LMFDB - Embedded newform 25.3.f.a.13.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,3,Mod(2,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("25.2");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	25.f (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:	$0.681200660901$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$4$ over $\Q(\zeta_{20})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			13.2
Character	$\chi$	$=$	25.13
Dual form			25.3.f.a.2.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.86717 + 0.295731i) q^{2} +(-2.19472 + 4.30737i) q^{3} +(-0.405347 + 0.131705i) q^{4} +(4.99561 - 0.209511i) q^{5} +(2.82409 - 8.69166i) q^{6} +(-3.57009 + 3.57009i) q^{7} +(7.45551 - 3.79877i) q^{8} +(-8.44662 - 11.6258i) q^{9} +O(q^{10})$	\(q+(-1.86717 + 0.295731i) q^{2} +(-2.19472 + 4.30737i) q^{3} +(-0.405347 + 0.131705i) q^{4} +(4.99561 - 0.209511i) q^{5} +(2.82409 - 8.69166i) q^{6} +(-3.57009 + 3.57009i) q^{7} +(7.45551 - 3.79877i) q^{8} +(-8.44662 - 11.6258i) q^{9} +(-9.26571 + 1.86855i) q^{10} +(11.7507 + 8.53735i) q^{11} +(0.322318 - 2.03504i) q^{12} +(1.48281 + 0.234854i) q^{13} +(5.61018 - 7.72176i) q^{14} +(-10.0615 + 21.9778i) q^{15} +(-11.4181 + 8.29572i) q^{16} +(0.980634 + 1.92460i) q^{17} +(19.2094 + 19.2094i) q^{18} +(-0.665919 - 0.216370i) q^{19} +(-1.99736 + 0.742872i) q^{20} +(-7.54237 - 23.2130i) q^{21} +(-24.4653 - 12.4657i) q^{22} +(-5.44617 - 34.3858i) q^{23} +40.4509i q^{24} +(24.9122 - 2.09327i) q^{25} -2.83811 q^{26} +(25.6417 - 4.06124i) q^{27} +(0.976924 - 1.91732i) q^{28} +(23.5192 - 7.64185i) q^{29} +(12.2871 - 44.0118i) q^{30} +(-0.269813 + 0.830398i) q^{31} +(-4.80067 + 4.80067i) q^{32} +(-62.5629 + 31.8774i) q^{33} +(-2.40018 - 3.30356i) q^{34} +(-17.0868 + 18.5827i) q^{35} +(4.95498 + 3.60001i) q^{36} +(3.63763 - 22.9671i) q^{37} +(1.30737 + 0.207068i) q^{38} +(-4.26594 + 5.87157i) q^{39} +(36.4489 - 20.5392i) q^{40} +(-17.9244 + 13.0228i) q^{41} +(20.9477 + 41.1122i) q^{42} +(7.47137 + 7.47137i) q^{43} +(-5.88750 - 1.91297i) q^{44} +(-44.6317 - 56.3082i) q^{45} +(20.3379 + 62.5936i) q^{46} +(69.0671 + 35.1914i) q^{47} +(-10.6733 - 67.3887i) q^{48} +23.5090i q^{49} +(-45.8964 + 11.2758i) q^{50} -10.4422 q^{51} +(-0.631983 + 0.100096i) q^{52} +(11.3757 - 22.3261i) q^{53} +(-46.6764 + 15.1661i) q^{54} +(60.4904 + 40.1874i) q^{55} +(-13.0549 + 40.1788i) q^{56} +(2.39349 - 2.39349i) q^{57} +(-41.6545 + 21.2240i) q^{58} +(-38.5765 - 53.0960i) q^{59} +(1.18381 - 10.2338i) q^{60} +(-71.2176 - 51.7426i) q^{61} +(0.258213 - 1.63029i) q^{62} +(71.6602 + 11.3499i) q^{63} +(40.7269 - 56.0557i) q^{64} +(7.45673 + 0.862573i) q^{65} +(107.389 - 78.0225i) q^{66} +(-40.4707 - 79.4283i) q^{67} +(-0.650977 - 0.650977i) q^{68} +(160.065 + 52.0084i) q^{69} +(26.4085 - 39.7503i) q^{70} +(-8.73781 - 26.8922i) q^{71} +(-107.138 - 54.5893i) q^{72} +(13.1161 + 82.8116i) q^{73} +43.9593i q^{74} +(-45.6588 + 111.900i) q^{75} +0.298425 q^{76} +(-72.4300 + 11.4718i) q^{77} +(6.22885 - 12.2248i) q^{78} +(-102.728 + 33.3782i) q^{79} +(-55.3022 + 43.8344i) q^{80} +(1.18297 - 3.64080i) q^{81} +(29.6167 - 29.6167i) q^{82} +(-22.5540 + 11.4919i) q^{83} +(6.11455 + 8.41596i) q^{84} +(5.30209 + 9.40911i) q^{85} +(-16.1599 - 11.7408i) q^{86} +(-18.7017 + 118.078i) q^{87} +(120.039 + 19.0122i) q^{88} +(21.8651 - 30.0947i) q^{89} +(99.9873 + 91.9381i) q^{90} +(-6.13220 + 4.45530i) q^{91} +(6.73637 + 13.2209i) q^{92} +(-2.98467 - 2.98467i) q^{93} +(-139.367 - 45.2832i) q^{94} +(-3.37200 - 0.941384i) q^{95} +(-10.1422 - 31.2144i) q^{96} +(53.1853 + 27.0993i) q^{97} +(-6.95233 - 43.8953i) q^{98} -208.722i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9}+O(q^{10}) $ 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19} + 130 q^{20} - 6 q^{21} + 70 q^{22} + 10 q^{23} - 40 q^{25} + 4 q^{26} - 100 q^{27} - 250 q^{28} - 110 q^{29} - 250 q^{30} - 6 q^{31} - 290 q^{32} - 190 q^{33} - 260 q^{34} - 120 q^{35} - 58 q^{36} + 50 q^{37} + 320 q^{38} + 390 q^{39} + 440 q^{40} - 86 q^{41} + 690 q^{42} + 230 q^{43} + 340 q^{44} + 310 q^{45} - 6 q^{46} + 70 q^{47} + 160 q^{48} - 100 q^{50} - 16 q^{51} - 320 q^{52} - 190 q^{53} - 660 q^{54} - 250 q^{55} - 70 q^{56} - 650 q^{57} - 640 q^{58} - 260 q^{59} - 550 q^{60} + 114 q^{61} + 60 q^{62} - 20 q^{63} + 340 q^{64} + 360 q^{65} + 138 q^{66} + 270 q^{67} + 710 q^{68} + 340 q^{69} + 310 q^{70} - 66 q^{71} + 360 q^{72} + 30 q^{73} - 90 q^{75} - 80 q^{76} - 250 q^{77} - 500 q^{78} - 210 q^{79} - 850 q^{80} + 62 q^{81} + 30 q^{82} - 10 q^{84} + 600 q^{85} - 6 q^{86} + 300 q^{87} + 190 q^{88} - 10 q^{89} + 380 q^{90} - 6 q^{91} - 30 q^{92} + 520 q^{93} + 790 q^{94} + 310 q^{95} + 174 q^{96} + 270 q^{97} + 170 q^{98}+O(q^{100}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9 - 10 * q^10 - 6 * q^11 - 10 * q^12 - 10 * q^13 - 10 * q^14 - 10 * q^15 + 2 * q^16 + 60 * q^17 + 140 * q^18 + 90 * q^19 + 130 * q^20 - 6 * q^21 + 70 * q^22 + 10 * q^23 - 40 * q^25 + 4 * q^26 - 100 * q^27 - 250 * q^28 - 110 * q^29 - 250 * q^30 - 6 * q^31 - 290 * q^32 - 190 * q^33 - 260 * q^34 - 120 * q^35 - 58 * q^36 + 50 * q^37 + 320 * q^38 + 390 * q^39 + 440 * q^40 - 86 * q^41 + 690 * q^42 + 230 * q^43 + 340 * q^44 + 310 * q^45 - 6 * q^46 + 70 * q^47 + 160 * q^48 - 100 * q^50 - 16 * q^51 - 320 * q^52 - 190 * q^53 - 660 * q^54 - 250 * q^55 - 70 * q^56 - 650 * q^57 - 640 * q^58 - 260 * q^59 - 550 * q^60 + 114 * q^61 + 60 * q^62 - 20 * q^63 + 340 * q^64 + 360 * q^65 + 138 * q^66 + 270 * q^67 + 710 * q^68 + 340 * q^69 + 310 * q^70 - 66 * q^71 + 360 * q^72 + 30 * q^73 - 90 * q^75 - 80 * q^76 - 250 * q^77 - 500 * q^78 - 210 * q^79 - 850 * q^80 + 62 * q^81 + 30 * q^82 - 10 * q^84 + 600 * q^85 - 6 * q^86 + 300 * q^87 + 190 * q^88 - 10 * q^89 + 380 * q^90 - 6 * q^91 - 30 * q^92 + 520 * q^93 + 790 * q^94 + 310 * q^95 + 174 * q^96 + 270 * q^97 + 170 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{19}{20}\right)$

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 $

$2$	−1.86717	+	0.295731i	−0.933587	+	0.147866i	−0.604654	−	0.796488i	$-0.706689\pi$
$2$	−1.86717	+	0.295731i	−0.933587	+	0.147866i	−0.328932	+	0.944354i	$0.606689\pi$
$3$	−2.19472	+	4.30737i	−0.731572	+	1.43579i	0.161962	+	0.986797i	$0.448218\pi$
$3$	−2.19472	+	4.30737i	−0.731572	+	1.43579i	−0.893535	+	0.448994i	$0.851782\pi$
$4$	−0.405347	+	0.131705i	−0.101337	+	0.0329263i
$5$	4.99561	−	0.209511i	0.999122	−	0.0419021i
$5$	4.99561	−	0.209511i	0.999122	−	0.0419021i
$6$	2.82409	−	8.69166i	0.470682	−	1.44861i
$7$	−3.57009	+	3.57009i	−0.510012	+	0.510012i	−0.914530	−	0.404518i	$-0.867439\pi$
$7$	−3.57009	+	3.57009i	−0.510012	+	0.510012i	0.404518	+	0.914530i	$0.367439\pi$
$8$	7.45551	−	3.79877i	0.931939	−	0.474846i
$9$	−8.44662	−	11.6258i	−0.938513	−	1.29175i
$10$	−9.26571	+	1.86855i	−0.926571	+	0.186855i
$11$	11.7507	+	8.53735i	1.06824	+	0.776123i	0.975595	−	0.219576i	$-0.0704674\pi$
$11$	11.7507	+	8.53735i	1.06824	+	0.776123i	0.0926463	+	0.995699i	$0.470467\pi$
$12$	0.322318	−	2.03504i	0.0268598	−	0.169586i
$13$	1.48281	+	0.234854i	0.114062	+	0.0180657i	0.213205	−	0.977008i	$-0.431610\pi$
$13$	1.48281	+	0.234854i	0.114062	+	0.0180657i	−0.0991424	+	0.995073i	$0.531610\pi$
$14$	5.61018	−	7.72176i	0.400727	−	0.551554i
$15$	−10.0615	+	21.9778i	−0.670767	+	1.46518i
$16$	−11.4181	+	8.29572i	−0.713630	+	0.518482i
$17$	0.980634	+	1.92460i	0.0576844	+	0.113212i	0.918049	−	0.396467i	$-0.129764\pi$
$17$	0.980634	+	1.92460i	0.0576844	+	0.113212i	−0.860364	+	0.509679i	$0.829764\pi$
$18$	19.2094	+	19.2094i	1.06719	+	1.06719i
$19$	−0.665919	−	0.216370i	−0.0350484	−	0.0113879i	0.291440	−	0.956589i	$-0.405866\pi$
$19$	−0.665919	−	0.216370i	−0.0350484	−	0.0113879i	−0.326489	+	0.945201i	$0.605866\pi$
$20$	−1.99736	+	0.742872i	−0.0998680	+	0.0371436i
$21$	−7.54237	−	23.2130i	−0.359160	−	1.10538i
$22$	−24.4653	−	12.4657i	−1.11206	−	0.566622i
$23$	−5.44617	−	34.3858i	−0.236790	−	1.49503i	−0.763954	−	0.645271i	$-0.776745\pi$
$23$	−5.44617	−	34.3858i	−0.236790	−	1.49503i	0.527164	−	0.849764i	$-0.323255\pi$
$24$			40.4509i			1.68545i
$25$	24.9122	−	2.09327i	0.996488	−	0.0837306i
$26$	−2.83811			−0.109158
$27$	25.6417	−	4.06124i	0.949691	−	0.150416i
$28$	0.976924	−	1.91732i	0.0348901	−	0.0684758i
$29$	23.5192	−	7.64185i	0.811007	−	0.263512i	0.125983	−	0.992032i	$-0.459792\pi$
$29$	23.5192	−	7.64185i	0.811007	−	0.263512i	0.685024	+	0.728520i	$0.259792\pi$
$30$	12.2871	−	44.0118i	0.409569	−	1.46706i
$31$	−0.269813	+	0.830398i	−0.00870364	+	0.0267870i	−0.955314	−	0.295593i	$-0.904483\pi$
$31$	−0.269813	+	0.830398i	−0.00870364	+	0.0267870i	0.946610	+	0.322380i	$0.104483\pi$
$32$	−4.80067	+	4.80067i	−0.150021	+	0.150021i
$33$	−62.5629	+	31.8774i	−1.89585	+	0.965982i
$34$	−2.40018	−	3.30356i	−0.0705935	−	0.0971636i
$35$	−17.0868	+	18.5827i	−0.488194	+	0.530935i
$36$	4.95498	+	3.60001i	0.137638	+	0.100000i
$37$	3.63763	−	22.9671i	0.0983144	−	0.620732i	−0.888500	−	0.458877i	$-0.848252\pi$
$37$	3.63763	−	22.9671i	0.0983144	−	0.620732i	0.986814	−	0.161856i	$-0.0517480\pi$
$38$	1.30737	+	0.207068i	0.0344046	+	0.00544915i
$39$	−4.26594	+	5.87157i	−0.109383	+	0.150553i
$40$	36.4489	−	20.5392i	0.911223	−	0.513480i
$41$	−17.9244	+	13.0228i	−0.437180	+	0.317630i	−0.784514	−	0.620112i	$-0.787087\pi$
$41$	−17.9244	+	13.0228i	−0.437180	+	0.317630i	0.347333	+	0.937742i	$0.387087\pi$
$42$	20.9477	+	41.1122i	0.498755	+	0.978863i
$43$	7.47137	+	7.47137i	0.173753	+	0.173753i	0.788626	−	0.614873i	$-0.210793\pi$
$43$	7.47137	+	7.47137i	0.173753	+	0.173753i	−0.614873	+	0.788626i	$0.710793\pi$
$44$	−5.88750	−	1.91297i	−0.133807	−	0.0434765i
$45$	−44.6317	−	56.3082i	−0.991816	−	1.25129i
$46$	20.3379	+	62.5936i	0.442128	+	1.36073i
$47$	69.0671	+	35.1914i	1.46951	+	0.748754i	0.991562	−	0.129633i	$-0.0413798\pi$
$47$	69.0671	+	35.1914i	1.46951	+	0.748754i	0.477951	+	0.878387i	$0.341380\pi$
$48$	−10.6733	−	67.3887i	−0.222361	−	1.40393i
$49$			23.5090i			0.479775i
$50$	−45.8964	+	11.2758i	−0.917927	+	0.225516i
$51$	−10.4422			−0.204749
$52$	−0.631983	+	0.100096i	−0.0121535	+	0.00192493i
$53$	11.3757	−	22.3261i	0.214636	−	0.421246i	−0.758436	−	0.651747i	$-0.774036\pi$
$53$	11.3757	−	22.3261i	0.214636	−	0.421246i	0.973072	+	0.230501i	$0.0740364\pi$
$54$	−46.6764	+	15.1661i	−0.864378	+	0.280853i
$55$	60.4904	+	40.1874i	1.09982	+	0.730680i
$56$	−13.0549	+	40.1788i	−0.233123	+	0.717478i
$57$	2.39349	−	2.39349i	0.0419911	−	0.0419911i
$58$	−41.6545	+	21.2240i	−0.718181	+	0.365931i
$59$	−38.5765	−	53.0960i	−0.653839	−	0.899932i	0.345419	−	0.938448i	$-0.387737\pi$
$59$	−38.5765	−	53.0960i	−0.653839	−	0.899932i	−0.999258	+	0.0385168i	$0.987737\pi$
$60$	1.18381	−	10.2338i	0.0197302	−	0.170563i
$61$	−71.2176	−	51.7426i	−1.16750	−	0.848239i	−0.176794	−	0.984248i	$-0.556573\pi$
$61$	−71.2176	−	51.7426i	−1.16750	−	0.848239i	−0.990708	+	0.136008i	$0.956573\pi$
$62$	0.258213	−	1.63029i	0.00416472	−	0.0262950i
$63$	71.6602	+	11.3499i	1.13746	+	0.180157i
$64$	40.7269	−	56.0557i	0.636357	−	0.875870i
$65$	7.45673	+	0.862573i	0.114719	+	0.0132704i
$66$	107.389	−	78.0225i	1.62710	−	1.18216i
$67$	−40.4707	−	79.4283i	−0.604041	−	1.18550i	−0.967259	−	0.253793i	$-0.918322\pi$
$67$	−40.4707	−	79.4283i	−0.604041	−	1.18550i	0.363218	−	0.931704i	$-0.381678\pi$
$68$	−0.650977	−	0.650977i	−0.00957319	−	0.00957319i
$69$	160.065	+	52.0084i	2.31979	+	0.753744i
$70$	26.4085	−	39.7503i	0.377264	−	0.567861i
$71$	−8.73781	−	26.8922i	−0.123068	−	0.378763i	0.870476	−	0.492210i	$-0.163811\pi$
$71$	−8.73781	−	26.8922i	−0.123068	−	0.378763i	−0.993544	+	0.113447i	$0.963811\pi$
$72$	−107.138	−	54.5893i	−1.48802	−	0.758185i
$73$	13.1161	+	82.8116i	0.179672	+	1.13441i	0.898421	+	0.439136i	$0.144715\pi$
$73$	13.1161	+	82.8116i	0.179672	+	1.13441i	−0.718749	+	0.695270i	$0.755285\pi$
$74$			43.9593i			0.594045i
$75$	−45.6588	+	111.900i	−0.608784	+	1.49200i
$76$	0.298425			0.00392665
$77$	−72.4300	+	11.4718i	−0.940649	+	0.148984i
$78$	6.22885	−	12.2248i	0.0798571	−	0.156728i
$79$	−102.728	+	33.3782i	−1.30035	+	0.422509i	−0.875703	−	0.482850i	$-0.839602\pi$
$79$	−102.728	+	33.3782i	−1.30035	+	0.422509i	−0.424646	+	0.905359i	$0.639602\pi$
$80$	−55.3022	+	43.8344i	−0.691278	+	0.547930i
$81$	1.18297	−	3.64080i	0.0146045	−	0.0449481i
$82$	29.6167	−	29.6167i	0.361179	−	0.361179i
$83$	−22.5540	+	11.4919i	−0.271735	+	0.138456i	−0.584549	−	0.811358i	$-0.698729\pi$
$83$	−22.5540	+	11.4919i	−0.271735	+	0.138456i	0.312813	+	0.949815i	$0.398729\pi$
$84$	6.11455	+	8.41596i	0.0727923	+	0.100190i
$85$	5.30209	+	9.40911i	0.0623775	+	0.110695i
$86$	−16.1599	−	11.7408i	−0.187905	−	0.136521i
$87$	−18.7017	+	118.078i	−0.214962	+	1.35721i
$88$	120.039	+	19.0122i	1.36407	+	0.216048i
$89$	21.8651	−	30.0947i	0.245675	−	0.338143i	−0.668316	−	0.743878i	$-0.732984\pi$
$89$	21.8651	−	30.0947i	0.245675	−	0.338143i	0.913991	+	0.405735i	$0.132984\pi$
$90$	99.9873	+	91.9381i	1.11097	+	1.02153i
$91$	−6.13220	+	4.45530i	−0.0673868	+	0.0489594i
$92$	6.73637	+	13.2209i	0.0732215	+	0.143705i
$93$	−2.98467	−	2.98467i	−0.0320933	−	0.0320933i
$94$	−139.367	−	45.2832i	−1.48263	−	0.481736i
$95$	−3.37200	−	0.941384i	−0.0354948	−	0.00990930i
$96$	−10.1422	−	31.2144i	−0.105648	−	0.325150i
$97$	53.1853	+	27.0993i	0.548302	+	0.279374i	0.706117	−	0.708095i	$-0.250445\pi$
$97$	53.1853	+	27.0993i	0.548302	+	0.279374i	−0.157815	+	0.987469i	$0.550445\pi$
$98$	−6.95233	−	43.8953i	−0.0709422	−	0.447911i
$99$		−	208.722i		−	2.10831i
$100$	−9.82239	+	4.12956i	−0.0982239	+	0.0412956i
$101$	125.096			1.23857			0.619287	−	0.785164i	$-0.287422\pi$
$101$	125.096			1.23857			0.619287	+	0.785164i	$0.287422\pi$
$102$	19.4974	−	3.08808i	0.191151	−	0.0302753i
$103$	10.0578	−	19.7396i	0.0976487	−	0.191646i	−0.837015	−	0.547181i	$-0.815701\pi$
$103$	10.0578	−	19.7396i	0.0976487	−	0.191646i	0.934663	+	0.355534i	$0.115701\pi$
$104$	11.9472	−	3.88189i	0.114877	−	0.0373259i
$105$	−42.5421	−	114.383i	−0.405163	−	1.08936i
$106$	−14.6379	+	45.0508i	−0.138093	+	0.425007i
$107$	−35.6587	+	35.6587i	−0.333259	+	0.333259i	−0.853823	−	0.520564i	$-0.825722\pi$
$107$	−35.6587	+	35.6587i	−0.333259	+	0.333259i	0.520564	+	0.853823i	$0.325722\pi$
$108$	−9.85888	+	5.02335i	−0.0912859	+	0.0465125i
$109$	16.9971	+	23.3945i	0.155937	+	0.214628i	0.879836	−	0.475277i	$-0.157652\pi$
$109$	16.9971	+	23.3945i	0.155937	+	0.214628i	−0.723900	+	0.689905i	$0.757652\pi$
$110$	−124.831	−	57.1479i	−1.13482	−	0.519527i
$111$	90.9443	+	66.0749i	0.819318	+	0.595269i
$112$	11.1471	−	70.3800i	0.0995276	−	0.628393i
$113$	−85.3823	−	13.5232i	−0.755596	−	0.119675i	−0.233260	−	0.972414i	$-0.574939\pi$
$113$	−85.3823	−	13.5232i	−0.755596	−	0.119675i	−0.522336	+	0.852740i	$0.674939\pi$
$114$	−3.76123	+	5.17689i	−0.0329933	+	0.0454113i
$115$	−34.4111	−	170.637i	−0.299227	−	1.48380i
$116$	−8.52696	+	6.19520i	−0.0735082	+	0.0534069i
$117$	−9.79436	−	19.2225i	−0.0837124	−	0.164295i
$118$	87.7311	+	87.7311i	0.743484	+	0.743484i
$119$	−10.3719	−	3.37005i	−0.0871592	−	0.0283198i
$120$	8.47489	+	202.077i	0.0706241	+	1.68397i
$121$	27.8005	+	85.5612i	0.229756	+	0.707117i
$122$	148.277	+	75.5511i	1.21539	+	0.619272i
$123$	−16.7553	−	105.789i	−0.136222	−	0.860069i
$124$		−	0.372135i		−	0.00300109i
$125$	124.013	−	15.6765i	0.992105	−	0.125412i
$126$	−137.159			−1.08856
$127$	−41.0976	+	6.50923i	−0.323603	+	0.0512538i	−0.316123	−	0.948718i	$-0.602381\pi$
$127$	−41.0976	+	6.50923i	−0.323603	+	0.0512538i	−0.00748062	+	0.999972i	$0.502381\pi$
$128$	−47.1378	+	92.5131i	−0.368264	+	0.722759i
$129$	−48.5795	+	15.7844i	−0.376585	+	0.122360i
$130$	−14.1781	+	0.594614i	−0.109062	+	0.00457396i
$131$	71.9522	−	221.446i	0.549253	−	1.69043i	−0.161403	−	0.986889i	$-0.551602\pi$
$131$	71.9522	−	221.446i	0.549253	−	1.69043i	0.710657	−	0.703539i	$-0.248398\pi$
$132$	21.1613	−	21.1613i	0.160313	−	0.160313i
$133$	3.14985	−	1.60493i	0.0236831	−	0.0120671i
$134$	99.0553	+	136.338i	0.739219	+	1.01745i
$135$	127.245	−	25.6606i	0.942554	−	0.190078i
$136$	14.6223	+	10.6237i	0.107517	+	0.0781154i
$137$	1.52175	−	9.60794i	0.0111076	−	0.0701309i	−0.981512	−	0.191401i	$-0.938697\pi$
$137$	1.52175	−	9.60794i	0.0111076	−	0.0701309i	0.992620	+	0.121270i	$0.0386968\pi$
$138$	−314.250	−	49.7723i	−2.27717	−	0.360669i
$139$	−97.0770	+	133.615i	−0.698395	+	0.961259i	0.301574	+	0.953443i	$0.402488\pi$
$139$	−97.0770	+	133.615i	−0.698395	+	0.961259i	−0.999969	+	0.00781597i	$0.997512\pi$
$140$	4.47863	−	9.78286i	0.0319902	−	0.0698776i
$141$	−303.165	+	220.263i	−2.15011	+	1.56215i
$142$	24.2679	+	47.6284i	0.170900	+	0.335411i
$143$	15.4189	+	15.4189i	0.107825	+	0.107825i
$144$	192.888	+	62.6732i	1.33950	+	0.435231i
$145$	115.892	−	43.1032i	0.799253	−	0.297263i
$146$	−48.9800	−	150.745i	−0.335479	−	1.03250i
$147$	−101.262	−	51.5955i	−0.688856	−	0.350990i
$148$	1.55038	+	9.78873i	0.0104756	+	0.0661401i
$149$			182.741i			1.22645i	0.789908	+	0.613225i	$0.210128\pi$
$149$			182.741i			1.22645i	−0.789908	+	0.613225i	$0.789872\pi$
$150$	52.1604	−	222.440i	0.347736	−	1.48293i
$151$	−46.5918			−0.308555			−0.154277	−	0.988028i	$-0.549305\pi$
$151$	−46.5918			−0.308555			−0.154277	+	0.988028i	$0.549305\pi$
$152$	−5.78671	+	0.916524i	−0.0380704	+	0.00602976i
$153$	14.0920	−	27.6570i	0.0921043	−	0.180765i
$154$	131.847	−	42.8396i	0.856148	−	0.278179i
$155$	−1.17390	+	4.20487i	−0.00757356	+	0.0271282i
$156$	0.955871	−	2.94187i	0.00612738	−	0.0188581i
$157$	113.507	−	113.507i	0.722972	−	0.722972i	−0.246237	−	0.969210i	$-0.579194\pi$
$157$	113.507	−	113.507i	0.722972	−	0.722972i	0.969210	+	0.246237i	$0.0791943\pi$
$158$	181.939	−	92.7027i	1.15151	−	0.586726i
$159$	71.2003	+	97.9987i	0.447800	+	0.616344i
$160$	−22.9765	+	24.9881i	−0.143603	+	0.156175i
$161$	142.204	+	103.317i	0.883252	+	0.641720i
$162$	−1.13211	+	7.14784i	−0.00698832	+	0.0441225i
$163$	51.9393	+	8.22637i	0.318646	+	0.0504685i	0.313709	−	0.949519i	$-0.398428\pi$
$163$	51.9393	+	8.22637i	0.318646	+	0.0504685i	0.00493714	+	0.999988i	$0.498428\pi$
$164$	5.55042	−	7.63950i	0.0338440	−	0.0465823i
$165$	−305.861	+	172.355i	−1.85370	+	1.04457i
$166$	38.7138	−	28.1272i	0.233216	−	0.169441i
$167$	−80.6381	−	158.261i	−0.482863	−	0.947672i	−0.995999	−	0.0893646i	$-0.971516\pi$
$167$	−80.6381	−	158.261i	−0.482863	−	0.947672i	0.513136	−	0.858307i	$-0.328484\pi$
$168$	−144.413	−	144.413i	−0.859602	−	0.859602i
$169$	−158.585	−	51.5274i	−0.938373	−	0.304896i
$170$	−12.6825	−	16.0004i	−0.0746029	−	0.0941203i
$171$	3.10929	+	9.56942i	0.0181830	+	0.0559615i
$172$	−4.01251	−	2.04448i	−0.0233286	−	0.0118865i
$173$	14.6263	+	92.3468i	0.0845450	+	0.533796i	0.993216	+	0.116283i	$0.0370981\pi$
$173$	14.6263	+	92.3468i	0.0845450	+	0.533796i	−0.908671	+	0.417513i	$0.862902\pi$
$174$		−	226.002i		−	1.29886i
$175$	−81.4656	+	96.4119i	−0.465518	+	0.550925i
$176$	−204.993			−1.16474
$177$	313.369	−	49.6327i	1.77044	−	0.280411i
$178$	−31.9260	+	62.6582i	−0.179359	+	0.352013i
$179$	148.821	−	48.3547i	0.831400	−	0.270138i	0.137765	−	0.990465i	$-0.456008\pi$
$179$	148.821	−	48.3547i	0.831400	−	0.270138i	0.693635	+	0.720327i	$0.256008\pi$
$180$	25.5074	+	16.9461i	0.141708	+	0.0941450i
$181$	−78.4020	+	241.296i	−0.433160	+	1.33313i	0.461800	+	0.886984i	$0.347204\pi$
$181$	−78.4020	+	241.296i	−0.433160	+	1.33313i	−0.894960	+	0.446146i	$0.852796\pi$
$182$	10.1323	−	10.1323i	0.0556720	−	0.0556720i
$183$	379.177	−	193.200i	2.07201	−	1.05574i
$184$	−171.228	−	235.675i	−0.930586	−	1.28084i
$185$	13.3603	−	115.497i	0.0722180	−	0.624307i
$186$	6.45556	+	4.69024i	0.0347073	+	0.0252164i
$187$	−4.90792	+	30.9874i	−0.0262456	+	0.165708i
$188$	−32.6310	−	5.16825i	−0.173569	−	0.0274907i
$189$	−77.0440	+	106.042i	−0.407640	+	0.561068i
$190$	6.57451	+	0.760520i	0.0346027	+	0.00400274i
$191$	122.790	−	89.2124i	0.642881	−	0.467081i	−0.217958	−	0.975958i	$-0.569939\pi$
$191$	122.790	−	89.2124i	0.642881	−	0.467081i	0.860839	+	0.508878i	$0.169939\pi$
$192$	152.069	+	298.452i	0.792026	+	1.55444i
$193$	−235.980	−	235.980i	−1.22269	−	1.22269i	−0.966671	−	0.256021i	$-0.917588\pi$
$193$	−235.980	−	235.980i	−1.22269	−	1.22269i	−0.256021	−	0.966671i	$-0.582412\pi$
$194$	−107.320	−	34.8705i	−0.553198	−	0.179745i
$195$	−20.0808	+	30.2258i	−0.102979	+	0.155004i
$196$	−3.09625	−	9.52928i	−0.0157972	−	0.0486188i
$197$	−29.8286	−	15.1984i	−0.151414	−	0.0771494i	0.376642	−	0.926359i	$-0.377079\pi$
$197$	−29.8286	−	15.1984i	−0.151414	−	0.0771494i	−0.528056	+	0.849210i	$0.677079\pi$
$198$	61.7257	+	389.721i	0.311746	+	1.96829i
$199$			169.710i			0.852815i	0.904531	+	0.426407i	$0.140221\pi$
$199$			169.710i			0.852815i	−0.904531	+	0.426407i	$0.859779\pi$
$200$	177.781	−	110.242i	0.888907	−	0.551211i
$201$	430.949			2.14403
$202$	−233.576	+	36.9948i	−1.15632	+	0.183143i
$203$	−56.6835	+	111.248i	−0.279229	+	0.548018i
$204$	4.23271	−	1.37529i	0.0207486	−	0.00674162i
$205$	−86.8148	+	68.8123i	−0.423487	+	0.335670i
$206$	−12.9421	+	39.8316i	−0.0628256	+	0.193357i
$207$	−353.760	+	353.760i	−1.70898	+	1.70898i
$208$	−18.8791	+	9.61938i	−0.0907649	+	0.0462470i
$209$	−5.97776	−	8.22768i	−0.0286017	−	0.0393669i
$210$	113.260	+	200.992i	0.539334	+	0.957104i
$211$	−258.395	−	187.735i	−1.22462	−	0.889739i	−0.228145	−	0.973627i	$-0.573266\pi$
$211$	−258.395	−	187.735i	−1.22462	−	0.889739i	−0.996475	+	0.0838886i	$0.973266\pi$
$212$	−1.67064	+	10.5480i	−0.00788040	+	0.0497549i
$213$	135.012	+	21.3838i	0.633858	+	0.100393i
$214$	56.0357	−	77.1265i	0.261849	−	0.360404i
$215$	38.8894	+	35.7587i	0.180881	+	0.166320i
$216$	175.744	−	127.685i	0.813629	−	0.591136i
$217$	−2.00134	−	3.92785i	−0.00922276	−	0.0181007i
$218$	−38.6550	−	38.6550i	−0.177316	−	0.177316i
$219$	−385.487	−	125.252i	−1.76021	−	0.571928i
$220$	−29.8125	−	8.32294i	−0.135511	−	0.0378315i
$221$	1.00209	+	3.08412i	0.00453435	+	0.0139553i
$222$	−189.349	−	96.4782i	−0.852924	−	0.434587i
$223$	45.5256	+	287.438i	0.204151	+	1.28896i	0.850524	+	0.525936i	$0.176285\pi$
$223$	45.5256	+	287.438i	0.204151	+	1.28896i	−0.646373	+	0.763021i	$0.723715\pi$
$224$		−	34.2776i		−	0.153025i
$225$	−234.760	−	271.943i	−1.04338	−	1.20863i
$226$	163.423			0.723110
$227$	−69.1857	+	10.9579i	−0.304783	+	0.0482728i	−0.306953	−	0.951725i	$-0.599309\pi$
$227$	−69.1857	+	10.9579i	−0.304783	+	0.0482728i	0.00216992	+	0.999998i	$0.499309\pi$
$228$	−0.654959	+	1.28543i	−0.00287263	+	0.00563785i
$229$	308.912	−	100.371i	1.34896	−	0.438303i	0.456617	−	0.889663i	$-0.349061\pi$
$229$	308.912	−	100.371i	1.34896	−	0.438303i	0.892342	+	0.451360i	$0.149061\pi$
$230$	114.714	+	308.432i	0.498757	+	1.34101i
$231$	109.550	−	337.160i	0.474242	−	1.45957i
$232$	146.318	−	146.318i	0.630681	−	0.630681i
$233$	−252.995	+	128.908i	−1.08582	+	0.553252i	−0.902889	−	0.429875i	$-0.858558\pi$
$233$	−252.995	+	128.908i	−1.08582	+	0.553252i	−0.182929	+	0.983126i	$0.558558\pi$
$234$	23.9725	+	32.9953i	0.102446	+	0.141005i
$235$	352.405	+	161.332i	1.49960	+	0.686521i
$236$	22.6299	+	16.4416i	0.0958892	+	0.0696676i
$237$	81.6855	−	515.742i	0.344665	−	2.17613i
$238$	20.3629	+	3.22516i	0.0855582	+	0.0135511i
$239$	94.5343	−	130.115i	0.395541	−	0.544416i	−0.564077	−	0.825722i	$-0.690768\pi$
$239$	94.5343	−	130.115i	0.395541	−	0.544416i	0.959618	+	0.281307i	$0.0907678\pi$
$240$	−67.4384	−	334.411i	−0.280993	−	1.39338i
$241$	215.316	−	156.436i	0.893427	−	0.649113i	−0.0433422	−	0.999060i	$-0.513801\pi$
$241$	215.316	−	156.436i	0.893427	−	0.649113i	0.936769	+	0.349948i	$0.113801\pi$
$242$	−77.2115	−	151.536i	−0.319056	−	0.626182i
$243$	178.303	+	178.303i	0.733756	+	0.733756i
$244$	35.6826	+	11.5940i	0.146240	+	0.0475163i
$245$	4.92538	+	117.442i	0.0201036	+	0.479353i
$246$	62.5699	+	192.570i	0.254349	+	0.782807i
$247$	−0.936614	−	0.477229i	−0.00379196	−	0.00193210i
$248$	1.14290	+	7.21600i	0.00460848	+	0.0290968i
$249$		−	122.370i		−	0.491446i
$250$	−226.918	+	65.9453i	−0.907672	+	0.263781i
$251$	−304.349			−1.21255			−0.606273	−	0.795257i	$-0.707336\pi$
$251$	−304.349			−1.21255			−0.606273	+	0.795257i	$0.707336\pi$
$252$	−30.5421	+	4.83739i	−0.121199	+	0.0191960i
$253$	229.567	−	450.552i	0.907381	−	1.78084i
$254$	74.8114	−	24.3077i	0.294533	−	0.0956996i
$255$	−52.1651	+	2.18775i	−0.204569	+	0.00857941i
$256$	−24.9901	+	76.9116i	−0.0976176	+	0.300436i
$257$	−328.140	+	328.140i	−1.27681	+	1.27681i	−0.334364	+	0.942444i	$0.608522\pi$
$257$	−328.140	+	328.140i	−1.27681	+	1.27681i	−0.942444	+	0.334364i	$0.891478\pi$
$258$	86.0384	−	43.8388i	0.333482	−	0.169918i
$259$	69.0079	+	94.9812i	0.266440	+	0.366723i
$260$	−3.13617	+	0.632448i	−0.0120622	+	0.00243249i
$261$	−287.500	−	208.881i	−1.10153	−	0.800311i
$262$	−68.8587	+	434.757i	−0.262819	+	1.65938i
$263$	−98.9066	−	15.6653i	−0.376071	−	0.0595638i	−0.0344620	−	0.999406i	$-0.510972\pi$
$263$	−98.9066	−	15.6653i	−0.376071	−	0.0595638i	−0.341609	+	0.939842i	$0.610972\pi$
$264$	−345.344	+	475.325i	−1.30812	+	1.80047i
$265$	52.1510	−	113.916i	0.196796	−	0.429870i
$266$	−5.40669	+	3.92819i	−0.0203259	+	0.0147676i
$267$	81.6415	+	160.230i	0.305773	+	0.600114i
$268$	26.8658	+	26.8658i	0.100246	+	0.100246i
$269$	−104.699	−	34.0186i	−0.389214	−	0.126463i	0.107872	−	0.994165i	$-0.465596\pi$
$269$	−104.699	−	34.0186i	−0.389214	−	0.126463i	−0.497085	+	0.867702i	$0.665596\pi$
$270$	−230.000	+	85.5430i	−0.851850	+	0.316826i
$271$	86.7259	+	266.915i	0.320022	+	0.984926i	0.973638	+	0.228100i	$0.0732512\pi$
$271$	86.7259	+	266.915i	0.320022	+	0.984926i	−0.653616	+	0.756826i	$0.726749\pi$
$272$	−27.1629	−	13.8402i	−0.0998637	−	0.0508831i
$273$	−5.73222	−	36.1918i	−0.0209971	−	0.132571i
$274$			18.3897i			0.0671157i
$275$	310.606	+	188.087i	1.12948	+	0.683953i
$276$	−71.7317			−0.259897
$277$	278.815	−	44.1599i	1.00655	−	0.159422i	0.368673	−	0.929559i	$-0.379812\pi$
$277$	278.815	−	44.1599i	1.00655	−	0.159422i	0.637878	+	0.770137i	$0.279812\pi$
$278$	141.745	−	278.191i	0.509875	−	1.00069i
$279$	11.9330	−	3.87728i	0.0427707	−	0.0138971i
$280$	−56.7991	+	203.452i	−0.202854	+	0.726616i
$281$	−168.715	+	519.250i	−0.600408	+	1.84786i	−0.0746877	+	0.997207i	$0.523796\pi$
$281$	−168.715	+	519.250i	−0.600408	+	1.84786i	−0.525720	+	0.850658i	$0.676204\pi$
$282$	500.924	−	500.924i	1.77633	−	1.77633i
$283$	53.0066	−	27.0082i	0.187302	−	0.0954353i	−0.357825	−	0.933789i	$-0.616481\pi$
$283$	53.0066	−	27.0082i	0.187302	−	0.0954353i	0.545127	+	0.838353i	$0.316481\pi$
$284$	7.08368	+	9.74985i	0.0249425	+	0.0343305i
$285$	11.4555	−	12.4584i	0.0401947	−	0.0437137i
$286$	−33.3497	−	24.2300i	−0.116607	−	0.0847201i
$287$	17.4990	−	110.484i	0.0609721	−	0.384963i
$288$	96.3610	+	15.2621i	0.334587	+	0.0529934i
$289$	167.127	−	230.031i	0.578296	−	0.795956i
$290$	−203.643	+	114.754i	−0.702217	+	0.395703i
$291$	−233.453	+	169.614i	−0.802245	+	0.582865i
$292$	−16.2233	−	31.8400i	−0.0555591	−	0.109041i
$293$	−83.9701	−	83.9701i	−0.286587	−	0.286587i	0.549142	−	0.835729i	$-0.314955\pi$
$293$	−83.9701	−	83.9701i	−0.286587	−	0.286587i	−0.835729	+	0.549142i	$0.814955\pi$
$294$	204.332	+	66.3915i	0.695007	+	0.225821i
$295$	−203.837	−	257.164i	−0.690973	−	0.871744i
$296$	−60.1264	−	185.050i	−0.203130	−	0.625169i
$297$	335.979	+	171.190i	1.13124	+	0.576396i
$298$	−54.0422	−	341.209i	−0.181350	−	1.14500i
$299$		−	52.2666i		−	0.174805i
$300$	3.76978	−	51.3719i	0.0125659	−	0.171240i
$301$	−53.3469			−0.177232
$302$	86.9949	−	13.7786i	0.288063	−	0.0456247i
$303$	−274.550	+	538.836i	−0.906107	+	1.77834i
$304$	9.39846	−	3.05375i	0.0309160	−	0.0100452i
$305$	−366.616	−	243.565i	−1.20202	−	0.798574i
$306$	−18.1331	+	55.8079i	−0.0592585	+	0.182379i
$307$	28.0098	−	28.0098i	0.0912370	−	0.0912370i	−0.660015	−	0.751252i	$-0.729450\pi$
$307$	28.0098	−	28.0098i	0.0912370	−	0.0912370i	0.751252	+	0.660015i	$0.229450\pi$
$308$	27.8484	−	14.1894i	0.0904167	−	0.0460696i
$309$	62.9517	+	86.6456i	0.203727	+	0.280406i
$310$	0.948366	−	8.19839i	0.00305924	−	0.0264464i
$311$	286.986	+	208.507i	0.922784	+	0.670442i	0.944215	−	0.329328i	$-0.106822\pi$
$311$	286.986	+	208.507i	0.922784	+	0.670442i	−0.0214313	+	0.999770i	$0.506822\pi$
$312$	−9.50004	+	59.9809i	−0.0304488	+	0.192246i
$313$	−250.103	−	39.6125i	−0.799052	−	0.126557i	−0.256461	−	0.966554i	$-0.582557\pi$
$313$	−250.103	−	39.6125i	−0.799052	−	0.126557i	−0.542591	+	0.839997i	$0.682557\pi$
$314$	−178.369	+	245.504i	−0.568055	+	0.781860i
$315$	360.364	+	41.6859i	1.14401	+	0.132336i
$316$	37.2442	−	27.0595i	0.117861	−	0.0856314i
$317$	−125.982	−	247.254i	−0.397420	−	0.779980i	0.602414	−	0.798183i	$-0.294205\pi$
$317$	−125.982	−	247.254i	−0.397420	−	0.779980i	−0.999834	+	0.0182030i	$0.994205\pi$
$318$	−161.925	−	161.925i	−0.509197	−	0.509197i
$319$	341.607	+	110.995i	1.07087	+	0.347946i
$320$	191.711	−	288.565i	0.599097	−	0.901766i
$321$	−75.3347	−	231.856i	−0.234688	−	0.722294i
$322$	−296.073	−	150.857i	−0.919480	−	0.468499i
$323$	−0.236596	−	1.49381i	−0.000732496	−	0.00462480i
$324$			1.63159i			0.00503577i
$325$	37.4316	+	2.74681i	0.115174	+	0.00845173i
$326$	−99.4124			−0.304946
$327$	−138.073	+	21.8685i	−0.422240	+	0.0668763i
$328$	−84.1647	+	165.183i	−0.256600	+	0.503605i
$329$	−372.212	+	120.939i	−1.13134	+	0.367596i
$330$	520.125	−	412.269i	1.57614	−	1.24930i
$331$	142.165	−	437.539i	0.429501	−	1.32187i	−0.469116	−	0.883136i	$-0.655427\pi$
$331$	142.165	−	437.539i	0.429501	−	1.32187i	0.898618	−	0.438733i	$-0.144573\pi$
$332$	7.62867	−	7.62867i	0.0229779	−	0.0229779i
$333$	−297.736	+	151.704i	−0.894102	+	0.455568i
$334$	197.368	+	271.654i	0.590923	+	0.813335i
$335$	−218.817	−	388.314i	−0.653185	−	1.15915i
$336$	278.688	+	202.479i	0.829429	+	0.602615i
$337$	−95.9825	+	606.010i	−0.284815	+	1.79825i	0.266376	+	0.963869i	$0.414174\pi$
$337$	−95.9825	+	606.010i	−0.284815	+	1.79825i	−0.551190	+	0.834380i	$0.685826\pi$
$338$	311.344	+	49.3120i	0.921136	+	0.145894i
$339$	245.640	−	338.094i	0.724601	−	0.997327i
$340$	−3.38841	−	3.11564i	−0.00996592	−	0.00916365i
$341$	−10.2599	+	7.45424i	−0.0300876	+	0.0218599i
$342$	−8.63557	−	16.9483i	−0.0252502	−	0.0495563i
$343$	−258.863	−	258.863i	−0.754703	−	0.754703i
$344$	84.0849	+	27.3208i	0.244433	+	0.0794210i
$345$	810.520	+	226.278i	2.34933	+	0.655878i
$346$	−54.6196	−	168.102i	−0.157860	−	0.485844i
$347$	471.200	+	240.088i	1.35792	+	0.691897i	0.972947	−	0.231029i	$-0.0742093\pi$
$347$	471.200	+	240.088i	1.35792	+	0.691897i	0.384977	+	0.922926i	$0.374209\pi$
$348$	−7.97077	−	50.3255i	−0.0229045	−	0.144613i
$349$			189.896i			0.544113i	0.962281	+	0.272057i	$0.0877038\pi$
$349$			189.896i			0.544113i	−0.962281	+	0.272057i	$0.912296\pi$
$350$	123.598	−	204.110i	0.353138	−	0.583170i
$351$	38.9754			0.111041
$352$	−97.3961	+	15.4260i	−0.276694	+	0.0438239i
$353$	−103.285	+	202.708i	−0.292591	+	0.574242i	−0.989773	−	0.142652i	$-0.954437\pi$
$353$	−103.285	+	202.708i	−0.292591	+	0.574242i	0.697182	+	0.716894i	$0.254437\pi$
$354$	−570.436	+	185.346i	−1.61140	+	0.523576i
$355$	−49.2849	−	132.512i	−0.138831	−	0.373274i
$356$	−4.89931	+	15.0785i	−0.0137621	+	0.0423554i
$357$	37.2796	−	37.2796i	0.104425	−	0.104425i
$358$	−263.574	+	134.298i	−0.736239	+	0.375133i
$359$	−177.619	−	244.471i	−0.494760	−	0.680979i	0.486497	−	0.873682i	$-0.338274\pi$
$359$	−177.619	−	244.471i	−0.494760	−	0.680979i	−0.981257	+	0.192703i	$0.938274\pi$
$360$	−546.654	−	250.260i	−1.51848	−	0.695168i
$361$	−291.659	−	211.902i	−0.807918	−	0.586987i
$362$	75.0312	−	473.728i	0.207268	−	1.30864i
$363$	−429.558	−	68.0354i	−1.18336	−	0.187425i
$364$	1.89888	−	2.61358i	0.00521670	−	0.00718018i
$365$	82.8727	+	410.946i	0.227048	+	1.12588i
$366$	−650.854	+	472.873i	−1.77829	+	1.29200i
$367$	114.708	+	225.127i	0.312556	+	0.613425i	0.992830	−	0.119532i	$-0.0381395\pi$
$367$	114.708	+	225.127i	0.312556	+	0.613425i	−0.680275	+	0.732957i	$0.738140\pi$
$368$	347.440	+	347.440i	0.944130	+	0.944130i
$369$	302.801	+	98.3861i	0.820599	+	0.266629i
$370$	9.20994	+	219.604i	0.0248917	+	0.593523i
$371$	39.0937	+	120.318i	0.105374	+	0.324308i
$372$	1.60292	+	0.816731i	0.00430894	+	0.00219551i
$373$	−20.8557	−	131.678i	−0.0559135	−	0.353024i	−0.999745	−	0.0225959i	$-0.992807\pi$
$373$	−20.8557	−	131.678i	−0.0559135	−	0.353024i	0.943831	−	0.330428i	$-0.107193\pi$
$374$		−	59.3102i		−	0.158583i
$375$	−204.649	+	568.576i	−0.545731	+	1.51620i
$376$	648.615			1.72504
$377$	36.6691	−	5.80782i	0.0972656	−	0.0154054i
$378$	112.495	−	220.783i	0.297605	−	0.584082i
$379$	−210.936	+	68.5373i	−0.556560	+	0.180837i	−0.573773	−	0.819015i	$-0.694521\pi$
$379$	−210.936	+	68.5373i	−0.556560	+	0.180837i	0.0172129	+	0.999852i	$0.494521\pi$
$380$	1.49082	−	0.0625232i	0.00392320	−	0.000164535i
$381$	62.1600	−	191.309i	0.163150	−	0.502123i
$382$	−202.888	+	202.888i	−0.531120	+	0.531120i
$383$	636.506	−	324.316i	1.66190	−	0.846778i	0.667091	−	0.744976i	$-0.267539\pi$
$383$	636.506	−	324.316i	1.66190	−	0.846778i	0.994805	−	0.101802i	$-0.0324608\pi$
$384$	−295.035	−	406.080i	−0.768319	−	1.05750i
$385$	−359.428	+	72.4833i	−0.933580	+	0.188268i
$386$	510.401	+	370.828i	1.32228	+	0.960695i
$387$	23.7526	−	149.968i	0.0613763	−	0.387515i
$388$	−25.1276	−	3.97982i	−0.0647619	−	0.0102573i
$389$	225.276	−	310.066i	0.579116	−	0.797085i	−0.414482	−	0.910057i	$-0.636037\pi$
$389$	225.276	−	310.066i	0.579116	−	0.797085i	0.993598	+	0.112973i	$0.0360373\pi$
$390$	28.5557	−	62.3754i	0.0732197	−	0.159937i
$391$	60.8383	−	44.2016i	0.155597	−	0.113048i
$392$	89.3052	+	175.271i	0.227819	+	0.447121i
$393$	795.936	+	795.936i	2.02528	+	2.02528i
$394$	60.1898	+	19.5569i	0.152766	+	0.0496367i
$395$	−506.194	+	188.267i	−1.28150	+	0.476625i
$396$	27.4898	+	84.6049i	0.0694187	+	0.213649i
$397$	−179.280	−	91.3478i	−0.451587	−	0.230095i	0.213378	−	0.976970i	$-0.431554\pi$
$397$	−179.280	−	91.3478i	−0.451587	−	0.230095i	−0.664965	+	0.746875i	$0.731554\pi$
$398$	−50.1886	−	316.878i	−0.126102	−	0.796176i
$399$			17.0899i			0.0428319i
$400$	−267.084	+	230.566i	−0.667711	+	0.576414i
$401$	−334.385			−0.833878			−0.416939	−	0.908935i	$-0.636897\pi$
$401$	−334.385			−0.833878			−0.416939	+	0.908935i	$0.636897\pi$
$402$	−804.657	+	127.445i	−2.00163	+	0.317028i
$403$	−0.595102	+	1.16795i	−0.00147668	+	0.00289815i
$404$	−50.7073	+	16.4758i	−0.125513	+	0.0407817i
$405$	5.14686	−	18.4359i	0.0127083	−	0.0455206i
$406$	72.9385	−	224.482i	0.179651	−	0.552910i
$407$	238.823	−	238.823i	0.586788	−	0.586788i
$408$	−77.8519	+	39.6675i	−0.190814	+	0.0972243i
$409$	89.2243	+	122.807i	0.218152	+	0.300261i	0.904041	−	0.427445i	$-0.140586\pi$
$409$	89.2243	+	122.807i	0.218152	+	0.300261i	−0.685889	+	0.727706i	$0.740586\pi$
$410$	141.748	−	154.158i	0.345728	−	0.375996i
$411$	38.0452	+	27.6414i	0.0925673	+	0.0672541i
$412$	−1.47710	+	9.32604i	−0.00358519	+	0.0226360i
$413$	327.279	+	51.8358i	0.792442	+	0.125510i
$414$	555.913	−	765.148i	1.34278	−	1.84818i
$415$	−110.264	+	62.1341i	−0.265695	+	0.149721i
$416$	−8.24593	+	5.99102i	−0.0198219	+	0.0144015i
$417$	−362.473	−	711.394i	−0.869240	−	1.70598i
$418$	13.5947	+	13.5947i	0.0325232	+	0.0325232i
$419$	−245.486	−	79.7632i	−0.585885	−	0.190366i	0.00105020	−	0.999999i	$-0.499666\pi$
$419$	−245.486	−	79.7632i	−0.585885	−	0.190366i	−0.586935	+	0.809634i	$0.699666\pi$
$420$	32.3091	+	40.7618i	0.0769265	+	0.0970518i
$421$	−67.3265	−	207.210i	−0.159920	−	0.492184i	0.838706	−	0.544585i	$-0.183313\pi$
$421$	−67.3265	−	207.210i	−0.159920	−	0.492184i	−0.998626	+	0.0524005i	$0.983313\pi$
$422$	537.987	+	274.118i	1.27485	+	0.649569i
$423$	−174.256	−	1100.21i	−0.411952	−	2.60096i
$424$		−	209.666i		−	0.494495i
$425$	28.4585	+	45.8934i	0.0669611	+	0.107984i
$426$	−258.414			−0.606606
$427$	438.979	−	69.5274i	1.02805	−	0.162828i
$428$	9.75772	−	19.1506i	0.0227984	−	0.0447444i
$429$	−100.255	+	32.5749i	−0.233695	+	0.0759322i
$430$	−83.1882	−	55.2669i	−0.193461	−	0.128528i
$431$	61.9145	−	190.553i	0.143653	−	0.442119i	−0.853182	−	0.521613i	$-0.825331\pi$
$431$	61.9145	−	190.553i	0.143653	−	0.442119i	0.996835	+	0.0794942i	$0.0253305\pi$
$432$	−259.088	+	259.088i	−0.599740	+	0.599740i
$433$	−424.969	+	216.532i	−0.981452	+	0.500075i	−0.869657	−	0.493657i	$-0.835660\pi$
$433$	−424.969	+	216.532i	−0.981452	+	0.500075i	−0.111795	+	0.993731i	$0.535660\pi$
$434$	4.89843	+	6.74212i	0.0112867	+	0.0155348i
$435$	−68.6877	+	593.788i	−0.157903	+	1.36503i
$436$	−9.97089	−	7.24427i	−0.0228690	−	0.0166153i
$437$	−3.81335	+	24.0765i	−0.00872620	+	0.0550951i
$438$	756.811	+	119.867i	1.72788	+	0.273669i
$439$	−444.956	+	612.429i	−1.01357	+	1.39506i	−0.0969494	+	0.995289i	$0.530909\pi$
$439$	−444.956	+	612.429i	−1.01357	+	1.39506i	−0.916617	+	0.399766i	$0.869091\pi$
$440$	603.649	+	69.8284i	1.37193	+	0.158701i
$441$	273.310	−	198.571i	0.619751	−	0.450275i
$442$	−2.78315	−	5.46224i	−0.00629672	−	0.0123580i
$443$	243.432	+	243.432i	0.549509	+	0.549509i	0.926299	−	0.376790i	$-0.122972\pi$
$443$	243.432	+	243.432i	0.549509	+	0.549509i	−0.376790	+	0.926299i	$0.622972\pi$
$444$	−45.5664	−	14.8054i	−0.102627	−	0.0333455i
$445$	102.924	−	154.922i	0.231290	−	0.348140i
$446$	−170.008	−	523.232i	−0.381185	−	1.17317i
$447$	−787.134	−	401.065i	−1.76093	−	0.897237i
$448$	54.7253	+	345.522i	0.122155	+	0.771255i
$449$		−	404.772i		−	0.901496i	−0.892651	−	0.450748i	$-0.851157\pi$
$449$		−	404.772i		−	0.901496i	0.892651	−	0.450748i	$-0.148843\pi$
$450$	518.759	+	438.338i	1.15280	+	0.974086i
$451$	−321.804			−0.713534
$452$	36.3905	−	5.76369i	0.0805100	−	0.0127515i
$453$	102.256	−	200.688i	0.225730	−	0.443020i
$454$	125.941	−	40.9207i	0.277403	−	0.0901337i
$455$	−29.7006	+	23.5417i	−0.0652761	+	0.0517400i
$456$	8.75237	−	26.9370i	0.0191938	−	0.0590724i
$457$	166.102	−	166.102i	0.363461	−	0.363461i	−0.501625	−	0.865085i	$-0.667264\pi$
$457$	166.102	−	166.102i	0.363461	−	0.363461i	0.865085	+	0.501625i	$0.167264\pi$
$458$	−547.109	+	278.766i	−1.19456	+	0.608659i
$459$	32.9614	+	45.3674i	0.0718113	+	0.0988397i
$460$	36.4222	+	64.6350i	0.0791787	+	0.140511i
$461$	88.2257	+	64.0997i	0.191379	+	0.139045i	0.679349	−	0.733816i	$-0.262262\pi$
$461$	88.2257	+	64.0997i	0.191379	+	0.139045i	−0.487970	+	0.872861i	$0.662262\pi$
$462$	−104.840	+	661.934i	−0.226926	+	1.43276i
$463$	413.975	+	65.5672i	0.894114	+	0.141614i	0.586549	−	0.809913i	$-0.300486\pi$
$463$	413.975	+	65.5672i	0.894114	+	0.141614i	0.307565	+	0.951527i	$0.400486\pi$
$464$	−205.149	+	282.364i	−0.442132	+	0.608543i
$465$	−15.5356	−	14.2849i	−0.0334099	−	0.0307203i
$466$	434.264	−	315.512i	0.931898	−	0.677063i
$467$	33.4938	+	65.7354i	0.0717213	+	0.140761i	0.924083	−	0.382191i	$-0.124831\pi$
$467$	33.4938	+	65.7354i	0.0717213	+	0.140761i	−0.852362	+	0.522952i	$0.824831\pi$
$468$	6.50181	+	6.50181i	0.0138928	+	0.0138928i
$469$	428.050	+	139.082i	0.912686	+	0.296550i
$470$	−705.713	−	197.018i	−1.50152	−	0.419188i
$471$	239.801	+	738.030i	0.509131	+	1.56694i
$472$	−489.307	−	249.314i	−1.03667	−	0.528208i
$473$	24.0078	+	151.579i	0.0507564	+	0.320464i
$474$			987.137i			2.08257i
$475$	−17.0424	−	3.99631i	−0.0358788	−	0.00841329i
$476$	4.64809			0.00976489
$477$	−355.644	+	56.3285i	−0.745585	+	0.118089i
$478$	−138.033	+	270.905i	−0.288772	+	0.566746i
$479$	133.246	−	43.2942i	0.278175	−	0.0903846i	−0.166607	−	0.986023i	$-0.553281\pi$
$479$	133.246	−	43.2942i	0.278175	−	0.0903846i	0.444782	+	0.895639i	$0.353281\pi$
$480$	−57.2061	−	153.810i	−0.119179	−	0.320438i
$481$	10.7878	−	33.2015i	0.0224279	−	0.0690259i
$482$	−355.769	+	355.769i	−0.738110	+	0.738110i
$483$	−757.121	+	385.772i	−1.56754	+	0.798701i
$484$	−22.5377	−	31.0205i	−0.0465655	−	0.0640919i
$485$	271.371	+	124.234i	0.559527	+	0.256154i
$486$	−385.652	−	280.192i	−0.793522	−	0.576527i
$487$	19.9189	−	125.763i	0.0409012	−	0.258240i	−0.958761	−	0.284212i	$-0.908268\pi$
$487$	19.9189	−	125.763i	0.0409012	−	0.258240i	0.999663	+	0.0259720i	$0.00826807\pi$
$488$	−727.522	−	115.228i	−1.49082	−	0.236123i
$489$	−149.426	+	205.667i	−0.305575	+	0.420588i
$490$	−43.9277	−	217.827i	−0.0896483	−	0.444545i
$491$	242.641	−	176.289i	0.494178	−	0.359041i	−0.312611	−	0.949881i	$-0.601204\pi$
$491$	242.641	−	176.289i	0.494178	−	0.359041i	0.806789	+	0.590840i	$0.201204\pi$
$492$	20.7246	+	40.6743i	0.0421231	+	0.0826713i
$493$	37.7713	+	37.7713i	0.0766151	+	0.0766151i
$494$	1.88995	+	0.614083i	0.00382581	+	0.00124308i
$495$	−43.7295	−	1042.69i	−0.0883425	−	2.10645i
$496$	−3.80801	−	11.7198i	−0.00767744	−	0.0236287i
$497$	127.202	+	64.8128i	0.255940	+	0.130408i
$498$	36.1887	+	228.486i	0.0726680	+	0.458808i
$499$		−	438.153i		−	0.878063i	−0.898472	−	0.439031i	$-0.855322\pi$
$499$		−	438.153i		−	0.878063i	0.898472	−	0.439031i	$-0.144678\pi$
$500$	−48.2036	+	22.6876i	−0.0964073	+	0.0453752i
$501$	858.668			1.71391
$502$	568.272	−	90.0055i	1.13202	−	0.179294i
$503$	21.9783	−	43.1348i	0.0436944	−	0.0857550i	−0.868127	−	0.496342i	$-0.834676\pi$
$503$	21.9783	−	43.1348i	0.0436944	−	0.0857550i	0.911821	+	0.410587i	$0.134676\pi$
$504$	577.379	−	187.602i	1.14559	−	0.372226i
$505$	624.931	−	26.2089i	1.23749	−	0.0518989i
$506$	−295.400	+	909.148i	−0.583795	+	1.79674i
$507$	569.997	−	569.997i	1.12425	−	1.12425i
$508$	15.8015	−	8.05126i	0.0311053	−	0.0158489i
$509$	−380.749	−	524.056i	−0.748034	−	1.02958i	−0.998116	−	0.0613557i	$-0.980458\pi$
$509$	−380.749	−	524.056i	−0.748034	−	1.02958i	0.250082	−	0.968225i	$-0.419542\pi$
$510$	96.7544	−	19.5118i	0.189714	−	0.0382584i
$511$	−342.470	−	248.819i	−0.670196	−	0.486926i
$512$	88.8860	−	561.204i	0.173605	−	1.09610i
$513$	−17.9540	−	2.84363i	−0.0349980	−	0.00554315i
$514$	515.653	−	709.735i	1.00322	−	1.38081i
$515$	46.1093	−	100.718i	0.0895326	−	0.195570i
$516$	17.6127	−	12.7963i	0.0341331	−	0.0247991i
$517$	511.142	+	1003.17i	0.988669	+	1.94037i
$518$	−156.939	−	156.939i	−0.302970	−	0.302970i
$519$	−429.873	−	139.674i	−0.828271	−	0.269122i
$520$	58.8704	−	21.8955i	0.113212	−	0.0421067i
$521$	32.4116	+	99.7526i	0.0622103	+	0.191464i	0.977331	−	0.211716i	$-0.0679051\pi$
$521$	32.4116	+	99.7526i	0.0622103	+	0.191464i	−0.915121	+	0.403179i	$0.867905\pi$
$522$	598.585	+	304.994i	1.14671	+	0.584280i
$523$	−55.9046	−	352.968i	−0.106892	−	0.674891i	−0.981702	−	0.190424i	$-0.939014\pi$
$523$	−55.9046	−	352.968i	−0.106892	−	0.674891i	0.874810	−	0.484467i	$-0.160986\pi$
$524$			99.2389i			0.189387i
$525$	−236.488	−	562.500i	−0.450454	−	1.07143i
$526$	189.309			0.359902
$527$	−1.86278	+	0.295035i	−0.00353468	+	0.000559838i
$528$	449.902	−	882.983i	0.852088	−	1.67232i
$529$	−649.613	+	211.072i	−1.22800	+	0.399002i
$530$	−63.6865	+	228.123i	−0.120163	+	0.430420i
$531$	−291.441	+	896.963i	−0.548853	+	1.68920i
$532$	−1.06540	+	1.06540i	−0.00200264	+	0.00200264i
$533$	−29.6369	+	15.1007i	−0.0556039	+	0.0283316i
$534$	−199.824	−	275.034i	−0.374202	−	0.515045i
$535$	−170.666	+	185.608i	−0.319002	+	0.346931i
$536$	−603.460	−	438.439i	−1.12586	−	0.817984i
$537$	−118.337	+	747.151i	−0.220367	+	1.39134i
$538$	205.551	+	32.5560i	0.382064	+	0.0605131i
$539$	−200.704	+	276.246i	−0.372364	+	0.512515i
$540$	−48.1986	+	27.1602i	−0.0892567	+	0.0502967i
$541$	−221.720	+	161.089i	−0.409834	+	0.297762i	−0.773535	−	0.633754i	$-0.781513\pi$
$541$	−221.720	+	161.089i	−0.409834	+	0.297762i	0.363700	+	0.931516i	$0.381513\pi$
$542$	−240.867	−	472.729i	−0.444405	−	0.872193i
$543$	−867.284	−	867.284i	−1.59721	−	1.59721i
$544$	−13.9471	−	4.53169i	−0.0256380	−	0.00833031i
$545$	89.8122	+	113.309i	0.164793	+	0.207906i
$546$	21.4061	+	65.8812i	0.0392053	+	0.120661i
$547$	559.689	+	285.176i	1.02320	+	0.521345i	0.883294	−	0.468820i	$-0.155321\pi$
$547$	559.689	+	285.176i	1.02320	+	0.521345i	0.139904	+	0.990165i	$0.455321\pi$
$548$	0.648579	+	4.09497i	0.00118354	+	0.00747257i
$549$			1265.01i			2.30421i
$550$	−635.578	−	259.335i	−1.15560	−	0.471519i
$551$	−17.3153			−0.0314253
$552$	1390.94	−	220.303i	2.51981	−	0.399099i
$553$	247.583	−	485.910i	0.447709	−	0.878679i
$554$	−507.536	+	164.908i	−0.916130	+	0.297669i
$555$	468.166	+	311.031i	0.843542	+	0.560416i
$556$	21.7520	−	66.9459i	0.0391224	−	0.120406i
$557$	−770.632	+	770.632i	−1.38354	+	1.38354i	−0.545300	+	0.838241i	$0.683584\pi$
$557$	−770.632	+	770.632i	−1.38354	+	1.38354i	−0.838241	+	0.545300i	$0.816416\pi$
$558$	−21.1344	+	10.7685i	−0.0378753	+	0.0192984i
$559$	9.32392	+	12.8333i	0.0166796	+	0.0229576i
$560$	40.9412	−	353.926i	0.0731092	−	0.632011i
$561$	−122.703	−	89.1487i	−0.218721	−	0.158910i
$562$	161.461	−	1019.42i	0.287297	−	1.81392i
$563$	479.058	+	75.8754i	0.850903	+	0.134770i	0.566629	−	0.823973i	$-0.308247\pi$
$563$	479.058	+	75.8754i	0.850903	+	0.134770i	0.284274	+	0.958743i	$0.408247\pi$
$564$	93.8774	−	129.211i	0.166449	−	0.229098i
$565$	−429.370	−	49.6683i	−0.759947	−	0.0879085i
$566$	−90.9853	+	66.1047i	−0.160751	+	0.116793i
$567$	8.77467	+	17.2213i	0.0154756	+	0.0303726i
$568$	−167.302	−	167.302i	−0.294546	−	0.294546i
$569$	862.709	+	280.311i	1.51619	+	0.492638i	0.944689	−	0.327967i	$-0.106363\pi$
$569$	862.709	+	280.311i	1.51619	+	0.492638i	0.571496	+	0.820605i	$0.306363\pi$
$570$	−17.7050	+	26.6497i	−0.0310615	+	0.0467539i
$571$	298.299	+	918.071i	0.522416	+	1.60783i	0.769371	+	0.638803i	$0.220570\pi$
$571$	298.299	+	918.071i	0.522416	+	1.60783i	−0.246955	+	0.969027i	$0.579430\pi$
$572$	−8.28077	−	4.21926i	−0.0144769	−	0.00737633i
$573$	114.781	+	724.700i	0.200316	+	1.26475i
$574$			211.468i			0.368412i
$575$	−207.655	−	845.226i	−0.361139	−	1.46996i
$576$	−995.696			−1.72864
$577$	−1072.44	+	169.858i	−1.85865	+	0.294381i	−0.982303	−	0.187298i	$-0.940027\pi$
$577$	−1072.44	+	169.858i	−1.85865	+	0.294381i	−0.876348	+	0.481679i	$0.840027\pi$
$578$	−244.029	+	478.933i	−0.422195	+	0.828604i
$579$	1534.36	−	498.544i	2.65002	−	0.861043i
$580$	−41.2994	+	32.7353i	−0.0712058	+	0.0564401i
$581$	39.4930	−	121.547i	0.0679741	−	0.209203i
$582$	385.738	−	385.738i	0.662780	−	0.662780i
$583$	324.277	−	165.228i	0.556222	−	0.283409i
$584$	412.369	+	567.578i	0.706112	+	0.971880i
$585$	−52.9561	−	93.9761i	−0.0905232	−	0.160643i
$586$	181.619	+	131.954i	0.309930	+	0.225178i
$587$	126.992	−	801.794i	0.216340	−	1.36592i	−0.605339	−	0.795968i	$-0.706963\pi$
$587$	126.992	−	801.794i	0.216340	−	1.36592i	0.821679	−	0.569950i	$-0.193037\pi$
$588$	47.8416	+	7.57736i	0.0813632	+	0.0128867i
$589$	0.359347	−	0.494599i	0.000610097	−	0.000839726i
$590$	456.651	+	419.890i	0.773984	+	0.711677i
$591$	130.931	−	95.1267i	0.221541	−	0.160959i
$592$	148.994	+	292.417i	0.251679	+	0.493947i
$593$	−104.789	−	104.789i	−0.176710	−	0.176710i	0.613210	−	0.789920i	$-0.289878\pi$
$593$	−104.789	−	104.789i	−0.176710	−	0.176710i	−0.789920	+	0.613210i	$0.789878\pi$
$594$	−677.956	−	220.281i	−1.14134	−	0.370844i
$595$	−52.5203	−	14.6624i	−0.0882693	−	0.0246427i
$596$	−24.0679	−	74.0735i	−0.0403824	−	0.124284i
$597$	−731.005	−	372.466i	−1.22446	−	0.623896i
$598$	15.4568	+	97.5907i	0.0258476	+	0.163195i
$599$			683.205i			1.14058i	0.821445	+	0.570288i	$0.193168\pi$
$599$			683.205i			1.14058i	−0.821445	+	0.570288i	$0.806832\pi$
$600$	84.6744	+	1007.72i	0.141124	+	1.67954i
$601$	−227.072			−0.377823			−0.188912	−	0.981994i	$-0.560496\pi$
$601$	−227.072			−0.377823			−0.188912	+	0.981994i	$0.560496\pi$
$602$	99.6079	−	15.7763i	0.165462	−	0.0262065i
$603$	−581.575	+	1141.40i	−0.964469	+	1.89288i
$604$	18.8858	−	6.13638i	0.0312679	−	0.0101596i
$605$	156.806	+	421.606i	0.259184	+	0.696869i
$606$	353.283	−	1087.29i	0.582975	−	1.79421i
$607$	−65.4899	+	65.4899i	−0.107891	+	0.107891i	−0.758992	−	0.651101i	$-0.774308\pi$
$607$	−65.4899	+	65.4899i	−0.107891	+	0.107891i	0.651101	+	0.758992i	$0.274308\pi$
$608$	4.23558	−	2.15814i	0.00696642	−	0.00354957i
$609$	−354.781	−	488.314i	−0.582563	−	0.801829i
$610$	756.565	+	346.358i	1.24027	+	0.567800i
$611$	94.1484	+	68.4028i	0.154089	+	0.111952i
$612$	−2.06956	+	13.0667i	−0.00338163	+	0.0213508i
$613$	−522.470	−	82.7511i	−0.852316	−	0.134994i	−0.285034	−	0.958517i	$-0.592005\pi$
$613$	−522.470	−	82.7511i	−0.852316	−	0.134994i	−0.567282	+	0.823524i	$0.692005\pi$
$614$	−44.0157	+	60.5824i	−0.0716868	+	0.0986685i
$615$	−105.866	−	524.968i	−0.172141	−	0.853606i
$616$	−496.424	+	360.673i	−0.805882	+	0.585508i
$617$	−126.641	−	248.548i	−0.205254	−	0.402833i	0.765316	−	0.643655i	$-0.222583\pi$
$617$	−126.641	−	248.548i	−0.205254	−	0.402833i	−0.970569	+	0.240822i	$0.922583\pi$
$618$	−143.166	−	143.166i	−0.231659	−	0.231659i
$619$	81.1742	+	26.3751i	0.131138	+	0.0426092i	0.373851	−	0.927489i	$-0.378037\pi$
$619$	81.1742	+	26.3751i	0.131138	+	0.0426092i	−0.242713	+	0.970098i	$0.578037\pi$
$620$	−0.0779662	−	1.85904i	−0.000125752	−	0.00299845i
$621$	−279.298	−	859.590i	−0.449755	−	1.38420i
$622$	−597.515	−	304.449i	−0.960634	−	0.489468i
$623$	29.3805	+	185.501i	0.0471597	+	0.297754i
$624$		−	102.431i		−	0.164152i
$625$	616.236	−	104.296i	0.985978	−	0.166873i
$626$	478.701			0.764698
$627$	48.5592	−	7.69102i	0.0774468	−	0.0122664i
$628$	−31.0601	+	60.9590i	−0.0494588	+	0.0970684i
$629$	47.7697	−	15.5213i	0.0759455	−	0.0246762i
$630$	−685.190	+	28.7362i	−1.08760	+	0.0456129i
$631$	−124.769	+	384.001i	−0.197733	+	0.608559i	0.802201	+	0.597054i	$0.203662\pi$
$631$	−124.769	+	384.001i	−0.197733	+	0.608559i	−0.999934	+	0.0115048i	$0.996338\pi$
$632$	−639.090	+	639.090i	−1.01122	+	1.01122i
$633$	1375.75	−	700.978i	2.17338	−	1.10739i
$634$	308.351	+	424.409i	0.486358	+	0.669415i
$635$	−203.944	+	41.1279i	−0.321172	+	0.0647684i
$636$	−41.7677	−	30.3460i	−0.0656725	−	0.0477139i
$637$	−5.52117	+	34.8593i	−0.00866745	+	0.0547241i
$638$	−670.664	−	106.223i	−1.05120	−	0.166493i
$639$	−238.838	+	328.732i	−0.373768	+	0.514448i
$640$	−216.099	+	472.035i	−0.337655	+	0.737555i
$641$	418.717	−	304.216i	0.653225	−	0.474596i	−0.211143	−	0.977455i	$-0.567719\pi$
$641$	418.717	−	304.216i	0.653225	−	0.474596i	0.864368	+	0.502859i	$0.167719\pi$
$642$	209.230	+	410.637i	0.325904	+	0.639622i
$643$	435.521	+	435.521i	0.677326	+	0.677326i	0.959394	−	0.282068i	$-0.0910204\pi$
$643$	435.521	+	435.521i	0.677326	+	0.677326i	−0.282068	+	0.959394i	$0.591020\pi$
$644$	−71.2491	−	23.1502i	−0.110635	−	0.0359476i
$645$	−239.377	+	89.0308i	−0.371128	+	0.138032i
$646$	0.883532	+	2.71923i	0.00136770	+	0.00420934i
$647$	−182.235	−	92.8532i	−0.281661	−	0.143513i	0.307453	−	0.951563i	$-0.400523\pi$
$647$	−182.235	−	92.8532i	−0.281661	−	0.143513i	−0.589114	+	0.808050i	$0.700523\pi$
$648$	−5.01094	−	31.6378i	−0.00773293	−	0.0488238i
$649$		−	953.254i		−	1.46880i
$650$	−70.7036	+	5.94092i	−0.108775	+	0.00913988i
$651$	21.3111			0.0327359
$652$	−22.1369	+	3.50614i	−0.0339523	+	0.00537751i
$653$	366.165	−	718.639i	0.560743	−	1.10052i	−0.420419	−	0.907330i	$-0.638117\pi$
$653$	366.165	−	718.639i	0.560743	−	1.10052i	0.981161	−	0.193189i	$-0.0618832\pi$
$654$	251.338	−	81.6647i	0.384309	−	0.124870i
$655$	313.050	−	1121.33i	0.477938	−	1.71196i
$656$	96.6284	−	297.392i	0.147299	−	0.453341i
$657$	851.963	−	851.963i	1.29675	−	1.29675i
$658$	659.219	−	335.889i	1.00185	−	0.510469i
$659$	426.426	+	586.925i	0.647081	+	0.890630i	0.998968	−	0.0454122i	$-0.0144601\pi$
$659$	426.426	+	586.925i	0.647081	+	0.890630i	−0.351888	+	0.936042i	$0.614460\pi$
$660$	101.280	−	110.147i	0.153454	−	0.166889i
$661$	562.862	+	408.943i	0.851531	+	0.618674i	0.925568	−	0.378582i	$-0.123588\pi$
$661$	562.862	+	408.943i	0.851531	+	0.618674i	−0.0740365	+	0.997256i	$0.523588\pi$
$662$	−136.053	+	859.003i	−0.205518	+	1.29759i
$663$	−15.4838	−	2.45239i	−0.0233541	−	0.00369893i
$664$	−124.497	+	171.355i	−0.187495	+	0.258065i
$665$	15.3992	−	8.67752i	0.0231566	−	0.0130489i
$666$	511.061	−	371.308i	0.767359	−	0.557519i
$667$	−390.861	−	767.107i	−0.585998	−	1.15009i
$668$	53.5302	+	53.5302i	0.0801350	+	0.0801350i
$669$	−1338.02	−	434.748i	−2.00003	−	0.649848i
$670$	523.406	+	660.338i	0.781203	+	0.985579i
$671$	−395.109	−	1216.02i	−0.588836	−	1.81225i
$672$	147.647	+	75.2297i	0.219712	+	0.111949i
$673$	−6.25856	−	39.5150i	−0.00929950	−	0.0587147i	0.982602	−	0.185723i	$-0.0594626\pi$
$673$	−6.25856	−	39.5150i	−0.00929950	−	0.0587147i	−0.991902	+	0.127008i	$0.959463\pi$
$674$		−	1159.91i		−	1.72094i
$675$	630.289	−	154.849i	0.933762	−	0.229406i
$676$	71.0683			0.105131
$677$	32.0421	−	5.07497i	0.0473296	−	0.00749627i	−0.132725	−	0.991153i	$-0.542373\pi$
$677$	32.0421	−	5.07497i	0.0473296	−	0.00749627i	0.180054	+	0.983657i	$0.442373\pi$
$678$	−358.667	+	703.923i	−0.529007	+	1.03824i
$679$	−286.623	+	93.1294i	−0.422125	+	0.137157i
$680$	75.2728	+	50.0083i	0.110695	+	0.0735416i
$681$	104.643	−	322.058i	0.153661	−	0.472919i
$682$	16.9525	−	16.9525i	0.0248571	−	0.0248571i
$683$	−245.294	+	124.983i	−0.359142	+	0.182992i	−0.624246	−	0.781228i	$-0.714594\pi$
$683$	−245.294	+	124.983i	−0.359142	+	0.182992i	0.265104	+	0.964220i	$0.414594\pi$
$684$	−2.52068	−	3.46942i	−0.00368521	−	0.00507226i
$685$	5.58909	−	48.3163i	0.00815926	−	0.0705348i
$686$	559.897	+	406.789i	0.816176	+	0.592986i
$687$	−245.636	+	1550.88i	−0.357549	+	2.25747i
$688$	−147.289	−	23.3283i	−0.214083	−	0.0339074i
$689$	22.1113	−	30.4336i	0.0320919	−	0.0441707i
$690$	−1580.30	−	182.804i	−2.29029	−	0.264934i
$691$	−825.186	+	599.532i	−1.19419	+	0.867630i	−0.993701	−	0.112066i	$-0.964253\pi$
$691$	−825.186	+	599.532i	−1.19419	+	0.867630i	−0.200490	+	0.979696i	$0.564253\pi$
$692$	−18.0913	−	35.5061i	−0.0261434	−	0.0513094i
$693$	745.157	+	745.157i	1.07526	+	1.07526i
$694$	−950.813	−	308.938i	−1.37005	−	0.445155i
$695$	−456.965	+	687.827i	−0.657503	+	0.989679i
$696$	309.120	+	951.372i	0.444137	+	1.36691i
$697$	−42.6411	−	21.7267i	−0.0611780	−	0.0311718i
$698$	−56.1580	−	354.568i	−0.0804556	−	0.507977i
$699$		−	1372.66i		−	1.96375i
$700$	20.3239	−	49.8097i	0.0290341	−	0.0711567i
$701$	−356.349			−0.508344			−0.254172	−	0.967159i	$-0.581803\pi$
$701$	−356.349			−0.508344			−0.254172	+	0.967159i	$0.581803\pi$
$702$	−72.7739	+	11.5263i	−0.103667	+	0.0164192i
$703$	−7.39176	+	14.5072i	−0.0105146	+	0.0206361i
$704$	957.135	−	310.992i	1.35957	−	0.441750i
$705$	−1468.35	+	1163.86i	−2.08276	+	1.65087i
$706$	132.903	−	409.035i	0.188248	−	0.579369i
$707$	−446.604	+	446.604i	−0.631689	+	0.631689i
$708$	−120.486	+	61.3907i	−0.170178	+	0.0867100i
$709$	−672.951	−	926.237i	−0.949155	−	1.30640i	−0.951902	−	0.306403i	$-0.900875\pi$
$709$	−672.951	−	926.237i	−0.949155	−	1.30640i	0.00274737	−	0.999996i	$-0.499125\pi$
$710$	131.211	+	232.848i	0.184805	+	0.327955i
$711$	1255.75	+	912.355i	1.76617	+	1.28320i
$712$	48.6924	−	307.432i	0.0683882	−	0.431786i
$713$	30.0233	+	4.75523i	0.0421085	+	0.00666933i
$714$	−58.5827	+	80.6321i	−0.0820486	+	0.112930i
$715$	80.2574	+	73.7965i	0.112248	+	0.103212i
$716$	−53.9553	+	39.2009i	−0.0753566	+	0.0547498i
$717$	352.979	+	692.761i	0.492300	+	0.966194i
$718$	403.943	+	403.943i	0.562595	+	0.562595i
$719$	876.169	+	284.685i	1.21859	+	0.395945i	0.846570	−	0.532278i	$-0.178664\pi$
$719$	876.169	+	284.685i	1.21859	+	0.395945i	0.372024	+	0.928223i	$0.378664\pi$
$720$	976.725	+	272.679i	1.35656	+	0.378721i
$721$	34.5647	+	106.379i	0.0479400	+	0.147544i
$722$	607.243	+	309.406i	0.841057	+	0.428540i
$723$	201.272	+	1270.78i	0.278384	+	1.75765i
$724$		−	108.135i		−	0.149357i
$725$	569.919	−	239.607i	0.786095	−	0.330493i
$726$	822.180			1.13248
$727$	−321.634	+	50.9418i	−0.442413	+	0.0700713i	−0.373667	−	0.927563i	$-0.621900\pi$
$727$	−321.634	+	50.9418i	−0.442413	+	0.0700713i	−0.0687456	+	0.997634i	$0.521900\pi$
$728$	−28.7940	+	56.5114i	−0.0395522	+	0.0776255i
$729$	−1126.57	+	366.046i	−1.54537	+	0.502120i
$730$	−276.267	−	742.800i	−0.378448	−	1.01753i
$731$	−7.05274	+	21.7061i	−0.00964807	+	0.0296937i
$732$	−128.253	+	128.253i	−0.175209	+	0.175209i
$733$	46.2214	−	23.5510i	0.0630579	−	0.0321296i	−0.422177	−	0.906513i	$-0.638734\pi$
$733$	46.2214	−	23.5510i	0.0630579	−	0.0321296i	0.485235	+	0.874384i	$0.338734\pi$
$734$	−280.757	−	386.428i	−0.382502	−	0.526469i
$735$	−516.675	−	236.536i	−0.702959	−	0.321817i
$736$	191.220	+	138.930i	0.259810	+	0.188763i
$737$	202.550	−	1278.85i	0.274830	−	1.73521i
$738$	−594.478	−	94.1561i	−0.805526	−	0.127583i
$739$	−513.049	+	706.151i	−0.694247	+	0.955550i	0.305747	+	0.952113i	$0.401094\pi$
$739$	−513.049	+	706.151i	−0.694247	+	0.955550i	−0.999994	+	0.00343667i	$0.998906\pi$
$740$	9.79595	+	48.5759i	0.0132378	+	0.0656431i
$741$	4.11121	−	2.98697i	0.00554819	−	0.00403099i
$742$	−108.577	−	213.094i	−0.146330	−	0.287188i
$743$	−739.686	−	739.686i	−0.995540	−	0.995540i	0.00444973	−	0.999990i	$-0.498584\pi$
$743$	−739.686	−	739.686i	−0.995540	−	0.995540i	−0.999990	+	0.00444973i	$0.998584\pi$
$744$	−33.5904	−	10.9142i	−0.0451483	−	0.0146696i
$745$	38.2862	+	912.903i	0.0513908	+	1.22537i
$746$	77.8826	+	239.698i	0.104400	+	0.321311i
$747$	324.107	+	165.141i	0.433879	+	0.221072i
$748$	−2.09179	−	13.2070i	−0.00279651	−	0.0176565i
$749$		−	254.610i		−	0.339933i
$750$	213.969	−	1122.15i	0.285293	−	1.49620i
$751$	95.9204			0.127724			0.0638618	−	0.997959i	$-0.479658\pi$
$751$	95.9204			0.127724			0.0638618	+	0.997959i	$0.479658\pi$
$752$	−1080.55	+	171.143i	−1.43690	+	0.227583i
$753$	667.960	−	1310.94i	0.887064	−	1.74096i
$754$	−66.7501	+	21.6884i	−0.0885280	+	0.0287645i
$755$	−232.754	+	9.76147i	−0.308284	+	0.0129291i
$756$	17.2633	−	53.1308i	0.0228350	−	0.0702789i
$757$	475.737	−	475.737i	0.628451	−	0.628451i	−0.319227	−	0.947678i	$-0.603423\pi$
$757$	475.737	−	475.737i	0.628451	−	0.628451i	0.947678	+	0.319227i	$0.103423\pi$
$758$	373.586	−	190.351i	0.492857	−	0.251123i
$759$	1436.86	+	1977.67i	1.89309	+	2.60562i
$760$	−28.7161	+	5.79097i	−0.0377843	+	0.00761970i
$761$	−491.896	−	357.383i	−0.646381	−	0.469623i	0.215655	−	0.976470i	$-0.430811\pi$
$761$	−491.896	−	357.383i	−0.646381	−	0.469623i	−0.862036	+	0.506846i	$0.830811\pi$
$762$	−59.4875	+	375.589i	−0.0780676	+	0.492899i
$763$	−144.201	−	22.8393i	−0.188993	−	0.0299335i
$764$	−38.0229	+	52.3341i	−0.0497682	+	0.0685001i
$765$	64.6035	−	141.116i	0.0844490	−	0.184466i
$766$	−1092.56	+	793.789i	−1.42631	+	1.03628i
$767$	−44.7317	−	87.7909i	−0.0583203	−	0.114460i
$768$	−276.441	−	276.441i	−0.359949	−	0.359949i
$769$	805.996	+	261.884i	1.04811	+	0.340551i	0.781926	−	0.623371i	$-0.214238\pi$
$769$	805.996	+	261.884i	1.04811	+	0.340551i	0.266183	+	0.963923i	$0.414238\pi$
$770$	649.679	−	241.633i	0.843739	−	0.313809i
$771$	−693.247	−	2133.59i	−0.899153	−	2.76731i
$772$	126.733	+	64.5738i	0.164162	+	0.0836448i
$773$	34.6368	+	218.688i	0.0448083	+	0.282909i	0.999911	−	0.0133675i	$-0.00425513\pi$
$773$	34.6368	+	218.688i	0.0448083	+	0.282909i	−0.955102	+	0.296276i	$0.904255\pi$
$774$			287.041i			0.370854i
$775$	−4.98339	+	21.2518i	−0.00643018	+	0.0274217i
$776$	499.468			0.643644
$777$	−560.572	+	88.7859i	−0.721457	+	0.114268i
$778$	−328.933	+	645.568i	−0.422794	+	0.829779i
$779$	14.7539	−	4.79385i	0.0189396	−	0.00615385i
$780$	4.15880	−	14.8967i	0.00533180	−	0.0190983i
$781$	126.913	−	390.599i	0.162501	−	0.500127i
$782$	−100.524	+	100.524i	−0.128547	+	0.128547i
$783$	572.036	−	291.467i	0.730569	−	0.372244i
$784$	−195.024	−	268.427i	−0.248755	−	0.342382i
$785$	543.254	−	590.816i	0.692043	−	0.752631i
$786$	−1721.53	−	1250.77i	−2.19025	−	1.59131i
$787$	32.8697	−	207.531i	0.0417658	−	0.263699i	−0.957965	−	0.286884i	$-0.907381\pi$
$787$	32.8697	−	207.531i	0.0417658	−	0.263699i	0.999731	+	0.0231849i	$0.00738066\pi$
$788$	14.0926	+	2.23206i	0.0178841	+	0.00283256i
$789$	284.548	−	391.647i	0.360644	−	0.496384i
$790$	889.475	−	501.225i	1.12592	−	0.634461i
$791$	353.101	−	256.543i	0.446399	−	0.324328i
$792$	−792.888	−	1556.13i	−1.00112	−	1.96481i
$793$	−93.4500	−	93.4500i	−0.117844	−	0.117844i
$794$	361.761	+	117.543i	0.455619	+	0.148040i
$795$	376.220	+	474.646i	0.473233	+	0.597039i
$796$	−22.3517	−	68.7915i	−0.0280800	−	0.0864214i
$797$	533.202	+	271.680i	0.669011	+	0.340878i	0.755288	−	0.655393i	$-0.227497\pi$
$797$	533.202	+	271.680i	0.669011	+	0.340878i	−0.0862771	+	0.996271i	$0.527497\pi$
$798$	−5.05403	−	31.9099i	−0.00633337	−	0.0399873i
$799$			167.437i			0.209558i
$800$	−109.546	+	129.644i	−0.136933	+	0.162056i
$801$	−534.561			−0.667366
$802$	624.355	−	98.8880i	0.778497	−	0.123302i
$803$	−552.869	+	1085.07i	−0.688505	+	1.35127i
$804$	−174.684	+	56.7582i	−0.217268	+	0.0705948i
$805$	732.039	+	486.338i	0.909366	+	0.604146i
$806$	0.765759	−	2.35676i	0.000950073	−	0.00292402i
$807$	376.314	−	376.314i	0.466313	−	0.466313i
$808$	932.655	−	475.211i	1.15428	−	0.588133i
$809$	668.464	+	920.062i	0.826285	+	1.13728i	0.988603	+	0.150545i	$0.0481028\pi$
$809$	668.464	+	920.062i	0.826285	+	1.13728i	−0.162318	+	0.986738i	$0.551897\pi$
$810$	−4.15802	+	35.9450i	−0.00513335	+	0.0443766i
$811$	193.105	+	140.299i	0.238108	+	0.172995i	0.700440	−	0.713711i	$-0.252987\pi$
$811$	193.105	+	140.299i	0.238108	+	0.172995i	−0.462332	+	0.886707i	$0.652987\pi$
$812$	8.32459	−	52.5594i	0.0102520	−	0.0647283i
$813$	−1340.04	−	212.242i	−1.64827	−	0.261060i
$814$	−375.296	+	516.551i	−0.461052	+	0.634583i
$815$	261.192	+	30.2139i	0.320481	+	0.0370723i
$816$	119.230	−	86.6256i	0.146115	−	0.106159i
$817$	−3.35875	−	6.59191i	−0.00411107	−	0.00806843i
$818$	−202.915	−	202.915i	−0.248062	−	0.248062i
$819$	103.593	+	33.6593i	0.126487	+	0.0410981i
$820$	26.1272	−	39.3268i	0.0318624	−	0.0479595i
$821$	413.541	+	1272.75i	0.503704	+	1.55024i	0.802938	+	0.596062i	$0.203269\pi$
$821$	413.541	+	1272.75i	0.503704	+	1.55024i	−0.299234	+	0.954180i	$0.596731\pi$
$822$	−79.2114	−	40.3602i	−0.0963642	−	0.0491000i
$823$	100.444	+	634.180i	0.122046	+	0.770571i	0.970464	+	0.241244i	$0.0775554\pi$
$823$	100.444	+	634.180i	0.122046	+	0.770571i	−0.848418	+	0.529327i	$0.822445\pi$
$824$		−	185.376i		−	0.224971i
$825$	−1491.85	+	925.098i	−1.80831	+	1.12133i
$826$	−626.415			−0.758372
$827$	677.919	−	107.372i	0.819732	−	0.129833i	0.267537	−	0.963548i	$-0.413790\pi$
$827$	677.919	−	107.372i	0.819732	−	0.129833i	0.552195	+	0.833715i	$0.313790\pi$
$828$	96.8034	−	189.987i	0.116912	−	0.229453i
$829$	466.331	−	151.520i	0.562522	−	0.182774i	−0.0139337	−	0.999903i	$-0.504435\pi$
$829$	466.331	−	151.520i	0.562522	−	0.182774i	0.576456	+	0.817129i	$0.304435\pi$
$830$	187.506	−	148.624i	0.225911	−	0.179065i
$831$	−421.706	+	1297.88i	−0.507468	+	1.56183i
$832$	73.5550	−	73.5550i	0.0884074	−	0.0884074i
$833$	−45.2454	+	23.0537i	−0.0543162	+	0.0276755i
$834$	887.182	+	1221.10i	1.06377	+	1.46415i
$835$	−435.994	−	773.717i	−0.522148	−	0.926607i
$836$	3.50669	+	2.54776i	0.00419461	+	0.00304756i
$837$	−3.54600	+	22.3886i	−0.00423656	+	0.0267486i
$838$	481.953	+	76.3339i	0.575123	+	0.0910905i
$839$	351.074	−	483.211i	0.418443	−	0.575937i	−0.546809	−	0.837257i	$-0.684158\pi$
$839$	351.074	−	483.211i	0.418443	−	0.575937i	0.965252	+	0.261320i	$0.0841578\pi$
$840$	−751.688	−	691.176i	−0.894866	−	0.822828i
$841$	−185.629	+	134.867i	−0.220724	+	0.160365i
$842$	186.989	+	366.986i	0.222077	+	0.435850i
$843$	−1866.32	−	1866.32i	−2.21391	−	2.21391i
$844$	129.465	+	42.0658i	0.153395	+	0.0498410i
$845$	−803.024	−	224.185i	−0.950324	−	0.265308i
$846$	650.731	+	2002.74i	0.769186	+	2.36731i
$847$	−404.711	−	206.211i	−0.477817	−	0.243460i
$848$	55.3221	+	349.290i	0.0652384	+	0.411899i
$849$			287.594i			0.338745i
$850$	−66.7090	−	77.2749i	−0.0784812	−	0.0909116i
$851$	−809.553			−0.951296
$852$	−57.5429	+	9.11391i	−0.0675387	+	0.0106971i
$853$	−361.364	+	709.217i	−0.423639	+	0.831438i	0.576261	+	0.817266i	$0.304511\pi$
$853$	−361.364	+	709.217i	−0.423639	+	0.831438i	−0.999900	+	0.0141723i	$0.995489\pi$
$854$	−799.088	+	259.639i	−0.935700	+	0.304027i
$855$	17.5377	+	47.1537i	0.0205119	+	0.0551505i
$856$	−130.395	+	401.314i	−0.152330	+	0.468824i
$857$	574.113	−	574.113i	0.669910	−	0.669910i	−0.287785	−	0.957695i	$-0.592919\pi$
$857$	574.113	−	574.113i	0.669910	−	0.669910i	0.957695	+	0.287785i	$0.0929188\pi$
$858$	177.561	−	90.4716i	0.206947	−	0.105445i
$859$	−478.848	−	659.078i	−0.557448	−	0.767262i	0.433551	−	0.901129i	$-0.357260\pi$
$859$	−478.848	−	659.078i	−0.557448	−	0.767262i	−0.990999	+	0.133867i	$0.957260\pi$
$860$	−20.4733	−	9.37275i	−0.0238061	−	0.0108985i
$861$	437.492	+	317.856i	0.508121	+	0.369171i
$862$	−59.2525	+	374.106i	−0.0687384	+	0.433997i
$863$	813.474	+	128.842i	0.942611	+	0.149295i	0.608781	−	0.793338i	$-0.291659\pi$
$863$	813.474	+	128.842i	0.942611	+	0.149295i	0.333830	+	0.942633i	$0.391659\pi$
$864$	−103.601	+	142.594i	−0.119908	+	0.165039i
$865$	92.4148	+	458.264i	0.106838	+	0.529785i
$866$	729.455	−	529.980i	0.842326	−	0.611986i
$867$	624.033	+	1224.73i	0.719761	+	1.41261i
$868$	1.32855	+	1.32855i	0.00153059	+	0.00153059i
$869$	−1492.08	−	484.806i	−1.71701	−	0.557889i
$870$	−47.3498	−	1129.02i	−0.0544251	−	1.29772i
$871$	−41.3563	−	127.282i	−0.0474814	−	0.146133i
$872$	215.592	+	109.850i	0.247239	+	0.125974i
$873$	−134.186	−	847.218i	−0.153707	−	0.970467i
$874$		−	46.0828i		−	0.0527263i
$875$	−386.771	+	498.704i	−0.442024	+	0.569947i
$876$	172.752			0.197206
$877$	883.498	−	139.932i	1.00741	−	0.159558i	0.369142	−	0.929373i	$-0.379652\pi$
$877$	883.498	−	139.932i	1.00741	−	0.159558i	0.638267	+	0.769815i	$0.279652\pi$
$878$	649.695	−	1275.10i	0.739972	−	1.45228i
$879$	545.981	−	177.400i	0.621139	−	0.201820i
$880$	−1024.07	+	42.9483i	−1.16371	+	0.0488049i
$881$	−34.0309	+	104.736i	−0.0386276	+	0.118883i	−0.968511	−	0.248971i	$-0.919908\pi$
$881$	−34.0309	+	104.736i	−0.0386276	+	0.118883i	0.929883	+	0.367855i	$0.119908\pi$
$882$	−451.593	+	451.593i	−0.512011	+	0.512011i
$883$	−375.623	+	191.389i	−0.425394	+	0.216749i	−0.653562	−	0.756873i	$-0.726726\pi$
$883$	−375.623	+	191.389i	−0.425394	+	0.216749i	0.228169	+	0.973622i	$0.426726\pi$
$884$	−0.812389	−	1.11816i	−0.000918992	−	0.00126488i
$885$	1555.07	−	313.600i	1.75714	−	0.354350i
$886$	−526.521	−	382.540i	−0.594268	−	0.431761i
$887$	−58.4169	+	368.830i	−0.0658589	+	0.415817i	0.932629	+	0.360838i	$0.117509\pi$
$887$	−58.4169	+	368.830i	−0.0658589	+	0.415817i	−0.998488	+	0.0549791i	$0.982491\pi$
$888$	929.040	+	147.145i	1.04622	+	0.165704i
$889$	123.484	−	169.961i	0.138902	−	0.191182i
$890$	−146.362	+	319.705i	−0.164452	+	0.359219i
$891$	44.9834	−	32.6824i	0.0504865	−	0.0366806i
$892$	−56.3107	−	110.516i	−0.0631286	−	0.123897i
$893$	−38.3787	−	38.3787i	−0.0429773	−	0.0429773i
$894$	1588.32	+	516.077i	1.77665	+	0.577268i
$895$	733.318	−	272.741i	0.819350	−	0.304738i
$896$	−161.994	−	498.566i	−0.180797	−	0.556435i
$897$	225.132	+	114.710i	0.250983	+	0.127882i
$898$	119.704	+	755.779i	0.133300	+	0.841624i
$899$			21.5922i			0.0240180i
$900$	130.975	+	79.3120i	0.145528	+	0.0881245i
$901$	54.1242			0.0600713
$902$	600.864	−	95.1675i	0.666146	−	0.105507i
$903$	117.081	−	229.785i	0.129658	−	0.254468i
$904$	−687.940	+	223.525i	−0.760996	+	0.247263i
$905$	−341.111	+	1221.85i	−0.376919	+	1.35011i
$906$	−131.579	+	404.960i	−0.145231	+	0.446976i
$907$	605.651	−	605.651i	0.667752	−	0.667752i	−0.289443	−	0.957195i	$-0.593470\pi$
$907$	605.651	−	605.651i	0.667752	−	0.667752i	0.957195	+	0.289443i	$0.0934701\pi$
$908$	26.6010	−	13.5539i	0.0292962	−	0.0149272i
$909$	−1056.64	−	1454.34i	−1.16242	−	1.59993i
$910$	48.4942	−	52.7399i	0.0532903	−	0.0579559i
$911$	−457.690	−	332.532i	−0.502404	−	0.365018i	0.307530	−	0.951538i	$-0.400497\pi$
$911$	−457.690	−	332.532i	−0.502404	−	0.365018i	−0.809935	+	0.586520i	$0.800497\pi$
$912$	−7.47334	+	47.1848i	−0.00819445	+	0.0517377i
$913$	−363.135	−	57.5149i	−0.397738	−	0.0629955i
$914$	−261.019	+	359.262i	−0.285579	+	0.393065i
$915$	1853.74	−	1044.60i	2.02595	−	1.14163i
$916$	−111.997	+	81.3705i	−0.122267	+	0.0888324i
$917$	533.706	+	1047.46i	0.582013	+	1.14226i
$918$	−74.9611	−	74.9611i	−0.0816570	−	0.0816570i
$919$	−1251.04	−	406.488i	−1.36131	−	0.442315i	−0.464827	−	0.885401i	$-0.653884\pi$
$919$	−1251.04	−	406.488i	−1.36131	−	0.442315i	−0.896479	+	0.443086i	$0.853884\pi$
$920$	−904.763	−	1141.46i	−0.983438	−	1.24072i
$921$	59.1750	+	182.122i	0.0642508	+	0.197744i
$922$	−183.689	−	93.5942i	−0.199229	−	0.101512i
$923$	−6.64075	−	41.9281i	−0.00719475	−	0.0454259i
$924$			151.095i			0.163523i
$925$	42.5452	−	579.776i	0.0459948	−	0.626785i
$926$	−792.353			−0.855673
$927$	−314.443	+	49.8028i	−0.339204	+	0.0537247i
$928$	−76.2219	+	149.594i	−0.0821357	+	0.161200i
$929$	−743.446	+	241.560i	−0.800265	+	0.260022i	−0.680469	−	0.732777i	$-0.738224\pi$
$929$	−743.446	+	241.560i	−0.800265	+	0.260022i	−0.119796	+	0.992799i	$0.538224\pi$
$930$	33.2321	+	22.0781i	0.0357335	+	0.0237399i
$931$	5.08664	−	15.6551i	0.00546363	−	0.0168153i
$932$	85.5731	−	85.5731i	0.0918166	−	0.0918166i
$933$	−1527.97	+	778.541i	−1.63770	+	0.834449i
$934$	−81.9788	−	112.834i	−0.0877718	−	0.120807i
$935$	−18.0259	+	155.829i	−0.0192790	+	0.166662i
$936$	−146.044	−	106.107i	−0.156030	−	0.113362i
$937$	−144.725	+	913.755i	−0.154455	+	0.975193i	0.781712	+	0.623639i	$0.214346\pi$
$937$	−144.725	+	913.755i	−0.154455	+	0.975193i	−0.936168	+	0.351554i	$0.885654\pi$
$938$	−840.374	−	133.102i	−0.895921	−	0.141900i
$939$	719.532	−	990.350i	0.766274	−	1.05469i
$940$	−164.095	−	18.9820i	−0.174569	−	0.0201936i
$941$	1236.27	−	898.202i	1.31378	−	0.954518i	0.313795	−	0.949491i	$-0.398400\pi$
$941$	1236.27	−	898.202i	1.31378	−	0.954518i	0.999987	−	0.00502752i	$-0.00160032\pi$
$942$	−666.008	−	1307.11i	−0.707015	−	1.38759i
$943$	545.420	+	545.420i	0.578388	+	0.578388i
$944$	880.938	+	286.234i	0.933198	+	0.303214i
$945$	−362.665	+	545.885i	−0.383772	+	0.577657i
$946$	−89.6534	−	275.925i	−0.0947711	−	0.291675i
$947$	−301.102	−	153.419i	−0.317953	−	0.162005i	0.287729	−	0.957712i	$-0.407100\pi$
$947$	−301.102	−	153.419i	−0.317953	−	0.162005i	−0.605682	+	0.795707i	$0.707100\pi$
$948$	34.8149	+	219.813i	0.0367246	+	0.231870i
$949$			125.874i			0.132639i
$950$	33.0030	+	2.42183i	0.0347400	+	0.00254930i
$951$	1341.51			1.41063
$952$	−90.1302	+	14.2752i	−0.0946746	+	0.0149950i
$953$	257.411	−	505.198i	0.270106	−	0.530114i	−0.715616	−	0.698494i	$-0.753854\pi$
$953$	257.411	−	505.198i	0.270106	−	0.530114i	0.985722	+	0.168381i	$0.0538538\pi$
$954$	647.391	−	210.350i	0.678607	−	0.220493i
$955$	594.721	−	471.396i	0.622745	−	0.493608i
$956$	−21.1823	+	65.1925i	−0.0221572	+	0.0681930i
$957$	−1227.83	+	1227.83i	−1.28300	+	1.28300i
$958$	−235.990	+	120.243i	−0.246336	+	0.125514i
$959$	28.8684	+	39.7339i	0.0301026	+	0.0414327i
$960$	822.206	+	1459.09i	0.856465	+	1.51989i
$961$	776.849	+	564.414i	0.808375	+	0.587319i
$962$	−10.3240	+	65.1832i	−0.0107318	+	0.0677580i
$963$	715.757	+	113.365i	0.743257	+	0.117720i
$964$	−66.6742	+	91.7691i	−0.0691641	+	0.0951962i
$965$	−1228.30	−	1129.42i	−1.27285	−	1.17038i
$966$	1299.59	−	944.208i	1.34533	−	0.977441i
$967$	−497.530	−	976.458i	−0.514509	−	1.00978i	−0.991406	−	0.130822i	$-0.958238\pi$
$967$	−497.530	−	976.458i	−0.514509	−	1.00978i	0.476897	−	0.878959i	$-0.341762\pi$
$968$	532.294	+	532.294i	0.549891	+	0.549891i
$969$	6.95366	+	2.25938i	0.00717612	+	0.00233166i
$970$	−543.436	−	151.715i	−0.560243	−	0.156407i
$971$	26.3844	+	81.2029i	0.0271724	+	0.0836281i	0.963723	−	0.266904i	$-0.0860007\pi$
$971$	26.3844	+	81.2029i	0.0271724	+	0.0836281i	−0.936551	+	0.350532i	$0.886001\pi$
$972$	−95.7578	−	48.7910i	−0.0985162	−	0.0501965i
$973$	−130.444	−	823.590i	−0.134064	−	0.846444i
$974$			240.712i			0.247137i
$975$	−93.9833	+	155.203i	−0.0963932	+	0.159183i
$976$	1242.41			1.27296
$977$	−599.515	+	94.9539i	−0.613629	+	0.0971893i	−0.455510	−	0.890231i	$-0.650543\pi$
$977$	−599.515	+	94.9539i	−0.613629	+	0.0971893i	−0.158119	+	0.987420i	$0.550543\pi$
$978$	218.182	−	428.206i	0.223090	−	0.437839i
$979$	513.858	−	166.963i	0.524881	−	0.170544i
$980$	−17.4641	−	46.9559i	−0.0178206	−	0.0479142i
$981$	128.411	−	395.209i	0.130898	−	0.402863i
$982$	−400.919	+	400.919i	−0.408268	+	0.408268i
$983$	−1531.04	+	780.104i	−1.55752	+	0.793595i	−0.999347	−	0.0361319i	$-0.988496\pi$
$983$	−1531.04	+	780.104i	−1.55752	+	0.793595i	−0.558170	+	0.829727i	$0.688496\pi$
$984$	−526.785	−	725.058i	−0.535351	−	0.736847i
$985$	−152.196	−	69.6760i	−0.154514	−	0.0707371i
$986$	−81.6956	−	59.3553i	−0.0828556	−	0.0601981i
$987$	295.970	−	1868.68i	0.299869	−	1.89330i
$988$	0.442507	+	0.0700862i	0.000447882	+	7.09375e-5i
$989$	216.219	−	297.599i	0.218623	−	0.300909i
$990$	390.008	+	1933.96i	0.393948	+	1.95350i
$991$	374.757	−	272.277i	0.378160	−	0.274749i	−0.382426	−	0.923986i	$-0.624911\pi$
$991$	374.757	−	272.277i	0.378160	−	0.274749i	0.760587	+	0.649236i	$0.224911\pi$
$992$	−2.69119	−	5.28175i	−0.00271289	−	0.00532435i
$993$	1572.63	+	1572.63i	1.58372	+	1.58372i
$994$	−256.676	−	83.3990i	−0.258225	−	0.0839024i
$995$	35.5561	+	847.805i	0.0357347	+	0.852066i
$996$	16.1168	+	49.6023i	0.0161815	+	0.0498015i
$997$	−977.886	−	498.258i	−0.980828	−	0.499757i	−0.111379	−	0.993778i	$-0.535527\pi$
$997$	−977.886	−	498.258i	−0.980828	−	0.499757i	−0.869450	+	0.494021i	$0.835527\pi$
$998$	129.576	+	818.108i	0.129835	+	0.819748i
$999$		−	603.688i		−	0.604292i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.3.f.a.13.2	yes	32
3.2	odd	2		225.3.r.a.163.3		32
4.3	odd	2		400.3.bg.c.113.4		32
5.2	odd	4		125.3.f.a.82.2		32
5.3	odd	4		125.3.f.b.82.3		32
5.4	even	2		125.3.f.c.43.3		32
25.2	odd	20	inner	25.3.f.a.2.2	✓	32
25.11	even	5		125.3.f.a.93.2		32
25.14	even	10		125.3.f.b.93.3		32
25.23	odd	20		125.3.f.c.32.3		32
75.2	even	20		225.3.r.a.127.3		32
100.27	even	20		400.3.bg.c.177.4		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
25.3.f.a.2.2	✓	32	25.2	odd	20	inner
25.3.f.a.13.2	yes	32	1.1	even	1	trivial
125.3.f.a.82.2		32	5.2	odd	4
125.3.f.a.93.2		32	25.11	even	5
125.3.f.b.82.3		32	5.3	odd	4
125.3.f.b.93.3		32	25.14	even	10
125.3.f.c.32.3		32	25.23	odd	20
125.3.f.c.43.3		32	5.4	even	2
225.3.r.a.127.3		32	75.2	even	20
225.3.r.a.163.3		32	3.2	odd	2
400.3.bg.c.113.4		32	4.3	odd	2
400.3.bg.c.177.4		32	100.27	even	20

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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	25.f (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.86717 + 0.295731i) q^{2} +(-2.19472 + 4.30737i) q^{3} +(-0.405347 + 0.131705i) q^{4} +(4.99561 - 0.209511i) q^{5} +(2.82409 - 8.69166i) q^{6} +(-3.57009 + 3.57009i) q^{7} +(7.45551 - 3.79877i) q^{8} +(-8.44662 - 11.6258i) q^{9} +O(q^{10})\)	\(q+(-1.86717 + 0.295731i) q^{2} +(-2.19472 + 4.30737i) q^{3} +(-0.405347 + 0.131705i) q^{4} +(4.99561 - 0.209511i) q^{5} +(2.82409 - 8.69166i) q^{6} +(-3.57009 + 3.57009i) q^{7} +(7.45551 - 3.79877i) q^{8} +(-8.44662 - 11.6258i) q^{9} +(-9.26571 + 1.86855i) q^{10} +(11.7507 + 8.53735i) q^{11} +(0.322318 - 2.03504i) q^{12} +(1.48281 + 0.234854i) q^{13} +(5.61018 - 7.72176i) q^{14} +(-10.0615 + 21.9778i) q^{15} +(-11.4181 + 8.29572i) q^{16} +(0.980634 + 1.92460i) q^{17} +(19.2094 + 19.2094i) q^{18} +(-0.665919 - 0.216370i) q^{19} +(-1.99736 + 0.742872i) q^{20} +(-7.54237 - 23.2130i) q^{21} +(-24.4653 - 12.4657i) q^{22} +(-5.44617 - 34.3858i) q^{23} +40.4509i q^{24} +(24.9122 - 2.09327i) q^{25} -2.83811 q^{26} +(25.6417 - 4.06124i) q^{27} +(0.976924 - 1.91732i) q^{28} +(23.5192 - 7.64185i) q^{29} +(12.2871 - 44.0118i) q^{30} +(-0.269813 + 0.830398i) q^{31} +(-4.80067 + 4.80067i) q^{32} +(-62.5629 + 31.8774i) q^{33} +(-2.40018 - 3.30356i) q^{34} +(-17.0868 + 18.5827i) q^{35} +(4.95498 + 3.60001i) q^{36} +(3.63763 - 22.9671i) q^{37} +(1.30737 + 0.207068i) q^{38} +(-4.26594 + 5.87157i) q^{39} +(36.4489 - 20.5392i) q^{40} +(-17.9244 + 13.0228i) q^{41} +(20.9477 + 41.1122i) q^{42} +(7.47137 + 7.47137i) q^{43} +(-5.88750 - 1.91297i) q^{44} +(-44.6317 - 56.3082i) q^{45} +(20.3379 + 62.5936i) q^{46} +(69.0671 + 35.1914i) q^{47} +(-10.6733 - 67.3887i) q^{48} +23.5090i q^{49} +(-45.8964 + 11.2758i) q^{50} -10.4422 q^{51} +(-0.631983 + 0.100096i) q^{52} +(11.3757 - 22.3261i) q^{53} +(-46.6764 + 15.1661i) q^{54} +(60.4904 + 40.1874i) q^{55} +(-13.0549 + 40.1788i) q^{56} +(2.39349 - 2.39349i) q^{57} +(-41.6545 + 21.2240i) q^{58} +(-38.5765 - 53.0960i) q^{59} +(1.18381 - 10.2338i) q^{60} +(-71.2176 - 51.7426i) q^{61} +(0.258213 - 1.63029i) q^{62} +(71.6602 + 11.3499i) q^{63} +(40.7269 - 56.0557i) q^{64} +(7.45673 + 0.862573i) q^{65} +(107.389 - 78.0225i) q^{66} +(-40.4707 - 79.4283i) q^{67} +(-0.650977 - 0.650977i) q^{68} +(160.065 + 52.0084i) q^{69} +(26.4085 - 39.7503i) q^{70} +(-8.73781 - 26.8922i) q^{71} +(-107.138 - 54.5893i) q^{72} +(13.1161 + 82.8116i) q^{73} +43.9593i q^{74} +(-45.6588 + 111.900i) q^{75} +0.298425 q^{76} +(-72.4300 + 11.4718i) q^{77} +(6.22885 - 12.2248i) q^{78} +(-102.728 + 33.3782i) q^{79} +(-55.3022 + 43.8344i) q^{80} +(1.18297 - 3.64080i) q^{81} +(29.6167 - 29.6167i) q^{82} +(-22.5540 + 11.4919i) q^{83} +(6.11455 + 8.41596i) q^{84} +(5.30209 + 9.40911i) q^{85} +(-16.1599 - 11.7408i) q^{86} +(-18.7017 + 118.078i) q^{87} +(120.039 + 19.0122i) q^{88} +(21.8651 - 30.0947i) q^{89} +(99.9873 + 91.9381i) q^{90} +(-6.13220 + 4.45530i) q^{91} +(6.73637 + 13.2209i) q^{92} +(-2.98467 - 2.98467i) q^{93} +(-139.367 - 45.2832i) q^{94} +(-3.37200 - 0.941384i) q^{95} +(-10.1422 - 31.2144i) q^{96} +(53.1853 + 27.0993i) q^{97} +(-6.95233 - 43.8953i) q^{98} -208.722i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9}+O(q^{10}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9	\( 32 q - 10 q^{2} - 10 q^{3} - 10 q^{4} - 10 q^{5} - 6 q^{6} - 10 q^{7} - 10 q^{8} - 10 q^{9} - 10 q^{10} - 6 q^{11} - 10 q^{12} - 10 q^{13} - 10 q^{14} - 10 q^{15} + 2 q^{16} + 60 q^{17} + 140 q^{18} + 90 q^{19} + 130 q^{20} - 6 q^{21} + 70 q^{22} + 10 q^{23} - 40 q^{25} + 4 q^{26} - 100 q^{27} - 250 q^{28} - 110 q^{29} - 250 q^{30} - 6 q^{31} - 290 q^{32} - 190 q^{33} - 260 q^{34} - 120 q^{35} - 58 q^{36} + 50 q^{37} + 320 q^{38} + 390 q^{39} + 440 q^{40} - 86 q^{41} + 690 q^{42} + 230 q^{43} + 340 q^{44} + 310 q^{45} - 6 q^{46} + 70 q^{47} + 160 q^{48} - 100 q^{50} - 16 q^{51} - 320 q^{52} - 190 q^{53} - 660 q^{54} - 250 q^{55} - 70 q^{56} - 650 q^{57} - 640 q^{58} - 260 q^{59} - 550 q^{60} + 114 q^{61} + 60 q^{62} - 20 q^{63} + 340 q^{64} + 360 q^{65} + 138 q^{66} + 270 q^{67} + 710 q^{68} + 340 q^{69} + 310 q^{70} - 66 q^{71} + 360 q^{72} + 30 q^{73} - 90 q^{75} - 80 q^{76} - 250 q^{77} - 500 q^{78} - 210 q^{79} - 850 q^{80} + 62 q^{81} + 30 q^{82} - 10 q^{84} + 600 q^{85} - 6 q^{86} + 300 q^{87} + 190 q^{88} - 10 q^{89} + 380 q^{90} - 6 q^{91} - 30 q^{92} + 520 q^{93} + 790 q^{94} + 310 q^{95} + 174 q^{96} + 270 q^{97} + 170 q^{98}+O(q^{100}) \) 32 * q - 10 * q^2 - 10 * q^3 - 10 * q^4 - 10 * q^5 - 6 * q^6 - 10 * q^7 - 10 * q^8 - 10 * q^9 - 10 * q^10 - 6 * q^11 - 10 * q^12 - 10 * q^13 - 10 * q^14 - 10 * q^15 + 2 * q^16 + 60 * q^17 + 140 * q^18 + 90 * q^19 + 130 * q^20 - 6 * q^21 + 70 * q^22 + 10 * q^23 - 40 * q^25 + 4 * q^26 - 100 * q^27 - 250 * q^28 - 110 * q^29 - 250 * q^30 - 6 * q^31 - 290 * q^32 - 190 * q^33 - 260 * q^34 - 120 * q^35 - 58 * q^36 + 50 * q^37 + 320 * q^38 + 390 * q^39 + 440 * q^40 - 86 * q^41 + 690 * q^42 + 230 * q^43 + 340 * q^44 + 310 * q^45 - 6 * q^46 + 70 * q^47 + 160 * q^48 - 100 * q^50 - 16 * q^51 - 320 * q^52 - 190 * q^53 - 660 * q^54 - 250 * q^55 - 70 * q^56 - 650 * q^57 - 640 * q^58 - 260 * q^59 - 550 * q^60 + 114 * q^61 + 60 * q^62 - 20 * q^63 + 340 * q^64 + 360 * q^65 + 138 * q^66 + 270 * q^67 + 710 * q^68 + 340 * q^69 + 310 * q^70 - 66 * q^71 + 360 * q^72 + 30 * q^73 - 90 * q^75 - 80 * q^76 - 250 * q^77 - 500 * q^78 - 210 * q^79 - 850 * q^80 + 62 * q^81 + 30 * q^82 - 10 * q^84 + 600 * q^85 - 6 * q^86 + 300 * q^87 + 190 * q^88 - 10 * q^89 + 380 * q^90 - 6 * q^91 - 30 * q^92 + 520 * q^93 + 790 * q^94 + 310 * q^95 + 174 * q^96 + 270 * q^97 + 170 * q^98

Introduction

L-functions

Modular forms

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