LMFDB - Embedded newform 338.4.c.o.191.6

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			191.6
Root			$-2.42606 + 4.20205i$ of defining polynomial
Character	$\chi$	$=$	338.191
Dual form			338.4.c.o.315.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 + 1.73205i) q^{2} +(4.07401 - 7.05638i) q^{3} +(-2.00000 - 3.46410i) q^{4} -12.6646 q^{5} +(8.14801 + 14.1128i) q^{6} +(14.3853 + 24.9160i) q^{7} +8.00000 q^{8} +(-19.6950 - 34.1128i) q^{9} +(12.6646 - 21.9357i) q^{10} +(26.4203 - 45.7613i) q^{11} -32.5920 q^{12} -57.5411 q^{14} +(-51.5957 + 89.3664i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-35.5161 - 61.5158i) q^{17} +78.7801 q^{18} +(-32.8843 - 56.9572i) q^{19} +(25.3292 + 43.8715i) q^{20} +234.423 q^{21} +(52.8406 + 91.5226i) q^{22} +(22.2154 - 38.4783i) q^{23} +(32.5920 - 56.4511i) q^{24} +35.3924 q^{25} -100.954 q^{27} +(57.5411 - 99.6641i) q^{28} +(39.2189 - 67.9292i) q^{29} +(-103.191 - 178.733i) q^{30} -195.024 q^{31} +(-16.0000 - 27.7128i) q^{32} +(-215.273 - 372.863i) q^{33} +142.065 q^{34} +(-182.184 - 315.552i) q^{35} +(-78.7801 + 136.451i) q^{36} +(-116.595 + 201.948i) q^{37} +131.537 q^{38} -101.317 q^{40} +(-60.2286 + 104.319i) q^{41} +(-234.423 + 406.032i) q^{42} +(-202.551 - 350.829i) q^{43} -211.362 q^{44} +(249.430 + 432.025i) q^{45} +(44.4309 + 76.9566i) q^{46} -400.779 q^{47} +(65.1841 + 112.902i) q^{48} +(-242.372 + 419.800i) q^{49} +(-35.3924 + 61.3014i) q^{50} -578.772 q^{51} +116.566 q^{53} +(100.954 - 174.858i) q^{54} +(-334.603 + 579.549i) q^{55} +(115.082 + 199.328i) q^{56} -535.883 q^{57} +(78.4379 + 135.858i) q^{58} +(-390.718 - 676.744i) q^{59} +412.765 q^{60} +(-26.2781 - 45.5149i) q^{61} +(195.024 - 337.792i) q^{62} +(566.637 - 981.444i) q^{63} +64.0000 q^{64} +861.091 q^{66} +(402.652 - 697.414i) q^{67} +(-142.065 + 246.063i) q^{68} +(-181.012 - 313.521i) q^{69} +728.735 q^{70} +(200.786 + 347.771i) q^{71} +(-157.560 - 272.902i) q^{72} +323.057 q^{73} +(-233.189 - 403.895i) q^{74} +(144.189 - 249.742i) q^{75} +(-131.537 + 227.829i) q^{76} +1520.25 q^{77} -794.845 q^{79} +(101.317 - 175.486i) q^{80} +(120.477 - 208.673i) q^{81} +(-120.457 - 208.638i) q^{82} +444.820 q^{83} +(-468.845 - 812.064i) q^{84} +(449.798 + 779.073i) q^{85} +810.205 q^{86} +(-319.556 - 553.488i) q^{87} +(211.362 - 366.090i) q^{88} +(-39.5736 + 68.5435i) q^{89} -997.720 q^{90} -177.724 q^{92} +(-794.529 + 1376.16i) q^{93} +(400.779 - 694.169i) q^{94} +(416.467 + 721.341i) q^{95} -260.736 q^{96} +(-1.94818 - 3.37434i) q^{97} +(-484.744 - 839.601i) q^{98} -2081.39 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 $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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
$3$	4.07401	−	7.05638i	0.784043	−	1.35800i	−0.145527	−	0.989354i	$-0.546488\pi$
$3$	4.07401	−	7.05638i	0.784043	−	1.35800i	0.929569	−	0.368647i	$-0.120179\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	−12.6646			−1.13276			−0.566379	−	0.824145i	$-0.691656\pi$
$5$	−12.6646			−1.13276			−0.566379	+	0.824145i	$0.691656\pi$
$6$	8.14801	+	14.1128i	0.554402	+	0.960252i
$7$	14.3853	+	24.9160i	0.776732	+	1.34534i	0.933816	+	0.357753i	$0.116457\pi$
$7$	14.3853	+	24.9160i	0.776732	+	1.34534i	−0.157085	+	0.987585i	$0.550210\pi$
$8$	8.00000			0.353553
$9$	−19.6950	−	34.1128i	−0.729446	−	1.26344i
$10$	12.6646	−	21.9357i	0.400490	−	0.693669i
$11$	26.4203	−	45.7613i	0.724183	−	1.25432i	−0.235126	−	0.971965i	$-0.575550\pi$
$11$	26.4203	−	45.7613i	0.724183	−	1.25432i	0.959309	−	0.282357i	$-0.0911164\pi$
$12$	−32.5920			−0.784043
$13$		0			0
$13$		0			0
$14$	−57.5411			−1.09846
$15$	−51.5957	+	89.3664i	−0.888130	+	1.53829i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−35.5161	−	61.5158i	−0.506702	−	0.877633i	−0.999970	−	0.00775579i	$-0.997531\pi$
$17$	−35.5161	−	61.5158i	−0.506702	−	0.877633i	0.493268	−	0.869877i	$-0.335802\pi$
$18$	78.7801			1.03159
$19$	−32.8843	−	56.9572i	−0.397062	−	0.687731i	0.596300	−	0.802761i	$-0.296637\pi$
$19$	−32.8843	−	56.9572i	−0.397062	−	0.687731i	−0.993362	+	0.115030i	$0.963303\pi$
$20$	25.3292	+	43.8715i	0.283189	+	0.490498i
$21$	234.423			2.43596
$22$	52.8406	+	91.5226i	0.512075	+	0.886940i
$23$	22.2154	−	38.4783i	0.201402	−	0.348838i	−0.747579	−	0.664173i	$-0.768784\pi$
$23$	22.2154	−	38.4783i	0.201402	−	0.348838i	0.948980	+	0.315335i	$0.102117\pi$
$24$	32.5920	−	56.4511i	0.277201	−	0.480126i
$25$	35.3924			0.283139
$26$		0			0
$27$	−100.954			−0.719581
$28$	57.5411	−	99.6641i	0.388366	−	0.672669i
$29$	39.2189	−	67.9292i	0.251130	−	0.434970i	−0.712707	−	0.701462i	$-0.752531\pi$
$29$	39.2189	−	67.9292i	0.251130	−	0.434970i	0.963837	+	0.266492i	$0.0858645\pi$
$30$	−103.191	−	178.733i	−0.628003	−	1.08773i
$31$	−195.024			−1.12991			−0.564957	−	0.825120i	$-0.691107\pi$
$31$	−195.024			−1.12991			−0.564957	+	0.825120i	$0.691107\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	−215.273	−	372.863i	−1.13558	−	1.96688i
$34$	142.065			0.716584
$35$	−182.184	−	315.552i	−0.879848	−	1.52394i
$36$	−78.7801	+	136.451i	−0.364723	+	0.631719i
$37$	−116.595	+	201.948i	−0.518055	+	0.897297i	0.481725	+	0.876322i	$0.340010\pi$
$37$	−116.595	+	201.948i	−0.518055	+	0.897297i	−0.999780	+	0.0209750i	$0.993323\pi$
$38$	131.537			0.561530
$39$		0			0
$40$	−101.317			−0.400490
$41$	−60.2286	+	104.319i	−0.229418	+	0.397363i	−0.957636	−	0.287983i	$-0.907015\pi$
$41$	−60.2286	+	104.319i	−0.229418	+	0.397363i	0.728218	+	0.685345i	$0.240349\pi$
$42$	−234.423	+	406.032i	−0.861243	+	1.49172i
$43$	−202.551	−	350.829i	−0.718344	−	1.24421i	−0.961656	−	0.274260i	$-0.911567\pi$
$43$	−202.551	−	350.829i	−0.718344	−	1.24421i	0.243312	−	0.969948i	$-0.421766\pi$
$44$	−211.362			−0.724183
$45$	249.430	+	432.025i	0.826285	+	1.43117i
$46$	44.4309	+	76.9566i	0.142413	+	0.246666i
$47$	−400.779			−1.24382			−0.621911	−	0.783088i	$-0.713643\pi$
$47$	−400.779			−1.24382			−0.621911	+	0.783088i	$0.713643\pi$
$48$	65.1841	+	112.902i	0.196011	+	0.339500i
$49$	−242.372	+	419.800i	−0.706624	+	1.22391i
$50$	−35.3924	+	61.3014i	−0.100105	+	0.173386i
$51$	−578.772			−1.58910
$52$		0			0
$53$	116.566			0.302105			0.151052	−	0.988526i	$-0.451734\pi$
$53$	116.566			0.302105			0.151052	+	0.988526i	$0.451734\pi$
$54$	100.954	−	174.858i	0.254410	−	0.440652i
$55$	−334.603	+	579.549i	−0.820324	+	1.42084i
$56$	115.082	+	199.328i	0.274616	+	0.475649i
$57$	−535.883			−1.24525
$58$	78.4379	+	135.858i	0.177576	+	0.307570i
$59$	−390.718	−	676.744i	−0.862155	−	1.49330i	−0.869844	−	0.493326i	$-0.835781\pi$
$59$	−390.718	−	676.744i	−0.862155	−	1.49330i	0.00768919	−	0.999970i	$-0.497552\pi$
$60$	412.765			0.888130
$61$	−26.2781	−	45.5149i	−0.0551567	−	0.0955343i	0.837129	−	0.547006i	$-0.184233\pi$
$61$	−26.2781	−	45.5149i	−0.0551567	−	0.0955343i	−0.892285	+	0.451472i	$0.850899\pi$
$62$	195.024	−	337.792i	0.399485	−	0.691929i
$63$	566.637	−	981.444i	1.13317	−	1.96270i
$64$	64.0000			0.125000
$65$		0			0
$66$	861.091			1.60595
$67$	402.652	−	697.414i	0.734206	−	1.27168i	−0.220864	−	0.975305i	$-0.570888\pi$
$67$	402.652	−	697.414i	0.734206	−	1.27168i	0.955071	−	0.296378i	$-0.0957789\pi$
$68$	−142.065	+	246.063i	−0.253351	+	0.438817i
$69$	−181.012	−	313.521i	−0.315815	−	0.547008i
$70$	728.735			1.24429
$71$	200.786	+	347.771i	0.335618	+	0.581307i	0.983603	−	0.180345i	$-0.0577216\pi$
$71$	200.786	+	347.771i	0.335618	+	0.581307i	−0.647985	+	0.761653i	$0.724388\pi$
$72$	−157.560	−	272.902i	−0.257898	−	0.446692i
$73$	323.057			0.517958			0.258979	−	0.965883i	$-0.416614\pi$
$73$	323.057			0.517958			0.258979	+	0.965883i	$0.416614\pi$
$74$	−233.189	−	403.895i	−0.366320	−	0.634485i
$75$	144.189	−	249.742i	0.221993	−	0.384503i
$76$	−131.537	+	227.829i	−0.198531	+	0.343865i
$77$	1520.25			2.24998
$78$		0			0
$79$	−794.845			−1.13199			−0.565994	−	0.824409i	$-0.691507\pi$
$79$	−794.845			−1.13199			−0.565994	+	0.824409i	$0.691507\pi$
$80$	101.317	−	175.486i	0.141595	−	0.245249i
$81$	120.477	−	208.673i	0.165264	−	0.286245i
$82$	−120.457	−	208.638i	−0.162223	−	0.280978i
$83$	444.820			0.588258			0.294129	−	0.955766i	$-0.404971\pi$
$83$	444.820			0.588258			0.294129	+	0.955766i	$0.404971\pi$
$84$	−468.845	−	812.064i	−0.608991	−	1.05480i
$85$	449.798	+	779.073i	0.573970	+	0.994145i
$86$	810.205			1.01589
$87$	−319.556	−	553.488i	−0.393793	−	0.682070i
$88$	211.362	−	366.090i	0.256037	−	0.443470i
$89$	−39.5736	+	68.5435i	−0.0471325	+	0.0816359i	−0.888629	−	0.458626i	$-0.848342\pi$
$89$	−39.5736	+	68.5435i	−0.0471325	+	0.0816359i	0.841497	+	0.540262i	$0.181675\pi$
$90$	−997.720			−1.16854
$91$		0			0
$92$	−177.724			−0.201402
$93$	−794.529	+	1376.16i	−0.885901	+	1.53443i
$94$	400.779	−	694.169i	0.439757	−	0.761682i
$95$	416.467	+	721.341i	0.449774	+	0.779032i
$96$	−260.736			−0.277201
$97$	−1.94818	−	3.37434i	−0.00203925	−	0.00353209i	0.865004	−	0.501765i	$-0.167316\pi$
$97$	−1.94818	−	3.37434i	−0.00203925	−	0.00353209i	−0.867043	+	0.498233i	$0.833982\pi$
$98$	−484.744	−	839.601i	−0.499658	−	0.865434i
$99$	−2081.39			−2.11301
$100$	−70.7847	−	122.603i	−0.0707847	−	0.122603i
$101$	517.657	−	896.609i	0.509988	−	0.883326i	−0.489945	−	0.871754i	$-0.662983\pi$
$101$	517.657	−	896.609i	0.509988	−	0.883326i	0.999933	−	0.0115723i	$-0.00368367\pi$
$102$	578.772	−	1002.46i	0.561833	−	0.973123i
$103$	1248.51			1.19436			0.597181	−	0.802107i	$-0.296287\pi$
$103$	1248.51			1.19436			0.597181	+	0.802107i	$0.296287\pi$
$104$		0			0
$105$	−2968.87			−2.75935
$106$	−116.566	+	201.898i	−0.106810	+	0.185001i
$107$	581.006	−	1006.33i	0.524934	−	0.909212i	−0.474644	−	0.880178i	$-0.657423\pi$
$107$	581.006	−	1006.33i	0.524934	−	0.909212i	0.999578	−	0.0290348i	$-0.00924335\pi$
$108$	201.909	+	349.716i	0.179895	+	0.311588i
$109$	−1003.58			−0.881885			−0.440943	−	0.897535i	$-0.645356\pi$
$109$	−1003.58			−0.881885			−0.440943	+	0.897535i	$0.645356\pi$
$110$	−669.205	−	1159.10i	−0.580057	−	1.00469i
$111$	950.014	+	1645.47i	0.812354	+	1.40704i
$112$	−460.329			−0.388366
$113$	372.206	+	644.679i	0.309860	+	0.536693i	0.978332	−	0.207045i	$-0.0663845\pi$
$113$	372.206	+	644.679i	0.309860	+	0.536693i	−0.668472	+	0.743738i	$0.733051\pi$
$114$	535.883	−	928.176i	0.440263	−	0.762559i
$115$	−281.350	+	487.312i	−0.228139	+	0.395149i
$116$	−313.751			−0.251130
$117$		0			0
$118$	1562.87			1.21927
$119$	1021.82	−	1769.84i	0.787142	−	1.36337i
$120$	−412.765	+	714.931i	−0.314001	+	0.543866i
$121$	−730.563	−	1265.37i	−0.548883	−	0.950694i
$122$	105.112			0.0780034
$123$	490.743	+	849.992i	0.359746	+	0.623099i
$124$	390.048	+	675.583i	0.282479	+	0.489267i
$125$	1134.85			0.812030
$126$	1133.27	+	1962.89i	0.801270	+	1.38784i
$127$	−841.759	+	1457.97i	−0.588142	+	1.01869i	0.406334	+	0.913725i	$0.366807\pi$
$127$	−841.759	+	1457.97i	−0.588142	+	1.01869i	−0.994476	+	0.104967i	$0.966526\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	−3300.78			−2.25285
$130$		0			0
$131$	2177.87			1.45253			0.726266	−	0.687414i	$-0.241254\pi$
$131$	2177.87			1.45253			0.726266	+	0.687414i	$0.241254\pi$
$132$	−861.091	+	1491.45i	−0.567791	+	0.983442i
$133$	946.098	−	1638.69i	0.616821	−	1.06836i
$134$	805.305	+	1394.83i	0.519162	+	0.899215i
$135$	1278.55			0.815110
$136$	−284.129	−	492.126i	−0.179146	−	0.310290i
$137$	883.829	+	1530.84i	0.551172	+	0.954658i	0.998190	+	0.0601334i	$0.0191526\pi$
$137$	883.829	+	1530.84i	0.551172	+	0.954658i	−0.447018	+	0.894525i	$0.647514\pi$
$138$	724.047			0.446630
$139$	−502.768	−	870.819i	−0.306793	−	0.531381i	0.670866	−	0.741579i	$-0.265923\pi$
$139$	−502.768	−	870.819i	−0.306793	−	0.531381i	−0.977659	+	0.210198i	$0.932589\pi$
$140$	−728.735	+	1262.21i	−0.439924	+	0.761971i
$141$	−1632.78	+	2828.05i	−0.975209	+	1.68911i
$142$	−803.143			−0.474635
$143$		0			0
$144$	630.241			0.364723
$145$	−496.692	+	860.297i	−0.284469	+	0.492715i
$146$	−323.057	+	559.551i	−0.183126	+	0.317183i
$147$	1974.85	+	3420.54i	1.10805	+	1.91919i
$148$	932.757			0.518055
$149$	68.1369	+	118.017i	0.0374631	+	0.0648879i	0.884149	−	0.467205i	$-0.154739\pi$
$149$	68.1369	+	118.017i	0.0374631	+	0.0648879i	−0.846686	+	0.532093i	$0.821406\pi$
$150$	288.377	+	499.484i	0.156973	+	0.271885i
$151$	−804.394			−0.433514			−0.216757	−	0.976226i	$-0.569548\pi$
$151$	−804.394			−0.433514			−0.216757	+	0.976226i	$0.569548\pi$
$152$	−263.074	−	455.658i	−0.140383	−	0.243150i
$153$	−1398.98	+	2423.11i	−0.739223	+	1.28037i
$154$	−1520.25	+	2633.15i	−0.795490	+	1.37783i
$155$	2469.90			1.27992
$156$		0			0
$157$	3730.07			1.89613			0.948064	−	0.318079i	$-0.103038\pi$
$157$	3730.07			1.89613			0.948064	+	0.318079i	$0.103038\pi$
$158$	794.845	−	1376.71i	0.400218	−	0.693198i
$159$	474.890	−	822.534i	0.236863	−	0.410259i
$160$	202.634	+	350.972i	0.100123	+	0.173417i
$161$	1278.30			0.625740
$162$	240.954	+	417.345i	0.116859	+	0.202406i
$163$	−1311.63	−	2271.80i	−0.630273	−	1.09166i	−0.987496	−	0.157646i	$-0.949610\pi$
$163$	−1311.63	−	2271.80i	−0.630273	−	1.09166i	0.357223	−	0.934019i	$-0.383724\pi$
$164$	481.828			0.229418
$165$	2726.35	+	4722.17i	1.28634	+	2.22800i
$166$	−444.820	+	770.451i	−0.207980	+	0.360233i
$167$	639.001	−	1106.78i	0.296092	−	0.512847i	−0.679146	−	0.734003i	$-0.737650\pi$
$167$	639.001	−	1106.78i	0.296092	−	0.512847i	0.975238	+	0.221156i	$0.0709831\pi$
$168$	1875.38			0.861243
$169$		0			0
$170$	−1799.19			−0.811716
$171$	−1295.31	+	2243.55i	−0.579270	+	1.00332i
$172$	−810.205	+	1403.32i	−0.359172	+	0.622104i
$173$	−534.991	−	926.631i	−0.235113	−	0.407228i	0.724192	−	0.689598i	$-0.242213\pi$
$173$	−534.991	−	926.631i	−0.235113	−	0.407228i	−0.959306	+	0.282370i	$0.908879\pi$
$174$	1278.22			0.556908
$175$	509.129	+	881.836i	0.219923	+	0.380918i
$176$	422.725	+	732.181i	0.181046	+	0.313581i
$177$	−6367.15			−2.70387
$178$	−79.1472	−	137.087i	−0.0333277	−	0.0577253i
$179$	−368.774	+	638.736i	−0.153986	+	0.266712i	−0.932689	−	0.360681i	$-0.882544\pi$
$179$	−368.774	+	638.736i	−0.153986	+	0.266712i	0.778703	+	0.627392i	$0.215878\pi$
$180$	997.720	−	1728.10i	0.413142	−	0.715584i
$181$	−1457.02			−0.598338			−0.299169	−	0.954200i	$-0.596709\pi$
$181$	−1457.02			−0.598338			−0.299169	+	0.954200i	$0.596709\pi$
$182$		0			0
$183$	−428.228			−0.172981
$184$	177.724	−	307.826i	0.0712063	−	0.123333i
$185$	1476.62	−	2557.59i	0.586830	−	1.01642i
$186$	−1589.06	−	2752.33i	−0.626427	−	1.08500i
$187$	−3753.39			−1.46778
$188$	801.558	+	1388.34i	0.310955	+	0.538591i
$189$	−1452.26	−	2515.38i	−0.558921	−	0.968080i
$190$	−1665.87			−0.636077
$191$	−287.715	−	498.337i	−0.108997	−	0.188788i	0.806367	−	0.591415i	$-0.201430\pi$
$191$	−287.715	−	498.337i	−0.108997	−	0.188788i	−0.915364	+	0.402627i	$0.868097\pi$
$192$	260.736	−	451.609i	0.0980053	−	0.169750i
$193$	−1219.36	+	2112.00i	−0.454775	+	0.787694i	−0.998675	−	0.0514564i	$-0.983614\pi$
$193$	−1219.36	+	2112.00i	−0.454775	+	0.787694i	0.543900	+	0.839150i	$0.316947\pi$
$194$	7.79271			0.00288394
$195$		0			0
$196$	1938.98			0.706624
$197$	−1911.76	+	3311.27i	−0.691408	+	1.19755i	0.279969	+	0.960009i	$0.409676\pi$
$197$	−1911.76	+	3311.27i	−0.691408	+	1.19755i	−0.971377	+	0.237544i	$0.923658\pi$
$198$	2081.39	−	3605.08i	0.747062	−	1.29395i
$199$	1078.71	+	1868.37i	0.384258	+	0.665555i	0.991666	−	0.128835i	$-0.0411238\pi$
$199$	1078.71	+	1868.37i	0.384258	+	0.665555i	−0.607408	+	0.794390i	$0.707790\pi$
$200$	283.139			0.100105
$201$	−3280.82	−	5682.54i	−1.15130	−	1.99411i
$202$	1035.31	+	1793.22i	0.360616	+	0.624606i
$203$	2256.70			0.780243
$204$	1157.54	+	2004.92i	0.397276	+	0.688102i
$205$	762.771	−	1321.16i	0.259874	−	0.450116i
$206$	−1248.51	+	2162.48i	−0.422271	+	0.731394i
$207$	−1750.14			−0.587647
$208$		0			0
$209$	−3475.25			−1.15018
$210$	2968.87	−	5142.24i	0.975579	−	1.68975i
$211$	−1681.93	+	2913.19i	−0.548762	+	0.950484i	0.449598	+	0.893231i	$0.351567\pi$
$211$	−1681.93	+	2913.19i	−0.548762	+	0.950484i	−0.998360	+	0.0572525i	$0.981766\pi$
$212$	−233.132	−	403.796i	−0.0755262	−	0.130815i
$213$	3272.01			1.05255
$214$	1162.01	+	2012.66i	0.371184	+	0.642910i
$215$	2565.23	+	4443.11i	0.813709	+	1.40939i
$216$	−807.635			−0.254410
$217$	−2805.47	−	4859.22i	−0.877640	−	1.52012i
$218$	1003.58	−	1738.25i	0.311794	−	0.540042i
$219$	1316.13	−	2279.61i	0.406101	−	0.703388i
$220$	2676.82			0.820324
$221$		0			0
$222$	−3800.06			−1.14884
$223$	1646.95	−	2852.61i	0.494566	−	0.856613i	−0.505415	−	0.862877i	$-0.668660\pi$
$223$	1646.95	−	2852.61i	0.494566	−	0.856613i	0.999980	+	0.00626360i	$0.00199378\pi$
$224$	460.329	−	797.313i	0.137308	−	0.237824i
$225$	−697.054	−	1207.33i	−0.206534	−	0.357728i
$226$	−1488.82			−0.438208
$227$	−271.743	−	470.673i	−0.0794547	−	0.137620i	0.823560	−	0.567229i	$-0.191985\pi$
$227$	−271.743	−	470.673i	−0.0794547	−	0.137620i	−0.903015	+	0.429609i	$0.858651\pi$
$228$	1071.77	+	1856.35i	0.311313	+	0.539210i
$229$	3071.66			0.886379			0.443189	−	0.896428i	$-0.353847\pi$
$229$	3071.66			0.886379			0.443189	+	0.896428i	$0.353847\pi$
$230$	−562.700	−	974.625i	−0.161319	−	0.279412i
$231$	6193.51	−	10727.5i	1.76408	−	3.05548i
$232$	313.751	−	543.433i	0.0887879	−	0.153785i
$233$	3383.06			0.951208			0.475604	−	0.879660i	$-0.342230\pi$
$233$	3383.06			0.951208			0.475604	+	0.879660i	$0.342230\pi$
$234$		0			0
$235$	5075.71			1.40895
$236$	−1562.87	+	2706.97i	−0.431078	+	0.746648i
$237$	−3238.20	+	5608.73i	−0.887527	+	1.53724i
$238$	2043.64	+	3539.68i	0.556594	+	0.964049i
$239$	698.550			0.189060			0.0945302	−	0.995522i	$-0.469865\pi$
$239$	698.550			0.189060			0.0945302	+	0.995522i	$0.469865\pi$
$240$	−825.531	−	1429.86i	−0.222032	−	0.384572i
$241$	−1857.72	−	3217.67i	−0.496541	−	0.860034i	0.503451	−	0.864024i	$-0.332063\pi$
$241$	−1857.72	−	3217.67i	−0.496541	−	0.860034i	−0.999992	+	0.00398962i	$0.998730\pi$
$242$	2922.25			0.776238
$243$	−2344.53	−	4060.85i	−0.618938	−	1.07203i
$244$	−105.112	+	182.060i	−0.0275784	+	0.0477671i
$245$	3069.55	−	5316.61i	0.800433	−	1.38639i
$246$	−1962.97			−0.508758
$247$		0			0
$248$	−1560.19			−0.399485
$249$	1812.20	−	3138.82i	0.461219	−	0.798855i
$250$	−1134.85	+	1965.61i	−0.287096	+	0.497265i
$251$	1926.42	+	3336.65i	0.484440	+	0.839074i	0.999840	−	0.0178750i	$-0.00569010\pi$
$251$	1926.42	+	3336.65i	0.484440	+	0.839074i	−0.515400	+	0.856950i	$0.672357\pi$
$252$	−4533.09			−1.13317
$253$	−1173.88	−	2033.21i	−0.291704	−	0.505245i
$254$	−1683.52	−	2915.94i	−0.415879	−	0.720324i
$255$	7329.92			1.80007
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−2288.73	+	3964.19i	−0.555513	+	0.962177i	0.442350	+	0.896842i	$0.354145\pi$
$257$	−2288.73	+	3964.19i	−0.555513	+	0.962177i	−0.997863	+	0.0653345i	$0.979189\pi$
$258$	3300.78	−	5717.12i	0.796502	−	1.37958i
$259$	−6708.98			−1.60956
$260$		0			0
$261$	−3089.67			−0.732743
$262$	−2177.87	+	3772.19i	−0.513547	+	0.889490i
$263$	2411.71	−	4177.21i	0.565447	−	0.979383i	−0.431561	−	0.902084i	$-0.642037\pi$
$263$	2411.71	−	4177.21i	0.565447	−	0.979383i	0.997008	−	0.0772990i	$-0.0246296\pi$
$264$	−1722.18	−	2982.91i	−0.401489	−	0.695399i
$265$	−1476.26			−0.342212
$266$	1892.20	+	3277.38i	0.436158	+	0.755448i
$267$	322.446	+	558.493i	0.0739078	+	0.128012i
$268$	−3221.22			−0.734206
$269$	982.898	+	1702.43i	0.222782	+	0.385870i	0.955652	−	0.294499i	$-0.0951529\pi$
$269$	982.898	+	1702.43i	0.222782	+	0.385870i	−0.732870	+	0.680369i	$0.761820\pi$
$270$	−1278.55	+	2214.51i	−0.288185	+	0.499151i
$271$	2207.96	−	3824.29i	0.494922	−	0.857230i	−0.505061	−	0.863084i	$-0.668530\pi$
$271$	2207.96	−	3824.29i	0.494922	−	0.857230i	0.999983	+	0.00585389i	$0.00186336\pi$
$272$	1136.52			0.253351
$273$		0			0
$274$	−3535.32			−0.779475
$275$	935.076	−	1619.60i	0.205044	−	0.355147i
$276$	−724.047	+	1254.09i	−0.157908	+	0.273504i
$277$	−1806.11	−	3128.28i	−0.391765	−	0.678557i	0.600917	−	0.799311i	$-0.294802\pi$
$277$	−1806.11	−	3128.28i	−0.391765	−	0.678557i	−0.992682	+	0.120754i	$0.961469\pi$
$278$	2011.07			0.433871
$279$	3841.01	+	6652.82i	0.824212	+	1.42758i
$280$	−1457.47	−	2524.41i	−0.311073	−	0.538795i
$281$	4095.02			0.869353			0.434676	−	0.900587i	$-0.356863\pi$
$281$	4095.02			0.869353			0.434676	+	0.900587i	$0.356863\pi$
$282$	−3265.55	−	5656.10i	−0.689577	−	1.19438i
$283$	−3363.10	+	5825.05i	−0.706415	+	1.22355i	0.259764	+	0.965672i	$0.416355\pi$
$283$	−3363.10	+	5825.05i	−0.706415	+	1.22355i	−0.966179	+	0.257874i	$0.916978\pi$
$284$	803.143	−	1391.08i	0.167809	−	0.290654i
$285$	6786.75			1.41057
$286$		0			0
$287$	−3465.62			−0.712783
$288$	−630.241	+	1091.61i	−0.128949	+	0.223346i
$289$	−66.2919	+	114.821i	−0.0134932	+	0.0233709i
$290$	−993.385	−	1720.59i	−0.201150	−	0.348402i
$291$	−31.7475			−0.00639544
$292$	−646.114	−	1119.10i	−0.129490	−	0.224282i
$293$	−2251.72	−	3900.10i	−0.448966	−	0.777632i	0.549353	−	0.835590i	$-0.314874\pi$
$293$	−2251.72	−	3900.10i	−0.448966	−	0.777632i	−0.998319	+	0.0579584i	$0.981541\pi$
$294$	−7899.40			−1.56701
$295$	4948.29	+	8570.69i	0.976613	+	1.69154i
$296$	−932.757	+	1615.58i	−0.183160	+	0.317243i
$297$	−2667.24	+	4619.80i	−0.521109	+	0.902586i
$298$	−272.548			−0.0529808
$299$		0			0
$300$	−1153.51			−0.221993
$301$	5827.51	−	10093.5i	1.11592	−	1.93283i
$302$	804.394	−	1393.25i	0.153270	−	0.265472i
$303$	−4217.88	−	7305.58i	−0.799705	−	1.38513i
$304$	1052.30			0.198531
$305$	332.801	+	576.429i	0.0624792	+	0.108217i
$306$	−2797.97	−	4846.22i	−0.522709	−	0.905359i
$307$	−1934.75			−0.359681			−0.179841	−	0.983696i	$-0.557558\pi$
$307$	−1934.75			−0.359681			−0.179841	+	0.983696i	$0.557558\pi$
$308$	−3040.50	−	5266.31i	−0.562496	−	0.974272i
$309$	5086.43	−	8809.96i	0.936431	−	1.62195i
$310$	−2469.90	+	4278.00i	−0.452520	+	0.783787i
$311$	−2655.72			−0.484219			−0.242110	−	0.970249i	$-0.577839\pi$
$311$	−2655.72			−0.484219			−0.242110	+	0.970249i	$0.577839\pi$
$312$		0			0
$313$	6102.36			1.10200			0.550999	−	0.834506i	$-0.314247\pi$
$313$	6102.36			1.10200			0.550999	+	0.834506i	$0.314247\pi$
$314$	−3730.07	+	6460.67i	−0.670383	+	1.16114i
$315$	−7176.23	+	12429.6i	−1.28360	+	2.22327i
$316$	1589.69	+	2753.42i	0.282997	+	0.490165i
$317$	1382.99			0.245037			0.122518	−	0.992466i	$-0.460903\pi$
$317$	1382.99			0.245037			0.122518	+	0.992466i	$0.460903\pi$
$318$	949.781	+	1645.07i	0.167488	+	0.290097i
$319$	−2072.35	−	3589.42i	−0.363728	−	0.629996i
$320$	−810.535			−0.141595
$321$	−4734.04	−	8199.60i	−0.823141	−	1.42572i
$322$	−1278.30	+	2214.08i	−0.221233	+	0.383186i
$323$	−2335.85	+	4045.80i	−0.402384	+	0.696949i
$324$	−963.817			−0.165264
$325$		0			0
$326$	5246.50			0.891340
$327$	−4088.59	+	7081.64i	−0.691436	+	1.19760i
$328$	−481.828	+	834.551i	−0.0811114	+	0.140489i
$329$	−5765.31	−	9985.81i	−0.966115	−	1.67336i
$330$	−10905.4			−1.81916
$331$	5003.33	+	8666.02i	0.830839	+	1.43906i	0.897374	+	0.441271i	$0.145472\pi$
$331$	5003.33	+	8666.02i	0.830839	+	1.43906i	−0.0665347	+	0.997784i	$0.521194\pi$
$332$	−889.641	−	1540.90i	−0.147064	−	0.254723i
$333$	9185.34			1.51157
$334$	1278.00	+	2213.57i	0.209369	+	0.362637i
$335$	−5099.44	+	8832.48i	−0.831678	+	1.44051i
$336$	−1875.38	+	3248.26i	−0.304495	+	0.527401i
$337$	11057.1			1.78730			0.893649	−	0.448767i	$-0.148137\pi$
$337$	11057.1			1.78730			0.893649	+	0.448767i	$0.148137\pi$
$338$		0			0
$339$	6065.47			0.971773
$340$	1799.19	−	3116.29i	0.286985	−	0.497073i
$341$	−5152.59	+	8924.55i	−0.818266	+	1.41728i
$342$	−2590.63	−	4487.10i	−0.409606	−	0.709458i
$343$	−4078.05			−0.641964
$344$	−1620.41	−	2806.63i	−0.253973	−	0.439894i
$345$	2292.44	+	3970.63i	0.357742	+	0.619627i
$346$	2139.96			0.332500
$347$	4316.98	+	7477.22i	0.667860	+	1.15677i	0.978501	+	0.206240i	$0.0661228\pi$
$347$	4316.98	+	7477.22i	0.667860	+	1.15677i	−0.310642	+	0.950527i	$0.600544\pi$
$348$	−1278.22	+	2213.95i	−0.196897	+	0.341035i
$349$	−4684.53	+	8113.84i	−0.718502	+	1.24448i	0.243092	+	0.970003i	$0.421838\pi$
$349$	−4684.53	+	8113.84i	−0.718502	+	1.24448i	−0.961593	+	0.274478i	$0.911495\pi$
$350$	−2036.51			−0.311018
$351$		0			0
$352$	−1690.90			−0.256037
$353$	2508.93	−	4345.59i	0.378291	−	0.655220i	−0.612522	−	0.790453i	$-0.709845\pi$
$353$	2508.93	−	4345.59i	0.378291	−	0.655220i	0.990814	+	0.135233i	$0.0431784\pi$
$354$	6367.15	−	11028.2i	0.955961	−	1.65577i
$355$	−2542.87	−	4404.38i	−0.380174	−	0.658480i
$356$	316.589			0.0471325
$357$	−8325.79	−	14420.7i	−1.23431	−	2.13788i
$358$	−737.549	−	1277.47i	−0.108885	−	0.188594i
$359$	7268.33			1.06855			0.534273	−	0.845312i	$-0.320586\pi$
$359$	7268.33			1.06855			0.534273	+	0.845312i	$0.320586\pi$
$360$	1995.44	+	3456.20i	0.292136	+	0.505994i
$361$	1266.75	−	2194.07i	0.184684	−	0.319882i
$362$	1457.02	−	2523.63i	0.211545	−	0.366406i
$363$	−11905.3			−1.72139
$364$		0			0
$365$	−4091.39			−0.586721
$366$	428.228	−	741.712i	0.0611580	−	0.105929i
$367$	−5943.72	+	10294.8i	−0.845394	+	1.46427i	0.0398848	+	0.999204i	$0.487301\pi$
$367$	−5943.72	+	10294.8i	−0.845394	+	1.46427i	−0.885279	+	0.465061i	$0.846032\pi$
$368$	355.447	+	615.652i	0.0503504	+	0.0872095i
$369$	4744.81			0.669391
$370$	2953.25	+	5115.18i	0.414952	+	0.718718i
$371$	1676.83	+	2904.36i	0.234654	+	0.406433i
$372$	6356.23			0.885901
$373$	7117.28	+	12327.5i	0.987986	+	1.71124i	0.627830	+	0.778350i	$0.283943\pi$
$373$	7117.28	+	12327.5i	0.987986	+	1.71124i	0.360156	+	0.932892i	$0.382723\pi$
$374$	3753.39	−	6501.06i	0.518939	−	0.898828i
$375$	4623.37	−	8007.91i	0.636666	−	1.10274i
$376$	−3206.23			−0.439757
$377$		0			0
$378$	5809.03			0.790434
$379$	−3960.04	+	6859.00i	−0.536712	+	0.929612i	0.462366	+	0.886689i	$0.347000\pi$
$379$	−3960.04	+	6859.00i	−0.536712	+	0.929612i	−0.999078	+	0.0429233i	$0.986333\pi$
$380$	1665.87	−	2885.37i	0.224887	−	0.389516i
$381$	6858.66	+	11879.5i	0.922257	+	1.59740i
$382$	1150.86			0.154144
$383$	−5313.47	−	9203.20i	−0.708892	−	1.22784i	−0.965268	−	0.261260i	$-0.915862\pi$
$383$	−5313.47	−	9203.20i	−0.708892	−	1.22784i	0.256376	−	0.966577i	$-0.417471\pi$
$384$	521.473	+	903.217i	0.0693002	+	0.120032i
$385$	−19253.4			−2.54869
$386$	−2438.72	−	4223.99i	−0.321575	−	0.556983i
$387$	−7978.51	+	13819.2i	−1.04799	+	1.81516i
$388$	−7.79271	+	13.4974i	−0.00101963	+	0.00176604i
$389$	−10183.7			−1.32733			−0.663667	−	0.748028i	$-0.731001\pi$
$389$	−10183.7			−1.32733			−0.663667	+	0.748028i	$0.731001\pi$
$390$		0			0
$391$	−3156.03			−0.408202
$392$	−1938.98	+	3358.40i	−0.249829	+	0.432717i
$393$	8872.66	−	15367.9i	1.13885	−	1.97254i
$394$	−3823.52	−	6622.53i	−0.488899	−	0.846798i
$395$	10066.4			1.28227
$396$	4162.79	+	7210.16i	0.528252	+	0.914960i
$397$	−1826.03	−	3162.78i	−0.230846	−	0.399837i	0.727211	−	0.686414i	$-0.240816\pi$
$397$	−1826.03	−	3162.78i	−0.230846	−	0.399837i	−0.958057	+	0.286577i	$0.907483\pi$
$398$	−4314.82			−0.543424
$399$	−7708.82	−	13352.1i	−0.967227	−	1.67529i
$400$	−283.139	+	490.411i	−0.0353924	+	0.0613014i
$401$	4442.35	−	7694.37i	0.553217	−	0.958200i	−0.444823	−	0.895619i	$-0.646733\pi$
$401$	4442.35	−	7694.37i	0.553217	−	0.958200i	0.998040	−	0.0625817i	$-0.0199334\pi$
$402$	13123.3			1.62818
$403$		0			0
$404$	−4141.26			−0.509988
$405$	−1525.80	+	2642.76i	−0.187204	+	0.324246i
$406$	−2256.70	+	3908.72i	−0.275857	+	0.477799i
$407$	6160.93	+	10671.0i	0.750334	+	1.29962i
$408$	−4630.17			−0.561833
$409$	5733.99	+	9931.55i	0.693221	+	1.20069i	0.970777	+	0.239984i	$0.0771423\pi$
$409$	5733.99	+	9931.55i	0.693221	+	1.20069i	−0.277556	+	0.960709i	$0.589524\pi$
$410$	1525.54	+	2642.32i	0.183759	+	0.318280i
$411$	14402.9			1.72857
$412$	−2497.02	−	4324.96i	−0.298590	−	0.517174i
$413$	11241.2	−	19470.3i	1.33933	−	2.31978i
$414$	1750.14	−	3031.32i	0.207764	−	0.359859i
$415$	−5633.48			−0.666353
$416$		0			0
$417$	−8193.11			−0.962155
$418$	3475.25	−	6019.31i	0.406651	−	0.704340i
$419$	7957.04	−	13782.0i	0.927749	−	1.60691i	0.140669	−	0.990057i	$-0.455075\pi$
$419$	7957.04	−	13782.0i	0.927749	−	1.60691i	0.787080	−	0.616851i	$-0.211592\pi$
$420$	5937.74	+	10284.5i	0.689839	+	1.19484i
$421$	−3091.64			−0.357904			−0.178952	−	0.983858i	$-0.557271\pi$
$421$	−3091.64			−0.357904			−0.178952	+	0.983858i	$0.557271\pi$
$422$	−3363.86	−	5826.37i	−0.388033	−	0.672093i
$423$	7893.35	+	13671.7i	0.907300	+	1.57149i
$424$	932.528			0.106810
$425$	−1257.00	−	2177.19i	−0.143467	−	0.248492i
$426$	−3272.01	+	5667.28i	−0.372134	+	0.644556i
$427$	756.034	−	1309.49i	0.0856840	−	0.148409i
$428$	−4648.05			−0.524934
$429$		0			0
$430$	−10260.9			−1.15076
$431$	−2498.35	+	4327.26i	−0.279214	+	0.483612i	−0.971190	−	0.238308i	$-0.923407\pi$
$431$	−2498.35	+	4327.26i	−0.279214	+	0.483612i	0.691976	+	0.721921i	$0.256740\pi$
$432$	807.635	−	1398.87i	0.0899476	−	0.155794i
$433$	920.918	+	1595.08i	0.102209	+	0.177031i	0.912594	−	0.408866i	$-0.134076\pi$
$433$	920.918	+	1595.08i	0.102209	+	0.177031i	−0.810386	+	0.585897i	$0.800742\pi$
$434$	11221.9			1.24117
$435$	4047.06	+	7009.71i	0.446072	+	0.772620i
$436$	2007.16	+	3476.50i	0.220471	+	0.381868i
$437$	−2922.16			−0.319876
$438$	2632.27	+	4559.23i	0.287157	+	0.497370i
$439$	−4981.61	+	8628.40i	−0.541593	+	0.938066i	0.457220	+	0.889354i	$0.348845\pi$
$439$	−4981.61	+	8628.40i	−0.541593	+	0.938066i	−0.998813	+	0.0487128i	$0.984488\pi$
$440$	−2676.82	+	4636.39i	−0.290028	+	0.502344i
$441$	19094.1			2.06177
$442$		0			0
$443$	−8480.02			−0.909476			−0.454738	−	0.890625i	$-0.650267\pi$
$443$	−8480.02			−0.909476			−0.454738	+	0.890625i	$0.650267\pi$
$444$	3800.06	−	6581.89i	0.406177	−	0.703519i
$445$	501.184	−	868.076i	0.0533897	−	0.0924736i
$446$	3293.91	+	5705.21i	0.349711	+	0.605717i
$447$	1110.36			0.117491
$448$	920.657	+	1594.63i	0.0970914	+	0.168167i
$449$	−1725.34	−	2988.37i	−0.181344	−	0.314098i	0.760994	−	0.648759i	$-0.224712\pi$
$449$	−1725.34	−	2988.37i	−0.181344	−	0.314098i	−0.942339	+	0.334661i	$0.891378\pi$
$450$	2788.21			0.292084
$451$	3182.51	+	5512.27i	0.332281	+	0.575527i
$452$	1488.82	−	2578.72i	0.154930	−	0.268347i
$453$	−3277.10	+	5676.11i	−0.339893	+	0.588713i
$454$	1086.97			0.112366
$455$		0			0
$456$	−4287.06			−0.440263
$457$	−3270.61	+	5664.87i	−0.334776	+	0.579850i	−0.983442	−	0.181224i	$-0.941994\pi$
$457$	−3270.61	+	5664.87i	−0.334776	+	0.579850i	0.648666	+	0.761074i	$0.275327\pi$
$458$	−3071.66	+	5320.27i	−0.313382	+	0.542794i
$459$	3585.51	+	6210.29i	0.364613	+	0.631528i
$460$	2250.80			0.228139
$461$	−7306.92	−	12656.0i	−0.738215	−	1.27863i	−0.953298	−	0.302030i	$-0.902336\pi$
$461$	−7306.92	−	12656.0i	−0.738215	−	1.27863i	0.215083	−	0.976596i	$-0.430998\pi$
$462$	12387.0	+	21455.0i	1.24740	+	2.16055i
$463$	−3680.01			−0.369383			−0.184692	−	0.982797i	$-0.559129\pi$
$463$	−3680.01			−0.369383			−0.184692	+	0.982797i	$0.559129\pi$
$464$	627.503	+	1086.87i	0.0627825	+	0.108743i
$465$	10062.4	−	17428.6i	1.00351	−	1.73813i
$466$	−3383.06	+	5859.63i	−0.336303	+	0.582494i
$467$	457.544			0.0453375			0.0226687	−	0.999743i	$-0.492784\pi$
$467$	457.544			0.0453375			0.0226687	+	0.999743i	$0.492784\pi$
$468$		0			0
$469$	23169.1			2.28112
$470$	−5075.71	+	8791.39i	−0.498138	+	0.862801i
$471$	15196.3	−	26320.8i	1.48665	−	2.57495i
$472$	−3125.74	−	5413.95i	−0.304818	−	0.527960i
$473$	−21405.9			−2.08085
$474$	−6476.40	−	11217.5i	−0.627576	−	1.08699i
$475$	−1163.85	−	2015.85i	−0.112424	−	0.194723i
$476$	−8174.55			−0.787142
$477$	−2295.77	−	3976.39i	−0.220369	−	0.381691i
$478$	−698.550	+	1209.92i	−0.0668429	+	0.115775i
$479$	4885.47	−	8461.88i	0.466018	−	0.807167i	−0.533229	−	0.845971i	$-0.679021\pi$
$479$	4885.47	−	8461.88i	0.466018	−	0.807167i	0.999247	+	0.0388039i	$0.0123548\pi$
$480$	3302.12			0.314001
$481$		0			0
$482$	7430.89			0.702215
$483$	5207.80	−	9020.18i	0.490607	−	0.849756i
$484$	−2922.25	+	5061.49i	−0.274442	+	0.475347i
$485$	24.6729	+	42.7347i	0.00230998	+	0.00400100i
$486$	9378.13			0.875310
$487$	−10125.1	−	17537.2i	−0.942118	−	1.63180i	−0.761421	−	0.648258i	$-0.775498\pi$
$487$	−10125.1	−	17537.2i	−0.942118	−	1.63180i	−0.180698	−	0.983539i	$-0.557836\pi$
$488$	−210.225	−	364.120i	−0.0195009	−	0.0337765i
$489$	−21374.3			−1.97664
$490$	6139.09	+	10633.2i	0.565992	+	0.980326i
$491$	8639.72	−	14964.4i	0.794104	−	1.37543i	−0.129303	−	0.991605i	$-0.541274\pi$
$491$	8639.72	−	14964.4i	0.794104	−	1.37543i	0.923407	−	0.383823i	$-0.125393\pi$
$492$	1962.97	−	3399.97i	0.179873	−	0.311549i
$493$	−5571.62			−0.508992
$494$		0			0
$495$	26360.0			2.39353
$496$	1560.19	−	2702.33i	0.141239	−	0.244634i
$497$	−5776.71	+	10005.6i	−0.521370	+	0.903039i
$498$	3624.40	+	6277.65i	0.326131	+	0.564876i
$499$	16994.7			1.52462			0.762310	−	0.647212i	$-0.224065\pi$
$499$	16994.7			1.52462			0.762310	+	0.647212i	$0.224065\pi$
$500$	−2269.69	−	3931.22i	−0.203007	−	0.351619i
$501$	−5206.59	−	9018.08i	−0.464298	−	0.804188i
$502$	−7705.67			−0.685101
$503$	−1550.97	−	2686.35i	−0.137483	−	0.238128i	0.789060	−	0.614316i	$-0.210568\pi$
$503$	−1550.97	−	2686.35i	−0.137483	−	0.238128i	−0.926543	+	0.376188i	$0.877235\pi$
$504$	4533.09	−	7851.55i	0.400635	−	0.693920i
$505$	−6555.93	+	11355.2i	−0.577693	+	1.00059i
$506$	4695.51			0.412531
$507$		0			0
$508$	6734.07			0.588142
$509$	9973.82	−	17275.2i	0.868530	−	1.50434i	0.00503052	−	0.999987i	$-0.498399\pi$
$509$	9973.82	−	17275.2i	0.868530	−	1.50434i	0.863499	−	0.504350i	$-0.168268\pi$
$510$	−7329.92	+	12695.8i	−0.636420	+	1.10231i
$511$	4647.26	+	8049.29i	0.402314	+	0.696829i
$512$	512.000			0.0441942
$513$	3319.81	+	5750.09i	0.285718	+	0.494878i
$514$	−4577.45	−	7928.38i	−0.392807	−	0.680362i
$515$	−15811.9			−1.35292
$516$	6601.56	+	11434.2i	0.563212	+	0.975512i
$517$	−10588.7	+	18340.2i	−0.900755	+	1.56015i
$518$	6708.98	−	11620.3i	0.569065	−	0.985649i
$519$	−8718.22			−0.737355
$520$		0			0
$521$	−18106.1			−1.52254			−0.761270	−	0.648436i	$-0.775424\pi$
$521$	−18106.1			−1.52254			−0.761270	+	0.648436i	$0.775424\pi$
$522$	3089.67	−	5351.47i	0.259064	−	0.448712i
$523$	427.606	−	740.635i	0.0357512	−	0.0619229i	−0.847596	−	0.530642i	$-0.821951\pi$
$523$	427.606	−	740.635i	0.0357512	−	0.0619229i	0.883347	+	0.468719i	$0.155284\pi$
$524$	−4355.74	−	7544.37i	−0.363133	−	0.628964i
$525$	8296.77			0.689716
$526$	4823.42	+	8354.42i	0.399831	+	0.692528i
$527$	6926.50	+	11997.1i	0.572530	+	0.991651i
$528$	6888.73			0.567791
$529$	5096.45	+	8827.31i	0.418875	+	0.725512i
$530$	1476.26	−	2556.96i	0.120990	−	0.209561i
$531$	−15390.4	+	26657.0i	−1.25779	+	2.17856i
$532$	−7568.79			−0.616821
$533$		0			0
$534$	−1289.78			−0.104521
$535$	−7358.21	+	12744.8i	−0.594623	+	1.02992i
$536$	3221.22	−	5579.32i	0.259581	−	0.449608i
$537$	3004.78	+	5204.43i	0.241463	+	0.418226i
$538$	−3931.59			−0.315061
$539$	12807.1	+	22182.5i	1.02345	+	1.77267i
$540$	−2557.10	−	4429.02i	−0.203778	−	0.352953i
$541$	−12326.5			−0.979592			−0.489796	−	0.871837i	$-0.662929\pi$
$541$	−12326.5			−0.979592			−0.489796	+	0.871837i	$0.662929\pi$
$542$	4415.91	+	7648.59i	0.349963	+	0.606153i
$543$	−5935.90	+	10281.3i	−0.469123	+	0.812544i
$544$	−1136.52	+	1968.50i	−0.0895730	+	0.155145i
$545$	12709.9			0.998962
$546$		0			0
$547$	7326.20			0.572661			0.286330	−	0.958131i	$-0.407564\pi$
$547$	7326.20			0.572661			0.286330	+	0.958131i	$0.407564\pi$
$548$	3535.32	−	6123.35i	0.275586	−	0.477329i
$549$	−1035.09	+	1792.84i	−0.0804677	+	0.139374i
$550$	1870.15	+	3239.20i	0.144988	+	0.251127i
$551$	−5158.75			−0.398857
$552$	−1448.09	−	2508.17i	−0.111658	−	0.193396i
$553$	−11434.1	−	19804.4i	−0.879251	−	1.52291i
$554$	7224.46			0.554039
$555$	−12031.6	−	20839.3i	−0.920200	−	1.59383i
$556$	−2011.07	+	3483.28i	−0.153396	+	0.265690i
$557$	−291.685	+	505.212i	−0.0221886	+	0.0384318i	−0.876907	−	0.480661i	$-0.840397\pi$
$557$	−291.685	+	505.212i	−0.0221886	+	0.0384318i	0.854718	+	0.519093i	$0.173730\pi$
$558$	−15364.0			−1.16561
$559$		0			0
$560$	5829.88			0.439924
$561$	−15291.3	+	26485.3i	−1.15080	+	1.99325i
$562$	−4095.02	+	7092.78i	−0.307363	+	0.532368i
$563$	−2719.97	−	4711.13i	−0.203611	−	0.352665i	0.746078	−	0.665858i	$-0.231935\pi$
$563$	−2719.97	−	4711.13i	−0.203611	−	0.352665i	−0.949689	+	0.313193i	$0.898601\pi$
$564$	13062.2			0.975209
$565$	−4713.84	−	8164.61i	−0.350996	−	0.607943i
$566$	−6726.19	−	11650.1i	−0.499511	−	0.865178i
$567$	6932.39			0.513462
$568$	1606.29	+	2782.17i	0.118659	+	0.205523i
$569$	−9071.62	+	15712.5i	−0.668369	+	1.15765i	0.309991	+	0.950739i	$0.399674\pi$
$569$	−9071.62	+	15712.5i	−0.668369	+	1.15765i	−0.978360	+	0.206910i	$0.933659\pi$
$570$	−6786.75	+	11755.0i	−0.498712	+	0.863794i
$571$	12916.3			0.946634			0.473317	−	0.880892i	$-0.343056\pi$
$571$	12916.3			0.946634			0.473317	+	0.880892i	$0.343056\pi$
$572$		0			0
$573$	−4688.61			−0.341832
$574$	3465.62	−	6002.62i	0.252007	−	0.436489i
$575$	786.257	−	1361.84i	0.0570247	−	0.0987696i
$576$	−1260.48	−	2183.22i	−0.0911807	−	0.157930i
$577$	1345.12			0.0970504			0.0485252	−	0.998822i	$-0.484548\pi$
$577$	1345.12			0.0970504			0.0485252	+	0.998822i	$0.484548\pi$
$578$	−132.584	−	229.642i	−0.00954111	−	0.0165257i
$579$	9935.37	+	17208.6i	0.713126	+	1.23517i
$580$	3973.54			0.284469
$581$	6398.86	+	11083.2i	0.456918	+	0.791405i
$582$	31.7475	−	54.9883i	0.00226113	−	0.00391639i
$583$	3079.71	−	5334.21i	0.218779	−	0.378937i
$584$	2584.45			0.183126
$585$		0			0
$586$	9006.89			0.634934
$587$	4968.49	−	8605.67i	0.349355	−	0.605100i	−0.636780	−	0.771045i	$-0.719734\pi$
$587$	4968.49	−	8605.67i	0.349355	−	0.605100i	0.986135	+	0.165945i	$0.0530674\pi$
$588$	7899.40	−	13682.2i	0.554023	−	0.959596i
$589$	6413.23	+	11108.0i	0.448646	+	0.777077i
$590$	−19793.2			−1.38114
$591$	15577.0	+	26980.2i	1.08419	+	1.87787i
$592$	−1865.51	−	3231.16i	−0.129514	−	0.224324i
$593$	−15740.8			−1.09005			−0.545024	−	0.838420i	$-0.683480\pi$
$593$	−15740.8			−1.09005			−0.545024	+	0.838420i	$0.683480\pi$
$594$	−5334.49	−	9239.61i	−0.368479	−	0.638225i
$595$	−12940.9	+	22414.4i	−0.891641	+	1.54437i
$596$	272.548	−	472.067i	0.0187315	−	0.0324440i
$597$	17578.6			1.20510
$598$		0			0
$599$	−6079.68			−0.414706			−0.207353	−	0.978266i	$-0.566485\pi$
$599$	−6079.68			−0.414706			−0.207353	+	0.978266i	$0.566485\pi$
$600$	1153.51	−	1997.94i	0.0784863	−	0.135942i
$601$	6882.14	−	11920.2i	0.467102	−	0.809045i	−0.532191	−	0.846624i	$-0.678631\pi$
$601$	6882.14	−	11920.2i	0.467102	−	0.809045i	0.999294	+	0.0375793i	$0.0119647\pi$
$602$	11655.0	+	20187.1i	0.789075	+	1.36672i
$603$	−31721.0			−2.14225
$604$	1608.79	+	2786.50i	0.108379	+	0.187717i
$605$	9252.30	+	16025.5i	0.621751	+	1.07690i
$606$	16871.5			1.13095
$607$	−8132.99	−	14086.8i	−0.543835	−	0.941950i	−0.998679	−	0.0513790i	$-0.983638\pi$
$607$	−8132.99	−	14086.8i	−0.543835	−	0.941950i	0.454844	−	0.890571i	$-0.349695\pi$
$608$	−1052.30	+	1822.63i	−0.0701913	+	0.121575i
$609$	9193.81	−	15924.1i	0.611743	−	1.05957i
$610$	−1331.21			−0.0883589
$611$		0			0
$612$	11191.9			0.739223
$613$	6247.17	−	10820.4i	0.411616	−	0.712940i	−0.583450	−	0.812149i	$-0.698298\pi$
$613$	6247.17	−	10820.4i	0.411616	−	0.712940i	0.995067	+	0.0992084i	$0.0316310\pi$
$614$	1934.75	−	3351.09i	0.127167	−	0.220259i
$615$	−6215.07	−	10764.8i	−0.407505	−	0.705820i
$616$	12162.0			0.795490
$617$	7233.90	+	12529.5i	0.472003	+	0.817534i	0.999487	−	0.0320316i	$-0.0101977\pi$
$617$	7233.90	+	12529.5i	0.472003	+	0.817534i	−0.527484	+	0.849565i	$0.676864\pi$
$618$	10172.9	+	17619.9i	0.662156	+	1.14689i
$619$	7989.85			0.518803			0.259401	−	0.965770i	$-0.416475\pi$
$619$	7989.85			0.518803			0.259401	+	0.965770i	$0.416475\pi$
$620$	−4939.81	−	8556.00i	−0.319980	−	0.554221i
$621$	−2242.75	+	3884.55i	−0.144925	+	0.251017i
$622$	2655.72	−	4599.85i	0.171197	−	0.296523i
$623$	−2277.11			−0.146437
$624$		0			0
$625$	−18796.4			−1.20297
$626$	−6102.36	+	10569.6i	−0.389615	+	0.674834i
$627$	−14158.2	+	24522.7i	−0.901792	+	1.56195i
$628$	−7460.14	−	12921.3i	−0.474032	−	0.821048i
$629$	16564.0			1.05000
$630$	−14352.5	−	24859.2i	−0.907644	−	1.57209i
$631$	−9484.25	−	16427.2i	−0.598355	−	1.03638i	−0.993064	−	0.117575i	$-0.962488\pi$
$631$	−9484.25	−	16427.2i	−0.598355	−	1.03638i	0.394709	−	0.918806i	$-0.370845\pi$
$632$	−6358.76			−0.400218
$633$	13704.4	+	23736.7i	0.860506	+	1.49044i
$634$	−1382.99	+	2395.42i	−0.0866336	+	0.150054i
$635$	10660.5	−	18464.6i	0.666222	−	1.15393i
$636$	−3799.12			−0.236863
$637$		0			0
$638$	8289.40			0.514390
$639$	7908.96	−	13698.7i	0.489630	−	0.848064i
$640$	810.535	−	1403.89i	0.0500613	−	0.0867087i
$641$	−12260.2	−	21235.3i	−0.755459	−	1.30849i	−0.945146	−	0.326649i	$-0.894081\pi$
$641$	−12260.2	−	21235.3i	−0.755459	−	1.30849i	0.189687	−	0.981845i	$-0.439253\pi$
$642$	18936.2			1.16410
$643$	−5887.83	−	10198.0i	−0.361110	−	0.625460i	0.627034	−	0.778992i	$-0.284269\pi$
$643$	−5887.83	−	10198.0i	−0.361110	−	0.625460i	−0.988144	+	0.153532i	$0.950935\pi$
$644$	−2556.60	−	4428.16i	−0.156435	−	0.270954i
$645$	41803.1			2.55193
$646$	−4671.69	−	8091.61i	−0.284528	−	0.492817i
$647$	10917.4	−	18909.5i	0.663382	−	1.14901i	−0.316340	−	0.948646i	$-0.602454\pi$
$647$	10917.4	−	18909.5i	0.663382	−	1.14901i	0.979721	−	0.200365i	$-0.0642128\pi$
$648$	963.817	−	1669.38i	0.0584295	−	0.101203i
$649$	−41291.5			−2.49743
$650$		0			0
$651$	−45718.1			−2.75243
$652$	−5246.50	+	9087.21i	−0.315136	+	0.545832i
$653$	−3663.85	+	6345.98i	−0.219567	+	0.380302i	−0.954676	−	0.297648i	$-0.903798\pi$
$653$	−3663.85	+	6345.98i	−0.219567	+	0.380302i	0.735108	+	0.677950i	$0.237131\pi$
$654$	−8177.18	−	14163.3i	−0.488919	−	0.846832i
$655$	−27581.9			−1.64537
$656$	−963.657	−	1669.10i	−0.0573544	−	0.0993407i
$657$	−6362.61	−	11020.4i	−0.377822	−	0.654407i
$658$	23061.2			1.36629
$659$	4184.17	+	7247.20i	0.247333	+	0.428393i	0.962785	−	0.270269i	$-0.0871126\pi$
$659$	4184.17	+	7247.20i	0.247333	+	0.428393i	−0.715452	+	0.698662i	$0.753779\pi$
$660$	10905.4	−	18888.7i	0.643169	−	1.11400i
$661$	−7591.06	+	13148.1i	−0.446684	+	0.773679i	−0.998168	−	0.0605065i	$-0.980728\pi$
$661$	−7591.06	+	13148.1i	−0.446684	+	0.773679i	0.551484	+	0.834185i	$0.314062\pi$
$662$	−20013.3			−1.17498
$663$		0			0
$664$	3558.56			0.207980
$665$	−11982.0	+	20753.4i	−0.698708	+	1.21020i
$666$	−9185.34	+	15909.5i	−0.534421	+	0.925645i
$667$	−1742.53	−	3018.15i	−0.101156	−	0.175207i
$668$	−5112.01			−0.296092
$669$	−13419.4	−	23243.1i	−0.775521	−	1.34324i
$670$	−10198.9	−	17665.0i	−0.588085	−	1.01859i
$671$	−2777.10			−0.159774
$672$	−3750.76	−	6496.51i	−0.215311	−	0.372929i
$673$	9952.15	−	17237.6i	0.570026	−	0.987314i	−0.426537	−	0.904470i	$-0.640267\pi$
$673$	9952.15	−	17237.6i	0.570026	−	0.987314i	0.996563	−	0.0828434i	$-0.0264001\pi$
$674$	−11057.1	+	19151.5i	−0.631905	+	1.09449i
$675$	−3573.01			−0.203741
$676$		0			0
$677$	−10760.9			−0.610896			−0.305448	−	0.952209i	$-0.598806\pi$
$677$	−10760.9			−0.610896			−0.305448	+	0.952209i	$0.598806\pi$
$678$	−6065.47	+	10505.7i	−0.343574	+	0.595087i
$679$	56.0501	−	97.0816i	0.00316790	−	0.00548697i
$680$	3598.38	+	6232.58i	0.202929	+	0.351483i
$681$	−4428.33			−0.249183
$682$	−10305.2	−	17849.1i	−0.578601	−	1.00217i
$683$	11589.1	+	20073.0i	0.649262	+	1.12456i	0.983299	+	0.181995i	$0.0582556\pi$
$683$	11589.1	+	20073.0i	0.649262	+	1.12456i	−0.334037	+	0.942560i	$0.608411\pi$
$684$	10362.5			0.579270
$685$	−11193.3	−	19387.4i	−0.624344	−	1.08140i
$686$	4078.05	−	7063.38i	0.226969	−	0.393121i
$687$	12513.9	−	21674.8i	0.694959	−	1.20370i
$688$	6481.64			0.359172
$689$		0			0
$690$	−9169.77			−0.505923
$691$	−8675.41	+	15026.3i	−0.477610	+	0.827244i	−0.999671	−	0.0256641i	$-0.991830\pi$
$691$	−8675.41	+	15026.3i	−0.477610	+	0.827244i	0.522061	+	0.852908i	$0.325163\pi$
$692$	−2139.96	+	3706.53i	−0.117557	+	0.203614i
$693$	−29941.4	−	51860.1i	−1.64124	−	2.84271i
$694$	−17267.9			−0.944497
$695$	6367.36	+	11028.6i	0.347522	+	0.601925i
$696$	−2556.45	−	4427.90i	−0.139227	−	0.241148i
$697$	8556.34			0.464985
$698$	−9369.06	−	16227.7i	−0.508057	−	0.879981i
$699$	13782.6	−	23872.2i	0.745788	−	1.29174i
$700$	2036.51	−	3527.35i	0.109961	−	0.190459i
$701$	50.2552			0.00270772			0.00135386	−	0.999999i	$-0.499569\pi$
$701$	50.2552			0.00270772			0.00135386	+	0.999999i	$0.499569\pi$
$702$		0			0
$703$	15336.5			0.822799
$704$	1690.90	−	2928.72i	0.0905229	−	0.156790i
$705$	20678.5	−	35816.1i	1.10468	−	1.91335i
$706$	5017.86	+	8691.19i	0.267492	+	0.463311i
$707$	29786.6			1.58450
$708$	12734.3	+	22056.5i	0.675966	+	1.17081i
$709$	12727.2	+	22044.2i	0.674163	+	1.16768i	0.976713	+	0.214550i	$0.0688286\pi$
$709$	12727.2	+	22044.2i	0.674163	+	1.16768i	−0.302550	+	0.953133i	$0.597838\pi$
$710$	10171.5			0.537647
$711$	15654.5	+	27114.4i	0.825724	+	1.43020i
$712$	−316.589	+	548.348i	−0.0166639	+	0.0288626i
$713$	−4332.55	+	7504.19i	−0.227567	+	0.394157i
$714$	33303.1			1.74557
$715$		0			0
$716$	2950.20			0.153986
$717$	2845.90	−	4929.24i	0.148231	−	0.256744i
$718$	−7268.33	+	12589.1i	−0.377788	+	0.654348i
$719$	−3742.99	−	6483.06i	−0.194145	−	0.336269i	0.752475	−	0.658621i	$-0.228860\pi$
$719$	−3742.99	−	6483.06i	−0.194145	−	0.336269i	−0.946620	+	0.322352i	$0.895527\pi$
$720$	−7981.76			−0.413142
$721$	17960.1	+	31107.9i	0.927698	+	1.60682i
$722$	2533.50	+	4388.14i	0.130591	+	0.226191i
$723$	−30273.5			−1.55724
$724$	2914.03	+	5047.26i	0.149585	+	0.259088i
$725$	1388.05	−	2404.17i	0.0711047	−	0.123157i
$726$	11905.3	−	20620.5i	0.608604	−	1.05413i
$727$	19443.6			0.991919			0.495959	−	0.868346i	$-0.334817\pi$
$727$	19443.6			0.991919			0.495959	+	0.868346i	$0.334817\pi$
$728$		0			0
$729$	−31700.8			−1.61057
$730$	4091.39	−	7086.49i	0.207437	−	0.359292i
$731$	−14387.7	+	24920.2i	−0.727972	+	1.26088i
$732$	856.456	+	1483.42i	0.0432452	+	0.0749030i
$733$	24222.3			1.22056			0.610280	−	0.792186i	$-0.291057\pi$
$733$	24222.3			1.22056			0.610280	+	0.792186i	$0.291057\pi$
$734$	−11887.4	−	20589.6i	−0.597784	−	1.03539i
$735$	−25010.7	−	43319.8i	−1.25515	−	2.17398i
$736$	−1421.79			−0.0712063
$737$	−21276.4	−	36851.8i	−1.06340	−	1.84186i
$738$	−4744.81	+	8218.26i	−0.236665	+	0.409916i
$739$	−1805.33	+	3126.92i	−0.0898647	+	0.155650i	−0.907454	−	0.420152i	$-0.861977\pi$
$739$	−1805.33	+	3126.92i	−0.0898647	+	0.155650i	0.817589	+	0.575802i	$0.195310\pi$
$740$	−11813.0			−0.586830
$741$		0			0
$742$	−6707.33			−0.331852
$743$	13089.8	−	22672.2i	0.646324	−	1.11947i	−0.337670	−	0.941264i	$-0.609639\pi$
$743$	13089.8	−	22672.2i	0.646324	−	1.11947i	0.983994	−	0.178201i	$-0.0570278\pi$
$744$	−6356.23	+	11009.3i	−0.313213	+	0.542502i
$745$	−862.928	−	1494.63i	−0.0424365	−	0.0735022i
$746$	−28469.1			−1.39722
$747$	−8760.75	−	15174.1i	−0.429102	−	0.743226i
$748$	7506.77	+	13002.1i	0.366945	+	0.635567i
$749$	33431.7			1.63093
$750$	9246.74	+	16015.8i	0.450191	+	0.779753i
$751$	−6379.01	+	11048.8i	−0.309951	+	0.536851i	−0.978351	−	0.206950i	$-0.933646\pi$
$751$	−6379.01	+	11048.8i	−0.309951	+	0.536851i	0.668400	+	0.743802i	$0.266979\pi$
$752$	3206.23	−	5553.36i	0.155478	−	0.269295i
$753$	31392.9			1.51929
$754$		0			0
$755$	10187.3			0.491066
$756$	−5809.03	+	10061.5i	−0.279461	+	0.484040i
$757$	−39.2371	+	67.9606i	−0.00188388	+	0.00326297i	−0.866966	−	0.498368i	$-0.833933\pi$
$757$	−39.2371	+	67.9606i	−0.00188388	+	0.00326297i	0.865082	+	0.501631i	$0.167266\pi$
$758$	−7920.09	−	13718.0i	−0.379513	−	0.657335i
$759$	−19129.5			−0.914832
$760$	3331.73	+	5770.73i	0.159019	+	0.275429i
$761$	8488.84	+	14703.1i	0.404363	+	0.700377i	0.994247	−	0.107111i	$-0.0341600\pi$
$761$	8488.84	+	14703.1i	0.404363	+	0.700377i	−0.589884	+	0.807488i	$0.700827\pi$
$762$	−27434.6			−1.30427
$763$	−14436.8	−	25005.2i	−0.684988	−	1.18643i
$764$	−1150.86	+	1993.35i	−0.0544983	+	0.0943938i
$765$	17717.6	−	30687.7i	0.837360	−	1.45035i
$766$	21253.9			1.00252
$767$		0			0
$768$	−2085.89			−0.0980053
$769$	11494.7	−	19909.4i	0.539024	−	0.933616i	−0.459933	−	0.887954i	$-0.652127\pi$
$769$	11494.7	−	19909.4i	0.539024	−	0.933616i	0.998957	−	0.0456629i	$-0.0145400\pi$
$770$	19253.4	−	33347.9i	0.901096	−	1.56074i
$771$	18648.6	+	32300.3i	0.871092	+	1.50878i
$772$	9754.90			0.454775
$773$	3016.71	+	5225.10i	0.140367	+	0.243123i	0.927635	−	0.373488i	$-0.121838\pi$
$773$	3016.71	+	5225.10i	0.140367	+	0.243123i	−0.787268	+	0.616611i	$0.788505\pi$
$774$	−15957.0	−	27638.4i	−0.741038	−	1.28351i
$775$	−6902.36			−0.319923
$776$	−15.5854	−	26.9947i	−0.000720984	−	0.00124878i
$777$	−27332.4	+	47341.1i	−1.26196	+	2.18578i
$778$	10183.7	−	17638.6i	0.469283	−	0.812823i
$779$	7922.29			0.364372
$780$		0			0
$781$	21219.3			0.972196
$782$	3156.03	−	5466.40i	0.144321	−	0.249972i
$783$	−3959.32	+	6857.75i	−0.180708	+	0.312996i
$784$	−3877.95	−	6716.81i	−0.176656	−	0.305977i
$785$	−47239.9			−2.14785
$786$	17745.3	+	30735.8i	0.805286	+	1.39480i
$787$	−18827.9	−	32610.9i	−0.852786	−	1.47707i	−0.878684	−	0.477404i	$-0.841578\pi$
$787$	−18827.9	−	32610.9i	−0.852786	−	1.47707i	0.0258980	−	0.999665i	$-0.491755\pi$
$788$	15294.1			0.691408
$789$	−19650.7	−	34035.9i	−0.886669	−	1.53576i
$790$	−10066.4	+	17435.5i	−0.453350	+	0.785225i
$791$	−10708.6	+	18547.8i	−0.481356	+	0.833733i
$792$	−16651.2			−0.747062
$793$		0			0
$794$	7304.13			0.326466
$795$	−6014.30	+	10417.1i	−0.268308	+	0.464724i
$796$	4314.82	−	7473.49i	0.192129	−	0.332778i
$797$	−12114.0	−	20982.1i	−0.538395	−	0.932527i	−0.998991	−	0.0449170i	$-0.985698\pi$
$797$	−12114.0	−	20982.1i	−0.538395	−	0.932527i	0.460596	−	0.887610i	$-0.347636\pi$
$798$	30835.3			1.36787
$799$	14234.1	+	24654.2i	0.630246	+	1.09162i
$800$	−566.278	−	980.822i	−0.0250262	−	0.0433466i
$801$	3117.61			0.137522
$802$	8884.69	+	15388.7i	0.391184	+	0.677550i
$803$	8535.25	−	14783.5i	0.375097	−	0.649686i
$804$	−13123.3	+	22730.2i	−0.575649	+	0.997053i
$805$	−16189.2			−0.708812
$806$		0			0
$807$	16017.3			0.698682
$808$	4141.26	−	7172.87i	0.180308	−	0.312303i
$809$	−19987.2	+	34618.9i	−0.868621	+	1.50450i	−0.00521394	+	0.999986i	$0.501660\pi$
$809$	−19987.2	+	34618.9i	−0.868621	+	1.50450i	−0.863407	+	0.504509i	$0.831674\pi$
$810$	−3051.59	−	5285.51i	−0.132373	−	0.229277i
$811$	13394.4			0.579953			0.289977	−	0.957034i	$-0.406352\pi$
$811$	13394.4			0.579953			0.289977	+	0.957034i	$0.406352\pi$
$812$	−4513.40	−	7817.44i	−0.195061	−	0.337855i
$813$	−17990.5	−	31160.4i	−0.776080	−	1.34421i
$814$	−24643.7			−1.06113
$815$	16611.2	+	28771.5i	0.713946	+	1.23659i
$816$	4630.17	−	8019.70i	0.198638	−	0.344051i
$817$	−13321.5	+	23073.5i	−0.570453	+	0.988054i
$818$	−22935.9			−0.980362
$819$		0			0
$820$	−6102.17			−0.259874
$821$	−15769.6	+	27313.8i	−0.670358	+	1.16109i	0.307445	+	0.951566i	$0.400526\pi$
$821$	−15769.6	+	27313.8i	−0.670358	+	1.16109i	−0.977803	+	0.209528i	$0.932807\pi$
$822$	−14402.9	+	24946.5i	−0.611142	+	1.05853i
$823$	13443.2	+	23284.2i	0.569379	+	0.986193i	0.996627	+	0.0820590i	$0.0261496\pi$
$823$	13443.2	+	23284.2i	0.569379	+	0.986193i	−0.427249	+	0.904134i	$0.640517\pi$
$824$	9988.07			0.422271
$825$	−7619.01	−	13196.5i	−0.321527	−	0.556901i
$826$	22482.3	+	38940.5i	0.947047	+	1.64033i
$827$	16064.3			0.675466			0.337733	−	0.941242i	$-0.390340\pi$
$827$	16064.3			0.675466			0.337733	+	0.941242i	$0.390340\pi$
$828$	3500.27	+	6062.65i	0.146912	+	0.254458i
$829$	−3927.65	+	6802.90i	−0.164551	+	0.285011i	−0.936496	−	0.350679i	$-0.885951\pi$
$829$	−3927.65	+	6802.90i	−0.164551	+	0.285011i	0.771945	+	0.635690i	$0.219284\pi$
$830$	5633.48	−	9757.47i	0.235591	−	0.408056i
$831$	−29432.5			−1.22864
$832$		0			0
$833$	34432.5			1.43219
$834$	8193.11	−	14190.9i	0.340173	−	0.589197i
$835$	−8092.70	+	14017.0i	−0.335401	+	0.580931i
$836$	6950.50	+	12038.6i	0.287545	+	0.498043i
$837$	19688.5			0.813065
$838$	15914.1	+	27564.0i	0.656017	+	1.13626i
$839$	−2603.26	−	4508.98i	−0.107121	−	0.185539i	0.807482	−	0.589892i	$-0.200830\pi$
$839$	−2603.26	−	4508.98i	−0.107121	−	0.185539i	−0.914603	+	0.404354i	$0.867497\pi$
$840$	−23751.0			−0.975579
$841$	9118.25	+	15793.3i	0.373867	+	0.647557i
$842$	3091.64	−	5354.88i	0.126538	−	0.219170i
$843$	16683.1	−	28896.0i	0.681610	−	1.18058i
$844$	13455.4			0.548762
$845$		0			0
$846$	−31573.4			−1.28312
$847$	21018.7	−	36405.5i	0.852670	−	1.47687i
$848$	−932.528	+	1615.19i	−0.0377631	+	0.0654077i
$849$	27402.5	+	47462.6i	1.10772	+	1.91862i
$850$	5028.00			0.202893
$851$	5180.40	+	8972.72i	0.208674	+	0.361435i
$852$	−6544.01	−	11334.6i	−0.263139	−	0.455770i
$853$	−11007.6			−0.441842			−0.220921	−	0.975292i	$-0.570906\pi$
$853$	−11007.6			−0.441842			−0.220921	+	0.975292i	$0.570906\pi$
$854$	1512.07	+	2618.98i	0.0605877	+	0.104941i
$855$	16404.6	−	28413.7i	0.656172	−	1.13652i
$856$	4648.05	−	8050.65i	0.185592	−	0.321455i
$857$	−15769.9			−0.628576			−0.314288	−	0.949328i	$-0.601766\pi$
$857$	−15769.9			−0.628576			−0.314288	+	0.949328i	$0.601766\pi$
$858$		0			0
$859$	13386.6			0.531716			0.265858	−	0.964012i	$-0.414345\pi$
$859$	13386.6			0.531716			0.265858	+	0.964012i	$0.414345\pi$
$860$	10260.9	−	17772.5i	0.406854	−	0.704693i
$861$	−14118.9	+	24454.7i	−0.558853	+	0.967961i
$862$	−4996.69	−	8654.52i	−0.197434	−	0.341965i
$863$	13233.1			0.521968			0.260984	−	0.965343i	$-0.415953\pi$
$863$	13233.1			0.521968			0.260984	+	0.965343i	$0.415953\pi$
$864$	1615.27	+	2797.73i	0.0636026	+	0.110163i
$865$	6775.45	+	11735.4i	0.266326	+	0.461291i
$866$	−3683.67			−0.144545
$867$	540.147	+	935.563i	0.0211584	+	0.0366475i
$868$	−11221.9	+	19436.9i	−0.438820	+	0.760059i
$869$	−21000.0	+	36373.1i	−0.819767	+	1.41988i
$870$	−16188.2			−0.630841
$871$		0			0
$872$	−8028.64			−0.311794
$873$	−76.7388	+	132.916i	−0.00297505	+	0.00515293i
$874$	2922.16	−	5061.32i	0.113093	−	0.195883i
$875$	16325.1	+	28275.8i	0.630729	+	1.09245i
$876$	−10529.1			−0.406101
$877$	−17860.3	−	30934.9i	−0.687684	−	1.19110i	−0.972585	−	0.232547i	$-0.925294\pi$
$877$	−17860.3	−	30934.9i	−0.687684	−	1.19110i	0.284901	−	0.958557i	$-0.408039\pi$
$878$	−9963.22	−	17256.8i	−0.382964	−	0.663313i
$879$	−36694.1			−1.40803
$880$	−5353.64	−	9272.78i	−0.205081	−	0.355211i
$881$	−263.170	+	455.824i	−0.0100641	+	0.0174315i	−0.871014	−	0.491259i	$-0.836537\pi$
$881$	−263.170	+	455.824i	−0.0100641	+	0.0174315i	0.860950	+	0.508690i	$0.169870\pi$
$882$	−19094.1	+	33071.9i	−0.728947	+	1.26257i
$883$	39626.2			1.51022			0.755112	−	0.655596i	$-0.227583\pi$
$883$	39626.2			1.51022			0.755112	+	0.655596i	$0.227583\pi$
$884$		0			0
$885$	80637.5			3.06282
$886$	8480.02	−	14687.8i	0.321548	−	0.556938i
$887$	18332.2	−	31752.3i	0.693951	−	1.20196i	−0.276582	−	0.960990i	$-0.589202\pi$
$887$	18332.2	−	31752.3i	0.693951	−	1.20196i	0.970533	−	0.240968i	$-0.0774650\pi$
$888$	7600.11	+	13163.8i	0.287211	+	0.497463i
$889$	−48435.7			−1.82731
$890$	1002.37	+	1736.15i	0.0377522	+	0.0653887i
$891$	−6366.08	−	11026.4i	−0.239362	−	0.414588i
$892$	−13175.6			−0.494566
$893$	13179.3	+	22827.3i	0.493874	+	0.855415i
$894$	−1110.36	+	1923.20i	−0.0415392	+	0.0719480i
$895$	4670.38	−	8089.34i	0.174429	−	0.302119i
$896$	−3682.63			−0.137308
$897$		0			0
$898$	6901.34			0.256460
$899$	−7648.64	+	13247.8i	−0.283756	+	0.491479i
$900$	−2788.21	+	4829.33i	−0.103267	+	0.178864i
$901$	−4139.97	−	7170.64i	−0.153077	−	0.265137i
$902$	−12730.0			−0.469916
$903$	−47482.6	−	82242.3i	−1.74986	−	3.03084i
$904$	2977.65	+	5157.43i	0.109552	+	0.189750i
$905$	18452.6			0.677772
$906$	−6554.21	−	11352.2i	−0.240341	−	0.416283i
$907$	17715.0	−	30683.3i	0.648530	−	1.12329i	−0.334944	−	0.942238i	$-0.608717\pi$
$907$	17715.0	−	30683.3i	0.648530	−	1.12329i	0.983474	−	0.181049i	$-0.0579493\pi$
$908$	−1086.97	+	1882.69i	−0.0397273	+	0.0688098i
$909$	−40781.1			−1.48804
$910$		0			0
$911$	−1970.18			−0.0716521			−0.0358261	−	0.999358i	$-0.511406\pi$
$911$	−1970.18			−0.0716521			−0.0358261	+	0.999358i	$0.511406\pi$
$912$	4287.06	−	7425.41i	0.155657	−	0.269605i
$913$	11752.3	−	20355.6i	0.426006	−	0.737865i
$914$	−6541.22	−	11329.7i	−0.236723	−	0.410016i
$915$	5423.34			0.195945
$916$	−6143.31	−	10640.5i	−0.221595	−	0.383813i
$917$	31329.3	+	54263.9i	1.12823	+	1.95415i
$918$	−14342.0			−0.515640
$919$	−3499.62	−	6061.52i	−0.125617	−	0.217575i	0.796357	−	0.604827i	$-0.206758\pi$
$919$	−3499.62	−	6061.52i	−0.125617	−	0.217575i	−0.921974	+	0.387252i	$0.873424\pi$
$920$	−2250.80	+	3898.50i	−0.0806594	+	0.139706i
$921$	−7882.19	+	13652.4i	−0.282005	+	0.488448i
$922$	29227.7			1.04399
$923$		0			0
$924$	−49548.1			−1.76408
$925$	−4126.56	+	7147.41i	−0.146681	+	0.254060i
$926$	3680.01	−	6373.96i	0.130597	−	0.226200i
$927$	−24589.4	−	42590.1i	−0.871222	−	1.50900i
$928$	−2510.01			−0.0887879
$929$	−11816.3	−	20466.4i	−0.417309	−	0.722801i	0.578358	−	0.815783i	$-0.303694\pi$
$929$	−11816.3	−	20466.4i	−0.417309	−	0.722801i	−0.995668	+	0.0929817i	$0.970360\pi$
$930$	20124.8	+	34857.2i	0.709590	+	1.22905i
$931$	31880.9			1.12229
$932$	−6766.11	−	11719.3i	−0.237802	−	0.411885i
$933$	−10819.4	+	18739.8i	−0.379649	+	0.657571i
$934$	−457.544	+	792.489i	−0.0160292	+	0.0277634i
$935$	47535.2			1.66264
$936$		0			0
$937$	−30872.4			−1.07637			−0.538183	−	0.842828i	$-0.680889\pi$
$937$	−30872.4			−1.07637			−0.538183	+	0.842828i	$0.680889\pi$
$938$	−23169.1	+	40130.0i	−0.806499	+	1.39690i
$939$	24861.0	−	43060.6i	0.864014	−	1.49652i
$940$	−10151.4	−	17582.8i	−0.352237	−	0.610092i
$941$	−6690.77			−0.231788			−0.115894	−	0.993262i	$-0.536973\pi$
$941$	−6690.77			−0.231788			−0.115894	+	0.993262i	$0.536973\pi$
$942$	30392.7	+	52641.6i	1.05122	+	1.82076i
$943$	2676.01	+	4634.98i	0.0924102	+	0.160059i
$944$	12503.0			0.431078
$945$	18392.3	+	31856.3i	0.633122	+	1.09660i
$946$	21405.9	−	37076.0i	0.735692	−	1.27426i
$947$	−10738.6	+	18599.7i	−0.368486	+	0.638237i	−0.989329	−	0.145698i	$-0.953457\pi$
$947$	−10738.6	+	18599.7i	−0.368486	+	0.638237i	0.620843	+	0.783935i	$0.286791\pi$
$948$	25905.6			0.887527
$949$		0			0
$950$	4655.41			0.158991
$951$	5634.33	−	9758.94i	0.192119	−	0.332761i
$952$	8174.55	−	14158.7i	0.278297	−	0.482024i
$953$	3925.25	+	6798.73i	0.133422	+	0.231094i	0.924994	−	0.379983i	$-0.124070\pi$
$953$	3925.25	+	6798.73i	0.133422	+	0.231094i	−0.791571	+	0.611077i	$0.790737\pi$
$954$	9183.08			0.311649
$955$	3643.80	+	6311.25i	0.123467	+	0.213851i
$956$	−1397.10	−	2419.85i	−0.0472651	−	0.0818656i
$957$	−33771.1			−1.14071
$958$	9770.94	+	16923.8i	0.329525	+	0.570753i
$959$	−25428.2	+	44043.0i	−0.856226	+	1.48303i
$960$	−3302.12	+	5719.45i	−0.111016	+	0.192286i
$961$	8243.39			0.276707
$962$		0			0
$963$	−45771.7			−1.53164
$964$	−7430.89	+	12870.7i	−0.248270	+	0.430017i
$965$	15442.7	−	26747.6i	0.515150	−	0.892266i
$966$	10415.6	+	18040.4i	0.346912	+	0.600869i
$967$	44143.2			1.46799			0.733997	−	0.679152i	$-0.237652\pi$
$967$	44143.2			1.46799			0.733997	+	0.679152i	$0.237652\pi$
$968$	−5844.51	−	10123.0i	−0.194060	−	0.336121i
$969$	19032.5	+	32965.2i	0.630972	+	1.09288i
$970$	−98.6916			−0.00326680
$971$	−14315.9	−	24795.8i	−0.473139	−	0.819500i	0.526389	−	0.850244i	$-0.323546\pi$
$971$	−14315.9	−	24795.8i	−0.473139	−	0.819500i	−0.999527	+	0.0307439i	$0.990212\pi$
$972$	−9378.13	+	16243.4i	−0.309469	+	0.536016i
$973$	14464.9	−	25053.9i	0.476591	−	0.825481i
$974$	40500.4			1.33236
$975$		0			0
$976$	840.898			0.0275784
$977$	4652.80	−	8058.88i	0.152360	−	0.263896i	−0.779734	−	0.626110i	$-0.784646\pi$
$977$	4652.80	−	8058.88i	0.152360	−	0.263896i	0.932095	+	0.362215i	$0.117979\pi$
$978$	21374.3	−	37021.3i	0.698849	−	1.21044i
$979$	2091.09	+	3621.88i	0.0682651	+	0.118239i
$980$	−24556.4			−0.800433
$981$	19765.5	+	34234.9i	0.643287	+	1.11421i
$982$	17279.4	+	29928.9i	0.561516	+	0.972574i
$983$	−28467.2			−0.923666			−0.461833	−	0.886967i	$-0.652808\pi$
$983$	−28467.2			−0.923666			−0.461833	+	0.886967i	$0.652808\pi$
$984$	3925.94	+	6799.93i	0.127190	+	0.220299i
$985$	24211.7	−	41935.9i	0.783197	−	1.35654i
$986$	5571.62	−	9650.33i	0.179956	−	0.311693i
$987$	−93951.6			−3.02990
$988$		0			0
$989$	−17999.1			−0.578703
$990$	−26360.0	+	45656.9i	−0.846240	+	1.46573i
$991$	−7749.06	+	13421.8i	−0.248393	+	0.430229i	−0.963080	−	0.269215i	$-0.913236\pi$
$991$	−7749.06	+	13421.8i	−0.248393	+	0.430229i	0.714687	+	0.699444i	$0.246569\pi$
$992$	3120.39	+	5404.67i	0.0998713	+	0.172982i
$993$	81534.3			2.60565
$994$	−11553.4	−	20011.1i	−0.368664	−	0.638545i
$995$	−13661.4	−	23662.2i	−0.435272	−	0.753912i
$996$	−14497.6			−0.461219
$997$	−630.399	−	1091.88i	−0.0200250	−	0.0346844i	0.855839	−	0.517242i	$-0.173041\pi$
$997$	−630.399	−	1091.88i	−0.0200250	−	0.0346844i	−0.875864	+	0.482558i	$0.839708\pi$
$998$	−16994.7	+	29435.6i	−0.539035	+	0.933636i
$999$	11770.7	−	20387.5i	0.372782	−	0.645678i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.4.c.o.191.6		12
13.2	odd	12		338.4.e.i.23.5		24
13.3	even	3	inner	338.4.c.o.315.6		12
13.4	even	6		338.4.a.n.1.1	✓	6
13.5	odd	4		338.4.e.i.147.12		24
13.6	odd	12		338.4.b.h.337.1		12
13.7	odd	12		338.4.b.h.337.7		12
13.8	odd	4		338.4.e.i.147.5		24
13.9	even	3		338.4.a.o.1.1	yes	6
13.10	even	6		338.4.c.p.315.6		12
13.11	odd	12		338.4.e.i.23.12		24
13.12	even	2		338.4.c.p.191.6		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
338.4.a.n.1.1	✓	6	13.4	even	6
338.4.a.o.1.1	yes	6	13.9	even	3
338.4.b.h.337.1		12	13.6	odd	12
338.4.b.h.337.7		12	13.7	odd	12
338.4.c.o.191.6		12	1.1	even	1	trivial
338.4.c.o.315.6		12	13.3	even	3	inner
338.4.c.p.191.6		12	13.12	even	2
338.4.c.p.315.6		12	13.10	even	6
338.4.e.i.23.5		24	13.2	odd	12
338.4.e.i.23.12		24	13.11	odd	12
338.4.e.i.147.5		24	13.8	odd	4
338.4.e.i.147.12		24	13.5	odd	4

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} +(4.07401 - 7.05638i) q^{3} +(-2.00000 - 3.46410i) q^{4} -12.6646 q^{5} +(8.14801 + 14.1128i) q^{6} +(14.3853 + 24.9160i) q^{7} +8.00000 q^{8} +(-19.6950 - 34.1128i) q^{9} +(12.6646 - 21.9357i) q^{10} +(26.4203 - 45.7613i) q^{11} -32.5920 q^{12} -57.5411 q^{14} +(-51.5957 + 89.3664i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-35.5161 - 61.5158i) q^{17} +78.7801 q^{18} +(-32.8843 - 56.9572i) q^{19} +(25.3292 + 43.8715i) q^{20} +234.423 q^{21} +(52.8406 + 91.5226i) q^{22} +(22.2154 - 38.4783i) q^{23} +(32.5920 - 56.4511i) q^{24} +35.3924 q^{25} -100.954 q^{27} +(57.5411 - 99.6641i) q^{28} +(39.2189 - 67.9292i) q^{29} +(-103.191 - 178.733i) q^{30} -195.024 q^{31} +(-16.0000 - 27.7128i) q^{32} +(-215.273 - 372.863i) q^{33} +142.065 q^{34} +(-182.184 - 315.552i) q^{35} +(-78.7801 + 136.451i) q^{36} +(-116.595 + 201.948i) q^{37} +131.537 q^{38} -101.317 q^{40} +(-60.2286 + 104.319i) q^{41} +(-234.423 + 406.032i) q^{42} +(-202.551 - 350.829i) q^{43} -211.362 q^{44} +(249.430 + 432.025i) q^{45} +(44.4309 + 76.9566i) q^{46} -400.779 q^{47} +(65.1841 + 112.902i) q^{48} +(-242.372 + 419.800i) q^{49} +(-35.3924 + 61.3014i) q^{50} -578.772 q^{51} +116.566 q^{53} +(100.954 - 174.858i) q^{54} +(-334.603 + 579.549i) q^{55} +(115.082 + 199.328i) q^{56} -535.883 q^{57} +(78.4379 + 135.858i) q^{58} +(-390.718 - 676.744i) q^{59} +412.765 q^{60} +(-26.2781 - 45.5149i) q^{61} +(195.024 - 337.792i) q^{62} +(566.637 - 981.444i) q^{63} +64.0000 q^{64} +861.091 q^{66} +(402.652 - 697.414i) q^{67} +(-142.065 + 246.063i) q^{68} +(-181.012 - 313.521i) q^{69} +728.735 q^{70} +(200.786 + 347.771i) q^{71} +(-157.560 - 272.902i) q^{72} +323.057 q^{73} +(-233.189 - 403.895i) q^{74} +(144.189 - 249.742i) q^{75} +(-131.537 + 227.829i) q^{76} +1520.25 q^{77} -794.845 q^{79} +(101.317 - 175.486i) q^{80} +(120.477 - 208.673i) q^{81} +(-120.457 - 208.638i) q^{82} +444.820 q^{83} +(-468.845 - 812.064i) q^{84} +(449.798 + 779.073i) q^{85} +810.205 q^{86} +(-319.556 - 553.488i) q^{87} +(211.362 - 366.090i) q^{88} +(-39.5736 + 68.5435i) q^{89} -997.720 q^{90} -177.724 q^{92} +(-794.529 + 1376.16i) q^{93} +(400.779 - 694.169i) q^{94} +(416.467 + 721.341i) q^{95} -260.736 q^{96} +(-1.94818 - 3.37434i) q^{97} +(-484.744 - 839.601i) q^{98} -2081.39 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

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