LMFDB - Embedded newform 15.4.e.a.2.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [15,4,Mod(2,15)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(15, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1]))

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

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

chi := DirichletCharacter("15.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 15 = 3 \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	15.e (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:	$0.885028650086$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.28356903014400.8
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 209x^{4} + 1600 $ x^8 + 209*x^4 + 1600
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			2.4
Root			$2.66260 + 2.66260i$ of defining polynomial
Character	$\chi$	$=$	15.2
Dual form			15.4.e.a.8.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.66260 - 2.66260i) q^{2} +(-2.80471 + 4.37420i) q^{3} -6.17891i q^{4} +(-9.55729 - 5.80157i) q^{5} +(4.17891 + 19.1146i) q^{6} +(9.35782 + 9.35782i) q^{7} +(4.84884 + 4.84884i) q^{8} +(-11.2672 - 24.5367i) q^{9} +O(q^{10})$	\(q+(2.66260 - 2.66260i) q^{2} +(-2.80471 + 4.37420i) q^{3} -6.17891i q^{4} +(-9.55729 - 5.80157i) q^{5} +(4.17891 + 19.1146i) q^{6} +(9.35782 + 9.35782i) q^{7} +(4.84884 + 4.84884i) q^{8} +(-11.2672 - 24.5367i) q^{9} +(-40.8945 + 10.0000i) q^{10} -34.1375i q^{11} +(27.0278 + 17.3301i) q^{12} +(2.82109 - 2.82109i) q^{13} +49.8323 q^{14} +(52.1826 - 25.5337i) q^{15} +75.2524 q^{16} +(-64.2384 + 64.2384i) q^{17} +(-95.3316 - 35.3316i) q^{18} -19.0735i q^{19} +(-35.8474 + 59.0536i) q^{20} +(-67.1789 + 14.6869i) q^{21} +(-90.8945 - 90.8945i) q^{22} +(51.4018 + 51.4018i) q^{23} +(-34.8094 + 7.61018i) q^{24} +(57.6836 + 110.895i) q^{25} -15.0229i q^{26} +(138.930 + 19.5337i) q^{27} +(57.8211 - 57.8211i) q^{28} -50.5042 q^{29} +(70.9555 - 206.928i) q^{30} -93.3673 q^{31} +(161.576 - 161.576i) q^{32} +(149.324 + 95.7458i) q^{33} +342.083i q^{34} +(-35.1454 - 143.725i) q^{35} +(-151.610 + 69.6188i) q^{36} +(-161.537 - 161.537i) q^{37} +(-50.7850 - 50.7850i) q^{38} +(4.42765 + 20.2524i) q^{39} +(-18.2109 - 74.4727i) q^{40} +88.7935i q^{41} +(-139.765 + 217.976i) q^{42} +(176.399 - 176.399i) q^{43} -210.932 q^{44} +(-34.6678 + 299.872i) q^{45} +273.725 q^{46} +(-38.2843 + 38.2843i) q^{47} +(-211.061 + 329.169i) q^{48} -167.863i q^{49} +(448.857 + 141.680i) q^{50} +(-100.821 - 461.162i) q^{51} +(-17.4313 - 17.4313i) q^{52} +(-344.569 - 344.569i) q^{53} +(421.925 - 317.904i) q^{54} +(-198.051 + 326.262i) q^{55} +90.7492i q^{56} +(83.4310 + 53.4956i) q^{57} +(-134.473 + 134.473i) q^{58} +421.133 q^{59} +(-157.771 - 322.432i) q^{60} +2.00000 q^{61} +(-248.600 + 248.600i) q^{62} +(124.174 - 335.046i) q^{63} -258.409i q^{64} +(-43.3287 + 10.5952i) q^{65} +(652.524 - 142.657i) q^{66} +(430.987 + 430.987i) q^{67} +(396.923 + 396.923i) q^{68} +(-369.009 + 80.6742i) q^{69} +(-476.262 - 289.105i) q^{70} +733.866i q^{71} +(64.3420 - 173.607i) q^{72} +(-348.073 + 348.073i) q^{73} -860.216 q^{74} +(-646.860 - 58.7079i) q^{75} -117.853 q^{76} +(319.452 - 319.452i) q^{77} +(65.7131 + 42.1349i) q^{78} -588.019i q^{79} +(-719.209 - 436.582i) q^{80} +(-475.102 + 552.919i) q^{81} +(236.422 + 236.422i) q^{82} +(217.997 + 217.997i) q^{83} +(90.7492 + 415.092i) q^{84} +(986.629 - 241.262i) q^{85} -939.362i q^{86} +(141.650 - 220.915i) q^{87} +(165.527 - 165.527i) q^{88} +1272.00 q^{89} +(706.133 + 890.746i) q^{90} +52.7985 q^{91} +(317.607 - 317.607i) q^{92} +(261.868 - 408.407i) q^{93} +203.872i q^{94} +(-110.656 + 182.291i) q^{95} +(253.591 + 1159.94i) q^{96} +(-432.111 - 432.111i) q^{97} +(-446.951 - 446.951i) q^{98} +(-837.622 + 384.633i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 6 q^{3} - 12 q^{6} - 16 q^{7}+O(q^{10}) $ 8 * q - 6 * q^3 - 12 * q^6 - 16 * q^7	$ 8 q - 6 q^{3} - 12 q^{6} - 16 q^{7} - 100 q^{10} + 132 q^{12} + 68 q^{13} + 90 q^{15} + 284 q^{16} - 240 q^{18} - 492 q^{21} - 500 q^{22} - 220 q^{25} + 702 q^{27} + 508 q^{28} + 660 q^{30} + 616 q^{31} - 240 q^{33} - 804 q^{36} - 1156 q^{37} - 600 q^{40} + 540 q^{42} + 548 q^{43} + 180 q^{45} + 736 q^{46} - 1116 q^{48} - 852 q^{51} + 224 q^{52} + 460 q^{55} + 684 q^{57} + 60 q^{58} + 540 q^{60} + 16 q^{61} + 1428 q^{63} + 2040 q^{66} + 404 q^{67} - 2220 q^{70} - 1800 q^{72} - 2512 q^{73} - 2910 q^{75} - 1488 q^{76} - 360 q^{78} + 288 q^{81} + 2800 q^{82} + 4940 q^{85} - 1680 q^{87} + 2460 q^{88} + 600 q^{90} - 1304 q^{91} + 3408 q^{93} + 4164 q^{96} + 1904 q^{97}+O(q^{100}) $ 8 * q - 6 * q^3 - 12 * q^6 - 16 * q^7 - 100 * q^10 + 132 * q^12 + 68 * q^13 + 90 * q^15 + 284 * q^16 - 240 * q^18 - 492 * q^21 - 500 * q^22 - 220 * q^25 + 702 * q^27 + 508 * q^28 + 660 * q^30 + 616 * q^31 - 240 * q^33 - 804 * q^36 - 1156 * q^37 - 600 * q^40 + 540 * q^42 + 548 * q^43 + 180 * q^45 + 736 * q^46 - 1116 * q^48 - 852 * q^51 + 224 * q^52 + 460 * q^55 + 684 * q^57 + 60 * q^58 + 540 * q^60 + 16 * q^61 + 1428 * q^63 + 2040 * q^66 + 404 * q^67 - 2220 * q^70 - 1800 * q^72 - 2512 * q^73 - 2910 * q^75 - 1488 * q^76 - 360 * q^78 + 288 * q^81 + 2800 * q^82 + 4940 * q^85 - 1680 * q^87 + 2460 * q^88 + 600 * q^90 - 1304 * q^91 + 3408 * q^93 + 4164 * q^96 + 1904 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/15\mathbb{Z}\right)^\times$.

$n$	$7$	$11$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$

Coefficient data

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

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

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

$2$	2.66260	−	2.66260i	0.941372	−	0.941372i	−0.0570018	−	0.998374i	$-0.518154\pi$
$2$	2.66260	−	2.66260i	0.941372	−	0.941372i	0.998374	+	0.0570018i	$0.0181541\pi$
$3$	−2.80471	+	4.37420i	−0.539767	+	0.841814i
$3$	−2.80471	+	4.37420i	−0.539767	+	0.841814i
$4$		−	6.17891i		−	0.772364i
$5$	−9.55729	−	5.80157i	−0.854830	−	0.518908i
$5$	−9.55729	−	5.80157i	−0.854830	−	0.518908i
$6$	4.17891	+	19.1146i	0.284339	+	1.30058i
$7$	9.35782	+	9.35782i	0.505275	+	0.505275i	0.913072	−	0.407798i	$-0.133703\pi$
$7$	9.35782	+	9.35782i	0.505275	+	0.505275i	−0.407798	+	0.913072i	$0.633703\pi$
$8$	4.84884	+	4.84884i	0.214291	+	0.214291i
$9$	−11.2672	−	24.5367i	−0.417303	−	0.908768i
$10$	−40.8945	+	10.0000i	−1.29320	+	0.316228i
$11$		−	34.1375i		−	0.935712i	−0.883805	−	0.467856i	$-0.845027\pi$
$11$		−	34.1375i		−	0.935712i	0.883805	−	0.467856i	$-0.154973\pi$
$12$	27.0278	+	17.3301i	0.650187	+	0.416897i
$13$	2.82109	−	2.82109i	0.0601869	−	0.0601869i	−0.676373	−	0.736560i	$-0.736449\pi$
$13$	2.82109	−	2.82109i	0.0601869	−	0.0601869i	0.736560	+	0.676373i	$0.236449\pi$
$14$	49.8323			0.951303
$15$	52.1826	−	25.5337i	0.898233	−	0.439519i
$16$	75.2524			1.17582
$17$	−64.2384	+	64.2384i	−0.916477	+	0.916477i	−0.996771	−	0.0802942i	$-0.974414\pi$
$17$	−64.2384	+	64.2384i	−0.916477	+	0.916477i	0.0802942	+	0.996771i	$0.474414\pi$
$18$	−95.3316	−	35.3316i	−1.24833	−	0.462652i
$19$		−	19.0735i		−	0.230303i	−0.993348	−	0.115151i	$-0.963265\pi$
$19$		−	19.0735i		−	0.230303i	0.993348	−	0.115151i	$-0.0367353\pi$
$20$	−35.8474	+	59.0536i	−0.400786	+	0.660240i
$21$	−67.1789	+	14.6869i	−0.698078	+	0.152617i
$22$	−90.8945	−	90.8945i	−0.880854	−	0.880854i
$23$	51.4018	+	51.4018i	0.466001	+	0.466001i	0.900616	−	0.434616i	$-0.143116\pi$
$23$	51.4018	+	51.4018i	0.466001	+	0.466001i	−0.434616	+	0.900616i	$0.643116\pi$
$24$	−34.8094	+	7.61018i	−0.296060	+	0.0647259i
$25$	57.6836	+	110.895i	0.461469	+	0.887156i
$26$		−	15.0229i		−	0.113317i
$27$	138.930	+	19.5337i	0.990260	+	0.139232i
$28$	57.8211	−	57.8211i	0.390256	−	0.390256i
$29$	−50.5042			−0.323393			−0.161697	−	0.986841i	$-0.551697\pi$
$29$	−50.5042			−0.323393			−0.161697	+	0.986841i	$0.551697\pi$
$30$	70.9555	−	206.928i	0.431821	−	1.25932i
$31$	−93.3673			−0.540944			−0.270472	−	0.962728i	$-0.587180\pi$
$31$	−93.3673			−0.540944			−0.270472	+	0.962728i	$0.587180\pi$
$32$	161.576	−	161.576i	0.892592	−	0.892592i
$33$	149.324	+	95.7458i	0.787696	+	0.505067i
$34$			342.083i			1.72549i
$35$	−35.1454	−	143.725i	−0.169733	−	0.694115i
$36$	−151.610	+	69.6188i	−0.701899	+	0.322309i
$37$	−161.537	−	161.537i	−0.717743	−	0.717743i	0.250400	−	0.968142i	$-0.419438\pi$
$37$	−161.537	−	161.537i	−0.717743	−	0.717743i	−0.968142	+	0.250400i	$0.919438\pi$
$38$	−50.7850	−	50.7850i	−0.216800	−	0.216800i
$39$	4.42765	+	20.2524i	0.0181793	+	0.0831531i
$40$	−18.2109	−	74.4727i	−0.0719850	−	0.294379i
$41$			88.7935i			0.338225i	0.985597	+	0.169112i	$0.0540901\pi$
$41$			88.7935i			0.338225i	−0.985597	+	0.169112i	$0.945910\pi$
$42$	−139.765	+	217.976i	−0.513482	+	0.800820i
$43$	176.399	−	176.399i	0.625596	−	0.625596i	−0.321361	−	0.946957i	$-0.604140\pi$
$43$	176.399	−	176.399i	0.625596	−	0.625596i	0.946957	+	0.321361i	$0.104140\pi$
$44$	−210.932			−0.722710
$45$	−34.6678	+	299.872i	−0.114844	+	0.993384i
$46$	273.725			0.877360
$47$	−38.2843	+	38.2843i	−0.118816	+	0.118816i	−0.764015	−	0.645199i	$-0.776775\pi$
$47$	−38.2843	+	38.2843i	−0.118816	+	0.118816i	0.645199	+	0.764015i	$0.276775\pi$
$48$	−211.061	+	329.169i	−0.634668	+	0.989820i
$49$		−	167.863i		−	0.489395i
$50$	448.857	+	141.680i	1.26956	+	0.400730i
$51$	−100.821	−	461.162i	−0.276819	−	1.26619i
$52$	−17.4313	−	17.4313i	−0.0464862	−	0.0464862i
$53$	−344.569	−	344.569i	−0.893022	−	0.893022i	0.101784	−	0.994806i	$-0.467545\pi$
$53$	−344.569	−	344.569i	−0.893022	−	0.893022i	−0.994806	+	0.101784i	$0.967545\pi$
$54$	421.925	−	317.904i	1.06327	−	0.801134i
$55$	−198.051	+	326.262i	−0.485549	+	0.799875i
$56$			90.7492i			0.216551i
$57$	83.4310	+	53.4956i	0.193872	+	0.124310i
$58$	−134.473	+	134.473i	−0.304433	+	0.304433i
$59$	421.133			0.929268			0.464634	−	0.885503i	$-0.346186\pi$
$59$	421.133			0.929268			0.464634	+	0.885503i	$0.346186\pi$
$60$	−157.771	−	322.432i	−0.339468	−	0.693763i
$61$	2.00000			0.00419793			0.00209897	−	0.999998i	$-0.499332\pi$
$61$	2.00000			0.00419793			0.00209897	+	0.999998i	$0.499332\pi$
$62$	−248.600	+	248.600i	−0.509229	+	0.509229i
$63$	124.174	−	335.046i	0.248325	−	0.670030i
$64$		−	258.409i		−	0.504704i
$65$	−43.3287	+	10.5952i	−0.0826811	+	0.0202181i
$66$	652.524	−	142.657i	1.21697	−	0.266059i
$67$	430.987	+	430.987i	0.785872	+	0.785872i	0.980815	−	0.194943i	$-0.0624521\pi$
$67$	430.987	+	430.987i	0.785872	+	0.785872i	−0.194943	+	0.980815i	$0.562452\pi$
$68$	396.923	+	396.923i	0.707853	+	0.707853i
$69$	−369.009	+	80.6742i	−0.643818	+	0.140754i
$70$	−476.262	−	289.105i	−0.813202	−	0.493639i
$71$			733.866i			1.22667i	0.789822	+	0.613337i	$0.210173\pi$
$71$			733.866i			1.22667i	−0.789822	+	0.613337i	$0.789827\pi$
$72$	64.3420	−	173.607i	0.105316	−	0.284164i
$73$	−348.073	+	348.073i	−0.558067	+	0.558067i	−0.928757	−	0.370690i	$-0.879121\pi$
$73$	−348.073	+	348.073i	−0.558067	+	0.558067i	0.370690	+	0.928757i	$0.379121\pi$
$74$	−860.216			−1.35133
$75$	−646.860	−	58.7079i	−0.995907	−	0.0903867i
$76$	−117.853			−0.177877
$77$	319.452	−	319.452i	0.472792	−	0.472792i
$78$	65.7131	+	42.1349i	0.0953915	+	0.0611646i
$79$		−	588.019i		−	0.837434i	−0.908117	−	0.418717i	$-0.862480\pi$
$79$		−	588.019i		−	0.837434i	0.908117	−	0.418717i	$-0.137520\pi$
$80$	−719.209	−	436.582i	−1.00512	−	0.610141i
$81$	−475.102	+	552.919i	−0.651717	+	0.758462i
$82$	236.422	+	236.422i	0.318395	+	0.318395i
$83$	217.997	+	217.997i	0.288293	+	0.288293i	0.836405	−	0.548112i	$-0.184653\pi$
$83$	217.997	+	217.997i	0.288293	+	0.288293i	−0.548112	+	0.836405i	$0.684653\pi$
$84$	90.7492	+	415.092i	0.117876	+	0.539170i
$85$	986.629	−	241.262i	1.25900	−	0.307865i
$86$		−	939.362i		−	1.17784i
$87$	141.650	−	220.915i	0.174557	−	0.272237i
$88$	165.527	−	165.527i	0.200514	−	0.200514i
$89$	1272.00			1.51497			0.757483	−	0.652855i	$-0.226429\pi$
$89$	1272.00			1.51497			0.757483	+	0.652855i	$0.226429\pi$
$90$	706.133	+	890.746i	0.827033	+	1.04325i
$91$	52.7985			0.0608219
$92$	317.607	−	317.607i	0.359922	−	0.359922i
$93$	261.868	−	408.407i	0.291984	−	0.455374i
$94$			203.872i			0.223700i
$95$	−110.656	+	182.291i	−0.119506	+	0.196870i
$96$	253.591	+	1159.94i	0.269605	+	1.23319i
$97$	−432.111	−	432.111i	−0.452312	−	0.452312i	0.443809	−	0.896121i	$-0.353627\pi$
$97$	−432.111	−	432.111i	−0.452312	−	0.452312i	−0.896121	+	0.443809i	$0.853627\pi$
$98$	−446.951	−	446.951i	−0.460703	−	0.460703i
$99$	−837.622	+	384.633i	−0.850345	+	0.390475i
$100$	685.207	−	356.422i	0.685207	−	0.356422i
$101$		−	1662.30i		−	1.63767i	−0.574029	−	0.818835i	$-0.694620\pi$
$101$		−	1662.30i		−	1.63767i	0.574029	−	0.818835i	$-0.305380\pi$
$102$	−1496.34	−	959.444i	−1.45254	−	0.931364i
$103$	−774.495	+	774.495i	−0.740906	+	0.740906i	−0.972752	−	0.231847i	$-0.925523\pi$
$103$	−774.495	+	774.495i	−0.740906	+	0.740906i	0.231847	+	0.972752i	$0.425523\pi$
$104$	27.3581			0.0257950
$105$	727.256	+	249.376i	0.675932	+	0.231777i
$106$	−1834.90			−1.68133
$107$	−1170.26	+	1170.26i	−1.05732	+	1.05732i	−0.0590633	+	0.998254i	$0.518811\pi$
$107$	−1170.26	+	1170.26i	−1.05732	+	1.05732i	−0.998254	+	0.0590633i	$0.981189\pi$
$108$	120.697	−	858.433i	0.107537	−	0.764841i
$109$			1264.60i			1.11125i	0.831432	+	0.555627i	$0.187522\pi$
$109$			1264.60i			1.11125i	−0.831432	+	0.555627i	$0.812478\pi$
$110$	341.375	+	1396.04i	0.295898	+	1.21006i
$111$	1159.66	−	253.529i	0.991620	−	0.216792i
$112$	704.198	+	704.198i	0.594111	+	0.594111i
$113$	381.173	+	381.173i	0.317325	+	0.317325i	0.847739	−	0.530414i	$-0.177963\pi$
$113$	381.173	+	381.173i	0.317325	+	0.317325i	−0.530414	+	0.847739i	$0.677963\pi$
$114$	364.581	−	79.7062i	0.299528	−	0.0654839i
$115$	−193.051	−	789.473i	−0.156540	−	0.640163i
$116$			312.061i			0.249777i
$117$	−101.006	−	37.4346i	−0.0798121	−	0.0295798i
$118$	1121.31	−	1121.31i	0.874787	−	0.874787i
$119$	−1202.26			−0.926145
$120$	376.835	+	129.216i	0.286668	+	0.0982983i
$121$	165.633			0.124442
$122$	5.32521	−	5.32521i	0.00395182	−	0.00395182i
$123$	−388.400	−	249.040i	−0.284722	−	0.182563i
$124$			576.908i			0.417805i
$125$	92.0630	−	1394.51i	0.0658749	−	0.997828i
$126$	−561.469	−	1222.72i	−0.396981	−	0.864513i
$127$	−439.588	−	439.588i	−0.307142	−	0.307142i	0.536658	−	0.843800i	$-0.319687\pi$
$127$	−439.588	−	439.588i	−0.307142	−	0.307142i	−0.843800	+	0.536658i	$0.819687\pi$
$128$	604.571	+	604.571i	0.417477	+	0.417477i
$129$	276.856	+	1266.35i	0.188959	+	0.864312i
$130$	−87.1563	+	143.578i	−0.0588009	+	0.0968664i
$131$			1399.28i			0.933247i	0.884456	+	0.466623i	$0.154530\pi$
$131$			1399.28i			0.933247i	−0.884456	+	0.466623i	$0.845470\pi$
$132$	591.605	−	922.659i	0.390095	−	0.608388i
$133$	178.486	−	178.486i	0.116366	−	0.116366i
$134$	2295.09			1.47960
$135$	−1214.46	−	992.698i	−0.774255	−	0.632873i
$136$	−622.964			−0.392785
$137$	1092.28	−	1092.28i	0.681169	−	0.681169i	−0.279095	−	0.960264i	$-0.590034\pi$
$137$	1092.28	−	1092.28i	0.681169	−	0.681169i	0.960264	+	0.279095i	$0.0900344\pi$
$138$	−767.720	+	1197.33i	−0.473570	+	0.738574i
$139$		−	2498.43i		−	1.52456i	−0.647245	−	0.762282i	$-0.724079\pi$
$139$		−	2498.43i		−	1.52456i	0.647245	−	0.762282i	$-0.275921\pi$
$140$	−888.066	+	217.160i	−0.536109	+	0.131096i
$141$	−60.0866	−	274.840i	−0.0358880	−	0.164154i
$142$	1953.99	+	1953.99i	1.15476	+	1.15476i
$143$	−96.3049	−	96.3049i	−0.0563177	−	0.0563177i
$144$	−847.881	−	1846.45i	−0.490672	−	1.06855i
$145$	482.684	+	293.004i	0.276446	+	0.167811i
$146$			1853.56i			1.05070i
$147$	734.264	+	470.806i	0.411980	+	0.264159i
$148$	−998.121	+	998.121i	−0.554358	+	0.554358i
$149$	−3570.40			−1.96308			−0.981538	−	0.191270i	$-0.938739\pi$
$149$	−3570.40			−1.96308			−0.981538	+	0.191270i	$0.938739\pi$
$150$	−1878.65	+	1566.02i	−1.02261	+	0.852431i
$151$	2687.14			1.44819			0.724094	−	0.689701i	$-0.242258\pi$
$151$	2687.14			1.44819			0.724094	+	0.689701i	$0.242258\pi$
$152$	92.4842	−	92.4842i	0.0493517	−	0.0493517i
$153$	2299.99	+	852.415i	1.21531	+	0.450416i
$154$		−	1701.15i		−	0.890146i
$155$	892.338	+	541.676i	0.462415	+	0.280700i
$156$	125.137	−	27.3581i	0.0642245	−	0.0140410i
$157$	−1810.48	−	1810.48i	−0.920333	−	0.920333i	0.0767201	−	0.997053i	$-0.475555\pi$
$157$	−1810.48	−	1810.48i	−0.920333	−	0.920333i	−0.997053	+	0.0767201i	$0.975555\pi$
$158$	−1565.66	−	1565.66i	−0.788337	−	0.788337i
$159$	2473.63	−	540.795i	1.23378	−	0.269735i
$160$	−2481.63	+	606.836i	−1.22619	+	0.299841i
$161$			962.017i			0.470916i
$162$	207.196	+	2737.21i	0.100487	+	1.32750i
$163$	−2679.06	+	2679.06i	−1.28736	+	1.28736i	−0.350982	+	0.936382i	$0.614152\pi$
$163$	−2679.06	+	2679.06i	−1.28736	+	1.28736i	−0.936382	+	0.350982i	$0.885848\pi$
$164$	548.647			0.261232
$165$	−871.657	−	1781.38i	−0.411263	−	0.840488i
$166$	1160.88			0.542782
$167$	139.543	−	139.543i	0.0646597	−	0.0646597i	−0.674037	−	0.738697i	$-0.735441\pi$
$167$	139.543	−	139.543i	0.0646597	−	0.0646597i	0.738697	+	0.674037i	$0.235441\pi$
$168$	−396.955	−	254.525i	−0.182296	−	0.116887i
$169$			2181.08i			0.992755i
$170$	1984.62	−	3269.39i	0.895372	−	1.47500i
$171$	−468.000	+	214.904i	−0.209292	+	0.0961059i
$172$	−1089.95	−	1089.95i	−0.483188	−	0.483188i
$173$	−881.613	−	881.613i	−0.387444	−	0.387444i	0.486331	−	0.873775i	$-0.338335\pi$
$173$	−881.613	−	881.613i	−0.387444	−	0.387444i	−0.873775	+	0.486331i	$0.838335\pi$
$174$	−211.053	−	965.367i	−0.0919532	−	0.420599i
$175$	−497.938	+	1577.52i	−0.215089	+	0.681426i
$176$		−	2568.93i		−	1.10023i
$177$	−1181.16	+	1842.12i	−0.501588	+	0.782271i
$178$	3386.84	−	3386.84i	1.42615	−	1.42615i
$179$	2512.87			1.04928			0.524638	−	0.851325i	$-0.324201\pi$
$179$	2512.87			1.04928			0.524638	+	0.851325i	$0.324201\pi$
$180$	1852.88	+	214.209i	0.767253	+	0.0887013i
$181$	269.796			0.110795			0.0553973	−	0.998464i	$-0.482357\pi$
$181$	269.796			0.110795			0.0553973	+	0.998464i	$0.482357\pi$
$182$	140.581	−	140.581i	0.0572560	−	0.0572560i
$183$	−5.60943	+	8.74839i	−0.00226591	+	0.00353388i
$184$			498.478i			0.199719i
$185$	606.687	+	2481.02i	0.241106	+	0.985990i
$186$	−390.173	−	1784.68i	−0.153811	−	0.703542i
$187$	2192.94	+	2192.94i	0.857559	+	0.857559i
$188$	236.555	+	236.555i	0.0917690	+	0.0917690i
$189$	1117.29	+	1482.87i	0.430003	+	0.570703i
$190$	190.735	+	780.000i	0.0728281	+	0.297827i
$191$		−	2420.22i		−	0.916864i	−0.888729	−	0.458432i	$-0.848411\pi$
$191$		−	2420.22i		−	0.916864i	0.888729	−	0.458432i	$-0.151589\pi$
$192$	1130.33	+	724.762i	0.424867	+	0.272423i
$193$	1965.28	−	1965.28i	0.732973	−	0.732973i	−0.238234	−	0.971208i	$-0.576569\pi$
$193$	1965.28	−	1965.28i	0.732973	−	0.732973i	0.971208	+	0.238234i	$0.0765686\pi$
$194$	−2301.08			−0.851588
$195$	75.1791	−	219.245i	0.0276086	−	0.0805152i
$196$	−1037.21			−0.377991
$197$	−832.602	+	832.602i	−0.301119	+	0.301119i	−0.841452	−	0.540333i	$-0.818298\pi$
$197$	−832.602	+	832.602i	−0.301119	+	0.301119i	0.540333	+	0.841452i	$0.318298\pi$
$198$	−1206.13	+	3254.38i	−0.432909	+	1.16807i
$199$		−	1540.54i		−	0.548775i	−0.961619	−	0.274387i	$-0.911525\pi$
$199$		−	1540.54i		−	0.548775i	0.961619	−	0.274387i	$-0.0884750\pi$
$200$	−258.011	+	817.409i	−0.0912208	+	0.288998i
$201$	−3094.02	+	676.426i	−1.08575	+	0.237370i
$202$	−4426.04	−	4426.04i	−1.54166	−	1.54166i
$203$	−472.609	−	472.609i	−0.163402	−	0.163402i
$204$	−2849.48	+	622.964i	−0.977957	+	0.213805i
$205$	515.142	−	848.625i	0.175508	−	0.289125i
$206$			4124.35i			1.39494i
$207$	682.079	−	1840.38i	0.229023	−	0.617949i
$208$	212.294	−	212.294i	0.0707689	−	0.0707689i
$209$	−651.119			−0.215497
$210$	2600.38	−	1272.40i	0.854492	−	0.418115i
$211$	−10.9380			−0.00356874			−0.00178437	−	0.999998i	$-0.500568\pi$
$211$	−10.9380			−0.00356874			−0.00178437	+	0.999998i	$0.500568\pi$
$212$	−2129.06	+	2129.06i	−0.689738	+	0.689738i
$213$	−3210.07	−	2058.28i	−1.03263	−	0.662118i
$214$			6231.86i			1.99066i
$215$	−2709.29	+	662.507i	−0.859405	+	0.210152i
$216$	578.932	+	768.364i	0.182367	+	0.242039i
$217$	−873.714	−	873.714i	−0.273325	−	0.273325i
$218$	3367.13	+	3367.13i	1.04610	+	1.04610i
$219$	−546.295	−	2498.79i	−0.168563	−	0.771016i
$220$	2015.94	+	1223.74i	0.617794	+	0.375020i
$221$			362.445i			0.110320i
$222$	2412.66	−	3762.75i	0.729401	−	1.13757i
$223$	831.512	−	831.512i	0.249696	−	0.249696i	−0.571150	−	0.820846i	$-0.693503\pi$
$223$	831.512	−	831.512i	0.249696	−	0.249696i	0.820846	+	0.571150i	$0.193503\pi$
$224$	3024.00			0.902008
$225$	2071.06	−	2664.83i	0.613647	−	0.789581i
$226$	2029.83			0.597443
$227$	3441.18	−	3441.18i	1.00616	−	1.00616i	0.00618314	−	0.999981i	$-0.498032\pi$
$227$	3441.18	−	3441.18i	1.00616	−	1.00616i	0.999981	−	0.00618314i	$-0.00196817\pi$
$228$	330.544	−	515.512i	0.0960124	−	0.149740i
$229$			1680.38i			0.484903i	0.970164	+	0.242451i	$0.0779515\pi$
$229$			1680.38i			0.484903i	−0.970164	+	0.242451i	$0.922049\pi$
$230$	−2616.07	−	1588.03i	−0.749994	−	0.455269i
$231$	501.375	+	2293.32i	0.142805	+	0.653200i
$232$	−244.887	−	244.887i	−0.0693001	−	0.0693001i
$233$	2106.74	+	2106.74i	0.592348	+	0.592348i	0.938265	−	0.345917i	$-0.112432\pi$
$233$	2106.74	+	2106.74i	0.592348	+	0.592348i	−0.345917	+	0.938265i	$0.612432\pi$
$234$	−368.613	+	169.265i	−0.102978	+	0.0472873i
$235$	588.004	−	143.785i	0.163222	−	0.0399129i
$236$		−	2602.14i		−	0.717733i
$237$	2572.11	+	1649.22i	0.704964	+	0.452019i
$238$	−3201.15	+	3201.15i	−0.871847	+	0.871847i
$239$	−261.125			−0.0706728			−0.0353364	−	0.999375i	$-0.511250\pi$
$239$	−261.125			−0.0706728			−0.0353364	+	0.999375i	$0.511250\pi$
$240$	3926.87	−	1921.47i	1.05616	−	0.516794i
$241$	−6001.45			−1.60410			−0.802048	−	0.597259i	$-0.796256\pi$
$241$	−6001.45			−1.60410			−0.802048	+	0.597259i	$0.796256\pi$
$242$	441.014	−	441.014i	0.117147	−	0.117147i
$243$	−1086.05	−	3628.97i	−0.286709	−	0.958018i
$244$		−	12.3578i		−	0.00324233i
$245$	−973.866	+	1604.31i	−0.253951	+	0.418350i
$246$	−1697.25	+	371.060i	−0.439889	+	0.0961704i
$247$	−53.8080	−	53.8080i	−0.0138612	−	0.0138612i
$248$	−452.723	−	452.723i	−0.115919	−	0.115919i
$249$	−1564.98	+	342.143i	−0.398300	+	0.0870781i
$250$	−3467.89	−	3958.15i	−0.877315	−	1.00134i
$251$		−	3044.59i		−	0.765630i	−0.923825	−	0.382815i	$-0.874955\pi$
$251$		−	3044.59i		−	0.765630i	0.923825	−	0.382815i	$-0.125045\pi$
$252$	−2070.22	−	767.260i	−0.517506	−	0.191797i
$253$	1754.73	−	1754.73i	0.436042	−	0.436042i
$254$	−2340.89			−0.578271
$255$	−1711.89	+	4992.38i	−0.420402	+	1.22602i
$256$	5286.74			1.29071
$257$	−946.317	+	946.317i	−0.229687	+	0.229687i	−0.812562	−	0.582875i	$-0.801928\pi$
$257$	−946.317	+	946.317i	−0.229687	+	0.229687i	0.582875	+	0.812562i	$0.301928\pi$
$258$	4108.95	+	2634.64i	0.991521	+	0.635758i
$259$		−	3023.26i		−	0.725314i
$260$	65.4670	+	267.724i	0.0156157	+	0.0638598i
$261$	569.040	+	1239.21i	0.134953	+	0.293889i
$262$	3725.72	+	3725.72i	0.878532	+	0.878532i
$263$	67.0257	+	67.0257i	0.0157148	+	0.0157148i	0.714921	−	0.699206i	$-0.246463\pi$
$263$	67.0257	+	67.0257i	0.0157148	+	0.0157148i	−0.699206	+	0.714921i	$0.746463\pi$
$264$	259.792	+	1188.31i	0.0605648	+	0.277027i
$265$	1294.11	+	5292.18i	0.299986	+	1.22678i
$266$		−	950.474i		−	0.219088i
$267$	−3567.60	+	5563.99i	−0.817729	+	1.27532i
$268$	2663.03	−	2663.03i	0.606979	−	0.606979i
$269$	2658.15			0.602492			0.301246	−	0.953546i	$-0.402597\pi$
$269$	2658.15			0.602492			0.301246	+	0.953546i	$0.402597\pi$
$270$	−5876.80	+	590.476i	−1.32463	+	0.133093i
$271$	145.673			0.0326530			0.0163265	−	0.999867i	$-0.494803\pi$
$271$	145.673			0.0326530			0.0163265	+	0.999867i	$0.494803\pi$
$272$	−4834.09	+	4834.09i	−1.07761	+	1.07761i
$273$	−148.085	+	230.951i	−0.0328296	+	0.0512007i
$274$		−	5816.64i		−	1.28247i
$275$	3785.66	−	1969.17i	0.830123	−	0.431802i
$276$	498.478	+	2280.07i	0.108713	+	0.497261i
$277$	−1074.57	−	1074.57i	−0.233085	−	0.233085i	0.580894	−	0.813979i	$-0.302703\pi$
$277$	−1074.57	−	1074.57i	−0.233085	−	0.233085i	−0.813979	+	0.580894i	$0.802703\pi$
$278$	−6652.34	−	6652.34i	−1.43518	−	1.43518i
$279$	1051.98	+	2290.93i	0.225737	+	0.491592i
$280$	526.488	−	867.316i	0.112370	−	0.185115i
$281$		−	2020.29i		−	0.428898i	−0.976735	−	0.214449i	$-0.931204\pi$
$281$		−	2020.29i		−	0.428898i	0.976735	−	0.214449i	$-0.0687956\pi$
$282$	−891.776	−	571.802i	−0.188314	−	0.120746i
$283$	−2400.34	+	2400.34i	−0.504189	+	0.504189i	−0.912737	−	0.408548i	$-0.866035\pi$
$283$	−2400.34	+	2400.34i	−0.504189	+	0.504189i	0.408548	+	0.912737i	$0.366035\pi$
$284$	4534.49			0.947438
$285$	−487.016	−	995.303i	−0.101222	−	0.206866i
$286$	−512.844			−0.106032
$287$	−830.913	+	830.913i	−0.170896	+	0.170896i
$288$	−5785.06	−	2144.05i	−1.18364	−	0.438678i
$289$		−	3340.15i		−	0.679860i
$290$	2065.35	−	505.042i	0.418212	−	0.102266i
$291$	3102.09	−	678.191i	0.624906	−	0.136619i
$292$	2150.71	+	2150.71i	0.431031	+	0.431031i
$293$	2533.13	+	2533.13i	0.505075	+	0.505075i	0.913011	−	0.407936i	$-0.133751\pi$
$293$	2533.13	+	2533.13i	0.505075	+	0.505075i	−0.407936	+	0.913011i	$0.633751\pi$
$294$	3208.62	−	701.482i	0.636499	−	0.139154i
$295$	−4024.89	−	2443.23i	−0.794366	−	0.482204i
$296$		−	1566.53i		−	0.307611i
$297$	666.830	−	4742.71i	0.130281	−	0.926598i
$298$	−9506.54	+	9506.54i	−1.84798	+	1.84798i
$299$	290.018			0.0560943
$300$	−362.751	+	3996.89i	−0.0698114	+	0.769202i
$301$	3301.42			0.632196
$302$	7154.79	−	7154.79i	1.36328	−	1.36328i
$303$	7271.21	+	4662.27i	1.37861	+	0.883961i
$304$		−	1435.32i		−	0.270794i
$305$	−19.1146	−	11.6031i	−0.00358852	−	0.00217834i
$306$	8393.59	−	3854.31i	1.56807	−	0.720052i
$307$	3159.93	+	3159.93i	0.587449	+	0.587449i	0.936940	−	0.349491i	$-0.113645\pi$
$307$	3159.93	+	3159.93i	0.587449	+	0.587449i	−0.349491	+	0.936940i	$0.613645\pi$
$308$	−1973.87	−	1973.87i	−0.365167	−	0.365167i
$309$	−1215.56	−	5560.03i	−0.223788	−	1.02362i
$310$	3818.21	−	933.673i	0.699548	−	0.171061i
$311$			7206.19i			1.31391i	0.753931	+	0.656954i	$0.228155\pi$
$311$			7206.19i			1.31391i	−0.753931	+	0.656954i	$0.771845\pi$
$312$	−76.7315	+	119.670i	−0.0139233	+	0.0217146i
$313$	2029.31	−	2029.31i	0.366464	−	0.366464i	−0.499722	−	0.866186i	$-0.666564\pi$
$313$	2029.31	−	2029.31i	0.366464	−	0.366464i	0.866186	+	0.499722i	$0.166564\pi$
$314$	−9641.19			−1.73275
$315$	−3130.56	+	2481.73i	−0.559959	+	0.443904i
$316$	−3633.31			−0.646804
$317$	−689.223	+	689.223i	−0.122116	+	0.122116i	−0.765524	−	0.643408i	$-0.777520\pi$
$317$	−689.223	+	689.223i	−0.122116	+	0.122116i	0.643408	+	0.765524i	$0.277520\pi$
$318$	5146.37	−	8026.21i	0.907528	−	1.41537i
$319$			1724.09i			0.302603i
$320$	−1499.18	+	2469.69i	−0.261895	+	0.431437i
$321$	−1836.70	−	8401.16i	−0.319360	−	1.46077i
$322$	2561.47	+	2561.47i	0.443308	+	0.443308i
$323$	1225.25	+	1225.25i	0.211067	+	0.211067i
$324$	3416.44	+	2935.61i	0.585809	+	0.503363i
$325$	475.574	+	150.113i	0.0811696	+	0.0256208i
$326$			14266.6i			2.42378i
$327$	−5531.60	−	3546.84i	−0.935469	−	0.599818i
$328$	−430.546	+	430.546i	−0.0724784	+	0.0724784i
$329$	−716.516			−0.120069
$330$	−7063.99	−	2422.24i	−1.17836	−	0.404061i
$331$	−8226.53			−1.36608			−0.683038	−	0.730383i	$-0.739342\pi$
$331$	−8226.53			−1.36608			−0.683038	+	0.730383i	$0.739342\pi$
$332$	1346.99	−	1346.99i	0.222667	−	0.222667i
$333$	−2143.52	+	5783.64i	−0.352745	+	0.951777i
$334$		−	743.096i		−	0.121738i
$335$	−1618.67	−	6619.47i	−0.263992	−	1.07958i
$336$	−5055.37	+	1105.23i	−0.820813	+	0.179449i
$337$	1777.34	+	1777.34i	0.287294	+	0.287294i	0.836009	−	0.548715i	$-0.184883\pi$
$337$	1777.34	+	1777.34i	0.287294	+	0.287294i	−0.548715	+	0.836009i	$0.684883\pi$
$338$	5807.36	+	5807.36i	0.934552	+	0.934552i
$339$	−2736.41	+	598.245i	−0.438411	+	0.0958472i
$340$	−1490.73	−	6096.29i	−0.237784	−	0.972405i
$341$			3187.32i			0.506168i
$342$	−673.895	+	1818.30i	−0.106550	+	0.287493i
$343$	4780.56	−	4780.56i	0.752554	−	0.752554i
$344$	1710.66			0.268119
$345$	3994.76	+	1369.80i	0.623393	+	0.213761i
$346$	−4694.77			−0.729458
$347$	−1715.22	+	1715.22i	−0.265354	+	0.265354i	−0.827225	−	0.561871i	$-0.810082\pi$
$347$	−1715.22	+	1715.22i	−0.265354	+	0.265354i	0.561871	+	0.827225i	$0.310082\pi$
$348$	−1365.02	−	875.242i	−0.210266	−	0.134821i
$349$			8603.96i			1.31965i	0.751417	+	0.659827i	$0.229371\pi$
$349$			8603.96i			1.31965i	−0.751417	+	0.659827i	$0.770629\pi$
$350$	2874.51	+	5526.13i	0.438997	+	0.843954i
$351$	447.039	−	336.827i	0.0679806	−	0.0512208i
$352$	−5515.81	−	5515.81i	−0.835209	−	0.835209i
$353$	−5425.13	−	5425.13i	−0.817990	−	0.817990i	0.167827	−	0.985816i	$-0.446325\pi$
$353$	−5425.13	−	5425.13i	−0.817990	−	0.817990i	−0.985816	+	0.167827i	$0.946325\pi$
$354$	1759.87	+	8049.77i	0.264227	+	1.20859i
$355$	4257.57	−	7013.77i	0.636531	−	1.04860i
$356$		−	7859.58i		−	1.17010i
$357$	3372.00	−	5258.93i	0.499903	−	0.779642i
$358$	6690.76	−	6690.76i	0.987759	−	0.987759i
$359$	−11418.9			−1.67874			−0.839370	−	0.543560i	$-0.817076\pi$
$359$	−11418.9			−1.67874			−0.839370	+	0.543560i	$0.817076\pi$
$360$	−1622.13	+	1285.93i	−0.237483	+	0.188263i
$361$	6495.20			0.946961
$362$	718.361	−	718.361i	0.104299	−	0.104299i
$363$	−464.552	+	724.510i	−0.0671699	+	0.104757i
$364$		−	326.237i		−	0.0469766i
$365$	5346.01	−	1307.27i	0.766638	−	0.187467i
$366$	8.35782	+	38.2292i	0.00119363	+	0.00545976i
$367$	6554.73	+	6554.73i	0.932299	+	0.932299i	0.997849	−	0.0655499i	$-0.0208802\pi$
$367$	6554.73	+	6554.73i	0.932299	+	0.932299i	−0.0655499	+	0.997849i	$0.520880\pi$
$368$	3868.11	+	3868.11i	0.547932	+	0.547932i
$369$	2178.70	−	1000.45i	0.307368	−	0.141142i
$370$	8221.34	+	4990.60i	1.15515	+	0.701214i
$371$		−	6448.83i		−	0.902443i
$372$	−2523.51	−	1618.06i	−0.351714	−	0.225518i
$373$	−5967.46	+	5967.46i	−0.828374	+	0.828374i	−0.987292	−	0.158918i	$-0.949199\pi$
$373$	−5967.46	+	5967.46i	−0.828374	+	0.828374i	0.158918	+	0.987292i	$0.449199\pi$
$374$	11677.8			1.61456
$375$	5841.64	+	4313.89i	0.804429	+	0.594049i
$376$	−371.270			−0.0509222
$377$	−142.477	+	142.477i	−0.0194640	+	0.0194640i
$378$	6923.18	+	973.408i	0.942037	+	0.132452i
$379$			1680.48i			0.227758i	0.993495	+	0.113879i	$0.0363276\pi$
$379$			1680.48i			0.227758i	−0.993495	+	0.113879i	$0.963672\pi$
$380$	1126.36	+	683.733i	0.152055	+	0.0923020i
$381$	3155.76	−	689.925i	0.424342	−	0.0927715i
$382$	−6444.09	−	6444.09i	−0.863110	−	0.863110i
$383$	−7493.42	−	7493.42i	−0.999728	−	0.999728i	0.000271480	−	1.00000i	$-0.499914\pi$
$383$	−7493.42	−	7493.42i	−0.999728	−	0.999728i	−1.00000		0.000271480i	$0.999914\pi$
$384$	−4340.16	+	948.864i	−0.576779	+	0.126098i
$385$	−4906.42	+	1199.77i	−0.649492	+	0.158821i
$386$		−	10465.5i		−	1.38000i
$387$	−6315.78	−	2340.74i	−0.829584	−	0.307459i
$388$	−2669.98	+	2669.98i	−0.349349	+	0.349349i
$389$	7966.97			1.03841			0.519205	−	0.854650i	$-0.326228\pi$
$389$	7966.97			1.03841			0.519205	+	0.854650i	$0.326228\pi$
$390$	−383.590	−	783.934i	−0.0498048	−	0.101785i
$391$	−6603.94			−0.854158
$392$	813.939	−	813.939i	0.104873	−	0.104873i
$393$	−6120.71	−	3924.57i	−0.785620	−	0.503736i
$394$			4433.78i			0.566930i
$395$	−3411.43	+	5619.87i	−0.434551	+	0.715864i
$396$	2376.61	+	5175.59i	0.301589	+	0.656776i
$397$	−8188.88	−	8188.88i	−1.03523	−	1.03523i	−0.999356	−	0.0358786i	$-0.988577\pi$
$397$	−8188.88	−	8188.88i	−1.03523	−	1.03523i	−0.0358786	−	0.999356i	$-0.511423\pi$
$398$	−4101.85	−	4101.85i	−0.516601	−	0.516601i
$399$	280.130	+	1281.33i	0.0351480	+	0.160769i
$400$	4340.83	+	8345.08i	0.542604	+	1.04313i
$401$			5167.66i			0.643542i	0.946817	+	0.321771i	$0.104278\pi$
$401$			5167.66i			0.643542i	−0.946817	+	0.321771i	$0.895722\pi$
$402$	−6437.08	+	10039.2i	−0.798638	+	1.24555i
$403$	−263.398	+	263.398i	−0.0325577	+	0.0325577i
$404$	−10271.2			−1.26488
$405$	7748.48	−	2528.07i	0.950679	−	0.310175i
$406$	−2516.74			−0.307645
$407$	−5514.46	+	5514.46i	−0.671601	+	0.671601i
$408$	1747.24	−	2724.97i	0.212012	−	0.330652i
$409$		−	8514.82i		−	1.02941i	−0.857366	−	0.514707i	$-0.827901\pi$
$409$		−	8514.82i		−	1.02941i	0.857366	−	0.514707i	$-0.172099\pi$
$410$	−887.935	−	3631.17i	−0.106956	−	0.437392i
$411$	1714.32	+	7841.41i	0.205745	+	0.941090i
$412$	4785.54	+	4785.54i	0.572249	+	0.572249i
$413$	3940.88	+	3940.88i	0.469535	+	0.469535i
$414$	−3084.11	−	6716.32i	−0.366125	−	0.797316i
$415$	−818.738	−	3348.19i	−0.0968440	−	0.396039i
$416$		−	911.644i		−	0.107445i
$417$	10928.6	+	7007.39i	1.28340	+	0.822910i
$418$	−1733.67	+	1733.67i	−0.202863	+	0.202863i
$419$	11939.7			1.39211			0.696053	−	0.717990i	$-0.254938\pi$
$419$	11939.7			1.39211			0.696053	+	0.717990i	$0.254938\pi$
$420$	1540.87	−	4493.65i	0.179016	−	0.522065i
$421$	10873.3			1.25875			0.629373	−	0.777103i	$-0.283312\pi$
$421$	10873.3			1.25875			0.629373	+	0.777103i	$0.283312\pi$
$422$	−29.1236	+	29.1236i	−0.00335951	+	0.00335951i
$423$	1370.73	+	508.016i	0.157558	+	0.0583938i
$424$		−	3341.52i		−	0.382733i
$425$	−10829.2	−	3418.19i	−1.23598	−	0.390133i
$426$	−14027.5	+	3066.76i	−1.59539	+	0.348791i
$427$	18.7156	+	18.7156i	0.00212111	+	0.00212111i
$428$	7230.91	+	7230.91i	0.816634	+	0.816634i
$429$	691.364	−	151.149i	0.0778074	−	0.0170106i
$430$	−5449.77	+	8977.76i	−0.611189	+	1.00685i
$431$		−	7603.48i		−	0.849760i	−0.905250	−	0.424880i	$-0.860316\pi$
$431$		−	7603.48i		−	0.849760i	0.905250	−	0.424880i	$-0.139684\pi$
$432$	10454.8	+	1469.95i	1.16437	+	0.163711i
$433$	4681.19	−	4681.19i	0.519547	−	0.519547i	−0.397887	−	0.917434i	$-0.630257\pi$
$433$	4681.19	−	4681.19i	0.519547	−	0.519547i	0.917434	+	0.397887i	$0.130257\pi$
$434$	−4652.70			−0.514601
$435$	−2635.44	+	1289.56i	−0.290483	+	0.142137i
$436$	7813.84			0.858292
$437$	980.409	−	980.409i	0.107321	−	0.107321i
$438$	−8107.85	−	5198.71i	−0.884493	−	0.567133i
$439$			8608.08i			0.935857i	0.883766	+	0.467929i	$0.155000\pi$
$439$			8608.08i			0.935857i	−0.883766	+	0.467929i	$0.845000\pi$
$440$	−2542.31	+	621.675i	−0.275454	+	0.0673572i
$441$	−4118.80	+	1891.34i	−0.444746	+	0.204226i
$442$	965.047	+	965.047i	0.103852	+	0.103852i
$443$	6466.81	+	6466.81i	0.693561	+	0.693561i	0.963014	−	0.269453i	$-0.0868428\pi$
$443$	6466.81	+	6466.81i	0.693561	+	0.693561i	−0.269453	+	0.963014i	$0.586843\pi$
$444$	−1566.53	−	7165.42i	−0.167442	−	0.765891i
$445$	−12156.9	−	7379.61i	−1.29504	−	0.786128i
$446$		−	4427.97i		−	0.470113i
$447$	10013.9	−	15617.6i	1.05960	−	1.65254i
$448$	2418.14	−	2418.14i	0.255014	−	0.255014i
$449$	356.370			0.0374569			0.0187284	−	0.999825i	$-0.494038\pi$
$449$	356.370			0.0374569			0.0187284	+	0.999825i	$0.494038\pi$
$450$	−1580.99	−	12609.8i	−0.165619	−	1.32096i
$451$	3031.19			0.316481
$452$	2355.24	−	2355.24i	0.245091	−	0.245091i
$453$	−7536.66	+	11754.1i	−0.781685	+	1.21911i
$454$		−	18325.0i		−	1.89435i
$455$	−504.611	−	306.314i	−0.0519923	−	0.0315609i
$456$	145.152	+	663.935i	0.0149065	+	0.0681834i
$457$	1512.80	+	1512.80i	0.154849	+	0.154849i	0.780280	−	0.625431i	$-0.215077\pi$
$457$	1512.80	+	1512.80i	0.154849	+	0.154849i	−0.625431	+	0.780280i	$0.715077\pi$
$458$	4474.19	+	4474.19i	0.456474	+	0.456474i
$459$	−10179.4	+	7669.81i	−1.03515	+	0.779948i
$460$	−4878.08	+	1192.84i	−0.494438	+	0.120906i
$461$			13307.9i			1.34449i	0.740327	+	0.672246i	$0.234670\pi$
$461$			13307.9i			1.34449i	−0.740327	+	0.672246i	$0.765330\pi$
$462$	7441.16	+	4771.23i	0.749338	+	0.480472i
$463$	−1237.43	+	1237.43i	−0.124208	+	0.124208i	−0.766478	−	0.642270i	$-0.777993\pi$
$463$	−1237.43	+	1237.43i	−0.124208	+	0.124208i	0.642270	+	0.766478i	$0.277993\pi$
$464$	−3800.56			−0.380251
$465$	−4872.15	+	2384.01i	−0.485894	+	0.237755i
$466$	11218.8			1.11524
$467$	8201.87	−	8201.87i	0.812713	−	0.812713i	−0.172327	−	0.985040i	$-0.555128\pi$
$467$	8201.87	−	8201.87i	0.812713	−	0.812713i	0.985040	+	0.172327i	$0.0551285\pi$
$468$	−231.305	+	624.107i	−0.0228463	+	0.0616439i
$469$			8066.19i			0.794162i
$470$	1182.78	−	1948.46i	0.116080	−	0.191225i
$471$	12997.3	−	2841.52i	1.27151	−	0.277984i
$472$	2042.01	+	2042.01i	0.199133	+	0.199133i
$473$	−6021.83	−	6021.83i	−0.585378	−	0.585378i
$474$	11239.7	−	2457.28i	1.08915	−	0.238115i
$475$	2115.14	−	1100.23i	0.204314	−	0.106278i
$476$			7428.67i			0.715321i
$477$	−4572.28	+	12336.9i	−0.438889	+	1.18421i
$478$	−695.273	+	695.273i	−0.0665294	+	0.0665294i
$479$	11419.1			1.08926			0.544629	−	0.838677i	$-0.316671\pi$
$479$	11419.1			1.08926			0.544629	+	0.838677i	$0.316671\pi$
$480$	4305.84	−	12557.1i	0.409445	−	1.19407i
$481$	−911.420			−0.0863974
$482$	−15979.5	+	15979.5i	−1.51005	+	1.51005i
$483$	−4208.05	−	2698.18i	−0.396424	−	0.254185i
$484$		−	1023.43i		−	0.0961147i
$485$	1622.89	+	6636.73i	0.151942	+	0.621358i
$486$	−12554.2	−	6770.77i	−1.17175	−	0.631952i
$487$	−6066.93	−	6066.93i	−0.564515	−	0.564515i	0.366071	−	0.930587i	$-0.380703\pi$
$487$	−6066.93	−	6066.93i	−0.564515	−	0.564515i	−0.930587	+	0.366071i	$0.880703\pi$
$488$	9.69769	+	9.69769i	0.000899577	+	0.000899577i
$489$	−4204.74	−	19232.7i	−0.388845	−	1.77860i
$490$	1678.63	+	6864.66i	0.154760	+	0.632885i
$491$			8978.88i			0.825277i	0.910895	+	0.412639i	$0.135393\pi$
$491$			8978.88i			0.825277i	−0.910895	+	0.412639i	$0.864607\pi$
$492$	−1538.80	+	2399.89i	−0.141005	+	0.219909i
$493$	3244.31	−	3244.31i	0.296382	−	0.296382i
$494$	−286.538			−0.0260971
$495$	10236.9	+	1183.47i	0.929521	+	0.107461i
$496$	−7026.11			−0.636051
$497$	−6867.38	+	6867.38i	−0.619807	+	0.619807i
$498$	−3255.94	+	5077.92i	−0.292976	+	0.456922i
$499$			7674.34i			0.688478i	0.938882	+	0.344239i	$0.111863\pi$
$499$			7674.34i			0.688478i	−0.938882	+	0.344239i	$0.888137\pi$
$500$	−8616.53	−	568.849i	−0.770686	−	0.0508794i
$501$	219.010	+	1001.77i	0.0195303	+	0.0893326i
$502$	−8106.54	−	8106.54i	−0.720743	−	0.720743i
$503$	−4044.23	−	4044.23i	−0.358496	−	0.358496i	0.504762	−	0.863258i	$-0.331580\pi$
$503$	−4044.23	−	4044.23i	−0.358496	−	0.358496i	−0.863258	+	0.504762i	$0.831580\pi$
$504$	2226.69	−	1022.49i	0.196795	−	0.0903674i
$505$	−9643.93	+	15887.1i	−0.849800	+	1.39993i
$506$		−	9344.28i		−	0.820957i
$507$	−9540.48	−	6117.31i	−0.835715	−	0.535857i
$508$	−2716.17	+	2716.17i	−0.237226	+	0.237226i
$509$	−12532.5			−1.09134			−0.545672	−	0.837999i	$-0.683725\pi$
$509$	−12532.5			−1.09134			−0.545672	+	0.837999i	$0.683725\pi$
$510$	8734.65	+	17850.8i	0.758386	+	1.54989i
$511$	−6514.42			−0.563955
$512$	9239.91	−	9239.91i	0.797559	−	0.797559i
$513$	372.574	−	2649.87i	0.0320654	−	0.228059i
$514$			5039.33i			0.432443i
$515$	11895.4	−	2908.79i	1.01781	−	0.248887i
$516$	7824.69	−	1710.66i	0.667563	−	0.145945i
$517$	1306.93	+	1306.93i	0.111177	+	0.111177i
$518$	−8049.75	−	8049.75i	−0.682791	−	0.682791i
$519$	6329.02	−	1383.68i	0.535285	−	0.117026i
$520$	−261.469	−	158.720i	−0.0220503	−	0.0133852i
$521$		−	19201.8i		−	1.61468i	−0.590089	−	0.807338i	$-0.700907\pi$
$521$		−	19201.8i		−	1.61468i	0.590089	−	0.807338i	$-0.299093\pi$
$522$	4814.65	+	1784.39i	0.403700	+	0.149618i
$523$	5472.69	−	5472.69i	0.457560	−	0.457560i	−0.440294	−	0.897854i	$-0.645126\pi$
$523$	5472.69	−	5472.69i	0.457560	−	0.457560i	0.897854	+	0.440294i	$0.145126\pi$
$524$	8646.00			0.720806
$525$	−5503.82	−	6602.58i	−0.457536	−	0.548877i
$526$	356.926			0.0295869
$527$	5997.77	−	5997.77i	0.495762	−	0.495762i
$528$	11237.0	+	7205.10i	0.926187	+	0.593867i
$529$		−	6882.71i		−	0.565687i
$530$	17536.7	+	10645.3i	1.43725	+	0.872457i
$531$	−4744.97	−	10333.2i	−0.387786	−	0.844488i
$532$	−1102.85	−	1102.85i	−0.0898769	−	0.0898769i
$533$	250.495	+	250.495i	0.0203567	+	0.0203567i
$534$	5315.58	+	24313.8i	0.430763	+	1.97034i
$535$	17973.8	−	4395.16i	1.45248	−	0.355176i
$536$			4179.58i			0.336810i
$537$	−7047.87	+	10991.8i	−0.566365	+	0.883295i
$538$	7077.60	−	7077.60i	0.567169	−	0.567169i
$539$	−5730.40			−0.457933
$540$	−6133.79	+	7504.07i	−0.488808	+	0.598007i
$541$	12778.2			1.01548			0.507741	−	0.861510i	$-0.330481\pi$
$541$	12778.2			1.01548			0.507741	+	0.861510i	$0.330481\pi$
$542$	387.868	−	387.868i	0.0307387	−	0.0307387i
$543$	−756.702	+	1180.14i	−0.0598033	+	0.0932684i
$544$			20758.8i			1.63608i
$545$	7336.66	−	12086.1i	0.576638	−	0.949933i
$546$	220.640	+	1009.22i	0.0172940	+	0.0791038i
$547$	−2414.12	−	2414.12i	−0.188702	−	0.188702i	0.606433	−	0.795135i	$-0.292600\pi$
$547$	−2414.12	−	2414.12i	−0.188702	−	0.188702i	−0.795135	+	0.606433i	$0.792600\pi$
$548$	−6749.12	−	6749.12i	−0.526110	−	0.526110i
$549$	−22.5343	−	49.0735i	−0.00175181	−	0.00381494i
$550$	4836.58	−	15322.8i	0.374968	−	1.18794i
$551$			963.290i			0.0744783i
$552$	−2180.44	−	1398.09i	−0.168126	−	0.107802i
$553$	5502.57	−	5502.57i	0.423134	−	0.423134i
$554$	−5722.30			−0.438840
$555$	−12554.0	−	4304.78i	−0.960162	−	0.329239i
$556$	−15437.6			−1.17752
$557$	5573.05	−	5573.05i	0.423946	−	0.423946i	−0.462614	−	0.886560i	$-0.653088\pi$
$557$	5573.05	−	5573.05i	0.423946	−	0.423946i	0.886560	+	0.462614i	$0.153088\pi$
$558$	8900.85	+	3298.81i	0.675274	+	0.250268i
$559$		−	995.277i		−	0.0753054i
$560$	−2644.77	−	10815.7i	−0.199575	−	0.816153i
$561$	−15742.9	+	3441.78i	−1.18479	+	0.259023i
$562$	−5379.23	−	5379.23i	−0.403753	−	0.403753i
$563$	3488.75	+	3488.75i	0.261160	+	0.261160i	0.825525	−	0.564365i	$-0.190879\pi$
$563$	3488.75	+	3488.75i	0.261160	+	0.261160i	−0.564365	+	0.825525i	$0.690879\pi$
$564$	−1698.21	+	371.270i	−0.126786	+	0.0277186i
$565$	−1431.58	−	5854.39i	−0.106597	−	0.435922i
$566$			12782.3i			0.949260i
$567$	−9620.03	+	728.199i	−0.712528	+	0.0539356i
$568$	−3558.40	+	3558.40i	−0.262865	+	0.262865i
$569$	−4924.15			−0.362796			−0.181398	−	0.983410i	$-0.558062\pi$
$569$	−4924.15			−0.362796			−0.181398	+	0.983410i	$0.558062\pi$
$570$	−3946.83	−	1353.37i	−0.290025	−	0.0994496i
$571$	−5642.12			−0.413512			−0.206756	−	0.978393i	$-0.566291\pi$
$571$	−5642.12			−0.413512			−0.206756	+	0.978393i	$0.566291\pi$
$572$	−595.059	+	595.059i	−0.0434977	+	0.0434977i
$573$	10586.5	+	6788.02i	0.771829	+	0.494893i
$574$			4424.78i			0.321754i
$575$	−2735.14	+	8665.22i	−0.198371	+	0.628460i
$576$	−6340.50	+	2911.53i	−0.458659	+	0.210614i
$577$	8505.39	+	8505.39i	0.613663	+	0.613663i	0.943899	−	0.330235i	$-0.107128\pi$
$577$	8505.39	+	8505.39i	0.613663	+	0.613663i	−0.330235	+	0.943899i	$0.607128\pi$
$578$	−8893.50	−	8893.50i	−0.640002	−	0.640002i
$579$	3084.47	+	14108.6i	0.221392	+	1.01266i
$580$	1810.44	−	2982.46i	0.129611	−	0.213517i
$581$			4079.96i			0.291334i
$582$	6453.87	−	10065.4i	0.459659	−	0.716879i
$583$	−11762.7	+	11762.7i	−0.835612	+	0.835612i
$584$	−3375.51			−0.239177
$585$	748.165	+	943.767i	0.0528766	+	0.0667008i
$586$	13489.4			0.950927
$587$	−1464.72	+	1464.72i	−0.102990	+	0.102990i	−0.756724	−	0.653734i	$-0.773202\pi$
$587$	−1464.72	+	1464.72i	−0.102990	+	0.102990i	0.653734	+	0.756724i	$0.273202\pi$
$588$	2909.07	−	4536.95i	0.204027	−	0.318198i
$589$			1780.84i			0.124581i
$590$	−17222.0	+	4211.33i	−1.20173	+	0.293860i
$591$	−1306.75	−	5977.17i	−0.0909521	−	0.416020i
$592$	−12156.0	−	12156.0i	−0.843935	−	0.843935i
$593$	18086.4	+	18086.4i	1.25248	+	1.25248i	0.954606	+	0.297871i	$0.0962766\pi$
$593$	18086.4	+	18086.4i	1.25248	+	1.25248i	0.297871	+	0.954606i	$0.403723\pi$
$594$	−10852.4	−	14403.4i	−0.749631	−	0.994917i
$595$	11490.4	+	6975.01i	0.791697	+	0.480584i
$596$			22061.1i			1.51621i
$597$	6738.63	+	4320.78i	0.461966	+	0.296211i
$598$	772.204	−	772.204i	0.0528056	−	0.0528056i
$599$	−21899.3			−1.49379			−0.746897	−	0.664940i	$-0.768457\pi$
$599$	−21899.3			−1.49379			−0.746897	+	0.664940i	$0.768457\pi$
$600$	−2851.86	−	3421.19i	−0.194044	−	0.232783i
$601$	−12431.8			−0.843766			−0.421883	−	0.906650i	$-0.638631\pi$
$601$	−12431.8			−0.843766			−0.421883	+	0.906650i	$0.638631\pi$
$602$	8790.38	−	8790.38i	0.595132	−	0.595132i
$603$	5719.00	−	15431.0i	0.386229	−	1.04212i
$604$		−	16603.6i		−	1.11853i
$605$	−1583.00	−	960.930i	−0.106377	−	0.0645741i
$606$	31774.1	−	6946.59i	2.12993	−	0.465653i
$607$	8237.79	+	8237.79i	0.550843	+	0.550843i	0.926684	−	0.375841i	$-0.122646\pi$
$607$	8237.79	+	8237.79i	0.550843	+	0.550843i	−0.375841	+	0.926684i	$0.622646\pi$
$608$	−3081.82	−	3081.82i	−0.205566	−	0.205566i
$609$	3392.82	−	741.752i	0.225754	−	0.0493552i
$610$	−81.7891	+	20.0000i	−0.00542876	+	0.00132750i
$611$			216.007i			0.0143023i
$612$	5267.00	−	14211.4i	0.347885	−	0.938663i
$613$	−8913.02	+	8913.02i	−0.587265	+	0.587265i	−0.936890	−	0.349625i	$-0.886309\pi$
$613$	−8913.02	+	8913.02i	−0.587265	+	0.587265i	0.349625	+	0.936890i	$0.386309\pi$
$614$	16827.3			1.10602
$615$	2267.23	+	4633.48i	0.148656	+	0.303805i
$616$	3097.95			0.202630
$617$	1378.18	−	1378.18i	0.0899244	−	0.0899244i	−0.660714	−	0.750638i	$-0.729746\pi$
$617$	1378.18	−	1378.18i	0.0899244	−	0.0899244i	0.750638	+	0.660714i	$0.229746\pi$
$618$	−18040.7	−	11567.6i	−1.17428	−	0.752941i
$619$		−	18926.2i		−	1.22893i	−0.788945	−	0.614464i	$-0.789372\pi$
$619$		−	18926.2i		−	1.22893i	0.788945	−	0.614464i	$-0.210628\pi$
$620$	3346.97	−	5513.67i	0.216802	−	0.357152i
$621$	6137.16	+	8145.29i	0.396580	+	0.526344i
$622$	19187.2	+	19187.2i	1.23688	+	1.23688i
$623$	11903.2	+	11903.2i	0.765474	+	0.765474i
$624$	333.191	+	1524.04i	0.0213755	+	0.0977730i
$625$	−8970.20	+	12793.6i	−0.574093	+	0.818790i
$626$		−	10806.5i		−	0.689959i
$627$	1826.20	−	2848.12i	0.116318	−	0.181408i
$628$	−11186.8	+	11186.8i	−0.710831	+	0.710831i
$629$	20753.7			1.31559
$630$	−1727.58	+	14943.3i	−0.109251	+	0.945009i
$631$	−26118.8			−1.64782			−0.823909	−	0.566723i	$-0.808211\pi$
$631$	−26118.8			−1.64782			−0.823909	+	0.566723i	$0.808211\pi$
$632$	2851.21	−	2851.21i	0.179454	−	0.179454i
$633$	30.6780	−	47.8450i	0.00192629	−	0.00300421i
$634$			3670.26i			0.229912i
$635$	1650.97	+	6751.56i	0.103176	+	0.421933i
$636$	−3341.52	−	15284.3i	−0.208333	−	0.952929i
$637$	−473.556	−	473.556i	−0.0294552	−	0.0294552i
$638$	4590.56	+	4590.56i	0.284862	+	0.284862i
$639$	18006.7	−	8268.59i	1.11476	−	0.511894i
$640$	−2270.60	−	9285.53i	−0.140240	−	0.573504i
$641$		−	15846.5i		−	0.976442i	−0.872720	−	0.488221i	$-0.837646\pi$
$641$		−	15846.5i		−	0.976442i	0.872720	−	0.488221i	$-0.162354\pi$
$642$	−27259.4	−	17478.6i	−1.67577	−	1.07449i
$643$	89.9404	−	89.9404i	0.00551618	−	0.00551618i	−0.704343	−	0.709859i	$-0.748758\pi$
$643$	89.9404	−	89.9404i	0.00551618	−	0.00551618i	0.709859	+	0.704343i	$0.248758\pi$
$644$	5944.21			0.363719
$645$	4700.85	−	13709.1i	0.286970	−	0.836893i
$646$	6524.70			0.397385
$647$	−20057.0	+	20057.0i	−1.21874	+	1.21874i	−0.250665	+	0.968074i	$0.580649\pi$
$647$	−20057.0	+	20057.0i	−1.21874	+	1.21874i	−0.968074	+	0.250665i	$0.919351\pi$
$648$	−4984.71	+	377.323i	−0.302188	+	0.0228745i
$649$		−	14376.4i		−	0.869527i
$650$	1665.96	−	866.575i	0.100530	−	0.0522921i
$651$	6272.31	−	1371.28i	0.377621	−	0.0825570i
$652$	16553.7	+	16553.7i	0.994313	+	0.994313i
$653$	−20478.4	−	20478.4i	−1.22723	−	1.22723i	−0.965007	−	0.262225i	$-0.915544\pi$
$653$	−20478.4	−	20478.4i	−1.22723	−	1.22723i	−0.262225	−	0.965007i	$-0.584456\pi$
$654$	−24172.3	+	5284.64i	−1.44528	+	0.315972i
$655$	8117.99	−	13373.3i	0.484269	−	0.797767i
$656$			6681.92i			0.397691i
$657$	12462.4	+	4618.78i	0.740036	+	0.274271i
$658$	−1907.80	+	1907.80i	−0.113030	+	0.113030i
$659$	1169.87			0.0691529			0.0345765	−	0.999402i	$-0.488992\pi$
$659$	1169.87			0.0691529			0.0345765	+	0.999402i	$0.488992\pi$
$660$	−11007.0	+	5385.89i	−0.649162	+	0.317645i
$661$	19622.6			1.15466			0.577329	−	0.816511i	$-0.304095\pi$
$661$	19622.6			1.15466			0.577329	+	0.816511i	$0.304095\pi$
$662$	−21904.0	+	21904.0i	−1.28599	+	1.28599i
$663$	−1585.41	−	1016.55i	−0.0928688	−	0.0595471i
$664$			2114.07i			0.123557i
$665$	−2741.34	+	670.343i	−0.159856	+	0.0390899i
$666$	9692.20	+	21106.9i	0.563912	+	1.22804i
$667$	−2596.01	−	2596.01i	−0.150701	−	0.150701i
$668$	−862.224	−	862.224i	−0.0499408	−	0.0499408i
$669$	1305.04	+	5969.35i	0.0754199	+	0.344975i
$670$	−21934.9	−	13315.1i	−1.26480	−	0.767774i
$671$		−	68.2750i		−	0.00392806i
$672$	−8481.46	+	13227.6i	−0.486874	+	0.759323i
$673$	15256.3	−	15256.3i	0.873830	−	0.873830i	−0.119057	−	0.992887i	$-0.537987\pi$
$673$	15256.3	−	15256.3i	0.873830	−	0.873830i	0.992887	+	0.119057i	$0.0379872\pi$
$674$	9464.72			0.540901
$675$	5847.79	+	16533.3i	0.333454	+	0.942766i
$676$	13476.7			0.766768
$677$	−16.1429	+	16.1429i	−0.000916428	+	0.000916428i	−0.707565	−	0.706648i	$-0.750206\pi$
$677$	−16.1429	+	16.1429i	−0.000916428	+	0.000916428i	0.706648	+	0.707565i	$0.250206\pi$
$678$	−5693.08	+	8878.86i	−0.322480	+	0.502936i
$679$		−	8087.23i		−	0.457083i
$680$	5953.85	+	3614.17i	0.335764	+	0.203819i
$681$	5400.87	+	24703.9i	0.303909	+	1.39010i
$682$	8486.57	+	8486.57i	0.476492	+	0.476492i
$683$	−3894.05	−	3894.05i	−0.218157	−	0.218157i	0.589564	−	0.807722i	$-0.299300\pi$
$683$	−3894.05	−	3894.05i	−0.218157	−	0.218157i	−0.807722	+	0.589564i	$0.799300\pi$
$684$	1327.87	+	2891.73i	0.0742287	+	0.161649i
$685$	−16776.2	+	4102.32i	−0.935747	+	0.228820i
$686$		−	25457.5i		−	1.41687i
$687$	−7350.31	−	4712.99i	−0.408198	−	0.261735i
$688$	13274.5	−	13274.5i	0.735587	−	0.735587i
$689$	−1944.12			−0.107497
$690$	14283.7	−	6989.22i	0.788074	−	0.385616i
$691$	−1041.11			−0.0573163			−0.0286581	−	0.999589i	$-0.509123\pi$
$691$	−1041.11			−0.0573163			−0.0286581	+	0.999589i	$0.509123\pi$
$692$	−5447.40	+	5447.40i	−0.299247	+	0.299247i
$693$	−11437.6	−	4238.99i	−0.626955	−	0.232361i
$694$			9133.91i			0.499594i
$695$	−14494.8	+	23878.3i	−0.791108	+	1.30324i
$696$	1758.02	−	384.346i	0.0957438	−	0.0209319i
$697$	−5703.96	−	5703.96i	−0.309975	−	0.309975i
$698$	22908.9	+	22908.9i	1.24229	+	1.24229i
$699$	−15124.1	+	3306.49i	−0.818378	+	0.178917i
$700$	9747.37	+	3076.71i	0.526309	+	0.166127i
$701$		−	29885.3i		−	1.61020i	−0.593138	−	0.805101i	$-0.702111\pi$
$701$		−	29885.3i		−	1.61020i	0.593138	−	0.805101i	$-0.297889\pi$
$702$	293.452	−	2087.12i	0.0157773	−	0.112213i
$703$	−3081.06	+	3081.06i	−0.165298	+	0.165298i
$704$	−8821.42			−0.472258
$705$	−1020.24	+	2975.32i	−0.0545026	+	0.158946i
$706$	−28889.9			−1.54007
$707$	15555.5	−	15555.5i	0.827473	−	0.827473i
$708$	11382.3	+	7298.26i	0.604198	+	0.387409i
$709$		−	12115.0i		−	0.641734i	−0.947124	−	0.320867i	$-0.896026\pi$
$709$		−	12115.0i		−	0.641734i	0.947124	−	0.320867i	$-0.103974\pi$
$710$	−7338.66	−	30011.1i	−0.387908	−	1.58633i
$711$	−14428.1	+	6625.31i	−0.761033	+	0.349463i
$712$	6167.74	+	6167.74i	0.324643	+	0.324643i
$713$	−4799.24	−	4799.24i	−0.252080	−	0.252080i
$714$	−5024.15	−	22980.8i	−0.263339	−	1.20453i
$715$	361.695	+	1479.13i	0.0189183	+	0.0773657i
$716$		−	15526.8i		−	0.810422i
$717$	732.381	−	1142.21i	0.0381468	−	0.0594933i
$718$	−30404.1	+	30404.1i	−1.58032	+	1.58032i
$719$	−6371.24			−0.330469			−0.165234	−	0.986254i	$-0.552838\pi$
$719$	−6371.24			−0.330469			−0.165234	+	0.986254i	$0.552838\pi$
$720$	−2608.84	+	22566.1i	−0.135036	+	1.16804i
$721$	−14495.2			−0.748722
$722$	17294.1	−	17294.1i	0.891443	−	0.891443i
$723$	16832.3	−	26251.5i	0.865839	−	1.35035i
$724$		−	1667.05i		−	0.0855737i
$725$	−2913.27	−	5600.64i	−0.149236	−	0.286900i
$726$	692.164	+	3166.00i	0.0353838	+	0.161848i
$727$	15771.9	+	15771.9i	0.804604	+	0.804604i	0.983811	−	0.179207i	$-0.0573532\pi$
$727$	15771.9	+	15771.9i	0.804604	+	0.804604i	−0.179207	+	0.983811i	$0.557353\pi$
$728$	256.012	+	256.012i	0.0130336	+	0.0130336i
$729$	18919.9	+	5427.61i	0.961229	+	0.275751i
$730$	10753.6	−	17715.0i	0.545216	−	0.898168i
$731$			22663.2i			1.14669i
$732$	54.0555	+	34.6601i	0.00272944	+	0.00175010i
$733$	−5626.05	+	5626.05i	−0.283496	+	0.283496i	−0.834502	−	0.551005i	$-0.814244\pi$
$733$	−5626.05	+	5626.05i	−0.283496	+	0.283496i	0.551005	+	0.834502i	$0.314244\pi$
$734$	34905.3			1.75528
$735$	−4286.16	−	8759.51i	−0.215098	−	0.439591i
$736$	16610.6			0.831897
$737$	14712.8	−	14712.8i	0.735350	−	0.735350i
$738$	3137.21	−	8464.82i	0.156480	−	0.422215i
$739$			30340.1i			1.51026i	0.655577	+	0.755129i	$0.272426\pi$
$739$			30340.1i			1.51026i	−0.655577	+	0.755129i	$0.727574\pi$
$740$	15330.0	−	3748.66i	0.761543	−	0.186221i
$741$	386.282	−	84.4506i	0.0191504	−	0.00418674i
$742$	−17170.7	−	17170.7i	−0.849535	−	0.849535i
$743$	−2368.77	−	2368.77i	−0.116961	−	0.116961i	0.646204	−	0.763165i	$-0.276355\pi$
$743$	−2368.77	−	2368.77i	−0.116961	−	0.116961i	−0.763165	+	0.646204i	$0.776355\pi$
$744$	3250.06	−	710.541i	0.160152	−	0.0350130i
$745$	34123.3	+	20713.9i	1.67810	+	1.01866i
$746$			31778.0i			1.55962i
$747$	2892.73	−	7805.16i	0.141686	−	0.382297i
$748$	13550.0	−	13550.0i	0.662347	−	0.662347i
$749$	−21902.1			−1.06847
$750$	27040.1	−	4067.77i	1.31649	−	0.198045i
$751$	10606.2			0.515346			0.257673	−	0.966232i	$-0.417044\pi$
$751$	10606.2			0.515346			0.257673	+	0.966232i	$0.417044\pi$
$752$	−2880.99	+	2880.99i	−0.139706	+	0.139706i
$753$	13317.6	+	8539.21i	0.644518	+	0.413262i
$754$			758.720i			0.0366458i
$755$	−25681.8	−	15589.6i	−1.23796	−	0.751477i
$756$	9162.52	−	6903.60i	0.440790	−	0.332119i
$757$	−18470.4	−	18470.4i	−0.886812	−	0.886812i	0.107404	−	0.994215i	$-0.465746\pi$
$757$	−18470.4	−	18470.4i	−0.886812	−	0.886812i	−0.994215	+	0.107404i	$0.965746\pi$
$758$	4474.44	+	4474.44i	0.214405	+	0.214405i
$759$	2754.01	+	12597.0i	0.131705	+	0.602428i
$760$	−1420.45	+	347.345i	−0.0677963	+	0.0165783i
$761$			13568.0i			0.646307i	0.946347	+	0.323153i	$0.104743\pi$
$761$			13568.0i			0.646307i	−0.946347	+	0.323153i	$0.895257\pi$
$762$	6565.54	−	10239.5i	0.312132	−	0.486797i
$763$	−11833.9	+	11833.9i	−0.561488	+	0.561488i
$764$	−14954.3			−0.708152
$765$	−17036.3	−	21490.3i	−0.805161	−	1.01566i
$766$	−39904.0			−1.88223
$767$	1188.05	−	1188.05i	0.0559298	−	0.0559298i
$768$	−14827.8	+	23125.2i	−0.696682	+	1.08654i
$769$			11029.1i			0.517190i	0.965986	+	0.258595i	$0.0832594\pi$
$769$			11029.1i			0.517190i	−0.965986	+	0.258595i	$0.916741\pi$
$770$	−9869.33	+	16258.4i	−0.461904	+	0.760924i
$771$	−1485.23	−	6793.52i	−0.0693764	−	0.317332i
$772$	−12143.3	−	12143.3i	−0.566122	−	0.566122i
$773$	−7090.94	−	7090.94i	−0.329940	−	0.329940i	0.522624	−	0.852563i	$-0.324953\pi$
$773$	−7090.94	−	7090.94i	−0.329940	−	0.329940i	−0.852563	+	0.522624i	$0.824953\pi$
$774$	−23048.9	+	10584.0i	−1.07038	+	0.491515i
$775$	−5385.76	−	10353.9i	−0.249629	−	0.479902i
$776$		−	4190.48i		−	0.193852i
$777$	13224.3	+	8479.38i	0.610580	+	0.391501i
$778$	21212.9	−	21212.9i	0.977530	−	0.977530i
$779$	1693.60			0.0778940
$780$	−1354.69	−	464.524i	−0.0621870	−	0.0213239i
$781$	25052.3			1.14781
$782$	−17583.7	+	17583.7i	−0.804080	+	0.804080i
$783$	−7016.53	−	986.533i	−0.320243	−	0.0450266i
$784$		−	12632.1i		−	0.575440i
$785$	6799.67	+	27806.9i	0.309160	+	1.26430i
$786$	−26746.6	+	5847.45i	−1.21376	+	0.265358i
$787$	−17915.0	−	17915.0i	−0.811437	−	0.811437i	0.173412	−	0.984849i	$-0.444521\pi$
$787$	−17915.0	−	17915.0i	−0.811437	−	0.811437i	−0.984849	+	0.173412i	$0.944521\pi$
$788$	5144.57	+	5144.57i	0.232573	+	0.232573i
$789$	−481.172	+	105.196i	−0.0217112	+	0.00474660i
$790$	5880.19	+	24046.8i	0.264820	+	1.08297i
$791$			7133.90i			0.320673i
$792$	−5926.52	−	2196.47i	−0.265896	−	0.0985458i
$793$	5.64218	−	5.64218i	0.000252661	−	0.000252661i
$794$	−43607.5			−1.94908
$795$	−26778.6	−	9182.39i	−1.19464	−	0.409643i
$796$	−9518.87			−0.423854
$797$	6043.79	−	6043.79i	0.268610	−	0.268610i	−0.559930	−	0.828540i	$-0.689172\pi$
$797$	6043.79	−	6043.79i	0.268610	−	0.268610i	0.828540	+	0.559930i	$0.189172\pi$
$798$	4157.56	+	2665.81i	0.184431	+	0.118256i
$799$		−	4918.65i		−	0.217784i
$800$	27238.3	+	8597.63i	1.20377	+	0.379965i
$801$	−14331.9	−	31210.8i	−0.632199	−	1.37675i
$802$	13759.4	+	13759.4i	0.605813	+	0.605813i
$803$	11882.3	+	11882.3i	0.522191	+	0.522191i
$804$	4179.58	+	19117.6i	0.183336	+	0.838591i
$805$	5581.21	−	9194.28i	0.244362	−	0.402554i
$806$			1402.65i			0.0612979i
$807$	−7455.35	+	11627.3i	−0.325205	+	0.507186i
$808$	8060.22	−	8060.22i	0.350937	−	0.350937i
$809$	35063.4			1.52381			0.761905	−	0.647689i	$-0.224264\pi$
$809$	35063.4			1.52381			0.761905	+	0.647689i	$0.224264\pi$
$810$	13899.9	−	27362.4i	0.602953	−	1.18693i
$811$	24621.3			1.06605			0.533027	−	0.846098i	$-0.321054\pi$
$811$	24621.3			1.06605			0.533027	+	0.846098i	$0.321054\pi$
$812$	−2920.21	+	2920.21i	−0.126206	+	0.126206i
$813$	−408.570	+	637.200i	−0.0176250	+	0.0274878i
$814$			29365.6i			1.26445i
$815$	41147.3	−	10061.8i	1.76850	−	0.432454i
$816$	−7587.02	−	34703.5i	−0.325489	−	1.48881i
$817$	−3364.54	−	3364.54i	−0.144076	−	0.144076i
$818$	−22671.6	−	22671.6i	−0.969063	−	0.969063i
$819$	−594.890	−	1295.50i	−0.0253811	−	0.0552729i
$820$	−5243.58	−	3183.01i	−0.223309	−	0.135556i
$821$			14268.3i			0.606538i	0.952905	+	0.303269i	$0.0980781\pi$
$821$			14268.3i			0.606538i	−0.952905	+	0.303269i	$0.901922\pi$
$822$	25443.1	+	16314.0i	1.07960	+	0.692234i
$823$	13764.1	−	13764.1i	0.582972	−	0.582972i	−0.352747	−	0.935719i	$-0.614752\pi$
$823$	13764.1	−	13764.1i	0.582972	−	0.582972i	0.935719	+	0.352747i	$0.114752\pi$
$824$	−7510.81			−0.317538
$825$	−2004.14	+	22082.2i	−0.0845760	+	0.931882i
$826$	20986.0			0.884015
$827$	−27442.5	+	27442.5i	−1.15389	+	1.15389i	−0.168128	+	0.985765i	$0.553772\pi$
$827$	−27442.5	+	27442.5i	−1.15389	+	1.15389i	−0.985765	+	0.168128i	$0.946228\pi$
$828$	−11371.6	−	4214.50i	−0.477282	−	0.176889i
$829$			12176.9i			0.510159i	0.966920	+	0.255080i	$0.0821016\pi$
$829$			12176.9i			0.510159i	−0.966920	+	0.255080i	$0.917898\pi$
$830$	−11094.9	−	6734.93i	−0.463987	−	0.281654i
$831$	7714.23	−	1686.52i	0.322026	−	0.0704027i
$832$	−728.995	−	728.995i	−0.0303766	−	0.0303766i
$833$	10783.2	+	10783.2i	0.448519	+	0.448519i
$834$	47756.5	−	10440.7i	1.98282	−	0.433492i
$835$	−2143.22	+	524.085i	−0.0888255	+	0.0217206i
$836$			4023.21i			0.166442i
$837$	−12971.5	−	1823.80i	−0.535675	−	0.0753165i
$838$	31790.7	−	31790.7i	1.31049	−	1.31049i
$839$	13942.3			0.573710			0.286855	−	0.957974i	$-0.407390\pi$
$839$	13942.3			0.573710			0.286855	+	0.957974i	$0.407390\pi$
$840$	2317.16	+	4735.53i	0.0951783	+	0.194514i
$841$	−21838.3			−0.895417
$842$	28951.3	−	28951.3i	1.18495	−	1.18495i
$843$	8837.14	+	5666.33i	0.361053	+	0.231505i
$844$			67.5849i			0.00275636i
$845$	12653.7	−	20845.2i	0.515149	−	0.848637i
$846$	5002.35	−	2297.06i	0.203291	−	0.0933505i
$847$	1549.96	+	1549.96i	0.0628776	+	0.0628776i
$848$	−25929.6	−	25929.6i	−1.05003	−	1.05003i
$849$	−3767.30	−	17231.8i	−0.152289	−	0.696579i
$850$	−37935.1	+	19732.6i	−1.53078	+	0.796261i
$851$		−	16606.6i		−	0.668937i
$852$	−12717.9	+	19834.7i	−0.511396	+	0.797567i
$853$	−32654.2	+	32654.2i	−1.31074	+	1.31074i	−0.389866	+	0.920871i	$0.627479\pi$
$853$	−32654.2	+	32654.2i	−1.31074	+	1.31074i	−0.920871	+	0.389866i	$0.872521\pi$
$854$	99.6646			0.00399350
$855$	5719.59	+	661.235i	0.228779	+	0.0264489i
$856$	−11348.8			−0.453147
$857$	−10358.9	+	10358.9i	−0.412898	+	0.412898i	−0.882747	−	0.469849i	$-0.844308\pi$
$857$	−10358.9	+	10358.9i	−0.412898	+	0.412898i	0.469849	+	0.882747i	$0.344308\pi$
$858$	1438.38	−	2243.28i	0.0572325	−	0.0892590i
$859$		−	14100.5i		−	0.560072i	−0.959990	−	0.280036i	$-0.909654\pi$
$859$		−	14100.5i		−	0.560072i	0.959990	−	0.280036i	$-0.0903464\pi$
$860$	4093.57	+	16740.5i	0.162313	+	0.663773i
$861$	−1304.10	−	5965.05i	−0.0516187	−	0.236107i
$862$	−20245.0	−	20245.0i	−0.799941	−	0.799941i
$863$	−16830.6	−	16830.6i	−0.663872	−	0.663872i	0.292419	−	0.956290i	$-0.405540\pi$
$863$	−16830.6	−	16830.6i	−0.663872	−	0.663872i	−0.956290	+	0.292419i	$0.905540\pi$
$864$	25603.9	−	19291.6i	1.00818	−	0.759621i
$865$	3311.09	+	13540.6i	0.130151	+	0.532246i
$866$		−	24928.3i		−	0.978174i
$867$	14610.5	+	9368.17i	0.572316	+	0.366966i
$868$	−5398.60	+	5398.60i	−0.211106	+	0.211106i
$869$	−20073.5			−0.783597
$870$	−3583.55	+	10450.7i	−0.139648	+	0.407256i
$871$	2431.71			0.0945984
$872$	−6131.84	+	6131.84i	−0.238131	+	0.238131i
$873$	−5733.92	+	15471.3i	−0.222295	+	0.599797i
$874$		−	5220.88i		−	0.202058i
$875$	13911.0	−	12188.0i	0.537462	−	0.470892i
$876$	−15439.8	+	3375.51i	−0.595504	+	0.130192i
$877$	9832.57	+	9832.57i	0.378589	+	0.378589i	0.870593	−	0.492004i	$-0.163736\pi$
$877$	9832.57	+	9832.57i	0.378589	+	0.378589i	−0.492004	+	0.870593i	$0.663736\pi$
$878$	22919.9	+	22919.9i	0.880990	+	0.880990i
$879$	−18185.1	+	3975.70i	−0.697802	+	0.152556i
$880$	−14903.8	+	24552.0i	−0.570917	+	0.940508i
$881$			41729.4i			1.59580i	0.602789	+	0.797900i	$0.294056\pi$
$881$			41729.4i			1.59580i	−0.602789	+	0.797900i	$0.705944\pi$
$882$	−5930.84	+	16002.6i	−0.226419	+	0.610925i
$883$	−11757.3	+	11757.3i	−0.448090	+	0.448090i	−0.894719	−	0.446629i	$-0.852624\pi$
$883$	−11757.3	+	11757.3i	−0.448090	+	0.448090i	0.446629	+	0.894719i	$0.352624\pi$
$884$	2239.51			0.0852070
$885$	21975.8	−	10753.1i	0.834699	−	0.408431i
$886$	34437.1			1.30580
$887$	24303.5	−	24303.5i	0.919989	−	0.919989i	−0.0770388	−	0.997028i	$-0.524547\pi$
$887$	24303.5	−	24303.5i	0.919989	−	0.919989i	0.997028	+	0.0770388i	$0.0245465\pi$
$888$	6852.32	+	4393.67i	0.258951	+	0.166038i
$889$		−	8227.16i		−	0.310383i
$890$	−52017.9	+	12720.0i	−1.95915	+	0.479074i
$891$	18875.3	+	16218.8i	0.709702	+	0.609820i
$892$	−5137.84	−	5137.84i	−0.192856	−	0.192856i
$893$	730.214	+	730.214i	0.0273636	+	0.0273636i
$894$	−14920.4	−	68246.6i	−0.558178	−	2.55314i
$895$	−24016.2	−	14578.6i	−0.896953	−	0.544478i
$896$			11314.9i			0.421881i
$897$	−813.418	+	1268.60i	−0.0302779	+	0.0472210i
$898$	948.871	−	948.871i	0.0352609	−	0.0352609i
$899$	4715.44			0.174937
$900$	−16465.8	−	12796.9i	−0.609843	−	0.473958i
$901$	44269.1			1.63687
$902$	8070.84	−	8070.84i	0.297927	−	0.297927i
$903$	−9259.55	+	14441.1i	−0.341239	+	0.532191i
$904$			3696.50i			0.136000i
$905$	−2578.52	−	1565.24i	−0.0947105	−	0.0574922i
$906$	11229.3	+	51363.6i	0.411776	+	1.88349i
$907$	1017.75	+	1017.75i	0.0372589	+	0.0372589i	0.725491	−	0.688232i	$-0.241613\pi$
$907$	1017.75	+	1017.75i	0.0372589	+	0.0372589i	−0.688232	+	0.725491i	$0.741613\pi$
$908$	−21262.7	−	21262.7i	−0.777124	−	0.777124i
$909$	−40787.3	+	18729.4i	−1.48826	+	0.683404i
$910$	−2159.17	+	527.985i	−0.0786548	+	0.0192336i
$911$		−	33165.2i		−	1.20616i	−0.797681	−	0.603080i	$-0.793940\pi$
$911$		−	33165.2i		−	1.20616i	0.797681	−	0.603080i	$-0.206060\pi$
$912$	6278.38	+	4025.67i	0.227958	+	0.146166i
$913$	7441.88	−	7441.88i	0.269759	−	0.269759i
$914$	8056.00			0.291541
$915$	104.365	−	51.0675i	0.00377072	−	0.00184507i
$916$	10382.9			0.374521
$917$	−13094.2	+	13094.2i	−0.471546	+	0.471546i
$918$	−6682.13	+	47525.4i	−0.240243	+	1.70869i
$919$		−	2162.18i		−	0.0776103i	−0.999247	−	0.0388051i	$-0.987645\pi$
$919$		−	2162.18i		−	0.0776103i	0.999247	−	0.0388051i	$-0.0123552\pi$
$920$	2891.96	−	4764.10i	0.103636	−	0.170726i
$921$	−22684.9	+	4959.46i	−0.811609	+	0.177437i
$922$	35433.7	+	35433.7i	1.26567	+	1.26567i
$923$	2070.30	+	2070.30i	0.0738297	+	0.0738297i
$924$	14170.2	−	3097.95i	0.504508	−	0.110298i
$925$	8595.52	−	27231.6i	0.305534	−	0.967966i
$926$			6589.59i			0.233852i
$927$	27729.9	+	10277.2i	0.982493	+	0.364129i
$928$	−8160.29	+	8160.29i	−0.288658	+	0.288658i
$929$	−17695.1			−0.624929			−0.312464	−	0.949930i	$-0.601154\pi$
$929$	−17695.1			−0.624929			−0.312464	+	0.949930i	$0.601154\pi$
$930$	−6624.92	+	19320.3i	−0.233591	+	0.681223i
$931$	−3201.72			−0.112709
$932$	13017.4	−	13017.4i	0.457508	−	0.457508i
$933$	−31521.3	−	20211.3i	−1.10607	−	0.709204i
$934$		−	43676.6i		−	1.53013i
$935$	−8236.07	−	33681.0i	−0.288073	−	1.17806i
$936$	−308.248	−	671.277i	−0.0107643	−	0.0234417i
$937$	−30208.0	−	30208.0i	−1.05320	−	1.05320i	−0.998503	−	0.0547017i	$-0.982579\pi$
$937$	−30208.0	−	30208.0i	−1.05320	−	1.05320i	−0.0547017	−	0.998503i	$-0.517421\pi$
$938$	21477.1	+	21477.1i	0.747602	+	0.747602i
$939$	3184.96	+	14568.2i	0.110689	+	0.506300i
$940$	−888.437	−	3633.22i	−0.0308272	−	0.126067i
$941$		−	1499.59i		−	0.0519503i	−0.999663	−	0.0259752i	$-0.991731\pi$
$941$		−	1499.59i		−	0.0519503i	0.999663	−	0.0259752i	$-0.00826908\pi$
$942$	27040.8	−	42172.4i	0.935282	−	1.45865i
$943$	−4564.14	+	4564.14i	−0.157613	+	0.157613i
$944$	31691.2			1.09265
$945$	−2075.25	−	20654.2i	−0.0714369	−	0.710986i
$946$	−32067.5			−1.10212
$947$	13763.8	−	13763.8i	0.472294	−	0.472294i	−0.430362	−	0.902656i	$-0.641614\pi$
$947$	13763.8	−	13763.8i	0.472294	−	0.472294i	0.902656	+	0.430362i	$0.141614\pi$
$948$	10190.4	−	15892.8i	0.349123	−	0.544488i
$949$			1963.89i			0.0671767i
$950$	2702.32	−	8561.25i	0.0922892	−	0.292383i
$951$	−1081.72	−	4947.87i	−0.0368847	−	0.168713i
$952$	−5829.59	−	5829.59i	−0.198464	−	0.198464i
$953$	14570.7	+	14570.7i	0.495268	+	0.495268i	0.909961	−	0.414693i	$-0.136111\pi$
$953$	14570.7	+	14570.7i	0.495268	+	0.495268i	−0.414693	+	0.909961i	$0.636111\pi$
$954$	20674.1	+	45022.4i	0.701625	+	1.52794i
$955$	−14041.1	+	23130.8i	−0.475768	+	0.783763i
$956$			1613.47i			0.0545851i
$957$	−7541.49	−	4835.57i	−0.254735	−	0.163335i
$958$	30404.7	−	30404.7i	1.02540	−	1.02540i
$959$	20442.8			0.688355
$960$	−6598.14	−	13484.5i	−0.221827	−	0.453342i
$961$	−21073.6			−0.707380
$962$	−2426.75	+	2426.75i	−0.0813322	+	0.0813322i
$963$	41899.7	+	15528.8i	1.40208	+	0.519635i
$964$			37082.4i			1.23895i
$965$	−30184.4	+	7381.04i	−1.00691	+	0.246222i
$966$	−18388.6	+	4020.18i	−0.612466	+	0.133900i
$967$	28409.1	+	28409.1i	0.944752	+	0.944752i	0.998552	−	0.0538000i	$-0.0171333\pi$
$967$	28409.1	+	28409.1i	0.944752	+	0.944752i	−0.0538000	+	0.998552i	$0.517133\pi$
$968$	803.127	+	803.127i	0.0266668	+	0.0266668i
$969$	−8795.95	+	1923.01i	−0.291606	+	0.0637522i
$970$	21992.1	+	13349.9i	0.727963	+	0.441896i
$971$		−	18059.4i		−	0.596864i	−0.954431	−	0.298432i	$-0.903536\pi$
$971$		−	18059.4i		−	0.596864i	0.954431	−	0.298432i	$-0.0964637\pi$
$972$	−22423.1	+	6710.61i	−0.739938	+	0.221443i
$973$	23379.9	−	23379.9i	0.770323	−	0.770323i
$974$	−32307.7			−1.06284
$975$	−1990.47	+	1659.23i	−0.0653807	+	0.0545005i
$976$	150.505			0.00493600
$977$	−31166.3	+	31166.3i	−1.02057	+	1.02057i	−0.0207872	+	0.999784i	$0.506617\pi$
$977$	−31166.3	+	31166.3i	−1.02057	+	1.02057i	−0.999784	+	0.0207872i	$0.993383\pi$
$978$	−62404.7	−	40013.6i	−2.04037	−	1.30828i
$979$		−	43422.9i		−	1.41757i
$980$	9912.89	+	6017.43i	0.323118	+	0.196143i
$981$	31029.1	−	14248.5i	1.00987	−	0.463729i
$982$	23907.2	+	23907.2i	0.776893	+	0.776893i
$983$	13839.4	+	13839.4i	0.449042	+	0.449042i	0.895036	−	0.445994i	$-0.147150\pi$
$983$	13839.4	+	13839.4i	0.449042	+	0.449042i	−0.445994	+	0.895036i	$0.647150\pi$
$984$	−675.734	−	3090.85i	−0.0218919	−	0.100135i
$985$	12787.8	−	3127.02i	0.413659	−	0.101153i
$986$		−	17276.6i		−	0.558012i
$987$	2009.62	−	3134.18i	0.0648095	−	0.101076i
$988$	−332.474	+	332.474i	−0.0107059	+	0.0107059i
$989$	18134.5			0.583056
$990$	30407.8	−	24105.6i	0.976186	−	0.773865i
$991$	17820.9			0.571242			0.285621	−	0.958343i	$-0.407800\pi$
$991$	17820.9			0.571242			0.285621	+	0.958343i	$0.407800\pi$
$992$	−15085.9	+	15085.9i	−0.482842	+	0.482842i
$993$	23073.1	−	35984.5i	0.737363	−	1.14998i
$994$			36570.2i			1.16694i
$995$	−8937.56	+	14723.4i	−0.284764	+	0.469109i
$996$	2114.07	+	9669.89i	0.0672559	+	0.307633i
$997$	−36985.0	−	36985.0i	−1.17485	−	1.17485i	−0.981038	−	0.193814i	$-0.937914\pi$
$997$	−36985.0	−	36985.0i	−1.17485	−	1.17485i	−0.193814	−	0.981038i	$-0.562086\pi$
$998$	20433.7	+	20433.7i	0.648114	+	0.648114i
$999$	−19286.8	−	25597.6i	−0.610819	−	0.810684i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	15.4.e.a.2.4	yes	8
3.2	odd	2	inner	15.4.e.a.2.1	✓	8
4.3	odd	2		240.4.v.c.17.3		8
5.2	odd	4		75.4.e.c.68.4		8
5.3	odd	4	inner	15.4.e.a.8.1	yes	8
5.4	even	2		75.4.e.c.32.1		8
12.11	even	2		240.4.v.c.17.4		8
15.2	even	4		75.4.e.c.68.1		8
15.8	even	4	inner	15.4.e.a.8.4	yes	8
15.14	odd	2		75.4.e.c.32.4		8
20.3	even	4		240.4.v.c.113.4		8
60.23	odd	4		240.4.v.c.113.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
15.4.e.a.2.1	✓	8	3.2	odd	2	inner
15.4.e.a.2.4	yes	8	1.1	even	1	trivial
15.4.e.a.8.1	yes	8	5.3	odd	4	inner
15.4.e.a.8.4	yes	8	15.8	even	4	inner
75.4.e.c.32.1		8	5.4	even	2
75.4.e.c.32.4		8	15.14	odd	2
75.4.e.c.68.1		8	15.2	even	4
75.4.e.c.68.4		8	5.2	odd	4
240.4.v.c.17.3		8	4.3	odd	2
240.4.v.c.17.4		8	12.11	even	2
240.4.v.c.113.3		8	60.23	odd	4
240.4.v.c.113.4		8	20.3	even	4

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:	\( N \)	\(=\)	\( 15 = 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	15.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.66260 - 2.66260i) q^{2} +(-2.80471 + 4.37420i) q^{3} -6.17891i q^{4} +(-9.55729 - 5.80157i) q^{5} +(4.17891 + 19.1146i) q^{6} +(9.35782 + 9.35782i) q^{7} +(4.84884 + 4.84884i) q^{8} +(-11.2672 - 24.5367i) q^{9} +O(q^{10})\)	\(q+(2.66260 - 2.66260i) q^{2} +(-2.80471 + 4.37420i) q^{3} -6.17891i q^{4} +(-9.55729 - 5.80157i) q^{5} +(4.17891 + 19.1146i) q^{6} +(9.35782 + 9.35782i) q^{7} +(4.84884 + 4.84884i) q^{8} +(-11.2672 - 24.5367i) q^{9} +(-40.8945 + 10.0000i) q^{10} -34.1375i q^{11} +(27.0278 + 17.3301i) q^{12} +(2.82109 - 2.82109i) q^{13} +49.8323 q^{14} +(52.1826 - 25.5337i) q^{15} +75.2524 q^{16} +(-64.2384 + 64.2384i) q^{17} +(-95.3316 - 35.3316i) q^{18} -19.0735i q^{19} +(-35.8474 + 59.0536i) q^{20} +(-67.1789 + 14.6869i) q^{21} +(-90.8945 - 90.8945i) q^{22} +(51.4018 + 51.4018i) q^{23} +(-34.8094 + 7.61018i) q^{24} +(57.6836 + 110.895i) q^{25} -15.0229i q^{26} +(138.930 + 19.5337i) q^{27} +(57.8211 - 57.8211i) q^{28} -50.5042 q^{29} +(70.9555 - 206.928i) q^{30} -93.3673 q^{31} +(161.576 - 161.576i) q^{32} +(149.324 + 95.7458i) q^{33} +342.083i q^{34} +(-35.1454 - 143.725i) q^{35} +(-151.610 + 69.6188i) q^{36} +(-161.537 - 161.537i) q^{37} +(-50.7850 - 50.7850i) q^{38} +(4.42765 + 20.2524i) q^{39} +(-18.2109 - 74.4727i) q^{40} +88.7935i q^{41} +(-139.765 + 217.976i) q^{42} +(176.399 - 176.399i) q^{43} -210.932 q^{44} +(-34.6678 + 299.872i) q^{45} +273.725 q^{46} +(-38.2843 + 38.2843i) q^{47} +(-211.061 + 329.169i) q^{48} -167.863i q^{49} +(448.857 + 141.680i) q^{50} +(-100.821 - 461.162i) q^{51} +(-17.4313 - 17.4313i) q^{52} +(-344.569 - 344.569i) q^{53} +(421.925 - 317.904i) q^{54} +(-198.051 + 326.262i) q^{55} +90.7492i q^{56} +(83.4310 + 53.4956i) q^{57} +(-134.473 + 134.473i) q^{58} +421.133 q^{59} +(-157.771 - 322.432i) q^{60} +2.00000 q^{61} +(-248.600 + 248.600i) q^{62} +(124.174 - 335.046i) q^{63} -258.409i q^{64} +(-43.3287 + 10.5952i) q^{65} +(652.524 - 142.657i) q^{66} +(430.987 + 430.987i) q^{67} +(396.923 + 396.923i) q^{68} +(-369.009 + 80.6742i) q^{69} +(-476.262 - 289.105i) q^{70} +733.866i q^{71} +(64.3420 - 173.607i) q^{72} +(-348.073 + 348.073i) q^{73} -860.216 q^{74} +(-646.860 - 58.7079i) q^{75} -117.853 q^{76} +(319.452 - 319.452i) q^{77} +(65.7131 + 42.1349i) q^{78} -588.019i q^{79} +(-719.209 - 436.582i) q^{80} +(-475.102 + 552.919i) q^{81} +(236.422 + 236.422i) q^{82} +(217.997 + 217.997i) q^{83} +(90.7492 + 415.092i) q^{84} +(986.629 - 241.262i) q^{85} -939.362i q^{86} +(141.650 - 220.915i) q^{87} +(165.527 - 165.527i) q^{88} +1272.00 q^{89} +(706.133 + 890.746i) q^{90} +52.7985 q^{91} +(317.607 - 317.607i) q^{92} +(261.868 - 408.407i) q^{93} +203.872i q^{94} +(-110.656 + 182.291i) q^{95} +(253.591 + 1159.94i) q^{96} +(-432.111 - 432.111i) q^{97} +(-446.951 - 446.951i) q^{98} +(-837.622 + 384.633i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 6 q^{3} - 12 q^{6} - 16 q^{7}+O(q^{10}) \) 8 * q - 6 * q^3 - 12 * q^6 - 16 * q^7	\( 8 q - 6 q^{3} - 12 q^{6} - 16 q^{7} - 100 q^{10} + 132 q^{12} + 68 q^{13} + 90 q^{15} + 284 q^{16} - 240 q^{18} - 492 q^{21} - 500 q^{22} - 220 q^{25} + 702 q^{27} + 508 q^{28} + 660 q^{30} + 616 q^{31} - 240 q^{33} - 804 q^{36} - 1156 q^{37} - 600 q^{40} + 540 q^{42} + 548 q^{43} + 180 q^{45} + 736 q^{46} - 1116 q^{48} - 852 q^{51} + 224 q^{52} + 460 q^{55} + 684 q^{57} + 60 q^{58} + 540 q^{60} + 16 q^{61} + 1428 q^{63} + 2040 q^{66} + 404 q^{67} - 2220 q^{70} - 1800 q^{72} - 2512 q^{73} - 2910 q^{75} - 1488 q^{76} - 360 q^{78} + 288 q^{81} + 2800 q^{82} + 4940 q^{85} - 1680 q^{87} + 2460 q^{88} + 600 q^{90} - 1304 q^{91} + 3408 q^{93} + 4164 q^{96} + 1904 q^{97}+O(q^{100}) \) 8 * q - 6 * q^3 - 12 * q^6 - 16 * q^7 - 100 * q^10 + 132 * q^12 + 68 * q^13 + 90 * q^15 + 284 * q^16 - 240 * q^18 - 492 * q^21 - 500 * q^22 - 220 * q^25 + 702 * q^27 + 508 * q^28 + 660 * q^30 + 616 * q^31 - 240 * q^33 - 804 * q^36 - 1156 * q^37 - 600 * q^40 + 540 * q^42 + 548 * q^43 + 180 * q^45 + 736 * q^46 - 1116 * q^48 - 852 * q^51 + 224 * q^52 + 460 * q^55 + 684 * q^57 + 60 * q^58 + 540 * q^60 + 16 * q^61 + 1428 * q^63 + 2040 * q^66 + 404 * q^67 - 2220 * q^70 - 1800 * q^72 - 2512 * q^73 - 2910 * q^75 - 1488 * q^76 - 360 * q^78 + 288 * q^81 + 2800 * q^82 + 4940 * q^85 - 1680 * q^87 + 2460 * q^88 + 600 * q^90 - 1304 * q^91 + 3408 * q^93 + 4164 * q^96 + 1904 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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