LMFDB - Embedded newform 950.2.e.o.201.4

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			201.4
Root			$-0.664633 + 1.15118i$ of defining polynomial
Character	$\chi$	$=$	950.201
Dual form			950.2.e.o.501.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.664633 - 1.15118i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.664633 - 1.15118i) q^{6} +2.32927 q^{7} -1.00000 q^{8} +(0.616527 + 1.06786i) q^{9} +O(q^{10})$	\(q+(0.500000 - 0.866025i) q^{2} +(0.664633 - 1.15118i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.664633 - 1.15118i) q^{6} +2.32927 q^{7} -1.00000 q^{8} +(0.616527 + 1.06786i) q^{9} +6.39380 q^{11} -1.32927 q^{12} +(0.429320 + 0.743604i) q^{13} +(1.16463 - 2.01720i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.34506 + 4.06176i) q^{17} +1.23305 q^{18} +(3.75178 - 2.21903i) q^{19} +(1.54811 - 2.68140i) q^{21} +(3.19690 - 5.53719i) q^{22} +(-1.73531 - 3.00565i) q^{23} +(-0.664633 + 1.15118i) q^{24} +0.858640 q^{26} +5.62685 q^{27} +(-1.16463 - 2.01720i) q^{28} +(2.21048 + 3.82866i) q^{29} -8.25244 q^{31} +(0.500000 + 0.866025i) q^{32} +(4.24953 - 7.36040i) q^{33} +(2.34506 + 4.06176i) q^{34} +(0.616527 - 1.06786i) q^{36} -9.76821 q^{37} +(-0.0458469 - 4.35866i) q^{38} +1.14136 q^{39} +(-1.84506 + 3.19574i) q^{41} +(-1.54811 - 2.68140i) q^{42} +(3.56232 - 6.17012i) q^{43} +(-3.19690 - 5.53719i) q^{44} -3.47063 q^{46} +(-3.59684 - 6.22992i) q^{47} +(0.664633 + 1.15118i) q^{48} -1.57452 q^{49} +(3.11721 + 5.39916i) q^{51} +(0.429320 - 0.743604i) q^{52} +(-3.10295 - 5.37446i) q^{53} +(2.81343 - 4.87300i) q^{54} -2.32927 q^{56} +(-0.0609427 - 5.79381i) q^{57} +4.42096 q^{58} +(3.09395 - 5.35888i) q^{59} +(4.01037 + 6.94616i) q^{61} +(-4.12622 + 7.14682i) q^{62} +(1.43605 + 2.48732i) q^{63} +1.00000 q^{64} +(-4.24953 - 7.36040i) q^{66} +(-2.45257 - 4.24798i) q^{67} +4.69012 q^{68} -4.61338 q^{69} +(-1.10005 + 1.90535i) q^{71} +(-0.616527 - 1.06786i) q^{72} +(-2.32859 + 4.03323i) q^{73} +(-4.88411 + 8.45952i) q^{74} +(-3.79763 - 2.13962i) q^{76} +14.8928 q^{77} +(0.570680 - 0.988447i) q^{78} +(-5.79153 + 10.0312i) q^{79} +(1.89021 - 3.27394i) q^{81} +(1.84506 + 3.19574i) q^{82} -6.07809 q^{83} -3.09621 q^{84} +(-3.56232 - 6.17012i) q^{86} +5.87663 q^{87} -6.39380 q^{88} +(-5.64947 - 9.78517i) q^{89} +(1.00000 + 1.73205i) q^{91} +(-1.73531 + 3.00565i) q^{92} +(-5.48484 + 9.50002i) q^{93} -7.19369 q^{94} +1.32927 q^{96} +(-5.67500 + 9.82939i) q^{97} +(-0.787262 + 1.36358i) q^{98} +(3.94195 + 6.82766i) 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
$3$	0.664633	−	1.15118i	0.383726	−	0.664633i	−0.607866	−	0.794040i	$-0.707974\pi$
$3$	0.664633	−	1.15118i	0.383726	−	0.664633i	0.991592	+	0.129407i	$0.0413074\pi$
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$		0			0
$5$		0			0
$6$	−0.664633	−	1.15118i	−0.271335	−	0.469966i
$7$	2.32927			0.880379			0.440190	−	0.897905i	$-0.354911\pi$
$7$	2.32927			0.880379			0.440190	+	0.897905i	$0.354911\pi$
$8$	−1.00000			−0.353553
$9$	0.616527	+	1.06786i	0.205509	+	0.355952i
$10$		0			0
$11$	6.39380			1.92780			0.963901	−	0.266260i	$-0.0857880\pi$
$11$	6.39380			1.92780			0.963901	+	0.266260i	$0.0857880\pi$
$12$	−1.32927			−0.383726
$13$	0.429320	+	0.743604i	0.119072	+	0.206239i	0.919400	−	0.393324i	$-0.128675\pi$
$13$	0.429320	+	0.743604i	0.119072	+	0.206239i	−0.800328	+	0.599562i	$0.795341\pi$
$14$	1.16463	−	2.01720i	0.311261	−	0.539120i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.34506	+	4.06176i	−0.568760	+	0.985122i	0.427929	+	0.903813i	$0.359243\pi$
$17$	−2.34506	+	4.06176i	−0.568760	+	0.985122i	−0.996689	+	0.0813093i	$0.974090\pi$
$18$	1.23305			0.290634
$19$	3.75178	−	2.21903i	0.860718	−	0.509081i
$19$	3.75178	−	2.21903i	0.860718	−	0.509081i
$20$		0			0
$21$	1.54811	−	2.68140i	0.337824	−	0.585129i
$22$	3.19690	−	5.53719i	0.681581	−	1.18053i
$23$	−1.73531	−	3.00565i	−0.361838	−	0.626721i	0.626426	−	0.779481i	$-0.284517\pi$
$23$	−1.73531	−	3.00565i	−0.361838	−	0.626721i	−0.988263	+	0.152760i	$0.951184\pi$
$24$	−0.664633	+	1.15118i	−0.135668	+	0.234983i
$25$		0			0
$26$	0.858640			0.168393
$27$	5.62685			1.08289
$28$	−1.16463	−	2.01720i	−0.220095	−	0.381216i
$29$	2.21048	+	3.82866i	0.410476	+	0.710965i	0.994942	−	0.100453i	$-0.0320293\pi$
$29$	2.21048	+	3.82866i	0.410476	+	0.710965i	−0.584466	+	0.811418i	$0.698696\pi$
$30$		0			0
$31$	−8.25244			−1.48218			−0.741091	−	0.671405i	$-0.765691\pi$
$31$	−8.25244			−1.48218			−0.741091	+	0.671405i	$0.765691\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	4.24953	−	7.36040i	0.739748	−	1.28128i
$34$	2.34506	+	4.06176i	0.402174	+	0.696586i
$35$		0			0
$36$	0.616527	−	1.06786i	0.102754	−	0.177976i
$37$	−9.76821			−1.60588			−0.802942	−	0.596057i	$-0.796733\pi$
$37$	−9.76821			−1.60588			−0.802942	+	0.596057i	$0.796733\pi$
$38$	−0.0458469	−	4.35866i	−0.00743735	−	0.707068i
$39$	1.14136			0.182764
$40$		0			0
$41$	−1.84506	+	3.19574i	−0.288150	+	0.499090i	−0.973368	−	0.229248i	$-0.926373\pi$
$41$	−1.84506	+	3.19574i	−0.288150	+	0.499090i	0.685218	+	0.728338i	$0.259707\pi$
$42$	−1.54811	−	2.68140i	−0.238878	−	0.413749i
$43$	3.56232	−	6.17012i	0.543249	−	0.940934i	−0.455466	−	0.890253i	$-0.650527\pi$
$43$	3.56232	−	6.17012i	0.543249	−	0.940934i	0.998715	−	0.0506811i	$-0.0161392\pi$
$44$	−3.19690	−	5.53719i	−0.481951	−	0.834763i
$45$		0			0
$46$	−3.47063			−0.511716
$47$	−3.59684	−	6.22992i	−0.524654	−	0.908727i	−0.999588	−	0.0287055i	$-0.990862\pi$
$47$	−3.59684	−	6.22992i	−0.524654	−	0.908727i	0.474934	−	0.880021i	$-0.342472\pi$
$48$	0.664633	+	1.15118i	0.0959315	+	0.166158i
$49$	−1.57452			−0.224932
$50$		0			0
$51$	3.11721	+	5.39916i	0.436496	+	0.756033i
$52$	0.429320	−	0.743604i	0.0595360	−	0.103119i
$53$	−3.10295	−	5.37446i	−0.426222	−	0.738239i	0.570311	−	0.821429i	$-0.306823\pi$
$53$	−3.10295	−	5.37446i	−0.426222	−	0.738239i	−0.996534	+	0.0831897i	$0.973489\pi$
$54$	2.81343	−	4.87300i	0.382859	−	0.663131i
$55$		0			0
$56$	−2.32927			−0.311261
$57$	−0.0609427	−	5.79381i	−0.00807206	−	0.767409i
$58$	4.42096			0.580500
$59$	3.09395	−	5.35888i	0.402798	−	0.697667i	−0.591264	−	0.806478i	$-0.701371\pi$
$59$	3.09395	−	5.35888i	0.402798	−	0.697667i	0.994062	+	0.108811i	$0.0347043\pi$
$60$		0			0
$61$	4.01037	+	6.94616i	0.513475	+	0.889365i	0.999878	+	0.0156304i	$0.00497553\pi$
$61$	4.01037	+	6.94616i	0.513475	+	0.889365i	−0.486403	+	0.873735i	$0.661691\pi$
$62$	−4.12622	+	7.14682i	−0.524030	+	0.907647i
$63$	1.43605	+	2.48732i	0.180926	+	0.313373i
$64$	1.00000			0.125000
$65$		0			0
$66$	−4.24953	−	7.36040i	−0.523081	−	0.906002i
$67$	−2.45257	−	4.24798i	−0.299629	−	0.518973i	0.676422	−	0.736515i	$-0.263530\pi$
$67$	−2.45257	−	4.24798i	−0.299629	−	0.518973i	−0.976051	+	0.217541i	$0.930196\pi$
$68$	4.69012			0.568760
$69$	−4.61338			−0.555386
$70$		0			0
$71$	−1.10005	+	1.90535i	−0.130552	+	0.226124i	−0.923890	−	0.382659i	$-0.875008\pi$
$71$	−1.10005	+	1.90535i	−0.130552	+	0.226124i	0.793337	+	0.608782i	$0.208342\pi$
$72$	−0.616527	−	1.06786i	−0.0726584	−	0.125848i
$73$	−2.32859	+	4.03323i	−0.272540	+	0.472054i	−0.969512	−	0.245045i	$-0.921197\pi$
$73$	−2.32859	+	4.03323i	−0.272540	+	0.472054i	0.696971	+	0.717099i	$0.254531\pi$
$74$	−4.88411	+	8.45952i	−0.567766	+	0.983399i
$75$		0			0
$76$	−3.79763	−	2.13962i	−0.435618	−	0.245432i
$77$	14.8928			1.69720
$78$	0.570680	−	0.988447i	0.0646168	−	0.111920i
$79$	−5.79153	+	10.0312i	−0.651598	+	1.12860i	0.331137	+	0.943583i	$0.392568\pi$
$79$	−5.79153	+	10.0312i	−0.651598	+	1.12860i	−0.982735	+	0.185018i	$0.940766\pi$
$80$		0			0
$81$	1.89021	−	3.27394i	0.210023	−	0.363771i
$82$	1.84506	+	3.19574i	0.203753	+	0.352910i
$83$	−6.07809			−0.667157			−0.333579	−	0.942722i	$-0.608256\pi$
$83$	−6.07809			−0.667157			−0.333579	+	0.942722i	$0.608256\pi$
$84$	−3.09621			−0.337824
$85$		0			0
$86$	−3.56232	−	6.17012i	−0.384135	−	0.665341i
$87$	5.87663			0.630041
$88$	−6.39380			−0.681581
$89$	−5.64947	−	9.78517i	−0.598843	−	1.03723i	−0.992992	−	0.118180i	$-0.962294\pi$
$89$	−5.64947	−	9.78517i	−0.598843	−	1.03723i	0.394149	−	0.919046i	$-0.371039\pi$
$90$		0			0
$91$	1.00000	+	1.73205i	0.104828	+	0.181568i
$92$	−1.73531	+	3.00565i	−0.180919	+	0.313361i
$93$	−5.48484	+	9.50002i	−0.568751	+	0.985106i
$94$	−7.19369			−0.741972
$95$		0			0
$96$	1.32927			0.135668
$97$	−5.67500	+	9.82939i	−0.576209	+	0.998024i	0.419700	+	0.907663i	$0.362135\pi$
$97$	−5.67500	+	9.82939i	−0.576209	+	0.998024i	−0.995909	+	0.0903607i	$0.971198\pi$
$98$	−0.787262	+	1.36358i	−0.0795254	+	0.137742i
$99$	3.94195	+	6.82766i	0.396181	+	0.686205i
$100$		0			0
$101$	−1.11042	−	1.92331i	−0.110491	−	0.191377i	0.805477	−	0.592627i	$-0.201909\pi$
$101$	−1.11042	−	1.92331i	−0.110491	−	0.191377i	−0.915968	+	0.401250i	$0.868576\pi$
$102$	6.23441			0.617299
$103$	3.26464			0.321675			0.160837	−	0.986981i	$-0.448581\pi$
$103$	3.26464			0.321675			0.160837	+	0.986981i	$0.448581\pi$
$104$	−0.429320	−	0.743604i	−0.0420983	−	0.0729164i
$105$		0			0
$106$	−6.20589			−0.602770
$107$	10.0000			0.966736			0.483368	−	0.875417i	$-0.339413\pi$
$107$	10.0000			0.966736			0.483368	+	0.875417i	$0.339413\pi$
$108$	−2.81343	−	4.87300i	−0.270722	−	0.468904i
$109$	1.51717	−	2.62782i	0.145319	−	0.251699i	−0.784173	−	0.620542i	$-0.786913\pi$
$109$	1.51717	−	2.62782i	0.145319	−	0.251699i	0.929492	+	0.368843i	$0.120246\pi$
$110$		0			0
$111$	−6.49227	+	11.2449i	−0.616219	+	1.06732i
$112$	−1.16463	+	2.01720i	−0.110047	+	0.190608i
$113$	4.97420			0.467933			0.233966	−	0.972245i	$-0.424829\pi$
$113$	4.97420			0.467933			0.233966	+	0.972245i	$0.424829\pi$
$114$	−5.04806	−	2.84413i	−0.472794	−	0.266377i
$115$		0			0
$116$	2.21048	−	3.82866i	0.205238	−	0.355482i
$117$	−0.529375	+	0.916904i	−0.0489407	+	0.0847678i
$118$	−3.09395	−	5.35888i	−0.284821	−	0.493325i
$119$	−5.46226	+	9.46092i	−0.500725	+	0.867281i
$120$		0			0
$121$	29.8806			2.71642
$122$	8.02074			0.726164
$123$	2.45257	+	4.24798i	0.221141	+	0.383028i
$124$	4.12622	+	7.14682i	0.370545	+	0.641803i
$125$		0			0
$126$	2.87211			0.255868
$127$	−7.14949	−	12.3833i	−0.634415	−	1.09884i	−0.986639	−	0.162923i	$-0.947908\pi$
$127$	−7.14949	−	12.3833i	−0.634415	−	1.09884i	0.352224	−	0.935916i	$-0.385426\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	−4.73527	−	8.20172i	−0.416917	−	0.722121i
$130$		0			0
$131$	−1.18947	+	2.06022i	−0.103924	+	0.180002i	−0.913298	−	0.407292i	$-0.866473\pi$
$131$	−1.18947	+	2.06022i	−0.103924	+	0.180002i	0.809374	+	0.587294i	$0.199807\pi$
$132$	−8.49905			−0.739748
$133$	8.73890	−	5.16872i	0.757759	−	0.448185i
$134$	−4.90515			−0.423740
$135$		0			0
$136$	2.34506	−	4.06176i	0.201087	−	0.348293i
$137$	−4.54585	−	7.87364i	−0.388378	−	0.672690i	0.603854	−	0.797095i	$-0.293631\pi$
$137$	−4.54585	−	7.87364i	−0.388378	−	0.672690i	−0.992232	+	0.124405i	$0.960298\pi$
$138$	−2.30669	+	3.99531i	−0.196359	+	0.340103i
$139$	10.5329	+	18.2435i	0.893389	+	1.54739i	0.835786	+	0.549055i	$0.185012\pi$
$139$	10.5329	+	18.2435i	0.893389	+	1.54739i	0.0576028	+	0.998340i	$0.481654\pi$
$140$		0			0
$141$	−9.56232			−0.805293
$142$	1.10005	+	1.90535i	0.0923145	+	0.159893i
$143$	2.74498	+	4.75445i	0.229547	+	0.397587i
$144$	−1.23305			−0.102754
$145$		0			0
$146$	2.32859	+	4.03323i	0.192715	+	0.333793i
$147$	−1.04648	+	1.81256i	−0.0863122	+	0.149497i
$148$	4.88411	+	8.45952i	0.401471	+	0.695368i
$149$	3.17889	−	5.50600i	0.260425	−	0.451069i	−0.705930	−	0.708282i	$-0.749471\pi$
$149$	3.17889	−	5.50600i	0.260425	−	0.451069i	0.966355	+	0.257212i	$0.0828040\pi$
$150$		0			0
$151$	−3.05559			−0.248660			−0.124330	−	0.992241i	$-0.539678\pi$
$151$	−3.05559			−0.248660			−0.124330	+	0.992241i	$0.539678\pi$
$152$	−3.75178	+	2.21903i	−0.304310	+	0.179987i
$153$	−5.78317			−0.467541
$154$	7.44642	−	12.8976i	0.600050	−	1.03932i
$155$		0			0
$156$	−0.570680	−	0.988447i	−0.0456910	−	0.0791391i
$157$	−4.07136	+	7.05180i	−0.324930	+	0.562795i	−0.981498	−	0.191472i	$-0.938674\pi$
$157$	−4.07136	+	7.05180i	−0.324930	+	0.562795i	0.656568	+	0.754267i	$0.272007\pi$
$158$	5.79153	+	10.0312i	0.460749	+	0.798041i
$159$	−8.24928			−0.654210
$160$		0			0
$161$	−4.04200	−	7.00096i	−0.318554	−	0.551753i
$162$	−1.89021	−	3.27394i	−0.148509	−	0.257225i
$163$	−13.4100			−1.05035			−0.525177	−	0.850993i	$-0.676001\pi$
$163$	−13.4100			−1.05035			−0.525177	+	0.850993i	$0.676001\pi$
$164$	3.69012			0.288150
$165$		0			0
$166$	−3.03905	+	5.26378i	−0.235876	+	0.408549i
$167$	6.49232	+	11.2450i	0.502391	+	0.870166i	0.999996	+	0.00276265i	$0.000879380\pi$
$167$	6.49232	+	11.2450i	0.502391	+	0.870166i	−0.497606	+	0.867403i	$0.665787\pi$
$168$	−1.54811	+	2.68140i	−0.119439	+	0.206874i
$169$	6.13137	−	10.6198i	0.471644	−	0.816911i
$170$		0			0
$171$	4.68269	+	2.63827i	0.358094	+	0.201754i
$172$	−7.12464			−0.543249
$173$	−1.05780	+	1.83216i	−0.0804228	+	0.139296i	−0.903432	−	0.428732i	$-0.858960\pi$
$173$	−1.05780	+	1.83216i	−0.0804228	+	0.139296i	0.823009	+	0.568029i	$0.192294\pi$
$174$	2.93831	−	5.08931i	0.222753	−	0.385819i
$175$		0			0
$176$	−3.19690	+	5.53719i	−0.240975	+	0.417381i
$177$	−4.11268	−	7.12338i	−0.309128	−	0.535426i
$178$	−11.2989			−0.846892
$179$	−9.87938			−0.738420			−0.369210	−	0.929346i	$-0.620372\pi$
$179$	−9.87938			−0.738420			−0.369210	+	0.929346i	$0.620372\pi$
$180$		0			0
$181$	−7.53974	−	13.0592i	−0.560425	−	0.970684i	−0.997459	−	0.0712395i	$-0.977305\pi$
$181$	−7.53974	−	13.0592i	−0.560425	−	0.970684i	0.437034	−	0.899445i	$-0.356029\pi$
$182$	2.00000			0.148250
$183$	10.6617			0.788135
$184$	1.73531	+	3.00565i	0.127929	+	0.221579i
$185$		0			0
$186$	5.48484	+	9.50002i	0.402168	+	0.696575i
$187$	−14.9938	+	25.9701i	−1.09646	+	1.89912i
$188$	−3.59684	+	6.22992i	−0.262327	+	0.454363i
$189$	13.1064			0.953352
$190$		0			0
$191$	8.84192			0.639779			0.319889	−	0.947455i	$-0.396354\pi$
$191$	8.84192			0.639779			0.319889	+	0.947455i	$0.396354\pi$
$192$	0.664633	−	1.15118i	0.0479657	−	0.0830791i
$193$	−9.34642	+	16.1885i	−0.672770	+	1.16527i	0.304346	+	0.952562i	$0.401562\pi$
$193$	−9.34642	+	16.1885i	−0.672770	+	1.16527i	−0.977115	+	0.212710i	$0.931771\pi$
$194$	5.67500	+	9.82939i	0.407441	+	0.705709i
$195$		0			0
$196$	0.787262	+	1.36358i	0.0562330	+	0.0973984i
$197$	16.3169			1.16253			0.581267	−	0.813713i	$-0.302557\pi$
$197$	16.3169			1.16253			0.581267	+	0.813713i	$0.302557\pi$
$198$	7.88390			0.560284
$199$	1.57452	+	2.72715i	0.111615	+	0.193323i	0.916422	−	0.400214i	$-0.131064\pi$
$199$	1.57452	+	2.72715i	0.111615	+	0.193323i	−0.804807	+	0.593537i	$0.797731\pi$
$200$		0			0
$201$	−6.52024			−0.459902
$202$	−2.22085			−0.156258
$203$	5.14879	+	8.91797i	0.361374	+	0.625919i
$204$	3.11721	−	5.39916i	0.218248	−	0.378017i
$205$		0			0
$206$	1.63232	−	2.82726i	0.113729	−	0.196985i
$207$	2.13973	−	3.70613i	0.148722	−	0.257594i
$208$	−0.858640			−0.0595360
$209$	23.9882	−	14.1881i	1.65930	−	0.981408i
$210$		0			0
$211$	3.95415	−	6.84879i	0.272215	−	0.471490i	−0.697214	−	0.716863i	$-0.745577\pi$
$211$	3.95415	−	6.84879i	0.272215	−	0.471490i	0.969429	+	0.245373i	$0.0789104\pi$
$212$	−3.10295	+	5.37446i	−0.213111	+	0.369119i
$213$	1.46226	+	2.53272i	0.100193	+	0.173539i
$214$	5.00000	−	8.66025i	0.341793	−	0.592003i
$215$		0			0
$216$	−5.62685			−0.382859
$217$	−19.2221			−1.30488
$218$	−1.51717	−	2.62782i	−0.102756	−	0.177978i
$219$	3.09531	+	5.36123i	0.209162	+	0.362279i
$220$		0			0
$221$	−4.02712			−0.270894
$222$	6.49227	+	11.2449i	0.435733	+	0.754711i
$223$	4.16463	−	7.21336i	0.278884	−	0.483042i	−0.692223	−	0.721683i	$-0.743369\pi$
$223$	4.16463	−	7.21336i	0.278884	−	0.483042i	0.971108	+	0.238641i	$0.0767020\pi$
$224$	1.16463	+	2.01720i	0.0778153	+	0.134780i
$225$		0			0
$226$	2.48710	−	4.30778i	0.165439	−	0.286549i
$227$	11.3680			0.754523			0.377261	−	0.926107i	$-0.376866\pi$
$227$	11.3680			0.754523			0.377261	+	0.926107i	$0.376866\pi$
$228$	−4.98712	+	2.94968i	−0.330280	+	0.195348i
$229$	−2.25560			−0.149054			−0.0745270	−	0.997219i	$-0.523745\pi$
$229$	−2.25560			−0.149054			−0.0745270	+	0.997219i	$0.523745\pi$
$230$		0			0
$231$	9.89827	−	17.1443i	0.651259	−	1.12801i
$232$	−2.21048	−	3.82866i	−0.145125	−	0.251364i
$233$	−7.96900	+	13.8027i	−0.522067	+	0.904246i	0.477604	+	0.878575i	$0.341505\pi$
$233$	−7.96900	+	13.8027i	−0.522067	+	0.904246i	−0.999670	+	0.0256705i	$0.991828\pi$
$234$	0.529375	+	0.916904i	0.0346063	+	0.0599399i
$235$		0			0
$236$	−6.18791			−0.402798
$237$	7.69848	+	13.3342i	0.500070	+	0.866147i
$238$	5.46226	+	9.46092i	0.354066	+	0.613260i
$239$	6.63412			0.429126			0.214563	−	0.976710i	$-0.431167\pi$
$239$	6.63412			0.429126			0.214563	+	0.976710i	$0.431167\pi$
$240$		0			0
$241$	11.0397	+	19.1213i	0.711130	+	1.23171i	0.964433	+	0.264326i	$0.0851494\pi$
$241$	11.0397	+	19.1213i	0.711130	+	1.23171i	−0.253304	+	0.967387i	$0.581517\pi$
$242$	14.9403	−	25.8774i	0.960400	−	1.66346i
$243$	5.92769	+	10.2671i	0.380261	+	0.658632i
$244$	4.01037	−	6.94616i	0.256738	−	0.444683i
$245$		0			0
$246$	4.90515			0.312741
$247$	3.26080	+	1.83717i	0.207480	+	0.116896i
$248$	8.25244			0.524030
$249$	−4.03970	+	6.99696i	−0.256006	+	0.443415i
$250$		0			0
$251$	−4.72558	−	8.18494i	−0.298276	−	0.516629i	0.677466	−	0.735554i	$-0.263078\pi$
$251$	−4.72558	−	8.18494i	−0.298276	−	0.516629i	−0.975742	+	0.218926i	$0.929745\pi$
$252$	1.43605	−	2.48732i	0.0904630	−	0.156686i
$253$	−11.0952	−	19.2175i	−0.697552	−	1.20819i
$254$	−14.2990			−0.897198
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−13.3945	−	23.1999i	−0.835524	−	1.44717i	−0.893603	−	0.448859i	$-0.851831\pi$
$257$	−13.3945	−	23.1999i	−0.835524	−	1.44717i	0.0580783	−	0.998312i	$-0.481503\pi$
$258$	−9.47053			−0.589610
$259$	−22.7528			−1.41379
$260$		0			0
$261$	−2.72564	+	4.72095i	−0.168713	+	0.292219i
$262$	1.18947	+	2.06022i	0.0734854	+	0.127281i
$263$	7.19364	−	12.4598i	0.443579	−	0.768301i	−0.554373	−	0.832268i	$-0.687042\pi$
$263$	7.19364	−	12.4598i	0.443579	−	0.768301i	0.997952	+	0.0639670i	$0.0203752\pi$
$264$	−4.24953	+	7.36040i	−0.261540	+	0.453001i
$265$		0			0
$266$	−0.106790	−	10.1525i	−0.00654769	−	0.622488i
$267$	−15.0193			−0.919166
$268$	−2.45257	+	4.24798i	−0.149815	+	0.259487i
$269$	−6.44486	+	11.1628i	−0.392950	+	0.680609i	−0.992837	−	0.119475i	$-0.961879\pi$
$269$	−6.44486	+	11.1628i	−0.392950	+	0.680609i	0.599887	+	0.800085i	$0.295212\pi$
$270$		0			0
$271$	−10.0907	+	17.4776i	−0.612966	+	1.06169i	0.377772	+	0.925899i	$0.376690\pi$
$271$	−10.0907	+	17.4776i	−0.612966	+	1.06169i	−0.990738	+	0.135790i	$0.956643\pi$
$272$	−2.34506	−	4.06176i	−0.142190	−	0.246280i
$273$	2.65853			0.160902
$274$	−9.09169			−0.549249
$275$		0			0
$276$	2.30669	+	3.99531i	0.138846	+	0.240489i
$277$	−7.40098			−0.444682			−0.222341	−	0.974969i	$-0.571370\pi$
$277$	−7.40098			−0.444682			−0.222341	+	0.974969i	$0.571370\pi$
$278$	21.0658			1.26344
$279$	−5.08785	−	8.81242i	−0.304602	−	0.527586i
$280$		0			0
$281$	−1.36083	−	2.35703i	−0.0811805	−	0.140609i	0.822577	−	0.568654i	$-0.192536\pi$
$281$	−1.36083	−	2.35703i	−0.0811805	−	0.140609i	−0.903757	+	0.428045i	$0.859202\pi$
$282$	−4.78116	+	8.28121i	−0.284714	+	0.493139i
$283$	−10.2721	+	17.7918i	−0.610613	+	1.05761i	0.380524	+	0.924771i	$0.375744\pi$
$283$	−10.2721	+	17.7918i	−0.610613	+	1.05761i	−0.991137	+	0.132842i	$0.957590\pi$
$284$	2.20011			0.130552
$285$		0			0
$286$	5.48997			0.324629
$287$	−4.29763	+	7.44372i	−0.253681	+	0.439389i
$288$	−0.616527	+	1.06786i	−0.0363292	+	0.0629240i
$289$	−2.49860	−	4.32771i	−0.146977	−	0.254571i
$290$		0			0
$291$	7.54358	+	13.0659i	0.442213	+	0.765935i
$292$	4.65717			0.272540
$293$	−26.7315			−1.56167			−0.780836	−	0.624736i	$-0.785206\pi$
$293$	−26.7315			−1.56167			−0.780836	+	0.624736i	$0.785206\pi$
$294$	1.04648	+	1.81256i	0.0610319	+	0.105710i
$295$		0			0
$296$	9.76821			0.567766
$297$	35.9769			2.08759
$298$	−3.17889	−	5.50600i	−0.184148	−	0.318954i
$299$	1.49001	−	2.58077i	0.0861694	−	0.149250i
$300$		0			0
$301$	8.29759	−	14.3718i	0.478265	−	0.828379i
$302$	−1.52779	+	2.64622i	−0.0879147	+	0.152273i
$303$	−2.95210			−0.169594
$304$	0.0458469	+	4.35866i	0.00262950	+	0.249986i
$305$		0			0
$306$	−2.89158	+	5.00837i	−0.165301	+	0.286310i
$307$	−6.38026	+	11.0509i	−0.364141	+	0.630710i	−0.988638	−	0.150317i	$-0.951971\pi$
$307$	−6.38026	+	11.0509i	−0.364141	+	0.630710i	0.624497	+	0.781027i	$0.285304\pi$
$308$	−7.44642	−	12.8976i	−0.424299	−	0.734908i
$309$	2.16979	−	3.75818i	0.123435	−	0.213795i
$310$		0			0
$311$	−6.96646			−0.395031			−0.197516	−	0.980300i	$-0.563287\pi$
$311$	−6.96646			−0.395031			−0.197516	+	0.980300i	$0.563287\pi$
$312$	−1.14136			−0.0646168
$313$	13.0846	+	22.6632i	0.739585	+	1.28100i	0.952682	+	0.303968i	$0.0983115\pi$
$313$	13.0846	+	22.6632i	0.739585	+	1.28100i	−0.213097	+	0.977031i	$0.568355\pi$
$314$	4.07136	+	7.05180i	0.229760	+	0.397956i
$315$		0			0
$316$	11.5831			0.651598
$317$	4.37870	+	7.58413i	0.245932	+	0.425967i	0.962393	−	0.271660i	$-0.0875725\pi$
$317$	4.37870	+	7.58413i	0.245932	+	0.425967i	−0.716461	+	0.697627i	$0.754239\pi$
$318$	−4.12464	+	7.14408i	−0.231298	+	0.400620i
$319$	14.1334	+	24.4797i	0.791316	+	1.37060i
$320$		0			0
$321$	6.64633	−	11.5118i	0.370962	−	0.642525i
$322$	−8.08401			−0.450504
$323$	0.215028	+	20.4426i	0.0119645	+	1.13746i
$324$	−3.78042			−0.210023
$325$		0			0
$326$	−6.70501	+	11.6134i	−0.371356	+	0.643208i
$327$	−2.01672	−	3.49306i	−0.111525	−	0.193167i
$328$	1.84506	−	3.19574i	0.101876	−	0.176455i
$329$	−8.37800	−	14.5111i	−0.461894	−	0.800024i
$330$		0			0
$331$	−9.34738			−0.513779			−0.256889	−	0.966441i	$-0.582698\pi$
$331$	−9.34738			−0.513779			−0.256889	+	0.966441i	$0.582698\pi$
$332$	3.03905	+	5.26378i	0.166789	+	0.288888i
$333$	−6.02237	−	10.4310i	−0.330024	−	0.571618i
$334$	12.9846			0.710488
$335$		0			0
$336$	1.54811	+	2.68140i	0.0844561	+	0.146282i
$337$	4.87376	−	8.44159i	0.265490	−	0.459843i	−0.702202	−	0.711978i	$-0.747799\pi$
$337$	4.87376	−	8.44159i	0.265490	−	0.459843i	0.967692	+	0.252135i	$0.0811328\pi$
$338$	−6.13137	−	10.6198i	−0.333502	−	0.577643i
$339$	3.30601	−	5.72618i	0.179558	−	0.311003i
$340$		0			0
$341$	−52.7644			−2.85735
$342$	4.62615	−	2.73619i	0.250154	−	0.147956i
$343$	−19.9723			−1.07840
$344$	−3.56232	+	6.17012i	−0.192067	+	0.332670i
$345$		0			0
$346$	1.05780	+	1.83216i	0.0568675	+	0.0984975i
$347$	7.38162	−	12.7853i	0.396266	−	0.686353i	−0.596996	−	0.802244i	$-0.703639\pi$
$347$	7.38162	−	12.7853i	0.396266	−	0.686353i	0.993262	+	0.115891i	$0.0369724\pi$
$348$	−2.93831	−	5.08931i	−0.157510	−	0.272816i
$349$	14.8315			0.793913			0.396956	−	0.917837i	$-0.370066\pi$
$349$	14.8315			0.793913			0.396956	+	0.917837i	$0.370066\pi$
$350$		0			0
$351$	2.41572	+	4.18415i	0.128942	+	0.223333i
$352$	3.19690	+	5.53719i	0.170395	+	0.295133i
$353$	26.8115			1.42703			0.713516	−	0.700639i	$-0.247102\pi$
$353$	26.8115			1.42703			0.713516	+	0.700639i	$0.247102\pi$
$354$	−8.22537			−0.437173
$355$		0			0
$356$	−5.64947	+	9.78517i	−0.299421	+	0.518613i
$357$	7.26080	+	12.5761i	0.384282	+	0.665596i
$358$	−4.93969	+	8.55579i	−0.261071	+	0.452188i
$359$	−0.197846	+	0.342680i	−0.0104419	+	0.0180859i	−0.871199	−	0.490930i	$-0.836657\pi$
$359$	−0.197846	+	0.342680i	−0.0104419	+	0.0180859i	0.860757	+	0.509016i	$0.169990\pi$
$360$		0			0
$361$	9.15178	−	16.6507i	0.481673	−	0.876351i
$362$	−15.0795			−0.792560
$363$	19.8597	−	34.3979i	1.04236	−	1.80542i
$364$	1.00000	−	1.73205i	0.0524142	−	0.0907841i
$365$		0			0
$366$	5.33085	−	9.23330i	0.278648	−	0.482632i
$367$	−3.49227	−	6.04879i	−0.182295	−	0.315744i	0.760367	−	0.649494i	$-0.225019\pi$
$367$	−3.49227	−	6.04879i	−0.182295	−	0.315744i	−0.942662	+	0.333750i	$0.891686\pi$
$368$	3.47063			0.180919
$369$	−4.55011			−0.236870
$370$		0			0
$371$	−7.22758	−	12.5185i	−0.375237	−	0.649930i
$372$	10.9697			0.568751
$373$	2.52621			0.130802			0.0654012	−	0.997859i	$-0.479167\pi$
$373$	2.52621			0.130802			0.0654012	+	0.997859i	$0.479167\pi$
$374$	14.9938	+	25.9701i	0.775313	+	1.34288i
$375$		0			0
$376$	3.59684	+	6.22992i	0.185493	+	0.321283i
$377$	−1.89801	+	3.28744i	−0.0977523	+	0.169312i
$378$	6.55321	−	11.3505i	0.337061	−	0.583807i
$379$	−29.3075			−1.50543			−0.752713	−	0.658349i	$-0.771255\pi$
$379$	−29.3075			−1.50543			−0.752713	+	0.658349i	$0.771255\pi$
$380$		0			0
$381$	−19.0071			−0.973765
$382$	4.42096	−	7.65733i	0.226196	−	0.391783i
$383$	−3.11717	+	5.39911i	−0.159280	+	0.275881i	−0.934609	−	0.355676i	$-0.884251\pi$
$383$	−3.11717	+	5.39911i	−0.159280	+	0.275881i	0.775329	+	0.631557i	$0.217584\pi$
$384$	−0.664633	−	1.15118i	−0.0339169	−	0.0587458i
$385$		0			0
$386$	9.34642	+	16.1885i	0.475720	+	0.823971i
$387$	8.78506			0.446570
$388$	11.3500			0.576209
$389$	−13.2183	−	22.8947i	−0.670193	−	1.16081i	−0.977849	−	0.209311i	$-0.932878\pi$
$389$	−13.2183	−	22.8947i	−0.670193	−	1.16081i	0.307656	−	0.951498i	$-0.400455\pi$
$390$		0			0
$391$	16.2776			0.823196
$392$	1.57452			0.0795254
$393$	1.58112	+	2.73857i	0.0797567	+	0.138143i
$394$	8.15847	−	14.1309i	0.411018	−	0.711903i
$395$		0			0
$396$	3.94195	−	6.82766i	0.198090	−	0.343103i
$397$	4.36575	−	7.56171i	0.219111	−	0.379511i	−0.735426	−	0.677606i	$-0.763018\pi$
$397$	4.36575	−	7.56171i	0.219111	−	0.379511i	0.954536	+	0.298094i	$0.0963510\pi$
$398$	3.14905			0.157847
$399$	−0.141952	−	13.4953i	−0.00710648	−	0.675611i
$400$		0			0
$401$	1.58356	−	2.74281i	0.0790794	−	0.136969i	−0.823774	−	0.566919i	$-0.808135\pi$
$401$	1.58356	−	2.74281i	0.0790794	−	0.136969i	0.902853	+	0.429949i	$0.141469\pi$
$402$	−3.26012	+	5.64669i	−0.162600	+	0.281631i
$403$	−3.54294	−	6.13654i	−0.176486	−	0.305683i
$404$	−1.11042	+	1.92331i	−0.0552457	+	0.0956884i
$405$		0			0
$406$	10.2976			0.511061
$407$	−62.4560			−3.09583
$408$	−3.11721	−	5.39916i	−0.154325	−	0.267298i
$409$	−8.54431	−	14.7992i	−0.422489	−	0.731773i	0.573693	−	0.819070i	$-0.305510\pi$
$409$	−8.54431	−	14.7992i	−0.422489	−	0.731773i	−0.996182	+	0.0872978i	$0.972177\pi$
$410$		0			0
$411$	−12.0853			−0.596123
$412$	−1.63232	−	2.82726i	−0.0804187	−	0.139289i
$413$	7.20664	−	12.4823i	0.354615	−	0.614212i
$414$	−2.13973	−	3.70613i	−0.105162	−	0.182146i
$415$		0			0
$416$	−0.429320	+	0.743604i	−0.0210491	+	0.0364582i
$417$	28.0020			1.37127
$418$	−0.293136	−	27.8684i	−0.0143378	−	1.36309i
$419$	7.80296			0.381200			0.190600	−	0.981668i	$-0.438957\pi$
$419$	7.80296			0.381200			0.190600	+	0.981668i	$0.438957\pi$
$420$		0			0
$421$	−16.9845	+	29.4180i	−0.827773	+	1.43374i	0.0720091	+	0.997404i	$0.477059\pi$
$421$	−16.9845	+	29.4180i	−0.827773	+	1.43374i	−0.899782	+	0.436340i	$0.856274\pi$
$422$	−3.95415	−	6.84879i	−0.192485	−	0.333394i
$423$	4.43510	−	7.68182i	0.215642	−	0.373503i
$424$	3.10295	+	5.37446i	0.150692	+	0.261007i
$425$		0			0
$426$	2.92453			0.141694
$427$	9.34122	+	16.1795i	0.452053	+	0.782979i
$428$	−5.00000	−	8.66025i	−0.241684	−	0.418609i
$429$	7.29763			0.352333
$430$		0			0
$431$	−9.07565	−	15.7195i	−0.437158	−	0.757181i	0.560311	−	0.828283i	$-0.310682\pi$
$431$	−9.07565	−	15.7195i	−0.437158	−	0.757181i	−0.997469	+	0.0711019i	$0.977348\pi$
$432$	−2.81343	+	4.87300i	−0.135361	+	0.234452i
$433$	0.157154	+	0.272199i	0.00755234	+	0.0130810i	0.869777	−	0.493445i	$-0.164263\pi$
$433$	0.157154	+	0.272199i	0.00755234	+	0.0130810i	−0.862225	+	0.506526i	$0.830929\pi$
$434$	−9.61106	+	16.6468i	−0.461346	+	0.799074i
$435$		0			0
$436$	−3.03434			−0.145319
$437$	−13.1802	−	7.42583i	−0.630492	−	0.355226i
$438$	6.19062			0.295799
$439$	−4.33220	+	7.50359i	−0.206765	+	0.358127i	−0.950694	−	0.310132i	$-0.899627\pi$
$439$	−4.33220	+	7.50359i	−0.206765	+	0.358127i	0.743929	+	0.668259i	$0.232960\pi$
$440$		0			0
$441$	−0.970736	−	1.68136i	−0.0462255	−	0.0800650i
$442$	−2.01356	+	3.48759i	−0.0957753	+	0.165888i
$443$	−1.94419	−	3.36744i	−0.0923714	−	0.159992i	0.816137	−	0.577858i	$-0.196111\pi$
$443$	−1.94419	−	3.36744i	−0.0923714	−	0.159992i	−0.908509	+	0.417866i	$0.862778\pi$
$444$	12.9845			0.616219
$445$		0			0
$446$	−4.16463	−	7.21336i	−0.197201	−	0.341562i
$447$	−4.22559	−	7.31894i	−0.199864	−	0.346174i
$448$	2.32927			0.110047
$449$	32.9375			1.55442			0.777208	−	0.629243i	$-0.216635\pi$
$449$	32.9375			1.55442			0.777208	+	0.629243i	$0.216635\pi$
$450$		0			0
$451$	−11.7969	+	20.4329i	−0.555496	+	0.962147i
$452$	−2.48710	−	4.30778i	−0.116983	−	0.202621i
$453$	−2.03084	+	3.51752i	−0.0954174	+	0.165268i
$454$	5.68402	−	9.84500i	0.266764	−	0.462049i
$455$		0			0
$456$	0.0609427	+	5.79381i	0.00285390	+	0.271320i
$457$	−1.22533			−0.0573184			−0.0286592	−	0.999589i	$-0.509124\pi$
$457$	−1.22533			−0.0573184			−0.0286592	+	0.999589i	$0.509124\pi$
$458$	−1.12780	+	1.95341i	−0.0526986	+	0.0912766i
$459$	−13.1953	+	22.8549i	−0.615904	+	1.06678i
$460$		0			0
$461$	19.5927	−	33.9356i	0.912524	−	1.58054i	0.102038	−	0.994781i	$-0.467464\pi$
$461$	19.5927	−	33.9356i	0.912524	−	1.58054i	0.810486	−	0.585758i	$-0.199203\pi$
$462$	−9.89827	−	17.1443i	−0.460509	−	0.797626i
$463$	32.5754			1.51391			0.756953	−	0.653469i	$-0.226687\pi$
$463$	32.5754			1.51391			0.756953	+	0.653469i	$0.226687\pi$
$464$	−4.42096			−0.205238
$465$		0			0
$466$	7.96900	+	13.8027i	0.369157	+	0.639398i
$467$	16.9079			0.782406			0.391203	−	0.920304i	$-0.372059\pi$
$467$	16.9079			0.782406			0.391203	+	0.920304i	$0.372059\pi$
$468$	1.05875			0.0489407
$469$	−5.71269	−	9.89467i	−0.263788	−	0.456894i
$470$		0			0
$471$	5.41192	+	9.37371i	0.249368	+	0.431918i
$472$	−3.09395	+	5.35888i	−0.142411	+	0.246663i
$473$	22.7767	−	39.4505i	1.04728	−	1.81394i
$474$	15.3970			0.707206
$475$		0			0
$476$	10.9245			0.500725
$477$	3.82610	−	6.62700i	0.175185	−	0.303429i
$478$	3.31706	−	5.74532i	0.151719	−	0.262785i
$479$	−1.82570	−	3.16220i	−0.0834181	−	0.144484i	0.821298	−	0.570500i	$-0.193250\pi$
$479$	−1.82570	−	3.16220i	−0.0834181	−	0.144484i	−0.904716	+	0.426015i	$0.859917\pi$
$480$		0			0
$481$	−4.19369	−	7.26368i	−0.191216	−	0.331195i
$482$	22.0794			1.00569
$483$	−10.7458			−0.488950
$484$	−14.9403	−	25.8774i	−0.679106	−	1.17625i
$485$		0			0
$486$	11.8554			0.537771
$487$	13.7416			0.622691			0.311346	−	0.950297i	$-0.399220\pi$
$487$	13.7416			0.622691			0.311346	+	0.950297i	$0.399220\pi$
$488$	−4.01037	−	6.94616i	−0.181541	−	0.314438i
$489$	−8.91274	+	15.4373i	−0.403048	+	0.698099i
$490$		0			0
$491$	17.3839	−	30.1098i	0.784525	−	1.35884i	−0.144758	−	0.989467i	$-0.546240\pi$
$491$	17.3839	−	30.1098i	0.784525	−	1.35884i	0.929283	−	0.369369i	$-0.120426\pi$
$492$	2.45257	−	4.24798i	0.110571	−	0.191514i
$493$	−20.7348			−0.933849
$494$	3.22143	−	1.90535i	0.144939	−	0.0857258i
$495$		0			0
$496$	4.12622	−	7.14682i	0.185273	−	0.320902i
$497$	−2.56232	+	4.43807i	−0.114936	+	0.199075i
$498$	4.03970	+	6.99696i	0.181023	+	0.313541i
$499$	−8.31410	+	14.4005i	−0.372190	+	0.644653i	−0.989902	−	0.141752i	$-0.954726\pi$
$499$	−8.31410	+	14.4005i	−0.372190	+	0.644653i	0.617712	+	0.786405i	$0.288060\pi$
$500$		0			0
$501$	17.2600			0.771121
$502$	−9.45115			−0.421825
$503$	2.37970	+	4.12176i	0.106106	+	0.183780i	0.914189	−	0.405287i	$-0.132829\pi$
$503$	2.37970	+	4.12176i	0.106106	+	0.183780i	−0.808084	+	0.589068i	$0.799495\pi$
$504$	−1.43605	−	2.48732i	−0.0639670	−	0.110794i
$505$		0			0
$506$	−22.1905			−0.986487
$507$	−8.15022	−	14.1166i	−0.361964	−	0.626940i
$508$	−7.14949	+	12.3833i	−0.317207	+	0.549419i
$509$	1.41576	+	2.45217i	0.0627524	+	0.108690i	0.895695	−	0.444669i	$-0.146679\pi$
$509$	1.41576	+	2.45217i	0.0627524	+	0.108690i	−0.832942	+	0.553360i	$0.813345\pi$
$510$		0			0
$511$	−5.42390	+	9.39446i	−0.239939	+	0.415587i
$512$	−1.00000			−0.0441942
$513$	21.1107	−	12.4862i	0.932062	−	0.551278i
$514$	−26.7890			−1.18161
$515$		0			0
$516$	−4.73527	+	8.20172i	−0.208459	+	0.361061i
$517$	−22.9975	−	39.8328i	−1.01143	−	1.75185i
$518$	−11.3764	+	19.7045i	−0.499849	+	0.865764i
$519$	1.40609	+	2.43542i	0.0617206	+	0.106903i
$520$		0			0
$521$	4.92317			0.215688			0.107844	−	0.994168i	$-0.465605\pi$
$521$	4.92317			0.215688			0.107844	+	0.994168i	$0.465605\pi$
$522$	2.72564	+	4.72095i	0.119298	+	0.206630i
$523$	−14.4447	−	25.0190i	−0.631624	−	1.09400i	−0.987220	−	0.159365i	$-0.949055\pi$
$523$	−14.4447	−	25.0190i	−0.631624	−	1.09400i	0.355596	−	0.934640i	$-0.384278\pi$
$524$	2.37893			0.103924
$525$		0			0
$526$	−7.19364	−	12.4598i	−0.313658	−	0.543271i
$527$	19.3525	−	33.5194i	0.843006	−	1.46013i
$528$	4.24953	+	7.36040i	0.184937	+	0.320320i
$529$	5.47738	−	9.48710i	0.238147	−	0.412483i
$530$		0			0
$531$	7.63002			0.331115
$532$	−8.84569	−	4.98375i	−0.383509	−	0.216073i
$533$	−3.16848			−0.137242
$534$	−7.50965	+	13.0071i	−0.324974	+	0.562872i
$535$		0			0
$536$	2.45257	+	4.24798i	0.105935	+	0.183485i
$537$	−6.56616	+	11.3729i	−0.283351	+	0.490778i
$538$	6.44486	+	11.1628i	0.277858	+	0.481264i
$539$	−10.0672			−0.433624
$540$		0			0
$541$	−2.30730	−	3.99637i	−0.0991987	−	0.171817i	0.812154	−	0.583442i	$-0.198295\pi$
$541$	−2.30730	−	3.99637i	−0.0991987	−	0.171817i	−0.911353	+	0.411625i	$0.864961\pi$
$542$	10.0907	+	17.4776i	0.433433	+	0.750727i
$543$	−20.0446			−0.860198
$544$	−4.69012			−0.201087
$545$		0			0
$546$	1.32927	−	2.30235i	0.0568873	−	0.0985317i
$547$	12.1562	+	21.0552i	0.519763	+	0.900255i	0.999736	+	0.0229724i	$0.00731297\pi$
$547$	12.1562	+	21.0552i	0.519763	+	0.900255i	−0.479973	+	0.877283i	$0.659354\pi$
$548$	−4.54585	+	7.87364i	−0.194189	+	0.336345i
$549$	−4.94500	+	8.56500i	−0.211048	+	0.365545i
$550$		0			0
$551$	16.7892	+	9.45919i	0.715243	+	0.402975i
$552$	4.61338			0.196359
$553$	−13.4900	+	23.3654i	−0.573654	+	0.993597i
$554$	−3.70049	+	6.40943i	−0.157219	+	0.272311i
$555$		0			0
$556$	10.5329	−	18.2435i	0.446694	−	0.773697i
$557$	12.2154	+	21.1577i	0.517582	+	0.896479i	0.999791	+	0.0204227i	$0.00650119\pi$
$557$	12.2154	+	21.1577i	0.517582	+	0.896479i	−0.482209	+	0.876056i	$0.660165\pi$
$558$	−10.1757			−0.430772
$559$	6.11750			0.258743
$560$		0			0
$561$	19.9308	+	34.5211i	0.841478	+	1.45748i
$562$	−2.72167			−0.114807
$563$	19.7981			0.834390			0.417195	−	0.908817i	$-0.363013\pi$
$563$	19.7981			0.834390			0.417195	+	0.908817i	$0.363013\pi$
$564$	4.78116	+	8.28121i	0.201323	+	0.348702i
$565$		0			0
$566$	10.2721	+	17.7918i	0.431769	+	0.747845i
$567$	4.40280	−	7.62587i	0.184900	−	0.320256i
$568$	1.10005	−	1.90535i	0.0461573	−	0.0799467i
$569$	−39.9935			−1.67662			−0.838308	−	0.545197i	$-0.816455\pi$
$569$	−39.9935			−1.67662			−0.838308	+	0.545197i	$0.816455\pi$
$570$		0			0
$571$	−30.3255			−1.26908			−0.634542	−	0.772889i	$-0.718811\pi$
$571$	−30.3255			−1.26908			−0.634542	+	0.772889i	$0.718811\pi$
$572$	2.74498	−	4.75445i	0.114774	−	0.198794i
$573$	5.87663	−	10.1786i	0.245500	−	0.425218i
$574$	4.29763	+	7.44372i	0.179380	+	0.310695i
$575$		0			0
$576$	0.616527	+	1.06786i	0.0256886	+	0.0444940i
$577$	−31.8330			−1.32523			−0.662613	−	0.748962i	$-0.730552\pi$
$577$	−31.8330			−1.32523			−0.662613	+	0.748962i	$0.730552\pi$
$578$	−4.99721			−0.207856
$579$	12.4239	+	21.5188i	0.516318	+	0.894289i
$580$		0			0
$581$	−14.1575			−0.587352
$582$	15.0872			0.625383
$583$	−19.8396	−	34.3632i	−0.821673	−	1.42318i
$584$	2.32859	−	4.03323i	0.0963576	−	0.166896i
$585$		0			0
$586$	−13.3658	+	23.1502i	−0.552134	+	0.956324i
$587$	0.530771	−	0.919322i	0.0219073	−	0.0379445i	−0.854864	−	0.518852i	$-0.826359\pi$
$587$	0.530771	−	0.919322i	0.0219073	−	0.0379445i	0.876771	+	0.480908i	$0.159693\pi$
$588$	2.09296			0.0863122
$589$	−30.9614	+	18.3124i	−1.27574	+	0.754551i
$590$		0			0
$591$	10.8448	−	18.7837i	0.446094	−	0.772657i
$592$	4.88411	−	8.45952i	0.200736	−	0.347684i
$593$	−18.7747	−	32.5188i	−0.770985	−	1.33539i	−0.937024	−	0.349266i	$-0.886431\pi$
$593$	−18.7747	−	32.5188i	−0.770985	−	1.33539i	0.166039	−	0.986119i	$-0.446902\pi$
$594$	17.9885	−	31.1570i	0.738076	−	1.27839i
$595$		0			0
$596$	−6.35778			−0.260425
$597$	4.18592			0.171318
$598$	−1.49001	−	2.58077i	−0.0609310	−	0.105536i
$599$	5.02165	+	8.69775i	0.205179	+	0.355380i	0.950190	−	0.311672i	$-0.100889\pi$
$599$	5.02165	+	8.69775i	0.205179	+	0.355380i	−0.745011	+	0.667052i	$0.767556\pi$
$600$		0			0
$601$	7.56630			0.308636			0.154318	−	0.988021i	$-0.450682\pi$
$601$	7.56630			0.308636			0.154318	+	0.988021i	$0.450682\pi$
$602$	−8.29759	−	14.3718i	−0.338184	−	0.585753i
$603$	3.02415	−	5.23799i	0.123153	−	0.213307i
$604$	1.52779	+	2.64622i	0.0621651	+	0.107673i
$605$		0			0
$606$	−1.47605	+	2.55659i	−0.0599604	+	0.103854i
$607$	−30.8174			−1.25084			−0.625420	−	0.780288i	$-0.715072\pi$
$607$	−30.8174			−1.25084			−0.625420	+	0.780288i	$0.715072\pi$
$608$	3.79763	+	2.13962i	0.154014	+	0.0867732i
$609$	13.6882			0.554675
$610$		0			0
$611$	3.08839	−	5.34925i	0.124943	−	0.216408i
$612$	2.89158	+	5.00837i	0.116885	+	0.202451i
$613$	9.36510	−	16.2208i	0.378253	−	0.655153i	−0.612555	−	0.790428i	$-0.709858\pi$
$613$	9.36510	−	16.2208i	0.378253	−	0.655153i	0.990808	+	0.135275i	$0.0431916\pi$
$614$	6.38026	+	11.0509i	0.257486	+	0.445980i
$615$		0			0
$616$	−14.8928			−0.600050
$617$	23.1741	+	40.1386i	0.932952	+	1.61592i	0.778245	+	0.627960i	$0.216110\pi$
$617$	23.1741	+	40.1386i	0.932952	+	1.61592i	0.154707	+	0.987960i	$0.450557\pi$
$618$	−2.16979	−	3.75818i	−0.0872816	−	0.151176i
$619$	11.5591			0.464600			0.232300	−	0.972644i	$-0.425375\pi$
$619$	11.5591			0.464600			0.232300	+	0.972644i	$0.425375\pi$
$620$		0			0
$621$	−9.76435	−	16.9123i	−0.391830	−	0.678669i
$622$	−3.48323	+	6.03313i	−0.139665	+	0.241906i
$623$	−13.1591	−	22.7923i	−0.527209	−	0.913153i
$624$	−0.570680	+	0.988447i	−0.0228455	+	0.0395695i
$625$		0			0
$626$	26.1692			1.04593
$627$	−0.389655	−	37.0445i	−0.0155613	−	1.47941i
$628$	8.14272			0.324930
$629$	22.9070	−	39.6761i	0.913363	−	1.58199i
$630$		0			0
$631$	−22.4567	−	38.8962i	−0.893989	−	1.54843i	−0.835051	−	0.550173i	$-0.814562\pi$
$631$	−22.4567	−	38.8962i	−0.893989	−	1.54843i	−0.0589383	−	0.998262i	$-0.518772\pi$
$632$	5.79153	−	10.0312i	0.230375	−	0.399021i
$633$	−5.25612	−	9.10386i	−0.208912	−	0.361846i
$634$	8.75740			0.347801
$635$		0			0
$636$	4.12464	+	7.14408i	0.163553	+	0.283281i
$637$	−0.675974	−	1.17082i	−0.0267831	−	0.0463897i
$638$	28.2667			1.11909
$639$	−2.71285			−0.107319
$640$		0			0
$641$	17.3522	−	30.0549i	0.685371	−	1.18710i	−0.287949	−	0.957646i	$-0.592973\pi$
$641$	17.3522	−	30.0549i	0.685371	−	1.18710i	0.973320	−	0.229451i	$-0.0736932\pi$
$642$	−6.64633	−	11.5118i	−0.262310	−	0.454333i
$643$	−18.7485	+	32.4734i	−0.739369	+	1.28062i	0.213411	+	0.976963i	$0.431543\pi$
$643$	−18.7485	+	32.4734i	−0.739369	+	1.28062i	−0.952780	+	0.303662i	$0.901791\pi$
$644$	−4.04200	+	7.00096i	−0.159277	+	0.275876i
$645$		0			0
$646$	17.8113	+	10.0351i	0.700778	+	0.394825i
$647$	22.6592			0.890823			0.445412	−	0.895326i	$-0.353057\pi$
$647$	22.6592			0.890823			0.445412	+	0.895326i	$0.353057\pi$
$648$	−1.89021	+	3.27394i	−0.0742544	+	0.128612i
$649$	19.7821	−	34.2636i	0.776516	−	1.34496i
$650$		0			0
$651$	−12.7756	+	22.1281i	−0.500717	+	0.867267i
$652$	6.70501	+	11.6134i	0.262588	+	0.454817i
$653$	17.7667			0.695266			0.347633	−	0.937631i	$-0.386986\pi$
$653$	17.7667			0.695266			0.347633	+	0.937631i	$0.386986\pi$
$654$	−4.03344			−0.157720
$655$		0			0
$656$	−1.84506	−	3.19574i	−0.0720375	−	0.124773i
$657$	−5.74255			−0.224038
$658$	−16.7560			−0.653217
$659$	−0.991869	−	1.71797i	−0.0386377	−	0.0669225i	0.846060	−	0.533088i	$-0.178969\pi$
$659$	−0.991869	−	1.71797i	−0.0386377	−	0.0669225i	−0.884698	+	0.466165i	$0.845635\pi$
$660$		0			0
$661$	−13.1253	−	22.7337i	−0.510515	−	0.884237i	−0.999926	−	0.0121841i	$-0.996122\pi$
$661$	−13.1253	−	22.7337i	−0.510515	−	0.884237i	0.489411	−	0.872053i	$-0.337212\pi$
$662$	−4.67369	+	8.09507i	−0.181648	+	0.314624i
$663$	−2.67656	+	4.63593i	−0.103949	+	0.180045i
$664$	6.07809			0.235876
$665$		0			0
$666$	−12.0447			−0.466724
$667$	7.67175	−	13.2879i	0.297051	−	0.514508i
$668$	6.49232	−	11.2450i	0.251195	−	0.435083i
$669$	−5.53590	−	9.58846i	−0.214030	−	0.370711i
$670$		0			0
$671$	25.6415	+	44.4124i	0.989879	+	1.71452i
$672$	3.09621			0.119439
$673$	16.0432			0.618418			0.309209	−	0.950994i	$-0.399936\pi$
$673$	16.0432			0.618418			0.309209	+	0.950994i	$0.399936\pi$
$674$	−4.87376	−	8.44159i	−0.187730	−	0.325158i
$675$		0			0
$676$	−12.2627			−0.471644
$677$	48.5483			1.86586			0.932931	−	0.360056i	$-0.117243\pi$
$677$	48.5483			1.86586			0.932931	+	0.360056i	$0.117243\pi$
$678$	−3.30601	−	5.72618i	−0.126967	−	0.219913i
$679$	−13.2186	+	22.8953i	−0.507283	+	0.878640i
$680$		0			0
$681$	7.55556	−	13.0866i	0.289530	−	0.501480i
$682$	−26.3822	+	45.6953i	−1.01023	+	1.74976i
$683$	13.3802			0.511981			0.255990	−	0.966679i	$-0.417598\pi$
$683$	13.3802			0.511981			0.255990	+	0.966679i	$0.417598\pi$
$684$	−0.0565317	−	5.37446i	−0.00216155	−	0.205498i
$685$		0			0
$686$	−9.98617	+	17.2966i	−0.381274	+	0.660385i
$687$	−1.49914	+	2.59659i	−0.0571959	+	0.0990662i
$688$	3.56232	+	6.17012i	0.135812	+	0.235234i
$689$	2.66431	−	4.61473i	0.101502	−	0.175807i
$690$		0			0
$691$	−25.8354			−0.982825			−0.491413	−	0.870927i	$-0.663519\pi$
$691$	−25.8354			−0.982825			−0.491413	+	0.870927i	$0.663519\pi$
$692$	2.11559			0.0804228
$693$	9.18184	+	15.9034i	0.348789	+	0.604121i
$694$	−7.38162	−	12.7853i	−0.280202	−	0.485325i
$695$		0			0
$696$	−5.87663			−0.222753
$697$	−8.65354	−	14.9884i	−0.327776	−	0.567725i
$698$	7.41576	−	12.8445i	0.280691	−	0.486170i
$699$	10.5929	+	18.3475i	0.400661	+	0.693965i
$700$		0			0
$701$	−24.6167	+	42.6373i	−0.929758	+	1.61039i	−0.146034	+	0.989280i	$0.546651\pi$
$701$	−24.6167	+	42.6373i	−0.929758	+	1.61039i	−0.783724	+	0.621109i	$0.786682\pi$
$702$	4.83144			0.182351
$703$	−36.6482	+	21.6760i	−1.38221	+	0.817525i
$704$	6.39380			0.240975
$705$		0			0
$706$	13.4058	−	23.2194i	0.504532	−	0.873875i
$707$	−2.58647	−	4.47990i	−0.0972744	−	0.168484i
$708$	−4.11268	+	7.12338i	−0.154564	+	0.267713i
$709$	−5.44796	−	9.43614i	−0.204602	−	0.354382i	0.745404	−	0.666613i	$-0.232257\pi$
$709$	−5.44796	−	9.43614i	−0.204602	−	0.354382i	−0.950006	+	0.312232i	$0.898923\pi$
$710$		0			0
$711$	−14.2825			−0.535637
$712$	5.64947	+	9.78517i	0.211723	+	0.366715i
$713$	14.3206	+	24.8039i	0.536309	+	0.928915i
$714$	14.5216			0.543457
$715$		0			0
$716$	4.93969	+	8.55579i	0.184605	+	0.319745i
$717$	4.40925	−	7.63705i	0.164667	−	0.285211i
$718$	0.197846	+	0.342680i	0.00738355	+	0.0127887i
$719$	16.9141	−	29.2961i	0.630789	−	1.09256i	−0.356602	−	0.934257i	$-0.616065\pi$
$719$	16.9141	−	29.2961i	0.630789	−	1.09256i	0.987391	−	0.158302i	$-0.0506020\pi$
$720$		0			0
$721$	7.60422			0.283196
$722$	−9.84402	−	16.2510i	−0.366356	−	0.604800i
$723$	29.3494			1.09152
$724$	−7.53974	+	13.0592i	−0.280212	+	0.485342i
$725$		0			0
$726$	−19.8597	−	34.3979i	−0.737061	−	1.27663i
$727$	−25.4674	+	44.1108i	−0.944533	+	1.63598i	−0.187848	+	0.982198i	$0.560151\pi$
$727$	−25.4674	+	44.1108i	−0.944533	+	1.63598i	−0.756684	+	0.653780i	$0.773182\pi$
$728$	−1.00000	−	1.73205i	−0.0370625	−	0.0641941i
$729$	27.1002			1.00371
$730$		0			0
$731$	16.7077	+	28.9386i	0.617957	+	1.07033i
$732$	−5.33085	−	9.23330i	−0.197034	−	0.341272i
$733$	30.8270			1.13862			0.569310	−	0.822123i	$-0.307210\pi$
$733$	30.8270			1.13862			0.569310	+	0.822123i	$0.307210\pi$
$734$	−6.98454			−0.257804
$735$		0			0
$736$	1.73531	−	3.00565i	0.0639645	−	0.110790i
$737$	−15.6813	−	27.1607i	−0.577626	−	1.00048i
$738$	−2.27506	+	3.94052i	−0.0837460	+	0.145052i
$739$	18.8645	−	32.6742i	0.693941	−	1.20194i	−0.276596	−	0.960986i	$-0.589206\pi$
$739$	18.8645	−	32.6742i	0.693941	−	1.20194i	0.970536	−	0.240954i	$-0.0774604\pi$
$740$		0			0
$741$	4.28214	−	2.53272i	0.157308	−	0.0930417i
$742$	−14.4552			−0.530666
$743$	−16.3990	+	28.4038i	−0.601619	+	1.04204i	0.390957	+	0.920409i	$0.372144\pi$
$743$	−16.3990	+	28.4038i	−0.601619	+	1.04204i	−0.992576	+	0.121626i	$0.961189\pi$
$744$	5.48484	−	9.50002i	0.201084	−	0.348288i
$745$		0			0
$746$	1.26311	−	2.18777i	0.0462456	−	0.0800998i
$747$	−3.74731	−	6.49053i	−0.137107	−	0.237476i
$748$	29.9877			1.09646
$749$	23.2927			0.851095
$750$		0			0
$751$	−2.19685	−	3.80505i	−0.0801641	−	0.138848i	0.823156	−	0.567815i	$-0.192211\pi$
$751$	−2.19685	−	3.80505i	−0.0801641	−	0.138848i	−0.903320	+	0.428967i	$0.858878\pi$
$752$	7.19369			0.262327
$753$	−12.5631			−0.457824
$754$	1.89801	+	3.28744i	0.0691213	+	0.119722i
$755$		0			0
$756$	−6.55321	−	11.3505i	−0.238338	−	0.412814i
$757$	−25.4884	+	44.1472i	−0.926391	+	1.60456i	−0.137082	+	0.990560i	$0.543773\pi$
$757$	−25.4884	+	44.1472i	−0.926391	+	1.60456i	−0.789309	+	0.613997i	$0.789561\pi$
$758$	−14.6538	+	25.3811i	−0.532248	+	0.921881i
$759$	−29.4970			−1.07067
$760$		0			0
$761$	10.5364			0.381945			0.190973	−	0.981595i	$-0.438836\pi$
$761$	10.5364			0.381945			0.190973	+	0.981595i	$0.438836\pi$
$762$	−9.50357	+	16.4607i	−0.344278	+	0.596307i
$763$	3.53389	−	6.12088i	0.127935	−	0.221591i
$764$	−4.42096	−	7.65733i	−0.159945	−	0.277032i
$765$		0			0
$766$	3.11717	+	5.39911i	0.112628	+	0.195078i
$767$	5.31318			0.191848
$768$	−1.32927			−0.0479657
$769$	22.2243	+	38.4936i	0.801429	+	1.38812i	0.918676	+	0.395013i	$0.129260\pi$
$769$	22.2243	+	38.4936i	0.801429	+	1.38812i	−0.117246	+	0.993103i	$0.537407\pi$
$770$		0			0
$771$	−35.6096			−1.28245
$772$	18.6928			0.672770
$773$	23.1902	+	40.1667i	0.834095	+	1.44469i	0.894766	+	0.446536i	$0.147343\pi$
$773$	23.1902	+	40.1667i	0.834095	+	1.44469i	−0.0606710	+	0.998158i	$0.519324\pi$
$774$	4.39253	−	7.60809i	0.157886	−	0.273467i
$775$		0			0
$776$	5.67500	−	9.82939i	0.203721	−	0.352855i
$777$	−15.1222	+	26.1925i	−0.542507	+	0.939649i
$778$	−26.4365			−0.947796
$779$	0.169181	+	16.0840i	0.00606152	+	0.576268i
$780$		0			0
$781$	−7.03353	+	12.1824i	−0.251679	+	0.435921i
$782$	8.13882	−	14.0969i	0.291044	−	0.504102i
$783$	12.4380	+	21.5433i	0.444499	+	0.769895i
$784$	0.787262	−	1.36358i	0.0281165	−	0.0486992i
$785$		0			0
$786$	3.16223			0.112793
$787$	13.6958			0.488204			0.244102	−	0.969750i	$-0.421507\pi$
$787$	13.6958			0.488204			0.244102	+	0.969750i	$0.421507\pi$
$788$	−8.15847	−	14.1309i	−0.290633	−	0.503392i
$789$	−9.56226	−	16.5623i	−0.340425	−	0.589634i
$790$		0			0
$791$	11.5862			0.411959
$792$	−3.94195	−	6.82766i	−0.140071	−	0.242610i
$793$	−3.44346	+	5.96425i	−0.122281	+	0.211797i
$794$	−4.36575	−	7.56171i	−0.154935	−	0.268355i
$795$		0			0
$796$	1.57452	−	2.72715i	0.0558075	−	0.0966614i
$797$	−30.5751			−1.08303			−0.541513	−	0.840692i	$-0.682148\pi$
$797$	−30.5751			−1.08303			−0.541513	+	0.840692i	$0.682148\pi$
$798$	−11.7583	−	6.62473i	−0.416238	−	0.234513i
$799$	33.7392			1.19361
$800$		0			0
$801$	6.96610	−	12.0656i	0.246135	−	0.426319i
$802$	−1.58356	−	2.74281i	−0.0559175	−	0.0968520i
$803$	−14.8885	+	25.7877i	−0.525404	+	0.910027i
$804$	3.26012	+	5.64669i	0.114976	+	0.199144i
$805$		0			0
$806$	−7.08587			−0.249589
$807$	8.56693	+	14.8384i	0.301570	+	0.522335i
$808$	1.11042	+	1.92331i	0.0390646	+	0.0676619i
$809$	−27.5436			−0.968381			−0.484191	−	0.874963i	$-0.660886\pi$
$809$	−27.5436			−0.968381			−0.484191	+	0.874963i	$0.660886\pi$
$810$		0			0
$811$	9.07845	+	15.7243i	0.318787	+	0.552156i	0.980235	−	0.197835i	$-0.0633911\pi$
$811$	9.07845	+	15.7243i	0.318787	+	0.552156i	−0.661448	+	0.749991i	$0.730058\pi$
$812$	5.14879	−	8.91797i	0.180687	−	0.312959i
$813$	13.4132	+	23.2324i	0.470422	+	0.814795i
$814$	−31.2280	+	54.0885i	−1.09454	+	1.89580i
$815$		0			0
$816$	−6.23441			−0.218248
$817$	−0.326643	−	31.0539i	−0.0114278	−	1.08644i
$818$	−17.0886			−0.597490
$819$	−1.23305	+	2.13571i	−0.0430864	+	0.0746278i
$820$		0			0
$821$	12.2072	+	21.1436i	0.426036	+	0.737916i	0.996517	−	0.0833952i	$-0.0265764\pi$
$821$	12.2072	+	21.1436i	0.426036	+	0.737916i	−0.570481	+	0.821311i	$0.693243\pi$
$822$	−6.04264	+	10.4662i	−0.210761	+	0.365049i
$823$	5.62916	+	9.74999i	0.196220	+	0.339863i	0.947300	−	0.320348i	$-0.103800\pi$
$823$	5.62916	+	9.74999i	0.196220	+	0.339863i	−0.751080	+	0.660212i	$0.770467\pi$
$824$	−3.26464			−0.113729
$825$		0			0
$826$	−7.20664	−	12.4823i	−0.250751	−	0.434313i
$827$	27.1179	+	46.9696i	0.942983	+	1.63329i	0.759740	+	0.650227i	$0.225326\pi$
$827$	27.1179	+	46.9696i	0.942983	+	1.63329i	0.183243	+	0.983068i	$0.441340\pi$
$828$	−4.27947			−0.148722
$829$	1.30919			0.0454701			0.0227350	−	0.999742i	$-0.492763\pi$
$829$	1.30919			0.0454701			0.0227350	+	0.999742i	$0.492763\pi$
$830$		0			0
$831$	−4.91893	+	8.51984i	−0.170636	+	0.295550i
$832$	0.429320	+	0.743604i	0.0148840	+	0.0257798i
$833$	3.69235	−	6.39534i	0.127932	−	0.221585i
$834$	14.0010	−	24.2505i	0.484816	−	0.839725i
$835$		0			0
$836$	−24.2813	−	13.6803i	−0.839786	−	0.473144i
$837$	−46.4352			−1.60504
$838$	3.90148	−	6.75756i	0.134774	−	0.233436i
$839$	14.7642	−	25.5723i	0.509716	−	0.882854i	−0.490220	−	0.871598i	$-0.663084\pi$
$839$	14.7642	−	25.5723i	0.509716	−	0.882854i	0.999937	−	0.0112559i	$-0.00358294\pi$
$840$		0			0
$841$	4.72756	−	8.18837i	0.163019	−	0.282358i
$842$	16.9845	+	29.4180i	0.585324	+	1.01381i
$843$	−3.61782			−0.124604
$844$	−7.90831			−0.272215
$845$		0			0
$846$	−4.43510	−	7.68182i	−0.152482	−	0.264107i
$847$	69.5999			2.39148
$848$	6.20589			0.213111
$849$	13.6543	+	23.6500i	0.468616	+	0.811667i
$850$		0			0
$851$	16.9509	+	29.3598i	0.581069	+	1.00644i
$852$	1.46226	−	2.53272i	0.0500964	−	0.0867694i
$853$	−4.20847	+	7.28928i	−0.144095	+	0.249580i	−0.929035	−	0.369992i	$-0.879361\pi$
$853$	−4.20847	+	7.28928i	−0.144095	+	0.249580i	0.784940	+	0.619572i	$0.212694\pi$
$854$	18.6824			0.639300
$855$		0			0
$856$	−10.0000			−0.341793
$857$	−6.82088	+	11.8141i	−0.232997	+	0.403562i	−0.958689	−	0.284458i	$-0.908187\pi$
$857$	−6.82088	+	11.8141i	−0.232997	+	0.403562i	0.725692	+	0.688020i	$0.241520\pi$
$858$	3.64881	−	6.31993i	0.124568	−	0.215759i
$859$	7.70524	+	13.3459i	0.262899	+	0.455355i	0.967011	−	0.254734i	$-0.0819879\pi$
$859$	7.70524	+	13.3459i	0.262899	+	0.455355i	−0.704112	+	0.710089i	$0.748655\pi$
$860$		0			0
$861$	5.71269	+	9.89467i	0.194688	+	0.337210i
$862$	−18.1513			−0.618235
$863$	−45.4425			−1.54688			−0.773440	−	0.633869i	$-0.781466\pi$
$863$	−45.4425			−1.54688			−0.773440	+	0.633869i	$0.781466\pi$
$864$	2.81343	+	4.87300i	0.0957147	+	0.165783i
$865$		0			0
$866$	0.314308			0.0106806
$867$	−6.64261			−0.225595
$868$	9.61106	+	16.6468i	0.326221	+	0.565031i
$869$	−37.0299	+	64.1376i	−1.25615	+	2.17572i
$870$		0			0
$871$	2.10588	−	3.64749i	0.0713549	−	0.123590i
$872$	−1.51717	+	2.62782i	−0.0513779	+	0.0889891i
$873$	−13.9952			−0.473665
$874$	−13.0210	+	7.70143i	−0.440443	+	0.260505i
$875$		0			0
$876$	3.09531	−	5.36123i	0.104581	−	0.181139i
$877$	18.7041	−	32.3964i	0.631591	−	1.09395i	−0.355635	−	0.934625i	$-0.615735\pi$
$877$	18.7041	−	32.3964i	0.631591	−	1.09395i	0.987226	−	0.159323i	$-0.0509312\pi$
$878$	4.33220	+	7.50359i	0.146205	+	0.253234i
$879$	−17.7666	+	30.7727i	−0.599254	+	1.03794i
$880$		0			0
$881$	3.04062			0.102441			0.0512206	−	0.998687i	$-0.483689\pi$
$881$	3.04062			0.102441			0.0512206	+	0.998687i	$0.483689\pi$
$882$	−1.94147			−0.0653728
$883$	4.07515	+	7.05837i	0.137140	+	0.237533i	0.926413	−	0.376509i	$-0.122876\pi$
$883$	4.07515	+	7.05837i	0.137140	+	0.237533i	−0.789273	+	0.614042i	$0.789542\pi$
$884$	2.01356	+	3.48759i	0.0677234	+	0.117300i
$885$		0			0
$886$	−3.88838			−0.130633
$887$	−23.0769	−	39.9704i	−0.774847	−	1.34207i	−0.934881	−	0.354963i	$-0.884494\pi$
$887$	−23.0769	−	39.9704i	−0.774847	−	1.34207i	0.160034	−	0.987112i	$-0.448840\pi$
$888$	6.49227	−	11.2449i	0.217866	−	0.377356i
$889$	−16.6531	−	28.8439i	−0.558526	−	0.967395i
$890$		0			0
$891$	12.0856	−	20.9329i	0.404883	−	0.701278i
$892$	−8.32927			−0.278884
$893$	−27.3190	−	15.3918i	−0.914195	−	0.515067i
$894$	−8.45118			−0.282650
$895$		0			0
$896$	1.16463	−	2.01720i	0.0389076	−	0.0673900i
$897$	−1.98062	−	3.43053i	−0.0661309	−	0.114542i
$898$	16.4687	−	28.5247i	0.549569	−	0.951882i
$899$	−18.2418	−	31.5958i	−0.608400	−	1.05378i
$900$		0			0
$901$	29.1064			0.969674
$902$	11.7969	+	20.4329i	0.392795	+	0.680341i
$903$	−11.0297	−	19.1040i	−0.367045	−	0.635741i
$904$	−4.97420			−0.165439
$905$		0			0
$906$	2.03084	+	3.51752i	0.0674703	+	0.116862i
$907$	15.6360	−	27.0823i	0.519184	−	0.899252i	−0.480568	−	0.876958i	$-0.659569\pi$
$907$	15.6360	−	27.0823i	0.519184	−	0.899252i	0.999751	−	0.0222948i	$-0.00709723\pi$
$908$	−5.68402	−	9.84500i	−0.188631	−	0.326718i
$909$	1.36921	−	2.37155i	0.0454140	−	0.0786593i
$910$		0			0
$911$	40.3430			1.33662			0.668312	−	0.743881i	$-0.267017\pi$
$911$	40.3430			1.33662			0.668312	+	0.743881i	$0.267017\pi$
$912$	5.04806	+	2.84413i	0.167158	+	0.0941785i
$913$	−38.8621			−1.28615
$914$	−0.612664	+	1.06116i	−0.0202651	+	0.0351002i
$915$		0			0
$916$	1.12780	+	1.95341i	0.0372635	+	0.0645423i
$917$	−2.77058	+	4.79879i	−0.0914927	+	0.158470i
$918$	13.1953	+	22.8549i	0.435510	+	0.754325i
$919$	33.5859			1.10790			0.553948	−	0.832552i	$-0.313121\pi$
$919$	33.5859			1.10790			0.553948	+	0.832552i	$0.313121\pi$
$920$		0			0
$921$	8.48106	+	14.6896i	0.279460	+	0.484040i
$922$	−19.5927	−	33.9356i	−0.645252	−	1.11761i
$923$	−1.88910			−0.0621805
$924$	−19.7965			−0.651259
$925$		0			0
$926$	16.2877	−	28.2111i	0.535247	−	0.927075i
$927$	2.01274	+	3.48617i	0.0661070	+	0.114501i
$928$	−2.21048	+	3.82866i	−0.0725625	+	0.125682i
$929$	−4.06819	+	7.04632i	−0.133473	+	0.231182i	−0.925013	−	0.379935i	$-0.875946\pi$
$929$	−4.06819	+	7.04632i	−0.133473	+	0.231182i	0.791540	+	0.611117i	$0.209280\pi$
$930$		0			0
$931$	−5.90727	+	3.49392i	−0.193603	+	0.114509i
$932$	15.9380			0.522067
$933$	−4.63013	+	8.01963i	−0.151584	+	0.262551i
$934$	8.45397	−	14.6427i	0.276622	−	0.479124i
$935$		0			0
$936$	0.529375	−	0.916904i	0.0173032	−	0.0299699i
$937$	7.30278	+	12.6488i	0.238571	+	0.413218i	0.960305	−	0.278953i	$-0.0899875\pi$
$937$	7.30278	+	12.6488i	0.238571	+	0.413218i	−0.721733	+	0.692171i	$0.756654\pi$
$938$	−11.4254			−0.373052
$939$	34.7858			1.13519
$940$		0			0
$941$	9.92629	+	17.1928i	0.323588	+	0.560471i	0.981226	−	0.192864i	$-0.0617775\pi$
$941$	9.92629	+	17.1928i	0.323588	+	0.560471i	−0.657638	+	0.753334i	$0.728444\pi$
$942$	10.8238			0.352659
$943$	12.8070			0.417054
$944$	3.09395	+	5.35888i	0.100700	+	0.174417i
$945$		0			0
$946$	−22.7767	−	39.4505i	−0.740536	−	1.28265i
$947$	−10.9218	+	18.9171i	−0.354911	+	0.614724i	−0.987103	−	0.160088i	$-0.948822\pi$
$947$	−10.9218	+	18.9171i	−0.354911	+	0.614724i	0.632191	+	0.774812i	$0.282156\pi$
$948$	7.69848	−	13.3342i	0.250035	−	0.433073i
$949$	−3.99883			−0.129808
$950$		0			0
$951$	11.6409			0.377482
$952$	5.46226	−	9.46092i	0.177033	−	0.306630i
$953$	2.75267	−	4.76776i	0.0891676	−	0.154443i	−0.817992	−	0.575230i	$-0.804913\pi$
$953$	2.75267	−	4.76776i	0.0891676	−	0.154443i	0.907160	+	0.420787i	$0.138246\pi$
$954$	−3.82610	−	6.62700i	−0.123875	−	0.214557i
$955$		0			0
$956$	−3.31706	−	5.74532i	−0.107281	−	0.185817i
$957$	37.5740			1.21459
$958$	−3.65139			−0.117971
$959$	−10.5885	−	18.3398i	−0.341920	−	0.592223i
$960$		0			0
$961$	37.1027			1.19686
$962$	−8.38738			−0.270420
$963$	6.16527	+	10.6786i	0.198673	+	0.344112i
$964$	11.0397	−	19.1213i	0.355565	−	0.615856i
$965$		0			0
$966$	−5.37289	+	9.30613i	−0.172870	+	0.299420i
$967$	−28.3693	+	49.1371i	−0.912295	+	1.58014i	−0.101481	+	0.994837i	$0.532358\pi$
$967$	−28.3693	+	49.1371i	−0.912295	+	1.58014i	−0.810814	+	0.585304i	$0.800975\pi$
$968$	−29.8806			−0.960400
$969$	23.6760	+	13.3393i	0.760583	+	0.428520i
$970$		0			0
$971$	7.20815	−	12.4849i	0.231321	−	0.400659i	−0.726876	−	0.686768i	$-0.759029\pi$
$971$	7.20815	−	12.4849i	0.231321	−	0.400659i	0.958197	+	0.286109i	$0.0923620\pi$
$972$	5.92769	−	10.2671i	0.190131	−	0.329316i
$973$	24.5339	+	42.4940i	0.786521	+	1.36229i
$974$	6.87080	−	11.9006i	0.220155	−	0.381319i
$975$		0			0
$976$	−8.02074			−0.256738
$977$	31.9776			1.02305			0.511527	−	0.859267i	$-0.329080\pi$
$977$	31.9776			1.02305			0.511527	+	0.859267i	$0.329080\pi$
$978$	8.91274	+	15.4373i	0.284998	+	0.493631i
$979$	−36.1216	−	62.5644i	−1.15445	−	1.99957i
$980$		0			0
$981$	3.74151			0.119457
$982$	−17.3839	−	30.1098i	−0.554743	−	0.960842i
$983$	−7.61623	+	13.1917i	−0.242920	+	0.420750i	−0.961545	−	0.274648i	$-0.911439\pi$
$983$	−7.61623	+	13.1917i	−0.242920	+	0.420750i	0.718625	+	0.695398i	$0.244772\pi$
$984$	−2.45257	−	4.24798i	−0.0781852	−	0.135421i
$985$		0			0
$986$	−10.3674	+	17.9569i	−0.330166	+	0.571864i
$987$	−22.2732			−0.708963
$988$	−0.0393660	−	3.74252i	−0.00125240	−	0.119065i
$989$	−24.7270			−0.786271
$990$		0			0
$991$	8.16214	−	14.1372i	0.259279	−	0.449084i	−0.706770	−	0.707443i	$-0.749848\pi$
$991$	8.16214	−	14.1372i	0.259279	−	0.449084i	0.966049	+	0.258359i	$0.0831818\pi$
$992$	−4.12622	−	7.14682i	−0.131008	−	0.226912i
$993$	−6.21258	+	10.7605i	−0.197150	+	0.341474i
$994$	2.56232	+	4.43807i	0.0812718	+	0.140767i
$995$		0			0
$996$	8.07940			0.256006
$997$	11.1218	+	19.2635i	0.352230	+	0.610081i	0.986640	−	0.162916i	$-0.0520901\pi$
$997$	11.1218	+	19.2635i	0.352230	+	0.610081i	−0.634410	+	0.772997i	$0.718757\pi$
$998$	8.31410	+	14.4005i	0.263178	+	0.455838i
$999$	−54.9643			−1.73899

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.e.o.201.4		10
5.2	odd	4		190.2.i.a.49.7	yes	20
5.3	odd	4		190.2.i.a.49.4	✓	20
5.4	even	2		950.2.e.n.201.2		10
15.2	even	4		1710.2.t.d.1189.1		20
15.8	even	4		1710.2.t.d.1189.9		20
19.7	even	3	inner	950.2.e.o.501.4		10
95.7	odd	12		190.2.i.a.159.4	yes	20
95.64	even	6		950.2.e.n.501.2		10
95.83	odd	12		190.2.i.a.159.7	yes	20
285.83	even	12		1710.2.t.d.919.1		20
285.197	even	12		1710.2.t.d.919.9		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
190.2.i.a.49.4	✓	20	5.3	odd	4
190.2.i.a.49.7	yes	20	5.2	odd	4
190.2.i.a.159.4	yes	20	95.7	odd	12
190.2.i.a.159.7	yes	20	95.83	odd	12
950.2.e.n.201.2		10	5.4	even	2
950.2.e.n.501.2		10	95.64	even	6
950.2.e.o.201.4		10	1.1	even	1	trivial
950.2.e.o.501.4		10	19.7	even	3	inner
1710.2.t.d.919.1		20	285.83	even	12
1710.2.t.d.919.9		20	285.197	even	12
1710.2.t.d.1189.1		20	15.2	even	4
1710.2.t.d.1189.9		20	15.8	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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.664633 - 1.15118i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.664633 - 1.15118i) q^{6} +2.32927 q^{7} -1.00000 q^{8} +(0.616527 + 1.06786i) q^{9} +O(q^{10})\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.664633 - 1.15118i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.664633 - 1.15118i) q^{6} +2.32927 q^{7} -1.00000 q^{8} +(0.616527 + 1.06786i) q^{9} +6.39380 q^{11} -1.32927 q^{12} +(0.429320 + 0.743604i) q^{13} +(1.16463 - 2.01720i) q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.34506 + 4.06176i) q^{17} +1.23305 q^{18} +(3.75178 - 2.21903i) q^{19} +(1.54811 - 2.68140i) q^{21} +(3.19690 - 5.53719i) q^{22} +(-1.73531 - 3.00565i) q^{23} +(-0.664633 + 1.15118i) q^{24} +0.858640 q^{26} +5.62685 q^{27} +(-1.16463 - 2.01720i) q^{28} +(2.21048 + 3.82866i) q^{29} -8.25244 q^{31} +(0.500000 + 0.866025i) q^{32} +(4.24953 - 7.36040i) q^{33} +(2.34506 + 4.06176i) q^{34} +(0.616527 - 1.06786i) q^{36} -9.76821 q^{37} +(-0.0458469 - 4.35866i) q^{38} +1.14136 q^{39} +(-1.84506 + 3.19574i) q^{41} +(-1.54811 - 2.68140i) q^{42} +(3.56232 - 6.17012i) q^{43} +(-3.19690 - 5.53719i) q^{44} -3.47063 q^{46} +(-3.59684 - 6.22992i) q^{47} +(0.664633 + 1.15118i) q^{48} -1.57452 q^{49} +(3.11721 + 5.39916i) q^{51} +(0.429320 - 0.743604i) q^{52} +(-3.10295 - 5.37446i) q^{53} +(2.81343 - 4.87300i) q^{54} -2.32927 q^{56} +(-0.0609427 - 5.79381i) q^{57} +4.42096 q^{58} +(3.09395 - 5.35888i) q^{59} +(4.01037 + 6.94616i) q^{61} +(-4.12622 + 7.14682i) q^{62} +(1.43605 + 2.48732i) q^{63} +1.00000 q^{64} +(-4.24953 - 7.36040i) q^{66} +(-2.45257 - 4.24798i) q^{67} +4.69012 q^{68} -4.61338 q^{69} +(-1.10005 + 1.90535i) q^{71} +(-0.616527 - 1.06786i) q^{72} +(-2.32859 + 4.03323i) q^{73} +(-4.88411 + 8.45952i) q^{74} +(-3.79763 - 2.13962i) q^{76} +14.8928 q^{77} +(0.570680 - 0.988447i) q^{78} +(-5.79153 + 10.0312i) q^{79} +(1.89021 - 3.27394i) q^{81} +(1.84506 + 3.19574i) q^{82} -6.07809 q^{83} -3.09621 q^{84} +(-3.56232 - 6.17012i) q^{86} +5.87663 q^{87} -6.39380 q^{88} +(-5.64947 - 9.78517i) q^{89} +(1.00000 + 1.73205i) q^{91} +(-1.73531 + 3.00565i) q^{92} +(-5.48484 + 9.50002i) q^{93} -7.19369 q^{94} +1.32927 q^{96} +(-5.67500 + 9.82939i) q^{97} +(-0.787262 + 1.36358i) q^{98} +(3.94195 + 6.82766i) 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