LMFDB - Embedded newform 39.4.k.a.20.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [39,4,Mod(2,39)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(39, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 1]))

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

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

chi := DirichletCharacter("39.2");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 39 = 3 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	39.k (of order $12$, degree $4$, 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:	$2.30107449022$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			20.3
Character	$\chi$	$=$	39.20
Dual form			39.4.k.a.2.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.908381 - 3.39012i) q^{2} +(2.68627 + 4.44791i) q^{3} +(-3.73959 + 2.15905i) q^{4} +(12.1413 - 12.1413i) q^{5} +(12.6388 - 13.1472i) q^{6} +(-3.81863 - 1.02320i) q^{7} +(-9.13753 - 9.13753i) q^{8} +(-12.5679 + 23.8966i) q^{9} +O(q^{10})$	\(q+(-0.908381 - 3.39012i) q^{2} +(2.68627 + 4.44791i) q^{3} +(-3.73959 + 2.15905i) q^{4} +(12.1413 - 12.1413i) q^{5} +(12.6388 - 13.1472i) q^{6} +(-3.81863 - 1.02320i) q^{7} +(-9.13753 - 9.13753i) q^{8} +(-12.5679 + 23.8966i) q^{9} +(-52.1894 - 30.1316i) q^{10} +(7.61210 - 2.03966i) q^{11} +(-19.6488 - 10.8336i) q^{12} +(44.8076 + 13.7578i) q^{13} +13.8751i q^{14} +(86.6183 + 21.3886i) q^{15} +(-39.9494 + 69.1944i) q^{16} +(-17.2612 - 29.8972i) q^{17} +(92.4289 + 20.8994i) q^{18} +(-26.2557 + 97.9877i) q^{19} +(-19.1897 + 71.6171i) q^{20} +(-5.70678 - 19.7335i) q^{21} +(-13.8294 - 23.9532i) q^{22} +(-98.5614 + 170.713i) q^{23} +(16.0970 - 65.1888i) q^{24} -169.822i q^{25} +(5.93819 - 164.401i) q^{26} +(-140.051 + 8.29199i) q^{27} +(16.4892 - 4.41828i) q^{28} +(60.6266 + 35.0028i) q^{29} +(-6.17235 - 313.076i) q^{30} +(-70.3210 - 70.3210i) q^{31} +(171.010 + 45.8220i) q^{32} +(29.5204 + 28.3789i) q^{33} +(-85.6755 + 85.6755i) q^{34} +(-58.7861 + 33.9402i) q^{35} +(-4.59536 - 116.498i) q^{36} +(38.6098 + 144.094i) q^{37} +356.041 q^{38} +(59.1721 + 236.258i) q^{39} -221.883 q^{40} +(-82.0241 - 306.118i) q^{41} +(-61.7152 + 37.2723i) q^{42} +(410.811 - 237.182i) q^{43} +(-24.0624 + 24.0624i) q^{44} +(137.546 + 442.726i) q^{45} +(668.271 + 179.063i) q^{46} +(-150.769 - 150.769i) q^{47} +(-415.086 + 8.18350i) q^{48} +(-283.512 - 163.686i) q^{49} +(-575.718 + 154.263i) q^{50} +(86.6120 - 157.088i) q^{51} +(-197.266 + 45.2935i) q^{52} -401.876i q^{53} +(155.330 + 467.258i) q^{54} +(67.6567 - 117.185i) q^{55} +(25.5433 + 44.2423i) q^{56} +(-506.371 + 146.438i) q^{57} +(63.5918 - 237.328i) q^{58} +(-146.297 + 545.989i) q^{59} +(-370.096 + 107.029i) q^{60} +(272.211 + 471.484i) q^{61} +(-174.519 + 302.275i) q^{62} +(72.4431 - 78.3929i) q^{63} +17.8207i q^{64} +(711.060 - 376.985i) q^{65} +(69.3922 - 125.857i) q^{66} +(490.625 - 131.463i) q^{67} +(129.099 + 74.5354i) q^{68} +(-1024.08 + 20.1900i) q^{69} +(168.462 + 168.462i) q^{70} +(-138.288 - 37.0542i) q^{71} +(333.195 - 103.517i) q^{72} +(74.5809 - 74.5809i) q^{73} +(453.424 - 261.784i) q^{74} +(755.354 - 456.188i) q^{75} +(-113.375 - 423.121i) q^{76} -31.1548 q^{77} +(747.192 - 415.213i) q^{78} -341.608 q^{79} +(355.072 + 1325.15i) q^{80} +(-413.097 - 600.660i) q^{81} +(-963.269 + 556.144i) q^{82} +(465.533 - 465.533i) q^{83} +(63.9467 + 61.4740i) q^{84} +(-572.564 - 153.418i) q^{85} +(-1177.25 - 1177.25i) q^{86} +(7.17021 + 363.689i) q^{87} +(-88.1932 - 50.9184i) q^{88} +(-514.593 + 137.885i) q^{89} +(1375.95 - 868.461i) q^{90} +(-157.027 - 98.3830i) q^{91} -851.196i q^{92} +(123.880 - 501.683i) q^{93} +(-374.170 + 648.081i) q^{94} +(870.919 + 1508.48i) q^{95} +(255.567 + 883.729i) q^{96} +(437.699 - 1633.51i) q^{97} +(-297.378 + 1109.83i) q^{98} +(-46.9271 + 207.538i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{3} - 12 q^{4} - 50 q^{6} + 20 q^{7} - 2 q^{9}+O(q^{10}) $ 48 * q - 2 * q^3 - 12 * q^4 - 50 * q^6 + 20 * q^7 - 2 * q^9	$ 48 q - 2 q^{3} - 12 q^{4} - 50 q^{6} + 20 q^{7} - 2 q^{9} - 156 q^{10} - 80 q^{13} + 70 q^{15} + 260 q^{16} + 256 q^{18} + 260 q^{19} + 82 q^{21} + 212 q^{22} - 1194 q^{24} - 248 q^{27} - 756 q^{28} - 1062 q^{30} - 180 q^{31} + 10 q^{33} - 396 q^{34} + 3060 q^{36} + 1932 q^{37} + 538 q^{39} + 360 q^{40} + 968 q^{42} + 1416 q^{43} - 386 q^{45} - 144 q^{46} - 410 q^{48} - 3000 q^{49} - 4336 q^{52} + 1930 q^{54} - 1012 q^{55} - 1274 q^{57} + 908 q^{58} - 2860 q^{60} + 836 q^{61} - 5150 q^{63} + 1376 q^{66} - 136 q^{67} - 1674 q^{69} + 1808 q^{70} - 3900 q^{72} + 3572 q^{73} + 5796 q^{75} + 8400 q^{76} + 12292 q^{78} - 3760 q^{79} + 2494 q^{81} + 2544 q^{82} + 1084 q^{84} + 4980 q^{85} + 2318 q^{87} - 8436 q^{88} - 8908 q^{91} - 1214 q^{93} - 8464 q^{94} - 6968 q^{96} - 204 q^{97} - 13094 q^{99}+O(q^{100}) $ 48 * q - 2 * q^3 - 12 * q^4 - 50 * q^6 + 20 * q^7 - 2 * q^9 - 156 * q^10 - 80 * q^13 + 70 * q^15 + 260 * q^16 + 256 * q^18 + 260 * q^19 + 82 * q^21 + 212 * q^22 - 1194 * q^24 - 248 * q^27 - 756 * q^28 - 1062 * q^30 - 180 * q^31 + 10 * q^33 - 396 * q^34 + 3060 * q^36 + 1932 * q^37 + 538 * q^39 + 360 * q^40 + 968 * q^42 + 1416 * q^43 - 386 * q^45 - 144 * q^46 - 410 * q^48 - 3000 * q^49 - 4336 * q^52 + 1930 * q^54 - 1012 * q^55 - 1274 * q^57 + 908 * q^58 - 2860 * q^60 + 836 * q^61 - 5150 * q^63 + 1376 * q^66 - 136 * q^67 - 1674 * q^69 + 1808 * q^70 - 3900 * q^72 + 3572 * q^73 + 5796 * q^75 + 8400 * q^76 + 12292 * q^78 - 3760 * q^79 + 2494 * q^81 + 2544 * q^82 + 1084 * q^84 + 4980 * q^85 + 2318 * q^87 - 8436 * q^88 - 8908 * q^91 - 1214 * q^93 - 8464 * q^94 - 6968 * q^96 - 204 * q^97 - 13094 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/39\mathbb{Z}\right)^\times$.

$n$	$14$	$28$
$\chi(n)$	$-1$	$e\left(\frac{11}{12}\right)$

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 $

$2$	−0.908381	−	3.39012i	−0.321161	−	1.19859i	−0.918115	−	0.396314i	$-0.870289\pi$
$2$	−0.908381	−	3.39012i	−0.321161	−	1.19859i	0.596954	−	0.802276i	$-0.296378\pi$
$3$	2.68627	+	4.44791i	0.516973	+	0.856001i
$3$	2.68627	+	4.44791i	0.516973	+	0.856001i
$4$	−3.73959	+	2.15905i	−0.467448	+	0.269881i
$5$	12.1413	−	12.1413i	1.08595	−	1.08595i	0.0900095	−	0.995941i	$-0.471310\pi$
$5$	12.1413	−	12.1413i	1.08595	−	1.08595i	0.995941	−	0.0900095i	$-0.0286898\pi$
$6$	12.6388	−	13.1472i	0.859963	−	0.894554i
$7$	−3.81863	−	1.02320i	−0.206187	−	0.0552475i	0.154247	−	0.988032i	$-0.450705\pi$
$7$	−3.81863	−	1.02320i	−0.206187	−	0.0552475i	−0.360434	+	0.932785i	$0.617371\pi$
$8$	−9.13753	−	9.13753i	−0.403825	−	0.403825i
$9$	−12.5679	+	23.8966i	−0.465477	+	0.885060i
$10$	−52.1894	−	30.1316i	−1.65037	−	0.952844i
$11$	7.61210	−	2.03966i	0.208649	−	0.0559072i	−0.152981	−	0.988229i	$-0.548887\pi$
$11$	7.61210	−	2.03966i	0.208649	−	0.0559072i	0.361629	+	0.932322i	$0.382221\pi$
$12$	−19.6488	−	10.8336i	−0.472677	−	0.260615i
$13$	44.8076	+	13.7578i	0.955954	+	0.293517i
$13$	44.8076	+	13.7578i	0.955954	+	0.293517i
$14$			13.8751i			0.264877i
$15$	86.6183	+	21.3886i	1.49098	+	0.368168i
$16$	−39.9494	+	69.1944i	−0.624209	+	1.08116i
$17$	−17.2612	−	29.8972i	−0.246261	−	0.426537i	0.716224	−	0.697870i	$-0.245869\pi$
$17$	−17.2612	−	29.8972i	−0.246261	−	0.426537i	−0.962486	+	0.271333i	$0.912536\pi$
$18$	92.4289	+	20.8994i	1.21032	+	0.273669i
$19$	−26.2557	+	97.9877i	−0.317025	+	1.18315i	0.605064	+	0.796177i	$0.293147\pi$
$19$	−26.2557	+	97.9877i	−0.317025	+	1.18315i	−0.922089	+	0.386977i	$0.873519\pi$
$20$	−19.1897	+	71.6171i	−0.214548	+	0.800703i
$21$	−5.70678	−	19.7335i	−0.0593010	−	0.205058i
$22$	−13.8294	−	23.9532i	−0.134020	−	0.232129i
$23$	−98.5614	+	170.713i	−0.893542	+	1.54766i	−0.0579429	+	0.998320i	$0.518454\pi$
$23$	−98.5614	+	170.713i	−0.893542	+	1.54766i	−0.835599	+	0.549340i	$0.814879\pi$
$24$	16.0970	−	65.1888i	0.136908	−	0.554442i
$25$		−	169.822i		−	1.35858i
$26$	5.93819	−	164.401i	0.0447913	−	1.24006i
$27$	−140.051	+	8.29199i	−0.998252	+	0.0591035i
$28$	16.4892	−	4.41828i	0.111292	−	0.0298206i
$29$	60.6266	+	35.0028i	0.388210	+	0.224133i	0.681384	−	0.731926i	$-0.261378\pi$
$29$	60.6266	+	35.0028i	0.388210	+	0.224133i	−0.293174	+	0.956059i	$0.594712\pi$
$30$	−6.17235	−	313.076i	−0.0375637	−	1.90532i
$31$	−70.3210	−	70.3210i	−0.407420	−	0.407420i	0.473418	−	0.880838i	$-0.343020\pi$
$31$	−70.3210	−	70.3210i	−0.407420	−	0.407420i	−0.880838	+	0.473418i	$0.843020\pi$
$32$	171.010	+	45.8220i	0.944707	+	0.253133i
$33$	29.5204	+	28.3789i	0.155722	+	0.149701i
$34$	−85.6755	+	85.6755i	−0.432154	+	0.432154i
$35$	−58.7861	+	33.9402i	−0.283905	+	0.163912i
$36$	−4.59536	−	116.498i	−0.0212748	−	0.539343i
$37$	38.6098	+	144.094i	0.171552	+	0.640240i	0.997113	+	0.0759278i	$0.0241919\pi$
$37$	38.6098	+	144.094i	0.171552	+	0.640240i	−0.825562	+	0.564312i	$0.809141\pi$
$38$	356.041			1.51993
$39$	59.1721	+	236.258i	0.242952	+	0.970038i
$40$	−221.883			−0.877069
$41$	−82.0241	−	306.118i	−0.312439	−	1.16604i	−0.926350	−	0.376664i	$-0.877071\pi$
$41$	−82.0241	−	306.118i	−0.312439	−	1.16604i	0.613911	−	0.789376i	$-0.289595\pi$
$42$	−61.7152	+	37.2723i	−0.226735	+	0.136934i
$43$	410.811	−	237.182i	1.45693	−	0.841161i	0.458074	−	0.888914i	$-0.348539\pi$
$43$	410.811	−	237.182i	1.45693	−	0.841161i	0.998859	+	0.0477533i	$0.0152061\pi$
$44$	−24.0624	+	24.0624i	−0.0824441	+	0.0824441i
$45$	137.546	+	442.726i	0.455646	+	1.46662i
$46$	668.271	+	179.063i	2.14198	+	0.573942i
$47$	−150.769	−	150.769i	−0.467913	−	0.467913i	0.433325	−	0.901238i	$-0.357340\pi$
$47$	−150.769	−	150.769i	−0.467913	−	0.467913i	−0.901238	+	0.433325i	$0.857340\pi$
$48$	−415.086	+	8.18350i	−1.24818	+	0.0246081i
$49$	−283.512	−	163.686i	−0.826565	−	0.477217i
$50$	−575.718	+	154.263i	−1.62838	+	0.436322i
$51$	86.6120	−	157.088i	0.237806	−	0.431309i
$52$	−197.266	+	45.2935i	−0.526074	+	0.120790i
$53$		−	401.876i		−	1.04155i	−0.853695	−	0.520773i	$-0.825644\pi$
$53$		−	401.876i		−	1.04155i	0.853695	−	0.520773i	$-0.174356\pi$
$54$	155.330	+	467.258i	0.391441	+	1.17751i
$55$	67.6567	−	117.185i	0.165870	−	0.287295i
$56$	25.5433	+	44.2423i	0.0609530	+	0.105574i
$57$	−506.371	+	146.438i	−1.17668	+	0.340285i
$58$	63.5918	−	237.328i	0.143966	−	0.537287i
$59$	−146.297	+	545.989i	−0.322819	+	1.20478i	0.593668	+	0.804710i	$0.297679\pi$
$59$	−146.297	+	545.989i	−0.322819	+	1.20478i	−0.916487	+	0.400066i	$0.868987\pi$
$60$	−370.096	+	107.029i	−0.796319	+	0.230289i
$61$	272.211	+	471.484i	0.571362	+	0.989628i	0.996426	+	0.0844650i	$0.0269181\pi$
$61$	272.211	+	471.484i	0.571362	+	0.989628i	−0.425064	+	0.905163i	$0.639749\pi$
$62$	−174.519	+	302.275i	−0.357482	+	0.619178i
$63$	72.4431	−	78.3929i	0.144873	−	0.156771i
$64$			17.8207i			0.0348062i
$65$	711.060	−	376.985i	1.35686	−	0.719374i
$66$	69.3922	−	125.857i	0.129418	−	0.234726i
$67$	490.625	−	131.463i	0.894618	−	0.239712i	0.217915	−	0.975968i	$-0.430075\pi$
$67$	490.625	−	131.463i	0.894618	−	0.239712i	0.676703	+	0.736256i	$0.263408\pi$
$68$	129.099	+	74.5354i	0.230229	+	0.132923i
$69$	−1024.08	+	20.1900i	−1.78674	+	0.0352259i
$70$	168.462	+	168.462i	0.287643	+	0.287643i
$71$	−138.288	−	37.0542i	−0.231152	−	0.0619370i	0.141384	−	0.989955i	$-0.454845\pi$
$71$	−138.288	−	37.0542i	−0.231152	−	0.0619370i	−0.372536	+	0.928018i	$0.621512\pi$
$72$	333.195	−	103.517i	0.545381	−	0.169438i
$73$	74.5809	−	74.5809i	0.119576	−	0.119576i	−0.644787	−	0.764363i	$-0.723054\pi$
$73$	74.5809	−	74.5809i	0.119576	−	0.119576i	0.764363	+	0.644787i	$0.223054\pi$
$74$	453.424	−	261.784i	0.712289	−	0.411241i
$75$	755.354	−	456.188i	1.16294	−	0.702348i
$76$	−113.375	−	423.121i	−0.171118	−	0.638622i
$77$	−31.1548			−0.0461093
$78$	747.192	−	415.213i	1.08465	−	0.602738i
$79$	−341.608			−0.486505			−0.243253	−	0.969963i	$-0.578214\pi$
$79$	−341.608			−0.486505			−0.243253	+	0.969963i	$0.578214\pi$
$80$	355.072	+	1325.15i	0.496228	+	1.85195i
$81$	−413.097	−	600.660i	−0.566662	−	0.823950i
$82$	−963.269	+	556.144i	−1.29726	+	0.748973i
$83$	465.533	−	465.533i	0.615649	−	0.615649i	−0.328763	−	0.944412i	$-0.606632\pi$
$83$	465.533	−	465.533i	0.615649	−	0.615649i	0.944412	+	0.328763i	$0.106632\pi$
$84$	63.9467	+	61.4740i	0.0830614	+	0.0798496i
$85$	−572.564	−	153.418i	−0.730626	−	0.195771i
$86$	−1177.25	−	1177.25i	−1.47612	−	1.47612i
$87$	7.17021	+	363.689i	0.00883594	+	0.448179i
$88$	−88.1932	−	50.9184i	−0.106834	−	0.0616809i
$89$	−514.593	+	137.885i	−0.612885	+	0.164222i	−0.551891	−	0.833916i	$-0.686094\pi$
$89$	−514.593	+	137.885i	−0.612885	+	0.164222i	−0.0609935	+	0.998138i	$0.519427\pi$
$90$	1375.95	−	868.461i	1.61154	−	1.01715i
$91$	−157.027	−	98.3830i	−0.180889	−	0.113333i
$92$		−	851.196i		−	0.964601i
$93$	123.880	−	501.683i	0.138127	−	0.559378i
$94$	−374.170	+	648.081i	−0.410560	+	0.711111i
$95$	870.919	+	1508.48i	0.940573	+	1.62912i
$96$	255.567	+	883.729i	0.271706	+	0.939534i
$97$	437.699	−	1633.51i	0.458161	−	1.70988i	−0.220466	−	0.975395i	$-0.570758\pi$
$97$	437.699	−	1633.51i	0.458161	−	1.70988i	0.678626	−	0.734484i	$-0.262576\pi$
$98$	−297.378	+	1109.83i	−0.306527	+	1.14398i
$99$	−46.9271	+	207.538i	−0.0476399	+	0.210690i
$100$	366.655	+	635.064i	0.366655	+	0.635064i
$101$	225.303	−	390.237i	0.221966	−	0.384456i	−0.733439	−	0.679755i	$-0.762086\pi$
$101$	225.303	−	390.237i	0.221966	−	0.384456i	0.955405	+	0.295299i	$0.0954194\pi$
$102$	−611.225	−	150.930i	−0.593336	−	0.146512i
$103$		−	197.100i		−	0.188552i	−0.995546	−	0.0942758i	$-0.969946\pi$
$103$		−	197.100i		−	0.188552i	0.995546	−	0.0942758i	$-0.0300536\pi$
$104$	−283.719	−	535.143i	−0.267509	−	0.504568i
$105$	−308.878	−	170.303i	−0.287080	−	0.158284i
$106$	−1362.41	+	365.057i	−1.24839	+	0.334504i
$107$	415.798	+	240.061i	0.375670	+	0.216893i	0.675933	−	0.736963i	$-0.263741\pi$
$107$	415.798	+	240.061i	0.375670	+	0.216893i	−0.300263	+	0.953857i	$0.597074\pi$
$108$	505.829	−	333.386i	0.450680	−	0.297037i
$109$	−572.401	−	572.401i	−0.502992	−	0.502992i	0.409375	−	0.912366i	$-0.365747\pi$
$109$	−572.401	−	572.401i	−0.502992	−	0.502992i	−0.912366	+	0.409375i	$0.865747\pi$
$110$	−458.729	−	122.916i	−0.397619	−	0.106542i
$111$	−537.200	+	558.808i	−0.459359	+	0.477836i
$112$	223.352	−	223.352i	0.188435	−	0.188435i
$113$	−1108.35	+	639.907i	−0.922699	+	0.532720i	−0.884495	−	0.466550i	$-0.845497\pi$
$113$	−1108.35	+	639.907i	−0.922699	+	0.532720i	−0.0382036	+	0.999270i	$0.512164\pi$
$114$	956.423	+	1583.64i	0.785765	+	1.30106i
$115$	876.018	+	3269.34i	0.710340	+	2.65102i
$116$	−302.291			−0.241957
$117$	−891.901	+	897.845i	−0.704755	+	0.709451i
$118$	1983.87			1.54771
$119$	35.3232	+	131.828i	0.0272107	+	0.101552i
$120$	−596.038	−	986.916i	−0.453421	−	0.750772i
$121$	−1098.90	+	634.448i	−0.825617	+	0.476670i
$122$	1351.12	−	1351.12i	1.00266	−	1.00266i
$123$	1141.25	−	1187.15i	0.836609	−	0.870260i
$124$	414.798	+	111.145i	0.300403	+	0.0804928i
$125$	−544.198	−	544.198i	−0.389397	−	0.389397i
$126$	−331.568	−	174.380i	−0.234432	−	0.123294i
$127$	658.601	+	380.243i	0.460168	+	0.265678i	0.712115	−	0.702063i	$-0.247737\pi$
$127$	658.601	+	380.243i	0.460168	+	0.265678i	−0.251947	+	0.967741i	$0.581071\pi$
$128$	1428.50	−	382.764i	0.986425	−	0.264312i
$129$	2158.52	+	1190.12i	1.47323	+	0.812279i
$130$	−1923.94	−	2068.14i	−1.29801	−	1.39529i
$131$			553.309i			0.369029i	0.982830	+	0.184515i	$0.0590713\pi$
$131$			553.309i			0.369029i	−0.982830	+	0.184515i	$0.940929\pi$
$132$	−171.666	−	42.3893i	−0.113194	−	0.0279509i
$133$	200.522	−	347.314i	0.130733	−	0.226436i
$134$	−891.349	−	1543.86i	−0.574633	−	0.995294i
$135$	−1599.72	+	1801.07i	−1.01987	+	1.14824i
$136$	−115.462	+	430.911i	−0.0728000	+	0.271693i
$137$	−187.774	+	700.782i	−0.117099	+	0.437021i	−0.999435	−	0.0335993i	$-0.989303\pi$
$137$	−187.774	+	700.782i	−0.117099	+	0.437021i	0.882336	+	0.470620i	$0.155970\pi$
$138$	998.702	+	3453.42i	0.616052	+	2.13025i
$139$	−1421.79	−	2462.62i	−0.867589	−	1.50271i	−0.864454	−	0.502713i	$-0.832335\pi$
$139$	−1421.79	−	2462.62i	−0.867589	−	1.50271i	−0.00313509	−	0.999995i	$-0.500998\pi$
$140$	146.557	−	253.844i	0.0884738	−	0.153241i
$141$	265.601	−	1075.61i	0.158635	−	0.642432i
$142$			502.474i			0.296948i
$143$	369.141	+	13.3335i	0.215868	+	0.00779720i
$144$	−1151.43	−	1824.28i	−0.666339	−	1.05572i
$145$	1161.07	−	311.107i	0.664974	−	0.178179i
$146$	−320.587	−	185.091i	−0.181726	−	0.104919i
$147$	−33.5304	−	1700.74i	−0.0188132	−	0.954249i
$148$	−455.491	−	455.491i	−0.252980	−	0.252980i
$149$	−1175.67	−	315.021i	−0.646409	−	0.173205i	−0.0793044	−	0.996850i	$-0.525270\pi$
$149$	−1175.67	−	315.021i	−0.646409	−	0.173205i	−0.567105	+	0.823646i	$0.691937\pi$
$150$	−2232.69	−	2146.35i	−1.21532	−	1.16833i
$151$	30.1761	−	30.1761i	0.0162629	−	0.0162629i	−0.698929	−	0.715191i	$-0.746339\pi$
$151$	30.1761	−	30.1761i	0.0162629	−	0.0162629i	0.715191	+	0.698929i	$0.246339\pi$
$152$	1135.28	−	655.453i	0.605810	−	0.349765i
$153$	931.378	−	36.7389i	0.492140	−	0.0194128i
$154$	28.3004	+	105.619i	0.0148085	+	0.0552661i
$155$	−1707.58			−0.884877
$156$	−731.371	−	755.750i	−0.375363	−	0.387875i
$157$	461.168			0.234428			0.117214	−	0.993107i	$-0.462604\pi$
$157$	461.168			0.234428			0.117214	+	0.993107i	$0.462604\pi$
$158$	310.310	+	1158.09i	0.156247	+	0.583120i
$159$	1787.51	−	1079.55i	0.891565	−	0.538451i
$160$	2632.62	−	1519.95i	1.30080	−	0.751014i
$161$	551.043	−	551.043i	0.269741	−	0.269741i
$162$	−1661.06	+	1946.08i	−0.805588	+	0.943817i
$163$	1530.57	+	410.115i	0.735482	+	0.197072i	0.607069	−	0.794649i	$-0.292345\pi$
$163$	1530.57	+	410.115i	0.735482	+	0.197072i	0.128413	+	0.991721i	$0.459012\pi$
$164$	967.661	+	967.661i	0.460742	+	0.460742i
$165$	702.972	−	13.8592i	0.331675	−	0.00653904i
$166$	−2001.09	−	1155.33i	−0.935633	−	0.540188i
$167$	2143.03	−	574.224i	0.993012	−	0.266077i	0.274497	−	0.961588i	$-0.411489\pi$
$167$	2143.03	−	574.224i	0.993012	−	0.266077i	0.718515	+	0.695511i	$0.244822\pi$
$168$	−128.170	+	232.462i	−0.0588602	+	0.106755i
$169$	1818.45	+	1232.91i	0.827695	+	0.561178i
$170$			2080.42i			0.938595i
$171$	−2011.60	−	1858.92i	−0.899594	−	0.831317i
$172$	−1024.18	+	1773.92i	−0.454027	+	0.786398i
$173$	830.033	+	1437.66i	0.364776	+	0.631810i	0.988740	−	0.149642i	$-0.0478123\pi$
$173$	830.033	+	1437.66i	0.364776	+	0.631810i	−0.623964	+	0.781453i	$0.714479\pi$
$174$	1226.44	−	354.676i	0.534345	−	0.154528i
$175$	−173.762	+	648.488i	−0.0750580	+	0.280120i
$176$	−162.966	+	608.198i	−0.0697956	+	0.260481i
$177$	−2821.51	+	815.958i	−1.19818	+	0.346504i
$178$	934.893	+	1619.28i	0.393670	+	0.681856i
$179$	188.911	−	327.203i	0.0788818	−	0.136627i	−0.823886	−	0.566756i	$-0.808198\pi$
$179$	188.911	−	327.203i	0.0788818	−	0.136627i	0.902768	+	0.430128i	$0.141532\pi$
$180$	−1470.23	−	1358.64i	−0.608803	−	0.562597i
$181$			3097.32i			1.27194i	0.771712	+	0.635972i	$0.219401\pi$
$181$			3097.32i			1.27194i	−0.771712	+	0.635972i	$0.780599\pi$
$182$	−190.890	+	621.710i	−0.0777458	+	0.253210i
$183$	−1365.89	+	2477.31i	−0.551744	+	1.00070i
$184$	2460.50	−	659.290i	0.985819	−	0.264150i
$185$	2218.26	+	1280.71i	0.881566	+	0.508972i
$186$	−1813.30	+	35.7496i	−0.714826	+	0.0140929i
$187$	−192.374	−	192.374i	−0.0752286	−	0.0752286i
$188$	889.330	+	238.295i	0.345006	+	0.0924440i
$189$	543.287	+	111.636i	0.209092	+	0.0429646i
$190$	4322.80	−	4322.80i	1.65057	−	1.65057i
$191$	−3184.42	+	1838.53i	−1.20637	+	0.696498i	−0.961964	−	0.273176i	$-0.911926\pi$
$191$	−3184.42	+	1838.53i	−1.20637	+	0.696498i	−0.244405	+	0.969673i	$0.578593\pi$
$192$	−79.2652	+	47.8714i	−0.0297941	+	0.0179939i
$193$	−444.429	−	1658.63i	−0.165755	−	0.618606i	−0.997943	−	0.0641123i	$-0.979578\pi$
$193$	−444.429	−	1658.63i	−0.165755	−	0.618606i	0.832188	−	0.554494i	$-0.187088\pi$
$194$	−5935.41			−2.19659
$195$	3586.90	+	2150.05i	1.31725	+	0.789580i
$196$	1413.62			0.515168
$197$	−1050.21	−	3919.42i	−0.379818	−	1.41750i	−0.846176	−	0.532903i	$-0.821101\pi$
$197$	−1050.21	−	3919.42i	−0.379818	−	1.41750i	0.466359	−	0.884596i	$-0.345566\pi$
$198$	746.206	−	29.4347i	0.267831	−	0.0105648i
$199$	−378.747	+	218.669i	−0.134918	+	0.0778948i	−0.565940	−	0.824447i	$-0.691486\pi$
$199$	−378.747	+	218.669i	−0.134918	+	0.0778948i	0.431022	+	0.902341i	$0.358153\pi$
$200$	−1551.75	+	1551.75i	−0.548628	+	0.548628i
$201$	1902.69	+	1829.11i	0.667688	+	0.641870i
$202$	−1527.61	−	409.323i	−0.532092	−	0.142574i
$203$	−195.696	−	195.696i	−0.0676609	−	0.0676609i
$204$	15.2683	+	774.444i	0.00524018	+	0.265794i
$205$	−4712.55	−	2720.79i	−1.60555	−	0.926967i
$206$	−668.193	+	179.042i	−0.225996	+	0.0605555i
$207$	−2840.76	−	4500.79i	−0.953849	−	1.51124i
$208$	−2742.00	+	2550.82i	−0.914055	+	0.850325i
$209$			799.445i			0.264587i
$210$	−296.769	+	1201.84i	−0.0975190	+	0.394926i
$211$	−1419.10	+	2457.95i	−0.463009	+	0.801955i	−0.999109	−	0.0421995i	$-0.986563\pi$
$211$	−1419.10	+	2457.95i	−0.463009	+	0.801955i	0.536100	+	0.844154i	$0.319897\pi$
$212$	867.671	+	1502.85i	0.281094	+	0.486869i
$213$	−206.666	−	714.632i	−0.0664813	−	0.229886i
$214$	436.134	−	1627.67i	0.139315	−	0.519932i
$215$	2108.08	−	7867.48i	0.668698	−	2.49562i
$216$	1355.49	+	1203.95i	0.426987	+	0.379252i
$217$	196.578	+	340.482i	0.0614957	+	0.106514i
$218$	−1420.55	+	2460.47i	−0.441339	+	0.764422i
$219$	532.074	+	131.385i	0.164175	+	0.0405396i
$220$			584.297i			0.179060i
$221$	−362.112	−	1577.10i	−0.110219	−	0.480032i
$222$	2382.41	+	1313.57i	0.720257	+	0.397120i
$223$	−4541.81	+	1216.97i	−1.36387	+	0.365447i	−0.865235	−	0.501367i	$-0.832831\pi$
$223$	−4541.81	+	1216.97i	−1.36387	+	0.365447i	−0.498632	+	0.866814i	$0.666164\pi$
$224$	−606.140	−	349.955i	−0.180801	−	0.104385i
$225$	4058.17	+	2134.30i	1.20242	+	0.632386i
$226$	3176.17	+	3176.17i	0.934848	+	0.934848i
$227$	−466.796	−	125.078i	−0.136486	−	0.0365714i	0.189929	−	0.981798i	$-0.439174\pi$
$227$	−466.796	−	125.078i	−0.136486	−	0.0365714i	−0.326415	+	0.945226i	$0.605841\pi$
$228$	1577.45	−	1640.90i	0.458198	−	0.476628i
$229$	3411.67	−	3411.67i	0.984495	−	0.984495i	−0.0153867	−	0.999882i	$-0.504898\pi$
$229$	3411.67	−	3411.67i	0.984495	−	0.984495i	0.999882	+	0.0153867i	$0.00489795\pi$
$230$	10287.7	−	5939.62i	2.94936	−	1.70281i
$231$	−83.6902	−	138.574i	−0.0238373	−	0.0394696i
$232$	−234.138	−	873.817i	−0.0662584	−	0.247280i
$233$	3579.31			1.00639			0.503194	−	0.864173i	$-0.332158\pi$
$233$	3579.31			1.00639			0.503194	+	0.864173i	$0.332158\pi$
$234$	3853.99	+	2208.07i	1.07668	+	0.616864i
$235$	−3661.06			−1.01626
$236$	−631.727	−	2357.64i	−0.174246	−	0.650293i
$237$	−917.652	−	1519.44i	−0.251510	−	0.416449i
$238$	414.826	−	239.500i	0.112980	−	0.0652289i
$239$	1878.30	−	1878.30i	0.508355	−	0.508355i	−0.405666	−	0.914021i	$-0.632960\pi$
$239$	1878.30	−	1878.30i	0.508355	−	0.508355i	0.914021	+	0.405666i	$0.132960\pi$
$240$	−4940.32	+	5139.04i	−1.32873	+	1.38218i
$241$	2449.04	+	656.217i	0.654591	+	0.175397i	0.570804	−	0.821087i	$-0.306632\pi$
$241$	2449.04	+	656.217i	0.654591	+	0.175397i	0.0837870	+	0.996484i	$0.473298\pi$
$242$	3149.07	+	3149.07i	0.836488	+	0.836488i
$243$	1561.99	−	3450.95i	0.412353	−	0.911024i
$244$	−2035.92	−	1175.44i	−0.534164	−	0.308400i
$245$	−5429.55	+	1454.84i	−1.41584	+	0.379374i
$246$	−5061.28	−	2790.59i	−1.31177	−	0.723257i
$247$	−2524.55	+	4029.38i	−0.650337	+	1.03799i
$248$			1285.12i			0.329053i
$249$	3321.20	+	820.102i	0.845270	+	0.208722i
$250$	−1350.56	+	2339.24i	−0.341668	+	0.591786i
$251$	452.836	+	784.334i	0.113875	+	0.197238i	0.917330	−	0.398129i	$-0.130340\pi$
$251$	452.836	+	784.334i	0.113875	+	0.197238i	−0.803454	+	0.595367i	$0.797007\pi$
$252$	−101.653	+	449.565i	−0.0254108	+	0.112381i
$253$	−402.063	+	1500.52i	−0.0999109	+	0.372873i
$254$	690.812	−	2578.14i	0.170651	−	0.636879i
$255$	−855.672	−	2958.84i	−0.210134	−	0.726625i
$256$	−2523.95	−	4371.62i	−0.616200	−	1.06729i
$257$	−1243.46	+	2153.73i	−0.301809	+	0.522748i	−0.976546	−	0.215310i	$-0.930924\pi$
$257$	−1243.46	+	2153.73i	−0.301809	+	0.522748i	0.674737	+	0.738058i	$0.264257\pi$
$258$	2073.89	−	8398.72i	0.500445	−	2.02667i
$259$		−	589.747i		−	0.141487i
$260$	−1845.14	+	2944.98i	−0.440118	+	0.702462i
$261$	−1598.40	+	1008.86i	−0.379074	+	0.239260i
$262$	1875.79	−	502.616i	0.442315	−	0.118518i
$263$	−2758.53	−	1592.64i	−0.646762	−	0.373408i	0.140452	−	0.990087i	$-0.455144\pi$
$263$	−2758.53	−	1592.64i	−0.646762	−	0.373408i	−0.787215	+	0.616679i	$0.788478\pi$
$264$	−10.4305	−	529.056i	−0.00243163	−	0.123338i
$265$	−4879.30	−	4879.30i	−1.13107	−	1.13107i
$266$	−1359.59	−	364.301i	−0.313390	−	0.0839725i
$267$	−1995.64	−	1918.47i	−0.457419	−	0.439732i
$268$	−1550.90	+	1550.90i	−0.353494	+	0.353494i
$269$	−4084.79	+	2358.36i	−0.925852	+	0.534541i	−0.885497	−	0.464644i	$-0.846182\pi$
$269$	−4084.79	+	2358.36i	−0.925852	+	0.534541i	−0.0403548	+	0.999185i	$0.512849\pi$
$270$	7559.03	+	3787.20i	1.70381	+	0.853636i
$271$	678.212	+	2531.12i	0.152024	+	0.567361i	0.999342	+	0.0362748i	$0.0115492\pi$
$271$	678.212	+	2531.12i	0.152024	+	0.567361i	−0.847318	+	0.531086i	$0.821784\pi$
$272$	2758.29			0.614875
$273$	15.7823	−	962.725i	0.00349885	−	0.213431i
$274$	2546.31			0.561416
$275$	−346.379	−	1292.70i	−0.0759543	−	0.283465i
$276$	3786.05	−	2286.54i	0.825700	−	0.498673i
$277$	1856.32	−	1071.75i	0.402655	−	0.232473i	−0.284974	−	0.958535i	$-0.591985\pi$
$277$	1856.32	−	1071.75i	0.402655	−	0.232473i	0.687629	+	0.726062i	$0.258652\pi$
$278$	−7057.05	+	7057.05i	−1.52249	+	1.52249i
$279$	2564.22	−	796.649i	0.550236	−	0.170947i
$280$	847.288	+	227.030i	0.180840	+	0.0484559i
$281$	4186.02	+	4186.02i	0.888673	+	0.888673i	0.994396	−	0.105723i	$-0.0337155\pi$
$281$	4186.02	+	4186.02i	0.888673	+	0.888673i	−0.105723	+	0.994396i	$0.533716\pi$
$282$	−3887.73	+	76.6474i	−0.820960	+	0.0161854i
$283$	926.666	+	535.011i	0.194645	+	0.112378i	0.594155	−	0.804350i	$-0.297486\pi$
$283$	926.666	+	535.011i	0.194645	+	0.112378i	−0.399510	+	0.916729i	$0.630820\pi$
$284$	597.143	−	160.004i	0.124767	−	0.0334313i
$285$	−4370.05	+	7925.95i	−0.908278	+	1.64734i
$286$	−290.119	−	1263.55i	−0.0599828	−	0.261242i
$287$			1252.88i			0.257683i
$288$	−3244.23	+	3510.68i	−0.663777	+	0.718294i
$289$	1860.60	−	3222.66i	0.378711	−	0.655946i
$290$	−2109.38	−	3653.55i	−0.427128	−	0.739807i
$291$	8441.51	−	2441.22i	1.70052	−	0.491776i
$292$	−117.878	+	439.926i	−0.0236242	+	0.0881668i
$293$	100.539	−	375.215i	0.0200462	−	0.0748133i	−0.955178	−	0.296032i	$-0.904337\pi$
$293$	100.539	−	375.215i	0.0200462	−	0.0748133i	0.975224	+	0.221218i	$0.0710033\pi$
$294$	−5735.26	+	1658.59i	−1.13771	+	0.329017i
$295$	4852.78	+	8405.26i	0.957762	+	1.65889i
$296$	963.863	−	1669.46i	0.189268	−	0.327822i
$297$	−1049.17	+	348.775i	−0.204980	+	0.0681414i
$298$			4271.84i			0.830406i
$299$	−6764.94	+	6293.27i	−1.30845	+	1.21722i
$300$	−1839.78	+	3336.80i	−0.354065	+	0.642168i
$301$	−1811.42	+	485.369i	−0.346872	+	0.0929441i
$302$	−129.712	−	74.8894i	−0.0247156	−	0.0142695i
$303$	2340.97	−	46.1527i	0.443845	−	0.00875050i
$304$	−5731.30	−	5731.30i	−1.08129	−	1.08129i
$305$	9029.42	+	2419.43i	1.69516	+	0.454216i
$306$	−970.596	−	3124.12i	−0.181324	−	0.583640i
$307$	−1020.49	+	1020.49i	−0.189716	+	0.189716i	−0.795573	−	0.605857i	$-0.792830\pi$
$307$	−1020.49	+	1020.49i	−0.189716	+	0.189716i	0.605857	+	0.795573i	$0.292830\pi$
$308$	116.506	−	67.2647i	0.0215537	−	0.0124440i
$309$	876.683	−	529.464i	0.161400	−	0.0974762i
$310$	1551.13	+	5788.90i	0.284188	+	1.06060i
$311$	2120.90			0.386705			0.193353	−	0.981129i	$-0.438064\pi$
$311$	2120.90			0.386705			0.193353	+	0.981129i	$0.438064\pi$
$312$	1618.12	−	2699.50i	0.293616	−	0.489836i
$313$	9662.69			1.74494			0.872472	−	0.488665i	$-0.162516\pi$
$313$	9662.69			1.74494			0.872472	+	0.488665i	$0.162516\pi$
$314$	−418.917	−	1563.42i	−0.0752893	−	0.280983i
$315$	−72.2387	−	1831.34i	−0.0129212	−	0.327570i
$316$	1277.47	−	737.549i	0.227416	−	0.131299i
$317$	−491.570	+	491.570i	−0.0870956	+	0.0870956i	−0.749312	−	0.662217i	$-0.769616\pi$
$317$	−491.570	+	491.570i	−0.0870956	+	0.0870956i	0.662217	+	0.749312i	$0.269616\pi$
$318$	−5283.54	−	5079.24i	−0.931718	−	0.895691i
$319$	532.890	+	142.787i	0.0935301	+	0.0250613i
$320$	216.367	+	216.367i	0.0377978	+	0.0377978i
$321$	49.1757	+	2494.30i	0.00855053	+	0.433702i
$322$	−2368.66	−	1367.55i	−0.409939	−	0.236678i
$323$	3382.76	−	906.408i	0.582730	−	0.156142i
$324$	2841.67	+	1354.32i	0.487254	+	0.232222i
$325$	2336.38	−	7609.33i	0.398765	−	1.29874i
$326$		−	5561.37i		−	0.944833i
$327$	1008.37	−	4083.62i	0.170528	−	0.690595i
$328$	−2047.66	+	3546.66i	−0.344705	+	0.597047i
$329$	421.464	+	729.997i	0.0706263	+	0.122328i
$330$	−685.551	−	2370.57i	−0.114359	−	0.395442i
$331$	1112.92	−	4153.46i	0.184808	−	0.689713i	−0.809864	−	0.586618i	$-0.800459\pi$
$331$	1112.92	−	4153.46i	0.184808	−	0.689713i	0.994672	−	0.103095i	$-0.0328744\pi$
$332$	−735.791	+	2746.01i	−0.121632	+	0.453936i
$333$	−3928.60	−	888.309i	−0.646504	−	0.146183i
$334$	−3893.38	−	6743.54i	−0.637834	−	1.10476i
$335$	4360.70	−	7552.95i	0.711195	−	1.23183i
$336$	1593.43	+	393.465i	0.258717	+	0.0638848i
$337$		−	671.879i		−	0.108604i	−0.998525	−	0.0543021i	$-0.982707\pi$
$337$		−	671.879i		−	0.108604i	0.998525	−	0.0543021i	$-0.0172934\pi$
$338$	2527.87	−	7284.71i	0.406798	−	1.17230i
$339$	−5823.59	−	3210.89i	−0.933020	−	0.514429i
$340$	2472.39	−	662.474i	0.394365	−	0.105670i
$341$	−678.722	−	391.860i	−0.107785	−	0.0622299i
$342$	−4474.68	+	8508.17i	−0.707494	+	1.34523i
$343$	1873.98	+	1873.98i	0.295001	+	0.295001i
$344$	−5921.06	−	1586.54i	−0.928029	−	0.248665i
$345$	−12188.5	+	12678.8i	−1.90205	+	1.97856i
$346$	4119.86	−	4119.86i	0.640130	−	0.640130i
$347$	−4427.93	+	2556.47i	−0.685026	+	0.395500i	−0.801746	−	0.597665i	$-0.796095\pi$
$347$	−4427.93	+	2556.47i	−0.685026	+	0.395500i	0.116720	+	0.993165i	$0.462762\pi$
$348$	−812.037	−	1344.57i	−0.125085	−	0.207116i
$349$	867.927	+	3239.15i	0.133121	+	0.496813i	0.999999	−	0.00170778i	$-0.000543604\pi$
$349$	867.927	+	3239.15i	0.133121	+	0.496813i	−0.866878	+	0.498520i	$0.833877\pi$
$350$	2356.30			0.359855
$351$	−6389.43	−	1555.24i	−0.971631	−	0.236504i
$352$	1395.21			0.211264
$353$	1172.37	+	4375.36i	0.176768	+	0.659708i	0.996244	+	0.0865939i	$0.0275983\pi$
$353$	1172.37	+	4375.36i	0.176768	+	0.659708i	−0.819475	+	0.573114i	$0.805735\pi$
$354$	5329.21	+	8824.07i	0.800124	+	1.32484i
$355$	−2128.89	+	1229.11i	−0.318280	+	0.183759i
$356$	1626.66	−	1626.66i	0.242171	−	0.242171i
$357$	−491.472	+	511.240i	−0.0728612	+	0.0757919i
$358$	−1280.86	−	343.206i	−0.189094	−	0.0506676i
$359$	259.074	+	259.074i	0.0380875	+	0.0380875i	0.725894	−	0.687807i	$-0.241426\pi$
$359$	259.074	+	259.074i	0.0380875	+	0.0380875i	−0.687807	+	0.725894i	$0.741426\pi$
$360$	2788.60	−	5302.25i	0.408255	−	0.776259i
$361$	−2972.16	−	1715.98i	−0.433323	−	0.250179i
$362$	10500.3	−	2813.55i	1.52454	−	0.408499i
$363$	−5773.90	−	3183.49i	−0.834852	−	0.460303i
$364$	799.629	+	28.8828i	0.115143	+	0.00415898i
$365$		−	1811.02i		−	0.259707i
$366$	9639.12	+	2380.18i	1.37663	+	0.339930i
$367$	3092.81	−	5356.90i	0.439900	−	0.761929i	−0.557782	−	0.829988i	$-0.688347\pi$
$367$	3092.81	−	5356.90i	0.439900	−	0.761929i	0.997681	+	0.0680592i	$0.0216807\pi$
$368$	−7874.93	−	13639.8i	−1.11551	−	1.93213i
$369$	8346.06	+	1887.16i	1.17745	+	0.266237i
$370$	2326.75	−	8683.55i	0.326924	−	1.22010i
$371$	−411.199	+	1534.62i	−0.0575428	+	0.214753i
$372$	619.898	+	2143.55i	0.0863985	+	0.298758i
$373$	2844.30	+	4926.47i	0.394832	+	0.683869i	0.993080	−	0.117442i	$-0.0374695\pi$
$373$	2844.30	+	4926.47i	0.394832	+	0.683869i	−0.598248	+	0.801311i	$0.704136\pi$
$374$	−477.422	+	826.919i	−0.0660078	+	0.114329i
$375$	958.682	−	3882.41i	0.132016	−	0.534632i
$376$			2755.31i			0.377910i
$377$	2234.97	+	2402.48i	0.305324	+	0.328207i
$378$	−115.052	−	1943.22i	−0.0156551	−	0.264414i
$379$	−8959.05	+	2400.57i	−1.21424	+	0.325354i	−0.808423	−	0.588602i	$-0.799678\pi$
$379$	−8959.05	+	2400.57i	−1.21424	+	0.325354i	−0.405813	+	0.913956i	$0.633012\pi$
$380$	−6513.75	−	3760.72i	−0.879338	−	0.507686i
$381$	77.8916	+	3950.84i	0.0104738	+	0.531253i
$382$	9125.50	+	9125.50i	1.22225	+	1.22225i
$383$	−9166.11	−	2456.05i	−1.22289	−	0.327672i	−0.411082	−	0.911598i	$-0.634849\pi$
$383$	−9166.11	−	2456.05i	−1.22289	−	0.327672i	−0.811806	+	0.583927i	$0.801516\pi$
$384$	5539.83	+	5325.62i	0.736207	+	0.707739i
$385$	−378.259	+	378.259i	−0.0500724	+	0.0500724i
$386$	−5219.26	+	3013.34i	−0.688221	+	0.397345i
$387$	504.822	+	12797.9i	0.0663089	+	1.68101i
$388$	1890.03	+	7053.68i	0.247298	+	0.922929i
$389$	12465.5			1.62475			0.812374	−	0.583137i	$-0.198175\pi$
$389$	12465.5			1.62475			0.812374	+	0.583137i	$0.198175\pi$
$390$	4030.66	−	14113.1i	0.523334	−	1.83242i
$391$	6805.13			0.880180
$392$	1094.91	+	4086.28i	0.141075	+	0.526500i
$393$	−2461.07	+	1486.34i	−0.315890	+	0.190778i
$394$	−12333.3	+	7120.66i	−1.57702	+	0.910491i
$395$	−4147.56	+	4147.56i	−0.528320	+	0.528320i
$396$	−272.597	−	877.423i	−0.0345921	−	0.111344i
$397$	−8807.73	−	2360.02i	−1.11347	−	0.298353i	−0.345231	−	0.938518i	$-0.612200\pi$
$397$	−8807.73	−	2360.02i	−1.11347	−	0.298353i	−0.768238	+	0.640164i	$0.778866\pi$
$398$	1085.36	+	1085.36i	0.136694	+	0.136694i
$399$	2083.48	−	41.0762i	0.261415	−	0.00515384i
$400$	11750.7	+	6784.29i	1.46884	+	0.848036i
$401$	−7739.54	+	2073.80i	−0.963826	+	0.258256i	−0.706219	−	0.707993i	$-0.749601\pi$
$401$	−7739.54	+	2073.80i	−0.963826	+	0.258256i	−0.257607	+	0.966250i	$0.582934\pi$
$402$	4472.56	−	8111.88i	0.554903	−	1.00643i
$403$	−2183.46	−	4118.38i	−0.269890	−	0.509060i
$404$			1945.77i			0.239618i
$405$	−12308.3	−	2277.25i	−1.51014	−	0.279402i
$406$	−485.667	+	841.200i	−0.0593676	+	0.102828i
$407$	587.804	+	1018.11i	0.0715881	+	0.123994i
$408$	−2226.82	+	643.978i	−0.270206	+	0.0781413i
$409$	1991.30	−	7431.64i	0.240742	−	0.898462i	−0.734734	−	0.678356i	$-0.762693\pi$
$409$	1991.30	−	7431.64i	0.240742	−	0.898462i	0.975476	−	0.220107i	$-0.0706405\pi$
$410$	−4943.03	+	18447.6i	−0.595412	+	2.22211i
$411$	−3621.43	+	1047.29i	−0.434627	+	0.125691i
$412$	425.548	+	737.071i	0.0508866	+	0.0881381i
$413$	1117.31	−	1935.24i	0.133122	−	0.230574i
$414$	−12677.7	+	13719.0i	−1.50502	+	1.62862i
$415$		−	11304.3i		−	1.33713i
$416$	7032.15	+	4405.90i	0.828797	+	0.519271i
$417$	7134.18	−	12939.3i	0.837800	−	1.51952i
$418$	2710.22	−	726.201i	0.317132	−	0.0849752i
$419$	9959.13	+	5749.91i	1.16118	+	0.670409i	0.951587	−	0.307379i	$-0.0994521\pi$
$419$	9959.13	+	5749.91i	1.16118	+	0.670409i	0.209595	+	0.977788i	$0.432785\pi$
$420$	1522.77	−	30.0217i	0.176913	−	0.00348788i
$421$	3360.79	+	3360.79i	0.389061	+	0.389061i	0.874353	−	0.485291i	$-0.161286\pi$
$421$	3360.79	+	3360.79i	0.389061	+	0.389061i	−0.485291	+	0.874353i	$0.661286\pi$
$422$	9621.85	+	2578.17i	1.10992	+	0.297401i
$423$	5497.71	−	1708.02i	0.631933	−	0.196328i
$424$	−3672.15	+	3672.15i	−0.420603	+	0.420603i
$425$	−5077.20	+	2931.33i	−0.579484	+	0.334565i
$426$	−2234.96	+	1349.78i	−0.254188	+	0.153514i
$427$	−557.053	−	2078.95i	−0.0631327	−	0.235614i
$428$	−2073.22			−0.234142
$429$	932.308	+	1677.73i	0.104924	+	0.188814i
$430$	−28586.7			−3.20598
$431$	542.052	+	2022.97i	0.0605794	+	0.226086i	0.989578	−	0.143998i	$-0.0459958\pi$
$431$	542.052	+	2022.97i	0.0605794	+	0.226086i	−0.928999	+	0.370083i	$0.879329\pi$
$432$	5021.19	−	10022.0i	0.559218	−	1.11617i
$433$	5424.28	−	3131.71i	0.602019	−	0.347576i	−0.167817	−	0.985818i	$-0.553672\pi$
$433$	5424.28	−	3131.71i	0.602019	−	0.347576i	0.769835	+	0.638243i	$0.220338\pi$
$434$	975.710	−	975.710i	0.107916	−	0.107916i
$435$	4502.71	+	4328.60i	0.496296	+	0.477105i
$436$	3376.39	+	904.700i	0.370871	+	0.0993745i
$437$	−14140.0	−	14140.0i	−1.54784	−	1.54784i
$438$	−37.9152	−	1923.15i	−0.00413621	−	0.209798i
$439$	661.172	+	381.728i	0.0718816	+	0.0415008i	0.535510	−	0.844529i	$-0.320119\pi$
$439$	661.172	+	381.728i	0.0718816	+	0.0415008i	−0.463628	+	0.886030i	$0.653453\pi$
$440$	−1688.99	+	452.565i	−0.182999	+	0.0490345i
$441$	7474.67	−	4717.79i	0.807113	−	0.509426i
$442$	−5017.62	+	2660.21i	−0.539964	+	0.286275i
$443$		−	4069.14i		−	0.436412i	−0.975903	−	0.218206i	$-0.929980\pi$
$443$		−	4069.14i		−	0.436412i	0.975903	−	0.218206i	$-0.0700204\pi$
$444$	802.411	−	3249.56i	0.0857675	−	0.347336i
$445$	−4573.72	+	7921.92i	−0.487225	+	0.843899i
$446$	8251.39	+	14291.8i	0.876042	+	1.51735i
$447$	−1757.00	−	6075.53i	−0.185913	−	0.642870i
$448$	18.2342	−	68.0508i	0.00192295	−	0.00717656i
$449$	2907.56	−	10851.2i	0.305604	−	1.14053i	−0.626820	−	0.779164i	$-0.715644\pi$
$449$	2907.56	−	10851.2i	0.305604	−	1.14053i	0.932424	−	0.361366i	$-0.117690\pi$
$450$	3549.19	−	15696.5i	0.371801	−	1.64431i
$451$	−1248.75	−	2162.90i	−0.130380	−	0.225825i
$452$	2763.18	−	4785.97i	0.287543	−	0.498038i
$453$	215.282	+	53.1595i	0.0223286	+	0.00551358i
$454$			1696.12i			0.175336i
$455$	−3101.01	+	712.012i	−0.319511	+	0.0733618i
$456$	5965.06	+	3288.89i	0.612587	+	0.337756i
$457$	7290.21	−	1953.41i	0.746218	−	0.199948i	0.134378	−	0.990930i	$-0.457096\pi$
$457$	7290.21	−	1953.41i	0.746218	−	0.199948i	0.611840	+	0.790982i	$0.290430\pi$
$458$	−14665.1	−	8466.88i	−1.49619	−	0.863824i
$459$	2665.35	+	4044.00i	0.271041	+	0.411237i
$460$	−10334.6	−	10334.6i	−1.04751	−	1.04751i
$461$	13023.1	+	3489.53i	1.31572	+	0.352546i	0.847373	−	0.530998i	$-0.178183\pi$
$461$	13023.1	+	3489.53i	1.31572	+	0.352546i	0.468347	+	0.883544i	$0.344850\pi$
$462$	−393.760	+	409.598i	−0.0396523	+	0.0412472i
$463$	−11452.3	+	11452.3i	−1.14953	+	1.14953i	−0.162888	+	0.986645i	$0.552081\pi$
$463$	−11452.3	+	11452.3i	−1.14953	+	1.14953i	−0.986645	+	0.162888i	$0.947919\pi$
$464$	−4844.00	+	2796.68i	−0.484648	+	0.279812i
$465$	−4587.02	−	7595.16i	−0.457458	−	0.757456i
$466$	−3251.38	−	12134.3i	−0.323213	−	1.20625i
$467$	1285.62			0.127390			0.0636951	−	0.997969i	$-0.479711\pi$
$467$	1285.62			0.127390			0.0636951	+	0.997969i	$0.479711\pi$
$468$	1396.85	−	5283.23i	0.137969	−	0.521832i
$469$	−2008.03			−0.197702
$470$	3325.64	+	12411.4i	0.326383	+	1.21808i
$471$	1238.82	+	2051.24i	0.121193	+	0.200671i
$472$	6325.79	−	3652.20i	0.616882	−	0.356157i
$473$	2643.37	−	2643.37i	0.256960	−	0.256960i
$474$	−4317.52	+	4491.19i	−0.418376	+	0.435205i
$475$	16640.5	+	4458.80i	1.60741	+	0.430703i
$476$	−416.717	−	416.717i	−0.0401265	−	0.0401265i
$477$	9603.48	+	5050.73i	0.921830	+	0.484816i
$478$	−8073.87	−	4661.45i	−0.772573	−	0.446045i
$479$	−447.867	+	120.006i	−0.0427214	+	0.0114472i	−0.280116	−	0.959966i	$-0.590373\pi$
$479$	−447.867	+	120.006i	−0.0427214	+	0.0114472i	0.237395	+	0.971413i	$0.423706\pi$
$480$	13832.5	+	7626.70i	1.31535	+	0.725228i
$481$	−252.397	+	6987.69i	−0.0239258	+	0.662393i
$482$		−	8898.64i		−	0.840916i
$483$	3931.24	+	970.740i	0.370347	+	0.0914497i
$484$	2739.61	−	4745.14i	0.257289	−	0.445637i
$485$	−14518.7	−	25147.2i	−1.35930	−	2.35438i
$486$	−13118.1	−	2160.56i	−1.22438	−	0.201657i
$487$	−4042.62	+	15087.3i	−0.376157	+	1.40384i	0.475489	+	0.879722i	$0.342271\pi$
$487$	−4042.62	+	15087.3i	−0.376157	+	1.40384i	−0.851646	+	0.524117i	$0.824396\pi$
$488$	1820.86	−	6795.53i	0.168906	−	0.630368i
$489$	2287.37	+	7909.53i	0.211531	+	0.731454i
$490$	9864.21	+	17085.3i	0.909428	+	1.57517i
$491$	3841.67	−	6653.97i	0.353100	−	0.611588i	−0.633691	−	0.773587i	$-0.718461\pi$
$491$	3841.67	−	6653.97i	0.353100	−	0.611588i	0.986791	+	0.161999i	$0.0517941\pi$
$492$	−1704.67	+	6903.47i	−0.156204	+	0.632587i
$493$		−	2416.76i		−	0.220781i
$494$	15953.3	+	4898.33i	1.45299	+	0.446126i
$495$	1950.02	+	3089.53i	0.177064	+	0.280534i
$496$	7675.11	−	2056.54i	0.694803	−	0.186172i
$497$	490.158	+	282.993i	0.0442386	+	0.0255412i
$498$	−236.666	−	12004.2i	−0.0212957	−	1.08017i
$499$	−7453.43	−	7453.43i	−0.668660	−	0.668660i	0.288746	−	0.957406i	$-0.406762\pi$
$499$	−7453.43	−	7453.43i	−0.668660	−	0.668660i	−0.957406	+	0.288746i	$0.906762\pi$
$500$	3210.03	+	860.124i	0.287114	+	0.0769319i
$501$	8310.88	+	7989.51i	0.741123	+	0.712465i
$502$	2247.64	−	2247.64i	0.199835	−	0.199835i
$503$	5226.31	−	3017.41i	0.463279	−	0.267474i	−0.250143	−	0.968209i	$-0.580478\pi$
$503$	5226.31	−	3017.41i	0.463279	−	0.267474i	0.713422	+	0.700735i	$0.247144\pi$
$504$	−1378.27	+	54.3668i	−0.121811	+	0.00480494i
$505$	−2002.51	−	7473.46i	−0.176456	−	0.658544i
$506$	5452.17			0.479009
$507$	−599.020	+	11400.2i	−0.0524722	+	0.998622i
$508$	−3283.86			−0.286806
$509$	2423.31	+	9043.90i	0.211024	+	0.787552i	0.987529	+	0.157440i	$0.0503242\pi$
$509$	2423.31	+	9043.90i	0.211024	+	0.787552i	−0.776505	+	0.630112i	$0.783009\pi$
$510$	−9253.55	+	5588.59i	−0.803439	+	0.485229i
$511$	−361.108	+	208.486i	−0.0312612	+	0.0180487i
$512$	−4161.76	+	4161.76i	−0.359230	+	0.359230i
$513$	2864.62	−	13941.0i	0.246542	−	1.19982i
$514$	8430.96	+	2259.07i	0.723489	+	0.193858i
$515$	−2393.05	−	2393.05i	−0.204758	−	0.204758i
$516$	−10641.5	+	209.799i	−0.907878	+	0.0178990i
$517$	−1455.18	−	840.151i	−0.123789	−	0.0714696i
$518$	−1999.31	+	535.715i	−0.169585	+	0.0454401i
$519$	−4164.89	+	7553.86i	−0.352251	+	0.638878i
$520$	−9942.04	−	3052.62i	−0.838437	−	0.257435i
$521$			12006.6i			1.00963i	0.863228	+	0.504814i	$0.168439\pi$
$521$			12006.6i			1.00963i	−0.863228	+	0.504814i	$0.831561\pi$
$522$	4872.12	+	4502.33i	0.408519	+	0.377513i
$523$	−733.643	+	1270.71i	−0.0613384	+	0.106241i	−0.895064	−	0.445938i	$-0.852870\pi$
$523$	−733.643	+	1270.71i	−0.0613384	+	0.106241i	0.833726	+	0.552179i	$0.186204\pi$
$524$	−1194.62	−	2069.15i	−0.0995941	−	0.172502i
$525$	−3351.19	+	969.137i	−0.278586	+	0.0805650i
$526$	−2893.45	+	10798.5i	−0.239849	+	0.895127i
$527$	−888.580	+	3316.22i	−0.0734481	+	0.274112i
$528$	−3142.98	+	908.926i	−0.259055	+	0.0749165i
$529$	−13345.2	−	23114.5i	−1.09683	−	1.89977i
$530$	−12109.2	+	20973.7i	−0.992431	+	1.71894i
$531$	−11208.7	−	10357.9i	−0.916034	−	0.846509i
$532$			1731.75i			0.141129i
$533$	536.200	−	14844.9i	0.0435749	−	1.20639i
$534$	−4691.05	+	8508.15i	−0.380153	+	0.689483i
$535$	7962.98	−	2133.67i	0.643495	−	0.172424i
$536$	−5684.34	−	3281.86i	−0.458071	−	0.264468i
$537$	1962.84	−	38.6977i	0.157733	−	0.00310974i
$538$	11705.7	+	11705.7i	0.938043	+	0.938043i
$539$	−2491.98	−	667.725i	−0.199141	−	0.0533598i
$540$	2093.69	−	10189.2i	0.166848	−	0.811984i
$541$	1953.57	−	1953.57i	0.155250	−	0.155250i	−0.625208	−	0.780458i	$-0.714986\pi$
$541$	1953.57	−	1953.57i	0.155250	−	0.155250i	0.780458	+	0.625208i	$0.214986\pi$
$542$	7964.74	−	4598.45i	0.631209	−	0.364428i
$543$	−13776.6	+	8320.25i	−1.08879	+	0.657562i
$544$	−1581.88	−	5903.67i	−0.124674	−	0.465290i
$545$	−13899.4			−1.09245
$546$	−3278.10	+	821.018i	−0.256941	+	0.0643522i
$547$	8662.27			0.677097			0.338548	−	0.940949i	$-0.390064\pi$
$547$	8662.27			0.677097			0.338548	+	0.940949i	$0.390064\pi$
$548$	−810.827	−	3026.05i	−0.0632058	−	0.235887i
$549$	−14688.0	+	579.379i	−1.14184	+	0.0450406i
$550$	−4067.78	+	2348.53i	−0.315365	+	0.182076i
$551$	−5021.64	+	5021.64i	−0.388256	+	0.388256i
$552$	9542.05	+	9173.08i	0.735755	+	0.707305i
$553$	1304.47	+	349.533i	0.100311	+	0.0268782i
$554$	−5319.61	−	5319.61i	−0.407957	−	0.407957i
$555$	262.350	+	13307.0i	0.0200651	+	1.01775i
$556$	10633.8	+	6139.44i	0.811106	+	0.468292i
$557$	−22323.8	+	5981.64i	−1.69819	+	0.455027i	−0.972482	−	0.232980i	$-0.925152\pi$
$557$	−22323.8	+	5981.64i	−1.69819	+	0.455027i	−0.725704	+	0.688007i	$0.758486\pi$
$558$	−5030.03	−	7969.37i	−0.381610	−	0.604606i
$559$	21670.6	−	4975.71i	1.63966	−	0.376476i
$560$		−	5423.56i		−	0.409263i
$561$	338.893	−	1372.43i	0.0255046	−	0.103287i
$562$	10388.6	−	17993.6i	0.779747	−	1.35056i
$563$	10615.8	+	18387.2i	0.794680	+	1.37643i	0.923042	+	0.384698i	$0.125694\pi$
$563$	10615.8	+	18387.2i	0.794680	+	1.37643i	−0.128363	+	0.991727i	$0.540972\pi$
$564$	1329.07	+	4595.79i	0.0992266	+	0.343117i
$565$	−5687.52	+	21226.1i	−0.423497	+	1.58051i
$566$	971.987	−	3627.51i	0.0721832	−	0.269391i
$567$	962.870	+	2716.38i	0.0713170	+	0.201194i
$568$	925.029	+	1602.20i	0.0683334	+	0.118357i
$569$	4933.98	−	8545.90i	0.363520	−	0.629636i	−0.625017	−	0.780611i	$-0.714908\pi$
$569$	4933.98	−	8545.90i	0.363520	−	0.629636i	0.988538	+	0.150975i	$0.0482413\pi$
$570$	30839.6	+	7615.22i	2.26619	+	0.559590i
$571$		−	7247.66i		−	0.531182i	−0.964086	−	0.265591i	$-0.914433\pi$
$571$		−	7247.66i		−	0.531182i	0.964086	−	0.265591i	$-0.0855671\pi$
$572$	−1409.22	+	747.133i	−0.103012	+	0.0546140i
$573$	−16731.8	−	9225.24i	−1.21986	−	0.672583i
$574$	4247.42	−	1138.09i	0.308857	−	0.0827579i
$575$	28990.9	+	16737.9i	2.10261	+	1.21395i
$576$	−425.856	−	223.969i	−0.0308055	−	0.0162015i
$577$	4490.73	+	4490.73i	0.324006	+	0.324006i	0.850302	−	0.526296i	$-0.176419\pi$
$577$	4490.73	+	4490.73i	0.324006	+	0.324006i	−0.526296	+	0.850302i	$0.676419\pi$
$578$	−12615.4	−	3380.28i	−0.907837	−	0.243254i
$579$	6183.60	−	6432.33i	0.443837	−	0.461690i
$580$	−3670.21	+	3670.21i	−0.262754	+	0.262754i
$581$	−2254.03	+	1301.36i	−0.160952	+	0.0929255i
$582$	−15944.1	−	26400.2i	−1.13558	−	1.88028i
$583$	−819.689	−	3059.12i	−0.0582299	−	0.217317i
$584$	−1362.97			−0.0965756
$585$	72.1610	+	21729.8i	0.00509999	+	1.53576i
$586$	−1363.35			−0.0961085
$587$	−3555.07	−	13267.7i	−0.249972	−	0.932908i	−0.970819	−	0.239814i	$-0.922914\pi$
$587$	−3555.07	−	13267.7i	−0.249972	−	0.932908i	0.720847	−	0.693094i	$-0.243753\pi$
$588$	3797.37	+	6287.67i	0.266328	+	0.440985i
$589$	8736.93	−	5044.27i	0.611203	−	0.352878i
$590$	24086.7	−	24086.7i	1.68074	−	1.68074i
$591$	14612.1	−	15199.9i	1.01703	−	1.05793i
$592$	−11512.9	−	3084.88i	−0.799288	−	0.214168i
$593$	9349.96	+	9349.96i	0.647482	+	0.647482i	0.952384	−	0.304902i	$-0.0986236\pi$
$593$	9349.96	+	9349.96i	0.647482	+	0.647482i	−0.304902	+	0.952384i	$0.598624\pi$
$594$	2135.44	+	3239.99i	0.147505	+	0.223802i
$595$	2029.43	+	1171.69i	0.139830	+	0.0807306i
$596$	5076.68	−	1360.29i	0.348908	−	0.0934895i
$597$	−1990.04	−	1097.23i	−0.136427	−	0.0752203i
$598$	27480.1	+	17217.3i	1.87917	+	1.17737i
$599$			3874.90i			0.264314i	0.991229	+	0.132157i	$0.0421903\pi$
$599$			3874.90i			0.264314i	−0.991229	+	0.132157i	$0.957810\pi$
$600$	−11070.5	−	2733.63i	−0.753252	−	0.186000i
$601$	−11379.1	+	19709.2i	−0.772320	+	1.33770i	0.163969	+	0.986466i	$0.447570\pi$
$601$	−11379.1	+	19709.2i	−0.772320	+	1.33770i	−0.936289	+	0.351232i	$0.885763\pi$
$602$	3290.92	+	5700.04i	0.222804	+	0.385908i
$603$	−3024.61	+	13376.5i	−0.204264	+	0.903371i
$604$	−47.6944	+	177.998i	−0.00321301	+	0.0119911i
$605$	−5639.00	+	21045.0i	−0.378939	+	1.41422i
$606$	−2282.95	−	7894.25i	−0.153034	−	0.529178i
$607$	−284.462	−	492.703i	−0.0190214	−	0.0329460i	0.856358	−	0.516383i	$-0.172722\pi$
$607$	−284.462	−	492.703i	−0.0190214	−	0.0329460i	−0.875379	+	0.483437i	$0.839388\pi$
$608$	−8979.99	+	15553.8i	−0.598992	+	1.03748i
$609$	344.746	−	1396.13i	0.0229389	−	0.0928967i
$610$		−	32808.6i		−	2.17768i
$611$	−4681.35	−	8829.84i	−0.309963	−	0.584643i
$612$	−3403.65	+	2148.28i	−0.224811	+	0.141894i
$613$	−25978.0	+	6960.77i	−1.71165	+	0.458634i	−0.975827	−	0.218543i	$-0.929870\pi$
$613$	−25978.0	+	6960.77i	−1.71165	+	0.458634i	−0.735820	+	0.677178i	$0.763203\pi$
$614$	4386.60	+	2532.61i	0.288321	+	0.166462i
$615$	−557.345	−	28269.8i	−0.0365436	−	1.85357i
$616$	284.678	+	284.678i	0.0186201	+	0.0186201i
$617$	−5424.03	−	1453.36i	−0.353911	−	0.0948302i	0.0774833	−	0.996994i	$-0.475312\pi$
$617$	−5424.03	−	1453.36i	−0.353911	−	0.0948302i	−0.431394	+	0.902163i	$0.641978\pi$
$618$	−2591.31	−	2491.11i	−0.168670	−	0.162147i
$619$	1641.77	−	1641.77i	0.106605	−	0.106605i	−0.651792	−	0.758397i	$-0.725983\pi$
$619$	1641.77	−	1641.77i	0.106605	−	0.106605i	0.758397	+	0.651792i	$0.225983\pi$
$620$	6385.63	−	3686.75i	0.413634	−	0.238812i
$621$	12388.0	−	24725.8i	0.800508	−	1.59777i
$622$	−1926.59	−	7190.12i	−0.124195	−	0.463501i
$623$	2106.12			0.135441
$624$	−18711.6	−	5343.98i	−1.20042	−	0.342837i
$625$	8013.22			0.512846
$626$	−8777.40	−	32757.7i	−0.560408	−	2.09147i
$627$	−3555.86	+	2147.53i	−0.226487	+	0.136785i
$628$	−1724.58	+	995.686i	−0.109583	+	0.0632678i
$629$	3641.55	−	3641.55i	0.230840	−	0.230840i
$630$	−6142.86	+	1908.46i	−0.388472	+	0.120690i
$631$	−15867.0	−	4251.56i	−1.00104	−	0.268228i	−0.279159	−	0.960245i	$-0.590056\pi$
$631$	−15867.0	−	4251.56i	−1.00104	−	0.268228i	−0.721881	+	0.692017i	$0.756722\pi$
$632$	3121.45	+	3121.45i	0.196463	+	0.196463i
$633$	−14744.9	+	290.698i	−0.925838	+	0.0182531i
$634$	2113.02	+	1219.95i	0.132364	+	0.0764202i
$635$	12612.9	−	3379.62i	0.788233	−	0.211206i
$636$	−4353.75	+	7896.39i	−0.271442	+	0.492315i
$637$	−10451.5	−	11234.9i	−0.650086	−	0.698809i
$638$		−	1936.27i		−	0.120153i
$639$	2623.46	−	2838.93i	0.162414	−	0.175753i
$640$	12696.5	−	21991.0i	0.784179	−	1.35824i
$641$	8349.97	+	14462.6i	0.514515	+	0.891166i	0.999858	+	0.0168423i	$0.00536132\pi$
$641$	8349.97	+	14462.6i	0.514515	+	0.891166i	−0.485343	+	0.874324i	$0.661305\pi$
$642$	8411.33	−	2432.49i	0.517085	−	0.149537i
$643$	1936.20	−	7226.00i	0.118750	−	0.443182i	−0.880790	−	0.473507i	$-0.842988\pi$
$643$	1936.20	−	7226.00i	0.118750	−	0.443182i	0.999540	+	0.0303256i	$0.00965443\pi$
$644$	−870.943	+	3250.40i	−0.0532918	+	0.198888i
$645$	40656.7	−	11757.6i	2.48195	−	0.717760i
$646$	−6145.68	−	10644.6i	−0.374301	−	0.648308i
$647$	−13586.9	+	23533.1i	−0.825587	+	1.42996i	0.0758823	+	0.997117i	$0.475823\pi$
$647$	−13586.9	+	23533.1i	−0.825587	+	1.42996i	−0.901470	+	0.432842i	$0.857511\pi$
$648$	−1713.86	+	9263.23i	−0.103899	+	0.561565i
$649$			4454.52i			0.269423i
$650$	−27918.9	−	1008.44i	−1.68472	−	0.0608524i
$651$	−986.375	+	1788.99i	−0.0593842	+	0.107705i
$652$	−6609.16	+	1770.92i	−0.396986	+	0.106372i
$653$	9441.34	+	5450.96i	0.565801	+	0.326665i	0.755471	−	0.655183i	$-0.227408\pi$
$653$	9441.34	+	5450.96i	0.565801	+	0.326665i	−0.189670	+	0.981848i	$0.560742\pi$
$654$	−14760.0	+	290.996i	−0.882507	+	0.0173988i
$655$	6717.89	+	6717.89i	0.400747	+	0.400747i
$656$	24458.5	+	6553.63i	1.45571	+	0.390055i
$657$	844.908	+	2719.56i	0.0501720	+	0.161492i
$658$	2091.93	−	2091.93i	0.123939	−	0.123939i
$659$	10745.6	−	6203.98i	0.635189	−	0.366726i	−0.147570	−	0.989052i	$-0.547145\pi$
$659$	10745.6	−	6203.98i	0.635189	−	0.366726i	0.782759	+	0.622325i	$0.213812\pi$
$660$	−2598.90	+	1569.58i	−0.153276	+	0.0925695i
$661$	4727.57	+	17643.5i	0.278186	+	1.03820i	0.953676	+	0.300835i	$0.0972655\pi$
$661$	4727.57	+	17643.5i	0.278186	+	1.03820i	−0.675490	+	0.737369i	$0.736068\pi$
$662$	−15091.7			−0.886036
$663$	6042.06	−	5847.16i	0.353928	−	0.342511i
$664$	−8507.63			−0.497229
$665$	−1782.25	−	6651.44i	−0.103929	−	0.387867i
$666$	557.186	+	14125.4i	0.0324182	+	0.821842i
$667$	−11950.9	+	6899.85i	−0.693763	+	0.400544i
$668$	−6774.28	+	6774.28i	−0.392373	+	0.392373i
$669$	−17613.5	−	16932.5i	−1.01791	−	0.978545i
$670$	−29566.6	−	7922.35i	−1.70486	−	0.456817i
$671$	3033.76	+	3033.76i	0.174541	+	0.174541i
$672$	−71.6871	−	3636.13i	−0.00411516	−	0.208730i
$673$	17305.3	+	9991.24i	0.991191	+	0.572264i	0.905630	−	0.424068i	$-0.139398\pi$
$673$	17305.3	+	9991.24i	0.991191	+	0.572264i	0.0855610	+	0.996333i	$0.472732\pi$
$674$	−2277.75	+	610.322i	−0.130172	+	0.0348794i
$675$	1408.16	+	23783.7i	0.0802966	+	1.35620i
$676$	−9462.15	−	684.442i	−0.538356	−	0.0389419i
$677$			4772.11i			0.270912i	0.990783	+	0.135456i	$0.0432499\pi$
$677$			4772.11i			0.270912i	−0.990783	+	0.135456i	$0.956750\pi$
$678$	−5595.27	+	22659.4i	−0.316940	+	1.28352i
$679$	−3342.82	+	5789.93i	−0.188933	+	0.327242i
$680$	3829.95	+	6633.67i	0.215988	+	0.374103i
$681$	−697.607	−	2412.26i	−0.0392546	−	0.135739i
$682$	−711.917	+	2656.91i	−0.0399717	+	0.149176i
$683$	4930.13	−	18399.5i	0.276202	−	1.03080i	−0.678830	−	0.734296i	$-0.737512\pi$
$683$	4930.13	−	18399.5i	0.276202	−	1.03080i	0.955032	−	0.296504i	$-0.0958209\pi$
$684$	11536.0	+	2608.46i	0.644871	+	0.145814i
$685$	6228.58	+	10788.2i	0.347419	+	0.601747i
$686$	4650.73	−	8055.30i	0.258842	−	0.448328i
$687$	24339.5	+	6010.13i	1.35169	+	0.333771i
$688$			37901.1i			2.10024i
$689$	5528.92	−	18007.1i	0.305711	−	0.995670i
$690$	54054.5	+	29803.5i	2.98235	+	1.64435i
$691$	20245.2	−	5424.70i	1.11457	−	0.298647i	0.345883	−	0.938277i	$-0.387579\pi$
$691$	20245.2	−	5424.70i	1.11457	−	0.298647i	0.768683	+	0.639630i	$0.220913\pi$
$692$	−6207.96	−	3584.17i	−0.341028	−	0.196892i
$693$	391.549	−	744.494i	0.0214628	−	0.0408095i
$694$	12689.0	+	12689.0i	0.694046	+	0.694046i
$695$	−47161.7	−	12637.0i	−2.57402	−	0.689708i
$696$	3257.70	−	3388.74i	0.177418	−	0.184554i
$697$	−7736.24	+	7736.24i	−0.420418	+	0.420418i
$698$	10192.7	−	5884.76i	0.552721	−	0.319114i
$699$	9615.01	+	15920.5i	0.520276	+	0.861470i
$700$	−750.321	−	2800.24i	−0.0405135	−	0.151199i
$701$	−24971.3			−1.34544			−0.672719	−	0.739898i	$-0.734874\pi$
$701$	−24971.3			−1.34544			−0.672719	+	0.739898i	$0.734874\pi$
$702$	531.562	+	23073.7i	0.0285791	+	1.24054i
$703$	−15133.2			−0.811889
$704$	36.3482	+	135.653i	0.00194592	+	0.00726226i
$705$	−9834.60	−	16284.1i	−0.525379	−	0.869920i
$706$	13768.1	−	7948.99i	0.733949	−	0.423745i
$707$	−1259.64	+	1259.64i	−0.0670066	+	0.0670066i
$708$	8789.58	−	9143.13i	0.466572	−	0.485339i
$709$	5068.00	+	1357.97i	0.268453	+	0.0719317i	0.390534	−	0.920588i	$-0.372290\pi$
$709$	5068.00	+	1357.97i	0.268453	+	0.0719317i	−0.122082	+	0.992520i	$0.538957\pi$
$710$	6100.69	+	6100.69i	0.322471	+	0.322471i
$711$	4293.29	−	8163.27i	0.226457	−	0.430586i
$712$	5962.03	+	3442.18i	0.313815	+	0.181181i
$713$	18935.7	−	5073.80i	0.994595	−	0.266501i
$714$	2179.61	+	1201.75i	0.114244	+	0.0629893i
$715$	4643.74	−	4319.97i	0.242890	−	0.225955i
$716$			1631.47i			0.0851549i
$717$	13400.1	+	3308.88i	0.697959	+	0.172347i
$718$	642.956	−	1113.63i	0.0334191	−	0.0578835i
$719$	922.227	+	1597.34i	0.0478348	+	0.0828524i	0.888951	−	0.458001i	$-0.151435\pi$
$719$	922.227	+	1597.34i	0.0478348	+	0.0828524i	−0.841117	+	0.540854i	$0.818101\pi$
$720$	−36129.0	−	8169.27i	−1.87007	−	0.422848i
$721$	−201.672	+	752.651i	−0.0104170	+	0.0388768i
$722$	−3117.52	+	11634.8i	−0.160696	+	0.599724i
$723$	3659.98	+	12655.9i	0.188266	+	0.651006i
$724$	−6687.27	−	11582.7i	−0.343274	−	0.594568i
$725$	5944.25	−	10295.7i	0.304502	−	0.527413i
$726$	−5547.54	+	22466.1i	−0.283593	+	1.14848i
$727$			7138.12i			0.364152i	0.983284	+	0.182076i	$0.0582816\pi$
$727$			7138.12i			0.364152i	−0.983284	+	0.182076i	$0.941718\pi$
$728$	535.859	+	2333.81i	0.0272806	+	0.118814i
$729$	19545.5	−	2322.60i	0.993014	−	0.118000i
$730$	−6139.58	+	1645.10i	−0.311282	+	0.0834078i
$731$	−14182.2	−	8188.07i	−0.717573	−	0.414291i
$732$	−240.784	−	12213.1i	−0.0121580	−	0.616680i
$733$	−22501.4	−	22501.4i	−1.13385	−	1.13385i	−0.989532	−	0.144315i	$-0.953902\pi$
$733$	−22501.4	−	22501.4i	−1.13385	−	1.13385i	−0.144315	−	0.989532i	$-0.546098\pi$
$734$	−20970.0	−	5618.89i	−1.05452	−	0.282557i
$735$	−21056.3	−	20242.1i	−1.05670	−	1.01584i
$736$	−24677.4	+	24677.4i	−1.23590	+	1.23590i
$737$	3466.55	−	2001.41i	0.173259	−	0.100031i
$738$	−1183.71	−	30008.4i	−0.0590417	−	1.49678i
$739$	−8568.92	−	31979.6i	−0.426540	−	1.59187i	−0.760538	−	0.649294i	$-0.775065\pi$
$739$	−8568.92	−	31979.6i	−0.426540	−	1.59187i	0.333998	−	0.942574i	$-0.391602\pi$
$740$	−11060.5			−0.549448
$741$	−24704.0	−	404.979i	−1.22473	−	0.0200773i
$742$	5576.06			0.275881
$743$	6828.91	+	25485.8i	0.337185	+	1.25839i	0.901481	+	0.432819i	$0.142481\pi$
$743$	6828.91	+	25485.8i	0.337185	+	1.25839i	−0.564296	+	0.825573i	$0.690852\pi$
$744$	−5716.11	+	3452.18i	−0.281670	+	0.170112i
$745$	−18099.0	+	10449.4i	−0.890060	+	0.513877i
$746$	14117.7	−	14117.7i	0.692874	−	0.692874i
$747$	5273.90	+	16975.4i	0.258316	+	0.831456i
$748$	1134.74	+	304.053i	0.0554683	+	0.0148627i
$749$	−1342.15	−	1342.15i	−0.0654753	−	0.0654753i
$750$	−14032.7	+	276.658i	−0.683203	+	0.0134695i
$751$	9953.95	+	5746.92i	0.483655	+	0.279238i	0.721938	−	0.691957i	$-0.243251\pi$
$751$	9953.95	+	5746.92i	0.483655	+	0.279238i	−0.238283	+	0.971196i	$0.576585\pi$
$752$	16455.5	−	4409.23i	0.797965	−	0.213814i
$753$	−2272.21	+	4121.11i	−0.109965	+	0.199444i
$754$	6114.50	−	9759.21i	0.295328	−	0.471365i
$755$		−	732.755i		−	0.0353214i
$756$	−2272.70	+	755.512i	−0.109335	+	0.0363462i
$757$	19937.2	−	34532.3i	0.957240	−	1.65799i	0.228085	−	0.973641i	$-0.426754\pi$
$757$	19937.2	−	34532.3i	0.957240	−	1.65799i	0.729156	−	0.684348i	$-0.239913\pi$
$758$	16276.5	+	28191.7i	0.779931	+	1.35088i
$759$	−7754.22	+	2242.46i	−0.370831	+	0.107241i
$760$	5825.70	−	21741.8i	0.278053	−	1.03771i
$761$	5142.64	−	19192.6i	0.244968	−	0.914233i	−0.728432	−	0.685119i	$-0.759750\pi$
$761$	5142.64	−	19192.6i	0.244968	−	0.914233i	0.973400	−	0.229114i	$-0.0735829\pi$
$762$	13323.1	−	3852.93i	0.633391	−	0.183172i
$763$	1600.11	+	2771.47i	0.0759211	+	0.131499i
$764$	7938.94	−	13750.6i	0.375943	−	0.651153i
$765$	10862.1	−	11754.2i	0.513359	−	0.555521i
$766$			33305.3i			1.57098i
$767$	−14066.8	+	22451.8i	−0.662222	+	1.05696i
$768$	12664.6	−	22969.7i	0.595042	−	1.07923i
$769$	−26357.0	+	7062.33i	−1.23597	+	0.331176i	−0.816900	−	0.576780i	$-0.804309\pi$
$769$	−26357.0	+	7062.33i	−1.23597	+	0.331176i	−0.419066	+	0.907956i	$0.637642\pi$
$770$	1625.95	+	938.742i	0.0760976	+	0.0439350i
$771$	−12919.9	+	254.718i	−0.603500	+	0.0118981i
$772$	5243.06	+	5243.06i	0.244432	+	0.244432i
$773$	22429.1	+	6009.86i	1.04362	+	0.279637i	0.739613	−	0.673033i	$-0.235009\pi$
$773$	22429.1	+	6009.86i	1.04362	+	0.279637i	0.304007	+	0.952670i	$0.401675\pi$
$774$	42927.8	−	13336.8i	1.99355	−	0.619354i
$775$	−11942.1	+	11942.1i	−0.553512	+	0.553512i
$776$	−18925.8	+	10926.8i	−0.875509	+	0.505476i
$777$	2623.14	−	1584.22i	0.121113	−	0.0731449i
$778$	−11323.4	−	42259.7i	−0.521806	−	1.94741i
$779$	32149.4			1.47866
$780$	−18055.6	−	295.991i	−0.828838	−	0.0135874i
$781$	−1128.24			−0.0516923
$782$	−6181.65	−	23070.2i	−0.282680	−	1.05497i
$783$	−8781.06	−	4399.46i	−0.400778	−	0.200797i
$784$	22652.2	−	13078.3i	1.03190	−	0.595767i
$785$	5599.18	−	5599.18i	0.254578	−	0.254578i
$786$	7274.46	+	6993.18i	0.330116	+	0.317352i
$787$	−41410.9	−	11096.0i	−1.87565	−	0.502580i	−0.999800	−	0.0200060i	$-0.993631\pi$
$787$	−41410.9	−	11096.0i	−1.87565	−	0.502580i	−0.875855	−	0.482574i	$-0.839702\pi$
$788$	12389.6	+	12389.6i	0.560102	+	0.560102i
$789$	−326.247	−	16548.0i	−0.0147208	−	0.746671i
$790$	17828.3	+	10293.2i	0.802916	+	0.463563i
$791$	4887.14	−	1309.50i	0.219680	−	0.0588630i
$792$	2325.18	−	1467.58i	0.104320	−	0.0658438i
$793$	5710.57	+	24871.1i	0.255723	+	1.11374i
$794$			32003.1i			1.43041i
$795$	8595.57	−	34809.8i	0.383463	−	1.55293i
$796$	944.237	−	1635.47i	0.0420447	−	0.0728236i
$797$	3398.97	+	5887.19i	0.151064	+	0.261650i	0.931619	−	0.363437i	$-0.118397\pi$
$797$	3398.97	+	5887.19i	0.151064	+	0.261650i	−0.780555	+	0.625087i	$0.785063\pi$
$798$	−2031.85	−	7025.94i	−0.0901336	−	0.311674i
$799$	−1905.12	+	7110.01i	−0.0843534	+	0.314811i
$800$	7781.59	−	29041.3i	0.343901	−	1.28346i
$801$	3172.36	−	14029.9i	0.139937	−	0.618881i
$802$	14060.9	+	24354.2i	0.619087	+	1.07229i
$803$	415.598	−	719.837i	0.0182642	−	0.0316345i
$804$	−11064.4	−	2732.13i	−0.485338	−	0.119844i
$805$		−	13380.8i		−	0.585850i
$806$	−11978.4	+	11143.3i	−0.523476	+	0.486978i
$807$	−21462.6	−	11833.6i	−0.936209	−	0.516187i
$808$	−5624.52	+	1507.09i	−0.244888	+	0.0656177i
$809$	−9299.83	−	5369.26i	−0.404159	−	0.233341i	0.284118	−	0.958789i	$-0.408299\pi$
$809$	−9299.83	−	5369.26i	−0.404159	−	0.233341i	−0.688277	+	0.725448i	$0.741633\pi$
$810$	3460.46	+	43795.3i	0.150109	+	1.89977i
$811$	−5639.22	−	5639.22i	−0.244167	−	0.244167i	0.574404	−	0.818572i	$-0.305234\pi$
$811$	−5639.22	−	5639.22i	−0.244167	−	0.244167i	−0.818572	+	0.574404i	$0.805234\pi$
$812$	1154.34	+	309.304i	0.0498884	+	0.0133675i
$813$	−9436.35	+	9815.91i	−0.407069	+	0.423443i
$814$	2917.56	−	2917.56i	0.125627	−	0.125627i
$815$	23562.4	−	13603.8i	1.01271	−	0.584687i
$816$	7409.52	+	12268.6i	0.317874	+	0.526334i
$817$	12454.8	+	46481.8i	0.533338	+	1.99045i
$818$	−27003.1			−1.15421
$819$	4324.51	−	2515.94i	0.184506	−	0.107343i
$820$	23497.3			1.00068
$821$	2815.57	+	10507.9i	0.119688	+	0.446683i	0.999595	−	0.0284640i	$-0.00906159\pi$
$821$	2815.57	+	10507.9i	0.119688	+	0.446683i	−0.879906	+	0.475147i	$0.842395\pi$
$822$	6840.08	+	11325.8i	0.290237	+	0.480573i
$823$	−15883.7	+	9170.43i	−0.672745	+	0.388410i	−0.797116	−	0.603826i	$-0.793642\pi$
$823$	−15883.7	+	9170.43i	−0.672745	+	0.388410i	0.124371	+	0.992236i	$0.460309\pi$
$824$	−1801.00	+	1801.00i	−0.0761419	+	0.0761419i
$825$	4819.36	−	5013.22i	0.203380	−	0.211561i
$826$	−7575.65	−	2029.89i	−0.319117	−	0.0855071i
$827$	−23293.7	−	23293.7i	−0.979446	−	0.979446i	0.0203468	−	0.999793i	$-0.493523\pi$
$827$	−23293.7	−	23293.7i	−0.979446	−	0.979446i	−0.999793	+	0.0203468i	$0.993523\pi$
$828$	20340.7	+	10697.7i	0.853730	+	0.449000i
$829$	23850.6	+	13770.1i	0.999233	+	0.576908i	0.908021	−	0.418924i	$-0.137593\pi$
$829$	23850.6	+	13770.1i	0.999233	+	0.576908i	0.0912120	+	0.995831i	$0.470926\pi$
$830$	−38323.1	+	10268.6i	−1.60267	+	0.429434i
$831$	9753.63	+	5377.75i	0.407160	+	0.224491i
$832$	−245.174	+	798.505i	−0.0102162	+	0.0332731i
$833$			11301.6i			0.470081i
$834$	−50346.3	−	12432.0i	−2.09035	−	0.516168i
$835$	19047.4	−	32991.0i	0.789416	−	1.36731i
$836$	−1726.04	−	2989.59i	−0.0714072	−	0.123681i
$837$	10431.6	+	9265.42i	0.430788	+	0.382628i
$838$	10446.2	−	38985.8i	0.430619	−	1.60709i
$839$	−4649.08	+	17350.6i	−0.191304	+	0.713957i	0.801888	+	0.597474i	$0.203829\pi$
$839$	−4649.08	+	17350.6i	−0.191304	+	0.713957i	−0.993193	+	0.116483i	$0.962838\pi$
$840$	1266.24	+	4378.53i	0.0520111	+	0.179850i
$841$	−9744.11	−	16877.3i	−0.399529	−	0.692004i
$842$	8340.62	−	14446.4i	0.341374	−	0.591277i
$843$	−7374.27	+	29863.9i	−0.301285	+	1.22013i
$844$		−	12255.6i		−	0.499830i
$845$	37047.4	−	7109.21i	1.50825	−	0.289425i
$846$	−10784.4	−	17086.4i	−0.438269	−	0.694376i
$847$	4845.44	−	1298.33i	0.196566	−	0.0526697i
$848$	27807.6	+	16054.7i	1.12608	+	0.650143i
$849$	109.595	+	5558.91i	0.00443027	+	0.224713i
$850$	14549.6	+	14549.6i	0.587114	+	0.587114i
$851$	−28404.2	−	7610.87i	−1.14416	−	0.306577i
$852$	2315.77	+	2226.23i	0.0931186	+	0.0895179i
$853$	29113.2	−	29113.2i	1.16860	−	1.16860i	0.186062	−	0.982538i	$-0.440427\pi$
$853$	29113.2	−	29113.2i	1.16860	−	1.16860i	0.982538	−	0.186062i	$-0.0595726\pi$
$854$	−6541.88	+	3776.96i	−0.262129	+	0.151340i
$855$	−46993.1	+	1853.68i	−1.87968	+	0.0741455i
$856$	−1605.80	−	5992.93i	−0.0641181	−	0.239292i
$857$	−34473.1			−1.37407			−0.687035	−	0.726625i	$-0.741088\pi$
$857$	−34473.1			−1.37407			−0.687035	+	0.726625i	$0.741088\pi$
$858$	4840.81	−	4684.66i	0.192614	−	0.186400i
$859$	18058.4			0.717281			0.358641	−	0.933476i	$-0.383240\pi$
$859$	18058.4			0.717281			0.358641	+	0.933476i	$0.383240\pi$
$860$	9102.92	+	33972.6i	0.360938	+	1.34704i
$861$	−5572.70	+	3365.57i	−0.220577	+	0.133215i
$862$	6365.72	−	3675.25i	0.251528	−	0.145220i
$863$	−7395.61	+	7395.61i	−0.291714	+	0.291714i	−0.837757	−	0.546043i	$-0.816134\pi$
$863$	−7395.61	+	7395.61i	−0.291714	+	0.291714i	0.546043	+	0.837757i	$0.316134\pi$
$864$	−24330.1	−	4999.40i	−0.958016	−	0.196855i
$865$	27532.7	+	7377.37i	1.08224	+	0.289986i
$866$	−15544.2	−	15544.2i	−0.609946	−	0.609946i
$867$	19332.2	−	381.139i	0.757274	−	0.0149298i
$868$	−1470.24	−	848.842i	−0.0574921	−	0.0331931i
$869$	−2600.35	+	696.763i	−0.101509	+	0.0271991i
$870$	10584.3	−	19196.8i	0.412462	−	0.748082i
$871$	23792.4	+	859.386i	0.925573	+	0.0334319i
$872$			10460.7i			0.406242i
$873$	33534.5	+	30989.3i	1.30008	+	1.20141i
$874$	−35091.9	+	60780.9i	−1.35812	+	2.35234i
$875$	1521.27	+	2634.91i	0.0587752	+	0.101802i
$876$	−2273.40	+	657.451i	−0.0876840	+	0.0253575i
$877$	−10247.7	+	38245.0i	−0.394573	+	1.47257i	0.427932	+	0.903811i	$0.359242\pi$
$877$	−10247.7	+	38245.0i	−0.394573	+	1.47257i	−0.822506	+	0.568757i	$0.807424\pi$
$878$	693.508	−	2588.21i	0.0266569	−	0.0994850i
$879$	1939.00	−	560.743i	0.0744036	−	0.0215169i
$880$	5405.69	+	9362.93i	0.207075	+	0.358664i
$881$	−17073.5	+	29572.3i	−0.652920	+	1.13089i	0.329491	+	0.944159i	$0.393123\pi$
$881$	−17073.5	+	29572.3i	−0.652920	+	1.13089i	−0.982411	+	0.186732i	$0.940210\pi$
$882$	−22783.8	−	21054.5i	−0.869806	−	0.803790i
$883$		−	21483.1i		−	0.818760i	−0.912364	−	0.409380i	$-0.865745\pi$
$883$		−	21483.1i		−	0.818760i	0.912364	−	0.409380i	$-0.134255\pi$
$884$	4759.18	+	5115.87i	0.181073	+	0.194644i
$885$	−24350.0	+	44163.6i	−0.924877	+	1.67745i
$886$	−13794.9	+	3696.33i	−0.523079	+	0.140159i
$887$	−36778.2	−	21233.9i	−1.39221	−	0.803794i	−0.398653	−	0.917102i	$-0.630522\pi$
$887$	−36778.2	−	21233.9i	−1.39221	−	0.803794i	−0.993560	+	0.113308i	$0.963855\pi$
$888$	10014.8	−	197.444i	0.378463	−	0.00746147i
$889$	−2125.89	−	2125.89i	−0.0802025	−	0.0802025i
$890$	31011.0	+	8309.37i	1.16797	+	0.312956i
$891$	−4369.67	−	3729.71i	−0.164298	−	0.140236i
$892$	14357.0	−	14357.0i	0.538910	−	0.538910i
$893$	18732.0	−	10814.9i	0.701953	−	0.405273i
$894$	−19000.8	+	11475.3i	−0.710829	+	0.429298i
$895$	−1679.05	−	6266.29i	−0.0627087	−	0.234032i
$896$	−5846.54			−0.217990
$897$	−46164.4	−	13184.4i	−1.71838	−	0.490763i
$898$	−39428.0			−1.46518
$899$	−1801.89	−	6724.76i	−0.0668482	−	0.249481i
$900$	−19784.0	+	780.393i	−0.732739	+	0.0289035i
$901$	−12015.0	+	6936.84i	−0.444258	+	0.256493i
$902$	−6198.16	+	6198.16i	−0.228798	+	0.228798i
$903$	−7024.85	−	6753.21i	−0.258884	−	0.248873i
$904$	15974.8	+	4280.42i	0.587735	+	0.157483i
$905$	37605.5	+	37605.5i	1.38127	+	1.38127i
$906$	−15.3408	−	778.122i	−0.000562545	−	0.0285335i
$907$	−30030.0	−	17337.9i	−1.09937	−	0.634723i	−0.163317	−	0.986574i	$-0.552219\pi$
$907$	−30030.0	−	17337.9i	−1.09937	−	0.634723i	−0.936056	+	0.351851i	$0.885553\pi$
$908$	2015.67	−	540.098i	0.0736702	−	0.0197399i
$909$	6493.76	+	10288.4i	0.236947	+	0.375408i
$910$	5230.70	+	9866.02i	0.190545	+	0.359401i
$911$		−	54012.5i		−	1.96434i	−0.187993	−	0.982170i	$-0.560198\pi$
$911$		−	54012.5i		−	1.96434i	0.187993	−	0.982170i	$-0.439802\pi$
$912$	10096.5	−	40888.2i	0.366588	−	1.48459i
$913$	2594.16	−	4493.21i	0.0940351	−	0.162873i
$914$	−13244.6	−	22940.3i	−0.479313	−	0.830194i
$915$	13494.1	+	46661.3i	0.487542	+	1.68588i
$916$	−5392.26	+	20124.2i	−0.194504	+	0.725897i
$917$	566.145	−	2112.88i	0.0203880	−	0.0760889i
$918$	11288.5	−	12709.4i	0.405857	−	0.456940i
$919$	−12062.7	−	20893.3i	−0.432984	−	0.749951i	0.564144	−	0.825676i	$-0.309206\pi$
$919$	−12062.7	−	20893.3i	−0.432984	−	0.749951i	−0.997129	+	0.0757251i	$0.975873\pi$
$920$	21869.1	−	37878.3i	0.783698	−	1.35740i
$921$	−7280.40	−	1797.75i	−0.260475	−	0.0643189i
$922$		−	47319.8i		−	1.69023i
$923$	−5686.59	−	3562.85i	−0.202791	−	0.127056i
$924$	612.155	+	337.517i	0.0217948	+	0.0120168i
$925$	24470.3	−	6556.80i	0.869815	−	0.233066i
$926$	49227.8	+	28421.7i	1.74700	+	1.00863i
$927$	4710.02	+	2477.13i	0.166879	+	0.0877664i
$928$	8763.87	+	8763.87i	0.310009	+	0.310009i
$929$	7607.96	+	2038.55i	0.268686	+	0.0719941i	0.390646	−	0.920541i	$-0.372251\pi$
$929$	7607.96	+	2038.55i	0.268686	+	0.0719941i	−0.121961	+	0.992535i	$0.538918\pi$
$930$	−21581.8	+	22449.9i	−0.760961	+	0.791570i
$931$	23483.0	−	23483.0i	0.826663	−	0.826663i
$932$	−13385.1	+	7727.92i	−0.470435	+	0.271606i
$933$	5697.32	+	9433.59i	0.199916	+	0.331020i
$934$	−1167.83	−	4358.40i	−0.0409128	−	0.152689i
$935$	−4671.33			−0.163389
$936$	16353.9	−	54.3083i	0.571092	−	0.00189650i
$937$	14122.0			0.492366			0.246183	−	0.969223i	$-0.420824\pi$
$937$	14122.0			0.492366			0.246183	+	0.969223i	$0.420824\pi$
$938$	1824.06	+	6807.47i	0.0634942	+	0.236963i
$939$	25956.6	+	42978.8i	0.902089	+	1.49367i
$940$	13690.8	−	7904.41i	0.475049	−	0.274270i
$941$	−10737.8	+	10737.8i	−0.371989	+	0.371989i	−0.868201	−	0.496213i	$-0.834724\pi$
$941$	−10737.8	+	10737.8i	−0.371989	+	0.371989i	0.496213	+	0.868201i	$0.334724\pi$
$942$	5828.63	−	6063.07i	0.201600	−	0.209709i
$943$	60342.8	+	16168.8i	2.08381	+	0.558355i
$944$	−31934.9	−	31934.9i	−1.10105	−	1.10105i
$945$	7951.61	−	5240.80i	0.273720	−	0.180406i
$946$	−11362.5	−	6560.16i	−0.390515	−	0.225464i
$947$	48011.3	−	12864.6i	1.64747	−	0.441440i	0.688570	−	0.725169i	$-0.258239\pi$
$947$	48011.3	−	12864.6i	1.64747	−	0.441440i	0.958904	+	0.283730i	$0.0915719\pi$
$948$	6712.19	+	3700.83i	0.229960	+	0.126790i
$949$	4367.86	−	2315.73i	0.149407	−	0.0792115i
$950$		−	60463.6i		−	2.06495i
$951$	−3506.95	−	865.970i	−0.119580	−	0.0295279i
$952$	881.815	−	1527.35i	0.0300208	−	0.0519975i
$953$	−27366.1	−	47399.5i	−0.930195	−	1.61114i	−0.782986	−	0.622039i	$-0.786305\pi$
$953$	−27366.1	−	47399.5i	−0.930195	−	1.61114i	−0.147208	−	0.989106i	$-0.547029\pi$
$954$	8398.98	−	37145.0i	0.285039	−	1.26060i
$955$	−16340.9	+	60985.1i	−0.553695	+	2.06642i
$956$	−2968.71	+	11079.4i	−0.100434	+	0.374825i
$957$	796.381	+	2753.81i	0.0269001	+	0.0930179i
$958$	813.668	+	1409.31i	0.0274409	+	0.0475291i
$959$	1434.08	−	2483.90i	0.0482886	−	0.0836384i
$960$	−381.161	+	1543.60i	−0.0128145	+	0.0518954i
$961$		−	19900.9i		−	0.668017i
$962$	23918.4	−	5491.83i	0.801622	−	0.184058i
$963$	−10962.3	+	6919.11i	−0.366829	+	0.231532i
$964$	−10575.2	+	2833.61i	−0.353324	+	0.0946728i
$965$	−25533.9	−	14742.0i	−0.851778	−	0.491774i
$966$	−280.137	−	14209.2i	−0.00933051	−	0.473265i
$967$	−10124.2	−	10124.2i	−0.336684	−	0.336684i	0.518434	−	0.855118i	$-0.326515\pi$
$967$	−10124.2	−	10124.2i	−0.336684	−	0.336684i	−0.855118	+	0.518434i	$0.826515\pi$
$968$	15838.5	+	4243.91i	0.525897	+	0.140914i
$969$	13118.6	+	12611.4i	0.434914	+	0.418097i
$970$	−72063.6	+	72063.6i	−2.38538	+	2.38538i
$971$	−44168.5	+	25500.7i	−1.45977	+	0.842798i	−0.998999	−	0.0447227i	$-0.985760\pi$
$971$	−44168.5	+	25500.7i	−1.45977	+	0.842798i	−0.460769	+	0.887520i	$0.652426\pi$
$972$	1609.59	+	16277.6i	0.0531147	+	0.537143i
$973$	2909.55	+	10858.6i	0.0958643	+	0.357770i
$974$	54819.9			1.80343
$975$	40121.8	−	10048.7i	1.31787	−	0.330069i
$976$	−43498.7			−1.42660
$977$	−2049.26	−	7647.92i	−0.0671049	−	0.250439i	0.924222	−	0.381854i	$-0.124714\pi$
$977$	−2049.26	−	7647.92i	−0.0671049	−	0.250439i	−0.991327	+	0.131416i	$0.958048\pi$
$978$	24736.5	−	14939.3i	0.808778	−	0.488454i
$979$	−3635.89	+	2099.18i	−0.118696	+	0.0685293i
$980$	17163.2	−	17163.2i	0.559447	−	0.559447i
$981$	20872.3	−	6484.59i	0.679309	−	0.211047i
$982$	−26047.5	−	6979.41i	−0.846445	−	0.226804i
$983$	−6675.46	−	6675.46i	−0.216596	−	0.216596i	0.590466	−	0.807062i	$-0.298944\pi$
$983$	−6675.46	−	6675.46i	−0.216596	−	0.216596i	−0.807062	+	0.590466i	$0.798944\pi$
$984$	−21275.8	+	419.457i	−0.689277	+	0.0135892i
$985$	−60337.7	−	34836.0i	−1.95180	−	1.12687i
$986$	−8193.10	+	2195.34i	−0.264626	+	0.0709064i
$987$	−2114.80	+	3835.61i	−0.0682013	+	0.123697i
$988$	741.144	−	20518.8i	0.0238653	−	0.660720i
$989$			93507.9i			3.00645i
$990$	8702.53	−	9417.28i	0.279378	−	0.302324i
$991$	11699.3	−	20263.8i	0.375016	−	0.649547i	−0.615313	−	0.788283i	$-0.710971\pi$
$991$	11699.3	−	20263.8i	0.375016	−	0.649547i	0.990329	+	0.138736i	$0.0443038\pi$
$992$	−8803.36	−	15247.9i	−0.281761	−	0.488024i
$993$	21463.8	−	6207.17i	0.685936	−	0.198367i
$994$	514.131	−	1918.76i	0.0164057	−	0.0612268i
$995$	−1943.54	+	7253.41i	−0.0619241	+	0.231104i
$996$	−14190.5	+	4103.79i	−0.451450	+	0.130556i
$997$	17787.2	+	30808.4i	0.565022	+	0.978647i	0.997048	+	0.0767856i	$0.0244657\pi$
$997$	17787.2	+	30808.4i	0.565022	+	0.978647i	−0.432026	+	0.901861i	$0.642201\pi$
$998$	−18497.5	+	32038.6i	−0.586702	+	1.01620i
$999$	−6602.16	−	19860.3i	−0.209092	−	0.628981i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	39.4.k.a.20.3	yes	48
3.2	odd	2	inner	39.4.k.a.20.10	yes	48
13.2	odd	12	inner	39.4.k.a.2.10	yes	48
39.2	even	12	inner	39.4.k.a.2.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
39.4.k.a.2.3	✓	48	39.2	even	12	inner
39.4.k.a.2.10	yes	48	13.2	odd	12	inner
39.4.k.a.20.3	yes	48	1.1	even	1	trivial
39.4.k.a.20.10	yes	48	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 39 = 3 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	39.k (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.908381 - 3.39012i) q^{2} +(2.68627 + 4.44791i) q^{3} +(-3.73959 + 2.15905i) q^{4} +(12.1413 - 12.1413i) q^{5} +(12.6388 - 13.1472i) q^{6} +(-3.81863 - 1.02320i) q^{7} +(-9.13753 - 9.13753i) q^{8} +(-12.5679 + 23.8966i) q^{9} +O(q^{10})\)	\(q+(-0.908381 - 3.39012i) q^{2} +(2.68627 + 4.44791i) q^{3} +(-3.73959 + 2.15905i) q^{4} +(12.1413 - 12.1413i) q^{5} +(12.6388 - 13.1472i) q^{6} +(-3.81863 - 1.02320i) q^{7} +(-9.13753 - 9.13753i) q^{8} +(-12.5679 + 23.8966i) q^{9} +(-52.1894 - 30.1316i) q^{10} +(7.61210 - 2.03966i) q^{11} +(-19.6488 - 10.8336i) q^{12} +(44.8076 + 13.7578i) q^{13} +13.8751i q^{14} +(86.6183 + 21.3886i) q^{15} +(-39.9494 + 69.1944i) q^{16} +(-17.2612 - 29.8972i) q^{17} +(92.4289 + 20.8994i) q^{18} +(-26.2557 + 97.9877i) q^{19} +(-19.1897 + 71.6171i) q^{20} +(-5.70678 - 19.7335i) q^{21} +(-13.8294 - 23.9532i) q^{22} +(-98.5614 + 170.713i) q^{23} +(16.0970 - 65.1888i) q^{24} -169.822i q^{25} +(5.93819 - 164.401i) q^{26} +(-140.051 + 8.29199i) q^{27} +(16.4892 - 4.41828i) q^{28} +(60.6266 + 35.0028i) q^{29} +(-6.17235 - 313.076i) q^{30} +(-70.3210 - 70.3210i) q^{31} +(171.010 + 45.8220i) q^{32} +(29.5204 + 28.3789i) q^{33} +(-85.6755 + 85.6755i) q^{34} +(-58.7861 + 33.9402i) q^{35} +(-4.59536 - 116.498i) q^{36} +(38.6098 + 144.094i) q^{37} +356.041 q^{38} +(59.1721 + 236.258i) q^{39} -221.883 q^{40} +(-82.0241 - 306.118i) q^{41} +(-61.7152 + 37.2723i) q^{42} +(410.811 - 237.182i) q^{43} +(-24.0624 + 24.0624i) q^{44} +(137.546 + 442.726i) q^{45} +(668.271 + 179.063i) q^{46} +(-150.769 - 150.769i) q^{47} +(-415.086 + 8.18350i) q^{48} +(-283.512 - 163.686i) q^{49} +(-575.718 + 154.263i) q^{50} +(86.6120 - 157.088i) q^{51} +(-197.266 + 45.2935i) q^{52} -401.876i q^{53} +(155.330 + 467.258i) q^{54} +(67.6567 - 117.185i) q^{55} +(25.5433 + 44.2423i) q^{56} +(-506.371 + 146.438i) q^{57} +(63.5918 - 237.328i) q^{58} +(-146.297 + 545.989i) q^{59} +(-370.096 + 107.029i) q^{60} +(272.211 + 471.484i) q^{61} +(-174.519 + 302.275i) q^{62} +(72.4431 - 78.3929i) q^{63} +17.8207i q^{64} +(711.060 - 376.985i) q^{65} +(69.3922 - 125.857i) q^{66} +(490.625 - 131.463i) q^{67} +(129.099 + 74.5354i) q^{68} +(-1024.08 + 20.1900i) q^{69} +(168.462 + 168.462i) q^{70} +(-138.288 - 37.0542i) q^{71} +(333.195 - 103.517i) q^{72} +(74.5809 - 74.5809i) q^{73} +(453.424 - 261.784i) q^{74} +(755.354 - 456.188i) q^{75} +(-113.375 - 423.121i) q^{76} -31.1548 q^{77} +(747.192 - 415.213i) q^{78} -341.608 q^{79} +(355.072 + 1325.15i) q^{80} +(-413.097 - 600.660i) q^{81} +(-963.269 + 556.144i) q^{82} +(465.533 - 465.533i) q^{83} +(63.9467 + 61.4740i) q^{84} +(-572.564 - 153.418i) q^{85} +(-1177.25 - 1177.25i) q^{86} +(7.17021 + 363.689i) q^{87} +(-88.1932 - 50.9184i) q^{88} +(-514.593 + 137.885i) q^{89} +(1375.95 - 868.461i) q^{90} +(-157.027 - 98.3830i) q^{91} -851.196i q^{92} +(123.880 - 501.683i) q^{93} +(-374.170 + 648.081i) q^{94} +(870.919 + 1508.48i) q^{95} +(255.567 + 883.729i) q^{96} +(437.699 - 1633.51i) q^{97} +(-297.378 + 1109.83i) q^{98} +(-46.9271 + 207.538i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{3} - 12 q^{4} - 50 q^{6} + 20 q^{7} - 2 q^{9}+O(q^{10}) \) 48 * q - 2 * q^3 - 12 * q^4 - 50 * q^6 + 20 * q^7 - 2 * q^9	\( 48 q - 2 q^{3} - 12 q^{4} - 50 q^{6} + 20 q^{7} - 2 q^{9} - 156 q^{10} - 80 q^{13} + 70 q^{15} + 260 q^{16} + 256 q^{18} + 260 q^{19} + 82 q^{21} + 212 q^{22} - 1194 q^{24} - 248 q^{27} - 756 q^{28} - 1062 q^{30} - 180 q^{31} + 10 q^{33} - 396 q^{34} + 3060 q^{36} + 1932 q^{37} + 538 q^{39} + 360 q^{40} + 968 q^{42} + 1416 q^{43} - 386 q^{45} - 144 q^{46} - 410 q^{48} - 3000 q^{49} - 4336 q^{52} + 1930 q^{54} - 1012 q^{55} - 1274 q^{57} + 908 q^{58} - 2860 q^{60} + 836 q^{61} - 5150 q^{63} + 1376 q^{66} - 136 q^{67} - 1674 q^{69} + 1808 q^{70} - 3900 q^{72} + 3572 q^{73} + 5796 q^{75} + 8400 q^{76} + 12292 q^{78} - 3760 q^{79} + 2494 q^{81} + 2544 q^{82} + 1084 q^{84} + 4980 q^{85} + 2318 q^{87} - 8436 q^{88} - 8908 q^{91} - 1214 q^{93} - 8464 q^{94} - 6968 q^{96} - 204 q^{97} - 13094 q^{99}+O(q^{100}) \) 48 * q - 2 * q^3 - 12 * q^4 - 50 * q^6 + 20 * q^7 - 2 * q^9 - 156 * q^10 - 80 * q^13 + 70 * q^15 + 260 * q^16 + 256 * q^18 + 260 * q^19 + 82 * q^21 + 212 * q^22 - 1194 * q^24 - 248 * q^27 - 756 * q^28 - 1062 * q^30 - 180 * q^31 + 10 * q^33 - 396 * q^34 + 3060 * q^36 + 1932 * q^37 + 538 * q^39 + 360 * q^40 + 968 * q^42 + 1416 * q^43 - 386 * q^45 - 144 * q^46 - 410 * q^48 - 3000 * q^49 - 4336 * q^52 + 1930 * q^54 - 1012 * q^55 - 1274 * q^57 + 908 * q^58 - 2860 * q^60 + 836 * q^61 - 5150 * q^63 + 1376 * q^66 - 136 * q^67 - 1674 * q^69 + 1808 * q^70 - 3900 * q^72 + 3572 * q^73 + 5796 * q^75 + 8400 * q^76 + 12292 * q^78 - 3760 * q^79 + 2494 * q^81 + 2544 * q^82 + 1084 * q^84 + 4980 * q^85 + 2318 * q^87 - 8436 * q^88 - 8908 * q^91 - 1214 * q^93 - 8464 * q^94 - 6968 * q^96 - 204 * q^97 - 13094 * q^99

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