LMFDB - Embedded newform 46.4.c.a.9.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [46,4,Mod(3,46)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("46.3"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(46, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([16])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 46 = 2 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	46.c (of order $11$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [30,-6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.71408786026$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$3$ over $\Q(\zeta_{11})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			9.2
Character	$\chi$	$=$	46.9
Dual form			46.4.c.a.41.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.91899 + 0.563465i) q^{2} +(-1.12472 - 1.29799i) q^{3} +(3.36501 - 2.16256i) q^{4} +(0.231505 + 1.61016i) q^{5} +(2.88969 + 1.85709i) q^{6} +(13.5480 - 29.6661i) q^{7} +(-5.23889 + 6.04600i) q^{8} +(3.42270 - 23.8054i) q^{9} +(-1.35152 - 2.95942i) q^{10} +(45.3795 + 13.3246i) q^{11} +(-6.59169 - 1.93549i) q^{12} +(-8.13276 - 17.8083i) q^{13} +(-9.28270 + 64.5626i) q^{14} +(1.82959 - 2.11146i) q^{15} +(6.64664 - 14.5541i) q^{16} +(-42.8901 - 27.5638i) q^{17} +(6.84541 + 47.6108i) q^{18} +(-123.133 + 79.1329i) q^{19} +(4.26108 + 4.91755i) q^{20} +(-53.7441 + 15.7807i) q^{21} -94.5906 q^{22} +(98.5556 + 49.5358i) q^{23} +13.7399 q^{24} +(117.398 - 34.4711i) q^{25} +(25.6410 + 29.5913i) q^{26} +(-73.7597 + 47.4025i) q^{27} +(-18.5654 - 129.125i) q^{28} +(31.8434 + 20.4645i) q^{29} +(-2.32123 + 5.08278i) q^{30} +(-12.2652 + 14.1548i) q^{31} +(-4.55407 + 31.6743i) q^{32} +(-33.7439 - 73.8888i) q^{33} +(97.8367 + 28.7274i) q^{34} +(50.9034 + 14.9466i) q^{35} +(-39.9633 - 87.5074i) q^{36} +(29.8058 - 207.304i) q^{37} +(191.702 - 221.236i) q^{38} +(-13.9680 + 30.5856i) q^{39} +(-10.9478 - 7.03574i) q^{40} +(16.1193 + 112.112i) q^{41} +(94.2423 - 60.5659i) q^{42} +(133.101 + 153.607i) q^{43} +(181.518 - 53.2985i) q^{44} +39.1228 q^{45} +(-217.039 - 39.5258i) q^{46} +105.031 q^{47} +(-26.3668 + 7.74198i) q^{48} +(-471.908 - 544.611i) q^{49} +(-205.861 + 132.299i) q^{50} +(12.4616 + 86.6726i) q^{51} +(-65.8783 - 42.3374i) q^{52} +(-179.403 + 392.838i) q^{53} +(114.834 - 132.526i) q^{54} +(-10.9491 + 76.1527i) q^{55} +(108.384 + 237.328i) q^{56} +(241.204 + 70.8240i) q^{57} +(-72.6382 - 21.3285i) q^{58} +(335.938 + 735.601i) q^{59} +(1.59044 - 11.0617i) q^{60} +(-62.6333 + 72.2826i) q^{61} +(15.5610 - 34.0738i) q^{62} +(-659.842 - 424.055i) q^{63} +(-9.10815 - 63.3486i) q^{64} +(26.7913 - 17.2177i) q^{65} +(106.388 + 122.778i) q^{66} +(360.939 - 105.981i) q^{67} -203.934 q^{68} +(-46.5502 - 183.638i) q^{69} -106.105 q^{70} +(-607.699 + 178.437i) q^{71} +(125.996 + 145.408i) q^{72} +(62.1324 - 39.9300i) q^{73} +(59.6116 + 414.608i) q^{74} +(-176.783 - 113.611i) q^{75} +(-243.215 + 532.567i) q^{76} +(1010.09 - 1165.71i) q^{77} +(9.57042 - 66.5637i) q^{78} +(521.624 + 1142.20i) q^{79} +(24.9731 + 7.33277i) q^{80} +(-478.565 - 140.519i) q^{81} +(-94.1040 - 206.059i) q^{82} +(74.1514 - 515.734i) q^{83} +(-146.723 + 169.327i) q^{84} +(34.4527 - 75.4408i) q^{85} +(-341.972 - 219.772i) q^{86} +(-9.25205 - 64.3495i) q^{87} +(-318.299 + 204.558i) q^{88} +(84.5663 + 97.5947i) q^{89} +(-75.0761 + 22.0443i) q^{90} -638.484 q^{91} +(438.765 - 46.4442i) q^{92} +32.1677 q^{93} +(-201.554 + 59.1815i) q^{94} +(-155.922 - 179.944i) q^{95} +(46.2351 - 29.7135i) q^{96} +(-160.779 - 1118.24i) q^{97} +(1212.46 + 779.198i) q^{98} +(472.519 - 1034.67i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q - 6 q^{2} + 6 q^{3} - 12 q^{4} + 10 q^{5} + 12 q^{6} + 107 q^{7} - 24 q^{8} - 63 q^{9} + 20 q^{10} + 64 q^{11} - 20 q^{12} + 8 q^{13} + 16 q^{14} + 252 q^{15} - 48 q^{16} - 126 q^{17} - 126 q^{18}+ \cdots + 1377 q^{99}+O(q^{100}) $ 30 * q - 6 * q^2 + 6 * q^3 - 12 * q^4 + 10 * q^5 + 12 * q^6 + 107 * q^7 - 24 * q^8 - 63 * q^9 + 20 * q^10 + 64 * q^11 - 20 * q^12 + 8 * q^13 + 16 * q^14 + 252 * q^15 - 48 * q^16 - 126 * q^17 - 126 * q^18 + 123 * q^19 - 136 * q^20 - 514 * q^21 - 356 * q^22 - 507 * q^23 + 48 * q^24 - 419 * q^25 - 94 * q^26 - 657 * q^27 + 32 * q^28 + 757 * q^29 + 240 * q^30 + 840 * q^31 - 96 * q^32 + 1948 * q^33 + 936 * q^34 - 785 * q^35 - 164 * q^36 - 444 * q^37 + 554 * q^38 + 1954 * q^39 + 80 * q^40 - 771 * q^41 + 72 * q^42 - 789 * q^43 + 256 * q^44 - 2596 * q^45 + 1230 * q^46 - 1748 * q^47 - 80 * q^48 - 720 * q^49 - 2026 * q^50 + 1641 * q^51 + 472 * q^52 - 785 * q^53 + 2030 * q^54 + 967 * q^55 + 856 * q^56 + 5918 * q^57 + 1052 * q^58 + 2307 * q^59 - 444 * q^60 + 877 * q^61 - 278 * q^62 - 5708 * q^63 - 192 * q^64 - 3846 * q^65 - 4156 * q^66 + 1763 * q^67 - 2528 * q^68 - 1970 * q^69 - 3968 * q^70 - 6362 * q^71 - 152 * q^72 - 3584 * q^73 - 888 * q^74 + 3143 * q^75 + 360 * q^76 + 6347 * q^77 - 1460 * q^78 + 2642 * q^79 + 864 * q^80 + 1043 * q^81 + 5542 * q^82 - 372 * q^83 + 2212 * q^84 + 5136 * q^85 - 2326 * q^86 + 5451 * q^87 - 104 * q^88 - 4283 * q^89 + 5104 * q^90 - 6182 * q^91 - 92 * q^92 - 8734 * q^93 - 2550 * q^94 + 9449 * q^95 + 192 * q^96 + 7599 * q^97 + 3928 * q^98 + 1377 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/46\mathbb{Z}\right)^\times$.

$n$	$5$
$\chi(n)$	$e\left(\frac{5}{11}\right)$

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 $

$2$	−1.91899	+	0.563465i	−0.678464	+	0.199215i
$2$	−1.91899	+	0.563465i	−0.678464	+	0.199215i
$3$	−1.12472	−	1.29799i	−0.216452	−	0.249799i	0.637131	−	0.770755i	$-0.280121\pi$
$3$	−1.12472	−	1.29799i	−0.216452	−	0.249799i	−0.853583	+	0.520956i	$0.825575\pi$
$4$	3.36501	−	2.16256i	0.420627	−	0.270320i
$5$	0.231505	+	1.61016i	0.0207065	+	0.144017i	0.997552	−	0.0699294i	$-0.0222774\pi$
$5$	0.231505	+	1.61016i	0.0207065	+	0.144017i	−0.976845	+	0.213946i	$0.931368\pi$
$6$	2.88969	+	1.85709i	0.196619	+	0.126359i
$7$	13.5480	−	29.6661i	0.731525	−	1.60182i	−0.0654873	−	0.997853i	$-0.520860\pi$
$7$	13.5480	−	29.6661i	0.731525	−	1.60182i	0.797012	−	0.603963i	$-0.206413\pi$
$8$	−5.23889	+	6.04600i	−0.231528	+	0.267198i
$9$	3.42270	−	23.8054i	0.126767	−	0.881682i
$10$	−1.35152	−	2.95942i	−0.0427389	−	0.0935851i
$11$	45.3795	+	13.3246i	1.24386	+	0.365229i	0.836463	−	0.548023i	$-0.184619\pi$
$11$	45.3795	+	13.3246i	1.24386	+	0.365229i	0.407394	+	0.913252i	$0.366438\pi$
$12$	−6.59169	−	1.93549i	−0.158571	−	0.0465608i
$13$	−8.13276	−	17.8083i	−0.173509	−	0.379933i	0.802820	−	0.596221i	$-0.203332\pi$
$13$	−8.13276	−	17.8083i	−0.173509	−	0.379933i	−0.976329	+	0.216289i	$0.930605\pi$
$14$	−9.28270	+	64.5626i	−0.177208	+	1.23251i
$15$	1.82959	−	2.11146i	0.0314933	−	0.0363452i
$16$	6.64664	−	14.5541i	0.103854	−	0.227408i
$17$	−42.8901	−	27.5638i	−0.611904	−	0.393247i	0.197667	−	0.980269i	$-0.436664\pi$
$17$	−42.8901	−	27.5638i	−0.611904	−	0.393247i	−0.809571	+	0.587022i	$0.800300\pi$
$18$	6.84541	+	47.6108i	0.0896376	+	0.623444i
$19$	−123.133	+	79.1329i	−1.48677	+	0.955492i	−0.490303	+	0.871552i	$0.663114\pi$
$19$	−123.133	+	79.1329i	−1.48677	+	0.955492i	−0.996471	+	0.0839396i	$0.973250\pi$
$20$	4.26108	+	4.91755i	0.0476403	+	0.0549799i
$21$	−53.7441	+	15.7807i	−0.558473	+	0.163982i
$22$	−94.5906			−0.916672
$23$	98.5556	+	49.5358i	0.893490	+	0.449084i
$23$	98.5556	+	49.5358i	0.893490	+	0.449084i
$24$	13.7399			0.116861
$25$	117.398	−	34.4711i	0.939181	−	0.275768i
$26$	25.6410	+	29.5913i	0.193408	+	0.223205i
$27$	−73.7597	+	47.4025i	−0.525743	+	0.337875i
$28$	−18.5654	−	129.125i	−0.125305	−	0.871513i
$29$	31.8434	+	20.4645i	0.203903	+	0.131040i	0.638607	−	0.769533i	$-0.279511\pi$
$29$	31.8434	+	20.4645i	0.203903	+	0.131040i	−0.434705	+	0.900573i	$0.643147\pi$
$30$	−2.32123	+	5.08278i	−0.0141266	+	0.0309328i
$31$	−12.2652	+	14.1548i	−0.0710610	+	0.0820088i	−0.790167	−	0.612892i	$-0.790006\pi$
$31$	−12.2652	+	14.1548i	−0.0710610	+	0.0820088i	0.719106	+	0.694901i	$0.244552\pi$
$32$	−4.55407	+	31.6743i	−0.0251579	+	0.174977i
$33$	−33.7439	−	73.8888i	−0.178002	−	0.389769i
$34$	97.8367	+	28.7274i	0.493496	+	0.144903i
$35$	50.9034	+	14.9466i	0.245836	+	0.0721838i
$36$	−39.9633	−	87.5074i	−0.185015	−	0.405127i
$37$	29.8058	−	207.304i	0.132434	−	0.921095i	−0.809935	−	0.586519i	$-0.800498\pi$
$37$	29.8058	−	207.304i	0.132434	−	0.921095i	0.942369	−	0.334576i	$-0.108593\pi$
$38$	191.702	−	221.236i	0.818374	−	0.944454i
$39$	−13.9680	+	30.5856i	−0.0573503	+	0.125580i
$40$	−10.9478	−	7.03574i	−0.0432751	−	0.0278112i
$41$	16.1193	+	112.112i	0.0614003	+	0.427048i	0.997217	+	0.0745601i	$0.0237553\pi$
$41$	16.1193	+	112.112i	0.0614003	+	0.427048i	−0.935816	+	0.352488i	$0.885336\pi$
$42$	94.2423	−	60.5659i	0.346236	−	0.222512i
$43$	133.101	+	153.607i	0.472041	+	0.544764i	0.940978	−	0.338467i	$-0.109908\pi$
$43$	133.101	+	153.607i	0.472041	+	0.544764i	−0.468937	+	0.883231i	$0.655363\pi$
$44$	181.518	−	53.2985i	0.621929	−	0.182615i
$45$	39.1228			0.129602
$46$	−217.039	−	39.5258i	−0.695665	−	0.126690i
$47$	105.031			0.325966			0.162983	−	0.986629i	$-0.447888\pi$
$47$	105.031			0.325966			0.162983	+	0.986629i	$0.447888\pi$
$48$	−26.3668	+	7.74198i	−0.0792857	+	0.0232804i
$49$	−471.908	−	544.611i	−1.37583	−	1.58779i
$50$	−205.861	+	132.299i	−0.582263	+	0.374198i
$51$	12.4616	+	86.6726i	0.0342152	+	0.237972i
$52$	−65.8783	−	42.3374i	−0.175686	−	0.112907i
$53$	−179.403	+	392.838i	−0.464961	+	1.01812i	0.521368	+	0.853332i	$0.325422\pi$
$53$	−179.403	+	392.838i	−0.464961	+	1.01812i	−0.986329	+	0.164790i	$0.947305\pi$
$54$	114.834	−	132.526i	0.289388	−	0.333972i
$55$	−10.9491	+	76.1527i	−0.0268432	+	0.186699i
$56$	108.384	+	237.328i	0.258633	+	0.566328i
$57$	241.204	+	70.8240i	0.560496	+	0.164577i
$58$	−72.6382	−	21.3285i	−0.164446	−	0.0482857i
$59$	335.938	+	735.601i	0.741277	+	1.62317i	0.781442	+	0.623978i	$0.214485\pi$
$59$	335.938	+	735.601i	0.741277	+	1.62317i	−0.0401644	+	0.999193i	$0.512788\pi$
$60$	1.59044	−	11.0617i	0.00342207	−	0.0238010i
$61$	−62.6333	+	72.2826i	−0.131465	+	0.151719i	−0.817665	−	0.575694i	$-0.804732\pi$
$61$	−62.6333	+	72.2826i	−0.131465	+	0.151719i	0.686200	+	0.727413i	$0.259277\pi$
$62$	15.5610	−	34.0738i	0.0318750	−	0.0697964i
$63$	−659.842	−	424.055i	−1.31956	−	0.848030i
$64$	−9.10815	−	63.3486i	−0.0177894	−	0.123728i
$65$	26.7913	−	17.2177i	0.0511238	−	0.0328553i
$66$	106.388	+	122.778i	0.198416	+	0.228984i
$67$	360.939	−	105.981i	0.658145	−	0.193249i	0.0644276	−	0.997922i	$-0.479478\pi$
$67$	360.939	−	105.981i	0.658145	−	0.193249i	0.593718	+	0.804674i	$0.297660\pi$
$68$	−203.934			−0.363686
$69$	−46.5502	−	183.638i	−0.0812171	−	0.320398i
$70$	−106.105			−0.181171
$71$	−607.699	+	178.437i	−1.01578	+	0.298261i	−0.746918	−	0.664916i	$-0.768467\pi$
$71$	−607.699	+	178.437i	−1.01578	+	0.298261i	−0.268866	+	0.963178i	$0.586649\pi$
$72$	125.996	+	145.408i	0.206234	+	0.238006i
$73$	62.1324	−	39.9300i	0.0996170	−	0.0640200i	−0.489884	−	0.871788i	$-0.662961\pi$
$73$	62.1324	−	39.9300i	0.0996170	−	0.0640200i	0.589501	+	0.807768i	$0.299324\pi$
$74$	59.6116	+	414.608i	0.0936446	+	0.651313i
$75$	−176.783	−	113.611i	−0.272174	−	0.174916i
$76$	−243.215	+	532.567i	−0.367088	+	0.803811i
$77$	1010.09	−	1165.71i	1.49494	−	1.72526i
$78$	9.57042	−	66.5637i	0.0138928	−	0.0966264i
$79$	521.624	+	1142.20i	0.742877	+	1.62667i	0.778764	+	0.627317i	$0.215847\pi$
$79$	521.624	+	1142.20i	0.742877	+	1.62667i	−0.0358875	+	0.999356i	$0.511426\pi$
$80$	24.9731	+	7.33277i	0.0349010	+	0.0102479i
$81$	−478.565	−	140.519i	−0.656468	−	0.192756i
$82$	−94.1040	−	206.059i	−0.126732	−	0.277505i
$83$	74.1514	−	515.734i	0.0980623	−	0.682039i	−0.880190	−	0.474621i	$-0.842585\pi$
$83$	74.1514	−	515.734i	0.0980623	−	0.682039i	0.978253	−	0.207417i	$-0.0665058\pi$
$84$	−146.723	+	169.327i	−0.190581	+	0.219942i
$85$	34.4527	−	75.4408i	0.0439637	−	0.0962671i
$86$	−341.972	−	219.772i	−0.428788	−	0.275565i
$87$	−9.25205	−	64.3495i	−0.0114014	−	0.0792987i
$88$	−318.299	+	204.558i	−0.385577	+	0.247795i
$89$	84.5663	+	97.5947i	0.100719	+	0.116236i	0.803871	−	0.594803i	$-0.202770\pi$
$89$	84.5663	+	97.5947i	0.100719	+	0.116236i	−0.703152	+	0.711040i	$0.748225\pi$
$90$	−75.0761	+	22.0443i	−0.0879302	+	0.0258186i
$91$	−638.484			−0.735509
$92$	438.765	−	46.4442i	0.497222	−	0.0526320i
$93$	32.1677			0.0358670
$94$	−201.554	+	59.1815i	−0.221156	+	0.0649373i
$95$	−155.922	−	179.944i	−0.168393	−	0.194335i
$96$	46.2351	−	29.7135i	0.0491547	−	0.0315898i
$97$	−160.779	−	1118.24i	−0.168295	−	1.17052i	−0.882408	−	0.470486i	$-0.844079\pi$
$97$	−160.779	−	1118.24i	−0.168295	−	1.17052i	0.714113	−	0.700031i	$-0.246830\pi$
$98$	1212.46	+	779.198i	1.24976	+	0.803172i
$99$	472.519	−	1034.67i	0.479696	−	1.05039i
$100$	320.499	−	369.875i	0.320499	−	0.369875i
$101$	−111.116	+	772.828i	−0.109470	+	0.761379i	0.858951	+	0.512058i	$0.171117\pi$
$101$	−111.116	+	772.828i	−0.109470	+	0.761379i	−0.968421	+	0.249321i	$0.919792\pi$
$102$	−72.7507	−	159.302i	−0.0706215	−	0.154639i
$103$	1690.30	+	496.317i	1.61699	+	0.474792i	0.960208	−	0.279285i	$-0.0900973\pi$
$103$	1690.30	+	496.317i	1.61699	+	0.474792i	0.656786	+	0.754077i	$0.271915\pi$
$104$	150.275	+	44.1248i	0.141689	+	0.0416038i
$105$	−37.8514	−	82.8830i	−0.0351802	−	0.0770339i
$106$	122.922	−	854.939i	0.112634	−	0.783387i
$107$	1025.30	−	1183.26i	0.926352	−	1.06907i	−0.0710816	−	0.997471i	$-0.522645\pi$
$107$	1025.30	−	1183.26i	0.926352	−	1.06907i	0.997434	−	0.0715968i	$-0.0228095\pi$
$108$	−145.692	+	319.020i	−0.129807	+	0.284238i
$109$	311.025	+	199.884i	0.273310	+	0.175646i	0.670115	−	0.742257i	$-0.266245\pi$
$109$	311.025	+	199.884i	0.273310	+	0.175646i	−0.396805	+	0.917903i	$0.629881\pi$
$110$	−21.8982	−	152.305i	−0.0189810	−	0.132016i
$111$	−302.602	+	194.471i	−0.258754	+	0.166291i
$112$	−341.714	−	394.359i	−0.288294	−	0.332709i
$113$	−1320.33	+	387.685i	−1.09917	+	0.322746i	−0.780523	−	0.625127i	$-0.785047\pi$
$113$	−1320.33	+	387.685i	−1.09917	+	0.322746i	−0.318649	+	0.947873i	$0.603229\pi$
$114$	−502.775			−0.413063
$115$	−56.9441	+	170.158i	−0.0461745	+	0.137976i
$116$	151.409			0.121190
$117$	−451.769	+	132.651i	−0.356975	+	0.104817i
$118$	−1059.15	−	1222.32i	−0.826290	−	0.953590i
$119$	−1398.78	+	898.944i	−1.07753	+	0.692488i
$120$	3.18087	+	22.1234i	0.00241977	+	0.0168299i
$121$	762.044	+	489.736i	0.572535	+	0.367946i
$122$	79.4636	−	174.001i	0.0589696	−	0.129125i
$123$	127.391	−	147.017i	0.0933861	−	0.107773i
$124$	−10.6619	+	74.1552i	−0.00772152	+	0.0537043i
$125$	167.152	+	366.012i	0.119604	+	0.261897i
$126$	1505.17	+	441.957i	1.06421	+	0.312482i
$127$	507.961	+	149.151i	0.354915	+	0.104212i	0.454330	−	0.890834i	$-0.349879\pi$
$127$	507.961	+	149.151i	0.354915	+	0.104212i	−0.0994145	+	0.995046i	$0.531697\pi$
$128$	53.1731	+	116.433i	0.0367178	+	0.0804009i
$129$	49.6796	−	345.529i	0.0339074	−	0.235831i
$130$	−41.7105	+	48.1365i	−0.0281404	+	0.0324758i
$131$	−114.479	+	250.674i	−0.0763518	+	0.167187i	−0.943959	−	0.330064i	$-0.892930\pi$
$131$	−114.479	+	250.674i	−0.0763518	+	0.167187i	0.867607	+	0.497251i	$0.165657\pi$
$132$	−273.338	−	175.663i	−0.180235	−	0.115830i
$133$	679.349	+	4724.97i	0.442910	+	3.08051i
$134$	−632.920	+	406.753i	−0.408030	+	0.262225i
$135$	−93.4012	−	107.791i	−0.0595459	−	0.0687196i
$136$	391.347	−	114.910i	0.246748	−	0.0724517i
$137$	−2834.77			−1.76781			−0.883907	−	0.467662i	$-0.845096\pi$
$137$	−2834.77			−1.76781			−0.883907	+	0.467662i	$0.845096\pi$
$138$	192.803	+	326.170i	0.118931	+	0.201199i
$139$	−3161.97			−1.92946			−0.964728	−	0.263247i	$-0.915206\pi$
$139$	−3161.97			−1.92946			−0.964728	+	0.263247i	$0.915206\pi$
$140$	203.614	−	59.7863i	0.122918	−	0.0360919i
$141$	−118.131	−	136.330i	−0.0705560	−	0.0814260i
$142$	1065.62	−	684.835i	0.629755	−	0.404719i
$143$	−131.772	−	916.496i	−0.0770583	−	0.535953i
$144$	−323.717	−	208.040i	−0.187336	−	0.120394i
$145$	−25.5792	+	56.0105i	−0.0146499	+	0.0320788i
$146$	−96.7319	+	111.635i	−0.0548328	+	0.0632805i
$147$	−176.138	+	1225.07i	−0.0988275	+	0.687360i
$148$	−348.011	−	762.037i	−0.193286	−	0.423237i
$149$	1791.00	+	525.884i	0.984726	+	0.289142i	0.734174	−	0.678961i	$-0.237570\pi$
$149$	1791.00	+	525.884i	0.984726	+	0.289142i	0.250552	+	0.968103i	$0.419388\pi$
$150$	403.259	+	118.408i	0.219506	+	0.0644529i
$151$	−520.022	−	1138.69i	−0.280257	−	0.613677i	0.716189	−	0.697906i	$-0.245885\pi$
$151$	−520.022	−	1138.69i	−0.280257	−	0.613677i	−0.996446	+	0.0842286i	$0.973157\pi$
$152$	166.644	−	1159.03i	0.0889249	−	0.618486i
$153$	−802.967	+	926.674i	−0.424288	+	0.489654i
$154$	−1281.52	+	2806.13i	−0.670568	+	1.46834i
$155$	−25.6308	−	16.4719i	−0.0132821	−	0.00853586i
$156$	19.1408	+	133.127i	0.00982367	+	0.0683252i
$157$	1733.44	−	1114.01i	0.881168	−	0.566292i	−0.0199817	−	0.999800i	$-0.506361\pi$
$157$	1733.44	−	1114.01i	0.881168	−	0.566292i	0.901150	+	0.433508i	$0.142724\pi$
$158$	−1644.58	−	1897.94i	−0.828073	−	0.955647i
$159$	711.680	−	208.968i	0.354968	−	0.104228i
$160$	−52.0548			−0.0257206
$161$	2804.77	−	2252.64i	1.37296	−	1.10269i
$162$	997.538			0.483790
$163$	1283.79	−	376.954i	0.616896	−	0.181137i	0.0416696	−	0.999131i	$-0.486732\pi$
$163$	1283.79	−	376.954i	0.616896	−	0.181137i	0.575226	+	0.817995i	$0.304914\pi$
$164$	296.691	+	342.400i	0.141266	+	0.163030i
$165$	111.160	−	71.4385i	0.0524475	−	0.0337059i
$166$	148.303	+	1031.47i	0.0693406	+	0.482274i
$167$	−1568.99	−	1008.33i	−0.727020	−	0.467227i	0.124053	−	0.992276i	$-0.460411\pi$
$167$	−1568.99	−	1008.33i	−0.727020	−	0.467227i	−0.851072	+	0.525049i	$0.824047\pi$
$168$	186.149	−	407.610i	0.0854864	−	0.187189i
$169$	1187.74	−	1370.72i	0.540618	−	0.623906i
$170$	−23.6059	+	164.183i	−0.0106499	+	0.0740720i
$171$	1462.34	+	3202.09i	0.653966	+	1.43199i
$172$	780.073	+	229.050i	0.345814	+	0.101540i
$173$	−2576.33	−	756.480i	−1.13223	−	0.332452i	−0.338644	−	0.940915i	$-0.609968\pi$
$173$	−2576.33	−	756.480i	−1.13223	−	0.332452i	−0.793582	+	0.608463i	$0.791786\pi$
$174$	54.0132	+	118.272i	0.0235329	+	0.0515300i
$175$	567.887	−	3949.74i	0.245304	−	1.70613i
$176$	495.549	−	571.894i	0.212235	−	0.244933i
$177$	576.971	−	1263.39i	0.245016	−	0.536509i
$178$	−217.273	−	139.633i	−0.0914903	−	0.0587973i
$179$	−270.465	−	1881.12i	−0.112936	−	0.785485i	−0.965038	−	0.262110i	$-0.915582\pi$
$179$	−270.465	−	1881.12i	−0.112936	−	0.785485i	0.852102	−	0.523375i	$-0.175327\pi$
$180$	131.649	−	84.6055i	0.0545140	−	0.0350340i
$181$	1267.40	+	1462.66i	0.520472	+	0.600657i	0.953749	−	0.300604i	$-0.0971883\pi$
$181$	1267.40	+	1462.66i	0.520472	+	0.600657i	−0.433277	+	0.901261i	$0.642643\pi$
$182$	1225.24	−	359.763i	0.499016	−	0.146524i
$183$	164.267			0.0663551
$184$	−815.815	+	336.355i	−0.326862	+	0.134763i
$185$	340.691			0.135395
$186$	−61.7294	+	18.1254i	−0.0243345	+	0.00714525i
$187$	−1579.05	−	1822.32i	−0.617496	−	0.712628i
$188$	353.432	−	227.137i	0.137110	−	0.0881152i
$189$	406.946	+	2830.37i	0.156619	+	1.08931i
$190$	400.605	+	257.453i	0.152963	+	0.0983032i
$191$	853.816	−	1869.60i	0.323455	−	0.708268i	−0.676138	−	0.736775i	$-0.736348\pi$
$191$	853.816	−	1869.60i	0.323455	−	0.708268i	0.999594	+	0.0285066i	$0.00907515\pi$
$192$	−71.9820	+	83.0716i	−0.0270565	+	0.0312249i
$193$	−428.140	+	2977.78i	−0.159680	+	1.11060i	0.739544	+	0.673109i	$0.235041\pi$
$193$	−428.140	+	2977.78i	−0.159680	+	1.11060i	−0.899224	+	0.437489i	$0.855868\pi$
$194$	938.621	+	2055.29i	0.347366	+	0.760626i
$195$	−52.4812	−	15.4099i	−0.0192731	−	0.00565909i
$196$	−2765.73	−	812.093i	−1.00792	−	0.295952i
$197$	461.599	+	1010.76i	0.166942	+	0.365552i	0.974551	−	0.224167i	$-0.0719660\pi$
$197$	461.599	+	1010.76i	0.166942	+	0.365552i	−0.807609	+	0.589718i	$0.799239\pi$
$198$	−323.755	+	2251.77i	−0.116203	+	0.808213i
$199$	2269.10	−	2618.69i	0.808304	−	0.932833i	−0.190502	−	0.981687i	$-0.561011\pi$
$199$	2269.10	−	2618.69i	0.808304	−	0.932833i	0.998806	+	0.0488539i	$0.0155569\pi$
$200$	−406.621	+	890.375i	−0.143762	+	0.314795i
$201$	−543.518	−	349.298i	−0.190730	−	0.122575i
$202$	−222.232	−	1545.66i	−0.0774068	−	0.538376i
$203$	1038.52	−	667.415i	0.359062	−	0.230755i
$204$	229.368	+	264.705i	0.0787206	+	0.0908484i
$205$	−176.786	+	51.9091i	−0.0602307	+	0.0176853i
$206$	−3523.32			−1.19166
$207$	1516.55	−	2176.61i	0.509214	−	0.730845i
$208$	−313.239			−0.104419
$209$	−6642.14	+	1950.31i	−2.19831	+	0.645482i
$210$	119.338	+	137.723i	0.0392148	+	0.0452563i
$211$	−1818.08	+	1168.41i	−0.593183	+	0.381215i	−0.802517	−	0.596629i	$-0.796507\pi$
$211$	−1818.08	+	1168.41i	−0.593183	+	0.381215i	0.209335	+	0.977844i	$0.432870\pi$
$212$	245.843	+	1709.88i	0.0796443	+	0.553938i
$213$	915.101	+	588.099i	0.294374	+	0.189183i
$214$	−1300.81	+	2848.38i	−0.415522	+	0.909867i
$215$	−216.518	+	249.875i	−0.0686808	+	0.0792619i
$216$	99.8235	−	694.288i	0.0314450	−	0.218705i
$217$	253.747	+	555.629i	0.0793801	+	0.173818i
$218$	−709.480	−	208.322i	−0.220422	−	0.0647218i
$219$	−121.710	−	35.7374i	−0.0375545	−	0.0110270i
$220$	127.841	+	279.933i	0.0391775	+	0.0857868i
$221$	−142.048	+	987.967i	−0.0432362	+	0.300714i
$222$	471.112	−	543.692i	0.142428	−	0.164370i
$223$	−1801.86	+	3945.52i	−0.541082	+	1.18481i	0.419741	+	0.907644i	$0.362121\pi$
$223$	−1801.86	+	3945.52i	−0.541082	+	1.18481i	−0.960823	+	0.277161i	$0.910606\pi$
$224$	877.952	+	564.226i	0.261878	+	0.168299i
$225$	−418.781	−	2912.68i	−0.124083	−	0.863017i
$226$	2315.25	−	1487.92i	0.681453	−	0.437943i
$227$	291.779	+	336.731i	0.0853130	+	0.0984565i	0.796801	−	0.604242i	$-0.206524\pi$
$227$	291.779	+	336.731i	0.0853130	+	0.0984565i	−0.711488	+	0.702698i	$0.751978\pi$
$228$	964.817	−	283.296i	0.280248	−	0.0822883i
$229$	4629.74			1.33599			0.667995	−	0.744166i	$-0.267153\pi$
$229$	4629.74			1.33599			0.667995	+	0.744166i	$0.267153\pi$
$230$	13.3971	−	358.616i	0.00384077	−	0.102811i
$231$	−2649.15			−0.754551
$232$	−290.553	+	85.3140i	−0.0822229	+	0.0241428i
$233$	−1860.90	−	2147.60i	−0.523226	−	0.603836i	0.431209	−	0.902252i	$-0.358087\pi$
$233$	−1860.90	−	2147.60i	−0.523226	−	0.603836i	−0.954436	+	0.298416i	$0.903542\pi$
$234$	792.194	−	509.112i	0.221313	−	0.142230i
$235$	24.3153	+	169.117i	0.00674960	+	0.0469445i
$236$	2721.22	+	1748.82i	0.750577	+	0.482367i
$237$	895.885	−	1961.71i	0.245544	−	0.537667i
$238$	2177.72	−	2513.23i	0.593113	−	0.684489i
$239$	−812.554	+	5651.43i	−0.219915	+	1.52954i	0.518430	+	0.855120i	$0.326517\pi$
$239$	−812.554	+	5651.43i	−0.219915	+	1.52954i	−0.738345	+	0.674423i	$0.764392\pi$
$240$	−18.5698	−	40.6623i	−0.00499449	−	0.0109364i
$241$	−3726.11	−	1094.08i	−0.995932	−	0.292432i	−0.257146	−	0.966373i	$-0.582782\pi$
$241$	−3726.11	−	1094.08i	−0.995932	−	0.292432i	−0.738786	+	0.673941i	$0.764600\pi$
$242$	−1738.30	−	510.411i	−0.461745	−	0.135580i
$243$	1339.28	+	2932.61i	0.353558	+	0.774184i
$244$	−54.4460	+	378.680i	−0.0142850	+	0.0993546i
$245$	767.659	−	885.926i	0.200179	−	0.231019i
$246$	−161.623	+	353.905i	−0.0418890	+	0.0917242i
$247$	2410.63	+	1549.22i	0.620992	+	0.399087i
$248$	−21.3238	−	148.310i	−0.00545994	−	0.0379747i
$249$	−752.820	+	483.808i	−0.191598	+	0.123133i
$250$	−526.997	−	608.187i	−0.133321	−	0.153861i
$251$	−813.948	+	238.997i	−0.204685	+	0.0601010i	−0.382468	−	0.923969i	$-0.624926\pi$
$251$	−813.948	+	238.997i	−0.204685	+	0.0601010i	0.177783	+	0.984070i	$0.443108\pi$
$252$	−3137.42			−0.784282
$253$	3812.36	+	3561.12i	0.947355	+	0.884925i
$254$	−1058.81			−0.261558
$255$	−136.671	+	40.1303i	−0.0335635	+	0.00985513i
$256$	−167.644	−	193.472i	−0.0409288	−	0.0472343i
$257$	4438.57	−	2852.50i	1.07732	−	0.692350i	0.123381	−	0.992359i	$-0.460626\pi$
$257$	4438.57	−	2852.50i	1.07732	−	0.692350i	0.953936	+	0.300010i	$0.0969899\pi$
$258$	99.3593	+	691.059i	0.0239761	+	0.166758i
$259$	−5746.08	−	3692.78i	−1.37855	−	0.885939i
$260$	52.9187	−	115.876i	0.0126226	−	0.0276396i
$261$	596.158	−	688.002i	0.141384	−	0.163166i
$262$	78.4376	−	545.546i	0.0184958	−	0.128641i
$263$	−846.091	−	1852.68i	−0.198373	−	0.434377i	0.784136	−	0.620589i	$-0.213106\pi$
$263$	−846.091	−	1852.68i	−0.198373	−	0.434377i	−0.982510	+	0.186212i	$0.940379\pi$
$264$	623.512	+	183.079i	0.145358	+	0.0426809i
$265$	−674.063	−	197.923i	−0.156254	−	0.0458804i
$266$	−3966.02	−	8684.37i	−0.914181	−	2.00178i
$267$	31.5641	−	219.533i	0.00723480	−	0.0503191i
$268$	985.374	−	1137.18i	0.224594	−	0.259196i
$269$	−643.299	+	1408.63i	−0.145809	+	0.319277i	−0.968419	−	0.249329i	$-0.919790\pi$
$269$	−643.299	+	1408.63i	−0.145809	+	0.319277i	0.822610	+	0.568606i	$0.192517\pi$
$270$	239.972	+	154.221i	0.0540897	+	0.0347613i
$271$	834.718	+	5805.59i	0.187105	+	1.30135i	0.839456	+	0.543428i	$0.182874\pi$
$271$	834.718	+	5805.59i	0.187105	+	1.30135i	−0.652351	+	0.757917i	$0.726217\pi$
$272$	−686.241	+	441.020i	−0.152976	+	0.0983117i
$273$	718.115	+	828.748i	0.159202	+	0.183729i
$274$	5439.88	−	1597.29i	1.19940	−	0.352175i
$275$	5786.76			1.26893
$276$	−553.772	−	517.278i	−0.120772	−	0.112813i
$277$	−3843.04			−0.833595			−0.416798	−	0.908999i	$-0.636848\pi$
$277$	−3843.04			−0.833595			−0.416798	+	0.908999i	$0.636848\pi$
$278$	6067.77	−	1781.66i	1.30907	−	0.384377i
$279$	294.980	+	340.425i	0.0632975	+	0.0730492i
$280$	−357.044	+	229.458i	−0.0762052	+	0.0489741i
$281$	−584.795	−	4067.34i	−0.124149	−	0.863477i	−0.952776	−	0.303675i	$-0.901786\pi$
$281$	−584.795	−	4067.34i	−0.124149	−	0.863477i	0.828626	−	0.559802i	$-0.189123\pi$
$282$	303.508	+	195.053i	0.0640910	+	0.0411888i
$283$	525.746	−	1151.22i	0.110432	−	0.241813i	−0.846345	−	0.532636i	$-0.821202\pi$
$283$	525.746	−	1151.22i	0.110432	−	0.241813i	0.956777	+	0.290822i	$0.0939289\pi$
$284$	−1659.04	+	1914.63i	−0.346640	+	0.400044i
$285$	−58.1975	+	404.773i	−0.0120959	+	0.0841286i
$286$	769.282	+	1684.49i	0.159051	+	0.348273i
$287$	3544.31	+	1040.70i	0.728969	+	0.214045i
$288$	738.433	+	216.823i	0.151085	+	0.0443626i
$289$	−961.138	−	2104.60i	−0.195632	−	0.428373i
$290$	17.5261	−	121.896i	0.00354885	−	0.0246828i
$291$	−1270.64	+	1466.40i	−0.255966	+	0.295401i
$292$	122.725	−	268.730i	0.0245957	−	0.0538570i
$293$	−4290.75	−	2757.50i	−0.855524	−	0.549812i	0.0377694	−	0.999286i	$-0.487975\pi$
$293$	−4290.75	−	2757.50i	−0.855524	−	0.549812i	−0.893293	+	0.449475i	$0.851611\pi$
$294$	−352.277	−	2450.14i	−0.0698816	−	0.486037i
$295$	−1106.66	+	711.208i	−0.218414	+	0.140366i
$296$	1097.21	+	1266.25i	0.215453	+	0.248646i
$297$	−3978.80	+	1168.28i	−0.777351	+	0.228251i
$298$	−3733.22			−0.725703
$299$	80.6167	−	2157.97i	0.0155926	−	0.417386i
$300$	−840.567			−0.161767
$301$	6360.18	−	1867.52i	1.21792	−	0.357614i
$302$	1639.53	+	1892.12i	0.312398	+	0.360527i
$303$	1128.10	−	724.986i	0.213887	−	0.137457i
$304$	333.287	+	2318.06i	0.0628794	+	0.437336i
$305$	−130.886	−	84.1154i	−0.0245722	−	0.0157916i
$306$	1018.73	−	2230.72i	0.190318	−	0.416737i
$307$	−3251.79	+	3752.77i	−0.604526	+	0.697660i	−0.972692	−	0.232100i	$-0.925440\pi$
$307$	−3251.79	+	3752.77i	−0.604526	+	0.697660i	0.368166	+	0.929760i	$0.379986\pi$
$308$	878.056	−	6107.01i	0.162441	−	1.12980i
$309$	−1256.90	−	2752.22i	−0.231399	−	0.506694i
$310$	58.4666	+	17.1673i	0.0107119	+	0.00314529i
$311$	3799.90	+	1115.75i	0.692838	+	0.203436i	0.609148	−	0.793056i	$-0.291511\pi$
$311$	3799.90	+	1115.75i	0.692838	+	0.203436i	0.0836898	+	0.996492i	$0.473330\pi$
$312$	−111.744	−	244.684i	−0.0202764	−	0.0443991i
$313$	270.221	−	1879.43i	0.0487981	−	0.339398i	−0.950767	−	0.309907i	$-0.899702\pi$
$313$	270.221	−	1879.43i	0.0487981	−	0.339398i	0.999565	−	0.0294914i	$-0.00938878\pi$
$314$	−2698.73	+	3114.51i	−0.485027	+	0.559751i
$315$	530.037	−	1160.62i	0.0948070	−	0.207598i
$316$	4225.34	+	2715.46i	0.752197	+	0.483407i
$317$	1436.21	+	9989.08i	0.254466	+	1.76985i	0.570690	+	0.821165i	$0.306676\pi$
$317$	1436.21	+	9989.08i	0.254466	+	1.76985i	−0.316224	+	0.948684i	$0.602415\pi$
$318$	−1247.96	+	802.014i	−0.220069	+	0.141430i
$319$	1172.36	+	1352.97i	0.205766	+	0.237467i
$320$	99.8925	−	29.3311i	0.0174505	−	0.00512393i
$321$	−2689.04			−0.467563
$322$	−4113.02	+	5903.18i	−0.711831	+	1.02165i
$323$	7462.40			1.28551
$324$	−1914.26	+	562.078i	−0.328234	+	0.0963782i
$325$	−1568.64	−	1810.30i	−0.267730	−	0.308977i
$326$	−2251.17	+	1446.74i	−0.382456	+	0.245790i
$327$	−90.3678	−	628.522i	−0.0152824	−	0.106292i
$328$	−762.277	−	489.886i	−0.128322	−	0.0824677i
$329$	1422.97	−	3115.86i	0.238452	−	0.522137i
$330$	−173.062	+	199.725i	−0.0288690	+	0.0333166i
$331$	605.997	−	4214.80i	0.100630	−	0.699899i	−0.875580	−	0.483073i	$-0.839521\pi$
$331$	605.997	−	4214.80i	0.100630	−	0.699899i	0.976210	−	0.216826i	$-0.0695703\pi$
$332$	−865.788	−	1895.81i	−0.143121	−	0.313392i
$333$	−4832.94	−	1419.08i	−0.795325	−	0.233529i
$334$	3579.03	+	1050.90i	0.586335	+	0.172164i
$335$	254.206	+	556.633i	0.0414589	+	0.0907824i
$336$	−127.544	+	887.086i	−0.0207086	+	0.144031i
$337$	3032.77	−	3500.00i	0.490224	−	0.565749i	−0.455701	−	0.890133i	$-0.650612\pi$
$337$	3032.77	−	3500.00i	0.490224	−	0.565749i	0.945926	+	0.324384i	$0.105157\pi$
$338$	−1506.90	+	3299.64i	−0.242498	+	0.530997i
$339$	1988.22	+	1277.75i	0.318540	+	0.204713i
$340$	−47.2118	−	328.366i	−0.00753065	−	0.0523768i
$341$	−745.195	+	478.908i	−0.118342	+	0.0760537i
$342$	−4610.48	−	5320.78i	−0.728966	−	0.841272i
$343$	−11816.7	+	3469.69i	−1.86018	+	0.546197i
$344$	−1626.01			−0.254851
$345$	284.910	−	117.466i	0.0444609	−	0.0183309i
$346$	5370.20			0.834404
$347$	−6474.83	+	1901.18i	−1.00169	+	0.294123i	−0.741150	−	0.671339i	$-0.765719\pi$
$347$	−6474.83	+	1901.18i	−1.00169	+	0.294123i	−0.260542	+	0.965463i	$0.583901\pi$
$348$	−170.293	−	196.529i	−0.0262318	−	0.0302731i
$349$	−1147.25	+	737.296i	−0.175963	+	0.113085i	−0.625658	−	0.780098i	$-0.715169\pi$
$349$	−1147.25	+	737.296i	−0.175963	+	0.113085i	0.449694	+	0.893182i	$0.351533\pi$
$350$	1135.77	+	7899.48i	0.173456	+	1.20641i
$351$	1444.03	+	928.020i	0.219591	+	0.141123i
$352$	−628.709	+	1376.68i	−0.0951998	+	0.208458i
$353$	−5190.94	+	5990.67i	−0.782680	+	0.903261i	−0.997300	−	0.0734367i	$-0.976603\pi$
$353$	−5190.94	+	5990.67i	−0.782680	+	0.903261i	0.214620	+	0.976698i	$0.431149\pi$
$354$	−395.323	+	2749.53i	−0.0593536	+	0.412813i
$355$	−427.996	−	937.181i	−0.0639879	−	0.140114i
$356$	495.622	+	145.528i	0.0737862	+	0.0216656i
$357$	2740.06	+	804.555i	0.406217	+	0.119276i
$358$	1578.97	+	3457.45i	0.233103	+	0.510425i
$359$	−602.794	+	4192.52i	−0.0886190	+	0.616359i	0.896314	+	0.443421i	$0.146235\pi$
$359$	−602.794	+	4192.52i	−0.0886190	+	0.616359i	−0.984933	+	0.172938i	$0.944674\pi$
$360$	−204.960	+	236.536i	−0.0300065	+	0.0346293i
$361$	6050.44	−	13248.6i	0.882118	−	1.93157i
$362$	−3256.29	−	2092.69i	−0.472781	−	0.303838i
$363$	−221.410	−	1539.94i	−0.0320139	−	0.222661i
$364$	−2148.51	+	1380.76i	−0.309375	+	0.198823i
$365$	78.6775	+	90.7987i	0.0112827	+	0.0130209i
$366$	−315.226	+	92.5589i	−0.0450195	+	0.0132189i
$367$	−2804.27			−0.398861			−0.199430	−	0.979912i	$-0.563909\pi$
$367$	−2804.27			−0.398861			−0.199430	+	0.979912i	$0.563909\pi$
$368$	1376.01	−	1105.14i	0.194917	−	0.156548i
$369$	2724.05			0.384304
$370$	−653.782	+	191.968i	−0.0918608	+	0.0269728i
$371$	9223.40	+	10644.4i	1.29071	+	1.48956i
$372$	108.245	−	69.5647i	0.0150866	−	0.00969559i
$373$	−667.928	−	4645.54i	−0.0927185	−	0.644872i	−0.982191	−	0.187883i	$-0.939837\pi$
$373$	−667.928	−	4645.54i	−0.0927185	−	0.644872i	0.889473	−	0.456988i	$-0.151072\pi$
$374$	4057.00	+	2607.27i	0.560915	+	0.360478i
$375$	287.082	−	628.623i	0.0395330	−	0.0865652i
$376$	−550.247	+	635.019i	−0.0754703	+	0.0870973i
$377$	105.463	−	733.509i	0.0144074	−	0.100206i
$378$	−2375.74	−	5202.14i	−0.323267	−	0.707856i
$379$	−6470.89	−	1900.02i	−0.877011	−	0.257514i	−0.187916	−	0.982185i	$-0.560173\pi$
$379$	−6470.89	−	1900.02i	−0.877011	−	0.257514i	−0.689095	+	0.724671i	$0.741992\pi$
$380$	−913.821	−	268.322i	−0.123363	−	0.0362227i
$381$	−377.716	−	827.083i	−0.0507900	−	0.111215i
$382$	−585.008	+	4068.82i	−0.0783551	+	0.544972i
$383$	−4397.05	+	5074.46i	−0.586628	+	0.677005i	−0.969016	−	0.246997i	$-0.920556\pi$
$383$	−4397.05	+	5074.46i	−0.586628	+	0.677005i	0.382388	+	0.924002i	$0.375102\pi$
$384$	91.3245	−	199.973i	0.0121364	−	0.0265750i
$385$	2110.81	+	1356.54i	0.279421	+	0.179573i
$386$	−856.281	−	5955.56i	−0.112911	−	0.785311i
$387$	4112.25	−	2642.78i	0.540148	−	0.347132i
$388$	−2959.29	−	3415.20i	−0.387204	−	0.446857i
$389$	8818.16	−	2589.25i	1.14935	−	0.337481i	0.349067	−	0.937098i	$-0.386499\pi$
$389$	8818.16	−	2589.25i	1.14935	−	0.337481i	0.800287	+	0.599617i	$0.204680\pi$
$390$	109.394			0.0142035
$391$	−2861.66	−	4841.16i	−0.370129	−	0.626158i
$392$	5764.99			0.742796
$393$	454.131	−	133.345i	0.0582897	−	0.0171154i
$394$	−1455.33	−	1679.54i	−0.186087	−	0.214756i
$395$	−1718.36	+	1104.32i	−0.218886	+	0.140669i
$396$	−647.511	−	4503.54i	−0.0821683	−	0.571493i
$397$	−7230.55	−	4646.79i	−0.914082	−	0.587445i	−0.00314742	−	0.999995i	$-0.501002\pi$
$397$	−7230.55	−	4646.79i	−0.914082	−	0.587445i	−0.910935	+	0.412550i	$0.864638\pi$
$398$	−2878.84	+	6303.78i	−0.362571	+	0.793920i
$399$	5368.91	−	6196.06i	0.673639	−	0.777421i
$400$	278.604	−	1937.73i	0.0348255	−	0.242217i
$401$	1946.73	+	4262.74i	0.242432	+	0.530851i	0.991262	−	0.131911i	$-0.0421113\pi$
$401$	1946.73	+	4262.74i	0.242432	+	0.530851i	−0.748830	+	0.662762i	$0.769384\pi$
$402$	1239.82	+	364.044i	0.153822	+	0.0451664i
$403$	351.822	+	103.304i	0.0434876	+	0.0127691i
$404$	1297.38	+	2840.87i	0.159770	+	0.349848i
$405$	115.468	−	803.095i	0.0141670	−	0.0985337i
$406$	−1616.84	+	1865.93i	−0.197641	+	0.228090i
$407$	4114.81	−	9010.19i	0.501140	−	1.09734i
$408$	−589.307	−	378.725i	−0.0715075	−	0.0459551i
$409$	−1707.03	−	11872.7i	−0.206375	−	1.43537i	−0.784858	−	0.619676i	$-0.787264\pi$
$409$	−1707.03	−	11872.7i	−0.206375	−	1.43537i	0.578483	−	0.815695i	$-0.303645\pi$
$410$	310.001	−	199.226i	0.0373412	−	0.0239977i
$411$	3188.32	+	3679.51i	0.382647	+	0.441599i
$412$	6761.21	−	1985.27i	0.808497	−	0.237396i
$413$	26373.7			3.14229
$414$	−1683.79	+	5031.41i	−0.199888	+	0.597295i
$415$	847.579			0.100255
$416$	601.101	−	176.499i	0.0708447	−	0.0208019i
$417$	3556.32	+	4104.21i	0.417635	+	0.481977i
$418$	11647.2	−	7485.23i	1.36288	−	0.875872i
$419$	−987.782	−	6870.18i	−0.115170	−	0.801027i	−0.962757	−	0.270369i	$-0.912854\pi$
$419$	−987.782	−	6870.18i	−0.115170	−	0.801027i	0.847586	−	0.530657i	$-0.178055\pi$
$420$	−306.610	−	197.046i	−0.0356216	−	0.0228926i
$421$	−4054.74	+	8878.64i	−0.469397	+	1.02784i	0.515848	+	0.856680i	$0.327477\pi$
$421$	−4054.74	+	8878.64i	−0.469397	+	1.02784i	−0.985244	+	0.171155i	$0.945250\pi$
$422$	2830.51	−	3266.58i	0.326509	−	0.376812i
$423$	359.491	−	2500.31i	0.0413216	−	0.287398i
$424$	−1435.23	−	3142.71i	−0.164389	−	0.359961i
$425$	−5985.34	−	1757.46i	−0.683134	−	0.200586i
$426$	−2087.44	−	612.927i	−0.237410	−	0.0697099i
$427$	1295.78	+	2837.37i	0.146856	+	0.321569i
$428$	891.278	−	6198.97i	0.100658	−	0.700090i
$429$	−1041.40	+	1201.84i	−0.117201	+	0.135257i
$430$	274.699	−	601.506i	0.0308073	−	0.0674586i
$431$	−2432.96	−	1563.57i	−0.271906	−	0.174744i	0.397581	−	0.917567i	$-0.369850\pi$
$431$	−2432.96	−	1563.57i	−0.271906	−	0.174744i	−0.669487	+	0.742823i	$0.733486\pi$
$432$	199.647	+	1388.58i	0.0222350	+	0.154648i
$433$	−11356.5	+	7298.36i	−1.26041	+	0.810016i	−0.988340	−	0.152261i	$-0.951344\pi$
$433$	−11356.5	+	7298.36i	−1.26041	+	0.810016i	−0.272070	+	0.962278i	$0.587708\pi$
$434$	−800.015	−	923.266i	−0.0884837	−	0.102116i
$435$	101.471	−	29.7945i	0.0111842	−	0.00328399i
$436$	1478.87			0.162442
$437$	−16055.4	+	1699.49i	−1.75751	+	0.186036i
$438$	253.697			0.0276761
$439$	−2054.26	+	603.185i	−0.223336	+	0.0655773i	−0.391486	−	0.920184i	$-0.628039\pi$
$439$	−2054.26	+	603.185i	−0.223336	+	0.0655773i	0.168150	+	0.985761i	$0.446221\pi$
$440$	−403.058	−	465.154i	−0.0436705	−	0.0503985i
$441$	−14579.9	+	9369.94i	−1.57433	+	1.01176i
$442$	−284.096	−	1975.93i	−0.0305726	−	0.212637i
$443$	4316.44	+	2774.01i	0.462935	+	0.297510i	0.751241	−	0.660028i	$-0.229456\pi$
$443$	4316.44	+	2774.01i	0.462935	+	0.297510i	−0.288306	+	0.957538i	$0.593092\pi$
$444$	−597.706	+	1308.79i	−0.0638871	+	0.139893i
$445$	−137.565	+	158.759i	−0.0146544	+	0.0169121i
$446$	1234.58	−	8586.68i	0.131074	−	0.911639i
$447$	−1331.77	−	2916.18i	−0.140919	−	0.308569i
$448$	−2002.70	−	588.046i	−0.211202	−	0.0620146i
$449$	6536.38	+	1919.25i	0.687018	+	0.201727i	0.606567	−	0.795032i	$-0.292546\pi$
$449$	6536.38	+	1919.25i	0.687018	+	0.201727i	0.0804502	+	0.996759i	$0.474364\pi$
$450$	2444.83	+	5353.43i	0.256112	+	0.560807i
$451$	−762.367	+	5302.38i	−0.0795974	+	0.553612i
$452$	−3604.55	+	4159.87i	−0.375096	+	0.432884i
$453$	−893.135	+	1955.69i	−0.0926338	+	0.202840i
$454$	−749.656	−	481.775i	−0.0774958	−	0.0498035i
$455$	−147.812	−	1028.06i	−0.0152298	−	0.105925i
$456$	−1691.84	+	1087.28i	−0.173745	+	0.111659i
$457$	9683.93	+	11175.8i	0.991236	+	1.14395i	0.989585	+	0.143949i	$0.0459801\pi$
$457$	9683.93	+	11175.8i	0.991236	+	1.14395i	0.00165102	+	0.999999i	$0.499474\pi$
$458$	−8884.41	+	2608.70i	−0.906421	+	0.266149i
$459$	4470.15			0.454573
$460$	176.359	+	695.728i	0.0178756	+	0.0705185i
$461$	−17270.1			−1.74479			−0.872395	−	0.488801i	$-0.837434\pi$
$461$	−17270.1			−1.74479			−0.872395	+	0.488801i	$0.837434\pi$
$462$	5083.68	−	1492.70i	0.511936	−	0.150318i
$463$	3115.99	+	3596.04i	0.312769	+	0.360955i	0.890268	−	0.455436i	$-0.150517\pi$
$463$	3115.99	+	3596.04i	0.312769	+	0.360955i	−0.577499	+	0.816391i	$0.695971\pi$
$464$	509.495	−	327.433i	0.0509757	−	0.0327601i
$465$	7.44699	+	51.7950i	0.000742680	+	0.00516545i
$466$	4781.14	+	3072.65i	0.475283	+	0.305446i
$467$	−4717.29	+	10329.4i	−0.467430	+	1.02353i	0.518300	+	0.855199i	$0.326565\pi$
$467$	−4717.29	+	10329.4i	−0.467430	+	1.02353i	−0.985731	+	0.168331i	$0.946162\pi$
$468$	−1233.34	+	1423.35i	−0.121819	+	0.140587i
$469$	1745.97	−	12143.5i	0.171900	−	1.19559i
$470$	−141.952	−	310.832i	−0.0139314	−	0.0305055i
$471$	−3395.61	−	997.041i	−0.332190	−	0.0975398i
$472$	−6207.38	−	1822.65i	−0.605334	−	0.177742i
$473$	3993.31	+	8744.13i	0.388188	+	0.850012i
$474$	−613.833	+	4269.30i	−0.0594816	+	0.413704i
$475$	−11727.8	+	13534.6i	−1.13286	+	1.30738i
$476$	−2762.91	+	6049.92i	−0.266045	+	0.582558i
$477$	8737.64	+	5615.34i	0.838719	+	0.539012i
$478$	−1625.11	−	11302.9i	−0.155503	−	1.08155i
$479$	14554.7	−	9353.72i	1.38835	−	0.892239i	0.388774	−	0.921333i	$-0.372899\pi$
$479$	14554.7	−	9353.72i	1.38835	−	0.892239i	0.999577	+	0.0290939i	$0.00926217\pi$
$480$	58.5470	+	67.5669i	0.00556728	+	0.00642498i
$481$	−3934.12	+	1155.16i	−0.372933	+	0.109503i
$482$	7766.82			0.733961
$483$	−6078.49	−	1106.98i	−0.572631	−	0.104284i
$484$	3623.37			0.340287
$485$	1763.32	−	517.757i	0.165089	−	0.0484745i
$486$	−4222.47	−	4873.00i	−0.394106	−	0.454822i
$487$	−870.906	+	559.697i	−0.0810360	+	0.0520787i	−0.580531	−	0.814238i	$-0.697155\pi$
$487$	−870.906	+	559.697i	−0.0810360	+	0.0520787i	0.499495	+	0.866317i	$0.333519\pi$
$488$	−108.892	−	757.361i	−0.0101010	−	0.0702543i
$489$	−1933.18	−	1242.38i	−0.178776	−	0.114893i
$490$	−973.939	+	2132.63i	−0.0897920	+	0.196617i
$491$	−3727.66	+	4301.95i	−0.342621	+	0.395406i	−0.900743	−	0.434353i	$-0.856977\pi$
$491$	−3727.66	+	4301.95i	−0.342621	+	0.395406i	0.558121	+	0.829759i	$0.311522\pi$
$492$	110.739	−	770.207i	0.0101474	−	0.0705765i
$493$	−801.687	−	1755.45i	−0.0732377	−	0.160368i
$494$	−5498.90	−	1614.62i	−0.500825	−	0.147055i
$495$	1775.37	+	521.296i	0.161206	+	0.0473344i
$496$	124.488	+	272.591i	0.0112695	+	0.0246768i
$497$	−2939.62	+	20445.5i	−0.265312	+	1.84528i
$498$	1172.04	−	1352.61i	0.105463	−	0.121711i
$499$	8697.80	−	19045.5i	0.780295	−	1.70861i	0.0777445	−	0.996973i	$-0.475228\pi$
$499$	8697.80	−	19045.5i	0.780295	−	1.70861i	0.702550	−	0.711634i	$-0.252045\pi$
$500$	1353.99	+	870.158i	0.121105	+	0.0778293i
$501$	455.868	+	3170.63i	0.0406520	+	0.282741i
$502$	1427.29	−	917.263i	0.126898	−	0.0815527i
$503$	−7576.78	−	8744.07i	−0.671634	−	0.775107i	0.312997	−	0.949754i	$-0.398667\pi$
$503$	−7576.78	−	8744.07i	−0.671634	−	0.775107i	−0.984631	+	0.174647i	$0.944122\pi$
$504$	6020.67	−	1767.83i	0.532107	−	0.156241i
$505$	−1270.10			−0.111918
$506$	−9322.43	−	4685.62i	−0.819037	−	0.411662i
$507$	−3115.06			−0.272869
$508$	2031.84	−	596.603i	0.177458	−	0.0521062i
$509$	−3703.55	−	4274.13i	−0.322509	−	0.372195i	0.571224	−	0.820794i	$-0.306469\pi$
$509$	−3703.55	−	4274.13i	−0.322509	−	0.372195i	−0.893733	+	0.448599i	$0.851923\pi$
$510$	239.658	−	154.019i	0.0208083	−	0.0133727i
$511$	−342.796	−	2384.20i	−0.0296759	−	0.206400i
$512$	430.722	+	276.808i	0.0371785	+	0.0238932i
$513$	5331.18	−	11673.7i	0.458825	−	1.00469i
$514$	−6910.27	+	7974.88i	−0.592994	+	0.684352i
$515$	−407.834	+	2836.55i	−0.0348958	+	0.242705i
$516$	−580.057	−	1270.15i	−0.0494875	−	0.108363i
$517$	4766.27	+	1399.50i	0.405455	+	0.119052i
$518$	13107.4	+	3848.68i	1.11179	+	0.326450i
$519$	1915.74	+	4194.89i	0.162027	+	0.354789i
$520$	−36.2582	+	252.182i	−0.00305775	+	0.0212671i
$521$	10308.3	−	11896.4i	0.866820	−	1.00036i	−0.133137	−	0.991098i	$-0.542505\pi$
$521$	10308.3	−	11896.4i	0.866820	−	1.00036i	0.999957	−	0.00926607i	$-0.00294953\pi$
$522$	−756.353	+	1656.18i	−0.0634189	+	0.138868i
$523$	−9755.14	−	6269.25i	−0.815607	−	0.524159i	0.0650671	−	0.997881i	$-0.479274\pi$
$523$	−9755.14	−	6269.25i	−0.815607	−	0.524159i	−0.880675	+	0.473722i	$0.842910\pi$
$524$	156.875	+	1091.09i	0.0130785	+	0.0909629i
$525$	−5765.45	+	3705.23i	−0.479286	+	0.308018i
$526$	2667.56	+	3078.53i	0.221124	+	0.255190i
$527$	916.213	−	269.025i	0.0757322	−	0.0222370i
$528$	−1299.67			−0.107123
$529$	7259.42	+	9764.06i	0.596648	+	0.802503i
$530$	1405.04			0.115153
$531$	18661.1	−	5479.40i	1.52509	−	0.447807i
$532$	12504.1	+	14430.5i	1.01902	+	1.17602i
$533$	1865.43	−	1198.84i	0.151596	−	0.0974248i
$534$	63.1282	+	439.066i	0.00511578	+	0.0355810i
$535$	2142.60	+	1376.96i	0.173145	+	0.111274i
$536$	−1250.16	+	2737.46i	−0.100744	+	0.220598i
$537$	−2137.49	+	2466.80i	−0.171768	+	0.198231i
$538$	440.769	−	3065.62i	0.0353214	−	0.245666i
$539$	−14158.2	−	31002.2i	−1.13142	−	2.47747i
$540$	−547.401	−	160.731i	−0.0436229	−	0.0128088i
$541$	5114.40	+	1501.72i	0.406442	+	0.119342i	0.478562	−	0.878054i	$-0.341158\pi$
$541$	5114.40	+	1501.72i	0.406442	+	0.119342i	−0.0721197	+	0.997396i	$0.522976\pi$
$542$	−4873.06	−	10670.5i	−0.386192	−	0.845642i
$543$	473.055	−	3290.17i	0.0373862	−	0.260027i
$544$	1068.39	−	1232.98i	0.0842036	−	0.0971761i
$545$	−249.840	+	547.073i	−0.0196366	+	0.0429982i
$546$	−1845.02	−	1185.72i	−0.144615	−	0.0929383i
$547$	−1322.47	−	9197.99i	−0.103373	−	0.718972i	−0.973921	−	0.226889i	$-0.927145\pi$
$547$	−1322.47	−	9197.99i	−0.103373	−	0.718972i	0.870548	−	0.492083i	$-0.163764\pi$
$548$	−9539.04	+	6130.37i	−0.743590	+	0.477876i
$549$	1506.34	+	1738.41i	0.117102	+	0.135143i
$550$	−11104.7	+	3260.64i	−0.860920	+	0.252789i
$551$	−5540.41			−0.428365
$552$	1354.15	+	680.619i	0.104414	+	0.0524802i
$553$	40951.4			3.14906
$554$	7374.74	−	2165.42i	0.565564	−	0.166065i
$555$	−383.182	−	442.216i	−0.0293066	−	0.0338216i
$556$	−10640.1	+	6837.95i	−0.811581	+	0.521572i
$557$	−1804.40	−	12549.9i	−0.137262	−	0.954676i	−0.935750	−	0.352665i	$-0.885275\pi$
$557$	−1804.40	−	12549.9i	−0.137262	−	0.954676i	0.798488	−	0.602011i	$-0.205634\pi$
$558$	−757.881	−	487.060i	−0.0574976	−	0.0369515i
$559$	1652.99	−	3619.55i	0.125070	−	0.273865i
$560$	555.871	−	641.509i	0.0419461	−	0.0484084i
$561$	−589.376	+	4099.20i	−0.0443556	+	0.308500i
$562$	3414.02	+	7475.65i	0.256248	+	0.561106i
$563$	53.5432	+	15.7217i	0.00400813	+	0.00117689i	0.283736	−	0.958902i	$-0.408426\pi$
$563$	53.5432	+	15.7217i	0.00400813	+	0.00117689i	−0.279728	+	0.960079i	$0.590244\pi$
$564$	−692.334	−	203.288i	−0.0516888	−	0.0151772i
$565$	−929.897	−	2036.19i	−0.0692408	−	0.151616i
$566$	−360.225	+	2505.42i	−0.0267516	+	0.186061i
$567$	−10652.3	+	12293.4i	−0.788983	+	0.910535i
$568$	2104.84	−	4608.96i	0.155488	−	0.340471i
$569$	−7570.93	−	4865.54i	−0.557803	−	0.358478i	0.231163	−	0.972915i	$-0.425747\pi$
$569$	−7570.93	−	4865.54i	−0.557803	−	0.358478i	−0.788966	+	0.614437i	$0.789383\pi$
$570$	−116.395	−	809.545i	−0.00855307	−	0.0594879i
$571$	6307.50	−	4053.58i	0.462278	−	0.297088i	−0.288695	−	0.957421i	$-0.593221\pi$
$571$	6307.50	−	4053.58i	0.462278	−	0.297088i	0.750973	+	0.660333i	$0.229585\pi$
$572$	−2425.39	−	2799.05i	−0.177292	−	0.204606i
$573$	−3387.03	+	994.521i	−0.246937	+	0.0725073i
$574$	−7387.88			−0.537220
$575$	13277.7	+	2418.07i	0.962992	+	0.175374i
$576$	−1539.21			−0.111344
$577$	−6389.91	+	1876.25i	−0.461032	+	0.135371i	−0.503997	−	0.863705i	$-0.668138\pi$
$577$	−6389.91	+	1876.25i	−0.461032	+	0.135371i	0.0429650	+	0.999077i	$0.486320\pi$
$578$	3030.28	+	3497.13i	0.218067	+	0.251663i
$579$	4346.68	−	2793.44i	0.311990	−	0.200503i
$580$	35.0521	+	243.793i	0.00250941	+	0.0174534i
$581$	−14295.2	−	9186.97i	−1.02077	−	0.656006i
$582$	1612.08	−	3529.95i	0.114816	−	0.251411i
$583$	−13375.6	+	15436.3i	−0.950193	+	1.09658i
$584$	−84.0874	+	584.841i	−0.00595816	+	0.0414399i
$585$	−318.176	−	696.709i	−0.0224871	−	0.0492399i
$586$	9787.65	+	2873.91i	0.689973	+	0.202594i
$587$	9550.54	+	2804.29i	0.671538	+	0.197181i	0.599688	−	0.800234i	$-0.295291\pi$
$587$	9550.54	+	2804.29i	0.671538	+	0.197181i	0.0718503	+	0.997415i	$0.477110\pi$
$588$	2056.58	+	4503.28i	0.144238	+	0.315837i
$589$	390.143	−	2713.50i	0.0272930	−	0.189827i
$590$	1722.93	−	1988.36i	0.120223	−	0.138745i
$591$	792.793	−	1735.97i	0.0551796	−	0.120826i
$592$	−2819.01	−	1811.67i	−0.195711	−	0.125776i
$593$	−1526.60	−	10617.7i	−0.105716	−	0.735273i	−0.971874	−	0.235502i	$-0.924327\pi$
$593$	−1526.60	−	10617.7i	−0.105716	−	0.735273i	0.866158	−	0.499771i	$-0.166583\pi$
$594$	6976.98	−	4483.83i	0.481934	−	0.309720i
$595$	−1771.27	−	2044.15i	−0.122042	−	0.140844i
$596$	7163.99	−	2103.54i	0.492363	−	0.144571i
$597$	−5951.14			−0.407980
$598$	1061.24	+	4186.53i	0.0725705	+	0.286288i
$599$	−3905.82			−0.266423			−0.133212	−	0.991088i	$-0.542529\pi$
$599$	−3905.82			−0.266423			−0.133212	+	0.991088i	$0.542529\pi$
$600$	1613.04	−	473.630i	0.109753	−	0.0322265i
$601$	18376.0	+	21207.0i	1.24721	+	1.43935i	0.854305	+	0.519772i	$0.173983\pi$
$601$	18376.0	+	21207.0i	1.24721	+	1.43935i	0.392901	+	0.919581i	$0.371471\pi$
$602$	−11152.8	+	7167.48i	−0.755074	+	0.485257i
$603$	−1287.54	−	8955.05i	−0.0869532	−	0.604773i
$604$	−4212.37	−	2707.13i	−0.283773	−	0.182370i
$605$	−612.133	+	1340.39i	−0.0411351	+	0.0900734i
$606$	−1756.31	+	2026.88i	−0.117731	+	0.135869i
$607$	1687.73	−	11738.4i	0.112855	−	0.784924i	−0.852264	−	0.523112i	$-0.824771\pi$
$607$	1687.73	−	11738.4i	0.112855	−	0.784924i	0.965119	−	0.261812i	$-0.0843200\pi$
$608$	−1945.72	−	4260.54i	−0.129785	−	0.284190i
$609$	−2034.34	−	597.337i	−0.135362	−	0.0397460i
$610$	298.565	+	87.6666i	0.0198173	+	0.00581888i
$611$	−854.194	−	1870.42i	−0.0565581	−	0.123845i
$612$	−698.006	+	4854.74i	−0.0461033	+	0.320655i
$613$	−3394.57	+	3917.55i	−0.223663	+	0.258121i	−0.856480	−	0.516181i	$-0.827353\pi$
$613$	−3394.57	+	3917.55i	−0.223663	+	0.258121i	0.632817	+	0.774302i	$0.281899\pi$
$614$	4125.59	−	9033.77i	0.271165	−	0.593768i
$615$	266.213	+	171.084i	0.0174548	+	0.0112175i
$616$	1756.11	+	12214.0i	0.114863	+	0.798891i
$617$	−17332.0	+	11138.6i	−1.13089	+	0.726782i	−0.965747	−	0.259487i	$-0.916446\pi$
$617$	−17332.0	+	11138.6i	−1.13089	+	0.726782i	−0.165148	+	0.986269i	$0.552810\pi$
$618$	3962.75	+	4573.25i	0.257937	+	0.297675i
$619$	−11571.5	+	3397.69i	−0.751368	+	0.220622i	−0.634923	−	0.772575i	$-0.718968\pi$
$619$	−11571.5	+	3397.69i	−0.751368	+	0.220622i	−0.116445	+	0.993197i	$0.537150\pi$
$620$	−121.870			−0.00789421
$621$	−9617.56	+	1018.04i	−0.621480	+	0.0657849i
$622$	−7920.65			−0.510593
$623$	4040.96	−	1186.53i	0.259868	−	0.0763040i
$624$	352.306	+	406.582i	0.0226018	+	0.0260838i
$625$	12315.7	−	7914.81i	0.788204	−	0.506548i
$626$	540.442	+	3758.86i	0.0345055	+	0.239991i
$627$	10002.0	+	6427.91i	0.637069	+	0.409420i
$628$	3423.92	−	7497.34i	0.217562	−	0.476395i
$629$	−6992.45	+	8069.71i	−0.443254	+	0.511543i
$630$	−363.165	+	2525.87i	−0.0229664	+	0.159735i
$631$	6005.72	+	13150.7i	0.378897	+	0.829668i	0.998981	+	0.0451328i	$0.0143711\pi$
$631$	6005.72	+	13150.7i	0.378897	+	0.829668i	−0.620084	+	0.784535i	$0.712902\pi$
$632$	−9638.44	−	2830.10i	−0.606640	−	0.178126i
$633$	3561.41	+	1045.72i	0.223623	+	0.0656616i
$634$	−8384.57	−	18359.6i	−0.525227	−	1.15009i
$635$	−122.560	+	852.425i	−0.00765930	+	0.0532716i
$636$	1942.91	−	2242.23i	0.121134	−	0.139796i
$637$	−5860.66	+	12833.1i	−0.364534	+	0.798217i
$638$	−3012.09	−	1935.75i	−0.186912	−	0.120121i
$639$	2167.79	+	15077.3i	0.134204	+	0.933408i
$640$	−175.165	+	112.572i	−0.0108188	+	0.00695280i
$641$	−2164.03	−	2497.43i	−0.133345	−	0.153888i	0.685150	−	0.728402i	$-0.259737\pi$
$641$	−2164.03	−	2497.43i	−0.133345	−	0.153888i	−0.818495	+	0.574514i	$0.805191\pi$
$642$	5160.24	−	1515.18i	0.317225	−	0.0931456i
$643$	13873.9			0.850905			0.425452	−	0.904981i	$-0.360115\pi$
$643$	13873.9			0.850905			0.425452	+	0.904981i	$0.360115\pi$
$644$	4566.59	−	13645.7i	0.279424	−	0.834960i
$645$	567.857			0.0346657
$646$	−14320.2	+	4204.80i	−0.872170	+	0.256092i
$647$	−11566.4	−	13348.3i	−0.702817	−	0.811094i	0.286314	−	0.958136i	$-0.407570\pi$
$647$	−11566.4	−	13348.3i	−0.702817	−	0.811094i	−0.989130	+	0.147042i	$0.953025\pi$
$648$	3356.73	−	2157.24i	0.203495	−	0.130778i
$649$	5443.08	+	37857.4i	0.329213	+	2.28973i
$650$	4030.23	+	2590.07i	0.243198	+	0.156294i
$651$	435.809	−	954.289i	0.0262376	−	0.0574524i
$652$	3504.78	−	4044.73i	0.210518	−	0.242950i
$653$	1786.21	−	12423.4i	0.107044	−	0.744508i	−0.863633	−	0.504121i	$-0.831817\pi$
$653$	1786.21	−	12423.4i	0.107044	−	0.744508i	0.970677	−	0.240387i	$-0.0772743\pi$
$654$	527.565	+	1155.21i	0.0315434	+	0.0690705i
$655$	−430.127	−	126.297i	−0.0256587	−	0.00753408i
$656$	1738.83	+	510.567i	0.103491	+	0.0303877i
$657$	−737.891	−	1615.76i	−0.0438172	−	0.0959462i
$658$	−974.974	+	6781.09i	−0.0577636	+	0.401755i
$659$	4972.74	−	5738.84i	0.293946	−	0.339232i	−0.589497	−	0.807771i	$-0.700674\pi$
$659$	4972.74	−	5738.84i	0.293946	−	0.339232i	0.883443	+	0.468539i	$0.155219\pi$
$660$	219.566	−	480.783i	0.0129494	−	0.0283552i
$661$	11185.7	+	7188.61i	0.658204	+	0.423002i	0.826656	−	0.562708i	$-0.190240\pi$
$661$	11185.7	+	7188.61i	0.658204	+	0.423002i	−0.168452	+	0.985710i	$0.553877\pi$
$662$	1211.99	+	8429.60i	0.0711563	+	0.494903i
$663$	1442.14	−	926.807i	0.0844767	−	0.0542899i
$664$	2729.66	+	3150.19i	0.159535	+	0.184113i
$665$	−7450.67	+	2187.71i	−0.434473	+	0.127573i
$666$	10073.9			0.586122
$667$	2124.62	+	3594.28i	0.123337	+	0.208653i
$668$	−7460.26			−0.432105
$669$	7147.85	−	2098.80i	0.413082	−	0.121292i
$670$	−801.460	−	924.934i	−0.0462136	−	0.0533333i
$671$	−3805.40	+	2445.58i	−0.218936	+	0.140702i
$672$	−255.087	−	1774.17i	−0.0146432	−	0.101846i
$673$	−13601.2	−	8740.94i	−0.779029	−	0.500651i	0.0896824	−	0.995970i	$-0.471415\pi$
$673$	−13601.2	−	8740.94i	−0.779029	−	0.500651i	−0.868711	+	0.495319i	$0.835051\pi$
$674$	−3847.71	+	8425.32i	−0.219894	+	0.481500i
$675$	−7025.20	+	8107.52i	−0.400593	+	0.462309i
$676$	1032.48	−	7181.05i	0.0587437	−	0.408571i
$677$	3099.35	+	6786.62i	0.175949	+	0.385275i	0.976975	−	0.213355i	$-0.0684392\pi$
$677$	3099.35	+	6786.62i	0.175949	+	0.385275i	−0.801026	+	0.598630i	$0.795712\pi$
$678$	−4535.32	−	1331.69i	−0.256900	−	0.0754326i
$679$	−35352.0	−	10380.3i	−1.99806	−	0.586685i
$680$	275.621	+	603.527i	0.0155435	+	0.0340356i
$681$	108.906	−	757.455i	0.00612815	−	0.0426222i
$682$	1160.17	−	1338.91i	0.0651396	−	0.0751751i
$683$	−12295.3	+	26923.0i	−0.688825	+	1.50832i	0.164188	+	0.986429i	$0.447499\pi$
$683$	−12295.3	+	26923.0i	−0.688825	+	1.50832i	−0.853014	+	0.521888i	$0.825228\pi$
$684$	11845.5	+	7612.66i	0.662171	+	0.425552i
$685$	−656.264	−	4564.42i	−0.0366052	−	0.254595i
$686$	20721.0	−	13316.6i	1.15325	−	0.741151i
$687$	−5207.15	−	6009.38i	−0.289178	−	0.333729i
$688$	3120.29	−	916.200i	0.172907	−	0.0507701i
$689$	8454.81			0.467493
$690$	−480.550	+	385.953i	−0.0265134	+	0.0212942i
$691$	−25075.2			−1.38047			−0.690236	−	0.723585i	$-0.742493\pi$
$691$	−25075.2			−1.38047			−0.690236	+	0.723585i	$0.742493\pi$
$692$	−10305.3	+	3025.92i	−0.566113	+	0.166226i
$693$	−24292.9	−	28035.5i	−1.33162	−	1.53677i
$694$	11353.9	−	7296.68i	0.621018	−	0.399104i
$695$	−732.012	−	5091.26i	−0.0399522	−	0.277874i
$696$	437.527	+	281.182i	0.0238282	+	0.0153134i
$697$	2398.88	−	5252.81i	0.130364	−	0.285458i
$698$	1786.13	−	2061.30i	0.0968565	−	0.111778i
$699$	−694.576	+	4830.88i	−0.0375841	+	0.261403i
$700$	−6630.61	−	14519.0i	−0.358020	−	0.783953i
$701$	−21340.1	−	6266.01i	−1.14979	−	0.337609i	−0.349333	−	0.936998i	$-0.613592\pi$
$701$	−21340.1	−	6266.01i	−1.14979	−	0.337609i	−0.800458	+	0.599389i	$0.795410\pi$
$702$	−3293.97	−	967.198i	−0.177098	−	0.0520008i
$703$	12734.5	+	27884.6i	0.683200	+	1.49600i
$704$	430.772	−	2996.09i	0.0230616	−	0.160397i
$705$	192.165	−	221.770i	0.0102657	−	0.0118473i
$706$	6585.82	−	14420.9i	0.351077	−	0.768752i
$707$	21421.4	+	13766.7i	1.13951	+	0.732318i
$708$	−790.645	−	5499.06i	−0.0419693	−	0.291903i
$709$	3390.19	−	2178.74i	0.179579	−	0.115408i	−0.447763	−	0.894152i	$-0.647779\pi$
$709$	3390.19	−	2178.74i	0.179579	−	0.115408i	0.627342	+	0.778744i	$0.284143\pi$
$710$	1349.39	+	1557.28i	0.0713262	+	0.0823149i
$711$	28975.8	−	8508.07i	1.52838	−	0.448773i
$712$	−1033.09			−0.0543774
$713$	−1909.97	+	787.467i	−0.100321	+	0.0413617i
$714$	−5711.48			−0.299365
$715$	1445.19	−	424.347i	0.0755905	−	0.0221954i
$716$	−4978.17	−	5745.11i	−0.259836	−	0.299867i
$717$	8249.42	−	5301.58i	0.429680	−	0.276138i
$718$	−1205.59	−	8385.04i	−0.0626631	−	0.435832i
$719$	26642.6	+	17122.1i	1.38192	+	0.888106i	0.999358	−	0.0358237i	$-0.0114055\pi$
$719$	26642.6	+	17122.1i	1.38192	+	0.888106i	0.382562	+	0.923930i	$0.375042\pi$
$720$	260.035	−	569.398i	0.0134596	−	0.0294725i
$721$	37624.1	−	43420.5i	1.94340	−	2.24281i
$722$	−4145.58	+	28833.1i	−0.213688	+	1.48623i
$723$	2770.71	+	6067.00i	0.142522	+	0.312080i
$724$	7427.94	+	2181.04i	0.381294	+	0.111958i
$725$	4443.78	+	1304.81i	0.227638	+	0.0668406i
$726$	1292.59	+	2830.37i	0.0660777	+	0.144690i
$727$	2251.65	−	15660.6i	0.114868	−	0.798924i	−0.848202	−	0.529673i	$-0.822315\pi$
$727$	2251.65	−	15660.6i	0.114868	−	0.798924i	0.963070	−	0.269251i	$-0.0867762\pi$
$728$	3344.94	−	3860.27i	0.170291	−	0.196526i
$729$	−3294.10	+	7213.07i	−0.167357	+	0.366462i
$730$	−202.143	−	129.909i	−0.0102488	−	0.00658653i
$731$	−1474.73	−	10257.0i	−0.0746169	−	0.518972i
$732$	552.762	−	355.238i	0.0279107	−	0.0179371i
$733$	4493.55	+	5185.84i	0.226430	+	0.261314i	0.857585	−	0.514343i	$-0.171964\pi$
$733$	4493.55	+	5185.84i	0.226430	+	0.261314i	−0.631155	+	0.775657i	$0.717419\pi$
$734$	5381.36	−	1580.11i	0.270613	−	0.0794590i
$735$	−2013.33			−0.101038
$736$	−2017.84	+	2896.09i	−0.101058	+	0.145042i
$737$	17791.4			0.889219
$738$	−5227.41	+	1534.91i	−0.260737	+	0.0765592i
$739$	12914.8	+	14904.4i	0.642866	+	0.741907i	0.979879	−	0.199593i	$-0.0639621\pi$
$739$	12914.8	+	14904.4i	0.642866	+	0.741907i	−0.337013	+	0.941500i	$0.609417\pi$
$740$	1146.43	−	736.767i	0.0569509	−	0.0366001i
$741$	−700.405	−	4871.42i	−0.0347234	−	0.241506i
$742$	−23697.3	−	15229.3i	−1.17245	−	0.753486i
$743$	−5747.52	+	12585.3i	−0.283790	+	0.621414i	−0.996817	−	0.0797229i	$-0.974596\pi$
$743$	−5747.52	+	12585.3i	−0.283790	+	0.621414i	0.713027	+	0.701137i	$0.247324\pi$
$744$	−168.523	+	194.486i	−0.00830423	+	0.00958360i
$745$	−432.130	+	3005.53i	−0.0212510	+	0.147804i
$746$	3899.35	+	8538.38i	0.191374	+	0.419051i
$747$	−12023.5	−	3530.41i	−0.588910	−	0.172920i
$748$	−9254.42	−	2717.34i	−0.452373	−	0.132829i
$749$	−21211.9	−	46447.5i	−1.03480	−	2.26590i
$750$	−196.700	+	1368.08i	−0.00957663	+	0.0666069i
$751$	3158.86	−	3645.52i	0.153487	−	0.177133i	−0.673799	−	0.738915i	$-0.735339\pi$
$751$	3158.86	−	3645.52i	0.153487	−	0.177133i	0.827285	+	0.561782i	$0.189884\pi$
$752$	698.105	−	1528.64i	0.0338528	−	0.0741272i
$753$	1225.68	+	787.696i	0.0593177	+	0.0381212i
$754$	210.925	+	1467.02i	0.0101876	+	0.0708563i
$755$	1713.08	−	1100.93i	0.0825766	−	0.0530688i
$756$	7490.24	+	8644.19i	0.360340	+	0.415855i
$757$	13620.5	−	3999.33i	0.653955	−	0.192018i	0.0621087	−	0.998069i	$-0.480217\pi$
$757$	13620.5	−	3999.33i	0.653955	−	0.192018i	0.591846	+	0.806051i	$0.298399\pi$
$758$	13488.1			0.646321
$759$	334.489	−	8953.68i	0.0159963	−	0.428192i
$760$	1904.80			0.0909136
$761$	−28405.2	+	8340.53i	−1.35307	+	0.397298i	−0.876316	−	0.481736i	$-0.840006\pi$
$761$	−28405.2	+	8340.53i	−1.35307	+	0.397298i	−0.476758	+	0.879035i	$0.658188\pi$
$762$	1190.86	+	1374.33i	0.0566148	+	0.0653369i
$763$	10143.5	−	6518.86i	0.481285	−	0.309303i
$764$	−1170.02	−	8137.65i	−0.0554054	−	0.385353i
$765$	−1677.98	−	1078.37i	−0.0793039	−	0.0509655i
$766$	5578.59	−	12215.4i	0.263136	−	0.576189i
$767$	10367.7	−	11964.9i	0.488077	−	0.563271i
$768$	−62.5727	+	435.203i	−0.00293997	+	0.0204480i
$769$	6796.44	+	14882.1i	0.318707	+	0.697872i	0.999398	−	0.0346993i	$-0.0110473\pi$
$769$	6796.44	+	14882.1i	0.318707	+	0.697872i	−0.680690	+	0.732571i	$0.738320\pi$
$770$	−4814.98	−	1413.81i	−0.225350	−	0.0661689i
$771$	−8694.67	−	2552.99i	−0.406136	−	0.119252i
$772$	4998.94	+	10946.2i	0.233052	+	0.510312i
$773$	2888.91	−	20092.8i	0.134420	−	0.934914i	−0.805275	−	0.592901i	$-0.797982\pi$
$773$	2888.91	−	20092.8i	0.134420	−	0.934914i	0.939695	−	0.342012i	$-0.111109\pi$
$774$	−6402.23	+	7388.57i	−0.297317	+	0.343122i
$775$	−951.973	+	2084.53i	−0.0441237	+	0.0966175i
$776$	7603.18	+	4886.26i	0.351724	+	0.226040i
$777$	1669.51	+	11611.7i	0.0770829	+	0.536123i
$778$	−15463.0	+	9937.45i	−0.712564	+	0.457937i
$779$	−10856.6	−	12529.2i	−0.499329	−	0.576257i
$780$	−209.925	+	61.6394i	−0.00963655	+	0.00282955i
$781$	−29954.7			−1.37242
$782$	8219.32	+	7677.66i	0.375860	+	0.351090i
$783$	−3318.83			−0.151476
$784$	−11062.9	+	3248.37i	−0.503960	+	0.147976i
$785$	2195.03	+	2533.20i	0.0998014	+	0.115177i
$786$	−796.336	+	511.774i	−0.0361378	+	0.0232244i
$787$	4933.59	+	34313.9i	0.223460	+	1.55420i	0.724805	+	0.688954i	$0.241930\pi$
$787$	4933.59	+	34313.9i	0.223460	+	1.55420i	−0.501345	+	0.865248i	$0.667161\pi$
$788$	3739.12	+	2402.99i	0.169036	+	0.108633i
$789$	−1453.16	+	3181.97i	−0.0655687	+	0.143575i
$790$	2675.25	−	3087.41i	0.120483	−	0.139044i
$791$	−6386.84	+	44421.4i	−0.287092	+	1.99677i
$792$	3780.15	+	8277.37i	0.169598	+	0.371368i
$793$	1796.61	+	527.532i	0.0804533	+	0.0236232i
$794$	16493.6	+	4842.96i	0.737200	+	0.216461i
$795$	501.229	+	1097.54i	0.0223607	+	0.0489631i
$796$	1972.49	−	13719.0i	0.0878307	−	0.610876i
$797$	13952.7	−	16102.3i	0.620114	−	0.715649i	−0.355615	−	0.934633i	$-0.615729\pi$
$797$	13952.7	−	16102.3i	0.620114	−	0.715649i	0.975729	+	0.218983i	$0.0702740\pi$
$798$	−6811.61	+	14915.3i	−0.302166	+	0.661651i
$799$	−4504.80	−	2895.06i	−0.199460	−	0.128185i
$800$	557.208	+	3875.47i	0.0246254	+	0.171273i
$801$	2612.73	−	1679.10i	0.115251	−	0.0740675i
$802$	−6137.65	−	7083.23i	−0.270235	−	0.311867i
$803$	3351.59	−	984.115i	0.147291	−	0.0432486i
$804$	−2584.32			−0.113361
$805$	4276.42	+	3994.61i	0.187235	+	0.174896i
$806$	−733.349			−0.0320485
$807$	2551.92	−	749.312i	0.111316	−	0.0326853i
$808$	−4090.39	−	4720.57i	−0.178093	−	0.205531i
$809$	4143.74	−	2663.02i	0.180082	−	0.115731i	−0.447494	−	0.894287i	$-0.647684\pi$
$809$	4143.74	−	2663.02i	0.180082	−	0.115731i	0.627576	+	0.778555i	$0.284047\pi$
$810$	230.935	+	1606.19i	0.0100176	+	0.0696738i
$811$	−9075.17	−	5832.26i	−0.392938	−	0.252526i	0.329221	−	0.944253i	$-0.393214\pi$
$811$	−9075.17	−	5832.26i	−0.392938	−	0.252526i	−0.722159	+	0.691727i	$0.756850\pi$
$812$	2051.30	−	4491.72i	0.0886534	−	0.194124i
$813$	6596.80	−	7613.12i	0.284576	−	0.328418i
$814$	−2819.35	+	19609.0i	−0.121398	+	0.844342i
$815$	904.158	+	1979.83i	0.0388605	+	0.0850925i
$816$	1344.27	+	394.713i	0.0576702	+	0.0169335i
$817$	−28544.6	−	8381.44i	−1.22234	−	0.358910i
$818$	9965.62	+	21821.7i	0.425965	+	0.932734i
$819$	−2185.34	+	15199.4i	−0.0932381	+	0.648485i
$820$	−482.632	+	556.987i	−0.0205539	+	0.0237205i
$821$	−980.400	+	2146.78i	−0.0416762	+	0.0912582i	−0.929325	−	0.369263i	$-0.879610\pi$
$821$	−980.400	+	2146.78i	−0.0416762	+	0.0912582i	0.887649	+	0.460521i	$0.152337\pi$
$822$	−8191.61	−	5264.43i	−0.347586	−	0.223380i
$823$	−4543.88	−	31603.4i	−0.192454	−	1.33855i	−0.825486	−	0.564422i	$-0.809099\pi$
$823$	−4543.88	−	31603.4i	−0.192454	−	1.33855i	0.633032	−	0.774126i	$-0.281810\pi$
$824$	−11856.0	+	7619.41i	−0.501243	+	0.322130i
$825$	−6508.47	−	7511.18i	−0.274662	−	0.316977i
$826$	−50610.7	+	14860.6i	−2.13193	+	0.625990i
$827$	−35715.7			−1.50176			−0.750880	−	0.660438i	$-0.770370\pi$
$827$	−35715.7			−1.50176			−0.750880	+	0.660438i	$0.770370\pi$
$828$	396.140	−	10604.0i	0.0166266	−	0.445064i
$829$	−21139.2			−0.885641			−0.442820	−	0.896610i	$-0.646022\pi$
$829$	−21139.2			−0.885641			−0.442820	+	0.896610i	$0.646022\pi$
$830$	−1626.49	+	477.581i	−0.0680197	+	0.0199724i
$831$	4322.34	+	4988.25i	0.180434	+	0.208231i
$832$	−1054.05	+	677.399i	−0.0439215	+	0.0282267i
$833$	5228.64	+	36366.0i	0.217481	+	1.51261i
$834$	−9137.11	−	5872.07i	−0.379367	−	0.243805i
$835$	1260.34	−	2759.75i	0.0522345	−	0.114378i
$836$	−18133.2	+	20926.9i	−0.750180	+	0.865754i
$837$	233.705	−	1625.45i	0.00965116	−	0.0671253i
$838$	5766.65	+	12627.2i	0.237715	+	0.520524i
$839$	37211.9	+	10926.4i	1.53122	+	0.449608i	0.935425	−	0.353525i	$-0.115017\pi$
$839$	37211.9	+	10926.4i	1.53122	+	0.449608i	0.595799	+	0.803133i	$0.296835\pi$
$840$	699.410	+	205.365i	0.0287285	+	0.00843544i
$841$	−9536.35	−	20881.7i	−0.391010	−	0.856193i
$842$	2778.18	−	19322.7i	0.113709	−	0.790860i
$843$	−4621.65	+	5333.67i	−0.188823	+	0.217914i
$844$	−3591.10	+	7863.41i	−0.146458	+	0.320699i
$845$	2482.04	+	1595.11i	0.101047	+	0.0649390i
$846$	718.982	+	5000.63i	0.0292188	+	0.203221i
$847$	24852.7	−	15971.9i	1.00821	−	0.647934i
$848$	4524.98	+	5222.11i	0.183241	+	0.211472i
$849$	−2085.60	+	612.387i	−0.0843081	+	0.0247551i
$850$	12476.1			0.503441
$851$	13206.5	−	18954.5i	0.531977	−	0.763516i
$852$	4351.13			0.174962
$853$	6503.61	−	1909.63i	0.261054	−	0.0766525i	−0.148586	−	0.988899i	$-0.547472\pi$
$853$	6503.61	−	1909.63i	0.261054	−	0.0766525i	0.409641	+	0.912247i	$0.365654\pi$
$854$	−4085.35	−	4714.74i	−0.163698	−	0.188917i
$855$	−4817.32	+	3095.90i	−0.192689	+	0.123833i
$856$	1782.56	+	12397.9i	0.0711758	+	0.495039i
$857$	34148.1	+	21945.6i	1.36112	+	0.874736i	0.998366	−	0.0571498i	$-0.0182013\pi$
$857$	34148.1	+	21945.6i	1.36112	+	0.874736i	0.362751	+	0.931886i	$0.381838\pi$
$858$	1321.24	−	2893.10i	0.0525714	−	0.115115i
$859$	−20567.4	+	23736.1i	−0.816940	+	0.942799i	−0.999181	−	0.0404546i	$-0.987119\pi$
$859$	−20567.4	+	23736.1i	−0.816940	+	0.942799i	0.182241	+	0.983254i	$0.441665\pi$
$860$	−188.215	+	1309.06i	−0.00746288	+	0.0519055i
$861$	−2635.53	−	5770.99i	−0.104319	−	0.228426i
$862$	5549.84	+	1629.58i	0.219290	+	0.0643894i
$863$	15964.7	+	4687.67i	0.629717	+	0.184902i	0.580990	−	0.813910i	$-0.302665\pi$
$863$	15964.7	+	4687.67i	0.629717	+	0.184902i	0.0487270	+	0.998812i	$0.484484\pi$
$864$	−1165.53	−	2552.16i	−0.0458938	−	0.100493i
$865$	621.615	−	4323.43i	0.0244342	−	0.169943i
$866$	17680.5	−	20404.4i	0.693775	−	0.800659i
$867$	−1650.75	+	3614.63i	−0.0646624	+	0.141591i
$868$	2055.45	+	1320.95i	0.0803760	+	0.0516545i
$869$	8451.68	+	58782.7i	0.329924	+	2.29467i
$870$	−177.933	+	114.350i	−0.00693389	+	0.00445614i
$871$	−4822.77	−	5565.78i	−0.187616	−	0.216520i
$872$	−2837.92	+	833.289i	−0.110211	+	0.0323609i
$873$	−27170.5			−1.05336
$874$	29852.4	−	12308.0i	1.15535	−	0.476342i
$875$	13122.7			0.507004
$876$	−486.842	+	142.950i	−0.0187772	+	0.00551349i
$877$	−24305.9	−	28050.5i	−0.935863	−	1.08004i	−0.996641	−	0.0818927i	$-0.973904\pi$
$877$	−24305.9	−	28050.5i	−0.935863	−	1.08004i	0.0607777	−	0.998151i	$-0.480642\pi$
$878$	3602.22	−	2315.01i	0.138461	−	0.0889837i
$879$	1246.67	+	8670.78i	0.0478375	+	0.332717i
$880$	1035.56	+	665.514i	0.0396690	+	0.0254937i
$881$	10104.7	−	22126.1i	0.386418	−	0.846138i	−0.612050	−	0.790819i	$-0.709655\pi$
$881$	10104.7	−	22126.1i	0.386418	−	0.846138i	0.998469	−	0.0553192i	$-0.0176177\pi$
$882$	22699.0	−	26196.0i	0.866570	−	1.00008i
$883$	3516.70	−	24459.2i	0.134028	−	0.932184i	−0.806201	−	0.591641i	$-0.798480\pi$
$883$	3516.70	−	24459.2i	0.134028	−	0.932184i	0.940229	−	0.340542i	$-0.110611\pi$
$884$	1658.55	+	3631.71i	0.0631029	+	0.138176i
$885$	2167.83	+	636.531i	0.0823397	+	0.0241771i
$886$	−9846.24	−	2891.12i	−0.373353	−	0.109626i
$887$	−14767.7	−	32336.8i	−0.559021	−	1.22409i	−0.952440	−	0.304726i	$-0.901435\pi$
$887$	−14767.7	−	32336.8i	−0.559021	−	1.22409i	0.393419	−	0.919359i	$-0.371292\pi$
$888$	409.530	−	2848.34i	0.0154763	−	0.107640i
$889$	11306.6	−	13048.5i	0.426559	−	0.492275i
$890$	174.531	−	382.169i	0.00657335	−	0.0143936i
$891$	−19844.7	−	12753.4i	−0.746152	−	0.479523i
$892$	2469.16	+	17173.4i	0.0926833	+	0.644626i
$893$	−12932.8	+	8311.44i	−0.484637	+	0.311458i
$894$	4198.82	+	4845.69i	0.157080	+	0.181280i
$895$	2966.29	−	870.981i	0.110784	−	0.0325292i
$896$	4174.50			0.155647
$897$	−2891.70	+	2322.46i	−0.107638	+	0.0864491i
$898$	−13624.7			−0.506304
$899$	−680.236	+	199.735i	−0.0252360	+	0.00740996i
$900$	−7708.07	−	8895.58i	−0.285484	−	0.329466i
$901$	18522.7	−	11903.8i	0.684885	−	0.440149i
$902$	−1524.73	−	10604.8i	−0.0562839	−	0.391463i
$903$	−9577.44	−	6155.04i	−0.352954	−	0.226830i
$904$	4573.13	−	10013.8i	0.168252	−	0.368421i
$905$	−2061.70	+	2379.33i	−0.0757275	+	0.0873941i
$906$	611.949	−	4256.20i	0.0224400	−	0.156074i
$907$	10928.4	+	23929.9i	0.400079	+	0.876052i	0.997262	+	0.0739465i	$0.0235594\pi$
$907$	10928.4	+	23929.9i	0.400079	+	0.876052i	−0.597183	+	0.802105i	$0.703713\pi$
$908$	1710.04	+	502.114i	0.0624997	+	0.0183516i
$909$	18017.2	+	5290.32i	0.657417	+	0.193035i
$910$	862.925	+	1889.54i	0.0314348	+	0.0688326i
$911$	−2204.60	+	15333.4i	−0.0801776	+	0.557648i	0.909650	+	0.415376i	$0.136350\pi$
$911$	−2204.60	+	15333.4i	−0.0801776	+	0.557648i	−0.989828	+	0.142272i	$0.954559\pi$
$912$	2633.98	−	3039.77i	0.0956357	−	0.110369i
$913$	10236.9	−	22415.7i	0.371076	−	0.812543i
$914$	−24880.5	−	15989.7i	−0.900410	−	0.578658i
$915$	38.0287	+	264.496i	0.00137398	+	0.00955624i
$916$	15579.1	−	10012.1i	0.561953	−	0.361146i
$917$	5885.55	+	6792.29i	0.211950	+	0.244603i
$918$	−8578.16	+	2518.78i	−0.308411	+	0.0905577i
$919$	−41556.7			−1.49165			−0.745826	−	0.666140i	$-0.767945\pi$
$919$	−41556.7			−1.49165			−0.745826	+	0.666140i	$0.767945\pi$
$920$	−730.449	−	1235.72i	−0.0261763	−	0.0442831i
$921$	8528.42			0.305126
$922$	33141.1	−	9731.09i	1.18378	−	0.347588i
$923$	8119.92	+	9370.89i	0.289567	+	0.334178i
$924$	−8914.43	+	5728.96i	−0.317384	+	0.203971i
$925$	−3646.85	−	25364.4i	−0.129630	−	0.901596i
$926$	−8005.78	−	5145.00i	−0.284110	−	0.182587i
$927$	17600.4	−	38539.6i	0.623597	−	1.36549i
$928$	−793.217	+	915.421i	−0.0280589	+	0.0323817i
$929$	−1421.83	+	9889.07i	−0.0502140	+	0.349246i	0.949189	+	0.314706i	$0.101906\pi$
$929$	−1421.83	+	9889.07i	−0.0502140	+	0.349246i	−0.999403	+	0.0345405i	$0.989003\pi$
$930$	−43.4753	−	95.1977i	−0.00153292	−	0.00335662i
$931$	101204.	+	29716.3i	3.56266	+	1.04609i
$932$	−10906.3	−	3202.37i	−0.383312	−	0.112551i
$933$	−2825.58	−	6187.16i	−0.0991483	−	0.217104i
$934$	3232.14	−	22480.0i	0.113232	−	0.787547i
$935$	2568.66	−	2964.40i	0.0898442	−	0.103686i
$936$	1564.76	−	3426.34i	0.0546428	−	0.119651i
$937$	−9526.12	−	6122.06i	−0.332129	−	0.213446i	0.363938	−	0.931423i	$-0.381432\pi$
$937$	−9526.12	−	6122.06i	−0.332129	−	0.213446i	−0.696067	+	0.717977i	$0.745068\pi$
$938$	3491.94	+	24287.0i	0.121552	+	0.845413i
$939$	−2743.41	+	1763.08i	−0.0953439	+	0.0612738i
$940$	447.547	+	516.497i	0.0155291	+	0.0179216i
$941$	50644.8	−	14870.6i	1.75449	−	0.515164i	0.763117	−	0.646260i	$-0.223668\pi$
$941$	50644.8	−	14870.6i	1.75449	−	0.515164i	0.991370	+	0.131097i	$0.0418498\pi$
$942$	7077.93			0.244810
$943$	−3964.92	+	11847.8i	−0.136920	+	0.409137i
$944$	12938.9			0.446107
$945$	−4463.13	+	1310.49i	−0.153636	+	0.0451115i
$946$	−12590.1	−	14529.8i	−0.432706	−	0.499370i
$947$	−34504.4	+	22174.6i	−1.18399	+	0.760907i	−0.976117	−	0.217248i	$-0.930292\pi$
$947$	−34504.4	+	22174.6i	−1.18399	+	0.760907i	−0.207878	+	0.978155i	$0.566656\pi$
$948$	−1227.67	−	8538.60i	−0.0420598	−	0.292533i
$949$	−1216.39	−	781.728i	−0.0416078	−	0.0267397i
$950$	14879.1	−	32580.8i	0.508151	−	1.11270i
$951$	11350.4	−	13099.1i	0.387027	−	0.446653i
$952$	1893.06	−	13166.5i	0.0644479	−	0.448245i
$953$	−1866.59	−	4087.27i	−0.0634469	−	0.138929i	0.875252	−	0.483667i	$-0.160695\pi$
$953$	−1866.59	−	4087.27i	−0.0634469	−	0.138929i	−0.938699	+	0.344737i	$0.887968\pi$
$954$	−19931.5	−	5852.40i	−0.676420	−	0.198615i
$955$	3208.00	+	941.954i	0.108700	+	0.0319172i
$956$	9487.33	+	20774.4i	0.320965	+	0.702814i
$957$	437.578	−	3043.43i	0.0147805	−	0.102800i
$958$	−22659.7	+	26150.7i	−0.764199	+	0.881932i
$959$	−38405.5	+	84096.4i	−1.29320	+	2.83171i
$960$	−150.422	−	96.6706i	−0.00505715	−	0.00325003i
$961$	4189.78	+	29140.5i	0.140639	+	0.978166i
$962$	6898.63	−	4433.48i	0.231207	−	0.148588i
$963$	−24658.7	−	28457.7i	−0.825147	−	0.952270i
$964$	−14904.4	+	4376.33i	−0.497966	+	0.146216i
$965$	−4893.81			−0.163251
$966$	12288.3	−	1300.74i	0.409285	−	0.0433236i
$967$	−52311.8			−1.73964			−0.869822	−	0.493366i	$-0.835766\pi$
$967$	−52311.8			−1.73964			−0.869822	+	0.493366i	$0.835766\pi$
$968$	−6953.20	+	2041.64i	−0.230872	+	0.0677902i
$969$	−8393.10	−	9686.15i	−0.278251	−	0.321119i
$970$	−3092.05	+	1987.14i	−0.102350	+	0.0657764i
$971$	−6083.50	−	42311.7i	−0.201059	−	1.39840i	−0.801148	−	0.598466i	$-0.795777\pi$
$971$	−6083.50	−	42311.7i	−0.201059	−	1.39840i	0.600089	−	0.799933i	$-0.295132\pi$
$972$	10848.6	+	6971.99i	0.357994	+	0.230069i
$973$	−42838.4	+	93803.1i	−1.41145	+	3.09064i
$974$	1355.89	−	1564.78i	0.0446051	−	0.0514771i
$975$	−585.488	+	4072.16i	−0.0192314	+	0.133757i
$976$	635.709	+	1392.01i	0.0208489	+	0.0456528i
$977$	16039.5	+	4709.62i	0.525229	+	0.154221i	0.533589	−	0.845744i	$-0.320843\pi$
$977$	16039.5	+	4709.62i	0.525229	+	0.154221i	−0.00835985	+	0.999965i	$0.502661\pi$
$978$	4409.79	+	1294.83i	0.144182	+	0.0423355i
$979$	2537.16	+	5555.61i	0.0828274	+	0.181367i
$980$	667.313	−	4641.27i	0.0217516	−	0.151286i
$981$	5822.86	−	6719.94i	0.189510	−	0.218707i
$982$	4729.33	−	10355.8i	0.153685	−	0.336524i
$983$	−10521.5	−	6761.79i	−0.341389	−	0.219397i	0.358700	−	0.933453i	$-0.383220\pi$
$983$	−10521.5	−	6761.79i	−0.341389	−	0.219397i	−0.700089	+	0.714056i	$0.746856\pi$
$984$	221.478	+	1540.41i	0.00717527	+	0.0499051i
$985$	−1520.62	+	977.242i	−0.0491888	+	0.0316117i
$986$	2527.56	+	2916.96i	0.0816369	+	0.0942140i
$987$	−5644.81	+	1657.47i	−0.182043	+	0.0534526i
$988$	11462.1			0.369087
$989$	5508.83	+	21732.1i	0.177119	+	0.698727i
$990$	−3700.65			−0.118802
$991$	−2335.80	+	685.852i	−0.0748729	+	0.0219847i	−0.318954	−	0.947770i	$-0.603332\pi$
$991$	−2335.80	+	685.852i	−0.0748729	+	0.0219847i	0.244082	+	0.969755i	$0.421514\pi$
$992$	−392.486	−	452.953i	−0.0125619	−	0.0144972i
$993$	−6152.37	+	3953.89i	−0.196616	+	0.126357i
$994$	−5879.24	−	40891.0i	−0.187604	−	1.30481i
$995$	4741.80	+	3047.37i	0.151081	+	0.0970936i
$996$	−1486.98	+	3256.04i	−0.0473061	+	0.103586i
$997$	−2578.28	+	2975.49i	−0.0819006	+	0.0945183i	−0.795221	−	0.606320i	$-0.792645\pi$
$997$	−2578.28	+	2975.49i	−0.0819006	+	0.0945183i	0.713320	+	0.700838i	$0.247191\pi$
$998$	−5959.47	+	41449.0i	−0.189022	+	1.31467i
$999$	7628.25	+	16703.5i	0.241589	+	0.529006i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	46.4.c.a.9.2	✓	30
23.8	even	11		1058.4.a.v.1.9		15
23.15	odd	22		1058.4.a.w.1.9		15
23.18	even	11	inner	46.4.c.a.41.2	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
46.4.c.a.9.2	✓	30	1.1	even	1	trivial
46.4.c.a.41.2	yes	30	23.18	even	11	inner
1058.4.a.v.1.9		15	23.8	even	11
1058.4.a.w.1.9		15	23.15	odd	22

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 46 = 2 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	46.c (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.91899 + 0.563465i) q^{2} +(-1.12472 - 1.29799i) q^{3} +(3.36501 - 2.16256i) q^{4} +(0.231505 + 1.61016i) q^{5} +(2.88969 + 1.85709i) q^{6} +(13.5480 - 29.6661i) q^{7} +(-5.23889 + 6.04600i) q^{8} +(3.42270 - 23.8054i) q^{9} +(-1.35152 - 2.95942i) q^{10} +(45.3795 + 13.3246i) q^{11} +(-6.59169 - 1.93549i) q^{12} +(-8.13276 - 17.8083i) q^{13} +(-9.28270 + 64.5626i) q^{14} +(1.82959 - 2.11146i) q^{15} +(6.64664 - 14.5541i) q^{16} +(-42.8901 - 27.5638i) q^{17} +(6.84541 + 47.6108i) q^{18} +(-123.133 + 79.1329i) q^{19} +(4.26108 + 4.91755i) q^{20} +(-53.7441 + 15.7807i) q^{21} -94.5906 q^{22} +(98.5556 + 49.5358i) q^{23} +13.7399 q^{24} +(117.398 - 34.4711i) q^{25} +(25.6410 + 29.5913i) q^{26} +(-73.7597 + 47.4025i) q^{27} +(-18.5654 - 129.125i) q^{28} +(31.8434 + 20.4645i) q^{29} +(-2.32123 + 5.08278i) q^{30} +(-12.2652 + 14.1548i) q^{31} +(-4.55407 + 31.6743i) q^{32} +(-33.7439 - 73.8888i) q^{33} +(97.8367 + 28.7274i) q^{34} +(50.9034 + 14.9466i) q^{35} +(-39.9633 - 87.5074i) q^{36} +(29.8058 - 207.304i) q^{37} +(191.702 - 221.236i) q^{38} +(-13.9680 + 30.5856i) q^{39} +(-10.9478 - 7.03574i) q^{40} +(16.1193 + 112.112i) q^{41} +(94.2423 - 60.5659i) q^{42} +(133.101 + 153.607i) q^{43} +(181.518 - 53.2985i) q^{44} +39.1228 q^{45} +(-217.039 - 39.5258i) q^{46} +105.031 q^{47} +(-26.3668 + 7.74198i) q^{48} +(-471.908 - 544.611i) q^{49} +(-205.861 + 132.299i) q^{50} +(12.4616 + 86.6726i) q^{51} +(-65.8783 - 42.3374i) q^{52} +(-179.403 + 392.838i) q^{53} +(114.834 - 132.526i) q^{54} +(-10.9491 + 76.1527i) q^{55} +(108.384 + 237.328i) q^{56} +(241.204 + 70.8240i) q^{57} +(-72.6382 - 21.3285i) q^{58} +(335.938 + 735.601i) q^{59} +(1.59044 - 11.0617i) q^{60} +(-62.6333 + 72.2826i) q^{61} +(15.5610 - 34.0738i) q^{62} +(-659.842 - 424.055i) q^{63} +(-9.10815 - 63.3486i) q^{64} +(26.7913 - 17.2177i) q^{65} +(106.388 + 122.778i) q^{66} +(360.939 - 105.981i) q^{67} -203.934 q^{68} +(-46.5502 - 183.638i) q^{69} -106.105 q^{70} +(-607.699 + 178.437i) q^{71} +(125.996 + 145.408i) q^{72} +(62.1324 - 39.9300i) q^{73} +(59.6116 + 414.608i) q^{74} +(-176.783 - 113.611i) q^{75} +(-243.215 + 532.567i) q^{76} +(1010.09 - 1165.71i) q^{77} +(9.57042 - 66.5637i) q^{78} +(521.624 + 1142.20i) q^{79} +(24.9731 + 7.33277i) q^{80} +(-478.565 - 140.519i) q^{81} +(-94.1040 - 206.059i) q^{82} +(74.1514 - 515.734i) q^{83} +(-146.723 + 169.327i) q^{84} +(34.4527 - 75.4408i) q^{85} +(-341.972 - 219.772i) q^{86} +(-9.25205 - 64.3495i) q^{87} +(-318.299 + 204.558i) q^{88} +(84.5663 + 97.5947i) q^{89} +(-75.0761 + 22.0443i) q^{90} -638.484 q^{91} +(438.765 - 46.4442i) q^{92} +32.1677 q^{93} +(-201.554 + 59.1815i) q^{94} +(-155.922 - 179.944i) q^{95} +(46.2351 - 29.7135i) q^{96} +(-160.779 - 1118.24i) q^{97} +(1212.46 + 779.198i) q^{98} +(472.519 - 1034.67i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q - 6 q^{2} + 6 q^{3} - 12 q^{4} + 10 q^{5} + 12 q^{6} + 107 q^{7} - 24 q^{8} - 63 q^{9} + 20 q^{10} + 64 q^{11} - 20 q^{12} + 8 q^{13} + 16 q^{14} + 252 q^{15} - 48 q^{16} - 126 q^{17} - 126 q^{18}+ \cdots + 1377 q^{99}+O(q^{100}) \) 30 * q - 6 * q^2 + 6 * q^3 - 12 * q^4 + 10 * q^5 + 12 * q^6 + 107 * q^7 - 24 * q^8 - 63 * q^9 + 20 * q^10 + 64 * q^11 - 20 * q^12 + 8 * q^13 + 16 * q^14 + 252 * q^15 - 48 * q^16 - 126 * q^17 - 126 * q^18 + 123 * q^19 - 136 * q^20 - 514 * q^21 - 356 * q^22 - 507 * q^23 + 48 * q^24 - 419 * q^25 - 94 * q^26 - 657 * q^27 + 32 * q^28 + 757 * q^29 + 240 * q^30 + 840 * q^31 - 96 * q^32 + 1948 * q^33 + 936 * q^34 - 785 * q^35 - 164 * q^36 - 444 * q^37 + 554 * q^38 + 1954 * q^39 + 80 * q^40 - 771 * q^41 + 72 * q^42 - 789 * q^43 + 256 * q^44 - 2596 * q^45 + 1230 * q^46 - 1748 * q^47 - 80 * q^48 - 720 * q^49 - 2026 * q^50 + 1641 * q^51 + 472 * q^52 - 785 * q^53 + 2030 * q^54 + 967 * q^55 + 856 * q^56 + 5918 * q^57 + 1052 * q^58 + 2307 * q^59 - 444 * q^60 + 877 * q^61 - 278 * q^62 - 5708 * q^63 - 192 * q^64 - 3846 * q^65 - 4156 * q^66 + 1763 * q^67 - 2528 * q^68 - 1970 * q^69 - 3968 * q^70 - 6362 * q^71 - 152 * q^72 - 3584 * q^73 - 888 * q^74 + 3143 * q^75 + 360 * q^76 + 6347 * q^77 - 1460 * q^78 + 2642 * q^79 + 864 * q^80 + 1043 * q^81 + 5542 * q^82 - 372 * q^83 + 2212 * q^84 + 5136 * q^85 - 2326 * q^86 + 5451 * q^87 - 104 * q^88 - 4283 * q^89 + 5104 * q^90 - 6182 * q^91 - 92 * q^92 - 8734 * q^93 - 2550 * q^94 + 9449 * q^95 + 192 * q^96 + 7599 * q^97 + 3928 * q^98 + 1377 * q^99

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