LMFDB - Embedded newform 684.2.ce.a.575.4

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			575.4
Character	$\chi$	$=$	684.575
Dual form			684.2.ce.a.251.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.37170 - 0.344141i) q^{2} +(1.76313 + 0.944117i) q^{4} +(-1.97780 + 2.35705i) q^{5} +(0.213423 - 0.123220i) q^{7} +(-2.09359 - 1.90181i) q^{8} +O(q^{10})$	\(q+(-1.37170 - 0.344141i) q^{2} +(1.76313 + 0.944117i) q^{4} +(-1.97780 + 2.35705i) q^{5} +(0.213423 - 0.123220i) q^{7} +(-2.09359 - 1.90181i) q^{8} +(3.52410 - 2.55252i) q^{10} +(1.66759 - 2.88835i) q^{11} +(0.255665 + 1.44995i) q^{13} +(-0.335157 + 0.0955732i) q^{14} +(2.21729 + 3.32921i) q^{16} +(1.37907 + 3.78896i) q^{17} +(4.21099 - 1.12585i) q^{19} +(-5.71245 + 2.28852i) q^{20} +(-3.28143 + 3.38807i) q^{22} +(-1.15211 + 0.966731i) q^{23} +(-0.775745 - 4.39947i) q^{25} +(0.148290 - 2.07688i) q^{26} +(0.492626 - 0.0157568i) q^{28} +(-3.23621 + 8.89141i) q^{29} +(-8.51714 + 4.91737i) q^{31} +(-1.89574 - 5.32974i) q^{32} +(-0.587737 - 5.67192i) q^{34} +(-0.131672 + 0.746750i) q^{35} -8.95491 q^{37} +(-6.16368 + 0.0951602i) q^{38} +(8.62335 - 1.17328i) q^{40} +(-2.41466 - 0.425770i) q^{41} +(-0.532361 + 0.634443i) q^{43} +(5.66712 - 3.51815i) q^{44} +(1.91304 - 0.929581i) q^{46} +(-4.56635 - 1.66202i) q^{47} +(-3.46963 + 6.00958i) q^{49} +(-0.449945 + 6.30173i) q^{50} +(-0.918148 + 2.79783i) q^{52} +(-1.74518 - 2.07983i) q^{53} +(3.50982 + 9.64314i) q^{55} +(-0.681159 - 0.147919i) q^{56} +(7.49901 - 11.0827i) q^{58} +(4.48342 - 1.63183i) q^{59} +(4.36183 - 3.66001i) q^{61} +(13.3753 - 3.81408i) q^{62} +(0.766209 + 7.96322i) q^{64} +(-3.92324 - 2.26509i) q^{65} +(-3.69523 + 10.1526i) q^{67} +(-1.14574 + 7.98245i) q^{68} +(0.437602 - 0.979005i) q^{70} +(11.7439 + 9.85428i) q^{71} +(-0.863085 + 4.89480i) q^{73} +(12.2835 + 3.08175i) q^{74} +(8.48748 + 1.99064i) q^{76} -0.821918i q^{77} +(-7.00868 - 1.23582i) q^{79} +(-12.2324 - 1.35826i) q^{80} +(3.16567 + 1.41501i) q^{82} +(-1.94795 - 3.37394i) q^{83} +(-11.6583 - 4.24326i) q^{85} +(0.948578 - 0.687060i) q^{86} +(-8.98434 + 2.87556i) q^{88} +(-3.87464 + 0.683204i) q^{89} +(0.233226 + 0.277948i) q^{91} +(-2.94402 + 0.616755i) q^{92} +(5.69171 + 3.85126i) q^{94} +(-5.67480 + 12.1522i) q^{95} +(-0.106910 + 0.0389119i) q^{97} +(6.82745 - 7.04932i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.37170	−	0.344141i	−0.969940	−	0.243344i
$2$	−1.37170	−	0.344141i	−0.969940	−	0.243344i
$3$		0			0
$3$		0			0
$4$	1.76313	+	0.944117i	0.881567	+	0.472059i
$5$	−1.97780	+	2.35705i	−0.884497	+	1.05410i	0.113666	+	0.993519i	$0.463741\pi$
$5$	−1.97780	+	2.35705i	−0.884497	+	1.05410i	−0.998163	+	0.0605837i	$0.980704\pi$
$6$		0			0
$7$	0.213423	−	0.123220i	0.0806661	−	0.0465726i	−0.459124	−	0.888372i	$-0.651837\pi$
$7$	0.213423	−	0.123220i	0.0806661	−	0.0465726i	0.539791	+	0.841799i	$0.318503\pi$
$8$	−2.09359	−	1.90181i	−0.740195	−	0.672393i
$9$		0			0
$10$	3.52410	−	2.55252i	1.11442	−	0.807179i
$11$	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	$0.878994\pi$
$14$	−0.335157	+	0.0955732i	−0.0895745	+	0.0255430i
$15$		0			0
$16$	2.21729	+	3.32921i	0.554321	+	0.832303i
$17$	1.37907	+	3.78896i	0.334473	+	0.918958i	0.986933	+	0.161134i	$0.0515152\pi$
$17$	1.37907	+	3.78896i	0.334473	+	0.918958i	−0.652459	+	0.757824i	$0.726263\pi$
$18$		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
$22$	−3.28143	+	3.38807i	−0.699604	+	0.722338i
$23$	−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
$26$	0.148290	−	2.07688i	0.0290820	−	0.407310i
$27$		0			0
$28$	0.492626	−	0.0157568i	0.0930976	−	0.00297775i
$29$	−3.23621	+	8.89141i	−0.600949	+	1.65109i	0.148407	+	0.988926i	$0.452586\pi$
$29$	−3.23621	+	8.89141i	−0.600949	+	1.65109i	−0.749356	+	0.662168i	$0.769637\pi$
$30$		0			0
$31$	−8.51714	+	4.91737i	−1.52972	+	0.883186i	−0.530351	+	0.847778i	$0.677940\pi$
$31$	−8.51714	+	4.91737i	−1.52972	+	0.883186i	−0.999373	+	0.0354082i	$0.988727\pi$
$32$	−1.89574	−	5.32974i	−0.335123	−	0.942175i
$33$		0			0
$34$	−0.587737	−	5.67192i	−0.100796	−	0.972726i
$35$	−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	$0.763330\pi$
$38$	−6.16368	+	0.0951602i	−0.999881	+	0.0154370i
$39$		0			0
$40$	8.62335	−	1.17328i	1.36347	−	0.185512i
$41$	−2.41466	−	0.425770i	−0.377106	−	0.0664940i	−0.0181175	−	0.999836i	$-0.505767\pi$
$41$	−2.41466	−	0.425770i	−0.377106	−	0.0664940i	−0.358989	+	0.933342i	$0.616878\pi$
$42$		0			0
$43$	−0.532361	+	0.634443i	−0.0811843	+	0.0967517i	−0.805108	−	0.593129i	$-0.797892\pi$
$43$	−0.532361	+	0.634443i	−0.0811843	+	0.0967517i	0.723923	+	0.689880i	$0.242337\pi$
$44$	5.66712	−	3.51815i	0.854350	−	0.530380i
$45$		0			0
$46$	1.91304	−	0.929581i	0.282062	−	0.137059i
$47$	−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
$50$	−0.449945	+	6.30173i	−0.0636318	+	0.891199i
$51$		0			0
$52$	−0.918148	+	2.79783i	−0.127324	+	0.387989i
$53$	−1.74518	−	2.07983i	−0.239719	−	0.285686i	0.632749	−	0.774357i	$-0.281926\pi$
$53$	−1.74518	−	2.07983i	−0.239719	−	0.285686i	−0.872468	+	0.488671i	$0.837482\pi$
$54$		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	$0.159011\pi$
$62$	13.3753	−	3.81408i	1.69866	−	0.484388i
$63$		0			0
$64$	0.766209	+	7.96322i	0.0957761	+	0.995403i
$65$	−3.92324	−	2.26509i	−0.486618	−	0.280949i
$66$		0			0
$67$	−3.69523	+	10.1526i	−0.451444	+	1.24033i	0.480264	+	0.877124i	$0.340541\pi$
$67$	−3.69523	+	10.1526i	−0.451444	+	1.24033i	−0.931708	+	0.363209i	$0.881681\pi$
$68$	−1.14574	+	7.98245i	−0.138941	+	0.968014i
$69$		0			0
$70$	0.437602	−	0.979005i	0.0523034	−	0.117013i
$71$	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	$0.961612\pi$
$74$	12.2835	+	3.08175i	1.42792	+	0.358246i
$75$		0			0
$76$	8.48748	+	1.99064i	0.973581	+	0.228342i
$77$		−	0.821918i		−	0.0936662i
$78$		0			0
$79$	−7.00868	−	1.23582i	−0.788539	−	0.139041i	−0.235145	−	0.971960i	$-0.575556\pi$
$79$	−7.00868	−	1.23582i	−0.788539	−	0.139041i	−0.553394	+	0.832920i	$0.686668\pi$
$80$	−12.2324	−	1.35826i	−1.36763	−	0.151858i
$81$		0			0
$82$	3.16567	+	1.41501i	0.349590	+	0.156262i
$83$	−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
$86$	0.948578	−	0.687060i	0.102288	−	0.0740876i
$87$		0			0
$88$	−8.98434	+	2.87556i	−0.957734	+	0.306536i
$89$	−3.87464	+	0.683204i	−0.410711	+	0.0724194i	−0.375186	−	0.926949i	$-0.622421\pi$
$89$	−3.87464	+	0.683204i	−0.410711	+	0.0724194i	−0.0355246	+	0.999369i	$0.511310\pi$
$90$		0			0
$91$	0.233226	+	0.277948i	0.0244488	+	0.0291369i
$92$	−2.94402	+	0.616755i	−0.306936	+	0.0643011i
$93$		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	$0.390727\pi$
$98$	6.82745	−	7.04932i	0.689676	−	0.712088i
$99$		0			0
$100$	2.78587	−	8.48925i	0.278587	−	0.848925i
$101$	11.1632	−	1.96838i	1.11078	−	0.195861i	0.411993	−	0.911187i	$-0.364833\pi$
$101$	11.1632	−	1.96838i	1.11078	−	0.195861i	0.698791	+	0.715326i	$0.253722\pi$
$102$		0			0
$103$	−3.25834	−	1.88120i	−0.321054	−	0.185360i	0.330808	−	0.943698i	$-0.392679\pi$
$103$	−3.25834	−	1.88120i	−0.321054	−	0.185360i	−0.651862	+	0.758337i	$0.726012\pi$
$104$	2.22227	−	3.52182i	0.217912	−	0.345342i
$105$		0			0
$106$	1.67812	+	3.45349i	0.162993	+	0.335433i
$107$	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	$0.792277\pi$
$110$	−1.49583	−	14.4354i	−0.142621	−	1.37636i
$111$		0			0
$112$	0.883443	+	0.437316i	0.0834775	+	0.0413224i
$113$			7.15002i			0.672617i	0.941752	+	0.336309i	$0.109179\pi$
$113$			7.15002i			0.672617i	−0.941752	+	0.336309i	$0.890821\pi$
$114$		0			0
$115$		−	4.62756i		−	0.431522i
$116$	−14.1004	+	12.6214i	−1.30919	+	1.17187i
$117$		0			0
$118$	−6.71150	+	0.695460i	−0.617843	+	0.0640223i
$119$	0.761199	+	0.638721i	0.0697790	+	0.0585515i
$120$		0			0
$121$	−0.0617000	−	0.106868i	−0.00560909	−	0.00971523i
$122$	−7.24268	+	3.51936i	−0.655722	+	0.318628i
$123$		0			0
$124$	−19.6594	+	0.628813i	−1.76547	+	0.0564691i
$125$	−1.41937	−	0.819473i	−0.126952	−	0.0732959i
$126$		0			0
$127$	8.24054	−	1.45303i	0.731229	−	0.128935i	0.204377	−	0.978892i	$-0.434483\pi$
$127$	8.24054	−	1.45303i	0.731229	−	0.128935i	0.526852	+	0.849957i	$0.323372\pi$
$128$	1.68946	−	11.1869i	0.149328	−	0.988788i
$129$		0			0
$130$	4.60201	+	4.45717i	0.403623	+	0.390920i
$131$	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
$136$	4.31870	−	10.5553i	0.370325	−	0.905105i
$137$	5.93591	+	7.07414i	0.507139	+	0.604385i	0.957490	−	0.288467i	$-0.0931455\pi$
$137$	5.93591	+	7.07414i	0.507139	+	0.604385i	−0.450351	+	0.892852i	$0.648701\pi$
$138$		0			0
$139$	16.4760	−	2.90516i	1.39747	−	0.246412i	0.576369	−	0.817190i	$-0.304469\pi$
$139$	16.4760	−	2.90516i	1.39747	−	0.246412i	0.821105	+	0.570777i	$0.193358\pi$
$140$	−0.937175	+	1.19231i	−0.0792057	+	0.100768i
$141$		0			0
$142$	−12.7178	−	17.5587i	−1.06726	−	1.47349i
$143$	4.61429	+	1.67947i	0.385867	+	0.140444i
$144$		0			0
$145$	−14.5569	−	25.2133i	−1.20888	−	2.09385i
$146$	2.86839	−	6.41718i	0.237390	−	0.531090i
$147$		0			0
$148$	−15.7887	−	8.45448i	−1.29782	−	0.694954i
$149$	16.0696	+	2.83351i	1.31647	+	0.232130i	0.787399	−	0.616444i	$-0.211427\pi$
$149$	16.0696	+	2.83351i	1.31647	+	0.232130i	0.529076	+	0.848574i	$0.322539\pi$
$150$		0			0
$151$		−	11.9193i		−	0.969982i	−0.874519	−	0.484991i	$-0.838823\pi$
$151$		−	11.9193i		−	0.969982i	0.874519	−	0.484991i	$-0.161177\pi$
$152$	−10.9572	−	5.65145i	−0.888749	−	0.458394i
$153$		0			0
$154$	−0.282855	+	1.12743i	−0.0227931	+	0.0908506i
$155$	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	$0.620795\pi$
$158$	9.18853	+	4.10715i	0.731000	+	0.326747i
$159$		0			0
$160$	16.3118	+	6.07280i	1.28956	+	0.480097i
$161$	−0.126765	+	0.348284i	−0.00999048	+	0.0274486i
$162$		0			0
$163$	−15.8808	−	9.16880i	−1.24388	−	0.718156i	−0.274000	−	0.961730i	$-0.588347\pi$
$163$	−15.8808	−	9.16880i	−1.24388	−	0.718156i	−0.969882	+	0.243574i	$0.921680\pi$
$164$	−3.85539	−	3.03041i	−0.301056	−	0.236635i
$165$		0			0
$166$	1.51089	+	5.29841i	0.117268	+	0.411236i
$167$	−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	$-0.846348\pi$
$173$	−6.65005	−	18.2709i	−0.505594	−	1.38911i	0.380146	−	0.924927i	$-0.375874\pi$
$174$		0			0
$175$	−0.707662	−	0.843359i	−0.0534943	−	0.0637520i
$176$	13.3134	−	0.852540i	1.00354	−	0.0642626i
$177$		0			0
$178$	5.54997	+	0.396269i	0.415988	+	0.0297016i
$179$	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	$0.574150\pi$
$182$	−0.224264	−	0.461525i	−0.0166235	−	0.0342105i
$183$		0			0
$184$	4.25057	+	0.167154i	0.313356	+	0.0123228i
$185$	17.7110	−	21.1071i	1.30214	−	1.55183i
$186$		0			0
$187$	13.2436	+	2.33520i	0.968465	+	0.170766i
$188$	−6.48195	−	7.24153i	−0.472745	−	0.528143i
$189$		0			0
$190$	11.9662	−	14.7163i	0.868120	−	1.06763i
$191$	−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	$0.783266\pi$
$194$	0.160039	−	0.0165836i	0.0114901	−	0.00119063i
$195$		0			0
$196$	−11.7912	+	7.31996i	−0.842227	+	0.522854i
$197$	−7.25620	+	4.18937i	−0.516983	+	0.298480i	−0.735699	−	0.677308i	$-0.763146\pi$
$197$	−7.25620	+	4.18937i	−0.516983	+	0.298480i	0.218716	+	0.975788i	$0.429813\pi$
$198$		0			0
$199$	−5.03053	+	13.8213i	−0.356605	+	0.979764i	0.623594	+	0.781749i	$0.285672\pi$
$199$	−5.03053	+	13.8213i	−0.356605	+	0.979764i	−0.980199	+	0.198016i	$0.936550\pi$
$200$	−6.74288	+	10.6860i	−0.476794	+	0.755614i
$201$		0			0
$202$	−15.9900	−	1.14169i	−1.12506	−	0.0803292i
$203$	0.404916	+	2.29639i	0.0284195	+	0.161175i
$204$		0			0
$205$	5.77926	−	4.84938i	0.403641	−	0.338695i
$206$	3.82207	+	3.70178i	0.266296	+	0.257915i
$207$		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	0.843534	−	0.537076i	$-0.180471\pi$
$211$	−2.14803	−	5.90166i	−0.147876	−	0.406287i	−0.991410	+	0.130789i	$0.958249\pi$
$212$	−1.11339	−	5.31467i	−0.0764680	−	0.365013i
$213$		0			0
$214$	−1.58249	−	5.54951i	−0.108177	−	0.379357i
$215$	−0.442510	−	2.50960i	−0.0301789	−	0.171153i
$216$		0			0
$217$	−1.21183	+	2.09896i	−0.0822646	+	0.142486i
$218$	3.78159	+	5.22099i	0.256121	+	0.353610i
$219$		0			0
$220$	−2.91598	+	20.3158i	−0.196595	+	1.36969i
$221$	−5.14121	+	2.96828i	−0.345835	+	0.199668i
$222$		0			0
$223$	8.31587	−	9.91046i	0.556872	−	0.663654i	−0.412010	−	0.911179i	$-0.635173\pi$
$223$	8.31587	−	9.91046i	0.556872	−	0.663654i	0.968881	+	0.247526i	$0.0796175\pi$
$224$	−1.06132	−	0.903895i	−0.0709126	−	0.0603940i
$225$		0			0
$226$	2.46061	−	9.80770i	0.163678	−	0.652398i
$227$	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	$0.161865\pi$
$230$	−1.59253	+	6.34764i	−0.105008	+	0.418551i
$231$		0			0
$232$	23.6851	−	12.4603i	1.55500	−	0.818057i
$233$	−16.4095	+	19.5561i	−1.07502	+	1.28116i	−0.117416	+	0.993083i	$0.537461\pi$
$233$	−16.4095	+	19.5561i	−1.07502	+	1.28116i	−0.957606	+	0.288080i	$0.906983\pi$
$234$		0			0
$235$	12.9488	−	7.47597i	0.844684	−	0.487678i
$236$	9.44551	+	1.35573i	0.614850	+	0.0882508i
$237$		0			0
$238$	−0.824328	−	1.13810i	−0.0534332	−	0.0737718i
$239$	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	$0.979955\pi$
$242$	0.0478566	+	0.167824i	0.00307634	+	0.0107881i
$243$		0			0
$244$	11.1460	−	2.33501i	0.713547	−	0.149484i
$245$	−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
$250$	1.66494	+	1.61254i	0.105300	+	0.101986i
$251$	−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
$254$	−11.8036	−	0.842780i	−0.740624	−	0.0528807i
$255$		0			0
$256$	−6.16729	+	14.7636i	−0.385455	+	0.922726i
$257$	4.78659	−	13.1511i	0.298579	−	0.820340i	−0.696158	−	0.717888i	$-0.745109\pi$
$257$	4.78659	−	13.1511i	0.298579	−	0.820340i	0.994738	−	0.102452i	$-0.0326689\pi$
$258$		0			0
$259$	−1.91118	+	1.10342i	−0.118755	+	0.0685632i
$260$	−4.77870	−	7.69765i	−0.296362	−	0.477388i
$261$		0			0
$262$	−23.4330	+	2.42818i	−1.44770	+	0.150013i
$263$	−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
$266$	−1.30374	+	0.779795i	−0.0799376	+	0.0478123i
$267$		0			0
$268$	−16.1004	+	14.4116i	−0.983488	+	0.880329i
$269$	6.42853	+	1.13352i	0.391954	+	0.0691121i	0.366152	−	0.930555i	$-0.380675\pi$
$269$	6.42853	+	1.13352i	0.391954	+	0.0691121i	0.0258020	+	0.999667i	$0.491786\pi$
$270$		0			0
$271$	10.1845	−	12.1374i	0.618662	−	0.737292i	−0.362178	−	0.932109i	$-0.617967\pi$
$271$	10.1845	−	12.1374i	0.618662	−	0.737292i	0.980840	+	0.194817i	$0.0624112\pi$
$272$	−9.55646	+	12.9924i	−0.579445	+	0.787781i
$273$		0			0
$274$	−5.70780	−	11.7464i	−0.344821	−	0.709626i
$275$	−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	$0.891160\pi$
$278$	−23.5999	−	1.68504i	−1.41543	−	0.101062i
$279$		0			0
$280$	1.69585	−	1.31297i	0.101346	−	0.0784649i
$281$	−9.25260	−	11.0268i	−0.551964	−	0.657805i	0.415862	−	0.909428i	$-0.363480\pi$
$281$	−9.25260	−	11.0268i	−0.551964	−	0.657805i	−0.967825	+	0.251623i	$0.919036\pi$
$282$		0			0
$283$	−4.54878	−	12.4977i	−0.270397	−	0.742909i	−0.998358	−	0.0572904i	$-0.981754\pi$
$283$	−4.54878	−	12.4977i	−0.270397	−	0.742909i	0.727961	−	0.685619i	$-0.240468\pi$
$284$	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
$290$	11.2908	+	39.5948i	0.663020	+	2.32508i
$291$		0			0
$292$	−6.14299	+	7.81533i	−0.359492	+	0.457358i
$293$	−14.6509	−	8.45871i	−0.855916	−	0.494163i	0.00672667	−	0.999977i	$-0.497859\pi$
$293$	−14.6509	−	8.45871i	−0.855916	−	0.494163i	−0.862642	+	0.505814i	$0.831192\pi$
$294$		0			0
$295$	−5.02099	+	13.7951i	−0.292333	+	0.803179i
$296$	18.7479	+	17.0306i	1.08970	+	0.989882i
$297$		0			0
$298$	−21.0676	−	9.41694i	−1.22041	−	0.545509i
$299$	−1.69626	−	1.42333i	−0.0980973	−	0.0823134i
$300$		0			0
$301$	−0.0354420	+	0.201002i	−0.00204284	+	0.0115855i
$302$	−4.10193	+	16.3498i	−0.236040	+	0.940824i
$303$		0			0
$304$	13.0852	+	11.5229i	0.750486	+	0.660886i
$305$			17.5198i			1.00318i
$306$		0			0
$307$	−26.4339	−	4.66100i	−1.50866	−	0.266018i	−0.642695	−	0.766122i	$-0.722184\pi$
$307$	−26.4339	−	4.66100i	−1.50866	−	0.266018i	−0.865965	+	0.500104i	$0.833295\pi$
$308$	0.775987	−	1.44915i	0.0442159	−	0.0825731i
$309$		0			0
$310$	−17.4636	+	39.0695i	−0.991864	+	2.21900i
$311$	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	$0.612493\pi$
$314$	−6.51275	−	8.99173i	−0.367536	−	0.507433i
$315$		0			0
$316$	−11.1905	−	8.79594i	−0.629514	−	0.494810i
$317$	28.3064	−	4.99119i	1.58985	−	0.280333i	0.692420	−	0.721495i	$-0.256545\pi$
$317$	28.3064	−	4.99119i	1.58985	−	0.280333i	0.897427	+	0.441162i	$0.145434\pi$
$318$		0			0
$319$	20.2848	+	24.1745i	1.13573	+	1.35351i
$320$	−20.2851	−	13.9436i	−1.13397	−	0.779473i
$321$		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
$326$	18.6284	+	18.0421i	1.03173	+	0.999260i
$327$		0			0
$328$	4.24556	+	5.48362i	0.234422	+	0.302782i
$329$	−1.17936	+	0.207952i	−0.0650200	+	0.0114648i
$330$		0			0
$331$	−11.7645	−	6.79225i	−0.646637	−	0.373336i	0.140530	−	0.990076i	$-0.455119\pi$
$331$	−11.7645	−	6.79225i	−0.646637	−	0.373336i	−0.787166	+	0.616741i	$0.788453\pi$
$332$	−0.249095	−	7.78780i	−0.0136709	−	0.427411i
$333$		0			0
$334$	27.2452	−	13.2390i	1.49079	−	0.724403i
$335$	−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	$0.280680\pi$
$338$	−15.2376	+	1.57895i	−0.828815	+	0.0858836i
$339$		0			0
$340$	−16.5490	−	18.4882i	−0.897493	−	1.00266i
$341$			32.8006i			1.77625i
$342$		0			0
$343$			3.43518i			0.185482i
$344$	2.32114	−	0.315810i	0.125147	−	0.0170273i
$345$		0			0
$346$	2.83414	+	27.3507i	0.152365	+	1.47039i
$347$	−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	$0.746553\pi$
$350$	0.680468	+	1.40037i	0.0363725	+	0.0748531i
$351$		0			0
$352$	−18.5555	−	3.41226i	−0.989010	−	0.181874i
$353$	11.6772	+	6.74186i	0.621517	+	0.358833i	0.777460	−	0.628933i	$-0.216508\pi$
$353$	11.6772	+	6.74186i	0.621517	+	0.358833i	−0.155942	+	0.987766i	$0.549841\pi$
$354$		0			0
$355$	−46.4540	+	8.19109i	−2.46552	+	0.434738i
$356$	−7.47653	−	2.45353i	−0.396256	−	0.130037i
$357$		0			0
$358$	−10.4927	+	10.8337i	−0.554558	+	0.572579i
$359$	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
$364$	0.148794	+	0.710254i	0.00779891	+	0.0372274i
$365$	−9.83025	−	11.7152i	−0.514539	−	0.613204i
$366$		0			0
$367$	20.3080	−	3.58085i	1.06007	−	0.186919i	0.383683	−	0.923465i	$-0.374656\pi$
$367$	20.3080	−	3.58085i	1.06007	−	0.186919i	0.676387	+	0.736546i	$0.263545\pi$
$368$	−5.77300	−	1.69208i	−0.300938	−	0.0882058i
$369$		0			0
$370$	−31.5580	+	22.8576i	−1.64062	+	1.18831i
$371$	−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	$0.667786\pi$
$374$	−17.3626	−	7.76084i	−0.897798	−	0.401303i
$375$		0			0
$376$	6.39921	+	12.1639i	0.330014	+	0.627307i
$377$	−13.7195	−	2.41911i	−0.706588	−	0.124591i
$378$		0			0
$379$		−	29.7966i		−	1.53055i	−0.643703	−	0.765275i	$-0.722603\pi$
$379$		−	29.7966i		−	1.53055i	0.643703	−	0.765275i	$-0.277397\pi$
$380$	−21.4785	+	16.0683i	−1.10183	+	0.824286i
$381$		0			0
$382$	33.9415	+	8.51544i	1.73660	+	0.435688i
$383$	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
$386$	12.1039	−	27.0788i	0.616070	−	1.37827i
$387$		0			0
$388$	−0.225233	−	0.0323282i	−0.0114345	−	0.00164122i
$389$	−5.26027	+	14.4525i	−0.266706	+	0.732769i	0.731970	+	0.681337i	$0.238601\pi$
$389$	−5.26027	+	14.4525i	−0.266706	+	0.732769i	−0.998676	+	0.0514328i	$0.983621\pi$
$390$		0			0
$391$	−5.25174	−	3.03209i	−0.265592	−	0.153340i
$392$	18.6931	−	5.98298i	0.944143	−	0.302186i
$393$		0			0
$394$	11.3951	−	3.24942i	0.574076	−	0.163703i
$395$	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	0.924188	−	0.381938i	$-0.124743\pi$
$401$	−0.586459	−	1.61128i	−0.0292864	−	0.0804636i	−0.953474	+	0.301475i	$0.902521\pi$
$402$		0			0
$403$	−9.30746	−	11.0922i	−0.463638	−	0.552542i
$404$	21.5407	+	7.06889i	1.07169	+	0.351690i
$405$		0			0
$406$	0.234858	−	3.28932i	0.0116558	−	0.163246i
$407$	−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	$0.579162\pi$
$410$	−9.59629	+	4.66302i	−0.473927	+	0.230290i
$411$		0			0
$412$	−3.96881	−	6.39307i	−0.195529	−	0.314964i
$413$	0.755789	−	0.900715i	0.0371900	−	0.0443213i
$414$		0			0
$415$	11.8052	+	2.08157i	0.579493	+	0.102180i
$416$	7.24317	−	4.11135i	0.355126	−	0.201575i
$417$		0			0
$418$	−10.0036	+	17.9615i	−0.489293	+	0.878527i
$419$	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	$-0.145314\pi$
$422$	0.915454	+	8.83454i	0.0445636	+	0.430059i
$423$		0			0
$424$	−0.301754	+	7.67331i	−0.0146545	+	0.372649i
$425$	15.5996	−	9.00644i	0.756693	−	0.436877i
$426$		0			0
$427$	0.479928	−	1.31859i	0.0232253	−	0.0638111i
$428$	0.260900	+	8.15687i	0.0126111	+	0.394277i
$429$		0			0
$430$	−0.256663	+	3.59471i	−0.0123774	+	0.173352i
$431$	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	$0.209080\pi$
$434$	2.38461	−	2.46210i	0.114465	−	0.118185i
$435$		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	$0.304111\pi$
$439$	13.8269	+	37.9891i	0.659922	+	1.81312i	0.0826331	+	0.996580i	$0.473667\pi$
$440$	10.9914	−	26.8638i	0.523992	−	1.28068i
$441$		0			0
$442$	8.07372	−	2.30230i	0.384028	−	0.109509i
$443$	−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
$446$	−14.8175	+	10.7324i	−0.701628	+	0.508193i
$447$		0			0
$448$	1.14475	+	1.60512i	0.0540844	+	0.0758348i
$449$	−16.2879	+	9.40383i	−0.768674	+	0.443794i	−0.832401	−	0.554173i	$-0.813035\pi$
$449$	−16.2879	+	9.40383i	−0.768674	+	0.443794i	0.0637273	+	0.997967i	$0.479701\pi$
$450$		0			0
$451$	−5.25643	+	6.26437i	−0.247515	+	0.294977i
$452$	−6.75046	+	12.6064i	−0.317515	+	0.592957i
$453$		0			0
$454$	−20.4068	−	5.11977i	−0.957737	−	0.240283i
$455$	−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	$0.539290\pi$
$458$	−36.2623	−	9.09769i	−1.69442	−	0.425107i
$459$		0			0
$460$	4.36896	−	8.15901i	0.203704	−	0.380416i
$461$	−1.19127	+	1.41971i	−0.0554832	+	0.0661223i	−0.793072	−	0.609128i	$-0.791520\pi$
$461$	−1.19127	+	1.41971i	−0.0554832	+	0.0661223i	0.737589	+	0.675250i	$0.235964\pi$
$462$		0			0
$463$	25.5804	−	14.7688i	1.18882	−	0.686367i	0.230783	−	0.973005i	$-0.425871\pi$
$463$	25.5804	−	14.7688i	1.18882	−	0.686367i	0.958039	+	0.286639i	$0.0925379\pi$
$464$	−36.7770	+	8.94078i	−1.70733	+	0.415065i
$465$		0			0
$466$	29.2390	−	21.1780i	1.35447	−	0.981050i
$467$	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
$470$	−20.3346	+	5.79861i	−0.937966	+	0.267470i
$471$		0			0
$472$	−12.4899	−	5.11025i	−0.574893	−	0.235218i
$473$	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
$478$	−7.85090	+	8.10603i	−0.359092	+	0.370761i
$479$	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
$482$	−0.348142	+	4.87593i	−0.0158574	+	0.222092i
$483$		0			0
$484$	−0.00788993	−	0.246674i	−0.000358633	−	0.0112124i
$485$	0.119728	−	0.328950i	0.00543657	−	0.0149369i
$486$		0			0
$487$	23.0078	−	13.2835i	1.04258	−	0.601935i	0.122018	−	0.992528i	$-0.461063\pi$
$487$	23.0078	−	13.2835i	1.04258	−	0.601935i	0.920564	+	0.390593i	$0.127730\pi$
$488$	−16.0925	−	0.632840i	−0.728474	−	0.0286473i
$489$		0			0
$490$	3.11226	+	30.0347i	0.140598	+	1.35683i
$491$	−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
$494$	−1.71381	−	8.91268i	−0.0771081	−	0.401000i
$495$		0			0
$496$	−35.2559	−	17.4521i	−1.58304	−	0.783624i
$497$	3.72065	+	0.656051i	0.166894	+	0.0294279i
$498$		0			0
$499$	11.1494	−	13.2873i	0.499116	−	0.594823i	−0.456396	−	0.889777i	$-0.650860\pi$
$499$	11.1494	−	13.2873i	0.499116	−	0.594823i	0.955511	+	0.294954i	$0.0953043\pi$
$500$	−1.72886	−	2.78489i	−0.0773169	−	0.124544i
$501$		0			0
$502$	33.5247	−	16.2903i	1.49628	−	0.727071i
$503$	−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
$506$	0.505205	−	7.07567i	0.0224591	−	0.314552i
$507$		0			0
$508$	15.9010	+	5.21815i	0.705493	+	0.231518i
$509$	6.48586	+	7.72955i	0.287481	+	0.342606i	0.890386	−	0.455207i	$-0.150435\pi$
$509$	6.48586	+	7.72955i	0.287481	+	0.342606i	−0.602905	+	0.797813i	$0.705990\pi$
$510$		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
$518$	3.00130	−	0.855849i	0.131870	−	0.0376039i
$519$		0			0
$520$	3.90588	+	12.2034i	0.171284	+	0.535156i
$521$	5.66567	+	3.27108i	0.248218	+	0.143308i	0.618948	−	0.785432i	$-0.287559\pi$
$521$	5.66567	+	3.27108i	0.248218	+	0.143308i	−0.370730	+	0.928741i	$0.620893\pi$
$522$		0			0
$523$	−5.57060	+	15.3051i	−0.243585	+	0.669245i	0.756302	+	0.654223i	$0.227004\pi$
$523$	−5.57060	+	15.3051i	−0.243585	+	0.669245i	−0.999887	+	0.0150224i	$0.995218\pi$
$524$	32.9787	+	4.73351i	1.44068	+	0.206784i
$525$		0			0
$526$	14.0920	−	31.5268i	0.614442	−	1.37463i
$527$	−30.3775	−	25.4897i	−1.32326	−	1.11035i
$528$		0			0
$529$	−3.60113	+	20.4230i	−0.156571	+	0.887958i
$530$	−11.4590	−	2.87490i	−0.497748	−	0.124878i
$531$		0			0
$532$	2.05671	−	0.620976i	0.0891695	−	0.0269227i
$533$		−	3.60998i		−	0.156366i
$534$		0			0
$535$	−12.3646	−	2.18022i	−0.534570	−	0.0942591i
$536$	27.0446	−	14.2276i	1.16815	−	0.614540i
$537$		0			0
$538$	−8.42793	−	3.76717i	−0.363354	−	0.162414i
$539$	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	$0.775207\pi$
$542$	−18.1470	+	13.1440i	−0.779480	+	0.564582i
$543$		0			0
$544$	17.5798	−	14.5330i	0.753729	−	0.623096i
$545$	13.8129	−	2.43558i	0.591678	−	0.104329i
$546$		0			0
$547$	17.4752	+	20.8261i	0.747183	+	0.890459i	0.996966	−	0.0778435i	$-0.0248034\pi$
$547$	17.4752	+	20.8261i	0.747183	+	0.890459i	−0.249782	+	0.968302i	$0.580359\pi$
$548$	3.78699	+	18.0769i	0.161772	+	0.772205i
$549$		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
$554$	24.9373	−	25.7477i	1.05949	−	1.09392i
$555$		0			0
$556$	31.7922	+	10.4331i	1.34829	+	0.442460i
$557$	−11.9988	+	2.11571i	−0.508405	+	0.0896456i	−0.421966	−	0.906612i	$-0.638660\pi$
$557$	−11.9988	+	2.11571i	−0.508405	+	0.0896456i	−0.0864392	+	0.996257i	$0.527549\pi$
$558$		0			0
$559$	−1.05601	−	0.609690i	−0.0446647	−	0.0257872i
$560$	−2.77804	+	1.21739i	−0.117394	+	0.0514443i
$561$		0			0
$562$	8.89703	+	18.3097i	0.375299	+	0.772348i
$563$	−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
$566$	1.93862	+	18.7085i	0.0814861	+	0.786377i
$567$		0			0
$568$	−5.84581	−	42.9655i	−0.245285	−	1.80279i
$569$		−	4.26367i		−	0.178742i	−0.995998	−	0.0893711i	$-0.971514\pi$
$569$		−	4.26367i		−	0.178742i	0.995998	−	0.0893711i	$-0.0284857\pi$
$570$		0			0
$571$		−	3.11580i		−	0.130392i	−0.997872	−	0.0651961i	$-0.979233\pi$
$571$		−	3.11580i		−	0.130392i	0.997872	−	0.0651961i	$-0.0207673\pi$
$572$	6.55001	+	7.31756i	0.273870	+	0.305962i
$573$		0			0
$574$	0.849982	−	0.0880770i	0.0354776	−	0.00367626i
$575$	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	$-0.506381\pi$
$578$	−0.943744	+	0.458583i	−0.0392546	+	0.0190745i
$579$		0			0
$580$	−1.86147	−	58.1978i	−0.0772935	−	2.41653i
$581$	−0.831471	−	0.480050i	−0.0344952	−	0.0199158i
$582$		0			0
$583$	−8.91751	+	1.57240i	−0.369326	+	0.0651221i
$584$	11.1159	−	8.60625i	0.459981	−	0.356129i
$585$		0			0
$586$	17.1857	+	16.6448i	0.709935	+	0.687591i
$587$	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
$592$	−19.8556	−	29.8128i	−0.816060	−	1.22530i
$593$	−17.7846	−	21.1948i	−0.730325	−	0.870368i	0.265265	−	0.964176i	$-0.414541\pi$
$593$	−17.7846	−	21.1948i	−0.730325	−	0.870368i	−0.995590	+	0.0938076i	$0.970096\pi$
$594$		0			0
$595$	−3.01099	+	0.530919i	−0.123439	+	0.0217656i
$596$	25.6577	+	20.1675i	1.05098	+	0.826091i
$597$		0			0
$598$	1.83694	+	2.53614i	0.0751180	+	0.103710i
$599$	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	$-0.361990\pi$
$602$	0.117789	−	0.263518i	0.00480071	−	0.0107402i
$603$		0			0
$604$	11.2533	−	21.0154i	0.457888	−	0.855104i
$605$	0.373922	+	0.0659325i	0.0152021	+	0.00268054i
$606$		0			0
$607$		−	19.2213i		−	0.780168i	−0.920779	−	0.390084i	$-0.872446\pi$
$607$		−	19.2213i		−	0.780168i	0.920779	−	0.390084i	$-0.127554\pi$
$608$	−13.9834	−	20.3092i	−0.567104	−	0.823646i
$609$		0			0
$610$	6.02926	−	24.0319i	0.244118	−	0.973023i
$611$	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	$0.778157\pi$
$614$	34.6554	+	15.4905i	1.39858	+	0.625145i
$615$		0			0
$616$	−1.56313	+	1.72076i	−0.0629805	+	0.0693312i
$617$	2.95958	−	8.13138i	0.119148	−	0.327357i	−0.865754	−	0.500470i	$-0.833160\pi$
$617$	2.95958	−	8.13138i	0.119148	−	0.327357i	0.984902	+	0.173113i	$0.0553826\pi$
$618$		0			0
$619$	22.1734	+	12.8018i	0.891223	+	0.514548i	0.874342	−	0.485310i	$-0.161293\pi$
$619$	22.1734	+	12.8018i	0.891223	+	0.514548i	0.0168807	+	0.999858i	$0.494626\pi$
$620$	37.4002	−	47.5819i	1.50203	−	1.91093i
$621$		0			0
$622$	−0.0835966	−	0.293158i	−0.00335192	−	0.0117545i
$623$	−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	$0.00878069\pi$
$631$	21.4321	+	25.5418i	0.853200	+	1.01680i	−0.146419	+	0.989223i	$0.546775\pi$
$632$	12.3230	+	15.9165i	0.490182	+	0.633125i
$633$		0			0
$634$	−40.5457	−	2.89497i	−1.61027	−	0.114974i
$635$	−12.8732	+	22.2971i	−0.510859	+	0.884834i
$636$		0			0
$637$	−9.60064	−	3.49435i	−0.380391	−	0.138451i
$638$	−19.5053	−	40.1411i	−0.772223	−	1.58920i
$639$		0			0
$640$	23.0265	+	26.1074i	0.910203	+	1.03199i
$641$	−6.22612	+	7.42000i	−0.245917	+	0.293073i	−0.874857	−	0.484381i	$-0.839045\pi$
$641$	−6.22612	+	7.42000i	−0.245917	+	0.293073i	0.628940	+	0.777454i	$0.283489\pi$
$642$		0			0
$643$	−26.3570	−	4.64744i	−1.03942	−	0.183277i	−0.372209	−	0.928149i	$-0.621400\pi$
$643$	−26.3570	−	4.64744i	−1.03942	−	0.183277i	−0.667208	+	0.744872i	$0.732511\pi$
$644$	−0.552325	+	0.494391i	−0.0217646	+	0.0194817i
$645$		0			0
$646$	−8.86070	−	23.2227i	−0.348620	−	0.913685i
$647$	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
$650$	−9.25221	+	0.958734i	−0.362901	+	0.0376046i
$651$		0			0
$652$	−19.3436	−	31.1592i	−0.757554	−	1.22029i
$653$	−9.69258	+	5.59601i	−0.379300	+	0.218989i	−0.677514	−	0.735510i	$-0.736943\pi$
$653$	−9.69258	+	5.59601i	−0.379300	+	0.218989i	0.298214	+	0.954499i	$0.403609\pi$
$654$		0			0
$655$	−17.5306	+	48.1651i	−0.684979	+	1.88196i
$656$	−3.93651	−	8.98296i	−0.153695	−	0.350726i
$657$		0			0
$658$	1.68929	+	0.120616i	0.0658554	+	0.00470209i
$659$	−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	$0.111372\pi$
$662$	13.7999	+	13.3656i	0.536350	+	0.519469i
$663$		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
$668$	−41.9283	+	8.78373i	−1.62226	+	0.339853i
$669$		0			0
$670$	12.8923	+	45.2108i	0.498073	+	1.74665i
$671$	−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	$0.972161\pi$
$674$	−29.9458	−	41.3441i	−1.15347	−	1.59252i
$675$		0			0
$676$	21.4448	+	3.07802i	0.824800	+	0.118385i
$677$	35.3561	−	20.4129i	1.35885	−	0.784530i	0.369377	−	0.929280i	$-0.379571\pi$
$677$	35.3561	−	20.4129i	1.35885	−	0.784530i	0.989468	+	0.144750i	$0.0462378\pi$
$678$		0			0
$679$	−0.0180222	+	0.0214780i	−0.000691628	+	0.000824251i
$680$	16.3377	+	31.0555i	0.626522	+	1.19092i
$681$		0			0
$682$	11.2880	−	44.9927i	0.432241	−	1.72286i
$683$	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
$686$	1.18219	−	4.71205i	0.0451361	−	0.179907i
$687$		0			0
$688$	−3.29259	−	0.365600i	−0.125529	−	0.0139384i
$689$	2.56946	−	3.06216i	0.0978886	−	0.116659i
$690$		0			0
$691$	−36.4703	+	21.0561i	−1.38740	+	0.801013i	−0.993021	−	0.117937i	$-0.962372\pi$
$691$	−36.4703	+	21.0561i	−1.38740	+	0.801013i	−0.394374	+	0.918950i	$0.629039\pi$
$692$	5.52490	−	38.4924i	0.210025	−	1.46326i
$693$		0			0
$694$	13.6534	+	18.8503i	0.518274	+	0.715547i
$695$	−25.7385	+	44.5804i	−0.976318	+	1.69103i
$696$		0			0
$697$	−1.71676	−	9.73622i	−0.0650268	−	0.368785i
$698$	−3.90163	−	13.6823i	−0.147679	−	0.517882i
$699$		0			0
$700$	−0.451474	−	2.15507i	−0.0170641	−	0.0814541i
$701$	6.73810	+	18.5128i	0.254495	+	0.699218i	0.999483	+	0.0321412i	$0.0102326\pi$
$701$	6.73810	+	18.5128i	0.254495	+	0.699218i	−0.744989	+	0.667077i	$0.767545\pi$
$702$		0			0
$703$	−37.7091	+	10.0819i	−1.42222	+	0.380246i
$704$	24.2783	+	11.0663i	0.915022	+	0.417077i
$705$		0			0
$706$	−13.6976	−	13.2664i	−0.515515	−	0.499289i
$707$	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	$-0.378737\pi$
$710$	66.5399	+	4.75097i	2.49720	+	0.178301i
$711$		0			0
$712$	9.41122	+	5.93850i	0.352700	+	0.222555i
$713$	5.05886	−	13.8991i	0.189456	−	0.520526i
$714$		0			0
$715$	−13.0847	+	7.55446i	−0.489340	+	0.282521i
$716$	18.1212	−	11.2497i	0.677222	−	0.420419i
$717$		0			0
$718$	−1.38405	+	0.143418i	−0.0516522	+	0.00535232i
$719$	−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
$722$	−25.8481	+	7.34011i	−0.961966	+	0.273171i
$723$		0			0
$724$	4.15825	+	4.64553i	0.154540	+	0.172650i
$725$	41.6280	+	7.34014i	1.54602	+	0.272606i
$726$		0			0
$727$	19.4476	−	23.1768i	0.721273	−	0.859580i	−0.273481	−	0.961877i	$-0.588175\pi$
$727$	19.4476	−	23.1768i	0.721273	−	0.859580i	0.994754	+	0.102298i	$0.0326195\pi$
$728$	0.0403265	−	1.02546i	0.00149460	−	0.0380062i
$729$		0			0
$730$	9.45249	+	19.4528i	0.349852	+	0.719981i
$731$	−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	$0.138264\pi$
$734$	−29.0889	−	2.07695i	−1.07369	−	0.0766617i
$735$		0			0
$736$	7.33652	+	4.30776i	0.270428	+	0.158786i
$737$	23.1620	+	27.6034i	0.853183	+	1.01678i
$738$		0			0
$739$	7.50914	+	20.6312i	0.276228	+	0.758931i	0.997782	+	0.0665720i	$0.0212062\pi$
$739$	7.50914	+	20.6312i	0.276228	+	0.758931i	−0.721553	+	0.692359i	$0.756572\pi$
$740$	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
$746$	−7.44430	−	26.1058i	−0.272555	−	0.955800i
$747$		0			0
$748$	21.1455	+	16.6207i	0.773155	+	0.607714i
$749$	0.870876	+	0.502800i	0.0318211	+	0.0183719i
$750$		0			0
$751$	−0.816742	+	2.24398i	−0.0298033	+	0.0818840i	−0.953702	−	0.300753i	$-0.902762\pi$
$751$	−0.816742	+	2.24398i	−0.0298033	+	0.0818840i	0.923899	+	0.382637i	$0.124984\pi$
$752$	−4.59171	−	18.8875i	−0.167442	−	0.688757i
$753$		0			0
$754$	17.9865	+	8.03972i	0.655030	+	0.292789i
$755$	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	$0.855090\pi$
$758$	−10.2542	+	40.8721i	−0.372451	+	1.48454i
$759$		0			0
$760$	34.9919	−	14.6493i	1.26929	−	0.531385i
$761$			0.616585i			0.0223512i	0.999938	+	0.0111756i	$0.00355737\pi$
$761$			0.616585i			0.0223512i	−0.999938	+	0.0111756i	$0.996443\pi$
$762$		0			0
$763$	−1.10632	−	0.195073i	−0.0400513	−	0.00706213i
$764$	−43.6271	−	23.3613i	−1.57837	−	0.845182i
$765$		0			0
$766$	−14.0560	+	31.4461i	−0.507863	+	1.13619i
$767$	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	$0.739816\pi$
$770$	−2.09797	−	2.89652i	−0.0756054	−	0.104383i
$771$		0			0
$772$	−25.9218	+	32.9786i	−0.932946	+	1.18693i
$773$	−27.5367	+	4.85547i	−0.990427	+	0.174639i	−0.645310	−	0.763921i	$-0.723272\pi$
$773$	−27.5367	+	4.85547i	−0.990427	+	0.174639i	−0.345117	+	0.938560i	$0.612161\pi$
$774$		0			0
$775$	28.2410	+	33.6563i	1.01445	+	1.20897i
$776$	0.297827	+	0.121857i	0.0106914	+	0.00437440i
$777$		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
$782$	6.16036	+	5.96647i	0.220294	+	0.213360i
$783$		0			0
$784$	−27.7003	+	1.77382i	−0.989298	+	0.0633507i
$785$	−23.7889	+	4.19462i	−0.849062	+	0.149713i
$786$		0			0
$787$	5.75195	+	3.32089i	0.205035	+	0.118377i	0.599002	−	0.800748i	$-0.295564\pi$
$787$	5.75195	+	3.32089i	0.205035	+	0.118377i	−0.393967	+	0.919125i	$0.628898\pi$
$788$	−16.7489	+	0.535719i	−0.596656	+	0.0190842i
$789$		0			0
$790$	−27.8538	+	13.5347i	−0.990993	+	0.481542i
$791$	0.881022	+	1.52598i	0.0313256	+	0.0542574i
$792$		0			0
$793$	6.42198	+	5.38868i	0.228051	+	0.191358i
$794$	−44.9264	+	4.65537i	−1.59438	+	0.165213i
$795$		0			0
$796$	−21.9184	+	19.6194i	−0.776878	+	0.695390i
$797$			15.9835i			0.566166i	0.959095	+	0.283083i	$0.0913572\pi$
$797$			15.9835i			0.566166i	−0.959095	+	0.283083i	$0.908643\pi$
$798$		0			0
$799$		−	19.5938i		−	0.693178i
$800$	−21.9774	+	12.4748i	−0.777020	+	0.441050i
$801$		0			0
$802$	0.249939	+	2.41202i	0.00882566	+	0.0851715i
$803$	12.6986	+	10.6554i	0.448124	+	0.376021i
$804$		0			0
$805$	−0.570206	−	0.987626i	−0.0200971	−	0.0348092i
$806$	8.94979	+	18.4183i	0.315243	+	0.648756i
$807$		0			0
$808$	−27.1147	−	17.1094i	−0.953892	−	0.601908i
$809$	14.9242	+	8.61649i	0.524707	+	0.302940i	0.738858	−	0.673861i	$-0.235365\pi$
$809$	14.9242	+	8.61649i	0.524707	+	0.302940i	−0.214151	+	0.976800i	$0.568699\pi$
$810$		0			0
$811$	−21.8280	+	3.84886i	−0.766484	+	0.135152i	−0.543202	−	0.839602i	$-0.682788\pi$
$811$	−21.8280	+	3.84886i	−0.766484	+	0.135152i	−0.223282	+	0.974754i	$0.571677\pi$
$812$	−1.45414	+	4.43114i	−0.0510304	+	0.155502i
$813$		0			0
$814$	29.3849	−	30.3398i	1.02994	−	1.06341i
$815$	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
$820$	14.7680	−	3.09380i	0.515721	−	0.108040i
$821$	24.1163	+	28.7407i	0.841665	+	1.00306i	0.999877	+	0.0156524i	$0.00498252\pi$
$821$	24.1163	+	28.7407i	0.841665	+	1.00306i	−0.158212	+	0.987405i	$0.550573\pi$
$822$		0			0
$823$	8.47209	−	1.49386i	0.295319	−	0.0520726i	−0.0240259	−	0.999711i	$-0.507648\pi$
$823$	8.47209	−	1.49386i	0.295319	−	0.0520726i	0.319344	+	0.947639i	$0.396537\pi$
$824$	3.24392	+	10.1352i	0.113007	+	0.353077i
$825$		0			0
$826$	−1.34669	+	0.975414i	−0.0468574	+	0.0339390i
$827$	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	$0.836624\pi$
$830$	−15.4768	−	6.91793i	−0.537209	−	0.240125i
$831$		0			0
$832$	−11.3504	+	3.14688i	−0.393503	+	0.109098i
$833$	−27.5549	−	4.85868i	−0.954722	−	0.168343i
$834$		0			0
$835$		−	65.9050i		−	2.28074i
$836$	19.9033	−	21.1952i	0.688370	−	0.733052i
$837$		0			0
$838$	−41.2775	−	10.3559i	−1.42591	−	0.357740i
$839$	−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
$842$	−13.9725	+	31.2593i	−0.481523	+	1.07727i
$843$		0			0
$844$	1.78459	−	12.4334i	0.0614283	−	0.427976i
$845$	−11.3995	+	31.3199i	−0.392155	+	1.07744i
$846$		0			0
$847$	−0.0263363	−	0.0152053i	−0.000904927	−	0.000522460i
$848$	3.05462	−	10.4217i	0.104896	−	0.357881i
$849$		0			0
$850$	−24.4975	+	6.98570i	−0.840258	+	0.239607i
$851$	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	$0.150897\pi$
$857$	14.6838	+	40.3434i	0.501589	+	1.37810i	−0.388134	+	0.921603i	$0.626880\pi$
$858$		0			0
$859$	−2.82888	−	3.37133i	−0.0965201	−	0.115028i	0.715622	−	0.698487i	$-0.246143\pi$
$859$	−2.82888	−	3.37133i	−0.0965201	−	0.115028i	−0.812142	+	0.583459i	$0.801699\pi$
$860$	1.58915	−	4.84254i	0.0541896	−	0.165129i
$861$		0			0
$862$	1.94439	−	27.2323i	0.0662262	−	0.927535i
$863$	−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
$866$	−11.3364	+	5.50858i	−0.385227	+	0.187189i
$867$		0			0
$868$	−4.11829	+	2.55663i	−0.139784	+	0.0867777i
$869$	−15.2571	+	18.1827i	−0.517561	+	0.616805i
$870$		0			0
$871$	−15.6654	−	2.76224i	−0.530802	−	0.0935948i
$872$	1.73822	+	12.7756i	0.0588637	+	0.432635i
$873$		0			0
$874$	7.00921	−	6.06825i	0.237090	−	0.205262i
$875$	−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	$0.0757749\pi$
$878$	−5.89280	−	56.8681i	−0.198872	−	1.91921i
$879$		0			0
$880$	−24.3218	+	33.0665i	−0.819887	+	1.11467i
$881$	−41.4405	+	23.9257i	−1.39617	+	0.806077i	−0.993989	−	0.109484i	$-0.965080\pi$
$881$	−41.4405	+	23.9257i	−1.39617	+	0.806077i	−0.402178	+	0.915561i	$0.631747\pi$
$882$		0			0
$883$	8.28536	−	22.7638i	0.278825	−	0.766064i	−0.718672	−	0.695349i	$-0.755250\pi$
$883$	8.28536	−	22.7638i	0.278825	−	0.766064i	0.997497	−	0.0707151i	$-0.0225281\pi$
$884$	−11.8671	+	0.379571i	−0.399132	+	0.0127664i
$885$		0			0
$886$	−2.46858	+	34.5739i	−0.0829337	+	1.16153i
$887$	−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
$890$	−11.9107	+	12.2978i	−0.399249	+	0.412223i
$891$		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
$896$	−1.01787	−	2.59570i	−0.0340047	−	0.0867163i
$897$		0			0
$898$	25.5784	−	7.29392i	0.853563	−	0.243401i
$899$	−16.1591	−	91.6431i	−0.538938	−	3.05647i
$900$		0			0
$901$	5.47366	−	9.48066i	0.182354	−	0.315847i
$902$	9.36608	−	6.78389i	0.311856	−	0.225879i
$903$		0			0
$904$	13.5980	−	14.9692i	0.452263	−	0.497868i
$905$	−8.30679	+	4.79592i	−0.276127	+	0.159422i
$906$		0			0
$907$	−33.7466	+	40.2176i	−1.12054	+	1.33540i	−0.184772	+	0.982781i	$0.559155\pi$
$907$	−33.7466	+	40.2176i	−1.12054	+	1.33540i	−0.935765	+	0.352624i	$0.885290\pi$
$908$	26.2301	+	14.0456i	0.870476	+	0.466120i
$909$		0			0
$910$	1.53138	+	0.384203i	0.0507649	+	0.0127362i
$911$	−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
$914$	7.22068	+	1.81157i	0.238839	+	0.0599213i
$915$		0			0
$916$	46.6101	+	24.9586i	1.54004	+	0.824656i
$917$	2.63882	−	3.14482i	0.0871414	−	0.103851i
$918$		0			0
$919$	0.745464	−	0.430394i	0.0245906	−	0.0141974i	−0.487654	−	0.873037i	$-0.662147\pi$
$919$	0.745464	−	0.430394i	0.0245906	−	0.0141974i	0.512245	+	0.858839i	$0.328814\pi$
$920$	−8.80076	+	9.68820i	−0.290152	+	0.319410i
$921$		0			0
$922$	2.12265	−	1.53745i	0.0699058	−	0.0506331i
$923$	−11.2857	+	19.5474i	−0.371473	+	0.643410i
$924$		0			0
$925$	6.94673	+	39.3969i	0.228407	+	1.29536i
$926$	−40.1712	+	11.4552i	−1.32011	+	0.376442i
$927$		0			0
$928$	53.5240	+	0.392365i	1.75701	+	0.0128800i
$929$	−7.06094	−	19.3998i	−0.231662	−	0.636486i	0.768332	−	0.640052i	$-0.221087\pi$
$929$	−7.06094	−	19.3998i	−0.231662	−	0.636486i	−0.999994	+	0.00356601i	$0.998865\pi$
$930$		0			0
$931$	−7.84470	+	29.2126i	−0.257100	+	0.957404i
$932$	−47.3954	+	18.9875i	−1.55249	+	0.621957i
$933$		0			0
$934$	−10.6044	+	10.9490i	−0.346986	+	0.358262i
$935$	−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	$0.750294\pi$
$938$	0.268170	−	3.75587i	0.00875606	−	0.122633i
$939$		0			0
$940$	29.8886	−	0.955995i	0.974858	−	0.0311811i
$941$	14.2489	−	39.1485i	0.464500	−	1.27620i	−0.457568	−	0.889175i	$-0.651279\pi$
$941$	14.2489	−	39.1485i	0.464500	−	1.27620i	0.922068	−	0.387029i	$-0.126499\pi$
$942$		0			0
$943$	3.19355	−	1.84379i	0.103996	−	0.0600422i
$944$	15.3737	+	11.3080i	0.500372	+	0.368044i
$945$		0			0
$946$	−0.402630	−	3.88556i	−0.0130906	−	0.126330i
$947$	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
$950$	5.20010	+	27.0431i	0.168714	+	0.877394i
$951$		0			0
$952$	−0.378906	−	2.78488i	−0.0122804	−	0.0902584i
$953$	11.9736	+	2.11127i	0.387864	+	0.0683909i	0.364180	−	0.931329i	$-0.381349\pi$
$953$	11.9736	+	2.11127i	0.387864	+	0.0683909i	0.0236840	+	0.999719i	$0.492460\pi$
$954$		0			0
$955$	48.9387	−	58.3229i	1.58362	−	1.88728i
$956$	13.5587	−	8.41724i	0.438520	−	0.272233i
$957$		0			0
$958$	−0.710983	+	0.345480i	−0.0229708	+	0.0111620i
$959$	2.13853	+	0.778361i	0.0690567	+	0.0251346i
$960$		0			0
$961$	32.8611	−	56.9172i	1.06004	−	1.83604i
$962$	−1.32792	+	18.5983i	−0.0428139	+	0.599632i
$963$		0			0
$964$	2.15555	−	6.56851i	0.0694257	−	0.211557i
$965$	−41.4810	−	49.4352i	−1.33532	−	1.59137i
$966$		0			0
$967$	11.4177	+	31.3699i	0.367169	+	1.00879i	0.976433	+	0.215820i	$0.0692426\pi$
$967$	11.4177	+	31.3699i	0.367169	+	1.00879i	−0.609264	+	0.792967i	$0.708535\pi$
$968$	−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
$974$	−36.1312	+	10.3032i	−1.15772	+	0.330135i
$975$		0			0
$976$	21.8563	+	6.40616i	0.699605	+	0.205056i
$977$	37.5428	+	21.6754i	1.20110	+	0.693456i	0.960800	−	0.277242i	$-0.0894205\pi$
$977$	37.5428	+	21.6754i	1.20110	+	0.693456i	0.240301	+	0.970698i	$0.422754\pi$
$978$		0			0
$979$	−4.48797	+	12.3306i	−0.143436	+	0.394088i
$980$	6.06707	−	42.2697i	0.193805	−	1.35026i
$981$		0			0
$982$	19.1328	−	42.8040i	0.610553	−	1.36593i
$983$	−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
$986$	52.3334	+	13.1297i	1.66664	+	0.418135i
$987$		0			0
$988$	−0.716374	+	12.8153i	−0.0227909	+	0.407710i
$989$		−	1.24559i		−	0.0396076i
$990$		0			0
$991$	−19.9299	−	3.51419i	−0.633095	−	0.111632i	−0.152115	−	0.988363i	$-0.548608\pi$
$991$	−19.9299	−	3.51419i	−0.633095	−	0.111632i	−0.480981	+	0.876731i	$0.659719\pi$
$992$	42.3546	+	36.0721i	1.34476	+	1.14529i
$993$		0			0
$994$	−4.87785	−	2.18033i	−0.154716	−	0.0691559i
$995$	−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	$0.348731\pi$
$998$	−19.8664	+	14.3893i	−0.628859	+	0.455486i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.37170 - 0.344141i) q^{2} +(1.76313 + 0.944117i) q^{4} +(-1.97780 + 2.35705i) q^{5} +(0.213423 - 0.123220i) q^{7} +(-2.09359 - 1.90181i) q^{8} +O(q^{10})\)	\(q+(-1.37170 - 0.344141i) q^{2} +(1.76313 + 0.944117i) q^{4} +(-1.97780 + 2.35705i) q^{5} +(0.213423 - 0.123220i) q^{7} +(-2.09359 - 1.90181i) q^{8} +(3.52410 - 2.55252i) q^{10} +(1.66759 - 2.88835i) q^{11} +(0.255665 + 1.44995i) q^{13} +(-0.335157 + 0.0955732i) q^{14} +(2.21729 + 3.32921i) q^{16} +(1.37907 + 3.78896i) q^{17} +(4.21099 - 1.12585i) q^{19} +(-5.71245 + 2.28852i) q^{20} +(-3.28143 + 3.38807i) q^{22} +(-1.15211 + 0.966731i) q^{23} +(-0.775745 - 4.39947i) q^{25} +(0.148290 - 2.07688i) q^{26} +(0.492626 - 0.0157568i) q^{28} +(-3.23621 + 8.89141i) q^{29} +(-8.51714 + 4.91737i) q^{31} +(-1.89574 - 5.32974i) q^{32} +(-0.587737 - 5.67192i) q^{34} +(-0.131672 + 0.746750i) q^{35} -8.95491 q^{37} +(-6.16368 + 0.0951602i) q^{38} +(8.62335 - 1.17328i) q^{40} +(-2.41466 - 0.425770i) q^{41} +(-0.532361 + 0.634443i) q^{43} +(5.66712 - 3.51815i) q^{44} +(1.91304 - 0.929581i) q^{46} +(-4.56635 - 1.66202i) q^{47} +(-3.46963 + 6.00958i) q^{49} +(-0.449945 + 6.30173i) q^{50} +(-0.918148 + 2.79783i) q^{52} +(-1.74518 - 2.07983i) q^{53} +(3.50982 + 9.64314i) q^{55} +(-0.681159 - 0.147919i) q^{56} +(7.49901 - 11.0827i) q^{58} +(4.48342 - 1.63183i) q^{59} +(4.36183 - 3.66001i) q^{61} +(13.3753 - 3.81408i) q^{62} +(0.766209 + 7.96322i) q^{64} +(-3.92324 - 2.26509i) q^{65} +(-3.69523 + 10.1526i) q^{67} +(-1.14574 + 7.98245i) q^{68} +(0.437602 - 0.979005i) q^{70} +(11.7439 + 9.85428i) q^{71} +(-0.863085 + 4.89480i) q^{73} +(12.2835 + 3.08175i) q^{74} +(8.48748 + 1.99064i) q^{76} -0.821918i q^{77} +(-7.00868 - 1.23582i) q^{79} +(-12.2324 - 1.35826i) q^{80} +(3.16567 + 1.41501i) q^{82} +(-1.94795 - 3.37394i) q^{83} +(-11.6583 - 4.24326i) q^{85} +(0.948578 - 0.687060i) q^{86} +(-8.98434 + 2.87556i) q^{88} +(-3.87464 + 0.683204i) q^{89} +(0.233226 + 0.277948i) q^{91} +(-2.94402 + 0.616755i) q^{92} +(5.69171 + 3.85126i) q^{94} +(-5.67480 + 12.1522i) q^{95} +(-0.106910 + 0.0389119i) q^{97} +(6.82745 - 7.04932i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 12 q^{4}+O(q^{10}) \) 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

L-functions

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