			0
$801$			6.44188i			0.227613i
$802$	12.5627	−	21.7592i	0.443604	−	0.768345i
$803$	13.7996	+	23.9016i	0.486978	+	0.843470i
$804$	2.48644	−	1.43555i	0.0876900	−	0.0506278i
$805$		0			0
$806$	−19.2303	−	12.1317i	−0.677358	−	0.427322i
$807$	6.40981			0.225636
$808$	12.6990	−	7.33175i	0.446748	−	0.257930i
$809$	−4.98796	−	8.63940i	−0.175367	−	0.303745i	0.764921	−	0.644124i	$-0.222778\pi$
$809$	−4.98796	−	8.63940i	−0.175367	−	0.303745i	−0.940288	+	0.340379i	$0.889445\pi$
$810$		0			0
$811$			4.85013i			0.170311i	0.996368	+	0.0851555i	$0.0271387\pi$
$811$			4.85013i			0.170311i	−0.996368	+	0.0851555i	$0.972861\pi$
$812$	15.5691	+	8.98884i	0.546369	+	0.315447i
$813$	13.6919	+	7.90503i	0.480196	+	0.277242i
$814$		−	46.7657i		−	1.63914i
$815$		0			0
$816$	0.641326	+	1.11081i	0.0224509	+	0.0388861i
$817$	25.0960	−	14.4892i	0.877998	−	0.506913i
$818$	−5.24767			−0.183480
$819$	9.86942	−	15.6443i	0.344866	−	0.546655i
$820$		0			0
$821$	21.9722	−	12.6857i	0.766836	−	0.442733i	−0.0649085	−	0.997891i	$-0.520676\pi$
$821$	21.9722	−	12.6857i	0.766836	−	0.442733i	0.831745	+	0.555158i	$0.187342\pi$
$822$	−0.444016	−	0.769058i	−0.0154868	−	0.0268240i
$823$	−13.2535	+	22.9557i	−0.461986	+	0.800184i	−0.999060	−	0.0433515i	$-0.986196\pi$
$823$	−13.2535	+	22.9557i	−0.461986	+	0.800184i	0.537073	+	0.843536i	$0.319530\pi$
$824$			4.04929i			0.141064i
$825$		0			0
$826$	6.74990	+	3.89706i	0.234859	+	0.135596i
$827$			21.7678i			0.756941i	0.925613	+	0.378470i	$0.123550\pi$
$827$			21.7678i			0.756941i	−0.925613	+	0.378470i	$0.876450\pi$
$828$	3.43113	−	5.94290i	0.119240	−	0.206530i
$829$	1.09376	+	1.89444i	0.0379878	+	0.0657968i	0.884394	−	0.466741i	$-0.154572\pi$
$829$	1.09376	+	1.89444i	0.0379878	+	0.0657968i	−0.846406	+	0.532537i	$0.821239\pi$
$830$		0			0
$831$	−4.98637			−0.172975
$832$	−3.19076	+	1.67900i	−0.110620	+	0.0582088i
$833$	−24.7797			−0.858567
$834$	0.461208	−	0.266279i	0.0159703	−	0.00922047i
$835$		0			0
$836$	−18.5508	+	32.1309i	−0.641591	+	1.11127i
$837$		−	6.30618i		−	0.217974i
$838$	−15.6114	−	9.01326i	−0.539288	−	0.311358i
$839$	21.7825	+	12.5761i	0.752016	+	0.434177i	0.826422	−	0.563051i	$-0.190373\pi$
$839$	21.7825	+	12.5761i	0.752016	+	0.434177i	−0.0744057	+	0.997228i	$0.523706\pi$
$840$		0			0
$841$	8.36004	−	14.4800i	0.288277	−	0.499311i
$842$	−3.96185	−	6.86213i	−0.136534	−	0.236485i
$843$	−0.446632	+	0.257863i	−0.0153828	+	0.00888127i
$844$	−26.8342			−0.923671
$845$		0			0
$846$	5.02353			0.172712
$847$	−89.4449	+	51.6411i	−3.07336	+	1.77441i
$848$	−3.15309	−	5.46131i	−0.108278	−	0.187542i
$849$	−8.97308	+	15.5418i	−0.307955	+	0.533394i
$850$		0			0
$851$	−49.8106	−	28.7581i	−1.70748	−	0.985816i
$852$	9.44775	+	5.45466i	0.323675	+	0.186874i
$853$			36.1721i			1.23851i	0.785190	+	0.619255i	$0.212565\pi$
$853$			36.1721i			1.23851i	−0.785190	+	0.619255i	$0.787435\pi$
$854$	26.6297	−	46.1241i	0.911251	−	1.57833i
$855$		0			0
$856$	6.72112	−	3.88044i	0.229723	−	0.132631i
$857$	18.5471			0.633556			0.316778	−	0.948500i	$-0.397399\pi$
$857$	18.5471			0.633556			0.316778	+	0.948500i	$0.397399\pi$
$858$	17.8032	−	9.36816i	0.607792	−	0.319824i
$859$	−21.5386			−0.734887			−0.367443	−	0.930046i	$-0.619767\pi$
$859$	−21.5386			−0.734887			−0.367443	+	0.930046i	$0.619767\pi$
$860$		0			0
$861$	−3.29014	−	5.69870i	−0.112128	−	0.194211i
$862$	−19.1537	+	33.1752i	−0.652379	+	1.12995i
$863$			32.1136i			1.09316i	0.837407	+	0.546580i	$0.184070\pi$
$863$			32.1136i			1.09316i	−0.837407	+	0.546580i	$0.815930\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$		0			0
$866$		−	20.0052i		−	0.679803i
$867$	−7.67740	+	13.2976i	−0.260738	+	0.451612i
$868$	−16.1760	−	28.0177i	−0.549051	−	0.950984i
$869$	−49.0382	+	28.3122i	−1.66351	+	0.960427i
$870$		0			0
$871$	5.52336	−	8.75522i	0.187152	−	0.296659i
$872$	−0.792690			−0.0268439
$873$	6.20806	−	3.58423i	0.210111	−	0.121308i
$874$	22.8152	+	39.5172i	0.771737	+	1.33669i
$875$		0			0
$876$		−	4.94644i		−	0.167125i
$877$	27.7681	+	16.0319i	0.937664	+	0.541360i	0.889227	−	0.457466i	$-0.151243\pi$
$877$	27.7681	+	16.0319i	0.937664	+	0.541360i	0.0484365	+	0.998826i	$0.484576\pi$
$878$	−10.3345	−	5.96660i	−0.348771	−	0.201363i
$879$			17.2711i			0.582538i
$880$		0			0
$881$	9.47244	+	16.4067i	0.319135	+	0.552757i	0.980308	−	0.197476i	$-0.0632745\pi$
$881$	9.47244	+	16.4067i	0.319135	+	0.552757i	−0.661173	+	0.750233i	$0.729941\pi$
$882$	16.7309	−	9.65957i	0.563357	−	0.325255i
$883$	−38.0685			−1.28111			−0.640554	−	0.767914i	$-0.721295\pi$
$883$	−38.0685			−1.28111			−0.640554	+	0.767914i	$0.721295\pi$
$884$	3.91137	+	2.46755i	0.131554	+	0.0829925i
$885$		0			0
$886$	−22.5656	+	13.0282i	−0.758105	+	0.437692i
$887$	6.75421	+	11.6986i	0.226784	+	0.392802i	0.956853	−	0.290572i	$-0.0938455\pi$
$887$	6.75421	+	11.6986i	0.226784	+	0.392802i	−0.730069	+	0.683373i	$0.760512\pi$
$888$	−4.19076	+	7.25861i	−0.140633	+	0.243583i
$889$		−	83.3815i		−	2.79653i
$890$		0			0
$891$	4.83209	+	2.78981i	0.161881	+	0.0934621i
$892$		−	0.0691851i		−	0.00231649i
$893$	−16.7019	+	28.9286i	−0.558908	+	0.968058i
$894$	−10.3988	−	18.0113i	−0.347789	−	0.602388i
$895$		0			0
$896$	−5.13022			−0.171389
$897$	0.969820	−	24.7232i	0.0323814	−	0.825485i
$898$	16.7392			0.558594
$899$	19.1379	−	11.0493i	0.638286	−	0.368515i
$900$		0			0
$901$	−4.04432	+	7.00497i	−0.134736	+	0.233369i
$902$		−	7.15671i		−	0.238292i
$903$	−19.3621	−	11.1787i	−0.644332	−	0.372005i
$904$		0			0
$905$		0			0
$906$	1.07700	−	1.86541i	0.0357808	−	0.0619742i
$907$	5.43460	+	9.41300i	0.180453	+	0.312554i	0.942035	−	0.335515i	$-0.108910\pi$
$907$	5.43460	+	9.41300i	0.180453	+	0.312554i	−0.761582	+	0.648069i	$0.775577\pi$
$908$	−5.36241	+	3.09599i	−0.177958	+	0.102744i
$909$	14.6635			0.486358
$910$		0			0
$911$	9.20770			0.305065			0.152532	−	0.988298i	$-0.451257\pi$
$911$	9.20770			0.305065			0.152532	+	0.988298i	$0.451257\pi$
$912$	5.75861	−	3.32474i	0.190687	−	0.110093i
$913$	−48.5112	−	84.0238i	−1.60549	−	2.78078i
$914$	−3.55432	+	6.15626i	−0.117566	+	0.203631i
$915$		0			0
$916$	15.0564	+	8.69283i	0.497478	+	0.287219i
$917$	−31.3049	−	18.0739i	−1.03378	−	0.596852i
$918$			1.28265i			0.0423339i
$919$	−0.0963564	+	0.166894i	−0.00317850	+	0.00550533i	−0.867610	−	0.497245i	$-0.834345\pi$
$919$	−0.0963564	+	0.166894i	−0.00317850	+	0.00550533i	0.864432	+	0.502750i	$0.167678\pi$
$920$		0			0
$921$	12.3559	−	7.13366i	0.407140	−	0.235062i
$922$	5.51635			0.181671
$923$	39.3039	+	1.54178i	1.29370	+	0.0507482i
$924$	28.6246			0.941682
$925$		0			0
$926$	2.49379	+	4.31938i	0.0819511	+	0.141943i
$927$	−2.02465	+	3.50679i	−0.0664981	+	0.115178i
$928$		−	3.50427i		−	0.115033i
$929$	−10.3702	−	5.98725i	−0.340236	−	0.196435i	0.320140	−	0.947370i	$-0.396270\pi$
$929$	−10.3702	−	5.98725i	−0.340236	−	0.196435i	−0.660376	+	0.750935i	$0.729603\pi$
$930$		0			0
$931$			128.462i			4.21018i
$932$	8.88580	−	15.3907i	0.291064	−	0.504138i
$933$	−11.5743	−	20.0473i	−0.378927	−	0.656320i
$934$	17.0962	−	9.87051i	0.559406	−	0.322973i
$935$		0			0
$936$	−3.60278	−	0.141326i	−0.117761	−	0.00461940i
$937$	32.1031			1.04876			0.524381	−	0.851484i	$-0.324297\pi$
$937$	32.1031			1.04876			0.524381	+	0.851484i	$0.324297\pi$
$938$	12.7560	−	7.36467i	0.416498	−	0.240465i
$939$	7.05609	+	12.2215i	0.230267	+	0.398834i
$940$		0			0
$941$			6.36756i			0.207577i	0.994599	+	0.103788i	$0.0330964\pi$
$941$			6.36756i			0.207577i	−0.994599	+	0.103788i	$0.966904\pi$
$942$	6.67044	+	3.85118i	0.217335	+	0.125478i
$943$	−7.62268	−	4.40095i	−0.248229	−	0.143315i
$944$		−	1.51926i		−	0.0494476i
$945$		0			0
$946$	−12.1580	−	21.0582i	−0.395290	−	0.684662i
$947$	51.2658	−	29.5983i	1.66591	−	0.961816i	0.696110	−	0.717936i	$-0.254913\pi$
$947$	51.2658	−	29.5983i	1.66591	−	0.961816i	0.969805	−	0.243881i	$-0.0784205\pi$
$948$	10.1485			0.329606
$949$	−8.30506	−	15.7829i	−0.269594	−	0.512335i
$950$		0			0
$951$	10.5494	−	6.09070i	0.342088	−	0.197505i
$952$	3.29014	+	5.69870i	0.106634	+	0.184696i
$953$	7.49699	−	12.9852i	0.242851	−	0.420631i	−0.718674	−	0.695347i	$-0.755251\pi$
$953$	7.49699	−	12.9852i	0.242851	−	0.420631i	0.961525	+	0.274716i	$0.0885840\pi$
$954$		−	6.30618i		−	0.204170i
$955$		0			0
$956$	−14.8512	−	8.57433i	−0.480321	−	0.277314i
$957$			19.5525i			0.632042i
$958$	4.30812	−	7.46188i	0.139189	−	0.241083i
$959$	−2.27790	−	3.94544i	−0.0735572	−	0.127405i
$960$		0			0
$961$	−8.76794			−0.282837
$962$	−1.18453	+	30.1968i	−0.0381908	+	0.973584i
$963$	7.76088			0.250091
$964$	−15.1831	+	8.76597i	−0.489015	+	0.282333i
$965$		0			0
$966$	17.6025	−	30.4884i	0.566350	−	0.980947i
$967$			43.4352i			1.39678i	0.715717	+	0.698390i	$0.246100\pi$
$967$			43.4352i			1.39678i	−0.715717	+	0.698390i	$0.753900\pi$
$968$	17.4349	+	10.0661i	0.560380	+	0.323535i
$969$	−7.38630	−	4.26448i	−0.237282	−	0.136995i
$970$		0			0
$971$	−24.4673	+	42.3786i	−0.785192	+	1.35999i	0.143692	+	0.989622i	$0.454103\pi$
$971$	−24.4673	+	42.3786i	−0.785192	+	1.35999i	−0.928884	+	0.370370i	$0.879231\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	2.36610	−	1.36607i	0.0758536	−	0.0437941i
$974$	−19.6205			−0.628682
$975$		0			0
$976$	−10.3815			−0.332305
$977$	−46.3031	+	26.7331i	−1.48137	+	0.855267i	−0.999777	−	0.0211299i	$-0.993274\pi$
$977$	−46.3031	+	26.7331i	−1.48137	+	0.855267i	−0.481589	+	0.876397i	$0.659940\pi$
$978$	−0.220942	−	0.382683i	−0.00706496	−	0.0122369i
$979$	−17.9716	+	31.1278i	−0.574375	+	0.994848i
$980$		0			0
$981$	−0.686490	−	0.396345i	−0.0219179	−	0.0126543i
$982$	34.4541	+	19.8921i	1.09948	+	0.634782i
$983$			26.5785i			0.847723i	0.905727	+	0.423862i	$0.139326\pi$
$983$			26.5785i			0.847723i	−0.905727	+	0.423862i	$0.860674\pi$
$984$	−0.641326	+	1.11081i	−0.0204447	+	0.0354113i
$985$		0			0
$986$	−3.89258	+	2.24738i	−0.123965	+	0.0715713i
$987$	25.7718			0.820325
$988$	12.7921	−	20.2771i	0.406972	−	0.645102i
$989$	−29.9057			−0.950947
$990$		0			0
$991$	18.1688	+	31.4693i	0.577152	+	0.999657i	0.995804	+	0.0915100i	$0.0291694\pi$
$991$	18.1688	+	31.4693i	0.577152	+	0.999657i	−0.418652	+	0.908147i	$0.637497\pi$
$992$	−3.15309	+	5.46131i	−0.100111	+	0.173397i
$993$			4.46249i			0.141613i
$994$	48.4690	+	27.9836i	1.53734	+	0.887586i
$995$		0			0
$996$			17.3887i			0.550983i
$997$	−15.2257	+	26.3716i	−0.482202	+	0.835198i	−0.999791	−	0.0204312i	$-0.993496\pi$
$997$	−15.2257	+	26.3716i	−0.482202	+	0.835198i	0.517590	+	0.855629i	$0.326829\pi$
$998$	3.92041	+	6.79035i	0.124098	+	0.214945i
$999$	−7.25861	+	4.19076i	−0.229652	+	0.132590i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.k.751.1	yes	12
5.2	odd	4		1950.2.y.m.49.6		12
5.3	odd	4		1950.2.y.n.49.1		12
5.4	even	2		1950.2.bc.h.751.6	✓	12
13.4	even	6	inner	1950.2.bc.k.901.1	yes	12
65.4	even	6		1950.2.bc.h.901.6	yes	12
65.17	odd	12		1950.2.y.n.199.1		12
65.43	odd	12		1950.2.y.m.199.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.y.m.49.6		12	5.2	odd	4
1950.2.y.m.199.6		12	65.43	odd	12
1950.2.y.n.49.1		12	5.3	odd	4
1950.2.y.n.199.1		12	65.17	odd	12
1950.2.bc.h.751.6	✓	12	5.4	even	2
1950.2.bc.h.901.6	yes	12	65.4	even	6
1950.2.bc.k.751.1	yes	12	1.1	even	1	trivial
1950.2.bc.k.901.1	yes	12	13.4	even	6	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:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.bc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-4.44290 - 2.56511i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-4.44290 - 2.56511i) q^{7} +1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-4.83209 + 2.78981i) q^{11} +1.00000 q^{12} +(3.19076 - 1.67900i) q^{13} +5.13022 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-0.641326 + 1.11081i) q^{17} -1.00000i q^{18} +(5.75861 + 3.32474i) q^{19} -5.13022i q^{21} +(2.78981 - 4.83209i) q^{22} +(-3.43113 - 5.94290i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(-1.92378 + 3.04944i) q^{26} -1.00000 q^{27} +(-4.44290 + 2.56511i) q^{28} +(-1.75214 - 3.03479i) q^{29} +6.30618i q^{31} +(0.866025 + 0.500000i) q^{32} +(-4.83209 - 2.78981i) q^{33} -1.28265i q^{34} +(0.500000 + 0.866025i) q^{36} +(7.25861 - 4.19076i) q^{37} -6.64947 q^{38} +(3.04944 + 1.92378i) q^{39} +(1.11081 - 0.641326i) q^{41} +(2.56511 + 4.44290i) q^{42} +(2.17900 - 3.77414i) q^{43} +5.57962i q^{44} +(5.94290 + 3.43113i) q^{46} +5.02353i q^{47} +(0.500000 - 0.866025i) q^{48} +(9.65957 + 16.7309i) q^{49} -1.28265 q^{51} +(0.141326 - 3.60278i) q^{52} +6.30618 q^{53} +(0.866025 - 0.500000i) q^{54} +(2.56511 - 4.44290i) q^{56} +6.64947i q^{57} +(3.03479 + 1.75214i) q^{58} +(1.31571 + 0.759628i) q^{59} +(5.19076 - 8.99066i) q^{61} +(-3.15309 - 5.46131i) q^{62} +(4.44290 - 2.56511i) q^{63} -1.00000 q^{64} +5.57962 q^{66} +(2.48644 - 1.43555i) q^{67} +(0.641326 + 1.11081i) q^{68} +(3.43113 - 5.94290i) q^{69} +(9.44775 + 5.45466i) q^{71} +(-0.866025 - 0.500000i) q^{72} -4.94644i q^{73} +(-4.19076 + 7.25861i) q^{74} +(5.75861 - 3.32474i) q^{76} +28.6246 q^{77} +(-3.60278 - 0.141326i) q^{78} +10.1485 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-0.641326 + 1.11081i) q^{82} +17.3887i q^{83} +(-4.44290 - 2.56511i) q^{84} +4.35800i q^{86} +(1.75214 - 3.03479i) q^{87} +(-2.78981 - 4.83209i) q^{88} +(5.57884 - 3.22094i) q^{89} +(-18.4830 - 0.725036i) q^{91} -6.86227 q^{92} +(-5.46131 + 3.15309i) q^{93} +(-2.51176 - 4.35050i) q^{94} +1.00000i q^{96} +(-6.20806 - 3.58423i) q^{97} +(-16.7309 - 9.65957i) q^{98} -5.57962i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 6 q^{4} + 6 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 + 6 * q^4 + 6 * q^7 - 6 * q^9	\( 12 q + 6 q^{3} + 6 q^{4} + 6 q^{7} - 6 q^{9} - 12 q^{11} + 12 q^{12} + 8 q^{14} - 6 q^{16} - 6 q^{19} + 4 q^{22} - 4 q^{23} - 4 q^{26} - 12 q^{27} + 6 q^{28} - 12 q^{33} + 6 q^{36} + 12 q^{37} - 24 q^{38} + 6 q^{39} + 4 q^{42} + 10 q^{43} + 12 q^{46} + 6 q^{48} + 32 q^{49} - 6 q^{52} + 16 q^{53} + 4 q^{56} + 24 q^{61} - 8 q^{62} - 6 q^{63} - 12 q^{64} + 8 q^{66} - 6 q^{67} + 4 q^{69} + 12 q^{71} - 12 q^{74} - 6 q^{76} + 48 q^{77} - 8 q^{78} + 52 q^{79} - 6 q^{81} + 6 q^{84} - 4 q^{88} + 24 q^{89} - 54 q^{91} - 8 q^{92} - 8 q^{94} - 12 q^{97} - 36 q^{98}+O(q^{100}) \) 12 * q + 6 * q^3 + 6 * q^4 + 6 * q^7 - 6 * q^9 - 12 * q^11 + 12 * q^12 + 8 * q^14 - 6 * q^16 - 6 * q^19 + 4 * q^22 - 4 * q^23 - 4 * q^26 - 12 * q^27 + 6 * q^28 - 12 * q^33 + 6 * q^36 + 12 * q^37 - 24 * q^38 + 6 * q^39 + 4 * q^42 + 10 * q^43 + 12 * q^46 + 6 * q^48 + 32 * q^49 - 6 * q^52 + 16 * q^53 + 4 * q^56 + 24 * q^61 - 8 * q^62 - 6 * q^63 - 12 * q^64 + 8 * q^66 - 6 * q^67 + 4 * q^69 + 12 * q^71 - 12 * q^74 - 6 * q^76 + 48 * q^77 - 8 * q^78 + 52 * q^79 - 6 * q^81 + 6 * q^84 - 4 * q^88 + 24 * q^89 - 54 * q^91 - 8 * q^92 - 8 * q^94 - 12 * q^97 - 36 * q^98

Introduction

L-functions

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