LMFDB - Embedded newform 220.3.w.a.7.9

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			7.9
Character	$\chi$	$=$	220.7
Dual form			220.3.w.a.63.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.88014 + 0.681953i) q^{2} +(1.94413 - 0.990585i) q^{3} +(3.06988 - 2.56434i) q^{4} +(-3.70748 + 3.35479i) q^{5} +(-2.97971 + 3.18825i) q^{6} +(1.57918 - 3.09932i) q^{7} +(-4.02306 + 6.91484i) q^{8} +(-2.49168 + 3.42950i) q^{9} +(4.68278 - 8.83581i) q^{10} +(-6.04402 + 9.19075i) q^{11} +(3.42806 - 8.02639i) q^{12} +(0.557233 + 3.51823i) q^{13} +(-0.855500 + 6.90410i) q^{14} +(-3.88462 + 10.1947i) q^{15} +(2.84833 - 15.7444i) q^{16} +(-1.87144 + 11.8158i) q^{17} +(2.34595 - 8.14716i) q^{18} +(3.77795 + 1.22753i) q^{19} +(-2.77869 + 19.8060i) q^{20} -7.58980i q^{21} +(5.09597 - 21.4017i) q^{22} +(27.4174 + 27.4174i) q^{23} +(-0.971620 + 17.4285i) q^{24} +(2.49076 - 24.8756i) q^{25} +(-3.44694 - 6.23477i) q^{26} +(-4.51893 + 28.5314i) q^{27} +(-3.09981 - 13.5641i) q^{28} +(-6.37004 - 19.6050i) q^{29} +(0.351317 - 21.8167i) q^{30} +(-33.6775 + 46.3530i) q^{31} +(5.38169 + 31.5442i) q^{32} +(-2.64616 + 23.8551i) q^{33} +(-4.53924 - 23.4916i) q^{34} +(4.54279 + 16.7885i) q^{35} +(1.14525 + 16.9177i) q^{36} +(-10.3741 + 20.3602i) q^{37} +(-7.94021 + 0.268451i) q^{38} +(4.56844 + 6.28792i) q^{39} +(-8.28245 - 39.1331i) q^{40} +(-66.3703 - 21.5650i) q^{41} +(5.17589 + 14.2699i) q^{42} +(3.10057 - 3.10057i) q^{43} +(5.01378 + 43.7134i) q^{44} +(-2.26742 - 21.0738i) q^{45} +(-70.2459 - 32.8512i) q^{46} +(17.8070 + 34.9482i) q^{47} +(-10.0587 - 33.4308i) q^{48} +(21.6895 + 29.8530i) q^{49} +(12.2810 + 48.4683i) q^{50} +(8.06622 + 24.8253i) q^{51} +(10.7326 + 9.37161i) q^{52} +(30.8259 - 4.88234i) q^{53} +(-10.9608 - 56.7248i) q^{54} +(-8.42498 - 54.3509i) q^{55} +(15.0782 + 23.3885i) q^{56} +(8.56081 - 1.35590i) q^{57} +(25.3462 + 32.5161i) q^{58} +(-26.3599 - 81.1273i) q^{59} +(14.2174 + 41.2581i) q^{60} +(8.24903 + 11.3538i) q^{61} +(31.7079 - 110.117i) q^{62} +(6.69431 + 13.1383i) q^{63} +(-31.6300 - 55.6376i) q^{64} +(-13.8689 - 11.1744i) q^{65} +(-11.2929 - 46.6556i) q^{66} +(39.5762 - 39.5762i) q^{67} +(24.5546 + 41.0721i) q^{68} +(80.4622 + 26.1438i) q^{69} +(-19.9901 - 28.4668i) q^{70} +(38.5603 + 53.0737i) q^{71} +(-13.6903 - 31.0266i) q^{72} +(54.8494 - 107.648i) q^{73} +(5.62000 - 45.3548i) q^{74} +(-19.7990 - 50.8288i) q^{75} +(14.7457 - 5.91958i) q^{76} +(18.9405 + 33.2462i) q^{77} +(-12.8774 - 8.70672i) q^{78} +(32.9819 - 45.3957i) q^{79} +(42.2591 + 67.9276i) q^{80} +(7.68780 + 23.6606i) q^{81} +(139.492 - 4.71609i) q^{82} +(14.8404 - 93.6988i) q^{83} +(-19.4628 - 23.2998i) q^{84} +(-32.7012 - 50.0851i) q^{85} +(-3.71507 + 7.94396i) q^{86} +(-31.8046 - 31.8046i) q^{87} +(-39.2371 - 78.7683i) q^{88} -6.98261i q^{89} +(18.6344 + 38.0756i) q^{90} +(11.7841 + 3.82889i) q^{91} +(154.475 + 13.8606i) q^{92} +(-19.5568 + 123.477i) q^{93} +(-57.3127 - 53.5641i) q^{94} +(-18.1248 + 8.12320i) q^{95} +(41.7099 + 55.9951i) q^{96} +(7.72602 + 48.7802i) q^{97} +(-61.1378 - 41.3368i) q^{98} +(-16.4599 - 43.6283i) 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 $

$2$	−1.88014	+	0.681953i	−0.940072	+	0.340976i
$2$	−1.88014	+	0.681953i	−0.940072	+	0.340976i
$3$	1.94413	−	0.990585i	0.648044	−	0.330195i	−0.0988849	−	0.995099i	$-0.531528\pi$
$3$	1.94413	−	0.990585i	0.648044	−	0.330195i	0.746929	+	0.664904i	$0.231528\pi$
$4$	3.06988	−	2.56434i	0.767470	−	0.641085i
$5$	−3.70748	+	3.35479i	−0.741495	+	0.670958i
$5$	−3.70748	+	3.35479i	−0.741495	+	0.670958i
$6$	−2.97971	+	3.18825i	−0.496619	+	0.531375i
$7$	1.57918	−	3.09932i	0.225598	−	0.442760i	−0.750268	−	0.661134i	$-0.770075\pi$
$7$	1.57918	−	3.09932i	0.225598	−	0.442760i	0.975865	+	0.218374i	$0.0700753\pi$
$8$	−4.02306	+	6.91484i	−0.502882	+	0.864355i
$9$	−2.49168	+	3.42950i	−0.276853	+	0.381055i
$10$	4.68278	−	8.83581i	0.468278	−	0.883581i
$11$	−6.04402	+	9.19075i	−0.549456	+	0.835523i
$11$	−6.04402	+	9.19075i	−0.549456	+	0.835523i
$12$	3.42806	−	8.02639i	0.285671	−	0.668866i
$13$	0.557233	+	3.51823i	0.0428641	+	0.270633i	0.999807	−	0.0196429i	$-0.00625292\pi$
$13$	0.557233	+	3.51823i	0.0428641	+	0.270633i	−0.956943	+	0.290276i	$0.906253\pi$
$14$	−0.855500	+	6.90410i	−0.0611071	+	0.493150i
$15$	−3.88462	+	10.1947i	−0.258974	+	0.679648i
$16$	2.84833	−	15.7444i	0.178021	−	0.984027i
$17$	−1.87144	+	11.8158i	−0.110085	+	0.695047i	0.869488	+	0.493955i	$0.164449\pi$
$17$	−1.87144	+	11.8158i	−0.110085	+	0.695047i	−0.979572	+	0.201092i	$0.935551\pi$
$18$	2.34595	−	8.14716i	0.130331	−	0.452620i
$19$	3.77795	+	1.22753i	0.198840	+	0.0646069i	0.406744	−	0.913542i	$-0.366664\pi$
$19$	3.77795	+	1.22753i	0.198840	+	0.0646069i	−0.207904	+	0.978149i	$0.566664\pi$
$20$	−2.77869	+	19.8060i	−0.138934	+	0.990302i
$21$		−	7.58980i		−	0.361419i
$22$	5.09597	−	21.4017i	0.231635	−	0.972803i
$23$	27.4174	+	27.4174i	1.19206	+	1.19206i	0.976488	+	0.215571i	$0.0691614\pi$
$23$	27.4174	+	27.4174i	1.19206	+	1.19206i	0.215571	+	0.976488i	$0.430839\pi$
$24$	−0.971620	+	17.4285i	−0.0404842	+	0.726189i
$25$	2.49076	−	24.8756i	0.0996302	−	0.995025i
$26$	−3.44694	−	6.23477i	−0.132575	−	0.239799i
$27$	−4.51893	+	28.5314i	−0.167368	+	1.05672i
$28$	−3.09981	−	13.5641i	−0.110707	−	0.484432i
$29$	−6.37004	−	19.6050i	−0.219656	−	0.676033i	−0.998790	−	0.0491753i	$-0.984341\pi$
$29$	−6.37004	−	19.6050i	−0.219656	−	0.676033i	0.779134	−	0.626858i	$-0.215659\pi$
$30$	0.351317	−	21.8167i	0.0117106	−	0.727222i
$31$	−33.6775	+	46.3530i	−1.08637	+	1.49526i	−0.234059	+	0.972222i	$0.575201\pi$
$31$	−33.6775	+	46.3530i	−1.08637	+	1.49526i	−0.852310	+	0.523037i	$0.824799\pi$
$32$	5.38169	+	31.5442i	0.168178	+	0.985757i
$33$	−2.64616	+	23.8551i	−0.0801865	+	0.722883i
$34$	−4.53924	−	23.4916i	−0.133507	−	0.690930i
$35$	4.54279	+	16.7885i	0.129794	+	0.479671i
$36$	1.14525	+	16.9177i	0.0318124	+	0.469935i
$37$	−10.3741	+	20.3602i	−0.280380	+	0.550277i	−0.987652	−	0.156665i	$-0.949926\pi$
$37$	−10.3741	+	20.3602i	−0.280380	+	0.550277i	0.707272	+	0.706942i	$0.249926\pi$
$38$	−7.94021	+	0.268451i	−0.208953	+	0.00706450i
$39$	4.56844	+	6.28792i	0.117139	+	0.161229i
$40$	−8.28245	−	39.1331i	−0.207061	−	0.978328i
$41$	−66.3703	−	21.5650i	−1.61879	−	0.525976i	−0.647132	−	0.762378i	$-0.724032\pi$
$41$	−66.3703	−	21.5650i	−1.61879	−	0.525976i	−0.971655	+	0.236402i	$0.924032\pi$
$42$	5.17589	+	14.2699i	0.123235	+	0.339760i
$43$	3.10057	−	3.10057i	0.0721063	−	0.0721063i	−0.670134	−	0.742240i	$-0.733763\pi$
$43$	3.10057	−	3.10057i	0.0721063	−	0.0721063i	0.742240	+	0.670134i	$0.233763\pi$
$44$	5.01378	+	43.7134i	0.113950	+	0.993487i
$45$	−2.26742	−	21.0738i	−0.0503871	−	0.468308i
$46$	−70.2459	−	32.8512i	−1.52709	−	0.714157i
$47$	17.8070	+	34.9482i	0.378872	+	0.743578i	0.999168	−	0.0407899i	$-0.0129874\pi$
$47$	17.8070	+	34.9482i	0.378872	+	0.743578i	−0.620296	+	0.784368i	$0.712987\pi$
$48$	−10.0587	−	33.4308i	−0.209555	−	0.696474i
$49$	21.6895	+	29.8530i	0.442643	+	0.609246i
$50$	12.2810	+	48.4683i	0.245620	+	0.969366i
$51$	8.06622	+	24.8253i	0.158161	+	0.486770i
$52$	10.7326	+	9.37161i	0.206396	+	0.180223i
$53$	30.8259	−	4.88234i	0.581620	−	0.0921196i	0.141310	−	0.989965i	$-0.454868\pi$
$53$	30.8259	−	4.88234i	0.581620	−	0.0921196i	0.440310	+	0.897846i	$0.354868\pi$
$54$	−10.9608	−	56.7248i	−0.202978	−	1.05046i
$55$	−8.42498	−	54.3509i	−0.153182	−	0.988198i
$56$	15.0782	+	23.3885i	0.269253	+	0.417653i
$57$	8.56081	−	1.35590i	0.150190	−	0.0237877i
$58$	25.3462	+	32.5161i	0.437004	+	0.560622i
$59$	−26.3599	−	81.1273i	−0.446777	−	1.37504i	−0.880523	−	0.474004i	$-0.842808\pi$
$59$	−26.3599	−	81.1273i	−0.446777	−	1.37504i	0.433745	−	0.901036i	$-0.357192\pi$
$60$	14.2174	+	41.2581i	0.236957	+	0.687634i
$61$	8.24903	+	11.3538i	0.135230	+	0.186128i	0.871261	−	0.490819i	$-0.163302\pi$
$61$	8.24903	+	11.3538i	0.135230	+	0.186128i	−0.736031	+	0.676947i	$0.763302\pi$
$62$	31.7079	−	110.117i	0.511417	−	1.77608i
$63$	6.69431	+	13.1383i	0.106259	+	0.208545i
$64$	−31.6300	−	55.6376i	−0.494219	−	0.869337i
$65$	−13.8689	−	11.1744i	−0.213367	−	0.171913i
$66$	−11.2929	−	46.6556i	−0.171105	−	0.706904i
$67$	39.5762	−	39.5762i	0.590690	−	0.590690i	−0.347128	−	0.937818i	$-0.612843\pi$
$67$	39.5762	−	39.5762i	0.590690	−	0.590690i	0.937818	+	0.347128i	$0.112843\pi$
$68$	24.5546	+	41.0721i	0.361097	+	0.604001i
$69$	80.4622	+	26.1438i	1.16612	+	0.378895i
$70$	−19.9901	−	28.4668i	−0.285572	−	0.406669i
$71$	38.5603	+	53.0737i	0.543102	+	0.747516i	0.989056	−	0.147540i	$-0.0471354\pi$
$71$	38.5603	+	53.0737i	0.543102	+	0.747516i	−0.445954	+	0.895056i	$0.647135\pi$
$72$	−13.6903	−	31.0266i	−0.190143	−	0.430925i
$73$	54.8494	−	107.648i	0.751362	−	1.47463i	−0.124578	−	0.992210i	$-0.539758\pi$
$73$	54.8494	−	107.648i	0.751362	−	1.47463i	0.875940	−	0.482421i	$-0.160242\pi$
$74$	5.62000	−	45.3548i	0.0759459	−	0.612903i
$75$	−19.7990	−	50.8288i	−0.263987	−	0.677717i
$76$	14.7457	−	5.91958i	0.194022	−	0.0778892i
$77$	18.9405	+	33.2462i	0.245980	+	0.431769i
$78$	−12.8774	−	8.70672i	−0.165095	−	0.111625i
$79$	32.9819	−	45.3957i	0.417492	−	0.574629i	−0.547533	−	0.836784i	$-0.684433\pi$
$79$	32.9819	−	45.3957i	0.417492	−	0.574629i	0.965026	+	0.262155i	$0.0844331\pi$
$80$	42.2591	+	67.9276i	0.528239	+	0.849096i
$81$	7.68780	+	23.6606i	0.0949111	+	0.292106i
$82$	139.492	−	4.71609i	1.70112	−	0.0575133i
$83$	14.8404	−	93.6988i	0.178800	−	1.12890i	−0.721108	−	0.692822i	$-0.756367\pi$
$83$	14.8404	−	93.6988i	0.178800	−	1.12890i	0.899909	−	0.436079i	$-0.143633\pi$
$84$	−19.4628	−	23.2998i	−0.231700	−	0.277378i
$85$	−32.7012	−	50.0851i	−0.384720	−	0.589236i
$86$	−3.71507	+	7.94396i	−0.0431985	+	0.0923716i
$87$	−31.8046	−	31.8046i	−0.365570	−	0.365570i
$88$	−39.2371	−	78.7683i	−0.445876	−	0.895095i
$89$		−	6.98261i		−	0.0784563i	−0.999230	−	0.0392281i	$-0.987510\pi$
$89$		−	6.98261i		−	0.0784563i	0.999230	−	0.0392281i	$-0.0124899\pi$
$90$	18.6344	+	38.0756i	0.207049	+	0.423062i
$91$	11.7841	+	3.82889i	0.129496	+	0.0420757i
$92$	154.475	+	13.8606i	1.67908	+	0.150659i
$93$	−19.5568	+	123.477i	−0.210288	+	1.32771i
$94$	−57.3127	−	53.5641i	−0.609709	−	0.569830i
$95$	−18.1248	+	8.12320i	−0.190787	+	0.0855073i
$96$	41.7099	+	55.9951i	0.434478	+	0.583282i
$97$	7.72602	+	48.7802i	0.0796497	+	0.502889i	0.994971	+	0.100164i	$0.0319368\pi$
$97$	7.72602	+	48.7802i	0.0796497	+	0.502889i	−0.915321	+	0.402725i	$0.868063\pi$
$98$	−61.1378	−	41.3368i	−0.623855	−	0.421804i
$99$	−16.4599	−	43.6283i	−0.166262	−	0.440690i
$100$	−56.1432	−	82.7523i	−0.561432	−	0.827523i
$101$	−4.59972	+	6.33098i	−0.0455418	+	0.0626830i	−0.831181	−	0.556003i	$-0.812334\pi$
$101$	−4.59972	+	6.33098i	−0.0455418	+	0.0626830i	0.785639	+	0.618685i	$0.212334\pi$
$102$	−32.0953	−	41.1743i	−0.314660	−	0.403670i
$103$	−66.9723	+	131.440i	−0.650216	+	1.27612i	0.296801	+	0.954939i	$0.404080\pi$
$103$	−66.9723	+	131.440i	−0.650216	+	1.27612i	−0.947018	+	0.321182i	$0.895920\pi$
$104$	−26.5698	−	10.3009i	−0.255479	−	0.0990468i
$105$	25.4622	+	28.1390i	0.242497	+	0.267991i
$106$	−54.6276	+	30.2013i	−0.515354	+	0.284918i
$107$	13.8933	−	7.07899i	0.129844	−	0.0661588i	−0.387862	−	0.921718i	$-0.626786\pi$
$107$	13.8933	−	7.07899i	0.129844	−	0.0661588i	0.517706	+	0.855559i	$0.326786\pi$
$108$	59.2916	+	99.1760i	0.548996	+	0.918297i
$109$	−180.398			−1.65503			−0.827515	−	0.561443i	$-0.810246\pi$
$109$	−180.398			−1.65503			−0.827515	+	0.561443i	$0.810246\pi$
$110$	52.9049	+	96.4420i	0.480954	+	0.876746i
$111$			49.8594i			0.449184i
$112$	−44.2990	−	33.6912i	−0.395527	−	0.300815i
$113$	−26.7276	−	52.4558i	−0.236527	−	0.464211i	0.741980	−	0.670422i	$-0.233887\pi$
$113$	−26.7276	−	52.4558i	−0.236527	−	0.464211i	−0.978508	+	0.206211i	$0.933887\pi$
$114$	−15.1709	+	8.38736i	−0.133078	+	0.0735733i
$115$	−193.629	−	9.66969i	−1.68373	−	0.0840843i
$116$	−69.8290	−	43.8499i	−0.601974	−	0.378017i
$117$	−13.4542	−	6.85526i	−0.114993	−	0.0585920i
$118$	104.885	+	134.555i	0.888859	+	1.14030i
$119$	33.6656	+	24.4595i	0.282904	+	0.205542i
$120$	−54.8668	−	67.8755i	−0.457224	−	0.565629i
$121$	−47.9397	−	111.098i	−0.396196	−	0.918166i
$122$	−23.2521	−	15.7214i	−0.190591	−	0.128864i
$123$	−150.395	+	23.8202i	−1.22272	+	0.193660i
$124$	15.4792	+	228.659i	0.124832	+	1.84402i
$125$	74.2181	+	100.582i	0.593745	+	0.804654i
$126$	−21.5460	−	20.1367i	−0.171000	−	0.159815i
$127$	186.451	+	29.5310i	1.46812	+	0.232528i	0.838724	−	0.544556i	$-0.183302\pi$
$127$	186.451	+	29.5310i	1.46812	+	0.232528i	0.629397	+	0.777084i	$0.283302\pi$
$128$	97.4112	+	83.0365i	0.761025	+	0.648723i
$129$	2.95654	−	9.09929i	0.0229189	−	0.0705371i
$130$	33.6958	+	11.5515i	0.259199	+	0.0888576i
$131$	63.9787			0.488387			0.244193	−	0.969727i	$-0.421477\pi$
$131$	63.9787			0.488387			0.244193	+	0.969727i	$0.421477\pi$
$132$	53.0493	+	80.0181i	0.401888	+	0.606197i
$133$	9.77059	−	9.77059i	0.0734631	−	0.0734631i
$134$	−47.4199	+	101.398i	−0.353880	+	0.756702i
$135$	−78.9630	−	120.940i	−0.584911	−	0.895848i
$136$	−74.1754	−	60.4763i	−0.545408	−	0.444679i
$137$	−48.0255	−	7.60649i	−0.350551	−	0.0555218i	−0.0213240	−	0.999773i	$-0.506788\pi$
$137$	−48.0255	−	7.60649i	−0.350551	−	0.0555218i	−0.329227	+	0.944251i	$0.606788\pi$
$138$	−169.109	+	5.71742i	−1.22543	+	0.0414306i
$139$	115.416	−	37.5009i	0.830330	−	0.269790i	0.137145	−	0.990551i	$-0.456207\pi$
$139$	115.416	−	37.5009i	0.830330	−	0.269790i	0.693184	+	0.720760i	$0.256207\pi$
$140$	56.9972	+	39.8894i	0.407123	+	0.284924i
$141$	69.2382	+	50.3045i	0.491051	+	0.356770i
$142$	−108.693	−	73.4898i	−0.765441	−	0.517534i
$143$	−35.7031	−	16.1429i	−0.249672	−	0.112887i
$144$	46.8984	+	48.9984i	0.325683	+	0.340266i
$145$	89.3873	+	51.3148i	0.616464	+	0.353895i
$146$	−29.7139	+	239.798i	−0.203520	+	1.64246i
$147$	71.7392	+	36.5530i	0.488022	+	0.248660i
$148$	20.3634	+	89.1061i	0.137591	+	0.602068i
$149$	−91.0686	+	66.1652i	−0.611199	+	0.444062i	−0.849836	−	0.527047i	$-0.823299\pi$
$149$	−91.0686	+	66.1652i	−0.611199	+	0.444062i	0.238637	+	0.971109i	$0.423299\pi$
$150$	71.8879	+	82.0634i	0.479253	+	0.547089i
$151$	23.3079	−	71.7345i	0.154357	−	0.475063i	−0.843738	−	0.536755i	$-0.819650\pi$
$151$	23.3079	−	71.7345i	0.154357	−	0.475063i	0.998095	+	0.0616926i	$0.0196498\pi$
$152$	−23.6871	+	21.1855i	−0.155836	+	0.139378i
$153$	−35.8592	−	35.8592i	−0.234374	−	0.234374i
$154$	−58.2832	−	49.5912i	−0.378462	−	0.322021i
$155$	−30.6464	−	284.834i	−0.197719	−	1.83764i
$156$	30.1489	+	7.58812i	0.193262	+	0.0486418i
$157$	157.719	−	80.3619i	1.00458	−	0.511860i	0.127314	−	0.991862i	$-0.459364\pi$
$157$	157.719	−	80.3619i	1.00458	−	0.511860i	0.877267	+	0.480003i	$0.159364\pi$
$158$	−31.0530	+	107.843i	−0.196538	+	0.682548i
$159$	55.0932	−	40.0276i	0.346498	−	0.251746i
$160$	−125.777	−	98.8950i	−0.786105	−	0.618094i
$161$	128.272	−	41.6782i	0.796722	−	0.258871i
$162$	−30.5896	−	39.2426i	−0.188825	−	0.242238i
$163$	5.58571	+	35.2668i	0.0342681	+	0.216361i	0.998880	−	0.0473130i	$-0.0150658\pi$
$163$	5.58571	+	35.2668i	0.0342681	+	0.216361i	−0.964612	+	0.263674i	$0.915066\pi$
$164$	−259.049	+	103.994i	−1.57957	+	0.634109i
$165$	−70.2184	−	97.3196i	−0.425566	−	0.589816i
$166$	35.9960	+	186.288i	0.216844	+	1.12221i
$167$	22.2971	+	140.778i	0.133515	+	0.842983i	0.959995	+	0.280017i	$0.0903400\pi$
$167$	22.2971	+	140.778i	0.133515	+	0.842983i	−0.826480	+	0.562967i	$0.809660\pi$
$168$	52.4823	+	30.5342i	0.312394	+	0.181751i
$169$	148.661	−	48.3029i	0.879652	−	0.285816i
$170$	95.6386	+	71.8664i	0.562580	+	0.422744i
$171$	−13.6233	+	9.89787i	−0.0796681	+	0.0578823i
$172$	1.56747	−	17.4693i	0.00911317	−	0.101566i
$173$	4.39809	−	2.24094i	0.0254225	−	0.0129534i	−0.441233	−	0.897393i	$-0.645459\pi$
$173$	4.39809	−	2.24094i	0.0254225	−	0.0129534i	0.466656	+	0.884439i	$0.345459\pi$
$174$	81.4864	+	38.1079i	0.468312	+	0.219011i
$175$	−73.1642	−	47.0028i	−0.418081	−	0.268587i
$176$	127.488	+	121.338i	0.724362	+	0.689420i
$177$	−131.611	−	131.611i	−0.743562	−	0.743562i
$178$	4.76181	+	13.1283i	0.0267517	+	0.0737545i
$179$	−36.8391	+	113.379i	−0.205805	+	0.633403i	0.793874	+	0.608082i	$0.208061\pi$
$179$	−36.8391	+	113.379i	−0.205805	+	0.633403i	−0.999679	+	0.0253208i	$0.991939\pi$
$180$	−61.0012	−	58.8797i	−0.338895	−	0.327110i
$181$	−213.562	+	155.162i	−1.17990	+	0.857248i	−0.992160	−	0.124971i	$-0.960116\pi$
$181$	−213.562	+	155.162i	−1.17990	+	0.857248i	−0.187740	+	0.982219i	$0.560116\pi$
$182$	−24.7669	+	0.837345i	−0.136082	+	0.00460080i
$183$	27.2841	+	13.9020i	0.149094	+	0.0759670i
$184$	−299.888	+	79.2851i	−1.62983	+	0.430897i
$185$	−29.8428	−	110.288i	−0.161312	−	0.596151i
$186$	−47.4358	−	245.491i	−0.255031	−	1.31984i
$187$	−97.2850	−	88.6148i	−0.520241	−	0.473876i
$188$	144.284	+	61.6236i	0.767469	+	0.327785i
$189$	81.2917	+	59.0619i	0.430115	+	0.312497i
$190$	28.5375	−	27.6330i	0.150198	−	0.145437i
$191$	35.4160	−	11.5074i	0.185424	−	0.0602480i	−0.214833	−	0.976651i	$-0.568921\pi$
$191$	35.4160	−	11.5074i	0.185424	−	0.0602480i	0.400257	+	0.916403i	$0.368921\pi$
$192$	−116.607	−	76.8346i	−0.607326	−	0.400180i
$193$	−224.593	−	35.5721i	−1.16370	−	0.184311i	−0.455440	−	0.890267i	$-0.650518\pi$
$193$	−224.593	−	35.5721i	−1.16370	−	0.184311i	−0.708256	+	0.705955i	$0.750518\pi$
$194$	−47.7918	−	86.4450i	−0.246350	−	0.445593i
$195$	−38.0320	−	7.98614i	−0.195036	−	0.0409546i
$196$	143.137	+	36.0260i	0.730293	+	0.183806i
$197$	−23.5094	+	23.5094i	−0.119337	+	0.119337i	−0.764253	−	0.644916i	$-0.776892\pi$
$197$	−23.5094	+	23.5094i	−0.119337	+	0.119337i	0.644916	+	0.764253i	$0.276892\pi$
$198$	60.6995	+	70.8026i	0.306563	+	0.357589i
$199$	250.493			1.25876			0.629379	−	0.777098i	$-0.283309\pi$
$199$	250.493			1.25876			0.629379	+	0.777098i	$0.283309\pi$
$200$	161.990	+	117.299i	0.809952	+	0.586496i
$201$	37.7378	−	116.145i	0.187750	−	0.577836i
$202$	4.33071	−	15.0399i	0.0214392	−	0.0744552i
$203$	−70.8215	−	11.2170i	−0.348875	−	0.0552563i
$204$	88.4228	+	55.5261i	0.433445	+	0.272187i
$205$	318.412	−	142.707i	1.55323	−	0.696130i
$206$	36.2813	−	292.799i	0.176123	−	1.42135i
$207$	−162.343	+	25.7126i	−0.784266	+	0.124216i
$208$	56.9797	+	1.24777i	0.273941	+	0.00599889i
$209$	−34.1159	+	27.3030i	−0.163234	+	0.130636i
$210$	−67.0621	−	35.5414i	−0.319343	−	0.169245i
$211$	71.3005	+	51.8028i	0.337917	+	0.245511i	0.743782	−	0.668422i	$-0.233030\pi$
$211$	71.3005	+	51.8028i	0.337917	+	0.245511i	−0.405866	+	0.913933i	$0.633030\pi$
$212$	82.1118	−	94.0362i	0.387320	−	0.443567i
$213$	127.540	+	64.9850i	0.598780	+	0.305094i
$214$	−21.2939	+	22.7841i	−0.0995041	+	0.106468i
$215$	−1.09352	+	21.8970i	−0.00508616	+	0.101847i
$216$	−179.110	−	146.031i	−0.829213	−	0.676070i
$217$	90.4801	+	177.577i	0.416959	+	0.818328i
$218$	339.175	−	123.023i	1.55585	−	0.564326i
$219$		−	263.615i		−	1.20372i
$220$	−165.238	−	145.246i	−0.751081	−	0.660210i
$221$	−42.6135			−0.192821
$222$	−34.0018	−	93.7428i	−0.153161	−	0.422265i
$223$	84.0151	−	42.8079i	0.376750	−	0.191963i	−0.255354	−	0.966848i	$-0.582192\pi$
$223$	84.0151	−	42.8079i	0.376750	−	0.191963i	0.632103	+	0.774884i	$0.282192\pi$
$224$	106.264	+	33.1345i	0.474394	+	0.147922i
$225$	79.1047	+	70.5240i	0.351577	+	0.313440i
$226$	86.0241	+	80.3976i	0.380638	+	0.355741i
$227$	−137.275	+	269.416i	−0.604734	+	1.18686i	0.362265	+	0.932075i	$0.382004\pi$
$227$	−137.275	+	269.416i	−0.604734	+	1.18686i	−0.966999	+	0.254781i	$0.917996\pi$
$228$	22.8037	−	26.1153i	0.100016	−	0.114541i
$229$	148.072	−	203.804i	0.646604	−	0.889973i	−0.352343	−	0.935871i	$-0.614615\pi$
$229$	148.072	−	203.804i	0.646604	−	0.889973i	0.998946	+	0.0458977i	$0.0146148\pi$
$230$	370.644	−	113.865i	1.61150	−	0.495067i
$231$	69.7560	+	45.8729i	0.301974	+	0.198584i
$232$	161.192	+	34.8241i	0.694794	+	0.150104i
$233$	34.1396	+	215.549i	0.146522	+	0.925104i	0.945943	+	0.324333i	$0.105140\pi$
$233$	34.1396	+	215.549i	0.146522	+	0.925104i	−0.799421	+	0.600771i	$0.794860\pi$
$234$	29.9708	+	3.71374i	0.128080	+	0.0158707i
$235$	−183.263	−	69.8308i	−0.779842	−	0.297152i
$236$	−288.960	−	181.456i	−1.22441	−	0.768880i
$237$	19.1529	−	120.927i	0.0808139	−	0.510239i
$238$	−79.9764	−	23.0290i	−0.336035	−	0.0967605i
$239$	129.224	+	41.9874i	0.540686	+	0.175680i	0.566613	−	0.823984i	$-0.308254\pi$
$239$	129.224	+	41.9874i	0.540686	+	0.175680i	−0.0259265	+	0.999664i	$0.508254\pi$
$240$	149.445	+	90.1990i	0.622689	+	0.375829i
$241$			361.662i			1.50067i	0.661056	+	0.750337i	$0.270109\pi$
$241$			361.662i			1.50067i	−0.661056	+	0.750337i	$0.729891\pi$
$242$	165.897	+	176.188i	0.685525	+	0.728049i
$243$	−145.452	−	145.452i	−0.598568	−	0.598568i
$244$	54.4386	+	13.7016i	0.223109	+	0.0561539i
$245$	−180.564	−	37.9157i	−0.736996	−	0.154758i
$246$	266.519	−	147.347i	1.08341	−	0.598973i
$247$	−2.21354	+	13.9757i	−0.00896169	+	0.0565819i
$248$	−185.037	−	419.355i	−0.746119	−	1.69095i
$249$	−63.9648	−	196.864i	−0.256887	−	0.790616i
$250$	−208.133	−	138.495i	−0.832530	−	0.553979i
$251$	92.2195	−	126.929i	0.367408	−	0.505694i	−0.584786	−	0.811188i	$-0.698821\pi$
$251$	92.2195	−	126.929i	0.367408	−	0.505694i	0.952194	+	0.305494i	$0.0988215\pi$
$252$	54.2418	+	23.1666i	0.215245	+	0.0919309i
$253$	−417.697	+	86.2750i	−1.65098	+	0.341008i
$254$	−370.694	+	71.6286i	−1.45943	+	0.282002i
$255$	−113.189	−	64.9786i	−0.443878	−	0.254818i
$256$	−239.774	−	89.6907i	−0.936617	−	0.350354i
$257$	−76.3507	+	149.847i	−0.297084	+	0.583061i	−0.990506	−	0.137471i	$-0.956103\pi$
$257$	−76.3507	+	149.847i	−0.297084	+	0.583061i	0.693421	+	0.720532i	$0.256103\pi$
$258$	0.646571	+	19.1242i	0.00250609	+	0.0741248i
$259$	46.7204	+	64.3051i	0.180388	+	0.248282i
$260$	−71.2305	+	1.26052i	−0.273964	+	0.00484814i
$261$	83.1073	+	27.0032i	0.318419	+	0.103460i
$262$	−120.289	+	43.6305i	−0.459119	+	0.166528i
$263$	−14.7959	+	14.7959i	−0.0562583	+	0.0562583i	−0.734676	−	0.678418i	$-0.762666\pi$
$263$	−14.7959	+	14.7959i	−0.0562583	+	0.0562583i	0.678418	+	0.734676i	$0.262666\pi$
$264$	−154.309	−	114.268i	−0.584503	−	0.432835i
$265$	−97.9070	+	121.516i	−0.369460	+	0.458549i
$266$	−11.7070	+	25.0332i	−0.0440114	+	0.0941098i
$267$	−6.91687	−	13.5751i	−0.0259059	−	0.0508431i
$268$	20.0074	−	222.981i	0.0746545	−	0.832019i
$269$	51.4570	+	70.8245i	0.191290	+	0.263288i	0.893880	−	0.448307i	$-0.147973\pi$
$269$	51.4570	+	70.8245i	0.191290	+	0.263288i	−0.702589	+	0.711595i	$0.747973\pi$
$270$	230.937	+	173.535i	0.855322	+	0.642721i
$271$	110.965	+	341.514i	0.409464	+	1.26020i	0.917110	+	0.398634i	$0.130516\pi$
$271$	110.965	+	341.514i	0.409464	+	1.26020i	−0.507647	+	0.861565i	$0.669484\pi$
$272$	180.702	+	63.1200i	0.664347	+	0.232059i
$273$	26.7027	−	4.22929i	0.0978120	−	0.0154919i
$274$	95.4821	−	18.4498i	0.348475	−	0.0673352i
$275$	213.571	+	173.241i	0.776623	+	0.629966i
$276$	314.051	−	126.074i	1.13787	−	0.456790i
$277$	−220.021	+	34.8479i	−0.794301	+	0.125805i	−0.540381	−	0.841420i	$-0.681720\pi$
$277$	−220.021	+	34.8479i	−0.794301	+	0.125805i	−0.253920	+	0.967225i	$0.581720\pi$
$278$	−191.424	+	149.215i	−0.688577	+	0.536745i
$279$	−75.0544	−	230.994i	−0.269012	−	0.827934i
$280$	−134.366	−	36.1284i	−0.479877	−	0.129030i
$281$	211.184	+	290.669i	0.751543	+	1.03441i	0.997871	+	0.0652239i	$0.0207762\pi$
$281$	211.184	+	290.669i	0.751543	+	1.03441i	−0.246327	+	0.969187i	$0.579224\pi$
$282$	−164.483	−	47.3625i	−0.583274	−	0.167952i
$283$	−64.8838	−	127.342i	−0.229271	−	0.449970i	0.747498	−	0.664264i	$-0.231255\pi$
$283$	−64.8838	−	127.342i	−0.229271	−	0.449970i	−0.976769	+	0.214294i	$0.931255\pi$
$284$	254.474	+	64.0482i	0.896036	+	0.225522i
$285$	−27.1902	+	33.7467i	−0.0954044	+	0.118409i
$286$	78.1356	+	6.00307i	0.273201	+	0.0209898i
$287$	−171.648	+	171.648i	−0.598076	+	0.598076i
$288$	−121.590	−	60.1415i	−0.422188	−	0.208825i
$289$	138.745	+	45.0809i	0.480085	+	0.155989i
$290$	−203.055	−	35.5212i	−0.700191	−	0.122487i
$291$	63.3413	+	87.1819i	0.217668	+	0.299594i
$292$	−107.665	−	471.119i	−0.368715	−	1.61342i
$293$	244.018	−	478.913i	0.832827	−	1.63451i	0.0614722	−	0.998109i	$-0.480420\pi$
$293$	244.018	−	478.913i	0.832827	−	1.63451i	0.771355	−	0.636406i	$-0.219580\pi$
$294$	−159.807	−	19.8020i	−0.543563	−	0.0673539i
$295$	369.894	+	212.346i	1.25388	+	0.719816i
$296$	−99.0524	−	153.645i	−0.334636	−	0.519072i
$297$	−234.912	−	213.977i	−0.790951	−	0.720460i
$298$	126.101	−	186.505i	0.423156	−	0.625855i
$299$	−81.1827	+	111.738i	−0.271514	+	0.373707i
$300$	−191.123	−	105.267i	−0.637076	−	0.350889i
$301$	−4.71329	−	14.5060i	−0.0156588	−	0.0481928i
$302$	5.09725	+	150.766i	0.0168783	+	0.499225i
$303$	−2.67110	+	16.8647i	−0.00881552	+	0.0556590i
$304$	30.0876	−	55.9853i	0.0989725	−	0.184162i
$305$	−68.6728	−	14.4202i	−0.225157	−	0.0472795i
$306$	91.8748	+	42.9662i	0.300245	+	0.140412i
$307$	175.853	+	175.853i	0.572811	+	0.572811i	0.932913	−	0.360102i	$-0.117258\pi$
$307$	175.853	+	175.853i	0.572811	+	0.572811i	−0.360102	+	0.932913i	$0.617258\pi$
$308$	143.400	+	53.4922i	0.465583	+	0.173676i
$309$			321.879i			1.04168i
$310$	251.863	+	514.629i	0.812460	+	1.66009i
$311$	−19.8837	−	6.46060i	−0.0639347	−	0.0207736i	0.276875	−	0.960906i	$-0.410701\pi$
$311$	−19.8837	−	6.46060i	−0.0639347	−	0.0207736i	−0.340810	+	0.940132i	$0.610701\pi$
$312$	−61.8590	+	6.29337i	−0.198266	+	0.0201711i
$313$	31.9632	−	201.807i	0.102119	−	0.644752i	−0.882537	−	0.470243i	$-0.844166\pi$
$313$	31.9632	−	201.807i	0.102119	−	0.644752i	0.984656	−	0.174509i	$-0.0558338\pi$
$314$	−241.732	+	258.649i	−0.769846	+	0.823723i
$315$	−68.8953	−	26.2520i	−0.218715	−	0.0833396i
$316$	−15.1595	−	223.936i	−0.0479730	−	0.708659i
$317$	−60.4218	−	381.488i	−0.190605	−	1.20343i	−0.878543	−	0.477664i	$-0.841484\pi$
$317$	−60.4218	−	381.488i	−0.190605	−	1.20343i	0.687938	−	0.725770i	$-0.258516\pi$
$318$	−76.2862	+	112.829i	−0.239894	+	0.354807i
$319$	218.685	+	59.9473i	0.685533	+	0.187923i
$320$	303.920	+	100.163i	0.949750	+	0.313009i
$321$	19.9981	−	27.5250i	0.0622993	−	0.0857476i
$322$	−212.748	+	165.837i	−0.660707	+	0.515021i
$323$	−21.5745	+	42.3423i	−0.0667940	+	0.131091i
$324$	84.2745	+	52.9211i	0.260106	+	0.163337i
$325$	88.9060	−	5.09846i	0.273557	−	0.0156876i
$326$	−34.5522	−	62.4974i	−0.105988	−	0.191710i
$327$	−350.718	+	178.700i	−1.07253	+	0.546483i
$328$	416.130	−	372.183i	1.26869	−	1.13470i
$329$	136.436			0.414699
$330$	198.388	+	135.089i	0.601176	+	0.409361i
$331$			236.229i			0.713683i	0.934165	+	0.356842i	$0.116146\pi$
$331$			236.229i			0.713683i	−0.934165	+	0.356842i	$0.883854\pi$
$332$	−194.717	−	325.700i	−0.586497	−	0.981024i
$333$	−43.9766	−	86.3090i	−0.132062	−	0.259186i
$334$	−137.926	−	249.478i	−0.412952	−	0.746939i
$335$	−13.9579	+	279.498i	−0.0416655	+	0.834322i
$336$	−119.497	−	21.6183i	−0.355646	−	0.0643401i
$337$	302.087	+	153.921i	0.896400	+	0.456739i	0.840571	−	0.541702i	$-0.182220\pi$
$337$	302.087	+	153.921i	0.896400	+	0.456739i	0.0558293	+	0.998440i	$0.482220\pi$
$338$	−246.564	+	192.196i	−0.729479	+	0.568628i
$339$	−103.924	−	75.5051i	−0.306560	−	0.222729i
$340$	−228.824	−	69.8981i	−0.673011	−	0.205583i
$341$	−222.472	−	589.680i	−0.652410	−	1.72927i
$342$	18.8638	−	27.8998i	0.0551573	−	0.0815785i
$343$	295.121	−	46.7426i	0.860412	−	0.136276i
$344$	8.96617	+	33.9137i	0.0260645	+	0.0985864i
$345$	−386.018	+	173.007i	−1.11889	+	0.501468i
$346$	−6.74083	+	7.21258i	−0.0194822	+	0.0208456i
$347$	−391.496	−	62.0068i	−1.12823	−	0.178694i	−0.435706	−	0.900089i	$-0.643501\pi$
$347$	−391.496	−	62.0068i	−1.12823	−	0.178694i	−0.692524	+	0.721395i	$0.743501\pi$
$348$	−179.194	−	16.0785i	−0.514925	−	0.0462027i
$349$	−96.3407	+	296.506i	−0.276048	+	0.849588i	0.712892	+	0.701273i	$0.247385\pi$
$349$	−96.3407	+	296.506i	−0.276048	+	0.849588i	−0.988940	+	0.148314i	$0.952615\pi$
$350$	169.613	+	38.4775i	0.484608	+	0.109936i
$351$	−102.898			−0.293157
$352$	−322.442	−	141.192i	−0.916028	−	0.401114i
$353$	−121.881	+	121.881i	−0.345273	+	0.345273i	−0.858345	−	0.513072i	$-0.828507\pi$
$353$	−121.881	+	121.881i	−0.345273	+	0.345273i	0.513072	+	0.858345i	$0.328507\pi$
$354$	337.199	+	157.695i	0.952539	+	0.445465i
$355$	−321.012	−	67.4077i	−0.904260	−	0.189881i
$356$	−17.9058	−	21.4358i	−0.0502971	−	0.0602129i
$357$	89.6796	+	14.2038i	0.251203	+	0.0397867i
$358$	−8.05640	−	238.291i	−0.0225039	−	0.665619i
$359$	668.725	−	217.282i	1.86274	−	0.605242i	0.868826	−	0.495118i	$-0.164875\pi$
$359$	668.725	−	217.282i	1.86274	−	0.605242i	0.993918	−	0.110124i	$-0.0351249\pi$
$360$	154.844	+	69.1024i	0.430123	+	0.191951i
$361$	−279.289	−	202.915i	−0.773654	−	0.562092i
$362$	295.714	−	437.366i	0.816890	−	1.20819i
$363$	−203.253	−	168.501i	−0.559926	−	0.464190i
$364$	45.9943	−	18.4642i	0.126358	−	0.0507258i
$365$	157.784	+	583.111i	0.432284	+	1.59756i
$366$	−60.7786	−	7.53119i	−0.166062	−	0.0205770i
$367$	302.226	+	153.992i	0.823504	+	0.419596i	0.814359	−	0.580362i	$-0.197089\pi$
$367$	302.226	+	153.992i	0.823504	+	0.419596i	0.00914512	+	0.999958i	$0.497089\pi$
$368$	509.765	−	353.577i	1.38523	−	0.960807i
$369$	239.330	−	173.884i	0.648592	−	0.471230i
$370$	131.320	+	187.006i	0.354919	+	0.505421i
$371$	33.5478	−	103.249i	0.0904253	−	0.278300i
$372$	256.599	+	429.209i	0.689783	+	1.15379i
$373$	395.322	+	395.322i	1.05984	+	1.05984i	0.998092	+	0.0617522i	$0.0196688\pi$
$373$	395.322	+	395.322i	1.05984	+	1.05984i	0.0617522	+	0.998092i	$0.480331\pi$
$374$	243.341	+	100.265i	0.650644	+	0.268088i
$375$	243.924	+	122.025i	0.650465	+	0.325399i
$376$	−313.299	−	17.4661i	−0.833243	−	0.0464523i
$377$	65.4252	−	33.3358i	0.173542	−	0.0884238i
$378$	−193.118	−	55.6077i	−0.510893	−	0.147110i
$379$	368.733	−	267.900i	0.972910	−	0.706860i	0.0167970	−	0.999859i	$-0.494653\pi$
$379$	368.733	−	267.900i	0.972910	−	0.706860i	0.956113	+	0.292999i	$0.0946531\pi$
$380$	−34.8103	+	71.4153i	−0.0916060	+	0.187935i
$381$	391.739	−	127.284i	1.02819	−	0.334078i
$382$	−58.7397	+	45.7876i	−0.153769	+	0.119863i
$383$	64.7246	+	408.655i	0.168994	+	1.06698i	0.915709	+	0.401841i	$0.131630\pi$
$383$	64.7246	+	408.655i	0.168994	+	1.06698i	−0.746716	+	0.665144i	$0.768370\pi$
$384$	271.635	+	64.9398i	0.707382	+	0.169114i
$385$	−181.755	−	59.7183i	−0.472092	−	0.155112i
$386$	446.526	−	86.2815i	1.15680	−	0.223527i
$387$	2.90778	+	18.3590i	0.00751365	+	0.0474393i
$388$	148.807	+	129.937i	0.383523	+	0.334890i
$389$	−208.934	+	67.8868i	−0.537105	+	0.174516i	−0.564994	−	0.825095i	$-0.691122\pi$
$389$	−208.934	+	67.8868i	−0.537105	+	0.174516i	0.0278887	+	0.999611i	$0.491122\pi$
$390$	76.9518	−	10.9210i	0.197312	−	0.0280024i
$391$	−375.268	+	272.648i	−0.959764	+	0.697310i
$392$	−293.687	+	29.8789i	−0.749202	+	0.0762218i
$393$	124.383	−	63.3763i	0.316496	−	0.161263i
$394$	28.1688	−	60.2334i	0.0714943	−	0.152877i
$395$	30.0135	+	278.951i	0.0759834	+	0.706205i
$396$	−162.408	−	91.7249i	−0.410121	−	0.231629i
$397$	−302.419	−	302.419i	−0.761762	−	0.761762i	0.214879	−	0.976641i	$-0.431064\pi$
$397$	−302.419	−	302.419i	−0.761762	−	0.761762i	−0.976641	+	0.214879i	$0.931064\pi$
$398$	−470.963	+	170.824i	−1.18332	+	0.429207i
$399$	9.31672	−	28.6739i	0.0233502	−	0.0718644i
$400$	−384.558	−	110.069i	−0.961395	−	0.275174i
$401$	−84.2984	+	61.2463i	−0.210220	+	0.152734i	−0.687913	−	0.725793i	$-0.741473\pi$
$401$	−84.2984	+	61.2463i	−0.210220	+	0.152734i	0.477693	+	0.878527i	$0.341473\pi$
$402$	8.25294	+	244.105i	0.0205297	+	0.607225i
$403$	−181.847	−	92.6556i	−0.451233	−	0.229915i
$404$	2.11417	+	31.2306i	0.00523309	+	0.0773035i
$405$	−107.879	−	61.9302i	−0.266367	−	0.152914i
$406$	140.804	−	27.2073i	0.346808	−	0.0670131i
$407$	−124.425	−	218.403i	−0.305712	−	0.536617i
$408$	−204.114	−	44.0969i	−0.500279	−	0.108081i
$409$	−405.406	−	294.545i	−0.991212	−	0.720158i	−0.0310261	−	0.999519i	$-0.509878\pi$
$409$	−405.406	−	294.545i	−0.991212	−	0.720158i	−0.960186	+	0.279361i	$0.909878\pi$
$410$	−501.342	+	485.451i	−1.22278	+	1.18403i
$411$	−100.903	+	32.7853i	−0.245506	+	0.0797696i
$412$	131.461	+	575.246i	0.319080	+	1.39623i
$413$	−293.067	−	46.4172i	−0.709605	−	0.112390i
$414$	287.693	−	159.054i	0.694912	−	0.384188i
$415$	259.319	+	397.173i	0.624866	+	0.957042i
$416$	−107.981	+	36.5115i	−0.259570	+	0.0877680i
$417$	187.236	−	187.236i	0.449007	−	0.449007i
$418$	45.5235	−	74.5990i	0.108908	−	0.178467i
$419$	−704.010			−1.68022			−0.840108	−	0.542419i	$-0.817508\pi$
$419$	−704.010			−1.68022			−0.840108	+	0.542419i	$0.817508\pi$
$420$	150.324	+	21.0897i	0.357914	+	0.0502135i
$421$	74.0084	−	227.774i	0.175792	−	0.541032i	−0.823877	−	0.566769i	$-0.808193\pi$
$421$	74.0084	−	227.774i	0.175792	−	0.541032i	0.999669	+	0.0257370i	$0.00819325\pi$
$422$	−169.382	−	48.7732i	−0.401380	−	0.115576i
$423$	−164.224	−	26.0105i	−0.388236	−	0.0614906i
$424$	−90.2537	+	232.798i	−0.212863	+	0.549052i
$425$	289.264	+	75.9834i	0.680621	+	0.178785i
$426$	−284.111	−	35.2047i	−0.666926	−	0.0826401i
$427$	48.2159	−	7.63664i	0.112918	−	0.0178844i
$428$	24.4979	−	57.3588i	0.0572380	−	0.134016i
$429$	−85.4024	+	3.98308i	−0.199073	+	0.00928458i
$430$	−12.8768	−	41.9153i	−0.0299460	−	0.0974775i
$431$	−484.030	−	351.669i	−1.12304	−	0.815936i	−0.138373	−	0.990380i	$-0.544187\pi$
$431$	−484.030	−	351.669i	−1.12304	−	0.815936i	−0.984667	+	0.174444i	$0.944187\pi$
$432$	436.339	+	152.415i	1.01004	+	0.352812i
$433$	584.794	+	297.967i	1.35056	+	0.688146i	0.971459	−	0.237208i	$-0.0762323\pi$
$433$	584.794	+	297.967i	1.35056	+	0.688146i	0.379104	+	0.925354i	$0.376232\pi$
$434$	−291.215	−	272.167i	−0.671002	−	0.627114i
$435$	224.612	+	11.2170i	0.516350	+	0.0257862i
$436$	−553.801	+	462.602i	−1.27019	+	1.06101i
$437$	69.9258	+	137.237i	0.160013	+	0.314044i
$438$	179.773	+	495.634i	0.410441	+	1.13158i
$439$			870.670i			1.98330i	0.128945	+	0.991652i	$0.458841\pi$
$439$			870.670i			1.98330i	−0.128945	+	0.991652i	$0.541159\pi$
$440$	409.722	+	160.399i	0.931186	+	0.364544i
$441$	−156.424			−0.354703
$442$	80.1195	−	29.0604i	0.181266	−	0.0657475i
$443$	268.280	−	136.695i	0.605598	−	0.308567i	−0.124172	−	0.992261i	$-0.539627\pi$
$443$	268.280	−	136.695i	0.605598	−	0.308567i	0.729769	+	0.683693i	$0.239627\pi$
$444$	127.856	+	153.062i	0.287965	+	0.344735i
$445$	23.4252	+	25.8879i	0.0526409	+	0.0581750i
$446$	−128.768	+	137.779i	−0.288717	+	0.308922i
$447$	−111.507	+	218.845i	−0.249457	+	0.489586i
$448$	−222.388	+	10.1696i	−0.496403	+	0.0227001i
$449$	−62.6109	+	86.1766i	−0.139445	+	0.191930i	−0.873028	−	0.487670i	$-0.837847\pi$
$449$	−62.6109	+	86.1766i	−0.139445	+	0.191930i	0.733583	+	0.679600i	$0.237847\pi$
$450$	−196.822	−	78.6496i	−0.437383	−	0.174777i
$451$	599.342	−	479.653i	1.32892	−	1.06353i
$452$	−216.565	−	92.4946i	−0.479126	−	0.204634i
$453$	−25.7454	−	162.550i	−0.0568330	−	0.358829i
$454$	74.3665	−	600.156i	0.163803	−	1.32193i
$455$	−56.5344	+	25.3377i	−0.124251	+	0.0556872i
$456$	−25.0648	+	64.6515i	−0.0549667	+	0.141780i
$457$	−111.870	+	706.318i	−0.244792	+	1.54555i	0.492701	+	0.870198i	$0.336009\pi$
$457$	−111.870	+	706.318i	−0.244792	+	1.54555i	−0.737493	+	0.675355i	$0.763991\pi$
$458$	−139.412	+	484.159i	−0.304394	+	1.05712i
$459$	−328.664	−	106.789i	−0.716044	−	0.232657i
$460$	−619.214	+	466.845i	−1.34612	+	1.01488i
$461$			67.6639i			0.146776i	0.997303	+	0.0733882i	$0.0233812\pi$
$461$			67.6639i			0.146776i	−0.997303	+	0.0733882i	$0.976619\pi$
$462$	−162.434	−	38.6774i	−0.351590	−	0.0837173i
$463$	−10.1650	−	10.1650i	−0.0219545	−	0.0219545i	0.696044	−	0.717999i	$-0.254942\pi$
$463$	−10.1650	−	10.1650i	−0.0219545	−	0.0219545i	−0.717999	+	0.696044i	$0.754942\pi$
$464$	−326.813	+	44.4512i	−0.704338	+	0.0958000i
$465$	−341.732	−	523.396i	−0.734908	−	1.12558i
$466$	−211.182	−	381.982i	−0.453180	−	0.819704i
$467$	59.7144	−	377.022i	0.127868	−	0.807327i	−0.837500	−	0.546437i	$-0.815984\pi$
$467$	59.7144	−	377.022i	0.127868	−	0.807327i	0.965368	−	0.260890i	$-0.0840161\pi$
$468$	−58.8820	+	13.4563i	−0.125816	+	0.0287528i
$469$	−60.1613	−	185.158i	−0.128276	−	0.394792i
$470$	392.182	+	6.31535i	0.834429	+	0.0134369i
$471$	227.022	−	312.468i	0.481999	−	0.663415i
$472$	667.030	+	144.106i	1.41320	+	0.305309i
$473$	9.75665	+	47.2365i	0.0206272	+	0.0998656i
$474$	46.4561	+	240.421i	0.0980086	+	0.507217i
$475$	39.9455	−	90.9214i	0.0840959	−	0.191413i
$476$	166.072	−	11.2423i	0.348890	−	0.0236183i
$477$	−60.0642	+	117.883i	−0.125921	+	0.247133i
$478$	−271.593	+	9.18230i	−0.568187	+	0.0192098i
$479$	−199.241	−	274.232i	−0.415952	−	0.572509i	0.548705	−	0.836016i	$-0.315121\pi$
$479$	−199.241	−	274.232i	−0.415952	−	0.572509i	−0.964658	+	0.263506i	$0.915121\pi$
$480$	−342.490	−	67.6724i	−0.713522	−	0.140984i
$481$	−77.4128	−	25.1529i	−0.160941	−	0.0522930i
$482$	−246.637	−	679.977i	−0.511695	−	1.41074i
$483$	208.092	−	208.092i	0.430833	−	0.430833i
$484$	−432.062	−	218.124i	−0.892691	−	0.450670i
$485$	−192.291	−	154.932i	−0.396477	−	0.319448i
$486$	372.662	+	174.279i	0.766795	+	0.358599i
$487$	347.474	+	681.957i	0.713500	+	1.40032i	0.907810	+	0.419382i	$0.137753\pi$
$487$	347.474	+	681.957i	0.713500	+	1.40032i	−0.194310	+	0.980940i	$0.562247\pi$
$488$	−111.696	+	11.3637i	−0.228886	+	0.0232862i
$489$	45.7941	+	63.0301i	0.0936484	+	0.128896i
$490$	365.343	−	51.8492i	0.745598	−	0.105815i
$491$	−245.327	−	755.039i	−0.499648	−	1.53776i	−0.809586	−	0.587001i	$-0.800308\pi$
$491$	−245.327	−	755.039i	−0.499648	−	1.53776i	0.309939	−	0.950757i	$-0.399692\pi$
$492$	−400.610	+	458.788i	−0.814248	+	0.932495i
$493$	243.569	−	38.5776i	0.494055	−	0.0782507i
$494$	−5.36902	−	27.7859i	−0.0108685	−	0.0562468i
$495$	207.389	+	106.531i	0.418967	+	0.215215i
$496$	633.878	+	662.261i	1.27798	+	1.33520i
$497$	225.386	−	35.6976i	0.453493	−	0.0718263i
$498$	254.515	+	326.511i	0.511074	+	0.655644i
$499$	45.2225	+	139.180i	0.0906262	+	0.278919i	0.986089	−	0.166217i	$-0.0531553\pi$
$499$	45.2225	+	139.180i	0.0906262	+	0.278919i	−0.895463	+	0.445136i	$0.853155\pi$
$500$	485.766	+	118.454i	0.971532	+	0.236907i
$501$	182.801	+	251.604i	0.364873	+	0.502204i
$502$	−86.8261	+	301.535i	−0.172960	+	0.600666i
$503$	−254.510	−	499.503i	−0.505983	−	0.993048i	−0.992827	−	0.119559i	$-0.961852\pi$
$503$	−254.510	−	499.503i	−0.505983	−	0.993048i	0.486844	−	0.873489i	$-0.338148\pi$
$504$	−117.781	−	6.56614i	−0.233692	−	0.0130281i
$505$	−4.18574	−	38.9031i	−0.00828859	−	0.0770358i
$506$	726.495	−	447.059i	1.43576	−	0.883516i
$507$	241.169	−	241.169i	0.475678	−	0.475678i
$508$	648.111	−	387.468i	1.27581	−	0.762732i
$509$	−159.906	−	51.9565i	−0.314157	−	0.102076i	0.147695	−	0.989033i	$-0.452815\pi$
$509$	−159.906	−	51.9565i	−0.314157	−	0.102076i	−0.461851	+	0.886957i	$0.652815\pi$
$510$	257.124	+	44.9796i	0.504164	+	0.0881954i
$511$	−247.019	−	339.992i	−0.483402	−	0.665346i
$512$	511.974	+	5.11675i	0.999950	+	0.00999366i
$513$	−52.0955	+	102.243i	−0.101551	+	0.199304i
$514$	41.3619	−	333.801i	0.0804706	−	0.649418i
$515$	−192.657	−	711.990i	−0.374092	−	1.38251i
$516$	−14.2574	−	35.5153i	−0.0276307	−	0.0688281i
$517$	−428.826	−	47.5679i	−0.829450	−	0.0920076i
$518$	−131.694	−	89.0417i	−0.254236	−	0.171895i
$519$	6.33063	−	8.71336i	0.0121977	−	0.0167887i
$520$	133.064	−	50.9458i	0.255892	−	0.0979727i
$521$	289.060	+	889.635i	0.554818	+	1.70755i	0.696424	+	0.717630i	$0.254773\pi$
$521$	289.060	+	889.635i	0.554818	+	1.70755i	−0.141607	+	0.989923i	$0.545227\pi$
$522$	−174.669	+	5.90537i	−0.334614	+	0.0113130i
$523$	97.1674	−	613.491i	0.185789	−	1.17302i	−0.701796	−	0.712378i	$-0.747618\pi$
$523$	97.1674	−	613.491i	0.185789	−	1.17302i	0.887585	−	0.460645i	$-0.152382\pi$
$524$	196.407	−	164.063i	0.374822	−	0.313097i
$525$	−188.801	−	18.9043i	−0.359621	−	0.0360083i
$526$	17.7283	−	37.9086i	0.0337041	−	0.0720696i
$527$	−484.673	−	484.673i	−0.919682	−	0.919682i
$528$	368.048	+	109.610i	0.697061	+	0.207594i
$529$			974.424i			1.84201i
$530$	101.211	−	295.235i	0.190965	−	0.557047i
$531$	343.906	+	111.742i	0.647658	+	0.210437i
$532$	4.93944	−	55.0497i	0.00928466	−	0.103477i
$533$	38.8870	−	245.523i	0.0729586	−	0.460643i
$534$	22.2623	+	20.8062i	0.0416897	+	0.0389629i
$535$	−27.7606	+	72.8543i	−0.0518889	+	0.136176i
$536$	114.446	+	432.881i	0.213518	+	0.807613i
$537$	40.6915	+	256.916i	0.0757756	+	0.478428i
$538$	−145.046	−	98.0690i	−0.269601	−	0.182284i
$539$	−405.464	+	18.9104i	−0.752251	+	0.0350843i
$540$	−552.537	−	168.782i	−1.02322	−	0.312559i
$541$	406.346	−	559.287i	0.751102	−	1.03380i	−0.246801	−	0.969066i	$-0.579379\pi$
$541$	406.346	−	559.287i	0.751102	−	1.03380i	0.997902	−	0.0647367i	$-0.0206207\pi$
$542$	−441.526	−	566.423i	−0.814623	−	1.04506i
$543$	−261.492	+	513.206i	−0.481569	+	0.945132i
$544$	−382.791	+	4.55588i	−0.703661	+	0.00837478i
$545$	668.822	−	605.199i	1.22720	−	1.11046i
$546$	−47.3207	+	26.1616i	−0.0866679	+	0.0479151i
$547$	890.035	−	453.495i	1.62712	−	0.829059i	0.628431	−	0.777865i	$-0.283697\pi$
$547$	890.035	−	453.495i	1.62712	−	0.829059i	0.998689	−	0.0511942i	$-0.0163027\pi$
$548$	−166.938	+	99.8026i	−0.304632	+	0.182122i
$549$	−59.4918			−0.108364
$550$	−519.687	−	180.072i	−0.944885	−	0.327403i
$551$		−	81.8860i		−	0.148613i
$552$	−504.484	+	451.205i	−0.913920	+	0.817401i
$553$	−88.6114	−	173.910i	−0.160238	−	0.314484i
$554$	389.907	−	215.563i	0.703803	−	0.389103i
$555$	−167.268	−	184.852i	−0.301383	−	0.333068i
$556$	258.148	−	411.088i	0.464295	−	0.739368i
$557$	737.242	+	375.643i	1.32359	+	0.674405i	0.965774	−	0.259386i	$-0.0835202\pi$
$557$	737.242	+	375.643i	1.32359	+	0.674405i	0.357820	+	0.933791i	$0.383520\pi$
$558$	298.640	+	383.118i	0.535197	+	0.686591i
$559$	12.6363	+	9.18078i	0.0226051	+	0.0164236i
$560$	277.265	−	23.7045i	0.495115	−	0.0423294i
$561$	−276.915	−	75.9098i	−0.493610	−	0.135312i
$562$	−595.278	−	402.483i	−1.05921	−	0.716162i
$563$	462.401	−	73.2371i	0.821316	−	0.130084i	0.268386	−	0.963311i	$-0.413510\pi$
$563$	462.401	−	73.2371i	0.821316	−	0.130084i	0.552930	+	0.833228i	$0.313510\pi$
$564$	341.551	−	23.1214i	0.605587	−	0.0409955i
$565$	275.070	+	104.813i	0.486850	+	0.185510i
$566$	208.832	+	195.173i	0.368961	+	0.344828i
$567$	85.4723	+	13.5375i	0.150745	+	0.0238756i
$568$	−522.126	+	53.1197i	−0.919236	+	0.0935206i
$569$	314.641	−	968.366i	0.552972	−	1.70187i	−0.148266	−	0.988947i	$-0.547369\pi$
$569$	314.641	−	968.366i	0.552972	−	1.70187i	0.701239	−	0.712927i	$-0.252631\pi$
$570$	28.1079	−	81.9911i	0.0493121	−	0.143844i
$571$	−626.329			−1.09690			−0.548449	−	0.836184i	$-0.684781\pi$
$571$	−626.329			−1.09690			−0.548449	+	0.836184i	$0.684781\pi$
$572$	−151.000	+	41.9982i	−0.263986	+	0.0734234i
$573$	57.4544	−	57.4544i	0.100269	−	0.100269i
$574$	205.667	−	439.778i	0.358304	−	0.766164i
$575$	750.314	−	613.734i	1.30489	−	1.06736i
$576$	269.621	+	30.1558i	0.468092	+	0.0523538i
$577$	−233.889	−	37.0444i	−0.405353	−	0.0642017i	−0.0495713	−	0.998771i	$-0.515785\pi$
$577$	−233.889	−	37.0444i	−0.405353	−	0.0642017i	−0.355782	+	0.934569i	$0.615785\pi$
$578$	−291.603	+	9.85881i	−0.504503	+	0.0170568i
$579$	−471.876	+	153.322i	−0.814985	+	0.264805i
$580$	405.997	−	71.6891i	0.699995	−	0.123602i
$581$	−266.967	−	193.963i	−0.459496	−	0.333843i
$582$	−178.545	−	120.719i	−0.306778	−	0.207420i
$583$	−141.440	+	312.822i	−0.242607	+	0.536573i
$584$	523.707	+	812.349i	0.896758	+	1.39101i
$585$	72.8791	−	19.7203i	0.124580	−	0.0337100i
$586$	−132.193	+	1066.83i	−0.225586	+	1.82054i
$587$	−815.832	−	415.687i	−1.38983	−	0.708155i	−0.410775	−	0.911737i	$-0.634742\pi$
$587$	−815.832	−	415.687i	−1.38983	−	0.708155i	−0.979058	+	0.203581i	$0.934742\pi$
$588$	313.965	−	71.7505i	0.533954	−	0.122025i
$589$	−184.132	+	133.779i	−0.312617	+	0.227130i
$590$	−840.263	−	146.990i	−1.42418	−	0.249136i
$591$	−22.4173	+	68.9934i	−0.0379312	+	0.116740i
$592$	291.012	+	221.326i	0.491574	+	0.373862i
$593$	259.129	+	259.129i	0.436979	+	0.436979i	0.890994	−	0.454015i	$-0.150009\pi$
$593$	259.129	+	259.129i	0.436979	+	0.436979i	−0.454015	+	0.890994i	$0.650009\pi$
$594$	587.591	+	242.108i	0.989210	+	0.407589i
$595$	−206.871	+	22.2581i	−0.347682	+	0.0374085i
$596$	−109.900	+	436.650i	−0.184395	+	0.732635i
$597$	486.991	−	248.134i	0.815731	−	0.415636i
$598$	76.4348	−	265.447i	0.127817	−	0.443892i
$599$	−157.968	+	114.770i	−0.263719	+	0.191603i	−0.711785	−	0.702397i	$-0.752113\pi$
$599$	−157.968	+	114.770i	−0.263719	+	0.191603i	0.448066	+	0.894001i	$0.352113\pi$
$600$	431.126	+	67.5799i	0.718543	+	0.112633i
$601$	−81.2154	+	26.3885i	−0.135134	+	0.0439076i	−0.375803	−	0.926700i	$-0.622633\pi$
$601$	−81.2154	+	26.3885i	−0.135134	+	0.0439076i	0.240669	+	0.970607i	$0.422633\pi$
$602$	18.7541	+	24.0592i	0.0311530	+	0.0399654i
$603$	37.1154	+	234.338i	0.0615513	+	0.388620i
$604$	−112.399	−	279.986i	−0.186091	−	0.463552i
$605$	550.446	+	251.066i	0.909828	+	0.414985i
$606$	−6.47886	−	33.5296i	−0.0106912	−	0.0553293i
$607$	−85.5908	−	540.399i	−0.141006	−	0.890278i	−0.952194	−	0.305493i	$-0.901179\pi$
$607$	−85.5908	−	540.399i	−0.141006	−	0.890278i	0.811188	−	0.584785i	$-0.198821\pi$
$608$	−18.3897	+	125.779i	−0.0302463	+	0.206873i
$609$	−148.798	+	48.3473i	−0.244331	+	0.0793881i
$610$	138.949	−	19.7195i	0.227785	−	0.0323271i
$611$	−113.033	+	82.1233i	−0.184997	+	0.134408i
$612$	−202.039	−	18.1283i	−0.330129	−	0.0296214i
$613$	−472.612	+	240.808i	−0.770982	+	0.392835i	−0.794792	−	0.606882i	$-0.792420\pi$
$613$	−472.612	+	240.808i	−0.770982	+	0.392835i	0.0238104	+	0.999716i	$0.492420\pi$
$614$	−450.553	−	210.706i	−0.733799	−	0.343169i
$615$	477.672	−	592.855i	0.776703	−	0.963992i
$616$	−306.091	−	2.78119i	−0.496901	−	0.00451492i
$617$	−607.931	−	607.931i	−0.985301	−	0.985301i	0.0145927	−	0.999894i	$-0.495355\pi$
$617$	−607.931	−	607.931i	−0.985301	−	0.985301i	−0.999894	+	0.0145927i	$0.995355\pi$
$618$	−219.507	−	605.179i	−0.355189	−	0.979255i
$619$	−152.133	+	468.218i	−0.245773	+	0.756411i	0.749736	+	0.661738i	$0.230181\pi$
$619$	−152.133	+	468.218i	−0.245773	+	0.756411i	−0.995508	+	0.0946734i	$0.969819\pi$
$620$	−824.491	−	795.817i	−1.32982	−	1.28358i
$621$	−906.153	+	658.359i	−1.45918	+	1.06016i
$622$	41.7900	−	1.41288i	0.0671865	−	0.00227151i
$623$	−21.6414	−	11.0268i	−0.0347373	−	0.0176995i
$624$	112.012	−	54.0174i	0.179507	−	0.0865663i
$625$	−612.592	−	123.918i	−0.980148	−	0.198269i
$626$	77.5279	+	401.224i	0.123846	+	0.640934i
$627$	−39.2800	+	86.8753i	−0.0626475	+	0.138557i
$628$	278.104	−	651.147i	0.442840	−	1.03686i
$629$	−221.158	−	160.681i	−0.351603	−	0.255454i
$630$	147.436	+	2.37417i	0.234025	+	0.00376853i
$631$	1126.54	−	366.036i	1.78533	−	0.580089i	0.786056	−	0.618155i	$-0.212120\pi$
$631$	1126.54	−	366.036i	1.78533	−	0.580089i	0.999275	+	0.0380658i	$0.0121196\pi$
$632$	181.216	+	410.694i	0.286734	+	0.649832i
$633$	189.933	+	30.0824i	0.300051	+	0.0475235i
$634$	373.759	+	676.048i	0.589525	+	1.06632i
$635$	−790.334	+	516.020i	−1.24462	+	0.812630i
$636$	66.4853	−	264.157i	0.104537	−	0.415342i
$637$	−92.9437	+	92.9437i	−0.145909	+	0.145909i
$638$	−452.040	+	36.4232i	−0.708527	+	0.0570896i
$639$	−278.096			−0.435205
$640$	−639.720	+	18.9384i	−0.999562	+	0.0295913i
$641$	314.274	−	967.234i	0.490286	−	1.50895i	−0.333890	−	0.942612i	$-0.608361\pi$
$641$	314.274	−	967.234i	0.490286	−	1.50895i	0.824176	−	0.566334i	$-0.191639\pi$
$642$	−18.8285	+	65.3887i	−0.0293279	+	0.101852i
$643$	−106.617	−	16.8864i	−0.165811	−	0.0262619i	0.0729767	−	0.997334i	$-0.476750\pi$
$643$	−106.617	−	16.8864i	−0.165811	−	0.0262619i	−0.238788	+	0.971072i	$0.576750\pi$
$644$	286.904	−	456.881i	0.445502	−	0.709442i
$645$	19.5649	+	43.6540i	0.0303332	+	0.0676806i
$646$	11.6877	−	94.3223i	0.0180923	−	0.146010i
$647$	245.112	−	38.8219i	0.378843	−	0.0600029i	0.0358910	−	0.999356i	$-0.488573\pi$
$647$	245.112	−	38.8219i	0.378843	−	0.0600029i	0.342952	+	0.939353i	$0.388573\pi$
$648$	−194.538	−	42.0281i	−0.300213	−	0.0648582i
$649$	904.940	+	248.068i	1.39436	+	0.382231i
$650$	−163.679	+	70.2156i	−0.251814	+	0.108024i
$651$	351.810	+	255.605i	0.540415	+	0.392635i
$652$	107.583	+	93.9411i	0.165005	+	0.144081i
$653$	544.207	+	277.287i	0.833395	+	0.424636i	0.817981	−	0.575245i	$-0.195093\pi$
$653$	544.207	+	277.287i	0.833395	+	0.424636i	0.0154138	+	0.999881i	$0.495093\pi$
$654$	537.536	−	575.154i	0.821920	−	0.879441i
$655$	−237.199	+	214.635i	−0.362137	+	0.327687i
$656$	−528.573	+	983.538i	−0.805752	+	1.49930i
$657$	232.512	+	456.330i	0.353899	+	0.694566i
$658$	−256.519	+	93.0430i	−0.389847	+	0.141403i
$659$			269.497i			0.408949i	0.978872	+	0.204474i	$0.0655485\pi$
$659$			269.497i			0.408949i	−0.978872	+	0.204474i	$0.934451\pi$
$660$	−465.123	−	118.696i	−0.704731	−	0.179842i
$661$	761.720			1.15237			0.576187	−	0.817318i	$-0.304540\pi$
$661$	761.720			1.15237			0.576187	+	0.817318i	$0.304540\pi$
$662$	−161.097	−	444.145i	−0.243349	−	0.670914i
$663$	−82.8463	+	42.2123i	−0.124957	+	0.0636686i
$664$	588.208	+	479.575i	0.885856	+	0.722251i
$665$	−3.44594	+	69.0025i	−0.00518187	+	0.103763i
$666$	141.541	+	132.283i	0.212524	+	0.198624i
$667$	362.867	−	712.166i	0.544028	−	1.06772i
$668$	429.452	+	374.995i	0.642893	+	0.561370i
$669$	120.932	−	166.448i	0.180765	−	0.248802i
$670$	−164.361	−	535.015i	−0.245316	−	0.798529i
$671$	−154.207	+	7.19208i	−0.229817	+	0.0107185i
$672$	239.414	−	40.8460i	0.356271	−	0.0607827i
$673$	−151.222	−	954.776i	−0.224698	−	1.41869i	−0.799634	−	0.600488i	$-0.794973\pi$
$673$	−151.222	−	954.776i	−0.224698	−	1.41869i	0.574936	−	0.818198i	$-0.305027\pi$
$674$	−672.934	−	83.3845i	−0.998418	−	0.123716i
$675$	698.480	+	183.476i	1.03479	+	0.271816i
$676$	332.507	−	529.502i	0.491874	−	0.783287i
$677$	20.3733	−	128.632i	0.0300935	−	0.190003i	−0.968062	−	0.250711i	$-0.919336\pi$
$677$	20.3733	−	128.632i	0.0300935	−	0.190003i	0.998156	+	0.0607076i	$0.0193357\pi$
$678$	246.883	+	71.0893i	0.364134	+	0.104851i
$679$	163.386	+	53.0874i	0.240628	+	0.0781847i
$680$	477.889	−	24.6286i	0.702778	−	0.0362185i
$681$			659.763i			0.968815i
$682$	820.413	+	956.967i	1.20295	+	1.40318i
$683$	700.152	+	700.152i	1.02511	+	1.02511i	0.999676	+	0.0254362i	$0.00809747\pi$
$683$	700.152	+	700.152i	1.02511	+	1.02511i	0.0254362	+	0.999676i	$0.491903\pi$
$684$	−16.4403	+	65.3199i	−0.0240355	+	0.0954970i
$685$	203.572	−	132.915i	0.297185	−	0.194036i
$686$	−522.994	+	289.142i	−0.762383	+	0.421490i
$687$	85.9869	−	542.900i	0.125163	−	0.790247i
$688$	−39.9852	−	57.6481i	−0.0581181	−	0.0837909i
$689$	34.3544	+	105.732i	0.0498612	+	0.153457i
$690$	607.788	−	588.524i	0.880852	−	0.852933i
$691$	−357.515	+	492.078i	−0.517388	+	0.712124i	−0.985143	−	0.171734i	$-0.945063\pi$
$691$	−357.515	+	492.078i	−0.517388	+	0.712124i	0.467755	+	0.883858i	$0.345063\pi$
$692$	7.75508	−	18.1576i	0.0112068	−	0.0262393i
$693$	−161.211	−	17.8825i	−0.232628	−	0.0258045i
$694$	778.354	−	150.400i	1.12155	−	0.216714i
$695$	−302.094	+	526.230i	−0.434667	+	0.757165i
$696$	347.875	−	91.9719i	0.499821	−	0.132144i
$697$	379.016	−	743.860i	0.543781	−	1.06723i
$698$	−21.0689	−	623.174i	−0.0301847	−	0.892799i
$699$	279.892	+	385.238i	0.400417	+	0.551127i
$700$	−345.136	+	43.3247i	−0.493052	+	0.0618925i
$701$	−421.132	−	136.834i	−0.600759	−	0.195198i	−0.00718020	−	0.999974i	$-0.502286\pi$
$701$	−421.132	−	136.834i	−0.600759	−	0.195198i	−0.593579	+	0.804776i	$0.702286\pi$
$702$	193.463	−	70.1717i	0.275589	−	0.0999596i
$703$	−64.1855	+	64.1855i	−0.0913023	+	0.0913023i
$704$	702.524	+	45.5712i	0.997903	+	0.0647318i
$705$	−425.460	+	45.7770i	−0.603490	+	0.0649319i
$706$	146.037	−	312.272i	0.206852	−	0.442312i
$707$	12.3579	+	24.2538i	0.0174794	+	0.0343052i
$708$	−741.523	−	66.5346i	−1.04735	−	0.0939754i
$709$	−168.577	−	232.026i	−0.237767	−	0.327259i	0.673413	−	0.739267i	$-0.264828\pi$
$709$	−168.577	−	232.026i	−0.237767	−	0.327259i	−0.911180	+	0.412008i	$0.864828\pi$
$710$	649.518	−	92.1792i	0.914814	−	0.129830i
$711$	73.5042	+	226.223i	0.103381	+	0.318176i
$712$	48.2836	+	28.0914i	0.0678141	+	0.0394543i
$713$	−2194.23	+	347.531i	−3.07745	+	0.487421i
$714$	−178.297	+	34.4520i	−0.249715	+	0.0482521i
$715$	186.524	−	59.9271i	0.260873	−	0.0838142i
$716$	177.651	+	442.528i	0.248116	+	0.618056i
$717$	292.821	−	46.3782i	0.408397	−	0.0646837i
$718$	−1109.12	+	864.560i	−1.54474	+	1.20412i
$719$	−15.9495	−	49.0876i	−0.0221829	−	0.0682721i	0.939352	−	0.342954i	$-0.111427\pi$
$719$	−15.9495	−	49.0876i	−0.0221829	−	0.0682721i	−0.961535	+	0.274682i	$0.911427\pi$
$720$	−338.254	−	24.3260i	−0.469797	−	0.0337862i
$721$	301.615	+	415.137i	0.418328	+	0.575780i
$722$	663.482	+	191.048i	0.918950	+	0.264609i
$723$	358.257	+	703.119i	0.495515	+	0.972503i
$724$	−257.722	+	1023.97i	−0.355970	+	1.41433i
$725$	−503.552	+	109.627i	−0.694554	+	0.151210i
$726$	497.055	+	178.197i	0.684649	+	0.245451i
$727$	74.3118	−	74.3118i	0.102217	−	0.102217i	−0.654149	−	0.756366i	$-0.726973\pi$
$727$	74.3118	−	74.3118i	0.102217	−	0.102217i	0.756366	+	0.654149i	$0.226973\pi$
$728$	−73.8842	+	66.0813i	−0.101489	+	0.0907710i
$729$	−639.806	−	207.886i	−0.877649	−	0.285165i
$730$	−694.310	−	988.731i	−0.951110	−	1.35443i
$731$	30.8332	+	42.4382i	0.0421794	+	0.0580550i
$732$	119.408	−	27.2884i	0.163126	−	0.0372792i
$733$	114.982	−	225.665i	0.156865	−	0.307865i	−0.799176	−	0.601097i	$-0.794731\pi$
$733$	114.982	−	225.665i	0.156865	−	0.307865i	0.956041	+	0.293232i	$0.0947307\pi$
$734$	−673.243	−	83.4228i	−0.917225	−	0.113655i
$735$	−388.599	+	105.151i	−0.528706	+	0.143062i
$736$	−717.308	+	1012.41i	−0.974603	+	1.37556i
$737$	124.536	+	602.934i	0.168976	+	0.818093i
$738$	−331.395	+	490.138i	−0.449045	+	0.664144i
$739$	−313.964	+	432.134i	−0.424849	+	0.584755i	−0.966761	−	0.255680i	$-0.917701\pi$
$739$	−313.964	+	432.134i	−0.424849	+	0.584755i	0.541912	+	0.840435i	$0.317701\pi$
$740$	−374.429	−	262.044i	−0.505986	−	0.354113i
$741$	9.54073	+	29.3633i	0.0128755	+	0.0396266i
$742$	7.33662	+	217.002i	0.00988763	+	0.292455i
$743$	−98.4216	+	621.410i	−0.132465	+	0.836352i	0.828562	+	0.559898i	$0.189160\pi$
$743$	−98.4216	+	621.410i	−0.132465	+	0.836352i	−0.961027	+	0.276455i	$0.910840\pi$
$744$	−775.144	−	631.986i	−1.04186	−	0.849444i
$745$	115.664	−	550.822i	0.155254	−	0.739359i
$746$	−1012.85	−	473.671i	−1.35771	−	0.634947i
$747$	284.362	+	284.362i	0.380672	+	0.380672i
$748$	−525.892	−	22.5652i	−0.703064	−	0.0301673i
$749$		−	54.2389i		−	0.0724150i
$750$	−541.828	−	63.0792i	−0.722437	−	0.0841056i
$751$	−788.214	−	256.106i	−1.04955	−	0.341020i	−0.267060	−	0.963680i	$-0.586052\pi$
$751$	−788.214	−	256.106i	−1.04955	−	0.341020i	−0.782493	+	0.622660i	$0.786052\pi$
$752$	600.959	−	180.817i	0.799148	−	0.240448i
$753$	53.5527	−	338.118i	0.0711191	−	0.449028i
$754$	−100.275	+	107.293i	−0.132991	+	0.142298i
$755$	154.241	+	344.147i	0.204292	+	0.455824i
$756$	401.011	−	27.1466i	0.530437	−	0.0359082i
$757$	174.782	+	1103.53i	0.230887	+	1.45777i	0.781971	+	0.623315i	$0.214215\pi$
$757$	174.782	+	1103.53i	0.230887	+	1.45777i	−0.551083	+	0.834450i	$0.685785\pi$
$758$	−510.575	+	755.149i	−0.673582	+	0.996239i
$759$	−726.596	+	581.494i	−0.957307	+	0.766132i
$760$	16.7464	−	158.010i	0.0220347	−	0.207908i
$761$	406.881	−	560.023i	0.534666	−	0.735905i	−0.453167	−	0.891426i	$-0.649706\pi$
$761$	406.881	−	560.023i	0.534666	−	0.735905i	0.987833	+	0.155521i	$0.0497057\pi$
$762$	−649.724	+	506.459i	−0.852656	+	0.664645i
$763$	−284.882	+	559.112i	−0.373371	+	0.732782i
$764$	79.2142	−	126.145i	0.103683	−	0.165111i
$765$	253.247	+	12.6470i	0.331042	+	0.0165320i
$766$	−400.375	−	724.191i	−0.522683	−	0.945420i
$767$	270.736	−	137.947i	0.352980	−	0.179853i
$768$	−554.999	+	63.1460i	−0.722654	+	0.0822213i
$769$	−539.723			−0.701850			−0.350925	−	0.936404i	$-0.614133\pi$

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+(-1.88014 + 0.681953i) q^{2} +(1.94413 - 0.990585i) q^{3} +(3.06988 - 2.56434i) q^{4} +(-3.70748 + 3.35479i) q^{5} +(-2.97971 + 3.18825i) q^{6} +(1.57918 - 3.09932i) q^{7} +(-4.02306 + 6.91484i) q^{8} +(-2.49168 + 3.42950i) q^{9} +(4.68278 - 8.83581i) q^{10} +(-6.04402 + 9.19075i) q^{11} +(3.42806 - 8.02639i) q^{12} +(0.557233 + 3.51823i) q^{13} +(-0.855500 + 6.90410i) q^{14} +(-3.88462 + 10.1947i) q^{15} +(2.84833 - 15.7444i) q^{16} +(-1.87144 + 11.8158i) q^{17} +(2.34595 - 8.14716i) q^{18} +(3.77795 + 1.22753i) q^{19} +(-2.77869 + 19.8060i) q^{20} -7.58980i q^{21} +(5.09597 - 21.4017i) q^{22} +(27.4174 + 27.4174i) q^{23} +(-0.971620 + 17.4285i) q^{24} +(2.49076 - 24.8756i) q^{25} +(-3.44694 - 6.23477i) q^{26} +(-4.51893 + 28.5314i) q^{27} +(-3.09981 - 13.5641i) q^{28} +(-6.37004 - 19.6050i) q^{29} +(0.351317 - 21.8167i) q^{30} +(-33.6775 + 46.3530i) q^{31} +(5.38169 + 31.5442i) q^{32} +(-2.64616 + 23.8551i) q^{33} +(-4.53924 - 23.4916i) q^{34} +(4.54279 + 16.7885i) q^{35} +(1.14525 + 16.9177i) q^{36} +(-10.3741 + 20.3602i) q^{37} +(-7.94021 + 0.268451i) q^{38} +(4.56844 + 6.28792i) q^{39} +(-8.28245 - 39.1331i) q^{40} +(-66.3703 - 21.5650i) q^{41} +(5.17589 + 14.2699i) q^{42} +(3.10057 - 3.10057i) q^{43} +(5.01378 + 43.7134i) q^{44} +(-2.26742 - 21.0738i) q^{45} +(-70.2459 - 32.8512i) q^{46} +(17.8070 + 34.9482i) q^{47} +(-10.0587 - 33.4308i) q^{48} +(21.6895 + 29.8530i) q^{49} +(12.2810 + 48.4683i) q^{50} +(8.06622 + 24.8253i) q^{51} +(10.7326 + 9.37161i) q^{52} +(30.8259 - 4.88234i) q^{53} +(-10.9608 - 56.7248i) q^{54} +(-8.42498 - 54.3509i) q^{55} +(15.0782 + 23.3885i) q^{56} +(8.56081 - 1.35590i) q^{57} +(25.3462 + 32.5161i) q^{58} +(-26.3599 - 81.1273i) q^{59} +(14.2174 + 41.2581i) q^{60} +(8.24903 + 11.3538i) q^{61} +(31.7079 - 110.117i) q^{62} +(6.69431 + 13.1383i) q^{63} +(-31.6300 - 55.6376i) q^{64} +(-13.8689 - 11.1744i) q^{65} +(-11.2929 - 46.6556i) q^{66} +(39.5762 - 39.5762i) q^{67} +(24.5546 + 41.0721i) q^{68} +(80.4622 + 26.1438i) q^{69} +(-19.9901 - 28.4668i) q^{70} +(38.5603 + 53.0737i) q^{71} +(-13.6903 - 31.0266i) q^{72} +(54.8494 - 107.648i) q^{73} +(5.62000 - 45.3548i) q^{74} +(-19.7990 - 50.8288i) q^{75} +(14.7457 - 5.91958i) q^{76} +(18.9405 + 33.2462i) q^{77} +(-12.8774 - 8.70672i) q^{78} +(32.9819 - 45.3957i) q^{79} +(42.2591 + 67.9276i) q^{80} +(7.68780 + 23.6606i) q^{81} +(139.492 - 4.71609i) q^{82} +(14.8404 - 93.6988i) q^{83} +(-19.4628 - 23.2998i) q^{84} +(-32.7012 - 50.0851i) q^{85} +(-3.71507 + 7.94396i) q^{86} +(-31.8046 - 31.8046i) q^{87} +(-39.2371 - 78.7683i) q^{88} -6.98261i q^{89} +(18.6344 + 38.0756i) q^{90} +(11.7841 + 3.82889i) q^{91} +(154.475 + 13.8606i) q^{92} +(-19.5568 + 123.477i) q^{93} +(-57.3127 - 53.5641i) q^{94} +(-18.1248 + 8.12320i) q^{95} +(41.7099 + 55.9951i) q^{96} +(7.72602 + 48.7802i) q^{97} +(-61.1378 - 41.3368i) q^{98} +(-16.4599 - 43.6283i) 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

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