LMFDB - Embedded newform 304.5.r.d.65.5

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:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 152)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			65.5
Character	$\chi$	$=$	304.65
Dual form			304.5.r.d.145.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-9.48048 - 5.47356i) q^{3} +(-15.3284 + 26.5496i) q^{5} -33.8970 q^{7} +(19.4197 + 33.6359i) q^{9} +O(q^{10})$	\(q+(-9.48048 - 5.47356i) q^{3} +(-15.3284 + 26.5496i) q^{5} -33.8970 q^{7} +(19.4197 + 33.6359i) q^{9} -179.466 q^{11} +(-117.643 + 67.9213i) q^{13} +(290.642 - 167.802i) q^{15} +(-208.267 + 360.729i) q^{17} +(-60.5460 - 355.886i) q^{19} +(321.359 + 185.537i) q^{21} +(251.149 + 435.003i) q^{23} +(-157.422 - 272.663i) q^{25} +461.538i q^{27} +(-878.069 + 506.954i) q^{29} -509.130i q^{31} +(1701.42 + 982.315i) q^{33} +(519.587 - 899.952i) q^{35} -1666.41i q^{37} +1487.08 q^{39} +(1694.69 + 978.431i) q^{41} +(104.281 - 180.620i) q^{43} -1190.69 q^{45} +(-1440.60 - 2495.19i) q^{47} -1252.00 q^{49} +(3948.95 - 2279.92i) q^{51} +(3899.24 - 2251.22i) q^{53} +(2750.93 - 4764.75i) q^{55} +(-1373.96 + 3705.38i) q^{57} +(-1295.56 - 747.992i) q^{59} +(-373.780 - 647.406i) q^{61} +(-658.268 - 1140.15i) q^{63} -4164.51i q^{65} +(-4164.10 + 2404.15i) q^{67} -5498.72i q^{69} +(-2018.19 - 1165.20i) q^{71} +(2272.15 - 3935.47i) q^{73} +3446.63i q^{75} +6083.34 q^{77} +(5716.90 + 3300.65i) q^{79} +(4099.25 - 7100.10i) q^{81} -7055.25 q^{83} +(-6384.82 - 11058.8i) q^{85} +11099.4 q^{87} +(8103.90 - 4678.79i) q^{89} +(3987.74 - 2302.33i) q^{91} +(-2786.76 + 4826.80i) q^{93} +(10376.7 + 3847.71i) q^{95} +(5571.32 + 3216.61i) q^{97} +(-3485.16 - 6036.48i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) $ 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9	$ 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9} - 24 q^{11} + 264 q^{13} - 624 q^{15} + 216 q^{17} + 652 q^{19} - 216 q^{21} + 1296 q^{23} - 3044 q^{25} + 288 q^{29} - 6660 q^{33} - 360 q^{35} - 3184 q^{39} + 1260 q^{41} - 632 q^{43} + 256 q^{45} - 1248 q^{47} + 16696 q^{49} + 8064 q^{51} - 3672 q^{53} + 3408 q^{55} - 4552 q^{57} - 12492 q^{59} + 2720 q^{61} - 12472 q^{63} - 16260 q^{67} + 504 q^{71} + 9220 q^{73} - 14688 q^{77} + 28944 q^{79} - 1660 q^{81} + 39192 q^{83} - 18632 q^{85} + 34400 q^{87} + 3456 q^{89} - 54432 q^{91} - 17208 q^{93} - 44520 q^{95} - 30540 q^{97} + 10096 q^{99}+O(q^{100}) $ 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9 - 24 * q^11 + 264 * q^13 - 624 * q^15 + 216 * q^17 + 652 * q^19 - 216 * q^21 + 1296 * q^23 - 3044 * q^25 + 288 * q^29 - 6660 * q^33 - 360 * q^35 - 3184 * q^39 + 1260 * q^41 - 632 * q^43 + 256 * q^45 - 1248 * q^47 + 16696 * q^49 + 8064 * q^51 - 3672 * q^53 + 3408 * q^55 - 4552 * q^57 - 12492 * q^59 + 2720 * q^61 - 12472 * q^63 - 16260 * q^67 + 504 * q^71 + 9220 * q^73 - 14688 * q^77 + 28944 * q^79 - 1660 * q^81 + 39192 * q^83 - 18632 * q^85 + 34400 * q^87 + 3456 * q^89 - 54432 * q^91 - 17208 * q^93 - 44520 * q^95 - 30540 * q^97 + 10096 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$3$	−9.48048	−	5.47356i	−1.05339	−	0.608173i	−0.129791	−	0.991541i	$-0.541431\pi$
$3$	−9.48048	−	5.47356i	−1.05339	−	0.608173i	−0.923596	+	0.383368i	$0.874764\pi$
$4$		0			0
$5$	−15.3284	+	26.5496i	−0.613138	+	1.06199i	0.377571	+	0.925981i	$0.376760\pi$
$5$	−15.3284	+	26.5496i	−0.613138	+	1.06199i	−0.990708	+	0.136005i	$0.956574\pi$
$6$		0			0
$7$	−33.8970			−0.691775			−0.345887	−	0.938276i	$-0.612422\pi$
$7$	−33.8970			−0.691775			−0.345887	+	0.938276i	$0.612422\pi$
$8$		0			0
$9$	19.4197	+	33.6359i	0.239749	+	0.415258i
$10$		0			0
$11$	−179.466			−1.48319			−0.741593	−	0.670850i	$-0.765930\pi$
$11$	−179.466			−1.48319			−0.741593	+	0.670850i	$0.765930\pi$
$12$		0			0
$13$	−117.643	+	67.9213i	−0.696113	+	0.401901i	−0.805898	−	0.592054i	$-0.798317\pi$
$13$	−117.643	+	67.9213i	−0.696113	+	0.401901i	0.109785	+	0.993955i	$0.464984\pi$
$14$		0			0
$15$	290.642	−	167.802i	1.29174	−	0.745787i
$16$		0			0
$17$	−208.267	+	360.729i	−0.720648	+	1.24820i	0.240093	+	0.970750i	$0.422822\pi$
$17$	−208.267	+	360.729i	−0.720648	+	1.24820i	−0.960741	+	0.277448i	$0.910511\pi$
$18$		0			0
$19$	−60.5460	−	355.886i	−0.167717	−	0.985835i
$19$	−60.5460	−	355.886i	−0.167717	−	0.985835i
$20$		0			0
$21$	321.359	+	185.537i	0.728706	+	0.420719i
$22$		0			0
$23$	251.149	+	435.003i	0.474762	+	0.822312i	0.999582	−	0.0289008i	$-0.00920070\pi$
$23$	251.149	+	435.003i	0.474762	+	0.822312i	−0.524820	+	0.851213i	$0.675867\pi$
$24$		0			0
$25$	−157.422	−	272.663i	−0.251875	−	0.436261i
$26$		0			0
$27$			461.538i			0.633111i
$28$		0			0
$29$	−878.069	+	506.954i	−1.04408	+	0.602798i	−0.920986	−	0.389597i	$-0.872614\pi$
$29$	−878.069	+	506.954i	−1.04408	+	0.602798i	−0.123092	+	0.992395i	$0.539281\pi$
$30$		0			0
$31$		−	509.130i		−	0.529792i	−0.964277	−	0.264896i	$-0.914662\pi$
$31$		−	509.130i		−	0.529792i	0.964277	−	0.264896i	$-0.0853377\pi$
$32$		0			0
$33$	1701.42	+	982.315i	1.56237	+	0.902034i
$34$		0			0
$35$	519.587	−	899.952i	0.424153	−	0.734655i
$36$		0			0
$37$		−	1666.41i		−	1.21725i	−0.793458	−	0.608625i	$-0.791722\pi$
$37$		−	1666.41i		−	1.21725i	0.793458	−	0.608625i	$-0.208278\pi$
$38$		0			0
$39$	1487.08			0.977702
$40$		0			0
$41$	1694.69	+	978.431i	1.00814	+	0.582053i	0.910648	−	0.413183i	$-0.135583\pi$
$41$	1694.69	+	978.431i	1.00814	+	0.582053i	0.0974969	+	0.995236i	$0.468916\pi$
$42$		0			0
$43$	104.281	−	180.620i	0.0563987	−	0.0976855i	−0.836448	−	0.548047i	$-0.815372\pi$
$43$	104.281	−	180.620i	0.0563987	−	0.0976855i	0.892846	+	0.450361i	$0.148705\pi$
$44$		0			0
$45$	−1190.69			−0.587997
$46$		0			0
$47$	−1440.60	−	2495.19i	−0.652150	−	1.12956i	−0.982600	−	0.185733i	$-0.940534\pi$
$47$	−1440.60	−	2495.19i	−0.652150	−	1.12956i	0.330450	−	0.943823i	$-0.392799\pi$
$48$		0			0
$49$	−1252.00			−0.521448
$50$		0			0
$51$	3948.95	−	2279.92i	1.51824	−	0.876557i
$52$		0			0
$53$	3899.24	−	2251.22i	1.38812	−	0.801433i	0.395019	−	0.918673i	$-0.370738\pi$
$53$	3899.24	−	2251.22i	1.38812	−	0.801433i	0.993104	+	0.117240i	$0.0374047\pi$
$54$		0			0
$55$	2750.93	−	4764.75i	0.909397	−	1.57512i
$56$		0			0
$57$	−1373.96	+	3705.38i	−0.422887	+	1.14047i
$58$		0			0
$59$	−1295.56	−	747.992i	−0.372180	−	0.214878i	0.302230	−	0.953235i	$-0.402269\pi$
$59$	−1295.56	−	747.992i	−0.372180	−	0.214878i	−0.674411	+	0.738357i	$0.735602\pi$
$60$		0			0
$61$	−373.780	−	647.406i	−0.100452	−	0.173987i	0.811419	−	0.584465i	$-0.198695\pi$
$61$	−373.780	−	647.406i	−0.100452	−	0.173987i	−0.911871	+	0.410477i	$0.865362\pi$
$62$		0			0
$63$	−658.268	−	1140.15i	−0.165852	−	0.287265i
$64$		0			0
$65$		−	4164.51i		−	0.985683i
$66$		0			0
$67$	−4164.10	+	2404.15i	−0.927623	+	0.535564i	−0.886059	−	0.463572i	$-0.846567\pi$
$67$	−4164.10	+	2404.15i	−0.927623	+	0.535564i	−0.0415642	+	0.999136i	$0.513234\pi$
$68$		0			0
$69$		−	5498.72i		−	1.15495i
$70$		0			0
$71$	−2018.19	−	1165.20i	−0.400356	−	0.231145i	0.286282	−	0.958145i	$-0.407581\pi$
$71$	−2018.19	−	1165.20i	−0.400356	−	0.231145i	−0.686637	+	0.727000i	$0.740914\pi$
$72$		0			0
$73$	2272.15	−	3935.47i	0.426374	−	0.738501i	−0.570174	−	0.821524i	$-0.693124\pi$
$73$	2272.15	−	3935.47i	0.426374	−	0.738501i	0.996548	+	0.0830230i	$0.0264575\pi$
$74$		0			0
$75$			3446.63i			0.612735i
$76$		0			0
$77$	6083.34			1.02603
$78$		0			0
$79$	5716.90	+	3300.65i	0.916023	+	0.528866i	0.882364	−	0.470567i	$-0.155951\pi$
$79$	5716.90	+	3300.65i	0.916023	+	0.528866i	0.0336589	+	0.999433i	$0.489284\pi$
$80$		0			0
$81$	4099.25	−	7100.10i	0.624790	−	1.08217i
$82$		0			0
$83$	−7055.25			−1.02413			−0.512066	−	0.858946i	$-0.671120\pi$
$83$	−7055.25			−1.02413			−0.512066	+	0.858946i	$0.671120\pi$
$84$		0			0
$85$	−6384.82	−	11058.8i	−0.883712	−	1.53063i
$86$		0			0
$87$	11099.4			1.46642
$88$		0			0
$89$	8103.90	−	4678.79i	1.02309	−	0.590681i	0.108093	−	0.994141i	$-0.465526\pi$
$89$	8103.90	−	4678.79i	1.02309	−	0.590681i	0.914997	+	0.403460i	$0.132192\pi$
$90$		0			0
$91$	3987.74	−	2302.33i	0.481553	−	0.278025i
$92$		0			0
$93$	−2786.76	+	4826.80i	−0.322205	+	0.558076i
$94$		0			0
$95$	10376.7	+	3847.71i	1.14978	+	0.426339i
$96$		0			0
$97$	5571.32	+	3216.61i	0.592127	+	0.341865i	0.765938	−	0.642914i	$-0.222275\pi$
$97$	5571.32	+	3216.61i	0.592127	+	0.341865i	−0.173811	+	0.984779i	$0.555608\pi$
$98$		0			0
$99$	−3485.16	−	6036.48i	−0.355593	−	0.615904i
$100$		0			0
$101$	−723.847	−	1253.74i	−0.0709585	−	0.122904i	0.828363	−	0.560191i	$-0.189272\pi$
$101$	−723.847	−	1253.74i	−0.0709585	−	0.122904i	−0.899322	+	0.437288i	$0.855939\pi$
$102$		0			0
$103$			12679.6i			1.19517i	0.801804	+	0.597587i	$0.203874\pi$
$103$			12679.6i			1.19517i	−0.801804	+	0.597587i	$0.796126\pi$
$104$		0			0
$105$	−9851.88	+	5687.98i	−0.893594	+	0.515917i
$106$		0			0
$107$			19138.3i			1.67161i	0.549026	+	0.835805i	$0.314999\pi$
$107$			19138.3i			1.67161i	−0.549026	+	0.835805i	$0.685001\pi$
$108$		0			0
$109$	2824.67	+	1630.82i	0.237747	+	0.137263i	0.614141	−	0.789197i	$-0.289503\pi$
$109$	2824.67	+	1630.82i	0.237747	+	0.137263i	−0.376394	+	0.926460i	$0.622836\pi$
$110$		0			0
$111$	−9121.22	+	15798.4i	−0.740298	+	1.28223i
$112$		0			0
$113$			18765.2i			1.46959i	0.678288	+	0.734796i	$0.262722\pi$
$113$			18765.2i			1.46959i	−0.678288	+	0.734796i	$0.737278\pi$
$114$		0			0
$115$	−15398.9			−1.16438
$116$		0			0
$117$	−4569.18	−	2638.02i	−0.333785	−	0.192711i
$118$		0			0
$119$	7059.62	−	12227.6i	0.498526	−	0.863472i
$120$		0			0
$121$	17566.9			1.19984
$122$		0			0
$123$	−10711.0	−	18552.0i	−0.707978	−	1.22625i
$124$		0			0
$125$	−9508.41			−0.608539
$126$		0			0
$127$	17203.1	−	9932.22i	1.06659	−	0.615799i	0.139346	−	0.990244i	$-0.455500\pi$
$127$	17203.1	−	9932.22i	1.06659	−	0.615799i	0.927249	+	0.374445i	$0.122167\pi$
$128$		0			0
$129$	−1977.27	+	1141.58i	−0.118819	+	0.0686004i
$130$		0			0
$131$	−12624.3	+	21865.9i	−0.735639	+	1.27416i	0.218804	+	0.975769i	$0.429785\pi$
$131$	−12624.3	+	21865.9i	−0.735639	+	1.27416i	−0.954443	+	0.298395i	$0.903549\pi$
$132$		0			0
$133$	2052.32	+	12063.5i	0.116023	+	0.681976i
$134$		0			0
$135$	−12253.7	−	7074.65i	−0.672354	−	0.388184i
$136$		0			0
$137$	−1334.82	−	2311.97i	−0.0711182	−	0.123180i	0.828273	−	0.560324i	$-0.189323\pi$
$137$	−1334.82	−	2311.97i	−0.0711182	−	0.123180i	−0.899392	+	0.437144i	$0.855990\pi$
$138$		0			0
$139$	−8741.17	−	15140.2i	−0.452418	−	0.783611i	0.546118	−	0.837709i	$-0.316105\pi$
$139$	−8741.17	−	15140.2i	−0.452418	−	0.783611i	−0.998536	+	0.0540974i	$0.982772\pi$
$140$		0			0
$141$			31540.8i			1.58648i
$142$		0			0
$143$	21112.9	−	12189.5i	1.03247	−	0.596095i
$144$		0			0
$145$		−	31083.2i		−	1.47839i
$146$		0			0
$147$	11869.5	+	6852.87i	0.549286	+	0.317131i
$148$		0			0
$149$	421.955	−	730.848i	0.0190061	−	0.0329196i	−0.856366	−	0.516369i	$-0.827283\pi$
$149$	421.955	−	730.848i	0.0190061	−	0.0329196i	0.875372	+	0.483450i	$0.160616\pi$
$150$		0			0
$151$		−	24101.3i		−	1.05703i	−0.848925	−	0.528513i	$-0.822750\pi$
$151$		−	24101.3i		−	1.05703i	0.848925	−	0.528513i	$-0.177250\pi$
$152$		0			0
$153$	−16177.9			−0.691098
$154$		0			0
$155$	13517.2	+	7804.17i	0.562632	+	0.324836i
$156$		0			0
$157$	667.366	−	1155.91i	0.0270748	−	0.0468949i	−0.852171	−	0.523264i	$-0.824714\pi$
$157$	667.366	−	1155.91i	0.0270748	−	0.0468949i	0.879245	+	0.476369i	$0.158047\pi$
$158$		0			0
$159$	−49288.8			−1.94964
$160$		0			0
$161$	−8513.20	−	14745.3i	−0.328429	−	0.568855i
$162$		0			0
$163$	13269.9			0.499451			0.249725	−	0.968317i	$-0.419660\pi$
$163$	13269.9			0.499451			0.249725	+	0.968317i	$0.419660\pi$
$164$		0			0
$165$	−52160.2	+	30114.7i	−1.91589	+	1.10614i
$166$		0			0
$167$	−20509.9	+	11841.4i	−0.735413	+	0.424591i	−0.820399	−	0.571791i	$-0.806249\pi$
$167$	−20509.9	+	11841.4i	−0.735413	+	0.424591i	0.0849864	+	0.996382i	$0.472915\pi$
$168$		0			0
$169$	−5053.89	+	8753.60i	−0.176951	+	0.306488i
$170$		0			0
$171$	10794.8	−	8947.72i	0.369165	−	0.305999i
$172$		0			0
$173$	−27585.3	−	15926.4i	−0.921690	−	0.532138i	−0.0375165	−	0.999296i	$-0.511945\pi$
$173$	−27585.3	−	15926.4i	−0.921690	−	0.532138i	−0.884174	+	0.467158i	$0.845278\pi$
$174$		0			0
$175$	5336.13	+	9242.44i	0.174241	+	0.301794i
$176$		0			0
$177$	8188.35	+	14182.6i	0.261367	+	0.452700i
$178$		0			0
$179$			12434.6i			0.388083i	0.980993	+	0.194042i	$0.0621597\pi$
$179$			12434.6i			0.388083i	−0.980993	+	0.194042i	$0.937840\pi$
$180$		0			0
$181$	−25342.4	+	14631.4i	−0.773553	+	0.446611i	−0.834141	−	0.551552i	$-0.814036\pi$
$181$	−25342.4	+	14631.4i	−0.773553	+	0.446611i	0.0605874	+	0.998163i	$0.480703\pi$
$182$		0			0
$183$			8183.63i			0.244368i
$184$		0			0
$185$	44242.7	+	25543.5i	1.29270	+	0.746341i
$186$		0			0
$187$	37376.8	−	64738.5i	1.06886	−	1.85131i
$188$		0			0
$189$		−	15644.7i		−	0.437970i
$190$		0			0
$191$	−39035.3			−1.07002			−0.535009	−	0.844847i	$-0.679692\pi$
$191$	−39035.3			−1.07002			−0.535009	+	0.844847i	$0.679692\pi$
$192$		0			0
$193$	−19097.8	−	11026.1i	−0.512707	−	0.296012i	0.221238	−	0.975220i	$-0.428990\pi$
$193$	−19097.8	−	11026.1i	−0.512707	−	0.296012i	−0.733946	+	0.679208i	$0.762323\pi$
$194$		0			0
$195$	−22794.7	+	39481.6i	−0.599466	+	1.03831i
$196$		0			0
$197$	69187.8			1.78278			0.891389	−	0.453240i	$-0.149732\pi$
$197$	69187.8			1.78278			0.891389	+	0.453240i	$0.149732\pi$
$198$		0			0
$199$	20717.4	+	35883.6i	0.523154	+	0.906130i	0.999637	+	0.0269458i	$0.00857814\pi$
$199$	20717.4	+	35883.6i	0.523154	+	0.906130i	−0.476483	+	0.879184i	$0.658089\pi$
$200$		0			0
$201$	52636.9			1.30286
$202$		0			0
$203$	29763.9	−	17184.2i	0.722266	−	0.417001i
$204$		0			0
$205$	−51953.9	+	29995.6i	−1.23626	+	0.713757i
$206$		0			0
$207$	−9754.47	+	16895.2i	−0.227648	+	0.394297i
$208$		0			0
$209$	10865.9	+	63869.4i	0.248756	+	1.46218i
$210$		0			0
$211$	5100.77	+	2944.93i	0.114570	+	0.0661470i	0.556190	−	0.831055i	$-0.312263\pi$
$211$	5100.77	+	2944.93i	0.114570	+	0.0661470i	−0.441620	+	0.897202i	$0.645596\pi$
$212$		0			0
$213$	12755.6	+	22093.4i	0.281153	+	0.486971i
$214$		0			0
$215$	3196.94	+	5537.26i	0.0691603	+	0.119789i
$216$		0			0
$217$			17258.0i			0.366497i
$218$		0			0
$219$	−43082.1	+	24873.4i	−0.898273	+	0.518618i
$220$		0			0
$221$		−	56583.1i		−	1.15852i
$222$		0			0
$223$	−59745.8	−	34494.2i	−1.20143	−	0.693644i	−0.240555	−	0.970636i	$-0.577329\pi$
$223$	−59745.8	−	34494.2i	−1.20143	−	0.693644i	−0.960872	+	0.276991i	$0.910663\pi$
$224$		0			0
$225$	6114.17	−	10590.0i	0.120774	−	0.209186i
$226$		0			0
$227$		−	36818.1i		−	0.714512i	−0.934007	−	0.357256i	$-0.883712\pi$
$227$		−	36818.1i		−	0.714512i	0.934007	−	0.357256i	$-0.116288\pi$
$228$		0			0
$229$	−77979.6			−1.48700			−0.743498	−	0.668738i	$-0.766835\pi$
$229$	−77979.6			−1.48700			−0.743498	+	0.668738i	$0.766835\pi$
$230$		0			0
$231$	−57673.0	−	33297.5i	−1.08081	−	0.624004i
$232$		0			0
$233$	−19521.8	+	33812.8i	−0.359591	+	0.622830i	−0.987892	−	0.155140i	$-0.950417\pi$
$233$	−19521.8	+	33812.8i	−0.359591	+	0.622830i	0.628302	+	0.777970i	$0.283750\pi$
$234$		0			0
$235$	88328.5			1.59943
$236$		0			0
$237$	−36132.6	−	62583.6i	−0.643284	−	1.11420i
$238$		0			0
$239$	2431.84			0.0425735			0.0212868	−	0.999773i	$-0.493224\pi$
$239$	2431.84			0.0425735			0.0212868	+	0.999773i	$0.493224\pi$
$240$		0			0
$241$	−16215.8	+	9362.20i	−0.279193	+	0.161192i	−0.633058	−	0.774104i	$-0.718201\pi$
$241$	−16215.8	+	9362.20i	−0.279193	+	0.161192i	0.353865	+	0.935296i	$0.384867\pi$
$242$		0			0
$243$	−45349.7	+	26182.7i	−0.768001	+	0.443405i
$244$		0			0
$245$	19191.1	−	33240.0i	0.319719	−	0.553770i
$246$		0			0
$247$	31295.1	+	37755.2i	0.512959	+	0.618847i
$248$		0			0
$249$	66887.1	+	38617.3i	1.07881	+	0.622850i
$250$		0			0
$251$	50002.5	+	86606.8i	0.793678	+	1.37469i	0.923676	+	0.383176i	$0.125170\pi$
$251$	50002.5	+	86606.8i	0.793678	+	1.37469i	−0.129998	+	0.991514i	$0.541497\pi$
$252$		0			0
$253$	−45072.7	−	78068.1i	−0.704161	−	1.21964i
$254$		0			0
$255$			139791.i			2.14980i
$256$		0			0
$257$	92634.5	−	53482.6i	1.40251	−	0.809741i	0.407862	−	0.913044i	$-0.366274\pi$
$257$	92634.5	−	53482.6i	1.40251	−	0.809741i	0.994650	+	0.103303i	$0.0329411\pi$
$258$		0			0
$259$			56486.4i			0.842062i
$260$		0			0
$261$	−34103.6	−	19689.7i	−0.500633	−	0.289041i
$262$		0			0
$263$	44960.8	−	77874.4i	0.650014	−	1.12586i	−0.333105	−	0.942890i	$-0.608096\pi$
$263$	44960.8	−	77874.4i	0.650014	−	1.12586i	0.983119	−	0.182968i	$-0.0585704\pi$
$264$		0			0
$265$			138031.i			1.96555i
$266$		0			0
$267$	−102438.			−1.43695
$268$		0			0
$269$	−60756.8	−	35077.9i	−0.839634	−	0.484763i	0.0175056	−	0.999847i	$-0.494428\pi$
$269$	−60756.8	−	35077.9i	−0.839634	−	0.484763i	−0.857140	+	0.515084i	$0.827761\pi$
$270$		0			0
$271$	−65719.3	+	113829.i	−0.894859	+	1.54994i	−0.0608794	+	0.998145i	$0.519390\pi$
$271$	−65719.3	+	113829.i	−0.894859	+	1.54994i	−0.833979	+	0.551796i	$0.813943\pi$
$272$		0			0
$273$	−50407.6			−0.676349
$274$		0			0
$275$	28251.8	+	48933.6i	0.373578	+	0.647056i
$276$		0			0
$277$	70772.2			0.922365			0.461183	−	0.887305i	$-0.347425\pi$
$277$	70772.2			0.922365			0.461183	+	0.887305i	$0.347425\pi$
$278$		0			0
$279$	17125.0	−	9887.15i	0.220000	−	0.127017i
$280$		0			0
$281$	136027.	−	78535.3i	1.72271	−	0.994609i	0.809509	−	0.587108i	$-0.199734\pi$
$281$	136027.	−	78535.3i	1.72271	−	0.994609i	0.913205	−	0.407501i	$-0.133600\pi$
$282$		0			0
$283$	51019.9	−	88369.1i	0.637041	−	1.10339i	−0.349038	−	0.937108i	$-0.613492\pi$
$283$	51019.9	−	88369.1i	0.637041	−	1.10339i	0.986079	−	0.166278i	$-0.0531750\pi$
$284$		0			0
$285$	−77315.7	−	93275.8i	−0.951871	−	1.14836i
$286$		0			0
$287$	−57444.9	−	33165.8i	−0.697409	−	0.402649i
$288$		0			0
$289$	−44989.9	−	77924.8i	−0.538666	−	0.932997i
$290$		0			0
$291$	−35212.6	−	60989.9i	−0.415826	−	0.720232i
$292$		0			0
$293$			132475.i			1.54311i	0.636160	+	0.771557i	$0.280522\pi$
$293$			132475.i			1.54311i	−0.636160	+	0.771557i	$0.719478\pi$
$294$		0			0
$295$	39717.8	−	22931.1i	0.456395	−	0.263500i
$296$		0			0
$297$		−	82830.1i		−	0.939021i
$298$		0			0
$299$	−59092.0	−	34116.8i	−0.660977	−	0.381615i
$300$		0			0
$301$	−3534.82	+	6122.48i	−0.0390152	+	0.0675763i
$302$		0			0
$303$			15848.1i			0.172620i
$304$		0			0
$305$	22917.9			0.246362
$306$		0			0
$307$	−17692.4	−	10214.7i	−0.187720	−	0.108380i	0.403195	−	0.915114i	$-0.367900\pi$
$307$	−17692.4	−	10214.7i	−0.187720	−	0.108380i	−0.590915	+	0.806734i	$0.701233\pi$
$308$		0			0
$309$	69402.6	−	120209.i	0.726873	−	1.25898i
$310$		0			0
$311$	23016.2			0.237965			0.118982	−	0.992896i	$-0.462037\pi$
$311$	23016.2			0.237965			0.118982	+	0.992896i	$0.462037\pi$
$312$		0			0
$313$	54014.9	+	93556.6i	0.551347	+	0.954961i	0.998178	+	0.0603425i	$0.0192193\pi$
$313$	54014.9	+	93556.6i	0.551347	+	0.954961i	−0.446831	+	0.894619i	$0.647447\pi$
$314$		0			0
$315$	40360.9			0.406761
$316$		0			0
$317$	−15916.9	+	9189.64i	−0.158395	+	0.0914492i	−0.577102	−	0.816672i	$-0.695817\pi$
$317$	−15916.9	+	9189.64i	−0.158395	+	0.0914492i	0.418708	+	0.908121i	$0.362483\pi$
$318$		0			0
$319$	157583.	−	90980.7i	1.54856	−	0.894063i
$320$		0			0
$321$	104754.	−	181440.i	1.01663	−	1.76085i
$322$		0			0
$323$	140988.	+	52278.8i	1.35138	+	0.501095i
$324$		0			0
$325$	37039.2	+	21384.6i	0.350667	+	0.202458i
$326$		0			0
$327$	−17852.8	−	30922.0i	−0.166960	−	0.289182i
$328$		0			0
$329$	48831.9	+	84579.4i	0.451141	+	0.781399i
$330$		0			0
$331$		−	33591.5i		−	0.306601i	−0.988180	−	0.153300i	$-0.951010\pi$
$331$		−	33591.5i		−	0.306601i	0.988180	−	0.153300i	$-0.0489902\pi$
$332$		0			0
$333$	56051.3	−	32361.2i	0.505472	−	0.291834i
$334$		0			0
$335$		−	147407.i		−	1.31350i
$336$		0			0
$337$	−92938.2	−	53657.9i	−0.818341	−	0.472469i	0.0315031	−	0.999504i	$-0.489971\pi$
$337$	−92938.2	−	53657.9i	−0.818341	−	0.472469i	−0.849844	+	0.527034i	$0.823304\pi$
$338$		0			0
$339$	102713.	−	177903.i	0.893766	−	1.54805i
$340$		0			0
$341$			91371.4i			0.785781i
$342$		0			0
$343$	123825.			1.05250
$344$		0			0
$345$	145989.	+	84286.8i	1.22654	+	0.708144i
$346$		0			0
$347$	108233.	−	187464.i	0.898874	−	1.55690i	0.0699395	−	0.997551i	$-0.477719\pi$
$347$	108233.	−	187464.i	0.898874	−	1.55690i	0.828935	−	0.559345i	$-0.188947\pi$
$348$		0			0
$349$	−79695.7			−0.654311			−0.327155	−	0.944971i	$-0.606090\pi$
$349$	−79695.7			−0.654311			−0.327155	+	0.944971i	$0.606090\pi$
$350$		0			0
$351$	−31348.2	−	54296.7i	−0.254448	−	0.440717i
$352$		0			0
$353$	183135.			1.46968			0.734839	−	0.678242i	$-0.237258\pi$
$353$	183135.			1.46968			0.734839	+	0.678242i	$0.237258\pi$
$354$		0			0
$355$	61871.5	−	35721.5i	0.490946	−	0.283448i
$356$		0			0
$357$	−133857.	+	77282.5i	−1.05028	+	0.606380i
$358$		0			0
$359$	32187.7	−	55750.8i	0.249748	−	0.432576i	−0.713708	−	0.700443i	$-0.752986\pi$
$359$	32187.7	−	55750.8i	0.249748	−	0.432576i	0.963456	+	0.267868i	$0.0863189\pi$
$360$		0			0
$361$	−122989.	+	43095.0i	−0.943742	+	0.330683i
$362$		0			0
$363$	−166543.	−	96153.5i	−1.26390	−	0.729712i
$364$		0			0
$365$	69656.9	+	120649.i	0.522851	+	0.905605i
$366$		0			0
$367$	7978.67	+	13819.5i	0.0592377	+	0.102603i	0.894123	−	0.447821i	$-0.147800\pi$
$367$	7978.67	+	13819.5i	0.0592377	+	0.102603i	−0.834886	+	0.550423i	$0.814466\pi$
$368$		0			0
$369$			76003.2i			0.558186i
$370$		0			0
$371$	−132172.	+	76309.7i	−0.960268	+	0.554411i
$372$		0			0
$373$		−	92394.5i		−	0.664092i	−0.943263	−	0.332046i	$-0.892261\pi$
$373$		−	92394.5i		−	0.664092i	0.943263	−	0.332046i	$-0.107739\pi$
$374$		0			0
$375$	90144.3	+	52044.9i	0.641026	+	0.370097i
$376$		0			0
$377$	68865.9	−	119279.i	0.484531	−	0.839232i
$378$		0			0
$379$			94895.2i			0.660641i	0.943869	+	0.330321i	$0.107157\pi$
$379$			94895.2i			0.660641i	−0.943869	+	0.330321i	$0.892843\pi$
$380$		0			0
$381$	−217458.			−1.49805
$382$		0			0
$383$	−79076.5	−	45654.8i	−0.539076	−	0.311235i	0.205629	−	0.978630i	$-0.434076\pi$
$383$	−79076.5	−	45654.8i	−0.539076	−	0.311235i	−0.744704	+	0.667395i	$0.767409\pi$
$384$		0			0
$385$	−93248.1	+	161510.i	−0.629098	+	1.08963i
$386$		0			0
$387$	8100.43			0.0540862
$388$		0			0
$389$	−81286.0	−	140792.i	−0.537176	−	0.930417i	−0.999055	−	0.0434733i	$-0.986158\pi$
$389$	−81286.0	−	140792.i	−0.537176	−	0.930417i	0.461878	−	0.886943i	$-0.347176\pi$
$390$		0			0
$391$	−209225.			−1.36855
$392$		0			0
$393$	239369.	−	138200.i	1.54982	−	0.894791i
$394$		0			0
$395$	−175262.	+	101188.i	−1.12330	+	0.648535i
$396$		0			0
$397$	119488.	−	206959.i	0.758128	−	1.31312i	−0.185676	−	0.982611i	$-0.559448\pi$
$397$	119488.	−	206959.i	0.758128	−	1.31312i	0.943804	−	0.330505i	$-0.107219\pi$
$398$		0			0
$399$	46573.1	−	125601.i	0.292543	−	0.788946i
$400$		0			0
$401$	−231188.	−	133476.i	−1.43773	−	0.830072i	−0.440035	−	0.897981i	$-0.645034\pi$
$401$	−231188.	−	133476.i	−1.43773	−	0.830072i	−0.997692	+	0.0679090i	$0.978367\pi$
$402$		0			0
$403$	34580.8	+	59895.7i	0.212924	+	0.368796i
$404$		0			0
$405$	125670.	+	217667.i	0.766164	+	1.32704i
$406$		0			0
$407$			299064.i			1.80541i
$408$		0			0
$409$	−255050.	+	147253.i	−1.52468	+	0.880273i	−0.525105	+	0.851038i	$0.675974\pi$
$409$	−255050.	+	147253.i	−1.52468	+	0.880273i	−0.999573	+	0.0292353i	$0.990693\pi$
$410$		0			0
$411$			29224.8i			0.173009i
$412$		0			0
$413$	43915.5	+	25354.6i	0.257465	+	0.148647i
$414$		0			0
$415$	108146.	−	187314.i	0.627934	−	1.08761i
$416$		0			0
$417$			191381.i			1.10059i
$418$		0			0
$419$	314560.			1.79174			0.895871	−	0.444314i	$-0.146553\pi$
$419$	314560.			1.79174			0.895871	+	0.444314i	$0.146553\pi$
$420$		0			0
$421$	104.430	+	60.2929i	0.000589200	+	0.000340175i	0.500295	−	0.865855i	$-0.333225\pi$
$421$	104.430	+	60.2929i	0.000589200	+	0.000340175i	−0.499705	+	0.866195i	$0.666558\pi$
$422$		0			0
$423$	55951.9	−	96911.6i	0.312705	−	0.541620i
$424$		0			0
$425$	131143.			0.726053
$426$		0			0
$427$	12670.0	+	21945.1i	0.0694898	+	0.120360i
$428$		0			0
$429$	−266881.			−1.45011
$430$		0			0
$431$	−109472.	+	63203.6i	−0.589316	+	0.340242i	−0.764827	−	0.644236i	$-0.777176\pi$
$431$	−109472.	+	63203.6i	−0.589316	+	0.340242i	0.175511	+	0.984477i	$0.443842\pi$
$432$		0			0
$433$	136983.	−	79087.1i	0.730619	−	0.421823i	−0.0880298	−	0.996118i	$-0.528057\pi$
$433$	136983.	−	79087.1i	0.730619	−	0.421823i	0.818648	+	0.574295i	$0.194724\pi$
$434$		0			0
$435$	−170136.	+	294684.i	−0.899119	+	1.55732i
$436$		0			0
$437$	139606.	−	115718.i	0.731039	−	0.605953i
$438$		0			0
$439$	1420.75	+	820.270i	0.00737205	+	0.00425625i	0.503681	−	0.863889i	$-0.331979\pi$
$439$	1420.75	+	820.270i	0.00737205	+	0.00425625i	−0.496309	+	0.868146i	$0.665312\pi$
$440$		0			0
$441$	−24313.4	−	42112.0i	−0.125017	−	0.216535i
$442$		0			0
$443$	85903.4	+	148789.i	0.437726	+	0.758164i	0.997514	−	0.0704719i	$-0.0224505\pi$
$443$	85903.4	+	148789.i	0.437726	+	0.758164i	−0.559787	+	0.828636i	$0.689117\pi$
$444$		0			0
$445$			286874.i			1.44868i
$446$		0			0
$447$	−8000.68	+	4619.19i	−0.0400416	+	0.0231180i
$448$		0			0
$449$		−	118361.i		−	0.587106i	−0.955943	−	0.293553i	$-0.905162\pi$
$449$		−	118361.i		−	0.587106i	0.955943	−	0.293553i	$-0.0948377\pi$
$450$		0			0
$451$	−304139.	−	175595.i	−1.49527	−	0.863293i
$452$		0			0
$453$	−131920.	+	228492.i	−0.642855	+	1.11346i
$454$		0			0
$455$			141164.i			0.681870i
$456$		0			0
$457$	−242945.			−1.16326			−0.581628	−	0.813455i	$-0.697584\pi$
$457$	−242945.			−1.16326			−0.581628	+	0.813455i	$0.697584\pi$
$458$		0			0
$459$	−166490.	−	96123.1i	−0.790247	−	0.456250i
$460$		0			0
$461$	−158783.	+	275021.i	−0.747141	+	1.29409i	0.202046	+	0.979376i	$0.435241\pi$
$461$	−158783.	+	275021.i	−0.747141	+	1.29409i	−0.949188	+	0.314711i	$0.898092\pi$
$462$		0			0
$463$	257398.			1.20072			0.600361	−	0.799729i	$-0.295023\pi$
$463$	257398.			1.20072			0.600361	+	0.799729i	$0.295023\pi$
$464$		0			0
$465$	−85433.2	−	147975.i	−0.395113	−	0.684355i
$466$		0			0
$467$	−71993.1			−0.330109			−0.165054	−	0.986284i	$-0.552780\pi$
$467$	−71993.1			−0.330109			−0.165054	+	0.986284i	$0.552780\pi$
$468$		0			0
$469$	141150.	−	81493.2i	0.641706	−	0.370489i
$470$		0			0
$471$	−12653.9	+	7305.74i	−0.0570404	+	0.0329323i
$472$		0			0
$473$	−18714.9	+	32415.2i	−0.0836498	+	0.144886i
$474$		0			0
$475$	−87505.8	+	72533.0i	−0.387837	+	0.321476i
$476$		0			0
$477$	151444.	+	87436.1i	0.665602	+	0.384286i
$478$		0			0
$479$	−63162.8	−	109401.i	−0.275290	−	0.476816i	0.694918	−	0.719089i	$-0.255441\pi$
$479$	−63162.8	−	109401.i	−0.275290	−	0.476816i	−0.970208	+	0.242272i	$0.922107\pi$
$480$		0			0
$481$	113185.	+	196042.i	0.489214	+	0.847343i
$482$		0			0
$483$			186390.i			0.798966i
$484$		0			0
$485$	−170799.	+	98611.1i	−0.726111	+	0.419220i
$486$		0			0
$487$			301108.i			1.26959i	0.772680	+	0.634796i	$0.218916\pi$
$487$			301108.i			1.26959i	−0.772680	+	0.634796i	$0.781084\pi$
$488$		0			0
$489$	−125805.	−	72633.6i	−0.526115	−	0.303753i
$490$		0			0
$491$	−129539.	+	224368.i	−0.537326	+	0.930677i	0.461720	+	0.887026i	$0.347232\pi$
$491$	−129539.	+	224368.i	−0.537326	+	0.930677i	−0.999047	+	0.0436511i	$0.986101\pi$
$492$		0			0
$493$		−	422327.i		−	1.73762i
$494$		0			0
$495$	213688.			0.872109
$496$		0			0
$497$	68410.6	+	39496.9i	0.276956	+	0.159901i
$498$		0			0
$499$	−34514.7	+	59781.2i	−0.138613	+	0.240084i	−0.926972	−	0.375131i	$-0.877598\pi$
$499$	−34514.7	+	59781.2i	−0.138613	+	0.240084i	0.788359	+	0.615215i	$0.210931\pi$
$500$		0			0
$501$	259259.			1.03290
$502$		0			0
$503$	−67756.8	−	117358.i	−0.267804	−	0.463850i	0.700491	−	0.713662i	$-0.252965\pi$
$503$	−67756.8	−	117358.i	−0.267804	−	0.463850i	−0.968294	+	0.249812i	$0.919631\pi$
$504$		0			0
$505$	44381.8			0.174029
$506$		0			0
$507$	95826.7	−	55325.6i	0.372795	−	0.215234i
$508$		0			0
$509$	391155.	−	225833.i	1.50978	−	0.871671i	0.509843	−	0.860267i	$-0.329703\pi$
$509$	391155.	−	225833.i	1.50978	−	0.871671i	0.999935	−	0.0114038i	$-0.00363001\pi$
$510$		0			0
$511$	−77018.8	+	133401.i	−0.294955	+	0.510876i
$512$		0			0
$513$	164255.	−	27944.2i	0.624143	−	0.106184i
$514$		0			0
$515$	−336639.	−	194359.i	−1.26926	−	0.732806i
$516$		0			0
$517$	258538.	+	447801.i	0.967260	+	1.67534i
$518$		0			0
$519$	174348.	+	301979.i	0.647264	+	1.12109i
$520$		0			0
$521$		−	252354.i		−	0.929684i	−0.885394	−	0.464842i	$-0.846111\pi$
$521$		−	252354.i		−	0.929684i	0.885394	−	0.464842i	$-0.153889\pi$
$522$		0			0
$523$	−115469.	+	66665.8i	−0.422144	+	0.243725i	−0.695994	−	0.718048i	$-0.745036\pi$
$523$	−115469.	+	66665.8i	−0.422144	+	0.243725i	0.273850	+	0.961772i	$0.411703\pi$
$524$		0			0
$525$		−	116830.i		−	0.423874i
$526$		0			0
$527$	183658.	+	106035.i	0.661286	+	0.381794i
$528$		0			0
$529$	13768.6	−	23847.9i	0.0492016	−	0.0852196i
$530$		0			0
$531$		−	58103.0i		−	0.206068i
$532$		0			0
$533$	−265825.			−0.935711
$534$		0			0
$535$	−508114.	−	293360.i	−1.77523	−	1.02493i
$536$		0			0
$537$	68061.4	−	117886.i	0.236022	−	0.408802i
$538$		0			0
$539$	224690.			0.773405
$540$		0			0
$541$	−234153.	−	405564.i	−0.800027	−	1.38569i	−0.919597	−	0.392862i	$-0.871485\pi$
$541$	−234153.	−	405564.i	−0.800027	−	1.38569i	0.119570	−	0.992826i	$-0.461848\pi$
$542$		0			0
$543$	320344.			1.08647
$544$		0			0
$545$	−86595.5	+	49996.0i	−0.291543	+	0.168322i
$546$		0			0
$547$	−1971.15	+	1138.04i	−0.00658786	+	0.00380350i	−0.503290	−	0.864117i	$-0.667877\pi$
$547$	−1971.15	+	1138.04i	−0.00658786	+	0.00380350i	0.496702	+	0.867921i	$0.334544\pi$
$548$		0			0
$549$	14517.4	−	25144.8i	0.0481663	−	0.0834265i
$550$		0			0
$551$	233581.	+	281799.i	0.769370	+	0.928189i
$552$		0			0
$553$	−193785.	−	111882.i	−0.633681	−	0.365856i
$554$		0			0
$555$	−279628.	−	484330.i	−0.907809	−	1.57237i
$556$		0			0
$557$	−153377.	−	265657.i	−0.494369	−	0.856272i	0.505610	−	0.862762i	$-0.331267\pi$
$557$	−153377.	−	265657.i	−0.494369	−	0.856272i	−0.999979	+	0.00649020i	$0.997934\pi$
$558$		0			0
$559$			28331.7i			0.0906669i
$560$		0			0
$561$	−708700.	+	409168.i	−2.25184	+	1.30010i
$562$		0			0
$563$			255569.i			0.806290i	0.915136	+	0.403145i	$0.132083\pi$
$563$			255569.i			0.806290i	−0.915136	+	0.403145i	$0.867917\pi$
$564$		0			0
$565$	−498210.	−	287642.i	−1.56069	−	0.901062i
$566$		0			0
$567$	−138952.	+	240672.i	−0.432214	+	0.748616i
$568$		0			0
$569$		−	101724.i		−	0.314196i	−0.987583	−	0.157098i	$-0.949786\pi$
$569$		−	101724.i		−	0.314196i	0.987583	−	0.157098i	$-0.0502138\pi$
$570$		0			0
$571$	−140519.			−0.430986			−0.215493	−	0.976505i	$-0.569136\pi$
$571$	−140519.			−0.430986			−0.215493	+	0.976505i	$0.569136\pi$
$572$		0			0
$573$	370073.	+	213662.i	1.12714	+	0.650756i
$574$		0			0
$575$	79072.8	−	136958.i	0.239162	−	0.414240i
$576$		0			0
$577$	−465912.			−1.39943			−0.699717	−	0.714420i	$-0.746691\pi$
$577$	−465912.			−1.39943			−0.699717	+	0.714420i	$0.746691\pi$
$578$		0			0
$579$	120704.	+	209066.i	0.360053	+	0.623630i
$580$		0			0
$581$	239151.			0.708469
$582$		0			0
$583$	−699779.	+	404017.i	−2.05884	+	1.18867i
$584$		0			0
$585$	140077.	−	80873.4i	0.409312	−	0.236316i
$586$		0			0
$587$	159891.	−	276939.i	0.464031	−	0.803726i	−0.535126	−	0.844772i	$-0.679736\pi$
$587$	159891.	−	276939.i	0.464031	−	0.803726i	0.999157	+	0.0410463i	$0.0130691\pi$
$588$		0			0
$589$	−181193.	+	30825.8i	−0.522288	+	0.0888554i
$590$		0			0
$591$	−655934.	−	378703.i	−1.87795	−	1.08424i
$592$		0			0
$593$	313390.	+	542808.i	0.891202	+	1.54361i	0.838436	+	0.545000i	$0.183471\pi$
$593$	313390.	+	542808.i	0.891202	+	1.54361i	0.0527664	+	0.998607i	$0.483196\pi$
$594$		0			0
$595$	216426.	+	374861.i	0.611330	+	1.05885i
$596$		0			0
$597$		−	453592.i		−	1.27267i
$598$		0			0
$599$	121207.	−	69978.9i	0.337811	−	0.195035i	−0.321492	−	0.946912i	$-0.604184\pi$
$599$	121207.	−	69978.9i	0.337811	−	0.195035i	0.659304	+	0.751877i	$0.270851\pi$
$600$		0			0
$601$			124892.i			0.345768i	0.984942	+	0.172884i	$0.0553086\pi$
$601$			124892.i			0.345768i	−0.984942	+	0.172884i	$0.944691\pi$
$602$		0			0
$603$	−161731.	−	93375.4i	−0.444794	−	0.256802i
$604$		0			0
$605$	−269273.	+	466395.i	−0.735669	+	1.27422i
$606$		0			0
$607$		−	518090.i		−	1.40614i	−0.711122	−	0.703069i	$-0.751813\pi$
$607$		−	518090.i		−	1.40614i	0.711122	−	0.703069i	$-0.248187\pi$
$608$		0			0
$609$	−376234.			−1.01443
$610$		0			0
$611$	338953.	+	195695.i	0.907940	+	0.524200i
$612$		0			0
$613$	−9188.49	+	15914.9i	−0.0244525	+	0.0423530i	−0.877993	−	0.478674i	$-0.841118\pi$
$613$	−9188.49	+	15914.9i	−0.0244525	+	0.0423530i	0.853540	+	0.521027i	$0.174451\pi$
$614$		0			0
$615$	656731.			1.73635
$616$		0			0
$617$	347784.	+	602379.i	0.913564	+	1.58234i	0.808990	+	0.587822i	$0.200014\pi$
$617$	347784.	+	602379.i	0.913564	+	1.58234i	0.104574	+	0.994517i	$0.466652\pi$
$618$		0			0
$619$	347922.			0.908031			0.454016	−	0.890994i	$-0.349991\pi$
$619$	347922.			0.908031			0.454016	+	0.890994i	$0.349991\pi$
$620$		0			0
$621$	−200770.	+	115915.i	−0.520615	+	0.300577i
$622$		0			0
$623$	−274697.	+	158597.i	−0.707748	+	0.408618i
$624$		0			0
$625$	244138.	−	422859.i	0.624993	−	1.08252i
$626$		0			0
$627$	246579.	−	664988.i	0.627221	−	1.69153i
$628$		0			0
$629$	601125.	+	347059.i	1.51937	+	0.877208i
$630$		0			0
$631$	−330309.	−	572111.i	−0.829585	−	1.43688i	−0.898364	−	0.439252i	$-0.855244\pi$
$631$	−330309.	−	572111.i	−0.829585	−	1.43688i	0.0687786	−	0.997632i	$-0.478090\pi$
$632$		0			0
$633$	−32238.5	−	55838.7i	−0.0804576	−	0.139357i
$634$		0			0
$635$			608982.i			1.51028i
$636$		0			0
$637$	147289.	−	85037.2i	0.362987	−	0.209570i
$638$		0			0
$639$		−	90511.5i		−	0.221668i
$640$		0			0
$641$	171627.	+	99088.7i	0.417704	+	0.241162i	0.694095	−	0.719884i	$-0.255805\pi$
$641$	171627.	+	99088.7i	0.417704	+	0.241162i	−0.276390	+	0.961045i	$0.589138\pi$
$642$		0			0
$643$	19414.6	−	33627.1i	0.0469576	−	0.0813330i	−0.841591	−	0.540115i	$-0.818381\pi$
$643$	19414.6	−	33627.1i	0.0469576	−	0.0813330i	0.888549	+	0.458782i	$0.151714\pi$
$644$		0			0
$645$		−	69994.5i		−	0.168246i
$646$		0			0
$647$	344258.			0.822385			0.411193	−	0.911549i	$-0.365112\pi$
$647$	344258.			0.822385			0.411193	+	0.911549i	$0.365112\pi$
$648$		0			0
$649$	232508.	+	134239.i	0.552013	+	0.318705i
$650$		0			0
$651$	94462.5	−	163614.i	0.222894	−	0.386063i
$652$		0			0
$653$	522523.			1.22540			0.612702	−	0.790314i	$-0.290083\pi$
$653$	522523.			1.22540			0.612702	+	0.790314i	$0.290083\pi$
$654$		0			0
$655$	−387021.	−	670341.i	−0.902095	−	1.56248i
$656$		0			0
$657$	176497.			0.408891
$658$		0			0
$659$	398216.	−	229910.i	0.916956	−	0.529405i	0.0342930	−	0.999412i	$-0.489082\pi$
$659$	398216.	−	229910.i	0.916956	−	0.529405i	0.882663	+	0.470007i	$0.155749\pi$
$660$		0			0
$661$	31560.1	−	18221.2i	0.0722329	−	0.0417037i	−0.463449	−	0.886124i	$-0.653388\pi$
$661$	31560.1	−	18221.2i	0.0722329	−	0.0417037i	0.535681	+	0.844420i	$0.320055\pi$
$662$		0			0
$663$	−309711.	+	536435.i	−0.704579	+	1.22037i
$664$		0			0
$665$	−351740.	−	130426.i	−0.795386	−	0.294931i
$666$		0			0
$667$	−441053.	−	254642.i	−0.991377	−	0.572372i
$668$		0			0
$669$	377612.	+	654044.i	0.843712	+	1.46135i
$670$		0			0
$671$	67080.7	+	116187.i	0.148988	+	0.258055i
$672$		0			0
$673$		−	353081.i		−	0.779550i	−0.920910	−	0.389775i	$-0.872553\pi$
$673$		−	353081.i		−	0.779550i	0.920910	−	0.389775i	$-0.127447\pi$
$674$		0			0
$675$	125844.	−	72656.2i	0.276201	−	0.159465i
$676$		0			0
$677$			106207.i			0.231727i	0.993265	+	0.115864i	$0.0369636\pi$
$677$			106207.i			0.231727i	−0.993265	+	0.115864i	$0.963036\pi$
$678$		0			0
$679$	−188851.	−	109033.i	−0.409619	−	0.236493i
$680$		0			0
$681$	−201526.	+	349053.i	−0.434547	+	0.752657i
$682$		0			0
$683$		−	566466.i		−	1.21432i	−0.794580	−	0.607159i	$-0.792309\pi$
$683$		−	566466.i		−	1.21432i	0.794580	−	0.607159i	$-0.207691\pi$
$684$		0			0
$685$	81842.6			0.174421
$686$		0			0
$687$	739284.	+	426826.i	1.56638	+	0.904351i
$688$		0			0
$689$	−305812.	+	529682.i	−0.644194	+	1.11578i
$690$		0			0
$691$	459078.			0.961459			0.480729	−	0.876869i	$-0.340372\pi$
$691$	459078.			0.961459			0.480729	+	0.876869i	$0.340372\pi$
$692$		0			0
$693$	118136.	+	204618.i	0.245990	+	0.426067i
$694$		0			0
$695$	535954.			1.10958
$696$		0			0
$697$	−705897.	+	407550.i	−1.45303	+	0.838910i
$698$		0			0
$699$	370153.	−	213708.i	0.757577	−	0.437387i
$700$		0			0
$701$	−102547.	+	177616.i	−0.208682	+	0.361448i	−0.951300	−	0.308268i	$-0.900251\pi$
$701$	−102547.	+	177616.i	−0.208682	+	0.361448i	0.742618	+	0.669716i	$0.233584\pi$
$702$		0			0
$703$	−593054.	+	100895.i	−1.20001	+	0.204154i
$704$		0			0
$705$	−837397.	−	483471.i	−1.68482	−	0.972730i
$706$		0			0
$707$	24536.2	+	42498.0i	0.0490873	+	0.0850216i
$708$		0			0
$709$	241646.	+	418544.i	0.480715	+	0.832623i	0.999755	−	0.0221266i	$-0.00704369\pi$
$709$	241646.	+	418544.i	0.480715	+	0.832623i	−0.519040	+	0.854750i	$0.673710\pi$
$710$		0			0
$711$			256390.i			0.507181i
$712$		0			0
$713$	221473.	−	127868.i	0.435655	−	0.251525i
$714$		0			0
$715$			747386.i			1.46195i
$716$		0			0
$717$	−23055.0	−	13310.8i	−0.0448464	−	0.0258921i
$718$		0			0
$719$	193030.	−	334338.i	0.373394	−	0.646737i	−0.616691	−	0.787205i	$-0.711527\pi$
$719$	193030.	−	334338.i	0.373394	−	0.646737i	0.990085	+	0.140468i	$0.0448607\pi$
$720$		0			0
$721$		−	429800.i		−	0.826791i
$722$		0			0
$723$	204978.			0.392131
$724$		0			0
$725$	276455.	+	159611.i	0.525954	+	0.303660i
$726$		0			0
$727$	111901.	−	193818.i	0.211721	−	0.366711i	−0.740532	−	0.672021i	$-0.765427\pi$
$727$	111901.	−	193818.i	0.211721	−	0.366711i	0.952253	+	0.305309i	$0.0987599\pi$
$728$		0			0
$729$	−90828.8			−0.170910
$730$		0			0
$731$	43436.7	+	75234.6i	0.0812872	+	0.140794i
$732$		0			0
$733$	434997.			0.809615			0.404807	−	0.914402i	$-0.367339\pi$
$733$	434997.			0.809615			0.404807	+	0.914402i	$0.367339\pi$
$734$		0			0
$735$	−363883.	+	210088.i	−0.673576	+	0.388889i
$736$		0			0
$737$	747313.	−	431461.i	1.37584	−	0.794341i
$738$		0			0
$739$	28247.0	−	48925.2i	0.0517229	−	0.0895867i	−0.839005	−	0.544124i	$-0.816862\pi$
$739$	28247.0	−	48925.2i	0.0517229	−	0.0895867i	0.890728	+	0.454537i	$0.150195\pi$
$740$		0			0
$741$	−90037.0	−	529233.i	−0.163978	−	0.963853i
$742$		0			0
$743$	−483600.	−	279207.i	−0.876010	−	0.505764i	−0.00666907	−	0.999978i	$-0.502123\pi$
$743$	−483600.	−	279207.i	−0.876010	−	0.505764i	−0.869341	+	0.494213i	$0.835456\pi$
$744$		0			0
$745$	12935.8	+	22405.5i	0.0233068	+	0.0403685i
$746$		0			0
$747$	−137011.	−	237309.i	−0.245535	−	0.425279i
$748$		0			0
$749$		−	648729.i		−	1.15638i
$750$		0			0
$751$	−27544.3	+	15902.7i	−0.0488373	+	0.0281962i	−0.524220	−	0.851583i	$-0.675643\pi$
$751$	−27544.3	+	15902.7i	−0.0488373	+	0.0281962i	0.475383	+	0.879779i	$0.342310\pi$
$752$		0			0
$753$		−	1.09477e6i		−	1.93077i
$754$		0			0
$755$	639880.	+	369435.i	1.12255	+	0.648103i
$756$		0			0
$757$	320867.	−	555757.i	0.559929	−	0.969825i	−0.437573	−	0.899183i	$-0.644162\pi$
$757$	320867.	−	555757.i	0.559929	−	0.969825i	0.997502	−	0.0706421i	$-0.0225048\pi$
$758$		0			0
$759$			986831.i			1.71301i
$760$		0			0
$761$	−1.07940e6			−1.86386			−0.931931	−	0.362636i	$-0.881877\pi$
$761$	−1.07940e6			−1.86386			−0.931931	+	0.362636i	$0.881877\pi$
$762$		0			0
$763$	−95747.7	−	55280.0i	−0.164467	−	0.0949552i
$764$		0			0
$765$	247982.	−	429518.i	0.423738	−	0.733936i
$766$		0			0
$767$	203218.			0.345440
$768$		0			0
$769$	−395789.	−	685527.i	−0.669286	−	1.15924i	−0.978104	−	0.208116i	$-0.933267\pi$
$769$	−395789.	−	685527.i	−0.669286	−	1.15924i	0.308819	−	0.951121i	$-0.400066\pi$
$770$		0			0
$771$	−1.17096e6			−1.96985
$772$		0			0
$773$	642395.	−	370887.i	1.07509	−	0.620701i	0.145519	−	0.989355i	$-0.453515\pi$
$773$	642395.	−	370887.i	1.07509	−	0.620701i	0.929566	+	0.368655i	$0.120181\pi$
$774$		0			0
$775$	−138821.	+	80148.3i	−0.231128	+	0.133442i
$776$		0			0
$777$	309181.	−	535518.i	0.512120	−	0.887017i
$778$		0			0
$779$	245603.	−	662358.i	0.404725	−	1.09148i
$780$		0			0
$781$	362196.	+	209114.i	0.593802	+	0.342832i
$782$		0			0
$783$	−233978.	−	405262.i	−0.381638	−	0.661017i
$784$		0			0
$785$	20459.4	+	35436.7i	0.0332011	+	0.0575061i
$786$		0			0
$787$		−	28275.8i		−	0.0456527i	−0.999739	−	0.0228263i	$-0.992734\pi$
$787$		−	28275.8i		−	0.0456527i	0.999739	−	0.0228263i	$-0.00726648\pi$
$788$		0			0
$789$	−852500.	+	492191.i	−1.36943	+	0.790642i
$790$		0			0
$791$		−	636084.i		−	1.01663i
$792$		0			0
$793$	87945.3	+	50775.3i	0.139851	+	0.0807432i
$794$		0			0
$795$	755521.	−	1.30860e6i	1.19540	−	2.07049i
$796$		0			0
$797$			1.04149e6i			1.63960i	0.572653	+	0.819798i	$0.305914\pi$
$797$			1.04149e6i			1.63960i	−0.572653	+	0.819798i	$0.694086\pi$
$798$		0			0
$799$	1.20012e6			1.87988
$800$		0			0
$801$	314750.	+	181721.i	0.490570	+	0.283231i
$802$		0			0
$803$	−407772.	+	706282.i	−0.632392	+	1.09533i
$804$		0			0
$805$	521976.			0.805487
$806$		0			0
$807$	384002.	+	665111.i	0.589640	+	1.02129i
$808$		0			0
$809$	130350.			0.199166			0.0995828	−	0.995029i	$-0.468249\pi$
$809$	130350.			0.199166			0.0995828	+	0.995029i	$0.468249\pi$
$810$		0			0
$811$	−731310.	+	422222.i	−1.11188	+	0.641947i	−0.939317	−	0.343051i	$-0.888540\pi$
$811$	−731310.	+	422222.i	−1.11188	+	0.641947i	−0.172568	+	0.984998i	$0.555206\pi$
$812$		0			0
$813$	1.24610e6	−	719437.i	1.88526	−	1.08846i
$814$		0			0
$815$	−203407.	+	352311.i	−0.306232	+	0.530409i
$816$		0			0
$817$	−70594.2	−	26176.4i	−0.105761	−	0.0392163i
$818$		0			0
$819$	154881.	+	89420.8i	0.230904	+	0.133312i
$820$		0			0
$821$	−419231.	−	726130.i	−0.621967	−	1.07728i	−0.989119	−	0.147117i	$-0.953001\pi$
$821$	−419231.	−	726130.i	−0.621967	−	1.07728i	0.367152	−	0.930161i	$-0.380333\pi$
$822$		0			0
$823$	10599.2	+	18358.3i	0.0156485	+	0.0271040i	0.873744	−	0.486387i	$-0.161685\pi$
$823$	10599.2	+	18358.3i	0.0156485	+	0.0271040i	−0.858095	+	0.513491i	$0.828352\pi$
$824$		0			0
$825$		−	618552.i		−	0.908800i
$826$		0			0
$827$	979412.	−	565464.i	1.43204	−	0.826787i	0.434761	−	0.900546i	$-0.356833\pi$
$827$	979412.	−	565464.i	1.43204	−	0.826787i	0.997276	+	0.0737589i	$0.0234995\pi$
$828$		0			0
$829$			420408.i			0.611733i	0.952074	+	0.305867i	$0.0989461\pi$
$829$			420408.i			0.611733i	−0.952074	+	0.305867i	$0.901054\pi$
$830$		0			0
$831$	−670954.	−	387376.i	−0.971607	−	0.560958i
$832$		0			0
$833$	260750.	−	451632.i	0.375780	−	0.650870i
$834$		0			0
$835$		−	726041.i		−	1.04133i
$836$		0			0
$837$	234983.			0.335417
$838$		0			0
$839$	−140137.	−	80908.3i	−0.199081	−	0.114939i	0.397146	−	0.917756i	$-0.370001\pi$
$839$	−140137.	−	80908.3i	−0.199081	−	0.114939i	−0.596227	+	0.802816i	$0.703334\pi$
$840$		0			0
$841$	160363.	−	277757.i	0.226732	−	0.392711i
$842$		0			0
$843$	−1.71947e6			−2.41958
$844$		0			0
$845$	−154937.	−	268358.i	−0.216990	−	0.375839i
$846$		0			0
$847$	−595465.			−0.830021
$848$		0			0
$849$	−967387.	+	558521.i	−1.34210	+	0.774862i
$850$		0			0
$851$	724896.	−	418519.i	1.00096	−	0.577904i
$852$		0			0
$853$	198807.	−	344344.i	0.273234	−	0.473255i	−0.696454	−	0.717601i	$-0.745240\pi$
$853$	198807.	−	344344.i	0.273234	−	0.473255i	0.969688	+	0.244347i	$0.0785735\pi$
$854$		0			0
$855$	72091.7	+	423752.i	0.0986172	+	0.579668i
$856$		0			0
$857$	−288557.	−	166599.i	−0.392890	−	0.226835i	0.290522	−	0.956868i	$-0.406171\pi$
$857$	−288557.	−	166599.i	−0.392890	−	0.226835i	−0.683411	+	0.730033i	$0.739504\pi$
$858$		0			0
$859$	607402.	+	1.05205e6i	0.823170	+	1.42577i	0.903310	+	0.428989i	$0.141130\pi$
$859$	607402.	+	1.05205e6i	0.823170	+	1.42577i	−0.0801396	+	0.996784i	$0.525537\pi$
$860$		0			0
$861$	363070.	+	628856.i	0.489761	+	0.848291i
$862$		0			0
$863$		−	636900.i		−	0.855165i	−0.903976	−	0.427582i	$-0.859365\pi$
$863$		−	636900.i		−	0.855165i	0.903976	−	0.427582i	$-0.140635\pi$
$864$		0			0
$865$	845678.	−	488253.i	1.13025	−	0.652548i
$866$		0			0
$867$			985020.i			1.31041i
$868$		0			0
$869$	−1.02599e6	−	592354.i	−1.35863	−	0.784407i
$870$		0			0
$871$	326585.	−	565662.i	0.430487	−	0.745626i
$872$		0			0
$873$			249862.i			0.327847i
$874$		0			0
$875$	322306.			0.420972
$876$		0			0
$877$	928722.	+	536198.i	1.20750	+	0.697149i	0.962212	−	0.272301i	$-0.0877847\pi$
$877$	928722.	+	536198.i	1.20750	+	0.697149i	0.245286	+	0.969451i	$0.421118\pi$
$878$		0			0
$879$	725109.	−	1.25593e6i	0.938481	−	1.62550i
$880$		0			0
$881$	−684257.			−0.881591			−0.440796	−	0.897607i	$-0.645304\pi$
$881$	−684257.			−0.881591			−0.440796	+	0.897607i	$0.645304\pi$
$882$		0			0
$883$	750981.	+	1.30074e6i	0.963180	+	1.66828i	0.714428	+	0.699709i	$0.246687\pi$
$883$	750981.	+	1.30074e6i	0.963180	+	1.66828i	0.248752	+	0.968567i	$0.419980\pi$
$884$		0			0
$885$	−502059.			−0.641015
$886$		0			0
$887$	−219926.	+	126974.i	−0.279530	+	0.161387i	−0.633211	−	0.773979i	$-0.718263\pi$
$887$	−219926.	+	126974.i	−0.279530	+	0.161387i	0.353681	+	0.935366i	$0.384930\pi$
$888$		0			0
$889$	−583133.	+	336672.i	−0.737843	+	0.425994i
$890$		0			0
$891$	−735674.	+	1.27422e6i	−0.926680	+	1.60506i
$892$		0			0
$893$	−800782.	+	663763.i	−1.00418	+	0.832359i
$894$		0			0
$895$	−330133.	−	190603.i	−0.412139	−	0.237948i
$896$		0			0
$897$	373480.	+	646887.i	0.464176	+	0.803976i
$898$		0			0
$899$	258106.	+	447052.i	0.319358	+	0.553144i
$900$		0			0
$901$			1.87542e6i			2.31020i
$902$		0			0
$903$	67023.5	−	38696.0i	0.0821962	−	0.0474560i
$904$		0			0
$905$		−	897108.i		−	1.09534i
$906$		0			0
$907$	−1.04761e6	−	604840.i	−1.27346	−	0.735235i	−0.297826	−	0.954620i	$-0.596262\pi$
$907$	−1.04761e6	−	604840.i	−1.27346	−	0.735235i	−0.975638	+	0.219385i	$0.929595\pi$
$908$		0			0
$909$	28113.8	−	48694.5i	0.0340244	−	0.0589321i
$910$		0			0
$911$		−	116317.i		−	0.140154i	−0.997542	−	0.0700771i	$-0.977675\pi$
$911$		−	116317.i		−	0.140154i	0.997542	−	0.0700771i	$-0.0223245\pi$
$912$		0			0
$913$	1.26617e6			1.51898
$914$		0			0
$915$	−217272.	−	125442.i	−0.259515	−	0.149831i
$916$		0			0
$917$	427925.	−	741188.i	0.508896	−	0.881434i
$918$		0			0
$919$	−270448.			−0.320223			−0.160112	−	0.987099i	$-0.551185\pi$
$919$	−270448.			−0.320223			−0.160112	+	0.987099i	$0.551185\pi$
$920$		0			0
$921$	111822.	+	193681.i	0.131828	+	0.228332i
$922$		0			0
$923$	316569.			0.371590
$924$		0			0
$925$	−454369.	+	262330.i	−0.531038	+	0.306595i
$926$		0			0
$927$	−426489.	+	246234.i	−0.496305	+	0.286542i
$928$		0			0
$929$	−719592.	+	1.24637e6i	−0.833786	+	1.44416i	0.0612290	+	0.998124i	$0.480498\pi$
$929$	−719592.	+	1.24637e6i	−0.833786	+	1.44416i	−0.895015	+	0.446036i	$0.852835\pi$
$930$		0			0
$931$	75803.3	+	445569.i	0.0874559	+	0.514062i
$932$		0			0
$933$	−218205.	−	125980.i	−0.250669	−	0.144724i
$934$		0			0
$935$	1.14586e6	+	1.98468e6i	1.31071	+	2.27022i
$936$		0			0
$937$	−393574.	−	681690.i	−0.448277	−	0.776439i	0.549997	−	0.835167i	$-0.314629\pi$
$937$	−393574.	−	681690.i	−0.448277	−	0.776439i	−0.998274	+	0.0587275i	$0.981296\pi$
$938$		0			0
$939$		−	1.18262e6i		−	1.34126i
$940$		0			0
$941$	1.04526e6	−	603479.i	1.18044	−	0.681527i	0.224323	−	0.974515i	$-0.427983\pi$
$941$	1.04526e6	−	603479.i	1.18044	−	0.681527i	0.956116	+	0.292988i	$0.0946496\pi$
$942$		0			0
$943$			982928.i			1.10535i
$944$		0			0
$945$	415362.	+	239809.i	0.465117	+	0.268536i
$946$		0			0
$947$	−355556.	+	615841.i	−0.396468	+	0.686703i	−0.993287	−	0.115673i	$-0.963098\pi$
$947$	−355556.	+	615841.i	−0.396468	+	0.686703i	0.596819	+	0.802376i	$0.296431\pi$
$948$		0			0
$949$			617308.i			0.685440i
$950$		0			0
$951$	201200.			0.222468
$952$		0			0
$953$	82892.0	+	47857.7i	0.0912698	+	0.0526946i	0.544940	−	0.838475i	$-0.316552\pi$
$953$	82892.0	+	47857.7i	0.0912698	+	0.0526946i	−0.453670	+	0.891170i	$0.649886\pi$
$954$		0			0
$955$	598350.	−	1.03637e6i	0.656068	−	1.13634i
$956$		0			0
$957$	−1.99195e6			−2.17498
$958$		0			0
$959$	45246.2	+	78368.8i	0.0491977	+	0.0852130i
$960$		0			0
$961$	664307.			0.719320
$962$		0			0
$963$	−643732.	+	371659.i	−0.694149	+	0.400767i
$964$		0			0
$965$	585480.	−	338027.i	0.628720	−	0.362992i
$966$		0			0
$967$	−467521.	+	809769.i	−0.499974	+	0.865981i	−1.00000		2.95638e-5i	$-0.999991\pi$
$967$	−467521.	+	809769.i	−0.499974	+	0.865981i	0.500026	+	0.866011i	$0.333324\pi$
$968$		0			0
$969$	−1.05049e6	−	1.26734e6i	−1.11878	−	1.34972i
$970$		0			0
$971$	−1.11760e6	−	645245.i	−1.18535	−	0.684362i	−0.228104	−	0.973637i	$-0.573253\pi$
$971$	−1.11760e6	−	645245.i	−1.18535	−	0.684362i	−0.957246	+	0.289274i	$0.906586\pi$
$972$		0			0
$973$	296299.	+	513205.i	0.312971	+	0.542082i
$974$		0			0
$975$	−234100.	−	405473.i	−0.246259	−	0.426533i
$976$		0			0
$977$			1.41146e6i			1.47870i	0.673321	+	0.739350i	$0.264867\pi$
$977$			1.41146e6i			1.47870i	−0.673321	+	0.739350i	$0.735133\pi$
$978$		0			0
$979$	−1.45437e6	+	839681.i	−1.51743	+	0.876091i
$980$		0			0
$981$			126680.i			0.131635i
$982$		0			0
$983$	1.01698e6	+	587156.i	1.05246	+	0.607640i	0.923338	−	0.383989i	$-0.125450\pi$
$983$	1.01698e6	+	587156.i	1.05246	+	0.607640i	0.129125	+	0.991628i	$0.458783\pi$
$984$		0			0
$985$	−1.06054e6	+	1.83691e6i	−1.09309	+	1.89328i
$986$		0			0
$987$		−	1.06914e6i		−	1.09749i
$988$		0			0
$989$	104761.			0.107104
$990$		0			0
$991$	−13570.4	−	7834.85i	−0.0138180	−	0.00797781i	0.493075	−	0.869987i	$-0.335873\pi$
$991$	−13570.4	−	7834.85i	−0.0138180	−	0.00797781i	−0.506893	+	0.862009i	$0.669206\pi$
$992$		0			0
$993$	−183865.	+	318464.i	−0.186466	+	0.322969i
$994$		0			0
$995$	−1.27026e6			−1.28306
$996$		0			0
$997$	−584068.	−	1.01163e6i	−0.587588	−	1.01773i	−0.994547	−	0.104286i	$-0.966744\pi$
$997$	−584068.	−	1.01163e6i	−0.587588	−	1.01773i	0.406959	−	0.913446i	$-0.366589\pi$
$998$		0			0
$999$	769113.			0.770653

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	304.5.r.d.65.5		40
4.3	odd	2		152.5.n.a.65.16	✓	40
19.12	odd	6	inner	304.5.r.d.145.5		40
76.31	even	6		152.5.n.a.145.16	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.5.n.a.65.16	✓	40	4.3	odd	2
152.5.n.a.145.16	yes	40	76.31	even	6
304.5.r.d.65.5		40	1.1	even	1	trivial
304.5.r.d.145.5		40	19.12	odd	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-9.48048 - 5.47356i) q^{3} +(-15.3284 + 26.5496i) q^{5} -33.8970 q^{7} +(19.4197 + 33.6359i) q^{9} +O(q^{10})\)	\(q+(-9.48048 - 5.47356i) q^{3} +(-15.3284 + 26.5496i) q^{5} -33.8970 q^{7} +(19.4197 + 33.6359i) q^{9} -179.466 q^{11} +(-117.643 + 67.9213i) q^{13} +(290.642 - 167.802i) q^{15} +(-208.267 + 360.729i) q^{17} +(-60.5460 - 355.886i) q^{19} +(321.359 + 185.537i) q^{21} +(251.149 + 435.003i) q^{23} +(-157.422 - 272.663i) q^{25} +461.538i q^{27} +(-878.069 + 506.954i) q^{29} -509.130i q^{31} +(1701.42 + 982.315i) q^{33} +(519.587 - 899.952i) q^{35} -1666.41i q^{37} +1487.08 q^{39} +(1694.69 + 978.431i) q^{41} +(104.281 - 180.620i) q^{43} -1190.69 q^{45} +(-1440.60 - 2495.19i) q^{47} -1252.00 q^{49} +(3948.95 - 2279.92i) q^{51} +(3899.24 - 2251.22i) q^{53} +(2750.93 - 4764.75i) q^{55} +(-1373.96 + 3705.38i) q^{57} +(-1295.56 - 747.992i) q^{59} +(-373.780 - 647.406i) q^{61} +(-658.268 - 1140.15i) q^{63} -4164.51i q^{65} +(-4164.10 + 2404.15i) q^{67} -5498.72i q^{69} +(-2018.19 - 1165.20i) q^{71} +(2272.15 - 3935.47i) q^{73} +3446.63i q^{75} +6083.34 q^{77} +(5716.90 + 3300.65i) q^{79} +(4099.25 - 7100.10i) q^{81} -7055.25 q^{83} +(-6384.82 - 11058.8i) q^{85} +11099.4 q^{87} +(8103.90 - 4678.79i) q^{89} +(3987.74 - 2302.33i) q^{91} +(-2786.76 + 4826.80i) q^{93} +(10376.7 + 3847.71i) q^{95} +(5571.32 + 3216.61i) q^{97} +(-3485.16 - 6036.48i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9}+O(q^{10}) \) 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9	\( 40 q - 12 q^{3} + 32 q^{7} + 624 q^{9} - 24 q^{11} + 264 q^{13} - 624 q^{15} + 216 q^{17} + 652 q^{19} - 216 q^{21} + 1296 q^{23} - 3044 q^{25} + 288 q^{29} - 6660 q^{33} - 360 q^{35} - 3184 q^{39} + 1260 q^{41} - 632 q^{43} + 256 q^{45} - 1248 q^{47} + 16696 q^{49} + 8064 q^{51} - 3672 q^{53} + 3408 q^{55} - 4552 q^{57} - 12492 q^{59} + 2720 q^{61} - 12472 q^{63} - 16260 q^{67} + 504 q^{71} + 9220 q^{73} - 14688 q^{77} + 28944 q^{79} - 1660 q^{81} + 39192 q^{83} - 18632 q^{85} + 34400 q^{87} + 3456 q^{89} - 54432 q^{91} - 17208 q^{93} - 44520 q^{95} - 30540 q^{97} + 10096 q^{99}+O(q^{100}) \) 40 * q - 12 * q^3 + 32 * q^7 + 624 * q^9 - 24 * q^11 + 264 * q^13 - 624 * q^15 + 216 * q^17 + 652 * q^19 - 216 * q^21 + 1296 * q^23 - 3044 * q^25 + 288 * q^29 - 6660 * q^33 - 360 * q^35 - 3184 * q^39 + 1260 * q^41 - 632 * q^43 + 256 * q^45 - 1248 * q^47 + 16696 * q^49 + 8064 * q^51 - 3672 * q^53 + 3408 * q^55 - 4552 * q^57 - 12492 * q^59 + 2720 * q^61 - 12472 * q^63 - 16260 * q^67 + 504 * q^71 + 9220 * q^73 - 14688 * q^77 + 28944 * q^79 - 1660 * q^81 + 39192 * q^83 - 18632 * q^85 + 34400 * q^87 + 3456 * q^89 - 54432 * q^91 - 17208 * q^93 - 44520 * q^95 - 30540 * q^97 + 10096 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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