LMFDB - Embedded newform 500.4.i.b.449.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [500,4,Mod(49,500)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(500, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("500.49");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 500 = 2^{2} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	500.i (of order $10$, degree $4$, 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:	$29.5009550029$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 100)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			449.14
Character	$\chi$	$=$	500.449
Dual form			500.4.i.b.49.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(8.18380 + 2.65908i) q^{3} +17.7526i q^{7} +(38.0604 + 27.6525i) q^{9} +O(q^{10})$	\(q+(8.18380 + 2.65908i) q^{3} +17.7526i q^{7} +(38.0604 + 27.6525i) q^{9} +(-23.4721 + 17.0535i) q^{11} +(-32.1054 + 44.1893i) q^{13} +(-65.0309 + 21.1298i) q^{17} +(16.6150 + 51.1357i) q^{19} +(-47.2055 + 145.284i) q^{21} +(-97.9692 - 134.843i) q^{23} +(101.386 + 139.546i) q^{27} +(78.8623 - 242.713i) q^{29} +(63.8593 + 196.539i) q^{31} +(-237.438 + 77.1482i) q^{33} +(-143.243 + 197.157i) q^{37} +(-380.247 + 276.266i) q^{39} +(38.2337 + 27.7784i) q^{41} +35.8364i q^{43} +(444.972 + 144.580i) q^{47} +27.8456 q^{49} -588.385 q^{51} +(640.594 + 208.142i) q^{53} +462.665i q^{57} +(-267.341 - 194.235i) q^{59} +(320.417 - 232.797i) q^{61} +(-490.904 + 675.671i) q^{63} +(-339.004 + 110.149i) q^{67} +(-443.202 - 1364.04i) q^{69} +(-104.255 + 320.863i) q^{71} +(427.809 + 588.829i) q^{73} +(-302.744 - 416.691i) q^{77} +(392.901 - 1209.22i) q^{79} +(66.1401 + 203.558i) q^{81} +(61.1687 - 19.8749i) q^{83} +(1290.79 - 1776.61i) q^{87} +(-565.265 + 410.689i) q^{89} +(-784.474 - 569.954i) q^{91} +1778.24i q^{93} +(917.209 + 298.019i) q^{97} -1364.93 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 26 q^{9}+O(q^{10}) $ 56 * q + 26 * q^9	$ 56 q + 26 q^{9} - 40 q^{11} - 4 q^{19} + 216 q^{21} - 384 q^{29} + 756 q^{31} - 1184 q^{39} + 596 q^{41} - 288 q^{49} - 3328 q^{51} - 288 q^{59} + 1032 q^{61} - 5992 q^{69} - 4052 q^{71} - 1792 q^{79} - 4406 q^{81} + 334 q^{89} + 4424 q^{91} + 4200 q^{99}+O(q^{100}) $ 56 * q + 26 * q^9 - 40 * q^11 - 4 * q^19 + 216 * q^21 - 384 * q^29 + 756 * q^31 - 1184 * q^39 + 596 * q^41 - 288 * q^49 - 3328 * q^51 - 288 * q^59 + 1032 * q^61 - 5992 * q^69 - 4052 * q^71 - 1792 * q^79 - 4406 * q^81 + 334 * q^89 + 4424 * q^91 + 4200 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/500\mathbb{Z}\right)^\times$.

$n$	$251$	$377$
$\chi(n)$	$1$	$e\left(\frac{3}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	8.18380	+	2.65908i	1.57497	+	0.511740i	0.960755	−	0.277397i	$-0.0894718\pi$
$3$	8.18380	+	2.65908i	1.57497	+	0.511740i	0.614217	+	0.789137i	$0.289472\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$			17.7526i			0.958550i	0.877665	+	0.479275i	$0.159100\pi$
$7$			17.7526i			0.958550i	−0.877665	+	0.479275i	$0.840900\pi$
$8$		0			0
$9$	38.0604	+	27.6525i	1.40964	+	1.02417i
$10$		0			0
$11$	−23.4721	+	17.0535i	−0.643374	+	0.467439i	−0.861008	−	0.508592i	$-0.830166\pi$
$11$	−23.4721	+	17.0535i	−0.643374	+	0.467439i	0.217634	+	0.976031i	$0.430166\pi$
$12$		0			0
$13$	−32.1054	+	44.1893i	−0.684957	+	0.942762i	−0.999980	−	0.00632198i	$-0.997988\pi$
$13$	−32.1054	+	44.1893i	−0.684957	+	0.942762i	0.315023	+	0.949084i	$0.397988\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−65.0309	+	21.1298i	−0.927782	+	0.301455i	−0.733655	−	0.679522i	$-0.762187\pi$
$17$	−65.0309	+	21.1298i	−0.927782	+	0.301455i	−0.194127	+	0.980976i	$0.562187\pi$
$18$		0			0
$19$	16.6150	+	51.1357i	0.200618	+	0.617438i	0.999865	+	0.0164357i	$0.00523188\pi$
$19$	16.6150	+	51.1357i	0.200618	+	0.617438i	−0.799247	+	0.601003i	$0.794768\pi$
$20$		0			0
$21$	−47.2055	+	145.284i	−0.490528	+	1.50969i
$22$		0			0
$23$	−97.9692	−	134.843i	−0.888173	−	1.22247i	−0.974089	−	0.226163i	$-0.927382\pi$
$23$	−97.9692	−	134.843i	−0.888173	−	1.22247i	0.0859161	−	0.996302i	$-0.472618\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	101.386	+	139.546i	0.722659	+	0.994654i
$28$		0			0
$29$	78.8623	−	242.713i	0.504978	−	1.55416i	−0.295830	−	0.955241i	$-0.595596\pi$
$29$	78.8623	−	242.713i	0.504978	−	1.55416i	0.800808	−	0.598921i	$-0.204404\pi$
$30$		0			0
$31$	63.8593	+	196.539i	0.369983	+	1.13869i	0.946802	+	0.321818i	$0.104294\pi$
$31$	63.8593	+	196.539i	0.369983	+	1.13869i	−0.576819	+	0.816872i	$0.695706\pi$
$32$		0			0
$33$	−237.438	+	77.1482i	−1.25250	+	0.406963i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−143.243	+	197.157i	−0.636459	+	0.876011i	−0.998421	−	0.0561822i	$-0.982107\pi$
$37$	−143.243	+	197.157i	−0.636459	+	0.876011i	0.361961	+	0.932193i	$0.382107\pi$
$38$		0			0
$39$	−380.247	+	276.266i	−1.56124	+	1.13430i
$40$		0			0
$41$	38.2337	+	27.7784i	0.145636	+	0.105811i	0.658218	−	0.752828i	$-0.271311\pi$
$41$	38.2337	+	27.7784i	0.145636	+	0.105811i	−0.512581	+	0.858639i	$0.671311\pi$
$42$		0			0
$43$			35.8364i			0.127093i	0.997979	+	0.0635464i	$0.0202411\pi$
$43$			35.8364i			0.127093i	−0.997979	+	0.0635464i	$0.979759\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	444.972	+	144.580i	1.38098	+	0.448706i	0.902990	−	0.429662i	$-0.141367\pi$
$47$	444.972	+	144.580i	1.38098	+	0.448706i	0.477985	+	0.878368i	$0.341367\pi$
$48$		0			0
$49$	27.8456			0.0811824
$50$		0			0
$51$	−588.385			−1.61550
$52$		0			0
$53$	640.594	+	208.142i	1.66023	+	0.539442i	0.980921	−	0.194407i	$-0.0622782\pi$
$53$	640.594	+	208.142i	1.66023	+	0.539442i	0.679312	+	0.733849i	$0.262278\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			462.665i			1.07511i
$58$		0			0
$59$	−267.341	−	194.235i	−0.589913	−	0.428597i	0.252371	−	0.967630i	$-0.418790\pi$
$59$	−267.341	−	194.235i	−0.589913	−	0.428597i	−0.842284	+	0.539034i	$0.818790\pi$
$60$		0			0
$61$	320.417	−	232.797i	0.672545	−	0.488633i	−0.198331	−	0.980135i	$-0.563552\pi$
$61$	320.417	−	232.797i	0.672545	−	0.488633i	0.870876	+	0.491502i	$0.163552\pi$
$62$		0			0
$63$	−490.904	+	675.671i	−0.981715	+	1.35121i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−339.004	+	110.149i	−0.618149	+	0.200849i	−0.601318	−	0.799010i	$-0.705358\pi$
$67$	−339.004	+	110.149i	−0.618149	+	0.200849i	−0.0168306	+	0.999858i	$0.505358\pi$
$68$		0			0
$69$	−443.202	−	1364.04i	−0.773265	−	2.37986i
$70$		0			0
$71$	−104.255	+	320.863i	−0.174264	+	0.536331i	−0.999599	−	0.0283132i	$-0.990986\pi$
$71$	−104.255	+	320.863i	−0.174264	+	0.536331i	0.825335	+	0.564644i	$0.190986\pi$
$72$		0			0
$73$	427.809	+	588.829i	0.685908	+	0.944072i	0.999986	−	0.00532550i	$-0.00169517\pi$
$73$	427.809	+	588.829i	0.685908	+	0.944072i	−0.314077	+	0.949397i	$0.601695\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−302.744	−	416.691i	−0.448063	−	0.616706i
$78$		0			0
$79$	392.901	−	1209.22i	0.559554	−	1.72213i	−0.124047	−	0.992276i	$-0.539587\pi$
$79$	392.901	−	1209.22i	0.559554	−	1.72213i	0.683602	−	0.729855i	$-0.260413\pi$
$80$		0			0
$81$	66.1401	+	203.558i	0.0907272	+	0.279230i
$82$		0			0
$83$	61.1687	−	19.8749i	0.0808932	−	0.0262838i	−0.268291	−	0.963338i	$-0.586459\pi$
$83$	61.1687	−	19.8749i	0.0808932	−	0.0262838i	0.349184	+	0.937054i	$0.386459\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	1290.79	−	1776.61i	1.59065	−	2.18935i
$88$		0			0
$89$	−565.265	+	410.689i	−0.673236	+	0.489134i	−0.871107	−	0.491094i	$-0.836597\pi$
$89$	−565.265	+	410.689i	−0.673236	+	0.489134i	0.197871	+	0.980228i	$0.436597\pi$
$90$		0			0
$91$	−784.474	−	569.954i	−0.903684	−	0.656565i
$92$		0			0
$93$			1778.24i			1.98274i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	917.209	+	298.019i	0.960088	+	0.311951i	0.746808	−	0.665040i	$-0.231585\pi$
$97$	917.209	+	298.019i	0.960088	+	0.311951i	0.213280	+	0.976991i	$0.431585\pi$
$98$		0			0
$99$	−1364.93			−1.38566
$100$		0			0
$101$	−45.8510			−0.0451718			−0.0225859	−	0.999745i	$-0.507190\pi$
$101$	−45.8510			−0.0451718			−0.0225859	+	0.999745i	$0.507190\pi$
$102$		0			0
$103$	−1082.31	−	351.665i	−1.03537	−	0.336413i	−0.258461	−	0.966022i	$-0.583215\pi$
$103$	−1082.31	−	351.665i	−1.03537	−	0.336413i	−0.776913	+	0.629608i	$0.783215\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$			1828.84i			1.65234i	0.563422	+	0.826169i	$0.309484\pi$
$107$			1828.84i			1.65234i	−0.563422	+	0.826169i	$0.690516\pi$
$108$		0			0
$109$	1699.65	+	1234.87i	1.49355	+	1.08513i	0.972864	+	0.231376i	$0.0743227\pi$
$109$	1699.65	+	1234.87i	1.49355	+	1.08513i	0.520683	+	0.853750i	$0.325677\pi$
$110$		0			0
$111$	−1696.53	+	1232.60i	−1.45070	+	1.05399i
$112$		0			0
$113$	878.927	−	1209.74i	0.731704	−	1.00710i	−0.267349	−	0.963600i	$-0.586148\pi$
$113$	878.927	−	1209.74i	0.731704	−	1.00710i	0.999053	−	0.0435042i	$-0.0138522\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2443.89	+	794.068i	−1.93109	+	0.627450i
$118$		0			0
$119$	−375.109	−	1154.47i	−0.288959	−	0.889326i
$120$		0			0
$121$	−151.183	+	465.292i	−0.113586	+	0.349581i
$122$		0			0
$123$	239.032	+	328.999i	0.175226	+	0.241178i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	1191.90	+	1640.51i	0.832787	+	1.14623i	0.987398	+	0.158257i	$0.0505876\pi$
$127$	1191.90	+	1640.51i	0.832787	+	1.14623i	−0.154611	+	0.987975i	$0.549412\pi$
$128$		0			0
$129$	−95.2917	+	293.278i	−0.0650385	+	0.200168i
$130$		0			0
$131$	−106.950	−	329.158i	−0.0713303	−	0.219532i	0.909036	−	0.416718i	$-0.136820\pi$
$131$	−106.950	−	329.158i	−0.0713303	−	0.219532i	−0.980366	+	0.197186i	$0.936820\pi$
$132$		0			0
$133$	−907.791	+	294.959i	−0.591845	+	0.192302i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−443.616	+	610.585i	−0.276647	+	0.380772i	−0.924620	−	0.380892i	$-0.875617\pi$
$137$	−443.616	+	610.585i	−0.276647	+	0.380772i	0.647973	+	0.761664i	$0.275617\pi$
$138$		0			0
$139$	−1619.65	+	1176.75i	−0.988325	+	0.718060i	−0.959554	−	0.281526i	$-0.909159\pi$
$139$	−1619.65	+	1176.75i	−0.988325	+	0.718060i	−0.0287710	+	0.999586i	$0.509159\pi$
$140$		0			0
$141$	3257.11	+	2366.43i	1.94538	+	1.41340i
$142$		0			0
$143$		−	1584.73i		−	0.926724i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	227.882	+	74.0435i	0.127860	+	0.0415442i
$148$		0			0
$149$	1066.44			0.586348			0.293174	−	0.956059i	$-0.405289\pi$
$149$	1066.44			0.586348			0.293174	+	0.956059i	$0.405289\pi$
$150$		0			0
$151$	763.019			0.411216			0.205608	−	0.978634i	$-0.434083\pi$
$151$	763.019			0.411216			0.205608	+	0.978634i	$0.434083\pi$
$152$		0			0
$153$	−3059.39	−	994.057i	−1.61658	−	0.525260i
$154$		0			0
$155$		0			0
$156$		0			0
$157$			62.3483i			0.0316939i	0.999874	+	0.0158469i	$0.00504445\pi$
$157$			62.3483i			0.0316939i	−0.999874	+	0.0158469i	$0.994956\pi$
$158$		0			0
$159$	4689.03	+	3406.78i	2.33877	+	1.69921i
$160$		0			0
$161$	2393.81	−	1739.21i	1.17179	−	0.851358i
$162$		0			0
$163$	212.733	−	292.802i	0.102224	−	0.140700i	−0.754840	−	0.655909i	$-0.772286\pi$
$163$	212.733	−	292.802i	0.102224	−	0.140700i	0.857065	+	0.515209i	$0.172286\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−1382.91	+	449.335i	−0.640795	+	0.208207i	−0.611351	−	0.791359i	$-0.709374\pi$
$167$	−1382.91	+	449.335i	−0.640795	+	0.208207i	−0.0294442	+	0.999566i	$0.509374\pi$
$168$		0			0
$169$	−243.027	−	747.959i	−0.110617	−	0.340446i
$170$		0			0
$171$	−781.656	+	2405.69i	−0.349560	+	1.07583i
$172$		0			0
$173$	−1189.07	−	1636.62i	−0.522564	−	0.719248i	0.463411	−	0.886144i	$-0.346626\pi$
$173$	−1189.07	−	1636.62i	−0.522564	−	0.719248i	−0.985974	+	0.166896i	$0.946626\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−1671.38	−	2300.46i	−0.709767	−	0.976910i
$178$		0			0
$179$	393.779	−	1211.93i	0.164427	−	0.506054i	−0.834567	−	0.550907i	$-0.814282\pi$
$179$	393.779	−	1211.93i	0.164427	−	0.506054i	0.998994	+	0.0448528i	$0.0142819\pi$
$180$		0			0
$181$	−1331.48	−	4097.87i	−0.546784	−	1.68283i	−0.716709	−	0.697372i	$-0.754353\pi$
$181$	−1331.48	−	4097.87i	−0.546784	−	1.68283i	0.169925	−	0.985457i	$-0.445647\pi$
$182$		0			0
$183$	3241.26	−	1053.15i	1.30929	−	0.425415i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	1166.08	−	1604.97i	0.456000	−	0.627630i
$188$		0			0
$189$	−2477.31	+	1799.87i	−0.953426	+	0.692704i
$190$		0			0
$191$	251.826	+	182.962i	0.0954004	+	0.0693124i	0.634463	−	0.772953i	$-0.281221\pi$
$191$	251.826	+	182.962i	0.0954004	+	0.0693124i	−0.539062	+	0.842266i	$0.681221\pi$
$192$		0			0
$193$		−	2675.32i		−	0.997790i	−0.866662	−	0.498895i	$-0.833739\pi$
$193$		−	2675.32i		−	0.997790i	0.866662	−	0.498895i	$-0.166261\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	881.549	+	286.433i	0.318821	+	0.103591i	0.464056	−	0.885806i	$-0.346394\pi$
$197$	881.549	+	286.433i	0.318821	+	0.103591i	−0.145235	+	0.989397i	$0.546394\pi$
$198$		0			0
$199$	444.199			0.158233			0.0791166	−	0.996865i	$-0.474790\pi$
$199$	444.199			0.158233			0.0791166	+	0.996865i	$0.474790\pi$
$200$		0			0
$201$	−3067.24			−1.07635
$202$		0			0
$203$	4308.79	+	1400.01i	1.48974	+	0.484046i
$204$		0			0
$205$		0			0
$206$		0			0
$207$		−	7841.27i		−	2.63288i
$208$		0			0
$209$	−1262.03	−	916.920i	−0.417687	−	0.303467i
$210$		0			0
$211$	785.213	−	570.491i	0.256191	−	0.186134i	−0.452275	−	0.891878i	$-0.649387\pi$
$211$	785.213	−	570.491i	0.256191	−	0.186134i	0.708466	+	0.705745i	$0.249387\pi$
$212$		0			0
$213$	−1706.40	+	2348.66i	−0.548923	+	0.755528i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−3489.07	+	1133.67i	−1.09149	+	0.354647i
$218$		0			0
$219$	1935.36	+	5956.44i	0.597168	+	1.83789i
$220$		0			0
$221$	1154.13	−	3552.05i	0.351291	−	1.08116i
$222$		0			0
$223$	2222.31	+	3058.75i	0.667342	+	0.918517i	0.999696	−	0.0246375i	$-0.00784316\pi$
$223$	2222.31	+	3058.75i	0.667342	+	0.918517i	−0.332355	+	0.943154i	$0.607843\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	2661.76	+	3663.59i	0.778269	+	1.07120i	0.995471	+	0.0950686i	$0.0303070\pi$
$227$	2661.76	+	3663.59i	0.778269	+	1.07120i	−0.217202	+	0.976127i	$0.569693\pi$
$228$		0			0
$229$	1260.02	−	3877.95i	0.363601	−	1.11905i	−0.587251	−	0.809405i	$-0.699790\pi$
$229$	1260.02	−	3877.95i	0.363601	−	1.11905i	0.950852	−	0.309644i	$-0.100210\pi$
$230$		0			0
$231$	−1369.58	−	4215.14i	−0.390094	−	1.20059i
$232$		0			0
$233$	−634.732	+	206.237i	−0.178466	+	0.0579873i	−0.396887	−	0.917867i	$-0.629910\pi$
$233$	−634.732	+	206.237i	−0.178466	+	0.0579873i	0.218421	+	0.975855i	$0.429910\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	6430.84	−	8851.30i	1.76257	−	2.42596i
$238$		0			0
$239$	2791.34	−	2028.03i	0.755468	−	0.548880i	−0.142049	−	0.989860i	$-0.545369\pi$
$239$	2791.34	−	2028.03i	0.755468	−	0.548880i	0.897517	+	0.440980i	$0.145369\pi$
$240$		0			0
$241$	−1805.47	−	1311.75i	−0.482575	−	0.350611i	0.319747	−	0.947503i	$-0.396402\pi$
$241$	−1805.47	−	1311.75i	−0.482575	−	0.350611i	−0.802322	+	0.596892i	$0.796402\pi$
$242$		0			0
$243$		−	2815.44i		−	0.743252i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−2793.08	−	907.527i	−0.719512	−	0.233784i
$248$		0			0
$249$	553.441			0.140855
$250$		0			0
$251$	433.464			0.109004			0.0545021	−	0.998514i	$-0.482643\pi$
$251$	433.464			0.109004			0.0545021	+	0.998514i	$0.482643\pi$
$252$		0			0
$253$	4599.09	+	1494.34i	1.14286	+	0.371336i
$254$		0			0
$255$		0			0
$256$		0			0
$257$		−	5696.10i		−	1.38254i	−0.722596	−	0.691270i	$-0.757051\pi$
$257$		−	5696.10i		−	1.38254i	0.722596	−	0.691270i	$-0.242949\pi$
$258$		0			0
$259$	−3500.05	−	2542.93i	−0.839700	−	0.610078i
$260$		0			0
$261$	9713.16	−	7057.02i	2.30356	−	1.67363i
$262$		0			0
$263$	2151.57	−	2961.39i	0.504455	−	0.694323i	−0.478517	−	0.878078i	$-0.658825\pi$
$263$	2151.57	−	2961.39i	0.504455	−	0.694323i	0.982972	+	0.183755i	$0.0588254\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−5718.07	+	1857.91i	−1.31064	+	0.425852i
$268$		0			0
$269$	−786.765	−	2421.41i	−0.178327	−	0.548833i	0.821443	−	0.570291i	$-0.193169\pi$
$269$	−786.765	−	2421.41i	−0.178327	−	0.548833i	−0.999770	+	0.0214573i	$0.993169\pi$
$270$		0			0
$271$	1452.10	−	4469.10i	0.325493	−	1.00177i	−0.645724	−	0.763571i	$-0.723444\pi$
$271$	1452.10	−	4469.10i	0.325493	−	1.00177i	0.971217	−	0.238195i	$-0.0765557\pi$
$272$		0			0
$273$	−4904.43	−	6750.37i	−1.08729	−	1.49652i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−39.3464	−	54.1557i	−0.00853465	−	0.0117469i	0.804728	−	0.593643i	$-0.202311\pi$
$277$	−39.3464	−	54.1557i	−0.00853465	−	0.0117469i	−0.813263	+	0.581896i	$0.802311\pi$
$278$		0			0
$279$	−3004.27	+	9246.21i	−0.644664	+	1.98407i
$280$		0			0
$281$	1462.28	+	4500.43i	0.310435	+	0.955420i	0.977593	+	0.210504i	$0.0675104\pi$
$281$	1462.28	+	4500.43i	0.310435	+	0.955420i	−0.667158	+	0.744916i	$0.732490\pi$
$282$		0			0
$283$	3564.15	−	1158.06i	0.748645	−	0.243250i	0.0902471	−	0.995919i	$-0.471234\pi$
$283$	3564.15	−	1158.06i	0.748645	−	0.243250i	0.658398	+	0.752670i	$0.271234\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−493.138	+	678.747i	−0.101425	+	0.139600i
$288$		0			0
$289$	−192.156	+	139.609i	−0.0391117	+	0.0284163i
$290$		0			0
$291$	6713.80	+	4877.86i	1.35247	+	0.982630i
$292$		0			0
$293$			1309.24i			0.261046i	0.991445	+	0.130523i	$0.0416657\pi$
$293$			1309.24i			0.261046i	−0.991445	+	0.130523i	$0.958334\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−4759.50	−	1546.46i	−0.929880	−	0.302136i
$298$		0			0
$299$	9103.96			1.76085
$300$		0			0
$301$	−636.188			−0.121825
$302$		0			0
$303$	−375.236	−	121.921i	−0.0711443	−	0.0231162i
$304$		0			0
$305$		0			0
$306$		0			0
$307$			5371.12i			0.998521i	0.866452	+	0.499260i	$0.166395\pi$
$307$			5371.12i			0.998521i	−0.866452	+	0.499260i	$0.833605\pi$
$308$		0			0
$309$	−7922.33	−	5755.91i	−1.45853	−	1.05968i
$310$		0			0
$311$	−3016.82	+	2191.85i	−0.550058	+	0.399640i	−0.827807	−	0.561013i	$-0.810412\pi$
$311$	−3016.82	+	2191.85i	−0.550058	+	0.399640i	0.277749	+	0.960654i	$0.410412\pi$
$312$		0			0
$313$	1713.05	−	2357.81i	0.309352	−	0.425787i	−0.625827	−	0.779962i	$-0.715238\pi$
$313$	1713.05	−	2357.81i	0.309352	−	0.425787i	0.935179	+	0.354175i	$0.115238\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	3440.56	−	1117.90i	0.609593	−	0.198069i	0.0120786	−	0.999927i	$-0.496155\pi$
$317$	3440.56	−	1117.90i	0.609593	−	0.198069i	0.597514	+	0.801858i	$0.296155\pi$
$318$		0			0
$319$	2288.04	+	7041.87i	0.401586	+	1.23595i
$320$		0			0
$321$	−4863.02	+	14966.8i	−0.845567	+	2.60239i
$322$		0			0
$323$	−2160.97	−	2974.33i	−0.372259	−	0.512371i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	10626.0	+	14625.4i	1.79699	+	2.47335i
$328$		0			0
$329$	−2566.67	+	7899.41i	−0.430107	+	1.32373i
$330$		0			0
$331$	−3240.51	−	9973.25i	−0.538110	−	1.65613i	−0.736832	−	0.676076i	$-0.763679\pi$
$331$	−3240.51	−	9973.25i	−0.538110	−	1.65613i	0.198722	−	0.980056i	$-0.436321\pi$
$332$		0			0
$333$	−10903.8	+	3542.85i	−1.79436	+	0.583024i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	−5491.44	+	7558.32i	−0.887650	+	1.22175i	0.0865929	+	0.996244i	$0.472402\pi$
$337$	−5491.44	+	7558.32i	−0.887650	+	1.22175i	−0.974243	+	0.225502i	$0.927598\pi$
$338$		0			0
$339$	10409.8	−	7563.13i	1.66779	−	1.21172i
$340$		0			0
$341$	−4850.58	−	3524.16i	−0.770305	−	0.559659i
$342$		0			0
$343$			6583.47i			1.03637i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	−1094.97	−	355.778i	−0.169398	−	0.0550408i	0.223090	−	0.974798i	$-0.428386\pi$
$347$	−1094.97	−	355.778i	−0.169398	−	0.0550408i	−0.392488	+	0.919757i	$0.628386\pi$
$348$		0			0
$349$	−8519.22			−1.30666			−0.653329	−	0.757074i	$-0.726628\pi$
$349$	−8519.22			−1.30666			−0.653329	+	0.757074i	$0.726628\pi$
$350$		0			0
$351$	−9421.49			−1.43271
$352$		0			0
$353$	−6065.69	−	1970.86i	−0.914572	−	0.297163i	−0.186334	−	0.982486i	$-0.559661\pi$
$353$	−6065.69	−	1970.86i	−0.914572	−	0.297163i	−0.728238	+	0.685324i	$0.759661\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$		−	10445.4i		−	1.54854i
$358$		0			0
$359$	4907.70	+	3565.65i	0.721500	+	0.524200i	0.886863	−	0.462032i	$-0.152880\pi$
$359$	4907.70	+	3565.65i	0.721500	+	0.524200i	−0.165363	+	0.986233i	$0.552880\pi$
$360$		0			0
$361$	3210.25	−	2332.38i	0.468034	−	0.340047i
$362$		0			0
$363$	−2474.50	+	3405.85i	−0.357789	+	0.492454i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−295.041	+	95.8646i	−0.0419646	+	0.0136351i	−0.329924	−	0.944007i	$-0.607023\pi$
$367$	−295.041	+	95.8646i	−0.0419646	+	0.0136351i	0.287959	+	0.957643i	$0.407023\pi$
$368$		0			0
$369$	687.047	+	2114.51i	0.0969275	+	0.298312i
$370$		0			0
$371$	−3695.05	+	11372.2i	−0.517082	+	1.59142i
$372$		0			0
$373$	2579.60	+	3550.51i	0.358087	+	0.492865i	0.949615	−	0.313420i	$-0.101475\pi$
$373$	2579.60	+	3550.51i	0.358087	+	0.492865i	−0.591527	+	0.806285i	$0.701475\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	8193.42	+	11277.3i	1.11932	+	1.54061i
$378$		0			0
$379$	−498.339	+	1533.73i	−0.0675408	+	0.207869i	−0.979131	−	0.203232i	$-0.934856\pi$
$379$	−498.339	+	1533.73i	−0.0675408	+	0.207869i	0.911590	+	0.411101i	$0.134856\pi$
$380$		0			0
$381$	5392.02	+	16594.9i	0.725044	+	2.23146i
$382$		0			0
$383$	4779.61	−	1552.99i	0.637667	−	0.207191i	0.0276987	−	0.999616i	$-0.491182\pi$
$383$	4779.61	−	1552.99i	0.637667	−	0.207191i	0.609968	+	0.792426i	$0.291182\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−990.965	+	1363.95i	−0.130164	+	0.179156i
$388$		0			0
$389$	9215.13	−	6695.18i	1.20109	−	0.872646i	0.206702	−	0.978404i	$-0.433727\pi$
$389$	9215.13	−	6695.18i	1.20109	−	0.872646i	0.994392	+	0.105758i	$0.0337268\pi$
$390$		0			0
$391$	9220.23	+	6698.89i	1.19255	+	0.866438i
$392$		0			0
$393$		−	2978.15i		−	0.382259i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	−7570.75	−	2459.89i	−0.957091	−	0.310978i	−0.211498	−	0.977379i	$-0.567834\pi$
$397$	−7570.75	−	2459.89i	−0.957091	−	0.310978i	−0.745594	+	0.666401i	$0.767834\pi$
$398$		0			0
$399$	−8213.49			−1.03055
$400$		0			0
$401$	−7624.87			−0.949546			−0.474773	−	0.880108i	$-0.657470\pi$
$401$	−7624.87			−0.949546			−0.474773	+	0.880108i	$0.657470\pi$
$402$		0			0
$403$	−10735.1	−	3488.05i	−1.32694	−	0.431147i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	7070.49i		−	0.861108i
$408$		0			0
$409$	−8492.31	−	6170.03i	−1.02669	−	0.745937i	−0.0590496	−	0.998255i	$-0.518807\pi$
$409$	−8492.31	−	6170.03i	−1.02669	−	0.745937i	−0.967644	+	0.252318i	$0.918807\pi$
$410$		0			0
$411$	−5254.05	+	3817.29i	−0.630568	+	0.458134i
$412$		0			0
$413$	3448.17	−	4746.00i	0.410831	−	0.565461i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−16384.0	+	5323.47i	−1.92404	+	0.625160i
$418$		0			0
$419$	−1278.02	−	3933.33i	−0.149010	−	0.458605i	0.848495	−	0.529203i	$-0.177509\pi$
$419$	−1278.02	−	3933.33i	−0.149010	−	0.458605i	−0.997505	+	0.0705983i	$0.977509\pi$
$420$		0			0
$421$	1907.69	−	5871.26i	0.220843	−	0.679685i	−0.777844	−	0.628458i	$-0.783687\pi$
$421$	1907.69	−	5871.26i	0.220843	−	0.679685i	0.998687	−	0.0512278i	$-0.0163135\pi$
$422$		0			0
$423$	12937.8	+	17807.4i	1.48713	+	2.04687i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	4132.75	+	5688.24i	0.468379	+	0.644668i
$428$		0			0
$429$	4213.91	−	12969.1i	0.474241	−	1.45956i
$430$		0			0
$431$	−3461.82	−	10654.4i	−0.386891	−	1.19073i	−0.935099	−	0.354387i	$-0.884690\pi$
$431$	−3461.82	−	10654.4i	−0.386891	−	1.19073i	0.548207	−	0.836342i	$-0.315310\pi$
$432$		0			0
$433$	−12879.2	+	4184.71i	−1.42941	+	0.464444i	−0.918579	−	0.395237i	$-0.870662\pi$
$433$	−12879.2	+	4184.71i	−1.42941	+	0.464444i	−0.510832	+	0.859681i	$0.670662\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	5267.53	−	7250.13i	0.576614	−	0.793641i
$438$		0			0
$439$	−1753.39	+	1273.91i	−0.190626	+	0.138498i	−0.679005	−	0.734134i	$-0.737588\pi$
$439$	−1753.39	+	1273.91i	−0.190626	+	0.138498i	0.488379	+	0.872632i	$0.337588\pi$
$440$		0			0
$441$	1059.81	+	769.999i	0.114438	+	0.0831443i
$442$		0			0
$443$			13212.9i			1.41708i	0.705672	+	0.708539i	$0.250645\pi$
$443$			13212.9i			1.41708i	−0.705672	+	0.708539i	$0.749355\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	8727.50	+	2835.74i	0.923482	+	0.300057i
$448$		0			0
$449$	1921.34			0.201946			0.100973	−	0.994889i	$-0.467805\pi$
$449$	1921.34			0.201946			0.100973	+	0.994889i	$0.467805\pi$
$450$		0			0
$451$	−1371.14			−0.143159
$452$		0			0
$453$	6244.39	+	2028.93i	0.647654	+	0.210435i
$454$		0			0
$455$		0			0
$456$		0			0
$457$		−	117.313i		−	0.0120080i	−0.999982	−	0.00600399i	$-0.998089\pi$
$457$		−	117.313i		−	0.0120080i	0.999982	−	0.00600399i	$-0.00191114\pi$
$458$		0			0
$459$	−9541.82	−	6932.53i	−0.970313	−	0.704974i
$460$		0			0
$461$	7795.85	−	5664.02i	0.787611	−	0.572233i	−0.119642	−	0.992817i	$-0.538175\pi$
$461$	7795.85	−	5664.02i	0.787611	−	0.572233i	0.907254	+	0.420584i	$0.138175\pi$
$462$		0			0
$463$	−3728.95	+	5132.47i	−0.374296	+	0.515175i	−0.954062	−	0.299608i	$-0.903144\pi$
$463$	−3728.95	+	5132.47i	−0.374296	+	0.515175i	0.579766	+	0.814783i	$0.303144\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	10087.4	−	3277.59i	0.999548	−	0.324773i	0.236863	−	0.971543i	$-0.423881\pi$
$467$	10087.4	−	3277.59i	0.999548	−	0.324773i	0.762685	+	0.646770i	$0.223881\pi$
$468$		0			0
$469$	−1955.43	−	6018.21i	−0.192524	−	0.592526i
$470$		0			0
$471$	−165.789	+	510.246i	−0.0162190	+	0.0499170i
$472$		0			0
$473$	−611.136	−	841.156i	−0.0594081	−	0.0817683i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	18625.6	+	25636.0i	1.78786	+	2.46078i
$478$		0			0
$479$	−2570.20	+	7910.25i	−0.245168	+	0.754548i	0.750441	+	0.660937i	$0.229841\pi$
$479$	−2570.20	+	7910.25i	−0.245168	+	0.754548i	−0.995609	+	0.0936111i	$0.970159\pi$
$480$		0			0
$481$	−4113.36	−	12659.6i	−0.389923	−	1.20006i
$482$		0			0
$483$	24215.2	−	7867.98i	2.28122	−	0.741213i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−1312.02	+	1805.83i	−0.122080	+	0.168029i	−0.865683	−	0.500593i	$-0.833115\pi$
$487$	−1312.02	+	1805.83i	−0.122080	+	0.168029i	0.743603	+	0.668622i	$0.233115\pi$
$488$		0			0
$489$	2519.55	−	1830.56i	0.233002	−	0.169286i
$490$		0			0
$491$	6421.33	+	4665.37i	0.590205	+	0.428809i	0.842389	−	0.538871i	$-0.181149\pi$
$491$	6421.33	+	4665.37i	0.590205	+	0.428809i	−0.252184	+	0.967679i	$0.581149\pi$
$492$		0			0
$493$			17450.2i			1.59415i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	−5696.16	−	1850.79i	−0.514100	−	0.167041i
$498$		0			0
$499$	−16900.0			−1.51612			−0.758062	−	0.652182i	$-0.773854\pi$
$499$	−16900.0			−1.51612			−0.758062	+	0.652182i	$0.773854\pi$
$500$		0			0
$501$	−12512.3			−1.11578
$502$		0			0
$503$	248.961	+	80.8923i	0.0220688	+	0.00717059i	0.320031	−	0.947407i	$-0.396307\pi$
$503$	248.961	+	80.8923i	0.0220688	+	0.00717059i	−0.297962	+	0.954578i	$0.596307\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$		−	6767.37i		−	0.592800i
$508$		0			0
$509$	−15761.2	−	11451.2i	−1.37250	−	0.997181i	−0.997537	−	0.0701412i	$-0.977655\pi$
$509$	−15761.2	−	11451.2i	−1.37250	−	0.997181i	−0.374964	−	0.927039i	$-0.622345\pi$
$510$		0			0
$511$	−10453.2	+	7594.73i	−0.904940	+	0.657477i
$512$		0			0
$513$	−5451.26	+	7503.01i	−0.469159	+	0.645743i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−12910.0	+	4194.73i	−1.09823	+	0.356835i
$518$		0			0
$519$	−5379.24	−	16555.6i	−0.454956	−	1.40021i
$520$		0			0
$521$	−3787.38	+	11656.3i	−0.318480	+	0.980180i	0.655819	+	0.754918i	$0.272324\pi$
$521$	−3787.38	+	11656.3i	−0.318480	+	0.980180i	−0.974298	+	0.225261i	$0.927676\pi$
$522$		0			0
$523$	−6951.42	−	9567.80i	−0.581193	−	0.799944i	0.412632	−	0.910898i	$-0.364610\pi$
$523$	−6951.42	−	9567.80i	−0.581193	−	0.799944i	−0.993826	+	0.110954i	$0.964610\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−8305.65	−	11431.7i	−0.686527	−	0.944923i
$528$		0			0
$529$	−4824.87	+	14849.4i	−0.396553	+	1.22047i
$530$		0			0
$531$	−4804.04	−	14785.3i	−0.392613	−	1.20834i
$532$		0			0
$533$	−2455.01	+	797.683i	−0.199509	+	0.0648245i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	6445.22	−	8871.08i	0.517936	−	0.712878i
$538$		0			0
$539$	−653.595	+	474.864i	−0.0522306	+	0.0379478i
$540$		0			0
$541$	−675.028	−	490.436i	−0.0536446	−	0.0389751i	0.560640	−	0.828060i	$-0.310555\pi$
$541$	−675.028	−	490.436i	−0.0536446	−	0.0389751i	−0.614284	+	0.789085i	$0.710555\pi$
$542$		0			0
$543$		−	37076.6i		−	2.93022i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	12248.2	+	3979.68i	0.957396	+	0.311077i	0.745717	−	0.666263i	$-0.232107\pi$
$547$	12248.2	+	3979.68i	0.957396	+	0.311077i	0.211679	+	0.977339i	$0.432107\pi$
$548$		0			0
$549$	18632.6			1.44849
$550$		0			0
$551$	13721.6			1.06091
$552$		0			0
$553$	21466.9	+	6975.01i	1.65075	+	0.536361i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	10133.4i		−	0.770852i	−0.922739	−	0.385426i	$-0.874055\pi$
$557$		−	10133.4i		−	0.770852i	0.922739	−	0.385426i	$-0.125945\pi$
$558$		0			0
$559$	−1583.58	−	1150.54i	−0.119818	−	0.0870531i
$560$		0			0
$561$	13810.7	−	10034.0i	1.03937	−	0.755146i
$562$		0			0
$563$	−11369.2	+	15648.3i	−0.851073	+	1.17140i	0.132552	+	0.991176i	$0.457683\pi$
$563$	−11369.2	+	15648.3i	−0.851073	+	1.17140i	−0.983625	+	0.180226i	$0.942317\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−3613.69	+	1174.16i	−0.267656	+	0.0869666i
$568$		0			0
$569$	5265.90	+	16206.8i	0.387975	+	1.19407i	0.934299	+	0.356491i	$0.116027\pi$
$569$	5265.90	+	16206.8i	0.387975	+	1.19407i	−0.546323	+	0.837574i	$0.683973\pi$
$570$		0			0
$571$	−5894.02	+	18139.9i	−0.431974	+	1.32948i	0.464182	+	0.885740i	$0.346348\pi$
$571$	−5894.02	+	18139.9i	−0.431974	+	1.32948i	−0.896156	+	0.443739i	$0.853652\pi$
$572$		0			0
$573$	1574.38	+	2166.95i	0.114783	+	0.157985i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−5664.97	−	7797.16i	−0.408727	−	0.562565i	0.554180	−	0.832397i	$-0.313032\pi$
$577$	−5664.97	−	7797.16i	−0.408727	−	0.562565i	−0.962907	+	0.269832i	$0.913032\pi$
$578$		0			0
$579$	7113.88	−	21894.3i	0.510609	−	1.57149i
$580$		0			0
$581$	352.831	+	1085.90i	0.0251943	+	0.0775401i
$582$		0			0
$583$	−18585.7	+	6038.84i	−1.32031	+	0.428994i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	41.5642	−	57.2082i	0.00292255	−	0.00402255i	−0.807553	−	0.589795i	$-0.799209\pi$
$587$	41.5642	−	57.2082i	0.00292255	−	0.00402255i	0.810476	+	0.585772i	$0.199209\pi$
$588$		0			0
$589$	−8989.11	+	6530.97i	−0.628845	+	0.456883i
$590$		0			0
$591$	6452.78	+	4688.22i	0.449123	+	0.326307i
$592$		0			0
$593$		−	10023.6i		−	0.694134i	−0.937840	−	0.347067i	$-0.887178\pi$
$593$		−	10023.6i		−	0.694134i	0.937840	−	0.347067i	$-0.112822\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	3635.23	+	1181.16i	0.249213	+	0.0809742i
$598$		0			0
$599$	20888.2			1.42483			0.712413	−	0.701761i	$-0.247602\pi$
$599$	20888.2			1.42483			0.712413	+	0.701761i	$0.247602\pi$
$600$		0			0
$601$	15619.9			1.06015			0.530073	−	0.847952i	$-0.322165\pi$
$601$	15619.9			1.06015			0.530073	+	0.847952i	$0.322165\pi$
$602$		0			0
$603$	−15948.5	−	5182.00i	−1.07707	−	0.349962i
$604$		0			0
$605$		0			0
$606$		0			0
$607$			12370.5i			0.827190i	0.910461	+	0.413595i	$0.135727\pi$
$607$			12370.5i			0.827190i	−0.910461	+	0.413595i	$0.864273\pi$
$608$		0			0
$609$	31539.5	+	22914.8i	2.09860	+	1.52472i
$610$		0			0
$611$	−20674.9	+	15021.2i	−1.36893	+	0.994587i
$612$		0			0
$613$	−1380.50	+	1900.10i	−0.0909591	+	0.125194i	−0.852071	−	0.523426i	$-0.824654\pi$
$613$	−1380.50	+	1900.10i	−0.0909591	+	0.125194i	0.761112	+	0.648620i	$0.224654\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−4704.81	+	1528.69i	−0.306983	+	0.0997449i	−0.458458	−	0.888716i	$-0.651598\pi$
$617$	−4704.81	+	1528.69i	−0.306983	+	0.0997449i	0.151474	+	0.988461i	$0.451598\pi$
$618$		0			0
$619$	3757.04	+	11563.0i	0.243955	+	0.750816i	0.995807	+	0.0914835i	$0.0291609\pi$
$619$	3757.04	+	11563.0i	0.243955	+	0.750816i	−0.751852	+	0.659332i	$0.770839\pi$
$620$		0			0
$621$	8884.10	−	27342.4i	0.574085	−	1.76685i
$622$		0			0
$623$	−7290.80	−	10034.9i	−0.468860	−	0.645330i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−7890.05	−	10859.7i	−0.502549	−	0.691700i
$628$		0			0
$629$	5149.32	−	15848.0i	0.326418	−	1.00461i
$630$		0			0
$631$	−569.989	−	1754.25i	−0.0359603	−	0.110674i	0.931465	−	0.363831i	$-0.118531\pi$
$631$	−569.989	−	1754.25i	−0.0359603	−	0.110674i	−0.967425	+	0.253156i	$0.918531\pi$
$632$		0			0
$633$	7943.01	−	2580.84i	0.498746	−	0.162052i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−893.993	+	1230.48i	−0.0556064	+	0.0765357i
$638$		0			0
$639$	−12840.7	+	9329.28i	−0.794943	+	0.577560i
$640$		0			0
$641$	10619.6	+	7715.58i	0.654365	+	0.475424i	0.864755	−	0.502193i	$-0.167473\pi$
$641$	10619.6	+	7715.58i	0.654365	+	0.475424i	−0.210390	+	0.977618i	$0.567473\pi$
$642$		0			0
$643$			16752.9i			1.02748i	0.857946	+	0.513740i	$0.171740\pi$
$643$			16752.9i			1.02748i	−0.857946	+	0.513740i	$0.828260\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−7413.87	−	2408.91i	−0.450493	−	0.146374i	0.0749785	−	0.997185i	$-0.476111\pi$
$647$	−7413.87	−	2408.91i	−0.450493	−	0.146374i	−0.525472	+	0.850811i	$0.676111\pi$
$648$		0			0
$649$	9587.45			0.579877
$650$		0			0
$651$	−31568.3			−1.90055
$652$		0			0
$653$	11467.0	+	3725.85i	0.687194	+	0.223283i	0.631742	−	0.775178i	$-0.282340\pi$
$653$	11467.0	+	3725.85i	0.687194	+	0.223283i	0.0554519	+	0.998461i	$0.482340\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$			34241.1i			2.03329i
$658$		0			0
$659$	17896.8	+	13002.8i	1.05791	+	0.768615i	0.973700	−	0.227834i	$-0.0731642\pi$
$659$	17896.8	+	13002.8i	1.05791	+	0.768615i	0.0842072	+	0.996448i	$0.473164\pi$
$660$		0			0
$661$	5644.88	−	4101.24i	0.332164	−	0.241331i	−0.409184	−	0.912452i	$-0.634187\pi$
$661$	5644.88	−	4101.24i	0.332164	−	0.241331i	0.741348	+	0.671121i	$0.234187\pi$
$662$		0			0
$663$	18890.3	−	26000.3i	1.10655	−	1.52303i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−40454.2	+	13144.4i	−2.34842	+	0.763047i
$668$		0			0
$669$	10053.5	+	30941.5i	0.581003	+	1.78814i
$670$		0			0
$671$	−3550.88	+	10928.5i	−0.204292	+	0.628747i
$672$		0			0
$673$	−3213.35	−	4422.80i	−0.184050	−	0.253323i	0.707015	−	0.707198i	$-0.250041\pi$
$673$	−3213.35	−	4422.80i	−0.184050	−	0.253323i	−0.891065	+	0.453875i	$0.850041\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	952.371	+	1310.83i	0.0540659	+	0.0744153i	0.835194	−	0.549956i	$-0.185355\pi$
$677$	952.371	+	1310.83i	0.0540659	+	0.0744153i	−0.781128	+	0.624371i	$0.785355\pi$
$678$		0			0
$679$	−5290.62	+	16282.8i	−0.299021	+	0.920292i
$680$		0			0
$681$	12041.5	+	37059.9i	0.677579	+	2.08537i
$682$		0			0
$683$	2183.24	−	709.376i	0.122312	−	0.0397416i	−0.247221	−	0.968959i	$-0.579517\pi$
$683$	2183.24	−	709.376i	0.122312	−	0.0397416i	0.369534	+	0.929217i	$0.379517\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	20623.5	−	28385.9i	1.14532	−	1.57640i
$688$		0			0
$689$	−29764.2	+	21624.9i	−1.64575	+	1.19571i
$690$		0			0
$691$	−20404.4	−	14824.6i	−1.12333	−	0.816144i	−0.138616	−	0.990346i	$-0.544266\pi$
$691$	−20404.4	−	14824.6i	−1.12333	−	0.816144i	−0.984710	+	0.174202i	$0.944266\pi$
$692$		0			0
$693$		−	24231.1i		−	1.32823i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−3073.32	−	998.582i	−0.167016	−	0.0542669i
$698$		0			0
$699$	−5742.92			−0.310754
$700$		0			0
$701$	9744.88			0.525049			0.262524	−	0.964925i	$-0.415445\pi$
$701$	9744.88			0.525049			0.262524	+	0.964925i	$0.415445\pi$
$702$		0			0
$703$	−12461.7	−	4049.06i	−0.668568	−	0.217231i
$704$		0			0
$705$		0			0
$706$		0			0
$707$		−	813.974i		−	0.0432994i
$708$		0			0
$709$	26149.3	+	18998.6i	1.38513	+	1.00636i	0.996380	+	0.0850142i	$0.0270936\pi$
$709$	26149.3	+	18998.6i	1.38513	+	1.00636i	0.388752	+	0.921343i	$0.372906\pi$
$710$		0			0
$711$	48392.1	−	35158.9i	2.55252	−	1.85452i
$712$		0			0
$713$	20245.6	−	27865.7i	1.06340	−	1.46364i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	28236.5	−	9174.58i	1.47072	−	0.477867i
$718$		0			0
$719$	−11657.9	−	35879.3i	−0.604681	−	1.86102i	−0.498970	−	0.866619i	$-0.666288\pi$
$719$	−11657.9	−	35879.3i	−0.604681	−	1.86102i	−0.105711	−	0.994397i	$-0.533712\pi$
$720$		0			0
$721$	6242.96	−	19213.9i	0.322469	−	0.992457i
$722$		0			0
$723$	−11287.5	−	15536.0i	−0.580620	−	0.799155i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−10307.5	−	14187.1i	−0.525840	−	0.723756i	0.460650	−	0.887582i	$-0.347616\pi$
$727$	−10307.5	−	14187.1i	−0.525840	−	0.723756i	−0.986489	+	0.163826i	$0.947616\pi$
$728$		0			0
$729$	9272.25	−	28537.0i	0.471079	−	1.44983i
$730$		0			0
$731$	−757.216	−	2330.47i	−0.0383128	−	0.117915i
$732$		0			0
$733$	−12326.0	+	4004.96i	−0.621107	+	0.201810i	−0.602632	−	0.798020i	$-0.705881\pi$
$733$	−12326.0	+	4004.96i	−0.621107	+	0.201810i	−0.0184751	+	0.999829i	$0.505881\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	6078.73	−	8366.65i	0.303816	−	0.418168i
$738$		0			0
$739$	−14750.5	+	10716.9i	−0.734245	+	0.533460i	−0.890903	−	0.454193i	$-0.849928\pi$
$739$	−14750.5	+	10716.9i	−0.734245	+	0.533460i	0.156659	+	0.987653i	$0.449928\pi$
$740$		0			0
$741$	−20444.8	−	14854.0i	−1.01358	−	0.736406i
$742$		0			0
$743$		−	11715.5i		−	0.578464i	−0.957259	−	0.289232i	$-0.906600\pi$
$743$		−	11715.5i		−	0.578464i	0.957259	−	0.289232i	$-0.0933999\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	2877.70	+	935.020i	0.140950	+	0.0457973i
$748$		0			0
$749$	−32466.6			−1.58385
$750$		0			0
$751$	37841.6			1.83870			0.919348	−	0.393444i	$-0.128717\pi$
$751$	37841.6			1.83870			0.919348	+	0.393444i	$0.128717\pi$
$752$		0			0
$753$	3547.39	+	1152.62i	0.171679	+	0.0557817i
$754$		0			0
$755$		0			0
$756$		0			0
$757$		−	19408.2i		−	0.931841i	−0.884826	−	0.465921i	$-0.845723\pi$
$757$		−	19408.2i		−	0.931841i	0.884826	−	0.465921i	$-0.154277\pi$
$758$		0			0
$759$	33664.5	+	24458.7i	1.60994	+	1.16969i
$760$		0			0
$761$	−16492.9	+	11982.8i	−0.785635	+	0.570797i	−0.906665	−	0.421852i	$-0.861380\pi$
$761$	−16492.9	+	11982.8i	−0.785635	+	0.570797i	0.121030	+	0.992649i	$0.461380\pi$
$762$		0			0
$763$	−21922.1	+	30173.1i	−1.04015	+	1.43164i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	17166.2	−	5577.63i	0.808130	−	0.262577i
$768$		0			0
$769$	−9147.67	−	28153.6i	−0.428964	−	1.32022i	−0.899147	−	0.437647i	$-0.855812\pi$
$769$	−9147.67	−	28153.6i	−0.428964	−	1.32022i	0.470183	−	0.882569i	$-0.344188\pi$
$770$		0			0
$771$	15146.4	−	46615.7i	0.707501	−	2.17746i
$772$		0			0
$773$	−2635.58	−	3627.57i	−0.122633	−	0.168790i	0.743287	−	0.668973i	$-0.233266\pi$
$773$	−2635.58	−	3627.57i	−0.122633	−	0.168790i	−0.865920	+	0.500183i	$0.833266\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−21881.8	−	30117.7i	−1.01030	−	1.39056i
$778$		0			0
$779$	−785.215	+	2416.64i	−0.0361145	+	0.111149i
$780$		0			0
$781$	−3024.76	−	9309.26i	−0.138584	−	0.426519i
$782$		0			0
$783$	41865.2	−	13602.8i	1.91078	−	0.620850i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	5565.14	−	7659.76i	0.252066	−	0.346939i	−0.664168	−	0.747584i	$-0.731214\pi$
$787$	5565.14	−	7659.76i	0.252066	−	0.346939i	0.916233	+	0.400645i	$0.131214\pi$
$788$		0			0
$789$	25482.6	−	18514.2i	1.14982	−	0.835390i
$790$		0			0
$791$	21476.0	+	15603.2i	0.965359	+	0.701374i
$792$		0			0
$793$			21633.1i			0.968742i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	1631.39	+	530.071i	0.0725054	+	0.0235584i	0.345045	−	0.938586i	$-0.387864\pi$
$797$	1631.39	+	530.071i	0.0725054	+	0.0235584i	−0.272540	+	0.962145i	$0.587864\pi$
$798$		0			0
$799$	−31991.9			−1.41651
$800$		0			0
$801$	−32870.8			−1.44998
$802$		0			0
$803$	−20083.2	−	6525.43i	−0.882591	−	0.286771i
$804$		0			0
$805$		0			0
$806$		0			0
$807$		−	21908.4i		−	0.955654i
$808$		0			0
$809$	1951.87	+	1418.12i	0.0848260	+	0.0616297i	0.629390	−	0.777090i	$-0.283305\pi$
$809$	1951.87	+	1418.12i	0.0848260	+	0.0616297i	−0.544564	+	0.838719i	$0.683305\pi$
$810$		0			0
$811$	14561.4	−	10579.5i	0.630481	−	0.458071i	−0.226086	−	0.974107i	$-0.572593\pi$
$811$	14561.4	−	10579.5i	0.630481	−	0.458071i	0.856567	+	0.516036i	$0.172593\pi$
$812$		0			0
$813$	23767.4	−	32713.0i	1.02529	−	1.41119i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−1832.52	+	595.421i	−0.0784720	+	0.0254971i
$818$		0			0
$819$	−14096.8	−	43385.4i	−0.601442	−	1.85105i
$820$		0			0
$821$	−7847.92	+	24153.4i	−0.333610	+	1.02675i	0.633792	+	0.773503i	$0.281497\pi$
$821$	−7847.92	+	24153.4i	−0.333610	+	1.02675i	−0.967402	+	0.253244i	$0.918503\pi$
$822$		0			0
$823$	20539.4	+	28270.1i	0.869939	+	1.19737i	0.979107	+	0.203345i	$0.0651814\pi$
$823$	20539.4	+	28270.1i	0.869939	+	1.19737i	−0.109168	+	0.994023i	$0.534819\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	−2137.14	−	2941.52i	−0.0898617	−	0.123684i	0.761719	−	0.647907i	$-0.224356\pi$
$827$	−2137.14	−	2941.52i	−0.0898617	−	0.123684i	−0.851581	+	0.524223i	$0.824356\pi$
$828$		0			0
$829$	−2810.25	+	8649.07i	−0.117737	+	0.362358i	−0.992508	−	0.122179i	$-0.961012\pi$
$829$	−2810.25	+	8649.07i	−0.117737	+	0.362358i	0.874771	+	0.484537i	$0.161012\pi$
$830$		0			0
$831$	−177.999	−	547.825i	−0.00743047	−	0.0228686i
$832$		0			0
$833$	−1810.82	+	588.371i	−0.0753196	+	0.0244728i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−20951.8	+	28837.6i	−0.865231	+	1.19089i
$838$		0			0
$839$	−1495.42	+	1086.49i	−0.0615349	+	0.0447077i	−0.618127	−	0.786078i	$-0.712108\pi$
$839$	−1495.42	+	1086.49i	−0.0615349	+	0.0447077i	0.556593	+	0.830786i	$0.312108\pi$
$840$		0			0
$841$	−32959.3	−	23946.3i	−1.35140	−	0.981850i
$842$		0			0
$843$			40718.9i			1.66362i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−8260.14	−	2683.88i	−0.335091	−	0.108878i
$848$		0			0
$849$	32247.6			1.30358
$850$		0			0
$851$	40618.6			1.63618
$852$		0			0
$853$	23043.7	+	7487.34i	0.924970	+	0.300541i	0.732504	−	0.680762i	$-0.238351\pi$
$853$	23043.7	+	7487.34i	0.924970	+	0.300541i	0.192466	+	0.981304i	$0.438351\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$		−	34.5262i		−	0.00137619i	−1.00000		0.000688093i	$-0.999781\pi$
$857$		−	34.5262i		−	0.00137619i	1.00000		0.000688093i	$-0.000219027\pi$
$858$		0			0
$859$	−13264.5	−	9637.23i	−0.526868	−	0.382792i	0.292317	−	0.956321i	$-0.405574\pi$
$859$	−13264.5	−	9637.23i	−0.526868	−	0.382792i	−0.819185	+	0.573530i	$0.805574\pi$
$860$		0			0
$861$	−5840.58	+	4243.43i	−0.231181	+	0.167963i
$862$		0			0
$863$	21789.5	−	29990.7i	0.859470	−	1.18296i	−0.122225	−	0.992502i	$-0.539003\pi$
$863$	21789.5	−	29990.7i	0.859470	−	1.18296i	0.981696	−	0.190457i	$-0.0609969\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−1943.80	+	631.578i	−0.0761416	+	0.0247399i
$868$		0			0
$869$	11399.3	+	35083.4i	0.444988	+	1.36953i
$870$		0			0
$871$	6016.46	−	18516.7i	0.234053	−	0.720340i
$872$		0			0
$873$	26668.4	+	36705.9i	1.03389	+	1.42303i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	−17075.4	−	23502.3i	−0.657464	−	0.904922i	0.341930	−	0.939725i	$-0.388919\pi$
$877$	−17075.4	−	23502.3i	−0.657464	−	0.904922i	−0.999394	+	0.0348035i	$0.988919\pi$
$878$		0			0
$879$	−3481.37	+	10714.6i	−0.133588	+	0.411141i
$880$		0			0
$881$	−11842.9	−	36448.7i	−0.452891	−	1.39386i	−0.873593	−	0.486657i	$-0.838216\pi$
$881$	−11842.9	−	36448.7i	−0.452891	−	1.39386i	0.420702	−	0.907199i	$-0.361784\pi$
$882$		0			0
$883$	−7636.32	+	2481.19i	−0.291033	+	0.0945625i	−0.450895	−	0.892577i	$-0.648895\pi$
$883$	−7636.32	+	2481.19i	−0.291033	+	0.0945625i	0.159862	+	0.987139i	$0.448895\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	2384.12	−	3281.46i	0.0902491	−	0.124217i	−0.761505	−	0.648159i	$-0.775539\pi$
$887$	2384.12	−	3281.46i	0.0902491	−	0.124217i	0.851754	+	0.523942i	$0.175539\pi$
$888$		0			0
$889$	−29123.3	+	21159.3i	−1.09872	+	0.798268i
$890$		0			0
$891$	−5023.83	−	3650.03i	−0.188894	−	0.137240i
$892$		0			0
$893$			25156.1i			0.942686i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	74504.9	+	24208.1i	2.77330	+	0.901099i
$898$		0			0
$899$	52738.6			1.95654
$900$		0			0
$901$	−46056.4			−1.70295
$902$		0			0
$903$	−5206.44	−	1691.67i	−0.191871	−	0.0623426i
$904$		0			0
$905$		0			0
$906$		0			0
$907$			30499.8i			1.11657i	0.829649	+	0.558285i	$0.188540\pi$
$907$			30499.8i			1.11657i	−0.829649	+	0.558285i	$0.811460\pi$
$908$		0			0
$909$	−1745.11	−	1267.90i	−0.0636761	−	0.0462634i
$910$		0			0
$911$	−26299.5	+	19107.7i	−0.956468	+	0.694915i	−0.952328	−	0.305076i	$-0.901318\pi$
$911$	−26299.5	+	19107.7i	−0.956468	+	0.694915i	−0.00414055	+	0.999991i	$0.501318\pi$
$912$		0			0
$913$	−1096.82	+	1509.65i	−0.0397585	+	0.0547229i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	5843.41	−	1898.64i	0.210432	−	0.0683736i
$918$		0			0
$919$	5998.77	+	18462.3i	0.215322	+	0.662694i	0.999131	+	0.0416910i	$0.0132745\pi$
$919$	5998.77	+	18462.3i	0.215322	+	0.662694i	−0.783808	+	0.621003i	$0.786725\pi$
$920$		0			0
$921$	−14282.2	+	43956.2i	−0.510983	+	1.57264i
$922$		0			0
$923$	−10831.6	−	14908.4i	−0.386269	−	0.531653i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−31468.9	−	43313.2i	−1.11497	−	1.53462i
$928$		0			0
$929$	7828.35	−	24093.2i	0.276469	−	0.850884i	−0.712358	−	0.701816i	$-0.752373\pi$
$929$	7828.35	−	24093.2i	0.276469	−	0.850884i	0.988827	−	0.149068i	$-0.0476273\pi$
$930$		0			0
$931$	462.654	+	1423.90i	0.0162866	+	0.0501251i
$932$		0			0
$933$	−30517.3	+	9915.67i	−1.07084	+	0.347936i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	3008.82	−	4141.28i	0.104903	−	0.144386i	−0.753338	−	0.657633i	$-0.771558\pi$
$937$	3008.82	−	4141.28i	0.104903	−	0.144386i	0.858241	+	0.513247i	$0.171558\pi$
$938$		0			0
$939$	20288.9	−	14740.7i	0.705114	−	0.512295i
$940$		0			0
$941$	19877.8	+	14442.1i	0.688627	+	0.500317i	0.876208	−	0.481932i	$-0.160065\pi$
$941$	19877.8	+	14442.1i	0.688627	+	0.500317i	−0.187582	+	0.982249i	$0.560065\pi$
$942$		0			0
$943$		−	7876.97i		−	0.272014i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	6879.24	+	2235.20i	0.236056	+	0.0766994i	0.424656	−	0.905355i	$-0.360395\pi$
$947$	6879.24	+	2235.20i	0.236056	+	0.0766994i	−0.188600	+	0.982054i	$0.560395\pi$
$948$		0			0
$949$	−39754.9			−1.35985
$950$		0			0
$951$	31129.4			1.06145
$952$		0			0
$953$	−22830.0	−	7417.92i	−0.776009	−	0.252141i	−0.105874	−	0.994380i	$-0.533764\pi$
$953$	−22830.0	−	7417.92i	−0.776009	−	0.252141i	−0.670135	+	0.742239i	$0.733764\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			63713.4i			2.15210i
$958$		0			0
$959$	−10839.5	−	7875.33i	−0.364989	−	0.265180i
$960$		0			0
$961$	−10448.0	+	7590.91i	−0.350709	+	0.254805i
$962$		0			0
$963$	−50571.9	+	69606.2i	−1.69227	+	2.32921i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	15008.5	−	4876.55i	0.499111	−	0.162171i	−0.0486335	−	0.998817i	$-0.515487\pi$
$967$	15008.5	−	4876.55i	0.499111	−	0.162171i	0.547744	+	0.836646i	$0.315487\pi$
$968$		0			0
$969$	−9776.01	−	30087.5i	−0.324098	−	0.997471i
$970$		0			0
$971$	5684.38	−	17494.7i	0.187869	−	0.578200i	−0.812117	−	0.583494i	$-0.801685\pi$
$971$	5684.38	−	17494.7i	0.187869	−	0.578200i	0.999986	+	0.00529403i	$0.00168515\pi$
$972$		0			0
$973$	−20890.3	−	28753.0i	−0.688296	−	0.947358i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	437.771	+	602.540i	0.0143352	+	0.0197308i	0.816124	−	0.577876i	$-0.196118\pi$
$977$	437.771	+	602.540i	0.0143352	+	0.0197308i	−0.801789	+	0.597607i	$0.796118\pi$
$978$		0			0
$979$	6264.29	−	19279.5i	0.204502	−	0.629393i
$980$		0			0
$981$	30542.1	+	93999.0i	0.994022	+	3.05928i
$982$		0			0
$983$	−12769.9	+	4149.20i	−0.414341	+	0.134627i	−0.508767	−	0.860904i	$-0.669898\pi$
$983$	−12769.9	+	4149.20i	−0.414341	+	0.134627i	0.0944260	+	0.995532i	$0.469898\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−42010.3	+	57822.2i	−1.35481	+	1.86474i
$988$		0			0
$989$	4832.28	−	3510.86i	0.155367	−	0.112881i
$990$		0			0
$991$	10603.6	+	7704.00i	0.339895	+	0.246948i	0.744617	−	0.667491i	$-0.232632\pi$
$991$	10603.6	+	7704.00i	0.339895	+	0.246948i	−0.404723	+	0.914439i	$0.632632\pi$
$992$		0			0
$993$		−	90235.9i		−	2.88373i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	−25995.8	−	8446.56i	−0.825774	−	0.268310i	−0.134510	−	0.990912i	$-0.542946\pi$
$997$	−25995.8	−	8446.56i	−0.825774	−	0.268310i	−0.691264	+	0.722602i	$0.742946\pi$
$998$		0			0
$999$	−42035.3			−1.33127

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	500.4.i.b.449.14		56
5.2	odd	4		500.4.g.a.301.7		28
5.3	odd	4		100.4.g.a.61.1	yes	28
5.4	even	2	inner	500.4.i.b.449.1		56
25.3	odd	20		2500.4.a.c.1.2		14
25.9	even	10	inner	500.4.i.b.49.14		56
25.12	odd	20		500.4.g.a.201.7		28
25.13	odd	20		100.4.g.a.41.1	✓	28
25.16	even	5	inner	500.4.i.b.49.1		56
25.22	odd	20		2500.4.a.d.1.13		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
100.4.g.a.41.1	✓	28	25.13	odd	20
100.4.g.a.61.1	yes	28	5.3	odd	4
500.4.g.a.201.7		28	25.12	odd	20
500.4.g.a.301.7		28	5.2	odd	4
500.4.i.b.49.1		56	25.16	even	5	inner
500.4.i.b.49.14		56	25.9	even	10	inner
500.4.i.b.449.1		56	5.4	even	2	inner
500.4.i.b.449.14		56	1.1	even	1	trivial
2500.4.a.c.1.2		14	25.3	odd	20
2500.4.a.d.1.13		14	25.22	odd	20

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:	\( N \)	\(=\)	\( 500 = 2^{2} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	500.i (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(8.18380 + 2.65908i) q^{3} +17.7526i q^{7} +(38.0604 + 27.6525i) q^{9} +O(q^{10})\)	\(q+(8.18380 + 2.65908i) q^{3} +17.7526i q^{7} +(38.0604 + 27.6525i) q^{9} +(-23.4721 + 17.0535i) q^{11} +(-32.1054 + 44.1893i) q^{13} +(-65.0309 + 21.1298i) q^{17} +(16.6150 + 51.1357i) q^{19} +(-47.2055 + 145.284i) q^{21} +(-97.9692 - 134.843i) q^{23} +(101.386 + 139.546i) q^{27} +(78.8623 - 242.713i) q^{29} +(63.8593 + 196.539i) q^{31} +(-237.438 + 77.1482i) q^{33} +(-143.243 + 197.157i) q^{37} +(-380.247 + 276.266i) q^{39} +(38.2337 + 27.7784i) q^{41} +35.8364i q^{43} +(444.972 + 144.580i) q^{47} +27.8456 q^{49} -588.385 q^{51} +(640.594 + 208.142i) q^{53} +462.665i q^{57} +(-267.341 - 194.235i) q^{59} +(320.417 - 232.797i) q^{61} +(-490.904 + 675.671i) q^{63} +(-339.004 + 110.149i) q^{67} +(-443.202 - 1364.04i) q^{69} +(-104.255 + 320.863i) q^{71} +(427.809 + 588.829i) q^{73} +(-302.744 - 416.691i) q^{77} +(392.901 - 1209.22i) q^{79} +(66.1401 + 203.558i) q^{81} +(61.1687 - 19.8749i) q^{83} +(1290.79 - 1776.61i) q^{87} +(-565.265 + 410.689i) q^{89} +(-784.474 - 569.954i) q^{91} +1778.24i q^{93} +(917.209 + 298.019i) q^{97} -1364.93 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 26 q^{9}+O(q^{10}) \) 56 * q + 26 * q^9	\( 56 q + 26 q^{9} - 40 q^{11} - 4 q^{19} + 216 q^{21} - 384 q^{29} + 756 q^{31} - 1184 q^{39} + 596 q^{41} - 288 q^{49} - 3328 q^{51} - 288 q^{59} + 1032 q^{61} - 5992 q^{69} - 4052 q^{71} - 1792 q^{79} - 4406 q^{81} + 334 q^{89} + 4424 q^{91} + 4200 q^{99}+O(q^{100}) \) 56 * q + 26 * q^9 - 40 * q^11 - 4 * q^19 + 216 * q^21 - 384 * q^29 + 756 * q^31 - 1184 * q^39 + 596 * q^41 - 288 * q^49 - 3328 * q^51 - 288 * q^59 + 1032 * q^61 - 5992 * q^69 - 4052 * q^71 - 1792 * q^79 - 4406 * q^81 + 334 * q^89 + 4424 * q^91 + 4200 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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