LMFDB - Embedded newform 76.4.k.a.3.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [76,4,Mod(3,76)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(76, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 13]))

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

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

chi := DirichletCharacter("76.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 76 = 2^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	76.k (of order $18$, degree $6$, 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:	$4.48414516044$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$28$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			3.15
Character	$\chi$	$=$	76.3
Dual form			76.4.k.a.51.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0378098 + 2.82817i) q^{2} +(2.57091 - 0.935735i) q^{3} +(-7.99714 - 0.213866i) q^{4} +(-1.56986 + 8.90313i) q^{5} +(2.54921 + 7.30636i) q^{6} +(-16.8987 + 9.75650i) q^{7} +(0.907220 - 22.6092i) q^{8} +(-14.9492 + 12.5439i) q^{9} +O(q^{10})$	\(q+(-0.0378098 + 2.82817i) q^{2} +(2.57091 - 0.935735i) q^{3} +(-7.99714 - 0.213866i) q^{4} +(-1.56986 + 8.90313i) q^{5} +(2.54921 + 7.30636i) q^{6} +(-16.8987 + 9.75650i) q^{7} +(0.907220 - 22.6092i) q^{8} +(-14.9492 + 12.5439i) q^{9} +(-25.1202 - 4.77647i) q^{10} +(44.7480 + 25.8353i) q^{11} +(-20.7600 + 6.93337i) q^{12} +(-18.1005 + 49.7308i) q^{13} +(-26.9541 - 48.1615i) q^{14} +(4.29499 + 24.3581i) q^{15} +(63.9085 + 3.42063i) q^{16} +(-104.717 - 87.8680i) q^{17} +(-34.9111 - 42.7533i) q^{18} +(64.2076 - 52.3104i) q^{19} +(14.4585 - 70.8638i) q^{20} +(-34.3157 + 40.8958i) q^{21} +(-74.7586 + 125.578i) q^{22} +(101.067 - 17.8209i) q^{23} +(-18.8239 - 58.9752i) q^{24} +(40.6603 + 14.7992i) q^{25} +(-139.963 - 53.0717i) q^{26} +(-63.6301 + 110.211i) q^{27} +(137.228 - 74.4100i) q^{28} +(179.400 + 213.801i) q^{29} +(-69.0514 + 11.2260i) q^{30} +(30.7849 + 53.3210i) q^{31} +(-12.0905 + 180.615i) q^{32} +(139.218 + 24.5479i) q^{33} +(252.465 - 292.836i) q^{34} +(-60.3346 - 165.768i) q^{35} +(122.234 - 97.1181i) q^{36} -126.535i q^{37} +(145.515 + 183.568i) q^{38} +144.791i q^{39} +(199.869 + 43.5705i) q^{40} +(5.64850 + 15.5191i) q^{41} +(-114.363 - 98.5969i) q^{42} +(308.578 + 54.4106i) q^{43} +(-352.331 - 216.179i) q^{44} +(-88.2116 - 152.787i) q^{45} +(46.5792 + 286.509i) q^{46} +(-77.9316 - 92.8752i) q^{47} +(167.504 - 51.0073i) q^{48} +(18.8784 - 32.6984i) q^{49} +(-43.3919 + 114.435i) q^{50} +(-351.439 - 127.913i) q^{51} +(155.388 - 393.833i) q^{52} +(-227.255 + 40.0712i) q^{53} +(-309.289 - 184.124i) q^{54} +(-300.263 + 357.840i) q^{55} +(205.256 + 390.919i) q^{56} +(116.123 - 194.567i) q^{57} +(-611.449 + 499.291i) q^{58} +(-370.549 - 310.928i) q^{59} +(-29.1383 - 195.714i) q^{60} +(33.0594 + 187.489i) q^{61} +(-151.965 + 85.0490i) q^{62} +(130.239 - 357.828i) q^{63} +(-510.354 - 41.0231i) q^{64} +(-414.344 - 239.222i) q^{65} +(-74.6896 + 392.805i) q^{66} +(472.421 - 396.409i) q^{67} +(818.645 + 725.088i) q^{68} +(243.159 - 140.388i) q^{69} +(471.102 - 164.369i) q^{70} +(-19.6586 + 111.490i) q^{71} +(270.045 + 349.370i) q^{72} +(413.529 - 150.512i) q^{73} +(357.862 + 4.78425i) q^{74} +118.382 q^{75} +(-524.665 + 404.602i) q^{76} -1008.25 q^{77} +(-409.493 - 5.47451i) q^{78} +(-782.608 + 284.846i) q^{79} +(-130.782 + 563.616i) q^{80} +(31.0359 - 176.013i) q^{81} +(-44.1044 + 15.3882i) q^{82} +(-608.348 + 351.230i) q^{83} +(283.173 - 319.711i) q^{84} +(946.691 - 794.368i) q^{85} +(-165.550 + 870.655i) q^{86} +(661.283 + 381.792i) q^{87} +(624.712 - 988.280i) q^{88} +(-243.556 + 669.166i) q^{89} +(435.444 - 243.701i) q^{90} +(-179.322 - 1016.99i) q^{91} +(-812.059 + 120.901i) q^{92} +(129.040 + 108.277i) q^{93} +(265.614 - 216.892i) q^{94} +(364.929 + 653.769i) q^{95} +(137.924 + 475.659i) q^{96} +(-366.498 + 436.776i) q^{97} +(91.7630 + 54.6278i) q^{98} +(-993.024 + 175.097i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 6 q^{2} - 24 q^{4} - 12 q^{5} - 24 q^{6} - 9 q^{8} + 18 q^{9}+O(q^{10}) $ 168 * q - 6 * q^2 - 24 * q^4 - 12 * q^5 - 24 * q^6 - 9 * q^8 + 18 * q^9	$ 168 q - 6 q^{2} - 24 q^{4} - 12 q^{5} - 24 q^{6} - 9 q^{8} + 18 q^{9} - 105 q^{10} - 9 q^{12} - 120 q^{13} + 69 q^{14} + 192 q^{16} - 12 q^{17} + 558 q^{20} + 6 q^{21} - 30 q^{22} + 96 q^{24} - 12 q^{25} - 411 q^{26} + 756 q^{28} - 12 q^{29} + 276 q^{30} - 471 q^{32} - 576 q^{33} + 36 q^{34} - 2673 q^{36} - 648 q^{38} - 2298 q^{40} - 606 q^{41} - 321 q^{42} - 1203 q^{44} - 6 q^{45} + 1566 q^{46} + 3237 q^{48} + 2346 q^{49} + 3204 q^{50} + 1077 q^{52} + 576 q^{53} - 627 q^{54} - 12 q^{57} - 4116 q^{58} + 90 q^{60} + 3528 q^{61} - 3300 q^{62} - 381 q^{64} + 1242 q^{65} + 276 q^{66} + 1170 q^{68} - 4770 q^{69} + 1449 q^{70} + 1146 q^{72} - 3468 q^{73} + 3105 q^{74} + 4386 q^{76} - 9396 q^{77} + 6939 q^{78} + 2133 q^{80} + 1980 q^{81} + 7299 q^{82} + 315 q^{84} - 516 q^{85} - 3804 q^{86} - 5841 q^{88} + 3576 q^{89} - 8898 q^{90} - 7668 q^{92} + 5694 q^{93} + 18942 q^{96} + 774 q^{97} + 8745 q^{98}+O(q^{100}) $ 168 * q - 6 * q^2 - 24 * q^4 - 12 * q^5 - 24 * q^6 - 9 * q^8 + 18 * q^9 - 105 * q^10 - 9 * q^12 - 120 * q^13 + 69 * q^14 + 192 * q^16 - 12 * q^17 + 558 * q^20 + 6 * q^21 - 30 * q^22 + 96 * q^24 - 12 * q^25 - 411 * q^26 + 756 * q^28 - 12 * q^29 + 276 * q^30 - 471 * q^32 - 576 * q^33 + 36 * q^34 - 2673 * q^36 - 648 * q^38 - 2298 * q^40 - 606 * q^41 - 321 * q^42 - 1203 * q^44 - 6 * q^45 + 1566 * q^46 + 3237 * q^48 + 2346 * q^49 + 3204 * q^50 + 1077 * q^52 + 576 * q^53 - 627 * q^54 - 12 * q^57 - 4116 * q^58 + 90 * q^60 + 3528 * q^61 - 3300 * q^62 - 381 * q^64 + 1242 * q^65 + 276 * q^66 + 1170 * q^68 - 4770 * q^69 + 1449 * q^70 + 1146 * q^72 - 3468 * q^73 + 3105 * q^74 + 4386 * q^76 - 9396 * q^77 + 6939 * q^78 + 2133 * q^80 + 1980 * q^81 + 7299 * q^82 + 315 * q^84 - 516 * q^85 - 3804 * q^86 - 5841 * q^88 + 3576 * q^89 - 8898 * q^90 - 7668 * q^92 + 5694 * q^93 + 18942 * q^96 + 774 * q^97 + 8745 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/76\mathbb{Z}\right)^\times$.

$n$	$21$	$39$
$\chi(n)$	$e\left(\frac{13}{18}\right)$	$-1$

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 $

$2$	−0.0378098	+	2.82817i	−0.0133678	+	0.999911i
$2$	−0.0378098	+	2.82817i	−0.0133678	+	0.999911i
$3$	2.57091	−	0.935735i	0.494772	−	0.180082i	−0.0825692	−	0.996585i	$-0.526313\pi$
$3$	2.57091	−	0.935735i	0.494772	−	0.180082i	0.577341	+	0.816503i	$0.304090\pi$
$4$	−7.99714	−	0.213866i	−0.999643	−	0.0267332i
$5$	−1.56986	+	8.90313i	−0.140413	+	0.796320i	0.830524	+	0.556983i	$0.188041\pi$
$5$	−1.56986	+	8.90313i	−0.140413	+	0.796320i	−0.970937	+	0.239337i	$0.923070\pi$
$6$	2.54921	+	7.30636i	0.173452	+	0.497135i
$7$	−16.8987	+	9.75650i	−0.912447	+	0.526801i	−0.881218	−	0.472711i	$-0.843275\pi$
$7$	−16.8987	+	9.75650i	−0.912447	+	0.526801i	−0.0312291	+	0.999512i	$0.509942\pi$
$8$	0.907220	−	22.6092i	0.0400938	−	0.999196i
$9$	−14.9492	+	12.5439i	−0.553675	+	0.464588i
$10$	−25.1202	−	4.77647i	−0.794372	−	0.151045i
$11$	44.7480	+	25.8353i	1.22655	+	0.708149i	0.966306	−	0.257394i	$-0.0828640\pi$
$11$	44.7480	+	25.8353i	1.22655	+	0.708149i	0.260243	+	0.965543i	$0.416197\pi$
$12$	−20.7600	+	6.93337i	−0.499409	+	0.166791i
$13$	−18.1005	+	49.7308i	−0.386168	+	1.06099i	0.582544	+	0.812799i	$0.302057\pi$
$13$	−18.1005	+	49.7308i	−0.386168	+	1.06099i	−0.968712	+	0.248188i	$0.920165\pi$
$14$	−26.9541	−	48.1615i	−0.514557	−	0.919407i
$15$	4.29499	+	24.3581i	0.0739308	+	0.419283i
$16$	63.9085	+	3.42063i	0.998571	+	0.0534473i
$17$	−104.717	−	87.8680i	−1.49398	−	1.25360i	−0.889469	−	0.456996i	$-0.848925\pi$
$17$	−104.717	−	87.8680i	−1.49398	−	1.25360i	−0.604508	−	0.796599i	$-0.706630\pi$
$18$	−34.9111	−	42.7533i	−0.457146	−	0.559836i
$19$	64.2076	−	52.3104i	0.775276	−	0.631623i
$19$	64.2076	−	52.3104i	0.775276	−	0.631623i
$20$	14.4585	−	70.8638i	0.161651	−	0.792282i
$21$	−34.3157	+	40.8958i	−0.356585	+	0.424962i
$22$	−74.7586	+	125.578i	−0.724482	+	1.21697i
$23$	101.067	−	17.8209i	0.916259	−	0.161561i	0.304415	−	0.952540i	$-0.401539\pi$
$23$	101.067	−	17.8209i	0.916259	−	0.161561i	0.611844	+	0.790979i	$0.290428\pi$
$24$	−18.8239	−	58.9752i	−0.160100	−	0.501594i
$25$	40.6603	+	14.7992i	0.325283	+	0.118393i
$26$	−139.963	−	53.0717i	−1.05573	−	0.400316i
$27$	−63.6301	+	110.211i	−0.453541	+	0.785556i
$28$	137.228	−	74.4100i	0.926204	−	0.502220i
$29$	179.400	+	213.801i	1.14875	+	1.36903i	0.918271	+	0.395952i	$0.129585\pi$
$29$	179.400	+	213.801i	1.14875	+	1.36903i	0.230480	+	0.973077i	$0.425970\pi$
$30$	−69.0514	+	11.2260i	−0.420233	+	0.0683193i
$31$	30.7849	+	53.3210i	0.178359	+	0.308927i	0.941319	−	0.337519i	$-0.109588\pi$
$31$	30.7849	+	53.3210i	0.178359	+	0.308927i	−0.762960	+	0.646446i	$0.776254\pi$
$32$	−12.0905	+	180.615i	−0.0667912	+	0.997767i
$33$	139.218	+	24.5479i	0.734387	+	0.129492i
$34$	252.465	−	292.836i	1.27345	−	1.47709i
$35$	−60.3346	−	165.768i	−0.291383	−	0.800569i
$36$	122.234	−	97.1181i	0.565897	−	0.449621i
$37$		−	126.535i		−	0.562220i	−0.959676	−	0.281110i	$-0.909297\pi$
$37$		−	126.535i		−	0.562220i	0.959676	−	0.281110i	$-0.0907026\pi$
$38$	145.515	+	183.568i	0.621203	+	0.783650i
$39$			144.791i			0.594488i
$40$	199.869	+	43.5705i	0.790050	+	0.172227i
$41$	5.64850	+	15.5191i	0.0215158	+	0.0591142i	0.949986	−	0.312294i	$-0.101097\pi$
$41$	5.64850	+	15.5191i	0.0215158	+	0.0591142i	−0.928470	+	0.371408i	$0.878875\pi$
$42$	−114.363	−	98.5969i	−0.420157	−	0.362234i
$43$	308.578	+	54.4106i	1.09437	+	0.192966i	0.691560	−	0.722319i	$-0.256924\pi$
$43$	308.578	+	54.4106i	1.09437	+	0.192966i	0.402806	+	0.915285i	$0.368035\pi$
$44$	−352.331	−	216.179i	−1.20718	−	0.740685i
$45$	−88.2116	−	152.787i	−0.292218	−	0.506137i
$46$	46.5792	+	286.509i	0.149298	+	0.918336i
$47$	−77.9316	−	92.8752i	−0.241861	−	0.288239i	0.631435	−	0.775429i	$-0.282466\pi$
$47$	−77.9316	−	92.8752i	−0.241861	−	0.288239i	−0.873296	+	0.487190i	$0.838022\pi$
$48$	167.504	−	51.0073i	0.503689	−	0.153381i
$49$	18.8784	−	32.6984i	0.0550392	−	0.0953306i
$50$	−43.3919	+	114.435i	−0.122731	+	0.323671i
$51$	−351.439	−	127.913i	−0.964928	−	0.351205i
$52$	155.388	−	393.833i	0.414393	−	1.05028i
$53$	−227.255	+	40.0712i	−0.588979	+	0.103853i	−0.460192	−	0.887819i	$-0.652219\pi$
$53$	−227.255	+	40.0712i	−0.588979	+	0.103853i	−0.128787	+	0.991672i	$0.541108\pi$
$54$	−309.289	−	184.124i	−0.779423	−	0.464002i
$55$	−300.263	+	357.840i	−0.736136	+	0.877293i
$56$	205.256	+	390.919i	0.489794	+	0.932834i
$57$	116.123	−	194.567i	0.269841	−	0.452122i
$58$	−611.449	+	499.291i	−1.38426	+	1.13035i
$59$	−370.549	−	310.928i	−0.817651	−	0.686091i	0.134770	−	0.990877i	$-0.456971\pi$
$59$	−370.549	−	310.928i	−0.817651	−	0.686091i	−0.952421	+	0.304786i	$0.901415\pi$
$60$	−29.1383	−	195.714i	−0.0626956	−	0.421109i
$61$	33.0594	+	187.489i	0.0693905	+	0.393533i	0.999646	+	0.0266197i	$0.00847431\pi$
$61$	33.0594	+	187.489i	0.0693905	+	0.393533i	−0.930255	+	0.366913i	$0.880415\pi$
$62$	−151.965	+	85.0490i	−0.311284	+	0.174214i
$63$	130.239	−	357.828i	0.260453	−	0.715589i
$64$	−510.354	−	41.0231i	−0.996785	−	0.0801232i
$65$	−414.344	−	239.222i	−0.790662	−	0.456489i
$66$	−74.6896	+	392.805i	−0.139298	+	0.732590i
$67$	472.421	−	396.409i	0.861425	−	0.722821i	−0.100850	−	0.994902i	$-0.532156\pi$
$67$	472.421	−	396.409i	0.861425	−	0.722821i	0.962274	+	0.272081i	$0.0877118\pi$
$68$	818.645	+	725.088i	1.45993	+	1.29309i
$69$	243.159	−	140.388i	0.424245	−	0.244938i
$70$	471.102	−	164.369i	0.804393	−	0.280655i
$71$	−19.6586	+	111.490i	−0.0328599	+	0.186358i	−0.996820	−	0.0796903i	$-0.974607\pi$
$71$	−19.6586	+	111.490i	−0.0328599	+	0.186358i	0.963960	+	0.266048i	$0.0857180\pi$
$72$	270.045	+	349.370i	0.442016	+	0.571857i
$73$	413.529	−	150.512i	0.663013	−	0.241317i	0.0114763	−	0.999934i	$-0.496347\pi$
$73$	413.529	−	150.512i	0.663013	−	0.241317i	0.651537	+	0.758617i	$0.274125\pi$
$74$	357.862	+	4.78425i	0.562170	+	0.00751564i
$75$	118.382			0.182261
$76$	−524.665	+	404.602i	−0.791884	+	0.610671i
$77$	−1008.25			−1.49221
$78$	−409.493	−	5.47451i	−0.594435	−	0.00794700i
$79$	−782.608	+	284.846i	−1.11456	+	0.405667i	−0.832664	−	0.553778i	$-0.813186\pi$
$79$	−782.608	+	284.846i	−1.11456	+	0.405667i	−0.281896	+	0.959445i	$0.590963\pi$
$80$	−130.782	+	563.616i	−0.182773	+	0.787677i
$81$	31.0359	−	176.013i	0.0425733	−	0.241445i
$82$	−44.1044	+	15.3882i	−0.0593965	+	0.0207236i
$83$	−608.348	+	351.230i	−0.804516	+	0.464487i	−0.845048	−	0.534691i	$-0.820428\pi$
$83$	−608.348	+	351.230i	−0.804516	+	0.464487i	0.0405319	+	0.999178i	$0.487095\pi$
$84$	283.173	−	319.711i	0.367818	−	0.415277i
$85$	946.691	−	794.368i	1.20804	−	1.01366i
$86$	−165.550	+	870.655i	−0.207578	+	1.09169i
$87$	661.283	+	381.792i	0.814908	+	0.470487i
$88$	624.712	−	988.280i	0.756756	−	1.19717i
$89$	−243.556	+	669.166i	−0.290078	+	0.796983i	0.705976	+	0.708235i	$0.250509\pi$
$89$	−243.556	+	669.166i	−0.290078	+	0.796983i	−0.996054	+	0.0887471i	$0.971714\pi$
$90$	435.444	−	243.701i	0.509998	−	0.285426i
$91$	−179.322	−	1016.99i	−0.206572	−	1.17153i
$92$	−812.059	+	120.901i	−0.920250	+	0.137009i
$93$	129.040	+	108.277i	0.143879	+	0.120729i
$94$	265.614	−	216.892i	0.291447	−	0.237987i
$95$	364.929	+	653.769i	0.394115	+	0.706056i
$96$	137.924	+	475.659i	0.146634	+	0.505695i
$97$	−366.498	+	436.776i	−0.383632	+	0.457194i	−0.922957	−	0.384903i	$-0.874235\pi$
$97$	−366.498	+	436.776i	−0.383632	+	0.457194i	0.539325	+	0.842097i	$0.318679\pi$
$98$	91.7630	+	54.6278i	0.0945864	+	0.0563086i
$99$	−993.024	+	175.097i	−1.00811	+	0.177757i
$100$	−322.001	−	127.047i	−0.322001	−	0.127047i
$101$	1437.86	+	523.337i	1.41656	+	0.515584i	0.933047	−	0.359755i	$-0.117140\pi$
$101$	1437.86	+	523.337i	1.41656	+	0.515584i	0.483510	+	0.875339i	$0.339362\pi$
$102$	375.049	−	989.094i	0.364073	−	0.960147i
$103$	407.687	−	706.135i	0.390006	−	0.675510i	−0.602444	−	0.798161i	$-0.705806\pi$
$103$	407.687	−	706.135i	0.390006	−	0.675510i	0.992450	+	0.122651i	$0.0391396\pi$
$104$	1107.95	+	454.355i	1.04465	+	0.428396i
$105$	−310.230	−	369.718i	−0.288336	−	0.343626i
$106$	−104.736	−	644.232i	−0.0959703	−	0.590315i
$107$	−346.162	−	599.570i	−0.312754	−	0.541707i	0.666203	−	0.745770i	$-0.267918\pi$
$107$	−346.162	−	599.570i	−0.312754	−	0.541707i	−0.978958	+	0.204064i	$0.934585\pi$
$108$	532.429	−	867.761i	0.474380	−	0.773151i
$109$	297.910	+	52.5296i	0.261785	+	0.0461598i	0.303000	−	0.952990i	$-0.402012\pi$
$109$	297.910	+	52.5296i	0.261785	+	0.0461598i	−0.0412149	+	0.999150i	$0.513123\pi$
$110$	−1000.68	−	862.727i	−0.867374	−	0.747798i
$111$	−118.403	−	325.309i	−0.101246	−	0.278171i
$112$	−1113.35	+	565.719i	−0.939298	+	0.477281i
$113$		−	650.922i		−	0.541890i	−0.962595	−	0.270945i	$-0.912664\pi$
$113$		−	650.922i		−	0.541890i	0.962595	−	0.270945i	$-0.0873362\pi$
$114$	545.878	+	335.774i	0.448475	+	0.275860i
$115$			927.790i			0.752320i
$116$	−1388.96	−	1748.16i	−1.11174	−	1.39925i
$117$	−353.228	−	970.487i	−0.279111	−	0.766851i
$118$	893.369	−	1036.22i	0.696960	−	0.808407i
$119$	2626.87	+	463.188i	2.02357	+	0.356810i
$120$	554.614	−	75.0083i	0.421910	−	0.0570607i
$121$	669.425	+	1159.48i	0.502949	+	0.871133i
$122$	−531.502	+	86.4088i	−0.394425	+	0.0641236i
$123$	29.0436	+	34.6128i	0.0212908	+	0.0253734i
$124$	−234.788	−	433.000i	−0.170037	−	0.313585i
$125$	−760.620	+	1317.43i	−0.544255	+	0.942677i
$126$	1007.08	+	381.867i	0.712043	+	0.269996i
$127$	2327.78	+	847.243i	1.62643	+	0.591974i	0.984593	−	0.174864i	$-0.0559484\pi$
$127$	2327.78	+	847.243i	1.62643	+	0.591974i	0.641842	+	0.766837i	$0.278171\pi$
$128$	135.317	−	1441.82i	0.0934408	−	0.995625i
$129$	844.240	−	148.862i	0.576211	−	0.101602i
$130$	692.227	−	1162.79i	0.467018	−	0.784490i
$131$	−299.837	+	357.332i	−0.199976	+	0.238322i	−0.856708	−	0.515802i	$-0.827494\pi$
$131$	−299.837	+	357.332i	−0.199976	+	0.238322i	0.656732	+	0.754124i	$0.271938\pi$
$132$	−1108.10	−	226.087i	−0.730663	−	0.149078i
$133$	−574.662	+	1510.42i	−0.374658	+	0.984738i
$134$	1103.25	+	1351.08i	0.711241	+	0.871010i
$135$	−881.328	−	739.522i	−0.561871	−	0.471466i
$136$	−2081.63	+	2287.85i	−1.31249	+	1.44251i
$137$	−262.598	−	1489.27i	−0.163761	−	0.928736i	−0.950333	−	0.311236i	$-0.899257\pi$
$137$	−262.598	−	1489.27i	−0.163761	−	0.928736i	0.786571	−	0.617499i	$-0.211854\pi$
$138$	387.847	+	693.003i	0.239245	+	0.427481i
$139$	406.305	−	1116.31i	0.247931	−	0.681184i	−0.751831	−	0.659356i	$-0.770829\pi$
$139$	406.305	−	1116.31i	0.247931	−	0.681184i	0.999762	−	0.0218279i	$-0.00694859\pi$
$140$	447.053	+	1338.57i	0.269877	+	0.808073i
$141$	−287.262	−	165.851i	−0.171573	−	0.0990577i
$142$	−314.569	−	59.8135i	−0.185902	−	0.0353481i
$143$	−2094.77	+	1757.72i	−1.22499	+	1.02789i
$144$	−998.291	+	750.526i	−0.577715	+	0.434332i
$145$	−2185.13	+	1261.59i	−1.25148	+	0.722545i
$146$	410.040	+	1175.22i	0.232432	+	0.666180i
$147$	17.9377	−	101.730i	0.0100645	−	0.0570785i
$148$	−27.0614	+	1011.91i	−0.0150299	+	0.562019i
$149$	−2353.47	+	856.593i	−1.29398	+	0.470972i	−0.895033	−	0.446000i	$-0.852848\pi$
$149$	−2353.47	+	856.593i	−1.29398	+	0.470972i	−0.398952	+	0.916972i	$0.630626\pi$
$150$	−4.47601	+	334.805i	−0.00243643	+	0.182245i
$151$	1474.31			0.794556			0.397278	−	0.917698i	$-0.369955\pi$
$151$	1474.31			0.794556			0.397278	+	0.917698i	$0.369955\pi$
$152$	−1124.45	−	1499.14i	−0.600031	−	0.799977i
$153$	2667.64			1.40958
$154$	38.1217	−	2851.50i	0.0199476	−	1.49208i
$155$	−523.052	+	190.375i	−0.271049	+	0.0986537i
$156$	30.9657	−	1157.91i	0.0158926	−	0.594276i
$157$	193.970	−	1100.06i	0.0986017	−	0.559198i	−0.894982	−	0.446101i	$-0.852812\pi$
$157$	193.970	−	1100.06i	0.0986017	−	0.559198i	0.993584	−	0.113096i	$-0.0360768\pi$
$158$	−776.004	−	2224.12i	−0.390731	−	1.11988i
$159$	−546.756	+	315.670i	−0.272708	+	0.157448i
$160$	−1589.06	−	391.184i	−0.785164	−	0.193286i
$161$	−1534.04	+	1287.21i	−0.750926	+	0.630102i
$162$	496.623	+	94.4300i	0.240854	+	0.0457970i
$163$	1761.79	+	1017.17i	0.846588	+	0.488778i	0.859498	−	0.511139i	$-0.170776\pi$
$163$	1761.79	+	1017.17i	0.846588	+	0.488778i	−0.0129098	+	0.999917i	$0.504109\pi$
$164$	−41.8528	−	125.317i	−0.0199278	−	0.0596682i
$165$	−437.107	+	1200.94i	−0.206235	+	0.566625i
$166$	−970.337	−	1733.79i	−0.453691	−	0.810653i
$167$	257.696	+	1461.47i	0.119408	+	0.677197i	0.984473	+	0.175537i	$0.0561661\pi$
$167$	257.696	+	1461.47i	0.119408	+	0.677197i	−0.865065	+	0.501660i	$0.832723\pi$
$168$	893.491	+	812.952i	0.410323	+	0.373337i
$169$	−462.520	−	388.101i	−0.210524	−	0.176650i
$170$	2210.82	+	2707.44i	0.997423	+	1.22148i
$171$	−303.678	+	1587.41i	−0.135806	+	0.709898i
$172$	−2456.11	−	501.124i	−1.08882	−	0.222153i
$173$	1061.08	−	1264.55i	0.466316	−	0.555734i	−0.480714	−	0.876877i	$-0.659623\pi$
$173$	1061.08	−	1264.55i	0.466316	−	0.555734i	0.947031	+	0.321143i	$0.104067\pi$
$174$	−1104.78	+	1855.79i	−0.481339	+	0.808545i
$175$	−831.497	+	146.615i	−0.359173	+	0.0633319i
$176$	2771.41	+	1804.16i	1.18695	+	0.772692i
$177$	−1243.59	−	452.632i	−0.528103	−	0.192214i
$178$	−1883.31	−	714.121i	−0.793034	−	0.300706i
$179$	2256.70	−	3908.72i	0.942311	−	1.63213i	0.181264	−	0.983435i	$-0.441981\pi$
$179$	2256.70	−	3908.72i	0.942311	−	1.63213i	0.761047	−	0.648696i	$-0.224685\pi$
$180$	672.765	+	1240.72i	0.278583	+	0.513768i
$181$	−623.519	−	743.081i	−0.256054	−	0.305153i	0.622669	−	0.782485i	$-0.286048\pi$
$181$	−623.519	−	743.081i	−0.256054	−	0.305153i	−0.878723	+	0.477332i	$0.841604\pi$
$182$	2882.99	−	468.702i	1.17418	−	0.190893i
$183$	260.433	+	451.083i	0.105201	+	0.182213i
$184$	−311.226	−	2301.22i	−0.124695	−	0.921999i
$185$	1126.55	+	198.642i	0.447707	+	0.0789429i
$186$	−311.105	+	360.852i	−0.122642	+	0.142253i
$187$	−2415.79	−	6637.32i	−0.944704	−	2.59555i
$188$	603.367	+	759.403i	0.234069	+	0.294602i
$189$		−	2483.23i		−	0.955704i
$190$	−1862.77	+	1007.36i	−0.711261	+	0.384642i
$191$			713.098i			0.270147i	0.990836	+	0.135073i	$0.0431270\pi$
$191$			713.098i			0.270147i	−0.990836	+	0.135073i	$0.956873\pi$
$192$	−1350.46	+	372.089i	−0.507610	+	0.139861i
$193$	798.274	+	2193.24i	0.297726	+	0.817994i	0.994879	+	0.101072i	$0.0322273\pi$
$193$	798.274	+	2193.24i	0.297726	+	0.817994i	−0.697154	+	0.716922i	$0.745550\pi$
$194$	−1221.42	−	1053.04i	−0.452025	−	0.389709i
$195$	−1289.09	−	227.301i	−0.473403	−	0.0834737i
$196$	−157.967	+	257.456i	−0.0575680	+	0.0938252i
$197$	−228.430	−	395.653i	−0.0826142	−	0.143092i	0.821758	−	0.569837i	$-0.192994\pi$
$197$	−228.430	−	395.653i	−0.0826142	−	0.143092i	−0.904372	+	0.426745i	$0.859660\pi$
$198$	−457.658	−	2815.06i	−0.164264	−	1.01039i
$199$	2719.66	+	3241.17i	0.968803	+	1.15457i	0.987953	+	0.154757i	$0.0494596\pi$
$199$	2719.66	+	3241.17i	0.968803	+	1.15457i	−0.0191499	+	0.999817i	$0.506096\pi$
$200$	371.485	−	905.873i	0.131340	−	0.320274i
$201$	843.619	−	1461.19i	0.296041	−	0.512759i
$202$	−1534.45	+	4046.73i	−0.534475	+	1.40954i
$203$	−5117.59	−	1862.65i	−1.76938	−	0.644002i
$204$	2783.15	+	1098.10i	0.955194	+	0.376875i
$205$	−147.036	+	25.9264i	−0.0500949	+	0.00883308i
$206$	1981.66	+	1179.71i	0.670236	+	0.399001i
$207$	−1287.33	+	1534.18i	−0.432250	+	0.515135i
$208$	−1326.89	+	3116.30i	−0.442323	+	1.03883i
$209$	4224.62	−	681.966i	1.39820	−	0.225706i
$210$	1057.36	−	863.405i	0.347450	−	0.283717i
$211$	−409.295	−	343.440i	−0.133541	−	0.112054i	0.573571	−	0.819156i	$-0.305558\pi$
$211$	−409.295	−	343.440i	−0.133541	−	0.112054i	−0.707112	+	0.707102i	$0.750002\pi$
$212$	1825.96	−	271.853i	0.591545	−	0.0880705i
$213$	53.7842	+	305.025i	0.0173016	+	0.0981220i
$214$	1708.78	−	956.336i	0.545839	−	0.305485i
$215$	−968.850	+	2661.89i	−0.307326	+	0.844370i
$216$	2434.05	+	1538.61i	0.766741	+	0.484672i
$217$	−1040.45	−	600.706i	−0.325486	−	0.187920i
$218$	−159.827	+	840.555i	−0.0496552	+	0.261145i
$219$	922.307	−	773.907i	0.284583	−	0.238794i
$220$	2477.78	−	2797.48i	0.759326	−	0.857300i
$221$	6265.17	−	3617.20i	1.90697	−	1.10099i
$222$	924.507	−	322.564i	0.279499	−	0.0975183i
$223$	338.146	−	1917.72i	0.101542	−	0.575875i	−0.891003	−	0.453998i	$-0.849997\pi$
$223$	338.146	−	1917.72i	0.101542	−	0.575875i	0.992545	−	0.121878i	$-0.0388915\pi$
$224$	−1557.86	−	3170.13i	−0.464682	−	0.945595i
$225$	−793.479	+	288.803i	−0.235105	+	0.0855712i
$226$	1840.92	+	24.6113i	0.541842	+	0.00724388i
$227$	−2456.17			−0.718158			−0.359079	−	0.933307i	$-0.616909\pi$
$227$	−2456.17			−0.718158			−0.359079	+	0.933307i	$0.616909\pi$
$228$	−970.266	+	1531.14i	−0.281831	+	0.444747i
$229$	2550.20			0.735902			0.367951	−	0.929845i	$-0.380059\pi$
$229$	2550.20			0.735902			0.367951	+	0.929845i	$0.380059\pi$
$230$	−2623.95	−	35.0796i	−0.752253	−	0.0100569i
$231$	−2592.11	+	943.452i	−0.738306	+	0.268721i
$232$	4996.63	−	3862.14i	1.41399	−	1.09294i
$233$	−60.3358	+	342.181i	−0.0169645	+	0.0962104i	−0.992114	−	0.125336i	$-0.959999\pi$
$233$	−60.3358	+	342.181i	−0.0169645	+	0.0962104i	0.975150	+	0.221546i	$0.0711103\pi$
$234$	2758.06	−	962.298i	0.770514	−	0.268835i
$235$	949.222	−	548.034i	0.263491	−	0.152127i
$236$	2896.84	+	2565.78i	0.799018	+	0.707704i
$237$	−1745.47	+	1464.63i	−0.478400	+	0.401425i
$238$	−1409.30	+	7411.73i	−0.383829	+	2.01862i
$239$	−1825.38	−	1053.88i	−0.494033	−	0.285230i	0.232213	−	0.972665i	$-0.425403\pi$
$239$	−1825.38	−	1053.88i	−0.494033	−	0.285230i	−0.726246	+	0.687435i	$0.758737\pi$
$240$	191.167	+	1571.38i	0.0514156	+	0.422635i
$241$	−138.281	+	379.925i	−0.0369605	+	0.101548i	−0.956800	−	0.290746i	$-0.906096\pi$
$241$	−138.281	+	379.925i	−0.0369605	+	0.101548i	0.919840	+	0.392295i	$0.128319\pi$
$242$	−3304.52	+	1849.41i	−0.877779	+	0.491259i
$243$	−681.571	−	3865.38i	−0.179929	−	1.02043i
$244$	−224.283	−	1506.45i	−0.0588453	−	0.395247i
$245$	261.482	+	219.409i	0.0681855	+	0.0572144i
$246$	−98.9891	+	80.8316i	−0.0256557	+	0.0209497i
$247$	1439.25	+	4139.94i	0.370757	+	1.06647i
$248$	1233.48	−	647.649i	0.315830	−	0.165830i
$249$	−1235.35	+	1472.23i	−0.314406	+	0.374694i
$250$	−3697.17	−	2200.98i	−0.935318	−	0.556808i
$251$	3251.86	−	573.390i	0.817751	−	0.144191i	0.250901	−	0.968013i	$-0.419273\pi$
$251$	3251.86	−	573.390i	0.817751	−	0.144191i	0.566850	+	0.823821i	$0.308162\pi$
$252$	−1118.06	+	2833.75i	−0.279490	+	0.708370i
$253$	4982.96	+	1813.65i	1.23825	+	0.450685i
$254$	−2484.16	+	6551.34i	−0.613663	+	1.61838i
$255$	1690.54	−	2928.10i	0.415160	−	0.719078i
$256$	4072.60	+	437.214i	0.994287	+	0.106742i
$257$	−3532.16	−	4209.47i	−0.857317	−	1.02171i	−0.999492	−	0.0318687i	$-0.989854\pi$
$257$	−3532.16	−	4209.47i	−0.857317	−	1.02171i	0.142175	−	0.989841i	$-0.454590\pi$
$258$	389.088	+	2393.29i	0.0938898	+	0.577518i
$259$	1234.53	+	2138.27i	0.296178	+	0.512996i
$260$	3262.41	+	2001.70i	0.778176	+	0.477463i
$261$	−5363.79	−	945.781i	−1.27207	−	0.224300i
$262$	−999.260	−	861.502i	−0.235628	−	0.203144i
$263$	−1691.96	−	4648.62i	−0.396695	−	1.08991i	−0.963884	−	0.266323i	$-0.914191\pi$
$263$	−1691.96	−	4648.62i	−0.396695	−	1.08991i	0.567189	−	0.823588i	$-0.308031\pi$
$264$	681.311	−	3125.34i	0.158833	−	0.728605i
$265$		−	2086.19i		−	0.483598i
$266$	−4250.01	−	1682.35i	−0.979642	−	0.387788i
$267$			1948.27i			0.446562i
$268$	−3862.80	+	3069.10i	−0.880440	+	0.699534i
$269$	−1680.24	−	4616.42i	−0.380840	−	1.04635i	−0.971003	−	0.239065i	$-0.923159\pi$
$269$	−1680.24	−	4616.42i	−0.380840	−	1.04635i	0.590164	−	0.807284i	$-0.299063\pi$
$270$	2124.82	−	2464.59i	0.478935	−	0.555519i
$271$	2266.13	+	399.579i	0.507961	+	0.0895672i	0.421754	−	0.906710i	$-0.361414\pi$
$271$	2266.13	+	399.579i	0.507961	+	0.0895672i	0.0862063	+	0.996277i	$0.472526\pi$
$272$	−6391.74	−	5973.71i	−1.42484	−	1.33165i
$273$	−1412.65	−	2446.78i	−0.313177	−	0.542439i
$274$	4221.84	−	686.364i	0.930842	−	0.151331i
$275$	1437.13	+	1712.71i	0.315135	+	0.375564i
$276$	−1974.60	+	1070.70i	−0.430641	+	0.233509i
$277$	−1748.00	+	3027.62i	−0.379159	+	0.656723i	−0.990940	−	0.134304i	$-0.957120\pi$
$277$	−1748.00	+	3027.62i	−0.379159	+	0.656723i	0.611781	+	0.791027i	$0.290453\pi$
$278$	3141.77	+	1191.31i	0.677808	+	0.257014i
$279$	−1129.06	−	410.945i	−0.242277	−	0.0881816i
$280$	−3802.62	+	1213.73i	−0.811608	+	0.259051i
$281$	2346.19	−	413.696i	0.498085	−	0.0878258i	0.0810384	−	0.996711i	$-0.474176\pi$
$281$	2346.19	−	413.696i	0.498085	−	0.0878258i	0.417046	+	0.908885i	$0.363065\pi$
$282$	479.916	−	806.155i	0.101342	−	0.170233i
$283$	−389.540	+	464.235i	−0.0818224	+	0.0975121i	−0.805402	−	0.592728i	$-0.798051\pi$
$283$	−389.540	+	464.235i	−0.0818224	+	0.0975121i	0.723580	+	0.690240i	$0.242495\pi$
$284$	181.057	−	887.394i	0.0378301	−	0.185413i
$285$	1549.95	+	1339.30i	0.322145	+	0.278363i
$286$	−4891.94	−	5990.84i	−1.01142	−	1.23862i
$287$	−246.865	−	207.144i	−0.0507734	−	0.0426040i
$288$	−2084.87	−	2851.72i	−0.426570	−	0.583469i
$289$	2391.73	+	13564.2i	0.486817	+	2.76088i
$290$	−3485.37	−	6227.63i	−0.705751	−	1.26103i
$291$	−533.528	+	1465.86i	−0.107478	+	0.295292i
$292$	−3339.24	+	1115.23i	−0.669227	+	0.223506i
$293$	−3587.51	−	2071.25i	−0.715306	−	0.412982i	0.0977169	−	0.995214i	$-0.468846\pi$
$293$	−3587.51	−	2071.25i	−0.715306	−	0.412982i	−0.813022	+	0.582232i	$0.802179\pi$
$294$	287.032	+	54.5774i	0.0569388	+	0.0108266i
$295$	3349.94	−	2810.94i	0.661157	−	0.554776i
$296$	−2860.85	−	114.795i	−0.561768	−	0.0225416i
$297$	−5694.64	+	3287.80i	−1.11258	+	0.642349i
$298$	−2333.61	−	6688.41i	−0.453632	−	1.30016i
$299$	−943.122	+	5348.71i	−0.182415	+	1.03453i
$300$	−946.719	−	25.3179i	−0.182196	−	0.00487243i
$301$	−5745.44	+	2091.17i	−1.10020	+	0.400442i
$302$	−55.7436	+	4169.62i	−0.0106215	+	0.794485i
$303$	4186.31			0.793720
$304$	4282.35	−	3123.45i	0.807926	−	0.589284i
$305$	−1721.14			−0.323121
$306$	−100.863	+	7544.56i	−0.0188430	+	1.40946i
$307$	−818.237	+	297.814i	−0.152115	+	0.0553652i	−0.416955	−	0.908927i	$-0.636903\pi$
$307$	−818.237	+	297.814i	−0.152115	+	0.0553652i	0.264841	+	0.964292i	$0.414681\pi$
$308$	8063.10	+	215.630i	1.49168	+	0.0398917i
$309$	387.372	−	2196.90i	0.0713166	−	0.404456i
$310$	−518.638	−	1486.48i	−0.0950215	−	0.272343i
$311$	1174.63	−	678.172i	0.214171	−	0.123651i	−0.389078	−	0.921205i	$-0.627206\pi$
$311$	1174.63	−	678.172i	0.214171	−	0.123651i	0.603248	+	0.797554i	$0.293873\pi$
$312$	3273.60	+	131.357i	0.594010	+	0.0238353i
$313$	3095.14	−	2597.13i	0.558938	−	0.469004i	−0.319016	−	0.947749i	$-0.603353\pi$
$313$	3095.14	−	2597.13i	0.558938	−	0.469004i	0.877954	+	0.478745i	$0.158908\pi$
$314$	3103.82	+	590.173i	0.557830	+	0.106068i
$315$	2981.33	+	1721.27i	0.533267	+	0.307882i
$316$	6319.54	−	2110.58i	1.12501	−	0.375726i
$317$	−1696.99	+	4662.45i	−0.300671	+	0.826087i	0.693713	+	0.720252i	$0.255974\pi$
$317$	−1696.99	+	4662.45i	−0.300671	+	0.826087i	−0.994384	+	0.105835i	$0.966249\pi$
$318$	−872.097	−	1558.26i	−0.153789	−	0.274789i
$319$	2504.20	+	14202.0i	0.439525	+	2.49267i
$320$	1166.42	−	4479.35i	0.203765	−	0.782510i
$321$	−1450.99	−	1217.52i	−0.252294	−	0.211700i
$322$	−3582.46	−	4387.20i	−0.620008	−	0.759282i
$323$	−11320.0	−	164.006i	−1.95004	−	0.0282525i
$324$	−285.842	+	1400.97i	−0.0490126	+	0.240221i
$325$	−1471.95	+	1754.20i	−0.251227	+	0.299401i
$326$	−2943.34	+	4944.19i	−0.500051	+	0.839979i
$327$	815.053	−	143.716i	0.137837	−	0.0243043i
$328$	356.000	−	113.629i	0.0599293	−	0.0191284i
$329$	2223.08	+	809.136i	0.372530	+	0.135590i
$330$	−3379.94	−	1281.62i	−0.563817	−	0.213791i
$331$	2713.25	−	4699.48i	0.450554	−	0.780383i	−0.547866	−	0.836566i	$-0.684560\pi$
$331$	2713.25	−	4699.48i	0.450554	−	0.780383i	0.998420	+	0.0561829i	$0.0178930\pi$
$332$	4940.16	−	2678.73i	0.816646	−	0.442814i
$333$	1587.23	+	1891.59i	0.261201	+	0.311287i
$334$	−4143.03	+	673.553i	−0.678733	+	0.110345i
$335$	2787.64	+	4828.33i	0.454642	+	0.787463i
$336$	−2332.95	+	2496.21i	−0.378789	+	0.405296i
$337$	4173.02	+	735.816i	0.674537	+	0.118939i	0.500416	−	0.865785i	$-0.333180\pi$
$337$	4173.02	+	735.816i	0.674537	+	0.118939i	0.174121	+	0.984724i	$0.444292\pi$
$338$	1115.10	−	1293.41i	0.179449	−	0.208143i
$339$	−609.090	−	1673.46i	−0.0975848	−	0.268112i
$340$	−7740.71	+	6150.21i	−1.23470	+	0.981006i
$341$			3181.35i			0.505219i
$342$	−4478.00	−	918.875i	−0.708019	−	0.145284i
$343$		−	5956.21i		−	0.937624i
$344$	1510.13	−	6927.35i	0.236688	−	1.08575i
$345$	868.165	+	2385.26i	0.135479	+	0.372227i
$346$	3536.25	+	3048.74i	0.549451	+	0.473704i
$347$	5771.70	+	1017.71i	0.892913	+	0.157445i	0.601235	−	0.799072i	$-0.294675\pi$
$347$	5771.70	+	1017.71i	0.892913	+	0.157445i	0.291678	+	0.956517i	$0.405786\pi$
$348$	−5206.72	−	3194.67i	−0.802039	−	0.492104i
$349$	778.340	+	1348.12i	0.119380	+	0.206772i	0.919522	−	0.393038i	$-0.128576\pi$
$349$	778.340	+	1348.12i	0.119380	+	0.206772i	−0.800142	+	0.599810i	$0.795243\pi$
$350$	−383.215	−	2357.16i	−0.0585249	−	0.359987i
$351$	−4329.12	−	5159.24i	−0.658322	−	0.784558i
$352$	−5207.27	+	7769.81i	−0.788490	+	1.17651i
$353$	5397.59	−	9348.91i	0.813838	−	1.40961i	−0.0963205	−	0.995350i	$-0.530707\pi$
$353$	5397.59	−	9348.91i	0.813838	−	1.40961i	0.910159	−	0.414259i	$-0.135959\pi$
$354$	1327.14	−	3499.99i	0.199256	−	0.525487i
$355$	−961.746	−	350.047i	−0.143786	−	0.0523340i
$356$	2090.87	−	5299.33i	0.311280	−	0.788943i
$357$	7186.87	−	1267.24i	1.06546	−	0.187869i
$358$	10969.2	+	6530.13i	1.61939	+	0.964045i
$359$	6851.17	−	8164.91i	1.00722	−	1.20035i	0.0275718	−	0.999620i	$-0.491223\pi$
$359$	6851.17	−	8164.91i	1.00722	−	1.20035i	0.979646	−	0.200735i	$-0.0643330\pi$
$360$	−3534.42	+	1855.79i	−0.517446	+	0.271690i
$361$	1386.24	−	6717.46i	0.202105	−	0.979364i
$362$	2125.14	−	1735.32i	0.308549	−	0.251952i
$363$	2806.00	+	2354.51i	0.405721	+	0.340440i
$364$	1216.56	+	8171.32i	0.175179	+	1.17663i
$365$	690.847	+	3917.99i	0.0990701	+	0.561854i
$366$	−1285.59	+	719.494i	−0.183603	+	0.102756i
$367$	−2419.64	+	6647.92i	−0.344154	+	0.945554i	0.640022	+	0.768357i	$0.278925\pi$
$367$	−2419.64	+	6647.92i	−0.344154	+	0.945554i	−0.984175	+	0.177197i	$0.943297\pi$
$368$	6520.01	−	793.192i	0.923584	−	0.112359i
$369$	−279.111	−	161.145i	−0.0393765	−	0.0227340i
$370$	−604.388	+	3178.58i	−0.0849207	+	0.446612i
$371$	3449.37	−	2894.37i	0.482702	−	0.405035i
$372$	−1008.79	−	893.504i	−0.140600	−	0.124532i
$373$	−5493.34	+	3171.58i	−0.762559	+	0.440264i	−0.830214	−	0.557445i	$-0.811782\pi$
$373$	−5493.34	+	3171.58i	−0.762559	+	0.440264i	0.0676547	+	0.997709i	$0.478448\pi$
$374$	18862.8	−	6581.31i	2.60795	−	0.909923i
$375$	−722.718	+	4098.74i	−0.0995226	+	0.564421i
$376$	−2170.54	+	1677.71i	−0.297705	+	0.230110i
$377$	−13879.7	+	5051.80i	−1.89613	+	0.690136i
$378$	7023.00	+	93.8904i	0.955619	+	0.0127757i
$379$	7387.64			1.00126			0.500630	−	0.865661i	$-0.333102\pi$
$379$	7387.64			1.00126			0.500630	+	0.865661i	$0.333102\pi$
$380$	−2778.57	−	5306.33i	−0.375099	−	0.716339i
$381$	6777.31			0.911318
$382$	−2016.77	−	26.9621i	−0.270122	−	0.00361126i
$383$	1239.16	−	451.017i	0.165321	−	0.0601720i	−0.258034	−	0.966136i	$-0.583075\pi$
$383$	1239.16	−	451.017i	0.165321	−	0.0601720i	0.423355	+	0.905964i	$0.360852\pi$
$384$	−1001.27	−	3833.41i	−0.133062	−	0.509434i
$385$	1582.81	−	8976.56i	0.209526	−	1.18828i
$386$	−6233.05	+	2174.73i	−0.821901	+	0.286764i
$387$	−5295.52	+	3057.37i	−0.695573	+	0.401589i
$388$	3024.35	−	3414.58i	0.395717	−	0.446775i
$389$	1287.54	−	1080.37i	0.167817	−	0.140815i	−0.555011	−	0.831843i	$-0.687286\pi$
$389$	1287.54	−	1080.37i	0.167817	−	0.140815i	0.722828	+	0.691027i	$0.242842\pi$
$390$	691.588	−	3637.17i	0.0897946	−	0.472245i
$391$	−12149.3	−	7014.42i	−1.57140	−	0.907249i
$392$	−722.159	−	456.491i	−0.0930473	−	0.0588171i
$393$	−436.486	+	1199.24i	−0.0560249	+	0.153927i
$394$	1127.61	−	631.082i	0.144184	−	0.0806940i
$395$	−1307.43	−	7414.83i	−0.166542	−	0.944507i
$396$	7978.80	−	1187.90i	1.01250	−	0.150743i
$397$	−2041.97	−	1713.42i	−0.258145	−	0.216610i	0.504525	−	0.863397i	$-0.331668\pi$
$397$	−2041.97	−	1713.42i	−0.258145	−	0.216610i	−0.762670	+	0.646788i	$0.776112\pi$
$398$	−9269.41	+	7569.13i	−1.16742	+	0.953282i
$399$	−64.0504	+	4420.89i	−0.00803642	+	0.554690i
$400$	2547.92	+	1084.88i	0.318490	+	0.135609i
$401$	5033.85	−	5999.10i	0.626878	−	0.747085i	−0.355358	−	0.934730i	$-0.615641\pi$
$401$	5033.85	−	5999.10i	0.626878	−	0.747085i	0.982237	+	0.187645i	$0.0600856\pi$
$402$	4100.61	+	2441.15i	0.508755	+	0.302869i
$403$	−3208.92	+	565.819i	−0.396644	+	0.0699391i
$404$	−11386.8	−	4492.71i	−1.40227	−	0.553269i
$405$	1518.35	+	552.633i	0.186290	+	0.0678039i
$406$	5461.39	−	14403.0i	0.667597	−	1.76061i
$407$	3269.06	−	5662.17i	0.398135	−	0.689591i
$408$	−3210.85	+	7829.72i	−0.389610	+	0.950071i
$409$	140.872	+	167.884i	0.0170309	+	0.0202967i	0.774493	−	0.632583i	$-0.218005\pi$
$409$	140.872	+	167.884i	0.0170309	+	0.0202967i	−0.757462	+	0.652880i	$0.773561\pi$
$410$	−67.7651	−	416.824i	−0.00816263	−	0.0502085i
$411$	−2068.68	−	3583.05i	−0.248273	−	0.430022i
$412$	−3411.35	+	5559.87i	−0.407925	+	0.664843i
$413$	9295.39	+	1639.03i	1.10750	+	0.195282i
$414$	−4290.26	−	3698.81i	−0.509311	−	0.439098i
$415$	−2172.02	−	5967.58i	−0.256916	−	0.705872i
$416$	−8763.28	−	3870.50i	−1.03283	−	0.456170i
$417$		−	3250.14i		−	0.381678i
$418$	1768.99	+	11973.8i	0.206995	+	1.40109i
$419$			14922.5i			1.73988i	0.493155	+	0.869941i	$0.335844\pi$
$419$			14922.5i			1.73988i	−0.493155	+	0.869941i	$0.664156\pi$
$420$	2401.88	+	3023.03i	0.279047	+	0.351211i
$421$	−1727.05	−	4745.03i	−0.199932	−	0.549308i	0.798693	−	0.601739i	$-0.205525\pi$
$421$	−1727.05	−	4745.03i	−0.199932	−	0.549308i	−0.998625	+	0.0524308i	$0.983303\pi$
$422$	986.782	−	1144.57i	0.113829	−	0.132031i
$423$	2330.03	+	410.848i	0.267825	+	0.0472248i
$424$	699.809	+	5174.41i	0.0801550	+	0.592669i
$425$	−2957.46	−	5122.47i	−0.337548	−	0.584650i
$426$	−864.698	+	140.578i	−0.0983445	+	0.0159883i
$427$	−2387.90	−	2845.79i	−0.270629	−	0.322523i
$428$	2640.08	+	4868.88i	0.298161	+	0.549874i
$429$	−3740.71	+	6479.10i	−0.420986	+	0.729169i
$430$	−7491.67	−	2840.72i	−0.840187	−	0.318586i
$431$	−12462.1	−	4535.82i	−1.39275	−	0.506921i	−0.466734	−	0.884398i	$-0.654570\pi$
$431$	−12462.1	−	4535.82i	−1.39275	−	0.506921i	−0.926019	+	0.377477i	$0.876792\pi$
$432$	−4443.49	+	6825.74i	−0.494879	+	0.760193i
$433$	−6122.74	+	1079.60i	−0.679538	+	0.119821i	−0.502755	−	0.864429i	$-0.667680\pi$
$433$	−6122.74	+	1079.60i	−0.679538	+	0.119821i	−0.176783	+	0.984250i	$0.556569\pi$
$434$	1738.24	−	2919.87i	0.192254	−	0.322945i
$435$	−4437.26	+	5288.13i	−0.489082	+	0.582865i
$436$	−2371.19	−	483.799i	−0.260458	−	0.0531417i
$437$	5557.06	−	6431.10i	0.608307	−	0.703984i
$438$	2153.87	+	2637.71i	0.234968	+	0.287750i
$439$	−4601.39	−	3861.02i	−0.500256	−	0.419764i	0.357429	−	0.933940i	$-0.383653\pi$
$439$	−4601.39	−	3861.02i	−0.500256	−	0.419764i	−0.857685	+	0.514176i	$0.828098\pi$
$440$	7818.07	+	7113.36i	0.847073	+	0.770718i
$441$	127.947	+	725.625i	0.0138157	+	0.0783528i
$442$	9993.19	+	17855.8i	1.07540	+	1.92152i
$443$	−2823.80	+	7758.31i	−0.302850	+	0.832074i	0.691152	+	0.722710i	$0.257104\pi$
$443$	−2823.80	+	7758.31i	−0.302850	+	0.832074i	−0.994002	+	0.109364i	$0.965119\pi$
$444$	877.311	+	2626.86i	0.0937733	+	0.280778i
$445$	−5575.32	−	3218.91i	−0.593923	−	0.342901i
$446$	5410.87	+	1028.85i	0.574467	+	0.109231i
$447$	−5249.01	+	4404.45i	−0.555413	+	0.466047i
$448$	9024.58	−	4286.03i	0.951722	−	0.451999i
$449$	−6037.19	+	3485.57i	−0.634549	+	0.366357i	−0.782512	−	0.622636i	$-0.786062\pi$
$449$	−6037.19	+	3485.57i	−0.634549	+	0.366357i	0.147963	+	0.988993i	$0.452728\pi$
$450$	−786.784	−	2255.02i	−0.0824207	−	0.236228i
$451$	−148.182	+	840.381i	−0.0154714	+	0.0877428i
$452$	−139.210	+	5205.52i	−0.0144865	+	0.541697i
$453$	3790.33	−	1379.57i	0.393124	−	0.143085i
$454$	92.8675	−	6946.49i	0.00960019	−	0.718094i
$455$	9335.86			0.961916
$456$	−4293.65	−	2801.97i	−0.440940	−	0.287751i
$457$	−790.730			−0.0809382			−0.0404691	−	0.999181i	$-0.512885\pi$
$457$	−790.730			−0.0809382			−0.0404691	+	0.999181i	$0.512885\pi$
$458$	−96.4224	+	7212.40i	−0.00983739	+	0.735837i
$459$	16347.1	−	5949.87i	1.66235	−	0.605046i
$460$	198.422	−	7419.66i	0.0201119	−	0.752051i
$461$	−1083.44	+	6144.50i	−0.109460	+	0.620777i	0.879885	+	0.475186i	$0.157619\pi$
$461$	−1083.44	+	6144.50i	−0.109460	+	0.620777i	−0.989345	+	0.145590i	$0.953492\pi$
$462$	−2570.24	−	7366.62i	−0.258828	−	0.741832i
$463$	4779.60	−	2759.50i	0.479756	−	0.276987i	−0.240559	−	0.970635i	$-0.577331\pi$
$463$	4779.60	−	2759.50i	0.479756	−	0.276987i	0.720315	+	0.693648i	$0.243997\pi$
$464$	10733.9	+	14277.4i	1.07394	+	1.42847i
$465$	−1166.58	+	978.876i	−0.116341	+	0.0976221i
$466$	−965.466	−	183.578i	−0.0959750	−	0.0182491i
$467$	−2305.58	−	1331.13i	−0.228457	−	0.131900i	0.381403	−	0.924409i	$-0.375441\pi$
$467$	−2305.58	−	1331.13i	−0.228457	−	0.131900i	−0.609860	+	0.792509i	$0.708774\pi$
$468$	2617.26	+	7836.67i	0.258511	+	0.774038i
$469$	−4115.77	+	11308.0i	−0.405221	+	1.11334i
$470$	1514.04	+	2705.29i	0.148591	+	0.265501i
$471$	−530.682	−	3009.65i	−0.0519162	−	0.294432i
$472$	−7366.01	+	8095.75i	−0.718322	+	0.789486i
$473$	12402.6	+	10407.0i	1.20564	+	1.01166i
$474$	−4076.22	−	4991.88i	−0.394994	−	0.483723i
$475$	3384.85	−	1176.74i	0.326964	−	0.113669i
$476$	−20908.4	−	4265.98i	−2.01331	−	0.410779i
$477$	2894.64	−	3449.70i	0.277854	−	0.331134i
$478$	3049.58	−	5122.64i	0.291809	−	0.490176i
$479$	−17848.2	+	3147.12i	−1.70252	+	0.300200i	−0.938572	−	0.345082i	$-0.887851\pi$
$479$	−17848.2	+	3147.12i	−1.70252	+	0.300200i	−0.763944	+	0.645282i	$0.776740\pi$
$480$	−4451.37	+	481.239i	−0.423284	+	0.0457613i
$481$	6292.66	+	2290.34i	0.596508	+	0.217111i
$482$	−1069.27	−	405.449i	−0.101045	−	0.0383147i
$483$	−2739.39	+	4744.76i	−0.258067	+	0.446985i
$484$	−5105.51	−	9415.68i	−0.479481	−	0.884267i
$485$	−3313.32	−	3948.66i	−0.310206	−	0.369689i
$486$	10957.7	−	1781.45i	1.02274	−	0.166272i
$487$	−5746.44	−	9953.12i	−0.534694	−	0.926117i	−0.999178	−	0.0405354i	$-0.987094\pi$
$487$	−5746.44	−	9953.12i	−0.534694	−	0.926117i	0.464484	−	0.885581i	$-0.346240\pi$
$488$	4268.97	−	577.353i	0.395999	−	0.0535564i
$489$	5481.20	+	966.483i	0.506888	+	0.0893781i
$490$	−630.414	+	731.220i	−0.0581208	+	0.0674146i
$491$	4419.24	+	12141.8i	0.406186	+	1.11599i	0.959178	+	0.282801i	$0.0912637\pi$
$491$	4419.24	+	12141.8i	0.406186	+	1.11599i	−0.552992	+	0.833186i	$0.686514\pi$
$492$	−224.863	−	283.015i	−0.0206049	−	0.0259335i
$493$		−	38152.1i		−	3.48537i
$494$	−11762.9	+	3913.91i	−1.07133	+	0.356468i
$495$		−	9115.90i		−	0.827735i
$496$	1785.03	+	3512.97i	0.161593	+	0.318018i
$497$	−755.542	−	2075.84i	−0.0681906	−	0.187352i
$498$	−4117.02	−	3549.45i	−0.370458	−	0.319387i
$499$	−7414.13	−	1307.31i	−0.665134	−	0.117281i	−0.169120	−	0.985595i	$-0.554093\pi$
$499$	−7414.13	−	1307.31i	−0.665134	−	0.117281i	−0.496014	+	0.868314i	$0.665204\pi$
$500$	6364.53	−	10373.0i	0.569261	−	0.927791i
$501$	2030.06	+	3516.17i	0.181031	+	0.313555i
$502$	1498.70	+	9218.50i	0.133247	+	0.819605i
$503$	−315.093	−	375.513i	−0.0279310	−	0.0332869i	0.751898	−	0.659279i	$-0.229139\pi$
$503$	−315.093	−	375.513i	−0.0279310	−	0.0332869i	−0.779829	+	0.625992i	$0.784694\pi$
$504$	−7972.06	−	3269.23i	−0.704571	−	0.288934i
$505$	−6916.58	+	11979.9i	−0.609473	+	1.05564i
$506$	−5317.72	+	14024.1i	−0.467197	+	1.23211i
$507$	−1552.26	−	564.975i	−0.135973	−	0.0494900i
$508$	−18434.4	−	7273.35i	−1.61003	−	0.635242i
$509$	−10966.2	+	1933.63i	−0.954945	+	0.168383i	−0.629346	−	0.777125i	$-0.716677\pi$
$509$	−10966.2	+	1933.63i	−0.954945	+	0.168383i	−0.325599	+	0.945508i	$0.605566\pi$
$510$	8217.26	+	4891.85i	0.713464	+	0.424735i
$511$	−5519.65	+	6578.07i	−0.477838	+	0.569465i
$512$	−1390.50	+	11501.5i	−0.120024	+	0.992771i
$513$	1679.62	+	10404.9i	0.144556	+	0.895490i
$514$	12038.7	−	9830.42i	1.03308	−	0.843582i
$515$	5646.80	+	4738.23i	0.483160	+	0.405420i
$516$	−6783.34	+	1009.92i	−0.578721	+	0.0861613i
$517$	−1087.83	−	6169.37i	−0.0925388	−	0.524814i
$518$	−6094.09	+	3410.63i	−0.516909	+	0.289294i
$519$	1544.67	−	4243.94i	0.130642	−	0.358937i
$520$	−5784.52	+	9150.97i	−0.487823	+	0.771724i
$521$	−4207.49	−	2429.19i	−0.353807	−	0.204270i	0.312554	−	0.949900i	$-0.398816\pi$
$521$	−4207.49	−	2429.19i	−0.353807	−	0.204270i	−0.666361	+	0.745630i	$0.732149\pi$
$522$	2877.64	−	15134.0i	0.241285	−	1.26896i
$523$	9905.73	−	8311.89i	0.828197	−	0.694940i	−0.126679	−	0.991944i	$-0.540432\pi$
$523$	9905.73	−	8311.89i	0.828197	−	0.694940i	0.954876	+	0.297004i	$0.0959874\pi$
$524$	2474.26	−	2793.51i	0.206276	−	0.232891i
$525$	−2000.51	+	1154.99i	−0.166304	+	0.0960154i
$526$	13211.1	−	4609.40i	1.09512	−	0.382090i
$527$	1461.51	−	8288.63i	0.120805	−	0.685120i
$528$	8813.26	+	2045.03i	0.726416	+	0.168558i
$529$	−1536.26	+	559.154i	−0.126265	+	0.0459566i
$530$	5900.10	+	78.8784i	0.483555	+	0.00646464i
$531$	9439.67			0.771463
$532$	4918.68	−	11956.2i	0.400849	−	0.974371i
$533$	−874.019			−0.0710281
$534$	−5510.05	−	73.6637i	−0.446522	−	0.00596955i
$535$	5881.47	−	2140.68i	0.475286	−	0.172990i
$536$	−8533.90	−	11040.7i	−0.687702	−	0.889713i
$537$	2144.25	−	12160.6i	0.172311	−	0.977226i
$538$	13119.6	−	4577.46i	1.05135	−	0.366818i
$539$	1689.55	−	975.460i	0.135017	−	0.0779518i
$540$	6889.95	+	6102.55i	0.549067	+	0.486318i
$541$	−13830.6	+	11605.2i	−1.09912	+	0.922271i	−0.997366	−	0.0725385i	$-0.976890\pi$
$541$	−13830.6	+	11605.2i	−1.09912	+	0.922271i	−0.101754	+	0.994810i	$0.532446\pi$
$542$	−1215.76	+	6393.89i	−0.0963495	+	0.506718i
$543$	−2298.34	−	1326.95i	−0.181641	−	0.104870i
$544$	17136.4	−	17851.1i	1.35058	−	1.40691i
$545$	−935.355	+	2569.87i	−0.0735160	+	0.201983i
$546$	6973.33	−	3902.70i	0.546577	−	0.305898i
$547$	3024.74	+	17154.1i	0.236432	+	1.34087i	0.839576	+	0.543242i	$0.182803\pi$
$547$	3024.74	+	17154.1i	0.236432	+	1.34087i	−0.603144	+	0.797632i	$0.706086\pi$
$548$	1781.53	+	11966.0i	0.138875	+	0.932782i
$549$	−2846.05	−	2388.12i	−0.221251	−	0.185651i
$550$	−4898.17	+	3999.70i	−0.379743	+	0.310087i
$551$	22702.9	+	4343.15i	1.75531	+	0.335797i
$552$	−2953.46	−	5624.99i	−0.227731	−	0.433724i
$553$	10446.0	−	12449.0i	0.803271	−	0.957301i
$554$	−8496.55	−	5058.12i	−0.651595	−	0.387904i
$555$	3082.14	−	543.465i	0.235729	−	0.0415654i
$556$	−3488.02	+	8840.43i	−0.266052	+	0.674312i
$557$	13992.3	+	5092.79i	1.06441	+	0.387412i	0.814082	−	0.580750i	$-0.197241\pi$
$557$	13992.3	+	5092.79i	1.06441	+	0.387412i	0.250324	+	0.968162i	$0.419463\pi$
$558$	1204.92	−	3177.65i	0.0914124	−	0.241076i
$559$	−8291.31	+	14361.0i	−0.627343	+	1.08659i
$560$	−3288.87	−	10800.4i	−0.248179	−	0.814998i
$561$	−12421.5	−	14803.4i	−0.934826	−	1.11408i
$562$	1081.30	+	6651.07i	0.0811597	+	0.499214i
$563$	−6152.33	−	10656.1i	−0.460550	−	0.797696i	0.538438	−	0.842665i	$-0.319014\pi$
$563$	−6152.33	−	10656.1i	−0.460550	−	0.797696i	−0.998988	+	0.0449689i	$0.985681\pi$
$564$	2261.80	+	1387.77i	0.168864	+	0.103609i
$565$	5795.24	+	1021.86i	0.431518	+	0.0760883i
$566$	−1298.21	−	1119.24i	−0.0964096	−	0.0831186i
$567$	1192.81	+	3277.21i	0.0883477	+	0.242733i
$568$	2502.86	+	545.612i	0.184890	+	0.0403052i
$569$			22841.0i			1.68285i	0.540373	+	0.841426i	$0.318283\pi$
$569$			22841.0i			1.68285i	−0.540373	+	0.841426i	$0.681717\pi$
$570$	−3846.39	+	4332.90i	−0.282645	+	0.318395i
$571$			4995.30i			0.366107i	0.983103	+	0.183053i	$0.0585981\pi$
$571$			4995.30i			0.366107i	−0.983103	+	0.183053i	$0.941402\pi$
$572$	17128.1	−	13608.8i	1.25203	−	0.994774i
$573$	667.271	+	1833.31i	0.0486486	+	0.133661i
$574$	595.174	−	690.345i	0.0432789	−	0.0501994i
$575$	4373.16	+	771.105i	0.317171	+	0.0559258i
$576$	8143.98	−	5788.56i	0.589119	−	0.418733i
$577$	10355.4	+	17936.1i	0.747143	+	1.29409i	0.949187	+	0.314714i	$0.101908\pi$
$577$	10355.4	+	17936.1i	0.747143	+	1.29409i	−0.202043	+	0.979377i	$0.564758\pi$
$578$	−38452.3	+	6251.37i	−2.76714	+	0.449867i
$579$	4104.58	+	4891.65i	0.294612	+	0.351105i
$580$	17744.6	−	9621.76i	1.27035	−	0.688830i
$581$	6853.54	−	11870.7i	0.489385	−	0.847640i
$582$	−4125.52	−	1564.33i	−0.293829	−	0.111415i
$583$	−11204.5	−	4078.10i	−0.795955	−	0.289704i
$584$	−3027.81	−	9486.12i	−0.214540	−	0.672155i
$585$	9194.89	−	1621.31i	0.649850	−	0.114586i
$586$	5993.50	−	10067.8i	0.422507	−	0.709721i
$587$	14600.6	−	17400.3i	1.02663	−	1.22349i	0.0522334	−	0.998635i	$-0.483366\pi$
$587$	14600.6	−	17400.3i	1.02663	−	1.22349i	0.974393	−	0.224851i	$-0.0721895\pi$
$588$	−165.207	+	809.712i	−0.0115868	+	0.0567890i
$589$	4765.87	+	1813.25i	0.333403	+	0.126848i
$590$	7823.15	+	9580.50i	0.545888	+	0.668514i
$591$	−957.500	−	803.438i	−0.0666435	−	0.0559205i
$592$	432.827	−	8086.63i	0.0300491	−	0.561417i
$593$	4572.64	+	25932.7i	0.316654	+	1.79583i	0.562792	+	0.826599i	$0.309727\pi$
$593$	4572.64	+	25932.7i	0.316654	+	1.79583i	−0.246138	+	0.969235i	$0.579162\pi$
$594$	−9083.17	−	16229.8i	−0.627419	−	1.12107i
$595$	−8247.65	+	22660.2i	−0.568270	+	1.56131i
$596$	19004.2	−	6346.97i	1.30611	−	0.436211i
$597$	10024.9	+	5787.86i	0.687254	+	0.396787i
$598$	−15091.4	−	2869.55i	−1.03200	−	0.196228i
$599$	8900.03	−	7468.01i	0.607087	−	0.509407i	−0.286628	−	0.958042i	$-0.592534\pi$
$599$	8900.03	−	7468.01i	0.607087	−	0.509407i	0.893715	+	0.448635i	$0.148090\pi$
$600$	107.399	−	2676.53i	0.00730755	−	0.182115i
$601$	20557.8	−	11869.1i	1.39529	−	0.805573i	0.401398	−	0.915904i	$-0.368524\pi$
$601$	20557.8	−	11869.1i	1.39529	−	0.805573i	0.993895	+	0.110331i	$0.0351911\pi$
$602$	−5696.96	−	16328.2i	−0.385699	−	1.10546i
$603$	−2089.83	+	11852.0i	−0.141135	+	0.800416i
$604$	−11790.3	−	315.305i	−0.794272	−	0.0212410i
$605$	−11373.9	+	4139.76i	−0.764321	+	0.278190i
$606$	−158.284	+	11839.6i	−0.0106103	+	0.793649i
$607$	−16196.4			−1.08302			−0.541508	−	0.840696i	$-0.682146\pi$
$607$	−16196.4			−1.08302			−0.541508	+	0.840696i	$0.682146\pi$
$608$	8671.75	+	12229.3i	0.578431	+	0.815732i
$609$	−14899.8			−0.991413
$610$	65.0759	−	4867.68i	0.00431942	−	0.323093i
$611$	6029.36	−	2194.51i	0.399217	−	0.145303i
$612$	−21333.5	−	570.517i	−1.40908	−	0.0376827i
$613$	888.187	−	5037.16i	0.0585213	−	0.331891i	−0.941465	−	0.337110i	$-0.890550\pi$
$613$	888.187	−	5037.16i	0.0585213	−	0.331891i	0.999986	+	0.00521984i	$0.00166153\pi$
$614$	−811.332	−	2325.38i	−0.0533269	−	0.152841i
$615$	−353.756	+	204.241i	−0.0231949	+	0.0133916i
$616$	−914.702	+	22795.7i	−0.0598286	+	1.49101i
$617$	−13364.3	+	11214.0i	−0.872002	+	0.731697i	−0.964519	−	0.264015i	$-0.914953\pi$
$617$	−13364.3	+	11214.0i	−0.872002	+	0.731697i	0.0925167	+	0.995711i	$0.470509\pi$
$618$	6198.56	+	1178.62i	0.403467	+	0.0767169i
$619$	15855.3	+	9154.09i	1.02953	+	0.594400i	0.916850	−	0.399231i	$-0.130723\pi$
$619$	15855.3	+	9154.09i	1.02953	+	0.594400i	0.112681	+	0.993631i	$0.464056\pi$
$620$	4223.64	−	1410.60i	0.273589	−	0.0913724i
$621$	−4466.86	+	12272.6i	−0.288646	+	0.793047i
$622$	1873.58	+	3347.69i	0.120777	+	0.215804i
$623$	−2412.92	−	13684.3i	−0.155171	−	0.880017i
$624$	−495.274	+	9253.35i	−0.0317738	+	0.593639i
$625$	−6391.87	−	5363.42i	−0.409080	−	0.343259i
$626$	7228.11	+	8851.78i	0.461491	+	0.565157i
$627$	10223.0	−	5706.40i	0.651143	−	0.363463i
$628$	−1786.47	+	8755.82i	−0.113516	+	0.556362i
$629$	−11118.3	+	13250.3i	−0.704796	+	0.839944i
$630$	−4980.78	+	8366.65i	−0.314983	+	0.529103i
$631$	−15916.9	+	2806.58i	−1.00419	+	0.177065i	−0.651478	−	0.758668i	$-0.725851\pi$
$631$	−15916.9	+	2806.58i	−1.00419	+	0.177065i	−0.352709	+	0.935733i	$0.614739\pi$
$632$	5730.15	+	17952.6i	0.360654	+	1.12993i
$633$	−1373.63	−	499.960i	−0.0862510	−	0.0313928i
$634$	−13122.1	−	4975.68i	−0.821993	−	0.311687i
$635$	−11197.4	+	19394.5i	−0.699773	+	1.21204i
$636$	4440.00	−	2407.52i	0.276820	−	0.150101i
$637$	1284.41	+	1530.70i	0.0798902	+	0.0952095i
$638$	−40260.5	+	6545.34i	−2.49832	+	0.406164i
$639$	−1104.63	−	1913.28i	−0.0683859	−	0.118448i
$640$	12624.3	+	3468.20i	0.779716	+	0.214207i
$641$	9457.04	+	1667.53i	0.582731	+	0.102751i	0.457240	−	0.889344i	$-0.348838\pi$
$641$	9457.04	+	1667.53i	0.582731	+	0.102751i	0.125491	+	0.992095i	$0.459949\pi$
$642$	3498.23	−	4057.61i	0.215053	−	0.249441i
$643$	−6725.34	−	18477.7i	−0.412475	−	1.13327i	−0.955870	−	0.293790i	$-0.905084\pi$
$643$	−6725.34	−	18477.7i	−0.412475	−	1.13327i	0.543395	−	0.839477i	$-0.317139\pi$
$644$	12543.2	−	9965.93i	0.767503	−	0.609802i
$645$			7750.07i			0.473114i
$646$	891.847	−	32008.9i	0.0543177	−	1.94949i
$647$			1603.82i			0.0974542i	0.998812	+	0.0487271i	$0.0155165\pi$
$647$			1603.82i			0.0974542i	−0.998812	+	0.0487271i	$0.984484\pi$
$648$	−3951.37	−	861.381i	−0.239544	−	0.0522195i
$649$	−8548.45	−	23486.7i	−0.517035	−	1.42054i
$650$	−4905.52	−	4229.25i	−0.296016	−	0.255207i
$651$	−3237.01	−	570.772i	−0.194882	−	0.0343630i
$652$	−13871.7	−	8511.23i	−0.833219	−	0.511235i
$653$	−9186.54	−	15911.6i	−0.550532	−	0.953549i	−0.998236	−	0.0593672i	$-0.981092\pi$
$653$	−9186.54	−	15911.6i	−0.550532	−	0.953549i	0.447705	−	0.894182i	$-0.352242\pi$
$654$	375.637	+	2310.55i	0.0224596	+	0.138149i
$655$	−2710.67	−	3230.45i	−0.161702	−	0.192708i
$656$	307.902	+	1011.13i	0.0183255	+	0.0601796i
$657$	−4293.93	+	7437.31i	−0.254981	+	0.441639i
$658$	−2372.43	+	6256.67i	−0.140558	+	0.370685i
$659$	10283.1	+	3742.73i	0.607848	+	0.221239i	0.627561	−	0.778567i	$-0.284053\pi$
$659$	10283.1	+	3742.73i	0.607848	+	0.221239i	−0.0197134	+	0.999806i	$0.506275\pi$
$660$	3752.44	−	9510.61i	0.221309	−	0.560909i
$661$	10166.3	−	1792.60i	0.598220	−	0.105482i	0.133665	−	0.991027i	$-0.457325\pi$
$661$	10166.3	−	1792.60i	0.598220	−	0.105482i	0.464555	+	0.885544i	$0.346214\pi$
$662$	13188.4	+	7851.22i	0.774290	+	0.460946i
$663$	12722.5	−	15162.0i	0.745248	−	0.888152i
$664$	7389.12	+	14072.9i	0.431858	+	0.822492i
$665$	−12545.3	−	7487.45i	−0.731560	−	0.436618i
$666$	−5409.77	+	4417.46i	−0.314751	+	0.257016i
$667$	21941.6	+	18411.2i	1.27374	+	1.06879i
$668$	−1748.28	−	11742.7i	−0.101262	−	0.680147i
$669$	−925.136	−	5246.71i	−0.0534646	−	0.303213i
$670$	−13760.8	+	7701.37i	−0.793470	+	0.444075i
$671$	−3364.49	+	9243.87i	−0.193569	+	0.531826i
$672$	−6971.51	−	6692.38i	−0.400196	−	0.384173i
$673$	−26787.8	−	15465.9i	−1.53431	−	0.885836i	−0.999156	−	0.0410834i	$-0.986919\pi$
$673$	−26787.8	−	15465.9i	−1.53431	−	0.885836i	−0.535157	−	0.844753i	$-0.679748\pi$
$674$	−2238.80	+	11774.2i	−0.127946	+	0.672887i
$675$	−4218.24	+	3539.53i	−0.240534	+	0.201832i
$676$	3615.84	+	3202.61i	0.205726	+	0.182215i
$677$	−16723.7	+	9655.43i	−0.949400	+	0.548136i	−0.892894	−	0.450266i	$-0.851329\pi$
$677$	−16723.7	+	9655.43i	−0.949400	+	0.548136i	−0.0565054	+	0.998402i	$0.517996\pi$
$678$	4755.87	−	1659.34i	0.269393	−	0.0939920i
$679$	1931.96	−	10956.7i	0.109193	−	0.619263i
$680$	−17101.2	−	22124.6i	−0.964413	−	1.24771i
$681$	−6314.60	+	2298.33i	−0.355324	+	0.129328i
$682$	−8997.41	−	120.286i	−0.505174	−	0.00675366i
$683$	4486.80			0.251366			0.125683	−	0.992070i	$-0.459888\pi$
$683$	4486.80			0.251366			0.125683	+	0.992070i	$0.459888\pi$
$684$	2768.05	−	12629.8i	0.154735	−	0.706014i
$685$	13671.4			0.762565
$686$	16845.2	+	225.203i	0.937540	+	0.0125340i
$687$	6556.32	−	2386.31i	0.364104	−	0.132523i
$688$	19534.7	+	4532.83i	1.08249	+	0.251181i
$689$	2120.66	−	12026.9i	0.117258	−	0.665004i
$690$	−6778.77	+	2365.14i	−0.374005	+	0.130492i
$691$	−9559.91	+	5519.41i	−0.526304	+	0.303862i	−0.739510	−	0.673146i	$-0.764943\pi$
$691$	−9559.91	+	5519.41i	−0.526304	+	0.303862i	0.213206	+	0.977007i	$0.431609\pi$
$692$	−8756.08	+	9885.86i	−0.481006	+	0.543070i
$693$	15072.5	−	12647.3i	0.826202	−	0.693266i
$694$	−3096.48	+	16284.9i	−0.169367	+	0.890729i
$695$	9300.84	+	5369.84i	0.507628	+	0.293079i
$696$	9231.94	−	14604.7i	0.502782	−	0.795389i
$697$	772.141	−	2121.44i	0.0419611	−	0.115287i
$698$	−3842.16	+	2150.31i	−0.208349	+	0.116605i
$699$	165.073	+	936.175i	0.00893223	+	0.0506572i
$700$	6680.95	−	994.675i	0.360738	−	0.0537074i
$701$	−14540.7	−	12201.1i	−0.783443	−	0.657387i	0.160670	−	0.987008i	$-0.448634\pi$
$701$	−14540.7	−	12201.1i	−0.783443	−	0.657387i	−0.944113	+	0.329621i	$0.893079\pi$
$702$	14754.9	−	12048.4i	0.793288	−	0.647776i
$703$	−6619.07	−	8124.48i	−0.355111	−	0.435876i
$704$	−21777.5	−	15020.8i	−1.16587	−	0.804147i
$705$	1927.55	−	2297.16i	0.102973	−	0.122718i
$706$	26236.3	+	15618.8i	1.39860	+	0.832609i
$707$	−29403.9	+	5184.71i	−1.56414	+	0.275801i
$708$	9848.40	+	3885.72i	0.522776	+	0.206263i
$709$	−526.758	−	191.724i	−0.0279024	−	0.0101556i	0.328031	−	0.944667i	$-0.393615\pi$
$709$	−526.758	−	191.724i	−0.0279024	−	0.0101556i	−0.355934	+	0.934511i	$0.615837\pi$
$710$	1026.36	−	2706.75i	0.0542514	−	0.143074i
$711$	8126.30	−	14075.2i	0.428636	−	0.742419i
$712$	14908.4	+	6113.70i	0.784711	+	0.321799i
$713$	4061.57	+	4840.39i	0.213334	+	0.254241i
$714$	3312.24	+	20373.6i	0.173610	+	1.06788i
$715$	−12360.7	−	21409.4i	−0.646524	−	1.11981i
$716$	−18883.1	+	30775.9i	−0.985606	+	1.60636i
$717$	−5679.04	−	1001.37i	−0.295799	−	0.0521573i
$718$	22832.7	+	19685.0i	1.18678	+	1.02317i
$719$	7806.79	+	21449.0i	0.404929	+	1.11253i	0.959821	+	0.280611i	$0.0905372\pi$
$719$	7806.79	+	21449.0i	0.404929	+	1.11253i	−0.554892	+	0.831922i	$0.687241\pi$
$720$	−5114.85	−	10066.1i	−0.264749	−	0.521031i
$721$			15910.4i			0.821823i
$722$	18945.7	+	4174.52i	0.976575	+	0.215179i
$723$			1106.15i			0.0568991i
$724$	4827.45	+	6075.87i	0.247805	+	0.311889i
$725$	4130.40	+	11348.2i	0.211585	+	0.581326i
$726$	−6765.06	+	7846.82i	−0.345833	+	0.401133i
$727$	−23015.7	−	4058.28i	−1.17415	−	0.207034i	−0.447653	−	0.894207i	$-0.647740\pi$
$727$	−23015.7	−	4058.28i	−1.17415	−	0.207034i	−0.726493	+	0.687174i	$0.758851\pi$
$728$	−23155.9	+	3131.70i	−1.17887	+	0.159435i
$729$	−2956.39	−	5120.61i	−0.150200	−	0.260154i
$730$	−11106.9	+	1805.70i	−0.563129	+	0.0915505i
$731$	−27532.4	−	32811.9i	−1.39306	−	1.66018i
$732$	−1986.25	−	3663.07i	−0.100292	−	0.184960i
$733$	−2935.90	+	5085.13i	−0.147940	+	0.256239i	−0.930466	−	0.366378i	$-0.880598\pi$
$733$	−2935.90	+	5085.13i	−0.147940	+	0.256239i	0.782526	+	0.622618i	$0.213931\pi$
$734$	−18710.0	−	7094.53i	−0.940869	−	0.356763i
$735$	877.554	+	319.404i	0.0440396	+	0.0160291i
$736$	1996.76	+	18469.7i	0.100002	+	0.925003i
$737$	31381.3	−	5533.36i	1.56844	−	0.276559i
$738$	466.299	−	783.281i	0.0232584	−	0.0390691i
$739$	−14256.5	+	16990.3i	−0.709655	+	0.845734i	−0.993582	−	0.113112i	$-0.963918\pi$
$739$	−14256.5	+	16990.3i	−0.709655	+	0.845734i	0.283927	+	0.958846i	$0.408363\pi$
$740$	−8966.72	−	1829.50i	−0.445437	−	0.0908833i
$741$	7574.05	+	9296.66i	0.375492	+	0.460892i
$742$	8055.35	+	9864.86i	0.398546	+	0.488073i
$743$	−7821.99	−	6563.43i	−0.386219	−	0.324077i	0.428919	−	0.903343i	$-0.358895\pi$
$743$	−7821.99	−	6563.43i	−0.386219	−	0.324077i	−0.815138	+	0.579266i	$0.803339\pi$
$744$	2565.13	−	2819.25i	0.126401	−	0.138923i
$745$	−3931.73	−	22298.0i	−0.193352	−	1.09656i
$746$	−8762.09	−	15656.1i	−0.430031	−	0.768376i
$747$	4688.54	−	12881.7i	0.229645	−	0.630944i
$748$	17899.9	+	53596.2i	0.874979	+	2.61988i
$749$	11699.4	+	6754.65i	0.570743	+	0.329519i
$750$	−11564.6	−	2198.94i	−0.563040	−	0.107059i
$751$	11888.5	−	9975.64i	0.577653	−	0.484709i	−0.306522	−	0.951864i	$-0.599165\pi$
$751$	11888.5	−	9975.64i	0.577653	−	0.484709i	0.884176	+	0.467155i	$0.154721\pi$
$752$	−4662.80	−	6202.09i	−0.226110	−	0.300754i
$753$	7823.69	−	4517.01i	0.378634	−	0.218604i
$754$	−13762.6	−	39445.3i	−0.664727	−	1.90519i
$755$	−2314.47	+	13126.0i	−0.111566	+	0.632721i
$756$	−531.077	+	19858.7i	−0.0255490	+	0.955363i
$757$	34145.7	−	12428.0i	1.63943	−	0.596703i	0.652488	−	0.757799i	$-0.273725\pi$
$757$	34145.7	−	12428.0i	1.63943	−	0.596703i	0.986939	+	0.161097i	$0.0515031\pi$
$758$	−279.325	+	20893.5i	−0.0133846	+	1.00117i
$759$	14507.8			0.693809
$760$	15112.3	−	7657.65i	0.721289	−	0.365490i
$761$	24054.3			1.14582			0.572910	−	0.819618i	$-0.305814\pi$
$761$	24054.3			1.14582			0.572910	+	0.819618i	$0.305814\pi$
$762$	−256.249	+	19167.4i	−0.0121823	+	0.911236i
$763$	−5546.81	+	2018.87i	−0.263182	+	0.0957905i
$764$	152.507	−	5702.75i	0.00722188	−	0.270050i
$765$	−4187.83	+	23750.4i	−0.197923	+	1.12248i
$766$	1228.70	+	3521.61i	0.0579566	+	0.166111i
$767$	22169.8	−	12799.7i	1.04368	−	0.602571i
$768$	10879.4	−	2686.83i	0.511167	−	0.126241i
$769$	10067.3	−	8447.46i	0.472088	−	0.396129i	−0.375468	−	0.926836i	$-0.622518\pi$
$769$	10067.3	−	8447.46i	0.472088	−	0.396129i	0.847556	+	0.530707i	$0.178073\pi$
$770$	25327.4	+	4815.86i	1.18537	+	0.225392i
$771$	−13019.8	−	7517.00i	−0.608168	−	0.351126i
$772$	−5914.85	−	17710.4i	−0.275752	−	0.825661i
$773$	1126.46	−	3094.94i	0.0524141	−	0.144007i	−0.910723	−	0.413018i	$-0.864475\pi$
$773$	1126.46	−	3094.94i	0.0524141	−	0.144007i	0.963137	+	0.269011i	$0.0866969\pi$
$774$	−8446.56	−	15092.3i	−0.392255	−	0.700879i
$775$	462.619	+	2623.64i	0.0214423	+	0.121605i
$776$	9542.67	+	8682.49i	0.441446	+	0.401654i
$777$	5174.73	+	4342.12i	0.238922	+	0.200479i
$778$	3006.81	+	3682.24i	0.138559	+	0.169685i
$779$	1174.49	+	700.971i	0.0540185	+	0.0322399i
$780$	10260.4	+	2093.45i	0.471002	+	0.0960995i
$781$	−3760.05	+	4481.06i	−0.172273	+	0.205307i
$782$	20297.4	−	34095.2i	0.928174	−	1.55913i
$783$	−34978.4	+	6167.63i	−1.59646	+	0.281498i
$784$	1318.34	−	2025.13i	0.0600557	−	0.0922527i
$785$	9489.44	+	3453.87i	0.431455	+	0.157037i
$786$	−3375.14	−	1279.80i	−0.153165	−	0.0580776i
$787$	−4719.34	+	8174.13i	−0.213756	+	0.370237i	−0.952887	−	0.303325i	$-0.901903\pi$
$787$	−4719.34	+	8174.13i	−0.213756	+	0.370237i	0.739131	+	0.673562i	$0.235237\pi$
$788$	1742.17	+	3212.95i	0.0787594	+	0.145249i
$789$	−8699.76	−	10368.0i	−0.392547	−	0.467819i
$790$	21019.9	−	3417.30i	0.946649	−	0.153901i
$791$	6350.72	+	10999.8i	0.285468	+	0.494446i
$792$	3057.91	+	22610.3i	0.137195	+	1.01442i
$793$	−9922.36	−	1749.58i	−0.444330	−	0.0783473i
$794$	4923.05	−	5710.27i	0.220041	−	0.255226i
$795$	−1952.12	−	5363.40i	−0.0870874	−	0.239271i
$796$	−21056.3	−	26501.7i	−0.937591	−	1.18006i
$797$		−	30429.6i		−	1.35241i	−0.736713	−	0.676206i	$-0.763623\pi$
$797$		−	30429.6i		−	1.35241i	0.736713	−	0.676206i	$-0.236377\pi$
$798$	−12500.6	−	348.299i	−0.554533	−	0.0154507i
$799$			16573.3i			0.733819i
$800$	−3164.55	+	7164.94i	−0.139855	+	0.316649i
$801$	−4752.96	−	13058.7i	−0.209660	−	0.576036i
$802$	16776.2	+	14463.4i	0.738638	+	0.636809i
$803$	22393.2	+	3948.52i	0.984106	+	0.173525i
$804$	−7059.04	+	11504.9i	−0.309643	+	0.504661i
$805$	−9051.98	−	15678.5i	−0.396323	−	0.686452i
$806$	−1478.91	−	9096.77i	−0.0646306	−	0.397544i
$807$	−8639.48	−	10296.1i	−0.376858	−	0.449121i
$808$	13136.7	−	32034.1i	0.571965	−	1.39475i
$809$	−10850.4	+	18793.4i	−0.471544	+	0.816738i	−0.999470	−	0.0325521i	$-0.989637\pi$
$809$	−10850.4	+	18793.4i	−0.471544	+	0.816738i	0.527926	+	0.849290i	$0.322970\pi$
$810$	−1620.35	+	4273.26i	−0.0702881	+	0.185367i
$811$	−481.539	−	175.266i	−0.0208497	−	0.00758868i	0.331574	−	0.943429i	$-0.392420\pi$
$811$	−481.539	−	175.266i	−0.0208497	−	0.00758868i	−0.352424	+	0.935840i	$0.614642\pi$
$812$	40527.7	+	15990.3i	1.75153	+	0.691073i
$813$	6199.90	−	1093.21i	0.267454	−	0.0471594i
$814$	15890.0	+	9459.55i	0.684207	+	0.407318i
$815$	−11821.8	+	14088.6i	−0.508096	+	0.605525i
$816$	−22022.4	−	9376.89i	−0.944777	−	0.402276i
$817$	22659.3	−	12648.3i	0.970317	−	0.541624i
$818$	−480.132	+	392.062i	−0.0205225	+	0.0167581i
$819$	15437.7	+	12953.7i	0.658652	+	0.552675i
$820$	1181.41	−	175.891i	0.0503131	−	0.00749073i
$821$	1362.93	+	7729.55i	0.0579373	+	0.328579i	0.999976	−	0.00692543i	$-0.00220445\pi$
$821$	1362.93	+	7729.55i	0.0579373	+	0.328579i	−0.942039	+	0.335504i	$0.891093\pi$
$822$	10211.7	−	5715.10i	0.433302	−	0.242503i
$823$	14029.3	−	38545.1i	0.594204	−	1.63256i	−0.168417	−	0.985716i	$-0.553866\pi$
$823$	14029.3	−	38545.1i	0.594204	−	1.63256i	0.762621	−	0.646846i	$-0.223912\pi$
$824$	−15595.3	−	9858.11i	−0.659330	−	0.416776i
$825$	5297.37	+	3058.44i	0.223552	+	0.129068i
$826$	−4986.91	+	26227.0i	−0.210069	+	1.10479i
$827$	10319.4	−	8659.04i	0.433908	−	0.364092i	−0.399516	−	0.916726i	$-0.630822\pi$
$827$	10319.4	−	8659.04i	0.433908	−	0.364092i	0.833424	+	0.552634i	$0.186377\pi$
$828$	10623.1	−	11993.8i	0.445867	−	0.503396i
$829$	−4941.50	+	2852.98i	−0.207027	+	0.119527i	−0.599929	−	0.800053i	$-0.704805\pi$
$829$	−4941.50	+	2852.98i	−0.207027	+	0.119527i	0.392902	+	0.919580i	$0.371471\pi$
$830$	16959.5	−	5917.22i	0.709243	−	0.247458i
$831$	−1660.90	+	9419.40i	−0.0693331	+	0.393208i
$832$	11277.8	−	24637.7i	0.469936	−	1.02663i
$833$	−4850.04	+	1765.27i	−0.201733	+	0.0734249i
$834$	9191.95	+	122.887i	0.381644	+	0.00510220i
$835$	−13416.2			−0.556032
$836$	−33930.7	+	4550.27i	−1.40373	+	0.188247i
$837$	−7835.38			−0.323573
$838$	−42203.4	−	564.217i	−1.73973	−	0.0232584i
$839$	−4622.73	+	1682.53i	−0.190220	+	0.0692343i	−0.435374	−	0.900250i	$-0.643384\pi$
$839$	−4622.73	+	1682.53i	−0.190220	+	0.0692343i	0.245154	+	0.969484i	$0.421161\pi$
$840$	−8640.47	+	6678.64i	−0.354910	+	0.274327i
$841$	−9291.27	+	52693.4i	−0.380961	+	2.16054i
$842$	13485.1	−	4704.99i	0.551932	−	0.192571i
$843$	5644.73	−	3258.98i	0.230622	−	0.133150i
$844$	3199.74	+	2834.07i	0.130497	+	0.115584i
$845$	4181.40	−	3508.61i	0.170230	−	0.142840i
$846$	−1250.05	+	6574.20i	−0.0508008	+	0.267170i
$847$	−22624.9	−	13062.5i	−0.917828	−	0.529908i
$848$	−14660.6	+	1783.54i	−0.593688	+	0.0722251i
$849$	−567.070	+	1558.01i	−0.0229232	+	0.0629810i
$850$	14599.0	−	8170.52i	0.589110	−	0.329702i
$851$	−2254.95	−	12788.5i	−0.0908329	−	0.515139i
$852$	−364.885	−	2450.83i	−0.0146723	−	0.0985494i
$853$	−1151.07	−	965.866i	−0.0462040	−	0.0387698i	0.619393	−	0.785081i	$-0.287379\pi$
$853$	−1151.07	−	965.866i	−0.0462040	−	0.0387698i	−0.665597	+	0.746311i	$0.731823\pi$
$854$	8138.67	−	6645.79i	0.326112	−	0.266293i
$855$	−13656.2	−	5195.71i	−0.546237	−	0.207824i
$856$	−13869.9	+	7282.51i	−0.553810	+	0.290784i
$857$	−3638.05	+	4335.66i	−0.145010	+	0.172816i	−0.833661	−	0.552277i	$-0.813759\pi$
$857$	−3638.05	+	4335.66i	−0.145010	+	0.172816i	0.688651	+	0.725093i	$0.258203\pi$
$858$	−18182.6	−	10824.3i	−0.723477	−	0.430696i
$859$	40249.9	−	7097.14i	1.59873	−	0.281899i	0.697941	−	0.716156i	$-0.254100\pi$
$859$	40249.9	−	7097.14i	1.59873	−	0.281899i	0.900789	+	0.434256i	$0.142989\pi$
$860$	8317.32	−	21080.3i	0.329789	−	0.835853i
$861$	−828.499	−	301.549i	−0.0327935	−	0.0119358i
$862$	13299.3	−	35073.4i	0.525493	−	1.38585i
$863$	−13973.3	+	24202.5i	−0.551168	+	0.954651i	0.447023	+	0.894523i	$0.352484\pi$
$863$	−13973.3	+	24202.5i	−0.551168	+	0.954651i	−0.998191	+	0.0601281i	$0.980849\pi$
$864$	−19136.4	−	12825.1i	−0.753510	−	0.504997i
$865$	9592.70	+	11432.1i	0.377066	+	0.449369i
$866$	−2821.81	−	17357.0i	−0.110726	−	0.681079i
$867$	18841.4	+	32634.3i	0.738048	+	1.27834i
$868$	8192.18	+	5026.44i	0.320346	+	0.196554i
$869$	−42379.2	−	7472.61i	−1.65434	−	0.291704i
$870$	−14788.0	−	12749.3i	−0.576275	−	0.496830i
$871$	11162.6	+	30669.1i	0.434249	+	1.19309i
$872$	1457.92	−	6687.86i	0.0566187	−	0.259724i
$873$		−	11126.8i		−	0.431368i
$874$	17978.2	+	15959.5i	0.695790	+	0.617664i
$875$		−	29683.9i		−	1.14686i
$876$	−7541.33	+	5991.80i	−0.290865	+	0.231100i
$877$	2630.31	+	7226.72i	0.101276	+	0.278254i	0.979974	−	0.199124i	$-0.0638095\pi$
$877$	2630.31	+	7226.72i	0.101276	+	0.278254i	−0.878698	+	0.477378i	$0.841587\pi$
$878$	11093.6	−	12867.5i	0.426414	−	0.494600i
$879$	−11161.3	−	1968.04i	−0.428284	−	0.0755180i
$880$	−20413.4	+	21841.9i	−0.781973	+	0.836694i
$881$	−10516.5	−	18215.0i	−0.402166	−	0.696573i	0.591821	−	0.806070i	$-0.298409\pi$
$881$	−10516.5	−	18215.0i	−0.402166	−	0.696573i	−0.993987	+	0.109497i	$0.965076\pi$
$882$	−2057.03	+	334.421i	−0.0785304	+	0.0127671i
$883$	4242.43	+	5055.93i	0.161686	+	0.192690i	0.840805	−	0.541338i	$-0.182082\pi$
$883$	4242.43	+	5055.93i	0.161686	+	0.192690i	−0.679118	+	0.734029i	$0.737638\pi$
$884$	−50877.1	+	27587.4i	−1.93573	+	1.04962i
$885$	5982.11	−	10361.3i	0.227216	−	0.393550i
$886$	−21835.1	−	8279.53i	−0.827951	−	0.313946i
$887$	30205.5	+	10993.9i	1.14341	+	0.416166i	0.843142	−	0.537691i	$-0.180703\pi$
$887$	30205.5	+	10993.9i	1.14341	+	0.416166i	0.300263	+	0.953856i	$0.402925\pi$
$888$	−7462.40	+	2381.87i	−0.282006	+	0.0900115i
$889$	−47602.7	+	8393.64i	−1.79589	+	0.316663i
$890$	9314.45	−	15646.3i	0.350810	−	0.589286i
$891$	5936.15	−	7074.43i	0.223197	−	0.265996i
$892$	−3114.34	+	15264.0i	−0.116901	+	0.572955i
$893$	−9862.14	−	1886.67i	−0.369568	−	0.0706997i
$894$	−12258.1	−	15011.7i	−0.458581	−	0.561594i
$895$	31257.1	+	26227.8i	1.16739	+	0.979553i
$896$	11780.4	+	25685.1i	0.439237	+	0.957679i
$897$	2580.29	+	14633.6i	0.0960462	+	0.544705i
$898$	−9629.54	−	17206.0i	−0.357842	−	0.639390i
$899$	−5877.26	+	16147.6i	−0.218040	+	0.599059i
$900$	6407.33	−	2139.90i	0.237309	−	0.0792555i
$901$	27318.4	+	15772.3i	1.01011	+	0.583188i
$902$	−2371.14	−	450.859i	−0.0875282	−	0.0166430i
$903$	−12814.2	+	10752.4i	−0.472238	+	0.396255i
$904$	−14716.8	−	590.529i	−0.541455	−	0.0217265i
$905$	7594.58	−	4384.73i	0.278953	−	0.161054i
$906$	3758.34	+	10771.9i	0.137817	+	0.395001i
$907$	4565.42	−	25891.8i	0.167136	−	0.947875i	−0.779699	−	0.626155i	$-0.784628\pi$
$907$	4565.42	−	25891.8i	0.167136	−	0.947875i	0.946835	−	0.321720i	$-0.104261\pi$
$908$	19642.4	+	525.291i	0.717902	+	0.0191987i
$909$	−28059.5	+	10212.8i	−1.02385	+	0.372650i
$910$	−352.987	+	26403.4i	−0.0128587	+	0.961830i
$911$	−26457.1			−0.962200			−0.481100	−	0.876666i	$-0.659763\pi$
$911$	−26457.1			−0.962200			−0.481100	+	0.876666i	$0.659763\pi$
$912$	8086.81	−	12037.3i	0.293620	−	0.437054i
$913$	−36296.5			−1.31570
$914$	29.8974	−	2236.32i	0.00108197	−	0.0809310i
$915$	−4424.89	+	1610.53i	−0.159871	+	0.0581884i
$916$	−20394.3	−	545.399i	−0.735639	−	0.0196730i
$917$	1580.56	−	8963.82i	0.0569191	−	0.322804i
$918$	16209.2	+	46457.5i	0.582770	+	1.67029i
$919$	38407.1	−	22174.4i	1.37860	−	0.795936i	0.386610	−	0.922243i	$-0.373646\pi$
$919$	38407.1	−	22174.4i	1.37860	−	0.795936i	0.991991	+	0.126308i	$0.0403127\pi$
$920$	20976.6	+	841.709i	0.751715	+	0.0301634i
$921$	−1824.94	+	1531.30i	−0.0652918	+	0.0547863i
$922$	−17336.8	−	3296.48i	−0.619258	−	0.117748i
$923$	−5188.64	−	2995.66i	−0.185034	−	0.106829i
$924$	20931.3	−	6990.56i	0.745226	−	0.248888i
$925$	1872.60	−	5144.94i	0.0665631	−	0.182881i
$926$	7623.64	+	13621.9i	0.270549	+	0.483415i
$927$	2763.07	+	15670.2i	0.0978977	+	0.555205i
$928$	−40784.7	+	29817.4i	−1.44270	+	1.05475i
$929$	2662.47	+	2234.08i	0.0940288	+	0.0788995i	0.688590	−	0.725151i	$-0.258230\pi$
$929$	2662.47	+	2234.08i	0.0940288	+	0.0788995i	−0.594561	+	0.804050i	$0.702674\pi$
$930$	−2724.32	−	3336.30i	−0.0960581	−	0.117636i
$931$	−498.328	−	3087.03i	−0.0175425	−	0.108672i
$932$	555.694	−	2723.57i	0.0195304	−	0.0957225i
$933$	2385.27	−	2842.66i	0.0836981	−	0.0997475i
$934$	3851.83	−	6470.25i	0.134942	−	0.226673i
$935$	62885.3	−	11088.4i	2.19954	−	0.387838i
$936$	−22262.4	+	7105.77i	−0.777425	+	0.248141i
$937$	−23089.3	−	8403.81i	−0.805010	−	0.293000i	−0.0934489	−	0.995624i	$-0.529789\pi$
$937$	−23089.3	−	8403.81i	−0.805010	−	0.293000i	−0.711561	+	0.702624i	$0.752011\pi$
$938$	−31825.3	−	12067.7i	−1.10782	−	0.420067i
$939$	5527.09	−	9573.21i	0.192087	−	0.332705i
$940$	−7708.27	+	4179.70i	−0.267464	+	0.145028i
$941$	17898.9	+	21331.0i	0.620070	+	0.738971i	0.981082	−	0.193590i	$-0.0620132\pi$
$941$	17898.9	+	21331.0i	0.620070	+	0.738971i	−0.361012	+	0.932561i	$0.617569\pi$
$942$	8531.88	−	1387.07i	0.295099	−	0.0479757i
$943$	847.442	+	1467.81i	0.0292646	+	0.0506877i
$944$	−22617.7	−	21138.5i	−0.779813	−	0.728811i
$945$	22108.5	+	3898.32i	0.761046	+	0.134193i
$946$	−29901.7	+	34683.1i	−1.02768	+	1.19201i
$947$	−16384.4	−	45015.6i	−0.562217	−	1.54468i	−0.816378	−	0.577518i	$-0.804021\pi$
$947$	−16384.4	−	45015.6i	−0.562217	−	1.54468i	0.254161	−	0.967162i	$-0.418201\pi$
$948$	14272.0	−	11339.5i	0.488960	−	0.388492i
$949$			23289.5i			0.796637i
$950$	3200.05	+	9617.45i	0.109288	+	0.328454i
$951$			13574.7i			0.462870i
$952$	12855.5	−	58971.3i	0.437656	−	2.00764i
$953$	8020.66	+	22036.6i	0.272628	+	0.749040i	0.998148	+	0.0608384i	$0.0193774\pi$
$953$	8020.66	+	22036.6i	0.272628	+	0.749040i	−0.725519	+	0.688202i	$0.758400\pi$
$954$	9646.90	+	8316.98i	0.327390	+	0.282256i
$955$	−6348.81	−	1119.47i	−0.215123	−	0.0379320i
$956$	14372.4	+	8818.43i	0.486231	+	0.298335i
$957$	19727.4	+	34168.9i	0.666350	+	1.15415i
$958$	−8225.77	−	50596.8i	−0.277414	−	1.70638i
$959$	18967.6	+	22604.7i	0.638682	+	0.761152i
$960$	−1192.72	−	12607.5i	−0.0400989	−	0.423858i
$961$	13000.1	−	22516.8i	0.436376	−	0.755825i
$962$	−6715.41	+	17710.1i	−0.225066	+	0.593553i
$963$	12695.8	+	4620.89i	0.424835	+	0.154627i
$964$	1187.11	−	3008.74i	0.0396620	−	0.100524i
$965$	−20779.9	+	3664.05i	−0.693190	+	0.122228i
$966$	−13315.4	−	7926.86i	−0.443495	−	0.264019i
$967$	−26560.0	+	31653.0i	−0.883260	+	1.05263i	0.114982	+	0.993368i	$0.463319\pi$
$967$	−26560.0	+	31653.0i	−0.883260	+	1.05263i	−0.998243	+	0.0592610i	$0.981126\pi$
$968$	26822.2	−	14083.3i	0.890598	−	0.467618i
$969$	−29256.3	+	10170.9i	−0.969914	+	0.337190i
$970$	11292.8	−	9221.35i	0.373803	−	0.305237i
$971$	−37610.0	−	31558.6i	−1.24301	−	1.04301i	−0.997283	−	0.0736705i	$-0.976529\pi$
$971$	−37610.0	−	31558.6i	−1.24301	−	1.04301i	−0.245728	−	0.969339i	$-0.579027\pi$
$972$	4623.94	+	31057.7i	0.152585	+	1.02487i
$973$	4025.27	+	22828.4i	0.132625	+	0.752154i
$974$	28366.4	−	15875.6i	0.933182	−	0.522266i
$975$	−2142.78	+	5887.23i	−0.0703834	+	0.193377i
$976$	1471.45	+	12095.2i	0.0482580	+	0.396679i
$977$	−11941.1	−	6894.21i	−0.391024	−	0.225758i	0.291580	−	0.956547i	$-0.405819\pi$
$977$	−11941.1	−	6894.21i	−0.391024	−	0.225758i	−0.682604	+	0.730789i	$0.739152\pi$
$978$	−2940.63	+	15465.2i	−0.0961461	+	0.505648i
$979$	−28186.8	+	23651.5i	−0.920177	+	0.772120i
$980$	−2044.18	−	1810.57i	−0.0666316	−	0.0590168i
$981$	−5112.45	+	2951.67i	−0.166389	+	0.0960649i
$982$	−34506.1	+	12039.3i	−1.12132	+	0.391232i
$983$	−8933.86	+	50666.4i	−0.289874	+	1.64396i	0.397464	+	0.917618i	$0.369890\pi$
$983$	−8933.86	+	50666.4i	−0.289874	+	1.64396i	−0.687338	+	0.726338i	$0.741221\pi$
$984$	808.917	−	625.251i	0.0262066	−	0.0202564i
$985$	3881.16	−	1412.63i	0.125547	−	0.0456954i
$986$	107901.	+	1442.53i	3.48505	+	0.0465917i
$987$	6472.48			0.208735
$988$	−10624.5	−	33415.5i	−0.342114	−	1.07600i
$989$	32156.7			1.03390
$990$	25781.3	+	344.670i	0.827661	+	0.0110650i
$991$	29953.8	−	10902.3i	0.960155	−	0.349468i	0.186061	−	0.982538i	$-0.440428\pi$
$991$	29953.8	−	10902.3i	0.960155	−	0.349468i	0.774094	+	0.633070i	$0.218206\pi$
$992$	−10002.8	+	4915.54i	−0.320150	+	0.157327i
$993$	2578.04	−	14620.8i	0.0823885	−	0.467248i
$994$	5899.39	−	2058.32i	0.188247	−	0.0656800i
$995$	−33126.0	+	19125.3i	−1.05544	+	0.609360i
$996$	10194.1	−	11509.4i	0.324310	−	0.366155i
$997$	−9386.69	+	7876.37i	−0.298174	+	0.250198i	−0.779584	−	0.626298i	$-0.784569\pi$
$997$	−9386.69	+	7876.37i	−0.298174	+	0.250198i	0.481410	+	0.876496i	$0.340125\pi$
$998$	3977.63	−	20919.0i	0.126162	−	0.663507i
$999$	13945.4	+	8051.40i	0.441656	+	0.254990i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.4.k.a.3.15	yes	168
4.3	odd	2	inner	76.4.k.a.3.2	✓	168
19.13	odd	18	inner	76.4.k.a.51.2	yes	168
76.51	even	18	inner	76.4.k.a.51.15	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.4.k.a.3.2	✓	168	4.3	odd	2	inner
76.4.k.a.3.15	yes	168	1.1	even	1	trivial
76.4.k.a.51.2	yes	168	19.13	odd	18	inner
76.4.k.a.51.15	yes	168	76.51	even	18	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 76 = 2^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	76.k (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0378098 + 2.82817i) q^{2} +(2.57091 - 0.935735i) q^{3} +(-7.99714 - 0.213866i) q^{4} +(-1.56986 + 8.90313i) q^{5} +(2.54921 + 7.30636i) q^{6} +(-16.8987 + 9.75650i) q^{7} +(0.907220 - 22.6092i) q^{8} +(-14.9492 + 12.5439i) q^{9} +O(q^{10})\)	\(q+(-0.0378098 + 2.82817i) q^{2} +(2.57091 - 0.935735i) q^{3} +(-7.99714 - 0.213866i) q^{4} +(-1.56986 + 8.90313i) q^{5} +(2.54921 + 7.30636i) q^{6} +(-16.8987 + 9.75650i) q^{7} +(0.907220 - 22.6092i) q^{8} +(-14.9492 + 12.5439i) q^{9} +(-25.1202 - 4.77647i) q^{10} +(44.7480 + 25.8353i) q^{11} +(-20.7600 + 6.93337i) q^{12} +(-18.1005 + 49.7308i) q^{13} +(-26.9541 - 48.1615i) q^{14} +(4.29499 + 24.3581i) q^{15} +(63.9085 + 3.42063i) q^{16} +(-104.717 - 87.8680i) q^{17} +(-34.9111 - 42.7533i) q^{18} +(64.2076 - 52.3104i) q^{19} +(14.4585 - 70.8638i) q^{20} +(-34.3157 + 40.8958i) q^{21} +(-74.7586 + 125.578i) q^{22} +(101.067 - 17.8209i) q^{23} +(-18.8239 - 58.9752i) q^{24} +(40.6603 + 14.7992i) q^{25} +(-139.963 - 53.0717i) q^{26} +(-63.6301 + 110.211i) q^{27} +(137.228 - 74.4100i) q^{28} +(179.400 + 213.801i) q^{29} +(-69.0514 + 11.2260i) q^{30} +(30.7849 + 53.3210i) q^{31} +(-12.0905 + 180.615i) q^{32} +(139.218 + 24.5479i) q^{33} +(252.465 - 292.836i) q^{34} +(-60.3346 - 165.768i) q^{35} +(122.234 - 97.1181i) q^{36} -126.535i q^{37} +(145.515 + 183.568i) q^{38} +144.791i q^{39} +(199.869 + 43.5705i) q^{40} +(5.64850 + 15.5191i) q^{41} +(-114.363 - 98.5969i) q^{42} +(308.578 + 54.4106i) q^{43} +(-352.331 - 216.179i) q^{44} +(-88.2116 - 152.787i) q^{45} +(46.5792 + 286.509i) q^{46} +(-77.9316 - 92.8752i) q^{47} +(167.504 - 51.0073i) q^{48} +(18.8784 - 32.6984i) q^{49} +(-43.3919 + 114.435i) q^{50} +(-351.439 - 127.913i) q^{51} +(155.388 - 393.833i) q^{52} +(-227.255 + 40.0712i) q^{53} +(-309.289 - 184.124i) q^{54} +(-300.263 + 357.840i) q^{55} +(205.256 + 390.919i) q^{56} +(116.123 - 194.567i) q^{57} +(-611.449 + 499.291i) q^{58} +(-370.549 - 310.928i) q^{59} +(-29.1383 - 195.714i) q^{60} +(33.0594 + 187.489i) q^{61} +(-151.965 + 85.0490i) q^{62} +(130.239 - 357.828i) q^{63} +(-510.354 - 41.0231i) q^{64} +(-414.344 - 239.222i) q^{65} +(-74.6896 + 392.805i) q^{66} +(472.421 - 396.409i) q^{67} +(818.645 + 725.088i) q^{68} +(243.159 - 140.388i) q^{69} +(471.102 - 164.369i) q^{70} +(-19.6586 + 111.490i) q^{71} +(270.045 + 349.370i) q^{72} +(413.529 - 150.512i) q^{73} +(357.862 + 4.78425i) q^{74} +118.382 q^{75} +(-524.665 + 404.602i) q^{76} -1008.25 q^{77} +(-409.493 - 5.47451i) q^{78} +(-782.608 + 284.846i) q^{79} +(-130.782 + 563.616i) q^{80} +(31.0359 - 176.013i) q^{81} +(-44.1044 + 15.3882i) q^{82} +(-608.348 + 351.230i) q^{83} +(283.173 - 319.711i) q^{84} +(946.691 - 794.368i) q^{85} +(-165.550 + 870.655i) q^{86} +(661.283 + 381.792i) q^{87} +(624.712 - 988.280i) q^{88} +(-243.556 + 669.166i) q^{89} +(435.444 - 243.701i) q^{90} +(-179.322 - 1016.99i) q^{91} +(-812.059 + 120.901i) q^{92} +(129.040 + 108.277i) q^{93} +(265.614 - 216.892i) q^{94} +(364.929 + 653.769i) q^{95} +(137.924 + 475.659i) q^{96} +(-366.498 + 436.776i) q^{97} +(91.7630 + 54.6278i) q^{98} +(-993.024 + 175.097i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 6 q^{2} - 24 q^{4} - 12 q^{5} - 24 q^{6} - 9 q^{8} + 18 q^{9}+O(q^{10}) \) 168 * q - 6 * q^2 - 24 * q^4 - 12 * q^5 - 24 * q^6 - 9 * q^8 + 18 * q^9	\( 168 q - 6 q^{2} - 24 q^{4} - 12 q^{5} - 24 q^{6} - 9 q^{8} + 18 q^{9} - 105 q^{10} - 9 q^{12} - 120 q^{13} + 69 q^{14} + 192 q^{16} - 12 q^{17} + 558 q^{20} + 6 q^{21} - 30 q^{22} + 96 q^{24} - 12 q^{25} - 411 q^{26} + 756 q^{28} - 12 q^{29} + 276 q^{30} - 471 q^{32} - 576 q^{33} + 36 q^{34} - 2673 q^{36} - 648 q^{38} - 2298 q^{40} - 606 q^{41} - 321 q^{42} - 1203 q^{44} - 6 q^{45} + 1566 q^{46} + 3237 q^{48} + 2346 q^{49} + 3204 q^{50} + 1077 q^{52} + 576 q^{53} - 627 q^{54} - 12 q^{57} - 4116 q^{58} + 90 q^{60} + 3528 q^{61} - 3300 q^{62} - 381 q^{64} + 1242 q^{65} + 276 q^{66} + 1170 q^{68} - 4770 q^{69} + 1449 q^{70} + 1146 q^{72} - 3468 q^{73} + 3105 q^{74} + 4386 q^{76} - 9396 q^{77} + 6939 q^{78} + 2133 q^{80} + 1980 q^{81} + 7299 q^{82} + 315 q^{84} - 516 q^{85} - 3804 q^{86} - 5841 q^{88} + 3576 q^{89} - 8898 q^{90} - 7668 q^{92} + 5694 q^{93} + 18942 q^{96} + 774 q^{97} + 8745 q^{98}+O(q^{100}) \) 168 * q - 6 * q^2 - 24 * q^4 - 12 * q^5 - 24 * q^6 - 9 * q^8 + 18 * q^9 - 105 * q^10 - 9 * q^12 - 120 * q^13 + 69 * q^14 + 192 * q^16 - 12 * q^17 + 558 * q^20 + 6 * q^21 - 30 * q^22 + 96 * q^24 - 12 * q^25 - 411 * q^26 + 756 * q^28 - 12 * q^29 + 276 * q^30 - 471 * q^32 - 576 * q^33 + 36 * q^34 - 2673 * q^36 - 648 * q^38 - 2298 * q^40 - 606 * q^41 - 321 * q^42 - 1203 * q^44 - 6 * q^45 + 1566 * q^46 + 3237 * q^48 + 2346 * q^49 + 3204 * q^50 + 1077 * q^52 + 576 * q^53 - 627 * q^54 - 12 * q^57 - 4116 * q^58 + 90 * q^60 + 3528 * q^61 - 3300 * q^62 - 381 * q^64 + 1242 * q^65 + 276 * q^66 + 1170 * q^68 - 4770 * q^69 + 1449 * q^70 + 1146 * q^72 - 3468 * q^73 + 3105 * q^74 + 4386 * q^76 - 9396 * q^77 + 6939 * q^78 + 2133 * q^80 + 1980 * q^81 + 7299 * q^82 + 315 * q^84 - 516 * q^85 - 3804 * q^86 - 5841 * q^88 + 3576 * q^89 - 8898 * q^90 - 7668 * q^92 + 5694 * q^93 + 18942 * q^96 + 774 * q^97 + 8745 * q^98

Introduction

L-functions

Modular forms

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