LMFDB - Embedded newform 525.2.j.b.407.6

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			407.6
Character	$\chi$	$=$	525.407
Dual form			525.2.j.b.218.6

$q$-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 $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

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

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	−0.793111	−	0.609077i	$-0.791540\pi$
$2$	−0.260263	+	0.260263i	−0.184034	+	0.184034i	0.609077	+	0.793111i	$0.291540\pi$
$3$	−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	$-0.829392\pi$
$11$		−	3.38750i		−	1.02137i	0.859768	−	0.510684i	$-0.170608\pi$
$12$	2.83765	−	1.54179i	0.819158	−	0.445077i
$13$	−1.59420	+	1.59420i	−0.442151	+	0.442151i	−0.892734	−	0.450583i	$-0.851216\pi$
$13$	−1.59420	+	1.59420i	−0.442151	+	0.442151i	0.450583	+	0.892734i	$0.351216\pi$
$14$	0.368068			0.0983703
$15$		0			0
$16$	−3.20551			−0.801377
$17$	−0.140684	+	0.140684i	−0.0341210	+	0.0341210i	−0.723961	−	0.689840i	$-0.757681\pi$
$17$	−0.140684	+	0.140684i	−0.0341210	+	0.0341210i	0.689840	+	0.723961i	$0.257681\pi$
$18$	−0.230209	−	1.07994i	−0.0542609	−	0.254544i
$19$		−	7.34691i		−	1.68550i	−0.538308	−	0.842748i	$-0.680936\pi$
$19$		−	7.34691i		−	1.68550i	0.538308	−	0.842748i	$-0.319064\pi$
$20$		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	0.437484	−	0.899226i	$-0.355870\pi$
$23$	−2.21444	−	2.21444i	−0.461742	−	0.461742i	−0.899226	+	0.437484i	$0.855870\pi$
$24$	−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	0.0271173	−	0.999632i	$-0.491367\pi$
$37$	−5.91558	−	5.91558i	−0.972515	−	0.972515i	−0.999632	+	0.0271173i	$0.991367\pi$
$38$	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	$0.0346818\pi$
$41$			1.39256i			0.217481i	−0.994070	+	0.108741i	$0.965318\pi$
$42$	−0.304359	−	0.560167i	−0.0469636	−	0.0864357i
$43$	−0.864526	+	0.864526i	−0.131839	+	0.131839i	−0.769947	−	0.638108i	$-0.779717\pi$
$43$	−0.864526	+	0.864526i	−0.131839	+	0.131839i	0.638108	+	0.769947i	$0.279717\pi$
$44$	6.31608			0.952184
$45$		0			0
$46$	1.15267			0.169952
$47$	−0.651346	+	0.651346i	−0.0950085	+	0.0950085i	−0.753014	−	0.658005i	$-0.771401\pi$
$47$	−0.651346	+	0.651346i	−0.0950085	+	0.0950085i	0.658005	+	0.753014i	$0.271401\pi$
$48$	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	0.0968158	−	0.995302i	$-0.469134\pi$
$53$	−6.54108	−	6.54108i	−0.898486	−	0.898486i	−0.995302	+	0.0968158i	$0.969134\pi$
$54$	−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	0.755165	−	0.655535i	$-0.227557\pi$
$67$	0.815500	+	0.815500i	0.0996292	+	0.0996292i	−0.655535	+	0.755165i	$0.727557\pi$
$68$	−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	$0.196998\pi$
$71$			9.77651i			1.16026i	−0.814524	+	0.580129i	$0.803002\pi$
$72$	4.17345	−	0.889650i	0.491846	−	0.104846i
$73$	4.80768	−	4.80768i	0.562697	−	0.562697i	−0.367376	−	0.930073i	$-0.619744\pi$
$73$	4.80768	−	4.80768i	0.562697	−	0.562697i	0.930073	+	0.367376i	$0.119744\pi$
$74$	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	$-0.938429\pi$
$79$		−	3.41711i		−	0.384455i	0.981350	−	0.192228i	$-0.0615712\pi$
$80$		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	0.961817	−	0.273693i	$-0.0882453\pi$
$83$	6.26911	+	6.26911i	0.688124	+	0.688124i	−0.273693	+	0.961817i	$0.588245\pi$
$84$	−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	0.960367	−	0.278739i	$-0.0899164\pi$
$97$	6.71326	+	6.71326i	0.681628	+	0.681628i	−0.278739	+	0.960367i	$0.589916\pi$
$98$	−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	$0.212675\pi$
$101$			12.4523i			1.23905i	−0.784976	+	0.619526i	$0.787325\pi$
$102$	−0.111450	+	0.0605545i	−0.0110352	+	0.00599579i
$103$	9.78924	−	9.78924i	0.964563	−	0.964563i	−0.0348303	−	0.999393i	$-0.511089\pi$
$103$	9.78924	−	9.78924i	0.964563	−	0.964563i	0.999393	+	0.0348303i	$0.0110891\pi$
$104$	3.20687			0.314459
$105$		0			0
$106$	3.40481			0.330704
$107$	−5.21866	+	5.21866i	−0.504507	+	0.504507i	−0.912835	−	0.408328i	$-0.866112\pi$
$107$	−5.21866	+	5.21866i	−0.504507	+	0.504507i	0.408328	+	0.912835i	$0.366112\pi$
$108$	−0.751653	+	9.65916i	−0.0723279	+	0.929453i
$109$		−	6.67661i		−	0.639504i	−0.947501	−	0.319752i	$-0.896400\pi$
$109$		−	6.67661i		−	0.639504i	0.947501	−	0.319752i	$-0.103600\pi$
$110$		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	0.978913	−	0.204276i	$-0.0654841\pi$
$113$	8.23451	+	8.23451i	0.774637	+	0.774637i	−0.204276	+	0.978913i	$0.565484\pi$
$114$	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	0.618669	−	0.785652i	$-0.287672\pi$
$127$	−1.88180	−	1.88180i	−0.166983	−	0.166983i	−0.785652	+	0.618669i	$0.787672\pi$
$128$	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	$-0.871821\pi$
$131$		−	8.97080i		−	0.783783i	0.920012	−	0.391891i	$-0.128179\pi$
$132$	−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	−0.372924	−	0.927862i	$-0.621645\pi$
$137$	6.49538	−	6.49538i	0.554938	−	0.554938i	0.927862	+	0.372924i	$0.121645\pi$
$138$	−0.953156	−	1.75427i	−0.0811380	−	0.149333i
$139$			1.83916i			0.155995i	0.996954	+	0.0779976i	$0.0248526\pi$
$139$			1.83916i			0.155995i	−0.996954	+	0.0779976i	$0.975147\pi$
$140$		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	0.465179	−	0.885217i	$-0.345990\pi$
$157$	−5.26306	−	5.26306i	−0.420038	−	0.420038i	−0.885217	+	0.465179i	$0.845990\pi$
$158$	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	−0.115041	+	0.993361i	$0.536700\pi$
$163$	−14.1511	+	14.1511i	−1.10840	+	1.10840i	−0.993361	+	0.115041i	$0.963300\pi$
$164$	−2.59646			−0.202750
$165$		0			0
$166$	−3.26324			−0.253276
$167$	−17.4876	+	17.4876i	−1.35323	+	1.35323i	−0.471215	+	0.882018i	$0.656184\pi$
$167$	−17.4876	+	17.4876i	−1.35323	+	1.35323i	−0.882018	+	0.471215i	$0.843816\pi$
$168$	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	0.160150	−	0.987093i	$-0.448802\pi$
$173$	−10.8767	−	10.8767i	−0.826942	−	0.826942i	−0.987093	+	0.160150i	$0.948802\pi$
$174$	−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	$-0.777509\pi$
$191$		−	17.7849i		−	1.28687i	0.765501	−	0.643435i	$-0.222491\pi$
$192$	−7.50253	+	4.07639i	−0.541449	+	0.294188i
$193$	−14.3394	+	14.3394i	−1.03217	+	1.03217i	−0.0327052	+	0.999465i	$0.510412\pi$
$193$	−14.3394	+	14.3394i	−1.03217	+	1.03217i	−0.999465	+	0.0327052i	$0.989588\pi$
$194$	−3.49443			−0.250885
$195$		0			0
$196$	−1.86453			−0.133180
$197$	4.10678	−	4.10678i	0.292596	−	0.292596i	−0.545509	−	0.838105i	$-0.683664\pi$
$197$	4.10678	−	4.10678i	0.292596	−	0.292596i	0.838105	+	0.545509i	$0.183664\pi$
$198$	−3.65829	+	0.779834i	−0.259983	+	0.0554204i
$199$		−	13.4148i		−	0.950949i	−0.879730	−	0.475474i	$-0.842276\pi$
$199$		−	13.4148i		−	0.950949i	0.879730	−	0.475474i	$-0.157724\pi$
$200$		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	−0.205643	−	0.978627i	$-0.565928\pi$
$223$	11.5431	−	11.5431i	0.772984	−	0.772984i	0.978627	+	0.205643i	$0.0659285\pi$
$224$	−4.02466			−0.268909
$225$		0			0
$226$	−4.28628			−0.285119
$227$	7.04578	−	7.04578i	0.467645	−	0.467645i	−0.433506	−	0.901151i	$-0.642724\pi$
$227$	7.04578	−	7.04578i	0.467645	−	0.467645i	0.901151	+	0.433506i	$0.142724\pi$
$228$	−11.3274	−	20.8479i	−0.750176	−	1.38069i
$229$		−	4.80117i		−	0.317270i	−0.987337	−	0.158635i	$-0.949291\pi$
$229$		−	4.80117i		−	0.317270i	0.987337	−	0.158635i	$-0.0507093\pi$
$230$		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	0.0625851	−	0.998040i	$-0.480066\pi$
$233$	−14.2791	−	14.2791i	−0.935455	−	0.935455i	−0.998040	+	0.0625851i	$0.980066\pi$
$234$	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	$0.0815426\pi$
$251$			8.02862i			0.506762i	−0.967367	+	0.253381i	$0.918457\pi$
$252$	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	0.0368323	−	0.999321i	$-0.488273\pi$
$257$	16.6108	−	16.6108i	1.03615	−	1.03615i	0.999321	−	0.0368323i	$-0.0117267\pi$
$258$	−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	0.137350	−	0.990523i	$-0.456142\pi$
$263$	−13.8361	−	13.8361i	−0.853173	−	0.853173i	−0.990523	+	0.137350i	$0.956142\pi$
$264$	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	0.212293	−	0.977206i	$-0.431907\pi$
$277$	−12.7307	−	12.7307i	−0.764914	−	0.764914i	−0.977206	+	0.212293i	$0.931907\pi$
$278$	−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	$-0.957984\pi$
$281$		−	4.41251i		−	0.263228i	0.991301	−	0.131614i	$-0.0420160\pi$
$282$	−0.515994	+	0.280357i	−0.0307270	+	0.0166950i
$283$	−2.07246	+	2.07246i	−0.123195	+	0.123195i	−0.766016	−	0.642821i	$-0.777764\pi$
$283$	−2.07246	+	2.07246i	−0.123195	+	0.123195i	0.642821	+	0.766016i	$0.277764\pi$
$284$	−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	0.458029	−	0.888937i	$-0.348555\pi$
$293$	−7.37595	−	7.37595i	−0.430908	−	0.430908i	−0.888937	+	0.458029i	$0.848555\pi$
$294$	−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	0.304209	−	0.952605i	$-0.401608\pi$
$307$	−11.3608	−	11.3608i	−0.648396	−	0.648396i	−0.952605	+	0.304209i	$0.901608\pi$
$308$	−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	$-0.918401\pi$
$311$		−	8.94291i		−	0.507106i	0.967322	−	0.253553i	$-0.0815992\pi$
$312$	−2.65179	−	4.88058i	−0.150128	−	0.276308i
$313$	−4.52473	+	4.52473i	−0.255753	+	0.255753i	−0.823324	−	0.567571i	$-0.807883\pi$
$313$	−4.52473	+	4.52473i	−0.255753	+	0.255753i	0.567571	+	0.823324i	$0.307883\pi$
$314$	2.73956			0.154602
$315$		0			0
$316$	6.37130			0.358414
$317$	1.78453	−	1.78453i	0.100229	−	0.100229i	−0.655214	−	0.755443i	$-0.727422\pi$
$317$	1.78453	−	1.78453i	0.100229	−	0.100229i	0.755443	+	0.655214i	$0.227422\pi$
$318$	−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	0.997779	−	0.0666042i	$-0.0212165\pi$
$337$	17.0941	+	17.0941i	0.931175	+	0.931175i	−0.0666042	+	0.997779i	$0.521216\pi$
$338$	−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	−0.838851	−	0.544361i	$-0.816772\pi$
$347$	−5.48573	+	5.48573i	−0.294489	+	0.294489i	0.544361	+	0.838851i	$0.316772\pi$
$348$	−26.9340	+	14.6342i	−1.44381	+	0.784474i
$349$		−	14.8272i		−	0.793681i	−0.917888	−	0.396841i	$-0.870107\pi$
$349$		−	14.8272i		−	0.793681i	0.917888	−	0.396841i	$-0.129893\pi$
$350$		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	0.476841	−	0.878990i	$-0.341782\pi$
$353$	−7.55570	−	7.55570i	−0.402149	−	0.402149i	−0.878990	+	0.476841i	$0.841782\pi$
$354$	−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	0.609019	−	0.793155i	$-0.291563\pi$
$367$	−3.52753	−	3.52753i	−0.184136	−	0.184136i	−0.793155	+	0.609019i	$0.791563\pi$
$368$	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	−0.499942	−	0.866059i	$-0.666645\pi$
$373$	7.07089	−	7.07089i	0.366117	−	0.366117i	0.866059	+	0.499942i	$0.166645\pi$
$374$	−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	$-0.814071\pi$
$379$		−	21.4715i		−	1.10292i	0.834202	−	0.551459i	$-0.185929\pi$
$380$		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	0.974269	−	0.225388i	$-0.0723648\pi$
$383$	14.6559	+	14.6559i	0.748882	+	0.748882i	−0.225388	+	0.974269i	$0.572365\pi$
$384$	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	0.962886	+	0.269907i	$0.0869929\pi$
$397$	24.5632	+	24.5632i	1.23279	+	1.23279i	0.269907	+	0.962886i	$0.413007\pi$
$398$	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	$0.126504\pi$
$401$			15.5011i			0.774088i	−0.922061	+	0.387044i	$0.873496\pi$
$402$	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	$0.291050\pi$
$409$			32.0414i			1.58434i	−0.610298	+	0.792172i	$0.708950\pi$
$410$		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	$0.0875271\pi$
$431$			11.2739i			0.543045i	−0.962432	+	0.271523i	$0.912473\pi$
$432$	−16.6061	−	1.29225i	−0.798962	−	0.0621733i
$433$	−9.75098	+	9.75098i	−0.468602	+	0.468602i	−0.901462	−	0.432859i	$-0.857505\pi$
$433$	−9.75098	+	9.75098i	−0.468602	+	0.468602i	0.432859	+	0.901462i	$0.357505\pi$
$434$	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	$-0.762576\pi$
$439$		−	28.4375i		−	1.35725i	0.734485	−	0.678625i	$-0.237424\pi$
$440$		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	0.996491	−	0.0836955i	$-0.0266723\pi$
$443$	19.2121	+	19.2121i	0.912796	+	0.912796i	−0.0836955	+	0.996491i	$0.526672\pi$
$444$	−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	0.546617	−	0.837383i	$-0.315916\pi$
$457$	−6.21588	−	6.21588i	−0.290767	−	0.290767i	−0.837383	+	0.546617i	$0.815916\pi$
$458$	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	$-0.691231\pi$
$461$		−	35.4227i		−	1.64980i	0.565278	−	0.824900i	$-0.308769\pi$
$462$	−1.89757	+	1.03101i	−0.0882827	+	0.0479671i
$463$	20.0869	−	20.0869i	0.933519	−	0.933519i	−0.0644045	−	0.997924i	$-0.520515\pi$
$463$	20.0869	−	20.0869i	0.933519	−	0.933519i	0.997924	+	0.0644045i	$0.0205148\pi$
$464$	30.4256			1.41247
$465$		0			0
$466$	7.43265			0.344311
$467$	5.80567	−	5.80567i	0.268654	−	0.268654i	−0.559903	−	0.828558i	$-0.689162\pi$
$467$	5.80567	−	5.80567i	0.268654	−	0.268654i	0.828558	+	0.559903i	$0.189162\pi$
$468$	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	0.0980363	−	0.995183i	$-0.468744\pi$
$487$	−19.7983	−	19.7983i	−0.897147	−	0.897147i	−0.995183	+	0.0980363i	$0.968744\pi$
$488$	−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	$-0.689506\pi$
$491$		−	36.6924i		−	1.65590i	0.560798	−	0.827952i	$-0.310494\pi$
$492$	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	$0.0545970\pi$
$499$			7.62548i			0.341363i	−0.985326	+	0.170682i	$0.945403\pi$
$500$		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	0.964926	−	0.262521i	$-0.0845538\pi$
$503$	15.7533	+	15.7533i	0.702406	+	0.702406i	−0.262521	+	0.964926i	$0.584554\pi$
$504$	−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	$-0.812309\pi$
$521$		−	25.3850i		−	1.11214i	0.831136	−	0.556069i	$-0.187691\pi$
$522$	2.18507	+	10.2504i	0.0956378	+	0.448648i
$523$	16.0464	−	16.0464i	0.701661	−	0.701661i	−0.263106	−	0.964767i	$-0.584747\pi$
$523$	16.0464	−	16.0464i	0.701661	−	0.701661i	0.964767	+	0.263106i	$0.0847470\pi$
$524$	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	0.210929	−	0.977501i	$-0.432351\pi$
$547$	−17.9286	−	17.9286i	−0.766572	−	0.766572i	−0.977501	+	0.210929i	$0.932351\pi$
$548$	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	−0.589301	−	0.807914i	$-0.700597\pi$
$557$	5.15944	−	5.15944i	0.218613	−	0.218613i	0.807914	+	0.589301i	$0.200597\pi$
$558$	−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	0.999805	−	0.0197332i	$-0.00628169\pi$
$563$	23.2548	+	23.2548i	0.980072	+	0.980072i	−0.0197332	+	0.999805i	$0.506282\pi$
$564$	−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	0.822957	−	0.568104i	$-0.192323\pi$
$577$	6.12177	+	6.12177i	0.254853	+	0.254853i	−0.568104	+	0.822957i	$0.692323\pi$
$578$	−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	−0.624992	−	0.780632i	$-0.714898\pi$
$587$	3.77086	−	3.77086i	0.155640	−	0.155640i	0.780632	+	0.624992i	$0.214898\pi$
$588$	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	0.857918	−	0.513786i	$-0.171758\pi$
$593$	8.38017	+	8.38017i	0.344132	+	0.344132i	−0.513786	+	0.857918i	$0.671758\pi$
$594$	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	0.649641	−	0.760241i	$-0.274919\pi$
$607$	−2.72491	−	2.72491i	−0.110601	−	0.110601i	−0.760241	+	0.649641i	$0.774919\pi$
$608$	−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	−0.948323	−	0.317306i	$-0.897222\pi$
$613$	−15.6232	+	15.6232i	−0.631017	+	0.631017i	0.317306	+	0.948323i	$0.397222\pi$
$614$	5.91361			0.238654
$615$		0			0
$616$	4.81840			0.194139
$617$	−5.47009	+	5.47009i	−0.220218	+	0.220218i	−0.808590	−	0.588373i	$-0.799769\pi$
$617$	−5.47009	+	5.47009i	−0.220218	+	0.220218i	0.588373	+	0.808590i	$0.299769\pi$
$618$	7.75500	−	4.21357i	0.311952	−	0.169494i
$619$		−	42.9951i		−	1.72812i	−0.503389	−	0.864060i	$-0.667914\pi$
$619$		−	42.9951i		−	1.72812i	0.503389	−	0.864060i	$-0.332086\pi$
$620$		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	$0.208141\pi$
$641$			30.8009i			1.21656i	−0.793721	+	0.608282i	$0.791859\pi$
$642$	−4.13420	+	2.24626i	−0.163164	+	0.0886527i
$643$	6.17366	−	6.17366i	0.243465	−	0.243465i	−0.574817	−	0.818282i	$-0.694927\pi$
$643$	6.17366	−	6.17366i	0.243465	−	0.243465i	0.818282	+	0.574817i	$0.194927\pi$
$644$	−5.83911			−0.230093
$645$		0			0
$646$	−0.538014			−0.0211679
$647$	23.4296	−	23.4296i	0.921112	−	0.921112i	−0.0759964	−	0.997108i	$-0.524214\pi$
$647$	23.4296	−	23.4296i	0.921112	−	0.921112i	0.997108	+	0.0759964i	$0.0242137\pi$
$648$	−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	0.285557	−	0.958362i	$-0.407821\pi$
$653$	−17.1928	−	17.1928i	−0.672805	−	0.672805i	−0.958362	+	0.285557i	$0.907821\pi$
$654$	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	−0.618651	−	0.785666i	$-0.712320\pi$
$673$	4.33276	−	4.33276i	0.167016	−	0.167016i	0.785666	+	0.618651i	$0.212320\pi$
$674$	−8.89793			−0.342736
$675$		0			0
$676$	−14.7616			−0.567753
$677$	−3.64637	+	3.64637i	−0.140142	+	0.140142i	−0.773697	−	0.633556i	$-0.781595\pi$
$677$	−3.64637	+	3.64637i	−0.140142	+	0.140142i	0.633556	+	0.773697i	$0.281595\pi$
$678$	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	0.933830	+	0.357718i	$0.116445\pi$
$683$	33.7536	+	33.7536i	1.29155	+	1.29155i	0.357718	+	0.933830i	$0.383555\pi$
$684$	−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	$0.134999\pi$
$701$			21.7907i			0.823024i	−0.911404	+	0.411512i	$0.865001\pi$
$702$	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	$0.0856814\pi$
$709$			14.1622i			0.531874i	−0.963990	+	0.265937i	$0.914319\pi$
$710$		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	0.496585	−	0.867988i	$-0.334587\pi$
$727$	−10.0141	−	10.0141i	−0.371403	−	0.371403i	−0.867988	+	0.496585i	$0.834587\pi$
$728$	−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	0.138967	−	0.990297i	$-0.455622\pi$
$733$	30.5737	−	30.5737i	1.12926	−	1.12926i	0.990297	−	0.138967i	$-0.0443783\pi$
$734$	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	$-0.904247\pi$
$739$		−	16.1095i		−	0.592598i	0.955095	−	0.296299i	$-0.0957525\pi$
$740$		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	0.140180	−	0.990126i	$-0.455232\pi$
$743$	−23.1679	−	23.1679i	−0.849946	−	0.849946i	−0.990126	+	0.140180i	$0.955232\pi$
$744$	−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	0.730166	−	0.683270i	$-0.239443\pi$
$757$	1.29026	+	1.29026i	0.0468952	+	0.0468952i	−0.683270	+	0.730166i	$0.739443\pi$
$758$	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	$-0.788674\pi$
$761$		−	33.9969i		−	1.23239i	0.787596	−	0.616193i	$-0.211326\pi$
$762$	−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	$0.126221\pi$
$769$			21.4206i			0.772448i	−0.922405	+	0.386224i	$0.873779\pi$
$770$		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	0.515192	−	0.857075i	$-0.327721\pi$
$773$	−9.50533	−	9.50533i	−0.341883	−	0.341883i	−0.857075	+	0.515192i	$0.827721\pi$
$774$	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	0.598015	−	0.801485i	$-0.295956\pi$
$787$	−5.70807	−	5.70807i	−0.203471	−	0.203471i	−0.801485	+	0.598015i	$0.795956\pi$
$788$	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	−0.555740	−	0.831356i	$-0.687565\pi$
$797$	7.78096	−	7.78096i	0.275616	−	0.275616i	0.831356	+	0.555740i	$0.187565\pi$
$798$	−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	$-0.794062\pi$
$821$		−	34.5427i		−	1.20555i	0.797911	−	0.602775i	$-0.205938\pi$
$822$	5.14561	−	2.79579i	0.179474	−	0.0975145i
$823$	11.9459	−	11.9459i	0.416409	−	0.416409i	−0.467555	−	0.883964i	$-0.654865\pi$
$823$	11.9459	−	11.9459i	0.416409	−	0.416409i	0.883964	+	0.467555i	$0.154865\pi$
$824$	−19.6919			−0.686001
$825$		0			0
$826$	−2.30054			−0.0800460
$827$	20.8624	−	20.8624i	0.725457	−	0.725457i	−0.244254	−	0.969711i	$-0.578543\pi$
$827$	20.8624	−	20.8624i	0.725457	−	0.725457i	0.969711	+	0.244254i	$0.0785431\pi$
$828$	3.65210	+	17.1324i	0.126919	+	0.595392i
$829$			34.6491i			1.20341i	0.798717	+	0.601706i	$0.205512\pi$
$829$			34.6491i			1.20341i	−0.798717	+	0.601706i	$0.794488\pi$
$830$		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	−0.555063	−	0.831808i	$-0.687306\pi$
$853$	8.08267	−	8.08267i	0.276745	−	0.276745i	0.831808	+	0.555063i	$0.187306\pi$
$854$	0.674527			0.0230818
$855$		0			0
$856$	10.4978			0.358807
$857$	14.3191	−	14.3191i	0.489131	−	0.489131i	−0.418901	−	0.908032i	$-0.637585\pi$
$857$	14.3191	−	14.3191i	0.489131	−	0.489131i	0.908032	+	0.418901i	$0.137585\pi$
$858$	2.32446	+	4.27813i	0.0793557	+	0.146053i
$859$		−	25.0614i		−	0.855084i	−0.903995	−	0.427542i	$-0.859380\pi$
$859$		−	25.0614i		−	0.855084i	0.903995	−	0.427542i	$-0.140620\pi$
$860$		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	−0.992170	−	0.124896i	$-0.960140\pi$
$863$	−32.8159	−	32.8159i	−1.11707	−	1.11707i	−0.124896	−	0.992170i	$-0.539860\pi$
$864$	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	0.400170	−	0.916441i	$-0.368951\pi$
$877$	−15.2890	−	15.2890i	−0.516271	−	0.516271i	−0.916441	+	0.400170i	$0.868951\pi$
$878$	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	$-0.836315\pi$
$881$		−	29.1988i		−	0.983734i	0.870670	−	0.491867i	$-0.163685\pi$
$882$	1.07994	−	0.230209i	0.0363634	−	0.00775156i
$883$	24.7944	−	24.7944i	0.834397	−	0.834397i	−0.153718	−	0.988115i	$-0.549125\pi$
$883$	24.7944	−	24.7944i	0.834397	−	0.834397i	0.988115	+	0.153718i	$0.0491247\pi$
$884$	0.836347			0.0281294
$885$		0			0
$886$	−10.0004			−0.335971
$887$	−18.5532	+	18.5532i	−0.622956	+	0.622956i	−0.946286	−	0.323331i	$-0.895197\pi$
$887$	−18.5532	+	18.5532i	−0.622956	+	0.622956i	0.323331	+	0.946286i	$0.395197\pi$
$888$	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	0.648545	−	0.761177i	$-0.275378\pi$
$907$	−3.39207	−	3.39207i	−0.112632	−	0.112632i	−0.761177	+	0.648545i	$0.775378\pi$
$908$	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	$-0.913441\pi$
$911$		−	16.2139i		−	0.537190i	0.963253	−	0.268595i	$-0.0865592\pi$
$912$	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	$0.0291605\pi$
$919$			5.54658i			0.182965i	−0.995807	+	0.0914823i	$0.970839\pi$
$920$		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	0.185119	−	0.982716i	$-0.440733\pi$
$937$	−24.4148	−	24.4148i	−0.797598	−	0.797598i	−0.982716	+	0.185119i	$0.940733\pi$
$938$	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	$0.0193351\pi$
$941$			3.72437i			0.121411i	−0.998156	+	0.0607055i	$0.980665\pi$
$942$	−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	−0.124186	+	0.992259i	$0.539632\pi$
$947$	−34.3568	+	34.3568i	−1.11644	+	1.11644i	−0.992259	+	0.124186i	$0.960368\pi$
$948$	−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	0.965177	−	0.261599i	$-0.0842497\pi$
$953$	21.7199	+	21.7199i	0.703578	+	0.703578i	−0.261599	+	0.965177i	$0.584250\pi$
$954$	−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	0.880616	+	0.473831i	$0.157129\pi$
$967$	42.1187	+	42.1187i	1.35445	+	1.35445i	0.473831	+	0.880616i	$0.342871\pi$
$968$	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	$0.145135\pi$
$971$			27.4414i			0.880638i	−0.897841	+	0.440319i	$0.854865\pi$
$972$	−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	−0.367531	+	0.930011i	$0.619797\pi$
$977$	−40.5573	+	40.5573i	−1.29754	+	1.29754i	−0.930011	+	0.367531i	$0.880203\pi$
$978$	−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	0.381218	−	0.924485i	$-0.375505\pi$
$983$	−17.0329	−	17.0329i	−0.543267	−	0.543267i	−0.924485	+	0.381218i	$0.875505\pi$
$984$	−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	−0.999967	−	0.00814356i	$-0.997408\pi$
$997$	−31.8314	−	31.8314i	−1.00811	−	1.00811i	−0.00814356	−	0.999967i	$-0.502592\pi$
$998$	−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.407.6		24
3.2	odd	2	inner	525.2.j.b.407.7		24
5.2	odd	4		105.2.j.a.8.6	✓	24
5.3	odd	4	inner	525.2.j.b.218.7		24
5.4	even	2		105.2.j.a.92.7	yes	24
15.2	even	4		105.2.j.a.8.7	yes	24
15.8	even	4	inner	525.2.j.b.218.6		24
15.14	odd	2		105.2.j.a.92.6	yes	24
35.2	odd	12		735.2.y.j.263.6		48
35.4	even	6		735.2.y.j.422.7		48
35.9	even	6		735.2.y.j.557.6		48
35.12	even	12		735.2.y.g.263.6		48
35.17	even	12		735.2.y.g.128.7		48
35.19	odd	6		735.2.y.g.557.6		48
35.24	odd	6		735.2.y.g.422.7		48
35.27	even	4		735.2.j.h.638.6		24
35.32	odd	12		735.2.y.j.128.7		48
35.34	odd	2		735.2.j.h.197.7		24
105.2	even	12		735.2.y.j.263.7		48
105.17	odd	12		735.2.y.g.128.6		48
105.32	even	12		735.2.y.j.128.6		48
105.44	odd	6		735.2.y.j.557.7		48
105.47	odd	12		735.2.y.g.263.7		48
105.59	even	6		735.2.y.g.422.6		48
105.62	odd	4		735.2.j.h.638.7		24
105.74	odd	6		735.2.y.j.422.6		48
105.89	even	6		735.2.y.g.557.7		48
105.104	even	2		735.2.j.h.197.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.6	✓	24	5.2	odd	4
105.2.j.a.8.7	yes	24	15.2	even	4
105.2.j.a.92.6	yes	24	15.14	odd	2
105.2.j.a.92.7	yes	24	5.4	even	2
525.2.j.b.218.6		24	15.8	even	4	inner
525.2.j.b.218.7		24	5.3	odd	4	inner
525.2.j.b.407.6		24	1.1	even	1	trivial
525.2.j.b.407.7		24	3.2	odd	2	inner
735.2.j.h.197.6		24	105.104	even	2
735.2.j.h.197.7		24	35.34	odd	2
735.2.j.h.638.6		24	35.27	even	4
735.2.j.h.638.7		24	105.62	odd	4
735.2.y.g.128.6		48	105.17	odd	12
735.2.y.g.128.7		48	35.17	even	12
735.2.y.g.263.6		48	35.12	even	12
735.2.y.g.263.7		48	105.47	odd	12
735.2.y.g.422.6		48	105.59	even	6
735.2.y.g.422.7		48	35.24	odd	6
735.2.y.g.557.6		48	35.19	odd	6
735.2.y.g.557.7		48	105.89	even	6
735.2.y.j.128.6		48	105.32	even	12
735.2.y.j.128.7		48	35.32	odd	12
735.2.y.j.263.6		48	35.2	odd	12
735.2.y.j.263.7		48	105.2	even	12
735.2.y.j.422.6		48	105.74	odd	6
735.2.y.j.422.7		48	35.4	even	6
735.2.y.j.557.6		48	35.9	even	6
735.2.y.j.557.7		48	105.44	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
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