LMFDB - Embedded newform 1950.2.y.n.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

chi = DirichletCharacter(H, H._module([0, 3, 5]))

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

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

chi := DirichletCharacter("1950.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			199.3
Root			$0.500000 + 4.71596i$ of defining polynomial
Character	$\chi$	$=$	1950.199
Dual form			1950.2.y.n.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(2.29099 + 3.96812i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(2.29099 + 3.96812i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.563824 - 0.325524i) q^{11} +1.00000i q^{12} +(3.35747 - 1.31432i) q^{13} +4.58199 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.03194 + 1.75049i) q^{17} +1.00000 q^{18} +(-2.50851 + 1.44829i) q^{19} -4.58199i q^{21} +(-0.563824 + 0.325524i) q^{22} +(-2.46812 - 1.42497i) q^{23} +(0.866025 + 0.500000i) q^{24} +(0.540502 - 3.56481i) q^{26} -1.00000i q^{27} +(2.29099 - 3.96812i) q^{28} +(-4.78243 + 8.28342i) q^{29} +5.58728i q^{31} +(0.500000 + 0.866025i) q^{32} +(0.325524 + 0.563824i) q^{33} +3.50098i q^{34} +(0.500000 - 0.866025i) q^{36} +(-2.31432 + 4.00851i) q^{37} +2.89658i q^{38} +(-3.56481 - 0.540502i) q^{39} +(-3.03194 - 1.75049i) q^{41} +(-3.96812 - 2.29099i) q^{42} +(6.68133 - 3.85747i) q^{43} +0.651048i q^{44} +(-2.46812 + 1.42497i) q^{46} -2.08630 q^{47} +(0.866025 - 0.500000i) q^{48} +(-6.99731 + 12.1197i) q^{49} +3.50098 q^{51} +(-2.81696 - 2.25049i) q^{52} +5.58728i q^{53} +(-0.866025 - 0.500000i) q^{54} +(-2.29099 - 3.96812i) q^{56} +2.89658 q^{57} +(4.78243 + 8.28342i) q^{58} +(-6.47663 + 3.73928i) q^{59} +(3.31432 + 5.74056i) q^{61} +(4.83873 + 2.79364i) q^{62} +(-2.29099 + 3.96812i) q^{63} +1.00000 q^{64} +0.651048 q^{66} +(4.58365 - 7.93912i) q^{67} +(3.03194 + 1.75049i) q^{68} +(1.42497 + 2.46812i) q^{69} +(-11.2778 + 6.51127i) q^{71} +(-0.500000 - 0.866025i) q^{72} +1.04861 q^{73} +(2.31432 + 4.00851i) q^{74} +(2.50851 + 1.44829i) q^{76} -2.98309i q^{77} +(-2.25049 + 2.81696i) q^{78} +3.46158 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-3.03194 + 1.75049i) q^{82} +10.5722 q^{83} +(-3.96812 + 2.29099i) q^{84} -7.71493i q^{86} +(8.28342 - 4.78243i) q^{87} +(0.563824 + 0.325524i) q^{88} +(7.10045 + 4.09944i) q^{89} +(12.9073 + 10.3117i) q^{91} +2.84994i q^{92} +(2.79364 - 4.83873i) q^{93} +(-1.04315 + 1.80679i) q^{94} -1.00000i q^{96} +(7.21861 + 12.5030i) q^{97} +(6.99731 + 12.1197i) q^{98} -0.651048i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - 6 q^{4} - 4 q^{7} - 12 q^{8} + 6 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 - 6 * q^4 - 4 * q^7 - 12 * q^8 + 6 * q^9	$ 12 q + 6 q^{2} - 6 q^{4} - 4 q^{7} - 12 q^{8} + 6 q^{9} - 12 q^{11} + 4 q^{13} - 8 q^{14} - 6 q^{16} + 12 q^{18} + 6 q^{19} - 12 q^{22} + 12 q^{23} - 4 q^{26} - 4 q^{28} + 6 q^{32} + 4 q^{33} + 6 q^{36} - 12 q^{37} - 6 q^{39} - 6 q^{42} + 12 q^{43} + 12 q^{46} + 16 q^{47} - 32 q^{49} - 8 q^{52} + 4 q^{56} + 24 q^{57} + 24 q^{61} + 4 q^{63} + 12 q^{64} + 8 q^{66} + 24 q^{67} - 4 q^{69} + 12 q^{71} - 6 q^{72} - 40 q^{73} + 12 q^{74} - 6 q^{76} - 6 q^{78} - 52 q^{79} - 6 q^{81} + 32 q^{83} - 6 q^{84} + 12 q^{88} - 24 q^{89} - 54 q^{91} - 8 q^{93} + 8 q^{94} + 24 q^{97} + 32 q^{98}+O(q^{100}) $ 12 * q + 6 * q^2 - 6 * q^4 - 4 * q^7 - 12 * q^8 + 6 * q^9 - 12 * q^11 + 4 * q^13 - 8 * q^14 - 6 * q^16 + 12 * q^18 + 6 * q^19 - 12 * q^22 + 12 * q^23 - 4 * q^26 - 4 * q^28 + 6 * q^32 + 4 * q^33 + 6 * q^36 - 12 * q^37 - 6 * q^39 - 6 * q^42 + 12 * q^43 + 12 * q^46 + 16 * q^47 - 32 * q^49 - 8 * q^52 + 4 * q^56 + 24 * q^57 + 24 * q^61 + 4 * q^63 + 12 * q^64 + 8 * q^66 + 24 * q^67 - 4 * q^69 + 12 * q^71 - 6 * q^72 - 40 * q^73 + 12 * q^74 - 6 * q^76 - 6 * q^78 - 52 * q^79 - 6 * q^81 + 32 * q^83 - 6 * q^84 + 12 * q^88 - 24 * q^89 - 54 * q^91 - 8 * q^93 + 8 * q^94 + 24 * q^97 + 32 * q^98

Display 100 coefficients 10 coefficients

Character values

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

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

Coefficient data

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

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

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

$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$2$	0.500000	−	0.866025i	0.353553	−	0.612372i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$3$	−0.866025	−	0.500000i	−0.500000	−	0.288675i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.866025	+	0.500000i	−0.353553	+	0.204124i
$7$	2.29099	+	3.96812i	0.865914	+	1.49981i	0.866137	+	0.499808i	$0.166596\pi$
$7$	2.29099	+	3.96812i	0.865914	+	1.49981i	−0.000222235		1.00000i	$0.500071\pi$
$8$	−1.00000			−0.353553
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−0.563824	−	0.325524i	−0.169999	−	0.0981491i	0.412586	−	0.910919i	$-0.364626\pi$
$11$	−0.563824	−	0.325524i	−0.169999	−	0.0981491i	−0.582585	+	0.812769i	$0.697959\pi$
$12$			1.00000i			0.288675i
$13$	3.35747	−	1.31432i	0.931193	−	0.364526i
$13$	3.35747	−	1.31432i	0.931193	−	0.364526i
$14$	4.58199			1.22459
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−3.03194	+	1.75049i	−0.735354	+	0.424557i	−0.820378	−	0.571822i	$-0.806237\pi$
$17$	−3.03194	+	1.75049i	−0.735354	+	0.424557i	0.0850238	+	0.996379i	$0.472903\pi$
$18$	1.00000			0.235702
$19$	−2.50851	+	1.44829i	−0.575492	+	0.332261i	−0.759340	−	0.650694i	$-0.774478\pi$
$19$	−2.50851	+	1.44829i	−0.575492	+	0.332261i	0.183848	+	0.982955i	$0.441145\pi$
$20$		0			0
$21$		−	4.58199i		−	0.999872i
$22$	−0.563824	+	0.325524i	−0.120208	+	0.0694019i
$23$	−2.46812	−	1.42497i	−0.514638	−	0.297126i	0.220100	−	0.975477i	$-0.429362\pi$
$23$	−2.46812	−	1.42497i	−0.514638	−	0.297126i	−0.734738	+	0.678351i	$0.762695\pi$
$24$	0.866025	+	0.500000i	0.176777	+	0.102062i
$25$		0			0
$26$	0.540502	−	3.56481i	0.106001	−	0.699116i
$27$		−	1.00000i		−	0.192450i
$28$	2.29099	−	3.96812i	0.432957	−	0.749904i
$29$	−4.78243	+	8.28342i	−0.888076	+	1.53819i	−0.0459282	+	0.998945i	$0.514625\pi$
$29$	−4.78243	+	8.28342i	−0.888076	+	1.53819i	−0.842147	+	0.539247i	$0.818709\pi$
$30$		0			0
$31$			5.58728i			1.00351i	0.865011	+	0.501753i	$0.167311\pi$
$31$			5.58728i			1.00351i	−0.865011	+	0.501753i	$0.832689\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	0.325524	+	0.563824i	0.0566664	+	0.0981491i
$34$			3.50098i			0.600414i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	−2.31432	+	4.00851i	−0.380471	+	0.658995i	−0.991130	−	0.132899i	$-0.957572\pi$
$37$	−2.31432	+	4.00851i	−0.380471	+	0.658995i	0.610658	+	0.791894i	$0.290905\pi$
$38$			2.89658i			0.469888i
$39$	−3.56481	−	0.540502i	−0.570826	−	0.0865495i
$40$		0			0
$41$	−3.03194	−	1.75049i	−0.473510	−	0.273381i	0.244198	−	0.969725i	$-0.421475\pi$
$41$	−3.03194	−	1.75049i	−0.473510	−	0.273381i	−0.717708	+	0.696344i	$0.754809\pi$
$42$	−3.96812	−	2.29099i	−0.612294	−	0.353508i
$43$	6.68133	−	3.85747i	1.01889	−	0.588258i	0.105110	−	0.994461i	$-0.466481\pi$
$43$	6.68133	−	3.85747i	1.01889	−	0.588258i	0.913783	+	0.406203i	$0.133147\pi$
$44$			0.651048i			0.0981491i
$45$		0			0
$46$	−2.46812	+	1.42497i	−0.363904	+	0.210100i
$47$	−2.08630			−0.304318			−0.152159	−	0.988356i	$-0.548623\pi$
$47$	−2.08630			−0.304318			−0.152159	+	0.988356i	$0.548623\pi$
$48$	0.866025	−	0.500000i	0.125000	−	0.0721688i
$49$	−6.99731	+	12.1197i	−0.999615	+	1.73138i
$50$		0			0
$51$	3.50098			0.490236
$52$	−2.81696	−	2.25049i	−0.390643	−	0.312087i
$53$			5.58728i			0.767472i	0.923443	+	0.383736i	$0.125363\pi$
$53$			5.58728i			0.767472i	−0.923443	+	0.383736i	$0.874637\pi$
$54$	−0.866025	−	0.500000i	−0.117851	−	0.0680414i
$55$		0			0
$56$	−2.29099	−	3.96812i	−0.306147	−	0.530262i
$57$	2.89658			0.383662
$58$	4.78243	+	8.28342i	0.627964	+	1.08767i
$59$	−6.47663	+	3.73928i	−0.843185	+	0.486813i	−0.858346	−	0.513072i	$-0.828507\pi$
$59$	−6.47663	+	3.73928i	−0.843185	+	0.486813i	0.0151603	+	0.999885i	$0.495174\pi$
$60$		0			0
$61$	3.31432	+	5.74056i	0.424355	+	0.735004i	0.996360	−	0.0852461i	$-0.0271676\pi$
$61$	3.31432	+	5.74056i	0.424355	+	0.735004i	−0.572005	+	0.820250i	$0.693834\pi$
$62$	4.83873	+	2.79364i	0.614519	+	0.354793i
$63$	−2.29099	+	3.96812i	−0.288638	+	0.499936i
$64$	1.00000			0.125000
$65$		0			0
$66$	0.651048			0.0801384
$67$	4.58365	−	7.93912i	0.559982	−	0.969917i	−0.437515	−	0.899211i	$-0.644141\pi$
$67$	4.58365	−	7.93912i	0.559982	−	0.969917i	0.997497	−	0.0707063i	$-0.0225253\pi$
$68$	3.03194	+	1.75049i	0.367677	+	0.212278i
$69$	1.42497	+	2.46812i	0.171546	+	0.297126i
$70$		0			0
$71$	−11.2778	+	6.51127i	−1.33843	+	0.772745i	−0.986575	−	0.163308i	$-0.947784\pi$
$71$	−11.2778	+	6.51127i	−1.33843	+	0.772745i	−0.351859	+	0.936053i	$0.614450\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	1.04861			0.122731			0.0613655	−	0.998115i	$-0.480454\pi$
$73$	1.04861			0.122731			0.0613655	+	0.998115i	$0.480454\pi$
$74$	2.31432	+	4.00851i	0.269034	+	0.465980i
$75$		0			0
$76$	2.50851	+	1.44829i	0.287746	+	0.166130i
$77$		−	2.98309i		−	0.339955i
$78$	−2.25049	+	2.81696i	−0.254818	+	0.318958i
$79$	3.46158			0.389458			0.194729	−	0.980857i	$-0.437617\pi$
$79$	3.46158			0.389458			0.194729	+	0.980857i	$0.437617\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−3.03194	+	1.75049i	−0.334822	+	0.193310i
$83$	10.5722			1.16045			0.580226	−	0.814455i	$-0.302964\pi$
$83$	10.5722			1.16045			0.580226	+	0.814455i	$0.302964\pi$
$84$	−3.96812	+	2.29099i	−0.432957	+	0.249968i
$85$		0			0
$86$		−	7.71493i		−	0.831922i
$87$	8.28342	−	4.78243i	0.888076	−	0.512731i
$88$	0.563824	+	0.325524i	0.0601038	+	0.0347010i
$89$	7.10045	+	4.09944i	0.752646	+	0.434540i	0.826649	−	0.562718i	$-0.190244\pi$
$89$	7.10045	+	4.09944i	0.752646	+	0.434540i	−0.0740033	+	0.997258i	$0.523578\pi$
$90$		0			0
$91$	12.9073	+	10.3117i	1.35305	+	1.08096i
$92$			2.84994i			0.297126i
$93$	2.79364	−	4.83873i	0.289687	−	0.501753i
$94$	−1.04315	+	1.80679i	−0.107593	+	0.186356i
$95$		0			0
$96$		−	1.00000i		−	0.102062i
$97$	7.21861	+	12.5030i	0.732939	+	1.26949i	0.955622	+	0.294596i	$0.0951852\pi$
$97$	7.21861	+	12.5030i	0.732939	+	1.26949i	−0.222683	+	0.974891i	$0.571481\pi$
$98$	6.99731	+	12.1197i	0.706835	+	1.22427i
$99$		−	0.651048i		−	0.0654328i
$100$		0			0
$101$	4.13139	−	7.15577i	0.411088	−	0.712026i	−0.583921	−	0.811811i	$-0.698482\pi$
$101$	4.13139	−	7.15577i	0.411088	−	0.712026i	0.995009	+	0.0997849i	$0.0318155\pi$
$102$	1.75049	−	3.03194i	0.173325	−	0.300207i
$103$		−	19.7208i		−	1.94315i	−0.236734	−	0.971575i	$-0.576077\pi$
$103$		−	19.7208i		−	1.94315i	0.236734	−	0.971575i	$-0.423923\pi$
$104$	−3.35747	+	1.31432i	−0.329227	+	0.128879i
$105$		0			0
$106$	4.83873	+	2.79364i	0.469979	+	0.271342i
$107$	2.21785	+	1.28048i	0.214408	+	0.123789i	0.603358	−	0.797470i	$-0.293829\pi$
$107$	2.21785	+	1.28048i	0.214408	+	0.123789i	−0.388950	+	0.921259i	$0.627162\pi$
$108$	−0.866025	+	0.500000i	−0.0833333	+	0.0481125i
$109$			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
$112$	−4.58199			−0.432957
$113$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$113$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$114$	1.44829	−	2.50851i	0.135645	−	0.234944i
$115$		0			0
$116$	9.56487			0.888076
$117$	2.81696	+	2.25049i	0.260428	+	0.208058i
$118$			7.47857i			0.688458i
$119$	−13.8923	−	8.02073i	−1.27351	−	0.735259i
$120$		0			0
$121$	−5.28807	−	9.15920i	−0.480733	−	0.832655i
$122$	6.62863			0.600128
$123$	1.75049	+	3.03194i	0.157837	+	0.273381i
$124$	4.83873	−	2.79364i	0.434531	−	0.250876i
$125$		0			0
$126$	2.29099	+	3.96812i	0.204098	+	0.353508i
$127$	−7.76012	−	4.48031i	−0.688600	−	0.397563i	0.114488	−	0.993425i	$-0.463477\pi$
$127$	−7.76012	−	4.48031i	−0.688600	−	0.397563i	−0.803087	+	0.595861i	$0.796811\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−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	$0.620805\pi$
$132$	0.325524	−	0.563824i	0.0283332	−	0.0490746i
$133$	−11.4940	−	6.63605i	−0.996654	−	0.575418i
$134$	−4.58365	−	7.93912i	−0.395967	−	0.685835i
$135$		0			0
$136$	3.03194	−	1.75049i	0.259987	−	0.150103i
$137$	6.97859	+	12.0873i	0.596221	+	1.03268i	0.993373	+	0.114932i	$0.0366651\pi$
$137$	6.97859	+	12.0873i	0.596221	+	1.03268i	−0.397152	+	0.917753i	$0.630002\pi$
$138$	2.84994			0.242603
$139$	4.91182	+	8.50753i	0.416615	+	0.721599i	0.995597	−	0.0937420i	$-0.0298829\pi$
$139$	4.91182	+	8.50753i	0.416615	+	0.721599i	−0.578981	+	0.815341i	$0.696550\pi$
$140$		0			0
$141$	1.80679	+	1.04315i	0.152159	+	0.0878490i
$142$			13.0225i			1.09283i
$143$	−2.32086	−	0.351892i	−0.194080	−	0.0294267i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	0.524307	−	0.908126i	0.0433919	−	0.0751570i
$147$	12.1197	−	6.99731i	0.999615	−	0.577128i
$148$	4.62863			0.380471
$149$	17.6473	−	10.1887i	1.44572	−	0.834689i	0.447502	−	0.894283i	$-0.352314\pi$
$149$	17.6473	−	10.1887i	1.44572	−	0.834689i	0.998223	+	0.0595936i	$0.0189805\pi$
$150$		0			0
$151$		−	22.5840i		−	1.83786i	−0.394422	−	0.918930i	$-0.629055\pi$
$151$		−	22.5840i		−	1.83786i	0.394422	−	0.918930i	$-0.370945\pi$
$152$	2.50851	−	1.44829i	0.203467	−	0.117472i
$153$	−3.03194	−	1.75049i	−0.245118	−	0.141519i
$154$	−2.58343	−	1.49155i	−0.208179	−	0.120192i
$155$		0			0
$156$	1.31432	+	3.35747i	0.105230	+	0.268812i
$157$			6.54245i			0.522145i	0.965319	+	0.261072i	$0.0840761\pi$
$157$			6.54245i			0.522145i	−0.965319	+	0.261072i	$0.915924\pi$
$158$	1.73079	−	2.99781i	0.137694	−	0.238493i
$159$	2.79364	−	4.83873i	0.221550	−	0.383736i
$160$		0			0
$161$		−	13.0584i		−	1.02914i
$162$	0.500000	+	0.866025i	0.0392837	+	0.0680414i
$163$	7.09944	+	12.2966i	0.556071	+	0.963144i	0.997819	+	0.0660047i	$0.0210252\pi$
$163$	7.09944	+	12.2966i	0.556071	+	0.963144i	−0.441748	+	0.897139i	$0.645641\pi$
$164$			3.50098i			0.273381i
$165$		0			0
$166$	5.28611	−	9.15582i	0.410282	−	0.710629i
$167$	1.42497	−	2.46812i	0.110267	−	0.190989i	−0.805611	−	0.592445i	$-0.798163\pi$
$167$	1.42497	−	2.46812i	0.110267	−	0.190989i	0.915878	+	0.401457i	$0.131496\pi$
$168$			4.58199i			0.353508i
$169$	9.54515	−	8.82554i	0.734242	−	0.678888i
$170$		0			0
$171$	−2.50851	−	1.44829i	−0.191831	−	0.110754i
$172$	−6.68133	−	3.85747i	−0.509446	−	0.294129i
$173$	−5.80397	+	3.35092i	−0.441267	+	0.254766i	−0.704135	−	0.710066i	$-0.748665\pi$
$173$	−5.80397	+	3.35092i	−0.441267	+	0.254766i	0.262868	+	0.964832i	$0.415332\pi$
$174$		−	9.56487i		−	0.725111i
$175$		0			0
$176$	0.563824	−	0.325524i	0.0424998	−	0.0245373i
$177$	7.47857			0.562124
$178$	7.10045	−	4.09944i	0.532201	−	0.307266i
$179$	−9.98128	+	17.2881i	−0.746036	+	1.29217i	0.203673	+	0.979039i	$0.434712\pi$
$179$	−9.98128	+	17.2881i	−0.746036	+	1.29217i	−0.949709	+	0.313133i	$0.898621\pi$
$180$		0			0
$181$	−3.19889			−0.237772			−0.118886	−	0.992908i	$-0.537932\pi$
$181$	−3.19889			−0.237772			−0.118886	+	0.992908i	$0.537932\pi$
$182$	15.3839	−	6.02218i	1.14033	−	0.446394i
$183$		−	6.62863i		−	0.490003i
$184$	2.46812	+	1.42497i	0.181952	+	0.105050i
$185$		0			0
$186$	−2.79364	−	4.83873i	−0.204840	−	0.354793i
$187$	2.27931			0.166679
$188$	1.04315	+	1.80679i	0.0760795	+	0.131774i
$189$	3.96812	−	2.29099i	0.288638	−	0.166645i
$190$		0			0
$191$	12.5366	+	21.7141i	0.907118	+	1.57117i	0.818048	+	0.575149i	$0.195056\pi$
$191$	12.5366	+	21.7141i	0.907118	+	1.57117i	0.0890697	+	0.996025i	$0.471611\pi$
$192$	−0.866025	−	0.500000i	−0.0625000	−	0.0360844i
$193$	4.49546	−	7.78636i	0.323590	−	0.560474i	−0.657636	−	0.753336i	$-0.728443\pi$
$193$	4.49546	−	7.78636i	0.323590	−	0.560474i	0.981226	+	0.192862i	$0.0617768\pi$
$194$	14.4372			1.03653
$195$		0			0
$196$	13.9946			0.999615
$197$	10.8923	−	18.8660i	0.776043	−	1.34415i	−0.158163	−	0.987413i	$-0.550557\pi$
$197$	10.8923	−	18.8660i	0.776043	−	1.34415i	0.934206	−	0.356733i	$-0.116110\pi$
$198$	−0.563824	−	0.325524i	−0.0400692	−	0.0231340i
$199$	−0.295538	−	0.511887i	−0.0209501	−	0.0362867i	0.855360	−	0.518034i	$-0.173336\pi$
$199$	−0.295538	−	0.511887i	−0.0209501	−	0.0362867i	−0.876310	+	0.481747i	$0.840002\pi$
$200$		0			0
$201$	−7.93912	+	4.58365i	−0.559982	+	0.323306i
$202$	−4.13139	−	7.15577i	−0.290683	−	0.503478i
$203$	−43.8261			−3.07599
$204$	−1.75049	−	3.03194i	−0.122559	−	0.212278i
$205$		0			0
$206$	−17.0787	−	9.86041i	−1.18993	−	0.687007i
$207$		−	2.84994i		−	0.198084i
$208$	−0.540502	+	3.56481i	−0.0374770	+	0.247175i
$209$	1.88581			0.130444
$210$		0			0
$211$	−6.09671	+	10.5598i	−0.419715	+	0.726967i	−0.995911	−	0.0903445i	$-0.971203\pi$
$211$	−6.09671	+	10.5598i	−0.419715	+	0.726967i	0.576196	+	0.817312i	$0.304537\pi$
$212$	4.83873	−	2.79364i	0.332325	−	0.191868i
$213$	13.0225			0.892289
$214$	2.21785	−	1.28048i	0.151609	−	0.0875317i
$215$		0			0
$216$			1.00000i			0.0680414i
$217$	−22.1710	+	12.8004i	−1.50507	+	0.868950i
$218$	11.8792	+	6.85845i	0.804560	+	0.464513i
$219$	−0.908126	−	0.524307i	−0.0613655	−	0.0354294i
$220$		0			0
$221$	−7.87894	+	9.86215i	−0.529995	+	0.663400i
$222$		−	4.62863i		−	0.310653i
$223$	−6.57244	+	11.3838i	−0.440123	+	0.762316i	−0.997698	−	0.0678107i	$-0.978399\pi$
$223$	−6.57244	+	11.3838i	−0.440123	+	0.762316i	0.557575	+	0.830127i	$0.311732\pi$
$224$	−2.29099	+	3.96812i	−0.153073	+	0.265131i
$225$		0			0
$226$		0			0
$227$	11.2618	+	19.5059i	0.747469	+	1.29465i	0.949032	+	0.315179i	$0.102065\pi$
$227$	11.2618	+	19.5059i	0.747469	+	1.29465i	−0.201563	+	0.979476i	$0.564602\pi$
$228$	−1.44829	−	2.50851i	−0.0959154	−	0.166130i
$229$			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
$232$	4.78243	−	8.28342i	0.313982	−	0.543833i
$233$			15.8725i			1.03984i	0.854215	+	0.519920i	$0.174038\pi$
$233$			15.8725i			1.03984i	−0.854215	+	0.519920i	$0.825962\pi$
$234$	3.35747	−	1.31432i	0.219484	−	0.0859195i
$235$		0			0
$236$	6.47663	+	3.73928i	0.421593	+	0.243407i
$237$	−2.99781	−	1.73079i	−0.194729	−	0.112427i
$238$	−13.8923	+	8.02073i	−0.900505	+	0.519907i
$239$		−	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	−0.664048	−	0.747690i	$-0.731163\pi$
$241$	−5.41101	+	3.12405i	−0.348554	+	0.201238i	0.315494	+	0.948927i	$0.397830\pi$
$242$	−10.5761			−0.679860
$243$	0.866025	−	0.500000i	0.0555556	−	0.0320750i
$244$	3.31432	−	5.74056i	0.212177	−	0.367502i
$245$		0			0
$246$	3.50098			0.223215
$247$	−6.51873	+	8.15956i	−0.414777	+	0.519181i
$248$		−	5.58728i		−	0.354793i
$249$	−9.15582	−	5.28611i	−0.580226	−	0.334994i
$250$		0			0
$251$	−12.9759	−	22.4749i	−0.819031	−	1.41860i	−0.906397	−	0.422427i	$-0.861178\pi$
$251$	−12.9759	−	22.4749i	−0.819031	−	1.41860i	0.0873659	−	0.996176i	$-0.472155\pi$
$252$	4.58199			0.288638
$253$	0.927722	+	1.60686i	0.0583254	+	0.101023i
$254$	−7.76012	+	4.48031i	−0.486914	+	0.281120i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−5.97280	−	3.44840i	−0.372573	−	0.215105i	0.302009	−	0.953305i	$-0.402343\pi$
$257$	−5.97280	−	3.44840i	−0.372573	−	0.215105i	−0.674582	+	0.738200i	$0.735676\pi$
$258$	−3.85747	+	6.68133i	−0.240155	+	0.415961i
$259$	−21.2083			−1.31782
$260$		0			0
$261$	−9.56487			−0.592050
$262$	−4.24027	+	7.34436i	−0.261965	+	0.453736i
$263$	7.10511	+	4.10214i	0.438120	+	0.252949i	0.702800	−	0.711388i	$-0.251933\pi$
$263$	7.10511	+	4.10214i	0.438120	+	0.252949i	−0.264680	+	0.964336i	$0.585266\pi$
$264$	−0.325524	−	0.563824i	−0.0200346	−	0.0347010i
$265$		0			0
$266$	−11.4940	+	6.63605i	−0.704741	+	0.406882i
$267$	−4.09944	−	7.10045i	−0.250882	−	0.434540i
$268$	−9.16730			−0.559982
$269$	−12.5086	−	21.6655i	−0.762661	−	1.32097i	−0.941474	−	0.337085i	$-0.890559\pi$
$269$	−12.5086	−	21.6655i	−0.762661	−	1.32097i	0.178813	−	0.983883i	$-0.442774\pi$
$270$		0			0
$271$	0.233654	+	0.134900i	0.0141934	+	0.00819459i	0.507080	−	0.861899i	$-0.330725\pi$
$271$	0.233654	+	0.134900i	0.0141934	+	0.00819459i	−0.492886	+	0.870094i	$0.664058\pi$
$272$		−	3.50098i		−	0.212278i
$273$	−6.02218	−	15.3839i	−0.364479	−	0.931074i
$274$	13.9572			0.843184
$275$		0			0
$276$	1.42497	−	2.46812i	0.0857730	−	0.148563i
$277$	−13.8324	+	7.98616i	−0.831110	+	0.479842i	−0.854233	−	0.519891i	$-0.825973\pi$
$277$	−13.8324	+	7.98616i	−0.831110	+	0.479842i	0.0231225	+	0.999733i	$0.492639\pi$
$278$	9.82364			0.589183
$279$	−4.83873	+	2.79364i	−0.289687	+	0.167251i
$280$		0			0
$281$		−	5.58923i		−	0.333425i	−0.986006	−	0.166713i	$-0.946685\pi$
$281$		−	5.58923i		−	0.333425i	0.986006	−	0.166713i	$-0.0533152\pi$
$282$	1.80679	−	1.04315i	0.107593	−	0.0621186i
$283$	8.45566	+	4.88188i	0.502637	+	0.290198i	0.729802	−	0.683659i	$-0.239612\pi$
$283$	8.45566	+	4.88188i	0.502637	+	0.290198i	−0.227165	+	0.973856i	$0.572946\pi$
$284$	11.2778	+	6.51127i	0.669217	+	0.386373i
$285$		0			0
$286$	−1.46518	+	1.83398i	−0.0866378	+	0.108445i
$287$		−	16.0415i		−	0.946898i
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−2.37155	+	4.10765i	−0.139503	+	0.241627i
$290$		0			0
$291$		−	14.4372i		−	0.846325i
$292$	−0.524307	−	0.908126i	−0.0306827	−	0.0531440i
$293$	−7.50680	−	13.0022i	−0.438552	−	0.759595i	0.559026	−	0.829150i	$-0.311175\pi$
$293$	−7.50680	−	13.0022i	−0.438552	−	0.759595i	−0.997578	+	0.0695556i	$0.977842\pi$
$294$		−	13.9946i		−	0.816182i
$295$		0			0
$296$	2.31432	−	4.00851i	0.134517	−	0.232990i
$297$	−0.325524	+	0.563824i	−0.0188888	+	0.0327164i
$298$		−	20.3774i		−	1.18043i
$299$	−10.1595	−	1.54040i	−0.587538	−	0.0890834i
$300$		0			0
$301$	30.6138	+	17.6749i	1.76455	+	1.01876i
$302$	−19.5583	−	11.2920i	−1.12545	−	0.649781i
$303$	−7.15577	+	4.13139i	−0.411088	+	0.237342i
$304$		−	2.89658i		−	0.166130i
$305$		0			0
$306$	−3.03194	+	1.75049i	−0.173325	+	0.100069i
$307$	6.30760			0.359994			0.179997	−	0.983667i	$-0.442391\pi$
$307$	6.30760			0.359994			0.179997	+	0.983667i	$0.442391\pi$
$308$	−2.58343	+	1.49155i	−0.147205	+	0.0849887i
$309$	−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	$0.777099\pi$
$312$	3.56481	+	0.540502i	0.201818	+	0.0305999i
$313$		−	18.4747i		−	1.04425i	−0.852869	−	0.522126i	$-0.825139\pi$
$313$		−	18.4747i		−	1.04425i	0.852869	−	0.522126i	$-0.174861\pi$
$314$	5.66593	+	3.27123i	0.319747	+	0.184606i
$315$		0			0
$316$	−1.73079	−	2.99781i	−0.0973645	−	0.168640i
$317$	2.85533			0.160371			0.0801856	−	0.996780i	$-0.474449\pi$
$317$	2.85533			0.160371			0.0801856	+	0.996780i	$0.474449\pi$
$318$	−2.79364	−	4.83873i	−0.156660	−	0.271342i
$319$	5.39290	−	3.11359i	0.301944	−	0.174328i
$320$		0			0
$321$	−1.28048	−	2.21785i	−0.0714693	−	0.123789i
$322$	−11.3089	−	6.52919i	−0.630219	−	0.363857i
$323$	5.07044	−	8.78226i	0.282127	−	0.488658i
$324$	1.00000			0.0555556
$325$		0			0
$326$	14.1989			0.786404
$327$	6.85845	−	11.8792i	0.379273	−	0.656920i
$328$	3.03194	+	1.75049i	0.167411	+	0.0966548i
$329$	−4.77970	−	8.27868i	−0.263513	−	0.456418i
$330$		0			0
$331$	−4.20347	+	2.42688i	−0.231044	+	0.133393i	−0.611054	−	0.791589i	$-0.709254\pi$
$331$	−4.20347	+	2.42688i	−0.231044	+	0.133393i	0.380010	+	0.924983i	$0.375921\pi$
$332$	−5.28611	−	9.15582i	−0.290113	−	0.502491i
$333$	−4.62863			−0.253647
$334$	−1.42497	−	2.46812i	−0.0779708	−	0.135049i
$335$		0			0
$336$	3.96812	+	2.29099i	0.216479	+	0.124984i
$337$			6.21782i			0.338706i	0.985555	+	0.169353i	$0.0541679\pi$
$337$			6.21782i			0.338706i	−0.985555	+	0.169353i	$0.945832\pi$
$338$	−2.87057	−	12.6791i	−0.156138	−	0.689653i
$339$		0			0
$340$		0			0
$341$	1.81879	−	3.15024i	0.0984932	−	0.170595i
$342$	−2.50851	+	1.44829i	−0.135645	+	0.0783146i
$343$	−32.0492			−1.73050
$344$	−6.68133	+	3.85747i	−0.360233	+	0.207981i
$345$		0			0
$346$			6.70184i			0.360293i
$347$	−7.30853	+	4.21958i	−0.392342	+	0.226519i	−0.683175	−	0.730255i	$-0.739401\pi$
$347$	−7.30853	+	4.21958i	−0.392342	+	0.226519i	0.290832	+	0.956774i	$0.406068\pi$
$348$	−8.28342	−	4.78243i	−0.444038	−	0.256365i
$349$	18.9617	+	10.9476i	1.01500	+	0.586009i	0.912651	−	0.408740i	$-0.134032\pi$
$349$	18.9617	+	10.9476i	1.01500	+	0.586009i	0.102346	+	0.994749i	$0.467365\pi$
$350$		0			0
$351$	−1.31432	−	3.35747i	−0.0701530	−	0.179208i
$352$		−	0.651048i		−	0.0347010i
$353$	−4.45302	+	7.71285i	−0.237010	+	0.410514i	−0.959855	−	0.280497i	$-0.909501\pi$
$353$	−4.45302	+	7.71285i	−0.237010	+	0.410514i	0.722845	+	0.691010i	$0.242834\pi$
$354$	3.73928	−	6.47663i	0.198741	−	0.344229i
$355$		0			0
$356$		−	8.19889i		−	0.434540i
$357$	8.02073	+	13.8923i	0.424502	+	0.735259i
$358$	9.98128	+	17.2881i	0.527527	+	0.913704i
$359$		−	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
$362$	−1.59944	+	2.77032i	−0.0840649	+	0.145605i
$363$			10.5761i			0.555103i
$364$	2.47657	−	16.3339i	0.129808	−	0.856129i
$365$		0			0
$366$	−5.74056	−	3.31432i	−0.300064	−	0.173242i
$367$	−17.3875	−	10.0387i	−0.907622	−	0.524016i	−0.0279569	−	0.999609i	$-0.508900\pi$
$367$	−17.3875	−	10.0387i	−0.907622	−	0.524016i	−0.879665	+	0.475593i	$0.842233\pi$
$368$	2.46812	−	1.42497i	0.128660	−	0.0742816i
$369$		−	3.50098i		−	0.182254i
$370$		0			0
$371$	−22.1710	+	12.8004i	−1.15106	+	0.664565i
$372$	−5.58728			−0.289687
$373$	28.8651	−	16.6653i	1.49458	−	0.862896i	0.494600	−	0.869121i	$-0.335315\pi$
$373$	28.8651	−	16.6653i	1.49458	−	0.862896i	0.999981	+	0.00622457i	$0.00198136\pi$
$374$	1.13965	−	1.97394i	0.0589301	−	0.102070i
$375$		0			0
$376$	2.08630			0.107593
$377$	−5.16983	+	34.0969i	−0.266260	+	1.75608i
$378$		−	4.58199i		−	0.235672i
$379$	1.43619	+	0.829184i	0.0737721	+	0.0425923i	0.536432	−	0.843943i	$-0.319772\pi$
$379$	1.43619	+	0.829184i	0.0737721	+	0.0425923i	−0.462660	+	0.886536i	$0.653105\pi$
$380$		0			0
$381$	4.48031	+	7.76012i	0.229533	+	0.397563i
$382$	25.0732			1.28286
$383$	−12.7966	−	22.1644i	−0.653877	−	1.13255i	−0.982174	−	0.187974i	$-0.939808\pi$
$383$	−12.7966	−	22.1644i	−0.653877	−	1.13255i	0.328297	−	0.944574i	$-0.393525\pi$
$384$	−0.866025	+	0.500000i	−0.0441942	+	0.0255155i
$385$		0			0
$386$	−4.49546	−	7.78636i	−0.228813	−	0.396315i
$387$	6.68133	+	3.85747i	0.339631	+	0.196086i
$388$	7.21861	−	12.5030i	0.366469	−	0.634744i
$389$	9.56487			0.484958			0.242479	−	0.970157i	$-0.422039\pi$
$389$	9.56487			0.484958			0.242479	+	0.970157i	$0.422039\pi$
$390$		0			0
$391$	9.97758			0.504588
$392$	6.99731	−	12.1197i	0.353417	−	0.612137i
$393$	7.34436	+	4.24027i	0.370474	+	0.213893i
$394$	−10.8923	−	18.8660i	−0.548746	−	0.950455i
$395$		0			0
$396$	−0.563824	+	0.325524i	−0.0283332	+	0.0163582i
$397$	−0.231927	−	0.401710i	−0.0116401	−	0.0201612i	0.860147	−	0.510047i	$-0.170372\pi$
$397$	−0.231927	−	0.401710i	−0.0116401	−	0.0201612i	−0.871787	+	0.489886i	$0.837039\pi$
$398$	−0.591076			−0.0296279
$399$	6.63605	+	11.4940i	0.332218	+	0.575418i
$400$		0			0
$401$	17.6992	+	10.2187i	0.883857	+	0.510295i	0.871928	−	0.489634i	$-0.162870\pi$
$401$	17.6992	+	10.2187i	0.883857	+	0.510295i	0.0119289	+	0.999929i	$0.496203\pi$
$402$			9.16730i			0.457223i
$403$	7.34346	+	18.7591i	0.365804	+	0.934458i
$404$	−8.26277			−0.411088
$405$		0			0
$406$	−21.9131	+	37.9545i	−1.08753	+	1.88365i
$407$	2.60973	−	1.50673i	0.129360	−	0.0746858i
$408$	−3.50098			−0.173325
$409$	9.15283	−	5.28439i	0.452578	−	0.261296i	−0.256340	−	0.966587i	$-0.582517\pi$
$409$	9.15283	−	5.28439i	0.452578	−	0.261296i	0.708919	+	0.705290i	$0.249183\pi$
$410$		0			0
$411$		−	13.9572i		−	0.688457i
$412$	−17.0787	+	9.86041i	−0.841408	+	0.485787i
$413$	−29.6758	−	17.1334i	−1.46025	−	0.843077i
$414$	−2.46812	−	1.42497i	−0.121301	−	0.0700334i
$415$		0			0
$416$	2.81696	+	2.25049i	0.138113	+	0.110339i
$417$		−	9.82364i		−	0.481066i
$418$	0.942906	−	1.63316i	0.0461191	−	0.0798805i
$419$	14.2835	−	24.7397i	0.697793	−	1.20861i	−0.271437	−	0.962456i	$-0.587499\pi$
$419$	14.2835	−	24.7397i	0.697793	−	1.20861i	0.969230	−	0.246156i	$-0.0791677\pi$
$420$		0			0
$421$			38.4187i			1.87241i	0.351450	+	0.936207i	$0.385689\pi$
$421$			38.4187i			1.87241i	−0.351450	+	0.936207i	$0.614311\pi$
$422$	6.09671	+	10.5598i	0.296783	+	0.514043i
$423$	−1.04315	−	1.80679i	−0.0507197	−	0.0878490i
$424$		−	5.58728i		−	0.271342i
$425$		0			0
$426$	6.51127	−	11.2778i	0.315472	−	0.546413i
$427$	−15.1862	+	26.3032i	−0.734910	+	1.27290i
$428$		−	2.56096i		−	0.123789i
$429$	1.83398	+	1.46518i	0.0885453	+	0.0707394i
$430$		0			0
$431$	−6.84351	−	3.95111i	−0.329641	−	0.190318i	0.326041	−	0.945356i	$-0.394285\pi$
$431$	−6.84351	−	3.95111i	−0.329641	−	0.190318i	−0.655681	+	0.755038i	$0.727619\pi$
$432$	0.866025	+	0.500000i	0.0416667	+	0.0240563i
$433$	14.4301	−	8.33120i	0.693465	−	0.400372i	−0.111444	−	0.993771i	$-0.535548\pi$
$433$	14.4301	−	8.33120i	0.693465	−	0.400372i	0.804909	+	0.593399i	$0.202214\pi$
$434$			25.6009i			1.22888i
$435$		0			0
$436$	11.8792	−	6.85845i	0.568910	−	0.328460i
$437$	8.25507			0.394894
$438$	−0.908126	+	0.524307i	−0.0433919	+	0.0250523i
$439$	11.1728	−	19.3519i	0.533250	−	0.923616i	−0.465996	−	0.884787i	$-0.654304\pi$
$439$	11.1728	−	19.3519i	0.533250	−	0.923616i	0.999246	−	0.0388290i	$-0.0123628\pi$
$440$		0			0
$441$	−13.9946			−0.666410
$442$	4.60140	+	11.7544i	0.218866	+	0.559101i
$443$		−	17.5200i		−	0.832398i	−0.909274	−	0.416199i	$-0.863362\pi$
$443$		−	17.5200i		−	0.832398i	0.909274	−	0.416199i	$-0.136638\pi$
$444$	−4.00851	−	2.31432i	−0.190236	−	0.109833i
$445$		0			0
$446$	6.57244	+	11.3838i	0.311214	+	0.539039i
$447$	−20.3774			−0.963816
$448$	2.29099	+	3.96812i	0.108239	+	0.187476i
$449$	16.9571	−	9.79019i	0.800255	−	0.462028i	−0.0433051	−	0.999062i	$-0.513789\pi$
$449$	16.9571	−	9.79019i	0.800255	−	0.462028i	0.843560	+	0.537034i	$0.180455\pi$
$450$		0			0
$451$	1.13965	+	1.97394i	0.0536642	+	0.0929491i
$452$		0			0
$453$	−11.2920	+	19.5583i	−0.530544	+	0.918930i
$454$	22.5235			1.05708
$455$		0			0
$456$	−2.89658			−0.135645
$457$	11.3375	−	19.6371i	0.530345	−	0.918585i	−0.469028	−	0.883183i	$-0.655396\pi$
$457$	11.3375	−	19.6371i	0.530345	−	0.918585i	0.999373	−	0.0354015i	$-0.0112710\pi$
$458$	19.5097	+	11.2639i	0.911630	+	0.526330i
$459$	1.75049	+	3.03194i	0.0817060	+	0.141519i
$460$		0			0
$461$	28.4102	−	16.4026i	1.32319	−	0.763947i	0.338957	−	0.940802i	$-0.389926\pi$
$461$	28.4102	−	16.4026i	1.32319	−	0.763947i	0.984237	+	0.176855i	$0.0565924\pi$
$462$	1.49155	+	2.58343i	0.0693930	+	0.120192i
$463$	−20.6472			−0.959555			−0.479778	−	0.877390i	$-0.659283\pi$
$463$	−20.6472			−0.959555			−0.479778	+	0.877390i	$0.659283\pi$
$464$	−4.78243	−	8.28342i	−0.222019	−	0.384548i
$465$		0			0
$466$	13.7460	+	7.93624i	0.636769	+	0.367639i
$467$		−	7.77136i		−	0.359616i	−0.983702	−	0.179808i	$-0.942452\pi$
$467$		−	7.77136i		−	0.359616i	0.983702	−	0.179808i	$-0.0575476\pi$
$468$	0.540502	−	3.56481i	0.0249847	−	0.164783i
$469$	42.0045			1.93959
$470$		0			0
$471$	3.27123	−	5.66593i	0.150730	−	0.261072i
$472$	6.47663	−	3.73928i	0.298111	−	0.172115i
$473$	−5.02279			−0.230948
$474$	−2.99781	+	1.73079i	−0.137694	+	0.0794978i
$475$		0			0
$476$			16.0415i			0.735259i
$477$	−4.83873	+	2.79364i	−0.221550	+	0.127912i
$478$	−18.1608	−	10.4851i	−0.830656	−	0.479579i
$479$	−15.1745	−	8.76102i	−0.693342	−	0.400301i	0.111521	−	0.993762i	$-0.464428\pi$
$479$	−15.1745	−	8.76102i	−0.693342	−	0.400301i	−0.804863	+	0.593461i	$0.797761\pi$
$480$		0			0
$481$	−2.50178	+	16.5002i	−0.114071	+	0.752344i
$482$			6.24809i			0.284593i
$483$	−6.52919	+	11.3089i	−0.297088	+	0.514572i
$484$	−5.28807	+	9.15920i	−0.240367	+	0.416327i
$485$		0			0
$486$		−	1.00000i		−	0.0453609i
$487$	−10.4412	−	18.0846i	−0.473135	−	0.819494i	0.526392	−	0.850242i	$-0.323544\pi$
$487$	−10.4412	−	18.0846i	−0.473135	−	0.819494i	−0.999527	+	0.0307482i	$0.990211\pi$
$488$	−3.31432	−	5.74056i	−0.150032	−	0.259863i
$489$		−	14.1989i		−	0.642096i
$490$		0			0
$491$	−7.97312	+	13.8098i	−0.359822	+	0.623230i	−0.987931	−	0.154896i	$-0.950496\pi$
$491$	−7.97312	+	13.8098i	−0.359822	+	0.623230i	0.628109	+	0.778125i	$0.283829\pi$
$492$	1.75049	−	3.03194i	0.0789183	−	0.136690i
$493$		−	33.4865i		−	1.50815i
$494$	3.80702	+	9.72517i	0.171286	+	0.437556i
$495$		0			0
$496$	−4.83873	−	2.79364i	−0.217265	−	0.125438i
$497$	−51.6749	−	29.8345i	−2.31794	−	1.33826i
$498$	−9.15582	+	5.28611i	−0.410282	+	0.236876i
$499$			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
$502$	−25.9518			−1.15828
$503$	−16.3588	+	9.44473i	−0.729401	+	0.421120i	−0.818203	−	0.574930i	$-0.805029\pi$
$503$	−16.3588	+	9.44473i	−0.729401	+	0.421120i	0.0888021	+	0.996049i	$0.471696\pi$
$504$	2.29099	−	3.96812i	0.102049	−	0.176754i
$505$		0			0
$506$	1.85544			0.0824846
$507$	−12.6791	+	2.87057i	−0.563099	+	0.127486i
$508$			8.96062i			0.397563i
$509$	−16.2075	−	9.35742i	−0.718386	−	0.414761i	0.0957722	−	0.995403i	$-0.469468\pi$
$509$	−16.2075	−	9.35742i	−0.718386	−	0.414761i	−0.814158	+	0.580643i	$0.802801\pi$
$510$		0			0
$511$	2.40237	+	4.16102i	0.106274	+	0.184073i
$512$	−1.00000			−0.0441942
$513$	1.44829	+	2.50851i	0.0639436	+	0.110754i
$514$	−5.97280	+	3.44840i	−0.263449	+	0.152102i
$515$		0			0
$516$	3.85747	+	6.68133i	0.169815	+	0.294129i
$517$	1.17630	+	0.679140i	0.0517338	+	0.0298685i
$518$	−10.6042	+	18.3670i	−0.465920	+	0.806998i
$519$	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	$0.145635\pi$
$522$	−4.78243	+	8.28342i	−0.209321	+	0.362555i
$523$	35.0978	+	20.2637i	1.53472	+	0.886072i	0.999135	+	0.0415914i	$0.0132428\pi$
$523$	35.0978	+	20.2637i	1.53472	+	0.886072i	0.535587	+	0.844480i	$0.320091\pi$
$524$	4.24027	+	7.34436i	0.185237	+	0.320840i
$525$		0			0
$526$	7.10511	−	4.10214i	0.309798	−	0.178862i
$527$	−9.78050	−	16.9403i	−0.426045	−	0.737932i
$528$	−0.651048			−0.0283332
$529$	−7.43893	−	12.8846i	−0.323432	−	0.560200i
$530$		0			0
$531$	−6.47663	−	3.73928i	−0.281062	−	0.162271i
$532$			13.2721i			0.575418i
$533$	−12.4803	−	1.89229i	−0.540583	−	0.0819641i
$534$	−8.19889			−0.354801
$535$		0			0
$536$	−4.58365	+	7.93912i	−0.197984	+	0.342918i
$537$	17.2881	−	9.98128i	0.746036	−	0.430724i
$538$	−25.0171			−1.07857
$539$	7.89049	−	4.55558i	0.339868	−	0.196223i
$540$		0			0
$541$		−	26.2949i		−	1.13050i	−0.824918	−	0.565252i	$-0.808779\pi$
$541$		−	26.2949i		−	1.13050i	0.824918	−	0.565252i	$-0.191221\pi$
$542$	0.233654	−	0.134900i	0.0100363	−	0.00579445i
$543$	2.77032	+	1.59944i	0.118886	+	0.0686387i
$544$	−3.03194	−	1.75049i	−0.129993	−	0.0750517i
$545$		0			0
$546$	−16.3339	−	2.47657i	−0.699027	−	0.105987i
$547$		−	33.5445i		−	1.43426i	−0.696940	−	0.717130i	$-0.745455\pi$
$547$		−	33.5445i		−	1.43426i	0.696940	−	0.717130i	$-0.254545\pi$
$548$	6.97859	−	12.0873i	0.298110	−	0.516342i
$549$	−3.31432	+	5.74056i	−0.141452	+	0.245001i
$550$		0			0
$551$		−	27.7054i		−	1.18029i
$552$	−1.42497	−	2.46812i	−0.0606507	−	0.105050i
$553$	7.93045	+	13.7359i	0.337237	+	0.584112i
$554$			15.9723i			0.678599i
$555$		0			0
$556$	4.91182	−	8.50753i	0.208308	−	0.360799i
$557$	−6.56478	+	11.3705i	−0.278159	+	0.481785i	−0.970927	−	0.239375i	$-0.923057\pi$
$557$	−6.56478	+	11.3705i	−0.278159	+	0.481785i	0.692768	+	0.721160i	$0.256391\pi$
$558$			5.58728i			0.236529i
$559$	17.3624	−	21.7327i	0.734351	−	0.919194i
$560$		0			0
$561$	−1.97394	−	1.13965i	−0.0833397	−	0.0481162i
$562$	−4.84041	−	2.79461i	−0.204180	−	0.117884i
$563$	17.0622	−	9.85086i	0.719086	−	0.415164i	−0.0953304	−	0.995446i	$-0.530391\pi$
$563$	17.0622	−	9.85086i	0.719086	−	0.415164i	0.814416	+	0.580281i	$0.197057\pi$
$564$		−	2.08630i		−	0.0878490i
$565$		0			0
$566$	8.45566	−	4.88188i	0.355418	−	0.205201i
$567$	−4.58199			−0.192425
$568$	11.2778	−	6.51127i	0.473208	−	0.273207i
$569$	−10.1979	+	17.6633i	−0.427519	+	0.740485i	−0.996652	−	0.0817607i	$-0.973946\pi$
$569$	−10.1979	+	17.6633i	−0.427519	+	0.740485i	0.569133	+	0.822246i	$0.307279\pi$
$570$		0			0
$571$	−19.7935			−0.828333			−0.414167	−	0.910201i	$-0.635927\pi$
$571$	−19.7935			−0.828333			−0.414167	+	0.910201i	$0.635927\pi$
$572$	0.855682	+	2.18587i	0.0357779	+	0.0913958i
$573$		−	25.0732i		−	1.04745i
$574$	−13.8923	−	8.02073i	−0.579854	−	0.334779i
$575$		0			0
$576$	0.500000	+	0.866025i	0.0208333	+	0.0360844i
$577$	−14.1729			−0.590024			−0.295012	−	0.955493i	$-0.595324\pi$
$577$	−14.1729			−0.590024			−0.295012	+	0.955493i	$0.595324\pi$
$578$	2.37155	+	4.10765i	0.0986436	+	0.170856i
$579$	−7.78636	+	4.49546i	−0.323590	+	0.186825i
$580$		0			0
$581$	24.2209	+	41.9518i	1.00485	+	1.74046i
$582$	−12.5030	−	7.21861i	−0.518266	−	0.299221i
$583$	1.81879	−	3.15024i	0.0753267	−	0.130470i
$584$	−1.04861			−0.0433919
$585$		0			0
$586$	−15.0136			−0.620206
$587$	10.7608	−	18.6382i	0.444145	−	0.769281i	−0.553847	−	0.832618i	$-0.686841\pi$
$587$	10.7608	−	18.6382i	0.444145	−	0.769281i	0.997992	+	0.0633369i	$0.0201743\pi$
$588$	−12.1197	−	6.99731i	−0.499808	−	0.288564i
$589$	−8.09201	−	14.0158i	−0.333425	−	0.577510i
$590$		0			0
$591$	−18.8660	+	10.8923i	−0.776043	+	0.448049i
$592$	−2.31432	−	4.00851i	−0.0951178	−	0.164749i
$593$	37.9368			1.55788			0.778938	−	0.627101i	$-0.215759\pi$
$593$	37.9368			1.55788			0.778938	+	0.627101i	$0.215759\pi$
$594$	0.325524	+	0.563824i	0.0133564	+	0.0231340i
$595$		0			0
$596$	−17.6473	−	10.1887i	−0.722862	−	0.417345i
$597$			0.591076i			0.0241911i
$598$	−6.41376	+	8.02817i	−0.262278	+	0.328296i
$599$	22.4129			0.915765			0.457883	−	0.889013i	$-0.348608\pi$
$599$	22.4129			0.915765			0.457883	+	0.889013i	$0.348608\pi$
$600$		0			0
$601$	−16.6804	+	28.8913i	−0.680407	+	1.17850i	0.294450	+	0.955667i	$0.404863\pi$
$601$	−16.6804	+	28.8913i	−0.680407	+	1.17850i	−0.974857	+	0.222832i	$0.928470\pi$
$602$	30.6138	−	17.6749i	1.24772	−	0.720373i
$603$	9.16730			0.373321
$604$	−19.5583	+	11.2920i	−0.795816	+	0.459465i
$605$		0			0
$606$			8.26277i			0.335652i
$607$	−13.9037	+	8.02733i	−0.564335	+	0.325819i	−0.754884	−	0.655859i	$-0.772307\pi$
$607$	−13.9037	+	8.02733i	−0.564335	+	0.325819i	0.190548	+	0.981678i	$0.438973\pi$
$608$	−2.50851	−	1.44829i	−0.101734	−	0.0587359i
$609$	37.9545	+	21.9131i	1.53799	+	0.887962i
$610$		0			0
$611$	−7.00467	+	2.74206i	−0.283379	+	0.110932i
$612$			3.50098i			0.141519i
$613$	−19.0929	+	33.0698i	−0.771154	+	1.33568i	0.165777	+	0.986163i	$0.446987\pi$
$613$	−19.0929	+	33.0698i	−0.771154	+	1.33568i	−0.936931	+	0.349514i	$0.886347\pi$
$614$	3.15380	−	5.46254i	0.127277	−	0.220450i
$615$		0			0
$616$			2.98309i			0.120192i
$617$	−21.5003	−	37.2397i	−0.865571	−	1.49921i	−0.866479	−	0.499213i	$-0.833622\pi$
$617$	−21.5003	−	37.2397i	−0.865571	−	1.49921i	0.000908306	−	1.00000i	$-0.499711\pi$
$618$	9.86041	+	17.0787i	0.396644	+	0.687007i
$619$			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
$622$	−13.4851	+	23.3570i	−0.540705	+	0.936529i
$623$			37.5672i			1.50510i
$624$	2.25049	−	2.81696i	0.0900918	−	0.112769i
$625$		0			0
$626$	−15.9996	−	9.23735i	−0.639471	−	0.369199i
$627$	−1.63316	−	0.942906i	−0.0652222	−	0.0376560i
$628$	5.66593	−	3.27123i	0.226095	−	0.130536i
$629$		−	16.2048i		−	0.646126i
$630$		0			0
$631$	−3.08250	+	1.77968i	−0.122713	+	0.0708481i	−0.560100	−	0.828425i	$-0.689237\pi$
$631$	−3.08250	+	1.77968i	−0.122713	+	0.0708481i	0.437387	+	0.899273i	$0.355904\pi$
$632$	−3.46158			−0.137694
$633$	10.5598	−	6.09671i	0.419715	−	0.242322i
$634$	1.42766	−	2.47279i	0.0566997	−	0.0982068i
$635$		0			0
$636$	−5.58728			−0.221550
$637$	−7.56411	+	49.8881i	−0.299701	+	1.97664i
$638$		−	6.22718i		−	0.246537i
$639$	−11.2778	−	6.51127i	−0.446145	−	0.257582i
$640$		0			0
$641$	19.4394	+	33.6701i	0.767812	+	1.32989i	0.938747	+	0.344607i	$0.111988\pi$
$641$	19.4394	+	33.6701i	0.767812	+	1.32989i	−0.170935	+	0.985282i	$0.554679\pi$
$642$	−2.56096			−0.101073
$643$	−7.50930	−	13.0065i	−0.296138	−	0.512926i	0.679111	−	0.734035i	$-0.262365\pi$
$643$	−7.50930	−	13.0065i	−0.296138	−	0.512926i	−0.975249	+	0.221110i	$0.929032\pi$
$644$	−11.3089	+	6.52919i	−0.445632	+	0.257286i
$645$		0			0
$646$	−5.07044	−	8.78226i	−0.199494	−	0.345534i
$647$	−25.8429	−	14.9204i	−1.01599	−	0.586581i	−0.103049	−	0.994676i	$-0.532860\pi$
$647$	−25.8429	−	14.9204i	−1.01599	−	0.586581i	−0.912939	+	0.408095i	$0.866193\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	4.86890			0.191121
$650$		0			0
$651$	25.6009			1.00338
$652$	7.09944	−	12.2966i	0.278036	−	0.481572i
$653$	−2.67950	−	1.54701i	−0.104857	−	0.0605393i	0.446654	−	0.894707i	$-0.352615\pi$
$653$	−2.67950	−	1.54701i	−0.104857	−	0.0605393i	−0.551511	+	0.834167i	$0.685949\pi$
$654$	−6.85845	−	11.8792i	−0.268187	−	0.464513i
$655$		0			0
$656$	3.03194	−	1.75049i	0.118377	−	0.0683452i
$657$	0.524307	+	0.908126i	0.0204552	+	0.0354294i
$658$	−9.55939			−0.372664
$659$	2.65012	+	4.59015i	0.103234	+	0.178807i	0.913015	−	0.407925i	$-0.133748\pi$
$659$	2.65012	+	4.59015i	0.103234	+	0.178807i	−0.809781	+	0.586732i	$0.800414\pi$
$660$		0			0
$661$	−27.0453	−	15.6146i	−1.05194	−	0.607337i	−0.128747	−	0.991677i	$-0.541096\pi$
$661$	−27.0453	−	15.6146i	−1.05194	−	0.607337i	−0.923191	+	0.384340i	$0.874429\pi$
$662$			4.85375i			0.188646i
$663$	11.7544	−	4.60140i	0.456504	−	0.178704i
$664$	−10.5722			−0.410282
$665$		0			0
$666$	−2.31432	+	4.00851i	−0.0896779	+	0.155327i
$667$	23.6072	−	13.6296i	0.914075	−	0.527742i
$668$	−2.84994			−0.110267
$669$	11.3838	−	6.57244i	0.440123	−	0.254105i
$670$		0			0
$671$		−	4.31556i		−	0.166600i
$672$	3.96812	−	2.29099i	0.153073	−	0.0883770i
$673$	31.2197	+	18.0247i	1.20343	+	0.694801i	0.961316	−	0.275447i	$-0.0888259\pi$
$673$	31.2197	+	18.0247i	1.20343	+	0.694801i	0.242114	+	0.970248i	$0.422159\pi$
$674$	5.38479	+	3.10891i	0.207414	+	0.119751i
$675$		0			0
$676$	−12.4157	−	3.85357i	−0.477528	−	0.148214i
$677$			23.2219i			0.892491i	0.894911	+	0.446245i	$0.147239\pi$
$677$			23.2219i			0.892491i	−0.894911	+	0.446245i	$0.852761\pi$
$678$		0			0
$679$	−33.0756	+	57.2886i	−1.26932	+	2.19853i
$680$		0			0
$681$		−	22.5235i		−	0.863103i
$682$	−1.81879	−	3.15024i	−0.0696452	−	0.120629i
$683$	14.8652	+	25.7473i	0.568802	+	0.985195i	0.996685	+	0.0813602i	$0.0259264\pi$
$683$	14.8652	+	25.7473i	0.568802	+	0.985195i	−0.427882	+	0.903834i	$0.640740\pi$
$684$			2.89658i			0.110754i
$685$		0			0
$686$	−16.0246	+	27.7554i	−0.611822	+	1.05971i
$687$	11.2639	−	19.5097i	0.429746	−	0.744342i
$688$			7.71493i			0.294129i
$689$	7.34346	+	18.7591i	0.279763	+	0.714665i
$690$		0			0
$691$	−19.7614	−	11.4092i	−0.751758	−	0.434028i	0.0745709	−	0.997216i	$-0.476241\pi$
$691$	−19.7614	−	11.4092i	−0.751758	−	0.434028i	−0.826329	+	0.563188i	$0.809575\pi$
$692$	5.80397	+	3.35092i	0.220634	+	0.127383i
$693$	2.58343	−	1.49155i	0.0981365	−	0.0566592i
$694$			8.43916i			0.320346i
$695$		0			0
$696$	−8.28342	+	4.78243i	−0.313982	+	0.181278i
$697$	12.2569			0.464263
$698$	18.9617	−	10.9476i	0.717712	−	0.414371i
$699$	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	$0.195527\pi$
$702$	−3.56481	−	0.540502i	−0.134545	−	0.0203999i
$703$		−	13.4072i		−	0.505662i
$704$	−0.563824	−	0.325524i	−0.0212499	−	0.0122686i
$705$		0			0
$706$	4.45302	+	7.71285i	0.167592	+	0.290277i
$707$	37.8599			1.42387
$708$	−3.73928	−	6.47663i	−0.140531	−	0.243407i
$709$	−15.8342	+	9.14186i	−0.594664	+	0.343330i	−0.766940	−	0.641719i	$-0.778221\pi$
$709$	−15.8342	+	9.14186i	−0.594664	+	0.343330i	0.172275	+	0.985049i	$0.444888\pi$
$710$		0			0
$711$	1.73079	+	2.99781i	0.0649096	+	0.112427i
$712$	−7.10045	−	4.09944i	−0.266100	−	0.153633i
$713$	7.96170	−	13.7901i	0.298168	−	0.516442i
$714$	16.0415			0.600337
$715$		0			0
$716$	19.9626			0.746036
$717$	−10.4851	+	18.1608i	−0.391575	+	0.678228i
$718$	−32.0401	−	18.4983i	−1.19572	−	0.690352i
$719$	−13.6420	−	23.6287i	−0.508762	−	0.881201i	−0.999949	−	0.0101468i	$-0.996770\pi$
$719$	−13.6420	−	23.6287i	−0.508762	−	0.881201i	0.491187	−	0.871054i	$-0.336563\pi$
$720$		0			0
$721$	78.2545	−	45.1803i	2.91435	−	1.68260i
$722$	5.30491	+	9.18837i	0.197428	+	0.341956i
$723$	6.24809			0.232369
$724$	1.59944	+	2.77032i	0.0594429	+	0.102958i
$725$		0			0
$726$	9.15920	+	5.28807i	0.339930	+	0.196259i
$727$		−	17.0453i		−	0.632176i	−0.948730	−	0.316088i	$-0.897631\pi$
$727$		−	17.0453i		−	0.632176i	0.948730	−	0.316088i	$-0.102369\pi$
$728$	−12.9073	−	10.3117i	−0.478376	−	0.382178i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−13.5049	+	23.3912i	−0.499498	+	0.865155i
$732$	−5.74056	+	3.31432i	−0.212177	+	0.122501i
$733$	−11.2472			−0.415424			−0.207712	−	0.978190i	$-0.566602\pi$
$733$	−11.2472			−0.415424			−0.207712	+	0.978190i	$0.566602\pi$
$734$	−17.3875	+	10.0387i	−0.641786	+	0.370535i
$735$		0			0
$736$		−	2.84994i		−	0.105050i
$737$	−5.16874	+	2.98418i	−0.190393	+	0.109924i
$738$	−3.03194	−	1.75049i	−0.111607	−	0.0644365i
$739$	−9.24885	−	5.33982i	−0.340224	−	0.196429i	0.320147	−	0.947368i	$-0.396268\pi$
$739$	−9.24885	−	5.33982i	−0.340224	−	0.196429i	−0.660371	+	0.750939i	$0.729601\pi$
$740$		0			0
$741$	9.72517	−	3.80702i	0.357263	−	0.139854i
$742$			25.6009i			0.939837i
$743$	−13.5160	+	23.4105i	−0.495855	+	0.858847i	−0.999989	−	0.00477910i	$-0.998479\pi$
$743$	−13.5160	+	23.4105i	−0.495855	+	0.858847i	0.504133	+	0.863626i	$0.331812\pi$
$744$	−2.79364	+	4.83873i	−0.102420	+	0.177396i
$745$		0			0
$746$		−	33.3306i		−	1.22032i
$747$	5.28611	+	9.15582i	0.193409	+	0.334994i
$748$	−1.13965	−	1.97394i	−0.0416699	−	0.0721743i
$749$			11.7343i			0.428761i
$750$		0			0
$751$	12.7159	−	22.0246i	0.464010	−	0.803688i	−0.535147	−	0.844759i	$-0.679744\pi$
$751$	12.7159	−	22.0246i	0.464010	−	0.803688i	0.999156	+	0.0410709i	$0.0130769\pi$
$752$	1.04315	−	1.80679i	0.0380397	−	0.0658868i
$753$			25.9518i			0.945736i
$754$	26.9439	+	21.5257i	0.981238	+	0.783918i
$755$		0			0
$756$	−3.96812	−	2.29099i	−0.144319	−	0.0833226i
$757$	37.5693	+	21.6906i	1.36548	+	0.788359i	0.990347	−	0.138612i	$-0.0442641\pi$
$757$	37.5693	+	21.6906i	1.36548	+	0.788359i	0.375132	+	0.926971i	$0.377597\pi$
$758$	1.43619	−	0.829184i	0.0521648	−	0.0301173i
$759$		−	1.85544i		−	0.0673484i
$760$		0			0
$761$	−15.5138	+	8.95691i	−0.562376	+	0.324688i	−0.754099	−	0.656761i	$-0.771926\pi$
$761$	−15.5138	+	8.95691i	−0.562376	+	0.324688i	0.191723	+	0.981449i	$0.438593\pi$
$762$	8.96062			0.324609
$763$	−54.4303	+	31.4253i	−1.97051	+	1.13767i
$764$	12.5366	−	21.7141i	0.453559	−	0.785587i
$765$		0			0
$766$	−25.5932			−0.924722
$767$	−16.8305	+	21.0669i	−0.607713	+	0.760680i
$768$			1.00000i			0.0360844i
$769$	−6.17619	−	3.56583i	−0.222719	−	0.128587i	0.384490	−	0.923129i	$-0.374377\pi$
$769$	−6.17619	−	3.56583i	−0.222719	−	0.128587i	−0.607209	+	0.794542i	$0.707711\pi$
$770$		0			0
$771$	3.44840	+	5.97280i	0.124191	+	0.215105i
$772$	−8.99091			−0.323590
$773$	17.9169	+	31.0330i	0.644427	+	1.11618i	0.984434	+	0.175757i	$0.0562374\pi$
$773$	17.9169	+	31.0330i	0.644427	+	1.11618i	−0.340006	+	0.940423i	$0.610429\pi$
$774$	6.68133	−	3.85747i	0.240155	−	0.138654i
$775$		0			0
$776$	−7.21861	−	12.5030i	−0.259133	−	0.448832i
$777$	18.3670	+	10.6042i	0.658911	+	0.380422i
$778$	4.78243	−	8.28342i	0.171459	−	0.296975i
$779$	10.1409			0.363335
$780$		0			0
$781$	8.47829			0.303377
$782$	4.98879	−	8.64084i	0.178399	−	0.308996i
$783$	8.28342	+	4.78243i	0.296025	+	0.170910i
$784$	−6.99731	−	12.1197i	−0.249904	−	0.432846i
$785$		0			0
$786$	7.34436	−	4.24027i	0.261965	−	0.151245i
$787$	−8.71109	−	15.0880i	−0.310517	−	0.537831i	0.667958	−	0.744199i	$-0.267169\pi$
$787$	−8.71109	−	15.0880i	−0.310517	−	0.537831i	−0.978474	+	0.206369i	$0.933835\pi$
$788$	−21.7846			−0.776043
$789$	−4.10214	−	7.10511i	−0.146040	−	0.252949i
$790$		0			0
$791$		0			0
$792$			0.651048i			0.0231340i
$793$	18.6726	+	14.9177i	0.663084	+	0.529743i
$794$	−0.463855			−0.0164616
$795$		0			0
$796$	−0.295538	+	0.511887i	−0.0104751	+	0.0181433i
$797$	22.2653	−	12.8548i	0.788676	−	0.455342i	−0.0508204	−	0.998708i	$-0.516184\pi$
$797$	22.2653	−	12.8548i	0.788676	−	0.455342i	0.839496	+	0.543366i	$0.182850\pi$
$798$	13.2721			0.469827
$799$	6.32554	−	3.65205i	0.223781	−	0.129200i
$800$		0			0
$801$			8.19889i			0.289694i
$802$	17.6992	−	10.2187i	0.624981	−	0.360833i
$803$	−0.591233	−	0.341349i	−0.0208642	−	0.0120459i
$804$	7.93912	+	4.58365i	0.279991	+	0.161653i
$805$		0			0
$806$	19.9176	+	3.01994i	0.701567	+	0.106373i
$807$			25.0171i			0.880645i
$808$	−4.13139	+	7.15577i	−0.145342	+	0.251739i
$809$	1.44563	−	2.50390i	0.0508255	−	0.0880323i	−0.839493	−	0.543370i	$-0.817148\pi$
$809$	1.44563	−	2.50390i	0.0508255	−	0.0880323i	0.890319	+	0.455338i	$0.150481\pi$
$810$		0			0
$811$		−	47.4396i		−	1.66583i	−0.553400	−	0.832916i	$-0.686670\pi$
$811$		−	47.4396i		−	1.66583i	0.553400	−	0.832916i	$-0.313330\pi$
$812$	21.9131	+	37.9545i	0.768997	+	1.33194i
$813$	−0.134900	−	0.233654i	−0.00473115	−	0.00819459i
$814$		−	3.01346i		−	0.105622i
$815$		0			0
$816$	−1.75049	+	3.03194i	−0.0612795	+	0.106139i
$817$	−11.1735	+	19.3530i	−0.390910	+	0.677076i
$818$		−	10.5688i		−	0.369529i
$819$	−2.47657	+	16.3339i	−0.0865384	+	0.570753i
$820$		0			0
$821$	−26.7086	−	15.4202i	−0.932135	−	0.538168i	−0.0446489	−	0.999003i	$-0.514217\pi$
$821$	−26.7086	−	15.4202i	−0.932135	−	0.538168i	−0.887486	+	0.460834i	$0.847550\pi$
$822$	−12.0873	−	6.97859i	−0.421592	−	0.243406i
$823$	19.7529	−	11.4043i	0.688542	−	0.397530i	−0.114523	−	0.993421i	$-0.536534\pi$
$823$	19.7529	−	11.4043i	0.688542	−	0.397530i	0.803066	+	0.595890i	$0.203201\pi$
$824$			19.7208i			0.687007i
$825$		0			0
$826$	−29.6758	+	17.1334i	−1.03255	+	0.596146i
$827$	43.7321			1.52071			0.760357	−	0.649506i	$-0.225024\pi$
$827$	43.7321			1.52071			0.760357	+	0.649506i	$0.225024\pi$
$828$	−2.46812	+	1.42497i	−0.0857730	+	0.0495211i
$829$	−7.34530	+	12.7224i	−0.255113	+	0.441869i	−0.964926	−	0.262521i	$-0.915446\pi$
$829$	−7.34530	+	12.7224i	−0.255113	+	0.441869i	0.709813	+	0.704390i	$0.248779\pi$
$830$		0			0
$831$	15.9723			0.554073
$832$	3.35747	−	1.31432i	0.116399	−	0.0455657i
$833$		−	48.9949i		−	1.69757i
$834$	−8.50753	−	4.91182i	−0.294592	−	0.170082i
$835$		0			0
$836$	−0.942906	−	1.63316i	−0.0326111	−	0.0564841i
$837$	5.58728			0.193125
$838$	−14.2835	−	24.7397i	−0.493414	−	0.854618i
$839$	−11.8808	+	6.85939i	−0.410171	+	0.236812i	−0.690863	−	0.722985i	$-0.742769\pi$
$839$	−11.8808	+	6.85939i	−0.410171	+	0.236812i	0.280692	+	0.959798i	$0.409436\pi$
$840$		0			0
$841$	−31.2433	−	54.1151i	−1.07736	−	1.86604i
$842$	33.2716	+	19.2094i	1.14661	+	0.661998i
$843$	−2.79461	+	4.84041i	−0.0962516	+	0.166713i
$844$	12.1934			0.419715
$845$		0			0
$846$	−2.08630			−0.0717284
$847$	24.2299	−	41.9674i	0.832548	−	1.44202i
$848$	−4.83873	−	2.79364i	−0.166163	−	0.0959340i
$849$	−4.88188	−	8.45566i	−0.167546	−	0.290198i
$850$		0			0
$851$	11.4240	−	6.59565i	0.391610	−	0.226096i
$852$	−6.51127	−	11.2778i	−0.223072	−	0.386373i
$853$	−5.80880			−0.198890			−0.0994448	−	0.995043i	$-0.531707\pi$
$853$	−5.80880			−0.198890			−0.0994448	+	0.995043i	$0.531707\pi$
$854$	15.1862	+	26.3032i	0.519660	+	0.900077i
$855$		0			0
$856$	−2.21785	−	1.28048i	−0.0758047	−	0.0437658i
$857$			49.9085i			1.70484i	0.522855	+	0.852421i	$0.324867\pi$
$857$			49.9085i			1.70484i	−0.522855	+	0.852421i	$0.675133\pi$
$858$	2.18587	−	0.855682i	0.0746244	−	0.0292125i
$859$	5.11251			0.174436			0.0872182	−	0.996189i	$-0.472202\pi$
$859$	5.11251			0.174436			0.0872182	+	0.996189i	$0.472202\pi$
$860$		0			0
$861$	−8.02073	+	13.8923i	−0.273346	+	0.473449i
$862$	−6.84351	+	3.95111i	−0.233091	+	0.134575i
$863$	18.5089			0.630051			0.315025	−	0.949083i	$-0.397987\pi$
$863$	18.5089			0.630051			0.315025	+	0.949083i	$0.397987\pi$
$864$	0.866025	−	0.500000i	0.0294628	−	0.0170103i
$865$		0			0
$866$		−	16.6624i		−	0.566211i
$867$	4.10765	−	2.37155i	0.139503	−	0.0805422i
$868$	22.1710	+	12.8004i	0.752533	+	0.434475i
$869$	−1.95172	−	1.12683i	−0.0662076	−	0.0382250i
$870$		0			0
$871$	4.95494	−	32.6797i	0.167892	−	1.10731i
$872$		−	13.7169i		−	0.464513i
$873$	−7.21861	+	12.5030i	−0.244313	+	0.423162i
$874$	4.12754	−	7.14910i	0.139616	−	0.241822i
$875$		0			0
$876$			1.04861i			0.0354294i
$877$	−1.97186	−	3.41536i	−0.0665850	−	0.115329i	0.830811	−	0.556555i	$-0.187877\pi$
$877$	−1.97186	−	3.41536i	−0.0665850	−	0.115329i	−0.897396	+	0.441226i	$0.854544\pi$
$878$	−11.1728	−	19.3519i	−0.377065	−	0.653095i
$879$			15.0136i			0.506396i
$880$		0			0
$881$	18.2883	−	31.6762i	0.616147	−	1.06720i	−0.374035	−	0.927415i	$-0.622026\pi$
$881$	18.2883	−	31.6762i	0.616147	−	1.06720i	0.990182	−	0.139784i	$-0.0446407\pi$
$882$	−6.99731	+	12.1197i	−0.235612	+	0.408091i
$883$		−	22.7956i		−	0.767134i	−0.923513	−	0.383567i	$-0.874696\pi$
$883$		−	22.7956i		−	0.767134i	0.923513	−	0.383567i	$-0.125304\pi$
$884$	12.4803	+	1.89229i	0.419759	+	0.0636445i
$885$		0			0
$886$	−15.1727	−	8.75998i	−0.509738	−	0.294297i
$887$	−9.83830	−	5.68015i	−0.330338	−	0.190721i	0.325653	−	0.945489i	$-0.394416\pi$
$887$	−9.83830	−	5.68015i	−0.330338	−	0.190721i	−0.655991	+	0.754769i	$0.727749\pi$
$888$	−4.00851	+	2.31432i	−0.134517	+	0.0776634i
$889$		−	41.0574i		−	1.37702i
$890$		0			0
$891$	0.563824	−	0.325524i	0.0188888	−	0.0109055i
$892$	13.1449			0.440123
$893$	5.23351	−	3.02157i	0.175133	−	0.101113i
$894$	−10.1887	+	17.6473i	−0.340761	+	0.590215i
$895$		0			0
$896$	4.58199			0.153073
$897$	8.02817	+	6.41376i	0.268053	+	0.214149i
$898$		−	19.5804i		−	0.653406i
$899$	−46.2818	−	26.7208i	−1.54358	−	0.891189i
$900$		0			0
$901$	−9.78050	−	16.9403i	−0.325836	−	0.564364i
$902$	2.27931			0.0758926
$903$	−17.6749	−	30.6138i	−0.588182	−	1.01876i
$904$		0			0
$905$		0			0
$906$	11.2920	+	19.5583i	0.375151	+	0.649781i
$907$	28.9626	+	16.7215i	0.961686	+	0.555230i	0.896692	−	0.442656i	$-0.145964\pi$
$907$	28.9626	+	16.7215i	0.961686	+	0.555230i	0.0649947	+	0.997886i	$0.479297\pi$
$908$	11.2618	−	19.5059i	0.373735	−	0.647327i
$909$	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	$0.262433\pi$
$912$	−1.44829	+	2.50851i	−0.0479577	+	0.0830652i
$913$	−5.96087	−	3.44151i	−0.197276	−	0.113897i
$914$	−11.3375	−	19.6371i	−0.375011	−	0.649538i
$915$		0			0
$916$	19.5097	−	11.2639i	0.644619	−	0.372171i
$917$	−19.4289	−	33.6518i	−0.641597	−	1.11128i
$918$	3.50098			0.115550
$919$	6.47104	+	11.2082i	0.213460	+	0.369724i	0.952795	−	0.303614i	$-0.0981933\pi$
$919$	6.47104	+	11.2082i	0.213460	+	0.369724i	−0.739335	+	0.673338i	$0.764860\pi$
$920$		0			0
$921$	−5.46254	−	3.15380i	−0.179997	−	0.103921i
$922$		−	32.8053i		−	1.08038i
$923$	−29.3071	+	36.6840i	−0.964655	+	1.20747i
$924$	2.98309			0.0981365
$925$		0			0
$926$	−10.3236	+	17.8810i	−0.339254	+	0.587605i
$927$	17.0787	−	9.86041i	0.560939	−	0.323858i
$928$	−9.56487			−0.313982
$929$	29.1850	−	16.8500i	0.957529	−	0.552830i	0.0621173	−	0.998069i	$-0.480215\pi$
$929$	29.1850	−	16.8500i	0.957529	−	0.552830i	0.895412	+	0.445239i	$0.146881\pi$
$930$		0			0
$931$		−	40.5365i		−	1.32853i
$932$	13.7460	−	7.93624i	0.450264	−	0.259960i
$933$	23.3570	+	13.4851i	0.764672	+	0.441484i
$934$	−6.73020	−	3.88568i	−0.220219	−	0.127143i
$935$		0			0
$936$	−2.81696	−	2.25049i	−0.0920753	−	0.0735596i
$937$			12.3888i			0.404724i	0.979311	+	0.202362i	$0.0648618\pi$
$937$			12.3888i			0.404724i	−0.979311	+	0.202362i	$0.935138\pi$
$938$	21.0022	−	36.3769i	0.685747	−	1.18775i
$939$	−9.23735	+	15.9996i	−0.301449	+	0.522126i
$940$		0			0
$941$			5.26120i			0.171510i	0.996316	+	0.0857551i	$0.0273303\pi$
$941$			5.26120i			0.171510i	−0.996316	+	0.0857551i	$0.972670\pi$
$942$	−3.27123	−	5.66593i	−0.106582	−	0.184606i
$943$	4.98879	+	8.64084i	0.162457	+	0.281385i
$944$		−	7.47857i		−	0.243407i
$945$		0			0
$946$	−2.51139	+	4.34986i	−0.0816525	+	0.141426i
$947$	−3.34711	+	5.79737i	−0.108766	+	0.188389i	−0.915271	−	0.402839i	$-0.868023\pi$
$947$	−3.34711	+	5.79737i	−0.108766	+	0.188389i	0.806504	+	0.591228i	$0.201357\pi$
$948$			3.46158i			0.112427i
$949$	3.52068	−	1.37821i	0.114286	−	0.0447386i
$950$		0			0
$951$	−2.47279	−	1.42766i	−0.0801856	−	0.0462952i
$952$	13.8923	+	8.02073i	0.450253	+	0.259953i
$953$	35.2569	−	20.3556i	1.14208	−	0.659382i	0.195137	−	0.980776i	$-0.437485\pi$
$953$	35.2569	−	20.3556i	1.14208	−	0.659382i	0.946945	+	0.321394i	$0.104152\pi$
$954$			5.58728i			0.180895i
$955$		0			0
$956$	−18.1608	+	10.4851i	−0.587362	+	0.339114i
$957$	−6.22718			−0.201296
$958$	−15.1745	+	8.76102i	−0.490267	+	0.283056i
$959$	−31.9758	+	55.3837i	−1.03255	+	1.78843i
$960$		0			0
$961$	−0.217731			−0.00702359
$962$	13.0387	+	10.4167i	0.420384	+	0.335848i
$963$			2.56096i			0.0825257i
$964$	5.41101	+	3.12405i	0.174277	+	0.100619i
$965$		0			0
$966$	6.52919	+	11.3089i	0.210073	+	0.363857i
$967$	60.9859			1.96117			0.980587	−	0.196085i	$-0.0628228\pi$
$967$	60.9859			1.96117			0.980587	+	0.196085i	$0.0628228\pi$
$968$	5.28807	+	9.15920i	0.169965	+	0.294388i
$969$	−8.78226	+	5.07044i	−0.282127	+	0.162886i
$970$		0			0
$971$	23.2702	+	40.3052i	0.746776	+	1.29345i	0.949360	+	0.314189i	$0.101733\pi$
$971$	23.2702	+	40.3052i	0.746776	+	1.29345i	−0.202584	+	0.979265i	$0.564934\pi$
$972$	−0.866025	−	0.500000i	−0.0277778	−	0.0160375i
$973$	−22.5059	+	38.9814i	−0.721506	+	1.24969i
$974$	−20.8824			−0.669114
$975$		0			0
$976$	−6.62863			−0.212177
$977$	−18.8296	+	32.6138i	−0.602413	+	1.04341i	0.390042	+	0.920797i	$0.372460\pi$
$977$	−18.8296	+	32.6138i	−0.602413	+	1.04341i	−0.992455	+	0.122612i	$0.960873\pi$
$978$	−12.2966	−	7.09944i	−0.393202	−	0.227015i
$979$	−2.66893	−	4.62273i	−0.0852995	−	0.147743i
$980$		0			0
$981$	−11.8792	+	6.85845i	−0.379273	+	0.218973i
$982$	7.97312	+	13.8098i	0.254432	+	0.440690i
$983$	32.9140			1.04979			0.524896	−	0.851166i	$-0.324104\pi$
$983$	32.9140			1.04979			0.524896	+	0.851166i	$0.324104\pi$
$984$	−1.75049	−	3.03194i	−0.0558037	−	0.0966548i
$985$		0			0
$986$	−29.0001	−	16.7432i	−0.923552	−	0.533213i
$987$			9.55939i			0.304279i
$988$	10.3258	+	1.56561i	0.328506	+	0.0498086i
$989$	−21.9871			−0.699148
$990$		0			0
$991$	−29.9561	+	51.8855i	−0.951588	+	1.64820i	−0.209597	+	0.977788i	$0.567215\pi$
$991$	−29.9561	+	51.8855i	−0.951588	+	1.64820i	−0.741991	+	0.670410i	$0.766118\pi$
$992$	−4.83873	+	2.79364i	−0.153630	+	0.0886982i
$993$	4.85375			0.154029
$994$	−51.6749	+	29.8345i	−1.63903	+	0.946294i
$995$		0			0
$996$			10.5722i			0.334994i
$997$	−46.1811	+	26.6627i	−1.46257	+	0.844416i	−0.999130	−	0.0417112i	$-0.986719\pi$
$997$	−46.1811	+	26.6627i	−1.46257	+	0.844416i	−0.463442	+	0.886127i	$0.653386\pi$
$998$	16.6250	+	9.59847i	0.526256	+	0.303834i
$999$	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.y.n.199.3		12
5.2	odd	4		1950.2.bc.h.901.4	yes	12
5.3	odd	4		1950.2.bc.k.901.3	yes	12
5.4	even	2		1950.2.y.m.199.4		12
13.10	even	6		1950.2.y.m.49.4		12
65.23	odd	12		1950.2.bc.k.751.3	yes	12
65.49	even	6	inner	1950.2.y.n.49.3		12
65.62	odd	12		1950.2.bc.h.751.4	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1950.2.y.m.49.4		12	13.10	even	6
1950.2.y.m.199.4		12	5.4	even	2
1950.2.y.n.49.3		12	65.49	even	6	inner
1950.2.y.n.199.3		12	1.1	even	1	trivial
1950.2.bc.h.751.4	✓	12	65.62	odd	12
1950.2.bc.h.901.4	yes	12	5.2	odd	4
1950.2.bc.k.751.3	yes	12	65.23	odd	12
1950.2.bc.k.901.3	yes	12	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(2.29099 + 3.96812i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(-0.866025 - 0.500000i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.866025 + 0.500000i) q^{6} +(2.29099 + 3.96812i) q^{7} -1.00000 q^{8} +(0.500000 + 0.866025i) q^{9} +(-0.563824 - 0.325524i) q^{11} +1.00000i q^{12} +(3.35747 - 1.31432i) q^{13} +4.58199 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-3.03194 + 1.75049i) q^{17} +1.00000 q^{18} +(-2.50851 + 1.44829i) q^{19} -4.58199i q^{21} +(-0.563824 + 0.325524i) q^{22} +(-2.46812 - 1.42497i) q^{23} +(0.866025 + 0.500000i) q^{24} +(0.540502 - 3.56481i) q^{26} -1.00000i q^{27} +(2.29099 - 3.96812i) q^{28} +(-4.78243 + 8.28342i) q^{29} +5.58728i q^{31} +(0.500000 + 0.866025i) q^{32} +(0.325524 + 0.563824i) q^{33} +3.50098i q^{34} +(0.500000 - 0.866025i) q^{36} +(-2.31432 + 4.00851i) q^{37} +2.89658i q^{38} +(-3.56481 - 0.540502i) q^{39} +(-3.03194 - 1.75049i) q^{41} +(-3.96812 - 2.29099i) q^{42} +(6.68133 - 3.85747i) q^{43} +0.651048i q^{44} +(-2.46812 + 1.42497i) q^{46} -2.08630 q^{47} +(0.866025 - 0.500000i) q^{48} +(-6.99731 + 12.1197i) q^{49} +3.50098 q^{51} +(-2.81696 - 2.25049i) q^{52} +5.58728i q^{53} +(-0.866025 - 0.500000i) q^{54} +(-2.29099 - 3.96812i) q^{56} +2.89658 q^{57} +(4.78243 + 8.28342i) q^{58} +(-6.47663 + 3.73928i) q^{59} +(3.31432 + 5.74056i) q^{61} +(4.83873 + 2.79364i) q^{62} +(-2.29099 + 3.96812i) q^{63} +1.00000 q^{64} +0.651048 q^{66} +(4.58365 - 7.93912i) q^{67} +(3.03194 + 1.75049i) q^{68} +(1.42497 + 2.46812i) q^{69} +(-11.2778 + 6.51127i) q^{71} +(-0.500000 - 0.866025i) q^{72} +1.04861 q^{73} +(2.31432 + 4.00851i) q^{74} +(2.50851 + 1.44829i) q^{76} -2.98309i q^{77} +(-2.25049 + 2.81696i) q^{78} +3.46158 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-3.03194 + 1.75049i) q^{82} +10.5722 q^{83} +(-3.96812 + 2.29099i) q^{84} -7.71493i q^{86} +(8.28342 - 4.78243i) q^{87} +(0.563824 + 0.325524i) q^{88} +(7.10045 + 4.09944i) q^{89} +(12.9073 + 10.3117i) q^{91} +2.84994i q^{92} +(2.79364 - 4.83873i) q^{93} +(-1.04315 + 1.80679i) q^{94} -1.00000i q^{96} +(7.21861 + 12.5030i) q^{97} +(6.99731 + 12.1197i) q^{98} -0.651048i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - 6 q^{4} - 4 q^{7} - 12 q^{8} + 6 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 - 6 * q^4 - 4 * q^7 - 12 * q^8 + 6 * q^9	\( 12 q + 6 q^{2} - 6 q^{4} - 4 q^{7} - 12 q^{8} + 6 q^{9} - 12 q^{11} + 4 q^{13} - 8 q^{14} - 6 q^{16} + 12 q^{18} + 6 q^{19} - 12 q^{22} + 12 q^{23} - 4 q^{26} - 4 q^{28} + 6 q^{32} + 4 q^{33} + 6 q^{36} - 12 q^{37} - 6 q^{39} - 6 q^{42} + 12 q^{43} + 12 q^{46} + 16 q^{47} - 32 q^{49} - 8 q^{52} + 4 q^{56} + 24 q^{57} + 24 q^{61} + 4 q^{63} + 12 q^{64} + 8 q^{66} + 24 q^{67} - 4 q^{69} + 12 q^{71} - 6 q^{72} - 40 q^{73} + 12 q^{74} - 6 q^{76} - 6 q^{78} - 52 q^{79} - 6 q^{81} + 32 q^{83} - 6 q^{84} + 12 q^{88} - 24 q^{89} - 54 q^{91} - 8 q^{93} + 8 q^{94} + 24 q^{97} + 32 q^{98}+O(q^{100}) \) 12 * q + 6 * q^2 - 6 * q^4 - 4 * q^7 - 12 * q^8 + 6 * q^9 - 12 * q^11 + 4 * q^13 - 8 * q^14 - 6 * q^16 + 12 * q^18 + 6 * q^19 - 12 * q^22 + 12 * q^23 - 4 * q^26 - 4 * q^28 + 6 * q^32 + 4 * q^33 + 6 * q^36 - 12 * q^37 - 6 * q^39 - 6 * q^42 + 12 * q^43 + 12 * q^46 + 16 * q^47 - 32 * q^49 - 8 * q^52 + 4 * q^56 + 24 * q^57 + 24 * q^61 + 4 * q^63 + 12 * q^64 + 8 * q^66 + 24 * q^67 - 4 * q^69 + 12 * q^71 - 6 * q^72 - 40 * q^73 + 12 * q^74 - 6 * q^76 - 6 * q^78 - 52 * q^79 - 6 * q^81 + 32 * q^83 - 6 * q^84 + 12 * q^88 - 24 * q^89 - 54 * q^91 - 8 * q^93 + 8 * q^94 + 24 * q^97 + 32 * q^98

Introduction

L-functions

Modular forms

Varieties

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Database

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