LMFDB - Embedded newform 76.4.k.a.3.9

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			3.9
Character	$\chi$	$=$	76.3
Dual form			76.4.k.a.51.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.70042 - 2.26022i) q^{2} +(5.85727 - 2.13187i) q^{3} +(-2.21716 + 7.68663i) q^{4} +(0.184577 - 1.04679i) q^{5} +(-14.7783 - 9.61362i) q^{6} +(24.9926 - 14.4295i) q^{7} +(21.1435 - 8.05922i) q^{8} +(9.07949 - 7.61860i) q^{9} +O(q^{10})$	\(q+(-1.70042 - 2.26022i) q^{2} +(5.85727 - 2.13187i) q^{3} +(-2.21716 + 7.68663i) q^{4} +(0.184577 - 1.04679i) q^{5} +(-14.7783 - 9.61362i) q^{6} +(24.9926 - 14.4295i) q^{7} +(21.1435 - 8.05922i) q^{8} +(9.07949 - 7.61860i) q^{9} +(-2.67983 + 1.36279i) q^{10} +(-11.5175 - 6.64963i) q^{11} +(3.40041 + 49.7493i) q^{12} +(4.71264 - 12.9479i) q^{13} +(-75.1115 - 31.9525i) q^{14} +(-1.15050 - 6.52481i) q^{15} +(-54.1684 - 34.0849i) q^{16} +(-2.09249 - 1.75581i) q^{17} +(-32.6586 - 7.56682i) q^{18} +(14.4557 - 81.5477i) q^{19} +(7.63703 + 3.73967i) q^{20} +(115.626 - 137.798i) q^{21} +(4.55495 + 37.3392i) q^{22} +(-157.313 + 27.7384i) q^{23} +(106.662 - 92.2803i) q^{24} +(116.400 + 42.3661i) q^{25} +(-37.2784 + 11.3652i) q^{26} +(-47.2087 + 81.7678i) q^{27} +(55.5014 + 224.101i) q^{28} +(108.216 + 128.967i) q^{29} +(-12.7912 + 13.6953i) q^{30} +(49.0642 + 84.9816i) q^{31} +(15.0696 + 180.391i) q^{32} +(-81.6372 - 14.3948i) q^{33} +(-0.410397 + 7.71508i) q^{34} +(-10.4915 - 28.8253i) q^{35} +(38.4306 + 86.6823i) q^{36} +90.3215i q^{37} +(-208.896 + 105.992i) q^{38} -85.8859i q^{39} +(-4.53369 - 23.6204i) q^{40} +(20.7248 + 56.9408i) q^{41} +(-508.066 - 27.0262i) q^{42} +(244.517 + 43.1149i) q^{43} +(76.6493 - 73.7874i) q^{44} +(-6.29920 - 10.9105i) q^{45} +(330.192 + 308.393i) q^{46} +(242.225 + 288.672i) q^{47} +(-389.943 - 84.1644i) q^{48} +(244.919 - 424.211i) q^{49} +(-102.172 - 335.129i) q^{50} +(-15.9994 - 5.82331i) q^{51} +(89.0768 + 64.9318i) q^{52} +(-680.228 + 119.943i) q^{53} +(265.088 - 32.3377i) q^{54} +(-9.08662 + 10.8290i) q^{55} +(412.141 - 506.510i) q^{56} +(-89.1781 - 508.464i) q^{57} +(107.481 - 463.891i) q^{58} +(-542.903 - 455.550i) q^{59} +(52.7046 + 5.62307i) q^{60} +(98.4793 + 558.504i) q^{61} +(108.647 - 255.400i) q^{62} +(116.987 - 321.420i) q^{63} +(382.098 - 340.801i) q^{64} +(-12.6838 - 7.32302i) q^{65} +(106.282 + 208.995i) q^{66} +(-236.636 + 198.561i) q^{67} +(18.1356 - 12.1913i) q^{68} +(-862.287 + 497.841i) q^{69} +(-47.3113 + 72.7281i) q^{70} +(1.39776 - 7.92710i) q^{71} +(130.573 - 234.258i) q^{72} +(-362.644 + 131.992i) q^{73} +(204.146 - 153.584i) q^{74} +772.104 q^{75} +(594.776 + 291.920i) q^{76} -383.802 q^{77} +(-194.121 + 146.042i) q^{78} +(-1028.57 + 374.370i) q^{79} +(-45.6780 + 50.4116i) q^{80} +(-157.766 + 894.733i) q^{81} +(93.4578 - 143.666i) q^{82} +(600.705 - 346.817i) q^{83} +(802.840 + 1194.30i) q^{84} +(-2.22418 + 1.86631i) q^{85} +(-318.332 - 625.975i) q^{86} +(908.794 + 524.692i) q^{87} +(-297.111 - 47.7747i) q^{88} +(341.851 - 939.228i) q^{89} +(-13.9489 + 32.7900i) q^{90} +(-69.0499 - 391.601i) q^{91} +(135.572 - 1270.70i) q^{92} +(468.552 + 393.161i) q^{93} +(240.578 - 1038.34i) q^{94} +(-82.6950 - 30.1839i) q^{95} +(472.837 + 1024.47i) q^{96} +(947.847 - 1129.60i) q^{97} +(-1375.27 + 167.768i) q^{98} +(-155.234 + 27.3719i) 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 $

$2$	−1.70042	−	2.26022i	−0.601189	−	0.799107i
$2$	−1.70042	−	2.26022i	−0.601189	−	0.799107i
$3$	5.85727	−	2.13187i	1.12723	−	0.410279i	0.289945	−	0.957043i	$-0.406363\pi$
$3$	5.85727	−	2.13187i	1.12723	−	0.410279i	0.837286	+	0.546765i	$0.184141\pi$
$4$	−2.21716	+	7.68663i	−0.277145	+	0.960828i
$5$	0.184577	−	1.04679i	0.0165091	−	0.0936276i	−0.975440	−	0.220266i	$-0.929308\pi$
$5$	0.184577	−	1.04679i	0.0165091	−	0.0936276i	0.991949	+	0.126638i	$0.0404187\pi$
$6$	−14.7783	−	9.61362i	−1.00554	−	0.654124i
$7$	24.9926	−	14.4295i	1.34947	−	0.779117i	0.361297	−	0.932451i	$-0.382334\pi$
$7$	24.9926	−	14.4295i	1.34947	−	0.779117i	0.988175	+	0.153333i	$0.0490009\pi$
$8$	21.1435	−	8.05922i	0.934421	−	0.356170i
$9$	9.07949	−	7.61860i	0.336278	−	0.282170i
$10$	−2.67983	+	1.36279i	−0.0847436	+	0.0430953i
$11$	−11.5175	−	6.64963i	−0.315696	−	0.182267i	0.333777	−	0.942652i	$-0.391677\pi$
$11$	−11.5175	−	6.64963i	−0.315696	−	0.182267i	−0.649473	+	0.760385i	$0.725010\pi$
$12$	3.40041	+	49.7493i	0.0818011	+	1.19678i
$13$	4.71264	−	12.9479i	0.100542	−	0.276238i	−0.879215	−	0.476424i	$-0.841933\pi$
$13$	4.71264	−	12.9479i	0.100542	−	0.276238i	0.979758	+	0.200186i	$0.0641548\pi$
$14$	−75.1115	−	31.9525i	−1.43388	−	0.609976i
$15$	−1.15050	−	6.52481i	−0.0198039	−	0.112313i
$16$	−54.1684	−	34.0849i	−0.846382	−	0.532577i
$17$	−2.09249	−	1.75581i	−0.0298531	−	0.0250497i	0.627739	−	0.778424i	$-0.283981\pi$
$17$	−2.09249	−	1.75581i	−0.0298531	−	0.0250497i	−0.657592	+	0.753374i	$0.728425\pi$
$18$	−32.6586	−	7.56682i	−0.427651	−	0.0990842i
$19$	14.4557	−	81.5477i	0.174546	−	0.984649i
$19$	14.4557	−	81.5477i	0.174546	−	0.984649i
$20$	7.63703	+	3.73967i	0.0853846	+	0.0418108i
$21$	115.626	−	137.798i	1.20151	−	1.43190i
$22$	4.55495	+	37.3392i	0.0441418	+	0.361852i
$23$	−157.313	+	27.7384i	−1.42617	+	0.251472i	−0.832852	−	0.553495i	$-0.813294\pi$
$23$	−157.313	+	27.7384i	−1.42617	+	0.251472i	−0.593319	+	0.804968i	$0.702183\pi$
$24$	106.662	−	92.2803i	0.907179	−	0.784860i
$25$	116.400	+	42.3661i	0.931199	+	0.338929i
$26$	−37.2784	+	11.3652i	−0.281189	+	0.0857269i
$27$	−47.2087	+	81.7678i	−0.336493	+	0.582823i
$28$	55.5014	+	224.101i	0.374599	+	1.51254i
$29$	108.216	+	128.967i	0.692941	+	0.825815i	0.991708	−	0.128511i	$-0.0410199\pi$
$29$	108.216	+	128.967i	0.692941	+	0.825815i	−0.298767	+	0.954326i	$0.596575\pi$
$30$	−12.7912	+	13.6953i	−0.0778445	+	0.0833469i
$31$	49.0642	+	84.9816i	0.284264	+	0.492360i	0.972430	−	0.233193i	$-0.0749175\pi$
$31$	49.0642	+	84.9816i	0.284264	+	0.492360i	−0.688166	+	0.725553i	$0.741584\pi$
$32$	15.0696	+	180.391i	0.0832488	+	0.996529i
$33$	−81.6372	−	14.3948i	−0.430643	−	0.0759339i
$34$	−0.410397	+	7.71508i	−0.00207008	+	0.0389154i
$35$	−10.4915	−	28.8253i	−0.0506684	−	0.139210i
$36$	38.4306	+	86.6823i	0.177920	+	0.401307i
$37$			90.3215i			0.401318i	0.979661	+	0.200659i	$0.0643083\pi$
$37$			90.3215i			0.401318i	−0.979661	+	0.200659i	$0.935692\pi$
$38$	−208.896	+	105.992i	−0.891775	+	0.452479i
$39$		−	85.8859i		−	0.352634i
$40$	−4.53369	−	23.6204i	−0.0179210	−	0.0933677i
$41$	20.7248	+	56.9408i	0.0789430	+	0.216894i	0.972885	−	0.231288i	$-0.0742939\pi$
$41$	20.7248	+	56.9408i	0.0789430	+	0.216894i	−0.893942	+	0.448182i	$0.852072\pi$
$42$	−508.066	−	27.0262i	−1.86658	−	0.0992912i
$43$	244.517	+	43.1149i	0.867174	+	0.152906i	0.589499	−	0.807769i	$-0.299325\pi$
$43$	244.517	+	43.1149i	0.867174	+	0.152906i	0.277675	+	0.960675i	$0.410436\pi$
$44$	76.6493	−	73.7874i	0.262621	−	0.252815i
$45$	−6.29920	−	10.9105i	−0.0208673	−	0.0361432i
$46$	330.192	+	308.393i	1.05835	+	0.988481i
$47$	242.225	+	288.672i	0.751747	+	0.895897i	0.997296	−	0.0734872i	$-0.0234128\pi$
$47$	242.225	+	288.672i	0.751747	+	0.895897i	−0.245549	+	0.969384i	$0.578968\pi$
$48$	−389.943	−	84.1644i	−1.17257	−	0.253085i
$49$	244.919	−	424.211i	0.714048	−	1.23677i
$50$	−102.172	−	335.129i	−0.288986	−	0.947888i
$51$	−15.9994	−	5.82331i	−0.0439287	−	0.0159887i
$52$	89.0768	+	64.9318i	0.237552	+	0.173162i
$53$	−680.228	+	119.943i	−1.76295	+	0.310856i	−0.958909	−	0.283713i	$-0.908434\pi$
$53$	−680.228	+	119.943i	−1.76295	+	0.310856i	−0.804044	+	0.594570i	$0.797323\pi$
$54$	265.088	−	32.3377i	0.668034	−	0.0814925i
$55$	−9.08662	+	10.8290i	−0.0222771	+	0.0265488i
$56$	412.141	−	506.510i	0.983475	−	1.20867i
$57$	−89.1781	−	508.464i	−0.207227	−	1.18154i
$58$	107.481	−	463.891i	0.243326	−	1.05020i
$59$	−542.903	−	455.550i	−1.19797	−	1.00521i	−0.999686	−	0.0250673i	$-0.992020\pi$
$59$	−542.903	−	455.550i	−1.19797	−	1.00521i	−0.198280	−	0.980145i	$-0.563536\pi$
$60$	52.7046	+	5.62307i	0.113402	+	0.0120989i
$61$	98.4793	+	558.504i	0.206705	+	1.17228i	0.894735	+	0.446598i	$0.147365\pi$
$61$	98.4793	+	558.504i	0.206705	+	1.17228i	−0.688030	+	0.725682i	$0.741524\pi$
$62$	108.647	−	255.400i	0.222552	−	0.523158i
$63$	116.987	−	321.420i	0.233953	−	0.642780i
$64$	382.098	−	340.801i	0.746285	−	0.665626i
$65$	−12.6838	−	7.32302i	−0.0242036	−	0.0139740i
$66$	106.282	+	208.995i	0.198218	+	0.389780i
$67$	−236.636	+	198.561i	−0.431488	+	0.362062i	−0.832513	−	0.554006i	$-0.813099\pi$
$67$	−236.636	+	198.561i	−0.431488	+	0.362062i	0.401025	+	0.916067i	$0.368654\pi$
$68$	18.1356	−	12.1913i	0.0323421	−	0.0217413i
$69$	−862.287	+	497.841i	−1.50445	+	0.868595i
$70$	−47.3113	+	72.7281i	−0.0807827	+	0.124181i
$71$	1.39776	−	7.92710i	0.00233639	−	0.0132503i	−0.983617	−	0.180269i	$-0.942303\pi$
$71$	1.39776	−	7.92710i	0.00233639	−	0.0132503i	0.985954	+	0.167019i	$0.0534142\pi$
$72$	130.573	−	234.258i	0.213724	−	0.383438i
$73$	−362.644	+	131.992i	−0.581428	+	0.211623i	−0.615955	−	0.787781i	$-0.711230\pi$
$73$	−362.644	+	131.992i	−0.581428	+	0.211623i	0.0345269	+	0.999404i	$0.489008\pi$
$74$	204.146	−	153.584i	0.320696	−	0.241268i
$75$	772.104			1.18873
$76$	594.776	+	291.920i	0.897704	+	0.440599i
$77$	−383.802			−0.568030
$78$	−194.121	+	146.042i	−0.281793	+	0.212000i
$79$	−1028.57	+	374.370i	−1.46485	+	0.533163i	−0.946698	−	0.322123i	$-0.895603\pi$
$79$	−1028.57	+	374.370i	−1.46485	+	0.533163i	−0.518156	+	0.855286i	$0.673381\pi$
$80$	−45.6780	+	50.4116i	−0.0638369	+	0.0704523i
$81$	−157.766	+	894.733i	−0.216414	+	1.22734i
$82$	93.4578	−	143.666i	0.125862	−	0.193478i
$83$	600.705	−	346.817i	0.794409	−	0.458652i	−0.0471036	−	0.998890i	$-0.514999\pi$
$83$	600.705	−	346.817i	0.794409	−	0.458652i	0.841512	+	0.540238i	$0.181666\pi$
$84$	802.840	+	1194.30i	1.04282	+	1.55129i
$85$	−2.22418	+	1.86631i	−0.00283819	+	0.00238153i
$86$	−318.332	−	625.975i	−0.399147	−	0.784890i
$87$	908.794	+	524.692i	1.11992	+	0.646585i
$88$	−297.111	−	47.7747i	−0.359911	−	0.0578727i
$89$	341.851	−	939.228i	0.407147	−	1.11863i	−0.551535	−	0.834152i	$-0.685958\pi$
$89$	341.851	−	939.228i	0.407147	−	1.11863i	0.958683	−	0.284477i	$-0.0918199\pi$
$90$	−13.9489	+	32.7900i	−0.0163371	+	0.0384041i
$91$	−69.0499	−	391.601i	−0.0795428	−	0.451109i
$92$	135.572	−	1270.70i	0.153634	−	1.44000i
$93$	468.552	+	393.161i	0.522436	+	0.438376i
$94$	240.578	−	1038.34i	0.263976	−	1.13933i
$95$	−82.6950	−	30.1839i	−0.0893087	−	0.0325980i
$96$	472.837	+	1024.47i	0.502695	+	1.08916i
$97$	947.847	−	1129.60i	0.992158	−	1.18241i	0.00894206	−	0.999960i	$-0.497154\pi$
$97$	947.847	−	1129.60i	0.992158	−	1.18241i	0.983216	−	0.182447i	$-0.0584019\pi$
$98$	−1375.27	+	167.768i	−1.41759	+	0.172929i
$99$	−155.234	+	27.3719i	−0.157592	+	0.0277877i
$100$	−583.729	+	800.790i	−0.583729	+	0.800790i
$101$	−721.549	−	262.622i	−0.710860	−	0.258732i	−0.0388193	−	0.999246i	$-0.512360\pi$
$101$	−721.549	−	262.622i	−0.710860	−	0.258732i	−0.672040	+	0.740514i	$0.734582\pi$
$102$	14.0437	+	46.0642i	0.0136327	+	0.0447160i
$103$	−780.680	+	1352.18i	−0.746822	+	1.29353i	0.202517	+	0.979279i	$0.435088\pi$
$103$	−780.680	+	1352.18i	−0.746822	+	1.29353i	−0.949339	+	0.314254i	$0.898245\pi$
$104$	−4.70787	−	311.744i	−0.00443889	−	0.293933i
$105$	−122.903	−	146.471i	−0.114230	−	0.136134i
$106$	1427.77	+	1333.51i	1.30827	+	1.22191i
$107$	−607.899	−	1052.91i	−0.549232	−	0.951298i	−0.998327	−	0.0578141i	$-0.981587\pi$
$107$	−607.899	−	1052.91i	−0.549232	−	0.951298i	0.449095	−	0.893484i	$-0.351746\pi$
$108$	−523.850	−	544.168i	−0.466736	−	0.484839i
$109$	1751.68	+	308.868i	1.53927	+	0.271414i	0.877972	−	0.478712i	$-0.158896\pi$
$109$	1751.68	+	308.868i	1.53927	+	0.271414i	0.661295	+	0.750126i	$0.270007\pi$
$110$	39.9270	+	2.12388i	0.0346081	+	0.00184095i
$111$	192.554	+	529.037i	0.164652	+	0.452378i
$112$	−1845.63	−	70.2484i	−1.55711	−	0.0592665i
$113$			1361.22i			1.13321i	0.823989	+	0.566605i	$0.191743\pi$
$113$			1361.22i			1.13321i	−0.823989	+	0.566605i	$0.808257\pi$
$114$	−997.600	+	1066.16i	−0.819595	+	0.875925i
$115$			169.793i			0.137681i
$116$	−1231.26	+	545.878i	−0.985511	+	0.436927i
$117$	−55.8563	−	153.464i	−0.0441360	−	0.121263i
$118$	−106.479	+	2001.70i	−0.0830694	+	1.56163i
$119$	−77.6319	−	13.6886i	−0.0598026	−	0.0105448i
$120$	−76.9105	−	128.685i	−0.0585078	−	0.0978944i
$121$	−577.065	−	999.506i	−0.433557	−	0.750943i
$122$	1094.88	−	1172.27i	0.812509	−	0.869940i
$123$	242.781	+	289.335i	0.177974	+	0.212101i
$124$	−762.005	+	188.720i	−0.551855	+	0.136674i
$125$	132.267	−	229.093i	0.0946423	−	0.163925i
$126$	−925.407	+	282.132i	−0.654300	+	0.199479i
$127$	592.211	+	215.547i	0.413781	+	0.150604i	0.540518	−	0.841332i	$-0.318228\pi$
$127$	592.211	+	215.547i	0.413781	+	0.150604i	−0.126737	+	0.991936i	$0.540450\pi$
$128$	−1420.01	−	284.121i	−0.980565	−	0.196195i
$129$	1524.12	−	268.743i	1.04024	−	0.183422i
$130$	5.01622	+	41.1204i	0.00338424	+	0.0277423i
$131$	−66.4305	+	79.1688i	−0.0443058	+	0.0528016i	−0.787742	−	0.616005i	$-0.788750\pi$
$131$	−66.4305	+	79.1688i	−0.0443058	+	0.0528016i	0.743436	+	0.668807i	$0.233195\pi$
$132$	291.650	−	595.599i	0.192310	−	0.392729i
$133$	−815.404	−	2246.67i	−0.531613	−	1.46475i
$134$	851.172	+	197.212i	0.548732	+	0.127138i
$135$	76.8800	+	64.5100i	0.0490132	+	0.0411269i
$136$	−58.3930	−	20.2601i	−0.0368173	−	0.0127742i
$137$	401.306	+	2275.92i	0.250262	+	1.41930i	0.807948	+	0.589253i	$0.200578\pi$
$137$	401.306	+	2275.92i	0.250262	+	1.41930i	−0.557687	+	0.830052i	$0.688311\pi$
$138$	2591.48	+	1102.42i	1.59856	+	0.680028i
$139$	411.878	−	1131.63i	0.251331	−	0.690527i	−0.748300	−	0.663361i	$-0.769130\pi$
$139$	411.878	−	1131.63i	0.251331	−	0.690527i	0.999631	−	0.0271659i	$-0.00864823\pi$
$140$	244.830	−	16.7344i	0.147800	−	0.0101022i
$141$	2034.19	+	1174.44i	1.21496	+	0.701457i
$142$	−20.2937	+	10.3201i	−0.0119930	+	0.00609892i
$143$	−140.376	+	117.790i	−0.0820899	+	0.0688816i
$144$	−751.501	+	103.214i	−0.434896	+	0.0597301i
$145$	154.976	−	89.4753i	0.0887589	−	0.0512450i
$146$	914.976	+	595.213i	0.518657	+	0.337398i
$147$	530.189	−	3006.85i	0.297478	−	1.68708i
$148$	−694.268	−	200.257i	−0.385598	−	0.111223i
$149$	1535.26	−	558.787i	0.844114	−	0.307232i	0.116476	−	0.993194i	$-0.462840\pi$
$149$	1535.26	−	558.787i	0.844114	−	0.307232i	0.727638	+	0.685961i	$0.240618\pi$
$150$	−1312.90	−	1745.12i	−0.714652	−	0.949924i
$151$	−777.881			−0.419226			−0.209613	−	0.977784i	$-0.567220\pi$
$151$	−777.881			−0.419226			−0.209613	+	0.977784i	$0.567220\pi$
$152$	−351.566	−	1840.71i	−0.187604	−	0.982245i
$153$	−32.3755			−0.0171072
$154$	652.624	+	867.476i	0.341493	+	0.453917i
$155$	98.0139	−	35.6741i	0.0507914	−	0.0184866i
$156$	660.172	+	190.423i	0.338821	+	0.0977308i
$157$	608.943	−	3453.49i	0.309548	−	1.75553i	−0.291739	−	0.956498i	$-0.594234\pi$
$157$	608.943	−	3453.49i	0.309548	−	1.75553i	0.601286	−	0.799034i	$-0.294655\pi$
$158$	2595.16	+	1688.21i	1.30671	+	0.850043i
$159$	−3728.58	+	2152.69i	−1.85972	+	1.07371i
$160$	191.613	+	17.5213i	0.0946770	+	0.00865738i
$161$	−3531.39	+	2963.19i	−1.72865	+	1.45051i
$162$	2290.56	−	1164.84i	1.11088	−	0.564927i
$163$	−18.7113	−	10.8030i	−0.00899130	−	0.00519113i	0.495498	−	0.868609i	$-0.334986\pi$
$163$	−18.7113	−	10.8030i	−0.00899130	−	0.00519113i	−0.504489	+	0.863418i	$0.668319\pi$
$164$	−483.633	+	33.0567i	−0.230277	+	0.0157396i
$165$	−30.1367	+	82.7999i	−0.0142190	+	0.0390665i
$166$	−1805.33	−	767.989i	−0.844102	−	0.359081i
$167$	−448.491	−	2543.52i	−0.207816	−	1.17858i	−0.892946	−	0.450163i	$-0.851366\pi$
$167$	−448.491	−	2543.52i	−0.207816	−	1.17858i	0.685130	−	0.728421i	$-0.259745\pi$
$168$	1334.20	−	3845.40i	0.612715	−	1.76594i
$169$	1537.56	+	1290.17i	0.699846	+	0.587240i
$170$	8.00031	+	1.85363i	0.00360938	+	0.000836274i
$171$	−490.029	−	850.544i	−0.219143	−	0.380367i
$172$	−873.541	+	1783.92i	−0.387249	+	0.790828i
$173$	873.807	−	1041.36i	0.384013	−	0.457649i	−0.539063	−	0.842265i	$-0.681222\pi$
$173$	873.807	−	1041.36i	0.384013	−	0.457649i	0.923077	+	0.384616i	$0.125666\pi$
$174$	−359.411	−	2946.27i	−0.156591	−	1.28365i
$175$	3520.45	−	620.750i	1.52069	−	0.268139i
$176$	397.233	+	752.773i	0.170128	+	0.322400i
$177$	−4151.10	−	1510.88i	−1.76280	−	0.641607i
$178$	−2704.15	+	824.422i	−1.13868	+	0.347152i
$179$	1243.07	−	2153.06i	0.519057	−	0.899033i	−0.480698	−	0.876886i	$-0.659617\pi$
$179$	1243.07	−	2153.06i	0.519057	−	0.899033i	0.999755	−	0.0221467i	$-0.00705009\pi$
$180$	97.8314	−	24.2292i	0.0405107	−	0.0100330i
$181$	−760.314	−	906.107i	−0.312230	−	0.372102i	0.586993	−	0.809592i	$-0.300312\pi$
$181$	−760.314	−	906.107i	−0.312230	−	0.372102i	−0.899223	+	0.437491i	$0.855867\pi$
$182$	−767.690	+	821.953i	−0.312665	+	0.334765i
$183$	1767.48	+	3061.36i	0.713965	+	1.23662i
$184$	−3102.59	+	1854.31i	−1.24308	+	0.742941i
$185$	94.5476	+	16.6713i	0.0375745	+	0.00662539i
$186$	91.8965	−	1727.57i	0.0362268	−	0.681029i
$187$	12.4248	+	34.1368i	0.00485876	+	0.0133493i
$188$	−2755.96	+	1221.86i	−1.06915	+	0.474006i
$189$			2724.78i			1.04867i
$190$	72.3939	+	238.234i	0.0276421	+	0.0909648i
$191$			3365.08i			1.27481i	0.770529	+	0.637405i	$0.219992\pi$
$191$			3365.08i			1.27481i	−0.770529	+	0.637405i	$0.780008\pi$
$192$	1511.51	−	2810.74i	0.568144	−	1.05650i
$193$	−822.828	−	2260.70i	−0.306883	−	0.843155i	−0.993260	−	0.115909i	$-0.963022\pi$
$193$	−822.828	−	2260.70i	−0.306883	−	0.843155i	0.686377	−	0.727246i	$-0.259200\pi$
$194$	−4164.88	−	221.547i	−1.54134	−	0.0819906i
$195$	−89.9043	−	15.8526i	−0.0330163	−	0.00582167i
$196$	2717.73	+	2823.14i	0.990427	+	1.02884i
$197$	−464.886	−	805.206i	−0.168131	−	0.291211i	0.769632	−	0.638488i	$-0.220440\pi$
$197$	−464.886	−	805.206i	−0.168131	−	0.291211i	−0.937763	+	0.347277i	$0.887106\pi$
$198$	325.829	+	304.319i	0.116948	+	0.109227i
$199$	1418.91	+	1690.99i	0.505447	+	0.602368i	0.957076	−	0.289838i	$-0.0936014\pi$
$199$	1418.91	+	1690.99i	0.505447	+	0.602368i	−0.451629	+	0.892206i	$0.649157\pi$
$200$	2802.54	−	42.3232i	0.990848	−	0.0149635i
$201$	−962.734	+	1667.50i	−0.337841	+	0.585158i
$202$	633.352	+	2077.43i	0.220606	+	0.723600i
$203$	4565.53	+	1661.72i	1.57851	+	0.574531i
$204$	80.2348	−	110.070i	0.0275371	−	0.0377768i
$205$	63.4303	−	11.1845i	0.0216106	−	0.00381052i
$206$	4383.69	−	534.760i	1.48265	−	0.180867i
$207$	−1216.99	+	1450.35i	−0.408631	+	0.486988i
$208$	−696.603	+	540.736i	−0.232215	+	0.180256i
$209$	−708.756	+	843.101i	−0.234573	+	0.279036i
$210$	−122.068	+	526.850i	−0.0401119	+	0.173124i
$211$	−3690.36	−	3096.58i	−1.20405	−	1.01032i	−0.999505	−	0.0314639i	$-0.989983\pi$
$211$	−3690.36	−	3096.58i	−1.20405	−	1.01032i	−0.204548	−	0.978857i	$-0.565572\pi$
$212$	586.220	−	5494.59i	0.189914	−	1.78005i
$213$	−8.71249	−	49.4110i	−0.00280267	−	0.0158948i
$214$	−1346.13	+	3164.38i	−0.429997	+	1.01080i
$215$	90.2644	−	247.999i	0.0286325	−	0.0786671i
$216$	−339.174	+	2109.33i	−0.106842	+	0.664451i
$217$	2452.48	+	1415.94i	0.767212	+	0.442950i
$218$	−2280.47	−	4484.37i	−0.708500	−	1.39321i
$219$	−1842.71	+	1546.22i	−0.568580	+	0.477095i
$220$	−63.0921	−	93.8551i	−0.0193349	−	0.0287623i
$221$	−32.5951	+	18.8188i	−0.00992119	+	0.00572800i
$222$	868.317	−	1334.80i	0.262512	−	0.403539i
$223$	235.607	−	1336.19i	0.0707506	−	0.401247i	−0.928781	−	0.370630i	$-0.879142\pi$
$223$	235.607	−	1336.19i	0.0707506	−	0.401247i	0.999531	−	0.0306166i	$-0.00974710\pi$
$224$	2979.57	+	4290.98i	0.888755	+	1.27993i
$225$	1379.62	−	502.141i	0.408777	−	0.148783i
$226$	3076.65	−	2314.64i	0.905556	−	0.681273i
$227$	−5141.79			−1.50340			−0.751702	−	0.659503i	$-0.770767\pi$
$227$	−5141.79			−1.50340			−0.751702	+	0.659503i	$0.770767\pi$
$228$	4106.10	+	441.867i	1.19269	+	0.128348i
$229$	−3718.68			−1.07309			−0.536545	−	0.843872i	$-0.680271\pi$
$229$	−3718.68			−1.07309			−0.536545	+	0.843872i	$0.680271\pi$
$230$	383.769	−	288.719i	0.110022	−	0.0827720i
$231$	−2248.03	+	818.217i	−0.640301	+	0.233051i
$232$	3327.45	+	1854.68i	0.941629	+	0.524853i
$233$	−704.774	+	3996.97i	−0.198160	+	1.12382i	0.709686	+	0.704518i	$0.248837\pi$
$233$	−704.774	+	3996.97i	−0.198160	+	1.12382i	−0.907846	+	0.419303i	$0.862274\pi$
$234$	−251.882	+	387.200i	−0.0703678	+	0.108171i
$235$	346.888	−	200.276i	0.0962913	−	0.0555938i
$236$	4705.34	−	3163.07i	1.29785	−	0.872450i
$237$	−5226.51	+	4385.57i	−1.43248	+	1.20200i
$238$	101.068	+	198.741i	0.0275262	+	0.0541281i
$239$	431.358	+	249.045i	0.116746	+	0.0674032i	0.557236	−	0.830354i	$-0.311862\pi$
$239$	431.358	+	249.045i	0.116746	+	0.0674032i	−0.440490	+	0.897758i	$0.645195\pi$
$240$	−160.077	+	392.654i	−0.0430538	+	0.105607i
$241$	−175.396	+	481.898i	−0.0468808	+	0.128804i	−0.960924	−	0.276814i	$-0.910721\pi$
$241$	−175.396	+	481.898i	−0.0468808	+	0.128804i	0.914043	+	0.405618i	$0.132944\pi$
$242$	−1277.85	+	3003.87i	−0.339435	+	0.797917i
$243$	540.704	+	3066.48i	0.142741	+	0.809527i
$244$	−4511.35	−	481.318i	−1.18365	−	0.126284i
$245$	−398.853	−	334.678i	−0.104007	−	0.0872725i
$246$	241.131	−	1040.73i	0.0624957	−	0.269733i
$247$	−987.745	−	571.476i	−0.254448	−	0.147215i
$248$	1722.27	+	1401.39i	0.440986	+	0.358825i
$249$	2779.12	−	3312.03i	0.707307	−	0.842936i
$250$	−742.707	+	90.6018i	−0.187892	+	0.0229206i
$251$	4205.10	−	741.473i	1.05747	−	0.186460i	0.382234	−	0.924066i	$-0.375155\pi$
$251$	4205.10	−	741.473i	1.05747	−	0.186460i	0.675231	+	0.737606i	$0.264044\pi$
$252$	2211.26	+	1611.88i	0.552763	+	0.402932i
$253$	1996.30	+	726.593i	0.496072	+	0.180555i
$254$	−519.822	−	1705.04i	−0.128412	−	0.421197i
$255$	−9.04890	+	15.6731i	−0.00222221	+	0.00384898i
$256$	1772.44	+	3692.65i	0.432724	+	0.901527i
$257$	−884.840	−	1054.51i	−0.214766	−	0.255948i	0.647896	−	0.761728i	$-0.275649\pi$
$257$	−884.840	−	1054.51i	−0.214766	−	0.255948i	−0.862662	+	0.505781i	$0.831205\pi$
$258$	−3199.05	−	2987.86i	−0.771954	−	0.720992i
$259$	1303.29	+	2257.37i	0.312674	+	0.541567i
$260$	84.4114	−	81.2596i	0.0201345	−	0.0193827i
$261$	1965.10	+	346.500i	0.466041	+	0.0821756i
$262$	291.898	+	15.5273i	0.0688303	+	0.00366137i
$263$	1952.07	+	5363.26i	0.457679	+	1.25746i	0.927208	+	0.374546i	$0.122201\pi$
$263$	1952.07	+	5363.26i	0.457679	+	1.25746i	−0.469529	+	0.882917i	$0.655576\pi$
$264$	−1842.11	+	353.574i	−0.429447	+	0.0824280i
$265$			734.194i			0.170193i
$266$	−3691.44	+	5663.27i	−0.850891	+	1.30540i
$267$		−	6230.09i		−	1.42800i
$268$	−1001.61	−	2259.18i	−0.228294	−	0.514930i
$269$	−1033.68	−	2840.01i	−0.234292	−	0.643712i	−1.00000		0.000523251i	$-0.999833\pi$
$269$	−1033.68	−	2840.01i	−0.234292	−	0.643712i	0.765708	−	0.643188i	$-0.222389\pi$
$270$	15.0784	−	283.459i	0.00339867	−	0.0638918i
$271$	−6708.84	−	1182.95i	−1.50381	−	0.265163i	−0.639764	−	0.768572i	$-0.720968\pi$
$271$	−6708.84	−	1182.95i	−1.50381	−	0.265163i	−0.864048	+	0.503409i	$0.832079\pi$
$272$	53.5002	+	166.431i	0.0119262	+	0.0371007i
$273$	−1239.29	−	2146.51i	−0.274744	−	0.475870i
$274$	4461.68	−	4777.05i	0.983722	−	1.05326i
$275$	−1058.92	−	1261.97i	−0.232200	−	0.276725i
$276$	−1914.89	−	7731.87i	−0.417620	−	1.68625i
$277$	−78.3318	+	135.675i	−0.0169910	+	0.0294293i	−0.874396	−	0.485213i	$-0.838742\pi$
$277$	−78.3318	+	135.675i	−0.0169910	+	0.0294293i	0.857405	+	0.514642i	$0.172075\pi$
$278$	−3258.08	+	993.302i	−0.702902	+	0.214296i
$279$	1092.92	+	397.790i	0.234521	+	0.0853586i
$280$	−454.137	−	524.914i	−0.0969282	−	0.112034i
$281$	731.992	−	129.070i	0.155398	−	0.0274009i	−0.0954076	−	0.995438i	$-0.530415\pi$
$281$	731.992	−	129.070i	0.155398	−	0.0274009i	0.250806	+	0.968037i	$0.419304\pi$
$282$	−804.482	−	6594.74i	−0.169880	−	1.39259i
$283$	3506.44	−	4178.82i	0.736525	−	0.877756i	−0.259599	−	0.965716i	$-0.583590\pi$
$283$	3506.44	−	4178.82i	0.736525	−	0.877756i	0.996124	+	0.0879605i	$0.0280349\pi$
$284$	57.8336	+	28.3197i	0.0120838	+	0.00591713i
$285$	−548.715	−	0.500226i	−0.114046	−	0.000103968i
$286$	504.929	+	116.989i	0.104395	+	0.0241878i
$287$	1339.59	+	1124.05i	0.275517	+	0.231187i
$288$	1511.15	+	1523.05i	0.309186	+	0.311620i
$289$	−851.838	−	4831.01i	−0.173384	−	0.983312i
$290$	−465.757	−	198.133i	−0.0943110	−	0.0401200i
$291$	3143.63	−	8637.06i	0.633275	−	1.73991i
$292$	−210.531	−	3080.15i	−0.0421932	−	0.617303i
$293$	−635.714	−	367.030i	−0.126754	−	0.0731812i	0.435283	−	0.900294i	$-0.356648\pi$
$293$	−635.714	−	367.030i	−0.126754	−	0.0731812i	−0.562036	+	0.827113i	$0.689982\pi$
$294$	−7697.68	+	3914.56i	−1.52700	+	0.776537i
$295$	−577.072	+	484.221i	−0.113893	+	0.0955676i
$296$	727.921	+	1909.72i	0.142938	+	0.375000i
$297$	1087.45	−	627.841i	0.212459	−	0.122663i
$298$	−3873.56	−	2519.84i	−0.752983	−	0.489833i
$299$	−382.204	+	2167.58i	−0.0739244	+	0.419246i
$300$	−1711.88	+	5934.87i	−0.329451	+	1.14217i
$301$	6733.23	−	2450.69i	1.28936	−	0.469288i
$302$	1322.72	+	1758.18i	0.252034	+	0.335006i
$303$	−4786.18			−0.907456
$304$	−3562.59	+	3924.59i	−0.672134	+	0.740430i
$305$	602.812			0.113170
$306$	55.0519	+	73.1756i	0.0102847	+	0.0136705i
$307$	−527.866	+	192.128i	−0.0981333	+	0.0357176i	−0.390620	−	0.920552i	$-0.627739\pi$
$307$	−527.866	+	192.128i	−0.0981333	+	0.0357176i	0.292487	+	0.956270i	$0.405517\pi$
$308$	850.950	−	2950.14i	0.157427	−	0.545779i
$309$	−1689.98	+	9584.37i	−0.311132	+	1.76452i
$310$	−247.296	−	160.872i	−0.0453079	−	0.0294739i
$311$	3840.96	−	2217.58i	0.700325	−	0.404333i	−0.107143	−	0.994244i	$-0.534170\pi$
$311$	3840.96	−	2217.58i	0.700325	−	0.404333i	0.807468	+	0.589911i	$0.200837\pi$
$312$	−692.173	−	1815.93i	−0.125598	−	0.329509i
$313$	6616.32	−	5551.76i	1.19481	−	1.00257i	0.195051	−	0.980793i	$-0.437513\pi$
$313$	6616.32	−	5551.76i	1.19481	−	1.00257i	0.999763	−	0.0217748i	$-0.00693169\pi$
$314$	−8841.09	+	4496.03i	−1.58895	+	0.808044i
$315$	−314.866	−	181.788i	−0.0563196	−	0.0325162i
$316$	−597.132	−	8736.29i	−0.106302	−	1.55524i
$317$	1183.34	−	3251.19i	0.209662	−	0.576041i	−0.789633	−	0.613579i	$-0.789729\pi$
$317$	1183.34	−	3251.19i	0.209662	−	0.576041i	0.999295	+	0.0375379i	$0.0119515\pi$
$318$	11205.7	+	4766.91i	1.97605	+	0.840613i
$319$	−388.797	−	2204.98i	−0.0682397	−	0.387007i
$320$	−286.220	−	462.880i	−0.0500005	−	0.0808618i
$321$	−5805.30	−	4871.23i	−1.00941	−	0.846995i
$322$	12702.3	+	2943.05i	2.19836	+	0.509347i
$323$	−173.430	+	145.256i	−0.0298759	+	0.0250225i
$324$	−6527.69	−	3196.45i	−1.11929	−	0.548088i
$325$	1097.10	−	1307.47i	0.187250	−	0.223156i
$326$	7.39997	+	60.6612i	0.00125720	+	0.0103059i
$327$	10918.5	−	1925.22i	1.84646	−	0.325582i
$328$	897.093	+	1036.90i	0.151017	+	0.174553i
$329$	10219.2	+	3719.48i	1.71247	+	0.623288i
$330$	238.391	−	72.6790i	0.0397666	−	0.0121238i
$331$	−1295.41	+	2243.72i	−0.215112	+	0.372585i	−0.953307	−	0.302002i	$-0.902345\pi$
$331$	−1295.41	+	2243.72i	−0.215112	+	0.372585i	0.738195	+	0.674587i	$0.235678\pi$
$332$	1334.00	+	5386.34i	0.220520	+	0.890403i
$333$	688.124	+	820.074i	0.113240	+	0.134954i
$334$	−4986.29	+	5338.74i	−0.816879	+	0.874619i
$335$	164.174	+	284.358i	0.0267755	+	0.0463765i
$336$	−10960.1	+	3523.19i	−1.77954	+	0.572041i
$337$	2577.53	+	454.488i	0.416638	+	0.0734645i	0.378038	−	0.925790i	$-0.376599\pi$
$337$	2577.53	+	454.488i	0.416638	+	0.0734645i	0.0386001	+	0.999255i	$0.487710\pi$
$338$	301.560	−	5669.04i	0.0485288	−	0.912294i
$339$	2901.94	+	7973.02i	0.464932	+	1.27739i
$340$	−9.41427	−	21.2344i	−0.00150165	−	0.00338704i
$341$		−	1305.03i		−	0.207248i
$342$	−1089.16	+	2553.85i	−0.172208	+	0.403791i
$343$		−	4237.56i		−	0.667075i
$344$	5517.42	−	1059.01i	0.864766	−	0.165983i
$345$	361.976	+	994.522i	0.0564874	+	0.155198i
$346$	−3839.54	−	204.241i	−0.596575	−	0.0317343i
$347$	2258.72	+	398.272i	0.349436	+	0.0616149i	0.345611	−	0.938378i	$-0.387672\pi$
$347$	2258.72	+	398.272i	0.349436	+	0.0616149i	0.00382436	+	0.999993i	$0.498783\pi$
$348$	−6048.05	+	5822.23i	−0.931637	+	0.896852i
$349$	3591.15	+	6220.05i	0.550801	+	0.954016i	0.998217	+	0.0596899i	$0.0190112\pi$
$349$	3591.15	+	6220.05i	0.550801	+	0.954016i	−0.447416	+	0.894326i	$0.647655\pi$
$350$	−7389.27	−	6901.44i	−1.12849	−	1.05399i
$351$	836.242	+	996.594i	0.127166	+	0.151551i
$352$	1025.97	−	2177.86i	0.155353	−	0.329774i
$353$	−2297.99	+	3980.23i	−0.346486	+	0.600131i	−0.985623	−	0.168962i	$-0.945959\pi$
$353$	−2297.99	+	3980.23i	−0.346486	+	0.600131i	0.639137	+	0.769093i	$0.279292\pi$
$354$	3643.70	+	11951.5i	0.547063	+	1.79439i
$355$	−8.04000	−	2.92632i	−0.00120203	−	0.000437501i
$356$	6461.55	+	4710.10i	0.961971	+	0.701221i
$357$	−483.893	+	85.3234i	−0.0717377	+	0.0126493i
$358$	−6980.11	+	851.493i	−1.03047	+	0.125706i
$359$	−5270.44	+	6281.07i	−0.774829	+	0.923405i	−0.998688	−	0.0512169i	$-0.983690\pi$
$359$	−5270.44	+	6281.07i	−0.774829	+	0.923405i	0.223859	+	0.974622i	$0.428134\pi$
$360$	−221.118	−	179.921i	−0.0323720	−	0.0263407i
$361$	−6441.06	−	2357.66i	−0.939067	−	0.343733i
$362$	−755.146	+	3259.23i	−0.109640	+	0.473209i
$363$	−5510.84	−	4624.14i	−0.796815	−	0.668608i
$364$	3163.19	+	337.481i	0.455484	+	0.0485957i
$365$	71.2315	+	403.974i	0.0102149	+	0.0579314i
$366$	3913.89	−	9200.47i	0.558968	−	1.31398i
$367$	871.872	−	2395.45i	0.124009	−	0.340712i	−0.862117	−	0.506709i	$-0.830862\pi$
$367$	871.872	−	2395.45i	0.124009	−	0.340712i	0.986126	+	0.165997i	$0.0530841\pi$
$368$	9466.84	+	3859.44i	1.34101	+	0.546704i
$369$	621.979	+	359.100i	0.0877479	+	0.0506612i
$370$	−123.090	−	242.046i	−0.0172949	−	0.0340091i
$371$	−15269.9	+	12813.0i	−2.13686	+	1.79304i
$372$	−4060.94	+	2729.88i	−0.565994	+	0.380478i
$373$	−6681.84	+	3857.76i	−0.927540	+	0.535515i	−0.886033	−	0.463623i	$-0.846549\pi$
$373$	−6681.84	+	3857.76i	−0.927540	+	0.535515i	−0.0415071	+	0.999138i	$0.513216\pi$
$374$	56.0292	−	86.1294i	0.00774652	−	0.0119081i
$375$	286.325	−	1623.83i	0.0394287	−	0.223611i
$376$	7447.96	+	4151.41i	1.02154	+	0.569395i
$377$	2179.84	−	793.396i	0.297791	−	0.108387i
$378$	6158.60	−	4633.27i	0.838001	−	0.630449i
$379$	−5539.89			−0.750831			−0.375415	−	0.926857i	$-0.622500\pi$
$379$	−5539.89			−0.750831			−0.375415	+	0.926857i	$0.622500\pi$
$380$	415.361	−	568.723i	0.0560725	−	0.0767760i
$381$	3928.25			0.528217
$382$	7605.81	−	5722.05i	1.01871	−	0.766401i
$383$	−9879.75	+	3595.93i	−1.31810	+	0.479748i	−0.902848	−	0.429959i	$-0.858528\pi$
$383$	−9879.75	+	3595.93i	−1.31810	+	0.479748i	−0.415249	+	0.909708i	$0.636306\pi$
$384$	−8923.08	+	1363.11i	−1.18582	+	0.181148i
$385$	−70.8411	+	401.760i	−0.00937765	+	0.0531833i
$386$	−3710.52	+	5703.91i	−0.489276	+	0.752128i
$387$	2548.56	−	1471.41i	0.334757	−	0.193272i
$388$	6581.29	+	9790.25i	0.861119	+	1.28099i
$389$	11304.8	−	9485.82i	1.47345	−	1.23638i	0.560603	−	0.828085i	$-0.310569\pi$
$389$	11304.8	−	9485.82i	1.47345	−	1.23638i	0.912852	−	0.408291i	$-0.133875\pi$
$390$	117.045	+	230.159i	0.0151969	+	0.0298835i
$391$	377.878	+	218.168i	0.0488750	+	0.0282180i
$392$	1759.63	−	10943.2i	0.226721	−	1.40998i
$393$	−220.323	+	605.334i	−0.0282795	+	0.0776973i
$394$	−1029.44	+	2419.93i	−0.131630	+	0.309427i
$395$	202.035	+	1145.80i	0.0257354	+	0.145953i
$396$	133.780	−	1253.91i	0.0169766	−	0.159120i
$397$	−3983.16	−	3342.27i	−0.503550	−	0.422528i	0.355303	−	0.934751i	$-0.384378\pi$
$397$	−3983.16	−	3342.27i	−0.503550	−	0.422528i	−0.858853	+	0.512223i	$0.828822\pi$
$398$	1409.27	−	6082.44i	0.177488	−	0.766043i
$399$	−9565.66	−	11421.0i	−1.20020	−	1.43300i
$400$	−4861.15	−	6262.39i	−0.607644	−	0.782798i
$401$	−3859.81	+	4599.95i	−0.480673	+	0.572844i	−0.950820	−	0.309744i	$-0.899757\pi$
$401$	−3859.81	+	4599.95i	−0.480673	+	0.572844i	0.470147	+	0.882588i	$0.344201\pi$
$402$	5405.97	−	659.467i	0.670710	−	0.0818189i
$403$	1331.55	−	234.789i	0.164589	−	0.0290215i
$404$	3618.47	−	4964.00i	0.445608	−	0.611308i
$405$	907.476	+	330.294i	0.111340	+	0.0405246i
$406$	−4007.47	−	13144.7i	−0.489871	−	1.60680i
$407$	600.605	−	1040.28i	0.0731471	−	0.126695i
$408$	−385.215	+	5.81741i	−0.0467426	+	0.000705894i
$409$	6177.27	+	7361.78i	0.746812	+	0.890016i	0.996938	−	0.0781974i	$-0.0249164\pi$
$409$	6177.27	+	7361.78i	0.746812	+	0.890016i	−0.250126	+	0.968213i	$0.580472\pi$
$410$	−133.137	−	124.348i	−0.0160370	−	0.0149783i
$411$	7202.52	+	12475.1i	0.864413	+	1.49721i
$412$	−8662.79	−	8998.78i	−1.03589	−	1.07606i
$413$	−20141.9	−	3551.56i	−2.39980	−	0.423149i
$414$	5347.50	+	284.456i	0.634820	+	0.0337687i
$415$	−252.168	−	692.826i	−0.0298276	−	0.0819505i
$416$	2406.70	+	654.998i	0.283649	+	0.0771969i
$417$		−	7506.30i		−	0.881499i
$418$	3110.77	+	168.319i	0.364002	+	0.0196956i
$419$		−	14712.5i		−	1.71540i	−0.514149	−	0.857701i	$-0.671892\pi$
$419$		−	14712.5i		−	1.71540i	0.514149	−	0.857701i	$-0.328108\pi$
$420$	1398.36	−	619.964i	0.162460	−	0.0720266i
$421$	−476.694	−	1309.71i	−0.0551844	−	0.151618i	0.909038	−	0.416714i	$-0.136818\pi$
$421$	−476.694	−	1309.71i	−0.0551844	−	0.151618i	−0.964222	+	0.265096i	$0.914596\pi$
$422$	−723.787	+	13606.5i	−0.0834915	+	1.56956i
$423$	4398.55	+	775.584i	0.505591	+	0.0891493i
$424$	−13415.8	+	8018.12i	−1.53662	+	0.918383i
$425$	−169.179	−	293.026i	−0.0193091	−	0.0334444i
$426$	−96.8646	+	103.711i	−0.0110167	+	0.0117954i
$427$	10520.2	+	12537.4i	1.19229	+	1.42091i
$428$	9441.15	−	2338.22i	1.06625	−	0.264070i
$429$	−571.109	+	989.190i	−0.0642737	+	0.111325i
$430$	−714.020	+	217.686i	−0.0800769	+	0.0244133i
$431$	12195.4	+	4438.75i	1.36295	+	0.496072i	0.916964	−	0.398969i	$-0.130632\pi$
$431$	12195.4	+	4438.75i	1.36295	+	0.496072i	0.445983	+	0.895041i	$0.352854\pi$
$432$	5344.27	−	2820.13i	0.595200	−	0.314082i
$433$	−12254.7	+	2160.84i	−1.36010	+	0.239823i	−0.805650	−	0.592392i	$-0.798184\pi$
$433$	−12254.7	+	2160.84i	−1.36010	+	0.239823i	−0.554453	+	0.832215i	$0.687073\pi$
$434$	−969.909	−	7950.82i	−0.107274	−	0.879381i
$435$	716.984	−	854.469i	0.0790271	−	0.0941808i
$436$	−6257.89	+	12779.7i	−0.687382	+	1.40375i
$437$	−12.0604	+	13229.5i	−0.00132020	+	1.44817i
$438$	6628.17	+	1535.71i	0.723074	+	0.167532i
$439$	10846.2	+	9101.07i	1.17919	+	0.989454i	0.999984	+	0.00564215i	$0.00179596\pi$
$439$	10846.2	+	9101.07i	1.17919	+	0.989454i	0.179202	+	0.983812i	$0.442648\pi$
$440$	−104.850	+	302.195i	−0.0113603	+	0.0327422i
$441$	−1008.16	−	5717.56i	−0.108861	−	0.617380i
$442$	97.9598	+	41.6722i	0.0105418	+	0.00448448i
$443$	3469.78	−	9533.13i	0.372131	−	1.02242i	−0.602405	−	0.798191i	$-0.705791\pi$
$443$	3469.78	−	9533.13i	0.372131	−	1.02242i	0.974536	−	0.224231i	$-0.0719870\pi$
$444$	−4493.43	+	307.130i	−0.480290	+	0.0328282i
$445$	−920.075	−	531.206i	−0.0980129	−	0.0565878i
$446$	−3420.71	+	1739.56i	−0.363174	+	0.184688i
$447$	7801.14	−	6545.93i	0.825461	−	0.692644i
$448$	4632.04	−	14030.9i	0.488489	−	1.47969i
$449$	3387.68	−	1955.88i	0.356068	−	0.205576i	−0.311287	−	0.950316i	$-0.600760\pi$
$449$	3387.68	−	1955.88i	0.356068	−	0.205576i	0.667355	+	0.744740i	$0.267427\pi$
$450$	−3480.88	−	2264.39i	−0.364645	−	0.237210i
$451$	139.938	−	793.628i	0.0146107	−	0.0828613i
$452$	−10463.2	−	3018.04i	−1.08882	−	0.314063i
$453$	−4556.26	+	1658.34i	−0.472564	+	0.171999i
$454$	8743.19	+	11621.6i	0.903829	+	1.20138i
$455$	−422.669			−0.0435495
$456$	−5983.37	−	10032.0i	−0.614467	−	1.03025i
$457$	−9650.53			−0.987818			−0.493909	−	0.869514i	$-0.664432\pi$
$457$	−9650.53			−0.987818			−0.493909	+	0.869514i	$0.664432\pi$
$458$	6323.31	+	8405.03i	0.645129	+	0.857513i
$459$	242.352	−	88.2089i	0.0246449	−	0.00897002i
$460$	−1305.13	−	376.458i	−0.132287	−	0.0381574i
$461$	−1076.22	+	6103.52i	−0.108730	+	0.616636i	0.880935	+	0.473237i	$0.156915\pi$
$461$	−1076.22	+	6103.52i	−0.108730	+	0.616636i	−0.989665	+	0.143400i	$0.954197\pi$
$462$	5671.94	+	3689.73i	0.571174	+	0.371562i
$463$	−2740.77	+	1582.38i	−0.275107	+	0.158833i	−0.631206	−	0.775615i	$-0.717440\pi$
$463$	−2740.77	+	1582.38i	−0.275107	+	0.158833i	0.356099	+	0.934448i	$0.384106\pi$
$464$	−1466.07	−	10674.5i	−0.146682	−	1.06800i
$465$	498.041	−	417.906i	0.0496690	−	0.0416772i
$466$	10232.4	−	5203.58i	1.01719	−	0.517277i
$467$	3874.51	+	2236.95i	0.383920	+	0.221656i	0.679523	−	0.733655i	$-0.262187\pi$
$467$	3874.51	+	2236.95i	0.383920	+	0.221656i	−0.295602	+	0.955311i	$0.595520\pi$
$468$	1303.46	−	89.0926i	0.128745	−	0.00879980i
$469$	−3049.01	+	8377.09i	−0.300192	+	0.824772i
$470$	−1042.52	−	443.489i	−0.102315	−	0.0435247i
$471$	−3795.65	−	21526.2i	−0.371325	−	2.10589i
$472$	−15150.3	−	5256.56i	−1.47743	−	0.512612i
$473$	−2529.52	−	2122.52i	−0.245894	−	0.206329i
$474$	18799.6	+	4355.76i	1.82172	+	0.422081i
$475$	5137.50	−	8879.71i	0.496263	−	0.857746i
$476$	277.341	−	566.378i	0.0267057	−	0.0545376i
$477$	−5262.33	+	6271.40i	−0.505127	+	0.601987i
$478$	−170.594	−	1398.44i	−0.0163238	−	0.133814i
$479$	3211.41	−	566.258i	0.306332	−	0.0540146i	−0.0183692	−	0.999831i	$-0.505847\pi$
$479$	3211.41	−	566.258i	0.306332	−	0.0540146i	0.324701	+	0.945817i	$0.394736\pi$
$480$	1159.68	−	305.867i	0.110275	−	0.0290851i
$481$	1169.47	+	425.653i	0.110859	+	0.0403495i
$482$	1387.44	−	422.994i	0.131112	−	0.0399727i
$483$	−14367.2	+	24884.7i	−1.35348	+	2.34429i
$484$	8962.27	−	2219.62i	0.841686	−	0.208454i
$485$	−1007.50	−	1200.69i	−0.0943264	−	0.112414i
$486$	6011.50	−	6436.41i	0.561084	−	0.600744i
$487$	−7137.83	−	12363.1i	−0.664160	−	1.15036i	−0.979512	−	0.201384i	$-0.935456\pi$
$487$	−7137.83	−	12363.1i	−0.664160	−	1.15036i	0.315352	−	0.948975i	$-0.397877\pi$
$488$	6583.30	+	11015.1i	0.610681	+	1.02178i
$489$	−132.628	−	23.3858i	−0.0122651	−	0.00216267i
$490$	−78.2267	+	1470.59i	−0.00721208	+	0.135580i
$491$	1561.10	+	4289.10i	0.143486	+	0.394224i	0.990530	−	0.137299i	$-0.0438420\pi$
$491$	1561.10	+	4289.10i	0.143486	+	0.394224i	−0.847044	+	0.531523i	$0.821620\pi$
$492$	−2762.29	+	1224.66i	−0.253117	+	0.112220i
$493$		−	459.869i		−	0.0420111i
$494$	387.919	+	3204.26i	0.0353306	+	0.291835i
$495$			167.549i			0.0152137i
$496$	238.864	−	6275.67i	0.0216236	−	0.568116i
$497$	−79.4501	−	218.287i	−0.00717067	−	0.0197013i
$498$	−12211.6	−	649.584i	−1.09882	−	0.0584509i
$499$	−15549.5	−	2741.80i	−1.39497	−	0.245971i	−0.574896	−	0.818226i	$-0.694958\pi$
$499$	−15549.5	−	2741.80i	−1.39497	−	0.245971i	−0.820076	+	0.572255i	$0.806069\pi$
$500$	1467.69	+	1524.62i	0.131274	+	0.136366i
$501$	−8049.39	−	13942.0i	−0.717805	−	1.24327i
$502$	−8826.32	−	8243.63i	−0.784737	−	0.732931i
$503$	−4319.74	−	5148.06i	−0.382918	−	0.456343i	0.539815	−	0.841784i	$-0.318494\pi$
$503$	−4319.74	−	5148.06i	−0.382918	−	0.456343i	−0.922733	+	0.385440i	$0.874050\pi$
$504$	−116.869	−	7738.79i	−0.0103289	−	0.683955i
$505$	−408.092	+	706.835i	−0.0359601	+	0.0622847i
$506$	−1752.28	−	5747.58i	−0.153950	−	0.504962i
$507$	11756.4	+	4278.97i	1.02982	+	0.374824i
$508$	−2969.85	+	4074.20i	−0.259382	+	0.355833i
$509$	14662.6	−	2585.41i	1.27683	−	0.225140i	0.506199	−	0.862417i	$-0.331050\pi$
$509$	14662.6	−	2585.41i	1.27683	−	0.225140i	0.770635	+	0.637276i	$0.219939\pi$
$510$	50.8116	−	6.19844i	0.00441172	−	0.000538179i
$511$	−7158.83	+	8531.56i	−0.619742	+	0.738580i
$512$	5332.31	−	10285.1i	0.460268	−	0.887780i
$513$	5985.55	+	5031.78i	0.515143	+	0.433057i
$514$	−878.826	+	3793.04i	−0.0754151	+	0.325494i
$515$	1271.35	+	1066.79i	0.108781	+	0.0912782i
$516$	−1313.48	+	12311.2i	−0.112060	+	1.05033i
$517$	−870.259	−	4935.48i	−0.0740309	−	0.419850i
$518$	2886.00	−	6784.19i	0.244794	−	0.575444i
$519$	2898.07	−	7962.38i	0.245108	−	0.673429i
$520$	−327.199	−	52.6126i	−0.0275935	−	0.00443696i
$521$	6110.52	+	3527.91i	0.513833	+	0.296661i	0.734408	−	0.678709i	$-0.237460\pi$
$521$	6110.52	+	3527.91i	0.513833	+	0.296661i	−0.220575	+	0.975370i	$0.570793\pi$
$522$	−2558.33	−	5030.75i	−0.214511	−	0.421820i
$523$	−8712.77	+	7310.88i	−0.728457	+	0.611248i	−0.929710	−	0.368291i	$-0.879943\pi$
$523$	−8712.77	+	7310.88i	−0.728457	+	0.611248i	0.201254	+	0.979539i	$0.435498\pi$
$524$	−461.254	−	686.156i	−0.0384541	−	0.0572039i
$525$	19296.9	−	11141.0i	1.60416	−	0.926162i
$526$	8802.80	−	13531.9i	0.729696	−	1.12171i
$527$	46.5450	−	263.970i	0.00384731	−	0.0218192i
$528$	3931.51	+	3562.34i	0.324047	+	0.293620i
$529$	12544.6	−	4565.85i	1.03103	−	0.375265i
$530$	1659.44	−	1248.44i	0.136003	−	0.102318i
$531$	−8399.94			−0.686490
$532$	19077.2	−	1286.47i	1.55470	−	0.104841i
$533$	834.931			0.0678515
$534$	−14081.3	+	10593.8i	−1.14112	+	0.858495i
$535$	−1214.38	+	441.999i	−0.0981351	+	0.0357182i
$536$	−3403.08	+	6105.39i	−0.274236	+	0.492001i
$537$	2690.94	−	15261.1i	0.216243	−	1.22638i
$538$	−4661.35	+	7165.54i	−0.373541	+	0.574216i
$539$	−5641.70	+	3257.24i	−0.450844	+	0.260295i
$540$	−666.319	+	447.919i	−0.0530997	+	0.0356951i
$541$	−3793.90	+	3183.46i	−0.301502	+	0.252990i	−0.780969	−	0.624570i	$-0.785274\pi$
$541$	−3793.90	+	3183.46i	−0.301502	+	0.252990i	0.479467	+	0.877560i	$0.340830\pi$
$542$	8734.11	+	17174.9i	0.692181	+	1.36112i
$543$	−6385.06	−	3686.42i	−0.504621	−	0.291343i
$544$	285.198	−	403.925i	0.0224775	−	0.0318348i
$545$	646.638	−	1776.62i	0.0508237	−	0.139637i
$546$	−2744.27	+	6451.01i	−0.215098	+	0.505637i
$547$	2943.86	+	16695.5i	0.230110	+	1.30502i	0.852671	+	0.522449i	$0.174981\pi$
$547$	2943.86	+	16695.5i	0.230110	+	1.30502i	−0.622560	+	0.782572i	$0.713907\pi$
$548$	−18383.9	−	1961.38i	−1.43307	−	0.152894i
$549$	5149.16	+	4320.66i	0.400293	+	0.335885i
$550$	−1051.72	+	4539.25i	−0.0815372	+	0.351917i
$551$	12081.3	−	6960.49i	0.934088	−	0.538161i
$552$	−14219.6	+	17475.5i	−1.09642	+	1.34747i
$553$	−20304.7	+	24198.2i	−1.56138	+	1.86078i
$554$	439.851	−	53.6568i	0.0337319	−	0.00411491i
$555$	589.331	−	103.915i	0.0450734	−	0.00794765i
$556$	7785.18	+	5674.94i	0.593822	+	0.432862i
$557$	−12078.4	−	4396.19i	−0.918815	−	0.334421i	−0.161048	−	0.986947i	$-0.551487\pi$
$557$	−12078.4	−	4396.19i	−0.918815	−	0.334421i	−0.757767	+	0.652525i	$0.773710\pi$
$558$	−959.327	−	3146.64i	−0.0727806	−	0.238724i
$559$	1710.57	−	2962.79i	0.129426	−	0.224173i
$560$	−414.197	+	1919.02i	−0.0312554	+	0.144810i
$561$	145.550	+	173.460i	0.0109539	+	0.0130543i
$562$	−1536.42	−	1434.99i	−0.115320	−	0.107707i
$563$	−3738.33	−	6474.99i	−0.279844	−	0.484704i	0.691502	−	0.722375i	$-0.256949\pi$
$563$	−3738.33	−	6474.99i	−0.279844	−	0.484704i	−0.971346	+	0.237671i	$0.923616\pi$
$564$	−13537.6	+	13032.1i	−1.01070	+	0.972962i
$565$	1424.91	+	251.250i	0.106100	+	0.0187083i
$566$	−15407.5	−	819.587i	−1.14421	−	0.0608654i
$567$	8967.55	+	24638.1i	0.664200	+	1.82488i
$568$	−34.3326	−	178.872i	−0.00253620	−	0.0132135i
$569$		−	16728.9i		−	1.23253i	−0.787539	−	0.616265i	$-0.788645\pi$
$569$		−	16728.9i		−	1.23253i	0.787539	−	0.616265i	$-0.211355\pi$
$570$	931.914	+	1241.07i	0.0684800	+	0.0911974i
$571$			11784.3i			0.863676i	0.901951	+	0.431838i	$0.142135\pi$
$571$			11784.3i			0.863676i	−0.901951	+	0.431838i	$0.857865\pi$
$572$	−594.169	−	1340.18i	−0.0434326	−	0.0979645i
$573$	7173.92	+	19710.2i	0.523027	+	1.43701i
$574$	262.732	−	4939.12i	0.0191049	−	0.359155i
$575$	−19486.3	−	3435.97i	−1.41328	−	0.249199i
$576$	872.832	−	6005.35i	0.0631389	−	0.434415i
$577$	13565.5	+	23496.2i	0.978752	+	1.69525i	0.666953	+	0.745100i	$0.267598\pi$
$577$	13565.5	+	23496.2i	0.978752	+	1.69525i	0.311799	+	0.950148i	$0.399068\pi$
$578$	−9470.65	+	10140.1i	−0.681535	+	0.729709i
$579$	−9639.05	−	11487.4i	−0.691857	−	0.824523i
$580$	344.157	+	1389.62i	0.0246385	+	0.0994843i
$581$	10008.8	−	17335.7i	0.714688	−	1.23788i
$582$	−24867.1	+	7581.32i	−1.77109	+	0.539958i
$583$	8632.10	+	3141.83i	0.613216	+	0.223192i
$584$	−6603.83	+	5713.40i	−0.467925	+	0.404832i
$585$	−170.954	+	30.1438i	−0.0120822	+	0.00213041i
$586$	251.413	+	2060.96i	0.0177232	+	0.145285i
$587$	10297.8	−	12272.4i	0.724080	−	0.862926i	−0.270940	−	0.962596i	$-0.587334\pi$
$587$	10297.8	−	12272.4i	0.724080	−	0.862926i	0.995020	+	0.0996707i	$0.0317789\pi$
$588$	21937.0	+	10742.0i	1.53855	+	0.753391i
$589$	7639.31	−	2772.60i	0.534418	−	0.193961i
$590$	2075.71	+	480.930i	0.144840	+	0.0335586i
$591$	−4439.55	−	3725.23i	−0.309000	−	0.259282i
$592$	3078.60	−	4892.58i	0.213733	−	0.339668i
$593$	51.1753	+	290.230i	0.00354388	+	0.0200983i	0.986528	−	0.163590i	$-0.0523074\pi$
$593$	51.1753	+	290.230i	0.00354388	+	0.0200983i	−0.982985	+	0.183688i	$0.941196\pi$
$594$	−3268.18	−	1390.29i	−0.225749	−	0.0960338i
$595$	−28.6581	+	78.7376i	−0.00197457	+	0.00542509i
$596$	891.285	+	13039.9i	0.0612558	+	0.896197i
$597$	11915.9	+	6879.65i	0.816894	+	0.471634i
$598$	5549.11	−	2821.94i	0.379465	−	0.192972i
$599$	10701.5	−	8979.59i	0.729967	−	0.612515i	−0.200156	−	0.979764i	$-0.564145\pi$
$599$	10701.5	−	8979.59i	0.729967	−	0.612515i	0.930123	+	0.367249i	$0.119700\pi$
$600$	16325.0	−	6222.56i	1.11078	−	0.423391i
$601$	−9437.66	+	5448.83i	−0.640549	+	0.369821i	−0.784826	−	0.619716i	$-0.787248\pi$
$601$	−9437.66	+	5448.83i	−0.640549	+	0.369821i	0.144277	+	0.989537i	$0.453914\pi$
$602$	−16988.4	−	11051.3i	−1.15016	−	0.748205i
$603$	−635.777	+	3605.67i	−0.0429367	+	0.243506i
$604$	1724.69	−	5979.28i	0.116186	−	0.402804i
$605$	−1152.78	+	419.579i	−0.0774667	+	0.0281956i
$606$	8138.51	+	10817.8i	0.545552	+	0.725154i
$607$	−5148.93			−0.344298			−0.172149	−	0.985071i	$-0.555071\pi$
$607$	−5148.93			−0.344298			−0.172149	+	0.985071i	$0.555071\pi$
$608$	14928.3	+	1378.79i	0.995762	+	0.0919692i
$609$	30284.1			2.01506
$610$	−1025.03	−	1362.49i	−0.0680367	−	0.0904352i
$611$	4879.21	−	1775.89i	0.323063	−	0.117585i
$612$	71.7816	−	248.858i	0.00474118	−	0.0164371i
$613$	5084.34	−	28834.7i	0.334999	−	1.89988i	−0.0922382	−	0.995737i	$-0.529402\pi$
$613$	5084.34	−	28834.7i	0.334999	−	1.89988i	0.427238	−	0.904139i	$-0.359487\pi$
$614$	1331.84	+	866.395i	0.0875388	+	0.0569460i
$615$	347.684	−	200.736i	0.0227967	−	0.0131617i
$616$	−8114.94	+	3093.15i	−0.530779	+	0.202316i
$617$	2369.19	−	1987.99i	0.154587	−	0.129714i	−0.562214	−	0.826992i	$-0.690050\pi$
$617$	2369.19	−	1987.99i	0.154587	−	0.129714i	0.716801	+	0.697278i	$0.245606\pi$
$618$	24536.4	−	12477.7i	1.59709	−	0.812179i
$619$	22684.7	+	13097.0i	1.47298	+	0.850426i	0.999538	−	0.0303985i	$-0.00967762\pi$
$619$	22684.7	+	13097.0i	1.47298	+	0.850426i	0.473443	+	0.880824i	$0.343011\pi$
$620$	56.9015	+	832.491i	0.00368584	+	0.0539252i
$621$	5158.41	−	14172.6i	0.333333	−	0.915825i
$622$	−11543.5	−	4910.59i	−0.744133	−	0.316555i
$623$	−5008.82	−	28406.4i	−0.322109	−	1.82677i
$624$	−2927.41	+	4652.30i	−0.187805	+	0.298463i
$625$	11645.9	+	9772.04i	0.745335	+	0.625410i
$626$	−23798.7	−	5514.02i	−1.51947	−	0.352052i
$627$	−2353.99	+	6449.24i	−0.149935	+	0.410778i
$628$	25195.6	+	12337.7i	1.60097	+	0.783958i
$629$	158.587	−	188.997i	0.0100529	−	0.0119806i
$630$	124.524	+	1020.78i	0.00787482	+	0.0645538i
$631$	18940.9	−	3339.80i	1.19497	−	0.210706i	0.459448	−	0.888205i	$-0.348047\pi$
$631$	18940.9	−	3339.80i	1.19497	−	0.210706i	0.735524	+	0.677499i	$0.236936\pi$
$632$	−18730.5	+	16205.0i	−1.17889	+	1.01994i
$633$	−28217.0	−	10270.1i	−1.77176	−	0.644868i
$634$	−9360.56	+	2853.78i	−0.586365	+	0.178767i
$635$	334.941	−	580.134i	0.0209318	−	0.0362550i
$636$	−8280.11	−	33433.0i	−0.516239	−	2.08444i
$637$	−4338.42	−	5170.33i	−0.269850	−	0.321595i
$638$	−4322.61	+	4628.15i	−0.268235	+	0.287195i
$639$	−47.7024	−	82.6230i	−0.00295317	−	0.00511505i
$640$	−559.515	+	1434.01i	−0.0345575	+	0.0885690i
$641$	−6922.66	−	1220.65i	−0.426566	−	0.0752151i	−0.0437561	−	0.999042i	$-0.513932\pi$
$641$	−6922.66	−	1220.65i	−0.426566	−	0.0752151i	−0.382810	+	0.923827i	$0.625044\pi$
$642$	−1138.59	+	21404.4i	−0.0699945	+	1.31583i
$643$	2984.74	+	8200.51i	0.183059	+	0.502949i	0.996948	−	0.0780707i	$-0.0248760\pi$
$643$	2984.74	+	8200.51i	0.183059	+	0.502949i	−0.813889	+	0.581020i	$0.802654\pi$
$644$	−14947.3	−	33714.3i	−0.914604	−	2.06294i
$645$		−	1645.03i		−	0.100423i
$646$	623.215	+	144.994i	0.0379567	+	0.00883083i
$647$			6656.75i			0.404488i	0.979335	+	0.202244i	$0.0648234\pi$
$647$			6656.75i			0.404488i	−0.979335	+	0.202244i	$0.935177\pi$
$648$	3875.13	+	20189.3i	0.234922	+	1.22393i
$649$	3223.65	+	8856.90i	0.194976	+	0.535692i
$650$	−4820.71	−	256.434i	−0.290898	−	0.0154741i
$651$	17383.4	+	3065.16i	1.04656	+	0.184536i
$652$	124.524	−	119.875i	0.00747968	−	0.00720040i
$653$	2924.35	+	5065.13i	0.175251	+	0.303543i	0.940248	−	0.340490i	$-0.110593\pi$
$653$	2924.35	+	5065.13i	0.175251	+	0.303543i	−0.764997	+	0.644034i	$0.777260\pi$
$654$	−22917.4	−	21404.5i	−1.37025	−	1.27979i
$655$	70.6114	+	84.1514i	0.00421224	+	0.00501995i
$656$	818.196	−	3790.80i	0.0486969	−	0.225618i
$657$	−2287.03	+	3961.26i	−0.135808	+	0.235226i
$658$	−8970.06	−	29422.3i	−0.531443	−	1.74316i
$659$	−2067.32	−	752.443i	−0.122202	−	0.0444780i	0.280195	−	0.959943i	$-0.409601\pi$
$659$	−2067.32	−	752.443i	−0.122202	−	0.0444780i	−0.402398	+	0.915465i	$0.631823\pi$
$660$	−569.634	−	415.230i	−0.0335954	−	0.0244891i
$661$	−5992.85	+	1056.70i	−0.352640	+	0.0621799i	−0.347162	−	0.937805i	$-0.612855\pi$
$661$	−5992.85	+	1056.70i	−0.352640	+	0.0621799i	−0.00547757	+	0.999985i	$0.501744\pi$
$662$	7274.02	−	887.347i	0.427059	−	0.0520963i
$663$	−150.799	+	179.715i	−0.00883340	+	0.0105272i
$664$	9905.95	−	12174.2i	0.578954	−	0.711519i
$665$	−2502.30	+	438.871i	−0.145917	+	0.0255920i
$666$	683.447	−	2949.78i	0.0397643	−	0.171624i
$667$	−20601.2	−	17286.4i	−1.19592	−	1.00350i
$668$	20545.5	+	2192.00i	1.19001	+	0.126963i
$669$	−1468.58	−	8328.71i	−0.0848706	−	0.481325i
$670$	363.546	−	854.596i	0.0209627	−	0.0492775i
$671$	2579.61	−	7087.42i	0.148412	−	0.407760i
$672$	26600.0	+	18781.4i	1.52696	+	1.07814i
$673$	−21656.1	−	12503.2i	−1.24039	−	0.716138i	−0.271215	−	0.962519i	$-0.587425\pi$
$673$	−21656.1	−	12503.2i	−1.24039	−	0.716138i	−0.969173	+	0.246380i	$0.920759\pi$
$674$	−3355.63	−	6598.59i	−0.191772	−	0.377104i
$675$	−8959.27	+	7517.72i	−0.510878	+	0.428677i
$676$	−13326.0	+	8958.15i	−0.758196	+	0.509681i
$677$	960.612	−	554.610i	0.0545337	−	0.0314850i	−0.472485	−	0.881339i	$-0.656643\pi$
$677$	960.612	−	554.610i	0.0545337	−	0.0314850i	0.527019	+	0.849854i	$0.323310\pi$
$678$	13086.2	−	20116.5i	0.741260	−	1.13948i
$679$	7389.60	−	41908.5i	0.417654	−	2.36863i
$680$	−31.9861	+	57.3856i	−0.00180384	+	0.00323623i
$681$	−30116.8	+	10961.6i	−1.69468	+	0.616814i
$682$	−2949.66	+	2219.10i	−0.165613	+	0.124595i
$683$	−21480.4			−1.20340			−0.601702	−	0.798720i	$-0.705511\pi$
$683$	−21480.4			−1.20340			−0.601702	+	0.798720i	$0.705511\pi$
$684$	7624.29	−	1880.88i	0.426202	−	0.105142i
$685$	2456.48			0.137018
$686$	−9577.80	+	7205.62i	−0.533064	+	0.401038i
$687$	−21781.3	+	7927.75i	−1.20962	+	0.440266i
$688$	−11775.5	−	10669.8i	−0.652526	−	0.591254i
$689$	−1652.67	+	9372.75i	−0.0913812	+	0.518249i
$690$	1632.32	−	2509.25i	0.0900602	−	0.138443i
$691$	4501.47	−	2598.93i	0.247821	−	0.143079i	−0.370945	−	0.928655i	$-0.620966\pi$
$691$	4501.47	−	2598.93i	0.247821	−	0.143079i	0.618766	+	0.785575i	$0.287633\pi$
$692$	6067.19	+	9025.49i	0.333295	+	0.495806i
$693$	−3484.73	+	2924.04i	−0.191016	+	0.160281i
$694$	−2940.58	−	5782.42i	−0.160840	−	0.316279i
$695$	−1108.55	−	640.021i	−0.0605031	−	0.0349315i
$696$	23443.7	+	3769.68i	1.27677	+	0.205301i
$697$	56.6107	−	155.537i	0.00307645	−	0.00845247i
$698$	7952.21	−	18693.5i	0.431226	−	1.01369i
$699$	4392.98	+	24913.8i	0.237708	+	1.34811i
$700$	−3033.92	+	28436.7i	−0.163816	+	1.53544i
$701$	−4062.13	−	3408.53i	−0.218865	−	0.183650i	0.526763	−	0.850012i	$-0.323406\pi$
$701$	−4062.13	−	3408.53i	−0.218865	−	0.183650i	−0.745628	+	0.666363i	$0.767850\pi$
$702$	830.558	−	3584.71i	0.0446544	−	0.192730i
$703$	7365.52	+	1305.66i	0.395157	+	0.0700484i
$704$	−6667.01	+	1384.36i	−0.356921	+	0.0741123i
$705$	1604.85	−	1912.59i	0.0857336	−	0.102173i
$706$	12903.7	−	1574.11i	0.687873	−	0.0839126i
$707$	−21822.9	+	3847.96i	−1.16087	+	0.204692i
$708$	20817.2	−	28558.1i	1.10503	−	1.51593i
$709$	2645.27	+	962.798i	0.140120	+	0.0509995i	0.411128	−	0.911578i	$-0.365135\pi$
$709$	2645.27	+	962.798i	0.140120	+	0.0509995i	−0.271008	+	0.962577i	$0.587357\pi$
$710$	7.05724	+	23.1481i	0.000373033	+	0.00122357i
$711$	−6486.74	+	11235.4i	−0.342154	+	0.592629i
$712$	−341.505	−	22613.6i	−0.0179753	−	1.19028i
$713$	−10075.7	−	12007.7i	−0.529224	−	0.630704i
$714$	1015.67	+	948.618i	0.0532360	+	0.0497215i
$715$	97.3907	+	168.686i	0.00509399	+	0.00882306i
$716$	13793.7	+	14328.7i	0.719962	+	0.747887i
$717$	3057.51	+	539.122i	0.159254	+	0.0280807i
$718$	23158.5	+	1231.90i	1.20372	+	0.0640308i
$719$	1841.60	+	5059.76i	0.0955218	+	0.262444i	0.978246	−	0.207447i	$-0.0665155\pi$
$719$	1841.60	+	5059.76i	0.0955218	+	0.262444i	−0.882724	+	0.469891i	$0.844293\pi$
$720$	−30.6670	+	805.714i	−0.00158735	+	0.0417044i
$721$			45059.1i			2.32745i
$722$	5623.67	+	18567.2i	0.289877	+	0.957064i
$723$			3196.53i			0.164426i
$724$	8650.64	−	3835.27i	0.444059	−	0.196874i
$725$	7132.54	+	19596.5i	0.365373	+	1.00386i
$726$	−1080.84	+	20318.7i	−0.0552528	+	1.03870i
$727$	−6940.94	−	1223.87i	−0.354092	−	0.0624360i	−0.00622714	−	0.999981i	$-0.501982\pi$
$727$	−6940.94	−	1223.87i	−0.354092	−	0.0624360i	−0.347865	+	0.937545i	$0.613093\pi$
$728$	−4615.96	−	7723.34i	−0.234998	−	0.393195i
$729$	−2560.84	−	4435.50i	−0.130104	−	0.225347i
$730$	791.946	−	847.924i	0.0401524	−	0.0429905i
$731$	−435.947	−	519.542i	−0.0220576	−	0.0262872i
$732$	−27450.3	+	6798.41i	−1.38605	+	0.343274i
$733$	−1741.41	+	3016.21i	−0.0877495	+	0.151987i	−0.906560	−	0.422078i	$-0.861301\pi$
$733$	−1741.41	+	3016.21i	−0.0877495	+	0.151987i	0.818810	+	0.574065i	$0.194634\pi$
$734$	−6896.78	+	2102.64i	−0.346818	+	0.105736i
$735$	−3049.68	−	1109.99i	−0.153046	−	0.0557043i
$736$	−7374.41	−	27959.8i	−0.369327	−	1.40029i
$737$	4045.82	−	713.387i	0.202211	−	0.0356553i
$738$	−245.981	−	2016.43i	−0.0122692	−	0.100577i
$739$	334.771	−	398.965i	0.0166641	−	0.0198595i	−0.757648	−	0.652663i	$-0.773652\pi$
$739$	334.771	−	398.965i	0.0166641	−	0.0198595i	0.774312	+	0.632804i	$0.218096\pi$
$740$	−337.773	+	689.789i	−0.0167794	+	0.0342664i
$741$	−7003.80	−	1241.54i	−0.347221	−	0.0615509i
$742$	54925.4	+	12725.9i	2.71749	+	0.629626i
$743$	17248.0	+	14472.8i	0.851637	+	0.714608i	0.960150	−	0.279487i	$-0.0901643\pi$
$743$	17248.0	+	14472.8i	0.851637	+	0.714608i	−0.108513	+	0.994095i	$0.534609\pi$
$744$	13075.4	+	4536.66i	0.644312	+	0.223551i
$745$	−301.559	−	1710.23i	−0.0148299	−	0.0841045i
$746$	20081.3	+	8542.59i	0.985560	+	0.419258i
$747$	2811.84	−	7725.45i	0.137724	−	0.378393i
$748$	−289.944	+	19.8179i	−0.0141730	+	0.000968737i
$749$	−30385.9	−	17543.3i	−1.48235	−	0.855833i
$750$	−4157.08	+	2114.03i	−0.202394	+	0.102925i
$751$	−431.212	+	361.830i	−0.0209523	+	0.0175810i	−0.653204	−	0.757182i	$-0.726575\pi$
$751$	−431.212	+	361.830i	−0.0209523	+	0.0175810i	0.632251	+	0.774763i	$0.282131\pi$
$752$	−3281.56	−	23893.1i	−0.159131	−	1.15863i
$753$	23049.7	−	13307.7i	1.11551	−	0.644038i
$754$	−5499.88	−	3577.80i	−0.265642	−	0.172806i
$755$	−143.579	+	814.277i	−0.00692103	+	0.0392511i
$756$	−20944.4	−	6041.27i	−1.00759	−	0.290634i
$757$	−19882.7	+	7236.71i	−0.954622	+	0.347454i	−0.771924	−	0.635715i	$-0.780705\pi$
$757$	−19882.7	+	7236.71i	−0.954622	+	0.347454i	−0.182698	+	0.983169i	$0.558483\pi$
$758$	9420.13	+	12521.3i	0.451391	+	0.599994i
$759$	13241.8			0.633266
$760$	−1991.72	+	28.2623i	−0.0950624	+	0.00134892i
$761$	−9826.65			−0.468089			−0.234044	−	0.972226i	$-0.575196\pi$
$761$	−9826.65			−0.468089			−0.234044	+	0.972226i	$0.575196\pi$
$762$	−6679.67	−	8878.70i	−0.317558	−	0.422102i
$763$	48235.6	−	17556.3i	2.28866	−	0.833004i
$764$	−25866.1	−	7460.92i	−1.22487	−	0.353307i
$765$	−5.97578	+	33.8903i	−0.000282424	+	0.00160171i
$766$	24927.3	+	16215.8i	1.17580	+	0.764882i
$767$	−8456.91	+	4882.60i	−0.398124	+	0.229857i
$768$	18253.9	+	17850.2i	0.857657	+	0.838692i
$769$	8048.65	−	6753.62i	0.377428	−	0.316699i	−0.434264	−	0.900786i	$-0.642991\pi$
$769$	8048.65	−	6753.62i	0.377428	−	0.316699i	0.811692	+	0.584086i	$0.198547\pi$
$770$	1028.52	−	523.043i	0.0481369	−	0.0244794i
$771$	−7430.82	−	4290.19i	−0.347101	−	0.200399i
$772$	19201.5	−	1312.44i	0.895178	−	0.0611862i
$773$	−496.926	+	1365.29i	−0.0231218	+	0.0635268i	−0.950717	−	0.310061i	$-0.899650\pi$
$773$	−496.926	+	1365.29i	−0.0231218	+	0.0635268i	0.927595	+	0.373588i	$0.121873\pi$
$774$	−7659.34	−	3258.29i	−0.355697	−	0.151314i
$775$	2110.72	+	11970.5i	0.0978315	+	0.554830i
$776$	10937.1	−	31522.6i	0.505954	−	1.45824i
$777$	12446.1	+	10443.5i	0.574649	+	0.482188i
$778$	−40662.8	−	9421.35i	−1.87382	−	0.434154i
$779$	4942.99	−	866.936i	0.227344	−	0.0398732i
$780$	321.185	−	655.913i	0.0147439	−	0.0301096i
$781$	−68.8110	+	82.0057i	−0.00315269	+	0.00375723i
$782$	−149.444	−	1225.06i	−0.00683388	−	0.0560206i
$783$	−15654.1	+	2760.25i	−0.714474	+	0.125981i
$784$	−27726.1	+	14630.8i	−1.26303	+	0.666492i
$785$	−3502.68	−	1274.87i	−0.159256	−	0.0579644i
$786$	1742.83	−	531.342i	0.0790898	−	0.0241124i
$787$	−6913.60	+	11974.7i	−0.313142	+	0.542379i	−0.979041	−	0.203664i	$-0.934715\pi$
$787$	−6913.60	+	11974.7i	−0.313142	+	0.542379i	0.665898	+	0.746042i	$0.268048\pi$
$788$	7220.04	−	1788.13i	0.326400	−	0.0808371i
$789$	22867.6	+	27252.5i	1.03182	+	1.22968i
$790$	2246.21	−	2404.98i	0.101160	−	0.108310i
$791$	19641.7	+	34020.3i	0.882904	+	1.52923i
$792$	−3061.60	+	1829.80i	−0.137360	+	0.0820950i
$793$	7695.53	+	1356.93i	0.344611	+	0.0607642i
$794$	−781.214	+	14686.1i	−0.0349172	+	0.656409i
$795$	1565.21	+	4300.37i	0.0698266	+	0.191847i
$796$	−16144.0	+	7157.44i	−0.718854	+	0.318704i
$797$			23052.5i			1.02455i	0.858823	+	0.512273i	$0.171196\pi$
$797$			23052.5i			1.02455i	−0.858823	+	0.512273i	$0.828804\pi$
$798$	−9548.40	+	41041.0i	−0.423571	+	1.82060i
$799$		−	1029.34i		−	0.0455764i
$800$	−5888.36	+	21635.9i	−0.260231	+	0.956182i
$801$	−4051.77	−	11132.1i	−0.178729	−	0.491055i
$802$	16960.2	+	902.183i	0.746739	+	0.0397222i
$803$	5054.45	+	891.235i	0.222126	+	0.0391669i
$804$	−10682.9	−	11097.3i	−0.468605	−	0.486780i
$805$	2450.02	+	4243.56i	0.107269	+	0.185796i
$806$	−2794.87	−	2610.36i	−0.122140	−	0.114077i
$807$	−12109.1	−	14431.0i	−0.528202	−	0.629487i
$808$	−17372.6	+	262.356i	−0.756395	+	0.0114229i
$809$	18016.9	−	31206.2i	0.782991	−	1.35618i	−0.147200	−	0.989107i	$-0.547026\pi$
$809$	18016.9	−	31206.2i	0.782991	−	1.35618i	0.930192	−	0.367074i	$-0.119641\pi$
$810$	−796.552	−	2612.73i	−0.0345531	−	0.113336i
$811$	10280.7	+	3741.88i	0.445136	+	0.162016i	0.554856	−	0.831946i	$-0.312773\pi$
$811$	10280.7	+	3741.88i	0.445136	+	0.162016i	−0.109720	+	0.993962i	$0.534996\pi$
$812$	−22895.5	+	31409.2i	−0.989501	+	1.35745i
$813$	−41817.4	+	7373.53i	−1.80393	+	0.318082i
$814$	−3372.53	+	411.411i	−0.145218	+	0.0177149i
$815$	−14.7621	+	17.5928i	−0.000634471	+	0.000756133i
$816$	668.176	+	860.778i	0.0286652	+	0.0369280i
$817$	7050.59	−	19316.5i	0.301921	−	0.827173i
$818$	6135.28	−	26480.1i	0.262243	−	1.13185i
$819$	−3610.39	−	3029.48i	−0.154038	−	0.129253i
$820$	−54.6641	+	512.363i	−0.00232799	+	0.0218201i
$821$	1603.63	+	9094.66i	0.0681696	+	0.386609i	0.999735	+	0.0230344i	$0.00733272\pi$
$821$	1603.63	+	9094.66i	0.0681696	+	0.386609i	−0.931565	+	0.363575i	$0.881556\pi$
$822$	15949.2	−	37492.2i	0.676754	−	1.59086i
$823$	−7493.02	+	20586.9i	−0.317364	+	0.871950i	0.673753	+	0.738957i	$0.264681\pi$
$823$	−7493.02	+	20586.9i	−0.317364	+	0.871950i	−0.991117	+	0.132993i	$0.957541\pi$
$824$	−5608.84	+	34881.5i	−0.237128	+	1.47470i
$825$	−8892.71	−	5134.21i	−0.375278	−	0.216667i
$826$	26222.3	+	51564.1i	1.10459	+	2.17209i
$827$	−4233.70	+	3552.49i	−0.178017	+	0.149374i	−0.727442	−	0.686169i	$-0.759291\pi$
$827$	−4233.70	+	3552.49i	−0.178017	+	0.149374i	0.549425	+	0.835543i	$0.314847\pi$
$828$	−8450.06	−	12570.2i	−0.354662	−	0.527590i
$829$	−38214.5	+	22063.1i	−1.60102	+	0.924348i	−0.609733	+	0.792607i	$0.708723\pi$
$829$	−38214.5	+	22063.1i	−1.60102	+	0.924348i	−0.991284	+	0.131741i	$0.957943\pi$
$830$	−1137.14	+	1748.05i	−0.0475553	+	0.0731031i
$831$	−169.569	+	961.676i	−0.00707858	+	0.0401446i
$832$	−2611.95	−	6553.43i	−0.108838	−	0.273076i
$833$	−1257.32	+	457.628i	−0.0522972	+	0.0190346i
$834$	−16965.9	+	12763.8i	−0.704412	+	0.529947i
$835$	−2745.31			−0.113779
$836$	−4909.17	−	7317.23i	−0.203095	−	0.302717i
$837$	−9265.02			−0.382612
$838$	−33253.5	+	25017.4i	−1.37079	+	1.03128i
$839$	8042.40	−	2927.19i	0.330935	−	0.120451i	−0.171208	−	0.985235i	$-0.554767\pi$
$839$	8042.40	−	2927.19i	0.330935	−	0.120451i	0.502144	+	0.864784i	$0.332545\pi$
$840$	−3779.05	−	2106.40i	−0.155226	−	0.0865211i
$841$	−686.666	+	3894.28i	−0.0281547	+	0.159673i
$842$	−2149.64	+	3304.48i	−0.0879828	+	0.135249i
$843$	4012.31	−	2316.51i	0.163928	−	0.0946439i
$844$	31984.4	−	21500.8i	1.30444	−	0.876883i
$845$	1634.33	−	1371.37i	0.0665357	−	0.0558301i
$846$	−5726.39	−	11260.5i	−0.232716	−	0.457617i
$847$	−28844.6	−	16653.5i	−1.17015	−	0.675584i
$848$	40935.1	+	16688.4i	1.65769	+	0.675805i
$849$	11629.5	−	31951.7i	0.470109	−	1.29161i
$850$	−374.628	+	880.647i	−0.0151172	+	0.0355364i
$851$	−2505.38	−	14208.7i	−0.100920	−	0.572348i
$852$	399.121	+	42.5823i	0.0160489	+	0.00171226i
$853$	28713.4	+	24093.4i	1.15255	+	0.967108i	0.999776	−	0.0211524i	$-0.00673353\pi$
$853$	28713.4	+	24093.4i	1.15255	+	0.967108i	0.152778	+	0.988260i	$0.451178\pi$
$854$	10448.7	−	45096.7i	0.418672	−	1.80700i
$855$	−980.788	+	355.965i	−0.0392307	+	0.0142383i
$856$	−21338.8	−	17363.1i	−0.852038	−	0.693293i
$857$	26897.2	−	32054.9i	1.07210	−	1.27768i	0.113314	−	0.993559i	$-0.463853\pi$
$857$	26897.2	−	32054.9i	1.07210	−	1.27768i	0.958788	−	0.284122i	$-0.0917022\pi$
$858$	3206.91	−	391.206i	0.127601	−	0.0155659i
$859$	2169.77	−	382.589i	0.0861835	−	0.0151965i	−0.130390	−	0.991463i	$-0.541623\pi$
$859$	2169.77	−	382.589i	0.0861835	−	0.0151965i	0.216574	+	0.976266i	$0.430512\pi$
$860$	1706.15	+	1243.68i	0.0676502	+	0.0493131i
$861$	10242.7	+	3728.02i	0.405423	+	0.147562i
$862$	−10704.7	−	35111.9i	−0.422973	−	1.38737i
$863$	−5425.91	+	9397.95i	−0.214021	+	0.370695i	−0.952969	−	0.303067i	$-0.901989\pi$
$863$	−5425.91	+	9397.95i	−0.214021	+	0.370695i	0.738948	+	0.673762i	$0.235323\pi$
$864$	−15461.6	−	7283.81i	−0.608813	−	0.286806i
$865$	−928.801	−	1106.90i	−0.0365089	−	0.0435096i
$866$	25722.1	+	24024.0i	1.00932	+	0.942689i
$867$	−15288.5	−	26480.5i	−0.598876	−	1.03728i
$868$	−16321.3	+	15711.9i	−0.638228	+	0.614398i
$869$	14336.0	+	2527.82i	0.559626	+	0.0986772i
$870$	−3150.46	−	167.586i	−0.122771	−	0.00653069i
$871$	1455.77	+	3999.68i	0.0566323	+	0.155596i
$872$	39525.8	−	7586.58i	1.53499	−	0.294626i
$873$		−	17477.5i		−	0.677574i
$874$	29922.0	−	22468.4i	1.15804	−	0.869569i
$875$		−	7634.14i		−	0.294950i
$876$	−7799.63	−	17592.5i	−0.300828	−	0.678532i
$877$	−11247.2	−	30901.4i	−0.433056	−	1.18981i	−0.943927	−	0.330154i	$-0.892899\pi$
$877$	−11247.2	−	30901.4i	−0.433056	−	1.18981i	0.510871	−	0.859657i	$-0.329323\pi$
$878$	2127.26	−	39990.5i	0.0817672	−	1.53714i
$879$	−4506.01	−	794.531i	−0.172905	−	0.0304879i
$880$	861.314	−	276.874i	0.0329942	−	0.0106062i
$881$	3244.19	+	5619.10i	0.124063	+	0.214883i	0.921366	−	0.388696i	$-0.127074\pi$
$881$	3244.19	+	5619.10i	0.124063	+	0.214883i	−0.797303	+	0.603579i	$0.793741\pi$
$882$	−11208.6	+	12000.9i	−0.427907	+	0.458153i
$883$	−6218.29	−	7410.67i	−0.236990	−	0.282434i	0.634421	−	0.772988i	$-0.281239\pi$
$883$	−6218.29	−	7410.67i	−0.236990	−	0.282434i	−0.871411	+	0.490554i	$0.836794\pi$
$884$	−72.3845	−	292.270i	−0.00275402	−	0.0111200i
$885$	−2347.77	+	4066.45i	−0.0891744	+	0.154455i
$886$	−27447.0	+	8367.86i	−1.04075	+	0.317295i
$887$	−19584.0	−	7127.99i	−0.741337	−	0.269825i	−0.0563813	−	0.998409i	$-0.517956\pi$
$887$	−19584.0	−	7127.99i	−0.741337	−	0.269825i	−0.684956	+	0.728585i	$0.740178\pi$
$888$	8334.90	+	9633.88i	0.314978	+	0.364068i
$889$	17911.1	−	3158.21i	0.675724	−	0.119148i
$890$	363.872	+	2982.84i	0.0137045	+	0.112343i
$891$	7766.71	−	9256.00i	0.292025	−	0.348022i
$892$	9748.43	+	4773.57i	0.365921	+	0.179183i
$893$	27042.1	−	15579.9i	1.01336	−	0.583832i
$894$	−28060.4	−	6501.44i	−1.04975	−	0.243222i
$895$	−2024.35	−	1698.63i	−0.0756052	−	0.0634403i
$896$	−39589.4	+	13389.1i	−1.47610	+	0.499216i
$897$	2382.34	+	13510.9i	0.0886778	+	0.502917i
$898$	−10181.2	−	4331.08i	−0.378341	−	0.160947i
$899$	−5650.30	+	15524.1i	−0.209620	+	0.575925i
$900$	800.933	+	11718.0i	0.0296642	+	0.433999i
$901$	1633.96	+	943.370i	0.0604165	+	0.0348815i
$902$	−2031.72	+	1033.21i	−0.0749989	+	0.0381398i
$903$	34213.7	−	28708.7i	1.26087	−	1.05799i
$904$	10970.4	+	28781.0i	0.403616	+	1.05890i
$905$	−1088.84	+	628.641i	−0.0399936	+	0.0230903i
$906$	11495.8	+	7478.25i	0.421546	+	0.274226i
$907$	−5808.38	+	32941.0i	−0.212640	+	1.20594i	0.672316	+	0.740264i	$0.265299\pi$
$907$	−5808.38	+	32941.0i	−0.212640	+	1.20594i	−0.884956	+	0.465675i	$0.845812\pi$
$908$	11400.2	−	39523.0i	0.416660	−	1.44451i
$909$	−8552.12	+	3112.72i	−0.312053	+	0.113578i
$910$	718.713	+	955.323i	0.0261814	+	0.0348007i
$911$	15560.7			0.565915			0.282958	−	0.959132i	$-0.408684\pi$
$911$	15560.7			0.565915			0.282958	+	0.959132i	$0.408684\pi$
$912$	−12500.3	+	30582.3i	−0.453868	+	1.11040i
$913$	−9224.82			−0.334389
$914$	16409.9	+	21812.3i	0.593865	+	0.789373i
$915$	3530.83	−	1285.12i	0.127569	−	0.0464313i
$916$	8244.90	−	28584.1i	0.297401	−	1.03105i
$917$	−517.905	+	2937.19i	−0.0186507	+	0.105774i
$918$	−611.471	−	397.776i	−0.0219843	−	0.0143013i
$919$	13493.8	−	7790.67i	0.484353	−	0.279641i	−0.237876	−	0.971296i	$-0.576451\pi$
$919$	13493.8	−	7790.67i	0.484353	−	0.279641i	0.722229	+	0.691654i	$0.243118\pi$
$920$	1368.40	+	3590.02i	0.0490378	+	0.128652i
$921$	−2682.26	+	2250.68i	−0.0959647	+	0.0805240i
$922$	15625.3	−	7946.06i	0.558126	−	0.283828i
$923$	−96.0519	−	55.4556i	−0.00342534	−	0.00197762i
$924$	−1305.08	−	19093.9i	−0.0464655	−	0.679808i
$925$	−3826.57	+	10513.4i	−0.136018	+	0.373707i
$926$	8236.99	+	3504.02i	0.292316	+	0.124351i
$927$	3213.52	+	18224.8i	0.113857	+	0.645717i
$928$	−21633.8	+	21464.8i	−0.765262	+	0.759283i
$929$	−10191.1	−	8551.39i	−0.359915	−	0.302004i	0.444842	−	0.895609i	$-0.353260\pi$
$929$	−10191.1	−	8551.39i	−0.359915	−	0.302004i	−0.804757	+	0.593605i	$0.797704\pi$
$930$	−1791.44	−	415.065i	−0.0631650	−	0.0146350i
$931$	−31053.0	−	26104.8i	−1.09315	−	0.918960i
$932$	−29160.6	−	14279.3i	−1.02488	−	0.501859i
$933$	17769.9	−	21177.4i	0.623539	−	0.743105i
$934$	−1532.29	−	12561.0i	−0.0536812	−	0.440051i
$935$	38.0273	−	6.70524i	0.00133008	−	0.000234529i
$936$	−2417.80	−	2794.61i	−0.0844318	−	0.0975904i
$937$	20867.3	+	7595.08i	0.727540	+	0.264803i	0.679123	−	0.734024i	$-0.262360\pi$
$937$	20867.3	+	7595.08i	0.727540	+	0.264803i	0.0484170	+	0.998827i	$0.484582\pi$
$938$	24118.6	−	7353.12i	0.839553	−	0.255957i
$939$	26917.9	−	46623.3i	0.935499	−	1.62033i
$940$	770.340	+	3110.44i	0.0267295	+	0.107927i
$941$	25400.9	+	30271.6i	0.879964	+	1.04870i	0.998445	+	0.0557437i	$0.0177530\pi$
$941$	25400.9	+	30271.6i	0.879964	+	1.04870i	−0.118481	+	0.992956i	$0.537803\pi$
$942$	−42199.7	+	45182.5i	−1.45960	+	1.56277i
$943$	−4839.71	−	8382.63i	−0.167129	−	0.289476i
$944$	13880.8	+	43181.2i	0.478583	+	1.48880i
$945$	2852.27	+	502.932i	0.0981846	+	0.0173126i
$946$	−496.113	+	9326.45i	−0.0170508	+	0.320538i
$947$	−16505.5	−	45348.4i	−0.566373	−	1.55610i	−0.810124	−	0.586259i	$-0.800600\pi$
$947$	−16505.5	−	45348.4i	−0.566373	−	1.55610i	0.243751	−	0.969838i	$-0.421622\pi$
$948$	−22122.2	−	49897.7i	−0.757907	−	1.70950i
$949$			5317.50i			0.181890i
$950$	−28806.0	+	3487.35i	−0.983778	+	0.119100i
$951$		−	21565.8i		−	0.735351i
$952$	−1751.73	+	336.227i	−0.0596365	+	0.0114466i
$953$	16765.1	+	46061.8i	0.569859	+	1.56567i	0.804726	+	0.593647i	$0.202312\pi$
$953$	16765.1	+	46061.8i	0.569859	+	1.56567i	−0.234867	+	0.972028i	$0.575465\pi$
$954$	23122.9	+	1230.00i	0.784729	+	0.0417430i
$955$	3522.53	+	621.117i	0.119357	+	0.0210459i
$956$	−2870.70	+	2763.52i	−0.0971184	+	0.0934922i
$957$	−6978.02	−	12086.3i	−0.235703	−	0.408249i
$958$	−6740.60	−	6295.60i	−0.227327	−	0.212319i
$959$	42869.9	+	51090.4i	1.44353	+	1.72033i
$960$	−2663.26	−	2101.03i	−0.0895380	−	0.0706358i
$961$	10080.9	−	17460.7i	0.338388	−	0.586105i
$962$	−1026.52	−	3367.05i	−0.0344038	−	0.112846i
$963$	−13541.1	−	4928.57i	−0.453122	−	0.164923i
$964$	−3315.29	−	2416.65i	−0.110766	−	0.0807418i
$965$	−2518.35	+	444.053i	−0.0840089	+	0.0148130i
$966$	80674.9	−	9841.42i	2.68703	−	0.327787i
$967$	−11757.0	+	14011.4i	−0.390982	+	0.465954i	−0.925248	−	0.379362i	$-0.876143\pi$
$967$	−11757.0	+	14011.4i	−0.390982	+	0.465954i	0.534266	+	0.845316i	$0.320588\pi$
$968$	−20256.4	−	16482.4i	−0.672589	−	0.547277i
$969$	−706.161	+	1220.54i	−0.0234109	+	0.0404636i
$970$	−1000.65	+	4318.85i	−0.0331227	+	0.142959i
$971$	−2170.58	−	1821.33i	−0.0717377	−	0.0601951i	0.606214	−	0.795302i	$-0.292688\pi$
$971$	−2170.58	−	1821.33i	−0.0717377	−	0.0601951i	−0.677951	+	0.735107i	$0.737132\pi$
$972$	−24769.7	−	2642.69i	−0.817376	−	0.0872061i
$973$	−6034.86	−	34225.4i	−0.198837	−	1.12766i
$974$	−15806.0	+	37155.5i	−0.519975	+	1.22232i
$975$	3638.65	−	9997.10i	0.119518	−	0.328373i
$976$	13702.1	−	33609.9i	0.449378	−	1.10228i
$977$	−15365.8	−	8871.46i	−0.503169	−	0.290505i	0.226852	−	0.973929i	$-0.427157\pi$
$977$	−15365.8	−	8871.46i	−0.503169	−	0.290505i	−0.730021	+	0.683424i	$0.760490\pi$
$978$	172.665	+	339.533i	0.00564543	+	0.0111013i
$979$	−10182.8	+	8544.37i	−0.332424	+	0.278937i
$980$	3456.86	−	2323.80i	0.112679	−	0.0757461i
$981$	18257.5	−	10540.9i	0.594206	−	0.343065i
$982$	7039.76	−	10821.7i	0.228765	−	0.351664i
$983$	−5304.76	+	30084.8i	−0.172122	+	0.976150i	0.769292	+	0.638897i	$0.220609\pi$
$983$	−5304.76	+	30084.8i	−0.172122	+	0.976150i	−0.941414	+	0.337253i	$0.890502\pi$
$984$	7465.06	+	4160.94i	0.241847	+	0.134803i
$985$	−928.687	+	338.015i	−0.0300411	+	0.0109340i
$986$	−1039.40	+	781.970i	−0.0335714	+	0.0252566i
$987$	67786.0			2.18607
$988$	6582.71	−	6325.37i	0.211967	−	0.203681i
$989$	−39661.5			−1.27519
$990$	378.698	−	284.904i	0.0121574	−	0.00914630i
$991$	−52421.6	+	19079.9i	−1.68035	+	0.611597i	−0.993358	−	0.115068i	$-0.963291\pi$
$991$	−52421.6	+	19079.9i	−1.68035	+	0.611597i	−0.686992	+	0.726665i	$0.741069\pi$
$992$	−14590.5	+	10131.4i	−0.466986	+	0.324266i
$993$	−2804.25	+	15903.7i	−0.0896174	+	0.508246i
$994$	−358.278	+	550.754i	−0.0114325	+	0.0175743i
$995$	2032.01	−	1173.18i	0.0647427	−	0.0373792i
$996$	19296.6	+	28705.3i	0.613890	+	0.913216i
$997$	3330.32	−	2794.47i	0.105790	−	0.0887680i	−0.588359	−	0.808600i	$-0.700226\pi$
$997$	3330.32	−	2794.47i	0.105790	−	0.0887680i	0.694148	+	0.719832i	$0.255781\pi$
$998$	20243.6	+	39807.4i	0.642084	+	1.26261i
$999$	−7385.40	−	4263.96i	−0.233898	−	0.135041i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	76.4.k.a.3.9	✓	168
4.3	odd	2	inner	76.4.k.a.3.24	yes	168
19.13	odd	18	inner	76.4.k.a.51.24	yes	168
76.51	even	18	inner	76.4.k.a.51.9	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
76.4.k.a.3.9	✓	168	1.1	even	1	trivial
76.4.k.a.3.24	yes	168	4.3	odd	2	inner
76.4.k.a.51.9	yes	168	76.51	even	18	inner
76.4.k.a.51.24	yes	168	19.13	odd	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)

\(f(q)\)	\(=\)	\(q+(-1.70042 - 2.26022i) q^{2} +(5.85727 - 2.13187i) q^{3} +(-2.21716 + 7.68663i) q^{4} +(0.184577 - 1.04679i) q^{5} +(-14.7783 - 9.61362i) q^{6} +(24.9926 - 14.4295i) q^{7} +(21.1435 - 8.05922i) q^{8} +(9.07949 - 7.61860i) q^{9} +O(q^{10})\)	\(q+(-1.70042 - 2.26022i) q^{2} +(5.85727 - 2.13187i) q^{3} +(-2.21716 + 7.68663i) q^{4} +(0.184577 - 1.04679i) q^{5} +(-14.7783 - 9.61362i) q^{6} +(24.9926 - 14.4295i) q^{7} +(21.1435 - 8.05922i) q^{8} +(9.07949 - 7.61860i) q^{9} +(-2.67983 + 1.36279i) q^{10} +(-11.5175 - 6.64963i) q^{11} +(3.40041 + 49.7493i) q^{12} +(4.71264 - 12.9479i) q^{13} +(-75.1115 - 31.9525i) q^{14} +(-1.15050 - 6.52481i) q^{15} +(-54.1684 - 34.0849i) q^{16} +(-2.09249 - 1.75581i) q^{17} +(-32.6586 - 7.56682i) q^{18} +(14.4557 - 81.5477i) q^{19} +(7.63703 + 3.73967i) q^{20} +(115.626 - 137.798i) q^{21} +(4.55495 + 37.3392i) q^{22} +(-157.313 + 27.7384i) q^{23} +(106.662 - 92.2803i) q^{24} +(116.400 + 42.3661i) q^{25} +(-37.2784 + 11.3652i) q^{26} +(-47.2087 + 81.7678i) q^{27} +(55.5014 + 224.101i) q^{28} +(108.216 + 128.967i) q^{29} +(-12.7912 + 13.6953i) q^{30} +(49.0642 + 84.9816i) q^{31} +(15.0696 + 180.391i) q^{32} +(-81.6372 - 14.3948i) q^{33} +(-0.410397 + 7.71508i) q^{34} +(-10.4915 - 28.8253i) q^{35} +(38.4306 + 86.6823i) q^{36} +90.3215i q^{37} +(-208.896 + 105.992i) q^{38} -85.8859i q^{39} +(-4.53369 - 23.6204i) q^{40} +(20.7248 + 56.9408i) q^{41} +(-508.066 - 27.0262i) q^{42} +(244.517 + 43.1149i) q^{43} +(76.6493 - 73.7874i) q^{44} +(-6.29920 - 10.9105i) q^{45} +(330.192 + 308.393i) q^{46} +(242.225 + 288.672i) q^{47} +(-389.943 - 84.1644i) q^{48} +(244.919 - 424.211i) q^{49} +(-102.172 - 335.129i) q^{50} +(-15.9994 - 5.82331i) q^{51} +(89.0768 + 64.9318i) q^{52} +(-680.228 + 119.943i) q^{53} +(265.088 - 32.3377i) q^{54} +(-9.08662 + 10.8290i) q^{55} +(412.141 - 506.510i) q^{56} +(-89.1781 - 508.464i) q^{57} +(107.481 - 463.891i) q^{58} +(-542.903 - 455.550i) q^{59} +(52.7046 + 5.62307i) q^{60} +(98.4793 + 558.504i) q^{61} +(108.647 - 255.400i) q^{62} +(116.987 - 321.420i) q^{63} +(382.098 - 340.801i) q^{64} +(-12.6838 - 7.32302i) q^{65} +(106.282 + 208.995i) q^{66} +(-236.636 + 198.561i) q^{67} +(18.1356 - 12.1913i) q^{68} +(-862.287 + 497.841i) q^{69} +(-47.3113 + 72.7281i) q^{70} +(1.39776 - 7.92710i) q^{71} +(130.573 - 234.258i) q^{72} +(-362.644 + 131.992i) q^{73} +(204.146 - 153.584i) q^{74} +772.104 q^{75} +(594.776 + 291.920i) q^{76} -383.802 q^{77} +(-194.121 + 146.042i) q^{78} +(-1028.57 + 374.370i) q^{79} +(-45.6780 + 50.4116i) q^{80} +(-157.766 + 894.733i) q^{81} +(93.4578 - 143.666i) q^{82} +(600.705 - 346.817i) q^{83} +(802.840 + 1194.30i) q^{84} +(-2.22418 + 1.86631i) q^{85} +(-318.332 - 625.975i) q^{86} +(908.794 + 524.692i) q^{87} +(-297.111 - 47.7747i) q^{88} +(341.851 - 939.228i) q^{89} +(-13.9489 + 32.7900i) q^{90} +(-69.0499 - 391.601i) q^{91} +(135.572 - 1270.70i) q^{92} +(468.552 + 393.161i) q^{93} +(240.578 - 1038.34i) q^{94} +(-82.6950 - 30.1839i) q^{95} +(472.837 + 1024.47i) q^{96} +(947.847 - 1129.60i) q^{97} +(-1375.27 + 167.768i) q^{98} +(-155.234 + 27.3719i) 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

Varieties

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Representations

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Database

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