LMFDB - Embedded newform 220.3.w.a.7.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [220,3,Mod(7,220)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(220, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 5, 14]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("220.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 220 = 2^{2} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	220.w (of order $20$, degree $8$, 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:	$5.99456581593$
Analytic rank:	$0$
Dimension:	$544$
Relative dimension:	$68$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			7.10
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.82522 - 0.817668i) q^{2} +(-2.40882 + 1.22736i) q^{3} +(2.66284 + 2.98484i) q^{4} +(-4.64336 - 1.85452i) q^{5} +(5.40020 - 0.270575i) q^{6} +(0.118689 - 0.232940i) q^{7} +(-2.41965 - 7.62531i) q^{8} +(-0.994045 + 1.36819i) q^{9} +(6.95876 + 7.18162i) q^{10} +(-6.29422 + 9.02124i) q^{11} +(-10.0778 - 3.92171i) q^{12} +(-0.636813 - 4.02068i) q^{13} +(-0.407100 + 0.328118i) q^{14} +(13.4612 - 1.23185i) q^{15} +(-1.81859 + 15.8963i) q^{16} +(4.69785 - 29.6611i) q^{17} +(2.93307 - 1.68444i) q^{18} +(22.0109 + 7.15178i) q^{19} +(-6.82906 - 18.7980i) q^{20} +0.706783i q^{21} +(18.8647 - 11.3191i) q^{22} +(25.1629 + 25.1629i) q^{23} +(15.1875 + 15.3982i) q^{24} +(18.1215 + 17.2224i) q^{25} +(-2.12526 + 7.85931i) q^{26} +(4.52149 - 28.5476i) q^{27} +(1.01134 - 0.266013i) q^{28} +(-14.7711 - 45.4607i) q^{29} +(-25.5768 - 8.75838i) q^{30} +(15.0900 - 20.7696i) q^{31} +(16.3172 - 27.5272i) q^{32} +(4.08939 - 29.4558i) q^{33} +(-32.8275 + 50.2966i) q^{34} +(-0.983104 + 0.861511i) q^{35} +(-6.73080 + 0.676187i) q^{36} +(16.1966 - 31.7877i) q^{37} +(-34.3269 - 31.0512i) q^{38} +(6.46877 + 8.90350i) q^{39} +(-2.90599 + 39.8943i) q^{40} +(49.9808 + 16.2397i) q^{41} +(0.577914 - 1.29003i) q^{42} +(-4.30965 + 4.30965i) q^{43} +(-43.6875 + 5.23483i) q^{44} +(7.15303 - 4.50950i) q^{45} +(-25.3529 - 66.5028i) q^{46} +(-1.77867 - 3.49084i) q^{47} +(-15.1298 - 40.5235i) q^{48} +(28.7613 + 39.5865i) q^{49} +(-18.9935 - 46.2520i) q^{50} +(25.0884 + 77.2142i) q^{51} +(10.3054 - 12.6072i) q^{52} +(-39.3423 + 6.23122i) q^{53} +(-31.5951 + 48.4084i) q^{54} +(45.9564 - 30.2161i) q^{55} +(-2.06342 - 0.341406i) q^{56} +(-61.7982 + 9.78787i) q^{57} +(-10.2113 + 95.0535i) q^{58} +(-11.9586 - 36.8047i) q^{59} +(39.5218 + 36.8993i) q^{60} +(50.3282 + 69.2708i) q^{61} +(-44.5251 + 25.5704i) q^{62} +(0.200723 + 0.393940i) q^{63} +(-52.2906 + 36.9011i) q^{64} +(-4.49947 + 19.8504i) q^{65} +(-31.5491 + 50.4195i) q^{66} +(-45.0546 + 45.0546i) q^{67} +(101.043 - 64.9603i) q^{68} +(-91.4969 - 29.7292i) q^{69} +(2.49881 - 0.768592i) q^{70} +(-32.7548 - 45.0831i) q^{71} +(12.8381 + 4.26937i) q^{72} +(4.51537 - 8.86192i) q^{73} +(-55.5542 + 44.7760i) q^{74} +(-64.7895 - 19.2441i) q^{75} +(37.2646 + 84.7432i) q^{76} +(1.35435 + 2.53689i) q^{77} +(-4.52681 - 21.5401i) q^{78} +(61.1887 - 84.2190i) q^{79} +(37.9244 - 70.4396i) q^{80} +(19.4432 + 59.8399i) q^{81} +(-77.9471 - 70.5087i) q^{82} +(-14.1953 + 89.6254i) q^{83} +(-2.10964 + 1.88205i) q^{84} +(-76.8208 + 129.015i) q^{85} +(11.3899 - 4.34218i) q^{86} +(91.3773 + 91.3773i) q^{87} +(84.0195 + 26.1672i) q^{88} +15.7814i q^{89} +(-16.7431 + 2.38201i) q^{90} +(-1.01216 - 0.328870i) q^{91} +(-8.10262 + 142.112i) q^{92} +(-10.8574 + 68.5509i) q^{93} +(0.392115 + 7.82590i) q^{94} +(-88.9414 - 74.0279i) q^{95} +(-5.51958 + 86.3353i) q^{96} +(-22.3539 - 141.137i) q^{97} +(-20.1270 - 95.7712i) q^{98} +(-6.08599 - 17.5792i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) $ 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/220\mathbb{Z}\right)^\times$.

$n$	$101$	$111$	$177$
$\chi(n)$	$e\left(\frac{7}{10}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−1.82522	−	0.817668i	−0.912609	−	0.408834i
$2$	−1.82522	−	0.817668i	−0.912609	−	0.408834i
$3$	−2.40882	+	1.22736i	−0.802941	+	0.409119i	−0.806764	−	0.590874i	$-0.798783\pi$
$3$	−2.40882	+	1.22736i	−0.802941	+	0.409119i	0.00382307	+	0.999993i	$0.498783\pi$
$4$	2.66284	+	2.98484i	0.665710	+	0.746211i
$5$	−4.64336	−	1.85452i	−0.928671	−	0.370904i
$5$	−4.64336	−	1.85452i	−0.928671	−	0.370904i
$6$	5.40020	−	0.270575i	0.900033	−	0.0450959i
$7$	0.118689	−	0.232940i	0.0169555	−	0.0332771i	−0.882373	−	0.470550i	$-0.844056\pi$
$7$	0.118689	−	0.232940i	0.0169555	−	0.0332771i	0.899329	+	0.437273i	$0.144056\pi$
$8$	−2.41965	−	7.62531i	−0.302456	−	0.953163i
$9$	−0.994045	+	1.36819i	−0.110449	+	0.152021i
$10$	6.95876	+	7.18162i	0.695876	+	0.718162i
$11$	−6.29422	+	9.02124i	−0.572202	+	0.820113i
$11$	−6.29422	+	9.02124i	−0.572202	+	0.820113i
$12$	−10.0778	−	3.92171i	−0.839814	−	0.326809i
$13$	−0.636813	−	4.02068i	−0.0489856	−	0.309283i	−1.00000		0.000136283i	$-0.999957\pi$
$13$	−0.636813	−	4.02068i	−0.0489856	−	0.309283i	0.951014	−	0.309147i	$-0.100043\pi$
$14$	−0.407100	+	0.328118i	−0.0290786	+	0.0234370i
$15$	13.4612	−	1.23185i	0.897412	−	0.0821232i
$16$	−1.81859	+	15.8963i	−0.113662	+	0.993520i
$17$	4.69785	−	29.6611i	0.276344	−	1.74477i	−0.324941	−	0.945734i	$-0.605344\pi$
$17$	4.69785	−	29.6611i	0.276344	−	1.74477i	0.601285	−	0.799035i	$-0.294656\pi$
$18$	2.93307	−	1.68444i	0.162948	−	0.0935798i
$19$	22.0109	+	7.15178i	1.15847	+	0.376410i	0.824327	−	0.566113i	$-0.191554\pi$
$19$	22.0109	+	7.15178i	1.15847	+	0.376410i	0.334142	+	0.942523i	$0.391554\pi$
$20$	−6.82906	−	18.7980i	−0.341453	−	0.939899i
$21$			0.706783i			0.0336564i
$22$	18.8647	−	11.3191i	0.857487	−	0.514506i
$23$	25.1629	+	25.1629i	1.09404	+	1.09404i	0.995093	+	0.0989481i	$0.0315478\pi$
$23$	25.1629	+	25.1629i	1.09404	+	1.09404i	0.0989481	+	0.995093i	$0.468452\pi$
$24$	15.1875	+	15.3982i	0.632811	+	0.641593i
$25$	18.1215	+	17.2224i	0.724861	+	0.688895i
$26$	−2.12526	+	7.85931i	−0.0817407	+	0.302281i
$27$	4.52149	−	28.5476i	0.167463	−	1.05732i
$28$	1.01134	−	0.266013i	0.0361192	−	0.00950047i
$29$	−14.7711	−	45.4607i	−0.509347	−	1.56761i	−0.793337	−	0.608782i	$-0.791658\pi$
$29$	−14.7711	−	45.4607i	−0.509347	−	1.56761i	0.283990	−	0.958827i	$-0.408342\pi$
$30$	−25.5768	−	8.75838i	−0.852561	−	0.291946i
$31$	15.0900	−	20.7696i	0.486773	−	0.669986i	−0.493016	−	0.870020i	$-0.664106\pi$
$31$	15.0900	−	20.7696i	0.486773	−	0.669986i	0.979789	+	0.200035i	$0.0641055\pi$
$32$	16.3172	−	27.5272i	0.509913	−	0.860226i
$33$	4.08939	−	29.4558i	0.123921	−	0.892601i
$34$	−32.8275	+	50.2966i	−0.965515	+	1.47931i
$35$	−0.983104	+	0.861511i	−0.0280887	+	0.0246146i
$36$	−6.73080	+	0.676187i	−0.186967	+	0.0187830i
$37$	16.1966	−	31.7877i	0.437747	−	0.859127i	−0.561746	−	0.827309i	$-0.689870\pi$
$37$	16.1966	−	31.7877i	0.437747	−	0.859127i	0.999494	−	0.0318179i	$-0.0101297\pi$
$38$	−34.3269	−	31.0512i	−0.903340	−	0.817136i
$39$	6.46877	+	8.90350i	0.165866	+	0.228295i
$40$	−2.90599	+	39.8943i	−0.0726497	+	0.997358i
$41$	49.9808	+	16.2397i	1.21904	+	0.396091i	0.846733	−	0.532017i	$-0.178566\pi$
$41$	49.9808	+	16.2397i	1.21904	+	0.396091i	0.372310	+	0.928108i	$0.378566\pi$
$42$	0.577914	−	1.29003i	0.0137599	−	0.0307151i
$43$	−4.30965	+	4.30965i	−0.100224	+	0.100224i	−0.755441	−	0.655217i	$-0.772577\pi$
$43$	−4.30965	+	4.30965i	−0.100224	+	0.100224i	0.655217	+	0.755441i	$0.272577\pi$
$44$	−43.6875	+	5.23483i	−0.992897	+	0.118973i
$45$	7.15303	−	4.50950i	0.158956	−	0.100211i
$46$	−25.3529	−	66.5028i	−0.551150	−	1.44571i
$47$	−1.77867	−	3.49084i	−0.0378441	−	0.0742732i	0.871310	−	0.490733i	$-0.163271\pi$
$47$	−1.77867	−	3.49084i	−0.0378441	−	0.0742732i	−0.909154	+	0.416459i	$0.863271\pi$
$48$	−15.1298	−	40.5235i	−0.315204	−	0.844239i
$49$	28.7613	+	39.5865i	0.586965	+	0.807889i
$50$	−18.9935	−	46.2520i	−0.379871	−	0.925040i
$51$	25.0884	+	77.2142i	0.491930	+	1.51400i
$52$	10.3054	−	12.6072i	0.198180	−	0.242446i
$53$	−39.3423	+	6.23122i	−0.742308	+	0.117570i	−0.516123	−	0.856514i	$-0.672625\pi$
$53$	−39.3423	+	6.23122i	−0.742308	+	0.117570i	−0.226185	+	0.974084i	$0.572625\pi$
$54$	−31.5951	+	48.4084i	−0.585095	+	0.896453i
$55$	45.9564	−	30.2161i	0.835570	−	0.549383i
$56$	−2.06342	−	0.341406i	−0.0368468	−	0.00609653i
$57$	−61.7982	+	9.78787i	−1.08418	+	0.171717i
$58$	−10.2113	+	95.0535i	−0.176057	+	1.63885i
$59$	−11.9586	−	36.8047i	−0.202688	−	0.623809i	−0.999800	−	0.0199783i	$-0.993640\pi$
$59$	−11.9586	−	36.8047i	−0.202688	−	0.623809i	0.797113	−	0.603831i	$-0.206360\pi$
$60$	39.5218	+	36.8993i	0.658697	+	0.614988i
$61$	50.3282	+	69.2708i	0.825052	+	1.13559i	0.988824	+	0.149089i	$0.0476340\pi$
$61$	50.3282	+	69.2708i	0.825052	+	1.13559i	−0.163772	+	0.986498i	$0.552366\pi$
$62$	−44.5251	+	25.5704i	−0.718146	+	0.412425i
$63$	0.200723	+	0.393940i	0.00318607	+	0.00625302i
$64$	−52.2906	+	36.9011i	−0.817041	+	0.576580i
$65$	−4.49947	+	19.8504i	−0.0692226	+	0.305391i
$66$	−31.5491	+	50.4195i	−0.478017	+	0.763932i
$67$	−45.0546	+	45.0546i	−0.672457	+	0.672457i	−0.958282	−	0.285825i	$-0.907732\pi$
$67$	−45.0546	+	45.0546i	−0.672457	+	0.672457i	0.285825	+	0.958282i	$0.407732\pi$
$68$	101.043	−	64.9603i	1.48593	−	0.955298i
$69$	−91.4969	−	29.7292i	−1.32604	−	0.430857i
$70$	2.49881	−	0.768592i	0.0356973	−	0.0109799i
$71$	−32.7548	−	45.0831i	−0.461335	−	0.634974i	0.513450	−	0.858120i	$-0.328367\pi$
$71$	−32.7548	−	45.0831i	−0.461335	−	0.634974i	−0.974785	+	0.223146i	$0.928367\pi$
$72$	12.8381	+	4.26937i	0.178307	+	0.0592968i
$73$	4.51537	−	8.86192i	0.0618544	−	0.121396i	−0.858009	−	0.513634i	$-0.828299\pi$
$73$	4.51537	−	8.86192i	0.0618544	−	0.121396i	0.919864	+	0.392238i	$0.128299\pi$
$74$	−55.5542	+	44.7760i	−0.750732	+	0.605081i
$75$	−64.7895	−	19.2441i	−0.863860	−	0.256588i
$76$	37.2646	+	84.7432i	0.490323	+	1.11504i
$77$	1.35435	+	2.53689i	0.0175890	+	0.0329467i
$78$	−4.52681	−	21.5401i	−0.0580360	−	0.276156i
$79$	61.1887	−	84.2190i	0.774540	−	1.06606i	−0.221323	−	0.975201i	$-0.571037\pi$
$79$	61.1887	−	84.2190i	0.774540	−	1.06606i	0.995863	−	0.0908629i	$-0.0289625\pi$
$80$	37.9244	−	70.4396i	0.474054	−	0.880496i
$81$	19.4432	+	59.8399i	0.240039	+	0.738764i
$82$	−77.9471	−	70.5087i	−0.950574	−	0.859863i
$83$	−14.1953	+	89.6254i	−0.171027	+	1.07982i	0.741543	+	0.670905i	$0.234094\pi$
$83$	−14.1953	+	89.6254i	−0.171027	+	1.07982i	−0.912571	+	0.408919i	$0.865906\pi$
$84$	−2.10964	+	1.88205i	−0.0251147	+	0.0224054i
$85$	−76.8208	+	129.015i	−0.903774	+	1.51782i
$86$	11.3899	−	4.34218i	0.132441	−	0.0504905i
$87$	91.3773	+	91.3773i	1.05031	+	1.05031i
$88$	84.0195	+	26.1672i	0.954767	+	0.297354i
$89$			15.7814i			0.177319i	0.996062	+	0.0886595i	$0.0282583\pi$
$89$			15.7814i			0.177319i	−0.996062	+	0.0886595i	$0.971742\pi$
$90$	−16.7431	+	2.38201i	−0.186035	+	0.0264668i
$91$	−1.01216	−	0.328870i	−0.0111226	−	0.00361395i
$92$	−8.10262	+	142.112i	−0.0880719	+	1.54470i
$93$	−10.8574	+	68.5509i	−0.116746	+	0.737107i
$94$	0.392115	+	7.82590i	0.00417143	+	0.0832543i
$95$	−88.9414	−	74.0279i	−0.936226	−	0.779241i
$96$	−5.51958	+	86.3353i	−0.0574956	+	0.899326i
$97$	−22.3539	−	141.137i	−0.230453	−	1.45502i	−0.783251	−	0.621705i	$-0.786440\pi$
$97$	−22.3539	−	141.137i	−0.230453	−	1.45502i	0.552799	−	0.833315i	$-0.313560\pi$
$98$	−20.1270	−	95.7712i	−0.205377	−	0.977258i
$99$	−6.08599	−	17.5792i	−0.0614746	−	0.177567i
$100$	−3.15144	+	99.9503i	−0.0315144	+	0.999503i
$101$	84.9980	−	116.990i	0.841564	−	1.15831i	−0.144095	−	0.989564i	$-0.546027\pi$
$101$	84.9980	−	116.990i	0.841564	−	1.15831i	0.985659	−	0.168750i	$-0.0539729\pi$
$102$	17.3438	−	161.447i	0.170037	−	1.58281i
$103$	23.9681	−	47.0400i	0.232700	−	0.456699i	−0.744899	−	0.667178i	$-0.767502\pi$
$103$	23.9681	−	47.0400i	0.232700	−	0.456699i	0.977598	+	0.210479i	$0.0675022\pi$
$104$	−29.1180	+	14.5845i	−0.279981	+	0.140236i
$105$	1.31074	−	3.28185i	0.0124833	−	0.0312557i
$106$	76.9034	+	20.7957i	0.725504	+	0.196185i
$107$	−34.5441	+	17.6011i	−0.322842	+	0.164496i	−0.607899	−	0.794014i	$-0.707987\pi$
$107$	−34.5441	+	17.6011i	−0.322842	+	0.164496i	0.285057	+	0.958511i	$0.407987\pi$
$108$	97.2500	−	62.5216i	0.900463	−	0.578904i
$109$	−16.3137			−0.149667			−0.0748337	−	0.997196i	$-0.523843\pi$
$109$	−16.3137			−0.149667			−0.0748337	+	0.997196i	$0.523843\pi$
$110$	−108.587	+	17.5739i	−0.987155	+	0.159762i
$111$			96.4500i			0.868919i
$112$	3.48703	+	2.31033i	0.0311342	+	0.0206280i
$113$	6.99939	+	13.7371i	0.0619415	+	0.121567i	0.919902	−	0.392149i	$-0.128268\pi$
$113$	6.99939	+	13.7371i	0.0619415	+	0.121567i	−0.857960	+	0.513716i	$0.828268\pi$
$114$	120.798	+	32.6654i	1.05963	+	0.286539i
$115$	−70.1754	−	163.506i	−0.610221	−	1.42179i
$116$	96.3601	−	165.144i	0.830690	−	1.42365i
$117$	6.13405	+	3.12546i	0.0524278	+	0.0267133i
$118$	−8.26704	+	76.9548i	−0.0700596	+	0.652159i
$119$	−6.35166	−	4.61475i	−0.0533753	−	0.0387794i
$120$	−41.9645	−	99.6650i	−0.349704	−	0.830541i
$121$	−41.7655	−	113.563i	−0.345170	−	0.938540i
$122$	−35.2194	−	167.586i	−0.288683	−	1.37366i
$123$	−140.327	+	22.2256i	−1.14087	+	0.180696i
$124$	102.176	−	10.2648i	0.824000	−	0.0827804i
$125$	−52.2055	−	113.576i	−0.417644	−	0.908611i
$126$	−0.0442501	−	0.883152i	−0.000351191	−	0.00700914i
$127$	63.2375	+	10.0158i	0.497933	+	0.0788649i	0.400350	−	0.916362i	$-0.368889\pi$
$127$	63.2375	+	10.0158i	0.497933	+	0.0788649i	0.0975836	+	0.995227i	$0.468889\pi$
$128$	125.615	−	24.5962i	0.981364	−	0.192158i
$129$	5.09170	−	15.6706i	0.0394706	−	0.121478i
$130$	24.4436	−	32.5523i	0.188027	−	0.250402i
$131$	183.238			1.39877			0.699383	−	0.714747i	$-0.253458\pi$
$131$	183.238			1.39877			0.699383	+	0.714747i	$0.253458\pi$
$132$	98.8104	−	66.2299i	0.748564	−	0.501742i
$133$	4.27838	−	4.27838i	0.0321683	−	0.0321683i
$134$	119.074	−	45.3947i	0.888613	−	0.338767i
$135$	−73.9369	+	124.171i	−0.547681	+	0.919788i
$136$	−237.542	+	35.9468i	−1.74663	+	0.264314i
$137$	104.651	+	16.5752i	0.763879	+	0.120987i	0.526204	−	0.850358i	$-0.323615\pi$
$137$	104.651	+	16.5752i	0.763879	+	0.120987i	0.237675	+	0.971345i	$0.423615\pi$
$138$	142.693	+	129.076i	1.03401	+	0.935336i
$139$	−224.699	+	73.0090i	−1.61654	+	0.525244i	−0.971121	−	0.238587i	$-0.923316\pi$
$139$	−224.699	+	73.0090i	−1.61654	+	0.525244i	−0.645415	+	0.763832i	$0.723316\pi$
$140$	−5.18932	−	0.640348i	−0.0370666	−	0.00457392i
$141$	8.56901	+	6.22575i	0.0607731	+	0.0441542i
$142$	22.9216	+	109.069i	0.161420	+	0.768092i
$143$	40.2797	+	19.5622i	0.281676	+	0.136799i
$144$	−19.9413	−	18.2898i	−0.138482	−	0.127013i
$145$	−15.7203	+	238.483i	−0.108416	+	1.64471i
$146$	−15.4876	+	12.4828i	−0.106080	+	0.0854990i
$147$	−117.868	−	60.0566i	−0.801821	−	0.408548i
$148$	138.010	−	36.3011i	0.932503	−	0.245277i
$149$	23.0847	−	16.7721i	0.154931	−	0.112564i	−0.507619	−	0.861582i	$-0.669474\pi$
$149$	23.0847	−	16.7721i	0.154931	−	0.112564i	0.662550	+	0.749018i	$0.269474\pi$
$150$	102.520	+	88.1010i	0.683465	+	0.587340i
$151$	−9.30741	+	28.6453i	−0.0616385	+	0.189704i	−0.977134	−	0.212624i	$-0.931799\pi$
$151$	−9.30741	+	28.6453i	−0.0616385	+	0.189704i	0.915496	+	0.402328i	$0.131799\pi$
$152$	1.27587	−	185.145i	0.00839387	−	1.21806i
$153$	35.9120	+	35.9120i	0.234719	+	0.234719i
$154$	−0.397650	−	5.73779i	−0.00258214	−	0.0372584i
$155$	−108.586	+	68.4558i	−0.700552	+	0.441650i
$156$	−9.35027	+	43.0169i	−0.0599376	+	0.275749i
$157$	18.1367	−	9.24111i	0.115520	−	0.0588606i	−0.395275	−	0.918563i	$-0.629351\pi$
$157$	18.1367	−	9.24111i	0.115520	−	0.0588606i	0.510796	+	0.859702i	$0.329351\pi$
$158$	−180.546	+	103.686i	−1.14270	+	0.656240i
$159$	87.1208	−	63.2970i	0.547930	−	0.398094i
$160$	−126.816	+	97.5581i	−0.792603	+	0.609738i
$161$	8.84800	−	2.87489i	0.0549565	−	0.0178565i
$162$	13.4412	−	125.119i	0.0829702	−	0.772339i
$163$	−31.5130	−	198.965i	−0.193331	−	1.22065i	−0.873219	−	0.487329i	$-0.837971\pi$
$163$	−31.5130	−	198.965i	−0.193331	−	1.22065i	0.679887	−	0.733317i	$-0.262029\pi$
$164$	84.6176	+	192.429i	0.515961	+	1.17335i
$165$	−73.6148	+	129.190i	−0.446151	+	0.782970i
$166$	99.1933	−	151.979i	0.597550	−	0.915535i
$167$	−0.639994	−	4.04076i	−0.00383230	−	0.0241962i	0.985698	−	0.168521i	$-0.0538990\pi$
$167$	−0.639994	−	4.04076i	−0.00383230	−	0.0241962i	−0.989530	+	0.144325i	$0.953899\pi$
$168$	5.38944	−	1.71017i	0.0320800	−	0.0101796i
$169$	144.968	−	47.1030i	0.857800	−	0.278716i
$170$	245.706	−	172.666i	1.44533	−	1.01568i
$171$	−31.6648	+	23.0058i	−0.185174	+	0.134537i
$172$	−24.3395	−	1.38773i	−0.141509	−	0.00806821i
$173$	46.1040	−	23.4912i	0.266497	−	0.135787i	−0.315636	−	0.948880i	$-0.602218\pi$
$173$	46.1040	−	23.4912i	0.266497	−	0.135787i	0.582134	+	0.813093i	$0.302218\pi$
$174$	−92.0672	−	241.500i	−0.529122	−	1.38793i
$175$	6.16259	−	2.17712i	0.0352148	−	0.0124407i
$176$	−131.958	−	116.461i	−0.749761	−	0.661709i
$177$	73.9786	+	73.9786i	0.417958	+	0.417958i
$178$	12.9039	−	28.8045i	0.0724941	−	0.161823i
$179$	92.5331	−	284.788i	0.516945	−	1.59099i	−0.262771	−	0.964858i	$-0.584636\pi$
$179$	92.5331	−	284.788i	0.516945	−	1.59099i	0.779716	−	0.626134i	$-0.215364\pi$
$180$	32.5075	+	9.34261i	0.180597	+	0.0519034i
$181$	−41.4561	+	30.1196i	−0.229039	+	0.166407i	−0.696386	−	0.717667i	$-0.745210\pi$
$181$	−41.4561	+	30.1196i	−0.229039	+	0.166407i	0.467347	+	0.884074i	$0.345210\pi$
$182$	1.57850	+	1.42787i	0.00867308	+	0.00784543i
$183$	−206.252	−	105.090i	−1.12706	−	0.574265i
$184$	130.990	−	252.761i	0.711900	−	1.37370i
$185$	−134.158	+	117.565i	−0.725177	+	0.635485i
$186$	75.8690	−	116.243i	0.407898	−	0.624960i
$187$	238.010	+	229.074i	1.27278	+	1.22499i
$188$	5.68330	−	14.6046i	0.0302303	−	0.0776840i
$189$	−6.11321	−	4.44151i	−0.0323450	−	0.0235000i
$190$	101.807	+	207.842i	0.535827	+	1.09390i
$191$	22.7883	−	7.40436i	0.119310	−	0.0387663i	−0.248753	−	0.968567i	$-0.580021\pi$
$191$	22.7883	−	7.40436i	0.119310	−	0.0387663i	0.368064	+	0.929801i	$0.380021\pi$
$192$	80.6680	−	153.067i	0.420146	−	0.797226i
$193$	227.586	+	36.0460i	1.17920	+	0.186767i	0.715104	−	0.699018i	$-0.246379\pi$
$193$	227.586	+	36.0460i	1.17920	+	0.186767i	0.464096	+	0.885785i	$0.346379\pi$
$194$	−74.6025	+	275.884i	−0.384549	+	1.42208i
$195$	−13.5251	−	53.3386i	−0.0693596	−	0.273531i
$196$	−41.5729	+	191.261i	−0.212107	+	0.975819i
$197$	−7.47757	+	7.47757i	−0.0379572	+	0.0379572i	−0.725831	−	0.687873i	$-0.758544\pi$
$197$	−7.47757	+	7.47757i	−0.0379572	+	0.0379572i	0.687873	+	0.725831i	$0.258544\pi$
$198$	−3.26568	+	37.0621i	−0.0164933	+	0.187183i
$199$	311.254			1.56409			0.782046	−	0.623221i	$-0.214176\pi$
$199$	311.254			1.56409			0.782046	+	0.623221i	$0.214176\pi$
$200$	87.4782	−	179.854i	0.437391	−	0.899271i
$201$	53.2305	−	163.827i	0.264828	−	0.815058i
$202$	−250.798	+	144.031i	−1.24158	+	0.713027i
$203$	−12.3427	−	1.95490i	−0.0608017	−	0.00963005i
$204$	−163.666	+	280.494i	−0.802284	+	1.37497i
$205$	−201.962	−	168.097i	−0.985179	−	0.819986i
$206$	−82.2101	+	66.2603i	−0.399078	+	0.321652i
$207$	−59.4406	+	9.41447i	−0.287153	+	0.0454805i
$208$	65.0720	−	2.81102i	0.312846	−	0.0135145i
$209$	−203.060	+	153.551i	−0.971577	+	0.734693i
$210$	−5.07585	+	4.91833i	−0.0241707	+	0.0234206i
$211$	−10.3525	−	7.52157i	−0.0490642	−	0.0356472i	0.562983	−	0.826469i	$-0.309654\pi$
$211$	−10.3525	−	7.52157i	−0.0490642	−	0.0356472i	−0.612047	+	0.790821i	$0.709654\pi$
$212$	−123.362	−	100.838i	−0.581894	−	0.475651i
$213$	134.234	+	68.3954i	0.630205	+	0.321105i
$214$	77.4424	−	3.88023i	0.361880	−	0.0181319i
$215$	28.0036	−	12.0189i	0.130249	−	0.0559019i
$216$	−228.624	+	34.5973i	−1.05845	+	0.160173i
$217$	−3.04704	−	5.98016i	−0.0140417	−	0.0275583i
$218$	29.7761	+	13.3392i	0.136588	+	0.0611891i
$219$			26.8888i			0.122780i
$220$	212.565	+	56.7121i	0.966203	+	0.257782i
$221$	−122.249			−0.553164
$222$	78.8641	−	176.042i	0.355244	−	0.792983i
$223$	−112.164	+	57.1506i	−0.502979	+	0.256281i	−0.687021	−	0.726638i	$-0.741082\pi$
$223$	−112.164	+	57.1506i	−0.502979	+	0.256281i	0.184042	+	0.982918i	$0.441082\pi$
$224$	−4.47551	−	7.06810i	−0.0199800	−	0.0315540i
$225$	−41.5770	+	7.67378i	−0.184787	+	0.0341057i
$226$	−1.54304	−	30.7964i	−0.00682762	−	0.136267i
$227$	−134.651	+	264.267i	−0.593175	+	1.16417i	0.378001	+	0.925805i	$0.376612\pi$
$227$	−134.651	+	264.267i	−0.593175	+	1.16417i	−0.971176	+	0.238365i	$0.923388\pi$
$228$	−193.774	−	158.394i	−0.849885	−	0.694712i
$229$	30.6482	−	42.1836i	0.133835	−	0.184208i	−0.736840	−	0.676068i	$-0.763683\pi$
$229$	30.6482	−	42.1836i	0.133835	−	0.184208i	0.870675	+	0.491860i	$0.163683\pi$
$230$	−5.60801	+	355.813i	−0.0243827	+	1.54702i
$231$	−6.37606	−	4.44865i	−0.0276020	−	0.0192582i
$232$	−310.911	+	222.633i	−1.34013	+	0.959624i
$233$	5.07822	+	32.0626i	0.0217949	+	0.137608i	0.996186	−	0.0872505i	$-0.0278081\pi$
$233$	5.07822	+	32.0626i	0.0217949	+	0.137608i	−0.974391	+	0.224858i	$0.927808\pi$
$234$	−8.64039	−	10.7203i	−0.0369248	−	0.0458131i
$235$	1.78518	+	19.5078i	0.00759651	+	0.0830119i
$236$	78.0126	−	133.700i	0.330562	−	0.566524i
$237$	−44.0260	+	277.969i	−0.185764	+	1.17286i
$238$	7.81982	+	13.6165i	0.0328564	+	0.0572120i
$239$	242.479	+	78.7861i	1.01456	+	0.329649i	0.768667	−	0.639649i	$-0.220920\pi$
$239$	242.479	+	78.7861i	1.01456	+	0.329649i	0.245888	+	0.969298i	$0.420920\pi$
$240$	−4.89849	+	216.223i	−0.0204104	+	0.900930i
$241$		−	55.0838i		−	0.228564i	−0.993448	−	0.114282i	$-0.963543\pi$
$241$		−	55.0838i		−	0.228564i	0.993448	−	0.114282i	$-0.0364567\pi$
$242$	−16.6260	+	241.428i	−0.0687023	+	0.997637i
$243$	63.6602	+	63.6602i	0.261976	+	0.261976i
$244$	−72.7467	+	334.679i	−0.298142	+	1.37163i
$245$	−60.1350	−	237.153i	−0.245449	−	0.967971i
$246$	274.300	+	74.1742i	1.11504	+	0.301521i
$247$	14.7382	−	93.0531i	0.0596687	−	0.376733i
$248$	−194.887	−	64.8106i	−0.785833	−	0.261333i
$249$	−75.8084	−	233.314i	−0.304452	−	0.937006i
$250$	2.41860	+	249.988i	0.00967439	+	0.999953i
$251$	−210.055	+	289.115i	−0.836871	+	1.15185i	0.149734	+	0.988726i	$0.452158\pi$
$251$	−210.055	+	289.115i	−0.836871	+	1.15185i	−0.986605	+	0.163128i	$0.947842\pi$
$252$	−0.641359	+	1.64813i	−0.00254507	+	0.00654018i
$253$	−385.382	+	68.6198i	−1.52325	+	0.271224i
$254$	−107.233	−	69.9884i	−0.422176	−	0.275545i
$255$	26.7007	−	405.060i	0.104709	−	1.58847i
$256$	−249.385	−	57.8177i	−0.974162	−	0.225850i
$257$	−43.4164	+	85.2094i	−0.168935	+	0.331554i	−0.959916	−	0.280286i	$-0.909571\pi$
$257$	−43.4164	+	85.2094i	−0.168935	+	0.331554i	0.790981	+	0.611841i	$0.209571\pi$
$258$	−22.1069	+	24.4390i	−0.0856855	+	0.0947249i
$259$	−5.48226	−	7.54568i	−0.0211670	−	0.0291339i
$260$	−71.2318	+	39.4282i	−0.273968	+	0.151647i
$261$	76.8817	+	24.9804i	0.294566	+	0.0957103i
$262$	−334.450	−	149.828i	−1.27653	−	0.571863i
$263$	86.6193	−	86.6193i	0.329351	−	0.329351i	−0.522989	−	0.852340i	$-0.675183\pi$
$263$	86.6193	−	86.6193i	0.329351	−	0.329351i	0.852340	+	0.522989i	$0.175183\pi$
$264$	−234.505	+	40.0898i	−0.888275	+	0.151855i
$265$	194.236	+	44.0274i	0.732968	+	0.166141i
$266$	−11.3073	+	4.31068i	−0.0425085	+	0.0162056i
$267$	−19.3694	−	38.0146i	−0.0725446	−	0.142377i
$268$	−254.454	−	14.5078i	−0.949455	−	0.0541338i
$269$	45.3303	+	62.3919i	0.168514	+	0.231940i	0.884919	−	0.465745i	$-0.154214\pi$
$269$	45.3303	+	62.3919i	0.168514	+	0.231940i	−0.716405	+	0.697685i	$0.754214\pi$
$270$	236.482	−	166.184i	0.875859	−	0.615496i
$271$	−9.80192	−	30.1672i	−0.0361694	−	0.111318i	0.931342	−	0.364146i	$-0.118639\pi$
$271$	−9.80192	−	30.1672i	−0.0361694	−	0.111318i	−0.967511	+	0.252828i	$0.918639\pi$
$272$	462.958	+	128.620i	1.70205	+	0.472867i
$273$	2.84175	−	0.450089i	0.0104093	−	0.00164868i
$274$	−177.459	−	115.823i	−0.647659	−	0.422713i
$275$	−269.428	+	55.0771i	−0.979739	+	0.200280i
$276$	−154.905	−	352.268i	−0.561249	−	1.27633i
$277$	369.430	−	58.5120i	1.33368	−	0.211235i	0.551443	−	0.834212i	$-0.314077\pi$
$277$	369.430	−	58.5120i	1.33368	−	0.211235i	0.782240	+	0.622978i	$0.214077\pi$
$278$	469.821	+	50.4715i	1.69000	+	0.181552i
$279$	13.4165	+	41.2917i	0.0480878	+	0.147999i
$280$	8.94805	+	5.41192i	0.0319573	+	0.0193283i
$281$	−148.433	−	204.301i	−0.528231	−	0.727048i	0.458628	−	0.888628i	$-0.348341\pi$
$281$	−148.433	−	204.301i	−0.528231	−	0.727048i	−0.986860	+	0.161580i	$0.948341\pi$
$282$	−10.5497	−	18.3699i	−0.0374103	−	0.0651417i
$283$	5.59113	+	10.9732i	0.0197567	+	0.0387746i	0.900674	−	0.434496i	$-0.143073\pi$
$283$	5.59113	+	10.9732i	0.0197567	+	0.0387746i	−0.880917	+	0.473270i	$0.843073\pi$
$284$	47.3453	−	217.817i	0.166709	−	0.766961i
$285$	305.103	+	69.1573i	1.07054	+	0.242657i
$286$	−57.5239	−	68.6407i	−0.201133	−	0.240003i
$287$	9.71503	−	9.71503i	0.0338503	−	0.0338503i
$288$	21.4423	+	49.6883i	0.0744524	+	0.172529i
$289$	−582.854	−	189.381i	−2.01680	−	0.655297i
$290$	223.693	−	422.430i	0.771356	−	1.45666i
$291$	227.072	+	312.538i	0.780316	+	1.07401i
$292$	38.4751	−	10.1202i	0.131764	−	0.0346581i
$293$	179.659	−	352.601i	0.613170	−	1.20341i	−0.350561	−	0.936540i	$-0.614009\pi$
$293$	179.659	−	352.601i	0.613170	−	1.20341i	0.963731	−	0.266875i	$-0.0859910\pi$
$294$	166.028	+	205.993i	0.564720	+	0.700656i
$295$	−12.7271	+	193.075i	−0.0431427	+	0.654491i
$296$	−281.581	−	46.5894i	−0.951288	−	0.157397i
$297$	229.075	+	220.474i	0.771297	+	0.742337i
$298$	−55.8487	+	11.7370i	−0.187412	+	0.0393858i
$299$	85.1480	−	117.196i	0.284776	−	0.391960i
$300$	−115.083	−	244.631i	−0.383611	−	0.815435i
$301$	0.492381	+	1.51539i	0.00163582	+	0.00503453i
$302$	40.4104	−	44.6735i	0.133809	−	0.147925i
$303$	−61.1570	+	386.130i	−0.201838	+	1.27436i
$304$	−153.716	+	336.886i	−0.505644	+	1.10818i
$305$	−105.228	−	414.984i	−0.345009	−	1.36060i
$306$	−36.1831	−	94.9112i	−0.118245	−	0.310167i
$307$	−206.158	−	206.158i	−0.671526	−	0.671526i	0.286542	−	0.958068i	$-0.407494\pi$
$307$	−206.158	−	206.158i	−0.671526	−	0.671526i	−0.958068	+	0.286542i	$0.907494\pi$
$308$	−3.96581	+	10.7979i	−0.0128760	+	0.0350580i
$309$			142.728i			0.461904i
$310$	254.166	−	36.1598i	0.819892	−	0.116645i
$311$	88.9741	+	28.9094i	0.286090	+	0.0929564i	0.448547	−	0.893759i	$-0.351942\pi$
$311$	88.9741	+	28.9094i	0.286090	+	0.0929564i	−0.162456	+	0.986716i	$0.551942\pi$
$312$	52.2398	−	70.8697i	0.167435	−	0.227147i
$313$	3.80615	−	24.0311i	0.0121602	−	0.0767766i	−0.980862	−	0.194705i	$-0.937625\pi$
$313$	3.80615	−	24.0311i	0.0121602	−	0.0767766i	0.993022	+	0.117928i	$0.0376252\pi$
$314$	−40.6596	+	2.03724i	−0.129489	+	0.00648802i
$315$	−0.201457	−	2.20145i	−0.000639547	−	0.00698873i
$316$	414.316	−	41.6229i	1.31113	−	0.131718i
$317$	20.7094	+	130.754i	0.0653292	+	0.412472i	0.998581	+	0.0532500i	$0.0169580\pi$
$317$	20.7094	+	130.754i	0.0653292	+	0.412472i	−0.933252	+	0.359222i	$0.883042\pi$
$318$	−210.770	+	44.2948i	−0.662800	+	0.139292i
$319$	503.084	+	152.886i	1.57707	+	0.479267i
$320$	311.238	−	74.3711i	0.972618	−	0.232410i
$321$	61.6078	−	84.7959i	0.191925	−	0.264162i
$322$	−18.5002	−	1.98743i	−0.0574541	−	0.00617214i
$323$	315.534	−	619.269i	0.976884	−	1.91724i
$324$	−126.839	+	217.379i	−0.391478	+	0.670922i
$325$	57.7056	−	83.8282i	0.177556	−	0.257933i
$326$	−105.169	+	388.922i	−0.322606	+	1.19301i
$327$	39.2969	−	20.0228i	0.120174	−	0.0612317i
$328$	2.89715	−	420.413i	0.00883277	−	1.28175i
$329$	−1.02426			−0.00311326
$330$	239.998	−	175.607i	0.727266	−	0.532144i
$331$		−	330.941i		−	0.999822i	−0.866077	−	0.499911i	$-0.833366\pi$
$331$		−	330.941i		−	0.999822i	0.866077	−	0.499911i	$-0.166634\pi$
$332$	−305.318	+	196.287i	−0.919631	+	0.591227i
$333$	27.3913	+	53.7584i	0.0822561	+	0.161437i
$334$	−2.13587	+	7.89857i	−0.00639483	+	0.0236484i
$335$	292.759	−	125.650i	0.873908	−	0.375075i
$336$	−11.2352	−	1.28535i	−0.0334382	−	0.00382544i
$337$	−251.656	−	128.225i	−0.746753	−	0.380489i	0.0388303	−	0.999246i	$-0.487637\pi$
$337$	−251.656	−	128.225i	−0.746753	−	0.380489i	−0.785583	+	0.618756i	$0.787637\pi$
$338$	−303.113	−	32.5626i	−0.896785	−	0.0963391i
$339$	−33.7206	−	24.4995i	−0.0994708	−	0.0722698i
$340$	−589.650	+	114.247i	−1.73426	+	0.336021i
$341$	92.3875	+	266.858i	0.270931	+	0.782576i
$342$	76.6063	−	16.0993i	0.223995	−	0.0470741i
$343$	25.2875	−	4.00514i	0.0737244	−	0.0116768i
$344$	43.2902	+	22.4346i	0.125844	+	0.0652167i
$345$	369.720	+	307.726i	1.07165	+	0.891959i
$346$	−103.358	+	5.17872i	−0.298722	+	0.0149674i
$347$	−238.755	−	37.8151i	−0.688054	−	0.108977i	−0.197389	−	0.980325i	$-0.563246\pi$
$347$	−238.755	−	37.8151i	−0.688054	−	0.108977i	−0.490665	+	0.871348i	$0.663246\pi$
$348$	−29.4240	+	516.070i	−0.0845519	+	1.48296i
$349$	171.175	−	526.823i	0.490474	−	1.50952i	−0.333420	−	0.942778i	$-0.608203\pi$
$349$	171.175	−	526.823i	0.490474	−	1.50952i	0.823894	−	0.566744i	$-0.191797\pi$
$350$	−13.0282	−	1.06524i	−0.0372235	−	0.00304354i
$351$	−117.660			−0.335213
$352$	145.625	+	320.464i	0.413709	+	0.910409i
$353$	−162.563	+	162.563i	−0.460518	+	0.460518i	−0.898825	−	0.438307i	$-0.855578\pi$
$353$	−162.563	+	162.563i	−0.460518	+	0.460518i	0.438307	+	0.898825i	$0.355578\pi$
$354$	−74.5371	−	195.517i	−0.210557	−	0.552308i
$355$	68.4848	+	270.081i	0.192915	+	0.760793i
$356$	−47.1050	+	42.0233i	−0.132317	+	0.118043i
$357$	20.9640	+	3.32036i	0.0587226	+	0.00930074i
$358$	−401.755	+	444.138i	−1.12222	+	1.24061i
$359$	−287.976	+	93.5692i	−0.802163	+	0.260638i	−0.681275	−	0.732028i	$-0.738574\pi$
$359$	−287.976	+	93.5692i	−0.802163	+	0.260638i	−0.120888	+	0.992666i	$0.538574\pi$
$360$	−51.6941	−	43.6326i	−0.143595	−	0.121202i
$361$	141.277	+	102.644i	0.391350	+	0.284333i
$362$	100.294	−	21.0775i	0.277056	−	0.0582252i
$363$	239.988	+	222.293i	0.661125	+	0.612377i
$364$	−1.71359	−	3.89686i	−0.00470765	−	0.0107057i
$365$	−37.4011	+	32.7752i	−0.102469	+	0.0897951i
$366$	290.525	+	360.458i	0.793784	+	0.984859i
$367$	362.988	+	184.952i	0.989069	+	0.503956i	0.872178	−	0.489189i	$-0.162707\pi$
$367$	362.988	+	184.952i	0.989069	+	0.503956i	0.116891	+	0.993145i	$0.462707\pi$
$368$	−445.759	+	354.237i	−1.21130	+	0.962600i
$369$	−71.9021	+	52.2399i	−0.194857	+	0.141572i
$370$	340.996	−	104.885i	0.921611	−	0.283472i
$371$	−3.21799	+	9.90397i	−0.00867384	+	0.0266953i
$372$	−233.525	+	150.132i	−0.627756	+	0.403582i
$373$	259.854	+	259.854i	0.696659	+	0.696659i	0.963688	−	0.267029i	$-0.0860421\pi$
$373$	259.854	+	259.854i	0.696659	+	0.696659i	−0.267029	+	0.963688i	$0.586042\pi$
$374$	−247.114	−	612.723i	−0.660733	−	1.63830i
$375$	265.152	+	209.511i	0.707073	+	0.558695i
$376$	−22.3150	+	22.0095i	−0.0593483	+	0.0585359i
$377$	−173.376	+	88.3396i	−0.459884	+	0.234323i
$378$	7.52626	+	13.1053i	0.0199107	+	0.0346701i
$379$	−94.3847	+	68.5745i	−0.249036	+	0.180935i	−0.705300	−	0.708909i	$-0.749187\pi$
$379$	−94.3847	+	68.5745i	−0.249036	+	0.180935i	0.456263	+	0.889845i	$0.349187\pi$
$380$	−15.8748	−	462.601i	−0.0417759	−	1.21737i
$381$	−164.621	+	53.4886i	−0.432076	+	0.140390i
$382$	−47.6478	−	5.11867i	−0.124733	−	0.0133997i
$383$	35.1135	+	221.698i	0.0916802	+	0.578846i	0.990172	+	0.139856i	$0.0446638\pi$
$383$	35.1135	+	221.698i	0.0916802	+	0.578846i	−0.898492	+	0.438991i	$0.855336\pi$
$384$	−272.395	+	213.422i	−0.709362	+	0.555786i
$385$	−1.58402	−	14.2914i	−0.00411434	−	0.0371204i
$386$	−385.920	−	251.881i	−0.999792	−	0.652543i
$387$	−1.61241	−	10.1804i	−0.00416644	−	0.0263059i
$388$	361.747	−	442.548i	0.932338	−	1.14059i
$389$	546.922	−	177.706i	1.40597	−	0.456827i	0.494852	−	0.868977i	$-0.335222\pi$
$389$	546.922	−	177.706i	1.40597	−	0.456827i	0.911116	+	0.412150i	$0.135222\pi$
$390$	−18.9270	+	108.414i	−0.0485307	+	0.277984i
$391$	864.571	−	628.148i	2.21118	−	1.60652i
$392$	232.267	−	315.099i	0.592519	−	0.803825i
$393$	−441.389	+	224.899i	−1.12313	+	0.572261i
$394$	19.7624	−	7.53402i	0.0501583	−	0.0191219i
$395$	−440.307	+	277.583i	−1.11470	+	0.702743i
$396$	36.2651	−	64.9762i	0.0915785	−	0.164081i
$397$	−277.982	−	277.982i	−0.700207	−	0.700207i	0.264248	−	0.964455i	$-0.414876\pi$
$397$	−277.982	−	277.982i	−0.700207	−	0.700207i	−0.964455	+	0.264248i	$0.914876\pi$
$398$	−568.107	−	254.503i	−1.42740	−	0.639454i
$399$	−5.05476	+	15.5570i	−0.0126686	+	0.0389899i
$400$	−306.728	+	256.745i	−0.766820	+	0.641862i
$401$	−266.732	+	193.792i	−0.665167	+	0.483272i	−0.868404	−	0.495857i	$-0.834854\pi$
$401$	−266.732	+	193.792i	−0.665167	+	0.483272i	0.203237	+	0.979130i	$0.434854\pi$
$402$	−231.113	+	255.494i	−0.574908	+	0.635558i
$403$	−93.1171	−	47.4456i	−0.231060	−	0.117731i
$404$	575.532	−	57.8189i	1.42458	−	0.143116i
$405$	20.6927	−	313.916i	0.0510930	−	0.775101i
$406$	20.9297	+	13.6604i	0.0515511	+	0.0336463i
$407$	184.819	+	346.193i	0.454101	+	0.850597i
$408$	528.077	−	378.138i	1.29431	−	0.926809i
$409$	−197.724	−	143.655i	−0.483433	−	0.351235i	0.319220	−	0.947681i	$-0.396579\pi$
$409$	−197.724	−	143.655i	−0.483433	−	0.351235i	−0.802653	+	0.596446i	$0.796579\pi$
$410$	231.176	+	471.952i	0.563845	+	1.15110i
$411$	−272.430	+	88.5180i	−0.662848	+	0.215372i
$412$	204.230	−	53.7189i	0.495704	−	0.130386i
$413$	−9.99263	−	1.58268i	−0.0241952	−	0.00383215i
$414$	116.190	+	31.4193i	0.280652	+	0.0758919i
$415$	232.126	−	389.837i	0.559339	−	0.939367i
$416$	−121.069	−	48.0766i	−0.291032	−	0.115569i
$417$	451.651	−	451.651i	1.08310	−	1.08310i
$418$	496.181	−	114.228i	1.18704	−	0.273274i
$419$	478.038			1.14090			0.570451	−	0.821332i	$-0.306768\pi$
$419$	478.038			1.14090			0.570451	+	0.821332i	$0.306768\pi$
$420$	13.2861	−	4.82667i	0.0316336	−	0.0114921i
$421$	86.2908	−	265.576i	0.204966	−	0.630821i	−0.794748	−	0.606939i	$-0.792397\pi$
$421$	86.2908	−	265.576i	0.204966	−	0.630821i	0.999715	−	0.0238825i	$-0.00760274\pi$
$422$	12.7455	+	22.1934i	0.0302026	+	0.0525911i
$423$	6.54419	+	1.03650i	0.0154709	+	0.00245035i
$424$	142.710	+	284.920i	0.336579	+	0.671981i
$425$	595.967	−	456.596i	1.40227	−	1.07434i
$426$	−189.081	−	234.595i	−0.443851	−	0.550693i
$427$	22.1093	−	3.50177i	0.0517782	−	0.00820086i
$428$	−144.522	−	56.2399i	−0.337668	−	0.131402i
$429$	−121.037	+	2.31573i	−0.282136	+	0.00539797i
$430$	−60.9401	−	0.960482i	−0.141721	−	0.00223368i
$431$	−115.362	−	83.8154i	−0.267661	−	0.194467i	0.445856	−	0.895104i	$-0.352899\pi$
$431$	−115.362	−	83.8154i	−0.267661	−	0.194467i	−0.713518	+	0.700637i	$0.752899\pi$
$432$	445.578	+	123.791i	1.03143	+	0.286554i
$433$	−312.649	−	159.303i	−0.722054	−	0.367905i	0.0540261	−	0.998540i	$-0.482795\pi$
$433$	−312.649	−	159.303i	−0.722054	−	0.367905i	−0.776080	+	0.630635i	$0.782795\pi$
$434$	0.671732	+	13.4066i	0.00154777	+	0.0308907i
$435$	−254.837	−	593.759i	−0.585831	−	1.36496i
$436$	−43.4409	−	48.6940i	−0.0996350	−	0.111683i
$437$	373.900	+	733.819i	0.855605	+	1.67922i
$438$	21.9861	−	49.0778i	0.0501965	−	0.112050i
$439$		−	371.749i		−	0.846809i	−0.905941	−	0.423405i	$-0.860835\pi$
$439$		−	371.749i		−	0.846809i	0.905941	−	0.423405i	$-0.139165\pi$
$440$	−341.605	−	277.319i	−0.776375	−	0.630271i
$441$	−82.7517			−0.187646
$442$	223.131	+	99.9593i	0.504822	+	0.226152i
$443$	−631.406	+	321.718i	−1.42530	+	0.726225i	−0.985149	−	0.171701i	$-0.945074\pi$
$443$	−631.406	+	321.718i	−1.42530	+	0.726225i	−0.440147	+	0.897926i	$0.645074\pi$
$444$	−287.888	+	256.831i	−0.648397	+	0.578448i
$445$	29.2669	−	73.2787i	0.0657683	−	0.164671i
$446$	251.455	−	12.5991i	0.563799	−	0.0282490i
$447$	−35.0218	+	68.7341i	−0.0783485	+	0.153768i
$448$	2.38943	+	16.5603i	0.00533354	+	0.0369649i
$449$	−10.8111	+	14.8802i	−0.0240781	+	0.0331407i	−0.820886	−	0.571092i	$-0.806520\pi$
$449$	−10.8111	+	14.8802i	−0.0240781	+	0.0331407i	0.796808	+	0.604232i	$0.206520\pi$
$450$	82.1617	+	19.9899i	0.182582	+	0.0444219i
$451$	−461.093	+	348.672i	−1.02238	+	0.773109i
$452$	−22.3648	+	57.4717i	−0.0494797	+	0.127150i
$453$	−12.7380	−	80.4249i	−0.0281193	−	0.177538i
$454$	461.849	−	372.245i	1.01729	−	0.819922i
$455$	4.08991	+	3.40412i	0.00898882	+	0.00748159i
$456$	224.165	+	447.547i	0.491591	+	0.981463i
$457$	68.7689	−	434.189i	0.150479	−	0.950086i	−0.790706	−	0.612196i	$-0.790287\pi$
$457$	68.7689	−	434.189i	0.150479	−	0.950086i	0.941185	−	0.337891i	$-0.109713\pi$
$458$	−90.4319	+	51.9343i	−0.197449	+	0.113394i
$459$	−825.510	−	268.225i	−1.79850	−	0.584367i
$460$	301.173	−	644.852i	0.654724	−	1.40185i
$461$			518.031i			1.12371i	0.827235	+	0.561856i	$0.189912\pi$
$461$			518.031i			1.12371i	−0.827235	+	0.561856i	$0.810088\pi$
$462$	8.00018	+	13.3333i	0.0173164	+	0.0288599i
$463$	−636.948	−	636.948i	−1.37570	−	1.37570i	−0.851750	−	0.523949i	$-0.824458\pi$
$463$	−636.948	−	636.948i	−1.37570	−	1.37570i	−0.523949	−	0.851750i	$-0.675542\pi$
$464$	749.520	−	152.131i	1.61534	−	0.327869i
$465$	177.544	−	298.171i	0.381814	−	0.641228i
$466$	16.9477	−	62.6736i	0.0363685	−	0.134493i
$467$	−57.4408	+	362.667i	−0.123000	+	0.776588i	0.846661	+	0.532133i	$0.178609\pi$
$467$	−57.4408	+	362.667i	−0.123000	+	0.776588i	−0.969660	+	0.244456i	$0.921391\pi$
$468$	7.00499	+	26.6318i	0.0149679	+	0.0569055i
$469$	5.14753	+	15.8425i	0.0109755	+	0.0337793i
$470$	12.6926	−	37.0656i	0.0270054	−	0.0788631i
$471$	−32.3460	+	44.5204i	−0.0686751	+	0.0945231i
$472$	−251.712	+	180.242i	−0.533288	+	0.381869i
$473$	−11.7525	−	66.0042i	−0.0248467	−	0.139544i
$474$	307.643	−	471.355i	0.649037	−	0.994420i
$475$	275.701	+	508.682i	0.580422	+	1.07091i
$476$	−3.13913	−	31.2470i	−0.00659481	−	0.0656450i
$477$	30.5826	−	60.0217i	0.0641145	−	0.125832i
$478$	−378.155	−	342.069i	−0.791120	−	0.715625i
$479$	−51.8442	−	71.3574i	−0.108234	−	0.148972i	0.751464	−	0.659774i	$-0.229348\pi$
$479$	−51.8442	−	71.3574i	−0.108234	−	0.148972i	−0.859698	+	0.510803i	$0.829348\pi$
$480$	185.740	−	390.649i	0.386958	−	0.813853i
$481$	−138.122	−	44.8787i	−0.287157	−	0.0933029i
$482$	−45.0403	+	100.540i	−0.0934446	+	0.208589i
$483$	−17.7847	+	17.7847i	−0.0368214	+	0.0368214i
$484$	227.754	−	427.064i	0.470566	−	0.882365i
$485$	−157.944	+	696.805i	−0.325658	+	1.43671i
$486$	−64.1408	−	168.247i	−0.131977	−	0.346186i
$487$	−189.407	−	371.733i	−0.388927	−	0.763312i	0.610664	−	0.791889i	$-0.290902\pi$
$487$	−189.407	−	371.733i	−0.388927	−	0.763312i	−0.999592	+	0.0285770i	$0.990902\pi$
$488$	406.435	−	551.379i	0.832858	−	1.12987i
$489$	320.110	+	440.594i	0.654623	+	0.901011i
$490$	−84.1527	+	482.026i	−0.171740	+	0.983726i
$491$	−3.50929	−	10.8005i	−0.00714722	−	0.0219969i	0.947419	−	0.319995i	$-0.103681\pi$
$491$	−3.50929	−	10.8005i	−0.00714722	−	0.0219969i	−0.954567	+	0.297998i	$0.903681\pi$
$492$	−440.007	−	359.670i	−0.894324	−	0.731037i
$493$	−1417.80	+	224.558i	−2.87587	+	0.455493i
$494$	−102.987	+	157.791i	−0.208476	+	0.319416i
$495$	−4.34149	+	92.9130i	−0.00877070	+	0.187703i
$496$	302.717	+	277.646i	0.610316	+	0.559770i
$497$	−14.3893	+	2.27904i	−0.0289522	+	0.00458559i
$498$	−52.4068	+	487.836i	−0.105235	+	0.979590i
$499$	−25.3376	−	77.9810i	−0.0507767	−	0.156275i	0.922453	−	0.386110i	$-0.126181\pi$
$499$	−25.3376	−	77.9810i	−0.0507767	−	0.156275i	−0.973230	+	0.229835i	$0.926181\pi$
$500$	199.993	−	458.261i	0.399986	−	0.916521i
$501$	6.50109	+	8.94798i	0.0129762	+	0.0178602i
$502$	619.796	−	355.944i	1.23465	−	0.709051i
$503$	312.391	+	613.102i	0.621056	+	1.21889i	0.960504	+	0.278266i	$0.0897596\pi$
$503$	312.391	+	613.102i	0.621056	+	1.21889i	−0.339448	+	0.940625i	$0.610240\pi$
$504$	2.51824	−	2.48377i	0.00499651	−	0.00492811i
$505$	−611.635	+	385.594i	−1.21116	+	0.763553i
$506$	759.514	+	189.869i	1.50102	+	0.375234i
$507$	−291.391	+	291.391i	−0.574735	+	0.574735i
$508$	138.496	+	215.425i	0.272629	+	0.424064i
$509$	610.099	+	198.233i	1.19862	+	0.389456i	0.839254	−	0.543740i	$-0.182992\pi$
$509$	610.099	+	198.233i	1.19862	+	0.389456i	0.359368	+	0.933196i	$0.382992\pi$
$510$	−379.939	+	717.490i	−0.744979	+	1.40684i
$511$	−1.52837	−	2.10362i	−0.00299093	−	0.00411667i
$512$	407.907	+	309.444i	0.796694	+	0.604383i
$513$	303.688	−	596.021i	0.591985	−	1.16184i
$514$	148.917	−	120.026i	0.289722	−	0.233513i
$515$	−198.529	+	173.974i	−0.385493	+	0.337814i
$516$	60.3328	−	26.5305i	0.116924	−	0.0514156i
$517$	42.6870	+	5.92630i	0.0825668	+	0.0114629i
$518$	3.83645	+	18.2552i	0.00740628	+	0.0352417i
$519$	−82.2244	+	113.172i	−0.158429	+	0.218058i
$520$	162.253	−	13.7212i	0.312024	−	0.0263869i
$521$	97.7205	+	300.753i	0.187563	+	0.577261i	0.999983	−	0.00581228i	$-0.00185012\pi$
$521$	97.7205	+	300.753i	0.187563	+	0.577261i	−0.812420	+	0.583073i	$0.801850\pi$
$522$	−119.900	−	108.458i	−0.229694	−	0.207775i
$523$	14.8497	−	93.7574i	0.0283933	−	0.179269i	−0.969416	−	0.245423i	$-0.921073\pi$
$523$	14.8497	−	93.7574i	0.0283933	−	0.179269i	0.997809	+	0.0661547i	$0.0210731\pi$
$524$	487.934	+	546.938i	0.931172	+	1.04377i
$525$	−12.1725	+	12.8080i	−0.0231857	+	0.0243962i
$526$	−228.925	+	87.2733i	−0.435219	+	0.165919i
$527$	−545.157	−	545.157i	−1.03445	−	1.03445i
$528$	460.802	+	118.574i	0.872731	+	0.224572i
$529$			737.347i			1.39385i
$530$	−318.524	−	239.180i	−0.600989	−	0.451284i
$531$	62.2431	+	20.2240i	0.117219	+	0.0380866i
$532$	24.1629	+	1.37766i	0.0454190	+	0.00258959i
$533$	33.4664	−	211.298i	0.0627887	−	0.396432i
$534$	4.27006	+	85.2226i	0.00799636	+	0.159593i
$535$	193.042	−	17.6655i	0.360827	−	0.0330197i
$536$	452.571	+	234.539i	0.844350	+	0.437573i
$537$	126.640	+	799.574i	0.235829	+	1.48896i
$538$	−31.7219	−	150.944i	−0.0589627	−	0.280565i
$539$	−538.150	+	10.2961i	−0.998422	+	0.0191023i
$540$	−567.514	+	109.958i	−1.05095	+	0.203626i
$541$	53.7552	−	73.9877i	0.0993626	−	0.136761i	−0.756441	−	0.654062i	$-0.773063\pi$
$541$	53.7552	−	73.9877i	0.0993626	−	0.136761i	0.855803	+	0.517301i	$0.173063\pi$
$542$	−6.77612	+	63.0764i	−0.0125021	+	0.116377i
$543$	62.8928	−	123.434i	0.115825	−	0.227319i
$544$	−739.831	−	613.305i	−1.35998	−	1.12740i
$545$	75.7505	+	30.2541i	0.138992	+	0.0555122i
$546$	−5.55483	−	1.50210i	−0.0101737	−	0.00275109i
$547$	273.634	−	139.424i	0.500245	−	0.254888i	−0.185613	−	0.982623i	$-0.559427\pi$
$547$	273.634	−	139.424i	0.500245	−	0.254888i	0.685858	+	0.727735i	$0.259427\pi$
$548$	229.196	+	356.505i	0.418240	+	0.650557i
$549$	−144.804			−0.263759
$550$	536.800	+	119.775i	0.975999	+	0.217773i
$551$		−	1106.27i		−	2.00775i
$552$	−5.30364	+	769.626i	−0.00960805	+	1.39425i
$553$	−12.3555	−	24.2491i	−0.0223427	−	0.0438501i
$554$	−722.134	−	195.274i	−1.30349	−	0.352480i
$555$	178.868	−	447.852i	0.322285	−	0.806940i
$556$	−816.256	−	476.279i	−1.46809	−	0.856617i
$557$	−490.021	−	249.678i	−0.879751	−	0.448255i	−0.0450664	−	0.998984i	$-0.514350\pi$
$557$	−490.021	−	249.678i	−0.879751	−	0.448255i	−0.834684	+	0.550729i	$0.814350\pi$
$558$	9.27490	−	86.3366i	0.0166217	−	0.154725i
$559$	20.0721	+	14.5833i	0.0359072	+	0.0260881i
$560$	−11.9070	−	17.1945i	−0.0212625	−	0.0307044i
$561$	−854.480	−	259.675i	−1.52314	−	0.462878i
$562$	103.873	+	494.262i	0.184827	+	0.879470i
$563$	−104.018	+	16.4749i	−0.184757	+	0.0292626i	−0.248127	−	0.968727i	$-0.579815\pi$
$563$	−104.018	+	16.4749i	−0.184757	+	0.0292626i	0.0633702	+	0.997990i	$0.479815\pi$
$564$	4.23499	+	42.1553i	0.00750885	+	0.0747435i
$565$	−7.02501	−	76.7667i	−0.0124336	−	0.135870i
$566$	−1.23259	−	24.6002i	−0.00217771	−	0.0434633i
$567$	16.2468	+	2.57324i	0.0286539	+	0.00453833i
$568$	−264.518	+	358.851i	−0.465700	+	0.631779i
$569$	−158.054	+	486.440i	−0.277775	+	0.854903i	0.710697	+	0.703498i	$0.248380\pi$
$569$	−158.054	+	486.440i	−0.277775	+	0.854903i	−0.988472	+	0.151405i	$0.951620\pi$
$570$	−500.331	−	375.700i	−0.877774	−	0.659123i
$571$	627.155			1.09834			0.549172	−	0.835709i	$-0.314943\pi$
$571$	627.155			1.09834			0.549172	+	0.835709i	$0.314943\pi$
$572$	48.8683	+	172.320i	0.0854341	+	0.301258i
$573$	−45.8051	+	45.8051i	−0.0799391	+	0.0799391i
$574$	−25.6757	+	9.78837i	−0.0447312	+	0.0170529i
$575$	22.6251	+	889.356i	0.0393480	+	1.54671i
$576$	1.49166	−	108.225i	0.00258969	−	0.187890i
$577$	−369.214	−	58.4778i	−0.639886	−	0.101348i	−0.171943	−	0.985107i	$-0.555005\pi$
$577$	−369.214	−	58.4778i	−0.639886	−	0.101348i	−0.467942	+	0.883759i	$0.655005\pi$
$578$	908.985	+	822.242i	1.57264	+	1.42256i
$579$	−592.455	+	192.500i	−1.02324	+	0.332470i
$580$	−753.696	+	588.120i	−1.29948	+	1.01400i
$581$	19.1925	+	13.9442i	0.0330335	+	0.0240003i
$582$	−158.904	−	756.119i	−0.273030	−	1.29917i
$583$	191.416	−	394.137i	0.328330	−	0.676050i
$584$	−78.5004	−	12.9884i	−0.134419	−	0.0222404i
$585$	−22.6864	−	25.8883i	−0.0387801	−	0.0442535i
$586$	−616.227	+	496.671i	−1.05158	+	0.847562i
$587$	−826.097	−	420.918i	−1.40732	−	0.717066i	−0.425162	−	0.905117i	$-0.639783\pi$
$587$	−826.097	−	420.918i	−1.40732	−	0.717066i	−0.982159	+	0.188051i	$0.939783\pi$
$588$	−134.603	−	511.738i	−0.228917	−	0.870302i
$589$	480.683	−	349.237i	0.816101	−	0.592932i
$590$	181.101	−	341.997i	0.306951	−	0.579656i
$591$	8.83449	−	27.1898i	0.0149484	−	0.0460064i
$592$	475.852	+	315.276i	0.803805	+	0.532560i
$593$	390.551	+	390.551i	0.658602	+	0.658602i	0.955049	−	0.296447i	$-0.0958019\pi$
$593$	390.551	+	390.551i	0.658602	+	0.658602i	−0.296447	+	0.955049i	$0.595802\pi$
$594$	−237.837	−	589.721i	−0.400400	−	0.992796i
$595$	20.9349	+	33.2072i	0.0351847	+	0.0558104i
$596$	111.533	+	24.2431i	0.187136	+	0.0406764i
$597$	−749.756	+	382.020i	−1.25587	+	0.639899i
$598$	−251.241	+	144.286i	−0.420136	+	0.241280i
$599$	−555.361	+	403.493i	−0.927147	+	0.673612i	−0.945293	−	0.326224i	$-0.894224\pi$
$599$	−555.361	+	403.493i	−0.927147	+	0.673612i	0.0181456	+	0.999835i	$0.494224\pi$
$600$	10.0257	+	540.604i	0.0167095	+	0.901007i
$601$	487.260	−	158.320i	0.810749	−	0.263428i	0.125834	−	0.992051i	$-0.459839\pi$
$601$	487.260	−	158.320i	0.810749	−	0.263428i	0.684915	+	0.728623i	$0.259839\pi$
$602$	0.340386	−	3.16853i	0.000565425	−	0.00526333i
$603$	−16.8568	−	106.429i	−0.0279548	−	0.176500i
$604$	−110.286	+	48.4965i	−0.182592	+	0.0802923i
$605$	−16.6731	+	604.770i	−0.0275589	+	0.999620i
$606$	427.351	−	654.765i	0.705200	−	1.08047i
$607$	79.9289	+	504.651i	0.131679	+	0.831386i	0.961790	+	0.273788i	$0.0882767\pi$
$607$	79.9289	+	504.651i	0.131679	+	0.831386i	−0.830111	+	0.557598i	$0.811723\pi$
$608$	556.026	−	489.202i	0.914516	−	0.804609i
$609$	32.1309	−	10.4399i	0.0527600	−	0.0171428i
$610$	−147.255	+	843.477i	−0.241402	+	1.38275i
$611$	−12.9029	+	9.37447i	−0.0211176	+	0.0153428i
$612$	−11.5639	+	202.819i	−0.0188952	+	0.331404i
$613$	186.867	−	95.2135i	0.304840	−	0.155324i	−0.294878	−	0.955535i	$-0.595279\pi$
$613$	186.867	−	95.2135i	0.304840	−	0.155324i	0.599719	+	0.800211i	$0.295279\pi$
$614$	207.715	+	544.853i	0.338298	+	0.887383i
$615$	692.805	+	157.037i	1.12651	+	0.255345i
$616$	16.0675	−	16.4657i	0.0260837	−	0.0267301i
$617$	−359.894	−	359.894i	−0.583296	−	0.583296i	0.352511	−	0.935808i	$-0.385328\pi$
$617$	−359.894	−	359.894i	−0.583296	−	0.583296i	−0.935808	+	0.352511i	$0.885328\pi$
$618$	116.704	−	260.510i	0.188842	−	0.421538i
$619$	−353.068	+	1086.63i	−0.570385	+	1.75546i	0.0809973	+	0.996714i	$0.474189\pi$
$619$	−353.068	+	1086.63i	−0.570385	+	1.75546i	−0.651382	+	0.758750i	$0.725811\pi$
$620$	−493.476	−	141.824i	−0.795929	−	0.228749i
$621$	832.115	−	604.567i	1.33996	−	0.973537i
$622$	−138.759	−	125.517i	−0.223085	−	0.201796i
$623$	3.67611	+	1.87307i	0.00590066	+	0.00300654i
$624$	−153.297	+	86.6378i	−0.245668	+	0.138843i
$625$	31.7792	+	624.192i	0.0508467	+	0.998706i
$626$	−26.5965	+	40.7498i	−0.0424864	+	0.0650955i
$627$	300.673	−	619.103i	0.479542	−	0.987405i
$628$	75.8784	+	29.5276i	0.120825	+	0.0470185i
$629$	−866.768	−	629.744i	−1.37801	−	1.00118i
$630$	−1.43235	+	4.18285i	−0.00227357	+	0.00663944i
$631$	−944.582	+	306.913i	−1.49696	+	0.486392i	−0.939130	−	0.343563i	$-0.888366\pi$
$631$	−944.582	+	306.913i	−1.49696	+	0.486392i	−0.557831	+	0.829955i	$0.688366\pi$
$632$	−790.251	−	262.802i	−1.25040	−	0.415826i
$633$	34.1691	+	5.41185i	0.0539796	+	0.00854953i
$634$	69.1141	−	255.587i	0.109013	−	0.403135i
$635$	−275.060	−	163.782i	−0.433165	−	0.257925i
$636$	420.920	+	91.4924i	0.661824	+	0.143856i
$637$	140.849	−	140.849i	0.221113	−	0.221113i
$638$	−793.228	−	690.406i	−1.24330	−	1.08214i
$639$	94.2418			0.147483
$640$	−628.887	−	118.746i	−0.982637	−	0.185540i
$641$	−320.214	+	985.517i	−0.499554	+	1.53747i	0.310184	+	0.950677i	$0.399609\pi$
$641$	−320.214	+	985.517i	−0.499554	+	1.53747i	−0.809738	+	0.586792i	$0.800391\pi$
$642$	−181.783	+	104.396i	−0.283150	+	0.162611i
$643$	891.746	+	141.239i	1.38685	+	0.219656i	0.804825	−	0.593513i	$-0.202259\pi$
$643$	891.746	+	141.239i	1.38685	+	0.219656i	0.582028	+	0.813169i	$0.302259\pi$
$644$	32.1419	+	18.7545i	0.0499098	+	0.0291219i
$645$	−52.7041	+	63.3218i	−0.0817118	+	0.0981733i
$646$	−1082.27	+	872.300i	−1.67535	+	1.35031i
$647$	977.200	−	154.773i	1.51035	−	0.239217i	0.654353	−	0.756189i	$-0.272941\pi$
$647$	977.200	−	154.773i	1.51035	−	0.239217i	0.856002	+	0.516973i	$0.172941\pi$
$648$	409.252	−	293.052i	0.631562	−	0.452240i
$649$	407.294	+	123.776i	0.627572	+	0.190718i
$650$	−173.869	+	105.821i	−0.267491	+	0.162801i
$651$	14.6796	+	10.6653i	0.0225493	+	0.0163830i
$652$	509.966	−	623.873i	0.782157	−	0.956861i
$653$	1102.90	+	561.957i	1.68898	+	0.860578i	0.989261	+	0.146159i	$0.0466912\pi$
$653$	1102.90	+	561.957i	1.68898	+	0.860578i	0.699718	+	0.714419i	$0.253309\pi$
$654$	−88.0974	+	4.41410i	−0.134706	+	0.00674938i
$655$	−850.841	−	339.819i	−1.29899	−	0.518807i
$656$	−349.046	+	764.977i	−0.532083	+	1.16612i
$657$	7.63626	+	14.9870i	0.0116229	+	0.0228113i
$658$	1.86950	+	0.837507i	0.00284119	+	0.00127281i
$659$		−	208.811i		−	0.316860i	−0.987370	−	0.158430i	$-0.949357\pi$
$659$		−	208.811i		−	0.316860i	0.987370	−	0.158430i	$-0.0506433\pi$
$660$	−581.637	+	124.283i	−0.881267	+	0.188308i
$661$	109.752			0.166040			0.0830200	−	0.996548i	$-0.473543\pi$
$661$	109.752			0.166040			0.0830200	+	0.996548i	$0.473543\pi$
$662$	−270.600	+	604.039i	−0.408761	+	0.912446i
$663$	294.477	−	150.043i	0.444158	−	0.226310i
$664$	717.769	−	108.619i	1.08098	−	0.163582i
$665$	−27.8004	+	11.9317i	−0.0418051	+	0.0179424i
$666$	−6.03851	−	120.518i	−0.00906683	−	0.180958i
$667$	772.241	−	1515.61i	1.15778	−	2.27228i
$668$	10.3568	−	12.6702i	0.0155043	−	0.0189673i
$669$	200.040	−	275.331i	0.299013	−	0.411556i
$670$	−637.089	−	10.0412i	−0.950879	−	0.0149869i
$671$	−941.685	+	18.0168i	−1.40341	+	0.0268506i
$672$	19.4558	+	11.5327i	0.0289521	+	0.0171618i
$673$	142.691	+	900.918i	0.212023	+	1.33866i	0.832321	+	0.554294i	$0.187012\pi$
$673$	142.691	+	900.918i	0.212023	+	1.33866i	−0.620298	+	0.784366i	$0.712988\pi$
$674$	354.481	+	439.809i	0.525936	+	0.652536i
$675$	573.593	−	439.455i	0.849768	−	0.651044i
$676$	526.622	+	307.280i	0.779027	+	0.454556i
$677$	−69.4858	+	438.716i	−0.102638	+	0.648030i	0.881710	+	0.471792i	$0.156393\pi$
$677$	−69.4858	+	438.716i	−0.102638	+	0.648030i	−0.984348	+	0.176238i	$0.943607\pi$
$678$	41.5150	+	72.2891i	0.0612316	+	0.106621i
$679$	−35.5295	−	11.5442i	−0.0523263	−	0.0170018i
$680$	1169.66	+	273.612i	1.72008	+	0.402371i
$681$		−	801.836i		−	1.17744i
$682$	49.5742	−	562.617i	0.0726895	−	0.824951i
$683$	839.835	+	839.835i	1.22963	+	1.22963i	0.964105	+	0.265522i	$0.0855443\pi$
$683$	839.835	+	839.835i	1.22963	+	1.22963i	0.265522	+	0.964105i	$0.414456\pi$
$684$	−152.987	−	33.2537i	−0.223665	−	0.0486165i
$685$	−455.195	−	271.042i	−0.664518	−	0.395682i
$686$	−49.4300	−	13.3665i	−0.0720554	−	0.0194847i
$687$	−22.0517	+	139.229i	−0.0320986	+	0.202663i
$688$	−60.6700	−	76.3450i	−0.0881832	−	0.110967i
$689$	50.1074	+	154.215i	0.0727248	+	0.223824i
$690$	−423.201	−	863.975i	−0.613335	−	1.25214i
$691$	−68.3233	+	94.0389i	−0.0988759	+	0.136091i	−0.855588	−	0.517657i	$-0.826804\pi$
$691$	−68.3233	+	94.0389i	−0.0988759	+	0.136091i	0.756712	+	0.653748i	$0.226804\pi$
$692$	192.885	+	75.0602i	0.278736	+	0.108468i
$693$	−4.81722	−	0.668781i	−0.00695126	−	0.000965052i
$694$	404.859	+	264.243i	0.583371	+	0.380754i
$695$	1178.75	+	77.7008i	1.69605	+	0.111800i
$696$	475.679	−	917.881i	0.683447	−	1.31879i
$697$	716.490	−	1406.19i	1.02796	−	2.01749i
$698$	−743.199	+	821.603i	−1.06475	+	1.17708i
$699$	−51.5848	−	71.0004i	−0.0737980	−	0.101574i
$700$	22.9083	+	12.5971i	0.0327262	+	0.0179958i
$701$	−620.160	−	201.502i	−0.884678	−	0.287449i	−0.168780	−	0.985654i	$-0.553983\pi$
$701$	−620.160	−	201.502i	−0.884678	−	0.287449i	−0.715899	+	0.698204i	$0.753983\pi$
$702$	214.755	+	96.2067i	0.305919	+	0.137047i
$703$	583.842	−	583.842i	0.830501	−	0.830501i
$704$	−3.76495	−	703.990i	−0.00534795	−	0.999986i
$705$	−28.2432	−	44.7997i	−0.0400613	−	0.0635457i
$706$	429.635	−	163.790i	0.608548	−	0.231997i
$707$	−17.1632	−	33.6847i	−0.0242761	−	0.0476446i
$708$	−23.8216	+	417.808i	−0.0336463	+	0.590124i
$709$	666.474	+	917.322i	0.940019	+	1.29383i	0.955821	+	0.293950i	$0.0949700\pi$
$709$	666.474	+	917.322i	0.940019	+	1.29383i	−0.0158017	+	0.999875i	$0.505030\pi$
$710$	95.8373	−	548.955i	0.134982	−	0.773176i
$711$	54.4029	+	167.435i	0.0765160	+	0.235492i
$712$	120.338	−	38.1854i	0.169014	−	0.0536312i
$713$	902.331	−	142.915i	1.26554	−	0.200442i
$714$	−35.5488	−	23.2019i	−0.0497883	−	0.0324957i
$715$	−150.755	−	165.534i	−0.210846	−	0.231516i
$716$	1096.45	−	482.146i	1.53135	−	0.673389i
$717$	−680.787	+	107.826i	−0.949493	+	0.150385i
$718$	602.128	+	64.6849i	0.838619	+	0.0900905i
$719$	157.762	+	485.542i	0.219419	+	0.675302i	0.998810	+	0.0487648i	$0.0155285\pi$
$719$	157.762	+	485.542i	0.219419	+	0.675302i	−0.779391	+	0.626538i	$0.784472\pi$
$720$	58.6760	+	121.908i	0.0814944	+	0.169316i
$721$	−8.11274	−	11.1662i	−0.0112521	−	0.0154871i
$722$	−173.933	−	302.866i	−0.240905	−	0.419482i
$723$	67.6075	+	132.687i	0.0935097	+	0.183523i
$724$	−200.293	−	43.5363i	−0.276648	−	0.0601330i
$725$	515.267	−	1078.21i	0.710713	−	1.48719i
$726$	−256.269	−	601.964i	−0.352988	−	0.829151i
$727$	−687.504	+	687.504i	−0.945672	+	0.945672i	−0.998598	−	0.0529261i	$-0.983145\pi$
$727$	−687.504	+	687.504i	−0.945672	+	0.945672i	0.0529261	+	0.998598i	$0.483145\pi$
$728$	−0.0586700	+	8.51376i	−8.05906e−5	+	0.0116947i
$729$	−770.039	−	250.201i	−1.05629	−	0.343211i
$730$	95.0643	−	29.2402i	0.130225	−	0.0400551i
$731$	107.583	+	148.075i	0.147172	+	0.202565i
$732$	−235.536	−	895.468i	−0.321771	−	1.22332i
$733$	238.263	−	467.618i	0.325052	−	0.637951i	−0.669428	−	0.742877i	$-0.733461\pi$
$733$	238.263	−	467.618i	0.325052	−	0.637951i	0.994480	+	0.104926i	$0.0334606\pi$
$734$	−511.304	−	634.381i	−0.696599	−	0.864280i
$735$	435.926	+	497.452i	0.593096	+	0.676805i
$736$	1103.26	−	282.077i	1.49899	−	0.383256i
$737$	−122.865	−	690.032i	−0.166709	−	0.936271i
$738$	173.952	−	36.5572i	0.235707	−	0.0495355i
$739$	−555.216	+	764.189i	−0.751307	+	1.03408i	0.246581	+	0.969122i	$0.420693\pi$
$739$	−555.216	+	764.189i	−0.751307	+	1.03408i	−0.997888	+	0.0649628i	$0.979307\pi$
$740$	−708.153	−	87.3841i	−0.956963	−	0.118087i
$741$	78.7077	+	242.238i	0.106218	+	0.326906i
$742$	13.9717	−	15.4456i	0.0188298	−	0.0208162i
$743$	−47.8436	+	302.073i	−0.0643925	+	0.406558i	0.934347	+	0.356365i	$0.115984\pi$
$743$	−47.8436	+	302.073i	−0.0643925	+	0.406558i	−0.998740	+	0.0501937i	$0.984016\pi$
$744$	548.993	−	83.0780i	0.737894	−	0.111664i
$745$	−138.295	+	35.0675i	−0.185631	+	0.0470705i
$746$	−261.816	−	686.764i	−0.350959	−	0.920595i
$747$	−108.513	−	108.513i	−0.145266	−	0.145266i
$748$	−49.9668	+	1320.41i	−0.0668005	+	1.76525i
$749$			10.1357i			0.0135324i
$750$	−312.651	−	599.209i	−0.416868	−	0.798945i
$751$	−413.712	−	134.423i	−0.550882	−	0.178992i	0.0203325	−	0.999793i	$-0.493528\pi$
$751$	−413.712	−	134.423i	−0.550882	−	0.178992i	−0.571214	+	0.820801i	$0.693528\pi$
$752$	58.7261	−	21.9259i	0.0780933	−	0.0291568i
$753$	151.137	−	954.240i	0.200713	−	1.26725i
$754$	388.682	−	19.4748i	0.515493	−	0.0258286i
$755$	96.3408	−	115.749i	0.127604	−	0.153311i
$756$	−3.02128	−	30.0740i	−0.00399640	−	0.0397804i
$757$	−121.827	−	769.187i	−0.160934	−	1.01610i	−0.927470	−	0.373897i	$-0.878021\pi$
$757$	−121.827	−	769.187i	−0.160934	−	1.01610i	0.766536	−	0.642201i	$-0.221979\pi$
$758$	228.344	−	47.9880i	0.301245	−	0.0633087i
$759$	844.096	−	638.294i	1.11212	−	0.840967i
$760$	−349.279	+	857.327i	−0.459577	+	1.12806i
$761$	449.036	−	618.045i	0.590060	−	0.812148i	−0.404693	−	0.914453i	$-0.632622\pi$
$761$	449.036	−	618.045i	0.590060	−	0.812148i	0.994753	+	0.102304i	$0.0326216\pi$
$762$	344.205	+	36.9770i	0.451713	+	0.0485262i
$763$	−1.93626	+	3.80012i	−0.00253769	+	0.00498049i
$764$	82.7823	+	48.3028i	0.108354	+	0.0632236i
$765$	−100.153	−	233.351i	−0.130919	−	0.305035i
$766$	117.186	−	433.358i	0.152984	−	0.565742i
$767$	−140.365	+	71.5193i	−0.183005	+	0.0932455i
$768$	671.688	−	166.812i	0.874594	−	0.217204i
$769$	452.899			0.588946			0.294473	−

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:	\( N \)	\(=\)	\( 220 = 2^{2} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	220.w (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.82522 - 0.817668i) q^{2} +(-2.40882 + 1.22736i) q^{3} +(2.66284 + 2.98484i) q^{4} +(-4.64336 - 1.85452i) q^{5} +(5.40020 - 0.270575i) q^{6} +(0.118689 - 0.232940i) q^{7} +(-2.41965 - 7.62531i) q^{8} +(-0.994045 + 1.36819i) q^{9} +(6.95876 + 7.18162i) q^{10} +(-6.29422 + 9.02124i) q^{11} +(-10.0778 - 3.92171i) q^{12} +(-0.636813 - 4.02068i) q^{13} +(-0.407100 + 0.328118i) q^{14} +(13.4612 - 1.23185i) q^{15} +(-1.81859 + 15.8963i) q^{16} +(4.69785 - 29.6611i) q^{17} +(2.93307 - 1.68444i) q^{18} +(22.0109 + 7.15178i) q^{19} +(-6.82906 - 18.7980i) q^{20} +0.706783i q^{21} +(18.8647 - 11.3191i) q^{22} +(25.1629 + 25.1629i) q^{23} +(15.1875 + 15.3982i) q^{24} +(18.1215 + 17.2224i) q^{25} +(-2.12526 + 7.85931i) q^{26} +(4.52149 - 28.5476i) q^{27} +(1.01134 - 0.266013i) q^{28} +(-14.7711 - 45.4607i) q^{29} +(-25.5768 - 8.75838i) q^{30} +(15.0900 - 20.7696i) q^{31} +(16.3172 - 27.5272i) q^{32} +(4.08939 - 29.4558i) q^{33} +(-32.8275 + 50.2966i) q^{34} +(-0.983104 + 0.861511i) q^{35} +(-6.73080 + 0.676187i) q^{36} +(16.1966 - 31.7877i) q^{37} +(-34.3269 - 31.0512i) q^{38} +(6.46877 + 8.90350i) q^{39} +(-2.90599 + 39.8943i) q^{40} +(49.9808 + 16.2397i) q^{41} +(0.577914 - 1.29003i) q^{42} +(-4.30965 + 4.30965i) q^{43} +(-43.6875 + 5.23483i) q^{44} +(7.15303 - 4.50950i) q^{45} +(-25.3529 - 66.5028i) q^{46} +(-1.77867 - 3.49084i) q^{47} +(-15.1298 - 40.5235i) q^{48} +(28.7613 + 39.5865i) q^{49} +(-18.9935 - 46.2520i) q^{50} +(25.0884 + 77.2142i) q^{51} +(10.3054 - 12.6072i) q^{52} +(-39.3423 + 6.23122i) q^{53} +(-31.5951 + 48.4084i) q^{54} +(45.9564 - 30.2161i) q^{55} +(-2.06342 - 0.341406i) q^{56} +(-61.7982 + 9.78787i) q^{57} +(-10.2113 + 95.0535i) q^{58} +(-11.9586 - 36.8047i) q^{59} +(39.5218 + 36.8993i) q^{60} +(50.3282 + 69.2708i) q^{61} +(-44.5251 + 25.5704i) q^{62} +(0.200723 + 0.393940i) q^{63} +(-52.2906 + 36.9011i) q^{64} +(-4.49947 + 19.8504i) q^{65} +(-31.5491 + 50.4195i) q^{66} +(-45.0546 + 45.0546i) q^{67} +(101.043 - 64.9603i) q^{68} +(-91.4969 - 29.7292i) q^{69} +(2.49881 - 0.768592i) q^{70} +(-32.7548 - 45.0831i) q^{71} +(12.8381 + 4.26937i) q^{72} +(4.51537 - 8.86192i) q^{73} +(-55.5542 + 44.7760i) q^{74} +(-64.7895 - 19.2441i) q^{75} +(37.2646 + 84.7432i) q^{76} +(1.35435 + 2.53689i) q^{77} +(-4.52681 - 21.5401i) q^{78} +(61.1887 - 84.2190i) q^{79} +(37.9244 - 70.4396i) q^{80} +(19.4432 + 59.8399i) q^{81} +(-77.9471 - 70.5087i) q^{82} +(-14.1953 + 89.6254i) q^{83} +(-2.10964 + 1.88205i) q^{84} +(-76.8208 + 129.015i) q^{85} +(11.3899 - 4.34218i) q^{86} +(91.3773 + 91.3773i) q^{87} +(84.0195 + 26.1672i) q^{88} +15.7814i q^{89} +(-16.7431 + 2.38201i) q^{90} +(-1.01216 - 0.328870i) q^{91} +(-8.10262 + 142.112i) q^{92} +(-10.8574 + 68.5509i) q^{93} +(0.392115 + 7.82590i) q^{94} +(-88.9414 - 74.0279i) q^{95} +(-5.51958 + 86.3353i) q^{96} +(-22.3539 - 141.137i) q^{97} +(-20.1270 - 95.7712i) q^{98} +(-6.08599 - 17.5792i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 544 q - 10 q^{2} - 12 q^{5} - 20 q^{6} - 10 q^{8} - 28 q^{12} - 20 q^{13} - 36 q^{16} - 20 q^{17} - 10 q^{18} - 40 q^{20} + 86 q^{22} - 12 q^{25} + 140 q^{26} - 10 q^{28} - 370 q^{30} - 100 q^{33} - 476 q^{36}+ \cdots + 148 q^{97}+O(q^{100}) \) 544 * q - 10 * q^2 - 12 * q^5 - 20 * q^6 - 10 * q^8 - 28 * q^12 - 20 * q^13 - 36 * q^16 - 20 * q^17 - 10 * q^18 - 40 * q^20 + 86 * q^22 - 12 * q^25 + 140 * q^26 - 10 * q^28 - 370 * q^30 - 100 * q^33 - 476 * q^36 - 12 * q^37 + 6 * q^38 - 10 * q^40 + 40 * q^41 + 198 * q^42 - 232 * q^45 + 340 * q^46 - 42 * q^48 - 10 * q^50 + 510 * q^52 - 156 * q^53 + 216 * q^56 - 20 * q^57 + 238 * q^58 + 118 * q^60 - 40 * q^61 + 440 * q^62 - 348 * q^66 - 10 * q^68 - 106 * q^70 - 1060 * q^72 - 580 * q^73 + 132 * q^77 - 1076 * q^78 + 614 * q^80 + 624 * q^81 - 490 * q^82 - 20 * q^85 - 772 * q^86 + 446 * q^88 - 820 * q^90 - 244 * q^92 - 132 * q^93 - 1840 * q^96 + 148 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more