LMFDB - Embedded newform 525.2.j.b.218.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(218,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("525.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.j (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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			218.6
Character	$\chi$	$=$	525.218
Dual form			525.2.j.b.407.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.260263 - 0.260263i) q^{2} +(-0.826909 + 1.52191i) q^{3} -1.86453i q^{4} +(0.611312 - 0.180884i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.00579 + 1.00579i) q^{8} +(-1.63244 - 2.51697i) q^{9} +O(q^{10})$	\(q+(-0.260263 - 0.260263i) q^{2} +(-0.826909 + 1.52191i) q^{3} -1.86453i q^{4} +(0.611312 - 0.180884i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.00579 + 1.00579i) q^{8} +(-1.63244 - 2.51697i) q^{9} +3.38750i q^{11} +(2.83765 + 1.54179i) q^{12} +(-1.59420 - 1.59420i) q^{13} +0.368068 q^{14} -3.20551 q^{16} +(-0.140684 - 0.140684i) q^{17} +(-0.230209 + 1.07994i) q^{18} +7.34691i q^{19} +(-0.491443 - 1.66087i) q^{21} +(0.881641 - 0.881641i) q^{22} +(-2.21444 + 2.21444i) q^{23} +(-0.699032 - 2.36243i) q^{24} +0.829822i q^{26} +(5.18049 - 0.403134i) q^{27} +(1.31842 + 1.31842i) q^{28} -9.49165 q^{29} +0.922582 q^{31} +(2.84586 + 2.84586i) q^{32} +(-5.15548 - 2.80115i) q^{33} +0.0732300i q^{34} +(-4.69295 + 3.04373i) q^{36} +(-5.91558 + 5.91558i) q^{37} +(1.91213 - 1.91213i) q^{38} +(3.74449 - 1.10797i) q^{39} -1.39256i q^{41} +(-0.304359 + 0.560167i) q^{42} +(-0.864526 - 0.864526i) q^{43} +6.31608 q^{44} +1.15267 q^{46} +(-0.651346 - 0.651346i) q^{47} +(2.65066 - 4.87851i) q^{48} -1.00000i q^{49} +(0.330443 - 0.0977764i) q^{51} +(-2.97242 + 2.97242i) q^{52} +(-6.54108 + 6.54108i) q^{53} +(-1.45321 - 1.24337i) q^{54} -1.42241i q^{56} +(-11.1814 - 6.07522i) q^{57} +(2.47033 + 2.47033i) q^{58} -6.25032 q^{59} +1.83261 q^{61} +(-0.240114 - 0.240114i) q^{62} +(2.93408 + 0.625454i) q^{63} +4.92967i q^{64} +(0.612745 + 2.07082i) q^{66} +(0.815500 - 0.815500i) q^{67} +(-0.262310 + 0.262310i) q^{68} +(-1.53904 - 5.20132i) q^{69} -9.77651i q^{71} +(4.17345 + 0.889650i) q^{72} +(4.80768 + 4.80768i) q^{73} +3.07921 q^{74} +13.6985 q^{76} +(-2.39532 - 2.39532i) q^{77} +(-1.26292 - 0.686187i) q^{78} +3.41711i q^{79} +(-3.67026 + 8.21761i) q^{81} +(-0.362432 + 0.362432i) q^{82} +(6.26911 - 6.26911i) q^{83} +(-3.09673 + 0.916307i) q^{84} +0.450009i q^{86} +(7.84873 - 14.4455i) q^{87} +(-3.40712 - 3.40712i) q^{88} +12.3767 q^{89} +2.25454 q^{91} +(4.12888 + 4.12888i) q^{92} +(-0.762891 + 1.40409i) q^{93} +0.339043i q^{94} +(-6.68443 + 1.97789i) q^{96} +(6.71326 - 6.71326i) q^{97} +(-0.260263 + 0.260263i) q^{98} +(8.52622 - 5.52990i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3}+O(q^{10}) $ 24 * q + 4 * q^3	$ 24 q + 4 q^{3} - 16 q^{12} + 8 q^{13} - 16 q^{16} + 20 q^{18} + 4 q^{21} - 8 q^{22} + 16 q^{27} - 28 q^{33} + 16 q^{36} + 16 q^{37} + 20 q^{42} + 40 q^{43} - 64 q^{46} - 16 q^{48} - 20 q^{51} - 4 q^{57} - 40 q^{58} + 32 q^{61} + 8 q^{63} - 16 q^{66} - 24 q^{67} + 8 q^{72} - 32 q^{73} + 32 q^{76} - 60 q^{78} + 52 q^{81} + 80 q^{82} - 4 q^{87} - 96 q^{88} - 24 q^{91} + 76 q^{93} - 96 q^{96} - 24 q^{97}+O(q^{100}) $ 24 * q + 4 * q^3 - 16 * q^12 + 8 * q^13 - 16 * q^16 + 20 * q^18 + 4 * q^21 - 8 * q^22 + 16 * q^27 - 28 * q^33 + 16 * q^36 + 16 * q^37 + 20 * q^42 + 40 * q^43 - 64 * q^46 - 16 * q^48 - 20 * q^51 - 4 * q^57 - 40 * q^58 + 32 * q^61 + 8 * q^63 - 16 * q^66 - 24 * q^67 + 8 * q^72 - 32 * q^73 + 32 * q^76 - 60 * q^78 + 52 * q^81 + 80 * q^82 - 4 * q^87 - 96 * q^88 - 24 * q^91 + 76 * q^93 - 96 * q^96 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	−0.260263	−	0.260263i	−0.184034	−	0.184034i	0.609077	−	0.793111i	$-0.291540\pi$
$2$	−0.260263	−	0.260263i	−0.184034	−	0.184034i	−0.793111	+	0.609077i	$0.791540\pi$
$3$	−0.826909	+	1.52191i	−0.477416	+	0.878677i
$3$	−0.826909	+	1.52191i	−0.477416	+	0.878677i
$4$		−	1.86453i		−	0.932263i
$5$		0			0
$5$		0			0
$6$	0.611312	−	0.180884i	0.249567	−	0.0738457i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$7$	−0.707107	+	0.707107i	−0.267261	+	0.267261i
$8$	−1.00579	+	1.00579i	−0.355602	+	0.355602i
$9$	−1.63244	−	2.51697i	−0.544148	−	0.838989i
$10$		0			0
$11$			3.38750i			1.02137i	0.859768	+	0.510684i	$0.170608\pi$
$11$			3.38750i			1.02137i	−0.859768	+	0.510684i	$0.829392\pi$
$12$	2.83765	+	1.54179i	0.819158	+	0.445077i
$13$	−1.59420	−	1.59420i	−0.442151	−	0.442151i	0.450583	−	0.892734i	$-0.351216\pi$
$13$	−1.59420	−	1.59420i	−0.442151	−	0.442151i	−0.892734	+	0.450583i	$0.851216\pi$
$14$	0.368068			0.0983703
$15$		0			0
$16$	−3.20551			−0.801377
$17$	−0.140684	−	0.140684i	−0.0341210	−	0.0341210i	0.689840	−	0.723961i	$-0.257681\pi$
$17$	−0.140684	−	0.140684i	−0.0341210	−	0.0341210i	−0.723961	+	0.689840i	$0.757681\pi$
$18$	−0.230209	+	1.07994i	−0.0542609	+	0.254544i
$19$			7.34691i			1.68550i	0.538308	+	0.842748i	$0.319064\pi$
$19$			7.34691i			1.68550i	−0.538308	+	0.842748i	$0.680936\pi$
$20$		0			0
$21$	−0.491443	−	1.66087i	−0.107242	−	0.362431i
$22$	0.881641	−	0.881641i	0.187966	−	0.187966i
$23$	−2.21444	+	2.21444i	−0.461742	+	0.461742i	−0.899226	−	0.437484i	$-0.855870\pi$
$23$	−2.21444	+	2.21444i	−0.461742	+	0.461742i	0.437484	+	0.899226i	$0.355870\pi$
$24$	−0.699032	−	2.36243i	−0.142689	−	0.482229i
$25$		0			0
$26$			0.829822i			0.162741i
$27$	5.18049	−	0.403134i	0.996986	−	0.0775831i
$28$	1.31842	+	1.31842i	0.249158	+	0.249158i
$29$	−9.49165			−1.76256			−0.881278	−	0.472598i	$-0.843316\pi$
$29$	−9.49165			−1.76256			−0.881278	+	0.472598i	$0.843316\pi$
$30$		0			0
$31$	0.922582			0.165701			0.0828503	−	0.996562i	$-0.473598\pi$
$31$	0.922582			0.165701			0.0828503	+	0.996562i	$0.473598\pi$
$32$	2.84586	+	2.84586i	0.503083	+	0.503083i
$33$	−5.15548	−	2.80115i	−0.897454	−	0.487618i
$34$			0.0732300i			0.0125588i
$35$		0			0
$36$	−4.69295	+	3.04373i	−0.782159	+	0.507289i
$37$	−5.91558	+	5.91558i	−0.972515	+	0.972515i	−0.999632	−	0.0271173i	$-0.991367\pi$
$37$	−5.91558	+	5.91558i	−0.972515	+	0.972515i	0.0271173	+	0.999632i	$0.491367\pi$
$38$	1.91213	−	1.91213i	0.310188	−	0.310188i
$39$	3.74449	−	1.10797i	0.599598	−	0.177418i
$40$		0			0
$41$		−	1.39256i		−	0.217481i	−0.994070	−	0.108741i	$-0.965318\pi$
$41$		−	1.39256i		−	0.217481i	0.994070	−	0.108741i	$-0.0346818\pi$
$42$	−0.304359	+	0.560167i	−0.0469636	+	0.0864357i
$43$	−0.864526	−	0.864526i	−0.131839	−	0.131839i	0.638108	−	0.769947i	$-0.279717\pi$
$43$	−0.864526	−	0.864526i	−0.131839	−	0.131839i	−0.769947	+	0.638108i	$0.779717\pi$
$44$	6.31608			0.952184
$45$		0			0
$46$	1.15267			0.169952
$47$	−0.651346	−	0.651346i	−0.0950085	−	0.0950085i	0.658005	−	0.753014i	$-0.271401\pi$
$47$	−0.651346	−	0.651346i	−0.0950085	−	0.0950085i	−0.753014	+	0.658005i	$0.771401\pi$
$48$	2.65066	−	4.87851i	0.382591	−	0.704152i
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	0.330443	−	0.0977764i	0.0462713	−	0.0136914i
$52$	−2.97242	+	2.97242i	−0.412201	+	0.412201i
$53$	−6.54108	+	6.54108i	−0.898486	+	0.898486i	−0.995302	−	0.0968158i	$-0.969134\pi$
$53$	−6.54108	+	6.54108i	−0.898486	+	0.898486i	0.0968158	+	0.995302i	$0.469134\pi$
$54$	−1.45321	−	1.24337i	−0.197757	−	0.169201i
$55$		0			0
$56$		−	1.42241i		−	0.190077i
$57$	−11.1814	−	6.07522i	−1.48101	−	0.804683i
$58$	2.47033	+	2.47033i	0.324370	+	0.324370i
$59$	−6.25032			−0.813722			−0.406861	−	0.913490i	$-0.633377\pi$
$59$	−6.25032			−0.813722			−0.406861	+	0.913490i	$0.633377\pi$
$60$		0			0
$61$	1.83261			0.234642			0.117321	−	0.993094i	$-0.462569\pi$
$61$	1.83261			0.234642			0.117321	+	0.993094i	$0.462569\pi$
$62$	−0.240114	−	0.240114i	−0.0304945	−	0.0304945i
$63$	2.93408	+	0.625454i	0.369659	+	0.0787998i
$64$			4.92967i			0.616209i
$65$		0			0
$66$	0.612745	+	2.07082i	0.0754237	+	0.254900i
$67$	0.815500	−	0.815500i	0.0996292	−	0.0996292i	−0.655535	−	0.755165i	$-0.727557\pi$
$67$	0.815500	−	0.815500i	0.0996292	−	0.0996292i	0.755165	+	0.655535i	$0.227557\pi$
$68$	−0.262310	+	0.262310i	−0.0318097	+	0.0318097i
$69$	−1.53904	−	5.20132i	−0.185279	−	0.626166i
$70$		0			0
$71$		−	9.77651i		−	1.16026i	−0.814524	−	0.580129i	$-0.803002\pi$
$71$		−	9.77651i		−	1.16026i	0.814524	−	0.580129i	$-0.196998\pi$
$72$	4.17345	+	0.889650i	0.491846	+	0.104846i
$73$	4.80768	+	4.80768i	0.562697	+	0.562697i	0.930073	−	0.367376i	$-0.119744\pi$
$73$	4.80768	+	4.80768i	0.562697	+	0.562697i	−0.367376	+	0.930073i	$0.619744\pi$
$74$	3.07921			0.357951
$75$		0			0
$76$	13.6985			1.57133
$77$	−2.39532	−	2.39532i	−0.272972	−	0.272972i
$78$	−1.26292	−	0.686187i	−0.142997	−	0.0776954i
$79$			3.41711i			0.384455i	0.981350	+	0.192228i	$0.0615712\pi$
$79$			3.41711i			0.384455i	−0.981350	+	0.192228i	$0.938429\pi$
$80$		0			0
$81$	−3.67026	+	8.21761i	−0.407807	+	0.913068i
$82$	−0.362432	+	0.362432i	−0.0400239	+	0.0400239i
$83$	6.26911	−	6.26911i	0.688124	−	0.688124i	−0.273693	−	0.961817i	$-0.588245\pi$
$83$	6.26911	−	6.26911i	0.688124	−	0.688124i	0.961817	+	0.273693i	$0.0882453\pi$
$84$	−3.09673	+	0.916307i	−0.337881	+	0.0999773i
$85$		0			0
$86$			0.450009i			0.0485257i
$87$	7.84873	−	14.4455i	0.841473	−	1.54872i
$88$	−3.40712	−	3.40712i	−0.363201	−	0.363201i
$89$	12.3767			1.31192			0.655962	−	0.754794i	$-0.272263\pi$
$89$	12.3767			1.31192			0.655962	+	0.754794i	$0.272263\pi$
$90$		0			0
$91$	2.25454			0.236340
$92$	4.12888	+	4.12888i	0.430465	+	0.430465i
$93$	−0.762891	+	1.40409i	−0.0791082	+	0.145597i
$94$			0.339043i			0.0349696i
$95$		0			0
$96$	−6.68443	+	1.97789i	−0.682227	+	0.201867i
$97$	6.71326	−	6.71326i	0.681628	−	0.681628i	−0.278739	−	0.960367i	$-0.589916\pi$
$97$	6.71326	−	6.71326i	0.681628	−	0.681628i	0.960367	+	0.278739i	$0.0899164\pi$
$98$	−0.260263	+	0.260263i	−0.0262906	+	0.0262906i
$99$	8.52622	−	5.52990i	0.856918	−	0.555775i
$100$		0			0
$101$		−	12.4523i		−	1.23905i	−0.784976	−	0.619526i	$-0.787325\pi$
$101$		−	12.4523i		−	1.23905i	0.784976	−	0.619526i	$-0.212675\pi$
$102$	−0.111450	−	0.0605545i	−0.0110352	−	0.00599579i
$103$	9.78924	+	9.78924i	0.964563	+	0.964563i	0.999393	−	0.0348303i	$-0.0110891\pi$
$103$	9.78924	+	9.78924i	0.964563	+	0.964563i	−0.0348303	+	0.999393i	$0.511089\pi$
$104$	3.20687			0.314459
$105$		0			0
$106$	3.40481			0.330704
$107$	−5.21866	−	5.21866i	−0.504507	−	0.504507i	0.408328	−	0.912835i	$-0.366112\pi$
$107$	−5.21866	−	5.21866i	−0.504507	−	0.504507i	−0.912835	+	0.408328i	$0.866112\pi$
$108$	−0.751653	−	9.65916i	−0.0723279	−	0.929453i
$109$			6.67661i			0.639504i	0.947501	+	0.319752i	$0.103600\pi$
$109$			6.67661i			0.639504i	−0.947501	+	0.319752i	$0.896400\pi$
$110$		0			0
$111$	−4.11135	−	13.8946i	−0.390233	−	1.31882i
$112$	2.26664	−	2.26664i	0.214177	−	0.214177i
$113$	8.23451	−	8.23451i	0.774637	−	0.774637i	−0.204276	−	0.978913i	$-0.565484\pi$
$113$	8.23451	−	8.23451i	0.774637	−	0.774637i	0.978913	+	0.204276i	$0.0654841\pi$
$114$	1.32894	+	4.49125i	0.124467	+	0.420644i
$115$		0			0
$116$			17.6974i			1.64317i
$117$	−1.41011	+	6.61498i	−0.130365	+	0.611555i
$118$	1.62673	+	1.62673i	0.149752	+	0.149752i
$119$	0.198958			0.0182384
$120$		0			0
$121$	−0.475134			−0.0431940
$122$	−0.476962	−	0.476962i	−0.0431821	−	0.0431821i
$123$	2.11936	+	1.15152i	0.191096	+	0.103829i
$124$		−	1.72018i		−	0.154477i
$125$		0			0
$126$	−0.600850	−	0.926415i	−0.0535279	−	0.0825316i
$127$	−1.88180	+	1.88180i	−0.166983	+	0.166983i	−0.785652	−	0.618669i	$-0.787672\pi$
$127$	−1.88180	+	1.88180i	−0.166983	+	0.166983i	0.618669	+	0.785652i	$0.287672\pi$
$128$	6.97474	−	6.97474i	0.616486	−	0.616486i
$129$	2.03062	−	0.600850i	0.178786	−	0.0529019i
$130$		0			0
$131$			8.97080i			0.783783i	0.920012	+	0.391891i	$0.128179\pi$
$131$			8.97080i			0.783783i	−0.920012	+	0.391891i	$0.871821\pi$
$132$	−5.22282	+	9.61252i	−0.454588	+	0.836663i
$133$	−5.19505	−	5.19505i	−0.450468	−	0.450468i
$134$	−0.424489			−0.0366703
$135$		0			0
$136$	0.282999			0.0242670
$137$	6.49538	+	6.49538i	0.554938	+	0.554938i	0.927862	−	0.372924i	$-0.121645\pi$
$137$	6.49538	+	6.49538i	0.554938	+	0.554938i	−0.372924	+	0.927862i	$0.621645\pi$
$138$	−0.953156	+	1.75427i	−0.0811380	+	0.149333i
$139$		−	1.83916i		−	0.155995i	−0.996954	−	0.0779976i	$-0.975147\pi$
$139$		−	1.83916i		−	0.155995i	0.996954	−	0.0779976i	$-0.0248526\pi$
$140$		0			0
$141$	1.52990	−	0.452688i	0.128840	−	0.0381232i
$142$	−2.54447	+	2.54447i	−0.213527	+	0.213527i
$143$	5.40034	−	5.40034i	0.451599	−	0.451599i
$144$	5.23281	+	8.06817i	0.436068	+	0.672347i
$145$		0			0
$146$		−	2.50253i		−	0.207110i
$147$	1.52191	+	0.826909i	0.125525	+	0.0682023i
$148$	11.0297	+	11.0297i	0.906640	+	0.906640i
$149$	−0.987227			−0.0808768			−0.0404384	−	0.999182i	$-0.512875\pi$
$149$	−0.987227			−0.0808768			−0.0404384	+	0.999182i	$0.512875\pi$
$150$		0			0
$151$	−8.71084			−0.708878			−0.354439	−	0.935079i	$-0.615328\pi$
$151$	−8.71084			−0.708878			−0.354439	+	0.935079i	$0.615328\pi$
$152$	−7.38948	−	7.38948i	−0.599366	−	0.599366i
$153$	−0.124439	+	0.583758i	−0.0100603	+	0.0471940i
$154$			1.24683i			0.100472i
$155$		0			0
$156$	−2.06585	−	6.98169i	−0.165400	−	0.558983i
$157$	−5.26306	+	5.26306i	−0.420038	+	0.420038i	−0.885217	−	0.465179i	$-0.845990\pi$
$157$	−5.26306	+	5.26306i	−0.420038	+	0.420038i	0.465179	+	0.885217i	$0.345990\pi$
$158$	0.889349	−	0.889349i	0.0707528	−	0.0707528i
$159$	−4.54608	−	15.3638i	−0.360528	−	1.21843i
$160$		0			0
$161$		−	3.13169i		−	0.246812i
$162$	3.09398	−	1.18351i	0.243086	−	0.0929853i
$163$	−14.1511	−	14.1511i	−1.10840	−	1.10840i	−0.993361	−	0.115041i	$-0.963300\pi$
$163$	−14.1511	−	14.1511i	−1.10840	−	1.10840i	−0.115041	−	0.993361i	$-0.536700\pi$
$164$	−2.59646			−0.202750
$165$		0			0
$166$	−3.26324			−0.253276
$167$	−17.4876	−	17.4876i	−1.35323	−	1.35323i	−0.882018	−	0.471215i	$-0.843816\pi$
$167$	−17.4876	−	17.4876i	−1.35323	−	1.35323i	−0.471215	−	0.882018i	$-0.656184\pi$
$168$	2.16478	+	1.17620i	0.167017	+	0.0907459i
$169$		−	7.91707i		−	0.609005i
$170$		0			0
$171$	18.4919	−	11.9934i	1.41411	−	0.917159i
$172$	−1.61193	+	1.61193i	−0.122909	+	0.122909i
$173$	−10.8767	+	10.8767i	−0.826942	+	0.826942i	−0.987093	−	0.160150i	$-0.948802\pi$
$173$	−10.8767	+	10.8767i	−0.826942	+	0.826942i	0.160150	+	0.987093i	$0.448802\pi$
$174$	−5.80236	+	1.71689i	−0.439876	+	0.130157i
$175$		0			0
$176$		−	10.8587i		−	0.818502i
$177$	5.16844	−	9.51244i	0.388484	−	0.714999i
$178$	−3.22119	−	3.22119i	−0.241439	−	0.241439i
$179$	17.6524			1.31941			0.659703	−	0.751527i	$-0.270682\pi$
$179$	17.6524			1.31941			0.659703	+	0.751527i	$0.270682\pi$
$180$		0			0
$181$	−11.9237			−0.886282			−0.443141	−	0.896452i	$-0.646136\pi$
$181$	−11.9237			−0.886282			−0.443141	+	0.896452i	$0.646136\pi$
$182$	−0.586773	−	0.586773i	−0.0434945	−	0.0434945i
$183$	−1.51541	+	2.78908i	−0.112022	+	0.206175i
$184$		−	4.45454i		−	0.328393i
$185$		0			0
$186$	0.563986	−	0.166881i	0.0413534	−	0.0122363i
$187$	0.476568	−	0.476568i	0.0348501	−	0.0348501i
$188$	−1.21445	+	1.21445i	−0.0885729	+	0.0885729i
$189$	−3.37810	+	3.94822i	−0.245721	+	0.287191i
$190$		0			0
$191$			17.7849i			1.28687i	0.765501	+	0.643435i	$0.222491\pi$
$191$			17.7849i			1.28687i	−0.765501	+	0.643435i	$0.777509\pi$
$192$	−7.50253	−	4.07639i	−0.541449	−	0.294188i
$193$	−14.3394	−	14.3394i	−1.03217	−	1.03217i	−0.999465	−	0.0327052i	$-0.989588\pi$
$193$	−14.3394	−	14.3394i	−1.03217	−	1.03217i	−0.0327052	−	0.999465i	$-0.510412\pi$
$194$	−3.49443			−0.250885
$195$		0			0
$196$	−1.86453			−0.133180
$197$	4.10678	+	4.10678i	0.292596	+	0.292596i	0.838105	−	0.545509i	$-0.183664\pi$
$197$	4.10678	+	4.10678i	0.292596	+	0.292596i	−0.545509	+	0.838105i	$0.683664\pi$
$198$	−3.65829	−	0.779834i	−0.259983	−	0.0554204i
$199$			13.4148i			0.950949i	0.879730	+	0.475474i	$0.157724\pi$
$199$			13.4148i			0.950949i	−0.879730	+	0.475474i	$0.842276\pi$
$200$		0			0
$201$	0.566776	+	1.91547i	0.0399773	+	0.135107i
$202$	−3.24088	+	3.24088i	−0.228027	+	0.228027i
$203$	6.71161	−	6.71161i	0.471063	−	0.471063i
$204$	−0.182307	−	0.616119i	−0.0127640	−	0.0431370i
$205$		0			0
$206$		−	5.09556i		−	0.355025i
$207$	9.18861	+	1.95873i	0.638653	+	0.136141i
$208$	5.11022	+	5.11022i	0.354330	+	0.354330i
$209$	−24.8876			−1.72151
$210$		0			0
$211$	8.11525			0.558677			0.279338	−	0.960193i	$-0.409885\pi$
$211$	8.11525			0.558677			0.279338	+	0.960193i	$0.409885\pi$
$212$	12.1960	+	12.1960i	0.837626	+	0.837626i
$213$	14.8790	+	8.08429i	1.01949	+	0.553926i
$214$			2.71645i			0.185693i
$215$		0			0
$216$	−4.80504	+	5.61598i	−0.326941	+	0.382119i
$217$	−0.652364	+	0.652364i	−0.0442854	+	0.0442854i
$218$	1.73768	−	1.73768i	0.117690	−	0.117690i
$219$	−11.2924	+	3.34136i	−0.763069	+	0.225788i
$220$		0			0
$221$			0.448558i			0.0301732i
$222$	−2.54623	+	4.68630i	−0.170892	+	0.314524i
$223$	11.5431	+	11.5431i	0.772984	+	0.772984i	0.978627	−	0.205643i	$-0.0659285\pi$
$223$	11.5431	+	11.5431i	0.772984	+	0.772984i	−0.205643	+	0.978627i	$0.565928\pi$
$224$	−4.02466			−0.268909
$225$		0			0
$226$	−4.28628			−0.285119
$227$	7.04578	+	7.04578i	0.467645	+	0.467645i	0.901151	−	0.433506i	$-0.142724\pi$
$227$	7.04578	+	7.04578i	0.467645	+	0.467645i	−0.433506	+	0.901151i	$0.642724\pi$
$228$	−11.3274	+	20.8479i	−0.750176	+	1.38069i
$229$			4.80117i			0.317270i	0.987337	+	0.158635i	$0.0507093\pi$
$229$			4.80117i			0.317270i	−0.987337	+	0.158635i	$0.949291\pi$
$230$		0			0
$231$	5.62619	−	1.66476i	0.370176	−	0.109533i
$232$	9.54665	−	9.54665i	0.626768	−	0.626768i
$233$	−14.2791	+	14.2791i	−0.935455	+	0.935455i	−0.998040	−	0.0625851i	$-0.980066\pi$
$233$	−14.2791	+	14.2791i	−0.935455	+	0.935455i	0.0625851	+	0.998040i	$0.480066\pi$
$234$	2.08864	−	1.35464i	0.136538	−	0.0885554i
$235$		0			0
$236$			11.6539i			0.758603i
$237$	−5.20055	−	2.82564i	−0.337812	−	0.183545i
$238$	−0.0517814	−	0.0517814i	−0.00335649	−	0.00335649i
$239$	12.8618			0.831961			0.415981	−	0.909373i	$-0.363438\pi$
$239$	12.8618			0.831961			0.415981	+	0.909373i	$0.363438\pi$
$240$		0			0
$241$	−16.1856			−1.04261			−0.521304	−	0.853371i	$-0.674554\pi$
$241$	−16.1856			−1.04261			−0.521304	+	0.853371i	$0.674554\pi$
$242$	0.123660	+	0.123660i	0.00794917	+	0.00794917i
$243$	−9.47153	−	12.3810i	−0.607599	−	0.794244i
$244$		−	3.41696i		−	0.218748i
$245$		0			0
$246$	−0.251892	−	0.851289i	−0.0160601	−	0.0542762i
$247$	11.7124	−	11.7124i	0.745243	−	0.745243i
$248$	−0.927928	+	0.927928i	−0.0589235	+	0.0589235i
$249$	4.35706	+	14.7250i	0.276117	+	0.933160i
$250$		0			0
$251$		−	8.02862i		−	0.506762i	−0.967367	−	0.253381i	$-0.918457\pi$
$251$		−	8.02862i		−	0.506762i	0.967367	−	0.253381i	$-0.0815426\pi$
$252$	1.16618	−	5.47066i	0.0734621	−	0.344619i
$253$	−7.50140	−	7.50140i	−0.471609	−	0.471609i
$254$	0.979525			0.0614609
$255$		0			0
$256$	6.22880			0.389300
$257$	16.6108	+	16.6108i	1.03615	+	1.03615i	0.999321	+	0.0368323i	$0.0117267\pi$
$257$	16.6108	+	16.6108i	1.03615	+	1.03615i	0.0368323	+	0.999321i	$0.488273\pi$
$258$	−0.684874	−	0.372116i	−0.0426384	−	0.0231669i
$259$		−	8.36589i		−	0.519831i
$260$		0			0
$261$	15.4946	+	23.8902i	0.959091	+	1.47877i
$262$	2.33477	−	2.33477i	0.144243	−	0.144243i
$263$	−13.8361	+	13.8361i	−0.853173	+	0.853173i	−0.990523	−	0.137350i	$-0.956142\pi$
$263$	−13.8361	+	13.8361i	−0.853173	+	0.853173i	0.137350	+	0.990523i	$0.456142\pi$
$264$	8.00273	−	2.36797i	0.492534	−	0.145738i
$265$		0			0
$266$			2.70416i			0.165803i
$267$	−10.2344	+	18.8362i	−0.626334	+	1.15276i
$268$	−1.52052	−	1.52052i	−0.0928806	−	0.0928806i
$269$	−11.4632			−0.698925			−0.349463	−	0.936950i	$-0.613636\pi$
$269$	−11.4632			−0.698925			−0.349463	+	0.936950i	$0.613636\pi$
$270$		0			0
$271$	8.42276			0.511646			0.255823	−	0.966724i	$-0.417654\pi$
$271$	8.42276			0.511646			0.255823	+	0.966724i	$0.417654\pi$
$272$	0.450965	+	0.450965i	0.0273438	+	0.0273438i
$273$	−1.86430	+	3.43121i	−0.112832	+	0.207666i
$274$		−	3.38102i		−	0.204255i
$275$		0			0
$276$	−9.69800	+	2.86959i	−0.583751	+	0.172729i
$277$	−12.7307	+	12.7307i	−0.764914	+	0.764914i	−0.977206	−	0.212293i	$-0.931907\pi$
$277$	−12.7307	+	12.7307i	−0.764914	+	0.764914i	0.212293	+	0.977206i	$0.431907\pi$
$278$	−0.478665	+	0.478665i	−0.0287084	+	0.0287084i
$279$	−1.50606	−	2.32211i	−0.0901656	−	0.139021i
$280$		0			0
$281$			4.41251i			0.263228i	0.991301	+	0.131614i	$0.0420160\pi$
$281$			4.41251i			0.263228i	−0.991301	+	0.131614i	$0.957984\pi$
$282$	−0.515994	−	0.280357i	−0.0307270	−	0.0166950i
$283$	−2.07246	−	2.07246i	−0.123195	−	0.123195i	0.642821	−	0.766016i	$-0.277764\pi$
$283$	−2.07246	−	2.07246i	−0.123195	−	0.123195i	−0.766016	+	0.642821i	$0.777764\pi$
$284$	−18.2286			−1.08167
$285$		0			0
$286$	−2.81102			−0.166219
$287$	0.984688	+	0.984688i	0.0581243	+	0.0581243i
$288$	2.51724	−	11.8087i	0.148330	−	0.695832i
$289$		−	16.9604i		−	0.997672i
$290$		0			0
$291$	4.66575	+	15.7683i	0.273511	+	0.924352i
$292$	8.96405	−	8.96405i	0.524581	−	0.524581i
$293$	−7.37595	+	7.37595i	−0.430908	+	0.430908i	−0.888937	−	0.458029i	$-0.848555\pi$
$293$	−7.37595	+	7.37595i	−0.430908	+	0.430908i	0.458029	+	0.888937i	$0.348555\pi$
$294$	−0.180884	−	0.611312i	−0.0105494	−	0.0356525i
$295$		0			0
$296$		−	11.8997i		−	0.691656i
$297$	1.36561	+	17.5489i	0.0792410	+	1.01829i
$298$	0.256939	+	0.256939i	0.0148841	+	0.0148841i
$299$	7.06050			0.408319
$300$		0			0
$301$	1.22262			0.0704709
$302$	2.26711	+	2.26711i	0.130458	+	0.130458i
$303$	18.9513	+	10.2969i	1.08873	+	0.591543i
$304$		−	23.5506i		−	1.35072i
$305$		0			0
$306$	0.184318	−	0.119544i	0.0105367	−	0.00683386i
$307$	−11.3608	+	11.3608i	−0.648396	+	0.648396i	−0.952605	−	0.304209i	$-0.901608\pi$
$307$	−11.3608	+	11.3608i	−0.648396	+	0.648396i	0.304209	+	0.952605i	$0.401608\pi$
$308$	−4.46614	+	4.46614i	−0.254482	+	0.254482i
$309$	−22.9932	+	6.80357i	−1.30804	+	0.387042i
$310$		0			0
$311$			8.94291i			0.507106i	0.967322	+	0.253553i	$0.0815992\pi$
$311$			8.94291i			0.507106i	−0.967322	+	0.253553i	$0.918401\pi$
$312$	−2.65179	+	4.88058i	−0.150128	+	0.276308i
$313$	−4.52473	−	4.52473i	−0.255753	−	0.255753i	0.567571	−	0.823324i	$-0.307883\pi$
$313$	−4.52473	−	4.52473i	−0.255753	−	0.255753i	−0.823324	+	0.567571i	$0.807883\pi$
$314$	2.73956			0.154602
$315$		0			0
$316$	6.37130			0.358414
$317$	1.78453	+	1.78453i	0.100229	+	0.100229i	0.755443	−	0.655214i	$-0.227422\pi$
$317$	1.78453	+	1.78453i	0.100229	+	0.100229i	−0.655214	+	0.755443i	$0.727422\pi$
$318$	−2.81546	+	5.18182i	−0.157883	+	0.290582i
$319$		−	32.1529i		−	1.80022i
$320$		0			0
$321$	12.2577	−	3.62699i	0.684158	−	0.202439i
$322$	−0.815063	+	0.815063i	−0.0454217	+	0.0454217i
$323$	1.03360	−	1.03360i	0.0575108	−	0.0575108i
$324$	15.3220	+	6.84330i	0.851220	+	0.380183i
$325$		0			0
$326$			7.36604i			0.407967i
$327$	−10.1612	−	5.52095i	−0.561917	−	0.305309i
$328$	1.40063	+	1.40063i	0.0773368	+	0.0773368i
$329$	0.921142			0.0507842
$330$		0			0
$331$	−3.61857			−0.198895			−0.0994474	−	0.995043i	$-0.531707\pi$
$331$	−3.61857			−0.198895			−0.0994474	+	0.995043i	$0.531707\pi$
$332$	−11.6889	−	11.6889i	−0.641512	−	0.641512i
$333$	24.5462	+	5.23248i	1.34512	+	0.286738i
$334$			9.10277i			0.498082i
$335$		0			0
$336$	1.57532	+	5.32393i	0.0859410	+	0.290444i
$337$	17.0941	−	17.0941i	0.931175	−	0.931175i	−0.0666042	−	0.997779i	$-0.521216\pi$
$337$	17.0941	−	17.0941i	0.931175	−	0.931175i	0.997779	+	0.0666042i	$0.0212165\pi$
$338$	−2.06052	+	2.06052i	−0.112078	+	0.112078i
$339$	5.72302	+	19.3414i	0.310832	+	1.05048i
$340$		0			0
$341$			3.12524i			0.169241i
$342$	−7.93421	−	1.69133i	−0.429033	−	0.0914565i
$343$	0.707107	+	0.707107i	0.0381802	+	0.0381802i
$344$	1.73907			0.0937644
$345$		0			0
$346$	5.66162			0.304371
$347$	−5.48573	−	5.48573i	−0.294489	−	0.294489i	0.544361	−	0.838851i	$-0.316772\pi$
$347$	−5.48573	−	5.48573i	−0.294489	−	0.294489i	−0.838851	+	0.544361i	$0.816772\pi$
$348$	−26.9340	−	14.6342i	−1.44381	−	0.784474i
$349$			14.8272i			0.793681i	0.917888	+	0.396841i	$0.129893\pi$
$349$			14.8272i			0.793681i	−0.917888	+	0.396841i	$0.870107\pi$
$350$		0			0
$351$	−8.90140	−	7.61605i	−0.475122	−	0.406515i
$352$	−9.64036	+	9.64036i	−0.513833	+	0.513833i
$353$	−7.55570	+	7.55570i	−0.402149	+	0.402149i	−0.878990	−	0.476841i	$-0.841782\pi$
$353$	−7.55570	+	7.55570i	−0.402149	+	0.402149i	0.476841	+	0.878990i	$0.341782\pi$
$354$	−3.82089	+	1.13058i	−0.203078	+	0.0600898i
$355$		0			0
$356$		−	23.0766i		−	1.22306i
$357$	−0.164520	+	0.302797i	−0.00870732	+	0.0160257i
$358$	−4.59428	−	4.59428i	−0.242815	−	0.242815i
$359$	−6.09504			−0.321684			−0.160842	−	0.986980i	$-0.551421\pi$
$359$	−6.09504			−0.321684			−0.160842	+	0.986980i	$0.551421\pi$
$360$		0			0
$361$	−34.9770			−1.84090
$362$	3.10330	+	3.10330i	0.163106	+	0.163106i
$363$	0.392893	−	0.723114i	0.0206215	−	0.0379536i
$364$		−	4.20364i		−	0.220331i
$365$		0			0
$366$	1.12030	−	0.331491i	0.0585590	−	0.0173273i
$367$	−3.52753	+	3.52753i	−0.184136	+	0.184136i	−0.793155	−	0.609019i	$-0.791563\pi$
$367$	−3.52753	+	3.52753i	−0.184136	+	0.184136i	0.609019	+	0.793155i	$0.291563\pi$
$368$	7.09840	−	7.09840i	0.370030	−	0.370030i
$369$	−3.50503	+	2.27327i	−0.182465	+	0.118342i
$370$		0			0
$371$		−	9.25048i		−	0.480261i
$372$	2.61796	+	1.42243i	0.135735	+	0.0737496i
$373$	7.07089	+	7.07089i	0.366117	+	0.366117i	0.866059	−	0.499942i	$-0.166645\pi$
$373$	7.07089	+	7.07089i	0.366117	+	0.366117i	−0.499942	+	0.866059i	$0.666645\pi$
$374$	−0.248066			−0.0128272
$375$		0			0
$376$	1.31024			0.0675704
$377$	15.1316	+	15.1316i	0.779315	+	0.779315i
$378$	1.90677	−	0.148381i	0.0980738	−	0.00763187i
$379$			21.4715i			1.10292i	0.834202	+	0.551459i	$0.185929\pi$
$379$			21.4715i			1.10292i	−0.834202	+	0.551459i	$0.814071\pi$
$380$		0			0
$381$	−1.30786	−	4.42001i	−0.0670036	−	0.226444i
$382$	4.62875	−	4.62875i	0.236828	−	0.236828i
$383$	14.6559	−	14.6559i	0.748882	−	0.748882i	−0.225388	−	0.974269i	$-0.572365\pi$
$383$	14.6559	−	14.6559i	0.748882	−	0.748882i	0.974269	+	0.225388i	$0.0723648\pi$
$384$	4.84748	+	16.3824i	0.247372	+	0.836012i
$385$		0			0
$386$			7.46402i			0.379909i
$387$	−0.764695	+	3.58727i	−0.0388716	+	0.182351i
$388$	−12.5170	−	12.5170i	−0.635457	−	0.635457i
$389$	13.6323			0.691185			0.345592	−	0.938385i	$-0.387678\pi$
$389$	13.6323			0.691185			0.345592	+	0.938385i	$0.387678\pi$
$390$		0			0
$391$	0.623074			0.0315102
$392$	1.00579	+	1.00579i	0.0508003	+	0.0508003i
$393$	−13.6528	−	7.41804i	−0.688692	−	0.374190i
$394$		−	2.13769i		−	0.107695i
$395$		0			0
$396$	−10.3106	−	15.8974i	−0.518129	−	0.798873i
$397$	24.5632	−	24.5632i	1.23279	−	1.23279i	0.269907	−	0.962886i	$-0.413007\pi$
$397$	24.5632	−	24.5632i	1.23279	−	1.23279i	0.962886	−	0.269907i	$-0.0869929\pi$
$398$	3.49137	−	3.49137i	0.175007	−	0.175007i
$399$	12.2022	−	3.61058i	0.610876	−	0.180755i
$400$		0			0
$401$		−	15.5011i		−	0.774088i	−0.922061	−	0.387044i	$-0.873496\pi$
$401$		−	15.5011i		−	0.774088i	0.922061	−	0.387044i	$-0.126504\pi$
$402$	0.351014	−	0.646036i	0.0175070	−	0.0322214i
$403$	−1.47078	−	1.47078i	−0.0732647	−	0.0732647i
$404$	−23.2177			−1.15512
$405$		0			0
$406$	−3.49357			−0.173383
$407$	−20.0390	−	20.0390i	−0.993296	−	0.993296i
$408$	−0.234015	+	0.430700i	−0.0115854	+	0.0213228i
$409$		−	32.0414i		−	1.58434i	−0.610298	−	0.792172i	$-0.708950\pi$
$409$		−	32.0414i		−	1.58434i	0.610298	−	0.792172i	$-0.291050\pi$
$410$		0			0
$411$	−15.2565	+	4.51432i	−0.752547	+	0.222675i
$412$	18.2523	−	18.2523i	0.899226	−	0.899226i
$413$	4.41964	−	4.41964i	0.217476	−	0.217476i
$414$	−1.88167	−	2.90124i	−0.0924792	−	0.142588i
$415$		0			0
$416$		−	9.07374i		−	0.444877i
$417$	2.79904	+	1.52081i	0.137069	+	0.0744746i
$418$	6.47733	+	6.47733i	0.316817	+	0.316817i
$419$	−5.95062			−0.290707			−0.145353	−	0.989380i	$-0.546432\pi$
$419$	−5.95062			−0.290707			−0.145353	+	0.989380i	$0.546432\pi$
$420$		0			0
$421$	−10.6388			−0.518504			−0.259252	−	0.965810i	$-0.583476\pi$
$421$	−10.6388			−0.518504			−0.259252	+	0.965810i	$0.583476\pi$
$422$	−2.11210	−	2.11210i	−0.102816	−	0.102816i
$423$	−0.576132	+	2.70270i	−0.0280125	+	0.131410i
$424$		−	13.1580i		−	0.639007i
$425$		0			0
$426$	−1.76842	−	5.97650i	−0.0856801	−	0.289563i
$427$	−1.29585	+	1.29585i	−0.0627108	+	0.0627108i
$428$	−9.73032	+	9.73032i	−0.470333	+	0.470333i
$429$	3.75326	+	12.6844i	0.181209	+	0.612410i
$430$		0			0
$431$		−	11.2739i		−	0.543045i	−0.962432	−	0.271523i	$-0.912473\pi$
$431$		−	11.2739i		−	0.543045i	0.962432	−	0.271523i	$-0.0875271\pi$
$432$	−16.6061	+	1.29225i	−0.798962	+	0.0621733i
$433$	−9.75098	−	9.75098i	−0.468602	−	0.468602i	0.432859	−	0.901462i	$-0.357505\pi$
$433$	−9.75098	−	9.75098i	−0.468602	−	0.468602i	−0.901462	+	0.432859i	$0.857505\pi$
$434$	0.339573			0.0163000
$435$		0			0
$436$	12.4487			0.596185
$437$	−16.2693	−	16.2693i	−0.778265	−	0.778265i
$438$	3.80863	+	2.06936i	0.181983	+	0.0988779i
$439$			28.4375i			1.35725i	0.734485	+	0.678625i	$0.237424\pi$
$439$			28.4375i			1.35725i	−0.734485	+	0.678625i	$0.762576\pi$
$440$		0			0
$441$	−2.51697	+	1.63244i	−0.119856	+	0.0777354i
$442$	0.116743	−	0.116743i	0.00555290	−	0.00555290i
$443$	19.2121	−	19.2121i	0.912796	−	0.912796i	−0.0836955	−	0.996491i	$-0.526672\pi$
$443$	19.2121	−	19.2121i	0.912796	−	0.912796i	0.996491	+	0.0836955i	$0.0266723\pi$
$444$	−25.9069	+	7.66573i	−1.22949	+	0.363799i
$445$		0			0
$446$		−	6.00850i		−	0.284511i
$447$	0.816347	−	1.50247i	0.0386119	−	0.0710646i
$448$	−3.48580	−	3.48580i	−0.164689	−	0.164689i
$449$	−2.40628			−0.113559			−0.0567796	−	0.998387i	$-0.518083\pi$
$449$	−2.40628			−0.113559			−0.0567796	+	0.998387i	$0.518083\pi$
$450$		0			0
$451$	4.71729			0.222129
$452$	−15.3534	−	15.3534i	−0.722166	−	0.722166i
$453$	7.20307	−	13.2572i	0.338430	−	0.622875i
$454$		−	3.66752i		−	0.172125i
$455$		0			0
$456$	17.3566	−	5.13572i	0.812796	−	0.240502i
$457$	−6.21588	+	6.21588i	−0.290767	+	0.290767i	−0.837383	−	0.546617i	$-0.815916\pi$
$457$	−6.21588	+	6.21588i	−0.290767	+	0.290767i	0.546617	+	0.837383i	$0.315916\pi$
$458$	1.24957	−	1.24957i	0.0583884	−	0.0583884i
$459$	−0.785529	−	0.672100i	−0.0366654	−	0.0313709i
$460$		0			0
$461$			35.4227i			1.64980i	0.565278	+	0.824900i	$0.308769\pi$
$461$			35.4227i			1.64980i	−0.565278	+	0.824900i	$0.691231\pi$
$462$	−1.89757	−	1.03101i	−0.0882827	−	0.0479671i
$463$	20.0869	+	20.0869i	0.933519	+	0.933519i	0.997924	−	0.0644045i	$-0.0205148\pi$
$463$	20.0869	+	20.0869i	0.933519	+	0.933519i	−0.0644045	+	0.997924i	$0.520515\pi$
$464$	30.4256			1.41247
$465$		0			0
$466$	7.43265			0.344311
$467$	5.80567	+	5.80567i	0.268654	+	0.268654i	0.828558	−	0.559903i	$-0.189162\pi$
$467$	5.80567	+	5.80567i	0.268654	+	0.268654i	−0.559903	+	0.828558i	$0.689162\pi$
$468$	12.3338	+	2.62918i	0.570130	+	0.121534i
$469$			1.15329i			0.0532540i
$470$		0			0
$471$	−3.65785	−	12.3620i	−0.168545	−	0.569610i
$472$	6.28653	−	6.28653i	0.289361	−	0.289361i
$473$	2.92858	−	2.92858i	0.134656	−	0.134656i
$474$	0.618102	+	2.08892i	0.0283904	+	0.0959475i
$475$		0			0
$476$		−	0.370962i		−	0.0170030i
$477$	27.1416	+	5.78575i	1.24273	+	0.264911i
$478$	−3.34746	−	3.34746i	−0.153109	−	0.153109i
$479$	40.3829			1.84514			0.922571	−	0.385828i	$-0.126084\pi$
$479$	40.3829			1.84514			0.922571	+	0.385828i	$0.126084\pi$
$480$		0			0
$481$	18.8612			0.859997
$482$	4.21252	+	4.21252i	0.191875	+	0.191875i
$483$	4.76616	+	2.58962i	0.216868	+	0.117832i
$484$			0.885900i			0.0402682i
$485$		0			0
$486$	−0.757238	+	5.68742i	−0.0343490	+	0.257987i
$487$	−19.7983	+	19.7983i	−0.897147	+	0.897147i	−0.995183	−	0.0980363i	$-0.968744\pi$
$487$	−19.7983	+	19.7983i	−0.897147	+	0.897147i	0.0980363	+	0.995183i	$0.468744\pi$
$488$	−1.84323	+	1.84323i	−0.0834393	+	0.0834393i
$489$	33.2385	−	9.83510i	1.50310	−	0.444759i
$490$		0			0
$491$			36.6924i			1.65590i	0.560798	+	0.827952i	$0.310494\pi$
$491$			36.6924i			1.65590i	−0.560798	+	0.827952i	$0.689506\pi$
$492$	2.14704	−	3.95159i	0.0967960	−	0.178152i
$493$	1.33533	+	1.33533i	0.0601402	+	0.0601402i
$494$	−6.09662			−0.274300
$495$		0			0
$496$	−2.95735			−0.132789
$497$	6.91304	+	6.91304i	0.310092	+	0.310092i
$498$	2.69840	−	4.96636i	0.120918	−	0.222548i
$499$		−	7.62548i		−	0.341363i	−0.985326	−	0.170682i	$-0.945403\pi$
$499$		−	7.62548i		−	0.341363i	0.985326	−	0.170682i	$-0.0545970\pi$
$500$		0			0
$501$	41.0753	−	12.1540i	1.83511	−	0.543000i
$502$	−2.08955	+	2.08955i	−0.0932614	+	0.0932614i
$503$	15.7533	−	15.7533i	0.702406	−	0.702406i	−0.262521	−	0.964926i	$-0.584554\pi$
$503$	15.7533	−	15.7533i	0.702406	−	0.702406i	0.964926	+	0.262521i	$0.0845538\pi$
$504$	−3.58016	+	2.32200i	−0.159473	+	0.103430i
$505$		0			0
$506$			3.90468i			0.173584i
$507$	12.0491	+	6.54670i	0.535119	+	0.290749i
$508$	3.50866	+	3.50866i	0.155672	+	0.155672i
$509$	14.4091			0.638673			0.319336	−	0.947641i	$-0.396540\pi$
$509$	14.4091			0.638673			0.319336	+	0.947641i	$0.396540\pi$
$510$		0			0
$511$	−6.79909			−0.300774
$512$	−15.5706	−	15.5706i	−0.688130	−	0.688130i
$513$	2.96178	+	38.0606i	0.130766	+	1.68042i
$514$		−	8.64637i		−	0.381375i
$515$		0			0
$516$	−1.12030	−	3.78614i	−0.0493185	−	0.166676i
$517$	2.20643	−	2.20643i	0.0970387	−	0.0970387i
$518$	−2.17733	+	2.17733i	−0.0956666	+	0.0956666i
$519$	−7.55938	−	25.5475i	−0.331820	−	1.12141i
$520$		0			0
$521$			25.3850i			1.11214i	0.831136	+	0.556069i	$0.187691\pi$
$521$			25.3850i			1.11214i	−0.831136	+	0.556069i	$0.812309\pi$
$522$	2.18507	−	10.2504i	0.0956378	−	0.448648i
$523$	16.0464	+	16.0464i	0.701661	+	0.701661i	0.964767	−	0.263106i	$-0.0847470\pi$
$523$	16.0464	+	16.0464i	0.701661	+	0.701661i	−0.263106	+	0.964767i	$0.584747\pi$
$524$	16.7263			0.730692
$525$		0			0
$526$	7.20208			0.314026
$527$	−0.129793	−	0.129793i	−0.00565387	−	0.00565387i
$528$	16.5259	+	8.97912i	0.719199	+	0.390766i
$529$			13.1925i			0.573588i
$530$		0			0
$531$	10.2033	+	15.7318i	0.442785	+	0.682704i
$532$	−9.68630	+	9.68630i	−0.419954	+	0.419954i
$533$	−2.22002	+	2.22002i	−0.0961595	+	0.0961595i
$534$	7.56601	−	2.23874i	0.327413	−	0.0968799i
$535$		0			0
$536$			1.64045i			0.0708567i
$537$	−14.5970	+	26.8655i	−0.629905	+	1.15933i
$538$	2.98346	+	2.98346i	0.128626	+	0.128626i
$539$	3.38750			0.145910
$540$		0			0
$541$	−26.9427			−1.15836			−0.579178	−	0.815201i	$-0.696626\pi$
$541$	−26.9427			−1.15836			−0.579178	+	0.815201i	$0.696626\pi$
$542$	−2.19213	−	2.19213i	−0.0941602	−	0.0941602i
$543$	9.85981	−	18.1468i	0.423125	−	0.778756i
$544$		−	0.800738i		−	0.0343313i
$545$		0			0
$546$	1.37823	−	0.407810i	0.0589826	−	0.0174527i
$547$	−17.9286	+	17.9286i	−0.766572	+	0.766572i	−0.977501	−	0.210929i	$-0.932351\pi$
$547$	−17.9286	+	17.9286i	−0.766572	+	0.766572i	0.210929	+	0.977501i	$0.432351\pi$
$548$	12.1108	−	12.1108i	0.517348	−	0.517348i
$549$	−2.99164	−	4.61263i	−0.127680	−	0.196862i
$550$		0			0
$551$		−	69.7343i		−	2.97078i
$552$	6.77942	+	3.68350i	0.288551	+	0.156780i
$553$	−2.41627	−	2.41627i	−0.102750	−	0.102750i
$554$	6.62667			0.281540
$555$		0			0
$556$	−3.42915			−0.145428
$557$	5.15944	+	5.15944i	0.218613	+	0.218613i	0.807914	−	0.589301i	$-0.200597\pi$
$557$	5.15944	+	5.15944i	0.218613	+	0.218613i	−0.589301	+	0.807914i	$0.700597\pi$
$558$	−0.212387	+	0.996333i	−0.00899106	+	0.0421781i
$559$			2.75645i			0.116585i
$560$		0			0
$561$	0.331217	+	1.11937i	0.0139840	+	0.0472600i
$562$	1.14841	−	1.14841i	0.0484429	−	0.0484429i
$563$	23.2548	−	23.2548i	0.980072	−	0.980072i	−0.0197332	−	0.999805i	$-0.506282\pi$
$563$	23.2548	−	23.2548i	0.980072	−	0.980072i	0.999805	+	0.0197332i	$0.00628169\pi$
$564$	−0.844049	−	2.85253i	−0.0355409	−	0.120113i
$565$		0			0
$566$			1.07877i			0.0453442i
$567$	−3.21547	−	8.40600i	−0.135037	−	0.353019i
$568$	9.83316	+	9.83316i	0.412590	+	0.412590i
$569$	−45.1914			−1.89452			−0.947260	−	0.320466i	$-0.896161\pi$
$569$	−45.1914			−1.89452			−0.947260	+	0.320466i	$0.896161\pi$
$570$		0			0
$571$	15.2468			0.638059			0.319029	−	0.947745i	$-0.396643\pi$
$571$	15.2468			0.638059			0.319029	+	0.947745i	$0.396643\pi$
$572$	−10.0691	−	10.0691i	−0.421009	−	0.421009i
$573$	−27.0671	−	14.7065i	−1.13074	−	0.614372i
$574$		−	0.512556i		−	0.0213937i
$575$		0			0
$576$	12.4078	−	8.04741i	0.516993	−	0.335309i
$577$	6.12177	−	6.12177i	0.254853	−	0.254853i	−0.568104	−	0.822957i	$-0.692323\pi$
$577$	6.12177	−	6.12177i	0.254853	−	0.254853i	0.822957	+	0.568104i	$0.192323\pi$
$578$	−4.41417	+	4.41417i	−0.183605	+	0.183605i
$579$	33.6806	−	9.96593i	1.39972	−	0.414170i
$580$		0			0
$581$			8.86586i			0.367818i
$582$	2.88958	−	5.31822i	0.119777	−	0.220447i
$583$	−22.1579	−	22.1579i	−0.917686	−	0.917686i
$584$	−9.67107			−0.400192
$585$		0			0
$586$	3.83938			0.158603
$587$	3.77086	+	3.77086i	0.155640	+	0.155640i	0.780632	−	0.624992i	$-0.214898\pi$
$587$	3.77086	+	3.77086i	0.155640	+	0.155640i	−0.624992	+	0.780632i	$0.714898\pi$
$588$	1.54179	−	2.83765i	0.0635825	−	0.117023i
$589$			6.77812i			0.279288i
$590$		0			0
$591$	−9.64610	+	2.85423i	−0.396787	+	0.117407i
$592$	18.9624	−	18.9624i	0.779352	−	0.779352i
$593$	8.38017	−	8.38017i	0.344132	−	0.344132i	−0.513786	−	0.857918i	$-0.671758\pi$
$593$	8.38017	−	8.38017i	0.344132	−	0.344132i	0.857918	+	0.513786i	$0.171758\pi$
$594$	4.21191	−	4.92275i	0.172817	−	0.201983i
$595$		0			0
$596$			1.84071i			0.0753985i
$597$	−20.4161	−	11.0928i	−0.835577	−	0.453998i
$598$	−1.83759	−	1.83759i	−0.0751446	−	0.0751446i
$599$	−6.75588			−0.276038			−0.138019	−	0.990430i	$-0.544073\pi$
$599$	−6.75588			−0.276038			−0.138019	+	0.990430i	$0.544073\pi$
$600$		0			0
$601$	21.2564			0.867068			0.433534	−	0.901137i	$-0.357266\pi$
$601$	21.2564			0.867068			0.433534	+	0.901137i	$0.357266\pi$
$602$	−0.318204	−	0.318204i	−0.0129690	−	0.0129690i
$603$	−3.38385	−	0.721331i	−0.137801	−	0.0293749i
$604$			16.2416i			0.660861i
$605$		0			0
$606$	−2.25243	−	7.61225i	−0.0914986	−	0.309227i
$607$	−2.72491	+	2.72491i	−0.110601	+	0.110601i	−0.760241	−	0.649641i	$-0.774919\pi$
$607$	−2.72491	+	2.72491i	−0.110601	+	0.110601i	0.649641	+	0.760241i	$0.274919\pi$
$608$	−20.9083	+	20.9083i	−0.847944	+	0.847944i
$609$	4.66460	+	15.7644i	0.189019	+	0.638805i
$610$		0			0
$611$			2.07675i			0.0840162i
$612$	1.08843	+	0.232020i	0.0439972	+	0.00937884i
$613$	−15.6232	−	15.6232i	−0.631017	−	0.631017i	0.317306	−	0.948323i	$-0.397222\pi$
$613$	−15.6232	−	15.6232i	−0.631017	−	0.631017i	−0.948323	+	0.317306i	$0.897222\pi$
$614$	5.91361			0.238654
$615$		0			0
$616$	4.81840			0.194139
$617$	−5.47009	−	5.47009i	−0.220218	−	0.220218i	0.588373	−	0.808590i	$-0.299769\pi$
$617$	−5.47009	−	5.47009i	−0.220218	−	0.220218i	−0.808590	+	0.588373i	$0.799769\pi$
$618$	7.75500	+	4.21357i	0.311952	+	0.169494i
$619$			42.9951i			1.72812i	0.503389	+	0.864060i	$0.332086\pi$
$619$			42.9951i			1.72812i	−0.503389	+	0.864060i	$0.667914\pi$
$620$		0			0
$621$	−10.5792	+	12.3646i	−0.424527	+	0.496174i
$622$	2.32751	−	2.32751i	0.0933247	−	0.0933247i
$623$	−8.75163	+	8.75163i	−0.350627	+	0.350627i
$624$	−12.0030	+	3.55162i	−0.480504	+	0.142179i
$625$		0			0
$626$			2.35524i			0.0941344i
$627$	20.5798	−	37.8768i	0.821878	−	1.51265i
$628$	9.81311	+	9.81311i	0.391586	+	0.391586i
$629$	1.66446			0.0663664
$630$		0			0
$631$	−38.0091			−1.51312			−0.756560	−	0.653925i	$-0.773121\pi$
$631$	−38.0091			−1.51312			−0.756560	+	0.653925i	$0.773121\pi$
$632$	−3.43691	−	3.43691i	−0.136713	−	0.136713i
$633$	−6.71057	+	12.3507i	−0.266721	+	0.490897i
$634$		−	0.928896i		−	0.0368912i
$635$		0			0
$636$	−28.6463	+	8.47629i	−1.13590	+	0.336107i
$637$	−1.59420	+	1.59420i	−0.0631644	+	0.0631644i
$638$	−8.36823	+	8.36823i	−0.331301	+	0.331301i
$639$	−24.6072	+	15.9596i	−0.973445	+	0.631352i
$640$		0			0
$641$		−	30.8009i		−	1.21656i	−0.793721	−	0.608282i	$-0.791859\pi$
$641$		−	30.8009i		−	1.21656i	0.793721	−	0.608282i	$-0.208141\pi$
$642$	−4.13420	−	2.24626i	−0.163164	−	0.0886527i
$643$	6.17366	+	6.17366i	0.243465	+	0.243465i	0.818282	−	0.574817i	$-0.194927\pi$
$643$	6.17366	+	6.17366i	0.243465	+	0.243465i	−0.574817	+	0.818282i	$0.694927\pi$
$644$	−5.83911			−0.230093
$645$		0			0
$646$	−0.538014			−0.0211679
$647$	23.4296	+	23.4296i	0.921112	+	0.921112i	0.997108	−	0.0759964i	$-0.0242137\pi$
$647$	23.4296	+	23.4296i	0.921112	+	0.921112i	−0.0759964	+	0.997108i	$0.524214\pi$
$648$	−4.57370	−	11.9568i	−0.179672	−	0.469706i
$649$		−	21.1729i		−	0.831110i
$650$		0			0
$651$	−0.453396	−	1.53229i	−0.0177700	−	0.0600551i
$652$	−26.3851	+	26.3851i	−1.03332	+	1.03332i
$653$	−17.1928	+	17.1928i	−0.672805	+	0.672805i	−0.958362	−	0.285557i	$-0.907821\pi$
$653$	−17.1928	+	17.1928i	−0.672805	+	0.672805i	0.285557	+	0.958362i	$0.407821\pi$
$654$	1.20769	+	4.08150i	0.0472246	+	0.159599i
$655$		0			0
$656$			4.46386i			0.174285i
$657$	4.25252	−	19.9490i	0.165906	−	0.778286i
$658$	−0.239739	−	0.239739i	−0.00934601	−	0.00934601i
$659$	0.0375362			0.00146220			0.000731101	−	1.00000i	$-0.499767\pi$
$659$	0.0375362			0.00146220			0.000731101		1.00000i	$0.499767\pi$
$660$		0			0
$661$	19.6937			0.765995			0.382998	−	0.923749i	$-0.374892\pi$
$661$	19.6937			0.765995			0.382998	+	0.923749i	$0.374892\pi$
$662$	0.941782	+	0.941782i	0.0366034	+	0.0366034i
$663$	−0.682666	−	0.370916i	−0.0265125	−	0.0144052i
$664$			12.6109i			0.489396i
$665$		0			0
$666$	−5.02664	−	7.75029i	−0.194778	−	0.300318i
$667$	21.0187	−	21.0187i	0.813846	−	0.813846i
$668$	−32.6061	+	32.6061i	−1.26157	+	1.26157i
$669$	−27.1127	+	8.02252i	−1.04824	+	0.310169i
$670$		0			0
$671$			6.20798i			0.239656i
$672$	3.32803	−	6.12519i	0.128381	−	0.236284i
$673$	4.33276	+	4.33276i	0.167016	+	0.167016i	0.785666	−	0.618651i	$-0.212320\pi$
$673$	4.33276	+	4.33276i	0.167016	+	0.167016i	−0.618651	+	0.785666i	$0.712320\pi$
$674$	−8.89793			−0.342736
$675$		0			0
$676$	−14.7616			−0.567753
$677$	−3.64637	−	3.64637i	−0.140142	−	0.140142i	0.633556	−	0.773697i	$-0.281595\pi$
$677$	−3.64637	−	3.64637i	−0.140142	−	0.140142i	−0.773697	+	0.633556i	$0.781595\pi$
$678$	3.54436	−	6.52335i	0.136120	−	0.250528i
$679$			9.49398i			0.364346i
$680$		0			0
$681$	−16.5493	+	4.89685i	−0.634170	+	0.187648i
$682$	0.813386	−	0.813386i	0.0311462	−	0.0311462i
$683$	33.7536	−	33.7536i	1.29155	−	1.29155i	0.357718	−	0.933830i	$-0.383555\pi$
$683$	33.7536	−	33.7536i	1.29155	−	1.29155i	0.933830	−	0.357718i	$-0.116445\pi$
$684$	−22.3620	−	34.4787i	−0.855033	−	1.31833i
$685$		0			0
$686$		−	0.368068i		−	0.0140529i
$687$	−7.30696	−	3.97013i	−0.278778	−	0.151470i
$688$	2.77125	+	2.77125i	0.105653	+	0.105653i
$689$	20.8555			0.794533
$690$		0			0
$691$	−12.2184			−0.464812			−0.232406	−	0.972619i	$-0.574660\pi$
$691$	−12.2184			−0.464812			−0.232406	+	0.972619i	$0.574660\pi$
$692$	20.2799	+	20.2799i	0.770928	+	0.770928i
$693$	−2.11872	+	9.93918i	−0.0804836	+	0.377558i
$694$			2.85547i			0.108392i
$695$		0			0
$696$	6.63497	+	22.4234i	0.251498	+	0.849956i
$697$	−0.195912	+	0.195912i	−0.00742068	+	0.00742068i
$698$	3.85897	−	3.85897i	0.146064	−	0.146064i
$699$	−9.92404	−	33.5391i	−0.375362	−	1.26856i
$700$		0			0
$701$		−	21.7907i		−	0.823024i	−0.911404	−	0.411512i	$-0.865001\pi$
$701$		−	21.7907i		−	0.823024i	0.911404	−	0.411512i	$-0.134999\pi$
$702$	0.334529	+	4.29889i	0.0126260	+	0.162251i
$703$	−43.4612	−	43.4612i	−1.63917	−	1.63917i
$704$	−16.6992			−0.629377
$705$		0			0
$706$	3.93294			0.148018
$707$	8.80511	+	8.80511i	0.331150	+	0.331150i
$708$	−17.7362	−	9.63670i	−0.666567	−	0.362169i
$709$		−	14.1622i		−	0.531874i	−0.963990	−	0.265937i	$-0.914319\pi$
$709$		−	14.1622i		−	0.531874i	0.963990	−	0.265937i	$-0.0856814\pi$
$710$		0			0
$711$	8.60077	−	5.57825i	0.322554	−	0.209201i
$712$	−12.4484	+	12.4484i	−0.466523	+	0.466523i
$713$	−2.04300	+	2.04300i	−0.0765110	+	0.0765110i
$714$	0.121625	−	0.0359883i	0.00455172	−	0.00134683i
$715$		0			0
$716$		−	32.9134i		−	1.23003i
$717$	−10.6355	+	19.5746i	−0.397192	+	0.731026i
$718$	1.58632	+	1.58632i	0.0592008	+	0.0592008i
$719$	−39.3153			−1.46621			−0.733106	−	0.680114i	$-0.761930\pi$
$719$	−39.3153			−1.46621			−0.733106	+	0.680114i	$0.761930\pi$
$720$		0			0
$721$	−13.8441			−0.515581
$722$	9.10324	+	9.10324i	0.338787	+	0.338787i
$723$	13.3840	−	24.6331i	0.497757	−	0.916115i
$724$			22.2320i			0.826248i
$725$		0			0
$726$	−0.290455	+	0.0859443i	−0.0107798	+	0.00318969i
$727$	−10.0141	+	10.0141i	−0.371403	+	0.371403i	−0.867988	−	0.496585i	$-0.834587\pi$
$727$	−10.0141	+	10.0141i	−0.371403	+	0.371403i	0.496585	+	0.867988i	$0.334587\pi$
$728$	−2.26760	+	2.26760i	−0.0840428	+	0.0840428i
$729$	26.6750	−	4.17686i	0.987962	−	0.154699i
$730$		0			0
$731$			0.243251i			0.00899695i
$732$	5.20032	+	2.82551i	0.192209	+	0.104434i
$733$	30.5737	+	30.5737i	1.12926	+	1.12926i	0.990297	+	0.138967i	$0.0443783\pi$
$733$	30.5737	+	30.5737i	1.12926	+	1.12926i	0.138967	+	0.990297i	$0.455622\pi$
$734$	1.83618			0.0677745
$735$		0			0
$736$	−12.6040			−0.464589
$737$	2.76250	+	2.76250i	0.101758	+	0.101758i
$738$	1.50388	+	0.320580i	0.0553586	+	0.0118007i
$739$			16.1095i			0.592598i	0.955095	+	0.296299i	$0.0957525\pi$
$739$			16.1095i			0.592598i	−0.955095	+	0.296299i	$0.904247\pi$
$740$		0			0
$741$	8.14019	+	27.5104i	0.299037	+	1.01062i
$742$	−2.40756	+	2.40756i	−0.0883844	+	0.0883844i
$743$	−23.1679	+	23.1679i	−0.849946	+	0.849946i	−0.990126	−	0.140180i	$-0.955232\pi$
$743$	−23.1679	+	23.1679i	−0.849946	+	0.849946i	0.140180	+	0.990126i	$0.455232\pi$
$744$	−0.644914	−	2.17954i	−0.0236437	−	0.0799057i
$745$		0			0
$746$		−	3.68059i		−	0.134756i
$747$	−26.0131	−	5.54518i	−0.951770	−	0.202888i
$748$	−0.888574	−	0.888574i	−0.0324895	−	0.0324895i
$749$	7.38030			0.269670
$750$		0			0
$751$	28.7540			1.04925			0.524625	−	0.851334i	$-0.324206\pi$
$751$	28.7540			1.04925			0.524625	+	0.851334i	$0.324206\pi$
$752$	2.08789	+	2.08789i	0.0761377	+	0.0761377i
$753$	12.2189	+	6.63894i	0.445280	+	0.241936i
$754$		−	7.87638i		−	0.286841i
$755$		0			0
$756$	7.36156	+	6.29856i	0.267737	+	0.229076i
$757$	1.29026	−	1.29026i	0.0468952	−	0.0468952i	−0.683270	−	0.730166i	$-0.739443\pi$
$757$	1.29026	−	1.29026i	0.0468952	−	0.0468952i	0.730166	+	0.683270i	$0.239443\pi$
$758$	5.58825	−	5.58825i	0.202974	−	0.202974i
$759$	17.6195	−	5.21351i	0.639546	−	0.189238i
$760$		0			0
$761$			33.9969i			1.23239i	0.787596	+	0.616193i	$0.211326\pi$
$761$			33.9969i			1.23239i	−0.787596	+	0.616193i	$0.788674\pi$
$762$	−0.809978	+	1.49075i	−0.0293424	+	0.0540043i
$763$	−4.72108	−	4.72108i	−0.170915	−	0.170915i
$764$	33.1604			1.19970
$765$		0			0
$766$	−7.62879			−0.275639
$767$	9.96424	+	9.96424i	0.359788	+	0.359788i
$768$	−5.15065	+	9.47970i	−0.185858	+	0.342069i
$769$		−	21.4206i		−	0.772448i	−0.922405	−	0.386224i	$-0.873779\pi$
$769$		−	21.4206i		−	0.772448i	0.922405	−	0.386224i	$-0.126221\pi$
$770$		0			0
$771$	−39.0158	+	11.5446i	−1.40512	+	0.415768i
$772$	−26.7361	+	26.7361i	−0.962254	+	0.962254i
$773$	−9.50533	+	9.50533i	−0.341883	+	0.341883i	−0.857075	−	0.515192i	$-0.827721\pi$
$773$	−9.50533	+	9.50533i	−0.341883	+	0.341883i	0.515192	+	0.857075i	$0.327721\pi$
$774$	1.13266	−	0.734614i	0.0407125	−	0.0264051i
$775$		0			0
$776$			13.5043i			0.484777i
$777$	12.7322	+	6.91783i	0.456764	+	0.248176i
$778$	−3.54798	−	3.54798i	−0.127201	−	0.127201i
$779$	10.2310			0.366564
$780$		0			0
$781$	33.1179			1.18505
$782$	−0.162163	−	0.162163i	−0.00579895	−	0.00579895i
$783$	−49.1714	+	3.82640i	−1.75724	+	0.136745i
$784$			3.20551i			0.114482i
$785$		0			0
$786$	1.62268	+	5.48396i	0.0578789	+	0.195606i
$787$	−5.70807	+	5.70807i	−0.203471	+	0.203471i	−0.801485	−	0.598015i	$-0.795956\pi$
$787$	−5.70807	+	5.70807i	−0.203471	+	0.203471i	0.598015	+	0.801485i	$0.295956\pi$
$788$	7.65720	−	7.65720i	0.272776	−	0.272776i
$789$	−9.61618	−	32.4986i	−0.342345	−	1.15698i
$790$		0			0
$791$			11.6453i			0.414061i
$792$	−3.01369	+	14.1376i	−0.107087	+	0.502356i
$793$	−2.92155	−	2.92155i	−0.103747	−	0.103747i
$794$	−12.7858			−0.453752
$795$		0			0
$796$	25.0122			0.886534
$797$	7.78096	+	7.78096i	0.275616	+	0.275616i	0.831356	−	0.555740i	$-0.187565\pi$
$797$	7.78096	+	7.78096i	0.275616	+	0.275616i	−0.555740	+	0.831356i	$0.687565\pi$
$798$	−4.11550	−	2.23609i	−0.145687	−	0.0791569i
$799$			0.183268i			0.00648357i
$800$		0			0
$801$	−20.2042	−	31.1517i	−0.713881	−	1.10069i
$802$	−4.03437	+	4.03437i	−0.142458	+	0.142458i
$803$	−16.2860	+	16.2860i	−0.574721	+	0.574721i
$804$	3.57144	−	1.05677i	0.125955	−	0.0372694i
$805$		0			0
$806$			0.765579i			0.0269664i
$807$	9.47905	−	17.4460i	0.333678	−	0.614130i
$808$	12.5245	+	12.5245i	0.440609	+	0.440609i
$809$	−28.7871			−1.01210			−0.506051	−	0.862504i	$-0.668895\pi$
$809$	−28.7871			−1.01210			−0.506051	+	0.862504i	$0.668895\pi$
$810$		0			0
$811$	−9.83136			−0.345226			−0.172613	−	0.984990i	$-0.555221\pi$
$811$	−9.83136			−0.345226			−0.172613	+	0.984990i	$0.555221\pi$
$812$	−12.5140	−	12.5140i	−0.439155	−	0.439155i
$813$	−6.96485	+	12.8187i	−0.244268	+	0.449572i
$814$			10.4308i			0.365600i
$815$		0			0
$816$	−1.05924	+	0.313423i	−0.0370807	+	0.0109720i
$817$	6.35159	−	6.35159i	0.222214	−	0.222214i
$818$	−8.33920	+	8.33920i	−0.291573	+	0.291573i
$819$	−3.68040	−	5.67459i	−0.128604	−	0.198286i
$820$		0			0
$821$			34.5427i			1.20555i	0.797911	+	0.602775i	$0.205938\pi$
$821$			34.5427i			1.20555i	−0.797911	+	0.602775i	$0.794062\pi$
$822$	5.14561	+	2.79579i	0.179474	+	0.0975145i
$823$	11.9459	+	11.9459i	0.416409	+	0.416409i	0.883964	−	0.467555i	$-0.154865\pi$
$823$	11.9459	+	11.9459i	0.416409	+	0.416409i	−0.467555	+	0.883964i	$0.654865\pi$
$824$	−19.6919			−0.686001
$825$		0			0
$826$	−2.30054			−0.0800460
$827$	20.8624	+	20.8624i	0.725457	+	0.725457i	0.969711	−	0.244254i	$-0.0785431\pi$
$827$	20.8624	+	20.8624i	0.725457	+	0.725457i	−0.244254	+	0.969711i	$0.578543\pi$
$828$	3.65210	−	17.1324i	0.126919	−	0.595392i
$829$		−	34.6491i		−	1.20341i	−0.798717	−	0.601706i	$-0.794488\pi$
$829$		−	34.6491i		−	1.20341i	0.798717	−	0.601706i	$-0.205512\pi$
$830$		0			0
$831$	−8.84790	−	29.9022i	−0.306930	−	1.03729i
$832$	7.85887	−	7.85887i	0.272457	−	0.272457i
$833$	−0.140684	+	0.140684i	−0.00487443	+	0.00487443i
$834$	−0.332674	−	1.12430i	−0.0115196	−	0.0389313i
$835$		0			0
$836$			46.4036i			1.60490i
$837$	4.77943	−	0.371924i	0.165201	−	0.0128556i
$838$	1.54873	+	1.54873i	0.0534999	+	0.0534999i
$839$	10.9282			0.377283			0.188642	−	0.982046i	$-0.439592\pi$
$839$	10.9282			0.377283			0.188642	+	0.982046i	$0.439592\pi$
$840$		0			0
$841$	61.0915			2.10660
$842$	2.76889	+	2.76889i	0.0954223	+	0.0954223i
$843$	−6.71546	−	3.64874i	−0.231293	−	0.125669i
$844$		−	15.1311i		−	0.520834i
$845$		0			0
$846$	0.853360	−	0.553468i	0.0293391	−	0.0190286i
$847$	0.335971	−	0.335971i	0.0115441	−	0.0115441i
$848$	20.9675	−	20.9675i	0.720027	−	0.720027i
$849$	4.86785	−	1.44037i	0.167064	−	0.0494335i
$850$		0			0
$851$		−	26.1994i		−	0.898102i
$852$	15.0734	−	27.7423i	0.516405	−	0.950436i
$853$	8.08267	+	8.08267i	0.276745	+	0.276745i	0.831808	−	0.555063i	$-0.187306\pi$
$853$	8.08267	+	8.08267i	0.276745	+	0.276745i	−0.555063	+	0.831808i	$0.687306\pi$
$854$	0.674527			0.0230818
$855$		0			0
$856$	10.4978			0.358807
$857$	14.3191	+	14.3191i	0.489131	+	0.489131i	0.908032	−	0.418901i	$-0.137585\pi$
$857$	14.3191	+	14.3191i	0.489131	+	0.489131i	−0.418901	+	0.908032i	$0.637585\pi$
$858$	2.32446	−	4.27813i	0.0793557	−	0.146053i
$859$			25.0614i			0.855084i	0.903995	+	0.427542i	$0.140620\pi$
$859$			25.0614i			0.855084i	−0.903995	+	0.427542i	$0.859380\pi$
$860$		0			0
$861$	−2.31286	+	0.684363i	−0.0788220	+	0.0233230i
$862$	−2.93418	+	2.93418i	−0.0999387	+	0.0999387i
$863$	−32.8159	+	32.8159i	−1.11707	+	1.11707i	−0.124896	+	0.992170i	$0.539860\pi$
$863$	−32.8159	+	32.8159i	−1.11707	+	1.11707i	−0.992170	+	0.124896i	$0.960140\pi$
$864$	15.8902	+	13.5957i	0.540597	+	0.462535i
$865$		0			0
$866$			5.07564i			0.172477i
$867$	25.8123	+	14.0247i	0.876631	+	0.476304i
$868$	1.21635	+	1.21635i	0.0412856	+	0.0412856i
$869$	−11.5755			−0.392671
$870$		0			0
$871$	−2.60014			−0.0881023
$872$	−6.71530	−	6.71530i	−0.227409	−	0.227409i
$873$	−27.8561	−	5.93805i	−0.942785	−	0.200972i
$874$			8.46858i			0.286454i
$875$		0			0
$876$	6.23006	+	21.0550i	0.210494	+	0.711381i
$877$	−15.2890	+	15.2890i	−0.516271	+	0.516271i	−0.916441	−	0.400170i	$-0.868951\pi$
$877$	−15.2890	+	15.2890i	−0.516271	+	0.516271i	0.400170	+	0.916441i	$0.368951\pi$
$878$	7.40125	−	7.40125i	0.249780	−	0.249780i
$879$	−5.12632	−	17.3248i	−0.172906	−	0.584351i
$880$		0			0
$881$			29.1988i			0.983734i	0.870670	+	0.491867i	$0.163685\pi$
$881$			29.1988i			0.983734i	−0.870670	+	0.491867i	$0.836315\pi$
$882$	1.07994	+	0.230209i	0.0363634	+	0.00775156i
$883$	24.7944	+	24.7944i	0.834397	+	0.834397i	0.988115	−	0.153718i	$-0.0491247\pi$
$883$	24.7944	+	24.7944i	0.834397	+	0.834397i	−0.153718	+	0.988115i	$0.549125\pi$
$884$	0.836347			0.0281294
$885$		0			0
$886$	−10.0004			−0.335971
$887$	−18.5532	−	18.5532i	−0.622956	−	0.622956i	0.323331	−	0.946286i	$-0.395197\pi$
$887$	−18.5532	−	18.5532i	−0.622956	−	0.622956i	−0.946286	+	0.323331i	$0.895197\pi$
$888$	18.1103	+	9.83997i	0.607743	+	0.330208i
$889$		−	2.66126i		−	0.0892559i
$890$		0			0
$891$	−27.8371	−	12.4330i	−0.932579	−	0.416521i
$892$	21.5224	−	21.5224i	0.720625	−	0.720625i
$893$	4.78537	−	4.78537i	0.160136	−	0.160136i
$894$	−0.603504	+	0.178574i	−0.0201842	+	0.00597240i
$895$		0			0
$896$			9.86377i			0.329526i
$897$	−5.83839	+	10.7455i	−0.194938	+	0.358781i
$898$	0.626265	+	0.626265i	0.0208987	+	0.0208987i
$899$	−8.75683			−0.292057
$900$		0			0
$901$	1.84046			0.0613145
$902$	−1.22774	−	1.22774i	−0.0408792	−	0.0408792i
$903$	−1.01100	+	1.86073i	−0.0336439	+	0.0619212i
$904$			16.5644i			0.550925i
$905$		0			0
$906$	−5.32504	+	1.57565i	−0.176913	+	0.0523476i
$907$	−3.39207	+	3.39207i	−0.112632	+	0.112632i	−0.761177	−	0.648545i	$-0.775378\pi$
$907$	−3.39207	+	3.39207i	−0.112632	+	0.112632i	0.648545	+	0.761177i	$0.275378\pi$
$908$	13.1370	−	13.1370i	0.435968	−	0.435968i
$909$	−31.3421	+	20.3277i	−1.03955	+	0.674227i
$910$		0			0
$911$			16.2139i			0.537190i	0.963253	+	0.268595i	$0.0865592\pi$
$911$			16.2139i			0.537190i	−0.963253	+	0.268595i	$0.913441\pi$
$912$	35.8419	+	19.4742i	1.18685	+	0.644855i
$913$	21.2366	+	21.2366i	0.702828	+	0.702828i
$914$	3.23553			0.107022
$915$		0			0
$916$	8.95190			0.295779
$917$	−6.34331	−	6.34331i	−0.209475	−	0.209475i
$918$	0.0295215	+	0.379367i	0.000974354	+	0.0125210i
$919$		−	5.54658i		−	0.182965i	−0.995807	−	0.0914823i	$-0.970839\pi$
$919$		−	5.54658i		−	0.182965i	0.995807	−	0.0914823i	$-0.0291605\pi$
$920$		0			0
$921$	−7.89582	−	26.6845i	−0.260176	−	0.879286i
$922$	9.21923	−	9.21923i	0.303619	−	0.303619i
$923$	−15.5857	+	15.5857i	−0.513009	+	0.513009i
$924$	−3.10399	−	10.4902i	−0.102114	−	0.345101i
$925$		0			0
$926$		−	10.4558i		−	0.343598i
$927$	8.65884	−	40.6196i	0.284393	−	1.33412i
$928$	−27.0120	−	27.0120i	−0.886711	−	0.886711i
$929$	12.7978			0.419884			0.209942	−	0.977714i	$-0.432673\pi$
$929$	12.7978			0.419884			0.209942	+	0.977714i	$0.432673\pi$
$930$		0			0
$931$	7.34691			0.240785
$932$	26.6237	+	26.6237i	0.872090	+	0.872090i
$933$	−13.6103	−	7.39497i	−0.445582	−	0.242100i
$934$		−	3.02201i		−	0.0988830i
$935$		0			0
$936$	−5.23503	−	8.07159i	−0.171112	−	0.263828i
$937$	−24.4148	+	24.4148i	−0.797598	+	0.797598i	−0.982716	−	0.185119i	$-0.940733\pi$
$937$	−24.4148	+	24.4148i	−0.797598	+	0.797598i	0.185119	+	0.982716i	$0.440733\pi$
$938$	0.300159	−	0.300159i	0.00980055	−	0.00980055i
$939$	10.6278	−	3.14471i	0.346825	−	0.102624i
$940$		0			0
$941$		−	3.72437i		−	0.121411i	−0.998156	−	0.0607055i	$-0.980665\pi$
$941$		−	3.72437i		−	0.121411i	0.998156	−	0.0607055i	$-0.0193351\pi$
$942$	−2.26537	+	4.16938i	−0.0738097	+	0.135846i
$943$	3.08374	+	3.08374i	0.100420	+	0.100420i
$944$	20.0354			0.652098
$945$		0			0
$946$	−1.52440			−0.0495626
$947$	−34.3568	−	34.3568i	−1.11644	−	1.11644i	−0.992259	−	0.124186i	$-0.960368\pi$
$947$	−34.3568	−	34.3568i	−1.11644	−	1.11644i	−0.124186	−	0.992259i	$-0.539632\pi$
$948$	−5.26849	+	9.69657i	−0.171112	+	0.314930i
$949$		−	15.3288i		−	0.497593i
$950$		0			0
$951$	−4.19155	+	1.24026i	−0.135920	+	0.0402181i
$952$	−0.200111	+	0.200111i	−0.00648562	+	0.00648562i
$953$	21.7199	−	21.7199i	0.703578	−	0.703578i	−0.261599	−	0.965177i	$-0.584250\pi$
$953$	21.7199	−	21.7199i	0.703578	−	0.703578i	0.965177	+	0.261599i	$0.0842497\pi$
$954$	−5.55815	−	8.56979i	−0.179952	−	0.277457i
$955$		0			0
$956$		−	23.9812i		−	0.775607i
$957$	48.9340	+	26.5876i	1.58181	+	0.859454i
$958$	−10.5102	−	10.5102i	−0.339569	−	0.339569i
$959$	−9.18585			−0.296627
$960$		0			0
$961$	−30.1488			−0.972543
$962$	−4.90888	−	4.90888i	−0.158269	−	0.158269i
$963$	−4.61604	+	21.6544i	−0.148750	+	0.697802i
$964$			30.1785i			0.971984i
$965$		0			0
$966$	−0.566473	−	1.91444i	−0.0182260	−	0.0615961i
$967$	42.1187	−	42.1187i	1.35445	−	1.35445i	0.473831	−	0.880616i	$-0.342871\pi$
$967$	42.1187	−	42.1187i	1.35445	−	1.35445i	0.880616	−	0.473831i	$-0.157129\pi$
$968$	0.477887	−	0.477887i	0.0153599	−	0.0153599i
$969$	0.718354	+	2.42773i	0.0230768	+	0.0779900i
$970$		0			0
$971$		−	27.4414i		−	0.880638i	−0.897841	−	0.440319i	$-0.854865\pi$
$971$		−	27.4414i		−	0.880638i	0.897841	−	0.440319i	$-0.145135\pi$
$972$	−23.0848	+	17.6599i	−0.740444	+	0.566442i
$973$	1.30048	+	1.30048i	0.0416915	+	0.0416915i
$974$	10.3055			0.330211
$975$		0			0
$976$	−5.87447			−0.188037
$977$	−40.5573	−	40.5573i	−1.29754	−	1.29754i	−0.930011	−	0.367531i	$-0.880203\pi$
$977$	−40.5573	−	40.5573i	−1.29754	−	1.29754i	−0.367531	−	0.930011i	$-0.619797\pi$
$978$	−11.2105	−	6.09104i	−0.358471	−	0.194770i
$979$			41.9259i			1.33996i
$980$		0			0
$981$	16.8048	−	10.8992i	0.536537	−	0.347984i
$982$	9.54968	−	9.54968i	0.304743	−	0.304743i
$983$	−17.0329	+	17.0329i	−0.543267	+	0.543267i	−0.924485	−	0.381218i	$-0.875505\pi$
$983$	−17.0329	+	17.0329i	−0.543267	+	0.543267i	0.381218	+	0.924485i	$0.375505\pi$
$984$	−3.28983	+	0.973443i	−0.104876	+	0.0310322i
$985$		0			0
$986$		−	0.695074i		−	0.0221357i
$987$	−0.761700	+	1.40190i	−0.0242452	+	0.0446229i
$988$	−21.8381	−	21.8381i	−0.694763	−	0.694763i
$989$	3.82888			0.121751
$990$		0			0
$991$	22.4760			0.713973			0.356986	−	0.934110i	$-0.383804\pi$
$991$	22.4760			0.713973			0.356986	+	0.934110i	$0.383804\pi$
$992$	2.62554	+	2.62554i	0.0833611	+	0.0833611i
$993$	2.99223	−	5.50716i	0.0949556	−	0.174764i
$994$		−	3.59842i		−	0.114135i
$995$		0			0
$996$	27.4552	−	8.12385i	0.869951	−	0.257414i
$997$	−31.8314	+	31.8314i	−1.00811	+	1.00811i	−0.00814356	+	0.999967i	$0.502592\pi$
$997$	−31.8314	+	31.8314i	−1.00811	+	1.00811i	−0.999967	+	0.00814356i	$0.997408\pi$
$998$	−1.98463	+	1.98463i	−0.0628224	+	0.0628224i
$999$	−28.2608	+	33.0304i	−0.894133	+	1.04503i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.j.b.218.6		24
3.2	odd	2	inner	525.2.j.b.218.7		24
5.2	odd	4	inner	525.2.j.b.407.7		24
5.3	odd	4		105.2.j.a.92.6	yes	24
5.4	even	2		105.2.j.a.8.7	yes	24
15.2	even	4	inner	525.2.j.b.407.6		24
15.8	even	4		105.2.j.a.92.7	yes	24
15.14	odd	2		105.2.j.a.8.6	✓	24
35.3	even	12		735.2.y.g.422.6		48
35.4	even	6		735.2.y.j.128.6		48
35.9	even	6		735.2.y.j.263.7		48
35.13	even	4		735.2.j.h.197.6		24
35.18	odd	12		735.2.y.j.422.6		48
35.19	odd	6		735.2.y.g.263.7		48
35.23	odd	12		735.2.y.j.557.7		48
35.24	odd	6		735.2.y.g.128.6		48
35.33	even	12		735.2.y.g.557.7		48
35.34	odd	2		735.2.j.h.638.7		24
105.23	even	12		735.2.y.j.557.6		48
105.38	odd	12		735.2.y.g.422.7		48
105.44	odd	6		735.2.y.j.263.6		48
105.53	even	12		735.2.y.j.422.7		48
105.59	even	6		735.2.y.g.128.7		48
105.68	odd	12		735.2.y.g.557.6		48
105.74	odd	6		735.2.y.j.128.7		48
105.83	odd	4		735.2.j.h.197.7		24
105.89	even	6		735.2.y.g.263.6		48
105.104	even	2		735.2.j.h.638.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.6	✓	24	15.14	odd	2
105.2.j.a.8.7	yes	24	5.4	even	2
105.2.j.a.92.6	yes	24	5.3	odd	4
105.2.j.a.92.7	yes	24	15.8	even	4
525.2.j.b.218.6		24	1.1	even	1	trivial
525.2.j.b.218.7		24	3.2	odd	2	inner
525.2.j.b.407.6		24	15.2	even	4	inner
525.2.j.b.407.7		24	5.2	odd	4	inner
735.2.j.h.197.6		24	35.13	even	4
735.2.j.h.197.7		24	105.83	odd	4
735.2.j.h.638.6		24	105.104	even	2
735.2.j.h.638.7		24	35.34	odd	2
735.2.y.g.128.6		48	35.24	odd	6
735.2.y.g.128.7		48	105.59	even	6
735.2.y.g.263.6		48	105.89	even	6
735.2.y.g.263.7		48	35.19	odd	6
735.2.y.g.422.6		48	35.3	even	12
735.2.y.g.422.7		48	105.38	odd	12
735.2.y.g.557.6		48	105.68	odd	12
735.2.y.g.557.7		48	35.33	even	12
735.2.y.j.128.6		48	35.4	even	6
735.2.y.j.128.7		48	105.74	odd	6
735.2.y.j.263.6		48	105.44	odd	6
735.2.y.j.263.7		48	35.9	even	6
735.2.y.j.422.6		48	35.18	odd	12
735.2.y.j.422.7		48	105.53	even	12
735.2.y.j.557.6		48	105.23	even	12
735.2.y.j.557.7		48	35.23	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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.260263 - 0.260263i) q^{2} +(-0.826909 + 1.52191i) q^{3} -1.86453i q^{4} +(0.611312 - 0.180884i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.00579 + 1.00579i) q^{8} +(-1.63244 - 2.51697i) q^{9} +O(q^{10})\)	\(q+(-0.260263 - 0.260263i) q^{2} +(-0.826909 + 1.52191i) q^{3} -1.86453i q^{4} +(0.611312 - 0.180884i) q^{6} +(-0.707107 + 0.707107i) q^{7} +(-1.00579 + 1.00579i) q^{8} +(-1.63244 - 2.51697i) q^{9} +3.38750i q^{11} +(2.83765 + 1.54179i) q^{12} +(-1.59420 - 1.59420i) q^{13} +0.368068 q^{14} -3.20551 q^{16} +(-0.140684 - 0.140684i) q^{17} +(-0.230209 + 1.07994i) q^{18} +7.34691i q^{19} +(-0.491443 - 1.66087i) q^{21} +(0.881641 - 0.881641i) q^{22} +(-2.21444 + 2.21444i) q^{23} +(-0.699032 - 2.36243i) q^{24} +0.829822i q^{26} +(5.18049 - 0.403134i) q^{27} +(1.31842 + 1.31842i) q^{28} -9.49165 q^{29} +0.922582 q^{31} +(2.84586 + 2.84586i) q^{32} +(-5.15548 - 2.80115i) q^{33} +0.0732300i q^{34} +(-4.69295 + 3.04373i) q^{36} +(-5.91558 + 5.91558i) q^{37} +(1.91213 - 1.91213i) q^{38} +(3.74449 - 1.10797i) q^{39} -1.39256i q^{41} +(-0.304359 + 0.560167i) q^{42} +(-0.864526 - 0.864526i) q^{43} +6.31608 q^{44} +1.15267 q^{46} +(-0.651346 - 0.651346i) q^{47} +(2.65066 - 4.87851i) q^{48} -1.00000i q^{49} +(0.330443 - 0.0977764i) q^{51} +(-2.97242 + 2.97242i) q^{52} +(-6.54108 + 6.54108i) q^{53} +(-1.45321 - 1.24337i) q^{54} -1.42241i q^{56} +(-11.1814 - 6.07522i) q^{57} +(2.47033 + 2.47033i) q^{58} -6.25032 q^{59} +1.83261 q^{61} +(-0.240114 - 0.240114i) q^{62} +(2.93408 + 0.625454i) q^{63} +4.92967i q^{64} +(0.612745 + 2.07082i) q^{66} +(0.815500 - 0.815500i) q^{67} +(-0.262310 + 0.262310i) q^{68} +(-1.53904 - 5.20132i) q^{69} -9.77651i q^{71} +(4.17345 + 0.889650i) q^{72} +(4.80768 + 4.80768i) q^{73} +3.07921 q^{74} +13.6985 q^{76} +(-2.39532 - 2.39532i) q^{77} +(-1.26292 - 0.686187i) q^{78} +3.41711i q^{79} +(-3.67026 + 8.21761i) q^{81} +(-0.362432 + 0.362432i) q^{82} +(6.26911 - 6.26911i) q^{83} +(-3.09673 + 0.916307i) q^{84} +0.450009i q^{86} +(7.84873 - 14.4455i) q^{87} +(-3.40712 - 3.40712i) q^{88} +12.3767 q^{89} +2.25454 q^{91} +(4.12888 + 4.12888i) q^{92} +(-0.762891 + 1.40409i) q^{93} +0.339043i q^{94} +(-6.68443 + 1.97789i) q^{96} +(6.71326 - 6.71326i) q^{97} +(-0.260263 + 0.260263i) q^{98} +(8.52622 - 5.52990i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3}+O(q^{10}) \) 24 * q + 4 * q^3	\( 24 q + 4 q^{3} - 16 q^{12} + 8 q^{13} - 16 q^{16} + 20 q^{18} + 4 q^{21} - 8 q^{22} + 16 q^{27} - 28 q^{33} + 16 q^{36} + 16 q^{37} + 20 q^{42} + 40 q^{43} - 64 q^{46} - 16 q^{48} - 20 q^{51} - 4 q^{57} - 40 q^{58} + 32 q^{61} + 8 q^{63} - 16 q^{66} - 24 q^{67} + 8 q^{72} - 32 q^{73} + 32 q^{76} - 60 q^{78} + 52 q^{81} + 80 q^{82} - 4 q^{87} - 96 q^{88} - 24 q^{91} + 76 q^{93} - 96 q^{96} - 24 q^{97}+O(q^{100}) \) 24 * q + 4 * q^3 - 16 * q^12 + 8 * q^13 - 16 * q^16 + 20 * q^18 + 4 * q^21 - 8 * q^22 + 16 * q^27 - 28 * q^33 + 16 * q^36 + 16 * q^37 + 20 * q^42 + 40 * q^43 - 64 * q^46 - 16 * q^48 - 20 * q^51 - 4 * q^57 - 40 * q^58 + 32 * q^61 + 8 * q^63 - 16 * q^66 - 24 * q^67 + 8 * q^72 - 32 * q^73 + 32 * q^76 - 60 * q^78 + 52 * q^81 + 80 * q^82 - 4 * q^87 - 96 * q^88 - 24 * q^91 + 76 * q^93 - 96 * q^96 - 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more