LMFDB - Embedded newform 975.2.w.f.199.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [975,2,Mod(49,975)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(975, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("975.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 975 = 3 \cdot 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	975.w (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.78541419707$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 195)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.2
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	975.199
Dual form			975.2.w.f.49.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.36603 - 2.36603i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-2.73205 - 4.73205i) q^{4} +(2.36603 - 1.36603i) q^{6} +(-1.23205 - 2.13397i) q^{7} -9.46410 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(1.36603 - 2.36603i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-2.73205 - 4.73205i) q^{4} +(2.36603 - 1.36603i) q^{6} +(-1.23205 - 2.13397i) q^{7} -9.46410 q^{8} +(0.500000 + 0.866025i) q^{9} +(-3.00000 - 1.73205i) q^{11} -5.46410i q^{12} +(-3.50000 + 0.866025i) q^{13} -6.73205 q^{14} +(-7.46410 + 12.9282i) q^{16} +(2.83013 - 1.63397i) q^{17} +2.73205 q^{18} +(1.26795 - 0.732051i) q^{19} -2.46410i q^{21} +(-8.19615 + 4.73205i) q^{22} +(6.46410 + 3.73205i) q^{23} +(-8.19615 - 4.73205i) q^{24} +(-2.73205 + 9.46410i) q^{26} +1.00000i q^{27} +(-6.73205 + 11.6603i) q^{28} +(0.366025 - 0.633975i) q^{29} -7.19615i q^{31} +(10.9282 + 18.9282i) q^{32} +(-1.73205 - 3.00000i) q^{33} -8.92820i q^{34} +(2.73205 - 4.73205i) q^{36} +(2.00000 - 3.46410i) q^{37} -4.00000i q^{38} +(-3.46410 - 1.00000i) q^{39} +(-7.56218 - 4.36603i) q^{41} +(-5.83013 - 3.36603i) q^{42} +(-3.23205 + 1.86603i) q^{43} +18.9282i q^{44} +(17.6603 - 10.1962i) q^{46} -10.1962 q^{47} +(-12.9282 + 7.46410i) q^{48} +(0.464102 - 0.803848i) q^{49} +3.26795 q^{51} +(13.6603 + 14.1962i) q^{52} -6.92820i q^{53} +(2.36603 + 1.36603i) q^{54} +(11.6603 + 20.1962i) q^{56} +1.46410 q^{57} +(-1.00000 - 1.73205i) q^{58} +(9.29423 - 5.36603i) q^{59} +(1.23205 + 2.13397i) q^{61} +(-17.0263 - 9.83013i) q^{62} +(1.23205 - 2.13397i) q^{63} +29.8564 q^{64} -9.46410 q^{66} +(-2.76795 + 4.79423i) q^{67} +(-15.4641 - 8.92820i) q^{68} +(3.73205 + 6.46410i) q^{69} +(8.02628 - 4.63397i) q^{71} +(-4.73205 - 8.19615i) q^{72} +5.39230 q^{73} +(-5.46410 - 9.46410i) q^{74} +(-6.92820 - 4.00000i) q^{76} +8.53590i q^{77} +(-7.09808 + 6.83013i) q^{78} +11.9282 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-20.6603 + 11.9282i) q^{82} +9.46410 q^{83} +(-11.6603 + 6.73205i) q^{84} +10.1962i q^{86} +(0.633975 - 0.366025i) q^{87} +(28.3923 + 16.3923i) q^{88} +(-4.09808 - 2.36603i) q^{89} +(6.16025 + 6.40192i) q^{91} -40.7846i q^{92} +(3.59808 - 6.23205i) q^{93} +(-13.9282 + 24.1244i) q^{94} +21.8564i q^{96} +(4.76795 + 8.25833i) q^{97} +(-1.26795 - 2.19615i) q^{98} -3.46410i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} - 4 q^{4} + 6 q^{6} + 2 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 2 * q^2 - 4 * q^4 + 6 * q^6 + 2 * q^7 - 24 * q^8 + 2 * q^9	$ 4 q + 2 q^{2} - 4 q^{4} + 6 q^{6} + 2 q^{7} - 24 q^{8} + 2 q^{9} - 12 q^{11} - 14 q^{13} - 20 q^{14} - 16 q^{16} - 6 q^{17} + 4 q^{18} + 12 q^{19} - 12 q^{22} + 12 q^{23} - 12 q^{24} - 4 q^{26} - 20 q^{28} - 2 q^{29} + 16 q^{32} + 4 q^{36} + 8 q^{37} - 6 q^{41} - 6 q^{42} - 6 q^{43} + 36 q^{46} - 20 q^{47} - 24 q^{48} - 12 q^{49} + 20 q^{51} + 20 q^{52} + 6 q^{54} + 12 q^{56} - 8 q^{57} - 4 q^{58} + 6 q^{59} - 2 q^{61} - 30 q^{62} - 2 q^{63} + 64 q^{64} - 24 q^{66} - 18 q^{67} - 48 q^{68} + 8 q^{69} - 6 q^{71} - 12 q^{72} - 20 q^{73} - 8 q^{74} - 18 q^{78} + 20 q^{79} - 2 q^{81} - 48 q^{82} + 24 q^{83} - 12 q^{84} + 6 q^{87} + 72 q^{88} - 6 q^{89} - 10 q^{91} + 4 q^{93} - 28 q^{94} + 26 q^{97} - 12 q^{98}+O(q^{100}) $ 4 * q + 2 * q^2 - 4 * q^4 + 6 * q^6 + 2 * q^7 - 24 * q^8 + 2 * q^9 - 12 * q^11 - 14 * q^13 - 20 * q^14 - 16 * q^16 - 6 * q^17 + 4 * q^18 + 12 * q^19 - 12 * q^22 + 12 * q^23 - 12 * q^24 - 4 * q^26 - 20 * q^28 - 2 * q^29 + 16 * q^32 + 4 * q^36 + 8 * q^37 - 6 * q^41 - 6 * q^42 - 6 * q^43 + 36 * q^46 - 20 * q^47 - 24 * q^48 - 12 * q^49 + 20 * q^51 + 20 * q^52 + 6 * q^54 + 12 * q^56 - 8 * q^57 - 4 * q^58 + 6 * q^59 - 2 * q^61 - 30 * q^62 - 2 * q^63 + 64 * q^64 - 24 * q^66 - 18 * q^67 - 48 * q^68 + 8 * q^69 - 6 * q^71 - 12 * q^72 - 20 * q^73 - 8 * q^74 - 18 * q^78 + 20 * q^79 - 2 * q^81 - 48 * q^82 + 24 * q^83 - 12 * q^84 + 6 * q^87 + 72 * q^88 - 6 * q^89 - 10 * q^91 + 4 * q^93 - 28 * q^94 + 26 * q^97 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/975\mathbb{Z}\right)^\times$.

$n$	$301$	$326$	$352$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$	1.36603	−	2.36603i	0.965926	−	1.67303i	0.258819	−	0.965926i	$-0.416667\pi$
$2$	1.36603	−	2.36603i	0.965926	−	1.67303i	0.707107	−	0.707107i	$-0.250000\pi$
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$3$	0.866025	+	0.500000i	0.500000	+	0.288675i
$4$	−2.73205	−	4.73205i	−1.36603	−	2.36603i
$5$		0			0
$5$		0			0
$6$	2.36603	−	1.36603i	0.965926	−	0.557678i
$7$	−1.23205	−	2.13397i	−0.465671	−	0.806567i	0.533560	−	0.845762i	$-0.320854\pi$
$7$	−1.23205	−	2.13397i	−0.465671	−	0.806567i	−0.999232	+	0.0391956i	$0.987520\pi$
$8$	−9.46410			−3.34607
$9$	0.500000	+	0.866025i	0.166667	+	0.288675i
$10$		0			0
$11$	−3.00000	−	1.73205i	−0.904534	−	0.522233i	−0.0258656	−	0.999665i	$-0.508234\pi$
$11$	−3.00000	−	1.73205i	−0.904534	−	0.522233i	−0.878668	+	0.477432i	$0.841568\pi$
$12$		−	5.46410i		−	1.57735i
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$13$	−3.50000	+	0.866025i	−0.970725	+	0.240192i
$14$	−6.73205			−1.79922
$15$		0			0
$16$	−7.46410	+	12.9282i	−1.86603	+	3.23205i
$17$	2.83013	−	1.63397i	0.686407	−	0.396297i	−0.115858	−	0.993266i	$-0.536962\pi$
$17$	2.83013	−	1.63397i	0.686407	−	0.396297i	0.802264	+	0.596969i	$0.203628\pi$
$18$	2.73205			0.643951
$19$	1.26795	−	0.732051i	0.290887	−	0.167944i	−0.347455	−	0.937697i	$-0.612954\pi$
$19$	1.26795	−	0.732051i	0.290887	−	0.167944i	0.638342	+	0.769753i	$0.279621\pi$
$20$		0			0
$21$		−	2.46410i		−	0.537711i
$22$	−8.19615	+	4.73205i	−1.74743	+	1.00888i
$23$	6.46410	+	3.73205i	1.34786	+	0.778186i	0.987946	−	0.154800i	$-0.0494732\pi$
$23$	6.46410	+	3.73205i	1.34786	+	0.778186i	0.359912	+	0.932986i	$0.382807\pi$
$24$	−8.19615	−	4.73205i	−1.67303	−	0.965926i
$25$		0			0
$26$	−2.73205	+	9.46410i	−0.535799	+	1.85606i
$27$			1.00000i			0.192450i
$28$	−6.73205	+	11.6603i	−1.27224	+	2.20358i
$29$	0.366025	−	0.633975i	0.0679692	−	0.117726i	−0.830038	−	0.557707i	$-0.811681\pi$
$29$	0.366025	−	0.633975i	0.0679692	−	0.117726i	0.898007	+	0.439981i	$0.145015\pi$
$30$		0			0
$31$		−	7.19615i		−	1.29247i	−0.763140	−	0.646234i	$-0.776343\pi$
$31$		−	7.19615i		−	1.29247i	0.763140	−	0.646234i	$-0.223657\pi$
$32$	10.9282	+	18.9282i	1.93185	+	3.34607i
$33$	−1.73205	−	3.00000i	−0.301511	−	0.522233i
$34$		−	8.92820i		−	1.53117i
$35$		0			0
$36$	2.73205	−	4.73205i	0.455342	−	0.788675i
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	−0.653476	−	0.756948i	$-0.726690\pi$
$37$	2.00000	−	3.46410i	0.328798	−	0.569495i	0.982274	+	0.187453i	$0.0600231\pi$
$38$		−	4.00000i		−	0.648886i
$39$	−3.46410	−	1.00000i	−0.554700	−	0.160128i
$40$		0			0
$41$	−7.56218	−	4.36603i	−1.18101	−	0.681859i	−0.224765	−	0.974413i	$-0.572161\pi$
$41$	−7.56218	−	4.36603i	−1.18101	−	0.681859i	−0.956249	+	0.292554i	$0.905495\pi$
$42$	−5.83013	−	3.36603i	−0.899608	−	0.519389i
$43$	−3.23205	+	1.86603i	−0.492883	+	0.284566i	−0.725770	−	0.687938i	$-0.758516\pi$
$43$	−3.23205	+	1.86603i	−0.492883	+	0.284566i	0.232887	+	0.972504i	$0.425183\pi$
$44$			18.9282i			2.85353i
$45$		0			0
$46$	17.6603	−	10.1962i	2.60386	−	1.50334i
$47$	−10.1962			−1.48726			−0.743631	−	0.668590i	$-0.766898\pi$
$47$	−10.1962			−1.48726			−0.743631	+	0.668590i	$0.766898\pi$
$48$	−12.9282	+	7.46410i	−1.86603	+	1.07735i
$49$	0.464102	−	0.803848i	0.0663002	−	0.114835i
$50$		0			0
$51$	3.26795			0.457604
$52$	13.6603	+	14.1962i	1.89434	+	1.96865i
$53$		−	6.92820i		−	0.951662i	−0.879537	−	0.475831i	$-0.842147\pi$
$53$		−	6.92820i		−	0.951662i	0.879537	−	0.475831i	$-0.157853\pi$
$54$	2.36603	+	1.36603i	0.321975	+	0.185893i
$55$		0			0
$56$	11.6603	+	20.1962i	1.55817	+	2.69882i
$57$	1.46410			0.193925
$58$	−1.00000	−	1.73205i	−0.131306	−	0.227429i
$59$	9.29423	−	5.36603i	1.21001	−	0.698597i	0.247245	−	0.968953i	$-0.420475\pi$
$59$	9.29423	−	5.36603i	1.21001	−	0.698597i	0.962760	+	0.270356i	$0.0871414\pi$
$60$		0			0
$61$	1.23205	+	2.13397i	0.157748	+	0.273227i	0.934056	−	0.357126i	$-0.116243\pi$
$61$	1.23205	+	2.13397i	0.157748	+	0.273227i	−0.776308	+	0.630353i	$0.782910\pi$
$62$	−17.0263	−	9.83013i	−2.16234	−	1.24843i
$63$	1.23205	−	2.13397i	0.155224	−	0.268856i
$64$	29.8564			3.73205
$65$		0			0
$66$	−9.46410			−1.16495
$67$	−2.76795	+	4.79423i	−0.338159	+	0.585708i	−0.984086	−	0.177690i	$-0.943137\pi$
$67$	−2.76795	+	4.79423i	−0.338159	+	0.585708i	0.645928	+	0.763399i	$0.276471\pi$
$68$	−15.4641	−	8.92820i	−1.87530	−	1.08270i
$69$	3.73205	+	6.46410i	0.449286	+	0.778186i
$70$		0			0
$71$	8.02628	−	4.63397i	0.952544	−	0.549952i	0.0586738	−	0.998277i	$-0.481313\pi$
$71$	8.02628	−	4.63397i	0.952544	−	0.549952i	0.893870	+	0.448326i	$0.147979\pi$
$72$	−4.73205	−	8.19615i	−0.557678	−	0.965926i
$73$	5.39230			0.631122			0.315561	−	0.948905i	$-0.397807\pi$
$73$	5.39230			0.631122			0.315561	+	0.948905i	$0.397807\pi$
$74$	−5.46410	−	9.46410i	−0.635189	−	1.10018i
$75$		0			0
$76$	−6.92820	−	4.00000i	−0.794719	−	0.458831i
$77$			8.53590i			0.972756i
$78$	−7.09808	+	6.83013i	−0.803699	+	0.773360i
$79$	11.9282			1.34203			0.671014	−	0.741445i	$-0.265859\pi$
$79$	11.9282			1.34203			0.671014	+	0.741445i	$0.265859\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−20.6603	+	11.9282i	−2.28154	+	1.31725i
$83$	9.46410			1.03882			0.519410	−	0.854525i	$-0.326152\pi$
$83$	9.46410			1.03882			0.519410	+	0.854525i	$0.326152\pi$
$84$	−11.6603	+	6.73205i	−1.27224	+	0.734527i
$85$		0			0
$86$			10.1962i			1.09948i
$87$	0.633975	−	0.366025i	0.0679692	−	0.0392420i
$88$	28.3923	+	16.3923i	3.02663	+	1.74743i
$89$	−4.09808	−	2.36603i	−0.434395	−	0.250798i	0.266822	−	0.963746i	$-0.414026\pi$
$89$	−4.09808	−	2.36603i	−0.434395	−	0.250798i	−0.701217	+	0.712948i	$0.747360\pi$
$90$		0			0
$91$	6.16025	+	6.40192i	0.645770	+	0.671104i
$92$		−	40.7846i		−	4.25209i
$93$	3.59808	−	6.23205i	0.373103	−	0.646234i
$94$	−13.9282	+	24.1244i	−1.43658	+	2.48824i
$95$		0			0
$96$			21.8564i			2.23071i
$97$	4.76795	+	8.25833i	0.484112	+	0.838506i	0.999833	−	0.0182499i	$-0.00580943\pi$
$97$	4.76795	+	8.25833i	0.484112	+	0.838506i	−0.515722	+	0.856756i	$0.672476\pi$
$98$	−1.26795	−	2.19615i	−0.128082	−	0.221845i
$99$		−	3.46410i		−	0.348155i
$100$		0			0
$101$	4.46410	−	7.73205i	0.444195	−	0.769368i	−0.553801	−	0.832649i	$-0.686823\pi$
$101$	4.46410	−	7.73205i	0.444195	−	0.769368i	0.997996	+	0.0632812i	$0.0201565\pi$
$102$	4.46410	−	7.73205i	0.442012	−	0.765587i
$103$			7.19615i			0.709058i	0.935045	+	0.354529i	$0.115359\pi$
$103$			7.19615i			0.709058i	−0.935045	+	0.354529i	$0.884641\pi$
$104$	33.1244	−	8.19615i	3.24811	−	0.803699i
$105$		0			0
$106$	−16.3923	−	9.46410i	−1.59216	−	0.919235i
$107$	6.16987	+	3.56218i	0.596464	+	0.344369i	0.767649	−	0.640870i	$-0.221426\pi$
$107$	6.16987	+	3.56218i	0.596464	+	0.344369i	−0.171185	+	0.985239i	$0.554760\pi$
$108$	4.73205	−	2.73205i	0.455342	−	0.262892i
$109$		−	11.7321i		−	1.12373i	−0.827230	−	0.561863i	$-0.810085\pi$
$109$		−	11.7321i		−	1.12373i	0.827230	−	0.561863i	$-0.189915\pi$
$110$		0			0
$111$	3.46410	−	2.00000i	0.328798	−	0.189832i
$112$	36.7846			3.47582
$113$	−10.8564	+	6.26795i	−1.02128	+	0.589639i	−0.914476	−	0.404640i	$-0.867397\pi$
$113$	−10.8564	+	6.26795i	−1.02128	+	0.589639i	−0.106809	+	0.994280i	$0.534063\pi$
$114$	2.00000	−	3.46410i	0.187317	−	0.324443i
$115$		0			0
$116$	−4.00000			−0.371391
$117$	−2.50000	−	2.59808i	−0.231125	−	0.240192i
$118$		−	29.3205i		−	2.69917i
$119$	−6.97372	−	4.02628i	−0.639280	−	0.369088i
$120$		0			0
$121$	0.500000	+	0.866025i	0.0454545	+	0.0787296i
$122$	6.73205			0.609491
$123$	−4.36603	−	7.56218i	−0.393671	−	0.681859i
$124$	−34.0526	+	19.6603i	−3.05801	+	1.76554i
$125$		0			0
$126$	−3.36603	−	5.83013i	−0.299869	−	0.519389i
$127$	−2.30385	−	1.33013i	−0.204433	−	0.118030i	0.394288	−	0.918987i	$-0.370991\pi$
$127$	−2.30385	−	1.33013i	−0.204433	−	0.118030i	−0.598722	+	0.800957i	$0.704324\pi$
$128$	18.9282	−	32.7846i	1.67303	−	2.89778i
$129$	−3.73205			−0.328589
$130$		0			0
$131$	4.73205			0.413441			0.206721	−	0.978400i	$-0.433721\pi$
$131$	4.73205			0.413441			0.206721	+	0.978400i	$0.433721\pi$
$132$	−9.46410	+	16.3923i	−0.823744	+	1.42677i
$133$	−3.12436	−	1.80385i	−0.270916	−	0.156413i
$134$	7.56218	+	13.0981i	0.653273	+	1.13150i
$135$		0			0
$136$	−26.7846	+	15.4641i	−2.29676	+	1.32604i
$137$	−7.56218	−	13.0981i	−0.646080	−	1.11904i	−0.984051	−	0.177887i	$-0.943074\pi$
$137$	−7.56218	−	13.0981i	−0.646080	−	1.11904i	0.337970	−	0.941157i	$-0.390260\pi$
$138$	20.3923			1.73591
$139$	−2.03590	−	3.52628i	−0.172683	−	0.299095i	0.766674	−	0.642036i	$-0.221910\pi$
$139$	−2.03590	−	3.52628i	−0.172683	−	0.299095i	−0.939357	+	0.342941i	$0.888577\pi$
$140$		0			0
$141$	−8.83013	−	5.09808i	−0.743631	−	0.429335i
$142$		−	25.3205i		−	2.12485i
$143$	12.0000	+	3.46410i	1.00349	+	0.289683i
$144$	−14.9282			−1.24402
$145$		0			0
$146$	7.36603	−	12.7583i	0.609617	−	1.05589i
$147$	0.803848	−	0.464102i	0.0663002	−	0.0382785i
$148$	−21.8564			−1.79659
$149$	−3.46410	+	2.00000i	−0.283790	+	0.163846i	−0.635138	−	0.772399i	$-0.719057\pi$
$149$	−3.46410	+	2.00000i	−0.283790	+	0.163846i	0.351348	+	0.936245i	$0.385723\pi$
$150$		0			0
$151$			9.85641i			0.802103i	0.916056	+	0.401051i	$0.131355\pi$
$151$			9.85641i			0.802103i	−0.916056	+	0.401051i	$0.868645\pi$
$152$	−12.0000	+	6.92820i	−0.973329	+	0.561951i
$153$	2.83013	+	1.63397i	0.228802	+	0.132099i
$154$	20.1962	+	11.6603i	1.62745	+	0.939610i
$155$		0			0
$156$	4.73205	+	19.1244i	0.378867	+	1.53117i
$157$			6.26795i			0.500237i	0.968215	+	0.250118i	$0.0804695\pi$
$157$			6.26795i			0.500237i	−0.968215	+	0.250118i	$0.919530\pi$
$158$	16.2942	−	28.2224i	1.29630	−	2.24526i
$159$	3.46410	−	6.00000i	0.274721	−	0.475831i
$160$		0			0
$161$		−	18.3923i		−	1.44952i
$162$	1.36603	+	2.36603i	0.107325	+	0.185893i
$163$	6.23205	+	10.7942i	0.488132	+	0.845469i	0.999907	−	0.0136503i	$-0.00434517\pi$
$163$	6.23205	+	10.7942i	0.488132	+	0.845469i	−0.511775	+	0.859120i	$0.671012\pi$
$164$			47.7128i			3.72574i
$165$		0			0
$166$	12.9282	−	22.3923i	1.00342	−	1.73798i
$167$	−5.26795	+	9.12436i	−0.407646	+	0.706064i	−0.994625	−	0.103538i	$-0.966984\pi$
$167$	−5.26795	+	9.12436i	−0.407646	+	0.706064i	0.586979	+	0.809602i	$0.300317\pi$
$168$			23.3205i			1.79922i
$169$	11.5000	−	6.06218i	0.884615	−	0.466321i
$170$		0			0
$171$	1.26795	+	0.732051i	0.0969625	+	0.0559813i
$172$	17.6603	+	10.1962i	1.34658	+	0.777449i
$173$	5.83013	−	3.36603i	0.443256	−	0.255914i	−0.261722	−	0.965143i	$-0.584290\pi$
$173$	5.83013	−	3.36603i	0.443256	−	0.255914i	0.704978	+	0.709229i	$0.250957\pi$
$174$		−	2.00000i		−	0.151620i
$175$		0			0
$176$	44.7846	−	25.8564i	3.37577	−	1.94900i
$177$	10.7321			0.806670
$178$	−11.1962	+	6.46410i	−0.839187	+	0.484505i
$179$	7.56218	−	13.0981i	0.565224	−	0.978996i	−0.431805	−	0.901967i	$-0.642123\pi$
$179$	7.56218	−	13.0981i	0.565224	−	0.978996i	0.997029	−	0.0770293i	$-0.0245435\pi$
$180$		0			0
$181$	21.4641			1.59541			0.797707	−	0.603045i	$-0.206046\pi$
$181$	21.4641			1.59541			0.797707	+	0.603045i	$0.206046\pi$
$182$	23.5622	−	5.83013i	1.74654	−	0.432158i
$183$			2.46410i			0.182152i
$184$	−61.1769	−	35.3205i	−4.51002	−	2.60386i
$185$		0			0
$186$	−9.83013	−	17.0263i	−0.720780	−	1.24843i
$187$	−11.3205			−0.827838
$188$	27.8564	+	48.2487i	2.03164	+	3.51890i
$189$	2.13397	−	1.23205i	0.155224	−	0.0896185i
$190$		0			0
$191$	−8.75833	−	15.1699i	−0.633731	−	1.09765i	−0.986783	−	0.162050i	$-0.948189\pi$
$191$	−8.75833	−	15.1699i	−0.633731	−	1.09765i	0.353052	−	0.935604i	$-0.385144\pi$
$192$	25.8564	+	14.9282i	1.86603	+	1.07735i
$193$	−9.96410	+	17.2583i	−0.717232	+	1.24228i	0.244861	+	0.969558i	$0.421258\pi$
$193$	−9.96410	+	17.2583i	−0.717232	+	1.24228i	−0.962092	+	0.272724i	$0.912076\pi$
$194$	26.0526			1.87046
$195$		0			0
$196$	−5.07180			−0.362271
$197$	5.46410	−	9.46410i	0.389301	−	0.674289i	−0.603055	−	0.797700i	$-0.706050\pi$
$197$	5.46410	−	9.46410i	0.389301	−	0.674289i	0.992356	+	0.123411i	$0.0393832\pi$
$198$	−8.19615	−	4.73205i	−0.582475	−	0.336292i
$199$	7.50000	+	12.9904i	0.531661	+	0.920864i	0.999317	+	0.0369532i	$0.0117652\pi$
$199$	7.50000	+	12.9904i	0.531661	+	0.920864i	−0.467656	+	0.883911i	$0.654901\pi$
$200$		0			0
$201$	−4.79423	+	2.76795i	−0.338159	+	0.195236i
$202$	−12.1962	−	21.1244i	−0.858118	−	1.48630i
$203$	−1.80385			−0.126605
$204$	−8.92820	−	15.4641i	−0.625099	−	1.08270i
$205$		0			0
$206$	17.0263	+	9.83013i	1.18628	+	0.684897i
$207$			7.46410i			0.518791i
$208$	14.9282	−	51.7128i	1.03508	−	3.58564i
$209$	−5.07180			−0.350824
$210$		0			0
$211$	−9.23205	+	15.9904i	−0.635561	+	1.10082i	0.350835	+	0.936437i	$0.385898\pi$
$211$	−9.23205	+	15.9904i	−0.635561	+	1.10082i	−0.986396	+	0.164386i	$0.947436\pi$
$212$	−32.7846	+	18.9282i	−2.25166	+	1.29999i
$213$	9.26795			0.635029
$214$	16.8564	−	9.73205i	1.15228	−	0.665269i
$215$		0			0
$216$		−	9.46410i		−	0.643951i
$217$	−15.3564	+	8.86603i	−1.04246	+	0.601865i
$218$	−27.7583	−	16.0263i	−1.88003	−	1.08544i
$219$	4.66987	+	2.69615i	0.315561	+	0.182189i
$220$		0			0
$221$	−8.49038	+	8.16987i	−0.571125	+	0.549565i
$222$		−	10.9282i		−	0.733453i
$223$	−7.92820	+	13.7321i	−0.530912	+	0.919566i	0.468438	+	0.883497i	$0.344817\pi$
$223$	−7.92820	+	13.7321i	−0.530912	+	0.919566i	−0.999349	+	0.0360695i	$0.988516\pi$
$224$	26.9282	−	46.6410i	1.79922	−	3.11633i
$225$		0			0
$226$			34.2487i			2.27819i
$227$	2.83013	+	4.90192i	0.187842	+	0.325352i	0.944531	−	0.328424i	$-0.106517\pi$
$227$	2.83013	+	4.90192i	0.187842	+	0.325352i	−0.756688	+	0.653776i	$0.773184\pi$
$228$	−4.00000	−	6.92820i	−0.264906	−	0.458831i
$229$			2.39230i			0.158088i	0.996871	+	0.0790440i	$0.0251868\pi$
$229$			2.39230i			0.158088i	−0.996871	+	0.0790440i	$0.974813\pi$
$230$		0			0
$231$	−4.26795	+	7.39230i	−0.280810	+	0.486378i
$232$	−3.46410	+	6.00000i	−0.227429	+	0.393919i
$233$		−	3.85641i		−	0.252642i	−0.991989	−	0.126321i	$-0.959683\pi$
$233$		−	3.85641i		−	0.252642i	0.991989	−	0.126321i	$-0.0403169\pi$
$234$	−9.56218	+	2.36603i	−0.625099	+	0.154672i
$235$		0			0
$236$	−50.7846	−	29.3205i	−3.30580	−	1.90860i
$237$	10.3301	+	5.96410i	0.671014	+	0.387410i
$238$	−19.0526	+	11.0000i	−1.23499	+	0.713024i
$239$			1.46410i			0.0947049i	0.998878	+	0.0473524i	$0.0150784\pi$
$239$			1.46410i			0.0947049i	−0.998878	+	0.0473524i	$0.984922\pi$
$240$		0			0
$241$	−19.3923	+	11.1962i	−1.24917	+	0.721208i	−0.970944	−	0.239308i	$-0.923079\pi$
$241$	−19.3923	+	11.1962i	−1.24917	+	0.721208i	−0.278225	+	0.960516i	$0.589746\pi$
$242$	2.73205			0.175623
$243$	−0.866025	+	0.500000i	−0.0555556	+	0.0320750i
$244$	6.73205	−	11.6603i	0.430975	−	0.746471i
$245$		0			0
$246$	−23.8564			−1.52103
$247$	−3.80385	+	3.66025i	−0.242033	+	0.232896i
$248$			68.1051i			4.32468i
$249$	8.19615	+	4.73205i	0.519410	+	0.299882i
$250$		0			0
$251$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$251$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$252$	−13.4641			−0.848159
$253$	−12.9282	−	22.3923i	−0.812789	−	1.40779i
$254$	−6.29423	+	3.63397i	−0.394935	+	0.228016i
$255$		0			0
$256$	−21.8564	−	37.8564i	−1.36603	−	2.36603i
$257$	6.29423	+	3.63397i	0.392623	+	0.226681i	0.683296	−	0.730141i	$-0.260546\pi$
$257$	6.29423	+	3.63397i	0.392623	+	0.226681i	−0.290673	+	0.956822i	$0.593879\pi$
$258$	−5.09808	+	8.83013i	−0.317392	+	0.549740i
$259$	−9.85641			−0.612447
$260$		0			0
$261$	0.732051			0.0453128
$262$	6.46410	−	11.1962i	0.399354	−	0.691701i
$263$	−20.4904	−	11.8301i	−1.26349	−	0.729477i	−0.289743	−	0.957105i	$-0.593570\pi$
$263$	−20.4904	−	11.8301i	−1.26349	−	0.729477i	−0.973748	+	0.227628i	$0.926903\pi$
$264$	16.3923	+	28.3923i	1.00888	+	1.74743i
$265$		0			0
$266$	−8.53590	+	4.92820i	−0.523370	+	0.302168i
$267$	−2.36603	−	4.09808i	−0.144798	−	0.250798i
$268$	30.2487			1.84773
$269$	−0.830127	−	1.43782i	−0.0506137	−	0.0876656i	0.839609	−	0.543192i	$-0.182784\pi$
$269$	−0.830127	−	1.43782i	−0.0506137	−	0.0876656i	−0.890222	+	0.455526i	$0.849451\pi$
$270$		0			0
$271$	0.232051	+	0.133975i	0.0140961	+	0.00813838i	0.507031	−	0.861928i	$-0.330743\pi$
$271$	0.232051	+	0.133975i	0.0140961	+	0.00813838i	−0.492935	+	0.870066i	$0.664076\pi$
$272$			48.7846i			2.95800i
$273$	2.13397	+	8.62436i	0.129154	+	0.521970i
$274$	−41.3205			−2.49626
$275$		0			0
$276$	20.3923	−	35.3205i	1.22747	−	2.12604i
$277$	24.4641	−	14.1244i	1.46991	−	0.848650i	0.470476	−	0.882413i	$-0.344082\pi$
$277$	24.4641	−	14.1244i	1.46991	−	0.848650i	0.999430	+	0.0337628i	$0.0107491\pi$
$278$	−11.1244			−0.667195
$279$	6.23205	−	3.59808i	0.373103	−	0.215411i
$280$		0			0
$281$			3.12436i			0.186383i	0.995648	+	0.0931917i	$0.0297070\pi$
$281$			3.12436i			0.186383i	−0.995648	+	0.0931917i	$0.970293\pi$
$282$	−24.1244	+	13.9282i	−1.43658	+	0.829412i
$283$	3.23205	+	1.86603i	0.192125	+	0.110924i	0.592977	−	0.805219i	$-0.297952\pi$
$283$	3.23205	+	1.86603i	0.192125	+	0.110924i	−0.400852	+	0.916143i	$0.631286\pi$
$284$	−43.8564	−	25.3205i	−2.60240	−	1.50250i
$285$		0			0
$286$	24.5885	−	23.6603i	1.45395	−	1.39906i
$287$			21.5167i			1.27009i
$288$	−10.9282	+	18.9282i	−0.643951	+	1.11536i
$289$	−3.16025	+	5.47372i	−0.185897	+	0.321984i
$290$		0			0
$291$			9.53590i			0.559004i
$292$	−14.7321	−	25.5167i	−0.862128	−	1.49325i
$293$	−3.29423	−	5.70577i	−0.192451	−	0.333335i	0.753611	−	0.657321i	$-0.228310\pi$
$293$	−3.29423	−	5.70577i	−0.192451	−	0.333335i	−0.946062	+	0.323986i	$0.894977\pi$
$294$		−	2.53590i		−	0.147897i
$295$		0			0
$296$	−18.9282	+	32.7846i	−1.10018	+	1.90557i
$297$	1.73205	−	3.00000i	0.100504	−	0.174078i
$298$			10.9282i			0.633054i
$299$	−25.8564	−	7.46410i	−1.49531	−	0.431660i
$300$		0			0
$301$	7.96410	+	4.59808i	0.459043	+	0.265029i
$302$	23.3205	+	13.4641i	1.34194	+	0.774772i
$303$	7.73205	−	4.46410i	0.444195	−	0.256456i
$304$			21.8564i			1.25355i
$305$		0			0
$306$	7.73205	−	4.46410i	0.442012	−	0.255196i
$307$	25.9282			1.47980			0.739900	−	0.672716i	$-0.234873\pi$
$307$	25.9282			1.47980			0.739900	+	0.672716i	$0.234873\pi$
$308$	40.3923	−	23.3205i	2.30157	−	1.32881i
$309$	−3.59808	+	6.23205i	−0.204687	+	0.354529i
$310$		0			0
$311$	0.196152			0.0111228			0.00556139	−	0.999985i	$-0.498230\pi$
$311$	0.196152			0.0111228			0.00556139	+	0.999985i	$0.498230\pi$
$312$	32.7846	+	9.46410i	1.85606	+	0.535799i
$313$			21.1962i			1.19808i	0.800720	+	0.599039i	$0.204450\pi$
$313$			21.1962i			1.19808i	−0.800720	+	0.599039i	$0.795550\pi$
$314$	14.8301	+	8.56218i	0.836912	+	0.483192i
$315$		0			0
$316$	−32.5885	−	56.4449i	−1.83324	−	3.17527i
$317$	10.5359			0.591755			0.295878	−	0.955226i	$-0.404388\pi$
$317$	10.5359			0.591755			0.295878	+	0.955226i	$0.404388\pi$
$318$	−9.46410	−	16.3923i	−0.530720	−	0.919235i
$319$	−2.19615	+	1.26795i	−0.122961	+	0.0709915i
$320$		0			0
$321$	3.56218	+	6.16987i	0.198821	+	0.344369i
$322$	−43.5167	−	25.1244i	−2.42509	−	1.40013i
$323$	2.39230	−	4.14359i	0.133111	−	0.230556i
$324$	5.46410			0.303561
$325$		0			0
$326$	34.0526			1.88600
$327$	5.86603	−	10.1603i	0.324392	−	0.561863i
$328$	71.5692	+	41.3205i	3.95175	+	2.28154i
$329$	12.5622	+	21.7583i	0.692575	+	1.19958i
$330$		0			0
$331$	13.9641	−	8.06218i	0.767536	−	0.443137i	−0.0644586	−	0.997920i	$-0.520532\pi$
$331$	13.9641	−	8.06218i	0.767536	−	0.443137i	0.831995	+	0.554783i	$0.187199\pi$
$332$	−25.8564	−	44.7846i	−1.41905	−	2.45787i
$333$	4.00000			0.219199
$334$	14.3923	+	24.9282i	0.787512	+	1.36401i
$335$		0			0
$336$	31.8564	+	18.3923i	1.73791	+	1.00338i
$337$			7.05256i			0.384177i	0.981378	+	0.192089i	$0.0615261\pi$
$337$			7.05256i			0.384177i	−0.981378	+	0.192089i	$0.938474\pi$
$338$	1.36603	−	35.4904i	0.0743020	−	1.93042i
$339$	−12.5359			−0.680857
$340$		0			0
$341$	−12.4641	+	21.5885i	−0.674969	+	1.16908i
$342$	3.46410	−	2.00000i	0.187317	−	0.108148i
$343$	−19.5359			−1.05484
$344$	30.5885	−	17.6603i	1.64922	−	0.952177i
$345$		0			0
$346$		−	18.3923i		−	0.988776i
$347$	11.6603	−	6.73205i	0.625955	−	0.361395i	−0.153229	−	0.988191i	$-0.548967\pi$
$347$	11.6603	−	6.73205i	0.625955	−	0.361395i	0.779184	+	0.626795i	$0.215634\pi$
$348$	−3.46410	−	2.00000i	−0.185695	−	0.107211i
$349$	−19.0359	−	10.9904i	−1.01897	−	0.588302i	−0.105163	−	0.994455i	$-0.533537\pi$
$349$	−19.0359	−	10.9904i	−1.01897	−	0.588302i	−0.913805	+	0.406153i	$0.866870\pi$
$350$		0			0
$351$	−0.866025	−	3.50000i	−0.0462250	−	0.186816i
$352$		−	75.7128i		−	4.03551i
$353$	11.5359	−	19.9808i	0.613994	−	1.06347i	−0.376566	−	0.926390i	$-0.622895\pi$
$353$	11.5359	−	19.9808i	0.613994	−	1.06347i	0.990560	−	0.137079i	$-0.0437714\pi$
$354$	14.6603	−	25.3923i	0.779184	−	1.34959i
$355$		0			0
$356$			25.8564i			1.37039i
$357$	−4.02628	−	6.97372i	−0.213093	−	0.369088i
$358$	−20.6603	−	35.7846i	−1.09193	−	1.89128i
$359$		−	16.3397i		−	0.862379i	−0.902261	−	0.431189i	$-0.858094\pi$
$359$		−	16.3397i		−	0.862379i	0.902261	−	0.431189i	$-0.141906\pi$
$360$		0			0
$361$	−8.42820	+	14.5981i	−0.443590	+	0.768320i
$362$	29.3205	−	50.7846i	1.54105	−	2.66918i
$363$			1.00000i			0.0524864i
$364$	13.4641	−	46.6410i	0.705711	−	2.44465i
$365$		0			0
$366$	5.83013	+	3.36603i	0.304746	+	0.175945i
$367$	−5.30385	−	3.06218i	−0.276859	−	0.159844i	0.355142	−	0.934812i	$-0.384433\pi$
$367$	−5.30385	−	3.06218i	−0.276859	−	0.159844i	−0.632000	+	0.774968i	$0.717766\pi$
$368$	−96.4974	+	55.7128i	−5.03028	+	2.90423i
$369$		−	8.73205i		−	0.454572i
$370$		0			0
$371$	−14.7846	+	8.53590i	−0.767579	+	0.443162i
$372$	−39.3205			−2.03867
$373$	22.6244	−	13.0622i	1.17144	−	0.676334i	0.217425	−	0.976077i	$-0.430234\pi$
$373$	22.6244	−	13.0622i	1.17144	−	0.676334i	0.954020	+	0.299743i	$0.0969010\pi$
$374$	−15.4641	+	26.7846i	−0.799630	+	1.38500i
$375$		0			0
$376$	96.4974			4.97647
$377$	−0.732051	+	2.53590i	−0.0377025	+	0.130605i
$378$		−	6.73205i		−	0.346259i
$379$	−14.0885	−	8.13397i	−0.723675	−	0.417814i	0.0924285	−	0.995719i	$-0.470537\pi$
$379$	−14.0885	−	8.13397i	−0.723675	−	0.417814i	−0.816104	+	0.577905i	$0.803870\pi$
$380$		0			0
$381$	−1.33013	−	2.30385i	−0.0681445	−	0.118030i
$382$	−47.8564			−2.44855
$383$	12.8301	+	22.2224i	0.655589	+	1.13551i	0.981746	+	0.190198i	$0.0609129\pi$
$383$	12.8301	+	22.2224i	0.655589	+	1.13551i	−0.326157	+	0.945316i	$0.605754\pi$
$384$	32.7846	−	18.9282i	1.67303	−	0.965926i
$385$		0			0
$386$	27.2224	+	47.1506i	1.38559	+	2.39990i
$387$	−3.23205	−	1.86603i	−0.164294	−	0.0948554i
$388$	26.0526	−	45.1244i	1.32262	−	2.29084i
$389$	10.5359			0.534191			0.267096	−	0.963670i	$-0.413936\pi$
$389$	10.5359			0.534191			0.267096	+	0.963670i	$0.413936\pi$
$390$		0			0
$391$	24.3923			1.23357
$392$	−4.39230	+	7.60770i	−0.221845	+	0.384247i
$393$	4.09808	+	2.36603i	0.206721	+	0.119350i
$394$	−14.9282	−	25.8564i	−0.752072	−	1.30263i
$395$		0			0
$396$	−16.3923	+	9.46410i	−0.823744	+	0.475589i
$397$	5.16025	+	8.93782i	0.258986	+	0.448576i	0.965970	−	0.258652i	$-0.0832784\pi$
$397$	5.16025	+	8.93782i	0.258986	+	0.448576i	−0.706985	+	0.707229i	$0.749945\pi$
$398$	40.9808			2.05418
$399$	−1.80385	−	3.12436i	−0.0903053	−	0.156413i
$400$		0			0
$401$	−16.7321	−	9.66025i	−0.835559	−	0.482410i	0.0201934	−	0.999796i	$-0.493572\pi$
$401$	−16.7321	−	9.66025i	−0.835559	−	0.482410i	−0.855752	+	0.517386i	$0.826905\pi$
$402$			15.1244i			0.754334i
$403$	6.23205	+	25.1865i	0.310441	+	1.25463i
$404$	−48.7846			−2.42713
$405$		0			0
$406$	−2.46410	+	4.26795i	−0.122291	+	0.211815i
$407$	−12.0000	+	6.92820i	−0.594818	+	0.343418i
$408$	−30.9282			−1.53117
$409$	−12.6962	+	7.33013i	−0.627784	+	0.362451i	−0.779893	−	0.625912i	$-0.784727\pi$
$409$	−12.6962	+	7.33013i	−0.627784	+	0.362451i	0.152109	+	0.988364i	$0.451393\pi$
$410$		0			0
$411$		−	15.1244i		−	0.746029i
$412$	34.0526	−	19.6603i	1.67765	−	0.968591i
$413$	−22.9019	−	13.2224i	−1.12693	−	0.650633i
$414$	17.6603	+	10.1962i	0.867954	+	0.501114i
$415$		0			0
$416$	−54.6410	−	56.7846i	−2.67900	−	2.78409i
$417$		−	4.07180i		−	0.199397i
$418$	−6.92820	+	12.0000i	−0.338869	+	0.586939i
$419$	−19.2224	+	33.2942i	−0.939077	+	1.62653i	−0.171880	+	0.985118i	$0.554984\pi$
$419$	−19.2224	+	33.2942i	−0.939077	+	1.62653i	−0.767197	+	0.641412i	$0.778349\pi$
$420$		0			0
$421$		−	7.58846i		−	0.369839i	−0.982754	−	0.184919i	$-0.940798\pi$
$421$		−	7.58846i		−	0.369839i	0.982754	−	0.184919i	$-0.0592024\pi$
$422$	25.2224	+	43.6865i	1.22781	+	2.12663i
$423$	−5.09808	−	8.83013i	−0.247877	−	0.429335i
$424$			65.5692i			3.18432i
$425$		0			0
$426$	12.6603	−	21.9282i	0.613391	−	1.06242i
$427$	3.03590	−	5.25833i	0.146917	−	0.254468i
$428$		−	38.9282i		−	1.88167i
$429$	8.66025	+	9.00000i	0.418121	+	0.434524i
$430$		0			0
$431$	−9.80385	−	5.66025i	−0.472235	−	0.272645i	0.244940	−	0.969538i	$-0.421232\pi$
$431$	−9.80385	−	5.66025i	−0.472235	−	0.272645i	−0.717175	+	0.696893i	$0.754565\pi$
$432$	−12.9282	−	7.46410i	−0.622008	−	0.359117i
$433$	13.1603	−	7.59808i	0.632441	−	0.365140i	−0.149256	−	0.988799i	$-0.547688\pi$
$433$	13.1603	−	7.59808i	0.632441	−	0.365140i	0.781697	+	0.623658i	$0.214354\pi$
$434$			48.4449i			2.32543i
$435$		0			0
$436$	−55.5167	+	32.0526i	−2.65877	+	1.53504i
$437$	10.9282			0.522767
$438$	12.7583	−	7.36603i	0.609617	−	0.351962i
$439$	2.69615	−	4.66987i	0.128680	−	0.222881i	−0.794485	−	0.607284i	$-0.792259\pi$
$439$	2.69615	−	4.66987i	0.128680	−	0.222881i	0.923166	+	0.384403i	$0.125593\pi$
$440$		0			0
$441$	0.928203			0.0442002
$442$	7.73205	+	31.2487i	0.367776	+	1.48635i
$443$			21.1244i			1.00365i	0.864970	+	0.501824i	$0.167338\pi$
$443$			21.1244i			1.00365i	−0.864970	+	0.501824i	$0.832662\pi$
$444$	−18.9282	−	10.9282i	−0.898293	−	0.518630i
$445$		0			0
$446$	21.6603	+	37.5167i	1.02564	+	1.77647i
$447$	−4.00000			−0.189194
$448$	−36.7846	−	63.7128i	−1.73791	−	3.01015i
$449$	21.5885	−	12.4641i	1.01882	−	0.588217i	0.105060	−	0.994466i	$-0.466497\pi$
$449$	21.5885	−	12.4641i	1.01882	−	0.588217i	0.913763	+	0.406249i	$0.133163\pi$
$450$		0			0
$451$	15.1244	+	26.1962i	0.712178	+	1.23353i
$452$	59.3205	+	34.2487i	2.79020	+	1.61092i
$453$	−4.92820	+	8.53590i	−0.231547	+	0.401051i
$454$	15.4641			0.725766
$455$		0			0
$456$	−13.8564			−0.648886
$457$	7.69615	−	13.3301i	0.360011	−	0.623557i	−0.627951	−	0.778253i	$-0.716106\pi$
$457$	7.69615	−	13.3301i	0.360011	−	0.623557i	0.987962	+	0.154696i	$0.0494397\pi$
$458$	5.66025	+	3.26795i	0.264486	+	0.152701i
$459$	1.63397	+	2.83013i	0.0762674	+	0.132099i
$460$		0			0
$461$	29.0263	−	16.7583i	1.35189	−	0.780513i	0.363375	−	0.931643i	$-0.381624\pi$
$461$	29.0263	−	16.7583i	1.35189	−	0.780513i	0.988514	+	0.151130i	$0.0482912\pi$
$462$	11.6603	+	20.1962i	0.542484	+	0.939610i
$463$	−39.7846			−1.84895			−0.924474	−	0.381246i	$-0.875495\pi$
$463$	−39.7846			−1.84895			−0.924474	+	0.381246i	$0.875495\pi$
$464$	5.46410	+	9.46410i	0.253665	+	0.439360i
$465$		0			0
$466$	−9.12436	−	5.26795i	−0.422678	−	0.244033i
$467$			6.33975i			0.293368i	0.989183	+	0.146684i	$0.0468601\pi$
$467$			6.33975i			0.293368i	−0.989183	+	0.146684i	$0.953140\pi$
$468$	−5.46410	+	18.9282i	−0.252578	+	0.874957i
$469$	13.6410			0.629884
$470$		0			0
$471$	−3.13397	+	5.42820i	−0.144406	+	0.250118i
$472$	−87.9615	+	50.7846i	−4.04876	+	2.33755i
$473$	12.9282			0.594439
$474$	28.2224	−	16.2942i	1.29630	−	0.748419i
$475$		0			0
$476$			44.0000i			2.01674i
$477$	6.00000	−	3.46410i	0.274721	−	0.158610i
$478$	3.46410	+	2.00000i	0.158444	+	0.0914779i
$479$	25.9019	+	14.9545i	1.18349	+	0.683288i	0.956819	−	0.290684i	$-0.0938828\pi$
$479$	25.9019	+	14.9545i	1.18349	+	0.683288i	0.226670	+	0.973972i	$0.427216\pi$
$480$		0			0
$481$	−4.00000	+	13.8564i	−0.182384	+	0.631798i
$482$			61.1769i			2.78653i
$483$	9.19615	−	15.9282i	0.418439	−	0.724758i
$484$	2.73205	−	4.73205i	0.124184	−	0.215093i
$485$		0			0
$486$			2.73205i			0.123928i
$487$	10.3923	+	18.0000i	0.470920	+	0.815658i	0.999447	−	0.0332590i	$-0.0105886\pi$
$487$	10.3923	+	18.0000i	0.470920	+	0.815658i	−0.528526	+	0.848917i	$0.677255\pi$
$488$	−11.6603	−	20.1962i	−0.527835	−	0.914237i
$489$			12.4641i			0.563646i
$490$		0			0
$491$	−8.56218	+	14.8301i	−0.386406	+	0.669274i	−0.991963	−	0.126527i	$-0.959617\pi$
$491$	−8.56218	+	14.8301i	−0.386406	+	0.669274i	0.605557	+	0.795802i	$0.292950\pi$
$492$	−23.8564	+	41.3205i	−1.07553	+	1.86287i
$493$		−	2.39230i		−	0.107744i
$494$	3.46410	+	14.0000i	0.155857	+	0.629890i
$495$		0			0
$496$	93.0333	+	53.7128i	4.17732	+	2.41178i
$497$	−19.7776	−	11.4186i	−0.887145	−	0.512194i
$498$	22.3923	−	12.9282i	1.00342	−	0.579327i
$499$			20.3923i			0.912885i	0.889753	+	0.456442i	$0.150877\pi$
$499$			20.3923i			0.912885i	−0.889753	+	0.456442i	$0.849123\pi$
$500$		0			0
$501$	−9.12436	+	5.26795i	−0.407646	+	0.235355i
$502$		0			0
$503$	−9.33975	+	5.39230i	−0.416439	+	0.240431i	−0.693552	−	0.720406i	$-0.743955\pi$
$503$	−9.33975	+	5.39230i	−0.416439	+	0.240431i	0.277114	+	0.960837i	$0.410622\pi$
$504$	−11.6603	+	20.1962i	−0.519389	+	0.899608i
$505$		0			0
$506$	−70.6410			−3.14038
$507$	12.9904	+	0.500000i	0.576923	+	0.0222058i
$508$			14.5359i			0.644926i
$509$	−0.803848	−	0.464102i	−0.0356299	−	0.0205709i	0.482079	−	0.876128i	$-0.339882\pi$
$509$	−0.803848	−	0.464102i	−0.0356299	−	0.0205709i	−0.517709	+	0.855557i	$0.673215\pi$
$510$		0			0
$511$	−6.64359	−	11.5070i	−0.293895	−	0.509042i
$512$	−43.7128			−1.93185
$513$	0.732051	+	1.26795i	0.0323208	+	0.0559813i
$514$	17.1962	−	9.92820i	0.758490	−	0.437914i
$515$		0			0
$516$	10.1962	+	17.6603i	0.448861	+	0.777449i
$517$	30.5885	+	17.6603i	1.34528	+	0.776697i
$518$	−13.4641	+	23.3205i	−0.591579	+	1.02464i
$519$	6.73205			0.295504
$520$		0			0
$521$	−9.26795			−0.406036			−0.203018	−	0.979175i	$-0.565075\pi$
$521$	−9.26795			−0.406036			−0.203018	+	0.979175i	$0.565075\pi$
$522$	1.00000	−	1.73205i	0.0437688	−	0.0758098i
$523$	−26.4449	−	15.2679i	−1.15635	−	0.667621i	−0.205926	−	0.978568i	$-0.566021\pi$
$523$	−26.4449	−	15.2679i	−1.15635	−	0.667621i	−0.950427	+	0.310947i	$0.899354\pi$
$524$	−12.9282	−	22.3923i	−0.564771	−	0.978212i
$525$		0			0
$526$	−55.9808	+	32.3205i	−2.44088	+	1.40924i
$527$	−11.7583	−	20.3660i	−0.512201	−	0.887158i
$528$	51.7128			2.25051
$529$	16.3564	+	28.3301i	0.711148	+	1.23174i
$530$		0			0
$531$	9.29423	+	5.36603i	0.403335	+	0.232866i
$532$			19.7128i			0.854659i
$533$	30.2487	+	8.73205i	1.31022	+	0.378227i
$534$	−12.9282			−0.559458
$535$		0			0
$536$	26.1962	−	45.3731i	1.13150	−	1.95982i
$537$	13.0981	−	7.56218i	0.565224	−	0.326332i
$538$	−4.53590			−0.195556
$539$	−2.78461	+	1.60770i	−0.119942	+	0.0692483i
$540$		0			0
$541$			13.5885i			0.584213i	0.956386	+	0.292107i	$0.0943562\pi$
$541$			13.5885i			0.584213i	−0.956386	+	0.292107i	$0.905644\pi$
$542$	0.633975	−	0.366025i	0.0272315	−	0.0157221i
$543$	18.5885	+	10.7321i	0.797707	+	0.460556i
$544$	61.8564	+	35.7128i	2.65207	+	1.53117i
$545$		0			0
$546$	23.3205	+	6.73205i	0.998026	+	0.288105i
$547$		−	7.33975i		−	0.313825i	−0.987613	−	0.156912i	$-0.949846\pi$
$547$		−	7.33975i		−	0.313825i	0.987613	−	0.156912i	$-0.0501540\pi$
$548$	−41.3205	+	71.5692i	−1.76512	+	3.05729i
$549$	−1.23205	+	2.13397i	−0.0525826	+	0.0910758i
$550$		0			0
$551$		−	1.07180i		−	0.0456601i
$552$	−35.3205	−	61.1769i	−1.50334	−	2.60386i
$553$	−14.6962	−	25.4545i	−0.624944	−	1.08243i
$554$		−	77.1769i		−	3.27893i
$555$		0			0
$556$	−11.1244	+	19.2679i	−0.471778	+	0.817143i
$557$	−7.26795	+	12.5885i	−0.307953	+	0.533390i	−0.977914	−	0.209006i	$-0.932977\pi$
$557$	−7.26795	+	12.5885i	−0.307953	+	0.533390i	0.669962	+	0.742396i	$0.266311\pi$
$558$		−	19.6603i		−	0.832285i
$559$	9.69615	−	9.33013i	0.410104	−	0.394622i
$560$		0			0
$561$	−9.80385	−	5.66025i	−0.413919	−	0.238976i
$562$	7.39230	+	4.26795i	0.311826	+	0.180033i
$563$	3.00000	−	1.73205i	0.126435	−	0.0729972i	−0.435449	−	0.900214i	$-0.643410\pi$
$563$	3.00000	−	1.73205i	0.126435	−	0.0729972i	0.561884	+	0.827216i	$0.310077\pi$
$564$			55.7128i			2.34593i
$565$		0			0
$566$	8.83013	−	5.09808i	0.371158	−	0.214288i
$567$	2.46410			0.103483
$568$	−75.9615	+	43.8564i	−3.18727	+	1.84017i
$569$	16.9019	−	29.2750i	0.708566	−	1.22727i	−0.256824	−	0.966458i	$-0.582676\pi$
$569$	16.9019	−	29.2750i	0.708566	−	1.22727i	0.965389	−	0.260813i	$-0.0839907\pi$
$570$		0			0
$571$	−23.8564			−0.998360			−0.499180	−	0.866498i	$-0.666365\pi$
$571$	−23.8564			−0.998360			−0.499180	+	0.866498i	$0.666365\pi$
$572$	−16.3923	−	66.2487i	−0.685397	−	2.77000i
$573$		−	17.5167i		−	0.731769i
$574$	50.9090	+	29.3923i	2.12490	+	1.22681i
$575$		0			0
$576$	14.9282	+	25.8564i	0.622008	+	1.07735i
$577$	−43.7128			−1.81979			−0.909894	−	0.414841i	$-0.863837\pi$
$577$	−43.7128			−1.81979			−0.909894	+	0.414841i	$0.863837\pi$
$578$	8.63397	+	14.9545i	0.359126	+	0.622024i
$579$	−17.2583	+	9.96410i	−0.717232	+	0.414094i
$580$		0			0
$581$	−11.6603	−	20.1962i	−0.483749	−	0.837878i
$582$	22.5622	+	13.0263i	0.935232	+	0.539957i
$583$	−12.0000	+	20.7846i	−0.496989	+	0.860811i
$584$	−51.0333			−2.11177
$585$		0			0
$586$	−18.0000			−0.743573
$587$	−4.16987	+	7.22243i	−0.172109	+	0.298102i	−0.939157	−	0.343488i	$-0.888391\pi$
$587$	−4.16987	+	7.22243i	−0.172109	+	0.298102i	0.767048	+	0.641590i	$0.221725\pi$
$588$	−4.39230	−	2.53590i	−0.181136	−	0.104579i
$589$	−5.26795	−	9.12436i	−0.217062	−	0.375963i
$590$		0			0
$591$	9.46410	−	5.46410i	0.389301	−	0.224763i
$592$	29.8564	+	51.7128i	1.22709	+	2.12538i
$593$	13.3205			0.547008			0.273504	−	0.961871i	$-0.411817\pi$
$593$	13.3205			0.547008			0.273504	+	0.961871i	$0.411817\pi$
$594$	−4.73205	−	8.19615i	−0.194158	−	0.336292i
$595$		0			0
$596$	18.9282	+	10.9282i	0.775329	+	0.447637i
$597$			15.0000i			0.613909i
$598$	−52.9808	+	50.9808i	−2.16654	+	2.08476i
$599$	−1.12436			−0.0459399			−0.0229700	−	0.999736i	$-0.507312\pi$
$599$	−1.12436			−0.0459399			−0.0229700	+	0.999736i	$0.507312\pi$
$600$		0			0
$601$	−13.1244	+	22.7321i	−0.535354	+	0.927260i	0.463793	+	0.885944i	$0.346488\pi$
$601$	−13.1244	+	22.7321i	−0.535354	+	0.927260i	−0.999146	+	0.0413158i	$0.986845\pi$
$602$	21.7583	−	12.5622i	0.886803	−	0.511996i
$603$	−5.53590			−0.225439
$604$	46.6410	−	26.9282i	1.89780	−	1.09569i
$605$		0			0
$606$		−	24.3923i		−	0.990870i
$607$	33.2487	−	19.1962i	1.34952	−	0.779148i	0.361342	−	0.932433i	$-0.382319\pi$
$607$	33.2487	−	19.1962i	1.34952	−	0.779148i	0.988182	+	0.153286i	$0.0489855\pi$
$608$	27.7128	+	16.0000i	1.12390	+	0.648886i
$609$	−1.56218	−	0.901924i	−0.0633026	−	0.0365478i
$610$		0			0
$611$	35.6865	−	8.83013i	1.44372	−	0.357229i
$612$		−	17.8564i		−	0.721802i
$613$	21.8923	−	37.9186i	0.884222	−	1.53152i	0.0376189	−	0.999292i	$-0.488023\pi$
$613$	21.8923	−	37.9186i	0.884222	−	1.53152i	0.846603	−	0.532225i	$-0.178644\pi$
$614$	35.4186	−	61.3468i	1.42938	−	2.47575i
$615$		0			0
$616$		−	80.7846i		−	3.25490i
$617$	−22.3205	−	38.6603i	−0.898590	−	1.55640i	−0.829298	−	0.558807i	$-0.811259\pi$
$617$	−22.3205	−	38.6603i	−0.898590	−	1.55640i	−0.0692919	−	0.997596i	$-0.522074\pi$
$618$	9.83013	+	17.0263i	0.395426	+	0.684897i
$619$			19.5885i			0.787327i	0.919255	+	0.393663i	$0.128792\pi$
$619$			19.5885i			0.787327i	−0.919255	+	0.393663i	$0.871208\pi$
$620$		0			0
$621$	−3.73205	+	6.46410i	−0.149762	+	0.259395i
$622$	0.267949	−	0.464102i	0.0107438	−	0.0186088i
$623$			11.6603i			0.467158i
$624$	38.7846	−	37.3205i	1.55263	−	1.49402i
$625$		0			0
$626$	50.1506	+	28.9545i	2.00442	+	1.15725i
$627$	−4.39230	−	2.53590i	−0.175412	−	0.101274i
$628$	29.6603	−	17.1244i	1.18357	−	0.683336i
$629$		−	13.0718i		−	0.521207i
$630$		0			0
$631$	36.0167	−	20.7942i	1.43380	−	0.827805i	0.436392	−	0.899756i	$-0.356256\pi$
$631$	36.0167	−	20.7942i	1.43380	−	0.827805i	0.997408	+	0.0719512i	$0.0229226\pi$
$632$	−112.890			−4.49051
$633$	−15.9904	+	9.23205i	−0.635561	+	0.366941i
$634$	14.3923	−	24.9282i	0.571591	−	0.990025i
$635$		0			0
$636$	−37.8564			−1.50110
$637$	−0.928203	+	3.21539i	−0.0367768	+	0.127398i
$638$			6.92820i			0.274290i
$639$	8.02628	+	4.63397i	0.317515	+	0.183317i
$640$		0			0
$641$	−1.39230	−	2.41154i	−0.0549927	−	0.0952502i	0.837219	−	0.546868i	$-0.184180\pi$
$641$	−1.39230	−	2.41154i	−0.0549927	−	0.0952502i	−0.892211	+	0.451618i	$0.850847\pi$
$642$	19.4641			0.768187
$643$	18.8923	+	32.7224i	0.745040	+	1.29045i	0.950176	+	0.311713i	$0.100903\pi$
$643$	18.8923	+	32.7224i	0.745040	+	1.29045i	−0.205136	+	0.978733i	$0.565764\pi$
$644$	−87.0333	+	50.2487i	−3.42959	+	1.98008i
$645$		0			0
$646$	−6.53590	−	11.3205i	−0.257151	−	0.445399i
$647$	1.73205	+	1.00000i	0.0680939	+	0.0393141i	0.533660	−	0.845699i	$-0.320816\pi$
$647$	1.73205	+	1.00000i	0.0680939	+	0.0393141i	−0.465566	+	0.885013i	$0.654149\pi$
$648$	4.73205	−	8.19615i	0.185893	−	0.321975i
$649$	−37.1769			−1.45932
$650$		0			0
$651$	−17.7321			−0.694974
$652$	34.0526	−	58.9808i	1.33360	−	2.30986i
$653$	−39.4186	−	22.7583i	−1.54257	−	0.890602i	−0.998676	−	0.0514475i	$-0.983617\pi$
$653$	−39.4186	−	22.7583i	−1.54257	−	0.890602i	−0.543893	−	0.839155i	$-0.683050\pi$
$654$	−16.0263	−	27.7583i	−0.626677	−	1.08544i
$655$		0			0
$656$	112.890	−	65.1769i	4.40760	−	2.54473i
$657$	2.69615	+	4.66987i	0.105187	+	0.182189i
$658$	68.6410			2.67591
$659$	12.5885	+	21.8038i	0.490377	+	0.849357i	0.999939	−	0.0110766i	$-0.00352588\pi$
$659$	12.5885	+	21.8038i	0.490377	+	0.849357i	−0.509562	+	0.860434i	$0.670193\pi$
$660$		0			0
$661$	14.7679	+	8.52628i	0.574407	+	0.331634i	0.758907	−	0.651199i	$-0.225733\pi$
$661$	14.7679	+	8.52628i	0.574407	+	0.331634i	−0.184501	+	0.982832i	$0.559067\pi$
$662$		−	44.0526i		−	1.71215i
$663$	−11.4378	+	2.83013i	−0.444208	+	0.109913i
$664$	−89.5692			−3.47596
$665$		0			0
$666$	5.46410	−	9.46410i	0.211730	−	0.366726i
$667$	4.73205	−	2.73205i	0.183226	−	0.105785i
$668$	57.5692			2.22742
$669$	−13.7321	+	7.92820i	−0.530912	+	0.306522i
$670$		0			0
$671$		−	8.53590i		−	0.329525i
$672$	46.6410	−	26.9282i	1.79922	−	1.03878i
$673$	1.16025	+	0.669873i	0.0447245	+	0.0258217i	0.522196	−	0.852826i	$-0.325113\pi$
$673$	1.16025	+	0.669873i	0.0447245	+	0.0258217i	−0.477471	+	0.878647i	$0.658446\pi$
$674$	16.6865	+	9.63397i	0.642741	+	0.371087i
$675$		0			0
$676$	−60.1051	−	37.8564i	−2.31174	−	1.45602i
$677$		−	8.78461i		−	0.337620i	−0.985649	−	0.168810i	$-0.946008\pi$
$677$		−	8.78461i		−	0.337620i	0.985649	−	0.168810i	$-0.0539924\pi$
$678$	−17.1244	+	29.6603i	−0.657657	+	1.13910i
$679$	11.7487	−	20.3494i	0.450874	−	0.780937i
$680$		0			0
$681$			5.66025i			0.216901i
$682$	34.0526	+	58.9808i	1.30394	+	2.25849i
$683$	22.3660	+	38.7391i	0.855812	+	1.48231i	0.875890	+	0.482512i	$0.160275\pi$
$683$	22.3660	+	38.7391i	0.855812	+	1.48231i	−0.0200773	+	0.999798i	$0.506391\pi$
$684$		−	8.00000i		−	0.305888i
$685$		0			0
$686$	−26.6865	+	46.2224i	−1.01890	+	1.76478i
$687$	−1.19615	+	2.07180i	−0.0456361	+	0.0790440i
$688$		−	55.7128i		−	2.12403i
$689$	6.00000	+	24.2487i	0.228582	+	0.923802i
$690$		0			0
$691$	10.7487	+	6.20577i	0.408900	+	0.236079i	0.690317	−	0.723507i	$-0.257471\pi$
$691$	10.7487	+	6.20577i	0.408900	+	0.236079i	−0.281417	+	0.959586i	$0.590804\pi$
$692$	−31.8564	−	18.3923i	−1.21100	−	0.699171i
$693$	−7.39230	+	4.26795i	−0.280810	+	0.162126i
$694$		−	36.7846i		−	1.39632i
$695$		0			0
$696$	−6.00000	+	3.46410i	−0.227429	+	0.131306i
$697$	−28.5359			−1.08087
$698$	−52.0070	+	30.0263i	−1.96850	+	1.13651i
$699$	1.92820	−	3.33975i	0.0729313	−	0.126321i
$700$		0			0
$701$	−32.7846			−1.23826			−0.619129	−	0.785289i	$-0.712514\pi$
$701$	−32.7846			−1.23826			−0.619129	+	0.785289i	$0.712514\pi$
$702$	−9.46410	−	2.73205i	−0.357199	−	0.103115i
$703$		−	5.85641i		−	0.220879i
$704$	−89.5692	−	51.7128i	−3.37577	−	1.94900i
$705$		0			0
$706$	−31.5167	−	54.5885i	−1.18615	−	2.05446i
$707$	−22.0000			−0.827395
$708$	−29.3205	−	50.7846i	−1.10193	−	1.90860i
$709$	−11.5526	+	6.66987i	−0.433865	+	0.250492i	−0.700992	−	0.713169i	$-0.747259\pi$
$709$	−11.5526	+	6.66987i	−0.433865	+	0.250492i	0.267127	+	0.963661i	$0.413926\pi$
$710$		0			0
$711$	5.96410	+	10.3301i	0.223671	+	0.387410i
$712$	38.7846	+	22.3923i	1.45351	+	0.839187i
$713$	26.8564	−	46.5167i	1.00578	−	1.74206i
$714$	−22.0000			−0.823329
$715$		0			0
$716$	−82.6410			−3.08844
$717$	−0.732051	+	1.26795i	−0.0273389	+	0.0473524i
$718$	−38.6603	−	22.3205i	−1.44279	−	0.832994i
$719$	−15.6340	−	27.0788i	−0.583049	−	1.00987i	−0.995116	−	0.0987166i	$-0.968526\pi$
$719$	−15.6340	−	27.0788i	−0.583049	−	1.00987i	0.412067	−	0.911154i	$-0.364807\pi$
$720$		0			0
$721$	15.3564	−	8.86603i	0.571902	−	0.330188i
$722$	23.0263	+	39.8827i	0.856949	+	1.48428i
$723$	−22.3923			−0.832779
$724$	−58.6410	−	101.569i	−2.17938	−	3.77479i
$725$		0			0
$726$	2.36603	+	1.36603i	0.0878114	+	0.0506980i
$727$			9.73205i			0.360942i	0.983580	+	0.180471i	$0.0577622\pi$
$727$			9.73205i			0.360942i	−0.983580	+	0.180471i	$0.942238\pi$
$728$	−58.3013	−	60.5885i	−2.16079	−	2.24556i
$729$	−1.00000			−0.0370370
$730$		0			0
$731$	−6.09808	+	10.5622i	−0.225545	+	0.390656i
$732$	11.6603	−	6.73205i	0.430975	−	0.248824i
$733$	32.3205			1.19379			0.596893	−	0.802321i	$-0.296402\pi$
$733$	32.3205			1.19379			0.596893	+	0.802321i	$0.296402\pi$
$734$	−14.4904	+	8.36603i	−0.534850	+	0.308796i
$735$		0			0
$736$			163.138i			6.01336i
$737$	16.6077	−	9.58846i	0.611752	−	0.353195i
$738$	−20.6603	−	11.9282i	−0.760514	−	0.439083i
$739$	−9.00000	−	5.19615i	−0.331070	−	0.191144i	0.325246	−	0.945629i	$-0.394553\pi$
$739$	−9.00000	−	5.19615i	−0.331070	−	0.191144i	−0.656316	+	0.754486i	$0.727886\pi$
$740$		0			0
$741$	−5.12436	+	1.26795i	−0.188248	+	0.0465793i
$742$			46.6410i			1.71225i
$743$	12.9545	−	22.4378i	0.475254	−	0.823164i	−0.524344	−	0.851506i	$-0.675690\pi$
$743$	12.9545	−	22.4378i	0.475254	−	0.823164i	0.999598	+	0.0283424i	$0.00902288\pi$
$744$	−34.0526	+	58.9808i	−1.24843	+	2.16234i
$745$		0			0
$746$		−	71.3731i		−	2.61315i
$747$	4.73205	+	8.19615i	0.173137	+	0.299882i
$748$	30.9282	+	53.5692i	1.13085	+	1.95868i
$749$		−	17.5551i		−	0.641451i
$750$		0			0
$751$	6.66025	−	11.5359i	0.243036	−	0.420951i	−0.718542	−	0.695484i	$-0.755190\pi$
$751$	6.66025	−	11.5359i	0.243036	−	0.420951i	0.961578	+	0.274533i	$0.0885233\pi$
$752$	76.1051	−	131.818i	2.77527	−	4.80691i
$753$		0			0
$754$	5.00000	+	5.19615i	0.182089	+	0.189233i
$755$		0			0
$756$	−11.6603	−	6.73205i	−0.424079	−	0.244842i
$757$	−11.3205	−	6.53590i	−0.411451	−	0.237551i	0.279962	−	0.960011i	$-0.409678\pi$
$757$	−11.3205	−	6.53590i	−0.411451	−	0.237551i	−0.691413	+	0.722460i	$0.743011\pi$
$758$	−38.4904	+	22.2224i	−1.39803	+	0.807155i
$759$		−	25.8564i		−	0.938528i
$760$		0			0
$761$	−18.9282	+	10.9282i	−0.686147	+	0.396147i	−0.802167	−	0.597100i	$-0.796320\pi$
$761$	−18.9282	+	10.9282i	−0.686147	+	0.396147i	0.116020	+	0.993247i	$0.462986\pi$
$762$	−7.26795			−0.263290
$763$	−25.0359	+	14.4545i	−0.906360	+	0.523287i
$764$	−47.8564	+	82.8897i	−1.73138	+	2.99885i
$765$		0			0
$766$	70.1051			2.53300
$767$	−27.8827	+	26.8301i	−1.00679	+	0.968780i
$768$		−	43.7128i		−	1.57735i
$769$	25.6410	+	14.8038i	0.924639	+	0.533840i	0.885112	−	0.465378i	$-0.154082\pi$
$769$	25.6410	+	14.8038i	0.924639	+	0.533840i	0.0395267	+	0.999219i	$0.487415\pi$
$770$		0			0
$771$	3.63397	+	6.29423i	0.130874	+	0.226681i
$772$	108.890			3.91903
$773$	−9.92820	−	17.1962i	−0.357093	−	0.618503i	0.630381	−	0.776286i	$-0.282899\pi$
$773$	−9.92820	−	17.1962i	−0.357093	−	0.618503i	−0.987474	+	0.157783i	$0.949565\pi$
$774$	−8.83013	+	5.09808i	−0.317392	+	0.183247i
$775$		0			0
$776$	−45.1244	−	78.1577i	−1.61987	−	2.80570i
$777$	−8.53590	−	4.92820i	−0.306224	−	0.176798i
$778$	14.3923	−	24.9282i	0.515989	−	0.893719i
$779$	−12.7846			−0.458056
$780$		0			0
$781$	−32.1051			−1.14881
$782$	33.3205	−	57.7128i	1.19154	−	2.06381i
$783$	0.633975	+	0.366025i	0.0226564	+	0.0130807i
$784$	6.92820	+	12.0000i	0.247436	+	0.428571i
$785$		0			0
$786$	11.1962	−	6.46410i	0.399354	−	0.230567i
$787$	14.2321	+	24.6506i	0.507318	+	0.878700i	0.999964	+	0.00847061i	$0.00269631\pi$
$787$	14.2321	+	24.6506i	0.507318	+	0.878700i	−0.492646	+	0.870230i	$0.663970\pi$
$788$	−59.7128			−2.12718
$789$	−11.8301	−	20.4904i	−0.421164	−	0.729477i
$790$		0			0
$791$	26.7513	+	15.4449i	0.951166	+	0.549156i
$792$			32.7846i			1.16495i
$793$	−6.16025	−	6.40192i	−0.218757	−	0.227339i
$794$	28.1962			1.00064
$795$		0			0
$796$	40.9808	−	70.9808i	1.45252	−	2.51585i
$797$	−24.6340	+	14.2224i	−0.872580	+	0.503784i	−0.868205	−	0.496206i	$-0.834726\pi$
$797$	−24.6340	+	14.2224i	−0.872580	+	0.503784i	−0.00437536	+	0.999990i	$0.501393\pi$
$798$	−9.85641			−0.348913
$799$	−28.8564	+	16.6603i	−1.02087	+	0.589397i
$800$		0			0
$801$		−	4.73205i		−	0.167199i
$802$	−45.7128	+	26.3923i	−1.61418	+	0.931945i
$803$	−16.1769	−	9.33975i	−0.570871	−	0.329592i
$804$	26.1962	+	15.1244i	0.923867	+	0.533395i
$805$		0			0
$806$	68.1051	+	19.6603i	2.39890	+	0.692503i
$807$		−	1.66025i		−	0.0584437i
$808$	−42.2487	+	73.1769i	−1.48630	+	2.57435i
$809$	18.0000	−	31.1769i	0.632846	−	1.09612i	−0.354121	−	0.935200i	$-0.615220\pi$
$809$	18.0000	−	31.1769i	0.632846	−	1.09612i	0.986967	−	0.160922i	$-0.0514468\pi$
$810$		0			0
$811$		−	39.0526i		−	1.37132i	−0.727922	−	0.685660i	$-0.759514\pi$
$811$		−	39.0526i		−	1.37132i	0.727922	−	0.685660i	$-0.240486\pi$
$812$	4.92820	+	8.53590i	0.172946	+	0.299551i
$813$	0.133975	+	0.232051i	0.00469869	+	0.00813838i
$814$			37.8564i			1.32687i
$815$		0			0
$816$	−24.3923	+	42.2487i	−0.853901	+	1.47900i
$817$	−2.73205	+	4.73205i	−0.0955824	+	0.165554i
$818$			40.0526i			1.40040i
$819$	−2.46410	+	8.53590i	−0.0861027	+	0.298268i
$820$		0			0
$821$	−11.1962	−	6.46410i	−0.390748	−	0.225599i	0.291736	−	0.956499i	$-0.405767\pi$
$821$	−11.1962	−	6.46410i	−0.390748	−	0.225599i	−0.682484	+	0.730900i	$0.739100\pi$
$822$	−35.7846	−	20.6603i	−1.24813	−	0.720609i
$823$	42.5885	−	24.5885i	1.48454	−	0.857100i	0.484695	−	0.874683i	$-0.338931\pi$
$823$	42.5885	−	24.5885i	1.48454	−	0.857100i	0.999845	+	0.0175835i	$0.00559731\pi$
$824$		−	68.1051i		−	2.37255i
$825$		0			0
$826$	−62.5692	+	36.1244i	−2.17706	+	1.25693i
$827$	28.5885			0.994118			0.497059	−	0.867717i	$-0.334413\pi$
$827$	28.5885			0.994118			0.497059	+	0.867717i	$0.334413\pi$
$828$	35.3205	−	20.3923i	1.22747	−	0.708682i
$829$	−12.0885	+	20.9378i	−0.419849	+	0.727201i	−0.995924	−	0.0901966i	$-0.971250\pi$
$829$	−12.0885	+	20.9378i	−0.419849	+	0.727201i	0.576075	+	0.817397i	$0.304584\pi$
$830$		0			0
$831$	28.2487			0.979937
$832$	−104.497	+	25.8564i	−3.62280	+	0.896410i
$833$		−	3.03332i		−	0.105098i
$834$	−9.63397	−	5.56218i	−0.333597	−	0.192602i
$835$		0			0
$836$	13.8564	+	24.0000i	0.479234	+	0.830057i
$837$	7.19615			0.248735
$838$	52.5167	+	90.9615i	1.81416	+	3.14221i
$839$	−23.7846	+	13.7321i	−0.821136	+	0.474083i	−0.850808	−	0.525477i	$-0.823887\pi$
$839$	−23.7846	+	13.7321i	−0.821136	+	0.474083i	0.0296721	+	0.999560i	$0.490554\pi$
$840$		0			0
$841$	14.2321	+	24.6506i	0.490760	+	0.850022i
$842$	−17.9545	−	10.3660i	−0.618752	−	0.357237i
$843$	−1.56218	+	2.70577i	−0.0538043	+	0.0931917i
$844$	100.890			3.47277
$845$		0			0
$846$	−27.8564			−0.957723
$847$	1.23205	−	2.13397i	0.0423338	−	0.0733242i
$848$	89.5692	+	51.7128i	3.07582	+	1.77583i
$849$	1.86603	+	3.23205i	0.0640418	+	0.110924i
$850$		0			0
$851$	25.8564	−	14.9282i	0.886346	−	0.511732i
$852$	−25.3205	−	43.8564i	−0.867466	−	1.50250i
$853$	37.3923			1.28029			0.640144	−	0.768255i	$-0.278875\pi$
$853$	37.3923			1.28029			0.640144	+	0.768255i	$0.278875\pi$
$854$	−8.29423	−	14.3660i	−0.283823	−	0.491595i
$855$		0			0
$856$	−58.3923	−	33.7128i	−1.99581	−	1.15228i
$857$		−	7.12436i		−	0.243363i	−0.992569	−	0.121682i	$-0.961171\pi$
$857$		−	7.12436i		−	0.243363i	0.992569	−	0.121682i	$-0.0388287\pi$
$858$	33.1244	−	8.19615i	1.13085	−	0.279812i
$859$	33.7846			1.15272			0.576358	−	0.817197i	$-0.304473\pi$
$859$	33.7846			1.15272			0.576358	+	0.817197i	$0.304473\pi$
$860$		0			0
$861$	−10.7583	+	18.6340i	−0.366643	+	0.635044i
$862$	−26.7846	+	15.4641i	−0.912287	+	0.526709i
$863$	13.6077			0.463211			0.231606	−	0.972810i	$-0.425602\pi$
$863$	13.6077			0.463211			0.231606	+	0.972810i	$0.425602\pi$
$864$	−18.9282	+	10.9282i	−0.643951	+	0.371785i
$865$		0			0
$866$		−	41.5167i		−	1.41079i
$867$	−5.47372	+	3.16025i	−0.185897	+	0.107328i
$868$	83.9090	+	48.4449i	2.84806	+	1.64433i
$869$	−35.7846	−	20.6603i	−1.21391	−	0.700851i
$870$		0			0
$871$	5.53590	−	19.1769i	0.187577	−	0.649785i
$872$			111.033i			3.76006i
$873$	−4.76795	+	8.25833i	−0.161371	+	0.279502i
$874$	14.9282	−	25.8564i	0.504954	−	0.874606i
$875$		0			0
$876$		−	29.4641i		−	0.995500i
$877$	−25.3205	−	43.8564i	−0.855013	−	1.48093i	−0.876633	−	0.481159i	$-0.840216\pi$
$877$	−25.3205	−	43.8564i	−0.855013	−	1.48093i	0.0216203	−	0.999766i	$-0.493117\pi$
$878$	−7.36603	−	12.7583i	−0.248591	−	0.430573i
$879$		−	6.58846i		−	0.222223i
$880$		0			0
$881$	18.5885	−	32.1962i	0.626261	−	1.08472i	−0.362035	−	0.932165i	$-0.617918\pi$
$881$	18.5885	−	32.1962i	0.626261	−	1.08472i	0.988296	−	0.152551i	$-0.0487489\pi$
$882$	1.26795	−	2.19615i	0.0426941	−	0.0739483i
$883$			16.6603i			0.560662i	0.959903	+	0.280331i	$0.0904443\pi$
$883$			16.6603i			0.560662i	−0.959903	+	0.280331i	$0.909556\pi$
$884$	61.8564	+	17.8564i	2.08046	+	0.600576i
$885$		0			0
$886$	49.9808	+	28.8564i	1.67914	+	0.969450i
$887$	−42.4186	−	24.4904i	−1.42428	−	0.822307i	−0.427616	−	0.903961i	$-0.640646\pi$
$887$	−42.4186	−	24.4904i	−1.42428	−	0.822307i	−0.996661	+	0.0816540i	$0.973980\pi$
$888$	−32.7846	+	18.9282i	−1.10018	+	0.635189i
$889$			6.55514i			0.219852i
$890$		0			0
$891$	3.00000	−	1.73205i	0.100504	−	0.0580259i
$892$	86.6410			2.90096
$893$	−12.9282	+	7.46410i	−0.432626	+	0.249777i
$894$	−5.46410	+	9.46410i	−0.182747	+	0.316527i
$895$		0			0
$896$	−93.2820			−3.11633
$897$	−18.6603	−	19.3923i	−0.623048	−	0.647490i
$898$		−	68.1051i		−	2.27270i
$899$	−4.56218	−	2.63397i	−0.152157	−	0.0878480i
$900$		0			0
$901$	−11.3205	−	19.6077i	−0.377141	−	0.653227i
$902$	82.6410			2.75164
$903$	4.59808	+	7.96410i	0.153014	+	0.265029i
$904$	102.746	−	59.3205i	3.41729	−	1.97297i
$905$		0			0
$906$	13.4641	+	23.3205i	0.447315	+	0.774772i
$907$	−27.2487	−	15.7321i	−0.904779	−	0.522374i	−0.0260311	−	0.999661i	$-0.508287\pi$
$907$	−27.2487	−	15.7321i	−0.904779	−	0.522374i	−0.878747	+	0.477287i	$0.841620\pi$
$908$	15.4641	−	26.7846i	0.513194	−	0.888878i
$909$	8.92820			0.296130
$910$		0			0
$911$	47.7128			1.58080			0.790398	−	0.612594i	$-0.209874\pi$
$911$	47.7128			1.58080			0.790398	+	0.612594i	$0.209874\pi$
$912$	−10.9282	+	18.9282i	−0.361869	+	0.626775i
$913$	−28.3923	−	16.3923i	−0.939648	−	0.542506i
$914$	−21.0263	−	36.4186i	−0.695488	−	1.20462i
$915$		0			0
$916$	11.3205	−	6.53590i	0.374040	−	0.215952i
$917$	−5.83013	−	10.0981i	−0.192528	−	0.333468i
$918$	8.92820			0.294675
$919$	−16.4641	−	28.5167i	−0.543101	−	0.940678i	−0.998724	−	0.0505051i	$-0.983917\pi$
$919$	−16.4641	−	28.5167i	−0.543101	−	0.940678i	0.455623	−	0.890173i	$-0.349416\pi$
$920$		0			0
$921$	22.4545	+	12.9641i	0.739900	+	0.427182i
$922$		−	91.5692i		−	3.01567i
$923$	−24.0788	+	23.1699i	−0.792565	+	0.762646i
$924$	46.6410			1.53438
$925$		0			0
$926$	−54.3468	+	94.1314i	−1.78595	+	3.09335i
$927$	−6.23205	+	3.59808i	−0.204687	+	0.118176i
$928$	16.0000			0.525226
$929$	16.7321	−	9.66025i	0.548961	−	0.316943i	−0.199742	−	0.979849i	$-0.564010\pi$
$929$	16.7321	−	9.66025i	0.548961	−	0.316943i	0.748703	+	0.662906i	$0.230677\pi$
$930$		0			0
$931$		−	1.35898i		−	0.0445389i
$932$	−18.2487	+	10.5359i	−0.597756	+	0.345115i
$933$	0.169873	+	0.0980762i	0.00556139	+	0.00321087i
$934$	15.0000	+	8.66025i	0.490815	+	0.283372i
$935$		0			0
$936$	23.6603	+	24.5885i	0.773360	+	0.803699i
$937$		−	16.2487i		−	0.530822i	−0.964135	−	0.265411i	$-0.914492\pi$
$937$		−	16.2487i		−	0.530822i	0.964135	−	0.265411i	$-0.0855077\pi$
$938$	18.6340	−	32.2750i	0.608421	−	1.05382i
$939$	−10.5981	+	18.3564i	−0.345855	+	0.599039i
$940$		0			0
$941$		−	40.5885i		−	1.32315i	−0.749881	−	0.661573i	$-0.769889\pi$
$941$		−	40.5885i		−	1.32315i	0.749881	−	0.661573i	$-0.230111\pi$
$942$	8.56218	+	14.8301i	0.278971	+	0.483192i
$943$	−32.5885	−	56.4449i	−1.06123	−	1.83810i
$944$			160.210i			5.21440i
$945$		0			0
$946$	17.6603	−	30.5885i	0.574184	−	0.994517i
$947$	−18.2942	+	31.6865i	−0.594483	+	1.02967i	0.399137	+	0.916891i	$0.369310\pi$
$947$	−18.2942	+	31.6865i	−0.594483	+	1.02967i	−0.993620	+	0.112783i	$0.964024\pi$
$948$		−	65.1769i		−	2.11685i
$949$	−18.8731	+	4.66987i	−0.612646	+	0.151590i
$950$		0			0
$951$	9.12436	+	5.26795i	0.295878	+	0.170825i
$952$	66.0000	+	38.1051i	2.13907	+	1.23499i
$953$	−21.0000	+	12.1244i	−0.680257	+	0.392746i	−0.799952	−	0.600064i	$-0.795142\pi$
$953$	−21.0000	+	12.1244i	−0.680257	+	0.392746i	0.119695	+	0.992811i	$0.461808\pi$
$954$		−	18.9282i		−	0.612823i
$955$		0			0
$956$	6.92820	−	4.00000i	0.224074	−	0.129369i
$957$	−2.53590			−0.0819740
$958$	70.7654	−	40.8564i	2.28633	−	1.32001i
$959$	−18.6340	+	32.2750i	−0.601722	+	1.04221i
$960$		0			0
$961$	−20.7846			−0.670471
$962$	27.3205	+	28.3923i	0.880849	+	0.915405i
$963$			7.12436i			0.229579i
$964$	105.962	+	61.1769i	3.41279	+	1.97038i
$965$		0			0
$966$	−25.1244	−	43.5167i	−0.808363	−	1.40013i
$967$	32.2487			1.03705			0.518524	−	0.855063i	$-0.326482\pi$
$967$	32.2487			1.03705			0.518524	+	0.855063i	$0.326482\pi$
$968$	−4.73205	−	8.19615i	−0.152094	−	0.263434i
$969$	4.14359	−	2.39230i	0.133111	−	0.0768519i
$970$		0			0
$971$	0.588457	+	1.01924i	0.0188845	+	0.0327089i	0.875313	−	0.483556i	$-0.160655\pi$
$971$	0.588457	+	1.01924i	0.0188845	+	0.0327089i	−0.856429	+	0.516265i	$0.827322\pi$
$972$	4.73205	+	2.73205i	0.151781	+	0.0876306i
$973$	−5.01666	+	8.68911i	−0.160827	+	0.278560i
$974$	56.7846			1.81950
$975$		0			0
$976$	−36.7846			−1.17745
$977$	−0.535898	+	0.928203i	−0.0171449	+	0.0296959i	−0.874471	−	0.485079i	$-0.838791\pi$
$977$	−0.535898	+	0.928203i	−0.0171449	+	0.0296959i	0.857326	+	0.514774i	$0.172124\pi$
$978$	29.4904	+	17.0263i	0.942998	+	0.544440i
$979$	8.19615	+	14.1962i	0.261950	+	0.453711i
$980$		0			0
$981$	10.1603	−	5.86603i	0.324392	−	0.187288i
$982$	23.3923	+	40.5167i	0.746478	+	1.29294i
$983$	−23.8564			−0.760901			−0.380451	−	0.924801i	$-0.624231\pi$
$983$	−23.8564			−0.760901			−0.380451	+	0.924801i	$0.624231\pi$
$984$	41.3205	+	71.5692i	1.31725	+	2.28154i
$985$		0			0
$986$	−5.66025	−	3.26795i	−0.180259	−	0.104073i
$987$			25.1244i			0.799717i
$988$	27.7128	+	8.00000i	0.881662	+	0.254514i
$989$	−27.8564			−0.885782
$990$		0			0
$991$	−14.4641	+	25.0526i	−0.459467	+	0.795821i	−0.998933	−	0.0461870i	$-0.985293\pi$
$991$	−14.4641	+	25.0526i	−0.459467	+	0.795821i	0.539465	+	0.842008i	$0.318626\pi$
$992$	136.210	−	78.6410i	4.32468	−	2.49685i
$993$	16.1244			0.511691
$994$	−54.0333	+	31.1962i	−1.71383	+	0.989482i
$995$		0			0
$996$		−	51.7128i		−	1.63858i
$997$	−49.8731	+	28.7942i	−1.57950	+	0.911922i	−0.584567	+	0.811346i	$0.698735\pi$
$997$	−49.8731	+	28.7942i	−1.57950	+	0.911922i	−0.994929	+	0.100577i	$0.967931\pi$
$998$	48.2487	+	27.8564i	1.52729	+	0.881779i
$999$	3.46410	+	2.00000i	0.109599	+	0.0632772i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	975.2.w.f.199.2		4
5.2	odd	4		975.2.bc.h.901.2		4
5.3	odd	4		195.2.bb.a.121.1	✓	4
5.4	even	2		975.2.w.a.199.1		4
13.10	even	6		975.2.w.a.49.1		4
15.8	even	4		585.2.bu.a.316.2		4
65.23	odd	12		195.2.bb.a.166.1	yes	4
65.33	even	12		2535.2.a.n.1.1		2
65.49	even	6	inner	975.2.w.f.49.2		4
65.58	even	12		2535.2.a.s.1.2		2
65.62	odd	12		975.2.bc.h.751.2		4
195.23	even	12		585.2.bu.a.361.2		4
195.98	odd	12		7605.2.a.bk.1.2		2
195.188	odd	12		7605.2.a.y.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
195.2.bb.a.121.1	✓	4	5.3	odd	4
195.2.bb.a.166.1	yes	4	65.23	odd	12
585.2.bu.a.316.2		4	15.8	even	4
585.2.bu.a.361.2		4	195.23	even	12
975.2.w.a.49.1		4	13.10	even	6
975.2.w.a.199.1		4	5.4	even	2
975.2.w.f.49.2		4	65.49	even	6	inner
975.2.w.f.199.2		4	1.1	even	1	trivial
975.2.bc.h.751.2		4	65.62	odd	12
975.2.bc.h.901.2		4	5.2	odd	4
2535.2.a.n.1.1		2	65.33	even	12
2535.2.a.s.1.2		2	65.58	even	12
7605.2.a.y.1.1		2	195.188	odd	12
7605.2.a.bk.1.2		2	195.98	odd	12

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:	\( N \)	\(=\)	\( 975 = 3 \cdot 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	975.w (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.36603 - 2.36603i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-2.73205 - 4.73205i) q^{4} +(2.36603 - 1.36603i) q^{6} +(-1.23205 - 2.13397i) q^{7} -9.46410 q^{8} +(0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(1.36603 - 2.36603i) q^{2} +(0.866025 + 0.500000i) q^{3} +(-2.73205 - 4.73205i) q^{4} +(2.36603 - 1.36603i) q^{6} +(-1.23205 - 2.13397i) q^{7} -9.46410 q^{8} +(0.500000 + 0.866025i) q^{9} +(-3.00000 - 1.73205i) q^{11} -5.46410i q^{12} +(-3.50000 + 0.866025i) q^{13} -6.73205 q^{14} +(-7.46410 + 12.9282i) q^{16} +(2.83013 - 1.63397i) q^{17} +2.73205 q^{18} +(1.26795 - 0.732051i) q^{19} -2.46410i q^{21} +(-8.19615 + 4.73205i) q^{22} +(6.46410 + 3.73205i) q^{23} +(-8.19615 - 4.73205i) q^{24} +(-2.73205 + 9.46410i) q^{26} +1.00000i q^{27} +(-6.73205 + 11.6603i) q^{28} +(0.366025 - 0.633975i) q^{29} -7.19615i q^{31} +(10.9282 + 18.9282i) q^{32} +(-1.73205 - 3.00000i) q^{33} -8.92820i q^{34} +(2.73205 - 4.73205i) q^{36} +(2.00000 - 3.46410i) q^{37} -4.00000i q^{38} +(-3.46410 - 1.00000i) q^{39} +(-7.56218 - 4.36603i) q^{41} +(-5.83013 - 3.36603i) q^{42} +(-3.23205 + 1.86603i) q^{43} +18.9282i q^{44} +(17.6603 - 10.1962i) q^{46} -10.1962 q^{47} +(-12.9282 + 7.46410i) q^{48} +(0.464102 - 0.803848i) q^{49} +3.26795 q^{51} +(13.6603 + 14.1962i) q^{52} -6.92820i q^{53} +(2.36603 + 1.36603i) q^{54} +(11.6603 + 20.1962i) q^{56} +1.46410 q^{57} +(-1.00000 - 1.73205i) q^{58} +(9.29423 - 5.36603i) q^{59} +(1.23205 + 2.13397i) q^{61} +(-17.0263 - 9.83013i) q^{62} +(1.23205 - 2.13397i) q^{63} +29.8564 q^{64} -9.46410 q^{66} +(-2.76795 + 4.79423i) q^{67} +(-15.4641 - 8.92820i) q^{68} +(3.73205 + 6.46410i) q^{69} +(8.02628 - 4.63397i) q^{71} +(-4.73205 - 8.19615i) q^{72} +5.39230 q^{73} +(-5.46410 - 9.46410i) q^{74} +(-6.92820 - 4.00000i) q^{76} +8.53590i q^{77} +(-7.09808 + 6.83013i) q^{78} +11.9282 q^{79} +(-0.500000 + 0.866025i) q^{81} +(-20.6603 + 11.9282i) q^{82} +9.46410 q^{83} +(-11.6603 + 6.73205i) q^{84} +10.1962i q^{86} +(0.633975 - 0.366025i) q^{87} +(28.3923 + 16.3923i) q^{88} +(-4.09808 - 2.36603i) q^{89} +(6.16025 + 6.40192i) q^{91} -40.7846i q^{92} +(3.59808 - 6.23205i) q^{93} +(-13.9282 + 24.1244i) q^{94} +21.8564i q^{96} +(4.76795 + 8.25833i) q^{97} +(-1.26795 - 2.19615i) q^{98} -3.46410i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} - 4 q^{4} + 6 q^{6} + 2 q^{7} - 24 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 2 * q^2 - 4 * q^4 + 6 * q^6 + 2 * q^7 - 24 * q^8 + 2 * q^9	\( 4 q + 2 q^{2} - 4 q^{4} + 6 q^{6} + 2 q^{7} - 24 q^{8} + 2 q^{9} - 12 q^{11} - 14 q^{13} - 20 q^{14} - 16 q^{16} - 6 q^{17} + 4 q^{18} + 12 q^{19} - 12 q^{22} + 12 q^{23} - 12 q^{24} - 4 q^{26} - 20 q^{28} - 2 q^{29} + 16 q^{32} + 4 q^{36} + 8 q^{37} - 6 q^{41} - 6 q^{42} - 6 q^{43} + 36 q^{46} - 20 q^{47} - 24 q^{48} - 12 q^{49} + 20 q^{51} + 20 q^{52} + 6 q^{54} + 12 q^{56} - 8 q^{57} - 4 q^{58} + 6 q^{59} - 2 q^{61} - 30 q^{62} - 2 q^{63} + 64 q^{64} - 24 q^{66} - 18 q^{67} - 48 q^{68} + 8 q^{69} - 6 q^{71} - 12 q^{72} - 20 q^{73} - 8 q^{74} - 18 q^{78} + 20 q^{79} - 2 q^{81} - 48 q^{82} + 24 q^{83} - 12 q^{84} + 6 q^{87} + 72 q^{88} - 6 q^{89} - 10 q^{91} + 4 q^{93} - 28 q^{94} + 26 q^{97} - 12 q^{98}+O(q^{100}) \) 4 * q + 2 * q^2 - 4 * q^4 + 6 * q^6 + 2 * q^7 - 24 * q^8 + 2 * q^9 - 12 * q^11 - 14 * q^13 - 20 * q^14 - 16 * q^16 - 6 * q^17 + 4 * q^18 + 12 * q^19 - 12 * q^22 + 12 * q^23 - 12 * q^24 - 4 * q^26 - 20 * q^28 - 2 * q^29 + 16 * q^32 + 4 * q^36 + 8 * q^37 - 6 * q^41 - 6 * q^42 - 6 * q^43 + 36 * q^46 - 20 * q^47 - 24 * q^48 - 12 * q^49 + 20 * q^51 + 20 * q^52 + 6 * q^54 + 12 * q^56 - 8 * q^57 - 4 * q^58 + 6 * q^59 - 2 * q^61 - 30 * q^62 - 2 * q^63 + 64 * q^64 - 24 * q^66 - 18 * q^67 - 48 * q^68 + 8 * q^69 - 6 * q^71 - 12 * q^72 - 20 * q^73 - 8 * q^74 - 18 * q^78 + 20 * q^79 - 2 * q^81 - 48 * q^82 + 24 * q^83 - 12 * q^84 + 6 * q^87 + 72 * q^88 - 6 * q^89 - 10 * q^91 + 4 * q^93 - 28 * q^94 + 26 * q^97 - 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more