LMFDB - Embedded newform 525.2.j.b.407.7

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			407.7
Character	$\chi$	$=$	525.407
Dual form			525.2.j.b.218.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.260263 - 0.260263i) q^{2} +(1.52191 + 0.826909i) q^{3} +1.86453i q^{4} +(0.611312 - 0.180884i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(1.00579 + 1.00579i) q^{8} +(1.63244 + 2.51697i) q^{9} +O(q^{10})$	\(q+(0.260263 - 0.260263i) q^{2} +(1.52191 + 0.826909i) 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} +(-1.54179 + 2.83765i) q^{12} +(-1.59420 + 1.59420i) q^{13} -0.368068 q^{14} -3.20551 q^{16} +(0.140684 - 0.140684i) q^{17} +(1.07994 + 0.230209i) 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} +(0.403134 + 5.18049i) q^{27} +(1.31842 - 1.31842i) q^{28} +9.49165 q^{29} +0.922582 q^{31} +(-2.84586 + 2.84586i) q^{32} +(-2.80115 + 5.15548i) 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} +(-0.560167 - 0.304359i) q^{42} +(-0.864526 + 0.864526i) q^{43} -6.31608 q^{44} +1.15267 q^{46} +(0.651346 - 0.651346i) q^{47} +(-4.87851 - 2.65066i) 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} +(6.07522 - 11.1814i) q^{57} +(2.47033 - 2.47033i) q^{58} +6.25032 q^{59} +1.83261 q^{61} +(0.240114 - 0.240114i) q^{62} +(0.625454 - 2.93408i) 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} +(-0.889650 + 4.17345i) q^{72} +(4.80768 - 4.80768i) q^{73} -3.07921 q^{74} +13.6985 q^{76} +(2.39532 - 2.39532i) q^{77} +(-0.686187 + 1.26292i) 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} +(14.4455 + 7.84873i) q^{87} +(-3.40712 + 3.40712i) q^{88} -12.3767 q^{89} +2.25454 q^{91} +(-4.12888 + 4.12888i) q^{92} +(1.40409 + 0.762891i) 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	−0.609077	−	0.793111i	$-0.708460\pi$
$2$	0.260263	−	0.260263i	0.184034	−	0.184034i	0.793111	+	0.609077i	$0.208460\pi$
$3$	1.52191	+	0.826909i	0.878677	+	0.477416i
$3$	1.52191	+	0.826909i	0.878677	+	0.477416i
$4$			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	$0.829392\pi$
$12$	−1.54179	+	2.83765i	−0.445077	+	0.819158i
$13$	−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	−0.689840	−	0.723961i	$-0.742319\pi$
$17$	0.140684	−	0.140684i	0.0341210	−	0.0341210i	0.723961	+	0.689840i	$0.242319\pi$
$18$	1.07994	+	0.230209i	0.254544	+	0.0542609i
$19$		−	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	0.899226	−	0.437484i	$-0.144130\pi$
$23$	2.21444	+	2.21444i	0.461742	+	0.461742i	−0.437484	+	0.899226i	$0.644130\pi$
$24$	0.699032	+	2.36243i	0.142689	+	0.482229i
$25$		0			0
$26$			0.829822i			0.162741i
$27$	0.403134	+	5.18049i	0.0775831	+	0.996986i
$28$	1.31842	−	1.31842i	0.249158	−	0.249158i
$29$	9.49165			1.76256			0.881278	−	0.472598i	$-0.156684\pi$
$29$	9.49165			1.76256			0.881278	+	0.472598i	$0.156684\pi$
$30$		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
$33$	−2.80115	+	5.15548i	−0.487618	+	0.897454i
$34$		−	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	$-0.965318\pi$
$41$		−	1.39256i		−	0.217481i	0.994070	−	0.108741i	$-0.0346818\pi$
$42$	−0.560167	−	0.304359i	−0.0864357	−	0.0469636i
$43$	−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	−0.658005	−	0.753014i	$-0.728599\pi$
$47$	0.651346	−	0.651346i	0.0950085	−	0.0950085i	0.753014	+	0.658005i	$0.228599\pi$
$48$	−4.87851	−	2.65066i	−0.704152	−	0.382591i
$49$			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	$-0.0308658\pi$
$53$	6.54108	+	6.54108i	0.898486	+	0.898486i	−0.0968158	+	0.995302i	$0.530866\pi$
$54$	1.45321	+	1.24337i	0.197757	+	0.169201i
$55$		0			0
$56$		−	1.42241i		−	0.190077i
$57$	6.07522	−	11.1814i	0.804683	−	1.48101i
$58$	2.47033	−	2.47033i	0.324370	−	0.324370i
$59$	6.25032			0.813722			0.406861	−	0.913490i	$-0.366623\pi$
$59$	6.25032			0.813722			0.406861	+	0.913490i	$0.366623\pi$
$60$		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
$63$	0.625454	−	2.93408i	0.0787998	−	0.369659i
$64$		−	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	$-0.803002\pi$
$71$		−	9.77651i		−	1.16026i	0.814524	−	0.580129i	$-0.196998\pi$
$72$	−0.889650	+	4.17345i	−0.104846	+	0.491846i
$73$	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
$78$	−0.686187	+	1.26292i	−0.0776954	+	0.142997i
$79$		−	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	0.273693	−	0.961817i	$-0.411755\pi$
$83$	−6.26911	−	6.26911i	−0.688124	−	0.688124i	−0.961817	+	0.273693i	$0.911755\pi$
$84$	3.09673	−	0.916307i	0.337881	−	0.0999773i
$85$		0			0
$86$			0.450009i			0.0485257i
$87$	14.4455	+	7.84873i	1.54872	+	0.841473i
$88$	−3.40712	+	3.40712i	−0.363201	+	0.363201i
$89$	−12.3767			−1.31192			−0.655962	−	0.754794i	$-0.727737\pi$
$89$	−12.3767			−1.31192			−0.655962	+	0.754794i	$0.727737\pi$
$90$		0			0
$91$	2.25454			0.236340
$92$	−4.12888	+	4.12888i	−0.430465	+	0.430465i
$93$	1.40409	+	0.762891i	0.145597	+	0.0791082i
$94$		−	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	$-0.787325\pi$
$101$		−	12.4523i		−	1.23905i	0.784976	−	0.619526i	$-0.212675\pi$
$102$	0.0605545	−	0.111450i	0.00599579	−	0.0110352i
$103$	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	−0.408328	−	0.912835i	$-0.633888\pi$
$107$	5.21866	−	5.21866i	0.504507	−	0.504507i	0.912835	+	0.408328i	$0.133888\pi$
$108$	−9.65916	+	0.751653i	−0.929453	+	0.0723279i
$109$		−	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	0.204276	−	0.978913i	$-0.434516\pi$
$113$	−8.23451	−	8.23451i	−0.774637	−	0.774637i	−0.978913	+	0.204276i	$0.934516\pi$
$114$	−1.32894	−	4.49125i	−0.124467	−	0.420644i
$115$		0			0
$116$			17.6974i			1.64317i
$117$	−6.61498	−	1.41011i	−0.611555	−	0.130365i
$118$	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
$123$	1.15152	−	2.11936i	0.103829	−	0.191096i
$124$			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	$0.128179\pi$
$131$			8.97080i			0.783783i	−0.920012	+	0.391891i	$0.871821\pi$
$132$	−9.61252	−	5.22282i	−0.836663	−	0.454588i
$133$	−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	$-0.878355\pi$
$137$	−6.49538	+	6.49538i	−0.554938	+	0.554938i	0.372924	+	0.927862i	$0.378355\pi$
$138$	1.75427	+	0.953156i	0.149333	+	0.0811380i
$139$			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
$147$	−0.826909	+	1.52191i	−0.0682023	+	0.125525i
$148$	11.0297	−	11.0297i	0.906640	−	0.906640i
$149$	0.987227			0.0808768			0.0404384	−	0.999182i	$-0.487125\pi$
$149$	0.987227			0.0808768			0.0404384	+	0.999182i	$0.487125\pi$
$150$		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
$153$	0.583758	+	0.124439i	0.0471940	+	0.0100603i
$154$		−	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
$162$	1.18351	+	3.09398i	0.0929853	+	0.243086i
$163$	−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	$-0.343816\pi$
$167$	17.4876	−	17.4876i	1.35323	−	1.35323i	0.882018	−	0.471215i	$-0.156184\pi$
$168$	1.17620	−	2.16478i	0.0907459	−	0.167017i
$169$			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	$-0.0511979\pi$
$173$	10.8767	+	10.8767i	0.826942	+	0.826942i	−0.160150	+	0.987093i	$0.551198\pi$
$174$	5.80236	−	1.71689i	0.439876	−	0.130157i
$175$		0			0
$176$		−	10.8587i		−	0.818502i
$177$	9.51244	+	5.16844i	0.714999	+	0.388484i
$178$	−3.22119	+	3.22119i	−0.241439	+	0.241439i
$179$	−17.6524			−1.31941			−0.659703	−	0.751527i	$-0.729318\pi$
$179$	−17.6524			−1.31941			−0.659703	+	0.751527i	$0.729318\pi$
$180$		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
$183$	2.78908	+	1.51541i	0.206175	+	0.112022i
$184$			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	$0.777509\pi$
$192$	4.07639	−	7.50253i	0.294188	−	0.541449i
$193$	−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	−0.838105	−	0.545509i	$-0.816336\pi$
$197$	−4.10678	+	4.10678i	−0.292596	+	0.292596i	0.545509	+	0.838105i	$0.316336\pi$
$198$	−0.779834	+	3.65829i	−0.0554204	+	0.259983i
$199$		−	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
$207$	−1.95873	+	9.18861i	−0.136141	+	0.638653i
$208$	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
$213$	8.08429	−	14.8790i	0.553926	−	1.01949i
$214$		−	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
$222$	−4.68630	−	2.54623i	−0.314524	−	0.170892i
$223$	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	−0.901151	−	0.433506i	$-0.857276\pi$
$227$	−7.04578	+	7.04578i	−0.467645	+	0.467645i	0.433506	+	0.901151i	$0.357276\pi$
$228$	20.8479	+	11.3274i	1.38069	+	0.750176i
$229$		−	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	0.998040	−	0.0625851i	$-0.0199345\pi$
$233$	14.2791	+	14.2791i	0.935455	+	0.935455i	−0.0625851	+	0.998040i	$0.519934\pi$
$234$	−2.08864	+	1.35464i	−0.136538	+	0.0885554i
$235$		0			0
$236$			11.6539i			0.758603i
$237$	2.82564	−	5.20055i	0.183545	−	0.337812i
$238$	−0.0517814	+	0.0517814i	−0.00335649	+	0.00335649i
$239$	−12.8618			−0.831961			−0.415981	−	0.909373i	$-0.636562\pi$
$239$	−12.8618			−0.831961			−0.415981	+	0.909373i	$0.636562\pi$
$240$		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
$243$	−12.3810	+	9.47153i	−0.794244	+	0.607599i
$244$			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	$-0.0815426\pi$
$252$	5.47066	+	1.16618i	0.344619	+	0.0734621i
$253$	−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	$0.511727\pi$
$257$	−16.6108	+	16.6108i	−1.03615	+	1.03615i	−0.999321	+	0.0368323i	$0.988273\pi$
$258$	−0.372116	+	0.684874i	−0.0231669	+	0.0426384i
$259$			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	$-0.0438584\pi$
$263$	13.8361	+	13.8361i	0.853173	+	0.853173i	−0.137350	+	0.990523i	$0.543858\pi$
$264$	−8.00273	+	2.36797i	−0.492534	+	0.145738i
$265$		0			0
$266$			2.70416i			0.165803i
$267$	−18.8362	−	10.2344i	−1.15276	−	0.626334i
$268$	−1.52052	+	1.52052i	−0.0928806	+	0.0928806i
$269$	11.4632			0.698925			0.349463	−	0.936950i	$-0.386364\pi$
$269$	11.4632			0.698925			0.349463	+	0.936950i	$0.386364\pi$
$270$		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
$273$	3.43121	+	1.86430i	0.207666	+	0.112832i
$274$			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	$0.0420160\pi$
$281$			4.41251i			0.263228i	−0.991301	+	0.131614i	$0.957984\pi$
$282$	0.280357	−	0.515994i	0.0166950	−	0.0307270i
$283$	−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
$288$	−11.8087	−	2.51724i	−0.695832	−	0.148330i
$289$			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	$-0.151445\pi$
$293$	7.37595	+	7.37595i	0.430908	+	0.430908i	−0.458029	+	0.888937i	$0.651445\pi$
$294$	0.180884	+	0.611312i	0.0105494	+	0.0356525i
$295$		0			0
$296$		−	11.8997i		−	0.691656i
$297$	−17.5489	+	1.36561i	−1.01829	+	0.0792410i
$298$	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
$303$	10.2969	−	18.9513i	0.591543	−	1.08873i
$304$			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	$0.0815992\pi$
$311$			8.94291i			0.507106i	−0.967322	+	0.253553i	$0.918401\pi$
$312$	−4.88058	−	2.65179i	−0.276308	−	0.150128i
$313$	−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	−0.755443	−	0.655214i	$-0.772578\pi$
$317$	−1.78453	+	1.78453i	−0.100229	+	0.100229i	0.655214	+	0.755443i	$0.272578\pi$
$318$	5.18182	+	2.81546i	0.290582	+	0.157883i
$319$			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
$327$	5.52095	−	10.1612i	0.305309	−	0.561917i
$328$	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
$333$	5.23248	−	24.5462i	0.286738	−	1.34512i
$334$		−	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
$342$	1.69133	−	7.93421i	0.0914565	−	0.429033i
$343$	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	$-0.683228\pi$
$347$	5.48573	−	5.48573i	0.294489	−	0.294489i	0.838851	+	0.544361i	$0.183228\pi$
$348$	−14.6342	+	26.9340i	−0.784474	+	1.44381i
$349$		−	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	0.878990	−	0.476841i	$-0.158218\pi$
$353$	7.55570	+	7.55570i	0.402149	+	0.402149i	−0.476841	+	0.878990i	$0.658218\pi$
$354$	3.82089	−	1.13058i	0.203078	−	0.0600898i
$355$		0			0
$356$		−	23.0766i		−	1.22306i
$357$	−0.302797	−	0.164520i	−0.0160257	−	0.00870732i
$358$	−4.59428	+	4.59428i	−0.242815	+	0.242815i
$359$	6.09504			0.321684			0.160842	−	0.986980i	$-0.448579\pi$
$359$	6.09504			0.321684			0.160842	+	0.986980i	$0.448579\pi$
$360$		0			0
$361$	−34.9770			−1.84090
$362$	−3.10330	+	3.10330i	−0.163106	+	0.163106i
$363$	−0.723114	−	0.392893i	−0.0379536	−	0.0206215i
$364$			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
$372$	−1.42243	+	2.61796i	−0.0737496	+	0.135735i
$373$	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
$378$	−0.148381	−	1.90677i	−0.00763187	−	0.0980738i
$379$		−	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	0.225388	−	0.974269i	$-0.427635\pi$
$383$	−14.6559	−	14.6559i	−0.748882	−	0.748882i	−0.974269	+	0.225388i	$0.927635\pi$
$384$	−4.84748	−	16.3824i	−0.247372	−	0.836012i
$385$		0			0
$386$			7.46402i			0.379909i
$387$	−3.58727	−	0.764695i	−0.182351	−	0.0388716i
$388$	−12.5170	+	12.5170i	−0.635457	+	0.635457i
$389$	−13.6323			−0.691185			−0.345592	−	0.938385i	$-0.612322\pi$
$389$	−13.6323			−0.691185			−0.345592	+	0.938385i	$0.612322\pi$
$390$		0			0
$391$	0.623074			0.0315102
$392$	−1.00579	+	1.00579i	−0.0508003	+	0.0508003i
$393$	−7.41804	+	13.6528i	−0.374190	+	0.688692i
$394$			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	$-0.873496\pi$
$401$		−	15.5011i		−	0.774088i	0.922061	−	0.387044i	$-0.126504\pi$
$402$	0.646036	+	0.351014i	0.0322214	+	0.0175070i
$403$	−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
$408$	0.430700	+	0.234015i	0.0213228	+	0.0115854i
$409$			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
$417$	−1.52081	+	2.79904i	−0.0744746	+	0.137069i
$418$	6.47733	−	6.47733i	0.316817	−	0.316817i
$419$	5.95062			0.290707			0.145353	−	0.989380i	$-0.453568\pi$
$419$	5.95062			0.290707			0.145353	+	0.989380i	$0.453568\pi$
$420$		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
$423$	2.70270	+	0.576132i	0.131410	+	0.0280125i
$424$			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	$-0.0875271\pi$
$432$	−1.29225	−	16.6061i	−0.0621733	−	0.798962i
$433$	−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
$438$	2.06936	−	3.80863i	0.0988779	−	0.181983i
$439$		−	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	0.0836955	−	0.996491i	$-0.473328\pi$
$443$	−19.2121	−	19.2121i	−0.912796	−	0.912796i	−0.996491	+	0.0836955i	$0.973328\pi$
$444$	25.9069	−	7.66573i	1.22949	−	0.363799i
$445$		0			0
$446$		−	6.00850i		−	0.284511i
$447$	1.50247	+	0.816347i	0.0710646	+	0.0386119i
$448$	−3.48580	+	3.48580i	−0.164689	+	0.164689i
$449$	2.40628			0.113559			0.0567796	−	0.998387i	$-0.481917\pi$
$449$	2.40628			0.113559			0.0567796	+	0.998387i	$0.481917\pi$
$450$		0			0
$451$	4.71729			0.222129
$452$	15.3534	−	15.3534i	0.722166	−	0.722166i
$453$	−13.2572	−	7.20307i	−0.622875	−	0.338430i
$454$			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	$0.308769\pi$
$461$			35.4227i			1.64980i	−0.565278	+	0.824900i	$0.691231\pi$
$462$	1.03101	−	1.89757i	0.0479671	−	0.0882827i
$463$	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	−0.828558	−	0.559903i	$-0.810838\pi$
$467$	−5.80567	+	5.80567i	−0.268654	+	0.268654i	0.559903	+	0.828558i	$0.310838\pi$
$468$	2.62918	−	12.3338i	0.121534	−	0.570130i
$469$		−	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
$477$	−5.78575	+	27.1416i	−0.264911	+	1.24273i
$478$	−3.34746	+	3.34746i	−0.153109	+	0.153109i
$479$	−40.3829			−1.84514			−0.922571	−	0.385828i	$-0.873916\pi$
$479$	−40.3829			−1.84514			−0.922571	+	0.385828i	$0.873916\pi$
$480$		0			0
$481$	18.8612			0.859997
$482$	−4.21252	+	4.21252i	−0.191875	+	0.191875i
$483$	2.58962	−	4.76616i	0.117832	−	0.216868i
$484$		−	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	$0.310494\pi$
$491$			36.6924i			1.65590i	−0.560798	+	0.827952i	$0.689506\pi$
$492$	3.95159	+	2.14704i	0.178152	+	0.0967960i
$493$	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
$498$	−4.96636	−	2.69840i	−0.222548	−	0.120918i
$499$			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	0.262521	−	0.964926i	$-0.415446\pi$
$503$	−15.7533	−	15.7533i	−0.702406	−	0.702406i	−0.964926	+	0.262521i	$0.915446\pi$
$504$	3.58016	−	2.32200i	0.159473	−	0.103430i
$505$		0			0
$506$			3.90468i			0.173584i
$507$	−6.54670	+	12.0491i	−0.290749	+	0.535119i
$508$	3.50866	−	3.50866i	0.155672	−	0.155672i
$509$	−14.4091			−0.638673			−0.319336	−	0.947641i	$-0.603460\pi$
$509$	−14.4091			−0.638673			−0.319336	+	0.947641i	$0.603460\pi$
$510$		0			0
$511$	−6.79909			−0.300774
$512$	15.5706	−	15.5706i	0.688130	−	0.688130i
$513$	38.0606	−	2.96178i	1.68042	−	0.130766i
$514$			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	$0.812309\pi$
$522$	10.2504	+	2.18507i	0.448648	+	0.0956378i
$523$	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
$528$	8.97912	−	16.5259i	0.390766	−	0.719199i
$529$		−	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
$537$	−26.8655	−	14.5970i	−1.15933	−	0.629905i
$538$	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
$543$	−18.1468	−	9.85981i	−0.778756	−	0.423125i
$544$			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
$552$	−3.68350	+	6.77942i	−0.156780	+	0.288551i
$553$	−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	$-0.799403\pi$
$557$	−5.15944	+	5.15944i	−0.218613	+	0.218613i	0.589301	+	0.807914i	$0.299403\pi$
$558$	0.996333	+	0.212387i	0.0421781	+	0.00899106i
$559$		−	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	$-0.493718\pi$
$563$	−23.2548	−	23.2548i	−0.980072	−	0.980072i	−0.999805	+	0.0197332i	$0.993718\pi$
$564$	0.844049	+	2.85253i	0.0355409	+	0.120113i
$565$		0			0
$566$			1.07877i			0.0453442i
$567$	8.40600	−	3.21547i	0.353019	−	0.135037i
$568$	9.83316	−	9.83316i	0.412590	−	0.412590i
$569$	45.1914			1.89452			0.947260	−	0.320466i	$-0.103839\pi$
$569$	45.1914			1.89452			0.947260	+	0.320466i	$0.103839\pi$
$570$		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
$573$	−14.7065	+	27.0671i	−0.614372	+	1.13074i
$574$			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
$582$	5.31822	+	2.88958i	0.220447	+	0.119777i
$583$	−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	$-0.785102\pi$
$587$	−3.77086	+	3.77086i	−0.155640	+	0.155640i	0.624992	+	0.780632i	$0.285102\pi$
$588$	−2.83765	−	1.54179i	−0.117023	−	0.0635825i
$589$		−	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	$-0.328242\pi$
$593$	−8.38017	−	8.38017i	−0.344132	−	0.344132i	−0.857918	+	0.513786i	$0.828242\pi$
$594$	−4.21191	+	4.92275i	−0.172817	+	0.201983i
$595$		0			0
$596$			1.84071i			0.0753985i
$597$	11.0928	−	20.4161i	0.453998	−	0.835577i
$598$	−1.83759	+	1.83759i	−0.0751446	+	0.0751446i
$599$	6.75588			0.276038			0.138019	−	0.990430i	$-0.455927\pi$
$599$	6.75588			0.276038			0.138019	+	0.990430i	$0.455927\pi$
$600$		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
$603$	−0.721331	+	3.38385i	−0.0293749	+	0.137801i
$604$		−	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
$612$	−0.232020	+	1.08843i	−0.00937884	+	0.0439972i
$613$	−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	−0.588373	−	0.808590i	$-0.700231\pi$
$617$	5.47009	−	5.47009i	0.220218	−	0.220218i	0.808590	+	0.588373i	$0.200231\pi$
$618$	4.21357	−	7.75500i	0.169494	−	0.311952i
$619$		−	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
$627$	37.8768	+	20.5798i	1.51265	+	0.821878i
$628$	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
$633$	12.3507	+	6.71057i	0.490897	+	0.266721i
$634$			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	$-0.208141\pi$
$642$	2.24626	−	4.13420i	0.0886527	−	0.163164i
$643$	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	−0.997108	−	0.0759964i	$-0.975786\pi$
$647$	−23.4296	+	23.4296i	−0.921112	+	0.921112i	0.0759964	+	0.997108i	$0.475786\pi$
$648$	−11.9568	+	4.57370i	−0.469706	+	0.179672i
$649$			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	$-0.0921786\pi$
$653$	17.1928	+	17.1928i	0.672805	+	0.672805i	−0.285557	+	0.958362i	$0.592179\pi$
$654$	−1.20769	−	4.08150i	−0.0472246	−	0.159599i
$655$		0			0
$656$			4.46386i			0.174285i
$657$	19.9490	+	4.25252i	0.778286	+	0.165906i
$658$	−0.239739	+	0.239739i	−0.00934601	+	0.00934601i
$659$	−0.0375362			−0.00146220			−0.000731101	−	1.00000i	$-0.500233\pi$
$659$	−0.0375362			−0.00146220			−0.000731101		1.00000i	$0.500233\pi$
$660$		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
$663$	−0.370916	+	0.682666i	−0.0144052	+	0.0265125i
$664$		−	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
$672$	6.12519	+	3.32803i	0.236284	+	0.128381i
$673$	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	−0.633556	−	0.773697i	$-0.718405\pi$
$677$	3.64637	−	3.64637i	0.140142	−	0.140142i	0.773697	+	0.633556i	$0.218405\pi$
$678$	−6.52335	−	3.54436i	−0.250528	−	0.136120i
$679$		−	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	$-0.883555\pi$
$683$	−33.7536	−	33.7536i	−1.29155	−	1.29155i	−0.357718	−	0.933830i	$-0.616445\pi$
$684$	22.3620	+	34.4787i	0.855033	+	1.31833i
$685$		0			0
$686$		−	0.368068i		−	0.0140529i
$687$	3.97013	−	7.30696i	0.151470	−	0.278778i
$688$	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
$693$	9.93918	+	2.11872i	0.377558	+	0.0804836i
$694$		−	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	$-0.134999\pi$
$702$	−4.29889	+	0.334529i	−0.162251	+	0.0126260i
$703$	−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
$708$	−9.63670	+	17.7362i	−0.362169	+	0.666567i
$709$			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
$717$	−19.5746	−	10.6355i	−0.731026	−	0.397192i
$718$	1.58632	−	1.58632i	0.0592008	−	0.0592008i
$719$	39.3153			1.46621			0.733106	−	0.680114i	$-0.238070\pi$
$719$	39.3153			1.46621			0.733106	+	0.680114i	$0.238070\pi$
$720$		0			0
$721$	−13.8441			−0.515581
$722$	−9.10324	+	9.10324i	−0.338787	+	0.338787i
$723$	−24.6331	−	13.3840i	−0.916115	−	0.497757i
$724$		−	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
$732$	−2.82551	+	5.20032i	−0.104434	+	0.192209i
$733$	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
$738$	0.320580	−	1.50388i	0.0118007	−	0.0553586i
$739$		−	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	0.990126	−	0.140180i	$-0.0447681\pi$
$743$	23.1679	+	23.1679i	0.849946	+	0.849946i	−0.140180	+	0.990126i	$0.544768\pi$
$744$	0.644914	+	2.17954i	0.0236437	+	0.0799057i
$745$		0			0
$746$		−	3.68059i		−	0.134756i
$747$	5.54518	−	26.0131i	0.202888	−	0.951770i
$748$	−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
$753$	6.63894	−	12.2189i	0.241936	−	0.445280i
$754$			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	$0.211326\pi$
$761$			33.9969i			1.23239i	−0.787596	+	0.616193i	$0.788674\pi$
$762$	−1.49075	−	0.809978i	−0.0540043	−	0.0293424i
$763$	−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
$768$	9.47970	+	5.15065i	0.342069	+	0.185858i
$769$			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	0.857075	−	0.515192i	$-0.172279\pi$
$773$	9.50533	+	9.50533i	0.341883	+	0.341883i	−0.515192	+	0.857075i	$0.672279\pi$
$774$	−1.13266	+	0.734614i	−0.0407125	+	0.0264051i
$775$		0			0
$776$			13.5043i			0.484777i
$777$	−6.91783	+	12.7322i	−0.248176	+	0.456764i
$778$	−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
$783$	3.82640	+	49.1714i	0.136745	+	1.75724i
$784$		−	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
$792$	−14.1376	−	3.01369i	−0.502356	−	0.107087i
$793$	−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	$-0.812435\pi$
$797$	−7.78096	+	7.78096i	−0.275616	+	0.275616i	0.555740	+	0.831356i	$0.312435\pi$
$798$	−2.23609	+	4.11550i	−0.0791569	+	0.145687i
$799$		−	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
$807$	17.4460	+	9.47905i	0.614130	+	0.333678i
$808$	12.5245	−	12.5245i	0.440609	−	0.440609i
$809$	28.7871			1.01210			0.506051	−	0.862504i	$-0.331105\pi$
$809$	28.7871			1.01210			0.506051	+	0.862504i	$0.331105\pi$
$810$		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
$813$	12.8187	+	6.96485i	0.449572	+	0.244268i
$814$		−	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	$0.794062\pi$
$822$	−2.79579	+	5.14561i	−0.0975145	+	0.179474i
$823$	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	−0.969711	−	0.244254i	$-0.921457\pi$
$827$	−20.8624	+	20.8624i	−0.725457	+	0.725457i	0.244254	+	0.969711i	$0.421457\pi$
$828$	−17.1324	−	3.65210i	−0.595392	−	0.126919i
$829$			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
$837$	0.371924	+	4.77943i	0.0128556	+	0.165201i
$838$	1.54873	−	1.54873i	0.0534999	−	0.0534999i
$839$	−10.9282			−0.377283			−0.188642	−	0.982046i	$-0.560408\pi$
$839$	−10.9282			−0.377283			−0.188642	+	0.982046i	$0.560408\pi$
$840$		0			0
$841$	61.0915			2.10660
$842$	−2.76889	+	2.76889i	−0.0954223	+	0.0954223i
$843$	−3.64874	+	6.71546i	−0.125669	+	0.231293i
$844$			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
$852$	27.7423	+	15.0734i	0.950436	+	0.516405i
$853$	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	−0.908032	−	0.418901i	$-0.862415\pi$
$857$	−14.3191	+	14.3191i	−0.489131	+	0.489131i	0.418901	+	0.908032i	$0.362415\pi$
$858$	−4.27813	−	2.32446i	−0.146053	−	0.0793557i
$859$		−	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	$0.0398598\pi$
$863$	32.8159	+	32.8159i	1.11707	+	1.11707i	0.124896	+	0.992170i	$0.460140\pi$
$864$	−15.8902	−	13.5957i	−0.540597	−	0.462535i
$865$		0			0
$866$			5.07564i			0.172477i
$867$	−14.0247	+	25.8123i	−0.476304	+	0.876631i
$868$	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
$873$	−5.93805	+	27.8561i	−0.200972	+	0.942785i
$874$		−	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	$0.163685\pi$
$881$			29.1988i			0.983734i	−0.870670	+	0.491867i	$0.836315\pi$
$882$	−0.230209	+	1.07994i	−0.00775156	+	0.0363634i
$883$	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	−0.323331	−	0.946286i	$-0.604803\pi$
$887$	18.5532	−	18.5532i	0.622956	−	0.622956i	0.946286	+	0.323331i	$0.104803\pi$
$888$	9.83997	−	18.1103i	0.330208	−	0.607743i
$889$			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
$897$	−10.7455	−	5.83839i	−0.358781	−	0.194938i
$898$	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
$903$	1.86073	+	1.01100i	0.0619212	+	0.0336439i
$904$		−	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	$0.0865592\pi$
$911$			16.2139i			0.537190i	−0.963253	+	0.268595i	$0.913441\pi$
$912$	−19.4742	+	35.8419i	−0.644855	+	1.18685i
$913$	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
$918$	0.379367	−	0.0295215i	0.0125210	−	0.000974354i
$919$			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
$927$	40.6196	+	8.65884i	1.33412	+	0.284393i
$928$	−27.0120	+	27.0120i	−0.886711	+	0.886711i
$929$	−12.7978			−0.419884			−0.209942	−	0.977714i	$-0.567327\pi$
$929$	−12.7978			−0.419884			−0.209942	+	0.977714i	$0.567327\pi$
$930$		0			0
$931$	7.34691			0.240785
$932$	−26.6237	+	26.6237i	−0.872090	+	0.872090i
$933$	−7.39497	+	13.6103i	−0.242100	+	0.445582i
$934$			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	$-0.980665\pi$
$941$		−	3.72437i		−	0.121411i	0.998156	−	0.0607055i	$-0.0193351\pi$
$942$	−4.16938	−	2.26537i	−0.135846	−	0.0738097i
$943$	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	$-0.460368\pi$
$947$	34.3568	−	34.3568i	1.11644	−	1.11644i	0.992259	−	0.124186i	$-0.0396318\pi$
$948$	9.69657	+	5.26849i	0.314930	+	0.171112i
$949$			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	$-0.415750\pi$
$953$	−21.7199	−	21.7199i	−0.703578	−	0.703578i	−0.965177	+	0.261599i	$0.915750\pi$
$954$	5.55815	+	8.56979i	0.179952	+	0.277457i
$955$		0			0
$956$		−	23.9812i		−	0.775607i
$957$	−26.5876	+	48.9340i	−0.859454	+	1.58181i
$958$	−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
$963$	21.6544	+	4.61604i	0.697802	+	0.148750i
$964$		−	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	$-0.854865\pi$
$971$		−	27.4414i		−	0.880638i	0.897841	−	0.440319i	$-0.145135\pi$
$972$	−17.6599	−	23.0848i	−0.566442	−	0.740444i
$973$	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	$-0.380203\pi$
$977$	40.5573	−	40.5573i	1.29754	−	1.29754i	0.930011	−	0.367531i	$-0.119797\pi$
$978$	−6.09104	+	11.2105i	−0.194770	+	0.358471i
$979$		−	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	$-0.124495\pi$
$983$	17.0329	+	17.0329i	0.543267	+	0.543267i	−0.381218	+	0.924485i	$0.624495\pi$
$984$	3.28983	−	0.973443i	0.104876	−	0.0310322i
$985$		0			0
$986$		−	0.695074i		−	0.0221357i
$987$	−1.40190	−	0.761700i	−0.0446229	−	0.0242452i
$988$	−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
$993$	−5.50716	−	2.99223i	−0.174764	−	0.0949556i
$994$			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.407.7		24
3.2	odd	2	inner	525.2.j.b.407.6		24
5.2	odd	4		105.2.j.a.8.7	yes	24
5.3	odd	4	inner	525.2.j.b.218.6		24
5.4	even	2		105.2.j.a.92.6	yes	24
15.2	even	4		105.2.j.a.8.6	✓	24
15.8	even	4	inner	525.2.j.b.218.7		24
15.14	odd	2		105.2.j.a.92.7	yes	24
35.2	odd	12		735.2.y.j.263.7		48
35.4	even	6		735.2.y.j.422.6		48
35.9	even	6		735.2.y.j.557.7		48
35.12	even	12		735.2.y.g.263.7		48
35.17	even	12		735.2.y.g.128.6		48
35.19	odd	6		735.2.y.g.557.7		48
35.24	odd	6		735.2.y.g.422.6		48
35.27	even	4		735.2.j.h.638.7		24
35.32	odd	12		735.2.y.j.128.6		48
35.34	odd	2		735.2.j.h.197.6		24
105.2	even	12		735.2.y.j.263.6		48
105.17	odd	12		735.2.y.g.128.7		48
105.32	even	12		735.2.y.j.128.7		48
105.44	odd	6		735.2.y.j.557.6		48
105.47	odd	12		735.2.y.g.263.6		48
105.59	even	6		735.2.y.g.422.7		48
105.62	odd	4		735.2.j.h.638.6		24
105.74	odd	6		735.2.y.j.422.7		48
105.89	even	6		735.2.y.g.557.6		48
105.104	even	2		735.2.j.h.197.7		24

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.260263 - 0.260263i) q^{2} +(1.52191 + 0.826909i) q^{3} +1.86453i q^{4} +(0.611312 - 0.180884i) q^{6} +(-0.707107 - 0.707107i) q^{7} +(1.00579 + 1.00579i) q^{8} +(1.63244 + 2.51697i) q^{9} +O(q^{10})\)	\(q+(0.260263 - 0.260263i) q^{2} +(1.52191 + 0.826909i) 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} +(-1.54179 + 2.83765i) q^{12} +(-1.59420 + 1.59420i) q^{13} -0.368068 q^{14} -3.20551 q^{16} +(0.140684 - 0.140684i) q^{17} +(1.07994 + 0.230209i) 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} +(0.403134 + 5.18049i) q^{27} +(1.31842 - 1.31842i) q^{28} +9.49165 q^{29} +0.922582 q^{31} +(-2.84586 + 2.84586i) q^{32} +(-2.80115 + 5.15548i) 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} +(-0.560167 - 0.304359i) q^{42} +(-0.864526 + 0.864526i) q^{43} -6.31608 q^{44} +1.15267 q^{46} +(0.651346 - 0.651346i) q^{47} +(-4.87851 - 2.65066i) 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} +(6.07522 - 11.1814i) q^{57} +(2.47033 - 2.47033i) q^{58} +6.25032 q^{59} +1.83261 q^{61} +(0.240114 - 0.240114i) q^{62} +(0.625454 - 2.93408i) 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} +(-0.889650 + 4.17345i) q^{72} +(4.80768 - 4.80768i) q^{73} -3.07921 q^{74} +13.6985 q^{76} +(2.39532 - 2.39532i) q^{77} +(-0.686187 + 1.26292i) 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} +(14.4455 + 7.84873i) q^{87} +(-3.40712 + 3.40712i) q^{88} -12.3767 q^{89} +2.25454 q^{91} +(-4.12888 + 4.12888i) q^{92} +(1.40409 + 0.762891i) 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

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