LMFDB - Embedded newform 684.2.ce.a.575.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,2,Mod(35,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 4]))

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

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

chi := DirichletCharacter("684.35");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	684.ce (of order $18$, degree $6$, 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:	$5.46176749826$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			575.11
Character	$\chi$	$=$	684.575
Dual form			684.2.ce.a.251.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.829576 + 1.14534i) q^{2} +(-0.623609 - 1.90029i) q^{4} +(1.97780 - 2.35705i) q^{5} +(-0.213423 + 0.123220i) q^{7} +(2.69381 + 0.862192i) q^{8} +O(q^{10})$	\(q+(-0.829576 + 1.14534i) q^{2} +(-0.623609 - 1.90029i) q^{4} +(1.97780 - 2.35705i) q^{5} +(-0.213423 + 0.123220i) q^{7} +(2.69381 + 0.862192i) q^{8} +(1.05889 + 4.22060i) q^{10} +(1.66759 - 2.88835i) q^{11} +(0.255665 + 1.44995i) q^{13} +(0.0359218 - 0.346661i) q^{14} +(-3.22222 + 2.37008i) q^{16} +(-1.37907 - 3.78896i) q^{17} +(-4.21099 + 1.12585i) q^{19} +(-5.71245 - 2.28852i) q^{20} +(1.92475 + 4.30606i) q^{22} +(-1.15211 + 0.966731i) q^{23} +(-0.775745 - 4.39947i) q^{25} +(-1.87278 - 0.910017i) q^{26} +(0.367245 + 0.328725i) q^{28} +(3.23621 - 8.89141i) q^{29} +(8.51714 - 4.91737i) q^{31} +(-0.0414673 - 5.65670i) q^{32} +(5.48369 + 1.56373i) q^{34} +(-0.131672 + 0.746750i) q^{35} -8.95491 q^{37} +(2.20385 - 5.75700i) q^{38} +(7.36004 - 4.64420i) q^{40} +(2.41466 + 0.425770i) q^{41} +(0.532361 - 0.634443i) q^{43} +(-6.52863 - 1.36771i) q^{44} +(-0.151478 - 2.12153i) q^{46} +(-4.56635 - 1.66202i) q^{47} +(-3.46963 + 6.00958i) q^{49} +(5.68243 + 2.76120i) q^{50} +(2.59589 - 1.39004i) q^{52} +(1.74518 + 2.07983i) q^{53} +(-3.50982 - 9.64314i) q^{55} +(-0.681159 + 0.147919i) q^{56} +(7.49901 + 11.0827i) q^{58} +(4.48342 - 1.63183i) q^{59} +(4.36183 - 3.66001i) q^{61} +(-1.43355 + 13.8344i) q^{62} +(6.51325 + 4.64517i) q^{64} +(3.92324 + 2.26509i) q^{65} +(3.69523 - 10.1526i) q^{67} +(-6.34014 + 4.98346i) q^{68} +(-0.746051 - 0.770295i) q^{70} +(11.7439 + 9.85428i) q^{71} +(-0.863085 + 4.89480i) q^{73} +(7.42878 - 10.2564i) q^{74} +(4.76546 + 7.30003i) q^{76} +0.821918i q^{77} +(7.00868 + 1.23582i) q^{79} +(-0.786520 + 12.2825i) q^{80} +(-2.49079 + 2.41240i) q^{82} +(-1.94795 - 3.37394i) q^{83} +(-11.6583 - 4.24326i) q^{85} +(0.285020 + 1.13605i) q^{86} +(6.98248 - 6.34288i) q^{88} +(3.87464 - 0.683204i) q^{89} +(-0.233226 - 0.277948i) q^{91} +(2.55553 + 1.58648i) q^{92} +(5.69171 - 3.85126i) q^{94} +(-5.67480 + 12.1522i) q^{95} +(-0.106910 + 0.0389119i) q^{97} +(-4.00469 - 8.95931i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 12 q^{4}+O(q^{10}) $ 240 * q + 12 * q^4	$ 240 q + 12 q^{4} + 12 q^{10} + 24 q^{13} - 12 q^{16} - 12 q^{34} + 120 q^{49} - 48 q^{52} - 144 q^{58} + 48 q^{61} - 12 q^{64} - 72 q^{70} + 72 q^{73} - 144 q^{76} - 72 q^{82} + 240 q^{85} - 48 q^{88} - 48 q^{94}+O(q^{100}) $ 240 * q + 12 * q^4 + 12 * q^10 + 24 * q^13 - 12 * q^16 - 12 * q^34 + 120 * q^49 - 48 * q^52 - 144 * q^58 + 48 * q^61 - 12 * q^64 - 72 * q^70 + 72 * q^73 - 144 * q^76 - 72 * q^82 + 240 * q^85 - 48 * q^88 - 48 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$e\left(\frac{8}{9}\right)$	$-1$	$-1$

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 $

$2$	−0.829576	+	1.14534i	−0.586599	+	0.809878i
$2$	−0.829576	+	1.14534i	−0.586599	+	0.809878i
$3$		0			0
$3$		0			0
$4$	−0.623609	−	1.90029i	−0.311804	−	0.950146i
$5$	1.97780	−	2.35705i	0.884497	−	1.05410i	−0.113666	−	0.993519i	$-0.536259\pi$
$5$	1.97780	−	2.35705i	0.884497	−	1.05410i	0.998163	−	0.0605837i	$-0.0192962\pi$
$6$		0			0
$7$	−0.213423	+	0.123220i	−0.0806661	+	0.0465726i	−0.539791	−	0.841799i	$-0.681497\pi$
$7$	−0.213423	+	0.123220i	−0.0806661	+	0.0465726i	0.459124	+	0.888372i	$0.348163\pi$
$8$	2.69381	+	0.862192i	0.952406	+	0.304831i
$9$		0			0
$10$	1.05889	+	4.22060i	0.334850	+	1.33467i
$11$	1.66759	−	2.88835i	0.502797	−	0.870869i	−0.497198	−	0.867637i	$-0.665638\pi$
$11$	1.66759	−	2.88835i	0.502797	−	0.870869i	0.999995	−	0.00323239i	$-0.00102890\pi$
$12$		0			0
$13$	0.255665	+	1.44995i	0.0709086	+	0.402143i	0.999517	+	0.0310812i	$0.00989504\pi$
$13$	0.255665	+	1.44995i	0.0709086	+	0.402143i	−0.928608	+	0.371062i	$0.878994\pi$
$14$	0.0359218	−	0.346661i	0.00960051	−	0.0926492i
$15$		0			0
$16$	−3.22222	+	2.37008i	−0.805556	+	0.592520i
$17$	−1.37907	−	3.78896i	−0.334473	−	0.918958i	−0.986933	−	0.161134i	$-0.948485\pi$
$17$	−1.37907	−	3.78896i	−0.334473	−	0.918958i	0.652459	−	0.757824i	$-0.273737\pi$
$18$		0			0
$19$	−4.21099	+	1.12585i	−0.966068	+	0.258288i
$19$	−4.21099	+	1.12585i	−0.966068	+	0.258288i
$20$	−5.71245	−	2.28852i	−1.27734	−	0.511728i
$21$		0			0
$22$	1.92475	+	4.30606i	0.410358	+	0.918055i
$23$	−1.15211	+	0.966731i	−0.240231	+	0.201577i	−0.754952	−	0.655780i	$-0.772340\pi$
$23$	−1.15211	+	0.966731i	−0.240231	+	0.201577i	0.514721	+	0.857358i	$0.327895\pi$
$24$		0			0
$25$	−0.775745	−	4.39947i	−0.155149	−	0.879894i
$26$	−1.87278	−	0.910017i	−0.367282	−	0.178469i
$27$		0			0
$28$	0.367245	+	0.328725i	0.0694029	+	0.0621231i
$29$	3.23621	−	8.89141i	0.600949	−	1.65109i	−0.148407	−	0.988926i	$-0.547414\pi$
$29$	3.23621	−	8.89141i	0.600949	−	1.65109i	0.749356	−	0.662168i	$-0.230363\pi$
$30$		0			0
$31$	8.51714	−	4.91737i	1.52972	−	0.883186i	0.530351	−	0.847778i	$-0.322060\pi$
$31$	8.51714	−	4.91737i	1.52972	−	0.883186i	0.999373	−	0.0354082i	$-0.0112732\pi$
$32$	−0.0414673	−	5.65670i	−0.00733045	−	0.999973i
$33$		0			0
$34$	5.48369	+	1.56373i	0.940445	+	0.268177i
$35$	−0.131672	+	0.746750i	−0.0222567	+	0.126224i
$36$		0			0
$37$	−8.95491			−1.47218			−0.736089	−	0.676885i	$-0.763330\pi$
$37$	−8.95491			−1.47218			−0.736089	+	0.676885i	$0.763330\pi$
$38$	2.20385	−	5.75700i	0.357512	−	0.933908i
$39$		0			0
$40$	7.36004	−	4.64420i	1.16372	−	0.734312i
$41$	2.41466	+	0.425770i	0.377106	+	0.0664940i	0.358989	−	0.933342i	$-0.383122\pi$
$41$	2.41466	+	0.425770i	0.377106	+	0.0664940i	0.0181175	+	0.999836i	$0.494233\pi$
$42$		0			0
$43$	0.532361	−	0.634443i	0.0811843	−	0.0967517i	−0.723923	−	0.689880i	$-0.757663\pi$
$43$	0.532361	−	0.634443i	0.0811843	−	0.0967517i	0.805108	+	0.593129i	$0.202108\pi$
$44$	−6.52863	−	1.36771i	−0.984228	−	0.206190i
$45$		0			0
$46$	−0.151478	−	2.12153i	−0.0223342	−	0.312802i
$47$	−4.56635	−	1.66202i	−0.666071	−	0.242430i	−0.0132156	−	0.999913i	$-0.504207\pi$
$47$	−4.56635	−	1.66202i	−0.666071	−	0.242430i	−0.652855	+	0.757483i	$0.726429\pi$
$48$		0			0
$49$	−3.46963	+	6.00958i	−0.495662	+	0.858512i
$50$	5.68243	+	2.76120i	0.803617	+	0.390493i
$51$		0			0
$52$	2.59589	−	1.39004i	0.359985	−	0.192763i
$53$	1.74518	+	2.07983i	0.239719	+	0.285686i	0.872468	−	0.488671i	$-0.162518\pi$
$53$	1.74518	+	2.07983i	0.239719	+	0.285686i	−0.632749	+	0.774357i	$0.718074\pi$
$54$		0			0
$55$	−3.50982	−	9.64314i	−0.473264	−	1.30028i
$56$	−0.681159	+	0.147919i	−0.0910237	+	0.0197665i
$57$		0			0
$58$	7.49901	+	11.0827i	0.984669	+	1.45522i
$59$	4.48342	−	1.63183i	0.583691	−	0.212446i	−0.0332610	−	0.999447i	$-0.510589\pi$
$59$	4.48342	−	1.63183i	0.583691	−	0.212446i	0.616953	+	0.787000i	$0.288367\pi$
$60$		0			0
$61$	4.36183	−	3.66001i	0.558475	−	0.468616i	−0.319324	−	0.947646i	$-0.603456\pi$
$61$	4.36183	−	3.66001i	0.558475	−	0.468616i	0.877799	+	0.479030i	$0.159011\pi$
$62$	−1.43355	+	13.8344i	−0.182061	+	1.75697i
$63$		0			0
$64$	6.51325	+	4.64517i	0.814156	+	0.580646i
$65$	3.92324	+	2.26509i	0.486618	+	0.280949i
$66$		0			0
$67$	3.69523	−	10.1526i	0.451444	−	1.24033i	−0.480264	−	0.877124i	$-0.659459\pi$
$67$	3.69523	−	10.1526i	0.451444	−	1.24033i	0.931708	−	0.363209i	$-0.118319\pi$
$68$	−6.34014	+	4.98346i	−0.768854	+	0.604334i
$69$		0			0
$70$	−0.746051	−	0.770295i	−0.0891701	−	0.0920678i
$71$	11.7439	+	9.85428i	1.39374	+	1.16949i	0.963798	+	0.266632i	$0.0859109\pi$
$71$	11.7439	+	9.85428i	1.39374	+	1.16949i	0.429943	+	0.902856i	$0.358534\pi$
$72$		0			0
$73$	−0.863085	+	4.89480i	−0.101016	+	0.572893i	0.891720	+	0.452587i	$0.149499\pi$
$73$	−0.863085	+	4.89480i	−0.101016	+	0.572893i	−0.992737	+	0.120306i	$0.961612\pi$
$74$	7.42878	−	10.2564i	0.863578	−	1.19228i
$75$		0			0
$76$	4.76546	+	7.30003i	0.546636	+	0.837371i
$77$			0.821918i			0.0936662i
$78$		0			0
$79$	7.00868	+	1.23582i	0.788539	+	0.139041i	0.553394	−	0.832920i	$-0.313332\pi$
$79$	7.00868	+	1.23582i	0.788539	+	0.139041i	0.235145	+	0.971960i	$0.424444\pi$
$80$	−0.786520	+	12.2825i	−0.0879357	+	1.37322i
$81$		0			0
$82$	−2.49079	+	2.41240i	−0.275062	+	0.266405i
$83$	−1.94795	−	3.37394i	−0.213815	−	0.370338i	0.739090	−	0.673606i	$-0.235256\pi$
$83$	−1.94795	−	3.37394i	−0.213815	−	0.370338i	−0.952905	+	0.303268i	$0.901922\pi$
$84$		0			0
$85$	−11.6583	−	4.24326i	−1.26452	−	0.460247i
$86$	0.285020	+	1.13605i	0.0307344	+	0.122504i
$87$		0			0
$88$	6.98248	−	6.34288i	0.744335	−	0.676154i
$89$	3.87464	−	0.683204i	0.410711	−	0.0724194i	0.0355246	−	0.999369i	$-0.488690\pi$
$89$	3.87464	−	0.683204i	0.410711	−	0.0724194i	0.375186	+	0.926949i	$0.377579\pi$
$90$		0			0
$91$	−0.233226	−	0.277948i	−0.0244488	−	0.0291369i
$92$	2.55553	+	1.58648i	0.266433	+	0.165401i
$93$		0			0
$94$	5.69171	−	3.85126i	0.587055	−	0.397227i
$95$	−5.67480	+	12.1522i	−0.582222	+	1.24679i
$96$		0			0
$97$	−0.106910	+	0.0389119i	−0.0108550	+	0.00395090i	−0.347442	−	0.937701i	$-0.612950\pi$
$97$	−0.106910	+	0.0389119i	−0.0108550	+	0.00395090i	0.336587	+	0.941652i	$0.390727\pi$
$98$	−4.00469	−	8.95931i	−0.404535	−	0.905027i
$99$		0			0
$100$	−7.87652	+	4.21769i	−0.787652	+	0.421769i
$101$	−11.1632	+	1.96838i	−1.11078	+	0.195861i	−0.698791	−	0.715326i	$-0.746278\pi$
$101$	−11.1632	+	1.96838i	−1.11078	+	0.195861i	−0.411993	+	0.911187i	$0.635167\pi$
$102$		0			0
$103$	3.25834	+	1.88120i	0.321054	+	0.185360i	0.651862	−	0.758337i	$-0.273988\pi$
$103$	3.25834	+	1.88120i	0.321054	+	0.185360i	−0.330808	+	0.943698i	$0.607321\pi$
$104$	−0.561420	+	4.12632i	−0.0550518	+	0.404619i
$105$		0			0
$106$	−3.82987	+	0.273454i	−0.371990	+	0.0265602i
$107$	2.04026	+	3.53384i	0.197240	+	0.341629i	0.947632	−	0.319363i	$-0.103469\pi$
$107$	2.04026	+	3.53384i	0.197240	+	0.341629i	−0.750393	+	0.660992i	$0.770136\pi$
$108$		0			0
$109$	−3.49198	−	2.93012i	−0.334471	−	0.280655i	0.460047	−	0.887894i	$-0.347832\pi$
$109$	−3.49198	−	2.93012i	−0.334471	−	0.280655i	−0.794519	+	0.607240i	$0.792277\pi$
$110$	13.9563	+	3.97978i	1.33068	+	0.379457i
$111$		0			0
$112$	0.395655	−	0.902869i	0.0373859	−	0.0853131i
$113$		−	7.15002i		−	0.672617i	−0.941752	−	0.336309i	$-0.890821\pi$
$113$		−	7.15002i		−	0.672617i	0.941752	−	0.336309i	$-0.109179\pi$
$114$		0			0
$115$			4.62756i			0.431522i
$116$	−18.9144	−	0.604983i	−1.75616	−	0.0561713i
$117$		0			0
$118$	−1.85033	+	6.48877i	−0.170337	+	0.597340i
$119$	0.761199	+	0.638721i	0.0697790	+	0.0585515i
$120$		0			0
$121$	−0.0617000	−	0.106868i	−0.00560909	−	0.00971523i
$122$	0.573489	+	8.03203i	0.0519212	+	0.727186i
$123$		0			0
$124$	−14.6558	−	13.1185i	−1.31613	−	1.17808i
$125$	1.41937	+	0.819473i	0.126952	+	0.0732959i
$126$		0			0
$127$	−8.24054	+	1.45303i	−0.731229	+	0.128935i	−0.526852	−	0.849957i	$-0.676628\pi$
$127$	−8.24054	+	1.45303i	−0.731229	+	0.128935i	−0.204377	+	0.978892i	$0.565517\pi$
$128$	−10.7235	+	3.60637i	−0.947835	+	0.318761i
$129$		0			0
$130$	−5.84892	+	2.61439i	−0.512984	+	0.229297i
$131$	15.6537	−	5.69749i	1.36767	−	0.497792i	0.449255	−	0.893403i	$-0.351689\pi$
$131$	15.6537	−	5.69749i	1.36767	−	0.497792i	0.918418	+	0.395611i	$0.129467\pi$
$132$		0			0
$133$	0.759994	−	0.759159i	0.0658998	−	0.0658274i
$134$	8.56267	+	12.6546i	0.739702	+	1.09319i
$135$		0			0
$136$	−0.448140	−	11.3958i	−0.0384277	−	0.977179i
$137$	−5.93591	−	7.07414i	−0.507139	−	0.604385i	0.450351	−	0.892852i	$-0.351299\pi$
$137$	−5.93591	−	7.07414i	−0.507139	−	0.604385i	−0.957490	+	0.288467i	$0.906854\pi$
$138$		0			0
$139$	−16.4760	+	2.90516i	−1.39747	+	0.246412i	−0.821105	−	0.570777i	$-0.806642\pi$
$139$	−16.4760	+	2.90516i	−1.39747	+	0.246412i	−0.576369	+	0.817190i	$0.695531\pi$
$140$	1.50116	−	0.215464i	0.126871	−	0.0182100i
$141$		0			0
$142$	−21.0289	+	5.27586i	−1.76471	+	0.442741i
$143$	4.61429	+	1.67947i	0.385867	+	0.140444i
$144$		0			0
$145$	−14.5569	−	25.2133i	−1.20888	−	2.09385i
$146$	−4.89021	−	5.04913i	−0.404717	−	0.417869i
$147$		0			0
$148$	5.58436	+	17.0170i	0.459032	+	1.39878i
$149$	−16.0696	−	2.83351i	−1.31647	−	0.232130i	−0.529076	−	0.848574i	$-0.677461\pi$
$149$	−16.0696	−	2.83351i	−1.31647	−	0.232130i	−0.787399	+	0.616444i	$0.788573\pi$
$150$		0			0
$151$			11.9193i			0.969982i	0.874519	+	0.484991i	$0.161177\pi$
$151$			11.9193i			0.969982i	−0.874519	+	0.484991i	$0.838823\pi$
$152$	−12.3143	−	0.597851i	−0.998824	−	0.0484921i
$153$		0			0
$154$	−0.941376	−	0.681843i	−0.0758582	−	0.0549445i
$155$	5.25469	−	29.8009i	0.422067	−	2.39366i
$156$		0			0
$157$	6.01399	+	5.04634i	0.479969	+	0.402742i	0.850415	−	0.526112i	$-0.176351\pi$
$157$	6.01399	+	5.04634i	0.479969	+	0.402742i	−0.370446	+	0.928854i	$0.620795\pi$
$158$	−7.22967	+	7.00212i	−0.575162	+	0.557059i
$159$		0			0
$160$	−13.4151	−	11.0901i	−1.06056	−	0.876746i
$161$	0.126765	−	0.348284i	0.00999048	−	0.0274486i
$162$		0			0
$163$	15.8808	+	9.16880i	1.24388	+	0.718156i	0.969882	−	0.243574i	$-0.0783198\pi$
$163$	15.8808	+	9.16880i	1.24388	+	0.718156i	0.274000	+	0.961730i	$0.411653\pi$
$164$	−0.696716	−	4.85407i	−0.0544044	−	0.379039i
$165$		0			0
$166$	5.48028	+	0.567878i	0.425352	+	0.0440759i
$167$	−16.4081	+	13.7680i	−1.26970	+	1.06540i	−0.275119	+	0.961410i	$0.588717\pi$
$167$	−16.4081	+	13.7680i	−1.26970	+	1.06540i	−0.994578	+	0.103993i	$0.966838\pi$
$168$		0			0
$169$	10.1790	−	3.70486i	0.783002	−	0.284989i
$170$	14.5314	−	9.83258i	1.11451	−	0.754124i
$171$		0			0
$172$	−1.53761	−	0.615997i	−0.117242	−	0.0469694i
$173$	6.65005	+	18.2709i	0.505594	+	1.38911i	0.885740	+	0.464182i	$0.153652\pi$
$173$	6.65005	+	18.2709i	0.505594	+	1.38911i	−0.380146	+	0.924927i	$0.624126\pi$
$174$		0			0
$175$	0.707662	+	0.843359i	0.0534943	+	0.0637520i
$176$	1.47227	+	13.2592i	0.110976	+	0.999451i
$177$		0			0
$178$	−2.43181	+	5.00455i	−0.182272	+	0.375107i
$179$	5.33229	−	9.23580i	0.398554	−	0.690316i	−0.594994	−	0.803731i	$-0.702845\pi$
$179$	5.33229	−	9.23580i	0.398554	−	0.690316i	0.993548	+	0.113414i	$0.0361787\pi$
$180$		0			0
$181$	2.92937	+	1.06620i	0.217738	+	0.0792503i	0.448586	−	0.893740i	$-0.351928\pi$
$181$	2.92937	+	1.06620i	0.217738	+	0.0792503i	−0.230848	+	0.972990i	$0.574150\pi$
$182$	0.511824	−	0.0365444i	0.0379390	−	0.00270885i
$183$		0			0
$184$	−3.93706	+	1.61086i	−0.290244	+	0.118754i
$185$	−17.7110	+	21.1071i	−1.30214	+	1.55183i
$186$		0			0
$187$	−13.2436	−	2.33520i	−0.968465	−	0.170766i
$188$	−0.310700	+	9.71385i	−0.0226601	+	0.708456i
$189$		0			0
$190$	−9.21074	−	16.5807i	−0.668217	−	1.20289i
$191$	−24.7441			−1.79042			−0.895209	−	0.445647i	$-0.852974\pi$
$191$	−24.7441			−1.79042			−0.895209	+	0.445647i	$0.852974\pi$
$192$		0			0
$193$	−3.64199	+	20.6547i	−0.262156	+	1.48676i	0.514857	+	0.857276i	$0.327845\pi$
$193$	−3.64199	+	20.6547i	−0.262156	+	1.48676i	−0.777013	+	0.629484i	$0.783266\pi$
$194$	0.0441222	−	0.154728i	0.00316779	−	0.0111088i
$195$		0			0
$196$	13.5837	+	2.84569i	0.970261	+	0.203264i
$197$	7.25620	−	4.18937i	0.516983	−	0.298480i	−0.218716	−	0.975788i	$-0.570187\pi$
$197$	7.25620	−	4.18937i	0.516983	−	0.298480i	0.735699	+	0.677308i	$0.236854\pi$
$198$		0			0
$199$	5.03053	−	13.8213i	0.356605	−	0.979764i	−0.623594	−	0.781749i	$-0.714328\pi$
$199$	5.03053	−	13.8213i	0.356605	−	0.979764i	0.980199	−	0.198016i	$-0.0634498\pi$
$200$	1.70348	−	12.5202i	0.120454	−	0.885311i
$201$		0			0
$202$	7.00629	−	14.4186i	0.492961	−	1.01449i
$203$	0.404916	+	2.29639i	0.0284195	+	0.161175i
$204$		0			0
$205$	5.77926	−	4.84938i	0.403641	−	0.338695i
$206$	−4.85766	+	2.17131i	−0.338449	+	0.151282i
$207$		0			0
$208$	−4.26030	−	4.06611i	−0.295398	−	0.281934i
$209$	−3.77035	+	14.0403i	−0.260801	+	0.971186i
$210$		0			0
$211$	2.14803	+	5.90166i	0.147876	+	0.406287i	0.991410	−	0.130789i	$-0.0417511\pi$
$211$	2.14803	+	5.90166i	0.147876	+	0.406287i	−0.843534	+	0.537076i	$0.819529\pi$
$212$	2.86397	−	4.61336i	0.196698	−	0.316847i
$213$		0			0
$214$	−5.74000	−	0.594791i	−0.392378	−	0.0406591i
$215$	−0.442510	−	2.50960i	−0.0301789	−	0.171153i
$216$		0			0
$217$	−1.21183	+	2.09896i	−0.0822646	+	0.142486i
$218$	6.25285	−	1.56875i	0.423497	−	0.106249i
$219$		0			0
$220$	−16.1360	+	12.6832i	−1.08789	+	0.855103i
$221$	5.14121	−	2.96828i	0.345835	−	0.199668i
$222$		0			0
$223$	−8.31587	+	9.91046i	−0.556872	+	0.663654i	−0.968881	−	0.247526i	$-0.920383\pi$
$223$	−8.31587	+	9.91046i	−0.556872	+	0.663654i	0.412010	+	0.911179i	$0.364827\pi$
$224$	0.705866	+	1.20216i	0.0471627	+	0.0803226i
$225$		0			0
$226$	8.18921	+	5.93148i	0.544738	+	0.394556i
$227$	14.8770			0.987419			0.493709	−	0.869627i	$-0.335641\pi$
$227$	14.8770			0.987419			0.493709	+	0.869627i	$0.335641\pi$
$228$		0			0
$229$	26.4360			1.74694			0.873468	−	0.486881i	$-0.161865\pi$
$229$	26.4360			1.74694			0.873468	+	0.486881i	$0.161865\pi$
$230$	−5.30013	−	3.83891i	−0.349480	−	0.253130i
$231$		0			0
$232$	16.3838	−	21.1616i	1.07565	−	1.38932i
$233$	16.4095	−	19.5561i	1.07502	−	1.28116i	0.117416	−	0.993083i	$-0.462539\pi$
$233$	16.4095	−	19.5561i	1.07502	−	1.28116i	0.957606	−	0.288080i	$-0.0930167\pi$
$234$		0			0
$235$	−12.9488	+	7.47597i	−0.844684	+	0.487678i
$236$	−5.89686	−	7.50218i	−0.383853	−	0.488351i
$237$		0			0
$238$	−1.36303	+	0.341964i	−0.0883518	+	0.0221662i
$239$	3.98974	−	6.91044i	0.258075	−	0.446999i	−0.707651	−	0.706562i	$-0.750245\pi$
$239$	3.98974	−	6.91044i	0.258075	−	0.446999i	0.965726	+	0.259563i	$0.0835785\pi$
$240$		0			0
$241$	−0.600228	−	3.40406i	−0.0386641	−	0.219275i	0.959354	−	0.282206i	$-0.0910662\pi$
$241$	−0.600228	−	3.40406i	−0.0386641	−	0.219275i	−0.998018	+	0.0629312i	$0.979955\pi$
$242$	0.173585	+	0.0179872i	0.0111584	+	0.00115626i
$243$		0			0
$244$	−9.67516	−	6.00633i	−0.619388	−	0.384516i
$245$	7.30263	+	20.0638i	0.466548	+	1.28183i
$246$		0			0
$247$	−2.70903	−	5.81787i	−0.172371	−	0.370182i
$248$	27.1833	−	5.90307i	1.72614	−	0.374845i
$249$		0			0
$250$	−2.11605	+	0.945845i	−0.133831	+	0.0598205i
$251$	−20.1899	+	16.9413i	−1.27437	+	1.06933i	−0.280379	+	0.959889i	$0.590460\pi$
$251$	−20.1899	+	16.9413i	−1.27437	+	1.06933i	−0.993994	+	0.109437i	$0.965095\pi$
$252$		0			0
$253$	0.871018	+	4.93979i	0.0547604	+	0.310562i
$254$	5.17193	−	10.6436i	0.324516	−	0.667840i
$255$		0			0
$256$	4.76546	−	15.2738i	0.297841	−	0.954615i
$257$	−4.78659	+	13.1511i	−0.298579	+	0.820340i	0.696158	+	0.717888i	$0.254891\pi$
$257$	−4.78659	+	13.1511i	−0.298579	+	0.820340i	−0.994738	+	0.102452i	$0.967331\pi$
$258$		0			0
$259$	1.91118	−	1.10342i	0.118755	−	0.0685632i
$260$	1.85776	−	8.86784i	0.115213	−	0.549960i
$261$		0			0
$262$	−6.46039	+	22.6554i	−0.399124	+	1.39965i
$263$	−4.24022	+	24.0475i	−0.261463	+	1.48283i	0.517457	+	0.855709i	$0.326879\pi$
$263$	−4.24022	+	24.0475i	−0.261463	+	1.48283i	−0.778920	+	0.627123i	$0.784232\pi$
$264$		0			0
$265$	8.35387			0.513174
$266$	0.239023	+	1.50023i	0.0146554	+	0.0919851i
$267$		0			0
$268$	−21.5972	−	0.690793i	−1.31926	−	0.0421969i
$269$	−6.42853	−	1.13352i	−0.391954	−	0.0691121i	−0.0258020	−	0.999667i	$-0.508214\pi$
$269$	−6.42853	−	1.13352i	−0.391954	−	0.0691121i	−0.366152	+	0.930555i	$0.619325\pi$
$270$		0			0
$271$	−10.1845	+	12.1374i	−0.618662	+	0.737292i	−0.980840	−	0.194817i	$-0.937589\pi$
$271$	−10.1845	+	12.1374i	−0.618662	+	0.737292i	0.362178	+	0.932109i	$0.382033\pi$
$272$	13.4238	+	8.94038i	0.813938	+	0.542090i
$273$		0			0
$274$	13.0266	−	0.930101i	0.786965	−	0.0561895i
$275$	−14.0008	−	5.09588i	−0.844281	−	0.307293i
$276$		0			0
$277$	−12.6729	+	21.9501i	−0.761439	+	1.31885i	0.180669	+	0.983544i	$0.442174\pi$
$277$	−12.6729	+	21.9501i	−0.761439	+	1.31885i	−0.942109	+	0.335308i	$0.891160\pi$
$278$	10.3407	−	21.2806i	0.620192	−	1.27633i
$279$		0			0
$280$	−0.998542	+	1.89808i	−0.0596743	+	0.113432i
$281$	9.25260	+	11.0268i	0.551964	+	0.657805i	0.967825	−	0.251623i	$-0.0809644\pi$
$281$	9.25260	+	11.0268i	0.551964	+	0.657805i	−0.415862	+	0.909428i	$0.636520\pi$
$282$		0			0
$283$	4.54878	+	12.4977i	0.270397	+	0.742909i	0.998358	+	0.0572904i	$0.0182461\pi$
$283$	4.54878	+	12.4977i	0.270397	+	0.742909i	−0.727961	+	0.685619i	$0.759532\pi$
$284$	11.4024	−	28.4620i	0.676610	−	1.68891i
$285$		0			0
$286$	−5.75146	+	3.89169i	−0.340091	+	0.230121i
$287$	−0.567806	+	0.206664i	−0.0335165	+	0.0121990i
$288$		0			0
$289$	0.568359	−	0.476910i	0.0334329	−	0.0280535i
$290$	40.9539	+	4.24373i	2.40489	+	0.249200i
$291$		0			0
$292$	9.83977	−	1.41232i	0.575829	−	0.0826500i
$293$	14.6509	+	8.45871i	0.855916	+	0.494163i	0.862642	−	0.505814i	$-0.168808\pi$
$293$	14.6509	+	8.45871i	0.855916	+	0.494163i	−0.00672667	+	0.999977i	$0.502141\pi$
$294$		0			0
$295$	5.02099	−	13.7951i	0.292333	−	0.803179i
$296$	−24.1228	−	7.72085i	−1.40211	−	0.448766i
$297$		0			0
$298$	16.5763	−	16.0546i	0.960239	−	0.930017i
$299$	−1.69626	−	1.42333i	−0.0980973	−	0.0823134i
$300$		0			0
$301$	−0.0354420	+	0.201002i	−0.00204284	+	0.0115855i
$302$	−13.6517	−	9.88799i	−0.785567	−	0.568990i
$303$		0			0
$304$	10.9004	−	13.6081i	0.625181	−	0.780480i
$305$		−	17.5198i		−	1.00318i
$306$		0			0
$307$	26.4339	+	4.66100i	1.50866	+	0.266018i	0.865965	−	0.500104i	$-0.166705\pi$
$307$	26.4339	+	4.66100i	1.50866	+	0.266018i	0.642695	+	0.766122i	$0.277816\pi$
$308$	1.56188	−	0.512555i	0.0889966	−	0.0292055i
$309$		0			0
$310$	29.7730	+	30.7405i	1.69099	+	1.74594i
$311$	0.107779	+	0.186678i	0.00611156	+	0.0105855i	0.869065	−	0.494698i	$-0.164721\pi$
$311$	0.107779	+	0.186678i	0.00611156	+	0.0105855i	−0.862953	+	0.505283i	$0.831388\pi$
$312$		0			0
$313$	−0.144348	−	0.0525385i	−0.00815905	−	0.00296965i	0.337937	−	0.941169i	$-0.390271\pi$
$313$	−0.144348	−	0.0525385i	−0.00815905	−	0.00296965i	−0.346096	+	0.938199i	$0.612493\pi$
$314$	−10.7688	+	2.70175i	−0.607720	+	0.152468i
$315$		0			0
$316$	−2.02226	−	14.0892i	−0.113761	−	0.792581i
$317$	−28.3064	+	4.99119i	−1.58985	+	0.280333i	−0.897427	−	0.441162i	$-0.854566\pi$
$317$	−28.3064	+	4.99119i	−1.58985	+	0.280333i	−0.692420	+	0.721495i	$0.743455\pi$
$318$		0			0
$319$	−20.2848	−	24.1745i	−1.13573	−	1.35351i
$320$	23.8307	−	6.16483i	1.33218	−	0.344624i
$321$		0			0
$322$	0.293743	+	0.434117i	0.0163696	+	0.0241924i
$323$	10.0731	+	14.4027i	0.560480	+	0.801385i
$324$		0			0
$325$	6.18067	−	2.24958i	0.342842	−	0.124784i
$326$	−23.6757	+	10.5827i	−1.31128	+	0.586124i
$327$		0			0
$328$	6.13754	+	3.22884i	0.338889	+	0.178283i
$329$	1.17936	−	0.207952i	0.0650200	−	0.0114648i
$330$		0			0
$331$	11.7645	+	6.79225i	0.646637	+	0.373336i	0.787166	−	0.616741i	$-0.211547\pi$
$331$	11.7645	+	6.79225i	0.646637	+	0.373336i	−0.140530	+	0.990076i	$0.544881\pi$
$332$	−5.19672	+	5.80569i	−0.285207	+	0.318628i
$333$		0			0
$334$	−2.15732	−	30.2145i	−0.118043	−	1.65326i
$335$	−16.6216	−	28.7895i	−0.908137	−	1.57294i
$336$		0			0
$337$	27.6524	+	23.2032i	1.50632	+	1.26396i	0.870549	+	0.492082i	$0.163764\pi$
$337$	27.6524	+	23.2032i	1.50632	+	1.26396i	0.635776	+	0.771874i	$0.280680\pi$
$338$	−4.20094	+	14.7319i	−0.228501	+	0.801310i
$339$		0			0
$340$	−0.793243	+	24.8003i	−0.0430197	+	1.34498i
$341$		−	32.8006i		−	1.77625i
$342$		0			0
$343$		−	3.43518i		−	0.185482i
$344$	1.98109	−	1.25007i	0.106813	−	0.0673994i
$345$		0			0
$346$	−26.4431	−	7.54049i	−1.42159	−	0.405380i
$347$	−12.6077	−	10.5792i	−0.676819	−	0.567919i	0.238256	−	0.971202i	$-0.423424\pi$
$347$	−12.6077	−	10.5792i	−0.676819	−	0.567919i	−0.915075	+	0.403284i	$0.867869\pi$
$348$		0			0
$349$	5.03025	+	8.71265i	0.269263	+	0.466378i	0.968672	−	0.248345i	$-0.0798865\pi$
$349$	5.03025	+	8.71265i	0.269263	+	0.466378i	−0.699409	+	0.714722i	$0.746553\pi$
$350$	−1.55299	+	0.110884i	−0.0830110	+	0.00592700i
$351$		0			0
$352$	−16.4077	−	9.31328i	−0.874532	−	0.496399i
$353$	−11.6772	−	6.74186i	−0.621517	−	0.358833i	0.155942	−	0.987766i	$-0.450159\pi$
$353$	−11.6772	−	6.74186i	−0.621517	−	0.358833i	−0.777460	+	0.628933i	$0.783492\pi$
$354$		0			0
$355$	46.4540	−	8.19109i	2.46552	−	0.434738i
$356$	−3.71455	−	6.93690i	−0.196871	−	0.367655i
$357$		0			0
$358$	6.15460	+	13.7691i	0.325281	+	0.727719i
$359$	0.924573	−	0.336517i	0.0487971	−	0.0177607i	−0.317506	−	0.948256i	$-0.602845\pi$
$359$	0.924573	−	0.336517i	0.0487971	−	0.0177607i	0.366303	+	0.930495i	$0.380623\pi$
$360$		0			0
$361$	16.4649	−	9.48191i	0.866574	−	0.499048i
$362$	−3.65130	+	2.47063i	−0.191908	+	0.129853i
$363$		0			0
$364$	−0.382741	+	0.616530i	−0.0200611	+	0.0323149i
$365$	9.83025	+	11.7152i	0.514539	+	0.613204i
$366$		0			0
$367$	−20.3080	+	3.58085i	−1.06007	+	0.186919i	−0.676387	−	0.736546i	$-0.736455\pi$
$367$	−20.3080	+	3.58085i	−1.06007	+	0.186919i	−0.383683	+	0.923465i	$0.625344\pi$
$368$	1.42111	−	5.84560i	0.0740806	−	0.304723i
$369$		0			0
$370$	−9.48225	−	37.7951i	−0.492958	−	1.96487i
$371$	−0.628737	−	0.228842i	−0.0326424	−	0.0118809i
$372$		0			0
$373$	9.59771	+	16.6237i	0.496951	+	0.860744i	0.999994	−	0.00351758i	$-0.00111968\pi$
$373$	9.59771	+	16.6237i	0.496951	+	0.860744i	−0.503043	+	0.864261i	$0.667786\pi$
$374$	13.6611	−	13.2312i	0.706400	−	0.684167i
$375$		0			0
$376$	−10.8679	−	8.41423i	−0.560470	−	0.433931i
$377$	13.7195	+	2.41911i	0.706588	+	0.124591i
$378$		0			0
$379$			29.7966i			1.53055i	0.643703	+	0.765275i	$0.277397\pi$
$379$			29.7966i			1.53055i	−0.643703	+	0.765275i	$0.722603\pi$
$380$	26.6316	+	3.20556i	1.36617	+	0.164442i
$381$		0			0
$382$	20.5271	−	28.3404i	1.05026	−	1.45002i
$383$	4.22937	−	23.9859i	0.216111	−	1.22562i	−0.662858	−	0.748745i	$-0.730657\pi$
$383$	4.22937	−	23.9859i	0.216111	−	1.22562i	0.878969	−	0.476879i	$-0.158232\pi$
$384$		0			0
$385$	1.93730	+	1.62559i	0.0987338	+	0.0828475i
$386$	−20.6354	−	21.3060i	−1.05031	−	1.08445i
$387$		0			0
$388$	0.140614	+	0.178894i	0.00713858	+	0.00908194i
$389$	5.26027	−	14.4525i	0.266706	−	0.732769i	−0.731970	−	0.681337i	$-0.761399\pi$
$389$	5.26027	−	14.4525i	0.266706	−	0.732769i	0.998676	−	0.0514328i	$-0.0163788\pi$
$390$		0			0
$391$	5.25174	+	3.03209i	0.265592	+	0.153340i
$392$	−14.5280	+	13.1972i	−0.733773	+	0.666559i
$393$		0			0
$394$	−1.22131	+	11.7862i	−0.0615289	+	0.593781i
$395$	16.7746	−	14.0756i	0.844023	−	0.708220i
$396$		0			0
$397$	30.0118	−	10.9234i	1.50625	−	0.548229i	0.548578	−	0.836099i	$-0.315169\pi$
$397$	30.0118	−	10.9234i	1.50625	−	0.548229i	0.957669	+	0.287870i	$0.0929472\pi$
$398$	11.6569	+	17.2275i	0.584306	+	0.863535i
$399$		0			0
$400$	12.9267	+	12.3375i	0.646336	+	0.616875i
$401$	0.586459	+	1.61128i	0.0292864	+	0.0804636i	0.953474	−	0.301475i	$-0.0974789\pi$
$401$	0.586459	+	1.61128i	0.0292864	+	0.0804636i	−0.924188	+	0.381938i	$0.875257\pi$
$402$		0			0
$403$	9.30746	+	11.0922i	0.463638	+	0.552542i
$404$	10.7020	+	19.9859i	0.532444	+	0.994337i
$405$		0			0
$406$	−2.96606	−	1.44126i	−0.147203	−	0.0715288i
$407$	−14.9331	+	25.8649i	−0.740206	+	1.28208i
$408$		0			0
$409$	3.80858	+	1.38621i	0.188322	+	0.0685436i	0.434460	−	0.900691i	$-0.356939\pi$
$409$	3.80858	+	1.38621i	0.188322	+	0.0685436i	−0.246138	+	0.969235i	$0.579162\pi$
$410$	0.759852	+	10.6421i	0.0375264	+	0.525578i
$411$		0			0
$412$	1.54291	−	7.36493i	0.0760136	−	0.362844i
$413$	−0.755789	+	0.900715i	−0.0371900	+	0.0443213i
$414$		0			0
$415$	−11.8052	−	2.08157i	−0.579493	−	0.102180i
$416$	8.19132	−	1.50634i	0.401612	−	0.0738546i
$417$		0			0
$418$	−12.9531	−	15.9658i	−0.633556	−	0.780913i
$419$	30.0922			1.47010			0.735049	−	0.678014i	$-0.237159\pi$
$419$	30.0922			1.47010			0.735049	+	0.678014i	$0.237159\pi$
$420$		0			0
$421$	4.20424	−	23.8435i	0.204902	−	1.16206i	−0.692691	−	0.721234i	$-0.743575\pi$
$421$	4.20424	−	23.8435i	0.204902	−	1.16206i	0.897593	−	0.440824i	$-0.145314\pi$
$422$	−8.54136	−	2.43565i	−0.415787	−	0.118566i
$423$		0			0
$424$	2.90798	+	7.10735i	0.141224	+	0.345163i
$425$	−15.5996	+	9.00644i	−0.756693	+	0.436877i
$426$		0			0
$427$	−0.479928	+	1.31859i	−0.0232253	+	0.0638111i
$428$	5.44300	−	6.08083i	0.263097	−	0.293928i
$429$		0			0
$430$	3.24144	+	1.57508i	0.156316	+	0.0759569i
$431$	3.35230	+	19.0119i	0.161475	+	0.915769i	0.952625	+	0.304147i	$0.0983715\pi$
$431$	3.35230	+	19.0119i	0.161475	+	0.915769i	−0.791150	+	0.611622i	$0.790517\pi$
$432$		0			0
$433$	6.82724	−	5.72873i	0.328096	−	0.275305i	−0.463827	−	0.885926i	$-0.653524\pi$
$433$	6.82724	−	5.72873i	0.328096	−	0.275305i	0.791924	+	0.610620i	$0.209080\pi$
$434$	−1.39871	−	3.12921i	−0.0671404	−	0.150207i
$435$		0			0
$436$	−3.39046	+	8.46304i	−0.162373	+	0.405306i
$437$	3.76311	−	5.36800i	0.180014	−	0.256786i
$438$		0			0
$439$	−13.8269	−	37.9891i	−0.659922	−	1.81312i	−0.577289	−	0.816540i	$-0.695889\pi$
$439$	−13.8269	−	37.9891i	−0.659922	−	1.81312i	−0.0826331	−	0.996580i	$-0.526333\pi$
$440$	−1.14055	−	29.0030i	−0.0543734	−	1.38266i
$441$		0			0
$442$	−0.865333	+	8.35085i	−0.0411597	+	0.397209i
$443$	−4.25606	−	24.1373i	−0.202211	−	1.14680i	−0.901768	−	0.432221i	$-0.857730\pi$
$443$	−4.25606	−	24.1373i	−0.202211	−	1.14680i	0.699556	−	0.714577i	$-0.253381\pi$
$444$		0			0
$445$	6.05290	−	10.4839i	0.286935	−	0.496986i
$446$	−4.45221	−	17.7460i	−0.210818	−	0.840296i
$447$		0			0
$448$	−1.96245	−	0.188824i	−0.0927170	−	0.00892109i
$449$	16.2879	−	9.40383i	0.768674	−	0.443794i	−0.0637273	−	0.997967i	$-0.520299\pi$
$449$	16.2879	−	9.40383i	0.768674	−	0.443794i	0.832401	+	0.554173i	$0.186965\pi$
$450$		0			0
$451$	5.25643	−	6.26437i	0.247515	−	0.294977i
$452$	−13.5871	+	4.45882i	−0.639085	+	0.209725i
$453$		0			0
$454$	−12.3416	+	17.0392i	−0.579219	+	0.799689i
$455$	−1.11641			−0.0523382
$456$		0			0
$457$	−5.26403			−0.246241			−0.123120	−	0.992392i	$-0.539290\pi$
$457$	−5.26403			−0.246241			−0.123120	+	0.992392i	$0.539290\pi$
$458$	−21.9306	+	30.2782i	−1.02475	+	1.41481i
$459$		0			0
$460$	8.79372	−	2.88579i	0.410009	−	0.134551i
$461$	1.19127	−	1.41971i	0.0554832	−	0.0661223i	−0.737589	−	0.675250i	$-0.764036\pi$
$461$	1.19127	−	1.41971i	0.0554832	−	0.0661223i	0.793072	+	0.609128i	$0.208480\pi$
$462$		0			0
$463$	−25.5804	+	14.7688i	−1.18882	+	0.686367i	−0.958039	−	0.286639i	$-0.907462\pi$
$463$	−25.5804	+	14.7688i	−1.18882	+	0.686367i	−0.230783	+	0.973005i	$0.574129\pi$
$464$	10.6456	+	36.3202i	0.494207	+	1.68612i
$465$		0			0
$466$	8.78545	+	35.0177i	0.406978	+	1.62217i
$467$	5.38903	−	9.33408i	0.249375	−	0.431930i	−0.713978	−	0.700168i	$-0.753108\pi$
$467$	5.38903	−	9.33408i	0.249375	−	0.431930i	0.963353	+	0.268239i	$0.0864416\pi$
$468$		0			0
$469$	0.462349	+	2.62211i	0.0213493	+	0.121078i
$470$	2.17945	−	21.0326i	0.100530	−	0.970162i
$471$		0			0
$472$	13.4844	−	0.530278i	0.620672	−	0.0244080i
$473$	−0.944733	−	2.59563i	−0.0434389	−	0.119347i
$474$		0			0
$475$	8.21981	+	17.6528i	0.377151	+	0.809964i
$476$	0.739068	−	1.84481i	0.0338751	−	0.0845568i
$477$		0			0
$478$	4.60501	+	10.3023i	0.210628	+	0.471218i
$479$	0.428182	−	0.359287i	0.0195641	−	0.0164162i	−0.632953	−	0.774190i	$-0.718157\pi$
$479$	0.428182	−	0.359287i	0.0195641	−	0.0164162i	0.652517	+	0.757774i	$0.273713\pi$
$480$		0			0
$481$	−2.28945	−	12.9841i	−0.104390	−	0.592026i
$482$	4.39675	+	2.13646i	0.200266	+	0.0973132i
$483$		0			0
$484$	−0.164603	+	0.183892i	−0.00748195	+	0.00835871i
$485$	−0.119728	+	0.328950i	−0.00543657	+	0.0149369i
$486$		0			0
$487$	−23.0078	+	13.2835i	−1.04258	+	0.601935i	−0.920564	−	0.390593i	$-0.872270\pi$
$487$	−23.0078	+	13.2835i	−1.04258	+	0.601935i	−0.122018	+	0.992528i	$0.538937\pi$
$488$	14.9056	−	6.09864i	0.674743	−	0.276072i
$489$		0			0
$490$	−29.0380	−	8.28045i	−1.31180	−	0.374073i
$491$	−5.75697	+	32.6494i	−0.259808	+	1.47345i	0.523614	+	0.851956i	$0.324583\pi$
$491$	−5.75697	+	32.6494i	−0.259808	+	1.47345i	−0.783422	+	0.621490i	$0.786528\pi$
$492$		0			0
$493$	−38.1522			−1.71829
$494$	8.91079	+	1.72361i	0.400915	+	0.0775488i
$495$		0			0
$496$	−15.7896	+	36.0312i	−0.708973	+	1.61785i
$497$	−3.72065	−	0.656051i	−0.166894	−	0.0294279i
$498$		0			0
$499$	−11.1494	+	13.2873i	−0.499116	+	0.594823i	−0.955511	−	0.294954i	$-0.904696\pi$
$499$	−11.1494	+	13.2873i	−0.499116	+	0.594823i	0.456396	+	0.889777i	$0.349140\pi$
$500$	0.672108	−	3.20825i	0.0300576	−	0.143477i
$501$		0			0
$502$	−2.65454	−	37.1784i	−0.118478	−	1.65935i
$503$	−25.0227	−	9.10751i	−1.11571	−	0.406084i	−0.282623	−	0.959231i	$-0.591204\pi$
$503$	−25.0227	−	9.10751i	−1.11571	−	0.406084i	−0.833083	+	0.553147i	$0.813427\pi$
$504$		0			0
$505$	−17.4391	+	30.2053i	−0.776028	+	1.34412i
$506$	−6.38031	−	3.10032i	−0.283640	−	0.137826i
$507$		0			0
$508$	7.90005	+	14.7533i	0.350508	+	0.654572i
$509$	−6.48586	−	7.72955i	−0.287481	−	0.342606i	0.602905	−	0.797813i	$-0.294010\pi$
$509$	−6.48586	−	7.72955i	−0.287481	−	0.342606i	−0.890386	+	0.455207i	$0.849565\pi$
$510$		0			0
$511$	−0.418933	−	1.15101i	−0.0185325	−	0.0509176i
$512$	13.5404	+	18.1289i	0.598409	+	0.801191i
$513$		0			0
$514$	−11.0916	−	16.3921i	−0.489229	−	0.723023i
$515$	10.8784	−	3.95942i	0.479360	−	0.174473i
$516$		0			0
$517$	−12.4153	+	10.4177i	−0.546023	+	0.458168i
$518$	−0.321677	+	3.10432i	−0.0141337	+	0.136396i
$519$		0			0
$520$	8.61554	+	9.48430i	0.377816	+	0.415914i
$521$	−5.66567	−	3.27108i	−0.248218	−	0.143308i	0.370730	−	0.928741i	$-0.379107\pi$
$521$	−5.66567	−	3.27108i	−0.248218	−	0.143308i	−0.618948	+	0.785432i	$0.712441\pi$
$522$		0			0
$523$	5.57060	−	15.3051i	0.243585	−	0.669245i	−0.756302	−	0.654223i	$-0.772996\pi$
$523$	5.57060	−	15.3051i	0.243585	−	0.669245i	0.999887	−	0.0150224i	$-0.00478196\pi$
$524$	−20.5887	−	26.1937i	−0.899422	−	1.14428i
$525$		0			0
$526$	−24.0250	−	24.8057i	−1.04754	−	1.08158i
$527$	−30.3775	−	25.4897i	−1.32326	−	1.11035i
$528$		0			0
$529$	−3.60113	+	20.4230i	−0.156571	+	0.887958i
$530$	−6.93016	+	9.56802i	−0.301027	+	0.415608i
$531$		0			0
$532$	−1.91656	−	0.970792i	−0.0830935	−	0.0420892i
$533$			3.60998i			0.156366i
$534$		0			0
$535$	12.3646	+	2.18022i	0.534570	+	0.0942591i
$536$	18.7077	−	24.1631i	0.808050	−	1.04369i
$537$		0			0
$538$	6.63122	−	6.42251i	0.285892	−	0.276894i
$539$	11.5718	+	20.0430i	0.498434	+	0.863314i
$540$		0			0
$541$	−21.5503	−	7.84365i	−0.926518	−	0.337225i	−0.165689	−	0.986178i	$-0.552985\pi$
$541$	−21.5503	−	7.84365i	−0.926518	−	0.337225i	−0.760828	+	0.648953i	$0.775207\pi$
$542$	−5.45263	−	21.7335i	−0.234211	−	0.933535i
$543$		0			0
$544$	−21.3758	+	7.95810i	−0.916482	+	0.341201i
$545$	−13.8129	+	2.43558i	−0.591678	+	0.104329i
$546$		0			0
$547$	−17.4752	−	20.8261i	−0.747183	−	0.890459i	0.249782	−	0.968302i	$-0.419641\pi$
$547$	−17.4752	−	20.8261i	−0.747183	−	0.890459i	−0.996966	+	0.0778435i	$0.975197\pi$
$548$	−9.74126	+	15.6915i	−0.416126	+	0.670306i
$549$		0			0
$550$	17.4513	−	11.8083i	0.744124	−	0.503507i
$551$	−3.61724	+	41.0852i	−0.154100	+	1.75029i
$552$		0			0
$553$	−1.64809	+	0.599855i	−0.0700839	+	0.0255084i
$554$	−14.6272	−	32.7240i	−0.621450	−	1.39031i
$555$		0			0
$556$	15.7952	+	29.4975i	0.669866	+	1.25097i
$557$	11.9988	−	2.11571i	0.508405	−	0.0896456i	0.0864392	−	0.996257i	$-0.472451\pi$
$557$	11.9988	−	2.11571i	0.508405	−	0.0896456i	0.421966	+	0.906612i	$0.361340\pi$
$558$		0			0
$559$	1.05601	+	0.609690i	0.0446647	+	0.0257872i
$560$	−1.34558	−	2.71827i	−0.0568611	−	0.114868i
$561$		0			0
$562$	−20.3052	+	1.44980i	−0.856523	+	0.0611559i
$563$	−8.89467	−	15.4060i	−0.374865	−	0.649286i	0.615441	−	0.788183i	$-0.288978\pi$
$563$	−8.89467	−	15.4060i	−0.374865	−	0.649286i	−0.990307	+	0.138897i	$0.955644\pi$
$564$		0			0
$565$	−16.8529	−	14.1413i	−0.709008	−	0.594928i
$566$	−18.0876	−	5.15786i	−0.760280	−	0.216801i
$567$		0			0
$568$	23.1395	+	36.6711i	0.970912	+	1.53868i
$569$			4.26367i			0.178742i	0.995998	+	0.0893711i	$0.0284857\pi$
$569$			4.26367i			0.178742i	−0.995998	+	0.0893711i	$0.971514\pi$
$570$		0			0
$571$			3.11580i			0.130392i	0.997872	+	0.0651961i	$0.0207673\pi$
$571$			3.11580i			0.130392i	−0.997872	+	0.0651961i	$0.979233\pi$
$572$	0.313962	−	9.81584i	0.0131274	−	0.410421i
$573$		0			0
$574$	0.234337	−	0.821775i	0.00978103	−	0.0343002i
$575$	5.14684	+	4.31872i	0.214638	+	0.180103i
$576$		0			0
$577$	−21.0392	−	36.4410i	−0.875874	−	1.51706i	−0.855829	−	0.517259i	$-0.826952\pi$
$577$	−21.0392	−	36.4410i	−0.875874	−	1.51706i	−0.0200455	−	0.999799i	$-0.506381\pi$
$578$	0.0747273	+	1.04660i	0.00310825	+	0.0435327i
$579$		0			0
$580$	−38.8348	+	43.3856i	−1.61253	+	1.80149i
$581$	0.831471	+	0.480050i	0.0344952	+	0.0199158i
$582$		0			0
$583$	8.91751	−	1.57240i	0.369326	−	0.0651221i
$584$	−6.54524	+	12.4415i	−0.270844	+	0.514834i
$585$		0			0
$586$	−21.8421	+	9.76315i	−0.902291	+	0.403312i
$587$	35.6998	−	12.9937i	1.47349	−	0.536307i	0.524445	−	0.851445i	$-0.324273\pi$
$587$	35.6998	−	12.9937i	1.47349	−	0.536307i	0.949046	+	0.315138i	$0.102051\pi$
$588$		0			0
$589$	−30.3294	+	30.2961i	−1.24970	+	1.24833i
$590$	11.6347	+	17.1948i	0.478995	+	0.707898i
$591$		0			0
$592$	28.8547	−	21.2238i	1.18592	−	0.872294i
$593$	17.7846	+	21.1948i	0.730325	+	0.870368i	0.995590	−	0.0938076i	$-0.0299039\pi$
$593$	17.7846	+	21.1948i	0.730325	+	0.870368i	−0.265265	+	0.964176i	$0.585459\pi$
$594$		0			0
$595$	3.01099	−	0.530919i	0.123439	−	0.0217656i
$596$	4.63666	+	32.3040i	0.189925	+	1.32322i
$597$		0			0
$598$	3.03738	−	0.762035i	0.124208	−	0.0311619i
$599$	2.45106	+	0.892113i	0.100148	+	0.0364507i	0.391608	−	0.920132i	$-0.371919\pi$
$599$	2.45106	+	0.892113i	0.100148	+	0.0364507i	−0.291460	+	0.956583i	$0.594141\pi$
$600$		0			0
$601$	−14.1168	−	24.4510i	−0.575837	−	0.997379i	−0.995950	−	0.0899073i	$-0.971343\pi$
$601$	−14.1168	−	24.4510i	−0.575837	−	0.997379i	0.420113	−	0.907472i	$-0.361990\pi$
$602$	−0.200814	−	0.207339i	−0.00818455	−	0.00845052i
$603$		0			0
$604$	22.6502	−	7.43300i	0.921625	−	0.302445i
$605$	−0.373922	−	0.0659325i	−0.0152021	−	0.00268054i
$606$		0			0
$607$			19.2213i			0.780168i	0.920779	+	0.390084i	$0.127554\pi$
$607$			19.2213i			0.780168i	−0.920779	+	0.390084i	$0.872446\pi$
$608$	6.54323	+	23.7736i	0.265363	+	0.964149i
$609$		0			0
$610$	20.0661	+	14.5340i	0.812452	+	0.588463i
$611$	1.24238	−	7.04589i	0.0502613	−	0.285046i
$612$		0			0
$613$	−6.63150	−	5.56449i	−0.267844	−	0.224748i	0.498967	−	0.866621i	$-0.333713\pi$
$613$	−6.63150	−	5.56449i	−0.267844	−	0.224748i	−0.766811	+	0.641873i	$0.778157\pi$
$614$	−27.2673	+	26.4091i	−1.10042	+	1.06579i
$615$		0			0
$616$	−0.708651	+	2.21409i	−0.0285524	+	0.0892083i
$617$	−2.95958	+	8.13138i	−0.119148	+	0.327357i	−0.984902	−	0.173113i	$-0.944617\pi$
$617$	−2.95958	+	8.13138i	−0.119148	+	0.327357i	0.865754	+	0.500470i	$0.166840\pi$
$618$		0			0
$619$	−22.1734	−	12.8018i	−0.891223	−	0.514548i	−0.0168807	−	0.999858i	$-0.505374\pi$
$619$	−22.1734	−	12.8018i	−0.891223	−	0.514548i	−0.874342	+	0.485310i	$0.838707\pi$
$620$	−59.9072	+	8.59861i	−2.40593	+	0.345329i
$621$		0			0
$622$	−0.303220	−	0.0314203i	−0.0121580	−	0.00125984i
$623$	−0.742751	+	0.623242i	−0.0297577	+	0.0249697i
$624$		0			0
$625$	25.7284	−	9.36437i	1.02914	−	0.374575i
$626$	0.179922	−	0.121743i	0.00719114	−	0.00486584i
$627$		0			0
$628$	5.83914	−	14.5753i	0.233007	−	0.581617i
$629$	12.3494	+	33.9298i	0.492404	+	1.35287i
$630$		0			0
$631$	−21.4321	−	25.5418i	−0.853200	−	1.01680i	−0.999620	−	0.0275819i	$-0.991219\pi$
$631$	−21.4321	−	25.5418i	−0.853200	−	1.01680i	0.146419	−	0.989223i	$-0.453225\pi$
$632$	17.8146	+	9.37190i	0.708625	+	0.372794i
$633$		0			0
$634$	17.7657	−	36.5611i	0.705566	−	1.45202i
$635$	−12.8732	+	22.2971i	−0.510859	+	0.884834i
$636$		0			0
$637$	−9.60064	−	3.49435i	−0.380391	−	0.138451i
$638$	44.5158	−	3.17844i	1.76240	−	0.125836i
$639$		0			0
$640$	−12.7086	+	32.4085i	−0.502351	+	1.28106i
$641$	6.22612	−	7.42000i	0.245917	−	0.293073i	−0.628940	−	0.777454i	$-0.716511\pi$
$641$	6.22612	−	7.42000i	0.245917	−	0.293073i	0.874857	+	0.484381i	$0.160955\pi$
$642$		0			0
$643$	26.3570	+	4.64744i	1.03942	+	0.183277i	0.667208	−	0.744872i	$-0.267489\pi$
$643$	26.3570	+	4.64744i	1.03942	+	0.183277i	0.372209	+	0.928149i	$0.378600\pi$
$644$	−0.740893	−	0.0236977i	−0.0291953	−	0.000933820i
$645$		0			0
$646$	−24.8523	−	0.411014i	−0.977801	−	0.0161711i
$647$	44.0730			1.73269			0.866345	−	0.499446i	$-0.166463\pi$
$647$	44.0730			1.73269			0.866345	+	0.499446i	$0.166463\pi$
$648$		0			0
$649$	2.76320	−	15.6709i	0.108465	−	0.615136i
$650$	−2.55080	+	8.94516i	−0.100050	+	0.350858i
$651$		0			0
$652$	7.51998	−	35.8960i	0.294505	−	1.40579i
$653$	9.69258	−	5.59601i	0.379300	−	0.218989i	−0.298214	−	0.954499i	$-0.596391\pi$
$653$	9.69258	−	5.59601i	0.379300	−	0.218989i	0.677514	+	0.735510i	$0.263057\pi$
$654$		0			0
$655$	17.5306	−	48.1651i	0.684979	−	1.88196i
$656$	−8.78968	+	4.35101i	−0.343179	+	0.169878i
$657$		0			0
$658$	−0.740188	+	1.52328i	−0.0288555	+	0.0593835i
$659$	−3.28547	−	18.6328i	−0.127984	−	0.725831i	−0.979491	−	0.201488i	$-0.935422\pi$
$659$	−3.28547	−	18.6328i	−0.127984	−	0.725831i	0.851507	−	0.524343i	$-0.175689\pi$
$660$		0			0
$661$	19.6670	−	16.5026i	0.764958	−	0.641876i	−0.174454	−	0.984665i	$-0.555816\pi$
$661$	19.6670	−	16.5026i	0.764958	−	0.641876i	0.939412	+	0.342789i	$0.111372\pi$
$662$	−17.5390	+	7.83970i	−0.681673	+	0.304698i
$663$		0			0
$664$	−2.33841	−	10.7683i	−0.0907481	−	0.417890i
$665$	−0.286259	−	3.29280i	−0.0111007	−	0.127689i
$666$		0			0
$667$	4.86715	+	13.3724i	0.188457	+	0.517781i
$668$	36.3955	+	22.5943i	1.40819	+	0.874201i
$669$		0			0
$670$	46.7627	+	4.84565i	1.80660	+	0.187204i
$671$	−3.29764	−	18.7019i	−0.127304	−	0.721977i
$672$		0			0
$673$	−14.8840	+	25.7798i	−0.573734	+	0.993737i	0.422443	+	0.906389i	$0.361172\pi$
$673$	−14.8840	+	25.7798i	−0.573734	+	0.993737i	−0.996178	+	0.0873478i	$0.972161\pi$
$674$	−49.5153	+	12.4227i	−1.90726	+	0.478504i
$675$		0			0
$676$	−13.3880	−	17.0327i	−0.514925	−	0.655105i
$677$	−35.3561	+	20.4129i	−1.35885	+	0.784530i	−0.989468	−	0.144750i	$-0.953762\pi$
$677$	−35.3561	+	20.4129i	−1.35885	+	0.784530i	−0.369377	+	0.929280i	$0.620429\pi$
$678$		0			0
$679$	0.0180222	−	0.0214780i	0.000691628	−	0.000824251i
$680$	−27.7467	−	21.4822i	−1.06404	−	0.823806i
$681$		0			0
$682$	37.5679	+	27.2106i	1.43855	+	1.04195i
$683$	33.2434			1.27202			0.636011	−	0.771680i	$-0.280583\pi$
$683$	33.2434			1.27202			0.636011	+	0.771680i	$0.280583\pi$
$684$		0			0
$685$	−28.4141			−1.08565
$686$	3.93445	+	2.84974i	0.150218	+	0.108804i
$687$		0			0
$688$	−0.211707	+	3.30605i	−0.00807125	+	0.126042i
$689$	−2.56946	+	3.06216i	−0.0978886	+	0.116659i
$690$		0			0
$691$	36.4703	−	21.0561i	1.38740	−	0.801013i	0.394374	−	0.918950i	$-0.370961\pi$
$691$	36.4703	−	21.0561i	1.38740	−	0.801013i	0.993021	+	0.117937i	$0.0376280\pi$
$692$	30.5730	−	24.0309i	1.16221	−	0.913519i
$693$		0			0
$694$	22.5758	−	5.66395i	0.856966	−	0.215001i
$695$	−25.7385	+	44.5804i	−0.976318	+	1.69103i
$696$		0			0
$697$	−1.71676	−	9.73622i	−0.0650268	−	0.368785i
$698$	−14.1519	−	1.46645i	−0.535658	−	0.0555061i
$699$		0			0
$700$	1.16132	−	1.87069i	0.0438940	−	0.0707055i
$701$	−6.73810	−	18.5128i	−0.254495	−	0.699218i	−0.999483	−	0.0321412i	$-0.989767\pi$
$701$	−6.73810	−	18.5128i	−0.254495	−	0.699218i	0.744989	−	0.667077i	$-0.232455\pi$
$702$		0			0
$703$	37.7091	−	10.0819i	1.42222	−	0.380246i
$704$	24.2783	−	11.0663i	0.915022	−	0.417077i
$705$		0			0
$706$	17.4089	−	7.78154i	0.655192	−	0.292862i
$707$	2.13994	−	1.79563i	0.0804809	−	0.0675315i
$708$		0			0
$709$	−7.85703	−	44.5594i	−0.295077	−	1.67347i	−0.666889	−	0.745157i	$-0.732374\pi$
$709$	−7.85703	−	44.5594i	−0.295077	−	1.67347i	0.371812	−	0.928308i	$-0.378737\pi$
$710$	−29.1555	+	60.0007i	−1.09419	+	2.25179i
$711$		0			0
$712$	11.0266	+	1.50026i	0.413239	+	0.0562247i
$713$	−5.05886	+	13.8991i	−0.189456	+	0.520526i
$714$		0			0
$715$	13.0847	−	7.55446i	0.489340	−	0.282521i
$716$	−20.8760	−	4.37339i	−0.780172	−	0.163441i
$717$		0			0
$718$	−0.381577	+	1.33812i	−0.0142403	+	0.0499381i
$719$	−0.240541	+	1.36418i	−0.00897067	+	0.0508752i	−0.988965	−	0.148153i	$-0.952667\pi$
$719$	−0.240541	+	1.36418i	−0.00897067	+	0.0508752i	0.979994	+	0.199028i	$0.0637784\pi$
$720$		0			0
$721$	−0.927204			−0.0345309
$722$	−2.79888	+	26.7239i	−0.104163	+	0.994560i
$723$		0			0
$724$	0.199318	−	6.23155i	0.00740760	−	0.231594i
$725$	−41.6280	−	7.34014i	−1.54602	−	0.272606i
$726$		0			0
$727$	−19.4476	+	23.1768i	−0.721273	+	0.859580i	−0.994754	−	0.102298i	$-0.967381\pi$
$727$	−19.4476	+	23.1768i	−0.721273	+	0.859580i	0.273481	+	0.961877i	$0.411825\pi$
$728$	−0.388623	−	0.949827i	−0.0144033	−	0.0352029i
$729$		0			0
$730$	−21.5729	+	1.54031i	−0.798448	+	0.0570094i
$731$	−3.13804	−	1.14215i	−0.116065	−	0.0422441i
$732$		0			0
$733$	2.41258	−	4.17872i	0.0891108	−	0.154345i	−0.818025	−	0.575183i	$-0.804931\pi$
$733$	2.41258	−	4.17872i	0.0891108	−	0.154345i	0.907136	+	0.420839i	$0.138264\pi$
$734$	12.7457	−	26.2302i	0.470454	−	0.968174i
$735$		0			0
$736$	5.51628	+	6.47703i	0.203333	+	0.238746i
$737$	−23.1620	−	27.6034i	−0.853183	−	1.01678i
$738$		0			0
$739$	−7.50914	−	20.6312i	−0.276228	−	0.758931i	−0.997782	−	0.0665720i	$-0.978794\pi$
$739$	−7.50914	−	20.6312i	−0.276228	−	0.758931i	0.721553	−	0.692359i	$-0.243428\pi$
$740$	51.1544	+	20.4935i	1.88047	+	0.753355i
$741$		0			0
$742$	0.783686	−	0.530276i	0.0287700	−	0.0194671i
$743$	4.06599	−	1.47990i	0.149167	−	0.0542923i	−0.266358	−	0.963874i	$-0.585820\pi$
$743$	4.06599	−	1.47990i	0.149167	−	0.0542923i	0.415525	+	0.909582i	$0.363598\pi$
$744$		0			0
$745$	−38.4611	+	32.2727i	−1.40911	+	1.18238i
$746$	−27.0018	−	2.79799i	−0.988608	−	0.102442i
$747$		0			0
$748$	3.82124	+	26.6229i	0.139718	+	0.973429i
$749$	−0.870876	−	0.502800i	−0.0318211	−	0.0183719i
$750$		0			0
$751$	0.816742	−	2.24398i	0.0298033	−	0.0818840i	−0.923899	−	0.382637i	$-0.875016\pi$
$751$	0.816742	−	2.24398i	0.0298033	−	0.0818840i	0.953702	+	0.300753i	$0.0972381\pi$
$752$	18.6529	−	5.46722i	0.680202	−	0.199369i
$753$		0			0
$754$	−14.1520	+	13.7066i	−0.515387	+	0.499165i
$755$	28.0944	+	23.5740i	1.02246	+	0.857947i
$756$		0			0
$757$	−5.62782	+	31.9170i	−0.204547	+	1.16004i	0.693605	+	0.720356i	$0.256021\pi$
$757$	−5.62782	+	31.9170i	−0.204547	+	1.16004i	−0.898151	+	0.439686i	$0.855090\pi$
$758$	−34.1273	−	24.7186i	−1.23956	−	0.897819i
$759$		0			0
$760$	−25.7644	+	27.8430i	−0.934572	+	1.00997i
$761$		−	0.616585i		−	0.0223512i	−0.999938	−	0.0111756i	$-0.996443\pi$
$761$		−	0.616585i		−	0.0223512i	0.999938	−	0.0111756i	$-0.00355737\pi$
$762$		0			0
$763$	1.10632	+	0.195073i	0.0400513	+	0.00706213i
$764$	15.4306	+	47.0210i	0.558260	+	1.70116i
$765$		0			0
$766$	23.9635	+	24.7422i	0.865836	+	0.893973i
$767$	3.51232	+	6.08352i	0.126823	+	0.219663i
$768$		0			0
$769$	−20.5033	−	7.46261i	−0.739369	−	0.269108i	−0.0552440	−	0.998473i	$-0.517594\pi$
$769$	−20.5033	−	7.46261i	−0.739369	−	0.269108i	−0.684125	+	0.729364i	$0.739816\pi$
$770$	−3.46898	+	0.870319i	−0.125014	+	0.0313641i
$771$		0			0
$772$	41.5212	−	5.95963i	1.49438	−	0.214492i
$773$	27.5367	−	4.85547i	0.990427	−	0.174639i	0.345117	−	0.938560i	$-0.387839\pi$
$773$	27.5367	−	4.85547i	0.990427	−	0.174639i	0.645310	+	0.763921i	$0.276728\pi$
$774$		0			0
$775$	−28.2410	−	33.6563i	−1.01445	−	1.20897i
$776$	−0.321544	+	0.0126448i	−0.0115427	+	0.000453920i
$777$		0			0
$778$	12.1892	+	18.0142i	0.437004	+	0.645841i
$779$	−10.6475	+	0.925636i	−0.381485	+	0.0331644i
$780$		0			0
$781$	48.0465	−	17.4875i	1.71924	−	0.625752i
$782$	−7.82949	+	3.49968i	−0.279982	+	0.125148i
$783$		0			0
$784$	−3.06324	−	27.5875i	−0.109401	−	0.985269i
$785$	23.7889	−	4.19462i	0.849062	−	0.149713i
$786$		0			0
$787$	−5.75195	−	3.32089i	−0.205035	−	0.118377i	0.393967	−	0.919125i	$-0.371102\pi$
$787$	−5.75195	−	3.32089i	−0.205035	−	0.118377i	−0.599002	+	0.800748i	$0.704436\pi$
$788$	−12.4861	−	11.1764i	−0.444798	−	0.398142i
$789$		0			0
$790$	2.20551	+	30.8894i	0.0784686	+	1.09900i
$791$	0.881022	+	1.52598i	0.0313256	+	0.0542574i
$792$		0			0
$793$	6.42198	+	5.38868i	0.228051	+	0.191358i
$794$	−12.3860	+	43.4355i	−0.439564	+	1.54147i
$795$		0			0
$796$	−29.4016	−	0.940417i	−1.04211	−	0.0333322i
$797$		−	15.9835i		−	0.566166i	−0.959095	−	0.283083i	$-0.908643\pi$
$797$		−	15.9835i		−	0.566166i	0.959095	−	0.283083i	$-0.0913572\pi$
$798$		0			0
$799$			19.5938i			0.693178i
$800$	−24.8543	+	4.57059i	−0.878733	+	0.161595i
$801$		0			0
$802$	−2.33198	−	0.664986i	−0.0823450	−	0.0234815i
$803$	12.6986	+	10.6554i	0.448124	+	0.376021i
$804$		0			0
$805$	−0.570206	−	0.987626i	−0.0200971	−	0.0348092i
$806$	−20.4256	+	1.45839i	−0.719461	+	0.0513697i
$807$		0			0
$808$	−31.7688	−	4.32241i	−1.11762	−	0.152062i
$809$	−14.9242	−	8.61649i	−0.524707	−	0.302940i	0.214151	−	0.976800i	$-0.431301\pi$
$809$	−14.9242	−	8.61649i	−0.524707	−	0.302940i	−0.738858	+	0.673861i	$0.764635\pi$
$810$		0			0
$811$	21.8280	−	3.84886i	0.766484	−	0.135152i	0.223282	−	0.974754i	$-0.428323\pi$
$811$	21.8280	−	3.84886i	0.766484	−	0.135152i	0.543202	+	0.839602i	$0.317212\pi$
$812$	4.11131	−	2.20151i	0.144279	−	0.0772578i
$813$		0			0
$814$	−17.2360	−	38.5604i	−0.604120	−	1.35154i
$815$	53.0203	−	19.2978i	1.85722	−	0.675973i
$816$		0			0
$817$	−1.52748	+	3.27099i	−0.0534397	+	0.114438i
$818$	−4.74718	+	3.21215i	−0.165981	+	0.112310i
$819$		0			0
$820$	−12.8192	−	7.95817i	−0.447667	−	0.277911i
$821$	−24.1163	−	28.7407i	−0.841665	−	1.00306i	−0.999877	−	0.0156524i	$-0.995017\pi$
$821$	−24.1163	−	28.7407i	−0.841665	−	1.00306i	0.158212	−	0.987405i	$-0.449427\pi$
$822$		0			0
$823$	−8.47209	+	1.49386i	−0.295319	+	0.0520726i	−0.319344	−	0.947639i	$-0.603463\pi$
$823$	−8.47209	+	1.49386i	−0.295319	+	0.0520726i	0.0240259	+	0.999711i	$0.492352\pi$
$824$	7.15539	+	7.87692i	0.249270	+	0.274406i
$825$		0			0
$826$	−0.404640	−	1.61285i	−0.0140792	−	0.0561181i
$827$	30.1548	+	10.9754i	1.04858	+	0.381653i	0.808128	−	0.589007i	$-0.200481\pi$
$827$	30.1548	+	10.9754i	1.04858	+	0.381653i	0.240456	+	0.970660i	$0.422703\pi$
$828$		0			0
$829$	−0.297653	−	0.515550i	−0.0103379	−	0.0179058i	0.860810	−	0.508926i	$-0.169957\pi$
$829$	−0.297653	−	0.515550i	−0.0103379	−	0.0179058i	−0.871148	+	0.491020i	$0.836624\pi$
$830$	12.1774	−	11.7941i	0.422683	−	0.409380i
$831$		0			0
$832$	−5.07004	+	10.6315i	−0.175772	+	0.368580i
$833$	27.5549	+	4.85868i	0.954722	+	0.168343i
$834$		0			0
$835$			65.9050i			2.28074i
$836$	29.0318	−	1.59087i	1.00409	−	0.0550212i
$837$		0			0
$838$	−24.9637	+	34.4658i	−0.862358	+	1.19060i
$839$	−6.96153	+	39.4808i	−0.240339	+	1.36303i	0.590735	+	0.806866i	$0.298838\pi$
$839$	−6.96153	+	39.4808i	−0.240339	+	1.36303i	−0.831074	+	0.556162i	$0.812273\pi$
$840$		0			0
$841$	−46.3689	−	38.9081i	−1.59893	−	1.34166i
$842$	23.8211	+	24.5952i	0.820930	+	0.847608i
$843$		0			0
$844$	9.87535	−	7.76221i	0.339924	−	0.267186i
$845$	11.3995	−	31.3199i	0.392155	−	1.07744i
$846$		0			0
$847$	0.0263363	+	0.0152053i	0.000904927	+	0.000522460i
$848$	−10.5527	−	2.56545i	−0.362382	−	0.0880980i
$849$		0			0
$850$	2.62562	−	25.3384i	0.0900580	−	0.869100i
$851$	10.3170	−	8.65699i	0.353662	−	0.296758i
$852$		0			0
$853$	−13.9135	+	5.06408i	−0.476388	+	0.173391i	−0.569044	−	0.822307i	$-0.692686\pi$
$853$	−13.9135	+	5.06408i	−0.476388	+	0.173391i	0.0926562	+	0.995698i	$0.470464\pi$
$854$	−1.11210	−	1.64355i	−0.0380552	−	0.0562411i
$855$		0			0
$856$	2.44924	+	11.2786i	0.0837131	+	0.385494i
$857$	−14.6838	−	40.3434i	−0.501589	−	1.37810i	−0.889723	−	0.456501i	$-0.849103\pi$
$857$	−14.6838	−	40.3434i	−0.501589	−	1.37810i	0.388134	−	0.921603i	$-0.373120\pi$
$858$		0			0
$859$	2.82888	+	3.37133i	0.0965201	+	0.115028i	0.812142	−	0.583459i	$-0.198301\pi$
$859$	2.82888	+	3.37133i	0.0965201	+	0.115028i	−0.715622	+	0.698487i	$0.753857\pi$
$860$	−4.49302	+	2.40591i	−0.153211	+	0.0820407i
$861$		0			0
$862$	−24.5560	−	11.9322i	−0.836382	−	0.406414i
$863$	−8.01780	+	13.8872i	−0.272929	+	0.472727i	−0.969611	−	0.244653i	$-0.921326\pi$
$863$	−8.01780	+	13.8872i	−0.272929	+	0.472727i	0.696681	+	0.717381i	$0.254659\pi$
$864$		0			0
$865$	56.2177	+	20.4616i	1.91146	+	0.695714i
$866$	0.897638	+	12.5719i	0.0305030	+	0.427211i
$867$		0			0
$868$	4.74434	+	0.993910i	0.161033	+	0.0337355i
$869$	15.2571	−	18.1827i	0.517561	−	0.616805i
$870$		0			0
$871$	15.6654	+	2.76224i	0.530802	+	0.0935948i
$872$	−6.88042	−	10.9040i	−0.233000	−	0.369255i
$873$		0			0
$874$	3.02640	+	8.76320i	0.102369	+	0.296420i
$875$	−0.403900			−0.0136543
$876$		0			0
$877$	−0.652867	+	3.70259i	−0.0220458	+	0.125028i	−0.993844	−	0.110784i	$-0.964664\pi$
$877$	−0.652867	+	3.70259i	−0.0220458	+	0.125028i	0.971799	+	0.235812i	$0.0757749\pi$
$878$	54.9809	+	15.6783i	1.85552	+	0.529118i
$879$		0			0
$880$	34.1644	+	22.7538i	1.15168	+	0.767031i
$881$	41.4405	−	23.9257i	1.39617	−	0.806077i	0.402178	−	0.915561i	$-0.368253\pi$
$881$	41.4405	−	23.9257i	1.39617	−	0.806077i	0.993989	+	0.109484i	$0.0349199\pi$
$882$		0			0
$883$	−8.28536	+	22.7638i	−0.278825	+	0.766064i	0.718672	+	0.695349i	$0.244750\pi$
$883$	−8.28536	+	22.7638i	−0.278825	+	0.766064i	−0.997497	+	0.0707151i	$0.977472\pi$
$884$	−8.84671	−	7.91876i	−0.297547	−	0.266337i
$885$		0			0
$886$	31.1761	+	15.1491i	1.04738	+	0.508943i
$887$	−3.08697	−	17.5071i	−0.103650	−	0.587830i	−0.991751	−	0.128181i	$-0.959086\pi$
$887$	−3.08697	−	17.5071i	−0.103650	−	0.587830i	0.888101	−	0.459649i	$-0.152025\pi$
$888$		0			0
$889$	1.57967	−	1.32550i	0.0529806	−	0.0444560i
$890$	6.98634	+	15.6299i	0.234182	+	0.523914i
$891$		0			0
$892$	24.0186	+	9.62233i	0.804203	+	0.322179i
$893$	21.1001	+	1.85770i	0.706086	+	0.0621656i
$894$		0			0
$895$	−11.2230	−	30.8350i	−0.375144	−	1.03070i
$896$	1.84427	−	2.09103i	0.0616127	−	0.0698564i
$897$		0			0
$898$	−2.74147	+	26.4564i	−0.0914840	+	0.882861i
$899$	−16.1591	−	91.6431i	−0.538938	−	3.05647i
$900$		0			0
$901$	5.47366	−	9.48066i	0.182354	−	0.315847i
$902$	2.81423	+	11.2172i	0.0937035	+	0.373491i
$903$		0			0
$904$	6.16469	−	19.2608i	0.205035	−	0.640605i
$905$	8.30679	−	4.79592i	0.276127	−	0.159422i
$906$		0			0
$907$	33.7466	−	40.2176i	1.12054	−	1.33540i	0.184772	−	0.982781i	$-0.440845\pi$
$907$	33.7466	−	40.2176i	1.12054	−	1.33540i	0.935765	−	0.352624i	$-0.114710\pi$
$908$	−9.27741	−	28.2706i	−0.307882	−	0.938193i
$909$		0			0
$910$	0.926148	−	1.27867i	0.0307015	−	0.0423875i
$911$	−22.7591			−0.754043			−0.377021	−	0.926205i	$-0.623052\pi$
$911$	−22.7591			−0.754043			−0.377021	+	0.926205i	$0.623052\pi$
$912$		0			0
$913$	−12.9935			−0.430022
$914$	4.36691	−	6.02910i	0.144444	−	0.199425i
$915$		0			0
$916$	−16.4857	−	50.2360i	−0.544702	−	1.65985i
$917$	−2.63882	+	3.14482i	−0.0871414	+	0.103851i
$918$		0			0
$919$	−0.745464	+	0.430394i	−0.0245906	+	0.0141974i	−0.512245	−	0.858839i	$-0.671186\pi$
$919$	−0.745464	+	0.430394i	−0.0245906	+	0.0141974i	0.487654	+	0.873037i	$0.337853\pi$
$920$	−3.98985	+	12.4658i	−0.131541	+	0.410985i
$921$		0			0
$922$	0.637794	+	2.54217i	0.0210046	+	0.0837219i
$923$	−11.2857	+	19.5474i	−0.371473	+	0.643410i
$924$		0			0
$925$	6.94673	+	39.3969i	0.228407	+	1.29536i
$926$	4.30551	−	41.5501i	0.141488	−	1.36542i
$927$		0			0
$928$	−50.4303	−	17.9376i	−1.65545	−	0.588830i
$929$	7.06094	+	19.3998i	0.231662	+	0.636486i	0.999994	−	0.00356601i	$-0.00113510\pi$
$929$	7.06094	+	19.3998i	0.231662	+	0.636486i	−0.768332	+	0.640052i	$0.778913\pi$
$930$		0			0
$931$	7.84470	−	29.2126i	0.257100	−	0.957404i
$932$	−47.3954	−	18.9875i	−1.55249	−	0.621957i
$933$		0			0
$934$	6.22009	+	13.9156i	0.203528	+	0.455333i
$935$	−31.6972	+	26.5971i	−1.03661	+	0.869819i
$936$		0			0
$937$	6.08959	+	34.5358i	0.198938	+	1.12823i	0.906698	+	0.421781i	$0.138595\pi$
$937$	6.08959	+	34.5358i	0.198938	+	1.12823i	−0.707759	+	0.706454i	$0.750294\pi$
$938$	−3.38676	−	1.64569i	−0.110582	−	0.0537338i
$939$		0			0
$940$	22.2815	+	19.9444i	0.726742	+	0.650513i
$941$	−14.2489	+	39.1485i	−0.464500	+	1.27620i	0.457568	+	0.889175i	$0.348721\pi$
$941$	−14.2489	+	39.1485i	−0.464500	+	1.27620i	−0.922068	+	0.387029i	$0.873501\pi$
$942$		0			0
$943$	−3.19355	+	1.84379i	−0.103996	+	0.0600422i
$944$	−10.5790	+	15.8842i	−0.344318	+	0.516986i
$945$		0			0
$946$	3.75661	+	1.07123i	0.122138	+	0.0348288i
$947$	5.28231	−	29.9575i	0.171652	−	0.973487i	−0.770285	−	0.637699i	$-0.779886\pi$
$947$	5.28231	−	29.9575i	0.171652	−	0.973487i	0.941938	−	0.335788i	$-0.109003\pi$
$948$		0			0
$949$	−7.31785			−0.237548
$950$	−27.0374	−	5.22982i	−0.877208	−	0.169678i
$951$		0			0
$952$	1.49983	+	2.37690i	0.0486096	+	0.0770356i
$953$	−11.9736	−	2.11127i	−0.387864	−	0.0683909i	−0.0236840	−	0.999719i	$-0.507540\pi$
$953$	−11.9736	−	2.11127i	−0.387864	−	0.0683909i	−0.364180	+	0.931329i	$0.618651\pi$
$954$		0			0
$955$	−48.9387	+	58.3229i	−1.58362	+	1.88728i
$956$	−15.6199	−	3.27227i	−0.505183	−	0.105833i
$957$		0			0
$958$	0.0562969	+	0.788469i	0.00181887	+	0.0254743i
$959$	2.13853	+	0.778361i	0.0690567	+	0.0251346i
$960$		0			0
$961$	32.8611	−	56.9172i	1.06004	−	1.83604i
$962$	16.7705	+	8.14912i	0.540704	+	0.262738i
$963$		0			0
$964$	−6.09441	+	3.26341i	−0.196288	+	0.105107i
$965$	41.4810	+	49.4352i	1.33532	+	1.59137i
$966$		0			0
$967$	−11.4177	−	31.3699i	−0.367169	−	1.00879i	−0.976433	−	0.215820i	$-0.930757\pi$
$967$	−11.4177	−	31.3699i	−0.367169	−	1.00879i	0.609264	−	0.792967i	$-0.291465\pi$
$968$	−0.0740679	−	0.341078i	−0.00238063	−	0.0109627i
$969$		0			0
$970$	−0.277437	−	0.410019i	−0.00890795	−	0.0131649i
$971$	−45.0097	+	16.3822i	−1.44443	+	0.525730i	−0.941030	−	0.338323i	$-0.890140\pi$
$971$	−45.0097	+	16.3822i	−1.44443	+	0.525730i	−0.503401	+	0.864053i	$0.667918\pi$
$972$		0			0
$973$	3.15837	−	2.65019i	0.101253	−	0.0849611i
$974$	3.87251	−	37.3714i	0.124083	−	1.19746i
$975$		0			0
$976$	−5.38028	+	22.1312i	−0.172219	+	0.708403i
$977$	−37.5428	−	21.6754i	−1.20110	−	0.693456i	−0.240301	−	0.970698i	$-0.577246\pi$
$977$	−37.5428	−	21.6754i	−1.20110	−	0.693456i	−0.960800	+	0.277242i	$0.910579\pi$
$978$		0			0
$979$	4.48797	−	12.3306i	0.143436	−	0.394088i
$980$	33.5731	−	26.3891i	1.07245	−	0.842969i
$981$		0			0
$982$	−32.6188	−	33.6788i	−1.04091	−	1.07473i
$983$	−13.9950	−	11.7432i	−0.446371	−	0.374550i	0.391716	−	0.920086i	$-0.371882\pi$
$983$	−13.9950	−	11.7432i	−0.446371	−	0.374550i	−0.838087	+	0.545536i	$0.816326\pi$
$984$		0			0
$985$	4.47675	−	25.3889i	0.142641	−	0.808958i
$986$	31.6501	−	43.6972i	1.00795	−	1.39160i
$987$		0			0
$988$	−9.36629	+	8.77602i	−0.297981	+	0.279202i
$989$			1.24559i			0.0396076i
$990$		0			0
$991$	19.9299	+	3.51419i	0.633095	+	0.111632i	0.480981	−	0.876731i	$-0.340281\pi$
$991$	19.9299	+	3.51419i	0.633095	+	0.111632i	0.152115	+	0.988363i	$0.451392\pi$
$992$	−28.1693	−	47.9750i	−0.894376	−	1.52321i
$993$		0			0
$994$	3.83796	−	3.71716i	0.121733	−	0.117901i
$995$	−22.6280	−	39.1929i	−0.717356	−	1.24250i
$996$		0			0
$997$	43.5611	+	15.8549i	1.37959	+	0.502131i	0.922055	−	0.387059i	$-0.126509\pi$
$997$	43.5611	+	15.8549i	1.37959	+	0.502131i	0.457539	+	0.889190i	$0.348731\pi$
$998$	−5.96925	−	23.7927i	−0.188953	−	0.753145i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.2.ce.a.575.11	yes	240
3.2	odd	2	inner	684.2.ce.a.575.30	yes	240
4.3	odd	2	inner	684.2.ce.a.575.37	yes	240
12.11	even	2	inner	684.2.ce.a.575.4	yes	240
19.4	even	9	inner	684.2.ce.a.251.4	✓	240
57.23	odd	18	inner	684.2.ce.a.251.37	yes	240
76.23	odd	18	inner	684.2.ce.a.251.30	yes	240
228.23	even	18	inner	684.2.ce.a.251.11	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.2.ce.a.251.4	✓	240	19.4	even	9	inner
684.2.ce.a.251.11	yes	240	228.23	even	18	inner
684.2.ce.a.251.30	yes	240	76.23	odd	18	inner
684.2.ce.a.251.37	yes	240	57.23	odd	18	inner
684.2.ce.a.575.4	yes	240	12.11	even	2	inner
684.2.ce.a.575.11	yes	240	1.1	even	1	trivial
684.2.ce.a.575.30	yes	240	3.2	odd	2	inner
684.2.ce.a.575.37	yes	240	4.3	odd	2	inner

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:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	684.ce (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.829576 + 1.14534i) q^{2} +(-0.623609 - 1.90029i) q^{4} +(1.97780 - 2.35705i) q^{5} +(-0.213423 + 0.123220i) q^{7} +(2.69381 + 0.862192i) q^{8} +O(q^{10})\)	\(q+(-0.829576 + 1.14534i) q^{2} +(-0.623609 - 1.90029i) q^{4} +(1.97780 - 2.35705i) q^{5} +(-0.213423 + 0.123220i) q^{7} +(2.69381 + 0.862192i) q^{8} +(1.05889 + 4.22060i) q^{10} +(1.66759 - 2.88835i) q^{11} +(0.255665 + 1.44995i) q^{13} +(0.0359218 - 0.346661i) q^{14} +(-3.22222 + 2.37008i) q^{16} +(-1.37907 - 3.78896i) q^{17} +(-4.21099 + 1.12585i) q^{19} +(-5.71245 - 2.28852i) q^{20} +(1.92475 + 4.30606i) q^{22} +(-1.15211 + 0.966731i) q^{23} +(-0.775745 - 4.39947i) q^{25} +(-1.87278 - 0.910017i) q^{26} +(0.367245 + 0.328725i) q^{28} +(3.23621 - 8.89141i) q^{29} +(8.51714 - 4.91737i) q^{31} +(-0.0414673 - 5.65670i) q^{32} +(5.48369 + 1.56373i) q^{34} +(-0.131672 + 0.746750i) q^{35} -8.95491 q^{37} +(2.20385 - 5.75700i) q^{38} +(7.36004 - 4.64420i) q^{40} +(2.41466 + 0.425770i) q^{41} +(0.532361 - 0.634443i) q^{43} +(-6.52863 - 1.36771i) q^{44} +(-0.151478 - 2.12153i) q^{46} +(-4.56635 - 1.66202i) q^{47} +(-3.46963 + 6.00958i) q^{49} +(5.68243 + 2.76120i) q^{50} +(2.59589 - 1.39004i) q^{52} +(1.74518 + 2.07983i) q^{53} +(-3.50982 - 9.64314i) q^{55} +(-0.681159 + 0.147919i) q^{56} +(7.49901 + 11.0827i) q^{58} +(4.48342 - 1.63183i) q^{59} +(4.36183 - 3.66001i) q^{61} +(-1.43355 + 13.8344i) q^{62} +(6.51325 + 4.64517i) q^{64} +(3.92324 + 2.26509i) q^{65} +(3.69523 - 10.1526i) q^{67} +(-6.34014 + 4.98346i) q^{68} +(-0.746051 - 0.770295i) q^{70} +(11.7439 + 9.85428i) q^{71} +(-0.863085 + 4.89480i) q^{73} +(7.42878 - 10.2564i) q^{74} +(4.76546 + 7.30003i) q^{76} +0.821918i q^{77} +(7.00868 + 1.23582i) q^{79} +(-0.786520 + 12.2825i) q^{80} +(-2.49079 + 2.41240i) q^{82} +(-1.94795 - 3.37394i) q^{83} +(-11.6583 - 4.24326i) q^{85} +(0.285020 + 1.13605i) q^{86} +(6.98248 - 6.34288i) q^{88} +(3.87464 - 0.683204i) q^{89} +(-0.233226 - 0.277948i) q^{91} +(2.55553 + 1.58648i) q^{92} +(5.69171 - 3.85126i) q^{94} +(-5.67480 + 12.1522i) q^{95} +(-0.106910 + 0.0389119i) q^{97} +(-4.00469 - 8.95931i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{4}+O(q^{10}) \) 240 * q + 12 * q^4	\( 240 q + 12 q^{4} + 12 q^{10} + 24 q^{13} - 12 q^{16} - 12 q^{34} + 120 q^{49} - 48 q^{52} - 144 q^{58} + 48 q^{61} - 12 q^{64} - 72 q^{70} + 72 q^{73} - 144 q^{76} - 72 q^{82} + 240 q^{85} - 48 q^{88} - 48 q^{94}+O(q^{100}) \) 240 * q + 12 * q^4 + 12 * q^10 + 24 * q^13 - 12 * q^16 - 12 * q^34 + 120 * q^49 - 48 * q^52 - 144 * q^58 + 48 * q^61 - 12 * q^64 - 72 * q^70 + 72 * q^73 - 144 * q^76 - 72 * q^82 + 240 * q^85 - 48 * q^88 - 48 * q^94

Introduction

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