LMFDB - Embedded newform 1950.2.bc.j.751.6

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} - 2 x^{11} - 8 x^{10} + 34 x^{9} + 8 x^{8} - 134 x^{7} + 98 x^{6} + 154 x^{5} + 104 x^{4} + \cdots + 2197 $ x^12 - 2x^11 - 8x^10 + 34x^9 + 8x^8 - 134x^7 + 98x^6 + 154x^5 + 104x^4 + 190x^3 - 1196x^2 - 338*x + 2197
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 390)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.6
Root			$1.75374 - 1.62986i$ of defining polynomial
Character	$\chi$	$=$	1950.751
Dual form			1950.2.bc.j.901.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(1.32301 + 0.763837i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(1.32301 + 0.763837i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.14057 + 0.658509i) q^{11} +1.00000 q^{12} +(-2.67975 + 2.41225i) q^{13} +1.52767 q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.784645 - 1.35904i) q^{17} +1.00000i q^{18} +(4.18063 + 2.41369i) q^{19} +1.52767i q^{21} +(-0.658509 + 1.14057i) q^{22} +(4.22143 + 7.31172i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-1.11461 + 3.42894i) q^{26} -1.00000 q^{27} +(1.32301 - 0.763837i) q^{28} +(2.21438 + 3.83543i) q^{29} -1.62745i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.14057 - 0.658509i) q^{33} -1.56929i q^{34} +(0.500000 + 0.866025i) q^{36} +(2.42743 - 1.40148i) q^{37} +4.82738 q^{38} +(-3.42894 - 1.11461i) q^{39} +(1.35904 - 0.784645i) q^{41} +(0.763837 + 1.32301i) q^{42} +(-2.64430 + 4.58006i) q^{43} +1.31702i q^{44} +(7.31172 + 4.22143i) q^{46} +4.94552i q^{47} +(0.500000 - 0.866025i) q^{48} +(-2.33310 - 4.04106i) q^{49} +1.56929 q^{51} +(0.749192 + 3.52686i) q^{52} +13.9161 q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.763837 - 1.32301i) q^{56} +4.82738i q^{57} +(3.83543 + 2.21438i) q^{58} +(9.07005 + 5.23660i) q^{59} +(2.49134 - 4.31513i) q^{61} +(-0.813725 - 1.40941i) q^{62} +(-1.32301 + 0.763837i) q^{63} -1.00000 q^{64} -1.31702 q^{66} +(-2.40112 + 1.38628i) q^{67} +(-0.784645 - 1.35904i) q^{68} +(-4.22143 + 7.31172i) q^{69} +(-12.8513 - 7.41968i) q^{71} +(0.866025 + 0.500000i) q^{72} -5.98944i q^{73} +(1.40148 - 2.42743i) q^{74} +(4.18063 - 2.41369i) q^{76} -2.01198 q^{77} +(-3.52686 + 0.749192i) q^{78} -4.87632 q^{79} +(-0.500000 - 0.866025i) q^{81} +(0.784645 - 1.35904i) q^{82} +6.39020i q^{83} +(1.32301 + 0.763837i) q^{84} +5.28860i q^{86} +(-2.21438 + 3.83543i) q^{87} +(0.658509 + 1.14057i) q^{88} +(-15.9738 + 9.22251i) q^{89} +(-5.38789 + 1.14452i) q^{91} +8.44285 q^{92} +(1.40941 - 0.813725i) q^{93} +(2.47276 + 4.28295i) q^{94} -1.00000i q^{96} +(1.66801 + 0.963028i) q^{97} +(-4.04106 - 2.33310i) q^{98} -1.31702i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{3} + 6 q^{4} - 12 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^3 + 6 * q^4 - 12 * q^7 - 6 * q^9	$ 12 q + 6 q^{3} + 6 q^{4} - 12 q^{7} - 6 q^{9} + 6 q^{11} + 12 q^{12} + 4 q^{13} - 4 q^{14} - 6 q^{16} + 8 q^{17} + 6 q^{19} - 6 q^{22} + 16 q^{23} - 2 q^{26} - 12 q^{27} - 12 q^{28} - 14 q^{29} + 6 q^{33} + 6 q^{36} - 6 q^{37} - 8 q^{38} + 2 q^{39} - 18 q^{41} - 2 q^{42} + 10 q^{43} - 6 q^{46} + 6 q^{48} - 8 q^{49} + 16 q^{51} + 2 q^{52} - 2 q^{56} + 6 q^{58} + 36 q^{59} + 10 q^{61} + 16 q^{62} + 12 q^{63} - 12 q^{64} - 12 q^{66} + 24 q^{67} - 8 q^{68} - 16 q^{69} - 12 q^{71} + 12 q^{74} + 6 q^{76} + 24 q^{77} - 10 q^{78} - 4 q^{79} - 6 q^{81} + 8 q^{82} - 12 q^{84} + 14 q^{87} + 6 q^{88} - 18 q^{89} + 2 q^{91} + 32 q^{92} - 6 q^{93} + 8 q^{94} - 24 q^{97} + 24 q^{98}+O(q^{100}) $ 12 * q + 6 * q^3 + 6 * q^4 - 12 * q^7 - 6 * q^9 + 6 * q^11 + 12 * q^12 + 4 * q^13 - 4 * q^14 - 6 * q^16 + 8 * q^17 + 6 * q^19 - 6 * q^22 + 16 * q^23 - 2 * q^26 - 12 * q^27 - 12 * q^28 - 14 * q^29 + 6 * q^33 + 6 * q^36 - 6 * q^37 - 8 * q^38 + 2 * q^39 - 18 * q^41 - 2 * q^42 + 10 * q^43 - 6 * q^46 + 6 * q^48 - 8 * q^49 + 16 * q^51 + 2 * q^52 - 2 * q^56 + 6 * q^58 + 36 * q^59 + 10 * q^61 + 16 * q^62 + 12 * q^63 - 12 * q^64 - 12 * q^66 + 24 * q^67 - 8 * q^68 - 16 * q^69 - 12 * q^71 + 12 * q^74 + 6 * q^76 + 24 * q^77 - 10 * q^78 - 4 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^84 + 14 * q^87 + 6 * q^88 - 18 * q^89 + 2 * q^91 + 32 * q^92 - 6 * q^93 + 8 * q^94 - 24 * q^97 + 24 * 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
$7$	1.32301	+	0.763837i	0.500049	+	0.288703i	0.728734	−	0.684797i	$-0.240109\pi$
$7$	1.32301	+	0.763837i	0.500049	+	0.288703i	−0.228685	+	0.973501i	$0.573443\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−1.14057	+	0.658509i	−0.343895	+	0.198548i	−0.661993	−	0.749510i	$-0.730289\pi$
$11$	−1.14057	+	0.658509i	−0.343895	+	0.198548i	0.318098	+	0.948058i	$0.396956\pi$
$12$	1.00000			0.288675
$13$	−2.67975	+	2.41225i	−0.743229	+	0.669037i
$13$	−2.67975	+	2.41225i	−0.743229	+	0.669037i
$14$	1.52767			0.408288
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	0.784645	−	1.35904i	0.190304	−	0.329617i	−0.755047	−	0.655671i	$-0.772386\pi$
$17$	0.784645	−	1.35904i	0.190304	−	0.329617i	0.945351	+	0.326054i	$0.105719\pi$
$18$			1.00000i			0.235702i
$19$	4.18063	+	2.41369i	0.959103	+	0.553738i	0.895897	−	0.444262i	$-0.146534\pi$
$19$	4.18063	+	2.41369i	0.959103	+	0.553738i	0.0632058	+	0.998001i	$0.479868\pi$
$20$		0			0
$21$			1.52767i			0.333366i
$22$	−0.658509	+	1.14057i	−0.140395	+	0.243171i
$23$	4.22143	+	7.31172i	0.880228	+	1.52460i	0.851087	+	0.525025i	$0.175944\pi$
$23$	4.22143	+	7.31172i	0.880228	+	1.52460i	0.0291412	+	0.999575i	$0.490723\pi$
$24$	0.866025	−	0.500000i	0.176777	−	0.102062i
$25$		0			0
$26$	−1.11461	+	3.42894i	−0.218593	+	0.672471i
$27$	−1.00000			−0.192450
$28$	1.32301	−	0.763837i	0.250025	−	0.144352i
$29$	2.21438	+	3.83543i	0.411201	+	0.712221i	0.995021	−	0.0996620i	$-0.0317762\pi$
$29$	2.21438	+	3.83543i	0.411201	+	0.712221i	−0.583821	+	0.811883i	$0.698443\pi$
$30$		0			0
$31$		−	1.62745i		−	0.292299i	−0.989263	−	0.146149i	$-0.953312\pi$
$31$		−	1.62745i		−	0.292299i	0.989263	−	0.146149i	$-0.0466880\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	−1.14057	−	0.658509i	−0.198548	−	0.114632i
$34$		−	1.56929i		−	0.269131i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	2.42743	−	1.40148i	0.399067	−	0.230402i	−0.287014	−	0.957926i	$-0.592663\pi$
$37$	2.42743	−	1.40148i	0.399067	−	0.230402i	0.686081	+	0.727525i	$0.259329\pi$
$38$	4.82738			0.783104
$39$	−3.42894	−	1.11461i	−0.549070	−	0.178480i
$40$		0			0
$41$	1.35904	−	0.784645i	0.212247	−	0.122541i	−0.390108	−	0.920769i	$-0.627562\pi$
$41$	1.35904	−	0.784645i	0.212247	−	0.122541i	0.602355	+	0.798228i	$0.294229\pi$
$42$	0.763837	+	1.32301i	0.117863	+	0.204144i
$43$	−2.64430	+	4.58006i	−0.403252	+	0.698452i	−0.994116	−	0.108318i	$-0.965453\pi$
$43$	−2.64430	+	4.58006i	−0.403252	+	0.698452i	0.590865	+	0.806771i	$0.298787\pi$
$44$			1.31702i			0.198548i
$45$		0			0
$46$	7.31172	+	4.22143i	1.07805	+	0.622415i
$47$			4.94552i			0.721378i	0.932686	+	0.360689i	$0.117458\pi$
$47$			4.94552i			0.721378i	−0.932686	+	0.360689i	$0.882542\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−2.33310	−	4.04106i	−0.333301	−	0.577294i
$50$		0			0
$51$	1.56929			0.219744
$52$	0.749192	+	3.52686i	0.103894	+	0.489087i
$53$	13.9161			1.91152			0.955760	−	0.294148i	$-0.0950359\pi$
$53$	13.9161			1.91152			0.955760	+	0.294148i	$0.0950359\pi$
$54$	−0.866025	+	0.500000i	−0.117851	+	0.0680414i
$55$		0			0
$56$	0.763837	−	1.32301i	0.102072	−	0.176794i
$57$			4.82738i			0.639402i
$58$	3.83543	+	2.21438i	0.503616	+	0.290763i
$59$	9.07005	+	5.23660i	1.18082	+	0.681747i	0.956204	−	0.292700i	$-0.0945539\pi$
$59$	9.07005	+	5.23660i	1.18082	+	0.681747i	0.224616	+	0.974447i	$0.427887\pi$
$60$		0			0
$61$	2.49134	−	4.31513i	0.318984	−	0.552496i	−0.661293	−	0.750128i	$-0.729992\pi$
$61$	2.49134	−	4.31513i	0.318984	−	0.552496i	0.980276	+	0.197632i	$0.0633252\pi$
$62$	−0.813725	−	1.40941i	−0.103343	−	0.178996i
$63$	−1.32301	+	0.763837i	−0.166683	+	0.0962345i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	−1.31702			−0.162114
$67$	−2.40112	+	1.38628i	−0.293343	+	0.169362i	−0.639448	−	0.768834i	$-0.720837\pi$
$67$	−2.40112	+	1.38628i	−0.293343	+	0.169362i	0.346105	+	0.938196i	$0.387504\pi$
$68$	−0.784645	−	1.35904i	−0.0951521	−	0.164808i
$69$	−4.22143	+	7.31172i	−0.508200	+	0.880228i
$70$		0			0
$71$	−12.8513	−	7.41968i	−1.52516	−	0.880554i	−0.999555	−	0.0298269i	$-0.990504\pi$
$71$	−12.8513	−	7.41968i	−1.52516	−	0.880554i	−0.525608	−	0.850727i	$-0.676162\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$		−	5.98944i		−	0.701011i	−0.936561	−	0.350505i	$-0.886010\pi$
$73$		−	5.98944i		−	0.701011i	0.936561	−	0.350505i	$-0.113990\pi$
$74$	1.40148	−	2.42743i	0.162919	−	0.282183i
$75$		0			0
$76$	4.18063	−	2.41369i	0.479551	−	0.276869i
$77$	−2.01198			−0.229286
$78$	−3.52686	+	0.749192i	−0.399338	+	0.0848293i
$79$	−4.87632			−0.548629			−0.274315	−	0.961640i	$-0.588451\pi$
$79$	−4.87632			−0.548629			−0.274315	+	0.961640i	$0.588451\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.784645	−	1.35904i	0.0866495	−	0.150081i
$83$			6.39020i			0.701416i	0.936485	+	0.350708i	$0.114059\pi$
$83$			6.39020i			0.701416i	−0.936485	+	0.350708i	$0.885941\pi$
$84$	1.32301	+	0.763837i	0.144352	+	0.0833415i
$85$		0			0
$86$			5.28860i			0.570284i
$87$	−2.21438	+	3.83543i	−0.237407	+	0.411201i
$88$	0.658509	+	1.14057i	0.0701973	+	0.121585i
$89$	−15.9738	+	9.22251i	−1.69322	+	0.977584i	−0.741338	+	0.671131i	$0.765809\pi$
$89$	−15.9738	+	9.22251i	−1.69322	+	0.977584i	−0.951886	+	0.306452i	$0.900858\pi$
$90$		0			0
$91$	−5.38789	+	1.14452i	−0.564804	+	0.119978i
$92$	8.44285			0.880228
$93$	1.40941	−	0.813725i	0.146149	−	0.0843794i
$94$	2.47276	+	4.28295i	0.255046	+	0.441752i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	1.66801	+	0.963028i	0.169361	+	0.0977807i	0.582285	−	0.812985i	$-0.302159\pi$
$97$	1.66801	+	0.963028i	0.169361	+	0.0977807i	−0.412923	+	0.910766i	$0.635492\pi$
$98$	−4.04106	−	2.33310i	−0.408208	−	0.235679i
$99$		−	1.31702i		−	0.132365i
$100$		0			0
$101$	1.21929	+	2.11188i	0.121324	+	0.210140i	0.920290	−	0.391237i	$-0.127953\pi$
$101$	1.21929	+	2.11188i	0.121324	+	0.210140i	−0.798966	+	0.601376i	$0.794619\pi$
$102$	1.35904	−	0.784645i	0.134565	−	0.0776914i
$103$	12.4300			1.22477			0.612383	−	0.790561i	$-0.290211\pi$
$103$	12.4300			1.22477			0.612383	+	0.790561i	$0.290211\pi$
$104$	2.41225	+	2.67975i	0.236540	+	0.262771i
$105$		0			0
$106$	12.0517	−	6.95804i	1.17056	−	0.675824i
$107$	−5.23831	−	9.07302i	−0.506407	−	0.877122i	−0.999973	−	0.00741349i	$-0.997640\pi$
$107$	−5.23831	−	9.07302i	−0.506407	−	0.877122i	0.493566	−	0.869708i	$-0.335693\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$		−	17.1799i		−	1.64553i	−0.568379	−	0.822767i	$-0.692429\pi$
$109$		−	17.1799i		−	1.64553i	0.568379	−	0.822767i	$-0.307571\pi$
$110$		0			0
$111$	2.42743	+	1.40148i	0.230402	+	0.133022i
$112$		−	1.52767i		−	0.144352i
$113$	1.29991	−	2.25151i	0.122285	−	0.211805i	−0.798383	−	0.602150i	$-0.794311\pi$
$113$	1.29991	−	2.25151i	0.122285	−	0.211805i	0.920669	+	0.390345i	$0.127644\pi$
$114$	2.41369	+	4.18063i	0.226063	+	0.391552i
$115$		0			0
$116$	4.42877			0.411201
$117$	−0.749192	−	3.52686i	−0.0692628	−	0.326058i
$118$	10.4732			0.964136
$119$	2.07618	−	1.19868i	0.190323	−	0.109883i
$120$		0			0
$121$	−4.63273	+	8.02413i	−0.421157	+	0.729466i
$122$		−	4.98268i		−	0.451111i
$123$	1.35904	+	0.784645i	0.122541	+	0.0707490i
$124$	−1.40941	−	0.813725i	−0.126569	−	0.0730747i
$125$		0			0
$126$	−0.763837	+	1.32301i	−0.0680481	+	0.117863i
$127$	4.05041	+	7.01552i	0.359416	+	0.622527i	0.987863	−	0.155325i	$-0.0496426\pi$
$127$	4.05041	+	7.01552i	0.359416	+	0.622527i	−0.628447	+	0.777852i	$0.716309\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	−5.28860			−0.465635
$130$		0			0
$131$	−2.32506			−0.203141			−0.101571	−	0.994828i	$-0.532387\pi$
$131$	−2.32506			−0.203141			−0.101571	+	0.994828i	$0.532387\pi$
$132$	−1.14057	+	0.658509i	−0.0992740	+	0.0573158i
$133$	3.68733	+	6.38665i	0.319732	+	0.553792i
$134$	−1.38628	+	2.40112i	−0.119757	+	0.207425i
$135$		0			0
$136$	−1.35904	−	0.784645i	−0.116537	−	0.0672827i
$137$	10.6381	+	6.14192i	0.908876	+	0.524740i	0.880069	−	0.474845i	$-0.157496\pi$
$137$	10.6381	+	6.14192i	0.908876	+	0.524740i	0.0288066	+	0.999585i	$0.490829\pi$
$138$			8.44285i			0.718703i
$139$	3.32861	−	5.76531i	0.282329	−	0.489008i	−0.689629	−	0.724163i	$-0.742226\pi$
$139$	3.32861	−	5.76531i	0.282329	−	0.489008i	0.971958	+	0.235155i	$0.0755598\pi$
$140$		0			0
$141$	−4.28295	+	2.47276i	−0.360689	+	0.208244i
$142$	−14.8394			−1.24529
$143$	1.46796	−	4.51598i	0.122757	−	0.377645i
$144$	1.00000			0.0833333
$145$		0			0
$146$	−2.99472	−	5.18700i	−0.247845	−	0.429280i
$147$	2.33310	−	4.04106i	0.192431	−	0.333301i
$148$		−	2.80296i		−	0.230402i
$149$	2.60768	+	1.50554i	0.213629	+	0.123339i	0.602997	−	0.797744i	$-0.293973\pi$
$149$	2.60768	+	1.50554i	0.213629	+	0.123339i	−0.389368	+	0.921082i	$0.627306\pi$
$150$		0			0
$151$		−	12.0149i		−	0.977759i	−0.872351	−	0.488880i	$-0.837406\pi$
$151$		−	12.0149i		−	0.977759i	0.872351	−	0.488880i	$-0.162594\pi$
$152$	2.41369	−	4.18063i	0.195776	−	0.339094i
$153$	0.784645	+	1.35904i	0.0634348	+	0.109872i
$154$	−1.74242	+	1.00599i	−0.140408	+	0.0810648i
$155$		0			0
$156$	−2.67975	+	2.41225i	−0.214552	+	0.193134i
$157$	3.01556			0.240668			0.120334	−	0.992733i	$-0.461604\pi$
$157$	3.01556			0.240668			0.120334	+	0.992733i	$0.461604\pi$
$158$	−4.22302	+	2.43816i	−0.335965	+	0.193970i
$159$	6.95804	+	12.0517i	0.551808	+	0.955760i
$160$		0			0
$161$			12.8979i			1.01650i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	8.58772	+	4.95812i	0.672642	+	0.388350i	0.797077	−	0.603878i	$-0.206379\pi$
$163$	8.58772	+	4.95812i	0.672642	+	0.388350i	−0.124435	+	0.992228i	$0.539712\pi$
$164$		−	1.56929i		−	0.122541i
$165$		0			0
$166$	3.19510	+	5.53408i	0.247988	+	0.429528i
$167$	11.2492	−	6.49472i	0.870488	−	0.502576i	0.00297754	−	0.999996i	$-0.499052\pi$
$167$	11.2492	−	6.49472i	0.870488	−	0.502576i	0.867510	+	0.497419i	$0.165719\pi$
$168$	1.52767			0.117863
$169$	1.36213	−	12.9284i	0.104779	−	0.994496i
$170$		0			0
$171$	−4.18063	+	2.41369i	−0.319701	+	0.184579i
$172$	2.64430	+	4.58006i	0.201626	+	0.349226i
$173$	1.93848	−	3.35755i	0.147380	−	0.255270i	−0.782878	−	0.622175i	$-0.786249\pi$
$173$	1.93848	−	3.35755i	0.147380	−	0.255270i	0.930258	+	0.366905i	$0.119583\pi$
$174$			4.42877i			0.335744i
$175$		0			0
$176$	1.14057	+	0.658509i	0.0859738	+	0.0496370i
$177$			10.4732i			0.787213i
$178$	−9.22251	+	15.9738i	−0.691256	+	1.19729i
$179$	−7.05325	−	12.2166i	−0.527185	−	0.913111i	−0.999498	−	0.0316802i	$-0.989914\pi$
$179$	−7.05325	−	12.2166i	−0.527185	−	0.913111i	0.472313	−	0.881431i	$-0.343419\pi$
$180$		0			0
$181$	−26.1472			−1.94351			−0.971753	−	0.236001i	$-0.924163\pi$
$181$	−26.1472			−1.94351			−0.971753	+	0.236001i	$0.924163\pi$
$182$	−4.09379	+	3.68513i	−0.303452	+	0.273160i
$183$	4.98268			0.368331
$184$	7.31172	−	4.22143i	0.539027	−	0.311208i
$185$		0			0
$186$	0.813725	−	1.40941i	0.0596652	−	0.103343i
$187$			2.06678i			0.151138i
$188$	4.28295	+	2.47276i	0.312366	+	0.180345i
$189$	−1.32301	−	0.763837i	−0.0962345	−	0.0555610i
$190$		0			0
$191$	−9.42713	+	16.3283i	−0.682123	+	1.18147i	0.292208	+	0.956355i	$0.405610\pi$
$191$	−9.42713	+	16.3283i	−0.682123	+	1.18147i	−0.974332	+	0.225117i	$0.927723\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−15.4949	+	8.94600i	−1.11535	+	0.643947i	−0.940210	−	0.340596i	$-0.889371\pi$
$193$	−15.4949	+	8.94600i	−1.11535	+	0.643947i	−0.175140	+	0.984544i	$0.556038\pi$
$194$	1.92606			0.138283
$195$		0			0
$196$	−4.66621			−0.333301
$197$	−0.542008	+	0.312928i	−0.0386165	+	0.0222952i	−0.519184	−	0.854663i	$-0.673764\pi$
$197$	−0.542008	+	0.312928i	−0.0386165	+	0.0222952i	0.480567	+	0.876958i	$0.340431\pi$
$198$	−0.658509	−	1.14057i	−0.0467982	−	0.0810568i
$199$	8.84057	−	15.3123i	0.626691	−	1.08546i	−0.361520	−	0.932364i	$-0.617742\pi$
$199$	8.84057	−	15.3123i	0.626691	−	1.08546i	0.988211	−	0.153097i	$-0.0489246\pi$
$200$		0			0
$201$	−2.40112	−	1.38628i	−0.169362	−	0.0977810i
$202$	2.11188	+	1.21929i	0.148591	+	0.0857891i
$203$			6.76572i			0.474860i
$204$	0.784645	−	1.35904i	0.0549361	−	0.0951521i
$205$		0			0
$206$	10.7647	−	6.21501i	0.750013	−	0.433020i
$207$	−8.44285			−0.586819
$208$	3.42894	+	1.11461i	0.237754	+	0.0772842i
$209$	−6.35774			−0.439774
$210$		0			0
$211$	−8.62227	−	14.9342i	−0.593581	−	1.02811i	−0.993745	−	0.111669i	$-0.964380\pi$
$211$	−8.62227	−	14.9342i	−0.593581	−	1.02811i	0.400164	−	0.916443i	$-0.368953\pi$
$212$	6.95804	−	12.0517i	0.477880	−	0.827712i
$213$		−	14.8394i		−	1.01678i
$214$	−9.07302	−	5.23831i	−0.620219	−	0.358083i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	1.24311	−	2.15313i	0.0843877	−	0.146164i
$218$	−8.58994	−	14.8782i	−0.581784	−	1.00768i
$219$	5.18700	−	2.99472i	0.350505	−	0.202364i
$220$		0			0
$221$	1.17570	+	5.53466i	0.0790861	+	0.372301i
$222$	2.80296			0.188122
$223$	−4.24107	+	2.44858i	−0.284003	+	0.163969i	−0.635234	−	0.772320i	$-0.719096\pi$
$223$	−4.24107	+	2.44858i	−0.284003	+	0.163969i	0.351231	+	0.936289i	$0.385763\pi$
$224$	−0.763837	−	1.32301i	−0.0510360	−	0.0883970i
$225$		0			0
$226$		−	2.59982i		−	0.172938i
$227$	8.79132	+	5.07567i	0.583500	+	0.336884i	0.762523	−	0.646961i	$-0.223960\pi$
$227$	8.79132	+	5.07567i	0.583500	+	0.336884i	−0.179023	+	0.983845i	$0.557294\pi$
$228$	4.18063	+	2.41369i	0.276869	+	0.159850i
$229$		−	15.3959i		−	1.01739i	−0.860947	−	0.508694i	$-0.830129\pi$
$229$		−	15.3959i		−	1.01739i	0.860947	−	0.508694i	$-0.169871\pi$
$230$		0			0
$231$	−1.00599	−	1.74242i	−0.0661891	−	0.114643i
$232$	3.83543	−	2.21438i	0.251808	−	0.145381i
$233$	−9.91624			−0.649634			−0.324817	−	0.945777i	$-0.605303\pi$
$233$	−9.91624			−0.649634			−0.324817	+	0.945777i	$0.605303\pi$
$234$	−2.41225	−	2.67975i	−0.157694	−	0.175181i
$235$		0			0
$236$	9.07005	−	5.23660i	0.590410	−	0.340873i
$237$	−2.43816	−	4.22302i	−0.158376	−	0.274315i
$238$	1.19868	−	2.07618i	0.0776990	−	0.134579i
$239$		−	9.46167i		−	0.612024i	−0.952028	−	0.306012i	$-0.901005\pi$
$239$		−	9.46167i		−	0.612024i	0.952028	−	0.306012i	$-0.0989948\pi$
$240$		0			0
$241$	11.3482	+	6.55189i	0.731002	+	0.422044i	0.818789	−	0.574095i	$-0.194646\pi$
$241$	11.3482	+	6.55189i	0.731002	+	0.422044i	−0.0877865	+	0.996139i	$0.527979\pi$
$242$			9.26546i			0.595607i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−2.49134	−	4.31513i	−0.159492	−	0.276248i
$245$		0			0
$246$	1.56929			0.100054
$247$	−17.0255	+	3.61663i	−1.08330	+	0.230121i
$248$	−1.62745			−0.103343
$249$	−5.53408	+	3.19510i	−0.350708	+	0.202481i
$250$		0			0
$251$	11.5822	−	20.0610i	0.731062	−	1.26624i	−0.225367	−	0.974274i	$-0.572358\pi$
$251$	11.5822	−	20.0610i	0.731062	−	1.26624i	0.956430	−	0.291963i	$-0.0943085\pi$
$252$			1.52767i			0.0962345i
$253$	−9.62967	−	5.55969i	−0.605412	−	0.349535i
$254$	7.01552	+	4.05041i	0.440193	+	0.254146i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	1.92197	+	3.32895i	0.119889	+	0.207654i	0.919724	−	0.392566i	$-0.128413\pi$
$257$	1.92197	+	3.32895i	0.119889	+	0.207654i	−0.799834	+	0.600221i	$0.795079\pi$
$258$	−4.58006	+	2.64430i	−0.285142	+	0.164627i
$259$	4.28201			0.266071
$260$		0			0
$261$	−4.42877			−0.274134
$262$	−2.01356	+	1.16253i	−0.124398	+	0.0718213i
$263$	15.3032	+	26.5060i	0.943638	+	1.63443i	0.758455	+	0.651726i	$0.225955\pi$
$263$	15.3032	+	26.5060i	0.943638	+	1.63443i	0.185184	+	0.982704i	$0.440712\pi$
$264$	−0.658509	+	1.14057i	−0.0405284	+	0.0701973i
$265$		0			0
$266$	6.38665	+	3.68733i	0.391590	+	0.226085i
$267$	−15.9738	−	9.22251i	−0.977584	−	0.564408i
$268$			2.77257i			0.169362i
$269$	−9.04370	+	15.6641i	−0.551404	+	0.955060i	0.446769	+	0.894649i	$0.352574\pi$
$269$	−9.04370	+	15.6641i	−0.551404	+	0.955060i	−0.998174	+	0.0604109i	$0.980759\pi$
$270$		0			0
$271$	12.2869	−	7.09382i	0.746373	−	0.430919i	−0.0780089	−	0.996953i	$-0.524856\pi$
$271$	12.2869	−	7.09382i	0.746373	−	0.430919i	0.824382	+	0.566034i	$0.191523\pi$
$272$	−1.56929			−0.0951521
$273$	−3.68513	−	4.09379i	−0.223034	−	0.247767i
$274$	12.2838			0.742094
$275$		0			0
$276$	4.22143	+	7.31172i	0.254100	+	0.440114i
$277$	8.42097	−	14.5855i	0.505967	−	0.876360i	−0.494009	−	0.869457i	$-0.664469\pi$
$277$	8.42097	−	14.5855i	0.505967	−	0.876360i	0.999976	−	0.00690380i	$-0.00219757\pi$
$278$		−	6.65721i		−	0.399273i
$279$	1.40941	+	0.813725i	0.0843794	+	0.0487165i
$280$		0			0
$281$		−	8.61535i		−	0.513949i	−0.966418	−	0.256974i	$-0.917274\pi$
$281$		−	8.61535i		−	0.513949i	0.966418	−	0.256974i	$-0.0827256\pi$
$282$	−2.47276	+	4.28295i	−0.147251	+	0.255046i
$283$	−13.8098	−	23.9192i	−0.820905	−	1.42185i	−0.905009	−	0.425392i	$-0.860136\pi$
$283$	−13.8098	−	23.9192i	−0.820905	−	1.42185i	0.0841040	−	0.996457i	$-0.473197\pi$
$284$	−12.8513	+	7.41968i	−0.762582	+	0.440277i
$285$		0			0
$286$	−0.986699	−	4.64493i	−0.0583447	−	0.274661i
$287$	2.39736			0.141512
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	7.26867	+	12.5897i	0.427569	+	0.740570i
$290$		0			0
$291$			1.92606i			0.112907i
$292$	−5.18700	−	2.99472i	−0.303546	−	0.175253i
$293$	−26.1973	−	15.1250i	−1.53046	−	0.883614i	−0.999340	−	0.0363205i	$-0.988436\pi$
$293$	−26.1973	−	15.1250i	−1.53046	−	0.883614i	−0.531125	−	0.847294i	$-0.678230\pi$
$294$		−	4.66621i		−	0.272139i
$295$		0			0
$296$	−1.40148	−	2.42743i	−0.0814593	−	0.141092i
$297$	1.14057	−	0.658509i	0.0661826	−	0.0382106i
$298$	3.01108			0.174427
$299$	−28.9501	−	9.41048i	−1.67422	−	0.544222i
$300$		0			0
$301$	−6.99684	+	4.03963i	−0.403291	+	0.232840i
$302$	−6.00745	−	10.4052i	−0.345690	−	0.598753i
$303$	−1.21929	+	2.11188i	−0.0700465	+	0.121324i
$304$		−	4.82738i		−	0.276869i
$305$		0			0
$306$	1.35904	+	0.784645i	0.0776914	+	0.0448552i
$307$			14.1392i			0.806966i	0.914987	+	0.403483i	$0.132201\pi$
$307$			14.1392i			0.806966i	−0.914987	+	0.403483i	$0.867799\pi$
$308$	−1.00599	+	1.74242i	−0.0573215	+	0.0992837i
$309$	6.21501	+	10.7647i	0.353559	+	0.612383i
$310$		0			0
$311$	−9.97427			−0.565589			−0.282794	−	0.959181i	$-0.591261\pi$
$311$	−9.97427			−0.565589			−0.282794	+	0.959181i	$0.591261\pi$
$312$	−1.11461	+	3.42894i	−0.0631023	+	0.194126i
$313$	−3.08460			−0.174352			−0.0871760	−	0.996193i	$-0.527784\pi$
$313$	−3.08460			−0.174352			−0.0871760	+	0.996193i	$0.527784\pi$
$314$	2.61155	−	1.50778i	0.147378	−	0.0850888i
$315$		0			0
$316$	−2.43816	+	4.22302i	−0.137157	+	0.237563i
$317$		−	14.2980i		−	0.803054i	−0.915847	−	0.401527i	$-0.868480\pi$
$317$		−	14.2980i		−	0.803054i	0.915847	−	0.401527i	$-0.131520\pi$
$318$	12.0517	+	6.95804i	0.675824	+	0.390187i
$319$	−5.05132	−	2.91638i	−0.282820	−	0.163286i
$320$		0			0
$321$	5.23831	−	9.07302i	0.292374	−	0.506407i
$322$	6.44897	+	11.1699i	0.359387	+	0.622476i
$323$	6.56062	−	3.78778i	0.365043	−	0.210757i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	9.91624			0.549210
$327$	14.8782	−	8.58994i	0.822767	−	0.475025i
$328$	−0.784645	−	1.35904i	−0.0433248	−	0.0750407i
$329$	−3.77757	+	6.54295i	−0.208264	+	0.360724i
$330$		0			0
$331$	−9.89017	−	5.71009i	−0.543613	−	0.313855i	0.202929	−	0.979193i	$-0.434954\pi$
$331$	−9.89017	−	5.71009i	−0.543613	−	0.313855i	−0.746542	+	0.665338i	$0.768287\pi$
$332$	5.53408	+	3.19510i	0.303722	+	0.175354i
$333$			2.80296i			0.153601i
$334$	6.49472	−	11.2492i	0.355375	−	0.615528i
$335$		0			0
$336$	1.32301	−	0.763837i	0.0721759	−	0.0416708i
$337$	−5.53208			−0.301352			−0.150676	−	0.988583i	$-0.548145\pi$
$337$	−5.53208			−0.301352			−0.150676	+	0.988583i	$0.548145\pi$
$338$	−5.28458	−	11.8774i	−0.287443	−	0.646047i
$339$	2.59982			0.141203
$340$		0			0
$341$	1.07169	+	1.85622i	0.0580353	+	0.100520i
$342$	−2.41369	+	4.18063i	−0.130517	+	0.226063i
$343$		−	17.8222i		−	0.962307i
$344$	4.58006	+	2.64430i	0.246940	+	0.142571i
$345$		0			0
$346$		−	3.87696i		−	0.208427i
$347$	−1.41004	+	2.44226i	−0.0756949	+	0.131107i	−0.901388	−	0.433012i	$-0.857451\pi$
$347$	−1.41004	+	2.44226i	−0.0756949	+	0.131107i	0.825693	+	0.564119i	$0.190784\pi$
$348$	2.21438	+	3.83543i	0.118703	+	0.205600i
$349$	−23.0704	+	13.3197i	−1.23493	+	0.712986i	−0.968053	−	0.250745i	$-0.919324\pi$
$349$	−23.0704	+	13.3197i	−1.23493	+	0.712986i	−0.266875	+	0.963731i	$0.585991\pi$
$350$		0			0
$351$	2.67975	−	2.41225i	0.143035	−	0.128756i
$352$	1.31702			0.0701973
$353$	−11.4542	+	6.61308i	−0.609645	+	0.351979i	−0.772826	−	0.634617i	$-0.781158\pi$
$353$	−11.4542	+	6.61308i	−0.609645	+	0.351979i	0.163182	+	0.986596i	$0.447824\pi$
$354$	5.23660	+	9.07005i	0.278322	+	0.482068i
$355$		0			0
$356$			18.4450i			0.977584i
$357$	2.07618	+	1.19868i	0.109883	+	0.0634410i
$358$	−12.2166	−	7.05325i	−0.645667	−	0.372776i
$359$			12.3827i			0.653532i	0.945105	+	0.326766i	$0.105959\pi$
$359$			12.3827i			0.653532i	−0.945105	+	0.326766i	$0.894041\pi$
$360$		0			0
$361$	2.15178	+	3.72700i	0.113252	+	0.196158i
$362$	−22.6441	+	13.0736i	−1.19015	+	0.687133i
$363$	−9.26546			−0.486311
$364$	−1.70276	+	5.23831i	−0.0892489	+	0.274562i
$365$		0			0
$366$	4.31513	−	2.49134i	0.225556	−	0.130225i
$367$	−3.54624	−	6.14226i	−0.185112	−	0.320623i	0.758502	−	0.651670i	$-0.225931\pi$
$367$	−3.54624	−	6.14226i	−0.185112	−	0.320623i	−0.943614	+	0.331047i	$0.892598\pi$
$368$	4.22143	−	7.31172i	0.220057	−	0.381150i
$369$			1.56929i			0.0816939i
$370$		0			0
$371$	18.4110	+	10.6296i	0.955854	+	0.551862i
$372$		−	1.62745i		−	0.0843794i
$373$	18.4902	−	32.0259i	0.957384	−	1.65824i	0.228568	−	0.973528i	$-0.426596\pi$
$373$	18.4902	−	32.0259i	0.957384	−	1.65824i	0.728816	−	0.684709i	$-0.240071\pi$
$374$	1.03339	+	1.78989i	0.0534354	+	0.0925528i
$375$		0			0
$376$	4.94552			0.255046
$377$	−15.1860	−	4.93634i	−0.782118	−	0.254235i
$378$	−1.52767			−0.0785751
$379$	29.6252	−	17.1041i	1.52174	−	0.878580i	0.522075	−	0.852900i	$-0.325158\pi$
$379$	29.6252	−	17.1041i	1.52174	−	0.878580i	0.999670	−	0.0256802i	$-0.00817514\pi$
$380$		0			0
$381$	−4.05041	+	7.01552i	−0.207509	+	0.359416i
$382$			18.8543i			0.964668i
$383$	−22.5461	−	13.0170i	−1.15205	−	0.665137i	−0.202665	−	0.979248i	$-0.564960\pi$
$383$	−22.5461	−	13.0170i	−1.15205	−	0.665137i	−0.949386	+	0.314111i	$0.898294\pi$
$384$	−0.866025	−	0.500000i	−0.0441942	−	0.0255155i
$385$		0			0
$386$	−8.94600	+	15.4949i	−0.455340	+	0.788671i
$387$	−2.64430	−	4.58006i	−0.134417	−	0.232817i
$388$	1.66801	−	0.963028i	0.0846806	−	0.0488904i
$389$	6.23568			0.316162			0.158081	−	0.987426i	$-0.449469\pi$
$389$	6.23568			0.316162			0.158081	+	0.987426i	$0.449469\pi$
$390$		0			0
$391$	13.2493			0.670045
$392$	−4.04106	+	2.33310i	−0.204104	+	0.117840i
$393$	−1.16253	−	2.01356i	−0.0586419	−	0.101571i
$394$	−0.312928	+	0.542008i	−0.0157651	+	0.0273060i
$395$		0			0
$396$	−1.14057	−	0.658509i	−0.0573158	−	0.0330913i
$397$	−31.7827	−	18.3498i	−1.59513	−	0.920948i	−0.992407	−	0.122997i	$-0.960750\pi$
$397$	−31.7827	−	18.3498i	−1.59513	−	0.920948i	−0.602722	−	0.797951i	$-0.705917\pi$
$398$		−	17.6811i		−	0.886275i
$399$	−3.68733	+	6.38665i	−0.184597	+	0.319732i
$400$		0			0
$401$	24.5044	−	14.1476i	1.22369	−	0.706498i	0.257987	−	0.966148i	$-0.416941\pi$
$401$	24.5044	−	14.1476i	1.22369	−	0.706498i	0.965703	+	0.259651i	$0.0836074\pi$
$402$	−2.77257			−0.138283
$403$	3.92581	+	4.36116i	0.195559	+	0.217245i
$404$	2.43859			0.121324
$405$		0			0
$406$	3.38286	+	5.85928i	0.167888	+	0.290791i
$407$	−1.84577	+	3.19697i	−0.0914915	+	0.158468i
$408$		−	1.56929i		−	0.0776914i
$409$	−13.2744	−	7.66400i	−0.656379	−	0.378961i	0.134517	−	0.990911i	$-0.457052\pi$
$409$	−13.2744	−	7.66400i	−0.656379	−	0.378961i	−0.790896	+	0.611951i	$0.790385\pi$
$410$		0			0
$411$			12.2838i			0.605917i
$412$	6.21501	−	10.7647i	0.306191	−	0.530339i
$413$	7.99982	+	13.8561i	0.393645	+	0.681814i
$414$	−7.31172	+	4.22143i	−0.359352	+	0.207472i
$415$		0			0
$416$	3.52686	−	0.749192i	0.172918	−	0.0367322i
$417$	6.65721			0.326005
$418$	−5.50597	+	3.17887i	−0.269306	+	0.155484i
$419$	13.4692	+	23.3293i	0.658013	+	1.13971i	0.981129	+	0.193353i	$0.0619362\pi$
$419$	13.4692	+	23.3293i	0.658013	+	1.13971i	−0.323116	+	0.946359i	$0.604730\pi$
$420$		0			0
$421$		−	38.5359i		−	1.87812i	−0.343747	−	0.939062i	$-0.611696\pi$
$421$		−	38.5359i		−	1.87812i	0.343747	−	0.939062i	$-0.388304\pi$
$422$	−14.9342	−	8.62227i	−0.726986	−	0.419725i
$423$	−4.28295	−	2.47276i	−0.208244	−	0.120230i
$424$		−	13.9161i		−	0.675824i
$425$		0			0
$426$	−7.41968	−	12.8513i	−0.359484	−	0.622645i
$427$	6.59212	−	3.80596i	0.319015	−	0.184183i
$428$	−10.4766			−0.506407
$429$	4.64493	−	0.986699i	0.224259	−	0.0476383i
$430$		0			0
$431$	2.48744	−	1.43612i	0.119816	−	0.0691756i	−0.438894	−	0.898539i	$-0.644630\pi$
$431$	2.48744	−	1.43612i	0.119816	−	0.0691756i	0.558710	+	0.829363i	$0.311296\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−6.48619	+	11.2344i	−0.311706	+	0.539891i	−0.978732	−	0.205144i	$-0.934234\pi$
$433$	−6.48619	+	11.2344i	−0.311706	+	0.539891i	0.667026	+	0.745035i	$0.267567\pi$
$434$		−	2.48622i		−	0.119342i
$435$		0			0
$436$	−14.8782	−	8.58994i	−0.712537	−	0.411383i
$437$			40.7568i			1.94966i
$438$	2.99472	−	5.18700i	0.143093	−	0.247845i
$439$	1.02411	+	1.77380i	0.0488779	+	0.0846590i	0.889429	−	0.457073i	$-0.151102\pi$
$439$	1.02411	+	1.77380i	0.0488779	+	0.0846590i	−0.840551	+	0.541732i	$0.817769\pi$
$440$		0			0
$441$	4.66621			0.222200
$442$	3.78551	+	4.20530i	0.180059	+	0.200026i
$443$	25.7082			1.22143			0.610717	−	0.791849i	$-0.290881\pi$
$443$	25.7082			1.22143			0.610717	+	0.791849i	$0.290881\pi$
$444$	2.42743	−	1.40148i	0.115201	−	0.0665112i
$445$		0			0
$446$	−2.44858	+	4.24107i	−0.115944	+	0.200820i
$447$			3.01108i			0.142419i
$448$	−1.32301	−	0.763837i	−0.0625061	−	0.0360879i
$449$	16.0756	+	9.28127i	0.758656	+	0.438010i	0.828813	−	0.559526i	$-0.189017\pi$
$449$	16.0756	+	9.28127i	0.758656	+	0.438010i	−0.0701571	+	0.997536i	$0.522350\pi$
$450$		0			0
$451$	−1.03339	+	1.78989i	−0.0486605	+	0.0842824i
$452$	−1.29991	−	2.25151i	−0.0611427	−	0.105902i
$453$	10.4052	−	6.00745i	0.488880	−	0.282255i
$454$	10.1513			0.476426
$455$		0			0
$456$	4.82738			0.226063
$457$	21.3412	−	12.3213i	0.998299	−	0.576368i	0.0905546	−	0.995891i	$-0.471136\pi$
$457$	21.3412	−	12.3213i	0.998299	−	0.576368i	0.907745	+	0.419523i	$0.137803\pi$
$458$	−7.69794	−	13.3332i	−0.359701	−	0.623020i
$459$	−0.784645	+	1.35904i	−0.0366241	+	0.0634348i
$460$		0			0
$461$	−27.5693	−	15.9171i	−1.28403	−	0.741334i	−0.306446	−	0.951888i	$-0.599140\pi$
$461$	−27.5693	−	15.9171i	−1.28403	−	0.741334i	−0.977582	+	0.210554i	$0.932473\pi$
$462$	−1.74242	−	1.00599i	−0.0810648	−	0.0468028i
$463$		−	3.18319i		−	0.147936i	−0.997261	−	0.0739678i	$-0.976434\pi$
$463$		−	3.18319i		−	0.147936i	0.997261	−	0.0739678i	$-0.0235662\pi$
$464$	2.21438	−	3.83543i	0.102800	−	0.178055i
$465$		0			0
$466$	−8.58772	+	4.95812i	−0.397818	+	0.229680i
$467$	21.6747			1.00298			0.501492	−	0.865162i	$-0.332785\pi$
$467$	21.6747			1.00298			0.501492	+	0.865162i	$0.332785\pi$
$468$	−3.42894	−	1.11461i	−0.158503	−	0.0515228i
$469$	−4.23559			−0.195581
$470$		0			0
$471$	1.50778	+	2.61155i	0.0694747	+	0.120334i
$472$	5.23660	−	9.07005i	0.241034	−	0.417483i
$473$		−	6.96517i		−	0.320259i
$474$	−4.22302	−	2.43816i	−0.193970	−	0.111988i
$475$		0			0
$476$		−	2.39736i		−	0.109883i
$477$	−6.95804	+	12.0517i	−0.318587	+	0.551808i
$478$	−4.73083	−	8.19404i	−0.216383	−	0.374787i
$479$	25.3765	−	14.6511i	1.15948	−	0.669426i	0.208300	−	0.978065i	$-0.433207\pi$
$479$	25.3765	−	14.6511i	1.15948	−	0.669426i	0.951179	+	0.308639i	$0.0998735\pi$
$480$		0			0
$481$	−3.12420	+	9.61118i	−0.142451	+	0.438232i
$482$	13.1038			0.596861
$483$	−11.1699	+	6.44897i	−0.508250	+	0.293438i
$484$	4.63273	+	8.02413i	0.210579	+	0.364733i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	−36.8309	−	21.2643i	−1.66897	−	0.963579i	−0.968196	−	0.250194i	$-0.919506\pi$
$487$	−36.8309	−	21.2643i	−1.66897	−	0.963579i	−0.700772	−	0.713385i	$-0.747161\pi$
$488$	−4.31513	−	2.49134i	−0.195337	−	0.112778i
$489$			9.91624i			0.448428i
$490$		0			0
$491$	6.32521	+	10.9556i	0.285453	+	0.494418i	0.972719	−	0.231987i	$-0.0745228\pi$
$491$	6.32521	+	10.9556i	0.285453	+	0.494418i	−0.687266	+	0.726406i	$0.741189\pi$
$492$	1.35904	−	0.784645i	0.0612705	−	0.0353745i
$493$	6.95002			0.313013
$494$	−12.9362	+	11.6448i	−0.582026	+	0.523925i
$495$		0			0
$496$	−1.40941	+	0.813725i	−0.0632845	+	0.0365373i
$497$	−11.3349	−	19.6325i	−0.508438	−	0.880640i
$498$	−3.19510	+	5.53408i	−0.143176	+	0.247988i
$499$			4.54007i			0.203242i	0.994823	+	0.101621i	$0.0324028\pi$
$499$			4.54007i			0.203242i	−0.994823	+	0.101621i	$0.967597\pi$
$500$		0			0
$501$	11.2492	+	6.49472i	0.502576	+	0.290163i
$502$		−	23.1644i		−	1.03388i
$503$	−9.95791	+	17.2476i	−0.444001	+	0.769033i	−0.997982	−	0.0634967i	$-0.979775\pi$
$503$	−9.95791	+	17.2476i	−0.444001	+	0.769033i	0.553981	+	0.832529i	$0.313108\pi$
$504$	0.763837	+	1.32301i	0.0340240	+	0.0589313i
$505$		0			0
$506$	−11.1194			−0.494317
$507$	11.8774	−	5.28458i	0.527495	−	0.234697i
$508$	8.10083			0.359416
$509$	9.09532	−	5.25118i	0.403143	−	0.232755i	−0.284696	−	0.958618i	$-0.591893\pi$
$509$	9.09532	−	5.25118i	0.403143	−	0.232755i	0.687839	+	0.725863i	$0.258559\pi$
$510$		0			0
$511$	4.57496	−	7.92406i	0.202384	−	0.350540i
$512$			1.00000i			0.0441942i
$513$	−4.18063	−	2.41369i	−0.184579	−	0.106567i
$514$	3.32895	+	1.92197i	0.146834	+	0.0847746i
$515$		0			0
$516$	−2.64430	+	4.58006i	−0.116409	+	0.201626i
$517$	−3.25667	−	5.64072i	−0.143228	−	0.248078i
$518$	3.70833	−	2.14100i	0.162934	−	0.0940703i
$519$	3.87696			0.170180
$520$		0			0
$521$	−24.5221			−1.07433			−0.537166	−	0.843477i	$-0.680505\pi$
$521$	−24.5221			−1.07433			−0.537166	+	0.843477i	$0.680505\pi$
$522$	−3.83543	+	2.21438i	−0.167872	+	0.0969210i
$523$	−12.5241	−	21.6924i	−0.547641	−	0.948541i	−0.998436	−	0.0559138i	$-0.982193\pi$
$523$	−12.5241	−	21.6924i	−0.547641	−	0.948541i	0.450795	−	0.892627i	$-0.351141\pi$
$524$	−1.16253	+	2.01356i	−0.0507853	+	0.0879628i
$525$		0			0
$526$	26.5060	+	15.3032i	1.15572	+	0.667253i
$527$	−2.21178	−	1.27697i	−0.0963466	−	0.0556257i
$528$			1.31702i			0.0573158i
$529$	−24.1409	+	41.8132i	−1.04960	+	1.81797i
$530$		0			0
$531$	−9.07005	+	5.23660i	−0.393607	+	0.227249i
$532$	7.37466			0.319732
$533$	−1.74914	+	5.38100i	−0.0757638	+	0.233077i
$534$	−18.4450			−0.798194
$535$		0			0
$536$	1.38628	+	2.40112i	0.0598784	+	0.103712i
$537$	7.05325	−	12.2166i	0.304370	−	0.527185i
$538$			18.0874i			0.779803i
$539$	5.32214	+	3.07274i	0.229241	+	0.132352i
$540$		0			0
$541$			20.6859i			0.889356i	0.895690	+	0.444678i	$0.146682\pi$
$541$			20.6859i			0.889356i	−0.895690	+	0.444678i	$0.853318\pi$
$542$	7.09382	−	12.2869i	0.304705	−	0.527765i
$543$	−13.0736	−	22.6441i	−0.561042	−	0.971753i
$544$	−1.35904	+	0.784645i	−0.0582686	+	0.0336414i
$545$		0			0
$546$	−5.23831	−	1.70276i	−0.224179	−	0.0728714i
$547$	40.5960			1.73576			0.867880	−	0.496773i	$-0.165482\pi$
$547$	40.5960			1.73576			0.867880	+	0.496773i	$0.165482\pi$
$548$	10.6381	−	6.14192i	0.454438	−	0.262370i
$549$	2.49134	+	4.31513i	0.106328	+	0.184165i
$550$		0			0
$551$			21.3793i			0.910790i
$552$	7.31172	+	4.22143i	0.311208	+	0.179676i
$553$	−6.45140	−	3.72472i	−0.274342	−	0.158391i
$554$		−	16.8419i		−	0.715545i
$555$		0			0
$556$	−3.32861	−	5.76531i	−0.141164	−	0.244504i
$557$	−35.6858	+	20.6032i	−1.51205	+	0.872985i	−0.512153	+	0.858894i	$0.671152\pi$
$557$	−35.6858	+	20.6032i	−1.51205	+	0.872985i	−0.999901	+	0.0140907i	$0.995515\pi$
$558$	1.62745			0.0688955
$559$	−3.96217	−	18.6521i	−0.167582	−	0.788900i
$560$		0			0
$561$	−1.78989	+	1.03339i	−0.0755690	+	0.0436298i
$562$	−4.30768	−	7.46112i	−0.181708	−	0.314728i
$563$	−7.55940	+	13.0933i	−0.318591	+	0.551815i	−0.980194	−	0.198038i	$-0.936543\pi$
$563$	−7.55940	+	13.0933i	−0.318591	+	0.551815i	0.661603	+	0.749854i	$0.269876\pi$
$564$			4.94552i			0.208244i
$565$		0			0
$566$	−23.9192	−	13.8098i	−1.00540	−	0.580468i
$567$		−	1.52767i		−	0.0641563i
$568$	−7.41968	+	12.8513i	−0.311323	+	0.539227i
$569$	13.2995	+	23.0353i	0.557542	+	0.965692i	0.997701	+	0.0677716i	$0.0215889\pi$
$569$	13.2995	+	23.0353i	0.557542	+	0.965692i	−0.440159	+	0.897920i	$0.645078\pi$
$570$		0			0
$571$	31.8452			1.33268			0.666340	−	0.745648i	$-0.267860\pi$
$571$	31.8452			1.33268			0.666340	+	0.745648i	$0.267860\pi$
$572$	−3.17697	−	3.52928i	−0.132836	−	0.147567i
$573$	−18.8543			−0.787648
$574$	2.07618	−	1.19868i	0.0866580	−	0.0500320i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$		−	1.20258i		−	0.0500639i	−0.999687	−	0.0250319i	$-0.992031\pi$
$577$		−	1.20258i		−	0.0500639i	0.999687	−	0.0250319i	$-0.00796874\pi$
$578$	12.5897	+	7.26867i	0.523662	+	0.302337i
$579$	−15.4949	−	8.94600i	−0.643947	−	0.371783i
$580$		0			0
$581$	−4.88108	+	8.45427i	−0.202501	+	0.350742i
$582$	0.963028	+	1.66801i	0.0399188	+	0.0691414i
$583$	−15.8723	+	9.16386i	−0.657362	+	0.379528i
$584$	−5.98944			−0.247845
$585$		0			0
$586$	−30.2501			−1.24962
$587$	16.5107	−	9.53243i	0.681468	−	0.393446i	−0.118940	−	0.992901i	$-0.537950\pi$
$587$	16.5107	−	9.53243i	0.681468	−	0.393446i	0.800408	+	0.599456i	$0.204616\pi$
$588$	−2.33310	−	4.04106i	−0.0962156	−	0.166650i
$589$	3.92816	−	6.80377i	0.161857	−	0.280344i
$590$		0			0
$591$	−0.542008	−	0.312928i	−0.0222952	−	0.0128722i
$592$	−2.42743	−	1.40148i	−0.0997668	−	0.0576004i
$593$			11.8496i			0.486606i	0.969950	+	0.243303i	$0.0782309\pi$
$593$			11.8496i			0.486606i	−0.969950	+	0.243303i	$0.921769\pi$
$594$	0.658509	−	1.14057i	0.0270189	−	0.0467982i
$595$		0			0
$596$	2.60768	−	1.50554i	0.106815	−	0.0616694i
$597$	17.6811			0.723641
$598$	−29.7767	+	6.32532i	−1.21766	+	0.258661i
$599$	−13.1277			−0.536382			−0.268191	−	0.963366i	$-0.586426\pi$
$599$	−13.1277			−0.536382			−0.268191	+	0.963366i	$0.586426\pi$
$600$		0			0
$601$	17.8125	+	30.8522i	0.726589	+	1.25849i	0.958317	+	0.285708i	$0.0922288\pi$
$601$	17.8125	+	30.8522i	0.726589	+	1.25849i	−0.231728	+	0.972781i	$0.574438\pi$
$602$	−4.03963	+	6.99684i	−0.164643	+	0.285170i
$603$		−	2.77257i		−	0.112908i
$604$	−10.4052	−	6.00745i	−0.423382	−	0.244440i
$605$		0			0
$606$			2.43859i			0.0990608i
$607$	2.42530	−	4.20075i	0.0984400	−	0.170503i	−0.812599	−	0.582823i	$-0.801948\pi$
$607$	2.42530	−	4.20075i	0.0984400	−	0.170503i	0.911039	+	0.412320i	$0.135281\pi$
$608$	−2.41369	−	4.18063i	−0.0978880	−	0.169547i
$609$	−5.85928	+	3.38286i	−0.237430	+	0.137080i
$610$		0			0
$611$	−11.9298	−	13.2528i	−0.482629	−	0.536149i
$612$	1.56929			0.0634348
$613$	20.2948	−	11.7172i	0.819698	−	0.473253i	−0.0306146	−	0.999531i	$-0.509746\pi$
$613$	20.2948	−	11.7172i	0.819698	−	0.473253i	0.850312	+	0.526279i	$0.176413\pi$
$614$	7.06959	+	12.2449i	0.285306	+	0.494164i
$615$		0			0
$616$			2.01198i			0.0810648i
$617$	−12.1560	−	7.01830i	−0.489384	−	0.282546i	0.234935	−	0.972011i	$-0.424512\pi$
$617$	−12.1560	−	7.01830i	−0.489384	−	0.282546i	−0.724319	+	0.689465i	$0.757846\pi$
$618$	10.7647	+	6.21501i	0.433020	+	0.250004i
$619$		−	16.1470i		−	0.649002i	−0.945885	−	0.324501i	$-0.894804\pi$
$619$		−	16.1470i		−	0.649002i	0.945885	−	0.324501i	$-0.105196\pi$
$620$		0			0
$621$	−4.22143	−	7.31172i	−0.169400	−	0.293409i
$622$	−8.63797	+	4.98713i	−0.346351	+	0.199966i
$623$	−28.1780			−1.12893
$624$	0.749192	+	3.52686i	0.0299917	+	0.141187i
$625$		0			0
$626$	−2.67134	+	1.54230i	−0.106768	+	0.0616428i
$627$	−3.17887	−	5.50597i	−0.126952	−	0.219887i
$628$	1.50778	−	2.61155i	0.0601669	−	0.104212i
$629$		−	4.39865i		−	0.175386i
$630$		0			0
$631$	16.3611	+	9.44608i	0.651325	+	0.376043i	0.788964	−	0.614440i	$-0.210618\pi$
$631$	16.3611	+	9.44608i	0.651325	+	0.376043i	−0.137639	+	0.990483i	$0.543951\pi$
$632$			4.87632i			0.193970i
$633$	8.62227	−	14.9342i	0.342704	−	0.593581i
$634$	−7.14899	−	12.3824i	−0.283922	−	0.491768i
$635$		0			0
$636$	13.9161			0.551808
$637$	16.0002	+	5.20100i	0.633950	+	0.206071i
$638$	−5.83277			−0.230921
$639$	12.8513	−	7.41968i	0.508388	−	0.293518i
$640$		0			0
$641$	3.57648	−	6.19465i	0.141262	−	0.244674i	−0.786710	−	0.617323i	$-0.788217\pi$
$641$	3.57648	−	6.19465i	0.141262	−	0.244674i	0.927972	+	0.372649i	$0.121551\pi$
$642$		−	10.4766i		−	0.413479i
$643$	−34.5756	−	19.9623i	−1.36353	−	0.787235i	−0.373438	−	0.927655i	$-0.621821\pi$
$643$	−34.5756	−	19.9623i	−1.36353	−	0.787235i	−0.990092	+	0.140420i	$0.955155\pi$
$644$	11.1699	+	6.44897i	0.440157	+	0.254125i
$645$		0			0
$646$	3.78778	−	6.56062i	0.149028	−	0.258124i
$647$	6.96608	+	12.0656i	0.273865	+	0.474348i	0.969848	−	0.243710i	$-0.0783645\pi$
$647$	6.96608	+	12.0656i	0.273865	+	0.474348i	−0.695983	+	0.718058i	$0.745031\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−13.7934			−0.541438
$650$		0			0
$651$	2.48622			0.0974425
$652$	8.58772	−	4.95812i	0.336321	−	0.194175i
$653$	14.8766	+	25.7670i	0.582165	+	1.00834i	0.995222	+	0.0976340i	$0.0311274\pi$
$653$	14.8766	+	25.7670i	0.582165	+	1.00834i	−0.413058	+	0.910705i	$0.635539\pi$
$654$	8.58994	−	14.8782i	0.335893	−	0.581784i
$655$		0			0
$656$	−1.35904	−	0.784645i	−0.0530618	−	0.0306352i
$657$	5.18700	+	2.99472i	0.202364	+	0.116835i
$658$			7.55515i			0.294530i
$659$	14.6318	−	25.3431i	0.569975	−	0.987226i	−0.426593	−	0.904444i	$-0.640286\pi$
$659$	14.6318	−	25.3431i	0.569975	−	0.987226i	0.996568	−	0.0827819i	$-0.0263805\pi$
$660$		0			0
$661$	−30.0903	+	17.3726i	−1.17038	+	0.675717i	−0.953769	−	0.300541i	$-0.902833\pi$
$661$	−30.0903	+	17.3726i	−1.17038	+	0.675717i	−0.216608	+	0.976259i	$0.569499\pi$
$662$	−11.4202			−0.443858
$663$	−4.20530	+	3.78551i	−0.163320	+	0.147017i
$664$	6.39020			0.247988
$665$		0			0
$666$	1.40148	+	2.42743i	0.0543062	+	0.0940611i
$667$	−18.6957	+	32.3819i	−0.723901	+	1.25383i
$668$		−	12.9894i		−	0.502576i
$669$	−4.24107	−	2.44858i	−0.163969	−	0.0946676i
$670$		0			0
$671$			6.56228i			0.253334i
$672$	0.763837	−	1.32301i	0.0294657	−	0.0510360i
$673$	16.2786	+	28.1953i	0.627492	+	1.08685i	0.988053	+	0.154113i	$0.0492519\pi$
$673$	16.2786	+	28.1953i	0.627492	+	1.08685i	−0.360561	+	0.932736i	$0.617415\pi$
$674$	−4.79092	+	2.76604i	−0.184539	+	0.106544i
$675$		0			0
$676$	−10.5153	−	7.64386i	−0.404434	−	0.293995i
$677$	−32.2002			−1.23756			−0.618778	−	0.785566i	$-0.712372\pi$
$677$	−32.2002			−1.23756			−0.618778	+	0.785566i	$0.712372\pi$
$678$	2.25151	−	1.29991i	0.0864689	−	0.0499228i
$679$	1.47119	+	2.54818i	0.0564593	+	0.0977903i
$680$		0			0
$681$			10.1513i			0.389000i
$682$	1.85622	+	1.07169i	0.0710784	+	0.0410372i
$683$	−5.53009	−	3.19280i	−0.211603	−	0.122169i	0.390453	−	0.920623i	$-0.372318\pi$
$683$	−5.53009	−	3.19280i	−0.211603	−	0.122169i	−0.602056	+	0.798454i	$0.705652\pi$
$684$			4.82738i			0.184579i
$685$		0			0
$686$	−8.91109	−	15.4345i	−0.340227	−	0.589290i
$687$	13.3332	−	7.69794i	0.508694	−	0.293695i
$688$	5.28860			0.201626
$689$	−37.2916	+	33.5690i	−1.42070	+	1.27888i
$690$		0			0
$691$	13.6788	−	7.89748i	0.520368	−	0.300434i	−0.216717	−	0.976234i	$-0.569535\pi$
$691$	13.6788	−	7.89748i	0.520368	−	0.300434i	0.737085	+	0.675800i	$0.236202\pi$
$692$	−1.93848	−	3.35755i	−0.0736900	−	0.127635i
$693$	1.00599	−	1.74242i	0.0382143	−	0.0661891i
$694$			2.82008i			0.107049i
$695$		0			0
$696$	3.83543	+	2.21438i	0.145381	+	0.0839360i
$697$		−	2.46267i		−	0.0932803i
$698$	−13.3197	+	23.0704i	−0.504157	+	0.873226i
$699$	−4.95812	−	8.58772i	−0.187533	−	0.324817i
$700$		0			0
$701$	−43.7481			−1.65234			−0.826171	−	0.563420i	$-0.809485\pi$
$701$	−43.7481			−1.65234			−0.826171	+	0.563420i	$0.809485\pi$
$702$	1.11461	−	3.42894i	0.0420682	−	0.129417i
$703$	13.5309			0.510329
$704$	1.14057	−	0.658509i	0.0429869	−	0.0248185i
$705$		0			0
$706$	−6.61308	+	11.4542i	−0.248886	+	0.431084i
$707$			3.72537i			0.140107i
$708$	9.07005	+	5.23660i	0.340873	+	0.196803i
$709$	30.0167	+	17.3302i	1.12730	+	0.650848i	0.943255	−	0.332070i	$-0.107747\pi$
$709$	30.0167	+	17.3302i	1.12730	+	0.650848i	0.184046	+	0.982918i	$0.441080\pi$
$710$		0			0
$711$	2.43816	−	4.22302i	0.0914382	−	0.158376i
$712$	9.22251	+	15.9738i	0.345628	+	0.598645i
$713$	11.8995	−	6.87016i	0.445639	−	0.257290i
$714$	2.39736			0.0897191
$715$		0			0
$716$	−14.1065			−0.527185
$717$	8.19404	−	4.73083i	0.306012	−	0.176676i
$718$	6.19133	+	10.7237i	0.231058	+	0.400205i
$719$	21.9251	−	37.9755i	0.817670	−	1.41625i	−0.0897253	−	0.995967i	$-0.528599\pi$
$719$	21.9251	−	37.9755i	0.817670	−	1.41625i	0.907395	−	0.420279i	$-0.138068\pi$
$720$		0			0
$721$	16.4450	+	9.49451i	0.612443	+	0.353594i
$722$	3.72700	+	2.15178i	0.138704	+	0.0800811i
$723$			13.1038i			0.487335i
$724$	−13.0736	+	22.6441i	−0.485876	+	0.841563i
$725$		0			0
$726$	−8.02413	+	4.63273i	−0.297803	+	0.171937i
$727$	−17.2599			−0.640136			−0.320068	−	0.947395i	$-0.603706\pi$
$727$	−17.2599			−0.640136			−0.320068	+	0.947395i	$0.603706\pi$
$728$	1.14452	+	5.38789i	0.0424188	+	0.199688i
$729$	1.00000			0.0370370
$730$		0			0
$731$	4.14967	+	7.18744i	0.153481	+	0.265837i
$732$	2.49134	−	4.31513i	0.0920826	−	0.159492i
$733$			0.304799i			0.0112580i	0.999984	+	0.00562900i	$0.00179178\pi$
$733$			0.304799i			0.0112580i	−0.999984	+	0.00562900i	$0.998208\pi$
$734$	−6.14226	−	3.54624i	−0.226715	−	0.130894i
$735$		0			0
$736$		−	8.44285i		−	0.311208i
$737$	1.82576	−	3.16231i	0.0672528	−	0.116485i
$738$	0.784645	+	1.35904i	0.0288832	+	0.0500271i
$739$	−3.14941	+	1.81831i	−0.115853	+	0.0668877i	−0.556807	−	0.830642i	$-0.687974\pi$
$739$	−3.14941	+	1.81831i	−0.115853	+	0.0668877i	0.440954	+	0.897530i	$0.354640\pi$
$740$		0			0
$741$	−11.6448	−	12.9362i	−0.427783	−	0.475222i
$742$	21.2592			0.780451
$743$	26.1800	−	15.1150i	0.960451	−	0.554517i	0.0641394	−	0.997941i	$-0.479570\pi$
$743$	26.1800	−	15.1150i	0.960451	−	0.554517i	0.896312	+	0.443424i	$0.146236\pi$
$744$	−0.813725	−	1.40941i	−0.0298326	−	0.0516716i
$745$		0			0
$746$		−	36.9803i		−	1.35395i
$747$	−5.53408	−	3.19510i	−0.202481	−	0.116903i
$748$	1.78989	+	1.03339i	0.0654447	+	0.0377845i
$749$		−	16.0049i		−	0.584805i
$750$		0			0
$751$	−0.00159080	−	0.00275535i	−5.80493e−5	−	0.000100544i	0.865996	−	0.500050i	$-0.166685\pi$
$751$	−0.00159080	−	0.00275535i	−5.80493e−5	−	0.000100544i	−0.866054	+	0.499950i	$0.833352\pi$
$752$	4.28295	−	2.47276i	0.156183	−	0.0901723i
$753$	23.1644			0.844158
$754$	−15.6196	+	3.31800i	−0.568833	+	0.120834i
$755$		0			0
$756$	−1.32301	+	0.763837i	−0.0481172	+	0.0277805i
$757$	21.0345	+	36.4328i	0.764512	+	1.32417i	0.940504	+	0.339782i	$0.110353\pi$
$757$	21.0345	+	36.4328i	0.764512	+	1.32417i	−0.175992	+	0.984392i	$0.556313\pi$
$758$	17.1041	−	29.6252i	0.621250	−	1.07604i
$759$		−	11.1194i		−	0.403608i
$760$		0			0
$761$	21.1489	+	12.2103i	0.766646	+	0.442623i	0.831677	−	0.555260i	$-0.187381\pi$
$761$	21.1489	+	12.2103i	0.766646	+	0.442623i	−0.0650310	+	0.997883i	$0.520715\pi$
$762$			8.10083i			0.293462i
$763$	13.1226	−	22.7291i	0.475071	−	0.822847i
$764$	9.42713	+	16.3283i	0.341062	+	0.590736i
$765$		0			0
$766$	−26.0340			−0.940646
$767$	−36.9374	+	7.84643i	−1.33373	+	0.283318i
$768$	−1.00000			−0.0360844
$769$	28.1198	−	16.2350i	1.01403	−	0.585449i	0.101659	−	0.994819i	$-0.467585\pi$
$769$	28.1198	−	16.2350i	1.01403	−	0.585449i	0.912368	+	0.409370i	$0.134252\pi$
$770$		0			0
$771$	−1.92197	+	3.32895i	−0.0692182	+	0.119889i
$772$			17.8920i			0.643947i
$773$	7.16756	+	4.13819i	0.257799	+	0.148840i	0.623330	−	0.781959i	$-0.285779\pi$
$773$	7.16756	+	4.13819i	0.257799	+	0.148840i	−0.365531	+	0.930799i	$0.619113\pi$
$774$	−4.58006	−	2.64430i	−0.164627	−	0.0950473i
$775$		0			0
$776$	0.963028	−	1.66801i	0.0345707	−	0.0598782i
$777$	2.14100	+	3.70833i	0.0768081	+	0.133035i
$778$	5.40026	−	3.11784i	0.193609	−	0.111780i
$779$	7.57555			0.271422
$780$		0			0
$781$	19.5437			0.699328
$782$	11.4742	−	6.62464i	0.410317	−	0.236897i
$783$	−2.21438	−	3.83543i	−0.0791356	−	0.137067i
$784$	−2.33310	+	4.04106i	−0.0833252	+	0.144323i
$785$		0			0
$786$	−2.01356	−	1.16253i	−0.0718213	−	0.0414661i
$787$	−2.79726	−	1.61500i	−0.0997115	−	0.0575685i	0.449315	−	0.893373i	$-0.351668\pi$
$787$	−2.79726	−	1.61500i	−0.0997115	−	0.0575685i	−0.549027	+	0.835805i	$0.685001\pi$
$788$			0.625857i			0.0222952i
$789$	−15.3032	+	26.5060i	−0.544810	+	0.943638i
$790$		0			0
$791$	3.43958	−	1.98584i	0.122297	−	0.0706085i
$792$	−1.31702			−0.0467982
$793$	3.73299	+	17.5732i	0.132562	+	0.624043i
$794$	−36.6995			−1.30242
$795$		0			0
$796$	−8.84057	−	15.3123i	−0.313346	−	0.542731i
$797$	−20.3003	+	35.1612i	−0.719075	+	1.24547i	0.242292	+	0.970203i	$0.422101\pi$
$797$	−20.3003	+	35.1612i	−0.719075	+	1.24547i	−0.961367	+	0.275271i	$0.911232\pi$
$798$			7.37466i			0.261060i
$799$	6.72118	+	3.88048i	0.237778	+	0.137281i
$800$		0			0
$801$		−	18.4450i		−	0.651722i
$802$	14.1476	−	24.5044i	0.499569	−	0.865279i
$803$	3.94410	+	6.83138i	0.139184	+	0.241074i
$804$	−2.40112	+	1.38628i	−0.0846808	+	0.0488905i
$805$		0			0
$806$	5.58043	+	1.81397i	0.196562	+	0.0638944i
$807$	−18.0874			−0.636707
$808$	2.11188	−	1.21929i	0.0742956	−	0.0428946i
$809$	−0.000840236	−	0.00145533i	−2.95411e−5	−	5.11667e-5i	0.866011	−	0.500026i	$-0.166676\pi$
$809$	−0.000840236	−	0.00145533i	−2.95411e−5	−	5.11667e-5i	−0.866040	+	0.499974i	$0.833343\pi$
$810$		0			0
$811$		−	34.9476i		−	1.22718i	−0.789626	−	0.613588i	$-0.789726\pi$
$811$		−	34.9476i		−	1.22718i	0.789626	−	0.613588i	$-0.210274\pi$
$812$	5.85928	+	3.38286i	0.205621	+	0.118715i
$813$	12.2869	+	7.09382i	0.430919	+	0.248791i
$814$			3.69154i			0.129389i
$815$		0			0
$816$	−0.784645	−	1.35904i	−0.0274681	−	0.0475761i
$817$	−22.1097	+	12.7650i	−0.773519	+	0.446592i
$818$	−15.3280			−0.535931
$819$	1.70276	−	5.23831i	0.0594992	−	0.183041i
$820$		0			0
$821$	22.0044	−	12.7042i	0.767957	−	0.443380i	−0.0641882	−	0.997938i	$-0.520446\pi$
$821$	22.0044	−	12.7042i	0.767957	−	0.443380i	0.832145	+	0.554557i	$0.187112\pi$
$822$	6.14192	+	10.6381i	0.214224	+	0.371047i
$823$	10.9142	−	18.9040i	0.380446	−	0.658952i	−0.610680	−	0.791878i	$-0.709104\pi$
$823$	10.9142	−	18.9040i	0.380446	−	0.658952i	0.991126	+	0.132926i	$0.0424371\pi$
$824$		−	12.4300i		−	0.433020i
$825$		0			0
$826$	13.8561	+	7.99982i	0.482115	+	0.278349i
$827$			18.9366i			0.658492i	0.944244	+	0.329246i	$0.106794\pi$
$827$			18.9366i			0.658492i	−0.944244	+	0.329246i	$0.893206\pi$
$828$	−4.22143	+	7.31172i	−0.146705	+	0.254100i
$829$	0.304309	+	0.527078i	0.0105691	+	0.0183062i	0.871262	−	0.490819i	$-0.163302\pi$
$829$	0.304309	+	0.527078i	0.0105691	+	0.0183062i	−0.860692	+	0.509125i	$0.829969\pi$
$830$		0			0
$831$	16.8419			0.584240
$832$	2.67975	−	2.41225i	0.0929036	−	0.0836296i
$833$	−7.32263			−0.253714
$834$	5.76531	−	3.32861i	0.199637	−	0.115260i
$835$		0			0
$836$	−3.17887	+	5.50597i	−0.109944	+	0.190428i
$837$			1.62745i			0.0562529i
$838$	23.3293	+	13.4692i	0.805898	+	0.465286i
$839$	23.3215	+	13.4647i	0.805148	+	0.464853i	0.845268	−	0.534342i	$-0.179441\pi$
$839$	23.3215	+	13.4647i	0.805148	+	0.464853i	−0.0401198	+	0.999195i	$0.512774\pi$
$840$		0			0
$841$	4.69300	−	8.12852i	0.161828	−	0.280294i
$842$	−19.2679	−	33.3731i	−0.664017	−	1.15011i
$843$	7.46112	−	4.30768i	0.256974	−	0.148364i
$844$	−17.2445			−0.593581
$845$		0			0
$846$	−4.94552			−0.170030
$847$	−12.2583	+	7.07731i	−0.421199	+	0.243179i
$848$	−6.95804	−	12.0517i	−0.238940	−	0.413856i
$849$	13.8098	−	23.9192i	0.473950	−	0.820905i
$850$		0			0
$851$	20.4944	+	11.8325i	0.702541	+	0.405612i
$852$	−12.8513	−	7.41968i	−0.440277	−	0.254194i
$853$			41.3790i			1.41679i	0.705817	+	0.708394i	$0.250580\pi$
$853$			41.3790i			1.41679i	−0.705817	+	0.708394i	$0.749420\pi$
$854$	3.80596	−	6.59212i	0.130237	−	0.225578i
$855$		0			0
$856$	−9.07302	+	5.23831i	−0.310109	+	0.179042i
$857$	30.6051			1.04545			0.522726	−	0.852501i	$-0.324915\pi$
$857$	30.6051			1.04545			0.522726	+	0.852501i	$0.324915\pi$
$858$	3.52928	−	3.17697i	0.120488	−	0.108460i
$859$	−30.9385			−1.05561			−0.527803	−	0.849367i	$-0.676984\pi$
$859$	−30.9385			−1.05561			−0.527803	+	0.849367i	$0.676984\pi$
$860$		0			0
$861$	1.19868	+	2.07618i	0.0408510	+	0.0707560i
$862$	1.43612	−	2.48744i	0.0489145	−	0.0847225i
$863$			15.1133i			0.514464i	0.966350	+	0.257232i	$0.0828104\pi$
$863$			15.1133i			0.514464i	−0.966350	+	0.257232i	$0.917190\pi$
$864$	0.866025	+	0.500000i	0.0294628	+	0.0170103i
$865$		0			0
$866$			12.9724i			0.440819i
$867$	−7.26867	+	12.5897i	−0.246857	+	0.427569i
$868$	−1.24311	−	2.15313i	−0.0421938	−	0.0730819i
$869$	5.56179	−	3.21110i	0.188671	−	0.108929i
$870$		0			0
$871$	3.09033	−	9.50698i	0.104712	−	0.322132i
$872$	−17.1799			−0.581784
$873$	−1.66801	+	0.963028i	−0.0564537	+	0.0325936i
$874$	20.3784	+	35.2964i	0.689310	+	1.19392i
$875$		0			0
$876$		−	5.98944i		−	0.202364i
$877$	−9.60868	−	5.54757i	−0.324462	−	0.187328i	0.328918	−	0.944359i	$-0.393316\pi$
$877$	−9.60868	−	5.54757i	−0.324462	−	0.187328i	−0.653380	+	0.757030i	$0.726649\pi$
$878$	1.77380	+	1.02411i	0.0598629	+	0.0345619i
$879$		−	30.2501i		−	1.02031i
$880$		0			0
$881$	22.3598	+	38.7283i	0.753321	+	1.30479i	0.946205	+	0.323568i	$0.104883\pi$
$881$	22.3598	+	38.7283i	0.753321	+	1.30479i	−0.192884	+	0.981222i	$0.561784\pi$
$882$	4.04106	−	2.33310i	0.136069	−	0.0785597i
$883$	−10.9779			−0.369435			−0.184718	−	0.982792i	$-0.559137\pi$
$883$	−10.9779			−0.369435			−0.184718	+	0.982792i	$0.559137\pi$
$884$	5.38100	+	1.74914i	0.180983	+	0.0588301i
$885$		0			0
$886$	22.2640	−	12.8541i	0.747973	−	0.431842i
$887$	19.2001	+	33.2555i	0.644675	+	1.11661i	0.984377	+	0.176076i	$0.0563405\pi$
$887$	19.2001	+	33.2555i	0.644675	+	1.11661i	−0.339702	+	0.940533i	$0.610326\pi$
$888$	1.40148	−	2.42743i	0.0470305	−	0.0814593i
$889$			12.3754i			0.415059i
$890$		0			0
$891$	1.14057	+	0.658509i	0.0382106	+	0.0220609i
$892$			4.89716i			0.163969i
$893$	−11.9369	+	20.6754i	−0.399455	+	0.691876i
$894$	1.50554	+	2.60768i	0.0503529	+	0.0872137i
$895$		0			0
$896$	−1.52767			−0.0510360
$897$	−6.32532	−	29.7767i	−0.211196	−	0.994216i
$898$	18.5625			0.619440
$899$	6.24197	−	3.60380i	0.208181	−	0.120193i
$900$		0			0
$901$	10.9192	−	18.9126i	0.363770	−	0.630069i
$902$			2.06678i			0.0688163i
$903$	−6.99684	−	4.03963i	−0.232840	−	0.134430i
$904$	−2.25151	−	1.29991i	−0.0748842	−	0.0432344i
$905$		0			0
$906$	6.00745	−	10.4052i	0.199584	−	0.345690i
$907$	19.8581	+	34.3953i	0.659378	+	1.14208i	0.980777	+	0.195133i	$0.0625137\pi$
$907$	19.8581	+	34.3953i	0.659378	+	1.14208i	−0.321399	+	0.946944i	$0.604153\pi$
$908$	8.79132	−	5.07567i	0.291750	−	0.168442i
$909$	−2.43859			−0.0808828
$910$		0			0
$911$	17.9575			0.594959			0.297479	−	0.954728i	$-0.403854\pi$
$911$	17.9575			0.594959			0.297479	+	0.954728i	$0.403854\pi$
$912$	4.18063	−	2.41369i	0.138435	−	0.0799252i
$913$	−4.20801	−	7.28848i	−0.139265	−	0.241213i
$914$	12.3213	−	21.3412i	0.407554	−	0.705904i
$915$		0			0
$916$	−13.3332	−	7.69794i	−0.440542	−	0.254347i
$917$	−3.07607	−	1.77597i	−0.101581	−	0.0586476i
$918$			1.56929i			0.0517943i
$919$	−10.0149	+	17.3463i	−0.330361	+	0.572203i	−0.982583	−	0.185826i	$-0.940504\pi$
$919$	−10.0149	+	17.3463i	−0.330361	+	0.572203i	0.652221	+	0.758029i	$0.273837\pi$
$920$		0			0
$921$	−12.2449	+	7.06959i	−0.403483	+	0.232951i
$922$	−31.8342			−1.04840
$923$	52.3363	−	11.1175i	1.72267	−	0.365938i
$924$	−2.01198			−0.0661891
$925$		0			0
$926$	−1.59160	−	2.75673i	−0.0523031	−	0.0905916i
$927$	−6.21501	+	10.7647i	−0.204128	+	0.353559i
$928$		−	4.42877i		−	0.145381i
$929$	−35.1451	−	20.2910i	−1.15307	−	0.665727i	−0.203439	−	0.979088i	$-0.565212\pi$
$929$	−35.1451	−	20.2910i	−1.15307	−	0.665727i	−0.949634	+	0.313361i	$0.898545\pi$
$930$		0			0
$931$		−	22.5255i		−	0.738245i
$932$	−4.95812	+	8.58772i	−0.162409	+	0.281300i
$933$	−4.98713	−	8.63797i	−0.163271	−	0.282794i
$934$	18.7708	−	10.8373i	0.614200	−	0.354609i
$935$		0			0
$936$	−3.52686	+	0.749192i	−0.115279	+	0.0244881i
$937$	47.1112			1.53905			0.769527	−	0.638614i	$-0.220492\pi$
$937$	47.1112			1.53905			0.769527	+	0.638614i	$0.220492\pi$
$938$	−3.66812	+	2.11779i	−0.119769	+	0.0691484i
$939$	−1.54230	−	2.67134i	−0.0503311	−	0.0871760i
$940$		0			0
$941$		−	4.35101i		−	0.141839i	−0.997482	−	0.0709195i	$-0.977407\pi$
$941$		−	4.35101i		−	0.141839i	0.997482	−	0.0709195i	$-0.0225933\pi$
$942$	2.61155	+	1.50778i	0.0850888	+	0.0491261i
$943$	11.4742	+	6.62464i	0.373652	+	0.215728i
$944$		−	10.4732i		−	0.340873i
$945$		0			0
$946$	−3.48259	−	6.03202i	−0.113229	−	0.196118i
$947$	30.2381	−	17.4580i	0.982605	−	0.567307i	0.0795494	−	0.996831i	$-0.474652\pi$
$947$	30.2381	−	17.4580i	0.982605	−	0.567307i	0.903056	+	0.429524i	$0.141319\pi$
$948$	−4.87632			−0.158376
$949$	14.4480	+	16.0502i	0.469002	+	0.521011i
$950$		0			0
$951$	12.3824	−	7.14899i	0.401527	−	0.231822i
$952$	−1.19868	−	2.07618i	−0.0388495	−	0.0672893i
$953$	−4.84801	+	8.39700i	−0.157042	+	0.272005i	−0.933801	−	0.357793i	$-0.883529\pi$
$953$	−4.84801	+	8.39700i	−0.157042	+	0.272005i	0.776758	+	0.629799i	$0.216863\pi$
$954$			13.9161i			0.450550i
$955$		0			0
$956$	−8.19404	−	4.73083i	−0.265014	−	0.153006i
$957$		−	5.83277i		−	0.188547i
$958$	14.6511	−	25.3765i	0.473356	−	0.819876i
$959$	9.38286	+	16.2516i	0.302988	+	0.524791i
$960$		0			0
$961$	28.3514			0.914561
$962$	2.09995	+	9.88562i	0.0677052	+	0.318725i
$963$	10.4766			0.337604
$964$	11.3482	−	6.55189i	0.365501	−	0.211022i
$965$		0			0
$966$	−6.44897	+	11.1699i	−0.207492	+	0.359387i
$967$		−	36.1715i		−	1.16320i	−0.813476	−	0.581599i	$-0.802427\pi$
$967$		−	36.1715i		−	1.16320i	0.813476	−	0.581599i	$-0.197573\pi$
$968$	8.02413	+	4.63273i	0.257905	+	0.148902i
$969$	6.56062	+	3.78778i	0.210757	+	0.121681i
$970$		0			0
$971$	0.194688	−	0.337209i	0.00624783	−	0.0108216i	−0.862885	−	0.505401i	$-0.831345\pi$
$971$	0.194688	−	0.337209i	0.00624783	−	0.0108216i	0.869132	+	0.494579i	$0.164678\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	8.80753	−	5.08503i	0.282356	−	0.163019i
$974$	−42.5287			−1.36271
$975$		0			0
$976$	−4.98268			−0.159492
$977$	−4.67802	+	2.70086i	−0.149663	+	0.0864080i	−0.572961	−	0.819582i	$-0.694206\pi$
$977$	−4.67802	+	2.70086i	−0.149663	+	0.0864080i	0.423298	+	0.905990i	$0.360872\pi$
$978$	4.95812	+	8.58772i	0.158543	+	0.274605i
$979$	12.1462	−	21.0378i	0.388194	−	0.672372i
$980$		0			0
$981$	14.8782	+	8.58994i	0.475025	+	0.274256i
$982$	10.9556	+	6.32521i	0.349607	+	0.201845i
$983$			43.6819i			1.39324i	0.717442	+	0.696618i	$0.245313\pi$
$983$			43.6819i			1.39324i	−0.717442	+	0.696618i	$0.754687\pi$
$984$	0.784645	−	1.35904i	0.0250136	−	0.0433248i
$985$		0			0
$986$	6.01889	−	3.47501i	0.191681	−	0.110667i
$987$	−7.55515			−0.240483
$988$	−5.38064	+	16.5528i	−0.171181	+	0.526615i
$989$	−44.6508			−1.41981
$990$		0			0
$991$	27.9427	+	48.3981i	0.887628	+	1.53742i	0.842671	+	0.538428i	$0.180982\pi$
$991$	27.9427	+	48.3981i	0.887628	+	1.53742i	0.0449569	+	0.998989i	$0.485685\pi$
$992$	−0.813725	+	1.40941i	−0.0258358	+	0.0447489i
$993$		−	11.4202i		−	0.362409i
$994$	−19.6325	−	11.3349i	−0.622706	−	0.359520i
$995$		0			0
$996$			6.39020i			0.202481i
$997$	17.8901	−	30.9866i	0.566587	−	0.981357i	−0.430314	−	0.902680i	$-0.641597\pi$
$997$	17.8901	−	30.9866i	0.566587	−	0.981357i	0.996900	−	0.0786773i	$-0.0250697\pi$
$998$	2.27004	+	3.93182i	0.0718567	+	0.124460i
$999$	−2.42743	+	1.40148i	−0.0768005	+	0.0443408i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.j.751.6		12
5.2	odd	4		390.2.x.b.49.5	yes	12
5.3	odd	4		390.2.x.a.49.2	✓	12
5.4	even	2		1950.2.bc.i.751.1		12
13.4	even	6	inner	1950.2.bc.j.901.6		12
15.2	even	4		1170.2.bj.c.829.2		12
15.8	even	4		1170.2.bj.d.829.5		12
65.4	even	6		1950.2.bc.i.901.1		12
65.17	odd	12		390.2.x.a.199.2	yes	12
65.43	odd	12		390.2.x.b.199.5	yes	12
195.17	even	12		1170.2.bj.d.199.5		12
195.173	even	12		1170.2.bj.c.199.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.x.a.49.2	✓	12	5.3	odd	4
390.2.x.a.199.2	yes	12	65.17	odd	12
390.2.x.b.49.5	yes	12	5.2	odd	4
390.2.x.b.199.5	yes	12	65.43	odd	12
1170.2.bj.c.199.2		12	195.173	even	12
1170.2.bj.c.829.2		12	15.2	even	4
1170.2.bj.d.199.5		12	195.17	even	12
1170.2.bj.d.829.5		12	15.8	even	4
1950.2.bc.i.751.1		12	5.4	even	2
1950.2.bc.i.901.1		12	65.4	even	6
1950.2.bc.j.751.6		12	1.1	even	1	trivial
1950.2.bc.j.901.6		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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{6} +(1.32301 + 0.763837i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +(1.32301 + 0.763837i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.14057 + 0.658509i) q^{11} +1.00000 q^{12} +(-2.67975 + 2.41225i) q^{13} +1.52767 q^{14} +(-0.500000 - 0.866025i) q^{16} +(0.784645 - 1.35904i) q^{17} +1.00000i q^{18} +(4.18063 + 2.41369i) q^{19} +1.52767i q^{21} +(-0.658509 + 1.14057i) q^{22} +(4.22143 + 7.31172i) q^{23} +(0.866025 - 0.500000i) q^{24} +(-1.11461 + 3.42894i) q^{26} -1.00000 q^{27} +(1.32301 - 0.763837i) q^{28} +(2.21438 + 3.83543i) q^{29} -1.62745i q^{31} +(-0.866025 - 0.500000i) q^{32} +(-1.14057 - 0.658509i) q^{33} -1.56929i q^{34} +(0.500000 + 0.866025i) q^{36} +(2.42743 - 1.40148i) q^{37} +4.82738 q^{38} +(-3.42894 - 1.11461i) q^{39} +(1.35904 - 0.784645i) q^{41} +(0.763837 + 1.32301i) q^{42} +(-2.64430 + 4.58006i) q^{43} +1.31702i q^{44} +(7.31172 + 4.22143i) q^{46} +4.94552i q^{47} +(0.500000 - 0.866025i) q^{48} +(-2.33310 - 4.04106i) q^{49} +1.56929 q^{51} +(0.749192 + 3.52686i) q^{52} +13.9161 q^{53} +(-0.866025 + 0.500000i) q^{54} +(0.763837 - 1.32301i) q^{56} +4.82738i q^{57} +(3.83543 + 2.21438i) q^{58} +(9.07005 + 5.23660i) q^{59} +(2.49134 - 4.31513i) q^{61} +(-0.813725 - 1.40941i) q^{62} +(-1.32301 + 0.763837i) q^{63} -1.00000 q^{64} -1.31702 q^{66} +(-2.40112 + 1.38628i) q^{67} +(-0.784645 - 1.35904i) q^{68} +(-4.22143 + 7.31172i) q^{69} +(-12.8513 - 7.41968i) q^{71} +(0.866025 + 0.500000i) q^{72} -5.98944i q^{73} +(1.40148 - 2.42743i) q^{74} +(4.18063 - 2.41369i) q^{76} -2.01198 q^{77} +(-3.52686 + 0.749192i) q^{78} -4.87632 q^{79} +(-0.500000 - 0.866025i) q^{81} +(0.784645 - 1.35904i) q^{82} +6.39020i q^{83} +(1.32301 + 0.763837i) q^{84} +5.28860i q^{86} +(-2.21438 + 3.83543i) q^{87} +(0.658509 + 1.14057i) q^{88} +(-15.9738 + 9.22251i) q^{89} +(-5.38789 + 1.14452i) q^{91} +8.44285 q^{92} +(1.40941 - 0.813725i) q^{93} +(2.47276 + 4.28295i) q^{94} -1.00000i q^{96} +(1.66801 + 0.963028i) q^{97} +(-4.04106 - 2.33310i) q^{98} -1.31702i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{3} + 6 q^{4} - 12 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^3 + 6 * q^4 - 12 * q^7 - 6 * q^9	\( 12 q + 6 q^{3} + 6 q^{4} - 12 q^{7} - 6 q^{9} + 6 q^{11} + 12 q^{12} + 4 q^{13} - 4 q^{14} - 6 q^{16} + 8 q^{17} + 6 q^{19} - 6 q^{22} + 16 q^{23} - 2 q^{26} - 12 q^{27} - 12 q^{28} - 14 q^{29} + 6 q^{33} + 6 q^{36} - 6 q^{37} - 8 q^{38} + 2 q^{39} - 18 q^{41} - 2 q^{42} + 10 q^{43} - 6 q^{46} + 6 q^{48} - 8 q^{49} + 16 q^{51} + 2 q^{52} - 2 q^{56} + 6 q^{58} + 36 q^{59} + 10 q^{61} + 16 q^{62} + 12 q^{63} - 12 q^{64} - 12 q^{66} + 24 q^{67} - 8 q^{68} - 16 q^{69} - 12 q^{71} + 12 q^{74} + 6 q^{76} + 24 q^{77} - 10 q^{78} - 4 q^{79} - 6 q^{81} + 8 q^{82} - 12 q^{84} + 14 q^{87} + 6 q^{88} - 18 q^{89} + 2 q^{91} + 32 q^{92} - 6 q^{93} + 8 q^{94} - 24 q^{97} + 24 q^{98}+O(q^{100}) \) 12 * q + 6 * q^3 + 6 * q^4 - 12 * q^7 - 6 * q^9 + 6 * q^11 + 12 * q^12 + 4 * q^13 - 4 * q^14 - 6 * q^16 + 8 * q^17 + 6 * q^19 - 6 * q^22 + 16 * q^23 - 2 * q^26 - 12 * q^27 - 12 * q^28 - 14 * q^29 + 6 * q^33 + 6 * q^36 - 6 * q^37 - 8 * q^38 + 2 * q^39 - 18 * q^41 - 2 * q^42 + 10 * q^43 - 6 * q^46 + 6 * q^48 - 8 * q^49 + 16 * q^51 + 2 * q^52 - 2 * q^56 + 6 * q^58 + 36 * q^59 + 10 * q^61 + 16 * q^62 + 12 * q^63 - 12 * q^64 - 12 * q^66 + 24 * q^67 - 8 * q^68 - 16 * q^69 - 12 * q^71 + 12 * q^74 + 6 * q^76 + 24 * q^77 - 10 * q^78 - 4 * q^79 - 6 * q^81 + 8 * q^82 - 12 * q^84 + 14 * q^87 + 6 * q^88 - 18 * q^89 + 2 * q^91 + 32 * q^92 - 6 * q^93 + 8 * q^94 - 24 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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