LMFDB - Embedded newform 110.4.g.c.91.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [110,4,Mod(31,110)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("110.31"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(110, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 110 = 2 \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	110.g (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.49021010063$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 80 x^{10} - 71 x^{9} + 3603 x^{8} - 191 x^{7} + 110280 x^{6} + 142285 x^{5} + \cdots + 2085136 $ x^12 - x^11 + 80x^10 - 71x^9 + 3603x^8 - 191x^7 + 110280x^6 + 142285x^5 + 9710517x^4 - 1952612x^3 + 6445016x^2 - 5490088x + 2085136
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.2
Root			$-0.292839 + 0.901266i$ of defining polynomial
Character	$\chi$	$=$	110.91
Dual form			110.4.g.c.81.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.61803 - 1.17557i) q^{2} +(0.292839 + 0.901266i) q^{3} +(1.23607 - 3.80423i) q^{4} +(4.04508 + 2.93893i) q^{5} +(1.53333 + 1.11403i) q^{6} +(2.73261 - 8.41010i) q^{7} +(-2.47214 - 7.60845i) q^{8} +(21.1169 - 15.3423i) q^{9} +10.0000 q^{10} +(36.3409 + 3.21519i) q^{11} +3.79059 q^{12} +(2.56155 - 1.86107i) q^{13} +(-5.46521 - 16.8202i) q^{14} +(-1.46420 + 4.50633i) q^{15} +(-12.9443 - 9.40456i) q^{16} +(16.7782 + 12.1901i) q^{17} +(16.1319 - 49.6489i) q^{18} +(-14.3749 - 44.2414i) q^{19} +(16.1803 - 11.7557i) q^{20} +8.37995 q^{21} +(62.5805 - 37.5190i) q^{22} -43.9802 q^{23} +(6.13330 - 4.45611i) q^{24} +(7.72542 + 23.7764i) q^{25} +(1.95685 - 6.02256i) q^{26} +(40.7113 + 29.5785i) q^{27} +(-28.6162 - 20.7909i) q^{28} +(-13.0016 + 40.0149i) q^{29} +(2.92839 + 9.01266i) q^{30} +(-177.910 + 129.259i) q^{31} -32.0000 q^{32} +(7.74430 + 33.6944i) q^{33} +41.4780 q^{34} +(35.7703 - 25.9886i) q^{35} +(-32.2638 - 99.2978i) q^{36} +(-18.4828 + 56.8842i) q^{37} +(-75.2680 - 54.6854i) q^{38} +(2.42744 + 1.76364i) q^{39} +(12.3607 - 38.0423i) q^{40} +(22.2877 + 68.5944i) q^{41} +(13.5590 - 9.85122i) q^{42} -368.628 q^{43} +(57.1512 - 134.275i) q^{44} +130.510 q^{45} +(-71.1615 + 51.7018i) q^{46} +(83.7848 + 257.863i) q^{47} +(4.68543 - 14.4203i) q^{48} +(214.230 + 155.647i) q^{49} +(40.4508 + 29.3893i) q^{50} +(-6.07319 + 18.6914i) q^{51} +(-3.91370 - 12.0451i) q^{52} +(-460.619 + 334.659i) q^{53} +100.644 q^{54} +(137.553 + 119.809i) q^{55} -70.7432 q^{56} +(35.6637 - 25.9112i) q^{57} +(26.0032 + 80.0297i) q^{58} +(41.7199 - 128.401i) q^{59} +(15.3333 + 11.1403i) q^{60} +(-61.3552 - 44.5771i) q^{61} +(-135.911 + 418.291i) q^{62} +(-71.3264 - 219.520i) q^{63} +(-51.7771 + 37.6183i) q^{64} +15.8312 q^{65} +(52.1407 + 45.4147i) q^{66} +113.462 q^{67} +(67.1128 - 48.7603i) q^{68} +(-12.8791 - 39.6379i) q^{69} +(27.3261 - 84.1010i) q^{70} +(-458.437 - 333.074i) q^{71} +(-168.935 - 122.739i) q^{72} +(-215.017 + 661.755i) q^{73} +(36.9656 + 113.768i) q^{74} +(-19.1666 + 13.9253i) q^{75} -186.073 q^{76} +(126.345 - 296.845i) q^{77} +6.00097 q^{78} +(590.328 - 428.898i) q^{79} +(-24.7214 - 76.0845i) q^{80} +(203.044 - 624.907i) q^{81} +(116.700 + 84.7873i) q^{82} +(-924.224 - 671.488i) q^{83} +(10.3582 - 31.8792i) q^{84} +(32.0435 + 98.6198i) q^{85} +(-596.453 + 433.348i) q^{86} -39.8714 q^{87} +(-65.3771 - 284.447i) q^{88} +1086.57 q^{89} +(211.169 - 153.423i) q^{90} +(-8.65211 - 26.6284i) q^{91} +(-54.3625 + 167.311i) q^{92} +(-168.596 - 122.492i) q^{93} +(438.703 + 318.737i) q^{94} +(71.8745 - 221.207i) q^{95} +(-9.37085 - 28.8405i) q^{96} +(186.303 - 135.357i) q^{97} +529.606 q^{98} +(816.737 - 489.660i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} - q^{3} - 12 q^{4} + 15 q^{5} + 2 q^{6} + 38 q^{7} + 24 q^{8} - 78 q^{9} + 120 q^{10} + 66 q^{11} + 16 q^{12} + 57 q^{13} - 76 q^{14} + 5 q^{15} - 48 q^{16} - 157 q^{17} - 24 q^{18} + 331 q^{19}+ \cdots + 3455 q^{99}+O(q^{100}) $ 12 * q + 6 * q^2 - q^3 - 12 * q^4 + 15 * q^5 + 2 * q^6 + 38 * q^7 + 24 * q^8 - 78 * q^9 + 120 * q^10 + 66 * q^11 + 16 * q^12 + 57 * q^13 - 76 * q^14 + 5 * q^15 - 48 * q^16 - 157 * q^17 - 24 * q^18 + 331 * q^19 + 60 * q^20 - 588 * q^21 + 98 * q^22 + 472 * q^23 + 8 * q^24 - 75 * q^25 - 34 * q^26 + 80 * q^27 - 88 * q^28 + 477 * q^29 - 10 * q^30 - 18 * q^31 - 384 * q^32 + 1093 * q^33 + 4 * q^34 + 110 * q^35 + 48 * q^36 - 390 * q^37 + 748 * q^38 - 381 * q^39 - 120 * q^40 - 193 * q^41 - 1534 * q^42 + 1014 * q^43 - 296 * q^44 - 660 * q^45 + 666 * q^46 - 894 * q^47 - 16 * q^48 - 899 * q^49 + 150 * q^50 - 677 * q^51 + 68 * q^52 - 2377 * q^53 + 100 * q^54 - 330 * q^55 + 256 * q^56 + 535 * q^57 - 954 * q^58 - 621 * q^59 + 20 * q^60 - 1290 * q^61 - 674 * q^62 - 1456 * q^63 - 192 * q^64 + 740 * q^65 + 1424 * q^66 + 5566 * q^67 - 628 * q^68 - 699 * q^69 + 380 * q^70 + 1212 * q^71 + 624 * q^72 - 263 * q^73 + 780 * q^74 - 25 * q^75 + 344 * q^76 + 1822 * q^77 + 3572 * q^78 + 753 * q^79 + 240 * q^80 + 1755 * q^81 - 1034 * q^82 - 5555 * q^83 - 1892 * q^84 - 790 * q^85 + 92 * q^86 + 1770 * q^87 + 72 * q^88 + 5026 * q^89 - 780 * q^90 - 707 * q^91 + 388 * q^92 - 527 * q^93 - 1012 * q^94 - 1655 * q^95 + 32 * q^96 - 2276 * q^97 - 832 * q^98 + 3455 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/110\mathbb{Z}\right)^\times$.

$n$	$67$	$101$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	1.61803	−	1.17557i	0.572061	−	0.415627i
$2$	1.61803	−	1.17557i	0.572061	−	0.415627i
$3$	0.292839	+	0.901266i	0.0563569	+	0.173449i	0.975273	−	0.221005i	$-0.0709338\pi$
$3$	0.292839	+	0.901266i	0.0563569	+	0.173449i	−0.918916	+	0.394454i	$0.870934\pi$
$4$	1.23607	−	3.80423i	0.154508	−	0.475528i
$5$	4.04508	+	2.93893i	0.361803	+	0.262866i
$5$	4.04508	+	2.93893i	0.361803	+	0.262866i
$6$	1.53333	+	1.11403i	0.104330	+	0.0757999i
$7$	2.73261	−	8.41010i	0.147547	−	0.454102i	−0.849783	−	0.527133i	$-0.823267\pi$
$7$	2.73261	−	8.41010i	0.147547	−	0.454102i	0.997330	+	0.0730304i	$0.0232670\pi$
$8$	−2.47214	−	7.60845i	−0.109254	−	0.336249i
$9$	21.1169	−	15.3423i	0.782109	−	0.568235i
$10$	10.0000			0.316228
$11$	36.3409	+	3.21519i	0.996109	+	0.0881287i
$11$	36.3409	+	3.21519i	0.996109	+	0.0881287i
$12$	3.79059			0.0911874
$13$	2.56155	−	1.86107i	0.0546497	−	0.0397053i	−0.560125	−	0.828408i	$-0.689247\pi$
$13$	2.56155	−	1.86107i	0.0546497	−	0.0397053i	0.614775	+	0.788703i	$0.289247\pi$
$14$	−5.46521	−	16.8202i	−0.104331	−	0.321099i
$15$	−1.46420	+	4.50633i	−0.0252036	+	0.0775686i
$16$	−12.9443	−	9.40456i	−0.202254	−	0.146946i
$17$	16.7782	+	12.1901i	0.239371	+	0.173913i	0.701003	−	0.713158i	$-0.252736\pi$
$17$	16.7782	+	12.1901i	0.239371	+	0.173913i	−0.461632	+	0.887072i	$0.652736\pi$
$18$	16.1319	−	49.6489i	0.211240	−	0.650131i
$19$	−14.3749	−	44.2414i	−0.173570	−	0.534193i	0.825995	−	0.563677i	$-0.190614\pi$
$19$	−14.3749	−	44.2414i	−0.173570	−	0.534193i	−0.999565	+	0.0294837i	$0.990614\pi$
$20$	16.1803	−	11.7557i	0.180902	−	0.131433i
$21$	8.37995			0.0870788
$22$	62.5805	−	37.5190i	0.606464	−	0.363595i
$23$	−43.9802			−0.398718			−0.199359	−	0.979927i	$-0.563886\pi$
$23$	−43.9802			−0.398718			−0.199359	+	0.979927i	$0.563886\pi$
$24$	6.13330	−	4.45611i	0.0521648	−	0.0378999i
$25$	7.72542	+	23.7764i	0.0618034	+	0.190211i
$26$	1.95685	−	6.02256i	0.0147604	−	0.0454277i
$27$	40.7113	+	29.5785i	0.290181	+	0.210829i
$28$	−28.6162	−	20.7909i	−0.193141	−	0.140325i
$29$	−13.0016	+	40.0149i	−0.0832531	+	0.256227i	−0.984015	−	0.178087i	$-0.943009\pi$
$29$	−13.0016	+	40.0149i	−0.0832531	+	0.256227i	0.900762	+	0.434314i	$0.143009\pi$
$30$	2.92839	+	9.01266i	0.0178216	+	0.0548493i
$31$	−177.910	+	129.259i	−1.03076	+	0.748890i	−0.968460	−	0.249167i	$-0.919843\pi$
$31$	−177.910	+	129.259i	−1.03076	+	0.748890i	−0.0622986	+	0.998058i	$0.519843\pi$
$32$	−32.0000			−0.176777
$33$	7.74430	+	33.6944i	0.0408518	+	0.177741i
$34$	41.4780			0.209218
$35$	35.7703	−	25.9886i	0.172751	−	0.125511i
$36$	−32.2638	−	99.2978i	−0.149369	−	0.459712i
$37$	−18.4828	+	56.8842i	−0.0821230	+	0.252749i	−0.983684	−	0.179902i	$-0.942422\pi$
$37$	−18.4828	+	56.8842i	−0.0821230	+	0.252749i	0.901561	+	0.432651i	$0.142422\pi$
$38$	−75.2680	−	54.6854i	−0.321318	−	0.233451i
$39$	2.42744	+	1.76364i	0.00996672	+	0.00724125i
$40$	12.3607	−	38.0423i	0.0488599	−	0.150375i
$41$	22.2877	+	68.5944i	0.0848963	+	0.261284i	0.984489	−	0.175446i	$-0.0561366\pi$
$41$	22.2877	+	68.5944i	0.0848963	+	0.261284i	−0.899593	+	0.436730i	$0.856137\pi$
$42$	13.5590	−	9.85122i	0.0498144	−	0.0361923i
$43$	−368.628			−1.30733			−0.653666	−	0.756783i	$-0.726770\pi$
$43$	−368.628			−1.30733			−0.653666	+	0.756783i	$0.726770\pi$
$44$	57.1512	−	134.275i	0.195815	−	0.460061i
$45$	130.510			0.432339
$46$	−71.1615	+	51.7018i	−0.228091	+	0.165718i
$47$	83.7848	+	257.863i	0.260027	+	0.800281i	0.992797	+	0.119805i	$0.0382270\pi$
$47$	83.7848	+	257.863i	0.260027	+	0.800281i	−0.732770	+	0.680476i	$0.761773\pi$
$48$	4.68543	−	14.4203i	0.0140892	−	0.0433622i
$49$	214.230	+	155.647i	0.624578	+	0.453782i
$50$	40.4508	+	29.3893i	0.114412	+	0.0831254i
$51$	−6.07319	+	18.6914i	−0.0166748	+	0.0513199i
$52$	−3.91370	−	12.0451i	−0.0104372	−	0.0321223i
$53$	−460.619	+	334.659i	−1.19379	+	0.867339i	−0.993660	−	0.112430i	$-0.964136\pi$
$53$	−460.619	+	334.659i	−1.19379	+	0.867339i	−0.200130	+	0.979769i	$0.564136\pi$
$54$	100.644			0.253628
$55$	137.553	+	119.809i	0.337230	+	0.293728i
$56$	−70.7432			−0.168812
$57$	35.6637	−	25.9112i	0.0828733	−	0.0602110i
$58$	26.0032	+	80.0297i	0.0588688	+	0.181180i
$59$	41.7199	−	128.401i	0.0920588	−	0.283328i	−0.894417	−	0.447233i	$-0.852409\pi$
$59$	41.7199	−	128.401i	0.0920588	−	0.283328i	0.986476	+	0.163906i	$0.0524093\pi$
$60$	15.3333	+	11.1403i	0.0329919	+	0.0239700i
$61$	−61.3552	−	44.5771i	−0.128782	−	0.0935659i	0.521529	−	0.853233i	$-0.325362\pi$
$61$	−61.3552	−	44.5771i	−0.128782	−	0.0935659i	−0.650312	+	0.759667i	$0.725362\pi$
$62$	−135.911	+	418.291i	−0.278398	+	0.856822i
$63$	−71.3264	−	219.520i	−0.142639	−	0.438999i
$64$	−51.7771	+	37.6183i	−0.101127	+	0.0734732i
$65$	15.8312			0.0302096
$66$	52.1407	+	45.4147i	0.0972435	+	0.0846994i
$67$	113.462			0.206889			0.103445	−	0.994635i	$-0.467014\pi$
$67$	113.462			0.206889			0.103445	+	0.994635i	$0.467014\pi$
$68$	67.1128	−	48.7603i	0.119686	−	0.0869567i
$69$	−12.8791	−	39.6379i	−0.0224705	−	0.0691571i
$70$	27.3261	−	84.1010i	0.0466584	−	0.143600i
$71$	−458.437	−	333.074i	−0.766288	−	0.556741i	0.134545	−	0.990908i	$-0.457043\pi$
$71$	−458.437	−	333.074i	−0.766288	−	0.556741i	−0.900832	+	0.434167i	$0.857043\pi$
$72$	−168.935	−	122.739i	−0.276517	−	0.200901i
$73$	−215.017	+	661.755i	−0.344738	+	1.06099i	0.616986	+	0.786974i	$0.288353\pi$
$73$	−215.017	+	661.755i	−0.344738	+	1.06099i	−0.961724	+	0.274020i	$0.911647\pi$
$74$	36.9656	+	113.768i	0.0580697	+	0.178720i
$75$	−19.1666	+	13.9253i	−0.0295089	+	0.0214394i
$76$	−186.073			−0.280842
$77$	126.345	−	296.845i	0.186992	−	0.439333i
$78$	6.00097			0.00871124
$79$	590.328	−	428.898i	0.840722	−	0.610821i	−0.0818500	−	0.996645i	$-0.526083\pi$
$79$	590.328	−	428.898i	0.840722	−	0.610821i	0.922572	+	0.385824i	$0.126083\pi$
$80$	−24.7214	−	76.0845i	−0.0345492	−	0.106331i
$81$	203.044	−	624.907i	0.278525	−	0.857211i
$82$	116.700	+	84.7873i	0.157163	+	0.114185i
$83$	−924.224	−	671.488i	−1.22225	−	0.888017i	−0.225965	−	0.974135i	$-0.572554\pi$
$83$	−924.224	−	671.488i	−1.22225	−	0.888017i	−0.996285	+	0.0861189i	$0.972554\pi$
$84$	10.3582	−	31.8792i	0.0134544	−	0.0414084i
$85$	32.0435	+	98.6198i	0.0408895	+	0.125845i
$86$	−596.453	+	433.348i	−0.747874	+	0.543362i
$87$	−39.8714			−0.0491341
$88$	−65.3771	−	284.447i	−0.0791957	−	0.344569i
$89$	1086.57			1.29412			0.647058	−	0.762441i	$-0.275999\pi$
$89$	1086.57			1.29412			0.647058	+	0.762441i	$0.275999\pi$
$90$	211.169	−	153.423i	0.247324	−	0.179692i
$91$	−8.65211	−	26.6284i	−0.00996689	−	0.0306749i
$92$	−54.3625	+	167.311i	−0.0616053	+	0.189601i
$93$	−168.596	−	122.492i	−0.187985	−	0.136579i
$94$	438.703	+	318.737i	0.481370	+	0.349736i
$95$	71.8745	−	221.207i	0.0776228	−	0.238898i
$96$	−9.37085	−	28.8405i	−0.00996259	−	0.0306617i
$97$	186.303	−	135.357i	0.195012	−	0.141685i	−0.485994	−	0.873962i	$-0.661542\pi$
$97$	186.303	−	135.357i	0.195012	−	0.141685i	0.681007	+	0.732277i	$0.261542\pi$
$98$	529.606			0.545901
$99$	816.737	−	489.660i	0.829143	−	0.497098i
$100$	100.000			0.100000
$101$	722.831	−	525.168i	0.712123	−	0.517387i	−0.171735	−	0.985143i	$-0.554937\pi$
$101$	722.831	−	525.168i	0.712123	−	0.517387i	0.883858	+	0.467756i	$0.154937\pi$
$102$	12.1464	+	37.3827i	0.0117909	+	0.0362886i
$103$	−272.580	+	838.914i	−0.260758	+	0.802531i	0.731882	+	0.681431i	$0.238642\pi$
$103$	−272.580	+	838.914i	−0.260758	+	0.802531i	−0.992640	+	0.121100i	$0.961358\pi$
$104$	−20.4924	−	14.8886i	−0.0193216	−	0.0140379i
$105$	33.8976	+	24.6281i	0.0315054	+	0.0228900i
$106$	−351.881	+	1082.98i	−0.322432	+	0.992342i
$107$	−495.313	−	1524.42i	−0.447511	−	1.37730i	−0.879706	−	0.475518i	$-0.842261\pi$
$107$	−495.313	−	1524.42i	−0.447511	−	1.37730i	0.432195	−	0.901780i	$-0.357739\pi$
$108$	162.845	−	118.314i	0.145091	−	0.105415i
$109$	1757.55			1.54443			0.772214	−	0.635362i	$-0.219149\pi$
$109$	1757.55			1.54443			0.772214	+	0.635362i	$0.219149\pi$
$110$	363.409	+	32.1519i	0.314997	+	0.0278687i
$111$	−56.6803			−0.0484671
$112$	−114.465	+	83.1636i	−0.0965707	+	0.0701627i
$113$	80.3771	+	247.375i	0.0669136	+	0.205939i	0.978923	−	0.204231i	$-0.0654694\pi$
$113$	80.3771	+	247.375i	0.0669136	+	0.205939i	−0.912009	+	0.410170i	$0.865469\pi$
$114$	27.2447	−	83.8505i	0.0223833	−	0.0688887i
$115$	−177.904	−	129.255i	−0.144257	−	0.104809i
$116$	136.155	+	98.9222i	0.108980	+	0.0791784i
$117$	25.5388	−	78.6003i	0.0201800	−	0.0621077i
$118$	−83.4398	−	256.801i	−0.0650954	−	0.200343i
$119$	148.368	−	107.796i	0.114293	−	0.0830387i
$120$	37.9059			0.0288360
$121$	1310.33	+	233.686i	0.984467	+	0.175572i
$122$	−151.678			−0.112560
$123$	−55.2951	+	40.1742i	−0.0405349	+	0.0294503i
$124$	271.822	+	836.582i	0.196857	+	0.605865i
$125$	−38.6271	+	118.882i	−0.0276393	+	0.0850651i
$126$	−373.470	−	271.342i	−0.264058	−	0.191850i
$127$	−1696.77	−	1232.78i	−1.18554	−	0.861349i	−0.192759	−	0.981246i	$-0.561743\pi$
$127$	−1696.77	−	1232.78i	−1.18554	−	0.861349i	−0.992786	+	0.119897i	$0.961743\pi$
$128$	−39.5542	+	121.735i	−0.0273135	+	0.0840623i
$129$	−107.949	−	332.232i	−0.0736772	−	0.226755i
$130$	25.6155	−	18.6107i	0.0172817	−	0.0125559i
$131$	−335.582			−0.223816			−0.111908	−	0.993719i	$-0.535696\pi$
$131$	−335.582			−0.223816			−0.111908	+	0.993719i	$0.535696\pi$
$132$	137.754	+	12.1875i	0.0908326	+	0.00803623i
$133$	−411.355			−0.268188
$134$	183.585	−	133.382i	0.118353	−	0.0859887i
$135$	77.7517	+	239.295i	0.0495689	+	0.152557i
$136$	51.2696	−	157.792i	0.0323260	−	0.0994891i
$137$	−358.500	−	260.465i	−0.223567	−	0.162431i	0.470364	−	0.882473i	$-0.344123\pi$
$137$	−358.500	−	260.465i	−0.223567	−	0.162431i	−0.693931	+	0.720042i	$0.744123\pi$
$138$	−67.4360	−	48.9951i	−0.0415981	−	0.0302228i
$139$	−668.437	+	2057.24i	−0.407886	+	1.25534i	0.510576	+	0.859833i	$0.329432\pi$
$139$	−668.437	+	2057.24i	−0.407886	+	1.25534i	−0.918462	+	0.395510i	$0.870568\pi$
$140$	−54.6521	−	168.202i	−0.0329925	−	0.101540i
$141$	−207.868	+	151.025i	−0.124153	+	0.0902028i
$142$	−1133.32			−0.669760
$143$	99.0727	−	59.3973i	0.0579362	−	0.0347346i
$144$	−417.631			−0.241685
$145$	−170.193	+	123.653i	−0.0974744	+	0.0708193i
$146$	430.034	+	1323.51i	0.243766	+	0.750236i
$147$	−77.5447	+	238.658i	−0.0435087	+	0.133906i
$148$	193.554	+	140.625i	0.107500	+	0.0781036i
$149$	−1601.48	−	1163.54i	−0.880526	−	0.639739i	0.0528647	−	0.998602i	$-0.483165\pi$
$149$	−1601.48	−	1163.54i	−0.880526	−	0.639739i	−0.933391	+	0.358862i	$0.883165\pi$
$150$	−14.6420	+	45.0633i	−0.00797007	+	0.0245294i
$151$	124.274	+	382.475i	0.0669752	+	0.206128i	0.978943	−	0.204133i	$-0.0654375\pi$
$151$	124.274	+	382.475i	0.0669752	+	0.206128i	−0.911968	+	0.410261i	$0.865437\pi$
$152$	−301.072	+	218.741i	−0.160659	+	0.116726i
$153$	541.328			0.286038
$154$	−144.531	−	628.833i	−0.0756274	−	0.329044i
$155$	−1099.54			−0.569790
$156$	9.70978	−	7.05457i	0.00498336	−	0.00362062i
$157$	1116.61	+	3436.59i	0.567615	+	1.74694i	0.660051	+	0.751220i	$0.270534\pi$
$157$	1116.61	+	3436.59i	0.567615	+	1.74694i	−0.0924366	+	0.995719i	$0.529466\pi$
$158$	450.970	−	1387.94i	0.227071	−	0.698854i
$159$	−436.504	−	317.139i	−0.217717	−	0.158181i
$160$	−129.443	−	94.0456i	−0.0639584	−	0.0464685i
$161$	−120.181	+	369.878i	−0.0588295	+	0.181059i
$162$	−406.089	−	1249.81i	−0.196947	−	0.606139i
$163$	−2974.68	+	2161.23i	−1.42942	+	1.03853i	−0.439293	+	0.898344i	$0.644771\pi$
$163$	−2974.68	+	2161.23i	−1.42942	+	1.03853i	−0.990125	+	0.140189i	$0.955229\pi$
$164$	288.498			0.137365
$165$	−67.6989	+	159.057i	−0.0319415	+	0.0750457i
$166$	−2284.81			−1.06829
$167$	303.415	−	220.444i	0.140592	−	0.102146i	−0.515266	−	0.857030i	$-0.672307\pi$
$167$	303.415	−	220.444i	0.140592	−	0.102146i	0.655858	+	0.754884i	$0.272307\pi$
$168$	−20.7164	−	63.7584i	−0.00951371	−	0.0292802i
$169$	−675.812	+	2079.94i	−0.307607	+	0.946717i
$170$	167.782	+	121.901i	0.0756958	+	0.0549962i
$171$	−982.321	−	713.698i	−0.439298	−	0.319169i
$172$	−455.649	+	1402.34i	−0.201994	+	0.621673i
$173$	599.946	+	1846.44i	0.263659	+	0.811459i	0.991999	+	0.126243i	$0.0402921\pi$
$173$	599.946	+	1846.44i	0.263659	+	0.811459i	−0.728340	+	0.685216i	$0.759708\pi$
$174$	−64.5133	+	46.8717i	−0.0281077	+	0.0204215i
$175$	221.072			0.0954943
$176$	−440.169	−	383.389i	−0.188517	−	0.164199i
$177$	127.940			0.0543310
$178$	1758.11	−	1277.34i	0.740314	−	0.537870i
$179$	158.237	+	487.004i	0.0660738	+	0.203354i	0.978643	−	0.205569i	$-0.0659045\pi$
$179$	158.237	+	487.004i	0.0660738	+	0.203354i	−0.912569	+	0.408923i	$0.865904\pi$
$180$	161.319	−	496.489i	0.0668001	−	0.205589i
$181$	−23.0552	−	16.7506i	−0.00946784	−	0.00687879i	0.583041	−	0.812443i	$-0.301863\pi$
$181$	−23.0552	−	16.7506i	−0.00946784	−	0.00687879i	−0.592509	+	0.805564i	$0.701863\pi$
$182$	−45.3030	−	32.9146i	−0.0184510	−	0.0134054i
$183$	22.2087	−	68.3513i	0.00897111	−	0.0276102i
$184$	108.725	+	334.621i	0.0435615	+	0.134069i
$185$	−241.943	+	175.782i	−0.0961513	+	0.0698580i
$186$	−416.791			−0.164304
$187$	570.542	+	496.944i	0.223113	+	0.194332i
$188$	1084.53			0.420733
$189$	360.006	−	261.560i	0.138553	−	0.100665i
$190$	−143.749	−	442.414i	−0.0548876	−	0.168927i
$191$	427.810	−	1316.66i	0.162069	−	0.498799i	−0.836739	−	0.547602i	$-0.815541\pi$
$191$	427.810	−	1316.66i	0.162069	−	0.498799i	0.998808	+	0.0488034i	$0.0155408\pi$
$192$	−49.0664	−	35.6488i	−0.0184430	−	0.0133997i
$193$	−744.435	−	540.864i	−0.277646	−	0.201721i	0.440244	−	0.897878i	$-0.354892\pi$
$193$	−744.435	−	540.864i	−0.277646	−	0.201721i	−0.717890	+	0.696157i	$0.754892\pi$
$194$	142.323	−	438.024i	0.0526710	−	0.162105i
$195$	4.63601	+	14.2682i	0.00170252	+	0.00523982i
$196$	856.921	−	622.590i	0.312289	−	0.226891i
$197$	3563.23			1.28868			0.644339	−	0.764740i	$-0.277132\pi$
$197$	3563.23			1.28868			0.644339	+	0.764740i	$0.277132\pi$
$198$	745.879	−	1752.42i	0.267714	−	0.628985i
$199$	−1374.07			−0.489474			−0.244737	−	0.969589i	$-0.578702\pi$
$199$	−1374.07			−0.489474			−0.244737	+	0.969589i	$0.578702\pi$
$200$	161.803	−	117.557i	0.0572061	−	0.0415627i
$201$	33.2261	+	102.259i	0.0116596	+	0.0358847i
$202$	552.194	−	1699.48i	0.192338	−	0.591955i
$203$	301.001	+	218.690i	0.104069	+	0.0756109i
$204$	63.5993	+	46.2076i	0.0218276	+	0.0158587i
$205$	−111.438	+	342.972i	−0.0379668	+	0.116850i
$206$	545.159	+	1677.83i	0.184384	+	0.567475i
$207$	−928.727	+	674.760i	−0.311840	+	0.226565i
$208$	−50.6600			−0.0168877
$209$	−380.153	−	1653.99i	−0.125817	−	0.547411i
$210$	83.7995			0.0275367
$211$	3769.12	−	2738.43i	1.22975	−	0.893465i	0.232878	−	0.972506i	$-0.425186\pi$
$211$	3769.12	−	2738.43i	1.22975	−	0.893465i	0.996871	+	0.0790410i	$0.0251858\pi$
$212$	703.763	+	2165.96i	0.227994	+	0.701692i
$213$	165.940	−	510.711i	0.0533804	−	0.164288i
$214$	−2593.49	−	1884.28i	−0.828446	−	0.601901i
$215$	−1491.13	−	1083.37i	−0.472997	−	0.343652i
$216$	124.403	−	382.872i	0.0391876	−	0.120607i
$217$	600.923	+	1849.45i	0.187988	+	0.578567i
$218$	2843.77	−	2066.12i	0.883508	−	0.641906i
$219$	−659.383			−0.203456
$220$	625.805	−	375.190i	0.191781	−	0.114979i
$221$	65.6648			0.0199868
$222$	−91.7106	+	66.6316i	−0.0277262	+	0.0201442i
$223$	804.927	+	2477.31i	0.241713	+	0.743915i	0.996160	+	0.0875542i	$0.0279051\pi$
$223$	804.927	+	2477.31i	0.241713	+	0.743915i	−0.754447	+	0.656361i	$0.772095\pi$
$224$	−87.4434	+	269.123i	−0.0260828	+	0.0802747i
$225$	527.923	+	383.559i	0.156422	+	0.113647i
$226$	420.860	+	305.773i	0.123872	+	0.0899986i
$227$	1636.43	−	5036.43i	0.478476	−	1.47260i	−0.362736	−	0.931892i	$-0.618157\pi$
$227$	1636.43	−	5036.43i	0.478476	−	1.47260i	0.841212	−	0.540705i	$-0.181843\pi$
$228$	−54.4893	−	167.701i	−0.0158274	−	0.0487117i
$229$	−4104.78	+	2982.30i	−1.18450	+	0.860593i	−0.992673	−	0.120835i	$-0.961443\pi$
$229$	−4104.78	+	2982.30i	−1.18450	+	0.860593i	−0.191831	+	0.981428i	$0.561443\pi$
$230$	−439.802			−0.126086
$231$	304.535	+	26.9431i	0.0867400	+	0.00767414i
$232$	336.593			0.0952518
$233$	3858.93	−	2803.67i	1.08501	−	0.788304i	0.106458	−	0.994317i	$-0.466049\pi$
$233$	3858.93	−	2803.67i	1.08501	−	0.788304i	0.978549	+	0.206013i	$0.0660491\pi$
$234$	−51.0776	−	157.201i	−0.0142694	−	0.0439168i
$235$	−418.924	+	1289.32i	−0.116288	+	0.357897i
$236$	−436.896	−	317.424i	−0.120506	−	0.0875531i
$237$	559.423	+	406.444i	0.153327	+	0.111398i
$238$	113.343	−	348.834i	0.0308695	−	0.0950065i
$239$	−557.561	−	1716.00i	−0.150902	−	0.464429i	0.846820	−	0.531879i	$-0.178514\pi$
$239$	−557.561	−	1716.00i	−0.150902	−	0.464429i	−0.997723	+	0.0674496i	$0.978514\pi$
$240$	61.3330	−	44.5611i	0.0164960	−	0.0119850i
$241$	5868.14			1.56846			0.784232	−	0.620467i	$-0.213057\pi$
$241$	5868.14			1.56846			0.784232	+	0.620467i	$0.213057\pi$
$242$	2394.86	−	1162.27i	0.636148	−	0.308733i
$243$	1981.36			0.523063
$244$	−245.421	+	178.309i	−0.0643912	+	0.0467829i
$245$	409.143	+	1259.21i	0.106691	+	0.328360i
$246$	−42.2417	+	130.007i	−0.0109481	+	0.0336948i
$247$	−119.158	−	86.5737i	−0.0306958	−	0.0223018i
$248$	1423.28	+	1034.07i	0.364428	+	0.264773i
$249$	334.540	−	1029.61i	0.0851431	−	0.262044i
$250$	77.2542	+	237.764i	0.0195440	+	0.0601501i
$251$	463.933	−	337.067i	0.116666	−	0.0847629i	−0.527922	−	0.849293i	$-0.677029\pi$
$251$	463.933	−	337.067i	0.116666	−	0.0847629i	0.644588	+	0.764530i	$0.277029\pi$
$252$	−923.268			−0.230795
$253$	−1598.28	−	141.405i	−0.397166	−	0.0351385i
$254$	−4194.65			−1.03620
$255$	−79.4991	+	57.7595i	−0.0195232	+	0.0141845i
$256$	79.1084	+	243.470i	0.0193136	+	0.0594410i
$257$	811.525	−	2497.62i	0.196971	−	0.606214i	−0.802977	−	0.596010i	$-0.796752\pi$
$257$	811.525	−	2497.62i	0.196971	−	0.606214i	0.999948	−	0.0102041i	$-0.00324811\pi$
$258$	−565.227	−	410.661i	−0.136393	−	0.0990956i
$259$	427.895	+	310.884i	0.102657	+	0.0745845i
$260$	19.5685	−	60.2256i	0.00466764	−	0.0143655i
$261$	339.368	+	1044.47i	0.0804841	+	0.247704i
$262$	−542.983	+	394.500i	−0.128037	+	0.0930240i
$263$	1403.11			0.328972			0.164486	−	0.986379i	$-0.447403\pi$
$263$	1403.11			0.328972			0.164486	+	0.986379i	$0.447403\pi$
$264$	237.217	−	142.219i	0.0553019	−	0.0331553i
$265$	−2846.78			−0.659911
$266$	−665.587	+	483.577i	−0.153420	+	0.111466i
$267$	318.191	+	979.290i	0.0729324	+	0.224463i
$268$	140.247	−	431.635i	0.0319661	−	0.0983816i
$269$	−6577.55	−	4778.87i	−1.49086	−	1.08317i	−0.973851	−	0.227189i	$-0.927047\pi$
$269$	−6577.55	−	4778.87i	−1.49086	−	1.08317i	−0.517006	−	0.855982i	$-0.672953\pi$
$270$	407.113	+	295.785i	0.0917634	+	0.0666700i
$271$	190.126	−	585.148i	0.0426175	−	0.131163i	−0.927484	−	0.373863i	$-0.878033\pi$
$271$	190.126	−	585.148i	0.0426175	−	0.131163i	0.970101	+	0.242700i	$0.0780330\pi$
$272$	−102.539	−	315.583i	−0.0228579	−	0.0703494i
$273$	21.4656	−	15.5957i	0.00475883	−	0.00345749i
$274$	−886.260			−0.195405
$275$	204.303	+	888.895i	0.0447999	+	0.194918i
$276$	−166.711			−0.0363580
$277$	−2454.03	+	1782.96i	−0.532305	+	0.386742i	−0.821219	−	0.570613i	$-0.806706\pi$
$277$	−2454.03	+	1782.96i	−0.532305	+	0.386742i	0.288914	+	0.957355i	$0.406706\pi$
$278$	1336.87	+	4114.48i	0.288419	+	0.887661i
$279$	−1773.77	+	5459.11i	−0.380620	+	1.17143i
$280$	−286.162	−	207.909i	−0.0610767	−	0.0443748i
$281$	−5061.51	−	3677.40i	−1.07454	−	0.780696i	−0.0978135	−	0.995205i	$-0.531185\pi$
$281$	−5061.51	−	3677.40i	−1.07454	−	0.780696i	−0.976722	+	0.214509i	$0.931185\pi$
$282$	−158.797	+	488.727i	−0.0335327	+	0.103203i
$283$	322.022	+	991.082i	0.0676404	+	0.208176i	0.979164	−	0.203073i	$-0.0650928\pi$
$283$	322.022	+	991.082i	0.0676404	+	0.208176i	−0.911523	+	0.411249i	$0.865093\pi$
$284$	−1833.75	+	1332.30i	−0.383144	+	0.278370i
$285$	220.414			0.0458112
$286$	90.4774	−	212.574i	0.0187064	−	0.0439502i
$287$	637.789			0.131176
$288$	−675.742	+	490.955i	−0.138259	+	0.100451i
$289$	−1385.29	−	4263.49i	−0.281964	−	0.867797i
$290$	−130.016	+	400.149i	−0.0263269	+	0.0810260i
$291$	176.549	+	128.271i	0.0355653	+	0.0258397i
$292$	2251.69	+	1635.95i	0.451267	+	0.327865i
$293$	752.555	−	2316.13i	0.150050	−	0.461808i	−0.847575	−	0.530675i	$-0.821939\pi$
$293$	752.555	−	2316.13i	0.150050	−	0.461808i	0.997626	+	0.0688673i	$0.0219385\pi$
$294$	155.089	+	477.316i	0.0307653	+	0.0946859i
$295$	546.120	−	396.780i	0.107784	−	0.0783099i
$296$	478.492			0.0939588
$297$	1384.39	+	1205.80i	0.270472	+	0.235582i
$298$	−3959.08			−0.769608
$299$	−112.657	+	81.8504i	−0.0217898	+	0.0158312i
$300$	29.2839	+	90.1266i	0.00563569	+	0.0173449i
$301$	−1007.32	+	3100.20i	−0.192893	+	0.593662i
$302$	650.706	+	472.766i	0.123986	+	0.0900815i
$303$	684.989	+	497.674i	0.129873	+	0.0943585i
$304$	−229.998	+	707.862i	−0.0433925	+	0.133548i
$305$	−117.178	−	360.637i	−0.0219987	−	0.0677049i
$306$	875.888	−	636.370i	0.163631	−	0.118885i
$307$	2029.56			0.377306			0.188653	−	0.982044i	$-0.439588\pi$
$307$	2029.56			0.377306			0.188653	+	0.982044i	$0.439588\pi$
$308$	−973.093	−	847.567i	−0.180023	−	0.156801i
$309$	−835.907			−0.153893
$310$	−1779.10	+	1292.59i	−0.325955	+	0.236820i
$311$	940.534	+	2894.67i	0.171488	+	0.527786i	0.999456	−	0.0329899i	$-0.0105029\pi$
$311$	940.534	+	2894.67i	0.171488	+	0.527786i	−0.827968	+	0.560776i	$0.810503\pi$
$312$	7.41761	−	22.8291i	0.00134596	−	0.00414244i
$313$	−1850.98	−	1344.81i	−0.334260	−	0.242854i	0.407976	−	0.912993i	$-0.366235\pi$
$313$	−1850.98	−	1344.81i	−0.334260	−	0.242854i	−0.742236	+	0.670138i	$0.766235\pi$
$314$	5846.67	+	4247.85i	1.05079	+	0.763440i
$315$	356.632	−	1097.60i	0.0637903	−	0.196326i
$316$	−901.941	−	2775.89i	−0.160564	−	0.494164i
$317$	−3361.40	+	2442.20i	−0.595568	+	0.432706i	−0.844303	−	0.535866i	$-0.819985\pi$
$317$	−3361.40	+	2442.20i	−0.595568	+	0.432706i	0.248735	+	0.968572i	$0.419985\pi$
$318$	−1079.10			−0.190292
$319$	−601.146	+	1412.37i	−0.105510	+	0.247893i
$320$	−320.000			−0.0559017
$321$	1228.86	−	892.818i	0.213670	−	0.155241i
$322$	240.361	+	739.755i	0.0415988	+	0.128028i
$323$	298.121	−	917.522i	0.0513557	−	0.158057i
$324$	−2126.31	−	1544.85i	−0.364593	−	0.264893i
$325$	64.0387	+	46.5268i	0.0109299	+	0.00794106i
$326$	−2272.46	+	6993.90i	−0.386073	+	1.18821i
$327$	514.679	+	1584.02i	0.0870392	+	0.267879i
$328$	466.799	−	339.149i	0.0785813	−	0.0570926i
$329$	2397.61			0.401776
$330$	77.4430	+	336.944i	0.0129185	+	0.0562065i
$331$	2672.79			0.443837			0.221919	−	0.975065i	$-0.428768\pi$
$331$	2672.79			0.443837			0.221919	+	0.975065i	$0.428768\pi$
$332$	−3696.90	+	2685.95i	−0.611125	+	0.444008i
$333$	482.437	+	1484.79i	0.0793915	+	0.244342i
$334$	231.788	−	713.371i	0.0379727	−	0.116868i
$335$	458.963	+	333.456i	0.0748532	+	0.0543840i
$336$	−108.472	−	78.8098i	−0.0176121	−	0.0127959i
$337$	1500.33	−	4617.54i	0.242517	−	0.746391i	−0.753518	−	0.657427i	$-0.771645\pi$
$337$	1500.33	−	4617.54i	0.242517	−	0.746391i	0.996035	−	0.0889633i	$-0.0283554\pi$
$338$	1351.62	+	4159.87i	0.217511	+	0.669430i
$339$	−199.413	+	144.882i	−0.0319488	+	0.0232122i
$340$	414.780			0.0661606
$341$	−6881.00	+	4125.38i	−1.09275	+	0.655137i
$342$	−2428.43			−0.383960
$343$	4348.26	−	3159.19i	0.684501	−	0.497319i
$344$	911.299	+	2804.69i	0.142831	+	0.439589i
$345$	64.3956	−	198.189i	0.0100491	−	0.0309280i
$346$	3141.36	+	2282.33i	0.488093	+	0.354621i
$347$	−6236.00	−	4530.72i	−0.964743	−	0.700927i	−0.0104957	−	0.999945i	$-0.503341\pi$
$347$	−6236.00	−	4530.72i	−0.964743	−	0.700927i	−0.954247	+	0.299018i	$0.903341\pi$
$348$	−49.2838	+	151.680i	−0.00759164	+	0.0233647i
$349$	−1152.36	−	3546.60i	−0.176746	−	0.543969i	0.822963	−	0.568095i	$-0.192320\pi$
$349$	−1152.36	−	3546.60i	−0.176746	−	0.543969i	−0.999709	+	0.0241265i	$0.992320\pi$
$350$	357.703	−	259.886i	0.0546286	−	0.0396900i
$351$	159.332			0.0242293
$352$	−1162.91	−	102.886i	−0.176089	−	0.0155791i
$353$	6438.64			0.970805			0.485403	−	0.874291i	$-0.338673\pi$
$353$	6438.64			0.970805			0.485403	+	0.874291i	$0.338673\pi$
$354$	207.012	−	150.403i	0.0310807	−	0.0225814i
$355$	−875.536	−	2694.62i	−0.130898	−	0.402861i
$356$	1343.08	−	4133.56i	0.199952	−	0.615389i
$357$	140.600	+	102.152i	0.0208442	+	0.0151442i
$358$	828.541	+	601.970i	0.122318	+	0.0888690i
$359$	322.358	−	992.117i	0.0473911	−	0.145855i	−0.924561	−	0.381035i	$-0.875568\pi$
$359$	322.358	−	992.117i	0.0473911	−	0.145855i	0.971952	+	0.235180i	$0.0755679\pi$
$360$	−322.638	−	992.978i	−0.0472348	−	0.145374i
$361$	3798.38	−	2759.69i	0.553781	−	0.402346i
$362$	−56.9956			−0.00827520
$363$	173.101	+	1249.38i	0.0250288	+	0.180649i
$364$	−111.995			−0.0161268
$365$	−2814.61	+	2044.93i	−0.403626	+	0.293251i
$366$	−44.4174	−	136.703i	−0.00634353	−	0.0195234i
$367$	2119.87	−	6524.29i	0.301516	−	0.927970i	−0.679439	−	0.733732i	$-0.737777\pi$
$367$	2119.87	−	6524.29i	0.301516	−	0.927970i	0.980954	−	0.194238i	$-0.0622234\pi$
$368$	569.292	+	413.615i	0.0806423	+	0.0585901i
$369$	1523.05	+	1106.56i	0.214869	+	0.156111i
$370$	−184.828	+	568.842i	−0.0259696	+	0.0799261i
$371$	1555.83	+	4788.34i	0.217721	+	0.670076i
$372$	−674.383	+	489.968i	−0.0939923	+	0.0682894i
$373$	−9922.63			−1.37741			−0.688705	−	0.725041i	$-0.741821\pi$
$373$	−9922.63			−1.37741			−0.688705	+	0.725041i	$0.741821\pi$
$374$	1507.35	+	133.360i	0.208404	+	0.0184381i
$375$	−118.456			−0.0163121
$376$	1754.81	−	1274.95i	0.240685	−	0.174868i
$377$	41.1664	+	126.697i	0.00562381	+	0.0173083i
$378$	275.020	−	846.425i	0.0374220	−	0.115173i
$379$	4707.30	+	3420.05i	0.637988	+	0.463526i	0.859158	−	0.511710i	$-0.170988\pi$
$379$	4707.30	+	3420.05i	0.637988	+	0.463526i	−0.221170	+	0.975235i	$0.570988\pi$
$380$	−752.680	−	546.854i	−0.101610	−	0.0738237i
$381$	614.179	−	1890.25i	0.0825862	−	0.254174i
$382$	−855.621	−	2633.33i	−0.114600	−	0.352704i
$383$	−493.792	+	358.761i	−0.0658788	+	0.0478637i	−0.620237	−	0.784414i	$-0.712964\pi$
$383$	−493.792	+	358.761i	−0.0658788	+	0.0478637i	0.554358	+	0.832278i	$0.312964\pi$
$384$	−121.299			−0.0161198
$385$	1383.48	−	829.442i	0.183140	−	0.109798i
$386$	−1840.34			−0.242671
$387$	−7784.29	+	5655.62i	−1.02248	+	0.742872i
$388$	−284.645	−	876.048i	−0.0372440	−	0.114625i
$389$	−3717.57	+	11441.5i	−0.484546	+	1.49128i	0.348092	+	0.937460i	$0.386830\pi$
$389$	−3717.57	+	11441.5i	−0.484546	+	1.49128i	−0.832638	+	0.553818i	$0.813170\pi$
$390$	24.2744	+	17.6364i	0.00315175	+	0.00228988i
$391$	−737.908	−	536.122i	−0.0954415	−	0.0693423i
$392$	654.629	−	2014.74i	0.0843464	−	0.259591i
$393$	−98.2715	−	302.449i	−0.0126136	−	0.0388206i
$394$	5765.43	−	4188.83i	0.737203	−	0.535610i
$395$	3648.43			0.464740
$396$	−853.235	−	3712.31i	−0.108274	−	0.471087i
$397$	610.929			0.0772333			0.0386167	−	0.999254i	$-0.487705\pi$
$397$	610.929			0.0772333			0.0386167	+	0.999254i	$0.487705\pi$
$398$	−2223.30	+	1615.32i	−0.280009	+	0.203439i
$399$	−120.461	−	370.741i	−0.0151143	−	0.0465169i
$400$	123.607	−	380.423i	0.0154508	−	0.0475528i
$401$	−5130.18	−	3727.29i	−0.638875	−	0.464170i	0.220589	−	0.975367i	$-0.429202\pi$
$401$	−5130.18	−	3727.29i	−0.638875	−	0.464170i	−0.859463	+	0.511197i	$0.829202\pi$
$402$	173.974	+	126.400i	0.0215847	+	0.0156822i
$403$	−215.164	+	662.206i	−0.0265957	+	0.0818532i
$404$	−1104.39	−	3398.96i	−0.136003	−	0.418575i
$405$	2657.89	−	1931.07i	0.326102	−	0.236927i
$406$	744.114			0.0909600
$407$	−854.575	+	2007.80i	−0.104078	+	0.244528i
$408$	157.226			0.0190781
$409$	6923.18	−	5029.98i	0.836990	−	0.608109i	−0.0845379	−	0.996420i	$-0.526941\pi$
$409$	6923.18	−	5029.98i	0.836990	−	0.608109i	0.921528	+	0.388311i	$0.126941\pi$
$410$	222.877	+	685.944i	0.0268466	+	0.0826252i
$411$	129.766	−	399.378i	0.0155739	−	0.0479315i
$412$	2854.49	+	2073.91i	0.341337	+	0.247996i
$413$	−965.857	−	701.737i	−0.115077	−	0.0836082i
$414$	−709.484	+	2183.57i	−0.0842252	+	0.259219i
$415$	−1765.11	−	5432.45i	−0.208785	−	0.642575i
$416$	−81.9695	+	59.5544i	−0.00966079	+	0.00701897i
$417$	−2049.86			−0.240725
$418$	−2559.48	−	2229.32i	−0.299494	−	0.260860i
$419$	9840.45			1.14735			0.573673	−	0.819085i	$-0.305518\pi$
$419$	9840.45			1.14735			0.573673	+	0.819085i	$0.305518\pi$
$420$	135.590	−	98.5122i	0.0157527	−	0.0114450i
$421$	−1497.84	−	4609.88i	−0.173397	−	0.533662i	0.826159	−	0.563436i	$-0.190521\pi$
$421$	−1497.84	−	4609.88i	−0.173397	−	0.533662i	−0.999557	+	0.0297746i	$0.990521\pi$
$422$	2879.35	−	8861.74i	0.332144	−	1.02223i
$423$	5725.51	+	4159.82i	0.658117	+	0.478150i
$424$	3684.95	+	2677.27i	0.422068	+	0.306651i
$425$	−160.218	+	493.099i	−0.0182863	+	0.0562795i
$426$	−331.880	−	1021.42i	−0.0377456	−	0.116169i
$427$	−542.558	+	394.191i	−0.0614899	+	0.0446750i
$428$	−6411.46			−0.724088
$429$	82.5451	+	71.8971i	0.00928978	+	0.00809143i
$430$	−3686.28			−0.413414
$431$	−8873.74	+	6447.15i	−0.991723	+	0.720529i	−0.960298	−	0.278977i	$-0.910005\pi$
$431$	−8873.74	+	6447.15i	−0.991723	+	0.720529i	−0.0314256	+	0.999506i	$0.510005\pi$
$432$	−248.805	−	765.744i	−0.0277098	−	0.0852821i
$433$	1898.76	−	5843.77i	0.210735	−	0.648576i	−0.788694	−	0.614786i	$-0.789242\pi$
$433$	1898.76	−	5843.77i	0.210735	−	0.648576i	0.999429	−	0.0337901i	$-0.0107578\pi$
$434$	3146.48	+	2286.05i	0.348008	+	0.252843i
$435$	−161.283	−	117.179i	−0.0177769	−	0.0129157i
$436$	2172.45	−	6686.11i	0.238627	−	0.734419i
$437$	632.211	+	1945.75i	0.0692054	+	0.212992i
$438$	−1066.90	+	775.151i	−0.116390	+	0.0845619i
$439$	12752.7			1.38646			0.693229	−	0.720717i	$-0.256187\pi$
$439$	12752.7			1.38646			0.693229	+	0.720717i	$0.256187\pi$
$440$	571.512	−	1342.75i	0.0619221	−	0.145484i
$441$	6911.88			0.746343
$442$	106.248	−	77.1936i	0.0114337	−	0.00830707i
$443$	−2316.76	−	7130.27i	−0.248471	−	0.764716i	−0.995046	−	0.0994147i	$-0.968303\pi$
$443$	−2316.76	−	7130.27i	−0.248471	−	0.764716i	0.746575	−	0.665302i	$-0.231697\pi$
$444$	−70.0607	+	215.625i	−0.00748858	+	0.0230475i
$445$	4395.27	+	3193.35i	0.468216	+	0.340179i
$446$	4214.65	+	3062.13i	0.447466	+	0.325103i
$447$	579.686	−	1784.09i	0.0613383	−	0.188780i
$448$	174.887	+	538.246i	0.0184434	+	0.0567628i
$449$	11243.9	−	8169.20i	1.18181	−	0.858638i	0.189439	−	0.981892i	$-0.439333\pi$
$449$	11243.9	−	8169.20i	1.18181	−	0.858638i	0.992375	+	0.123254i	$0.0393331\pi$
$450$	1305.10			0.136718
$451$	589.410	+	2564.44i	0.0615394	+	0.267749i
$452$	1040.42			0.108269
$453$	−308.320	+	224.008i	−0.0319782	+	0.0232335i
$454$	−3272.87	−	10072.9i	−0.338333	−	1.04128i
$455$	43.2605	−	133.142i	0.00445733	−	0.0137183i
$456$	−285.310	−	207.290i	−0.0293001	−	0.0212878i
$457$	−4591.87	−	3336.19i	−0.470019	−	0.341489i	0.327430	−	0.944876i	$-0.393818\pi$
$457$	−4591.87	−	3336.19i	−0.470019	−	0.341489i	−0.797449	+	0.603387i	$0.793818\pi$
$458$	−3135.77	+	9650.91i	−0.319924	+	0.984624i
$459$	322.498	+	992.547i	0.0327950	+	0.100933i
$460$	−711.615	+	517.018i	−0.0721287	+	0.0524046i
$461$	−18025.9			−1.82115			−0.910574	−	0.413346i	$-0.864360\pi$
$461$	−18025.9			−1.82115			−0.910574	+	0.413346i	$0.864360\pi$
$462$	524.422	−	314.408i	0.0528102	−	0.0316614i
$463$	3950.70			0.396554			0.198277	−	0.980146i	$-0.436465\pi$
$463$	3950.70			0.396554			0.198277	+	0.980146i	$0.436465\pi$
$464$	544.619	−	395.689i	0.0544899	−	0.0395892i
$465$	−321.989	−	990.981i	−0.0321116	−	0.0988293i
$466$	2947.96	−	9072.88i	0.293050	−	0.901916i
$467$	9401.50	+	6830.59i	0.931584	+	0.676835i	0.946380	−	0.323055i	$-0.104710\pi$
$467$	9401.50	+	6830.59i	0.931584	+	0.676835i	−0.0147961	+	0.999891i	$0.504710\pi$
$468$	−267.446	−	194.311i	−0.0264160	−	0.0191923i
$469$	310.047	−	954.225i	0.0305258	−	0.0939489i
$470$	837.848	+	2578.63i	0.0822278	+	0.253071i
$471$	−2770.29	+	2012.73i	−0.271015	+	0.196904i
$472$	−1080.07			−0.105327
$473$	−13396.3	−	1185.21i	−1.30224	−	0.115213i
$474$	1382.97			0.134012
$475$	940.849	−	683.567i	0.0908824	−	0.0660299i
$476$	−226.686	−	697.668i	−0.0218280	−	0.0671797i
$477$	−4592.40	+	14133.9i	−0.440821	+	1.35671i
$478$	−2919.43	−	2121.09i	−0.279355	−	0.202963i
$479$	13228.5	+	9611.09i	1.26185	+	0.916789i	0.998847	−	0.0480052i	$-0.0152864\pi$
$479$	13228.5	+	9611.09i	1.26185	+	0.916789i	0.263005	+	0.964794i	$0.415286\pi$
$480$	46.8543	−	144.203i	0.00445541	−	0.0137123i
$481$	58.5211	+	180.109i	0.00554747	+	0.0170733i
$482$	9494.85	−	6898.41i	0.897258	−	0.651896i
$483$	−368.552			−0.0347199
$484$	2508.64	−	4695.92i	0.235598	−	0.441014i
$485$	1151.41			0.107800
$486$	3205.91	−	2329.23i	0.299224	−	0.217399i
$487$	−3168.88	−	9752.81i	−0.294858	−	0.907479i	−0.983269	−	0.182158i	$-0.941692\pi$
$487$	−3168.88	−	9752.81i	−0.294858	−	0.907479i	0.688412	−	0.725320i	$-0.258308\pi$
$488$	−187.485	+	577.019i	−0.0173915	+	0.0535254i
$489$	−2818.95	−	2048.09i	−0.260690	−	0.189402i
$490$	2142.30	+	1556.47i	0.197509	+	0.143499i
$491$	−3784.06	+	11646.1i	−0.347805	+	1.07043i	0.612261	+	0.790656i	$0.290260\pi$
$491$	−3784.06	+	11646.1i	−0.347805	+	1.07043i	−0.960065	+	0.279776i	$0.909740\pi$
$492$	84.4834	+	260.013i	0.00774147	+	0.0238258i
$493$	−705.928	+	512.887i	−0.0644896	+	0.0468545i
$494$	−294.576			−0.0268292
$495$	4742.85	+	419.614i	0.430657	+	0.0381015i
$496$	3518.54			0.318522
$497$	−4053.91	+	2945.34i	−0.365881	+	0.265828i
$498$	−669.081	−	2059.22i	−0.0602053	−	0.185293i
$499$	−6044.04	+	18601.7i	−0.542222	+	1.66879i	0.185284	+	0.982685i	$0.440679\pi$
$499$	−6044.04	+	18601.7i	−0.542222	+	1.66879i	−0.727506	+	0.686101i	$0.759321\pi$
$500$	404.508	+	293.893i	0.0361803	+	0.0262866i
$501$	287.530	+	208.903i	0.0256405	+	0.0186289i
$502$	354.414	−	1090.77i	0.0315105	−	0.0969792i
$503$	2388.74	+	7351.80i	0.211747	+	0.651691i	0.999369	+	0.0355313i	$0.0113124\pi$
$503$	2388.74	+	7351.80i	0.211747	+	0.651691i	−0.787621	+	0.616160i	$0.788688\pi$
$504$	−1493.88	+	1085.37i	−0.132029	+	0.0959248i
$505$	4467.34			0.393652
$506$	−2752.30	+	1650.09i	−0.241808	+	0.144972i
$507$	−2072.48			−0.181543
$508$	−6787.09	+	4931.11i	−0.592772	+	0.430674i
$509$	−6773.40	−	20846.4i	−0.589835	−	1.81532i	−0.578921	−	0.815384i	$-0.696526\pi$
$509$	−6773.40	−	20846.4i	−0.589835	−	1.81532i	−0.0109136	−	0.999940i	$-0.503474\pi$
$510$	−60.7319	+	186.914i	−0.00527304	+	0.0162288i
$511$	4977.86	+	3616.63i	0.430935	+	0.313092i
$512$	414.217	+	300.946i	0.0357538	+	0.0259767i
$513$	723.373	−	2226.31i	0.0622567	−	0.191606i
$514$	−1623.05	−	4995.23i	−0.139279	−	0.428658i
$515$	−3568.11	+	2592.39i	−0.305301	+	0.221814i
$516$	−1397.32			−0.119212
$517$	2215.74	+	9640.37i	0.188488	+	0.820083i
$518$	1057.81			0.0897253
$519$	−1488.45	+	1081.42i	−0.125888	+	0.0914627i
$520$	−39.1370	−	120.451i	−0.00330052	−	0.0101580i
$521$	−4030.20	+	12403.7i	−0.338899	+	1.04302i	0.625871	+	0.779927i	$0.284744\pi$
$521$	−4030.20	+	12403.7i	−0.338899	+	1.04302i	−0.964770	+	0.263096i	$0.915256\pi$
$522$	1776.95	+	1291.03i	0.148994	+	0.108251i
$523$	−5374.46	−	3904.77i	−0.449348	−	0.326470i	0.339991	−	0.940429i	$-0.389576\pi$
$523$	−5374.46	−	3904.77i	−0.449348	−	0.326470i	−0.789338	+	0.613959i	$0.789576\pi$
$524$	−414.802	+	1276.63i	−0.0345815	+	0.106431i
$525$	64.7387	+	199.245i	0.00538177	+	0.0165634i
$526$	2270.29	−	1649.46i	0.188192	−	0.136730i
$527$	−4560.68			−0.376976
$528$	216.637	−	508.981i	0.0178559	−	0.0419518i
$529$	−10232.7			−0.841024
$530$	−4606.19	+	3346.59i	−0.377509	+	0.274277i
$531$	−1088.97	−	3351.51i	−0.0889968	−	0.273904i
$532$	−508.463	+	1564.89i	−0.0414374	+	0.127531i
$533$	184.750	+	134.229i	0.0150139	+	0.0109082i
$534$	1666.07	+	1210.47i	0.135015	+	0.0980939i
$535$	2476.56	−	7622.08i	0.200133	−	0.615946i
$536$	−280.493	−	863.269i	−0.0226035	−	0.0695663i
$537$	−392.582	+	285.228i	−0.0315478	+	0.0229208i
$538$	−16260.6			−1.30306
$539$	7284.89	+	6345.16i	0.582157	+	0.507060i
$540$	1006.44			0.0802041
$541$	−1336.21	+	970.816i	−0.106189	+	0.0771509i	−0.639613	−	0.768697i	$-0.720905\pi$
$541$	−1336.21	+	970.816i	−0.106189	+	0.0771509i	0.533423	+	0.845848i	$0.320905\pi$
$542$	−380.252	−	1170.30i	−0.0301351	−	0.0927463i
$543$	8.34527	−	25.6841i	0.000659539	−	0.00202985i
$544$	−536.902	−	390.082i	−0.0423152	−	0.0307438i
$545$	7109.44	+	5165.31i	0.558779	+	0.405977i
$546$	16.3983	−	50.4688i	0.00128532	−	0.00395579i
$547$	−4701.87	−	14470.9i	−0.367527	−	1.13113i	−0.948383	−	0.317126i	$-0.897282\pi$
$547$	−4701.87	−	14470.9i	−0.367527	−	1.13113i	0.580856	−	0.814006i	$-0.302718\pi$
$548$	−1434.00	+	1041.86i	−0.111784	+	0.0812155i
$549$	−1979.55			−0.153889
$550$	1375.53	+	1198.09i	0.106641	+	0.0928850i
$551$	1957.21			0.151325
$552$	−269.744	+	195.980i	−0.0207990	+	0.0151114i
$553$	−1993.94	−	6136.72i	−0.153329	−	0.471899i
$554$	−1874.71	+	5769.77i	−0.143771	+	0.442480i
$555$	−229.276	−	166.579i	−0.0175356	−	0.0127403i
$556$	6999.96	+	5085.77i	0.533929	+	0.387922i
$557$	−4565.52	+	14051.2i	−0.347303	+	1.06889i	0.613037	+	0.790054i	$0.289948\pi$
$557$	−4565.52	+	14051.2i	−0.347303	+	1.06889i	−0.960340	+	0.278833i	$0.910052\pi$
$558$	3547.54	+	10918.2i	0.269139	+	0.828324i
$559$	−944.259	+	686.044i	−0.0714452	+	0.0519080i
$560$	−707.432			−0.0533830
$561$	−280.801	+	659.734i	−0.0211327	+	0.0496506i
$562$	−12512.7			−0.939178
$563$	3015.33	−	2190.77i	0.225722	−	0.163996i	−0.469177	−	0.883104i	$-0.655449\pi$
$563$	3015.33	−	2190.77i	0.225722	−	0.163996i	0.694898	+	0.719108i	$0.255449\pi$
$564$	317.594	+	977.454i	0.0237112	+	0.0729756i
$565$	−401.885	+	1236.88i	−0.0299247	+	0.0920987i
$566$	1686.13	+	1225.04i	0.125218	+	0.0909761i
$567$	−4700.68	−	3415.25i	−0.348166	−	0.252957i
$568$	−1400.86	+	4311.40i	−0.103484	+	0.318490i
$569$	−3595.21	−	11064.9i	−0.264884	−	0.815229i	−0.991720	−	0.128418i	$-0.959010\pi$
$569$	−3595.21	−	11064.9i	−0.264884	−	0.815229i	0.726836	−	0.686811i	$-0.240990\pi$
$570$	356.637	−	259.112i	0.0262068	−	0.0190404i
$571$	−16532.2			−1.21165			−0.605823	−	0.795600i	$-0.707156\pi$
$571$	−16532.2			−1.21165			−0.605823	+	0.795600i	$0.707156\pi$
$572$	−103.500	−	450.314i	−0.00756565	−	0.0329171i
$573$	1311.95			0.0956497
$574$	1031.96	−	749.765i	0.0750406	−	0.0545202i
$575$	−339.766	−	1045.69i	−0.0246421	−	0.0758406i
$576$	−516.221	+	1588.76i	−0.0373424	+	0.114928i
$577$	19449.1	+	14130.6i	1.40325	+	1.01952i	0.994261	+	0.106983i	$0.0341190\pi$
$577$	19449.1	+	14130.6i	1.40325	+	1.01952i	0.408990	+	0.912539i	$0.365881\pi$
$578$	−7253.48	−	5269.96i	−0.521981	−	0.379241i
$579$	269.462	−	829.320i	0.0193411	−	0.0595257i
$580$	260.032	+	800.297i	0.0186160	+	0.0572940i
$581$	−8172.82	+	5937.90i	−0.583590	+	0.424003i
$582$	436.454			0.0310852
$583$	−17815.3	+	10680.8i	−1.26558	+	0.758757i
$584$	5566.48			0.394422
$585$	334.307	−	242.888i	0.0236272	−	0.0171662i
$586$	−1505.11	−	4632.26i	−0.106102	−	0.326547i
$587$	7030.68	−	21638.2i	0.494357	−	1.52147i	−0.323600	−	0.946194i	$-0.604893\pi$
$587$	7030.68	−	21638.2i	0.494357	−	1.52147i	0.817957	−	0.575280i	$-0.195107\pi$
$588$	812.059	+	589.995i	0.0569537	+	0.0413793i
$589$	8276.03	+	6012.89i	0.578961	+	0.420640i
$590$	417.199	−	1284.01i	0.0291115	−	0.0895961i
$591$	1043.45	+	3211.42i	0.0726260	+	0.223520i
$592$	774.217	−	562.502i	0.0537502	−	0.0390518i
$593$	−12506.8			−0.866094			−0.433047	−	0.901371i	$-0.642562\pi$
$593$	−12506.8			−0.866094			−0.433047	+	0.901371i	$0.642562\pi$
$594$	3657.49	+	323.589i	0.252641	+	0.0223519i
$595$	916.964			0.0631796
$596$	−6405.92	+	4654.17i	−0.440263	+	0.319870i
$597$	−402.382	−	1238.40i	−0.0275853	−	0.0848987i
$598$	−86.0626	+	264.873i	−0.00588522	+	0.0181128i
$599$	−7388.22	−	5367.85i	−0.503964	−	0.366151i	0.306565	−	0.951850i	$-0.400820\pi$
$599$	−7388.22	−	5367.85i	−0.503964	−	0.366151i	−0.810529	+	0.585699i	$0.800820\pi$
$600$	153.333	+	111.403i	0.0104330	+	0.00757999i
$601$	5751.92	−	17702.6i	0.390392	−	1.20150i	−0.542101	−	0.840314i	$-0.682371\pi$
$601$	5751.92	−	17702.6i	0.390392	−	1.20150i	0.932493	−	0.361189i	$-0.117629\pi$
$602$	2014.63	+	6200.39i	0.136396	+	0.419783i
$603$	2395.97	−	1740.77i	0.161810	−	0.117562i
$604$	1608.63			0.108368
$605$	4613.59	+	4796.23i	0.310032	+	0.322305i
$606$	1693.39			0.113513
$607$	−13119.1	+	9531.56i	−0.877243	+	0.637354i	−0.932521	−	0.361117i	$-0.882396\pi$
$607$	−13119.1	+	9531.56i	−0.877243	+	0.637354i	0.0552775	+	0.998471i	$0.482396\pi$
$608$	459.997	+	1415.72i	0.0306831	+	0.0944329i
$609$	−108.953	+	335.323i	−0.00724958	+	0.0223119i
$610$	−613.552	−	445.771i	−0.0407246	−	0.0295881i
$611$	694.522	+	504.599i	0.0459858	+	0.0334106i
$612$	669.119	−	2059.34i	0.0441953	−	0.136019i
$613$	532.206	+	1637.96i	0.0350663	+	0.107923i	0.967058	−	0.254558i	$-0.0819299\pi$
$613$	532.206	+	1637.96i	0.0350663	+	0.107923i	−0.931991	+	0.362481i	$0.881930\pi$
$614$	3283.89	−	2385.89i	0.215842	−	0.156819i
$615$	−341.742			−0.0224071
$616$	−2570.87	−	227.453i	−0.168155	−	0.0148772i
$617$	21657.0			1.41309			0.706547	−	0.707666i	$-0.250252\pi$
$617$	21657.0			1.41309			0.706547	+	0.707666i	$0.250252\pi$
$618$	−1352.53	+	982.668i	−0.0880365	+	0.0639623i
$619$	−4699.18	−	14462.6i	−0.305131	−	0.939097i	−0.979628	−	0.200819i	$-0.935640\pi$
$619$	−4699.18	−	14462.6i	−0.305131	−	0.939097i	0.674497	−	0.738277i	$-0.264360\pi$
$620$	−1359.11	+	4182.91i	−0.0880373	+	0.270951i
$621$	−1790.49	−	1300.87i	−0.115700	−	0.0840613i
$622$	4924.70	+	3578.00i	0.317464	+	0.230651i
$623$	2969.17	−	9138.17i	0.190943	−	0.587661i
$624$	−14.8352	−	45.6581i	−0.000951737	−	0.00292915i
$625$	−505.636	+	367.366i	−0.0323607	+	0.0235114i
$626$	−4575.87			−0.292154
$627$	1379.36	−	826.972i	0.0878572	−	0.0526732i
$628$	14453.8			0.918420
$629$	−1003.53	+	729.107i	−0.0636142	+	0.0462184i
$630$	−713.264	−	2195.20i	−0.0451065	−	0.138824i
$631$	7357.85	−	22645.1i	0.464202	−	1.42867i	−0.395782	−	0.918344i	$-0.629526\pi$
$631$	7357.85	−	22645.1i	0.464202	−	1.42867i	0.859984	−	0.510321i	$-0.170474\pi$
$632$	−4722.62	−	3431.19i	−0.297240	−	0.215958i
$633$	3571.80	+	2595.06i	0.224275	+	0.162946i
$634$	−2567.88	+	7903.13i	−0.160857	+	0.495068i
$635$	−3240.55	−	9973.38i	−0.202515	−	0.623278i
$636$	−1746.02	+	1268.56i	−0.108859	+	0.0790904i
$637$	838.432			0.0521506
$638$	687.671	+	2991.96i	0.0426727	+	0.185663i
$639$	−14790.9			−0.915680
$640$	−517.771	+	376.183i	−0.0319792	+	0.0232343i
$641$	−1980.78	−	6096.23i	−0.122053	−	0.375642i	0.871299	−	0.490752i	$-0.163278\pi$
$641$	−1980.78	−	6096.23i	−0.122053	−	0.375642i	−0.993353	+	0.115110i	$0.963278\pi$
$642$	938.764	−	2889.22i	0.0577104	−	0.177614i
$643$	15209.2	+	11050.2i	0.932805	+	0.677722i	0.946678	−	0.322182i	$-0.104416\pi$
$643$	15209.2	+	11050.2i	0.932805	+	0.677722i	−0.0138733	+	0.999904i	$0.504416\pi$
$644$	1258.55	+	914.388i	0.0770089	+	0.0559502i
$645$	539.744	−	1661.16i	0.0329494	−	0.101408i
$646$	−596.242	−	1835.04i	−0.0363140	−	0.111763i
$647$	22016.7	−	15996.1i	1.33782	−	0.971981i	0.338296	−	0.941040i	$-0.390150\pi$
$647$	22016.7	−	15996.1i	1.33782	−	0.971981i	0.999521	−	0.0309413i	$-0.00985049\pi$
$648$	−5256.52			−0.318666
$649$	1928.97	−	4532.06i	0.116670	−	0.274112i
$650$	158.312			0.00955311
$651$	−1490.87	+	1083.18i	−0.0897573	+	0.0652125i
$652$	4544.91	+	13987.8i	0.272995	+	0.840191i
$653$	8559.40	−	26343.1i	0.512948	−	1.57869i	−0.274036	−	0.961719i	$-0.588359\pi$
$653$	8559.40	−	26343.1i	0.512948	−	1.57869i	0.786984	−	0.616973i	$-0.211641\pi$
$654$	2694.90	+	1957.96i	0.161130	+	0.117067i
$655$	−1357.46	−	986.250i	−0.0809775	−	0.0588336i
$656$	356.603	−	1097.51i	0.0212241	−	0.0653210i
$657$	5612.37	+	17273.1i	0.333271	+	1.02570i
$658$	3879.41	−	2818.55i	0.229840	−	0.166989i
$659$	20157.8			1.19156			0.595778	−	0.803149i	$-0.296844\pi$
$659$	20157.8			1.19156			0.595778	+	0.803149i	$0.296844\pi$
$660$	521.407	+	454.147i	0.0307511	+	0.0267843i
$661$	19540.5			1.14983			0.574916	−	0.818213i	$-0.305035\pi$
$661$	19540.5			1.14983			0.574916	+	0.818213i	$0.305035\pi$
$662$	4324.67	−	3142.06i	0.253902	−	0.184471i
$663$	19.2292	+	59.1815i	0.00112640	+	0.00346669i
$664$	−2824.18	+	8691.92i	−0.165059	+	0.508000i
$665$	−1663.97	−	1208.94i	−0.0970314	−	0.0704974i
$666$	2526.07	+	1835.30i	0.146972	+	0.106781i
$667$	571.814	−	1759.86i	0.0331945	−	0.102162i
$668$	−463.577	−	1426.74i	−0.0268508	−	0.0826382i
$669$	−1997.00	+	1450.91i	−0.115409	+	0.0838495i
$670$	1134.62			0.0654241
$671$	−2086.38	−	1817.24i	−0.120035	−	0.104551i
$672$	−268.158			−0.0153935
$673$	20412.0	−	14830.2i	1.16913	−	0.849421i	0.178224	−	0.983990i	$-0.442965\pi$
$673$	20412.0	−	14830.2i	1.16913	−	0.849421i	0.990904	+	0.134569i	$0.0429648\pi$
$674$	−3000.66	−	9235.09i	−0.171485	−	0.527778i
$675$	−388.758	+	1196.48i	−0.0221679	+	0.0682257i
$676$	7077.20	+	5141.89i	0.402663	+	0.292552i
$677$	1134.09	+	823.966i	0.0643821	+	0.0467764i	0.619511	−	0.784988i	$-0.287331\pi$
$677$	1134.09	+	823.966i	0.0643821	+	0.0467764i	−0.555129	+	0.831764i	$0.687331\pi$
$678$	−152.338	+	468.849i	−0.00862908	+	0.0265576i
$679$	−629.272	−	1936.70i	−0.0355659	−	0.109461i
$680$	671.128	−	487.603i	0.0378479	−	0.0274981i
$681$	5018.38			0.282386
$682$	−6284.01	+	14764.1i	−0.352826	+	0.828954i
$683$	24332.9			1.36321			0.681605	−	0.731721i	$-0.261282\pi$
$683$	24332.9			1.36321			0.681605	+	0.731721i	$0.261282\pi$
$684$	−3929.28	+	2854.79i	−0.219649	+	0.159584i
$685$	−684.673	−	2107.21i	−0.0381898	−	0.117536i
$686$	3321.77	−	10223.4i	0.184877	−	0.568994i
$687$	−3889.88	−	2826.17i	−0.216024	−	0.156950i
$688$	4771.62	+	3466.79i	0.264413	+	0.192108i
$689$	−557.072	+	1714.49i	−0.0308023	+	0.0947996i
$690$	−128.791	−	396.379i	−0.00710580	−	0.0218694i
$691$	−3194.79	+	2321.15i	−0.175884	+	0.127787i	−0.672244	−	0.740330i	$-0.734669\pi$
$691$	−3194.79	+	2321.15i	−0.175884	+	0.127787i	0.496360	+	0.868117i	$0.334669\pi$
$692$	7765.86			0.426609
$693$	−1886.27	−	8206.89i	−0.103396	−	0.449861i
$694$	−15416.2			−0.843216
$695$	−8749.96	+	6357.21i	−0.477561	+	0.346968i
$696$	98.5676	+	303.360i	0.00536810	+	0.0165213i
$697$	−462.224	+	1422.58i	−0.0251190	+	0.0773084i
$698$	−6033.84	−	4383.84i	−0.327198	−	0.237723i
$699$	3656.90	+	2656.89i	0.197878	+	0.143767i
$700$	273.261	−	841.010i	0.0147547	−	0.0454102i
$701$	6533.11	+	20106.9i	0.352000	+	1.08335i	0.957728	+	0.287674i	$0.0928819\pi$
$701$	6533.11	+	20106.9i	0.352000	+	1.08335i	−0.605728	+	0.795672i	$0.707118\pi$
$702$	257.804	−	187.306i	0.0138607	−	0.0100704i
$703$	2782.32			0.149271
$704$	−2002.58	+	1200.61i	−0.107209	+	0.0642751i
$705$	−1284.69			−0.0686304
$706$	10417.9	−	7569.08i	0.555360	−	0.403493i
$707$	−2441.50	−	7514.16i	−0.129875	−	0.399716i
$708$	158.143	−	486.714i	0.00839460	−	0.0258359i
$709$	−9818.78	−	7133.76i	−0.520101	−	0.377876i	0.296541	−	0.955020i	$-0.404167\pi$
$709$	−9818.78	−	7133.76i	−0.520101	−	0.377876i	−0.816642	+	0.577144i	$0.804167\pi$
$710$	−4584.37	−	3330.74i	−0.242321	−	0.176057i
$711$	5885.61	−	18114.0i	0.310446	−	0.955456i
$712$	−2686.15	−	8267.13i	−0.141387	−	0.435146i
$713$	7824.51	−	5684.84i	0.410982	−	0.298596i
$714$	347.583			0.0182185
$715$	575.322	+	50.9004i	0.0300921	+	0.00266233i
$716$	2048.26			0.106910
$717$	1383.29	−	1005.02i	0.0720503	−	0.0523476i
$718$	−644.716	−	1984.23i	−0.0335106	−	0.103135i
$719$	−5079.11	+	15631.9i	−0.263447	+	0.810808i	0.728600	+	0.684940i	$0.240172\pi$
$719$	−5079.11	+	15631.9i	−0.263447	+	0.810808i	−0.992047	+	0.125868i	$0.959828\pi$
$720$	−1689.35	−	1227.39i	−0.0874424	−	0.0635306i
$721$	6310.49	+	4584.84i	0.325957	+	0.236822i
$722$	2901.71	−	8930.54i	0.149571	−	0.460333i
$723$	1718.42	+	5288.75i	0.0883938	+	0.272048i
$724$	−92.2208	+	67.0023i	−0.00473392	+	0.00343939i
$725$	−1051.85			−0.0538825
$726$	1748.82	+	1818.05i	0.0894007	+	0.0929398i
$727$	−25394.7			−1.29551			−0.647757	−	0.761847i	$-0.724293\pi$
$727$	−25394.7			−1.29551			−0.647757	+	0.761847i	$0.724293\pi$
$728$	−181.212	+	131.658i	−0.00922550	+	0.00670272i
$729$	−4901.98	−	15086.7i	−0.249046	−	0.766486i
$730$	−2150.17	+	6617.55i	−0.109016	+	0.335516i
$731$	−6184.91	−	4493.60i	−0.312937	−	0.227362i
$732$	−232.572	−	168.974i	−0.0117433	−	0.00853203i
$733$	−4872.60	+	14996.3i	−0.245530	+	0.755664i	0.750019	+	0.661417i	$0.230044\pi$
$733$	−4872.60	+	14996.3i	−0.245530	+	0.755664i	−0.995549	+	0.0942474i	$0.969956\pi$
$734$	−4239.74	−	13048.6i	−0.213204	−	0.656174i
$735$	−1015.07	+	737.494i	−0.0509409	+	0.0370107i
$736$	1407.37			0.0704840
$737$	4123.31	+	364.801i	0.206084	+	0.0182329i
$738$	3765.18			0.187802
$739$	−30681.4	+	22291.3i	−1.52724	+	1.10961i	−0.569497	+	0.821993i	$0.692862\pi$
$739$	−30681.4	+	22291.3i	−1.52724	+	1.10961i	−0.957746	+	0.287614i	$0.907138\pi$
$740$	369.656	+	1137.68i	0.0183633	+	0.0565163i
$741$	43.1317	−	132.746i	0.00213830	−	0.00658102i
$742$	8146.41	+	5918.71i	0.403051	+	0.292834i
$743$	−10591.5	−	7695.18i	−0.522967	−	0.379958i	0.294753	−	0.955573i	$-0.404763\pi$
$743$	−10591.5	−	7695.18i	−0.522967	−	0.379958i	−0.817721	+	0.575615i	$0.804763\pi$
$744$	−515.183	+	1585.57i	−0.0253864	+	0.0781314i
$745$	−3058.55	−	9413.26i	−0.150412	−	0.462920i
$746$	−16055.1	+	11664.7i	−0.787963	+	0.572489i
$747$	−29819.0			−1.46053
$748$	2595.71	−	1556.21i	0.126883	−	0.0760706i
$749$	−14174.0			−0.691463
$750$	−191.666	+	139.253i	−0.00933152	+	0.00677975i
$751$	9043.08	+	27831.8i	0.439397	+	1.35232i	0.888513	+	0.458851i	$0.151739\pi$
$751$	9043.08	+	27831.8i	0.439397	+	1.35232i	−0.449117	+	0.893473i	$0.648261\pi$
$752$	1340.56	−	4125.81i	0.0650068	−	0.200070i
$753$	439.645	+	319.421i	0.0212770	+	0.0154586i
$754$	215.550	+	156.606i	0.0104110	+	0.00756400i
$755$	−621.369	+	1912.38i	−0.0299522	+	0.0921835i
$756$	−550.040	−	1692.85i	−0.0264613	−	0.0814396i
$757$	−4453.65	+	3235.77i	−0.213832	+	0.155358i	−0.689546	−	0.724242i	$-0.742190\pi$
$757$	−4453.65	+	3235.77i	−0.213832	+	0.155358i	0.475714	+	0.879600i	$0.342190\pi$
$758$	11637.1			0.557622
$759$	−340.596	−	1481.89i	−0.0162883	−	0.0708683i
$760$	−1860.73			−0.0888100
$761$	−6583.24	+	4783.00i	−0.313590	+	0.227837i	−0.733436	−	0.679759i	$-0.762084\pi$
$761$	−6583.24	+	4783.00i	−0.313590	+	0.227837i	0.419845	+	0.907596i	$0.362084\pi$
$762$	−1228.36	−	3780.50i	−0.0583973	−	0.179728i
$763$	4802.69	−	14781.2i	0.227876	−	0.701329i
$764$	−4480.09	−	3254.97i	−0.212152	−	0.154137i
$765$	2189.72	+	1590.92i	0.103489	+	0.0751895i
$766$	−377.223	+	1160.97i	−0.0177932	+	0.0547620i
$767$	−132.096	−	406.548i	−0.00621863	−	0.0191390i
$768$	−196.266	+	142.595i	−0.00922152	+	0.00669983i
$769$	16999.2			0.797150			0.398575	−	0.917136i	$-0.369505\pi$
$769$	16999.2			0.797150			0.398575	+	0.917136i	$0.369505\pi$
$770$	1263.45	−	2968.45i	0.0591321	−	0.138929i
$771$	2488.66			0.116248
$772$	−2977.74	+	2163.45i	−0.138823	+	0.100861i
$773$	7916.96	+	24365.9i	0.368374	+	1.13374i	0.947841	+	0.318743i	$0.103261\pi$
$773$	7916.96	+	24365.9i	0.368374	+	1.13374i	−0.579467	+	0.814996i	$0.696739\pi$
$774$	−5946.67	+	18302.0i	−0.276161	+	0.849936i
$775$	−4447.74	−	3231.47i	−0.206152	−	0.149778i
$776$	−1490.42	−	1082.86i	−0.0689472	−	0.0500931i
$777$	−154.885	+	476.686i	−0.00715117	+	0.0220090i
$778$	7435.14	+	22883.0i	0.342625	+	1.05449i
$779$	2714.33	−	1972.07i	0.124841	−	0.0907020i
$780$	60.0097			0.00275473
$781$	−15589.1	−	13578.2i	−0.714241	−	0.622106i
$782$	−1824.21			−0.0834189
$783$	−1712.89	+	1244.49i	−0.0781785	+	0.0568000i
$784$	−1309.26	−	4029.48i	−0.0596419	−	0.183559i
$785$	−5583.07	+	17182.9i	−0.253845	+	0.781255i
$786$	−514.556	−	373.847i	−0.0233507	−	0.0169652i
$787$	−9255.32	−	6724.38i	−0.419208	−	0.304572i	0.358111	−	0.933679i	$-0.383421\pi$
$787$	−9255.32	−	6724.38i	−0.419208	−	0.304572i	−0.777319	+	0.629107i	$0.783421\pi$
$788$	4404.40	−	13555.3i	0.199112	−	0.612803i
$789$	410.887	+	1264.58i	0.0185399	+	0.0570598i
$790$	5903.28	−	4288.98i	0.265860	−	0.193158i
$791$	2300.09			0.103390
$792$	−5744.64	−	5003.60i	−0.257736	−	0.224489i
$793$	−240.126			−0.0107530
$794$	988.503	−	718.190i	0.0441822	−	0.0321003i
$795$	−833.649	−	2565.71i	−0.0371905	−	0.114461i
$796$	−1698.45	+	5227.28i	−0.0756279	+	0.232759i
$797$	−14158.6	−	10286.8i	−0.629263	−	0.457186i	0.226882	−	0.973922i	$-0.427147\pi$
$797$	−14158.6	−	10286.8i	−0.629263	−	0.457186i	−0.856145	+	0.516736i	$0.827147\pi$
$798$	−630.742	−	458.261i	−0.0279800	−	0.0203286i
$799$	−1737.61	+	5347.82i	−0.0769366	+	0.236786i
$800$	−247.214	−	760.845i	−0.0109254	−	0.0336249i
$801$	22945.1	−	16670.6i	1.01214	−	0.735362i
$802$	−12682.5			−0.558397
$803$	−9941.59	+	23357.5i	−0.436900	+	1.02648i
$804$	430.087			0.0188657
$805$	−1573.18	+	1142.98i	−0.0688788	+	0.0500434i
$806$	430.328	+	1324.41i	0.0188060	+	0.0578790i
$807$	2380.87	−	7327.57i	0.103855	−	0.319631i
$808$	−5782.65	−	4201.34i	−0.251773	−	0.182924i
$809$	9687.92	+	7038.68i	0.421025	+	0.305892i	0.778050	−	0.628202i	$-0.216209\pi$
$809$	9687.92	+	7038.68i	0.421025	+	0.305892i	−0.357025	+	0.934095i	$0.616209\pi$
$810$	2030.44	−	6249.07i	0.0880772	−	0.271074i
$811$	860.778	+	2649.20i	0.0372700	+	0.114705i	0.967961	−	0.251102i	$-0.0807929\pi$
$811$	860.778	+	2649.20i	0.0372700	+	0.114705i	−0.930691	+	0.365807i	$0.880793\pi$
$812$	1204.00	−	874.759i	0.0520347	−	0.0378054i
$813$	583.051			0.0251519
$814$	977.576	+	4253.30i	0.0420934	+	0.183142i
$815$	−18384.6			−0.790163
$816$	254.397	−	184.830i	0.0109138	−	0.00792935i
$817$	5298.99	+	16308.6i	0.226913	+	0.698368i
$818$	5288.84	−	16277.4i	0.226063	−	0.695752i
$819$	−591.249	−	429.568i	−0.0252258	−	0.0183276i
$820$	1167.00	+	847.873i	0.0496992	+	0.0361085i
$821$	−9464.20	+	29127.8i	−0.402318	+	1.23821i	0.520797	+	0.853681i	$0.325635\pi$
$821$	−9464.20	+	29127.8i	−0.402318	+	1.23821i	−0.923114	+	0.384526i	$0.874365\pi$
$822$	−259.531	−	798.756i	−0.0110124	−	0.0338927i
$823$	−23238.3	+	16883.6i	−0.984248	+	0.715098i	−0.958654	−	0.284574i	$-0.908148\pi$
$823$	−23238.3	+	16883.6i	−0.984248	+	0.715098i	−0.0255942	+	0.999672i	$0.508148\pi$
$824$	7056.69			0.298339
$825$	−741.303	+	444.435i	−0.0312835	+	0.0187554i
$826$	−2387.73			−0.100581
$827$	5232.96	−	3801.97i	0.220034	−	0.159864i	−0.472308	−	0.881433i	$-0.656579\pi$
$827$	5232.96	−	3801.97i	0.220034	−	0.159864i	0.692342	+	0.721570i	$0.256579\pi$
$828$	1418.97	+	4367.14i	0.0595562	+	0.183295i
$829$	−13587.2	+	41817.2i	−0.569245	+	1.75196i	0.0857437	+	0.996317i	$0.472673\pi$
$829$	−13587.2	+	41817.2i	−0.569245	+	1.75196i	−0.654989	+	0.755639i	$0.727327\pi$
$830$	−9242.24	−	6714.88i	−0.386509	−	0.280815i
$831$	−2325.56	−	1689.62i	−0.0970790	−	0.0705320i
$832$	−62.6192	+	192.722i	−0.00260929	+	0.00803057i
$833$	1697.04	+	5222.96i	0.0705871	+	0.217245i
$834$	−3316.75	+	2409.76i	−0.137709	+	0.100052i
$835$	1875.21			0.0777176
$836$	−6762.05	−	598.259i	−0.279749	−	0.0247502i
$837$	−11066.2			−0.456995
$838$	15922.2	−	11568.1i	0.656352	−	0.476868i
$839$	1811.48	+	5575.18i	0.0745404	+	0.229412i	0.981384	−	0.192055i	$-0.0615153\pi$
$839$	1811.48	+	5575.18i	0.0745404	+	0.229412i	−0.906844	+	0.421467i	$0.861515\pi$
$840$	103.582	−	318.792i	0.00425466	−	0.0130945i
$841$	18299.0	+	13295.0i	0.750296	+	0.545122i
$842$	−7842.79	−	5698.12i	−0.320998	−	0.233219i
$843$	1832.11	−	5638.66i	0.0748532	−	0.230374i
$844$	−5758.71	−	17723.5i	−0.234861	−	0.722828i
$845$	−8846.50	+	6427.36i	−0.360152	+	0.261666i
$846$	14154.2			0.575216
$847$	5545.92	−	10381.4i	0.224982	−	0.421144i
$848$	9109.70			0.368901
$849$	−798.928	+	580.455i	−0.0322958	+	0.0234643i
$850$	320.435	+	986.198i	0.0129304	+	0.0397956i
$851$	812.877	−	2501.78i	0.0327439	−	0.100775i
$852$	−1737.75	−	1262.55i	−0.0698758	−	0.0507677i
$853$	25040.7	+	18193.2i	1.00513	+	0.730272i	0.963183	−	0.268848i	$-0.0866429\pi$
$853$	25040.7	+	18193.2i	1.00513	+	0.730272i	0.0419502	+	0.999120i	$0.486643\pi$
$854$	−414.477	+	1275.63i	−0.0166079	+	0.0511137i
$855$	−1876.07	−	5773.94i	−0.0750410	−	0.230953i
$856$	−10374.0	+	7537.13i	−0.414223	+	0.300951i
$857$	26330.4			1.04951			0.524754	−	0.851254i	$-0.324157\pi$
$857$	26330.4			1.04951			0.524754	+	0.851254i	$0.324157\pi$
$858$	218.081	+	19.2943i	0.00867734	+	0.000767710i
$859$	−48579.7			−1.92959			−0.964796	−	0.263000i	$-0.915288\pi$
$859$	−48579.7			−1.92959			−0.964796	+	0.263000i	$0.915288\pi$
$860$	−5964.53	+	4333.48i	−0.236498	+	0.171826i
$861$	186.769	+	574.817i	0.00739267	+	0.0227523i
$862$	−6778.93	+	20863.4i	−0.267855	+	0.824374i
$863$	9185.20	+	6673.44i	0.362304	+	0.263229i	0.754012	−	0.656860i	$-0.228116\pi$
$863$	9185.20	+	6673.44i	0.362304	+	0.263229i	−0.391709	+	0.920089i	$0.628116\pi$
$864$	−1302.76	−	946.512i	−0.0512973	−	0.0372697i
$865$	−2999.73	+	9232.21i	−0.117912	+	0.362896i
$866$	−3797.51	−	11687.5i	−0.149012	−	0.458613i
$867$	3436.87	−	2497.03i	0.134628	−	0.0978127i
$868$	7778.51			0.304170
$869$	22832.0	−	13688.5i	0.891282	−	0.534352i
$870$	−398.714			−0.0155376
$871$	290.638	−	211.161i	0.0113064	−	0.00821460i
$872$	−4344.90	−	13372.2i	−0.168735	−	0.519313i
$873$	1857.45	−	5716.64i	0.0720105	−	0.221626i
$874$	3310.30	+	2405.07i	0.128115	+	0.0930810i
$875$	894.257	+	649.716i	0.0345502	+	0.0251022i
$876$	−815.042	+	2508.44i	−0.0314357	+	0.0967492i
$877$	6716.63	+	20671.7i	0.258614	+	0.795932i	0.993096	+	0.117304i	$0.0374252\pi$
$877$	6716.63	+	20671.7i	0.258614	+	0.795932i	−0.734482	+	0.678628i	$0.762575\pi$
$878$	20634.4	−	14991.7i	0.793139	−	0.576249i
$879$	2307.83			0.0885563
$880$	−653.771	−	2844.47i	−0.0250439	−	0.108962i
$881$	20102.9			0.768769			0.384384	−	0.923173i	$-0.374414\pi$
$881$	20102.9			0.768769			0.384384	+	0.923173i	$0.374414\pi$
$882$	11183.7	−	8125.41i	0.426954	−	0.310200i
$883$	13265.2	+	40826.2i	0.505562	+	1.55596i	0.799825	+	0.600234i	$0.204926\pi$
$883$	13265.2	+	40826.2i	0.505562	+	1.55596i	−0.294263	+	0.955724i	$0.595074\pi$
$884$	81.1661	−	249.804i	0.00308814	−	0.00950431i
$885$	517.530	+	376.007i	0.0196571	+	0.0142817i
$886$	−12130.7	−	8813.50i	−0.459978	−	0.334193i
$887$	5201.22	−	16007.7i	0.196888	−	0.605960i	−0.803061	−	0.595897i	$-0.796797\pi$
$887$	5201.22	−	16007.7i	0.196888	−	0.605960i	0.999949	−	0.0100633i	$-0.00320330\pi$
$888$	140.121	+	431.249i	0.00529523	+	0.0162970i
$889$	−15004.4	+	10901.3i	−0.566064	+	0.411270i
$890$	10865.7			0.409236
$891$	9388.01	−	22056.9i	0.352986	−	0.829329i
$892$	10419.2			0.391099
$893$	10203.8	−	7413.52i	0.382372	−	0.277809i
$894$	−1159.37	−	3568.18i	−0.0433727	−	0.133488i
$895$	−791.186	+	2435.02i	−0.0295491	+	0.0909427i
$896$	915.719	+	665.309i	0.0341429	+	0.0248063i
$897$	−106.760	−	77.5653i	−0.00397391	−	0.00288721i
$898$	8589.61	−	26436.1i	0.319197	−	0.982388i
$899$	−2859.17	−	8799.61i	−0.106072	−	0.326455i
$900$	2111.69	−	1534.23i	0.0782109	−	0.0568235i
$901$	−11807.9			−0.436601
$902$	3968.37	+	3456.46i	0.146488	+	0.127592i
$903$	−3089.08			−0.113841
$904$	1683.44	−	1223.09i	0.0619362	−	0.0449993i
$905$	−44.0315	−	135.515i	−0.00161730	−	0.00497754i
$906$	−235.535	+	724.904i	−0.00863702	+	0.0265820i
$907$	−17973.7	−	13058.7i	−0.658001	−	0.478066i	0.207986	−	0.978132i	$-0.433309\pi$
$907$	−17973.7	−	13058.7i	−0.658001	−	0.478066i	−0.865987	+	0.500066i	$0.833309\pi$
$908$	−17137.0	−	12450.7i	−0.626333	−	0.455057i
$909$	7206.67	−	22179.9i	0.262960	−	0.809306i
$910$	−86.5211	−	266.284i	−0.00315181	−	0.00970027i
$911$	33409.8	−	24273.7i	1.21506	−	0.882791i	0.219377	−	0.975640i	$-0.429597\pi$
$911$	33409.8	−	24273.7i	1.21506	−	0.882791i	0.995680	+	0.0928491i	$0.0295974\pi$
$912$	−705.325			−0.0256093
$913$	−31428.2	−	27374.0i	−1.13923	−	0.992277i
$914$	−11351.7			−0.410812
$915$	290.715	−	211.217i	0.0105036	−	0.00763128i
$916$	6271.54	+	19301.8i	0.226220	+	0.696234i
$917$	−917.013	+	2822.28i	−0.0330234	+	0.101635i
$918$	1688.62	+	1226.86i	0.0607112	+	0.0441092i
$919$	12281.7	+	8923.19i	0.440845	+	0.320293i	0.785971	−	0.618264i	$-0.212164\pi$
$919$	12281.7	+	8923.19i	0.440845	+	0.320293i	−0.345126	+	0.938557i	$0.612164\pi$
$920$	−543.625	+	1673.11i	−0.0194813	+	0.0599573i
$921$	594.334	+	1829.17i	0.0212638	+	0.0654433i
$922$	−29166.5	+	21190.7i	−1.04181	+	0.756918i
$923$	−1794.18			−0.0639829
$924$	478.924	−	1125.22i	0.0170513	−	0.0400616i
$925$	−1495.29			−0.0531511
$926$	6392.36	−	4644.32i	0.226853	−	0.164818i
$927$	7114.87	+	21897.3i	0.252085	+	0.775838i
$928$	416.052	−	1280.48i	0.0147172	−	0.0452949i
$929$	−38956.8	−	28303.8i	−1.37581	−	0.999587i	−0.997258	−	0.0740084i	$-0.976421\pi$
$929$	−38956.8	−	28303.8i	−1.37581	−	0.999587i	−0.378556	−	0.925579i	$-0.623579\pi$
$930$	−1685.96	−	1224.92i	−0.0594459	−	0.0431900i
$931$	3806.52	−	11715.3i	0.134000	−	0.412408i
$932$	−5895.91	−	18145.8i	−0.207218	−	0.637751i
$933$	−2333.44	+	1695.34i	−0.0818793	+	0.0594888i
$934$	23241.8			0.814234
$935$	847.409	+	3686.96i	0.0296398	+	0.128959i
$936$	−661.162			−0.0230884
$937$	34360.7	−	24964.5i	1.19799	−	0.870391i	0.203905	−	0.978991i	$-0.434637\pi$
$937$	34360.7	−	24964.5i	1.19799	−	0.870391i	0.994086	+	0.108600i	$0.0346368\pi$
$938$	−620.093	−	1908.45i	−0.0215850	−	0.0664319i
$939$	669.997	−	2062.04i	0.0232849	−	0.0716635i
$940$	4387.03	+	3187.37i	0.152223	+	0.110596i
$941$	−18047.4	−	13112.2i	−0.625215	−	0.454245i	0.229524	−	0.973303i	$-0.426283\pi$
$941$	−18047.4	−	13112.2i	−0.625215	−	0.454245i	−0.854739	+	0.519058i	$0.826283\pi$
$942$	−2116.31	+	6513.34i	−0.0731988	+	0.225283i
$943$	−980.216	−	3016.79i	−0.0338496	−	0.104179i
$944$	−1747.59	+	1269.70i	−0.0602532	+	0.0437765i
$945$	2224.96			0.0765904
$946$	−23068.9	+	13830.6i	−0.792850	+	0.475339i
$947$	11025.1			0.378319			0.189160	−	0.981946i	$-0.439424\pi$
$947$	11025.1			0.378319			0.189160	+	0.981946i	$0.439424\pi$
$948$	2237.69	−	1625.78i	0.0766633	−	0.0556991i
$949$	680.798	+	2095.28i	0.0232873	+	0.0716709i
$950$	718.745	−	2212.07i	0.0245465	−	0.0755463i
$951$	−3185.42	−	2314.35i	−0.108617	−	0.0789146i
$952$	−1186.94	−	862.365i	−0.0404087	−	0.0293586i
$953$	−15810.9	+	48661.0i	−0.537425	+	1.65402i	0.200925	+	0.979607i	$0.435605\pi$
$953$	−15810.9	+	48661.0i	−0.537425	+	1.65402i	−0.738350	+	0.674418i	$0.764395\pi$
$954$	9184.80	+	28267.9i	0.311707	+	0.959336i
$955$	5600.11	−	4068.72i	0.189754	−	0.137865i
$956$	−7217.22			−0.244165
$957$	−1448.96	−	128.194i	−0.0489429	−	0.00433012i
$958$	32702.7			1.10290
$959$	−3170.17	+	2303.27i	−0.106747	+	0.0775562i
$960$	−93.7085	−	288.405i	−0.00315045	−	0.00969608i
$961$	5738.06	−	17659.9i	0.192611	−	0.592794i
$962$	306.420	+	222.627i	0.0102696	+	0.00746133i
$963$	−33847.6	−	24591.7i	−1.13263	−	0.822905i
$964$	7253.42	−	22323.7i	0.242341	−	0.745849i
$965$	−1421.74	−	4375.68i	−0.0474275	−	0.145967i
$966$	−596.329	+	433.259i	−0.0198619	+	0.0144305i
$967$	−5302.68			−0.176342			−0.0881710	−	0.996105i	$-0.528102\pi$
$967$	−5302.68			−0.176342			−0.0881710	+	0.996105i	$0.528102\pi$
$968$	−1461.31	−	10547.2i	−0.0485211	−	0.350208i
$969$	914.233			0.0303090
$970$	1863.03	−	1353.57i	0.0616683	−	0.0448046i
$971$	15769.3	+	48532.9i	0.521175	+	1.60401i	0.771757	+	0.635917i	$0.219378\pi$
$971$	15769.3	+	48532.9i	0.521175	+	1.60401i	−0.250582	+	0.968095i	$0.580622\pi$
$972$	2449.09	−	7537.54i	0.0808176	−	0.248731i
$973$	15475.0	+	11243.2i	0.509872	+	0.370444i
$974$	−16592.5	−	12055.1i	−0.545849	−	0.396583i
$975$	−23.1800	+	71.3408i	−0.000761390	+	0.00234332i
$976$	374.969	+	1154.04i	0.0122976	+	0.0378482i
$977$	−4157.57	+	3020.65i	−0.136144	+	0.0989141i	−0.653773	−	0.756691i	$-0.726815\pi$
$977$	−4157.57	+	3020.65i	−0.136144	+	0.0989141i	0.517629	+	0.855605i	$0.326815\pi$
$978$	−6968.83			−0.227851
$979$	39487.0	+	3493.53i	1.28908	+	0.114049i
$980$	5296.06			0.172629
$981$	37114.0	−	26964.9i	1.20791	−	0.877598i
$982$	7568.11	+	23292.2i	0.245935	+	0.756910i
$983$	16459.2	−	50656.1i	0.534045	−	1.64362i	−0.211659	−	0.977344i	$-0.567887\pi$
$983$	16459.2	−	50656.1i	0.534045	−	1.64362i	0.745704	−	0.666277i	$-0.232113\pi$
$984$	442.361	+	321.394i	0.0143312	+	0.0104123i
$985$	14413.6	+	10472.1i	0.466248	+	0.338749i
$986$	−539.281	+	1659.74i	−0.0174181	+	0.0536073i
$987$	702.113	+	2160.88i	0.0226429	+	0.0696875i
$988$	−476.634	+	346.295i	−0.0153479	+	0.0111509i
$989$	16212.3			0.521256
$990$	8167.37	−	4896.60i	0.262198	−	0.157196i
$991$	−26857.5			−0.860904			−0.430452	−	0.902613i	$-0.641646\pi$
$991$	−26857.5			−0.860904			−0.430452	+	0.902613i	$0.641646\pi$
$992$	5693.11	−	4136.29i	0.182214	−	0.132386i
$993$	782.699	+	2408.90i	0.0250133	+	0.0769830i
$994$	−3096.91	+	9531.31i	−0.0988210	+	0.304140i
$995$	−5558.24	−	4038.30i	−0.177093	−	0.128666i
$996$	−3503.35	−	2545.34i	−0.111454	−	0.0809759i
$997$	2090.10	−	6432.66i	0.0663932	−	0.204337i	−0.912356	−	0.409397i	$-0.865739\pi$
$997$	2090.10	−	6432.66i	0.0663932	−	0.204337i	0.978749	+	0.205060i	$0.0657390\pi$
$998$	12088.1	+	37203.3i	0.383409	+	1.18001i
$999$	−2435.01	+	1769.14i	−0.0771173	+	0.0560290i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	110.4.g.c.91.2	yes	12
11.2	odd	10		1210.4.a.bg.1.4		6
11.4	even	5	inner	110.4.g.c.81.2	✓	12
11.9	even	5		1210.4.a.bd.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
110.4.g.c.81.2	✓	12	11.4	even	5	inner
110.4.g.c.91.2	yes	12	1.1	even	1	trivial
1210.4.a.bd.1.4		6	11.9	even	5
1210.4.a.bg.1.4		6	11.2	odd	10

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 110 = 2 \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	110.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.61803 - 1.17557i) q^{2} +(0.292839 + 0.901266i) q^{3} +(1.23607 - 3.80423i) q^{4} +(4.04508 + 2.93893i) q^{5} +(1.53333 + 1.11403i) q^{6} +(2.73261 - 8.41010i) q^{7} +(-2.47214 - 7.60845i) q^{8} +(21.1169 - 15.3423i) q^{9} +10.0000 q^{10} +(36.3409 + 3.21519i) q^{11} +3.79059 q^{12} +(2.56155 - 1.86107i) q^{13} +(-5.46521 - 16.8202i) q^{14} +(-1.46420 + 4.50633i) q^{15} +(-12.9443 - 9.40456i) q^{16} +(16.7782 + 12.1901i) q^{17} +(16.1319 - 49.6489i) q^{18} +(-14.3749 - 44.2414i) q^{19} +(16.1803 - 11.7557i) q^{20} +8.37995 q^{21} +(62.5805 - 37.5190i) q^{22} -43.9802 q^{23} +(6.13330 - 4.45611i) q^{24} +(7.72542 + 23.7764i) q^{25} +(1.95685 - 6.02256i) q^{26} +(40.7113 + 29.5785i) q^{27} +(-28.6162 - 20.7909i) q^{28} +(-13.0016 + 40.0149i) q^{29} +(2.92839 + 9.01266i) q^{30} +(-177.910 + 129.259i) q^{31} -32.0000 q^{32} +(7.74430 + 33.6944i) q^{33} +41.4780 q^{34} +(35.7703 - 25.9886i) q^{35} +(-32.2638 - 99.2978i) q^{36} +(-18.4828 + 56.8842i) q^{37} +(-75.2680 - 54.6854i) q^{38} +(2.42744 + 1.76364i) q^{39} +(12.3607 - 38.0423i) q^{40} +(22.2877 + 68.5944i) q^{41} +(13.5590 - 9.85122i) q^{42} -368.628 q^{43} +(57.1512 - 134.275i) q^{44} +130.510 q^{45} +(-71.1615 + 51.7018i) q^{46} +(83.7848 + 257.863i) q^{47} +(4.68543 - 14.4203i) q^{48} +(214.230 + 155.647i) q^{49} +(40.4508 + 29.3893i) q^{50} +(-6.07319 + 18.6914i) q^{51} +(-3.91370 - 12.0451i) q^{52} +(-460.619 + 334.659i) q^{53} +100.644 q^{54} +(137.553 + 119.809i) q^{55} -70.7432 q^{56} +(35.6637 - 25.9112i) q^{57} +(26.0032 + 80.0297i) q^{58} +(41.7199 - 128.401i) q^{59} +(15.3333 + 11.1403i) q^{60} +(-61.3552 - 44.5771i) q^{61} +(-135.911 + 418.291i) q^{62} +(-71.3264 - 219.520i) q^{63} +(-51.7771 + 37.6183i) q^{64} +15.8312 q^{65} +(52.1407 + 45.4147i) q^{66} +113.462 q^{67} +(67.1128 - 48.7603i) q^{68} +(-12.8791 - 39.6379i) q^{69} +(27.3261 - 84.1010i) q^{70} +(-458.437 - 333.074i) q^{71} +(-168.935 - 122.739i) q^{72} +(-215.017 + 661.755i) q^{73} +(36.9656 + 113.768i) q^{74} +(-19.1666 + 13.9253i) q^{75} -186.073 q^{76} +(126.345 - 296.845i) q^{77} +6.00097 q^{78} +(590.328 - 428.898i) q^{79} +(-24.7214 - 76.0845i) q^{80} +(203.044 - 624.907i) q^{81} +(116.700 + 84.7873i) q^{82} +(-924.224 - 671.488i) q^{83} +(10.3582 - 31.8792i) q^{84} +(32.0435 + 98.6198i) q^{85} +(-596.453 + 433.348i) q^{86} -39.8714 q^{87} +(-65.3771 - 284.447i) q^{88} +1086.57 q^{89} +(211.169 - 153.423i) q^{90} +(-8.65211 - 26.6284i) q^{91} +(-54.3625 + 167.311i) q^{92} +(-168.596 - 122.492i) q^{93} +(438.703 + 318.737i) q^{94} +(71.8745 - 221.207i) q^{95} +(-9.37085 - 28.8405i) q^{96} +(186.303 - 135.357i) q^{97} +529.606 q^{98} +(816.737 - 489.660i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} - q^{3} - 12 q^{4} + 15 q^{5} + 2 q^{6} + 38 q^{7} + 24 q^{8} - 78 q^{9} + 120 q^{10} + 66 q^{11} + 16 q^{12} + 57 q^{13} - 76 q^{14} + 5 q^{15} - 48 q^{16} - 157 q^{17} - 24 q^{18} + 331 q^{19}+ \cdots + 3455 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 - q^3 - 12 * q^4 + 15 * q^5 + 2 * q^6 + 38 * q^7 + 24 * q^8 - 78 * q^9 + 120 * q^10 + 66 * q^11 + 16 * q^12 + 57 * q^13 - 76 * q^14 + 5 * q^15 - 48 * q^16 - 157 * q^17 - 24 * q^18 + 331 * q^19 + 60 * q^20 - 588 * q^21 + 98 * q^22 + 472 * q^23 + 8 * q^24 - 75 * q^25 - 34 * q^26 + 80 * q^27 - 88 * q^28 + 477 * q^29 - 10 * q^30 - 18 * q^31 - 384 * q^32 + 1093 * q^33 + 4 * q^34 + 110 * q^35 + 48 * q^36 - 390 * q^37 + 748 * q^38 - 381 * q^39 - 120 * q^40 - 193 * q^41 - 1534 * q^42 + 1014 * q^43 - 296 * q^44 - 660 * q^45 + 666 * q^46 - 894 * q^47 - 16 * q^48 - 899 * q^49 + 150 * q^50 - 677 * q^51 + 68 * q^52 - 2377 * q^53 + 100 * q^54 - 330 * q^55 + 256 * q^56 + 535 * q^57 - 954 * q^58 - 621 * q^59 + 20 * q^60 - 1290 * q^61 - 674 * q^62 - 1456 * q^63 - 192 * q^64 + 740 * q^65 + 1424 * q^66 + 5566 * q^67 - 628 * q^68 - 699 * q^69 + 380 * q^70 + 1212 * q^71 + 624 * q^72 - 263 * q^73 + 780 * q^74 - 25 * q^75 + 344 * q^76 + 1822 * q^77 + 3572 * q^78 + 753 * q^79 + 240 * q^80 + 1755 * q^81 - 1034 * q^82 - 5555 * q^83 - 1892 * q^84 - 790 * q^85 + 92 * q^86 + 1770 * q^87 + 72 * q^88 + 5026 * q^89 - 780 * q^90 - 707 * q^91 + 388 * q^92 - 527 * q^93 - 1012 * q^94 - 1655 * q^95 + 32 * q^96 - 2276 * q^97 - 832 * q^98 + 3455 * q^99

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