LMFDB - Embedded newform 175.4.x.a.3.50

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,4,Mod(3,175)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, 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:	$10.3253342510$
Analytic rank:	$0$
Dimension:	$928$
Relative dimension:	$58$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			3.50
Character	$\chi$	$=$	175.3
Dual form			175.4.x.a.117.50

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.31018 - 3.55736i) q^{2} +(2.03540 - 5.30240i) q^{3} +(-4.06400 - 9.12789i) q^{4} +(6.18963 - 9.31066i) q^{5} +(-14.1604 - 19.4901i) q^{6} +(-7.03669 - 17.1314i) q^{7} +(-8.34419 - 1.32159i) q^{8} +(-3.90766 - 3.51847i) q^{9} +(-18.8222 - 43.5280i) q^{10} +(44.5648 + 49.4942i) q^{11} +(-56.6716 + 2.97003i) q^{12} +(2.69963 + 1.37553i) q^{13} +(-77.1985 - 14.5445i) q^{14} +(-36.7705 - 51.7708i) q^{15} +(29.5082 - 32.7722i) q^{16} +(-87.7422 + 108.353i) q^{17} +(-21.5438 + 5.77266i) q^{18} +(27.4824 + 12.2359i) q^{19} +(-110.141 - 18.6598i) q^{20} +(-105.160 + 2.44206i) q^{21} +(279.021 - 44.1926i) q^{22} +(53.6397 + 34.8340i) q^{23} +(-23.9914 + 41.5543i) q^{24} +(-48.3769 - 115.259i) q^{25} +(11.1299 - 6.42583i) q^{26} +(110.026 - 56.0611i) q^{27} +(-127.776 + 133.852i) q^{28} +(-80.3234 + 110.556i) q^{29} +(-269.114 + 11.2060i) q^{30} +(-133.607 + 14.0427i) q^{31} +(-65.9057 - 245.963i) q^{32} +(353.145 - 135.560i) q^{33} +(182.749 + 562.444i) q^{34} +(-203.059 - 40.5209i) q^{35} +(-16.2355 + 49.9677i) q^{36} +(4.20638 + 80.2626i) q^{37} +(107.017 - 69.4975i) q^{38} +(12.7884 - 11.5148i) q^{39} +(-63.9524 + 69.5098i) q^{40} +(-157.315 + 51.1147i) q^{41} +(-234.251 + 379.733i) q^{42} +(52.0680 + 52.0680i) q^{43} +(270.666 - 607.927i) q^{44} +(-56.9463 + 14.6048i) q^{45} +(247.834 - 110.343i) q^{46} +(222.772 - 180.397i) q^{47} +(-113.710 - 223.169i) q^{48} +(-243.970 + 241.097i) q^{49} +(-521.777 - 94.1750i) q^{50} +(395.938 + 685.785i) q^{51} +(1.58440 - 30.2321i) q^{52} +(599.480 + 230.119i) q^{53} +(54.7502 - 520.913i) q^{54} +(736.663 - 108.577i) q^{55} +(36.0748 + 152.247i) q^{56} +(120.817 - 120.817i) q^{57} +(207.725 + 541.142i) q^{58} +(-816.097 - 173.467i) q^{59} +(-323.123 + 546.033i) q^{60} +(-156.072 - 734.259i) q^{61} +(-258.702 + 507.731i) q^{62} +(-32.7794 + 91.7021i) q^{63} +(-691.707 - 224.749i) q^{64} +(29.5168 - 16.6213i) q^{65} +(333.593 - 1569.43i) q^{66} +(-581.110 - 470.573i) q^{67} +(1345.61 + 360.556i) q^{68} +(293.882 - 213.518i) q^{69} +(-613.250 + 628.744i) q^{70} +(248.754 + 180.730i) q^{71} +(27.9563 + 34.5231i) q^{72} +(661.159 + 34.6499i) q^{73} +(295.240 + 170.457i) q^{74} +(-709.616 + 21.9151i) q^{75} -300.583i q^{76} +(534.317 - 1111.73i) q^{77} +(-11.4186 - 72.0941i) q^{78} +(-249.173 - 26.1891i) q^{79} +(-122.486 - 477.589i) q^{80} +(-88.1514 - 838.704i) q^{81} +(-181.592 + 677.709i) q^{82} +(-78.0327 + 492.679i) q^{83} +(449.661 + 949.964i) q^{84} +(465.743 + 1487.60i) q^{85} +(305.511 - 64.9383i) q^{86} +(422.720 + 650.932i) q^{87} +(-306.446 - 471.885i) q^{88} +(551.340 - 117.191i) q^{89} +(-79.6012 + 236.318i) q^{90} +(4.56831 - 55.9276i) q^{91} +(99.9695 - 631.183i) q^{92} +(-197.485 + 737.022i) q^{93} +(-127.095 - 1209.23i) q^{94} +(284.031 - 180.143i) q^{95} +(-1438.34 - 151.176i) q^{96} +(-162.001 - 1022.84i) q^{97} +(294.054 + 1424.86i) q^{98} -350.206i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) $ 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{20}\right)$

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 $

$2$	2.31018	−	3.55736i	0.816771	−	1.25772i	−0.146507	−	0.989210i	$-0.546803\pi$
$2$	2.31018	−	3.55736i	0.816771	−	1.25772i	0.963278	−	0.268507i	$-0.0865302\pi$
$3$	2.03540	−	5.30240i	0.391713	−	1.02045i	−0.585965	−	0.810337i	$-0.699284\pi$
$3$	2.03540	−	5.30240i	0.391713	−	1.02045i	0.977678	−	0.210110i	$-0.0673823\pi$
$4$	−4.06400	−	9.12789i	−0.508000	−	1.14099i
$5$	6.18963	−	9.31066i	0.553618	−	0.832771i
$5$	6.18963	−	9.31066i	0.553618	−	0.832771i
$6$	−14.1604	−	19.4901i	−0.963493	−	1.32613i
$7$	−7.03669	−	17.1314i	−0.379945	−	0.925009i
$7$	−7.03669	−	17.1314i	−0.379945	−	0.925009i
$8$	−8.34419	−	1.32159i	−0.368765	−	0.0584066i
$9$	−3.90766	−	3.51847i	−0.144728	−	0.130314i
$10$	−18.8222	−	43.5280i	−0.595211	−	1.37648i
$11$	44.5648	+	49.4942i	1.22153	+	1.35664i	0.914317	+	0.405000i	$0.132728\pi$
$11$	44.5648	+	49.4942i	1.22153	+	1.35664i	0.307209	+	0.951642i	$0.400605\pi$
$12$	−56.6716	+	2.97003i	−1.36331	+	0.0714478i
$13$	2.69963	+	1.37553i	0.0575956	+	0.0293464i	0.482551	−	0.875868i	$-0.339710\pi$
$13$	2.69963	+	1.37553i	0.0575956	+	0.0293464i	−0.424956	+	0.905214i	$0.639710\pi$
$14$	−77.1985	−	14.5445i	−1.47373	−	0.277656i
$15$	−36.7705	−	51.7708i	−0.632939	−	0.891144i
$16$	29.5082	−	32.7722i	0.461066	−	0.512065i
$17$	−87.7422	+	108.353i	−1.25180	+	1.54585i	−0.544989	+	0.838443i	$0.683466\pi$
$17$	−87.7422	+	108.353i	−1.25180	+	1.54585i	−0.706811	+	0.707402i	$0.749867\pi$
$18$	−21.5438	+	5.77266i	−0.282107	+	0.0755905i
$19$	27.4824	+	12.2359i	0.331836	+	0.147743i	0.565890	−	0.824481i	$-0.308533\pi$
$19$	27.4824	+	12.2359i	0.331836	+	0.147743i	−0.234054	+	0.972224i	$0.575199\pi$
$20$	−110.141	−	18.6598i	−1.23142	−	0.208622i
$21$	−105.160	+	2.44206i	−1.09275	+	0.0253762i
$22$	279.021	−	44.1926i	2.70398	−	0.428268i
$23$	53.6397	+	34.8340i	0.486289	+	0.315800i	0.764392	−	0.644751i	$-0.223039\pi$
$23$	53.6397	+	34.8340i	0.486289	+	0.315800i	−0.278103	+	0.960551i	$0.589706\pi$
$24$	−23.9914	+	41.5543i	−0.204051	+	0.353426i
$25$	−48.3769	−	115.259i	−0.387015	−	0.922073i
$26$	11.1299	−	6.42583i	0.0839518	−	0.0484696i
$27$	110.026	−	56.0611i	0.784242	−	0.399591i
$28$	−127.776	+	133.852i	−0.862410	+	0.903417i
$29$	−80.3234	+	110.556i	−0.514334	+	0.707920i	−0.984643	−	0.174582i	$-0.944143\pi$
$29$	−80.3234	+	110.556i	−0.514334	+	0.707920i	0.470309	+	0.882502i	$0.344143\pi$
$30$	−269.114	+	11.2060i	−1.63777	+	0.0681978i
$31$	−133.607	+	14.0427i	−0.774084	+	0.0813595i	−0.483330	−	0.875438i	$-0.660573\pi$
$31$	−133.607	+	14.0427i	−0.774084	+	0.0813595i	−0.290754	+	0.956798i	$0.593906\pi$
$32$	−65.9057	−	245.963i	−0.364081	−	1.35877i
$33$	353.145	−	135.560i	1.86287	−	0.715088i
$34$	182.749	+	562.444i	0.921801	+	2.83701i
$35$	−203.059	−	40.5209i	−0.980665	−	0.195694i
$36$	−16.2355	+	49.9677i	−0.0751644	+	0.231332i
$37$	4.20638	+	80.2626i	0.0186899	+	0.356624i	0.991926	+	0.126817i	$0.0404761\pi$
$37$	4.20638	+	80.2626i	0.0186899	+	0.356624i	−0.973236	+	0.229807i	$0.926191\pi$
$38$	107.017	−	69.4975i	0.456853	−	0.296684i
$39$	12.7884	−	11.5148i	0.0525074	−	0.0472778i
$40$	−63.9524	+	69.5098i	−0.252794	+	0.274762i
$41$	−157.315	+	51.1147i	−0.599230	+	0.194702i	−0.592897	−	0.805278i	$-0.702016\pi$
$41$	−157.315	+	51.1147i	−0.599230	+	0.194702i	−0.00633322	+	0.999980i	$0.502016\pi$
$42$	−234.251	+	379.733i	−0.860612	+	1.39510i
$43$	52.0680	+	52.0680i	0.184658	+	0.184658i	0.793382	−	0.608724i	$-0.208318\pi$
$43$	52.0680	+	52.0680i	0.184658	+	0.184658i	−0.608724	+	0.793382i	$0.708318\pi$
$44$	270.666	−	607.927i	0.927375	−	2.08292i
$45$	−56.9463	+	14.6048i	−0.188646	+	0.0483814i
$46$	247.834	−	110.343i	0.794374	−	0.353678i
$47$	222.772	−	180.397i	0.691376	−	0.559865i	−0.217945	−	0.975961i	$-0.569935\pi$
$47$	222.772	−	180.397i	0.691376	−	0.559865i	0.909321	+	0.416096i	$0.136602\pi$
$48$	−113.710	−	223.169i	−0.341930	−	0.671075i
$49$	−243.970	+	241.097i	−0.711283	+	0.702906i
$50$	−521.777	−	94.1750i	−1.47581	−	0.266367i
$51$	395.938	+	685.785i	1.08711	+	1.88292i
$52$	1.58440	−	30.2321i	0.00422531	−	0.0806237i
$53$	599.480	+	230.119i	1.55368	+	0.596401i	0.975595	−	0.219577i	$-0.0704678\pi$
$53$	599.480	+	230.119i	1.55368	+	0.596401i	0.578083	+	0.815978i	$0.303801\pi$
$54$	54.7502	−	520.913i	0.137973	−	1.31273i
$55$	736.663	−	108.577i	1.80603	−	0.266191i
$56$	36.0748	+	152.247i	0.0860838	+	0.363302i
$57$	120.817	−	120.817i	0.280748	−	0.280748i
$58$	207.725	+	541.142i	0.470270	+	1.22509i
$59$	−816.097	−	173.467i	−1.80079	−	0.382770i	−0.819163	−	0.573561i	$-0.805561\pi$
$59$	−816.097	−	173.467i	−1.80079	−	0.382770i	−0.981631	+	0.190791i	$0.938895\pi$
$60$	−323.123	+	546.033i	−0.695250	+	1.17488i
$61$	−156.072	−	734.259i	−0.327589	−	1.54118i	−0.766256	−	0.642535i	$-0.777883\pi$
$61$	−156.072	−	734.259i	−0.327589	−	1.54118i	0.438668	−	0.898649i	$-0.355451\pi$
$62$	−258.702	+	507.731i	−0.529922	+	1.04003i
$63$	−32.7794	+	91.7021i	−0.0655526	+	0.183387i
$64$	−691.707	−	224.749i	−1.35099	−	0.438963i
$65$	29.5168	−	16.6213i	0.0563247	−	0.0317172i
$66$	333.593	−	1569.43i	0.622158	−	2.92702i
$67$	−581.110	−	470.573i	−1.05961	−	0.858055i	−0.0693926	−	0.997589i	$-0.522106\pi$
$67$	−581.110	−	470.573i	−1.05961	−	0.858055i	−0.990217	+	0.139534i	$0.955439\pi$
$68$	1345.61	+	360.556i	2.39970	+	0.642998i
$69$	293.882	−	213.518i	0.512743	−	0.372530i
$70$	−613.250	+	628.744i	−1.04711	+	1.07356i
$71$	248.754	+	180.730i	0.415798	+	0.302095i	0.775945	−	0.630801i	$-0.217273\pi$
$71$	248.754	+	180.730i	0.415798	+	0.302095i	−0.360147	+	0.932896i	$0.617273\pi$
$72$	27.9563	+	34.5231i	0.0457594	+	0.0565082i
$73$	661.159	+	34.6499i	1.06004	+	0.0555542i	0.574375	−	0.818592i	$-0.305245\pi$
$73$	661.159	+	34.6499i	1.06004	+	0.0555542i	0.485663	+	0.874146i	$0.338578\pi$
$74$	295.240	+	170.457i	0.463797	+	0.267773i
$75$	−709.616	+	21.9151i	−1.09253	+	0.0337404i
$76$		−	300.583i		−	0.453674i
$77$	534.317	−	1111.73i	0.790793	−	1.64537i
$78$	−11.4186	−	72.0941i	−0.0165757	−	0.104655i
$79$	−249.173	−	26.1891i	−0.354862	−	0.0372975i	−0.0745796	−	0.997215i	$-0.523761\pi$
$79$	−249.173	−	26.1891i	−0.354862	−	0.0372975i	−0.280283	+	0.959918i	$0.590428\pi$
$80$	−122.486	−	477.589i	−0.171179	−	0.667450i
$81$	−88.1514	−	838.704i	−0.120921	−	1.15049i
$82$	−181.592	+	677.709i	−0.244554	+	0.912689i
$83$	−78.0327	+	492.679i	−0.103195	+	0.651549i	0.880818	+	0.473455i	$0.156993\pi$
$83$	−78.0327	+	492.679i	−0.103195	+	0.651549i	−0.984013	+	0.178094i	$0.943007\pi$
$84$	449.661	+	949.964i	0.584072	+	1.23392i
$85$	465.743	+	1487.60i	0.594316	+	1.89827i
$86$	305.511	−	64.9383i	0.383071	−	0.0814242i
$87$	422.720	+	650.932i	0.520923	+	0.802152i
$88$	−306.446	−	471.885i	−0.371219	−	0.571627i
$89$	551.340	−	117.191i	0.656651	−	0.139575i	0.132476	−	0.991186i	$-0.457707\pi$
$89$	551.340	−	117.191i	0.656651	−	0.139575i	0.524175	+	0.851611i	$0.324374\pi$
$90$	−79.6012	+	236.318i	−0.0932301	+	0.276779i
$91$	4.56831	−	55.9276i	0.00526252	−	0.0644264i
$92$	99.9695	−	631.183i	0.113289	−	0.715276i
$93$	−197.485	+	737.022i	−0.220196	+	0.821781i
$94$	−127.095	−	1209.23i	−0.139456	−	1.32684i
$95$	284.031	−	180.143i	0.306746	−	0.194550i
$96$	−1438.34	−	151.176i	−1.52917	−	0.160722i
$97$	−162.001	−	1022.84i	−0.169575	−	1.07065i	−0.914820	−	0.403862i	$-0.867668\pi$
$97$	−162.001	−	1022.84i	−0.169575	−	1.07065i	0.745245	−	0.666790i	$-0.232332\pi$
$98$	294.054	+	1424.86i	0.303101	+	1.46871i
$99$		−	350.206i		−	0.355526i
$100$	−855.469	+	909.992i	−0.855469	+	0.909992i
$101$	−509.671	−	294.259i	−0.502121	−	0.289900i	0.227468	−	0.973786i	$-0.426955\pi$
$101$	−509.671	−	294.259i	−0.502121	−	0.289900i	−0.729589	+	0.683886i	$0.760289\pi$
$102$	3354.27	+	175.790i	3.25610	+	0.170645i
$103$	307.265	+	379.440i	0.293939	+	0.362984i	0.902626	−	0.430426i	$-0.141637\pi$
$103$	307.265	+	379.440i	0.293939	+	0.362984i	−0.608687	+	0.793410i	$0.708303\pi$
$104$	−20.7083	−	15.0455i	−0.0195252	−	0.0141859i
$105$	−628.165	+	994.225i	−0.583834	+	0.924061i
$106$	2203.52	−	1600.95i	2.01910	−	1.46696i
$107$	−246.473	−	66.0424i	−0.222687	−	0.0596687i	0.145750	−	0.989321i	$-0.453440\pi$
$107$	−246.473	−	66.0424i	−0.222687	−	0.0596687i	−0.368437	+	0.929653i	$0.620107\pi$
$108$	−958.865	−	776.473i	−0.854322	−	0.691817i
$109$	2.90216	−	13.6536i	0.00255024	−	0.0119980i	−0.976854	−	0.213907i	$-0.931381\pi$
$109$	2.90216	−	13.6536i	0.00255024	−	0.0119980i	0.979404	+	0.201909i	$0.0647145\pi$
$110$	1315.58	−	2871.41i	1.14032	−	2.48889i
$111$	434.146	+	141.062i	0.371237	+	0.120622i
$112$	−769.073	−	274.909i	−0.648845	−	0.231933i
$113$	−156.936	+	308.004i	−0.130649	+	0.256412i	−0.947059	−	0.321060i	$-0.895961\pi$
$113$	−156.936	+	308.004i	−0.130649	+	0.256412i	0.816410	+	0.577472i	$0.195961\pi$
$114$	−150.681	−	708.901i	−0.123795	−	0.582409i
$115$	656.338	−	283.811i	0.532207	−	0.230135i
$116$	1335.57	+	283.885i	1.06901	+	0.227225i
$117$	−5.70947	−	14.8737i	−0.00451146	−	0.0117527i
$118$	−2502.41	+	2502.41i	−1.95225	+	1.95225i
$119$	2473.65	+	740.704i	1.90554	+	0.570590i
$120$	238.400	+	480.581i	0.181357	+	0.365590i
$121$	−324.529	+	3087.69i	−0.243823	+	2.31982i
$122$	−2972.58	−	1141.07i	−2.20594	−	0.846780i
$123$	−49.1682	+	938.184i	−0.0360434	+	0.687750i
$124$	671.161	+	1162.48i	0.486065	+	0.841888i
$125$	−1372.57	−	262.991i	−0.982134	−	0.188181i
$126$	250.491	+	328.456i	0.177107	+	0.232232i
$127$	415.931	+	816.310i	0.290613	+	0.570360i	0.989442	−	0.144928i	$-0.0462952\pi$
$127$	415.931	+	816.310i	0.290613	+	0.570360i	−0.698829	+	0.715289i	$0.746295\pi$
$128$	−814.337	+	659.437i	−0.562328	+	0.455364i
$129$	382.065	−	170.106i	0.260767	−	0.116101i
$130$	9.06104	−	143.400i	0.00611312	−	0.0967463i
$131$	−784.101	+	1761.12i	−0.522956	+	1.17458i	0.438277	+	0.898840i	$0.355589\pi$
$131$	−784.101	+	1761.12i	−0.522956	+	1.17458i	−0.961233	+	0.275739i	$0.911078\pi$
$132$	−2672.55	−	2672.55i	−1.76224	−	1.76224i
$133$	16.2340	−	556.912i	0.0105839	−	0.363086i
$134$	−3016.46	+	980.109i	−1.94465	+	0.631855i
$135$	159.055	−	1371.41i	0.101402	−	0.874314i
$136$	875.335	−	788.156i	0.551907	−	0.496940i
$137$	−167.649	+	108.872i	−0.104549	+	0.0678949i	−0.595855	−	0.803092i	$-0.703187\pi$
$137$	−167.649	+	108.872i	−0.104549	+	0.0678949i	0.491306	+	0.870987i	$0.336520\pi$
$138$	−80.6403	−	1538.71i	−0.0497432	−	0.949156i
$139$	−243.712	+	750.067i	−0.148715	+	0.457697i	−0.997470	−	0.0710891i	$-0.977353\pi$
$139$	−243.712	+	750.067i	−0.148715	+	0.457697i	0.848755	+	0.528786i	$0.177353\pi$
$140$	455.362	+	2018.18i	0.274894	+	1.21834i
$141$	−503.108	−	1548.41i	−0.300492	−	0.924819i
$142$	1217.59	−	467.388i	0.719561	−	0.276214i
$143$	52.2276	+	194.916i	0.0305419	+	0.113984i
$144$	−230.616	+	24.2387i	−0.133458	+	0.0140270i
$145$	532.174	+	1432.16i	0.304791	+	0.820239i
$146$	1650.65	−	2271.93i	0.935679	−	1.28785i
$147$	781.814	+	1784.35i	0.438659	+	1.00116i
$148$	715.533	−	364.582i	0.397408	−	0.202490i
$149$	−1050.16	+	606.309i	−0.577398	+	0.333361i	−0.760099	−	0.649808i	$-0.774849\pi$
$149$	−1050.16	+	606.309i	−0.577398	+	0.333361i	0.182701	+	0.983169i	$0.441516\pi$
$150$	−1561.38	+	2574.99i	−0.849907	+	1.40165i
$151$	−1463.51	+	2534.88i	−0.788735	+	1.36613i	0.138008	+	0.990431i	$0.455930\pi$
$151$	−1463.51	+	2534.88i	−0.788735	+	1.36613i	−0.926742	+	0.375697i	$0.877403\pi$
$152$	−213.147	−	138.419i	−0.113740	−	0.0738638i
$153$	724.102	−	114.687i	0.382616	−	0.0606004i
$154$	−2720.47	−	4469.05i	−1.42352	−	2.33848i
$155$	−696.234	+	1330.89i	−0.360793	+	0.689677i
$156$	−157.078	−	69.9354i	−0.0806171	−	0.0358930i
$157$	107.505	−	28.8060i	0.0546489	−	0.0146431i	−0.231391	−	0.972861i	$-0.574328\pi$
$157$	107.505	−	28.8060i	0.0546489	−	0.0146431i	0.286040	+	0.958218i	$0.407661\pi$
$158$	−668.797	+	825.895i	−0.336751	+	0.415852i
$159$	2440.36	−	2710.30i	1.21719	−	1.35183i
$160$	−2698.01	−	908.798i	−1.33311	−	0.449042i
$161$	219.310	−	1164.04i	0.107354	−	0.569809i
$162$	−3187.22	−	1623.97i	−1.54575	−	0.787599i
$163$	−1144.16	+	59.9630i	−0.549802	+	0.0288139i	−0.325215	−	0.945640i	$-0.605437\pi$
$163$	−1144.16	+	59.9630i	−0.549802	+	0.0288139i	−0.224587	+	0.974454i	$0.572103\pi$
$164$	1105.90	+	1228.22i	0.526561	+	0.584805i
$165$	923.687	−	4127.08i	0.435812	−	1.94723i
$166$	1572.37	+	1415.77i	0.735177	+	0.661956i
$167$	−216.388	−	34.2725i	−0.100267	−	0.0158808i	0.106099	−	0.994356i	$-0.466164\pi$
$167$	−216.388	−	34.2725i	−0.100267	−	0.0158808i	−0.206366	+	0.978475i	$0.566164\pi$
$168$	880.702	+	118.601i	0.404450	+	0.0544660i
$169$	−1285.97	−	1769.98i	−0.585329	−	0.805637i
$170$	6367.88	+	1779.81i	2.87291	+	0.802970i
$171$	−64.3399	−	144.510i	−0.0287731	−	0.0646254i
$172$	263.667	−	686.875i	0.116886	−	0.304499i
$173$	1453.28	−	2237.86i	0.638676	−	0.983475i	−0.360046	−	0.932935i	$-0.617239\pi$
$173$	1453.28	−	2237.86i	0.638676	−	0.983475i	0.998722	−	0.0505401i	$-0.0160943\pi$
$174$	3292.16			1.43435
$175$	−1634.14	+	1639.81i	−0.705881	+	0.708330i
$176$	2937.06			1.25789
$177$	−2580.87	+	3974.20i	−1.09599	+	1.68768i
$178$	856.803	−	2232.05i	0.360787	−	0.939882i
$179$	1265.30	+	2841.92i	0.528342	+	1.18668i	0.958804	+	0.284067i	$0.0916838\pi$
$179$	1265.30	+	2841.92i	0.528342	+	1.18668i	−0.430462	+	0.902608i	$0.641650\pi$
$180$	364.741	+	460.445i	0.151034	+	0.190664i
$181$	−1560.27	−	2147.53i	−0.640740	−	0.881904i	0.357914	−	0.933754i	$-0.383488\pi$
$181$	−1560.27	−	2147.53i	−0.640740	−	0.881904i	−0.998655	+	0.0518508i	$0.983488\pi$
$182$	−188.401	−	145.454i	−0.0767319	−	0.0592404i
$183$	−4211.00	−	666.957i	−1.70102	−	0.269415i
$184$	−401.544	−	361.552i	−0.160881	−	0.144858i
$185$	773.334	+	457.632i	0.307333	+	0.181869i
$186$	2165.63	+	2405.17i	0.853718	+	0.948150i
$187$	−9273.04	+	485.979i	−3.62627	+	0.190044i
$188$	−2551.99	−	1300.31i	−0.990017	−	0.504439i
$189$	−1734.62	−	1490.42i	−0.667594	−	0.573608i
$190$	15.3266	−	1426.56i	0.00585217	−	0.544703i
$191$	1807.43	−	2007.35i	0.684717	−	0.760456i	−0.296148	−	0.955142i	$-0.595702\pi$
$191$	1807.43	−	2007.35i	0.684717	−	0.760456i	0.980866	+	0.194686i	$0.0623689\pi$
$192$	−2599.61	+	3210.25i	−0.977139	+	1.20667i
$193$	3514.79	−	941.786i	1.31088	−	0.351250i	0.465328	−	0.885139i	$-0.345937\pi$
$193$	3514.79	−	941.786i	1.31088	−	0.351250i	0.845555	+	0.533889i	$0.179270\pi$
$194$	−4012.85	−	1786.63i	−1.48508	−	0.661200i
$195$	−28.0543	−	190.341i	−0.0103026	−	0.0699005i
$196$	3192.20	+	1247.12i	1.16334	+	0.454488i
$197$	−1769.50	+	280.261i	−0.639958	+	0.101359i	−0.467977	−	0.883741i	$-0.655017\pi$
$197$	−1769.50	+	280.261i	−0.639958	+	0.101359i	−0.171981	+	0.985100i	$0.555017\pi$
$198$	−1245.81	−	809.038i	−0.447151	−	0.290383i
$199$	1956.33	−	3388.46i	0.696886	−	1.20704i	−0.272654	−	0.962112i	$-0.587901\pi$
$199$	1956.33	−	3388.46i	0.696886	−	1.20704i	0.969541	−	0.244931i	$-0.0787652\pi$
$200$	251.341	+	1025.68i	0.0888623	+	0.362632i
$201$	−3677.96	+	2123.47i	−1.29066	+	0.745164i
$202$	−2224.22	+	1133.29i	−0.774729	+	0.394744i
$203$	2459.19	+	598.107i	0.850251	+	0.206793i
$204$	4650.68	−	6401.11i	1.59614	−	2.19690i
$205$	−497.809	+	1781.09i	−0.169602	+	0.606812i
$206$	2059.64	−	216.477i	0.696611	−	0.0732168i
$207$	−87.0431	−	324.849i	−0.0292266	−	0.109075i
$208$	124.740	−	47.8833i	0.0415826	−	0.0159621i
$209$	619.138	+	1905.51i	0.204912	+	0.630655i
$210$	2085.64	+	4531.44i	0.685348	+	1.48904i
$211$	−1222.38	+	3762.10i	−0.398825	+	1.22746i	0.527117	+	0.849793i	$0.323273\pi$
$211$	−1222.38	+	3762.10i	−0.398825	+	1.22746i	−0.925942	+	0.377665i	$0.876727\pi$
$212$	−335.787	−	6407.19i	−0.108783	−	2.07570i
$213$	1464.62	−	951.134i	0.471145	−	0.305965i
$214$	−804.333	+	724.225i	−0.256930	+	0.231341i
$215$	807.070	−	162.506i	0.256008	−	0.0515479i
$216$	−992.168	+	322.375i	−0.312539	+	0.101550i
$217$	1180.72	+	2190.07i	0.369368	+	0.685122i
$218$	−41.8662	−	41.8662i	−0.0130071	−	0.0130071i
$219$	1529.45	−	3435.20i	0.471921	−	1.05995i
$220$	−3984.87	−	6282.93i	−1.22118	−	1.92543i
$221$	−385.914	+	171.820i	−0.117463	+	0.0522980i
$222$	1504.76	−	1218.53i	0.454924	−	0.368390i
$223$	2268.46	+	4452.11i	0.681200	+	1.33693i	0.929707	+	0.368300i	$0.120060\pi$
$223$	2268.46	+	4452.11i	0.681200	+	1.33693i	−0.248507	+	0.968630i	$0.579940\pi$
$224$	−3749.94	+	2859.83i	−1.11854	+	0.853036i
$225$	−216.496	+	620.606i	−0.0641469	+	0.183883i
$226$	733.131	+	1269.82i	0.215784	+	0.373749i
$227$	86.8638	−	1657.46i	0.0253980	−	0.484624i	−0.956087	−	0.293084i	$-0.905319\pi$
$227$	86.8638	−	1657.46i	0.0253980	−	0.484624i	0.981485	−	0.191540i	$-0.0613481\pi$
$228$	−1593.81	−	611.806i	−0.462950	−	0.177710i
$229$	−21.8932	+	208.300i	−0.00631766	+	0.0601085i	−0.997227	−	0.0744265i	$-0.976287\pi$
$229$	−21.8932	+	208.300i	−0.00631766	+	0.0601085i	0.990909	+	0.134535i	$0.0429541\pi$
$230$	506.638	−	2990.49i	0.145246	−	0.857334i
$231$	−4807.30	−	5095.98i	−1.36925	−	1.45148i
$232$	816.343	−	816.343i	0.231015	−	0.231015i
$233$	481.950	+	1255.52i	0.135509	+	0.353013i	0.984498	−	0.175398i	$-0.0561213\pi$
$233$	481.950	+	1255.52i	0.135509	+	0.353013i	−0.848989	+	0.528411i	$0.822788\pi$
$234$	−66.1008	−	14.0502i	−0.0184664	−	0.00392516i
$235$	−300.741	−	3190.75i	−0.0834816	−	0.885709i
$236$	1733.23	+	8154.21i	0.478067	+	2.24913i
$237$	−646.031	+	1267.91i	−0.177064	+	0.347508i
$238$	8349.51	−	7088.49i	2.27403	−	1.93058i
$239$	4189.25	+	1361.17i	1.13381	+	0.368396i	0.815022	−	0.579430i	$-0.196725\pi$
$239$	4189.25	+	1361.17i	1.13381	+	0.368396i	0.318786	+	0.947827i	$0.396725\pi$
$240$	−2781.67	−	322.615i	−0.748151	−	0.0867698i
$241$	587.885	−	2765.78i	0.157133	−	0.739251i	−0.827055	−	0.562121i	$-0.809985\pi$
$241$	587.885	−	2765.78i	0.157133	−	0.739251i	0.984187	−	0.177130i	$-0.0566813\pi$
$242$	10234.3	+	8287.56i	2.71853	+	2.20142i
$243$	−1406.07	−	376.757i	−0.371192	−	0.0994607i
$244$	−6067.96	+	4408.63i	−1.59205	+	1.15670i
$245$	734.685	+	3763.82i	0.191581	+	0.981477i
$246$	3223.87	+	2342.28i	0.835555	+	0.607066i
$247$	57.3613	+	70.8353i	0.0147766	+	0.0182475i
$248$	1133.40	+	59.3992i	0.290207	+	0.0152091i
$249$	2453.55	+	1416.56i	0.624448	+	0.360525i
$250$	−4106.44	+	4275.19i	−1.03886	+	1.08155i
$251$			4488.21i			1.12866i	0.825550	+	0.564329i	$0.190865\pi$
$251$			4488.21i			1.12866i	−0.825550	+	0.564329i	$0.809135\pi$
$252$	970.262	−	73.4704i	0.242543	−	0.0183659i
$253$	666.359	+	4207.23i	0.165588	+	1.04548i
$254$	3864.78	+	406.205i	0.954716	+	0.100345i
$255$	8835.82	+	558.310i	2.16989	+	0.137109i
$256$	−143.598	−	1366.25i	−0.0350582	−	0.333556i
$257$	975.642	−	3641.15i	0.236805	−	0.883768i	−0.740522	−	0.672032i	$-0.765422\pi$
$257$	975.642	−	3641.15i	0.236805	−	0.883768i	0.977327	−	0.211736i	$-0.0679117\pi$
$258$	277.508	−	1752.12i	0.0669647	−	0.422798i
$259$	1345.41	−	636.844i	0.322779	−	0.152786i
$260$	−271.674	−	201.877i	−0.0648019	−	0.0481534i
$261$	702.864	−	149.398i	0.166690	−	0.0354311i
$262$	4453.53	+	6857.83i	1.05015	+	1.61709i
$263$	−2732.33	−	4207.42i	−0.640619	−	0.986467i	−0.998608	−	0.0527409i	$-0.983204\pi$
$263$	−2732.33	−	4207.42i	−0.640619	−	0.986467i	0.357989	−	0.933726i	$-0.383462\pi$
$264$	−3125.86	+	664.423i	−0.728726	+	0.154895i
$265$	5853.12	−	4157.21i	1.35681	−	0.963680i
$266$	−1943.63	−	1344.32i	−0.448014	−	0.309869i
$267$	500.805	−	3161.96i	0.114789	−	0.724751i
$268$	−1933.71	+	7216.72i	−0.440747	+	1.64489i
$269$	230.211	+	2190.31i	0.0521792	+	0.496452i	0.989136	+	0.147006i	$0.0469636\pi$
$269$	230.211	+	2190.31i	0.0521792	+	0.496452i	−0.936956	+	0.349446i	$0.886370\pi$
$270$	−4511.16	−	3734.02i	−1.01682	−	0.841649i
$271$	4624.34	+	486.038i	1.03656	+	0.108947i	0.607494	−	0.794324i	$-0.292175\pi$
$271$	4624.34	+	486.038i	1.03656	+	0.108947i	0.429069	+	0.903272i	$0.358842\pi$
$272$	961.836	+	6072.79i	0.214411	+	1.35374i
$273$	−287.252	−	138.058i	−0.0636824	−	0.0306068i
$274$			847.902i			0.186948i
$275$	3548.75	−	7530.87i	0.778174	−	1.65138i
$276$	−3143.30	−	1814.79i	−0.685524	−	0.395788i
$277$	3931.67	+	206.050i	0.852820	+	0.0446944i	0.473735	−	0.880668i	$-0.342906\pi$
$277$	3931.67	+	206.050i	0.852820	+	0.0446944i	0.379085	+	0.925362i	$0.376239\pi$
$278$	2105.24	+	2599.76i	0.454187	+	0.560874i
$279$	571.501	+	415.220i	0.122634	+	0.0890988i
$280$	1640.81	+	606.475i	0.350205	+	0.129442i
$281$	−2165.26	+	1573.16i	−0.459675	+	0.333974i	−0.793404	−	0.608695i	$-0.791693\pi$
$281$	−2165.26	+	1573.16i	−0.459675	+	0.333974i	0.333729	+	0.942669i	$0.391693\pi$
$282$	−6670.51	−	1787.36i	−1.40859	−	0.377431i
$283$	−200.128	−	162.060i	−0.0420366	−	0.0340405i	0.608072	−	0.793882i	$-0.291943\pi$
$283$	−200.128	−	162.060i	−0.0420366	−	0.0340405i	−0.650108	+	0.759841i	$0.725277\pi$
$284$	638.751	−	3005.09i	0.133461	−	0.627884i
$285$	−377.075	−	1872.71i	−0.0783719	−	0.389226i
$286$	814.042	+	264.498i	0.168305	+	0.0546857i
$287$	1982.64	+	2335.35i	0.407776	+	0.480317i
$288$	−607.878	+	1193.03i	−0.124374	+	0.244097i
$289$	−3020.12	−	14208.6i	−0.614720	−	2.89203i
$290$	6324.14	+	1415.41i	1.28057	+	0.286607i
$291$	−5753.22	−	1222.88i	−1.15897	−	0.246346i
$292$	−2370.67	−	6175.80i	−0.475112	−	1.23771i
$293$	−897.201	+	897.201i	−0.178891	+	0.178891i	−0.790872	−	0.611981i	$-0.790373\pi$
$293$	−897.201	+	897.201i	−0.178891	+	0.178891i	0.611981	+	0.790872i	$0.290373\pi$
$294$	8153.72	+	1340.98i	1.61746	+	0.266012i
$295$	−6666.43	+	6524.71i	−1.31571	+	1.28774i
$296$	70.9753	−	675.285i	0.0139370	−	0.132602i
$297$	7677.98	+	2947.30i	1.50007	+	0.575824i
$298$	−269.191	+	5136.47i	−0.0523283	+	0.998483i
$299$	96.8921	+	167.822i	0.0187405	+	0.0324595i
$300$	3083.92	+	6388.24i	0.593500	+	1.22942i
$301$	525.612	−	1258.38i	0.100650	−	0.240970i
$302$	5636.50	+	11062.3i	1.07399	+	2.10782i
$303$	−2597.66	+	2103.55i	−0.492514	+	0.398830i
$304$	1211.95	−	539.597i	0.228652	−	0.101803i
$305$	−7802.46	−	3091.66i	−1.46481	−	0.580420i
$306$	1264.82	−	2840.84i	0.236291	−	0.530719i
$307$	−259.479	−	259.479i	−0.0482385	−	0.0482385i	0.682576	−	0.730815i	$-0.260860\pi$
$307$	−259.479	−	259.479i	−0.0482385	−	0.0482385i	−0.730815	+	0.682576i	$0.760860\pi$
$308$	−12319.2	−	359.105i	−2.27907	−	0.0664348i
$309$	2637.35	−	856.927i	0.485545	−	0.157763i
$310$	3126.04	+	5551.35i	0.572733	+	1.01708i
$311$	−1387.25	+	1249.09i	−0.252939	+	0.227747i	−0.785839	−	0.618431i	$-0.787769\pi$
$311$	−1387.25	+	1249.09i	−0.252939	+	0.227747i	0.532901	+	0.846178i	$0.321102\pi$
$312$	−121.927	+	79.1802i	−0.0221242	+	0.0143676i
$313$	−131.228	−	2503.98i	−0.0236979	−	0.452183i	−0.984548	−	0.175114i	$-0.943971\pi$
$313$	−131.228	−	2503.98i	−0.0236979	−	0.452183i	0.960850	−	0.277068i	$-0.0893628\pi$
$314$	145.883	−	448.983i	0.0262187	−	0.0806929i
$315$	650.915	+	872.800i	0.116428	+	0.156117i
$316$	773.586	+	2380.85i	0.137714	+	0.423840i
$317$	5357.40	−	2056.51i	0.949217	−	0.364370i	0.166005	−	0.986125i	$-0.446913\pi$
$317$	5357.40	−	2056.51i	0.949217	−	0.364370i	0.783212	+	0.621755i	$0.213580\pi$
$318$	−4003.83	−	14942.5i	−0.706050	−	2.63501i
$319$	−9051.46	+	951.347i	−1.58867	+	0.166976i
$320$	−6373.97	+	5049.13i	−1.11349	+	0.882047i
$321$	−851.855	+	1172.48i	−0.148118	+	0.203867i
$322$	−3634.26	−	3469.30i	−0.628974	−	0.600424i
$323$	−3737.16	+	1904.18i	−0.643781	+	0.328023i
$324$	−7297.35	+	4213.13i	−1.25126	+	0.722416i
$325$	27.9427	−	377.701i	0.00476918	−	0.0644648i
$326$	−2429.91	+	4208.72i	−0.412822	+	0.715029i
$327$	−66.4897	−	43.1789i	−0.0112443	−	0.00730214i
$328$	1380.22	−	218.605i	0.232347	−	0.0368001i
$329$	−4658.04	−	2547.00i	−0.780565	−	0.426811i
$330$	−12547.6	−	12820.2i	−2.09310	−	2.13857i
$331$	−5208.20	−	2318.84i	−0.864860	−	0.385061i	−0.0741471	−	0.997247i	$-0.523623\pi$
$331$	−5208.20	−	2318.84i	−0.864860	−	0.385061i	−0.790713	+	0.612187i	$0.790290\pi$
$332$	4814.24	−	1289.97i	0.795831	−	0.213242i
$333$	265.964	−	328.439i	0.0437681	−	0.0540490i
$334$	−621.814	+	690.595i	−0.101869	+	0.113137i
$335$	−7978.21	+	2497.84i	−1.30118	+	0.407378i
$336$	−3023.05	+	3518.38i	−0.490836	+	0.571260i
$337$	−3659.10	−	1864.40i	−0.591465	−	0.301367i	0.132522	−	0.991180i	$-0.457692\pi$
$337$	−3659.10	−	1864.40i	−0.591465	−	0.301367i	−0.723987	+	0.689814i	$0.757692\pi$
$338$	−9267.28	+	485.678i	−1.49134	+	0.0781579i
$339$	1313.73	+	1459.05i	0.210478	+	0.233760i
$340$	11685.9	−	10296.9i	1.86399	−	1.64243i
$341$	−6649.22	−	5986.98i	−1.05594	−	0.950772i
$342$	−662.710	−	104.963i	−0.104781	−	0.0165957i
$343$	5847.07	+	2483.03i	0.920443	+	0.390877i
$344$	−365.653	−	503.278i	−0.0573101	−	0.0788806i
$345$	−168.971	−	4057.84i	−0.0263683	−	0.633236i
$346$	−4603.53	−	10339.7i	−0.715281	−	1.60655i
$347$	2387.62	−	6219.96i	0.369378	−	0.962262i	−0.615364	−	0.788243i	$-0.710991\pi$
$347$	2387.62	−	6219.96i	0.369378	−	0.962262i	0.984742	−	0.174019i	$-0.0556755\pi$
$348$	4223.70	−	6503.93i	0.650615	−	1.00186i
$349$	7761.05			1.19037			0.595185	−	0.803588i	$-0.297079\pi$
$349$	7761.05			1.19037			0.595185	+	0.803588i	$0.297079\pi$
$350$	2058.24	+	9601.46i	0.314335	+	1.46634i
$351$	374.143			0.0568954
$352$	9236.69	−	14223.3i	1.39863	−	2.15370i
$353$	2371.06	−	6176.83i	0.357504	−	0.931329i	−0.630401	−	0.776269i	$-0.717110\pi$
$353$	2371.06	−	6176.83i	0.357504	−	0.931329i	0.987905	−	0.155060i	$-0.0495570\pi$
$354$	8175.38	+	18362.2i	1.22745	+	2.75689i
$355$	3222.41	−	1197.41i	0.481769	−	0.179019i
$356$	−3310.35	−	4556.31i	−0.492832	−	0.678325i
$357$	8962.37	−	11608.6i	1.32868	−	1.72099i
$358$	13032.8	+	2064.19i	1.92404	+	0.304737i
$359$	−332.416	−	299.309i	−0.0488697	−	0.0440025i	0.644334	−	0.764744i	$-0.277135\pi$
$359$	−332.416	−	299.309i	−0.0488697	−	0.0440025i	−0.693204	+	0.720742i	$0.743801\pi$
$360$	494.472	−	46.6060i	0.0723916	−	0.00682320i
$361$	−3984.00	−	4424.68i	−0.580843	−	0.645092i
$362$	−11244.0	+	589.275i	−1.63252	+	0.0855569i
$363$	15711.6	+	8005.46i	2.27175	+	1.15751i
$364$	−529.067	+	185.591i	−0.0761830	+	0.0267242i
$365$	4414.94	−	5941.35i	0.633119	−	0.852013i
$366$	−12100.8	+	13439.3i	−1.72819	+	1.91935i
$367$	−2070.73	+	2557.14i	−0.294527	+	0.363711i	−0.902832	−	0.429992i	$-0.858516\pi$
$367$	−2070.73	+	2557.14i	−0.294527	+	0.363711i	0.608305	+	0.793703i	$0.291850\pi$
$368$	2724.40	−	730.000i	0.385921	−	0.103407i
$369$	794.578	+	353.769i	0.112098	+	0.0499091i
$370$	3414.50	−	1693.82i	0.479760	−	0.237993i
$371$	−276.095	−	11889.2i	−0.0386365	−	1.66377i
$372$	7530.03	−	1192.64i	1.04950	−	0.166224i
$373$	−11364.1	−	7379.96i	−1.57752	−	1.02445i	−0.973844	−	0.227218i	$-0.927037\pi$
$373$	−11364.1	−	7379.96i	−1.57752	−	1.02445i	−0.603672	−	0.797233i	$-0.706296\pi$
$374$	−19693.5	+	34110.2i	−2.72280	+	4.71604i
$375$	−4188.22	+	6742.64i	−0.576743	+	0.928503i
$376$	−2097.26	+	1210.86i	−0.287655	+	0.166078i
$377$	−368.916	+	187.972i	−0.0503983	+	0.0256792i
$378$	−9309.23	+	2727.56i	−1.26671	+	0.371138i
$379$	3920.25	−	5395.76i	0.531318	−	0.731297i	−0.456012	−	0.889973i	$-0.650723\pi$
$379$	3920.25	−	5395.76i	0.531318	−	0.731297i	0.987331	+	0.158677i	$0.0507227\pi$
$380$	−2798.63	−	1860.50i	−0.377807	−	0.251162i
$381$	5174.98	−	543.913i	0.695859	−	0.0731378i
$382$	−2965.40	−	11067.0i	−0.397181	−	1.48230i
$383$	−3153.52	+	1210.52i	−0.420724	+	0.161501i	−0.559514	−	0.828821i	$-0.689012\pi$
$383$	−3153.52	+	1210.52i	−0.420724	+	0.161501i	0.138790	+	0.990322i	$0.455679\pi$
$384$	1839.10	+	5660.16i	0.244404	+	0.752197i
$385$	−7043.74	−	11856.1i	−0.932422	−	1.56946i
$386$	4769.52	−	14679.1i	0.628917	−	1.93561i
$387$	−20.2642	−	386.664i	−0.00266172	−	0.0507887i
$388$	−8677.96	+	5635.53i	−1.13546	+	0.737373i
$389$	6118.84	−	5509.43i	0.797526	−	0.718096i	−0.165879	−	0.986146i	$-0.553046\pi$
$389$	6118.84	−	5509.43i	0.797526	−	0.718096i	0.963405	+	0.268051i	$0.0863794\pi$
$390$	−741.921	−	339.922i	−0.0963298	−	0.0441349i
$391$	−8480.83	+	2755.59i	−1.09692	+	0.356409i
$392$	2354.36	−	1689.33i	0.303350	−	0.217663i
$393$	7742.20	+	7742.20i	0.993747	+	0.993747i
$394$	−3090.87	+	6942.20i	−0.395217	+	0.887673i
$395$	−1786.13	+	2157.86i	−0.227518	+	0.274870i
$396$	−3196.64	+	1423.24i	−0.405650	+	0.180607i
$397$	−2374.67	+	1922.97i	−0.300204	+	0.243101i	−0.767573	−	0.640962i	$-0.778536\pi$
$397$	−2374.67	+	1922.97i	−0.300204	+	0.243101i	0.467368	+	0.884063i	$0.345202\pi$
$398$	−7534.50	−	14787.3i	−0.948921	−	1.86236i
$399$	−2919.93	−	1219.62i	−0.366364	−	0.153026i
$400$	−5204.81	−	1815.67i	−0.650601	−	0.226959i
$401$	5043.05	+	8734.82i	0.628025	+	1.08777i	0.987948	+	0.154789i	$0.0494698\pi$
$401$	5043.05	+	8734.82i	0.628025	+	1.08777i	−0.359922	+	0.932982i	$0.617197\pi$
$402$	−942.785	+	17989.4i	−0.116970	+	2.23192i
$403$	−380.007	−	145.871i	−0.0469714	−	0.0180306i
$404$	−614.659	+	5848.09i	−0.0756942	+	0.720182i
$405$	−8354.52	−	4370.52i	−1.02504	−	0.536230i
$406$	7808.83	−	7366.47i	0.954546	−	0.900473i
$407$	−3785.07	+	3785.07i	−0.460981	+	0.460981i
$408$	−2397.46	−	6245.59i	−0.290911	−	0.757850i
$409$	−6489.08	−	1379.30i	−0.784509	−	0.166753i	−0.201793	−	0.979428i	$-0.564677\pi$
$409$	−6489.08	−	1379.30i	−0.784509	−	0.166753i	−0.582716	+	0.812676i	$0.698010\pi$
$410$	5185.94	+	5885.51i	0.624671	+	0.708938i
$411$	236.053	+	1110.54i	0.0283300	+	0.133282i
$412$	2214.76	−	4346.72i	0.264839	−	0.519776i
$413$	2770.89	+	15201.5i	0.330137	+	1.81118i
$414$	−1356.69	−	440.816i	−0.161057	−	0.0523307i
$415$	4104.17	+	3776.04i	0.485460	+	0.446647i
$416$	160.409	−	754.665i	0.0189055	−	0.0889435i
$417$	3481.10	+	2818.94i	0.408802	+	0.331041i
$418$	8208.90	+	2199.57i	0.960551	+	0.257379i
$419$	−3112.59	+	2261.43i	−0.362912	+	0.263671i	−0.754266	−	0.656569i	$-0.772007\pi$
$419$	−3112.59	+	2261.43i	−0.362912	+	0.263671i	0.391354	+	0.920240i	$0.372007\pi$
$420$	11628.0	+	1693.29i	1.35093	+	0.196724i
$421$	2830.04	+	2056.14i	0.327619	+	0.238029i	0.739420	−	0.673245i	$-0.235100\pi$
$421$	2830.04	+	2056.14i	0.327619	+	0.238029i	−0.411800	+	0.911274i	$0.635100\pi$
$422$	10559.2	+	13039.6i	1.21805	+	1.50416i
$423$	−1505.24	−	78.8863i	−0.173020	−	0.00906757i
$424$	−4698.05	−	2712.42i	−0.538108	−	0.310677i
$425$	16733.3	+	4871.33i	1.90985	+	0.555987i
$426$		−	7407.46i		−	0.842471i
$427$	−11480.7	+	7840.48i	−1.30114	+	0.888589i
$428$	398.840	+	2518.18i	0.0450436	+	0.284394i
$429$	1139.83	+	119.801i	0.128278	+	0.0134826i
$430$	1286.38	−	3246.45i	0.144267	−	0.364088i
$431$	840.571	+	7997.49i	0.0939417	+	0.893795i	0.935428	+	0.353517i	$0.115014\pi$
$431$	840.571	+	7997.49i	0.0939417	+	0.893795i	−0.841486	+	0.540278i	$0.818319\pi$
$432$	1409.43	−	5260.05i	0.156970	−	0.585820i
$433$	166.411	−	1050.68i	0.0184693	−	0.116611i	−0.976731	−	0.214467i	$-0.931199\pi$
$433$	166.411	−	1050.68i	0.0184693	−	0.116611i	0.995201	+	0.0978563i	$0.0311986\pi$
$434$	10518.5	+	859.182i	1.16338	+	0.0950277i
$435$	8677.09	+	93.2247i	0.956401	+	0.0102754i
$436$	−136.423	+	28.9976i	−0.0149850	+	0.00318517i
$437$	1047.92	+	1613.65i	0.114711	+	0.176640i
$438$	−8686.94	−	13376.7i	−0.947667	−	1.45928i
$439$	−10295.6	+	2188.39i	−1.11932	+	0.237919i	−0.730177	−	0.683259i	$-0.760562\pi$
$439$	−10295.6	+	2188.39i	−1.11932	+	0.237919i	−0.389143	+	0.921177i	$0.627229\pi$
$440$	−6290.35	−	67.5821i	−0.681547	−	0.00732239i
$441$	1801.64	−	83.7218i	0.194541	−	0.00904025i
$442$	−280.304	+	1769.77i	−0.0301644	+	0.190451i
$443$	1994.42	−	7443.28i	0.213900	−	0.798286i	−0.772651	−	0.634831i	$-0.781070\pi$
$443$	1994.42	−	7443.28i	0.213900	−	0.798286i	0.986551	−	0.163455i	$-0.0522638\pi$
$444$	−476.765	−	4536.11i	−0.0509600	−	0.484852i
$445$	2321.47	−	5858.71i	0.247299	−	0.624111i
$446$	21078.3	+	2215.42i	2.23786	+	0.235209i
$447$	1077.40	+	6802.44i	0.114003	+	0.719786i
$448$	1017.06	+	13431.4i	0.107257	+	1.41646i
$449$			847.947i			0.0891249i	0.999007	+	0.0445625i	$0.0141894\pi$
$449$			847.947i			0.0891249i	−0.999007	+	0.0445625i	$0.985811\pi$
$450$	1707.58	+	2203.86i	0.178880	+	0.230869i
$451$	−9540.58	−	5508.26i	−0.996116	−	0.575108i
$452$	3449.21	+	180.766i	0.358932	+	0.0188108i
$453$	10462.1	+	12919.6i	1.08510	+	1.33999i
$454$	−5695.51	−	4138.03i	−0.588775	−	0.427770i
$455$	−492.447	−	388.705i	−0.0507391	−	0.0400501i
$456$	−1167.79	+	848.453i	−0.119928	+	0.0871325i
$457$	15249.8	+	4086.18i	1.56096	+	0.418257i	0.932967	−	0.359963i	$-0.117211\pi$
$457$	15249.8	+	4086.18i	1.56096	+	0.418257i	0.627991	+	0.778220i	$0.283877\pi$
$458$	690.421	+	559.092i	0.0704394	+	0.0570407i
$459$	−3579.57	+	16840.5i	−0.364008	+	1.71252i
$460$	−5257.96	−	4837.57i	−0.532942	−	0.490333i
$461$	13412.2	+	4357.90i	1.35503	+	0.440277i	0.894382	−	0.447304i	$-0.147616\pi$
$461$	13412.2	+	4357.90i	1.35503	+	0.440277i	0.460651	+	0.887581i	$0.347616\pi$
$462$	−29233.9	+	5328.68i	−2.94391	+	0.536607i
$463$	−2393.15	+	4696.83i	−0.240215	+	0.471448i	−0.979367	−	0.202091i	$-0.935226\pi$
$463$	−2393.15	+	4696.83i	−0.240215	+	0.471448i	0.739152	+	0.673538i	$0.235226\pi$
$464$	1252.95	+	5894.67i	0.125359	+	0.589770i
$465$	5639.81	+	6400.61i	0.562451	+	0.638325i
$466$	5579.74	+	1186.01i	0.554670	+	0.117899i
$467$	−3966.93	−	10334.2i	−0.393078	−	1.02400i	−0.977197	−	0.212335i	$-0.931893\pi$
$467$	−3966.93	−	10334.2i	−0.393078	−	1.02400i	0.584119	−	0.811668i	$-0.301440\pi$
$468$	−112.562	+	112.562i	−0.0111179	+	0.0111179i
$469$	−3972.50	+	13266.5i	−0.391115	+	1.30616i
$470$	−12045.4	−	6301.35i	−1.18216	−	0.618425i
$471$	66.0757	−	628.669i	0.00646414	−	0.0615022i
$472$	6580.42	+	2525.99i	0.641713	+	0.246330i
$473$	−256.665	+	4897.46i	−0.0249503	+	0.476079i
$474$	3017.96	+	5227.25i	0.292446	+	0.506531i
$475$	80.7924	−	3759.53i	0.00780423	−	0.363156i
$476$	−3291.83	−	25589.4i	−0.316977	−	2.46405i
$477$	−1532.90	−	3008.48i	−0.147142	−	0.288782i
$478$	14520.1	−	11758.1i	1.38940	−	1.12511i
$479$	−1566.19	+	697.311i	−0.149396	+	0.0665156i	−0.480073	−	0.877229i	$-0.659390\pi$
$479$	−1566.19	+	697.311i	−0.149396	+	0.0665156i	0.330676	+	0.943744i	$0.392723\pi$
$480$	−10310.3	+	12456.2i	−0.980418	+	1.18447i
$481$	−99.0479	+	222.465i	−0.00938918	+	0.0210884i
$482$	−8480.76	−	8480.76i	−0.801427	−	0.801427i
$483$	−5725.82	−	3532.16i	−0.539407	−	0.332751i
$484$	29502.9	−	9586.09i	2.77075	−	0.900271i
$485$	−10526.0	−	4822.64i	−0.985487	−	0.451515i
$486$	−4588.54	+	4131.54i	−0.428272	+	0.385618i
$487$	−2694.41	+	1749.77i	−0.250709	+	0.162812i	−0.663875	−	0.747843i	$-0.731089\pi$
$487$	−2694.41	+	1749.77i	−0.250709	+	0.162812i	0.413166	+	0.910656i	$0.364423\pi$
$488$	331.902	+	6333.06i	0.0307879	+	0.587468i
$489$	−2010.88	+	6188.85i	−0.185961	+	0.572330i
$490$	15086.5	+	6081.56i	1.39090	+	0.560687i
$491$	−1802.78	−	5548.37i	−0.165699	−	0.509969i	0.833388	−	0.552688i	$-0.186398\pi$
$491$	−1802.78	−	5548.37i	−0.165699	−	0.509969i	−0.999087	+	0.0427193i	$0.986398\pi$
$492$	8763.46	−	3363.98i	0.803023	−	0.308252i
$493$	−4931.24	−	18403.7i	−0.450491	−	1.68126i
$494$	384.501	−	40.4127i	0.0350193	−	0.00368068i
$495$	−3260.65	−	2167.65i	−0.296072	−	0.196825i
$496$	−3482.30	+	4792.98i	−0.315242	+	0.433894i
$497$	1345.76	−	5533.25i	0.121460	−	0.499397i
$498$	10707.3	−	5455.67i	0.963469	−	0.490912i
$499$	−3319.33	+	1916.42i	−0.297783	+	0.171925i	−0.641446	−	0.767168i	$-0.721665\pi$
$499$	−3319.33	+	1916.42i	−0.297783	+	0.171925i	0.343664	+	0.939093i	$0.388332\pi$
$500$	3177.59	+	13597.5i	0.284212	+	1.21620i
$501$	−622.163	+	1077.62i	−0.0554814	+	0.0960966i
$502$	15966.2	+	10368.6i	1.41953	+	0.921855i
$503$	−11789.3	+	1867.24i	−1.04504	+	0.165519i	−0.655272	−	0.755393i	$-0.727446\pi$
$503$	−11789.3	+	1867.24i	−1.04504	+	0.165519i	−0.389772	+	0.920911i	$0.627446\pi$
$504$	394.710	−	721.859i	0.0348845	−	0.0637979i
$505$	−5894.43	+	2924.02i	−0.519403	+	0.257658i
$506$	16506.0	+	7348.95i	1.45016	+	0.645654i
$507$	−12002.6	+	3216.09i	−1.05139	+	0.281719i
$508$	5760.84	−	7114.05i	0.503142	−	0.621328i
$509$	−898.103	+	997.444i	−0.0782077	+	0.0868584i	−0.780979	−	0.624558i	$-0.785279\pi$
$509$	−898.103	+	997.444i	−0.0782077	+	0.0868584i	0.702771	+	0.711416i	$0.251946\pi$
$510$	22398.4	−	30142.4i	1.94474	−	2.61711i
$511$	−4058.77	−	11570.4i	−0.351368	−	1.00165i
$512$	−12661.1	−	6451.17i	−1.09287	−	0.556844i
$513$	3709.74	−	194.419i	0.319277	−	0.0167326i
$514$	−10699.0	−	11882.4i	−0.918115	−	1.01967i
$515$	5434.69	−	512.242i	0.465012	−	0.0438293i
$516$	−3105.42	−	2796.13i	−0.264939	−	0.238552i
$517$	18856.4	+	2986.56i	1.60407	+	0.254060i
$518$	842.655	−	6257.33i	0.0714752	−	0.530756i
$519$	−8908.00	−	12260.8i	−0.753406	−	1.03697i
$520$	−268.260	+	99.6823i	−0.0226231	+	0.00840646i
$521$	626.637	+	1407.45i	0.0526938	+	0.118352i	0.937974	−	0.346706i	$-0.112700\pi$
$521$	626.637	+	1407.45i	0.0526938	+	0.118352i	−0.885280	+	0.465059i	$0.846033\pi$
$522$	1092.28	−	2845.47i	0.0915854	−	0.238588i
$523$	−5288.38	+	8143.39i	−0.442151	+	0.680852i	−0.987547	−	0.157326i	$-0.949713\pi$
$523$	−5288.38	+	8143.39i	−0.442151	+	0.680852i	0.545396	+	0.838178i	$0.316379\pi$
$524$	19261.9			1.60584
$525$	5368.78	+	12002.5i	0.446310	+	0.997776i
$526$	−21279.5			−1.76393
$527$	10201.4	−	15708.9i	0.843230	−	1.29846i
$528$	5978.09	−	15573.5i	0.492733	−	1.28361i
$529$	−3284.96	−	7378.13i	−0.269989	−	0.606405i
$530$	−1266.94	−	30425.5i	−0.103834	−	2.49359i
$531$	2578.69	+	3549.26i	0.210745	+	0.290066i
$532$	−5149.41	+	2115.11i	−0.419652	+	0.172371i
$533$	−495.001	−	78.4005i	−0.0402268	−	0.00637130i
$534$	−10091.3	−	9086.22i	−0.817775	−	0.736328i
$535$	−2140.48	+	1886.05i	−0.172974	+	0.152413i
$536$	4226.99	+	4694.54i	0.340631	+	0.378309i
$537$	17644.4	−	924.703i	1.41790	−	0.0743089i
$538$	8323.55	+	4241.06i	0.667014	+	0.339861i
$539$	−22805.4	−	1330.68i	−1.82244	−	0.106339i
$540$	−13164.5	+	4121.58i	−1.04909	+	0.328453i
$541$	1678.18	−	1863.81i	0.133365	−	0.148117i	−0.672763	−	0.739858i	$-0.734893\pi$
$541$	1678.18	−	1863.81i	0.133365	−	0.148117i	0.806128	+	0.591741i	$0.201559\pi$
$542$	12412.1	−	15327.6i	0.983659	−	1.21472i
$543$	−14562.8	+	3902.10i	−1.15092	+	0.308389i
$544$	32433.5	+	14440.3i	2.55620	+	1.13809i
$545$	−109.161	−	111.532i	−0.00857969	−	0.00876605i
$546$	−1154.72	+	702.920i	−0.0905085	+	0.0550956i
$547$	5003.83	−	792.528i	0.391130	−	0.0619489i	0.0422278	−	0.999108i	$-0.486554\pi$
$547$	5003.83	−	792.528i	0.391130	−	0.0619489i	0.348902	+	0.937159i	$0.386554\pi$
$548$	1675.10	+	1087.82i	0.130578	+	0.0847984i
$549$	−1973.60	+	3418.37i	−0.153426	+	0.265742i
$550$	−18591.8	−	30021.8i	−1.44137	−	2.32752i
$551$	−3560.23	+	2055.50i	−0.275265	+	0.158924i
$552$	−2734.39	+	1393.24i	−0.210840	+	0.107428i
$553$	1304.69	+	4452.96i	0.100328	+	0.342422i
$554$	9815.84	−	13510.3i	0.752771	−	1.03610i
$555$	4000.59	−	3169.06i	0.305974	−	0.242377i
$556$	7836.97	−	823.699i	0.597773	−	0.0628284i
$557$	−3131.95	−	11688.6i	−0.238249	−	0.889159i	−0.976657	−	0.214804i	$-0.931089\pi$
$557$	−3131.95	−	11688.6i	−0.238249	−	0.889159i	0.738408	−	0.674354i	$-0.235578\pi$
$558$	2797.35	−	1073.80i	0.212225	−	0.0814655i
$559$	68.9432	+	212.185i	0.00521643	+	0.0160545i
$560$	−7319.87	+	5459.00i	−0.552359	+	0.411937i
$561$	−16297.5	+	50158.5i	−1.22652	+	3.77485i
$562$	594.141	+	11336.9i	0.0445949	+	0.850921i
$563$	9406.94	−	6108.94i	0.704183	−	0.457302i	−0.142226	−	0.989834i	$-0.545426\pi$
$563$	9406.94	−	6108.94i	0.704183	−	0.457302i	0.846410	+	0.532532i	$0.178759\pi$
$564$	−12089.1	+	10885.0i	−0.902556	+	0.812665i
$565$	1896.35	+	3367.61i	0.141203	+	0.250755i
$566$	−1038.84	+	337.538i	−0.0771476	+	0.0250668i
$567$	−13747.9	+	7411.86i	−1.01827	+	0.548975i
$568$	−1836.80	−	1836.80i	−0.135687	−	0.135687i
$569$	−4405.48	+	9894.87i	−0.324582	+	0.729024i	−0.999964	−	0.00844429i	$-0.997312\pi$
$569$	−4405.48	+	9894.87i	−0.324582	+	0.729024i	0.675382	+	0.737468i	$0.263979\pi$
$570$	−7533.00	−	2984.89i	−0.553548	−	0.219339i
$571$	−11297.0	+	5029.77i	−0.827962	+	0.368633i	−0.776558	−	0.630045i	$-0.783036\pi$
$571$	−11297.0	+	5029.77i	−0.827962	+	0.368633i	−0.0514040	+	0.998678i	$0.516370\pi$
$572$	1566.92	−	1268.87i	0.114539	−	0.0927517i
$573$	−6964.95	−	13669.5i	−0.507792	−	0.996598i
$574$	12887.9	−	1657.91i	0.937162	−	0.120557i
$575$	1420.02	−	7867.63i	0.102989	−	0.570614i
$576$	1912.18	+	3311.99i	0.138323	+	0.239583i
$577$	−1052.36	+	20080.1i	−0.0759274	+	1.44878i	0.649436	+	0.760416i	$0.275005\pi$
$577$	−1052.36	+	20080.1i	−0.0759274	+	1.44878i	−0.725364	+	0.688366i	$0.758328\pi$
$578$	−57521.9	−	22080.6i	−4.13944	−	1.58898i
$579$	2160.28	−	20553.7i	0.155058	−	1.47527i
$580$	10909.9	−	10677.9i	0.781048	−	0.764444i
$581$	8989.37	−	2130.02i	0.641897	−	0.152096i
$582$	−17641.2	+	17641.2i	−1.25644	+	1.25644i
$583$	15326.1	+	39926.0i	1.08875	+	2.83630i
$584$	−5471.04	−	1162.91i	−0.387660	−	0.0823996i
$585$	−173.823	−	38.9036i	−0.0122850	−	0.00274952i
$586$	1118.97	+	5264.36i	0.0788812	+	0.371107i
$587$	1920.16	−	3768.53i	0.135015	−	0.264981i	−0.813594	−	0.581434i	$-0.802492\pi$
$587$	1920.16	−	3768.53i	0.135015	−	0.264981i	0.948608	+	0.316453i	$0.102492\pi$
$588$	13110.1	−	14387.9i	0.919475	−	1.00910i
$589$	−3843.67	−	1248.89i	−0.268889	−	0.0873675i
$590$	7810.10	+	38788.1i	0.544978	+	2.70658i
$591$	−2115.58	+	9953.04i	−0.147248	+	0.692747i
$592$	2754.50	+	2230.55i	0.191232	+	0.154857i
$593$	−15204.8	−	4074.11i	−1.05293	−	0.282131i	−0.309466	−	0.950910i	$-0.600150\pi$
$593$	−15204.8	−	4074.11i	−1.05293	−	0.282131i	−0.743461	+	0.668780i	$0.766817\pi$
$594$	28222.1	−	20504.6i	1.94944	−	1.41635i
$595$	22207.4	−	18446.6i	1.53011	−	1.27099i
$596$	9802.17	+	7121.69i	0.673678	+	0.489456i
$597$	−13985.0	−	17270.1i	−0.958744	−	1.18395i
$598$	820.841	+	43.0184i	0.0561316	+	0.00294173i
$599$	9585.15	+	5533.99i	0.653821	+	0.377484i	0.789919	−	0.613212i	$-0.210123\pi$
$599$	9585.15	+	5533.99i	0.653821	+	0.377484i	−0.136098	+	0.990695i	$0.543456\pi$
$600$	5950.14	+	754.958i	0.404855	+	0.0513684i
$601$			10243.2i			0.695222i	0.937639	+	0.347611i	$0.113007\pi$
$601$			10243.2i			0.695222i	−0.937639	+	0.347611i	$0.886993\pi$
$602$	−3262.27	−	4776.88i	−0.220864	−	0.323407i
$603$	615.079	+	3883.46i	0.0415389	+	0.262266i
$604$	29085.8	+	3057.04i	1.95941	+	0.205942i
$605$	26739.7	+	22133.2i	1.79690	+	1.48734i
$606$	1482.01	+	14100.4i	0.0993441	+	0.945196i
$607$	−3765.51	+	14053.1i	−0.251792	+	0.939699i	0.718056	+	0.695986i	$0.245032\pi$
$607$	−3765.51	+	14053.1i	−0.251792	+	0.939699i	−0.969847	+	0.243713i	$0.921634\pi$
$608$	1198.35	−	7566.08i	0.0799333	−	0.504679i
$609$	8176.83	−	11822.2i	0.544075	−	0.786633i
$610$	−29023.2	+	20613.9i	−1.92642	+	1.36825i
$611$	849.544	−	180.576i	0.0562502	−	0.0119564i
$612$	−3989.60	−	6143.44i	−0.263513	−	0.405774i
$613$	−2920.90	−	4497.79i	−0.192453	−	0.296352i	0.729250	−	0.684247i	$-0.239869\pi$
$613$	−2920.90	−	4497.79i	−0.192453	−	0.296352i	−0.921704	+	0.387895i	$0.873202\pi$
$614$	−1522.50	+	323.618i	−0.100070	+	0.0212706i
$615$	8430.79	+	6264.81i	0.552784	+	0.410766i
$616$	−5927.69	+	8570.36i	−0.387717	+	0.560567i
$617$	−364.999	+	2304.51i	−0.0238157	+	0.150367i	−0.996731	−	0.0807973i	$-0.974253\pi$
$617$	−364.999	+	2304.51i	−0.0238157	+	0.150367i	0.972915	+	0.231164i	$0.0742534\pi$
$618$	3044.34	−	11361.6i	0.198158	−	0.739535i
$619$	145.188	+	1381.37i	0.00942746	+	0.0896963i	0.998224	−	0.0595740i	$-0.0189742\pi$
$619$	145.188	+	1381.37i	0.00942746	+	0.0896963i	−0.988796	+	0.149270i	$0.952308\pi$
$620$	14977.7	+	946.400i	0.970194	+	0.0613038i
$621$	7854.60	+	825.552i	0.507559	+	0.0533466i
$622$	1238.66	+	7820.57i	0.0798483	+	0.504142i
$623$	−5887.25	−	8620.60i	−0.378600	−	0.554377i
$624$		−	758.884i		−	0.0486854i
$625$	−10944.4	+	11151.8i	−0.700439	+	0.713713i
$626$	−9210.70	−	5317.80i	−0.588073	−	0.339524i
$627$	11364.0	+	595.560i	0.723817	+	0.0379336i
$628$	−699.840	−	864.231i	−0.0444692	−	0.0549149i
$629$	−9065.73	−	6586.64i	−0.574681	−	0.417530i
$630$	4608.59	−	299.216i	0.291445	−	0.0189223i
$631$	−9104.72	+	6614.97i	−0.574411	+	0.417334i	−0.836705	−	0.547654i	$-0.815521\pi$
$631$	−9104.72	+	6614.97i	−0.574411	+	0.417334i	0.262294	+	0.964988i	$0.415521\pi$
$632$	2044.53	+	547.831i	0.128682	+	0.0344803i
$633$	17460.1	+	14138.9i	1.09633	+	0.887791i
$634$	5060.79	−	23809.1i	0.317018	−	1.49145i
$635$	10174.8	+	1180.07i	0.635868	+	0.0737473i
$636$	−34656.9	−	11260.7i	−2.16075	−	0.702070i
$637$	−990.264	+	315.284i	−0.0615945	+	0.0196107i
$638$	−17526.2	+	34397.1i	−1.08757	+	2.13447i
$639$	−336.151	−	1581.47i	−0.0208105	−	0.0979058i
$640$	1099.35	+	11663.7i	0.0678994	+	0.720388i
$641$	−4816.98	−	1023.88i	−0.296816	−	0.0630902i	0.0570966	−	0.998369i	$-0.481816\pi$
$641$	−4816.98	−	1023.88i	−0.296816	−	0.0630902i	−0.353913	+	0.935278i	$0.615149\pi$
$642$	2202.99	+	5738.98i	0.135428	+	0.352803i
$643$	−14072.7	+	14072.7i	−0.863100	+	0.863100i	−0.991697	−	0.128597i	$-0.958953\pi$
$643$	−14072.7	+	14072.7i	−0.863100	+	0.863100i	0.128597	+	0.991697i	$0.458953\pi$
$644$	−11516.5	+	2728.82i	−0.704680	+	0.166973i
$645$	781.039	−	4610.17i	0.0476796	−	0.281434i
$646$	−1859.65	+	17693.4i	−0.113262	+	1.07761i
$647$	2456.96	+	943.138i	0.149294	+	0.0573085i	0.431867	−	0.901937i	$-0.357855\pi$
$647$	2456.96	+	943.138i	0.149294	+	0.0573085i	−0.282574	+	0.959246i	$0.591188\pi$
$648$	−372.871	+	7114.81i	−0.0226046	+	0.431321i
$649$	−27783.6	−	48122.6i	−1.68043	−	2.91060i
$650$	−1279.06	−	971.958i	−0.0771832	−	0.0586513i
$651$	14015.9	−	1803.01i	0.843817	−	0.108549i
$652$	5197.21	+	10200.1i	0.312175	+	0.612679i
$653$	888.470	−	719.468i	0.0532443	−	0.0431164i	−0.602329	−	0.798248i	$-0.705760\pi$
$653$	888.470	−	719.468i	0.0532443	−	0.0431164i	0.655573	+	0.755132i	$0.272427\pi$
$654$	−307.206	+	136.777i	−0.0183681	+	0.00817798i
$655$	11543.9	+	18201.2i	0.688637	+	1.08577i
$656$	−2966.94	+	6663.85i	−0.176585	+	0.396615i
$657$	−2461.67	−	2461.67i	−0.146178	−	0.146178i
$658$	−19821.5	+	10686.3i	−1.17435	+	0.633123i
$659$	23640.4	−	7681.23i	1.39742	−	0.454049i	0.489064	−	0.872248i	$-0.337339\pi$
$659$	23640.4	−	7681.23i	1.39742	−	0.454049i	0.908355	+	0.418199i	$0.137339\pi$
$660$	−41425.4	+	8341.12i	−2.44315	+	0.491936i
$661$	−4572.05	+	4116.69i	−0.269035	+	0.242240i	−0.792595	−	0.609749i	$-0.791270\pi$
$661$	−4572.05	+	4116.69i	−0.269035	+	0.242240i	0.523560	+	0.851989i	$0.324604\pi$
$662$	−20280.8	+	13170.5i	−1.19069	+	0.773243i
$663$	125.568	+	2395.99i	0.00735547	+	0.140351i
$664$	1302.24	−	4007.88i	0.0761095	−	0.234241i
$665$	−5084.74	−	3598.23i	−0.296508	−	0.209825i
$666$	−553.950	−	1704.88i	−0.0322299	−	0.0991935i
$667$	−8159.63	+	3132.19i	−0.473676	+	0.181827i
$668$	566.565	+	2114.45i	0.0328160	+	0.122471i
$669$	28224.1	−	2966.47i	1.63110	−	0.171436i
$670$	−9545.35	+	34151.8i	−0.550401	+	1.96925i
$671$	29386.3	−	40446.7i	1.69068	−	2.32702i
$672$	7531.30	+	25704.6i	0.432331	+	1.47556i
$673$	3003.04	−	1530.12i	0.172004	−	0.0876403i	−0.365869	−	0.930666i	$-0.619228\pi$
$673$	3003.04	−	1530.12i	0.172004	−	0.0876403i	0.537873	+	0.843026i	$0.319228\pi$
$674$	−15085.5	+	8709.62i	−0.862125	+	0.497748i
$675$	−11784.3	−	9969.45i	−0.671966	−	0.568480i
$676$	−10930.0	+	18931.4i	−0.621873	+	1.07712i
$677$	−54.9689	−	35.6972i	−0.00312057	−	0.00202652i	0.543078	−	0.839682i	$-0.317259\pi$
$677$	−54.9689	−	35.6972i	−0.00312057	−	0.00202652i	−0.546198	+	0.837656i	$0.683926\pi$
$678$	8225.31	−	1302.76i	0.465916	−	0.0737938i
$679$	−16382.7	+	9972.68i	−0.925933	+	0.563647i
$680$	−1920.25	−	13028.3i	−0.108291	−	0.734727i
$681$	−8611.71	−	3834.18i	−0.484584	−	0.215751i
$682$	−36658.7	+	9822.67i	−2.05826	+	0.551510i
$683$	19321.5	−	23860.1i	1.08246	−	1.33672i	0.144683	−	0.989478i	$-0.453784\pi$
$683$	19321.5	−	23860.1i	1.08246	−	1.33672i	0.937774	−	0.347245i	$-0.112883\pi$
$684$	−1057.59	+	1174.58i	−0.0591200	+	0.0656594i
$685$	−24.0102	+	2234.80i	−0.00133925	+	0.124653i
$686$	22340.8	−	15063.9i	1.24340	−	0.838399i
$687$	1059.93	+	540.060i	0.0588629	+	0.0299921i
$688$	3242.82	−	169.949i	0.179696	−	0.00941749i
$689$	1301.84	+	1445.84i	0.0719827	+	0.0799449i
$690$	−14825.5	−	8773.23i	−0.817969	−	0.484045i
$691$	10742.0	+	9672.13i	0.591381	+	0.532482i	0.909573	−	0.415544i	$-0.136409\pi$
$691$	10742.0	+	9672.13i	0.591381	+	0.532482i	−0.318192	+	0.948026i	$0.603076\pi$
$692$	−26333.0	−	4170.74i	−1.44658	−	0.229115i
$693$	−5999.53	+	2464.29i	−0.328865	+	0.135080i
$694$	−16610.8	−	22862.8i	−0.908556	−	1.25052i
$695$	5475.14	+	6911.75i	0.298826	+	0.377234i
$696$	−2666.99	−	5990.16i	−0.145247	−	0.326231i
$697$	8264.74	−	21530.4i	0.449138	−	1.17005i
$698$	17929.4	−	27608.8i	0.972260	−	1.49715i
$699$	7638.25			0.413312
$700$	21609.1	+	8252.06i	1.16678	+	0.445569i
$701$	25466.1			1.37210			0.686050	−	0.727554i	$-0.259343\pi$
$701$	25466.1			1.37210			0.686050	+	0.727554i	$0.259343\pi$
$702$	864.336	−	1330.96i	0.0464705	−	0.0715583i
$703$	−866.487	+	2257.27i	−0.0464867	+	0.121102i
$704$	−19702.0	−	44251.4i	−1.05475	−	2.36901i
$705$	−17530.8	−	4899.80i	−0.936520	−	0.261755i
$706$	−16495.6	−	22704.3i	−0.879350	−	1.21032i
$707$	−1454.67	+	10802.0i	−0.0773812	+	0.574612i
$708$	46764.7	+	7406.80i	2.48238	+	0.393170i
$709$	8487.76	+	7642.41i	0.449597	+	0.404819i	0.862581	−	0.505919i	$-0.168847\pi$
$709$	8487.76	+	7642.41i	0.449597	+	0.404819i	−0.412984	+	0.910738i	$0.635513\pi$
$710$	3184.73	−	14229.5i	0.168339	−	0.752147i
$711$	881.536	+	979.045i	0.0464981	+	0.0516414i
$712$	−4755.37	+	249.218i	−0.250302	+	0.0131178i
$713$	−7655.83	−	3900.84i	−0.402122	−	0.204891i
$714$	−20591.4	−	58700.3i	−1.07929	−	3.07676i
$715$	2138.07	+	720.185i	0.111831	+	0.0376691i
$716$	20798.5	−	23099.1i	1.08558	−	1.20566i
$717$	15744.3	−	19442.5i	0.820056	−	1.01268i
$718$	−1832.69	+	491.067i	−0.0952580	+	0.0255243i
$719$	−13587.3	−	6049.48i	−0.704760	−	0.313779i	0.0228802	−	0.999738i	$-0.492716\pi$
$719$	−13587.3	−	6049.48i	−0.704760	−	0.313779i	−0.727640	+	0.685959i	$0.759383\pi$
$720$	−1201.75	+	2297.22i	−0.0622035	+	0.118906i
$721$	4338.22	−	7933.88i	0.224083	−	0.409810i
$722$	−24943.9	+	3950.73i	−1.28576	+	0.203644i
$723$	−13468.7	−	8746.67i	−0.692816	−	0.449920i
$724$	−13261.5	+	22969.5i	−0.680744	+	1.17908i
$725$	16628.4	+	3909.67i	0.851809	+	0.200278i
$726$	64774.8	−	37397.8i	3.31132	−	1.91179i
$727$	−20973.9	+	10686.7i	−1.06998	+	0.545183i	−0.898036	−	0.439923i	$-0.855006\pi$
$727$	−20973.9	+	10686.7i	−1.06998	+	0.545183i	−0.171947	+	0.985106i	$0.555006\pi$
$728$	−112.032	+	460.633i	−0.00570356	+	0.0234508i
$729$	8524.08	−	11732.4i	0.433068	−	0.596067i
$730$	−10936.2	−	29431.1i	−0.554477	−	1.49218i
$731$	−10210.3	+	1073.14i	−0.516608	+	0.0542977i
$732$	11025.6	+	41148.1i	0.556718	+	2.07770i
$733$	−24555.2	+	9425.84i	−1.23733	+	0.474968i	−0.887049	−	0.461676i	$-0.847248\pi$
$733$	−24555.2	+	9425.84i	−1.23733	+	0.474968i	−0.350284	+	0.936643i	$0.613915\pi$
$734$	4312.92	+	13273.8i	0.216884	+	0.667500i
$735$	21452.7	+	3765.29i	1.07659	+	0.188959i
$736$	5032.74	−	15489.2i	0.252050	−	0.775732i
$737$	−2606.37	−	49732.6i	−0.130267	−	2.48565i
$738$	3094.10	−	2009.33i	0.154330	−	0.100223i
$739$	−18186.9	+	16375.5i	−0.905297	+	0.815133i	−0.983332	−	0.181818i	$-0.941802\pi$
$739$	−18186.9	+	16375.5i	−0.905297	+	0.815133i	0.0780353	+	0.996951i	$0.475135\pi$
$740$	1034.38	−	8918.72i	0.0513847	−	0.443052i
$741$	492.350	−	159.974i	0.0244088	−	0.00793091i
$742$	−42932.0	−	26484.0i	−2.12410	−	1.31032i
$743$	8742.57	+	8742.57i	0.431674	+	0.431674i	0.889197	−	0.457524i	$-0.151263\pi$
$743$	8742.57	+	8742.57i	0.431674	+	0.431674i	−0.457524	+	0.889197i	$0.651263\pi$
$744$	2621.89	−	5888.86i	0.129198	−	0.290183i
$745$	−854.954	+	13530.5i	−0.0420444	+	0.665395i
$746$	−52506.4	+	23377.3i	−2.57694	+	1.14733i
$747$	2038.40	−	1650.67i	0.0998410	−	0.0808497i
$748$	42121.6	+	82668.2i	2.05898	+	4.04098i
$749$	602.958	+	4687.16i	0.0294147	+	0.228658i
$750$	14310.5	+	30475.7i	0.696727	+	1.48375i
$751$	−1217.17	−	2108.21i	−0.0591415	−	0.102436i	0.834939	−	0.550343i	$-0.185503\pi$
$751$	−1217.17	−	2108.21i	−0.0591415	−	0.102436i	−0.894080	+	0.447907i	$0.852170\pi$
$752$	661.592	−	12623.9i	0.0320822	−	0.612164i
$753$	23798.3	+	9135.30i	1.15174	+	0.442110i
$754$	−183.577	+	1746.62i	−0.00886667	+	0.0843607i
$755$	14542.8	+	29316.2i	0.701015	+	1.41315i
$756$	−6554.85	+	21890.5i	−0.315341	+	1.05311i
$757$	12552.5	−	12552.5i	0.602680	−	0.602680i	−0.338343	−	0.941023i	$-0.609866\pi$
$757$	12552.5	−	12552.5i	0.602680	−	0.602680i	0.941023	+	0.338343i	$0.109866\pi$
$758$	−10138.2	−	26410.9i	−0.485799	−	1.26555i
$759$	23664.7	+	5030.09i	1.13172	+	0.240554i
$760$	−2608.08	+	1127.78i	−0.124480	+	0.0538273i
$761$	−6628.81	−	31186.1i	−0.315761	−	1.48554i	−0.794328	−	0.607489i	$-0.792177\pi$
$761$	−6628.81	−	31186.1i	−0.315761	−	1.48554i	0.478567	−	0.878051i	$-0.341156\pi$
$762$	10020.2	−	19665.8i	0.476371	−	0.934930i
$763$	−254.327	+	46.3580i	−0.0120672	+	0.00219957i
$764$	−25668.3	−	8340.14i	−1.21551	−	0.394942i
$765$	3414.12	−	7451.74i	0.161356	−	0.352181i
$766$	−2978.92	+	14014.7i	−0.140513	+	0.661061i
$767$	−1964.55	−	1590.86i	−0.0924848	−	0.0748927i
$768$	−7536.66	−	2019.44i	−0.354109	−	0.0948833i
$769$	10119.6	−	7352.31i	0.474540	−	0.344774i	−0.324668	−	0.945828i	$-0.605252\pi$
$769$	10119.6	−	7352.31i	0.474540	−	0.344774i	0.799208	+	0.601054i	$0.205252\pi$
$770$	−58448.5	−	2332.46i	−2.73551	−	0.109164i
$771$	−17321.0	−	12584.4i	−0.809079	−	0.587830i
$772$	−22880.6	−	28255.2i	−1.06670	−	1.31726i
$773$	−15055.4	−	789.022i	−0.700526	−	0.0367130i	−0.301252	−	0.953545i	$-0.597404\pi$
$773$	−15055.4	−	789.022i	−0.700526	−	0.0367130i	−0.399274	+	0.916832i	$0.630738\pi$
$774$	−1422.32	−	821.175i	−0.0660518	−	0.0381350i
$775$	8082.06	+	14720.1i	0.374602	+	0.682275i
$776$			8748.83i			0.404723i
$777$	−638.349	−	8430.14i	−0.0294732	−	0.389227i
$778$	−5463.42	−	34494.7i	−0.251765	−	1.58958i
$779$	−4948.82	−	520.142i	−0.227612	−	0.0239230i
$780$	−1623.40	+	1029.62i	−0.0745217	+	0.0472646i
$781$	2140.56	+	20366.1i	0.0980734	+	0.933106i
$782$	−9789.59	+	36535.2i	−0.447666	+	1.67071i
$783$	−2639.80	+	16667.0i	−0.120484	+	0.760703i
$784$	702.146	+	15109.8i	0.0319855	+	0.688309i
$785$	397.216	−	1179.25i	0.0180602	−	0.0536167i
$786$	45427.6	−	9655.94i	2.06151	−	0.438188i
$787$	1924.03	+	2962.75i	0.0871464	+	0.134194i	0.879555	−	0.475796i	$-0.157840\pi$
$787$	1924.03	+	2962.75i	0.0871464	+	0.134194i	−0.792409	+	0.609990i	$0.791173\pi$
$788$	9749.44	+	15012.8i	0.440748	+	0.678693i
$789$	−27870.8	+	5924.12i	−1.25758	+	0.267306i
$790$	3550.03	+	11338.9i	0.159879	+	0.510659i
$791$	6380.85	+	521.204i	0.286823	+	0.0234284i
$792$	−462.829	+	2922.19i	−0.0207650	+	0.131105i
$793$	588.660	−	2196.91i	0.0263606	−	0.0983789i
$794$	1354.79	+	12889.9i	0.0605537	+	0.576130i
$795$	−10129.7	−	39497.1i	−0.451905	−	1.76204i
$796$	−38880.0	−	4086.45i	−1.73124	−	0.181960i
$797$	3248.96	+	20513.1i	0.144397	+	0.911685i	0.948404	+	0.317065i	$0.102697\pi$
$797$	3248.96	+	20513.1i	0.144397	+	0.911685i	−0.804007	+	0.594620i	$0.797303\pi$
$798$	−11084.2	+	7569.70i	−0.491698	+	0.335795i
$799$			39966.4i			1.76960i
$800$	−25161.2	+	19495.2i	−1.11198	+	0.861574i
$801$	−2566.78	−	1481.93i	−0.113224	−	0.0653702i
$802$	42723.2	+	2239.03i	1.88106	+	0.0985822i
$803$	27749.4	+	34267.7i	1.21950	+	1.50595i
$804$	34330.0	+	24942.2i	1.50588	+	1.09408i
$805$	−9480.54	−	9246.90i	−0.415087	−	0.404858i
$806$	−1396.80	+	1014.83i	−0.0610423	+	0.0443498i
$807$	12082.5	+	3237.49i	0.527042	+	0.141220i
$808$	3863.91	+	3128.93i	0.168232	+	0.136232i
$809$	−9323.35	+	43862.9i	−0.405181	+	1.90623i	0.0172876	+	0.999851i	$0.494497\pi$
$809$	−9323.35	+	43862.9i	−0.405181	+	1.90623i	−0.422469	+	0.906377i	$0.638836\pi$
$810$	−34847.9	+	19623.3i	−1.51164	+	0.851227i
$811$	34673.6	+	11266.1i	1.50130	+	0.487802i	0.940397	−	0.340079i	$-0.110454\pi$
$811$	34673.6	+	11266.1i	1.50130	+	0.487802i	0.560904	+	0.827881i	$0.310454\pi$
$812$	−4534.67	−	24877.9i	−0.195980	−	1.07518i
$813$	11989.5	−	23530.8i	0.517210	−	1.01508i
$814$	4720.68	+	22209.1i	0.203268	+	0.956299i
$815$	−6523.65	+	11024.1i	−0.280384	+	0.473811i
$816$	34158.1	+	7260.52i	1.46541	+	0.311482i
$817$	793.851	+	2068.05i	0.0339943	+	0.0885582i
$818$	−19897.6	+	19897.6i	−0.850491	+	0.850491i
$819$	−214.631	+	202.473i	−0.00915729	+	0.00863854i
$820$	18280.7	−	2694.38i	0.778522	−	0.114746i
$821$	−488.398	+	4646.80i	−0.0207615	+	0.197533i	−0.999986	−	0.00524535i	$-0.998330\pi$
$821$	−488.398	+	4646.80i	−0.0207615	+	0.197533i	0.979225	+	0.202778i	$0.0649970\pi$
$822$	4495.91	+	1725.82i	0.190770	+	0.0732298i
$823$	1601.00	−	30548.9i	0.0678096	−	1.29388i	−0.726836	−	0.686811i	$-0.759010\pi$
$823$	1601.00	−	30548.9i	0.0678096	−	1.29388i	0.794646	−	0.607073i	$-0.207657\pi$
$824$	−2062.41	−	3572.20i	−0.0871935	−	0.151024i
$825$	−32708.6	−	34145.2i	−1.38032	−	1.44095i
$826$	60478.5	+	25261.1i	2.54760	+	1.06410i
$827$	−11695.9	−	22954.5i	−0.491785	−	0.965183i	−0.994891	−	0.100958i	$-0.967809\pi$
$827$	−11695.9	−	22954.5i	−0.491785	−	0.965183i	0.503105	−	0.864225i	$-0.332191\pi$
$828$	−2611.45	+	2114.71i	−0.109606	+	0.0887574i
$829$	718.289	−	319.803i	0.0300931	−	0.0133983i	−0.391635	−	0.920121i	$-0.628090\pi$
$829$	718.289	−	319.803i	0.0300931	−	0.0133983i	0.421728	+	0.906722i	$0.361424\pi$
$830$	22914.1	−	5876.71i	0.958265	−	0.245763i
$831$	9095.08	−	20427.9i	0.379669	−	0.852750i
$832$	−1558.20	−	1558.20i	−0.0649290	−	0.0649290i
$833$	−4716.98	−	47589.1i	−0.196199	−	1.97943i
$834$	18069.9	−	5871.28i	0.750253	−	0.243772i
$835$	−1658.46	+	1802.58i	−0.0687347	+	0.0747077i
$836$	14877.1	−	13395.4i	0.615473	−	0.554174i
$837$	−13913.0	+	9035.24i	−0.574558	+	0.373122i
$838$	854.085	+	16296.9i	0.0352075	+	0.671799i
$839$	8246.02	−	25378.6i	0.339314	−	1.04430i	−0.625244	−	0.780429i	$-0.715001\pi$
$839$	8246.02	−	25378.6i	0.339314	−	1.04430i	0.964558	−	0.263871i	$-0.0849993\pi$
$840$	6555.48	−	7465.82i	0.269269	−	0.306661i
$841$	1765.90	+	5434.89i	0.0724058	+	0.222842i
$842$	13852.3	−	5317.41i	0.566963	−	0.217637i
$843$	3934.32	+	14683.1i	0.160742	+	0.599896i
$844$	39307.8	−	4131.41i	1.60312	−	0.168494i
$845$	−24439.4	+	1017.67i	−0.994959	+	0.0414307i
$846$	−3758.00	+	5172.44i	−0.152722	+	0.210204i
$847$	55180.0	−	16167.4i	2.23850	−	0.655868i
$848$	25231.1	−	12855.9i	1.02174	−	0.520604i
$849$	−1266.65	+	731.299i	−0.0512028	+	0.0295620i
$850$	55986.0	−	48272.8i	2.25918	−	1.94793i
$851$	−2570.24	+	4451.79i	−0.103533	+	0.179325i
$852$	−14634.0	−	9503.46i	−0.588444	−	0.382140i
$853$	−28772.9	+	4557.18i	−1.15494	+	0.182925i	−0.704382	−	0.709821i	$-0.748776\pi$
$853$	−28772.9	+	4557.18i	−1.15494	+	0.182925i	−0.450560	+	0.892746i	$0.648776\pi$
$854$	1369.04	+	58953.7i	0.0548567	+	2.36224i
$855$	−1743.72	−	295.415i	−0.0697474	−	0.0118164i
$856$	1969.34	+	876.807i	0.0786340	+	0.0350101i
$857$	−16621.8	+	4453.81i	−0.662533	+	0.177525i	−0.574389	−	0.818582i	$-0.694760\pi$
$857$	−16621.8	+	4453.81i	−0.662533	+	0.177525i	−0.0881442	+	0.996108i	$0.528094\pi$
$858$	3059.37	−	3778.01i	0.121731	−	0.150325i
$859$	4260.78	−	4732.07i	0.169238	−	0.187958i	−0.652559	−	0.757738i	$-0.726305\pi$
$859$	4260.78	−	4732.07i	0.169238	−	0.187958i	0.821798	+	0.569779i	$0.192971\pi$
$860$	−4763.26	−	6706.42i	−0.188867	−	0.265915i
$861$	16418.4	−	5759.39i	0.649869	−	0.227967i
$862$	30391.8	+	15485.4i	1.20087	+	0.611874i
$863$	−47241.5	+	2475.82i	−1.86340	+	0.0976569i	−0.950539	−	0.310605i	$-0.899468\pi$
$863$	−47241.5	+	2475.82i	−1.86340	+	0.0976569i	−0.912865	+	0.408262i	$0.866135\pi$
$864$	−21040.3	−	23367.6i	−0.828479	−	0.920119i
$865$	−11840.7	−	27382.5i	−0.465427	−	1.07634i
$866$	−3353.21	−	3019.24i	−0.131578	−	0.118473i
$867$	−81486.6	−	12906.2i	−3.19196	−	0.505557i
$868$	15192.2	−	19678.0i	0.594076	−	0.769486i
$869$	−9808.11	−	13499.7i	−0.382874	−	0.526981i
$870$	20377.2	−	30652.2i	0.794084	−	1.19449i
$871$	−921.493	−	2069.71i	−0.0358480	−	0.0805159i
$872$	−42.2606	+	110.093i	−0.00164120	+	0.00427547i
$873$	−2965.77	+	4566.89i	−0.114978	+	0.177051i
$874$	8161.23			0.315855
$875$	5152.97	+	25364.7i	0.199088	+	0.979982i
$876$	−37571.8			−1.44912
$877$	−17331.1	+	26687.6i	−0.667310	+	1.02757i	0.329213	+	0.944256i	$0.393216\pi$
$877$	−17331.1	+	26687.6i	−0.667310	+	1.02757i	−0.996524	+	0.0833119i	$0.973450\pi$
$878$	−15999.7	+	41680.7i	−0.614993	+	1.60211i
$879$	2931.15	+	6583.48i	0.112475	+	0.252623i
$880$	18179.3	−	27346.0i	0.696391	−	1.04754i
$881$	7456.01	+	10262.3i	0.285130	+	0.392448i	0.927425	−	0.374010i	$-0.122017\pi$
$881$	7456.01	+	10262.3i	0.285130	+	0.392448i	−0.642295	+	0.766458i	$0.722017\pi$
$882$	3864.29	−	6602.51i	0.147525	−	0.252061i
$883$	14411.3	+	2282.53i	0.549241	+	0.0869913i	0.424887	−	0.905247i	$-0.360314\pi$
$883$	14411.3	+	2282.53i	0.549241	+	0.0869913i	0.124355	+	0.992238i	$0.460314\pi$
$884$	3136.70	+	2824.30i	0.119343	+	0.107456i
$885$	21027.8	+	48628.5i	0.798690	+	1.84704i
$886$	−21871.0	−	24290.2i	−0.829310	−	0.921043i
$887$	50495.2	−	2646.34i	1.91146	−	0.100175i	0.940555	−	0.339642i	$-0.110306\pi$
$887$	50495.2	−	2646.34i	1.91146	−	0.100175i	0.970904	+	0.239467i	$0.0769727\pi$
$888$	−3436.17	−	1750.81i	−0.129854	−	0.0661638i
$889$	11057.8	−	12869.6i	0.417171	−	0.485526i
$890$	−15478.5	−	21793.0i	−0.582969	−	0.820788i
$891$	37582.5	−	41739.6i	1.41309	−	1.56939i
$892$	31419.3	−	38799.6i	1.17937	−	1.45640i
$893$	8329.64	−	2231.92i	0.312140	−	0.0836376i
$894$	26687.7	+	11882.1i	0.998401	+	0.444517i
$895$	34291.9	+	5809.61i	1.28073	+	0.216977i
$896$	17027.3	+	9310.49i	0.634869	+	0.347145i
$897$	1087.07	−	172.175i	0.0404641	−	0.00640889i
$898$	3016.45	+	1958.91i	0.112094	+	0.0727946i
$899$	9179.30	−	15899.0i	0.340542	−	0.589835i
$900$	6544.66	−	545.994i	0.242395	−	0.0202220i
$901$	−77533.7	+	44764.1i	−2.86684	+	1.65517i
$902$	−41635.3	+	21214.2i	−1.53692	+	0.783100i
$903$	−5602.62	−	5348.32i	−0.206471	−	0.197100i
$904$	1716.56	−	2362.64i	0.0631547	−	0.0869250i
$905$	−29652.4	+	1234.74i	−1.08915	+	0.0453528i
$906$	70129.0	−	7370.85i	2.57161	−	0.270287i
$907$	3120.34	+	11645.3i	0.114233	+	0.426323i	0.999228	−	0.0392764i	$-0.0125053\pi$
$907$	3120.34	+	11645.3i	0.114233	+	0.426323i	−0.884995	+	0.465600i	$0.845839\pi$
$908$	−15482.1	+	5943.03i	−0.565851	+	0.217210i
$909$	956.280	+	2943.13i	0.0348931	+	0.107390i
$910$	−2520.40	+	853.833i	−0.0918138	+	0.0311036i
$911$	10428.1	−	32094.3i	0.379250	−	1.16721i	−0.561316	−	0.827602i	$-0.689705\pi$
$911$	10428.1	−	32094.3i	0.379250	−	1.16721i	0.940566	−	0.339611i	$-0.110295\pi$
$912$	−394.345	−	7524.56i	−0.0143181	−	0.273205i
$913$	−27862.3	+	18094.0i	−1.00997	+	0.655885i
$914$	49765.9	−	44809.4i	1.80099	−	1.62162i
$915$	−32274.4	+	35079.0i	−1.16607	+	1.26741i
$916$	1990.31	−	646.692i	0.0717924	−	0.0233268i
$917$	35687.9	+	1040.30i	1.28519	+	0.0374633i
$918$	51638.4	+	51638.4i	1.85656	+	1.85656i
$919$	−1293.37	+	2904.96i	−0.0464249	+	0.104272i	−0.935269	−	0.353938i	$-0.884842\pi$
$919$	−1293.37	+	2904.96i	−0.0464249	+	0.104272i	0.888844	+	0.458210i	$0.151509\pi$
$920$	−5851.69	+	1500.77i	−0.209701	+	0.0537813i
$921$	−1904.00	+	847.717i	−0.0681205	+	0.0303292i
$922$	46487.2	−	37644.6i	1.66049	−	1.34464i
$923$	422.943	+	830.073i	0.0150827	+	0.0296015i
$924$	−26978.7	+	64590.5i	−0.960534	+	2.29965i
$925$	9047.50	−	4367.68i	0.321600	−	0.155252i
$926$	11179.7	+	19363.8i	0.396747	+	0.687186i
$927$	134.364	−	2563.82i	0.00476063	−	0.0908382i
$928$	32486.4	+	12470.4i	1.14916	+	0.441121i
$929$	−4367.92	+	41557.9i	−0.154259	+	1.46768i	0.594104	+	0.804388i	$0.297507\pi$
$929$	−4367.92	+	41557.9i	−0.154259	+	1.46768i	−0.748364	+	0.663289i	$0.769160\pi$
$930$	35798.2	−	5276.29i	1.26223	−	0.186039i
$931$	−9654.92	+	3640.71i	−0.339879	+	0.128163i
$932$	9501.63	−	9501.63i	0.333945	−	0.333945i
$933$	3799.55	+	9898.16i	0.133324	+	0.347322i
$934$	−45926.8	−	9762.03i	−1.60896	−	0.341995i
$935$	−52871.9	+	89346.1i	−1.84930	+	3.12506i
$936$	27.9840	+	131.654i	0.000977228	+	0.00459749i
$937$	19562.9	−	38394.4i	0.682064	−	1.33863i	−0.247112	−	0.968987i	$-0.579482\pi$
$937$	19562.9	−	38394.4i	0.682064	−	1.33863i	0.929176	−	0.369638i	$-0.120518\pi$
$938$	38016.6	+	44779.6i	1.32333	+	1.55875i
$939$	−13544.2	−	4400.77i	−0.470711	−	0.152943i
$940$	−27902.6	+	15712.3i	−0.968173	+	0.545191i
$941$	5546.15	−	26092.6i	0.192135	−	0.903926i	−0.771401	−	0.636349i	$-0.780444\pi$
$941$	5546.15	−	26092.6i	0.192135	−	0.903926i	0.963536	−	0.267577i	$-0.0862230\pi$
$942$	−2083.75	−	1687.39i	−0.0720726	−	0.0583632i
$943$	−10218.9	−	2738.13i	−0.352886	−	0.0945556i
$944$	−29766.4	+	21626.6i	−1.02629	+	0.745641i
$945$	−24613.4	+	6925.37i	−0.847276	+	0.238394i
$946$	16829.1	+	12227.1i	0.578394	+	0.420228i
$947$	−9901.93	−	12227.9i	−0.339778	−	0.419591i	0.578404	−	0.815751i	$-0.303676\pi$
$947$	−9901.93	−	12227.9i	−0.339778	−	0.419591i	−0.918181	+	0.396160i	$0.870343\pi$
$948$	14198.8	+	744.127i	0.486451	+	0.0254938i
$949$	1737.22	+	1002.98i	0.0594232	+	0.0343080i
$950$	−13187.4	−	8972.59i	−0.450373	−	0.306431i
$951$		−	32592.9i		−	1.11135i
$952$	−19661.7	−	9449.72i	−0.669368	−	0.321709i
$953$	−8610.79	−	54366.4i	−0.292687	−	1.84795i	−0.495335	−	0.868702i	$-0.664955\pi$
$953$	−8610.79	−	54366.4i	−0.292687	−	1.84795i	0.202648	−	0.979252i	$-0.435045\pi$
$954$	−14243.5	−	1497.05i	−0.483386	−	0.0508059i
$955$	−7502.47	−	29253.2i	−0.254214	−	0.991214i
$956$	−4600.50	−	43770.8i	−0.155639	−	1.48080i
$957$	−13378.9	+	49930.8i	−0.451911	+	1.68656i
$958$	−1137.58	+	7182.40i	−0.0383649	+	0.242226i
$959$	3044.83	+	2105.96i	0.102526	+	0.0709124i
$960$	13798.9	+	44074.3i	0.463915	+	1.48176i
$961$	−11486.2	+	2441.48i	−0.385561	+	0.0819535i
$962$	562.570	+	866.282i	0.0188545	+	0.0290333i
$963$	730.766	+	1125.28i	0.0244534	+	0.0376549i
$964$	−27634.9	+	5873.98i	−0.923299	+	0.196253i
$965$	12986.6	−	38554.4i	0.433217	−	1.28612i
$966$	−25792.8	+	12208.9i	−0.859078	+	0.406640i
$967$	3392.64	−	21420.3i	0.112823	−	0.712338i	−0.864822	−	0.502078i	$-0.832569\pi$
$967$	3392.64	−	21420.3i	0.112823	−	0.712338i	0.977646	−	0.210260i	$-0.0674310\pi$
$968$	6788.59	−	25335.3i	0.225406	−	0.841228i
$969$	2490.10	+	23691.7i	0.0825525	+	0.785435i
$970$	−41472.8	+	26303.6i	−1.37279	+	0.870680i
$971$	8832.35	+	928.317i	0.291909	+	0.0306809i	0.249351	−	0.968413i	$-0.419783\pi$
$971$	8832.35	+	928.317i	0.291909	+	0.0306809i	0.0425578	+	0.999094i	$0.486449\pi$
$972$	2275.29	+	14365.6i	0.0750823	+	0.474051i
$973$	14564.6	−	1102.87i	0.479877	−	0.0363374i
$974$			13627.3i			0.448301i
$975$	−1945.85	−	916.936i	−0.0639148	−	0.0301184i
$976$	−28668.7	−	16551.9i	−0.940227	−	0.542840i
$977$	−49501.1	−	2594.24i	−1.62096	−	0.0849510i	−0.779905	−	0.625898i	$-0.784733\pi$
$977$	−49501.1	−	2594.24i	−1.62096	−	0.0849510i	−0.841057	+	0.540947i	$0.818066\pi$
$978$	17370.5	+	21450.8i	0.567941	+	0.701349i
$979$	30370.6	+	22065.5i	0.991470	+	0.720345i
$980$	31370.0	−	22002.3i	1.02253	−	0.717181i
$981$	−59.3805	+	43.1424i	−0.00193259	+	0.00140411i
$982$	−23902.3	−	6404.60i	−0.776734	−	0.208125i
$983$	28564.4	+	23131.0i	0.926820	+	0.750524i	0.968606	−	0.248603i	$-0.0799714\pi$
$983$	28564.4	+	23131.0i	0.926820	+	0.750524i	−0.0417858	+	0.999127i	$0.513305\pi$
$984$	1650.16	−	7763.41i	0.0534607	−	0.251513i
$985$	−8343.14	+	18209.9i	−0.269883	+	0.589053i
$986$	−76860.4	−	24973.5i	−2.48249	−	0.806610i
$987$	−22986.2	+	19514.6i	−0.741295	+	0.629338i
$988$	413.461	−	811.462i	0.0133137	−	0.0261296i
$989$	979.174	+	4606.65i	0.0314822	+	0.148112i
$990$	−15243.8	+	6591.66i	−0.489373	+	0.211613i
$991$	18034.9	+	3833.44i	0.578101	+	0.122879i	0.487677	−	0.873024i	$-0.337844\pi$
$991$	18034.9	+	3833.44i	0.578101	+	0.122879i	0.0904243	+	0.995903i	$0.471178\pi$
$992$	12259.5	+	31937.0i	0.392378	+	1.02218i
$993$	−22896.2	+	22896.2i	−0.731711	+	0.731711i
$994$	−16574.8	−	17570.1i	−0.528894	−	0.560655i
$995$	−19439.9	−	39188.0i	−0.619382	−	1.24859i
$996$	2958.96	−	28152.6i	0.0941348	−	0.895633i
$997$	−29604.0	−	11363.9i	−0.940389	−	0.360982i	−0.160597	−	0.987020i	$-0.551342\pi$
$997$	−29604.0	−	11363.9i	−0.940389	−	0.360982i	−0.779792	+	0.626038i	$0.784675\pi$
$998$	−850.857	+	16235.3i	−0.0269874	+	0.514950i
$999$	4962.42	+	8595.16i	0.157161	+	0.272211i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.4.x.a.3.50	✓	928
7.5	odd	6	inner	175.4.x.a.103.9	yes	928
25.17	odd	20	inner	175.4.x.a.17.9	yes	928
175.117	even	60	inner	175.4.x.a.117.50	yes	928

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.4.x.a.3.50	✓	928	1.1	even	1	trivial
175.4.x.a.17.9	yes	928	25.17	odd	20	inner
175.4.x.a.103.9	yes	928	7.5	odd	6	inner
175.4.x.a.117.50	yes	928	175.117	even	60	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(2.31018 - 3.55736i) q^{2} +(2.03540 - 5.30240i) q^{3} +(-4.06400 - 9.12789i) q^{4} +(6.18963 - 9.31066i) q^{5} +(-14.1604 - 19.4901i) q^{6} +(-7.03669 - 17.1314i) q^{7} +(-8.34419 - 1.32159i) q^{8} +(-3.90766 - 3.51847i) q^{9} +(-18.8222 - 43.5280i) q^{10} +(44.5648 + 49.4942i) q^{11} +(-56.6716 + 2.97003i) q^{12} +(2.69963 + 1.37553i) q^{13} +(-77.1985 - 14.5445i) q^{14} +(-36.7705 - 51.7708i) q^{15} +(29.5082 - 32.7722i) q^{16} +(-87.7422 + 108.353i) q^{17} +(-21.5438 + 5.77266i) q^{18} +(27.4824 + 12.2359i) q^{19} +(-110.141 - 18.6598i) q^{20} +(-105.160 + 2.44206i) q^{21} +(279.021 - 44.1926i) q^{22} +(53.6397 + 34.8340i) q^{23} +(-23.9914 + 41.5543i) q^{24} +(-48.3769 - 115.259i) q^{25} +(11.1299 - 6.42583i) q^{26} +(110.026 - 56.0611i) q^{27} +(-127.776 + 133.852i) q^{28} +(-80.3234 + 110.556i) q^{29} +(-269.114 + 11.2060i) q^{30} +(-133.607 + 14.0427i) q^{31} +(-65.9057 - 245.963i) q^{32} +(353.145 - 135.560i) q^{33} +(182.749 + 562.444i) q^{34} +(-203.059 - 40.5209i) q^{35} +(-16.2355 + 49.9677i) q^{36} +(4.20638 + 80.2626i) q^{37} +(107.017 - 69.4975i) q^{38} +(12.7884 - 11.5148i) q^{39} +(-63.9524 + 69.5098i) q^{40} +(-157.315 + 51.1147i) q^{41} +(-234.251 + 379.733i) q^{42} +(52.0680 + 52.0680i) q^{43} +(270.666 - 607.927i) q^{44} +(-56.9463 + 14.6048i) q^{45} +(247.834 - 110.343i) q^{46} +(222.772 - 180.397i) q^{47} +(-113.710 - 223.169i) q^{48} +(-243.970 + 241.097i) q^{49} +(-521.777 - 94.1750i) q^{50} +(395.938 + 685.785i) q^{51} +(1.58440 - 30.2321i) q^{52} +(599.480 + 230.119i) q^{53} +(54.7502 - 520.913i) q^{54} +(736.663 - 108.577i) q^{55} +(36.0748 + 152.247i) q^{56} +(120.817 - 120.817i) q^{57} +(207.725 + 541.142i) q^{58} +(-816.097 - 173.467i) q^{59} +(-323.123 + 546.033i) q^{60} +(-156.072 - 734.259i) q^{61} +(-258.702 + 507.731i) q^{62} +(-32.7794 + 91.7021i) q^{63} +(-691.707 - 224.749i) q^{64} +(29.5168 - 16.6213i) q^{65} +(333.593 - 1569.43i) q^{66} +(-581.110 - 470.573i) q^{67} +(1345.61 + 360.556i) q^{68} +(293.882 - 213.518i) q^{69} +(-613.250 + 628.744i) q^{70} +(248.754 + 180.730i) q^{71} +(27.9563 + 34.5231i) q^{72} +(661.159 + 34.6499i) q^{73} +(295.240 + 170.457i) q^{74} +(-709.616 + 21.9151i) q^{75} -300.583i q^{76} +(534.317 - 1111.73i) q^{77} +(-11.4186 - 72.0941i) q^{78} +(-249.173 - 26.1891i) q^{79} +(-122.486 - 477.589i) q^{80} +(-88.1514 - 838.704i) q^{81} +(-181.592 + 677.709i) q^{82} +(-78.0327 + 492.679i) q^{83} +(449.661 + 949.964i) q^{84} +(465.743 + 1487.60i) q^{85} +(305.511 - 64.9383i) q^{86} +(422.720 + 650.932i) q^{87} +(-306.446 - 471.885i) q^{88} +(551.340 - 117.191i) q^{89} +(-79.6012 + 236.318i) q^{90} +(4.56831 - 55.9276i) q^{91} +(99.9695 - 631.183i) q^{92} +(-197.485 + 737.022i) q^{93} +(-127.095 - 1209.23i) q^{94} +(284.031 - 180.143i) q^{95} +(-1438.34 - 151.176i) q^{96} +(-162.001 - 1022.84i) q^{97} +(294.054 + 1424.86i) q^{98} -350.206i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 928 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 24 q^{7} + 84 q^{8} - 10 q^{9} - 96 q^{10} - 6 q^{11} - 72 q^{12} - 20 q^{14} - 368 q^{15} - 1670 q^{16} + 120 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} - 880 q^{22}+ \cdots - 19478 q^{98}+O(q^{100}) \) 928 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 24 * q^7 + 84 * q^8 - 10 * q^9 - 96 * q^10 - 6 * q^11 - 72 * q^12 - 20 * q^14 - 368 * q^15 - 1670 * q^16 + 120 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 - 880 * q^22 + 296 * q^23 + 32 * q^25 - 48 * q^26 + 226 * q^28 - 200 * q^29 - 38 * q^30 - 18 * q^31 - 964 * q^32 - 1092 * q^33 + 288 * q^35 + 7400 * q^36 - 392 * q^37 + 5424 * q^38 + 2430 * q^39 + 2172 * q^40 - 2098 * q^42 + 1560 * q^43 - 10 * q^44 - 4224 * q^45 - 6 * q^46 + 96 * q^47 + 6232 * q^50 - 16 * q^51 - 8928 * q^52 - 2384 * q^53 - 30 * q^54 + 244 * q^56 + 1556 * q^57 + 640 * q^58 + 4890 * q^59 + 3676 * q^60 - 18 * q^61 + 224 * q^63 - 9700 * q^64 - 1116 * q^65 - 2610 * q^66 - 2404 * q^67 - 13614 * q^68 - 1700 * q^70 - 24 * q^71 - 518 * q^72 - 4200 * q^73 - 16104 * q^75 - 722 * q^77 - 356 * q^78 - 10 * q^79 + 6414 * q^80 - 6810 * q^81 + 1692 * q^82 + 20620 * q^84 + 2712 * q^85 - 6 * q^86 + 9102 * q^87 + 1650 * q^88 + 20370 * q^89 - 12 * q^91 + 1612 * q^92 - 4604 * q^93 - 30 * q^94 + 1652 * q^95 - 2610 * q^96 - 19478 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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