LMFDB - Embedded newform 325.2.f.a.18.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(18,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("325.18");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.f (of order $4$, 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:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			18.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	325.18
Dual form			325.2.f.a.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.00000 - 1.00000i) q^{3} +1.00000 q^{4} +(1.00000 - 1.00000i) q^{6} +2.00000 q^{7} +3.00000i q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.00000 - 1.00000i) q^{3} +1.00000 q^{4} +(1.00000 - 1.00000i) q^{6} +2.00000 q^{7} +3.00000i q^{8} -1.00000i q^{9} +(-1.00000 - 1.00000i) q^{11} +(-1.00000 - 1.00000i) q^{12} +(2.00000 - 3.00000i) q^{13} +2.00000i q^{14} -1.00000 q^{16} +(1.00000 + 1.00000i) q^{17} +1.00000 q^{18} +(5.00000 + 5.00000i) q^{19} +(-2.00000 - 2.00000i) q^{21} +(1.00000 - 1.00000i) q^{22} +(3.00000 - 3.00000i) q^{23} +(3.00000 - 3.00000i) q^{24} +(3.00000 + 2.00000i) q^{26} +(-4.00000 + 4.00000i) q^{27} +2.00000 q^{28} +(5.00000 - 5.00000i) q^{31} +5.00000i q^{32} +2.00000i q^{33} +(-1.00000 + 1.00000i) q^{34} -1.00000i q^{36} +(-5.00000 + 5.00000i) q^{38} +(-5.00000 + 1.00000i) q^{39} +(-7.00000 + 7.00000i) q^{41} +(2.00000 - 2.00000i) q^{42} +(-1.00000 + 1.00000i) q^{43} +(-1.00000 - 1.00000i) q^{44} +(3.00000 + 3.00000i) q^{46} -6.00000 q^{47} +(1.00000 + 1.00000i) q^{48} -3.00000 q^{49} -2.00000i q^{51} +(2.00000 - 3.00000i) q^{52} +(-5.00000 - 5.00000i) q^{53} +(-4.00000 - 4.00000i) q^{54} +6.00000i q^{56} -10.0000i q^{57} +(7.00000 - 7.00000i) q^{59} -14.0000 q^{61} +(5.00000 + 5.00000i) q^{62} -2.00000i q^{63} -7.00000 q^{64} -2.00000 q^{66} -4.00000i q^{67} +(1.00000 + 1.00000i) q^{68} -6.00000 q^{69} +(1.00000 - 1.00000i) q^{71} +3.00000 q^{72} +10.0000i q^{73} +(5.00000 + 5.00000i) q^{76} +(-2.00000 - 2.00000i) q^{77} +(-1.00000 - 5.00000i) q^{78} +2.00000i q^{79} +5.00000 q^{81} +(-7.00000 - 7.00000i) q^{82} -6.00000 q^{83} +(-2.00000 - 2.00000i) q^{84} +(-1.00000 - 1.00000i) q^{86} +(3.00000 - 3.00000i) q^{88} +(-5.00000 + 5.00000i) q^{89} +(4.00000 - 6.00000i) q^{91} +(3.00000 - 3.00000i) q^{92} -10.0000 q^{93} -6.00000i q^{94} +(5.00000 - 5.00000i) q^{96} +2.00000i q^{97} -3.00000i q^{98} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{7}+O(q^{10}) $ 2 * q - 2 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^7	$ 2 q - 2 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{7} - 2 q^{11} - 2 q^{12} + 4 q^{13} - 2 q^{16} + 2 q^{17} + 2 q^{18} + 10 q^{19} - 4 q^{21} + 2 q^{22} + 6 q^{23} + 6 q^{24} + 6 q^{26} - 8 q^{27} + 4 q^{28} + 10 q^{31} - 2 q^{34} - 10 q^{38} - 10 q^{39} - 14 q^{41} + 4 q^{42} - 2 q^{43} - 2 q^{44} + 6 q^{46} - 12 q^{47} + 2 q^{48} - 6 q^{49} + 4 q^{52} - 10 q^{53} - 8 q^{54} + 14 q^{59} - 28 q^{61} + 10 q^{62} - 14 q^{64} - 4 q^{66} + 2 q^{68} - 12 q^{69} + 2 q^{71} + 6 q^{72} + 10 q^{76} - 4 q^{77} - 2 q^{78} + 10 q^{81} - 14 q^{82} - 12 q^{83} - 4 q^{84} - 2 q^{86} + 6 q^{88} - 10 q^{89} + 8 q^{91} + 6 q^{92} - 20 q^{93} + 10 q^{96} - 2 q^{99}+O(q^{100}) $ 2 * q - 2 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^7 - 2 * q^11 - 2 * q^12 + 4 * q^13 - 2 * q^16 + 2 * q^17 + 2 * q^18 + 10 * q^19 - 4 * q^21 + 2 * q^22 + 6 * q^23 + 6 * q^24 + 6 * q^26 - 8 * q^27 + 4 * q^28 + 10 * q^31 - 2 * q^34 - 10 * q^38 - 10 * q^39 - 14 * q^41 + 4 * q^42 - 2 * q^43 - 2 * q^44 + 6 * q^46 - 12 * q^47 + 2 * q^48 - 6 * q^49 + 4 * q^52 - 10 * q^53 - 8 * q^54 + 14 * q^59 - 28 * q^61 + 10 * q^62 - 14 * q^64 - 4 * q^66 + 2 * q^68 - 12 * q^69 + 2 * q^71 + 6 * q^72 + 10 * q^76 - 4 * q^77 - 2 * q^78 + 10 * q^81 - 14 * q^82 - 12 * q^83 - 4 * q^84 - 2 * q^86 + 6 * q^88 - 10 * q^89 + 8 * q^91 + 6 * q^92 - 20 * q^93 + 10 * q^96 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$			1.00000i			0.707107i	0.935414	+	0.353553i	$0.115027\pi$
$2$			1.00000i			0.707107i	−0.935414	+	0.353553i	$0.884973\pi$
$3$	−1.00000	−	1.00000i	−0.577350	−	0.577350i	0.356822	−	0.934172i	$-0.383860\pi$
$3$	−1.00000	−	1.00000i	−0.577350	−	0.577350i	−0.934172	+	0.356822i	$0.883860\pi$
$4$	1.00000			0.500000
$5$		0			0
$5$		0			0
$6$	1.00000	−	1.00000i	0.408248	−	0.408248i
$7$	2.00000			0.755929			0.377964	−	0.925820i	$-0.376624\pi$
$7$	2.00000			0.755929			0.377964	+	0.925820i	$0.376624\pi$
$8$			3.00000i			1.06066i
$9$		−	1.00000i		−	0.333333i
$10$		0			0
$11$	−1.00000	−	1.00000i	−0.301511	−	0.301511i	0.540094	−	0.841605i	$-0.318389\pi$
$11$	−1.00000	−	1.00000i	−0.301511	−	0.301511i	−0.841605	+	0.540094i	$0.818389\pi$
$12$	−1.00000	−	1.00000i	−0.288675	−	0.288675i
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$13$	2.00000	−	3.00000i	0.554700	−	0.832050i
$14$			2.00000i			0.534522i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	0.817898	−	0.575363i	$-0.195139\pi$
$17$	1.00000	+	1.00000i	0.242536	+	0.242536i	−0.575363	+	0.817898i	$0.695139\pi$
$18$	1.00000			0.235702
$19$	5.00000	+	5.00000i	1.14708	+	1.14708i	0.987124	+	0.159954i	$0.0511347\pi$
$19$	5.00000	+	5.00000i	1.14708	+	1.14708i	0.159954	+	0.987124i	$0.448865\pi$
$20$		0			0
$21$	−2.00000	−	2.00000i	−0.436436	−	0.436436i
$22$	1.00000	−	1.00000i	0.213201	−	0.213201i
$23$	3.00000	−	3.00000i	0.625543	−	0.625543i	−0.321400	−	0.946943i	$-0.604153\pi$
$23$	3.00000	−	3.00000i	0.625543	−	0.625543i	0.946943	+	0.321400i	$0.104153\pi$
$24$	3.00000	−	3.00000i	0.612372	−	0.612372i
$25$		0			0
$26$	3.00000	+	2.00000i	0.588348	+	0.392232i
$27$	−4.00000	+	4.00000i	−0.769800	+	0.769800i
$28$	2.00000			0.377964
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$	5.00000	−	5.00000i	0.898027	−	0.898027i	−0.0972349	−	0.995261i	$-0.531000\pi$
$31$	5.00000	−	5.00000i	0.898027	−	0.898027i	0.995261	+	0.0972349i	$0.0309998\pi$
$32$			5.00000i			0.883883i
$33$			2.00000i			0.348155i
$34$	−1.00000	+	1.00000i	−0.171499	+	0.171499i
$35$		0			0
$36$		−	1.00000i		−	0.166667i
$37$		0			0			−	1.00000i	$-0.5\pi$
$37$		0			0				1.00000i	$0.5\pi$
$38$	−5.00000	+	5.00000i	−0.811107	+	0.811107i
$39$	−5.00000	+	1.00000i	−0.800641	+	0.160128i
$40$		0			0
$41$	−7.00000	+	7.00000i	−1.09322	+	1.09322i	−0.0980332	+	0.995183i	$0.531255\pi$
$41$	−7.00000	+	7.00000i	−1.09322	+	1.09322i	−0.995183	+	0.0980332i	$0.968745\pi$
$42$	2.00000	−	2.00000i	0.308607	−	0.308607i
$43$	−1.00000	+	1.00000i	−0.152499	+	0.152499i	−0.779233	−	0.626734i	$-0.784391\pi$
$43$	−1.00000	+	1.00000i	−0.152499	+	0.152499i	0.626734	+	0.779233i	$0.284391\pi$
$44$	−1.00000	−	1.00000i	−0.150756	−	0.150756i
$45$		0			0
$46$	3.00000	+	3.00000i	0.442326	+	0.442326i
$47$	−6.00000			−0.875190			−0.437595	−	0.899172i	$-0.644170\pi$
$47$	−6.00000			−0.875190			−0.437595	+	0.899172i	$0.644170\pi$
$48$	1.00000	+	1.00000i	0.144338	+	0.144338i
$49$	−3.00000			−0.428571
$50$		0			0
$51$		−	2.00000i		−	0.280056i
$52$	2.00000	−	3.00000i	0.277350	−	0.416025i
$53$	−5.00000	−	5.00000i	−0.686803	−	0.686803i	0.274721	−	0.961524i	$-0.411414\pi$
$53$	−5.00000	−	5.00000i	−0.686803	−	0.686803i	−0.961524	+	0.274721i	$0.911414\pi$
$54$	−4.00000	−	4.00000i	−0.544331	−	0.544331i
$55$		0			0
$56$			6.00000i			0.801784i
$57$		−	10.0000i		−	1.32453i
$58$		0			0
$59$	7.00000	−	7.00000i	0.911322	−	0.911322i	−0.0850540	−	0.996376i	$-0.527106\pi$
$59$	7.00000	−	7.00000i	0.911322	−	0.911322i	0.996376	+	0.0850540i	$0.0271063\pi$
$60$		0			0
$61$	−14.0000			−1.79252			−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−14.0000			−1.79252			−0.896258	+	0.443533i	$0.853725\pi$
$62$	5.00000	+	5.00000i	0.635001	+	0.635001i
$63$		−	2.00000i		−	0.251976i
$64$	−7.00000			−0.875000
$65$		0			0
$66$	−2.00000			−0.246183
$67$		−	4.00000i		−	0.488678i	−0.969690	−	0.244339i	$-0.921429\pi$
$67$		−	4.00000i		−	0.488678i	0.969690	−	0.244339i	$-0.0785709\pi$
$68$	1.00000	+	1.00000i	0.121268	+	0.121268i
$69$	−6.00000			−0.722315
$70$		0			0
$71$	1.00000	−	1.00000i	0.118678	−	0.118678i	−0.645273	−	0.763952i	$-0.723257\pi$
$71$	1.00000	−	1.00000i	0.118678	−	0.118678i	0.763952	+	0.645273i	$0.223257\pi$
$72$	3.00000			0.353553
$73$			10.0000i			1.17041i	0.810885	+	0.585206i	$0.198986\pi$
$73$			10.0000i			1.17041i	−0.810885	+	0.585206i	$0.801014\pi$
$74$		0			0
$75$		0			0
$76$	5.00000	+	5.00000i	0.573539	+	0.573539i
$77$	−2.00000	−	2.00000i	−0.227921	−	0.227921i
$78$	−1.00000	−	5.00000i	−0.113228	−	0.566139i
$79$			2.00000i			0.225018i	0.993651	+	0.112509i	$0.0358886\pi$
$79$			2.00000i			0.225018i	−0.993651	+	0.112509i	$0.964111\pi$
$80$		0			0
$81$	5.00000			0.555556
$82$	−7.00000	−	7.00000i	−0.773021	−	0.773021i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	−2.00000	−	2.00000i	−0.218218	−	0.218218i
$85$		0			0
$86$	−1.00000	−	1.00000i	−0.107833	−	0.107833i
$87$		0			0
$88$	3.00000	−	3.00000i	0.319801	−	0.319801i
$89$	−5.00000	+	5.00000i	−0.529999	+	0.529999i	−0.920572	−	0.390573i	$-0.872277\pi$
$89$	−5.00000	+	5.00000i	−0.529999	+	0.529999i	0.390573	+	0.920572i	$0.372277\pi$
$90$		0			0
$91$	4.00000	−	6.00000i	0.419314	−	0.628971i
$92$	3.00000	−	3.00000i	0.312772	−	0.312772i
$93$	−10.0000			−1.03695
$94$		−	6.00000i		−	0.618853i
$95$		0			0
$96$	5.00000	−	5.00000i	0.510310	−	0.510310i
$97$			2.00000i			0.203069i	0.994832	+	0.101535i	$0.0323753\pi$
$97$			2.00000i			0.203069i	−0.994832	+	0.101535i	$0.967625\pi$
$98$		−	3.00000i		−	0.303046i
$99$	−1.00000	+	1.00000i	−0.100504	+	0.100504i
$100$		0			0
$101$			12.0000i			1.19404i	0.802225	+	0.597022i	$0.203650\pi$
$101$			12.0000i			1.19404i	−0.802225	+	0.597022i	$0.796350\pi$
$102$	2.00000			0.198030
$103$	7.00000	−	7.00000i	0.689730	−	0.689730i	−0.272442	−	0.962172i	$-0.587831\pi$
$103$	7.00000	−	7.00000i	0.689730	−	0.689730i	0.962172	+	0.272442i	$0.0878312\pi$
$104$	9.00000	+	6.00000i	0.882523	+	0.588348i
$105$		0			0
$106$	5.00000	−	5.00000i	0.485643	−	0.485643i
$107$	−7.00000	+	7.00000i	−0.676716	+	0.676716i	−0.959256	−	0.282540i	$-0.908823\pi$
$107$	−7.00000	+	7.00000i	−0.676716	+	0.676716i	0.282540	+	0.959256i	$0.408823\pi$
$108$	−4.00000	+	4.00000i	−0.384900	+	0.384900i
$109$	−9.00000	−	9.00000i	−0.862044	−	0.862044i	0.129532	−	0.991575i	$-0.458653\pi$
$109$	−9.00000	−	9.00000i	−0.862044	−	0.862044i	−0.991575	+	0.129532i	$0.958653\pi$
$110$		0			0
$111$		0			0
$112$	−2.00000			−0.188982
$113$	−5.00000	−	5.00000i	−0.470360	−	0.470360i	0.431671	−	0.902031i	$-0.357924\pi$
$113$	−5.00000	−	5.00000i	−0.470360	−	0.470360i	−0.902031	+	0.431671i	$0.857924\pi$
$114$	10.0000			0.936586
$115$		0			0
$116$		0			0
$117$	−3.00000	−	2.00000i	−0.277350	−	0.184900i
$118$	7.00000	+	7.00000i	0.644402	+	0.644402i
$119$	2.00000	+	2.00000i	0.183340	+	0.183340i
$120$		0			0
$121$		−	9.00000i		−	0.818182i
$122$		−	14.0000i		−	1.26750i
$123$	14.0000			1.26234
$124$	5.00000	−	5.00000i	0.449013	−	0.449013i
$125$		0			0
$126$	2.00000			0.178174
$127$	9.00000	+	9.00000i	0.798621	+	0.798621i	0.982878	−	0.184257i	$-0.0589879\pi$
$127$	9.00000	+	9.00000i	0.798621	+	0.798621i	−0.184257	+	0.982878i	$0.558988\pi$
$128$			3.00000i			0.265165i
$129$	2.00000			0.176090
$130$		0			0
$131$	−20.0000			−1.74741			−0.873704	−	0.486458i	$-0.838289\pi$
$131$	−20.0000			−1.74741			−0.873704	+	0.486458i	$0.838289\pi$
$132$			2.00000i			0.174078i
$133$	10.0000	+	10.0000i	0.867110	+	0.867110i
$134$	4.00000			0.345547
$135$		0			0
$136$	−3.00000	+	3.00000i	−0.257248	+	0.257248i
$137$	16.0000			1.36697			0.683486	−	0.729964i	$-0.260463\pi$
$137$	16.0000			1.36697			0.683486	+	0.729964i	$0.260463\pi$
$138$		−	6.00000i		−	0.510754i
$139$			14.0000i			1.18746i	0.804663	+	0.593732i	$0.202346\pi$
$139$			14.0000i			1.18746i	−0.804663	+	0.593732i	$0.797654\pi$
$140$		0			0
$141$	6.00000	+	6.00000i	0.505291	+	0.505291i
$142$	1.00000	+	1.00000i	0.0839181	+	0.0839181i
$143$	−5.00000	+	1.00000i	−0.418121	+	0.0836242i
$144$			1.00000i			0.0833333i
$145$		0			0
$146$	−10.0000			−0.827606
$147$	3.00000	+	3.00000i	0.247436	+	0.247436i
$148$		0			0
$149$	3.00000	+	3.00000i	0.245770	+	0.245770i	0.819232	−	0.573462i	$-0.194400\pi$
$149$	3.00000	+	3.00000i	0.245770	+	0.245770i	−0.573462	+	0.819232i	$0.694400\pi$
$150$		0			0
$151$	7.00000	+	7.00000i	0.569652	+	0.569652i	0.932031	−	0.362379i	$-0.118035\pi$
$151$	7.00000	+	7.00000i	0.569652	+	0.569652i	−0.362379	+	0.932031i	$0.618035\pi$
$152$	−15.0000	+	15.0000i	−1.21666	+	1.21666i
$153$	1.00000	−	1.00000i	0.0808452	−	0.0808452i
$154$	2.00000	−	2.00000i	0.161165	−	0.161165i
$155$		0			0
$156$	−5.00000	+	1.00000i	−0.400320	+	0.0800641i
$157$	−13.0000	+	13.0000i	−1.03751	+	1.03751i	−0.0382445	+	0.999268i	$0.512177\pi$
$157$	−13.0000	+	13.0000i	−1.03751	+	1.03751i	−0.999268	+	0.0382445i	$0.987823\pi$
$158$	−2.00000			−0.159111
$159$			10.0000i			0.793052i
$160$		0			0
$161$	6.00000	−	6.00000i	0.472866	−	0.472866i
$162$			5.00000i			0.392837i
$163$		−	4.00000i		−	0.313304i	−0.987654	−	0.156652i	$-0.949930\pi$
$163$		−	4.00000i		−	0.313304i	0.987654	−	0.156652i	$-0.0500701\pi$
$164$	−7.00000	+	7.00000i	−0.546608	+	0.546608i
$165$		0			0
$166$		−	6.00000i		−	0.465690i
$167$	18.0000			1.39288			0.696441	−	0.717614i	$-0.254766\pi$
$167$	18.0000			1.39288			0.696441	+	0.717614i	$0.254766\pi$
$168$	6.00000	−	6.00000i	0.462910	−	0.462910i
$169$	−5.00000	−	12.0000i	−0.384615	−	0.923077i
$170$		0			0
$171$	5.00000	−	5.00000i	0.382360	−	0.382360i
$172$	−1.00000	+	1.00000i	−0.0762493	+	0.0762493i
$173$	−11.0000	+	11.0000i	−0.836315	+	0.836315i	−0.988372	−	0.152057i	$-0.951410\pi$
$173$	−11.0000	+	11.0000i	−0.836315	+	0.836315i	0.152057	+	0.988372i	$0.451410\pi$
$174$		0			0
$175$		0			0
$176$	1.00000	+	1.00000i	0.0753778	+	0.0753778i
$177$	−14.0000			−1.05230
$178$	−5.00000	−	5.00000i	−0.374766	−	0.374766i
$179$	20.0000			1.49487			0.747435	−	0.664335i	$-0.231285\pi$
$179$	20.0000			1.49487			0.747435	+	0.664335i	$0.231285\pi$
$180$		0			0
$181$		−	8.00000i		−	0.594635i	−0.954779	−	0.297318i	$-0.903908\pi$
$181$		−	8.00000i		−	0.594635i	0.954779	−	0.297318i	$-0.0960920\pi$
$182$	6.00000	+	4.00000i	0.444750	+	0.296500i
$183$	14.0000	+	14.0000i	1.03491	+	1.03491i
$184$	9.00000	+	9.00000i	0.663489	+	0.663489i
$185$		0			0
$186$		−	10.0000i		−	0.733236i
$187$		−	2.00000i		−	0.146254i
$188$	−6.00000			−0.437595
$189$	−8.00000	+	8.00000i	−0.581914	+	0.581914i
$190$		0			0
$191$	8.00000			0.578860			0.289430	−	0.957199i	$-0.406534\pi$
$191$	8.00000			0.578860			0.289430	+	0.957199i	$0.406534\pi$
$192$	7.00000	+	7.00000i	0.505181	+	0.505181i
$193$		−	18.0000i		−	1.29567i	−0.761781	−	0.647834i	$-0.775675\pi$
$193$		−	18.0000i		−	1.29567i	0.761781	−	0.647834i	$-0.224325\pi$
$194$	−2.00000			−0.143592
$195$		0			0
$196$	−3.00000			−0.214286
$197$			6.00000i			0.427482i	0.976890	+	0.213741i	$0.0685649\pi$
$197$			6.00000i			0.427482i	−0.976890	+	0.213741i	$0.931435\pi$
$198$	−1.00000	−	1.00000i	−0.0710669	−	0.0710669i
$199$	8.00000			0.567105			0.283552	−	0.958957i	$-0.408487\pi$
$199$	8.00000			0.567105			0.283552	+	0.958957i	$0.408487\pi$
$200$		0			0
$201$	−4.00000	+	4.00000i	−0.282138	+	0.282138i
$202$	−12.0000			−0.844317
$203$		0			0
$204$		−	2.00000i		−	0.140028i
$205$		0			0
$206$	7.00000	+	7.00000i	0.487713	+	0.487713i
$207$	−3.00000	−	3.00000i	−0.208514	−	0.208514i
$208$	−2.00000	+	3.00000i	−0.138675	+	0.208013i
$209$		−	10.0000i		−	0.691714i
$210$		0			0
$211$	4.00000			0.275371			0.137686	−	0.990476i	$-0.456034\pi$
$211$	4.00000			0.275371			0.137686	+	0.990476i	$0.456034\pi$
$212$	−5.00000	−	5.00000i	−0.343401	−	0.343401i
$213$	−2.00000			−0.137038
$214$	−7.00000	−	7.00000i	−0.478510	−	0.478510i
$215$		0			0
$216$	−12.0000	−	12.0000i	−0.816497	−	0.816497i
$217$	10.0000	−	10.0000i	0.678844	−	0.678844i
$218$	9.00000	−	9.00000i	0.609557	−	0.609557i
$219$	10.0000	−	10.0000i	0.675737	−	0.675737i
$220$		0			0
$221$	5.00000	−	1.00000i	0.336336	−	0.0672673i
$222$		0			0
$223$	−2.00000			−0.133930			−0.0669650	−	0.997755i	$-0.521332\pi$
$223$	−2.00000			−0.133930			−0.0669650	+	0.997755i	$0.521332\pi$
$224$			10.0000i			0.668153i
$225$		0			0
$226$	5.00000	−	5.00000i	0.332595	−	0.332595i
$227$		−	12.0000i		−	0.796468i	−0.917284	−	0.398234i	$-0.869623\pi$
$227$		−	12.0000i		−	0.796468i	0.917284	−	0.398234i	$-0.130377\pi$
$228$		−	10.0000i		−	0.662266i
$229$	3.00000	−	3.00000i	0.198246	−	0.198246i	−0.601002	−	0.799248i	$-0.705232\pi$
$229$	3.00000	−	3.00000i	0.198246	−	0.198246i	0.799248	+	0.601002i	$0.205232\pi$
$230$		0			0
$231$			4.00000i			0.263181i
$232$		0			0
$233$	1.00000	−	1.00000i	0.0655122	−	0.0655122i	−0.673592	−	0.739104i	$-0.735249\pi$
$233$	1.00000	−	1.00000i	0.0655122	−	0.0655122i	0.739104	+	0.673592i	$0.235249\pi$
$234$	2.00000	−	3.00000i	0.130744	−	0.196116i
$235$		0			0
$236$	7.00000	−	7.00000i	0.455661	−	0.455661i
$237$	2.00000	−	2.00000i	0.129914	−	0.129914i
$238$	−2.00000	+	2.00000i	−0.129641	+	0.129641i
$239$	−3.00000	−	3.00000i	−0.194054	−	0.194054i	0.603391	−	0.797445i	$-0.293816\pi$
$239$	−3.00000	−	3.00000i	−0.194054	−	0.194054i	−0.797445	+	0.603391i	$0.793816\pi$
$240$		0			0
$241$	17.0000	+	17.0000i	1.09507	+	1.09507i	0.994979	+	0.100088i	$0.0319123\pi$
$241$	17.0000	+	17.0000i	1.09507	+	1.09507i	0.100088	+	0.994979i	$0.468088\pi$
$242$	9.00000			0.578542
$243$	7.00000	+	7.00000i	0.449050	+	0.449050i
$244$	−14.0000			−0.896258
$245$		0			0
$246$			14.0000i			0.892607i
$247$	25.0000	−	5.00000i	1.59071	−	0.318142i
$248$	15.0000	+	15.0000i	0.952501	+	0.952501i
$249$	6.00000	+	6.00000i	0.380235	+	0.380235i
$250$		0			0
$251$			2.00000i			0.126239i	0.998006	+	0.0631194i	$0.0201049\pi$
$251$			2.00000i			0.126239i	−0.998006	+	0.0631194i	$0.979895\pi$
$252$		−	2.00000i		−	0.125988i
$253$	−6.00000			−0.377217
$254$	−9.00000	+	9.00000i	−0.564710	+	0.564710i
$255$		0			0
$256$	−17.0000			−1.06250
$257$	−11.0000	−	11.0000i	−0.686161	−	0.686161i	0.275220	−	0.961381i	$-0.411249\pi$
$257$	−11.0000	−	11.0000i	−0.686161	−	0.686161i	−0.961381	+	0.275220i	$0.911249\pi$
$258$			2.00000i			0.124515i
$259$		0			0
$260$		0			0
$261$		0			0
$262$		−	20.0000i		−	1.23560i
$263$	−1.00000	−	1.00000i	−0.0616626	−	0.0616626i	0.675603	−	0.737266i	$-0.263883\pi$
$263$	−1.00000	−	1.00000i	−0.0616626	−	0.0616626i	−0.737266	+	0.675603i	$0.763883\pi$
$264$	−6.00000			−0.369274
$265$		0			0
$266$	−10.0000	+	10.0000i	−0.613139	+	0.613139i
$267$	10.0000			0.611990
$268$		−	4.00000i		−	0.244339i
$269$		−	12.0000i		−	0.731653i	−0.930683	−	0.365826i	$-0.880786\pi$
$269$		−	12.0000i		−	0.731653i	0.930683	−	0.365826i	$-0.119214\pi$
$270$		0			0
$271$	−9.00000	−	9.00000i	−0.546711	−	0.546711i	0.378777	−	0.925488i	$-0.376345\pi$
$271$	−9.00000	−	9.00000i	−0.546711	−	0.546711i	−0.925488	+	0.378777i	$0.876345\pi$
$272$	−1.00000	−	1.00000i	−0.0606339	−	0.0606339i
$273$	−10.0000	+	2.00000i	−0.605228	+	0.121046i
$274$			16.0000i			0.966595i
$275$		0			0
$276$	−6.00000			−0.361158
$277$	−15.0000	−	15.0000i	−0.901263	−	0.901263i	0.0942828	−	0.995545i	$-0.469944\pi$
$277$	−15.0000	−	15.0000i	−0.901263	−	0.901263i	−0.995545	+	0.0942828i	$0.969944\pi$
$278$	−14.0000			−0.839664
$279$	−5.00000	−	5.00000i	−0.299342	−	0.299342i
$280$		0			0
$281$	1.00000	+	1.00000i	0.0596550	+	0.0596550i	0.736305	−	0.676650i	$-0.236569\pi$
$281$	1.00000	+	1.00000i	0.0596550	+	0.0596550i	−0.676650	+	0.736305i	$0.736569\pi$
$282$	−6.00000	+	6.00000i	−0.357295	+	0.357295i
$283$	−9.00000	+	9.00000i	−0.534994	+	0.534994i	−0.922055	−	0.387060i	$-0.873491\pi$
$283$	−9.00000	+	9.00000i	−0.534994	+	0.534994i	0.387060	+	0.922055i	$0.373491\pi$
$284$	1.00000	−	1.00000i	0.0593391	−	0.0593391i
$285$		0			0
$286$	−1.00000	−	5.00000i	−0.0591312	−	0.295656i
$287$	−14.0000	+	14.0000i	−0.826394	+	0.826394i
$288$	5.00000			0.294628
$289$		−	15.0000i		−	0.882353i
$290$		0			0
$291$	2.00000	−	2.00000i	0.117242	−	0.117242i
$292$			10.0000i			0.585206i
$293$			6.00000i			0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$			6.00000i			0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$	−3.00000	+	3.00000i	−0.174964	+	0.174964i
$295$		0			0
$296$		0			0
$297$	8.00000			0.464207
$298$	−3.00000	+	3.00000i	−0.173785	+	0.173785i
$299$	−3.00000	−	15.0000i	−0.173494	−	0.867472i
$300$		0			0
$301$	−2.00000	+	2.00000i	−0.115278	+	0.115278i
$302$	−7.00000	+	7.00000i	−0.402805	+	0.402805i
$303$	12.0000	−	12.0000i	0.689382	−	0.689382i
$304$	−5.00000	−	5.00000i	−0.286770	−	0.286770i
$305$		0			0
$306$	1.00000	+	1.00000i	0.0571662	+	0.0571662i
$307$	−18.0000			−1.02731			−0.513657	−	0.857996i	$-0.671710\pi$
$307$	−18.0000			−1.02731			−0.513657	+	0.857996i	$0.671710\pi$
$308$	−2.00000	−	2.00000i	−0.113961	−	0.113961i
$309$	−14.0000			−0.796432
$310$		0			0
$311$			6.00000i			0.340229i	0.985424	+	0.170114i	$0.0544137\pi$
$311$			6.00000i			0.340229i	−0.985424	+	0.170114i	$0.945586\pi$
$312$	−3.00000	−	15.0000i	−0.169842	−	0.849208i
$313$	−9.00000	−	9.00000i	−0.508710	−	0.508710i	0.405420	−	0.914130i	$-0.367125\pi$
$313$	−9.00000	−	9.00000i	−0.508710	−	0.508710i	−0.914130	+	0.405420i	$0.867125\pi$
$314$	−13.0000	−	13.0000i	−0.733632	−	0.733632i
$315$		0			0
$316$			2.00000i			0.112509i
$317$		−	14.0000i		−	0.786318i	−0.919470	−	0.393159i	$-0.871382\pi$
$317$		−	14.0000i		−	0.786318i	0.919470	−	0.393159i	$-0.128618\pi$
$318$	−10.0000			−0.560772
$319$		0			0
$320$		0			0
$321$	14.0000			0.781404
$322$	6.00000	+	6.00000i	0.334367	+	0.334367i
$323$			10.0000i			0.556415i
$324$	5.00000			0.277778
$325$		0			0
$326$	4.00000			0.221540
$327$			18.0000i			0.995402i
$328$	−21.0000	−	21.0000i	−1.15953	−	1.15953i
$329$	−12.0000			−0.661581
$330$		0			0
$331$	−3.00000	+	3.00000i	−0.164895	+	0.164895i	−0.784731	−	0.619836i	$-0.787199\pi$
$331$	−3.00000	+	3.00000i	−0.164895	+	0.164895i	0.619836	+	0.784731i	$0.287199\pi$
$332$	−6.00000			−0.329293
$333$		0			0
$334$			18.0000i			0.984916i
$335$		0			0
$336$	2.00000	+	2.00000i	0.109109	+	0.109109i
$337$	13.0000	+	13.0000i	0.708155	+	0.708155i	0.966147	−	0.257992i	$-0.0830608\pi$
$337$	13.0000	+	13.0000i	0.708155	+	0.708155i	−0.257992	+	0.966147i	$0.583061\pi$
$338$	12.0000	−	5.00000i	0.652714	−	0.271964i
$339$			10.0000i			0.543125i
$340$		0			0
$341$	−10.0000			−0.541530
$342$	5.00000	+	5.00000i	0.270369	+	0.270369i
$343$	−20.0000			−1.07990
$344$	−3.00000	−	3.00000i	−0.161749	−	0.161749i
$345$		0			0
$346$	−11.0000	−	11.0000i	−0.591364	−	0.591364i
$347$	−3.00000	+	3.00000i	−0.161048	+	0.161048i	−0.783031	−	0.621983i	$-0.786327\pi$
$347$	−3.00000	+	3.00000i	−0.161048	+	0.161048i	0.621983	+	0.783031i	$0.286327\pi$
$348$		0			0
$349$	−9.00000	+	9.00000i	−0.481759	+	0.481759i	−0.905693	−	0.423934i	$-0.860649\pi$
$349$	−9.00000	+	9.00000i	−0.481759	+	0.481759i	0.423934	+	0.905693i	$0.360649\pi$
$350$		0			0
$351$	4.00000	+	20.0000i	0.213504	+	1.06752i
$352$	5.00000	−	5.00000i	0.266501	−	0.266501i
$353$	12.0000			0.638696			0.319348	−	0.947638i	$-0.396536\pi$
$353$	12.0000			0.638696			0.319348	+	0.947638i	$0.396536\pi$
$354$		−	14.0000i		−	0.744092i
$355$		0			0
$356$	−5.00000	+	5.00000i	−0.264999	+	0.264999i
$357$		−	4.00000i		−	0.211702i
$358$			20.0000i			1.05703i
$359$	−1.00000	+	1.00000i	−0.0527780	+	0.0527780i	−0.733003	−	0.680225i	$-0.761882\pi$
$359$	−1.00000	+	1.00000i	−0.0527780	+	0.0527780i	0.680225	+	0.733003i	$0.261882\pi$
$360$		0			0
$361$			31.0000i			1.63158i
$362$	8.00000			0.420471
$363$	−9.00000	+	9.00000i	−0.472377	+	0.472377i
$364$	4.00000	−	6.00000i	0.209657	−	0.314485i
$365$		0			0
$366$	−14.0000	+	14.0000i	−0.731792	+	0.731792i
$367$	1.00000	−	1.00000i	0.0521996	−	0.0521996i	−0.680525	−	0.732725i	$-0.738248\pi$
$367$	1.00000	−	1.00000i	0.0521996	−	0.0521996i	0.732725	+	0.680525i	$0.238248\pi$
$368$	−3.00000	+	3.00000i	−0.156386	+	0.156386i
$369$	7.00000	+	7.00000i	0.364405	+	0.364405i
$370$		0			0
$371$	−10.0000	−	10.0000i	−0.519174	−	0.519174i
$372$	−10.0000			−0.518476
$373$	15.0000	+	15.0000i	0.776671	+	0.776671i	0.979263	−	0.202593i	$-0.0649367\pi$
$373$	15.0000	+	15.0000i	0.776671	+	0.776671i	−0.202593	+	0.979263i	$0.564937\pi$
$374$	2.00000			0.103418
$375$		0			0
$376$		−	18.0000i		−	0.928279i
$377$		0			0
$378$	−8.00000	−	8.00000i	−0.411476	−	0.411476i
$379$	1.00000	+	1.00000i	0.0513665	+	0.0513665i	0.732323	−	0.680957i	$-0.238436\pi$
$379$	1.00000	+	1.00000i	0.0513665	+	0.0513665i	−0.680957	+	0.732323i	$0.738436\pi$
$380$		0			0
$381$		−	18.0000i		−	0.922168i
$382$			8.00000i			0.409316i
$383$	30.0000			1.53293			0.766464	−	0.642287i	$-0.222014\pi$
$383$	30.0000			1.53293			0.766464	+	0.642287i	$0.222014\pi$
$384$	3.00000	−	3.00000i	0.153093	−	0.153093i
$385$		0			0
$386$	18.0000			0.916176
$387$	1.00000	+	1.00000i	0.0508329	+	0.0508329i
$388$			2.00000i			0.101535i
$389$	18.0000			0.912636			0.456318	−	0.889817i	$-0.349168\pi$
$389$	18.0000			0.912636			0.456318	+	0.889817i	$0.349168\pi$
$390$		0			0
$391$	6.00000			0.303433
$392$		−	9.00000i		−	0.454569i
$393$	20.0000	+	20.0000i	1.00887	+	1.00887i
$394$	−6.00000			−0.302276
$395$		0			0
$396$	−1.00000	+	1.00000i	−0.0502519	+	0.0502519i
$397$	−16.0000			−0.803017			−0.401508	−	0.915855i	$-0.631514\pi$
$397$	−16.0000			−0.803017			−0.401508	+	0.915855i	$0.631514\pi$
$398$			8.00000i			0.401004i
$399$		−	20.0000i		−	1.00125i
$400$		0			0
$401$	−11.0000	−	11.0000i	−0.549314	−	0.549314i	0.376929	−	0.926242i	$-0.376980\pi$
$401$	−11.0000	−	11.0000i	−0.549314	−	0.549314i	−0.926242	+	0.376929i	$0.876980\pi$
$402$	−4.00000	−	4.00000i	−0.199502	−	0.199502i
$403$	−5.00000	−	25.0000i	−0.249068	−	1.24534i
$404$			12.0000i			0.597022i
$405$		0			0
$406$		0			0
$407$		0			0
$408$	6.00000			0.297044
$409$	7.00000	+	7.00000i	0.346128	+	0.346128i	0.858665	−	0.512537i	$-0.171294\pi$
$409$	7.00000	+	7.00000i	0.346128	+	0.346128i	−0.512537	+	0.858665i	$0.671294\pi$
$410$		0			0
$411$	−16.0000	−	16.0000i	−0.789222	−	0.789222i
$412$	7.00000	−	7.00000i	0.344865	−	0.344865i
$413$	14.0000	−	14.0000i	0.688895	−	0.688895i
$414$	3.00000	−	3.00000i	0.147442	−	0.147442i
$415$		0			0
$416$	15.0000	+	10.0000i	0.735436	+	0.490290i
$417$	14.0000	−	14.0000i	0.685583	−	0.685583i
$418$	10.0000			0.489116
$419$			38.0000i			1.85642i	0.372055	+	0.928211i	$0.378653\pi$
$419$			38.0000i			1.85642i	−0.372055	+	0.928211i	$0.621347\pi$
$420$		0			0
$421$	−11.0000	+	11.0000i	−0.536107	+	0.536107i	−0.922383	−	0.386276i	$-0.873761\pi$
$421$	−11.0000	+	11.0000i	−0.536107	+	0.536107i	0.386276	+	0.922383i	$0.373761\pi$
$422$			4.00000i			0.194717i
$423$			6.00000i			0.291730i
$424$	15.0000	−	15.0000i	0.728464	−	0.728464i
$425$		0			0
$426$		−	2.00000i		−	0.0969003i
$427$	−28.0000			−1.35501
$428$	−7.00000	+	7.00000i	−0.338358	+	0.338358i
$429$	6.00000	+	4.00000i	0.289683	+	0.193122i
$430$		0			0
$431$	13.0000	−	13.0000i	0.626188	−	0.626188i	−0.320919	−	0.947107i	$-0.603992\pi$
$431$	13.0000	−	13.0000i	0.626188	−	0.626188i	0.947107	+	0.320919i	$0.103992\pi$
$432$	4.00000	−	4.00000i	0.192450	−	0.192450i
$433$	17.0000	−	17.0000i	0.816968	−	0.816968i	−0.168700	−	0.985668i	$-0.553957\pi$
$433$	17.0000	−	17.0000i	0.816968	−	0.816968i	0.985668	+	0.168700i	$0.0539568\pi$
$434$	10.0000	+	10.0000i	0.480015	+	0.480015i
$435$		0			0
$436$	−9.00000	−	9.00000i	−0.431022	−	0.431022i
$437$	30.0000			1.43509
$438$	10.0000	+	10.0000i	0.477818	+	0.477818i
$439$		0			0			−	1.00000i	$-0.5\pi$
$439$		0			0				1.00000i	$0.5\pi$
$440$		0			0
$441$			3.00000i			0.142857i
$442$	1.00000	+	5.00000i	0.0475651	+	0.237826i
$443$	−25.0000	−	25.0000i	−1.18779	−	1.18779i	−0.977678	−	0.210108i	$-0.932619\pi$
$443$	−25.0000	−	25.0000i	−1.18779	−	1.18779i	−0.210108	−	0.977678i	$-0.567381\pi$
$444$		0			0
$445$		0			0
$446$		−	2.00000i		−	0.0947027i
$447$		−	6.00000i		−	0.283790i
$448$	−14.0000			−0.661438
$449$	3.00000	−	3.00000i	0.141579	−	0.141579i	−0.632765	−	0.774344i	$-0.718080\pi$
$449$	3.00000	−	3.00000i	0.141579	−	0.141579i	0.774344	+	0.632765i	$0.218080\pi$
$450$		0			0
$451$	14.0000			0.659234
$452$	−5.00000	−	5.00000i	−0.235180	−	0.235180i
$453$		−	14.0000i		−	0.657777i
$454$	12.0000			0.563188
$455$		0			0
$456$	30.0000			1.40488
$457$			2.00000i			0.0935561i	0.998905	+	0.0467780i	$0.0148953\pi$
$457$			2.00000i			0.0935561i	−0.998905	+	0.0467780i	$0.985105\pi$
$458$	3.00000	+	3.00000i	0.140181	+	0.140181i
$459$	−8.00000			−0.373408
$460$		0			0
$461$	17.0000	−	17.0000i	0.791769	−	0.791769i	−0.190013	−	0.981782i	$-0.560853\pi$
$461$	17.0000	−	17.0000i	0.791769	−	0.791769i	0.981782	+	0.190013i	$0.0608529\pi$
$462$	−4.00000			−0.186097
$463$			24.0000i			1.11537i	0.830051	+	0.557687i	$0.188311\pi$
$463$			24.0000i			1.11537i	−0.830051	+	0.557687i	$0.811689\pi$
$464$		0			0
$465$		0			0
$466$	1.00000	+	1.00000i	0.0463241	+	0.0463241i
$467$	9.00000	+	9.00000i	0.416470	+	0.416470i	0.883985	−	0.467515i	$-0.154851\pi$
$467$	9.00000	+	9.00000i	0.416470	+	0.416470i	−0.467515	+	0.883985i	$0.654851\pi$
$468$	−3.00000	−	2.00000i	−0.138675	−	0.0924500i
$469$		−	8.00000i		−	0.369406i
$470$		0			0
$471$	26.0000			1.19802
$472$	21.0000	+	21.0000i	0.966603	+	0.966603i
$473$	2.00000			0.0919601
$474$	2.00000	+	2.00000i	0.0918630	+	0.0918630i
$475$		0			0
$476$	2.00000	+	2.00000i	0.0916698	+	0.0916698i
$477$	−5.00000	+	5.00000i	−0.228934	+	0.228934i
$478$	3.00000	−	3.00000i	0.137217	−	0.137217i
$479$	7.00000	−	7.00000i	0.319838	−	0.319838i	−0.528867	−	0.848705i	$-0.677383\pi$
$479$	7.00000	−	7.00000i	0.319838	−	0.319838i	0.848705	+	0.528867i	$0.177383\pi$
$480$		0			0
$481$		0			0
$482$	−17.0000	+	17.0000i	−0.774329	+	0.774329i
$483$	−12.0000			−0.546019
$484$		−	9.00000i		−	0.409091i
$485$		0			0
$486$	−7.00000	+	7.00000i	−0.317526	+	0.317526i
$487$			16.0000i			0.725029i	0.931978	+	0.362515i	$0.118082\pi$
$487$			16.0000i			0.725029i	−0.931978	+	0.362515i	$0.881918\pi$
$488$		−	42.0000i		−	1.90125i
$489$	−4.00000	+	4.00000i	−0.180886	+	0.180886i
$490$		0			0
$491$		−	22.0000i		−	0.992846i	−0.868081	−	0.496423i	$-0.834646\pi$
$491$		−	22.0000i		−	0.992846i	0.868081	−	0.496423i	$-0.165354\pi$
$492$	14.0000			0.631169
$493$		0			0
$494$	5.00000	+	25.0000i	0.224961	+	1.12480i
$495$		0			0
$496$	−5.00000	+	5.00000i	−0.224507	+	0.224507i
$497$	2.00000	−	2.00000i	0.0897123	−	0.0897123i
$498$	−6.00000	+	6.00000i	−0.268866	+	0.268866i
$499$	−3.00000	−	3.00000i	−0.134298	−	0.134298i	0.636762	−	0.771060i	$-0.280273\pi$
$499$	−3.00000	−	3.00000i	−0.134298	−	0.134298i	−0.771060	+	0.636762i	$0.780273\pi$
$500$		0			0
$501$	−18.0000	−	18.0000i	−0.804181	−	0.804181i
$502$	−2.00000			−0.0892644
$503$	3.00000	+	3.00000i	0.133763	+	0.133763i	0.770818	−	0.637055i	$-0.219848\pi$
$503$	3.00000	+	3.00000i	0.133763	+	0.133763i	−0.637055	+	0.770818i	$0.719848\pi$
$504$	6.00000			0.267261
$505$		0			0
$506$		−	6.00000i		−	0.266733i
$507$	−7.00000	+	17.0000i	−0.310881	+	0.754997i
$508$	9.00000	+	9.00000i	0.399310	+	0.399310i
$509$	−13.0000	−	13.0000i	−0.576215	−	0.576215i	0.357643	−	0.933858i	$-0.383580\pi$
$509$	−13.0000	−	13.0000i	−0.576215	−	0.576215i	−0.933858	+	0.357643i	$0.883580\pi$
$510$		0			0
$511$			20.0000i			0.884748i
$512$		−	11.0000i		−	0.486136i
$513$	−40.0000			−1.76604
$514$	11.0000	−	11.0000i	0.485189	−	0.485189i
$515$		0			0
$516$	2.00000			0.0880451
$517$	6.00000	+	6.00000i	0.263880	+	0.263880i
$518$		0			0
$519$	22.0000			0.965693
$520$		0			0
$521$	−10.0000			−0.438108			−0.219054	−	0.975713i	$-0.570297\pi$
$521$	−10.0000			−0.438108			−0.219054	+	0.975713i	$0.570297\pi$
$522$		0			0
$523$	−9.00000	−	9.00000i	−0.393543	−	0.393543i	0.482405	−	0.875948i	$-0.339763\pi$
$523$	−9.00000	−	9.00000i	−0.393543	−	0.393543i	−0.875948	+	0.482405i	$0.839763\pi$
$524$	−20.0000			−0.873704
$525$		0			0
$526$	1.00000	−	1.00000i	0.0436021	−	0.0436021i
$527$	10.0000			0.435607
$528$		−	2.00000i		−	0.0870388i
$529$			5.00000i			0.217391i
$530$		0			0
$531$	−7.00000	−	7.00000i	−0.303774	−	0.303774i
$532$	10.0000	+	10.0000i	0.433555	+	0.433555i
$533$	7.00000	+	35.0000i	0.303204	+	1.51602i
$534$			10.0000i			0.432742i
$535$		0			0
$536$	12.0000			0.518321
$537$	−20.0000	−	20.0000i	−0.863064	−	0.863064i
$538$	12.0000			0.517357
$539$	3.00000	+	3.00000i	0.129219	+	0.129219i
$540$		0			0
$541$	9.00000	+	9.00000i	0.386940	+	0.386940i	0.873595	−	0.486654i	$-0.161783\pi$
$541$	9.00000	+	9.00000i	0.386940	+	0.386940i	−0.486654	+	0.873595i	$0.661783\pi$
$542$	9.00000	−	9.00000i	0.386583	−	0.386583i
$543$	−8.00000	+	8.00000i	−0.343313	+	0.343313i
$544$	−5.00000	+	5.00000i	−0.214373	+	0.214373i
$545$		0			0
$546$	−2.00000	−	10.0000i	−0.0855921	−	0.427960i
$547$	9.00000	−	9.00000i	0.384812	−	0.384812i	−0.488020	−	0.872832i	$-0.662281\pi$
$547$	9.00000	−	9.00000i	0.384812	−	0.384812i	0.872832	+	0.488020i	$0.162281\pi$
$548$	16.0000			0.683486
$549$			14.0000i			0.597505i
$550$		0			0
$551$		0			0
$552$		−	18.0000i		−	0.766131i
$553$			4.00000i			0.170097i
$554$	15.0000	−	15.0000i	0.637289	−	0.637289i
$555$		0			0
$556$			14.0000i			0.593732i
$557$	−24.0000			−1.01691			−0.508456	−	0.861088i	$-0.669784\pi$
$557$	−24.0000			−1.01691			−0.508456	+	0.861088i	$0.669784\pi$
$558$	5.00000	−	5.00000i	0.211667	−	0.211667i
$559$	1.00000	+	5.00000i	0.0422955	+	0.211477i
$560$		0			0
$561$	−2.00000	+	2.00000i	−0.0844401	+	0.0844401i
$562$	−1.00000	+	1.00000i	−0.0421825	+	0.0421825i
$563$	15.0000	−	15.0000i	0.632175	−	0.632175i	−0.316438	−	0.948613i	$-0.602487\pi$
$563$	15.0000	−	15.0000i	0.632175	−	0.632175i	0.948613	+	0.316438i	$0.102487\pi$
$564$	6.00000	+	6.00000i	0.252646	+	0.252646i
$565$		0			0
$566$	−9.00000	−	9.00000i	−0.378298	−	0.378298i
$567$	10.0000			0.419961
$568$	3.00000	+	3.00000i	0.125877	+	0.125877i
$569$	−6.00000			−0.251533			−0.125767	−	0.992060i	$-0.540139\pi$
$569$	−6.00000			−0.251533			−0.125767	+	0.992060i	$0.540139\pi$
$570$		0			0
$571$		−	6.00000i		−	0.251092i	−0.992088	−	0.125546i	$-0.959932\pi$
$571$		−	6.00000i		−	0.251092i	0.992088	−	0.125546i	$-0.0400683\pi$
$572$	−5.00000	+	1.00000i	−0.209061	+	0.0418121i
$573$	−8.00000	−	8.00000i	−0.334205	−	0.334205i
$574$	−14.0000	−	14.0000i	−0.584349	−	0.584349i
$575$		0			0
$576$			7.00000i			0.291667i
$577$			46.0000i			1.91501i	0.288425	+	0.957503i	$0.406868\pi$
$577$			46.0000i			1.91501i	−0.288425	+	0.957503i	$0.593132\pi$
$578$	15.0000			0.623918
$579$	−18.0000	+	18.0000i	−0.748054	+	0.748054i
$580$		0			0
$581$	−12.0000			−0.497844
$582$	2.00000	+	2.00000i	0.0829027	+	0.0829027i
$583$			10.0000i			0.414158i
$584$	−30.0000			−1.24141
$585$		0			0
$586$	−6.00000			−0.247858
$587$		−	4.00000i		−	0.165098i	−0.996587	−	0.0825488i	$-0.973694\pi$
$587$		−	4.00000i		−	0.165098i	0.996587	−	0.0825488i	$-0.0263060\pi$
$588$	3.00000	+	3.00000i	0.123718	+	0.123718i
$589$	50.0000			2.06021
$590$		0			0
$591$	6.00000	−	6.00000i	0.246807	−	0.246807i
$592$		0			0
$593$		−	10.0000i		−	0.410651i	−0.978694	−	0.205325i	$-0.934175\pi$
$593$		−	10.0000i		−	0.410651i	0.978694	−	0.205325i	$-0.0658253\pi$
$594$			8.00000i			0.328244i
$595$		0			0
$596$	3.00000	+	3.00000i	0.122885	+	0.122885i
$597$	−8.00000	−	8.00000i	−0.327418	−	0.327418i
$598$	15.0000	−	3.00000i	0.613396	−	0.122679i
$599$		−	30.0000i		−	1.22577i	−0.790173	−	0.612883i	$-0.790010\pi$
$599$		−	30.0000i		−	1.22577i	0.790173	−	0.612883i	$-0.209990\pi$
$600$		0			0
$601$	−38.0000			−1.55005			−0.775026	−	0.631929i	$-0.782263\pi$
$601$	−38.0000			−1.55005			−0.775026	+	0.631929i	$0.782263\pi$
$602$	−2.00000	−	2.00000i	−0.0815139	−	0.0815139i
$603$	−4.00000			−0.162893
$604$	7.00000	+	7.00000i	0.284826	+	0.284826i
$605$		0			0
$606$	12.0000	+	12.0000i	0.487467	+	0.487467i
$607$	13.0000	−	13.0000i	0.527654	−	0.527654i	−0.392218	−	0.919872i	$-0.628292\pi$
$607$	13.0000	−	13.0000i	0.527654	−	0.527654i	0.919872	+	0.392218i	$0.128292\pi$
$608$	−25.0000	+	25.0000i	−1.01388	+	1.01388i
$609$		0			0
$610$		0			0
$611$	−12.0000	+	18.0000i	−0.485468	+	0.728202i
$612$	1.00000	−	1.00000i	0.0404226	−	0.0404226i
$613$	20.0000			0.807792			0.403896	−	0.914805i	$-0.367656\pi$
$613$	20.0000			0.807792			0.403896	+	0.914805i	$0.367656\pi$
$614$		−	18.0000i		−	0.726421i
$615$		0			0
$616$	6.00000	−	6.00000i	0.241747	−	0.241747i
$617$		−	22.0000i		−	0.885687i	−0.896599	−	0.442843i	$-0.853970\pi$
$617$		−	22.0000i		−	0.885687i	0.896599	−	0.442843i	$-0.146030\pi$
$618$		−	14.0000i		−	0.563163i
$619$	−25.0000	+	25.0000i	−1.00483	+	1.00483i	−0.00484658	+	0.999988i	$0.501543\pi$
$619$	−25.0000	+	25.0000i	−1.00483	+	1.00483i	−0.999988	+	0.00484658i	$0.998457\pi$
$620$		0			0
$621$			24.0000i			0.963087i
$622$	−6.00000			−0.240578
$623$	−10.0000	+	10.0000i	−0.400642	+	0.400642i
$624$	5.00000	−	1.00000i	0.200160	−	0.0400320i
$625$		0			0
$626$	9.00000	−	9.00000i	0.359712	−	0.359712i
$627$	−10.0000	+	10.0000i	−0.399362	+	0.399362i
$628$	−13.0000	+	13.0000i	−0.518756	+	0.518756i
$629$		0			0
$630$		0			0
$631$	11.0000	+	11.0000i	0.437903	+	0.437903i	0.891306	−	0.453403i	$-0.149790\pi$
$631$	11.0000	+	11.0000i	0.437903	+	0.437903i	−0.453403	+	0.891306i	$0.649790\pi$
$632$	−6.00000			−0.238667
$633$	−4.00000	−	4.00000i	−0.158986	−	0.158986i
$634$	14.0000			0.556011
$635$		0			0
$636$			10.0000i			0.396526i
$637$	−6.00000	+	9.00000i	−0.237729	+	0.356593i
$638$		0			0
$639$	−1.00000	−	1.00000i	−0.0395594	−	0.0395594i
$640$		0			0
$641$		−	24.0000i		−	0.947943i	−0.880540	−	0.473972i	$-0.842820\pi$
$641$		−	24.0000i		−	0.947943i	0.880540	−	0.473972i	$-0.157180\pi$
$642$			14.0000i			0.552536i
$643$	34.0000			1.34083			0.670415	−	0.741987i	$-0.266116\pi$
$643$	34.0000			1.34083			0.670415	+	0.741987i	$0.266116\pi$
$644$	6.00000	−	6.00000i	0.236433	−	0.236433i
$645$		0			0
$646$	−10.0000			−0.393445
$647$	1.00000	+	1.00000i	0.0393141	+	0.0393141i	0.726491	−	0.687176i	$-0.241150\pi$
$647$	1.00000	+	1.00000i	0.0393141	+	0.0393141i	−0.687176	+	0.726491i	$0.741150\pi$
$648$			15.0000i			0.589256i
$649$	−14.0000			−0.549548
$650$		0			0
$651$	−20.0000			−0.783862
$652$		−	4.00000i		−	0.156652i
$653$	−13.0000	−	13.0000i	−0.508729	−	0.508729i	0.405407	−	0.914136i	$-0.367130\pi$
$653$	−13.0000	−	13.0000i	−0.508729	−	0.508729i	−0.914136	+	0.405407i	$0.867130\pi$
$654$	−18.0000			−0.703856
$655$		0			0
$656$	7.00000	−	7.00000i	0.273304	−	0.273304i
$657$	10.0000			0.390137
$658$		−	12.0000i		−	0.467809i
$659$		−	26.0000i		−	1.01282i	−0.862294	−	0.506408i	$-0.830973\pi$
$659$		−	26.0000i		−	1.01282i	0.862294	−	0.506408i	$-0.169027\pi$
$660$		0			0
$661$	17.0000	+	17.0000i	0.661223	+	0.661223i	0.955668	−	0.294445i	$-0.0951348\pi$
$661$	17.0000	+	17.0000i	0.661223	+	0.661223i	−0.294445	+	0.955668i	$0.595135\pi$
$662$	−3.00000	−	3.00000i	−0.116598	−	0.116598i
$663$	−6.00000	−	4.00000i	−0.233021	−	0.155347i
$664$		−	18.0000i		−	0.698535i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	18.0000			0.696441
$669$	2.00000	+	2.00000i	0.0773245	+	0.0773245i
$670$		0			0
$671$	14.0000	+	14.0000i	0.540464	+	0.540464i
$672$	10.0000	−	10.0000i	0.385758	−	0.385758i
$673$	−15.0000	+	15.0000i	−0.578208	+	0.578208i	−0.934409	−	0.356202i	$-0.884072\pi$
$673$	−15.0000	+	15.0000i	−0.578208	+	0.578208i	0.356202	+	0.934409i	$0.384072\pi$
$674$	−13.0000	+	13.0000i	−0.500741	+	0.500741i
$675$		0			0
$676$	−5.00000	−	12.0000i	−0.192308	−	0.461538i
$677$	23.0000	−	23.0000i	0.883962	−	0.883962i	−0.109973	−	0.993935i	$-0.535076\pi$
$677$	23.0000	−	23.0000i	0.883962	−	0.883962i	0.993935	+	0.109973i	$0.0350764\pi$
$678$	−10.0000			−0.384048
$679$			4.00000i			0.153506i
$680$		0			0
$681$	−12.0000	+	12.0000i	−0.459841	+	0.459841i
$682$		−	10.0000i		−	0.382920i
$683$			12.0000i			0.459167i	0.973289	+	0.229584i	$0.0737364\pi$
$683$			12.0000i			0.459167i	−0.973289	+	0.229584i	$0.926264\pi$
$684$	5.00000	−	5.00000i	0.191180	−	0.191180i
$685$		0			0
$686$		−	20.0000i		−	0.763604i
$687$	−6.00000			−0.228914
$688$	1.00000	−	1.00000i	0.0381246	−	0.0381246i
$689$	−25.0000	+	5.00000i	−0.952424	+	0.190485i
$690$		0			0
$691$	−3.00000	+	3.00000i	−0.114125	+	0.114125i	−0.761863	−	0.647738i	$-0.775715\pi$
$691$	−3.00000	+	3.00000i	−0.114125	+	0.114125i	0.647738	+	0.761863i	$0.275715\pi$
$692$	−11.0000	+	11.0000i	−0.418157	+	0.418157i
$693$	−2.00000	+	2.00000i	−0.0759737	+	0.0759737i
$694$	−3.00000	−	3.00000i	−0.113878	−	0.113878i
$695$		0			0
$696$		0			0
$697$	−14.0000			−0.530288
$698$	−9.00000	−	9.00000i	−0.340655	−	0.340655i
$699$	−2.00000			−0.0756469
$700$		0			0
$701$			12.0000i			0.453234i	0.973984	+	0.226617i	$0.0727665\pi$
$701$			12.0000i			0.453234i	−0.973984	+	0.226617i	$0.927233\pi$
$702$	−20.0000	+	4.00000i	−0.754851	+	0.150970i
$703$		0			0
$704$	7.00000	+	7.00000i	0.263822	+	0.263822i
$705$		0			0
$706$			12.0000i			0.451626i
$707$			24.0000i			0.902613i
$708$	−14.0000			−0.526152
$709$	−29.0000	+	29.0000i	−1.08912	+	1.08912i	−0.0934984	+	0.995619i	$0.529805\pi$
$709$	−29.0000	+	29.0000i	−1.08912	+	1.08912i	−0.995619	+	0.0934984i	$0.970195\pi$
$710$		0			0
$711$	2.00000			0.0750059
$712$	−15.0000	−	15.0000i	−0.562149	−	0.562149i
$713$		−	30.0000i		−	1.12351i
$714$	4.00000			0.149696
$715$		0			0
$716$	20.0000			0.747435
$717$			6.00000i			0.224074i
$718$	−1.00000	−	1.00000i	−0.0373197	−	0.0373197i
$719$	8.00000			0.298350			0.149175	−	0.988811i	$-0.452338\pi$
$719$	8.00000			0.298350			0.149175	+	0.988811i	$0.452338\pi$
$720$		0			0
$721$	14.0000	−	14.0000i	0.521387	−	0.521387i
$722$	−31.0000			−1.15370
$723$		−	34.0000i		−	1.26447i
$724$		−	8.00000i		−	0.297318i
$725$		0			0
$726$	−9.00000	−	9.00000i	−0.334021	−	0.334021i
$727$	−35.0000	−	35.0000i	−1.29808	−	1.29808i	−0.929660	−	0.368418i	$-0.879900\pi$
$727$	−35.0000	−	35.0000i	−1.29808	−	1.29808i	−0.368418	−	0.929660i	$-0.620100\pi$
$728$	18.0000	+	12.0000i	0.667124	+	0.444750i
$729$		−	29.0000i		−	1.07407i
$730$		0			0
$731$	−2.00000			−0.0739727
$732$	14.0000	+	14.0000i	0.517455	+	0.517455i
$733$	4.00000			0.147743			0.0738717	−	0.997268i	$-0.476464\pi$
$733$	4.00000			0.147743			0.0738717	+	0.997268i	$0.476464\pi$
$734$	1.00000	+	1.00000i	0.0369107	+	0.0369107i
$735$		0			0
$736$	15.0000	+	15.0000i	0.552907	+	0.552907i
$737$	−4.00000	+	4.00000i	−0.147342	+	0.147342i
$738$	−7.00000	+	7.00000i	−0.257674	+	0.257674i
$739$	3.00000	−	3.00000i	0.110357	−	0.110357i	−0.649772	−	0.760129i	$-0.725136\pi$
$739$	3.00000	−	3.00000i	0.110357	−	0.110357i	0.760129	+	0.649772i	$0.225136\pi$
$740$		0			0
$741$	−30.0000	−	20.0000i	−1.10208	−	0.734718i
$742$	10.0000	−	10.0000i	0.367112	−	0.367112i
$743$	−34.0000			−1.24734			−0.623670	−	0.781688i	$-0.714359\pi$
$743$	−34.0000			−1.24734			−0.623670	+	0.781688i	$0.714359\pi$
$744$		−	30.0000i		−	1.09985i
$745$		0			0
$746$	−15.0000	+	15.0000i	−0.549189	+	0.549189i
$747$			6.00000i			0.219529i
$748$		−	2.00000i		−	0.0731272i
$749$	−14.0000	+	14.0000i	−0.511549	+	0.511549i
$750$		0			0
$751$		−	50.0000i		−	1.82453i	−0.409605	−	0.912263i	$-0.634333\pi$
$751$		−	50.0000i		−	1.82453i	0.409605	−	0.912263i	$-0.365667\pi$
$752$	6.00000			0.218797
$753$	2.00000	−	2.00000i	0.0728841	−	0.0728841i
$754$		0			0
$755$		0			0
$756$	−8.00000	+	8.00000i	−0.290957	+	0.290957i
$757$	35.0000	−	35.0000i	1.27210	−	1.27210i	0.327111	−	0.944986i	$-0.393925\pi$
$757$	35.0000	−	35.0000i	1.27210	−	1.27210i	0.944986	−	0.327111i	$-0.106075\pi$
$758$	−1.00000	+	1.00000i	−0.0363216	+	0.0363216i
$759$	6.00000	+	6.00000i	0.217786	+	0.217786i
$760$		0			0
$761$	−7.00000	−	7.00000i	−0.253750	−	0.253750i	0.568756	−	0.822506i	$-0.307425\pi$
$761$	−7.00000	−	7.00000i	−0.253750	−	0.253750i	−0.822506	+	0.568756i	$0.807425\pi$
$762$	18.0000			0.652071
$763$	−18.0000	−	18.0000i	−0.651644	−	0.651644i
$764$	8.00000			0.289430
$765$		0			0
$766$			30.0000i			1.08394i
$767$	−7.00000	−	35.0000i	−0.252755	−	1.26378i
$768$	17.0000	+	17.0000i	0.613435	+	0.613435i
$769$	15.0000	+	15.0000i	0.540914	+	0.540914i	0.923797	−	0.382883i	$-0.125069\pi$
$769$	15.0000	+	15.0000i	0.540914	+	0.540914i	−0.382883	+	0.923797i	$0.625069\pi$
$770$		0			0
$771$			22.0000i			0.792311i
$772$		−	18.0000i		−	0.647834i
$773$	32.0000			1.15096			0.575480	−	0.817816i	$-0.304815\pi$
$773$	32.0000			1.15096			0.575480	+	0.817816i	$0.304815\pi$
$774$	−1.00000	+	1.00000i	−0.0359443	+	0.0359443i
$775$		0			0
$776$	−6.00000			−0.215387
$777$		0			0
$778$			18.0000i			0.645331i
$779$	−70.0000			−2.50801
$780$		0			0
$781$	&minu

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.00000 - 1.00000i) q^{3} +1.00000 q^{4} +(1.00000 - 1.00000i) q^{6} +2.00000 q^{7} +3.00000i q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.00000 - 1.00000i) q^{3} +1.00000 q^{4} +(1.00000 - 1.00000i) q^{6} +2.00000 q^{7} +3.00000i q^{8} -1.00000i q^{9} +(-1.00000 - 1.00000i) q^{11} +(-1.00000 - 1.00000i) q^{12} +(2.00000 - 3.00000i) q^{13} +2.00000i q^{14} -1.00000 q^{16} +(1.00000 + 1.00000i) q^{17} +1.00000 q^{18} +(5.00000 + 5.00000i) q^{19} +(-2.00000 - 2.00000i) q^{21} +(1.00000 - 1.00000i) q^{22} +(3.00000 - 3.00000i) q^{23} +(3.00000 - 3.00000i) q^{24} +(3.00000 + 2.00000i) q^{26} +(-4.00000 + 4.00000i) q^{27} +2.00000 q^{28} +(5.00000 - 5.00000i) q^{31} +5.00000i q^{32} +2.00000i q^{33} +(-1.00000 + 1.00000i) q^{34} -1.00000i q^{36} +(-5.00000 + 5.00000i) q^{38} +(-5.00000 + 1.00000i) q^{39} +(-7.00000 + 7.00000i) q^{41} +(2.00000 - 2.00000i) q^{42} +(-1.00000 + 1.00000i) q^{43} +(-1.00000 - 1.00000i) q^{44} +(3.00000 + 3.00000i) q^{46} -6.00000 q^{47} +(1.00000 + 1.00000i) q^{48} -3.00000 q^{49} -2.00000i q^{51} +(2.00000 - 3.00000i) q^{52} +(-5.00000 - 5.00000i) q^{53} +(-4.00000 - 4.00000i) q^{54} +6.00000i q^{56} -10.0000i q^{57} +(7.00000 - 7.00000i) q^{59} -14.0000 q^{61} +(5.00000 + 5.00000i) q^{62} -2.00000i q^{63} -7.00000 q^{64} -2.00000 q^{66} -4.00000i q^{67} +(1.00000 + 1.00000i) q^{68} -6.00000 q^{69} +(1.00000 - 1.00000i) q^{71} +3.00000 q^{72} +10.0000i q^{73} +(5.00000 + 5.00000i) q^{76} +(-2.00000 - 2.00000i) q^{77} +(-1.00000 - 5.00000i) q^{78} +2.00000i q^{79} +5.00000 q^{81} +(-7.00000 - 7.00000i) q^{82} -6.00000 q^{83} +(-2.00000 - 2.00000i) q^{84} +(-1.00000 - 1.00000i) q^{86} +(3.00000 - 3.00000i) q^{88} +(-5.00000 + 5.00000i) q^{89} +(4.00000 - 6.00000i) q^{91} +(3.00000 - 3.00000i) q^{92} -10.0000 q^{93} -6.00000i q^{94} +(5.00000 - 5.00000i) q^{96} +2.00000i q^{97} -3.00000i q^{98} +(-1.00000 + 1.00000i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{7}+O(q^{10}) \) 2 * q - 2 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^7	\( 2 q - 2 q^{3} + 2 q^{4} + 2 q^{6} + 4 q^{7} - 2 q^{11} - 2 q^{12} + 4 q^{13} - 2 q^{16} + 2 q^{17} + 2 q^{18} + 10 q^{19} - 4 q^{21} + 2 q^{22} + 6 q^{23} + 6 q^{24} + 6 q^{26} - 8 q^{27} + 4 q^{28} + 10 q^{31} - 2 q^{34} - 10 q^{38} - 10 q^{39} - 14 q^{41} + 4 q^{42} - 2 q^{43} - 2 q^{44} + 6 q^{46} - 12 q^{47} + 2 q^{48} - 6 q^{49} + 4 q^{52} - 10 q^{53} - 8 q^{54} + 14 q^{59} - 28 q^{61} + 10 q^{62} - 14 q^{64} - 4 q^{66} + 2 q^{68} - 12 q^{69} + 2 q^{71} + 6 q^{72} + 10 q^{76} - 4 q^{77} - 2 q^{78} + 10 q^{81} - 14 q^{82} - 12 q^{83} - 4 q^{84} - 2 q^{86} + 6 q^{88} - 10 q^{89} + 8 q^{91} + 6 q^{92} - 20 q^{93} + 10 q^{96} - 2 q^{99}+O(q^{100}) \) 2 * q - 2 * q^3 + 2 * q^4 + 2 * q^6 + 4 * q^7 - 2 * q^11 - 2 * q^12 + 4 * q^13 - 2 * q^16 + 2 * q^17 + 2 * q^18 + 10 * q^19 - 4 * q^21 + 2 * q^22 + 6 * q^23 + 6 * q^24 + 6 * q^26 - 8 * q^27 + 4 * q^28 + 10 * q^31 - 2 * q^34 - 10 * q^38 - 10 * q^39 - 14 * q^41 + 4 * q^42 - 2 * q^43 - 2 * q^44 + 6 * q^46 - 12 * q^47 + 2 * q^48 - 6 * q^49 + 4 * q^52 - 10 * q^53 - 8 * q^54 + 14 * q^59 - 28 * q^61 + 10 * q^62 - 14 * q^64 - 4 * q^66 + 2 * q^68 - 12 * q^69 + 2 * q^71 + 6 * q^72 + 10 * q^76 - 4 * q^77 - 2 * q^78 + 10 * q^81 - 14 * q^82 - 12 * q^83 - 4 * q^84 - 2 * q^86 + 6 * q^88 - 10 * q^89 + 8 * q^91 + 6 * q^92 - 20 * q^93 + 10 * q^96 - 2 * q^99

Introduction

L-functions

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Varieties

Fields

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Groups

Database

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