LMFDB - Embedded newform 1950.2.y.m.199.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1950,2,Mod(49,1950)]

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, 3, 5]))

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

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

chi := DirichletCharacter("1950.49");

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.y (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$15.5708283941$
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			199.6
Root			$0.500000 - 4.99624i$ of defining polynomial
Character	$\chi$	$=$	1950.199
Dual form			1950.2.y.m.49.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(2.56511 + 4.44290i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(2.56511 + 4.44290i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-4.83209 - 2.78981i) q^{11} -1.00000i q^{12} +(-1.67900 + 3.19076i) q^{13} -5.13022 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.11081 + 0.641326i) q^{17} -1.00000 q^{18} +(-5.75861 + 3.32474i) q^{19} +5.13022i q^{21} +(4.83209 - 2.78981i) q^{22} +(-5.94290 - 3.43113i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-1.92378 - 3.04944i) q^{26} +1.00000i q^{27} +(2.56511 - 4.44290i) q^{28} +(1.75214 - 3.03479i) q^{29} -6.30618i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.78981 - 4.83209i) q^{33} -1.28265i q^{34} +(0.500000 - 0.866025i) q^{36} +(4.19076 - 7.25861i) q^{37} -6.64947i q^{38} +(-3.04944 + 1.92378i) q^{39} +(1.11081 + 0.641326i) q^{41} +(-4.44290 - 2.56511i) q^{42} +(-3.77414 + 2.17900i) q^{43} +5.57962i q^{44} +(5.94290 - 3.43113i) q^{46} -5.02353 q^{47} +(-0.866025 + 0.500000i) q^{48} +(-9.65957 + 16.7309i) q^{49} -1.28265 q^{51} +(3.60278 - 0.141326i) q^{52} +6.30618i q^{53} +(-0.866025 - 0.500000i) q^{54} +(2.56511 + 4.44290i) q^{56} -6.64947 q^{57} +(1.75214 + 3.03479i) q^{58} +(-1.31571 + 0.759628i) q^{59} +(5.19076 + 8.99066i) q^{61} +(5.46131 + 3.15309i) q^{62} +(-2.56511 + 4.44290i) q^{63} +1.00000 q^{64} +5.57962 q^{66} +(1.43555 - 2.48644i) q^{67} +(1.11081 + 0.641326i) q^{68} +(-3.43113 - 5.94290i) q^{69} +(9.44775 - 5.45466i) q^{71} +(0.500000 + 0.866025i) q^{72} -4.94644 q^{73} +(4.19076 + 7.25861i) q^{74} +(5.75861 + 3.32474i) q^{76} -28.6246i q^{77} +(-0.141326 - 3.60278i) q^{78} -10.1485 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.11081 + 0.641326i) q^{82} +17.3887 q^{83} +(4.44290 - 2.56511i) q^{84} -4.35800i q^{86} +(3.03479 - 1.75214i) q^{87} +(-4.83209 - 2.78981i) q^{88} +(-5.57884 - 3.22094i) q^{89} +(-18.4830 + 0.725036i) q^{91} +6.86227i q^{92} +(3.15309 - 5.46131i) q^{93} +(2.51176 - 4.35050i) q^{94} -1.00000i q^{96} +(3.58423 + 6.20806i) q^{97} +(-9.65957 - 16.7309i) q^{98} -5.57962i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{2} - 6 q^{4} + 4 q^{7} + 12 q^{8} + 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^2 - 6 * q^4 + 4 * q^7 + 12 * q^8 + 6 * q^9	$ 12 q - 6 q^{2} - 6 q^{4} + 4 q^{7} + 12 q^{8} + 6 q^{9} - 12 q^{11} - 4 q^{13} - 8 q^{14} - 6 q^{16} - 12 q^{18} + 6 q^{19} + 12 q^{22} - 12 q^{23} - 4 q^{26} + 4 q^{28} - 6 q^{32} - 4 q^{33} + 6 q^{36} + 12 q^{37} - 6 q^{39} + 6 q^{42} - 12 q^{43} + 12 q^{46} - 16 q^{47} - 32 q^{49} + 8 q^{52} + 4 q^{56} - 24 q^{57} + 24 q^{61} - 4 q^{63} + 12 q^{64} + 8 q^{66} - 24 q^{67} - 4 q^{69} + 12 q^{71} + 6 q^{72} + 40 q^{73} + 12 q^{74} - 6 q^{76} + 6 q^{78} - 52 q^{79} - 6 q^{81} - 32 q^{83} - 6 q^{84} - 12 q^{88} - 24 q^{89} - 54 q^{91} + 8 q^{93} + 8 q^{94} - 24 q^{97} - 32 q^{98}+O(q^{100}) $ 12 * q - 6 * q^2 - 6 * q^4 + 4 * q^7 + 12 * q^8 + 6 * q^9 - 12 * q^11 - 4 * q^13 - 8 * q^14 - 6 * q^16 - 12 * q^18 + 6 * q^19 + 12 * q^22 - 12 * q^23 - 4 * q^26 + 4 * q^28 - 6 * q^32 - 4 * q^33 + 6 * q^36 + 12 * q^37 - 6 * q^39 + 6 * q^42 - 12 * q^43 + 12 * q^46 - 16 * q^47 - 32 * q^49 + 8 * q^52 + 4 * q^56 - 24 * q^57 + 24 * q^61 - 4 * q^63 + 12 * q^64 + 8 * q^66 - 24 * q^67 - 4 * q^69 + 12 * q^71 + 6 * q^72 + 40 * q^73 + 12 * q^74 - 6 * q^76 + 6 * q^78 - 52 * q^79 - 6 * q^81 - 32 * q^83 - 6 * q^84 - 12 * q^88 - 24 * q^89 - 54 * q^91 + 8 * q^93 + 8 * q^94 - 24 * q^97 - 32 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	2.56511	+	4.44290i	0.969520	+	1.67926i	0.696947	+	0.717123i	$0.254541\pi$
$7$	2.56511	+	4.44290i	0.969520	+	1.67926i	0.272574	+	0.962135i	$0.412125\pi$
$8$	1.00000			0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−4.83209	−	2.78981i	−1.45693	−	0.841159i	−0.458071	−	0.888916i	$-0.651459\pi$
$11$	−4.83209	−	2.78981i	−1.45693	−	0.841159i	−0.998859	+	0.0477570i	$0.984793\pi$
$12$		−	1.00000i		−	0.288675i
$13$	−1.67900	+	3.19076i	−0.465670	+	0.884958i
$13$	−1.67900	+	3.19076i	−0.465670	+	0.884958i
$14$	−5.13022			−1.37111
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.11081	+	0.641326i	−0.269411	+	0.155545i	−0.628620	−	0.777713i	$-0.716380\pi$
$17$	−1.11081	+	0.641326i	−0.269411	+	0.155545i	0.359209	+	0.933257i	$0.383047\pi$
$18$	−1.00000			−0.235702
$19$	−5.75861	+	3.32474i	−1.32112	+	0.762747i	−0.983907	−	0.178682i	$-0.942817\pi$
$19$	−5.75861	+	3.32474i	−1.32112	+	0.762747i	−0.337210	+	0.941430i	$0.609483\pi$
$20$		0			0
$21$			5.13022i			1.11951i
$22$	4.83209	−	2.78981i	1.03020	−	0.594789i
$23$	−5.94290	−	3.43113i	−1.23918	−	0.715441i	−0.270253	−	0.962789i	$-0.587108\pi$
$23$	−5.94290	−	3.43113i	−1.23918	−	0.715441i	−0.968927	+	0.247348i	$0.920441\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$		0			0
$26$	−1.92378	−	3.04944i	−0.377285	−	0.598044i
$27$			1.00000i			0.192450i
$28$	2.56511	−	4.44290i	0.484760	−	0.839629i
$29$	1.75214	−	3.03479i	0.325364	−	0.563546i	−0.656222	−	0.754568i	$-0.727847\pi$
$29$	1.75214	−	3.03479i	0.325364	−	0.563546i	0.981586	+	0.191021i	$0.0611800\pi$
$30$		0			0
$31$		−	6.30618i		−	1.13262i	−0.824191	−	0.566312i	$-0.808370\pi$
$31$		−	6.30618i		−	1.13262i	0.824191	−	0.566312i	$-0.191630\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−2.78981	−	4.83209i	−0.485643	−	0.841159i
$34$		−	1.28265i		−	0.219973i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	4.19076	−	7.25861i	0.688957	−	1.19331i	−0.283218	−	0.959055i	$-0.591402\pi$
$37$	4.19076	−	7.25861i	0.688957	−	1.19331i	0.972176	−	0.234253i	$-0.0752645\pi$
$38$		−	6.64947i		−	1.07869i
$39$	−3.04944	+	1.92378i	−0.488301	+	0.308052i
$40$		0			0
$41$	1.11081	+	0.641326i	0.173479	+	0.100158i	0.584225	−	0.811591i	$-0.301398\pi$
$41$	1.11081	+	0.641326i	0.173479	+	0.100158i	−0.410746	+	0.911750i	$0.634732\pi$
$42$	−4.44290	−	2.56511i	−0.685554	−	0.395805i
$43$	−3.77414	+	2.17900i	−0.575550	+	0.332294i	−0.759363	−	0.650667i	$-0.774489\pi$
$43$	−3.77414	+	2.17900i	−0.575550	+	0.332294i	0.183813	+	0.982961i	$0.441156\pi$
$44$			5.57962i			0.841159i
$45$		0			0
$46$	5.94290	−	3.43113i	0.876233	−	0.505893i
$47$	−5.02353			−0.732757			−0.366379	−	0.930466i	$-0.619402\pi$
$47$	−5.02353			−0.732757			−0.366379	+	0.930466i	$0.619402\pi$
$48$	−0.866025	+	0.500000i	−0.125000	+	0.0721688i
$49$	−9.65957	+	16.7309i	−1.37994	+	2.39012i
$50$		0			0
$51$	−1.28265			−0.179607
$52$	3.60278	−	0.141326i	0.499616	−	0.0195985i
$53$			6.30618i			0.866221i	0.901341	+	0.433110i	$0.142584\pi$
$53$			6.30618i			0.866221i	−0.901341	+	0.433110i	$0.857416\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$		0			0
$56$	2.56511	+	4.44290i	0.342777	+	0.593707i
$57$	−6.64947			−0.880744
$58$	1.75214	+	3.03479i	0.230067	+	0.398487i
$59$	−1.31571	+	0.759628i	−0.171291	+	0.0988952i	−0.583195	−	0.812332i	$-0.698198\pi$
$59$	−1.31571	+	0.759628i	−0.171291	+	0.0988952i	0.411903	+	0.911228i	$0.364864\pi$
$60$		0			0
$61$	5.19076	+	8.99066i	0.664609	+	1.15114i	0.979391	+	0.201973i	$0.0647352\pi$
$61$	5.19076	+	8.99066i	0.664609	+	1.15114i	−0.314782	+	0.949164i	$0.601931\pi$
$62$	5.46131	+	3.15309i	0.693588	+	0.400443i
$63$	−2.56511	+	4.44290i	−0.323173	+	0.559753i
$64$	1.00000			0.125000
$65$		0			0
$66$	5.57962			0.686803
$67$	1.43555	−	2.48644i	0.175380	−	0.303767i	−0.764913	−	0.644134i	$-0.777218\pi$
$67$	1.43555	−	2.48644i	0.175380	−	0.303767i	0.940293	+	0.340367i	$0.110551\pi$
$68$	1.11081	+	0.641326i	0.134706	+	0.0777723i
$69$	−3.43113	−	5.94290i	−0.413060	−	0.715441i
$70$		0			0
$71$	9.44775	−	5.45466i	1.12124	−	0.647350i	0.179524	−	0.983754i	$-0.442544\pi$
$71$	9.44775	−	5.45466i	1.12124	−	0.647350i	0.941718	+	0.336404i	$0.109211\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−4.94644			−0.578937			−0.289468	−	0.957188i	$-0.593478\pi$
$73$	−4.94644			−0.578937			−0.289468	+	0.957188i	$0.593478\pi$
$74$	4.19076	+	7.25861i	0.487166	+	0.843797i
$75$		0			0
$76$	5.75861	+	3.32474i	0.660558	+	0.381374i
$77$		−	28.6246i		−	3.26208i
$78$	−0.141326	−	3.60278i	−0.0160021	−	0.407935i
$79$	−10.1485			−1.14179			−0.570895	−	0.821023i	$-0.693404\pi$
$79$	−10.1485			−1.14179			−0.570895	+	0.821023i	$0.693404\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.11081	+	0.641326i	−0.122668	+	0.0708227i
$83$	17.3887			1.90866			0.954330	−	0.298755i	$-0.0965714\pi$
$83$	17.3887			1.90866			0.954330	+	0.298755i	$0.0965714\pi$
$84$	4.44290	−	2.56511i	0.484760	−	0.279876i
$85$		0			0
$86$		−	4.35800i		−	0.469935i
$87$	3.03479	−	1.75214i	0.325364	−	0.187849i
$88$	−4.83209	−	2.78981i	−0.515102	−	0.297395i
$89$	−5.57884	−	3.22094i	−0.591355	−	0.341419i	0.174278	−	0.984697i	$-0.444241\pi$
$89$	−5.57884	−	3.22094i	−0.591355	−	0.341419i	−0.765633	+	0.643277i	$0.777574\pi$
$90$		0			0
$91$	−18.4830	+	0.725036i	−1.93755	+	0.0760044i
$92$			6.86227i			0.715441i
$93$	3.15309	−	5.46131i	0.326960	−	0.566312i
$94$	2.51176	−	4.35050i	0.259069	−	0.448720i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	3.58423	+	6.20806i	0.363923	+	0.630333i	0.988603	−	0.150548i	$-0.0481038\pi$
$97$	3.58423	+	6.20806i	0.363923	+	0.630333i	−0.624680	+	0.780881i	$0.714770\pi$
$98$	−9.65957	−	16.7309i	−0.975764	−	1.69007i
$99$		−	5.57962i		−	0.560772i
$100$		0			0
$101$	−7.33175	+	12.6990i	−0.729537	+	1.26359i	0.227543	+	0.973768i	$0.426931\pi$
$101$	−7.33175	+	12.6990i	−0.729537	+	1.26359i	−0.957079	+	0.289826i	$0.906402\pi$
$102$	0.641326	−	1.11081i	0.0635008	−	0.109987i
$103$			4.04929i			0.398989i	0.979899	+	0.199494i	$0.0639299\pi$
$103$			4.04929i			0.398989i	−0.979899	+	0.199494i	$0.936070\pi$
$104$	−1.67900	+	3.19076i	−0.164639	+	0.312880i
$105$		0			0
$106$	−5.46131	−	3.15309i	−0.530450	−	0.306255i
$107$	6.72112	+	3.88044i	0.649755	+	0.375136i	0.788362	−	0.615211i	$-0.210929\pi$
$107$	6.72112	+	3.88044i	0.649755	+	0.375136i	−0.138608	+	0.990347i	$0.544263\pi$
$108$	0.866025	−	0.500000i	0.0833333	−	0.0481125i
$109$			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
$112$	−5.13022			−0.484760
$113$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$113$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$114$	3.32474	−	5.75861i	0.311390	−	0.539344i
$115$		0			0
$116$	−3.50427			−0.325364
$117$	−3.60278	+	0.141326i	−0.333077	+	0.0130656i
$118$		−	1.51926i		−	0.139859i
$119$	−5.69870	−	3.29014i	−0.522399	−	0.301607i
$120$		0			0
$121$	10.0661	+	17.4349i	0.915096	+	1.58499i
$122$	−10.3815			−0.939899
$123$	0.641326	+	1.11081i	0.0578265	+	0.100158i
$124$	−5.46131	+	3.15309i	−0.490440	+	0.283156i
$125$		0			0
$126$	−2.56511	−	4.44290i	−0.228518	−	0.395805i
$127$	−14.0755	−	8.12651i	−1.24900	−	0.721111i	−0.278090	−	0.960555i	$-0.589702\pi$
$127$	−14.0755	−	8.12651i	−1.24900	−	0.721111i	−0.970910	+	0.239444i	$0.923035\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−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	$0.400405\pi$
$132$	−2.78981	+	4.83209i	−0.242822	+	0.420579i
$133$	−29.5429	−	17.0566i	−2.56170	−	1.47900i
$134$	1.43555	+	2.48644i	0.124012	+	0.214796i
$135$		0			0
$136$	−1.11081	+	0.641326i	−0.0952512	+	0.0549933i
$137$	−0.444016	−	0.769058i	−0.0379348	−	0.0657051i	0.846435	−	0.532493i	$-0.178745\pi$
$137$	−0.444016	−	0.769058i	−0.0379348	−	0.0657051i	−0.884369	+	0.466788i	$0.845411\pi$
$138$	6.86227			0.584155
$139$	0.266279	+	0.461208i	0.0225854	+	0.0391191i	0.877097	−	0.480313i	$-0.159477\pi$
$139$	0.266279	+	0.461208i	0.0225854	+	0.0391191i	−0.854512	+	0.519432i	$0.826144\pi$
$140$		0			0
$141$	−4.35050	−	2.51176i	−0.366379	−	0.211529i
$142$			10.9093i			0.915490i
$143$	17.0147	−	10.7340i	1.42284	−	0.897619i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	2.47322	−	4.28374i	0.204685	−	0.354525i
$147$	−16.7309	+	9.65957i	−1.37994	+	0.796708i
$148$	−8.38153			−0.688957
$149$	−18.0113	+	10.3988i	−1.47554	+	0.851905i	−0.999620	−	0.0275822i	$-0.991219\pi$
$149$	−18.0113	+	10.3988i	−1.47554	+	0.851905i	−0.475923	+	0.879487i	$0.657886\pi$
$150$		0			0
$151$		−	2.15400i		−	0.175290i	−0.996152	−	0.0876448i	$-0.972066\pi$
$151$		−	2.15400i		−	0.175290i	0.996152	−	0.0876448i	$-0.0279341\pi$
$152$	−5.75861	+	3.32474i	−0.467085	+	0.269672i
$153$	−1.11081	−	0.641326i	−0.0898037	−	0.0518482i
$154$	24.7897	+	14.3123i	1.99761	+	1.15332i
$155$		0			0
$156$	3.19076	+	1.67900i	0.255465	+	0.134427i
$157$			7.70236i			0.614716i	0.951594	+	0.307358i	$0.0994448\pi$
$157$			7.70236i			0.614716i	−0.951594	+	0.307358i	$0.900555\pi$
$158$	5.07423	−	8.78882i	0.403684	−	0.699201i
$159$	−3.15309	+	5.46131i	−0.250056	+	0.433110i
$160$		0			0
$161$		−	35.2049i		−	2.77454i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	0.220942	+	0.382683i	0.0173055	+	0.0299741i	0.874548	−	0.484938i	$-0.161158\pi$
$163$	0.220942	+	0.382683i	0.0173055	+	0.0299741i	−0.857243	+	0.514912i	$0.827825\pi$
$164$		−	1.28265i		−	0.100158i
$165$		0			0
$166$	−8.69436	+	15.0591i	−0.674813	+	1.16881i
$167$	3.43113	−	5.94290i	0.265509	−	0.459875i	−0.702188	−	0.711992i	$-0.747793\pi$
$167$	3.43113	−	5.94290i	0.265509	−	0.459875i	0.967697	+	0.252116i	$0.0811266\pi$
$168$			5.13022i			0.395805i
$169$	−7.36193	−	10.7146i	−0.566302	−	0.824197i
$170$		0			0
$171$	−5.75861	−	3.32474i	−0.440372	−	0.254249i
$172$	3.77414	+	2.17900i	0.287775	+	0.166147i
$173$	−19.3036	+	11.1449i	−1.46762	+	0.847333i	−0.999343	−	0.0362472i	$-0.988460\pi$
$173$	−19.3036	+	11.1449i	−1.46762	+	0.847333i	−0.468280	+	0.883580i	$0.655126\pi$
$174$			3.50427i			0.265658i
$175$		0			0
$176$	4.83209	−	2.78981i	0.364232	−	0.210290i
$177$	−1.51926			−0.114194
$178$	5.57884	−	3.22094i	0.418151	−	0.241420i
$179$	−0.784447	+	1.35870i	−0.0586324	+	0.101554i	−0.893852	−	0.448363i	$-0.852007\pi$
$179$	−0.784447	+	1.35870i	−0.0586324	+	0.101554i	0.835219	+	0.549917i	$0.185341\pi$
$180$		0			0
$181$	11.4419			0.850469			0.425234	−	0.905083i	$-0.360192\pi$
$181$	11.4419			0.850469			0.425234	+	0.905083i	$0.360192\pi$
$182$	8.61363	−	16.3693i	0.638484	−	1.21337i
$183$			10.3815i			0.767424i
$184$	−5.94290	−	3.43113i	−0.438116	−	0.252947i
$185$		0			0
$186$	3.15309	+	5.46131i	0.231196	+	0.400443i
$187$	7.15671			0.523351
$188$	2.51176	+	4.35050i	0.183189	+	0.317293i
$189$	−4.44290	+	2.56511i	−0.323173	+	0.186584i
$190$		0			0
$191$	−4.41092	−	7.63995i	−0.319163	−	0.552807i	0.661150	−	0.750253i	$-0.270069\pi$
$191$	−4.41092	−	7.63995i	−0.319163	−	0.552807i	−0.980314	+	0.197446i	$0.936735\pi$
$192$	0.866025	+	0.500000i	0.0625000	+	0.0360844i
$193$	5.59403	−	9.68914i	0.402667	−	0.697440i	−0.591380	−	0.806393i	$-0.701417\pi$
$193$	5.59403	−	9.68914i	0.402667	−	0.697440i	0.994047	+	0.108953i	$0.0347499\pi$
$194$	−7.16845			−0.514665
$195$		0			0
$196$	19.3191			1.37994
$197$	−11.4675	+	19.8624i	−0.817029	+	1.41514i	0.0908332	+	0.995866i	$0.471047\pi$
$197$	−11.4675	+	19.8624i	−0.817029	+	1.41514i	−0.907862	+	0.419269i	$0.862286\pi$
$198$	4.83209	+	2.78981i	0.343402	+	0.198263i
$199$	−5.52892	−	9.57637i	−0.391935	−	0.678851i	0.600770	−	0.799422i	$-0.294861\pi$
$199$	−5.52892	−	9.57637i	−0.391935	−	0.678851i	−0.992705	+	0.120571i	$0.961527\pi$
$200$		0			0
$201$	2.48644	−	1.43555i	0.175380	−	0.101256i
$202$	−7.33175	−	12.6990i	−0.515860	−	0.893496i
$203$	17.9777			1.26179
$204$	0.641326	+	1.11081i	0.0449018	+	0.0777723i
$205$		0			0
$206$	−3.50679	−	2.02465i	−0.244330	−	0.141064i
$207$		−	6.86227i		−	0.476961i
$208$	−1.92378	−	3.04944i	−0.133390	−	0.211440i
$209$	37.1015			2.56637
$210$		0			0
$211$	−13.4171	+	23.2391i	−0.923671	+	1.59984i	−0.129986	+	0.991516i	$0.541493\pi$
$211$	−13.4171	+	23.2391i	−0.923671	+	1.59984i	−0.793685	+	0.608329i	$0.791840\pi$
$212$	5.46131	−	3.15309i	0.375085	−	0.216555i
$213$	10.9093			0.747495
$214$	−6.72112	+	3.88044i	−0.459446	+	0.265261i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	28.0177	−	16.1760i	1.90197	−	1.09810i
$218$	−0.686490	−	0.396345i	−0.0464949	−	0.0268439i
$219$	−4.28374	−	2.47322i	−0.289468	−	0.167125i
$220$		0			0
$221$	−0.181273	−	4.62112i	−0.0121937	−	0.310850i
$222$			8.38153i			0.562531i
$223$	−0.0345926	+	0.0599161i	−0.00231649	+	0.00401228i	−0.867181	−	0.497993i	$-0.834071\pi$
$223$	−0.0345926	+	0.0599161i	−0.00231649	+	0.00401228i	0.864865	+	0.502005i	$0.167404\pi$
$224$	2.56511	−	4.44290i	0.171389	−	0.296854i
$225$		0			0
$226$		0			0
$227$	3.09599	+	5.36241i	0.205488	+	0.355916i	0.950288	−	0.311372i	$-0.100788\pi$
$227$	3.09599	+	5.36241i	0.205488	+	0.355916i	−0.744800	+	0.667288i	$0.767455\pi$
$228$	3.32474	+	5.75861i	0.220186	+	0.381374i
$229$			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
$232$	1.75214	−	3.03479i	0.115033	−	0.199244i
$233$			17.7716i			1.16426i	0.813097	+	0.582128i	$0.197780\pi$
$233$			17.7716i			1.16426i	−0.813097	+	0.582128i	$0.802220\pi$
$234$	1.67900	−	3.19076i	0.109760	−	0.208587i
$235$		0			0
$236$	1.31571	+	0.759628i	0.0856457	+	0.0494476i
$237$	−8.78882	−	5.07423i	−0.570895	−	0.329606i
$238$	5.69870	−	3.29014i	0.369392	−	0.213268i
$239$		−	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	−0.901675	−	0.432415i	$-0.857661\pi$
$241$	−15.1831	+	8.76597i	−0.978029	+	0.564665i	−0.0763547	+	0.997081i	$0.524328\pi$
$242$	−20.1321			−1.29414
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	5.19076	−	8.99066i	0.332305	−	0.575568i
$245$		0			0
$246$	−1.28265			−0.0817790
$247$	−0.939747	−	23.9566i	−0.0597947	−	1.52432i
$248$		−	6.30618i		−	0.400443i
$249$	15.0591	+	8.69436i	0.954330	+	0.550983i
$250$		0			0
$251$	−9.10358	−	15.7679i	−0.574613	−	0.995259i	−0.996084	−	0.0884170i	$-0.971819\pi$
$251$	−9.10358	−	15.7679i	−0.574613	−	0.995259i	0.421470	−	0.906842i	$-0.361514\pi$
$252$	5.13022			0.323173
$253$	19.1444	+	33.1591i	1.20360	+	2.08469i
$254$	14.0755	−	8.12651i	0.883177	−	0.509902i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−15.2430	−	8.80056i	−0.950833	−	0.548964i	−0.0574935	−	0.998346i	$-0.518311\pi$
$257$	−15.2430	−	8.80056i	−0.950833	−	0.548964i	−0.893340	+	0.449382i	$0.851644\pi$
$258$	2.17900	−	3.77414i	0.135658	−	0.234967i
$259$	42.9991			2.67183
$260$		0			0
$261$	3.50427			0.216909
$262$	−3.52302	+	6.10206i	−0.217653	+	0.376986i
$263$	10.1853	+	5.88051i	0.628055	+	0.362608i	0.779999	−	0.625781i	$-0.215220\pi$
$263$	10.1853	+	5.88051i	0.628055	+	0.362608i	−0.151943	+	0.988389i	$0.548553\pi$
$264$	−2.78981	−	4.83209i	−0.171701	−	0.297395i
$265$		0			0
$266$	29.5429	−	17.0566i	1.81139	−	1.04581i
$267$	−3.22094	−	5.57884i	−0.197118	−	0.341419i
$268$	−2.87109			−0.175380
$269$	−3.20490	−	5.55106i	−0.195406	−	0.338454i	0.751627	−	0.659588i	$-0.229269\pi$
$269$	−3.20490	−	5.55106i	−0.195406	−	0.338454i	−0.947034	+	0.321134i	$0.895936\pi$
$270$		0			0
$271$	13.6919	+	7.90503i	0.831725	+	0.480196i	0.854443	−	0.519545i	$-0.173899\pi$
$271$	13.6919	+	7.90503i	0.831725	+	0.480196i	−0.0227182	+	0.999742i	$0.507232\pi$
$272$		−	1.28265i		−	0.0777723i
$273$	−16.3693	−	8.61363i	−0.990716	−	0.521320i
$274$	0.888032			0.0536480
$275$		0			0
$276$	−3.43113	+	5.94290i	−0.206530	+	0.357720i
$277$	−4.31832	+	2.49319i	−0.259463	+	0.149801i	−0.624090	−	0.781353i	$-0.714530\pi$
$277$	−4.31832	+	2.49319i	−0.259463	+	0.149801i	0.364627	+	0.931154i	$0.381197\pi$
$278$	−0.532557			−0.0319406
$279$	5.46131	−	3.15309i	0.326960	−	0.188771i
$280$		0			0
$281$		−	0.515726i		−	0.0307656i	−0.999882	−	0.0153828i	$-0.995103\pi$
$281$		−	0.515726i		−	0.0307656i	0.999882	−	0.0153828i	$-0.00489670\pi$
$282$	4.35050	−	2.51176i	0.259069	−	0.149573i
$283$	15.5418	+	8.97308i	0.923866	+	0.533394i	0.884866	−	0.465845i	$-0.154250\pi$
$283$	15.5418	+	8.97308i	0.923866	+	0.533394i	0.0389995	+	0.999239i	$0.487583\pi$
$284$	−9.44775	−	5.45466i	−0.560621	−	0.323675i
$285$		0			0
$286$	0.788547	+	20.1021i	0.0466278	+	1.18866i
$287$			6.58029i			0.388422i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	−7.67740	+	13.2976i	−0.451612	+	0.782215i
$290$		0			0
$291$			7.16845i			0.420222i
$292$	2.47322	+	4.28374i	0.144734	+	0.250687i
$293$	8.63553	+	14.9572i	0.504493	+	0.873808i	0.999987	+	0.00519587i	$0.00165390\pi$
$293$	8.63553	+	14.9572i	0.504493	+	0.873808i	−0.495493	+	0.868612i	$0.665013\pi$
$294$		−	19.3191i		−	1.12671i
$295$		0			0
$296$	4.19076	−	7.25861i	0.243583	−	0.421898i
$297$	2.78981	−	4.83209i	0.161881	−	0.280386i
$298$		−	20.7976i		−	1.20478i
$299$	20.9261	−	13.2015i	1.21018	−	0.763463i
$300$		0			0
$301$	−19.3621	−	11.1787i	−1.11601	−	0.644332i
$302$	1.86541	+	1.07700i	0.107343	+	0.0619742i
$303$	−12.6990	+	7.33175i	−0.729537	+	0.421198i
$304$		−	6.64947i		−	0.381374i
$305$		0			0
$306$	1.11081	−	0.641326i	0.0635008	−	0.0366622i
$307$	14.2673			0.814279			0.407140	−	0.913366i	$-0.366526\pi$
$307$	14.2673			0.814279			0.407140	+	0.913366i	$0.366526\pi$
$308$	−24.7897	+	14.3123i	−1.41252	+	0.815520i
$309$	−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	$0.727888\pi$
$312$	−3.04944	+	1.92378i	−0.172640	+	0.108913i
$313$			14.1122i			0.797667i	0.917023	+	0.398834i	$0.130585\pi$
$313$			14.1122i			0.797667i	−0.917023	+	0.398834i	$0.869415\pi$
$314$	−6.67044	−	3.85118i	−0.376435	−	0.217335i
$315$		0			0
$316$	5.07423	+	8.78882i	0.285448	+	0.494410i
$317$	12.1814			0.684176			0.342088	−	0.939668i	$-0.388866\pi$
$317$	12.1814			0.684176			0.342088	+	0.939668i	$0.388866\pi$
$318$	−3.15309	−	5.46131i	−0.176817	−	0.306255i
$319$	−16.9330	+	9.77625i	−0.948064	+	0.547365i
$320$		0			0
$321$	3.88044	+	6.72112i	0.216585	+	0.375136i
$322$	30.4884	+	17.6025i	1.69905	+	0.980947i
$323$	4.26448	−	7.38630i	0.237282	−	0.410985i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−0.441885			−0.0244737
$327$	−0.396345	+	0.686490i	−0.0219179	+	0.0379630i
$328$	1.11081	+	0.641326i	0.0613342	+	0.0354113i
$329$	−12.8859	−	22.3190i	−0.710423	−	1.23049i
$330$		0			0
$331$	3.86463	−	2.23125i	0.212419	−	0.122640i	−0.390016	−	0.920808i	$-0.627530\pi$
$331$	3.86463	−	2.23125i	0.212419	−	0.122640i	0.602435	+	0.798168i	$0.294197\pi$
$332$	−8.69436	−	15.0591i	−0.477165	−	0.826474i
$333$	8.38153			0.459305
$334$	3.43113	+	5.94290i	0.187743	+	0.325181i
$335$		0			0
$336$	−4.44290	−	2.56511i	−0.242380	−	0.139938i
$337$		−	6.04773i		−	0.329441i	−0.986340	−	0.164720i	$-0.947328\pi$
$337$		−	6.04773i		−	0.329441i	0.986340	−	0.164720i	$-0.0526722\pi$
$338$	12.9601	−	1.01834i	0.704934	−	0.0553902i
$339$		0			0
$340$		0			0
$341$	−17.5930	+	30.4720i	−0.952716	+	1.65015i
$342$	5.75861	−	3.32474i	0.311390	−	0.179781i
$343$	−63.1999			−3.41247
$344$	−3.77414	+	2.17900i	−0.203488	+	0.117484i
$345$		0			0
$346$		−	22.2898i		−	1.19831i
$347$	−5.49627	+	3.17327i	−0.295055	+	0.170350i	−0.640219	−	0.768192i	$-0.721157\pi$
$347$	−5.49627	+	3.17327i	−0.295055	+	0.170350i	0.345164	+	0.938542i	$0.387823\pi$
$348$	−3.03479	−	1.75214i	−0.162682	−	0.0939244i
$349$	24.4438	+	14.1126i	1.30844	+	0.755431i	0.981836	−	0.189729i	$-0.0607611\pi$
$349$	24.4438	+	14.1126i	1.30844	+	0.755431i	0.326608	+	0.945160i	$0.394094\pi$
$350$		0			0
$351$	−3.19076	−	1.67900i	−0.170310	−	0.0896183i
$352$			5.57962i			0.297395i
$353$	−8.04696	+	13.9378i	−0.428297	+	0.741832i	−0.996722	−	0.0809033i	$-0.974220\pi$
$353$	−8.04696	+	13.9378i	−0.428297	+	0.741832i	0.568425	+	0.822735i	$0.307553\pi$
$354$	0.759628	−	1.31571i	0.0403738	−	0.0699294i
$355$		0			0
$356$			6.44188i			0.341419i
$357$	−3.29014	−	5.69870i	−0.174133	−	0.301607i
$358$	−0.784447	−	1.35870i	−0.0414593	−	0.0718097i
$359$		−	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
$362$	−5.72094	+	9.90896i	−0.300686	+	0.520804i
$363$			20.1321i			1.05666i
$364$	9.86942	+	15.6443i	0.517298	+	0.819983i
$365$		0			0
$366$	−8.99066	−	5.19076i	−0.469950	−	0.271326i
$367$	32.9145	+	19.0032i	1.71812	+	0.991958i	0.922344	+	0.386371i	$0.126271\pi$
$367$	32.9145	+	19.0032i	1.71812	+	0.991958i	0.795779	+	0.605588i	$0.207062\pi$
$368$	5.94290	−	3.43113i	0.309795	−	0.178860i
$369$			1.28265i			0.0667722i
$370$		0			0
$371$	−28.0177	+	16.1760i	−1.45461	+	0.839818i
$372$	−6.30618			−0.326960
$373$	14.7361	−	8.50787i	0.763004	−	0.440521i	−0.0673691	−	0.997728i	$-0.521460\pi$
$373$	14.7361	−	8.50787i	0.763004	−	0.440521i	0.830373	+	0.557207i	$0.188127\pi$
$374$	−3.57836	+	6.19789i	−0.185032	+	0.320485i
$375$		0			0
$376$	−5.02353			−0.259069
$377$	6.74146	+	10.6861i	0.347203	+	0.550360i
$378$		−	5.13022i		−	0.263870i
$379$	−11.0257	−	6.36569i	−0.566352	−	0.326983i	0.189339	−	0.981912i	$-0.439365\pi$
$379$	−11.0257	−	6.36569i	−0.566352	−	0.326983i	−0.755691	+	0.654928i	$0.772699\pi$
$380$		0			0
$381$	−8.12651	−	14.0755i	−0.416334	−	0.721111i
$382$	8.82185			0.451365
$383$	−11.2859	−	19.5478i	−0.576683	−	0.998845i	−0.995857	−	0.0909383i	$-0.971013\pi$
$383$	−11.2859	−	19.5478i	−0.576683	−	0.998845i	0.419173	−	0.907906i	$-0.362320\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$		0			0
$386$	5.59403	+	9.68914i	0.284729	+	0.493164i
$387$	−3.77414	−	2.17900i	−0.191850	−	0.110765i
$388$	3.58423	−	6.20806i	0.181961	−	0.315167i
$389$	−3.50427			−0.177674			−0.0888368	−	0.996046i	$-0.528315\pi$
$389$	−3.50427			−0.177674			−0.0888368	+	0.996046i	$0.528315\pi$
$390$		0			0
$391$	8.80191			0.445132
$392$	−9.65957	+	16.7309i	−0.487882	+	0.845036i
$393$	6.10206	+	3.52302i	0.307808	+	0.177713i
$394$	−11.4675	−	19.8624i	−0.577727	−	1.00065i
$395$		0			0
$396$	−4.83209	+	2.78981i	−0.242822	+	0.140193i
$397$	14.9326	+	25.8640i	0.749445	+	1.29808i	0.948089	+	0.318005i	$0.103013\pi$
$397$	14.9326	+	25.8640i	0.749445	+	1.29808i	−0.198644	+	0.980072i	$0.563654\pi$
$398$	11.0578			0.554279
$399$	−17.0566	−	29.5429i	−0.853899	−	1.47900i
$400$		0			0
$401$	−21.7592	−	12.5627i	−1.08660	−	0.627351i	−0.153934	−	0.988081i	$-0.549194\pi$
$401$	−21.7592	−	12.5627i	−1.08660	−	0.627351i	−0.932670	+	0.360730i	$0.882528\pi$
$402$			2.87109i			0.143197i
$403$	20.1215	+	10.5881i	1.00232	+	0.527429i
$404$	14.6635			0.729537
$405$		0			0
$406$	−8.98884	+	15.5691i	−0.446109	+	0.772683i
$407$	−40.5003	+	23.3828i	−2.00752	+	1.15904i
$408$	−1.28265			−0.0635008
$409$	−4.54462	+	2.62384i	−0.224717	+	0.129740i	−0.608132	−	0.793836i	$-0.708081\pi$
$409$	−4.54462	+	2.62384i	−0.224717	+	0.129740i	0.383416	+	0.923576i	$0.374748\pi$
$410$		0			0
$411$		−	0.888032i		−	0.0438034i
$412$	3.50679	−	2.02465i	0.172767	−	0.0997472i
$413$	−6.74990	−	3.89706i	−0.332141	−	0.191762i
$414$	5.94290	+	3.43113i	0.292078	+	0.168631i
$415$		0			0
$416$	3.60278	−	0.141326i	0.176641	−	0.00692910i
$417$			0.532557i			0.0260794i
$418$	−18.5508	+	32.1309i	−0.907347	+	1.57157i
$419$	−9.01326	+	15.6114i	−0.440326	+	0.762668i	−0.997714	−	0.0675850i	$-0.978471\pi$
$419$	−9.01326	+	15.6114i	−0.440326	+	0.762668i	0.557387	+	0.830253i	$0.311804\pi$
$420$		0			0
$421$		−	7.92370i		−	0.386178i	−0.981181	−	0.193089i	$-0.938149\pi$
$421$		−	7.92370i		−	0.386178i	0.981181	−	0.193089i	$-0.0618506\pi$
$422$	−13.4171	−	23.2391i	−0.653134	−	1.13126i
$423$	−2.51176	−	4.35050i	−0.122126	−	0.211529i
$424$			6.30618i			0.306255i
$425$		0			0
$426$	−5.45466	+	9.44775i	−0.264279	+	0.457745i
$427$	−26.6297	+	46.1241i	−1.28870	+	2.23210i
$428$		−	7.76088i		−	0.375136i
$429$	20.1021	−	0.788547i	0.970540	−	0.0380714i
$430$		0			0
$431$	33.1752	+	19.1537i	1.59800	+	0.922603i	0.991873	+	0.127231i	$0.0406090\pi$
$431$	33.1752	+	19.1537i	1.59800	+	0.922603i	0.606122	+	0.795372i	$0.292724\pi$
$432$	−0.866025	−	0.500000i	−0.0416667	−	0.0240563i
$433$	17.3250	−	10.0026i	0.832585	−	0.480693i	−0.0221517	−	0.999755i	$-0.507052\pi$
$433$	17.3250	−	10.0026i	0.832585	−	0.480693i	0.854737	+	0.519061i	$0.173718\pi$
$434$			32.3521i			1.55295i
$435$		0			0
$436$	0.686490	−	0.396345i	0.0328769	−	0.0189815i
$437$	45.6305			2.18280
$438$	4.28374	−	2.47322i	0.204685	−	0.118175i
$439$	−5.96660	+	10.3345i	−0.284770	+	0.493237i	−0.972553	−	0.232680i	$-0.925251\pi$
$439$	−5.96660	+	10.3345i	−0.284770	+	0.493237i	0.687783	+	0.725916i	$0.258584\pi$
$440$		0			0
$441$	−19.3191			−0.919959
$442$	4.09264	+	2.15357i	0.194667	+	0.102435i
$443$			26.0565i			1.23798i	0.785399	+	0.618990i	$0.212458\pi$
$443$			26.0565i			1.23798i	−0.785399	+	0.618990i	$0.787542\pi$
$444$	−7.25861	−	4.19076i	−0.344479	−	0.198885i
$445$		0			0
$446$	−0.0345926	−	0.0599161i	−0.00163801	−	0.00283711i
$447$	−20.7976			−0.983695
$448$	2.56511	+	4.44290i	0.121190	+	0.209907i
$449$	14.4966	−	8.36959i	0.684135	−	0.394985i	−0.117276	−	0.993099i	$-0.537416\pi$
$449$	14.4966	−	8.36959i	0.684135	−	0.394985i	0.801411	+	0.598114i	$0.204083\pi$
$450$		0			0
$451$	−3.57836	−	6.19789i	−0.168498	−	0.291847i
$452$		0			0
$453$	1.07700	−	1.86541i	0.0506018	−	0.0876448i
$454$	−6.19198			−0.290604
$455$		0			0
$456$	−6.64947			−0.311390
$457$	3.55432	−	6.15626i	0.166264	−	0.287977i	−0.770840	−	0.637029i	$-0.780163\pi$
$457$	3.55432	−	6.15626i	0.166264	−	0.287977i	0.937103	+	0.349052i	$0.113496\pi$
$458$	−15.0564	−	8.69283i	−0.703540	−	0.406189i
$459$	−0.641326	−	1.11081i	−0.0299346	−	0.0518482i
$460$		0			0
$461$	−4.77730	+	2.75817i	−0.222501	+	0.128461i	−0.607108	−	0.794620i	$-0.707670\pi$
$461$	−4.77730	+	2.75817i	−0.222501	+	0.128461i	0.384607	+	0.923081i	$0.374337\pi$
$462$	14.3123	+	24.7897i	0.665870	+	1.15332i
$463$	−4.98759			−0.231793			−0.115896	−	0.993261i	$-0.536974\pi$
$463$	−4.98759			−0.231793			−0.115896	+	0.993261i	$0.536974\pi$
$464$	1.75214	+	3.03479i	0.0813409	+	0.140887i
$465$		0			0
$466$	−15.3907	−	8.88580i	−0.712958	−	0.411627i
$467$			19.7410i			0.913506i	0.889594	+	0.456753i	$0.150988\pi$
$467$			19.7410i			0.913506i	−0.889594	+	0.456753i	$0.849012\pi$
$468$	1.92378	+	3.04944i	0.0889269	+	0.140960i
$469$	14.7293			0.680138
$470$		0			0
$471$	−3.85118	+	6.67044i	−0.177453	+	0.307358i
$472$	−1.31571	+	0.759628i	−0.0605607	+	0.0349647i
$473$	24.3159			1.11805
$474$	8.78882	−	5.07423i	0.403684	−	0.233067i
$475$		0			0
$476$			6.58029i			0.301607i
$477$	−5.46131	+	3.15309i	−0.250056	+	0.144370i
$478$	14.8512	+	8.57433i	0.679277	+	0.392181i
$479$	7.46188	+	4.30812i	0.340942	+	0.196843i	0.660689	−	0.750660i	$-0.270264\pi$
$479$	7.46188	+	4.30812i	0.340942	+	0.196843i	−0.319746	+	0.947503i	$0.603598\pi$
$480$		0			0
$481$	16.1242	+	25.5589i	0.735202	+	1.16539i
$482$		−	17.5319i		−	0.798558i
$483$	17.6025	−	30.4884i	0.800940	−	1.38727i
$484$	10.0661	−	17.4349i	0.457548	−	0.792496i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	−9.81026	−	16.9919i	−0.444545	−	0.769975i	0.553475	−	0.832866i	$-0.313301\pi$
$487$	−9.81026	−	16.9919i	−0.444545	−	0.769975i	−0.998020	+	0.0628907i	$0.979968\pi$
$488$	5.19076	+	8.99066i	0.234975	+	0.406988i
$489$			0.441885i			0.0199827i
$490$		0			0
$491$	−19.8921	+	34.4541i	−0.897718	+	1.55489i	−0.0673138	+	0.997732i	$0.521443\pi$
$491$	−19.8921	+	34.4541i	−0.897718	+	1.55489i	−0.830404	+	0.557161i	$0.811890\pi$
$492$	0.641326	−	1.11081i	0.0289132	−	0.0500792i
$493$			4.49477i			0.202434i
$494$	21.2169	+	11.1645i	0.954593	+	0.502313i
$495$		0			0
$496$	5.46131	+	3.15309i	0.245220	+	0.141578i
$497$	48.4690	+	27.9836i	2.17413	+	1.25524i
$498$	−15.0591	+	8.69436i	−0.674813	+	0.389603i
$499$		−	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
$502$	18.2072			0.812626
$503$	−6.15215	+	3.55194i	−0.274311	+	0.158373i	−0.630845	−	0.775909i	$-0.717292\pi$
$503$	−6.15215	+	3.55194i	−0.274311	+	0.158373i	0.356534	+	0.934282i	$0.383958\pi$
$504$	−2.56511	+	4.44290i	−0.114259	+	0.197902i
$505$		0			0
$506$	−38.2888			−1.70215
$507$	−1.01834	−	12.9601i	−0.0452259	−	0.575576i
$508$			16.2530i			0.721111i
$509$	−34.0477	−	19.6575i	−1.50914	−	0.871302i	−0.999943	−	0.0106512i	$-0.996610\pi$
$509$	−34.0477	−	19.6575i	−1.50914	−	0.871302i	−0.509196	−	0.860651i	$-0.670057\pi$
$510$		0			0
$511$	−12.6882	−	21.9765i	−0.561291	−	0.972184i
$512$	1.00000			0.0441942
$513$	−3.32474	−	5.75861i	−0.146791	−	0.254249i
$514$	15.2430	−	8.80056i	0.672341	−	0.388176i
$515$		0			0
$516$	2.17900	+	3.77414i	0.0959250	+	0.166147i
$517$	24.2741	+	14.0147i	1.06758	+	0.616365i
$518$	−21.4995	+	37.2383i	−0.944635	+	1.63616i
$519$	−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	$0.171496\pi$
$522$	−1.75214	+	3.03479i	−0.0766889	+	0.132829i
$523$	7.33790	+	4.23654i	0.320864	+	0.185251i	0.651778	−	0.758410i	$-0.274024\pi$
$523$	7.33790	+	4.23654i	0.320864	+	0.185251i	−0.330914	+	0.943661i	$0.607357\pi$
$524$	−3.52302	−	6.10206i	−0.153904	−	0.266570i
$525$		0			0
$526$	−10.1853	+	5.88051i	−0.444102	+	0.256402i
$527$	4.04432	+	7.00497i	0.176173	+	0.305141i
$528$	5.57962			0.242822
$529$	12.0454	+	20.8632i	0.523712	+	0.907095i
$530$		0			0
$531$	−1.31571	−	0.759628i	−0.0570972	−	0.0329651i
$532$			34.1133i			1.47900i
$533$	−3.91137	+	2.46755i	−0.169420	+	0.106881i
$534$	6.44188			0.278768
$535$		0			0
$536$	1.43555	−	2.48644i	0.0620062	−	0.107398i
$537$	−1.35870	+	0.784447i	−0.0586324	+	0.0338514i
$538$	6.40981			0.276346
$539$	93.3518	−	53.8967i	4.02095	−	2.32149i
$540$		0			0
$541$		−	14.5899i		−	0.627269i	−0.949544	−	0.313634i	$-0.898453\pi$
$541$		−	14.5899i		−	0.627269i	0.949544	−	0.313634i	$-0.101547\pi$
$542$	−13.6919	+	7.90503i	−0.588118	+	0.339550i
$543$	9.90896	+	5.72094i	0.425234	+	0.245509i
$544$	1.11081	+	0.641326i	0.0476256	+	0.0274966i
$545$		0			0
$546$	15.6443	−	9.86942i	0.669513	−	0.422372i
$547$		−	14.2246i		−	0.608200i	−0.952640	−	0.304100i	$-0.901644\pi$
$547$		−	14.2246i		−	0.608200i	0.952640	−	0.304100i	$-0.0983557\pi$
$548$	−0.444016	+	0.769058i	−0.0189674	+	0.0328525i
$549$	−5.19076	+	8.99066i	−0.221536	+	0.383712i
$550$		0			0
$551$			23.3016i			0.992680i
$552$	−3.43113	−	5.94290i	−0.146039	−	0.252947i
$553$	−26.0319	−	45.0885i	−1.10699	−	1.91736i
$554$		−	4.98637i		−	0.211851i
$555$		0			0
$556$	0.266279	−	0.461208i	0.0112927	−	0.0195596i
$557$	17.4527	−	30.2289i	0.739493	−	1.28084i	−0.213231	−	0.977002i	$-0.568399\pi$
$557$	17.4527	−	30.2289i	0.739493	−	1.28084i	0.952724	−	0.303838i	$-0.0982681\pi$
$558$			6.30618i			0.266962i
$559$	−0.615900	−	15.7009i	−0.0260498	−	0.664077i
$560$		0			0
$561$	6.19789	+	3.57836i	0.261675	+	0.151078i
$562$	0.446632	+	0.257863i	0.0188400	+	0.0108773i
$563$	−13.6984	+	7.90879i	−0.577320	+	0.333316i	−0.760067	−	0.649844i	$-0.774834\pi$
$563$	−13.6984	+	7.90879i	−0.577320	+	0.333316i	0.182748	+	0.983160i	$0.441501\pi$
$564$			5.02353i			0.211529i
$565$		0			0
$566$	−15.5418	+	8.97308i	−0.653272	+	0.377167i
$567$	−5.13022			−0.215449
$568$	9.44775	−	5.45466i	0.396419	−	0.228873i
$569$	0.234472	−	0.406118i	0.00982959	−	0.0170253i	−0.861069	−	0.508489i	$-0.830204\pi$
$569$	0.234472	−	0.406118i	0.00982959	−	0.0170253i	0.870898	+	0.491463i	$0.163538\pi$
$570$		0			0
$571$	21.6325			0.905292			0.452646	−	0.891690i	$-0.350480\pi$
$571$	21.6325			0.905292			0.452646	+	0.891690i	$0.350480\pi$
$572$	−17.8032	−	9.36816i	−0.744390	−	0.391703i
$573$		−	8.82185i		−	0.368538i
$574$	−5.69870	−	3.29014i	−0.237859	−	0.137328i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	21.2140			0.883149			0.441574	−	0.897225i	$-0.354420\pi$
$577$	21.2140			0.883149			0.441574	+	0.897225i	$0.354420\pi$
$578$	−7.67740	−	13.2976i	−0.319338	−	0.553109i
$579$	9.68914	−	5.59403i	0.402667	−	0.232480i
$580$		0			0
$581$	44.6040	+	77.2563i	1.85048	+	3.20513i
$582$	−6.20806	−	3.58423i	−0.257332	−	0.148571i
$583$	17.5930	−	30.4720i	0.728629	−	1.26202i
$584$	−4.94644			−0.204685
$585$		0			0
$586$	−17.2711			−0.713461
$587$	−1.18666	+	2.05536i	−0.0489788	+	0.0848338i	−0.889475	−	0.456983i	$-0.848930\pi$
$587$	−1.18666	+	2.05536i	−0.0489788	+	0.0848338i	0.840497	+	0.541817i	$0.182263\pi$
$588$	16.7309	+	9.65957i	0.689969	+	0.398354i
$589$	20.9664	+	36.3149i	0.863905	+	1.49633i
$590$		0			0
$591$	−19.8624	+	11.4675i	−0.817029	+	0.471712i
$592$	4.19076	+	7.25861i	0.172239	+	0.298327i
$593$	2.26258			0.0929130			0.0464565	−	0.998920i	$-0.485207\pi$
$593$	2.26258			0.0929130			0.0464565	+	0.998920i	$0.485207\pi$
$594$	2.78981	+	4.83209i	0.114467	+	0.198263i
$595$		0			0
$596$	18.0113	+	10.3988i	0.737771	+	0.425952i
$597$		−	11.0578i		−	0.452567i
$598$	0.969820	+	24.7232i	0.0396589	+	1.01101i
$599$	8.04828			0.328844			0.164422	−	0.986390i	$-0.447424\pi$
$599$	8.04828			0.328844			0.164422	+	0.986390i	$0.447424\pi$
$600$		0			0
$601$	−1.32625	+	2.29713i	−0.0540988	+	0.0937019i	−0.891807	−	0.452417i	$-0.850562\pi$
$601$	−1.32625	+	2.29713i	−0.0540988	+	0.0937019i	0.837708	+	0.546119i	$0.183895\pi$
$602$	19.3621	−	11.1787i	0.789142	−	0.455611i
$603$	2.87109			0.116920
$604$	−1.86541	+	1.07700i	−0.0759026	+	0.0438224i
$605$		0			0
$606$		−	14.6635i		−	0.595664i
$607$	1.89971	−	1.09680i	0.0771070	−	0.0445177i	−0.460951	−	0.887426i	$-0.652492\pi$
$607$	1.89971	−	1.09680i	0.0771070	−	0.0445177i	0.538058	+	0.842908i	$0.319158\pi$
$608$	5.75861	+	3.32474i	0.233543	+	0.134836i
$609$	15.5691	+	8.98884i	0.630893	+	0.364246i
$610$		0			0
$611$	8.43450	−	16.0289i	0.341223	−	0.648459i
$612$			1.28265i			0.0518482i
$613$	−0.0485163	+	0.0840326i	−0.00195955	+	0.00339405i	−0.867004	−	0.498302i	$-0.833957\pi$
$613$	−0.0485163	+	0.0840326i	−0.00195955	+	0.00339405i	0.865044	+	0.501696i	$0.167290\pi$
$614$	−7.13366	+	12.3559i	−0.287891	+	0.498642i
$615$		0			0
$616$		−	28.6246i		−	1.15332i
$617$	−3.31734	−	5.74580i	−0.133551	−	0.231317i	0.791492	−	0.611180i	$-0.209305\pi$
$617$	−3.31734	−	5.74580i	−0.133551	−	0.231317i	−0.925043	+	0.379862i	$0.875971\pi$
$618$	−2.02465	−	3.50679i	−0.0814432	−	0.141064i
$619$		−	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
$622$	11.5743	−	20.0473i	0.464088	−	0.803824i
$623$		−	33.0483i		−	1.32405i
$624$	−0.141326	−	3.60278i	−0.00565759	−	0.144227i
$625$		0			0
$626$	−12.2215	−	7.05609i	−0.488469	−	0.282018i
$627$	32.1309	+	18.5508i	1.28318	+	0.740846i
$628$	6.67044	−	3.85118i	0.266180	−	0.153679i
$629$			10.7506i			0.428654i
$630$		0			0
$631$	−36.1445	+	20.8680i	−1.43889	+	0.830743i	−0.997773	−	0.0667070i	$-0.978751\pi$
$631$	−36.1445	+	20.8680i	−1.43889	+	0.830743i	−0.441116	+	0.897450i	$0.645417\pi$
$632$	−10.1485			−0.403684
$633$	−23.2391	+	13.4171i	−0.923671	+	0.533282i
$634$	−6.09070	+	10.5494i	−0.241893	+	0.418970i
$635$		0			0
$636$	6.30618			0.250056
$637$	−37.1658	−	58.9125i	−1.47256	−	2.33420i
$638$		−	19.5525i		−	0.774091i
$639$	9.44775	+	5.45466i	0.373747	+	0.215783i
$640$		0			0
$641$	−18.4382	−	31.9358i	−0.728264	−	1.26139i	−0.957617	−	0.288046i	$-0.906994\pi$
$641$	−18.4382	−	31.9358i	−0.728264	−	1.26139i	0.229353	−	0.973343i	$-0.426339\pi$
$642$	−7.76088			−0.306297
$643$	−10.9694	−	18.9996i	−0.432592	−	0.749271i	0.564504	−	0.825430i	$-0.309067\pi$
$643$	−10.9694	−	18.9996i	−0.432592	−	0.749271i	−0.997096	+	0.0761597i	$0.975734\pi$
$644$	−30.4884	+	17.6025i	−1.20141	+	0.693634i
$645$		0			0
$646$	4.26448	+	7.38630i	0.167784	+	0.290610i
$647$	1.68214	+	0.971183i	0.0661317	+	0.0381811i	0.532701	−	0.846303i	$-0.321177\pi$
$647$	1.68214	+	0.971183i	0.0661317	+	0.0381811i	−0.466570	+	0.884485i	$0.654510\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	8.47687			0.332746
$650$		0			0
$651$	32.3521			1.26798
$652$	0.220942	−	0.382683i	0.00865277	−	0.0149870i
$653$	9.14197	+	5.27812i	0.357753	+	0.206549i	0.668095	−	0.744076i	$-0.267110\pi$
$653$	9.14197	+	5.27812i	0.357753	+	0.206549i	−0.310342	+	0.950625i	$0.600443\pi$
$654$	−0.396345	−	0.686490i	−0.0154983	−	0.0268439i
$655$		0			0
$656$	−1.11081	+	0.641326i	−0.0433698	+	0.0250396i
$657$	−2.47322	−	4.28374i	−0.0964895	−	0.167125i
$658$	25.7718			1.00469
$659$	−0.191440	−	0.331584i	−0.00745746	−	0.0129167i	0.862273	−	0.506444i	$-0.169040\pi$
$659$	−0.191440	−	0.331584i	−0.00745746	−	0.0129167i	−0.869730	+	0.493528i	$0.835707\pi$
$660$		0			0
$661$	22.5877	+	13.0410i	0.878560	+	0.507237i	0.870183	−	0.492728i	$-0.164000\pi$
$661$	22.5877	+	13.0410i	0.878560	+	0.507237i	0.00837690	+	0.999965i	$0.497334\pi$
$662$			4.46249i			0.173440i
$663$	2.15357	−	4.09264i	0.0836378	−	0.158945i
$664$	17.3887			0.674813
$665$		0			0
$666$	−4.19076	+	7.25861i	−0.162389	+	0.281266i
$667$	−20.8255	+	12.0236i	−0.806368	+	0.465557i
$668$	−6.86227			−0.265509
$669$	−0.0599161	+	0.0345926i	−0.00231649	+	0.00133743i
$670$		0			0
$671$		−	57.9249i		−	2.23617i
$672$	4.44290	−	2.56511i	0.171389	−	0.0989512i
$673$	11.1123	+	6.41571i	0.428349	+	0.247307i	0.698643	−	0.715470i	$-0.253788\pi$
$673$	11.1123	+	6.41571i	0.428349	+	0.247307i	−0.270294	+	0.962778i	$0.587121\pi$
$674$	5.23749	+	3.02387i	0.201741	+	0.116475i
$675$		0			0
$676$	−5.59812	+	11.7329i	−0.215312	+	0.451266i
$677$			22.3408i			0.858626i	0.903156	+	0.429313i	$0.141244\pi$
$677$			22.3408i			0.858626i	−0.903156	+	0.429313i	$0.858756\pi$
$678$		0			0
$679$	−18.3879	+	31.8487i	−0.705661	+	1.22224i
$680$		0			0
$681$			6.19198i			0.237277i
$682$	−17.5930	−	30.4720i	−0.673672	−	1.16683i
$683$	−10.1071	−	17.5060i	−0.386738	−	0.669850i	0.605271	−	0.796020i	$-0.293065\pi$
$683$	−10.1071	−	17.5060i	−0.386738	−	0.669850i	−0.992009	+	0.126170i	$0.959732\pi$
$684$			6.64947i			0.254249i
$685$		0			0
$686$	31.5999	−	54.7327i	1.20649	−	2.08970i
$687$	−8.69283	+	15.0564i	−0.331652	+	0.574438i
$688$		−	4.35800i		−	0.166147i
$689$	−20.1215	−	10.5881i	−0.766569	−	0.403373i
$690$		0			0
$691$	21.3351	+	12.3178i	0.811625	+	0.468592i	0.847520	−	0.530764i	$-0.178095\pi$
$691$	21.3351	+	12.3178i	0.811625	+	0.468592i	−0.0358950	+	0.999356i	$0.511428\pi$
$692$	19.3036	+	11.1449i	0.733812	+	0.423666i
$693$	24.7897	−	14.3123i	0.941682	−	0.543680i
$694$		−	6.34654i		−	0.240911i
$695$		0			0
$696$	3.03479	−	1.75214i	0.115033	−	0.0664146i
$697$	−1.64520			−0.0623163
$698$	−24.4438	+	14.1126i	−0.925210	+	0.534170i
$699$	−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	$0.193474\pi$
$702$	3.04944	−	1.92378i	0.115094	−	0.0726085i
$703$			55.7327i			2.10200i
$704$	−4.83209	−	2.78981i	−0.182116	−	0.105145i
$705$		0			0
$706$	−8.04696	−	13.9378i	−0.302851	−	0.524554i
$707$	−75.2270			−2.82920
$708$	0.759628	+	1.31571i	0.0285486	+	0.0494476i
$709$	−4.05937	+	2.34368i	−0.152453	+	0.0880187i	−0.574286	−	0.818655i	$-0.694720\pi$
$709$	−4.05937	+	2.34368i	−0.152453	+	0.0880187i	0.421833	+	0.906674i	$0.361387\pi$
$710$		0			0
$711$	−5.07423	−	8.78882i	−0.190298	−	0.329606i
$712$	−5.57884	−	3.22094i	−0.209076	−	0.120710i
$713$	−21.6374	+	37.4770i	−0.810325	+	1.40352i
$714$	6.58029			0.246261
$715$		0			0
$716$	1.56889			0.0586324
$717$	8.57433	−	14.8512i	0.320214	−	0.554627i
$718$	7.61833	+	4.39845i	0.284314	+	0.164149i
$719$	−13.6893	−	23.7106i	−0.510526	−	0.884257i	−0.999926	−	0.0121971i	$-0.996117\pi$
$719$	−13.6893	−	23.7106i	−0.510526	−	0.884257i	0.489400	−	0.872060i	$-0.337216\pi$
$720$		0			0
$721$	−17.9906	+	10.3869i	−0.670005	+	0.386827i
$722$	12.6078	+	21.8373i	0.469212	+	0.812699i
$723$	−17.5319			−0.652020
$724$	−5.72094	−	9.90896i	−0.212617	−	0.368264i
$725$		0			0
$726$	−17.4349	−	10.0661i	−0.647071	−	0.373586i
$727$			12.4066i			0.460136i	0.973175	+	0.230068i	$0.0738948\pi$
$727$			12.4066i			0.460136i	−0.973175	+	0.230068i	$0.926105\pi$
$728$	−18.4830	+	0.725036i	−0.685027	+	0.0268716i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	2.79490	−	4.84091i	0.103373	−	0.179047i
$732$	8.99066	−	5.19076i	0.332305	−	0.191856i
$733$	−18.7638			−0.693056			−0.346528	−	0.938040i	$-0.612639\pi$
$733$	−18.7638			−0.693056			−0.346528	+	0.938040i	$0.612639\pi$
$734$	−32.9145	+	19.0032i	−1.21490	+	0.701420i
$735$		0			0
$736$			6.86227i			0.252947i
$737$	−13.8734	+	8.00980i	−0.511033	+	0.295045i
$738$	−1.11081	−	0.641326i	−0.0408895	−	0.0236076i
$739$	−44.5751	−	25.7355i	−1.63972	−	0.946694i	−0.980928	−	0.194370i	$-0.937734\pi$
$739$	−44.5751	−	25.7355i	−1.63972	−	0.946694i	−0.658794	−	0.752324i	$-0.728933\pi$
$740$		0			0
$741$	11.1645	−	21.2169i	0.410136	−	0.779422i
$742$		−	32.3521i		−	1.18768i
$743$	24.7999	−	42.9547i	0.909819	−	1.57585i	0.0955053	−	0.995429i	$-0.469553\pi$
$743$	24.7999	−	42.9547i	0.909819	−	1.57585i	0.814314	−	0.580424i	$-0.197113\pi$
$744$	3.15309	−	5.46131i	0.115598	−	0.200221i
$745$		0			0
$746$			17.0157i			0.622990i
$747$	8.69436	+	15.0591i	0.318110	+	0.550983i
$748$	−3.57836	−	6.19789i	−0.130838	−	0.226617i
$749$			39.8150i			1.45481i
$750$		0			0
$751$	5.15058	−	8.92107i	0.187947	−	0.325535i	−0.756618	−	0.653857i	$-0.773150\pi$
$751$	5.15058	−	8.92107i	0.187947	−	0.325535i	0.944566	+	0.328322i	$0.106483\pi$
$752$	2.51176	−	4.35050i	0.0915946	−	0.158647i
$753$		−	18.2072i		−	0.663506i
$754$	−12.6251	+	0.495247i	−0.459780	+	0.0180358i
$755$		0			0
$756$	4.44290	+	2.56511i	0.161587	+	0.0932921i
$757$	3.83773	+	2.21571i	0.139485	+	0.0805314i	0.568118	−	0.822947i	$-0.307672\pi$
$757$	3.83773	+	2.21571i	0.139485	+	0.0805314i	−0.428634	+	0.903478i	$0.641005\pi$
$758$	11.0257	−	6.36569i	0.400471	−	0.231212i
$759$			38.2888i			1.38980i
$760$		0			0
$761$	9.89888	−	5.71512i	0.358834	−	0.207173i	−0.309735	−	0.950823i	$-0.600240\pi$
$761$	9.89888	−	5.71512i	0.358834	−	0.207173i	0.668569	+	0.743650i	$0.266907\pi$
$762$	16.2530			0.588785
$763$	−3.52184	+	2.03334i	−0.127499	+	0.0736117i
$764$	−4.41092	+	7.63995i	−0.159582	+	0.276404i
$765$		0			0
$766$	22.5718			0.815553
$767$	−0.214711	−	5.47355i	−0.00775277	−	0.197638i
$768$		−	1.00000i		−	0.0360844i
$769$	−8.46766	−	4.88880i	−0.305352	−	0.176295i	0.339493	−	0.940609i	$-0.389745\pi$
$769$	−8.46766	−	4.88880i	−0.305352	−	0.176295i	−0.644844	+	0.764314i	$0.723078\pi$
$770$		0			0
$771$	−8.80056	−	15.2430i	−0.316944	−	0.548964i
$772$	−11.1881			−0.402667
$773$	−3.39593	−	5.88192i	−0.122143	−	0.211558i	0.798470	−	0.602035i	$-0.205643\pi$
$773$	−3.39593	−	5.88192i	−0.122143	−	0.211558i	−0.920613	+	0.390477i	$0.872310\pi$
$774$	3.77414	−	2.17900i	0.135658	−	0.0783225i
$775$		0			0
$776$	3.58423	+	6.20806i	0.128666	+	0.222856i
$777$	37.2383	+	21.4995i	1.33592	+	0.771291i
$778$	1.75214	−	3.03479i	0.0628171	−	0.108802i
$779$	−8.52897			−0.305582
$780$		0			0
$781$	−60.8699			−2.17809
$782$	−4.40095	+	7.62268i	−0.157378	+	0.272586i
$783$	3.03479	+	1.75214i	0.108455	+	0.0626163i
$784$	−9.65957	−	16.7309i	−0.344985	−	0.597531i
$785$		0			0
$786$	−6.10206	+	3.52302i	−0.217653	+	0.125662i
$787$	−2.50713	−	4.34247i	−0.0893694	−	0.154792i	0.817875	−	0.575395i	$-0.195152\pi$
$787$	−2.50713	−	4.34247i	−0.0893694	−	0.154792i	−0.907245	+	0.420603i	$0.861818\pi$
$788$	22.9351			0.817029
$789$	5.88051	+	10.1853i	0.209352	+	0.362608i
$790$		0			0
$791$		0			0
$792$		−	5.57962i		−	0.198263i
$793$	−37.4024	+	1.46718i	−1.32820	+	0.0521012i
$794$	−29.8652			−1.05988
$795$		0			0
$796$	−5.52892	+	9.57637i	−0.195967	+	0.339425i
$797$	8.59714	−	4.96356i	0.304526	−	0.175818i	−0.339948	−	0.940444i	$-0.610410\pi$
$797$	8.59714	−	4.96356i	0.304526	−	0.175818i	0.644474	+	0.764626i	$0.277076\pi$
$798$	34.1133			1.20760
$799$	5.58019	−	3.22172i	0.197413	−	0.113976i
$800$		0			0
$801$		−	6.44188i		−	0.227613i
$802$	21.7592	−	12.5627i	0.768345	−	0.443604i
$803$	23.9016	+	13.7996i	0.843470	+	0.486978i
$804$	−2.48644	−	1.43555i	−0.0876900	−	0.0506278i
$805$		0			0
$806$	−19.2303	+	12.1317i	−0.677358	+	0.427322i
$807$		−	6.40981i		−	0.225636i
$808$	−7.33175	+	12.6990i	−0.257930	+	0.446748i
$809$	4.98796	−	8.63940i	0.175367	−	0.303745i	−0.764921	−	0.644124i	$-0.777222\pi$
$809$	4.98796	−	8.63940i	0.175367	−	0.303745i	0.940288	+	0.340379i	$0.110555\pi$
$810$		0			0
$811$		−	4.85013i		−	0.170311i	−0.996368	−	0.0851555i	$-0.972861\pi$
$811$		−	4.85013i		−	0.170311i	0.996368	−	0.0851555i	$-0.0271387\pi$
$812$	−8.98884	−	15.5691i	−0.315447	−	0.546369i
$813$	7.90503	+	13.6919i	0.277242	+	0.480196i
$814$		−	46.7657i		−	1.63914i
$815$		0			0
$816$	0.641326	−	1.11081i	0.0224509	−	0.0388861i
$817$	14.4892	−	25.0960i	0.506913	−	0.877998i
$818$		−	5.24767i		−	0.183480i
$819$	−9.86942	−	15.6443i	−0.344866	−	0.546655i
$820$		0			0
$821$	21.9722	+	12.6857i	0.766836	+	0.442733i	0.831745	−	0.555158i	$-0.187342\pi$
$821$	21.9722	+	12.6857i	0.766836	+	0.442733i	−0.0649085	+	0.997891i	$0.520676\pi$
$822$	0.769058	+	0.444016i	0.0268240	+	0.0154868i
$823$	22.9557	−	13.2535i	0.800184	−	0.461986i	−0.0433515	−	0.999060i	$-0.513804\pi$
$823$	22.9557	−	13.2535i	0.800184	−	0.461986i	0.843536	+	0.537073i	$0.180470\pi$
$824$			4.04929i			0.141064i
$825$		0			0
$826$	6.74990	−	3.89706i	0.234859	−	0.135596i
$827$	−21.7678			−0.756941			−0.378470	−	0.925613i	$-0.623550\pi$
$827$	−21.7678			−0.756941			−0.378470	+	0.925613i	$0.623550\pi$
$828$	−5.94290	+	3.43113i	−0.206530	+	0.119240i
$829$	−1.09376	+	1.89444i	−0.0379878	+	0.0657968i	−0.884394	−	0.466741i	$-0.845428\pi$
$829$	−1.09376	+	1.89444i	−0.0379878	+	0.0657968i	0.846406	+	0.532537i	$0.178761\pi$
$830$		0			0
$831$	−4.98637			−0.172975
$832$	−1.67900	+	3.19076i	−0.0582088	+	0.110620i
$833$		−	24.7797i		−	0.858567i
$834$	−0.461208	−	0.266279i	−0.0159703	−	0.00922047i
$835$		0			0
$836$	−18.5508	−	32.1309i	−0.641591	−	1.11127i
$837$	6.30618			0.217974
$838$	−9.01326	−	15.6114i	−0.311358	−	0.539288i
$839$	−21.7825	+	12.5761i	−0.752016	+	0.434177i	−0.826422	−	0.563051i	$-0.809627\pi$
$839$	−21.7825	+	12.5761i	−0.752016	+	0.434177i	0.0744057	+	0.997228i	$0.476294\pi$
$840$		0			0
$841$	8.36004	+	14.4800i	0.288277	+	0.499311i
$842$	6.86213	+	3.96185i	0.236485	+	0.136534i
$843$	0.257863	−	0.446632i	0.00888127	−	0.0153828i
$844$	26.8342			0.923671
$845$		0			0
$846$	5.02353			0.172712
$847$	−51.6411	+	89.4449i	−1.77441	+	3.07336i
$848$	−5.46131	−	3.15309i	−0.187542	−	0.108278i
$849$	8.97308	+	15.5418i	0.307955	+	0.533394i
$850$		0			0
$851$	−49.8106	+	28.7581i	−1.70748	+	0.985816i
$852$	−5.45466	−	9.44775i	−0.186874	−	0.323675i
$853$	36.1721			1.23851			0.619255	−	0.785190i	$-0.287435\pi$
$853$	36.1721			1.23851			0.619255	+	0.785190i	$0.287435\pi$
$854$	−26.6297	−	46.1241i	−0.911251	−	1.57833i
$855$		0			0
$856$	6.72112	+	3.88044i	0.229723	+	0.132631i
$857$		−	18.5471i		−	0.633556i	−0.948500	−	0.316778i	$-0.897399\pi$
$857$		−	18.5471i		−	0.633556i	0.948500	−	0.316778i	$-0.102601\pi$
$858$	−9.36816	+	17.8032i	−0.319824	+	0.607792i
$859$	21.5386			0.734887			0.367443	−	0.930046i	$-0.380233\pi$
$859$	21.5386			0.734887			0.367443	+	0.930046i	$0.380233\pi$
$860$		0			0
$861$	−3.29014	+	5.69870i	−0.112128	+	0.194211i
$862$	−33.1752	+	19.1537i	−1.12995	+	0.652379i
$863$	32.1136			1.09316			0.546580	−	0.837407i	$-0.315930\pi$
$863$	32.1136			1.09316			0.546580	+	0.837407i	$0.315930\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$		0			0
$866$			20.0052i			0.679803i
$867$	−13.2976	+	7.67740i	−0.451612	+	0.260738i
$868$	−28.0177	−	16.1760i	−0.950984	−	0.549051i
$869$	49.0382	+	28.3122i	1.66351	+	0.960427i
$870$		0			0
$871$	5.52336	+	8.75522i	0.187152	+	0.296659i
$872$			0.792690i			0.0268439i
$873$	−3.58423	+	6.20806i	−0.121308	+	0.210111i
$874$	−22.8152	+	39.5172i	−0.771737	+	1.33669i
$875$		0			0
$876$			4.94644i			0.167125i
$877$	−16.0319	−	27.7681i	−0.541360	−	0.937664i	−0.998826	−	0.0484365i	$-0.984576\pi$
$877$	−16.0319	−	27.7681i	−0.541360	−	0.937664i	0.457466	−	0.889227i	$-0.348757\pi$
$878$	−5.96660	−	10.3345i	−0.201363	−	0.348771i
$879$			17.2711i			0.582538i
$880$		0			0
$881$	9.47244	−	16.4067i	0.319135	−	0.552757i	−0.661173	−	0.750233i	$-0.729941\pi$
$881$	9.47244	−	16.4067i	0.319135	−	0.552757i	0.980308	+	0.197476i	$0.0632745\pi$
$882$	9.65957	−	16.7309i	0.325255	−	0.563357i
$883$		−	38.0685i		−	1.28111i	−0.767914	−	0.640554i	$-0.778705\pi$
$883$		−	38.0685i		−	1.28111i	0.767914	−	0.640554i	$-0.221295\pi$
$884$	−3.91137	+	2.46755i	−0.131554	+	0.0829925i
$885$		0			0
$886$	−22.5656	−	13.0282i	−0.758105	−	0.437692i
$887$	−11.6986	−	6.75421i	−0.392802	−	0.226784i	0.290572	−	0.956853i	$-0.406155\pi$
$887$	−11.6986	−	6.75421i	−0.392802	−	0.226784i	−0.683373	+	0.730069i	$0.739488\pi$
$888$	7.25861	−	4.19076i	0.243583	−	0.140633i
$889$		−	83.3815i		−	2.79653i
$890$		0			0
$891$	4.83209	−	2.78981i	0.161881	−	0.0934621i
$892$	0.0691851			0.00231649
$893$	28.9286	−	16.7019i	0.968058	−	0.558908i
$894$	10.3988	−	18.0113i	0.347789	−	0.602388i
$895$		0			0
$896$	−5.13022			−0.171389
$897$	24.7232	−	0.969820i	0.825485	−	0.0323814i
$898$			16.7392i			0.558594i
$899$	−19.1379	−	11.0493i	−0.638286	−	0.368515i
$900$		0			0
$901$	−4.04432	−	7.00497i	−0.134736	−	0.233369i
$902$	7.15671			0.238292
$903$	−11.1787	−	19.3621i	−0.372005	−	0.644332i
$904$		0			0
$905$		0			0
$906$	1.07700	+	1.86541i	0.0357808	+	0.0619742i
$907$	−9.41300	−	5.43460i	−0.312554	−	0.180453i	0.335515	−	0.942035i	$-0.391090\pi$
$907$	−9.41300	−	5.43460i	−0.312554	−	0.180453i	−0.648069	+	0.761582i	$0.724423\pi$
$908$	3.09599	−	5.36241i	0.102744	−	0.177958i
$909$	−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	$0.451257\pi$
$912$	3.32474	−	5.75861i	0.110093	−	0.190687i
$913$	−84.0238	−	48.5112i	−2.78078	−	1.60549i
$914$	3.55432	+	6.15626i	0.117566	+	0.203631i
$915$		0			0
$916$	15.0564	−	8.69283i	0.497478	−	0.287219i
$917$	18.0739	+	31.3049i	0.596852	+	1.03378i
$918$	1.28265			0.0423339
$919$	0.0963564	+	0.166894i	0.00317850	+	0.00550533i	0.867610	−	0.497245i	$-0.165655\pi$
$919$	0.0963564	+	0.166894i	0.00317850	+	0.00550533i	−0.864432	+	0.502750i	$0.832322\pi$
$920$		0			0
$921$	12.3559	+	7.13366i	0.407140	+	0.235062i
$922$		−	5.51635i		−	0.181671i
$923$	1.54178	+	39.3039i	0.0507482	+	1.29370i
$924$	−28.6246			−0.941682
$925$		0			0
$926$	2.49379	−	4.31938i	0.0819511	−	0.141943i
$927$	−3.50679	+	2.02465i	−0.115178	+	0.0664981i
$928$	−3.50427			−0.115033
$929$	10.3702	−	5.98725i	0.340236	−	0.196435i	−0.320140	−	0.947370i	$-0.603730\pi$
$929$	10.3702	−	5.98725i	0.340236	−	0.196435i	0.660376	+	0.750935i	$0.270397\pi$
$930$		0			0
$931$		−	128.462i		−	4.21018i
$932$	15.3907	−	8.88580i	0.504138	−	0.291064i
$933$	−20.0473	−	11.5743i	−0.656320	−	0.378927i
$934$	−17.0962	−	9.87051i	−0.559406	−	0.322973i
$935$		0			0
$936$	−3.60278	+	0.141326i	−0.117761	+	0.00461940i
$937$		−	32.1031i		−	1.04876i	−0.851484	−	0.524381i	$-0.824297\pi$
$937$		−	32.1031i		−	1.04876i	0.851484	−	0.524381i	$-0.175703\pi$
$938$	−7.36467	+	12.7560i	−0.240465	+	0.416498i
$939$	−7.05609	+	12.2215i	−0.230267	+	0.398834i
$940$		0			0
$941$		−	6.36756i		−	0.207577i	−0.994599	−	0.103788i	$-0.966904\pi$
$941$		−	6.36756i		−	0.207577i	0.994599	−	0.103788i	$-0.0330964\pi$
$942$	−3.85118	−	6.67044i	−0.125478	−	0.217335i
$943$	−4.40095	−	7.62268i	−0.143315	−	0.248229i
$944$		−	1.51926i		−	0.0494476i
$945$		0			0
$946$	−12.1580	+	21.0582i	−0.395290	+	0.684662i
$947$	29.5983	−	51.2658i	0.961816	−	1.66591i	0.243881	−	0.969805i	$-0.421579\pi$
$947$	29.5983	−	51.2658i	0.961816	−	1.66591i	0.717936	−	0.696110i	$-0.245087\pi$
$948$			10.1485i			0.329606i
$949$	8.30506	−	15.7829i	0.269594	−	0.512335i
$950$		0			0
$951$	10.5494	+	6.09070i	0.342088	+	0.197505i
$952$	−5.69870	−	3.29014i	−0.184696	−	0.106634i
$953$	−12.9852	+	7.49699i	−0.420631	+	0.242851i	−0.695347	−	0.718674i	$-0.744749\pi$
$953$	−12.9852	+	7.49699i	−0.420631	+	0.242851i	0.274716	+	0.961525i	$0.411416\pi$
$954$		−	6.30618i		−	0.204170i
$955$		0			0
$956$	−14.8512	+	8.57433i	−0.480321	+	0.277314i
$957$	−19.5525			−0.632042
$958$	−7.46188	+	4.30812i	−0.241083	+	0.139189i
$959$	2.27790	−	3.94544i	0.0735572	−	0.127405i
$960$		0			0
$961$	−8.76794			−0.282837
$962$	−30.1968	+	1.18453i	−0.973584	+	0.0381908i
$963$			7.76088i			0.250091i
$964$	15.1831	+	8.76597i	0.489015	+	0.282333i
$965$		0			0
$966$	17.6025	+	30.4884i	0.566350	+	0.980947i
$967$	−43.4352			−1.39678			−0.698390	−	0.715717i	$-0.746100\pi$
$967$	−43.4352			−1.39678			−0.698390	+	0.715717i	$0.746100\pi$
$968$	10.0661	+	17.4349i	0.323535	+	0.560380i
$969$	7.38630	−	4.26448i	0.237282	−	0.136995i
$970$		0			0
$971$	−24.4673	−	42.3786i	−0.785192	−	1.35999i	−0.928884	−	0.370370i	$-0.879231\pi$
$971$	−24.4673	−	42.3786i	−0.785192	−	1.35999i	0.143692	−	0.989622i	$-0.454103\pi$
$972$	0.866025	+	0.500000i	0.0277778	+	0.0160375i
$973$	−1.36607	+	2.36610i	−0.0437941	+	0.0758536i
$974$	19.6205			0.628682
$975$		0			0
$976$	−10.3815			−0.332305
$977$	−26.7331	+	46.3031i	−0.855267	+	1.48137i	0.0211299	+	0.999777i	$0.493274\pi$
$977$	−26.7331	+	46.3031i	−0.855267	+	1.48137i	−0.876397	+	0.481589i	$0.840060\pi$
$978$	−0.382683	−	0.220942i	−0.0122369	−	0.00706496i
$979$	17.9716	+	31.1278i	0.574375	+	0.994848i
$980$		0			0
$981$	−0.686490	+	0.396345i	−0.0219179	+	0.0126543i
$982$	−19.8921	−	34.4541i	−0.634782	−	1.09948i
$983$	26.5785			0.847723			0.423862	−	0.905727i	$-0.360674\pi$
$983$	26.5785			0.847723			0.423862	+	0.905727i	$0.360674\pi$
$984$	0.641326	+	1.11081i	0.0204447	+	0.0354113i
$985$		0			0
$986$	−3.89258	−	2.24738i	−0.123965	−	0.0715713i
$987$		−	25.7718i		−	0.820325i
$988$	−20.2771	+	12.7921i	−0.645102	+	0.406972i
$989$	29.9057			0.950947
$990$		0			0
$991$	18.1688	−	31.4693i	0.577152	−	0.999657i	−0.418652	−	0.908147i	$-0.637497\pi$
$991$	18.1688	−	31.4693i	0.577152	−	0.999657i	0.995804	−	0.0915100i	$-0.0291694\pi$
$992$	−5.46131	+	3.15309i	−0.173397	+	0.100111i
$993$	4.46249			0.141613
$994$	−48.4690	+	27.9836i	−1.53734	+	0.887586i
$995$		0			0
$996$		−	17.3887i		−	0.550983i
$997$	−26.3716	+	15.2257i	−0.835198	+	0.482202i	−0.855629	−	0.517590i	$-0.826829\pi$
$997$	−26.3716	+	15.2257i	−0.835198	+	0.482202i	0.0204312	+	0.999791i	$0.493496\pi$
$998$	6.79035	+	3.92041i	0.214945	+	0.124098i
$999$	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.y.m.199.6		12
5.2	odd	4		1950.2.bc.k.901.1	yes	12
5.3	odd	4		1950.2.bc.h.901.6	yes	12
5.4	even	2		1950.2.y.n.199.1		12
13.10	even	6		1950.2.y.n.49.1		12
65.23	odd	12		1950.2.bc.h.751.6	✓	12
65.49	even	6	inner	1950.2.y.m.49.6		12
65.62	odd	12		1950.2.bc.k.751.1	yes	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.y.m.49.6		12	65.49	even	6	inner
1950.2.y.m.199.6		12	1.1	even	1	trivial
1950.2.y.n.49.1		12	13.10	even	6
1950.2.y.n.199.1		12	5.4	even	2
1950.2.bc.h.751.6	✓	12	65.23	odd	12
1950.2.bc.h.901.6	yes	12	5.3	odd	4
1950.2.bc.k.751.1	yes	12	65.62	odd	12
1950.2.bc.k.901.1	yes	12	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1950.y (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(2.56511 + 4.44290i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(2.56511 + 4.44290i) q^{7} +1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-4.83209 - 2.78981i) q^{11} -1.00000i q^{12} +(-1.67900 + 3.19076i) q^{13} -5.13022 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-1.11081 + 0.641326i) q^{17} -1.00000 q^{18} +(-5.75861 + 3.32474i) q^{19} +5.13022i q^{21} +(4.83209 - 2.78981i) q^{22} +(-5.94290 - 3.43113i) q^{23} +(0.866025 + 0.500000i) q^{24} +(-1.92378 - 3.04944i) q^{26} +1.00000i q^{27} +(2.56511 - 4.44290i) q^{28} +(1.75214 - 3.03479i) q^{29} -6.30618i q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.78981 - 4.83209i) q^{33} -1.28265i q^{34} +(0.500000 - 0.866025i) q^{36} +(4.19076 - 7.25861i) q^{37} -6.64947i q^{38} +(-3.04944 + 1.92378i) q^{39} +(1.11081 + 0.641326i) q^{41} +(-4.44290 - 2.56511i) q^{42} +(-3.77414 + 2.17900i) q^{43} +5.57962i q^{44} +(5.94290 - 3.43113i) q^{46} -5.02353 q^{47} +(-0.866025 + 0.500000i) q^{48} +(-9.65957 + 16.7309i) q^{49} -1.28265 q^{51} +(3.60278 - 0.141326i) q^{52} +6.30618i q^{53} +(-0.866025 - 0.500000i) q^{54} +(2.56511 + 4.44290i) q^{56} -6.64947 q^{57} +(1.75214 + 3.03479i) q^{58} +(-1.31571 + 0.759628i) q^{59} +(5.19076 + 8.99066i) q^{61} +(5.46131 + 3.15309i) q^{62} +(-2.56511 + 4.44290i) q^{63} +1.00000 q^{64} +5.57962 q^{66} +(1.43555 - 2.48644i) q^{67} +(1.11081 + 0.641326i) q^{68} +(-3.43113 - 5.94290i) q^{69} +(9.44775 - 5.45466i) q^{71} +(0.500000 + 0.866025i) q^{72} -4.94644 q^{73} +(4.19076 + 7.25861i) q^{74} +(5.75861 + 3.32474i) q^{76} -28.6246i q^{77} +(-0.141326 - 3.60278i) q^{78} -10.1485 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-1.11081 + 0.641326i) q^{82} +17.3887 q^{83} +(4.44290 - 2.56511i) q^{84} -4.35800i q^{86} +(3.03479 - 1.75214i) q^{87} +(-4.83209 - 2.78981i) q^{88} +(-5.57884 - 3.22094i) q^{89} +(-18.4830 + 0.725036i) q^{91} +6.86227i q^{92} +(3.15309 - 5.46131i) q^{93} +(2.51176 - 4.35050i) q^{94} -1.00000i q^{96} +(3.58423 + 6.20806i) q^{97} +(-9.65957 - 16.7309i) q^{98} -5.57962i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{2} - 6 q^{4} + 4 q^{7} + 12 q^{8} + 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^2 - 6 * q^4 + 4 * q^7 + 12 * q^8 + 6 * q^9	\( 12 q - 6 q^{2} - 6 q^{4} + 4 q^{7} + 12 q^{8} + 6 q^{9} - 12 q^{11} - 4 q^{13} - 8 q^{14} - 6 q^{16} - 12 q^{18} + 6 q^{19} + 12 q^{22} - 12 q^{23} - 4 q^{26} + 4 q^{28} - 6 q^{32} - 4 q^{33} + 6 q^{36} + 12 q^{37} - 6 q^{39} + 6 q^{42} - 12 q^{43} + 12 q^{46} - 16 q^{47} - 32 q^{49} + 8 q^{52} + 4 q^{56} - 24 q^{57} + 24 q^{61} - 4 q^{63} + 12 q^{64} + 8 q^{66} - 24 q^{67} - 4 q^{69} + 12 q^{71} + 6 q^{72} + 40 q^{73} + 12 q^{74} - 6 q^{76} + 6 q^{78} - 52 q^{79} - 6 q^{81} - 32 q^{83} - 6 q^{84} - 12 q^{88} - 24 q^{89} - 54 q^{91} + 8 q^{93} + 8 q^{94} - 24 q^{97} - 32 q^{98}+O(q^{100}) \) 12 * q - 6 * q^2 - 6 * q^4 + 4 * q^7 + 12 * q^8 + 6 * q^9 - 12 * q^11 - 4 * q^13 - 8 * q^14 - 6 * q^16 - 12 * q^18 + 6 * q^19 + 12 * q^22 - 12 * q^23 - 4 * q^26 + 4 * q^28 - 6 * q^32 - 4 * q^33 + 6 * q^36 + 12 * q^37 - 6 * q^39 + 6 * q^42 - 12 * q^43 + 12 * q^46 - 16 * q^47 - 32 * q^49 + 8 * q^52 + 4 * q^56 - 24 * q^57 + 24 * q^61 - 4 * q^63 + 12 * q^64 + 8 * q^66 - 24 * q^67 - 4 * q^69 + 12 * q^71 + 6 * q^72 + 40 * q^73 + 12 * q^74 - 6 * q^76 + 6 * q^78 - 52 * q^79 - 6 * q^81 - 32 * q^83 - 6 * q^84 - 12 * q^88 - 24 * q^89 - 54 * q^91 + 8 * q^93 + 8 * q^94 - 24 * q^97 - 32 * q^98

Introduction

L-functions

Modular forms

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Database

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