LMFDB - Embedded newform 950.2.e.n.201.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(201,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("950.201");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.e (of order $3$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 10x^{8} - 12x^{7} + 85x^{6} - 70x^{5} + 186x^{4} - 110x^{3} + 285x^{2} - 150x + 100 $ x^10 + 10x^8 - 12x^7 + 85x^6 - 70x^5 + 186x^4 - 110x^3 + 285x^2 - 150x + 100
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 190)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			201.3
Root			$0.341187 - 0.590953i$ of defining polynomial
Character	$\chi$	$=$	950.201
Dual form			950.2.e.n.501.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.341187 - 0.590953i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.341187 + 0.590953i) q^{6} -0.317626 q^{7} +1.00000 q^{8} +(1.26718 + 2.19482i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.341187 - 0.590953i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.341187 + 0.590953i) q^{6} -0.317626 q^{7} +1.00000 q^{8} +(1.26718 + 2.19482i) q^{9} -4.31087 q^{11} -0.682374 q^{12} +(-3.14836 - 5.45312i) q^{13} +(0.158813 - 0.275072i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.0669268 - 0.115921i) q^{17} -2.53437 q^{18} +(-4.05310 - 1.60387i) q^{19} +(-0.108370 + 0.187702i) q^{21} +(2.15544 - 3.73333i) q^{22} +(-1.98955 - 3.44600i) q^{23} +(0.341187 - 0.590953i) q^{24} +6.29672 q^{26} +3.77651 q^{27} +(0.158813 + 0.275072i) q^{28} +(4.57435 + 7.92301i) q^{29} -2.98584 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.47081 + 2.54753i) q^{33} +(0.0669268 + 0.115921i) q^{34} +(1.26718 - 2.19482i) q^{36} -5.07323 q^{37} +(3.41554 - 2.70815i) q^{38} -4.29672 q^{39} +(0.433073 - 0.750105i) q^{41} +(-0.108370 - 0.187702i) q^{42} +(-2.85199 + 4.93979i) q^{43} +(2.15544 + 3.73333i) q^{44} +3.97909 q^{46} +(-6.48617 - 11.2344i) q^{47} +(0.341187 + 0.590953i) q^{48} -6.89911 q^{49} +(-0.0456691 - 0.0791012i) q^{51} +(-3.14836 + 5.45312i) q^{52} +(-3.96261 - 6.86344i) q^{53} +(-1.88825 + 3.27055i) q^{54} -0.317626 q^{56} +(-2.33068 + 1.84797i) q^{57} -9.14871 q^{58} +(4.80717 - 8.32627i) q^{59} +(-3.08711 - 5.34704i) q^{61} +(1.49292 - 2.58582i) q^{62} +(-0.402490 - 0.697133i) q^{63} +1.00000 q^{64} +(-1.47081 - 2.54753i) q^{66} +(0.295518 + 0.511852i) q^{67} -0.133854 q^{68} -2.71523 q^{69} +(-5.83073 + 10.0991i) q^{71} +(1.26718 + 2.19482i) q^{72} +(4.13048 - 7.15420i) q^{73} +(2.53661 - 4.39354i) q^{74} +(0.637555 + 4.31202i) q^{76} +1.36924 q^{77} +(2.14836 - 3.72107i) q^{78} +(1.66112 - 2.87714i) q^{79} +(-2.51305 + 4.35273i) q^{81} +(0.433073 + 0.750105i) q^{82} -4.20708 q^{83} +0.216740 q^{84} +(-2.85199 - 4.93979i) q^{86} +6.24284 q^{87} -4.31087 q^{88} +(1.85992 + 3.22147i) q^{89} +(1.00000 + 1.73205i) q^{91} +(-1.98955 + 3.44600i) q^{92} +(-1.01873 + 1.76450i) q^{93} +12.9723 q^{94} -0.682374 q^{96} +(-2.42830 + 4.20594i) q^{97} +(3.44956 - 5.97481i) q^{98} +(-5.46266 - 9.46161i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 5 q^{2} - 5 q^{4} - 10 q^{7} + 10 q^{8} - 5 q^{9}+O(q^{10}) $ 10 * q - 5 * q^2 - 5 * q^4 - 10 * q^7 + 10 * q^8 - 5 * q^9	$ 10 q - 5 q^{2} - 5 q^{4} - 10 q^{7} + 10 q^{8} - 5 q^{9} - 6 q^{11} - 2 q^{13} + 5 q^{14} - 5 q^{16} + 4 q^{17} + 10 q^{18} + 11 q^{19} + 20 q^{21} + 3 q^{22} + 13 q^{23} + 4 q^{26} + 36 q^{27} + 5 q^{28} + 2 q^{29} - 8 q^{31} - 5 q^{32} + 2 q^{33} + 4 q^{34} - 5 q^{36} + 10 q^{37} - 13 q^{38} + 16 q^{39} + q^{41} + 20 q^{42} + 3 q^{44} - 26 q^{46} - 10 q^{47} - 20 q^{49} + 4 q^{51} - 2 q^{52} + 5 q^{53} - 18 q^{54} - 10 q^{56} - 10 q^{57} - 4 q^{58} + 22 q^{59} - 2 q^{61} + 4 q^{62} + 23 q^{63} + 10 q^{64} + 2 q^{66} + 4 q^{67} - 8 q^{68} - 24 q^{69} - 22 q^{71} - 5 q^{72} + 26 q^{73} - 5 q^{74} + 2 q^{76} + 10 q^{77} - 8 q^{78} + 2 q^{79} - 5 q^{81} + q^{82} + 12 q^{83} - 40 q^{84} - 20 q^{87} - 6 q^{88} - q^{89} + 10 q^{91} + 13 q^{92} + 6 q^{93} + 20 q^{94} + 8 q^{97} + 10 q^{98} + 13 q^{99}+O(q^{100}) $ 10 * q - 5 * q^2 - 5 * q^4 - 10 * q^7 + 10 * q^8 - 5 * q^9 - 6 * q^11 - 2 * q^13 + 5 * q^14 - 5 * q^16 + 4 * q^17 + 10 * q^18 + 11 * q^19 + 20 * q^21 + 3 * q^22 + 13 * q^23 + 4 * q^26 + 36 * q^27 + 5 * q^28 + 2 * q^29 - 8 * q^31 - 5 * q^32 + 2 * q^33 + 4 * q^34 - 5 * q^36 + 10 * q^37 - 13 * q^38 + 16 * q^39 + q^41 + 20 * q^42 + 3 * q^44 - 26 * q^46 - 10 * q^47 - 20 * q^49 + 4 * q^51 - 2 * q^52 + 5 * q^53 - 18 * q^54 - 10 * q^56 - 10 * q^57 - 4 * q^58 + 22 * q^59 - 2 * q^61 + 4 * q^62 + 23 * q^63 + 10 * q^64 + 2 * q^66 + 4 * q^67 - 8 * q^68 - 24 * q^69 - 22 * q^71 - 5 * q^72 + 26 * q^73 - 5 * q^74 + 2 * q^76 + 10 * q^77 - 8 * q^78 + 2 * q^79 - 5 * q^81 + q^82 + 12 * q^83 - 40 * q^84 - 20 * q^87 - 6 * q^88 - q^89 + 10 * q^91 + 13 * q^92 + 6 * q^93 + 20 * q^94 + 8 * q^97 + 10 * q^98 + 13 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	0.341187	−	0.590953i	0.196984	−	0.341187i	−0.750565	−	0.660797i	$-0.770218\pi$
$3$	0.341187	−	0.590953i	0.196984	−	0.341187i	0.947549	+	0.319610i	$0.103552\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	0.341187	+	0.590953i	0.139289	+	0.241256i
$7$	−0.317626			−0.120051			−0.0600256	−	0.998197i	$-0.519118\pi$
$7$	−0.317626			−0.120051			−0.0600256	+	0.998197i	$0.519118\pi$
$8$	1.00000			0.353553
$9$	1.26718	+	2.19482i	0.422394	+	0.731608i
$10$		0			0
$11$	−4.31087			−1.29978			−0.649889	−	0.760029i	$-0.725184\pi$
$11$	−4.31087			−1.29978			−0.649889	+	0.760029i	$0.725184\pi$
$12$	−0.682374			−0.196984
$13$	−3.14836	−	5.45312i	−0.873198	−	1.51242i	−0.858670	−	0.512528i	$-0.828709\pi$
$13$	−3.14836	−	5.45312i	−0.873198	−	1.51242i	−0.0145275	−	0.999894i	$-0.504624\pi$
$14$	0.158813	−	0.275072i	0.0424445	−	0.0735161i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	0.0669268	−	0.115921i	0.0162321	−	0.0281149i	−0.857795	−	0.513992i	$-0.828166\pi$
$17$	0.0669268	−	0.115921i	0.0162321	−	0.0281149i	0.874027	+	0.485877i	$0.161500\pi$
$18$	−2.53437			−0.597356
$19$	−4.05310	−	1.60387i	−0.929844	−	0.367953i
$19$	−4.05310	−	1.60387i	−0.929844	−	0.367953i
$20$		0			0
$21$	−0.108370	+	0.187702i	−0.0236482	+	0.0409599i
$22$	2.15544	−	3.73333i	0.459541	−	0.795948i
$23$	−1.98955	−	3.44600i	−0.414849	−	0.718540i	0.580564	−	0.814215i	$-0.302832\pi$
$23$	−1.98955	−	3.44600i	−0.414849	−	0.718540i	−0.995413	+	0.0956753i	$0.969499\pi$
$24$	0.341187	−	0.590953i	0.0696445	−	0.120628i
$25$		0			0
$26$	6.29672			1.23489
$27$	3.77651			0.726789
$28$	0.158813	+	0.275072i	0.0300128	+	0.0519837i
$29$	4.57435	+	7.92301i	0.849436	+	1.47127i	0.881712	+	0.471788i	$0.156391\pi$
$29$	4.57435	+	7.92301i	0.849436	+	1.47127i	−0.0322757	+	0.999479i	$0.510275\pi$
$30$		0			0
$31$	−2.98584			−0.536274			−0.268137	−	0.963381i	$-0.586408\pi$
$31$	−2.98584			−0.536274			−0.268137	+	0.963381i	$0.586408\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−1.47081	+	2.54753i	−0.256036	+	0.443467i
$34$	0.0669268	+	0.115921i	0.0114778	+	0.0198802i
$35$		0			0
$36$	1.26718	−	2.19482i	0.211197	−	0.365804i
$37$	−5.07323			−0.834033			−0.417017	−	0.908899i	$-0.636924\pi$
$37$	−5.07323			−0.834033			−0.417017	+	0.908899i	$0.636924\pi$
$38$	3.41554	−	2.70815i	0.554074	−	0.439320i
$39$	−4.29672			−0.688026
$40$		0			0
$41$	0.433073	−	0.750105i	0.0676347	−	0.117147i	−0.830225	−	0.557428i	$-0.811788\pi$
$41$	0.433073	−	0.750105i	0.0676347	−	0.117147i	0.897860	+	0.440282i	$0.145121\pi$
$42$	−0.108370	−	0.187702i	−0.0167218	−	0.0289631i
$43$	−2.85199	+	4.93979i	−0.434925	+	0.753311i	−0.997289	−	0.0735777i	$-0.976558\pi$
$43$	−2.85199	+	4.93979i	−0.434925	+	0.753311i	0.562365	+	0.826889i	$0.309892\pi$
$44$	2.15544	+	3.73333i	0.324944	+	0.562820i
$45$		0			0
$46$	3.97909			0.586685
$47$	−6.48617	−	11.2344i	−0.946105	−	1.63870i	−0.753523	−	0.657421i	$-0.771647\pi$
$47$	−6.48617	−	11.2344i	−0.946105	−	1.63870i	−0.192582	−	0.981281i	$-0.561686\pi$
$48$	0.341187	+	0.590953i	0.0492461	+	0.0852968i
$49$	−6.89911			−0.985588
$50$		0			0
$51$	−0.0456691	−	0.0791012i	−0.00639495	−	0.0110764i
$52$	−3.14836	+	5.45312i	−0.436599	+	0.756211i
$53$	−3.96261	−	6.86344i	−0.544306	−	0.942766i	−0.998650	−	0.0519397i	$-0.983460\pi$
$53$	−3.96261	−	6.86344i	−0.544306	−	0.942766i	0.454344	−	0.890826i	$-0.349874\pi$
$54$	−1.88825	+	3.27055i	−0.256959	+	0.445066i
$55$		0			0
$56$	−0.317626			−0.0424445
$57$	−2.33068	+	1.84797i	−0.308706	+	0.244770i
$58$	−9.14871			−1.20128
$59$	4.80717	−	8.32627i	0.625841	−	1.08399i	−0.362537	−	0.931969i	$-0.618089\pi$
$59$	4.80717	−	8.32627i	0.625841	−	1.08399i	0.988378	−	0.152018i	$-0.0485772\pi$
$60$		0			0
$61$	−3.08711	−	5.34704i	−0.395264	−	0.684618i	0.597871	−	0.801593i	$-0.296014\pi$
$61$	−3.08711	−	5.34704i	−0.395264	−	0.684618i	−0.993135	+	0.116975i	$0.962680\pi$
$62$	1.49292	−	2.58582i	0.189601	−	0.328399i
$63$	−0.402490	−	0.697133i	−0.0507090	−	0.0878305i
$64$	1.00000			0.125000
$65$		0			0
$66$	−1.47081	−	2.54753i	−0.181045	−	0.313579i
$67$	0.295518	+	0.511852i	0.0361033	+	0.0625327i	0.883512	−	0.468408i	$-0.155172\pi$
$67$	0.295518	+	0.511852i	0.0361033	+	0.0625327i	−0.847409	+	0.530940i	$0.821839\pi$
$68$	−0.133854			−0.0162321
$69$	−2.71523			−0.326875
$70$		0			0
$71$	−5.83073	+	10.0991i	−0.691981	+	1.19855i	0.279207	+	0.960231i	$0.409928\pi$
$71$	−5.83073	+	10.0991i	−0.691981	+	1.19855i	−0.971188	+	0.238315i	$0.923405\pi$
$72$	1.26718	+	2.19482i	0.149339	+	0.258663i
$73$	4.13048	−	7.15420i	0.483436	−	0.837335i	−0.516383	−	0.856358i	$-0.672722\pi$
$73$	4.13048	−	7.15420i	0.483436	−	0.837335i	0.999819	+	0.0190222i	$0.00605532\pi$
$74$	2.53661	−	4.39354i	0.294875	−	0.510739i
$75$		0			0
$76$	0.637555	+	4.31202i	0.0731326	+	0.494623i
$77$	1.36924			0.156040
$78$	2.14836	−	3.72107i	0.243254	−	0.421328i
$79$	1.66112	−	2.87714i	0.186890	−	0.323703i	−0.757322	−	0.653042i	$-0.773492\pi$
$79$	1.66112	−	2.87714i	0.186890	−	0.323703i	0.944212	+	0.329339i	$0.106826\pi$
$80$		0			0
$81$	−2.51305	+	4.35273i	−0.279228	+	0.483637i
$82$	0.433073	+	0.750105i	0.0478249	+	0.0828352i
$83$	−4.20708			−0.461787			−0.230894	−	0.972979i	$-0.574165\pi$
$83$	−4.20708			−0.461787			−0.230894	+	0.972979i	$0.574165\pi$
$84$	0.216740			0.0236482
$85$		0			0
$86$	−2.85199	−	4.93979i	−0.307538	−	0.532672i
$87$	6.24284			0.669303
$88$	−4.31087			−0.459541
$89$	1.85992	+	3.22147i	0.197151	+	0.341476i	0.947604	−	0.319449i	$-0.103498\pi$
$89$	1.85992	+	3.22147i	0.197151	+	0.341476i	−0.750453	+	0.660924i	$0.770164\pi$
$90$		0			0
$91$	1.00000	+	1.73205i	0.104828	+	0.181568i
$92$	−1.98955	+	3.44600i	−0.207425	+	0.359270i
$93$	−1.01873	+	1.76450i	−0.105638	+	0.182970i
$94$	12.9723			1.33799
$95$		0			0
$96$	−0.682374			−0.0696445
$97$	−2.42830	+	4.20594i	−0.246556	+	0.427048i	−0.962568	−	0.271040i	$-0.912632\pi$
$97$	−2.42830	+	4.20594i	−0.246556	+	0.427048i	0.716012	+	0.698088i	$0.245966\pi$
$98$	3.44956	−	5.97481i	0.348458	−	0.603547i
$99$	−5.46266	−	9.46161i	−0.549018	−	0.950928i
$100$		0			0
$101$	1.25638	+	2.17611i	0.125014	+	0.216531i	0.921739	−	0.387812i	$-0.126769\pi$
$101$	1.25638	+	2.17611i	0.125014	+	0.216531i	−0.796724	+	0.604343i	$0.793436\pi$
$102$	0.0913382			0.00904383
$103$	−4.03297			−0.397380			−0.198690	−	0.980062i	$-0.563669\pi$
$103$	−4.03297			−0.397380			−0.198690	+	0.980062i	$0.563669\pi$
$104$	−3.14836	−	5.45312i	−0.308722	−	0.534722i
$105$		0			0
$106$	7.92522			0.769765
$107$	−10.0000			−0.966736			−0.483368	−	0.875417i	$-0.660587\pi$
$107$	−10.0000			−0.966736			−0.483368	+	0.875417i	$0.660587\pi$
$108$	−1.88825	−	3.27055i	−0.181697	−	0.314709i
$109$	2.93197	−	5.07832i	0.280832	−	0.486415i	−0.690758	−	0.723086i	$-0.742723\pi$
$109$	2.93197	−	5.07832i	0.280832	−	0.486415i	0.971590	+	0.236671i	$0.0760564\pi$
$110$		0			0
$111$	−1.73092	+	2.99804i	−0.164292	+	0.284561i
$112$	0.158813	−	0.275072i	0.0150064	−	0.0259919i
$113$	18.0853			1.70132			0.850660	−	0.525716i	$-0.176202\pi$
$113$	18.0853			1.70132			0.850660	+	0.525716i	$0.176202\pi$
$114$	−0.435051	−	2.94241i	−0.0407463	−	0.275582i
$115$		0			0
$116$	4.57435	−	7.92301i	0.424718	−	0.735633i
$117$	7.97909	−	13.8202i	0.737667	−	1.27768i
$118$	4.80717	+	8.32627i	0.442536	+	0.766495i
$119$	−0.0212577	+	0.0368194i	−0.00194869	+	0.00337523i
$120$		0			0
$121$	7.58363			0.689421
$122$	6.17422			0.558988
$123$	−0.295518	−	0.511852i	−0.0266460	−	0.0461522i
$124$	1.49292	+	2.58582i	0.134068	+	0.232213i
$125$		0			0
$126$	0.804980			0.0717133
$127$	8.94845	+	15.4992i	0.794047	+	1.37533i	0.923443	+	0.383736i	$0.125363\pi$
$127$	8.94845	+	15.4992i	0.794047	+	1.37533i	−0.129396	+	0.991593i	$0.541304\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	1.94613	+	3.37079i	0.171347	+	0.296781i
$130$		0			0
$131$	5.90509	−	10.2279i	0.515930	−	0.893617i	−0.483899	−	0.875124i	$-0.660780\pi$
$131$	5.90509	−	10.2279i	0.515930	−	0.893617i	0.999829	−	0.0184931i	$-0.00588686\pi$
$132$	2.94163			0.256036
$133$	1.28737	+	0.509431i	0.111629	+	0.0441733i
$134$	−0.591036			−0.0510577
$135$		0			0
$136$	0.0669268	−	0.115921i	0.00573892	−	0.00994011i
$137$	7.91554	+	13.7101i	0.676270	+	1.17133i	0.976096	+	0.217341i	$0.0697382\pi$
$137$	7.91554	+	13.7101i	0.676270	+	1.17133i	−0.299825	+	0.953994i	$0.596928\pi$
$138$	1.35762	−	2.35146i	0.115568	−	0.200169i
$139$	−0.583681	−	1.01096i	−0.0495071	−	0.0857489i	0.840210	−	0.542261i	$-0.182432\pi$
$139$	−0.583681	−	1.01096i	−0.0495071	−	0.0857489i	−0.889717	+	0.456512i	$0.849098\pi$
$140$		0			0
$141$	−8.85199			−0.745472
$142$	−5.83073	−	10.0991i	−0.489304	−	0.847500i
$143$	13.5722	+	23.5077i	1.13496	+	1.96581i
$144$	−2.53437			−0.211197
$145$		0			0
$146$	4.13048	+	7.15420i	0.341841	+	0.592086i
$147$	−2.35389	+	4.07705i	−0.194145	+	0.336270i
$148$	2.53661	+	4.39354i	0.208508	+	0.361147i
$149$	6.07575	−	10.5235i	0.497745	−	0.862120i	−0.502252	−	0.864722i	$-0.667495\pi$
$149$	6.07575	−	10.5235i	0.497745	−	0.862120i	0.999997	+	0.00260182i	$0.000828187\pi$
$150$		0			0
$151$	−20.3803			−1.65853			−0.829263	−	0.558859i	$-0.811239\pi$
$151$	−20.3803			−1.65853			−0.829263	+	0.558859i	$0.811239\pi$
$152$	−4.05310	−	1.60387i	−0.328750	−	0.130091i
$153$	0.339234			0.0274254
$154$	−0.684622	+	1.18580i	−0.0551684	+	0.0955545i
$155$		0			0
$156$	2.14836	+	3.72107i	0.172006	+	0.297924i
$157$	−2.46121	+	4.26294i	−0.196426	+	0.340220i	−0.947367	−	0.320149i	$-0.896267\pi$
$157$	−2.46121	+	4.26294i	−0.196426	+	0.340220i	0.750941	+	0.660369i	$0.229600\pi$
$158$	1.66112	+	2.87714i	0.132151	+	0.228893i
$159$	−5.40796			−0.428879
$160$		0			0
$161$	0.631931	+	1.09454i	0.0498032	+	0.0862616i
$162$	−2.51305	−	4.35273i	−0.197444	−	0.341983i
$163$	−1.43727			−0.112576			−0.0562880	−	0.998415i	$-0.517927\pi$
$163$	−1.43727			−0.112576			−0.0562880	+	0.998415i	$0.517927\pi$
$164$	−0.866146			−0.0676347
$165$		0			0
$166$	2.10354	−	3.64344i	0.163266	−	0.282786i
$167$	−4.68750	−	8.11899i	−0.362730	−	0.628266i	0.625680	−	0.780080i	$-0.284822\pi$
$167$	−4.68750	−	8.11899i	−0.362730	−	0.628266i	−0.988409	+	0.151814i	$0.951488\pi$
$168$	−0.108370	+	0.187702i	−0.00836091	+	0.0144815i
$169$	−13.3243	+	23.0784i	−1.02495	+	1.77526i
$170$		0			0
$171$	−1.61580	−	10.9282i	−0.123563	−	0.835703i
$172$	5.70398			0.434925
$173$	−3.88263	+	6.72491i	−0.295191	+	0.511286i	−0.975029	−	0.222076i	$-0.928717\pi$
$173$	−3.88263	+	6.72491i	−0.295191	+	0.511286i	0.679838	+	0.733362i	$0.262050\pi$
$174$	−3.12142	+	5.40646i	−0.236634	+	0.409863i
$175$		0			0
$176$	2.15544	−	3.73333i	0.162472	−	0.281410i
$177$	−3.28029	−	5.68163i	−0.246562	−	0.427057i
$178$	−3.71984			−0.278814
$179$	−1.12249			−0.0838992			−0.0419496	−	0.999120i	$-0.513357\pi$
$179$	−1.12249			−0.0838992			−0.0419496	+	0.999120i	$0.513357\pi$
$180$		0			0
$181$	−7.89198	−	13.6693i	−0.586606	−	1.01603i	−0.994673	−	0.103080i	$-0.967130\pi$
$181$	−7.89198	−	13.6693i	−0.586606	−	1.01603i	0.408067	−	0.912952i	$-0.366203\pi$
$182$	−2.00000			−0.148250
$183$	−4.21313			−0.311444
$184$	−1.98955	−	3.44600i	−0.146671	−	0.254042i
$185$		0			0
$186$	−1.01873	−	1.76450i	−0.0746970	−	0.129379i
$187$	−0.288513	+	0.499719i	−0.0210982	+	0.0365431i
$188$	−6.48617	+	11.2344i	−0.473053	+	0.819351i
$189$	−1.19952			−0.0872520
$190$		0			0
$191$	18.2974			1.32395			0.661977	−	0.749524i	$-0.269717\pi$
$191$	18.2974			1.32395			0.661977	+	0.749524i	$0.269717\pi$
$192$	0.341187	−	0.590953i	0.0246231	−	0.0426484i
$193$	−0.558777	+	0.967830i	−0.0402216	+	0.0696659i	−0.885435	−	0.464762i	$-0.846140\pi$
$193$	−0.558777	+	0.967830i	−0.0402216	+	0.0696659i	0.845214	+	0.534428i	$0.179473\pi$
$194$	−2.42830	−	4.20594i	−0.174342	−	0.301969i
$195$		0			0
$196$	3.44956	+	5.97481i	0.246397	+	0.426772i
$197$	16.2594			1.15843			0.579217	−	0.815173i	$-0.303358\pi$
$197$	16.2594			1.15843			0.579217	+	0.815173i	$0.303358\pi$
$198$	10.9253			0.776429
$199$	6.89911	+	11.9496i	0.489065	+	0.847086i	0.999921	−	0.0125807i	$-0.00400467\pi$
$199$	6.89911	+	11.9496i	0.489065	+	0.847086i	−0.510856	+	0.859667i	$0.670671\pi$
$200$		0			0
$201$	0.403308			0.0284471
$202$	−2.51276			−0.176797
$203$	−1.45293	−	2.51655i	−0.101976	−	0.176627i
$204$	−0.0456691	+	0.0791012i	−0.00319748	+	0.00553819i
$205$		0			0
$206$	2.01648	−	3.49265i	0.140495	−	0.243345i
$207$	5.04224	−	8.73341i	0.350460	−	0.607014i
$208$	6.29672			0.436599
$209$	17.4724	+	6.91409i	1.20859	+	0.478257i
$210$		0			0
$211$	0.584458	−	1.01231i	0.0402358	−	0.0696904i	−0.845206	−	0.534440i	$-0.820522\pi$
$211$	0.584458	−	1.01231i	0.0402358	−	0.0696904i	0.885442	+	0.464750i	$0.153856\pi$
$212$	−3.96261	+	6.86344i	−0.272153	+	0.471383i
$213$	3.97874	+	6.89138i	0.272619	+	0.472190i
$214$	5.00000	−	8.66025i	0.341793	−	0.592003i
$215$		0			0
$216$	3.77651			0.256959
$217$	0.948381			0.0643803
$218$	2.93197	+	5.07832i	0.198578	+	0.343947i
$219$	−2.81853	−	4.88184i	−0.190459	−	0.329884i
$220$		0			0
$221$	−0.842838			−0.0566954
$222$	−1.73092	−	2.99804i	−0.116172	−	0.201215i
$223$	−3.15881	+	5.47122i	−0.211530	+	0.366380i	−0.952193	−	0.305496i	$-0.901178\pi$
$223$	−3.15881	+	5.47122i	−0.211530	+	0.366380i	0.740664	+	0.671876i	$0.234511\pi$
$224$	0.158813	+	0.275072i	0.0106111	+	0.0183790i
$225$		0			0
$226$	−9.04264	+	15.6623i	−0.601508	+	1.04184i
$227$	3.77942			0.250849			0.125424	−	0.992103i	$-0.459971\pi$
$227$	3.77942			0.250849			0.125424	+	0.992103i	$0.459971\pi$
$228$	2.76573	+	1.09444i	0.183165	+	0.0724811i
$229$	5.43628			0.359239			0.179620	−	0.983736i	$-0.442513\pi$
$229$	5.43628			0.359239			0.179620	+	0.983736i	$0.442513\pi$
$230$		0			0
$231$	0.467169	−	0.809160i	0.0307374	−	0.0532388i
$232$	4.57435	+	7.92301i	0.300321	+	0.520171i
$233$	−1.22461	+	2.12109i	−0.0802270	+	0.138957i	−0.903347	−	0.428910i	$-0.858898\pi$
$233$	−1.22461	+	2.12109i	−0.0802270	+	0.138957i	0.823120	+	0.567867i	$0.192231\pi$
$234$	7.97909	+	13.8202i	0.521610	+	0.903454i
$235$		0			0
$236$	−9.61434			−0.625841
$237$	−1.13350	−	1.96329i	−0.0736289	−	0.127529i
$238$	−0.0212577	−	0.0368194i	−0.00137793	−	0.00238664i
$239$	−9.45899			−0.611851			−0.305926	−	0.952055i	$-0.598966\pi$
$239$	−9.45899			−0.611851			−0.305926	+	0.952055i	$0.598966\pi$
$240$		0			0
$241$	8.43540	+	14.6105i	0.543372	+	0.941148i	0.998707	+	0.0508279i	$0.0161860\pi$
$241$	8.43540	+	14.6105i	0.543372	+	0.941148i	−0.455335	+	0.890320i	$0.650481\pi$
$242$	−3.79182	+	6.56762i	−0.243747	+	0.422183i
$243$	7.37960	+	12.7819i	0.473402	+	0.819956i
$244$	−3.08711	+	5.34704i	−0.197632	+	0.342309i
$245$		0			0
$246$	0.591036			0.0376831
$247$	4.01451	+	27.1516i	0.255437	+	1.72761i
$248$	−2.98584			−0.189601
$249$	−1.43540	+	2.48619i	−0.0909649	+	0.157556i
$250$		0			0
$251$	−1.32814	−	2.30040i	−0.0838311	−	0.145200i	0.821061	−	0.570840i	$-0.193382\pi$
$251$	−1.32814	−	2.30040i	−0.0838311	−	0.145200i	−0.904893	+	0.425640i	$0.860049\pi$
$252$	−0.402490	+	0.697133i	−0.0253545	+	0.0439152i
$253$	8.57668	+	14.8553i	0.539211	+	0.933942i
$254$	−17.8969			−1.12295
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−1.12373	−	1.94635i	−0.0700961	−	0.121410i	0.828847	−	0.559475i	$-0.188997\pi$
$257$	−1.12373	−	1.94635i	−0.0700961	−	0.121410i	−0.898943	+	0.438065i	$0.855664\pi$
$258$	−3.89225			−0.242321
$259$	1.61139			0.100127
$260$		0			0
$261$	−11.5931	+	20.0798i	−0.717594	+	1.24291i
$262$	5.90509	+	10.2279i	0.364818	+	0.631883i
$263$	15.9289	−	27.5897i	0.982219	−	1.70125i	0.328524	−	0.944496i	$-0.393449\pi$
$263$	15.9289	−	27.5897i	0.982219	−	1.70125i	0.653695	−	0.756758i	$-0.273218\pi$
$264$	−1.47081	+	2.54753i	−0.0905224	+	0.156789i
$265$		0			0
$266$	−1.08486	+	0.860178i	−0.0665173	+	0.0527409i
$267$	2.53832			0.155343
$268$	0.295518	−	0.511852i	0.0180516	−	0.0312663i
$269$	5.44763	−	9.43558i	0.332148	−	0.575297i	−0.650785	−	0.759262i	$-0.725560\pi$
$269$	5.44763	−	9.43558i	0.332148	−	0.575297i	0.982933	+	0.183965i	$0.0588933\pi$
$270$		0			0
$271$	5.96631	−	10.3340i	0.362428	−	0.627743i	−0.625932	−	0.779877i	$-0.715281\pi$
$271$	5.96631	−	10.3340i	0.362428	−	0.627743i	0.988360	+	0.152134i	$0.0486147\pi$
$272$	0.0669268	+	0.115921i	0.00405803	+	0.00702872i
$273$	1.36475			0.0825983
$274$	−15.8311			−0.956391
$275$		0			0
$276$	1.35762	+	2.35146i	0.0817188	+	0.141541i
$277$	−15.9065			−0.955730			−0.477865	−	0.878433i	$-0.658589\pi$
$277$	−15.9065			−0.955730			−0.477865	+	0.878433i	$0.658589\pi$
$278$	1.16736			0.0700137
$279$	−3.78361	−	6.55341i	−0.226519	−	0.392342i
$280$		0			0
$281$	10.4921	+	18.1729i	0.625909	+	1.08411i	0.988364	+	0.152105i	$0.0486052\pi$
$281$	10.4921	+	18.1729i	0.625909	+	1.08411i	−0.362455	+	0.932001i	$0.618062\pi$
$282$	4.42600	−	7.66605i	0.263564	−	0.456507i
$283$	6.43083	−	11.1385i	0.382273	−	0.662116i	−0.609114	−	0.793083i	$-0.708475\pi$
$283$	6.43083	−	11.1385i	0.382273	−	0.662116i	0.991387	+	0.130967i	$0.0418081\pi$
$284$	11.6615			0.691981
$285$		0			0
$286$	−27.1444			−1.60508
$287$	−0.137555	+	0.238253i	−0.00811963	+	0.0140636i
$288$	1.26718	−	2.19482i	0.0746695	−	0.129331i
$289$	8.49104	+	14.7069i	0.499473	+	0.865113i
$290$		0			0
$291$	1.65701	+	2.87002i	0.0971356	+	0.168244i
$292$	−8.26096			−0.483436
$293$	−12.1278			−0.708511			−0.354255	−	0.935149i	$-0.615266\pi$
$293$	−12.1278			−0.708511			−0.354255	+	0.935149i	$0.615266\pi$
$294$	−2.35389	−	4.07705i	−0.137282	−	0.237779i
$295$		0			0
$296$	−5.07323			−0.294875
$297$	−16.2801			−0.944664
$298$	6.07575	+	10.5235i	0.351959	+	0.609611i
$299$	−12.5276	+	21.6985i	−0.724491	+	1.25485i
$300$		0			0
$301$	0.905866	−	1.56901i	0.0522132	−	0.0904360i
$302$	10.1902	−	17.6499i	0.586377	−	1.01564i
$303$	1.71464			0.0985035
$304$	3.41554	−	2.70815i	0.195895	−	0.155323i
$305$		0			0
$306$	−0.169617	+	0.293785i	−0.00969635	+	0.0167946i
$307$	−9.08409	+	15.7341i	−0.518456	+	0.897992i	0.481314	+	0.876548i	$0.340160\pi$
$307$	−9.08409	+	15.7341i	−0.518456	+	0.897992i	−0.999770	+	0.0214442i	$0.993174\pi$
$308$	−0.684622	−	1.18580i	−0.0390100	−	0.0675673i
$309$	−1.37600	+	2.38330i	−0.0782777	+	0.135581i
$310$		0			0
$311$	19.4766			1.10442			0.552210	−	0.833705i	$-0.313785\pi$
$311$	19.4766			1.10442			0.552210	+	0.833705i	$0.313785\pi$
$312$	−4.29672			−0.243254
$313$	5.98987	+	10.3748i	0.338568	+	0.586416i	0.984164	−	0.177263i	$-0.0567243\pi$
$313$	5.98987	+	10.3748i	0.338568	+	0.586416i	−0.645596	+	0.763679i	$0.723391\pi$
$314$	−2.46121	−	4.26294i	−0.138894	−	0.240572i
$315$		0			0
$316$	−3.32223			−0.186890
$317$	0.564654	+	0.978009i	0.0317141	+	0.0549305i	0.881447	−	0.472283i	$-0.156570\pi$
$317$	0.564654	+	0.978009i	0.0317141	+	0.0549305i	−0.849733	+	0.527214i	$0.823237\pi$
$318$	2.70398	−	4.68343i	0.151632	−	0.262634i
$319$	−19.7195	−	34.1551i	−1.10408	−	1.91232i
$320$		0			0
$321$	−3.41187	+	5.90953i	−0.190432	+	0.329838i
$322$	−1.26386			−0.0704323
$323$	−0.457182	+	0.362495i	−0.0254383	+	0.0201698i
$324$	5.02610			0.279228
$325$		0			0
$326$	0.718637	−	1.24472i	0.0398016	−	0.0689385i
$327$	−2.00070	−	3.46532i	−0.110639	−	0.191632i
$328$	0.433073	−	0.750105i	0.0239125	−	0.0414176i
$329$	2.06017	+	3.56833i	0.113581	+	0.196728i
$330$		0			0
$331$	−14.3080			−0.786437			−0.393218	−	0.919445i	$-0.628638\pi$
$331$	−14.3080			−0.786437			−0.393218	+	0.919445i	$0.628638\pi$
$332$	2.10354	+	3.64344i	0.115447	+	0.199960i
$333$	−6.42871	−	11.1348i	−0.352291	−	0.610186i
$334$	9.37500			0.512977
$335$		0			0
$336$	−0.108370	−	0.187702i	−0.00591206	−	0.0102400i
$337$	−13.8589	+	24.0043i	−0.754941	+	1.30760i	0.190463	+	0.981694i	$0.439001\pi$
$337$	−13.8589	+	24.0043i	−0.754941	+	1.30760i	−0.945404	+	0.325901i	$0.894332\pi$
$338$	−13.3243	−	23.0784i	−0.724748	−	1.25530i
$339$	6.17047	−	10.6876i	0.335134	−	0.580469i
$340$		0			0
$341$	12.8716			0.697036
$342$	10.2720	+	4.06480i	0.555448	+	0.219799i
$343$	4.41472			0.238372
$344$	−2.85199	+	4.93979i	−0.153769	+	0.266336i
$345$		0			0
$346$	−3.88263	−	6.72491i	−0.208731	−	0.361534i
$347$	15.7098	−	27.2102i	0.843346	−	1.46072i	−0.0437044	−	0.999045i	$-0.513916\pi$
$347$	15.7098	−	27.2102i	0.843346	−	1.46072i	0.887050	−	0.461673i	$-0.152751\pi$
$348$	−3.12142	−	5.40646i	−0.167326	−	0.289817i
$349$	23.4539			1.25546			0.627729	−	0.778432i	$-0.283985\pi$
$349$	23.4539			1.25546			0.627729	+	0.778432i	$0.283985\pi$
$350$		0			0
$351$	−11.8898	−	20.5937i	−0.634631	−	1.09921i
$352$	2.15544	+	3.73333i	0.114885	+	0.198987i
$353$	−17.3468			−0.923277			−0.461638	−	0.887068i	$-0.652738\pi$
$353$	−17.3468			−0.923277			−0.461638	+	0.887068i	$0.652738\pi$
$354$	6.56058			0.348691
$355$		0			0
$356$	1.85992	−	3.22147i	0.0985755	−	0.170738i
$357$	0.0145057	+	0.0251246i	0.000767722	+	0.00132973i
$358$	0.561247	−	0.972108i	0.0296628	−	0.0513775i
$359$	−0.402934	+	0.697902i	−0.0212660	+	0.0368339i	−0.876463	−	0.481470i	$-0.840103\pi$
$359$	−0.402934	+	0.697902i	−0.0212660	+	0.0368339i	0.855197	+	0.518304i	$0.173436\pi$
$360$		0			0
$361$	13.8552	+	13.0013i	0.729221	+	0.684279i
$362$	15.7840			0.829587
$363$	2.58744	−	4.48157i	0.135805	−	0.235222i
$364$	1.00000	−	1.73205i	0.0524142	−	0.0907841i
$365$		0			0
$366$	2.10657	−	3.64868i	0.110112	−	0.190720i
$367$	−1.26908	−	2.19811i	−0.0662455	−	0.114740i	0.831000	−	0.556272i	$-0.187769\pi$
$367$	−1.26908	−	2.19811i	−0.0662455	−	0.114740i	−0.897246	+	0.441531i	$0.854435\pi$
$368$	3.97909			0.207425
$369$	2.19513			0.114274
$370$		0			0
$371$	1.25863	+	2.18001i	0.0653446	+	0.113180i
$372$	2.03746			0.105638
$373$	−12.4012			−0.642110			−0.321055	−	0.947060i	$-0.604038\pi$
$373$	−12.4012			−0.642110			−0.321055	+	0.947060i	$0.604038\pi$
$374$	−0.288513	−	0.499719i	−0.0149186	−	0.0258399i
$375$		0			0
$376$	−6.48617	−	11.2344i	−0.334499	−	0.579369i
$377$	28.8034	−	49.8890i	1.48345	−	2.56941i
$378$	0.599758	−	1.03881i	0.0308482	−	0.0534307i
$379$	−12.6756			−0.651100			−0.325550	−	0.945525i	$-0.605549\pi$
$379$	−12.6756			−0.651100			−0.325550	+	0.945525i	$0.605549\pi$
$380$		0			0
$381$	12.2124			0.625660
$382$	−9.14871	+	15.8460i	−0.468089	+	0.810753i
$383$	−7.97632	+	13.8154i	−0.407571	+	0.705934i	−0.994617	−	0.103620i	$-0.966957\pi$
$383$	−7.97632	+	13.8154i	−0.407571	+	0.705934i	0.587046	+	0.809554i	$0.300291\pi$
$384$	0.341187	+	0.590953i	0.0174111	+	0.0301570i
$385$		0			0
$386$	−0.558777	−	0.967830i	−0.0284410	−	0.0492612i
$387$	−14.4560			−0.734839
$388$	4.85660			0.246556
$389$	13.0991	+	22.6883i	0.664150	+	1.15034i	0.979515	+	0.201372i	$0.0645399\pi$
$389$	13.0991	+	22.6883i	0.664150	+	1.15034i	−0.315365	+	0.948971i	$0.602127\pi$
$390$		0			0
$391$	−0.532616			−0.0269355
$392$	−6.89911			−0.348458
$393$	−4.02948	−	6.97926i	−0.203260	−	0.352057i
$394$	−8.12970	+	14.0811i	−0.409568	+	0.709393i
$395$		0			0
$396$	−5.46266	+	9.46161i	−0.274509	+	0.475464i
$397$	15.0639	−	26.0914i	0.756034	−	1.30949i	−0.188824	−	0.982011i	$-0.560468\pi$
$397$	15.0639	−	26.0914i	0.756034	−	1.30949i	0.944858	−	0.327479i	$-0.106199\pi$
$398$	−13.7982			−0.691643
$399$	0.740283	−	0.586963i	0.0370605	−	0.0293849i
$400$		0			0
$401$	1.08591	−	1.88085i	0.0542278	−	0.0939254i	−0.837637	−	0.546227i	$-0.816064\pi$
$401$	1.08591	−	1.88085i	0.0542278	−	0.0939254i	0.891865	+	0.452302i	$0.149397\pi$
$402$	−0.201654	+	0.349275i	−0.0100576	+	0.0174202i
$403$	9.40051	+	16.2822i	0.468273	+	0.811072i
$404$	1.25638	−	2.17611i	0.0625072	−	0.108266i
$405$		0			0
$406$	2.90587			0.144216
$407$	21.8700			1.08406
$408$	−0.0456691	−	0.0791012i	−0.00226096	−	0.00391609i
$409$	−16.0832	−	27.8569i	−0.795262	−	1.37743i	−0.922673	−	0.385584i	$-0.874000\pi$
$409$	−16.0832	−	27.8569i	−0.795262	−	1.37743i	0.127410	−	0.991850i	$-0.459333\pi$
$410$		0			0
$411$	10.8027			0.532859
$412$	2.01648	+	3.49265i	0.0993450	+	0.172071i
$413$	−1.52688	+	2.64464i	−0.0751329	+	0.130134i
$414$	5.04224	+	8.73341i	0.247812	+	0.429224i
$415$		0			0
$416$	−3.14836	+	5.45312i	−0.154361	+	0.267361i
$417$	−0.796577			−0.0390085
$418$	−14.7240	+	11.6745i	−0.720173	+	0.571018i
$419$	−9.99674			−0.488373			−0.244186	−	0.969728i	$-0.578521\pi$
$419$	−9.99674			−0.488373			−0.244186	+	0.969728i	$0.578521\pi$
$420$		0			0
$421$	19.0856	−	33.0572i	0.930173	−	1.61111i	0.147150	−	0.989114i	$-0.452990\pi$
$421$	19.0856	−	33.0572i	0.930173	−	1.61111i	0.783023	−	0.621993i	$-0.213677\pi$
$422$	0.584458	+	1.01231i	0.0284510	+	0.0492785i
$423$	16.4383	−	28.4720i	0.799259	−	1.38436i
$424$	−3.96261	−	6.86344i	−0.192441	−	0.333318i
$425$		0			0
$426$	−7.95748			−0.385541
$427$	0.980546	+	1.69836i	0.0474520	+	0.0821892i
$428$	5.00000	+	8.66025i	0.241684	+	0.418609i
$429$	18.5226			0.894280
$430$		0			0
$431$	−1.73649	−	3.00769i	−0.0836437	−	0.144875i	0.821169	−	0.570685i	$-0.193322\pi$
$431$	−1.73649	−	3.00769i	−0.0836437	−	0.144875i	−0.904812	+	0.425810i	$0.859989\pi$
$432$	−1.88825	+	3.27055i	−0.0908487	+	0.157355i
$433$	5.54742	+	9.60841i	0.266592	+	0.461751i	0.967979	−	0.251029i	$-0.0807691\pi$
$433$	5.54742	+	9.60841i	0.266592	+	0.461751i	−0.701388	+	0.712780i	$0.747436\pi$
$434$	−0.474191	+	0.821322i	−0.0227619	+	0.0394247i
$435$		0			0
$436$	−5.86394			−0.280832
$437$	2.53689	+	17.1579i	0.121356	+	0.820775i
$438$	5.63706			0.269349
$439$	6.51914	−	11.2915i	0.311141	−	0.538913i	−0.667468	−	0.744638i	$-0.732622\pi$
$439$	6.51914	−	11.2915i	0.311141	−	0.538913i	0.978610	+	0.205725i	$0.0659554\pi$
$440$		0			0
$441$	−8.74244	−	15.1423i	−0.416307	−	0.721064i
$442$	0.421419	−	0.729919i	0.0200449	−	0.0347187i
$443$	−7.51250	−	13.0120i	−0.356930	−	0.618221i	0.630516	−	0.776176i	$-0.282843\pi$
$443$	−7.51250	−	13.0120i	−0.356930	−	0.618221i	−0.987446	+	0.157955i	$0.949510\pi$
$444$	3.46184			0.164292
$445$		0			0
$446$	−3.15881	−	5.47122i	−0.149574	−	0.259070i
$447$	−4.14594	−	7.18097i	−0.196096	−	0.339648i
$448$	−0.317626			−0.0150064
$449$	14.4251			0.680761			0.340381	−	0.940288i	$-0.389444\pi$
$449$	14.4251			0.680761			0.340381	+	0.940288i	$0.389444\pi$
$450$		0			0
$451$	−1.86692	+	3.23361i	−0.0879100	+	0.152265i
$452$	−9.04264	−	15.6623i	−0.425330	−	0.736693i
$453$	−6.95350	+	12.0438i	−0.326704	+	0.565868i
$454$	−1.88971	+	3.27307i	−0.0886884	+	0.153613i
$455$		0			0
$456$	−2.33068	+	1.84797i	−0.109144	+	0.0865392i
$457$	−32.1773			−1.50519			−0.752596	−	0.658483i	$-0.771199\pi$
$457$	−32.1773			−1.50519			−0.752596	+	0.658483i	$0.771199\pi$
$458$	−2.71814	+	4.70795i	−0.127010	+	0.219988i
$459$	0.252750	−	0.437775i	0.0117973	−	0.0204336i
$460$		0			0
$461$	7.75530	−	13.4326i	0.361200	−	0.625617i	−0.626958	−	0.779053i	$-0.715700\pi$
$461$	7.75530	−	13.4326i	0.361200	−	0.625617i	0.988159	+	0.153435i	$0.0490337\pi$
$462$	0.467169	+	0.809160i	0.0217347	+	0.0376455i
$463$	−30.1477			−1.40108			−0.700541	−	0.713612i	$-0.747058\pi$
$463$	−30.1477			−1.40108			−0.700541	+	0.713612i	$0.747058\pi$
$464$	−9.14871			−0.424718
$465$		0			0
$466$	−1.22461	−	2.12109i	−0.0567290	−	0.0982576i
$467$	−34.5731			−1.59985			−0.799927	−	0.600098i	$-0.795128\pi$
$467$	−34.5731			−1.59985			−0.799927	+	0.600098i	$0.795128\pi$
$468$	−15.9582			−0.737667
$469$	−0.0938641	−	0.162577i	−0.00433424	−	0.00750713i
$470$		0			0
$471$	1.67947	+	2.90892i	0.0773858	+	0.134036i
$472$	4.80717	−	8.32627i	0.221268	−	0.383247i
$473$	12.2946	−	21.2948i	0.565305	−	0.979137i
$474$	2.26701			0.104127
$475$		0			0
$476$	0.0425153			0.00194869
$477$	10.0427	−	17.3945i	0.459824	−	0.796438i
$478$	4.72950	−	8.19173i	0.216322	−	0.374681i
$479$	−15.4238	−	26.7148i	−0.704732	−	1.22063i	−0.966788	−	0.255579i	$-0.917734\pi$
$479$	−15.4238	−	26.7148i	−0.704732	−	1.22063i	0.262056	−	0.965053i	$-0.415600\pi$
$480$		0			0
$481$	15.9723	+	27.6649i	0.728276	+	1.26141i
$482$	−16.8708			−0.768444
$483$	0.862427			0.0392418
$484$	−3.79182	−	6.56762i	−0.172355	−	0.298528i
$485$		0			0
$486$	−14.7592			−0.669491
$487$	−30.7745			−1.39453			−0.697263	−	0.716815i	$-0.745599\pi$
$487$	−30.7745			−1.39453			−0.697263	+	0.716815i	$0.745599\pi$
$488$	−3.08711	−	5.34704i	−0.139747	−	0.242049i
$489$	−0.490380	+	0.849362i	−0.0221757	+	0.0384095i
$490$		0			0
$491$	12.8571	−	22.2692i	0.580234	−	1.00499i	−0.415218	−	0.909722i	$-0.636295\pi$
$491$	12.8571	−	22.2692i	0.580234	−	1.00499i	0.995451	−	0.0952719i	$-0.0303720\pi$
$492$	−0.295518	+	0.511852i	−0.0133230	+	0.0230761i
$493$	1.22459			0.0551526
$494$	−25.5212	−	10.0991i	−1.14825	−	0.454381i
$495$		0			0
$496$	1.49292	−	2.58582i	0.0670342	−	0.116107i
$497$	1.85199	−	3.20774i	0.0830732	−	0.143887i
$498$	−1.43540	−	2.48619i	−0.0643219	−	0.111409i
$499$	0.201106	−	0.348326i	0.00900274	−	0.0155932i	−0.861489	−	0.507776i	$-0.830468\pi$
$499$	0.201106	−	0.348326i	0.00900274	−	0.0155932i	0.870492	+	0.492183i	$0.163801\pi$
$500$		0			0
$501$	−6.39726			−0.285808
$502$	2.65627			0.118555
$503$	−20.2327	−	35.0441i	−0.902133	−	1.56254i	−0.824720	−	0.565542i	$-0.808667\pi$
$503$	−20.2327	−	35.0441i	−0.902133	−	1.56254i	−0.0774136	−	0.996999i	$-0.524666\pi$
$504$	−0.402490	−	0.697133i	−0.0179283	−	0.0310528i
$505$		0			0
$506$	−17.1534			−0.762560
$507$	9.09218	+	15.7481i	0.403798	+	0.699399i
$508$	8.94845	−	15.4992i	0.397023	−	0.687665i
$509$	5.72694	+	9.91935i	0.253842	+	0.439668i	0.964580	−	0.263789i	$-0.0849723\pi$
$509$	5.72694	+	9.91935i	0.253842	+	0.439668i	−0.710738	+	0.703457i	$0.751639\pi$
$510$		0			0
$511$	−1.31195	+	2.27236i	−0.0580371	+	0.100523i
$512$	1.00000			0.0441942
$513$	−15.3066	−	6.05703i	−0.675801	−	0.267425i
$514$	2.24745			0.0991308
$515$		0			0
$516$	1.94613	−	3.37079i	0.0856734	−	0.148391i
$517$	27.9611	+	48.4300i	1.22973	+	2.12995i
$518$	−0.805694	+	1.39550i	−0.0354002	+	0.0613149i
$519$	2.64941	+	4.58891i	0.116296	+	0.201431i
$520$		0			0
$521$	1.66822			0.0730860			0.0365430	−	0.999332i	$-0.488365\pi$
$521$	1.66822			0.0730860			0.0365430	+	0.999332i	$0.488365\pi$
$522$	−11.5931	−	20.0798i	−0.507416	−	0.878870i
$523$	−21.9775	−	38.0662i	−0.961011	−	1.66452i	−0.719971	−	0.694004i	$-0.755845\pi$
$523$	−21.9775	−	38.0662i	−0.961011	−	1.66452i	−0.241039	−	0.970515i	$-0.577488\pi$
$524$	−11.8102			−0.515930
$525$		0			0
$526$	15.9289	+	27.5897i	0.694534	+	1.20297i
$527$	−0.199833	+	0.346121i	−0.00870486	+	0.0150773i
$528$	−1.47081	−	2.54753i	−0.0640090	−	0.110867i
$529$	3.58341	−	6.20665i	0.155800	−	0.269854i
$530$		0			0
$531$	24.3663			1.05741
$532$	−0.202504	−	1.36961i	−0.00877966	−	0.0593801i
$533$	−5.45388			−0.236234
$534$	−1.26916	+	2.19825i	−0.0549220	+	0.0951276i
$535$		0			0
$536$	0.295518	+	0.511852i	0.0127644	+	0.0221086i
$537$	−0.382981	+	0.663342i	−0.0165268	+	0.0286253i
$538$	5.44763	+	9.43558i	0.234864	+	0.406797i
$539$	29.7412			1.28104
$540$		0			0
$541$	14.7202	+	25.4961i	0.632870	+	1.09616i	0.986962	+	0.160953i	$0.0514567\pi$
$541$	14.7202	+	25.4961i	0.632870	+	1.09616i	−0.354092	+	0.935211i	$0.615210\pi$
$542$	5.96631	+	10.3340i	0.256275	+	0.443881i
$543$	−10.7706			−0.462209
$544$	−0.133854			−0.00573892
$545$		0			0
$546$	−0.682374	+	1.18191i	−0.0292029	+	0.0505809i
$547$	−10.2026	−	17.6714i	−0.436231	−	0.755574i	0.561164	−	0.827704i	$-0.310354\pi$
$547$	−10.2026	−	17.6714i	−0.436231	−	0.755574i	−0.997395	+	0.0721302i	$0.977020\pi$
$548$	7.91554	−	13.7101i	0.338135	−	0.585667i
$549$	7.82387	−	13.5513i	0.333915	−	0.578357i
$550$		0			0
$551$	−5.83281	−	39.4494i	−0.248486	−	1.68060i
$552$	−2.71523			−0.115568
$553$	−0.527613	+	0.913853i	−0.0224364	+	0.0388610i
$554$	7.95326	−	13.7754i	0.337902	−	0.585263i
$555$		0			0
$556$	−0.583681	+	1.01096i	−0.0247536	+	0.0428744i
$557$	2.30575	+	3.99368i	0.0976977	+	0.169217i	0.910731	−	0.412999i	$-0.135519\pi$
$557$	2.30575	+	3.99368i	0.0976977	+	0.169217i	−0.813034	+	0.582217i	$0.802185\pi$
$558$	7.56722			0.320346
$559$	35.9164			1.51910
$560$		0			0
$561$	0.196874	+	0.340995i	0.00831202	+	0.0143968i
$562$	−20.9843			−0.885169
$563$	−5.13495			−0.216412			−0.108206	−	0.994128i	$-0.534511\pi$
$563$	−5.13495			−0.216412			−0.108206	+	0.994128i	$0.534511\pi$
$564$	4.42600	+	7.66605i	0.186368	+	0.322799i
$565$		0			0
$566$	6.43083	+	11.1385i	0.270308	+	0.468187i
$567$	0.798210	−	1.38254i	0.0335217	−	0.0580612i
$568$	−5.83073	+	10.0991i	−0.244652	+	0.423750i
$569$	−23.0698			−0.967135			−0.483568	−	0.875307i	$-0.660659\pi$
$569$	−23.0698			−0.967135			−0.483568	+	0.875307i	$0.660659\pi$
$570$		0			0
$571$	−24.7009			−1.03370			−0.516850	−	0.856076i	$-0.672896\pi$
$571$	−24.7009			−1.03370			−0.516850	+	0.856076i	$0.672896\pi$
$572$	13.5722	−	23.5077i	0.567481	−	0.982906i
$573$	6.24284	−	10.8129i	0.260799	−	0.451716i
$574$	−0.137555	−	0.238253i	−0.00574144	−	0.00994447i
$575$		0			0
$576$	1.26718	+	2.19482i	0.0527993	+	0.0914510i
$577$	−34.0569			−1.41781			−0.708903	−	0.705306i	$-0.750810\pi$
$577$	−34.0569			−1.41781			−0.708903	+	0.705306i	$0.750810\pi$
$578$	−16.9821			−0.706362
$579$	0.381295	+	0.660422i	0.0158461	+	0.0274462i
$580$		0			0
$581$	1.33628			0.0554381
$582$	−3.31402			−0.137370
$583$	17.0823	+	29.5874i	0.707477	+	1.22539i
$584$	4.13048	−	7.15420i	0.170920	−	0.296043i
$585$		0			0
$586$	6.06388	−	10.5029i	0.250496	−	0.433873i
$587$	−18.9701	+	32.8572i	−0.782981	+	1.35616i	0.147216	+	0.989104i	$0.452969\pi$
$587$	−18.9701	+	32.8572i	−0.782981	+	1.35616i	−0.930198	+	0.367059i	$0.880365\pi$
$588$	4.70778			0.194145
$589$	12.1019	+	4.78891i	0.498651	+	0.197324i
$590$		0			0
$591$	5.54750	−	9.60855i	0.228194	−	0.395243i
$592$	2.53661	−	4.39354i	0.104254	−	0.180574i
$593$	−4.85602	−	8.41087i	−0.199413	−	0.345393i	0.748925	−	0.662654i	$-0.230570\pi$
$593$	−4.85602	−	8.41087i	−0.199413	−	0.345393i	−0.948338	+	0.317261i	$0.897237\pi$
$594$	8.14003	−	14.0989i	0.333989	−	0.578486i
$595$		0			0
$596$	−12.1515			−0.497745
$597$	9.41556			0.385353
$598$	−12.5276	−	21.6985i	−0.512292	−	0.887316i
$599$	7.71001	+	13.3541i	0.315023	+	0.545635i	0.979442	−	0.201725i	$-0.0646546\pi$
$599$	7.71001	+	13.3541i	0.315023	+	0.545635i	−0.664420	+	0.747360i	$0.731321\pi$
$600$		0			0
$601$	−21.9383			−0.894881			−0.447441	−	0.894314i	$-0.647664\pi$
$601$	−21.9383			−0.894881			−0.447441	+	0.894314i	$0.647664\pi$
$602$	0.905866	+	1.56901i	0.0369203	+	0.0639479i
$603$	−0.748951	+	1.29722i	−0.0304996	+	0.0528269i
$604$	10.1902	+	17.6499i	0.414631	+	0.718163i
$605$		0			0
$606$	−0.857320	+	1.48492i	−0.0348263	+	0.0603209i
$607$	22.2900			0.904724			0.452362	−	0.891834i	$-0.350582\pi$
$607$	22.2900			0.904724			0.452362	+	0.891834i	$0.350582\pi$
$608$	0.637555	+	4.31202i	0.0258563	+	0.174876i
$609$	−1.98289			−0.0803507
$610$		0			0
$611$	−40.8416	+	70.7397i	−1.65227	+	2.86182i
$612$	−0.169617	−	0.293785i	−0.00685636	−	0.0118756i
$613$	12.6028	−	21.8287i	0.509023	−	0.881654i	−0.490922	−	0.871203i	$-0.663340\pi$
$613$	12.6028	−	21.8287i	0.509023	−	0.881654i	0.999945	−	0.0104504i	$-0.00332654\pi$
$614$	−9.08409	−	15.7341i	−0.366604	−	0.634977i
$615$		0			0
$616$	1.36924			0.0551684
$617$	−9.51333	−	16.4776i	−0.382992	−	0.663362i	0.608496	−	0.793557i	$-0.291773\pi$
$617$	−9.51333	−	16.4776i	−0.382992	−	0.663362i	−0.991488	+	0.130195i	$0.958440\pi$
$618$	−1.37600	−	2.38330i	−0.0553507	−	0.0958702i
$619$	−33.9075			−1.36286			−0.681429	−	0.731884i	$-0.738641\pi$
$619$	−33.9075			−1.36286			−0.681429	+	0.731884i	$0.738641\pi$
$620$		0			0
$621$	−7.51354	−	13.0138i	−0.301508	−	0.522227i
$622$	−9.73832	+	16.8673i	−0.390471	+	0.676316i
$623$	−0.590758	−	1.02322i	−0.0236682	−	0.0409946i
$624$	2.14836	−	3.72107i	0.0860032	−	0.148962i
$625$		0			0
$626$	−11.9797			−0.478807
$627$	10.0473	−	7.96637i	0.401249	−	0.318146i
$628$	4.92242			0.196426
$629$	−0.339535	+	0.588091i	−0.0135381	+	0.0234487i
$630$		0			0
$631$	−4.27169	−	7.39878i	−0.170053	−	0.294541i	0.768385	−	0.639988i	$-0.221061\pi$
$631$	−4.27169	−	7.39878i	−0.170053	−	0.294541i	−0.938438	+	0.345447i	$0.887727\pi$
$632$	1.66112	−	2.87714i	0.0660757	−	0.114446i
$633$	−0.398819	−	0.690775i	−0.0158516	−	0.0274558i
$634$	−1.12931			−0.0448505
$635$		0			0
$636$	2.70398	+	4.68343i	0.107220	+	0.185710i
$637$	21.7209	+	37.6217i	0.860613	+	1.49063i
$638$	39.4389			1.56140
$639$	−29.5544			−1.16915
$640$		0			0
$641$	−1.86302	+	3.22684i	−0.0735847	+	0.127453i	−0.900470	−	0.434918i	$-0.856777\pi$
$641$	−1.86302	+	3.22684i	−0.0735847	+	0.127453i	0.826885	+	0.562371i	$0.190111\pi$
$642$	−3.41187	−	5.90953i	−0.134656	−	0.233231i
$643$	−16.1350	+	27.9466i	−0.636300	+	1.10210i	0.349938	+	0.936773i	$0.386203\pi$
$643$	−16.1350	+	27.9466i	−0.636300	+	1.10210i	−0.986238	+	0.165332i	$0.947131\pi$
$644$	0.631931	−	1.09454i	0.0249016	−	0.0431308i
$645$		0			0
$646$	−0.0853390	−	0.577179i	−0.00335762	−	0.0227088i
$647$	48.1241			1.89195			0.945977	−	0.324234i	$-0.105107\pi$
$647$	48.1241			1.89195			0.945977	+	0.324234i	$0.105107\pi$
$648$	−2.51305	+	4.35273i	−0.0987220	+	0.170992i
$649$	−20.7231	+	35.8935i	−0.813453	+	1.40894i
$650$		0			0
$651$	0.323575	−	0.560449i	0.0126819	−	0.0219657i
$652$	0.718637	+	1.24472i	0.0281440	+	0.0487469i
$653$	13.9774			0.546979			0.273489	−	0.961875i	$-0.411822\pi$
$653$	13.9774			0.546979			0.273489	+	0.961875i	$0.411822\pi$
$654$	4.00140			0.156467
$655$		0			0
$656$	0.433073	+	0.750105i	0.0169087	+	0.0292867i
$657$	20.9363			0.816802
$658$	−4.12035			−0.160628
$659$	6.24517	+	10.8170i	0.243277	+	0.421369i	0.961646	−	0.274294i	$-0.0884441\pi$
$659$	6.24517	+	10.8170i	0.243277	+	0.421369i	−0.718369	+	0.695663i	$0.755111\pi$
$660$		0			0
$661$	−14.2429	−	24.6695i	−0.553986	−	0.959531i	−0.997982	−	0.0635024i	$-0.979773\pi$
$661$	−14.2429	−	24.6695i	−0.553986	−	0.959531i	0.443996	−	0.896029i	$-0.353560\pi$
$662$	7.15398	−	12.3911i	0.278047	−	0.481592i
$663$	−0.287566	+	0.498078i	−0.0111681	+	0.0193438i
$664$	−4.20708			−0.163266
$665$		0			0
$666$	12.8574			0.498215
$667$	18.2018	−	31.5264i	0.704776	−	1.22071i
$668$	−4.68750	+	8.11899i	−0.181365	+	0.314133i
$669$	2.15549	+	3.73342i	0.0833362	+	0.144342i
$670$		0			0
$671$	13.3082	+	23.0504i	0.513755	+	0.889851i
$672$	0.216740			0.00836091
$673$	31.6748			1.22097			0.610486	−	0.792027i	$-0.290974\pi$
$673$	31.6748			1.22097			0.610486	+	0.792027i	$0.290974\pi$
$674$	−13.8589	−	24.0043i	−0.533824	−	0.924610i
$675$		0			0
$676$	26.6487			1.02495
$677$	−49.3049			−1.89494			−0.947470	−	0.319844i	$-0.896369\pi$
$677$	−49.3049			−1.89494			−0.947470	+	0.319844i	$0.896369\pi$
$678$	6.17047	+	10.6876i	0.236975	+	0.410453i
$679$	0.771290	−	1.33591i	0.0295994	−	0.0512677i
$680$		0			0
$681$	1.28949	−	2.23346i	0.0494133	−	0.0855863i
$682$	−6.43580	+	11.1471i	−0.246440	+	0.426846i
$683$	−4.26771			−0.163299			−0.0816496	−	0.996661i	$-0.526019\pi$
$683$	−4.26771			−0.163299			−0.0816496	+	0.996661i	$0.526019\pi$
$684$	−8.65623	+	6.86344i	−0.330979	+	0.262430i
$685$		0			0
$686$	−2.20736	+	3.82326i	−0.0842773	+	0.145973i
$687$	1.85479	−	3.21259i	0.0707645	−	0.122568i
$688$	−2.85199	−	4.93979i	−0.108731	−	0.188328i
$689$	−24.9514	+	43.2172i	−0.950574	+	1.64644i
$690$		0			0
$691$	0.249546			0.00949319			0.00474659	−	0.999989i	$-0.498489\pi$
$691$	0.249546			0.00949319			0.00474659	+	0.999989i	$0.498489\pi$
$692$	7.76526			0.295191
$693$	1.73508	+	3.00525i	0.0659104	+	0.114160i
$694$	15.7098	+	27.2102i	0.596335	+	1.03288i
$695$		0			0
$696$	6.24284			0.236634
$697$	−0.0579684	−	0.100404i	−0.00219571	−	0.00380308i
$698$	−11.7269	+	20.3117i	−0.443871	+	0.768808i
$699$	0.835643	+	1.44738i	0.0316069	+	0.0547448i
$700$		0			0
$701$	−4.08961	+	7.08341i	−0.154462	+	0.267537i	−0.932863	−	0.360231i	$-0.882698\pi$
$701$	−4.08961	+	7.08341i	−0.154462	+	0.267537i	0.778401	+	0.627768i	$0.216031\pi$
$702$	23.7796			0.897504
$703$	20.5623	+	8.13680i	0.775521	+	0.306885i
$704$	−4.31087			−0.162472
$705$		0			0
$706$	8.67340	−	15.0228i	0.326428	−	0.565389i
$707$	−0.399058	−	0.691189i	−0.0150081	−	0.0259948i
$708$	−3.28029	+	5.68163i	−0.123281	+	0.213529i
$709$	6.85226	+	11.8685i	0.257342	+	0.445730i	0.965529	−	0.260295i	$-0.0838200\pi$
$709$	6.85226	+	11.8685i	0.257342	+	0.445730i	−0.708187	+	0.706025i	$0.750487\pi$
$710$		0			0
$711$	8.41975			0.315765
$712$	1.85992	+	3.22147i	0.0697034	+	0.120730i
$713$	5.94048	+	10.2892i	0.222473	+	0.385334i
$714$	−0.0290114			−0.00108572
$715$		0			0
$716$	0.561247	+	0.972108i	0.0209748	+	0.0363294i
$717$	−3.22729	+	5.58982i	−0.120525	+	0.208756i
$718$	−0.402934	−	0.697902i	−0.0150374	−	0.0260455i
$719$	−13.4178	+	23.2403i	−0.500398	+	0.866715i	0.499602	+	0.866255i	$0.333480\pi$
$719$	−13.4178	+	23.2403i	−0.500398	+	0.866715i	−1.00000		0.000460027i	$0.999854\pi$
$720$		0			0
$721$	1.28097			0.0477060
$722$	−18.1870	+	5.49830i	−0.676852	+	0.204626i
$723$	11.5122			0.428143
$724$	−7.89198	+	13.6693i	−0.293303	+	0.508016i
$725$		0			0
$726$	2.58744	+	4.48157i	0.0960288	+	0.166327i
$727$	14.5299	−	25.1665i	0.538883	−	0.933373i	−0.460081	−	0.887877i	$-0.652180\pi$
$727$	14.5299	−	25.1665i	0.538883	−	0.933373i	0.998965	−	0.0454961i	$-0.0144869\pi$
$728$	1.00000	+	1.73205i	0.0370625	+	0.0641941i
$729$	−5.00701			−0.185445
$730$		0			0
$731$	0.381749	+	0.661209i	0.0141195	+	0.0244557i
$732$	2.10657	+	3.64868i	0.0778609	+	0.134859i
$733$	−30.8850			−1.14076			−0.570381	−	0.821380i	$-0.693204\pi$
$733$	−30.8850			−1.14076			−0.570381	+	0.821380i	$0.693204\pi$
$734$	2.53816			0.0936852
$735$		0			0
$736$	−1.98955	+	3.44600i	−0.0733357	+	0.127021i
$737$	−1.27394	−	2.20653i	−0.0469262	−	0.0812786i
$738$	−1.09757	+	1.90104i	−0.0404020	+	0.0699782i
$739$	17.9491	−	31.0887i	0.660267	−	1.14362i	−0.320279	−	0.947323i	$-0.603777\pi$
$739$	17.9491	−	31.0887i	0.660267	−	1.14362i	0.980545	−	0.196292i	$-0.0628901\pi$
$740$		0			0
$741$	17.4150	+	6.89138i	0.639757	+	0.253161i
$742$	−2.51725			−0.0924113
$743$	3.15432	−	5.46344i	0.115721	−	0.200434i	−0.802347	−	0.596858i	$-0.796416\pi$
$743$	3.15432	−	5.46344i	0.115721	−	0.200434i	0.918068	+	0.396424i	$0.129749\pi$
$744$	−1.01873	+	1.76450i	−0.0373485	+	0.0646895i
$745$		0			0
$746$	6.20061	−	10.7398i	0.227020	−	0.393211i
$747$	−5.33114	−	9.23380i	−0.195056	−	0.337847i
$748$	0.577026			0.0210982
$749$	3.17626			0.116058
$750$		0			0
$751$	20.3945	+	35.3242i	0.744204	+	1.28900i	0.950566	+	0.310524i	$0.100505\pi$
$751$	20.3945	+	35.3242i	0.744204	+	1.28900i	−0.206361	+	0.978476i	$0.566162\pi$
$752$	12.9723			0.473053
$753$	−1.81257			−0.0660537
$754$	28.8034	+	49.8890i	1.04896	+	1.81685i
$755$		0			0
$756$	0.599758	+	1.03881i	0.0218130	+	0.0377812i
$757$	9.72687	−	16.8474i	0.353529	−	0.612330i	−0.633336	−	0.773877i	$-0.718315\pi$
$757$	9.72687	−	16.8474i	0.353529	−	0.612330i	0.986865	+	0.161547i	$0.0516482\pi$
$758$	6.33778	−	10.9774i	0.230199	−	0.398716i
$759$	11.7050			0.424865
$760$		0			0
$761$	−19.1465			−0.694058			−0.347029	−	0.937854i	$-0.612810\pi$
$761$	−19.1465			−0.694058			−0.347029	+	0.937854i	$0.612810\pi$
$762$	−6.10619	+	10.5762i	−0.221204	+	0.383137i
$763$	−0.931269	+	1.61301i	−0.0337142	+	0.0583947i
$764$	−9.14871	−	15.8460i	−0.330989	−	0.573289i
$765$		0			0
$766$	−7.97632	−	13.8154i	−0.288196	−	0.499170i
$767$	−60.5388			−2.18593
$768$	−0.682374			−0.0246231
$769$	−13.3405	−	23.1064i	−0.481070	−	0.833238i	0.518694	−	0.854960i	$-0.326418\pi$
$769$	−13.3405	−	23.1064i	−0.481070	−	0.833238i	−0.999764	+	0.0217222i	$0.993085\pi$
$770$		0			0
$771$	−1.53360			−0.0552314
$772$	1.11755			0.0402216
$773$	11.8521	+	20.5284i	0.426290	+	0.738356i	0.996540	−	0.0831151i	$-0.0264869\pi$
$773$	11.8521	+	20.5284i	0.426290	+	0.738356i	−0.570250	+	0.821471i	$0.693154\pi$
$774$	7.22799	−	12.5192i	0.259805	−	0.449995i
$775$		0			0
$776$	−2.42830	+	4.20594i	−0.0871709	+	0.150984i
$777$	0.549785	−	0.952255i	0.0197234	−	0.0341620i
$778$	−26.1982			−0.939250
$779$	−2.95836	+	2.34565i	−0.105994	+	0.0840418i
$780$		0			0
$781$	25.1356	−	43.5361i	0.899421	−	1.55784i
$782$	0.266308	−	0.461259i	0.00952315	−	0.0164946i
$783$	17.2751	+	29.9213i	0.617361	+	1.06930i
$784$	3.44956	−	5.97481i	0.123198	−	0.213386i
$785$		0			0
$786$	8.05896			0.287454
$787$	30.3141			1.08058			0.540291	−	0.841478i	$-0.318314\pi$
$787$	30.3141			1.08058			0.540291	+	0.841478i	$0.318314\pi$
$788$	−8.12970	−	14.0811i	−0.289609	−	0.501617i
$789$	−10.8695	−	18.8265i	−0.386964	−	0.670241i
$790$		0			0
$791$	−5.74435			−0.204246
$792$	−5.46266	−	9.46161i	−0.194107	−	0.336204i
$793$	−19.4387	+	33.6688i	−0.690288	+	1.19561i
$794$	15.0639	+	26.0914i	0.534597	+	0.925949i
$795$		0			0
$796$	6.89911	−	11.9496i	0.244533	−	0.423543i
$797$	0.460092			0.0162973			0.00814865	−	0.999967i	$-0.497406\pi$
$797$	0.460092			0.0162973			0.00814865	+	0.999967i	$0.497406\pi$
$798$	0.138183	+	0.934586i	0.00489164	+	0.0330840i
$799$	−1.73639			−0.0614292
$800$		0			0
$801$	−4.71371	+	8.16439i	−0.166551	+	0.288475i
$802$	1.08591	+	1.88085i	0.0383449	+	0.0664153i
$803$	−17.8060	+	30.8408i	−0.628359	+	1.08835i
$804$	−0.201654	−	0.349275i	−0.00711178	−	0.0123180i
$805$		0			0
$806$	−18.8010			−0.662238
$807$	−3.71733	−	6.43860i	−0.130856	−	0.226649i
$808$	1.25638	+	2.17611i	0.0441992	+	0.0765553i
$809$	43.3070			1.52259			0.761296	−	0.648404i	$-0.224563\pi$
$809$	43.3070			1.52259			0.761296	+	0.648404i	$0.224563\pi$
$810$		0			0
$811$	−15.9700	−	27.6609i	−0.560783	−	0.971305i	−0.997428	−	0.0716709i	$-0.977167\pi$
$811$	−15.9700	−	27.6609i	−0.560783	−	0.971305i	0.436645	−	0.899634i	$-0.356166\pi$
$812$	−1.45293	+	2.51655i	−0.0509880	+	0.0883137i
$813$	−4.07126	−	7.05162i	−0.142785	−	0.247311i
$814$	−10.9350	+	18.9400i	−0.383272	+	0.663847i
$815$		0			0
$816$	0.0913382			0.00319748
$817$	19.4822	−	15.4472i	0.681596	−	0.540430i
$818$	32.1664			1.12467
$819$	−2.53437	+	4.38965i	−0.0885579	+	0.153387i
$820$		0			0
$821$	−9.55092	−	16.5427i	−0.333329	−	0.577344i	0.649833	−	0.760077i	$-0.274839\pi$
$821$	−9.55092	−	16.5427i	−0.333329	−	0.577344i	−0.983162	+	0.182733i	$0.941505\pi$
$822$	−5.40136	+	9.35543i	−0.188394	+	0.326308i
$823$	−8.43860	−	14.6161i	−0.294151	−	0.509485i	0.680636	−	0.732622i	$-0.261704\pi$
$823$	−8.43860	−	14.6161i	−0.294151	−	0.509485i	−0.974787	+	0.223137i	$0.928370\pi$
$824$	−4.03297			−0.140495
$825$		0			0
$826$	−1.52688	−	2.64464i	−0.0531270	−	0.0920187i
$827$	11.9233	+	20.6518i	0.414615	+	0.718134i	0.995388	−	0.0959317i	$-0.0305830\pi$
$827$	11.9233	+	20.6518i	0.414615	+	0.718134i	−0.580773	+	0.814065i	$0.697250\pi$
$828$	−10.0845			−0.350460
$829$	−34.6508			−1.20347			−0.601735	−	0.798696i	$-0.705524\pi$
$829$	−34.6508			−1.20347			−0.601735	+	0.798696i	$0.705524\pi$
$830$		0			0
$831$	−5.42710	+	9.40001i	−0.188264	+	0.326083i
$832$	−3.14836	−	5.45312i	−0.109150	−	0.189053i
$833$	−0.461735	+	0.799749i	−0.0159982	+	0.0277097i
$834$	0.398289	−	0.689856i	0.0137916	−	0.0238878i
$835$		0			0
$836$	−2.74842	−	18.5886i	−0.0950561	−	0.642899i
$837$	−11.2761			−0.389758
$838$	4.99837	−	8.65743i	0.172666	−	0.299066i
$839$	4.08140	−	7.06919i	0.140906	−	0.244056i	−0.786932	−	0.617039i	$-0.788332\pi$
$839$	4.08140	−	7.06919i	0.140906	−	0.244056i	0.927838	+	0.372984i	$0.121665\pi$
$840$		0			0
$841$	−27.3494	+	47.3706i	−0.943084	+	1.63347i
$842$	19.0856	+	33.0572i	0.657732	+	1.13922i
$843$	14.3191			0.493177
$844$	−1.16892			−0.0402358
$845$		0			0
$846$	16.4383	+	28.4720i	0.565161	+	0.978888i
$847$	−2.40876			−0.0827659
$848$	7.92522			0.272153
$849$	−4.38823	−	7.60064i	−0.150604	−	0.260853i
$850$		0			0
$851$	10.0934	+	17.4823i	0.345998	+	0.599286i
$852$	3.97874	−	6.89138i	0.136309	−	0.236095i
$853$	11.6611	−	20.1976i	0.399269	−	0.691554i	−0.594367	−	0.804194i	$-0.702597\pi$
$853$	11.6611	−	20.1976i	0.399269	−	0.691554i	0.993636	+	0.112640i	$0.0359306\pi$
$854$	−1.96109			−0.0671072
$855$		0			0
$856$	−10.0000			−0.341793
$857$	−16.7728	+	29.0514i	−0.572949	+	0.992377i	0.423312	+	0.905984i	$0.360867\pi$
$857$	−16.7728	+	29.0514i	−0.572949	+	0.992377i	−0.996261	+	0.0863933i	$0.972466\pi$
$858$	−9.26131	+	16.0411i	−0.316176	+	0.547632i
$859$	−8.96416	−	15.5264i	−0.305853	−	0.529753i	0.671598	−	0.740916i	$-0.265608\pi$
$859$	−8.96416	−	15.5264i	−0.305853	−	0.529753i	−0.977451	+	0.211163i	$0.932275\pi$
$860$		0			0
$861$	0.0938641	+	0.162577i	0.00319888	+	0.00554062i
$862$	3.47298			0.118290
$863$	40.9267			1.39316			0.696580	−	0.717479i	$-0.254704\pi$
$863$	40.9267			1.39316			0.696580	+	0.717479i	$0.254704\pi$
$864$	−1.88825	−	3.27055i	−0.0642397	−	0.111266i
$865$		0			0
$866$	−11.0948			−0.377018
$867$	11.5881			0.393554
$868$	−0.474191	−	0.821322i	−0.0160951	−	0.0278775i
$869$	−7.16086	+	12.4030i	−0.242916	+	0.420742i
$870$		0			0
$871$	1.86079	−	3.22299i	0.0630506	−	0.109207i
$872$	2.93197	−	5.07832i	0.0992890	−	0.171974i
$873$	−12.3084			−0.416576
$874$	−16.1276	−	6.38195i	−0.545526	−	0.215873i
$875$		0			0
$876$	−2.81853	+	4.88184i	−0.0952294	+	0.164942i
$877$	−5.72299	+	9.91251i	−0.193252	+	0.334722i	−0.946326	−	0.323214i	$-0.895237\pi$
$877$	−5.72299	+	9.91251i	−0.193252	+	0.334722i	0.753074	+	0.657935i	$0.228570\pi$
$878$	6.51914	+	11.2915i	0.220010	+	0.381069i
$879$	−4.13783	+	7.16694i	−0.139566	+	0.241735i
$880$		0			0
$881$	−17.5970			−0.592860			−0.296430	−	0.955055i	$-0.595796\pi$
$881$	−17.5970			−0.592860			−0.296430	+	0.955055i	$0.595796\pi$
$882$	17.4849			0.588746
$883$	11.6528	+	20.1832i	0.392147	+	0.679218i	0.992732	−	0.120342i	$-0.0383992\pi$
$883$	11.6528	+	20.1832i	0.392147	+	0.679218i	−0.600586	+	0.799560i	$0.705066\pi$
$884$	0.421419	+	0.729919i	0.0141739	+	0.0245498i
$885$		0			0
$886$	15.0250			0.504775
$887$	2.19763	+	3.80640i	0.0737891	+	0.127806i	0.900559	−	0.434734i	$-0.143158\pi$
$887$	2.19763	+	3.80640i	0.0737891	+	0.127806i	−0.826770	+	0.562540i	$0.809824\pi$
$888$	−1.73092	+	2.99804i	−0.0580859	+	0.100608i
$889$	−2.84226	−	4.92294i	−0.0953263	−	0.165110i
$890$		0			0
$891$	10.8335	−	18.7641i	0.362934	−	0.628621i
$892$	6.31763			0.211530
$893$	8.27058	+	55.9370i	0.276765	+	1.87186i
$894$	8.29187			0.277322
$895$		0			0
$896$	0.158813	−	0.275072i	0.00530557	−	0.00918951i
$897$	8.54852	+	14.8065i	0.285427	+	0.494374i
$898$	−7.21254	+	12.4925i	−0.240686	+	0.416880i
$899$	−13.6583	−	23.6569i	−0.455530	−	0.789002i
$900$		0			0
$901$	−1.06082			−0.0353410
$902$	−1.86692	−	3.23361i	−0.0621618	−	0.107667i
$903$	−0.618140	−	1.07065i	−0.0205704	−	0.0356290i
$904$	18.0853			0.601508
$905$		0			0
$906$	−6.95350	−	12.0438i	−0.231014	−	0.400129i
$907$	−26.9577	+	46.6921i	−0.895115	+	1.55039i	−0.0614534	+	0.998110i	$0.519574\pi$
$907$	−26.9577	+	46.6921i	−0.895115	+	1.55039i	−0.833662	+	0.552275i	$0.813760\pi$
$908$	−1.88971	−	3.27307i	−0.0627122	−	0.108621i
$909$	−3.18412	+	5.51506i	−0.105611	+	0.182923i
$910$		0			0
$911$	−42.8496			−1.41967			−0.709835	−	0.704368i	$-0.751231\pi$
$911$	−42.8496			−1.41967			−0.709835	+	0.704368i	$0.751231\pi$
$912$	−0.435051	−	2.94241i	−0.0144060	−	0.0974330i
$913$	18.1362			0.600220
$914$	16.0887	−	27.8664i	0.532166	−	0.921738i
$915$		0			0
$916$	−2.71814	−	4.70795i	−0.0898098	−	0.155555i
$917$	−1.87561	+	3.24865i	−0.0619380	+	0.107280i
$918$	0.252750	+	0.437775i	0.00834198	+	0.0144487i
$919$	40.6599			1.34124			0.670622	−	0.741799i	$-0.266027\pi$
$919$	40.6599			1.34124			0.670622	+	0.741799i	$0.266027\pi$
$920$		0			0
$921$	6.19875	+	10.7365i	0.204256	+	0.353781i
$922$	7.75530	+	13.4326i	0.255407	+	0.442378i
$923$	73.4290			2.41694
$924$	−0.934337			−0.0307374
$925$		0			0
$926$	15.0739	−	26.1087i	0.495358	−	0.857985i
$927$	−5.11051	−	8.85166i	−0.167851	−	0.290727i
$928$	4.57435	−	7.92301i	0.150161	−	0.260086i
$929$	14.3215	−	24.8056i	0.469874	−	0.813846i	−0.529532	−	0.848290i	$-0.677633\pi$
$929$	14.3215	−	24.8056i	0.469874	−	0.813846i	0.999407	+	0.0344435i	$0.0109659\pi$
$930$		0			0
$931$	27.9628	+	11.0653i	0.916443	+	0.362650i
$932$	2.44922			0.0802270
$933$	6.64518	−	11.5098i	0.217553	−	0.376814i
$934$	17.2866	−	29.9412i	0.565634	−	0.979706i
$935$		0			0
$936$	7.97909	−	13.8202i	0.260805	−	0.451727i
$937$	13.9548	+	24.1704i	0.455884	+	0.789614i	0.998739	−	0.0502128i	$-0.0159899\pi$
$937$	13.9548	+	24.1704i	0.455884	+	0.789614i	−0.542855	+	0.839827i	$0.682657\pi$
$938$	0.187728			0.00612955
$939$	8.17467			0.266770
$940$		0			0
$941$	−14.3706	−	24.8907i	−0.468470	−	0.811413i	0.530881	−	0.847446i	$-0.321861\pi$
$941$	−14.3706	−	24.8907i	−0.468470	−	0.811413i	−0.999351	+	0.0360331i	$0.988528\pi$
$942$	−3.35893			−0.109440
$943$	−3.44648			−0.112233
$944$	4.80717	+	8.32627i	0.156460	+	0.270997i
$945$		0			0
$946$	12.2946	+	21.2948i	0.399731	+	0.692355i
$947$	15.2939	−	26.4899i	0.496986	−	0.860804i	−0.503008	−	0.864282i	$-0.667773\pi$
$947$	15.2939	−	26.4899i	0.496986	−	0.860804i	0.999994	+	0.00347712i	$0.00110680\pi$
$948$	−1.13350	+	1.96329i	−0.0368145	+	0.0637645i
$949$	−52.0169			−1.68854
$950$		0			0
$951$	0.770611			0.0249888
$952$	−0.0212577	+	0.0368194i	−0.000688965	+	0.00119332i
$953$	11.7597	−	20.3684i	0.380933	−	0.659796i	−0.610263	−	0.792199i	$-0.708936\pi$
$953$	11.7597	−	20.3684i	0.380933	−	0.659796i	0.991196	+	0.132403i	$0.0422694\pi$
$954$	10.0427	+	17.3945i	0.325144	+	0.563167i
$955$		0			0
$956$	4.72950	+	8.19173i	0.152963	+	0.264939i
$957$	−26.9121			−0.869945
$958$	30.8476			0.996642
$959$	−2.51418	−	4.35469i	−0.0811871	−	0.140620i
$960$		0			0
$961$	−22.0847			−0.712411
$962$	−31.9447			−1.02994
$963$	−12.6718	−	21.9482i	−0.408344	−	0.707272i
$964$	8.43540	−	14.6105i	0.271686	−	0.470574i
$965$		0			0
$966$	−0.431214	+	0.746884i	−0.0138741	+	0.0240306i
$967$	−0.318277	+	0.551272i	−0.0102351	+	0.0177277i	−0.871098	−	0.491110i	$-0.836591\pi$
$967$	−0.318277	+	0.551272i	−0.0102351	+	0.0177277i	0.860862	+	0.508838i	$0.169925\pi$
$968$	7.58363			0.243747
$969$	0.0582332	+	0.393852i	0.00187072	+	0.0126524i
$970$		0			0
$971$	−11.9491	+	20.6965i	−0.383466	+	0.664182i	−0.991555	−	0.129686i	$-0.958603\pi$
$971$	−11.9491	+	20.6965i	−0.383466	+	0.664182i	0.608089	+	0.793869i	$0.291936\pi$
$972$	7.37960	−	12.7819i	0.236701	−	0.409978i
$973$	0.185392	+	0.321108i	0.00594339	+	0.0102943i
$974$	15.3873	−	26.6515i	0.493040	−	0.853970i
$975$		0			0
$976$	6.17422			0.197632
$977$	7.29767			0.233473			0.116737	−	0.993163i	$-0.462757\pi$
$977$	7.29767			0.233473			0.116737	+	0.993163i	$0.462757\pi$
$978$	−0.490380	−	0.849362i	−0.0156806	−	0.0271596i
$979$	−8.01788	−	13.8874i	−0.256252	−	0.443842i
$980$		0			0
$981$	14.8614			0.474487
$982$	12.8571	+	22.2692i	0.410287	+	0.710638i
$983$	−24.6949	+	42.7727i	−0.787644	+	1.36424i	0.139763	+	0.990185i	$0.455366\pi$
$983$	−24.6949	+	42.7727i	−0.787644	+	1.36424i	−0.927407	+	0.374054i	$0.877968\pi$
$984$	−0.295518	−	0.511852i	−0.00942077	−	0.0163173i
$985$		0			0
$986$	−0.612294	+	1.06052i	−0.0194994	+	0.0337740i
$987$	2.81162			0.0894949
$988$	21.5067	−	17.0525i	0.684219	−	0.542511i
$989$	22.6967			0.721712
$990$		0			0
$991$	7.14580	−	12.3769i	0.226994	−	0.393165i	−0.729922	−	0.683531i	$-0.760444\pi$
$991$	7.14580	−	12.3769i	0.226994	−	0.393165i	0.956916	+	0.290366i	$0.0937769\pi$
$992$	1.49292	+	2.58582i	0.0474003	+	0.0820998i
$993$	−4.88169	+	8.45534i	−0.154916	+	0.268322i
$994$	1.85199	+	3.20774i	0.0587416	+	0.101743i
$995$		0			0
$996$	2.87080			0.0909649
$997$	−29.4280	−	50.9707i	−0.931993	−	1.61426i	−0.779910	−	0.625892i	$-0.784735\pi$
$997$	−29.4280	−	50.9707i	−0.931993	−	1.61426i	−0.152084	−	0.988368i	$-0.548598\pi$
$998$	0.201106	+	0.348326i	0.00636590	+	0.0110261i
$999$	−19.1591			−0.606167

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.e.n.201.3		10
5.2	odd	4		190.2.i.a.49.3	✓	20
5.3	odd	4		190.2.i.a.49.8	yes	20
5.4	even	2		950.2.e.o.201.3		10
15.2	even	4		1710.2.t.d.1189.10		20
15.8	even	4		1710.2.t.d.1189.3		20
19.7	even	3	inner	950.2.e.n.501.3		10
95.7	odd	12		190.2.i.a.159.8	yes	20
95.64	even	6		950.2.e.o.501.3		10
95.83	odd	12		190.2.i.a.159.3	yes	20
285.83	even	12		1710.2.t.d.919.10		20
285.197	even	12		1710.2.t.d.919.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.i.a.49.3	✓	20	5.2	odd	4
190.2.i.a.49.8	yes	20	5.3	odd	4
190.2.i.a.159.3	yes	20	95.83	odd	12
190.2.i.a.159.8	yes	20	95.7	odd	12
950.2.e.n.201.3		10	1.1	even	1	trivial
950.2.e.n.501.3		10	19.7	even	3	inner
950.2.e.o.201.3		10	5.4	even	2
950.2.e.o.501.3		10	95.64	even	6
1710.2.t.d.919.3		20	285.197	even	12
1710.2.t.d.919.10		20	285.83	even	12
1710.2.t.d.1189.3		20	15.8	even	4
1710.2.t.d.1189.10		20	15.2	even	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.341187 - 0.590953i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.341187 + 0.590953i) q^{6} -0.317626 q^{7} +1.00000 q^{8} +(1.26718 + 2.19482i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.341187 - 0.590953i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(0.341187 + 0.590953i) q^{6} -0.317626 q^{7} +1.00000 q^{8} +(1.26718 + 2.19482i) q^{9} -4.31087 q^{11} -0.682374 q^{12} +(-3.14836 - 5.45312i) q^{13} +(0.158813 - 0.275072i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(0.0669268 - 0.115921i) q^{17} -2.53437 q^{18} +(-4.05310 - 1.60387i) q^{19} +(-0.108370 + 0.187702i) q^{21} +(2.15544 - 3.73333i) q^{22} +(-1.98955 - 3.44600i) q^{23} +(0.341187 - 0.590953i) q^{24} +6.29672 q^{26} +3.77651 q^{27} +(0.158813 + 0.275072i) q^{28} +(4.57435 + 7.92301i) q^{29} -2.98584 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-1.47081 + 2.54753i) q^{33} +(0.0669268 + 0.115921i) q^{34} +(1.26718 - 2.19482i) q^{36} -5.07323 q^{37} +(3.41554 - 2.70815i) q^{38} -4.29672 q^{39} +(0.433073 - 0.750105i) q^{41} +(-0.108370 - 0.187702i) q^{42} +(-2.85199 + 4.93979i) q^{43} +(2.15544 + 3.73333i) q^{44} +3.97909 q^{46} +(-6.48617 - 11.2344i) q^{47} +(0.341187 + 0.590953i) q^{48} -6.89911 q^{49} +(-0.0456691 - 0.0791012i) q^{51} +(-3.14836 + 5.45312i) q^{52} +(-3.96261 - 6.86344i) q^{53} +(-1.88825 + 3.27055i) q^{54} -0.317626 q^{56} +(-2.33068 + 1.84797i) q^{57} -9.14871 q^{58} +(4.80717 - 8.32627i) q^{59} +(-3.08711 - 5.34704i) q^{61} +(1.49292 - 2.58582i) q^{62} +(-0.402490 - 0.697133i) q^{63} +1.00000 q^{64} +(-1.47081 - 2.54753i) q^{66} +(0.295518 + 0.511852i) q^{67} -0.133854 q^{68} -2.71523 q^{69} +(-5.83073 + 10.0991i) q^{71} +(1.26718 + 2.19482i) q^{72} +(4.13048 - 7.15420i) q^{73} +(2.53661 - 4.39354i) q^{74} +(0.637555 + 4.31202i) q^{76} +1.36924 q^{77} +(2.14836 - 3.72107i) q^{78} +(1.66112 - 2.87714i) q^{79} +(-2.51305 + 4.35273i) q^{81} +(0.433073 + 0.750105i) q^{82} -4.20708 q^{83} +0.216740 q^{84} +(-2.85199 - 4.93979i) q^{86} +6.24284 q^{87} -4.31087 q^{88} +(1.85992 + 3.22147i) q^{89} +(1.00000 + 1.73205i) q^{91} +(-1.98955 + 3.44600i) q^{92} +(-1.01873 + 1.76450i) q^{93} +12.9723 q^{94} -0.682374 q^{96} +(-2.42830 + 4.20594i) q^{97} +(3.44956 - 5.97481i) q^{98} +(-5.46266 - 9.46161i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 5 q^{2} - 5 q^{4} - 10 q^{7} + 10 q^{8} - 5 q^{9}+O(q^{10}) \) 10 * q - 5 * q^2 - 5 * q^4 - 10 * q^7 + 10 * q^8 - 5 * q^9	\( 10 q - 5 q^{2} - 5 q^{4} - 10 q^{7} + 10 q^{8} - 5 q^{9} - 6 q^{11} - 2 q^{13} + 5 q^{14} - 5 q^{16} + 4 q^{17} + 10 q^{18} + 11 q^{19} + 20 q^{21} + 3 q^{22} + 13 q^{23} + 4 q^{26} + 36 q^{27} + 5 q^{28} + 2 q^{29} - 8 q^{31} - 5 q^{32} + 2 q^{33} + 4 q^{34} - 5 q^{36} + 10 q^{37} - 13 q^{38} + 16 q^{39} + q^{41} + 20 q^{42} + 3 q^{44} - 26 q^{46} - 10 q^{47} - 20 q^{49} + 4 q^{51} - 2 q^{52} + 5 q^{53} - 18 q^{54} - 10 q^{56} - 10 q^{57} - 4 q^{58} + 22 q^{59} - 2 q^{61} + 4 q^{62} + 23 q^{63} + 10 q^{64} + 2 q^{66} + 4 q^{67} - 8 q^{68} - 24 q^{69} - 22 q^{71} - 5 q^{72} + 26 q^{73} - 5 q^{74} + 2 q^{76} + 10 q^{77} - 8 q^{78} + 2 q^{79} - 5 q^{81} + q^{82} + 12 q^{83} - 40 q^{84} - 20 q^{87} - 6 q^{88} - q^{89} + 10 q^{91} + 13 q^{92} + 6 q^{93} + 20 q^{94} + 8 q^{97} + 10 q^{98} + 13 q^{99}+O(q^{100}) \) 10 * q - 5 * q^2 - 5 * q^4 - 10 * q^7 + 10 * q^8 - 5 * q^9 - 6 * q^11 - 2 * q^13 + 5 * q^14 - 5 * q^16 + 4 * q^17 + 10 * q^18 + 11 * q^19 + 20 * q^21 + 3 * q^22 + 13 * q^23 + 4 * q^26 + 36 * q^27 + 5 * q^28 + 2 * q^29 - 8 * q^31 - 5 * q^32 + 2 * q^33 + 4 * q^34 - 5 * q^36 + 10 * q^37 - 13 * q^38 + 16 * q^39 + q^41 + 20 * q^42 + 3 * q^44 - 26 * q^46 - 10 * q^47 - 20 * q^49 + 4 * q^51 - 2 * q^52 + 5 * q^53 - 18 * q^54 - 10 * q^56 - 10 * q^57 - 4 * q^58 + 22 * q^59 - 2 * q^61 + 4 * q^62 + 23 * q^63 + 10 * q^64 + 2 * q^66 + 4 * q^67 - 8 * q^68 - 24 * q^69 - 22 * q^71 - 5 * q^72 + 26 * q^73 - 5 * q^74 + 2 * q^76 + 10 * q^77 - 8 * q^78 + 2 * q^79 - 5 * q^81 + q^82 + 12 * q^83 - 40 * q^84 - 20 * q^87 - 6 * q^88 - q^89 + 10 * q^91 + 13 * q^92 + 6 * q^93 + 20 * q^94 + 8 * q^97 + 10 * q^98 + 13 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more