LMFDB - Embedded newform 570.4.f.b.341.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,4,Mod(341,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 1]))

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

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

chi := DirichletCharacter("570.341");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	570.f (of order $2$, degree $1$, 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:	$33.6310887033$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			341.12
Character	$\chi$	$=$	570.341
Dual form			570.4.f.b.341.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +(-3.00767 + 4.23721i) q^{3} +4.00000 q^{4} +5.00000i q^{5} +(-6.01534 + 8.47441i) q^{6} +25.9641 q^{7} +8.00000 q^{8} +(-8.90783 - 25.4882i) q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +(-3.00767 + 4.23721i) q^{3} +4.00000 q^{4} +5.00000i q^{5} +(-6.01534 + 8.47441i) q^{6} +25.9641 q^{7} +8.00000 q^{8} +(-8.90783 - 25.4882i) q^{9} +10.0000i q^{10} -23.1314i q^{11} +(-12.0307 + 16.9488i) q^{12} -58.1664i q^{13} +51.9282 q^{14} +(-21.1860 - 15.0384i) q^{15} +16.0000 q^{16} -50.1706i q^{17} +(-17.8157 - 50.9765i) q^{18} +(76.5091 - 31.7073i) q^{19} +20.0000i q^{20} +(-78.0915 + 110.015i) q^{21} -46.2628i q^{22} -153.540i q^{23} +(-24.0614 + 33.8976i) q^{24} -25.0000 q^{25} -116.333i q^{26} +(134.791 + 38.9159i) q^{27} +103.856 q^{28} -110.700 q^{29} +(-42.3721 - 30.0767i) q^{30} -58.4782i q^{31} +32.0000 q^{32} +(98.0124 + 69.5716i) q^{33} -100.341i q^{34} +129.821i q^{35} +(-35.6313 - 101.953i) q^{36} +11.9874i q^{37} +(153.018 - 63.4145i) q^{38} +(246.463 + 174.945i) q^{39} +40.0000i q^{40} -208.349 q^{41} +(-156.183 + 220.031i) q^{42} +111.918 q^{43} -92.5255i q^{44} +(127.441 - 44.5392i) q^{45} -307.081i q^{46} +257.216i q^{47} +(-48.1227 + 67.7953i) q^{48} +331.135 q^{49} -50.0000 q^{50} +(212.583 + 150.897i) q^{51} -232.666i q^{52} -165.397 q^{53} +(269.582 + 77.8319i) q^{54} +115.657 q^{55} +207.713 q^{56} +(-95.7642 + 419.550i) q^{57} -221.401 q^{58} -138.661 q^{59} +(-84.7441 - 60.1534i) q^{60} +576.621 q^{61} -116.956i q^{62} +(-231.284 - 661.779i) q^{63} +64.0000 q^{64} +290.832 q^{65} +(196.025 + 139.143i) q^{66} -156.446i q^{67} -200.682i q^{68} +(650.582 + 461.799i) q^{69} +259.641i q^{70} +1093.46 q^{71} +(-71.2627 - 203.906i) q^{72} +507.186 q^{73} +23.9748i q^{74} +(75.1918 - 105.930i) q^{75} +(306.037 - 126.829i) q^{76} -600.586i q^{77} +(492.926 + 349.891i) q^{78} +702.983i q^{79} +80.0000i q^{80} +(-570.301 + 454.090i) q^{81} -416.698 q^{82} -658.626i q^{83} +(-312.366 + 440.061i) q^{84} +250.853 q^{85} +223.837 q^{86} +(332.950 - 469.060i) q^{87} -185.051i q^{88} +481.471 q^{89} +(254.882 - 89.0783i) q^{90} -1510.24i q^{91} -614.162i q^{92} +(247.784 + 175.883i) q^{93} +514.431i q^{94} +(158.536 + 382.546i) q^{95} +(-96.2455 + 135.591i) q^{96} +1513.98i q^{97} +662.270 q^{98} +(-589.578 + 206.050i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 80 q^{2} + 10 q^{3} + 160 q^{4} + 20 q^{6} - 20 q^{7} + 320 q^{8} + 10 q^{9}+O(q^{10}) $ 40 * q + 80 * q^2 + 10 * q^3 + 160 * q^4 + 20 * q^6 - 20 * q^7 + 320 * q^8 + 10 * q^9	$ 40 q + 80 q^{2} + 10 q^{3} + 160 q^{4} + 20 q^{6} - 20 q^{7} + 320 q^{8} + 10 q^{9} + 40 q^{12} - 40 q^{14} + 640 q^{16} + 20 q^{18} + 68 q^{19} - 78 q^{21} + 80 q^{24} - 1000 q^{25} + 292 q^{27} - 80 q^{28} - 60 q^{29} + 1280 q^{32} + 440 q^{33} + 40 q^{36} + 136 q^{38} - 634 q^{39} + 888 q^{41} - 156 q^{42} + 488 q^{43} + 160 q^{45} + 160 q^{48} + 924 q^{49} - 2000 q^{50} + 2098 q^{51} - 108 q^{53} + 584 q^{54} - 160 q^{56} + 1562 q^{57} - 120 q^{58} + 132 q^{59} - 1496 q^{61} + 762 q^{63} + 2560 q^{64} + 120 q^{65} + 880 q^{66} - 1222 q^{69} - 1128 q^{71} + 80 q^{72} - 316 q^{73} - 250 q^{75} + 272 q^{76} - 1268 q^{78} - 942 q^{81} + 1776 q^{82} - 312 q^{84} + 976 q^{86} + 1830 q^{87} + 1776 q^{89} + 320 q^{90} - 1568 q^{93} - 660 q^{95} + 320 q^{96} + 1848 q^{98} - 4016 q^{99}+O(q^{100}) $ 40 * q + 80 * q^2 + 10 * q^3 + 160 * q^4 + 20 * q^6 - 20 * q^7 + 320 * q^8 + 10 * q^9 + 40 * q^12 - 40 * q^14 + 640 * q^16 + 20 * q^18 + 68 * q^19 - 78 * q^21 + 80 * q^24 - 1000 * q^25 + 292 * q^27 - 80 * q^28 - 60 * q^29 + 1280 * q^32 + 440 * q^33 + 40 * q^36 + 136 * q^38 - 634 * q^39 + 888 * q^41 - 156 * q^42 + 488 * q^43 + 160 * q^45 + 160 * q^48 + 924 * q^49 - 2000 * q^50 + 2098 * q^51 - 108 * q^53 + 584 * q^54 - 160 * q^56 + 1562 * q^57 - 120 * q^58 + 132 * q^59 - 1496 * q^61 + 762 * q^63 + 2560 * q^64 + 120 * q^65 + 880 * q^66 - 1222 * q^69 - 1128 * q^71 + 80 * q^72 - 316 * q^73 - 250 * q^75 + 272 * q^76 - 1268 * q^78 - 942 * q^81 + 1776 * q^82 - 312 * q^84 + 976 * q^86 + 1830 * q^87 + 1776 * q^89 + 320 * q^90 - 1568 * q^93 - 660 * q^95 + 320 * q^96 + 1848 * q^98 - 4016 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$-1$	$1$

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 $

$2$	2.00000			0.707107
$2$	2.00000			0.707107
$3$	−3.00767	+	4.23721i	−0.578827	+	0.815451i
$3$	−3.00767	+	4.23721i	−0.578827	+	0.815451i
$4$	4.00000			0.500000
$5$			5.00000i			0.447214i
$5$			5.00000i			0.447214i
$6$	−6.01534	+	8.47441i	−0.409292	+	0.576611i
$7$	25.9641			1.40193			0.700965	−	0.713196i	$-0.252753\pi$
$7$	25.9641			1.40193			0.700965	+	0.713196i	$0.252753\pi$
$8$	8.00000			0.353553
$9$	−8.90783	−	25.4882i	−0.329920	−	0.944009i
$10$			10.0000i			0.316228i
$11$		−	23.1314i		−	0.634034i	−0.948420	−	0.317017i	$-0.897319\pi$
$11$		−	23.1314i		−	0.634034i	0.948420	−	0.317017i	$-0.102681\pi$
$12$	−12.0307	+	16.9488i	−0.289413	+	0.407725i
$13$		−	58.1664i		−	1.24096i	−0.784223	−	0.620479i	$-0.786938\pi$
$13$		−	58.1664i		−	1.24096i	0.784223	−	0.620479i	$-0.213062\pi$
$14$	51.9282			0.991314
$15$	−21.1860	−	15.0384i	−0.364681	−	0.258859i
$16$	16.0000			0.250000
$17$		−	50.1706i		−	0.715774i	−0.933765	−	0.357887i	$-0.883497\pi$
$17$		−	50.1706i		−	0.715774i	0.933765	−	0.357887i	$-0.116503\pi$
$18$	−17.8157	−	50.9765i	−0.233288	−	0.667515i
$19$	76.5091	−	31.7073i	0.923811	−	0.382850i
$19$	76.5091	−	31.7073i	0.923811	−	0.382850i
$20$			20.0000i			0.223607i
$21$	−78.0915	+	110.015i	−0.811474	+	1.14320i
$22$		−	46.2628i		−	0.448330i
$23$		−	153.540i		−	1.39197i	−0.718055	−	0.695987i	$-0.754967\pi$
$23$		−	153.540i		−	1.39197i	0.718055	−	0.695987i	$-0.245033\pi$
$24$	−24.0614	+	33.8976i	−0.204646	+	0.288305i
$25$	−25.0000			−0.200000
$26$		−	116.333i		−	0.877490i
$27$	134.791	+	38.9159i	0.960759	+	0.277384i
$28$	103.856			0.700965
$29$	−110.700			−0.708846			−0.354423	−	0.935085i	$-0.615323\pi$
$29$	−110.700			−0.708846			−0.354423	+	0.935085i	$0.615323\pi$
$30$	−42.3721	−	30.0767i	−0.257868	−	0.183041i
$31$		−	58.4782i		−	0.338806i	−0.985547	−	0.169403i	$-0.945816\pi$
$31$		−	58.4782i		−	0.338806i	0.985547	−	0.169403i	$-0.0541840\pi$
$32$	32.0000			0.176777
$33$	98.0124	+	69.5716i	0.517024	+	0.366996i
$34$		−	100.341i		−	0.506129i
$35$			129.821i			0.626962i
$36$	−35.6313	−	101.953i	−0.164960	−	0.472005i
$37$			11.9874i			0.0532627i	0.999645	+	0.0266313i	$0.00847802\pi$
$37$			11.9874i			0.0532627i	−0.999645	+	0.0266313i	$0.991522\pi$
$38$	153.018	−	63.4145i	0.653233	−	0.270716i
$39$	246.463	+	174.945i	1.01194	+	0.718299i
$40$			40.0000i			0.158114i
$41$	−208.349			−0.793625			−0.396813	−	0.917900i	$-0.629884\pi$
$41$	−208.349			−0.793625			−0.396813	+	0.917900i	$0.629884\pi$
$42$	−156.183	+	220.031i	−0.573799	+	0.808368i
$43$	111.918			0.396916			0.198458	−	0.980109i	$-0.436407\pi$
$43$	111.918			0.396916			0.198458	+	0.980109i	$0.436407\pi$
$44$		−	92.5255i		−	0.317017i
$45$	127.441	−	44.5392i	0.422174	−	0.147545i
$46$		−	307.081i		−	0.984274i
$47$			257.216i			0.798272i	0.916892	+	0.399136i	$0.130690\pi$
$47$			257.216i			0.798272i	−0.916892	+	0.399136i	$0.869310\pi$
$48$	−48.1227	+	67.7953i	−0.144707	+	0.203863i
$49$	331.135			0.965408
$50$	−50.0000			−0.141421
$51$	212.583	+	150.897i	0.583678	+	0.414309i
$52$		−	232.666i		−	0.620479i
$53$	−165.397			−0.428662			−0.214331	−	0.976761i	$-0.568757\pi$
$53$	−165.397			−0.428662			−0.214331	+	0.976761i	$0.568757\pi$
$54$	269.582	+	77.8319i	0.679359	+	0.196140i
$55$	115.657			0.283549
$56$	207.713			0.495657
$57$	−95.7642	+	419.550i	−0.222531	+	0.974926i
$58$	−221.401			−0.501230
$59$	−138.661			−0.305967			−0.152984	−	0.988229i	$-0.548888\pi$
$59$	−138.661			−0.305967			−0.152984	+	0.988229i	$0.548888\pi$
$60$	−84.7441	−	60.1534i	−0.182340	−	0.129430i
$61$	576.621			1.21031			0.605154	−	0.796109i	$-0.293112\pi$
$61$	576.621			1.21031			0.605154	+	0.796109i	$0.293112\pi$
$62$		−	116.956i		−	0.239572i
$63$	−231.284	−	661.779i	−0.462524	−	1.32343i
$64$	64.0000			0.125000
$65$	290.832			0.554973
$66$	196.025	+	139.143i	0.365591	+	0.259505i
$67$		−	156.446i		−	0.285267i	−0.989776	−	0.142634i	$-0.954443\pi$
$67$		−	156.446i		−	0.285267i	0.989776	−	0.142634i	$-0.0455571\pi$
$68$		−	200.682i		−	0.357887i
$69$	650.582	+	461.799i	1.13509	+	0.805711i
$70$			259.641i			0.443329i
$71$	1093.46			1.82775			0.913876	−	0.405994i	$-0.133075\pi$
$71$	1093.46			1.82775			0.913876	+	0.405994i	$0.133075\pi$
$72$	−71.2627	−	203.906i	−0.116644	−	0.333758i
$73$	507.186			0.813173			0.406586	−	0.913612i	$-0.366719\pi$
$73$	507.186			0.813173			0.406586	+	0.913612i	$0.366719\pi$
$74$			23.9748i			0.0376624i
$75$	75.1918	−	105.930i	0.115765	−	0.163090i
$76$	306.037	−	126.829i	0.461905	−	0.191425i
$77$		−	600.586i		−	0.888871i
$78$	492.926	+	349.891i	0.715550	+	0.507914i
$79$			702.983i			1.00116i	0.865690	+	0.500581i	$0.166880\pi$
$79$			702.983i			1.00116i	−0.865690	+	0.500581i	$0.833120\pi$
$80$			80.0000i			0.111803i
$81$	−570.301	+	454.090i	−0.782306	+	0.622894i
$82$	−416.698			−0.561178
$83$		−	658.626i		−	0.871008i	−0.900187	−	0.435504i	$-0.856570\pi$
$83$		−	658.626i		−	0.871008i	0.900187	−	0.435504i	$-0.143430\pi$
$84$	−312.366	+	440.061i	−0.405737	+	0.571602i
$85$	250.853			0.320104
$86$	223.837			0.280662
$87$	332.950	−	469.060i	0.410299	−	0.578029i
$88$		−	185.051i		−	0.224165i
$89$	481.471			0.573436			0.286718	−	0.958015i	$-0.407436\pi$
$89$	481.471			0.573436			0.286718	+	0.958015i	$0.407436\pi$
$90$	254.882	−	89.0783i	0.298522	−	0.104330i
$91$		−	1510.24i		−	1.73974i
$92$		−	614.162i		−	0.695987i
$93$	247.784	+	175.883i	0.276280	+	0.196110i
$94$			514.431i			0.564463i
$95$	158.536	+	382.546i	0.171216	+	0.413141i
$96$	−96.2455	+	135.591i	−0.102323	+	0.144153i
$97$			1513.98i			1.58475i	0.610032	+	0.792377i	$0.291157\pi$
$97$			1513.98i			1.58475i	−0.610032	+	0.792377i	$0.708843\pi$
$98$	662.270			0.682646
$99$	−589.578	+	206.050i	−0.598534	+	0.209180i
$100$	−100.000			−0.100000
$101$		−	1410.99i		−	1.39008i	−0.718970	−	0.695042i	$-0.755386\pi$
$101$		−	1410.99i		−	1.39008i	0.718970	−	0.695042i	$-0.244614\pi$
$102$	425.166	+	301.793i	0.412723	+	0.292961i
$103$		−	382.749i		−	0.366149i	−0.983099	−	0.183074i	$-0.941395\pi$
$103$		−	382.749i		−	0.366149i	0.983099	−	0.183074i	$-0.0586049\pi$
$104$		−	465.331i		−	0.438745i
$105$	−550.076	−	390.457i	−0.511257	−	0.362902i
$106$	−330.795			−0.303110
$107$	−1061.57			−0.959121			−0.479560	−	0.877509i	$-0.659204\pi$
$107$	−1061.57			−0.959121			−0.479560	+	0.877509i	$0.659204\pi$
$108$	539.163	+	155.664i	0.480380	+	0.138692i
$109$			1339.76i			1.17730i	0.808389	+	0.588649i	$0.200340\pi$
$109$			1339.76i			1.17730i	−0.808389	+	0.588649i	$0.799660\pi$
$110$	231.314			0.200499
$111$	−50.7932	−	36.0542i	−0.0434331	−	0.0308299i
$112$	415.426			0.350482
$113$	−1544.27			−1.28560			−0.642800	−	0.766034i	$-0.722227\pi$
$113$	−1544.27			−1.28560			−0.642800	+	0.766034i	$0.722227\pi$
$114$	−191.528	+	839.100i	−0.157353	+	0.689376i
$115$	767.702			0.622509
$116$	−442.801			−0.354423
$117$	−1482.56	+	518.136i	−1.17148	+	0.409416i
$118$	−277.321			−0.216351
$119$		−	1302.63i		−	1.00347i
$120$	−169.488	−	120.307i	−0.128934	−	0.0915205i
$121$	795.939			0.598001
$122$	1153.24			0.855817
$123$	626.645	−	882.817i	0.459371	−	0.647162i
$124$		−	233.913i		−	0.169403i
$125$		−	125.000i		−	0.0894427i
$126$	−462.568	−	1323.56i	−0.327054	−	0.935809i
$127$			1437.91i			1.00468i	0.864671	+	0.502339i	$0.167527\pi$
$127$			1437.91i			1.00468i	−0.864671	+	0.502339i	$0.832473\pi$
$128$	128.000			0.0883883
$129$	−336.613	+	474.221i	−0.229745	+	0.323665i
$130$	581.664			0.392425
$131$			1437.13i			0.958493i	0.877680	+	0.479247i	$0.159090\pi$
$131$			1437.13i			0.958493i	−0.877680	+	0.479247i	$0.840910\pi$
$132$	392.050	+	278.286i	0.258512	+	0.183498i
$133$	1986.49	−	823.251i	1.29512	−	0.536728i
$134$		−	312.892i		−	0.201714i
$135$	−194.580	+	673.954i	−0.124050	+	0.429665i
$136$		−	401.365i		−	0.253064i
$137$			1580.37i			0.985550i	0.870157	+	0.492775i	$0.164017\pi$
$137$			1580.37i			0.985550i	−0.870157	+	0.492775i	$0.835983\pi$
$138$	1301.16	+	923.598i	0.802627	+	0.569724i
$139$	−2879.51			−1.75710			−0.878550	−	0.477651i	$-0.841488\pi$
$139$	−2879.51			−1.75710			−0.878550	+	0.477651i	$0.841488\pi$
$140$			519.282i			0.313481i
$141$	−1089.88	−	773.620i	−0.650951	−	0.462061i
$142$	2186.93			1.29242
$143$	−1345.47			−0.786809
$144$	−142.525	−	407.812i	−0.0824799	−	0.236002i
$145$		−	553.501i		−	0.317005i
$146$	1014.37			0.575000
$147$	−995.944	+	1403.09i	−0.558803	+	0.787242i
$148$			47.9497i			0.0266313i
$149$		−	1365.03i		−	0.750523i	−0.926919	−	0.375262i	$-0.877553\pi$
$149$		−	1365.03i		−	0.750523i	0.926919	−	0.375262i	$-0.122447\pi$
$150$	150.384	−	211.860i	0.0818584	−	0.115322i
$151$			1319.33i			0.711028i	0.934671	+	0.355514i	$0.115694\pi$
$151$			1319.33i			0.711028i	−0.934671	+	0.355514i	$0.884306\pi$
$152$	612.073	−	253.658i	0.326616	−	0.135358i
$153$	−1278.76	+	446.911i	−0.675697	+	0.236148i
$154$		−	1201.17i		−	0.628527i
$155$	292.391			0.151519
$156$	985.852	+	699.781i	0.505970	+	0.359150i
$157$	−1696.71			−0.862497			−0.431249	−	0.902233i	$-0.641927\pi$
$157$	−1696.71			−0.862497			−0.431249	+	0.902233i	$0.641927\pi$
$158$			1405.97i			0.707928i
$159$	497.461	−	700.823i	0.248121	−	0.349553i
$160$			160.000i			0.0790569i
$161$		−	3986.54i		−	1.95145i
$162$	−1140.60	+	908.180i	−0.553174	+	0.440453i
$163$	2042.98			0.981707			0.490853	−	0.871242i	$-0.336685\pi$
$163$	2042.98			0.981707			0.490853	+	0.871242i	$0.336685\pi$
$164$	−833.396			−0.396813
$165$	−347.858	+	490.062i	−0.164125	+	0.231220i
$166$		−	1317.25i		−	0.615895i
$167$	1705.68			0.790357			0.395179	−	0.918604i	$-0.370683\pi$
$167$	1705.68			0.790357			0.395179	+	0.918604i	$0.370683\pi$
$168$	−624.732	+	880.122i	−0.286899	+	0.404184i
$169$	−1186.33			−0.539976
$170$	501.706			0.226348
$171$	−1489.69	−	1667.64i	−0.666197	−	0.745776i
$172$	447.673			0.198458
$173$	−2589.67			−1.13808			−0.569042	−	0.822308i	$-0.692686\pi$
$173$	−2589.67			−1.13808			−0.569042	+	0.822308i	$0.692686\pi$
$174$	665.900	−	938.120i	0.290125	−	0.408728i
$175$	−649.103			−0.280386
$176$		−	370.102i		−	0.158509i
$177$	417.045	−	587.533i	0.177102	−	0.249501i
$178$	962.942			0.405481
$179$	106.976			0.0446689			0.0223345	−	0.999751i	$-0.492890\pi$
$179$	106.976			0.0446689			0.0223345	+	0.999751i	$0.492890\pi$
$180$	509.765	−	178.157i	0.211087	−	0.0737723i
$181$		−	1644.50i		−	0.675331i	−0.941266	−	0.337666i	$-0.890363\pi$
$181$		−	1644.50i		−	0.675331i	0.941266	−	0.337666i	$-0.109637\pi$
$182$		−	3020.48i		−	1.23018i
$183$	−1734.29	+	2443.26i	−0.700558	+	0.986946i
$184$		−	1228.32i		−	0.492137i
$185$	−59.9371			−0.0238198
$186$	495.568	+	351.766i	0.195359	+	0.138671i
$187$	−1160.52			−0.453825
$188$			1028.86i			0.399136i
$189$	3499.72	+	1010.42i	1.34692	+	0.388873i
$190$	317.073	+	765.091i	0.121068	+	0.292135i
$191$		−	434.659i		−	0.164664i	−0.996605	−	0.0823320i	$-0.973763\pi$
$191$		−	434.659i		−	0.164664i	0.996605	−	0.0823320i	$-0.0262368\pi$
$192$	−192.491	+	271.181i	−0.0723533	+	0.101931i
$193$		−	949.089i		−	0.353974i	−0.984213	−	0.176987i	$-0.943365\pi$
$193$		−	949.089i		−	0.353974i	0.984213	−	0.176987i	$-0.0566350\pi$
$194$			3027.95i			1.12059i
$195$	−874.727	+	1232.31i	−0.321233	+	0.452553i
$196$	1324.54			0.482704
$197$			1450.85i			0.524714i	0.964971	+	0.262357i	$0.0844998\pi$
$197$			1450.85i			0.524714i	−0.964971	+	0.262357i	$0.915500\pi$
$198$	−1179.16	+	412.101i	−0.423227	+	0.147913i
$199$	−3324.15			−1.18414			−0.592068	−	0.805888i	$-0.701688\pi$
$199$	−3324.15			−1.18414			−0.592068	+	0.805888i	$0.701688\pi$
$200$	−200.000			−0.0707107
$201$	662.894	+	470.538i	0.232621	+	0.165120i
$202$		−	2821.97i		−	0.982937i
$203$	−2874.23			−0.993752
$204$	850.333	+	603.587i	0.291839	+	0.207155i
$205$		−	1041.74i		−	0.354920i
$206$		−	765.497i		−	0.258906i
$207$	−3913.48	+	1367.71i	−1.31404	+	0.459239i
$208$		−	930.662i		−	0.310239i
$209$	−733.433	−	1769.76i	−0.242740	−	0.585727i
$210$	−1100.15	−	780.915i	−0.361513	−	0.256611i
$211$		−	5869.12i		−	1.91491i	−0.288578	−	0.957456i	$-0.593182\pi$
$211$		−	5869.12i		−	1.91491i	0.288578	−	0.957456i	$-0.406818\pi$
$212$	−661.590			−0.214331
$213$	−3288.78	+	4633.23i	−1.05795	+	1.49044i
$214$	−2123.14			−0.678201
$215$			559.591i			0.177506i
$216$	1078.33	+	311.327i	0.339680	+	0.0980701i
$217$		−	1518.33i		−	0.474982i
$218$			2679.51i			0.832475i
$219$	−1525.45	+	2149.05i	−0.470686	+	0.663102i
$220$	462.628			0.141774
$221$	−2918.24			−0.888245
$222$	−101.586	−	72.1084i	−0.0307118	−	0.0218000i
$223$		−	345.304i		−	0.103692i	−0.998655	−	0.0518459i	$-0.983490\pi$
$223$		−	345.304i		−	0.103692i	0.998655	−	0.0518459i	$-0.0165105\pi$
$224$	830.851			0.247829
$225$	222.696	+	637.206i	0.0659839	+	0.188802i
$226$	−3088.54			−0.909056
$227$	1526.17			0.446237			0.223118	−	0.974791i	$-0.428376\pi$
$227$	1526.17			0.446237			0.223118	+	0.974791i	$0.428376\pi$
$228$	−383.057	+	1678.20i	−0.111266	+	0.487463i
$229$	3226.39			0.931028			0.465514	−	0.885040i	$-0.345869\pi$
$229$	3226.39			0.931028			0.465514	+	0.885040i	$0.345869\pi$
$230$	1535.40			0.440181
$231$	2544.81	+	1806.36i	0.724831	+	0.514502i
$232$	−885.602			−0.250615
$233$			4868.37i			1.36883i	0.729093	+	0.684415i	$0.239942\pi$
$233$			4868.37i			1.36883i	−0.729093	+	0.684415i	$0.760058\pi$
$234$	−2965.12	+	1036.27i	−0.828358	+	0.289501i
$235$	−1286.08			−0.356998
$236$	−554.642			−0.152984
$237$	−2978.68	−	2114.34i	−0.816398	−	0.579499i
$238$		−	2605.27i		−	0.709557i
$239$		−	2152.76i		−	0.582638i	−0.956626	−	0.291319i	$-0.905906\pi$
$239$		−	2152.76i		−	0.582638i	0.956626	−	0.291319i	$-0.0940941\pi$
$240$	−338.976	−	240.614i	−0.0911702	−	0.0647148i
$241$		−	2638.76i		−	0.705301i	−0.935755	−	0.352651i	$-0.885280\pi$
$241$		−	2638.76i		−	0.705301i	0.935755	−	0.352651i	$-0.114720\pi$
$242$	1591.88			0.422850
$243$	−208.795	−	3782.24i	−0.0551201	−	0.998480i
$244$	2306.48			0.605154
$245$			1655.67i			0.431743i
$246$	1253.29	−	1765.63i	0.324825	−	0.457613i
$247$	−1844.30	−	4450.26i	−0.475100	−	1.14641i
$248$		−	467.825i		−	0.119786i
$249$	2790.74	+	1980.93i	0.710264	+	0.504162i
$250$		−	250.000i		−	0.0632456i
$251$			3901.93i			0.981226i	0.871378	+	0.490613i	$0.163227\pi$
$251$			3901.93i			0.981226i	−0.871378	+	0.490613i	$0.836773\pi$
$252$	−925.136	−	2647.12i	−0.231262	−	0.661717i
$253$	−3551.60			−0.882559
$254$			2875.83i			0.710415i
$255$	−754.483	+	1062.92i	−0.185285	+	0.261029i
$256$	256.000			0.0625000
$257$	5501.83			1.33539			0.667694	−	0.744436i	$-0.267281\pi$
$257$	5501.83			1.33539			0.667694	+	0.744436i	$0.267281\pi$
$258$	−673.227	+	948.441i	−0.162454	+	0.228866i
$259$			311.243i			0.0746705i
$260$	1163.33			0.277487
$261$	986.099	+	2821.56i	0.233862	+	0.669157i
$262$			2874.26i			0.677757i
$263$			3601.59i			0.844424i	0.906497	+	0.422212i	$0.138746\pi$
$263$			3601.59i			0.844424i	−0.906497	+	0.422212i	$0.861254\pi$
$264$	784.100	+	556.573i	0.182795	+	0.129753i
$265$		−	826.987i		−	0.191703i
$266$	3972.98	−	1646.50i	0.915787	−	0.379524i
$267$	−1448.11	+	2040.09i	−0.331920	+	0.467609i
$268$		−	625.784i		−	0.142634i
$269$	6727.62			1.52487			0.762435	−	0.647064i	$-0.224004\pi$
$269$	6727.62			1.52487			0.762435	+	0.647064i	$0.224004\pi$
$270$	−389.159	+	1347.91i	−0.0877166	+	0.303819i
$271$	−7774.37			−1.74265			−0.871327	−	0.490702i	$-0.836740\pi$
$271$	−7774.37			−1.74265			−0.871327	+	0.490702i	$0.836740\pi$
$272$		−	802.730i		−	0.178944i
$273$	6399.19	+	4542.30i	1.41867	+	1.00701i
$274$			3160.74i			0.696889i
$275$			578.285i			0.126807i
$276$	2602.33	+	1847.20i	0.567543	+	0.402856i
$277$	5453.73			1.18297			0.591486	−	0.806315i	$-0.298542\pi$
$277$	5453.73			1.18297			0.591486	+	0.806315i	$0.298542\pi$
$278$	−5759.02			−1.24246
$279$	−1490.51	+	520.914i	−0.319836	+	0.111779i
$280$			1038.56i			0.221665i
$281$	2175.04			0.461750			0.230875	−	0.972983i	$-0.425841\pi$
$281$	2175.04			0.461750			0.230875	+	0.972983i	$0.425841\pi$
$282$	−2179.75	−	1547.24i	−0.460292	−	0.326726i
$283$	5433.29			1.14126			0.570629	−	0.821208i	$-0.306700\pi$
$283$	5433.29			1.14126			0.570629	+	0.821208i	$0.306700\pi$
$284$	4373.86			0.913876
$285$	−2097.75	−	478.821i	−0.436000	−	0.0995189i
$286$	−2690.94			−0.556358
$287$	−5409.59			−1.11261
$288$	−285.051	−	815.624i	−0.0583221	−	0.166879i
$289$	2395.91			0.487667
$290$		−	1107.00i		−	0.224157i
$291$	−6415.03	−	4553.55i	−1.29229	−	0.917298i
$292$	2028.74			0.406586
$293$	6781.93			1.35223			0.676117	−	0.736795i	$-0.263662\pi$
$293$	6781.93			1.35223			0.676117	+	0.736795i	$0.263662\pi$
$294$	−1991.89	+	2806.17i	−0.395134	+	0.556664i
$295$		−	693.303i		−	0.136833i
$296$			95.8993i			0.0188312i
$297$	900.179	−	3117.90i	0.175871	−	0.609154i
$298$		−	2730.07i		−	0.530700i
$299$	−8930.89			−1.72738
$300$	300.767	−	423.721i	0.0578827	−	0.0815451i
$301$	2905.86			0.556448
$302$			2638.65i			0.502773i
$303$	5978.64	+	4243.78i	1.13354	+	0.804617i
$304$	1224.15	−	507.316i	0.230953	−	0.0957124i
$305$			2883.10i			0.541266i
$306$	−2557.52	+	893.823i	−0.477790	+	0.166982i
$307$			7413.93i			1.37829i	0.724623	+	0.689146i	$0.242014\pi$
$307$			7413.93i			1.37829i	−0.724623	+	0.689146i	$0.757986\pi$
$308$		−	2402.34i		−	0.444436i
$309$	1621.78	+	1151.18i	0.298576	+	0.211937i
$310$	584.782			0.107140
$311$		−	1667.69i		−	0.304070i	−0.988375	−	0.152035i	$-0.951417\pi$
$311$		−	1667.69i		−	0.304070i	0.988375	−	0.152035i	$-0.0485827\pi$
$312$	1971.70	+	1399.56i	0.357775	+	0.253957i
$313$	6098.33			1.10127			0.550636	−	0.834745i	$-0.314385\pi$
$313$	6098.33			1.10127			0.550636	+	0.834745i	$0.314385\pi$
$314$	−3393.42			−0.609878
$315$	3308.90	−	1156.42i	0.591858	−	0.206847i
$316$			2811.93i			0.500581i
$317$	−10184.5			−1.80447			−0.902236	−	0.431243i	$-0.858075\pi$
$317$	−10184.5			−1.80447			−0.902236	+	0.431243i	$0.858075\pi$
$318$	994.922	−	1401.65i	0.175448	−	0.247171i
$319$			2560.65i			0.449432i
$320$			320.000i			0.0559017i
$321$	3192.86	−	4498.09i	0.555165	−	0.782116i
$322$		−	7973.08i		−	1.37988i
$323$	−1590.77	−	3838.51i	−0.274034	−	0.661240i
$324$	−2281.20	+	1816.36i	−0.391153	+	0.311447i
$325$			1454.16i			0.248192i
$326$	4085.95			0.694171
$327$	−5676.82	−	4029.55i	−0.960028	−	0.681451i
$328$	−1666.79			−0.280589
$329$			6678.38i			1.11912i
$330$	−695.716	+	980.124i	−0.116054	+	0.163497i
$331$		−	4765.45i		−	0.791337i	−0.918393	−	0.395669i	$-0.870513\pi$
$331$		−	4765.45i		−	0.791337i	0.918393	−	0.395669i	$-0.129487\pi$
$332$		−	2634.51i		−	0.435504i
$333$	305.538	−	106.782i	0.0502805	−	0.0175724i
$334$	3411.36			0.558867
$335$	782.230			0.127575
$336$	−1249.46	+	1760.24i	−0.202869	+	0.285801i
$337$		−	10633.4i		−	1.71881i	−0.511295	−	0.859405i	$-0.670834\pi$
$337$		−	10633.4i		−	1.71881i	0.511295	−	0.859405i	$-0.329166\pi$
$338$	−2372.66			−0.381821
$339$	4644.66	−	6543.39i	0.744139	−	1.04834i
$340$	1003.41			0.160052
$341$	−1352.68			−0.214815
$342$	−2979.39	−	3335.28i	−0.471072	−	0.527343i
$343$	−308.070			−0.0484963
$344$	895.346			0.140331
$345$	−2308.99	+	3252.91i	−0.360325	+	0.507626i
$346$	−5179.33			−0.804748
$347$			1231.94i			0.190588i	0.995449	+	0.0952939i	$0.0303791\pi$
$347$			1231.94i			0.190588i	−0.995449	+	0.0952939i	$0.969621\pi$
$348$	1331.80	−	1876.24i	0.205149	−	0.289014i
$349$	−9132.74			−1.40076			−0.700379	−	0.713771i	$-0.746986\pi$
$349$	−9132.74			−1.40076			−0.700379	+	0.713771i	$0.746986\pi$
$350$	−1298.21			−0.198263
$351$	2263.60	−	7840.29i	0.344222	−	1.19226i
$352$		−	740.204i		−	0.112082i
$353$			2908.49i			0.438536i	0.975665	+	0.219268i	$0.0703669\pi$
$353$			2908.49i			0.438536i	−0.975665	+	0.219268i	$0.929633\pi$
$354$	834.090	−	1175.07i	0.125230	−	0.176424i
$355$			5467.32i			0.817395i
$356$	1925.88			0.286718
$357$	5519.53	+	3917.90i	0.818276	+	0.580832i
$358$	213.951			0.0315857
$359$			3502.47i			0.514912i	0.966290	+	0.257456i	$0.0828843\pi$
$359$			3502.47i			0.514912i	−0.966290	+	0.257456i	$0.917116\pi$
$360$	1019.53	−	356.313i	0.149261	−	0.0521649i
$361$	4848.30	−	4851.79i	0.706852	−	0.707361i
$362$		−	3289.01i		−	0.477531i
$363$	−2393.92	+	3372.56i	−0.346139	+	0.487640i
$364$		−	6040.95i		−	0.869868i
$365$			2535.93i			0.363662i
$366$	−3468.57	+	4886.52i	−0.495369	+	0.697876i
$367$	−11546.8			−1.64234			−0.821168	−	0.570687i	$-0.806677\pi$
$367$	−11546.8			−1.64234			−0.821168	+	0.570687i	$0.806677\pi$
$368$		−	2456.65i		−	0.347993i
$369$	1855.94	+	5310.45i	0.261833	+	0.749189i
$370$	−119.874			−0.0168431
$371$	−4294.40			−0.600954
$372$	991.136	+	703.532i	0.138140	+	0.0980550i
$373$			6436.46i			0.893478i	0.894664	+	0.446739i	$0.147415\pi$
$373$			6436.46i			0.893478i	−0.894664	+	0.446739i	$0.852585\pi$
$374$	−2321.03			−0.320903
$375$	529.651	+	375.959i	0.0729361	+	0.0517718i
$376$			2057.73i			0.282232i
$377$			6439.03i			0.879648i
$378$	6999.44	+	2020.83i	0.952414	+	0.274975i
$379$		−	1779.37i		−	0.241161i	−0.992704	−	0.120580i	$-0.961524\pi$
$379$		−	1779.37i		−	0.241161i	0.992704	−	0.120580i	$-0.0384756\pi$
$380$	634.145	+	1530.18i	0.0856078	+	0.206570i
$381$	−6092.73	−	4324.77i	−0.819266	−	0.581535i
$382$		−	869.318i		−	0.116435i
$383$	−4165.28			−0.555707			−0.277854	−	0.960623i	$-0.589623\pi$
$383$	−4165.28			−0.555707			−0.277854	+	0.960623i	$0.589623\pi$
$384$	−384.982	+	542.362i	−0.0511615	+	0.0720763i
$385$	3002.93			0.397515
$386$		−	1898.18i		−	0.250297i
$387$	−996.949	−	2852.60i	−0.130950	−	0.374692i
$388$			6055.91i			0.792377i
$389$			13645.2i			1.77850i	0.457421	+	0.889250i	$0.348773\pi$
$389$			13645.2i			1.77850i	−0.457421	+	0.889250i	$0.651227\pi$
$390$	−1749.45	+	2464.63i	−0.227146	+	0.320003i
$391$	−7703.22			−0.996338
$392$	2649.08			0.341323
$393$	−6089.42	−	4322.41i	−0.781604	−	0.554801i
$394$			2901.70i			0.371029i
$395$	−3514.91			−0.447733
$396$	−2358.31	+	824.202i	−0.299267	+	0.104590i
$397$	−1255.11			−0.158671			−0.0793353	−	0.996848i	$-0.525280\pi$
$397$	−1255.11			−0.158671			−0.0793353	+	0.996848i	$0.525280\pi$
$398$	−6648.31			−0.837310
$399$	−2486.43	+	10893.2i	−0.311973	+	1.36678i
$400$	−400.000			−0.0500000
$401$	1549.54			0.192968			0.0964840	−	0.995335i	$-0.469240\pi$
$401$	1549.54			0.192968			0.0964840	+	0.995335i	$0.469240\pi$
$402$	1325.79	+	941.076i	0.164488	+	0.116758i
$403$	−3401.46			−0.420444
$404$		−	5643.95i		−	0.695042i
$405$	−2270.45	−	2851.51i	−0.278567	−	0.349858i
$406$	−5748.47			−0.702689
$407$	277.286			0.0337704
$408$	1700.67	+	1207.17i	0.206362	+	0.146480i
$409$		−	10794.8i		−	1.30506i	−0.757764	−	0.652528i	$-0.773708\pi$
$409$		−	10794.8i		−	1.30506i	0.757764	−	0.652528i	$-0.226292\pi$
$410$		−	2083.49i		−	0.250966i
$411$	−6696.36	−	4753.24i	−0.803667	−	0.570462i
$412$		−	1530.99i		−	0.183074i
$413$	−3600.20			−0.428945
$414$	−7826.95	+	2735.42i	−0.929163	+	0.324731i
$415$	3293.13			0.389526
$416$		−	1861.32i		−	0.219372i
$417$	8660.62	−	12201.1i	1.01706	−	1.43283i
$418$	−1466.87	−	3539.52i	−0.171643	−	0.414172i
$419$			307.106i			0.0358070i	0.999840	+	0.0179035i	$0.00569916\pi$
$419$			307.106i			0.0358070i	−0.999840	+	0.0179035i	$0.994301\pi$
$420$	−2200.31	−	1561.83i	−0.255628	−	0.181451i
$421$			3945.21i			0.456717i	0.973577	+	0.228359i	$0.0733359\pi$
$421$			3945.21i			0.456717i	−0.973577	+	0.228359i	$0.926664\pi$
$422$		−	11738.2i		−	1.35405i
$423$	6555.98	−	2291.23i	0.753576	−	0.263366i
$424$	−1323.18			−0.151555
$425$			1254.27i			0.143155i
$426$	−6577.56	+	9266.47i	−0.748084	+	1.05390i
$427$	14971.4			1.69677
$428$	−4246.28			−0.479560
$429$	4046.73	−	5701.03i	0.455426	−	0.641604i
$430$			1119.18i			0.125516i
$431$	−4659.79			−0.520775			−0.260388	−	0.965504i	$-0.583850\pi$
$431$	−4659.79			−0.520775			−0.260388	+	0.965504i	$0.583850\pi$
$432$	2156.65	+	622.655i	0.240190	+	0.0693461i
$433$		−	84.3083i		−	0.00935704i	−0.999989	−	0.00467852i	$-0.998511\pi$
$433$		−	84.3083i		−	0.00935704i	0.999989	−	0.00467852i	$-0.00148922\pi$
$434$		−	3036.67i		−	0.335863i
$435$	2345.30	+	1664.75i	0.258502	+	0.183491i
$436$			5359.03i			0.588649i
$437$	−4868.34	−	11747.2i	−0.532917	−	1.28592i
$438$	−3050.90	+	4298.10i	−0.332825	+	0.468884i
$439$		−	12577.7i		−	1.36743i	−0.729751	−	0.683713i	$-0.760364\pi$
$439$		−	12577.7i		−	1.36743i	0.729751	−	0.683713i	$-0.239636\pi$
$440$	925.255			0.100250
$441$	−2949.69	−	8440.04i	−0.318507	−	0.911353i
$442$	−5836.48			−0.628084
$443$			7670.68i			0.822675i	0.911483	+	0.411337i	$0.134938\pi$
$443$			7670.68i			0.822675i	−0.911483	+	0.411337i	$0.865062\pi$
$444$	−203.173	−	144.217i	−0.0217165	−	0.0154149i
$445$			2407.36i			0.256449i
$446$		−	690.609i		−	0.0733212i
$447$	5783.93	+	4105.57i	0.612015	+	0.434423i
$448$	1661.70			0.175241
$449$	8662.40			0.910477			0.455238	−	0.890370i	$-0.349554\pi$
$449$	8662.40			0.910477			0.455238	+	0.890370i	$0.349554\pi$
$450$	445.392	+	1274.41i	0.0466577	+	0.133503i
$451$			4819.40i			0.503185i
$452$	−6177.08			−0.642800
$453$	−5590.26	−	3968.10i	−0.579808	−	0.411562i
$454$	3052.35			0.315537
$455$	7551.19			0.778034
$456$	−766.113	+	3356.40i	−0.0786766	+	0.344688i
$457$	18520.9			1.89578			0.947891	−	0.318594i	$-0.103211\pi$
$457$	18520.9			1.89578			0.947891	+	0.318594i	$0.103211\pi$
$458$	6452.77			0.658337
$459$	1952.44	−	6762.53i	0.198544	−	0.687686i
$460$	3070.81			0.311255
$461$		−	10737.8i		−	1.08484i	−0.840108	−	0.542419i	$-0.817509\pi$
$461$		−	10737.8i		−	1.08484i	0.840108	−	0.542419i	$-0.182491\pi$
$462$	5089.61	+	3612.73i	0.512533	+	0.363808i
$463$	16128.6			1.61892			0.809459	−	0.587177i	$-0.199761\pi$
$463$	16128.6			1.61892			0.809459	+	0.587177i	$0.199761\pi$
$464$	−1771.20			−0.177211
$465$	−879.415	+	1238.92i	−0.0877030	+	0.123556i
$466$			9736.74i			0.967909i
$467$			2448.21i			0.242590i	0.992616	+	0.121295i	$0.0387048\pi$
$467$			2448.21i			0.242590i	−0.992616	+	0.121295i	$0.961295\pi$
$468$	−5930.24	+	2072.55i	−0.585738	+	0.204708i
$469$		−	4061.98i		−	0.399925i
$470$	−2572.16			−0.252436
$471$	5103.14	−	7189.30i	0.499236	−	0.703324i
$472$	−1109.28			−0.108176
$473$		−	2588.82i		−	0.251658i
$474$	−5957.37	−	4228.68i	−0.577280	−	0.409767i
$475$	−1912.73	+	792.681i	−0.184762	+	0.0765699i
$476$		−	5210.54i		−	0.501733i
$477$	1473.33	+	4215.69i	0.141424	+	0.404661i
$478$		−	4305.52i		−	0.411987i
$479$		−	6363.89i		−	0.607042i	−0.952825	−	0.303521i	$-0.901838\pi$
$479$		−	6363.89i		−	0.607042i	0.952825	−	0.303521i	$-0.0981623\pi$
$480$	−677.953	−	481.227i	−0.0644670	−	0.0457603i
$481$	697.265			0.0660967
$482$		−	5277.53i		−	0.498723i
$483$	16891.8	+	11990.2i	1.59131	+	1.12955i
$484$	3183.76			0.299000
$485$	−7569.89			−0.708723
$486$	−417.590	−	7564.47i	−0.0389758	−	0.706032i
$487$			14190.9i			1.32043i	0.751076	+	0.660216i	$0.229535\pi$
$487$			14190.9i			1.32043i	−0.751076	+	0.660216i	$0.770465\pi$
$488$	4612.97			0.427908
$489$	−6144.60	+	8656.51i	−0.568238	+	0.800533i
$490$			3311.35i			0.305289i
$491$		−	673.995i		−	0.0619491i	−0.999520	−	0.0309745i	$-0.990139\pi$
$491$		−	673.995i		−	0.0619491i	0.999520	−	0.0309745i	$-0.00986107\pi$
$492$	2506.58	−	3531.27i	0.229686	−	0.323581i
$493$			5553.90i			0.507373i
$494$	−3688.59	−	8900.52i	−0.335947	−	0.810634i
$495$	−1030.25	−	2947.89i	−0.0935483	−	0.267672i
$496$		−	935.651i		−	0.0847015i
$497$	28390.8			2.56238
$498$	5581.47	+	3961.86i	0.502232	+	0.356497i
$499$	5205.63			0.467006			0.233503	−	0.972356i	$-0.424981\pi$
$499$	5205.63			0.467006			0.233503	+	0.972356i	$0.424981\pi$
$500$		−	500.000i		−	0.0447214i
$501$	−5130.13	+	7227.33i	−0.457480	+	0.644497i
$502$			7803.86i			0.693832i
$503$			12520.8i			1.10989i	0.831887	+	0.554945i	$0.187261\pi$
$503$			12520.8i			1.10989i	−0.831887	+	0.554945i	$0.812739\pi$
$504$	−1850.27	−	5294.24i	−0.163527	−	0.467905i
$505$	7054.93			0.621664
$506$	−7103.20			−0.624063
$507$	3568.08	−	5026.71i	0.312553	−	0.440324i
$508$			5751.65i			0.502339i
$509$	18723.8			1.63049			0.815243	−	0.579119i	$-0.196603\pi$
$509$	18723.8			1.63049			0.815243	+	0.579119i	$0.196603\pi$
$510$	−1508.97	+	2125.83i	−0.131016	+	0.184575i
$511$	13168.6			1.14001
$512$	512.000			0.0441942
$513$	11546.6	−	1296.42i	0.993756	−	0.111576i
$514$	11003.7			0.944262
$515$	1913.74			0.163747
$516$	−1346.45	+	1896.88i	−0.114873	+	0.161833i
$517$	5949.76			0.506131
$518$			622.485i			0.0528000i
$519$	7788.86	−	10972.9i	0.658754	−	0.928052i
$520$	2326.66			0.196213
$521$	14307.6			1.20313			0.601563	−	0.798825i	$-0.294545\pi$
$521$	14307.6			1.20313			0.601563	+	0.798825i	$0.294545\pi$
$522$	1972.20	+	5643.11i	0.165366	+	0.473165i
$523$		−	16728.6i		−	1.39864i	−0.714808	−	0.699321i	$-0.753486\pi$
$523$		−	16728.6i		−	1.39864i	0.714808	−	0.699321i	$-0.246514\pi$
$524$			5748.52i			0.479247i
$525$	1952.29	−	2750.38i	0.162295	−	0.228641i
$526$			7203.18i			0.597098i
$527$	−2933.89			−0.242509
$528$	1568.20	+	1113.15i	0.129256	+	0.0917489i
$529$	−11407.7			−0.937590
$530$		−	1653.97i		−	0.135555i
$531$	1235.16	+	3534.21i	0.100945	+	0.288836i
$532$	7945.97	−	3293.00i	0.647559	−	0.268364i
$533$			12118.9i			0.984855i
$534$	−2896.21	+	4080.18i	−0.234703	+	0.330650i
$535$		−	5307.85i		−	0.428932i
$536$		−	1251.57i		−	0.100857i
$537$	−321.748	+	453.278i	−0.0258556	+	0.0364253i
$538$	13455.2			1.07825
$539$		−	7659.61i		−	0.612101i
$540$	−778.319	+	2695.82i	−0.0620250	+	0.214832i
$541$	−14692.2			−1.16759			−0.583796	−	0.811900i	$-0.698433\pi$
$541$	−14692.2			−1.16759			−0.583796	+	0.811900i	$0.698433\pi$
$542$	−15548.7			−1.23224
$543$	6968.10	+	4946.12i	0.550699	+	0.390900i
$544$		−	1605.46i		−	0.126532i
$545$	−6698.78			−0.526503
$546$	12798.4	+	9084.60i	1.00315	+	0.712060i
$547$		−	6578.82i		−	0.514241i	−0.966379	−	0.257121i	$-0.917226\pi$
$547$		−	6578.82i		−	0.514241i	0.966379	−	0.257121i	$-0.0827738\pi$
$548$			6321.49i			0.492775i
$549$	−5136.44	−	14697.1i	−0.399304	−	1.14254i
$550$			1156.57i			0.0896660i
$551$	−8469.58	+	3510.00i	−0.654839	+	0.271381i
$552$	5204.66	+	3694.39i	0.401313	+	0.284862i
$553$			18252.3i			1.40356i
$554$	10907.5			0.836487
$555$	180.271	−	253.966i	0.0137875	−	0.0194239i
$556$	−11518.0			−0.878550
$557$			2661.68i			0.202476i	0.994862	+	0.101238i	$0.0322804\pi$
$557$			2661.68i			0.202476i	−0.994862	+	0.101238i	$0.967720\pi$
$558$	−2981.01	+	1041.83i	−0.226158	+	0.0790395i
$559$		−	6509.88i		−	0.492556i
$560$			2077.13i			0.156741i
$561$	3490.45	−	4917.34i	0.262686	−	0.370072i
$562$	4350.08			0.326507
$563$	−21918.9			−1.64080			−0.820400	−	0.571790i	$-0.806249\pi$
$563$	−21918.9			−1.64080			−0.820400	+	0.571790i	$0.806249\pi$
$564$	−4359.50	−	3094.48i	−0.325476	−	0.231030i
$565$		−	7721.35i		−	0.574938i
$566$	10866.6			0.806991
$567$	−14807.4	+	11790.0i	−1.09674	+	0.873254i
$568$	8747.72			0.646208
$569$	20276.0			1.49388			0.746939	−	0.664893i	$-0.231523\pi$
$569$	20276.0			1.49388			0.746939	+	0.664893i	$0.231523\pi$
$570$	−4195.50	−	957.642i	−0.308299	−	0.0703705i
$571$	4446.53			0.325887			0.162943	−	0.986635i	$-0.447901\pi$
$571$	4446.53			0.325887			0.162943	+	0.986635i	$0.447901\pi$
$572$	−5381.88			−0.393405
$573$	1841.74	+	1307.31i	0.134275	+	0.0953119i
$574$	−10819.2			−0.786732
$575$			3838.51i			0.278395i
$576$	−570.101	−	1631.25i	−0.0412400	−	0.118001i
$577$	−16544.9			−1.19371			−0.596856	−	0.802349i	$-0.703584\pi$
$577$	−16544.9			−1.19371			−0.596856	+	0.802349i	$0.703584\pi$
$578$	4791.82			0.344833
$579$	4021.48	+	2854.55i	0.288648	+	0.204889i
$580$		−	2214.01i		−	0.158503i
$581$		−	17100.6i		−	1.22109i
$582$	−12830.1	−	9107.09i	−0.913786	−	0.648627i
$583$			3825.87i			0.271786i
$584$	4057.49			0.287500
$585$	−2590.68	−	7412.79i	−0.183097	−	0.523900i
$586$	13563.9			0.956173
$587$		−	17945.8i		−	1.26184i	−0.775846	−	0.630922i	$-0.782677\pi$
$587$		−	17945.8i		−	1.26184i	0.775846	−	0.630922i	$-0.217323\pi$
$588$	−3983.78	+	5612.35i	−0.279402	+	0.393621i
$589$	−1854.18	−	4474.11i	−0.129712	−	0.312993i
$590$		−	1386.61i		−	0.0967553i
$591$	−6147.55	−	4363.68i	−0.427879	−	0.303719i
$592$			191.799i			0.0133157i
$593$			21182.9i			1.46691i	0.679738	+	0.733455i	$0.262093\pi$
$593$			21182.9i			1.46691i	−0.679738	+	0.733455i	$0.737907\pi$
$594$	1800.36	−	6235.79i	0.124360	−	0.430737i
$595$	6513.17			0.448763
$596$		−	5460.14i		−	0.375262i
$597$	9997.96	−	14085.1i	0.685409	−	0.965604i
$598$	−17861.8			−1.22144
$599$	12924.5			0.881605			0.440802	−	0.897604i	$-0.354694\pi$
$599$	12924.5			0.881605			0.440802	+	0.897604i	$0.354694\pi$
$600$	601.534	−	847.441i	0.0409292	−	0.0576611i
$601$			22074.8i			1.49825i	0.662427	+	0.749127i	$0.269527\pi$
$601$			22074.8i			1.49825i	−0.662427	+	0.749127i	$0.730473\pi$
$602$	5811.71			0.393468
$603$	−3987.53	+	1393.59i	−0.269295	+	0.0941153i
$604$			5277.30i			0.355514i
$605$			3979.70i			0.267434i
$606$	11957.3	+	8487.57i	0.801537	+	0.568950i
$607$			18837.6i			1.25963i	0.776745	+	0.629815i	$0.216869\pi$
$607$			18837.6i			1.25963i	−0.776745	+	0.629815i	$0.783131\pi$
$608$	2448.29	−	1014.63i	0.163308	−	0.0676789i
$609$	8644.75	−	12178.7i	0.575210	−	0.810356i
$610$			5766.21i			0.382733i
$611$	14961.3			0.990622
$612$	−5115.04	+	1787.65i	−0.337849	+	0.118074i
$613$	5354.37			0.352791			0.176396	−	0.984319i	$-0.443556\pi$
$613$	5354.37			0.352791			0.176396	+	0.984319i	$0.443556\pi$
$614$			14827.9i			0.974599i
$615$	4414.09	+	3133.22i	0.289420	+	0.205437i
$616$		−	4804.69i		−	0.314263i
$617$			7515.14i			0.490354i	0.969478	+	0.245177i	$0.0788460\pi$
$617$			7515.14i			0.490354i	−0.969478	+	0.245177i	$0.921154\pi$
$618$	3243.57	+	2302.36i	0.211125	+	0.149862i
$619$	−23408.3			−1.51996			−0.759981	−	0.649945i	$-0.774792\pi$
$619$	−23408.3			−1.51996			−0.759981	+	0.649945i	$0.774792\pi$
$620$	1169.56			0.0757593
$621$	5975.17	−	20695.8i	0.386111	−	1.33735i
$622$		−	3335.37i		−	0.215010i
$623$	12501.0			0.803917
$624$	3943.41	+	2799.13i	0.252985	+	0.179575i
$625$	625.000			0.0400000
$626$	12196.7			0.778717
$627$	9704.77	+	2215.16i	0.618136	+	0.141092i
$628$	−6786.83			−0.431249
$629$	601.416			0.0381240
$630$	6617.79	−	2312.84i	0.418507	−	0.146263i
$631$	23718.7			1.49640			0.748200	−	0.663473i	$-0.230918\pi$
$631$	23718.7			1.49640			0.748200	+	0.663473i	$0.230918\pi$
$632$			5623.86i			0.353964i
$633$	24868.7	+	17652.4i	1.56152	+	1.10840i
$634$	−20369.0			−1.27595
$635$	−7189.57			−0.449306
$636$	1989.84	−	2803.29i	0.124060	−	0.174776i
$637$		−	19260.9i		−	1.19803i
$638$			5121.30i			0.317797i
$639$	−9740.40	−	27870.5i	−0.603011	−	1.72541i
$640$			640.000i			0.0395285i
$641$	−8452.72			−0.520846			−0.260423	−	0.965495i	$-0.583862\pi$
$641$	−8452.72			−0.520846			−0.260423	+	0.965495i	$0.583862\pi$
$642$	6385.71	−	8996.19i	0.392561	−	0.553039i
$643$	−22113.8			−1.35627			−0.678135	−	0.734937i	$-0.737212\pi$
$643$	−22113.8			−1.35627			−0.678135	+	0.734937i	$0.737212\pi$
$644$		−	15946.2i		−	0.975725i
$645$	−2371.10	−	1683.07i	−0.144747	−	0.102745i
$646$	−3181.54	−	7677.02i	−0.193771	−	0.467567i
$647$			30376.2i			1.84577i	0.385082	+	0.922883i	$0.374173\pi$
$647$			30376.2i			1.84577i	−0.385082	+	0.922883i	$0.625827\pi$
$648$	−4562.41	+	3632.72i	−0.276587	+	0.220226i
$649$			3207.41i			0.193994i
$650$			2908.32i			0.175498i
$651$	6433.49	+	4566.65i	0.387325	+	0.274932i
$652$	8171.90			0.490853
$653$			6862.48i			0.411255i	0.978630	+	0.205627i	$0.0659235\pi$
$653$			6862.48i			0.411255i	−0.978630	+	0.205627i	$0.934076\pi$
$654$	−11353.6	−	8059.09i	−0.678842	−	0.481859i
$655$	−7185.65			−0.428651
$656$	−3333.58			−0.198406
$657$	−4517.92	−	12927.3i	−0.268282	−	0.767642i
$658$			13356.8i			0.791338i
$659$	4672.30			0.276187			0.138093	−	0.990419i	$-0.455903\pi$
$659$	4672.30			0.276187			0.138093	+	0.990419i	$0.455903\pi$
$660$	−1391.43	+	1960.25i	−0.0820627	+	0.115610i
$661$		−	17433.0i		−	1.02581i	−0.858444	−	0.512907i	$-0.828568\pi$
$661$		−	17433.0i		−	1.02581i	0.858444	−	0.512907i	$-0.171432\pi$
$662$		−	9530.89i		−	0.559560i
$663$	8777.11	−	12365.2i	0.514140	−	0.724320i
$664$		−	5269.01i		−	0.307948i
$665$	4116.25	+	9932.46i	0.240032	+	0.579194i
$666$	611.076	−	213.564i	0.0355536	−	0.0124256i
$667$			16997.0i			0.986694i
$668$	6822.73			0.395179
$669$	1463.13	+	1038.56i	0.0845556	+	0.0600196i
$670$	1564.46			0.0902095
$671$		−	13338.0i		−	0.767376i
$672$	−2498.93	+	3520.49i	−0.143450	+	0.202092i
$673$		−	3592.04i		−	0.205740i	−0.994695	−	0.102870i	$-0.967197\pi$
$673$		−	3592.04i		−	0.205740i	0.994695	−	0.102870i	$-0.0328025\pi$
$674$		−	21266.8i		−	1.21538i
$675$	−3369.77	−	972.898i	−0.192152	−	0.0554768i
$676$	−4745.31			−0.269988
$677$	−23014.4			−1.30652			−0.653260	−	0.757133i	$-0.726599\pi$
$677$	−23014.4			−1.30652			−0.653260	+	0.757133i	$0.726599\pi$
$678$	9289.31	−	13086.8i	0.526186	−	0.741290i
$679$			39309.1i			2.22171i
$680$	2006.82			0.113174
$681$	−4590.23	+	6466.71i	−0.258294	+	0.363884i
$682$	−2705.36			−0.151897
$683$	−3158.45			−0.176947			−0.0884735	−	0.996079i	$-0.528199\pi$
$683$	−3158.45			−0.176947			−0.0884735	+	0.996079i	$0.528199\pi$
$684$	−5958.77	−	6670.56i	−0.333098	−	0.372888i
$685$	−7901.86			−0.440751
$686$	−616.140			−0.0342920
$687$	−9703.90	+	13670.9i	−0.538904	+	0.759208i
$688$	1790.69			0.0992289
$689$			9620.57i			0.531951i
$690$	−4617.99	+	6505.82i	−0.254788	+	0.358946i
$691$	−31700.5			−1.74522			−0.872609	−	0.488420i	$-0.837573\pi$
$691$	−31700.5			−1.74522			−0.872609	+	0.488420i	$0.837573\pi$
$692$	−10358.7			−0.569042
$693$	−15307.9	+	5349.92i	−0.839103	+	0.293256i
$694$			2463.88i			0.134766i
$695$		−	14397.5i		−	0.785799i
$696$	2663.60	−	3752.48i	0.145062	−	0.204364i
$697$			10453.0i			0.568056i
$698$	−18265.5			−0.990485
$699$	−20628.3	−	14642.4i	−1.11621	−	0.792315i
$700$	−2596.41			−0.140193
$701$		−	21202.2i		−	1.14236i	−0.820824	−	0.571181i	$-0.806485\pi$
$701$		−	21202.2i		−	1.14236i	0.820824	−	0.571181i	$-0.193515\pi$
$702$	4527.20	−	15680.6i	0.243402	−	0.843056i
$703$	380.088	+	917.147i	0.0203916	+	0.0492046i
$704$		−	1480.41i		−	0.0792543i
$705$	3868.10	−	5449.38i	0.206640	−	0.291114i
$706$			5816.98i			0.310092i
$707$		−	36635.0i		−	1.94880i
$708$	1668.18	−	2350.13i	0.0885510	−	0.124751i
$709$	9154.95			0.484938			0.242469	−	0.970159i	$-0.422043\pi$
$709$	9154.95			0.484938			0.242469	+	0.970159i	$0.422043\pi$
$710$			10934.6i			0.577986i
$711$	17917.8	−	6262.05i	0.945105	−	0.330303i
$712$	3851.77			0.202740
$713$	−8978.76			−0.471609
$714$	11039.1	+	7835.79i	0.578609	+	0.410710i
$715$		−	6727.34i		−	0.351872i
$716$	427.903			0.0223345
$717$	9121.69	+	6474.79i	0.475113	+	0.337246i
$718$			7004.95i			0.364098i
$719$		−	1688.03i		−	0.0875564i	−0.999041	−	0.0437782i	$-0.986061\pi$
$719$		−	1688.03i		−	0.0875564i	0.999041	−	0.0437782i	$-0.0139395\pi$
$720$	2039.06	−	712.627i	0.105543	−	0.0368861i
$721$		−	9937.73i		−	0.513315i
$722$	9696.60	−	9703.58i	0.499820	−	0.500180i
$723$	11181.0	+	7936.53i	0.575139	+	0.408247i
$724$		−	6578.01i		−	0.337666i
$725$	2767.51			0.141769
$726$	−4787.85	+	6745.12i	−0.244757	+	0.344814i
$727$	7106.99			0.362564			0.181282	−	0.983431i	$-0.441975\pi$
$727$	7106.99			0.362564			0.181282	+	0.983431i	$0.441975\pi$
$728$		−	12081.9i		−	0.615089i
$729$	16654.1	+	10491.0i	0.846116	+	0.532999i
$730$			5071.86i			0.257148i
$731$		−	5615.01i		−	0.284102i
$732$	−6937.14	+	9773.05i	−0.350279	+	0.493473i
$733$	7494.92			0.377669			0.188834	−	0.982009i	$-0.439529\pi$
$733$	7494.92			0.377669			0.188834	+	0.982009i	$0.439529\pi$
$734$	−23093.6			−1.16131
$735$	−7015.43	−	4979.72i	−0.352065	−	0.249905i
$736$		−	4913.29i		−	0.246068i
$737$	−3618.81			−0.180869
$738$	3711.87	+	10620.9i	0.185144	+	0.529757i
$739$	25847.8			1.28664			0.643320	−	0.765597i	$-0.277556\pi$
$739$	25847.8			1.28664			0.643320	+	0.765597i	$0.277556\pi$
$740$	−239.748			−0.0119099
$741$	24403.7	+	5570.25i	1.20984	+	0.276152i
$742$	−8588.79			−0.424939
$743$	−13250.6			−0.654265			−0.327133	−	0.944978i	$-0.606082\pi$
$743$	−13250.6			−0.654265			−0.327133	+	0.944978i	$0.606082\pi$
$744$	1982.27	+	1407.06i	0.0976796	+	0.0693353i
$745$	6825.17			0.335644
$746$			12872.9i			0.631784i
$747$	−16787.2	+	5866.93i	−0.822239	+	0.287363i
$748$	−4642.06			−0.226913
$749$	−27562.7			−1.34462
$750$	1059.30	+	751.918i	0.0515736	+	0.0366082i
$751$			15133.4i			0.735321i	0.929960	+	0.367661i	$0.119841\pi$
$751$			15133.4i			0.735321i	−0.929960	+	0.367661i	$0.880159\pi$
$752$			4115.45i			0.199568i
$753$	−16533.3	−	11735.7i	−0.800142	−	0.567960i
$754$			12878.1i			0.622005i
$755$	−6596.63			−0.317981
$756$	13998.9	+	4041.67i	0.673458	+	0.194437i
$757$	−35927.3			−1.72497			−0.862483	−	0.506086i	$-0.831092\pi$
$757$	−35927.3			−1.72497			−0.862483	+	0.506086i	$0.831092\pi$
$758$		−	3558.74i		−	0.170527i
$759$	10682.0	−	15048.9i	0.510848	−	0.719683i
$760$	1268.29	+	3060.37i	0.0605338	+	0.146067i
$761$		−	19449.5i		−	0.926470i	−0.886235	−	0.463235i	$-0.846689\pi$
$761$		−	19449.5i		−	0.926470i	0.886235	−	0.463235i	$-0.153311\pi$
$762$	−12185.5	−	8649.54i	−0.579308	−	0.411207i
$763$			34785.6i			1.65049i
$764$		−	1738.64i		−	0.0823320i
$765$	−2234.56	−	6393.80i	−0.105609	−	0.302181i
$766$	−8330.56			−0.392944
$767$			8065.38i			0.379692i
$768$	−769.964	+	1084.72i	−0.0361767	+	0.0509657i
$769$	−33564.3			−1.57394			−0.786971	−	0.616991i	$-0.788352\pi$
$769$	−33564.3			−1.57394			−0.786971	+	0.616991i	$0.788352\pi$
$770$	6005.86			0.281086
$771$	−16547.7	+	23312.4i	−0.772958	+	1.08894i
$772$		−	3796.35i		−	0.176987i
$773$	6946.21			0.323205			0.161603	−	0.986856i	$-0.448334\pi$
$773$	6946.21			0.323205			0.161603	+	0.986856i	$0.448334\pi$
$774$	−1993.90	−	5705.20i	−0.0925958	−	0.264947i
$775$			1461.95i			0.0677612i
$776$			12111.8i			0.560295i
$777$	−1318.80	−	936.115i	−0.0608901	−	0.0432213i
$778$			27290.3i			1.25759i
$779$	−15940.6	+	6606.17i	−0.733159	+	0.303839i
$780$	−3498.91	+	4929.26i	−0.160617	+	0.226277i
$781$		−	25293.3i		−	1.15886i
$782$	−15406.4			−0.704518
$783$	−14921.4	−	4308.00i	−0.681030	−	0.196623i
$784$	5298.16			0.241352
$785$		−	8483.54i		−	0.385721i
$786$	−12178.8	−	8644.83i	−0.552677	−	0.392304i
$787$			32763.8i			1.48400i	0.670403	+	0.741998i	$0.266121\pi$
$787$			32763.8i			1.48400i	−0.670403	+	0.741998i	$0.733879\pi$
$788$			5803.40i			0.262357i
$789$	−15260.7	−	10832.4i	−0.688586	−	0.488775i
$790$	−7029.83			−0.316595
$791$	−40095.6			−1.80232
$792$	−4716.63	+	1648.40i	−0.211614	+	0.0739564i
$793$		−	33540.0i		−	1.50194i
$794$	−2510.22			−0.112197
$795$	3504.12	+	2487.31i	0.156325	+	0.110963i
$796$	−13296.6			−0.592068
$797$	19292.5			0.857436			0.428718	−	0.903438i	$-0.358965\pi$
$797$	19292.5			0.857436			0.428718	+	0.903438i	$0.358965\pi$
$798$	−4972.86	+	21786.5i	−0.220598	+	0.966458i
$799$	12904.7			0.571382
$800$	−800.000			−0.0353553
$801$	−4288.86	−	12271.9i	−0.189188	−	0.541329i
$802$	3099.07			0.136449
$803$		−	11731.9i		−	0.515579i
$804$	2651.57	+	1882.15i	0.116311	+	0.0825602i
$805$	19932.7			0.872715
$806$	−6802.93			−0.297299
$807$	−20234.5	+	28506.3i	−0.882636	+	1.24346i
$808$		−	11287.9i		−	0.491469i
$809$			41116.0i			1.78685i	0.449211	+	0.893426i	$0.351705\pi$
$809$			41116.0i			1.78685i	−0.449211	+	0.893426i	$0.648295\pi$
$810$	−4540.90	−	5703.01i	−0.196976	−	0.247387i
$811$		−	6822.43i		−	0.295398i	−0.989032	−	0.147699i	$-0.952813\pi$
$811$		−	6822.43i		−	0.295398i	0.989032	−	0.147699i	$-0.0471867\pi$
$812$	−11496.9			−0.496876
$813$	23382.7	−	32941.6i	1.00869	−	1.42105i
$814$	554.571			0.0238792
$815$			10214.9i			0.439033i
$816$	3401.33	+	2414.35i	0.145920	+	0.103577i
$817$	8562.77	−	3548.62i	0.366675	−	0.151959i
$818$		−	21589.6i		−	0.922815i
$819$	−38493.3	+	13452.9i	−1.64233	+	0.573973i
$820$		−	4166.98i		−	0.177460i
$821$			36561.8i			1.55422i	0.629363	+	0.777112i	$0.283316\pi$
$821$			36561.8i			1.55422i	−0.629363	+	0.777112i	$0.716684\pi$
$822$	−13392.7	−	9506.48i	−0.568278	−	0.403378i
$823$	−16480.2			−0.698012			−0.349006	−	0.937120i	$-0.613481\pi$
$823$	−16480.2			−0.698012			−0.349006	+	0.937120i	$0.613481\pi$
$824$		−	3061.99i		−	0.129453i
$825$	−2450.31	−	1739.29i	−0.103405	−	0.0733991i
$826$	−7200.39			−0.303310
$827$	18317.9			0.770223			0.385111	−	0.922870i	$-0.374163\pi$
$827$	18317.9			0.770223			0.385111	+	0.922870i	$0.374163\pi$
$828$	−15653.9	+	5470.85i	−0.657018	+	0.229620i
$829$		−	312.485i		−	0.0130917i	−0.999979	−	0.00654587i	$-0.997916\pi$
$829$		−	312.485i		−	0.0130917i	0.999979	−	0.00654587i	$-0.00208363\pi$
$830$	6586.26			0.275437
$831$	−16403.0	+	23108.6i	−0.684735	+	0.964655i
$832$		−	3722.65i		−	0.155120i
$833$		−	16613.2i		−	0.691014i
$834$	17321.2	−	24402.2i	0.719167	−	1.01316i
$835$			8528.41i			0.353458i
$836$	−2933.73	−	7079.05i	−0.121370	−	0.292864i
$837$	2275.73	−	7882.32i	0.0939795	−	0.325511i
$838$			614.213i			0.0253194i
$839$	26576.9			1.09361			0.546804	−	0.837260i	$-0.315844\pi$
$839$	26576.9			1.09361			0.546804	+	0.837260i	$0.315844\pi$
$840$	−4400.61	−	3123.66i	−0.180757	−	0.128305i
$841$	−12134.5			−0.497538
$842$			7890.43i			0.322948i
$843$	−6541.80	+	9216.08i	−0.267273	+	0.376535i
$844$		−	23476.5i		−	0.957456i
$845$		−	5931.64i		−	0.241485i
$846$	13112.0	−	4582.47i	0.532859	−	0.186228i
$847$	20665.8			0.838355
$848$	−2646.36			−0.107166
$849$	−16341.6	+	23022.0i	−0.660590	+	0.930639i
$850$			2508.53i			0.101226i
$851$	1840.55			0.0741402
$852$	−13155.1	+	18532.9i	−0.528976	+	0.745221i
$853$	−12349.3			−0.495699			−0.247850	−	0.968798i	$-0.579724\pi$
$853$	−12349.3			−0.495699			−0.247850	+	0.968798i	$0.579724\pi$
$854$	29942.9			1.19979
$855$	8338.20	−	7448.46i	0.333521	−	0.297932i
$856$	−8492.57			−0.339100
$857$	−2704.97			−0.107818			−0.0539091	−	0.998546i	$-0.517168\pi$
$857$	−2704.97			−0.107818			−0.0539091	+	0.998546i	$0.517168\pi$
$858$	8093.45	−	11402.1i	0.322035	−	0.453683i
$859$	−42528.2			−1.68923			−0.844613	−	0.535377i	$-0.820169\pi$
$859$	−42528.2			−1.68923			−0.844613	+	0.535377i	$0.820169\pi$
$860$			2238.37i			0.0887530i
$861$	16270.3	−	22921.6i	0.644006	−	0.907276i
$862$	−9319.58			−0.368244
$863$	−9986.02			−0.393891			−0.196946	−	0.980414i	$-0.563102\pi$
$863$	−9986.02			−0.393891			−0.196946	+	0.980414i	$0.563102\pi$
$864$	4313.30	+	1245.31i	0.169840	+	0.0490351i
$865$		−	12948.3i		−	0.508967i
$866$		−	168.617i		−	0.00661642i
$867$	−7206.11	+	10152.0i	−0.282275	+	0.397669i
$868$		−	6073.33i		−	0.237491i
$869$	16261.0			0.634770
$870$	4690.60	+	3329.50i	0.182789	+	0.129748i
$871$	−9099.89			−0.354005
$872$			10718.1i			0.416237i
$873$	38588.6	−	13486.3i	1.49602	−	0.522841i
$874$	−9736.69	−	23494.5i	−0.376829	−	0.909283i
$875$		−	3245.51i		−	0.125392i
$876$	−6101.79	+	8596.20i	−0.235343	+	0.331551i
$877$			22352.6i			0.860653i	0.902673	+	0.430327i	$0.141602\pi$
$877$			22352.6i			0.860653i	−0.902673	+	0.430327i	$0.858398\pi$
$878$		−	25155.4i		−	0.966916i
$879$	−20397.8	+	28736.4i	−0.782709	+	1.10268i
$880$	1850.51			0.0708872
$881$			27588.4i			1.05502i	0.849548	+	0.527512i	$0.176875\pi$
$881$			27588.4i			1.05502i	−0.849548	+	0.527512i	$0.823125\pi$
$882$	−5899.39	−	16880.1i	−0.225218	−	0.644424i
$883$	−26845.4			−1.02312			−0.511562	−	0.859246i	$-0.670933\pi$
$883$	−26845.4			−1.02312			−0.511562	+	0.859246i	$0.670933\pi$
$884$	−11673.0			−0.444123
$885$	2937.67	+	2085.23i	0.111580	+	0.0792024i
$886$			15341.4i			0.581719i
$887$	18932.5			0.716677			0.358338	−	0.933592i	$-0.383343\pi$
$887$	18932.5			0.716677			0.358338	+	0.933592i	$0.383343\pi$
$888$	−406.345	−	288.434i	−0.0153559	−	0.0109000i
$889$			37334.1i			1.40849i
$890$			4814.71i			0.181336i
$891$	10503.7	+	13191.9i	0.394936	+	0.496009i
$892$		−	1381.22i		−	0.0518459i
$893$	8155.61	+	19679.4i	0.305618	+	0.737452i
$894$	11567.9	+	8211.15i	0.432760	+	0.307183i
$895$			534.879i			0.0199766i
$896$	3323.41			0.123914
$897$	26861.2	−	37842.0i	0.999853	−	1.40859i
$898$	17324.8			0.643804
$899$			6473.55i			0.240161i
$900$	890.783	+	2548.82i	0.0329920	+	0.0944009i
$901$			8298.09i			0.306825i
$902$			9638.80i			0.355806i
$903$	−8739.86	+	12312.7i	−0.322087	+	0.453756i
$904$	−12354.2			−0.454528
$905$	8222.51			0.302017
$906$	−11180.5	−	7936.20i	−0.409986	−	0.291018i
$907$			47316.4i			1.73221i	0.499861	+	0.866106i	$0.333385\pi$
$907$			47316.4i			1.73221i	−0.499861	+	0.866106i	$0.666615\pi$
$908$	6104.69			0.223118
$909$	−35963.6	+	12568.8i	−1.31225	+	0.458616i
$910$	15102.4			0.550153
$911$	−19239.4			−0.699703			−0.349851	−	0.936805i	$-0.613768\pi$
$911$	−19239.4			−0.699703			−0.349851	+	0.936805i	$0.613768\pi$
$912$	−1532.23	+	6712.80i	−0.0556328	+	0.243731i
$913$	−15234.9			−0.552248
$914$	37041.9			1.34052
$915$	−12216.3	−	8671.43i	−0.441376	−	0.313299i
$916$	12905.5			0.465514
$917$			37313.8i			1.34374i
$918$	3904.87	−	13525.1i	0.140392	−	0.486268i
$919$	14320.3			0.514019			0.257009	−	0.966409i	$-0.417263\pi$
$919$	14320.3			0.514019			0.257009	+	0.966409i	$0.417263\pi$
$920$	6141.62			0.220090
$921$	−31414.4	−	22298.7i	−1.12393	−	0.797792i
$922$		−	21475.6i		−	0.767096i
$923$		−	63602.9i		−	2.26816i
$924$	10179.2	+	7225.46i	0.362415	+	0.257251i
$925$		−	299.685i		−	0.0106525i
$926$	32257.2			1.14475
$927$	−9755.59	+	3409.46i	−0.345648	+	0.120800i
$928$	−3542.41			−0.125307
$929$		−	9405.31i		−	0.332162i	−0.986112	−	0.166081i	$-0.946889\pi$
$929$		−	9405.31i		−	0.332162i	0.986112	−	0.166081i	$-0.0531113\pi$
$930$	−1758.83	+	2477.84i	−0.0620154	+	0.0873673i
$931$	25334.8	−	10499.4i	0.891854	−	0.369606i
$932$			19473.5i			0.684415i
$933$	7066.34	+	5015.86i	0.247954	+	0.176004i
$934$			4896.42i			0.171537i
$935$		−	5802.58i		−	0.202957i
$936$	−11860.5	+	4145.09i	−0.414179	+	0.144751i
$937$	18063.6			0.629790			0.314895	−	0.949126i	$-0.398031\pi$
$937$	18063.6			0.629790			0.314895	+	0.949126i	$0.398031\pi$
$938$		−	8123.96i		−	0.282790i
$939$	−18341.8	+	25839.9i	−0.637445	+	0.898033i
$940$	−5144.31			−0.178499
$941$	10662.6			0.369386			0.184693	−	0.982796i	$-0.440871\pi$
$941$	10662.6			0.369386			0.184693	+	0.982796i	$0.440871\pi$
$942$	10206.3	−	14378.6i	0.353013	−	0.497325i
$943$			31990.0i			1.10471i
$944$	−2218.57			−0.0764918
$945$	−5052.09	+	17498.6i	−0.173909	+	0.602360i
$946$		−	5177.65i		−	0.177949i
$947$		−	32760.2i		−	1.12414i	−0.827089	−	0.562072i	$-0.810005\pi$
$947$		−	32760.2i		−	1.12414i	0.827089	−	0.562072i	$-0.189995\pi$
$948$	−11914.7	−	8457.36i	−0.408199	−	0.289749i
$949$		−	29501.2i		−	1.00911i
$950$	−3825.46	+	1585.36i	−0.130647	+	0.0541431i
$951$	30631.6	−	43153.7i	1.04448	−	1.47146i
$952$		−	10421.1i		−	0.354778i
$953$	−58609.6			−1.99218			−0.996092	−	0.0883161i	$-0.971851\pi$
$953$	−58609.6			−1.99218			−0.996092	+	0.0883161i	$0.971851\pi$
$954$	2946.67	+	8431.38i	0.100002	+	0.286138i
$955$	2173.29			0.0736400
$956$		−	8611.04i		−	0.291319i
$957$	−10850.0	−	7701.59i	−0.366490	−	0.260143i
$958$		−	12727.8i		−	0.429244i
$959$			41032.9i			1.38167i
$960$	−1355.91	−	962.455i	−0.0455851	−	0.0323574i
$961$	26371.3			0.885210
$962$	1394.53			0.0467375
$963$	9456.29	+	27057.6i	0.316433	+	0.905419i
$964$		−	10555.1i		−	0.352651i
$965$	4745.44			0.158302
$966$	33783.6	+	23980.4i	1.12523	+	0.798713i
$967$	3422.06			0.113802			0.0569008	−	0.998380i	$-0.481878\pi$
$967$	3422.06			0.113802			0.0569008	+	0.998380i	$0.481878\pi$
$968$	6367.51			0.211425
$969$	21049.1	+	4804.55i	0.697826	+	0.159282i
$970$	−15139.8			−0.501143
$971$	−29893.3			−0.987973			−0.493986	−	0.869470i	$-0.664461\pi$
$971$	−29893.3			−0.987973			−0.493986	+	0.869470i	$0.664461\pi$
$972$	−835.179	−	15128.9i	−0.0275601	−	0.499240i
$973$	−74763.9			−2.46333
$974$			28381.8i			0.933686i
$975$	−6161.57	−	4373.63i	−0.202388	−	0.143660i
$976$	9225.94			0.302577
$977$	10890.7			0.356628			0.178314	−	0.983974i	$-0.442936\pi$
$977$	10890.7			0.356628			0.178314	+	0.983974i	$0.442936\pi$
$978$	−12289.2	+	17313.0i	−0.401805	+	0.566063i
$979$		−	11137.1i		−	0.363578i
$980$			6622.70i			0.215872i
$981$	34148.0	−	11934.3i	1.11138	−	0.388414i
$982$		−	1347.99i		−	0.0438046i
$983$	4638.20			0.150494			0.0752471	−	0.997165i	$-0.476025\pi$
$983$	4638.20			0.150494			0.0752471	+	0.997165i	$0.476025\pi$
$984$	5013.16	−	7062.54i	0.162412	−	0.228806i
$985$	−7254.24			−0.234659
$986$			11107.8i			0.358767i
$987$	−28297.7	−	20086.4i	−0.912588	−	0.647777i
$988$	−7377.18	−	17801.0i	−0.237550	−	0.573205i
$989$		−	17184.0i		−	0.552496i
$990$	−2060.50	−	5895.78i	−0.0661486	−	0.189273i
$991$		−	56562.6i		−	1.81309i	−0.422113	−	0.906543i	$-0.638711\pi$
$991$		−	56562.6i		−	1.81309i	0.422113	−	0.906543i	$-0.361289\pi$
$992$		−	1871.30i		−	0.0598930i
$993$	20192.2	+	14332.9i	0.645296	+	0.458047i
$994$	56781.7			1.81188
$995$		−	16620.8i		−	0.529561i
$996$	11162.9	+	7923.72i	0.355132	+	0.252081i
$997$	−26733.8			−0.849215			−0.424607	−	0.905378i	$-0.639588\pi$
$997$	−26733.8			−0.849215			−0.424607	+	0.905378i	$0.639588\pi$
$998$	10411.3			0.330223
$999$	−466.501	+	1615.79i	−0.0147742	+	0.0511726i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.4.f.b.341.12	yes	40
3.2	odd	2		570.4.f.a.341.30	yes	40
19.18	odd	2		570.4.f.a.341.29	✓	40
57.56	even	2	inner	570.4.f.b.341.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.4.f.a.341.29	✓	40	19.18	odd	2
570.4.f.a.341.30	yes	40	3.2	odd	2
570.4.f.b.341.11	yes	40	57.56	even	2	inner
570.4.f.b.341.12	yes	40	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	570.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +(-3.00767 + 4.23721i) q^{3} +4.00000 q^{4} +5.00000i q^{5} +(-6.01534 + 8.47441i) q^{6} +25.9641 q^{7} +8.00000 q^{8} +(-8.90783 - 25.4882i) q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +(-3.00767 + 4.23721i) q^{3} +4.00000 q^{4} +5.00000i q^{5} +(-6.01534 + 8.47441i) q^{6} +25.9641 q^{7} +8.00000 q^{8} +(-8.90783 - 25.4882i) q^{9} +10.0000i q^{10} -23.1314i q^{11} +(-12.0307 + 16.9488i) q^{12} -58.1664i q^{13} +51.9282 q^{14} +(-21.1860 - 15.0384i) q^{15} +16.0000 q^{16} -50.1706i q^{17} +(-17.8157 - 50.9765i) q^{18} +(76.5091 - 31.7073i) q^{19} +20.0000i q^{20} +(-78.0915 + 110.015i) q^{21} -46.2628i q^{22} -153.540i q^{23} +(-24.0614 + 33.8976i) q^{24} -25.0000 q^{25} -116.333i q^{26} +(134.791 + 38.9159i) q^{27} +103.856 q^{28} -110.700 q^{29} +(-42.3721 - 30.0767i) q^{30} -58.4782i q^{31} +32.0000 q^{32} +(98.0124 + 69.5716i) q^{33} -100.341i q^{34} +129.821i q^{35} +(-35.6313 - 101.953i) q^{36} +11.9874i q^{37} +(153.018 - 63.4145i) q^{38} +(246.463 + 174.945i) q^{39} +40.0000i q^{40} -208.349 q^{41} +(-156.183 + 220.031i) q^{42} +111.918 q^{43} -92.5255i q^{44} +(127.441 - 44.5392i) q^{45} -307.081i q^{46} +257.216i q^{47} +(-48.1227 + 67.7953i) q^{48} +331.135 q^{49} -50.0000 q^{50} +(212.583 + 150.897i) q^{51} -232.666i q^{52} -165.397 q^{53} +(269.582 + 77.8319i) q^{54} +115.657 q^{55} +207.713 q^{56} +(-95.7642 + 419.550i) q^{57} -221.401 q^{58} -138.661 q^{59} +(-84.7441 - 60.1534i) q^{60} +576.621 q^{61} -116.956i q^{62} +(-231.284 - 661.779i) q^{63} +64.0000 q^{64} +290.832 q^{65} +(196.025 + 139.143i) q^{66} -156.446i q^{67} -200.682i q^{68} +(650.582 + 461.799i) q^{69} +259.641i q^{70} +1093.46 q^{71} +(-71.2627 - 203.906i) q^{72} +507.186 q^{73} +23.9748i q^{74} +(75.1918 - 105.930i) q^{75} +(306.037 - 126.829i) q^{76} -600.586i q^{77} +(492.926 + 349.891i) q^{78} +702.983i q^{79} +80.0000i q^{80} +(-570.301 + 454.090i) q^{81} -416.698 q^{82} -658.626i q^{83} +(-312.366 + 440.061i) q^{84} +250.853 q^{85} +223.837 q^{86} +(332.950 - 469.060i) q^{87} -185.051i q^{88} +481.471 q^{89} +(254.882 - 89.0783i) q^{90} -1510.24i q^{91} -614.162i q^{92} +(247.784 + 175.883i) q^{93} +514.431i q^{94} +(158.536 + 382.546i) q^{95} +(-96.2455 + 135.591i) q^{96} +1513.98i q^{97} +662.270 q^{98} +(-589.578 + 206.050i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 80 q^{2} + 10 q^{3} + 160 q^{4} + 20 q^{6} - 20 q^{7} + 320 q^{8} + 10 q^{9}+O(q^{10}) \) 40 * q + 80 * q^2 + 10 * q^3 + 160 * q^4 + 20 * q^6 - 20 * q^7 + 320 * q^8 + 10 * q^9	\( 40 q + 80 q^{2} + 10 q^{3} + 160 q^{4} + 20 q^{6} - 20 q^{7} + 320 q^{8} + 10 q^{9} + 40 q^{12} - 40 q^{14} + 640 q^{16} + 20 q^{18} + 68 q^{19} - 78 q^{21} + 80 q^{24} - 1000 q^{25} + 292 q^{27} - 80 q^{28} - 60 q^{29} + 1280 q^{32} + 440 q^{33} + 40 q^{36} + 136 q^{38} - 634 q^{39} + 888 q^{41} - 156 q^{42} + 488 q^{43} + 160 q^{45} + 160 q^{48} + 924 q^{49} - 2000 q^{50} + 2098 q^{51} - 108 q^{53} + 584 q^{54} - 160 q^{56} + 1562 q^{57} - 120 q^{58} + 132 q^{59} - 1496 q^{61} + 762 q^{63} + 2560 q^{64} + 120 q^{65} + 880 q^{66} - 1222 q^{69} - 1128 q^{71} + 80 q^{72} - 316 q^{73} - 250 q^{75} + 272 q^{76} - 1268 q^{78} - 942 q^{81} + 1776 q^{82} - 312 q^{84} + 976 q^{86} + 1830 q^{87} + 1776 q^{89} + 320 q^{90} - 1568 q^{93} - 660 q^{95} + 320 q^{96} + 1848 q^{98} - 4016 q^{99}+O(q^{100}) \) 40 * q + 80 * q^2 + 10 * q^3 + 160 * q^4 + 20 * q^6 - 20 * q^7 + 320 * q^8 + 10 * q^9 + 40 * q^12 - 40 * q^14 + 640 * q^16 + 20 * q^18 + 68 * q^19 - 78 * q^21 + 80 * q^24 - 1000 * q^25 + 292 * q^27 - 80 * q^28 - 60 * q^29 + 1280 * q^32 + 440 * q^33 + 40 * q^36 + 136 * q^38 - 634 * q^39 + 888 * q^41 - 156 * q^42 + 488 * q^43 + 160 * q^45 + 160 * q^48 + 924 * q^49 - 2000 * q^50 + 2098 * q^51 - 108 * q^53 + 584 * q^54 - 160 * q^56 + 1562 * q^57 - 120 * q^58 + 132 * q^59 - 1496 * q^61 + 762 * q^63 + 2560 * q^64 + 120 * q^65 + 880 * q^66 - 1222 * q^69 - 1128 * q^71 + 80 * q^72 - 316 * q^73 - 250 * q^75 + 272 * q^76 - 1268 * q^78 - 942 * q^81 + 1776 * q^82 - 312 * q^84 + 976 * q^86 + 1830 * q^87 + 1776 * q^89 + 320 * q^90 - 1568 * q^93 - 660 * q^95 + 320 * q^96 + 1848 * q^98 - 4016 * q^99

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