LMFDB - Embedded newform 338.4.e.h.23.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [338,4,Mod(23,338)]

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([5]))

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

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

chi := DirichletCharacter("338.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	338.e (of order $6$, 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 $\Q(\zeta_{6})$
Coefficient field:	12.0.17213603549184.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 5x^{10} + 19x^{8} - 28x^{6} + 31x^{4} - 6x^{2} + 1 $ x^12 - 5x^10 + 19x^8 - 28x^6 + 31x^4 - 6*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.6
Root			$1.56052 - 0.900969i$ of defining polynomial
Character	$\chi$	$=$	338.23
Dual form			338.4.e.h.147.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 - 1.00000i) q^{2} +(4.37047 + 7.56988i) q^{3} +(2.00000 - 3.46410i) q^{4} -14.1685i q^{5} +(15.1398 + 8.74094i) q^{6} +(24.8120 + 14.3252i) q^{7} -8.00000i q^{8} +(-24.7020 + 42.7851i) q^{9} +(-14.1685 - 24.5406i) q^{10} +(-8.22160 + 4.74674i) q^{11} +34.9638 q^{12} +57.3008 q^{14} +(107.254 - 61.9231i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(15.3052 - 26.5094i) q^{17} +98.8080i q^{18} +(133.247 + 76.9300i) q^{19} +(-49.0812 - 28.3370i) q^{20} +250.431i q^{21} +(-9.49349 + 16.4432i) q^{22} +(-18.0015 - 31.1795i) q^{23} +(60.5590 - 34.9638i) q^{24} -75.7470 q^{25} -195.832 q^{27} +(99.2479 - 57.3008i) q^{28} +(24.6283 + 42.6575i) q^{29} +(123.846 - 214.508i) q^{30} -166.984i q^{31} +(-27.7128 - 16.0000i) q^{32} +(-71.8645 - 41.4910i) q^{33} -61.2209i q^{34} +(202.967 - 351.549i) q^{35} +(98.8080 + 171.141i) q^{36} +(-20.6814 + 11.9404i) q^{37} +307.720 q^{38} -113.348 q^{40} +(-108.664 + 62.7371i) q^{41} +(250.431 + 433.760i) q^{42} +(-217.387 + 376.526i) q^{43} +37.9739i q^{44} +(606.202 + 349.991i) q^{45} +(-62.3591 - 36.0030i) q^{46} -186.017i q^{47} +(69.9275 - 121.118i) q^{48} +(238.923 + 413.826i) q^{49} +(-131.198 + 75.7470i) q^{50} +267.564 q^{51} -400.631 q^{53} +(-339.191 + 195.832i) q^{54} +(67.2543 + 116.488i) q^{55} +(114.602 - 198.496i) q^{56} +1344.88i q^{57} +(85.3151 + 49.2567i) q^{58} +(353.518 + 204.104i) q^{59} -495.385i q^{60} +(301.881 - 522.873i) q^{61} +(-166.984 - 289.225i) q^{62} +(-1225.81 + 707.722i) q^{63} -64.0000 q^{64} -165.964 q^{66} +(249.024 - 143.774i) q^{67} +(-61.2209 - 106.038i) q^{68} +(157.350 - 272.538i) q^{69} -811.868i q^{70} +(-832.946 - 480.901i) q^{71} +(342.281 + 197.616i) q^{72} +963.198i q^{73} +(-23.8808 + 41.3627i) q^{74} +(-331.050 - 573.396i) q^{75} +(532.986 - 307.720i) q^{76} -271.992 q^{77} -1043.18 q^{79} +(-196.325 + 113.348i) q^{80} +(-188.924 - 327.226i) q^{81} +(-125.474 + 217.328i) q^{82} -313.304i q^{83} +(867.520 + 500.863i) q^{84} +(-375.599 - 216.852i) q^{85} +869.549i q^{86} +(-215.275 + 372.867i) q^{87} +(37.9739 + 65.7728i) q^{88} +(585.220 - 337.877i) q^{89} +1399.96 q^{90} -144.012 q^{92} +(1264.05 - 729.799i) q^{93} +(-186.017 - 322.191i) q^{94} +(1089.98 - 1887.91i) q^{95} -279.710i q^{96} +(-235.935 - 136.217i) q^{97} +(827.653 + 477.845i) q^{98} -469.016i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 24 q^{3} + 24 q^{4} - 18 q^{9} - 48 q^{10} + 192 q^{12} + 216 q^{14} - 96 q^{16} - 180 q^{17} + 328 q^{22} + 38 q^{23} + 244 q^{25} - 276 q^{27} + 202 q^{29} + 360 q^{30} + 916 q^{35} + 72 q^{36}+ \cdots + 3658 q^{95}+O(q^{100}) $ 12 * q + 24 * q^3 + 24 * q^4 - 18 * q^9 - 48 * q^10 + 192 * q^12 + 216 * q^14 - 96 * q^16 - 180 * q^17 + 328 * q^22 + 38 * q^23 + 244 * q^25 - 276 * q^27 + 202 * q^29 + 360 * q^30 + 916 * q^35 + 72 * q^36 + 1040 * q^38 - 384 * q^40 + 936 * q^42 - 2410 * q^43 + 384 * q^48 - 368 * q^49 + 828 * q^51 - 4380 * q^53 + 1052 * q^55 + 432 * q^56 + 2216 * q^61 - 2076 * q^62 - 768 * q^64 + 1168 * q^66 + 720 * q^68 - 628 * q^69 + 336 * q^74 - 1010 * q^75 - 1920 * q^77 - 7844 * q^79 - 1830 * q^81 - 748 * q^82 - 3272 * q^87 - 1312 * q^88 + 5160 * q^90 + 304 * q^92 - 2144 * q^94 + 3658 * q^95

Character values

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

$n$	$171$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	4.37047	+	7.56988i	0.841097	+	1.45682i	0.888968	+	0.457970i	$0.151423\pi$
$3$	4.37047	+	7.56988i	0.841097	+	1.45682i	−0.0478706	+	0.998854i	$0.515244\pi$
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$		−	14.1685i		−	1.26727i	−0.773632	−	0.633636i	$-0.781562\pi$
$5$		−	14.1685i		−	1.26727i	0.773632	−	0.633636i	$-0.218438\pi$
$6$	15.1398	+	8.74094i	1.03013	+	0.594746i
$7$	24.8120	+	14.3252i	1.33972	+	0.773488i	0.986766	−	0.162152i	$-0.0518436\pi$
$7$	24.8120	+	14.3252i	1.33972	+	0.773488i	0.352955	+	0.935640i	$0.385177\pi$
$8$		−	8.00000i		−	0.353553i
$9$	−24.7020	+	42.7851i	−0.914889	+	1.58463i
$10$	−14.1685	−	24.5406i	−0.448048	−	0.776042i
$11$	−8.22160	+	4.74674i	−0.225355	+	0.130109i	−0.608427	−	0.793610i	$-0.708199\pi$
$11$	−8.22160	+	4.74674i	−0.225355	+	0.130109i	0.383072	+	0.923718i	$0.374866\pi$
$12$	34.9638			0.841097
$13$		0			0
$13$		0			0
$14$	57.3008			1.09388
$15$	107.254	−	61.9231i	1.84619	−	1.06590i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	15.3052	−	26.5094i	0.218356	−	0.378205i	−0.735949	−	0.677037i	$-0.763264\pi$
$17$	15.3052	−	26.5094i	0.218356	−	0.378205i	0.954306	+	0.298832i	$0.0965971\pi$
$18$			98.8080i			1.29385i
$19$	133.247	+	76.9300i	1.60889	+	0.928892i	0.989620	+	0.143712i	$0.0459040\pi$
$19$	133.247	+	76.9300i	1.60889	+	0.928892i	0.619268	+	0.785180i	$0.287429\pi$
$20$	−49.0812	−	28.3370i	−0.548745	−	0.316818i
$21$			250.431i			2.60231i
$22$	−9.49349	+	16.4432i	−0.0920008	+	0.159350i
$23$	−18.0015	−	31.1795i	−0.163199	−	0.282669i	0.772815	−	0.634631i	$-0.218848\pi$
$23$	−18.0015	−	31.1795i	−0.163199	−	0.282669i	−0.936014	+	0.351962i	$0.885515\pi$
$24$	60.5590	−	34.9638i	0.515065	−	0.297373i
$25$	−75.7470			−0.605976
$26$		0			0
$27$	−195.832			−1.39585
$28$	99.2479	−	57.3008i	0.669860	−	0.386744i
$29$	24.6283	+	42.6575i	0.157702	+	0.273148i	0.934040	−	0.357169i	$-0.116258\pi$
$29$	24.6283	+	42.6575i	0.157702	+	0.273148i	−0.776337	+	0.630318i	$0.782925\pi$
$30$	123.846	−	214.508i	0.753704	−	1.30545i
$31$		−	166.984i		−	0.967459i	−0.875217	−	0.483730i	$-0.839282\pi$
$31$		−	166.984i		−	0.967459i	0.875217	−	0.483730i	$-0.160718\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	−71.8645	−	41.4910i	−0.379091	−	0.218868i
$34$		−	61.2209i		−	0.308803i
$35$	202.967	−	351.549i	0.980219	−	1.69779i
$36$	98.8080	+	171.141i	0.457445	+	0.792317i
$37$	−20.6814	+	11.9404i	−0.0918917	+	0.0530537i	−0.545242	−	0.838279i	$-0.683562\pi$
$37$	−20.6814	+	11.9404i	−0.0918917	+	0.0530537i	0.453350	+	0.891333i	$0.350229\pi$
$38$	307.720			1.31365
$39$		0			0
$40$	−113.348			−0.448048
$41$	−108.664	+	62.7371i	−0.413913	+	0.238973i	−0.692470	−	0.721447i	$-0.743477\pi$
$41$	−108.664	+	62.7371i	−0.413913	+	0.238973i	0.278557	+	0.960420i	$0.410144\pi$
$42$	250.431	+	433.760i	0.920057	+	1.59359i
$43$	−217.387	+	376.526i	−0.770959	+	1.33534i	0.166079	+	0.986112i	$0.446889\pi$
$43$	−217.387	+	376.526i	−0.770959	+	1.33534i	−0.937038	+	0.349227i	$0.886444\pi$
$44$			37.9739i			0.130109i
$45$	606.202	+	349.991i	2.00816	+	1.15941i
$46$	−62.3591	−	36.0030i	−0.199877	−	0.115399i
$47$		−	186.017i		−	0.577306i	−0.957434	−	0.288653i	$-0.906793\pi$
$47$		−	186.017i		−	0.577306i	0.957434	−	0.288653i	$-0.0932073\pi$
$48$	69.9275	−	121.118i	0.210274	−	0.364206i
$49$	238.923	+	413.826i	0.696568	+	1.20649i
$50$	−131.198	+	75.7470i	−0.371083	+	0.214245i
$51$	267.564			0.734636
$52$		0			0
$53$	−400.631			−1.03832			−0.519159	−	0.854678i	$-0.673755\pi$
$53$	−400.631			−1.03832			−0.519159	+	0.854678i	$0.673755\pi$
$54$	−339.191	+	195.832i	−0.854779	+	0.493507i
$55$	67.2543	+	116.488i	0.164883	+	0.285586i
$56$	114.602	−	198.496i	0.273469	−	0.473663i
$57$			1344.88i			3.12515i
$58$	85.3151	+	49.2567i	0.193145	+	0.111512i
$59$	353.518	+	204.104i	0.780070	+	0.450374i	0.836455	−	0.548035i	$-0.184624\pi$
$59$	353.518	+	204.104i	0.780070	+	0.450374i	−0.0563849	+	0.998409i	$0.517957\pi$
$60$		−	495.385i		−	1.06590i
$61$	301.881	−	522.873i	0.633638	−	1.09749i	−0.353165	−	0.935561i	$-0.614894\pi$
$61$	301.881	−	522.873i	0.633638	−	1.09749i	0.986802	−	0.161931i	$-0.0517722\pi$
$62$	−166.984	−	289.225i	−0.342048	−	0.592445i
$63$	−1225.81	+	707.722i	−2.45139	+	1.41531i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	−165.964			−0.309527
$67$	249.024	−	143.774i	0.454076	−	0.262161i	−0.255474	−	0.966816i	$-0.582232\pi$
$67$	249.024	−	143.774i	0.454076	−	0.262161i	0.709550	+	0.704655i	$0.248898\pi$
$68$	−61.2209	−	106.038i	−0.109178	−	0.189102i
$69$	157.350	−	272.538i	0.274532	−	0.475504i
$70$		−	811.868i		−	1.38624i
$71$	−832.946	−	480.901i	−1.39229	−	0.803838i	−0.398720	−	0.917073i	$-0.630545\pi$
$71$	−832.946	−	480.901i	−1.39229	−	0.803838i	−0.993568	+	0.113235i	$0.963879\pi$
$72$	342.281	+	197.616i	0.560253	+	0.323462i
$73$			963.198i			1.54430i	0.635441	+	0.772149i	$0.280818\pi$
$73$			963.198i			1.54430i	−0.635441	+	0.772149i	$0.719182\pi$
$74$	−23.8808	+	41.3627i	−0.0375146	+	0.0649773i
$75$	−331.050	−	573.396i	−0.509685	−	0.882800i
$76$	532.986	−	307.720i	0.804444	−	0.464446i
$77$	−271.992			−0.402550
$78$		0			0
$79$	−1043.18			−1.48566			−0.742828	−	0.669482i	$-0.766516\pi$
$79$	−1043.18			−1.48566			−0.742828	+	0.669482i	$0.766516\pi$
$80$	−196.325	+	113.348i	−0.274372	+	0.158409i
$81$	−188.924	−	327.226i	−0.259155	−	0.448870i
$82$	−125.474	+	217.328i	−0.168979	+	0.292681i
$83$		−	313.304i		−	0.414332i	−0.978306	−	0.207166i	$-0.933576\pi$
$83$		−	313.304i		−	0.414332i	0.978306	−	0.207166i	$-0.0664240\pi$
$84$	867.520	+	500.863i	1.12684	+	0.650579i
$85$	−375.599	−	216.852i	−0.479288	−	0.276717i
$86$			869.549i			1.09030i
$87$	−215.275	+	372.867i	−0.265286	+	0.459489i
$88$	37.9739	+	65.7728i	0.0460004	+	0.0796750i
$89$	585.220	−	337.877i	0.697002	−	0.402414i	−0.109228	−	0.994017i	$-0.534838\pi$
$89$	585.220	−	337.877i	0.697002	−	0.402414i	0.806230	+	0.591602i	$0.201504\pi$
$90$	1399.96			1.63966
$91$		0			0
$92$	−144.012			−0.163199
$93$	1264.05	−	729.799i	1.40942	−	0.813727i
$94$	−186.017	−	322.191i	−0.204108	−	0.353526i
$95$	1089.98	−	1887.91i	1.17716	−	2.03890i
$96$		−	279.710i		−	0.297373i
$97$	−235.935	−	136.217i	−0.246965	−	0.142585i	0.371409	−	0.928469i	$-0.378875\pi$
$97$	−235.935	−	136.217i	−0.246965	−	0.142585i	−0.618374	+	0.785884i	$0.712208\pi$
$98$	827.653	+	477.845i	0.853118	+	0.492548i
$99$		−	469.016i		−	0.476140i
$100$	−151.494	+	262.395i	−0.151494	+	0.262395i
$101$	−330.780	−	572.928i	−0.325880	−	0.564441i	0.655810	−	0.754926i	$-0.272327\pi$
$101$	−330.780	−	572.928i	−0.325880	−	0.564441i	−0.981690	+	0.190485i	$0.938994\pi$
$102$	463.434	−	267.564i	0.449871	−	0.259733i
$103$	315.353			0.301676			0.150838	−	0.988558i	$-0.451803\pi$
$103$	315.353			0.301676			0.150838	+	0.988558i	$0.451803\pi$
$104$		0			0
$105$	3548.24			3.29784
$106$	−693.913	+	400.631i	−0.635838	+	0.367101i
$107$	−1060.66	−	1837.12i	−0.958299	−	1.65982i	−0.726632	−	0.687026i	$-0.758916\pi$
$107$	−1060.66	−	1837.12i	−0.958299	−	1.65982i	−0.231666	−	0.972795i	$-0.574418\pi$
$108$	−391.664	+	678.382i	−0.348962	+	0.604420i
$109$		−	884.432i		−	0.777185i	−0.921410	−	0.388593i	$-0.872961\pi$
$109$		−	884.432i		−	0.777185i	0.921410	−	0.388593i	$-0.127039\pi$
$110$	232.976	+	134.509i	0.201940	+	0.116590i
$111$	−180.774	−	104.370i	−0.154580	−	0.0892467i
$112$		−	458.406i		−	0.386744i
$113$	66.1023	−	114.493i	0.0550299	−	0.0953146i	−0.837198	−	0.546900i	$-0.815808\pi$
$113$	66.1023	−	114.493i	0.0550299	−	0.0953146i	0.892228	+	0.451585i	$0.149141\pi$
$114$	1344.88	+	2329.40i	1.10491	+	1.91376i
$115$	−441.768	+	255.055i	−0.358218	+	0.206817i
$116$	197.027			0.157702
$117$		0			0
$118$	816.415			0.636925
$119$	759.505	−	438.501i	0.585073	−	0.337792i
$120$	−495.385	−	858.032i	−0.376852	−	0.652727i
$121$	−620.437	+	1074.63i	−0.466143	+	0.807384i
$122$		−	1207.52i		−	0.896099i
$123$	−949.824	−	548.381i	−0.696282	−	0.401999i
$124$	−578.450	−	333.968i	−0.418922	−	0.241865i
$125$		−	697.842i		−	0.499335i
$126$	−1415.44	+	2451.62i	−1.00078	+	1.73340i
$127$	−936.404	−	1621.90i	−0.654271	−	1.13323i	−0.982076	−	0.188485i	$-0.939642\pi$
$127$	−936.404	−	1621.90i	−0.654271	−	1.13323i	0.327805	−	0.944745i	$-0.393691\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	−3800.34			−2.59381
$130$		0			0
$131$	−1850.21			−1.23400			−0.617000	−	0.786963i	$-0.711652\pi$
$131$	−1850.21			−1.23400			−0.617000	+	0.786963i	$0.711652\pi$
$132$	−287.458	+	165.964i	−0.189546	+	0.109434i
$133$	2204.07	+	3817.57i	1.43697	+	2.48891i
$134$	287.548	−	498.047i	0.185376	−	0.321080i
$135$			2774.65i			1.76892i
$136$	−212.075	−	122.442i	−0.133715	−	0.0772007i
$137$	−837.771	−	483.687i	−0.522450	−	0.301637i	0.215487	−	0.976507i	$-0.430866\pi$
$137$	−837.771	−	483.687i	−0.522450	−	0.301637i	−0.737936	+	0.674870i	$0.764200\pi$
$138$		−	629.401i		−	0.388247i
$139$	51.7985	−	89.7176i	0.0316078	−	0.0547464i	−0.849789	−	0.527123i	$-0.823271\pi$
$139$	51.7985	−	89.7176i	0.0316078	−	0.0547464i	0.881397	+	0.472377i	$0.156604\pi$
$140$	−811.868	−	1406.20i	−0.490110	−	0.848895i
$141$	1408.13	−	812.981i	0.841032	−	0.485570i
$142$	−1923.61			−1.13680
$143$		0			0
$144$	790.464			0.457445
$145$	604.394	−	348.947i	0.346153	−	0.199852i
$146$	963.198	+	1668.31i	0.545992	+	0.945686i
$147$	−2088.41	+	3617.23i	−1.17176	+	2.02955i
$148$			95.5231i			0.0530537i
$149$	−1660.55	−	958.718i	−0.913002	−	0.527122i	−0.0316065	−	0.999500i	$-0.510062\pi$
$149$	−1660.55	−	958.718i	−0.913002	−	0.527122i	−0.881396	+	0.472378i	$0.843396\pi$
$150$	−1146.79	−	662.100i	−0.624234	−	0.360402i
$151$		−	2035.28i		−	1.09688i	−0.836191	−	0.548439i	$-0.815222\pi$
$151$		−	2035.28i		−	1.09688i	0.836191	−	0.548439i	$-0.184778\pi$
$152$	615.440	−	1065.97i	0.328413	−	0.568828i
$153$	756.139	+	1309.67i	0.399544	+	0.692030i
$154$	−471.104	+	271.992i	−0.246511	+	0.142323i
$155$	−2365.92			−1.22603
$156$		0			0
$157$	−615.393			−0.312826			−0.156413	−	0.987692i	$-0.549993\pi$
$157$	−615.393			−0.312826			−0.156413	+	0.987692i	$0.549993\pi$
$158$	−1806.84	+	1043.18i	−0.909775	+	0.525259i
$159$	−1750.94	−	3032.73i	−0.873327	−	1.51265i
$160$	−226.696	+	392.650i	−0.112012	+	0.194010i
$161$		−	1031.50i		−	0.504930i
$162$	−654.452	−	377.848i	−0.317399	−	0.183250i
$163$	1004.67	+	580.046i	0.482771	+	0.278728i	0.721571	−	0.692341i	$-0.243421\pi$
$163$	1004.67	+	580.046i	0.482771	+	0.278728i	−0.238799	+	0.971069i	$0.576754\pi$
$164$			501.897i			0.238973i
$165$	−587.866	+	1018.21i	−0.277365	+	0.480411i
$166$	−313.304	−	542.658i	−0.146489	−	0.253726i
$167$	1757.39	−	1014.63i	0.814319	−	0.470147i	−0.0341344	−	0.999417i	$-0.510867\pi$
$167$	1757.39	−	1014.63i	0.814319	−	0.470147i	0.848454	+	0.529270i	$0.177534\pi$
$168$	2003.45			0.920057
$169$		0			0
$170$	−867.409			−0.391337
$171$	−6582.92	+	3800.65i	−2.94391	+	1.69967i
$172$	869.549	+	1506.10i	0.385479	+	0.667670i
$173$	−1536.80	+	2661.82i	−0.675380	+	1.16979i	0.300977	+	0.953631i	$0.402687\pi$
$173$	−1536.80	+	2661.82i	−0.675380	+	1.16979i	−0.976358	+	0.216162i	$0.930646\pi$
$174$			861.099i			0.375171i
$175$	−1879.43	−	1085.09i	−0.811839	−	0.468715i
$176$	131.546	+	75.9479i	0.0563388	+	0.0325272i
$177$			3568.12i			1.51523i
$178$	675.754	−	1170.44i	0.284550	−	0.492855i
$179$	1156.94	+	2003.88i	0.483095	+	0.836745i	0.999812	−	0.0194115i	$-0.00617925\pi$
$179$	1156.94	+	2003.88i	0.483095	+	0.836745i	−0.516717	+	0.856156i	$0.672846\pi$
$180$	2424.81	−	1399.96i	1.00408	−	0.579706i
$181$	1670.01			0.685805			0.342903	−	0.939371i	$-0.388590\pi$
$181$	1670.01			0.685805			0.342903	+	0.939371i	$0.388590\pi$
$182$		0			0
$183$	5277.44			2.13180
$184$	−249.436	+	144.012i	−0.0999385	+	0.0576995i
$185$	169.178	+	293.024i	0.0672334	+	0.116452i
$186$	1459.60	−	2528.10i	0.575392	−	0.996608i
$187$			290.600i			0.113640i
$188$	−644.382	−	372.034i	−0.249981	−	0.144326i
$189$	−4858.98	−	2805.33i	−1.87005	−	1.07967i
$190$		−	4359.94i		−	1.66475i
$191$	−1912.60	+	3312.73i	−0.724561	+	1.25498i	0.234594	+	0.972094i	$0.424624\pi$
$191$	−1912.60	+	3312.73i	−0.724561	+	1.25498i	−0.959154	+	0.282883i	$0.908709\pi$
$192$	−279.710	−	484.472i	−0.105137	−	0.182103i
$193$	−787.071	+	454.416i	−0.293547	+	0.169480i	−0.639540	−	0.768757i	$-0.720875\pi$
$193$	−787.071	+	454.416i	−0.293547	+	0.169480i	0.345993	+	0.938237i	$0.387542\pi$
$194$	−544.869			−0.201646
$195$		0			0
$196$	1911.38			0.696568
$197$	1158.45	−	668.833i	0.418966	−	0.241890i	−0.275669	−	0.961253i	$-0.588899\pi$
$197$	1158.45	−	668.833i	0.418966	−	0.241890i	0.694635	+	0.719362i	$0.255566\pi$
$198$	−469.016	−	812.360i	−0.168341	−	0.291575i
$199$	572.290	−	991.236i	0.203862	−	0.353100i	−0.745907	−	0.666050i	$-0.767984\pi$
$199$	572.290	−	991.236i	0.203862	−	0.353100i	0.949770	+	0.312950i	$0.101317\pi$
$200$			605.976i			0.214245i
$201$	2176.70	+	1256.72i	0.763844	+	0.441005i
$202$	−1145.86	−	661.561i	−0.399120	−	0.230432i
$203$			1411.22i			0.487924i
$204$	535.128	−	926.869i	0.183659	−	0.318107i
$205$	888.892	+	1539.61i	0.302843	+	0.524540i
$206$	546.207	−	315.353i	0.184738	−	0.106659i
$207$	1778.69			0.597236
$208$		0			0
$209$	−1460.67			−0.483428
$210$	6145.74	−	3548.24i	2.01951	−	1.16596i
$211$	5.61262	+	9.72134i	0.00183123	+	0.00317178i	0.866940	−	0.498413i	$-0.166084\pi$
$211$	5.61262	+	9.72134i	0.00183123	+	0.00317178i	−0.865108	+	0.501585i	$0.832750\pi$
$212$	−801.262	+	1387.83i	−0.259580	+	0.449605i
$213$		−	8407.06i		−	2.70442i
$214$	−3674.24	−	2121.32i	−1.17367	−	0.677619i
$215$	5334.81	+	3080.05i	1.69224	+	0.977014i
$216$			1566.66i			0.493507i
$217$	2392.08	−	4143.21i	0.748318	−	1.29613i
$218$	−884.432	−	1531.88i	−0.274777	−	0.475927i
$219$	−7291.29	+	4209.63i	−2.24977	+	1.29891i
$220$	538.035			0.164883
$221$		0			0
$222$	−417.481			−0.126214
$223$	2372.68	−	1369.87i	0.712497	−	0.411360i	−0.0994882	−	0.995039i	$-0.531721\pi$
$223$	2372.68	−	1369.87i	0.712497	−	0.411360i	0.811985	+	0.583679i	$0.198387\pi$
$224$	−458.406	−	793.983i	−0.136735	−	0.236831i
$225$	1871.10	−	3240.85i	0.554401	−	0.960251i
$226$		−	264.409i		−	0.0778241i
$227$	3922.88	+	2264.87i	1.14701	+	0.662225i	0.948156	−	0.317805i	$-0.102946\pi$
$227$	3922.88	+	2264.87i	1.14701	+	0.662225i	0.198851	+	0.980030i	$0.436279\pi$
$228$	4658.80	+	2689.76i	1.35323	+	0.781288i
$229$		−	867.892i		−	0.250445i	−0.992129	−	0.125222i	$-0.960036\pi$
$229$		−	867.892i		−	0.250445i	0.992129	−	0.125222i	$-0.0399645\pi$
$230$	−510.110	+	883.536i	−0.146242	+	0.253298i
$231$	−1188.73	−	2058.95i	−0.338584	−	0.586445i
$232$	341.260	−	197.027i	0.0965726	−	0.0557562i
$233$	−535.138			−0.150464			−0.0752319	−	0.997166i	$-0.523970\pi$
$233$	−535.138			−0.150464			−0.0752319	+	0.997166i	$0.523970\pi$
$234$		0			0
$235$	−2635.59			−0.731603
$236$	1414.07	−	816.415i	0.390035	−	0.225187i
$237$	−4559.18	−	7896.73i	−1.24958	−	2.16434i
$238$	877.001	−	1519.01i	0.238855	−	0.413709i
$239$			1146.73i			0.310359i	0.987886	+	0.155180i	$0.0495956\pi$
$239$			1146.73i			0.310359i	−0.987886	+	0.155180i	$0.950404\pi$
$240$	−1716.06	−	990.769i	−0.461547	−	0.266475i
$241$	2903.81	+	1676.52i	0.776145	+	0.448107i	0.835062	−	0.550155i	$-0.185432\pi$
$241$	2903.81	+	1676.52i	0.776145	+	0.448107i	−0.0589175	+	0.998263i	$0.518765\pi$
$242$			2481.75i			0.659226i
$243$	−992.360	+	1718.82i	−0.261975	+	0.453754i
$244$	−1207.52	−	2091.49i	−0.316819	−	0.548746i
$245$	5863.31	−	3385.18i	1.52895	−	0.882740i
$246$	−2193.52			−0.568512
$247$		0			0
$248$	−1335.87			−0.342048
$249$	2371.67	−	1369.29i	0.603609	−	0.348494i
$250$	−697.842	−	1208.70i	−0.176542	−	0.305779i
$251$	2678.98	−	4640.13i	0.673688	−	1.16686i	−0.303163	−	0.952939i	$-0.598043\pi$
$251$	2678.98	−	4640.13i	0.673688	−	1.16686i	0.976851	−	0.213923i	$-0.0686240\pi$
$252$			5661.78i			1.41531i
$253$	296.003	+	170.897i	0.0735554	+	0.0424672i
$254$	−3243.80	−	1872.81i	−0.801315	−	0.462639i
$255$		−	3790.99i		−	0.930983i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−3146.05	−	5449.12i	−0.763601	−	1.32260i	−0.940983	−	0.338453i	$-0.890096\pi$
$257$	−3146.05	−	5449.12i	−0.763601	−	1.32260i	0.177383	−	0.984142i	$-0.443237\pi$
$258$	−6582.37	+	3800.34i	−1.58837	+	0.917049i
$259$	−684.194			−0.164146
$260$		0			0
$261$	−2433.48			−0.577121
$262$	−3204.66	+	1850.21i	−0.755667	+	0.436285i
$263$	2398.88	+	4154.98i	0.562438	+	0.974171i	0.997283	+	0.0736656i	$0.0234697\pi$
$263$	2398.88	+	4154.98i	0.562438	+	0.974171i	−0.434845	+	0.900505i	$0.643197\pi$
$264$	−331.928	+	574.916i	−0.0773816	+	0.134029i
$265$			5676.35i			1.31583i
$266$	7635.14	+	4408.15i	1.75993	+	1.01609i
$267$	5115.37	+	2953.36i	1.17249	+	0.676939i
$268$		−	1150.19i		−	0.262161i
$269$	−3123.22	+	5409.57i	−0.707903	+	1.22612i	0.257731	+	0.966217i	$0.417025\pi$
$269$	−3123.22	+	5409.57i	−0.707903	+	1.22612i	−0.965634	+	0.259907i	$0.916308\pi$
$270$	2774.65	+	4805.84i	0.625407	+	1.08324i
$271$	1585.82	−	915.576i	0.355468	−	0.205230i	−0.311623	−	0.950206i	$-0.600872\pi$
$271$	1585.82	−	915.576i	0.355468	−	0.205230i	0.667091	+	0.744976i	$0.267539\pi$
$272$	−489.767			−0.109178
$273$		0			0
$274$	−1934.75			−0.426578
$275$	622.762	−	359.552i	0.136560	−	0.0788428i
$276$	−629.401	−	1090.15i	−0.137266	−	0.237752i
$277$	−800.712	+	1386.87i	−0.173683	+	0.300827i	−0.939705	−	0.341987i	$-0.888900\pi$
$277$	−800.712	+	1386.87i	−0.173683	+	0.300827i	0.766022	+	0.642814i	$0.222233\pi$
$278$		−	207.194i		−	0.0447002i
$279$	7144.44	+	4124.84i	1.53307	+	0.885118i
$280$	−2812.39	−	1623.74i	−0.600259	−	0.346560i
$281$			4516.64i			0.958861i	0.877580	+	0.479431i	$0.159157\pi$
$281$			4516.64i			0.958861i	−0.877580	+	0.479431i	$0.840843\pi$
$282$	1625.96	−	2816.25i	0.343350	−	0.594699i
$283$	3541.51	+	6134.08i	0.743890	+	1.28846i	0.950711	+	0.310077i	$0.100355\pi$
$283$	3541.51	+	6134.08i	0.743890	+	1.28846i	−0.206821	+	0.978379i	$0.566312\pi$
$284$	−3331.78	+	1923.61i	−0.696144	+	0.401919i
$285$	19055.0			3.96042
$286$		0			0
$287$	−3594.89			−0.739371
$288$	1369.12	−	790.464i	0.280126	−	0.161731i
$289$	1988.00	+	3443.32i	0.404641	+	0.700859i
$290$	697.894	−	1208.79i	0.141316	−	0.244767i
$291$		−	2381.34i		−	0.479713i
$292$	3336.62	+	1926.40i	0.668701	+	0.386075i
$293$	−5995.94	−	3461.76i	−1.19552	−	0.690233i	−0.235965	−	0.971762i	$-0.575825\pi$
$293$	−5995.94	−	3461.76i	−1.19552	−	0.690233i	−0.959553	+	0.281529i	$0.909158\pi$
$294$			8353.64i			1.65712i
$295$	2891.85	−	5008.83i	0.570746	−	0.988561i
$296$	95.5231	+	165.451i	0.0187573	+	0.0324886i
$297$	1610.05	−	929.565i	0.314561	−	0.181612i
$298$	−3834.87			−0.745463
$299$		0			0
$300$	−2648.40			−0.509685
$301$	−10787.6	+	6228.23i	−2.06574	+	1.19265i
$302$	−2035.28	−	3525.20i	−0.387805	−	0.671698i
$303$	2891.33	−	5007.93i	0.548194	−	0.949499i
$304$		−	2461.76i		−	0.464446i
$305$	−7408.34	−	4277.21i	−1.39082	−	0.802991i
$306$	2619.34	+	1512.28i	0.489339	+	0.282520i
$307$		−	8778.50i		−	1.63197i	−0.578071	−	0.815986i	$-0.696195\pi$
$307$		−	8778.50i		−	1.63197i	0.578071	−	0.815986i	$-0.303805\pi$
$308$	−543.984	+	942.208i	−0.100638	+	0.174309i
$309$	1378.24	+	2387.18i	0.253739	+	0.439489i
$310$	−4097.89	+	2365.92i	−0.750789	+	0.433468i
$311$	2197.35			0.400644			0.200322	−	0.979730i	$-0.435801\pi$
$311$	2197.35			0.400644			0.200322	+	0.979730i	$0.435801\pi$
$312$		0			0
$313$	−5052.55			−0.912419			−0.456209	−	0.889873i	$-0.650793\pi$
$313$	−5052.55			−0.912419			−0.456209	+	0.889873i	$0.650793\pi$
$314$	−1065.89	+	615.393i	−0.191566	+	0.110601i
$315$	10027.4	+	17367.9i	1.79358	+	3.10658i
$316$	−2086.36	+	3613.68i	−0.371414	+	0.643308i
$317$			1889.91i			0.334852i	0.985885	+	0.167426i	$0.0535455\pi$
$317$			1889.91i			0.334852i	−0.985885	+	0.167426i	$0.946455\pi$
$318$	−6065.45	−	3501.89i	−1.06960	−	0.617535i
$319$	−404.969	−	233.809i	−0.0710780	−	0.0410369i
$320$			906.785i			0.158409i
$321$	9271.17	−	16058.1i	1.61204	−	2.79214i
$322$	−1031.50	−	1786.61i	−0.178520	−	0.309205i
$323$	4078.74	−	2354.86i	0.702622	−	0.405659i
$324$	−1511.39			−0.259155
$325$		0			0
$326$	2320.18			0.394181
$327$	6695.04	−	3865.38i	1.13222	−	0.653688i
$328$	501.897	+	869.311i	0.0844897	+	0.146340i
$329$	2664.73	−	4615.45i	0.446539	−	0.773428i
$330$			2351.46i			0.392254i
$331$	2207.83	+	1274.69i	0.366627	+	0.211672i	0.671984	−	0.740566i	$-0.265442\pi$
$331$	2207.83	+	1274.69i	0.366627	+	0.211672i	−0.305357	+	0.952238i	$0.598776\pi$
$332$	−1085.32	−	626.608i	−0.179411	−	0.103583i
$333$		−	1179.81i		−	0.194153i
$334$	2029.26	−	3514.79i	0.332444	−	0.575811i
$335$	−2037.06	−	3528.30i	−0.332229	−	0.575437i
$336$	3470.08	−	2003.45i	0.563418	−	0.325289i
$337$	−140.649			−0.0227349			−0.0113674	−	0.999935i	$-0.503618\pi$
$337$	−140.649			−0.0227349			−0.0113674	+	0.999935i	$0.503618\pi$
$338$		0			0
$339$	1155.59			0.185142
$340$	−1502.40	+	867.409i	−0.239644	+	0.138358i
$341$	792.631	+	1372.88i	0.125875	+	0.218022i
$342$	−7601.30	+	13165.8i	−1.20185	+	2.08166i
$343$			3863.38i			0.608171i
$344$	3012.20	+	1739.10i	0.472114	+	0.272575i
$345$	−3861.47	−	2229.42i	−0.602593	−	0.347907i
$346$			6147.20i			0.955132i
$347$	−70.2566	+	121.688i	−0.0108691	+	0.0188258i	−0.871409	−	0.490558i	$-0.836793\pi$
$347$	−70.2566	+	121.688i	−0.0108691	+	0.0188258i	0.860540	+	0.509383i	$0.170126\pi$
$348$	861.099	+	1491.47i	0.132643	+	0.229744i
$349$	−10628.9	+	6136.62i	−1.63024	+	0.941220i	−0.646223	+	0.763148i	$0.723653\pi$
$349$	−10628.9	+	6136.62i	−1.63024	+	0.941220i	−0.984018	+	0.178072i	$0.943014\pi$
$350$	−4340.37			−0.662864
$351$		0			0
$352$	303.792			0.0460004
$353$	5099.13	−	2943.98i	0.768837	−	0.443888i	−0.0636228	−	0.997974i	$-0.520265\pi$
$353$	5099.13	−	2943.98i	0.768837	−	0.443888i	0.832459	+	0.554086i	$0.186932\pi$
$354$	3568.12	+	6180.16i	0.535716	+	0.927887i
$355$	−6813.66	+	11801.6i	−1.01868	+	1.76441i
$356$		−	2703.02i		−	0.402414i
$357$	6638.79	+	3832.91i	0.984207	+	0.568232i
$358$	4007.77	+	2313.89i	0.591668	+	0.341600i
$359$			5902.88i			0.867806i	0.900960	+	0.433903i	$0.142864\pi$
$359$			5902.88i			0.867806i	−0.900960	+	0.433903i	$0.857136\pi$
$360$	2799.93	−	4849.62i	0.409914	−	0.709992i
$361$	8406.94	+	14561.2i	1.22568	+	2.12294i
$362$	2892.54	−	1670.01i	0.419968	−	0.242469i
$363$	−10846.4			−1.56829
$364$		0			0
$365$	13647.1			1.95704
$366$	9140.80	−	5277.44i	1.30546	−	0.753706i
$367$	1659.47	+	2874.28i	0.236031	+	0.408818i	0.959572	−	0.281464i	$-0.0908200\pi$
$367$	1659.47	+	2874.28i	0.236031	+	0.408818i	−0.723541	+	0.690282i	$0.757487\pi$
$368$	−288.024	+	498.873i	−0.0407997	+	0.0706672i
$369$		−	6198.93i		−	0.874535i
$370$	586.049	+	338.355i	0.0823438	+	0.0475412i
$371$	−9940.44	−	5739.12i	−1.39106	−	0.803127i
$372$		−	5838.39i		−	0.813727i
$373$	−121.108	+	209.765i	−0.0168116	+	0.0291185i	−0.874309	−	0.485370i	$-0.838685\pi$
$373$	−121.108	+	209.765i	−0.0168116	+	0.0291185i	0.857497	+	0.514489i	$0.172018\pi$
$374$	290.600	+	503.333i	0.0401779	+	0.0695902i
$375$	5282.58	−	3049.90i	0.727443	−	0.419989i
$376$	−1488.14			−0.204108
$377$		0			0
$378$	−11221.3			−1.52689
$379$	−11175.4	+	6452.13i	−1.51462	+	0.874469i	−0.514772	+	0.857327i	$0.672123\pi$
$379$	−11175.4	+	6452.13i	−1.51462	+	0.874469i	−0.999853	+	0.0171418i	$0.994543\pi$
$380$	−4359.94	−	7551.63i	−0.588579	−	1.01945i
$381$	8185.05	−	14176.9i	1.10061	−	1.90631i
$382$			7650.41i			1.02468i
$383$	3975.94	+	2295.51i	0.530446	+	0.306253i	0.741198	−	0.671286i	$-0.234258\pi$
$383$	3975.94	+	2295.51i	0.530446	+	0.306253i	−0.210752	+	0.977540i	$0.567591\pi$
$384$	−968.944	−	559.420i	−0.128766	−	0.0743432i
$385$			3853.73i			0.510141i
$386$	−908.832	+	1574.14i	−0.119840	+	0.207569i
$387$	−10739.8	−	18601.9i	−1.41068	−	2.44338i
$388$	−943.742	+	544.869i	−0.123483	+	0.0712927i
$389$	13973.1			1.82125			0.910623	−	0.413239i	$-0.135603\pi$
$389$	13973.1			1.82125			0.910623	+	0.413239i	$0.135603\pi$
$390$		0			0
$391$	−1102.07			−0.142542
$392$	3310.61	−	1911.38i	0.426559	−	0.246274i
$393$	−8086.30	−	14005.9i	−1.03791	−	1.79772i
$394$	1337.67	−	2316.91i	0.171042	−	0.296254i
$395$			14780.3i			1.88273i
$396$	−1624.72	−	938.033i	−0.206175	−	0.119035i
$397$	2267.02	+	1308.87i	0.286596	+	0.165466i	0.636406	−	0.771355i	$-0.280420\pi$
$397$	2267.02	+	1308.87i	0.286596	+	0.165466i	−0.349810	+	0.936821i	$0.613754\pi$
$398$		−	2289.16i		−	0.288305i
$399$	−19265.7	+	33369.1i	−2.41727	+	4.18683i
$400$	605.976	+	1049.58i	0.0757470	+	0.131198i
$401$	−6832.24	+	3944.60i	−0.850838	+	0.491231i	−0.860933	−	0.508718i	$-0.830120\pi$
$401$	−6832.24	+	3944.60i	−0.850838	+	0.491231i	0.0100957	+	0.999949i	$0.496786\pi$
$402$	5026.87			0.623676
$403$		0			0
$404$	−2646.24			−0.325880
$405$	−4636.31	+	2676.77i	−0.568840	+	0.328420i
$406$	1411.22	+	2444.31i	0.172507	+	0.298791i
$407$	113.356	−	196.338i	0.0138055	−	0.0239118i
$408$		−	2140.51i		−	0.259733i
$409$	−6695.71	−	3865.77i	−0.809490	−	0.467359i	0.0372886	−	0.999305i	$-0.488128\pi$
$409$	−6695.71	−	3865.77i	−0.809490	−	0.467359i	−0.846779	+	0.531945i	$0.821461\pi$
$410$	3079.21	+	1777.78i	0.370906	+	0.214143i
$411$		−	8455.76i		−	1.01482i
$412$	630.706	−	1092.41i	0.0754191	−	0.130630i
$413$	5847.66	+	10128.4i	0.696718	+	1.20675i
$414$	3080.79	−	1778.69i	0.365731	−	0.211155i
$415$	−4439.05			−0.525071
$416$		0			0
$417$	905.535			0.106341
$418$	−2529.95	+	1460.67i	−0.296038	+	0.170918i
$419$	−1378.20	−	2387.12i	−0.160691	−	0.278326i	0.774425	−	0.632665i	$-0.218039\pi$
$419$	−1378.20	−	2387.12i	−0.160691	−	0.278326i	−0.935117	+	0.354340i	$0.884706\pi$
$420$	7096.49	−	12291.5i	0.824460	−	1.42801i
$421$		−	11815.2i		−	1.36778i	−0.729585	−	0.683890i	$-0.760287\pi$
$421$		−	11815.2i		−	1.36778i	0.729585	−	0.683890i	$-0.239713\pi$
$422$	19.4427	+	11.2252i	0.00224278	+	0.00129487i
$423$	7958.76	+	4594.99i	0.914818	+	0.528171i
$424$			3205.05i			0.367101i
$425$	−1159.32	+	2008.01i	−0.132319	+	0.229183i
$426$	−8407.06	−	14561.5i	−0.956158	−	1.65611i
$427$	14980.5	−	8649.01i	1.69779	−	0.980222i
$428$	−8485.29			−0.958299
$429$		0			0
$430$	12320.2			1.38171
$431$	9180.93	−	5300.61i	1.02605	−	0.592393i	0.110203	−	0.993909i	$-0.464850\pi$
$431$	9180.93	−	5300.61i	1.02605	−	0.592393i	0.915852	+	0.401516i	$0.131517\pi$
$432$	1566.66	+	2713.53i	0.174481	+	0.302210i
$433$	−4614.86	+	7993.17i	−0.512185	+	0.887130i	0.487716	+	0.873003i	$0.337830\pi$
$433$	−4614.86	+	7993.17i	−0.512185	+	0.887130i	−0.999900	+	0.0141273i	$0.995503\pi$
$434$		−	9568.32i		−	1.05828i
$435$	5282.97	+	3050.13i	0.582297	+	0.336189i
$436$	−3063.76	−	1768.86i	−0.336531	−	0.194296i
$437$		−	5539.42i		−	0.606377i
$438$	−8419.25	+	14582.6i	−0.918465	+	1.59083i
$439$	3600.83	+	6236.82i	0.391476	+	0.678057i	0.992645	−	0.121066i	$-0.0386311\pi$
$439$	3600.83	+	6236.82i	0.391476	+	0.678057i	−0.601168	+	0.799123i	$0.705298\pi$
$440$	931.903	−	538.035i	0.100970	−	0.0582950i
$441$	−23607.5			−2.54913
$442$		0			0
$443$	−3544.70			−0.380167			−0.190083	−	0.981768i	$-0.560876\pi$
$443$	−3544.70			−0.380167			−0.190083	+	0.981768i	$0.560876\pi$
$444$	−723.098	+	417.481i	−0.0772899	+	0.0446233i
$445$	−4787.22	−	8291.70i	−0.509968	−	0.883291i
$446$	2739.74	−	4745.37i	0.290876	−	0.503811i
$447$		−	16760.2i		−	1.77344i
$448$	−1587.97	−	916.813i	−0.167465	−	0.0966860i
$449$	15870.2	+	9162.68i	1.66807	+	0.963059i	0.968678	+	0.248319i	$0.0798780\pi$
$449$	15870.2	+	9162.68i	1.66807	+	0.963059i	0.699389	+	0.714741i	$0.253455\pi$
$450$		−	7484.41i		−	0.784041i
$451$	595.594	−	1031.60i	0.0621849	−	0.107707i
$452$	−264.409	−	457.970i	−0.0275150	−	0.0476573i
$453$	15406.8	−	8895.12i	1.59796	−	0.922581i
$454$	9059.50			0.936527
$455$		0			0
$456$	10759.0			1.10491
$457$	4662.54	−	2691.92i	0.477252	−	0.275542i	−0.242018	−	0.970272i	$-0.577809\pi$
$457$	4662.54	−	2691.92i	0.477252	−	0.275542i	0.719271	+	0.694730i	$0.244476\pi$
$458$	−867.892	−	1503.23i	−0.0885457	−	0.153366i
$459$	−2997.25	+	5191.39i	−0.304793	+	0.527916i
$460$			2040.44i			0.206817i
$461$	−9198.17	−	5310.57i	−0.929288	−	0.536525i	−0.0427015	−	0.999088i	$-0.513596\pi$
$461$	−9198.17	−	5310.57i	−0.929288	−	0.536525i	−0.886586	+	0.462563i	$0.846930\pi$
$462$	−4117.89	−	2377.47i	−0.414679	−	0.239415i
$463$			10407.3i			1.04464i	0.852751	+	0.522318i	$0.174933\pi$
$463$			10407.3i			1.04464i	−0.852751	+	0.522318i	$0.825067\pi$
$464$	394.053	−	682.521i	0.0394256	−	0.0682871i
$465$	−10340.2	−	17909.7i	−1.03121	−	1.78611i
$466$	−926.886	+	535.138i	−0.0921399	+	0.0531970i
$467$	15784.0			1.56402			0.782010	−	0.623266i	$-0.214195\pi$
$467$	15784.0			1.56402			0.782010	+	0.623266i	$0.214195\pi$
$468$		0			0
$469$	8238.36			0.811113
$470$	−4564.97	+	2635.59i	−0.448013	+	0.258661i
$471$	−2689.56	−	4658.45i	−0.263117	−	0.455732i
$472$	1632.83	−	2828.15i	0.159231	−	0.275796i
$473$		−	4127.52i		−	0.401234i
$474$	−15793.5	−	9118.36i	−1.53042	−	0.883587i
$475$	−10093.0	−	5827.22i	−0.974948	−	0.562886i
$476$		−	3508.00i		−	0.337792i
$477$	9896.38	−	17141.0i	0.949946	−	1.64536i
$478$	1146.73	+	1986.20i	0.109729	+	0.190055i
$479$	−15816.8	+	9131.86i	−1.50875	+	0.871075i	−0.508799	+	0.860885i	$0.669910\pi$
$479$	−15816.8	+	9131.86i	−1.50875	+	0.871075i	−0.999948	+	0.0101899i	$0.996756\pi$
$480$	−3963.08			−0.376852
$481$		0			0
$482$	6706.06			0.633720
$483$	7808.34	−	4508.15i	0.735593	−	0.424695i
$484$	2481.75	+	4298.51i	0.233072	+	0.403692i
$485$	−1930.00	+	3342.86i	−0.180694	+	0.312972i
$486$			3969.44i			0.370489i
$487$	−4649.70	−	2684.50i	−0.432645	−	0.249788i	0.267828	−	0.963467i	$-0.413694\pi$
$487$	−4649.70	−	2684.50i	−0.432645	−	0.249788i	−0.700473	+	0.713679i	$0.747027\pi$
$488$	−4182.98	−	2415.05i	−0.388022	−	0.224025i
$489$			10140.3i			0.937750i
$490$	6770.36	−	11726.6i	0.624192	−	1.08113i
$491$	−745.667	−	1291.53i	−0.0685366	−	0.118709i	0.829721	−	0.558179i	$-0.188500\pi$
$491$	−745.667	−	1291.53i	−0.0685366	−	0.118709i	−0.898257	+	0.439470i	$0.855166\pi$
$492$	−3799.30	+	2193.52i	−0.348141	+	0.200999i
$493$	1507.77			0.137741
$494$		0			0
$495$	−6645.27			−0.603399
$496$	−2313.80	+	1335.87i	−0.209461	+	0.120932i
$497$	−13778.0	−	23864.2i	−1.24352	−	2.15384i
$498$	2738.57	−	4743.34i	0.246422	−	0.426816i
$499$			10067.4i			0.903163i	0.892230	+	0.451582i	$0.149140\pi$
$499$			10067.4i			0.903163i	−0.892230	+	0.451582i	$0.850860\pi$
$500$	−2417.40	−	1395.68i	−0.216218	−	0.124834i
$501$	15361.3	+	8868.84i	1.36984	+	0.790879i
$502$		−	10715.9i		−	0.952738i
$503$	−2341.53	+	4055.65i	−0.207562	+	0.359508i	−0.950946	−	0.309357i	$-0.899886\pi$
$503$	−2341.53	+	4055.65i	−0.207562	+	0.359508i	0.743384	+	0.668865i	$0.233220\pi$
$504$	5661.78	+	9806.49i	0.500388	+	0.866698i
$505$	−8117.55	+	4686.67i	−0.715299	+	0.412978i
$506$	683.589			0.0600577
$507$		0			0
$508$	−7491.23			−0.654271
$509$	−9998.23	+	5772.48i	−0.870656	+	0.502673i	−0.867566	−	0.497322i	$-0.834317\pi$
$509$	−9998.23	+	5772.48i	−0.870656	+	0.502673i	−0.00308978	+	0.999995i	$0.500984\pi$
$510$	−3790.99	−	6566.18i	−0.329152	−	0.570108i
$511$	−13798.0	+	23898.8i	−1.19450	+	2.06893i
$512$			512.000i			0.0441942i
$513$	−26094.0	−	15065.4i	−2.24576	−	1.29659i
$514$	−10898.2	−	6292.11i	−0.935216	−	0.539947i
$515$		−	4468.09i		−	0.382306i
$516$	−7600.67	+	13164.7i	−0.648451	+	1.12315i
$517$	882.975	+	1529.36i	0.0751125	+	0.130099i
$518$	−1185.06	+	684.194i	−0.100518	+	0.0580343i
$519$	−26866.2			−2.27224
$520$		0			0
$521$	19889.6			1.67252			0.836258	−	0.548336i	$-0.184739\pi$
$521$	19889.6			1.67252			0.836258	+	0.548336i	$0.184739\pi$
$522$	−4214.91	+	2433.48i	−0.353413	+	0.204043i
$523$	2545.03	+	4408.13i	0.212785	+	0.368555i	0.952585	−	0.304272i	$-0.0984133\pi$
$523$	2545.03	+	4408.13i	0.212785	+	0.368555i	−0.739800	+	0.672827i	$0.765080\pi$
$524$	−3700.43	+	6409.33i	−0.308500	+	0.534337i
$525$		−	18969.4i		−	1.57694i
$526$	8309.96	+	4797.76i	0.688843	+	0.397704i
$527$	−4426.65	−	2555.73i	−0.365897	−	0.211251i
$528$			1327.71i			0.109434i
$529$	5435.39	−	9414.37i	0.446732	−	0.773763i
$530$	5676.35	+	9831.72i	0.465216	+	0.805779i
$531$	−17465.2	+	10083.5i	−1.42736	+	0.824084i
$532$	17632.6			1.43697
$533$		0			0
$534$	11813.4			0.957337
$535$	−26029.3	+	15028.0i	−2.10344	+	1.21442i
$536$	−1150.19	−	1992.19i	−0.0926879	−	0.160540i
$537$	−10112.8	+	17515.8i	−0.812660	+	1.40757i
$538$			12492.9i			1.00113i
$539$	−3928.65	−	2268.21i	−0.313950	−	0.181259i
$540$	9611.67	+	5549.30i	0.765964	+	0.442230i
$541$		−	5958.49i		−	0.473523i	−0.971568	−	0.236761i	$-0.923914\pi$
$541$		−	5958.49i		−	0.473523i	0.971568	−	0.236761i	$-0.0760859\pi$
$542$	1831.15	−	3171.65i	0.145119	−	0.251354i
$543$	7298.72	+	12641.8i	0.576829	+	0.999097i
$544$	−848.301	+	489.767i	−0.0668577	+	0.0386003i
$545$	−12531.1			−0.984905
$546$		0			0
$547$	2475.52			0.193502			0.0967509	−	0.995309i	$-0.469155\pi$
$547$	2475.52			0.193502			0.0967509	+	0.995309i	$0.469155\pi$
$548$	−3351.08	+	1934.75i	−0.261225	+	0.150818i
$549$	14914.1	+	25832.0i	1.15942	+	2.00817i
$550$	719.103	−	1245.52i	0.0557503	−	0.0965624i
$551$			7578.63i			0.585954i
$552$	−2180.31	−	1258.80i	−0.168116	−	0.0970619i
$553$	−25883.3	−	14943.7i	−1.99036	−	1.14914i
$554$			3202.85i			0.245624i
$555$	−1478.77	+	2561.31i	−0.113100	+	0.195894i
$556$	−207.194	−	358.870i	−0.0158039	−	0.0273732i
$557$	20188.4	−	11655.8i	1.53574	−	0.886662i	0.536664	−	0.843796i	$-0.319684\pi$
$557$	20188.4	−	11655.8i	1.53574	−	0.886662i	0.999081	−	0.0428662i	$-0.0136489\pi$
$558$	16499.4			1.25175
$559$		0			0
$560$	−6494.94			−0.490110
$561$	−2199.80	+	1270.06i	−0.165554	+	0.0955826i
$562$	4516.64	+	7823.04i	0.339009	+	0.587180i
$563$	12313.1	−	21326.9i	0.921733	−	1.59649i	0.125000	−	0.992157i	$-0.460107\pi$
$563$	12313.1	−	21326.9i	0.921733	−	1.59649i	0.796733	−	0.604332i	$-0.206560\pi$
$564$		−	6503.85i		−	0.485570i
$565$	−1622.19	−	936.572i	−0.120789	−	0.0697378i
$566$	12268.2	+	7083.02i	0.911076	+	0.526010i
$567$		−	10825.5i		−	0.801813i
$568$	−3847.21	+	6663.57i	−0.284200	+	0.492248i
$569$	−6599.29	−	11430.3i	−0.486215	−	0.842150i	0.513659	−	0.857994i	$-0.328290\pi$
$569$	−6599.29	−	11430.3i	−0.486215	−	0.842150i	−0.999874	+	0.0158447i	$0.994956\pi$
$570$	33004.2	−	19055.0i	2.42525	−	1.40022i
$571$	−20934.2			−1.53427			−0.767137	−	0.641483i	$-0.778319\pi$
$571$	−20934.2			−1.53427			−0.767137	+	0.641483i	$0.778319\pi$
$572$		0			0
$573$	−33435.9			−2.43770
$574$	−6226.52	+	3594.89i	−0.452770	+	0.261407i
$575$	1363.56	+	2361.76i	0.0988947	+	0.171291i
$576$	1580.93	−	2738.25i	0.114361	−	0.198079i
$577$			17083.2i			1.23255i	0.787531	+	0.616275i	$0.211359\pi$
$577$			17083.2i			1.23255i	−0.787531	+	0.616275i	$0.788641\pi$
$578$	6886.64	+	3976.00i	0.495582	+	0.286124i
$579$	−6879.74	−	3972.02i	−0.493804	−	0.285098i
$580$		−	2791.58i		−	0.199852i
$581$	4488.14	−	7773.69i	0.320481	−	0.555089i
$582$	−2381.34	−	4124.59i	−0.169604	−	0.293763i
$583$	3293.83	−	1901.69i	0.233990	−	0.135094i
$584$	7705.58			0.545992
$585$		0			0
$586$	−13847.0			−0.976136
$587$	3861.45	−	2229.41i	0.271515	−	0.156759i	−0.358061	−	0.933698i	$-0.616562\pi$
$587$	3861.45	−	2229.41i	0.271515	−	0.156759i	0.629576	+	0.776939i	$0.283229\pi$
$588$	8353.64	+	14468.9i	0.585881	+	1.01478i
$589$	12846.1	−	22250.1i	0.898665	−	1.55653i
$590$		−	11567.4i		−	0.807156i
$591$	10126.0	+	5846.23i	0.704783	+	0.406907i
$592$	330.902	+	191.046i	0.0229729	+	0.0132634i
$593$			3217.47i			0.222809i	0.993775	+	0.111404i	$0.0355349\pi$
$593$			3217.47i			0.222809i	−0.993775	+	0.111404i	$0.964465\pi$
$594$	1859.13	−	3220.11i	0.128419	−	0.222429i
$595$	−6212.91	−	10761.1i	−0.428074	−	0.741447i
$596$	−6642.19	+	3834.87i	−0.456501	+	0.263561i
$597$	10004.7			0.685872
$598$		0			0
$599$	−4495.37			−0.306637			−0.153319	−	0.988177i	$-0.548996\pi$
$599$	−4495.37			−0.306637			−0.153319	+	0.988177i	$0.548996\pi$
$600$	−4587.16	+	2648.40i	−0.312117	+	0.180201i
$601$	5459.23	+	9455.66i	0.370527	+	0.641771i	0.989647	−	0.143525i	$-0.0458438\pi$
$601$	5459.23	+	9455.66i	0.370527	+	0.641771i	−0.619120	+	0.785297i	$0.712510\pi$
$602$	−12456.5	+	21575.2i	−0.843334	+	1.46070i
$603$			14206.0i			0.959392i
$604$	−7050.41	−	4070.56i	−0.474962	−	0.274219i
$605$	15225.9	+	8790.67i	1.02317	+	0.590730i
$606$		−	11565.3i		−	0.775263i
$607$	−6243.51	+	10814.1i	−0.417490	+	0.723114i	−0.995686	−	0.0927838i	$-0.970423\pi$
$607$	−6243.51	+	10814.1i	−0.417490	+	0.723114i	0.578196	+	0.815898i	$0.303757\pi$
$608$	−2461.76	−	4263.89i	−0.164206	−	0.284414i
$609$	−10682.8	+	6167.71i	−0.710818	+	0.410391i
$610$	−17108.8			−1.13560
$611$		0			0
$612$	6049.11			0.399544
$613$	832.656	−	480.734i	0.0548624	−	0.0316748i	−0.472318	−	0.881428i	$-0.656583\pi$
$613$	832.656	−	480.734i	0.0548624	−	0.0316748i	0.527180	+	0.849753i	$0.323249\pi$
$614$	−8778.50	−	15204.8i	−0.576989	−	0.999375i
$615$	−7769.75	+	13457.6i	−0.509442	+	0.882379i
$616$			2175.94i			0.142323i
$617$	13365.8	+	7716.73i	0.872100	+	0.503507i	0.868046	−	0.496485i	$-0.165376\pi$
$617$	13365.8	+	7716.73i	0.872100	+	0.503507i	0.00405455	+	0.999992i	$0.498709\pi$
$618$	4774.37	+	2756.48i	0.310766	+	0.179421i
$619$		−	24569.6i		−	1.59537i	−0.603073	−	0.797686i	$-0.706057\pi$
$619$		−	24569.6i		−	1.59537i	0.603073	−	0.797686i	$-0.293943\pi$
$620$	−4731.84	+	8195.78i	−0.306508	+	0.530888i
$621$	3525.27	+	6105.96i	0.227801	+	0.394563i
$622$	3805.92	−	2197.35i	0.245343	−	0.141649i
$623$	19360.6			1.24505
$624$		0			0
$625$	−19355.8			−1.23877
$626$	−8751.27	+	5052.55i	−0.558740	+	0.322589i
$627$	−6383.80	−	11057.1i	−0.406610	−	0.704269i
$628$	−1230.79	+	2131.78i	−0.0782065	+	0.135458i
$629$			731.001i			0.0463385i
$630$	34735.9	+	20054.8i	2.19668	+	1.26826i
$631$	11537.4	+	6661.10i	0.727885	+	0.420245i	0.817648	−	0.575719i	$-0.195278\pi$
$631$	11537.4	+	6661.10i	0.727885	+	0.420245i	−0.0897629	+	0.995963i	$0.528611\pi$
$632$			8345.43i			0.525259i
$633$	−49.0596	+	84.9736i	−0.00308048	+	0.00533554i
$634$	1889.91	+	3273.42i	0.118388	+	0.205054i
$635$	−22979.9	+	13267.5i	−1.43611	+	0.829139i
$636$	−14007.6			−0.873327
$637$		0			0
$638$	−935.235			−0.0580350
$639$	41150.9	−	23758.5i	2.54758	−	1.47085i
$640$	906.785	+	1570.60i	0.0560060	+	0.0970052i
$641$	7447.28	−	12899.1i	0.458892	−	0.794824i	−0.540011	−	0.841658i	$-0.681580\pi$
$641$	7447.28	−	12899.1i	0.458892	−	0.794824i	0.998903	+	0.0468338i	$0.0149131\pi$
$642$		−	37084.7i		−	2.27978i
$643$	−8008.62	−	4623.78i	−0.491181	−	0.283583i	0.233883	−	0.972265i	$-0.424857\pi$
$643$	−8008.62	−	4623.78i	−0.491181	−	0.283583i	−0.725064	+	0.688681i	$0.758190\pi$
$644$	−3573.23	−	2063.00i	−0.218641	−	0.126232i
$645$			53845.1i			3.28705i
$646$	4709.72	−	8157.47i	0.286844	−	0.496829i
$647$	1367.07	+	2367.84i	0.0830681	+	0.143878i	0.904566	−	0.426333i	$-0.140195\pi$
$647$	1367.07	+	2367.84i	0.0830681	+	0.143878i	−0.821498	+	0.570211i	$0.806861\pi$
$648$	−2617.81	+	1511.39i	−0.158699	+	0.0916251i
$649$	−3875.31			−0.234390
$650$		0			0
$651$	41818.1			2.51763
$652$	4018.67	−	2320.18i	0.241386	−	0.139364i
$653$	3281.39	+	5683.53i	0.196647	+	0.340603i	0.947439	−	0.319936i	$-0.103661\pi$
$653$	3281.39	+	5683.53i	0.196647	+	0.340603i	−0.750792	+	0.660539i	$0.770328\pi$
$654$	7730.76	−	13390.1i	0.462228	−	0.800602i
$655$			26214.8i			1.56381i
$656$	1738.62	+	1003.79i	0.103478	+	0.0597432i
$657$	−41210.5	−	23792.9i	−2.44715	−	1.41286i
$658$		−	10658.9i		−	0.631501i
$659$	2476.92	−	4290.15i	0.146414	−	0.253597i	−0.783485	−	0.621410i	$-0.786560\pi$
$659$	2476.92	−	4290.15i	0.146414	−	0.253597i	0.929900	+	0.367813i	$0.119893\pi$
$660$	2351.46	+	4072.85i	0.138683	+	0.240206i
$661$	8094.98	−	4673.64i	0.476336	−	0.275013i	−0.242552	−	0.970138i	$-0.577985\pi$
$661$	8094.98	−	4673.64i	0.476336	−	0.275013i	0.718888	+	0.695126i	$0.244651\pi$
$662$	5098.78			0.299350
$663$		0			0
$664$	−2506.43			−0.146489
$665$	54089.3	−	31228.5i	3.15413	−	1.82104i
$666$	−1179.81	−	2043.48i	−0.0686435	−	0.118894i
$667$	886.695	−	1535.80i	0.0514737	−	0.0891551i
$668$		−	8117.06i		−	0.470147i
$669$	20739.5	+	11974.0i	1.19856	+	0.691988i
$670$	−7056.59	−	4074.13i	−0.406896	−	0.234921i
$671$			5731.80i			0.329767i
$672$	4006.90	−	6940.16i	0.230014	−	0.398396i
$673$	7709.51	+	13353.3i	0.441575	+	0.764830i	0.997807	−	0.0661971i	$-0.0210866\pi$
$673$	7709.51	+	13353.3i	0.441575	+	0.764830i	−0.556232	+	0.831027i	$0.687753\pi$
$674$	−243.611	+	140.649i	−0.0139222	+	0.00803798i
$675$	14833.7			0.845851
$676$		0			0
$677$	26079.0			1.48050			0.740248	−	0.672334i	$-0.234708\pi$
$677$	26079.0			1.48050			0.740248	+	0.672334i	$0.234708\pi$
$678$	2001.54	−	1155.59i	0.113376	−	0.0654576i
$679$	−3902.68	−	6759.64i	−0.220576	−	0.382049i
$680$	−1734.82	+	3004.79i	−0.0978342	+	0.169454i
$681$			39594.3i			2.22798i
$682$	2745.75	+	1585.26i	0.154165	+	0.0890070i
$683$	12895.2	+	7445.02i	0.722429	+	0.417095i	0.815646	−	0.578551i	$-0.196382\pi$
$683$	12895.2	+	7445.02i	0.722429	+	0.417095i	−0.0932168	+	0.995646i	$0.529715\pi$
$684$			30405.2i			1.69967i
$685$	−6853.14	+	11870.0i	−0.382255	+	0.662086i
$686$	3863.38	+	6691.56i	0.215021	+	0.372427i
$687$	6569.83	−	3793.09i	0.364854	−	0.210649i
$688$	6956.39			0.385479
$689$		0			0
$690$	−8917.68			−0.492015
$691$	3525.61	−	2035.51i	0.194096	−	0.112062i	−0.399802	−	0.916601i	$-0.630921\pi$
$691$	3525.61	−	2035.51i	0.194096	−	0.112062i	0.593899	+	0.804540i	$0.297588\pi$
$692$	6147.20	+	10647.3i	0.337690	+	0.584897i
$693$	6718.75	−	11637.2i	0.368289	−	0.637895i
$694$			281.026i			0.0153712i
$695$	−1271.17	−	733.908i	−0.0693785	−	0.0400557i
$696$	2982.94	+	1722.20i	0.162454	+	0.0937928i
$697$			3840.82i			0.208725i
$698$	−12273.2	+	21257.9i	−0.665543	+	1.15275i
$699$	−2338.80	−	4050.93i	−0.126555	−	0.219199i
$700$	−7517.73	+	4340.37i	−0.405919	+	0.234358i
$701$	−18378.1			−0.990200			−0.495100	−	0.868836i	$-0.664869\pi$
$701$	−18378.1			−0.990200			−0.495100	+	0.868836i	$0.664869\pi$
$702$		0			0
$703$	−3674.29			−0.197125
$704$	526.182	−	303.792i	0.0281694	−	0.0162636i
$705$	−11518.7	−	19951.1i	−0.615349	−	1.06582i
$706$	5887.97	−	10198.3i	0.313876	−	0.543650i
$707$		−	18954.0i		−	1.00826i
$708$	12360.3	+	7136.24i	0.656115	+	0.378808i
$709$	−12943.9	−	7473.18i	−0.685641	−	0.395855i	0.116336	−	0.993210i	$-0.462885\pi$
$709$	−12943.9	−	7473.18i	−0.685641	−	0.395855i	−0.801977	+	0.597355i	$0.796218\pi$
$710$			27254.7i			1.44063i
$711$	25768.6	−	44632.5i	1.35921	−	2.35422i
$712$	−2703.02	−	4681.76i	−0.142275	−	0.246428i
$713$	−5206.49	+	3005.97i	−0.273471	+	0.157888i
$714$	15331.6			0.803602
$715$		0			0
$716$	9255.55			0.483095
$717$	−8680.61	+	5011.75i	−0.452138	+	0.261042i
$718$	5902.88	+	10224.1i	0.306816	+	0.531420i
$719$	7502.92	−	12995.4i	0.389168	−	0.674058i	−0.603170	−	0.797613i	$-0.706096\pi$
$719$	7502.92	−	12995.4i	0.389168	−	0.674058i	0.992338	+	0.123554i	$0.0394294\pi$
$720$		−	11199.7i		−	0.579706i
$721$	7824.53	+	4517.49i	0.404162	+	0.233343i
$722$	29122.5	+	16813.9i	1.50115	+	0.866687i
$723$			29308.6i			1.50761i
$724$	3340.02	−	5785.08i	0.171451	−	0.296962i
$725$	−1865.52	−	3231.18i	−0.0955639	−	0.165521i
$726$	−18786.5	+	10846.4i	−0.960376	+	0.554473i
$727$	30390.1			1.55035			0.775177	−	0.631744i	$-0.217661\pi$
$727$	30390.1			1.55035			0.775177	+	0.631744i	$0.217661\pi$
$728$		0			0
$729$	−27550.2			−1.39970
$730$	23637.5	−	13647.1i	1.19844	−	0.691920i
$731$	6654.32	+	11525.6i	0.336688	+	0.583160i
$732$	10554.9	−	18281.6i	0.532951	−	0.923098i
$733$		−	31143.3i		−	1.56931i	−0.619932	−	0.784655i	$-0.712840\pi$
$733$		−	31143.3i		−	1.56931i	0.619932	−	0.784655i	$-0.287160\pi$
$734$	5748.56	+	3318.93i	0.289078	+	0.166899i
$735$	51250.8	+	29589.7i	2.57199	+	1.48494i
$736$			1152.10i			0.0576995i
$737$	−1364.92	+	2364.10i	−0.0682189	+	0.118159i
$738$	−6198.93	−	10736.9i	−0.309195	−	0.535541i
$739$	3364.34	−	1942.40i	0.167469	−	0.0966881i	−0.413923	−	0.910312i	$-0.635842\pi$
$739$	3364.34	−	1942.40i	0.167469	−	0.0966881i	0.581392	+	0.813624i	$0.302508\pi$
$740$	1353.42			0.0672334
$741$		0			0
$742$	−22956.5			−1.13579
$743$	−10058.7	+	5807.42i	−0.496661	+	0.286748i	−0.727334	−	0.686284i	$-0.759241\pi$
$743$	−10058.7	+	5807.42i	−0.496661	+	0.286748i	0.230672	+	0.973031i	$0.425907\pi$
$744$	−5838.39	−	10112.4i	−0.287696	−	0.498304i
$745$	−13583.6	+	23527.5i	−0.668007	+	1.15702i
$746$			484.431i			0.0237752i
$747$	13404.7	+	7739.23i	0.656565	+	0.379068i
$748$	1006.67	+	581.199i	0.0492077	+	0.0284101i
$749$		−	60776.7i		−	2.96493i
$750$	6099.79	−	10565.2i	0.296977	−	0.514380i
$751$	−17205.1	−	29800.1i	−0.835982	−	1.44796i	−0.893228	−	0.449604i	$-0.851565\pi$
$751$	−17205.1	−	29800.1i	−0.835982	−	1.44796i	0.0572461	−	0.998360i	$-0.481768\pi$
$752$	−2577.53	+	1488.14i	−0.124990	+	0.0721632i
$753$	46833.6			2.26655
$754$		0			0
$755$	−28836.9			−1.39004
$756$	−19435.9	+	11221.3i	−0.935023	+	0.539836i
$757$	14728.4	+	25510.3i	0.707150	+	1.22482i	0.965910	+	0.258879i	$0.0833529\pi$
$757$	14728.4	+	25510.3i	0.707150	+	1.22482i	−0.258760	+	0.965942i	$0.583314\pi$
$758$	−12904.3	+	22350.8i	−0.618343	+	1.07100i
$759$			2987.60i			0.142876i
$760$	−15103.3	−	8719.87i	−0.720859	−	0.416188i
$761$	−28535.7	−	16475.1i	−1.35929	−	0.784784i	−0.369759	−	0.929128i	$-0.620560\pi$
$761$	−28535.7	−	16475.1i	−1.35929	−	0.784784i	−0.989528	+	0.144343i	$0.953893\pi$
$762$		−	32740.2i		−	1.55650i
$763$	12669.7	−	21944.5i	0.601144	−	1.04121i
$764$	7650.41	+	13250.9i	0.362280	+	0.627488i
$765$	18556.1	−	10713.4i	0.876990	−	0.506331i
$766$	9182.04			0.433108
$767$		0			0
$768$	−2237.68			−0.105137
$769$	−8854.00	+	5111.86i	−0.415193	+	0.239712i	−0.693019	−	0.720920i	$-0.743720\pi$
$769$	−8854.00	+	5111.86i	−0.415193	+	0.239712i	0.277826	+	0.960632i	$0.410386\pi$
$770$	3853.73	+	6674.85i	0.180362	+	0.312396i
$771$	27499.5	−	47630.4i	1.28452	−	2.22486i
$772$			3635.33i			0.169480i
$773$	8781.56	+	5070.04i	0.408604	+	0.235908i	0.690190	−	0.723629i	$-0.257527\pi$
$773$	8781.56	+	5070.04i	0.408604	+	0.235908i	−0.281586	+	0.959536i	$0.590860\pi$
$774$	−37203.8	−	21479.6i	−1.72773	−	0.997504i
$775$			12648.6i			0.586257i
$776$	−1089.74	+	1887.48i	−0.0504115	+	0.0873153i
$777$	−2990.25	−	5179.26i	−0.138062	−	0.239131i
$778$	24202.1	−	13973.1i	1.11528	−	0.643907i
$779$	−19305.4			−0.887920
$780$		0			0
$781$	9130.86			0.418346
$782$	−1908.84	+	1102.07i	−0.0872889	+	0.0503963i
$783$	−4823.02	−	8353.71i	−0.220129	−	0.381274i
$784$	3822.76	−	6621.22i	0.174142	−	0.301623i
$785$			8719.21i			0.396435i
$786$	−28011.8	−	16172.6i	−1.27118	−	0.733916i
$787$	7870.90	+	4544.27i	0.356502	+	0.205827i	0.667545	−	0.744569i	$-0.267345\pi$
$787$	7870.90	+	4544.27i	0.356502	+	0.205827i	−0.311043	+	0.950396i	$0.600678\pi$
$788$		−	5350.67i		−	0.241890i
$789$	−20968.4	+	36318.4i	−0.946130	+	1.63874i
$790$	14780.3	+	25600.2i	0.665645	+	1.15293i
$791$	3280.26	−	1893.86i	0.147449	−	0.0851300i
$792$	−3752.13			−0.168341
$793$		0			0
$794$	5235.46			0.234004
$795$	−42969.2	+	24808.3i	−1.91693	+	1.10674i
$796$	−2289.16	−	3964.94i	−0.101931	−	0.176550i
$797$	−10516.2	+	18214.6i	−0.467382	+	0.809530i	−0.999305	−	0.0372629i	$-0.988136\pi$
$797$	−10516.2	+	18214.6i	−0.467382	+	0.809530i	0.531923	+	0.846792i	$0.321469\pi$
$798$			77062.7i			3.41853i
$799$	−4931.20	−	2847.03i	−0.218340	−	0.126058i
$800$	2099.16	+	1211.95i	0.0927708	+	0.0535612i
$801$			33385.0i			1.47266i
$802$	−7889.19	+	13664.5i	−0.347353	+	0.601633i
$803$	−4572.05	−	7919.03i	−0.200927	−	0.348015i
$804$	8706.80	−	5026.87i	0.381922	−	0.220503i
$805$	−14614.9			−0.639883
$806$		0			0
$807$	−54599.7			−2.38166
$808$	−4583.43	+	2646.24i	−0.199560	+	0.115216i
$809$	21822.5	+	37797.6i	0.948376	+	1.64264i	0.748846	+	0.662745i	$0.230608\pi$
$809$	21822.5	+	37797.6i	0.948376	+	1.64264i	0.199531	+	0.979892i	$0.436058\pi$
$810$	−5353.55	+	9272.62i	−0.232228	+	0.402230i
$811$		−	28688.1i		−	1.24214i	−0.783756	−	0.621069i	$-0.786699\pi$
$811$		−	28688.1i		−	1.24214i	0.783756	−	0.621069i	$-0.213301\pi$
$812$	4888.62	+	2822.45i	0.211277	+	0.121981i
$813$	13861.6	+	8002.99i	0.597967	+	0.345236i
$814$		−	453.424i		−	0.0195239i
$815$	8218.39	−	14234.7i	0.353224	−	0.611802i
$816$	−2140.51	−	3707.47i	−0.0918295	−	0.159053i
$817$	−57932.2	+	33447.2i	−2.48077	+	1.43227i
$818$	−15463.1			−0.660946
$819$		0			0
$820$	7111.14			0.302843
$821$	−13893.0	+	8021.12i	−0.590583	+	0.340973i	−0.765328	−	0.643640i	$-0.777423\pi$
$821$	−13893.0	+	8021.12i	−0.590583	+	0.340973i	0.174745	+	0.984614i	$0.444090\pi$
$822$	−8455.76	−	14645.8i	−0.358794	−	0.621449i
$823$	−6069.43	+	10512.6i	−0.257068	+	0.445255i	−0.965455	−	0.260569i	$-0.916090\pi$
$823$	−6069.43	+	10512.6i	−0.257068	+	0.445255i	0.708387	+	0.705824i	$0.249423\pi$
$824$		−	2522.82i		−	0.106659i
$825$	5443.52	+	3142.82i	0.229720	+	0.132629i
$826$	20256.9	+	11695.3i	0.853301	+	0.492654i
$827$		−	17136.2i		−	0.720538i	−0.932848	−	0.360269i	$-0.882685\pi$
$827$		−	17136.2i		−	0.720538i	0.932848	−	0.360269i	$-0.117315\pi$
$828$	3557.39	−	6161.58i	0.149309	−	0.258611i
$829$	5473.64	+	9480.61i	0.229321	+	0.397196i	0.957607	−	0.288077i	$-0.0930161\pi$
$829$	5473.64	+	9480.61i	0.229321	+	0.397196i	−0.728286	+	0.685273i	$0.759683\pi$
$830$	−7688.67	+	4439.05i	−0.321539	+	0.185641i
$831$	−13997.9			−0.584336
$832$		0			0
$833$	14627.1			0.608400
$834$	1568.43	−	905.535i	0.0651203	−	0.0375972i
$835$	−14375.8	−	24899.7i	−0.595804	−	1.03196i
$836$	−2921.33	+	5059.90i	−0.120857	+	0.209330i
$837$			32700.9i			1.35043i
$838$	−4774.24	−	2756.41i	−0.196806	−	0.113626i
$839$	−11802.8	−	6814.35i	−0.485671	−	0.280402i	0.237106	−	0.971484i	$-0.423801\pi$
$839$	−11802.8	−	6814.35i	−0.485671	−	0.280402i	−0.722777	+	0.691081i	$0.757135\pi$
$840$		−	28385.9i		−	1.16596i
$841$	10981.4	−	19020.3i	0.450260	−	0.779873i
$842$	−11815.2	−	20464.5i	−0.483584	−	0.837591i
$843$	−34190.4	+	19739.8i	−1.39689	+	0.806495i
$844$	44.9010			0.00183123
$845$		0			0
$846$	18380.0			0.746946
$847$	−30788.5	+	17775.8i	−1.24900	+	0.721113i
$848$	3205.05	+	5551.30i	0.129790	+	0.224803i
$849$	−30956.1	+	53617.6i	−1.25137	+	2.16743i
$850$			4637.30i			0.187127i
$851$	744.592	+	429.890i	0.0299933	+	0.0173166i
$852$	−29122.9	−	16814.1i	−1.17105	−	0.676106i
$853$		−	6645.59i		−	0.266753i	−0.991065	−	0.133377i	$-0.957418\pi$
$853$		−	6645.59i		−	0.266753i	0.991065	−	0.133377i	$-0.0425820\pi$
$854$	17298.0	−	29961.0i	0.693122	−	1.20052i
$855$	53849.6	+	93270.2i	2.15394	+	3.73073i
$856$	−14696.9	+	8485.29i	−0.586836	+	0.338810i
$857$	−15552.6			−0.619914			−0.309957	−	0.950751i	$-0.600315\pi$
$857$	−15552.6			−0.619914			−0.309957	+	0.950751i	$0.600315\pi$
$858$		0			0
$859$	−48006.5			−1.90682			−0.953412	−	0.301672i	$-0.902455\pi$
$859$	−48006.5			−1.90682			−0.953412	+	0.301672i	$0.902455\pi$
$860$	21339.2	−	12320.2i	0.846119	−	0.488507i
$861$	−15711.3	−	27212.8i	−0.621883	−	1.07713i
$862$	10601.2	−	18361.9i	0.418885	−	0.725530i
$863$		−	3572.64i		−	0.140920i	−0.997515	−	0.0704601i	$-0.977553\pi$
$863$		−	3572.64i		−	0.140920i	0.997515	−	0.0704601i	$-0.0224468\pi$
$864$	5427.06	+	3133.31i	0.213695	+	0.123377i
$865$	37714.0	+	21774.2i	1.48245	+	0.855890i
$866$			18459.4i			0.724339i
$867$	−17377.0	+	30097.8i	−0.680685	+	1.17898i
$868$	−9568.32	−	16572.8i	−0.374159	−	0.648063i
$869$	8576.60	−	4951.70i	0.334800	−	0.193297i
$870$	12200.5			0.475443
$871$		0			0
$872$	−7075.45			−0.274777
$873$	11656.2	−	6729.68i	0.451891	−	0.260900i
$874$	−5539.42	−	9594.56i	−0.214387	−	0.371328i
$875$	9996.72	−	17314.8i	0.386230	−	0.668969i
$876$			33677.0i			1.29891i
$877$	2338.13	+	1349.92i	0.0900262	+	0.0519767i	0.544337	−	0.838866i	$-0.316781\pi$
$877$	2338.13	+	1349.92i	0.0900262	+	0.0519767i	−0.454311	+	0.890843i	$0.650115\pi$
$878$	12473.6	+	7201.66i	0.479459	+	0.276816i
$879$		−	60518.1i		−	2.32221i
$880$	1076.07	−	1863.81i	0.0412208	−	0.0713965i
$881$	1991.23	+	3448.91i	0.0761477	+	0.131892i	0.901585	−	0.432602i	$-0.142405\pi$
$881$	1991.23	+	3448.91i	0.0761477	+	0.131892i	−0.825437	+	0.564494i	$0.809071\pi$
$882$	−40889.4	+	23607.5i	−1.56102	+	0.901253i
$883$	−21896.7			−0.834523			−0.417261	−	0.908787i	$-0.637010\pi$
$883$	−21896.7			−0.834523			−0.417261	+	0.908787i	$0.637010\pi$
$884$		0			0
$885$	50555.0			1.92021
$886$	−6139.61	+	3544.70i	−0.232804	+	0.134409i
$887$	10609.8	+	18376.8i	0.401627	+	0.695638i	0.993922	−	0.110082i	$-0.0351115\pi$
$887$	10609.8	+	18376.8i	0.401627	+	0.695638i	−0.592295	+	0.805721i	$0.701778\pi$
$888$	−834.962	+	1446.20i	−0.0315535	+	0.0546522i
$889$		−	53656.7i		−	2.02428i
$890$	−16583.4	−	9574.43i	−0.624581	−	0.360602i
$891$	3106.52	+	1793.55i	0.116804	+	0.0674367i
$892$		−	10959.0i		−	0.411360i
$893$	14310.3	−	24786.1i	0.536254	−	0.928820i
$894$	−16760.2	−	29029.5i	−0.627007	−	1.08601i
$895$	28392.1	−	16392.2i	1.06038	−	0.612212i
$896$	−3667.25			−0.136735
$897$		0			0
$898$	36650.7			1.36197
$899$	7123.13	−	4112.54i	0.264260	−	0.152571i
$900$	−7484.41	−	12963.4i	−0.277201	−	0.480125i
$901$	−6131.74	+	10620.5i	−0.226724	+	0.392697i
$902$		−	2382.37i		−	0.0879428i
$903$	−94293.8	−	54440.6i	−3.47497	−	2.00628i
$904$	−915.940	−	528.818i	−0.0336988	−	0.0194560i
$905$		−	23661.5i		−	0.869101i
$906$	17790.2	−	30813.6i	0.652363	−	1.12993i
$907$	−21436.8	−	37129.7i	−0.784783	−	1.35928i	−0.929129	−	0.369756i	$-0.879441\pi$
$907$	−21436.8	−	37129.7i	−0.784783	−	1.35928i	0.144346	−	0.989527i	$-0.453892\pi$
$908$	15691.5	−	9059.50i	0.573503	−	0.331112i
$909$	32683.8			1.19258
$910$		0			0
$911$	28943.9			1.05264			0.526319	−	0.850287i	$-0.323572\pi$
$911$	28943.9			1.05264			0.526319	+	0.850287i	$0.323572\pi$
$912$	18635.2	−	10759.0i	0.676616	−	0.390644i
$913$	1487.17	+	2575.86i	0.0539083	+	0.0933718i
$914$	5383.84	−	9325.08i	0.194838	−	0.337468i
$915$		−	74773.6i		−	2.70157i
$916$	−3006.46	−	1735.78i	−0.108446	−	0.0626112i
$917$	−45907.5	−	26504.7i	−1.65321	−	0.954484i
$918$			11989.0i			0.431042i
$919$	−1367.51	+	2368.60i	−0.0490860	+	0.0850194i	−0.889524	−	0.456888i	$-0.848964\pi$
$919$	−1367.51	+	2368.60i	−0.0490860	+	0.0850194i	0.840438	+	0.541907i	$0.182298\pi$
$920$	2040.44	+	3534.14i	0.0731210	+	0.126649i
$921$	66452.2	−	38366.2i	2.37749	−	1.37265i
$922$	−21242.3			−0.758760
$923$		0			0
$924$	−9509.87			−0.338584
$925$	1566.55	−	904.449i	0.0556842	−	0.0321493i
$926$	10407.3	+	18025.9i	0.369334	+	0.639706i
$927$	−7789.85	+	13492.4i	−0.276000	+	0.478047i
$928$		−	1576.21i		−	0.0557562i
$929$	13069.9	+	7545.90i	0.461581	+	0.266494i	0.712709	−	0.701460i	$-0.247468\pi$
$929$	13069.9	+	7545.90i	0.461581	+	0.266494i	−0.251128	+	0.967954i	$0.580801\pi$
$930$	−35819.4	−	20680.3i	−1.26297	−	0.729178i
$931$			73521.3i			2.58814i
$932$	−1070.28	+	1853.77i	−0.0376159	+	0.0651527i
$933$	9603.45	+	16633.7i	0.336980	+	0.583667i
$934$	27338.7	−	15784.0i	0.957763	−	0.552965i
$935$	4117.37			0.144013
$936$		0			0
$937$	−20974.5			−0.731278			−0.365639	−	0.930757i	$-0.619150\pi$
$937$	−20974.5			−0.731278			−0.365639	+	0.930757i	$0.619150\pi$
$938$	14269.3	−	8238.36i	0.496703	−	0.286772i
$939$	−22082.0	−	38247.2i	−0.767433	−	1.32923i
$940$	−5271.17	+	9129.94i	−0.182901	+	0.316793i
$941$			886.927i			0.0307258i	0.999882	+	0.0153629i	$0.00489036\pi$
$941$			886.927i			0.0307258i	−0.999882	+	0.0153629i	$0.995110\pi$
$942$	−9316.89	−	5379.11i	−0.322251	−	0.186052i
$943$	3912.23	+	2258.73i	0.135100	+	0.0780002i
$944$		−	6531.32i		−	0.225187i
$945$	−39747.4	+	68844.6i	−1.36824	+	2.36986i
$946$	−4127.52	−	7149.08i	−0.141858	−	0.245705i
$947$	37534.7	−	21670.7i	1.28798	−	0.743613i	0.309683	−	0.950840i	$-0.399777\pi$
$947$	37534.7	−	21670.7i	1.28798	−	0.743613i	0.978293	+	0.207226i	$0.0664437\pi$
$948$	−36473.5			−1.24958
$949$		0			0
$950$	−23308.9			−0.796041
$951$	−14306.4	+	8259.80i	−0.487820	+	0.281643i
$952$	−3508.00	−	6076.04i	−0.119428	−	0.206855i
$953$	8007.43	−	13869.3i	0.272178	−	0.471427i	−0.697241	−	0.716837i	$-0.745589\pi$
$953$	8007.43	−	13869.3i	0.272178	−	0.471427i	0.969419	+	0.245410i	$0.0789226\pi$
$954$		−	39585.5i		−	1.34343i
$955$	46936.4	+	27098.8i	1.59040	+	0.918215i
$956$	3972.39	+	2293.46i	0.134389	+	0.0775898i
$957$		−	4087.42i		−	0.138064i
$958$	−18263.7	+	31633.7i	−0.615943	+	1.06685i
$959$	−13857.8	−	24002.5i	−0.466624	−	0.808217i
$960$	−6864.25	+	3963.08i	−0.230774	+	0.133237i
$961$	1907.30			0.0640227
$962$		0			0
$963$	104802.			3.50695
$964$	11615.2	−	6706.06i	0.388072	−	0.224054i
$965$	6438.40	+	11151.6i	0.214777	+	0.372004i
$966$	9016.29	−	15616.7i	0.300305	−	0.520143i
$967$		−	7986.48i		−	0.265592i	−0.991143	−	0.132796i	$-0.957604\pi$
$967$		−	7986.48i		−	0.265592i	0.991143	−	0.132796i	$-0.0423956\pi$
$968$	8597.03	+	4963.49i	0.285453	+	0.164807i
$969$	35652.0	+	20583.7i	1.18195	+	0.682397i
$970$			7720.00i			0.255540i
$971$	−12622.7	+	21863.2i	−0.417180	+	0.722578i	−0.995655	−	0.0931229i	$-0.970315\pi$
$971$	−12622.7	+	21863.2i	−0.417180	+	0.722578i	0.578474	+	0.815701i	$0.303648\pi$
$972$	3969.44	+	6875.27i	0.130987	+	0.226877i
$973$	2570.45	−	1484.05i	0.0846914	−	0.0488966i
$974$	−10738.0			−0.353253
$975$		0			0
$976$	−9660.19			−0.316819
$977$	4530.83	−	2615.88i	0.148367	−	0.0856595i	−0.423979	−	0.905672i	$-0.639367\pi$
$977$	4530.83	−	2615.88i	0.148367	−	0.0856595i	0.572346	+	0.820013i	$0.306034\pi$
$978$	10140.3	+	17563.5i	0.331545	+	0.574252i
$979$	−3207.63	+	5555.78i	−0.104715	+	0.181372i
$980$		−	27081.5i		−	0.882740i
$981$	37840.5	+	21847.2i	1.23155	+	0.711038i
$982$	−2583.07	−	1491.33i	−0.0839399	−	0.0484627i
$983$			22720.8i			0.737212i	0.929586	+	0.368606i	$0.120165\pi$
$983$			22720.8i			0.737212i	−0.929586	+	0.368606i	$0.879835\pi$
$984$	−4387.05	+	7598.59i	−0.142128	+	0.246173i
$985$	−9476.38	−	16413.6i	−0.306541	−	0.530944i
$986$	2611.53	−	1507.77i	0.0843490	−	0.0486989i
$987$	46584.5			1.50233
$988$		0			0
$989$	15653.2			0.503279
$990$	−11509.9	+	6645.27i	−0.369505	+	0.213334i
$991$	−9502.55	−	16458.9i	−0.304600	−	0.527582i	0.672572	−	0.740031i	$-0.265189\pi$
$991$	−9502.55	−	16458.9i	−0.304600	−	0.527582i	−0.977172	+	0.212449i	$0.931856\pi$
$992$	−2671.75	+	4627.60i	−0.0855121	+	0.148111i
$993$			22284.0i			0.712148i
$994$	−47728.5	−	27556.0i	−1.52299	−	0.879300i
$995$	−14044.4	−	8108.51i	−0.447473	−	0.258349i
$996$		−	10954.3i		−	0.348494i
$997$	−24621.6	+	42645.9i	−0.782121	+	1.35467i	0.148583	+	0.988900i	$0.452529\pi$
$997$	−24621.6	+	42645.9i	−0.782121	+	1.35467i	−0.930704	+	0.365773i	$0.880805\pi$
$998$	10067.4	+	17437.2i	0.319316	+	0.553072i
$999$	4050.07	−	2338.31i	0.128267	−	0.0740549i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.4.e.h.23.6		12
13.2	odd	12		338.4.a.k.1.1	yes	3
13.3	even	3		338.4.b.f.337.4		6
13.4	even	6	inner	338.4.e.h.147.6		12
13.5	odd	4		338.4.c.k.315.3		6
13.6	odd	12		338.4.c.k.191.3		6
13.7	odd	12		338.4.c.l.191.3		6
13.8	odd	4		338.4.c.l.315.3		6
13.9	even	3	inner	338.4.e.h.147.3		12
13.10	even	6		338.4.b.f.337.1		6
13.11	odd	12		338.4.a.j.1.1	✓	3
13.12	even	2	inner	338.4.e.h.23.3		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
338.4.a.j.1.1	✓	3	13.11	odd	12
338.4.a.k.1.1	yes	3	13.2	odd	12
338.4.b.f.337.1		6	13.10	even	6
338.4.b.f.337.4		6	13.3	even	3
338.4.c.k.191.3		6	13.6	odd	12
338.4.c.k.315.3		6	13.5	odd	4
338.4.c.l.191.3		6	13.7	odd	12
338.4.c.l.315.3		6	13.8	odd	4
338.4.e.h.23.3		12	13.12	even	2	inner
338.4.e.h.23.6		12	1.1	even	1	trivial
338.4.e.h.147.3		12	13.9	even	3	inner
338.4.e.h.147.6		12	13.4	even	6	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:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	338.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(4.37047 + 7.56988i) q^{3} +(2.00000 - 3.46410i) q^{4} -14.1685i q^{5} +(15.1398 + 8.74094i) q^{6} +(24.8120 + 14.3252i) q^{7} -8.00000i q^{8} +(-24.7020 + 42.7851i) q^{9} +(-14.1685 - 24.5406i) q^{10} +(-8.22160 + 4.74674i) q^{11} +34.9638 q^{12} +57.3008 q^{14} +(107.254 - 61.9231i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(15.3052 - 26.5094i) q^{17} +98.8080i q^{18} +(133.247 + 76.9300i) q^{19} +(-49.0812 - 28.3370i) q^{20} +250.431i q^{21} +(-9.49349 + 16.4432i) q^{22} +(-18.0015 - 31.1795i) q^{23} +(60.5590 - 34.9638i) q^{24} -75.7470 q^{25} -195.832 q^{27} +(99.2479 - 57.3008i) q^{28} +(24.6283 + 42.6575i) q^{29} +(123.846 - 214.508i) q^{30} -166.984i q^{31} +(-27.7128 - 16.0000i) q^{32} +(-71.8645 - 41.4910i) q^{33} -61.2209i q^{34} +(202.967 - 351.549i) q^{35} +(98.8080 + 171.141i) q^{36} +(-20.6814 + 11.9404i) q^{37} +307.720 q^{38} -113.348 q^{40} +(-108.664 + 62.7371i) q^{41} +(250.431 + 433.760i) q^{42} +(-217.387 + 376.526i) q^{43} +37.9739i q^{44} +(606.202 + 349.991i) q^{45} +(-62.3591 - 36.0030i) q^{46} -186.017i q^{47} +(69.9275 - 121.118i) q^{48} +(238.923 + 413.826i) q^{49} +(-131.198 + 75.7470i) q^{50} +267.564 q^{51} -400.631 q^{53} +(-339.191 + 195.832i) q^{54} +(67.2543 + 116.488i) q^{55} +(114.602 - 198.496i) q^{56} +1344.88i q^{57} +(85.3151 + 49.2567i) q^{58} +(353.518 + 204.104i) q^{59} -495.385i q^{60} +(301.881 - 522.873i) q^{61} +(-166.984 - 289.225i) q^{62} +(-1225.81 + 707.722i) q^{63} -64.0000 q^{64} -165.964 q^{66} +(249.024 - 143.774i) q^{67} +(-61.2209 - 106.038i) q^{68} +(157.350 - 272.538i) q^{69} -811.868i q^{70} +(-832.946 - 480.901i) q^{71} +(342.281 + 197.616i) q^{72} +963.198i q^{73} +(-23.8808 + 41.3627i) q^{74} +(-331.050 - 573.396i) q^{75} +(532.986 - 307.720i) q^{76} -271.992 q^{77} -1043.18 q^{79} +(-196.325 + 113.348i) q^{80} +(-188.924 - 327.226i) q^{81} +(-125.474 + 217.328i) q^{82} -313.304i q^{83} +(867.520 + 500.863i) q^{84} +(-375.599 - 216.852i) q^{85} +869.549i q^{86} +(-215.275 + 372.867i) q^{87} +(37.9739 + 65.7728i) q^{88} +(585.220 - 337.877i) q^{89} +1399.96 q^{90} -144.012 q^{92} +(1264.05 - 729.799i) q^{93} +(-186.017 - 322.191i) q^{94} +(1089.98 - 1887.91i) q^{95} -279.710i q^{96} +(-235.935 - 136.217i) q^{97} +(827.653 + 477.845i) q^{98} -469.016i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 24 q^{3} + 24 q^{4} - 18 q^{9} - 48 q^{10} + 192 q^{12} + 216 q^{14} - 96 q^{16} - 180 q^{17} + 328 q^{22} + 38 q^{23} + 244 q^{25} - 276 q^{27} + 202 q^{29} + 360 q^{30} + 916 q^{35} + 72 q^{36}+ \cdots + 3658 q^{95}+O(q^{100}) \) 12 * q + 24 * q^3 + 24 * q^4 - 18 * q^9 - 48 * q^10 + 192 * q^12 + 216 * q^14 - 96 * q^16 - 180 * q^17 + 328 * q^22 + 38 * q^23 + 244 * q^25 - 276 * q^27 + 202 * q^29 + 360 * q^30 + 916 * q^35 + 72 * q^36 + 1040 * q^38 - 384 * q^40 + 936 * q^42 - 2410 * q^43 + 384 * q^48 - 368 * q^49 + 828 * q^51 - 4380 * q^53 + 1052 * q^55 + 432 * q^56 + 2216 * q^61 - 2076 * q^62 - 768 * q^64 + 1168 * q^66 + 720 * q^68 - 628 * q^69 + 336 * q^74 - 1010 * q^75 - 1920 * q^77 - 7844 * q^79 - 1830 * q^81 - 748 * q^82 - 3272 * q^87 - 1312 * q^88 + 5160 * q^90 + 304 * q^92 - 2144 * q^94 + 3658 * q^95

Introduction

L-functions

Modular forms

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