LMFDB - Embedded newform 52.4.f.b.31.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [52,4,Mod(31,52)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(52, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("52.31");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 52 = 2^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	52.f (of order $4$, degree $2$, 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:	$3.06809932030$
Analytic rank:	$0$
Dimension:	$36$
Relative dimension:	$18$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			31.5
Character	$\chi$	$=$	52.31
Dual form			52.4.f.b.47.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.84904 - 2.14034i) q^{2} -1.29511i q^{3} +(-1.16213 + 7.91514i) q^{4} +(-10.6631 + 10.6631i) q^{5} +(-2.77198 + 2.39471i) q^{6} +(-7.71781 + 7.71781i) q^{7} +(19.0899 - 12.1480i) q^{8} +25.3227 q^{9} +(42.5392 + 3.10621i) q^{10} +(-37.6703 + 37.6703i) q^{11} +(10.2510 + 1.50508i) q^{12} +(-12.8764 + 45.0688i) q^{13} +(30.7893 + 2.24823i) q^{14} +(13.8099 + 13.8099i) q^{15} +(-61.2989 - 18.3968i) q^{16} -74.8326i q^{17} +(-46.8226 - 54.1992i) q^{18} +(28.9136 + 28.9136i) q^{19} +(-72.0081 - 96.7919i) q^{20} +(9.99541 + 9.99541i) q^{21} +(150.281 + 10.9735i) q^{22} -197.094 q^{23} +(-15.7330 - 24.7235i) q^{24} -102.404i q^{25} +(120.272 - 55.7741i) q^{26} -67.7636i q^{27} +(-52.1185 - 70.0566i) q^{28} -50.4142 q^{29} +(4.02289 - 55.0929i) q^{30} +(118.823 + 118.823i) q^{31} +(73.9686 + 165.217i) q^{32} +(48.7871 + 48.7871i) q^{33} +(-160.167 + 138.368i) q^{34} -164.592i q^{35} +(-29.4281 + 200.433i) q^{36} +(16.2523 + 16.2523i) q^{37} +(8.42267 - 115.347i) q^{38} +(58.3691 + 16.6763i) q^{39} +(-74.0220 + 333.094i) q^{40} +(60.0957 - 60.0957i) q^{41} +(2.91171 - 39.8755i) q^{42} +454.584 q^{43} +(-254.388 - 341.943i) q^{44} +(-270.019 + 270.019i) q^{45} +(364.434 + 421.848i) q^{46} +(173.328 - 173.328i) q^{47} +(-23.8258 + 79.3888i) q^{48} +223.871i q^{49} +(-219.179 + 189.348i) q^{50} -96.9165 q^{51} +(-341.762 - 154.294i) q^{52} +312.128 q^{53} +(-145.037 + 125.297i) q^{54} -803.364i q^{55} +(-53.5761 + 241.089i) q^{56} +(37.4463 - 37.4463i) q^{57} +(93.2178 + 107.904i) q^{58} +(-313.025 + 313.025i) q^{59} +(-125.356 + 93.2584i) q^{60} +38.0900 q^{61} +(34.6136 - 474.028i) q^{62} +(-195.436 + 195.436i) q^{63} +(216.850 - 463.810i) q^{64} +(-343.272 - 617.876i) q^{65} +(14.2119 - 194.630i) q^{66} +(-29.1322 - 29.1322i) q^{67} +(592.311 + 86.9649i) q^{68} +255.258i q^{69} +(-352.282 + 304.336i) q^{70} +(366.856 + 366.856i) q^{71} +(483.408 - 307.621i) q^{72} +(-331.694 - 331.694i) q^{73} +(4.73436 - 64.8365i) q^{74} -132.624 q^{75} +(-262.456 + 195.254i) q^{76} -581.464i q^{77} +(-72.2336 - 155.765i) q^{78} +670.706i q^{79} +(849.804 - 457.470i) q^{80} +595.951 q^{81} +(-239.744 - 17.5062i) q^{82} +(94.6029 + 94.6029i) q^{83} +(-90.7310 + 67.4992i) q^{84} +(797.949 + 797.949i) q^{85} +(-840.543 - 972.966i) q^{86} +65.2919i q^{87} +(-261.502 + 1176.74i) q^{88} +(-750.787 - 750.787i) q^{89} +(1077.21 + 78.6577i) q^{90} +(-248.455 - 447.210i) q^{91} +(229.048 - 1560.02i) q^{92} +(153.888 - 153.888i) q^{93} +(-691.469 - 50.4912i) q^{94} -616.618 q^{95} +(213.974 - 95.7975i) q^{96} +(-477.621 + 477.621i) q^{97} +(479.160 - 413.945i) q^{98} +(-953.912 + 953.912i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 2 q^{2} - 20 q^{5} - 16 q^{6} - 40 q^{8} - 332 q^{9} - 96 q^{13} + 204 q^{14} + 52 q^{16} + 330 q^{18} + 500 q^{20} + 224 q^{21} - 48 q^{22} - 496 q^{24} + 570 q^{26} - 356 q^{28} + 560 q^{29} + 292 q^{32}+ \cdots + 3226 q^{98}+O(q^{100}) $ 36 * q + 2 * q^2 - 20 * q^5 - 16 * q^6 - 40 * q^8 - 332 * q^9 - 96 * q^13 + 204 * q^14 + 52 * q^16 + 330 * q^18 + 500 * q^20 + 224 * q^21 - 48 * q^22 - 496 * q^24 + 570 * q^26 - 356 * q^28 + 560 * q^29 + 292 * q^32 + 104 * q^33 - 416 * q^34 - 788 * q^37 - 2788 * q^40 + 1124 * q^41 - 1172 * q^42 - 156 * q^44 - 972 * q^45 - 668 * q^46 + 1332 * q^48 + 1354 * q^50 - 164 * q^52 + 1208 * q^53 + 2272 * q^54 - 1248 * q^57 - 2972 * q^58 + 692 * q^60 + 2632 * q^61 + 596 * q^65 + 3312 * q^66 + 2948 * q^68 - 1008 * q^70 - 908 * q^72 - 196 * q^73 - 1504 * q^74 - 3472 * q^76 - 2688 * q^78 - 1096 * q^80 - 764 * q^81 + 3744 * q^84 + 600 * q^85 - 3952 * q^86 - 2748 * q^89 - 1224 * q^92 - 6128 * q^93 + 2884 * q^94 + 4792 * q^96 - 1820 * q^97 + 3226 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/52\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.84904	−	2.14034i	−0.653733	−	0.756725i
$2$	−1.84904	−	2.14034i	−0.653733	−	0.756725i
$3$		−	1.29511i		−	0.249244i	−0.992204	−	0.124622i	$-0.960228\pi$
$3$		−	1.29511i		−	0.249244i	0.992204	−	0.124622i	$-0.0397718\pi$
$4$	−1.16213	+	7.91514i	−0.145266	+	0.989393i
$5$	−10.6631	+	10.6631i	−0.953737	+	0.953737i	−0.998976	−	0.0452389i	$-0.985595\pi$
$5$	−10.6631	+	10.6631i	−0.953737	+	0.953737i	0.0452389	+	0.998976i	$0.485595\pi$
$6$	−2.77198	+	2.39471i	−0.188609	+	0.162939i
$7$	−7.71781	+	7.71781i	−0.416723	+	0.416723i	−0.884072	−	0.467350i	$-0.845209\pi$
$7$	−7.71781	+	7.71781i	−0.416723	+	0.416723i	0.467350	+	0.884072i	$0.345209\pi$
$8$	19.0899	−	12.1480i	0.843663	−	0.536873i
$9$	25.3227			0.937877
$10$	42.5392	+	3.10621i	1.34521	+	0.0982271i
$11$	−37.6703	+	37.6703i	−1.03255	+	1.03255i	−0.0330942	+	0.999452i	$0.510536\pi$
$11$	−37.6703	+	37.6703i	−1.03255	+	1.03255i	−0.999452	+	0.0330942i	$0.989464\pi$
$12$	10.2510	+	1.50508i	0.246600	+	0.0362066i
$13$	−12.8764	+	45.0688i	−0.274712	+	0.961526i
$13$	−12.8764	+	45.0688i	−0.274712	+	0.961526i
$14$	30.7893	+	2.24823i	0.587770	+	0.0429190i
$15$	13.8099	+	13.8099i	0.237713	+	0.237713i
$16$	−61.2989	−	18.3968i	−0.957796	−	0.287449i
$17$		−	74.8326i		−	1.06762i	−0.845604	−	0.533811i	$-0.820759\pi$
$17$		−	74.8326i		−	1.06762i	0.845604	−	0.533811i	$-0.179241\pi$
$18$	−46.8226	−	54.1992i	−0.613122	−	0.709715i
$19$	28.9136	+	28.9136i	0.349118	+	0.349118i	0.859781	−	0.510663i	$-0.170600\pi$
$19$	28.9136	+	28.9136i	0.349118	+	0.349118i	−0.510663	+	0.859781i	$0.670600\pi$
$20$	−72.0081	−	96.7919i	−0.805076	−	1.08217i
$21$	9.99541	+	9.99541i	0.103866	+	0.103866i
$22$	150.281	+	10.9735i	1.45636	+	0.106344i
$23$	−197.094			−1.78682			−0.893410	−	0.449242i	$-0.851694\pi$
$23$	−197.094			−1.78682			−0.893410	+	0.449242i	$0.851694\pi$
$24$	−15.7330	−	24.7235i	−0.133812	−	0.210278i
$25$		−	102.404i		−	0.819230i
$26$	120.272	−	55.7741i	0.907200	−	0.420700i
$27$		−	67.7636i		−	0.483004i
$28$	−52.1185	−	70.0566i	−0.351767	−	0.472838i
$29$	−50.4142			−0.322817			−0.161408	−	0.986888i	$-0.551604\pi$
$29$	−50.4142			−0.322817			−0.161408	+	0.986888i	$0.551604\pi$
$30$	4.02289	−	55.0929i	0.0244825	−	0.335285i
$31$	118.823	+	118.823i	0.688425	+	0.688425i	0.961884	−	0.273459i	$-0.0881677\pi$
$31$	118.823	+	118.823i	0.688425	+	0.688425i	−0.273459	+	0.961884i	$0.588168\pi$
$32$	73.9686	+	165.217i	0.408623	+	0.912703i
$33$	48.7871	+	48.7871i	0.257356	+	0.257356i
$34$	−160.167	+	138.368i	−0.807897	+	0.697940i
$35$		−	164.592i		−	0.794888i
$36$	−29.4281	+	200.433i	−0.136241	+	0.927929i
$37$	16.2523	+	16.2523i	0.0722124	+	0.0722124i	0.742291	−	0.670078i	$-0.233739\pi$
$37$	16.2523	+	16.2523i	0.0722124	+	0.0722124i	−0.670078	+	0.742291i	$0.733739\pi$
$38$	8.42267	−	115.347i	0.0359563	−	0.492416i
$39$	58.3691	+	16.6763i	0.239655	+	0.0684704i
$40$	−74.0220	+	333.094i	−0.292597	+	1.31667i
$41$	60.0957	−	60.0957i	0.228911	−	0.228911i	−0.583326	−	0.812238i	$-0.698249\pi$
$41$	60.0957	−	60.0957i	0.228911	−	0.228911i	0.812238	+	0.583326i	$0.198249\pi$
$42$	2.91171	−	39.8755i	0.0106973	−	0.146498i
$43$	454.584			1.61217			0.806087	−	0.591798i	$-0.201581\pi$
$43$	454.584			1.61217			0.806087	+	0.591798i	$0.201581\pi$
$44$	−254.388	−	341.943i	−0.871600	−	1.17159i
$45$	−270.019	+	270.019i	−0.894489	+	0.894489i
$46$	364.434	+	421.848i	1.16810	+	1.35213i
$47$	173.328	−	173.328i	0.537924	−	0.537924i	−0.384995	−	0.922919i	$-0.625797\pi$
$47$	173.328	−	173.328i	0.537924	−	0.537924i	0.922919	+	0.384995i	$0.125797\pi$
$48$	−23.8258	+	79.3888i	−0.0716451	+	0.238725i
$49$			223.871i			0.652685i
$50$	−219.179	+	189.348i	−0.619932	+	0.535558i
$51$	−96.9165			−0.266098
$52$	−341.762	−	154.294i	−0.911421	−	0.411475i
$53$	312.128			0.808944			0.404472	−	0.914550i	$-0.367455\pi$
$53$	312.128			0.808944			0.404472	+	0.914550i	$0.367455\pi$
$54$	−145.037	+	125.297i	−0.365501	+	0.315756i
$55$		−	803.364i		−	1.96956i
$56$	−53.5761	+	241.089i	−0.127846	+	0.575300i
$57$	37.4463	−	37.4463i	0.0870155	−	0.0870155i
$58$	93.2178	+	107.904i	0.211036	+	0.244284i
$59$	−313.025	+	313.025i	−0.690717	+	0.690717i	−0.962390	−	0.271672i	$-0.912423\pi$
$59$	−313.025	+	313.025i	−0.690717	+	0.690717i	0.271672	+	0.962390i	$0.412423\pi$
$60$	−125.356	+	93.2584i	−0.269723	+	0.200660i
$61$	38.0900			0.0799497			0.0399748	−	0.999201i	$-0.487272\pi$
$61$	38.0900			0.0799497			0.0399748	+	0.999201i	$0.487272\pi$
$62$	34.6136	−	474.028i	0.0709021	−	0.970995i
$63$	−195.436	+	195.436i	−0.390835	+	0.390835i
$64$	216.850	−	463.810i	0.423535	−	0.905880i
$65$	−343.272	−	617.876i	−0.655040	−	1.17905i
$66$	14.2119	−	194.630i	0.0265056	−	0.362990i
$67$	−29.1322	−	29.1322i	−0.0531205	−	0.0531205i	0.680048	−	0.733168i	$-0.261959\pi$
$67$	−29.1322	−	29.1322i	−0.0531205	−	0.0531205i	−0.733168	+	0.680048i	$0.761959\pi$
$68$	592.311	+	86.9649i	1.05630	+	0.155089i
$69$			255.258i			0.445354i
$70$	−352.282	+	304.336i	−0.601511	+	0.519645i
$71$	366.856	+	366.856i	0.613208	+	0.613208i	0.943781	−	0.330572i	$-0.107242\pi$
$71$	366.856	+	366.856i	0.613208	+	0.613208i	−0.330572	+	0.943781i	$0.607242\pi$
$72$	483.408	−	307.621i	0.791253	−	0.503521i
$73$	−331.694	−	331.694i	−0.531805	−	0.531805i	0.389304	−	0.921109i	$-0.372716\pi$
$73$	−331.694	−	331.694i	−0.531805	−	0.531805i	−0.921109	+	0.389304i	$0.872716\pi$
$74$	4.73436	−	64.8365i	0.00743728	−	0.101853i
$75$	−132.624			−0.204188
$76$	−262.456	+	195.254i	−0.396129	+	0.294700i
$77$		−	581.464i		−	0.860571i
$78$	−72.2336	−	155.765i	−0.104857	−	0.226114i
$79$			670.706i			0.955193i	0.878579	+	0.477597i	$0.158492\pi$
$79$			670.706i			0.955193i	−0.878579	+	0.477597i	$0.841508\pi$
$80$	849.804	−	457.470i	1.18764	−	0.639334i
$81$	595.951			0.817492
$82$	−239.744	−	17.5062i	−0.322870	−	0.0235760i
$83$	94.6029	+	94.6029i	0.125109	+	0.125109i	0.766889	−	0.641780i	$-0.221804\pi$
$83$	94.6029	+	94.6029i	0.125109	+	0.125109i	−0.641780	+	0.766889i	$0.721804\pi$
$84$	−90.7310	+	67.4992i	−0.117852	+	0.0876758i
$85$	797.949	+	797.949i	1.01823	+	1.01823i
$86$	−840.543	−	972.966i	−1.05393	−	1.21997i
$87$			65.2919i			0.0804601i
$88$	−261.502	+	1176.74i	−0.316775	+	1.42547i
$89$	−750.787	−	750.787i	−0.894194	−	0.894194i	0.100721	−	0.994915i	$-0.467885\pi$
$89$	−750.787	−	750.787i	−0.894194	−	0.894194i	−0.994915	+	0.100721i	$0.967885\pi$
$90$	1077.21	+	78.6577i	1.26164	+	0.0921250i
$91$	−248.455	−	447.210i	−0.286211	−	0.515169i
$92$	229.048	−	1560.02i	0.259564	−	1.76787i
$93$	153.888	−	153.888i	0.171586	−	0.171586i
$94$	−691.469	−	50.4912i	−0.758719	−	0.0554018i
$95$	−616.618			−0.665933
$96$	213.974	−	95.7975i	0.227486	−	0.101847i
$97$	−477.621	+	477.621i	−0.499949	+	0.499949i	−0.911422	−	0.411473i	$-0.865014\pi$
$97$	−477.621	+	477.621i	−0.499949	+	0.499949i	0.411473	+	0.911422i	$0.365014\pi$
$98$	479.160	−	413.945i	0.493903	−	0.426682i
$99$	−953.912	+	953.912i	−0.968402	+	0.968402i
$100$	810.540	+	119.006i	0.810540	+	0.119006i
$101$			1306.08i			1.28673i	0.765561	+	0.643364i	$0.222462\pi$
$101$			1306.08i			1.28673i	−0.765561	+	0.643364i	$0.777538\pi$
$102$	179.202	+	207.434i	0.173957	+	0.201363i
$103$	−1592.54			−1.52347			−0.761737	−	0.647886i	$-0.775653\pi$
$103$	−1592.54			−1.52347			−0.761737	+	0.647886i	$0.775653\pi$
$104$	301.690	+	1016.78i	0.284453	+	0.958690i
$105$	−213.164			−0.198121
$106$	−577.135	−	668.060i	−0.528833	−	0.612148i
$107$			628.733i			0.568055i	0.958816	+	0.284028i	$0.0916707\pi$
$107$			628.733i			0.568055i	−0.958816	+	0.284028i	$0.908329\pi$
$108$	536.359	+	78.7498i	0.477881	+	0.0701639i
$109$	−693.576	+	693.576i	−0.609473	+	0.609473i	−0.942808	−	0.333336i	$-0.891826\pi$
$109$	−693.576	+	693.576i	−0.609473	+	0.609473i	0.333336	+	0.942808i	$0.391826\pi$
$110$	−1719.47	+	1485.45i	−1.49041	+	1.28756i
$111$	21.0485	−	21.0485i	0.0179985	−	0.0179985i
$112$	615.076	−	331.111i	0.518922	−	0.279348i
$113$	1989.07			1.65589			0.827947	−	0.560807i	$-0.189509\pi$
$113$	1989.07			1.65589			0.827947	+	0.560807i	$0.189509\pi$
$114$	−149.387	−	10.9083i	−0.122732	−	0.00896188i
$115$	2101.63	−	2101.63i	1.70416	−	1.70416i
$116$	58.5876	−	399.036i	0.0468942	−	0.319393i
$117$	−326.064	+	1141.26i	−0.257646	+	0.901794i
$118$	1248.77	+	91.1855i	0.974228	+	0.0711382i
$119$	577.544	+	577.544i	0.444902	+	0.444902i
$120$	431.393	+	95.8666i	0.328172	+	0.0729282i
$121$		−	1507.10i		−	1.13230i
$122$	−70.4299	−	81.5257i	−0.0522657	−	0.0604999i
$123$	−77.8305	−	77.8305i	−0.0570548	−	0.0570548i
$124$	−1078.58	+	802.411i	−0.781127	+	0.581118i
$125$	−240.946	−	240.946i	−0.172407	−	0.172407i
$126$	779.667	+	56.9314i	0.551256	+	0.0402528i
$127$	1889.18			1.31998			0.659990	−	0.751275i	$-0.270561\pi$
$127$	1889.18			1.31998			0.659990	+	0.751275i	$0.270561\pi$
$128$	−1393.68	+	393.469i	−0.962381	+	0.271704i
$129$		−	588.737i		−	0.401824i
$130$	−687.743	+	1877.19i	−0.463993	+	1.26647i
$131$			1935.37i			1.29080i	0.763846	+	0.645399i	$0.223309\pi$
$131$			1935.37i			1.29080i	−0.763846	+	0.645399i	$0.776691\pi$
$132$	−442.854	+	329.460i	−0.292011	+	0.217241i
$133$	−446.299			−0.290970
$134$	−8.48636	+	116.220i	−0.00547097	+	0.0749242i
$135$	722.571	+	722.571i	0.460659	+	0.460659i
$136$	−909.070	−	1428.55i	−0.573177	−	0.900714i
$137$	−371.694	−	371.694i	−0.231796	−	0.231796i	0.581646	−	0.813442i	$-0.302409\pi$
$137$	−371.694	−	371.694i	−0.231796	−	0.231796i	−0.813442	+	0.581646i	$0.802409\pi$
$138$	546.339	−	471.981i	0.337011	−	0.291143i
$139$		−	2312.75i		−	1.41126i	−0.708580	−	0.705630i	$-0.750664\pi$
$139$		−	2312.75i		−	1.41126i	0.708580	−	0.705630i	$-0.249336\pi$
$140$	1302.77	+	191.276i	0.786456	+	0.115470i
$141$	−224.478	−	224.478i	−0.134074	−	0.134074i
$142$	106.867	−	1463.53i	0.0631554	−	0.864905i
$143$	−1212.70	−	2182.81i	−0.709168	−	1.27647i
$144$	−1552.25	−	465.856i	−0.898295	−	0.269592i
$145$	537.572	−	537.572i	0.307882	−	0.307882i
$146$	−96.6239	+	1323.25i	−0.0547716	+	0.750089i
$147$	289.937			0.162678
$148$	−147.526	+	109.752i	−0.0819363	+	0.0609564i
$149$	−1220.44	+	1220.44i	−0.671020	+	0.671020i	−0.957951	−	0.286931i	$-0.907365\pi$
$149$	−1220.44	+	1220.44i	−0.671020	+	0.671020i	0.286931	+	0.957951i	$0.407365\pi$
$150$	245.227	+	283.861i	0.133485	+	0.154514i
$151$	691.393	−	691.393i	0.372614	−	0.372614i	−0.495814	−	0.868429i	$-0.665130\pi$
$151$	691.393	−	691.393i	0.372614	−	0.372614i	0.868429	+	0.495814i	$0.165130\pi$
$152$	903.202	+	200.715i	0.481969	+	0.107106i
$153$		−	1894.96i		−	1.00130i
$154$	−1244.53	+	1075.15i	−0.651215	+	0.562584i
$155$	−2534.04			−1.31315
$156$	−199.827	+	442.620i	−0.102558	+	0.227166i
$157$	1836.11			0.933359			0.466679	−	0.884427i	$-0.345450\pi$
$157$	1836.11			0.933359			0.466679	+	0.884427i	$0.345450\pi$
$158$	1435.54	−	1240.16i	0.722819	−	0.624442i
$159$		−	404.239i		−	0.201624i
$160$	−2550.46	−	972.991i	−1.26020	−	0.480761i
$161$	1521.13	−	1521.13i	0.744608	−	0.744608i
$162$	−1101.94	−	1275.54i	−0.534421	−	0.618616i
$163$	206.302	−	206.302i	0.0991338	−	0.0991338i	−0.655800	−	0.754934i	$-0.727669\pi$
$163$	206.302	−	206.302i	0.0991338	−	0.0991338i	0.754934	+	0.655800i	$0.227669\pi$
$164$	405.827	+	545.504i	0.193230	+	0.259736i
$165$	−1040.44			−0.490900
$166$	27.5583	−	377.407i	0.0128852	−	0.176461i
$167$	2095.93	−	2095.93i	0.971184	−	0.971184i	−0.0284121	−	0.999596i	$-0.509045\pi$
$167$	2095.93	−	2095.93i	0.971184	−	0.971184i	0.999596	+	0.0284121i	$0.00904506\pi$
$168$	312.236	+	69.3869i	0.143390	+	0.0318650i
$169$	−1865.40	−	1160.64i	−0.849066	−	0.528286i
$170$	232.446	−	3183.32i	0.104869	−	1.43617i
$171$	732.170	+	732.170i	0.327430	+	0.327430i
$172$	−528.284	+	3598.10i	−0.234193	+	1.59507i
$173$			3878.99i			1.70470i	0.522968	+	0.852352i	$0.324825\pi$
$173$			3878.99i			1.70470i	−0.522968	+	0.852352i	$0.675175\pi$
$174$	139.747	−	120.727i	0.0608862	−	0.0525995i
$175$	790.333	+	790.333i	0.341392	+	0.341392i
$176$	3002.16	−	1616.14i	1.28577	−	0.692164i
$177$	405.401	+	405.401i	0.172157	+	0.172157i
$178$	−218.708	+	2995.17i	−0.0920946	+	1.26122i
$179$	−1563.04			−0.652665			−0.326333	−	0.945255i	$-0.605813\pi$
$179$	−1563.04			−0.652665			−0.326333	+	0.945255i	$0.605813\pi$
$180$	−1823.44	−	2451.03i	−0.755062	−	1.01494i
$181$		−	1080.24i		−	0.443611i	−0.975091	−	0.221806i	$-0.928805\pi$
$181$		−	1080.24i		−	0.443611i	0.975091	−	0.221806i	$-0.0711951\pi$
$182$	−497.779	+	1358.69i	−0.202735	+	0.553366i
$183$		−	49.3308i		−	0.0199270i
$184$	−3762.50	+	2394.30i	−1.50747	+	0.959295i
$185$	−346.599			−0.137743
$186$	−613.919	−	44.8284i	−0.242015	−	0.0176719i
$187$	2818.96	+	2818.96i	1.10237	+	1.10237i
$188$	1170.48	+	1573.34i	0.454076	+	0.610360i
$189$	522.987	+	522.987i	0.201279	+	0.201279i
$190$	1140.15	+	1319.77i	0.435343	+	0.503928i
$191$			1684.06i			0.637982i	0.947758	+	0.318991i	$0.103344\pi$
$191$			1684.06i			0.637982i	−0.947758	+	0.318991i	$0.896656\pi$
$192$	−600.685	−	280.845i	−0.225785	−	0.105564i
$193$	1953.15	+	1953.15i	0.728450	+	0.728450i	0.970311	−	0.241861i	$-0.0777578\pi$
$193$	1953.15	+	1953.15i	0.728450	+	0.728450i	−0.241861	+	0.970311i	$0.577758\pi$
$194$	1905.41	+	139.133i	0.705157	+	0.0514906i
$195$	−800.217	+	444.575i	−0.293870	+	0.163265i
$196$	−1771.97	−	260.166i	−0.645761	−	0.0948126i
$197$	−418.716	+	418.716i	−0.151433	+	0.151433i	−0.778758	−	0.627325i	$-0.784150\pi$
$197$	−418.716	+	418.716i	−0.151433	+	0.151433i	0.627325	+	0.778758i	$0.284150\pi$
$198$	3805.52	+	277.879i	1.36589	+	0.0997375i
$199$	1261.88			0.449509			0.224755	−	0.974415i	$-0.427842\pi$
$199$	1261.88			0.449509			0.224755	+	0.974415i	$0.427842\pi$
$200$	−1244.01	−	1954.88i	−0.439822	−	0.691154i
$201$	−37.7295	+	37.7295i	−0.0132400	+	0.0132400i
$202$	2795.45	−	2414.98i	0.973699	−	0.841176i
$203$	389.087	−	389.087i	0.134525	−	0.134525i
$204$	112.629	−	767.108i	0.0386550	−	0.263276i
$205$			1281.61i			0.436643i
$206$	2944.67	+	3408.59i	0.995946	+	1.15285i
$207$	−4990.94			−1.67582
$208$	1618.43	−	2525.79i	0.539509	−	0.841980i
$209$	−2178.37			−0.720960
$210$	394.149	+	456.244i	0.129518	+	0.149923i
$211$		−	1974.61i		−	0.644256i	−0.946696	−	0.322128i	$-0.895602\pi$
$211$		−	1974.61i		−	0.644256i	0.946696	−	0.322128i	$-0.104398\pi$
$212$	−362.731	+	2470.53i	−0.117512	+	0.800363i
$213$	475.119	−	475.119i	0.152838	−	0.152838i
$214$	1345.70	−	1162.55i	0.429862	−	0.371357i
$215$	−4847.28	+	4847.28i	−1.53759	+	1.53759i
$216$	−823.195	−	1293.60i	−0.259312	−	0.407493i
$217$	−1834.10			−0.573764
$218$	2766.94	+	202.042i	0.859636	+	0.0627707i
$219$	−429.580	+	429.580i	−0.132549	+	0.132549i
$220$	6358.74	+	933.609i	1.94866	+	0.286109i
$221$	3372.62	+	963.572i	1.02655	+	0.293289i
$222$	−83.9703	−	6.13152i	−0.0253861	−	0.00185370i
$223$	−1248.10	−	1248.10i	−0.374795	−	0.374795i	0.494425	−	0.869220i	$-0.335379\pi$
$223$	−1248.10	−	1248.10i	−0.374795	−	0.374795i	−0.869220	+	0.494425i	$0.835379\pi$
$224$	−1845.99	−	704.237i	−0.550626	−	0.210062i
$225$		−	2593.14i		−	0.768337i
$226$	−3677.86	−	4257.29i	−1.08251	−	1.25306i
$227$	−2445.98	−	2445.98i	−0.715178	−	0.715178i	0.252436	−	0.967614i	$-0.418768\pi$
$227$	−2445.98	−	2445.98i	−0.715178	−	0.715178i	−0.967614	+	0.252436i	$0.918768\pi$
$228$	252.875	+	339.910i	0.0734521	+	0.0987328i
$229$	−2197.09	−	2197.09i	−0.634007	−	0.634007i	0.315064	−	0.949071i	$-0.397974\pi$
$229$	−2197.09	−	2197.09i	−0.634007	−	0.634007i	−0.949071	+	0.315064i	$0.897974\pi$
$230$	−8384.20	−	612.215i	−2.40364	−	0.175514i
$231$	−753.059			−0.214492
$232$	−962.403	+	612.434i	−0.272349	+	0.173312i
$233$			5676.88i			1.59616i	0.602553	+	0.798079i	$0.294150\pi$
$233$			5676.88i			1.59616i	−0.602553	+	0.798079i	$0.705850\pi$
$234$	3045.60	−	1412.35i	0.850842	−	0.394565i
$235$			3696.42i			1.02608i
$236$	−2113.86	−	2841.41i	−0.583053	−	0.783728i
$237$	868.637			0.238076
$238$	168.241	−	2304.04i	0.0458213	−	0.627516i
$239$	3427.55	+	3427.55i	0.927655	+	0.927655i	0.997554	−	0.0698990i	$-0.0222677\pi$
$239$	3427.55	+	3427.55i	0.927655	+	0.927655i	−0.0698990	+	0.997554i	$0.522268\pi$
$240$	−592.474	−	1100.59i	−0.159350	−	0.296011i
$241$	85.5677	+	85.5677i	0.0228710	+	0.0228710i	0.718450	−	0.695579i	$-0.244852\pi$
$241$	85.5677	+	85.5677i	0.0228710	+	0.0228710i	−0.695579	+	0.718450i	$0.744852\pi$
$242$	−3225.70	+	2786.68i	−0.856843	+	0.740225i
$243$		−	2601.44i		−	0.686759i
$244$	−44.2654	+	301.488i	−0.0116139	+	0.0791016i
$245$	−2387.16	−	2387.16i	−0.622490	−	0.622490i
$246$	−22.6724	+	310.495i	−0.00587617	+	0.0804734i
$247$	−1675.40	+	930.800i	−0.431593	+	0.239779i
$248$	3711.78	+	824.852i	0.950395	+	0.211202i
$249$	122.521	−	122.521i	0.0311826	−	0.0311826i
$250$	−70.1889	+	961.227i	−0.0177565	+	0.243173i
$251$	5442.95			1.36875			0.684374	−	0.729131i	$-0.260076\pi$
$251$	5442.95			1.36875			0.684374	+	0.729131i	$0.260076\pi$
$252$	−1319.78	−	1774.02i	−0.329914	−	0.443464i
$253$	7424.57	−	7424.57i	1.84498	−	1.84498i
$254$	−3493.16	−	4043.48i	−0.862914	−	0.998861i
$255$	1033.43	−	1033.43i	0.253788	−	0.253788i
$256$	3419.12	+	2255.40i	0.834746	+	0.550636i
$257$		−	2778.19i		−	0.674313i	−0.941449	−	0.337157i	$-0.890535\pi$
$257$		−	2778.19i		−	0.674313i	0.941449	−	0.337157i	$-0.109465\pi$
$258$	−1260.10	+	1088.60i	−0.304071	+	0.262686i
$259$	−250.864			−0.0601850
$260$	5289.50	−	1999.00i	1.26170	−	0.476817i
$261$	−1276.62			−0.302763
$262$	4142.36	−	3578.58i	0.976779	−	0.843837i
$263$		−	6299.91i		−	1.47707i	−0.674216	−	0.738534i	$-0.735518\pi$
$263$		−	6299.91i		−	1.47707i	0.674216	−	0.738534i	$-0.264482\pi$
$264$	1524.01	+	338.674i	0.355289	+	0.0789543i
$265$	−3328.25	+	3328.25i	−0.771520	+	0.771520i
$266$	825.224	+	955.233i	0.190217	+	0.220185i
$267$	−972.351	+	972.351i	−0.222872	+	0.222872i
$268$	264.441	−	196.731i	0.0602736	−	0.0448404i
$269$	−1220.79			−0.276702			−0.138351	−	0.990383i	$-0.544180\pi$
$269$	−1220.79			−0.276702			−0.138351	+	0.990383i	$0.544180\pi$
$270$	210.488	−	2882.61i	0.0474441	−	0.649741i
$271$	609.759	−	609.759i	0.136680	−	0.136680i	−0.635457	−	0.772137i	$-0.719188\pi$
$271$	609.759	−	609.759i	0.136680	−	0.136680i	0.772137	+	0.635457i	$0.219188\pi$
$272$	−1376.68	+	4587.16i	−0.306888	+	1.02256i
$273$	−579.186	+	321.777i	−0.128403	+	0.0713364i
$274$	−108.276	+	1482.83i	−0.0238730	+	0.326938i
$275$	3857.58	+	3857.58i	0.845893	+	0.845893i
$276$	−2020.40	−	296.642i	−0.440630	−	0.0646947i
$277$		−	2159.74i		−	0.468470i	−0.972180	−	0.234235i	$-0.924741\pi$
$277$		−	2159.74i		−	0.468470i	0.972180	−	0.234235i	$-0.0752585\pi$
$278$	−4950.08	+	4276.37i	−1.06794	+	0.922588i
$279$	3008.91	+	3008.91i	0.645658	+	0.645658i
$280$	−1999.47	−	3142.04i	−0.426754	−	0.670618i
$281$	4526.08	+	4526.08i	0.960866	+	0.960866i	0.999263	−	0.0383964i	$-0.0122249\pi$
$281$	4526.08	+	4526.08i	0.960866	+	0.960866i	−0.0383964	+	0.999263i	$0.512225\pi$
$282$	−65.3916	+	895.529i	−0.0138086	+	0.189106i
$283$	−7599.92			−1.59636			−0.798178	−	0.602422i	$-0.794202\pi$
$283$	−7599.92			−1.59636			−0.798178	+	0.602422i	$0.794202\pi$
$284$	−3330.05	+	2477.38i	−0.695782	+	0.517626i
$285$			798.588i			0.165980i
$286$	−2429.63	+	6631.69i	−0.502333	+	1.37112i
$287$			927.614i			0.190785i
$288$	1873.08	+	4183.74i	0.383238	+	0.856004i
$289$	−686.924			−0.139818
$290$	−2144.58	−	156.597i	−0.434255	−	0.0317094i
$291$	618.571	+	618.571i	0.124609	+	0.124609i
$292$	3010.87	−	2239.93i	0.603417	−	0.448911i
$293$	−3856.57	−	3856.57i	−0.768954	−	0.768954i	0.208968	−	0.977922i	$-0.432989\pi$
$293$	−3856.57	−	3856.57i	−0.768954	−	0.768954i	−0.977922	+	0.208968i	$0.932989\pi$
$294$	−536.105	−	620.565i	−0.106348	−	0.123102i
$295$		−	6675.63i		−	1.31753i
$296$	507.688	+	112.821i	0.0996917	+	0.0221541i
$297$	2552.67	+	2552.67i	0.498724	+	0.498724i
$298$	4868.78	+	355.519i	0.946445	+	0.0691095i
$299$	2537.85	−	8882.78i	0.490861	−	1.71808i
$300$	154.126	−	1049.74i	0.0296615	−	0.202022i
$301$	−3508.39	+	3508.39i	−0.671829	+	0.671829i
$302$	−2758.23	−	201.406i	−0.525557	−	0.0383762i
$303$	1691.51			0.320709
$304$	−1240.46	−	2304.29i	−0.234030	−	0.434737i
$305$	−406.158	+	406.158i	−0.0762510	+	0.0762510i
$306$	−4055.87	+	3503.86i	−0.757708	+	0.654582i
$307$	−669.061	+	669.061i	−0.124382	+	0.124382i	−0.766558	−	0.642176i	$-0.778032\pi$
$307$	−669.061	+	669.061i	−0.124382	+	0.124382i	0.642176	+	0.766558i	$0.278032\pi$
$308$	4602.37	+	675.734i	0.851442	+	0.125011i
$309$			2062.52i			0.379717i
$310$	4685.53	+	5423.71i	0.858452	+	0.993696i
$311$	2935.12			0.535162			0.267581	−	0.963535i	$-0.413776\pi$
$311$	2935.12			0.535162			0.267581	+	0.963535i	$0.413776\pi$
$312$	1316.85	−	390.721i	0.238948	−	0.0708982i
$313$	−2554.13			−0.461240			−0.230620	−	0.973044i	$-0.574075\pi$
$313$	−2554.13			−0.461240			−0.230620	+	0.973044i	$0.574075\pi$
$314$	−3395.03	−	3929.90i	−0.610168	−	0.706296i
$315$		−	4167.90i		−	0.745507i
$316$	−5308.73	−	779.444i	−0.945061	−	0.138757i
$317$	3207.19	−	3207.19i	0.568245	−	0.568245i	−0.363391	−	0.931637i	$-0.618381\pi$
$317$	3207.19	−	3207.19i	0.568245	−	0.568245i	0.931637	+	0.363391i	$0.118381\pi$
$318$	−865.210	+	747.454i	−0.152574	+	0.131809i
$319$	1899.12	−	1899.12i	0.333323	−	0.333323i
$320$	2633.36	+	7257.96i	0.460030	+	1.26791i
$321$	814.278			0.141584
$322$	−6068.37	−	443.113i	−1.05024	−	0.0766886i
$323$	2163.68	−	2163.68i	0.372726	−	0.372726i
$324$	−692.570	+	4717.04i	−0.118753	+	0.808820i
$325$	4615.22	+	1318.59i	0.787711	+	0.225052i
$326$	−823.016	−	60.0967i	−0.139824	−	0.0102100i
$327$	898.257	+	898.257i	0.151907	+	0.151907i
$328$	417.177	−	1877.27i	0.0702278	−	0.316020i
$329$			2675.42i			0.448330i
$330$	1923.82	+	2226.91i	0.320918	+	0.371476i
$331$	6722.96	+	6722.96i	1.11640	+	1.11640i	0.992266	+	0.124131i	$0.0396142\pi$
$331$	6722.96	+	6722.96i	1.11640	+	1.11640i	0.124131	+	0.992266i	$0.460386\pi$
$332$	−858.736	+	638.855i	−0.141956	+	0.105608i
$333$	411.551	+	411.551i	0.0677263	+	0.0677263i
$334$	−8361.45	−	610.554i	−1.36981	−	0.100024i
$335$	621.281			0.101326
$336$	−428.825	−	796.591i	−0.0696259	−	0.129338i
$337$			7362.48i			1.19009i	0.803693	+	0.595044i	$0.202866\pi$
$337$			7362.48i			1.19009i	−0.803693	+	0.595044i	$0.797134\pi$
$338$	965.015	+	6138.67i	0.155296	+	0.987868i
$339$		−	2576.06i		−	0.412722i
$340$	−7243.19	+	5388.56i	−1.15534	+	0.859517i
$341$	−8952.16			−1.42166
$342$	213.285	−	2920.90i	0.0337226	−	0.461826i
$343$	−4375.00	−	4375.00i	−0.688711	−	0.688711i
$344$	8677.98	−	5522.31i	1.36013	−	0.865532i
$345$	−2721.84	−	2721.84i	−0.424751	−	0.424751i
$346$	8302.35	−	7172.39i	1.28999	−	1.11442i
$347$			8192.41i			1.26741i	0.773574	+	0.633706i	$0.218467\pi$
$347$			8192.41i			1.26741i	−0.773574	+	0.633706i	$0.781533\pi$
$348$	−516.795	−	75.8774i	−0.0796067	−	0.0116881i
$349$	755.212	+	755.212i	0.115833	+	0.115833i	0.762647	−	0.646815i	$-0.223899\pi$
$349$	755.212	+	755.212i	0.115833	+	0.115833i	−0.646815	+	0.762647i	$0.723899\pi$
$350$	230.228	−	3152.94i	0.0351605	−	0.481519i
$351$	3054.03	+	872.549i	0.464421	+	0.132687i
$352$	−9010.18	−	3437.35i	−1.36433	−	0.520487i
$353$	4310.99	−	4310.99i	0.650003	−	0.650003i	−0.302991	−	0.952993i	$-0.597985\pi$
$353$	4310.99	−	4310.99i	0.650003	−	0.650003i	0.952993	+	0.302991i	$0.0979851\pi$
$354$	118.095	−	1617.30i	0.0177308	−	0.242820i
$355$	−7823.65			−1.16968
$356$	6815.09	−	5070.07i	1.01460	−	0.754813i
$357$	747.983	−	747.983i	0.110889	−	0.110889i
$358$	2890.12	+	3345.44i	0.426669	+	0.493888i
$359$	−3213.18	+	3213.18i	−0.472383	+	0.472383i	−0.902685	−	0.430302i	$-0.858407\pi$
$359$	−3213.18	+	3213.18i	−0.472383	+	0.472383i	0.430302	+	0.902685i	$0.358407\pi$
$360$	−1874.44	+	8434.83i	−0.274421	+	1.23487i
$361$		−	5187.01i		−	0.756234i
$362$	−2312.08	+	1997.41i	−0.335692	+	0.290004i
$363$	−1951.86			−0.282220
$364$	3828.47	−	1446.85i	0.551281	−	0.208339i
$365$	7073.77			1.01441
$366$	−105.585	+	91.2144i	−0.0150792	+	0.0130269i
$367$			7106.44i			1.01077i	0.862893	+	0.505386i	$0.168650\pi$
$367$			7106.44i			1.01077i	−0.862893	+	0.505386i	$0.831350\pi$
$368$	12081.6	+	3625.89i	1.71141	+	0.513621i
$369$	1521.78	−	1521.78i	0.214691	−	0.214691i
$370$	640.875	+	741.841i	0.0900473	+	0.104234i
$371$	−2408.94	+	2408.94i	−0.337105	+	0.337105i
$372$	1039.21	+	1396.89i	0.144840	+	0.194691i
$373$	−7742.45			−1.07477			−0.537384	−	0.843338i	$-0.680587\pi$
$373$	−7742.45			−1.07477			−0.537384	+	0.843338i	$0.680587\pi$
$374$	821.178	−	11245.9i	0.113535	−	1.55485i
$375$	−312.052	+	312.052i	−0.0429715	+	0.0429715i
$376$	1203.22	−	5414.40i	0.165030	−	0.742623i
$377$	649.151	−	2272.11i	0.0886817	−	0.310397i
$378$	152.349	−	2086.39i	0.0207301	−	0.283895i
$379$	−3219.19	−	3219.19i	−0.436302	−	0.436302i	0.454463	−	0.890766i	$-0.349831\pi$
$379$	−3219.19	−	3219.19i	−0.436302	−	0.436302i	−0.890766	+	0.454463i	$0.849831\pi$
$380$	716.587	−	4880.62i	0.0967372	−	0.658869i
$381$		−	2446.69i		−	0.328997i
$382$	3604.47	−	3113.90i	0.482777	−	0.417070i
$383$	−8174.66	−	8174.66i	−1.09062	−	1.09062i	−0.995463	−	0.0951528i	$-0.969666\pi$
$383$	−8174.66	−	8174.66i	−1.09062	−	1.09062i	−0.0951528	−	0.995463i	$-0.530334\pi$
$384$	509.586	+	1804.96i	0.0677206	+	0.239868i
$385$	6200.21	+	6200.21i	0.820758	+	0.820758i
$386$	568.962	−	7791.86i	0.0750244	−	1.02745i
$387$	11511.3			1.51202
$388$	−3225.38	−	4335.49i	−0.422020	−	0.567271i
$389$		−	12081.8i		−	1.57474i	−0.616483	−	0.787368i	$-0.711443\pi$
$389$		−	12081.8i		−	1.57474i	0.616483	−	0.787368i	$-0.288557\pi$
$390$	2431.17	+	890.703i	0.315659	+	0.115647i
$391$			14749.0i			1.90765i
$392$	2719.59	+	4273.68i	0.350409	+	0.550646i
$393$	2506.52			0.321723
$394$	1670.42	+	121.974i	0.213590	+	0.0155963i
$395$	−7151.81	−	7151.81i	−0.911003	−	0.911003i
$396$	−6441.79	−	8658.92i	−0.817454	−	1.09881i
$397$	−1696.03	−	1696.03i	−0.214411	−	0.214411i	0.591727	−	0.806138i	$-0.298446\pi$
$397$	−1696.03	−	1696.03i	−0.214411	−	0.214411i	−0.806138	+	0.591727i	$0.798446\pi$
$398$	−2333.26	−	2700.86i	−0.293859	−	0.340155i
$399$			578.007i			0.0725226i
$400$	−1883.90	+	6277.24i	−0.235487	+	0.784655i
$401$	3151.96	+	3151.96i	0.392522	+	0.392522i	0.875585	−	0.483063i	$-0.160476\pi$
$401$	3151.96	+	3151.96i	0.392522	+	0.392522i	−0.483063	+	0.875585i	$0.660476\pi$
$402$	150.517	+	10.9908i	0.0186744	+	0.00136361i
$403$	−6885.20	+	3825.19i	−0.851058	+	0.472820i
$404$	−10337.8	−	1517.82i	−1.27308	−	0.186917i
$405$	−6354.69	+	6354.69i	−0.779672	+	0.779672i
$406$	−1552.22	−	113.343i	−0.189742	−	0.0138550i
$407$	−1224.45			−0.149125
$408$	−1850.13	+	1177.35i	−0.224497	+	0.142861i
$409$	−4593.42	+	4593.42i	−0.555330	+	0.555330i	−0.927974	−	0.372644i	$-0.878451\pi$
$409$	−4593.42	+	4593.42i	−0.555330	+	0.555330i	0.372644	+	0.927974i	$0.378451\pi$
$410$	2743.09	−	2369.75i	0.330418	−	0.285448i
$411$	−481.385	+	481.385i	−0.0577736	+	0.0577736i
$412$	1850.73	−	12605.2i	0.221309	−	1.50731i
$413$		−	4831.73i		−	0.575675i
$414$	9228.44	+	10682.3i	1.09554	+	1.26813i
$415$	−2017.52			−0.238642
$416$	−8398.58	+	1206.29i	−0.989842	+	0.142171i
$417$	−2995.27			−0.351748
$418$	4027.88	+	4662.45i	0.471316	+	0.545569i
$419$			10024.7i			1.16882i	0.811457	+	0.584412i	$0.198675\pi$
$419$			10024.7i			1.16882i	−0.811457	+	0.584412i	$0.801325\pi$
$420$	247.724	−	1687.23i	0.0287802	−	0.196019i
$421$	4879.25	−	4879.25i	0.564846	−	0.564846i	−0.365834	−	0.930680i	$-0.619216\pi$
$421$	4879.25	−	4879.25i	0.564846	−	0.564846i	0.930680	+	0.365834i	$0.119216\pi$
$422$	−4226.35	+	3651.13i	−0.487524	+	0.421171i
$423$	4389.12	−	4389.12i	0.504507	−	0.504507i
$424$	5958.49	−	3791.74i	0.682476	−	0.434300i
$425$	−7663.14			−0.874628
$426$	−1895.43	−	138.404i	−0.215572	−	0.0157411i
$427$	−293.972	+	293.972i	−0.0333168	+	0.0333168i
$428$	−4976.51	−	730.666i	−0.562030	−	0.0825189i
$429$	−2826.98	+	1570.58i	−0.318153	+	0.176756i
$430$	19337.6	+	1412.04i	2.16871	+	0.158359i
$431$	−1254.56	−	1254.56i	−0.140209	−	0.140209i	0.633519	−	0.773727i	$-0.281610\pi$
$431$	−1254.56	−	1254.56i	−0.140209	−	0.140209i	−0.773727	+	0.633519i	$0.781610\pi$
$432$	−1246.63	+	4153.84i	−0.138839	+	0.462619i
$433$			4575.03i			0.507764i	0.967235	+	0.253882i	$0.0817074\pi$
$433$			4575.03i			0.507764i	−0.967235	+	0.253882i	$0.918293\pi$
$434$	3391.32	+	3925.60i	0.375089	+	0.434182i
$435$	−696.215	−	696.215i	−0.0767378	−	0.0767378i
$436$	−4683.73	−	6295.77i	−0.514472	−	0.691543i
$437$	−5698.69	−	5698.69i	−0.623811	−	0.623811i
$438$	1713.76	+	125.139i	0.186955	+	0.0136515i
$439$	1986.74			0.215995			0.107998	−	0.994151i	$-0.465556\pi$
$439$	1986.74			0.215995			0.107998	+	0.994151i	$0.465556\pi$
$440$	−9759.30	−	15336.2i	−1.05740	−	1.66164i
$441$			5669.01i			0.612138i
$442$	−4173.73	−	9000.24i	−0.449149	−	0.968547i
$443$		−	8531.36i		−	0.914982i	−0.889214	−	0.457491i	$-0.848748\pi$
$443$		−	8531.36i		−	0.914982i	0.889214	−	0.457491i	$-0.151252\pi$
$444$	142.141	+	191.063i	0.0151930	+	0.0204221i
$445$	16011.4			1.70565
$446$	−363.579	+	4979.16i	−0.0386008	+	0.528633i
$447$	1580.60	+	1580.60i	0.167248	+	0.167248i
$448$	1905.99	+	5253.21i	0.201004	+	0.553997i
$449$	10993.1	+	10993.1i	1.15545	+	1.15545i	0.985444	+	0.170001i	$0.0543772\pi$
$449$	10993.1	+	10993.1i	1.15545	+	1.15545i	0.170001	+	0.985444i	$0.445623\pi$
$450$	−5550.20	+	4794.81i	−0.581420	+	0.502288i
$451$			4527.64i			0.472723i
$452$	−2311.55	+	15743.8i	−0.240544	+	1.63833i
$453$	−895.429	−	895.429i	−0.0928718	−	0.0928718i
$454$	−712.526	+	9757.94i	−0.0736575	+	1.00873i
$455$	7417.95	+	2119.34i	0.764306	+	0.218365i
$456$	259.947	−	1169.75i	0.0266955	−	0.120128i
$457$	−742.547	+	742.547i	−0.0760063	+	0.0760063i	−0.744088	−	0.668082i	$-0.767116\pi$
$457$	−742.547	+	742.547i	−0.0760063	+	0.0760063i	0.668082	+	0.744088i	$0.267116\pi$
$458$	−640.022	+	8765.01i	−0.0652975	+	0.894241i
$459$	−5070.93			−0.515666
$460$	14192.4	+	19077.1i	1.43853	+	1.93364i
$461$	2813.63	−	2813.63i	0.284260	−	0.284260i	−0.550545	−	0.834805i	$-0.685580\pi$
$461$	2813.63	−	2813.63i	0.284260	−	0.284260i	0.834805	+	0.550545i	$0.185580\pi$
$462$	1392.43	+	1611.80i	0.140221	+	0.162312i
$463$	−2851.03	+	2851.03i	−0.286174	+	0.286174i	−0.835565	−	0.549391i	$-0.814860\pi$
$463$	−2851.03	+	2851.03i	−0.286174	+	0.286174i	0.549391	+	0.835565i	$0.314860\pi$
$464$	3090.34	+	927.459i	0.309193	+	0.0927935i
$465$			3281.86i			0.327296i
$466$	12150.5	−	10496.8i	1.20785	−	1.04346i
$467$	8885.31			0.880435			0.440218	−	0.897891i	$-0.354901\pi$
$467$	8885.31			0.880435			0.440218	+	0.897891i	$0.354901\pi$
$468$	−8654.34	−	3907.13i	−0.854801	−	0.385913i
$469$	449.674			0.0442730
$470$	7911.61	−	6834.82i	0.776458	−	0.670780i
$471$		−	2377.96i		−	0.232634i
$472$	−2172.98	+	9778.25i	−0.211905	+	0.953560i
$473$	−17124.3	+	17124.3i	−1.66464	+	1.66464i
$474$	−1606.14	−	1859.18i	−0.155638	−	0.180158i
$475$	2960.86	−	2960.86i	0.286008	−	0.286008i
$476$	−5242.52	+	3900.16i	−0.504812	+	0.375554i
$477$	7903.91			0.758690
$478$	998.461	−	13673.8i	0.0955409	−	1.30842i
$479$	−284.404	+	284.404i	−0.0271289	+	0.0271289i	−0.720541	−	0.693412i	$-0.756107\pi$
$479$	−284.404	+	284.404i	−0.0271289	+	0.0271289i	0.693412	+	0.720541i	$0.256107\pi$
$480$	−1260.13	+	3303.13i	−0.119827	+	0.314097i
$481$	−941.741	+	523.201i	−0.0892717	+	0.0495965i
$482$	24.9263	−	341.362i	0.00235552	−	0.0322585i
$483$	−1970.03	−	1970.03i	−0.185589	−	0.185589i
$484$	11928.9	+	1751.43i	1.12029	+	0.164485i
$485$		−	10185.8i		−	0.953639i
$486$	−5567.97	+	4810.16i	−0.519688	+	0.448957i
$487$	−954.466	−	954.466i	−0.0888110	−	0.0888110i	0.661306	−	0.750117i	$-0.270003\pi$
$487$	−954.466	−	954.466i	−0.0888110	−	0.0888110i	−0.750117	+	0.661306i	$0.770003\pi$
$488$	727.136	−	462.719i	0.0674506	−	0.0429228i
$489$	−267.183	−	267.183i	−0.0247085	−	0.0247085i
$490$	−695.391	+	9523.28i	−0.0641113	+	0.877996i
$491$	4904.82			0.450817			0.225409	−	0.974264i	$-0.427628\pi$
$491$	4904.82			0.450817			0.225409	+	0.974264i	$0.427628\pi$
$492$	706.488	−	525.590i	0.0647377	−	0.0481615i
$493$			3772.63i			0.344646i
$494$	5090.11	+	1864.85i	0.463593	+	0.169846i
$495$		−	20343.3i		−	1.84720i
$496$	−5097.75	−	9469.65i	−0.461483	−	0.857258i
$497$	−5662.65			−0.511075
$498$	−488.783	−	35.6910i	−0.0439817	−	0.00321155i
$499$	4836.83	+	4836.83i	0.433920	+	0.433920i	0.889960	−	0.456040i	$-0.150732\pi$
$499$	4836.83	+	4836.83i	0.433920	+	0.433920i	−0.456040	+	0.889960i	$0.650732\pi$
$500$	2187.14	−	1627.12i	0.195623	−	0.145534i
$501$	−2714.46	−	2714.46i	−0.242062	−	0.242062i
$502$	−10064.2	−	11649.8i	−0.894796	−	1.03577i
$503$			3132.50i			0.277677i	0.990315	+	0.138838i	$0.0443368\pi$
$503$			3132.50i			0.277677i	−0.990315	+	0.138838i	$0.955663\pi$
$504$	−1356.69	+	6105.01i	−0.119904	+	0.539561i
$505$	−13926.8	−	13926.8i	−1.22720	−	1.22720i
$506$	−29619.4	−	2162.81i	−2.60226	−	0.190017i
$507$	−1503.16	+	2415.90i	−0.131672	+	0.211625i
$508$	−2195.46	+	14953.1i	−0.191748	+	1.30598i
$509$	11951.2	−	11951.2i	1.04072	−	1.04072i	0.0415837	−	0.999135i	$-0.486760\pi$
$509$	11951.2	−	11951.2i	1.04072	−	1.04072i	0.999135	−	0.0415837i	$-0.0132403\pi$
$510$	−4122.75	−	301.043i	−0.357957	−	0.0261381i
$511$	5119.90			0.443231
$512$	−1494.74	−	11488.4i	−0.129021	−	0.991642i
$513$	1959.29	−	1959.29i	0.168625	−	0.168625i
$514$	−5946.27	+	5136.97i	−0.510270	+	0.440821i
$515$	16981.5	−	16981.5i	1.45299	−	1.45299i
$516$	4659.93	+	684.185i	0.397562	+	0.0583713i
$517$			13058.6i			1.11086i
$518$	463.857	+	536.934i	0.0393450	+	0.0455435i
$519$	5023.71			0.424887
$520$	−14059.0	−	7625.12i	−1.18563	−	0.643045i
$521$	−5743.31			−0.482954			−0.241477	−	0.970407i	$-0.577632\pi$
$521$	−5743.31			−0.482954			−0.241477	+	0.970407i	$0.577632\pi$
$522$	2360.52	+	2732.41i	0.197926	+	0.229108i
$523$			3548.61i			0.296692i	0.988936	+	0.148346i	$0.0473949\pi$
$523$			3548.61i			0.296692i	−0.988936	+	0.148346i	$0.952605\pi$
$524$	−15318.8	−	2249.15i	−1.27711	−	0.187508i
$525$	1023.57	−	1023.57i	0.0850898	−	0.0850898i
$526$	−13484.0	+	11648.8i	−1.11773	+	0.965609i
$527$	8891.81	−	8891.81i	0.734978	−	0.734978i
$528$	−2093.07	−	3888.12i	−0.172518	−	0.320471i
$529$	26678.9			2.19273
$530$	13277.6	+	969.535i	1.08820	+	0.0794602i
$531$	−7926.62	+	7926.62i	−0.647808	+	0.647808i
$532$	518.656	−	3532.52i	0.0422680	−	0.287884i
$533$	1934.63	+	3482.25i	0.157220	+	0.282989i
$534$	3879.08	+	283.250i	0.314352	+	0.0229540i
$535$	−6704.25	−	6704.25i	−0.541775	−	0.541775i
$536$	−910.032	−	202.232i	−0.0733347	−	0.0162968i
$537$			2024.31i			0.162673i
$538$	2257.28	+	2612.90i	0.180889	+	0.209387i
$539$	−8433.27	−	8433.27i	−0.673927	−	0.673927i
$540$	−6558.97	+	4879.53i	−0.522691	+	0.388855i
$541$	−17205.2	−	17205.2i	−1.36730	−	1.36730i	−0.864266	−	0.503035i	$-0.832217\pi$
$541$	−17205.2	−	17205.2i	−1.36730	−	1.36730i	−0.503035	−	0.864266i	$-0.667783\pi$
$542$	−2432.56	−	177.626i	−0.192781	−	0.0140769i
$543$	−1399.03			−0.110567
$544$	12363.6	−	5535.27i	0.974423	−	0.436255i
$545$		−	14791.3i		−	1.16255i
$546$	1759.65	+	644.678i	0.137923	+	0.0505306i
$547$		−	10030.1i		−	0.784014i	−0.919962	−	0.392007i	$-0.871781\pi$
$547$		−	10030.1i		−	0.784014i	0.919962	−	0.392007i	$-0.128219\pi$
$548$	3373.97	−	2510.06i	0.263009	−	0.195665i
$549$	964.542			0.0749830
$550$	1123.73	−	15389.3i	0.0871200	−	1.19310i
$551$	−1457.66	−	1457.66i	−0.112701	−	0.112701i
$552$	3100.88	+	4872.85i	0.239099	+	0.375729i
$553$	−5176.38	−	5176.38i	−0.398051	−	0.398051i
$554$	−4622.58	+	3993.44i	−0.354503	+	0.306254i
$555$			448.884i			0.0343317i
$556$	18305.8	+	2687.71i	1.39629	+	0.205008i
$557$	5210.40	+	5210.40i	0.396359	+	0.396359i	0.876947	−	0.480588i	$-0.159577\pi$
$557$	5210.40	+	5210.40i	0.396359	+	0.396359i	−0.480588	+	0.876947i	$0.659577\pi$
$558$	876.509	−	12003.7i	0.0664975	−	0.910674i
$559$	−5853.39	+	20487.6i	−0.442884	+	1.55015i
$560$	−3027.95	+	10089.3i	−0.228490	+	0.761340i
$561$	3650.87	−	3650.87i	0.274759	−	0.274759i
$562$	1318.47	−	18056.3i	0.0989613	−	1.35526i
$563$	−9904.62			−0.741438			−0.370719	−	0.928745i	$-0.620889\pi$
$563$	−9904.62			−0.741438			−0.370719	+	0.928745i	$0.620889\pi$
$564$	2037.65	−	1515.91i	0.152129	−	0.113176i
$565$	−21209.7	+	21209.7i	−1.57929	+	1.57929i
$566$	14052.5	+	16266.4i	1.04359	+	1.20800i
$567$	−4599.44	+	4599.44i	−0.340667	+	0.340667i
$568$	11459.8	+	2546.67i	0.846556	+	0.188126i
$569$			3377.53i			0.248846i	0.992229	+	0.124423i	$0.0397080\pi$
$569$			3377.53i			0.248846i	−0.992229	+	0.124423i	$0.960292\pi$
$570$	1709.25	−	1476.62i	0.125601	−	0.108507i
$571$	20372.0			1.49307			0.746533	−	0.665348i	$-0.231717\pi$
$571$	20372.0			1.49307			0.746533	+	0.665348i	$0.231717\pi$
$572$	18686.6	−	7061.98i	1.36595	−	0.516217i
$573$	2181.05			0.159013
$574$	1985.41	−	1715.19i	0.144372	−	0.124723i
$575$			20183.1i			1.46382i
$576$	5491.23	−	11744.9i	0.397224	−	0.849604i
$577$	12982.3	−	12982.3i	0.936669	−	0.936669i	−0.0614412	−	0.998111i	$-0.519570\pi$
$577$	12982.3	−	12982.3i	0.936669	−	0.936669i	0.998111	+	0.0614412i	$0.0195697\pi$
$578$	1270.15	+	1470.25i	0.0914035	+	0.105804i
$579$	2529.54	−	2529.54i	0.181562	−	0.181562i
$580$	3630.23	+	4879.69i	0.259892	+	0.349341i
$581$	−1460.25			−0.104271
$582$	180.193	−	2467.71i	0.0128337	−	0.175756i
$583$	−11757.9	+	11757.9i	−0.835272	+	0.835272i
$584$	−10361.4	−	2302.58i	−0.734176	−	0.163153i
$585$	−8692.57	−	15646.3i	−0.614348	−	1.10580i
$586$	−1123.44	+	15385.3i	−0.0791959	+	1.08458i
$587$	5331.07	+	5331.07i	0.374850	+	0.374850i	0.869240	−	0.494390i	$-0.164609\pi$
$587$	5331.07	+	5331.07i	0.374850	+	0.374850i	−0.494390	+	0.869240i	$0.664609\pi$
$588$	−336.943	+	2294.89i	−0.0236315	+	0.160952i
$589$			6871.18i			0.480683i
$590$	−14288.1	+	12343.5i	−0.997005	+	0.861311i
$591$	542.283	+	542.283i	0.0377437	+	0.0377437i
$592$	−697.258	−	1295.24i	−0.0484073	−	0.0899221i
$593$	7978.19	+	7978.19i	0.552488	+	0.552488i	0.927158	−	0.374670i	$-0.122244\pi$
$593$	7978.19	+	7978.19i	0.552488	+	0.552488i	−0.374670	+	0.927158i	$0.622244\pi$
$594$	743.606	−	10183.6i	0.0513645	−	0.703430i
$595$	−12316.8			−0.848640
$596$	−8241.62	−	11078.2i	−0.566426	−	0.761378i
$597$		−	1634.27i		−	0.112037i
$598$	−23704.8	+	10992.7i	−1.62100	+	0.751716i
$599$		−	17924.7i		−	1.22268i	−0.791368	−	0.611339i	$-0.790631\pi$
$599$		−	17924.7i		−	1.22268i	0.791368	−	0.611339i	$-0.209369\pi$
$600$	−2531.78	+	1611.12i	−0.172266	+	0.109623i
$601$	−190.129			−0.0129044			−0.00645220	−	0.999979i	$-0.502054\pi$
$601$	−190.129			−0.0129044			−0.00645220	+	0.999979i	$0.502054\pi$
$602$	13996.3	+	1022.01i	0.947587	+	0.0691929i
$603$	−737.707	−	737.707i	−0.0498205	−	0.0498205i
$604$	4668.99	+	6275.96i	0.314534	+	0.422790i
$605$	16070.3	+	16070.3i	1.07992	+	1.07992i
$606$	−3127.67	−	3620.41i	−0.209658	−	0.242689i
$607$		−	11485.0i		−	0.767979i	−0.923337	−	0.383990i	$-0.874550\pi$
$607$		−	11485.0i		−	0.767979i	0.923337	−	0.383990i	$-0.125450\pi$
$608$	−2638.32	+	6915.72i	−0.175983	+	0.461298i
$609$	−503.911	−	503.911i	−0.0335296	−	0.0335296i
$610$	1620.32	+	118.316i	0.107549	+	0.00785322i
$611$	5579.84	+	10043.5i	0.369454	+	0.665002i
$612$	14998.9	+	2202.18i	0.990678	+	0.145454i
$613$	−13721.8	+	13721.8i	−0.904106	+	0.904106i	−0.995788	−	0.0916819i	$-0.970776\pi$
$613$	−13721.8	+	13721.8i	−0.904106	+	0.904106i	0.0916819	+	0.995788i	$0.470776\pi$
$614$	2669.14	+	194.901i	0.175436	+	0.0128103i
$615$	1659.83			0.108831
$616$	−7063.65	−	11100.1i	−0.462017	−	0.726032i
$617$	−3021.17	+	3021.17i	−0.197127	+	0.197127i	−0.798767	−	0.601640i	$-0.794514\pi$
$617$	−3021.17	+	3021.17i	−0.197127	+	0.197127i	0.601640	+	0.798767i	$0.294514\pi$
$618$	4414.49	−	3813.67i	0.287341	−	0.248234i
$619$	−6921.94	+	6921.94i	−0.449461	+	0.449461i	−0.895175	−	0.445714i	$-0.852950\pi$
$619$	−6921.94	+	6921.94i	−0.449461	+	0.449461i	0.445714	+	0.895175i	$0.352950\pi$
$620$	2944.87	−	20057.3i	0.190756	−	1.29922i
$621$			13355.8i			0.863042i
$622$	−5427.14	−	6282.15i	−0.349853	−	0.404970i
$623$	11588.9			0.745261
$624$	−3271.17	−	2096.04i	−0.209858	−	0.134469i
$625$	17938.9			1.14809
$626$	4722.68	+	5466.71i	0.301528	+	0.349032i
$627$			2821.22i			0.179695i
$628$	−2133.79	+	14533.0i	−0.135585	+	0.923458i
$629$	1216.20	−	1216.20i	0.0770955	−	0.0770955i
$630$	−8920.74	+	7706.61i	−0.564144	+	0.487363i
$631$	458.535	−	458.535i	0.0289286	−	0.0289286i	−0.692495	−	0.721423i	$-0.743488\pi$
$631$	458.535	−	458.535i	0.0289286	−	0.0289286i	0.721423	+	0.692495i	$0.243488\pi$
$632$	8147.76	+	12803.7i	0.512817	+	0.805861i
$633$	−2557.34			−0.160577
$634$	−12794.7	−	934.270i	−0.801486	−	0.0585246i
$635$	−20144.5	+	20144.5i	−1.25891	+	1.25891i
$636$	3199.61	+	469.777i	0.199486	+	0.0292891i
$637$	−10089.6	−	2882.64i	−0.627574	−	0.179300i
$638$	−7576.30	−	553.222i	−0.470139	−	0.0343296i
$639$	9289.78	+	9289.78i	0.575114	+	0.575114i
$640$	10665.3	−	19056.5i	0.658724	−	1.17699i
$641$			24148.9i			1.48803i	0.668166	+	0.744013i	$0.267080\pi$
$641$			24148.9i			1.48803i	−0.668166	+	0.744013i	$0.732920\pi$
$642$	−1505.63	−	1742.83i	−0.0925584	−	0.107140i
$643$	−5593.24	−	5593.24i	−0.343042	−	0.343042i	0.514468	−	0.857510i	$-0.327990\pi$
$643$	−5593.24	−	5593.24i	−0.343042	−	0.343042i	−0.857510	+	0.514468i	$0.827990\pi$
$644$	10272.2	+	13807.7i	0.628544	+	0.844876i
$645$	6277.76	+	6277.76i	0.383235	+	0.383235i
$646$	−8631.74	−	630.291i	−0.525714	−	0.0383877i
$647$	−16876.3			−1.02547			−0.512733	−	0.858548i	$-0.671367\pi$
$647$	−16876.3			−1.02547			−0.512733	+	0.858548i	$0.671367\pi$
$648$	11376.7	−	7239.64i	0.689688	−	0.438889i
$649$		−	23583.4i		−	1.42640i
$650$	−5711.48	−	12316.3i	−0.344650	−	0.743205i
$651$			2375.36i			0.143007i
$652$	1393.16	+	1872.66i	0.0836815	+	0.112483i
$653$	−7246.31			−0.434257			−0.217129	−	0.976143i	$-0.569669\pi$
$653$	−7246.31			−0.434257			−0.217129	+	0.976143i	$0.569669\pi$
$654$	261.666	−	3583.49i	0.0156452	−	0.214259i
$655$	−20637.1	−	20637.1i	−1.23108	−	1.23108i
$656$	−4789.37	+	2578.23i	−0.285051	+	0.153450i
$657$	−8399.37	−	8399.37i	−0.498768	−	0.498768i
$658$	5726.31	−	4946.95i	0.339263	−	0.293088i
$659$			15428.5i			0.912000i	0.889980	+	0.456000i	$0.150718\pi$
$659$			15428.5i			0.912000i	−0.889980	+	0.456000i	$0.849282\pi$
$660$	1209.13	−	8235.27i	0.0713109	−	0.485693i
$661$	13135.2	+	13135.2i	0.772918	+	0.772918i	0.978616	−	0.205698i	$-0.0659464\pi$
$661$	13135.2	+	13135.2i	0.772918	+	0.772918i	−0.205698	+	0.978616i	$0.565946\pi$
$662$	1958.43	−	26820.4i	0.114980	−	1.57463i
$663$	1247.93	−	4367.91i	0.0731005	−	0.255861i
$664$	2955.20	+	656.722i	0.172717	+	0.0383821i
$665$	4758.94	−	4758.94i	0.277509	−	0.277509i
$666$	119.887	−	1641.83i	0.00697526	−	0.0955252i
$667$	9936.32			0.576816
$668$	14153.8	+	19025.3i	0.819803	+	1.10196i
$669$	−1616.43	+	1616.43i	−0.0934154	+	0.0934154i
$670$	−1148.77	−	1329.75i	−0.0662401	−	0.0766759i
$671$	−1434.86	+	1434.86i	−0.0825517	+	0.0825517i
$672$	−912.065	+	2390.76i	−0.0523566	+	0.137240i
$673$		−	23189.3i		−	1.32821i	−0.747641	−	0.664103i	$-0.768813\pi$
$673$		−	23189.3i		−	1.32821i	0.747641	−	0.664103i	$-0.231187\pi$
$674$	15758.2	−	13613.5i	0.900570	−	0.778001i
$675$	−6939.25			−0.395692
$676$	11354.5	−	13416.1i	0.646023	−	0.763318i
$677$	−15348.0			−0.871304			−0.435652	−	0.900115i	$-0.643482\pi$
$677$	−15348.0			−0.871304			−0.435652	+	0.900115i	$0.643482\pi$
$678$	−5513.66	+	4763.24i	−0.312317	+	0.269810i
$679$		−	7372.37i		−	0.416680i
$680$	24926.3	+	5539.26i	1.40571	+	0.312384i
$681$	−3167.81	+	3167.81i	−0.178254	+	0.178254i
$682$	16552.9	+	19160.7i	0.929387	+	1.07581i
$683$	−375.432	+	375.432i	−0.0210329	+	0.0210329i	−0.717545	−	0.696512i	$-0.754734\pi$
$683$	−375.432	+	375.432i	−0.0210329	+	0.0210329i	0.696512	+	0.717545i	$0.254734\pi$
$684$	−6646.10	+	4944.36i	−0.371521	+	0.276392i
$685$	7926.83			0.442144
$686$	−1274.46	+	17453.5i	−0.0709316	+	0.971398i
$687$	−2845.47	+	2845.47i	−0.158022	+	0.158022i
$688$	−27865.5	−	8362.88i	−1.54413	−	0.463418i
$689$	−4019.07	+	14067.2i	−0.222227	+	0.777821i
$690$	−792.886	+	10858.5i	−0.0437459	+	0.599094i
$691$	−18349.9	−	18349.9i	−1.01022	−	1.01022i	−0.999947	−	0.0102745i	$-0.996729\pi$
$691$	−18349.9	−	18349.9i	−1.01022	−	1.01022i	−0.0102745	−	0.999947i	$-0.503271\pi$
$692$	−30702.7	−	4507.87i	−1.68662	−	0.247635i
$693$		−	14724.2i		−	0.807110i
$694$	17534.6	−	15148.1i	0.959082	−	0.828549i
$695$	24661.1	+	24661.1i	1.34597	+	1.34597i
$696$	793.169	+	1246.42i	0.0431969	+	0.0678813i
$697$	−4497.12	−	4497.12i	−0.244391	−	0.244391i
$698$	219.997	−	3012.83i	0.0119298	−	0.163377i
$699$	7352.18			0.397833
$700$	−7174.06	+	5337.13i	−0.387363	+	0.288178i
$701$		−	2716.25i		−	0.146350i	−0.997319	−	0.0731750i	$-0.976687\pi$
$701$		−	2716.25i		−	0.146350i	0.997319	−	0.0731750i	$-0.0233132\pi$
$702$	−3779.46	−	8150.04i	−0.203200	−	0.438181i
$703$			939.823i			0.0504212i
$704$	9303.06	+	25640.7i	0.498043	+	1.37268i
$705$	4787.27			0.255743
$706$	−17198.2	−	1255.81i	−0.916802	−	0.0669449i
$707$	−10080.0	−	10080.0i	−0.536208	−	0.536208i
$708$	−3679.93	+	2737.68i	−0.195340	+	0.145323i
$709$	8379.79	+	8379.79i	0.443878	+	0.443878i	0.893313	−	0.449435i	$-0.148375\pi$
$709$	8379.79	+	8379.79i	0.443878	+	0.443878i	−0.449435	+	0.893313i	$0.648375\pi$
$710$	14466.2	+	16745.3i	0.764658	+	0.885126i
$711$			16984.1i			0.895854i
$712$	−23453.0	−	5211.87i	−1.23447	−	0.274330i
$713$	−23419.2	−	23419.2i	−1.23009	−	1.23009i
$714$	−2983.99	−	217.891i	−0.156405	−	0.0114207i
$715$	36206.7	+	10344.4i	1.89378	+	0.541061i
$716$	1816.45	−	12371.7i	0.0948098	−	0.645742i
$717$	4439.05	−	4439.05i	0.231212	−	0.231212i
$718$	12818.6	+	936.016i	0.666276	+	0.0486515i
$719$	−17298.3			−0.897245			−0.448623	−	0.893721i	$-0.648085\pi$
$719$	−17298.3			−0.897245			−0.448623	+	0.893721i	$0.648085\pi$
$720$	21519.3	−	11584.4i	1.11386	−	0.599617i
$721$	12290.9	−	12290.9i	0.634866	−	0.634866i
$722$	−11102.0	+	9590.97i	−0.572261	+	0.494375i
$723$	110.820	−	110.820i	0.00570045	−	0.00570045i
$724$	8550.26	+	1255.38i	0.438906	+	0.0644415i
$725$			5162.60i			0.264461i
$726$	3609.05	+	4177.64i	0.184497	+	0.213563i
$727$	29222.3			1.49078			0.745388	−	0.666631i	$-0.232264\pi$
$727$	29222.3			1.49078			0.745388	+	0.666631i	$0.232264\pi$
$728$	−10175.7	−	5518.95i	−0.518046	−	0.280970i
$729$	12721.5			0.646321
$730$	−13079.7	−	15140.3i	−0.663151	−	0.767626i
$731$		−	34017.7i		−	1.72119i
$732$	390.460	+	57.3285i	0.0197156	+	0.00289470i
$733$	−2106.22	+	2106.22i	−0.106133	+	0.106133i	−0.758179	−	0.652046i	$-0.773911\pi$
$733$	−2106.22	+	2106.22i	−0.106133	+	0.106133i	0.652046	+	0.758179i	$0.273911\pi$
$734$	15210.2	−	13140.1i	0.764876	−	0.660775i
$735$	−3091.63	+	3091.63i	−0.155152	+	0.155152i
$736$	−14578.7	−	32563.2i	−0.730136	−	1.63084i
$737$	2194.84			0.109699
$738$	−6070.97	−	443.303i	−0.302812	−	0.0221114i
$739$	13932.1	−	13932.1i	0.693503	−	0.693503i	−0.269498	−	0.963001i	$-0.586858\pi$
$739$	13932.1	−	13932.1i	0.693503	−	0.693503i	0.963001	+	0.269498i	$0.0868577\pi$
$740$	402.792	−	2743.38i	0.0200094	−	0.136282i
$741$	1205.49	+	2169.83i	0.0597635	+	0.107572i
$742$	9610.18	+	701.736i	0.475473	+	0.0347191i
$743$	−10931.3	−	10931.3i	−0.539747	−	0.539747i	0.383708	−	0.923455i	$-0.374647\pi$
$743$	−10931.3	−	10931.3i	−0.539747	−	0.539747i	−0.923455	+	0.383708i	$0.874647\pi$
$744$	1068.27	−	4807.16i	0.0526409	−	0.236880i
$745$		−	26027.3i		−	1.27995i
$746$	14316.1	+	16571.5i	0.702612	+	0.813304i
$747$	2395.60	+	2395.60i	0.117337	+	0.117337i
$748$	−25588.5	+	19036.5i	−1.25081	+	0.930540i
$749$	−4852.44	−	4852.44i	−0.236721	−	0.236721i
$750$	1244.89	+	90.9023i	0.0606095	+	0.00442571i
$751$	31170.2			1.51453			0.757267	−	0.653105i	$-0.226534\pi$
$751$	31170.2			1.51453			0.757267	+	0.653105i	$0.226534\pi$
$752$	−13813.5	+	7436.13i	−0.669847	+	0.360595i
$753$		−	7049.21i		−	0.341152i
$754$	−6063.40	+	2811.81i	−0.292859	+	0.135809i
$755$			14744.8i			0.710752i
$756$	−4747.29	+	3531.74i	−0.228383	+	0.169905i
$757$	−4743.32			−0.227740			−0.113870	−	0.993496i	$-0.536325\pi$
$757$	−4743.32			−0.227740			−0.113870	+	0.993496i	$0.536325\pi$
$758$	−937.765	+	12842.6i	−0.0449356	+	0.615386i
$759$	−9615.63	−	9615.63i	−0.459849	−	0.459849i
$760$	−11771.2	+	7490.70i	−0.561823	+	0.357521i
$761$	12027.9	+	12027.9i	0.572943	+	0.572943i	0.932950	−	0.360007i	$-0.117226\pi$
$761$	12027.9	+	12027.9i	0.572943	+	0.572943i	−0.360007	+	0.932950i	$0.617226\pi$
$762$	−5236.76	+	4524.02i	−0.248960	+	0.215076i
$763$		−	10705.8i		−	0.507962i
$764$	−13329.6	−	1957.09i	−0.631215	−	0.0926768i
$765$	20206.2	+	20206.2i	0.954976	+	0.954976i
$766$	−2381.32	+	32611.8i	−0.112324	+	1.53827i
$767$	−10077.0	−	18138.3i	−0.474395	−	0.853892i
$768$	2921.00	−	4428.13i	0.137243	−	0.208055i
$769$	−4224.75	+	4224.75i	−0.198112	+	0.198112i	−0.799190	−	0.601078i	$-0.794738\pi$
$769$	−4224.75	+	4224.75i	−0.198112	+	0.198112i	0.601078	+	0.799190i	$0.294738\pi$
$770$	1806.15	−	24735.0i	0.0845314	−	1.15765i
$771$	−3598.06			−0.168068
$772$	−17729.3	+	13189.7i	−0.826542	+	0.614904i
$773$	−1842.87	+	1842.87i	−0.0857482	+	0.0857482i	−0.748680	−	0.662932i	$-0.769312\pi$
$773$	−1842.87	+	1842.87i	−0.0857482	+	0.0857482i	0.662932	+	0.748680i	$0.269312\pi$
$774$	−21284.8	−	24638.1i	−0.988458	−	1.14418i
$775$	12167.9	−	12167.9i	0.563978	−	0.563978i
$776$	−3315.58	+	14919.9i	−0.153379	+	0.690197i
$777$			324.896i			0.0150008i
$778$	−25859.2	+	22339.7i	−1.19164	+	1.02946i
$779$	3475.16			0.159834
$780$	−2588.92	−	6850.48i	−0.118844	−	0.314470i
$781$	−27639.1			−1.26633
$782$	31568.0	−	27271.5i	1.44357	−	1.24709i
$783$			3416.25i			0.155922i
$784$	4118.50	−	13723.0i	0.187614	−	0.625139i
$785$	−19578.6	+	19578.6i	−0.890179	+	0.890179i
$786$	−4634.65	−	5364.81i	−0.210321	−	0.243456i
$787$	14175.0	−	14175.0i	0.642039	−	0.642039i	−0.309018	−	0.951056i	$-0.600000\pi$
$787$	14175.0	−	14175.0i	0.642039	−	0.642039i	0.951056	+	0.309018i	$0.100000\pi$
$788$	−2827.60	−	3800.80i	−0.127829	−	0.171825i
$789$	−8159.07			−0.368150
$790$	−2083.35	+	28531.3i	−0.0938259	+	1.28493i
$791$	−15351.3	+	15351.3i	−0.690048	+	0.690048i
$792$	−6621.94	+	29798.3i	−0.297096	+	1.33691i
$793$	−490.461	+	1716.67i	−0.0219631	+	0.0768737i
$794$	−494.061	+	6766.10i	−0.0220826	+	0.302418i
$795$	4310.45	+	4310.45i	0.192297	+	0.192297i
$796$	−1466.46	+	9987.96i	−0.0652982	+	0.444741i
$797$			12141.5i			0.539617i	0.962914	+	0.269809i	$0.0869604\pi$
$797$			12141.5i			0.539617i	−0.962914	+	0.269809i	$0.913040\pi$
$798$	1237.13	−	1068.76i	0.0548797	−	0.0474104i
$799$	−12970.6	−	12970.6i	−0.574300	−	0.574300i
$800$	16918.8	−	7574.66i	0.747714	−	0.334756i
$801$	−19011.9	−	19011.9i	−0.838644	−	0.838644i
$802$	918.181	−	12574.4i	0.0404265	−	0.553636i
$803$	24990.0			1.09823
$804$	−254.788	−	342.480i	−0.0111762	−	0.0150228i
$805$			32440.0i			1.42032i
$806$	20918.2	+	7663.75i	0.914160	+	0.334918i
$807$			1581.05i			0.0689662i
$808$	15866.3	+	24932.9i	0.690809	+	1.08556i
$809$	14477.2			0.629163			0.314581	−	0.949231i	$-0.398136\pi$
$809$	14477.2			0.629163			0.314581	+	0.949231i	$0.398136\pi$
$810$	25351.3	+	1851.15i	1.09970	+	0.0802998i
$811$	−21798.1	−	21798.1i	−0.943816	−	0.943816i	0.0546876	−	0.998504i	$-0.482584\pi$
$811$	−21798.1	−	21798.1i	−0.943816	−	0.943816i	−0.998504	+	0.0546876i	$0.982584\pi$
$812$	2627.51	+	3531.85i	0.113556	+	0.152640i
$813$	−789.705	−	789.705i	−0.0340666	−	0.0340666i
$814$	2264.06	+	2620.75i	0.0974881	+	0.112847i
$815$			4399.64i			0.189095i
$816$	5940.88	+	1782.95i	0.254868	+	0.0764899i
$817$	13143.7	+	13143.7i	0.562838	+	0.562838i
$818$	18324.9	+	1338.09i	0.783270	+	0.0571945i
$819$	−6291.56	−	11324.6i	−0.268431	−	0.483165i
$820$	−10144.1	−	1489.39i	−0.432011	−	0.0634292i
$821$	15143.8	−	15143.8i	0.643756	−	0.643756i	−0.307721	−	0.951477i	$-0.599566\pi$
$821$	15143.8	−	15143.8i	0.643756	−	0.643756i	0.951477	+	0.307721i	$0.0995663\pi$
$822$	1920.43	+	140.230i	0.0814873	+	0.00595021i
$823$	4405.55			0.186595			0.0932976	−	0.995638i	$-0.470259\pi$
$823$	4405.55			0.186595			0.0932976	+	0.995638i	$0.470259\pi$
$824$	−30401.5	+	19346.3i	−1.28530	+	0.817912i
$825$	4995.98	−	4995.98i	0.210834	−	0.210834i
$826$	−10341.5	+	8934.04i	−0.435628	+	0.376338i
$827$	−24831.2	+	24831.2i	−1.04409	+	1.04409i	−0.0451119	+	0.998982i	$0.514364\pi$
$827$	−24831.2	+	24831.2i	−1.04409	+	1.04409i	−0.998982	+	0.0451119i	$0.985636\pi$
$828$	5800.10	−	39504.0i	0.243439	−	1.65804i
$829$			11444.5i			0.479473i	0.970838	+	0.239736i	$0.0770610\pi$
$829$			11444.5i			0.479473i	−0.970838	+	0.239736i	$0.922939\pi$
$830$	3730.47	+	4318.19i	0.156008	+	0.180586i
$831$	−2797.10			−0.116763
$832$	18111.2	+	15745.4i	0.754677	+	0.656097i
$833$	16752.8			0.696821
$834$	5538.36	+	6410.90i	0.229949	+	0.266177i
$835$			44698.2i			1.85251i
$836$	2531.53	−	17242.1i	0.104731	−	0.713313i
$837$	8051.85	−	8051.85i	0.332512	−	0.332512i
$838$	21456.2	−	18536.0i	0.884479	−	0.764100i
$839$	21045.6	−	21045.6i	0.866001	−	0.866001i	−0.126026	−	0.992027i	$-0.540222\pi$
$839$	21045.6	−	21045.6i	0.866001	−	0.866001i	0.992027	+	0.126026i	$0.0402222\pi$
$840$	−4069.29	+	2589.53i	−0.167147	+	0.106366i
$841$	−21847.4			−0.895789
$842$	−19465.2	−	1421.35i	−0.796691	−	0.0581745i
$843$	5861.77	−	5861.77i	0.239490	−	0.239490i
$844$	15629.3	+	2294.75i	0.637422	+	0.0935882i
$845$	32267.0	−	7514.87i	1.31363	−	0.305940i
$846$	−17509.9	−	1278.57i	−0.711586	−	0.0519601i
$847$	11631.5	+	11631.5i	0.471857	+	0.471857i
$848$	−19133.1	−	5742.14i	−0.774803	−	0.232530i
$849$			9842.73i			0.397882i
$850$	14169.4	+	16401.7i	0.571774	+	0.661853i
$851$	−3203.22	−	3203.22i	−0.129031	−	0.129031i
$852$	3208.48	+	4312.78i	0.129015	+	0.173419i
$853$	26871.0	+	26871.0i	1.07860	+	1.07860i	0.996635	+	0.0819652i	$0.0261196\pi$
$853$	26871.0	+	26871.0i	1.07860	+	1.07860i	0.0819652	+	0.996635i	$0.473880\pi$
$854$	1172.76	+	85.6353i	0.0469920	+	0.00343136i
$855$	−15614.4			−0.624564
$856$	7637.87	+	12002.5i	0.304973	+	0.479247i
$857$			15017.2i			0.598574i	0.954163	+	0.299287i	$0.0967487\pi$
$857$			15017.2i			0.598574i	−0.954163	+	0.299287i	$0.903251\pi$
$858$	8588.76	+	3146.64i	0.341743	+	0.125204i
$859$			3581.12i			0.142243i	0.997468	+	0.0711213i	$0.0226577\pi$
$859$			3581.12i			0.142243i	−0.997468	+	0.0711213i	$0.977342\pi$
$860$	−32733.8	−	44000.1i	−1.29792	−	1.74464i
$861$	1201.36			0.0475520
$862$	−365.459	+	5004.90i	−0.0144403	+	0.197758i
$863$	26232.6	+	26232.6i	1.03472	+	1.03472i	0.999375	+	0.0353487i	$0.0112542\pi$
$863$	26232.6	+	26232.6i	1.03472	+	1.03472i	0.0353487	+	0.999375i	$0.488746\pi$
$864$	11195.7	−	5012.38i	0.440840	−	0.197367i
$865$	−41362.0	−	41362.0i	−1.62584	−	1.62584i
$866$	9792.12	−	8459.39i	0.384238	−	0.331942i
$867$			889.642i			0.0348487i
$868$	2131.45	−	14517.2i	0.0833483	−	0.567678i
$869$	−25265.7	−	25265.7i	−0.986281	−	0.986281i
$870$	−202.811	+	2777.47i	−0.00790337	+	0.108236i
$871$	1688.07	−	937.839i	0.0656696	−	0.0364839i
$872$	−4814.72	+	21665.9i	−0.186980	+	0.841399i
$873$	−12094.6	+	12094.6i	−0.468891	+	0.468891i
$874$	−1660.06	+	22734.2i	−0.0642474	+	0.879859i
$875$	3719.16			0.143692
$876$	−2900.96	−	3899.41i	−0.111888	−	0.150398i
$877$	−686.478	+	686.478i	−0.0264318	+	0.0264318i	−0.720199	−	0.693767i	$-0.755950\pi$
$877$	−686.478	+	686.478i	−0.0264318	+	0.0264318i	0.693767	+	0.720199i	$0.255950\pi$
$878$	−3673.56	−	4252.30i	−0.141203	−	0.163449i
$879$	−4994.69	+	4994.69i	−0.191657	+	0.191657i
$880$	−14779.3	+	49245.4i	−0.566148	+	1.88643i
$881$		−	20214.9i		−	0.773049i	−0.922279	−	0.386524i	$-0.873676\pi$
$881$		−	20214.9i		−	0.773049i	0.922279	−	0.386524i	$-0.126324\pi$
$882$	12133.6	−	10482.2i	0.463220	−	0.400175i
$883$	12482.3			0.475722			0.237861	−	0.971299i	$-0.423554\pi$
$883$	12482.3			0.475722			0.237861	+	0.971299i	$0.423554\pi$
$884$	−11546.2	+	25575.0i	−0.439300	+	0.973054i
$885$	−8645.67			−0.328385
$886$	−18260.0	+	15774.8i	−0.692390	+	0.598154i
$887$			13500.9i			0.511066i	0.966800	+	0.255533i	$0.0822510\pi$
$887$			13500.9i			0.511066i	−0.966800	+	0.255533i	$0.917749\pi$
$888$	146.116	−	657.511i	0.00552177	−	0.0248476i
$889$	−14580.3	+	14580.3i	−0.550065	+	0.550065i
$890$	−29605.7	−	34269.9i	−1.11504	−	1.29071i
$891$	−22449.6	+	22449.6i	−0.844098	+	0.844098i
$892$	11329.4	−	8428.47i	0.425264	−	0.316375i
$893$	10023.0			0.375598
$894$	460.436	−	6305.60i	0.0172251	−	0.235896i
$895$	16666.9	−	16666.9i	0.622471	−	0.622471i
$896$	7719.41	−	13792.9i	0.287821	−	0.514271i
$897$	−11504.2	−	3286.79i	−0.428220	−	0.122344i
$898$	3202.33	−	43855.5i	0.119001	−	1.62971i
$899$	−5990.35	−	5990.35i	−0.222235	−	0.222235i
$900$	20525.1	+	3013.55i	0.760187	+	0.111613i
$901$		−	23357.3i		−	0.863646i
$902$	9690.69	−	8371.77i	0.357721	−	0.309035i
$903$	4543.76	+	4543.76i	0.167449	+	0.167449i
$904$	37971.2	−	24163.3i	1.39702	−	0.889004i
$905$	11518.7	+	11518.7i	0.423089	+	0.423089i
$906$	−260.843	+	3572.21i	−0.00956504	+	0.130992i
$907$	−44925.7			−1.64469			−0.822344	−	0.568990i	$-0.807334\pi$
$907$	−44925.7			−1.64469			−0.822344	+	0.568990i	$0.807334\pi$
$908$	22202.8	−	16517.7i	0.811483	−	0.603701i
$909$			33073.4i			1.20679i
$910$	−9179.96	−	19795.7i	−0.334409	−	0.721122i
$911$		−	12642.9i		−	0.459801i	−0.973214	−	0.229901i	$-0.926160\pi$
$911$		−	12642.9i		−	0.459801i	0.973214	−	0.229901i	$-0.0738401\pi$
$912$	−2984.31	+	1606.53i	−0.108356	+	0.0583305i
$913$	−7127.43			−0.258361
$914$	2962.30	+	216.307i	0.107204	+	0.00782802i
$915$	526.019	+	526.019i	0.0190051	+	0.0190051i
$916$	19943.5	−	14837.0i	0.719381	−	0.535183i
$917$	−14936.9	−	14936.9i	−0.537904	−	0.537904i
$918$	9376.34	+	10853.5i	0.337108	+	0.390218i
$919$		−	261.747i		−	0.00939524i	−0.999989	−	0.00469762i	$-0.998505\pi$
$919$		−	261.747i		−	0.00939524i	0.999989	−	0.00469762i	$-0.00149530\pi$
$920$	14589.3	−	65650.7i	0.522819	−	2.35265i
$921$	866.507	+	866.507i	0.0310015	+	0.0310015i
$922$	−11224.7	−	819.625i	−0.400937	−	0.0292765i
$923$	−21257.5	+	11810.0i	−0.758072	+	0.421160i
$924$	875.149	−	5960.57i	0.0311583	−	0.212217i
$925$	1664.29	−	1664.29i	0.0591585	−	0.0591585i
$926$	11373.8	+	830.518i	0.403636	+	0.0294735i
$927$	−40327.5			−1.42883
$928$	−3729.07	−	8329.28i	−0.131910	−	0.294636i
$929$	34300.0	−	34300.0i	1.21135	−	1.21135i	0.240769	−	0.970583i	$-0.422600\pi$
$929$	34300.0	−	34300.0i	1.21135	−	1.21135i	0.970583	−	0.240769i	$-0.0773995\pi$
$930$	7024.29	−	6068.27i	0.247673	−	0.213964i
$931$	−6472.91	+	6472.91i	−0.227864	+	0.227864i
$932$	−44933.3	−	6597.24i	−1.57923	−	0.231867i
$933$		−	3801.30i		−	0.133386i
$934$	−16429.3	−	19017.6i	−0.575570	−	0.666247i
$935$	−60117.9			−2.10274
$936$	7639.59	+	25747.7i	0.266782	+	0.899134i
$937$	56131.0			1.95701			0.978505	−	0.206221i	$-0.0661167\pi$
$937$	56131.0			1.95701			0.978505	+	0.206221i	$0.0661167\pi$
$938$	−831.464	−	962.457i	−0.0289427	−	0.0335025i
$939$			3307.88i			0.114961i
$940$	−29257.7	−	4295.70i	−1.01519	−	0.149054i
$941$	35821.6	−	35821.6i	1.24097	−	1.24097i	0.281368	−	0.959600i	$-0.409212\pi$
$941$	35821.6	−	35821.6i	1.24097	−	1.24097i	0.959600	−	0.281368i	$-0.0907883\pi$
$942$	−5089.65	+	4396.94i	−0.176040	+	0.152081i
$943$	−11844.5	+	11844.5i	−0.409024	+	0.409024i
$944$	24946.7	−	13429.4i	0.860113	−	0.463020i
$945$	−11153.3			−0.383934
$946$	68315.3	+	4988.39i	2.34791	+	0.171445i
$947$	1240.29	−	1240.29i	0.0425596	−	0.0425596i	−0.685507	−	0.728066i	$-0.740419\pi$
$947$	1240.29	−	1240.29i	0.0425596	−	0.0425596i	0.728066	+	0.685507i	$0.240419\pi$
$948$	−1009.47	+	6875.39i	−0.0345843	+	0.235551i
$949$	19220.0	−	10678.0i	0.657438	−	0.365252i
$950$	−11812.0	−	862.513i	−0.403402	−	0.0294564i
$951$	−4153.66	−	4153.66i	−0.141632	−	0.141632i
$952$	18041.3	+	4009.24i	0.614204	+	0.136492i
$953$			29138.5i			0.990439i	0.868768	+	0.495219i	$0.164912\pi$
$953$			29138.5i			0.990439i	−0.868768	+	0.495219i	$0.835088\pi$
$954$	−14614.6	−	16917.1i	−0.495981	−	0.574120i
$955$	−17957.3	−	17957.3i	−0.608467	−	0.608467i
$956$	−31112.8	+	23146.3i	−1.05257	+	0.783059i
$957$	−2459.56	−	2459.56i	−0.0830788	−	0.0830788i
$958$	1134.60	+	82.8483i	0.0382642	+	0.00279406i
$959$	5737.33			0.193189
$960$	9399.85	−	3410.50i	0.316020	−	0.114660i
$961$		−	1553.36i		−	0.0521420i
$962$	2861.14	+	1048.23i	0.0958908	+	0.0351313i
$963$			15921.2i			0.532766i
$964$	−776.721	+	577.840i	−0.0259507	+	0.0193060i
$965$	−41653.3			−1.38950
$966$	−573.880	+	7859.20i	−0.0191142	+	0.261766i
$967$	32699.0	+	32699.0i	1.08741	+	1.08741i	0.995794	+	0.0916208i	$0.0292048\pi$
$967$	32699.0	+	32699.0i	1.08741	+	1.08741i	0.0916208	+	0.995794i	$0.470795\pi$
$968$	−18308.3	−	28770.4i	−0.607903	−	0.955283i
$969$	−2802.20	−	2802.20i	−0.0928997	−	0.0928997i
$970$	−21801.2	+	18834.0i	−0.721643	+	0.623426i
$971$		−	7154.75i		−	0.236464i	−0.992986	−	0.118232i	$-0.962277\pi$
$971$		−	7154.75i		−	0.236464i	0.992986	−	0.118232i	$-0.0377227\pi$
$972$	20590.8	+	3023.20i	0.679474	+	0.0997625i
$973$	17849.4	+	17849.4i	0.588104	+	0.588104i
$974$	−278.040	+	3807.73i	−0.00914681	+	0.125264i
$975$	1707.71	−	5977.21i	0.0560930	−	0.196332i
$976$	−2334.88	−	700.733i	−0.0765754	−	0.0229815i
$977$	−25772.9	+	25772.9i	−0.843960	+	0.843960i	−0.989371	−	0.145411i	$-0.953549\pi$
$977$	−25772.9	+	25772.9i	−0.843960	+	0.843960i	0.145411	+	0.989371i	$0.453549\pi$
$978$	−77.8318	+	1065.90i	−0.00254477	+	0.0348503i
$979$	56564.7			1.84659
$980$	21668.9	−	16120.5i	0.706313	−	0.525460i
$981$	−17563.2	+	17563.2i	−0.571611	+	0.571611i
$982$	−9069.19	−	10498.0i	−0.294714	−	0.341145i
$983$	25691.2	−	25691.2i	0.833593	−	0.833593i	−0.154413	−	0.988006i	$-0.549349\pi$
$983$	25691.2	−	25691.2i	0.833593	−	0.833593i	0.988006	+	0.154413i	$0.0493486\pi$
$984$	−2431.27	−	540.289i	−0.0787662	−	0.0175039i
$985$		−	8929.62i		−	0.288854i
$986$	8074.72	−	6975.73i	0.260803	−	0.225307i
$987$	3464.96			0.111744
$988$	−5420.39	−	14342.8i	−0.174540	−	0.461846i
$989$	−89595.7			−2.88066
$990$	−43541.7	+	37615.6i	−1.39782	+	1.20758i
$991$		−	31620.6i		−	1.01358i	−0.862068	−	0.506792i	$-0.830831\pi$
$991$		−	31620.6i		−	1.01358i	0.862068	−	0.506792i	$-0.169169\pi$
$992$	−10842.4	+	28420.7i	−0.347022	+	0.909634i
$993$	8706.97	−	8706.97i	0.278255	−	0.278255i
$994$	10470.4	+	12120.0i	0.334107	+	0.386744i
$995$	−13455.6	+	13455.6i	−0.428714	+	0.428714i
$996$	827.387	+	1112.16i	0.0263221	+	0.0353816i
$997$	−31973.5			−1.01566			−0.507828	−	0.861458i	$-0.669552\pi$
$997$	−31973.5			−1.01566			−0.507828	+	0.861458i	$0.669552\pi$
$998$	1408.99	−	19295.9i	0.0446902	−	0.612026i
$999$	1101.31	−	1101.31i	0.0348789	−	0.0348789i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	52.4.f.b.31.5	✓	36
4.3	odd	2	inner	52.4.f.b.31.14	yes	36
13.8	odd	4	inner	52.4.f.b.47.14	yes	36
52.47	even	4	inner	52.4.f.b.47.5	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
52.4.f.b.31.5	✓	36	1.1	even	1	trivial
52.4.f.b.31.14	yes	36	4.3	odd	2	inner
52.4.f.b.47.5	yes	36	52.47	even	4	inner
52.4.f.b.47.14	yes	36	13.8	odd	4	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:	\( N \)	\(=\)	\( 52 = 2^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	52.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.84904 - 2.14034i) q^{2} -1.29511i q^{3} +(-1.16213 + 7.91514i) q^{4} +(-10.6631 + 10.6631i) q^{5} +(-2.77198 + 2.39471i) q^{6} +(-7.71781 + 7.71781i) q^{7} +(19.0899 - 12.1480i) q^{8} +25.3227 q^{9} +(42.5392 + 3.10621i) q^{10} +(-37.6703 + 37.6703i) q^{11} +(10.2510 + 1.50508i) q^{12} +(-12.8764 + 45.0688i) q^{13} +(30.7893 + 2.24823i) q^{14} +(13.8099 + 13.8099i) q^{15} +(-61.2989 - 18.3968i) q^{16} -74.8326i q^{17} +(-46.8226 - 54.1992i) q^{18} +(28.9136 + 28.9136i) q^{19} +(-72.0081 - 96.7919i) q^{20} +(9.99541 + 9.99541i) q^{21} +(150.281 + 10.9735i) q^{22} -197.094 q^{23} +(-15.7330 - 24.7235i) q^{24} -102.404i q^{25} +(120.272 - 55.7741i) q^{26} -67.7636i q^{27} +(-52.1185 - 70.0566i) q^{28} -50.4142 q^{29} +(4.02289 - 55.0929i) q^{30} +(118.823 + 118.823i) q^{31} +(73.9686 + 165.217i) q^{32} +(48.7871 + 48.7871i) q^{33} +(-160.167 + 138.368i) q^{34} -164.592i q^{35} +(-29.4281 + 200.433i) q^{36} +(16.2523 + 16.2523i) q^{37} +(8.42267 - 115.347i) q^{38} +(58.3691 + 16.6763i) q^{39} +(-74.0220 + 333.094i) q^{40} +(60.0957 - 60.0957i) q^{41} +(2.91171 - 39.8755i) q^{42} +454.584 q^{43} +(-254.388 - 341.943i) q^{44} +(-270.019 + 270.019i) q^{45} +(364.434 + 421.848i) q^{46} +(173.328 - 173.328i) q^{47} +(-23.8258 + 79.3888i) q^{48} +223.871i q^{49} +(-219.179 + 189.348i) q^{50} -96.9165 q^{51} +(-341.762 - 154.294i) q^{52} +312.128 q^{53} +(-145.037 + 125.297i) q^{54} -803.364i q^{55} +(-53.5761 + 241.089i) q^{56} +(37.4463 - 37.4463i) q^{57} +(93.2178 + 107.904i) q^{58} +(-313.025 + 313.025i) q^{59} +(-125.356 + 93.2584i) q^{60} +38.0900 q^{61} +(34.6136 - 474.028i) q^{62} +(-195.436 + 195.436i) q^{63} +(216.850 - 463.810i) q^{64} +(-343.272 - 617.876i) q^{65} +(14.2119 - 194.630i) q^{66} +(-29.1322 - 29.1322i) q^{67} +(592.311 + 86.9649i) q^{68} +255.258i q^{69} +(-352.282 + 304.336i) q^{70} +(366.856 + 366.856i) q^{71} +(483.408 - 307.621i) q^{72} +(-331.694 - 331.694i) q^{73} +(4.73436 - 64.8365i) q^{74} -132.624 q^{75} +(-262.456 + 195.254i) q^{76} -581.464i q^{77} +(-72.2336 - 155.765i) q^{78} +670.706i q^{79} +(849.804 - 457.470i) q^{80} +595.951 q^{81} +(-239.744 - 17.5062i) q^{82} +(94.6029 + 94.6029i) q^{83} +(-90.7310 + 67.4992i) q^{84} +(797.949 + 797.949i) q^{85} +(-840.543 - 972.966i) q^{86} +65.2919i q^{87} +(-261.502 + 1176.74i) q^{88} +(-750.787 - 750.787i) q^{89} +(1077.21 + 78.6577i) q^{90} +(-248.455 - 447.210i) q^{91} +(229.048 - 1560.02i) q^{92} +(153.888 - 153.888i) q^{93} +(-691.469 - 50.4912i) q^{94} -616.618 q^{95} +(213.974 - 95.7975i) q^{96} +(-477.621 + 477.621i) q^{97} +(479.160 - 413.945i) q^{98} +(-953.912 + 953.912i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 2 q^{2} - 20 q^{5} - 16 q^{6} - 40 q^{8} - 332 q^{9} - 96 q^{13} + 204 q^{14} + 52 q^{16} + 330 q^{18} + 500 q^{20} + 224 q^{21} - 48 q^{22} - 496 q^{24} + 570 q^{26} - 356 q^{28} + 560 q^{29} + 292 q^{32}+ \cdots + 3226 q^{98}+O(q^{100}) \) 36 * q + 2 * q^2 - 20 * q^5 - 16 * q^6 - 40 * q^8 - 332 * q^9 - 96 * q^13 + 204 * q^14 + 52 * q^16 + 330 * q^18 + 500 * q^20 + 224 * q^21 - 48 * q^22 - 496 * q^24 + 570 * q^26 - 356 * q^28 + 560 * q^29 + 292 * q^32 + 104 * q^33 - 416 * q^34 - 788 * q^37 - 2788 * q^40 + 1124 * q^41 - 1172 * q^42 - 156 * q^44 - 972 * q^45 - 668 * q^46 + 1332 * q^48 + 1354 * q^50 - 164 * q^52 + 1208 * q^53 + 2272 * q^54 - 1248 * q^57 - 2972 * q^58 + 692 * q^60 + 2632 * q^61 + 596 * q^65 + 3312 * q^66 + 2948 * q^68 - 1008 * q^70 - 908 * q^72 - 196 * q^73 - 1504 * q^74 - 3472 * q^76 - 2688 * q^78 - 1096 * q^80 - 764 * q^81 + 3744 * q^84 + 600 * q^85 - 3952 * q^86 - 2748 * q^89 - 1224 * q^92 - 6128 * q^93 + 2884 * q^94 + 4792 * q^96 - 1820 * q^97 + 3226 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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