LMFDB - Embedded newform 324.4.b.c.323.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [324,4,Mod(323,324)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(324, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("324.323");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 324 = 2^{2} \cdot 3^{4} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	324.b (of order $2$, degree $1$, 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:	$19.1166188419$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.4
Character	$\chi$	$=$	324.323
Dual form			324.4.b.c.323.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.75517 + 0.639551i) q^{2} +(7.18195 - 3.52415i) q^{4} -5.44403i q^{5} -24.1745i q^{7} +(-17.5336 + 14.3029i) q^{8} +O(q^{10})$	\(q+(-2.75517 + 0.639551i) q^{2} +(7.18195 - 3.52415i) q^{4} -5.44403i q^{5} -24.1745i q^{7} +(-17.5336 + 14.3029i) q^{8} +(3.48173 + 14.9992i) q^{10} -50.7998 q^{11} -50.1766 q^{13} +(15.4609 + 66.6050i) q^{14} +(39.1608 - 50.6205i) q^{16} +51.7146i q^{17} +27.9305i q^{19} +(-19.1855 - 39.0987i) q^{20} +(139.962 - 32.4891i) q^{22} +7.87096 q^{23} +95.3626 q^{25} +(138.245 - 32.0905i) q^{26} +(-85.1946 - 173.620i) q^{28} +245.706i q^{29} -59.3526i q^{31} +(-75.5203 + 164.513i) q^{32} +(-33.0741 - 142.482i) q^{34} -131.607 q^{35} +295.334 q^{37} +(-17.8630 - 76.9533i) q^{38} +(77.8651 + 95.4536i) q^{40} -169.548i q^{41} +329.052i q^{43} +(-364.841 + 179.026i) q^{44} +(-21.6859 + 5.03388i) q^{46} +95.9484 q^{47} -241.409 q^{49} +(-262.740 + 60.9892i) q^{50} +(-360.365 + 176.830i) q^{52} +300.751i q^{53} +276.555i q^{55} +(345.765 + 423.868i) q^{56} +(-157.142 - 676.964i) q^{58} -226.546 q^{59} -347.445 q^{61} +(37.9590 + 163.527i) q^{62} +(102.857 - 501.562i) q^{64} +273.162i q^{65} +1044.63i q^{67} +(182.250 + 371.411i) q^{68} +(362.600 - 84.1693i) q^{70} +243.524 q^{71} -1094.68 q^{73} +(-813.696 + 188.881i) q^{74} +(98.4312 + 200.595i) q^{76} +1228.06i q^{77} +612.775i q^{79} +(-275.579 - 213.192i) q^{80} +(108.435 + 467.135i) q^{82} -566.126 q^{83} +281.535 q^{85} +(-210.446 - 906.596i) q^{86} +(890.705 - 726.582i) q^{88} -212.529i q^{89} +1213.00i q^{91} +(56.5288 - 27.7384i) q^{92} +(-264.354 + 61.3639i) q^{94} +152.054 q^{95} -468.597 q^{97} +(665.122 - 154.393i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{4}+O(q^{10}) $ 24 * q + 24 * q^4	$ 24 q + 24 q^{4} + 96 q^{10} + 432 q^{13} + 144 q^{16} + 384 q^{22} - 504 q^{25} - 672 q^{28} + 1320 q^{34} + 1248 q^{37} - 1272 q^{40} + 960 q^{46} - 696 q^{49} - 264 q^{52} - 1032 q^{58} + 528 q^{61} + 960 q^{64} - 1128 q^{70} - 4776 q^{73} + 1200 q^{76} - 4104 q^{82} - 1440 q^{85} - 3912 q^{88} + 2376 q^{94} - 1176 q^{97}+O(q^{100}) $ 24 * q + 24 * q^4 + 96 * q^10 + 432 * q^13 + 144 * q^16 + 384 * q^22 - 504 * q^25 - 672 * q^28 + 1320 * q^34 + 1248 * q^37 - 1272 * q^40 + 960 * q^46 - 696 * q^49 - 264 * q^52 - 1032 * q^58 + 528 * q^61 + 960 * q^64 - 1128 * q^70 - 4776 * q^73 + 1200 * q^76 - 4104 * q^82 - 1440 * q^85 - 3912 * q^88 + 2376 * q^94 - 1176 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/324\mathbb{Z}\right)^\times$.

$n$	$163$	$245$
$\chi(n)$	$-1$	$-1$

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 $

$2$	−2.75517	+	0.639551i	−0.974101	+	0.226115i
$2$	−2.75517	+	0.639551i	−0.974101	+	0.226115i
$3$		0			0
$3$		0			0
$4$	7.18195	−	3.52415i	0.897744	−	0.440518i
$5$		−	5.44403i		−	0.486928i	−0.969910	−	0.243464i	$-0.921716\pi$
$5$		−	5.44403i		−	0.486928i	0.969910	−	0.243464i	$-0.0782838\pi$
$6$		0			0
$7$		−	24.1745i		−	1.30530i	−0.757658	−	0.652651i	$-0.773657\pi$
$7$		−	24.1745i		−	1.30530i	0.757658	−	0.652651i	$-0.226343\pi$
$8$	−17.5336	+	14.3029i	−0.774885	+	0.632103i
$9$		0			0
$10$	3.48173	+	14.9992i	0.110102	+	0.474317i
$11$	−50.7998			−1.39243			−0.696214	−	0.717834i	$-0.745134\pi$
$11$	−50.7998			−1.39243			−0.696214	+	0.717834i	$0.745134\pi$
$12$		0			0
$13$	−50.1766			−1.07050			−0.535249	−	0.844694i	$-0.679782\pi$
$13$	−50.1766			−1.07050			−0.535249	+	0.844694i	$0.679782\pi$
$14$	15.4609	+	66.6050i	0.295149	+	1.27150i
$15$		0			0
$16$	39.1608	−	50.6205i	0.611887	−	0.790945i
$17$			51.7146i			0.737801i	0.929469	+	0.368901i	$0.120266\pi$
$17$			51.7146i			0.737801i	−0.929469	+	0.368901i	$0.879734\pi$
$18$		0			0
$19$			27.9305i			0.337247i	0.985681	+	0.168624i	$0.0539322\pi$
$19$			27.9305i			0.337247i	−0.985681	+	0.168624i	$0.946068\pi$
$20$	−19.1855	−	39.0987i	−0.214501	−	0.437137i
$21$		0			0
$22$	139.962	−	32.4891i	1.35637	−	0.314850i
$23$	7.87096			0.0713569			0.0356785	−	0.999363i	$-0.488641\pi$
$23$	7.87096			0.0713569			0.0356785	+	0.999363i	$0.488641\pi$
$24$		0			0
$25$	95.3626			0.762901
$26$	138.245	−	32.0905i	1.04277	−	0.242056i
$27$		0			0
$28$	−85.1946	−	173.620i	−0.575010	−	1.17183i
$29$			245.706i			1.57333i	0.617381	+	0.786665i	$0.288194\pi$
$29$			245.706i			1.57333i	−0.617381	+	0.786665i	$0.711806\pi$
$30$		0			0
$31$		−	59.3526i		−	0.343872i	−0.985108	−	0.171936i	$-0.944998\pi$
$31$		−	59.3526i		−	0.343872i	0.985108	−	0.171936i	$-0.0550023\pi$
$32$	−75.5203	+	164.513i	−0.417195	+	0.908817i
$33$		0			0
$34$	−33.0741	−	142.482i	−0.166828	−	0.718693i
$35$	−131.607			−0.635589
$36$		0			0
$37$	295.334			1.31223			0.656116	−	0.754660i	$-0.272198\pi$
$37$	295.334			1.31223			0.656116	+	0.754660i	$0.272198\pi$
$38$	−17.8630	−	76.9533i	−0.0762568	−	0.328513i
$39$		0			0
$40$	77.8651	+	95.4536i	0.307789	+	0.377313i
$41$		−	169.548i		−	0.645829i	−0.946428	−	0.322915i	$-0.895337\pi$
$41$		−	169.548i		−	0.645829i	0.946428	−	0.322915i	$-0.104663\pi$
$42$		0			0
$43$			329.052i			1.16698i	0.812122	+	0.583488i	$0.198313\pi$
$43$			329.052i			1.16698i	−0.812122	+	0.583488i	$0.801687\pi$
$44$	−364.841	+	179.026i	−1.25004	+	0.613390i
$45$		0			0
$46$	−21.6859	+	5.03388i	−0.0695088	+	0.0161349i
$47$	95.9484			0.297777			0.148888	−	0.988854i	$-0.452430\pi$
$47$	95.9484			0.297777			0.148888	+	0.988854i	$0.452430\pi$
$48$		0			0
$49$	−241.409			−0.703815
$50$	−262.740	+	60.9892i	−0.743142	+	0.172504i
$51$		0			0
$52$	−360.365	+	176.830i	−0.961033	+	0.471574i
$53$			300.751i			0.779459i	0.920929	+	0.389729i	$0.127431\pi$
$53$			300.751i			0.779459i	−0.920929	+	0.389729i	$0.872569\pi$
$54$		0			0
$55$			276.555i			0.678013i
$56$	345.765	+	423.868i	0.825086	+	1.01146i
$57$		0			0
$58$	−157.142	−	676.964i	−0.355754	−	1.53258i
$59$	−226.546			−0.499894			−0.249947	−	0.968259i	$-0.580413\pi$
$59$	−226.546			−0.499894			−0.249947	+	0.968259i	$0.580413\pi$
$60$		0			0
$61$	−347.445			−0.729274			−0.364637	−	0.931150i	$-0.618807\pi$
$61$	−347.445			−0.729274			−0.364637	+	0.931150i	$0.618807\pi$
$62$	37.9590	+	163.527i	0.0777548	+	0.334966i
$63$		0			0
$64$	102.857	−	501.562i	0.200892	−	0.979613i
$65$			273.162i			0.521256i
$66$		0			0
$67$			1044.63i			1.90480i	0.304849	+	0.952401i	$0.401394\pi$
$67$			1044.63i			1.90480i	−0.304849	+	0.952401i	$0.598606\pi$
$68$	182.250	+	371.411i	0.325015	+	0.662356i
$69$		0			0
$70$	362.600	−	84.1693i	0.619128	−	0.143716i
$71$	243.524			0.407057			0.203528	−	0.979069i	$-0.434759\pi$
$71$	243.524			0.407057			0.203528	+	0.979069i	$0.434759\pi$
$72$		0			0
$73$	−1094.68			−1.75510			−0.877552	−	0.479481i	$-0.840825\pi$
$73$	−1094.68			−1.75510			−0.877552	+	0.479481i	$0.840825\pi$
$74$	−813.696	+	188.881i	−1.27825	+	0.296716i
$75$		0			0
$76$	98.4312	+	200.595i	0.148564	+	0.302761i
$77$			1228.06i			1.81754i
$78$		0			0
$79$			612.775i			0.872691i	0.899779	+	0.436346i	$0.143728\pi$
$79$			612.775i			0.872691i	−0.899779	+	0.436346i	$0.856272\pi$
$80$	−275.579	−	213.192i	−0.385134	−	0.297945i
$81$		0			0
$82$	108.435	+	467.135i	0.146032	+	0.629103i
$83$	−566.126			−0.748680			−0.374340	−	0.927292i	$-0.622131\pi$
$83$	−566.126			−0.748680			−0.374340	+	0.927292i	$0.622131\pi$
$84$		0			0
$85$	281.535			0.359256
$86$	−210.446	−	906.596i	−0.263871	−	1.13675i
$87$		0			0
$88$	890.705	−	726.582i	1.07897	−	0.880158i
$89$		−	212.529i		−	0.253124i	−0.991959	−	0.126562i	$-0.959606\pi$
$89$		−	212.529i		−	0.253124i	0.991959	−	0.126562i	$-0.0403943\pi$
$90$		0			0
$91$			1213.00i			1.39732i
$92$	56.5288	−	27.7384i	0.0640602	−	0.0314340i
$93$		0			0
$94$	−264.354	+	61.3639i	−0.290065	+	0.0673320i
$95$	152.054			0.164215
$96$		0			0
$97$	−468.597			−0.490503			−0.245252	−	0.969459i	$-0.578871\pi$
$97$	−468.597			−0.490503			−0.245252	+	0.969459i	$0.578871\pi$
$98$	665.122	−	154.393i	0.685587	−	0.159143i
$99$		0			0
$100$	684.889	−	336.072i	0.684889	−	0.336072i
$101$		−	1793.23i		−	1.76666i	−0.468752	−	0.883330i	$-0.655296\pi$
$101$		−	1793.23i		−	1.76666i	0.468752	−	0.883330i	$-0.344704\pi$
$102$		0			0
$103$			138.415i			0.132412i	0.997806	+	0.0662059i	$0.0210894\pi$
$103$			138.415i			0.132412i	−0.997806	+	0.0662059i	$0.978911\pi$
$104$	879.778	−	717.668i	0.829512	−	0.676665i
$105$		0			0
$106$	−192.346	−	828.621i	−0.176248	−	0.759271i
$107$	−771.292			−0.696857			−0.348428	−	0.937335i	$-0.613285\pi$
$107$	−771.292			−0.696857			−0.348428	+	0.937335i	$0.613285\pi$
$108$		0			0
$109$	−275.772			−0.242332			−0.121166	−	0.992632i	$-0.538663\pi$
$109$	−275.772			−0.242332			−0.121166	+	0.992632i	$0.538663\pi$
$110$	−176.871	−	761.958i	−0.153309	−	0.660453i
$111$		0			0
$112$	−1223.73	−	946.694i	−1.03242	−	0.798698i
$113$		−	626.905i		−	0.521896i	−0.965353	−	0.260948i	$-0.915965\pi$
$113$		−	626.905i		−	0.521896i	0.965353	−	0.260948i	$-0.0840352\pi$
$114$		0			0
$115$		−	42.8497i		−	0.0347457i
$116$	865.906	+	1764.65i	0.693080	+	1.41245i
$117$		0			0
$118$	624.173	−	144.888i	0.486947	−	0.113034i
$119$	1250.18			0.963054
$120$		0			0
$121$	1249.62			0.938856
$122$	957.270	−	222.209i	0.710386	−	0.164900i
$123$		0			0
$124$	−209.167	−	426.267i	−0.151482	−	0.308709i
$125$		−	1199.66i		−	0.858406i
$126$		0			0
$127$			71.3408i			0.0498463i	0.999689	+	0.0249231i	$0.00793410\pi$
$127$			71.3408i			0.0498463i	−0.999689	+	0.0249231i	$0.992066\pi$
$128$	37.3866	+	1447.67i	0.0258167	+	0.999667i
$129$		0			0
$130$	−174.701	−	752.610i	−0.117864	−	0.507756i
$131$	717.805			0.478740			0.239370	−	0.970928i	$-0.423059\pi$
$131$	717.805			0.478740			0.239370	+	0.970928i	$0.423059\pi$
$132$		0			0
$133$	675.207			0.440210
$134$	−668.093	−	2878.13i	−0.430705	−	1.85547i
$135$		0			0
$136$	−739.666	−	906.744i	−0.466366	−	0.571711i
$137$		−	220.461i		−	0.137484i	−0.997634	−	0.0687420i	$-0.978101\pi$
$137$		−	220.461i		−	0.137484i	0.997634	−	0.0687420i	$-0.0218985\pi$
$138$		0			0
$139$			1402.62i			0.855889i	0.903805	+	0.427945i	$0.140762\pi$
$139$			1402.62i			0.855889i	−0.903805	+	0.427945i	$0.859238\pi$
$140$	−945.194	+	463.802i	−0.570596	+	0.279989i
$141$		0			0
$142$	−670.952	+	155.746i	−0.396514	+	0.0920418i
$143$	2548.96			1.49059
$144$		0			0
$145$	1337.63			0.766099
$146$	3016.03	−	700.104i	1.70965	−	0.396856i
$147$		0			0
$148$	2121.07	−	1040.80i	1.17805	−	0.578062i
$149$		−	1488.83i		−	0.818586i	−0.912403	−	0.409293i	$-0.865775\pi$
$149$		−	1488.83i		−	0.818586i	0.912403	−	0.409293i	$-0.134225\pi$
$150$		0			0
$151$			1967.81i			1.06051i	0.847837	+	0.530257i	$0.177905\pi$
$151$			1967.81i			1.06051i	−0.847837	+	0.530257i	$0.822095\pi$
$152$	−399.486	−	489.723i	−0.213175	−	0.261328i
$153$		0			0
$154$	−785.408	−	3383.52i	−0.410974	−	1.77047i
$155$	−323.117			−0.167441
$156$		0			0
$157$	−1128.24			−0.573527			−0.286763	−	0.958001i	$-0.592579\pi$
$157$	−1128.24			−0.573527			−0.286763	+	0.958001i	$0.592579\pi$
$158$	−391.901	−	1688.30i	−0.197329	−	0.850089i
$159$		0			0
$160$	895.616	+	411.134i	0.442529	+	0.203144i
$161$		−	190.277i		−	0.0931424i
$162$		0			0
$163$		−	1940.05i		−	0.932250i	−0.884719	−	0.466125i	$-0.845650\pi$
$163$		−	1940.05i		−	0.932250i	0.884719	−	0.466125i	$-0.154350\pi$
$164$	−597.513	−	1217.69i	−0.284500	−	0.579789i
$165$		0			0
$166$	1559.78	−	362.067i	0.729289	−	0.169288i
$167$	−2485.04			−1.15149			−0.575743	−	0.817630i	$-0.695287\pi$
$167$	−2485.04			−1.15149			−0.575743	+	0.817630i	$0.695287\pi$
$168$		0			0
$169$	320.687			0.145966
$170$	−775.678	+	180.056i	−0.349952	+	0.0812334i
$171$		0			0
$172$	1159.63	+	2363.24i	0.514075	+	1.04765i
$173$			2878.29i			1.26493i	0.774590	+	0.632464i	$0.217956\pi$
$173$			2878.29i			1.26493i	−0.774590	+	0.632464i	$0.782044\pi$
$174$		0			0
$175$		−	2305.35i		−	0.995816i
$176$	−1989.36	+	2571.51i	−0.852009	+	1.10133i
$177$		0			0
$178$	135.923	+	585.555i	0.0572353	+	0.246569i
$179$	−2965.78			−1.23840			−0.619198	−	0.785235i	$-0.712542\pi$
$179$	−2965.78			−1.23840			−0.619198	+	0.785235i	$0.712542\pi$
$180$		0			0
$181$	1250.55			0.513551			0.256776	−	0.966471i	$-0.417340\pi$
$181$	1250.55			0.513551			0.256776	+	0.966471i	$0.417340\pi$
$182$	−775.773	−	3342.01i	−0.315957	−	1.36113i
$183$		0			0
$184$	−138.007	+	112.577i	−0.0552934	+	0.0451049i
$185$		−	1607.80i		−	0.638963i
$186$		0			0
$187$		−	2627.09i		−	1.02734i
$188$	689.097	−	338.136i	0.267327	−	0.131176i
$189$		0			0
$190$	−418.936	+	97.2465i	−0.159962	+	0.0371316i
$191$	775.527			0.293796			0.146898	−	0.989152i	$-0.453071\pi$
$191$	775.527			0.293796			0.146898	+	0.989152i	$0.453071\pi$
$192$		0			0
$193$	−4371.42			−1.63037			−0.815185	−	0.579201i	$-0.803365\pi$
$193$	−4371.42			−1.63037			−0.815185	+	0.579201i	$0.803365\pi$
$194$	1291.06	−	299.692i	0.477799	−	0.110910i
$195$		0			0
$196$	−1733.78	+	850.759i	−0.631846	+	0.310044i
$197$			1648.60i			0.596233i	0.954530	+	0.298116i	$0.0963584\pi$
$197$			1648.60i			0.596233i	−0.954530	+	0.298116i	$0.903642\pi$
$198$		0			0
$199$			2946.42i			1.04958i	0.851232	+	0.524790i	$0.175856\pi$
$199$			2946.42i			1.04958i	−0.851232	+	0.524790i	$0.824144\pi$
$200$	−1672.05	+	1363.96i	−0.591160	+	0.482232i
$201$		0			0
$202$	1146.86	+	4940.65i	0.399469	+	1.72090i
$203$	5939.84			2.05367
$204$		0			0
$205$	−923.025			−0.314473
$206$	−88.5233	−	381.356i	−0.0299403	−	0.128982i
$207$		0			0
$208$	−1964.95	+	2539.96i	−0.655024	+	0.846705i
$209$		−	1418.86i		−	0.469592i
$210$		0			0
$211$		−	550.895i		−	0.179740i	−0.995954	−	0.0898700i	$-0.971355\pi$
$211$		−	550.895i		−	0.179740i	0.995954	−	0.0898700i	$-0.0286452\pi$
$212$	1059.89	+	2159.98i	0.343366	+	0.699754i
$213$		0			0
$214$	2125.04	−	493.281i	0.678808	−	0.157570i
$215$	1791.37			0.568234
$216$		0			0
$217$	−1434.82			−0.448857
$218$	759.801	−	176.371i	0.236056	−	0.0547951i
$219$		0			0
$220$	974.621	+	1986.21i	0.298677	+	0.608682i
$221$		−	2594.86i		−	0.789815i
$222$		0			0
$223$			1806.90i			0.542596i	0.962495	+	0.271298i	$0.0874529\pi$
$223$			1806.90i			0.542596i	−0.962495	+	0.271298i	$0.912547\pi$
$224$	3977.04	+	1825.67i	1.18628	+	0.544565i
$225$		0			0
$226$	400.938	+	1727.23i	0.118009	+	0.508380i
$227$	−1505.59			−0.440219			−0.220109	−	0.975475i	$-0.570641\pi$
$227$	−1505.59			−0.440219			−0.220109	+	0.975475i	$0.570641\pi$
$228$		0			0
$229$	1534.03			0.442671			0.221335	−	0.975198i	$-0.428958\pi$
$229$	1534.03			0.442671			0.221335	+	0.975198i	$0.428958\pi$
$230$	27.4046	+	118.058i	0.00785654	+	0.0338458i
$231$		0			0
$232$	−3514.30	−	4308.13i	−0.994506	−	1.21915i
$233$		−	1257.04i		−	0.353440i	−0.984261	−	0.176720i	$-0.943451\pi$
$233$		−	1257.04i		−	0.353440i	0.984261	−	0.176720i	$-0.0565487\pi$
$234$		0			0
$235$		−	522.346i		−	0.144996i
$236$	−1627.04	+	798.381i	−0.448777	+	0.220213i
$237$		0			0
$238$	−3444.45	+	799.551i	−0.938111	+	0.217761i
$239$	−1833.96			−0.496357			−0.248178	−	0.968714i	$-0.579832\pi$
$239$	−1833.96			−0.496357			−0.248178	+	0.968714i	$0.579832\pi$
$240$		0			0
$241$	717.542			0.191788			0.0958941	−	0.995392i	$-0.469429\pi$
$241$	717.542			0.191788			0.0958941	+	0.995392i	$0.469429\pi$
$242$	−3442.91	+	799.194i	−0.914540	+	0.212290i
$243$		0			0
$244$	−2495.33	+	1224.45i	−0.654701	+	0.321259i
$245$			1314.23i			0.342708i
$246$		0			0
$247$		−	1401.46i		−	0.361022i
$248$	848.912	+	1040.67i	0.217363	+	0.266461i
$249$		0			0
$250$	767.244	+	3305.27i	0.194099	+	0.836174i
$251$	1053.84			0.265010			0.132505	−	0.991182i	$-0.457698\pi$
$251$	1053.84			0.265010			0.132505	+	0.991182i	$0.457698\pi$
$252$		0			0
$253$	−399.843			−0.0993594
$254$	−45.6261	−	196.556i	−0.0112710	−	0.0485553i
$255$		0			0
$256$	−1028.87	−	3964.68i	−0.251188	−	0.967938i
$257$			6911.52i			1.67754i	0.544483	+	0.838772i	$0.316726\pi$
$257$			6911.52i			1.67754i	−0.544483	+	0.838772i	$0.683274\pi$
$258$		0			0
$259$		−	7139.56i		−	1.71286i
$260$	962.665	+	1961.84i	0.229623	+	0.467954i
$261$		0			0
$262$	−1977.68	+	459.073i	−0.466341	+	0.108251i
$263$	−2650.46			−0.621423			−0.310712	−	0.950504i	$-0.600567\pi$
$263$	−2650.46			−0.621423			−0.310712	+	0.950504i	$0.600567\pi$
$264$		0			0
$265$	1637.30			0.379541
$266$	−1860.31	+	431.829i	−0.428808	+	0.0995382i
$267$		0			0
$268$	3681.42	+	7502.47i	0.839100	+	1.71002i
$269$			2386.16i			0.540843i	0.962742	+	0.270422i	$0.0871631\pi$
$269$			2386.16i			0.540843i	−0.962742	+	0.270422i	$0.912837\pi$
$270$		0			0
$271$		−	4287.45i		−	0.961048i	−0.876982	−	0.480524i	$-0.840446\pi$
$271$		−	4287.45i		−	0.961048i	0.876982	−	0.480524i	$-0.159554\pi$
$272$	2617.82	+	2025.18i	0.583560	+	0.451451i
$273$		0			0
$274$	140.996	+	607.409i	0.0310872	+	0.133923i
$275$	−4844.40			−1.06228
$276$		0			0
$277$	4833.16			1.04836			0.524181	−	0.851607i	$-0.324371\pi$
$277$	4833.16			1.04836			0.524181	+	0.851607i	$0.324371\pi$
$278$	−897.046	−	3864.46i	−0.193530	−	0.833722i
$279$		0			0
$280$	2307.55	−	1882.35i	0.492508	−	0.401758i
$281$		−	1733.54i		−	0.368023i	−0.982924	−	0.184011i	$-0.941092\pi$
$281$		−	1733.54i		−	0.368023i	0.982924	−	0.184011i	$-0.0589083\pi$
$282$		0			0
$283$			3726.95i			0.782841i	0.920212	+	0.391420i	$0.128016\pi$
$283$			3726.95i			0.782841i	−0.920212	+	0.391420i	$0.871984\pi$
$284$	1748.98	−	858.216i	0.365433	−	0.179316i
$285$		0			0
$286$	−7022.82	+	1630.19i	−1.45199	+	0.337046i
$287$	−4098.75			−0.843003
$288$		0			0
$289$	2238.61			0.455649
$290$	−3685.41	+	855.484i	−0.746257	+	0.173227i
$291$		0			0
$292$	−7861.94	+	3857.81i	−1.57563	+	0.773156i
$293$			6471.64i			1.29037i	0.764028	+	0.645183i	$0.223219\pi$
$293$			6471.64i			1.29037i	−0.764028	+	0.645183i	$0.776781\pi$
$294$		0			0
$295$			1233.32i			0.243413i
$296$	−5178.28	+	4224.12i	−1.01683	+	0.829466i
$297$		0			0
$298$	952.180	+	4101.97i	0.185095	+	0.797386i
$299$	−394.938			−0.0763874
$300$		0			0
$301$	7954.69			1.52326
$302$	−1258.51	−	5421.64i	−0.239799	−	1.03305i
$303$		0			0
$304$	1413.86	+	1093.78i	0.266744	+	0.206357i
$305$			1891.50i			0.355104i
$306$		0			0
$307$		−	7858.86i		−	1.46101i	−0.682909	−	0.730503i	$-0.739285\pi$
$307$		−	7858.86i		−	1.46101i	0.682909	−	0.730503i	$-0.260715\pi$
$308$	4327.87	+	8819.88i	0.800660	+	1.63169i
$309$		0			0
$310$	890.243	−	206.650i	0.163105	−	0.0378610i
$311$	−7490.15			−1.36568			−0.682842	−	0.730566i	$-0.739256\pi$
$311$	−7490.15			−1.36568			−0.682842	+	0.730566i	$0.739256\pi$
$312$		0			0
$313$	−8608.77			−1.55462			−0.777310	−	0.629117i	$-0.783417\pi$
$313$	−8608.77			−1.55462			−0.777310	+	0.629117i	$0.783417\pi$
$314$	3108.51	−	721.570i	0.558672	−	0.129683i
$315$		0			0
$316$	2159.51	+	4400.92i	0.384437	+	0.783453i
$317$			5433.35i			0.962673i	0.876536	+	0.481336i	$0.159848\pi$
$317$			5433.35i			0.962673i	−0.876536	+	0.481336i	$0.840152\pi$
$318$		0			0
$319$		−	12481.8i		−	2.19075i
$320$	−2730.52	−	559.955i	−0.477002	−	0.0978200i
$321$		0			0
$322$	121.692	+	524.246i	0.0210609	+	0.0907300i
$323$	−1444.41			−0.248821
$324$		0			0
$325$	−4784.97			−0.816684
$326$	1240.76	+	5345.18i	0.210796	+	0.908105i
$327$		0			0
$328$	2425.02	+	2972.80i	0.408230	+	0.500443i
$329$		−	2319.51i		−	0.388689i
$330$		0			0
$331$		−	1578.72i		−	0.262158i	−0.991372	−	0.131079i	$-0.958156\pi$
$331$		−	1578.72i		−	0.262158i	0.991372	−	0.131079i	$-0.0418441\pi$
$332$	−4065.89	+	1995.11i	−0.672122	+	0.329807i
$333$		0			0
$334$	6846.72	−	1589.31i	1.12166	−	0.260369i
$335$	5686.98			0.927502
$336$		0			0
$337$	6800.75			1.09929			0.549645	−	0.835399i	$-0.314763\pi$
$337$	6800.75			1.09929			0.549645	+	0.835399i	$0.314763\pi$
$338$	−883.549	+	205.096i	−0.142186	+	0.0330052i
$339$		0			0
$340$	2021.97	−	992.172i	0.322520	−	0.158259i
$341$			3015.10i			0.478818i
$342$		0			0
$343$		−	2455.93i		−	0.386611i
$344$	−4706.39	−	5769.48i	−0.737649	−	0.904272i
$345$		0			0
$346$	−1840.81	−	7930.19i	−0.286020	−	1.23217i
$347$	12456.2			1.92704			0.963522	−	0.267629i	$-0.0862402\pi$
$347$	12456.2			1.92704			0.963522	+	0.267629i	$0.0862402\pi$
$348$		0			0
$349$	1821.46			0.279371			0.139685	−	0.990196i	$-0.455391\pi$
$349$	1821.46			0.279371			0.139685	+	0.990196i	$0.455391\pi$
$350$	1474.39	+	6351.63i	0.225169	+	0.970025i
$351$		0			0
$352$	3836.42	−	8357.25i	0.580914	−	1.26546i
$353$		−	6950.74i		−	1.04802i	−0.851712	−	0.524010i	$-0.824436\pi$
$353$		−	6950.74i		−	1.04802i	0.851712	−	0.524010i	$-0.175564\pi$
$354$		0			0
$355$		−	1325.75i		−	0.198208i
$356$	−748.985	−	1526.37i	−0.111506	−	0.227241i
$357$		0			0
$358$	8171.24	−	1896.77i	1.20632	−	0.280020i
$359$	−318.743			−0.0468597			−0.0234298	−	0.999725i	$-0.507459\pi$
$359$	−318.743			−0.0468597			−0.0234298	+	0.999725i	$0.507459\pi$
$360$		0			0
$361$	6078.89			0.886264
$362$	−3445.48	+	799.791i	−0.500250	+	0.116122i
$363$		0			0
$364$	4274.77	+	8711.67i	0.615547	+	1.25444i
$365$			5959.47i			0.854610i
$366$		0			0
$367$		−	6264.50i		−	0.891019i	−0.895277	−	0.445510i	$-0.853023\pi$
$367$		−	6264.50i		−	0.891019i	0.895277	−	0.445510i	$-0.146977\pi$
$368$	308.233	−	398.432i	0.0436624	−	0.0564394i
$369$		0			0
$370$	1028.27	+	4429.78i	0.144479	+	0.622414i
$371$	7270.52			1.01743
$372$		0			0
$373$	−12132.4			−1.68416			−0.842078	−	0.539355i	$-0.818668\pi$
$373$	−12132.4			−1.68416			−0.842078	+	0.539355i	$0.818668\pi$
$374$	1680.16	+	7238.08i	0.232296	+	1.00073i
$375$		0			0
$376$	−1682.32	+	1372.34i	−0.230743	+	0.188226i
$377$		−	12328.7i		−	1.68425i
$378$		0			0
$379$			1928.72i			0.261402i	0.991422	+	0.130701i	$0.0417229\pi$
$379$			1928.72i			0.261402i	−0.991422	+	0.130701i	$0.958277\pi$
$380$	1092.05	−	535.862i	0.147423	−	0.0723398i
$381$		0			0
$382$	−2136.71	+	495.989i	−0.286187	+	0.0664319i
$383$	−5949.87			−0.793796			−0.396898	−	0.917863i	$-0.629913\pi$
$383$	−5949.87			−0.793796			−0.396898	+	0.917863i	$0.629913\pi$
$384$		0			0
$385$	6685.60			0.885012
$386$	12044.0	−	2795.74i	1.58814	−	0.368652i
$387$		0			0
$388$	−3365.44	+	1651.40i	−0.440346	+	0.216076i
$389$		−	2336.09i		−	0.304485i	−0.988343	−	0.152242i	$-0.951351\pi$
$389$		−	2336.09i		−	0.304485i	0.988343	−	0.152242i	$-0.0486494\pi$
$390$		0			0
$391$			407.043i			0.0526472i
$392$	4232.77	−	3452.83i	0.545376	−	0.444884i
$393$		0			0
$394$	−1054.36	−	4542.18i	−0.134817	−	0.580791i
$395$	3335.97			0.424938
$396$		0			0
$397$	−6080.16			−0.768652			−0.384326	−	0.923198i	$-0.625566\pi$
$397$	−6080.16			−0.768652			−0.384326	+	0.923198i	$0.625566\pi$
$398$	−1884.39	−	8117.91i	−0.237326	−	1.02240i
$399$		0			0
$400$	3734.47	−	4827.30i	0.466809	−	0.603413i
$401$		−	13853.8i		−	1.72525i	−0.505843	−	0.862626i	$-0.668818\pi$
$401$		−	13853.8i		−	1.72525i	0.505843	−	0.862626i	$-0.331182\pi$
$402$		0			0
$403$			2978.11i			0.368115i
$404$	−6319.59	−	12878.9i	−0.778246	−	1.58601i
$405$		0			0
$406$	−16365.3	+	3798.83i	−2.00048	+	0.464367i
$407$	−15002.9			−1.82719
$408$		0			0
$409$	−270.871			−0.0327474			−0.0163737	−	0.999866i	$-0.505212\pi$
$409$	−270.871			−0.0327474			−0.0163737	+	0.999866i	$0.505212\pi$
$410$	2543.09	−	590.322i	0.306328	−	0.0711071i
$411$		0			0
$412$	487.794	+	994.087i	0.0583298	+	0.118872i
$413$			5476.64i			0.652513i
$414$		0			0
$415$			3082.01i			0.364553i
$416$	3789.35	−	8254.72i	0.446606	−	0.972887i
$417$		0			0
$418$	907.435	+	3909.21i	0.106182	+	0.457430i
$419$	7901.50			0.921274			0.460637	−	0.887589i	$-0.347621\pi$
$419$	7901.50			0.921274			0.460637	+	0.887589i	$0.347621\pi$
$420$		0			0
$421$	−6663.82			−0.771436			−0.385718	−	0.922617i	$-0.626046\pi$
$421$	−6663.82			−0.771436			−0.385718	+	0.922617i	$0.626046\pi$
$422$	352.325	+	1517.81i	0.0406420	+	0.175085i
$423$		0			0
$424$	−4301.60	−	5273.26i	−0.492698	−	0.603991i
$425$			4931.63i			0.562869i
$426$		0			0
$427$			8399.31i			0.951923i
$428$	−5539.38	+	2718.15i	−0.625599	+	0.306978i
$429$		0			0
$430$	−4935.53	+	1145.67i	−0.553517	+	0.128487i
$431$	14773.0			1.65102			0.825509	−	0.564388i	$-0.190888\pi$
$431$	14773.0			1.65102			0.825509	+	0.564388i	$0.190888\pi$
$432$		0			0
$433$	−2372.81			−0.263349			−0.131674	−	0.991293i	$-0.542035\pi$
$433$	−2372.81			−0.263349			−0.131674	+	0.991293i	$0.542035\pi$
$434$	3953.18	−	917.642i	0.437232	−	0.101494i
$435$		0			0
$436$	−1980.58	+	971.863i	−0.217552	+	0.106752i
$437$			219.840i			0.0240649i
$438$		0			0
$439$		−	2897.79i		−	0.315043i	−0.987516	−	0.157522i	$-0.949650\pi$
$439$		−	2897.79i		−	0.315043i	0.987516	−	0.157522i	$-0.0503504\pi$
$440$	−3955.53	−	4849.02i	−0.428574	−	0.525382i
$441$		0			0
$442$	1659.54	+	7149.28i	0.178589	+	0.769359i
$443$	−7864.13			−0.843422			−0.421711	−	0.906730i	$-0.638570\pi$
$443$	−7864.13			−0.843422			−0.421711	+	0.906730i	$0.638570\pi$
$444$		0			0
$445$	−1157.02			−0.123253
$446$	−1155.60	−	4978.32i	−0.122689	−	0.528543i
$447$		0			0
$448$	−12125.0	−	2486.51i	−1.27869	−	0.262225i
$449$			1335.91i			0.140413i	0.997532	+	0.0702064i	$0.0223658\pi$
$449$			1335.91i			0.140413i	−0.997532	+	0.0702064i	$0.977634\pi$
$450$		0			0
$451$			8613.02i			0.899271i
$452$	−2209.31	−	4502.40i	−0.229905	−	0.468529i
$453$		0			0
$454$	4148.17	−	962.904i	0.428818	−	0.0995403i
$455$	6603.58			0.680397
$456$		0			0
$457$	17393.0			1.78033			0.890164	−	0.455641i	$-0.150590\pi$
$457$	17393.0			1.78033			0.890164	+	0.455641i	$0.150590\pi$
$458$	−4226.52	+	981.091i	−0.431206	+	0.100095i
$459$		0			0
$460$	−151.009	−	307.744i	−0.0153061	−	0.0311927i
$461$			2232.20i			0.225518i	0.993622	+	0.112759i	$0.0359688\pi$
$461$			2232.20i			0.225518i	−0.993622	+	0.112759i	$0.964031\pi$
$462$		0			0
$463$			3967.51i			0.398241i	0.979975	+	0.199121i	$0.0638086\pi$
$463$			3967.51i			0.398241i	−0.979975	+	0.199121i	$0.936191\pi$
$464$	12437.8	+	9622.06i	1.24442	+	0.962700i
$465$		0			0
$466$	803.942	+	3463.37i	0.0799183	+	0.344286i
$467$	−8810.21			−0.872993			−0.436497	−	0.899706i	$-0.643781\pi$
$467$	−8810.21			−0.872993			−0.436497	+	0.899706i	$0.643781\pi$
$468$		0			0
$469$	25253.4			2.48634
$470$	334.067	+	1439.15i	0.0327858	+	0.141241i
$471$		0			0
$472$	3972.17	−	3240.25i	0.387360	−	0.315985i
$473$		−	16715.8i		−	1.62493i
$474$		0			0
$475$			2663.52i			0.257286i
$476$	8978.70	−	4405.80i	0.864576	−	0.424243i
$477$		0			0
$478$	5052.89	−	1172.91i	0.483502	−	0.112234i
$479$	19468.0			1.85703			0.928513	−	0.371300i	$-0.121088\pi$
$479$	19468.0			1.85703			0.928513	+	0.371300i	$0.121088\pi$
$480$		0			0
$481$	−14818.8			−1.40474
$482$	−1976.95	+	458.905i	−0.186821	+	0.0433663i
$483$		0			0
$484$	8974.69	−	4403.84i	0.842852	−	0.413583i
$485$			2551.05i			0.238840i
$486$		0			0
$487$			5226.26i			0.486293i	0.969990	+	0.243146i	$0.0781795\pi$
$487$			5226.26i			0.486293i	−0.969990	+	0.243146i	$0.921820\pi$
$488$	6091.97	−	4969.45i	0.565103	−	0.460976i
$489$		0			0
$490$	−840.520	−	3620.94i	−0.0774915	−	0.333832i
$491$	−9587.12			−0.881183			−0.440591	−	0.897708i	$-0.645231\pi$
$491$	−9587.12			−0.881183			−0.440591	+	0.897708i	$0.645231\pi$
$492$		0			0
$493$	−12706.6			−1.16080
$494$	896.303	+	3861.25i	0.0816327	+	0.351672i
$495$		0			0
$496$	−3004.46	−	2324.29i	−0.271984	−	0.210411i
$497$		−	5887.09i		−	0.531332i
$498$		0			0
$499$			2408.31i			0.216053i	0.994148	+	0.108027i	$0.0344532\pi$
$499$			2408.31i			0.216053i	−0.994148	+	0.108027i	$0.965547\pi$
$500$	−4227.78	−	8615.89i	−0.378144	−	0.770629i
$501$		0			0
$502$	−2903.50	+	673.982i	−0.258146	+	0.0599228i
$503$	−17192.1			−1.52397			−0.761985	−	0.647595i	$-0.775775\pi$
$503$	−17192.1			−1.52397			−0.761985	+	0.647595i	$0.775775\pi$
$504$		0			0
$505$	−9762.37			−0.860237
$506$	1101.64	−	255.720i	0.0967860	−	0.0224667i
$507$		0			0
$508$	251.416	+	512.366i	0.0219582	+	0.0447492i
$509$		−	2959.10i		−	0.257681i	−0.991665	−	0.128841i	$-0.958874\pi$
$509$		−	2959.10i		−	0.257681i	0.991665	−	0.128841i	$-0.0411256\pi$
$510$		0			0
$511$			26463.4i			2.29094i
$512$	5370.32	+	10265.4i	0.463548	+	0.886072i
$513$		0			0
$514$	−4420.27	−	19042.4i	−0.379319	−	1.63410i
$515$	753.533			0.0644750
$516$		0			0
$517$	−4874.16			−0.414633
$518$	4566.11	+	19670.7i	0.387304	+	1.66850i
$519$		0			0
$520$	−3907.00	−	4789.53i	−0.329487	−	0.403913i
$521$		−	12490.4i		−	1.05032i	−0.851004	−	0.525159i	$-0.824006\pi$
$521$		−	12490.4i		−	1.05032i	0.851004	−	0.525159i	$-0.175994\pi$
$522$		0			0
$523$			13273.1i			1.10974i	0.831939	+	0.554868i	$0.187231\pi$
$523$			13273.1i			1.10974i	−0.831939	+	0.554868i	$0.812769\pi$
$524$	5155.24	−	2529.65i	0.429786	−	0.210894i
$525$		0			0
$526$	7302.47	−	1695.10i	0.605329	−	0.140513i
$527$	3069.39			0.253709
$528$		0			0
$529$	−12105.0			−0.994908
$530$	−4511.03	+	1047.13i	−0.369711	+	0.0858200i
$531$		0			0
$532$	4849.30	−	2379.53i	0.395195	−	0.193920i
$533$			8507.35i			0.691359i
$534$		0			0
$535$			4198.94i			0.339319i
$536$	−14941.2	−	18316.1i	−1.20403	−	1.47600i
$537$		0			0
$538$	−1526.07	−	6574.29i	−0.122293	−	0.526836i
$539$	12263.5			0.980012
$540$		0			0
$541$	−12385.8			−0.984302			−0.492151	−	0.870510i	$-0.663789\pi$
$541$	−12385.8			−0.984302			−0.492151	+	0.870510i	$0.663789\pi$
$542$	2742.04	+	11812.7i	0.217308	+	0.936158i
$543$		0			0
$544$	−8507.74	−	3905.50i	−0.670526	−	0.307807i
$545$			1501.31i			0.117998i
$546$		0			0
$547$			18407.8i			1.43887i	0.694562	+	0.719433i	$0.255598\pi$
$547$			18407.8i			1.43887i	−0.694562	+	0.719433i	$0.744402\pi$
$548$	−776.939	−	1583.34i	−0.0605642	−	0.123425i
$549$		0			0
$550$	13347.2	−	3098.24i	1.03477	−	0.240199i
$551$	−6862.70			−0.530601
$552$		0			0
$553$	14813.6			1.13913
$554$	−13316.2	+	3091.05i	−1.02121	+	0.237051i
$555$		0			0
$556$	4943.04	+	10073.5i	0.377035	+	0.768369i
$557$		−	13864.9i		−	1.05472i	−0.849643	−	0.527358i	$-0.823183\pi$
$557$		−	13864.9i		−	1.05472i	0.849643	−	0.527358i	$-0.176817\pi$
$558$		0			0
$559$		−	16510.7i		−	1.24925i
$560$	−5153.83	+	6662.00i	−0.388909	+	0.502716i
$561$		0			0
$562$	1108.69	+	4776.20i	0.0832156	+	0.358491i
$563$	−14885.5			−1.11430			−0.557150	−	0.830412i	$-0.688105\pi$
$563$	−14885.5			−1.11430			−0.557150	+	0.830412i	$0.688105\pi$
$564$		0			0
$565$	−3412.89			−0.254126
$566$	−2383.57	−	10268.4i	−0.177012	−	0.762566i
$567$		0			0
$568$	−4269.87	+	3483.09i	−0.315422	+	0.257302i
$569$		−	6805.29i		−	0.501393i	−0.968066	−	0.250697i	$-0.919340\pi$
$569$		−	6805.29i		−	0.501393i	0.968066	−	0.250697i	$-0.0806596\pi$
$570$		0			0
$571$		−	8271.44i		−	0.606215i	−0.952956	−	0.303108i	$-0.901976\pi$
$571$		−	8271.44i		−	0.606215i	0.952956	−	0.303108i	$-0.0980242\pi$
$572$	18306.5	−	8982.90i	1.33817	−	0.656633i
$573$		0			0
$574$	11292.8	−	2621.36i	0.821169	−	0.190616i
$575$	750.595			0.0544382
$576$		0			0
$577$	−12153.3			−0.876863			−0.438432	−	0.898765i	$-0.644466\pi$
$577$	−12153.3			−0.876863			−0.438432	+	0.898765i	$0.644466\pi$
$578$	−6167.74	+	1431.70i	−0.443848	+	0.103029i
$579$		0			0
$580$	9606.81	−	4714.01i	0.687760	−	0.337481i
$581$			13685.8i			0.977254i
$582$		0			0
$583$		−	15278.1i		−	1.08534i
$584$	19193.7	−	15657.0i	1.36000	−	1.10941i
$585$		0			0
$586$	−4138.95	−	17830.5i	−0.291772	−	1.25695i
$587$	14331.6			1.00771			0.503856	−	0.863787i	$-0.331914\pi$
$587$	14331.6			1.00771			0.503856	+	0.863787i	$0.331914\pi$
$588$		0			0
$589$	1657.75			0.115970
$590$	−788.772	−	3398.01i	−0.0550394	−	0.237109i
$591$		0			0
$592$	11565.5	−	14949.9i	0.802938	−	1.03790i
$593$			17892.9i			1.23908i	0.784966	+	0.619539i	$0.212681\pi$
$593$			17892.9i			1.23908i	−0.784966	+	0.619539i	$0.787319\pi$
$594$		0			0
$595$		−	6805.99i		−	0.468938i
$596$	−5246.84	−	10692.7i	−0.360602	−	0.734881i
$597$		0			0
$598$	1088.12	−	252.583i	0.0744090	−	0.0172724i
$599$	11979.9			0.817172			0.408586	−	0.912720i	$-0.366022\pi$
$599$	11979.9			0.817172			0.408586	+	0.912720i	$0.366022\pi$
$600$		0			0
$601$	2946.95			0.200015			0.100007	−	0.994987i	$-0.468113\pi$
$601$	2946.95			0.200015			0.100007	+	0.994987i	$0.468113\pi$
$602$	−21916.5	+	5087.43i	−1.48381	+	0.344432i
$603$		0			0
$604$	6934.83	+	14132.7i	0.467176	+	0.952070i
$605$		−	6802.95i		−	0.457156i
$606$		0			0
$607$			25718.4i			1.71973i	0.510520	+	0.859866i	$0.329453\pi$
$607$			25718.4i			1.71973i	−0.510520	+	0.859866i	$0.670547\pi$
$608$	−4594.94	−	2109.32i	−0.306496	−	0.140698i
$609$		0			0
$610$	−1209.71	−	5211.40i	−0.0802946	−	0.345907i
$611$	−4814.36			−0.318770
$612$		0			0
$613$	−1851.43			−0.121988			−0.0609938	−	0.998138i	$-0.519427\pi$
$613$	−1851.43			−0.121988			−0.0609938	+	0.998138i	$0.519427\pi$
$614$	5026.15	+	21652.5i	0.330356	+	1.42317i
$615$		0			0
$616$	−17564.8	−	21532.4i	−1.14887	−	1.40838i
$617$			20049.5i			1.30821i	0.756405	+	0.654103i	$0.226954\pi$
$617$			20049.5i			1.30821i	−0.756405	+	0.654103i	$0.773046\pi$
$618$		0			0
$619$		−	22182.4i		−	1.44037i	−0.693784	−	0.720183i	$-0.744058\pi$
$619$		−	22182.4i		−	1.44037i	0.693784	−	0.720183i	$-0.255942\pi$
$620$	−2320.61	+	1138.71i	−0.150319	+	0.0737609i
$621$		0			0
$622$	20636.7	−	4790.34i	1.33031	−	0.308802i
$623$	−5137.80			−0.330404
$624$		0			0
$625$	5389.35			0.344918
$626$	23718.6	−	5505.75i	1.51436	−	0.351524i
$627$		0			0
$628$	−8102.99	+	3976.10i	−0.514880	+	0.252649i
$629$			15273.1i			0.968166i
$630$		0			0
$631$			28148.1i			1.77584i	0.459994	+	0.887922i	$0.347851\pi$
$631$			28148.1i			1.77584i	−0.459994	+	0.887922i	$0.652149\pi$
$632$	−8764.44	−	10744.2i	−0.551631	−	0.676235i
$633$		0			0
$634$	−3474.90	−	14969.8i	−0.217675	−	0.937740i
$635$	388.381			0.0242716
$636$		0			0
$637$	12113.1			0.753433
$638$	7982.77	+	34389.6i	0.495362	+	2.13401i
$639$		0			0
$640$	7881.16	−	203.534i	0.486766	−	0.0125709i
$641$		−	8060.46i		−	0.496676i	−0.968673	−	0.248338i	$-0.920116\pi$
$641$		−	8060.46i		−	0.496676i	0.968673	−	0.248338i	$-0.0798843\pi$
$642$		0			0
$643$		−	769.223i		−	0.0471776i	−0.999722	−	0.0235888i	$-0.992491\pi$
$643$		−	769.223i		−	0.0471776i	0.999722	−	0.0235888i	$-0.00750924\pi$
$644$	−670.564	−	1366.56i	−0.0410309	−	0.0836180i
$645$		0			0
$646$	3979.61	−	923.776i	0.242377	−	0.0562624i
$647$	25155.2			1.52852			0.764259	−	0.644909i	$-0.223105\pi$
$647$	25155.2			1.52852			0.764259	+	0.644909i	$0.223105\pi$
$648$		0			0
$649$	11508.5			0.696067
$650$	13183.4	−	3060.23i	0.795532	−	0.184665i
$651$		0			0
$652$	−6837.03	−	13933.4i	−0.410673	−	0.836921i
$653$			20613.8i			1.23534i	0.786436	+	0.617671i	$0.211924\pi$
$653$			20613.8i			1.23534i	−0.786436	+	0.617671i	$0.788076\pi$
$654$		0			0
$655$		−	3907.75i		−	0.233112i
$656$	−8582.62	−	6639.64i	−0.510815	−	0.395175i
$657$		0			0
$658$	1483.44	+	6390.65i	0.0878886	+	0.378622i
$659$	−24165.6			−1.42846			−0.714231	−	0.699910i	$-0.753223\pi$
$659$	−24165.6			−1.42846			−0.714231	+	0.699910i	$0.753223\pi$
$660$		0			0
$661$	19953.1			1.17411			0.587053	−	0.809549i	$-0.300288\pi$
$661$	19953.1			1.17411			0.587053	+	0.809549i	$0.300288\pi$
$662$	1009.67	+	4349.64i	0.0592779	+	0.255368i
$663$		0			0
$664$	9926.25	−	8097.22i	0.580140	−	0.473243i
$665$		−	3675.84i		−	0.214351i
$666$		0			0
$667$			1933.95i			0.112268i
$668$	−17847.4	+	8757.65i	−1.03374	+	0.507251i
$669$		0			0
$670$	−15668.6	+	3637.12i	−0.903480	+	0.209722i
$671$	17650.1			1.01546
$672$		0			0
$673$	−6899.20			−0.395163			−0.197581	−	0.980286i	$-0.563309\pi$
$673$	−6899.20			−0.395163			−0.197581	+	0.980286i	$0.563309\pi$
$674$	−18737.2	+	4349.43i	−1.07082	+	0.248566i
$675$		0			0
$676$	2303.16	−	1130.15i	0.131040	−	0.0643007i
$677$			9020.73i			0.512105i	0.966663	+	0.256052i	$0.0824220\pi$
$677$			9020.73i			0.512105i	−0.966663	+	0.256052i	$0.917578\pi$
$678$		0			0
$679$			11328.1i			0.640255i
$680$	−4936.34	+	4026.76i	−0.278382	+	0.227087i
$681$		0			0
$682$	−1928.31	−	8307.12i	−0.108268	−	0.466416i
$683$	−7388.19			−0.413911			−0.206956	−	0.978350i	$-0.566356\pi$
$683$	−7388.19			−0.413911			−0.206956	+	0.978350i	$0.566356\pi$
$684$		0			0
$685$	−1200.20			−0.0669448
$686$	1570.69	+	6766.50i	0.0874187	+	0.376598i
$687$		0			0
$688$	16656.8	+	12885.9i	0.923014	+	0.714058i
$689$		−	15090.6i		−	0.834409i
$690$		0			0
$691$			29990.9i			1.65110i	0.564330	+	0.825549i	$0.309134\pi$
$691$			29990.9i			1.65110i	−0.564330	+	0.825549i	$0.690866\pi$
$692$	10143.5	+	20671.7i	0.557224	+	1.13558i
$693$		0			0
$694$	−34319.0	+	7966.38i	−1.87713	+	0.435734i
$695$	7635.89			0.416757
$696$		0			0
$697$	8768.11			0.476494
$698$	−5018.43	+	1164.92i	−0.272135	+	0.0631701i
$699$		0			0
$700$	−8124.38	−	16556.9i	−0.438675	−	0.893988i
$701$			23559.3i			1.26936i	0.772774	+	0.634681i	$0.218869\pi$
$701$			23559.3i			1.26936i	−0.772774	+	0.634681i	$0.781131\pi$
$702$		0			0
$703$			8248.82i			0.442547i
$704$	−5225.10	+	25479.2i	−0.279728	+	1.36404i
$705$		0			0
$706$	4445.36	+	19150.5i	0.236973	+	1.02088i
$707$	−43350.4			−2.30603
$708$		0			0
$709$	12229.9			0.647820			0.323910	−	0.946088i	$-0.395003\pi$
$709$	12229.9			0.647820			0.323910	+	0.946088i	$0.395003\pi$
$710$	847.887	+	3652.68i	0.0448178	+	0.193074i
$711$		0			0
$712$	3039.78	+	3726.41i	0.160001	+	0.196142i
$713$		−	467.162i		−	0.0245377i
$714$		0			0
$715$		−	13876.6i		−	0.725811i
$716$	−21300.1	+	10451.8i	−1.11176	+	0.545536i
$717$		0			0
$718$	878.193	−	203.853i	0.0456460	−	0.0105957i
$719$	−37718.6			−1.95642			−0.978211	−	0.207613i	$-0.933431\pi$
$719$	−37718.6			−1.95642			−0.978211	+	0.207613i	$0.933431\pi$
$720$		0			0
$721$	3346.11			0.172837
$722$	−16748.4	+	3887.76i	−0.863311	+	0.200398i
$723$		0			0
$724$	8981.40	−	4407.13i	0.461037	−	0.226229i
$725$			23431.2i			1.20029i
$726$		0			0
$727$		−	8724.32i		−	0.445072i	−0.974924	−	0.222536i	$-0.928567\pi$
$727$		−	8724.32i		−	0.445072i	0.974924	−	0.222536i	$-0.0714335\pi$
$728$	−17349.3	−	21268.2i	−0.883252	−	1.08276i
$729$		0			0
$730$	−3811.38	−	16419.4i	−0.193241	−	0.832476i
$731$	−17016.8			−0.860997
$732$		0			0
$733$	−15921.9			−0.802306			−0.401153	−	0.916011i	$-0.631390\pi$
$733$	−15921.9			−0.802306			−0.401153	+	0.916011i	$0.631390\pi$
$734$	4006.46	+	17259.8i	0.201473	+	0.867942i
$735$		0			0
$736$	−594.417	+	1294.88i	−0.0297697	+	0.0648504i
$737$		−	53066.9i		−	2.65230i
$738$		0			0
$739$		−	21026.0i		−	1.04662i	−0.852141	−	0.523312i	$-0.824696\pi$
$739$		−	21026.0i		−	1.04662i	0.852141	−	0.523312i	$-0.175304\pi$
$740$	−5666.14	−	11547.2i	−0.281475	−	0.573625i
$741$		0			0
$742$	−20031.5	+	4649.87i	−0.991079	+	0.230057i
$743$	11626.2			0.574057			0.287029	−	0.957922i	$-0.407333\pi$
$743$	11626.2			0.574057			0.287029	+	0.957922i	$0.407333\pi$
$744$		0			0
$745$	−8105.21			−0.398593
$746$	33426.8	−	7759.27i	1.64054	−	0.380814i
$747$		0			0
$748$	−9258.24	−	18867.6i	−0.452560	−	0.922284i
$749$			18645.6i			0.909609i
$750$		0			0
$751$			7039.13i			0.342026i	0.985269	+	0.171013i	$0.0547040\pi$
$751$			7039.13i			0.342026i	−0.985269	+	0.171013i	$0.945296\pi$
$752$	3757.41	−	4856.95i	0.182206	−	0.235525i
$753$		0			0
$754$	7884.84	+	33967.7i	0.380834	+	1.64062i
$755$	10712.8			0.516395
$756$		0			0
$757$	−28354.3			−1.36137			−0.680685	−	0.732577i	$-0.738318\pi$
$757$	−28354.3			−1.36137			−0.680685	+	0.732577i	$0.738318\pi$
$758$	−1233.51	−	5313.95i	−0.0591071	−	0.254632i
$759$		0			0
$760$	−2666.07	+	2174.81i	−0.127248	+	0.103801i
$761$		−	23411.0i		−	1.11518i	−0.830118	−	0.557588i	$-0.811727\pi$
$761$		−	23411.0i		−	1.11518i	0.830118	−	0.557588i	$-0.188273\pi$
$762$		0			0
$763$			6666.67i			0.316317i
$764$	5569.79	−	2733.07i	0.263754	−	0.129423i
$765$		0			0
$766$	16392.9	−	3805.24i	0.773237	−	0.179490i
$767$	11367.3			0.535136
$768$		0			0
$769$	−25265.6			−1.18478			−0.592392	−	0.805650i	$-0.701816\pi$
$769$	−25265.6			−1.18478			−0.592392	+	0.805650i	$0.701816\pi$
$770$	−18420.0	+	4275.78i	−0.862091	+	0.200115i
$771$		0			0
$772$	−31395.3	+	15405.5i	−1.46365	+	0.718208i
$773$			31081.3i			1.44621i	0.690740	+	0.723103i	$0.257285\pi$
$773$			31081.3i			1.44621i	−0.690740	+	0.723103i	$0.742715\pi$
$774$		0			0
$775$		−	5660.02i		−	0.262340i
$776$	8216.21	−	6702.27i	0.380083	−	0.310048i
$777$		0			0
$778$	1494.05	+	6436.33i	0.0688487	+	0.296599i
$779$	4735.57			0.217804
$780$		0			0
$781$	−12371.0			−0.566797
$782$	−260.325	−	1121.47i	−0.0119043	−	0.0512837i
$783$		0			0
$784$	−9453.75	+	12220.2i	−0.430656	+	0.556679i
$785$			6142.19i			0.279266i
$786$		0			0
$787$		−	34241.6i		−	1.55093i	−0.631392	−	0.775463i	$-0.717516\pi$
$787$		−	34241.6i		−	1.55093i	0.631392	−	0.775463i	$-0.282484\pi$
$788$	5809.91	+	11840.2i	0.262651	+	0.535264i
$789$		0			0
$790$	−9191.16	+	2133.52i	−0.413933	+	0.0960851i
$791$	−15155.2			−0.681233
$792$		0			0
$793$	17433.6			0.780686
$794$	16751.9	−	3888.57i	0.748744	−	0.173804i
$795$		0			0
$796$	10383.6	+	21161.1i	0.462359	+	0.942254i
$797$		−	18168.2i		−	0.807465i	−0.914877	−	0.403732i	$-0.867713\pi$
$797$		−	18168.2i		−	0.807465i	0.914877	−	0.403732i	$-0.132287\pi$
$798$		0			0
$799$			4961.93i			0.219700i
$800$	−7201.81	+	15688.4i	−0.318278	+	0.693337i
$801$		0			0
$802$	8860.21	+	38169.6i	0.390106	+	1.68057i
$803$	55609.5			2.44386
$804$		0			0
$805$	−1035.87			−0.0453537
$806$	−1904.65	−	8205.20i	−0.0832364	−	0.358581i
$807$		0			0
$808$	25648.2	+	31441.8i	1.11671	+	1.36896i
$809$			24608.1i			1.06944i	0.845029	+	0.534720i	$0.179583\pi$
$809$			24608.1i			1.06944i	−0.845029	+	0.534720i	$0.820417\pi$
$810$		0			0
$811$			3293.86i			0.142618i	0.997454	+	0.0713089i	$0.0227176\pi$
$811$			3293.86i			0.142618i	−0.997454	+	0.0713089i	$0.977282\pi$
$812$	42659.6	−	20932.9i	1.84367	−	0.904680i
$813$		0			0
$814$	41335.6	−	9595.12i	1.77987	−	0.413156i
$815$	−10561.7			−0.453939
$816$		0			0
$817$	−9190.59			−0.393560
$818$	746.295	−	173.236i	0.0318993	−	0.00740470i
$819$		0			0
$820$	−6629.12	+	3252.88i	−0.282316	+	0.138531i
$821$			38410.9i			1.63283i	0.577467	+	0.816414i	$0.304041\pi$
$821$			38410.9i			1.63283i	−0.577467	+	0.816414i	$0.695959\pi$
$822$		0			0
$823$		−	613.495i		−	0.0259843i	−0.999916	−	0.0129922i	$-0.995864\pi$
$823$		−	613.495i		−	0.0259843i	0.999916	−	0.0129922i	$-0.00413565\pi$
$824$	−1979.73	−	2426.91i	−0.0836978	−	0.102604i
$825$		0			0
$826$	−3502.59	−	15089.1i	−0.147543	−	0.635614i
$827$	19933.1			0.838140			0.419070	−	0.907954i	$-0.362356\pi$
$827$	19933.1			0.838140			0.419070	+	0.907954i	$0.362356\pi$
$828$		0			0
$829$	32209.0			1.34941			0.674707	−	0.738086i	$-0.264270\pi$
$829$	32209.0			1.34941			0.674707	+	0.738086i	$0.264270\pi$
$830$	−1971.10	−	8491.46i	−0.0824312	−	0.355112i
$831$		0			0
$832$	−5161.00	+	25166.7i	−0.215054	+	1.04867i
$833$		−	12484.3i		−	0.519276i
$834$		0			0
$835$			13528.6i			0.560692i
$836$	−5000.28	−	10190.2i	−0.206864	−	0.421574i
$837$		0			0
$838$	−21770.0	+	5053.41i	−0.897413	+	0.208314i
$839$	−43832.6			−1.80366			−0.901828	−	0.432094i	$-0.857775\pi$
$839$	−43832.6			−1.80366			−0.901828	+	0.432094i	$0.857775\pi$
$840$		0			0
$841$	−35982.7			−1.47536
$842$	18360.0	−	4261.85i	0.751456	−	0.174434i
$843$		0			0
$844$	−1941.43	−	3956.50i	−0.0791788	−	0.161361i
$845$		−	1745.83i		−	0.0710750i
$846$		0			0
$847$		−	30208.9i		−	1.22549i
$848$	15224.2	+	11777.6i	0.616509	+	0.476941i
$849$		0			0
$850$	−3154.03	−	13587.5i	−0.127273	−	0.548291i
$851$	2324.56			0.0936368
$852$		0			0
$853$	12782.2			0.513074			0.256537	−	0.966534i	$-0.417418\pi$
$853$	12782.2			0.513074			0.256537	+	0.966534i	$0.417418\pi$
$854$	−5371.79	−	23141.6i	−0.215245	−	0.927269i
$855$		0			0
$856$	13523.6	−	11031.7i	0.539983	−	0.440485i
$857$		−	37157.1i		−	1.48105i	−0.672026	−	0.740527i	$-0.734576\pi$
$857$		−	37157.1i		−	1.48105i	0.672026	−	0.740527i	$-0.265424\pi$
$858$		0			0
$859$		−	8351.87i		−	0.331737i	−0.986148	−	0.165869i	$-0.946957\pi$
$859$		−	8351.87i		−	0.331737i	0.986148	−	0.165869i	$-0.0530427\pi$
$860$	12865.5	−	6313.05i	0.510129	−	0.250318i
$861$		0			0
$862$	−40702.1	+	9448.07i	−1.60826	+	0.373321i
$863$	11795.5			0.465265			0.232633	−	0.972565i	$-0.425266\pi$
$863$	11795.5			0.465265			0.232633	+	0.972565i	$0.425266\pi$
$864$		0			0
$865$	15669.5			0.615929
$866$	6537.50	−	1517.53i	0.256528	−	0.0595472i
$867$		0			0
$868$	−10304.8	+	5056.52i	−0.402959	+	0.197730i
$869$		−	31128.9i		−	1.21516i
$870$		0			0
$871$		−	52415.9i		−	2.03909i
$872$	4835.29	−	3944.33i	0.187780	−	0.153179i
$873$		0			0
$874$	−140.599	−	605.697i	−0.00544145	−	0.0234416i
$875$	−29001.2			−1.12048
$876$		0			0
$877$	−15657.9			−0.602886			−0.301443	−	0.953484i	$-0.597468\pi$
$877$	−15657.9			−0.602886			−0.301443	+	0.953484i	$0.597468\pi$
$878$	1853.28	+	7983.91i	0.0712361	+	0.306884i
$879$		0			0
$880$	13999.4	+	10830.1i	0.536271	+	0.414867i
$881$		−	39103.2i		−	1.49537i	−0.664054	−	0.747684i	$-0.731166\pi$
$881$		−	39103.2i		−	1.49537i	0.664054	−	0.747684i	$-0.268834\pi$
$882$		0			0
$883$			23664.8i			0.901907i	0.892547	+	0.450953i	$0.148916\pi$
$883$			23664.8i			0.901907i	−0.892547	+	0.450953i	$0.851084\pi$
$884$	−9144.66	−	18636.1i	−0.347928	−	0.709051i
$885$		0			0
$886$	21667.0	−	5029.51i	0.821578	−	0.190711i
$887$	44038.9			1.66706			0.833529	−	0.552476i	$-0.186317\pi$
$887$	44038.9			1.66706			0.833529	+	0.552476i	$0.186317\pi$
$888$		0			0
$889$	1724.63			0.0650645
$890$	3187.78	−	739.970i	0.120061	−	0.0278695i
$891$		0			0
$892$	6367.77	+	12977.1i	0.239023	+	0.487112i
$893$			2679.89i			0.100424i
$894$		0			0
$895$			16145.8i			0.603010i
$896$	34996.8	−	903.804i	1.30487	−	0.0336986i
$897$		0			0
$898$	−854.380	−	3680.65i	−0.0317495	−	0.136776i
$899$	14583.3			0.541024
$900$		0			0
$901$	−15553.2			−0.575086
$902$	−5508.46	−	23730.3i	−0.203339	−	0.875980i
$903$		0			0
$904$	8966.54	+	10991.9i	0.329892	+	0.404409i
$905$		−	6808.03i		−	0.250063i
$906$		0			0
$907$		−	32690.4i		−	1.19677i	−0.801210	−	0.598384i	$-0.795810\pi$
$907$		−	32690.4i		−	1.19677i	0.801210	−	0.598384i	$-0.204190\pi$
$908$	−10813.1	+	5305.93i	−0.395204	+	0.193925i
$909$		0			0
$910$	−18194.0	+	4223.33i	−0.662775	+	0.153848i
$911$	25499.9			0.927386			0.463693	−	0.885996i	$-0.346524\pi$
$911$	25499.9			0.927386			0.463693	+	0.885996i	$0.346524\pi$
$912$		0			0
$913$	28759.1			1.04248
$914$	−47920.7	+	11123.7i	−1.73422	+	0.402559i
$915$		0			0
$916$	11017.3	−	5406.15i	0.397405	−	0.195005i
$917$		−	17352.6i		−	0.624901i
$918$		0			0
$919$		−	20221.1i		−	0.725825i	−0.931823	−	0.362912i	$-0.881782\pi$
$919$		−	20221.1i		−	0.725825i	0.931823	−	0.362912i	$-0.118218\pi$
$920$	612.873	+	751.311i	0.0219629	+	0.0269239i
$921$		0			0
$922$	−1427.60	−	6150.08i	−0.0509931	−	0.219677i
$923$	−12219.2			−0.435754
$924$		0			0
$925$	28163.8			1.00110
$926$	−2537.42	−	10931.2i	−0.0900485	−	0.387927i
$927$		0			0
$928$	−40422.0	−	18555.8i	−1.42987	−	0.656385i
$929$		−	37318.6i		−	1.31796i	−0.752161	−	0.658979i	$-0.770989\pi$
$929$		−	37318.6i		−	1.31796i	0.752161	−	0.658979i	$-0.229011\pi$
$930$		0			0
$931$		−	6742.66i		−	0.237360i
$932$	−4430.00	−	9028.01i	−0.155697	−	0.317299i
$933$		0			0
$934$	24273.6	−	5634.58i	0.850383	−	0.197397i
$935$	−14301.9			−0.500239
$936$		0			0
$937$	−16237.5			−0.566121			−0.283060	−	0.959102i	$-0.591350\pi$
$937$	−16237.5			−0.566121			−0.283060	+	0.959102i	$0.591350\pi$
$938$	−69577.5	+	16150.8i	−2.42195	+	0.562200i
$939$		0			0
$940$	−1840.82	−	3751.46i	−0.0638734	−	0.130169i
$941$		−	2061.31i		−	0.0714100i	−0.999362	−	0.0357050i	$-0.988632\pi$
$941$		−	2061.31i		−	0.0714100i	0.999362	−	0.0357050i	$-0.0113677\pi$
$942$		0			0
$943$		−	1334.51i		−	0.0460844i
$944$	−8871.72	+	11467.9i	−0.305879	+	0.395389i
$945$		0			0
$946$	10690.6	+	46054.9i	0.367422	+	1.58285i
$947$	17909.0			0.614534			0.307267	−	0.951623i	$-0.400586\pi$
$947$	17909.0			0.614534			0.307267	+	0.951623i	$0.400586\pi$
$948$		0			0
$949$	54927.3			1.87884
$950$	−1703.46	−	7338.47i	−0.0581764	−	0.250623i
$951$		0			0
$952$	−21920.1	+	17881.1i	−0.746256	+	0.608749i
$953$			10905.6i			0.370689i	0.982674	+	0.185344i	$0.0593400\pi$
$953$			10905.6i			0.370689i	−0.982674	+	0.185344i	$0.940660\pi$
$954$		0			0
$955$		−	4221.99i		−	0.143058i
$956$	−13171.4	+	6463.16i	−0.445601	+	0.218654i
$957$		0			0
$958$	−53637.7	+	12450.8i	−1.80893	+	0.419902i
$959$	−5329.56			−0.179458
$960$		0			0
$961$	26268.3			0.881752
$962$	40828.4	−	9477.40i	1.36836	−	0.317634i
$963$		0			0
$964$	5153.35	−	2528.72i	0.172177	−	0.0844862i
$965$			23798.1i			0.793873i
$966$		0			0
$967$		−	48616.1i		−	1.61674i	−0.588674	−	0.808370i	$-0.700350\pi$
$967$		−	48616.1i		−	1.61674i	0.588674	−	0.808370i	$-0.299650\pi$
$968$	−21910.3	+	17873.1i	−0.727505	+	0.593454i
$969$		0			0
$970$	−1631.53	−	7028.59i	−0.0540054	−	0.232654i
$971$	24102.8			0.796596			0.398298	−	0.917256i	$-0.369601\pi$
$971$	24102.8			0.796596			0.398298	+	0.917256i	$0.369601\pi$
$972$		0			0
$973$	33907.7			1.11719
$974$	−3342.46	−	14399.2i	−0.109958	−	0.473698i
$975$		0			0
$976$	−13606.2	+	17587.8i	−0.446233	+	0.576816i
$977$			24660.1i			0.807521i	0.914865	+	0.403760i	$0.132297\pi$
$977$			24660.1i			0.807521i	−0.914865	+	0.403760i	$0.867703\pi$
$978$		0			0
$979$			10796.4i			0.352457i
$980$	4631.56	+	9438.77i	0.150969	+	0.307664i
$981$		0			0
$982$	26414.2	−	6131.46i	0.858361	−	0.199249i
$983$	−22001.9			−0.713887			−0.356943	−	0.934126i	$-0.616181\pi$
$983$	−22001.9			−0.713887			−0.356943	+	0.934126i	$0.616181\pi$
$984$		0			0
$985$	8975.02			0.290323
$986$	35008.9	−	8126.52i	1.13074	−	0.262476i
$987$		0			0
$988$	−4938.94	−	10065.2i	−0.159037	−	0.324106i
$989$			2589.96i			0.0832718i
$990$		0			0
$991$		−	21100.2i		−	0.676358i	−0.941082	−	0.338179i	$-0.890189\pi$
$991$		−	21100.2i		−	0.676358i	0.941082	−	0.338179i	$-0.109811\pi$
$992$	9764.30	+	4482.33i	0.312517	+	0.143462i
$993$		0			0
$994$	3765.10	+	16220.0i	0.120142	+	0.517571i
$995$	16040.4			0.511071
$996$		0			0
$997$	8283.41			0.263128			0.131564	−	0.991308i	$-0.458000\pi$
$997$	8283.41			0.263128			0.131564	+	0.991308i	$0.458000\pi$
$998$	−1540.23	−	6635.30i	−0.0488530	−	0.210458i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	324.4.b.c.323.4		24
3.2	odd	2	inner	324.4.b.c.323.21		24
4.3	odd	2	inner	324.4.b.c.323.22		24
9.2	odd	6		36.4.h.b.23.3	yes	24
9.4	even	3		36.4.h.b.11.8	yes	24
9.5	odd	6		108.4.h.b.35.5		24
9.7	even	3		108.4.h.b.71.10		24
12.11	even	2	inner	324.4.b.c.323.3		24
36.7	odd	6		108.4.h.b.71.5		24
36.11	even	6		36.4.h.b.23.8	yes	24
36.23	even	6		108.4.h.b.35.10		24
36.31	odd	6		36.4.h.b.11.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.b.11.3	✓	24	36.31	odd	6
36.4.h.b.11.8	yes	24	9.4	even	3
36.4.h.b.23.3	yes	24	9.2	odd	6
36.4.h.b.23.8	yes	24	36.11	even	6
108.4.h.b.35.5		24	9.5	odd	6
108.4.h.b.35.10		24	36.23	even	6
108.4.h.b.71.5		24	36.7	odd	6
108.4.h.b.71.10		24	9.7	even	3
324.4.b.c.323.3		24	12.11	even	2	inner
324.4.b.c.323.4		24	1.1	even	1	trivial
324.4.b.c.323.21		24	3.2	odd	2	inner
324.4.b.c.323.22		24	4.3	odd	2	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:	\( N \)	\(=\)	\( 324 = 2^{2} \cdot 3^{4} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	324.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.75517 + 0.639551i) q^{2} +(7.18195 - 3.52415i) q^{4} -5.44403i q^{5} -24.1745i q^{7} +(-17.5336 + 14.3029i) q^{8} +O(q^{10})\)	\(q+(-2.75517 + 0.639551i) q^{2} +(7.18195 - 3.52415i) q^{4} -5.44403i q^{5} -24.1745i q^{7} +(-17.5336 + 14.3029i) q^{8} +(3.48173 + 14.9992i) q^{10} -50.7998 q^{11} -50.1766 q^{13} +(15.4609 + 66.6050i) q^{14} +(39.1608 - 50.6205i) q^{16} +51.7146i q^{17} +27.9305i q^{19} +(-19.1855 - 39.0987i) q^{20} +(139.962 - 32.4891i) q^{22} +7.87096 q^{23} +95.3626 q^{25} +(138.245 - 32.0905i) q^{26} +(-85.1946 - 173.620i) q^{28} +245.706i q^{29} -59.3526i q^{31} +(-75.5203 + 164.513i) q^{32} +(-33.0741 - 142.482i) q^{34} -131.607 q^{35} +295.334 q^{37} +(-17.8630 - 76.9533i) q^{38} +(77.8651 + 95.4536i) q^{40} -169.548i q^{41} +329.052i q^{43} +(-364.841 + 179.026i) q^{44} +(-21.6859 + 5.03388i) q^{46} +95.9484 q^{47} -241.409 q^{49} +(-262.740 + 60.9892i) q^{50} +(-360.365 + 176.830i) q^{52} +300.751i q^{53} +276.555i q^{55} +(345.765 + 423.868i) q^{56} +(-157.142 - 676.964i) q^{58} -226.546 q^{59} -347.445 q^{61} +(37.9590 + 163.527i) q^{62} +(102.857 - 501.562i) q^{64} +273.162i q^{65} +1044.63i q^{67} +(182.250 + 371.411i) q^{68} +(362.600 - 84.1693i) q^{70} +243.524 q^{71} -1094.68 q^{73} +(-813.696 + 188.881i) q^{74} +(98.4312 + 200.595i) q^{76} +1228.06i q^{77} +612.775i q^{79} +(-275.579 - 213.192i) q^{80} +(108.435 + 467.135i) q^{82} -566.126 q^{83} +281.535 q^{85} +(-210.446 - 906.596i) q^{86} +(890.705 - 726.582i) q^{88} -212.529i q^{89} +1213.00i q^{91} +(56.5288 - 27.7384i) q^{92} +(-264.354 + 61.3639i) q^{94} +152.054 q^{95} -468.597 q^{97} +(665.122 - 154.393i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{4}+O(q^{10}) \) 24 * q + 24 * q^4	\( 24 q + 24 q^{4} + 96 q^{10} + 432 q^{13} + 144 q^{16} + 384 q^{22} - 504 q^{25} - 672 q^{28} + 1320 q^{34} + 1248 q^{37} - 1272 q^{40} + 960 q^{46} - 696 q^{49} - 264 q^{52} - 1032 q^{58} + 528 q^{61} + 960 q^{64} - 1128 q^{70} - 4776 q^{73} + 1200 q^{76} - 4104 q^{82} - 1440 q^{85} - 3912 q^{88} + 2376 q^{94} - 1176 q^{97}+O(q^{100}) \) 24 * q + 24 * q^4 + 96 * q^10 + 432 * q^13 + 144 * q^16 + 384 * q^22 - 504 * q^25 - 672 * q^28 + 1320 * q^34 + 1248 * q^37 - 1272 * q^40 + 960 * q^46 - 696 * q^49 - 264 * q^52 - 1032 * q^58 + 528 * q^61 + 960 * q^64 - 1128 * q^70 - 4776 * q^73 + 1200 * q^76 - 4104 * q^82 - 1440 * q^85 - 3912 * q^88 + 2376 * q^94 - 1176 * q^97

Introduction

L-functions

Modular forms

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