LMFDB - Embedded newform 338.4.c.l.191.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [338,4,Mod(191,338)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("338.191"); S:= CuspForms(chi, 4); N := Newforms(S);

sage: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")

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:traces = [6,6,12,-12,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$19.9426455819$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			191.3
Root			$0.222521 - 0.385418i$ of defining polynomial
Character	$\chi$	$=$	338.191
Dual form			338.4.c.l.315.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.00000 - 1.73205i) q^{2} +(4.37047 - 7.56988i) q^{3} +(-2.00000 - 3.46410i) q^{4} +14.1685 q^{5} +(-8.74094 - 15.1398i) q^{6} +(14.3252 + 24.8120i) q^{7} -8.00000 q^{8} +(-24.7020 - 42.7851i) q^{9} +(14.1685 - 24.5406i) q^{10} +(4.74674 - 8.22160i) q^{11} -34.9638 q^{12} +57.3008 q^{14} +(61.9231 - 107.254i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-15.3052 - 26.5094i) q^{17} -98.8080 q^{18} +(-76.9300 - 133.247i) q^{19} +(-28.3370 - 49.0812i) q^{20} +250.431 q^{21} +(-9.49349 - 16.4432i) q^{22} +(18.0015 - 31.1795i) q^{23} +(-34.9638 + 60.5590i) q^{24} +75.7470 q^{25} -195.832 q^{27} +(57.3008 - 99.2479i) q^{28} +(24.6283 - 42.6575i) q^{29} +(-123.846 - 214.508i) q^{30} +166.984 q^{31} +(16.0000 + 27.7128i) q^{32} +(-41.4910 - 71.8645i) q^{33} -61.2209 q^{34} +(202.967 + 351.549i) q^{35} +(-98.8080 + 171.141i) q^{36} +(11.9404 - 20.6814i) q^{37} -307.720 q^{38} -113.348 q^{40} +(-62.7371 + 108.664i) q^{41} +(250.431 - 433.760i) q^{42} +(217.387 + 376.526i) q^{43} -37.9739 q^{44} +(-349.991 - 606.202i) q^{45} +(-36.0030 - 62.3591i) q^{46} -186.017 q^{47} +(69.9275 + 121.118i) q^{48} +(-238.923 + 413.826i) q^{49} +(75.7470 - 131.198i) q^{50} -267.564 q^{51} -400.631 q^{53} +(-195.832 + 339.191i) q^{54} +(67.2543 - 116.488i) q^{55} +(-114.602 - 198.496i) q^{56} -1344.88 q^{57} +(-49.2567 - 85.3151i) q^{58} +(204.104 + 353.518i) q^{59} -495.385 q^{60} +(301.881 + 522.873i) q^{61} +(166.984 - 289.225i) q^{62} +(707.722 - 1225.81i) q^{63} +64.0000 q^{64} -165.964 q^{66} +(143.774 - 249.024i) q^{67} +(-61.2209 + 106.038i) q^{68} +(-157.350 - 272.538i) q^{69} +811.868 q^{70} +(480.901 + 832.946i) q^{71} +(197.616 + 342.281i) q^{72} +963.198 q^{73} +(-23.8808 - 41.3627i) q^{74} +(331.050 - 573.396i) q^{75} +(-307.720 + 532.986i) q^{76} +271.992 q^{77} -1043.18 q^{79} +(-113.348 + 196.325i) q^{80} +(-188.924 + 327.226i) q^{81} +(125.474 + 217.328i) q^{82} +313.304 q^{83} +(-500.863 - 867.520i) q^{84} +(-216.852 - 375.599i) q^{85} +869.549 q^{86} +(-215.275 - 372.867i) q^{87} +(-37.9739 + 65.7728i) q^{88} +(-337.877 + 585.220i) q^{89} -1399.96 q^{90} -144.012 q^{92} +(729.799 - 1264.05i) q^{93} +(-186.017 + 322.191i) q^{94} +(-1089.98 - 1887.91i) q^{95} +279.710 q^{96} +(136.217 + 235.935i) q^{97} +(477.845 + 827.653i) q^{98} -469.016 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 12 q^{3} - 12 q^{4} + 24 q^{5} - 24 q^{6} + 27 q^{7} - 48 q^{8} - 9 q^{9} + 24 q^{10} - 82 q^{11} - 96 q^{12} + 108 q^{14} + 90 q^{15} - 48 q^{16} + 90 q^{17} - 36 q^{18} - 130 q^{19} - 48 q^{20}+ \cdots - 4114 q^{99}+O(q^{100}) $ 6 * q + 6 * q^2 + 12 * q^3 - 12 * q^4 + 24 * q^5 - 24 * q^6 + 27 * q^7 - 48 * q^8 - 9 * q^9 + 24 * q^10 - 82 * q^11 - 96 * q^12 + 108 * q^14 + 90 * q^15 - 48 * q^16 + 90 * q^17 - 36 * q^18 - 130 * q^19 - 48 * q^20 + 468 * q^21 + 164 * q^22 - 19 * q^23 - 96 * q^24 - 122 * q^25 - 138 * q^27 + 108 * q^28 + 101 * q^29 - 180 * q^30 + 1038 * q^31 + 96 * q^32 + 146 * q^33 + 360 * q^34 + 458 * q^35 - 36 * q^36 - 84 * q^37 - 520 * q^38 - 192 * q^40 - 187 * q^41 + 468 * q^42 + 1205 * q^43 + 656 * q^44 - 645 * q^45 + 38 * q^46 - 1072 * q^47 + 192 * q^48 + 184 * q^49 - 122 * q^50 - 414 * q^51 - 2190 * q^53 - 138 * q^54 + 526 * q^55 - 216 * q^56 - 2818 * q^57 - 202 * q^58 + 1413 * q^59 - 720 * q^60 + 1108 * q^61 + 1038 * q^62 + 1404 * q^63 + 384 * q^64 + 584 * q^66 + 1605 * q^67 + 360 * q^68 + 314 * q^69 + 1832 * q^70 + 909 * q^71 + 72 * q^72 + 574 * q^73 + 168 * q^74 + 505 * q^75 - 520 * q^76 + 960 * q^77 - 3922 * q^79 - 192 * q^80 - 915 * q^81 + 374 * q^82 + 382 * q^83 - 936 * q^84 - 67 * q^85 + 4820 * q^86 - 1636 * q^87 + 656 * q^88 - 1091 * q^89 - 2580 * q^90 + 152 * q^92 + 1614 * q^93 - 1072 * q^94 - 1829 * q^95 + 768 * q^96 + 947 * q^97 - 368 * q^98 - 4114 * 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
$3$	4.37047	−	7.56988i	0.841097	−	1.45682i	−0.0478706	−	0.998854i	$-0.515244\pi$
$3$	4.37047	−	7.56988i	0.841097	−	1.45682i	0.888968	−	0.457970i	$-0.151423\pi$
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	14.1685			1.26727			0.633636	−	0.773632i	$-0.281562\pi$
$5$	14.1685			1.26727			0.633636	+	0.773632i	$0.281562\pi$
$6$	−8.74094	−	15.1398i	−0.594746	−	1.03013i
$7$	14.3252	+	24.8120i	0.773488	+	1.33972i	0.935640	+	0.352955i	$0.114823\pi$
$7$	14.3252	+	24.8120i	0.773488	+	1.33972i	−0.162152	+	0.986766i	$0.551844\pi$
$8$	−8.00000			−0.353553
$9$	−24.7020	−	42.7851i	−0.914889	−	1.58463i
$10$	14.1685	−	24.5406i	0.448048	−	0.776042i
$11$	4.74674	−	8.22160i	0.130109	−	0.225355i	−0.793610	−	0.608427i	$-0.791801\pi$
$11$	4.74674	−	8.22160i	0.130109	−	0.225355i	0.923718	+	0.383072i	$0.125134\pi$
$12$	−34.9638			−0.841097
$13$		0			0
$13$		0			0
$14$	57.3008			1.09388
$15$	61.9231	−	107.254i	1.06590	−	1.84619i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−15.3052	−	26.5094i	−0.218356	−	0.378205i	0.735949	−	0.677037i	$-0.236736\pi$
$17$	−15.3052	−	26.5094i	−0.218356	−	0.378205i	−0.954306	+	0.298832i	$0.903403\pi$
$18$	−98.8080			−1.29385
$19$	−76.9300	−	133.247i	−0.928892	−	1.60889i	−0.785180	−	0.619268i	$-0.787429\pi$
$19$	−76.9300	−	133.247i	−0.928892	−	1.60889i	−0.143712	−	0.989620i	$-0.545904\pi$
$20$	−28.3370	−	49.0812i	−0.316818	−	0.548745i
$21$	250.431			2.60231
$22$	−9.49349	−	16.4432i	−0.0920008	−	0.159350i
$23$	18.0015	−	31.1795i	0.163199	−	0.282669i	−0.772815	−	0.634631i	$-0.781152\pi$
$23$	18.0015	−	31.1795i	0.163199	−	0.282669i	0.936014	+	0.351962i	$0.114485\pi$
$24$	−34.9638	+	60.5590i	−0.297373	+	0.515065i
$25$	75.7470			0.605976
$26$		0			0
$27$	−195.832			−1.39585
$28$	57.3008	−	99.2479i	0.386744	−	0.669860i
$29$	24.6283	−	42.6575i	0.157702	−	0.273148i	−0.776337	−	0.630318i	$-0.782925\pi$
$29$	24.6283	−	42.6575i	0.157702	−	0.273148i	0.934040	+	0.357169i	$0.116258\pi$
$30$	−123.846	−	214.508i	−0.753704	−	1.30545i
$31$	166.984			0.967459			0.483730	−	0.875217i	$-0.339282\pi$
$31$	166.984			0.967459			0.483730	+	0.875217i	$0.339282\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	−41.4910	−	71.8645i	−0.218868	−	0.379091i
$34$	−61.2209			−0.308803
$35$	202.967	+	351.549i	0.980219	+	1.69779i
$36$	−98.8080	+	171.141i	−0.457445	+	0.792317i
$37$	11.9404	−	20.6814i	0.0530537	−	0.0918917i	−0.838279	−	0.545242i	$-0.816438\pi$
$37$	11.9404	−	20.6814i	0.0530537	−	0.0918917i	0.891333	+	0.453350i	$0.149771\pi$
$38$	−307.720			−1.31365
$39$		0			0
$40$	−113.348			−0.448048
$41$	−62.7371	+	108.664i	−0.238973	+	0.413913i	−0.960420	−	0.278557i	$-0.910144\pi$
$41$	−62.7371	+	108.664i	−0.238973	+	0.413913i	0.721447	+	0.692470i	$0.243477\pi$
$42$	250.431	−	433.760i	0.920057	−	1.59359i
$43$	217.387	+	376.526i	0.770959	+	1.33534i	0.937038	+	0.349227i	$0.113556\pi$
$43$	217.387	+	376.526i	0.770959	+	1.33534i	−0.166079	+	0.986112i	$0.553111\pi$
$44$	−37.9739			−0.130109
$45$	−349.991	−	606.202i	−1.15941	−	2.00816i
$46$	−36.0030	−	62.3591i	−0.115399	−	0.199877i
$47$	−186.017			−0.577306			−0.288653	−	0.957434i	$-0.593207\pi$
$47$	−186.017			−0.577306			−0.288653	+	0.957434i	$0.593207\pi$
$48$	69.9275	+	121.118i	0.210274	+	0.364206i
$49$	−238.923	+	413.826i	−0.696568	+	1.20649i
$50$	75.7470	−	131.198i	0.214245	−	0.371083i
$51$	−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	$0.673755\pi$
$54$	−195.832	+	339.191i	−0.493507	+	0.854779i
$55$	67.2543	−	116.488i	0.164883	−	0.285586i
$56$	−114.602	−	198.496i	−0.273469	−	0.473663i
$57$	−1344.88			−3.12515
$58$	−49.2567	−	85.3151i	−0.111512	−	0.193145i
$59$	204.104	+	353.518i	0.450374	+	0.780070i	0.998409	−	0.0563849i	$-0.0179574\pi$
$59$	204.104	+	353.518i	0.450374	+	0.780070i	−0.548035	+	0.836455i	$0.684624\pi$
$60$	−495.385			−1.06590
$61$	301.881	+	522.873i	0.633638	+	1.09749i	0.986802	+	0.161931i	$0.0517722\pi$
$61$	301.881	+	522.873i	0.633638	+	1.09749i	−0.353165	+	0.935561i	$0.614894\pi$
$62$	166.984	−	289.225i	0.342048	−	0.592445i
$63$	707.722	−	1225.81i	1.41531	−	2.45139i
$64$	64.0000			0.125000
$65$		0			0
$66$	−165.964			−0.309527
$67$	143.774	−	249.024i	0.262161	−	0.454076i	−0.704655	−	0.709550i	$-0.748898\pi$
$67$	143.774	−	249.024i	0.262161	−	0.454076i	0.966816	+	0.255474i	$0.0822316\pi$
$68$	−61.2209	+	106.038i	−0.109178	+	0.189102i
$69$	−157.350	−	272.538i	−0.274532	−	0.475504i
$70$	811.868			1.38624
$71$	480.901	+	832.946i	0.803838	+	1.39229i	0.917073	+	0.398720i	$0.130545\pi$
$71$	480.901	+	832.946i	0.803838	+	1.39229i	−0.113235	+	0.993568i	$0.536121\pi$
$72$	197.616	+	342.281i	0.323462	+	0.560253i
$73$	963.198			1.54430			0.772149	−	0.635441i	$-0.219182\pi$
$73$	963.198			1.54430			0.772149	+	0.635441i	$0.219182\pi$
$74$	−23.8808	−	41.3627i	−0.0375146	−	0.0649773i
$75$	331.050	−	573.396i	0.509685	−	0.882800i
$76$	−307.720	+	532.986i	−0.464446	+	0.804444i
$77$	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	$0.766516\pi$
$80$	−113.348	+	196.325i	−0.158409	+	0.274372i
$81$	−188.924	+	327.226i	−0.259155	+	0.448870i
$82$	125.474	+	217.328i	0.168979	+	0.292681i
$83$	313.304			0.414332			0.207166	−	0.978306i	$-0.433576\pi$
$83$	313.304			0.414332			0.207166	+	0.978306i	$0.433576\pi$
$84$	−500.863	−	867.520i	−0.650579	−	1.12684i
$85$	−216.852	−	375.599i	−0.276717	−	0.479288i
$86$	869.549			1.09030
$87$	−215.275	−	372.867i	−0.265286	−	0.459489i
$88$	−37.9739	+	65.7728i	−0.0460004	+	0.0796750i
$89$	−337.877	+	585.220i	−0.402414	+	0.697002i	−0.994017	−	0.109228i	$-0.965162\pi$
$89$	−337.877	+	585.220i	−0.402414	+	0.697002i	0.591602	+	0.806230i	$0.298496\pi$
$90$	−1399.96			−1.63966
$91$		0			0
$92$	−144.012			−0.163199
$93$	729.799	−	1264.05i	0.813727	−	1.40942i
$94$	−186.017	+	322.191i	−0.204108	+	0.353526i
$95$	−1089.98	−	1887.91i	−1.17716	−	2.03890i
$96$	279.710			0.297373
$97$	136.217	+	235.935i	0.142585	+	0.246965i	0.928469	−	0.371409i	$-0.121125\pi$
$97$	136.217	+	235.935i	0.142585	+	0.246965i	−0.785884	+	0.618374i	$0.787792\pi$
$98$	477.845	+	827.653i	0.492548	+	0.853118i
$99$	−469.016			−0.476140
$100$	−151.494	−	262.395i	−0.151494	−	0.262395i
$101$	330.780	−	572.928i	0.325880	−	0.564441i	−0.655810	−	0.754926i	$-0.727673\pi$
$101$	330.780	−	572.928i	0.325880	−	0.564441i	0.981690	+	0.190485i	$0.0610061\pi$
$102$	−267.564	+	463.434i	−0.259733	+	0.449871i
$103$	−315.353			−0.301676			−0.150838	−	0.988558i	$-0.548197\pi$
$103$	−315.353			−0.301676			−0.150838	+	0.988558i	$0.548197\pi$
$104$		0			0
$105$	3548.24			3.29784
$106$	−400.631	+	693.913i	−0.367101	+	0.635838i
$107$	−1060.66	+	1837.12i	−0.958299	+	1.65982i	−0.231666	+	0.972795i	$0.574418\pi$
$107$	−1060.66	+	1837.12i	−0.958299	+	1.65982i	−0.726632	+	0.687026i	$0.758916\pi$
$108$	391.664	+	678.382i	0.348962	+	0.604420i
$109$	884.432			0.777185			0.388593	−	0.921410i	$-0.372961\pi$
$109$	884.432			0.777185			0.388593	+	0.921410i	$0.372961\pi$
$110$	−134.509	−	232.976i	−0.116590	−	0.201940i
$111$	−104.370	−	180.774i	−0.0892467	−	0.154580i
$112$	−458.406			−0.386744
$113$	66.1023	+	114.493i	0.0550299	+	0.0953146i	0.892228	−	0.451585i	$-0.149141\pi$
$113$	66.1023	+	114.493i	0.0550299	+	0.0953146i	−0.837198	+	0.546900i	$0.815808\pi$
$114$	−1344.88	+	2329.40i	−1.10491	+	1.91376i
$115$	255.055	−	441.768i	0.206817	−	0.358218i
$116$	−197.027			−0.157702
$117$		0			0
$118$	816.415			0.636925
$119$	438.501	−	759.505i	0.337792	−	0.585073i
$120$	−495.385	+	858.032i	−0.376852	+	0.652727i
$121$	620.437	+	1074.63i	0.466143	+	0.807384i
$122$	1207.52			0.896099
$123$	548.381	+	949.824i	0.401999	+	0.696282i
$124$	−333.968	−	578.450i	−0.241865	−	0.418922i
$125$	−697.842			−0.499335
$126$	−1415.44	−	2451.62i	−1.00078	−	1.73340i
$127$	936.404	−	1621.90i	0.654271	−	1.13323i	−0.327805	−	0.944745i	$-0.606309\pi$
$127$	936.404	−	1621.90i	0.654271	−	1.13323i	0.982076	−	0.188485i	$-0.0603577\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	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	$0.711652\pi$
$132$	−165.964	+	287.458i	−0.109434	+	0.189546i
$133$	2204.07	−	3817.57i	1.43697	−	2.48891i
$134$	−287.548	−	498.047i	−0.185376	−	0.321080i
$135$	−2774.65			−1.76892
$136$	122.442	+	212.075i	0.0772007	+	0.133715i
$137$	−483.687	−	837.771i	−0.301637	−	0.522450i	0.674870	−	0.737936i	$-0.264200\pi$
$137$	−483.687	−	837.771i	−0.301637	−	0.522450i	−0.976507	+	0.215487i	$0.930866\pi$
$138$	−629.401			−0.388247
$139$	51.7985	+	89.7176i	0.0316078	+	0.0547464i	0.881397	−	0.472377i	$-0.156604\pi$
$139$	51.7985	+	89.7176i	0.0316078	+	0.0547464i	−0.849789	+	0.527123i	$0.823271\pi$
$140$	811.868	−	1406.20i	0.490110	−	0.848895i
$141$	−812.981	+	1408.13i	−0.485570	+	0.841032i
$142$	1923.61			1.13680
$143$		0			0
$144$	790.464			0.457445
$145$	348.947	−	604.394i	0.199852	−	0.346153i
$146$	963.198	−	1668.31i	0.545992	−	0.945686i
$147$	2088.41	+	3617.23i	1.17176	+	2.02955i
$148$	−95.5231			−0.0530537
$149$	958.718	+	1660.55i	0.527122	+	0.913002i	0.999500	+	0.0316065i	$0.0100623\pi$
$149$	958.718	+	1660.55i	0.527122	+	0.913002i	−0.472378	+	0.881396i	$0.656604\pi$
$150$	−662.100	−	1146.79i	−0.360402	−	0.624234i
$151$	−2035.28			−1.09688			−0.548439	−	0.836191i	$-0.684778\pi$
$151$	−2035.28			−1.09688			−0.548439	+	0.836191i	$0.684778\pi$
$152$	615.440	+	1065.97i	0.328413	+	0.568828i
$153$	−756.139	+	1309.67i	−0.399544	+	0.692030i
$154$	271.992	−	471.104i	0.142323	−	0.246511i
$155$	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	$0.549993\pi$
$158$	−1043.18	+	1806.84i	−0.525259	+	0.909775i
$159$	−1750.94	+	3032.73i	−0.873327	+	1.51265i
$160$	226.696	+	392.650i	0.112012	+	0.194010i
$161$	1031.50			0.504930
$162$	377.848	+	654.452i	0.183250	+	0.317399i
$163$	580.046	+	1004.67i	0.278728	+	0.482771i	0.971069	−	0.238799i	$-0.0767538\pi$
$163$	580.046	+	1004.67i	0.278728	+	0.482771i	−0.692341	+	0.721571i	$0.743421\pi$
$164$	501.897			0.238973
$165$	−587.866	−	1018.21i	−0.277365	−	0.480411i
$166$	313.304	−	542.658i	0.146489	−	0.253726i
$167$	−1014.63	+	1757.39i	−0.470147	+	0.814319i	−0.999417	−	0.0341344i	$-0.989133\pi$
$167$	−1014.63	+	1757.39i	−0.470147	+	0.814319i	0.529270	+	0.848454i	$0.322466\pi$
$168$	−2003.45			−0.920057
$169$		0			0
$170$	−867.409			−0.391337
$171$	−3800.65	+	6582.92i	−1.69967	+	2.94391i
$172$	869.549	−	1506.10i	0.385479	−	0.667670i
$173$	1536.80	+	2661.82i	0.675380	+	1.16979i	0.976358	+	0.216162i	$0.0693539\pi$
$173$	1536.80	+	2661.82i	0.675380	+	1.16979i	−0.300977	+	0.953631i	$0.597313\pi$
$174$	−861.099			−0.375171
$175$	1085.09	+	1879.43i	0.468715	+	0.811839i
$176$	75.9479	+	131.546i	0.0325272	+	0.0563388i
$177$	3568.12			1.51523
$178$	675.754	+	1170.44i	0.284550	+	0.492855i
$179$	−1156.94	+	2003.88i	−0.483095	+	0.836745i	−0.999812	−	0.0194115i	$-0.993821\pi$
$179$	−1156.94	+	2003.88i	−0.483095	+	0.836745i	0.516717	+	0.856156i	$0.327154\pi$
$180$	−1399.96	+	2424.81i	−0.579706	+	1.00408i
$181$	−1670.01			−0.685805			−0.342903	−	0.939371i	$-0.611410\pi$
$181$	−1670.01			−0.685805			−0.342903	+	0.939371i	$0.611410\pi$
$182$		0			0
$183$	5277.44			2.13180
$184$	−144.012	+	249.436i	−0.0576995	+	0.0999385i
$185$	169.178	−	293.024i	0.0672334	−	0.116452i
$186$	−1459.60	−	2528.10i	−0.575392	−	0.996608i
$187$	−290.600			−0.113640
$188$	372.034	+	644.382i	0.144326	+	0.249981i
$189$	−2805.33	−	4858.98i	−1.07967	−	1.87005i
$190$	−4359.94			−1.66475
$191$	−1912.60	−	3312.73i	−0.724561	−	1.25498i	−0.959154	−	0.282883i	$-0.908709\pi$
$191$	−1912.60	−	3312.73i	−0.724561	−	1.25498i	0.234594	−	0.972094i	$-0.424624\pi$
$192$	279.710	−	484.472i	0.105137	−	0.182103i
$193$	454.416	−	787.071i	0.169480	−	0.293547i	−0.768757	−	0.639540i	$-0.779125\pi$
$193$	454.416	−	787.071i	0.169480	−	0.293547i	0.938237	+	0.345993i	$0.112458\pi$
$194$	544.869			0.201646
$195$		0			0
$196$	1911.38			0.696568
$197$	668.833	−	1158.45i	0.241890	−	0.418966i	−0.719362	−	0.694635i	$-0.755566\pi$
$197$	668.833	−	1158.45i	0.241890	−	0.418966i	0.961253	+	0.275669i	$0.0888992\pi$
$198$	−469.016	+	812.360i	−0.168341	+	0.291575i
$199$	−572.290	−	991.236i	−0.203862	−	0.353100i	0.745907	−	0.666050i	$-0.232016\pi$
$199$	−572.290	−	991.236i	−0.203862	−	0.353100i	−0.949770	+	0.312950i	$0.898683\pi$
$200$	−605.976			−0.214245
$201$	−1256.72	−	2176.70i	−0.441005	−	0.763844i
$202$	−661.561	−	1145.86i	−0.230432	−	0.399120i
$203$	1411.22			0.487924
$204$	535.128	+	926.869i	0.183659	+	0.318107i
$205$	−888.892	+	1539.61i	−0.302843	+	0.524540i
$206$	−315.353	+	546.207i	−0.106659	+	0.184738i
$207$	−1778.69			−0.597236
$208$		0			0
$209$	−1460.67			−0.483428
$210$	3548.24	−	6145.74i	1.16596	−	2.01951i
$211$	5.61262	−	9.72134i	0.00183123	−	0.00317178i	−0.865108	−	0.501585i	$-0.832750\pi$
$211$	5.61262	−	9.72134i	0.00183123	−	0.00317178i	0.866940	+	0.498413i	$0.166084\pi$
$212$	801.262	+	1387.83i	0.259580	+	0.449605i
$213$	8407.06			2.70442
$214$	2121.32	+	3674.24i	0.677619	+	1.17367i
$215$	3080.05	+	5334.81i	0.977014	+	1.69224i
$216$	1566.66			0.493507
$217$	2392.08	+	4143.21i	0.748318	+	1.29613i
$218$	884.432	−	1531.88i	0.274777	−	0.475927i
$219$	4209.63	−	7291.29i	1.29891	−	2.24977i
$220$	−538.035			−0.164883
$221$		0			0
$222$	−417.481			−0.126214
$223$	1369.87	−	2372.68i	0.411360	−	0.712497i	−0.583679	−	0.811985i	$-0.698387\pi$
$223$	1369.87	−	2372.68i	0.411360	−	0.712497i	0.995039	+	0.0994882i	$0.0317205\pi$
$224$	−458.406	+	793.983i	−0.136735	+	0.236831i
$225$	−1871.10	−	3240.85i	−0.554401	−	0.960251i
$226$	264.409			0.0778241
$227$	−2264.87	−	3922.88i	−0.662225	−	1.14701i	−0.980030	−	0.198851i	$-0.936279\pi$
$227$	−2264.87	−	3922.88i	−0.662225	−	1.14701i	0.317805	−	0.948156i	$-0.397054\pi$
$228$	2689.76	+	4658.80i	0.781288	+	1.35323i
$229$	−867.892			−0.250445			−0.125222	−	0.992129i	$-0.539964\pi$
$229$	−867.892			−0.250445			−0.125222	+	0.992129i	$0.539964\pi$
$230$	−510.110	−	883.536i	−0.146242	−	0.253298i
$231$	1188.73	−	2058.95i	0.338584	−	0.586445i
$232$	−197.027	+	341.260i	−0.0557562	+	0.0965726i
$233$	535.138			0.150464			0.0752319	−	0.997166i	$-0.476030\pi$
$233$	535.138			0.150464			0.0752319	+	0.997166i	$0.476030\pi$
$234$		0			0
$235$	−2635.59			−0.731603
$236$	816.415	−	1414.07i	0.225187	−	0.390035i
$237$	−4559.18	+	7896.73i	−1.24958	+	2.16434i
$238$	−877.001	−	1519.01i	−0.238855	−	0.413709i
$239$	−1146.73			−0.310359			−0.155180	−	0.987886i	$-0.549596\pi$
$239$	−1146.73			−0.310359			−0.155180	+	0.987886i	$0.549596\pi$
$240$	990.769	+	1716.06i	0.266475	+	0.461547i
$241$	1676.52	+	2903.81i	0.448107	+	0.776145i	0.998263	−	0.0589175i	$-0.0187649\pi$
$241$	1676.52	+	2903.81i	0.448107	+	0.776145i	−0.550155	+	0.835062i	$0.685432\pi$
$242$	2481.75			0.659226
$243$	−992.360	−	1718.82i	−0.261975	−	0.453754i
$244$	1207.52	−	2091.49i	0.316819	−	0.548746i
$245$	−3385.18	+	5863.31i	−0.882740	+	1.52895i
$246$	2193.52			0.568512
$247$		0			0
$248$	−1335.87			−0.342048
$249$	1369.29	−	2371.67i	0.348494	−	0.603609i
$250$	−697.842	+	1208.70i	−0.176542	+	0.305779i
$251$	−2678.98	−	4640.13i	−0.673688	−	1.16686i	−0.976851	−	0.213923i	$-0.931376\pi$
$251$	−2678.98	−	4640.13i	−0.673688	−	1.16686i	0.303163	−	0.952939i	$-0.401957\pi$
$252$	−5661.78			−1.41531
$253$	−170.897	−	296.003i	−0.0424672	−	0.0735554i
$254$	−1872.81	−	3243.80i	−0.462639	−	0.801315i
$255$	−3790.99			−0.930983
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	3146.05	−	5449.12i	0.763601	−	1.32260i	−0.177383	−	0.984142i	$-0.556763\pi$
$257$	3146.05	−	5449.12i	0.763601	−	1.32260i	0.940983	−	0.338453i	$-0.109904\pi$
$258$	3800.34	−	6582.37i	0.917049	−	1.58837i
$259$	684.194			0.164146
$260$		0			0
$261$	−2433.48			−0.577121
$262$	−1850.21	+	3204.66i	−0.436285	+	0.755667i
$263$	2398.88	−	4154.98i	0.562438	−	0.974171i	−0.434845	−	0.900505i	$-0.643197\pi$
$263$	2398.88	−	4154.98i	0.562438	−	0.974171i	0.997283	−	0.0736656i	$-0.0234697\pi$
$264$	331.928	+	574.916i	0.0773816	+	0.134029i
$265$	−5676.35			−1.31583
$266$	−4408.15	−	7635.14i	−1.01609	−	1.75993i
$267$	2953.36	+	5115.37i	0.676939	+	1.17249i
$268$	−1150.19			−0.262161
$269$	−3123.22	−	5409.57i	−0.707903	−	1.22612i	−0.965634	−	0.259907i	$-0.916308\pi$
$269$	−3123.22	−	5409.57i	−0.707903	−	1.22612i	0.257731	−	0.966217i	$-0.417025\pi$
$270$	−2774.65	+	4805.84i	−0.625407	+	1.08324i
$271$	−915.576	+	1585.82i	−0.205230	+	0.355468i	−0.950206	−	0.311623i	$-0.899128\pi$
$271$	−915.576	+	1585.82i	−0.205230	+	0.355468i	0.744976	+	0.667091i	$0.232461\pi$
$272$	489.767			0.109178
$273$		0			0
$274$	−1934.75			−0.426578
$275$	359.552	−	622.762i	0.0788428	−	0.136560i
$276$	−629.401	+	1090.15i	−0.137266	+	0.237752i
$277$	800.712	+	1386.87i	0.173683	+	0.300827i	0.939705	−	0.341987i	$-0.111100\pi$
$277$	800.712	+	1386.87i	0.173683	+	0.300827i	−0.766022	+	0.642814i	$0.777767\pi$
$278$	207.194			0.0447002
$279$	−4124.84	−	7144.44i	−0.885118	−	1.53307i
$280$	−1623.74	−	2812.39i	−0.346560	−	0.600259i
$281$	4516.64			0.958861			0.479431	−	0.877580i	$-0.340843\pi$
$281$	4516.64			0.958861			0.479431	+	0.877580i	$0.340843\pi$
$282$	1625.96	+	2816.25i	0.343350	+	0.594699i
$283$	−3541.51	+	6134.08i	−0.743890	+	1.28846i	0.206821	+	0.978379i	$0.433688\pi$
$283$	−3541.51	+	6134.08i	−0.743890	+	1.28846i	−0.950711	+	0.310077i	$0.899645\pi$
$284$	1923.61	−	3331.78i	0.401919	−	0.696144i
$285$	−19055.0			−3.96042
$286$		0			0
$287$	−3594.89			−0.739371
$288$	790.464	−	1369.12i	0.161731	−	0.280126i
$289$	1988.00	−	3443.32i	0.404641	−	0.700859i
$290$	−697.894	−	1208.79i	−0.141316	−	0.244767i
$291$	2381.34			0.479713
$292$	−1926.40	−	3336.62i	−0.386075	−	0.668701i
$293$	−3461.76	−	5995.94i	−0.690233	−	1.19552i	−0.971762	−	0.235965i	$-0.924175\pi$
$293$	−3461.76	−	5995.94i	−0.690233	−	1.19552i	0.281529	−	0.959553i	$-0.409158\pi$
$294$	8353.64			1.65712
$295$	2891.85	+	5008.83i	0.570746	+	0.988561i
$296$	−95.5231	+	165.451i	−0.0187573	+	0.0324886i
$297$	−929.565	+	1610.05i	−0.181612	+	0.314561i
$298$	3834.87			0.745463
$299$		0			0
$300$	−2648.40			−0.509685
$301$	−6228.23	+	10787.6i	−1.19265	+	2.06574i
$302$	−2035.28	+	3525.20i	−0.387805	+	0.671698i
$303$	−2891.33	−	5007.93i	−0.548194	−	0.949499i
$304$	2461.76			0.464446
$305$	4277.21	+	7408.34i	0.802991	+	1.39082i
$306$	1512.28	+	2619.34i	0.282520	+	0.489339i
$307$	−8778.50			−1.63197			−0.815986	−	0.578071i	$-0.803805\pi$
$307$	−8778.50			−1.63197			−0.815986	+	0.578071i	$0.803805\pi$
$308$	−543.984	−	942.208i	−0.100638	−	0.174309i
$309$	−1378.24	+	2387.18i	−0.253739	+	0.439489i
$310$	2365.92	−	4097.89i	0.433468	−	0.750789i
$311$	−2197.35			−0.400644			−0.200322	−	0.979730i	$-0.564199\pi$
$311$	−2197.35			−0.400644			−0.200322	+	0.979730i	$0.564199\pi$
$312$		0			0
$313$	−5052.55			−0.912419			−0.456209	−	0.889873i	$-0.650793\pi$
$313$	−5052.55			−0.912419			−0.456209	+	0.889873i	$0.650793\pi$
$314$	−615.393	+	1065.89i	−0.110601	+	0.191566i
$315$	10027.4	−	17367.9i	1.79358	−	3.10658i
$316$	2086.36	+	3613.68i	0.371414	+	0.643308i
$317$	−1889.91			−0.334852			−0.167426	−	0.985885i	$-0.553545\pi$
$317$	−1889.91			−0.334852			−0.167426	+	0.985885i	$0.553545\pi$
$318$	3501.89	+	6065.45i	0.617535	+	1.06960i
$319$	−233.809	−	404.969i	−0.0410369	−	0.0710780i
$320$	906.785			0.158409
$321$	9271.17	+	16058.1i	1.61204	+	2.79214i
$322$	1031.50	−	1786.61i	0.178520	−	0.309205i
$323$	−2354.86	+	4078.74i	−0.405659	+	0.702622i
$324$	1511.39			0.259155
$325$		0			0
$326$	2320.18			0.394181
$327$	3865.38	−	6695.04i	0.653688	−	1.13222i
$328$	501.897	−	869.311i	0.0844897	−	0.146340i
$329$	−2664.73	−	4615.45i	−0.446539	−	0.773428i
$330$	−2351.46			−0.392254
$331$	−1274.69	−	2207.83i	−0.211672	−	0.366627i	0.740566	−	0.671984i	$-0.234558\pi$
$331$	−1274.69	−	2207.83i	−0.211672	−	0.366627i	−0.952238	+	0.305357i	$0.901224\pi$
$332$	−626.608	−	1085.32i	−0.103583	−	0.179411i
$333$	−1179.81			−0.194153
$334$	2029.26	+	3514.79i	0.332444	+	0.575811i
$335$	2037.06	−	3528.30i	0.332229	−	0.575437i
$336$	−2003.45	+	3470.08i	−0.325289	+	0.563418i
$337$	140.649			0.0227349			0.0113674	−	0.999935i	$-0.496382\pi$
$337$	140.649			0.0227349			0.0113674	+	0.999935i	$0.496382\pi$
$338$		0			0
$339$	1155.59			0.185142
$340$	−867.409	+	1502.40i	−0.138358	+	0.239644i
$341$	792.631	−	1372.88i	0.125875	−	0.218022i
$342$	7601.30	+	13165.8i	1.20185	+	2.08166i
$343$	−3863.38			−0.608171
$344$	−1739.10	−	3012.20i	−0.272575	−	0.472114i
$345$	−2229.42	−	3861.47i	−0.347907	−	0.602593i
$346$	6147.20			0.955132
$347$	−70.2566	−	121.688i	−0.0108691	−	0.0188258i	0.860540	−	0.509383i	$-0.170126\pi$
$347$	−70.2566	−	121.688i	−0.0108691	−	0.0188258i	−0.871409	+	0.490558i	$0.836793\pi$
$348$	−861.099	+	1491.47i	−0.132643	+	0.229744i
$349$	6136.62	−	10628.9i	0.941220	−	1.63024i	0.178072	−	0.984018i	$-0.443014\pi$
$349$	6136.62	−	10628.9i	0.941220	−	1.63024i	0.763148	−	0.646223i	$-0.223653\pi$
$350$	4340.37			0.662864
$351$		0			0
$352$	303.792			0.0460004
$353$	2943.98	−	5099.13i	0.443888	−	0.768837i	−0.554086	−	0.832459i	$-0.686932\pi$
$353$	2943.98	−	5099.13i	0.443888	−	0.768837i	0.997974	+	0.0636228i	$0.0202654\pi$
$354$	3568.12	−	6180.16i	0.535716	−	0.927887i
$355$	6813.66	+	11801.6i	1.01868	+	1.76441i
$356$	2703.02			0.402414
$357$	−3832.91	−	6638.79i	−0.568232	−	0.984207i
$358$	2313.89	+	4007.77i	0.341600	+	0.591668i
$359$	5902.88			0.867806			0.433903	−	0.900960i	$-0.357136\pi$
$359$	5902.88			0.867806			0.433903	+	0.900960i	$0.357136\pi$
$360$	2799.93	+	4849.62i	0.409914	+	0.709992i
$361$	−8406.94	+	14561.2i	−1.22568	+	2.12294i
$362$	−1670.01	+	2892.54i	−0.242469	+	0.419968i
$363$	10846.4			1.56829
$364$		0			0
$365$	13647.1			1.95704
$366$	5277.44	−	9140.80i	0.753706	−	1.30546i
$367$	1659.47	−	2874.28i	0.236031	−	0.408818i	−0.723541	−	0.690282i	$-0.757487\pi$
$367$	1659.47	−	2874.28i	0.236031	−	0.408818i	0.959572	+	0.281464i	$0.0908200\pi$
$368$	288.024	+	498.873i	0.0407997	+	0.0706672i
$369$	6198.93			0.874535
$370$	−338.355	−	586.049i	−0.0475412	−	0.0823438i
$371$	−5739.12	−	9940.44i	−0.803127	−	1.39106i
$372$	−5838.39			−0.813727
$373$	−121.108	−	209.765i	−0.0168116	−	0.0291185i	0.857497	−	0.514489i	$-0.172018\pi$
$373$	−121.108	−	209.765i	−0.0168116	−	0.0291185i	−0.874309	+	0.485370i	$0.838685\pi$
$374$	−290.600	+	503.333i	−0.0401779	+	0.0695902i
$375$	−3049.90	+	5282.58i	−0.419989	+	0.727443i
$376$	1488.14			0.204108
$377$		0			0
$378$	−11221.3			−1.52689
$379$	−6452.13	+	11175.4i	−0.874469	+	1.51462i	−0.0171418	+	0.999853i	$0.505457\pi$
$379$	−6452.13	+	11175.4i	−0.874469	+	1.51462i	−0.857327	+	0.514772i	$0.827877\pi$
$380$	−4359.94	+	7551.63i	−0.588579	+	1.01945i
$381$	−8185.05	−	14176.9i	−1.10061	−	1.90631i
$382$	−7650.41			−1.02468
$383$	−2295.51	−	3975.94i	−0.306253	−	0.530446i	0.671286	−	0.741198i	$-0.265742\pi$
$383$	−2295.51	−	3975.94i	−0.306253	−	0.530446i	−0.977540	+	0.210752i	$0.932409\pi$
$384$	−559.420	−	968.944i	−0.0743432	−	0.128766i
$385$	3853.73			0.510141
$386$	−908.832	−	1574.14i	−0.119840	−	0.207569i
$387$	10739.8	−	18601.9i	1.41068	−	2.44338i
$388$	544.869	−	943.742i	0.0712927	−	0.123483i
$389$	−13973.1			−1.82125			−0.910623	−	0.413239i	$-0.864397\pi$
$389$	−13973.1			−1.82125			−0.910623	+	0.413239i	$0.864397\pi$
$390$		0			0
$391$	−1102.07			−0.142542
$392$	1911.38	−	3310.61i	0.246274	−	0.426559i
$393$	−8086.30	+	14005.9i	−1.03791	+	1.79772i
$394$	−1337.67	−	2316.91i	−0.171042	−	0.296254i
$395$	−14780.3			−1.88273
$396$	938.033	+	1624.72i	0.119035	+	0.206175i
$397$	1308.87	+	2267.02i	0.165466	+	0.286596i	0.936821	−	0.349810i	$-0.113754\pi$
$397$	1308.87	+	2267.02i	0.165466	+	0.286596i	−0.771355	+	0.636406i	$0.780420\pi$
$398$	−2289.16			−0.288305
$399$	−19265.7	−	33369.1i	−2.41727	−	4.18683i
$400$	−605.976	+	1049.58i	−0.0757470	+	0.131198i
$401$	3944.60	−	6832.24i	0.491231	−	0.850838i	−0.508718	−	0.860933i	$-0.669880\pi$
$401$	3944.60	−	6832.24i	0.491231	−	0.850838i	0.999949	+	0.0100957i	$0.00321361\pi$
$402$	−5026.87			−0.623676
$403$		0			0
$404$	−2646.24			−0.325880
$405$	−2676.77	+	4636.31i	−0.328420	+	0.568840i
$406$	1411.22	−	2444.31i	0.172507	−	0.298791i
$407$	−113.356	−	196.338i	−0.0138055	−	0.0239118i
$408$	2140.51			0.259733
$409$	3865.77	+	6695.71i	0.467359	+	0.809490i	0.999305	−	0.0372886i	$-0.0118721\pi$
$409$	3865.77	+	6695.71i	0.467359	+	0.809490i	−0.531945	+	0.846779i	$0.678539\pi$
$410$	1777.78	+	3079.21i	0.214143	+	0.370906i
$411$	−8455.76			−1.01482
$412$	630.706	+	1092.41i	0.0754191	+	0.130630i
$413$	−5847.66	+	10128.4i	−0.696718	+	1.20675i
$414$	−1778.69	+	3080.79i	−0.211155	+	0.365731i
$415$	4439.05			0.525071
$416$		0			0
$417$	905.535			0.106341
$418$	−1460.67	+	2529.95i	−0.170918	+	0.296038i
$419$	−1378.20	+	2387.12i	−0.160691	+	0.278326i	−0.935117	−	0.354340i	$-0.884706\pi$
$419$	−1378.20	+	2387.12i	−0.160691	+	0.278326i	0.774425	+	0.632665i	$0.218039\pi$
$420$	−7096.49	−	12291.5i	−0.824460	−	1.42801i
$421$	11815.2			1.36778			0.683890	−	0.729585i	$-0.260287\pi$
$421$	11815.2			1.36778			0.683890	+	0.729585i	$0.260287\pi$
$422$	−11.2252	−	19.4427i	−0.00129487	−	0.00224278i
$423$	4594.99	+	7958.76i	0.528171	+	0.914818i
$424$	3205.05			0.367101
$425$	−1159.32	−	2008.01i	−0.132319	−	0.229183i
$426$	8407.06	−	14561.5i	0.956158	−	1.65611i
$427$	−8649.01	+	14980.5i	−0.980222	+	1.69779i
$428$	8485.29			0.958299
$429$		0			0
$430$	12320.2			1.38171
$431$	5300.61	−	9180.93i	0.592393	−	1.02605i	−0.401516	−	0.915852i	$-0.631517\pi$
$431$	5300.61	−	9180.93i	0.592393	−	1.02605i	0.993909	−	0.110203i	$-0.0351501\pi$
$432$	1566.66	−	2713.53i	0.174481	−	0.302210i
$433$	4614.86	+	7993.17i	0.512185	+	0.887130i	0.999900	+	0.0141273i	$0.00449701\pi$
$433$	4614.86	+	7993.17i	0.512185	+	0.887130i	−0.487716	+	0.873003i	$0.662170\pi$
$434$	9568.32			1.05828
$435$	−3050.13	−	5282.97i	−0.336189	−	0.582297i
$436$	−1768.86	−	3063.76i	−0.194296	−	0.336531i
$437$	−5539.42			−0.606377
$438$	−8419.25	−	14582.6i	−0.918465	−	1.59083i
$439$	−3600.83	+	6236.82i	−0.391476	+	0.678057i	−0.992645	−	0.121066i	$-0.961369\pi$
$439$	−3600.83	+	6236.82i	−0.391476	+	0.678057i	0.601168	+	0.799123i	$0.294702\pi$
$440$	−538.035	+	931.903i	−0.0582950	+	0.100970i
$441$	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	$0.560876\pi$
$444$	−417.481	+	723.098i	−0.0446233	+	0.0772899i
$445$	−4787.22	+	8291.70i	−0.509968	+	0.883291i
$446$	−2739.74	−	4745.37i	−0.290876	−	0.503811i
$447$	16760.2			1.77344
$448$	916.813	+	1587.97i	0.0966860	+	0.167465i
$449$	9162.68	+	15870.2i	0.963059	+	1.66807i	0.714741	+	0.699389i	$0.246545\pi$
$449$	9162.68	+	15870.2i	0.963059	+	1.66807i	0.248319	+	0.968678i	$0.420122\pi$
$450$	−7484.41			−0.784041
$451$	595.594	+	1031.60i	0.0621849	+	0.107707i
$452$	264.409	−	457.970i	0.0275150	−	0.0476573i
$453$	−8895.12	+	15406.8i	−0.922581	+	1.59796i
$454$	−9059.50			−0.936527
$455$		0			0
$456$	10759.0			1.10491
$457$	2691.92	−	4662.54i	0.275542	−	0.477252i	−0.694730	−	0.719271i	$-0.744476\pi$
$457$	2691.92	−	4662.54i	0.275542	−	0.477252i	0.970272	+	0.242018i	$0.0778094\pi$
$458$	−867.892	+	1503.23i	−0.0885457	+	0.153366i
$459$	2997.25	+	5191.39i	0.304793	+	0.527916i
$460$	−2040.44			−0.206817
$461$	5310.57	+	9198.17i	0.536525	+	0.929288i	0.999088	+	0.0427015i	$0.0135965\pi$
$461$	5310.57	+	9198.17i	0.536525	+	0.929288i	−0.462563	+	0.886586i	$0.653070\pi$
$462$	−2377.47	−	4117.89i	−0.239415	−	0.414679i
$463$	10407.3			1.04464			0.522318	−	0.852751i	$-0.325067\pi$
$463$	10407.3			1.04464			0.522318	+	0.852751i	$0.325067\pi$
$464$	394.053	+	682.521i	0.0394256	+	0.0682871i
$465$	10340.2	−	17909.7i	1.03121	−	1.78611i
$466$	535.138	−	926.886i	0.0531970	−	0.0921399i
$467$	−15784.0			−1.56402			−0.782010	−	0.623266i	$-0.785805\pi$
$467$	−15784.0			−1.56402			−0.782010	+	0.623266i	$0.785805\pi$
$468$		0			0
$469$	8238.36			0.811113
$470$	−2635.59	+	4564.97i	−0.258661	+	0.448013i
$471$	−2689.56	+	4658.45i	−0.263117	+	0.455732i
$472$	−1632.83	−	2828.15i	−0.159231	−	0.275796i
$473$	4127.52			0.401234
$474$	9118.36	+	15793.5i	0.883587	+	1.53042i
$475$	−5827.22	−	10093.0i	−0.562886	−	0.974948i
$476$	−3508.00			−0.337792
$477$	9896.38	+	17141.0i	0.949946	+	1.64536i
$478$	−1146.73	+	1986.20i	−0.109729	+	0.190055i
$479$	9131.86	−	15816.8i	0.871075	−	1.50875i	0.0101899	−	0.999948i	$-0.496756\pi$
$479$	9131.86	−	15816.8i	0.871075	−	1.50875i	0.860885	−	0.508799i	$-0.169910\pi$
$480$	3963.08			0.376852
$481$		0			0
$482$	6706.06			0.633720
$483$	4508.15	−	7808.34i	0.424695	−	0.735593i
$484$	2481.75	−	4298.51i	0.233072	−	0.403692i
$485$	1930.00	+	3342.86i	0.180694	+	0.312972i
$486$	−3969.44			−0.370489
$487$	2684.50	+	4649.70i	0.249788	+	0.432645i	0.963467	−	0.267828i	$-0.0863059\pi$
$487$	2684.50	+	4649.70i	0.249788	+	0.432645i	−0.713679	+	0.700473i	$0.752973\pi$
$488$	−2415.05	−	4182.98i	−0.224025	−	0.388022i
$489$	10140.3			0.937750
$490$	6770.36	+	11726.6i	0.624192	+	1.08113i
$491$	745.667	−	1291.53i	0.0685366	−	0.118709i	−0.829721	−	0.558179i	$-0.811500\pi$
$491$	745.667	−	1291.53i	0.0685366	−	0.118709i	0.898257	+	0.439470i	$0.144834\pi$
$492$	2193.52	−	3799.30i	0.200999	−	0.348141i
$493$	−1507.77			−0.137741
$494$		0			0
$495$	−6645.27			−0.603399
$496$	−1335.87	+	2313.80i	−0.120932	+	0.209461i
$497$	−13778.0	+	23864.2i	−1.24352	+	2.15384i
$498$	−2738.57	−	4743.34i	−0.246422	−	0.426816i
$499$	−10067.4			−0.903163			−0.451582	−	0.892230i	$-0.649140\pi$
$499$	−10067.4			−0.903163			−0.451582	+	0.892230i	$0.649140\pi$
$500$	1395.68	+	2417.40i	0.124834	+	0.216218i
$501$	8868.84	+	15361.3i	0.790879	+	1.36984i
$502$	−10715.9			−0.952738
$503$	−2341.53	−	4055.65i	−0.207562	−	0.359508i	0.743384	−	0.668865i	$-0.233220\pi$
$503$	−2341.53	−	4055.65i	−0.207562	−	0.359508i	−0.950946	+	0.309357i	$0.899886\pi$
$504$	−5661.78	+	9806.49i	−0.500388	+	0.866698i
$505$	4686.67	−	8117.55i	0.412978	−	0.715299i
$506$	−683.589			−0.0600577
$507$		0			0
$508$	−7491.23			−0.654271
$509$	−5772.48	+	9998.23i	−0.502673	+	0.870656i	0.497322	+	0.867566i	$0.334317\pi$
$509$	−5772.48	+	9998.23i	−0.502673	+	0.870656i	−0.999995	+	0.00308978i	$0.999016\pi$
$510$	−3790.99	+	6566.18i	−0.329152	+	0.570108i
$511$	13798.0	+	23898.8i	1.19450	+	2.06893i
$512$	−512.000			−0.0441942
$513$	15065.4	+	26094.0i	1.29659	+	2.24576i
$514$	−6292.11	−	10898.2i	−0.539947	−	0.935216i
$515$	−4468.09			−0.382306
$516$	−7600.67	−	13164.7i	−0.648451	−	1.12315i
$517$	−882.975	+	1529.36i	−0.0751125	+	0.130099i
$518$	684.194	−	1185.06i	0.0580343	−	0.100518i
$519$	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	$0.184739\pi$
$522$	−2433.48	+	4214.91i	−0.204043	+	0.353413i
$523$	2545.03	−	4408.13i	0.212785	−	0.368555i	−0.739800	−	0.672827i	$-0.765080\pi$
$523$	2545.03	−	4408.13i	0.212785	−	0.368555i	0.952585	+	0.304272i	$0.0984133\pi$
$524$	3700.43	+	6409.33i	0.308500	+	0.534337i
$525$	18969.4			1.57694
$526$	−4797.76	−	8309.96i	−0.397704	−	0.688843i
$527$	−2555.73	−	4426.65i	−0.211251	−	0.365897i
$528$	1327.71			0.109434
$529$	5435.39	+	9414.37i	0.446732	+	0.773763i
$530$	−5676.35	+	9831.72i	−0.465216	+	0.805779i
$531$	10083.5	−	17465.2i	0.824084	−	1.42736i
$532$	−17632.6			−1.43697
$533$		0			0
$534$	11813.4			0.957337
$535$	−15028.0	+	26029.3i	−1.21442	+	2.10344i
$536$	−1150.19	+	1992.19i	−0.0926879	+	0.160540i
$537$	10112.8	+	17515.8i	0.812660	+	1.40757i
$538$	−12492.9			−1.00113
$539$	2268.21	+	3928.65i	0.181259	+	0.313950i
$540$	5549.30	+	9611.67i	0.442230	+	0.765964i
$541$	−5958.49			−0.473523			−0.236761	−	0.971568i	$-0.576086\pi$
$541$	−5958.49			−0.473523			−0.236761	+	0.971568i	$0.576086\pi$
$542$	1831.15	+	3171.65i	0.145119	+	0.251354i
$543$	−7298.72	+	12641.8i	−0.576829	+	0.999097i
$544$	489.767	−	848.301i	0.0386003	−	0.0668577i
$545$	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	$0.469155\pi$
$548$	−1934.75	+	3351.08i	−0.150818	+	0.261225i
$549$	14914.1	−	25832.0i	1.15942	−	2.00817i
$550$	−719.103	−	1245.52i	−0.0557503	−	0.0965624i
$551$	−7578.63			−0.585954
$552$	1258.80	+	2180.31i	0.0970619	+	0.168116i
$553$	−14943.7	−	25883.3i	−1.14914	−	1.99036i
$554$	3202.85			0.245624
$555$	−1478.77	−	2561.31i	−0.113100	−	0.195894i
$556$	207.194	−	358.870i	0.0158039	−	0.0273732i
$557$	−11655.8	+	20188.4i	−0.886662	+	1.53574i	−0.0428662	+	0.999081i	$0.513649\pi$
$557$	−11655.8	+	20188.4i	−0.886662	+	1.53574i	−0.843796	+	0.536664i	$0.819684\pi$
$558$	−16499.4			−1.25175
$559$		0			0
$560$	−6494.94			−0.490110
$561$	−1270.06	+	2199.80i	−0.0955826	+	0.165554i
$562$	4516.64	−	7823.04i	0.339009	−	0.587180i
$563$	−12313.1	−	21326.9i	−0.921733	−	1.59649i	−0.796733	−	0.604332i	$-0.793440\pi$
$563$	−12313.1	−	21326.9i	−0.921733	−	1.59649i	−0.125000	−	0.992157i	$-0.539893\pi$
$564$	6503.85			0.485570
$565$	936.572	+	1622.19i	0.0697378	+	0.120789i
$566$	7083.02	+	12268.2i	0.526010	+	0.911076i
$567$	−10825.5			−0.801813
$568$	−3847.21	−	6663.57i	−0.284200	−	0.492248i
$569$	6599.29	−	11430.3i	0.486215	−	0.842150i	−0.513659	−	0.857994i	$-0.671710\pi$
$569$	6599.29	−	11430.3i	0.486215	−	0.842150i	0.999874	+	0.0158447i	$0.00504372\pi$
$570$	−19055.0	+	33004.2i	−1.40022	+	2.42525i
$571$	20934.2			1.53427			0.767137	−	0.641483i	$-0.221681\pi$
$571$	20934.2			1.53427			0.767137	+	0.641483i	$0.221681\pi$
$572$		0			0
$573$	−33435.9			−2.43770
$574$	−3594.89	+	6226.52i	−0.261407	+	0.452770i
$575$	1363.56	−	2361.76i	0.0988947	−	0.171291i
$576$	−1580.93	−	2738.25i	−0.114361	−	0.198079i
$577$	−17083.2			−1.23255			−0.616275	−	0.787531i	$-0.711359\pi$
$577$	−17083.2			−1.23255			−0.616275	+	0.787531i	$0.711359\pi$
$578$	−3976.00	−	6886.64i	−0.286124	−	0.495582i
$579$	−3972.02	−	6879.74i	−0.285098	−	0.493804i
$580$	−2791.58			−0.199852
$581$	4488.14	+	7773.69i	0.320481	+	0.555089i
$582$	2381.34	−	4124.59i	0.169604	−	0.293763i
$583$	−1901.69	+	3293.83i	−0.135094	+	0.233990i
$584$	−7705.58			−0.545992
$585$		0			0
$586$	−13847.0			−0.976136
$587$	2229.41	−	3861.45i	0.156759	−	0.271515i	−0.776939	−	0.629576i	$-0.783229\pi$
$587$	2229.41	−	3861.45i	0.156759	−	0.271515i	0.933698	+	0.358061i	$0.116562\pi$
$588$	8353.64	−	14468.9i	0.585881	−	1.01478i
$589$	−12846.1	−	22250.1i	−0.898665	−	1.55653i
$590$	11567.4			0.807156
$591$	−5846.23	−	10126.0i	−0.406907	−	0.704783i
$592$	191.046	+	330.902i	0.0132634	+	0.0229729i
$593$	3217.47			0.222809			0.111404	−	0.993775i	$-0.464465\pi$
$593$	3217.47			0.222809			0.111404	+	0.993775i	$0.464465\pi$
$594$	1859.13	+	3220.11i	0.128419	+	0.222429i
$595$	6212.91	−	10761.1i	0.428074	−	0.741447i
$596$	3834.87	−	6642.19i	0.263561	−	0.456501i
$597$	−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	$0.548996\pi$
$600$	−2648.40	+	4587.16i	−0.180201	+	0.312117i
$601$	5459.23	−	9455.66i	0.370527	−	0.641771i	−0.619120	−	0.785297i	$-0.712510\pi$
$601$	5459.23	−	9455.66i	0.370527	−	0.641771i	0.989647	+	0.143525i	$0.0458438\pi$
$602$	12456.5	+	21575.2i	0.843334	+	1.46070i
$603$	−14206.0			−0.959392
$604$	4070.56	+	7050.41i	0.274219	+	0.474962i
$605$	8790.67	+	15225.9i	0.590730	+	1.02317i
$606$	−11565.3			−0.775263
$607$	−6243.51	−	10814.1i	−0.417490	−	0.723114i	0.578196	−	0.815898i	$-0.303757\pi$
$607$	−6243.51	−	10814.1i	−0.417490	−	0.723114i	−0.995686	+	0.0927838i	$0.970423\pi$
$608$	2461.76	−	4263.89i	0.164206	−	0.284414i
$609$	6167.71	−	10682.8i	0.410391	−	0.710818i
$610$	17108.8			1.13560
$611$		0			0
$612$	6049.11			0.399544
$613$	480.734	−	832.656i	0.0316748	−	0.0548624i	−0.849753	−	0.527180i	$-0.823249\pi$
$613$	480.734	−	832.656i	0.0316748	−	0.0548624i	0.881428	+	0.472318i	$0.156583\pi$
$614$	−8778.50	+	15204.8i	−0.576989	+	0.999375i
$615$	7769.75	+	13457.6i	0.509442	+	0.882379i
$616$	−2175.94			−0.142323
$617$	−7716.73	−	13365.8i	−0.503507	−	0.872100i	−0.999992	−	0.00405455i	$-0.998709\pi$
$617$	−7716.73	−	13365.8i	−0.503507	−	0.872100i	0.496485	−	0.868046i	$-0.334624\pi$
$618$	2756.48	+	4774.37i	0.179421	+	0.310766i
$619$	−24569.6			−1.59537			−0.797686	−	0.603073i	$-0.793943\pi$
$619$	−24569.6			−1.59537			−0.797686	+	0.603073i	$0.793943\pi$
$620$	−4731.84	−	8195.78i	−0.306508	−	0.530888i
$621$	−3525.27	+	6105.96i	−0.227801	+	0.394563i
$622$	−2197.35	+	3805.92i	−0.141649	+	0.245343i
$623$	−19360.6			−1.24505
$624$		0			0
$625$	−19355.8			−1.23877
$626$	−5052.55	+	8751.27i	−0.322589	+	0.558740i
$627$	−6383.80	+	11057.1i	−0.406610	+	0.704269i
$628$	1230.79	+	2131.78i	0.0782065	+	0.135458i
$629$	−731.001			−0.0463385
$630$	−20054.8	−	34735.9i	−1.26826	−	2.19668i
$631$	6661.10	+	11537.4i	0.420245	+	0.727885i	0.995963	−	0.0897629i	$-0.0286109\pi$
$631$	6661.10	+	11537.4i	0.420245	+	0.727885i	−0.575719	+	0.817648i	$0.695278\pi$
$632$	8345.43			0.525259
$633$	−49.0596	−	84.9736i	−0.00308048	−	0.00533554i
$634$	−1889.91	+	3273.42i	−0.118388	+	0.205054i
$635$	13267.5	−	22979.9i	0.829139	−	1.43611i
$636$	14007.6			0.873327
$637$		0			0
$638$	−935.235			−0.0580350
$639$	23758.5	−	41150.9i	1.47085	−	2.54758i
$640$	906.785	−	1570.60i	0.0560060	−	0.0970052i
$641$	−7447.28	−	12899.1i	−0.458892	−	0.794824i	0.540011	−	0.841658i	$-0.318420\pi$
$641$	−7447.28	−	12899.1i	−0.458892	−	0.794824i	−0.998903	+	0.0468338i	$0.985087\pi$
$642$	37084.7			2.27978
$643$	4623.78	+	8008.62i	0.283583	+	0.491181i	0.972265	−	0.233883i	$-0.0751434\pi$
$643$	4623.78	+	8008.62i	0.283583	+	0.491181i	−0.688681	+	0.725064i	$0.741810\pi$
$644$	−2063.00	−	3573.23i	−0.126232	−	0.218641i
$645$	53845.1			3.28705
$646$	4709.72	+	8157.47i	0.286844	+	0.496829i
$647$	−1367.07	+	2367.84i	−0.0830681	+	0.143878i	−0.904566	−	0.426333i	$-0.859805\pi$
$647$	−1367.07	+	2367.84i	−0.0830681	+	0.143878i	0.821498	+	0.570211i	$0.193139\pi$
$648$	1511.39	−	2617.81i	0.0916251	−	0.158699i
$649$	3875.31			0.234390
$650$		0			0
$651$	41818.1			2.51763
$652$	2320.18	−	4018.67i	0.139364	−	0.241386i
$653$	3281.39	−	5683.53i	0.196647	−	0.340603i	−0.750792	−	0.660539i	$-0.770328\pi$
$653$	3281.39	−	5683.53i	0.196647	−	0.340603i	0.947439	+	0.319936i	$0.103661\pi$
$654$	−7730.76	−	13390.1i	−0.462228	−	0.800602i
$655$	−26214.8			−1.56381
$656$	−1003.79	−	1738.62i	−0.0597432	−	0.103478i
$657$	−23792.9	−	41210.5i	−1.41286	−	2.44715i
$658$	−10658.9			−0.631501
$659$	2476.92	+	4290.15i	0.146414	+	0.253597i	0.929900	−	0.367813i	$-0.119893\pi$
$659$	2476.92	+	4290.15i	0.146414	+	0.253597i	−0.783485	+	0.621410i	$0.786560\pi$
$660$	−2351.46	+	4072.85i	−0.138683	+	0.240206i
$661$	−4673.64	+	8094.98i	−0.275013	+	0.476336i	−0.970138	−	0.242552i	$-0.922015\pi$
$661$	−4673.64	+	8094.98i	−0.275013	+	0.476336i	0.695126	+	0.718888i	$0.255349\pi$
$662$	−5098.78			−0.299350
$663$		0			0
$664$	−2506.43			−0.146489
$665$	31228.5	−	54089.3i	1.82104	−	3.15413i
$666$	−1179.81	+	2043.48i	−0.0686435	+	0.118894i
$667$	−886.695	−	1535.80i	−0.0514737	−	0.0891551i
$668$	8117.06			0.470147
$669$	−11974.0	−	20739.5i	−0.691988	−	1.19856i
$670$	−4074.13	−	7056.59i	−0.234921	−	0.406896i
$671$	5731.80			0.329767
$672$	4006.90	+	6940.16i	0.230014	+	0.398396i
$673$	−7709.51	+	13353.3i	−0.441575	+	0.764830i	−0.997807	−	0.0661971i	$-0.978913\pi$
$673$	−7709.51	+	13353.3i	−0.441575	+	0.764830i	0.556232	+	0.831027i	$0.312247\pi$
$674$	140.649	−	243.611i	0.00803798	−	0.0139222i
$675$	−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	$0.234708\pi$
$678$	1155.59	−	2001.54i	0.0654576	−	0.113376i
$679$	−3902.68	+	6759.64i	−0.220576	+	0.382049i
$680$	1734.82	+	3004.79i	0.0978342	+	0.169454i
$681$	−39594.3			−2.22798
$682$	−1585.26	−	2745.75i	−0.0890070	−	0.154165i
$683$	7445.02	+	12895.2i	0.417095	+	0.722429i	0.995646	−	0.0932168i	$-0.0297150\pi$
$683$	7445.02	+	12895.2i	0.417095	+	0.722429i	−0.578551	+	0.815646i	$0.696382\pi$
$684$	30405.2			1.69967
$685$	−6853.14	−	11870.0i	−0.382255	−	0.662086i
$686$	−3863.38	+	6691.56i	−0.215021	+	0.372427i
$687$	−3793.09	+	6569.83i	−0.210649	+	0.364854i
$688$	−6956.39			−0.385479
$689$		0			0
$690$	−8917.68			−0.492015
$691$	2035.51	−	3525.61i	0.112062	−	0.194096i	−0.804540	−	0.593899i	$-0.797588\pi$
$691$	2035.51	−	3525.61i	0.112062	−	0.194096i	0.916601	+	0.399802i	$0.130921\pi$
$692$	6147.20	−	10647.3i	0.337690	−	0.584897i
$693$	−6718.75	−	11637.2i	−0.368289	−	0.637895i
$694$	−281.026			−0.0153712
$695$	733.908	+	1271.17i	0.0400557	+	0.0693785i
$696$	1722.20	+	2982.94i	0.0937928	+	0.162454i
$697$	3840.82			0.208725
$698$	−12273.2	−	21257.9i	−0.665543	−	1.15275i
$699$	2338.80	−	4050.93i	0.126555	−	0.219199i
$700$	4340.37	−	7517.73i	0.234358	−	0.405919i
$701$	18378.1			0.990200			0.495100	−	0.868836i	$-0.335131\pi$
$701$	18378.1			0.990200			0.495100	+	0.868836i	$0.335131\pi$
$702$		0			0
$703$	−3674.29			−0.197125
$704$	303.792	−	526.182i	0.0162636	−	0.0281694i
$705$	−11518.7	+	19951.1i	−0.615349	+	1.06582i
$706$	−5887.97	−	10198.3i	−0.313876	−	0.543650i
$707$	18954.0			1.00826
$708$	−7136.24	−	12360.3i	−0.378808	−	0.656115i
$709$	−7473.18	−	12943.9i	−0.395855	−	0.685641i	0.597355	−	0.801977i	$-0.296218\pi$
$709$	−7473.18	−	12943.9i	−0.395855	−	0.685641i	−0.993210	+	0.116336i	$0.962885\pi$
$710$	27254.7			1.44063
$711$	25768.6	+	44632.5i	1.35921	+	2.35422i
$712$	2703.02	−	4681.76i	0.142275	−	0.246428i
$713$	3005.97	−	5206.49i	0.157888	−	0.273471i
$714$	−15331.6			−0.803602
$715$		0			0
$716$	9255.55			0.483095
$717$	−5011.75	+	8680.61i	−0.261042	+	0.452138i
$718$	5902.88	−	10224.1i	0.306816	−	0.531420i
$719$	−7502.92	−	12995.4i	−0.389168	−	0.674058i	0.603170	−	0.797613i	$-0.293904\pi$
$719$	−7502.92	−	12995.4i	−0.389168	−	0.674058i	−0.992338	+	0.123554i	$0.960571\pi$
$720$	11199.7			0.579706
$721$	−4517.49	−	7824.53i	−0.233343	−	0.404162i
$722$	16813.9	+	29122.5i	0.866687	+	1.50115i
$723$	29308.6			1.50761
$724$	3340.02	+	5785.08i	0.171451	+	0.296962i
$725$	1865.52	−	3231.18i	0.0955639	−	0.165521i
$726$	10846.4	−	18786.5i	0.554473	−	0.960376i
$727$	−30390.1			−1.55035			−0.775177	−	0.631744i	$-0.782339\pi$
$727$	−30390.1			−1.55035			−0.775177	+	0.631744i	$0.782339\pi$
$728$		0			0
$729$	−27550.2			−1.39970
$730$	13647.1	−	23637.5i	0.691920	−	1.19844i
$731$	6654.32	−	11525.6i	0.336688	−	0.583160i
$732$	−10554.9	−	18281.6i	−0.532951	−	0.923098i
$733$	31143.3			1.56931			0.784655	−	0.619932i	$-0.212840\pi$
$733$	31143.3			1.56931			0.784655	+	0.619932i	$0.212840\pi$
$734$	−3318.93	−	5748.56i	−0.166899	−	0.289078i
$735$	29589.7	+	51250.8i	1.48494	+	2.57199i
$736$	1152.10			0.0576995
$737$	−1364.92	−	2364.10i	−0.0682189	−	0.118159i
$738$	6198.93	−	10736.9i	0.309195	−	0.535541i
$739$	−1942.40	+	3364.34i	−0.0966881	+	0.167469i	−0.910312	−	0.413923i	$-0.864158\pi$
$739$	−1942.40	+	3364.34i	−0.0966881	+	0.167469i	0.813624	+	0.581392i	$0.197492\pi$
$740$	−1353.42			−0.0672334
$741$		0			0
$742$	−22956.5			−1.13579
$743$	−5807.42	+	10058.7i	−0.286748	+	0.496661i	−0.973031	−	0.230672i	$-0.925907\pi$
$743$	−5807.42	+	10058.7i	−0.286748	+	0.496661i	0.686284	+	0.727334i	$0.259241\pi$
$744$	−5838.39	+	10112.4i	−0.287696	+	0.498304i
$745$	13583.6	+	23527.5i	0.668007	+	1.15702i
$746$	−484.431			−0.0237752
$747$	−7739.23	−	13404.7i	−0.379068	−	0.656565i
$748$	581.199	+	1006.67i	0.0284101	+	0.0492077i
$749$	−60776.7			−2.96493
$750$	6099.79	+	10565.2i	0.296977	+	0.514380i
$751$	17205.1	−	29800.1i	0.835982	−	1.44796i	−0.0572461	−	0.998360i	$-0.518232\pi$
$751$	17205.1	−	29800.1i	0.835982	−	1.44796i	0.893228	−	0.449604i	$-0.148435\pi$
$752$	1488.14	−	2577.53i	0.0721632	−	0.124990i
$753$	−46833.6			−2.26655
$754$		0			0
$755$	−28836.9			−1.39004
$756$	−11221.3	+	19435.9i	−0.539836	+	0.935023i
$757$	14728.4	−	25510.3i	0.707150	−	1.22482i	−0.258760	−	0.965942i	$-0.583314\pi$
$757$	14728.4	−	25510.3i	0.707150	−	1.22482i	0.965910	−	0.258879i	$-0.0833529\pi$
$758$	12904.3	+	22350.8i	0.618343	+	1.07100i
$759$	−2987.60			−0.142876
$760$	8719.87	+	15103.3i	0.416188	+	0.720859i
$761$	−16475.1	−	28535.7i	−0.784784	−	1.35929i	−0.929128	−	0.369759i	$-0.879440\pi$
$761$	−16475.1	−	28535.7i	−0.784784	−	1.35929i	0.144343	−	0.989528i	$-0.453893\pi$
$762$	−32740.2			−1.55650
$763$	12669.7	+	21944.5i	0.601144	+	1.04121i
$764$	−7650.41	+	13250.9i	−0.362280	+	0.627488i
$765$	−10713.4	+	18556.1i	−0.506331	+	0.876990i
$766$	−9182.04			−0.433108
$767$		0			0
$768$	−2237.68			−0.105137
$769$	−5111.86	+	8854.00i	−0.239712	+	0.415193i	−0.960632	−	0.277826i	$-0.910386\pi$
$769$	−5111.86	+	8854.00i	−0.239712	+	0.415193i	0.720920	+	0.693019i	$0.243720\pi$
$770$	3853.73	−	6674.85i	0.180362	−	0.312396i
$771$	−27499.5	−	47630.4i	−1.28452	−	2.22486i
$772$	−3635.33			−0.169480
$773$	−5070.04	−	8781.56i	−0.235908	−	0.408604i	0.723629	−	0.690190i	$-0.242473\pi$
$773$	−5070.04	−	8781.56i	−0.235908	−	0.408604i	−0.959536	+	0.281586i	$0.909140\pi$
$774$	−21479.6	−	37203.8i	−0.997504	−	1.72773i
$775$	12648.6			0.586257
$776$	−1089.74	−	1887.48i	−0.0504115	−	0.0873153i
$777$	2990.25	−	5179.26i	0.138062	−	0.239131i
$778$	−13973.1	+	24202.1i	−0.643907	+	1.11528i
$779$	19305.4			0.887920
$780$		0			0
$781$	9130.86			0.418346
$782$	−1102.07	+	1908.84i	−0.0503963	+	0.0872889i
$783$	−4823.02	+	8353.71i	−0.220129	+	0.381274i
$784$	−3822.76	−	6621.22i	−0.174142	−	0.301623i
$785$	−8719.21			−0.396435
$786$	16172.6	+	28011.8i	0.733916	+	1.27118i
$787$	4544.27	+	7870.90i	0.205827	+	0.356502i	0.950396	−	0.311043i	$-0.100678\pi$
$787$	4544.27	+	7870.90i	0.205827	+	0.356502i	−0.744569	+	0.667545i	$0.767345\pi$
$788$	−5350.67			−0.241890
$789$	−20968.4	−	36318.4i	−0.946130	−	1.63874i
$790$	−14780.3	+	25600.2i	−0.665645	+	1.15293i
$791$	−1893.86	+	3280.26i	−0.0851300	+	0.147449i
$792$	3752.13			0.168341
$793$		0			0
$794$	5235.46			0.234004
$795$	−24808.3	+	42969.2i	−1.10674	+	1.91693i
$796$	−2289.16	+	3964.94i	−0.101931	+	0.176550i
$797$	10516.2	+	18214.6i	0.467382	+	0.809530i	0.999305	−	0.0372629i	$-0.0118639\pi$
$797$	10516.2	+	18214.6i	0.467382	+	0.809530i	−0.531923	+	0.846792i	$0.678531\pi$
$798$	−77062.7			−3.41853
$799$	2847.03	+	4931.20i	0.126058	+	0.218340i
$800$	1211.95	+	2099.16i	0.0535612	+	0.0927708i
$801$	33385.0			1.47266
$802$	−7889.19	−	13664.5i	−0.347353	−	0.601633i
$803$	4572.05	−	7919.03i	0.200927	−	0.348015i
$804$	−5026.87	+	8706.80i	−0.220503	+	0.381922i
$805$	14614.9			0.639883
$806$		0			0
$807$	−54599.7			−2.38166
$808$	−2646.24	+	4583.43i	−0.115216	+	0.199560i
$809$	21822.5	−	37797.6i	0.948376	−	1.64264i	0.199531	−	0.979892i	$-0.436058\pi$
$809$	21822.5	−	37797.6i	0.948376	−	1.64264i	0.748846	−	0.662745i	$-0.230608\pi$
$810$	5353.55	+	9272.62i	0.232228	+	0.402230i
$811$	28688.1			1.24214			0.621069	−	0.783756i	$-0.286699\pi$
$811$	28688.1			1.24214			0.621069	+	0.783756i	$0.286699\pi$
$812$	−2822.45	−	4888.62i	−0.121981	−	0.211277i
$813$	8002.99	+	13861.6i	0.345236	+	0.597967i
$814$	−453.424			−0.0195239
$815$	8218.39	+	14234.7i	0.353224	+	0.611802i
$816$	2140.51	−	3707.47i	0.0918295	−	0.159053i
$817$	33447.2	−	57932.2i	1.43227	−	2.48077i
$818$	15463.1			0.660946
$819$		0			0
$820$	7111.14			0.302843
$821$	−8021.12	+	13893.0i	−0.340973	+	0.590583i	−0.984614	−	0.174745i	$-0.944090\pi$
$821$	−8021.12	+	13893.0i	−0.340973	+	0.590583i	0.643640	+	0.765328i	$0.277423\pi$
$822$	−8455.76	+	14645.8i	−0.358794	+	0.621449i
$823$	6069.43	+	10512.6i	0.257068	+	0.445255i	0.965455	−	0.260569i	$-0.0839101\pi$
$823$	6069.43	+	10512.6i	0.257068	+	0.445255i	−0.708387	+	0.705824i	$0.750577\pi$
$824$	2522.82			0.106659
$825$	−3142.82	−	5443.52i	−0.132629	−	0.229720i
$826$	11695.3	+	20256.9i	0.492654	+	0.853301i
$827$	−17136.2			−0.720538			−0.360269	−	0.932848i	$-0.617315\pi$
$827$	−17136.2			−0.720538			−0.360269	+	0.932848i	$0.617315\pi$
$828$	3557.39	+	6161.58i	0.149309	+	0.258611i
$829$	−5473.64	+	9480.61i	−0.229321	+	0.397196i	−0.957607	−	0.288077i	$-0.906984\pi$
$829$	−5473.64	+	9480.61i	−0.229321	+	0.397196i	0.728286	+	0.685273i	$0.240317\pi$
$830$	4439.05	−	7688.67i	0.185641	−	0.321539i
$831$	13997.9			0.584336
$832$		0			0
$833$	14627.1			0.608400
$834$	905.535	−	1568.43i	0.0375972	−	0.0651203i
$835$	−14375.8	+	24899.7i	−0.595804	+	1.03196i
$836$	2921.33	+	5059.90i	0.120857	+	0.209330i
$837$	−32700.9			−1.35043
$838$	2756.41	+	4774.24i	0.113626	+	0.196806i
$839$	−6814.35	−	11802.8i	−0.280402	−	0.485671i	0.691081	−	0.722777i	$-0.257135\pi$
$839$	−6814.35	−	11802.8i	−0.280402	−	0.485671i	−0.971484	+	0.237106i	$0.923801\pi$
$840$	−28385.9			−1.16596
$841$	10981.4	+	19020.3i	0.450260	+	0.779873i
$842$	11815.2	−	20464.5i	0.483584	−	0.837591i
$843$	19739.8	−	34190.4i	0.806495	−	1.39689i
$844$	−44.9010			−0.00183123
$845$		0			0
$846$	18380.0			0.746946
$847$	−17775.8	+	30788.5i	−0.721113	+	1.24900i
$848$	3205.05	−	5551.30i	0.129790	−	0.224803i
$849$	30956.1	+	53617.6i	1.25137	+	2.16743i
$850$	−4637.30			−0.187127
$851$	−429.890	−	744.592i	−0.0173166	−	0.0299933i
$852$	−16814.1	−	29122.9i	−0.676106	−	1.17105i
$853$	−6645.59			−0.266753			−0.133377	−	0.991065i	$-0.542582\pi$
$853$	−6645.59			−0.266753			−0.133377	+	0.991065i	$0.542582\pi$
$854$	17298.0	+	29961.0i	0.693122	+	1.20052i
$855$	−53849.6	+	93270.2i	−2.15394	+	3.73073i
$856$	8485.29	−	14696.9i	0.338810	−	0.586836i
$857$	15552.6			0.619914			0.309957	−	0.950751i	$-0.399685\pi$
$857$	15552.6			0.619914			0.309957	+	0.950751i	$0.399685\pi$
$858$		0			0
$859$	−48006.5			−1.90682			−0.953412	−	0.301672i	$-0.902455\pi$
$859$	−48006.5			−1.90682			−0.953412	+	0.301672i	$0.902455\pi$
$860$	12320.2	−	21339.2i	0.488507	−	0.846119i
$861$	−15711.3	+	27212.8i	−0.621883	+	1.07713i
$862$	−10601.2	−	18361.9i	−0.418885	−	0.725530i
$863$	3572.64			0.140920			0.0704601	−	0.997515i	$-0.477553\pi$
$863$	3572.64			0.140920			0.0704601	+	0.997515i	$0.477553\pi$
$864$	−3133.31	−	5427.06i	−0.123377	−	0.213695i
$865$	21774.2	+	37714.0i	0.855890	+	1.48245i
$866$	18459.4			0.724339
$867$	−17377.0	−	30097.8i	−0.680685	−	1.17898i
$868$	9568.32	−	16572.8i	0.374159	−	0.648063i
$869$	−4951.70	+	8576.60i	−0.193297	+	0.334800i
$870$	−12200.5			−0.475443
$871$		0			0
$872$	−7075.45			−0.274777
$873$	6729.68	−	11656.2i	0.260900	−	0.451891i
$874$	−5539.42	+	9594.56i	−0.214387	+	0.371328i
$875$	−9996.72	−	17314.8i	−0.386230	−	0.668969i
$876$	−33677.0			−1.29891
$877$	−1349.92	−	2338.13i	−0.0519767	−	0.0900262i	0.838866	−	0.544337i	$-0.183219\pi$
$877$	−1349.92	−	2338.13i	−0.0519767	−	0.0900262i	−0.890843	+	0.454311i	$0.849885\pi$
$878$	7201.66	+	12473.6i	0.276816	+	0.479459i
$879$	−60518.1			−2.32221
$880$	1076.07	+	1863.81i	0.0412208	+	0.0713965i
$881$	−1991.23	+	3448.91i	−0.0761477	+	0.131892i	−0.901585	−	0.432602i	$-0.857595\pi$
$881$	−1991.23	+	3448.91i	−0.0761477	+	0.131892i	0.825437	+	0.564494i	$0.190929\pi$
$882$	23607.5	−	40889.4i	0.901253	−	1.56102i
$883$	21896.7			0.834523			0.417261	−	0.908787i	$-0.362990\pi$
$883$	21896.7			0.834523			0.417261	+	0.908787i	$0.362990\pi$
$884$		0			0
$885$	50555.0			1.92021
$886$	−3544.70	+	6139.61i	−0.134409	+	0.232804i
$887$	10609.8	−	18376.8i	0.401627	−	0.695638i	−0.592295	−	0.805721i	$-0.701778\pi$
$887$	10609.8	−	18376.8i	0.401627	−	0.695638i	0.993922	+	0.110082i	$0.0351115\pi$
$888$	834.962	+	1446.20i	0.0315535	+	0.0546522i
$889$	53656.7			2.02428
$890$	9574.43	+	16583.4i	0.360602	+	0.624581i
$891$	1793.55	+	3106.52i	0.0674367	+	0.116804i
$892$	−10959.0			−0.411360
$893$	14310.3	+	24786.1i	0.536254	+	0.928820i
$894$	16760.2	−	29029.5i	0.627007	−	1.08601i
$895$	−16392.2	+	28392.1i	−0.612212	+	1.06038i
$896$	3667.25			0.136735
$897$		0			0
$898$	36650.7			1.36197
$899$	4112.54	−	7123.13i	0.152571	−	0.264260i
$900$	−7484.41	+	12963.4i	−0.277201	+	0.480125i
$901$	6131.74	+	10620.5i	0.226724	+	0.392697i
$902$	2382.37			0.0879428
$903$	54440.6	+	94293.8i	2.00628	+	3.47497i
$904$	−528.818	−	915.940i	−0.0194560	−	0.0336988i
$905$	−23661.5			−0.869101
$906$	17790.2	+	30813.6i	0.652363	+	1.12993i
$907$	21436.8	−	37129.7i	0.784783	−	1.35928i	−0.144346	−	0.989527i	$-0.546108\pi$
$907$	21436.8	−	37129.7i	0.784783	−	1.35928i	0.929129	−	0.369756i	$-0.120559\pi$
$908$	−9059.50	+	15691.5i	−0.331112	+	0.573503i
$909$	−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	$0.323572\pi$
$912$	10759.0	−	18635.2i	0.390644	−	0.676616i
$913$	1487.17	−	2575.86i	0.0539083	−	0.0933718i
$914$	−5383.84	−	9325.08i	−0.194838	−	0.337468i
$915$	74773.6			2.70157
$916$	1735.78	+	3006.46i	0.0626112	+	0.108446i
$917$	−26504.7	−	45907.5i	−0.954484	−	1.65321i
$918$	11989.0			0.431042
$919$	−1367.51	−	2368.60i	−0.0490860	−	0.0850194i	0.840438	−	0.541907i	$-0.182298\pi$
$919$	−1367.51	−	2368.60i	−0.0490860	−	0.0850194i	−0.889524	+	0.456888i	$0.848964\pi$
$920$	−2040.44	+	3534.14i	−0.0731210	+	0.126649i
$921$	−38366.2	+	66452.2i	−1.37265	+	2.37749i
$922$	21242.3			0.758760
$923$		0			0
$924$	−9509.87			−0.338584
$925$	904.449	−	1566.55i	0.0321493	−	0.0556842i
$926$	10407.3	−	18025.9i	0.369334	−	0.639706i
$927$	7789.85	+	13492.4i	0.276000	+	0.478047i
$928$	1576.21			0.0557562
$929$	−7545.90	−	13069.9i	−0.266494	−	0.461581i	0.701460	−	0.712709i	$-0.252532\pi$
$929$	−7545.90	−	13069.9i	−0.266494	−	0.461581i	−0.967954	+	0.251128i	$0.919199\pi$
$930$	−20680.3	−	35819.4i	−0.729178	−	1.26297i
$931$	73521.3			2.58814
$932$	−1070.28	−	1853.77i	−0.0376159	−	0.0651527i
$933$	−9603.45	+	16633.7i	−0.336980	+	0.583667i
$934$	−15784.0	+	27338.7i	−0.552965	+	0.957763i
$935$	−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	$0.619150\pi$
$938$	8238.36	−	14269.3i	0.286772	−	0.496703i
$939$	−22082.0	+	38247.2i	−0.767433	+	1.32923i
$940$	5271.17	+	9129.94i	0.182901	+	0.316793i
$941$	−886.927			−0.0307258			−0.0153629	−	0.999882i	$-0.504890\pi$
$941$	−886.927			−0.0307258			−0.0153629	+	0.999882i	$0.504890\pi$
$942$	5379.11	+	9316.89i	0.186052	+	0.322251i
$943$	2258.73	+	3912.23i	0.0780002	+	0.135100i
$944$	−6531.32			−0.225187
$945$	−39747.4	−	68844.6i	−1.36824	−	2.36986i
$946$	4127.52	−	7149.08i	0.141858	−	0.245705i
$947$	−21670.7	+	37534.7i	−0.743613	+	1.28798i	0.207226	+	0.978293i	$0.433556\pi$
$947$	−21670.7	+	37534.7i	−0.743613	+	1.28798i	−0.950840	+	0.309683i	$0.899777\pi$
$948$	36473.5			1.24958
$949$		0			0
$950$	−23308.9			−0.796041
$951$	−8259.80	+	14306.4i	−0.281643	+	0.487820i
$952$	−3508.00	+	6076.04i	−0.119428	+	0.206855i
$953$	−8007.43	−	13869.3i	−0.272178	−	0.471427i	0.697241	−	0.716837i	$-0.254411\pi$
$953$	−8007.43	−	13869.3i	−0.272178	−	0.471427i	−0.969419	+	0.245410i	$0.921077\pi$
$954$	39585.5			1.34343
$955$	−27098.8	−	46936.4i	−0.918215	−	1.59040i
$956$	2293.46	+	3972.39i	0.0775898	+	0.134389i
$957$	−4087.42			−0.138064
$958$	−18263.7	−	31633.7i	−0.615943	−	1.06685i
$959$	13857.8	−	24002.5i	0.466624	−	0.808217i
$960$	3963.08	−	6864.25i	0.133237	−	0.230774i
$961$	−1907.30			−0.0640227
$962$		0			0
$963$	104802.			3.50695
$964$	6706.06	−	11615.2i	0.224054	−	0.388072i
$965$	6438.40	−	11151.6i	0.214777	−	0.372004i
$966$	−9016.29	−	15616.7i	−0.300305	−	0.520143i
$967$	7986.48			0.265592			0.132796	−	0.991143i	$-0.457604\pi$
$967$	7986.48			0.265592			0.132796	+	0.991143i	$0.457604\pi$
$968$	−4963.49	−	8597.03i	−0.164807	−	0.285453i
$969$	20583.7	+	35652.0i	0.682397	+	1.18195i
$970$	7720.00			0.255540
$971$	−12622.7	−	21863.2i	−0.417180	−	0.722578i	0.578474	−	0.815701i	$-0.303648\pi$
$971$	−12622.7	−	21863.2i	−0.417180	−	0.722578i	−0.995655	+	0.0931229i	$0.970315\pi$
$972$	−3969.44	+	6875.27i	−0.130987	+	0.226877i
$973$	−1484.05	+	2570.45i	−0.0488966	+	0.0846914i
$974$	10738.0			0.353253
$975$		0			0
$976$	−9660.19			−0.316819
$977$	2615.88	−	4530.83i	0.0856595	−	0.148367i	−0.820013	−	0.572346i	$-0.806034\pi$
$977$	2615.88	−	4530.83i	0.0856595	−	0.148367i	0.905672	+	0.423979i	$0.139367\pi$
$978$	10140.3	−	17563.5i	0.331545	−	0.574252i
$979$	3207.63	+	5555.78i	0.104715	+	0.181372i
$980$	27081.5			0.882740
$981$	−21847.2	−	37840.5i	−0.711038	−	1.23155i
$982$	−1491.33	−	2583.07i	−0.0484627	−	0.0839399i
$983$	22720.8			0.737212			0.368606	−	0.929586i	$-0.379835\pi$
$983$	22720.8			0.737212			0.368606	+	0.929586i	$0.379835\pi$
$984$	−4387.05	−	7598.59i	−0.142128	−	0.246173i
$985$	9476.38	−	16413.6i	0.306541	−	0.530944i
$986$	−1507.77	+	2611.53i	−0.0486989	+	0.0843490i
$987$	−46584.5			−1.50233
$988$		0			0
$989$	15653.2			0.503279
$990$	−6645.27	+	11509.9i	−0.213334	+	0.369505i
$991$	−9502.55	+	16458.9i	−0.304600	+	0.527582i	−0.977172	−	0.212449i	$-0.931856\pi$
$991$	−9502.55	+	16458.9i	−0.304600	+	0.527582i	0.672572	+	0.740031i	$0.265189\pi$
$992$	2671.75	+	4627.60i	0.0855121	+	0.148111i
$993$	−22284.0			−0.712148
$994$	27556.0	+	47728.5i	0.879300	+	1.52299i
$995$	−8108.51	−	14044.4i	−0.258349	−	0.447473i
$996$	−10954.3			−0.348494
$997$	−24621.6	−	42645.9i	−0.782121	−	1.35467i	−0.930704	−	0.365773i	$-0.880805\pi$
$997$	−24621.6	−	42645.9i	−0.782121	−	1.35467i	0.148583	−	0.988900i	$-0.452529\pi$
$998$	−10067.4	+	17437.2i	−0.319316	+	0.553072i
$999$	−2338.31	+	4050.07i	−0.0740549	+	0.128267i

Twists

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

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

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} +(4.37047 - 7.56988i) q^{3} +(-2.00000 - 3.46410i) q^{4} +14.1685 q^{5} +(-8.74094 - 15.1398i) q^{6} +(14.3252 + 24.8120i) q^{7} -8.00000 q^{8} +(-24.7020 - 42.7851i) q^{9} +(14.1685 - 24.5406i) q^{10} +(4.74674 - 8.22160i) q^{11} -34.9638 q^{12} +57.3008 q^{14} +(61.9231 - 107.254i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-15.3052 - 26.5094i) q^{17} -98.8080 q^{18} +(-76.9300 - 133.247i) q^{19} +(-28.3370 - 49.0812i) q^{20} +250.431 q^{21} +(-9.49349 - 16.4432i) q^{22} +(18.0015 - 31.1795i) q^{23} +(-34.9638 + 60.5590i) q^{24} +75.7470 q^{25} -195.832 q^{27} +(57.3008 - 99.2479i) q^{28} +(24.6283 - 42.6575i) q^{29} +(-123.846 - 214.508i) q^{30} +166.984 q^{31} +(16.0000 + 27.7128i) q^{32} +(-41.4910 - 71.8645i) q^{33} -61.2209 q^{34} +(202.967 + 351.549i) q^{35} +(-98.8080 + 171.141i) q^{36} +(11.9404 - 20.6814i) q^{37} -307.720 q^{38} -113.348 q^{40} +(-62.7371 + 108.664i) q^{41} +(250.431 - 433.760i) q^{42} +(217.387 + 376.526i) q^{43} -37.9739 q^{44} +(-349.991 - 606.202i) q^{45} +(-36.0030 - 62.3591i) q^{46} -186.017 q^{47} +(69.9275 + 121.118i) q^{48} +(-238.923 + 413.826i) q^{49} +(75.7470 - 131.198i) q^{50} -267.564 q^{51} -400.631 q^{53} +(-195.832 + 339.191i) q^{54} +(67.2543 - 116.488i) q^{55} +(-114.602 - 198.496i) q^{56} -1344.88 q^{57} +(-49.2567 - 85.3151i) q^{58} +(204.104 + 353.518i) q^{59} -495.385 q^{60} +(301.881 + 522.873i) q^{61} +(166.984 - 289.225i) q^{62} +(707.722 - 1225.81i) q^{63} +64.0000 q^{64} -165.964 q^{66} +(143.774 - 249.024i) q^{67} +(-61.2209 + 106.038i) q^{68} +(-157.350 - 272.538i) q^{69} +811.868 q^{70} +(480.901 + 832.946i) q^{71} +(197.616 + 342.281i) q^{72} +963.198 q^{73} +(-23.8808 - 41.3627i) q^{74} +(331.050 - 573.396i) q^{75} +(-307.720 + 532.986i) q^{76} +271.992 q^{77} -1043.18 q^{79} +(-113.348 + 196.325i) q^{80} +(-188.924 + 327.226i) q^{81} +(125.474 + 217.328i) q^{82} +313.304 q^{83} +(-500.863 - 867.520i) q^{84} +(-216.852 - 375.599i) q^{85} +869.549 q^{86} +(-215.275 - 372.867i) q^{87} +(-37.9739 + 65.7728i) q^{88} +(-337.877 + 585.220i) q^{89} -1399.96 q^{90} -144.012 q^{92} +(729.799 - 1264.05i) q^{93} +(-186.017 + 322.191i) q^{94} +(-1089.98 - 1887.91i) q^{95} +279.710 q^{96} +(136.217 + 235.935i) q^{97} +(477.845 + 827.653i) q^{98} -469.016 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 12 q^{3} - 12 q^{4} + 24 q^{5} - 24 q^{6} + 27 q^{7} - 48 q^{8} - 9 q^{9} + 24 q^{10} - 82 q^{11} - 96 q^{12} + 108 q^{14} + 90 q^{15} - 48 q^{16} + 90 q^{17} - 36 q^{18} - 130 q^{19} - 48 q^{20}+ \cdots - 4114 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 12 * q^3 - 12 * q^4 + 24 * q^5 - 24 * q^6 + 27 * q^7 - 48 * q^8 - 9 * q^9 + 24 * q^10 - 82 * q^11 - 96 * q^12 + 108 * q^14 + 90 * q^15 - 48 * q^16 + 90 * q^17 - 36 * q^18 - 130 * q^19 - 48 * q^20 + 468 * q^21 + 164 * q^22 - 19 * q^23 - 96 * q^24 - 122 * q^25 - 138 * q^27 + 108 * q^28 + 101 * q^29 - 180 * q^30 + 1038 * q^31 + 96 * q^32 + 146 * q^33 + 360 * q^34 + 458 * q^35 - 36 * q^36 - 84 * q^37 - 520 * q^38 - 192 * q^40 - 187 * q^41 + 468 * q^42 + 1205 * q^43 + 656 * q^44 - 645 * q^45 + 38 * q^46 - 1072 * q^47 + 192 * q^48 + 184 * q^49 - 122 * q^50 - 414 * q^51 - 2190 * q^53 - 138 * q^54 + 526 * q^55 - 216 * q^56 - 2818 * q^57 - 202 * q^58 + 1413 * q^59 - 720 * q^60 + 1108 * q^61 + 1038 * q^62 + 1404 * q^63 + 384 * q^64 + 584 * q^66 + 1605 * q^67 + 360 * q^68 + 314 * q^69 + 1832 * q^70 + 909 * q^71 + 72 * q^72 + 574 * q^73 + 168 * q^74 + 505 * q^75 - 520 * q^76 + 960 * q^77 - 3922 * q^79 - 192 * q^80 - 915 * q^81 + 374 * q^82 + 382 * q^83 - 936 * q^84 - 67 * q^85 + 4820 * q^86 - 1636 * q^87 + 656 * q^88 - 1091 * q^89 - 2580 * q^90 + 152 * q^92 + 1614 * q^93 - 1072 * q^94 - 1829 * q^95 + 768 * q^96 + 947 * q^97 - 368 * q^98 - 4114 * q^99

Introduction

L-functions

Modular forms

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Database

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