LMFDB - Embedded newform 27.4.e.a.7.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [27,4,Mod(4,27)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(27, base_ring=CyclotomicField(18))

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

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

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

chi := DirichletCharacter("27.4");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 27 = 3^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	27.e (of order $9$, 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:	$1.59305157015$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$8$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			7.6
Character	$\chi$	$=$	27.7
Dual form			27.4.e.a.4.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.82340 - 0.663664i) q^{2} +(5.12138 - 0.878355i) q^{3} +(-3.24401 + 2.72205i) q^{4} +(-0.470388 - 2.66770i) q^{5} +(8.75540 - 5.00047i) q^{6} +(-9.12942 - 7.66050i) q^{7} +(-11.8703 + 20.5600i) q^{8} +(25.4570 - 8.99678i) q^{9} +O(q^{10})$	\(q+(1.82340 - 0.663664i) q^{2} +(5.12138 - 0.878355i) q^{3} +(-3.24401 + 2.72205i) q^{4} +(-0.470388 - 2.66770i) q^{5} +(8.75540 - 5.00047i) q^{6} +(-9.12942 - 7.66050i) q^{7} +(-11.8703 + 20.5600i) q^{8} +(25.4570 - 8.99678i) q^{9} +(-2.62817 - 4.55212i) q^{10} +(-3.88999 + 22.0612i) q^{11} +(-14.2229 + 16.7900i) q^{12} +(-63.1117 - 22.9708i) q^{13} +(-21.7306 - 7.90930i) q^{14} +(-4.75222 - 13.2491i) q^{15} +(-2.11657 + 12.0037i) q^{16} +(44.8404 + 77.6659i) q^{17} +(40.4475 - 33.2996i) q^{18} +(39.1643 - 67.8345i) q^{19} +(8.78755 + 7.37363i) q^{20} +(-53.4839 - 31.2134i) q^{21} +(7.54823 + 42.8081i) q^{22} +(76.3697 - 64.0818i) q^{23} +(-42.7333 + 115.722i) q^{24} +(110.566 - 40.2428i) q^{25} -130.323 q^{26} +(122.472 - 68.4362i) q^{27} +50.4682 q^{28} +(102.311 - 37.2381i) q^{29} +(-17.4582 - 21.0046i) q^{30} +(-170.780 + 143.301i) q^{31} +(-28.8731 - 163.747i) q^{32} +(-0.544499 + 116.401i) q^{33} +(133.306 + 111.857i) q^{34} +(-16.1416 + 27.9580i) q^{35} +(-58.0930 + 98.4807i) q^{36} +(-38.3904 - 66.4941i) q^{37} +(26.3929 - 149.681i) q^{38} +(-343.395 - 62.2075i) q^{39} +(60.4316 + 21.9953i) q^{40} +(-357.134 - 129.986i) q^{41} +(-118.238 - 21.4193i) q^{42} +(-80.7838 + 458.148i) q^{43} +(-47.4325 - 82.1555i) q^{44} +(-35.9754 - 63.6797i) q^{45} +(96.7239 - 167.531i) q^{46} +(289.529 + 242.944i) q^{47} +(-0.296266 + 63.3345i) q^{48} +(-34.8981 - 197.917i) q^{49} +(174.899 - 146.758i) q^{50} +(297.863 + 358.370i) q^{51} +(267.263 - 97.2756i) q^{52} -0.995976 q^{53} +(177.898 - 206.067i) q^{54} +60.6826 q^{55} +(265.869 - 96.7683i) q^{56} +(140.992 - 381.806i) q^{57} +(161.840 - 135.800i) q^{58} +(111.486 + 632.267i) q^{59} +(51.4810 + 30.0445i) q^{60} +(-282.916 - 237.395i) q^{61} +(-216.296 + 374.636i) q^{62} +(-301.327 - 112.878i) q^{63} +(-210.076 - 363.862i) q^{64} +(-31.5923 + 179.169i) q^{65} +(76.2581 + 212.606i) q^{66} +(-401.725 - 146.216i) q^{67} +(-356.873 - 129.891i) q^{68} +(334.831 - 395.267i) q^{69} +(-10.8778 + 61.6913i) q^{70} +(29.7664 + 51.5569i) q^{71} +(-117.209 + 630.189i) q^{72} +(-157.281 + 272.418i) q^{73} +(-114.131 - 95.7672i) q^{74} +(530.904 - 303.215i) q^{75} +(57.5994 + 326.663i) q^{76} +(204.513 - 171.607i) q^{77} +(-667.433 + 114.470i) q^{78} +(-164.373 + 59.8269i) q^{79} +33.0179 q^{80} +(567.116 - 458.062i) q^{81} -737.467 q^{82} +(-764.859 + 278.386i) q^{83} +(258.466 - 44.3290i) q^{84} +(186.097 - 156.154i) q^{85} +(156.755 + 889.001i) q^{86} +(491.265 - 280.576i) q^{87} +(-407.403 - 341.851i) q^{88} +(511.446 - 885.851i) q^{89} +(-107.860 - 92.2381i) q^{90} +(400.206 + 693.177i) q^{91} +(-73.3104 + 415.764i) q^{92} +(-748.757 + 883.904i) q^{93} +(689.161 + 250.834i) q^{94} +(-199.385 - 72.5701i) q^{95} +(-291.698 - 813.251i) q^{96} +(140.142 - 794.785i) q^{97} +(-194.984 - 337.722i) q^{98} +(99.4525 + 596.609i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) $ 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/27\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{8}{9}\right)$

Coefficient data

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

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

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

$2$	1.82340	−	0.663664i	0.644670	−	0.234641i	0.00106622	−	0.999999i	$-0.499661\pi$
$2$	1.82340	−	0.663664i	0.644670	−	0.234641i	0.643604	+	0.765359i	$0.277438\pi$
$3$	5.12138	−	0.878355i	0.985609	−	0.169040i
$3$	5.12138	−	0.878355i	0.985609	−	0.169040i
$4$	−3.24401	+	2.72205i	−0.405501	+	0.340256i
$5$	−0.470388	−	2.66770i	−0.0420728	−	0.238607i	0.956518	−	0.291673i	$-0.0942118\pi$
$5$	−0.470388	−	2.66770i	−0.0420728	−	0.238607i	−0.998591	+	0.0530660i	$0.983101\pi$
$6$	8.75540	−	5.00047i	0.595729	−	0.340239i
$7$	−9.12942	−	7.66050i	−0.492943	−	0.413628i	0.362137	−	0.932125i	$-0.382047\pi$
$7$	−9.12942	−	7.66050i	−0.492943	−	0.413628i	−0.855079	+	0.518497i	$0.826492\pi$
$8$	−11.8703	+	20.5600i	−0.524598	+	0.908631i
$9$	25.4570	−	8.99678i	0.942851	−	0.333214i
$10$	−2.62817	−	4.55212i	−0.0831099	−	0.143951i
$11$	−3.88999	+	22.0612i	−0.106625	+	0.604701i	0.883934	+	0.467612i	$0.154886\pi$
$11$	−3.88999	+	22.0612i	−0.106625	+	0.604701i	−0.990559	+	0.137088i	$0.956226\pi$
$12$	−14.2229	+	16.7900i	−0.342149	+	0.403905i
$13$	−63.1117	−	22.9708i	−1.34647	−	0.490073i	−0.434622	−	0.900613i	$-0.643118\pi$
$13$	−63.1117	−	22.9708i	−1.34647	−	0.490073i	−0.911843	+	0.410540i	$0.865340\pi$
$14$	−21.7306	−	7.90930i	−0.414839	−	0.150989i
$15$	−4.75222	−	13.2491i	−0.0818013	−	0.228061i
$16$	−2.11657	+	12.0037i	−0.0330715	+	0.187558i
$17$	44.8404	+	77.6659i	0.639729	+	1.10804i	0.985492	+	0.169722i	$0.0542869\pi$
$17$	44.8404	+	77.6659i	0.639729	+	1.10804i	−0.345763	+	0.938322i	$0.612380\pi$
$18$	40.4475	−	33.2996i	0.529643	−	0.436044i
$19$	39.1643	−	67.8345i	0.472889	−	0.819068i	−0.526629	−	0.850095i	$-0.676544\pi$
$19$	39.1643	−	67.8345i	0.472889	−	0.819068i	0.999519	+	0.0310268i	$0.00987773\pi$
$20$	8.78755	+	7.37363i	0.0982478	+	0.0824397i
$21$	−53.4839	−	31.2134i	−0.555768	−	0.324349i
$22$	7.54823	+	42.8081i	0.0731494	+	0.414851i
$23$	76.3697	−	64.0818i	0.692356	−	0.580956i	−0.227232	−	0.973841i	$-0.572967\pi$
$23$	76.3697	−	64.0818i	0.692356	−	0.580956i	0.919588	+	0.392885i	$0.128523\pi$
$24$	−42.7333	+	115.722i	−0.363454	+	0.984233i
$25$	110.566	−	40.2428i	0.884530	−	0.321942i
$26$	−130.323			−0.983017
$27$	122.472	−	68.4362i	0.872957	−	0.487798i
$28$	50.4682			0.340628
$29$	102.311	−	37.2381i	0.655126	−	0.238447i	0.00699560	−	0.999976i	$-0.497773\pi$
$29$	102.311	−	37.2381i	0.655126	−	0.238447i	0.648131	+	0.761529i	$0.275551\pi$
$30$	−17.4582	−	21.0046i	−0.106247	−	0.127830i
$31$	−170.780	+	143.301i	−0.989449	+	0.830246i	−0.985488	−	0.169746i	$-0.945705\pi$
$31$	−170.780	+	143.301i	−0.989449	+	0.830246i	−0.00396118	+	0.999992i	$0.501261\pi$
$32$	−28.8731	−	163.747i	−0.159503	−	0.904585i
$33$	−0.544499	+	116.401i	−0.00287228	+	0.614022i
$34$	133.306	+	111.857i	0.672407	+	0.564216i
$35$	−16.1416	+	27.9580i	−0.0779549	+	0.135022i
$36$	−58.0930	+	98.4807i	−0.268949	+	0.455929i
$37$	−38.3904	−	66.4941i	−0.170577	−	0.295448i	0.768045	−	0.640396i	$-0.221230\pi$
$37$	−38.3904	−	66.4941i	−0.170577	−	0.295448i	−0.938622	+	0.344948i	$0.887896\pi$
$38$	26.3929	−	149.681i	0.112671	−	0.638988i
$39$	−343.395	−	62.2075i	−1.40993	−	0.255415i
$40$	60.4316	+	21.9953i	0.238877	+	0.0869440i
$41$	−357.134	−	129.986i	−1.36037	−	0.495133i	−0.444198	−	0.895928i	$-0.646511\pi$
$41$	−357.134	−	129.986i	−1.36037	−	0.495133i	−0.916167	+	0.400796i	$0.868734\pi$
$42$	−118.238	−	21.4193i	−0.434393	−	0.0786921i
$43$	−80.7838	+	458.148i	−0.286498	+	1.62481i	0.413387	+	0.910555i	$0.364346\pi$
$43$	−80.7838	+	458.148i	−0.286498	+	1.62481i	−0.699885	+	0.714255i	$0.746766\pi$
$44$	−47.4325	−	82.1555i	−0.162516	−	0.281486i
$45$	−35.9754	−	63.6797i	−0.119175	−	0.210951i
$46$	96.7239	−	167.531i	0.310025	−	0.536980i
$47$	289.529	+	242.944i	0.898556	+	0.753978i	0.969908	−	0.243473i	$-0.0782867\pi$
$47$	289.529	+	242.944i	0.898556	+	0.753978i	−0.0713514	+	0.997451i	$0.522731\pi$
$48$	−0.296266	+	63.3345i	−0.000890883	+	0.190449i
$49$	−34.8981	−	197.917i	−0.101744	−	0.577018i
$50$	174.899	−	146.758i	0.494689	−	0.415093i
$51$	297.863	+	358.370i	0.817827	+	0.983959i
$52$	267.263	−	97.2756i	0.712743	−	0.259417i
$53$	−0.995976			−0.00258128			−0.00129064	−	0.999999i	$-0.500411\pi$
$53$	−0.995976			−0.00258128			−0.00129064	+	0.999999i	$0.500411\pi$
$54$	177.898	−	206.067i	0.448312	−	0.519300i
$55$	60.6826			0.148772
$56$	265.869	−	96.7683i	0.634432	−	0.230914i
$57$	140.992	−	381.806i	0.327629	−	0.887218i
$58$	161.840	−	135.800i	0.366391	−	0.307439i
$59$	111.486	+	632.267i	0.246003	+	1.39515i	0.818151	+	0.575003i	$0.194999\pi$
$59$	111.486	+	632.267i	0.246003	+	1.39515i	−0.572148	+	0.820151i	$0.693890\pi$
$60$	51.4810	+	30.0445i	0.110770	+	0.0646456i
$61$	−282.916	−	237.395i	−0.593831	−	0.498284i	0.295625	−	0.955304i	$-0.404472\pi$
$61$	−282.916	−	237.395i	−0.593831	−	0.498284i	−0.889456	+	0.457021i	$0.848917\pi$
$62$	−216.296	+	374.636i	−0.443059	+	0.767400i
$63$	−301.327	−	112.878i	−0.602598	−	0.225734i
$64$	−210.076	−	363.862i	−0.410304	−	0.710668i
$65$	−31.5923	+	179.169i	−0.0602852	+	0.341894i
$66$	76.2581	+	212.606i	0.142223	+	0.396516i
$67$	−401.725	−	146.216i	−0.732515	−	0.266614i	−0.0512858	−	0.998684i	$-0.516332\pi$
$67$	−401.725	−	146.216i	−0.732515	−	0.266614i	−0.681229	+	0.732070i	$0.738554\pi$
$68$	−356.873	−	129.891i	−0.636429	−	0.231641i
$69$	334.831	−	395.267i	0.584188	−	0.689631i
$70$	−10.8778	+	61.6913i	−0.0185736	+	0.105336i
$71$	29.7664	+	51.5569i	0.0497552	+	0.0861786i	0.889830	−	0.456291i	$-0.150823\pi$
$71$	29.7664	+	51.5569i	0.0497552	+	0.0861786i	−0.840075	+	0.542470i	$0.817489\pi$
$72$	−117.209	+	630.189i	−0.191850	+	1.03151i
$73$	−157.281	+	272.418i	−0.252169	+	0.436769i	−0.964123	−	0.265457i	$-0.914477\pi$
$73$	−157.281	+	272.418i	−0.252169	+	0.436769i	0.711954	+	0.702226i	$0.247810\pi$
$74$	−114.131	−	95.7672i	−0.179290	−	0.150442i
$75$	530.904	−	303.215i	0.817380	−	0.466830i
$76$	57.5994	+	326.663i	0.0869356	+	0.493036i
$77$	204.513	−	171.607i	0.302681	−	0.253980i
$78$	−667.433	+	114.470i	−0.968871	+	0.166169i
$79$	−164.373	+	59.8269i	−0.234094	+	0.0852032i	−0.456403	−	0.889773i	$-0.650863\pi$
$79$	−164.373	+	59.8269i	−0.234094	+	0.0852032i	0.222310	+	0.974976i	$0.428640\pi$
$80$	33.0179			0.0461439
$81$	567.116	−	458.062i	0.777937	−	0.628342i
$82$	−737.467			−0.993166
$83$	−764.859	+	278.386i	−1.01150	+	0.368155i	−0.794007	−	0.607908i	$-0.792009\pi$
$83$	−764.859	+	278.386i	−1.01150	+	0.368155i	−0.217489	+	0.976063i	$0.569787\pi$
$84$	258.466	−	44.3290i	0.335726	−	0.0575796i
$85$	186.097	−	156.154i	0.237471	−	0.199262i
$86$	156.755	+	889.001i	0.196550	+	1.11469i
$87$	491.265	−	280.576i	0.605392	−	0.345757i
$88$	−407.403	−	341.851i	−0.493514	−	0.414108i
$89$	511.446	−	885.851i	0.609137	−	1.05506i	−0.382246	−	0.924061i	$-0.624849\pi$
$89$	511.446	−	885.851i	0.609137	−	1.05506i	0.991383	−	0.130996i	$-0.0418174\pi$
$90$	−107.860	−	92.2381i	−0.126327	−	0.108031i
$91$	400.206	+	693.177i	0.461022	+	0.798514i
$92$	−73.3104	+	415.764i	−0.0830775	+	0.471156i
$93$	−748.757	+	883.904i	−0.834866	+	0.985555i
$94$	689.161	+	250.834i	0.756187	+	0.275229i
$95$	−199.385	−	72.5701i	−0.215331	−	0.0783740i
$96$	−291.698	−	813.251i	−0.310118	−	0.864605i
$97$	140.142	−	794.785i	0.146693	−	0.831940i	−0.819298	−	0.573367i	$-0.805637\pi$
$97$	140.142	−	794.785i	0.146693	−	0.831940i	0.965992	−	0.258572i	$-0.0832521\pi$
$98$	−194.984	−	337.722i	−0.200983	−	0.348113i
$99$	99.4525	+	596.609i	0.100963	+	0.605672i
$100$	−249.135	+	431.514i	−0.249135	+	0.431514i
$101$	−1271.64	−	1067.03i	−1.25280	−	1.05123i	−0.996410	−	0.0846544i	$-0.973021\pi$
$101$	−1271.64	−	1067.03i	−1.25280	−	1.05123i	−0.256393	−	0.966573i	$-0.582534\pi$
$102$	780.962	+	455.773i	0.758105	+	0.442433i
$103$	−19.4320	−	110.204i	−0.0185893	−	0.105425i	0.974101	−	0.226112i	$-0.0726014\pi$
$103$	−19.4320	−	110.204i	−0.0185893	−	0.105425i	−0.992691	+	0.120687i	$0.961490\pi$
$104$	1221.43	−	1024.91i	1.15165	−	0.966349i
$105$	−58.1099	+	157.361i	−0.0540090	+	0.146256i
$106$	−1.81607	+	0.660994i	−0.00166407	+	0.000605674i
$107$	1525.97			1.37870			0.689351	−	0.724428i	$-0.257896\pi$
$107$	1525.97			1.37870			0.689351	+	0.724428i	$0.257896\pi$
$108$	−211.015	+	555.383i	−0.188009	+	0.494831i
$109$	1838.03			1.61515			0.807573	−	0.589767i	$-0.200781\pi$
$109$	1838.03			1.61515			0.807573	+	0.589767i	$0.200781\pi$
$110$	110.649	−	40.2729i	0.0959086	−	0.0349079i
$111$	−255.017	−	306.821i	−0.218064	−	0.262362i
$112$	111.277	−	93.3727i	0.0938814	−	0.0787758i
$113$	265.502	+	1505.73i	0.221029	+	1.25352i	0.870132	+	0.492818i	$0.164033\pi$
$113$	265.502	+	1505.73i	0.221029	+	1.25352i	−0.649103	+	0.760700i	$0.724856\pi$
$114$	3.69433	−	789.758i	0.00303514	−	0.648838i
$115$	−206.875	−	173.588i	−0.167749	−	0.140758i
$116$	−230.534	+	399.296i	−0.184522	+	0.319601i
$117$	−1813.30	−	16.9649i	−1.43282	−	0.0134052i
$118$	622.896	+	1078.89i	0.485951	+	0.841692i
$119$	185.592	−	1052.54i	0.142968	−	0.810812i
$120$	328.812	+	59.5657i	0.250136	+	0.0453132i
$121$	779.166	+	283.593i	0.585399	+	0.213068i
$122$	−673.421	−	245.105i	−0.499743	−	0.181892i
$123$	−1943.19	−	352.018i	−1.42449	−	0.258052i
$124$	163.938	−	929.740i	0.118727	−	0.673331i
$125$	−328.668	−	569.270i	−0.235176	−	0.407337i
$126$	−624.354	−	5.84134i	−0.441444	−	0.00413007i
$127$	−307.885	+	533.273i	−0.215121	+	0.372601i	−0.953310	−	0.301993i	$-0.902348\pi$
$127$	−307.885	+	533.273i	−0.215121	+	0.372601i	0.738189	+	0.674594i	$0.235681\pi$
$128$	394.447	+	330.980i	0.272379	+	0.228553i
$129$	−11.3077	+	2417.30i	−0.00771772	+	1.64986i
$130$	61.3024	+	347.663i	0.0413583	+	0.234554i
$131$	570.558	−	478.755i	0.380534	−	0.319306i	−0.432378	−	0.901692i	$-0.642325\pi$
$131$	570.558	−	478.755i	0.380534	−	0.319306i	0.812912	+	0.582387i	$0.197881\pi$
$132$	−315.081	−	379.087i	−0.207760	−	0.249964i
$133$	−877.193	+	319.272i	−0.571897	+	0.208153i
$134$	−829.544			−0.534789
$135$	−240.177	−	294.528i	−0.153120	−	0.187770i
$136$	−2129.08			−1.34240
$137$	−1522.72	+	554.226i	−0.949599	+	0.345626i	−0.769950	−	0.638105i	$-0.779719\pi$
$137$	−1522.72	+	554.226i	−0.949599	+	0.345626i	−0.179650	+	0.983731i	$0.557496\pi$
$138$	348.208	−	942.946i	0.214793	−	0.581659i
$139$	587.030	−	492.576i	0.358210	−	0.300574i	−0.445867	−	0.895099i	$-0.647104\pi$
$139$	587.030	−	492.576i	0.358210	−	0.300574i	0.804077	+	0.594525i	$0.202660\pi$
$140$	−23.7396	−	134.634i	−0.0143312	−	0.0812761i
$141$	1696.18	+	989.897i	1.01308	+	0.591236i
$142$	88.4926	+	74.2541i	0.0522967	+	0.0438822i
$143$	752.268	−	1302.97i	0.439914	−	0.761954i
$144$	54.1129	+	324.620i	0.0313153	+	0.187859i
$145$	−147.466	−	255.419i	−0.0844579	−	0.146285i
$146$	−105.992	+	601.110i	−0.0600818	+	0.340741i
$147$	−352.568	−	982.955i	−0.197819	−	0.551516i
$148$	305.539	+	111.207i	0.169697	+	0.0617646i
$149$	−1030.41	−	375.040i	−0.566543	−	0.206205i	0.0428386	−	0.999082i	$-0.486360\pi$
$149$	−1030.41	−	375.040i	−0.566543	−	0.206205i	−0.609381	+	0.792877i	$0.708582\pi$
$150$	766.818	−	905.225i	0.417403	−	0.492742i
$151$	−171.346	+	971.751i	−0.0923439	+	0.523708i	0.903185	+	0.429251i	$0.141223\pi$
$151$	−171.346	+	971.751i	−0.0923439	+	0.523708i	−0.995529	+	0.0944569i	$0.969889\pi$
$152$	929.783	+	1610.43i	0.496154	+	0.859364i
$153$	1840.24	+	1573.72i	0.972385	+	0.831554i
$154$	259.021	−	448.637i	0.135536	−	0.234754i
$155$	462.617	+	388.182i	0.239731	+	0.201158i
$156$	1283.31	−	732.937i	0.658635	−	0.376166i
$157$	−391.084	−	2217.95i	−0.198802	−	1.12746i	−0.906900	−	0.421346i	$-0.861558\pi$
$157$	−391.084	−	2217.95i	−0.198802	−	1.12746i	0.708098	−	0.706114i	$-0.249553\pi$
$158$	−260.013	+	218.177i	−0.130921	+	0.109856i
$159$	−5.10077	+	0.874821i	−0.00254413	+	0.000436339i
$160$	−423.248	+	154.050i	−0.209129	+	0.0761168i
$161$	−1188.11			−0.581591
$162$	730.082	−	1211.61i	0.354078	−	0.587609i
$163$	84.6969			0.0406992			0.0203496	−	0.999793i	$-0.493522\pi$
$163$	84.6969			0.0406992			0.0203496	+	0.999793i	$0.493522\pi$
$164$	1512.37	−	550.459i	0.720101	−	0.262095i
$165$	310.778	−	53.3009i	0.146631	−	0.0251483i
$166$	−1209.89	+	1015.22i	−0.565698	+	0.474677i
$167$	539.897	+	3061.91i	0.250170	+	1.41879i	0.808172	+	0.588947i	$0.200457\pi$
$167$	539.897	+	3061.91i	0.250170	+	1.41879i	−0.558001	+	0.829840i	$0.688432\pi$
$168$	1276.62	−	729.114i	0.586269	−	0.334836i
$169$	1772.43	+	1487.25i	0.806752	+	0.676946i
$170$	235.696	−	408.238i	0.106336	−	0.184179i
$171$	386.712	−	2079.21i	0.172939	−	0.929833i
$172$	−985.036	−	1706.13i	−0.436676	−	0.756345i
$173$	80.8272	−	458.394i	0.0355213	−	0.201451i	−0.961883	−	0.273463i	$-0.911831\pi$
$173$	80.8272	−	458.394i	0.0355213	−	0.201451i	0.997404	+	0.0720120i	$0.0229420\pi$
$174$	709.565	−	837.638i	0.309149	−	0.364949i
$175$	−1317.69	−	479.598i	−0.569187	−	0.207167i
$176$	−256.582	−	93.3884i	−0.109890	−	0.0399967i
$177$	1126.31	+	3140.15i	0.478299	+	1.33349i
$178$	344.665	−	1954.69i	0.145133	−	0.823092i
$179$	−182.127	−	315.453i	−0.0760491	−	0.131721i	0.825493	−	0.564413i	$-0.190897\pi$
$179$	−182.127	−	315.453i	−0.0760491	−	0.131721i	−0.901542	+	0.432692i	$0.857564\pi$
$180$	290.043	+	108.651i	0.120103	+	0.0449908i
$181$	566.151	−	980.602i	0.232495	−	0.402694i	−0.726047	−	0.687646i	$-0.758644\pi$
$181$	566.151	−	980.602i	0.232495	−	0.402694i	0.958542	+	0.284952i	$0.0919776\pi$
$182$	1189.77	+	998.339i	0.484571	+	0.406603i
$183$	−1657.44	−	967.287i	−0.669515	−	0.390732i
$184$	410.988	+	2330.83i	0.164666	+	0.933865i
$185$	−159.328	+	133.692i	−0.0633191	+	0.0531311i
$186$	−778.670	+	2108.64i	−0.306962	+	0.831251i
$187$	−1887.83	+	687.115i	−0.738246	+	0.268700i
$188$	−1600.54			−0.620911
$189$	−1642.36	−	313.417i	−0.632084	−	0.120623i
$190$	−411.721			−0.157207
$191$	802.031	−	291.915i	0.303837	−	0.110588i	−0.185602	−	0.982625i	$-0.559424\pi$
$191$	802.031	−	291.915i	0.303837	−	0.110588i	0.489440	+	0.872037i	$0.337201\pi$
$192$	−1395.48	−	1678.95i	−0.524531	−	0.631083i
$193$	940.060	−	788.804i	0.350606	−	0.294194i	−0.450427	−	0.892813i	$-0.648728\pi$
$193$	940.060	−	788.804i	0.350606	−	0.294194i	0.801033	+	0.598620i	$0.204284\pi$
$194$	−271.935	−	1542.22i	−0.100638	−	0.570747i
$195$	−4.42211	+	945.339i	−0.00162397	+	0.347165i
$196$	651.950	+	547.051i	0.237591	+	0.199362i
$197$	−1699.66	+	2943.90i	−0.614700	+	1.06469i	0.375737	+	0.926726i	$0.377390\pi$
$197$	−1699.66	+	2943.90i	−0.614700	+	1.06469i	−0.990437	+	0.137965i	$0.955944\pi$
$198$	577.290	+	1021.86i	0.207203	+	0.366768i
$199$	−1604.48	−	2779.04i	−0.571550	−	0.989954i	−0.996407	−	0.0846936i	$-0.973009\pi$
$199$	−1604.48	−	2779.04i	−0.571550	−	0.989954i	0.424857	−	0.905261i	$-0.360324\pi$
$200$	−485.064	+	2750.93i	−0.171496	+	0.972602i
$201$	−2185.81	−	395.969i	−0.767041	−	0.138953i
$202$	−3026.87	−	1101.69i	−1.05431	−	0.383736i
$203$	−1219.30	−	443.790i	−0.421568	−	0.153438i
$204$	−1941.77	−	351.760i	−0.666427	−	0.120726i
$205$	−178.773	+	1013.87i	−0.0609075	+	0.345424i
$206$	−108.571	−	188.051i	−0.0367209	−	0.0636025i
$207$	1367.61	−	2318.41i	0.459206	−	0.778457i
$208$	409.315	−	708.954i	0.136447	−	0.236332i
$209$	1344.16	+	1127.89i	0.444869	+	0.373290i
$210$	−1.52262	+	325.499i	−0.000500337	+	0.106960i
$211$	236.185	+	1339.47i	0.0770600	+	0.437029i	0.998789	+	0.0491949i	$0.0156655\pi$
$211$	236.185	+	1339.47i	0.0770600	+	0.437029i	−0.921729	+	0.387834i	$0.873223\pi$
$212$	3.23096	−	2.71109i	0.00104671	−	0.000878296i
$213$	197.730	+	237.897i	0.0636068	+	0.0765278i
$214$	2782.46	−	1012.73i	0.888808	−	0.323500i
$215$	1260.20			0.399744
$216$	−46.7395	+	3330.39i	−0.0147232	+	1.04909i
$217$	2656.88			0.831155
$218$	3351.46	−	1219.83i	1.04124	−	0.378979i
$219$	−566.214	+	1533.30i	−0.174709	+	0.473110i
$220$	−196.855	+	165.181i	−0.0603270	+	0.0506204i
$221$	−1045.91	−	5931.65i	−0.318351	−	1.80546i
$222$	−668.625	−	390.212i	−0.202140	−	0.117970i
$223$	3380.21	+	2836.33i	1.01505	+	0.851725i	0.988997	−	0.147936i	$-0.0472629\pi$
$223$	3380.21	+	2836.33i	1.01505	+	0.851725i	0.0260491	+	0.999661i	$0.491707\pi$
$224$	−990.791	+	1716.10i	−0.295536	+	0.511883i
$225$	2452.63	−	2019.20i	0.726704	−	0.598281i
$226$	1483.42	+	2569.36i	0.436617	+	0.756244i
$227$	746.356	−	4232.80i	0.218226	−	1.23762i	−0.656993	−	0.753897i	$-0.728172\pi$
$227$	746.356	−	4232.80i	0.218226	−	1.23762i	0.875219	−	0.483726i	$-0.160717\pi$
$228$	581.914	+	1622.37i	0.169027	+	0.471246i
$229$	207.521	+	75.5316i	0.0598839	+	0.0217959i	0.371788	−	0.928317i	$-0.378745\pi$
$229$	207.521	+	75.5316i	0.0598839	+	0.0217959i	−0.311905	+	0.950113i	$0.600967\pi$
$230$	−492.420	−	179.226i	−0.141171	−	0.0513819i
$231$	896.657	−	1058.50i	0.255393	−	0.301490i
$232$	−448.847	+	2545.54i	−0.127018	+	0.720357i
$233$	40.7671	+	70.6107i	0.0114624	+	0.0198535i	0.871700	−	0.490040i	$-0.163018\pi$
$233$	40.7671	+	70.6107i	0.0114624	+	0.0198535i	−0.860237	+	0.509894i	$0.829685\pi$
$234$	−3317.63	+	1172.49i	−0.926839	+	0.327555i
$235$	511.911	−	886.655i	0.142099	−	0.246123i
$236$	−2082.72	−	1747.61i	−0.574464	−	0.482032i
$237$	−789.267	+	450.774i	−0.216322	+	0.123548i
$238$	−360.127	−	2042.38i	−0.0980823	−	0.556253i
$239$	1215.74	−	1020.13i	0.329036	−	0.276094i	−0.463271	−	0.886217i	$-0.653324\pi$
$239$	1215.74	−	1020.13i	0.329036	−	0.276094i	0.792307	+	0.610123i	$0.208880\pi$
$240$	169.097	−	29.0014i	0.0454798	−	0.00780014i
$241$	283.355	−	103.133i	0.0757365	−	0.0275658i	−0.303874	−	0.952712i	$-0.598280\pi$
$241$	283.355	−	103.133i	0.0757365	−	0.0275658i	0.379611	+	0.925146i	$0.376058\pi$
$242$	1608.94			0.427383
$243$	2502.07	−	2844.04i	0.660527	−	0.750802i
$244$	1563.98			0.410343
$245$	−511.569	+	186.196i	−0.133400	+	0.0485535i
$246$	−3776.84	+	647.758i	−0.978873	+	0.167884i
$247$	−4029.94	+	3381.52i	−1.03813	+	0.871097i
$248$	−919.061	−	5212.25i	−0.235324	−	1.33459i
$249$	−3672.61	+	2097.54i	−0.934707	+	0.533839i
$250$	−977.099	−	819.884i	−0.247189	−	0.207416i
$251$	−190.883	+	330.619i	−0.0480017	+	0.0831415i	−0.889028	−	0.457853i	$-0.848619\pi$
$251$	−190.883	+	330.619i	−0.0480017	+	0.0831415i	0.841026	+	0.540994i	$0.181952\pi$
$252$	1284.77	−	454.051i	0.321162	−	0.113502i
$253$	1116.65	+	1934.09i	0.277482	+	0.480612i
$254$	−207.485	+	1176.70i	−0.0512549	+	0.290681i
$255$	815.915	−	963.183i	0.200371	−	0.236537i
$256$	4097.40	+	1491.33i	1.00034	+	0.364095i
$257$	4491.22	+	1634.67i	1.09010	+	0.396762i	0.823656	−	0.567089i	$-0.191931\pi$
$257$	4491.22	+	1634.67i	1.09010	+	0.396762i	0.266439	+	0.963852i	$0.414153\pi$
$258$	1583.66	+	4415.22i	0.382149	+	1.06543i
$259$	−158.896	+	901.142i	−0.0381208	+	0.216194i
$260$	−385.220	−	667.220i	−0.0918858	−	0.159151i
$261$	2269.50	−	1868.44i	0.538233	−	0.443117i
$262$	722.625	−	1251.62i	0.170397	−	0.295136i
$263$	−450.407	−	377.936i	−0.105602	−	0.0886105i	0.588458	−	0.808528i	$-0.299735\pi$
$263$	−450.407	−	377.936i	−0.105602	−	0.0886105i	−0.694060	+	0.719917i	$0.744180\pi$
$264$	−2386.73	−	1392.91i	−0.556413	−	0.324725i
$265$	0.468495	+	2.65697i	0.000108602	+	0.000615911i
$266$	−1387.59	+	1164.32i	−0.319844	+	0.268381i
$267$	1841.22	−	4986.01i	0.422025	−	1.14284i
$268$	1701.20	−	619.188i	0.387752	−	0.141130i
$269$	−3125.47			−0.708413			−0.354206	−	0.935167i	$-0.615249\pi$
$269$	−3125.47			−0.708413			−0.354206	+	0.935167i	$0.615249\pi$
$270$	−633.407	−	377.647i	−0.142770	−	0.0851218i
$271$	153.883			0.0344935			0.0172467	−	0.999851i	$-0.494510\pi$
$271$	153.883			0.0344935			0.0172467	+	0.999851i	$0.494510\pi$
$272$	−1027.18	+	373.865i	−0.228979	+	0.0833415i
$273$	2658.46	+	3198.50i	0.589368	+	0.709091i
$274$	−2408.72	+	2021.16i	−0.531081	+	0.445629i
$275$	457.704	+	2595.77i	0.100366	+	0.569203i
$276$	−10.2616	+	2193.68i	−0.00223795	+	0.478419i
$277$	−6029.51	−	5059.36i	−1.30786	−	1.09743i	−0.988728	−	0.149720i	$-0.952163\pi$
$277$	−6029.51	−	5059.36i	−1.30786	−	1.09743i	−0.319136	−	0.947709i	$-0.603393\pi$
$278$	743.486	−	1287.76i	0.160400	−	0.277822i
$279$	−3058.29	+	5184.48i	−0.656254	+	1.11250i
$280$	−383.210	−	663.740i	−0.0817900	−	0.141664i
$281$	−89.6875	+	508.643i	−0.0190402	+	0.107983i	−0.992847	−	0.119396i	$-0.961904\pi$
$281$	−89.6875	+	508.643i	−0.0190402	+	0.107983i	0.973807	+	0.227378i	$0.0730154\pi$
$282$	3749.77	+	679.287i	0.791829	+	0.143443i
$283$	−3744.12	−	1362.75i	−0.786448	−	0.286244i	−0.0825895	−	0.996584i	$-0.526319\pi$
$283$	−3744.12	−	1362.75i	−0.786448	−	0.286244i	−0.703859	+	0.710340i	$0.748541\pi$
$284$	−236.903	−	86.2255i	−0.0494986	−	0.0180160i
$285$	−1084.87	−	196.528i	−0.225480	−	0.0408467i
$286$	506.955	−	2875.08i	0.104814	−	0.594431i
$287$	2264.67	+	3922.53i	0.465782	+	0.806757i
$288$	−2208.22	−	3908.75i	−0.451807	−	0.799740i
$289$	−1564.83	+	2710.36i	−0.318508	+	0.551671i
$290$	−438.403	−	367.863i	−0.0887720	−	0.0744886i
$291$	19.6163	−	4193.48i	0.00395165	−	0.844764i
$292$	−231.315	−	1311.85i	−0.0463585	−	0.262912i
$293$	−5284.93	+	4434.58i	−1.05375	+	0.884201i	−0.993483	−	0.113981i	$-0.963640\pi$
$293$	−5284.93	+	4434.58i	−1.05375	+	0.884201i	−0.0602672	+	0.998182i	$0.519195\pi$
$294$	−1295.23	−	1558.34i	−0.256936	−	0.309129i
$295$	1634.26	−	594.821i	0.322543	−	0.117396i
$296$	1822.82			0.357937
$297$	1033.37	+	2968.11i	0.201893	+	0.579889i
$298$	−2127.76			−0.413617
$299$	−6291.84	+	2290.04i	−1.21694	+	0.442931i
$300$	−896.891	+	2428.78i	−0.172607	+	0.467418i
$301$	4247.15	−	3563.78i	0.813294	−	0.682435i
$302$	332.484	+	1885.61i	0.0633520	+	0.359287i
$303$	−7449.79	−	4347.73i	−1.41247	−	0.824326i
$304$	731.370	+	613.692i	0.137983	+	0.115782i
$305$	−500.219	+	866.404i	−0.0939096	+	0.162656i
$306$	4399.93	+	1648.22i	0.821984	+	0.307917i
$307$	−2277.90	−	3945.44i	−0.423474	−	0.733479i	0.572802	−	0.819693i	$-0.305856\pi$
$307$	−2277.90	−	3945.44i	−0.423474	−	0.733479i	−0.996277	+	0.0862148i	$0.972523\pi$
$308$	−196.320	+	1113.39i	−0.0363195	+	0.205978i
$309$	−196.317	−	547.330i	−0.0361427	−	0.100765i
$310$	1101.16	+	400.790i	0.201747	+	0.0734301i
$311$	9326.41	+	3394.53i	1.70049	+	0.618927i	0.995881	−	0.0906698i	$-0.0289008\pi$
$311$	9326.41	+	3394.53i	1.70049	+	0.618927i	0.704608	+	0.709597i	$0.251123\pi$
$312$	5355.20	−	6321.78i	0.971725	−	1.14712i
$313$	−55.7874	+	316.386i	−0.0100744	+	0.0571348i	−0.989431	−	0.145008i	$-0.953679\pi$
$313$	−55.7874	+	316.386i	−0.0100744	+	0.0571348i	0.979356	+	0.202142i	$0.0647904\pi$
$314$	−2185.07	−	3784.66i	−0.392710	−	0.680193i
$315$	−159.383	+	856.948i	−0.0285087	+	0.153281i
$316$	370.376	−	641.510i	0.0659344	−	0.114202i
$317$	5963.31	+	5003.81i	1.05657	+	0.886569i	0.993769	−	0.111457i	$-0.0355519\pi$
$317$	5963.31	+	5003.81i	1.05657	+	0.886569i	0.0628021	+	0.998026i	$0.479996\pi$
$318$	−8.72017	+	4.98035i	−0.00153774	+	0.000878252i
$319$	423.530	+	2401.96i	0.0743359	+	0.421580i
$320$	−871.859	+	731.576i	−0.152307	+	0.127801i
$321$	7815.07	−	1340.34i	1.35886	−	0.233055i
$322$	−2166.40	+	788.506i	−0.374935	+	0.136465i
$323$	7024.57			1.21008
$324$	−592.864	+	3029.67i	−0.101657	+	0.519491i
$325$	−7902.44			−1.34876
$326$	154.437	−	56.2103i	0.0262376	−	0.00954969i
$327$	9413.22	−	1614.44i	1.59190	−	0.273024i
$328$	6911.81	−	5799.69i	1.16354	−	0.976325i
$329$	−782.164	−	4435.87i	−0.131070	−	0.743336i
$330$	531.300	−	303.441i	0.0886276	−	0.0506179i
$331$	−5277.52	−	4428.36i	−0.876370	−	0.735362i	0.0890590	−	0.996026i	$-0.471614\pi$
$331$	−5277.52	−	4428.36i	−0.876370	−	0.735362i	−0.965430	+	0.260664i	$0.916058\pi$
$332$	1723.43	−	2985.07i	0.284896	−	0.493455i
$333$	−1575.54	−	1347.35i	−0.259276	−	0.221725i
$334$	3016.53	+	5224.78i	0.494183	+	0.855950i
$335$	−201.094	+	1140.46i	−0.0327968	+	0.186000i
$336$	487.878	−	575.938i	0.0792141	−	0.0935119i
$337$	4167.84	+	1516.97i	0.673699	+	0.245206i	0.656140	−	0.754639i	$-0.272188\pi$
$337$	4167.84	+	1516.97i	0.673699	+	0.245206i	0.0175593	+	0.999846i	$0.494410\pi$
$338$	4218.90	+	1535.55i	0.678928	+	0.247110i
$339$	2682.30	+	7478.23i	0.429743	+	1.19812i
$340$	−178.642	+	1013.13i	−0.0284948	+	0.161602i
$341$	−2497.07	−	4325.04i	−0.396550	−	0.686845i
$342$	−674.768	−	4047.89i	−0.106688	−	0.640014i
$343$	−3241.42	+	5614.30i	−0.510262	+	0.883800i
$344$	−8460.58	−	7099.27i	−1.32606	−	1.11269i
$345$	−1211.95	−	707.302i	−0.189129	−	0.110376i
$346$	−156.839	−	889.479i	−0.0243691	−	0.138204i
$347$	−9392.82	+	7881.51i	−1.45312	+	1.21931i	−0.522858	+	0.852420i	$0.675134\pi$
$347$	−9392.82	+	7881.51i	−1.45312	+	1.21931i	−0.930263	+	0.366894i	$0.880421\pi$
$348$	−829.926	+	2247.44i	−0.127841	+	0.346193i
$349$	1132.53	−	412.208i	0.173705	−	0.0632234i	−0.253704	−	0.967282i	$-0.581649\pi$
$349$	1132.53	−	412.208i	0.173705	−	0.0632234i	0.427409	+	0.904059i	$0.359427\pi$
$350$	−2720.96			−0.415548
$351$	−9301.48	+	1505.84i	−1.41446	+	0.228990i
$352$	3724.78			0.564010
$353$	452.132	−	164.563i	0.0681716	−	0.0248124i	−0.307709	−	0.951480i	$-0.599562\pi$
$353$	452.132	−	164.563i	0.0681716	−	0.0248124i	0.375881	+	0.926668i	$0.377340\pi$
$354$	4137.73	+	4978.26i	0.621237	+	0.747434i
$355$	123.537	−	103.660i	0.0184694	−	0.0154977i
$356$	752.191	+	4265.89i	0.111983	+	0.635089i
$357$	25.9782	−	5553.49i	0.00385129	−	0.823311i
$358$	−541.445	−	454.326i	−0.0799337	−	0.0670723i
$359$	2984.85	−	5169.92i	0.438815	−	0.760050i	−0.558783	−	0.829314i	$-0.688732\pi$
$359$	2984.85	−	5169.92i	0.438815	−	0.760050i	0.997598	+	0.0692637i	$0.0220650\pi$
$360$	1736.29	+	16.2444i	0.254196	+	0.00237821i
$361$	361.822	+	626.695i	0.0527515	+	0.0913683i
$362$	381.530	−	2163.77i	0.0553944	−	0.314158i
$363$	4239.50	+	768.003i	0.612991	+	0.111046i
$364$	−3185.13	−	1159.29i	−0.458644	−	0.166933i
$365$	800.714	+	291.436i	0.114825	+	0.0417930i
$366$	−3664.13	−	663.772i	−0.523298	−	0.0947977i
$367$	−723.679	+	4104.19i	−0.102931	+	0.583752i	0.889095	+	0.457722i	$0.151335\pi$
$367$	−723.679	+	4104.19i	−0.102931	+	0.583752i	−0.992026	+	0.126030i	$0.959777\pi$
$368$	607.576	+	1052.35i	0.0860654	+	0.149070i
$369$	−10261.0	−	96.0002i	−1.44761	−	0.0135436i
$370$	−201.793	+	349.515i	−0.0283532	+	0.0491093i
$371$	9.09269	+	7.62967i	0.00127242	+	0.00106769i
$372$	22.9472	−	4905.54i	0.00319827	−	0.683711i
$373$	−261.404	−	1482.50i	−0.0362868	−	0.205793i	0.961274	−	0.275594i	$-0.0888746\pi$
$373$	−261.404	−	1482.50i	−0.0362868	−	0.205793i	−0.997561	+	0.0698013i	$0.977763\pi$
$374$	−2986.27	+	2505.77i	−0.412877	+	0.346445i
$375$	−2183.26	−	2626.76i	−0.300648	−	0.361721i
$376$	−8431.71	+	3068.89i	−1.15647	+	0.420920i
$377$	−7312.41			−0.998961
$378$	−3202.68	+	518.489i	−0.435789	+	0.0705508i
$379$	2159.41			0.292669			0.146334	−	0.989235i	$-0.453252\pi$
$379$	2159.41			0.292669			0.146334	+	0.989235i	$0.453252\pi$
$380$	844.344	−	307.316i	0.113984	−	0.0414868i
$381$	−1108.39	+	3001.52i	−0.149041	+	0.403603i
$382$	1268.69	−	1064.56i	0.169926	−	0.142585i
$383$	−1336.89	−	7581.86i	−0.178359	−	1.01153i	−0.934194	−	0.356764i	$-0.883880\pi$
$383$	−1336.89	−	7581.86i	−0.178359	−	1.01153i	0.755835	−	0.654762i	$-0.227231\pi$
$384$	2310.83	+	1348.61i	0.307094	+	0.179221i
$385$	−553.997	−	464.859i	−0.0733358	−	0.0615361i
$386$	1190.61	−	2062.19i	0.156996	−	0.271924i
$387$	2065.34	+	12389.8i	0.271285	+	1.62742i
$388$	1708.82	+	2959.76i	0.223588	+	0.387266i
$389$	1052.20	−	5967.31i	0.137143	−	0.777775i	−0.836201	−	0.548423i	$-0.815228\pi$
$389$	1052.20	−	5967.31i	0.137143	−	0.777775i	0.973344	−	0.229352i	$-0.0736607\pi$
$390$	619.324	+	1726.67i	0.0804121	+	0.224188i
$391$	8401.42	+	3057.87i	1.08664	+	0.395506i
$392$	4483.42	+	1631.83i	0.577671	+	0.210255i
$393$	2501.53	−	2953.04i	0.321082	−	0.379036i
$394$	−1145.41	+	6495.92i	−0.146459	+	0.830609i
$395$	236.919	+	410.357i	0.0301790	+	0.0522716i
$396$	−1946.62	−	1664.69i	−0.247024	−	0.211247i
$397$	−1243.55	+	2153.89i	−0.157209	+	0.272293i	−0.933861	−	0.357636i	$-0.883583\pi$
$397$	−1243.55	+	2153.89i	−0.157209	+	0.272293i	0.776652	+	0.629929i	$0.216916\pi$
$398$	−4769.96	−	4002.47i	−0.600745	−	0.504085i
$399$	−4212.00	+	2405.60i	−0.528481	+	0.301831i
$400$	249.040	+	1412.38i	0.0311301	+	0.176547i
$401$	9077.73	−	7617.12i	1.13047	−	0.948581i	0.131389	−	0.991331i	$-0.458056\pi$
$401$	9077.73	−	7617.12i	1.13047	−	0.948581i	0.999086	+	0.0427502i	$0.0136120\pi$
$402$	−4248.41	+	728.635i	−0.527093	+	0.0904005i
$403$	14069.9	−	5121.04i	1.73914	−	0.632995i
$404$	7029.74			0.865699
$405$	−1488.74	−	1297.43i	−0.182657	−	0.159185i
$406$	−2517.81			−0.307775
$407$	1616.28	−	588.277i	0.196845	−	0.0716458i
$408$	−10903.8	+	1870.09i	−1.32309	+	0.226919i
$409$	3363.12	−	2821.99i	0.406591	−	0.341170i	−0.416444	−	0.909161i	$-0.636724\pi$
$409$	3363.12	−	2821.99i	0.406591	−	0.341170i	0.823035	+	0.567991i	$0.192279\pi$
$410$	346.895	+	1967.34i	0.0417852	+	0.236976i
$411$	−7311.64	+	4175.89i	−0.877509	+	0.501172i
$412$	363.019	+	304.609i	0.0434094	+	0.0364248i
$413$	3825.68	−	6626.26i	0.455809	−	0.789485i
$414$	955.063	−	5135.03i	0.113379	−	0.609597i
$415$	1102.43	+	1909.47i	0.130401	+	0.225860i
$416$	−1939.18	+	10997.6i	−0.228548	+	1.29616i
$417$	2573.74	−	3038.29i	0.302246	−	0.356800i
$418$	3199.49	+	1164.52i	0.374383	+	0.136264i
$419$	−5014.25	−	1825.04i	−0.584635	−	0.212790i	0.0327330	−	0.999464i	$-0.489579\pi$
$419$	−5014.25	−	1825.04i	−0.584635	−	0.212790i	−0.617368	+	0.786674i	$0.711801\pi$
$420$	−239.836	−	668.660i	−0.0278638	−	0.0776839i
$421$	2614.12	−	14825.4i	0.302623	−	1.71626i	−0.331862	−	0.943328i	$-0.607677\pi$
$421$	2614.12	−	14825.4i	0.302623	−	1.71626i	0.634486	−	0.772935i	$-0.281212\pi$
$422$	1319.62	+	2285.65i	0.152223	+	0.263658i
$423$	9556.25	+	3579.79i	1.09844	+	0.411478i
$424$	11.8225	−	20.4773i	0.00135414	−	0.00234543i
$425$	8083.33	+	6782.72i	0.922586	+	0.774142i
$426$	518.425	+	302.555i	0.0589620	+	0.0344104i
$427$	764.299	+	4334.56i	0.0866207	+	0.491250i
$428$	−4950.26	+	4153.76i	−0.559065	+	0.469111i
$429$	2708.18	−	7333.73i	0.304783	−	0.825352i
$430$	2297.85	−	836.351i	0.257703	−	0.0937963i
$431$	−4779.82			−0.534190			−0.267095	−	0.963670i	$-0.586064\pi$
$431$	−4779.82			−0.534190			−0.267095	+	0.963670i	$0.586064\pi$
$432$	562.264	+	1614.97i	0.0626202	+	0.179862i
$433$	6331.13			0.702666			0.351333	−	0.936250i	$-0.385728\pi$
$433$	6331.13			0.702666			0.351333	+	0.936250i	$0.385728\pi$
$434$	4844.56	−	1763.27i	0.535821	−	0.195023i
$435$	−979.578	−	1178.57i	−0.107971	−	0.129903i
$436$	−5962.57	+	5003.19i	−0.654944	+	0.549563i
$437$	−1355.99	−	7690.22i	−0.148435	−	0.841814i
$438$	−14.8362	+	3171.61i	−0.00161849	+	0.345994i
$439$	4644.41	+	3897.12i	0.504933	+	0.423689i	0.859342	−	0.511402i	$-0.170874\pi$
$439$	4644.41	+	3897.12i	0.504933	+	0.423689i	−0.354409	+	0.935090i	$0.615318\pi$
$440$	−720.321	+	1247.63i	−0.0780453	+	0.135178i
$441$	−2669.02	−	4724.40i	−0.288200	−	0.510140i
$442$	−5843.74	−	10121.7i	−0.628865	−	1.08923i
$443$	486.378	−	2758.39i	0.0521637	−	0.295835i	−0.947554	−	0.319596i	$-0.896453\pi$
$443$	486.378	−	2758.39i	0.0521637	−	0.295835i	0.999718	+	0.0237606i	$0.00756396\pi$
$444$	1662.46	+	301.161i	0.177695	+	0.0321903i
$445$	−2603.77	−	947.693i	−0.277372	−	0.100955i
$446$	8045.85	+	2928.45i	0.854219	+	0.310910i
$447$	−5606.56	−	1015.65i	−0.593246	−	0.107469i
$448$	−869.493	+	4931.14i	−0.0916957	+	0.520032i
$449$	2667.38	+	4620.04i	0.280360	+	0.485598i	0.971473	−	0.237149i	$-0.0762128\pi$
$449$	2667.38	+	4620.04i	0.280360	+	0.485598i	−0.691113	+	0.722746i	$0.742880\pi$
$450$	3132.05	−	5309.54i	0.328103	−	0.556209i
$451$	4256.90	−	7373.17i	0.444456	−	0.769820i
$452$	−4959.97	−	4161.91i	−0.516144	−	0.433097i
$453$	−23.9841	+	5127.20i	−0.00248757	+	0.531782i
$454$	−1448.25	−	8213.42i	−0.149713	−	0.849064i
$455$	1660.94	−	1393.69i	0.171134	−	0.143599i
$456$	6176.30	+	7430.95i	0.634280	+	0.763127i
$457$	−12826.7	+	4668.55i	−1.31293	+	0.477868i	−0.901187	−	0.433431i	$-0.857303\pi$
$457$	−12826.7	+	4668.55i	−1.31293	+	0.477868i	−0.411745	+	0.911299i	$0.635081\pi$
$458$	428.523			0.0437196
$459$	10806.9	+	6443.22i	1.09896	+	0.655215i
$460$	1143.62			0.115916
$461$	−12782.7	+	4652.53i	−1.29143	+	0.470044i	−0.894198	−	0.447672i	$-0.852253\pi$
$461$	−12782.7	+	4652.53i	−1.29143	+	0.470044i	−0.397237	+	0.917716i	$0.630031\pi$
$462$	932.479	−	2525.15i	0.0939023	−	0.254287i
$463$	−12418.0	+	10419.9i	−1.24646	+	1.04591i	−0.249471	+	0.968382i	$0.580257\pi$
$463$	−12418.0	+	10419.9i	−1.24646	+	1.04591i	−0.996991	+	0.0775235i	$0.975299\pi$
$464$	230.446	+	1306.93i	0.0230565	+	0.130760i
$465$	2710.20	+	1581.68i	0.270285	+	0.157739i
$466$	121.197	+	101.696i	0.0120479	+	0.0101094i
$467$	−8459.62	+	14652.5i	−0.838254	+	1.45190i	0.0530989	+	0.998589i	$0.483090\pi$
$467$	−8459.62	+	14652.5i	−0.838254	+	1.45190i	−0.891353	+	0.453310i	$0.850243\pi$
$468$	5928.53	−	4880.85i	0.585569	−	0.482088i
$469$	2547.43	+	4412.28i	0.250809	+	0.434414i
$470$	344.978	−	1956.47i	0.0338567	−	0.192011i
$471$	−3951.03	−	11015.4i	−0.386526	−	1.07763i
$472$	−14322.8	−	5213.06i	−1.39673	−	0.508369i
$473$	−9793.04	−	3564.38i	−0.951976	−	0.346491i
$474$	−1139.99	+	1345.75i	−0.110467	+	0.130406i
$475$	1600.39	−	9076.28i	0.154592	−	0.876733i
$476$	2263.01	+	3919.65i	0.217910	+	0.377431i
$477$	−25.3546	+	8.96058i	−0.00243376	+	0.000860119i
$478$	1539.76	−	2666.95i	0.147337	−	0.255195i
$479$	776.983	+	651.966i	0.0741153	+	0.0621901i	0.679093	−	0.734053i	$-0.262373\pi$
$479$	776.983	+	651.966i	0.0741153	+	0.0621901i	−0.604977	+	0.796243i	$0.706818\pi$
$480$	−2032.30	+	1160.71i	−0.193253	+	0.110372i
$481$	895.462	+	5078.42i	0.0848847	+	0.481405i
$482$	448.225	−	376.105i	0.0423570	−	0.0355418i
$483$	−6084.76	+	1043.58i	−0.573222	+	0.0983119i
$484$	−3299.57	+	1200.95i	−0.309877	+	0.112786i
$485$	−2186.17			−0.204678
$486$	2674.80	−	6846.36i	0.249653	−	0.639006i
$487$	−4091.32			−0.380688			−0.190344	−	0.981717i	$-0.560960\pi$
$487$	−4091.32			−0.380688			−0.190344	+	0.981717i	$0.560960\pi$
$488$	8239.13	−	2998.80i	0.764279	−	0.278175i
$489$	433.765	−	74.3940i	0.0401135	−	0.00687978i
$490$	−809.224	+	679.020i	−0.0746062	+	0.0626020i
$491$	17.0256	+	96.5568i	0.00156487	+	0.00887484i	0.985580	−	0.169209i	$-0.0541213\pi$
$491$	17.0256	+	96.5568i	0.00156487	+	0.00887484i	−0.984015	+	0.178084i	$0.943010\pi$
$492$	7261.94	−	4147.51i	0.665434	−	0.380049i
$493$	7479.80	+	6276.30i	0.683313	+	0.573368i
$494$	−5104.00	+	8840.39i	−0.464858	+	0.805158i
$495$	1544.80	−	545.948i	0.140269	−	0.0495728i
$496$	−1358.67	−	2353.29i	−0.122996	−	0.213036i
$497$	123.201	−	698.710i	0.0111194	−	0.0630612i
$498$	−5304.59	+	6262.04i	−0.477318	+	0.563471i
$499$	−5691.89	−	2071.68i	−0.510629	−	0.185854i	0.0738395	−	0.997270i	$-0.476475\pi$
$499$	−5691.89	−	2071.68i	−0.510629	−	0.185854i	−0.584469	+	0.811416i	$0.698697\pi$
$500$	2615.78	+	952.067i	0.233963	+	0.0851555i
$501$	5454.46	+	15207.0i	0.486401	+	1.35608i
$502$	−128.637	+	729.535i	−0.0114369	+	0.0648620i
$503$	−4856.15	−	8411.10i	−0.430467	−	0.745591i	0.566446	−	0.824099i	$-0.308318\pi$
$503$	−4856.15	−	8411.10i	−0.430467	−	0.745591i	−0.996914	+	0.0785074i	$0.974985\pi$
$504$	5897.61	−	4855.39i	0.521231	−	0.429120i
$505$	−2248.37	+	3894.28i	−0.198121	+	0.343155i
$506$	3319.68	+	2785.54i	0.291655	+	0.244728i
$507$	10383.6	+	6059.94i	0.909573	+	0.530831i
$508$	−452.811	−	2568.02i	−0.0395477	−	0.224286i
$509$	7383.99	−	6195.90i	0.643005	−	0.539545i	−0.261935	−	0.965086i	$-0.584360\pi$
$509$	7383.99	−	6195.90i	0.643005	−	0.539545i	0.904939	+	0.425541i	$0.139916\pi$
$510$	848.511	−	2297.76i	0.0736719	−	0.199503i
$511$	3522.74	−	1282.17i	0.304965	−	0.110998i
$512$	4341.65			0.374757
$513$	154.210	−	10988.1i	0.0132720	−	0.945685i
$514$	9274.18			0.795849
$515$	−284.852	+	103.678i	−0.0243730	+	0.00887104i
$516$	−6543.33	−	7872.53i	−0.558244	−	0.671645i
$517$	−6485.90	+	5442.31i	−0.551740	+	0.462965i
$518$	308.325	+	1748.60i	0.0261526	+	0.148319i
$519$	11.3138	−	2418.60i	0.000956876	−	0.204557i
$520$	−3308.69	−	2776.32i	−0.279030	−	0.234134i
$521$	−8627.23	+	14942.8i	−0.725462	+	1.25654i	0.233321	+	0.972400i	$0.425041\pi$
$521$	−8627.23	+	14942.8i	−0.725462	+	1.25654i	−0.958783	+	0.284138i	$0.908293\pi$
$522$	2898.20	−	4913.11i	0.243010	−	0.411956i
$523$	−6426.55	−	11131.1i	−0.537311	−	0.930649i	−0.999048	−	0.0436325i	$-0.986107\pi$
$523$	−6426.55	−	11131.1i	−0.537311	−	0.930649i	0.461737	−	0.887017i	$-0.347226\pi$
$524$	−547.702	+	3106.17i	−0.0456612	+	0.258958i
$525$	−7169.62	−	1298.81i	−0.596015	−	0.107971i
$526$	−1072.10	−	390.211i	−0.0888700	−	0.0323460i
$527$	−18787.4	−	6838.07i	−1.55293	−	0.565220i
$528$	−1396.08	−	252.906i	−0.115070	−	0.0208453i
$529$	−386.921	+	2194.34i	−0.0318009	+	0.180352i
$530$	2.61759	+	4.53380i	0.000214530	+	0.000371577i
$531$	8526.45	+	15092.6i	0.696829	+	1.23345i
$532$	1976.55	−	3423.48i	0.161079	−	0.278998i
$533$	19553.5	+	16407.3i	1.58903	+	1.33336i
$534$	48.2443	−	10313.5i	0.00390962	−	0.835780i
$535$	−717.798	−	4070.83i	−0.0580058	−	0.328967i
$536$	7774.79	−	6523.82i	0.626529	−	0.525721i
$537$	−1209.82	−	1455.58i	−0.0972208	−	0.116970i
$538$	−5698.98	+	2074.26i	−0.456692	+	0.166222i
$539$	4502.05			0.359772
$540$	1580.86	+	301.680i	0.125980	+	0.0240412i
$541$	−9727.92			−0.773080			−0.386540	−	0.922273i	$-0.626330\pi$
$541$	−9727.92			−0.773080			−0.386540	+	0.922273i	$0.626330\pi$
$542$	280.591	−	102.127i	0.0222369	−	0.00809358i
$543$	2038.15	−	5519.31i	0.161078	−	0.436200i
$544$	11422.9	−	9584.95i	0.900281	−	0.755425i
$545$	−864.585	−	4903.31i	−0.0679537	−	0.385385i
$546$	6970.18	+	4067.83i	0.546330	+	0.318840i
$547$	18630.8	+	15633.1i	1.45630	+	1.22198i	0.927819	+	0.373031i	$0.121681\pi$
$547$	18630.8	+	15633.1i	1.45630	+	1.22198i	0.528478	+	0.848947i	$0.322763\pi$
$548$	3431.10	−	5942.84i	0.267462	−	0.463258i
$549$	−9337.98	−	3498.02i	−0.725929	−	0.271934i
$550$	2557.30	+	4429.37i	0.198261	+	0.343398i
$551$	1480.90	−	8398.61i	0.114498	−	0.649352i
$552$	4152.12	+	11576.1i	0.320156	+	0.892591i
$553$	1958.94	+	712.994i	0.150637	+	0.0548275i
$554$	−14352.0	−	5223.68i	−1.10064	−	0.400601i
$555$	−698.550	+	824.635i	−0.0534267	+	0.0630699i
$556$	−563.513	+	3195.84i	−0.0429825	+	0.243766i
$557$	7540.43	+	13060.4i	0.573606	+	0.993514i	0.996192	+	0.0871912i	$0.0277891\pi$
$557$	7540.43	+	13060.4i	0.573606	+	0.993514i	−0.422586	+	0.906323i	$0.638878\pi$
$558$	−2135.73	+	11483.1i	−0.162030	+	0.871178i
$559$	15622.4	−	27058.8i	1.18204	−	2.04735i
$560$	−301.434	−	252.933i	−0.0227463	−	0.0190864i
$561$	−9064.77	+	5177.16i	−0.682201	+	0.389626i
$562$	174.032	+	986.984i	0.0130624	+	0.0740808i
$563$	−1831.42	+	1536.74i	−0.137096	+	0.115037i	−0.708757	−	0.705453i	$-0.750744\pi$
$563$	−1831.42	+	1536.74i	−0.137096	+	0.115037i	0.571661	+	0.820490i	$0.306299\pi$
$564$	−8196.96	+	1405.84i	−0.611976	+	0.104959i
$565$	3891.96	−	1416.56i	0.289798	−	0.105478i
$566$	−7731.45			−0.574164
$567$	−8686.42	−	162.551i	−0.643378	−	0.0120397i
$568$	−1413.34			−0.104406
$569$	20151.9	−	7334.70i	1.48473	−	0.540398i	0.532675	−	0.846320i	$-0.321187\pi$
$569$	20151.9	−	7334.70i	1.48473	−	0.540398i	0.952057	+	0.305922i	$0.0989646\pi$
$570$	−2108.58	+	361.637i	−0.154945	+	0.0265742i
$571$	8824.02	−	7404.24i	0.646714	−	0.542658i	−0.259358	−	0.965781i	$-0.583511\pi$
$571$	8824.02	−	7404.24i	0.646714	−	0.542658i	0.906072	+	0.423124i	$0.139066\pi$
$572$	1106.37	+	6274.54i	0.0808735	+	0.458657i
$573$	3851.10	−	2199.48i	0.280771	−	0.160357i
$574$	6732.65	+	5649.36i	0.489574	+	0.410801i
$575$	5865.08	−	10158.6i	0.425375	−	0.736771i
$576$	−8621.49	−	7372.83i	−0.623661	−	0.533335i
$577$	4116.78	+	7130.48i	0.297026	+	0.514464i	0.975454	−	0.220203i	$-0.0706719\pi$
$577$	4116.78	+	7130.48i	0.297026	+	0.514464i	−0.678428	+	0.734667i	$0.737339\pi$
$578$	−1054.54	+	5980.60i	−0.0758878	+	0.430381i
$579$	4121.55	−	4865.47i	0.295830	−	0.349226i
$580$	1173.64	+	427.171i	0.0840222	+	0.0305816i
$581$	9115.30	+	3317.70i	0.650889	+	0.236904i
$582$	−2747.30	−	7659.43i	−0.195669	−	0.545522i
$583$	3.87434	−	21.9725i	0.000275229	−	0.00156090i
$584$	−3733.94	−	6467.37i	−0.264575	−	0.458257i
$585$	807.696	+	4845.32i	0.0570840	+	0.342443i
$586$	−6693.48	+	11593.4i	−0.471852	+	0.817271i
$587$	−13361.6	−	11211.7i	−0.939511	−	0.788343i	0.0379893	−	0.999278i	$-0.487905\pi$
$587$	−13361.6	−	11211.7i	−0.939511	−	0.788343i	−0.977500	+	0.210935i	$0.932349\pi$
$588$	3819.38	+	2229.01i	0.267872	+	0.156331i
$589$	3032.30	+	17197.0i	0.212129	+	1.20304i
$590$	2585.15	−	2169.20i	0.180388	−	0.151363i
$591$	−6118.82	+	16569.7i	−0.425879	+	1.15328i
$592$	879.430	−	320.086i	0.0610547	−	0.0222221i
$593$	−14432.2			−0.999423			−0.499712	−	0.866192i	$-0.666561\pi$
$593$	−14432.2			−0.999423			−0.499712	+	0.866192i	$0.666561\pi$
$594$	3854.07	+	4726.24i	0.266220	+	0.326465i
$595$	−2895.18			−0.199480
$596$	4363.55	−	1588.20i	0.299896	−	0.109153i
$597$	−10658.1	−	12823.2i	−0.730667	−	0.879093i
$598$	−9952.73	+	8351.33i	−0.680598	+	0.571089i
$599$	3220.81	+	18266.1i	0.219698	+	1.24597i	0.872566	+	0.488496i	$0.162454\pi$
$599$	3220.81	+	18266.1i	0.219698	+	1.24597i	−0.652868	+	0.757471i	$0.726435\pi$
$600$	−67.8966	+	14514.6i	−0.00461978	+	0.987595i
$601$	−16512.1	−	13855.3i	−1.12070	−	0.940382i	−0.122064	−	0.992522i	$-0.538951\pi$
$601$	−16512.1	−	13855.3i	−1.12070	−	0.940382i	−0.998640	+	0.0521402i	$0.983396\pi$
$602$	5379.11	−	9316.89i	0.364179	−	0.630777i
$603$	−11542.2	−	107.986i	−0.779492	−	0.00729278i
$604$	−2089.30	−	3618.78i	−0.140749	−	0.243785i
$605$	390.032	−	2211.98i	0.0262100	−	0.148644i
$606$	−16469.4	−	2983.50i	−1.10400	−	0.199994i
$607$	−7155.28	−	2604.31i	−0.478458	−	0.174144i	0.0915221	−	0.995803i	$-0.470827\pi$
$607$	−7155.28	−	2604.31i	−0.478458	−	0.174144i	−0.569980	+	0.821659i	$0.693049\pi$
$608$	−12238.5	−	4454.45i	−0.816344	−	0.297125i
$609$	−6634.31	−	1201.83i	−0.441438	−	0.0799684i
$610$	−337.098	+	1911.78i	−0.0223749	+	0.126895i
$611$	−12692.1	−	21983.3i	−0.840370	−	1.45556i
$612$	−10253.5	−	95.9300i	−0.677244	−	0.00633617i
$613$	−13145.6	+	22768.8i	−0.866142	+	1.50020i	−0.000232630		1.00000i	$0.500074\pi$
$613$	−13145.6	+	22768.8i	−0.866142	+	1.50020i	−0.865909	+	0.500201i	$0.833259\pi$
$614$	−6771.97	−	5682.36i	−0.445105	−	0.373488i
$615$	−25.0237	+	5349.45i	−0.00164073	+	0.350749i
$616$	1100.60	+	6241.81i	0.0719877	+	0.408263i
$617$	8444.18	−	7085.51i	0.550972	−	0.462321i	−0.324298	−	0.945955i	$-0.605128\pi$
$617$	8444.18	−	7085.51i	0.550972	−	0.462321i	0.875270	+	0.483634i	$0.160684\pi$
$618$	−721.209	−	867.714i	−0.0469438	−	0.0564799i
$619$	−4411.45	+	1605.63i	−0.286447	+	0.104258i	−0.481248	−	0.876585i	$-0.659816\pi$
$619$	−4411.45	+	1605.63i	−0.286447	+	0.104258i	0.194800	+	0.980843i	$0.437594\pi$
$620$	−2557.38			−0.165656
$621$	4967.67	−	13074.7i	0.321008	−	0.844879i
$622$	19258.6			1.24148
$623$	−11455.3	+	4169.38i	−0.736670	+	0.268126i
$624$	1473.54	−	3990.34i	0.0945334	−	0.255996i
$625$	9902.76	−	8309.40i	0.633776	−	0.531802i
$626$	108.251	+	613.923i	0.00691148	+	0.0391970i
$627$	7874.65	+	4595.68i	0.501568	+	0.292717i
$628$	7306.03	+	6130.48i	0.464239	+	0.389543i
$629$	3442.88	−	5963.25i	0.218246	−	0.378013i
$630$	278.106	+	1668.34i	0.0175873	+	0.105505i
$631$	1671.81	+	2895.66i	0.105473	+	0.182685i	0.913932	−	0.405868i	$-0.133031\pi$
$631$	1671.81	+	2895.66i	0.105473	+	0.182685i	−0.808458	+	0.588554i	$0.799698\pi$
$632$	721.119	−	4089.67i	0.0453870	−	0.257402i
$633$	2386.13	+	6652.49i	0.149826	+	0.417714i
$634$	14194.4	+	5166.33i	0.889165	+	0.323630i
$635$	1567.44	+	570.501i	0.0979558	+	0.0356530i
$636$	14.1656	−	16.7225i	0.000883182	−	0.00104259i
$637$	−2343.83	+	13292.5i	−0.145787	+	0.826797i
$638$	2366.36	+	4098.66i	0.146842	+	0.254338i
$639$	1221.61	+	1044.68i	0.0756277	+	0.0646744i
$640$	697.414	−	1207.96i	0.0430745	−	0.0746073i
$641$	5422.29	+	4549.84i	0.334114	+	0.280355i	0.794374	−	0.607429i	$-0.207799\pi$
$641$	5422.29	+	4549.84i	0.334114	+	0.280355i	−0.460259	+	0.887785i	$0.652244\pi$
$642$	13360.5	−	7630.57i	0.821333	−	0.469088i
$643$	−3327.12	−	18869.0i	−0.204057	−	1.15727i	−0.898917	−	0.438120i	$-0.855645\pi$
$643$	−3327.12	−	18869.0i	−0.204057	−	1.15727i	0.694860	−	0.719145i	$-0.255466\pi$
$644$	3854.24	−	3234.09i	0.235836	−	0.197890i
$645$	6453.96	−	1106.90i	0.393992	−	0.0675726i
$646$	12808.6	−	4661.95i	0.780106	−	0.283935i
$647$	26381.3			1.60302			0.801512	−	0.597978i	$-0.204029\pi$
$647$	26381.3			1.60302			0.801512	+	0.597978i	$0.204029\pi$
$648$	2685.89	+	17097.2i	0.162827	+	1.03649i
$649$	−14382.2			−0.869881
$650$	−14409.3	+	5244.56i	−0.869508	+	0.316475i
$651$	13606.9	−	2333.68i	0.819194	−	0.140498i
$652$	−274.757	+	230.549i	−0.0165036	+	0.0138481i
$653$	4445.74	+	25213.1i	0.266425	+	1.51097i	0.764947	+	0.644093i	$0.222765\pi$
$653$	4445.74	+	25213.1i	0.266425	+	1.51097i	−0.498522	+	0.866877i	$0.666124\pi$
$654$	16092.6	−	9190.99i	0.962190	−	0.549536i
$655$	−1545.56	−	1296.88i	−0.0921985	−	0.0773638i
$656$	2316.21	−	4011.80i	0.137855	−	0.238772i
$657$	−1553.01	+	8349.96i	−0.0922200	+	0.495834i
$658$	−4370.13	−	7569.29i	−0.258914	−	0.448452i
$659$	477.180	−	2706.22i	0.0282068	−	0.159969i	−0.967451	−	0.253059i	$-0.918563\pi$
$659$	477.180	−	2706.22i	0.0282068	−	0.159969i	0.995658	+	0.0930900i	$0.0296744\pi$
$660$	−863.080	+	1018.86i	−0.0509020	+	0.0600896i
$661$	26790.5	+	9750.96i	1.57645	+	0.573780i	0.974427	−	0.224702i	$-0.0721410\pi$
$661$	26790.5	+	9750.96i	1.57645	+	0.573780i	0.602019	+	0.798482i	$0.294363\pi$
$662$	−12562.0	−	4572.19i	−0.737516	−	0.268434i
$663$	−10566.6	−	29459.5i	−0.618963	−	1.72566i
$664$	3355.50	−	19030.0i	0.196113	−	1.11221i
$665$	1264.34	+	2189.91i	0.0737281	+	0.127701i
$666$	−3767.02	−	1411.13i	−0.219173	−	0.0821026i
$667$	5427.17	−	9400.14i	0.315054	−	0.545689i
$668$	−10086.1	−	8463.23i	−0.584195	−	0.490198i
$669$	19802.6	+	11556.9i	1.14441	+	0.667885i
$670$	390.208	+	2212.98i	0.0225001	+	0.127604i
$671$	6337.76	−	5318.01i	0.364630	−	0.305961i
$672$	−3566.87	+	9659.06i	−0.204754	+	0.554474i
$673$	−21228.1	+	7726.38i	−1.21587	+	0.442541i	−0.868737	−	0.495274i	$-0.835068\pi$
$673$	−21228.1	+	7726.38i	−1.21587	+	0.442541i	−0.347135	+	0.937815i	$0.612845\pi$
$674$	8606.40			0.491849
$675$	10787.2	−	12495.4i	0.615113	−	0.712514i
$676$	−9798.16			−0.557474
$677$	234.324	−	85.2870i	0.0133025	−	0.00484172i	−0.335360	−	0.942090i	$-0.608858\pi$
$677$	234.324	−	85.2870i	0.0133025	−	0.00484172i	0.348663	+	0.937248i	$0.386636\pi$
$678$	9853.95	+	11855.7i	0.558169	+	0.671555i
$679$	−7367.86	+	6182.37i	−0.416425	+	0.349422i
$680$	1001.49	+	5679.75i	0.0564787	+	0.320307i
$681$	104.471	−	22333.3i	0.00587861	−	1.25670i
$682$	−7423.53	−	6229.09i	−0.416806	−	0.349742i
$683$	−3696.21	+	6402.03i	−0.207074	+	0.358663i	−0.950792	−	0.309831i	$-0.899727\pi$
$683$	−3696.21	+	6402.03i	−0.207074	+	0.358663i	0.743717	+	0.668494i	$0.233061\pi$
$684$	4405.22	+	7797.63i	0.246254	+	0.435892i
$685$	2194.78	+	3801.47i	0.122421	+	0.212039i
$686$	−2184.40	+	12388.3i	−0.121575	+	0.689488i
$687$	1129.14	+	204.548i	0.0627065	+	0.0113595i
$688$	−5328.47	−	1939.41i	−0.295271	−	0.107470i
$689$	62.8578	+	22.8784i	0.00347560	+	0.00126502i
$690$	−2679.29	−	485.365i	−0.147825	−	0.0267790i
$691$	978.497	−	5549.33i	0.0538694	−	0.305509i	−0.945954	−	0.324301i	$-0.894871\pi$
$691$	978.497	−	5549.33i	0.0538694	−	0.305509i	0.999823	+	0.0187922i	$0.00598210\pi$
$692$	985.565	+	1707.05i	0.0541410	+	0.0937749i
$693$	3662.38	−	6208.56i	0.200754	−	0.340323i
$694$	−11896.2	+	20604.9i	−0.650683	+	1.12702i
$695$	−1590.18	−	1334.32i	−0.0867898	−	0.0728253i
$696$	−62.8272	+	13430.9i	−0.00342164	+	0.731462i
$697$	−5918.55	−	33565.8i	−0.321637	−	1.82410i
$698$	1791.49	−	1503.24i	0.0971476	−	0.0815165i
$699$	270.805	+	325.816i	0.0146535	+	0.0176302i
$700$	5580.07	−	2030.98i	0.301296	−	0.109663i
$701$	−3492.05			−0.188149			−0.0940747	−	0.995565i	$-0.529989\pi$
$701$	−3492.05			−0.188149			−0.0940747	+	0.995565i	$0.529989\pi$
$702$	−15961.0	+	8918.81i	−0.858131	+	0.479514i
$703$	−6014.12			−0.322656
$704$	8844.43	−	3219.11i	0.473490	−	0.172336i
$705$	1842.89	−	4990.53i	0.0984499	−	0.266602i
$706$	715.205	−	600.128i	0.0381262	−	0.0319917i
$707$	3435.35	+	19482.8i	0.182743	+	1.03639i
$708$	−12201.4	−	7120.79i	−0.647679	−	0.377988i
$709$	−26353.3	−	22113.0i	−1.39594	−	1.17133i	−0.962869	−	0.269968i	$-0.912987\pi$
$709$	−26353.3	−	22113.0i	−1.39594	−	1.17133i	−0.433067	−	0.901362i	$-0.642569\pi$
$710$	156.462	−	271.000i	0.00827030	−	0.0143246i
$711$	−3646.19	+	3001.84i	−0.192325	+	0.158337i
$712$	12142.1	+	21030.6i	0.639105	+	1.10696i
$713$	−3859.40	+	21887.7i	−0.202715	+	1.14965i
$714$	−3638.29	−	10143.5i	−0.190700	−	0.531668i
$715$	−3829.78	−	1393.93i	−0.200316	−	0.0729090i
$716$	1449.50	+	527.574i	0.0756568	+	0.0275368i
$717$	5330.23	−	6292.31i	0.277630	−	0.327741i
$718$	2011.50	−	11407.8i	0.104552	−	0.592946i
$719$	13224.9	+	22906.3i	0.685963	+	1.18812i	0.973133	+	0.230243i	$0.0739521\pi$
$719$	13224.9	+	22906.3i	0.685963	+	1.18812i	−0.287170	+	0.957880i	$0.592715\pi$
$720$	840.535	−	297.054i	0.0435068	−	0.0153758i
$721$	−666.817	+	1154.96i	−0.0344432	+	0.0596574i
$722$	1075.66	+	902.589i	0.0554460	+	0.0465247i
$723$	1360.58	−	777.069i	0.0699869	−	0.0399716i
$724$	832.646	+	4722.17i	0.0427418	+	0.242401i
$725$	9813.57	−	8234.56i	0.502713	−	0.421826i
$726$	8240.00	−	1413.22i	0.421233	−	0.0722447i
$727$	13632.0	−	4961.66i	0.695440	−	0.253119i	0.0299770	−	0.999551i	$-0.490457\pi$
$727$	13632.0	−	4961.66i	0.695440	−	0.253119i	0.665462	+	0.746431i	$0.268234\pi$
$728$	−19002.3			−0.967406
$729$	10316.0	−	16763.1i	0.524106	−	0.851653i
$730$	1653.44			0.0838309
$731$	−39204.8	+	14269.4i	−1.98364	+	0.721987i
$732$	8009.74	−	1373.73i	0.404438	−	0.0693642i
$733$	7600.74	−	6377.78i	0.383001	−	0.321376i	−0.430878	−	0.902410i	$-0.641796\pi$
$733$	7600.74	−	6377.78i	0.383001	−	0.321376i	0.813879	+	0.581034i	$0.197352\pi$
$734$	1404.24	+	7963.87i	0.0706153	+	0.400479i
$735$	−2456.39	+	1402.92i	−0.123272	+	0.0704046i
$736$	−12698.2	−	10655.1i	−0.635956	−	0.533630i
$737$	4788.40	−	8293.76i	0.239326	−	0.414524i
$738$	−18773.7	+	6634.82i	−0.936407	+	0.330937i
$739$	−894.624	−	1549.53i	−0.0445322	−	0.0771320i	0.842900	−	0.538070i	$-0.180846\pi$
$739$	−894.624	−	1549.53i	−0.0445322	−	0.0771320i	−0.887432	+	0.460938i	$0.847513\pi$
$740$	152.946	−	867.397i	0.00759782	−	0.0430894i
$741$	−17668.6	+	20857.7i	−0.875943	+	1.03405i
$742$	21.6432	+	7.87747i	0.00107082	+	0.000389746i
$743$	16623.9	+	6050.61i	0.820824	+	0.298755i	0.718087	−	0.695953i	$-0.245018\pi$
$743$	16623.9	+	6050.61i	0.820824	+	0.298755i	0.102737	+	0.994709i	$0.467240\pi$
$744$	−9285.07	−	25886.6i	−0.457536	−	1.27561i
$745$	−515.801	+	2925.25i	−0.0253658	+	0.143856i
$746$	−1460.52	−	2529.70i	−0.0716805	−	0.124154i
$747$	−16966.4	+	13968.1i	−0.831016	+	0.684160i
$748$	4253.79	−	7367.77i	0.207933	−	0.360150i
$749$	−13931.2	−	11689.7i	−0.679621	−	0.570270i
$750$	−5724.24	−	3340.69i	−0.278693	−	0.162646i
$751$	6988.63	+	39634.5i	0.339572	+	1.92581i	0.376328	+	0.926486i	$0.377186\pi$
$751$	6988.63	+	39634.5i	0.339572	+	1.92581i	−0.0367561	+	0.999324i	$0.511702\pi$
$752$	−3529.03	+	2961.21i	−0.171131	+	0.143596i
$753$	−687.183	+	1860.89i	−0.0332568	+	0.0900592i
$754$	−13333.5	+	4852.99i	−0.644001	+	0.234397i
$755$	2672.94			0.128845
$756$	6180.96	−	3453.85i	0.297353	−	0.166158i
$757$	28253.8			1.35654			0.678270	−	0.734813i	$-0.262730\pi$
$757$	28253.8			1.35654			0.678270	+	0.734813i	$0.262730\pi$
$758$	3937.47	−	1433.12i	0.188675	−	0.0686720i
$759$	7417.57	+	8924.37i	0.354731	+	0.426791i
$760$	3858.80	−	3237.91i	0.184175	−	0.154541i
$761$	511.044	+	2898.28i	0.0243434	+	0.138058i	0.994557	−	0.104192i	$-0.0332256\pi$
$761$	511.044	+	2898.28i	0.0243434	+	0.138058i	−0.970214	+	0.242250i	$0.922114\pi$
$762$	−29.0426	+	6208.59i	−0.00138071	+	0.295162i
$763$	−16780.1	−	14080.2i	−0.796175	−	0.668070i
$764$	−1807.19	+	3130.14i	−0.0855782	+	0.148226i
$765$	3332.59	−	5649.48i	0.157503	−	0.267003i
$766$	−7469.49	−	12937.5i	−0.352328	−	0.610251i
$767$	7487.61	−	42464.4i	0.352493	−	1.99909i
$768$	22294.3	+	4038.70i	1.04749	+	0.189758i
$769$	−35348.7	−	12865.9i	−1.65762	−	0.603323i	−0.667631	−	0.744492i	$-0.732692\pi$
$769$	−35348.7	−	12865.9i	−1.65762	−	0.603323i	−0.989986	+	0.141169i	$0.954914\pi$
$770$	−1318.67	−	479.956i	−0.0617163	−	0.0224629i
$771$	24437.0	+	4426.87i	1.14148	+	0.206783i
$772$	−902.401	+	5117.77i	−0.0420701	+	0.238592i
$773$	6917.54	+	11981.5i	0.321871	+	0.557497i	0.980874	−	0.194643i	$-0.0623549\pi$
$773$	6917.54	+	11981.5i	0.321871	+	0.557497i	−0.659003	+	0.752140i	$0.729022\pi$
$774$	11988.6	+	21221.0i	0.556748	+	0.985495i
$775$	−13115.6	+	22716.9i	−0.607905	+	1.05292i
$776$	14677.2	+	12315.7i	0.678971	+	0.569724i
$777$	−22.2414	+	4754.66i	−0.00102690	+	0.219527i
$778$	−2041.71	−	11579.1i	−0.0940859	−	0.533588i
$779$	−22804.4	+	19135.2i	−1.04885	+	0.880089i
$780$	−2558.91	−	3078.72i	−0.117466	−	0.141328i
$781$	−1253.20	+	456.127i	−0.0574174	+	0.0208982i
$782$	17348.6			0.793329
$783$	9981.83	−	11562.4i	0.455583	−	0.527723i
$784$	2449.60			0.111589
$785$	−5732.86	+	2086.59i	−0.260655	+	0.0948708i
$786$	2601.46	−	7044.75i	0.118055	−	0.319692i
$787$	9145.50	−	7673.98i	0.414233	−	0.347583i	−0.411731	−	0.911305i	$-0.635076\pi$
$787$	9145.50	−	7673.98i	0.414233	−	0.347583i	0.825964	+	0.563722i	$0.190631\pi$
$788$	−2499.72	−	14176.6i	−0.113006	−	0.640889i
$789$	−2638.67	−	1539.94i	−0.119061	−	0.0694844i
$790$	704.339	+	591.010i	0.0317206	+	0.0266167i
$791$	9110.80	−	15780.4i	0.409536	−	0.709336i
$792$	−13446.8	−	5037.20i	−0.603297	−	0.225996i
$793$	12402.2	+	21481.2i	0.555378	+	0.961942i
$794$	−838.029	+	4752.70i	−0.0374566	+	0.212427i
$795$	4.73310	+	13.1958i	0.000211152	+	0.000588689i
$796$	12769.6	+	4647.76i	0.568602	+	0.206954i
$797$	−13361.4	−	4863.17i	−0.593835	−	0.216138i	0.0275802	−	0.999620i	$-0.491220\pi$
$797$	−13361.4	−	4863.17i	−0.593835	−	0.216138i	−0.621415	+	0.783481i	$0.713442\pi$
$798$	−6083.66	+	7181.73i	−0.269874	+	0.318585i
$799$	−5885.83	+	33380.2i	−0.260608	+	1.47798i
$800$	−9782.04	−	16943.0i	−0.432309	−	0.748781i
$801$	5050.08	−	27152.5i	0.222766	−	1.19773i
$802$	11497.1	−	19913.6i	0.506208	−	0.876777i
$803$	−5398.06	−	4529.51i	−0.237227	−	0.199057i
$804$	8168.64	−	4665.36i	0.358316	−	0.204645i
$805$	558.873	+	3169.52i	0.0244692	+	0.138771i
$806$	22256.5	−	18675.4i	0.972645	−	0.816146i
$807$	−16006.7	+	2745.27i	−0.698218	+	0.119750i
$808$	37033.0	−	13478.9i	1.61240	−	0.586864i
$809$	−6797.07			−0.295392			−0.147696	−	0.989033i	$-0.547186\pi$
$809$	−6797.07			−0.295392			−0.147696	+	0.989033i	$0.547186\pi$
$810$	−3575.62	−	1377.72i	−0.155105	−	0.0597630i
$811$	−9855.20			−0.426711			−0.213356	−	0.976975i	$-0.568439\pi$
$811$	−9855.20			−0.426711			−0.213356	+	0.976975i	$0.568439\pi$
$812$	5163.44	−	1879.34i	0.223154	−	0.0812216i
$813$	788.094	−	135.164i	0.0339971	−	0.00583077i
$814$	2556.71	−	2145.33i	0.110089	−	0.0923758i
$815$	−39.8404	−	225.946i	−0.00171233	−	0.00971110i
$816$	−4932.21	+	2816.94i	−0.211596	+	0.120849i
$817$	27914.4	+	23422.9i	1.19535	+	1.00302i
$818$	4259.47	−	7377.61i	0.182065	−	0.315345i
$819$	16424.4	+	14045.6i	0.700751	+	0.599261i
$820$	−2179.87	−	3775.64i	−0.0928344	−	0.160794i
$821$	−1128.63	+	6400.80i	−0.0479776	+	0.272094i	−0.999354	−	0.0359361i	$-0.988559\pi$
$821$	−1128.63	+	6400.80i	−0.0479776	+	0.272094i	0.951377	+	0.308030i	$0.0996698\pi$
$822$	−10560.7	+	12466.8i	−0.448109	+	0.528990i
$823$	15173.9	+	5522.84i	0.642683	+	0.233917i	0.642742	−	0.766083i	$-0.277797\pi$
$823$	15173.9	+	5522.84i	0.642683	+	0.233917i	−5.94321e−5		1.00000i	$0.500019\pi$
$824$	2496.46	+	908.639i	0.105544	+	0.0384150i
$825$	4624.08	+	12891.9i	0.195139	+	0.544046i
$826$	2578.13	−	14621.3i	0.108601	−	0.615909i
$827$	−9781.92	−	16942.8i	−0.411307	−	0.712404i	0.583726	−	0.811950i	$-0.301594\pi$
$827$	−9781.92	−	16942.8i	−0.411307	−	0.712404i	−0.995033	+	0.0995466i	$0.968261\pi$
$828$	1874.27	+	11243.6i	0.0786661	+	0.471913i
$829$	3895.95	−	6747.99i	0.163223	−	0.282711i	−0.772800	−	0.634650i	$-0.781144\pi$
$829$	3895.95	−	6747.99i	0.163223	−	0.282711i	0.936023	+	0.351939i	$0.114478\pi$
$830$	3277.42	+	2750.08i	0.137061	+	0.115008i
$831$	−35323.3	−	20614.8i	−1.47455	−	0.860555i
$832$	4900.05	+	27789.6i	0.204181	+	1.15797i
$833$	13806.6	−	11585.1i	0.574273	−	0.481872i
$834$	2676.56	−	7248.13i	0.111129	−	0.300938i
$835$	7914.30	−	2880.57i	0.328007	−	0.119385i
$836$	−7430.63			−0.307409
$837$	−11108.8	+	29237.9i	−0.458754	+	1.20742i
$838$	−10354.2			−0.426826
$839$	11385.6	−	4144.01i	0.468502	−	0.170521i	−0.0969714	−	0.995287i	$-0.530916\pi$
$839$	11385.6	−	4144.01i	0.468502	−	0.170521i	0.565474	+	0.824766i	$0.308693\pi$
$840$	−2545.56	−	3062.67i	−0.104560	−	0.125800i
$841$	−9602.21	+	8057.21i	−0.393711	+	0.330362i
$842$	−5072.50	−	28767.6i	−0.207613	−	1.17743i
$843$	−12.5540	+	2683.73i	−0.000512908	+	0.109647i
$844$	−4412.29	−	3702.35i	−0.179950	−	0.150996i
$845$	3133.81	−	5427.91i	0.127581	−	0.220977i
$846$	19800.7	+	185.251i	0.804682	+	0.00752846i
$847$	−4940.87	−	8557.84i	−0.200437	−	0.347167i
$848$	2.10806	−	11.9554i	8.53667e−5	−	0.000484139i
$849$	−20372.0	−	3690.48i	−0.823517	−	0.149184i
$850$	19240.6	+	7003.01i	0.776409	+	0.282590i
$851$	−7192.92	−	2618.01i	−0.289742	−	0.105457i
$852$	−1289.00	−	233.509i	−0.0518317	−	0.00938952i
$853$	−4507.24	+	25561.8i	−0.180920	+	1.02605i	0.750166	+	0.661250i	$0.229974\pi$
$853$	−4507.24	+	25561.8i	−0.180920	+	1.02605i	−0.931086	+	0.364800i	$0.881137\pi$
$854$	4270.32	+	7396.40i	0.171109	+	0.296370i
$855$	−5728.63	−	53.5960i	−0.229140	−	0.00214379i
$856$	−18113.7	+	31373.9i	−0.723265	+	1.25273i
$857$	−10375.3	−	8705.89i	−0.413550	−	0.347010i	0.412153	−	0.911115i	$-0.364777\pi$
$857$	−10375.3	−	8705.89i	−0.413550	−	0.347010i	−0.825703	+	0.564105i	$0.809221\pi$
$858$	70.9608	−	15169.7i	0.00282350	−	0.603595i
$859$	−3637.04	−	20626.7i	−0.144464	−	0.819294i	−0.967796	−	0.251735i	$-0.918999\pi$
$859$	−3637.04	−	20626.7i	−0.144464	−	0.819294i	0.823333	−	0.567559i	$-0.192112\pi$
$860$	−4088.10	+	3430.33i	−0.162097	+	0.136015i
$861$	15043.6	+	18099.5i	0.595453	+	0.716412i
$862$	−8715.54	+	3172.20i	−0.344376	+	0.125343i
$863$	15861.7			0.625653			0.312826	−	0.949810i	$-0.398724\pi$
$863$	15861.7			0.625653			0.312826	+	0.949810i	$0.398724\pi$
$864$	−14742.4	−	18078.6i	−0.580493	−	0.711858i
$865$	−1260.88			−0.0495620
$866$	11544.2	−	4201.74i	0.452988	−	0.164874i
$867$	−5633.41	+	15255.3i	−0.220670	+	0.597573i
$868$	−8618.93	+	7232.14i	−0.337034	+	0.282805i
$869$	−680.445	−	3858.99i	−0.0265622	−	0.150641i
$870$	−2568.34	−	1498.89i	−0.100086	−	0.0584106i
$871$	21994.9	+	18455.9i	0.855645	+	0.717972i
$872$	−21817.9	+	37789.8i	−0.847303	+	1.46757i
$873$	−3582.91	−	21493.6i	−0.138904	−	0.833276i
$874$	−7576.24	−	13122.4i	−0.293215	−	0.507864i
$875$	−1360.34	+	7714.87i	−0.0525576	+	0.298069i
$876$	−2336.92	−	6515.31i	−0.0901339	−	0.251292i
$877$	931.001	+	338.857i	0.0358468	+	0.0130472i	0.359881	−	0.932998i	$-0.382817\pi$
$877$	931.001	+	338.857i	0.0358468	+	0.0130472i	−0.324035	+	0.946045i	$0.605039\pi$
$878$	11055.0	+	4023.69i	0.424930	+	0.154662i
$879$	−23171.0	+	27353.2i	−0.889121	+	1.04960i
$880$	−128.439	+	728.414i	−0.00492009	+	0.0279032i
$881$	−20960.4	−	36304.6i	−0.801561	−	1.38834i	−0.918588	−	0.395216i	$-0.870670\pi$
$881$	−20960.4	−	36304.6i	−0.801561	−	1.38834i	0.117027	−	0.993129i	$-0.462664\pi$
$882$	−8002.11	−	6843.16i	−0.305493	−	0.261248i
$883$	24426.1	−	42307.3i	0.930922	−	1.61240i	0.149174	−	0.988811i	$-0.452339\pi$
$883$	24426.1	−	42307.3i	0.930922	−	1.61240i	0.781749	−	0.623594i	$-0.214328\pi$
$884$	19539.2	+	16395.3i	0.743409	+	0.623794i
$885$	7847.18	−	4481.76i	0.298057	−	0.170229i
$886$	−943.781	−	5352.45i	−0.0357866	−	0.202956i
$887$	−21378.4	+	17938.6i	−0.809262	+	0.679051i	−0.950432	−	0.310934i	$-0.899358\pi$
$887$	−21378.4	+	17938.6i	−0.809262	+	0.679051i	0.141169	+	0.989985i	$0.454914\pi$
$888$	9335.36	−	1601.09i	0.352786	−	0.0605056i
$889$	6895.95	−	2509.92i	0.260161	−	0.0946907i
$890$	−5376.66			−0.202501
$891$	7899.32	+	14293.1i	0.297011	+	0.537416i
$892$	−18686.0			−0.701407
$893$	27819.1	−	10125.3i	1.04248	−	0.379431i
$894$	−10897.1	+	1868.93i	−0.407665	+	0.0699177i
$895$	−755.864	+	634.245i	−0.0282299	+	0.0236877i
$896$	−1065.60	−	6043.32i	−0.0397313	−	0.225327i
$897$	−30211.4	+	17254.6i	−1.12456	+	0.642269i
$898$	7929.87	+	6653.95i	0.294681	+	0.247266i
$899$	−12136.4	+	21020.8i	−0.450245	+	0.779847i
$900$	−2459.99	+	13226.5i	−0.0911106	+	0.489869i
$901$	−44.6600	−	77.3534i	−0.00165132	−	0.00286017i
$902$	2868.74	−	16269.4i	0.105896	−	0.600568i
$903$	18621.0	−	21982.0i	0.686232	−	0.810093i
$904$	−34109.5	−	12414.8i	−1.25494	−	0.456760i
$905$	−2882.26	−	1049.06i	−0.105867	−	0.0385325i
$906$	3359.01	+	9364.87i	0.123174	+	0.343407i
$907$	2493.90	−	14143.6i	0.0912995	−	0.517785i	−0.904519	−	0.426433i	$-0.859770\pi$
$907$	2493.90	−	14143.6i	0.0912995	−	0.517785i	0.995819	−	0.0913521i	$-0.0291189\pi$
$908$	9100.68	+	15762.8i	0.332617	+	0.576110i
$909$	−41972.1	−	15722.8i	−1.53149	−	0.573699i
$910$	2103.62	−	3643.57i	0.0766310	−	0.132729i
$911$	10096.6	+	8472.06i	0.367196	+	0.308114i	0.807651	−	0.589660i	$-0.200738\pi$
$911$	10096.6	+	8472.06i	0.367196	+	0.308114i	−0.440455	+	0.897775i	$0.645183\pi$
$912$	4284.66	+	2500.54i	0.155569	+	0.0907909i
$913$	−3166.24	−	17956.6i	−0.114772	−	0.650907i
$914$	−20290.0	+	17025.3i	−0.734281	+	0.616135i
$915$	−1800.80	+	4876.55i	−0.0650628	+	0.176190i
$916$	−878.802	+	319.858i	−0.0316992	+	0.0115376i
$917$	−8876.37			−0.319655
$918$	23981.4	+	4576.46i	0.862206	+	0.164538i
$919$	39299.4			1.41063			0.705314	−	0.708895i	$-0.250806\pi$
$919$	39299.4			1.41063			0.705314	+	0.708895i	$0.250806\pi$
$920$	6024.64	−	2192.79i	0.215898	−	0.0785806i
$921$	−15131.5	−	18205.3i	−0.541367	−	0.651339i
$922$	−20220.4	+	16966.9i	−0.722258	+	0.606046i
$923$	−694.306	−	3937.60i	−0.0247599	−	0.140420i
$924$	−27.4799	+	5874.52i	−0.000978378	+	0.209153i
$925$	−6920.59	−	5807.06i	−0.245997	−	0.206416i
$926$	−15727.6	+	27241.1i	−0.558145	+	0.966735i
$927$	−1486.16	−	2630.65i	−0.0526559	−	0.0932058i
$928$	−9051.68	−	15678.0i	−0.320189	−	0.554584i
$929$	−3239.00	+	18369.3i	−0.114390	+	0.648738i	0.872660	+	0.488327i	$0.162393\pi$
$929$	−3239.00	+	18369.3i	−0.114390	+	0.648738i	−0.987050	+	0.160410i	$0.948718\pi$
$930$	5991.49	+	1085.38i	0.211257	+	0.0382700i
$931$	−14792.4	−	5383.98i	−0.520731	−	0.189530i
$932$	−324.454	−	118.092i	−0.0114033	−	0.00415045i
$933$	50745.6	+	9192.79i	1.78064	+	0.322571i
$934$	−5700.96	+	32331.8i	−0.199723	+	1.13268i
$935$	2721.03	+	4712.97i	0.0951735	+	0.164845i
$936$	21873.2	−	37080.0i	0.763833	−	1.29487i
$937$	23914.1	−	41420.5i	0.833768	−	1.44413i	−0.0612608	−	0.998122i	$-0.519512\pi$
$937$	23914.1	−	41420.5i	0.833768	−	1.44413i	0.895029	−	0.446007i	$-0.147155\pi$
$938$	7573.26	+	6354.72i	0.263620	+	0.221204i
$939$	−7.80881	+	1669.33i	−0.000271385	+	0.0580155i
$940$	752.874	+	4269.76i	0.0261234	+	0.148153i
$941$	−5811.42	+	4876.36i	−0.201325	+	0.168932i	−0.737876	−	0.674936i	$-0.764171\pi$
$941$	−5811.42	+	4876.36i	−0.201325	+	0.168932i	0.536551	+	0.843868i	$0.319727\pi$
$942$	−14514.9	−	17463.4i	−0.502038	−	0.604021i
$943$	−35604.0	+	12958.8i	−1.22951	+	0.447504i
$944$	−7825.49			−0.269807
$945$	−63.5576	+	4528.75i	−0.00218786	+	0.155894i
$946$	−20222.2			−0.695012
$947$	28695.0	−	10444.1i	0.984649	−	0.358383i	0.201003	−	0.979591i	$-0.435580\pi$
$947$	28695.0	−	10444.1i	0.984649	−	0.358383i	0.783646	+	0.621208i	$0.213358\pi$
$948$	1333.36	−	3610.74i	0.0456810	−	0.123704i
$949$	16183.9	−	13579.9i	0.553585	−	0.464513i
$950$	−3105.44	−	17611.8i	−0.106057	−	0.601477i
$951$	34935.5	+	20388.5i	1.19123	+	0.695208i
$952$	19437.3	+	16309.8i	0.661728	+	0.555256i
$953$	11433.4	−	19803.3i	0.388631	−	0.673128i	−0.603635	−	0.797261i	$-0.706282\pi$
$953$	11433.4	−	19803.3i	0.388631	−	0.673128i	0.992266	+	0.124133i	$0.0396149\pi$
$954$	−40.2848	+	33.1657i	−0.00136716	+	0.00112555i
$955$	−1156.01	−	2002.27i	−0.0391702	−	0.0678449i
$956$	−1167.04	+	6618.60i	−0.0394819	+	0.223913i
$957$	4278.83	+	11929.3i	0.144530	+	0.402947i
$958$	1849.44	+	673.141i	0.0623723	+	0.0227017i
$959$	18147.2	+	6605.06i	0.611059	+	0.222407i
$960$	−3822.53	+	4512.48i	−0.128512	+	0.151708i
$961$	3457.31	−	19607.4i	0.116052	−	0.658165i
$962$	5003.15	+	8665.71i	0.167680	+	0.290430i
$963$	38846.6	−	13728.8i	1.29991	−	0.459403i
$964$	−638.474	+	1105.87i	−0.0213318	+	0.0369478i
$965$	−2546.49	−	2136.76i	−0.0849475	−	0.0712794i
$966$	−10402.4	+	5941.11i	−0.346471	+	0.197880i
$967$	−1845.61	−	10467.0i	−0.0613764	−	0.348083i	−0.999995	−	0.00312642i	$-0.999005\pi$
$967$	−1845.61	−	10467.0i	−0.0613764	−	0.348083i	0.938619	−	0.344956i	$-0.112106\pi$
$968$	−15079.6	+	12653.3i	−0.500699	+	0.420137i
$969$	35975.4	−	6170.07i	1.19267	−	0.204552i
$970$	−3986.27	+	1450.88i	−0.131950	+	0.0480258i
$971$	8417.86			0.278210			0.139105	−	0.990278i	$-0.455577\pi$
$971$	8417.86			0.278210			0.139105	+	0.990278i	$0.455577\pi$
$972$	−375.152	+	16036.8i	−0.0123796	+	0.529199i
$973$	−9132.62			−0.300903
$974$	−7460.12	+	2715.26i	−0.245418	+	0.0893250i
$975$	−40471.3	+	6941.15i	−1.32935	+	0.227994i
$976$	3448.43	−	2893.57i	0.113096	−	0.0948986i
$977$	−9134.62	−	51805.0i	−0.299122	−	1.69641i	−0.649959	−	0.759969i	$-0.725214\pi$
$977$	−9134.62	−	51805.0i	−0.299122	−	1.69641i	0.350837	−	0.936437i	$-0.385897\pi$
$978$	741.555	−	423.524i	0.0242457	−	0.0138475i
$979$	17553.4	+	14729.1i	0.573044	+	0.480841i
$980$	1152.70	−	1996.53i	0.0375731	−	0.0650785i
$981$	46790.6	−	16536.3i	1.52284	−	0.538189i
$982$	95.1258	+	164.763i	0.00309123	+	0.00535416i
$983$	−1781.78	+	10105.0i	−0.0578129	+	0.327873i	−0.999973	−	0.00728863i	$-0.997680\pi$
$983$	−1781.78	+	10105.0i	−0.0578129	+	0.327873i	0.942161	+	0.335162i	$0.108791\pi$
$984$	30303.8	−	35773.4i	0.981757	−	1.15896i
$985$	8652.95	+	3149.42i	0.279905	+	0.101877i
$986$	17804.0	+	6480.14i	0.575047	+	0.209300i
$987$	−7902.03	−	22030.8i	−0.254837	−	0.710483i
$988$	3868.50	−	21939.3i	0.124568	−	0.706461i
$989$	23189.5	+	40165.4i	0.745584	+	1.29139i
$990$	2454.46	−	2020.71i	0.0787957	−	0.0648710i
$991$	−26864.7	+	46531.1i	−0.861137	+	1.49153i	0.00969537	+	0.999953i	$0.496914\pi$
$991$	−26864.7	+	46531.1i	−0.861137	+	1.49153i	−0.870832	+	0.491580i	$0.836420\pi$
$992$	28396.1	+	23827.2i	0.908848	+	0.762614i
$993$	−30917.8	−	18043.8i	−0.988064	−	0.576638i
$994$	−239.063	−	1355.79i	−0.00762839	−	0.0432628i
$995$	−6658.92	+	5587.50i	−0.212163	+	0.178026i
$996$	6204.38	−	16801.4i	0.197383	−	0.534512i
$997$	17210.7	−	6264.17i	0.546707	−	0.198985i	−0.0538756	−	0.998548i	$-0.517157\pi$
$997$	17210.7	−	6264.17i	0.546707	−	0.198985i	0.600583	+	0.799562i	$0.294935\pi$
$998$	−11753.5			−0.372796
$999$	−9252.36	−	5516.40i	−0.293025	−	0.174706i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	27.4.e.a.7.6	yes	48
3.2	odd	2		81.4.e.a.19.3		48
9.2	odd	6		243.4.e.a.136.6		48
9.4	even	3		243.4.e.c.217.3		48
9.5	odd	6		243.4.e.b.217.6		48
9.7	even	3		243.4.e.d.136.3		48
27.2	odd	18		729.4.a.c.1.17		24
27.4	even	9	inner	27.4.e.a.4.6	✓	48
27.5	odd	18		243.4.e.b.28.6		48
27.13	even	9		243.4.e.d.109.3		48
27.14	odd	18		243.4.e.a.109.6		48
27.22	even	9		243.4.e.c.28.3		48
27.23	odd	18		81.4.e.a.64.3		48
27.25	even	9		729.4.a.d.1.8		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.4.e.a.4.6	✓	48	27.4	even	9	inner
27.4.e.a.7.6	yes	48	1.1	even	1	trivial
81.4.e.a.19.3		48	3.2	odd	2
81.4.e.a.64.3		48	27.23	odd	18
243.4.e.a.109.6		48	27.14	odd	18
243.4.e.a.136.6		48	9.2	odd	6
243.4.e.b.28.6		48	27.5	odd	18
243.4.e.b.217.6		48	9.5	odd	6
243.4.e.c.28.3		48	27.22	even	9
243.4.e.c.217.3		48	9.4	even	3
243.4.e.d.109.3		48	27.13	even	9
243.4.e.d.136.3		48	9.7	even	3
729.4.a.c.1.17		24	27.2	odd	18
729.4.a.d.1.8		24	27.25	even	9

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:	\( N \)	\(=\)	\( 27 = 3^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	27.e (of order \(9\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(1.82340 - 0.663664i) q^{2} +(5.12138 - 0.878355i) q^{3} +(-3.24401 + 2.72205i) q^{4} +(-0.470388 - 2.66770i) q^{5} +(8.75540 - 5.00047i) q^{6} +(-9.12942 - 7.66050i) q^{7} +(-11.8703 + 20.5600i) q^{8} +(25.4570 - 8.99678i) q^{9} +O(q^{10})\)	\(q+(1.82340 - 0.663664i) q^{2} +(5.12138 - 0.878355i) q^{3} +(-3.24401 + 2.72205i) q^{4} +(-0.470388 - 2.66770i) q^{5} +(8.75540 - 5.00047i) q^{6} +(-9.12942 - 7.66050i) q^{7} +(-11.8703 + 20.5600i) q^{8} +(25.4570 - 8.99678i) q^{9} +(-2.62817 - 4.55212i) q^{10} +(-3.88999 + 22.0612i) q^{11} +(-14.2229 + 16.7900i) q^{12} +(-63.1117 - 22.9708i) q^{13} +(-21.7306 - 7.90930i) q^{14} +(-4.75222 - 13.2491i) q^{15} +(-2.11657 + 12.0037i) q^{16} +(44.8404 + 77.6659i) q^{17} +(40.4475 - 33.2996i) q^{18} +(39.1643 - 67.8345i) q^{19} +(8.78755 + 7.37363i) q^{20} +(-53.4839 - 31.2134i) q^{21} +(7.54823 + 42.8081i) q^{22} +(76.3697 - 64.0818i) q^{23} +(-42.7333 + 115.722i) q^{24} +(110.566 - 40.2428i) q^{25} -130.323 q^{26} +(122.472 - 68.4362i) q^{27} +50.4682 q^{28} +(102.311 - 37.2381i) q^{29} +(-17.4582 - 21.0046i) q^{30} +(-170.780 + 143.301i) q^{31} +(-28.8731 - 163.747i) q^{32} +(-0.544499 + 116.401i) q^{33} +(133.306 + 111.857i) q^{34} +(-16.1416 + 27.9580i) q^{35} +(-58.0930 + 98.4807i) q^{36} +(-38.3904 - 66.4941i) q^{37} +(26.3929 - 149.681i) q^{38} +(-343.395 - 62.2075i) q^{39} +(60.4316 + 21.9953i) q^{40} +(-357.134 - 129.986i) q^{41} +(-118.238 - 21.4193i) q^{42} +(-80.7838 + 458.148i) q^{43} +(-47.4325 - 82.1555i) q^{44} +(-35.9754 - 63.6797i) q^{45} +(96.7239 - 167.531i) q^{46} +(289.529 + 242.944i) q^{47} +(-0.296266 + 63.3345i) q^{48} +(-34.8981 - 197.917i) q^{49} +(174.899 - 146.758i) q^{50} +(297.863 + 358.370i) q^{51} +(267.263 - 97.2756i) q^{52} -0.995976 q^{53} +(177.898 - 206.067i) q^{54} +60.6826 q^{55} +(265.869 - 96.7683i) q^{56} +(140.992 - 381.806i) q^{57} +(161.840 - 135.800i) q^{58} +(111.486 + 632.267i) q^{59} +(51.4810 + 30.0445i) q^{60} +(-282.916 - 237.395i) q^{61} +(-216.296 + 374.636i) q^{62} +(-301.327 - 112.878i) q^{63} +(-210.076 - 363.862i) q^{64} +(-31.5923 + 179.169i) q^{65} +(76.2581 + 212.606i) q^{66} +(-401.725 - 146.216i) q^{67} +(-356.873 - 129.891i) q^{68} +(334.831 - 395.267i) q^{69} +(-10.8778 + 61.6913i) q^{70} +(29.7664 + 51.5569i) q^{71} +(-117.209 + 630.189i) q^{72} +(-157.281 + 272.418i) q^{73} +(-114.131 - 95.7672i) q^{74} +(530.904 - 303.215i) q^{75} +(57.5994 + 326.663i) q^{76} +(204.513 - 171.607i) q^{77} +(-667.433 + 114.470i) q^{78} +(-164.373 + 59.8269i) q^{79} +33.0179 q^{80} +(567.116 - 458.062i) q^{81} -737.467 q^{82} +(-764.859 + 278.386i) q^{83} +(258.466 - 44.3290i) q^{84} +(186.097 - 156.154i) q^{85} +(156.755 + 889.001i) q^{86} +(491.265 - 280.576i) q^{87} +(-407.403 - 341.851i) q^{88} +(511.446 - 885.851i) q^{89} +(-107.860 - 92.2381i) q^{90} +(400.206 + 693.177i) q^{91} +(-73.3104 + 415.764i) q^{92} +(-748.757 + 883.904i) q^{93} +(689.161 + 250.834i) q^{94} +(-199.385 - 72.5701i) q^{95} +(-291.698 - 813.251i) q^{96} +(140.142 - 794.785i) q^{97} +(-194.984 - 337.722i) q^{98} +(99.4525 + 596.609i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9}+O(q^{10}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9	\( 48 q - 6 q^{2} - 6 q^{3} - 6 q^{4} + 6 q^{5} - 18 q^{6} - 6 q^{7} - 75 q^{8} - 54 q^{9} - 3 q^{10} + 57 q^{11} + 147 q^{12} - 6 q^{13} + 51 q^{14} - 36 q^{15} + 18 q^{16} - 207 q^{17} - 639 q^{18} - 3 q^{19} - 597 q^{20} - 138 q^{21} - 60 q^{22} + 402 q^{23} + 1170 q^{24} - 222 q^{25} + 1914 q^{26} + 1125 q^{27} - 12 q^{28} + 480 q^{29} + 459 q^{30} - 60 q^{31} - 648 q^{32} - 639 q^{33} + 288 q^{34} - 1257 q^{35} - 2088 q^{36} - 3 q^{37} - 1524 q^{38} - 768 q^{39} + 561 q^{40} - 1731 q^{41} - 3078 q^{42} + 507 q^{43} - 2211 q^{44} - 360 q^{45} - 3 q^{46} + 984 q^{47} + 2289 q^{48} - 600 q^{49} + 4359 q^{50} + 2655 q^{51} - 1431 q^{52} + 2736 q^{53} + 5454 q^{54} - 12 q^{55} + 5907 q^{56} + 3426 q^{57} - 897 q^{58} + 2238 q^{59} + 1314 q^{60} + 48 q^{61} - 2118 q^{62} - 2610 q^{63} - 195 q^{64} - 6990 q^{65} - 11115 q^{66} - 681 q^{67} - 11169 q^{68} - 6138 q^{69} - 33 q^{70} - 3105 q^{71} - 36 q^{72} - 219 q^{73} + 3543 q^{74} + 2604 q^{75} + 3426 q^{76} + 4722 q^{77} + 6066 q^{78} + 2802 q^{79} + 9870 q^{80} + 3438 q^{81} - 12 q^{82} + 3468 q^{83} + 7674 q^{84} + 2529 q^{85} + 3624 q^{86} + 2880 q^{87} + 2850 q^{88} - 5202 q^{89} - 12510 q^{90} + 267 q^{91} - 18453 q^{92} - 11802 q^{93} - 1653 q^{94} - 10113 q^{95} - 14094 q^{96} - 3381 q^{97} - 4392 q^{98} - 1242 q^{99}+O(q^{100}) \) 48 * q - 6 * q^2 - 6 * q^3 - 6 * q^4 + 6 * q^5 - 18 * q^6 - 6 * q^7 - 75 * q^8 - 54 * q^9 - 3 * q^10 + 57 * q^11 + 147 * q^12 - 6 * q^13 + 51 * q^14 - 36 * q^15 + 18 * q^16 - 207 * q^17 - 639 * q^18 - 3 * q^19 - 597 * q^20 - 138 * q^21 - 60 * q^22 + 402 * q^23 + 1170 * q^24 - 222 * q^25 + 1914 * q^26 + 1125 * q^27 - 12 * q^28 + 480 * q^29 + 459 * q^30 - 60 * q^31 - 648 * q^32 - 639 * q^33 + 288 * q^34 - 1257 * q^35 - 2088 * q^36 - 3 * q^37 - 1524 * q^38 - 768 * q^39 + 561 * q^40 - 1731 * q^41 - 3078 * q^42 + 507 * q^43 - 2211 * q^44 - 360 * q^45 - 3 * q^46 + 984 * q^47 + 2289 * q^48 - 600 * q^49 + 4359 * q^50 + 2655 * q^51 - 1431 * q^52 + 2736 * q^53 + 5454 * q^54 - 12 * q^55 + 5907 * q^56 + 3426 * q^57 - 897 * q^58 + 2238 * q^59 + 1314 * q^60 + 48 * q^61 - 2118 * q^62 - 2610 * q^63 - 195 * q^64 - 6990 * q^65 - 11115 * q^66 - 681 * q^67 - 11169 * q^68 - 6138 * q^69 - 33 * q^70 - 3105 * q^71 - 36 * q^72 - 219 * q^73 + 3543 * q^74 + 2604 * q^75 + 3426 * q^76 + 4722 * q^77 + 6066 * q^78 + 2802 * q^79 + 9870 * q^80 + 3438 * q^81 - 12 * q^82 + 3468 * q^83 + 7674 * q^84 + 2529 * q^85 + 3624 * q^86 + 2880 * q^87 + 2850 * q^88 - 5202 * q^89 - 12510 * q^90 + 267 * q^91 - 18453 * q^92 - 11802 * q^93 - 1653 * q^94 - 10113 * q^95 - 14094 * q^96 - 3381 * q^97 - 4392 * q^98 - 1242 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more