LMFDB - Embedded newform 1950.2.bc.h.751.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("1950.751");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1950 = 2 \cdot 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1950.bc (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$15.5708283941$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 6 x^{11} + 87 x^{10} - 380 x^{9} + 2556 x^{8} - 8010 x^{7} + 29687 x^{6} - 62556 x^{5} + \cdots + 14089 $ x^12 - 6x^11 + 87x^10 - 380x^9 + 2556x^8 - 8010x^7 + 29687x^6 - 62556x^5 + 115386x^4 - 135130x^3 + 113253x^2 - 54888*x + 14089
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			751.4
Root			$0.500000 + 4.71596i$ of defining polynomial
Character	$\chi$	$=$	1950.751
Dual form			1950.2.bc.h.901.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-3.96812 - 2.29099i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(-3.96812 - 2.29099i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.563824 + 0.325524i) q^{11} -1.00000 q^{12} +(-1.31432 + 3.35747i) q^{13} -4.58199 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.75049 + 3.03194i) q^{17} +1.00000i q^{18} +(2.50851 + 1.44829i) q^{19} +4.58199i q^{21} +(-0.325524 + 0.563824i) q^{22} +(-1.42497 - 2.46812i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.540502 + 3.56481i) q^{26} +1.00000 q^{27} +(-3.96812 + 2.29099i) q^{28} +(4.78243 + 8.28342i) q^{29} -5.58728i q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.563824 + 0.325524i) q^{33} +3.50098i q^{34} +(0.500000 + 0.866025i) q^{36} +(-4.00851 + 2.31432i) q^{37} +2.89658 q^{38} +(3.56481 - 0.540502i) q^{39} +(-3.03194 + 1.75049i) q^{41} +(2.29099 + 3.96812i) q^{42} +(-3.85747 + 6.68133i) q^{43} +0.651048i q^{44} +(-2.46812 - 1.42497i) q^{46} +2.08630i q^{47} +(-0.500000 + 0.866025i) q^{48} +(6.99731 + 12.1197i) q^{49} +3.50098 q^{51} +(2.25049 + 2.81696i) q^{52} +5.58728 q^{53} +(0.866025 - 0.500000i) q^{54} +(-2.29099 + 3.96812i) q^{56} -2.89658i q^{57} +(8.28342 + 4.78243i) q^{58} +(6.47663 + 3.73928i) q^{59} +(3.31432 - 5.74056i) q^{61} +(-2.79364 - 4.83873i) q^{62} +(3.96812 - 2.29099i) q^{63} -1.00000 q^{64} +0.651048 q^{66} +(7.93912 - 4.58365i) q^{67} +(1.75049 + 3.03194i) q^{68} +(-1.42497 + 2.46812i) q^{69} +(-11.2778 - 6.51127i) q^{71} +(0.866025 + 0.500000i) q^{72} +1.04861i q^{73} +(-2.31432 + 4.00851i) q^{74} +(2.50851 - 1.44829i) q^{76} +2.98309 q^{77} +(2.81696 - 2.25049i) q^{78} -3.46158 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.75049 + 3.03194i) q^{82} +10.5722i q^{83} +(3.96812 + 2.29099i) q^{84} +7.71493i q^{86} +(4.78243 - 8.28342i) q^{87} +(0.325524 + 0.563824i) q^{88} +(-7.10045 + 4.09944i) q^{89} +(12.9073 - 10.3117i) q^{91} -2.84994 q^{92} +(-4.83873 + 2.79364i) q^{93} +(1.04315 + 1.80679i) q^{94} +1.00000i q^{96} +(-12.5030 - 7.21861i) q^{97} +(12.1197 + 6.99731i) q^{98} -0.651048i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 6 q^{3} + 6 q^{4} - 6 q^{7} - 6 q^{9}+O(q^{10}) $ 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^7 - 6 * q^9	$ 12 q - 6 q^{3} + 6 q^{4} - 6 q^{7} - 6 q^{9} - 12 q^{11} - 12 q^{12} + 8 q^{14} - 6 q^{16} - 6 q^{19} - 4 q^{22} + 4 q^{23} - 4 q^{26} + 12 q^{27} - 6 q^{28} + 12 q^{33} + 6 q^{36} - 12 q^{37} + 24 q^{38} + 6 q^{39} - 4 q^{42} - 10 q^{43} + 12 q^{46} - 6 q^{48} + 32 q^{49} + 6 q^{52} - 16 q^{53} + 4 q^{56} + 24 q^{61} + 8 q^{62} + 6 q^{63} - 12 q^{64} + 8 q^{66} + 6 q^{67} + 4 q^{69} + 12 q^{71} - 12 q^{74} - 6 q^{76} - 48 q^{77} + 8 q^{78} + 52 q^{79} - 6 q^{81} + 6 q^{84} + 4 q^{88} + 24 q^{89} - 54 q^{91} + 8 q^{92} - 8 q^{94} + 12 q^{97} + 36 q^{98}+O(q^{100}) $ 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^7 - 6 * q^9 - 12 * q^11 - 12 * q^12 + 8 * q^14 - 6 * q^16 - 6 * q^19 - 4 * q^22 + 4 * q^23 - 4 * q^26 + 12 * q^27 - 6 * q^28 + 12 * q^33 + 6 * q^36 - 12 * q^37 + 24 * q^38 + 6 * q^39 - 4 * q^42 - 10 * q^43 + 12 * q^46 - 6 * q^48 + 32 * q^49 + 6 * q^52 - 16 * q^53 + 4 * q^56 + 24 * q^61 + 8 * q^62 + 6 * q^63 - 12 * q^64 + 8 * q^66 + 6 * q^67 + 4 * q^69 + 12 * q^71 - 12 * q^74 - 6 * q^76 - 48 * q^77 + 8 * q^78 + 52 * q^79 - 6 * q^81 + 6 * q^84 + 4 * q^88 + 24 * q^89 - 54 * q^91 + 8 * q^92 - 8 * q^94 + 12 * q^97 + 36 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.866025	−	0.500000i	−0.353553	−	0.204124i
$7$	−3.96812	−	2.29099i	−1.49981	−	0.865914i	−0.499808	−	0.866137i	$-0.666596\pi$
$7$	−3.96812	−	2.29099i	−1.49981	−	0.865914i	−1.00000		0.000222235i	$0.999929\pi$
$8$		−	1.00000i		−	0.353553i
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−0.563824	+	0.325524i	−0.169999	+	0.0981491i	−0.582585	−	0.812769i	$-0.697959\pi$
$11$	−0.563824	+	0.325524i	−0.169999	+	0.0981491i	0.412586	+	0.910919i	$0.364626\pi$
$12$	−1.00000			−0.288675
$13$	−1.31432	+	3.35747i	−0.364526	+	0.931193i
$13$	−1.31432	+	3.35747i	−0.364526	+	0.931193i
$14$	−4.58199			−1.22459
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.75049	+	3.03194i	−0.424557	+	0.735354i	−0.996379	−	0.0850238i	$-0.972903\pi$
$17$	−1.75049	+	3.03194i	−0.424557	+	0.735354i	0.571822	+	0.820378i	$0.306237\pi$
$18$			1.00000i			0.235702i
$19$	2.50851	+	1.44829i	0.575492	+	0.332261i	0.759340	−	0.650694i	$-0.225522\pi$
$19$	2.50851	+	1.44829i	0.575492	+	0.332261i	−0.183848	+	0.982955i	$0.558855\pi$
$20$		0			0
$21$			4.58199i			0.999872i
$22$	−0.325524	+	0.563824i	−0.0694019	+	0.120208i
$23$	−1.42497	−	2.46812i	−0.297126	−	0.514638i	0.678351	−	0.734738i	$-0.262695\pi$
$23$	−1.42497	−	2.46812i	−0.297126	−	0.514638i	−0.975477	+	0.220100i	$0.929362\pi$
$24$	−0.866025	+	0.500000i	−0.176777	+	0.102062i
$25$		0			0
$26$	0.540502	+	3.56481i	0.106001	+	0.699116i
$27$	1.00000			0.192450
$28$	−3.96812	+	2.29099i	−0.749904	+	0.432957i
$29$	4.78243	+	8.28342i	0.888076	+	1.53819i	0.842147	+	0.539247i	$0.181291\pi$
$29$	4.78243	+	8.28342i	0.888076	+	1.53819i	0.0459282	+	0.998945i	$0.485375\pi$
$30$		0			0
$31$		−	5.58728i		−	1.00351i	−0.865011	−	0.501753i	$-0.832689\pi$
$31$		−	5.58728i		−	1.00351i	0.865011	−	0.501753i	$-0.167311\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	0.563824	+	0.325524i	0.0981491	+	0.0566664i
$34$			3.50098i			0.600414i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	−4.00851	+	2.31432i	−0.658995	+	0.380471i	−0.791894	−	0.610658i	$-0.790905\pi$
$37$	−4.00851	+	2.31432i	−0.658995	+	0.380471i	0.132899	+	0.991130i	$0.457572\pi$
$38$	2.89658			0.469888
$39$	3.56481	−	0.540502i	0.570826	−	0.0865495i
$40$		0			0
$41$	−3.03194	+	1.75049i	−0.473510	+	0.273381i	−0.717708	−	0.696344i	$-0.754809\pi$
$41$	−3.03194	+	1.75049i	−0.473510	+	0.273381i	0.244198	+	0.969725i	$0.421475\pi$
$42$	2.29099	+	3.96812i	0.353508	+	0.612294i
$43$	−3.85747	+	6.68133i	−0.588258	+	1.01889i	0.406203	+	0.913783i	$0.366853\pi$
$43$	−3.85747	+	6.68133i	−0.588258	+	1.01889i	−0.994461	+	0.105110i	$0.966481\pi$
$44$			0.651048i			0.0981491i
$45$		0			0
$46$	−2.46812	−	1.42497i	−0.363904	−	0.210100i
$47$			2.08630i			0.304318i	0.988356	+	0.152159i	$0.0486226\pi$
$47$			2.08630i			0.304318i	−0.988356	+	0.152159i	$0.951377\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	6.99731	+	12.1197i	0.999615	+	1.73138i
$50$		0			0
$51$	3.50098			0.490236
$52$	2.25049	+	2.81696i	0.312087	+	0.390643i
$53$	5.58728			0.767472			0.383736	−	0.923443i	$-0.374637\pi$
$53$	5.58728			0.767472			0.383736	+	0.923443i	$0.374637\pi$
$54$	0.866025	−	0.500000i	0.117851	−	0.0680414i
$55$		0			0
$56$	−2.29099	+	3.96812i	−0.306147	+	0.530262i
$57$		−	2.89658i		−	0.383662i
$58$	8.28342	+	4.78243i	1.08767	+	0.627964i
$59$	6.47663	+	3.73928i	0.843185	+	0.486813i	0.858346	−	0.513072i	$-0.171493\pi$
$59$	6.47663	+	3.73928i	0.843185	+	0.486813i	−0.0151603	+	0.999885i	$0.504826\pi$
$60$		0			0
$61$	3.31432	−	5.74056i	0.424355	−	0.735004i	−0.572005	−	0.820250i	$-0.693834\pi$
$61$	3.31432	−	5.74056i	0.424355	−	0.735004i	0.996360	+	0.0852461i	$0.0271676\pi$
$62$	−2.79364	−	4.83873i	−0.354793	−	0.614519i
$63$	3.96812	−	2.29099i	0.499936	−	0.288638i
$64$	−1.00000			−0.125000
$65$		0			0
$66$	0.651048			0.0801384
$67$	7.93912	−	4.58365i	0.969917	−	0.559982i	0.0707063	−	0.997497i	$-0.477475\pi$
$67$	7.93912	−	4.58365i	0.969917	−	0.559982i	0.899211	+	0.437515i	$0.144141\pi$
$68$	1.75049	+	3.03194i	0.212278	+	0.367677i
$69$	−1.42497	+	2.46812i	−0.171546	+	0.297126i
$70$		0			0
$71$	−11.2778	−	6.51127i	−1.33843	−	0.772745i	−0.351859	−	0.936053i	$-0.614450\pi$
$71$	−11.2778	−	6.51127i	−1.33843	−	0.772745i	−0.986575	+	0.163308i	$0.947784\pi$
$72$	0.866025	+	0.500000i	0.102062	+	0.0589256i
$73$			1.04861i			0.122731i	0.998115	+	0.0613655i	$0.0195455\pi$
$73$			1.04861i			0.122731i	−0.998115	+	0.0613655i	$0.980454\pi$
$74$	−2.31432	+	4.00851i	−0.269034	+	0.465980i
$75$		0			0
$76$	2.50851	−	1.44829i	0.287746	−	0.166130i
$77$	2.98309			0.339955
$78$	2.81696	−	2.25049i	0.318958	−	0.254818i
$79$	−3.46158			−0.389458			−0.194729	−	0.980857i	$-0.562383\pi$
$79$	−3.46158			−0.389458			−0.194729	+	0.980857i	$0.562383\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.75049	+	3.03194i	−0.193310	+	0.334822i
$83$			10.5722i			1.16045i	0.814455	+	0.580226i	$0.197036\pi$
$83$			10.5722i			1.16045i	−0.814455	+	0.580226i	$0.802964\pi$
$84$	3.96812	+	2.29099i	0.432957	+	0.249968i
$85$		0			0
$86$			7.71493i			0.831922i
$87$	4.78243	−	8.28342i	0.512731	−	0.888076i
$88$	0.325524	+	0.563824i	0.0347010	+	0.0601038i
$89$	−7.10045	+	4.09944i	−0.752646	+	0.434540i	−0.826649	−	0.562718i	$-0.809756\pi$
$89$	−7.10045	+	4.09944i	−0.752646	+	0.434540i	0.0740033	+	0.997258i	$0.476422\pi$
$90$		0			0
$91$	12.9073	−	10.3117i	1.35305	−	1.08096i
$92$	−2.84994			−0.297126
$93$	−4.83873	+	2.79364i	−0.501753	+	0.289687i
$94$	1.04315	+	1.80679i	0.107593	+	0.186356i
$95$		0			0
$96$			1.00000i			0.102062i
$97$	−12.5030	−	7.21861i	−1.26949	−	0.732939i	−0.294596	−	0.955622i	$-0.595185\pi$
$97$	−12.5030	−	7.21861i	−1.26949	−	0.732939i	−0.974891	+	0.222683i	$0.928519\pi$
$98$	12.1197	+	6.99731i	1.22427	+	0.706835i
$99$		−	0.651048i		−	0.0654328i
$100$		0			0
$101$	4.13139	+	7.15577i	0.411088	+	0.712026i	0.995009	−	0.0997849i	$-0.0318155\pi$
$101$	4.13139	+	7.15577i	0.411088	+	0.712026i	−0.583921	+	0.811811i	$0.698482\pi$
$102$	3.03194	−	1.75049i	0.300207	−	0.173325i
$103$	−19.7208			−1.94315			−0.971575	−	0.236734i	$-0.923923\pi$
$103$	−19.7208			−1.94315			−0.971575	+	0.236734i	$0.923923\pi$
$104$	3.35747	+	1.31432i	0.329227	+	0.128879i
$105$		0			0
$106$	4.83873	−	2.79364i	0.469979	−	0.271342i
$107$	−1.28048	−	2.21785i	−0.123789	−	0.214408i	0.797470	−	0.603358i	$-0.206171\pi$
$107$	−1.28048	−	2.21785i	−0.123789	−	0.214408i	−0.921259	+	0.388950i	$0.872838\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$			13.7169i			1.31384i	0.753960	+	0.656920i	$0.228141\pi$
$109$			13.7169i			1.31384i	−0.753960	+	0.656920i	$0.771859\pi$
$110$		0			0
$111$	4.00851	+	2.31432i	0.380471	+	0.219665i
$112$			4.58199i			0.432957i
$113$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$113$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$114$	−1.44829	−	2.50851i	−0.135645	−	0.234944i
$115$		0			0
$116$	9.56487			0.888076
$117$	−2.25049	−	2.81696i	−0.208058	−	0.260428i
$118$	7.47857			0.688458
$119$	13.8923	−	8.02073i	1.27351	−	0.735259i
$120$		0			0
$121$	−5.28807	+	9.15920i	−0.480733	+	0.832655i
$122$		−	6.62863i		−	0.600128i
$123$	3.03194	+	1.75049i	0.273381	+	0.157837i
$124$	−4.83873	−	2.79364i	−0.434531	−	0.250876i
$125$		0			0
$126$	2.29099	−	3.96812i	0.204098	−	0.353508i
$127$	4.48031	+	7.76012i	0.397563	+	0.688600i	0.993425	−	0.114488i	$-0.0365226\pi$
$127$	4.48031	+	7.76012i	0.397563	+	0.688600i	−0.595861	+	0.803087i	$0.703189\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	7.71493			0.679262
$130$		0			0
$131$	−8.48054			−0.740948			−0.370474	−	0.928843i	$-0.620805\pi$
$131$	−8.48054			−0.740948			−0.370474	+	0.928843i	$0.620805\pi$
$132$	0.563824	−	0.325524i	0.0490746	−	0.0283332i
$133$	−6.63605	−	11.4940i	−0.575418	−	0.996654i
$134$	4.58365	−	7.93912i	0.395967	−	0.685835i
$135$		0			0
$136$	3.03194	+	1.75049i	0.259987	+	0.150103i
$137$	−12.0873	−	6.97859i	−1.03268	−	0.596221i	−0.114932	−	0.993373i	$-0.536665\pi$
$137$	−12.0873	−	6.97859i	−1.03268	−	0.596221i	−0.917753	+	0.397152i	$0.869998\pi$
$138$			2.84994i			0.242603i
$139$	−4.91182	+	8.50753i	−0.416615	+	0.721599i	−0.995597	−	0.0937420i	$-0.970117\pi$
$139$	−4.91182	+	8.50753i	−0.416615	+	0.721599i	0.578981	+	0.815341i	$0.303450\pi$
$140$		0			0
$141$	1.80679	−	1.04315i	0.152159	−	0.0878490i
$142$	−13.0225			−1.09283
$143$	−0.351892	−	2.32086i	−0.0294267	−	0.194080i
$144$	1.00000			0.0833333
$145$		0			0
$146$	0.524307	+	0.908126i	0.0433919	+	0.0751570i
$147$	6.99731	−	12.1197i	0.577128	−	0.999615i
$148$			4.62863i			0.380471i
$149$	−17.6473	−	10.1887i	−1.44572	−	0.834689i	−0.447502	−	0.894283i	$-0.647686\pi$
$149$	−17.6473	−	10.1887i	−1.44572	−	0.834689i	−0.998223	+	0.0595936i	$0.981020\pi$
$150$		0			0
$151$			22.5840i			1.83786i	0.394422	+	0.918930i	$0.370945\pi$
$151$			22.5840i			1.83786i	−0.394422	+	0.918930i	$0.629055\pi$
$152$	1.44829	−	2.50851i	0.117472	−	0.203467i
$153$	−1.75049	−	3.03194i	−0.141519	−	0.245118i
$154$	2.58343	−	1.49155i	0.208179	−	0.120192i
$155$		0			0
$156$	1.31432	−	3.35747i	0.105230	−	0.268812i
$157$	−6.54245			−0.522145			−0.261072	−	0.965319i	$-0.584076\pi$
$157$	−6.54245			−0.522145			−0.261072	+	0.965319i	$0.584076\pi$
$158$	−2.99781	+	1.73079i	−0.238493	+	0.137694i
$159$	−2.79364	−	4.83873i	−0.221550	−	0.383736i
$160$		0			0
$161$			13.0584i			1.02914i
$162$	−0.866025	−	0.500000i	−0.0680414	−	0.0392837i
$163$	12.2966	+	7.09944i	0.963144	+	0.556071i	0.897139	−	0.441748i	$-0.145641\pi$
$163$	12.2966	+	7.09944i	0.963144	+	0.556071i	0.0660047	+	0.997819i	$0.478975\pi$
$164$			3.50098i			0.273381i
$165$		0			0
$166$	5.28611	+	9.15582i	0.410282	+	0.710629i
$167$	2.46812	−	1.42497i	0.190989	−	0.110267i	−0.401457	−	0.915878i	$-0.631496\pi$
$167$	2.46812	−	1.42497i	0.190989	−	0.110267i	0.592445	+	0.805611i	$0.298163\pi$
$168$	4.58199			0.353508
$169$	−9.54515	−	8.82554i	−0.734242	−	0.678888i
$170$		0			0
$171$	−2.50851	+	1.44829i	−0.191831	+	0.110754i
$172$	3.85747	+	6.68133i	0.294129	+	0.509446i
$173$	3.35092	−	5.80397i	0.254766	−	0.441267i	−0.710066	−	0.704135i	$-0.751335\pi$
$173$	3.35092	−	5.80397i	0.254766	−	0.441267i	0.964832	+	0.262868i	$0.0846683\pi$
$174$		−	9.56487i		−	0.725111i
$175$		0			0
$176$	0.563824	+	0.325524i	0.0424998	+	0.0245373i
$177$		−	7.47857i		−	0.562124i
$178$	−4.09944	+	7.10045i	−0.307266	+	0.532201i
$179$	9.98128	+	17.2881i	0.746036	+	1.29217i	0.949709	+	0.313133i	$0.101379\pi$
$179$	9.98128	+	17.2881i	0.746036	+	1.29217i	−0.203673	+	0.979039i	$0.565288\pi$
$180$		0			0
$181$	−3.19889			−0.237772			−0.118886	−	0.992908i	$-0.537932\pi$
$181$	−3.19889			−0.237772			−0.118886	+	0.992908i	$0.537932\pi$
$182$	6.02218	−	15.3839i	0.446394	−	1.14033i
$183$	−6.62863			−0.490003
$184$	−2.46812	+	1.42497i	−0.181952	+	0.105050i
$185$		0			0
$186$	−2.79364	+	4.83873i	−0.204840	+	0.354793i
$187$		−	2.27931i		−	0.166679i
$188$	1.80679	+	1.04315i	0.131774	+	0.0760795i
$189$	−3.96812	−	2.29099i	−0.288638	−	0.166645i
$190$		0			0
$191$	12.5366	−	21.7141i	0.907118	−	1.57117i	0.0890697	−	0.996025i	$-0.471611\pi$
$191$	12.5366	−	21.7141i	0.907118	−	1.57117i	0.818048	−	0.575149i	$-0.195056\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−7.78636	+	4.49546i	−0.560474	+	0.323590i	−0.753336	−	0.657636i	$-0.771557\pi$
$193$	−7.78636	+	4.49546i	−0.560474	+	0.323590i	0.192862	+	0.981226i	$0.438223\pi$
$194$	−14.4372			−1.03653
$195$		0			0
$196$	13.9946			0.999615
$197$	18.8660	−	10.8923i	1.34415	−	0.776043i	0.356733	−	0.934206i	$-0.383890\pi$
$197$	18.8660	−	10.8923i	1.34415	−	0.776043i	0.987413	+	0.158163i	$0.0505571\pi$
$198$	−0.325524	−	0.563824i	−0.0231340	−	0.0400692i
$199$	0.295538	−	0.511887i	0.0209501	−	0.0362867i	−0.855360	−	0.518034i	$-0.826664\pi$
$199$	0.295538	−	0.511887i	0.0209501	−	0.0362867i	0.876310	+	0.481747i	$0.159998\pi$
$200$		0			0
$201$	−7.93912	−	4.58365i	−0.559982	−	0.323306i
$202$	7.15577	+	4.13139i	0.503478	+	0.290683i
$203$		−	43.8261i		−	3.07599i
$204$	1.75049	−	3.03194i	0.122559	−	0.212278i
$205$		0			0
$206$	−17.0787	+	9.86041i	−1.18993	+	0.687007i
$207$	2.84994			0.198084
$208$	3.56481	−	0.540502i	0.247175	−	0.0374770i
$209$	−1.88581			−0.130444
$210$		0			0
$211$	−6.09671	−	10.5598i	−0.419715	−	0.726967i	0.576196	−	0.817312i	$-0.304537\pi$
$211$	−6.09671	−	10.5598i	−0.419715	−	0.726967i	−0.995911	+	0.0903445i	$0.971203\pi$
$212$	2.79364	−	4.83873i	0.191868	−	0.332325i
$213$			13.0225i			0.892289i
$214$	−2.21785	−	1.28048i	−0.151609	−	0.0875317i
$215$		0			0
$216$		−	1.00000i		−	0.0680414i
$217$	−12.8004	+	22.1710i	−0.868950	+	1.50507i
$218$	6.85845	+	11.8792i	0.464513	+	0.804560i
$219$	0.908126	−	0.524307i	0.0613655	−	0.0354294i
$220$		0			0
$221$	−7.87894	−	9.86215i	−0.529995	−	0.663400i
$222$	4.62863			0.310653
$223$	11.3838	−	6.57244i	0.762316	−	0.440123i	−0.0678107	−	0.997698i	$-0.521601\pi$
$223$	11.3838	−	6.57244i	0.762316	−	0.440123i	0.830127	+	0.557575i	$0.188268\pi$
$224$	2.29099	+	3.96812i	0.153073	+	0.265131i
$225$		0			0
$226$		0			0
$227$	−19.5059	−	11.2618i	−1.29465	−	0.747469i	−0.315179	−	0.949032i	$-0.602065\pi$
$227$	−19.5059	−	11.2618i	−1.29465	−	0.747469i	−0.979476	+	0.201563i	$0.935398\pi$
$228$	−2.50851	−	1.44829i	−0.166130	−	0.0959154i
$229$			22.5279i			1.48868i	0.667798	+	0.744342i	$0.267237\pi$
$229$			22.5279i			1.48868i	−0.667798	+	0.744342i	$0.732763\pi$
$230$		0			0
$231$	−1.49155	−	2.58343i	−0.0981365	−	0.169977i
$232$	8.28342	−	4.78243i	0.543833	−	0.313982i
$233$	15.8725			1.03984			0.519920	−	0.854215i	$-0.325962\pi$
$233$	15.8725			1.03984			0.519920	+	0.854215i	$0.325962\pi$
$234$	−3.35747	−	1.31432i	−0.219484	−	0.0859195i
$235$		0			0
$236$	6.47663	−	3.73928i	0.421593	−	0.243407i
$237$	1.73079	+	2.99781i	0.112427	+	0.194729i
$238$	8.02073	−	13.8923i	0.519907	−	0.900505i
$239$		−	20.9703i		−	1.35646i	−0.734852	−	0.678228i	$-0.762748\pi$
$239$		−	20.9703i		−	1.35646i	0.734852	−	0.678228i	$-0.237252\pi$
$240$		0			0
$241$	−5.41101	−	3.12405i	−0.348554	−	0.201238i	0.315494	−	0.948927i	$-0.397830\pi$
$241$	−5.41101	−	3.12405i	−0.348554	−	0.201238i	−0.664048	+	0.747690i	$0.731163\pi$
$242$			10.5761i			0.679860i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−3.31432	−	5.74056i	−0.212177	−	0.367502i
$245$		0			0
$246$	3.50098			0.223215
$247$	−8.15956	+	6.51873i	−0.519181	+	0.414777i
$248$	−5.58728			−0.354793
$249$	9.15582	−	5.28611i	0.580226	−	0.334994i
$250$		0			0
$251$	−12.9759	+	22.4749i	−0.819031	+	1.41860i	0.0873659	+	0.996176i	$0.472155\pi$
$251$	−12.9759	+	22.4749i	−0.819031	+	1.41860i	−0.906397	+	0.422427i	$0.861178\pi$
$252$		−	4.58199i		−	0.288638i
$253$	1.60686	+	0.927722i	0.101023	+	0.0583254i
$254$	7.76012	+	4.48031i	0.486914	+	0.281120i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.44840	+	5.97280i	0.215105	+	0.372573i	0.953305	−	0.302009i	$-0.0976573\pi$
$257$	3.44840	+	5.97280i	0.215105	+	0.372573i	−0.738200	+	0.674582i	$0.764324\pi$
$258$	6.68133	−	3.85747i	0.415961	−	0.240155i
$259$	21.2083			1.31782
$260$		0			0
$261$	−9.56487			−0.592050
$262$	−7.34436	+	4.24027i	−0.453736	+	0.261965i
$263$	4.10214	+	7.10511i	0.252949	+	0.438120i	0.964336	−	0.264680i	$-0.0852663\pi$
$263$	4.10214	+	7.10511i	0.252949	+	0.438120i	−0.711388	+	0.702800i	$0.751933\pi$
$264$	0.325524	−	0.563824i	0.0200346	−	0.0347010i
$265$		0			0
$266$	−11.4940	−	6.63605i	−0.704741	−	0.406882i
$267$	7.10045	+	4.09944i	0.434540	+	0.250882i
$268$		−	9.16730i		−	0.559982i
$269$	12.5086	−	21.6655i	0.762661	−	1.32097i	−0.178813	−	0.983883i	$-0.557226\pi$
$269$	12.5086	−	21.6655i	0.762661	−	1.32097i	0.941474	−	0.337085i	$-0.109441\pi$
$270$		0			0
$271$	0.233654	−	0.134900i	0.0141934	−	0.00819459i	−0.492886	−	0.870094i	$-0.664058\pi$
$271$	0.233654	−	0.134900i	0.0141934	−	0.00819459i	0.507080	+	0.861899i	$0.330725\pi$
$272$	3.50098			0.212278
$273$	−15.3839	−	6.02218i	−0.931074	−	0.364479i
$274$	−13.9572			−0.843184
$275$		0			0
$276$	1.42497	+	2.46812i	0.0857730	+	0.148563i
$277$	−7.98616	+	13.8324i	−0.479842	+	0.831110i	−0.999733	−	0.0231225i	$-0.992639\pi$
$277$	−7.98616	+	13.8324i	−0.479842	+	0.831110i	0.519891	+	0.854233i	$0.325973\pi$
$278$			9.82364i			0.589183i
$279$	4.83873	+	2.79364i	0.289687	+	0.167251i
$280$		0			0
$281$			5.58923i			0.333425i	0.986006	+	0.166713i	$0.0533152\pi$
$281$			5.58923i			0.333425i	−0.986006	+	0.166713i	$0.946685\pi$
$282$	1.04315	−	1.80679i	0.0621186	−	0.107593i
$283$	4.88188	+	8.45566i	0.290198	+	0.502637i	0.973856	−	0.227165i	$-0.0729457\pi$
$283$	4.88188	+	8.45566i	0.290198	+	0.502637i	−0.683659	+	0.729802i	$0.739612\pi$
$284$	−11.2778	+	6.51127i	−0.669217	+	0.386373i
$285$		0			0
$286$	−1.46518	−	1.83398i	−0.0866378	−	0.108445i
$287$	16.0415			0.946898
$288$	0.866025	−	0.500000i	0.0510310	−	0.0294628i
$289$	2.37155	+	4.10765i	0.139503	+	0.241627i
$290$		0			0
$291$			14.4372i			0.846325i
$292$	0.908126	+	0.524307i	0.0531440	+	0.0306827i
$293$	−13.0022	−	7.50680i	−0.759595	−	0.438552i	0.0695556	−	0.997578i	$-0.477842\pi$
$293$	−13.0022	−	7.50680i	−0.759595	−	0.438552i	−0.829150	+	0.559026i	$0.811175\pi$
$294$		−	13.9946i		−	0.816182i
$295$		0			0
$296$	2.31432	+	4.00851i	0.134517	+	0.232990i
$297$	−0.563824	+	0.325524i	−0.0327164	+	0.0188888i
$298$	−20.3774			−1.18043
$299$	10.1595	−	1.54040i	0.587538	−	0.0890834i
$300$		0			0
$301$	30.6138	−	17.6749i	1.76455	−	1.01876i
$302$	11.2920	+	19.5583i	0.649781	+	1.12545i
$303$	4.13139	−	7.15577i	0.237342	−	0.411088i
$304$		−	2.89658i		−	0.166130i
$305$		0			0
$306$	−3.03194	−	1.75049i	−0.173325	−	0.100069i
$307$		−	6.30760i		−	0.359994i	−0.983667	−	0.179997i	$-0.942391\pi$
$307$		−	6.30760i		−	0.359994i	0.983667	−	0.179997i	$-0.0576088\pi$
$308$	1.49155	−	2.58343i	0.0849887	−	0.147205i
$309$	9.86041	+	17.0787i	0.560939	+	0.971575i
$310$		0			0
$311$	−26.9703			−1.52934			−0.764672	−	0.644419i	$-0.777099\pi$
$311$	−26.9703			−1.52934			−0.764672	+	0.644419i	$0.777099\pi$
$312$	−0.540502	−	3.56481i	−0.0305999	−	0.201818i
$313$	−18.4747			−1.04425			−0.522126	−	0.852869i	$-0.674861\pi$
$313$	−18.4747			−1.04425			−0.522126	+	0.852869i	$0.674861\pi$
$314$	−5.66593	+	3.27123i	−0.319747	+	0.184606i
$315$		0			0
$316$	−1.73079	+	2.99781i	−0.0973645	+	0.168640i
$317$		−	2.85533i		−	0.160371i	−0.996780	−	0.0801856i	$-0.974449\pi$
$317$		−	2.85533i		−	0.160371i	0.996780	−	0.0801856i	$-0.0255513\pi$
$318$	−4.83873	−	2.79364i	−0.271342	−	0.156660i
$319$	−5.39290	−	3.11359i	−0.301944	−	0.174328i
$320$		0			0
$321$	−1.28048	+	2.21785i	−0.0714693	+	0.123789i
$322$	6.52919	+	11.3089i	0.363857	+	0.630219i
$323$	−8.78226	+	5.07044i	−0.488658	+	0.282127i
$324$	−1.00000			−0.0555556
$325$		0			0
$326$	14.1989			0.786404
$327$	11.8792	−	6.85845i	0.656920	−	0.379273i
$328$	1.75049	+	3.03194i	0.0966548	+	0.167411i
$329$	4.77970	−	8.27868i	0.263513	−	0.456418i
$330$		0			0
$331$	−4.20347	−	2.42688i	−0.231044	−	0.133393i	0.380010	−	0.924983i	$-0.375921\pi$
$331$	−4.20347	−	2.42688i	−0.231044	−	0.133393i	−0.611054	+	0.791589i	$0.709254\pi$
$332$	9.15582	+	5.28611i	0.502491	+	0.290113i
$333$		−	4.62863i		−	0.253647i
$334$	1.42497	−	2.46812i	0.0779708	−	0.135049i
$335$		0			0
$336$	3.96812	−	2.29099i	0.216479	−	0.124984i
$337$	−6.21782			−0.338706			−0.169353	−	0.985555i	$-0.554168\pi$
$337$	−6.21782			−0.338706			−0.169353	+	0.985555i	$0.554168\pi$
$338$	−12.6791	−	2.87057i	−0.689653	−	0.156138i
$339$		0			0
$340$		0			0
$341$	1.81879	+	3.15024i	0.0984932	+	0.170595i
$342$	−1.44829	+	2.50851i	−0.0783146	+	0.135645i
$343$		−	32.0492i		−	1.73050i
$344$	6.68133	+	3.85747i	0.360233	+	0.207981i
$345$		0			0
$346$		−	6.70184i		−	0.360293i
$347$	−4.21958	+	7.30853i	−0.226519	+	0.392342i	−0.956774	−	0.290832i	$-0.906068\pi$
$347$	−4.21958	+	7.30853i	−0.226519	+	0.392342i	0.730255	+	0.683175i	$0.239401\pi$
$348$	−4.78243	−	8.28342i	−0.256365	−	0.444038i
$349$	−18.9617	+	10.9476i	−1.01500	+	0.586009i	−0.912651	−	0.408740i	$-0.865968\pi$
$349$	−18.9617	+	10.9476i	−1.01500	+	0.586009i	−0.102346	+	0.994749i	$0.532635\pi$
$350$		0			0
$351$	−1.31432	+	3.35747i	−0.0701530	+	0.179208i
$352$	0.651048			0.0347010
$353$	7.71285	−	4.45302i	0.410514	−	0.237010i	−0.280497	−	0.959855i	$-0.590499\pi$
$353$	7.71285	−	4.45302i	0.410514	−	0.237010i	0.691010	+	0.722845i	$0.257166\pi$
$354$	−3.73928	−	6.47663i	−0.198741	−	0.344229i
$355$		0			0
$356$			8.19889i			0.434540i
$357$	−13.8923	−	8.02073i	−0.735259	−	0.424502i
$358$	17.2881	+	9.98128i	0.913704	+	0.527527i
$359$		−	36.9967i		−	1.95261i	−0.216401	−	0.976305i	$-0.569432\pi$
$359$		−	36.9967i		−	1.95261i	0.216401	−	0.976305i	$-0.430568\pi$
$360$		0			0
$361$	−5.30491	−	9.18837i	−0.279206	−	0.483598i
$362$	−2.77032	+	1.59944i	−0.145605	+	0.0840649i
$363$	10.5761			0.555103
$364$	−2.47657	−	16.3339i	−0.129808	−	0.856129i
$365$		0			0
$366$	−5.74056	+	3.31432i	−0.300064	+	0.173242i
$367$	10.0387	+	17.3875i	0.524016	+	0.907622i	0.999609	+	0.0279569i	$0.00890013\pi$
$367$	10.0387	+	17.3875i	0.524016	+	0.907622i	−0.475593	+	0.879665i	$0.657767\pi$
$368$	−1.42497	+	2.46812i	−0.0742816	+	0.128660i
$369$		−	3.50098i		−	0.182254i
$370$		0			0
$371$	−22.1710	−	12.8004i	−1.15106	−	0.664565i
$372$			5.58728i			0.289687i
$373$	−16.6653	+	28.8651i	−0.862896	+	1.49458i	0.00622457	+	0.999981i	$0.498019\pi$
$373$	−16.6653	+	28.8651i	−0.862896	+	1.49458i	−0.869121	+	0.494600i	$0.835315\pi$
$374$	−1.13965	−	1.97394i	−0.0589301	−	0.102070i
$375$		0			0
$376$	2.08630			0.107593
$377$	−34.0969	+	5.16983i	−1.75608	+	0.266260i
$378$	−4.58199			−0.235672
$379$	−1.43619	+	0.829184i	−0.0737721	+	0.0425923i	−0.536432	−	0.843943i	$-0.680228\pi$
$379$	−1.43619	+	0.829184i	−0.0737721	+	0.0425923i	0.462660	+	0.886536i	$0.346895\pi$
$380$		0			0
$381$	4.48031	−	7.76012i	0.229533	−	0.397563i
$382$		−	25.0732i		−	1.28286i
$383$	−22.1644	−	12.7966i	−1.13255	−	0.653877i	−0.187974	−	0.982174i	$-0.560192\pi$
$383$	−22.1644	−	12.7966i	−1.13255	−	0.653877i	−0.944574	+	0.328297i	$0.893525\pi$
$384$	0.866025	+	0.500000i	0.0441942	+	0.0255155i
$385$		0			0
$386$	−4.49546	+	7.78636i	−0.228813	+	0.396315i
$387$	−3.85747	−	6.68133i	−0.196086	−	0.339631i
$388$	−12.5030	+	7.21861i	−0.634744	+	0.366469i
$389$	−9.56487			−0.484958			−0.242479	−	0.970157i	$-0.577961\pi$
$389$	−9.56487			−0.484958			−0.242479	+	0.970157i	$0.577961\pi$
$390$		0			0
$391$	9.97758			0.504588
$392$	12.1197	−	6.99731i	0.612137	−	0.353417i
$393$	4.24027	+	7.34436i	0.213893	+	0.370474i
$394$	10.8923	−	18.8660i	0.548746	−	0.950455i
$395$		0			0
$396$	−0.563824	−	0.325524i	−0.0283332	−	0.0163582i
$397$	0.401710	+	0.231927i	0.0201612	+	0.0116401i	0.510047	−	0.860147i	$-0.329628\pi$
$397$	0.401710	+	0.231927i	0.0201612	+	0.0116401i	−0.489886	+	0.871787i	$0.662961\pi$
$398$		−	0.591076i		−	0.0296279i
$399$	−6.63605	+	11.4940i	−0.332218	+	0.575418i
$400$		0			0
$401$	17.6992	−	10.2187i	0.883857	−	0.510295i	0.0119289	−	0.999929i	$-0.496203\pi$
$401$	17.6992	−	10.2187i	0.883857	−	0.510295i	0.871928	+	0.489634i	$0.162870\pi$
$402$	−9.16730			−0.457223
$403$	18.7591	+	7.34346i	0.934458	+	0.365804i
$404$	8.26277			0.411088
$405$		0			0
$406$	−21.9131	−	37.9545i	−1.08753	−	1.88365i
$407$	1.50673	−	2.60973i	0.0746858	−	0.129360i
$408$		−	3.50098i		−	0.173325i
$409$	−9.15283	−	5.28439i	−0.452578	−	0.261296i	0.256340	−	0.966587i	$-0.417483\pi$
$409$	−9.15283	−	5.28439i	−0.452578	−	0.261296i	−0.708919	+	0.705290i	$0.750817\pi$
$410$		0			0
$411$			13.9572i			0.688457i
$412$	−9.86041	+	17.0787i	−0.485787	+	0.841408i
$413$	−17.1334	−	29.6758i	−0.843077	−	1.46025i
$414$	2.46812	−	1.42497i	0.121301	−	0.0700334i
$415$		0			0
$416$	2.81696	−	2.25049i	0.138113	−	0.110339i
$417$	9.82364			0.481066
$418$	−1.63316	+	0.942906i	−0.0798805	+	0.0461191i
$419$	−14.2835	−	24.7397i	−0.697793	−	1.20861i	−0.969230	−	0.246156i	$-0.920832\pi$
$419$	−14.2835	−	24.7397i	−0.697793	−	1.20861i	0.271437	−	0.962456i	$-0.412501\pi$
$420$		0			0
$421$		−	38.4187i		−	1.87241i	−0.351450	−	0.936207i	$-0.614311\pi$
$421$		−	38.4187i		−	1.87241i	0.351450	−	0.936207i	$-0.385689\pi$
$422$	−10.5598	−	6.09671i	−0.514043	−	0.296783i
$423$	−1.80679	−	1.04315i	−0.0878490	−	0.0507197i
$424$		−	5.58728i		−	0.271342i
$425$		0			0
$426$	6.51127	+	11.2778i	0.315472	+	0.546413i
$427$	−26.3032	+	15.1862i	−1.27290	+	0.734910i
$428$	−2.56096			−0.123789
$429$	−1.83398	+	1.46518i	−0.0885453	+	0.0707394i
$430$		0			0
$431$	−6.84351	+	3.95111i	−0.329641	+	0.190318i	−0.655681	−	0.755038i	$-0.727619\pi$
$431$	−6.84351	+	3.95111i	−0.329641	+	0.190318i	0.326041	+	0.945356i	$0.394285\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−8.33120	+	14.4301i	−0.400372	+	0.693465i	−0.993771	−	0.111444i	$-0.964452\pi$
$433$	−8.33120	+	14.4301i	−0.400372	+	0.693465i	0.593399	+	0.804909i	$0.297786\pi$
$434$			25.6009i			1.22888i
$435$		0			0
$436$	11.8792	+	6.85845i	0.568910	+	0.328460i
$437$		−	8.25507i		−	0.394894i
$438$	0.524307	−	0.908126i	0.0250523	−	0.0433919i
$439$	−11.1728	−	19.3519i	−0.533250	−	0.923616i	−0.999246	−	0.0388290i	$-0.987637\pi$
$439$	−11.1728	−	19.3519i	−0.533250	−	0.923616i	0.465996	−	0.884787i	$-0.345696\pi$
$440$		0			0
$441$	−13.9946			−0.666410
$442$	−11.7544	−	4.60140i	−0.559101	−	0.218866i
$443$	−17.5200			−0.832398			−0.416199	−	0.909274i	$-0.636638\pi$
$443$	−17.5200			−0.832398			−0.416199	+	0.909274i	$0.636638\pi$
$444$	4.00851	−	2.31432i	0.190236	−	0.109833i
$445$		0			0
$446$	6.57244	−	11.3838i	0.311214	−	0.539039i
$447$			20.3774i			0.963816i
$448$	3.96812	+	2.29099i	0.187476	+	0.108239i
$449$	−16.9571	−	9.79019i	−0.800255	−	0.462028i	0.0433051	−	0.999062i	$-0.486211\pi$
$449$	−16.9571	−	9.79019i	−0.800255	−	0.462028i	−0.843560	+	0.537034i	$0.819545\pi$
$450$		0			0
$451$	1.13965	−	1.97394i	0.0536642	−	0.0929491i
$452$		0			0
$453$	19.5583	−	11.2920i	0.918930	−	0.530544i
$454$	−22.5235			−1.05708
$455$		0			0
$456$	−2.89658			−0.135645
$457$	19.6371	−	11.3375i	0.918585	−	0.530345i	0.0354015	−	0.999373i	$-0.488729\pi$
$457$	19.6371	−	11.3375i	0.918585	−	0.530345i	0.883183	+	0.469028i	$0.155396\pi$
$458$	11.2639	+	19.5097i	0.526330	+	0.911630i
$459$	−1.75049	+	3.03194i	−0.0817060	+	0.141519i
$460$		0			0
$461$	28.4102	+	16.4026i	1.32319	+	0.763947i	0.984237	−	0.176855i	$-0.0565924\pi$
$461$	28.4102	+	16.4026i	1.32319	+	0.763947i	0.338957	+	0.940802i	$0.389926\pi$
$462$	−2.58343	−	1.49155i	−0.120192	−	0.0693930i
$463$		−	20.6472i		−	0.959555i	−0.877390	−	0.479778i	$-0.840717\pi$
$463$		−	20.6472i		−	0.959555i	0.877390	−	0.479778i	$-0.159283\pi$
$464$	4.78243	−	8.28342i	0.222019	−	0.384548i
$465$		0			0
$466$	13.7460	−	7.93624i	0.636769	−	0.367639i
$467$	7.77136			0.359616			0.179808	−	0.983702i	$-0.442452\pi$
$467$	7.77136			0.359616			0.179808	+	0.983702i	$0.442452\pi$
$468$	−3.56481	+	0.540502i	−0.164783	+	0.0249847i
$469$	−42.0045			−1.93959
$470$		0			0
$471$	3.27123	+	5.66593i	0.150730	+	0.261072i
$472$	3.73928	−	6.47663i	0.172115	−	0.298111i
$473$		−	5.02279i		−	0.230948i
$474$	2.99781	+	1.73079i	0.137694	+	0.0794978i
$475$		0			0
$476$		−	16.0415i		−	0.735259i
$477$	−2.79364	+	4.83873i	−0.127912	+	0.221550i
$478$	−10.4851	−	18.1608i	−0.479579	−	0.830656i
$479$	15.1745	−	8.76102i	0.693342	−	0.400301i	−0.111521	−	0.993762i	$-0.535572\pi$
$479$	15.1745	−	8.76102i	0.693342	−	0.400301i	0.804863	+	0.593461i	$0.202239\pi$
$480$		0			0
$481$	−2.50178	−	16.5002i	−0.114071	−	0.752344i
$482$	−6.24809			−0.284593
$483$	11.3089	−	6.52919i	0.514572	−	0.297088i
$484$	5.28807	+	9.15920i	0.240367	+	0.416327i
$485$		0			0
$486$			1.00000i			0.0453609i
$487$	18.0846	+	10.4412i	0.819494	+	0.473135i	0.850242	−	0.526392i	$-0.176456\pi$
$487$	18.0846	+	10.4412i	0.819494	+	0.473135i	−0.0307482	+	0.999527i	$0.509789\pi$
$488$	−5.74056	−	3.31432i	−0.259863	−	0.150032i
$489$		−	14.1989i		−	0.642096i
$490$		0			0
$491$	−7.97312	−	13.8098i	−0.359822	−	0.623230i	0.628109	−	0.778125i	$-0.283829\pi$
$491$	−7.97312	−	13.8098i	−0.359822	−	0.623230i	−0.987931	+	0.154896i	$0.950496\pi$
$492$	3.03194	−	1.75049i	0.136690	−	0.0789183i
$493$	−33.4865			−1.50815
$494$	−3.80702	+	9.72517i	−0.171286	+	0.437556i
$495$		0			0
$496$	−4.83873	+	2.79364i	−0.217265	+	0.125438i
$497$	29.8345	+	51.6749i	1.33826	+	2.31794i
$498$	5.28611	−	9.15582i	0.236876	−	0.410282i
$499$			19.1969i			0.859373i	0.902978	+	0.429687i	$0.141376\pi$
$499$			19.1969i			0.859373i	−0.902978	+	0.429687i	$0.858624\pi$
$500$		0			0
$501$	−2.46812	−	1.42497i	−0.110267	−	0.0636629i
$502$			25.9518i			1.15828i
$503$	9.44473	−	16.3588i	0.421120	−	0.729401i	−0.574930	−	0.818203i	$-0.694971\pi$
$503$	9.44473	−	16.3588i	0.421120	−	0.729401i	0.996049	+	0.0888021i	$0.0283039\pi$
$504$	−2.29099	−	3.96812i	−0.102049	−	0.176754i
$505$		0			0
$506$	1.85544			0.0824846
$507$	−2.87057	+	12.6791i	−0.127486	+	0.563099i
$508$	8.96062			0.397563
$509$	16.2075	−	9.35742i	0.718386	−	0.414761i	−0.0957722	−	0.995403i	$-0.530532\pi$
$509$	16.2075	−	9.35742i	0.718386	−	0.414761i	0.814158	+	0.580643i	$0.197199\pi$
$510$		0			0
$511$	2.40237	−	4.16102i	0.106274	−	0.184073i
$512$			1.00000i			0.0441942i
$513$	2.50851	+	1.44829i	0.110754	+	0.0639436i
$514$	5.97280	+	3.44840i	0.263449	+	0.152102i
$515$		0			0
$516$	3.85747	−	6.68133i	0.169815	−	0.294129i
$517$	−0.679140	−	1.17630i	−0.0298685	−	0.0517338i
$518$	18.3670	−	10.6042i	0.806998	−	0.465920i
$519$	−6.70184			−0.294178
$520$		0			0
$521$	40.9556			1.79430			0.897149	−	0.441729i	$-0.145635\pi$
$521$	40.9556			1.79430			0.897149	+	0.441729i	$0.145635\pi$
$522$	−8.28342	+	4.78243i	−0.362555	+	0.209321i
$523$	20.2637	+	35.0978i	0.886072	+	1.53472i	0.844480	+	0.535587i	$0.179909\pi$
$523$	20.2637	+	35.0978i	0.886072	+	1.53472i	0.0415914	+	0.999135i	$0.486757\pi$
$524$	−4.24027	+	7.34436i	−0.185237	+	0.320840i
$525$		0			0
$526$	7.10511	+	4.10214i	0.309798	+	0.178862i
$527$	16.9403	+	9.78050i	0.737932	+	0.426045i
$528$		−	0.651048i		−	0.0283332i
$529$	7.43893	−	12.8846i	0.323432	−	0.560200i
$530$		0			0
$531$	−6.47663	+	3.73928i	−0.281062	+	0.162271i
$532$	−13.2721			−0.575418
$533$	−1.89229	−	12.4803i	−0.0819641	−	0.540583i
$534$	8.19889			0.354801
$535$		0			0
$536$	−4.58365	−	7.93912i	−0.197984	−	0.342918i
$537$	9.98128	−	17.2881i	0.430724	−	0.746036i
$538$		−	25.0171i		−	1.07857i
$539$	−7.89049	−	4.55558i	−0.339868	−	0.196223i
$540$		0			0
$541$			26.2949i			1.13050i	0.824918	+	0.565252i	$0.191221\pi$
$541$			26.2949i			1.13050i	−0.824918	+	0.565252i	$0.808779\pi$
$542$	0.134900	−	0.233654i	0.00579445	−	0.0100363i
$543$	1.59944	+	2.77032i	0.0686387	+	0.118886i
$544$	3.03194	−	1.75049i	0.129993	−	0.0750517i
$545$		0			0
$546$	−16.3339	+	2.47657i	−0.699027	+	0.105987i
$547$	33.5445			1.43426			0.717130	−	0.696940i	$-0.245455\pi$
$547$	33.5445			1.43426			0.717130	+	0.696940i	$0.245455\pi$
$548$	−12.0873	+	6.97859i	−0.516342	+	0.298110i
$549$	3.31432	+	5.74056i	0.141452	+	0.245001i
$550$		0			0
$551$			27.7054i			1.18029i
$552$	2.46812	+	1.42497i	0.105050	+	0.0606507i
$553$	13.7359	+	7.93045i	0.584112	+	0.337237i
$554$			15.9723i			0.678599i
$555$		0			0
$556$	4.91182	+	8.50753i	0.208308	+	0.360799i
$557$	−11.3705	+	6.56478i	−0.481785	+	0.278159i	−0.721160	−	0.692768i	$-0.756391\pi$
$557$	−11.3705	+	6.56478i	−0.481785	+	0.278159i	0.239375	+	0.970927i	$0.423057\pi$
$558$	5.58728			0.236529
$559$	−17.3624	−	21.7327i	−0.734351	−	0.919194i
$560$		0			0
$561$	−1.97394	+	1.13965i	−0.0833397	+	0.0481162i
$562$	2.79461	+	4.84041i	0.117884	+	0.204180i
$563$	−9.85086	+	17.0622i	−0.415164	+	0.719086i	−0.995446	−	0.0953304i	$-0.969609\pi$
$563$	−9.85086	+	17.0622i	−0.415164	+	0.719086i	0.580281	+	0.814416i	$0.302943\pi$
$564$		−	2.08630i		−	0.0878490i
$565$		0			0
$566$	8.45566	+	4.88188i	0.355418	+	0.205201i
$567$			4.58199i			0.192425i
$568$	−6.51127	+	11.2778i	−0.273207	+	0.473208i
$569$	10.1979	+	17.6633i	0.427519	+	0.740485i	0.996652	−	0.0817607i	$-0.0260543\pi$
$569$	10.1979	+	17.6633i	0.427519	+	0.740485i	−0.569133	+	0.822246i	$0.692721\pi$
$570$		0			0
$571$	−19.7935			−0.828333			−0.414167	−	0.910201i	$-0.635927\pi$
$571$	−19.7935			−0.828333			−0.414167	+	0.910201i	$0.635927\pi$
$572$	−2.18587	−	0.855682i	−0.0913958	−	0.0357779i
$573$	−25.0732			−1.04745
$574$	13.8923	−	8.02073i	0.579854	−	0.334779i
$575$		0			0
$576$	0.500000	−	0.866025i	0.0208333	−	0.0360844i
$577$			14.1729i			0.590024i	0.955493	+	0.295012i	$0.0953237\pi$
$577$			14.1729i			0.590024i	−0.955493	+	0.295012i	$0.904676\pi$
$578$	4.10765	+	2.37155i	0.170856	+	0.0986436i
$579$	7.78636	+	4.49546i	0.323590	+	0.186825i
$580$		0			0
$581$	24.2209	−	41.9518i	1.00485	−	1.74046i
$582$	7.21861	+	12.5030i	0.299221	+	0.518266i
$583$	−3.15024	+	1.81879i	−0.130470	+	0.0753267i
$584$	1.04861			0.0433919
$585$		0			0
$586$	−15.0136			−0.620206
$587$	18.6382	−	10.7608i	0.769281	−	0.444145i	−0.0633369	−	0.997992i	$-0.520174\pi$
$587$	18.6382	−	10.7608i	0.769281	−	0.444145i	0.832618	+	0.553847i	$0.186841\pi$
$588$	−6.99731	−	12.1197i	−0.288564	−	0.499808i
$589$	8.09201	−	14.0158i	0.333425	−	0.577510i
$590$		0			0
$591$	−18.8660	−	10.8923i	−0.776043	−	0.448049i
$592$	4.00851	+	2.31432i	0.164749	+	0.0951178i
$593$			37.9368i			1.55788i	0.627101	+	0.778938i	$0.284241\pi$
$593$			37.9368i			1.55788i	−0.627101	+	0.778938i	$0.715759\pi$
$594$	−0.325524	+	0.563824i	−0.0133564	+	0.0231340i
$595$		0			0
$596$	−17.6473	+	10.1887i	−0.722862	+	0.417345i
$597$	−0.591076			−0.0241911
$598$	8.02817	−	6.41376i	0.328296	−	0.262278i
$599$	−22.4129			−0.915765			−0.457883	−	0.889013i	$-0.651392\pi$
$599$	−22.4129			−0.915765			−0.457883	+	0.889013i	$0.651392\pi$
$600$		0			0
$601$	−16.6804	−	28.8913i	−0.680407	−	1.17850i	−0.974857	−	0.222832i	$-0.928470\pi$
$601$	−16.6804	−	28.8913i	−0.680407	−	1.17850i	0.294450	−	0.955667i	$-0.404863\pi$
$602$	17.6749	−	30.6138i	0.720373	−	1.24772i
$603$			9.16730i			0.373321i
$604$	19.5583	+	11.2920i	0.795816	+	0.459465i
$605$		0			0
$606$		−	8.26277i		−	0.335652i
$607$	−8.02733	+	13.9037i	−0.325819	+	0.564335i	−0.981678	−	0.190548i	$-0.938973\pi$
$607$	−8.02733	+	13.9037i	−0.325819	+	0.564335i	0.655859	+	0.754884i	$0.272307\pi$
$608$	−1.44829	−	2.50851i	−0.0587359	−	0.101734i
$609$	−37.9545	+	21.9131i	−1.53799	+	0.887962i
$610$		0			0
$611$	−7.00467	−	2.74206i	−0.283379	−	0.110932i
$612$	−3.50098			−0.141519
$613$	33.0698	−	19.0929i	1.33568	−	0.771154i	0.349514	−	0.936931i	$-0.386347\pi$
$613$	33.0698	−	19.0929i	1.33568	−	0.771154i	0.986163	+	0.165777i	$0.0530133\pi$
$614$	−3.15380	−	5.46254i	−0.127277	−	0.220450i
$615$		0			0
$616$		−	2.98309i		−	0.120192i
$617$	37.2397	+	21.5003i	1.49921	+	0.865571i	1.00000		0.000908306i	$-0.000289123\pi$
$617$	37.2397	+	21.5003i	1.49921	+	0.865571i	0.499213	+	0.866479i	$0.333622\pi$
$618$	17.0787	+	9.86041i	0.687007	+	0.396644i
$619$			6.35493i			0.255426i	0.991811	+	0.127713i	$0.0407636\pi$
$619$			6.35493i			0.255426i	−0.991811	+	0.127713i	$0.959236\pi$
$620$		0			0
$621$	−1.42497	−	2.46812i	−0.0571820	−	0.0990422i
$622$	−23.3570	+	13.4851i	−0.936529	+	0.540705i
$623$	37.5672			1.50510
$624$	−2.25049	−	2.81696i	−0.0900918	−	0.112769i
$625$		0			0
$626$	−15.9996	+	9.23735i	−0.639471	+	0.369199i
$627$	0.942906	+	1.63316i	0.0376560	+	0.0652222i
$628$	−3.27123	+	5.66593i	−0.130536	+	0.226095i
$629$		−	16.2048i		−	0.646126i
$630$		0			0
$631$	−3.08250	−	1.77968i	−0.122713	−	0.0708481i	0.437387	−	0.899273i	$-0.355904\pi$
$631$	−3.08250	−	1.77968i	−0.122713	−	0.0708481i	−0.560100	+	0.828425i	$0.689237\pi$
$632$			3.46158i			0.137694i
$633$	−6.09671	+	10.5598i	−0.242322	+	0.419715i
$634$	−1.42766	−	2.47279i	−0.0566997	−	0.0982068i
$635$		0			0
$636$	−5.58728			−0.221550
$637$	−49.8881	+	7.56411i	−1.97664	+	0.299701i
$638$	−6.22718			−0.246537
$639$	11.2778	−	6.51127i	0.446145	−	0.257582i
$640$		0			0
$641$	19.4394	−	33.6701i	0.767812	−	1.32989i	−0.170935	−	0.985282i	$-0.554679\pi$
$641$	19.4394	−	33.6701i	0.767812	−	1.32989i	0.938747	−	0.344607i	$-0.111988\pi$
$642$			2.56096i			0.101073i
$643$	−13.0065	−	7.50930i	−0.512926	−	0.296138i	0.221110	−	0.975249i	$-0.429032\pi$
$643$	−13.0065	−	7.50930i	−0.512926	−	0.296138i	−0.734035	+	0.679111i	$0.762365\pi$
$644$	11.3089	+	6.52919i	0.445632	+	0.257286i
$645$		0			0
$646$	−5.07044	+	8.78226i	−0.199494	+	0.345534i
$647$	14.9204	+	25.8429i	0.586581	+	1.01599i	0.994676	+	0.103049i	$0.0328599\pi$
$647$	14.9204	+	25.8429i	0.586581	+	1.01599i	−0.408095	+	0.912939i	$0.633807\pi$
$648$	−0.866025	+	0.500000i	−0.0340207	+	0.0196419i
$649$	−4.86890			−0.191121
$650$		0			0
$651$	25.6009			1.00338
$652$	12.2966	−	7.09944i	0.481572	−	0.278036i
$653$	−1.54701	−	2.67950i	−0.0605393	−	0.104857i	0.834167	−	0.551511i	$-0.185949\pi$
$653$	−1.54701	−	2.67950i	−0.0605393	−	0.104857i	−0.894707	+	0.446654i	$0.852615\pi$
$654$	6.85845	−	11.8792i	0.268187	−	0.464513i
$655$		0			0
$656$	3.03194	+	1.75049i	0.118377	+	0.0683452i
$657$	−0.908126	−	0.524307i	−0.0354294	−	0.0204552i
$658$		−	9.55939i		−	0.372664i
$659$	−2.65012	+	4.59015i	−0.103234	+	0.178807i	−0.913015	−	0.407925i	$-0.866252\pi$
$659$	−2.65012	+	4.59015i	−0.103234	+	0.178807i	0.809781	+	0.586732i	$0.199586\pi$
$660$		0			0
$661$	−27.0453	+	15.6146i	−1.05194	+	0.607337i	−0.923191	−	0.384340i	$-0.874429\pi$
$661$	−27.0453	+	15.6146i	−1.05194	+	0.607337i	−0.128747	+	0.991677i	$0.541096\pi$
$662$	−4.85375			−0.188646
$663$	−4.60140	+	11.7544i	−0.178704	+	0.456504i
$664$	10.5722			0.410282
$665$		0			0
$666$	−2.31432	−	4.00851i	−0.0896779	−	0.155327i
$667$	13.6296	−	23.6072i	0.527742	−	0.914075i
$668$		−	2.84994i		−	0.110267i
$669$	−11.3838	−	6.57244i	−0.440123	−	0.254105i
$670$		0			0
$671$			4.31556i			0.166600i
$672$	2.29099	−	3.96812i	0.0883770	−	0.153073i
$673$	18.0247	+	31.2197i	0.694801	+	1.20343i	0.970248	+	0.242114i	$0.0778408\pi$
$673$	18.0247	+	31.2197i	0.694801	+	1.20343i	−0.275447	+	0.961316i	$0.588826\pi$
$674$	−5.38479	+	3.10891i	−0.207414	+	0.119751i
$675$		0			0
$676$	−12.4157	+	3.85357i	−0.477528	+	0.148214i
$677$	−23.2219			−0.892491			−0.446245	−	0.894911i	$-0.647239\pi$
$677$	−23.2219			−0.892491			−0.446245	+	0.894911i	$0.647239\pi$
$678$		0			0
$679$	33.0756	+	57.2886i	1.26932	+	2.19853i
$680$		0			0
$681$			22.5235i			0.863103i
$682$	3.15024	+	1.81879i	0.120629	+	0.0696452i
$683$	25.7473	+	14.8652i	0.985195	+	0.568802i	0.903834	−	0.427882i	$-0.140740\pi$
$683$	25.7473	+	14.8652i	0.985195	+	0.568802i	0.0813602	+	0.996685i	$0.474074\pi$
$684$			2.89658i			0.110754i
$685$		0			0
$686$	−16.0246	−	27.7554i	−0.611822	−	1.05971i
$687$	19.5097	−	11.2639i	0.744342	−	0.429746i
$688$	7.71493			0.294129
$689$	−7.34346	+	18.7591i	−0.279763	+	0.714665i
$690$		0			0
$691$	−19.7614	+	11.4092i	−0.751758	+	0.434028i	−0.826329	−	0.563188i	$-0.809575\pi$
$691$	−19.7614	+	11.4092i	−0.751758	+	0.434028i	0.0745709	+	0.997216i	$0.476241\pi$
$692$	−3.35092	−	5.80397i	−0.127383	−	0.220634i
$693$	−1.49155	+	2.58343i	−0.0566592	+	0.0981365i
$694$			8.43916i			0.320346i
$695$		0			0
$696$	−8.28342	−	4.78243i	−0.313982	−	0.181278i
$697$		−	12.2569i		−	0.464263i
$698$	−10.9476	+	18.9617i	−0.414371	+	0.717712i
$699$	−7.93624	−	13.7460i	−0.300176	−	0.519920i
$700$		0			0
$701$	43.2728			1.63439			0.817196	−	0.576359i	$-0.195527\pi$
$701$	43.2728			1.63439			0.817196	+	0.576359i	$0.195527\pi$
$702$	0.540502	+	3.56481i	0.0203999	+	0.134545i
$703$	−13.4072			−0.505662
$704$	0.563824	−	0.325524i	0.0212499	−	0.0122686i
$705$		0			0
$706$	4.45302	−	7.71285i	0.167592	−	0.290277i
$707$		−	37.8599i		−	1.42387i
$708$	−6.47663	−	3.73928i	−0.243407	−	0.140531i
$709$	15.8342	+	9.14186i	0.594664	+	0.343330i	0.766940	−	0.641719i	$-0.221779\pi$
$709$	15.8342	+	9.14186i	0.594664	+	0.343330i	−0.172275	+	0.985049i	$0.555112\pi$
$710$		0			0
$711$	1.73079	−	2.99781i	0.0649096	−	0.112427i
$712$	4.09944	+	7.10045i	0.153633	+	0.266100i
$713$	−13.7901	+	7.96170i	−0.516442	+	0.298168i
$714$	−16.0415			−0.600337
$715$		0			0
$716$	19.9626			0.746036
$717$	−18.1608	+	10.4851i	−0.678228	+	0.391575i
$718$	−18.4983	−	32.0401i	−0.690352	−	1.19572i
$719$	13.6420	−	23.6287i	0.508762	−	0.881201i	−0.491187	−	0.871054i	$-0.663437\pi$
$719$	13.6420	−	23.6287i	0.508762	−	0.881201i	0.999949	−	0.0101468i	$-0.00322987\pi$
$720$		0			0
$721$	78.2545	+	45.1803i	2.91435	+	1.68260i
$722$	−9.18837	−	5.30491i	−0.341956	−	0.197428i
$723$			6.24809i			0.232369i
$724$	−1.59944	+	2.77032i	−0.0594429	+	0.102958i
$725$		0			0
$726$	9.15920	−	5.28807i	0.339930	−	0.196259i
$727$	17.0453			0.632176			0.316088	−	0.948730i	$-0.397631\pi$
$727$	17.0453			0.632176			0.316088	+	0.948730i	$0.397631\pi$
$728$	−10.3117	−	12.9073i	−0.382178	−	0.478376i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−13.5049	−	23.3912i	−0.499498	−	0.865155i
$732$	−3.31432	+	5.74056i	−0.122501	+	0.212177i
$733$		−	11.2472i		−	0.415424i	−0.978190	−	0.207712i	$-0.933398\pi$
$733$		−	11.2472i		−	0.415424i	0.978190	−	0.207712i	$-0.0666016\pi$
$734$	17.3875	+	10.0387i	0.641786	+	0.370535i
$735$		0			0
$736$			2.84994i			0.105050i
$737$	−2.98418	+	5.16874i	−0.109924	+	0.190393i
$738$	−1.75049	−	3.03194i	−0.0644365	−	0.111607i
$739$	9.24885	−	5.33982i	0.340224	−	0.196429i	−0.320147	−	0.947368i	$-0.603732\pi$
$739$	9.24885	−	5.33982i	0.340224	−	0.196429i	0.660371	+	0.750939i	$0.270399\pi$
$740$		0			0
$741$	9.72517	+	3.80702i	0.357263	+	0.139854i
$742$	−25.6009			−0.939837
$743$	23.4105	−	13.5160i	0.858847	−	0.495855i	−0.00477910	−	0.999989i	$-0.501521\pi$
$743$	23.4105	−	13.5160i	0.858847	−	0.495855i	0.863626	+	0.504133i	$0.168188\pi$
$744$	2.79364	+	4.83873i	0.102420	+	0.177396i
$745$		0			0
$746$			33.3306i			1.22032i
$747$	−9.15582	−	5.28611i	−0.334994	−	0.193409i
$748$	−1.97394	−	1.13965i	−0.0721743	−	0.0416699i
$749$			11.7343i			0.428761i
$750$		0			0
$751$	12.7159	+	22.0246i	0.464010	+	0.803688i	0.999156	−	0.0410709i	$-0.0130769\pi$
$751$	12.7159	+	22.0246i	0.464010	+	0.803688i	−0.535147	+	0.844759i	$0.679744\pi$
$752$	1.80679	−	1.04315i	0.0658868	−	0.0380397i
$753$	25.9518			0.945736
$754$	−26.9439	+	21.5257i	−0.981238	+	0.783918i
$755$		0			0
$756$	−3.96812	+	2.29099i	−0.144319	+	0.0833226i
$757$	−21.6906	−	37.5693i	−0.788359	−	1.36548i	−0.926971	−	0.375132i	$-0.877597\pi$
$757$	−21.6906	−	37.5693i	−0.788359	−	1.36548i	0.138612	−	0.990347i	$-0.455736\pi$
$758$	−0.829184	+	1.43619i	−0.0301173	+	0.0521648i
$759$		−	1.85544i		−	0.0673484i
$760$		0			0
$761$	−15.5138	−	8.95691i	−0.562376	−	0.324688i	0.191723	−	0.981449i	$-0.438593\pi$
$761$	−15.5138	−	8.95691i	−0.562376	−	0.324688i	−0.754099	+	0.656761i	$0.771926\pi$
$762$		−	8.96062i		−	0.324609i
$763$	31.4253	−	54.4303i	1.13767	−	1.97051i
$764$	−12.5366	−	21.7141i	−0.453559	−	0.785587i
$765$		0			0
$766$	−25.5932			−0.924722
$767$	−21.0669	+	16.8305i	−0.760680	+	0.607713i
$768$	1.00000			0.0360844
$769$	6.17619	−	3.56583i	0.222719	−	0.128587i	−0.384490	−	0.923129i	$-0.625623\pi$
$769$	6.17619	−	3.56583i	0.222719	−	0.128587i	0.607209	+	0.794542i	$0.292289\pi$
$770$		0			0
$771$	3.44840	−	5.97280i	0.124191	−	0.215105i
$772$			8.99091i			0.323590i
$773$	31.0330	+	17.9169i	1.11618	+	0.644427i	0.940423	−	0.340006i	$-0.110429\pi$
$773$	31.0330	+	17.9169i	1.11618	+	0.644427i	0.175757	+	0.984434i	$0.443763\pi$
$774$	−6.68133	−	3.85747i	−0.240155	−	0.138654i
$775$		0			0
$776$	−7.21861	+	12.5030i	−0.259133	+	0.448832i
$777$	−10.6042	−	18.3670i	−0.380422	−	0.658911i
$778$	−8.28342	+	4.78243i	−0.296975	+	0.171459i
$779$	−10.1409			−0.363335
$780$		0			0
$781$	8.47829			0.303377
$782$	8.64084	−	4.98879i	0.308996	−	0.178399i
$783$	4.78243	+	8.28342i	0.170910	+	0.296025i
$784$	6.99731	−	12.1197i	0.249904	−	0.432846i
$785$		0			0
$786$	7.34436	+	4.24027i	0.261965	+	0.151245i
$787$	15.0880	+	8.71109i	0.537831	+	0.310517i	0.744199	−	0.667958i	$-0.232831\pi$
$787$	15.0880	+	8.71109i	0.537831	+	0.310517i	−0.206369	+	0.978474i	$0.566165\pi$
$788$		−	21.7846i		−	0.776043i
$789$	4.10214	−	7.10511i	0.146040	−	0.252949i
$790$		0			0
$791$		0			0
$792$	−0.651048			−0.0231340
$793$	14.9177	+	18.6726i	0.529743	+	0.663084i
$794$	0.463855			0.0164616
$795$		0			0
$796$	−0.295538	−	0.511887i	−0.0104751	−	0.0181433i
$797$	12.8548	−	22.2653i	0.455342	−	0.788676i	−0.543366	−	0.839496i	$-0.682850\pi$
$797$	12.8548	−	22.2653i	0.455342	−	0.788676i	0.998708	+	0.0508204i	$0.0161836\pi$
$798$			13.2721i			0.469827i
$799$	−6.32554	−	3.65205i	−0.223781	−	0.129200i
$800$		0			0
$801$		−	8.19889i		−	0.289694i
$802$	10.2187	−	17.6992i	0.360833	−	0.624981i
$803$	−0.341349	−	0.591233i	−0.0120459	−	0.0208642i
$804$	−7.93912	+	4.58365i	−0.279991	+	0.161653i
$805$		0			0
$806$	19.9176	−	3.01994i	0.701567	−	0.106373i
$807$	−25.0171			−0.880645
$808$	7.15577	−	4.13139i	0.251739	−	0.145342i
$809$	−1.44563	−	2.50390i	−0.0508255	−	0.0880323i	0.839493	−	0.543370i	$-0.182852\pi$
$809$	−1.44563	−	2.50390i	−0.0508255	−	0.0880323i	−0.890319	+	0.455338i	$0.849519\pi$
$810$		0			0
$811$			47.4396i			1.66583i	0.553400	+	0.832916i	$0.313330\pi$
$811$			47.4396i			1.66583i	−0.553400	+	0.832916i	$0.686670\pi$
$812$	−37.9545	−	21.9131i	−1.33194	−	0.768997i
$813$	−0.233654	−	0.134900i	−0.00819459	−	0.00473115i
$814$		−	3.01346i		−	0.105622i
$815$		0			0
$816$	−1.75049	−	3.03194i	−0.0612795	−	0.106139i
$817$	−19.3530	+	11.1735i	−0.677076	+	0.390910i
$818$	−10.5688			−0.369529
$819$	2.47657	+	16.3339i	0.0865384	+	0.570753i
$820$		0			0
$821$	−26.7086	+	15.4202i	−0.932135	+	0.538168i	−0.887486	−	0.460834i	$-0.847550\pi$
$821$	−26.7086	+	15.4202i	−0.932135	+	0.538168i	−0.0446489	+	0.999003i	$0.514217\pi$
$822$	6.97859	+	12.0873i	0.243406	+	0.421592i
$823$	−11.4043	+	19.7529i	−0.397530	+	0.688542i	−0.993421	−	0.114523i	$-0.963466\pi$
$823$	−11.4043	+	19.7529i	−0.397530	+	0.688542i	0.595890	+	0.803066i	$0.296799\pi$
$824$			19.7208i			0.687007i
$825$		0			0
$826$	−29.6758	−	17.1334i	−1.03255	−	0.596146i
$827$		−	43.7321i		−	1.52071i	−0.649506	−	0.760357i	$-0.725024\pi$
$827$		−	43.7321i		−	1.52071i	0.649506	−	0.760357i	$-0.274976\pi$
$828$	1.42497	−	2.46812i	0.0495211	−	0.0857730i
$829$	7.34530	+	12.7224i	0.255113	+	0.441869i	0.964926	−	0.262521i	$-0.0845540\pi$
$829$	7.34530	+	12.7224i	0.255113	+	0.441869i	−0.709813	+	0.704390i	$0.751221\pi$
$830$		0			0
$831$	15.9723			0.554073
$832$	1.31432	−	3.35747i	0.0455657	−	0.116399i
$833$	−48.9949			−1.69757
$834$	8.50753	−	4.91182i	0.294592	−	0.170082i
$835$		0			0
$836$	−0.942906	+	1.63316i	−0.0326111	+	0.0564841i
$837$		−	5.58728i		−	0.193125i
$838$	−24.7397	−	14.2835i	−0.854618	−	0.493414i
$839$	11.8808	+	6.85939i	0.410171	+	0.236812i	0.690863	−	0.722985i	$-0.257231\pi$
$839$	11.8808	+	6.85939i	0.410171	+	0.236812i	−0.280692	+	0.959798i	$0.590564\pi$
$840$		0			0
$841$	−31.2433	+	54.1151i	−1.07736	+	1.86604i
$842$	−19.2094	−	33.2716i	−0.661998	−	1.14661i
$843$	4.84041	−	2.79461i	0.166713	−	0.0962516i
$844$	−12.1934			−0.419715
$845$		0			0
$846$	−2.08630			−0.0717284
$847$	41.9674	−	24.2299i	1.44202	−	0.832548i
$848$	−2.79364	−	4.83873i	−0.0959340	−	0.166163i
$849$	4.88188	−	8.45566i	0.167546	−	0.290198i
$850$		0			0
$851$	11.4240	+	6.59565i	0.391610	+	0.226096i
$852$	11.2778	+	6.51127i	0.386373	+	0.223072i
$853$		−	5.80880i		−	0.198890i	−0.995043	−	0.0994448i	$-0.968293\pi$
$853$		−	5.80880i		−	0.198890i	0.995043	−	0.0994448i	$-0.0317067\pi$
$854$	−15.1862	+	26.3032i	−0.519660	+	0.900077i
$855$		0			0
$856$	−2.21785	+	1.28048i	−0.0758047	+	0.0437658i
$857$	−49.9085			−1.70484			−0.852421	−	0.522855i	$-0.824867\pi$
$857$	−49.9085			−1.70484			−0.852421	+	0.522855i	$0.824867\pi$
$858$	−0.855682	+	2.18587i	−0.0292125	+	0.0746244i
$859$	−5.11251			−0.174436			−0.0872182	−	0.996189i	$-0.527798\pi$
$859$	−5.11251			−0.174436			−0.0872182	+	0.996189i	$0.527798\pi$
$860$		0			0
$861$	−8.02073	−	13.8923i	−0.273346	−	0.473449i
$862$	−3.95111	+	6.84351i	−0.134575	+	0.233091i
$863$			18.5089i			0.630051i	0.949083	+	0.315025i	$0.102013\pi$
$863$			18.5089i			0.630051i	−0.949083	+	0.315025i	$0.897987\pi$
$864$	−0.866025	−	0.500000i	−0.0294628	−	0.0170103i
$865$		0			0
$866$			16.6624i			0.566211i
$867$	2.37155	−	4.10765i	0.0805422	−	0.139503i
$868$	12.8004	+	22.1710i	0.434475	+	0.752533i
$869$	1.95172	−	1.12683i	0.0662076	−	0.0382250i
$870$		0			0
$871$	4.95494	+	32.6797i	0.167892	+	1.10731i
$872$	13.7169			0.464513
$873$	12.5030	−	7.21861i	0.423162	−	0.244313i
$874$	−4.12754	−	7.14910i	−0.139616	−	0.241822i
$875$		0			0
$876$		−	1.04861i		−	0.0354294i
$877$	3.41536	+	1.97186i	0.115329	+	0.0665850i	0.556555	−	0.830811i	$-0.312123\pi$
$877$	3.41536	+	1.97186i	0.115329	+	0.0665850i	−0.441226	+	0.897396i	$0.645456\pi$
$878$	−19.3519	−	11.1728i	−0.653095	−	0.377065i
$879$			15.0136i			0.506396i
$880$		0			0
$881$	18.2883	+	31.6762i	0.616147	+	1.06720i	0.990182	+	0.139784i	$0.0446407\pi$
$881$	18.2883	+	31.6762i	0.616147	+	1.06720i	−0.374035	+	0.927415i	$0.622026\pi$
$882$	−12.1197	+	6.99731i	−0.408091	+	0.235612i
$883$	−22.7956			−0.767134			−0.383567	−	0.923513i	$-0.625304\pi$
$883$	−22.7956			−0.767134			−0.383567	+	0.923513i	$0.625304\pi$
$884$	−12.4803	+	1.89229i	−0.419759	+	0.0636445i
$885$		0			0
$886$	−15.1727	+	8.75998i	−0.509738	+	0.294297i
$887$	5.68015	+	9.83830i	0.190721	+	0.330338i	0.945489	−	0.325653i	$-0.105584\pi$
$887$	5.68015	+	9.83830i	0.190721	+	0.330338i	−0.754769	+	0.655991i	$0.772251\pi$
$888$	2.31432	−	4.00851i	0.0776634	−	0.134517i
$889$		−	41.0574i		−	1.37702i
$890$		0			0
$891$	0.563824	+	0.325524i	0.0188888	+	0.0109055i
$892$		−	13.1449i		−	0.440123i
$893$	−3.02157	+	5.23351i	−0.101113	+	0.175133i
$894$	10.1887	+	17.6473i	0.340761	+	0.590215i
$895$		0			0
$896$	4.58199			0.153073
$897$	−6.41376	−	8.02817i	−0.214149	−	0.268053i
$898$	−19.5804			−0.653406
$899$	46.2818	−	26.7208i	1.54358	−	0.891189i
$900$		0			0
$901$	−9.78050	+	16.9403i	−0.325836	+	0.564364i
$902$		−	2.27931i		−	0.0758926i
$903$	−30.6138	−	17.6749i	−1.01876	−	0.588182i
$904$		0			0
$905$		0			0
$906$	11.2920	−	19.5583i	0.375151	−	0.649781i
$907$	−16.7215	−	28.9626i	−0.555230	−	0.961686i	−0.997886	−	0.0649947i	$-0.979297\pi$
$907$	−16.7215	−	28.9626i	−0.555230	−	0.961686i	0.442656	−	0.896692i	$-0.354036\pi$
$908$	−19.5059	+	11.2618i	−0.647327	+	0.373735i
$909$	−8.26277			−0.274059
$910$		0			0
$911$	40.9855			1.35791			0.678956	−	0.734179i	$-0.262433\pi$
$911$	40.9855			1.35791			0.678956	+	0.734179i	$0.262433\pi$
$912$	−2.50851	+	1.44829i	−0.0830652	+	0.0479577i
$913$	−3.44151	−	5.96087i	−0.113897	−	0.197276i
$914$	11.3375	−	19.6371i	0.375011	−	0.649538i
$915$		0			0
$916$	19.5097	+	11.2639i	0.644619	+	0.372171i
$917$	33.6518	+	19.4289i	1.11128	+	0.641597i
$918$			3.50098i			0.115550i
$919$	−6.47104	+	11.2082i	−0.213460	+	0.369724i	−0.952795	−	0.303614i	$-0.901807\pi$
$919$	−6.47104	+	11.2082i	−0.213460	+	0.369724i	0.739335	+	0.673338i	$0.235140\pi$
$920$		0			0
$921$	−5.46254	+	3.15380i	−0.179997	+	0.103921i
$922$	32.8053			1.08038
$923$	36.6840	−	29.3071i	1.20747	−	0.964655i
$924$	−2.98309			−0.0981365
$925$		0			0
$926$	−10.3236	−	17.8810i	−0.339254	−	0.587605i
$927$	9.86041	−	17.0787i	0.323858	−	0.560939i
$928$		−	9.56487i		−	0.313982i
$929$	−29.1850	−	16.8500i	−0.957529	−	0.552830i	−0.0621173	−	0.998069i	$-0.519785\pi$
$929$	−29.1850	−	16.8500i	−0.957529	−	0.552830i	−0.895412	+	0.445239i	$0.853119\pi$
$930$		0			0
$931$			40.5365i			1.32853i
$932$	7.93624	−	13.7460i	0.259960	−	0.450264i
$933$	13.4851	+	23.3570i	0.441484	+	0.764672i
$934$	6.73020	−	3.88568i	0.220219	−	0.127143i
$935$		0			0
$936$	−2.81696	+	2.25049i	−0.0920753	+	0.0735596i
$937$	−12.3888			−0.404724			−0.202362	−	0.979311i	$-0.564862\pi$
$937$	−12.3888			−0.404724			−0.202362	+	0.979311i	$0.564862\pi$
$938$	−36.3769	+	21.0022i	−1.18775	+	0.685747i
$939$	9.23735	+	15.9996i	0.301449	+	0.522126i
$940$		0			0
$941$		−	5.26120i		−	0.171510i	−0.996316	−	0.0857551i	$-0.972670\pi$
$941$		−	5.26120i		−	0.171510i	0.996316	−	0.0857551i	$-0.0273303\pi$
$942$	5.66593	+	3.27123i	0.184606	+	0.106582i
$943$	8.64084	+	4.98879i	0.281385	+	0.162457i
$944$		−	7.47857i		−	0.243407i
$945$		0			0
$946$	−2.51139	−	4.34986i	−0.0816525	−	0.141426i
$947$	−5.79737	+	3.34711i	−0.188389	+	0.108766i	−0.591228	−	0.806504i	$-0.701357\pi$
$947$	−5.79737	+	3.34711i	−0.188389	+	0.108766i	0.402839	+	0.915271i	$0.368023\pi$
$948$	3.46158			0.112427
$949$	−3.52068	−	1.37821i	−0.114286	−	0.0447386i
$950$		0			0
$951$	−2.47279	+	1.42766i	−0.0801856	+	0.0462952i
$952$	−8.02073	−	13.8923i	−0.259953	−	0.450253i
$953$	−20.3556	+	35.2569i	−0.659382	+	1.14208i	0.321394	+	0.946945i	$0.395848\pi$
$953$	−20.3556	+	35.2569i	−0.659382	+	1.14208i	−0.980776	+	0.195137i	$0.937485\pi$
$954$			5.58728i			0.180895i
$955$		0			0
$956$	−18.1608	−	10.4851i	−0.587362	−	0.339114i
$957$			6.22718i			0.201296i
$958$	8.76102	−	15.1745i	0.283056	−	0.490267i
$959$	31.9758	+	55.3837i	1.03255	+	1.78843i
$960$		0			0
$961$	−0.217731			−0.00702359
$962$	−10.4167	−	13.0387i	−0.335848	−	0.420384i
$963$	2.56096			0.0825257
$964$	−5.41101	+	3.12405i	−0.174277	+	0.100619i
$965$		0			0
$966$	6.52919	−	11.3089i	0.210073	−	0.363857i
$967$		−	60.9859i		−	1.96117i	−0.196085	−	0.980587i	$-0.562823\pi$
$967$		−	60.9859i		−	1.96117i	0.196085	−	0.980587i	$-0.437177\pi$
$968$	9.15920	+	5.28807i	0.294388	+	0.169965i
$969$	8.78226	+	5.07044i	0.282127	+	0.162886i
$970$		0			0
$971$	23.2702	−	40.3052i	0.746776	−	1.29345i	−0.202584	−	0.979265i	$-0.564934\pi$
$971$	23.2702	−	40.3052i	0.746776	−	1.29345i	0.949360	−	0.314189i	$-0.101733\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	38.9814	−	22.5059i	1.24969	−	0.721506i
$974$	20.8824			0.669114
$975$		0			0
$976$	−6.62863			−0.212177
$977$	−32.6138	+	18.8296i	−1.04341	+	0.602413i	−0.920797	−	0.390042i	$-0.872460\pi$
$977$	−32.6138	+	18.8296i	−1.04341	+	0.602413i	−0.122612	+	0.992455i	$0.539127\pi$
$978$	−7.09944	−	12.2966i	−0.227015	−	0.393202i
$979$	2.66893	−	4.62273i	0.0852995	−	0.147743i
$980$		0			0
$981$	−11.8792	−	6.85845i	−0.379273	−	0.218973i
$982$	−13.8098	−	7.97312i	−0.440690	−	0.254432i
$983$			32.9140i			1.04979i	0.851166	+	0.524896i	$0.175896\pi$
$983$			32.9140i			1.04979i	−0.851166	+	0.524896i	$0.824104\pi$
$984$	1.75049	−	3.03194i	0.0558037	−	0.0966548i
$985$		0			0
$986$	−29.0001	+	16.7432i	−0.923552	+	0.533213i
$987$	−9.55939			−0.304279
$988$	1.56561	+	10.3258i	0.0498086	+	0.328506i
$989$	21.9871			0.699148
$990$		0			0
$991$	−29.9561	−	51.8855i	−0.951588	−	1.64820i	−0.741991	−	0.670410i	$-0.766118\pi$
$991$	−29.9561	−	51.8855i	−0.951588	−	1.64820i	−0.209597	−	0.977788i	$-0.567215\pi$
$992$	−2.79364	+	4.83873i	−0.0886982	+	0.153630i
$993$			4.85375i			0.154029i
$994$	51.6749	+	29.8345i	1.63903	+	0.946294i
$995$		0			0
$996$		−	10.5722i		−	0.334994i
$997$	−26.6627	+	46.1811i	−0.844416	+	1.46257i	0.0417112	+	0.999130i	$0.486719\pi$
$997$	−26.6627	+	46.1811i	−0.844416	+	1.46257i	−0.886127	+	0.463442i	$0.846614\pi$
$998$	9.59847	+	16.6250i	0.303834	+	0.526256i
$999$	−4.00851	+	2.31432i	−0.126824	+	0.0732217i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1950.2.bc.h.751.4	✓	12
5.2	odd	4		1950.2.y.n.49.3		12
5.3	odd	4		1950.2.y.m.49.4		12
5.4	even	2		1950.2.bc.k.751.3	yes	12
13.4	even	6	inner	1950.2.bc.h.901.4	yes	12
65.4	even	6		1950.2.bc.k.901.3	yes	12
65.17	odd	12		1950.2.y.m.199.4		12
65.43	odd	12		1950.2.y.n.199.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.y.m.49.4		12	5.3	odd	4
1950.2.y.m.199.4		12	65.17	odd	12
1950.2.y.n.49.3		12	5.2	odd	4
1950.2.y.n.199.3		12	65.43	odd	12
1950.2.bc.h.751.4	✓	12	1.1	even	1	trivial
1950.2.bc.h.901.4	yes	12	13.4	even	6	inner
1950.2.bc.k.751.3	yes	12	5.4	even	2
1950.2.bc.k.901.3	yes	12	65.4	even	6

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)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.866025 - 0.500000i) q^{6} +(-3.96812 - 2.29099i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +(-3.96812 - 2.29099i) q^{7} -1.00000i q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.563824 + 0.325524i) q^{11} -1.00000 q^{12} +(-1.31432 + 3.35747i) q^{13} -4.58199 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.75049 + 3.03194i) q^{17} +1.00000i q^{18} +(2.50851 + 1.44829i) q^{19} +4.58199i q^{21} +(-0.325524 + 0.563824i) q^{22} +(-1.42497 - 2.46812i) q^{23} +(-0.866025 + 0.500000i) q^{24} +(0.540502 + 3.56481i) q^{26} +1.00000 q^{27} +(-3.96812 + 2.29099i) q^{28} +(4.78243 + 8.28342i) q^{29} -5.58728i q^{31} +(-0.866025 - 0.500000i) q^{32} +(0.563824 + 0.325524i) q^{33} +3.50098i q^{34} +(0.500000 + 0.866025i) q^{36} +(-4.00851 + 2.31432i) q^{37} +2.89658 q^{38} +(3.56481 - 0.540502i) q^{39} +(-3.03194 + 1.75049i) q^{41} +(2.29099 + 3.96812i) q^{42} +(-3.85747 + 6.68133i) q^{43} +0.651048i q^{44} +(-2.46812 - 1.42497i) q^{46} +2.08630i q^{47} +(-0.500000 + 0.866025i) q^{48} +(6.99731 + 12.1197i) q^{49} +3.50098 q^{51} +(2.25049 + 2.81696i) q^{52} +5.58728 q^{53} +(0.866025 - 0.500000i) q^{54} +(-2.29099 + 3.96812i) q^{56} -2.89658i q^{57} +(8.28342 + 4.78243i) q^{58} +(6.47663 + 3.73928i) q^{59} +(3.31432 - 5.74056i) q^{61} +(-2.79364 - 4.83873i) q^{62} +(3.96812 - 2.29099i) q^{63} -1.00000 q^{64} +0.651048 q^{66} +(7.93912 - 4.58365i) q^{67} +(1.75049 + 3.03194i) q^{68} +(-1.42497 + 2.46812i) q^{69} +(-11.2778 - 6.51127i) q^{71} +(0.866025 + 0.500000i) q^{72} +1.04861i q^{73} +(-2.31432 + 4.00851i) q^{74} +(2.50851 - 1.44829i) q^{76} +2.98309 q^{77} +(2.81696 - 2.25049i) q^{78} -3.46158 q^{79} +(-0.500000 - 0.866025i) q^{81} +(-1.75049 + 3.03194i) q^{82} +10.5722i q^{83} +(3.96812 + 2.29099i) q^{84} +7.71493i q^{86} +(4.78243 - 8.28342i) q^{87} +(0.325524 + 0.563824i) q^{88} +(-7.10045 + 4.09944i) q^{89} +(12.9073 - 10.3117i) q^{91} -2.84994 q^{92} +(-4.83873 + 2.79364i) q^{93} +(1.04315 + 1.80679i) q^{94} +1.00000i q^{96} +(-12.5030 - 7.21861i) q^{97} +(12.1197 + 6.99731i) q^{98} -0.651048i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 6 q^{3} + 6 q^{4} - 6 q^{7} - 6 q^{9}+O(q^{10}) \) 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^7 - 6 * q^9	\( 12 q - 6 q^{3} + 6 q^{4} - 6 q^{7} - 6 q^{9} - 12 q^{11} - 12 q^{12} + 8 q^{14} - 6 q^{16} - 6 q^{19} - 4 q^{22} + 4 q^{23} - 4 q^{26} + 12 q^{27} - 6 q^{28} + 12 q^{33} + 6 q^{36} - 12 q^{37} + 24 q^{38} + 6 q^{39} - 4 q^{42} - 10 q^{43} + 12 q^{46} - 6 q^{48} + 32 q^{49} + 6 q^{52} - 16 q^{53} + 4 q^{56} + 24 q^{61} + 8 q^{62} + 6 q^{63} - 12 q^{64} + 8 q^{66} + 6 q^{67} + 4 q^{69} + 12 q^{71} - 12 q^{74} - 6 q^{76} - 48 q^{77} + 8 q^{78} + 52 q^{79} - 6 q^{81} + 6 q^{84} + 4 q^{88} + 24 q^{89} - 54 q^{91} + 8 q^{92} - 8 q^{94} + 12 q^{97} + 36 q^{98}+O(q^{100}) \) 12 * q - 6 * q^3 + 6 * q^4 - 6 * q^7 - 6 * q^9 - 12 * q^11 - 12 * q^12 + 8 * q^14 - 6 * q^16 - 6 * q^19 - 4 * q^22 + 4 * q^23 - 4 * q^26 + 12 * q^27 - 6 * q^28 + 12 * q^33 + 6 * q^36 - 12 * q^37 + 24 * q^38 + 6 * q^39 - 4 * q^42 - 10 * q^43 + 12 * q^46 - 6 * q^48 + 32 * q^49 + 6 * q^52 - 16 * q^53 + 4 * q^56 + 24 * q^61 + 8 * q^62 + 6 * q^63 - 12 * q^64 + 8 * q^66 + 6 * q^67 + 4 * q^69 + 12 * q^71 - 12 * q^74 - 6 * q^76 - 48 * q^77 + 8 * q^78 + 52 * q^79 - 6 * q^81 + 6 * q^84 + 4 * q^88 + 24 * q^89 - 54 * q^91 + 8 * q^92 - 8 * q^94 + 12 * q^97 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more