LMFDB - Embedded newform 304.5.r.c.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [304,5,Mod(65,304)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(304, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("304.65");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 304 = 2^{4} \cdot 19 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	304.r (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$31.4244687775$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 1024 x^{14} - 7028 x^{13} + 404698 x^{12} - 2337188 x^{11} + 77836288 x^{10} + \cdots + 23840536514409 $ x^16 - 8x^15 + 1024x^14 - 7028x^13 + 404698x^12 - 2337188x^11 + 77836288x^10 - 367923764x^9 + 7565874847x^8 - 28081380444x^7 + 352870494000x^6 - 961846520868x^5 + 6856327325898x^4 - 12141615583188x^3 + 32749209391860x^2 - 26834137576128*x + 23840536514409
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5} $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			145.2
Root			$0.500000 + 14.3823i$ of defining polynomial
Character	$\chi$	$=$	304.145
Dual form			304.5.r.c.65.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-10.4807 + 6.05105i) q^{3} +(9.13314 + 15.8191i) q^{5} +40.6944 q^{7} +(32.7305 - 56.6909i) q^{9} +O(q^{10})$	\(q+(-10.4807 + 6.05105i) q^{3} +(9.13314 + 15.8191i) q^{5} +40.6944 q^{7} +(32.7305 - 56.6909i) q^{9} +52.4698 q^{11} +(133.461 + 77.0538i) q^{13} +(-191.444 - 110.530i) q^{15} +(-137.797 - 238.671i) q^{17} +(70.6137 - 354.026i) q^{19} +(-426.507 + 246.244i) q^{21} +(448.573 - 776.951i) q^{23} +(145.671 - 252.310i) q^{25} -188.055i q^{27} +(268.560 + 155.053i) q^{29} +904.934i q^{31} +(-549.921 + 317.497i) q^{33} +(371.668 + 643.747i) q^{35} +115.035i q^{37} -1865.03 q^{39} +(1836.56 - 1060.34i) q^{41} +(1000.64 + 1733.16i) q^{43} +1195.73 q^{45} +(-2012.65 + 3486.01i) q^{47} -744.965 q^{49} +(2888.42 + 1667.63i) q^{51} +(2557.89 + 1476.80i) q^{53} +(479.214 + 830.022i) q^{55} +(1402.15 + 4137.74i) q^{57} +(5202.69 - 3003.77i) q^{59} +(606.668 - 1050.78i) q^{61} +(1331.95 - 2307.00i) q^{63} +2814.97i q^{65} +(5554.61 + 3206.96i) q^{67} +10857.4i q^{69} +(2812.41 - 1623.75i) q^{71} +(-3824.61 - 6624.43i) q^{73} +3525.86i q^{75} +2135.23 q^{77} +(-5809.97 + 3354.39i) q^{79} +(3789.10 + 6562.91i) q^{81} -8748.10 q^{83} +(2517.03 - 4359.63i) q^{85} -3752.94 q^{87} +(6846.92 + 3953.07i) q^{89} +(5431.12 + 3135.66i) q^{91} +(-5475.80 - 9484.37i) q^{93} +(6245.29 - 2116.33i) q^{95} +(6081.56 - 3511.19i) q^{97} +(1717.36 - 2974.56i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 12 q^{3} - 18 q^{5} - 72 q^{7} + 352 q^{9}+O(q^{10}) $ 16 * q + 12 * q^3 - 18 * q^5 - 72 * q^7 + 352 * q^9	$ 16 q + 12 q^{3} - 18 q^{5} - 72 q^{7} + 352 q^{9} + 84 q^{11} + 450 q^{13} + 390 q^{15} + 606 q^{17} + 306 q^{19} - 2160 q^{21} + 54 q^{23} - 434 q^{25} - 4914 q^{29} + 7890 q^{33} - 2328 q^{35} - 7620 q^{39} - 1692 q^{41} + 7402 q^{43} - 16720 q^{45} - 3198 q^{47} + 24816 q^{49} - 10710 q^{51} + 3870 q^{53} + 13588 q^{55} + 3702 q^{57} + 18288 q^{59} - 6522 q^{61} + 15676 q^{63} + 30168 q^{67} - 35874 q^{71} - 8080 q^{73} + 34560 q^{77} + 30738 q^{79} - 30920 q^{81} + 1476 q^{83} + 33626 q^{85} - 113100 q^{87} + 19782 q^{89} + 34260 q^{91} - 4272 q^{93} + 23706 q^{95} - 9936 q^{97} - 3848 q^{99}+O(q^{100}) $ 16 * q + 12 * q^3 - 18 * q^5 - 72 * q^7 + 352 * q^9 + 84 * q^11 + 450 * q^13 + 390 * q^15 + 606 * q^17 + 306 * q^19 - 2160 * q^21 + 54 * q^23 - 434 * q^25 - 4914 * q^29 + 7890 * q^33 - 2328 * q^35 - 7620 * q^39 - 1692 * q^41 + 7402 * q^43 - 16720 * q^45 - 3198 * q^47 + 24816 * q^49 - 10710 * q^51 + 3870 * q^53 + 13588 * q^55 + 3702 * q^57 + 18288 * q^59 - 6522 * q^61 + 15676 * q^63 + 30168 * q^67 - 35874 * q^71 - 8080 * q^73 + 34560 * q^77 + 30738 * q^79 - 30920 * q^81 + 1476 * q^83 + 33626 * q^85 - 113100 * q^87 + 19782 * q^89 + 34260 * q^91 - 4272 * q^93 + 23706 * q^95 - 9936 * q^97 - 3848 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/304\mathbb{Z}\right)^\times$.

$n$	$97$	$191$	$229$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	−10.4807	+	6.05105i	−1.16453	+	0.672339i	−0.952384	−	0.304900i	$-0.901377\pi$
$3$	−10.4807	+	6.05105i	−1.16453	+	0.672339i	−0.212141	+	0.977239i	$0.568044\pi$
$4$		0			0
$5$	9.13314	+	15.8191i	0.365326	+	0.632763i	0.988828	−	0.149059i	$-0.0476243\pi$
$5$	9.13314	+	15.8191i	0.365326	+	0.632763i	−0.623503	+	0.781821i	$0.714291\pi$
$6$		0			0
$7$	40.6944			0.830498			0.415249	−	0.909708i	$-0.363694\pi$
$7$	40.6944			0.830498			0.415249	+	0.909708i	$0.363694\pi$
$8$		0			0
$9$	32.7305	−	56.6909i	0.404080	−	0.699887i
$10$		0			0
$11$	52.4698			0.433634			0.216817	−	0.976212i	$-0.430432\pi$
$11$	52.4698			0.433634			0.216817	+	0.976212i	$0.430432\pi$
$12$		0			0
$13$	133.461	+	77.0538i	0.789711	+	0.455940i	0.839861	−	0.542802i	$-0.182637\pi$
$13$	133.461	+	77.0538i	0.789711	+	0.455940i	−0.0501501	+	0.998742i	$0.515970\pi$
$14$		0			0
$15$	−191.444	−	110.530i	−0.850862	−	0.491245i
$16$		0			0
$17$	−137.797	−	238.671i	−0.476805	−	0.825850i	0.522842	−	0.852430i	$-0.324872\pi$
$17$	−137.797	−	238.671i	−0.476805	−	0.825850i	−0.999647	+	0.0265796i	$0.991538\pi$
$18$		0			0
$19$	70.6137	−	354.026i	0.195606	−	0.980683i
$19$	70.6137	−	354.026i	0.195606	−	0.980683i
$20$		0			0
$21$	−426.507	+	246.244i	−0.967136	+	0.558376i
$22$		0			0
$23$	448.573	−	776.951i	0.847964	−	1.46872i	−0.0350577	−	0.999385i	$-0.511162\pi$
$23$	448.573	−	776.951i	0.847964	−	1.46872i	0.883022	−	0.469332i	$-0.155505\pi$
$24$		0			0
$25$	145.671	−	252.310i	0.233074	−	0.403697i
$26$		0			0
$27$		−	188.055i		−	0.257963i
$28$		0			0
$29$	268.560	+	155.053i	0.319334	+	0.184368i	0.651096	−	0.758996i	$-0.274310\pi$
$29$	268.560	+	155.053i	0.319334	+	0.184368i	−0.331762	+	0.943363i	$0.607643\pi$
$30$		0			0
$31$			904.934i			0.941659i	0.882224	+	0.470829i	$0.156045\pi$
$31$			904.934i			0.941659i	−0.882224	+	0.470829i	$0.843955\pi$
$32$		0			0
$33$	−549.921	+	317.497i	−0.504978	+	0.291549i
$34$		0			0
$35$	371.668	+	643.747i	0.303402	+	0.525508i
$36$		0			0
$37$			115.035i			0.0840282i	0.999117	+	0.0420141i	$0.0133774\pi$
$37$			115.035i			0.0840282i	−0.999117	+	0.0420141i	$0.986623\pi$
$38$		0			0
$39$	−1865.03			−1.22618
$40$		0			0
$41$	1836.56	−	1060.34i	1.09254	−	0.630778i	0.158288	−	0.987393i	$-0.449402\pi$
$41$	1836.56	−	1060.34i	1.09254	−	0.630778i	0.934251	+	0.356615i	$0.116069\pi$
$42$		0			0
$43$	1000.64	+	1733.16i	0.541179	+	0.937350i	0.998837	+	0.0482214i	$0.0153553\pi$
$43$	1000.64	+	1733.16i	0.541179	+	0.937350i	−0.457657	+	0.889129i	$0.651311\pi$
$44$		0			0
$45$	1195.73			0.590483
$46$		0			0
$47$	−2012.65	+	3486.01i	−0.911113	+	1.57809i	−0.0986174	+	0.995125i	$0.531442\pi$
$47$	−2012.65	+	3486.01i	−0.911113	+	1.57809i	−0.812495	+	0.582968i	$0.801891\pi$
$48$		0			0
$49$	−744.965			−0.310273
$50$		0			0
$51$	2888.42	+	1667.63i	1.11050	+	0.641149i
$52$		0			0
$53$	2557.89	+	1476.80i	0.910607	+	0.525739i	0.880626	−	0.473811i	$-0.157122\pi$
$53$	2557.89	+	1476.80i	0.910607	+	0.525739i	0.0299806	+	0.999550i	$0.490455\pi$
$54$		0			0
$55$	479.214	+	830.022i	0.158418	+	0.274388i
$56$		0			0
$57$	1402.15	+	4137.74i	0.431563	+	1.27354i
$58$		0			0
$59$	5202.69	−	3003.77i	1.49460	−	0.862905i	0.494615	−	0.869112i	$-0.335309\pi$
$59$	5202.69	−	3003.77i	1.49460	−	0.862905i	0.999981	+	0.00620675i	$0.00197568\pi$
$60$		0			0
$61$	606.668	−	1050.78i	0.163039	−	0.282392i	−0.772918	−	0.634506i	$-0.781204\pi$
$61$	606.668	−	1050.78i	0.163039	−	0.282392i	0.935957	+	0.352114i	$0.114537\pi$
$62$		0			0
$63$	1331.95	−	2307.00i	0.335588	−	0.581255i
$64$		0			0
$65$			2814.97i			0.666266i
$66$		0			0
$67$	5554.61	+	3206.96i	1.23738	+	0.714404i	0.968559	−	0.248785i	$-0.0800314\pi$
$67$	5554.61	+	3206.96i	1.23738	+	0.714404i	0.268825	+	0.963189i	$0.413365\pi$
$68$		0			0
$69$			10857.4i			2.28048i
$70$		0			0
$71$	2812.41	−	1623.75i	0.557907	−	0.322108i	−0.194398	−	0.980923i	$-0.562275\pi$
$71$	2812.41	−	1623.75i	0.557907	−	0.322108i	0.752305	+	0.658815i	$0.228942\pi$
$72$		0			0
$73$	−3824.61	−	6624.43i	−0.717698	−	1.24309i	−0.961910	−	0.273368i	$-0.911862\pi$
$73$	−3824.61	−	6624.43i	−0.717698	−	1.24309i	0.244211	−	0.969722i	$-0.421471\pi$
$74$		0			0
$75$			3525.86i			0.626820i
$76$		0			0
$77$	2135.23			0.360133
$78$		0			0
$79$	−5809.97	+	3354.39i	−0.930936	+	0.537476i	−0.887107	−	0.461563i	$-0.847289\pi$
$79$	−5809.97	+	3354.39i	−0.930936	+	0.537476i	−0.0438282	+	0.999039i	$0.513955\pi$
$80$		0			0
$81$	3789.10	+	6562.91i	0.577519	+	1.00029i
$82$		0			0
$83$	−8748.10			−1.26986			−0.634932	−	0.772568i	$-0.718972\pi$
$83$	−8748.10			−1.26986			−0.634932	+	0.772568i	$0.718972\pi$
$84$		0			0
$85$	2517.03	−	4359.63i	0.348378	−	0.603408i
$86$		0			0
$87$	−3752.94			−0.495830
$88$		0			0
$89$	6846.92	+	3953.07i	0.864401	+	0.499062i	0.865483	−	0.500938i	$-0.167011\pi$
$89$	6846.92	+	3953.07i	0.864401	+	0.499062i	−0.00108292	+	0.999999i	$0.500345\pi$
$90$		0			0
$91$	5431.12	+	3135.66i	0.655853	+	0.378657i
$92$		0			0
$93$	−5475.80	−	9484.37i	−0.633114	−	1.09659i
$94$		0			0
$95$	6245.29	−	2116.33i	0.691999	−	0.234497i
$96$		0			0
$97$	6081.56	−	3511.19i	0.646356	−	0.373174i	−0.140703	−	0.990052i	$-0.544936\pi$
$97$	6081.56	−	3511.19i	0.646356	−	0.373174i	0.787059	+	0.616878i	$0.211603\pi$
$98$		0			0
$99$	1717.36	−	2974.56i	0.175223	−	0.303495i
$100$		0			0
$101$	−4727.68	+	8188.57i	−0.463452	+	0.802723i	−0.999130	−	0.0416997i	$-0.986723\pi$
$101$	−4727.68	+	8188.57i	−0.463452	+	0.802723i	0.535678	+	0.844422i	$0.320056\pi$
$102$		0			0
$103$		−	1584.35i		−	0.149340i	−0.997208	−	0.0746699i	$-0.976210\pi$
$103$		−	1584.35i		−	0.149340i	0.997208	−	0.0746699i	$-0.0237903\pi$
$104$		0			0
$105$	−7790.70	−	4497.96i	−0.706639	−	0.407978i
$106$		0			0
$107$		−	5489.78i		−	0.479498i	−0.970835	−	0.239749i	$-0.922935\pi$
$107$		−	5489.78i		−	0.479498i	0.970835	−	0.239749i	$-0.0770652\pi$
$108$		0			0
$109$	−1219.92	+	704.320i	−0.102678	+	0.0592812i	−0.550460	−	0.834862i	$-0.685548\pi$
$109$	−1219.92	+	704.320i	−0.102678	+	0.0592812i	0.447782	+	0.894143i	$0.352214\pi$
$110$		0			0
$111$	−696.080	−	1205.65i	−0.0564954	−	0.0978530i
$112$		0			0
$113$			2362.53i			0.185021i	0.995712	+	0.0925105i	$0.0294892\pi$
$113$			2362.53i			0.185021i	−0.995712	+	0.0925105i	$0.970511\pi$
$114$		0			0
$115$	16387.5			1.23913
$116$		0			0
$117$	8736.49	−	5044.02i	0.638212	−	0.368472i
$118$		0			0
$119$	−5607.55	−	9712.56i	−0.395985	−	0.685867i
$120$		0			0
$121$	−11887.9			−0.811961
$122$		0			0
$123$	−12832.3	+	22226.2i	−0.848194	+	1.46911i
$124$		0			0
$125$	16738.2			1.07124
$126$		0			0
$127$	−20297.0	−	11718.5i	−1.25842	−	0.726547i	−0.285650	−	0.958334i	$-0.592210\pi$
$127$	−20297.0	−	11718.5i	−1.25842	−	0.726547i	−0.972767	+	0.231786i	$0.925543\pi$
$128$		0			0
$129$	−20974.9	−	12109.9i	−1.26043	−	0.727712i
$130$		0			0
$131$	−1960.23	−	3395.22i	−0.114226	−	0.197845i	0.803244	−	0.595650i	$-0.203105\pi$
$131$	−1960.23	−	3395.22i	−0.114226	−	0.197845i	−0.917470	+	0.397805i	$0.869772\pi$
$132$		0			0
$133$	2873.58	−	14406.9i	0.162450	−	0.814455i
$134$		0			0
$135$	2974.86	−	1717.53i	0.163229	−	0.0942405i
$136$		0			0
$137$	−13070.8	+	22639.4i	−0.696406	+	1.20621i	0.273298	+	0.961929i	$0.411885\pi$
$137$	−13070.8	+	22639.4i	−0.696406	+	1.20621i	−0.969704	+	0.244281i	$0.921448\pi$
$138$		0			0
$139$	9845.46	−	17052.8i	0.509573	−	0.882606i	−0.490366	−	0.871517i	$-0.663137\pi$
$139$	9845.46	−	17052.8i	0.509573	−	0.882606i	0.999939	−	0.0110893i	$-0.00352992\pi$
$140$		0			0
$141$		−	48714.5i		−	2.45031i
$142$		0			0
$143$	7002.67	+	4042.99i	0.342446	+	0.197711i
$144$		0			0
$145$			5664.49i			0.269417i
$146$		0			0
$147$	7807.78	−	4507.82i	0.361321	−	0.208609i
$148$		0			0
$149$	10988.5	+	19032.6i	0.494953	+	0.857284i	0.999983	−	0.00581763i	$-0.00185182\pi$
$149$	10988.5	+	19032.6i	0.494953	+	0.857284i	−0.505030	+	0.863102i	$0.668518\pi$
$150$		0			0
$151$			22987.8i			1.00819i	0.863647	+	0.504096i	$0.168174\pi$
$151$			22987.8i			1.00819i	−0.863647	+	0.504096i	$0.831826\pi$
$152$		0			0
$153$	−18040.6			−0.770669
$154$		0			0
$155$	−14315.2	+	8264.89i	−0.595846	+	0.344012i
$156$		0			0
$157$	20607.3	+	35692.9i	0.836029	+	1.44804i	0.893190	+	0.449680i	$0.148462\pi$
$157$	20607.3	+	35692.9i	0.836029	+	1.44804i	−0.0571609	+	0.998365i	$0.518205\pi$
$158$		0			0
$159$	−35744.8			−1.41390
$160$		0			0
$161$	18254.4	−	31617.6i	0.704233	−	1.21977i
$162$		0			0
$163$	3003.65			0.113051			0.0565254	−	0.998401i	$-0.481998\pi$
$163$	3003.65			0.113051			0.0565254	+	0.998401i	$0.481998\pi$
$164$		0			0
$165$	−10045.0	−	5799.49i	−0.368963	−	0.213021i
$166$		0			0
$167$	28990.2	+	16737.5i	1.03949	+	0.600147i	0.919688	−	0.392651i	$-0.128442\pi$
$167$	28990.2	+	16737.5i	1.03949	+	0.600147i	0.119798	+	0.992798i	$0.461775\pi$
$168$		0			0
$169$	−2405.93	−	4167.19i	−0.0842381	−	0.145905i
$170$		0			0
$171$	−17758.8	−	15590.6i	−0.607327	−	0.533176i
$172$		0			0
$173$	24129.7	−	13931.3i	0.806231	−	0.465478i	−0.0394143	−	0.999223i	$-0.512549\pi$
$173$	24129.7	−	13931.3i	0.806231	−	0.465478i	0.845645	+	0.533745i	$0.179216\pi$
$174$		0			0
$175$	5928.01	−	10267.6i	0.193568	−	0.335269i
$176$		0			0
$177$	−36352.0	+	62963.5i	−1.16033	+	2.00975i
$178$		0			0
$179$		−	9775.14i		−	0.305082i	−0.988297	−	0.152541i	$-0.951254\pi$
$179$		−	9775.14i		−	0.305082i	0.988297	−	0.152541i	$-0.0487457\pi$
$180$		0			0
$181$	−20831.3	−	12027.0i	−0.635858	−	0.367113i	0.147159	−	0.989113i	$-0.452987\pi$
$181$	−20831.3	−	12027.0i	−0.635858	−	0.367113i	−0.783017	+	0.622000i	$0.786320\pi$
$182$		0			0
$183$			14683.9i			0.438470i
$184$		0			0
$185$	−1819.74	+	1050.63i	−0.0531699	+	0.0306977i
$186$		0			0
$187$	−7230.15	−	12523.0i	−0.206759	−	0.358117i
$188$		0			0
$189$		−	7652.79i		−	0.214238i
$190$		0			0
$191$	−6591.39			−0.180680			−0.0903400	−	0.995911i	$-0.528795\pi$
$191$	−6591.39			−0.180680			−0.0903400	+	0.995911i	$0.528795\pi$
$192$		0			0
$193$	11519.8	−	6650.95i	0.309264	−	0.178554i	−0.337333	−	0.941385i	$-0.609525\pi$
$193$	11519.8	−	6650.95i	0.309264	−	0.178554i	0.646597	+	0.762832i	$0.276192\pi$
$194$		0			0
$195$	−17033.5	−	29503.0i	−0.447957	−	0.775883i
$196$		0			0
$197$	−8607.77			−0.221798			−0.110899	−	0.993832i	$-0.535373\pi$
$197$	−8607.77			−0.221798			−0.110899	+	0.993832i	$0.535373\pi$
$198$		0			0
$199$	18628.0	−	32264.6i	0.470391	−	0.814742i	−0.529035	−	0.848600i	$-0.677446\pi$
$199$	18628.0	−	32264.6i	0.470391	−	0.814742i	0.999427	+	0.0338581i	$0.0107794\pi$
$200$		0			0
$201$	−77621.9			−1.92129
$202$		0			0
$203$	10928.9	+	6309.80i	0.265206	+	0.153117i
$204$		0			0
$205$	33547.1	+	19368.4i	0.798266	+	0.460879i
$206$		0			0
$207$	−29364.0	−	50860.0i	−0.685291	−	1.18696i
$208$		0			0
$209$	3705.08	−	18575.7i	0.0848214	−	0.425258i
$210$		0			0
$211$	−64223.3	+	37079.3i	−1.44254	+	0.832850i	−0.998019	−	0.0629190i	$-0.979959\pi$
$211$	−64223.3	+	37079.3i	−1.44254	+	0.832850i	−0.444520	+	0.895769i	$0.646626\pi$
$212$		0			0
$213$	−19650.7	+	34036.1i	−0.433131	+	0.750205i
$214$		0			0
$215$	−18278.0	+	31658.4i	−0.395413	+	0.684876i
$216$		0			0
$217$			36825.8i			0.782046i
$218$		0			0
$219$	80169.5	+	46285.9i	1.67156	+	0.965073i
$220$		0			0
$221$		−	42471.0i		−	0.869577i
$222$		0			0
$223$	73682.3	−	42540.5i	1.48168	−	0.855447i	0.481894	−	0.876230i	$-0.339949\pi$
$223$	73682.3	−	42540.5i	1.48168	−	0.855447i	0.999784	+	0.0207829i	$0.00661587\pi$
$224$		0			0
$225$	−9535.79	−	16516.5i	−0.188361	−	0.326251i
$226$		0			0
$227$		−	34377.0i		−	0.667140i	−0.942725	−	0.333570i	$-0.891747\pi$
$227$		−	34377.0i		−	0.667140i	0.942725	−	0.333570i	$-0.108253\pi$
$228$		0			0
$229$	−16889.2			−0.322062			−0.161031	−	0.986949i	$-0.551482\pi$
$229$	−16889.2			−0.322062			−0.161031	+	0.986949i	$0.551482\pi$
$230$		0			0
$231$	−22378.7	+	12920.4i	−0.419384	+	0.242131i
$232$		0			0
$233$	−7596.98	−	13158.4i	−0.139936	−	0.242376i	0.787536	−	0.616268i	$-0.211356\pi$
$233$	−7596.98	−	13158.4i	−0.139936	−	0.242376i	−0.927472	+	0.373892i	$0.878023\pi$
$234$		0			0
$235$	−73527.2			−1.33141
$236$		0			0
$237$	40595.1	−	70312.9i	0.722732	−	1.25181i
$238$		0			0
$239$	−35768.6			−0.626190			−0.313095	−	0.949722i	$-0.601366\pi$
$239$	−35768.6			−0.626190			−0.313095	+	0.949722i	$0.601366\pi$
$240$		0			0
$241$	−91819.3	−	53011.9i	−1.58088	−	0.912723i	−0.994731	−	0.102523i	$-0.967309\pi$
$241$	−91819.3	−	53011.9i	−1.58088	−	0.912723i	−0.586153	−	0.810201i	$-0.699358\pi$
$242$		0			0
$243$	−66233.4	−	38239.9i	−1.12167	−	0.647595i
$244$		0			0
$245$	−6803.87	−	11784.7i	−0.113351	−	0.196329i
$246$		0			0
$247$	36703.3	−	41807.7i	0.601604	−	0.685271i
$248$		0			0
$249$	91686.4	−	52935.2i	1.47879	−	0.853780i
$250$		0			0
$251$	27632.2	−	47860.4i	0.438600	−	0.759678i	−0.558982	−	0.829180i	$-0.688808\pi$
$251$	27632.2	−	47860.4i	0.438600	−	0.759678i	0.997582	+	0.0695024i	$0.0221411\pi$
$252$		0			0
$253$	23536.5	−	40766.4i	0.367706	−	0.636886i
$254$		0			0
$255$			60922.7i			0.936913i
$256$		0			0
$257$	38690.0	+	22337.7i	0.585778	+	0.338199i	0.763426	−	0.645895i	$-0.223516\pi$
$257$	38690.0	+	22337.7i	0.585778	+	0.338199i	−0.177649	+	0.984094i	$0.556849\pi$
$258$		0			0
$259$			4681.26i			0.0697853i
$260$		0			0
$261$	17580.2	−	10149.9i	0.258073	−	0.148999i
$262$		0			0
$263$	29030.4	+	50282.2i	0.419703	+	0.726947i	0.995909	−	0.0903572i	$-0.0288009\pi$
$263$	29030.4	+	50282.2i	0.419703	+	0.726947i	−0.576206	+	0.817304i	$0.695468\pi$
$264$		0			0
$265$			53951.3i			0.768264i
$266$		0			0
$267$	−95680.9			−1.34216
$268$		0			0
$269$	62637.7	−	36163.9i	0.865627	−	0.499770i	−0.000265353	−	1.00000i	$-0.500084\pi$
$269$	62637.7	−	36163.9i	0.865627	−	0.499770i	0.865893	+	0.500230i	$0.166751\pi$
$270$		0			0
$271$	43116.8	+	74680.5i	0.587094	+	1.01688i	0.994611	+	0.103680i	$0.0330616\pi$
$271$	43116.8	+	74680.5i	0.587094	+	1.01688i	−0.407516	+	0.913198i	$0.633605\pi$
$272$		0			0
$273$	−75896.1			−1.01834
$274$		0			0
$275$	7643.35	−	13238.7i	0.101069	−	0.175057i
$276$		0			0
$277$	133588.			1.74103			0.870516	−	0.492139i	$-0.163785\pi$
$277$	133588.			1.74103			0.870516	+	0.492139i	$0.163785\pi$
$278$		0			0
$279$	51301.5	+	29618.9i	0.659055	+	0.380505i
$280$		0			0
$281$	−67741.3	−	39110.5i	−0.857908	−	0.495314i	0.00540286	−	0.999985i	$-0.498280\pi$
$281$	−67741.3	−	39110.5i	−0.857908	−	0.495314i	−0.863311	+	0.504672i	$0.831614\pi$
$282$		0			0
$283$	−1941.73	−	3363.17i	−0.0242446	−	0.0419929i	0.853649	−	0.520849i	$-0.174385\pi$
$283$	−1941.73	−	3363.17i	−0.0242446	−	0.0419929i	−0.877893	+	0.478857i	$0.841051\pi$
$284$		0			0
$285$	−52649.2	+	59971.3i	−0.648189	+	0.738335i
$286$		0			0
$287$	74737.7	−	43149.8i	0.907352	−	0.523860i
$288$		0			0
$289$	3784.71	−	6555.31i	0.0453145	−	0.0784870i
$290$		0			0
$291$	−42492.8	+	73599.7i	−0.501799	+	0.869141i
$292$		0			0
$293$			115090.i			1.34061i	0.742087	+	0.670304i	$0.233836\pi$
$293$			115090.i			1.34061i	−0.742087	+	0.670304i	$0.766164\pi$
$294$		0			0
$295$	95033.8	+	54867.8i	1.09203	+	0.630483i
$296$		0			0
$297$		−	9867.21i		−	0.111862i
$298$		0			0
$299$	119734.	−	69128.5i	1.33929	−	0.773241i
$300$		0			0
$301$	40720.5	+	70529.9i	0.449448	+	0.778467i
$302$		0			0
$303$		−	114430.i		−	1.24639i
$304$		0			0
$305$	22163.1			0.238249
$306$		0			0
$307$	−24719.2	+	14271.7i	−0.262276	+	0.151425i	−0.625372	−	0.780327i	$-0.715053\pi$
$307$	−24719.2	+	14271.7i	−0.262276	+	0.151425i	0.363096	+	0.931752i	$0.381720\pi$
$308$		0			0
$309$	9586.96	+	16605.1i	0.100407	+	0.173910i
$310$		0			0
$311$	13146.5			0.135921			0.0679607	−	0.997688i	$-0.478351\pi$
$311$	13146.5			0.135921			0.0679607	+	0.997688i	$0.478351\pi$
$312$		0			0
$313$	−87731.9	+	151956.i	−0.895507	+	1.55106i	−0.0623313	+	0.998056i	$0.519854\pi$
$313$	−87731.9	+	151956.i	−0.895507	+	1.55106i	−0.833176	+	0.553008i	$0.813480\pi$
$314$		0			0
$315$	48659.5			0.490395
$316$		0			0
$317$	75547.7	+	43617.5i	0.751801	+	0.434052i	0.826344	−	0.563165i	$-0.190417\pi$
$317$	75547.7	+	43617.5i	0.751801	+	0.434052i	−0.0745435	+	0.997218i	$0.523750\pi$
$318$		0			0
$319$	14091.3	+	8135.60i	0.138474	+	0.0799482i
$320$		0			0
$321$	33218.9	+	57536.9i	0.322385	+	0.558388i
$322$		0			0
$323$	−94226.0	+	31930.2i	−0.903162	+	0.306053i
$324$		0			0
$325$	38882.9	−	22449.1i	0.368123	−	0.212536i
$326$		0			0
$327$	8523.75	−	14763.6i	0.0797141	−	0.138069i
$328$		0			0
$329$	−81903.5	+	141861.i	−0.756677	+	1.31060i
$330$		0			0
$331$			161860.i			1.47735i	0.674060	+	0.738677i	$0.264549\pi$
$331$			161860.i			1.47735i	−0.674060	+	0.738677i	$0.735451\pi$
$332$		0			0
$333$	6521.41	+	3765.14i	0.0588102	+	0.0339541i
$334$		0			0
$335$			117158.i			1.04396i
$336$		0			0
$337$	110393.	−	63735.2i	0.972031	−	0.561203i	0.0721764	−	0.997392i	$-0.477006\pi$
$337$	110393.	−	63735.2i	0.972031	−	0.561203i	0.899855	+	0.436189i	$0.143672\pi$
$338$		0			0
$339$	−14295.8	−	24761.1i	−0.124397	−	0.215462i
$340$		0			0
$341$			47481.7i			0.408336i
$342$		0			0
$343$	−128023.			−1.08818
$344$		0			0
$345$	−171753.	+	99161.8i	−1.44300	+	0.833117i
$346$		0			0
$347$	71952.7	+	124626.i	0.597569	+	1.03502i	0.993179	+	0.116602i	$0.0372001\pi$
$347$	71952.7	+	124626.i	0.597569	+	1.03502i	−0.395609	+	0.918419i	$0.629467\pi$
$348$		0			0
$349$	−66908.7			−0.549328			−0.274664	−	0.961540i	$-0.588567\pi$
$349$	−66908.7			−0.549328			−0.274664	+	0.961540i	$0.588567\pi$
$350$		0			0
$351$	14490.4	−	25098.0i	0.117616	−	0.203716i
$352$		0			0
$353$	116126.			0.931921			0.465961	−	0.884806i	$-0.345709\pi$
$353$	116126.			0.931921			0.465961	+	0.884806i	$0.345709\pi$
$354$		0			0
$355$	51372.3	+	29659.8i	0.407635	+	0.235348i
$356$		0			0
$357$	117542.	+	67863.2i	0.922270	+	0.532473i
$358$		0			0
$359$	−46490.7	−	80524.3i	−0.360726	−	0.624795i	0.627355	−	0.778734i	$-0.284138\pi$
$359$	−46490.7	−	80524.3i	−0.360726	−	0.624795i	−0.988080	+	0.153938i	$0.950804\pi$
$360$		0			0
$361$	−120348.	−	49998.2i	−0.923477	−	0.383654i
$362$		0			0
$363$	124594.	−	71934.5i	0.945550	−	0.545913i
$364$		0			0
$365$	69861.5	−	121004.i	0.524387	−	0.908265i
$366$		0			0
$367$	−5846.49	+	10126.4i	−0.0434073	+	0.0751837i	−0.886913	−	0.461937i	$-0.847155\pi$
$367$	−5846.49	+	10126.4i	−0.0434073	+	0.0751837i	0.843505	+	0.537121i	$0.180488\pi$
$368$		0			0
$369$		−	138821.i		−	1.01954i
$370$		0			0
$371$	104092.	+	60097.6i	0.756257	+	0.436625i
$372$		0			0
$373$		−	56159.4i		−	0.403650i	−0.979422	−	0.201825i	$-0.935313\pi$
$373$		−	56159.4i		−	0.403650i	0.979422	−	0.201825i	$-0.0646872\pi$
$374$		0			0
$375$	−175428.	+	101284.i	−1.24749	+	0.720239i
$376$		0			0
$377$	23894.9	+	41387.1i	0.168121	+	0.291194i
$378$		0			0
$379$			77613.7i			0.540331i	0.962814	+	0.270165i	$0.0870784\pi$
$379$			77613.7i			0.540331i	−0.962814	+	0.270165i	$0.912922\pi$
$380$		0			0
$381$	283637.			1.95395
$382$		0			0
$383$	203087.	−	117252.i	1.38447	−	0.799327i	0.391789	−	0.920055i	$-0.371856\pi$
$383$	203087.	−	117252.i	1.38447	−	0.799327i	0.992686	+	0.120728i	$0.0385229\pi$
$384$		0			0
$385$	19501.3	+	33777.3i	0.131566	+	0.227878i
$386$		0			0
$387$	131006.			0.874719
$388$		0			0
$389$	60585.7	−	104938.i	0.400379	−	0.693476i	−0.593393	−	0.804913i	$-0.702212\pi$
$389$	60585.7	−	104938.i	0.400379	−	0.693476i	0.993772	+	0.111437i	$0.0355453\pi$
$390$		0			0
$391$	−247247.			−1.61725
$392$		0			0
$393$	41089.3	+	23722.9i	0.266038	+	0.153597i
$394$		0			0
$395$	−106127.	−	61272.2i	−0.680189	−	0.392707i
$396$		0			0
$397$	−84743.0	−	146779.i	−0.537679	−	0.931287i	−0.999029	−	0.0440685i	$-0.985968\pi$
$397$	−84743.0	−	146779.i	−0.537679	−	0.931287i	0.461350	−	0.887218i	$-0.347365\pi$
$398$		0			0
$399$	57059.7	+	168383.i	0.358413	+	1.05768i
$400$		0			0
$401$	53887.1	−	31111.8i	0.335117	−	0.193480i	−0.322994	−	0.946401i	$-0.604689\pi$
$401$	53887.1	−	31111.8i	0.335117	−	0.193480i	0.658111	+	0.752921i	$0.271356\pi$
$402$		0			0
$403$	−69728.6	+	120773.i	−0.429339	+	0.743638i
$404$		0			0
$405$	−69212.8	+	119880.i	−0.421965	+	0.730864i
$406$		0			0
$407$			6035.84i			0.0364375i
$408$		0			0
$409$	−19314.6	−	11151.3i	−0.115462	−	0.0666621i	0.441157	−	0.897430i	$-0.354568\pi$
$409$	−19314.6	−	11151.3i	−0.115462	−	0.0666621i	−0.556619	+	0.830768i	$0.687902\pi$
$410$		0			0
$411$		−	316369.i		−	1.87288i
$412$		0			0
$413$	211720.	−	122237.i	1.24126	−	0.716641i
$414$		0			0
$415$	−79897.6	−	138387.i	−0.463914	−	0.803523i
$416$		0			0
$417$			238302.i			1.37042i
$418$		0			0
$419$	276136.			1.57288			0.786438	−	0.617669i	$-0.211923\pi$
$419$	276136.			1.57288			0.786438	+	0.617669i	$0.211923\pi$
$420$		0			0
$421$	−245912.	+	141977.i	−1.38744	+	0.801041i	−0.993027	−	0.117890i	$-0.962387\pi$
$421$	−245912.	+	141977.i	−1.38744	+	0.801041i	−0.394417	+	0.918931i	$0.629054\pi$
$422$		0			0
$423$	131750.	+	228197.i	0.736325	+	1.27535i
$424$		0			0
$425$	−80292.1			−0.444524
$426$		0			0
$427$	24688.0	−	42760.9i	0.135404	−	0.234526i
$428$		0			0
$429$	−97857.5			−0.531716
$430$		0			0
$431$	−91869.3	−	53040.8i	−0.494557	−	0.285532i	0.231906	−	0.972738i	$-0.425504\pi$
$431$	−91869.3	−	53040.8i	−0.494557	−	0.285532i	−0.726463	+	0.687206i	$0.758837\pi$
$432$		0			0
$433$	−154599.	−	89257.9i	−0.824577	−	0.476070i	0.0274149	−	0.999624i	$-0.491272\pi$
$433$	−154599.	−	89257.9i	−0.824577	−	0.476070i	−0.851992	+	0.523554i	$0.824606\pi$
$434$		0			0
$435$	−34276.1	−	59368.0i	−0.181140	−	0.313743i
$436$		0			0
$437$	−243386.	−	213670.i	−1.27448	−	1.11887i
$438$		0			0
$439$	156345.	−	90265.9i	0.811252	−	0.468376i	−0.0361388	−	0.999347i	$-0.511506\pi$
$439$	156345.	−	90265.9i	0.811252	−	0.468376i	0.847390	+	0.530970i	$0.178173\pi$
$440$		0			0
$441$	−24383.1	+	42232.7i	−0.125375	+	0.217156i
$442$		0			0
$443$	116330.	−	201489.i	0.592766	−	1.02670i	−0.401092	−	0.916038i	$-0.631369\pi$
$443$	116330.	−	201489.i	0.592766	−	1.02670i	0.993858	−	0.110663i	$-0.0352976\pi$
$444$		0			0
$445$			144416.i			0.729280i
$446$		0			0
$447$	−230334.	−	132983.i	−1.15277	−	0.665553i
$448$		0			0
$449$		−	182552.i		−	0.905510i	−0.891635	−	0.452755i	$-0.850441\pi$
$449$		−	182552.i		−	0.905510i	0.891635	−	0.452755i	$-0.149559\pi$
$450$		0			0
$451$	96363.8	−	55635.7i	0.473763	−	0.273527i
$452$		0			0
$453$	−139100.	−	240929.i	−0.677848	−	1.17407i
$454$		0			0
$455$			114554.i			0.553332i
$456$		0			0
$457$	78140.6			0.374149			0.187074	−	0.982346i	$-0.440099\pi$
$457$	78140.6			0.374149			0.187074	+	0.982346i	$0.440099\pi$
$458$		0			0
$459$	−44883.2	+	25913.4i	−0.213039	+	0.122998i
$460$		0			0
$461$	−110657.	−	191663.i	−0.520687	−	0.901856i	−0.999711	−	0.0240539i	$-0.992343\pi$
$461$	−110657.	−	191663.i	−0.520687	−	0.901856i	0.479024	−	0.877802i	$-0.340991\pi$
$462$		0			0
$463$	−330182.			−1.54025			−0.770126	−	0.637891i	$-0.779807\pi$
$463$	−330182.			−1.54025			−0.770126	+	0.637891i	$0.779807\pi$
$464$		0			0
$465$	100023.	−	173244.i	0.462586	−	0.801222i
$466$		0			0
$467$	−123478.			−0.566183			−0.283092	−	0.959093i	$-0.591360\pi$
$467$	−123478.			−0.566183			−0.283092	+	0.959093i	$0.591360\pi$
$468$		0			0
$469$	226042.	+	130505.i	1.02764	+	0.593311i
$470$		0			0
$471$	−431959.	−	249391.i	−1.94715	−	1.12419i
$472$		0			0
$473$	52503.4	+	90938.5i	0.234674	+	0.406467i
$474$		0			0
$475$	−79038.2	−	69388.1i	−0.350308	−	0.307537i
$476$		0			0
$477$	167442.	−	96672.8i	0.735916	−	0.424881i
$478$		0			0
$479$	−70014.4	+	121269.i	−0.305152	+	0.528539i	−0.977295	−	0.211882i	$-0.932041\pi$
$479$	−70014.4	+	121269.i	−0.305152	+	0.528539i	0.672143	+	0.740421i	$0.265374\pi$
$480$		0			0
$481$	−8863.85	+	15352.6i	−0.0383118	+	0.0663579i
$482$		0			0
$483$			441834.i			1.89393i
$484$		0			0
$485$	111088.	+	64136.4i	0.472261	+	0.272660i
$486$		0			0
$487$		−	141943.i		−	0.598489i	−0.954176	−	0.299245i	$-0.903265\pi$
$487$		−	141943.i		−	0.598489i	0.954176	−	0.299245i	$-0.0967347\pi$
$488$		0			0
$489$	−31480.4	+	18175.2i	−0.131650	+	0.0760084i
$490$		0			0
$491$	1364.05	+	2362.60i	0.00565804	+	0.00980001i	0.868841	−	0.495092i	$-0.164866\pi$
$491$	1364.05	+	2362.60i	0.00565804	+	0.00980001i	−0.863183	+	0.504892i	$0.831532\pi$
$492$		0			0
$493$		−	85463.2i		−	0.351630i
$494$		0			0
$495$	62739.6			0.256054
$496$		0			0
$497$	114449.	−	66077.3i	0.463341	−	0.267510i
$498$		0			0
$499$	105201.	+	182214.i	0.422494	+	0.731780i	0.996183	−	0.0872927i	$-0.0278215\pi$
$499$	105201.	+	182214.i	0.422494	+	0.731780i	−0.573689	+	0.819073i	$0.694488\pi$
$500$		0			0
$501$	−405118.			−1.61401
$502$		0			0
$503$	159932.	−	277011.i	0.632121	−	1.09486i	−0.354997	−	0.934867i	$-0.615518\pi$
$503$	159932.	−	277011.i	0.632121	−	1.09486i	0.987117	−	0.159997i	$-0.0511486\pi$
$504$		0			0
$505$	−172714.			−0.677244
$506$		0			0
$507$	50431.7	+	29116.8i	0.196195	+	0.113273i
$508$		0			0
$509$	−116894.	−	67488.9i	−0.451188	−	0.260493i	0.257144	−	0.966373i	$-0.417219\pi$
$509$	−116894.	−	67488.9i	−0.451188	−	0.260493i	−0.708332	+	0.705880i	$0.750552\pi$
$510$		0			0
$511$	−155640.	−	269577.i	−0.596047	−	1.03238i
$512$		0			0
$513$	−66576.5	−	13279.3i	−0.252980	−	0.0504591i
$514$		0			0
$515$	25062.9	−	14470.0i	0.0944966	−	0.0545576i
$516$		0			0
$517$	−105603.	+	182910.i	−0.395090	+	0.684315i
$518$		0			0
$519$	−168598.	+	292020.i	−0.625918	+	1.08412i
$520$		0			0
$521$			253689.i			0.934601i	0.884099	+	0.467300i	$0.154773\pi$
$521$			253689.i			0.934601i	−0.884099	+	0.467300i	$0.845227\pi$
$522$		0			0
$523$	−287975.	−	166262.i	−1.05281	−	0.607841i	−0.129377	−	0.991596i	$-0.541298\pi$
$523$	−287975.	−	166262.i	−1.05281	−	0.607841i	−0.923435	+	0.383754i	$0.874631\pi$
$524$		0			0
$525$			143483.i			0.520573i
$526$		0			0
$527$	215981.	−	124697.i	0.777669	−	0.448987i
$528$		0			0
$529$	−262515.	−	454689.i	−0.938087	−	1.62481i
$530$		0			0
$531$		−	393260.i		−	1.39473i
$532$		0			0
$533$	326812.			1.15039
$534$		0			0
$535$	86843.1	−	50138.9i	0.303409	−	0.175173i
$536$		0			0
$537$	59149.9	+	102451.i	0.205119	+	0.355276i
$538$		0			0
$539$	−39088.1			−0.134545
$540$		0			0
$541$	−156555.	+	271161.i	−0.534899	+	0.926473i	0.464269	+	0.885694i	$0.346317\pi$
$541$	−156555.	+	271161.i	−0.534899	+	0.926473i	−0.999168	+	0.0407784i	$0.987016\pi$
$542$		0			0
$543$	291104.			0.987297
$544$		0			0
$545$	−22283.4	−	12865.3i	−0.0750218	−	0.0433139i
$546$		0			0
$547$	54608.4	+	31528.2i	0.182509	+	0.105372i	0.588471	−	0.808518i	$-0.299730\pi$
$547$	54608.4	+	31528.2i	0.182509	+	0.105372i	−0.405962	+	0.913890i	$0.633063\pi$
$548$		0			0
$549$	−39713.1	−	68785.0i	−0.131762	−	0.228218i
$550$		0			0
$551$	73856.9	−	84128.5i	0.243270	−	0.277102i
$552$		0			0
$553$	−236433.	+	136505.i	−0.773140	+	0.446373i
$554$		0			0
$555$	12714.8	−	22022.7i	0.0412785	−	0.0714964i
$556$		0			0
$557$	−98461.3	+	170540.i	−0.317362	+	0.549688i	−0.979937	−	0.199308i	$-0.936130\pi$
$557$	−98461.3	+	170540.i	−0.317362	+	0.549688i	0.662575	+	0.748996i	$0.269464\pi$
$558$		0			0
$559$			308413.i			0.986980i
$560$		0			0
$561$	151555.	+	87500.1i	0.481552	+	0.278024i
$562$		0			0
$563$			307676.i			0.970681i	0.874325	+	0.485341i	$0.161304\pi$
$563$			307676.i			0.970681i	−0.874325	+	0.485341i	$0.838696\pi$
$564$		0			0
$565$	−37373.1	+	21577.3i	−0.117074	+	0.0675929i
$566$		0			0
$567$	154195.	+	267074.i	0.479628	+	0.830740i
$568$		0			0
$569$			249874.i			0.771785i	0.922544	+	0.385892i	$0.126106\pi$
$569$			249874.i			0.771785i	−0.922544	+	0.385892i	$0.873894\pi$
$570$		0			0
$571$	−333305.			−1.02228			−0.511140	−	0.859498i	$-0.670777\pi$
$571$	−333305.			−1.02228			−0.511140	+	0.859498i	$0.670777\pi$
$572$		0			0
$573$	69082.6	−	39884.8i	0.210407	−	0.121478i
$574$		0			0
$575$	−130689.	−	226359.i	−0.395277	−	0.684641i
$576$		0			0
$577$	452372.			1.35876			0.679382	−	0.733785i	$-0.262248\pi$
$577$	452372.			1.35876			0.679382	+	0.733785i	$0.262248\pi$
$578$		0			0
$579$	−80490.4	+	139414.i	−0.240097	+	0.415861i
$580$		0			0
$581$	−355999.			−1.05462
$582$		0			0
$583$	134212.	+	77487.4i	0.394870	+	0.227979i
$584$		0			0
$585$	159583.	+	92135.4i	0.466311	+	0.269225i
$586$		0			0
$587$	112606.	+	195040.i	0.326803	+	0.566040i	0.981876	−	0.189526i	$-0.0606953\pi$
$587$	112606.	+	195040.i	0.326803	+	0.566040i	−0.655072	+	0.755566i	$0.727362\pi$
$588$		0			0
$589$	320371.	+	63900.7i	0.923468	+	0.184194i
$590$		0			0
$591$	90215.7	−	52086.1i	0.258290	−	0.149124i
$592$		0			0
$593$	225542.	−	390650.i	0.641384	−	1.11091i	−0.343740	−	0.939065i	$-0.611694\pi$
$593$	225542.	−	390650.i	0.641384	−	1.11091i	0.985124	−	0.171844i	$-0.0549726\pi$
$594$		0			0
$595$	102429.	−	177412.i	0.289327	−	0.501129i
$596$		0			0
$597$			450875.i			1.26505i
$598$		0			0
$599$	376004.	+	217086.i	1.04795	+	0.605032i	0.922074	−	0.387014i	$-0.126494\pi$
$599$	376004.	+	217086.i	1.04795	+	0.605032i	0.125873	+	0.992046i	$0.459827\pi$
$600$		0			0
$601$		−	545183.i		−	1.50936i	−0.656091	−	0.754681i	$-0.727791\pi$
$601$		−	545183.i		−	1.50936i	0.656091	−	0.754681i	$-0.272209\pi$
$602$		0			0
$603$	363610.	−	209931.i	1.00000	−	0.577352i
$604$		0			0
$605$	−108574.	−	188056.i	−0.296630	−	0.513779i
$606$		0			0
$607$			2996.79i			0.00813352i	0.999992	+	0.00406676i	$0.00129449\pi$
$607$			2996.79i			0.00813352i	−0.999992	+	0.00406676i	$0.998706\pi$
$608$		0			0
$609$	−152724.			−0.411786
$610$		0			0
$611$	−537220.	+	310164.i	−1.43903	+	0.830825i
$612$		0			0
$613$	−42295.9	−	73258.7i	−0.112558	−	0.194957i	0.804243	−	0.594301i	$-0.202571\pi$
$613$	−42295.9	−	73258.7i	−0.112558	−	0.194957i	−0.916801	+	0.399344i	$0.869238\pi$
$614$		0			0
$615$	−468798.			−1.23947
$616$		0			0
$617$	276736.	−	479321.i	0.726935	−	1.25909i	−0.231238	−	0.972897i	$-0.574278\pi$
$617$	276736.	−	479321.i	0.726935	−	1.25909i	0.958173	−	0.286191i	$-0.0923891\pi$
$618$		0			0
$619$	−434064.			−1.13285			−0.566426	−	0.824113i	$-0.691674\pi$
$619$	−434064.			−1.13285			−0.566426	+	0.824113i	$0.691674\pi$
$620$		0			0
$621$	−146110.	−	84356.5i	−0.378875	−	0.218744i
$622$		0			0
$623$	278631.	+	160868.i	0.717883	+	0.414470i
$624$		0			0
$625$	61827.5	+	107088.i	0.158278	+	0.274146i
$626$		0			0
$627$	73570.5	+	217106.i	0.187141	+	0.552252i
$628$		0			0
$629$	27455.4	−	15851.4i	0.0693947	−	0.0400650i
$630$		0			0
$631$	−94963.7	+	164482.i	−0.238506	+	0.413104i	−0.960286	−	0.279018i	$-0.909991\pi$
$631$	−94963.7	+	164482.i	−0.238506	+	0.413104i	0.721780	+	0.692123i	$0.243324\pi$
$632$		0			0
$633$	448738.	−	777237.i	1.11992	−	1.93975i
$634$		0			0
$635$		−	428106.i		−	1.06171i
$636$		0			0
$637$	−99423.9	−	57402.4i	−0.245026	−	0.141466i
$638$		0			0
$639$		−	212584.i		−	0.520629i
$640$		0			0
$641$	−176029.	+	101631.i	−0.428419	+	0.247348i	−0.698673	−	0.715441i	$-0.746226\pi$
$641$	−176029.	+	101631.i	−0.428419	+	0.247348i	0.270254	+	0.962789i	$0.412892\pi$
$642$		0			0
$643$	−262304.	−	454324.i	−0.634430	−	1.09886i	−0.986636	−	0.162942i	$-0.947902\pi$
$643$	−262304.	−	454324.i	−0.634430	−	1.09886i	0.352206	−	0.935923i	$-0.385432\pi$
$644$		0			0
$645$		−	442404.i		−	1.06341i
$646$		0			0
$647$	−223408.			−0.533690			−0.266845	−	0.963739i	$-0.585981\pi$
$647$	−223408.			−0.533690			−0.266845	+	0.963739i	$0.585981\pi$
$648$		0			0
$649$	272984.	−	157607.i	0.648108	−	0.374185i
$650$		0			0
$651$	−222835.	−	385961.i	−0.525800	−	0.910712i
$652$		0			0
$653$	−333259.			−0.781548			−0.390774	−	0.920487i	$-0.627793\pi$
$653$	−333259.			−0.781548			−0.390774	+	0.920487i	$0.627793\pi$
$654$		0			0
$655$	35806.1	−	62018.0i	0.0834593	−	0.144556i
$656$		0			0
$657$	−500726.			−1.16003
$658$		0			0
$659$	−143860.	−	83057.9i	−0.331261	−	0.191254i	0.325140	−	0.945666i	$-0.394589\pi$
$659$	−143860.	−	83057.9i	−0.331261	−	0.191254i	−0.656401	+	0.754412i	$0.727922\pi$
$660$		0			0
$661$	−177769.	−	102635.i	−0.406867	−	0.234905i	0.282576	−	0.959245i	$-0.408811\pi$
$661$	−177769.	−	102635.i	−0.406867	−	0.234905i	−0.689443	+	0.724340i	$0.742144\pi$
$662$		0			0
$663$	256994.	+	445127.i	0.584650	+	1.01264i
$664$		0			0
$665$	254148.	−	86122.8i	0.574704	−	0.194749i
$666$		0			0
$667$	240938.	−	139105.i	0.541568	−	0.312674i
$668$		0			0
$669$	−514830.	+	891711.i	−1.15030	+	1.99238i
$670$		0			0
$671$	31831.7	−	55134.2i	0.0706993	−	0.122455i
$672$		0			0
$673$			589468.i			1.30146i	0.759310	+	0.650729i	$0.225537\pi$
$673$			589468.i			1.30146i	−0.759310	+	0.650729i	$0.774463\pi$
$674$		0			0
$675$	−47448.3	−	27394.3i	−0.104139	−	0.0601246i
$676$		0			0
$677$			197706.i			0.431362i	0.976464	+	0.215681i	$0.0691971\pi$
$677$			197706.i			0.431362i	−0.976464	+	0.215681i	$0.930803\pi$
$678$		0			0
$679$	247486.	−	142886.i	0.536797	−	0.309920i
$680$		0			0
$681$	208017.	+	360296.i	0.448544	+	0.776901i
$682$		0			0
$683$			450800.i			0.966368i	0.875519	+	0.483184i	$0.160520\pi$
$683$			450800.i			0.966368i	−0.875519	+	0.483184i	$0.839480\pi$
$684$		0			0
$685$	−477511.			−1.01766
$686$		0			0
$687$	177012.	−	102198.i	0.375049	−	0.216535i
$688$		0			0
$689$	227586.	+	394191.i	0.479411	+	0.830364i
$690$		0			0
$691$	−90174.6			−0.188855			−0.0944274	−	0.995532i	$-0.530102\pi$
$691$	−90174.6			−0.188855			−0.0944274	+	0.995532i	$0.530102\pi$
$692$		0			0
$693$	69887.0	−	121048.i	0.145522	−	0.252052i
$694$		0			0
$695$	359680.			0.744640
$696$		0			0
$697$	−506143.	−	292222.i	−1.04186	−	0.601516i
$698$		0			0
$699$	159244.	+	91939.5i	0.325918	+	0.188169i
$700$		0			0
$701$	52451.2	+	90848.2i	0.106738	+	0.184876i	0.914447	−	0.404706i	$-0.132626\pi$
$701$	52451.2	+	90848.2i	0.106738	+	0.184876i	−0.807709	+	0.589582i	$0.799293\pi$
$702$		0			0
$703$	40725.3	+	8123.01i	0.0824050	+	0.0164364i
$704$		0			0
$705$	770619.	−	444917.i	1.55046	−	0.895160i
$706$		0			0
$707$	−192390.	+	333229.i	−0.384896	+	0.666660i
$708$		0			0
$709$	−163355.	+	282939.i	−0.324968	+	0.562860i	−0.981506	−	0.191432i	$-0.938687\pi$
$709$	−163355.	+	282939.i	−0.324968	+	0.562860i	0.656538	+	0.754293i	$0.272020\pi$
$710$		0			0
$711$			439163.i			0.868733i
$712$		0			0
$713$	703090.	+	405929.i	1.38303	+	0.798493i
$714$		0			0
$715$			147701.i			0.288916i
$716$		0			0
$717$	374881.	−	216438.i	0.729214	−	0.421012i
$718$		0			0
$719$	−395433.	−	684910.i	−0.764919	−	1.32488i	−0.940289	−	0.340376i	$-0.889446\pi$
$719$	−395433.	−	684910.i	−0.764919	−	1.32488i	0.175371	−	0.984502i	$-0.443888\pi$
$720$		0			0
$721$		−	64474.0i		−	0.124026i
$722$		0			0
$723$	1.28311e6			2.45464
$724$		0			0
$725$	78243.1	−	45173.7i	0.148857	−	0.0859428i
$726$		0			0
$727$	−466495.	−	807992.i	−0.882628	−	1.52876i	−0.848408	−	0.529342i	$-0.822439\pi$
$727$	−466495.	−	807992.i	−0.882628	−	1.52876i	−0.0342199	−	0.999414i	$-0.510895\pi$
$728$		0			0
$729$	311731.			0.586578
$730$		0			0
$731$	275770.	−	477647.i	0.516074	−	0.893866i
$732$		0			0
$733$	27589.8			0.0513500			0.0256750	−	0.999670i	$-0.491826\pi$
$733$	27589.8			0.0513500			0.0256750	+	0.999670i	$0.491826\pi$
$734$		0			0
$735$	142619.	+	82341.2i	0.263999	+	0.152420i
$736$		0			0
$737$	291449.	+	168268.i	0.536572	+	0.309790i
$738$		0			0
$739$	86704.5	+	150177.i	0.158764	+	0.274988i	0.934423	−	0.356164i	$-0.115916\pi$
$739$	86704.5	+	150177.i	0.158764	+	0.274988i	−0.775659	+	0.631152i	$0.782582\pi$
$740$		0			0
$741$	−131696.	+	660269.i	−0.239849	+	1.20250i
$742$		0			0
$743$	84623.8	−	48857.6i	0.153290	−	0.0885022i	−0.421393	−	0.906878i	$-0.638459\pi$
$743$	84623.8	−	48857.6i	0.153290	−	0.0885022i	0.574683	+	0.818376i	$0.305125\pi$
$744$		0			0
$745$	−200718.	+	347654.i	−0.361638	+	0.626376i
$746$		0			0
$747$	−286329.	+	495937.i	−0.513127	+	0.888762i
$748$		0			0
$749$		−	223403.i		−	0.398222i
$750$		0			0
$751$	878645.	+	507286.i	1.55788	+	0.899442i	0.997460	+	0.0712325i	$0.0226932\pi$
$751$	878645.	+	507286.i	1.55788	+	0.899442i	0.560419	+	0.828209i	$0.310640\pi$
$752$		0			0
$753$			668817.i			1.17955i
$754$		0			0
$755$	−363646.	+	209951.i	−0.637947	+	0.368319i
$756$		0			0
$757$	−35978.1	−	62315.9i	−0.0627836	−	0.108744i	0.832925	−	0.553386i	$-0.186664\pi$
$757$	−35978.1	−	62315.9i	−0.0627836	−	0.108744i	−0.895709	+	0.444641i	$0.853331\pi$
$758$		0			0
$759$			569683.i			0.988894i
$760$		0			0
$761$	−376652.			−0.650386			−0.325193	−	0.945648i	$-0.605429\pi$
$761$	−376652.			−0.650386			−0.325193	+	0.945648i	$0.605429\pi$
$762$		0			0
$763$	−49643.8	+	28661.9i	−0.0852739	+	0.0492329i
$764$		0			0
$765$	−164767.	−	285385.i	−0.281545	−	0.487650i
$766$		0			0
$767$	925809.			1.57373
$768$		0			0
$769$	−148128.	+	256565.i	−0.250486	+	0.433855i	−0.963660	−	0.267132i	$-0.913924\pi$
$769$	−148128.	+	256565.i	−0.250486	+	0.433855i	0.713173	+	0.700988i	$0.247257\pi$
$770$		0			0
$771$	−540666.			−0.909537
$772$		0			0
$773$	876530.	+	506065.i	1.46693	+	0.846930i	0.999315	−	0.0370049i	$-0.0117817\pi$
$773$	876530.	+	506065.i	1.46693	+	0.846930i	0.467610	+	0.883935i	$0.345115\pi$
$774$		0			0
$775$	228324.	+	131823.i	0.380144	+	0.219477i
$776$		0			0
$777$	−28326.6	−	49063.1i	−0.0469194	−	0.0812667i
$778$		0			0
$779$	−245701.	−	725065.i	−0.404886	−	1.19482i
$780$		0			0
$781$	147566.	−	85197.5i	0.241928	−	0.139677i
$782$		0			0
$783$	29158.6	−	50504.1i	0.0475601	−	0.0823764i
$784$		0			0
$785$	−376418.	+	651976.i	−0.610846	+	1.05802i
$786$		0			0
$787$			1.06296e6i			1.71620i	0.513486	+	0.858098i	$0.328354\pi$
$787$			1.06296e6i			1.71620i	−0.513486	+	0.858098i	$0.671646\pi$
$788$		0			0
$789$	−608521.	−	351329.i	−0.977510	−	0.564366i
$790$		0			0
$791$			96141.9i			0.153660i
$792$		0			0
$793$	161933.	−	93492.1i	0.257507	−	0.148672i
$794$		0			0
$795$	−326462.	−	565449.i	−0.516534	−	0.894663i
$796$		0			0
$797$		−	492593.i		−	0.775482i	−0.921768	−	0.387741i	$-0.873255\pi$
$797$		−	492593.i		−	0.775482i	0.921768	−	0.387741i	$-0.126745\pi$
$798$		0			0
$799$	1.10934e6			1.73769
$800$		0			0
$801$	448206.	−	258772.i	0.698574	−	0.403322i
$802$		0			0
$803$	−200677.	−	347582.i	−0.311219	−	0.539046i
$804$		0			0
$805$	666881.			1.02910
$806$		0			0
$807$	−437659.	+	758048.i	−0.672030	+	1.16399i
$808$		0			0
$809$	955780.			1.46036			0.730181	−	0.683253i	$-0.239436\pi$
$809$	955780.			1.46036			0.730181	+	0.683253i	$0.239436\pi$
$810$		0			0
$811$	−159358.	−	92005.2i	−0.242288	−	0.139885i	0.373940	−	0.927453i	$-0.378007\pi$
$811$	−159358.	−	92005.2i	−0.242288	−	0.139885i	−0.616228	+	0.787568i	$0.711340\pi$
$812$		0			0
$813$	−903791.	−	521804.i	−1.36737	−	0.789453i
$814$		0			0
$815$	27432.7	+	47514.9i	0.0413003	+	0.0715343i
$816$		0			0
$817$	684243.	−	231868.i	1.02510	−	0.347374i
$818$		0			0
$819$	355526.	−	205263.i	0.530034	−	0.306015i
$820$		0			0
$821$	241392.	−	418103.i	0.358126	−	0.620293i	−0.629522	−	0.776983i	$-0.716749\pi$
$821$	241392.	−	418103.i	0.358126	−	0.620293i	0.987648	+	0.156690i	$0.0500824\pi$
$822$		0			0
$823$	−525182.	+	909641.i	−0.775372	+	1.34298i	0.159214	+	0.987244i	$0.449104\pi$
$823$	−525182.	+	909641.i	−0.775372	+	1.34298i	−0.934585	+	0.355739i	$0.884229\pi$
$824$		0			0
$825$			185001.i			0.271811i
$826$		0			0
$827$	297865.	+	171973.i	0.435521	+	0.251448i	0.701696	−	0.712477i	$-0.252427\pi$
$827$	297865.	+	171973.i	0.435521	+	0.251448i	−0.266175	+	0.963925i	$0.585760\pi$
$828$		0			0
$829$			655153.i			0.953309i	0.879091	+	0.476654i	$0.158151\pi$
$829$			655153.i			0.953309i	−0.879091	+	0.476654i	$0.841849\pi$
$830$		0			0
$831$	−1.40010e6	+	808346.i	−2.02748	+	1.17056i
$832$		0			0
$833$	102654.	+	177801.i	0.147940	+	0.256239i
$834$		0			0
$835$			611464.i			0.876997i
$836$		0			0
$837$	170177.			0.242913
$838$		0			0
$839$	−4544.02	+	2623.49i	−0.00645529	+	0.00372697i	−0.503224	−	0.864156i	$-0.667853\pi$
$839$	−4544.02	+	2623.49i	−0.00645529	+	0.00372697i	0.496769	+	0.867883i	$0.334520\pi$
$840$		0			0
$841$	−305558.	−	529241.i	−0.432017	−	0.748276i
$842$		0			0
$843$	946638.			1.33208
$844$		0			0
$845$	43947.3	−	76119.0i	0.0615487	−	0.106605i
$846$		0			0
$847$	−483772.			−0.674332
$848$		0			0
$849$	40701.4	+	23499.0i	0.0564669	+	0.0326012i
$850$		0			0
$851$	89376.3	+	51601.4i	0.123414	+	0.0712529i
$852$		0			0
$853$	263.952	+	457.177i	0.000362766	+	0.000628328i	0.866207	−	0.499686i	$-0.166551\pi$
$853$	263.952	+	457.177i	0.000362766	+	0.000628328i	−0.865844	+	0.500314i	$0.833218\pi$
$854$		0			0
$855$	84434.7	−	423319.i	0.115502	−	0.579077i
$856$		0			0
$857$	891345.	−	514618.i	1.21362	−	0.700686i	0.250078	−	0.968226i	$-0.419544\pi$
$857$	891345.	−	514618.i	1.21362	−	0.700686i	0.963547	+	0.267539i	$0.0862105\pi$
$858$		0			0
$859$	−145913.	+	252730.i	−0.197747	+	0.342507i	−0.947797	−	0.318873i	$-0.896696\pi$
$859$	−145913.	+	252730.i	−0.197747	+	0.342507i	0.750051	+	0.661380i	$0.230029\pi$
$860$		0			0
$861$	−522204.	+	904483.i	−0.704423	+	1.22010i
$862$		0			0
$863$		−	1.24371e6i		−	1.66993i	−0.550307	−	0.834963i	$-0.685489\pi$
$863$		−	1.24371e6i		−	1.66993i	0.550307	−	0.834963i	$-0.314511\pi$
$864$		0			0
$865$	440760.	+	254473.i	0.589074	+	0.340102i
$866$		0			0
$867$			91606.0i			0.121867i
$868$		0			0
$869$	−304848.	+	176004.i	−0.403686	+	0.233068i
$870$		0			0
$871$	494217.	+	856008.i	0.651450	+	1.12834i
$872$		0			0
$873$		−	459692.i		−	0.603168i
$874$		0			0
$875$	681150.			0.889666
$876$		0			0
$877$	−806389.	+	465569.i	−1.04844	+	0.605320i	−0.922214	−	0.386681i	$-0.873621\pi$
$877$	−806389.	+	465569.i	−1.04844	+	0.605320i	−0.126231	+	0.992001i	$0.540288\pi$
$878$		0			0
$879$	−696415.	−	1.20623e6i	−0.901343	−	1.56117i
$880$		0			0
$881$	−465283.			−0.599467			−0.299734	−	0.954023i	$-0.596898\pi$
$881$	−465283.			−0.599467			−0.299734	+	0.954023i	$0.596898\pi$
$882$		0			0
$883$	−208028.	+	360315.i	−0.266809	+	0.462126i	−0.968036	−	0.250812i	$-0.919302\pi$
$883$	−208028.	+	360315.i	−0.266809	+	0.462126i	0.701227	+	0.712938i	$0.252636\pi$
$884$		0			0
$885$	−1.32803e6			−1.69559
$886$		0			0
$887$	833217.	+	481058.i	1.05904	+	0.611435i	0.925166	−	0.379564i	$-0.123926\pi$
$887$	833217.	+	481058.i	1.05904	+	0.611435i	0.133871	+	0.990999i	$0.457259\pi$
$888$		0			0
$889$	−825975.	−	476877.i	−1.04511	−	0.603396i
$890$		0			0
$891$	198813.	+	344355.i	0.250432	+	0.433761i
$892$		0			0
$893$	1.09202e6	+	958690.i	1.36939	+	1.20220i
$894$		0			0
$895$	154634.	−	89277.7i	0.193045	−	0.111454i
$896$		0			0
$897$	−836601.	+	1.44903e6i	−1.03976	+	1.80092i
$898$		0			0
$899$	−140313.	+	243029.i	−0.173611	+	0.300704i
$900$		0			0
$901$		−	813993.i		−	1.00270i
$902$		0			0
$903$	−853561.	−	492803.i	−1.04679	−	0.604364i
$904$		0			0
$905$		−	439376.i		−	0.536463i
$906$		0			0
$907$	214782.	−	124005.i	0.261086	−	0.150738i	−0.363744	−	0.931499i	$-0.618502\pi$
$907$	214782.	−	124005.i	0.261086	−	0.150738i	0.624830	+	0.780761i	$0.285168\pi$
$908$		0			0
$909$	309478.	+	536032.i	0.374543	+	0.648728i
$910$		0			0
$911$		−	598290.i		−	0.720900i	−0.932779	−	0.360450i	$-0.882623\pi$
$911$		−	598290.i		−	0.720900i	0.932779	−	0.360450i	$-0.117377\pi$
$912$		0			0
$913$	−459010.			−0.550657
$914$		0			0
$915$	−232286.	+	134110.i	−0.277447	+	0.160184i
$916$		0			0
$917$	−79770.4	−	138166.i	−0.0948644	−	0.164310i
$918$		0			0
$919$	−1.03278e6			−1.22286			−0.611432	−	0.791297i	$-0.709406\pi$
$919$	−1.03278e6			−1.22286			−0.611432	+	0.791297i	$0.709406\pi$
$920$		0			0
$921$	172717.	−	299155.i	0.203618	−	0.352677i
$922$		0			0
$923$	500463.			0.587447
$924$		0			0
$925$	29024.4	+	16757.3i	0.0339219	+	0.0195848i
$926$		0			0
$927$	−89817.9	−	51856.4i	−0.104521	−	0.0603452i
$928$		0			0
$929$	−388831.	−	673475.i	−0.450536	−	0.780351i	0.547883	−	0.836555i	$-0.315434\pi$
$929$	−388831.	−	673475.i	−0.450536	−	0.780351i	−0.998419	+	0.0562037i	$0.982100\pi$
$930$		0			0
$931$	−52604.7	+	263737.i	−0.0606912	+	0.304279i
$932$		0			0
$933$	−137784.	+	79549.9i	−0.158284	+	0.0913853i
$934$		0			0
$935$	132068.	−	228748.i	0.151069	−	0.261659i
$936$		0			0
$937$	587086.	−	1.01686e6i	0.668686	−	1.15820i	−0.309585	−	0.950872i	$-0.600190\pi$
$937$	587086.	−	1.01686e6i	0.668686	−	1.15820i	0.978272	−	0.207327i	$-0.0664764\pi$
$938$		0			0
$939$		−	2.12348e6i		−	2.40834i
$940$		0			0
$941$	−698093.	−	403044.i	−0.788378	−	0.455170i	0.0510135	−	0.998698i	$-0.483755\pi$
$941$	−698093.	−	403044.i	−0.788378	−	0.455170i	−0.839391	+	0.543528i	$0.817088\pi$
$942$		0			0
$943$		−	1.90256e6i		−	2.13951i
$944$		0			0
$945$	121060.	−	69894.0i	0.135562	−	0.0782666i
$946$		0			0
$947$	−91047.7	−	157699.i	−0.101524	−	0.175845i	0.810789	−	0.585339i	$-0.199039\pi$
$947$	−91047.7	−	157699.i	−0.101524	−	0.175845i	−0.912313	+	0.409494i	$0.865705\pi$
$948$		0			0
$949$		−	1.17880e6i		−	1.30891i
$950$		0			0
$951$	−1.05573e6			−1.16732
$952$		0			0
$953$	−665244.	+	384079.i	−0.732479	+	0.422897i	−0.819328	−	0.573325i	$-0.805653\pi$
$953$	−665244.	+	384079.i	−0.732479	+	0.422897i	0.0868497	+	0.996221i	$0.472320\pi$
$954$		0			0
$955$	−60200.1	−	104270.i	−0.0660071	−	0.114328i
$956$		0			0
$957$	−196916.			−0.215009
$958$		0			0
$959$	−531910.	+	921296.i	−0.578364	+	1.00176i
$960$		0			0
$961$	104615.			0.113279
$962$		0			0
$963$	−311220.	−	179683.i	−0.335595	−	0.193756i
$964$		0			0
$965$	210423.	+	121488.i	0.225964	+	0.130460i
$966$		0			0
$967$	−42211.1	−	73111.7i	−0.0451412	−	0.0781869i	0.842572	−	0.538584i	$-0.181040\pi$
$967$	−42211.1	−	73111.7i	−0.0451412	−	0.0781869i	−0.887713	+	0.460397i	$0.847707\pi$
$968$		0			0
$969$	794346.	−	904819.i	0.845984	−	0.963638i
$970$		0			0
$971$	36053.5	−	20815.5i	0.0382392	−	0.0220774i	−0.480759	−	0.876853i	$-0.659639\pi$
$971$	36053.5	−	20815.5i	0.0382392	−	0.0220774i	0.518998	+	0.854776i	$0.326305\pi$
$972$		0			0
$973$	400655.	−	693955.i	0.423199	−	0.733003i
$974$		0			0
$975$	−271681.	+	470566.i	−0.285792	+	0.495006i
$976$		0			0
$977$			586443.i			0.614380i	0.951648	+	0.307190i	$0.0993887\pi$
$977$			586443.i			0.614380i	−0.951648	+	0.307190i	$0.900611\pi$
$978$		0			0
$979$	359256.	+	207417.i	0.374834	+	0.216410i
$980$		0			0
$981$			92210.9i			0.0958173i
$982$		0			0
$983$	516678.	−	298304.i	0.534703	−	0.308711i	−0.208226	−	0.978081i	$-0.566769\pi$
$983$	516678.	−	298304.i	0.534703	−	0.308711i	0.742930	+	0.669370i	$0.233436\pi$
$984$		0			0
$985$	−78616.0	−	136167.i	−0.0810286	−	0.140346i
$986$		0			0
$987$		−	1.98241e6i		−	2.03498i
$988$		0			0
$989$	1.79544e6			1.83560
$990$		0			0
$991$	−125022.	+	72181.2i	−0.127303	+	0.0734982i	−0.562299	−	0.826934i	$-0.690083\pi$
$991$	−125022.	+	72181.2i	−0.127303	+	0.0734982i	0.434996	+	0.900432i	$0.356750\pi$
$992$		0			0
$993$	−979425.	−	1.69641e6i	−0.993282	−	1.72042i
$994$		0			0
$995$	680527.			0.687384
$996$		0			0
$997$	−975015.	+	1.68878e6i	−0.980892	+	1.69895i	−0.321958	+	0.946754i	$0.604341\pi$
$997$	−975015.	+	1.68878e6i	−0.980892	+	1.69895i	−0.658934	+	0.752201i	$0.728992\pi$
$998$		0			0
$999$	21632.8			0.0216762

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.5.r.c.145.2		16
4.3	odd	2		38.5.d.a.31.8	yes	16
12.11	even	2		342.5.m.c.145.2		16
19.8	odd	6	inner	304.5.r.c.65.2		16
76.27	even	6		38.5.d.a.27.8	✓	16
228.179	odd	6		342.5.m.c.217.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.5.d.a.27.8	✓	16	76.27	even	6
38.5.d.a.31.8	yes	16	4.3	odd	2
304.5.r.c.65.2		16	19.8	odd	6	inner
304.5.r.c.145.2		16	1.1	even	1	trivial
342.5.m.c.145.2		16	12.11	even	2
342.5.m.c.217.2		16	228.179	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:	\( N \)	\(=\)	\( 304 = 2^{4} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	304.r (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-10.4807 + 6.05105i) q^{3} +(9.13314 + 15.8191i) q^{5} +40.6944 q^{7} +(32.7305 - 56.6909i) q^{9} +O(q^{10})\)	\(q+(-10.4807 + 6.05105i) q^{3} +(9.13314 + 15.8191i) q^{5} +40.6944 q^{7} +(32.7305 - 56.6909i) q^{9} +52.4698 q^{11} +(133.461 + 77.0538i) q^{13} +(-191.444 - 110.530i) q^{15} +(-137.797 - 238.671i) q^{17} +(70.6137 - 354.026i) q^{19} +(-426.507 + 246.244i) q^{21} +(448.573 - 776.951i) q^{23} +(145.671 - 252.310i) q^{25} -188.055i q^{27} +(268.560 + 155.053i) q^{29} +904.934i q^{31} +(-549.921 + 317.497i) q^{33} +(371.668 + 643.747i) q^{35} +115.035i q^{37} -1865.03 q^{39} +(1836.56 - 1060.34i) q^{41} +(1000.64 + 1733.16i) q^{43} +1195.73 q^{45} +(-2012.65 + 3486.01i) q^{47} -744.965 q^{49} +(2888.42 + 1667.63i) q^{51} +(2557.89 + 1476.80i) q^{53} +(479.214 + 830.022i) q^{55} +(1402.15 + 4137.74i) q^{57} +(5202.69 - 3003.77i) q^{59} +(606.668 - 1050.78i) q^{61} +(1331.95 - 2307.00i) q^{63} +2814.97i q^{65} +(5554.61 + 3206.96i) q^{67} +10857.4i q^{69} +(2812.41 - 1623.75i) q^{71} +(-3824.61 - 6624.43i) q^{73} +3525.86i q^{75} +2135.23 q^{77} +(-5809.97 + 3354.39i) q^{79} +(3789.10 + 6562.91i) q^{81} -8748.10 q^{83} +(2517.03 - 4359.63i) q^{85} -3752.94 q^{87} +(6846.92 + 3953.07i) q^{89} +(5431.12 + 3135.66i) q^{91} +(-5475.80 - 9484.37i) q^{93} +(6245.29 - 2116.33i) q^{95} +(6081.56 - 3511.19i) q^{97} +(1717.36 - 2974.56i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 12 q^{3} - 18 q^{5} - 72 q^{7} + 352 q^{9}+O(q^{10}) \) 16 * q + 12 * q^3 - 18 * q^5 - 72 * q^7 + 352 * q^9	\( 16 q + 12 q^{3} - 18 q^{5} - 72 q^{7} + 352 q^{9} + 84 q^{11} + 450 q^{13} + 390 q^{15} + 606 q^{17} + 306 q^{19} - 2160 q^{21} + 54 q^{23} - 434 q^{25} - 4914 q^{29} + 7890 q^{33} - 2328 q^{35} - 7620 q^{39} - 1692 q^{41} + 7402 q^{43} - 16720 q^{45} - 3198 q^{47} + 24816 q^{49} - 10710 q^{51} + 3870 q^{53} + 13588 q^{55} + 3702 q^{57} + 18288 q^{59} - 6522 q^{61} + 15676 q^{63} + 30168 q^{67} - 35874 q^{71} - 8080 q^{73} + 34560 q^{77} + 30738 q^{79} - 30920 q^{81} + 1476 q^{83} + 33626 q^{85} - 113100 q^{87} + 19782 q^{89} + 34260 q^{91} - 4272 q^{93} + 23706 q^{95} - 9936 q^{97} - 3848 q^{99}+O(q^{100}) \) 16 * q + 12 * q^3 - 18 * q^5 - 72 * q^7 + 352 * q^9 + 84 * q^11 + 450 * q^13 + 390 * q^15 + 606 * q^17 + 306 * q^19 - 2160 * q^21 + 54 * q^23 - 434 * q^25 - 4914 * q^29 + 7890 * q^33 - 2328 * q^35 - 7620 * q^39 - 1692 * q^41 + 7402 * q^43 - 16720 * q^45 - 3198 * q^47 + 24816 * q^49 - 10710 * q^51 + 3870 * q^53 + 13588 * q^55 + 3702 * q^57 + 18288 * q^59 - 6522 * q^61 + 15676 * q^63 + 30168 * q^67 - 35874 * q^71 - 8080 * q^73 + 34560 * q^77 + 30738 * q^79 - 30920 * q^81 + 1476 * q^83 + 33626 * q^85 - 113100 * q^87 + 19782 * q^89 + 34260 * q^91 - 4272 * q^93 + 23706 * q^95 - 9936 * q^97 - 3848 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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