LMFDB - Embedded newform 135.4.e.b.46.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,4,Mod(46,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 0]))

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

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

chi := DirichletCharacter("135.46");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	135.e (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:	$7.96525785077$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.15759792.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 16x^{4} - 27x^{3} + 52x^{2} - 39x + 9 $ x^6 - 3x^5 + 16x^4 - 27x^3 + 52x^2 - 39*x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{3} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			46.3
Root			$0.500000 - 0.0378788i$ of defining polynomial
Character	$\chi$	$=$	135.46
Dual form			135.4.e.b.91.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.87428 - 3.24635i) q^{2} +(-3.02587 - 5.24096i) q^{4} +(2.50000 + 4.33013i) q^{5} +(15.6746 - 27.1492i) q^{7} +7.30318 q^{8} +O(q^{10})$	\(q+(1.87428 - 3.24635i) q^{2} +(-3.02587 - 5.24096i) q^{4} +(2.50000 + 4.33013i) q^{5} +(15.6746 - 27.1492i) q^{7} +7.30318 q^{8} +18.7428 q^{10} +(-10.4166 + 18.0422i) q^{11} +(-29.9655 - 51.9018i) q^{13} +(-58.7572 - 101.770i) q^{14} +(37.8952 - 65.6364i) q^{16} +74.0460 q^{17} -63.8390 q^{19} +(15.1294 - 26.2048i) q^{20} +(39.0475 + 67.6322i) q^{22} +(-16.4247 - 28.4484i) q^{23} +(-12.5000 + 21.6506i) q^{25} -224.655 q^{26} -189.717 q^{28} +(-80.0044 + 138.572i) q^{29} +(127.187 + 220.294i) q^{31} +(-112.840 - 195.444i) q^{32} +(138.783 - 240.379i) q^{34} +156.746 q^{35} +215.365 q^{37} +(-119.652 + 207.244i) q^{38} +(18.2579 + 31.6237i) q^{40} +(70.8407 + 122.700i) q^{41} +(-68.9529 + 119.430i) q^{43} +126.078 q^{44} -123.138 q^{46} +(16.7895 - 29.0803i) q^{47} +(-319.885 - 554.058i) q^{49} +(46.8571 + 81.1588i) q^{50} +(-181.344 + 314.096i) q^{52} +41.9914 q^{53} -104.166 q^{55} +(114.474 - 198.275i) q^{56} +(299.902 + 519.445i) q^{58} +(307.571 + 532.728i) q^{59} +(67.1535 - 116.313i) q^{61} +953.535 q^{62} -239.652 q^{64} +(149.828 - 259.509i) q^{65} +(428.767 + 742.646i) q^{67} +(-224.054 - 388.072i) q^{68} +(293.786 - 508.852i) q^{70} -588.665 q^{71} -618.191 q^{73} +(403.655 - 699.152i) q^{74} +(193.169 + 334.578i) q^{76} +(326.553 + 565.607i) q^{77} +(172.644 - 299.029i) q^{79} +378.952 q^{80} +531.102 q^{82} +(-546.584 + 946.711i) q^{83} +(185.115 + 320.629i) q^{85} +(258.474 + 447.691i) q^{86} +(-76.0746 + 131.765i) q^{88} -414.849 q^{89} -1878.79 q^{91} +(-99.3979 + 172.162i) q^{92} +(-62.9366 - 109.009i) q^{94} +(-159.598 - 276.431i) q^{95} +(100.705 - 174.427i) q^{97} -2398.22 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - q^{2} - 11 q^{4} + 15 q^{5} + 43 q^{7} + 54 q^{8}+O(q^{10}) $ 6 * q - q^2 - 11 * q^4 + 15 * q^5 + 43 * q^7 + 54 * q^8	$ 6 q - q^{2} - 11 q^{4} + 15 q^{5} + 43 q^{7} + 54 q^{8} - 10 q^{10} + 14 q^{11} - 40 q^{13} - 27 q^{14} + 13 q^{16} + 332 q^{17} - 328 q^{19} + 55 q^{20} + 376 q^{22} + 171 q^{23} - 75 q^{25} - 868 q^{26} - 1034 q^{28} - 335 q^{29} + 352 q^{31} - 77 q^{32} + 52 q^{34} + 430 q^{35} + 804 q^{37} - 178 q^{38} + 135 q^{40} + 187 q^{41} + 602 q^{43} - 1964 q^{44} - 402 q^{46} + 665 q^{47} - 430 q^{49} - 25 q^{50} + 456 q^{52} + 1460 q^{53} + 140 q^{55} + 705 q^{56} - 217 q^{58} - 298 q^{59} + 1439 q^{61} + 3228 q^{62} - 3138 q^{64} + 200 q^{65} + 1849 q^{67} - 710 q^{68} + 135 q^{70} - 140 q^{71} - 736 q^{73} - 320 q^{74} - 204 q^{76} - 948 q^{77} + 382 q^{79} + 130 q^{80} - 1150 q^{82} - 831 q^{83} + 830 q^{85} + 1580 q^{86} + 1428 q^{88} - 3438 q^{89} - 1420 q^{91} - 1623 q^{92} + 2077 q^{94} - 820 q^{95} + 282 q^{97} - 4328 q^{98}+O(q^{100}) $ 6 * q - q^2 - 11 * q^4 + 15 * q^5 + 43 * q^7 + 54 * q^8 - 10 * q^10 + 14 * q^11 - 40 * q^13 - 27 * q^14 + 13 * q^16 + 332 * q^17 - 328 * q^19 + 55 * q^20 + 376 * q^22 + 171 * q^23 - 75 * q^25 - 868 * q^26 - 1034 * q^28 - 335 * q^29 + 352 * q^31 - 77 * q^32 + 52 * q^34 + 430 * q^35 + 804 * q^37 - 178 * q^38 + 135 * q^40 + 187 * q^41 + 602 * q^43 - 1964 * q^44 - 402 * q^46 + 665 * q^47 - 430 * q^49 - 25 * q^50 + 456 * q^52 + 1460 * q^53 + 140 * q^55 + 705 * q^56 - 217 * q^58 - 298 * q^59 + 1439 * q^61 + 3228 * q^62 - 3138 * q^64 + 200 * q^65 + 1849 * q^67 - 710 * q^68 + 135 * q^70 - 140 * q^71 - 736 * q^73 - 320 * q^74 - 204 * q^76 - 948 * q^77 + 382 * q^79 + 130 * q^80 - 1150 * q^82 - 831 * q^83 + 830 * q^85 + 1580 * q^86 + 1428 * q^88 - 3438 * q^89 - 1420 * q^91 - 1623 * q^92 + 2077 * q^94 - 820 * q^95 + 282 * q^97 - 4328 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/135\mathbb{Z}\right)^\times$.

$n$	$56$	$82$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	1.87428	−	3.24635i	0.662659	−	1.14776i	−0.317255	−	0.948340i	$-0.602761\pi$
$2$	1.87428	−	3.24635i	0.662659	−	1.14776i	0.979914	−	0.199419i	$-0.0639054\pi$
$3$		0			0
$3$		0			0
$4$	−3.02587	−	5.24096i	−0.378234	−	0.655120i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$		0			0
$7$	15.6746	−	27.1492i	0.846348	−	1.46592i	−0.0380969	−	0.999274i	$-0.512130\pi$
$7$	15.6746	−	27.1492i	0.846348	−	1.46592i	0.884445	−	0.466644i	$-0.154537\pi$
$8$	7.30318			0.322758
$9$		0			0
$10$	18.7428			0.592700
$11$	−10.4166	+	18.0422i	−0.285522	+	0.494538i	−0.972736	−	0.231917i	$-0.925500\pi$
$11$	−10.4166	+	18.0422i	−0.285522	+	0.494538i	0.687214	+	0.726455i	$0.258834\pi$
$12$		0			0
$13$	−29.9655	−	51.9018i	−0.639303	−	1.10731i	−0.985586	−	0.169175i	$-0.945890\pi$
$13$	−29.9655	−	51.9018i	−0.639303	−	1.10731i	0.346283	−	0.938130i	$-0.387444\pi$
$14$	−58.7572	−	101.770i	−1.12168	−	1.94281i
$15$		0			0
$16$	37.8952	−	65.6364i	0.592112	−	1.02557i
$17$	74.0460			1.05640			0.528200	−	0.849120i	$-0.322867\pi$
$17$	74.0460			1.05640			0.528200	+	0.849120i	$0.322867\pi$
$18$		0			0
$19$	−63.8390			−0.770825			−0.385413	−	0.922744i	$-0.625941\pi$
$19$	−63.8390			−0.770825			−0.385413	+	0.922744i	$0.625941\pi$
$20$	15.1294	−	26.2048i	0.169151	−	0.292979i
$21$		0			0
$22$	39.0475	+	67.6322i	0.378407	+	0.655420i
$23$	−16.4247	−	28.4484i	−0.148904	−	0.257909i	0.781919	−	0.623380i	$-0.214241\pi$
$23$	−16.4247	−	28.4484i	−0.148904	−	0.257909i	−0.930823	+	0.365472i	$0.880908\pi$
$24$		0			0
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−224.655			−1.69456
$27$		0			0
$28$	−189.717			−1.28047
$29$	−80.0044	+	138.572i	−0.512291	+	0.887314i	0.487607	+	0.873063i	$0.337870\pi$
$29$	−80.0044	+	138.572i	−0.512291	+	0.887314i	−0.999898	+	0.0142513i	$0.995464\pi$
$30$		0			0
$31$	127.187	+	220.294i	0.736884	+	1.27632i	0.953892	+	0.300151i	$0.0970371\pi$
$31$	127.187	+	220.294i	0.736884	+	1.27632i	−0.217007	+	0.976170i	$0.569630\pi$
$32$	−112.840	−	195.444i	−0.623358	−	1.07969i
$33$		0			0
$34$	138.783	−	240.379i	0.700033	−	1.21249i
$35$	156.746			0.756997
$36$		0			0
$37$	215.365			0.956914			0.478457	−	0.878111i	$-0.341196\pi$
$37$	215.365			0.956914			0.478457	+	0.878111i	$0.341196\pi$
$38$	−119.652	+	207.244i	−0.510794	+	0.884722i
$39$		0			0
$40$	18.2579	+	31.6237i	0.0721708	+	0.125004i
$41$	70.8407	+	122.700i	0.269841	+	0.467377i	0.968820	−	0.247764i	$-0.0796957\pi$
$41$	70.8407	+	122.700i	0.269841	+	0.467377i	−0.698980	+	0.715141i	$0.746362\pi$
$42$		0			0
$43$	−68.9529	+	119.430i	−0.244540	+	0.423556i	−0.962002	−	0.273042i	$-0.911970\pi$
$43$	−68.9529	+	119.430i	−0.244540	+	0.423556i	0.717462	+	0.696597i	$0.245304\pi$
$44$	126.078			0.431976
$45$		0			0
$46$	−123.138			−0.394689
$47$	16.7895	−	29.0803i	0.0521064	−	0.0902509i	−0.838796	−	0.544446i	$-0.816740\pi$
$47$	16.7895	−	29.0803i	0.0521064	−	0.0902509i	0.890902	+	0.454195i	$0.150073\pi$
$48$		0			0
$49$	−319.885	−	554.058i	−0.932611	−	1.61533i
$50$	46.8571	+	81.1588i	0.132532	+	0.229552i
$51$		0			0
$52$	−181.344	+	314.096i	−0.483612	+	0.837641i
$53$	41.9914			0.108829			0.0544147	−	0.998518i	$-0.482671\pi$
$53$	41.9914			0.108829			0.0544147	+	0.998518i	$0.482671\pi$
$54$		0			0
$55$	−104.166			−0.255378
$56$	114.474	−	198.275i	0.273166	−	0.473137i
$57$		0			0
$58$	299.902	+	519.445i	0.678949	+	1.17597i
$59$	307.571	+	532.728i	0.678683	+	1.17551i	0.975378	+	0.220541i	$0.0707824\pi$
$59$	307.571	+	532.728i	0.678683	+	1.17551i	−0.296694	+	0.954973i	$0.595884\pi$
$60$		0			0
$61$	67.1535	−	116.313i	0.140953	−	0.244137i	−0.786903	−	0.617077i	$-0.788317\pi$
$61$	67.1535	−	116.313i	0.140953	−	0.244137i	0.927856	+	0.372939i	$0.121650\pi$
$62$	953.535			1.95321
$63$		0			0
$64$	−239.652			−0.468071
$65$	149.828	−	259.509i	0.285905	−	0.495202i
$66$		0			0
$67$	428.767	+	742.646i	0.781824	+	1.35416i	0.930878	+	0.365329i	$0.119044\pi$
$67$	428.767	+	742.646i	0.781824	+	1.35416i	−0.149055	+	0.988829i	$0.547623\pi$
$68$	−224.054	−	388.072i	−0.399566	−	0.692069i
$69$		0			0
$70$	293.786	−	508.852i	0.501631	−	0.868850i
$71$	−588.665			−0.983968			−0.491984	−	0.870604i	$-0.663728\pi$
$71$	−588.665			−0.983968			−0.491984	+	0.870604i	$0.663728\pi$
$72$		0			0
$73$	−618.191			−0.991148			−0.495574	−	0.868566i	$-0.665042\pi$
$73$	−618.191			−0.991148			−0.495574	+	0.868566i	$0.665042\pi$
$74$	403.655	−	699.152i	0.634108	−	1.09831i
$75$		0			0
$76$	193.169	+	334.578i	0.291552	+	0.504983i
$77$	326.553	+	565.607i	0.483301	+	0.837103i
$78$		0			0
$79$	172.644	−	299.029i	0.245873	−	0.425865i	−0.716503	−	0.697584i	$-0.754259\pi$
$79$	172.644	−	299.029i	0.245873	−	0.425865i	0.962377	+	0.271718i	$0.0875919\pi$
$80$	378.952			0.529601
$81$		0			0
$82$	531.102			0.715249
$83$	−546.584	+	946.711i	−0.722836	+	1.25199i	0.237023	+	0.971504i	$0.423828\pi$
$83$	−546.584	+	946.711i	−0.722836	+	1.25199i	−0.959859	+	0.280484i	$0.909505\pi$
$84$		0			0
$85$	185.115	+	320.629i	0.236218	+	0.409142i
$86$	258.474	+	447.691i	0.324093	+	0.561346i
$87$		0			0
$88$	−76.0746	+	131.765i	−0.0921543	+	0.159616i
$89$	−414.849			−0.494089			−0.247045	−	0.969004i	$-0.579459\pi$
$89$	−414.849			−0.494089			−0.247045	+	0.969004i	$0.579459\pi$
$90$		0			0
$91$	−1878.79			−2.16429
$92$	−99.3979	+	172.162i	−0.112641	+	0.195100i
$93$		0			0
$94$	−62.9366	−	109.009i	−0.0690576	−	0.119611i
$95$	−159.598	−	276.431i	−0.172362	−	0.298539i
$96$		0			0
$97$	100.705	−	174.427i	0.105413	−	0.182581i	−0.808494	−	0.588505i	$-0.799717\pi$
$97$	100.705	−	174.427i	0.105413	−	0.182581i	0.913907	+	0.405924i	$0.133050\pi$
$98$	−2398.22			−2.47201
$99$		0			0
$100$	151.294			0.151294
$101$	132.691	−	229.828i	0.130726	−	0.226424i	−0.793231	−	0.608921i	$-0.791603\pi$
$101$	132.691	−	229.828i	0.130726	−	0.226424i	0.923957	+	0.382498i	$0.124936\pi$
$102$		0			0
$103$	263.809	+	456.931i	0.252368	+	0.437114i	0.964177	−	0.265259i	$-0.0854574\pi$
$103$	263.809	+	456.931i	0.252368	+	0.437114i	−0.711810	+	0.702373i	$0.752124\pi$
$104$	−218.843	−	379.048i	−0.206340	−	0.357391i
$105$		0			0
$106$	78.7038	−	136.319i	0.0721168	−	0.124910i
$107$	−2084.24			−1.88310			−0.941549	−	0.336877i	$-0.890629\pi$
$107$	−2084.24			−1.88310			−0.941549	+	0.336877i	$0.890629\pi$
$108$		0			0
$109$	925.651			0.813406			0.406703	−	0.913560i	$-0.366678\pi$
$109$	925.651			0.813406			0.406703	+	0.913560i	$0.366678\pi$
$110$	−195.237	+	338.161i	−0.169229	+	0.293113i
$111$		0			0
$112$	−1187.98	−	2057.65i	−1.00227	−	1.73598i
$113$	273.009	+	472.866i	0.227279	+	0.393659i	0.957001	−	0.290085i	$-0.0936836\pi$
$113$	273.009	+	472.866i	0.227279	+	0.393659i	−0.729721	+	0.683745i	$0.760350\pi$
$114$		0			0
$115$	82.1234	−	142.242i	0.0665917	−	0.115340i
$116$	968.332			0.775063
$117$		0			0
$118$	2305.90			1.79894
$119$	1160.64	−	2010.29i	0.894082	−	1.54860i
$120$		0			0
$121$	448.487	+	776.802i	0.336955	+	0.583623i
$122$	−251.729	−	436.008i	−0.186807	−	0.323560i
$123$		0			0
$124$	769.701	−	1333.16i	0.557429	−	0.965495i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	−975.972			−0.681918			−0.340959	−	0.940078i	$-0.610752\pi$
$127$	−975.972			−0.681918			−0.340959	+	0.940078i	$0.610752\pi$
$128$	453.543	−	785.559i	0.313187	−	0.542455i
$129$		0			0
$130$	−561.639	−	972.786i	−0.378915	−	0.656300i
$131$	−814.614	−	1410.95i	−0.543307	−	0.941035i	−0.998711	−	0.0507502i	$-0.983839\pi$
$131$	−814.614	−	1410.95i	−0.543307	−	0.941035i	0.455405	−	0.890285i	$-0.349495\pi$
$132$		0			0
$133$	−1000.65	+	1733.18i	−0.652387	+	1.12997i
$134$	3214.52			2.07233
$135$		0			0
$136$	540.771			0.340961
$137$	330.725	−	572.833i	0.206246	−	0.357229i	−0.744283	−	0.667865i	$-0.767208\pi$
$137$	330.725	−	572.833i	0.206246	−	0.357229i	0.950529	+	0.310635i	$0.100542\pi$
$138$		0			0
$139$	−691.495	−	1197.70i	−0.421955	−	0.730848i	0.574175	−	0.818732i	$-0.305323\pi$
$139$	−691.495	−	1197.70i	−0.421955	−	0.730848i	−0.996131	+	0.0878842i	$0.971989\pi$
$140$	−474.293	−	821.499i	−0.286322	−	0.495924i
$141$		0			0
$142$	−1103.33	+	1911.02i	−0.652035	+	1.12936i
$143$	1248.56			0.730139
$144$		0			0
$145$	−800.044			−0.458207
$146$	−1158.66	+	2006.87i	−0.656793	+	1.13760i
$147$		0			0
$148$	−651.667	−	1128.72i	−0.361937	−	0.626894i
$149$	1581.75	+	2739.66i	0.869676	+	1.50632i	0.862328	+	0.506349i	$0.169005\pi$
$149$	1581.75	+	2739.66i	0.869676	+	1.50632i	0.00734719	+	0.999973i	$0.497661\pi$
$150$		0			0
$151$	1279.40	−	2215.98i	0.689509	−	1.19427i	−0.282488	−	0.959271i	$-0.591160\pi$
$151$	1279.40	−	2215.98i	0.689509	−	1.19427i	0.971997	−	0.234994i	$-0.0755071\pi$
$152$	−466.228			−0.248790
$153$		0			0
$154$	2448.21			1.28106
$155$	−635.934	+	1101.47i	−0.329545	+	0.570788i
$156$		0			0
$157$	−1750.48	−	3031.92i	−0.889832	−	1.54123i	−0.840073	−	0.542474i	$-0.817488\pi$
$157$	−1750.48	−	3031.92i	−0.889832	−	1.54123i	−0.0497594	−	0.998761i	$-0.515845\pi$
$158$	−647.168	−	1120.93i	−0.325860	−	0.564407i
$159$		0			0
$160$	564.199	−	977.222i	0.278774	−	0.482851i
$161$	−1029.80			−0.504097
$162$		0			0
$163$	263.950			0.126835			0.0634176	−	0.997987i	$-0.479800\pi$
$163$	263.950			0.126835			0.0634176	+	0.997987i	$0.479800\pi$
$164$	428.710	−	742.547i	0.204126	−	0.353556i
$165$		0			0
$166$	2048.90	+	3548.81i	0.957987	+	1.65928i
$167$	−1794.53	−	3108.21i	−0.831524	−	1.44024i	−0.896829	−	0.442377i	$-0.854135\pi$
$167$	−1794.53	−	3108.21i	−0.831524	−	1.44024i	0.0653054	−	0.997865i	$-0.479198\pi$
$168$		0			0
$169$	−697.365	+	1207.87i	−0.317417	+	0.549782i
$170$	1387.83			0.626128
$171$		0			0
$172$	834.570			0.369973
$173$	185.228	−	320.824i	0.0814024	−	0.140993i	−0.822450	−	0.568837i	$-0.807393\pi$
$173$	185.228	−	320.824i	0.0814024	−	0.140993i	0.903853	+	0.427844i	$0.140727\pi$
$174$		0			0
$175$	391.865	+	678.730i	0.169270	+	0.293184i
$176$	789.482	+	1367.42i	0.338122	+	0.585644i
$177$		0			0
$178$	−777.545	+	1346.75i	−0.327413	+	0.567095i
$179$	−446.898			−0.186607			−0.0933036	−	0.995638i	$-0.529743\pi$
$179$	−446.898			−0.186607			−0.0933036	+	0.995638i	$0.529743\pi$
$180$		0			0
$181$	−904.046			−0.371255			−0.185628	−	0.982620i	$-0.559432\pi$
$181$	−904.046			−0.371255			−0.185628	+	0.982620i	$0.559432\pi$
$182$	−3521.38	+	6099.21i	−1.43419	+	2.48409i
$183$		0			0
$184$	−119.952	−	207.764i	−0.0480598	−	0.0832420i
$185$	538.413	+	932.559i	0.213973	+	0.370611i
$186$		0			0
$187$	−771.311	+	1335.95i	−0.301625	+	0.522430i
$188$	−203.211			−0.0788336
$189$		0			0
$190$	−1196.52			−0.456868
$191$	−299.793	+	519.257i	−0.113572	+	0.196713i	−0.917208	−	0.398409i	$-0.869563\pi$
$191$	−299.793	+	519.257i	−0.113572	+	0.196713i	0.803636	+	0.595121i	$0.202896\pi$
$192$		0			0
$193$	2206.87	+	3822.40i	0.823076	+	1.42561i	0.903381	+	0.428839i	$0.141077\pi$
$193$	2206.87	+	3822.40i	0.823076	+	1.42561i	−0.0803048	+	0.996770i	$0.525589\pi$
$194$	−377.500	−	653.850i	−0.139706	−	0.241978i
$195$		0			0
$196$	−1935.86	+	3353.01i	−0.705490	+	1.22194i
$197$	4807.15			1.73855			0.869277	−	0.494325i	$-0.164585\pi$
$197$	4807.15			1.73855			0.869277	+	0.494325i	$0.164585\pi$
$198$		0			0
$199$	313.833			0.111794			0.0558970	−	0.998437i	$-0.482198\pi$
$199$	313.833			0.111794			0.0558970	+	0.998437i	$0.482198\pi$
$200$	−91.2897	+	158.118i	−0.0322758	+	0.0559033i
$201$		0			0
$202$	−497.403	−	861.527i	−0.173253	−	0.300083i
$203$	2508.07	+	4344.11i	0.867153	+	1.50195i
$204$		0			0
$205$	−354.204	+	613.499i	−0.120676	+	0.209018i
$206$	1977.81			0.668935
$207$		0			0
$208$	−4542.20			−1.51416
$209$	664.989	−	1151.79i	0.220087	−	0.381202i
$210$		0			0
$211$	−1219.41	−	2112.08i	−0.397856	−	0.689106i	0.595605	−	0.803277i	$-0.296912\pi$
$211$	−1219.41	−	2112.08i	−0.397856	−	0.689106i	−0.993461	+	0.114171i	$0.963579\pi$
$212$	−127.061	−	220.075i	−0.0411630	−	0.0712964i
$213$		0			0
$214$	−3906.46	+	6766.19i	−1.24785	+	2.16134i
$215$	−689.529			−0.218723
$216$		0			0
$217$	7974.40			2.49464
$218$	1734.93	−	3004.99i	0.539011	−	0.933594i
$219$		0			0
$220$	315.194	+	545.933i	0.0965927	+	0.167303i
$221$	−2218.83	−	3843.12i	−0.675360	−	1.16976i
$222$		0			0
$223$	1166.71	−	2020.79i	0.350352	−	0.606827i	−0.635959	−	0.771722i	$-0.719395\pi$
$223$	1166.71	−	2020.79i	0.350352	−	0.606827i	0.986311	+	0.164896i	$0.0527288\pi$
$224$	−7074.87			−2.11031
$225$		0			0
$226$	2046.79			0.602435
$227$	−1361.85	+	2358.79i	−0.398189	+	0.689684i	−0.993503	−	0.113810i	$-0.963695\pi$
$227$	−1361.85	+	2358.79i	−0.398189	+	0.689684i	0.595313	+	0.803494i	$0.297028\pi$
$228$		0			0
$229$	1657.08	+	2870.15i	0.478179	+	0.828230i	0.999687	−	0.0250162i	$-0.00796375\pi$
$229$	1657.08	+	2870.15i	0.478179	+	0.828230i	−0.521508	+	0.853246i	$0.674630\pi$
$230$	−307.845	−	533.203i	−0.0882552	−	0.152863i
$231$		0			0
$232$	−584.286	+	1012.01i	−0.165346	+	0.286388i
$233$	3175.44			0.892833			0.446416	−	0.894825i	$-0.352700\pi$
$233$	3175.44			0.892833			0.446416	+	0.894825i	$0.352700\pi$
$234$		0			0
$235$	167.895			0.0466054
$236$	1861.34	−	3223.93i	0.513402	−	0.889238i
$237$		0			0
$238$	−4350.74	−	7535.70i	−1.18494	−	2.05238i
$239$	−123.062	−	213.150i	−0.0333064	−	0.0576884i	0.848892	−	0.528567i	$-0.177270\pi$
$239$	−123.062	−	213.150i	−0.0333064	−	0.0576884i	−0.882198	+	0.470878i	$0.843937\pi$
$240$		0			0
$241$	2643.87	−	4579.31i	0.706666	−	1.22398i	−0.259421	−	0.965764i	$-0.583532\pi$
$241$	2643.87	−	4579.31i	0.706666	−	1.22398i	0.966087	−	0.258217i	$-0.0831349\pi$
$242$	3362.36			0.893144
$243$		0			0
$244$	−812.791			−0.213252
$245$	1599.43	−	2770.29i	0.417076	−	0.722397i
$246$		0			0
$247$	1912.97	+	3313.36i	0.492791	+	0.853539i
$248$	928.867	+	1608.84i	0.237835	+	0.411943i
$249$		0			0
$250$	−234.285	+	405.794i	−0.0592700	+	0.102659i
$251$	−2821.23			−0.709459			−0.354730	−	0.934969i	$-0.615427\pi$
$251$	−2821.23			−0.709459			−0.354730	+	0.934969i	$0.615427\pi$
$252$		0			0
$253$	684.361			0.170061
$254$	−1829.25	+	3168.35i	−0.451879	+	0.782677i
$255$		0			0
$256$	−2658.74	−	4605.08i	−0.649107	−	1.12429i
$257$	−942.096	−	1631.76i	−0.228663	−	0.396056i	0.728749	−	0.684781i	$-0.240102\pi$
$257$	−942.096	−	1631.76i	−0.228663	−	0.396056i	−0.957412	+	0.288725i	$0.906769\pi$
$258$		0			0
$259$	3375.76	−	5846.99i	0.809883	−	1.40276i
$260$	−1813.44			−0.432556
$261$		0			0
$262$	−6107.27			−1.44011
$263$	276.506	−	478.922i	0.0648292	−	0.112287i	−0.831789	−	0.555092i	$-0.812683\pi$
$263$	276.506	−	478.922i	0.0648292	−	0.112287i	0.896618	+	0.442804i	$0.146016\pi$
$264$		0			0
$265$	104.979	+	181.828i	0.0243350	+	0.0421495i
$266$	3751.00	+	6496.93i	0.864620	+	1.49757i
$267$		0			0
$268$	2594.78	−	4494.30i	0.591424	−	1.02438i
$269$	−3363.48			−0.762361			−0.381180	−	0.924501i	$-0.624482\pi$
$269$	−3363.48			−0.762361			−0.381180	+	0.924501i	$0.624482\pi$
$270$		0			0
$271$	−3333.85			−0.747295			−0.373648	−	0.927571i	$-0.621893\pi$
$271$	−3333.85			−0.747295			−0.373648	+	0.927571i	$0.621893\pi$
$272$	2805.99	−	4860.11i	0.625507	−	1.08341i
$273$		0			0
$274$	−1239.75	−	2147.30i	−0.273342	−	0.473443i
$275$	−260.416	−	451.054i	−0.0571043	−	0.0989076i
$276$		0			0
$277$	2693.63	−	4665.50i	0.584275	−	1.01199i	−0.410690	−	0.911775i	$-0.634712\pi$
$277$	2693.63	−	4665.50i	0.584275	−	1.01199i	0.994965	−	0.100220i	$-0.0319546\pi$
$278$	−5184.23			−1.11845
$279$		0			0
$280$	1144.74			0.244327
$281$	1858.35	−	3218.76i	0.394519	−	0.683327i	−0.598521	−	0.801107i	$-0.704245\pi$
$281$	1858.35	−	3218.76i	0.394519	−	0.683327i	0.993040	+	0.117781i	$0.0375779\pi$
$282$		0			0
$283$	−1384.38	−	2397.81i	−0.290787	−	0.503658i	0.683209	−	0.730223i	$-0.260584\pi$
$283$	−1384.38	−	2397.81i	−0.290787	−	0.503658i	−0.973996	+	0.226565i	$0.927250\pi$
$284$	1781.23	+	3085.17i	0.372170	+	0.644617i
$285$		0			0
$286$	2340.16	−	4053.27i	0.483833	−	0.838024i
$287$	4441.60			0.913516
$288$		0			0
$289$	569.810			0.115980
$290$	−1499.51	+	2597.23i	−0.303635	+	0.525911i
$291$		0			0
$292$	1870.57	+	3239.91i	0.374886	+	0.649321i
$293$	−1740.00	−	3013.76i	−0.346934	−	0.600907i	0.638769	−	0.769398i	$-0.279444\pi$
$293$	−1740.00	−	3013.76i	−0.346934	−	0.600907i	−0.985703	+	0.168491i	$0.946110\pi$
$294$		0			0
$295$	−1537.85	+	2663.64i	−0.303516	+	0.525706i
$296$	1572.85			0.308852
$297$		0			0
$298$	11858.6			2.30519
$299$	−984.348	+	1704.94i	−0.190389	+	0.329764i
$300$		0			0
$301$	2161.62	+	3744.03i	0.413932	+	0.716951i
$302$	−4795.91	−	8306.75i	−0.913819	−	1.58278i
$303$		0			0
$304$	−2419.19	+	4190.16i	−0.456415	+	0.790534i
$305$	671.535			0.126072
$306$		0			0
$307$	−1810.36			−0.336555			−0.168278	−	0.985740i	$-0.553821\pi$
$307$	−1810.36			−0.336555			−0.168278	+	0.985740i	$0.553821\pi$
$308$	1976.22	−	3422.91i	0.365602	−	0.633241i
$309$		0			0
$310$	2383.84	+	4128.93i	0.436751	+	0.756476i
$311$	−443.649	−	768.422i	−0.0808907	−	0.140107i	0.822742	−	0.568415i	$-0.192443\pi$
$311$	−443.649	−	768.422i	−0.0808907	−	0.140107i	−0.903633	+	0.428308i	$0.859110\pi$
$312$		0			0
$313$	1107.57	−	1918.36i	0.200011	−	0.346429i	−0.748521	−	0.663111i	$-0.769236\pi$
$313$	1107.57	−	1918.36i	0.200011	−	0.346429i	0.948532	+	0.316682i	$0.102569\pi$
$314$	−13123.6			−2.35862
$315$		0			0
$316$	−2089.60			−0.371990
$317$	−329.023	+	569.884i	−0.0582958	+	0.100971i	−0.893700	−	0.448664i	$-0.851900\pi$
$317$	−329.023	+	569.884i	−0.0582958	+	0.100971i	0.835405	+	0.549635i	$0.185233\pi$
$318$		0			0
$319$	−1666.76	−	2886.91i	−0.292540	−	0.506695i
$320$	−599.130	−	1037.72i	−0.104664	−	0.181283i
$321$		0			0
$322$	−1930.14	+	3343.10i	−0.334045	+	0.578582i
$323$	−4727.03			−0.814299
$324$		0			0
$325$	1498.28			0.255721
$326$	494.717	−	856.875i	0.0840485	−	0.145576i
$327$		0			0
$328$	517.362	+	896.098i	0.0870931	+	0.150850i
$329$	−526.337	−	911.643i	−0.0882003	−	0.152767i
$330$		0			0
$331$	−2638.22	+	4569.53i	−0.438096	+	0.758804i	−0.997543	−	0.0700619i	$-0.977680\pi$
$331$	−2638.22	+	4569.53i	−0.438096	+	0.758804i	0.559447	+	0.828866i	$0.311014\pi$
$332$	6615.57			1.09360
$333$		0			0
$334$	−13453.8			−2.20407
$335$	−2143.83	+	3713.23i	−0.349642	+	0.605598i
$336$		0			0
$337$	1680.64	+	2910.95i	0.271662	+	0.470532i	0.969288	−	0.245930i	$-0.0790934\pi$
$337$	1680.64	+	2910.95i	0.271662	+	0.470532i	−0.697626	+	0.716462i	$0.745760\pi$
$338$	2614.12	+	4527.78i	0.420678	+	0.728636i
$339$		0			0
$340$	1120.27	−	1940.36i	0.178691	−	0.309503i
$341$	−5299.44			−0.841586
$342$		0			0
$343$	−9303.52			−1.46456
$344$	−503.575	+	872.218i	−0.0789272	+	0.136706i
$345$		0			0
$346$	−694.339	−	1202.63i	−0.107884	−	0.186861i
$347$	4677.77	+	8102.13i	0.723677	+	1.25344i	0.959516	+	0.281653i	$0.0908826\pi$
$347$	4677.77	+	8102.13i	0.723677	+	1.25344i	−0.235840	+	0.971792i	$0.575784\pi$
$348$		0			0
$349$	−3519.65	+	6096.22i	−0.539836	+	0.935023i	0.459077	+	0.888397i	$0.348180\pi$
$349$	−3519.65	+	6096.22i	−0.539836	+	0.935023i	−0.998912	+	0.0466263i	$0.985153\pi$
$350$	2937.86			0.448672
$351$		0			0
$352$	4701.65			0.711929
$353$	2101.09	−	3639.19i	0.316798	−	0.548710i	−0.663020	−	0.748602i	$-0.730726\pi$
$353$	2101.09	−	3639.19i	0.316798	−	0.548710i	0.979818	+	0.199891i	$0.0640589\pi$
$354$		0			0
$355$	−1471.66	−	2549.00i	−0.220022	−	0.381089i
$356$	1255.28	+	2174.21i	0.186881	+	0.323688i
$357$		0			0
$358$	−837.612	+	1450.79i	−0.123657	+	0.214180i
$359$	−588.013			−0.0864461			−0.0432230	−	0.999065i	$-0.513763\pi$
$359$	−588.013			−0.0864461			−0.0432230	+	0.999065i	$0.513763\pi$
$360$		0			0
$361$	−2783.58			−0.405828
$362$	−1694.44	+	2934.85i	−0.246016	+	0.426112i
$363$		0			0
$364$	5684.97	+	9846.66i	0.818608	+	1.41787i
$365$	−1545.48	−	2676.85i	−0.221627	−	0.383870i
$366$		0			0
$367$	3892.55	−	6742.10i	0.553650	−	0.958950i	−0.444357	−	0.895850i	$-0.646568\pi$
$367$	3892.55	−	6742.10i	0.553650	−	0.958950i	0.998007	−	0.0631004i	$-0.0200988\pi$
$368$	−2489.67			−0.352671
$369$		0			0
$370$	4036.55			0.567163
$371$	658.198	−	1140.03i	0.0921077	−	0.159535i
$372$		0			0
$373$	3912.02	+	6775.81i	0.543047	+	0.940585i	0.998727	+	0.0504412i	$0.0160627\pi$
$373$	3912.02	+	6775.81i	0.543047	+	0.940585i	−0.455680	+	0.890144i	$0.650604\pi$
$374$	2891.31	+	5007.90i	0.399749	+	0.692385i
$375$		0			0
$376$	122.617	−	212.378i	0.0168177	−	0.0291292i
$377$	9589.49			1.31004
$378$		0			0
$379$	−4679.90			−0.634275			−0.317138	−	0.948379i	$-0.602722\pi$
$379$	−4679.90			−0.634275			−0.317138	+	0.948379i	$0.602722\pi$
$380$	−965.843	+	1672.89i	−0.130386	+	0.225835i
$381$		0			0
$382$	1123.79	+	1946.47i	0.150519	+	0.260707i
$383$	−3363.82	−	5826.31i	−0.448782	−	0.777313i	0.549525	−	0.835477i	$-0.314809\pi$
$383$	−3363.82	−	5826.31i	−0.448782	−	0.777313i	−0.998307	+	0.0581644i	$0.981475\pi$
$384$		0			0
$385$	−1632.77	+	2828.04i	−0.216139	+	0.374364i
$386$	16545.2			2.18167
$387$		0			0
$388$	−1218.89			−0.159483
$389$	−2386.44	+	4133.43i	−0.311047	+	0.538749i	−0.978589	−	0.205823i	$-0.934013\pi$
$389$	−2386.44	+	4133.43i	−0.311047	+	0.538749i	0.667542	+	0.744572i	$0.267346\pi$
$390$		0			0
$391$	−1216.18	−	2106.49i	−0.157302	−	0.272455i
$392$	−2336.18	−	4046.38i	−0.301007	−	0.521360i
$393$		0			0
$394$	9009.95	−	15605.7i	1.15207	−	1.99544i
$395$	1726.44			0.219916
$396$		0			0
$397$	−4688.95			−0.592775			−0.296388	−	0.955068i	$-0.595782\pi$
$397$	−4688.95			−0.592775			−0.296388	+	0.955068i	$0.595782\pi$
$398$	588.211	−	1018.81i	0.0740813	−	0.128313i
$399$		0			0
$400$	947.379	+	1640.91i	0.118422	+	0.205114i
$401$	766.916	+	1328.34i	0.0955061	+	0.165421i	0.909820	−	0.415004i	$-0.136220\pi$
$401$	766.916	+	1328.34i	0.0955061	+	0.165421i	−0.814314	+	0.580425i	$0.802886\pi$
$402$		0			0
$403$	7622.43	−	13202.4i	0.942185	−	1.63191i
$404$	−1606.03			−0.197780
$405$		0			0
$406$	18803.3			2.29851
$407$	−2243.38	+	3885.66i	−0.273220	+	0.473230i
$408$		0			0
$409$	4389.41	+	7602.68i	0.530666	+	0.919140i	0.999360	+	0.0357796i	$0.0113914\pi$
$409$	4389.41	+	7602.68i	0.530666	+	0.919140i	−0.468694	+	0.883361i	$0.655275\pi$
$410$	1327.76	+	2299.74i	0.159935	+	0.277015i
$411$		0			0
$412$	1596.50	−	2765.23i	0.190908	−	0.330662i
$413$	19284.2			2.29761
$414$		0			0
$415$	−5465.84			−0.646524
$416$	−6762.61	+	11713.2i	−0.797029	+	1.38050i
$417$		0			0
$418$	−2492.75	−	4317.58i	−0.291686	−	0.505214i
$419$	−2138.02	−	3703.17i	−0.249282	−	0.431770i	0.714044	−	0.700100i	$-0.246861\pi$
$419$	−2138.02	−	3703.17i	−0.249282	−	0.431770i	−0.963327	+	0.268330i	$0.913528\pi$
$420$		0			0
$421$	−7231.64	+	12525.6i	−0.837169	+	1.45002i	0.0550823	+	0.998482i	$0.482458\pi$
$421$	−7231.64	+	12525.6i	−0.837169	+	1.45002i	−0.892252	+	0.451538i	$0.850875\pi$
$422$	−9142.07			−1.05457
$423$		0			0
$424$	306.671			0.0351256
$425$	−925.575	+	1603.14i	−0.105640	+	0.182974i
$426$		0			0
$427$	−2105.21	−	3646.32i	−0.238590	−	0.413250i
$428$	6306.65	+	10923.4i	0.712251	+	1.23366i
$429$		0			0
$430$	−1292.37	+	2238.45i	−0.144939	+	0.251042i
$431$	2208.11			0.246777			0.123389	−	0.992358i	$-0.460624\pi$
$431$	2208.11			0.246777			0.123389	+	0.992358i	$0.460624\pi$
$432$		0			0
$433$	−10062.3			−1.11677			−0.558386	−	0.829581i	$-0.688579\pi$
$433$	−10062.3			−1.11677			−0.558386	+	0.829581i	$0.688579\pi$
$434$	14946.3	−	25887.7i	1.65310	−	2.86325i
$435$		0			0
$436$	−2800.90	−	4851.30i	−0.307658	−	0.532879i
$437$	1048.54	+	1816.12i	0.114779	+	0.198803i
$438$		0			0
$439$	−6658.62	+	11533.1i	−0.723915	+	1.25386i	0.235504	+	0.971873i	$0.424326\pi$
$439$	−6658.62	+	11533.1i	−0.723915	+	1.25386i	−0.959419	+	0.281984i	$0.909008\pi$
$440$	−760.746			−0.0824253
$441$		0			0
$442$	−16634.8			−1.79013
$443$	−7137.55	+	12362.6i	−0.765497	+	1.32588i	0.174486	+	0.984660i	$0.444174\pi$
$443$	−7137.55	+	12362.6i	−0.765497	+	1.32588i	−0.939983	+	0.341220i	$0.889160\pi$
$444$		0			0
$445$	−1037.12	−	1796.35i	−0.110482	−	0.191360i
$446$	−4373.47	−	7575.08i	−0.464327	−	0.804238i
$447$		0			0
$448$	−3756.45	+	6506.36i	−0.396151	+	0.686153i
$449$	1690.02			0.177632			0.0888162	−	0.996048i	$-0.471692\pi$
$449$	1690.02			0.177632			0.0888162	+	0.996048i	$0.471692\pi$
$450$		0			0
$451$	−2951.69			−0.308181
$452$	1652.18	−	2861.66i	0.171929	−	0.297791i
$453$		0			0
$454$	5104.97	+	8842.07i	0.527727	+	0.914051i
$455$	−4696.97	−	8135.39i	−0.483950	−	0.838227i
$456$		0			0
$457$	3332.19	−	5771.53i	0.341080	−	0.590767i	−0.643554	−	0.765401i	$-0.722541\pi$
$457$	3332.19	−	5771.53i	0.341080	−	0.590767i	0.984634	+	0.174633i	$0.0558741\pi$
$458$	12423.3			1.26748
$459$		0			0
$460$	−993.979			−0.100749
$461$	833.712	−	1444.03i	0.0842295	−	0.145890i	−0.820833	−	0.571168i	$-0.806490\pi$
$461$	833.712	−	1444.03i	0.0842295	−	0.145890i	0.905063	+	0.425278i	$0.139824\pi$
$462$		0			0
$463$	2916.01	+	5050.68i	0.292697	+	0.506966i	0.974446	−	0.224620i	$-0.0721140\pi$
$463$	2916.01	+	5050.68i	0.292697	+	0.506966i	−0.681750	+	0.731585i	$0.738781\pi$
$464$	6063.56	+	10502.4i	0.606668	+	1.05078i
$465$		0			0
$466$	5951.67	−	10308.6i	0.591644	−	1.02476i
$467$	−17410.6			−1.72519			−0.862597	−	0.505892i	$-0.831163\pi$
$467$	−17410.6			−1.72519			−0.862597	+	0.505892i	$0.831163\pi$
$468$		0			0
$469$	26883.0			2.64678
$470$	314.683	−	545.047i	0.0308835	−	0.0534918i
$471$		0			0
$472$	2246.24	+	3890.61i	0.219050	+	0.379406i
$473$	−1436.52	−	2488.12i	−0.139643	−	0.241869i
$474$		0			0
$475$	797.988	−	1382.16i	0.0770825	−	0.133511i
$476$	−14047.8			−1.35269
$477$		0			0
$478$	−922.614			−0.0882832
$479$	−1639.67	+	2839.99i	−0.156406	+	0.270903i	−0.933570	−	0.358395i	$-0.883324\pi$
$479$	−1639.67	+	2839.99i	−0.156406	+	0.270903i	0.777164	+	0.629298i	$0.216657\pi$
$480$		0			0
$481$	−6453.53	−	11177.8i	−0.611758	−	1.05960i
$482$	−9910.71	−	17165.9i	−0.936557	−	1.62216i
$483$		0			0
$484$	2714.13	−	4701.00i	0.254895	−	0.441492i
$485$	1007.05			0.0942844
$486$		0			0
$487$	−10506.7			−0.977624			−0.488812	−	0.872389i	$-0.662570\pi$
$487$	−10506.7			−0.977624			−0.488812	+	0.872389i	$0.662570\pi$
$488$	490.433	−	849.456i	0.0454936	−	0.0787972i
$489$		0			0
$490$	−5995.56	−	10384.6i	−0.552759	−	0.957406i
$491$	−7132.25	−	12353.4i	−0.655548	−	1.13544i	−0.981756	−	0.190144i	$-0.939104\pi$
$491$	−7132.25	−	12353.4i	−0.655548	−	1.13544i	0.326208	−	0.945298i	$-0.394229\pi$
$492$		0			0
$493$	−5924.01	+	10260.7i	−0.541184	+	0.937359i
$494$	14341.8			1.30621
$495$		0			0
$496$	19279.1			1.74527
$497$	−9227.09	+	15981.8i	−0.832780	+	1.44242i
$498$		0			0
$499$	−4723.70	−	8181.68i	−0.423771	−	0.733993i	0.572534	−	0.819881i	$-0.305961\pi$
$499$	−4723.70	−	8181.68i	−0.423771	−	0.733993i	−0.996305	+	0.0858882i	$0.972627\pi$
$500$	378.234	+	655.120i	0.0338303	+	0.0585957i
$501$		0			0
$502$	−5287.78	+	9158.70i	−0.470130	+	0.814288i
$503$	−14579.2			−1.29235			−0.646177	−	0.763188i	$-0.723633\pi$
$503$	−14579.2			−1.29235			−0.646177	+	0.763188i	$0.723633\pi$
$504$		0			0
$505$	1326.91			0.116925
$506$	1282.69	−	2221.68i	0.112692	−	0.195189i
$507$		0			0
$508$	2953.17	+	5115.03i	0.257924	+	0.446738i
$509$	4205.32	+	7283.83i	0.366204	+	0.634283i	0.988969	−	0.148126i	$-0.0473240\pi$
$509$	4205.32	+	7283.83i	0.366204	+	0.634283i	−0.622765	+	0.782409i	$0.713991\pi$
$510$		0			0
$511$	−9689.89	+	16783.4i	−0.838856	+	1.45294i
$512$	−12676.3			−1.09417
$513$		0			0
$514$	−7063.02			−0.606102
$515$	−1319.04	+	2284.65i	−0.112862	+	0.195483i
$516$		0			0
$517$	349.781	+	605.838i	0.0297550	+	0.0515372i
$518$	−12654.3	−	21917.8i	−1.07335	−	1.85910i
$519$		0			0
$520$	1094.22	−	1895.24i	0.0922781	−	0.159830i
$521$	−10058.1			−0.845781			−0.422890	−	0.906181i	$-0.638984\pi$
$521$	−10058.1			−0.845781			−0.422890	+	0.906181i	$0.638984\pi$
$522$		0			0
$523$	20006.3			1.67269			0.836344	−	0.548205i	$-0.184688\pi$
$523$	20006.3			1.67269			0.836344	+	0.548205i	$0.184688\pi$
$524$	−4929.83	+	8538.72i	−0.410994	+	0.711862i
$525$		0			0
$526$	−1036.50	−	1795.27i	−0.0859192	−	0.148817i
$527$	9417.67	+	16311.9i	0.778444	+	1.34830i
$528$		0			0
$529$	5543.96	−	9602.42i	0.455655	−	0.789218i
$530$	787.038			0.0645033
$531$		0			0
$532$	12111.4			0.987019
$533$	4245.56	−	7353.52i	0.345020	−	0.597592i
$534$		0			0
$535$	−5210.61	−	9025.04i	−0.421073	−	0.729320i
$536$	3131.36	+	5423.67i	0.252340	+	0.437065i
$537$		0			0
$538$	−6304.11	+	10919.0i	−0.505185	+	0.875006i
$539$	13328.5			1.06512
$540$		0			0
$541$	−1884.15			−0.149734			−0.0748668	−	0.997194i	$-0.523853\pi$
$541$	−1884.15			−0.149734			−0.0748668	+	0.997194i	$0.523853\pi$
$542$	−6248.58	+	10822.9i	−0.495202	+	0.857715i
$543$		0			0
$544$	−8355.34	−	14471.9i	−0.658515	−	1.14058i
$545$	2314.13	+	4008.19i	0.181883	+	0.315031i
$546$		0			0
$547$	8998.24	−	15585.4i	0.703358	−	1.21825i	−0.263922	−	0.964544i	$-0.585016\pi$
$547$	8998.24	−	15585.4i	0.703358	−	1.21825i	0.967281	−	0.253708i	$-0.0816504\pi$
$548$	−4002.93			−0.312038
$549$		0			0
$550$	−1952.37			−0.151363
$551$	5107.40	−	8846.28i	0.394887	−	0.683964i
$552$		0			0
$553$	−5412.25	−	9374.30i	−0.416189	−	0.720860i
$554$	−10097.2	−	17488.9i	−0.774351	−	1.34121i
$555$		0			0
$556$	−4184.75	+	7248.19i	−0.319196	+	0.552863i
$557$	3615.76			0.275054			0.137527	−	0.990498i	$-0.456085\pi$
$557$	3615.76			0.275054			0.137527	+	0.990498i	$0.456085\pi$
$558$		0			0
$559$	8264.84			0.625341
$560$	5939.91	−	10288.2i	0.448227	−	0.776352i
$561$		0			0
$562$	−6966.14	−	12065.7i	−0.522863	−	0.905625i
$563$	7410.91	+	12836.1i	0.554765	+	0.960881i	0.997922	+	0.0644370i	$0.0205251\pi$
$563$	7410.91	+	12836.1i	0.554765	+	0.960881i	−0.443157	+	0.896444i	$0.646142\pi$
$564$		0			0
$565$	−1365.05	+	2364.33i	−0.101642	+	0.176050i
$566$	−10378.9			−0.770771
$567$		0			0
$568$	−4299.13			−0.317583
$569$	11224.7	−	19441.8i	0.827005	−	1.43241i	−0.0733726	−	0.997305i	$-0.523376\pi$
$569$	11224.7	−	19441.8i	0.827005	−	1.43241i	0.900377	−	0.435110i	$-0.143290\pi$
$570$		0			0
$571$	8006.75	+	13868.1i	0.586817	+	1.01640i	0.994646	+	0.103338i	$0.0329523\pi$
$571$	8006.75	+	13868.1i	0.586817	+	1.01640i	−0.407830	+	0.913058i	$0.633714\pi$
$572$	−3777.98	−	6543.66i	−0.276163	−	0.478329i
$573$		0			0
$574$	8324.81	−	14419.0i	0.605350	−	1.04850i
$575$	821.234			0.0595615
$576$		0			0
$577$	3096.97			0.223446			0.111723	−	0.993739i	$-0.464363\pi$
$577$	3096.97			0.223446			0.111723	+	0.993739i	$0.464363\pi$
$578$	1067.99	−	1849.81i	0.0768553	−	0.133117i
$579$		0			0
$580$	2420.83	+	4193.00i	0.173309	+	0.300181i
$581$	17135.0	+	29678.6i	1.22354	+	2.11924i
$582$		0			0
$583$	−437.410	+	757.616i	−0.0310732	+	0.0538203i
$584$	−4514.76			−0.319901
$585$		0			0
$586$	−13045.0			−0.919595
$587$	12312.4	−	21325.7i	0.865734	−	1.49950i	−0.000582275	−	1.00000i	$-0.500185\pi$
$587$	12312.4	−	21325.7i	0.865734	−	1.49950i	0.866316	−	0.499496i	$-0.166481\pi$
$588$		0			0
$589$	−8119.48	−	14063.3i	−0.568009	−	0.983820i
$590$	5764.75	+	9984.83i	0.402256	+	0.696727i
$591$		0			0
$592$	8161.30	−	14135.8i	0.566601	−	0.981381i
$593$	−27128.8			−1.87866			−0.939330	−	0.343014i	$-0.888552\pi$
$593$	−27128.8			−1.87866			−0.939330	+	0.343014i	$0.888552\pi$
$594$		0			0
$595$	11606.4			0.799691
$596$	9572.32	−	16579.7i	0.657881	−	1.13948i
$597$		0			0
$598$	3689.89	+	6391.08i	0.252326	+	0.437042i
$599$	2815.87	+	4877.24i	0.192076	+	0.332685i	0.945938	−	0.324347i	$-0.105145\pi$
$599$	2815.87	+	4877.24i	0.192076	+	0.332685i	−0.753862	+	0.657033i	$0.771811\pi$
$600$		0			0
$601$	7375.88	−	12775.4i	0.500613	−	0.867087i	−0.499387	−	0.866379i	$-0.666441\pi$
$601$	7375.88	−	12775.4i	0.500613	−	0.867087i	1.00000		0.000707853i	$-0.000225317\pi$
$602$	16205.9			1.09718
$603$		0			0
$604$	−15485.2			−1.04318
$605$	−2242.43	+	3884.01i	−0.150691	+	0.261004i
$606$		0			0
$607$	7391.04	+	12801.7i	0.494222	+	0.856018i	0.999978	−	0.00665872i	$-0.00211955\pi$
$607$	7391.04	+	12801.7i	0.494222	+	0.856018i	−0.505756	+	0.862677i	$0.668786\pi$
$608$	7203.59	+	12477.0i	0.480500	+	0.832251i
$609$		0			0
$610$	1258.65	−	2180.04i	0.0835427	−	0.144700i
$611$	−2012.43			−0.133247
$612$		0			0
$613$	4947.28			0.325969			0.162984	−	0.986629i	$-0.447888\pi$
$613$	4947.28			0.325969			0.162984	+	0.986629i	$0.447888\pi$
$614$	−3393.12	+	5877.06i	−0.223021	+	0.386284i
$615$		0			0
$616$	2384.88	+	4130.73i	0.155989	+	0.270181i
$617$	−1871.82	−	3242.09i	−0.122134	−	0.211543i	0.798475	−	0.602028i	$-0.205640\pi$
$617$	−1871.82	−	3242.09i	−0.122134	−	0.211543i	−0.920609	+	0.390485i	$0.872307\pi$
$618$		0			0
$619$	−3069.37	+	5316.30i	−0.199303	+	0.345202i	−0.948303	−	0.317368i	$-0.897201\pi$
$619$	−3069.37	+	5316.30i	−0.199303	+	0.345202i	0.749000	+	0.662570i	$0.230534\pi$
$620$	7697.01			0.498580
$621$		0			0
$622$	−3326.09			−0.214412
$623$	−6502.59	+	11262.8i	−0.418171	+	0.724294i
$624$		0			0
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−4151.79	−	7191.11i	−0.265078	−	0.459128i
$627$		0			0
$628$	−10593.5	+	18348.4i	−0.673129	+	1.16589i
$629$	15946.9			1.01088
$630$		0			0
$631$	−5548.00			−0.350019			−0.175010	−	0.984567i	$-0.555996\pi$
$631$	−5548.00			−0.350019			−0.175010	+	0.984567i	$0.555996\pi$
$632$	1260.85	−	2183.86i	0.0793575	−	0.137451i
$633$		0			0
$634$	1233.36	+	2136.25i	0.0772605	+	0.133819i
$635$	−2439.93	−	4226.08i	−0.152481	−	0.264106i
$636$		0			0
$637$	−19171.1	+	33205.3i	−1.19244	+	2.06537i
$638$	−12495.9			−0.775418
$639$		0			0
$640$	4535.43			0.280123
$641$	−5804.05	+	10052.9i	−0.357639	+	0.619448i	−0.987566	−	0.157206i	$-0.949751\pi$
$641$	−5804.05	+	10052.9i	−0.357639	+	0.619448i	0.629927	+	0.776654i	$0.283085\pi$
$642$		0			0
$643$	6360.85	+	11017.3i	0.390120	+	0.675708i	0.992465	−	0.122528i	$-0.0391001\pi$
$643$	6360.85	+	11017.3i	0.390120	+	0.675708i	−0.602345	+	0.798236i	$0.705767\pi$
$644$	3116.04	+	5397.15i	0.190667	+	0.330244i
$645$		0			0
$646$	−8859.78	+	15345.6i	−0.539603	+	0.934620i
$647$	28203.7			1.71376			0.856879	−	0.515518i	$-0.172400\pi$
$647$	28203.7			1.71376			0.856879	+	0.515518i	$0.172400\pi$
$648$		0			0
$649$	−12815.4			−0.775115
$650$	2808.19	−	4863.93i	0.169456	−	0.293506i
$651$		0			0
$652$	−798.678	−	1383.35i	−0.0479734	−	0.0830924i
$653$	−11346.4	−	19652.5i	−0.679966	−	1.17774i	−0.974991	−	0.222247i	$-0.928661\pi$
$653$	−11346.4	−	19652.5i	−0.679966	−	1.17774i	0.295024	−	0.955490i	$-0.404672\pi$
$654$		0			0
$655$	4073.07	−	7054.77i	0.242974	−	0.420844i
$656$	10738.1			0.639103
$657$		0			0
$658$	−3946.02			−0.233787
$659$	3002.00	−	5199.61i	0.177453	−	0.307357i	−0.763555	−	0.645743i	$-0.776548\pi$
$659$	3002.00	−	5199.61i	0.177453	−	0.307357i	0.941007	+	0.338386i	$0.109881\pi$
$660$		0			0
$661$	−5958.18	−	10319.9i	−0.350600	−	0.607256i	0.635755	−	0.771891i	$-0.280689\pi$
$661$	−5958.18	−	10319.9i	−0.350600	−	0.607256i	−0.986355	+	0.164635i	$0.947356\pi$
$662$	9889.54	+	17129.2i	0.580616	+	1.00566i
$663$		0			0
$664$	−3991.80	+	6914.00i	−0.233301	+	0.404089i
$665$	−10006.5			−0.583512
$666$		0			0
$667$	5256.19			0.305128
$668$	−10860.0	+	18810.1i	−0.629021	+	1.08950i
$669$		0			0
$670$	8036.30	+	13919.3i	0.463387	+	0.802610i
$671$	1399.03	+	2423.19i	0.0804901	+	0.139413i
$672$		0			0
$673$	8016.85	−	13885.6i	0.459178	−	0.795319i	−0.539740	−	0.841832i	$-0.681477\pi$
$673$	8016.85	−	13885.6i	0.459178	−	0.795319i	0.998918	+	0.0465125i	$0.0148107\pi$
$674$	12599.9			0.720077
$675$		0			0
$676$	8440.54			0.480231
$677$	5655.94	−	9796.38i	0.321086	−	0.556138i	−0.659626	−	0.751594i	$-0.729285\pi$
$677$	5655.94	−	9796.38i	0.321086	−	0.556138i	0.980712	+	0.195456i	$0.0626187\pi$
$678$		0			0
$679$	−3157.03	−	5468.14i	−0.178432	−	0.309054i
$680$	1351.93	+	2341.61i	0.0762413	+	0.132054i
$681$		0			0
$682$	−9932.64	+	17203.8i	−0.557684	+	0.965937i
$683$	652.395			0.0365493			0.0182747	−	0.999833i	$-0.494183\pi$
$683$	652.395			0.0365493			0.0182747	+	0.999833i	$0.494183\pi$
$684$		0			0
$685$	3307.25			0.184472
$686$	−17437.4	+	30202.5i	−0.970502	+	1.68096i
$687$		0			0
$688$	5225.96	+	9051.64i	0.289590	+	0.501585i
$689$	−1258.29	−	2179.43i	−0.0695750	−	0.120507i
$690$		0			0
$691$	−6268.93	+	10858.1i	−0.345125	+	0.597774i	−0.985376	−	0.170392i	$-0.945497\pi$
$691$	−6268.93	+	10858.1i	−0.345125	+	0.597774i	0.640252	+	0.768165i	$0.278830\pi$
$692$	−2241.90			−0.123157
$693$		0			0
$694$	35069.8			1.91820
$695$	3457.47	−	5988.52i	0.188704	−	0.326845i
$696$		0			0
$697$	5245.47	+	9085.42i	0.285059	+	0.493737i
$698$	13193.6	+	22852.1i	0.715454	+	1.23920i
$699$		0			0
$700$	2371.46	−	4107.50i	0.128047	−	0.221784i
$701$	−5880.60			−0.316844			−0.158422	−	0.987372i	$-0.550641\pi$
$701$	−5880.60			−0.316844			−0.158422	+	0.987372i	$0.550641\pi$
$702$		0			0
$703$	−13748.7			−0.737614
$704$	2496.37	−	4323.84i	0.133644	−	0.231479i
$705$		0			0
$706$	−7876.07	−	13641.8i	−0.419858	−	0.727216i
$707$	−4159.77	−	7204.93i	−0.221279	−	0.383266i
$708$		0			0
$709$	−3203.33	+	5548.33i	−0.169681	+	0.293895i	−0.938308	−	0.345802i	$-0.887607\pi$
$709$	−3203.33	+	5548.33i	−0.169681	+	0.293895i	0.768627	+	0.639697i	$0.220940\pi$
$710$	−11033.3			−0.583198
$711$		0			0
$712$	−3029.72			−0.159471
$713$	4178.00	−	7236.52i	0.219449	−	0.380098i
$714$		0			0
$715$	3121.40	+	5406.43i	0.163264	+	0.282782i
$716$	1352.25	+	2342.17i	0.0705812	+	0.122250i
$717$		0			0
$718$	−1102.10	+	1908.90i	−0.0572843	+	0.0992193i
$719$	−21907.0			−1.13629			−0.568144	−	0.822929i	$-0.692338\pi$
$719$	−21907.0			−1.13629			−0.568144	+	0.822929i	$0.692338\pi$
$720$		0			0
$721$	16540.4			0.854364
$722$	−5217.21	+	9036.47i	−0.268926	+	0.465793i
$723$		0			0
$724$	2735.53	+	4738.07i	0.140421	+	0.243217i
$725$	−2000.11	−	3464.29i	−0.102458	−	0.177463i
$726$		0			0
$727$	−6685.46	+	11579.6i	−0.341059	+	0.590732i	−0.984630	−	0.174655i	$-0.944119\pi$
$727$	−6685.46	+	11579.6i	−0.341059	+	0.590732i	0.643571	+	0.765387i	$0.277452\pi$
$728$	−13721.1			−0.698542
$729$		0			0
$730$	−11586.6			−0.587453
$731$	−5105.69	+	8843.31i	−0.258332	+	0.447444i
$732$		0			0
$733$	−15095.5	−	26146.2i	−0.760663	−	1.31751i	−0.942509	−	0.334181i	$-0.891540\pi$
$733$	−15095.5	−	26146.2i	−0.760663	−	1.31751i	0.181846	−	0.983327i	$-0.441793\pi$
$734$	−14591.5	−	25273.2i	−0.733762	−	1.27091i
$735$		0			0
$736$	−3706.72	+	6420.22i	−0.185641	+	0.321539i
$737$	−17865.2			−0.892910
$738$		0			0
$739$	−11624.7			−0.578650			−0.289325	−	0.957231i	$-0.593431\pi$
$739$	−11624.7			−0.578650			−0.289325	+	0.957231i	$0.593431\pi$
$740$	3258.34	−	5643.60i	0.161863	−	0.280355i
$741$		0			0
$742$	−2467.30	−	4273.49i	−0.122072	−	0.211435i
$743$	−2627.19	−	4550.42i	−0.129720	−	0.224682i	0.793848	−	0.608116i	$-0.208075\pi$
$743$	−2627.19	−	4550.42i	−0.129720	−	0.224682i	−0.923568	+	0.383434i	$0.874741\pi$
$744$		0			0
$745$	−7908.73	+	13698.3i	−0.388931	+	0.673648i
$746$	29328.9			1.43942
$747$		0			0
$748$	9335.55			0.456339
$749$	−32669.7	+	56585.5i	−1.59376	+	2.76047i
$750$		0			0
$751$	14614.4	+	25312.9i	0.710102	+	1.22993i	0.964819	+	0.262917i	$0.0846844\pi$
$751$	14614.4	+	25312.9i	0.710102	+	1.22993i	−0.254717	+	0.967016i	$0.581982\pi$
$752$	−1272.48	−	2204.00i	−0.0617057	−	0.106877i
$753$		0			0
$754$	17973.4	−	31130.9i	0.868108	−	1.50361i
$755$	12794.0			0.616716
$756$		0			0
$757$	32885.9			1.57894			0.789470	−	0.613789i	$-0.210355\pi$
$757$	32885.9			1.57894			0.789470	+	0.613789i	$0.210355\pi$
$758$	−8771.46	+	15192.6i	−0.420308	+	0.727995i
$759$		0			0
$760$	−1165.57	−	2018.83i	−0.0556311	−	0.0963559i
$761$	−6634.11	−	11490.6i	−0.316014	−	0.547352i	0.663639	−	0.748053i	$-0.269011\pi$
$761$	−6634.11	−	11490.6i	−0.316014	−	0.547352i	−0.979652	+	0.200702i	$0.935678\pi$
$762$		0			0
$763$	14509.2	−	25130.7i	0.688425	−	1.19239i
$764$	3628.54			0.171827
$765$		0			0
$766$	−25219.0			−1.18956
$767$	18433.0	−	31927.0i	0.867769	−	1.50302i
$768$		0			0
$769$	−17142.9	−	29692.4i	−0.803887	−	1.39237i	−0.917040	−	0.398796i	$-0.869428\pi$
$769$	−17142.9	−	29692.4i	−0.803887	−	1.39237i	0.113153	−	0.993578i	$-0.463905\pi$
$770$	6120.53	+	10601.1i	0.286453	+	0.496151i
$771$		0			0
$772$	13355.4	−	23132.2i	0.622630	−	1.07843i
$773$	27987.1			1.30223			0.651117	−	0.758978i	$-0.274301\pi$
$773$	27987.1			1.30223			0.651117	+	0.758978i	$0.274301\pi$
$774$		0			0
$775$	−6359.34			−0.294754
$776$	735.469	−	1273.87i	0.0340229	−	0.0589294i
$777$		0			0
$778$	8945.72	+	15494.4i	0.412236	+	0.714014i
$779$	−4522.40	−	7833.03i	−0.208000	−	0.360266i
$780$		0			0
$781$	6131.92	−	10620.8i	0.280944	−	0.486610i
$782$	−9117.88			−0.416950
$783$		0			0
$784$	−48488.5			−2.20884
$785$	8752.41	−	15159.6i	0.397945	−	0.689261i
$786$		0			0
$787$	−177.400	−	307.265i	−0.00803509	−	0.0139172i	0.861980	−	0.506942i	$-0.169224\pi$
$787$	−177.400	−	307.265i	−0.00803509	−	0.0139172i	−0.870015	+	0.493025i	$0.835891\pi$
$788$	−14545.8	−	25194.1i	−0.657580	−	1.13896i
$789$		0			0
$790$	3235.84	−	5604.64i	0.145729	−	0.252410i
$791$	17117.2			0.769430
$792$		0			0
$793$	−8049.15			−0.360446
$794$	−8788.42	+	15222.0i	−0.392808	+	0.680363i
$795$		0			0
$796$	−949.617	−	1644.78i	−0.0422843	−	0.0732385i
$797$	6400.65	+	11086.2i	0.284470	+	0.492717i	0.972481	−	0.232984i	$-0.0748490\pi$
$797$	6400.65	+	11086.2i	0.284470	+	0.492717i	−0.688011	+	0.725701i	$0.741516\pi$
$798$		0			0
$799$	1243.20	−	2153.28i	0.0550452	−	0.0953411i
$800$	5641.99			0.249343
$801$		0			0
$802$	5749.67			0.253152
$803$	6439.48	−	11153.5i	0.282994	−	0.490160i
$804$		0			0
$805$	−2574.50	−	4459.17i	−0.112720	−	0.195236i
$806$	−28573.2	−	49490.2i	−1.24869	−	2.16280i
$807$		0			0
$808$	969.069	−	1678.48i	0.0421927	−	0.0730800i
$809$	16374.9			0.711632			0.355816	−	0.934556i	$-0.384203\pi$
$809$	16374.9			0.711632			0.355816	+	0.934556i	$0.384203\pi$
$810$		0			0
$811$	−35518.2			−1.53787			−0.768936	−	0.639326i	$-0.779214\pi$
$811$	−35518.2			−1.53787			−0.768936	+	0.639326i	$0.779214\pi$
$812$	15178.2	−	26289.4i	0.655974	−	1.13618i
$813$		0			0
$814$	8409.47	+	14565.6i	0.362103	+	0.627181i
$815$	659.875	+	1142.94i	0.0283612	+	0.0491231i
$816$		0			0
$817$	4401.89	−	7624.29i	0.188498	−	0.326487i
$818$	32908.0			1.40660
$819$		0			0
$820$	4287.10			0.182576
$821$	21471.9	−	37190.5i	0.912760	−	1.58095i	0.102612	−	0.994721i	$-0.467280\pi$
$821$	21471.9	−	37190.5i	0.912760	−	1.58095i	0.810148	−	0.586226i	$-0.199387\pi$
$822$		0			0
$823$	3958.46	+	6856.26i	0.167659	+	0.290394i	0.937596	−	0.347726i	$-0.113046\pi$
$823$	3958.46	+	6856.26i	0.167659	+	0.290394i	−0.769937	+	0.638119i	$0.779713\pi$
$824$	1926.64	+	3337.04i	0.0814536	+	0.141082i
$825$		0			0
$826$	36144.0	−	62603.3i	1.52253	−	2.63710i
$827$	−18774.4			−0.789421			−0.394710	−	0.918806i	$-0.629155\pi$
$827$	−18774.4			−0.789421			−0.394710	+	0.918806i	$0.629155\pi$
$828$		0			0
$829$	22166.1			0.928661			0.464330	−	0.885662i	$-0.346295\pi$
$829$	22166.1			0.928661			0.464330	+	0.885662i	$0.346295\pi$
$830$	−10244.5	+	17744.0i	−0.428425	+	0.742054i
$831$		0			0
$832$	7181.30	+	12438.4i	0.299239	+	0.518297i
$833$	−23686.2	−	41025.8i	−0.985210	−	1.70643i
$834$		0			0
$835$	8972.63	−	15541.0i	0.371869	−	0.644096i
$836$	−8048.68			−0.332978
$837$		0			0
$838$	−16029.1			−0.660757
$839$	21295.4	−	36884.7i	0.876279	−	1.51776i	0.0208849	−	0.999782i	$-0.493352\pi$
$839$	21295.4	−	36884.7i	0.876279	−	1.51776i	0.855394	−	0.517978i	$-0.173315\pi$
$840$		0			0
$841$	−606.908	−	1051.20i	−0.0248845	−	0.0431012i
$842$	27108.3	+	46952.9i	1.10952	+	1.92174i
$843$		0			0
$844$	−7379.55	+	12781.7i	−0.300965	+	0.521287i
$845$	−6973.65			−0.283906
$846$		0			0
$847$	28119.4			1.14072
$848$	1591.27	−	2756.16i	0.0644393	−	0.111612i
$849$		0			0
$850$	3469.58	+	6009.49i	0.140007	+	0.242498i
$851$	−3537.31	−	6126.79i	−0.142488	−	0.246796i
$852$		0			0
$853$	−13230.6	+	22916.0i	−0.531074	+	0.919847i	0.468269	+	0.883586i	$0.344878\pi$
$853$	−13230.6	+	22916.0i	−0.531074	+	0.919847i	−0.999342	+	0.0362605i	$0.988455\pi$
$854$	−15783.0			−0.632416
$855$		0			0
$856$	−15221.6			−0.607784
$857$	−10004.5	+	17328.3i	−0.398772	+	0.690693i	−0.993575	−	0.113179i	$-0.963897\pi$
$857$	−10004.5	+	17328.3i	−0.398772	+	0.690693i	0.594803	+	0.803871i	$0.297230\pi$
$858$		0			0
$859$	8909.03	+	15430.9i	0.353868	+	0.612917i	0.986923	−	0.161189i	$-0.0515330\pi$
$859$	8909.03	+	15430.9i	0.353868	+	0.612917i	−0.633056	+	0.774106i	$0.718200\pi$
$860$	2086.43	+	3613.79i	0.0827285	+	0.143290i
$861$		0			0
$862$	4138.63	−	7168.31i	0.163529	−	0.283241i
$863$	−12769.5			−0.503683			−0.251841	−	0.967769i	$-0.581036\pi$
$863$	−12769.5			−0.503683			−0.251841	+	0.967769i	$0.581036\pi$
$864$		0			0
$865$	1852.28			0.0728085
$866$	−18859.6	+	32665.7i	−0.740039	+	1.28179i
$867$		0			0
$868$	−24129.5	−	41793.5i	−0.943558	−	1.63429i
$869$	3596.75	+	6229.75i	0.140404	+	0.243187i
$870$		0			0
$871$	25696.4	−	44507.5i	0.999644	−	1.73144i
$872$	6760.19			0.262533
$873$		0			0
$874$	7861.01			0.304236
$875$	−1959.32	+	3393.65i	−0.0756997	+	0.131116i
$876$		0			0
$877$	−13738.6	−	23796.0i	−0.528986	−	0.916231i	−0.999429	−	0.0338003i	$-0.989239\pi$
$877$	−13738.6	−	23796.0i	−0.528986	−	0.916231i	0.470442	−	0.882431i	$-0.344094\pi$
$878$	24960.3	+	43232.5i	0.959417	+	1.66176i
$879$		0			0
$880$	−3947.41	+	6837.11i	−0.151213	+	0.261908i
$881$	−31509.1			−1.20496			−0.602480	−	0.798134i	$-0.705821\pi$
$881$	−31509.1			−1.20496			−0.602480	+	0.798134i	$0.705821\pi$
$882$		0			0
$883$	5271.46			0.200905			0.100452	−	0.994942i	$-0.467971\pi$
$883$	5271.46			0.200905			0.100452	+	0.994942i	$0.467971\pi$
$884$	−13427.8	+	23257.6i	−0.510888	+	0.884883i
$885$		0			0
$886$	26755.6	+	46342.0i	1.01453	+	1.75721i
$887$	5216.89	+	9035.91i	0.197481	+	0.342048i	0.947711	−	0.319130i	$-0.103391\pi$
$887$	5216.89	+	9035.91i	0.197481	+	0.342048i	−0.750230	+	0.661177i	$0.770057\pi$
$888$		0			0
$889$	−15298.0	+	26496.9i	−0.577140	+	0.999636i
$890$	−7775.45			−0.292847
$891$		0			0
$892$	−14121.2			−0.530059
$893$	−1071.83	+	1856.46i	−0.0401649	+	0.0695677i
$894$		0			0
$895$	−1117.24	−	1935.12i	−0.0417266	−	0.0722727i
$896$	−14218.2	−	24626.6i	−0.530130	−	0.918212i
$897$		0			0
$898$	3167.57	−	5486.40i	0.117710	−	0.203879i
$899$	−40702.0			−1.51000
$900$		0			0
$901$	3109.30			0.114967
$902$	−5532.30	+	9582.23i	−0.204219	+	0.353718i
$903$		0			0
$904$	1993.84	+	3453.43i	0.0733562	+	0.127057i
$905$	−2260.11	−	3914.63i	−0.0830152	−	0.143787i
$906$		0			0
$907$	−10343.3	+	17915.1i	−0.378659	+	0.655856i	−0.990867	−	0.134840i	$-0.956948\pi$
$907$	−10343.3	+	17915.1i	−0.378659	+	0.655856i	0.612209	+	0.790696i	$0.290281\pi$
$908$	16483.1			0.602434
$909$		0			0
$910$	−35213.8			−1.28278
$911$	−11820.0	+	20472.9i	−0.429874	+	0.744563i	−0.996862	−	0.0791627i	$-0.974775\pi$
$911$	−11820.0	+	20472.9i	−0.429874	+	0.744563i	0.566988	+	0.823726i	$0.308109\pi$
$912$		0			0
$913$	−11387.1	−	19723.1i	−0.412770	−	0.714939i
$914$	−12490.9	−	21635.0i	−0.452039	−	0.782955i
$915$		0			0
$916$	10028.2	−	17369.4i	0.361727	−	0.626529i
$917$	−51075.0			−1.83931
$918$		0			0
$919$	27335.2			0.981180			0.490590	−	0.871390i	$-0.336781\pi$
$919$	27335.2			0.981180			0.490590	+	0.871390i	$0.336781\pi$
$920$	599.762	−	1038.82i	0.0214930	−	0.0372270i
$921$		0			0
$922$	−3125.22	−	5413.04i	−0.111631	−	0.193350i
$923$	17639.7	+	30552.8i	0.629054	+	1.08955i
$924$		0			0
$925$	−2692.07	+	4662.79i	−0.0956914	+	0.165742i
$926$	21861.7			0.775832
$927$		0			0
$928$	36110.7			1.27736
$929$	−6614.28	+	11456.3i	−0.233593	+	0.404594i	−0.958863	−	0.283870i	$-0.908382\pi$
$929$	−6614.28	+	11456.3i	−0.233593	+	0.404594i	0.725270	+	0.688464i	$0.241715\pi$
$930$		0			0
$931$	20421.2	+	35370.5i	0.718880	+	1.24514i
$932$	−9608.47	−	16642.4i	−0.337700	−	0.584913i
$933$		0			0
$934$	−32632.3	+	56520.9i	−1.14321	+	1.98011i
$935$	−7713.11			−0.269782
$936$		0			0
$937$	−18740.4			−0.653387			−0.326693	−	0.945130i	$-0.605934\pi$
$937$	−18740.4			−0.653387			−0.326693	+	0.945130i	$0.605934\pi$
$938$	50386.3	−	87271.6i	1.75391	−	3.03787i
$939$		0			0
$940$	−508.029	−	879.932i	−0.0176277	−	0.0305321i
$941$	27244.5	+	47188.9i	0.943832	+	1.63476i	0.758074	+	0.652169i	$0.226141\pi$
$941$	27244.5	+	47188.9i	0.943832	+	1.63476i	0.185758	+	0.982596i	$0.440526\pi$
$942$		0			0
$943$	2327.07	−	4030.61i	0.0803605	−	0.139188i
$944$	46621.8			1.60743
$945$		0			0
$946$	−10769.7			−0.370142
$947$	−5641.35	+	9771.11i	−0.193579	+	0.335289i	−0.946434	−	0.322898i	$-0.895343\pi$
$947$	−5641.35	+	9771.11i	−0.193579	+	0.335289i	0.752855	+	0.658187i	$0.228676\pi$
$948$		0			0
$949$	18524.4	+	32085.2i	0.633644	+	1.09750i
$950$	−2991.31	−	5181.10i	−0.102159	−	0.176944i
$951$		0			0
$952$	8476.36	−	14681.5i	0.288572	−	0.499821i
$953$	51190.0			1.73999			0.869994	−	0.493063i	$-0.164123\pi$
$953$	51190.0			1.73999			0.869994	+	0.493063i	$0.164123\pi$
$954$		0			0
$955$	−2997.93			−0.101582
$956$	−744.741	+	1289.93i	−0.0251952	+	0.0436394i
$957$		0			0
$958$	6146.41	+	10645.9i	0.207288	+	0.359033i
$959$	−10368.0	−	17957.8i	−0.349113	−	0.604681i
$960$		0			0
$961$	−17457.4	+	30237.2i	−0.585997	+	1.01498i
$962$	−48383.0			−1.62155
$963$		0			0
$964$	−32000.0			−1.06914
$965$	−11034.3	+	19112.0i	−0.368091	+	0.637552i
$966$		0			0
$967$	−11571.8	−	20042.9i	−0.384822	−	0.666530i	0.606923	−	0.794761i	$-0.292404\pi$
$967$	−11571.8	−	20042.9i	−0.384822	−	0.666530i	−0.991744	+	0.128230i	$0.959070\pi$
$968$	3275.38	+	5673.12i	0.108755	+	0.188369i
$969$		0			0
$970$	1887.50	−	3269.25i	0.0624784	−	0.108216i
$971$	34124.5			1.12782			0.563908	−	0.825838i	$-0.309297\pi$
$971$	34124.5			1.12782			0.563908	+	0.825838i	$0.309297\pi$
$972$		0			0
$973$	−43355.6			−1.42848
$974$	−19692.5	+	34108.4i	−0.647831	+	1.12208i
$975$		0			0
$976$	−5089.58	−	8815.42i	−0.166920	−	0.289113i
$977$	−18231.8	−	31578.5i	−0.597020	−	1.03407i	−0.993258	−	0.115921i	$-0.963018\pi$
$977$	−18231.8	−	31578.5i	−0.597020	−	1.03407i	0.396239	−	0.918148i	$-0.370315\pi$
$978$		0			0
$979$	4321.34	−	7484.78i	0.141073	−	0.244346i
$980$	−19358.6			−0.631009
$981$		0			0
$982$	−53471.4			−1.73762
$983$	−25770.8	+	44636.3i	−0.836176	+	1.44830i	0.0568941	+	0.998380i	$0.481880\pi$
$983$	−25770.8	+	44636.3i	−0.836176	+	1.44830i	−0.893070	+	0.449918i	$0.851453\pi$
$984$		0			0
$985$	12017.9	+	20815.6i	0.388752	+	0.673339i
$986$	22206.5	+	38462.8i	0.717241	+	1.24230i
$987$		0			0
$988$	11576.8	−	20051.6i	0.372780	−	0.645675i
$989$	4530.12			0.145652
$990$		0			0
$991$	34299.1			1.09944			0.549721	−	0.835348i	$-0.314734\pi$
$991$	34299.1			1.09944			0.549721	+	0.835348i	$0.314734\pi$
$992$	28703.5	−	49715.9i	0.918685	−	1.59121i
$993$		0			0
$994$	34588.3	+	59908.8i	1.10370	+	1.91166i
$995$	784.582	+	1358.94i	0.0249979	+	0.0432976i
$996$		0			0
$997$	−10648.5	+	18443.7i	−0.338256	+	0.585877i	−0.984105	−	0.177589i	$-0.943170\pi$
$997$	−10648.5	+	18443.7i	−0.338256	+	0.585877i	0.645849	+	0.763465i	$0.276504\pi$
$998$	−35414.2			−1.12326
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.4.e.b.46.3		6
3.2	odd	2		45.4.e.b.16.1	✓	6
9.2	odd	6		405.4.a.h.1.3		3
9.4	even	3	inner	135.4.e.b.91.3		6
9.5	odd	6		45.4.e.b.31.1	yes	6
9.7	even	3		405.4.a.j.1.1		3
15.2	even	4		225.4.k.c.124.2		12
15.8	even	4		225.4.k.c.124.5		12
15.14	odd	2		225.4.e.c.151.3		6
45.14	odd	6		225.4.e.c.76.3		6
45.23	even	12		225.4.k.c.49.2		12
45.29	odd	6		2025.4.a.s.1.1		3
45.32	even	12		225.4.k.c.49.5		12
45.34	even	6		2025.4.a.q.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.4.e.b.16.1	✓	6	3.2	odd	2
45.4.e.b.31.1	yes	6	9.5	odd	6
135.4.e.b.46.3		6	1.1	even	1	trivial
135.4.e.b.91.3		6	9.4	even	3	inner
225.4.e.c.76.3		6	45.14	odd	6
225.4.e.c.151.3		6	15.14	odd	2
225.4.k.c.49.2		12	45.23	even	12
225.4.k.c.49.5		12	45.32	even	12
225.4.k.c.124.2		12	15.2	even	4
225.4.k.c.124.5		12	15.8	even	4
405.4.a.h.1.3		3	9.2	odd	6
405.4.a.j.1.1		3	9.7	even	3
2025.4.a.q.1.3		3	45.34	even	6
2025.4.a.s.1.1		3	45.29	odd	6

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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	135.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.87428 - 3.24635i) q^{2} +(-3.02587 - 5.24096i) q^{4} +(2.50000 + 4.33013i) q^{5} +(15.6746 - 27.1492i) q^{7} +7.30318 q^{8} +O(q^{10})\)	\(q+(1.87428 - 3.24635i) q^{2} +(-3.02587 - 5.24096i) q^{4} +(2.50000 + 4.33013i) q^{5} +(15.6746 - 27.1492i) q^{7} +7.30318 q^{8} +18.7428 q^{10} +(-10.4166 + 18.0422i) q^{11} +(-29.9655 - 51.9018i) q^{13} +(-58.7572 - 101.770i) q^{14} +(37.8952 - 65.6364i) q^{16} +74.0460 q^{17} -63.8390 q^{19} +(15.1294 - 26.2048i) q^{20} +(39.0475 + 67.6322i) q^{22} +(-16.4247 - 28.4484i) q^{23} +(-12.5000 + 21.6506i) q^{25} -224.655 q^{26} -189.717 q^{28} +(-80.0044 + 138.572i) q^{29} +(127.187 + 220.294i) q^{31} +(-112.840 - 195.444i) q^{32} +(138.783 - 240.379i) q^{34} +156.746 q^{35} +215.365 q^{37} +(-119.652 + 207.244i) q^{38} +(18.2579 + 31.6237i) q^{40} +(70.8407 + 122.700i) q^{41} +(-68.9529 + 119.430i) q^{43} +126.078 q^{44} -123.138 q^{46} +(16.7895 - 29.0803i) q^{47} +(-319.885 - 554.058i) q^{49} +(46.8571 + 81.1588i) q^{50} +(-181.344 + 314.096i) q^{52} +41.9914 q^{53} -104.166 q^{55} +(114.474 - 198.275i) q^{56} +(299.902 + 519.445i) q^{58} +(307.571 + 532.728i) q^{59} +(67.1535 - 116.313i) q^{61} +953.535 q^{62} -239.652 q^{64} +(149.828 - 259.509i) q^{65} +(428.767 + 742.646i) q^{67} +(-224.054 - 388.072i) q^{68} +(293.786 - 508.852i) q^{70} -588.665 q^{71} -618.191 q^{73} +(403.655 - 699.152i) q^{74} +(193.169 + 334.578i) q^{76} +(326.553 + 565.607i) q^{77} +(172.644 - 299.029i) q^{79} +378.952 q^{80} +531.102 q^{82} +(-546.584 + 946.711i) q^{83} +(185.115 + 320.629i) q^{85} +(258.474 + 447.691i) q^{86} +(-76.0746 + 131.765i) q^{88} -414.849 q^{89} -1878.79 q^{91} +(-99.3979 + 172.162i) q^{92} +(-62.9366 - 109.009i) q^{94} +(-159.598 - 276.431i) q^{95} +(100.705 - 174.427i) q^{97} -2398.22 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - q^{2} - 11 q^{4} + 15 q^{5} + 43 q^{7} + 54 q^{8}+O(q^{10}) \) 6 * q - q^2 - 11 * q^4 + 15 * q^5 + 43 * q^7 + 54 * q^8	\( 6 q - q^{2} - 11 q^{4} + 15 q^{5} + 43 q^{7} + 54 q^{8} - 10 q^{10} + 14 q^{11} - 40 q^{13} - 27 q^{14} + 13 q^{16} + 332 q^{17} - 328 q^{19} + 55 q^{20} + 376 q^{22} + 171 q^{23} - 75 q^{25} - 868 q^{26} - 1034 q^{28} - 335 q^{29} + 352 q^{31} - 77 q^{32} + 52 q^{34} + 430 q^{35} + 804 q^{37} - 178 q^{38} + 135 q^{40} + 187 q^{41} + 602 q^{43} - 1964 q^{44} - 402 q^{46} + 665 q^{47} - 430 q^{49} - 25 q^{50} + 456 q^{52} + 1460 q^{53} + 140 q^{55} + 705 q^{56} - 217 q^{58} - 298 q^{59} + 1439 q^{61} + 3228 q^{62} - 3138 q^{64} + 200 q^{65} + 1849 q^{67} - 710 q^{68} + 135 q^{70} - 140 q^{71} - 736 q^{73} - 320 q^{74} - 204 q^{76} - 948 q^{77} + 382 q^{79} + 130 q^{80} - 1150 q^{82} - 831 q^{83} + 830 q^{85} + 1580 q^{86} + 1428 q^{88} - 3438 q^{89} - 1420 q^{91} - 1623 q^{92} + 2077 q^{94} - 820 q^{95} + 282 q^{97} - 4328 q^{98}+O(q^{100}) \) 6 * q - q^2 - 11 * q^4 + 15 * q^5 + 43 * q^7 + 54 * q^8 - 10 * q^10 + 14 * q^11 - 40 * q^13 - 27 * q^14 + 13 * q^16 + 332 * q^17 - 328 * q^19 + 55 * q^20 + 376 * q^22 + 171 * q^23 - 75 * q^25 - 868 * q^26 - 1034 * q^28 - 335 * q^29 + 352 * q^31 - 77 * q^32 + 52 * q^34 + 430 * q^35 + 804 * q^37 - 178 * q^38 + 135 * q^40 + 187 * q^41 + 602 * q^43 - 1964 * q^44 - 402 * q^46 + 665 * q^47 - 430 * q^49 - 25 * q^50 + 456 * q^52 + 1460 * q^53 + 140 * q^55 + 705 * q^56 - 217 * q^58 - 298 * q^59 + 1439 * q^61 + 3228 * q^62 - 3138 * q^64 + 200 * q^65 + 1849 * q^67 - 710 * q^68 + 135 * q^70 - 140 * q^71 - 736 * q^73 - 320 * q^74 - 204 * q^76 - 948 * q^77 + 382 * q^79 + 130 * q^80 - 1150 * q^82 - 831 * q^83 + 830 * q^85 + 1580 * q^86 + 1428 * q^88 - 3438 * q^89 - 1420 * q^91 - 1623 * q^92 + 2077 * q^94 - 820 * q^95 + 282 * q^97 - 4328 * q^98

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