LMFDB - Embedded newform 338.4.c.o.315.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [338,4,Mod(191,338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(338, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("338.191");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	338.c (of order $3$, degree $2$, not 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:	$19.9426455819$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
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} + 108 x^{10} - 63 x^{9} + 7831 x^{8} - 3348 x^{7} + 317885 x^{6} + 1680 x^{5} + \cdots + 1759886401 $ x^12 - x^11 + 108x^10 - 63x^9 + 7831x^8 - 3348x^7 + 317885x^6 + 1680x^5 + 9364467x^4 + 988393x^3 + 158096834x^2 + 69596709x + 1759886401
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 13^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			315.1
Root			$2.92486 + 5.06601i$ of defining polynomial
Character	$\chi$	$=$	338.315
Dual form			338.4.c.o.191.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.73205i) q^{2} +(-5.00428 - 8.66767i) q^{3} +(-2.00000 + 3.46410i) q^{4} -13.8136 q^{5} +(-10.0086 + 17.3353i) q^{6} +(0.131143 - 0.227146i) q^{7} +8.00000 q^{8} +(-36.5857 + 63.3682i) q^{9} +(13.8136 + 23.9258i) q^{10} +(-20.0079 - 34.6548i) q^{11} +40.0343 q^{12} -0.524571 q^{14} +(69.1270 + 119.731i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-39.8680 + 69.0534i) q^{17} +146.343 q^{18} +(11.2932 - 19.5604i) q^{19} +(27.6271 - 47.8516i) q^{20} -2.62510 q^{21} +(-40.0159 + 69.3096i) q^{22} +(32.7646 + 56.7499i) q^{23} +(-40.0343 - 69.3414i) q^{24} +65.8147 q^{25} +462.109 q^{27} +(0.524571 + 0.908583i) q^{28} +(-20.0684 - 34.7595i) q^{29} +(138.254 - 239.463i) q^{30} -113.748 q^{31} +(-16.0000 + 27.7128i) q^{32} +(-200.251 + 346.845i) q^{33} +159.472 q^{34} +(-1.81155 + 3.13770i) q^{35} +(-146.343 - 253.473i) q^{36} +(-60.5399 - 104.858i) q^{37} -45.1727 q^{38} -110.509 q^{40} +(-198.092 - 343.106i) q^{41} +(2.62510 + 4.54681i) q^{42} +(137.950 - 238.936i) q^{43} +160.064 q^{44} +(505.379 - 875.342i) q^{45} +(65.5291 - 113.500i) q^{46} -440.483 q^{47} +(-80.0685 + 138.683i) q^{48} +(171.466 + 296.987i) q^{49} +(-65.8147 - 113.994i) q^{50} +798.043 q^{51} -615.108 q^{53} +(-462.109 - 800.396i) q^{54} +(276.381 + 478.706i) q^{55} +(1.04914 - 1.81717i) q^{56} -226.057 q^{57} +(-40.1368 + 69.5190i) q^{58} +(115.454 - 199.972i) q^{59} -553.016 q^{60} +(54.7618 - 94.8501i) q^{61} +(113.748 + 197.017i) q^{62} +(9.59589 + 16.6206i) q^{63} +64.0000 q^{64} +801.003 q^{66} +(110.566 + 191.506i) q^{67} +(-159.472 - 276.214i) q^{68} +(327.926 - 567.985i) q^{69} +7.24620 q^{70} +(161.102 - 279.036i) q^{71} +(-292.685 + 506.946i) q^{72} -323.664 q^{73} +(-121.080 + 209.716i) q^{74} +(-329.355 - 570.460i) q^{75} +(45.1727 + 78.2415i) q^{76} -10.4956 q^{77} +743.263 q^{79} +(110.509 + 191.406i) q^{80} +(-1324.71 - 2294.46i) q^{81} +(-396.184 + 686.211i) q^{82} +539.296 q^{83} +(5.25020 - 9.09361i) q^{84} +(550.720 - 953.875i) q^{85} -551.800 q^{86} +(-200.856 + 347.893i) q^{87} +(-160.064 - 277.238i) q^{88} +(632.070 + 1094.78i) q^{89} -2021.51 q^{90} -262.116 q^{92} +(569.225 + 985.927i) q^{93} +(440.483 + 762.939i) q^{94} +(-155.999 + 270.199i) q^{95} +320.274 q^{96} +(-163.040 + 282.394i) q^{97} +(342.931 - 593.974i) q^{98} +2928.02 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 12 q^{2} - 9 q^{3} - 24 q^{4} + 36 q^{5} - 18 q^{6} - 25 q^{7} + 96 q^{8} - 113 q^{9} - 36 q^{10} - 37 q^{11} + 72 q^{12} + 100 q^{14} - 118 q^{15} - 96 q^{16} - 99 q^{17} + 452 q^{18} + 81 q^{19}+ \cdots - 2688 q^{99}+O(q^{100}) $ 12 * q - 12 * q^2 - 9 * q^3 - 24 * q^4 + 36 * q^5 - 18 * q^6 - 25 * q^7 + 96 * q^8 - 113 * q^9 - 36 * q^10 - 37 * q^11 + 72 * q^12 + 100 * q^14 - 118 * q^15 - 96 * q^16 - 99 * q^17 + 452 * q^18 + 81 * q^19 - 72 * q^20 - 52 * q^21 - 74 * q^22 - 267 * q^23 - 72 * q^24 + 736 * q^25 + 1338 * q^27 - 100 * q^28 + 119 * q^29 - 236 * q^30 - 1250 * q^31 - 192 * q^32 - 762 * q^33 + 396 * q^34 - 614 * q^35 - 452 * q^36 - 274 * q^37 - 324 * q^38 + 288 * q^40 - 1140 * q^41 + 52 * q^42 - 428 * q^43 + 296 * q^44 + 1215 * q^45 - 534 * q^46 - 1972 * q^47 - 144 * q^48 - 899 * q^49 - 736 * q^50 + 578 * q^51 + 178 * q^53 - 1338 * q^54 - 1126 * q^55 - 200 * q^56 - 5106 * q^57 + 238 * q^58 - 1088 * q^59 + 944 * q^60 - 1704 * q^61 + 1250 * q^62 + 3222 * q^63 + 768 * q^64 + 3048 * q^66 + 1692 * q^67 - 396 * q^68 - 1168 * q^69 + 2456 * q^70 + 1221 * q^71 - 904 * q^72 - 3108 * q^73 - 548 * q^74 - 1798 * q^75 + 324 * q^76 + 5580 * q^77 - 1750 * q^79 - 288 * q^80 - 3338 * q^81 - 2280 * q^82 - 252 * q^83 + 104 * q^84 + 3721 * q^85 + 1712 * q^86 - 1602 * q^87 - 296 * q^88 + 374 * q^89 - 4860 * q^90 + 2136 * q^92 + 1868 * q^93 + 1972 * q^94 + 4093 * q^95 + 576 * q^96 + 330 * q^97 - 1798 * q^98 - 2688 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$	−5.00428	−	8.66767i	−0.963074	−	1.66809i	−0.714702	−	0.699429i	$-0.753438\pi$
$3$	−5.00428	−	8.66767i	−0.963074	−	1.66809i	−0.248373	−	0.968665i	$-0.579896\pi$
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	−13.8136			−1.23552			−0.617762	−	0.786365i	$-0.711960\pi$
$5$	−13.8136			−1.23552			−0.617762	+	0.786365i	$0.711960\pi$
$6$	−10.0086	+	17.3353i	−0.680996	+	1.17952i
$7$	0.131143	−	0.227146i	0.00708104	−	0.0122647i	−0.862463	−	0.506120i	$-0.831079\pi$
$7$	0.131143	−	0.227146i	0.00708104	−	0.0122647i	0.869544	+	0.493855i	$0.164413\pi$
$8$	8.00000			0.353553
$9$	−36.5857	+	63.3682i	−1.35502	+	2.34697i
$10$	13.8136	+	23.9258i	0.436823	+	0.756600i
$11$	−20.0079	−	34.6548i	−0.548420	−	0.949892i	−0.998383	−	0.0568445i	$-0.981896\pi$
$11$	−20.0079	−	34.6548i	−0.548420	−	0.949892i	0.449963	−	0.893047i	$-0.351437\pi$
$12$	40.0343			0.963074
$13$		0			0
$13$		0			0
$14$	−0.524571			−0.0100141
$15$	69.1270	+	119.731i	1.18990	+	2.06097i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−39.8680	+	69.0534i	−0.568789	+	0.985172i	0.427897	+	0.903828i	$0.359255\pi$
$17$	−39.8680	+	69.0534i	−0.568789	+	0.985172i	−0.996686	+	0.0813443i	$0.974079\pi$
$18$	146.343			1.91629
$19$	11.2932	−	19.5604i	0.136360	−	0.236182i	−0.789756	−	0.613421i	$-0.789793\pi$
$19$	11.2932	−	19.5604i	0.136360	−	0.236182i	0.926116	+	0.377239i	$0.123126\pi$
$20$	27.6271	−	47.8516i	0.308881	−	0.534997i
$21$	−2.62510			−0.0272783
$22$	−40.0159	+	69.3096i	−0.387792	+	0.671675i
$23$	32.7646	+	56.7499i	0.297038	+	0.514485i	0.975457	−	0.220190i	$-0.0706678\pi$
$23$	32.7646	+	56.7499i	0.297038	+	0.514485i	−0.678419	+	0.734675i	$0.737334\pi$
$24$	−40.0343	−	69.3414i	−0.340498	−	0.589760i
$25$	65.8147			0.526518
$26$		0			0
$27$	462.109			3.29381
$28$	0.524571	+	0.908583i	0.00354052	+	0.00613236i
$29$	−20.0684	−	34.7595i	−0.128504	−	0.222575i	0.794593	−	0.607142i	$-0.207684\pi$
$29$	−20.0684	−	34.7595i	−0.128504	−	0.222575i	−0.923097	+	0.384567i	$0.874351\pi$
$30$	138.254	−	239.463i	0.841387	−	1.45732i
$31$	−113.748			−0.659022			−0.329511	−	0.944152i	$-0.606884\pi$
$31$	−113.748			−0.659022			−0.329511	+	0.944152i	$0.606884\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$	−200.251	+	346.845i	−1.05634	+	1.82963i
$34$	159.472			0.804389
$35$	−1.81155	+	3.13770i	−0.00874879	+	0.0151534i
$36$	−146.343	−	253.473i	−0.677512	−	1.17349i
$37$	−60.5399	−	104.858i	−0.268992	−	0.465908i	0.699610	−	0.714525i	$-0.253357\pi$
$37$	−60.5399	−	104.858i	−0.268992	−	0.465908i	−0.968602	+	0.248617i	$0.920024\pi$
$38$	−45.1727			−0.192842
$39$		0			0
$40$	−110.509			−0.436823
$41$	−198.092	−	343.106i	−0.754556	−	1.30693i	−0.945595	−	0.325347i	$-0.894519\pi$
$41$	−198.092	−	343.106i	−0.754556	−	1.30693i	0.191039	−	0.981583i	$-0.438814\pi$
$42$	2.62510	+	4.54681i	0.00964433	+	0.0167045i
$43$	137.950	−	238.936i	0.489237	−	0.847383i	−0.510687	−	0.859767i	$-0.670609\pi$
$43$	137.950	−	238.936i	0.489237	−	0.847383i	0.999923	+	0.0123841i	$0.00394208\pi$
$44$	160.064			0.548420
$45$	505.379	−	875.342i	1.67416	−	2.89974i
$46$	65.5291	−	113.500i	0.210038	−	0.363796i
$47$	−440.483			−1.36704			−0.683522	−	0.729930i	$-0.739553\pi$
$47$	−440.483			−1.36704			−0.683522	+	0.729930i	$0.739553\pi$
$48$	−80.0685	+	138.683i	−0.240769	+	0.417023i
$49$	171.466	+	296.987i	0.499900	+	0.865852i
$50$	−65.8147	−	113.994i	−0.186152	−	0.322425i
$51$	798.043			2.19115
$52$		0			0
$53$	−615.108			−1.59418			−0.797091	−	0.603860i	$-0.793629\pi$
$53$	−615.108			−1.59418			−0.797091	+	0.603860i	$0.793629\pi$
$54$	−462.109	−	800.396i	−1.16454	−	2.01704i
$55$	276.381	+	478.706i	0.677586	+	1.17361i
$56$	1.04914	−	1.81717i	0.00250353	−	0.00433623i
$57$	−226.057			−0.525298
$58$	−40.1368	+	69.5190i	−0.0908659	+	0.157384i
$59$	115.454	−	199.972i	0.254760	−	0.441257i	−0.710070	−	0.704131i	$-0.751337\pi$
$59$	115.454	−	199.972i	0.254760	−	0.441257i	0.964830	+	0.262874i	$0.0846702\pi$
$60$	−553.016			−1.18990
$61$	54.7618	−	94.8501i	0.114943	−	0.199087i	−0.802814	−	0.596230i	$-0.796665\pi$
$61$	54.7618	−	94.8501i	0.114943	−	0.199087i	0.917757	+	0.397142i	$0.129998\pi$
$62$	113.748	+	197.017i	0.232999	+	0.403567i
$63$	9.59589	+	16.6206i	0.0191900	+	0.0332380i
$64$	64.0000			0.125000
$65$		0			0
$66$	801.003			1.49389
$67$	110.566	+	191.506i	0.201609	+	0.349197i	0.949047	−	0.315135i	$-0.102050\pi$
$67$	110.566	+	191.506i	0.201609	+	0.349197i	−0.747438	+	0.664331i	$0.768716\pi$
$68$	−159.472	−	276.214i	−0.284395	−	0.492586i
$69$	327.926	−	567.985i	0.572140	−	0.990976i
$70$	7.24620			0.0123727
$71$	161.102	−	279.036i	0.269285	−	0.466416i	−0.699392	−	0.714738i	$-0.746546\pi$
$71$	161.102	−	279.036i	0.269285	−	0.466416i	0.968677	+	0.248322i	$0.0798792\pi$
$72$	−292.685	+	506.946i	−0.479074	+	0.829780i
$73$	−323.664			−0.518932			−0.259466	−	0.965752i	$-0.583547\pi$
$73$	−323.664			−0.518932			−0.259466	+	0.965752i	$0.583547\pi$
$74$	−121.080	+	209.716i	−0.190206	+	0.329446i
$75$	−329.355	−	570.460i	−0.507076	−	0.878281i
$76$	45.1727	+	78.2415i	0.0681799	+	0.118091i
$77$	−10.4956			−0.0155335
$78$		0			0
$79$	743.263			1.05853			0.529263	−	0.848458i	$-0.322468\pi$
$79$	743.263			1.05853			0.529263	+	0.848458i	$0.322468\pi$
$80$	110.509	+	191.406i	0.154440	+	0.267499i
$81$	−1324.71	−	2294.46i	−1.81716	−	3.14741i
$82$	−396.184	+	686.211i	−0.533552	+	0.924139i
$83$	539.296			0.713198			0.356599	−	0.934258i	$-0.383936\pi$
$83$	539.296			0.713198			0.356599	+	0.934258i	$0.383936\pi$
$84$	5.25020	−	9.09361i	0.00681957	−	0.0118118i
$85$	550.720	−	953.875i	0.702752	−	1.21720i
$86$	−551.800			−0.691885
$87$	−200.856	+	347.893i	−0.247517	+	0.428713i
$88$	−160.064	−	277.238i	−0.193896	−	0.335837i
$89$	632.070	+	1094.78i	0.752801	+	1.30389i	0.946460	+	0.322821i	$0.104631\pi$
$89$	632.070	+	1094.78i	0.752801	+	1.30389i	−0.193659	+	0.981069i	$0.562035\pi$
$90$	−2021.51			−2.36763
$91$		0			0
$92$	−262.116			−0.297038
$93$	569.225	+	985.927i	0.634687	+	1.09931i
$94$	440.483	+	762.939i	0.483323	+	0.837140i
$95$	−155.999	+	270.199i	−0.168476	+	0.291808i
$96$	320.274			0.340498
$97$	−163.040	+	282.394i	−0.170662	+	0.295596i	−0.938652	−	0.344867i	$-0.887924\pi$
$97$	−163.040	+	282.394i	−0.170662	+	0.295596i	0.767989	+	0.640463i	$0.221257\pi$
$98$	342.931	−	593.974i	0.353482	−	0.612250i
$99$	2928.02			2.97249
$100$	−131.629	+	227.989i	−0.131629	+	0.227989i
$101$	717.578	+	1242.88i	0.706948	+	1.22447i	0.965984	+	0.258602i	$0.0832618\pi$
$101$	717.578	+	1242.88i	0.706948	+	1.22447i	−0.259036	+	0.965868i	$0.583405\pi$
$102$	−798.043	−	1382.25i	−0.774687	−	1.34180i
$103$	1853.77			1.77337			0.886684	−	0.462375i	$-0.153003\pi$
$103$	1853.77			1.77337			0.886684	+	0.462375i	$0.153003\pi$
$104$		0			0
$105$	36.2620			0.0337029
$106$	615.108	+	1065.40i	0.563628	+	0.976233i
$107$	76.9627	+	133.303i	0.0695352	+	0.120438i	0.898697	−	0.438571i	$-0.144515\pi$
$107$	76.9627	+	133.303i	0.0695352	+	0.120438i	−0.829162	+	0.559009i	$0.811182\pi$
$108$	−924.217	+	1600.79i	−0.823452	+	1.42626i
$109$	1788.06			1.57124			0.785621	−	0.618708i	$-0.212343\pi$
$109$	1788.06			1.57124			0.785621	+	0.618708i	$0.212343\pi$
$110$	552.762	−	957.413i	0.479126	−	0.829870i
$111$	−605.917	+	1049.48i	−0.518118	+	0.897407i
$112$	−4.19657			−0.00354052
$113$	464.890	−	805.214i	0.387020	−	0.670338i	−0.605028	−	0.796205i	$-0.706838\pi$
$113$	464.890	−	805.214i	0.387020	−	0.670338i	0.992047	+	0.125867i	$0.0401712\pi$
$114$	226.057	+	391.542i	0.185721	+	0.321678i
$115$	−452.595	−	783.918i	−0.366998	−	0.635659i
$116$	160.547			0.128504
$117$		0			0
$118$	−461.816			−0.360285
$119$	10.4568	+	18.1117i	0.00805524	+	0.0139521i
$120$	553.016	+	957.852i	0.420693	+	0.728662i
$121$	−135.136	+	234.062i	−0.101530	+	0.175855i
$122$	−219.047			−0.162554
$123$	−1982.62	+	3433.99i	−1.45339	+	2.51734i
$124$	227.495	−	394.033i	0.164755	−	0.285365i
$125$	817.560			0.584998
$126$	19.1918	−	33.2411i	0.0135694	−	0.0235028i
$127$	392.742	+	680.249i	0.274411	+	0.475294i	0.969986	−	0.243159i	$-0.0781838\pi$
$127$	392.742	+	680.249i	0.274411	+	0.475294i	−0.695575	+	0.718453i	$0.744850\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$	−2761.36			−1.88469
$130$		0			0
$131$	−2851.17			−1.90159			−0.950793	−	0.309826i	$-0.899729\pi$
$131$	−2851.17			−1.90159			−0.950793	+	0.309826i	$0.899729\pi$
$132$	−801.003	−	1387.38i	−0.528170	−	0.914817i
$133$	−2.96204	−	5.13040i	−0.00193114	−	0.00334483i
$134$	221.132	−	383.012i	0.142559	−	0.246919i
$135$	−6383.37			−4.06958
$136$	−318.944	+	552.428i	−0.201097	+	0.348311i
$137$	201.039	−	348.210i	0.125372	−	0.217150i	−0.796506	−	0.604630i	$-0.793321\pi$
$137$	201.039	−	348.210i	0.125372	−	0.217150i	0.921878	+	0.387480i	$0.126654\pi$
$138$	−1311.70			−0.809128
$139$	−430.111	+	744.975i	−0.262457	+	0.454590i	−0.966894	−	0.255177i	$-0.917866\pi$
$139$	−430.111	+	744.975i	−0.262457	+	0.454590i	0.704437	+	0.709767i	$0.251200\pi$
$140$	−7.24620	−	12.5508i	−0.00437440	−	0.00757668i
$141$	2204.30	+	3817.96i	1.31657	+	2.28036i
$142$	−644.407			−0.380827
$143$		0			0
$144$	1170.74			0.677512
$145$	277.216	+	480.153i	0.158769	+	0.274997i
$146$	323.664	+	560.603i	0.183470	+	0.317780i
$147$	1716.12	−	2972.41i	0.962881	−	1.66776i
$148$	484.319			0.268992
$149$	715.006	−	1238.43i	0.393125	−	0.680912i	−0.599735	−	0.800199i	$-0.704727\pi$
$149$	715.006	−	1238.43i	0.393125	−	0.680912i	0.992860	+	0.119287i	$0.0380608\pi$
$150$	−658.711	+	1140.92i	−0.358557	+	0.621039i
$151$	−941.478			−0.507393			−0.253697	−	0.967284i	$-0.581646\pi$
$151$	−941.478			−0.507393			−0.253697	+	0.967284i	$0.581646\pi$
$152$	90.3455	−	156.483i	0.0482104	−	0.0835029i
$153$	−2917.20	−	5052.73i	−1.54145	−	2.66986i
$154$	10.4956	+	18.1789i	0.00549194	+	0.00951232i
$155$	1571.26			0.814237
$156$		0			0
$157$	−182.395			−0.0927179			−0.0463590	−	0.998925i	$-0.514762\pi$
$157$	−182.395			−0.0927179			−0.0463590	+	0.998925i	$0.514762\pi$
$158$	−743.263	−	1287.37i	−0.374246	−	0.648213i
$159$	3078.17	+	5331.55i	1.53532	+	2.65924i
$160$	221.017	−	382.813i	0.109206	−	0.189150i
$161$	17.1873			0.00841336
$162$	−2649.42	+	4588.93i	−1.28493	+	2.22556i
$163$	−443.611	+	768.356i	−0.213167	+	0.369217i	−0.952704	−	0.303900i	$-0.901711\pi$
$163$	−443.611	+	768.356i	−0.213167	+	0.369217i	0.739537	+	0.673116i	$0.235045\pi$
$164$	1584.74			0.754556
$165$	2766.18	−	4791.16i	1.30513	−	2.26055i
$166$	−539.296	−	934.088i	−0.252154	−	0.436743i
$167$	−1449.33	−	2510.32i	−0.671574	−	1.16320i	−0.977458	−	0.211131i	$-0.932285\pi$
$167$	−1449.33	−	2510.32i	−0.671574	−	1.16320i	0.305884	−	0.952069i	$-0.401048\pi$
$168$	−21.0008			−0.00964433
$169$		0			0
$170$	−2202.88			−0.993842
$171$	826.337	+	1431.26i	0.369542	+	0.640065i
$172$	551.800	+	955.746i	0.244618	+	0.423691i
$173$	−1378.49	+	2387.62i	−0.605808	+	1.04929i	0.386115	+	0.922451i	$0.373817\pi$
$173$	−1378.49	+	2387.62i	−0.605808	+	1.04929i	−0.991923	+	0.126840i	$0.959517\pi$
$174$	803.423			0.350042
$175$	8.63112	−	14.9495i	0.00372829	−	0.00645760i
$176$	−320.127	+	554.477i	−0.137105	+	0.237473i
$177$	−2311.06			−0.981411
$178$	1264.14	−	2189.56i	0.532311	−	0.921990i
$179$	1053.34	+	1824.44i	0.439834	+	0.761815i	0.997676	−	0.0681321i	$-0.0217039\pi$
$179$	1053.34	+	1824.44i	0.439834	+	0.761815i	−0.557842	+	0.829947i	$0.688371\pi$
$180$	2021.51	+	3501.37i	0.837082	+	1.44987i
$181$	778.123			0.319544			0.159772	−	0.987154i	$-0.448924\pi$
$181$	778.123			0.319544			0.159772	+	0.987154i	$0.448924\pi$
$182$		0			0
$183$	−1096.17			−0.442795
$184$	262.116	+	453.999i	0.105019	+	0.181898i
$185$	836.272	+	1448.47i	0.332346	+	0.575640i
$186$	1138.45	−	1971.85i	0.448792	−	0.777330i
$187$	3190.71			1.24774
$188$	880.967	−	1525.88i	0.341761	−	0.591948i
$189$	60.6022	−	104.966i	0.0233236	−	0.0403977i
$190$	623.997			0.238260
$191$	895.531	−	1551.11i	0.339259	−	0.587613i	−0.645035	−	0.764153i	$-0.723157\pi$
$191$	895.531	−	1551.11i	0.339259	−	0.587613i	0.984293	+	0.176540i	$0.0564905\pi$
$192$	−320.274	−	554.731i	−0.120384	−	0.208512i
$193$	−938.493	−	1625.52i	−0.350022	−	0.606255i	0.636231	−	0.771498i	$-0.280492\pi$
$193$	−938.493	−	1625.52i	−0.350022	−	0.606255i	−0.986253	+	0.165243i	$0.947159\pi$
$194$	652.161			0.241353
$195$		0			0
$196$	−1371.72			−0.499900
$197$	−792.022	−	1371.82i	−0.286443	−	0.496133i	0.686515	−	0.727115i	$-0.259139\pi$
$197$	−792.022	−	1371.82i	−0.286443	−	0.496133i	−0.972958	+	0.230982i	$0.925806\pi$
$198$	−2928.02	−	5071.47i	−1.05093	−	1.82027i
$199$	−2484.09	+	4302.57i	−0.884887	+	1.53267i	−0.0390430	+	0.999238i	$0.512431\pi$
$199$	−2484.09	+	4302.57i	−0.884887	+	1.53267i	−0.845844	+	0.533431i	$0.820902\pi$
$200$	526.518			0.186152
$201$	1106.61	−	1916.70i	0.388329	−	0.672605i
$202$	1435.16	−	2485.76i	0.499888	−	0.865831i
$203$	−10.5273			−0.00363976
$204$	−1596.09	+	2764.50i	−0.547786	+	0.948794i
$205$	2736.36	+	4739.51i	0.932272	+	1.61474i
$206$	−1853.77	−	3210.82i	−0.626980	−	1.08596i
$207$	−4794.85			−1.60998
$208$		0			0
$209$	−903.814			−0.299130
$210$	−36.2620	−	62.8076i	−0.0119158	−	0.0206388i
$211$	−1831.34	−	3171.97i	−0.597509	−	1.03492i	−0.993188	−	0.116527i	$-0.962824\pi$
$211$	−1831.34	−	3171.97i	−0.597509	−	1.03492i	0.395678	−	0.918389i	$-0.370509\pi$
$212$	1230.22	−	2130.80i	0.398545	−	0.690301i
$213$	−3224.79			−1.03737
$214$	153.925	−	266.607i	0.0491688	−	0.0851628i
$215$	−1905.58	+	3300.57i	−0.604463	+	1.04696i
$216$	3696.87			1.16454
$217$	−14.9172	+	25.8373i	−0.00466656	+	0.00808272i
$218$	−1788.06	−	3097.02i	−0.555518	−	0.962186i
$219$	1619.71	+	2805.41i	0.499770	+	0.865627i
$220$	−2211.05			−0.677586
$221$		0			0
$222$	2423.67			0.732730
$223$	2247.62	+	3892.99i	0.674940	+	1.16903i	0.976486	+	0.215579i	$0.0691640\pi$
$223$	2247.62	+	3892.99i	0.674940	+	1.16903i	−0.301546	+	0.953452i	$0.597503\pi$
$224$	4.19657	+	7.26867i	0.00125176	+	0.00216812i
$225$	−2407.88	+	4170.56i	−0.713445	+	1.23572i
$226$	−1859.56			−0.547328
$227$	−1800.81	+	3119.09i	−0.526536	+	0.911987i	0.472986	+	0.881070i	$0.343176\pi$
$227$	−1800.81	+	3119.09i	−0.526536	+	0.911987i	−0.999522	+	0.0309171i	$0.990157\pi$
$228$	452.114	−	783.085i	0.131325	−	0.227461i
$229$	5162.11			1.48962			0.744808	−	0.667279i	$-0.232541\pi$
$229$	5162.11			1.48962			0.744808	+	0.667279i	$0.232541\pi$
$230$	−905.191	+	1567.84i	−0.259507	+	0.449479i
$231$	52.5229	+	90.9723i	0.0149600	+	0.0259114i
$232$	−160.547	−	278.076i	−0.0454329	−	0.0786922i
$233$	−2022.92			−0.568781			−0.284390	−	0.958709i	$-0.591791\pi$
$233$	−2022.92			−0.568781			−0.284390	+	0.958709i	$0.591791\pi$
$234$		0			0
$235$	6084.65			1.68902
$236$	461.816	+	799.889i	0.127380	+	0.220629i
$237$	−3719.50	−	6442.36i	−1.01944	−	1.76572i
$238$	20.9136	−	36.2234i	0.00569592	−	0.00986561i
$239$	1423.12			0.385163			0.192581	−	0.981281i	$-0.438314\pi$
$239$	1423.12			0.385163			0.192581	+	0.981281i	$0.438314\pi$
$240$	1106.03	−	1915.70i	0.297475	−	0.515242i
$241$	1777.17	−	3078.15i	0.475011	−	0.822743i	−0.524580	−	0.851361i	$-0.675778\pi$
$241$	1777.17	−	3078.15i	0.475011	−	0.822743i	0.999590	+	0.0286187i	$0.00911086\pi$
$242$	540.544			0.143585
$243$	−7019.96	+	12158.9i	−1.85321	+	3.20986i
$244$	219.047	+	379.401i	0.0574715	+	0.0995436i
$245$	−2368.55	−	4102.45i	−0.617638	−	1.06978i
$246$	7930.47			2.05540
$247$		0			0
$248$	−909.981			−0.232999
$249$	−2698.79	−	4674.44i	−0.686863	−	1.18968i
$250$	−817.560	−	1416.06i	−0.206828	−	0.358237i
$251$	576.202	−	998.011i	0.144899	−	0.250972i	−0.784437	−	0.620209i	$-0.787048\pi$
$251$	576.202	−	998.011i	0.144899	−	0.250972i	0.929335	+	0.369237i	$0.120381\pi$
$252$	−76.7671			−0.0191900
$253$	1311.10	−	2270.90i	0.325804	−	0.564309i
$254$	785.484	−	1360.50i	0.194038	−	0.336083i
$255$	−11023.8			−2.70721
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	924.506	+	1601.29i	0.224393	+	0.388661i	0.956137	−	0.292919i	$-0.0946266\pi$
$257$	924.506	+	1601.29i	0.224393	+	0.388661i	−0.731744	+	0.681580i	$0.761293\pi$
$258$	2761.36	+	4782.82i	0.666337	+	1.15413i
$259$	−31.7575			−0.00761897
$260$		0			0
$261$	2936.86			0.696503
$262$	2851.17	+	4938.37i	0.672312	+	1.16448i
$263$	1675.44	+	2901.95i	0.392822	+	0.680387i	0.992820	−	0.119614i	$-0.0381657\pi$
$263$	1675.44	+	2901.95i	0.392822	+	0.680387i	−0.599999	+	0.800001i	$0.704832\pi$
$264$	−1602.01	+	2774.76i	−0.373472	+	0.646873i
$265$	8496.84			1.96965
$266$	−5.92408	+	10.2608i	−0.00136552	+	0.00236515i
$267$	6326.12	−	10957.2i	1.45001	−	2.51149i
$268$	−884.529			−0.201609
$269$	417.064	−	722.375i	0.0945309	−	0.163732i	−0.814882	−	0.579627i	$-0.803198\pi$
$269$	417.064	−	722.375i	0.0945309	−	0.163732i	0.909413	+	0.415895i	$0.136532\pi$
$270$	6383.37	+	11056.3i	1.43881	+	2.49210i
$271$	4030.53	+	6981.09i	0.903459	+	1.56484i	0.822973	+	0.568081i	$0.192314\pi$
$271$	4030.53	+	6981.09i	0.903459	+	1.56484i	0.0804861	+	0.996756i	$0.474353\pi$
$272$	1275.78			0.284395
$273$		0			0
$274$	−804.157			−0.177303
$275$	−1316.82	−	2280.80i	−0.288753	−	0.500135i
$276$	1311.70	+	2271.94i	0.286070	+	0.495488i
$277$	2354.77	−	4078.58i	0.510774	−	0.884687i	−0.489148	−	0.872201i	$-0.662692\pi$
$277$	2354.77	−	4078.58i	0.510774	−	0.884687i	0.999922	−	0.0124859i	$-0.00397448\pi$
$278$	1720.45			0.371171
$279$	4161.53	−	7207.99i	0.892991	−	1.54671i
$280$	−14.4924	+	25.1016i	−0.00309317	+	0.00535752i
$281$	2110.40			0.448028			0.224014	−	0.974586i	$-0.428084\pi$
$281$	2110.40			0.448028			0.224014	+	0.974586i	$0.428084\pi$
$282$	4408.60	−	7635.93i	0.930952	−	1.61246i
$283$	−546.796	−	947.078i	−0.114854	−	0.198933i	0.802867	−	0.596158i	$-0.203307\pi$
$283$	−546.796	−	947.078i	−0.114854	−	0.198933i	−0.917721	+	0.397225i	$0.869973\pi$
$284$	644.407	+	1116.15i	0.134643	+	0.233208i
$285$	3122.66			0.649018
$286$		0			0
$287$	−103.913			−0.0213722
$288$	−1170.74	−	2027.78i	−0.239537	−	0.414890i
$289$	−722.419	−	1251.27i	−0.147042	−	0.254685i
$290$	554.433	−	960.305i	0.112267	−	0.194452i
$291$	3263.60			0.657441
$292$	647.328	−	1121.21i	0.129733	−	0.224704i
$293$	−4802.59	+	8318.33i	−0.957578	+	1.65857i	−0.229223	+	0.973374i	$0.573619\pi$
$293$	−4802.59	+	8318.33i	−0.957578	+	1.65857i	−0.728355	+	0.685200i	$0.759715\pi$
$294$	−6864.50			−1.36172
$295$	−1594.83	+	2762.33i	−0.314762	+	0.545184i
$296$	−484.319	−	838.865i	−0.0951030	−	0.164723i
$297$	−9245.85	−	16014.3i	−1.80639	−	3.12876i
$298$	−2860.02			−0.555962
$299$		0			0
$300$	2634.84			0.507076
$301$	−36.1823	−	62.6695i	−0.00692861	−	0.0120007i
$302$	941.478	+	1630.69i	0.179391	+	0.310714i
$303$	7181.93	−	12439.5i	1.36169	−	2.35851i
$304$	−361.382			−0.0681799
$305$	−756.455	+	1310.22i	−0.142015	+	0.245977i
$306$	−5834.39	+	10105.5i	−1.08997	+	1.88788i
$307$	−4387.82			−0.815721			−0.407860	−	0.913044i	$-0.633725\pi$
$307$	−4387.82			−0.815721			−0.407860	+	0.913044i	$0.633725\pi$
$308$	20.9912	−	36.3578i	0.00388339	−	0.00672622i
$309$	−9276.77	−	16067.8i	−1.70789	−	2.95815i
$310$	−1571.26	−	2721.50i	−0.287876	−	0.498616i
$311$	2875.57			0.524304			0.262152	−	0.965027i	$-0.415568\pi$
$311$	2875.57			0.524304			0.262152	+	0.965027i	$0.415568\pi$
$312$		0			0
$313$	5715.61			1.03216			0.516078	−	0.856541i	$-0.327391\pi$
$313$	5715.61			1.03216			0.516078	+	0.856541i	$0.327391\pi$
$314$	182.395	+	315.918i	0.0327807	+	0.0567779i
$315$	−132.553	−	229.589i	−0.0237097	−	0.0410663i
$316$	−1486.53	+	2574.74i	−0.264632	+	0.458356i
$317$	−7381.87			−1.30791			−0.653954	−	0.756534i	$-0.726891\pi$
$317$	−7381.87			−1.30791			−0.653954	+	0.756534i	$0.726891\pi$
$318$	6156.35	−	10663.1i	1.08563	−	1.88037i
$319$	−803.055	+	1390.93i	−0.140948	+	0.244129i
$320$	−884.069			−0.154440
$321$	770.286	−	1334.17i	0.133935	−	0.231982i
$322$	−17.1873	−	29.7693i	−0.00297457	−	0.00515211i
$323$	900.474	+	1559.67i	0.155120	+	0.268676i
$324$	10597.7			1.81716
$325$		0			0
$326$	1774.44			0.301464
$327$	−8947.97	−	15498.3i	−1.51322	−	2.62098i
$328$	−1584.74	−	2744.85i	−0.266776	−	0.462069i
$329$	−57.7662	+	100.054i	−0.00968010	+	0.0167664i
$330$	−11064.7			−1.84573
$331$	−3027.29	+	5243.43i	−0.502704	+	0.870709i	0.497291	+	0.867584i	$0.334328\pi$
$331$	−3027.29	+	5243.43i	−0.502704	+	0.870709i	−0.999995	+	0.00312540i	$0.999005\pi$
$332$	−1078.59	+	1868.18i	−0.178299	+	0.308824i
$333$	8859.57			1.45796
$334$	−2898.67	+	5020.64i	−0.474874	+	0.822507i
$335$	−1527.31	−	2645.38i	−0.249092	−	0.431441i
$336$	21.0008	+	36.3745i	0.00340978	+	0.00590592i
$337$	−3686.95			−0.595967			−0.297984	−	0.954571i	$-0.596314\pi$
$337$	−3686.95			−0.595967			−0.297984	+	0.954571i	$0.596314\pi$
$338$		0			0
$339$	−9305.77			−1.49091
$340$	2202.88	+	3815.50i	0.351376	+	0.608601i
$341$	2275.86	+	3941.90i	0.361421	+	0.626000i
$342$	1652.67	−	2862.52i	0.261305	−	0.452594i
$343$	179.910			0.0283213
$344$	1103.60	−	1911.49i	0.172971	−	0.299595i
$345$	−4529.83	+	7845.90i	−0.706892	+	1.22437i
$346$	5513.97			0.856742
$347$	3267.55	−	5659.56i	0.505508	−	0.875566i	−0.494472	−	0.869194i	$-0.664638\pi$
$347$	3267.55	−	5659.56i	0.505508	−	0.875566i	0.999980	−	0.00637190i	$-0.00202825\pi$
$348$	−803.423	−	1391.57i	−0.123759	−	0.214356i
$349$	1486.70	+	2575.04i	0.228027	+	0.394954i	0.957223	−	0.289351i	$-0.0934393\pi$
$349$	1486.70	+	2575.04i	0.228027	+	0.394954i	−0.729197	+	0.684304i	$0.760106\pi$
$350$	−34.5245			−0.00527260
$351$		0			0
$352$	1280.51			0.193896
$353$	−5546.12	−	9606.15i	−0.836232	−	1.44840i	−0.893023	−	0.450011i	$-0.851420\pi$
$353$	−5546.12	−	9606.15i	−0.836232	−	1.44840i	0.0567910	−	0.998386i	$-0.481913\pi$
$354$	2311.06	+	4002.87i	0.346981	+	0.600989i
$355$	−2225.39	+	3854.49i	−0.332708	+	0.576268i
$356$	−5056.56			−0.752801
$357$	104.658	−	181.272i	0.0155156	−	0.0268738i
$358$	2106.68	−	3648.88i	0.311010	−	0.538684i
$359$	−5263.11			−0.773751			−0.386875	−	0.922132i	$-0.626446\pi$
$359$	−5263.11			−0.773751			−0.386875	+	0.922132i	$0.626446\pi$
$360$	4043.03	−	7002.73i	0.591907	−	1.02521i
$361$	3174.43	+	5498.27i	0.462812	+	0.801614i
$362$	−778.123	−	1347.75i	−0.112976	−	0.195680i
$363$	2705.03			0.391122
$364$		0			0
$365$	4470.96			0.641152
$366$	1096.17	+	1898.63i	0.156552	+	0.271155i
$367$	−4334.56	−	7507.68i	−0.616518	−	1.06784i	−0.990116	−	0.140250i	$-0.955209\pi$
$367$	−4334.56	−	7507.68i	−0.616518	−	1.06784i	0.373598	−	0.927591i	$-0.378124\pi$
$368$	524.233	−	907.998i	0.0742596	−	0.128621i
$369$	28989.3			4.08977
$370$	1672.54	−	2896.93i	0.235004	−	0.407039i
$371$	−80.6670	+	139.719i	−0.0112885	+	0.0195522i
$372$	−4553.80			−0.634687
$373$	−3929.86	+	6806.72i	−0.545524	+	0.944876i	0.453049	+	0.891486i	$0.350336\pi$
$373$	−3929.86	+	6806.72i	−0.545524	+	0.944876i	−0.998574	+	0.0533906i	$0.982997\pi$
$374$	−3190.71	−	5526.47i	−0.441144	−	0.764083i
$375$	−4091.30	−	7086.34i	−0.563397	−	0.975832i
$376$	−3523.87			−0.483323
$377$		0			0
$378$	−242.409			−0.0329846
$379$	1540.26	+	2667.80i	0.208754	+	0.361572i	0.951322	−	0.308198i	$-0.0997259\pi$
$379$	1540.26	+	2667.80i	0.208754	+	0.361572i	−0.742568	+	0.669770i	$0.766393\pi$
$380$	−623.997	−	1080.79i	−0.0842378	−	0.145904i
$381$	3930.78	−	6808.31i	0.528556	−	0.915487i
$382$	−3582.13			−0.479784
$383$	715.562	−	1239.39i	0.0954661	−	0.165352i	−0.814337	−	0.580392i	$-0.802899\pi$
$383$	715.562	−	1239.39i	0.0954661	−	0.165352i	0.909803	+	0.415040i	$0.136233\pi$
$384$	−640.548	+	1109.46i	−0.0851246	+	0.147440i
$385$	144.982			0.0191921
$386$	−1876.99	+	3251.03i	−0.247503	+	0.428687i
$387$	10094.0	+	17483.3i	1.32586	+	2.29645i
$388$	−652.161	−	1129.58i	−0.0853311	−	0.147798i
$389$	11639.0			1.51701			0.758507	−	0.651665i	$-0.225929\pi$
$389$	11639.0			1.51701			0.758507	+	0.651665i	$0.225929\pi$
$390$		0			0
$391$	−5225.03			−0.675809
$392$	1371.72	+	2375.90i	0.176741	+	0.306125i
$393$	14268.1	+	24713.0i	1.83137	+	3.17202i
$394$	−1584.04	+	2743.64i	−0.202546	+	0.350819i
$395$	−10267.1			−1.30783
$396$	−5856.03	+	10142.9i	−0.743123	+	1.28713i
$397$	−593.609	+	1028.16i	−0.0750438	+	0.129980i	−0.901105	−	0.433600i	$-0.857243\pi$
$397$	−593.609	+	1028.16i	−0.0750438	+	0.129980i	0.826062	+	0.563580i	$0.190576\pi$
$398$	9936.36			1.25142
$399$	−29.6457	+	51.3479i	−0.00371966	+	0.00644264i
$400$	−526.518	−	911.956i	−0.0658147	−	0.113994i
$401$	1674.14	+	2899.69i	0.208485	+	0.361106i	0.951237	−	0.308460i	$-0.0998135\pi$
$401$	1674.14	+	2899.69i	0.208485	+	0.361106i	−0.742753	+	0.669566i	$0.766480\pi$
$402$	−4426.43			−0.549180
$403$		0			0
$404$	−5740.63			−0.706948
$405$	18299.0	+	31694.7i	2.24514	+	3.88870i
$406$	10.5273	+	18.2338i	0.00128685	+	0.00222889i
$407$	−2422.56	+	4195.99i	−0.295041	+	0.511026i
$408$	6384.35			0.774687
$409$	−8069.81	+	13977.3i	−0.975615	+	1.68981i	−0.297723	+	0.954652i	$0.596227\pi$
$409$	−8069.81	+	13977.3i	−0.975615	+	1.68981i	−0.677892	+	0.735162i	$0.737106\pi$
$410$	5472.72	−	9479.03i	0.659216	−	1.14179i
$411$	−4024.23			−0.482970
$412$	−3707.53	+	6421.63i	−0.443342	+	0.767891i
$413$	−30.2819	−	52.4498i	−0.00360793	−	0.00624912i
$414$	4794.85	+	8304.93i	0.569213	+	0.985905i
$415$	−7449.60			−0.881173
$416$		0			0
$417$	8609.60			1.01106
$418$	903.814	+	1565.45i	0.105758	+	0.183179i
$419$	−3173.29	−	5496.30i	−0.369989	−	0.640840i	0.619574	−	0.784938i	$-0.287305\pi$
$419$	−3173.29	−	5496.30i	−0.369989	−	0.640840i	−0.989563	+	0.144098i	$0.953972\pi$
$420$	−72.5240	+	125.615i	−0.00842574	+	0.0145938i
$421$	−5135.18			−0.594473			−0.297236	−	0.954804i	$-0.596065\pi$
$421$	−5135.18			−0.594473			−0.297236	+	0.954804i	$0.596065\pi$
$422$	−3662.67	+	6343.94i	−0.422503	+	0.731796i
$423$	16115.4	−	27912.6i	1.85238	−	3.20841i
$424$	−4920.87			−0.563628
$425$	−2623.90	+	4544.73i	−0.299478	+	0.518711i
$426$	3224.79	+	5585.51i	0.366765	+	0.635255i
$427$	−14.3632	−	24.8778i	−0.00162783	−	0.00281949i
$428$	−615.701			−0.0695352
$429$		0			0
$430$	7622.33			0.854840
$431$	−3522.27	−	6100.75i	−0.393647	−	0.681816i	0.599281	−	0.800539i	$-0.295453\pi$
$431$	−3522.27	−	6100.75i	−0.393647	−	0.681816i	−0.992927	+	0.118723i	$0.962120\pi$
$432$	−3696.87	−	6403.17i	−0.411726	−	0.713131i
$433$	−5086.91	+	8810.79i	−0.564576	+	0.977874i	0.432513	+	0.901628i	$0.357627\pi$
$433$	−5086.91	+	8810.79i	−0.564576	+	0.977874i	−0.997089	+	0.0762465i	$0.975706\pi$
$434$	59.6687			0.00659951
$435$	2774.54	−	4805.64i	0.305813	−	0.529684i
$436$	−3576.13	+	6194.03i	−0.392811	+	0.680368i
$437$	1480.06			0.162016
$438$	3239.41	−	5610.83i	0.353391	−	0.612091i
$439$	−3192.79	−	5530.08i	−0.347116	−	0.601222i	0.638620	−	0.769522i	$-0.279505\pi$
$439$	−3192.79	−	5530.08i	−0.347116	−	0.601222i	−0.985736	+	0.168300i	$0.946172\pi$
$440$	2211.05	+	3829.65i	0.239563	+	0.414935i
$441$	−25092.7			−2.70951
$442$		0			0
$443$	2362.81			0.253410			0.126705	−	0.991940i	$-0.459560\pi$
$443$	2362.81			0.253410			0.126705	+	0.991940i	$0.459560\pi$
$444$	−2423.67	−	4197.92i	−0.259059	−	0.448704i
$445$	−8731.15	−	15122.8i	−0.930104	−	1.61099i
$446$	4495.24	−	7785.98i	0.477255	−	0.826630i
$447$	−14312.4			−1.51443
$448$	8.39313	−	14.5373i	0.000885130	−	0.00153309i
$449$	−4074.10	+	7056.55i	−0.428216	+	0.741691i	−0.996715	−	0.0809928i	$-0.974191\pi$
$449$	−4074.10	+	7056.55i	−0.428216	+	0.741691i	0.568499	+	0.822684i	$0.307524\pi$
$450$	9631.50			1.00896
$451$	−7926.84	+	13729.7i	−0.827628	+	1.43349i
$452$	1859.56	+	3220.86i	0.193510	+	0.335169i
$453$	4711.42	+	8160.42i	0.488657	+	0.846379i
$454$	7203.22			0.744634
$455$		0			0
$456$	−1808.46			−0.185721
$457$	7017.20	+	12154.1i	0.718273	+	1.24408i	0.961684	+	0.274162i	$0.0884003\pi$
$457$	7017.20	+	12154.1i	0.718273	+	1.24408i	−0.243411	+	0.969923i	$0.578266\pi$
$458$	−5162.11	−	8941.04i	−0.526658	−	0.912199i
$459$	−18423.4	+	31910.2i	−1.87348	+	3.24497i
$460$	3620.76			0.366998
$461$	3845.85	−	6661.21i	0.388545	−	0.672979i	−0.603709	−	0.797204i	$-0.706311\pi$
$461$	3845.85	−	6661.21i	0.388545	−	0.672979i	0.992254	+	0.124225i	$0.0396446\pi$
$462$	105.046	−	181.945i	0.0105783	−	0.0183221i
$463$	15555.9			1.56144			0.780719	−	0.624883i	$-0.214853\pi$
$463$	15555.9			1.56144			0.780719	+	0.624883i	$0.214853\pi$
$464$	−321.094	+	556.152i	−0.0321259	+	0.0556438i
$465$	−7863.03	−	13619.2i	−0.784171	−	1.35822i
$466$	2022.92	+	3503.80i	0.201094	+	0.348306i
$467$	−11941.8			−1.18330			−0.591648	−	0.806197i	$-0.701522\pi$
$467$	−11941.8			−1.18330			−0.591648	+	0.806197i	$0.701522\pi$
$468$		0			0
$469$	57.9997			0.00571040
$470$	−6084.65	−	10538.9i	−0.597157	−	1.03431i
$471$	912.757	+	1580.94i	0.0892943	+	0.154662i
$472$	923.633	−	1599.78i	0.0900713	−	0.156008i
$473$	−11040.4			−1.07323
$474$	−7438.99	+	12884.7i	−0.720853	+	1.24855i
$475$	743.258	−	1287.36i	0.0717958	−	0.124354i
$476$	−83.6544			−0.00805524
$477$	22504.1	−	38978.3i	2.16016	−	3.74150i
$478$	−1423.12	−	2464.91i	−0.136176	−	0.235863i
$479$	7428.22	+	12866.1i	0.708568	+	1.22728i	0.965388	+	0.260817i	$0.0839918\pi$
$479$	7428.22	+	12866.1i	0.708568	+	1.22728i	−0.256820	+	0.966459i	$0.582675\pi$
$480$	−4424.13			−0.420693
$481$		0			0
$482$	−7108.68			−0.671767
$483$	−86.0102	−	148.974i	−0.00810269	−	0.0140343i
$484$	−540.544	−	936.250i	−0.0507648	−	0.0879273i
$485$	2252.17	−	3900.87i	0.210857	−	0.365215i
$486$	28079.9			2.62084
$487$	−7031.81	+	12179.5i	−0.654295	+	1.13327i	0.327775	+	0.944756i	$0.393701\pi$
$487$	−7031.81	+	12179.5i	−0.654295	+	1.13327i	−0.982070	+	0.188516i	$0.939632\pi$
$488$	438.094	−	758.801i	0.0406385	−	0.0703879i
$489$	8879.81			0.821184
$490$	−4737.10	+	8204.91i	−0.436736	+	0.756449i
$491$	4109.04	+	7117.06i	0.377675	+	0.654151i	0.990723	−	0.135893i	$-0.0433905\pi$
$491$	4109.04	+	7117.06i	0.377675	+	0.654151i	−0.613049	+	0.790045i	$0.710057\pi$
$492$	−7930.47	−	13736.0i	−0.726694	−	1.25867i
$493$	3200.35			0.292366
$494$		0			0
$495$	−40446.4			−3.67258
$496$	909.981	+	1576.13i	0.0823777	+	0.142682i
$497$	−42.2546	−	73.1872i	−0.00381364	−	0.00660542i
$498$	−5397.58	+	9348.88i	−0.485685	+	0.841231i
$499$	−6081.91			−0.545619			−0.272809	−	0.962068i	$-0.587953\pi$
$499$	−6081.91			−0.545619			−0.272809	+	0.962068i	$0.587953\pi$
$500$	−1635.12	+	2832.11i	−0.146250	+	0.253312i
$501$	−14505.8	+	25124.7i	−1.29355	+	2.24050i
$502$	−2304.81			−0.204917
$503$	1613.35	−	2794.41i	0.143013	−	0.247707i	−0.785617	−	0.618714i	$-0.787654\pi$
$503$	1613.35	−	2794.41i	0.143013	−	0.247707i	0.928630	+	0.371007i	$0.120987\pi$
$504$	76.7671	+	132.965i	0.00678468	+	0.0117514i
$505$	−9912.32	−	17168.6i	−0.873450	−	1.51286i
$506$	−5244.41			−0.460756
$507$		0			0
$508$	−3141.93			−0.274411
$509$	−314.535	−	544.791i	−0.0273901	−	0.0474410i	0.852005	−	0.523533i	$-0.175386\pi$
$509$	−314.535	−	544.791i	−0.0273901	−	0.0474410i	−0.879396	+	0.476092i	$0.842053\pi$
$510$	11023.8	+	19093.8i	0.957144	+	1.65782i
$511$	−42.4462	+	73.5190i	−0.00367458	+	0.00636455i
$512$	512.000			0.0441942
$513$	5218.68	−	9039.02i	0.449143	−	0.777938i
$514$	1849.01	−	3202.58i	0.158670	−	0.274825i
$515$	−25607.1			−2.19104
$516$	5522.73	−	9565.64i	0.471171	−	0.816093i
$517$	8813.17	+	15264.9i	0.749715	+	1.29854i
$518$	31.7575	+	55.0055i	0.00269371	+	0.00466565i
$519$	27593.4			2.33375
$520$		0			0
$521$	−785.154			−0.0660235			−0.0330117	−	0.999455i	$-0.510510\pi$
$521$	−785.154			−0.0660235			−0.0330117	+	0.999455i	$0.510510\pi$
$522$	−2936.86	−	5086.80i	−0.246251	−	0.426519i
$523$	495.190	+	857.693i	0.0414018	+	0.0717100i	0.885984	−	0.463716i	$-0.153484\pi$
$523$	495.190	+	857.693i	0.0414018	+	0.0717100i	−0.844582	+	0.535426i	$0.820151\pi$
$524$	5702.34	−	9876.74i	0.475397	−	0.823411i
$525$	−172.770			−0.0143625
$526$	3350.88	−	5803.90i	0.277767	−	0.481106i
$527$	4534.89	−	7854.67i	0.374845	−	0.649250i
$528$	6408.03			0.528170
$529$	3936.47	−	6818.16i	0.323536	−	0.560382i
$530$	−8496.84	−	14717.0i	−0.696376	−	1.20616i
$531$	8447.93	+	14632.2i	0.690412	+	1.19583i
$532$	23.6963			0.00193114
$533$		0			0
$534$	−25304.5			−2.05062
$535$	−1063.13	−	1841.39i	−0.0859123	−	0.148804i
$536$	884.529	+	1532.05i	0.0712795	+	0.123460i
$537$	10542.4	−	18260.0i	0.847186	−	1.46737i
$538$	−1668.25			−0.133687
$539$	6861.35	−	11884.2i	0.548310	−	0.949701i
$540$	12766.7	−	22112.6i	1.01739	−	1.76218i
$541$	2509.00			0.199390			0.0996952	−	0.995018i	$-0.468213\pi$
$541$	2509.00			0.199390			0.0996952	+	0.995018i	$0.468213\pi$
$542$	8061.06	−	13962.2i	0.638842	−	1.10651i
$543$	−3893.94	−	6744.51i	−0.307744	−	0.533029i
$544$	−1275.78	−	2209.71i	−0.100549	−	0.174155i
$545$	−24699.5			−1.94131
$546$		0			0
$547$	24461.5			1.91206			0.956032	−	0.293264i	$-0.0947415\pi$
$547$	24461.5			1.91206			0.956032	+	0.293264i	$0.0947415\pi$
$548$	804.157	+	1392.84i	0.0626859	+	0.108575i
$549$	4006.99	+	6940.31i	0.311501	+	0.539536i
$550$	−2633.64	+	4561.59i	−0.204179	+	0.353649i
$551$	−906.545			−0.0700909
$552$	2623.41	−	4543.88i	0.202282	−	0.350363i
$553$	97.4735	−	168.829i	0.00749547	−	0.0129825i
$554$	−9419.08			−0.722344
$555$	8369.88	−	14497.1i	0.640147	−	1.10877i
$556$	−1720.45	−	2979.90i	−0.131229	−	0.227295i
$557$	6114.38	+	10590.4i	0.465125	+	0.805620i	0.999207	−	0.0398124i	$-0.0126760\pi$
$557$	6114.38	+	10590.4i	0.465125	+	0.805620i	−0.534082	+	0.845433i	$0.679343\pi$
$558$	−16646.1			−1.26288
$559$		0			0
$560$	57.9696			0.00437440
$561$	−15967.2	−	27656.0i	−1.20167	−	2.08135i
$562$	−2110.40	−	3655.32i	−0.158402	−	0.274360i
$563$	966.101	−	1673.34i	0.0723203	−	0.125262i	−0.827598	−	0.561322i	$-0.810293\pi$
$563$	966.101	−	1673.34i	0.0723203	−	0.125262i	0.899918	+	0.436060i	$0.143626\pi$
$564$	−17634.4			−1.31657
$565$	−6421.80	+	11122.9i	−0.478172	+	0.828218i
$566$	−1093.59	+	1894.16i	−0.0812139	+	0.140667i
$567$	−694.904			−0.0514695
$568$	1288.81	−	2232.29i	0.0952067	−	0.164903i
$569$	−9871.56	−	17098.1i	−0.727307	−	1.25973i	−0.958017	−	0.286710i	$-0.907438\pi$
$569$	−9871.56	−	17098.1i	−0.727307	−	1.25973i	0.230711	−	0.973022i	$-0.425895\pi$
$570$	−3122.66	−	5408.60i	−0.229463	−	0.397441i
$571$	1327.51			0.0972933			0.0486466	−	0.998816i	$-0.484509\pi$
$571$	1327.51			0.0972933			0.0486466	+	0.998816i	$0.484509\pi$
$572$		0			0
$573$	−17926.0			−1.30692
$574$	103.913	+	179.983i	0.00755620	+	0.0130877i
$575$	2156.39	+	3734.98i	0.156396	+	0.270886i
$576$	−2341.48	+	4055.57i	−0.169378	+	0.293371i
$577$	−15077.5			−1.08784			−0.543921	−	0.839137i	$-0.683061\pi$
$577$	−15077.5			−1.08784			−0.543921	+	0.839137i	$0.683061\pi$
$578$	−1444.84	+	2502.53i	−0.103975	+	0.180089i
$579$	−9392.96	+	16269.1i	−0.674194	+	1.16774i
$580$	−2217.73			−0.158769
$581$	70.7247	−	122.499i	0.00505018	−	0.00874717i
$582$	−3263.60	−	5652.72i	−0.232441	−	0.402599i
$583$	12307.1	+	21316.4i	0.874281	+	1.51430i
$584$	−2589.31			−0.183470
$585$		0			0
$586$	19210.4			1.35422
$587$	3578.28	+	6197.76i	0.251604	+	0.435790i	0.963967	−	0.266020i	$-0.0857087\pi$
$587$	3578.28	+	6197.76i	0.251604	+	0.435790i	−0.712364	+	0.701810i	$0.752375\pi$
$588$	6864.50	+	11889.7i	0.481441	+	0.833880i
$589$	−1284.57	+	2224.95i	−0.0898640	+	0.155649i
$590$	6379.33			0.445141
$591$	−7927.00	+	13730.0i	−0.551731	+	0.955627i
$592$	−968.638	+	1677.73i	−0.0672480	+	0.116477i
$593$	−14729.2			−1.01999			−0.509997	−	0.860176i	$-0.670354\pi$
$593$	−14729.2			−1.01999			−0.509997	+	0.860176i	$0.670354\pi$
$594$	−18491.7	+	32028.5i	−1.27731	+	2.21237i
$595$	−144.446	−	250.187i	−0.00995244	−	0.0172381i
$596$	2860.02	+	4953.71i	0.196562	+	0.340456i
$597$	49724.3			3.40885
$598$		0			0
$599$	28634.9			1.95324			0.976621	−	0.214970i	$-0.0689653\pi$
$599$	28634.9			1.95324			0.976621	+	0.214970i	$0.0689653\pi$
$600$	−2634.84	−	4563.68i	−0.179278	−	0.310519i
$601$	−2757.80	−	4776.64i	−0.187176	−	0.324199i	0.757131	−	0.653263i	$-0.226600\pi$
$601$	−2757.80	−	4776.64i	−0.187176	−	0.324199i	−0.944308	+	0.329064i	$0.893267\pi$
$602$	−72.3646	+	125.339i	−0.00489927	+	0.00848578i
$603$	−16180.5			−1.09274
$604$	1882.96	−	3261.37i	0.126848	−	0.219708i
$605$	1866.71	−	3233.24i	0.125442	−	0.217272i
$606$	−28727.7			−1.92572
$607$	−6449.07	+	11170.1i	−0.431235	+	0.746921i	−0.996980	−	0.0776591i	$-0.975255\pi$
$607$	−6449.07	+	11170.1i	−0.431235	+	0.746921i	0.565745	+	0.824580i	$0.308589\pi$
$608$	361.382	+	625.932i	0.0241052	+	0.0417515i
$609$	52.6816	+	91.2472i	0.00350536	+	0.00607146i
$610$	3025.82			0.200839
$611$		0			0
$612$	23337.6			1.54145
$613$	8040.16	+	13926.0i	0.529754	+	0.917560i	0.999398	+	0.0347045i	$0.0110490\pi$
$613$	8040.16	+	13926.0i	0.529754	+	0.917560i	−0.469644	+	0.882856i	$0.655618\pi$
$614$	4387.82	+	7599.93i	0.288401	+	0.499525i
$615$	27387.0	−	47435.7i	1.79569	−	3.11023i
$616$	−83.9647			−0.00549194
$617$	−461.623	+	799.555i	−0.0301203	+	0.0521700i	−0.880693	−	0.473688i	$-0.842922\pi$
$617$	−461.623	+	799.555i	−0.0301203	+	0.0521700i	0.850572	+	0.525858i	$0.176256\pi$
$618$	−18553.5	+	32135.7i	−1.20766	+	2.09172i
$619$	25650.3			1.66555			0.832773	−	0.553615i	$-0.186752\pi$
$619$	25650.3			1.66555			0.832773	+	0.553615i	$0.186752\pi$
$620$	−3142.52	+	5443.01i	−0.203559	+	0.352575i
$621$	15140.8	+	26224.6i	0.978388	+	1.69462i
$622$	−2875.57	−	4980.63i	−0.185370	−	0.321069i
$623$	331.566			0.0213225
$624$		0			0
$625$	−19520.3			−1.24930
$626$	−5715.61	−	9899.72i	−0.364923	−	0.632064i
$627$	4522.94	+	7833.96i	0.288084	+	0.498976i
$628$	364.790	−	631.835i	0.0231795	−	0.0401480i
$629$	9654.42			0.611999
$630$	−265.107	+	459.179i	−0.0167653	+	0.0290383i
$631$	10873.9	−	18834.2i	0.686029	−	1.18824i	−0.287083	−	0.957906i	$-0.592685\pi$
$631$	10873.9	−	18834.2i	0.686029	−	1.18824i	0.973112	−	0.230332i	$-0.0739812\pi$
$632$	5946.10			0.374246
$633$	−18329.0	+	31746.8i	−1.15089	+	1.99340i
$634$	7381.87	+	12785.8i	0.462416	+	0.800927i
$635$	−5425.17	−	9396.66i	−0.339041	−	0.587237i
$636$	−24625.4			−1.53532
$637$		0			0
$638$	3212.22			0.199331
$639$	11788.0	+	20417.5i	0.729776	+	1.26401i
$640$	884.069	+	1531.25i	0.0546029	+	0.0945751i
$641$	−11113.9	+	19249.8i	−0.684822	+	1.18615i	0.288671	+	0.957428i	$0.406787\pi$
$641$	−11113.9	+	19249.8i	−0.684822	+	1.18615i	−0.973493	+	0.228718i	$0.926547\pi$
$642$	−3081.14			−0.189413
$643$	−1424.23	+	2466.83i	−0.0873498	+	0.151294i	−0.906390	−	0.422442i	$-0.861173\pi$
$643$	−1424.23	+	2466.83i	−0.0873498	+	0.151294i	0.819040	+	0.573736i	$0.194506\pi$
$644$	−34.3747	+	59.5387i	−0.00210334	+	0.00364309i
$645$	38144.3			2.32857
$646$	1800.95	−	3119.33i	0.109686	−	0.189982i
$647$	−2074.43	−	3593.02i	−0.126050	−	0.218325i	0.796093	−	0.605174i	$-0.206897\pi$
$647$	−2074.43	−	3593.02i	−0.126050	−	0.218325i	−0.922143	+	0.386850i	$0.873563\pi$
$648$	−10597.7	−	18355.7i	−0.642463	−	1.11278i
$649$	−9240.00			−0.558862
$650$		0			0
$651$	298.599			0.0179770
$652$	−1774.44	−	3073.42i	−0.106584	−	0.184608i
$653$	−6208.89	−	10754.1i	−0.372087	−	0.644473i	0.617800	−	0.786335i	$-0.288024\pi$
$653$	−6208.89	−	10754.1i	−0.372087	−	0.644473i	−0.989886	+	0.141863i	$0.954691\pi$
$654$	−17895.9	+	30996.7i	−1.07001	+	1.85331i
$655$	39384.8			2.34945
$656$	−3169.47	+	5489.69i	−0.188639	+	0.326732i
$657$	11841.5	−	20510.0i	0.703165	−	1.21792i
$658$	231.065			0.0136897
$659$	7951.44	−	13772.3i	0.470022	−	0.814101i	−0.529391	−	0.848378i	$-0.677579\pi$
$659$	7951.44	−	13772.3i	0.470022	−	0.814101i	0.999412	+	0.0342768i	$0.0109128\pi$
$660$	11064.7	+	19164.6i	0.652566	+	1.13028i
$661$	−13162.3	−	22797.8i	−0.774514	−	1.34150i	−0.935067	−	0.354471i	$-0.884661\pi$
$661$	−13162.3	−	22797.8i	−0.774514	−	1.34150i	0.160553	−	0.987027i	$-0.448672\pi$
$662$	12109.2			0.710931
$663$		0			0
$664$	4314.37			0.252154
$665$	40.9163	+	70.8692i	0.00238597	+	0.00413261i
$666$	−8859.57	−	15345.2i	−0.515467	−	0.892816i
$667$	1315.06	−	2277.76i	0.0763411	−	0.132227i
$668$	11594.7			0.671574
$669$	22495.4	−	38963.2i	1.30004	−	2.25173i
$670$	−3054.62	+	5290.76i	−0.176135	+	0.305075i
$671$	−4382.68			−0.252148
$672$	42.0016	−	72.7489i	0.00241108	−	0.00417612i
$673$	−5793.31	−	10034.3i	−0.331821	−	0.574732i	0.651048	−	0.759037i	$-0.274330\pi$
$673$	−5793.31	−	10034.3i	−0.331821	−	0.574732i	−0.982869	+	0.184305i	$0.940996\pi$
$674$	3686.95	+	6385.99i	0.210706	+	0.364954i
$675$	30413.6			1.73425
$676$		0			0
$677$	−7512.76			−0.426498			−0.213249	−	0.976998i	$-0.568405\pi$
$677$	−7512.76			−0.426498			−0.213249	+	0.976998i	$0.568405\pi$
$678$	9305.77	+	16118.1i	0.527118	+	0.912995i
$679$	42.7631	+	74.0678i	0.00241693	+	0.00418625i
$680$	4405.76	−	7631.00i	0.248460	−	0.430346i
$681$	36047.0			2.02837
$682$	4551.71	−	7883.80i	0.255563	−	0.442649i
$683$	−2177.41	+	3771.38i	−0.121986	+	0.211285i	−0.920551	−	0.390623i	$-0.872260\pi$
$683$	−2177.41	+	3771.38i	−0.121986	+	0.211285i	0.798565	+	0.601909i	$0.205593\pi$
$684$	−6610.70			−0.369542
$685$	−2777.07	+	4810.03i	−0.154900	+	0.268294i
$686$	−179.910	−	311.613i	−0.0100131	−	0.0173432i
$687$	−25832.7	−	44743.5i	−1.43461	−	2.48482i
$688$	−4414.40			−0.244618
$689$		0			0
$690$	18119.3			0.999697
$691$	10267.4	+	17783.7i	0.565255	+	0.979051i	0.997026	+	0.0770672i	$0.0245556\pi$
$691$	10267.4	+	17783.7i	0.565255	+	0.979051i	−0.431771	+	0.901983i	$0.642111\pi$
$692$	−5513.97	−	9550.47i	−0.302904	−	0.524645i
$693$	383.988	−	665.087i	0.0210483	−	0.0364568i
$694$	−13070.2			−0.714896
$695$	5941.38	−	10290.8i	0.324272	−	0.561656i
$696$	−1606.85	+	2783.14i	−0.0875106	+	0.151573i
$697$	31590.2			1.71673
$698$	2973.40	−	5150.09i	0.161239	−	0.279275i
$699$	10123.3	+	17534.0i	0.547778	+	0.948779i
$700$	34.5245	+	59.7982i	0.00186415	+	0.00322880i
$701$	19666.5			1.05962			0.529810	−	0.848117i	$-0.322263\pi$
$701$	19666.5			1.05962			0.529810	+	0.848117i	$0.322263\pi$
$702$		0			0
$703$	−2734.75			−0.146719
$704$	−1280.51	−	2217.91i	−0.0685525	−	0.118736i
$705$	−30449.3	−	52739.7i	−1.62665	−	2.81744i
$706$	−11092.2	+	19212.3i	−0.591305	+	1.02417i
$707$	376.421			0.0200237
$708$	4622.12	−	8005.74i	0.245353	−	0.424964i
$709$	3716.84	−	6437.75i	0.196881	−	0.341008i	−0.750634	−	0.660718i	$-0.770252\pi$
$709$	3716.84	−	6437.75i	0.196881	−	0.341008i	0.947516	+	0.319709i	$0.103585\pi$
$710$	8901.56			0.470521
$711$	−27192.8	+	47099.3i	−1.43433	+	2.48433i
$712$	5056.56	+	8758.22i	0.266155	+	0.460995i
$713$	−3726.89	−	6455.16i	−0.195755	−	0.339057i
$714$	−418.630			−0.0219424
$715$		0			0
$716$	−8426.72			−0.439834
$717$	−7121.68	−	12335.1i	−0.370940	−	0.642487i
$718$	5263.11	+	9115.98i	0.273562	+	0.473823i
$719$	12422.6	−	21516.6i	0.644348	−	1.11604i	−0.340104	−	0.940388i	$-0.610462\pi$
$719$	12422.6	−	21516.6i	0.644348	−	1.11604i	0.984452	−	0.175655i	$-0.0562043\pi$
$720$	−16172.1			−0.837082
$721$	243.108	−	421.075i	0.0125573	−	0.0217499i
$722$	6348.86	−	10996.5i	0.327258	−	0.566827i
$723$	−35573.8			−1.82988
$724$	−1556.25	+	2695.50i	−0.0798859	+	0.138366i
$725$	−1320.80	−	2287.69i	−0.0676595	−	0.117190i
$726$	−2705.03	−	4685.26i	−0.138283	−	0.239513i
$727$	8215.91			0.419135			0.209568	−	0.977794i	$-0.432794\pi$
$727$	8215.91			0.419135			0.209568	+	0.977794i	$0.432794\pi$
$728$		0			0
$729$	68985.2			3.50481
$730$	−4470.96	−	7743.92i	−0.226682	−	0.392624i
$731$	10999.6	+	19051.8i	0.556545	+	0.963964i
$732$	2192.35	−	3797.25i	0.110699	−	0.191736i
$733$	−5235.91			−0.263838			−0.131919	−	0.991261i	$-0.542114\pi$
$733$	−5235.91			−0.263838			−0.131919	+	0.991261i	$0.542114\pi$
$734$	−8669.12	+	15015.4i	−0.435944	+	0.755077i
$735$	−23705.8	+	41059.7i	−1.18966	+	2.06056i
$736$	−2096.93			−0.105019
$737$	4424.40	−	7663.29i	0.221133	−	0.383013i
$738$	−28989.3	−	50211.0i	−1.44595	−	2.50446i
$739$	5792.55	+	10033.0i	0.288339	+	0.499418i	0.973413	−	0.229055i	$-0.0735637\pi$
$739$	5792.55	+	10033.0i	0.288339	+	0.499418i	−0.685074	+	0.728473i	$0.740230\pi$
$740$	−6690.18			−0.332346
$741$		0			0
$742$	322.668			0.0159643
$743$	13500.0	+	23382.7i	0.666578	+	1.15455i	0.978855	+	0.204556i	$0.0655751\pi$
$743$	13500.0	+	23382.7i	0.666578	+	1.15455i	−0.312277	+	0.949991i	$0.601092\pi$
$744$	4553.80	+	7887.42i	0.224396	+	0.388665i
$745$	−9876.79	+	17107.1i	−0.485715	+	0.841282i
$746$	15719.5			0.771488
$747$	−19730.5	+	34174.2i	−0.966401	+	1.67385i
$748$	−6381.42	+	11052.9i	−0.311936	+	0.540288i
$749$	40.3724			0.00196953
$750$	−8182.60	+	14172.7i	−0.398382	+	0.690017i
$751$	−3986.25	−	6904.39i	−0.193689	−	0.335479i	0.752781	−	0.658271i	$-0.228712\pi$
$751$	−3986.25	−	6904.39i	−0.193689	−	0.335479i	−0.946470	+	0.322792i	$0.895379\pi$
$752$	3523.87	+	6103.52i	0.170881	+	0.295974i
$753$	−11533.9			−0.558192
$754$		0			0
$755$	13005.2			0.626896
$756$	242.409	+	419.864i	0.0116618	+	0.0201988i
$757$	−10310.5	−	17858.3i	−0.495034	−	0.857424i	0.504949	−	0.863149i	$-0.331511\pi$
$757$	−10310.5	−	17858.3i	−0.495034	−	0.857424i	−0.999984	+	0.00572455i	$0.998178\pi$
$758$	3080.51	−	5335.61i	0.147611	−	0.255670i
$759$	−26244.5			−1.25509
$760$	−1247.99	+	2161.59i	−0.0595651	+	0.103170i
$761$	−12550.2	+	21737.6i	−0.597826	+	1.03546i	0.395316	+	0.918545i	$0.370635\pi$
$761$	−12550.2	+	21737.6i	−0.597826	+	1.03546i	−0.993141	+	0.116919i	$0.962698\pi$
$762$	−15723.1			−0.747492
$763$	234.492	−	406.151i	0.0111260	−	0.0192709i
$764$	3582.13	+	6204.42i	0.169629	+	0.293806i
$765$	40296.9	+	69796.3i	1.90449	+	3.29868i
$766$	−2862.25			−0.135009
$767$		0			0
$768$	2562.19			0.120384
$769$	−17181.7	−	29759.5i	−0.805705	−	1.39552i	−0.915814	−	0.401602i	$-0.868453\pi$
$769$	−17181.7	−	29759.5i	−0.805705	−	1.39552i	0.110109	−	0.993920i	$-0.464880\pi$
$770$	−144.982	−	251.115i	−0.00678542	−	0.0117527i
$771$	9252.97	−	16026.6i	0.432215	−	0.748618i
$772$	7507.94			0.350022
$773$	13633.4	−	23613.7i	0.634357	−	1.09874i	−0.352294	−	0.935889i	$-0.614598\pi$
$773$	13633.4	−	23613.7i	0.634357	−	1.09874i	0.986651	−	0.162849i	$-0.0520683\pi$
$774$	20188.0	−	34966.6i	0.937521	−	1.62383i
$775$	−7486.27			−0.346987
$776$	−1304.32	+	2259.15i	−0.0603382	+	0.104509i
$777$	158.923	+	275.263i	0.00733763	+	0.0127092i
$778$	−11639.0	−	20159.3i	−0.536346	−	0.928978i
$779$	−8948.37			−0.411564
$780$		0			0
$781$	−12893.3			−0.590726
$782$	5225.03	+	9050.02i	0.238934	+	0.413847i
$783$	−9273.78	−	16062.7i	−0.423267	−	0.733120i
$784$	2743.45	−	4751.79i	0.124975	−	0.216463i
$785$	2519.53			0.114555
$786$	28536.1	−	49426.0i	1.29497	−	2.24296i
$787$	−7310.34	+	12661.9i	−0.331112	+	0.573504i	−0.982730	−	0.185044i	$-0.940757\pi$
$787$	−7310.34	+	12661.9i	−0.331112	+	0.573504i	0.651618	+	0.758547i	$0.274091\pi$
$788$	6336.17			0.286443
$789$	16768.7	−	29044.3i	0.756633	−	1.31053i
$790$	10267.1	+	17783.2i	0.462389	+	0.800882i
$791$	−121.934	−	211.196i	−0.00548100	−	0.00949338i
$792$	23424.1			1.05093
$793$		0			0
$794$	2374.44			0.106128
$795$	−42520.6	−	73647.8i	−1.89692	−	3.28556i
$796$	−9936.36	−	17210.3i	−0.442443	−	0.766334i
$797$	−4136.59	+	7164.79i	−0.183846	+	0.318431i	−0.943187	−	0.332262i	$-0.892188\pi$
$797$	−4136.59	+	7164.79i	−0.183846	+	0.318431i	0.759341	+	0.650693i	$0.225522\pi$
$798$	118.583			0.00526039
$799$	17561.2	−	30416.9i	0.777560	−	1.34677i
$800$	−1053.04	+	1823.91i	−0.0465380	+	0.0806063i
$801$	−92498.9			−4.08026
$802$	3348.27	−	5799.38i	0.147421	−	0.255341i
$803$	6475.85	+	11216.5i	0.284593	+	0.492929i
$804$	4426.43	+	7666.80i	0.194164	+	0.336303i
$805$	−237.418			−0.0103949
$806$		0			0
$807$	−8348.41			−0.364161
$808$	5740.63	+	9943.06i	0.249944	+	0.432915i
$809$	22673.1	+	39271.0i	0.985346	+	1.70667i	0.640389	+	0.768051i	$0.278773\pi$
$809$	22673.1	+	39271.0i	0.985346	+	1.70667i	0.344957	+	0.938618i	$0.387893\pi$
$810$	36597.9	−	63389.4i	1.58756	−	2.74973i
$811$	20946.4			0.906940			0.453470	−	0.891272i	$-0.350186\pi$
$811$	20946.4			0.906940			0.453470	+	0.891272i	$0.350186\pi$
$812$	21.0546	−	36.4676i	0.000909940	−	0.00157606i
$813$	40339.8	−	69870.6i	1.74020	−	3.01411i
$814$	9690.23			0.417251
$815$	6127.85	−	10613.7i	0.263373	−	0.456176i
$816$	−6384.35	−	11058.0i	−0.273893	−	0.474397i
$817$	−3115.79	−	5396.71i	−0.133424	−	0.231098i
$818$	32279.2			1.37973
$819$		0			0
$820$	−21890.9			−0.932272
$821$	10766.6	+	18648.3i	0.457683	+	0.792731i	0.998838	−	0.0481924i	$-0.0153461\pi$
$821$	10766.6	+	18648.3i	0.457683	+	0.792731i	−0.541155	+	0.840923i	$0.682013\pi$
$822$	4024.23	+	6970.17i	0.170756	+	0.295757i
$823$	−10996.9	+	19047.3i	−0.465771	+	0.806739i	−0.999236	−	0.0390833i	$-0.987556\pi$
$823$	−10996.9	+	19047.3i	−0.465771	+	0.806739i	0.533465	+	0.845822i	$0.320890\pi$
$824$	14830.1			0.626980
$825$	−13179.5	+	22827.5i	−0.556181	+	0.963334i
$826$	−60.5638	+	104.900i	−0.00255119	+	0.00441880i
$827$	7954.97			0.334488			0.167244	−	0.985916i	$-0.446513\pi$
$827$	7954.97			0.334488			0.167244	+	0.985916i	$0.446513\pi$
$828$	9589.70	−	16609.9i	0.402494	−	0.697140i
$829$	−2288.22	−	3963.32i	−0.0958665	−	0.166046i	0.814103	−	0.580720i	$-0.197229\pi$
$829$	−2288.22	−	3963.32i	−0.0958665	−	0.166046i	−0.909970	+	0.414674i	$0.863896\pi$
$830$	7449.60	+	12903.1i	0.311542	+	0.539606i
$831$	−47135.7			−1.96765
$832$		0			0
$833$	−27344.0			−1.13735
$834$	−8609.60	−	14912.3i	−0.357465	−	0.619148i
$835$	20020.5	+	34676.5i	0.829745	+	1.43716i
$836$	1807.63	−	3130.90i	0.0747824	−	0.129527i
$837$	−52563.8			−2.17069
$838$	−6346.58	+	10992.6i	−0.261622	+	0.453142i
$839$	−4067.18	+	7044.57i	−0.167360	+	0.289876i	−0.937491	−	0.348010i	$-0.886857\pi$
$839$	−4067.18	+	7044.57i	−0.167360	+	0.289876i	0.770131	+	0.637886i	$0.220191\pi$
$840$	290.096			0.0119158
$841$	11389.0	−	19726.4i	0.466974	−	0.808822i
$842$	5135.18	+	8894.38i	0.210178	+	0.364039i
$843$	−10561.0	−	18292.3i	−0.431485	−	0.747353i
$844$	14650.7			0.597509
$845$		0			0
$846$	−64461.5			−2.61966
$847$	35.4442	+	61.3912i	0.00143787	+	0.00249047i
$848$	4920.87	+	8523.19i	0.199273	+	0.345150i
$849$	−5472.64	+	9478.89i	−0.221226	+	0.383174i
$850$	10495.6			0.423525
$851$	3967.12	−	6871.26i	0.159802	−	0.276785i
$852$	6449.59	−	11171.0i	0.259342	−	0.449193i
$853$	−44562.9			−1.78875			−0.894375	−	0.447317i	$-0.852380\pi$
$853$	−44562.9			−1.78875			−0.894375	+	0.447317i	$0.852380\pi$
$854$	−28.7264	+	49.7556i	−0.00115105	+	0.00199368i
$855$	−11414.7	−	19770.8i	−0.456577	−	0.790815i
$856$	615.701	+	1066.43i	0.0245844	+	0.0425814i
$857$	18917.8			0.754048			0.377024	−	0.926204i	$-0.376947\pi$
$857$	18917.8			0.754048			0.377024	+	0.926204i	$0.376947\pi$
$858$		0			0
$859$	−27153.9			−1.07855			−0.539277	−	0.842128i	$-0.681303\pi$
$859$	−27153.9			−1.07855			−0.539277	+	0.842128i	$0.681303\pi$
$860$	−7622.33	−	13202.3i	−0.302232	−	0.523481i
$861$	520.012	+	900.687i	0.0205830	+	0.0356508i
$862$	−7044.54	+	12201.5i	−0.278350	+	0.482117i
$863$	−33687.7			−1.32879			−0.664393	−	0.747384i	$-0.731310\pi$
$863$	−33687.7			−1.32879			−0.664393	+	0.747384i	$0.731310\pi$
$864$	−7393.74	+	12806.3i	−0.291134	+	0.504260i
$865$	19041.9	−	32981.5i	0.748490	−	1.29642i
$866$	20347.6			0.798431
$867$	−7230.38	+	12523.4i	−0.283225	+	0.490561i
$868$	−59.6687	−	103.349i	−0.00233328	−	0.00404136i
$869$	−14871.2	−	25757.6i	−0.580518	−	1.00549i
$870$	−11098.1			−0.432486
$871$		0			0
$872$	14304.5			0.555518
$873$	−11929.9	−	20663.1i	−0.462503	−	0.801078i
$874$	−1480.06	−	2563.55i	−0.0572814	−	0.0992143i
$875$	107.217	−	185.705i	0.00414240	−	0.00717484i
$876$	−12957.7			−0.499770
$877$	21238.0	−	36785.2i	0.817737	−	1.41636i	−0.0896088	−	0.995977i	$-0.528562\pi$
$877$	21238.0	−	36785.2i	0.817737	−	1.41636i	0.907346	−	0.420385i	$-0.138105\pi$
$878$	−6385.59	+	11060.2i	−0.245448	+	0.425128i
$879$	96134.1			3.68888
$880$	4422.10	−	7659.30i	0.169397	−	0.293403i
$881$	9903.32	+	17153.1i	0.378719	+	0.655961i	0.990876	−	0.134776i	$-0.0430314\pi$
$881$	9903.32	+	17153.1i	0.378719	+	0.655961i	−0.612157	+	0.790736i	$0.709698\pi$
$882$	25092.7	+	43461.9i	0.957955	+	1.65923i
$883$	29417.9			1.12117			0.560584	−	0.828098i	$-0.310577\pi$
$883$	29417.9			1.12117			0.560584	+	0.828098i	$0.310577\pi$
$884$		0			0
$885$	31924.0			1.21256
$886$	−2362.81	−	4092.51i	−0.0895939	−	0.155181i
$887$	16143.1	+	27960.7i	0.611084	+	1.05843i	0.991058	+	0.133432i	$0.0425998\pi$
$887$	16143.1	+	27960.7i	0.611084	+	1.05843i	−0.379974	+	0.924997i	$0.624067\pi$
$888$	−4847.34	+	8395.84i	−0.183182	+	0.317281i
$889$	206.021			0.00777246
$890$	−17462.3	+	30245.6i	−0.657683	+	1.13914i
$891$	−53009.4	+	91815.0i	−1.99313	+	3.45221i
$892$	−17980.9			−0.674940
$893$	−4974.46	+	8616.02i	−0.186410	+	0.322871i
$894$	14312.4	+	24789.7i	0.535433	+	0.927397i
$895$	−14550.4	−	25202.0i	−0.543425	−	0.941240i
$896$	−33.5725			−0.00125176
$897$		0			0
$898$	16296.4			0.605588
$899$	2282.73	+	3953.81i	0.0846868	+	0.146682i
$900$	−9631.50	−	16682.3i	−0.356722	−	0.617861i
$901$	24523.2	−	42475.3i	0.906753	−	1.57054i
$902$	31707.3			1.17044
$903$	−362.133	+	627.232i	−0.0133455	+	0.0231151i
$904$	3719.12	−	6441.71i	0.136832	−	0.237000i
$905$	−10748.7			−0.394804
$906$	9422.84	−	16320.8i	0.345533	−	0.598481i
$907$	−12873.2	−	22297.1i	−0.471278	−	0.816277i	0.528182	−	0.849131i	$-0.322874\pi$
$907$	−12873.2	−	22297.1i	−0.471278	−	0.816277i	−0.999460	+	0.0328538i	$0.989540\pi$
$908$	−7203.22	−	12476.3i	−0.263268	−	0.455994i
$909$	−105012.			−3.83173
$910$		0			0
$911$	7802.68			0.283770			0.141885	−	0.989883i	$-0.454684\pi$
$911$	7802.68			0.283770			0.141885	+	0.989883i	$0.454684\pi$
$912$	1808.46	+	3132.34i	0.0656623	+	0.113730i
$913$	−10790.2	−	18689.2i	−0.391132	−	0.677461i
$914$	14034.4	−	24308.3i	0.507896	−	0.879701i
$915$	15142.1			0.547083
$916$	−10324.2	+	17882.1i	−0.372404	+	0.645022i
$917$	−373.910	+	647.631i	−0.0134652	+	0.0233224i
$918$	73693.4			2.64951
$919$	206.449	−	357.580i	0.00741037	−	0.0128351i	−0.862296	−	0.506404i	$-0.830975\pi$
$919$	206.449	−	357.580i	0.00741037	−	0.0128351i	0.869707	+	0.493569i	$0.164308\pi$
$920$	−3620.76	−	6271.35i	−0.129753	−	0.224739i
$921$	21957.9	+	38032.2i	0.785600	+	1.36070i
$922$	−15383.4			−0.549485
$923$		0			0
$924$	−420.183			−0.0149600
$925$	−3984.42	−	6901.21i	−0.141629	−	0.245309i
$926$	−15555.9	−	26943.7i	−0.552051	−	0.956181i
$927$	−67821.3	+	117470.i	−2.40296	+	4.16205i
$928$	1284.38			0.0454329
$929$	−2628.93	+	4553.44i	−0.0928443	+	0.160811i	−0.908707	−	0.417435i	$-0.862929\pi$
$929$	−2628.93	+	4553.44i	−0.0928443	+	0.160811i	0.815863	+	0.578246i	$0.196263\pi$
$930$	−15726.1	+	27238.3i	−0.554492	+	0.960409i
$931$	7745.57			0.272665
$932$	4045.84	−	7007.60i	0.142195	−	0.246289i
$933$	−14390.2	−	24924.5i	−0.504944	−	0.874589i
$934$	11941.8	+	20683.7i	0.418358	+	0.724618i
$935$	−44075.1			−1.54161
$936$		0			0
$937$	−21763.7			−0.758793			−0.379396	−	0.925234i	$-0.623868\pi$
$937$	−21763.7			−0.758793			−0.379396	+	0.925234i	$0.623868\pi$
$938$	−57.9997	−	100.458i	−0.00201893	−	0.00349689i
$939$	−28602.5	−	49541.0i	−0.994044	−	1.72173i
$940$	−12169.3	+	21077.8i	−0.422254	+	0.731365i
$941$	−4630.07			−0.160400			−0.0801998	−	0.996779i	$-0.525556\pi$
$941$	−4630.07			−0.160400			−0.0801998	+	0.996779i	$0.525556\pi$
$942$	1825.51	−	3161.88i	0.0631406	−	0.109363i
$943$	12980.8	−	22483.4i	0.448264	−	0.776416i
$944$	−3694.53			−0.127380
$945$	−837.133	+	1449.96i	−0.0288169	+	0.0499123i
$946$	11040.4	+	19122.5i	0.379444	+	0.657216i
$947$	3815.83	+	6609.21i	0.130937	+	0.226790i	0.924038	−	0.382300i	$-0.124868\pi$
$947$	3815.83	+	6609.21i	0.130937	+	0.226790i	−0.793101	+	0.609090i	$0.791535\pi$
$948$	29756.0			1.01944
$949$		0			0
$950$	−2973.03			−0.101535
$951$	36940.9	+	63983.6i	1.25961	+	2.18171i
$952$	83.6544	+	144.894i	0.00284796	+	0.00493281i
$953$	−13227.6	+	22910.9i	−0.449617	+	0.778760i	−0.998361	−	0.0572307i	$-0.981773\pi$
$953$	−13227.6	+	22910.9i	−0.449617	+	0.778760i	0.548744	+	0.835991i	$0.315106\pi$
$954$	−90016.6			−3.05492
$955$	−12370.5	+	21426.3i	−0.419162	+	0.726010i
$956$	−2846.24	+	4929.83i	−0.0962906	+	0.166780i
$957$	16074.9			0.542974
$958$	14856.4	−	25732.1i	0.501033	−	0.867815i
$959$	−52.7297	−	91.3305i	−0.00177553	−	0.00307530i
$960$	4424.13	+	7662.81i	0.148738	+	0.257621i
$961$	−16852.5			−0.565690
$962$		0			0
$963$	−11262.9			−0.376887
$964$	7108.68	+	12312.6i	0.237505	+	0.411371i
$965$	12963.9	+	22454.2i	0.432460	+	0.749043i
$966$	−172.020	+	297.948i	−0.00572947	+	0.00992373i
$967$	18687.5			0.621457			0.310728	−	0.950499i	$-0.399427\pi$
$967$	18687.5			0.621457			0.310728	+	0.950499i	$0.399427\pi$
$968$	−1081.09	+	1872.50i	−0.0358962	+	0.0621740i
$969$	9012.45	−	15610.0i	0.298784	−	0.517509i
$970$	−9008.67			−0.298197
$971$	3140.93	−	5440.26i	0.103808	−	0.179800i	−0.809443	−	0.587199i	$-0.800231\pi$
$971$	3140.93	−	5440.26i	0.103808	−	0.179800i	0.913250	+	0.407398i	$0.133564\pi$
$972$	−28079.9	−	48635.7i	−0.926607	−	1.60493i
$973$	112.812	+	195.396i	0.00371694	+	0.00643794i
$974$	28127.2			0.925313
$975$		0			0
$976$	−1752.38			−0.0574715
$977$	21133.0	+	36603.4i	0.692021	+	1.19861i	0.971175	+	0.238368i	$0.0766126\pi$
$977$	21133.0	+	36603.4i	0.692021	+	1.19861i	−0.279154	+	0.960246i	$0.590054\pi$
$978$	−8879.81	−	15380.3i	−0.290332	−	0.502870i
$979$	25292.9	−	43808.5i	0.825703	−	1.43016i
$980$	18948.4			0.617638
$981$	−65417.5	+	113306.i	−2.12907	+	3.68766i
$982$	8218.07	−	14234.1i	0.267056	−	0.462555i
$983$	−41111.7			−1.33394			−0.666968	−	0.745086i	$-0.732408\pi$
$983$	−41111.7			−1.33394			−0.666968	+	0.745086i	$0.732408\pi$
$984$	−15860.9	+	27472.0i	−0.513850	+	0.890014i
$985$	10940.6	+	18949.8i	0.353907	+	0.612984i
$986$	−3200.35	−	5543.17i	−0.103367	−	0.179037i
$987$	1156.31			0.0372906
$988$		0			0
$989$	18079.5			0.581288
$990$	40446.4	+	70055.1i	1.29845	+	2.24899i
$991$	20023.5	+	34681.7i	0.641845	+	1.11171i	0.985021	+	0.172436i	$0.0551639\pi$
$991$	20023.5	+	34681.7i	0.641845	+	1.11171i	−0.343176	+	0.939271i	$0.611503\pi$
$992$	1819.96	−	3152.27i	0.0582499	−	0.100892i
$993$	60597.7			1.93657
$994$	−84.5093	+	146.374i	−0.00269665	+	0.00467074i
$995$	34314.1	−	59433.8i	1.09330	−	1.89365i
$996$	21590.3			0.686863
$997$	−11984.4	+	20757.6i	−0.380692	+	0.659377i	−0.991161	−	0.132663i	$-0.957647\pi$
$997$	−11984.4	+	20757.6i	−0.380692	+	0.659377i	0.610470	+	0.792040i	$0.290981\pi$
$998$	6081.91	+	10534.2i	0.192905	+	0.334122i
$999$	−27976.0	−	48455.9i	−0.886008	−	1.53461i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.4.c.o.315.1		12
13.2	odd	12		338.4.b.h.337.6		12
13.3	even	3		338.4.a.o.1.6	yes	6
13.4	even	6		338.4.c.p.191.1		12
13.5	odd	4		338.4.e.i.23.1		24
13.6	odd	12		338.4.e.i.147.10		24
13.7	odd	12		338.4.e.i.147.1		24
13.8	odd	4		338.4.e.i.23.10		24
13.9	even	3	inner	338.4.c.o.191.1		12
13.10	even	6		338.4.a.n.1.6	✓	6
13.11	odd	12		338.4.b.h.337.12		12
13.12	even	2		338.4.c.p.315.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
338.4.a.n.1.6	✓	6	13.10	even	6
338.4.a.o.1.6	yes	6	13.3	even	3
338.4.b.h.337.6		12	13.2	odd	12
338.4.b.h.337.12		12	13.11	odd	12
338.4.c.o.191.1		12	13.9	even	3	inner
338.4.c.o.315.1		12	1.1	even	1	trivial
338.4.c.p.191.1		12	13.4	even	6
338.4.c.p.315.1		12	13.12	even	2
338.4.e.i.23.1		24	13.5	odd	4
338.4.e.i.23.10		24	13.8	odd	4
338.4.e.i.147.1		24	13.7	odd	12
338.4.e.i.147.10		24	13.6	odd	12

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:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	338.c (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-5.00428 - 8.66767i) q^{3} +(-2.00000 + 3.46410i) q^{4} -13.8136 q^{5} +(-10.0086 + 17.3353i) q^{6} +(0.131143 - 0.227146i) q^{7} +8.00000 q^{8} +(-36.5857 + 63.3682i) q^{9} +(13.8136 + 23.9258i) q^{10} +(-20.0079 - 34.6548i) q^{11} +40.0343 q^{12} -0.524571 q^{14} +(69.1270 + 119.731i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(-39.8680 + 69.0534i) q^{17} +146.343 q^{18} +(11.2932 - 19.5604i) q^{19} +(27.6271 - 47.8516i) q^{20} -2.62510 q^{21} +(-40.0159 + 69.3096i) q^{22} +(32.7646 + 56.7499i) q^{23} +(-40.0343 - 69.3414i) q^{24} +65.8147 q^{25} +462.109 q^{27} +(0.524571 + 0.908583i) q^{28} +(-20.0684 - 34.7595i) q^{29} +(138.254 - 239.463i) q^{30} -113.748 q^{31} +(-16.0000 + 27.7128i) q^{32} +(-200.251 + 346.845i) q^{33} +159.472 q^{34} +(-1.81155 + 3.13770i) q^{35} +(-146.343 - 253.473i) q^{36} +(-60.5399 - 104.858i) q^{37} -45.1727 q^{38} -110.509 q^{40} +(-198.092 - 343.106i) q^{41} +(2.62510 + 4.54681i) q^{42} +(137.950 - 238.936i) q^{43} +160.064 q^{44} +(505.379 - 875.342i) q^{45} +(65.5291 - 113.500i) q^{46} -440.483 q^{47} +(-80.0685 + 138.683i) q^{48} +(171.466 + 296.987i) q^{49} +(-65.8147 - 113.994i) q^{50} +798.043 q^{51} -615.108 q^{53} +(-462.109 - 800.396i) q^{54} +(276.381 + 478.706i) q^{55} +(1.04914 - 1.81717i) q^{56} -226.057 q^{57} +(-40.1368 + 69.5190i) q^{58} +(115.454 - 199.972i) q^{59} -553.016 q^{60} +(54.7618 - 94.8501i) q^{61} +(113.748 + 197.017i) q^{62} +(9.59589 + 16.6206i) q^{63} +64.0000 q^{64} +801.003 q^{66} +(110.566 + 191.506i) q^{67} +(-159.472 - 276.214i) q^{68} +(327.926 - 567.985i) q^{69} +7.24620 q^{70} +(161.102 - 279.036i) q^{71} +(-292.685 + 506.946i) q^{72} -323.664 q^{73} +(-121.080 + 209.716i) q^{74} +(-329.355 - 570.460i) q^{75} +(45.1727 + 78.2415i) q^{76} -10.4956 q^{77} +743.263 q^{79} +(110.509 + 191.406i) q^{80} +(-1324.71 - 2294.46i) q^{81} +(-396.184 + 686.211i) q^{82} +539.296 q^{83} +(5.25020 - 9.09361i) q^{84} +(550.720 - 953.875i) q^{85} -551.800 q^{86} +(-200.856 + 347.893i) q^{87} +(-160.064 - 277.238i) q^{88} +(632.070 + 1094.78i) q^{89} -2021.51 q^{90} -262.116 q^{92} +(569.225 + 985.927i) q^{93} +(440.483 + 762.939i) q^{94} +(-155.999 + 270.199i) q^{95} +320.274 q^{96} +(-163.040 + 282.394i) q^{97} +(342.931 - 593.974i) q^{98} +2928.02 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 12 q^{2} - 9 q^{3} - 24 q^{4} + 36 q^{5} - 18 q^{6} - 25 q^{7} + 96 q^{8} - 113 q^{9} - 36 q^{10} - 37 q^{11} + 72 q^{12} + 100 q^{14} - 118 q^{15} - 96 q^{16} - 99 q^{17} + 452 q^{18} + 81 q^{19}+ \cdots - 2688 q^{99}+O(q^{100}) \) 12 * q - 12 * q^2 - 9 * q^3 - 24 * q^4 + 36 * q^5 - 18 * q^6 - 25 * q^7 + 96 * q^8 - 113 * q^9 - 36 * q^10 - 37 * q^11 + 72 * q^12 + 100 * q^14 - 118 * q^15 - 96 * q^16 - 99 * q^17 + 452 * q^18 + 81 * q^19 - 72 * q^20 - 52 * q^21 - 74 * q^22 - 267 * q^23 - 72 * q^24 + 736 * q^25 + 1338 * q^27 - 100 * q^28 + 119 * q^29 - 236 * q^30 - 1250 * q^31 - 192 * q^32 - 762 * q^33 + 396 * q^34 - 614 * q^35 - 452 * q^36 - 274 * q^37 - 324 * q^38 + 288 * q^40 - 1140 * q^41 + 52 * q^42 - 428 * q^43 + 296 * q^44 + 1215 * q^45 - 534 * q^46 - 1972 * q^47 - 144 * q^48 - 899 * q^49 - 736 * q^50 + 578 * q^51 + 178 * q^53 - 1338 * q^54 - 1126 * q^55 - 200 * q^56 - 5106 * q^57 + 238 * q^58 - 1088 * q^59 + 944 * q^60 - 1704 * q^61 + 1250 * q^62 + 3222 * q^63 + 768 * q^64 + 3048 * q^66 + 1692 * q^67 - 396 * q^68 - 1168 * q^69 + 2456 * q^70 + 1221 * q^71 - 904 * q^72 - 3108 * q^73 - 548 * q^74 - 1798 * q^75 + 324 * q^76 + 5580 * q^77 - 1750 * q^79 - 288 * q^80 - 3338 * q^81 - 2280 * q^82 - 252 * q^83 + 104 * q^84 + 3721 * q^85 + 1712 * q^86 - 1602 * q^87 - 296 * q^88 + 374 * q^89 - 4860 * q^90 + 2136 * q^92 + 1868 * q^93 + 1972 * q^94 + 4093 * q^95 + 576 * q^96 + 330 * q^97 - 1798 * q^98 - 2688 * q^99

Introduction

L-functions

Modular forms

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