LMFDB - Embedded newform 175.2.e.c.51.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(51,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("175.51");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.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:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			51.1
Root			$-0.707107 + 1.22474i$ of defining polynomial
Character	$\chi$	$=$	175.51
Dual form			175.2.e.c.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.207107 + 0.358719i) q^{2} +(1.20711 + 2.09077i) q^{3} +(0.914214 + 1.58346i) q^{4} -1.00000 q^{6} +(1.62132 - 2.09077i) q^{7} -1.58579 q^{8} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})$	\(q+(-0.207107 + 0.358719i) q^{2} +(1.20711 + 2.09077i) q^{3} +(0.914214 + 1.58346i) q^{4} -1.00000 q^{6} +(1.62132 - 2.09077i) q^{7} -1.58579 q^{8} +(-1.41421 + 2.44949i) q^{9} +(-2.41421 - 4.18154i) q^{11} +(-2.20711 + 3.82282i) q^{12} -0.828427 q^{13} +(0.414214 + 1.01461i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(-0.414214 - 0.717439i) q^{17} +(-0.585786 - 1.01461i) q^{18} +(1.41421 - 2.44949i) q^{19} +(6.32843 + 0.866025i) q^{21} +2.00000 q^{22} +(-1.20711 + 2.09077i) q^{23} +(-1.91421 - 3.31552i) q^{24} +(0.171573 - 0.297173i) q^{26} +0.414214 q^{27} +(4.79289 + 0.655892i) q^{28} -1.00000 q^{29} +(3.00000 + 5.19615i) q^{31} +(-2.20711 - 3.82282i) q^{32} +(5.82843 - 10.0951i) q^{33} +0.343146 q^{34} -5.17157 q^{36} +(0.585786 + 1.01461i) q^{38} +(-1.00000 - 1.73205i) q^{39} -2.17157 q^{41} +(-1.62132 + 2.09077i) q^{42} -6.41421 q^{43} +(4.41421 - 7.64564i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(1.00000 - 1.73205i) q^{47} -7.24264 q^{48} +(-1.74264 - 6.77962i) q^{49} +(1.00000 - 1.73205i) q^{51} +(-0.757359 - 1.31178i) q^{52} +(-3.41421 - 5.91359i) q^{53} +(-0.0857864 + 0.148586i) q^{54} +(-2.57107 + 3.31552i) q^{56} +6.82843 q^{57} +(0.207107 - 0.358719i) q^{58} +(6.24264 + 10.8126i) q^{59} +(5.74264 - 9.94655i) q^{61} -2.48528 q^{62} +(2.82843 + 6.92820i) q^{63} -4.17157 q^{64} +(2.41421 + 4.18154i) q^{66} +(6.20711 + 10.7510i) q^{67} +(0.757359 - 1.31178i) q^{68} -5.82843 q^{69} -12.4853 q^{71} +(2.24264 - 3.88437i) q^{72} +(2.41421 + 4.18154i) q^{73} +5.17157 q^{76} +(-12.6569 - 1.73205i) q^{77} +0.828427 q^{78} +(-4.58579 + 7.94282i) q^{79} +(4.74264 + 8.21449i) q^{81} +(0.449747 - 0.778985i) q^{82} +11.7279 q^{83} +(4.41421 + 10.8126i) q^{84} +(1.32843 - 2.30090i) q^{86} +(-1.20711 - 2.09077i) q^{87} +(3.82843 + 6.63103i) q^{88} +(-1.32843 + 2.30090i) q^{89} +(-1.34315 + 1.73205i) q^{91} -4.41421 q^{92} +(-7.24264 + 12.5446i) q^{93} +(0.414214 + 0.717439i) q^{94} +(5.32843 - 9.22911i) q^{96} -0.343146 q^{97} +(2.79289 + 0.778985i) q^{98} +13.6569 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{6} - 2 q^{7} - 12 q^{8}+O(q^{10}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^6 - 2 * q^7 - 12 * q^8	$ 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{6} - 2 q^{7} - 12 q^{8} - 4 q^{11} - 6 q^{12} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 4 q^{17} - 8 q^{18} + 14 q^{21} + 8 q^{22} - 2 q^{23} - 2 q^{24} + 12 q^{26} - 4 q^{27} + 22 q^{28} - 4 q^{29} + 12 q^{31} - 6 q^{32} + 12 q^{33} + 24 q^{34} - 32 q^{36} + 8 q^{38} - 4 q^{39} - 20 q^{41} + 2 q^{42} - 20 q^{43} + 12 q^{44} - 2 q^{46} + 4 q^{47} - 12 q^{48} + 10 q^{49} + 4 q^{51} - 20 q^{52} - 8 q^{53} - 6 q^{54} + 18 q^{56} + 16 q^{57} - 2 q^{58} + 8 q^{59} + 6 q^{61} + 24 q^{62} - 28 q^{64} + 4 q^{66} + 22 q^{67} + 20 q^{68} - 12 q^{69} - 16 q^{71} - 8 q^{72} + 4 q^{73} + 32 q^{76} - 28 q^{77} - 8 q^{78} - 24 q^{79} + 2 q^{81} - 18 q^{82} - 4 q^{83} + 12 q^{84} - 6 q^{86} - 2 q^{87} + 4 q^{88} + 6 q^{89} - 28 q^{91} - 12 q^{92} - 12 q^{93} - 4 q^{94} + 10 q^{96} - 24 q^{97} + 14 q^{98} + 32 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^6 - 2 * q^7 - 12 * q^8 - 4 * q^11 - 6 * q^12 + 8 * q^13 - 4 * q^14 - 6 * q^16 + 4 * q^17 - 8 * q^18 + 14 * q^21 + 8 * q^22 - 2 * q^23 - 2 * q^24 + 12 * q^26 - 4 * q^27 + 22 * q^28 - 4 * q^29 + 12 * q^31 - 6 * q^32 + 12 * q^33 + 24 * q^34 - 32 * q^36 + 8 * q^38 - 4 * q^39 - 20 * q^41 + 2 * q^42 - 20 * q^43 + 12 * q^44 - 2 * q^46 + 4 * q^47 - 12 * q^48 + 10 * q^49 + 4 * q^51 - 20 * q^52 - 8 * q^53 - 6 * q^54 + 18 * q^56 + 16 * q^57 - 2 * q^58 + 8 * q^59 + 6 * q^61 + 24 * q^62 - 28 * q^64 + 4 * q^66 + 22 * q^67 + 20 * q^68 - 12 * q^69 - 16 * q^71 - 8 * q^72 + 4 * q^73 + 32 * q^76 - 28 * q^77 - 8 * q^78 - 24 * q^79 + 2 * q^81 - 18 * q^82 - 4 * q^83 + 12 * q^84 - 6 * q^86 - 2 * q^87 + 4 * q^88 + 6 * q^89 - 28 * q^91 - 12 * q^92 - 12 * q^93 - 4 * q^94 + 10 * q^96 - 24 * q^97 + 14 * q^98 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.207107	+	0.358719i	−0.146447	+	0.253653i	−0.929912	−	0.367783i	$-0.880117\pi$
$2$	−0.207107	+	0.358719i	−0.146447	+	0.253653i	0.783465	+	0.621436i	$0.213450\pi$
$3$	1.20711	+	2.09077i	0.696923	+	1.20711i	0.969528	+	0.244981i	$0.0787816\pi$
$3$	1.20711	+	2.09077i	0.696923	+	1.20711i	−0.272605	+	0.962126i	$0.587885\pi$
$4$	0.914214	+	1.58346i	0.457107	+	0.791732i
$5$		0			0
$5$		0			0
$6$	−1.00000			−0.408248
$7$	1.62132	−	2.09077i	0.612801	−	0.790237i
$7$	1.62132	−	2.09077i	0.612801	−	0.790237i
$8$	−1.58579			−0.560660
$9$	−1.41421	+	2.44949i	−0.471405	+	0.816497i
$10$		0			0
$11$	−2.41421	−	4.18154i	−0.727913	−	1.26078i	−0.957764	−	0.287556i	$-0.907157\pi$
$11$	−2.41421	−	4.18154i	−0.727913	−	1.26078i	0.229851	−	0.973226i	$-0.426176\pi$
$12$	−2.20711	+	3.82282i	−0.637137	+	1.10355i
$13$	−0.828427			−0.229764			−0.114882	−	0.993379i	$-0.536649\pi$
$13$	−0.828427			−0.229764			−0.114882	+	0.993379i	$0.536649\pi$
$14$	0.414214	+	1.01461i	0.110703	+	0.271166i
$15$		0			0
$16$	−1.50000	+	2.59808i	−0.375000	+	0.649519i
$17$	−0.414214	−	0.717439i	−0.100462	−	0.174005i	0.811413	−	0.584473i	$-0.198699\pi$
$17$	−0.414214	−	0.717439i	−0.100462	−	0.174005i	−0.911875	+	0.410468i	$0.865365\pi$
$18$	−0.585786	−	1.01461i	−0.138071	−	0.239146i
$19$	1.41421	−	2.44949i	0.324443	−	0.561951i	−0.656957	−	0.753928i	$-0.728157\pi$
$19$	1.41421	−	2.44949i	0.324443	−	0.561951i	0.981399	+	0.191977i	$0.0614899\pi$
$20$		0			0
$21$	6.32843	+	0.866025i	1.38098	+	0.188982i
$22$	2.00000			0.426401
$23$	−1.20711	+	2.09077i	−0.251699	+	0.435956i	−0.963994	−	0.265925i	$-0.914323\pi$
$23$	−1.20711	+	2.09077i	−0.251699	+	0.435956i	0.712295	+	0.701881i	$0.247656\pi$
$24$	−1.91421	−	3.31552i	−0.390737	−	0.676777i
$25$		0			0
$26$	0.171573	−	0.297173i	0.0336482	−	0.0582804i
$27$	0.414214			0.0797154
$28$	4.79289	+	0.655892i	0.905772	+	0.123952i
$29$	−1.00000			−0.185695			−0.0928477	−	0.995680i	$-0.529597\pi$
$29$	−1.00000			−0.185695			−0.0928477	+	0.995680i	$0.529597\pi$
$30$		0			0
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	0.998968	+	0.0454165i	$0.0144615\pi$
$31$	3.00000	+	5.19615i	0.538816	+	0.933257i	−0.460152	+	0.887840i	$0.652205\pi$
$32$	−2.20711	−	3.82282i	−0.390165	−	0.675786i
$33$	5.82843	−	10.0951i	1.01460	−	1.75734i
$34$	0.343146			0.0588490
$35$		0			0
$36$	−5.17157			−0.861929
$37$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$37$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$38$	0.585786	+	1.01461i	0.0950271	+	0.164592i
$39$	−1.00000	−	1.73205i	−0.160128	−	0.277350i
$40$		0			0
$41$	−2.17157			−0.339143			−0.169571	−	0.985518i	$-0.554238\pi$
$41$	−2.17157			−0.339143			−0.169571	+	0.985518i	$0.554238\pi$
$42$	−1.62132	+	2.09077i	−0.250175	+	0.322613i
$43$	−6.41421			−0.978158			−0.489079	−	0.872239i	$-0.662667\pi$
$43$	−6.41421			−0.978158			−0.489079	+	0.872239i	$0.662667\pi$
$44$	4.41421	−	7.64564i	0.665468	−	1.15262i
$45$		0			0
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	−0.783830	−	0.620975i	$-0.786737\pi$
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	0.929695	+	0.368329i	$0.120070\pi$
$48$	−7.24264			−1.04539
$49$	−1.74264	−	6.77962i	−0.248949	−	0.968517i
$50$		0			0
$51$	1.00000	−	1.73205i	0.140028	−	0.242536i
$52$	−0.757359	−	1.31178i	−0.105027	−	0.181912i
$53$	−3.41421	−	5.91359i	−0.468978	−	0.812294i	0.530393	−	0.847752i	$-0.322044\pi$
$53$	−3.41421	−	5.91359i	−0.468978	−	0.812294i	−0.999371	+	0.0354577i	$0.988711\pi$
$54$	−0.0857864	+	0.148586i	−0.0116741	+	0.0202201i
$55$		0			0
$56$	−2.57107	+	3.31552i	−0.343573	+	0.443054i
$57$	6.82843			0.904447
$58$	0.207107	−	0.358719i	0.0271945	−	0.0471022i
$59$	6.24264	+	10.8126i	0.812723	+	1.40768i	0.910952	+	0.412513i	$0.135349\pi$
$59$	6.24264	+	10.8126i	0.812723	+	1.40768i	−0.0982291	+	0.995164i	$0.531318\pi$
$60$		0			0
$61$	5.74264	−	9.94655i	0.735270	−	1.27352i	−0.219335	−	0.975650i	$-0.570389\pi$
$61$	5.74264	−	9.94655i	0.735270	−	1.27352i	0.954605	−	0.297875i	$-0.0962779\pi$
$62$	−2.48528			−0.315631
$63$	2.82843	+	6.92820i	0.356348	+	0.872872i
$64$	−4.17157			−0.521447
$65$		0			0
$66$	2.41421	+	4.18154i	0.297169	+	0.514712i
$67$	6.20711	+	10.7510i	0.758319	+	1.31345i	0.943707	+	0.330781i	$0.107312\pi$
$67$	6.20711	+	10.7510i	0.758319	+	1.31345i	−0.185389	+	0.982665i	$0.559354\pi$
$68$	0.757359	−	1.31178i	0.0918433	−	0.159077i
$69$	−5.82843			−0.701660
$70$		0			0
$71$	−12.4853			−1.48173			−0.740865	−	0.671654i	$-0.765584\pi$
$71$	−12.4853			−1.48173			−0.740865	+	0.671654i	$0.765584\pi$
$72$	2.24264	−	3.88437i	0.264298	−	0.457777i
$73$	2.41421	+	4.18154i	0.282562	+	0.489412i	0.972015	−	0.234918i	$-0.0754823\pi$
$73$	2.41421	+	4.18154i	0.282562	+	0.489412i	−0.689453	+	0.724331i	$0.742149\pi$
$74$		0			0
$75$		0			0
$76$	5.17157			0.593220
$77$	−12.6569	−	1.73205i	−1.44238	−	0.197386i
$78$	0.828427			0.0938009
$79$	−4.58579	+	7.94282i	−0.515941	+	0.893637i	0.483887	+	0.875130i	$0.339224\pi$
$79$	−4.58579	+	7.94282i	−0.515941	+	0.893637i	−0.999829	+	0.0185063i	$0.994109\pi$
$80$		0			0
$81$	4.74264	+	8.21449i	0.526960	+	0.912722i
$82$	0.449747	−	0.778985i	0.0496663	−	0.0860246i
$83$	11.7279			1.28731			0.643653	−	0.765317i	$-0.277418\pi$
$83$	11.7279			1.28731			0.643653	+	0.765317i	$0.277418\pi$
$84$	4.41421	+	10.8126i	0.481630	+	1.17975i
$85$		0			0
$86$	1.32843	−	2.30090i	0.143248	−	0.248113i
$87$	−1.20711	−	2.09077i	−0.129415	−	0.224154i
$88$	3.82843	+	6.63103i	0.408112	+	0.706870i
$89$	−1.32843	+	2.30090i	−0.140813	+	0.243895i	−0.927803	−	0.373070i	$-0.878305\pi$
$89$	−1.32843	+	2.30090i	−0.140813	+	0.243895i	0.786990	+	0.616966i	$0.211638\pi$
$90$		0			0
$91$	−1.34315	+	1.73205i	−0.140800	+	0.181568i
$92$	−4.41421			−0.460214
$93$	−7.24264	+	12.5446i	−0.751027	+	1.30082i
$94$	0.414214	+	0.717439i	0.0427229	+	0.0739982i
$95$		0			0
$96$	5.32843	−	9.22911i	0.543830	−	0.941942i
$97$	−0.343146			−0.0348412			−0.0174206	−	0.999848i	$-0.505545\pi$
$97$	−0.343146			−0.0348412			−0.0174206	+	0.999848i	$0.505545\pi$
$98$	2.79289	+	0.778985i	0.282125	+	0.0786894i
$99$	13.6569			1.37257
$100$		0			0
$101$	−6.15685	−	10.6640i	−0.612630	−	1.06111i	−0.990795	−	0.135368i	$-0.956778\pi$
$101$	−6.15685	−	10.6640i	−0.612630	−	1.06111i	0.378165	−	0.925738i	$-0.376555\pi$
$102$	0.414214	+	0.717439i	0.0410133	+	0.0710370i
$103$	0.207107	−	0.358719i	0.0204068	−	0.0353457i	−0.855642	−	0.517569i	$-0.826837\pi$
$103$	0.207107	−	0.358719i	0.0204068	−	0.0353457i	0.876048	+	0.482223i	$0.160171\pi$
$104$	1.31371			0.128820
$105$		0			0
$106$	2.82843			0.274721
$107$	1.37868	−	2.38794i	0.133282	−	0.230851i	−0.791658	−	0.610965i	$-0.790782\pi$
$107$	1.37868	−	2.38794i	0.133282	−	0.230851i	0.924940	+	0.380113i	$0.124115\pi$
$108$	0.378680	+	0.655892i	0.0364385	+	0.0631133i
$109$	−1.74264	−	3.01834i	−0.166915	−	0.289105i	0.770419	−	0.637538i	$-0.220047\pi$
$109$	−1.74264	−	3.01834i	−0.166915	−	0.289105i	−0.937334	+	0.348433i	$0.886714\pi$
$110$		0			0
$111$		0			0
$112$	3.00000	+	7.34847i	0.283473	+	0.694365i
$113$	−12.4853			−1.17452			−0.587258	−	0.809400i	$-0.699793\pi$
$113$	−12.4853			−1.17452			−0.587258	+	0.809400i	$0.699793\pi$
$114$	−1.41421	+	2.44949i	−0.132453	+	0.229416i
$115$		0			0
$116$	−0.914214	−	1.58346i	−0.0848826	−	0.147021i
$117$	1.17157	−	2.02922i	0.108312	−	0.187602i
$118$	−5.17157			−0.476082
$119$	−2.17157	−	0.297173i	−0.199068	−	0.0272418i
$120$		0			0
$121$	−6.15685	+	10.6640i	−0.559714	+	0.969453i
$122$	2.37868	+	4.11999i	0.215356	+	0.373007i
$123$	−2.62132	−	4.54026i	−0.236356	−	0.409381i
$124$	−5.48528	+	9.50079i	−0.492593	+	0.853196i
$125$		0			0
$126$	−3.07107	−	0.420266i	−0.273592	−	0.0374403i
$127$	−13.3137			−1.18140			−0.590700	−	0.806891i	$-0.701148\pi$
$127$	−13.3137			−1.18140			−0.590700	+	0.806891i	$0.701148\pi$
$128$	5.27817	−	9.14207i	0.466529	−	0.808052i
$129$	−7.74264	−	13.4106i	−0.681702	−	1.18074i
$130$		0			0
$131$	−1.65685	+	2.86976i	−0.144760	+	0.250732i	−0.929283	−	0.369368i	$-0.879574\pi$
$131$	−1.65685	+	2.86976i	−0.144760	+	0.250732i	0.784523	+	0.620099i	$0.212908\pi$
$132$	21.3137			1.85512
$133$	−2.82843	−	6.92820i	−0.245256	−	0.600751i
$134$	−5.14214			−0.444213
$135$		0			0
$136$	0.656854	+	1.13770i	0.0563248	+	0.0975574i
$137$	0.828427	+	1.43488i	0.0707773	+	0.122590i	0.899242	−	0.437451i	$-0.144119\pi$
$137$	0.828427	+	1.43488i	0.0707773	+	0.122590i	−0.828465	+	0.560041i	$0.810785\pi$
$138$	1.20711	−	2.09077i	0.102756	−	0.177978i
$139$	12.1421			1.02988			0.514941	−	0.857225i	$-0.327814\pi$
$139$	12.1421			1.02988			0.514941	+	0.857225i	$0.327814\pi$
$140$		0			0
$141$	4.82843			0.406627
$142$	2.58579	−	4.47871i	0.216994	−	0.375845i
$143$	2.00000	+	3.46410i	0.167248	+	0.289683i
$144$	−4.24264	−	7.34847i	−0.353553	−	0.612372i
$145$		0			0
$146$	−2.00000			−0.165521
$147$	12.0711	−	11.8272i	0.995605	−	0.975490i
$148$		0			0
$149$	3.91421	−	6.77962i	0.320665	−	0.555408i	−0.659961	−	0.751300i	$-0.729427\pi$
$149$	3.91421	−	6.77962i	0.320665	−	0.555408i	0.980625	+	0.195892i	$0.0627603\pi$
$150$		0			0
$151$	−0.171573	−	0.297173i	−0.0139624	−	0.0241836i	0.858960	−	0.512043i	$-0.171111\pi$
$151$	−0.171573	−	0.297173i	−0.0139624	−	0.0241836i	−0.872922	+	0.487859i	$0.837778\pi$
$152$	−2.24264	+	3.88437i	−0.181902	+	0.315064i
$153$	2.34315			0.189432
$154$	3.24264	−	4.18154i	0.261299	−	0.336958i
$155$		0			0
$156$	1.82843	−	3.16693i	0.146391	−	0.253557i
$157$	−2.65685	−	4.60181i	−0.212040	−	0.367264i	0.740313	−	0.672263i	$-0.234677\pi$
$157$	−2.65685	−	4.60181i	−0.212040	−	0.367264i	−0.952353	+	0.304998i	$0.901344\pi$
$158$	−1.89949	−	3.29002i	−0.151116	−	0.261740i
$159$	8.24264	−	14.2767i	0.653684	−	1.13221i
$160$		0			0
$161$	2.41421	+	5.91359i	0.190267	+	0.466056i
$162$	−3.92893			−0.308686
$163$	11.8284	−	20.4874i	0.926474	−	1.60470i	0.137301	−	0.990529i	$-0.456157\pi$
$163$	11.8284	−	20.4874i	0.926474	−	1.60470i	0.789173	−	0.614170i	$-0.210509\pi$
$164$	−1.98528	−	3.43861i	−0.155024	−	0.268510i
$165$		0			0
$166$	−2.42893	+	4.20703i	−0.188522	+	0.326529i
$167$	−19.5858			−1.51559			−0.757797	−	0.652491i	$-0.773724\pi$
$167$	−19.5858			−1.51559			−0.757797	+	0.652491i	$0.773724\pi$
$168$	−10.0355	−	1.37333i	−0.774258	−	0.105955i
$169$	−12.3137			−0.947208
$170$		0			0
$171$	4.00000	+	6.92820i	0.305888	+	0.529813i
$172$	−5.86396	−	10.1567i	−0.447123	−	0.774439i
$173$	−9.65685	+	16.7262i	−0.734197	+	1.27167i	0.220878	+	0.975302i	$0.429108\pi$
$173$	−9.65685	+	16.7262i	−0.734197	+	1.27167i	−0.955075	+	0.296365i	$0.904226\pi$
$174$	1.00000			0.0758098
$175$		0			0
$176$	14.4853			1.09187
$177$	−15.0711	+	26.1039i	−1.13281	+	1.96209i
$178$	−0.550253	−	0.953065i	−0.0412432	−	0.0714353i
$179$	5.00000	+	8.66025i	0.373718	+	0.647298i	0.990134	−	0.140122i	$-0.0447496\pi$
$179$	5.00000	+	8.66025i	0.373718	+	0.647298i	−0.616417	+	0.787420i	$0.711416\pi$
$180$		0			0
$181$	−8.65685			−0.643459			−0.321729	−	0.946832i	$-0.604264\pi$
$181$	−8.65685			−0.643459			−0.321729	+	0.946832i	$0.604264\pi$
$182$	−0.343146	−	0.840532i	−0.0254357	−	0.0623044i
$183$	27.7279			2.04971
$184$	1.91421	−	3.31552i	0.141118	−	0.244423i
$185$		0			0
$186$	−3.00000	−	5.19615i	−0.219971	−	0.381000i
$187$	−2.00000	+	3.46410i	−0.146254	+	0.253320i
$188$	3.65685			0.266704
$189$	0.671573	−	0.866025i	0.0488497	−	0.0629941i
$190$		0			0
$191$	3.58579	−	6.21076i	0.259458	−	0.449395i	−0.706639	−	0.707575i	$-0.749789\pi$
$191$	3.58579	−	6.21076i	0.259458	−	0.449395i	0.966097	+	0.258180i	$0.0831226\pi$
$192$	−5.03553	−	8.72180i	−0.363408	−	0.629442i
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	0.827788	−	0.561041i	$-0.189599\pi$
$193$	−1.00000	−	1.73205i	−0.0719816	−	0.124676i	−0.899770	+	0.436365i	$0.856266\pi$
$194$	0.0710678	−	0.123093i	0.00510237	−	0.00883757i
$195$		0			0
$196$	9.14214	−	8.95743i	0.653010	−	0.639816i
$197$	23.6569			1.68548			0.842741	−	0.538320i	$-0.180941\pi$
$197$	23.6569			1.68548			0.842741	+	0.538320i	$0.180941\pi$
$198$	−2.82843	+	4.89898i	−0.201008	+	0.348155i
$199$	−0.828427	−	1.43488i	−0.0587256	−	0.101716i	0.835168	−	0.549995i	$-0.185370\pi$
$199$	−0.828427	−	1.43488i	−0.0587256	−	0.101716i	−0.893894	+	0.448279i	$0.852037\pi$
$200$		0			0
$201$	−14.9853	+	25.9553i	−1.05698	+	1.83074i
$202$	5.10051			0.358870
$203$	−1.62132	+	2.09077i	−0.113794	+	0.146743i
$204$	3.65685			0.256031
$205$		0			0
$206$	0.0857864	+	0.148586i	0.00597702	+	0.0103525i
$207$	−3.41421	−	5.91359i	−0.237304	−	0.411023i
$208$	1.24264	−	2.15232i	0.0861616	−	0.149236i
$209$	−13.6569			−0.944664
$210$		0			0
$211$	3.51472			0.241963			0.120982	−	0.992655i	$-0.461396\pi$
$211$	3.51472			0.241963			0.120982	+	0.992655i	$0.461396\pi$
$212$	6.24264	−	10.8126i	0.428746	−	0.742610i
$213$	−15.0711	−	26.1039i	−1.03265	−	1.78861i
$214$	0.571068	+	0.989118i	0.0390374	+	0.0676147i
$215$		0			0
$216$	−0.656854			−0.0446933
$217$	15.7279	+	2.15232i	1.06768	+	0.146109i
$218$	1.44365			0.0977764
$219$	−5.82843	+	10.0951i	−0.393849	+	0.682166i
$220$		0			0
$221$	0.343146	+	0.594346i	0.0230825	+	0.0399800i
$222$		0			0
$223$	−11.6569			−0.780601			−0.390300	−	0.920688i	$-0.627629\pi$
$223$	−11.6569			−0.780601			−0.390300	+	0.920688i	$0.627629\pi$
$224$	−11.5711	−	1.58346i	−0.773124	−	0.105800i
$225$		0			0
$226$	2.58579	−	4.47871i	0.172004	−	0.297920i
$227$	13.4853	+	23.3572i	0.895050	+	1.55027i	0.833743	+	0.552152i	$0.186193\pi$
$227$	13.4853	+	23.3572i	0.895050	+	1.55027i	0.0613063	+	0.998119i	$0.480473\pi$
$228$	6.24264	+	10.8126i	0.413429	+	0.716080i
$229$	0.171573	−	0.297173i	0.0113379	−	0.0196377i	−0.860301	−	0.509787i	$-0.829724\pi$
$229$	0.171573	−	0.297173i	0.0113379	−	0.0196377i	0.871639	+	0.490149i	$0.163058\pi$
$230$		0			0
$231$	−11.6569	−	28.5533i	−0.766965	−	1.87867i
$232$	1.58579			0.104112
$233$	−5.58579	+	9.67487i	−0.365937	+	0.633822i	−0.988926	−	0.148409i	$-0.952585\pi$
$233$	−5.58579	+	9.67487i	−0.365937	+	0.633822i	0.622989	+	0.782231i	$0.285918\pi$
$234$	0.485281	+	0.840532i	0.0317238	+	0.0549473i
$235$		0			0
$236$	−11.4142	+	19.7700i	−0.743002	+	1.28692i
$237$	−22.1421			−1.43829
$238$	0.556349	−	0.717439i	0.0360628	−	0.0465047i
$239$	1.31371			0.0849767			0.0424884	−	0.999097i	$-0.486471\pi$
$239$	1.31371			0.0849767			0.0424884	+	0.999097i	$0.486471\pi$
$240$		0			0
$241$	−8.17157	−	14.1536i	−0.526377	−	0.911712i	−0.999528	−	0.0307305i	$-0.990217\pi$
$241$	−8.17157	−	14.1536i	−0.526377	−	0.911712i	0.473150	−	0.880982i	$-0.343117\pi$
$242$	−2.55025	−	4.41717i	−0.163936	−	0.283946i
$243$	−10.8284	+	18.7554i	−0.694644	+	1.20316i
$244$	21.0000			1.34439
$245$		0			0
$246$	2.17157			0.138454
$247$	−1.17157	+	2.02922i	−0.0745454	+	0.129116i
$248$	−4.75736	−	8.23999i	−0.302093	−	0.523240i
$249$	14.1569	+	24.5204i	0.897154	+	1.55392i
$250$		0			0
$251$	13.3137			0.840354			0.420177	−	0.907442i	$-0.361968\pi$
$251$	13.3137			0.840354			0.420177	+	0.907442i	$0.361968\pi$
$252$	−8.38478	+	10.8126i	−0.528191	+	0.681128i
$253$	11.6569			0.732860
$254$	2.75736	−	4.77589i	0.173012	−	0.299666i
$255$		0			0
$256$	−1.98528	−	3.43861i	−0.124080	−	0.214913i
$257$	8.82843	−	15.2913i	0.550702	−	0.953844i	−0.447522	−	0.894273i	$-0.647693\pi$
$257$	8.82843	−	15.2913i	0.550702	−	0.953844i	0.998224	−	0.0595711i	$-0.0189733\pi$
$258$	6.41421			0.399331
$259$		0			0
$260$		0			0
$261$	1.41421	−	2.44949i	0.0875376	−	0.151620i
$262$	−0.686292	−	1.18869i	−0.0423992	−	0.0734376i
$263$	9.52082	+	16.4905i	0.587079	+	1.01685i	0.994613	+	0.103660i	$0.0330554\pi$
$263$	9.52082	+	16.4905i	0.587079	+	1.01685i	−0.407534	+	0.913190i	$0.633611\pi$
$264$	−9.24264	+	16.0087i	−0.568845	+	0.985269i
$265$		0			0
$266$	3.07107	+	0.420266i	0.188299	+	0.0257682i
$267$	−6.41421			−0.392543
$268$	−11.3492	+	19.6575i	−0.693265	+	1.20077i
$269$	15.2279	+	26.3755i	0.928463	+	1.60814i	0.785895	+	0.618360i	$0.212202\pi$
$269$	15.2279	+	26.3755i	0.928463	+	1.60814i	0.142568	+	0.989785i	$0.454464\pi$
$270$		0			0
$271$	0.242641	−	0.420266i	0.0147394	−	0.0255293i	−0.858562	−	0.512710i	$-0.828641\pi$
$271$	0.242641	−	0.420266i	0.0147394	−	0.0255293i	0.873301	+	0.487181i	$0.161975\pi$
$272$	2.48528			0.150692
$273$	−5.24264	−	0.717439i	−0.317299	−	0.0434214i
$274$	−0.686292			−0.0414604
$275$		0			0
$276$	−5.32843	−	9.22911i	−0.320734	−	0.555527i
$277$	−6.07107	−	10.5154i	−0.364775	−	0.631809i	0.623965	−	0.781452i	$-0.285521\pi$
$277$	−6.07107	−	10.5154i	−0.364775	−	0.631809i	−0.988740	+	0.149643i	$0.952187\pi$
$278$	−2.51472	+	4.35562i	−0.150823	+	0.261233i
$279$	−16.9706			−1.01600
$280$		0			0
$281$	26.2843			1.56799			0.783994	−	0.620768i	$-0.213179\pi$
$281$	26.2843			1.56799			0.783994	+	0.620768i	$0.213179\pi$
$282$	−1.00000	+	1.73205i	−0.0595491	+	0.103142i
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	0.995544	−	0.0942988i	$-0.0300609\pi$
$283$	7.00000	+	12.1244i	0.416107	+	0.720718i	−0.579437	+	0.815017i	$0.696728\pi$
$284$	−11.4142	−	19.7700i	−0.677309	−	1.17313i
$285$		0			0
$286$	−1.65685			−0.0979718
$287$	−3.52082	+	4.54026i	−0.207827	+	0.268003i
$288$	12.4853			0.735702
$289$	8.15685	−	14.1281i	0.479815	−	0.831064i
$290$		0			0
$291$	−0.414214	−	0.717439i	−0.0242816	−	0.0420570i
$292$	−4.41421	+	7.64564i	−0.258322	+	0.447427i
$293$	16.0000			0.934730			0.467365	−	0.884064i	$-0.345203\pi$
$293$	16.0000			0.934730			0.467365	+	0.884064i	$0.345203\pi$
$294$	1.74264	+	6.77962i	0.101633	+	0.395395i
$295$		0			0
$296$		0			0
$297$	−1.00000	−	1.73205i	−0.0580259	−	0.100504i
$298$	1.62132	+	2.80821i	0.0939206	+	0.162675i
$299$	1.00000	−	1.73205i	0.0578315	−	0.100167i
$300$		0			0
$301$	−10.3995	+	13.4106i	−0.599417	+	0.772977i
$302$	0.142136			0.00817899
$303$	14.8640	−	25.7451i	0.853912	−	1.47902i
$304$	4.24264	+	7.34847i	0.243332	+	0.421464i
$305$		0			0
$306$	−0.485281	+	0.840532i	−0.0277417	+	0.0480500i
$307$	13.2426			0.755797			0.377899	−	0.925847i	$-0.376647\pi$
$307$	13.2426			0.755797			0.377899	+	0.925847i	$0.376647\pi$
$308$	−8.82843	−	21.6251i	−0.503046	−	1.23221i
$309$	1.00000			0.0568880
$310$		0			0
$311$	9.41421	+	16.3059i	0.533831	+	0.924623i	0.999219	+	0.0395157i	$0.0125815\pi$
$311$	9.41421	+	16.3059i	0.533831	+	0.924623i	−0.465388	+	0.885107i	$0.654085\pi$
$312$	1.58579	+	2.74666i	0.0897775	+	0.155499i
$313$	−8.82843	+	15.2913i	−0.499012	+	0.864314i	−0.999999	−	0.00114023i	$-0.999637\pi$
$313$	−8.82843	+	15.2913i	−0.499012	+	0.864314i	0.500987	+	0.865455i	$0.332970\pi$
$314$	2.20101			0.124210
$315$		0			0
$316$	−16.7696			−0.943361
$317$	12.8995	−	22.3426i	0.724508	−	1.25488i	−0.234668	−	0.972075i	$-0.575400\pi$
$317$	12.8995	−	22.3426i	0.724508	−	1.25488i	0.959176	−	0.282809i	$-0.0912662\pi$
$318$	3.41421	+	5.91359i	0.191460	+	0.331618i
$319$	2.41421	+	4.18154i	0.135170	+	0.234121i
$320$		0			0
$321$	6.65685			0.371549
$322$	−2.62132	−	0.358719i	−0.146080	−	0.0199907i
$323$	−2.34315			−0.130376
$324$	−8.67157	+	15.0196i	−0.481754	+	0.834422i
$325$		0			0
$326$	4.89949	+	8.48617i	0.271358	+	0.470006i
$327$	4.20711	−	7.28692i	0.232654	−	0.402968i
$328$	3.44365			0.190144
$329$	−2.00000	−	4.89898i	−0.110264	−	0.270089i
$330$		0			0
$331$	5.48528	−	9.50079i	0.301498	−	0.522210i	−0.674977	−	0.737839i	$-0.735847\pi$
$331$	5.48528	−	9.50079i	0.301498	−	0.522210i	0.976476	+	0.215628i	$0.0691799\pi$
$332$	10.7218	+	18.5707i	0.588437	+	1.01920i
$333$		0			0
$334$	4.05635	−	7.02580i	0.221954	−	0.384435i
$335$		0			0
$336$	−11.7426	+	15.1427i	−0.640614	+	0.826102i
$337$	−14.8284			−0.807756			−0.403878	−	0.914813i	$-0.632338\pi$
$337$	−14.8284			−0.807756			−0.403878	+	0.914813i	$0.632338\pi$
$338$	2.55025	−	4.41717i	0.138715	−	0.240262i
$339$	−15.0711	−	26.1039i	−0.818548	−	1.41777i
$340$		0			0
$341$	14.4853	−	25.0892i	0.784422	−	1.35866i
$342$	−3.31371			−0.179185
$343$	−17.0000	−	7.34847i	−0.917914	−	0.396780i
$344$	10.1716			0.548414
$345$		0			0
$346$	−4.00000	−	6.92820i	−0.215041	−	0.372463i
$347$	11.0355	+	19.1141i	0.592418	+	1.02610i	0.993906	+	0.110234i	$0.0351601\pi$
$347$	11.0355	+	19.1141i	0.592418	+	1.02610i	−0.401487	+	0.915865i	$0.631507\pi$
$348$	2.20711	−	3.82282i	0.118313	−	0.204925i
$349$	−26.6569			−1.42691			−0.713454	−	0.700702i	$-0.752870\pi$
$349$	−26.6569			−1.42691			−0.713454	+	0.700702i	$0.752870\pi$
$350$		0			0
$351$	−0.343146			−0.0183158
$352$	−10.6569	+	18.4582i	−0.568012	+	0.983826i
$353$	−10.5858	−	18.3351i	−0.563425	−	0.975880i	−0.997194	−	0.0748562i	$-0.976150\pi$
$353$	−10.5858	−	18.3351i	−0.563425	−	0.975880i	0.433770	−	0.901024i	$-0.357183\pi$
$354$	−6.24264	−	10.8126i	−0.331793	−	0.574682i
$355$		0			0
$356$	−4.85786			−0.257466
$357$	−2.00000	−	4.89898i	−0.105851	−	0.259281i
$358$	−4.14214			−0.218919
$359$	5.00000	−	8.66025i	0.263890	−	0.457071i	−0.703382	−	0.710812i	$-0.748328\pi$
$359$	5.00000	−	8.66025i	0.263890	−	0.457071i	0.967272	+	0.253741i	$0.0816611\pi$
$360$		0			0
$361$	5.50000	+	9.52628i	0.289474	+	0.501383i
$362$	1.79289	−	3.10538i	0.0942324	−	0.163215i
$363$	−29.7279			−1.56031
$364$	−3.97056	−	0.543359i	−0.208114	−	0.0284798i
$365$		0			0
$366$	−5.74264	+	9.94655i	−0.300173	+	0.519914i
$367$	−5.62132	−	9.73641i	−0.293431	−	0.508237i	0.681188	−	0.732108i	$-0.261464\pi$
$367$	−5.62132	−	9.73641i	−0.293431	−	0.508237i	−0.974619	+	0.223872i	$0.928130\pi$
$368$	−3.62132	−	6.27231i	−0.188774	−	0.326967i
$369$	3.07107	−	5.31925i	0.159873	−	0.276909i
$370$		0			0
$371$	−17.8995	−	2.44949i	−0.929295	−	0.127171i
$372$	−26.4853			−1.37320
$373$	6.48528	−	11.2328i	0.335795	−	0.581614i	−0.647842	−	0.761775i	$-0.724328\pi$
$373$	6.48528	−	11.2328i	0.335795	−	0.581614i	0.983637	+	0.180160i	$0.0576617\pi$
$374$	−0.828427	−	1.43488i	−0.0428369	−	0.0741958i
$375$		0			0
$376$	−1.58579	+	2.74666i	−0.0817807	+	0.141648i
$377$	0.828427			0.0426662
$378$	0.171573	+	0.420266i	0.00882476	+	0.0216162i
$379$	21.1716			1.08751			0.543755	−	0.839244i	$-0.317002\pi$
$379$	21.1716			1.08751			0.543755	+	0.839244i	$0.317002\pi$
$380$		0			0
$381$	−16.0711	−	27.8359i	−0.823346	−	1.42608i
$382$	1.48528	+	2.57258i	0.0759936	+	0.131625i
$383$	8.44975	−	14.6354i	0.431762	−	0.747834i	−0.565263	−	0.824911i	$-0.691225\pi$
$383$	8.44975	−	14.6354i	0.431762	−	0.747834i	0.997025	+	0.0770770i	$0.0245587\pi$
$384$	25.4853			1.30054
$385$		0			0
$386$	0.828427			0.0421658
$387$	9.07107	−	15.7116i	0.461108	−	0.798663i
$388$	−0.313708	−	0.543359i	−0.0159261	−	0.0275849i
$389$	−6.17157	−	10.6895i	−0.312911	−	0.541978i	0.666080	−	0.745880i	$-0.267971\pi$
$389$	−6.17157	−	10.6895i	−0.312911	−	0.541978i	−0.978991	+	0.203902i	$0.934638\pi$
$390$		0			0
$391$	2.00000			0.101144
$392$	2.76346	+	10.7510i	0.139576	+	0.543009i
$393$	−8.00000			−0.403547
$394$	−4.89949	+	8.48617i	−0.246833	+	0.427527i
$395$		0			0
$396$	12.4853	+	21.6251i	0.627409	+	1.08670i
$397$	14.3137	−	24.7921i	0.718384	−	1.24428i	−0.243255	−	0.969962i	$-0.578215\pi$
$397$	14.3137	−	24.7921i	0.718384	−	1.24428i	0.961640	−	0.274316i	$-0.0884514\pi$
$398$	0.686292			0.0344007
$399$	11.0711	−	14.2767i	0.554247	−	0.714728i
$400$		0			0
$401$	−3.84315	+	6.65652i	−0.191918	+	0.332411i	−0.945886	−	0.324500i	$-0.894804\pi$
$401$	−3.84315	+	6.65652i	−0.191918	+	0.332411i	0.753968	+	0.656911i	$0.228137\pi$
$402$	−6.20711	−	10.7510i	−0.309582	−	0.536212i
$403$	−2.48528	−	4.30463i	−0.123801	−	0.214429i
$404$	11.2574	−	19.4983i	0.560075	−	0.970078i
$405$		0			0
$406$	−0.414214	−	1.01461i	−0.0205571	−	0.0503543i
$407$		0			0
$408$	−1.58579	+	2.74666i	−0.0785081	+	0.135980i
$409$	−12.3995	−	21.4766i	−0.613116	−	1.06195i	−0.990712	−	0.135977i	$-0.956583\pi$
$409$	−12.3995	−	21.4766i	−0.613116	−	1.06195i	0.377596	−	0.925970i	$-0.376751\pi$
$410$		0			0
$411$	−2.00000	+	3.46410i	−0.0986527	+	0.170872i
$412$	0.757359			0.0373124
$413$	32.7279	+	4.47871i	1.61044	+	0.220383i
$414$	2.82843			0.139010
$415$		0			0
$416$	1.82843	+	3.16693i	0.0896460	+	0.155271i
$417$	14.6569	+	25.3864i	0.717749	+	1.24318i
$418$	2.82843	−	4.89898i	0.138343	−	0.239617i
$419$	−23.3137			−1.13895			−0.569475	−	0.822009i	$-0.692853\pi$
$419$	−23.3137			−1.13895			−0.569475	+	0.822009i	$0.692853\pi$
$420$		0			0
$421$	−3.48528			−0.169862			−0.0849311	−	0.996387i	$-0.527067\pi$
$421$	−3.48528			−0.169862			−0.0849311	+	0.996387i	$0.527067\pi$
$422$	−0.727922	+	1.26080i	−0.0354347	+	0.0613747i
$423$	2.82843	+	4.89898i	0.137523	+	0.238197i
$424$	5.41421	+	9.37769i	0.262937	+	0.455421i
$425$		0			0
$426$	12.4853			0.604914
$427$	−11.4853	−	28.1331i	−0.555812	−	1.36146i
$428$	5.04163			0.243696
$429$	−4.82843	+	8.36308i	−0.233119	+	0.403773i
$430$		0			0
$431$	10.8995	+	18.8785i	0.525010	+	0.909344i	0.999576	+	0.0291242i	$0.00927183\pi$
$431$	10.8995	+	18.8785i	0.525010	+	0.909344i	−0.474566	+	0.880220i	$0.657395\pi$
$432$	−0.621320	+	1.07616i	−0.0298933	+	0.0517767i
$433$	31.7990			1.52816			0.764081	−	0.645120i	$-0.223193\pi$
$433$	31.7990			1.52816			0.764081	+	0.645120i	$0.223193\pi$
$434$	−4.02944	+	5.19615i	−0.193419	+	0.249423i
$435$		0			0
$436$	3.18629	−	5.51882i	0.152596	−	0.264303i
$437$	3.41421	+	5.91359i	0.163324	+	0.282885i
$438$	−2.41421	−	4.18154i	−0.115356	−	0.199802i
$439$	−16.9706	+	29.3939i	−0.809961	+	1.40289i	0.102930	+	0.994689i	$0.467178\pi$
$439$	−16.9706	+	29.3939i	−0.809961	+	1.40289i	−0.912890	+	0.408205i	$0.866155\pi$
$440$		0			0
$441$	19.0711	+	5.31925i	0.908146	+	0.253297i
$442$	−0.284271			−0.0135214
$443$	−6.10660	+	10.5769i	−0.290133	+	0.502526i	−0.973841	−	0.227230i	$-0.927033\pi$
$443$	−6.10660	+	10.5769i	−0.290133	+	0.502526i	0.683708	+	0.729756i	$0.260366\pi$
$444$		0			0
$445$		0			0
$446$	2.41421	−	4.18154i	0.114316	−	0.198002i
$447$	18.8995			0.893915
$448$	−6.76346	+	8.72180i	−0.319543	+	0.412066i
$449$	−1.82843			−0.0862888			−0.0431444	−	0.999069i	$-0.513738\pi$
$449$	−1.82843			−0.0862888			−0.0431444	+	0.999069i	$0.513738\pi$
$450$		0			0
$451$	5.24264	+	9.08052i	0.246866	+	0.427585i
$452$	−11.4142	−	19.7700i	−0.536879	−	0.929902i
$453$	0.414214	−	0.717439i	0.0194615	−	0.0337082i
$454$	−11.1716			−0.524308
$455$		0			0
$456$	−10.8284			−0.507088
$457$	−16.1421	+	27.9590i	−0.755097	+	1.30787i	0.190229	+	0.981740i	$0.439077\pi$
$457$	−16.1421	+	27.9590i	−0.755097	+	1.30787i	−0.945326	+	0.326127i	$0.894256\pi$
$458$	0.0710678	+	0.123093i	0.00332078	+	0.00575176i
$459$	−0.171573	−	0.297173i	−0.00800834	−	0.0138708i
$460$		0			0
$461$	18.6863			0.870307			0.435154	−	0.900356i	$-0.356694\pi$
$461$	18.6863			0.870307			0.435154	+	0.900356i	$0.356694\pi$
$462$	12.6569	+	1.73205i	0.588850	+	0.0805823i
$463$	−11.0416			−0.513148			−0.256574	−	0.966525i	$-0.582594\pi$
$463$	−11.0416			−0.513148			−0.256574	+	0.966525i	$0.582594\pi$
$464$	1.50000	−	2.59808i	0.0696358	−	0.120613i
$465$		0			0
$466$	−2.31371	−	4.00746i	−0.107180	−	0.185642i
$467$	−11.4497	+	19.8315i	−0.529831	+	0.917694i	0.469563	+	0.882899i	$0.344411\pi$
$467$	−11.4497	+	19.8315i	−0.529831	+	0.917694i	−0.999394	+	0.0347956i	$0.988922\pi$
$468$	4.28427			0.198041
$469$	32.5416	+	4.45322i	1.50263	+	0.205631i
$470$		0			0
$471$	6.41421	−	11.1097i	0.295551	−	0.511910i
$472$	−9.89949	−	17.1464i	−0.455661	−	0.789228i
$473$	15.4853	+	26.8213i	0.712014	+	1.23324i
$474$	4.58579	−	7.94282i	0.210632	−	0.364826i
$475$		0			0
$476$	−1.51472	−	3.71029i	−0.0694270	−	0.170061i
$477$	19.3137			0.884314
$478$	−0.272078	+	0.471253i	−0.0124446	+	0.0215546i
$479$	12.1716	+	21.0818i	0.556133	+	0.963251i	0.997814	+	0.0660791i	$0.0210490\pi$
$479$	12.1716	+	21.0818i	0.556133	+	0.963251i	−0.441681	+	0.897172i	$0.645618\pi$
$480$		0			0
$481$		0			0
$482$	6.76955			0.308345
$483$	−9.44975	+	12.1859i	−0.429978	+	0.554478i
$484$	−22.5147			−1.02340
$485$		0			0
$486$	−4.48528	−	7.76874i	−0.203456	−	0.352397i
$487$	7.82843	+	13.5592i	0.354740	+	0.614428i	0.987073	−	0.160269i	$-0.0512361\pi$
$487$	7.82843	+	13.5592i	0.354740	+	0.614428i	−0.632334	+	0.774696i	$0.717903\pi$
$488$	−9.10660	+	15.7731i	−0.412236	+	0.714015i
$489$	57.1127			2.58273
$490$		0			0
$491$	−13.3137			−0.600839			−0.300420	−	0.953807i	$-0.597127\pi$
$491$	−13.3137			−0.600839			−0.300420	+	0.953807i	$0.597127\pi$
$492$	4.79289	−	8.30153i	0.216080	−	0.374262i
$493$	0.414214	+	0.717439i	0.0186552	+	0.0323118i
$494$	−0.485281	−	0.840532i	−0.0218338	−	0.0378173i
$495$		0			0
$496$	−18.0000			−0.808224
$497$	−20.2426	+	26.1039i	−0.908007	+	1.17092i
$498$	−11.7279			−0.525541
$499$	−2.41421	+	4.18154i	−0.108075	+	0.187191i	−0.914990	−	0.403476i	$-0.867802\pi$
$499$	−2.41421	+	4.18154i	−0.108075	+	0.187191i	0.806915	+	0.590667i	$0.201135\pi$
$500$		0			0
$501$	−23.6421	−	40.9494i	−1.05625	−	1.82948i
$502$	−2.75736	+	4.77589i	−0.123067	+	0.213158i
$503$	−37.8701			−1.68854			−0.844271	−	0.535916i	$-0.819966\pi$
$503$	−37.8701			−1.68854			−0.844271	+	0.535916i	$0.819966\pi$
$504$	−4.48528	−	10.9867i	−0.199790	−	0.489384i
$505$		0			0
$506$	−2.41421	+	4.18154i	−0.107325	+	0.185892i
$507$	−14.8640	−	25.7451i	−0.660132	−	1.14338i
$508$	−12.1716	−	21.0818i	−0.540026	−	0.935353i
$509$	−12.3284	+	21.3535i	−0.546448	+	0.946476i	0.452066	+	0.891984i	$0.350687\pi$
$509$	−12.3284	+	21.3535i	−0.546448	+	0.946476i	−0.998514	+	0.0544912i	$0.982646\pi$
$510$		0			0
$511$	12.6569	+	1.73205i	0.559906	+	0.0766214i
$512$	22.7574			1.00574
$513$	0.585786	−	1.01461i	0.0258631	−	0.0447962i
$514$	3.65685	+	6.33386i	0.161297	+	0.279374i
$515$		0			0
$516$	14.1569	−	24.5204i	0.623221	−	1.07945i
$517$	−9.65685			−0.424708
$518$		0			0
$519$	−46.6274			−2.04672
$520$		0			0
$521$	9.48528	+	16.4290i	0.415558	+	0.719767i	0.995487	−	0.0948999i	$-0.0302531\pi$
$521$	9.48528	+	16.4290i	0.415558	+	0.719767i	−0.579929	+	0.814667i	$0.696920\pi$
$522$	0.585786	+	1.01461i	0.0256392	+	0.0444084i
$523$	12.1716	−	21.0818i	0.532226	−	0.921842i	−0.467066	−	0.884222i	$-0.654689\pi$
$523$	12.1716	−	21.0818i	0.532226	−	0.921842i	0.999292	−	0.0376197i	$-0.0119776\pi$
$524$	−6.05887			−0.264683
$525$		0			0
$526$	−7.88730			−0.343903
$527$	2.48528	−	4.30463i	0.108261	−	0.187513i
$528$	17.4853	+	30.2854i	0.760949	+	1.31800i
$529$	8.58579	+	14.8710i	0.373295	+	0.646566i
$530$		0			0
$531$	−35.3137			−1.53248
$532$	8.38478	−	10.8126i	0.363526	−	0.468784i
$533$	1.79899			0.0779229
$534$	1.32843	−	2.30090i	0.0574867	−	0.0995698i
$535$		0			0
$536$	−9.84315	−	17.0488i	−0.425159	−	0.736397i
$537$	−12.0711	+	20.9077i	−0.520905	+	0.902234i
$538$	−12.6152			−0.543881
$539$	−24.1421	+	23.6544i	−1.03988	+	1.01887i
$540$		0			0
$541$	−9.32843	+	16.1573i	−0.401060	+	0.694657i	−0.993854	−	0.110697i	$-0.964692\pi$
$541$	−9.32843	+	16.1573i	−0.401060	+	0.694657i	0.592794	+	0.805354i	$0.298025\pi$
$542$	0.100505	+	0.174080i	0.00431706	+	0.00747737i
$543$	−10.4497	−	18.0995i	−0.448442	−	0.776724i
$544$	−1.82843	+	3.16693i	−0.0783932	+	0.135781i
$545$		0			0
$546$	1.34315	−	1.73205i	0.0574813	−	0.0741249i
$547$	−5.10051			−0.218082			−0.109041	−	0.994037i	$-0.534778\pi$
$547$	−5.10051			−0.218082			−0.109041	+	0.994037i	$0.534778\pi$
$548$	−1.51472	+	2.62357i	−0.0647056	+	0.112073i
$549$	16.2426	+	28.1331i	0.693219	+	1.20069i
$550$		0			0
$551$	−1.41421	+	2.44949i	−0.0602475	+	0.104352i
$552$	9.24264			0.393393
$553$	9.17157	+	22.4657i	0.390015	+	0.955338i
$554$	5.02944			0.213680
$555$		0			0
$556$	11.1005	+	19.2266i	0.470766	+	0.815391i
$557$	−17.1421	−	29.6910i	−0.726336	−	1.25805i	−0.958422	−	0.285355i	$-0.907889\pi$
$557$	−17.1421	−	29.6910i	−0.726336	−	1.25805i	0.232086	−	0.972695i	$-0.425445\pi$
$558$	3.51472	−	6.08767i	0.148790	−	0.257712i
$559$	5.31371			0.224746
$560$		0			0
$561$	−9.65685			−0.407713
$562$	−5.44365	+	9.42868i	−0.229627	+	0.397725i
$563$	8.13604	+	14.0920i	0.342893	+	0.593908i	0.984969	−	0.172733i	$-0.0552598\pi$
$563$	8.13604	+	14.0920i	0.342893	+	0.593908i	−0.642076	+	0.766641i	$0.721926\pi$
$564$	4.41421	+	7.64564i	0.185872	+	0.321940i
$565$		0			0
$566$	−5.79899			−0.243750
$567$	24.8640	+	3.40256i	1.04419	+	0.142894i
$568$	19.7990			0.830747
$569$	1.82843	−	3.16693i	0.0766517	−	0.132765i	−0.825152	−	0.564911i	$-0.808910\pi$
$569$	1.82843	−	3.16693i	0.0766517	−	0.132765i	0.901803	+	0.432147i	$0.142244\pi$
$570$		0			0
$571$	−7.41421	−	12.8418i	−0.310275	−	0.537412i	0.668147	−	0.744030i	$-0.267088\pi$
$571$	−7.41421	−	12.8418i	−0.310275	−	0.537412i	−0.978422	+	0.206617i	$0.933755\pi$
$572$	−3.65685	+	6.33386i	−0.152901	+	0.264832i
$573$	17.3137			0.723291
$574$	−0.899495	−	2.20330i	−0.0375442	−	0.0919641i
$575$		0			0
$576$	5.89949	−	10.2182i	0.245812	−	0.425759i
$577$	11.9706	+	20.7336i	0.498341	+	0.863152i	0.999998	−	0.00191453i	$-0.000609416\pi$
$577$	11.9706	+	20.7336i	0.498341	+	0.863152i	−0.501657	+	0.865067i	$0.667276\pi$
$578$	3.37868	+	5.85204i	0.140535	+	0.243413i
$579$	2.41421	−	4.18154i	0.100331	−	0.173779i
$580$		0			0
$581$	19.0147	−	24.5204i	0.788863	−	1.01728i
$582$	0.343146			0.0142238
$583$	−16.4853	+	28.5533i	−0.682751	+	1.18256i
$584$	−3.82843	−	6.63103i	−0.158421	−	0.274394i
$585$		0			0
$586$	−3.31371	+	5.73951i	−0.136888	+	0.237097i
$587$	−22.2843			−0.919770			−0.459885	−	0.887978i	$-0.652109\pi$
$587$	−22.2843			−0.919770			−0.459885	+	0.887978i	$0.652109\pi$
$588$	29.7635	+	8.30153i	1.22742	+	0.342350i
$589$	16.9706			0.699260
$590$		0			0
$591$	28.5563	+	49.4610i	1.17465	+	2.03456i
$592$		0			0
$593$	21.8995	−	37.9310i	0.899304	−	1.55764i	0.0709193	−	0.997482i	$-0.477407\pi$
$593$	21.8995	−	37.9310i	0.899304	−	1.55764i	0.828385	−	0.560159i	$-0.189260\pi$
$594$	0.828427			0.0339908
$595$		0			0
$596$	14.3137			0.586312
$597$	2.00000	−	3.46410i	0.0818546	−	0.141776i
$598$	0.414214	+	0.717439i	0.0169385	+	0.0293383i
$599$	−8.82843	−	15.2913i	−0.360720	−	0.624785i	0.627360	−	0.778730i	$-0.284136\pi$
$599$	−8.82843	−	15.2913i	−0.360720	−	0.624785i	−0.988079	+	0.153945i	$0.950802\pi$
$600$		0			0
$601$	8.34315			0.340324			0.170162	−	0.985416i	$-0.445571\pi$
$601$	8.34315			0.340324			0.170162	+	0.985416i	$0.445571\pi$
$602$	−2.65685	−	6.50794i	−0.108285	−	0.265244i
$603$	−35.1127			−1.42990
$604$	0.313708	−	0.543359i	0.0127646	−	0.0221090i
$605$		0			0
$606$	6.15685	+	10.6640i	0.250105	+	0.433195i
$607$	−2.10660	+	3.64874i	−0.0855043	+	0.148098i	−0.905606	−	0.424120i	$-0.860583\pi$
$607$	−2.10660	+	3.64874i	−0.0855043	+	0.148098i	0.820102	+	0.572218i	$0.193917\pi$
$608$	−12.4853			−0.506345
$609$	−6.32843	−	0.866025i	−0.256441	−	0.0350931i
$610$		0			0
$611$	−0.828427	+	1.43488i	−0.0335146	+	0.0580489i
$612$	2.14214	+	3.71029i	0.0865907	+	0.149979i
$613$	−7.72792	−	13.3852i	−0.312128	−	0.540621i	0.666695	−	0.745331i	$-0.267708\pi$
$613$	−7.72792	−	13.3852i	−0.312128	−	0.540621i	−0.978823	+	0.204709i	$0.934375\pi$
$614$	−2.74264	+	4.75039i	−0.110684	+	0.191710i
$615$		0			0
$616$	20.0711	+	2.74666i	0.808686	+	0.110666i
$617$	11.3137			0.455473			0.227736	−	0.973723i	$-0.426868\pi$
$617$	11.3137			0.455473			0.227736	+	0.973723i	$0.426868\pi$
$618$	−0.207107	+	0.358719i	−0.00833106	+	0.0144298i
$619$	−21.2426	−	36.7933i	−0.853814	−	1.47885i	−0.877741	−	0.479135i	$-0.840950\pi$
$619$	−21.2426	−	36.7933i	−0.853814	−	1.47885i	0.0239273	−	0.999714i	$-0.492383\pi$
$620$		0			0
$621$	−0.500000	+	0.866025i	−0.0200643	+	0.0347524i
$622$	−7.79899			−0.312711
$623$	2.65685	+	6.50794i	0.106445	+	0.260735i
$624$	6.00000			0.240192
$625$		0			0
$626$	−3.65685	−	6.33386i	−0.146157	−	0.253152i
$627$	−16.4853	−	28.5533i	−0.658359	−	1.14031i
$628$	4.85786	−	8.41407i	0.193850	−	0.335758i
$629$		0			0
$630$		0			0
$631$	8.14214			0.324133			0.162067	−	0.986780i	$-0.448184\pi$
$631$	8.14214			0.324133			0.162067	+	0.986780i	$0.448184\pi$
$632$	7.27208	−	12.5956i	0.289268	−	0.501026i
$633$	4.24264	+	7.34847i	0.168630	+	0.292075i
$634$	5.34315	+	9.25460i	0.212203	+	0.367547i
$635$		0			0
$636$	30.1421			1.19521
$637$	1.44365	+	5.61642i	0.0571995	+	0.222531i
$638$	−2.00000			−0.0791808
$639$	17.6569	−	30.5826i	0.698494	−	1.20983i
$640$		0			0
$641$	−7.25736	−	12.5701i	−0.286648	−	0.496490i	0.686359	−	0.727263i	$-0.259208\pi$
$641$	−7.25736	−	12.5701i	−0.286648	−	0.496490i	−0.973008	+	0.230773i	$0.925875\pi$
$642$	−1.37868	+	2.38794i	−0.0544121	+	0.0942446i
$643$	30.2843			1.19430			0.597148	−	0.802131i	$-0.296301\pi$
$643$	30.2843			1.19430			0.597148	+	0.802131i	$0.296301\pi$
$644$	−7.15685	+	9.22911i	−0.282020	+	0.363678i
$645$		0			0
$646$	0.485281	−	0.840532i	0.0190931	−	0.0330703i
$647$	8.52082	+	14.7585i	0.334988	+	0.580216i	0.983482	−	0.181003i	$-0.0579345\pi$
$647$	8.52082	+	14.7585i	0.334988	+	0.580216i	−0.648495	+	0.761219i	$0.724601\pi$
$648$	−7.52082	−	13.0264i	−0.295446	−	0.511727i
$649$	30.1421	−	52.2077i	1.18318	−	2.04933i
$650$		0			0
$651$	14.4853	+	35.4815i	0.567723	+	1.39063i
$652$	43.2548			1.69399
$653$	−12.4142	+	21.5020i	−0.485806	+	0.841440i	−0.999867	−	0.0163133i	$-0.994807\pi$
$653$	−12.4142	+	21.5020i	−0.485806	+	0.841440i	0.514061	+	0.857754i	$0.328140\pi$
$654$	1.74264	+	3.01834i	0.0681426	+	0.118027i
$655$		0			0
$656$	3.25736	−	5.64191i	0.127179	−	0.220280i
$657$	−13.6569			−0.532805
$658$	2.17157	+	0.297173i	0.0846567	+	0.0115850i
$659$	26.8284			1.04509			0.522544	−	0.852613i	$-0.324983\pi$
$659$	26.8284			1.04509			0.522544	+	0.852613i	$0.324983\pi$
$660$		0			0
$661$	−13.0858	−	22.6652i	−0.508978	−	0.881576i	−0.999946	−	0.0103982i	$-0.996690\pi$
$661$	−13.0858	−	22.6652i	−0.508978	−	0.881576i	0.490968	−	0.871178i	$-0.336643\pi$
$662$	2.27208	+	3.93535i	0.0883068	+	0.152952i
$663$	−0.828427	+	1.43488i	−0.0321734	+	0.0557260i
$664$	−18.5980			−0.721742
$665$		0			0
$666$		0			0
$667$	1.20711	−	2.09077i	0.0467394	−	0.0809549i
$668$	−17.9056	−	31.0134i	−0.692788	−	1.19994i
$669$	−14.0711	−	24.3718i	−0.544019	−	0.942268i
$670$		0			0
$671$	−55.4558			−2.14085
$672$	−10.6569	−	26.1039i	−0.411097	−	1.00698i
$673$	−18.3431			−0.707076			−0.353538	−	0.935420i	$-0.615022\pi$
$673$	−18.3431			−0.707076			−0.353538	+	0.935420i	$0.615022\pi$
$674$	3.07107	−	5.31925i	0.118293	−	0.204890i
$675$		0			0
$676$	−11.2574	−	19.4983i	−0.432975	−	0.749935i
$677$	0.0710678	−	0.123093i	0.00273136	−	0.00473085i	−0.864656	−	0.502364i	$-0.832464\pi$
$677$	0.0710678	−	0.123093i	0.00273136	−	0.00473085i	0.867388	+	0.497633i	$0.165797\pi$
$678$	12.4853			0.479494
$679$	−0.556349	+	0.717439i	−0.0213507	+	0.0275328i
$680$		0			0
$681$	−32.5563	+	56.3893i	−1.24756	+	2.16084i
$682$	6.00000	+	10.3923i	0.229752	+	0.397942i
$683$	−21.6213	−	37.4492i	−0.827317	−	1.43295i	−0.900136	−	0.435610i	$-0.856533\pi$
$683$	−21.6213	−	37.4492i	−0.827317	−	1.43295i	0.0728189	−	0.997345i	$-0.476801\pi$
$684$	−7.31371	+	12.6677i	−0.279647	+	0.484362i
$685$		0			0
$686$	6.15685	−	4.57631i	0.235070	−	0.174724i
$687$	0.828427			0.0316065
$688$	9.62132	−	16.6646i	0.366809	−	0.635333i
$689$	2.82843	+	4.89898i	0.107754	+	0.186636i
$690$		0			0
$691$	2.41421	−	4.18154i	0.0918410	−	0.159073i	−0.816445	−	0.577423i	$-0.804058\pi$
$691$	2.41421	−	4.18154i	0.0918410	−	0.159073i	0.908286	+	0.418350i	$0.137392\pi$
$692$	−35.3137			−1.34243
$693$	22.1421	−	28.5533i	0.841110	−	1.08465i
$694$	−9.14214			−0.347031
$695$		0			0
$696$	1.91421	+	3.31552i	0.0725581	+	0.125674i
$697$	0.899495	+	1.55797i	0.0340708	+	0.0590124i
$698$	5.52082	−	9.56233i	0.208966	−	0.361940i
$699$	−26.9706			−1.02012
$700$		0			0
$701$	−42.7990			−1.61650			−0.808248	−	0.588843i	$-0.799584\pi$
$701$	−42.7990			−1.61650			−0.808248	+	0.588843i	$0.799584\pi$
$702$	0.0710678	−	0.123093i	0.00268228	−	0.00464585i
$703$		0			0
$704$	10.0711	+	17.4436i	0.379568	+	0.657430i
$705$		0			0
$706$	8.76955			0.330046
$707$	−32.2782	−	4.41717i	−1.21395	−	0.166125i
$708$	−55.1127			−2.07126
$709$	−19.1569	+	33.1806i	−0.719451	+	1.24613i	0.241767	+	0.970334i	$0.422273\pi$
$709$	−19.1569	+	33.1806i	−0.719451	+	1.24613i	−0.961218	+	0.275791i	$0.911060\pi$
$710$		0			0
$711$	−12.9706	−	22.4657i	−0.486434	−	0.842529i
$712$	2.10660	−	3.64874i	0.0789482	−	0.136742i
$713$	−14.4853			−0.542478
$714$	2.17157	+	0.297173i	0.0812691	+	0.0111214i
$715$		0			0
$716$	−9.14214	+	15.8346i	−0.341658	+	0.591768i
$717$	1.58579	+	2.74666i	0.0592223	+	0.102576i
$718$	2.07107	+	3.58719i	0.0772916	+	0.133873i
$719$	20.5563	−	35.6046i	0.766622	−	1.32783i	−0.172762	−	0.984964i	$-0.555269\pi$
$719$	20.5563	−	35.6046i	0.766622	−	1.32783i	0.939385	−	0.342865i	$-0.111398\pi$
$720$		0			0
$721$	−0.414214	−	1.01461i	−0.0154261	−	0.0377861i
$722$	−4.55635			−0.169570
$723$	19.7279	−	34.1698i	0.733689	−	1.27079i
$724$	−7.91421	−	13.7078i	−0.294129	−	0.509447i
$725$		0			0
$726$	6.15685	−	10.6640i	0.228502	−	0.395778i
$727$	40.4142			1.49888			0.749440	−	0.662072i	$-0.230323\pi$
$727$	40.4142			1.49888			0.749440	+	0.662072i	$0.230323\pi$
$728$	2.12994	−	2.74666i	0.0789409	−	0.101798i
$729$	−23.8284			−0.882534
$730$		0			0
$731$	2.65685	+	4.60181i	0.0982673	+	0.170204i
$732$	25.3492	+	43.9062i	0.936935	+	1.62282i
$733$	−11.0000	+	19.0526i	−0.406294	+	0.703722i	−0.994471	−	0.105010i	$-0.966513\pi$
$733$	−11.0000	+	19.0526i	−0.406294	+	0.703722i	0.588177	+	0.808732i	$0.299846\pi$
$734$	4.65685			0.171888
$735$		0			0
$736$	10.6569			0.392817
$737$	29.9706	−	51.9105i	1.10398	−	1.91215i
$738$	1.27208	+	2.20330i	0.0468258	+	0.0811047i
$739$	−20.5563	−	35.6046i	−0.756178	−	1.30974i	−0.944787	−	0.327686i	$-0.893731\pi$
$739$	−20.5563	−	35.6046i	−0.756178	−	1.30974i	0.188609	−	0.982052i	$-0.439602\pi$
$740$		0			0
$741$	−5.65685			−0.207810
$742$	4.58579	−	5.91359i	0.168350	−	0.217095i
$743$	1.92893			0.0707657			0.0353828	−	0.999374i	$-0.488735\pi$
$743$	1.92893			0.0707657			0.0353828	+	0.999374i	$0.488735\pi$
$744$	11.4853	−	19.8931i	0.421071	−	0.729316i
$745$		0			0
$746$	2.68629	+	4.65279i	0.0983521	+	0.170351i
$747$	−16.5858	+	28.7274i	−0.606842	+	1.05108i
$748$	−7.31371			−0.267416
$749$	−2.75736	−	6.75412i	−0.100752	−	0.246790i
$750$		0			0
$751$	20.8284	−	36.0759i	0.760040	−	1.31643i	−0.182789	−	0.983152i	$-0.558513\pi$
$751$	20.8284	−	36.0759i	0.760040	−	1.31643i	0.942829	−	0.333276i	$-0.108154\pi$
$752$	3.00000	+	5.19615i	0.109399	+	0.189484i
$753$	16.0711	+	27.8359i	0.585662	+	1.01440i
$754$	−0.171573	+	0.297173i	−0.00624832	+	0.0108224i
$755$		0			0
$756$	1.98528	+	0.271680i	0.0722040	+	0.00988089i
$757$	−19.4558			−0.707135			−0.353567	−	0.935409i	$-0.615031\pi$
$757$	−19.4558			−0.707135			−0.353567	+	0.935409i	$0.615031\pi$
$758$	−4.38478	+	7.59466i	−0.159262	+	0.275850i
$759$	14.0711	+	24.3718i	0.510747	+	0.884640i
$760$		0			0
$761$	6.65685	−	11.5300i	0.241311	−	0.417963i	−0.719777	−	0.694205i	$-0.755756\pi$
$761$	6.65685	−	11.5300i	0.241311	−	0.417963i	0.961088	+	0.276243i	$0.0890894\pi$
$762$	13.3137			0.482305
$763$	−9.13604	−	1.25024i	−0.330747	−	0.0452617i
$764$	13.1127			0.474401
$765$		0			0
$766$	3.50000	+	6.06218i	0.126460	+	0.219035i
$767$	−5.17157	−	8.95743i	−0.186735	−	0.323434i
$768$	4.79289	−	8.30153i	0.172949	−	0.299556i
$769$	44.6274			1.60931			0.804653	−	0.593745i	$-0.202351\pi$
$769$	44.6274			1.60931			0.804653	+	0.593745i	$0.202351\pi$
$770$		0			0
$771$	42.6274			1.53519
$772$	1.82843	−	3.16693i	0.0658065	−	0.113980i
$773$	12.5563	+	21.7482i	0.451620	+	0.782230i	0.998487	−	0.0549903i	$-0.0175128\pi$
$773$	12.5563	+	21.7482i	0.451620	+	0.782230i	−0.546866	+	0.837220i	$0.684179\pi$
$774$	3.75736	+	6.50794i	0.135055	+	0.233923i
$775$		0			0
$776$	0.544156			0.0195341
$777$		0			0
$778$	5.11270			0.183299
$779$	−3.07107	+	5.31925i	−0.110032	+	0.190582i
$780$		0			0
$781$	30.1421	+	52.2077i	1.07857	+	1.86814i
$782$	−0.414214	+	0.717439i	−0.0148122	+	0.0256556i
$783$	−0.414214			−0.0148028
$784$	20.2279	+	5.64191i	0.722426	+	0.201497i
$785$		0			0
$786$	1.65685	−	2.86976i	0.0590980	−	0.102361i
$787$	−14.2782	−	24.7305i	−0.508962	−	0.881548i	−0.999946	−	0.0103795i	$-0.996696\pi$
$787$	−14.2782	−	24.7305i	−0.508962	−	0.881548i	0.490984	−	0.871168i	$-0.336637\pi$
$788$	21.6274	+	37.4598i	0.770445	+	1.33445i
$789$	−22.9853	+	39.8117i	−0.818298	+	1.41733i
$790$		0			0
$791$	−20.2426	+	26.1039i	−0.719745	+	0.928146i
$792$	−21.6569			−0.769543
$793$	−4.75736	+	8.23999i	−0.168939	+	0.292611i
$794$	5.92893	+	10.2692i	0.210410	+	0.364441i
$795$		0			0
$796$	1.51472	−	2.62357i	0.0536878	−	0.0929900i
$797$	8.00000			0.283375			0.141687	−	0.989911i	$-0.454747\pi$
$797$	8.00000			0.283375			0.141687	+	0.989911i	$0.454747\pi$
$798$	2.82843	+	6.92820i	0.100125	+	0.245256i
$799$	−1.65685			−0.0586153
$800$		0			0
$801$	−3.75736	−	6.50794i	−0.132760	−	0.229947i
$802$	−1.59188	−	2.75722i	−0.0562113	−	0.0973609i
$803$	11.6569	−	20.1903i	0.411361	−	0.712499i
$804$	−54.7990			−1.93261
$805$		0			0
$806$	2.05887			0.0725208
$807$	−36.7635	+	63.6762i	−1.29413	+	2.24151i
$808$	9.76346	+	16.9108i	0.343477	+	0.594920i
$809$	4.81371	+	8.33759i	0.169241	+	0.293134i	0.938153	−	0.346220i	$-0.112535\pi$
$809$	4.81371	+	8.33759i	0.169241	+	0.293134i	−0.768912	+	0.639354i	$0.779202\pi$
$810$		0			0
$811$	24.6274			0.864786			0.432393	−	0.901685i	$-0.357669\pi$
$811$	24.6274			0.864786			0.432393	+	0.901685i	$0.357669\pi$
$812$	−4.79289	−	0.655892i	−0.168198	−	0.0230173i
$813$	1.17157			0.0410889
$814$		0			0
$815$		0			0
$816$	3.00000	+	5.19615i	0.105021	+	0.181902i
$817$	−9.07107	+	15.7116i	−0.317356	+	0.549678i
$818$	10.2721			0.359155
$819$	−2.34315	−	5.73951i	−0.0818761	−	0.200555i
$820$		0			0
$821$	9.97056	−	17.2695i	0.347975	−	0.602710i	−0.637915	−	0.770107i	$-0.720203\pi$
$821$	9.97056	−	17.2695i	0.347975	−	0.602710i	0.985890	+	0.167397i	$0.0535361\pi$
$822$	−0.828427	−	1.43488i	−0.0288947	−	0.0500471i
$823$	−6.03553	−	10.4539i	−0.210385	−	0.364398i	0.741450	−	0.671008i	$-0.234139\pi$
$823$	−6.03553	−	10.4539i	−0.210385	−	0.364398i	−0.951835	+	0.306610i	$0.900805\pi$
$824$	−0.328427	+	0.568852i	−0.0114413	+	0.0198169i
$825$		0			0
$826$	−8.38478	+	10.8126i	−0.291744	+	0.376217i
$827$	−16.2132			−0.563788			−0.281894	−	0.959446i	$-0.590963\pi$
$827$	−16.2132			−0.563788			−0.281894	+	0.959446i	$0.590963\pi$
$828$	6.24264	−	10.8126i	0.216947	−	0.375763i
$829$	−3.34315	−	5.79050i	−0.116112	−	0.201112i	0.802112	−	0.597174i	$-0.203710\pi$
$829$	−3.34315	−	5.79050i	−0.116112	−	0.201112i	−0.918224	+	0.396062i	$0.870377\pi$
$830$		0			0
$831$	14.6569	−	25.3864i	0.508441	−	0.880645i
$832$	3.45584			0.119810
$833$	−4.14214	+	4.05845i	−0.143516	+	0.140617i
$834$	−12.1421			−0.420448
$835$		0			0
$836$	−12.4853	−	21.6251i	−0.431812	−	0.747921i
$837$	1.24264	+	2.15232i	0.0429519	+	0.0743950i
$838$	4.82843	−	8.36308i	0.166795	−	0.288898i
$839$	20.8284			0.719077			0.359539	−	0.933130i	$-0.382934\pi$
$839$	20.8284			0.719077			0.359539	+	0.933130i	$0.382934\pi$
$840$		0			0
$841$	−28.0000			−0.965517
$842$	0.721825	−	1.25024i	0.0248757	−	0.0430861i
$843$	31.7279	+	54.9544i	1.09277	+	1.89273i
$844$	3.21320	+	5.56543i	0.110603	+	0.191570i
$845$		0			0
$846$	−2.34315			−0.0805590
$847$	12.3137	+	30.1623i	0.423104	+	1.03639i
$848$	20.4853			0.703467
$849$	−16.8995	+	29.2708i	−0.579989	+	1.00457i
$850$		0			0
$851$		0			0
$852$	27.5563	−	47.7290i	0.944065	−	1.63517i
$853$	−53.4558			−1.83029			−0.915147	−	0.403121i	$-0.867925\pi$
$853$	−53.4558			−1.83029			−0.915147	+	0.403121i	$0.867925\pi$
$854$	12.4706	+	1.70656i	0.426734	+	0.0583972i
$855$		0			0
$856$	−2.18629	+	3.78677i	−0.0747259	+	0.129429i
$857$	−11.1421	−	19.2987i	−0.380608	−	0.659233i	0.610541	−	0.791985i	$-0.290952\pi$
$857$	−11.1421	−	19.2987i	−0.380608	−	0.659233i	−0.991149	+	0.132752i	$0.957619\pi$
$858$	−2.00000	−	3.46410i	−0.0682789	−	0.118262i
$859$	−23.3137	+	40.3805i	−0.795453	+	1.37777i	0.127097	+	0.991890i	$0.459434\pi$
$859$	−23.3137	+	40.3805i	−0.795453	+	1.37777i	−0.922551	+	0.385876i	$0.873899\pi$
$860$		0			0
$861$	−13.7426	−	1.88064i	−0.468348	−	0.0640919i
$862$	−9.02944			−0.307544
$863$	−8.27817	+	14.3382i	−0.281792	+	0.488079i	−0.971826	−	0.235698i	$-0.924262\pi$
$863$	−8.27817	+	14.3382i	−0.281792	+	0.488079i	0.690034	+	0.723777i	$0.257596\pi$
$864$	−0.914214	−	1.58346i	−0.0311022	−	0.0538706i
$865$		0			0
$866$	−6.58579	+	11.4069i	−0.223794	+	0.387623i
$867$	39.3848			1.33758
$868$	10.9706	+	26.8723i	0.372365	+	0.912105i
$869$	44.2843			1.50224
$870$		0			0
$871$	−5.14214	−	8.90644i	−0.174235	−	0.301783i
$872$	2.76346	+	4.78645i	0.0935824	+	0.162090i
$873$	0.485281	−	0.840532i	0.0164243	−	0.0284477i
$874$	−2.82843			−0.0956730
$875$		0			0
$876$	−21.3137			−0.720123
$877$	15.4142	−	26.6982i	0.520501	−	0.901534i	−0.479215	−	0.877698i	$-0.659079\pi$
$877$	15.4142	−	26.6982i	0.520501	−	0.901534i	0.999716	−	0.0238366i	$-0.00758813\pi$
$878$	−7.02944	−	12.1753i	−0.237232	−	0.410898i
$879$	19.3137	+	33.4523i	0.651435	+	1.12832i
$880$		0			0
$881$	−3.82843			−0.128983			−0.0644915	−	0.997918i	$-0.520543\pi$
$881$	−3.82843			−0.128983			−0.0644915	+	0.997918i	$0.520543\pi$
$882$	−5.85786	+	5.73951i	−0.197245	+	0.193259i
$883$	38.2843			1.28837			0.644184	−	0.764870i	$-0.277197\pi$
$883$	38.2843			1.28837			0.644184	+	0.764870i	$0.277197\pi$
$884$	−0.627417	+	1.08672i	−0.0211023	+	0.0365503i
$885$		0			0
$886$	−2.52944	−	4.38111i	−0.0849781	−	0.147186i
$887$	22.0355	−	38.1667i	0.739881	−	1.28151i	−0.212668	−	0.977125i	$-0.568215\pi$
$887$	22.0355	−	38.1667i	0.739881	−	1.28151i	0.952549	−	0.304387i	$-0.0984515\pi$
$888$		0			0
$889$	−21.5858	+	27.8359i	−0.723964	+	0.933586i
$890$		0			0
$891$	22.8995	−	39.6631i	0.767162	−	1.32876i
$892$	−10.6569	−	18.4582i	−0.356818	−	0.618027i
$893$	−2.82843	−	4.89898i	−0.0946497	−	0.163938i
$894$	−3.91421	+	6.77962i	−0.130911	+	0.226744i
$895$		0			0
$896$	−10.5563	−	25.8577i	−0.352663	−	0.863844i
$897$	4.82843			0.161216
$898$	0.378680	−	0.655892i	0.0126367	−	0.0218874i
$899$	−3.00000	−	5.19615i	−0.100056	−	0.173301i
$900$		0			0
$901$	−2.82843	+	4.89898i	−0.0942286	+	0.163209i
$902$	−4.34315			−0.144611
$903$	−40.5919	−	5.55487i	−1.35081	−	0.184855i
$904$	19.7990			0.658505
$905$		0			0
$906$	0.171573	+	0.297173i	0.00570013	+	0.00987291i
$907$	14.1066	+	24.4334i	0.468402	+	0.811296i	0.999348	−	0.0361097i	$-0.0114966\pi$
$907$	14.1066	+	24.4334i	0.468402	+	0.811296i	−0.530946	+	0.847406i	$0.678163\pi$
$908$	−24.6569	+	42.7069i	−0.818266	+	1.41728i
$909$	34.8284			1.15519
$910$		0			0
$911$	−49.7990			−1.64991			−0.824957	−	0.565195i	$-0.808801\pi$
$911$	−49.7990			−1.64991			−0.824957	+	0.565195i	$0.808801\pi$
$912$	−10.2426	+	17.7408i	−0.339168	+	0.587456i
$913$	−28.3137	−	49.0408i	−0.937047	−	1.62301i
$914$	−6.68629	−	11.5810i	−0.221163	−	0.383065i
$915$		0			0
$916$	0.627417			0.0207304
$917$	3.31371	+	8.11689i	0.109428	+	0.268043i
$918$	0.142136			0.00469117
$919$	−9.55635	+	16.5521i	−0.315235	+	0.546003i	−0.979487	−	0.201505i	$-0.935417\pi$
$919$	−9.55635	+	16.5521i	−0.315235	+	0.546003i	0.664253	+	0.747508i	$0.268750\pi$
$920$		0			0
$921$	15.9853	+	27.6873i	0.526733	+	0.912328i
$922$	−3.87006	+	6.70314i	−0.127454	+	0.220756i
$923$	10.3431			0.340449
$924$	34.5563	−	44.5621i	1.13682	−	1.46598i
$925$		0			0
$926$	2.28680	−	3.96085i	0.0751488	−	0.130162i
$927$	0.585786	+	1.01461i	0.0192398	+	0.0333242i
$928$	2.20711	+	3.82282i	0.0724518	+	0.125490i
$929$	5.74264	−	9.94655i	0.188410	−	0.326336i	−0.756310	−	0.654213i	$-0.773000\pi$
$929$	5.74264	−	9.94655i	0.188410	−	0.326336i	0.944720	+	0.327877i	$0.106333\pi$
$930$		0			0
$931$	−19.0711	−	5.31925i	−0.625029	−	0.174331i
$932$	−20.4264			−0.669089
$933$	−22.7279	+	39.3659i	−0.744079	+	1.28878i
$934$	−4.74264	−	8.21449i	−0.155184	−	0.268786i
$935$		0			0
$936$	−1.85786	+	3.21792i	−0.0607262	+	0.105181i
$937$	10.6274			0.347183			0.173591	−	0.984818i	$-0.444463\pi$
$937$	10.6274			0.347183			0.173591	+	0.984818i	$0.444463\pi$
$938$	−8.33705	+	10.7510i	−0.272214	+	0.351033i
$939$	−42.6274			−1.39109
$940$		0			0
$941$	−5.14214	−	8.90644i	−0.167629	−	0.290342i	0.769957	−	0.638096i	$-0.220278\pi$
$941$	−5.14214	−	8.90644i	−0.167629	−	0.290342i	−0.937586	+	0.347754i	$0.886944\pi$
$942$	2.65685	+	4.60181i	0.0865650	+	0.149935i
$943$	2.62132	−	4.54026i	0.0853619	−	0.147851i
$944$	−37.4558			−1.21908
$945$		0			0
$946$	−12.8284			−0.417088
$947$	−21.5919	+	37.3982i	−0.701642	+	1.21528i	0.266248	+	0.963905i	$0.414216\pi$
$947$	−21.5919	+	37.3982i	−0.701642	+	1.21528i	−0.967890	+	0.251375i	$0.919117\pi$
$948$	−20.2426	−	35.0613i	−0.657450	−	1.13874i
$949$	−2.00000	−	3.46410i	−0.0649227	−	0.112449i
$950$		0			0
$951$	62.2843			2.01971
$952$	3.44365	+	0.471253i	0.111609	+	0.0152734i
$953$	2.34315			0.0759019			0.0379510	−	0.999280i	$-0.487917\pi$
$953$	2.34315			0.0759019			0.0379510	+	0.999280i	$0.487917\pi$
$954$	−4.00000	+	6.92820i	−0.129505	+	0.224309i
$955$		0			0
$956$	1.20101	+	2.08021i	0.0388434	+	0.0672788i
$957$	−5.82843	+	10.0951i	−0.188406	+	0.326329i
$958$	−10.0833			−0.325775
$959$	4.34315	+	0.594346i	0.140247	+	0.0191924i
$960$		0			0
$961$	−2.50000	+	4.33013i	−0.0806452	+	0.139682i
$962$		0			0
$963$	3.89949	+	6.75412i	0.125659	+	0.217649i
$964$	14.9411	−	25.8788i	0.481221	−	0.833500i
$965$		0			0
$966$	−2.41421	−	5.91359i	−0.0776760	−	0.190267i
$967$	27.5269			0.885206			0.442603	−	0.896718i	$-0.354055\pi$
$967$	27.5269			0.885206			0.442603	+	0.896718i	$0.354055\pi$
$968$	9.76346	−	16.9108i	0.313809	−	0.543534i
$969$	−2.82843	−	4.89898i	−0.0908622	−	0.157378i
$970$		0			0
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	−0.606685	−	0.794943i	$-0.707501\pi$
$971$	12.0000	−	20.7846i	0.385098	−	0.667010i	0.991783	+	0.127933i	$0.0408342\pi$
$972$	−39.5980			−1.27011
$973$	19.6863	−	25.3864i	0.631114	−	0.813851i
$974$	−6.48528			−0.207802
$975$		0			0
$976$	17.2279	+	29.8396i	0.551452	+	0.955143i
$977$	10.6569	+	18.4582i	0.340943	+	0.590531i	0.984608	−	0.174777i	$-0.0559204\pi$
$977$	10.6569	+	18.4582i	0.340943	+	0.590531i	−0.643665	+	0.765307i	$0.722587\pi$
$978$	−11.8284	+	20.4874i	−0.378231	+	0.655116i
$979$	12.8284			0.409998
$980$		0			0
$981$	9.85786			0.314737
$982$	2.75736	−	4.77589i	0.0879909	−	0.152405i
$983$	−7.10660	−	12.3090i	−0.226665	−	0.392596i	0.730152	−	0.683284i	$-0.239449\pi$
$983$	−7.10660	−	12.3090i	−0.226665	−	0.392596i	−0.956818	+	0.290688i	$0.906116\pi$
$984$	4.15685	+	7.19988i	0.132516	+	0.229524i
$985$		0			0
$986$	−0.343146			−0.0109280
$987$	7.82843	−	10.0951i	0.249182	−	0.321332i
$988$	−4.28427			−0.136301
$989$	7.74264	−	13.4106i	0.246202	−	0.426434i
$990$		0			0
$991$	7.82843	+	13.5592i	0.248678	+	0.430723i	0.963159	−	0.268931i	$-0.0866705\pi$
$991$	7.82843	+	13.5592i	0.248678	+	0.430723i	−0.714481	+	0.699655i	$0.753337\pi$
$992$	13.2426	−	22.9369i	0.420454	−	0.728248i
$993$	26.4853			0.840485
$994$	−5.17157	−	12.6677i	−0.164032	−	0.401796i
$995$		0			0
$996$	−25.8848	+	44.8337i	−0.820191	+	1.42061i
$997$	−8.72792	−	15.1172i	−0.276416	−	0.478767i	0.694075	−	0.719902i	$-0.255813\pi$
$997$	−8.72792	−	15.1172i	−0.276416	−	0.478767i	−0.970491	+	0.241136i	$0.922480\pi$
$998$	−1.00000	−	1.73205i	−0.0316544	−	0.0548271i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.e.c.51.1		4
5.2	odd	4		175.2.k.a.149.2		8
5.3	odd	4		175.2.k.a.149.3		8
5.4	even	2		35.2.e.a.16.2	yes	4
7.2	even	3		1225.2.a.k.1.2		2
7.4	even	3	inner	175.2.e.c.151.1		4
7.5	odd	6		1225.2.a.m.1.2		2
15.14	odd	2		315.2.j.e.226.1		4
20.19	odd	2		560.2.q.k.401.2		4
35.2	odd	12		1225.2.b.g.99.3		4
35.4	even	6		35.2.e.a.11.2	✓	4
35.9	even	6		245.2.a.h.1.1		2
35.12	even	12		1225.2.b.h.99.3		4
35.18	odd	12		175.2.k.a.74.2		8
35.19	odd	6		245.2.a.g.1.1		2
35.23	odd	12		1225.2.b.g.99.2		4
35.24	odd	6		245.2.e.e.116.2		4
35.32	odd	12		175.2.k.a.74.3		8
35.33	even	12		1225.2.b.h.99.2		4
35.34	odd	2		245.2.e.e.226.2		4
105.44	odd	6		2205.2.a.n.1.2		2
105.74	odd	6		315.2.j.e.46.1		4
105.89	even	6		2205.2.a.q.1.2		2
140.19	even	6		3920.2.a.bv.1.2		2
140.39	odd	6		560.2.q.k.81.2		4
140.79	odd	6		3920.2.a.bq.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.2.e.a.11.2	✓	4	35.4	even	6
35.2.e.a.16.2	yes	4	5.4	even	2
175.2.e.c.51.1		4	1.1	even	1	trivial
175.2.e.c.151.1		4	7.4	even	3	inner
175.2.k.a.74.2		8	35.18	odd	12
175.2.k.a.74.3		8	35.32	odd	12
175.2.k.a.149.2		8	5.2	odd	4
175.2.k.a.149.3		8	5.3	odd	4
245.2.a.g.1.1		2	35.19	odd	6
245.2.a.h.1.1		2	35.9	even	6
245.2.e.e.116.2		4	35.24	odd	6
245.2.e.e.226.2		4	35.34	odd	2
315.2.j.e.46.1		4	105.74	odd	6
315.2.j.e.226.1		4	15.14	odd	2
560.2.q.k.81.2		4	140.39	odd	6
560.2.q.k.401.2		4	20.19	odd	2
1225.2.a.k.1.2		2	7.2	even	3
1225.2.a.m.1.2		2	7.5	odd	6
1225.2.b.g.99.2		4	35.23	odd	12
1225.2.b.g.99.3		4	35.2	odd	12
1225.2.b.h.99.2		4	35.33	even	12
1225.2.b.h.99.3		4	35.12	even	12
2205.2.a.n.1.2		2	105.44	odd	6
2205.2.a.q.1.2		2	105.89	even	6
3920.2.a.bq.1.1		2	140.79	odd	6
3920.2.a.bv.1.2		2	140.19	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.207107 + 0.358719i) q^{2} +(1.20711 + 2.09077i) q^{3} +(0.914214 + 1.58346i) q^{4} -1.00000 q^{6} +(1.62132 - 2.09077i) q^{7} -1.58579 q^{8} +(-1.41421 + 2.44949i) q^{9} +O(q^{10})\)	\(q+(-0.207107 + 0.358719i) q^{2} +(1.20711 + 2.09077i) q^{3} +(0.914214 + 1.58346i) q^{4} -1.00000 q^{6} +(1.62132 - 2.09077i) q^{7} -1.58579 q^{8} +(-1.41421 + 2.44949i) q^{9} +(-2.41421 - 4.18154i) q^{11} +(-2.20711 + 3.82282i) q^{12} -0.828427 q^{13} +(0.414214 + 1.01461i) q^{14} +(-1.50000 + 2.59808i) q^{16} +(-0.414214 - 0.717439i) q^{17} +(-0.585786 - 1.01461i) q^{18} +(1.41421 - 2.44949i) q^{19} +(6.32843 + 0.866025i) q^{21} +2.00000 q^{22} +(-1.20711 + 2.09077i) q^{23} +(-1.91421 - 3.31552i) q^{24} +(0.171573 - 0.297173i) q^{26} +0.414214 q^{27} +(4.79289 + 0.655892i) q^{28} -1.00000 q^{29} +(3.00000 + 5.19615i) q^{31} +(-2.20711 - 3.82282i) q^{32} +(5.82843 - 10.0951i) q^{33} +0.343146 q^{34} -5.17157 q^{36} +(0.585786 + 1.01461i) q^{38} +(-1.00000 - 1.73205i) q^{39} -2.17157 q^{41} +(-1.62132 + 2.09077i) q^{42} -6.41421 q^{43} +(4.41421 - 7.64564i) q^{44} +(-0.500000 - 0.866025i) q^{46} +(1.00000 - 1.73205i) q^{47} -7.24264 q^{48} +(-1.74264 - 6.77962i) q^{49} +(1.00000 - 1.73205i) q^{51} +(-0.757359 - 1.31178i) q^{52} +(-3.41421 - 5.91359i) q^{53} +(-0.0857864 + 0.148586i) q^{54} +(-2.57107 + 3.31552i) q^{56} +6.82843 q^{57} +(0.207107 - 0.358719i) q^{58} +(6.24264 + 10.8126i) q^{59} +(5.74264 - 9.94655i) q^{61} -2.48528 q^{62} +(2.82843 + 6.92820i) q^{63} -4.17157 q^{64} +(2.41421 + 4.18154i) q^{66} +(6.20711 + 10.7510i) q^{67} +(0.757359 - 1.31178i) q^{68} -5.82843 q^{69} -12.4853 q^{71} +(2.24264 - 3.88437i) q^{72} +(2.41421 + 4.18154i) q^{73} +5.17157 q^{76} +(-12.6569 - 1.73205i) q^{77} +0.828427 q^{78} +(-4.58579 + 7.94282i) q^{79} +(4.74264 + 8.21449i) q^{81} +(0.449747 - 0.778985i) q^{82} +11.7279 q^{83} +(4.41421 + 10.8126i) q^{84} +(1.32843 - 2.30090i) q^{86} +(-1.20711 - 2.09077i) q^{87} +(3.82843 + 6.63103i) q^{88} +(-1.32843 + 2.30090i) q^{89} +(-1.34315 + 1.73205i) q^{91} -4.41421 q^{92} +(-7.24264 + 12.5446i) q^{93} +(0.414214 + 0.717439i) q^{94} +(5.32843 - 9.22911i) q^{96} -0.343146 q^{97} +(2.79289 + 0.778985i) q^{98} +13.6569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{6} - 2 q^{7} - 12 q^{8}+O(q^{10}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^6 - 2 * q^7 - 12 * q^8	\( 4 q + 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{6} - 2 q^{7} - 12 q^{8} - 4 q^{11} - 6 q^{12} + 8 q^{13} - 4 q^{14} - 6 q^{16} + 4 q^{17} - 8 q^{18} + 14 q^{21} + 8 q^{22} - 2 q^{23} - 2 q^{24} + 12 q^{26} - 4 q^{27} + 22 q^{28} - 4 q^{29} + 12 q^{31} - 6 q^{32} + 12 q^{33} + 24 q^{34} - 32 q^{36} + 8 q^{38} - 4 q^{39} - 20 q^{41} + 2 q^{42} - 20 q^{43} + 12 q^{44} - 2 q^{46} + 4 q^{47} - 12 q^{48} + 10 q^{49} + 4 q^{51} - 20 q^{52} - 8 q^{53} - 6 q^{54} + 18 q^{56} + 16 q^{57} - 2 q^{58} + 8 q^{59} + 6 q^{61} + 24 q^{62} - 28 q^{64} + 4 q^{66} + 22 q^{67} + 20 q^{68} - 12 q^{69} - 16 q^{71} - 8 q^{72} + 4 q^{73} + 32 q^{76} - 28 q^{77} - 8 q^{78} - 24 q^{79} + 2 q^{81} - 18 q^{82} - 4 q^{83} + 12 q^{84} - 6 q^{86} - 2 q^{87} + 4 q^{88} + 6 q^{89} - 28 q^{91} - 12 q^{92} - 12 q^{93} - 4 q^{94} + 10 q^{96} - 24 q^{97} + 14 q^{98} + 32 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^6 - 2 * q^7 - 12 * q^8 - 4 * q^11 - 6 * q^12 + 8 * q^13 - 4 * q^14 - 6 * q^16 + 4 * q^17 - 8 * q^18 + 14 * q^21 + 8 * q^22 - 2 * q^23 - 2 * q^24 + 12 * q^26 - 4 * q^27 + 22 * q^28 - 4 * q^29 + 12 * q^31 - 6 * q^32 + 12 * q^33 + 24 * q^34 - 32 * q^36 + 8 * q^38 - 4 * q^39 - 20 * q^41 + 2 * q^42 - 20 * q^43 + 12 * q^44 - 2 * q^46 + 4 * q^47 - 12 * q^48 + 10 * q^49 + 4 * q^51 - 20 * q^52 - 8 * q^53 - 6 * q^54 + 18 * q^56 + 16 * q^57 - 2 * q^58 + 8 * q^59 + 6 * q^61 + 24 * q^62 - 28 * q^64 + 4 * q^66 + 22 * q^67 + 20 * q^68 - 12 * q^69 - 16 * q^71 - 8 * q^72 + 4 * q^73 + 32 * q^76 - 28 * q^77 - 8 * q^78 - 24 * q^79 + 2 * q^81 - 18 * q^82 - 4 * q^83 + 12 * q^84 - 6 * q^86 - 2 * q^87 + 4 * q^88 + 6 * q^89 - 28 * q^91 - 12 * q^92 - 12 * q^93 - 4 * q^94 + 10 * q^96 - 24 * q^97 + 14 * q^98 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more