LMFDB - Embedded newform 135.4.f.b.53.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [135,4,Mod(53,135)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(135, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("135.53");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 135 = 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	135.f (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.96525785077$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.1
Character	$\chi$	$=$	135.53
Dual form			135.4.f.b.107.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.78617 - 3.78617i) q^{2} +20.6702i q^{4} +(-5.68236 - 9.62864i) q^{5} +(20.4442 - 20.4442i) q^{7} +(47.9717 - 47.9717i) q^{8} +O(q^{10})$	\(q+(-3.78617 - 3.78617i) q^{2} +20.6702i q^{4} +(-5.68236 - 9.62864i) q^{5} +(20.4442 - 20.4442i) q^{7} +(47.9717 - 47.9717i) q^{8} +(-14.9413 + 57.9701i) q^{10} -10.1550i q^{11} +(-37.3182 - 37.3182i) q^{13} -154.810 q^{14} -197.897 q^{16} +(27.8636 + 27.8636i) q^{17} -28.1493i q^{19} +(199.026 - 117.456i) q^{20} +(-38.4487 + 38.4487i) q^{22} +(-23.6065 + 23.6065i) q^{23} +(-60.4215 + 109.427i) q^{25} +282.587i q^{26} +(422.586 + 422.586i) q^{28} -247.001 q^{29} +125.187 q^{31} +(365.498 + 365.498i) q^{32} -210.993i q^{34} +(-313.021 - 80.6783i) q^{35} +(-76.0376 + 76.0376i) q^{37} +(-106.578 + 106.578i) q^{38} +(-734.496 - 189.310i) q^{40} +63.0208i q^{41} +(-124.728 - 124.728i) q^{43} +209.907 q^{44} +178.757 q^{46} +(-71.5882 - 71.5882i) q^{47} -492.927i q^{49} +(643.076 - 185.543i) q^{50} +(771.377 - 771.377i) q^{52} +(-148.544 + 148.544i) q^{53} +(-97.7790 + 57.7045i) q^{55} -1961.48i q^{56} +(935.190 + 935.190i) q^{58} -231.315 q^{59} -886.615 q^{61} +(-473.980 - 473.980i) q^{62} -1184.51i q^{64} +(-147.268 + 571.380i) q^{65} +(438.750 - 438.750i) q^{67} +(-575.948 + 575.948i) q^{68} +(879.689 + 1490.61i) q^{70} -729.974i q^{71} +(-186.217 - 186.217i) q^{73} +575.784 q^{74} +581.854 q^{76} +(-207.611 - 207.611i) q^{77} +919.171i q^{79} +(1124.52 + 1905.48i) q^{80} +(238.608 - 238.608i) q^{82} +(396.645 - 396.645i) q^{83} +(109.958 - 426.620i) q^{85} +944.487i q^{86} +(-487.154 - 487.154i) q^{88} +1389.76 q^{89} -1525.88 q^{91} +(-487.952 - 487.952i) q^{92} +542.091i q^{94} +(-271.040 + 159.955i) q^{95} +(951.496 - 951.496i) q^{97} +(-1866.31 + 1866.31i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{7}+O(q^{10}) $ 24 * q + 12 * q^7	$ 24 q + 12 q^{7} - 120 q^{10} - 72 q^{13} - 612 q^{16} - 552 q^{22} + 144 q^{25} + 1008 q^{28} + 456 q^{31} + 360 q^{37} - 1092 q^{40} - 1848 q^{43} + 732 q^{46} + 2868 q^{52} - 2052 q^{55} + 2424 q^{58} - 2544 q^{61} - 1776 q^{67} + 7332 q^{70} + 4236 q^{73} + 5844 q^{76} + 1188 q^{82} - 48 q^{85} - 8472 q^{88} - 7056 q^{91} + 2916 q^{97}+O(q^{100}) $ 24 * q + 12 * q^7 - 120 * q^10 - 72 * q^13 - 612 * q^16 - 552 * q^22 + 144 * q^25 + 1008 * q^28 + 456 * q^31 + 360 * q^37 - 1092 * q^40 - 1848 * q^43 + 732 * q^46 + 2868 * q^52 - 2052 * q^55 + 2424 * q^58 - 2544 * q^61 - 1776 * q^67 + 7332 * q^70 + 4236 * q^73 + 5844 * q^76 + 1188 * q^82 - 48 * q^85 - 8472 * q^88 - 7056 * q^91 + 2916 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$56$	$82$
$\chi(n)$	$-1$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−3.78617	−	3.78617i	−1.33861	−	1.33861i	−0.897403	−	0.441212i	$-0.854549\pi$
$2$	−3.78617	−	3.78617i	−1.33861	−	1.33861i	−0.441212	−	0.897403i	$-0.645451\pi$
$3$		0			0
$3$		0			0
$4$			20.6702i			2.58378i
$5$	−5.68236	−	9.62864i	−0.508246	−	0.861212i
$5$	−5.68236	−	9.62864i	−0.508246	−	0.861212i
$6$		0			0
$7$	20.4442	−	20.4442i	1.10388	−	1.10388i	0.109943	−	0.993938i	$-0.464933\pi$
$7$	20.4442	−	20.4442i	1.10388	−	1.10388i	0.993938	−	0.109943i	$-0.0350668\pi$
$8$	47.9717	−	47.9717i	2.12007	−	2.12007i
$9$		0			0
$10$	−14.9413	+	57.9701i	−0.472485	+	1.83318i
$11$		−	10.1550i		−	0.278350i	−0.990268	−	0.139175i	$-0.955555\pi$
$11$		−	10.1550i		−	0.278350i	0.990268	−	0.139175i	$-0.0444451\pi$
$12$		0			0
$13$	−37.3182	−	37.3182i	−0.796171	−	0.796171i	0.186319	−	0.982489i	$-0.440344\pi$
$13$	−37.3182	−	37.3182i	−0.796171	−	0.796171i	−0.982489	+	0.186319i	$0.940344\pi$
$14$	−154.810			−2.95534
$15$		0			0
$16$	−197.897			−3.09214
$17$	27.8636	+	27.8636i	0.397525	+	0.397525i	0.877359	−	0.479834i	$-0.159303\pi$
$17$	27.8636	+	27.8636i	0.397525	+	0.397525i	−0.479834	+	0.877359i	$0.659303\pi$
$18$		0			0
$19$		−	28.1493i		−	0.339890i	−0.985454	−	0.169945i	$-0.945641\pi$
$19$		−	28.1493i		−	0.339890i	0.985454	−	0.169945i	$-0.0543589\pi$
$20$	199.026	−	117.456i	2.22518	−	1.31320i
$21$		0			0
$22$	−38.4487	+	38.4487i	−0.372604	+	0.372604i
$23$	−23.6065	+	23.6065i	−0.214013	+	0.214013i	−0.805970	−	0.591957i	$-0.798356\pi$
$23$	−23.6065	+	23.6065i	−0.214013	+	0.214013i	0.591957	+	0.805970i	$0.298356\pi$
$24$		0			0
$25$	−60.4215	+	109.427i	−0.483372	+	0.875415i
$26$			282.587i			2.13153i
$27$		0			0
$28$	422.586	+	422.586i	2.85218	+	2.85218i
$29$	−247.001			−1.58162			−0.790810	−	0.612062i	$-0.790340\pi$
$29$	−247.001			−1.58162			−0.790810	+	0.612062i	$0.790340\pi$
$30$		0			0
$31$	125.187			0.725298			0.362649	−	0.931926i	$-0.381872\pi$
$31$	125.187			0.725298			0.362649	+	0.931926i	$0.381872\pi$
$32$	365.498	+	365.498i	2.01911	+	2.01911i
$33$		0			0
$34$		−	210.993i		−	1.06427i
$35$	−313.021	−	80.6783i	−1.51172	−	0.389632i
$36$		0			0
$37$	−76.0376	+	76.0376i	−0.337852	+	0.337852i	−0.855558	−	0.517707i	$-0.826786\pi$
$37$	−76.0376	+	76.0376i	−0.337852	+	0.337852i	0.517707	+	0.855558i	$0.326786\pi$
$38$	−106.578	+	106.578i	−0.454981	+	0.454981i
$39$		0			0
$40$	−734.496	−	189.310i	−2.90335	−	0.748313i
$41$			63.0208i			0.240053i	0.992771	+	0.120027i	$0.0382980\pi$
$41$			63.0208i			0.240053i	−0.992771	+	0.120027i	$0.961702\pi$
$42$		0			0
$43$	−124.728	−	124.728i	−0.442347	−	0.442347i	0.450453	−	0.892800i	$-0.351262\pi$
$43$	−124.728	−	124.728i	−0.442347	−	0.442347i	−0.892800	+	0.450453i	$0.851262\pi$
$44$	209.907			0.719196
$45$		0			0
$46$	178.757			0.572961
$47$	−71.5882	−	71.5882i	−0.222175	−	0.222175i	0.587239	−	0.809414i	$-0.300215\pi$
$47$	−71.5882	−	71.5882i	−0.222175	−	0.222175i	−0.809414	+	0.587239i	$0.800215\pi$
$48$		0			0
$49$		−	492.927i		−	1.43711i
$50$	643.076	−	185.543i	1.81889	−	0.524795i
$51$		0			0
$52$	771.377	−	771.377i	2.05713	−	2.05713i
$53$	−148.544	+	148.544i	−0.384984	+	0.384984i	−0.872894	−	0.487910i	$-0.837759\pi$
$53$	−148.544	+	148.544i	−0.384984	+	0.384984i	0.487910	+	0.872894i	$0.337759\pi$
$54$		0			0
$55$	−97.7790	+	57.7045i	−0.239719	+	0.141470i
$56$		−	1961.48i		−	4.68061i
$57$		0			0
$58$	935.190	+	935.190i	2.11718	+	2.11718i
$59$	−231.315			−0.510417			−0.255209	−	0.966886i	$-0.582144\pi$
$59$	−231.315			−0.510417			−0.255209	+	0.966886i	$0.582144\pi$
$60$		0			0
$61$	−886.615			−1.86098			−0.930488	−	0.366324i	$-0.880616\pi$
$61$	−886.615			−1.86098			−0.930488	+	0.366324i	$0.880616\pi$
$62$	−473.980	−	473.980i	−0.970895	−	0.970895i
$63$		0			0
$64$		−	1184.51i		−	2.31349i
$65$	−147.268	+	571.380i	−0.281021	+	1.09032i
$66$		0			0
$67$	438.750	−	438.750i	0.800028	−	0.800028i	−0.183072	−	0.983100i	$-0.558604\pi$
$67$	438.750	−	438.750i	0.800028	−	0.800028i	0.983100	+	0.183072i	$0.0586041\pi$
$68$	−575.948	+	575.948i	−1.02712	+	1.02712i
$69$		0			0
$70$	879.689	+	1490.61i	1.50204	+	2.54518i
$71$		−	729.974i		−	1.22017i	−0.792336	−	0.610084i	$-0.791136\pi$
$71$		−	729.974i		−	1.22017i	0.792336	−	0.610084i	$-0.208864\pi$
$72$		0			0
$73$	−186.217	−	186.217i	−0.298562	−	0.298562i	0.541888	−	0.840450i	$-0.317710\pi$
$73$	−186.217	−	186.217i	−0.298562	−	0.298562i	−0.840450	+	0.541888i	$0.817710\pi$
$74$	575.784			0.904507
$75$		0			0
$76$	581.854			0.878200
$77$	−207.611	−	207.611i	−0.307265	−	0.307265i
$78$		0			0
$79$			919.171i			1.30905i	0.756041	+	0.654524i	$0.227131\pi$
$79$			919.171i			1.30905i	−0.756041	+	0.654524i	$0.772869\pi$
$80$	1124.52	+	1905.48i	1.57157	+	2.66299i
$81$		0			0
$82$	238.608	−	238.608i	0.321339	−	0.321339i
$83$	396.645	−	396.645i	0.524547	−	0.524547i	−0.394394	−	0.918941i	$-0.629046\pi$
$83$	396.645	−	396.645i	0.524547	−	0.524547i	0.918941	+	0.394394i	$0.129046\pi$
$84$		0			0
$85$	109.958	−	426.620i	0.140313	−	0.544394i
$86$			944.487i			1.18426i
$87$		0			0
$88$	−487.154	−	487.154i	−0.590122	−	0.590122i
$89$	1389.76			1.65522			0.827609	−	0.561305i	$-0.189701\pi$
$89$	1389.76			1.65522			0.827609	+	0.561305i	$0.189701\pi$
$90$		0			0
$91$	−1525.88			−1.75776
$92$	−487.952	−	487.952i	−0.552962	−	0.552962i
$93$		0			0
$94$			542.091i			0.594813i
$95$	−271.040	+	159.955i	−0.292717	+	0.172748i
$96$		0			0
$97$	951.496	−	951.496i	0.995977	−	0.995977i	−0.00401445	−	0.999992i	$-0.501278\pi$
$97$	951.496	−	951.496i	0.995977	−	0.995977i	0.999992	+	0.00401445i	$0.00127784\pi$
$98$	−1866.31	+	1866.31i	−1.92373	+	1.92373i
$99$		0			0
$100$	−2261.88	−	1248.93i	−2.26188	−	1.24893i
$101$			974.619i			0.960180i	0.877219	+	0.480090i	$0.159396\pi$
$101$			974.619i			0.960180i	−0.877219	+	0.480090i	$0.840604\pi$
$102$		0			0
$103$	−594.952	−	594.952i	−0.569149	−	0.569149i	0.362741	−	0.931890i	$-0.381841\pi$
$103$	−594.952	−	594.952i	−0.569149	−	0.569149i	−0.931890	+	0.362741i	$0.881841\pi$
$104$	−3580.44			−3.37588
$105$		0			0
$106$	1124.83			1.03069
$107$	1002.53	+	1002.53i	0.905776	+	0.905776i	0.995928	−	0.0901521i	$-0.0287353\pi$
$107$	1002.53	+	1002.53i	0.905776	+	0.905776i	−0.0901521	+	0.995928i	$0.528735\pi$
$108$		0			0
$109$		−	9.66265i		−	0.00849095i	−0.999991	−	0.00424548i	$-0.998649\pi$
$109$		−	9.66265i		−	0.00849095i	0.999991	−	0.00424548i	$-0.00135138\pi$
$110$	588.688	+	151.729i	0.510265	+	0.131516i
$111$		0			0
$112$	−4045.84	+	4045.84i	−3.41335	+	3.41335i
$113$	1130.78	−	1130.78i	0.941366	−	0.941366i	−0.0570076	−	0.998374i	$-0.518156\pi$
$113$	1130.78	−	1130.78i	0.941366	−	0.941366i	0.998374	+	0.0570076i	$0.0181559\pi$
$114$		0			0
$115$	361.439	+	93.1577i	0.293081	+	0.0755392i
$116$		−	5105.58i		−	4.08656i
$117$		0			0
$118$	875.798	+	875.798i	0.683252	+	0.683252i
$119$	1139.30			0.877640
$120$		0			0
$121$	1227.88			0.922521
$122$	3356.88	+	3356.88i	2.49113	+	2.49113i
$123$		0			0
$124$			2587.65i			1.87401i
$125$	1396.97	−	40.0269i	0.999590	−	0.0286409i
$126$		0			0
$127$	−910.771	+	910.771i	−0.636361	+	0.636361i	−0.949656	−	0.313295i	$-0.898567\pi$
$127$	−910.771	+	910.771i	−0.636361	+	0.636361i	0.313295	+	0.949656i	$0.398567\pi$
$128$	−1560.76	+	1560.76i	−1.07776	+	1.07776i
$129$		0			0
$130$	2720.93	−	1605.76i	1.83570	−	1.08334i
$131$			69.5658i			0.0463969i	0.999731	+	0.0231985i	$0.00738496\pi$
$131$			69.5658i			0.0463969i	−0.999731	+	0.0231985i	$0.992615\pi$
$132$		0			0
$133$	−575.490	−	575.490i	−0.375198	−	0.375198i
$134$	−3322.37			−2.14186
$135$		0			0
$136$	2673.33			1.68556
$137$	−1504.67	−	1504.67i	−0.938338	−	0.938338i	0.0598684	−	0.998206i	$-0.480932\pi$
$137$	−1504.67	−	1504.67i	−0.938338	−	0.938338i	−0.998206	+	0.0598684i	$0.980932\pi$
$138$		0			0
$139$		−	943.775i		−	0.575899i	−0.957646	−	0.287950i	$-0.907026\pi$
$139$		−	943.775i		−	0.575899i	0.957646	−	0.287950i	$-0.0929735\pi$
$140$	1667.64	−	6470.21i	1.00672	−	3.90595i
$141$		0			0
$142$	−2763.81	+	2763.81i	−1.63334	+	1.63334i
$143$	−378.967	+	378.967i	−0.221614	+	0.221614i
$144$		0			0
$145$	1403.55	+	2378.29i	0.803852	+	1.36211i
$146$			1410.10i			0.799320i
$147$		0			0
$148$	−1571.72	−	1571.72i	−0.872934	−	0.872934i
$149$	−817.207			−0.449317			−0.224658	−	0.974438i	$-0.572127\pi$
$149$	−817.207			−0.449317			−0.224658	+	0.974438i	$0.572127\pi$
$150$		0			0
$151$	−2513.86			−1.35480			−0.677402	−	0.735613i	$-0.736894\pi$
$151$	−2513.86			−1.35480			−0.677402	+	0.735613i	$0.736894\pi$
$152$	−1350.37	−	1350.37i	−0.720590	−	0.720590i
$153$		0			0
$154$			1572.10i			0.822620i
$155$	−711.358	−	1205.38i	−0.368630	−	0.624636i
$156$		0			0
$157$	2469.84	−	2469.84i	1.25551	−	1.25551i	0.302289	−	0.953216i	$-0.402249\pi$
$157$	2469.84	−	2469.84i	1.25551	−	1.25551i	0.953216	−	0.302289i	$-0.0977509\pi$
$158$	3480.14	−	3480.14i	1.75231	−	1.75231i
$159$		0			0
$160$	1442.36	−	5596.15i	0.712677	−	2.76509i
$161$			965.230i			0.472489i
$162$		0			0
$163$	−2145.02	−	2145.02i	−1.03074	−	1.03074i	−0.999512	−	0.0312289i	$-0.990058\pi$
$163$	−2145.02	−	2145.02i	−1.03074	−	1.03074i	−0.0312289	−	0.999512i	$-0.509942\pi$
$164$	−1302.65			−0.620245
$165$		0			0
$166$	−3003.53			−1.40433
$167$	816.233	+	816.233i	0.378216	+	0.378216i	0.870458	−	0.492242i	$-0.163823\pi$
$167$	816.233	+	816.233i	0.378216	+	0.378216i	−0.492242	+	0.870458i	$0.663823\pi$
$168$		0			0
$169$			588.304i			0.267776i
$170$	−2031.58	+	1198.94i	−0.916558	+	0.540909i
$171$		0			0
$172$	2578.17	−	2578.17i	1.14293	−	1.14293i
$173$	−958.369	+	958.369i	−0.421176	+	0.421176i	−0.885608	−	0.464433i	$-0.846258\pi$
$173$	−958.369	+	958.369i	−0.421176	+	0.421176i	0.464433	+	0.885608i	$0.346258\pi$
$174$		0			0
$175$	1001.87	+	3472.41i	0.432769	+	1.49994i
$176$			2009.65i			0.860698i
$177$		0			0
$178$	−5261.88	−	5261.88i	−2.21570	−	2.21570i
$179$	3158.52			1.31888			0.659438	−	0.751759i	$-0.270794\pi$
$179$	3158.52			1.31888			0.659438	+	0.751759i	$0.270794\pi$
$180$		0			0
$181$	1360.25			0.558601			0.279301	−	0.960204i	$-0.409897\pi$
$181$	1360.25			0.558601			0.279301	+	0.960204i	$0.409897\pi$
$182$	5777.25	+	5777.25i	2.35296	+	2.35296i
$183$		0			0
$184$			2264.89i			0.907445i
$185$	1164.21	+	300.066i	0.462674	+	0.119250i
$186$		0			0
$187$	282.956	−	282.956i	0.110651	−	0.110651i
$188$	1479.75	−	1479.75i	0.574051	−	0.574051i
$189$		0			0
$190$	1631.82	+	420.588i	0.623078	+	0.160593i
$191$		−	766.758i		−	0.290475i	−0.989397	−	0.145237i	$-0.953605\pi$
$191$		−	766.758i		−	0.290475i	0.989397	−	0.145237i	$-0.0463946\pi$
$192$		0			0
$193$	−1347.92	−	1347.92i	−0.502722	−	0.502722i	0.409561	−	0.912283i	$-0.365682\pi$
$193$	−1347.92	−	1347.92i	−0.502722	−	0.502722i	−0.912283	+	0.409561i	$0.865682\pi$
$194$	−7205.06			−2.66646
$195$		0			0
$196$	10188.9			3.71316
$197$	−2533.99	−	2533.99i	−0.916445	−	0.916445i	0.0803240	−	0.996769i	$-0.474404\pi$
$197$	−2533.99	−	2533.99i	−0.916445	−	0.916445i	−0.996769	+	0.0803240i	$0.974404\pi$
$198$		0			0
$199$			5187.90i			1.84804i	0.382340	+	0.924022i	$0.375118\pi$
$199$			5187.90i			1.84804i	−0.382340	+	0.924022i	$0.624882\pi$
$200$	2350.88	+	8147.92i	0.831160	+	2.88073i
$201$		0			0
$202$	3690.08	−	3690.08i	1.28531	−	1.28531i
$203$	−5049.73	+	5049.73i	−1.74592	+	1.74592i
$204$		0			0
$205$	606.804	−	358.107i	0.206737	−	0.122006i
$206$			4505.19i			1.52374i
$207$		0			0
$208$	7385.17	+	7385.17i	2.46187	+	2.46187i
$209$	−285.857			−0.0946084
$210$		0			0
$211$	−327.540			−0.106866			−0.0534331	−	0.998571i	$-0.517016\pi$
$211$	−327.540			−0.106866			−0.0534331	+	0.998571i	$0.517016\pi$
$212$	−3070.45	−	3070.45i	−0.994713	−	0.994713i
$213$		0			0
$214$		−	7591.49i		−	2.42497i
$215$	−492.213	+	1909.72i	−0.156133	+	0.605775i
$216$		0			0
$217$	2559.34	−	2559.34i	0.800643	−	0.800643i
$218$	−36.5845	+	36.5845i	−0.0113661	+	0.0113661i
$219$		0			0
$220$	−1192.77	−	2021.12i	−0.365528	−	0.619380i
$221$		−	2079.64i		−	0.632995i
$222$		0			0
$223$	3604.24	+	3604.24i	1.08232	+	1.08232i	0.996293	+	0.0860278i	$0.0274174\pi$
$223$	3604.24	+	3604.24i	1.08232	+	1.08232i	0.0860278	+	0.996293i	$0.472583\pi$
$224$	14944.6			4.45772
$225$		0			0
$226$	−8562.63			−2.52025
$227$	−2208.02	−	2208.02i	−0.645602	−	0.645602i	0.306325	−	0.951927i	$-0.400900\pi$
$227$	−2208.02	−	2208.02i	−0.645602	−	0.645602i	−0.951927	+	0.306325i	$0.900900\pi$
$228$		0			0
$229$			1262.63i			0.364353i	0.983266	+	0.182177i	$0.0583143\pi$
$229$			1262.63i			0.364353i	−0.983266	+	0.182177i	$0.941686\pi$
$230$	−1015.76	−	1721.18i	−0.291205	−	0.493441i
$231$		0			0
$232$	−11849.1	+	11849.1i	−3.35315	+	3.35315i
$233$	3253.94	−	3253.94i	0.914904	−	0.914904i	−0.0817488	−	0.996653i	$-0.526051\pi$
$233$	3253.94	−	3253.94i	0.914904	−	0.914904i	0.996653	+	0.0817488i	$0.0260505\pi$
$234$		0			0
$235$	−282.507	+	1096.09i	−0.0784201	+	0.304259i
$236$		−	4781.33i		−	1.31881i
$237$		0			0
$238$	−4313.58	−	4313.58i	−1.17482	−	1.17482i
$239$	344.652			0.0932791			0.0466396	−	0.998912i	$-0.485149\pi$
$239$	344.652			0.0932791			0.0466396	+	0.998912i	$0.485149\pi$
$240$		0			0
$241$	−258.333			−0.0690485			−0.0345242	−	0.999404i	$-0.510992\pi$
$241$	−258.333			−0.0690485			−0.0345242	+	0.999404i	$0.510992\pi$
$242$	−4648.95	−	4648.95i	−1.23490	−	1.23490i
$243$		0			0
$244$		−	18326.6i		−	4.80835i
$245$	−4746.22	+	2800.99i	−1.23765	+	0.730403i
$246$		0			0
$247$	−1050.48	+	1050.48i	−0.270610	+	0.270610i
$248$	6005.44	−	6005.44i	1.53768	−	1.53768i
$249$		0			0
$250$	−5440.72	−	5137.62i	−1.37640	−	1.29973i
$251$		−	3294.81i		−	0.828553i	−0.910151	−	0.414277i	$-0.864035\pi$
$251$		−	3294.81i		−	0.828553i	0.910151	−	0.414277i	$-0.135965\pi$
$252$		0			0
$253$	239.724	+	239.724i	0.0595705	+	0.0595705i
$254$	6896.68			1.70368
$255$		0			0
$256$	2342.57			0.571918
$257$	−2188.15	−	2188.15i	−0.531101	−	0.531101i	0.389799	−	0.920900i	$-0.372544\pi$
$257$	−2188.15	−	2188.15i	−0.531101	−	0.531101i	−0.920900	+	0.389799i	$0.872544\pi$
$258$		0			0
$259$			3109.05i			0.745896i
$260$	−11810.6	−	3044.07i	−2.81715	−	0.726096i
$261$		0			0
$262$	263.388	−	263.388i	0.0621076	−	0.0621076i
$263$	−2742.43	+	2742.43i	−0.642987	+	0.642987i	−0.951289	−	0.308302i	$-0.900239\pi$
$263$	−2742.43	+	2742.43i	−0.642987	+	0.642987i	0.308302	+	0.951289i	$0.400239\pi$
$264$		0			0
$265$	2274.36	+	586.197i	0.527219	+	0.135886i
$266$			4357.81i			1.00449i
$267$		0			0
$268$	9069.07	+	9069.07i	2.06710	+	2.06710i
$269$	−2147.61			−0.486774			−0.243387	−	0.969929i	$-0.578259\pi$
$269$	−2147.61			−0.486774			−0.243387	+	0.969929i	$0.578259\pi$
$270$		0			0
$271$	−2160.12			−0.484198			−0.242099	−	0.970251i	$-0.577836\pi$
$271$	−2160.12			−0.484198			−0.242099	+	0.970251i	$0.577836\pi$
$272$	−5514.13	−	5514.13i	−1.22920	−	1.22920i
$273$		0			0
$274$			11393.9i			2.51215i
$275$	1111.23	+	613.581i	0.243672	+	0.134547i
$276$		0			0
$277$	3594.16	−	3594.16i	0.779611	−	0.779611i	−0.200154	−	0.979764i	$-0.564144\pi$
$277$	3594.16	−	3594.16i	0.779611	−	0.779611i	0.979764	+	0.200154i	$0.0641442\pi$
$278$	−3573.30	+	3573.30i	−0.770907	+	0.770907i
$279$		0			0
$280$	−18886.4	+	11145.9i	−4.03100	+	2.37890i
$281$			898.372i			0.190720i	0.995443	+	0.0953601i	$0.0304003\pi$
$281$			898.372i			0.190720i	−0.995443	+	0.0953601i	$0.969600\pi$
$282$		0			0
$283$	2274.76	+	2274.76i	0.477811	+	0.477811i	0.904431	−	0.426620i	$-0.140296\pi$
$283$	2274.76	+	2274.76i	0.477811	+	0.477811i	−0.426620	+	0.904431i	$0.640296\pi$
$284$	15088.7			3.15265
$285$		0			0
$286$	2869.67			0.593312
$287$	1288.41	+	1288.41i	0.264990	+	0.264990i
$288$		0			0
$289$		−	3360.24i		−	0.683948i
$290$	3690.52	−	14318.7i	0.747292	−	2.89939i
$291$		0			0
$292$	3849.15	−	3849.15i	0.771419	−	0.771419i
$293$	−1505.74	+	1505.74i	−0.300226	+	0.300226i	−0.841102	−	0.540876i	$-0.818093\pi$
$293$	−1505.74	+	1505.74i	−0.300226	+	0.300226i	0.540876	+	0.841102i	$0.318093\pi$
$294$		0			0
$295$	1314.41	+	2227.25i	0.259417	+	0.439577i
$296$			7295.32i			1.43254i
$297$		0			0
$298$	3094.09	+	3094.09i	0.601462	+	0.601462i
$299$	1761.91			0.340781
$300$		0			0
$301$	−5099.93			−0.976596
$302$	9517.93	+	9517.93i	1.81356	+	1.81356i
$303$		0			0
$304$			5570.67i			1.05099i
$305$	5038.07	+	8536.90i	0.945833	+	1.60269i
$306$		0			0
$307$	5663.48	−	5663.48i	1.05287	−	1.05287i	0.0543513	−	0.998522i	$-0.482691\pi$
$307$	5663.48	−	5663.48i	1.05287	−	1.05287i	0.998522	−	0.0543513i	$-0.0173091\pi$
$308$	4291.36	−	4291.36i	0.793906	−	0.793906i
$309$		0			0
$310$	−1870.46	+	7257.11i	−0.342693	+	1.32960i
$311$		−	7054.95i		−	1.28633i	−0.765726	−	0.643167i	$-0.777620\pi$
$311$		−	7054.95i		−	1.28633i	0.765726	−	0.643167i	$-0.222380\pi$
$312$		0			0
$313$	−573.433	−	573.433i	−0.103554	−	0.103554i	0.653432	−	0.756986i	$-0.273329\pi$
$313$	−573.433	−	573.433i	−0.103554	−	0.103554i	−0.756986	+	0.653432i	$0.773329\pi$
$314$	−18702.5			−3.36128
$315$		0			0
$316$	−18999.5			−3.38229
$317$	−1.62217	−	1.62217i	−0.000287413	−	0.000287413i	0.706963	−	0.707250i	$-0.250065\pi$
$317$	−1.62217	−	1.62217i	−0.000287413	−	0.000287413i	−0.707250	+	0.706963i	$0.750065\pi$
$318$		0			0
$319$			2508.30i			0.440244i
$320$	−11405.2	+	6730.80i	−1.99240	+	1.17582i
$321$		0			0
$322$	3654.53	−	3654.53i	0.632481	−	0.632481i
$323$	784.343	−	784.343i	0.135115	−	0.135115i
$324$		0			0
$325$	6338.44	−	1828.80i	1.08183	−	0.312134i
$326$			16242.8i			2.75953i
$327$		0			0
$328$	3023.22	+	3023.22i	0.508930	+	0.508930i
$329$	−2927.12			−0.490509
$330$		0			0
$331$	−4118.43			−0.683896			−0.341948	−	0.939719i	$-0.611087\pi$
$331$	−4118.43			−0.683896			−0.341948	+	0.939719i	$0.611087\pi$
$332$	8198.74	+	8198.74i	1.35531	+	1.35531i
$333$		0			0
$334$		−	6180.80i		−	1.01257i
$335$	−6717.70	−	1731.43i	−1.09560	−	0.282382i
$336$		0			0
$337$	−431.375	+	431.375i	−0.0697284	+	0.0697284i	−0.741111	−	0.671383i	$-0.765701\pi$
$337$	−431.375	+	431.375i	−0.0697284	+	0.0697284i	0.671383	+	0.741111i	$0.265701\pi$
$338$	2227.42	−	2227.42i	0.358449	−	0.358449i
$339$		0			0
$340$	8818.34	+	2272.85i	1.40659	+	0.362537i
$341$		−	1271.28i		−	0.201887i
$342$		0			0
$343$	−3065.13	−	3065.13i	−0.482512	−	0.482512i
$344$	−11966.9			−1.87561
$345$		0			0
$346$	7257.10			1.12758
$347$	−136.745	−	136.745i	−0.0211553	−	0.0211553i	0.696450	−	0.717605i	$-0.254762\pi$
$347$	−136.745	−	136.745i	−0.0211553	−	0.0211553i	−0.717605	+	0.696450i	$0.754762\pi$
$348$		0			0
$349$		−	5077.68i		−	0.778803i	−0.921068	−	0.389401i	$-0.872682\pi$
$349$		−	5077.68i		−	0.778803i	0.921068	−	0.389401i	$-0.127318\pi$
$350$	9353.87	−	16940.4i	1.42853	−	2.58715i
$351$		0			0
$352$	3711.64	−	3711.64i	0.562020	−	0.562020i
$353$	6459.49	−	6459.49i	0.973949	−	0.973949i	−0.0257198	−	0.999669i	$-0.508188\pi$
$353$	6459.49	−	6459.49i	0.973949	−	0.973949i	0.999669	+	0.0257198i	$0.00818777\pi$
$354$		0			0
$355$	−7028.66	+	4147.98i	−1.05082	+	0.620146i
$356$			28726.7i			4.27672i
$357$		0			0
$358$	−11958.7	−	11958.7i	−1.76547	−	1.76547i
$359$	5112.47			0.751604			0.375802	−	0.926700i	$-0.377367\pi$
$359$	5112.47			0.751604			0.375802	+	0.926700i	$0.377367\pi$
$360$		0			0
$361$	6066.61			0.884475
$362$	−5150.16	−	5150.16i	−0.747752	−	0.747752i
$363$		0			0
$364$		−	31540.3i		−	4.54165i
$365$	−734.863	+	2851.17i	−0.105382	+	0.408868i
$366$		0			0
$367$	−3508.76	+	3508.76i	−0.499063	+	0.499063i	−0.911146	−	0.412083i	$-0.864801\pi$
$367$	−3508.76	+	3508.76i	−0.499063	+	0.499063i	0.412083	+	0.911146i	$0.364801\pi$
$368$	4671.65	−	4671.65i	0.661757	−	0.661757i
$369$		0			0
$370$	−3271.81	−	5544.01i	−0.459712	−	0.778972i
$371$			6073.73i			0.849952i
$372$		0			0
$373$	3084.51	+	3084.51i	0.428177	+	0.428177i	0.888007	−	0.459830i	$-0.152090\pi$
$373$	3084.51	+	3084.51i	0.428177	+	0.428177i	−0.459830	+	0.888007i	$0.652090\pi$
$374$	−2142.64			−0.296239
$375$		0			0
$376$	−6868.43			−0.942053
$377$	9217.66	+	9217.66i	1.25924	+	1.25924i
$378$		0			0
$379$			6031.24i			0.817424i	0.912663	+	0.408712i	$0.134022\pi$
$379$			6031.24i			0.817424i	−0.912663	+	0.408712i	$0.865978\pi$
$380$	−3306.31	−	5602.46i	−0.446342	−	0.756316i
$381$		0			0
$382$	−2903.08	+	2903.08i	−0.388834	+	0.388834i
$383$	534.684	−	534.684i	0.0713344	−	0.0713344i	−0.670539	−	0.741874i	$-0.733937\pi$
$383$	534.684	−	534.684i	0.0713344	−	0.0713344i	0.741874	+	0.670539i	$0.233937\pi$
$384$		0			0
$385$	−819.289	+	3178.73i	−0.108454	+	0.420787i
$386$			10206.9i			1.34590i
$387$		0			0
$388$	19667.7	+	19667.7i	2.57339	+	2.57339i
$389$	14267.3			1.85960			0.929798	−	0.368071i	$-0.119982\pi$
$389$	14267.3			1.85960			0.929798	+	0.368071i	$0.119982\pi$
$390$		0			0
$391$	−1315.52			−0.170151
$392$	−23646.6	−	23646.6i	−3.04677	−	3.04677i
$393$		0			0
$394$			19188.3i			2.45353i
$395$	8850.37	−	5223.07i	1.12737	−	0.665319i
$396$		0			0
$397$	−1436.61	+	1436.61i	−0.181615	+	0.181615i	−0.792059	−	0.610444i	$-0.790991\pi$
$397$	−1436.61	+	1436.61i	−0.181615	+	0.181615i	0.610444	+	0.792059i	$0.290991\pi$
$398$	19642.3	−	19642.3i	2.47382	−	2.47382i
$399$		0			0
$400$	11957.2	−	21655.2i	1.49465	−	2.70691i
$401$		−	9080.34i		−	1.13080i	−0.824817	−	0.565400i	$-0.808722\pi$
$401$		−	9080.34i		−	1.13080i	0.824817	−	0.565400i	$-0.191278\pi$
$402$		0			0
$403$	−4671.76	−	4671.76i	−0.577461	−	0.577461i
$404$	−20145.6			−2.48090
$405$		0			0
$406$	38238.3			4.67423
$407$	772.164	+	772.164i	0.0940411	+	0.0940411i
$408$		0			0
$409$			1114.46i			0.134734i	0.997728	+	0.0673671i	$0.0214599\pi$
$409$			1114.46i			0.134734i	−0.997728	+	0.0673671i	$0.978540\pi$
$410$	−3653.32	−	941.612i	−0.440060	−	0.113422i
$411$		0			0
$412$	12297.8	−	12297.8i	1.47056	−	1.47056i
$413$	−4729.03	+	4729.03i	−0.563440	+	0.563440i
$414$		0			0
$415$	−6073.03	−	1565.27i	−0.718345	−	0.185147i
$416$		−	27279.5i		−	3.21512i
$417$		0			0
$418$	1082.30	+	1082.30i	0.126644	+	0.126644i
$419$	7176.27			0.836716			0.418358	−	0.908282i	$-0.362606\pi$
$419$	7176.27			0.836716			0.418358	+	0.908282i	$0.362606\pi$
$420$		0			0
$421$	12755.1			1.47659			0.738294	−	0.674479i	$-0.235632\pi$
$421$	12755.1			1.47659			0.738294	+	0.674479i	$0.235632\pi$
$422$	1240.12	+	1240.12i	0.143053	+	0.143053i
$423$		0			0
$424$			14251.9i			1.63239i
$425$	−4732.59	+	1365.47i	−0.540152	+	0.155847i
$426$		0			0
$427$	−18126.1	+	18126.1i	−2.05429	+	2.05429i
$428$	−20722.5	+	20722.5i	−2.34033	+	2.34033i
$429$		0			0
$430$	9094.13	−	5366.92i	1.01990	−	0.601897i
$431$		−	16292.2i		−	1.82081i	−0.413722	−	0.910403i	$-0.635771\pi$
$431$		−	16292.2i		−	1.82081i	0.413722	−	0.910403i	$-0.364229\pi$
$432$		0			0
$433$	−2314.16	−	2314.16i	−0.256840	−	0.256840i	0.566928	−	0.823767i	$-0.308132\pi$
$433$	−2314.16	−	2314.16i	−0.256840	−	0.256840i	−0.823767	+	0.566928i	$0.808132\pi$
$434$	−19380.2			−2.14350
$435$		0			0
$436$	199.729			0.0219387
$437$	664.507	+	664.507i	0.0727407	+	0.0727407i
$438$		0			0
$439$		−	13009.8i		−	1.41440i	−0.707012	−	0.707201i	$-0.749958\pi$
$439$		−	13009.8i		−	1.41440i	0.707012	−	0.707201i	$-0.250042\pi$
$440$	−1922.44	+	7458.82i	−0.208293	+	0.808148i
$441$		0			0
$442$	−7873.89	+	7873.89i	−0.847337	+	0.847337i
$443$	1676.93	−	1676.93i	0.179850	−	0.179850i	−0.611441	−	0.791290i	$-0.709410\pi$
$443$	1676.93	−	1676.93i	0.179850	−	0.179850i	0.791290	+	0.611441i	$0.209410\pi$
$444$		0			0
$445$	−7897.13	−	13381.5i	−0.841258	−	1.42549i
$446$		−	27292.5i		−	2.89762i
$447$		0			0
$448$	−24216.2	−	24216.2i	−2.55382	−	2.55382i
$449$	5946.29			0.624995			0.312497	−	0.949919i	$-0.398834\pi$
$449$	5946.29			0.624995			0.312497	+	0.949919i	$0.398834\pi$
$450$		0			0
$451$	639.977			0.0668189
$452$	23373.4	+	23373.4i	2.43228	+	2.43228i
$453$		0			0
$454$			16719.9i			1.72842i
$455$	8670.61	+	14692.2i	0.893372	+	1.51380i
$456$		0			0
$457$	10976.0	−	10976.0i	1.12349	−	1.12349i	0.132275	−	0.991213i	$-0.457772\pi$
$457$	10976.0	−	10976.0i	1.12349	−	1.12349i	0.991213	−	0.132275i	$-0.0422282\pi$
$458$	4780.54	−	4780.54i	0.487729	−	0.487729i
$459$		0			0
$460$	−1925.59	+	7471.03i	−0.195177	+	0.757258i
$461$			10224.1i			1.03294i	0.856305	+	0.516470i	$0.172754\pi$
$461$			10224.1i			1.03294i	−0.856305	+	0.516470i	$0.827246\pi$
$462$		0			0
$463$	−6754.83	−	6754.83i	−0.678020	−	0.678020i	0.281532	−	0.959552i	$-0.409158\pi$
$463$	−6754.83	−	6754.83i	−0.678020	−	0.678020i	−0.959552	+	0.281532i	$0.909158\pi$
$464$	48880.8			4.89059
$465$		0			0
$466$	−24640.0			−2.44941
$467$	−12272.2	−	12272.2i	−1.21604	−	1.21604i	−0.969009	−	0.247027i	$-0.920546\pi$
$467$	−12272.2	−	12272.2i	−1.21604	−	1.21604i	−0.247027	−	0.969009i	$-0.579454\pi$
$468$		0			0
$469$		−	17939.7i		−	1.76627i
$470$	5219.60	−	3080.36i	0.512260	−	0.302312i
$471$		0			0
$472$	−11096.6	+	11096.6i	−1.08212	+	1.08212i
$473$	−1266.62	+	1266.62i	−0.123127	+	0.123127i
$474$		0			0
$475$	3080.30	+	1700.82i	0.297545	+	0.164293i
$476$			23549.5i			2.26763i
$477$		0			0
$478$	−1304.91	−	1304.91i	−0.124865	−	0.124865i
$479$	−1290.56			−0.123105			−0.0615524	−	0.998104i	$-0.519605\pi$
$479$	−1290.56			−0.123105			−0.0615524	+	0.998104i	$0.519605\pi$
$480$		0			0
$481$	5675.18			0.537975
$482$	978.094	+	978.094i	0.0924293	+	0.0924293i
$483$		0			0
$484$			25380.5i			2.38359i
$485$	−14568.4	−	3754.87i	−1.36395	−	0.351546i
$486$		0			0
$487$	−3079.92	+	3079.92i	−0.286580	+	0.286580i	−0.835726	−	0.549146i	$-0.814953\pi$
$487$	−3079.92	+	3079.92i	−0.286580	+	0.286580i	0.549146	+	0.835726i	$0.314953\pi$
$488$	−42532.5	+	42532.5i	−3.94540	+	3.94540i
$489$		0			0
$490$	28575.1	+	7364.97i	2.63447	+	0.679011i
$491$		−	316.594i		−	0.0290992i	−0.999894	−	0.0145496i	$-0.995369\pi$
$491$		−	316.594i		−	0.0290992i	0.999894	−	0.0145496i	$-0.00463144\pi$
$492$		0			0
$493$	−6882.35	−	6882.35i	−0.628733	−	0.628733i
$494$	7954.63			0.724486
$495$		0			0
$496$	−24774.1			−2.24272
$497$	−14923.7	−	14923.7i	−1.34692	−	1.34692i
$498$		0			0
$499$		−	546.747i		−	0.0490496i	−0.999699	−	0.0245248i	$-0.992193\pi$
$499$		−	546.747i		−	0.0490496i	0.999699	−	0.0245248i	$-0.00780727\pi$
$500$	827.366	+	28875.7i	0.0740018	+	2.58272i
$501$		0			0
$502$	−12474.7	+	12474.7i	−1.10911	+	1.10911i
$503$	−11182.9	+	11182.9i	−0.991292	+	0.991292i	−0.999962	−	0.00867044i	$-0.997240\pi$
$503$	−11182.9	+	11182.9i	−0.991292	+	0.991292i	0.00867044	+	0.999962i	$0.497240\pi$
$504$		0			0
$505$	9384.26	−	5538.14i	0.826919	−	0.488008i
$506$		−	1815.28i		−	0.159484i
$507$		0			0
$508$	−18825.9	−	18825.9i	−1.64422	−	1.64422i
$509$	5644.09			0.491493			0.245747	−	0.969334i	$-0.420967\pi$
$509$	5644.09			0.491493			0.245747	+	0.969334i	$0.420967\pi$
$510$		0			0
$511$	−7614.09			−0.659154
$512$	3616.69	+	3616.69i	0.312181	+	0.312181i
$513$		0			0
$514$			16569.4i			1.42188i
$515$	−2347.85	+	9109.32i	−0.200890	+	0.779426i
$516$		0			0
$517$	−726.980	+	726.980i	−0.0618424	+	0.0618424i
$518$	11771.4	−	11771.4i	0.998467	−	0.998467i
$519$		0			0
$520$	20345.4	+	34474.8i	1.71578	+	2.90735i
$521$			7812.01i			0.656911i	0.944520	+	0.328455i	$0.106528\pi$
$521$			7812.01i			0.656911i	−0.944520	+	0.328455i	$0.893472\pi$
$522$		0			0
$523$	9750.12	+	9750.12i	0.815187	+	0.815187i	0.985406	−	0.170219i	$-0.0544476\pi$
$523$	9750.12	+	9750.12i	0.815187	+	0.815187i	−0.170219	+	0.985406i	$0.554448\pi$
$524$	−1437.94			−0.119879
$525$		0			0
$526$	20766.7			1.72142
$527$	3488.16	+	3488.16i	0.288324	+	0.288324i
$528$		0			0
$529$			11052.5i			0.908397i
$530$	−6391.69	−	10830.6i	−0.523844	−	0.887642i
$531$		0			0
$532$	11895.5	−	11895.5i	0.969428	−	0.969428i
$533$	2351.82	−	2351.82i	0.191123	−	0.191123i
$534$		0			0
$535$	3956.25	−	15349.7i	0.319708	−	1.24042i
$536$		−	42095.2i		−	3.39223i
$537$		0			0
$538$	8131.24	+	8131.24i	0.651603	+	0.651603i
$539$	−5005.68			−0.400019
$540$		0			0
$541$	−17446.9			−1.38650			−0.693252	−	0.720695i	$-0.743823\pi$
$541$	−17446.9			−1.38650			−0.693252	+	0.720695i	$0.743823\pi$
$542$	8178.58	+	8178.58i	0.648155	+	0.648155i
$543$		0			0
$544$			20368.2i			1.60529i
$545$	−93.0381	+	54.9067i	−0.00731251	+	0.00431549i
$546$		0			0
$547$	−6786.43	+	6786.43i	−0.530470	+	0.530470i	−0.920712	−	0.390242i	$-0.872391\pi$
$547$	−6786.43	+	6786.43i	−0.530470	+	0.530470i	0.390242	+	0.920712i	$0.372391\pi$
$548$	31101.8	−	31101.8i	2.42446	−	2.42446i
$549$		0			0
$550$	−1884.19	−	6530.44i	−0.146077	−	0.506289i
$551$			6952.92i			0.537576i
$552$		0			0
$553$	18791.7	+	18791.7i	1.44503	+	1.44503i
$554$	−27216.2			−2.08720
$555$		0			0
$556$	19508.1			1.48800
$557$	−2894.26	−	2894.26i	−0.220169	−	0.220169i	0.588401	−	0.808569i	$-0.299758\pi$
$557$	−2894.26	−	2894.26i	−0.220169	−	0.220169i	−0.808569	+	0.588401i	$0.799758\pi$
$558$		0			0
$559$			9309.29i			0.704367i
$560$	61945.8	+	15966.0i	4.67444	+	1.20480i
$561$		0			0
$562$	3401.39	−	3401.39i	0.255301	−	0.255301i
$563$	−15586.9	+	15586.9i	−1.16680	+	1.16680i	−0.183844	+	0.982955i	$0.558854\pi$
$563$	−15586.9	+	15586.9i	−1.16680	+	1.16680i	−0.982955	+	0.183844i	$0.941146\pi$
$564$		0			0
$565$	−17313.3	−	4462.35i	−1.28916	−	0.332270i
$566$		−	17225.3i		−	1.27921i
$567$		0			0
$568$	−35018.1	−	35018.1i	−2.58685	−	2.58685i
$569$	8467.77			0.623880			0.311940	−	0.950102i	$-0.399021\pi$
$569$	8467.77			0.623880			0.311940	+	0.950102i	$0.399021\pi$
$570$		0			0
$571$	856.979			0.0628081			0.0314041	−	0.999507i	$-0.490002\pi$
$571$	856.979			0.0628081			0.0314041	+	0.999507i	$0.490002\pi$
$572$	−7833.35	−	7833.35i	−0.572603	−	0.572603i
$573$		0			0
$574$		−	9756.26i		−	0.709440i
$575$	−1156.85	−	4009.52i	−0.0839023	−	0.290798i
$576$		0			0
$577$	−10900.1	+	10900.1i	−0.786446	+	0.786446i	−0.980910	−	0.194464i	$-0.937703\pi$
$577$	−10900.1	+	10900.1i	−0.786446	+	0.786446i	0.194464	+	0.980910i	$0.437703\pi$
$578$	−12722.4	+	12722.4i	−0.915543	+	0.915543i
$579$		0			0
$580$	−49159.8	+	29011.7i	−3.51939	+	2.07698i
$581$		−	16218.1i		−	1.15808i
$582$		0			0
$583$	1508.47	+	1508.47i	0.107160	+	0.107160i
$584$	−17866.3			−1.26595
$585$		0			0
$586$	11402.0			0.803774
$587$	−15691.7	−	15691.7i	−1.10335	−	1.10335i	−0.994004	−	0.109341i	$-0.965126\pi$
$587$	−15691.7	−	15691.7i	−1.10335	−	1.10335i	−0.109341	−	0.994004i	$-0.534874\pi$
$588$		0			0
$589$		−	3523.93i		−	0.246521i
$590$	3456.14	−	13409.3i	0.241165	−	0.935685i
$591$		0			0
$592$	15047.6	−	15047.6i	1.04468	−	1.04468i
$593$	−10530.3	+	10530.3i	−0.729217	+	0.729217i	−0.970464	−	0.241247i	$-0.922444\pi$
$593$	−10530.3	+	10530.3i	−0.729217	+	0.729217i	0.241247	+	0.970464i	$0.422444\pi$
$594$		0			0
$595$	−6473.90	−	10969.9i	−0.446057	−	0.755834i
$596$		−	16891.9i		−	1.16094i
$597$		0			0
$598$	−6670.88	−	6670.88i	−0.456175	−	0.456175i
$599$	−21508.5			−1.46714			−0.733568	−	0.679616i	$-0.762146\pi$
$599$	−21508.5			−1.46714			−0.733568	+	0.679616i	$0.762146\pi$
$600$		0			0
$601$	10931.5			0.741939			0.370969	−	0.928645i	$-0.379025\pi$
$601$	10931.5			0.741939			0.370969	+	0.928645i	$0.379025\pi$
$602$	19309.2	+	19309.2i	1.30729	+	1.30729i
$603$		0			0
$604$		−	51962.2i		−	3.50051i
$605$	−6977.24	−	11822.8i	−0.468868	−	0.794486i
$606$		0			0
$607$	8691.67	−	8691.67i	0.581193	−	0.581193i	−0.354038	−	0.935231i	$-0.615192\pi$
$607$	8691.67	−	8691.67i	0.581193	−	0.581193i	0.935231	+	0.354038i	$0.115192\pi$
$608$	10288.5	−	10288.5i	0.686275	−	0.686275i
$609$		0			0
$610$	13247.2	−	51397.2i	0.879283	−	3.41150i
$611$			5343.10i			0.353778i
$612$		0			0
$613$	−8301.57	−	8301.57i	−0.546978	−	0.546978i	0.378588	−	0.925565i	$-0.376410\pi$
$613$	−8301.57	−	8301.57i	−0.546978	−	0.546978i	−0.925565	+	0.378588i	$0.876410\pi$
$614$	−42885.9			−2.81878
$615$		0			0
$616$	−19918.9			−1.30285
$617$	−18758.4	−	18758.4i	−1.22396	−	1.22396i	−0.966211	−	0.257751i	$-0.917019\pi$
$617$	−18758.4	−	18758.4i	−1.22396	−	1.22396i	−0.257751	−	0.966211i	$-0.582981\pi$
$618$		0			0
$619$		−	1353.19i		−	0.0878662i	−0.999034	−	0.0439331i	$-0.986011\pi$
$619$		−	1353.19i		−	0.0878662i	0.999034	−	0.0439331i	$-0.0139888\pi$
$620$	24915.5	−	14703.9i	1.61392	−	0.952459i
$621$		0			0
$622$	−26711.3	+	26711.3i	−1.72190	+	1.72190i
$623$	28412.5	−	28412.5i	1.82716	−	1.82716i
$624$		0			0
$625$	−8323.49	−	13223.5i	−0.532704	−	0.846302i
$626$			4342.24i			0.277238i
$627$		0			0
$628$	51052.1	+	51052.1i	3.24395	+	3.24395i
$629$	−4237.37			−0.268609
$630$		0			0
$631$	16226.2			1.02370			0.511850	−	0.859075i	$-0.328960\pi$
$631$	16226.2			1.02370			0.511850	+	0.859075i	$0.328960\pi$
$632$	44094.3	+	44094.3i	2.77528	+	2.77528i
$633$		0			0
$634$			12.2836i			0.000769471i
$635$	13944.8	+	3594.15i	0.871470	+	0.224614i
$636$		0			0
$637$	−18395.2	+	18395.2i	−1.14418	+	1.14418i
$638$	9496.87	−	9496.87i	0.589318	−	0.589318i
$639$		0			0
$640$	23896.8	+	6159.19i	1.47594	+	0.380412i
$641$			24947.0i			1.53720i	0.639729	+	0.768600i	$0.279047\pi$
$641$			24947.0i			1.53720i	−0.639729	+	0.768600i	$0.720953\pi$
$642$		0			0
$643$	12652.5	+	12652.5i	0.775996	+	0.775996i	0.979147	−	0.203151i	$-0.0651183\pi$
$643$	12652.5	+	12652.5i	0.775996	+	0.775996i	−0.203151	+	0.979147i	$0.565118\pi$
$644$	−19951.5			−1.22081
$645$		0			0
$646$	−5939.32			−0.361733
$647$	11588.5	+	11588.5i	0.704162	+	0.704162i	0.965301	−	0.261139i	$-0.0840981\pi$
$647$	11588.5	+	11588.5i	0.704162	+	0.704162i	−0.261139	+	0.965301i	$0.584098\pi$
$648$		0			0
$649$			2349.00i			0.142075i
$650$	−30922.6	−	17074.3i	−1.86598	−	1.03032i
$651$		0			0
$652$	44338.0	−	44338.0i	2.66321	−	2.66321i
$653$	204.573	−	204.573i	0.0122597	−	0.0122597i	−0.700950	−	0.713210i	$-0.747241\pi$
$653$	204.573	−	204.573i	0.0122597	−	0.0122597i	0.713210	+	0.700950i	$0.247241\pi$
$654$		0			0
$655$	669.825	−	395.298i	0.0399576	−	0.0235811i
$656$		−	12471.6i		−	0.742279i
$657$		0			0
$658$	11082.6	+	11082.6i	0.656603	+	0.656603i
$659$	11765.7			0.695491			0.347745	−	0.937589i	$-0.386947\pi$
$659$	11765.7			0.695491			0.347745	+	0.937589i	$0.386947\pi$
$660$		0			0
$661$	16079.0			0.946144			0.473072	−	0.881024i	$-0.343145\pi$
$661$	16079.0			0.946144			0.473072	+	0.881024i	$0.343145\pi$
$662$	15593.1	+	15593.1i	0.915473	+	0.915473i
$663$		0			0
$664$		−	38055.5i		−	2.22416i
$665$	−2271.04	+	8811.33i	−0.132432	+	0.513817i
$666$		0			0
$667$	5830.83	−	5830.83i	0.338487	−	0.338487i
$668$	−16871.7	+	16871.7i	−0.977226	+	0.977226i
$669$		0			0
$670$	18878.9	+	31989.9i	1.08859	+	1.84459i
$671$			9003.59i			0.518003i
$672$		0			0
$673$	13328.5	+	13328.5i	0.763414	+	0.763414i	0.976938	−	0.213524i	$-0.0684941\pi$
$673$	13328.5	+	13328.5i	0.763414	+	0.763414i	−0.213524	+	0.976938i	$0.568494\pi$
$674$	3266.52			0.186679
$675$		0			0
$676$	−12160.4			−0.691874
$677$	14255.7	+	14255.7i	0.809295	+	0.809295i	0.984527	−	0.175232i	$-0.0560677\pi$
$677$	14255.7	+	14255.7i	0.809295	+	0.809295i	−0.175232	+	0.984527i	$0.556068\pi$
$678$		0			0
$679$		−	38905.1i		−	2.19888i
$680$	−15190.9	−	25740.6i	−0.856681	−	1.45163i
$681$		0			0
$682$	−4813.27	+	4813.27i	−0.270249	+	0.270249i
$683$	5144.86	−	5144.86i	0.288232	−	0.288232i	−0.548149	−	0.836381i	$-0.684667\pi$
$683$	5144.86	−	5144.86i	0.288232	−	0.288232i	0.836381	+	0.548149i	$0.184667\pi$
$684$		0			0
$685$	−5937.83	+	23037.9i	−0.331201	+	1.28501i
$686$			23210.3i			1.29180i
$687$		0			0
$688$	24683.4	+	24683.4i	1.36780	+	1.36780i
$689$	11086.8			0.613026
$690$		0			0
$691$	23827.2			1.31176			0.655882	−	0.754864i	$-0.272297\pi$
$691$	23827.2			1.31176			0.655882	+	0.754864i	$0.272297\pi$
$692$	−19809.7	−	19809.7i	−1.08823	−	1.08823i
$693$		0			0
$694$			1035.48i			0.0566375i
$695$	−9087.27	+	5362.87i	−0.495971	+	0.292698i
$696$		0			0
$697$	−1755.99	+	1755.99i	−0.0954272	+	0.0954272i
$698$	−19225.0	+	19225.0i	−1.04252	+	1.04252i
$699$		0			0
$700$	−71775.5	+	20709.0i	−3.87551	+	1.11818i
$701$		−	10688.6i		−	0.575896i	−0.957646	−	0.287948i	$-0.907027\pi$
$701$		−	10688.6i		−	0.575896i	0.957646	−	0.287948i	$-0.0929731\pi$
$702$		0			0
$703$	2140.41	+	2140.41i	0.114832	+	0.114832i
$704$	−12028.7			−0.643960
$705$		0			0
$706$	−48913.5			−2.60749
$707$	19925.3	+	19925.3i	1.05992	+	1.05992i
$708$		0			0
$709$		−	2343.05i		−	0.124112i	−0.998073	−	0.0620558i	$-0.980234\pi$
$709$		−	2343.05i		−	0.124112i	0.998073	−	0.0620558i	$-0.0197657\pi$
$710$	42316.7	+	10906.8i	2.23679	+	0.576512i
$711$		0			0
$712$	66669.3	−	66669.3i	3.50918	−	3.50918i
$713$	−2955.23	+	2955.23i	−0.155223	+	0.155223i
$714$		0			0
$715$	5802.37	+	1495.51i	0.303492	+	0.0782223i
$716$			65287.4i			3.40769i
$717$		0			0
$718$	−19356.7	−	19356.7i	−1.00611	−	1.00611i
$719$	−29082.3			−1.50847			−0.754234	−	0.656606i	$-0.771991\pi$
$719$	−29082.3			−1.50847			−0.754234	+	0.656606i	$0.771991\pi$
$720$		0			0
$721$	−24326.6			−1.25655
$722$	−22969.3	−	22969.3i	−1.18397	−	1.18397i
$723$		0			0
$724$			28116.8i			1.44330i
$725$	14924.2	−	27028.6i	0.764511	−	1.38457i
$726$		0			0
$727$	−16125.8	+	16125.8i	−0.822658	+	0.822658i	−0.986489	−	0.163830i	$-0.947615\pi$
$727$	−16125.8	+	16125.8i	−0.822658	+	0.822658i	0.163830	+	0.986489i	$0.447615\pi$
$728$	−73199.1	+	73199.1i	−3.72657	+	3.72657i
$729$		0			0
$730$	13577.3	−	8012.70i	0.688383	−	0.406251i
$731$		−	6950.77i		−	0.351688i
$732$		0			0
$733$	−18975.4	−	18975.4i	−0.956171	−	0.956171i	0.0429085	−	0.999079i	$-0.486338\pi$
$733$	−18975.4	−	18975.4i	−0.956171	−	0.956171i	−0.999079	+	0.0429085i	$0.986338\pi$
$734$	26569.6			1.33611
$735$		0			0
$736$	−17256.3			−0.864232
$737$	−4455.51	−	4455.51i	−0.222688	−	0.222688i
$738$		0			0
$739$			21228.6i			1.05671i	0.849024	+	0.528354i	$0.177190\pi$
$739$			21228.6i			1.05671i	−0.849024	+	0.528354i	$0.822810\pi$
$740$	−6202.43	+	24064.6i	−0.308116	+	1.19545i
$741$		0			0
$742$	22996.2	−	22996.2i	1.13776	−	1.13776i
$743$	4049.21	−	4049.21i	0.199934	−	0.199934i	−0.600038	−	0.799972i	$-0.704848\pi$
$743$	4049.21	−	4049.21i	0.199934	−	0.199934i	0.799972	+	0.600038i	$0.204848\pi$
$744$		0			0
$745$	4643.67	+	7868.59i	0.228363	+	0.386957i
$746$		−	23357.0i		−	1.14633i
$747$		0			0
$748$	5848.76	+	5848.76i	0.285898	+	0.285898i
$749$	40991.7			1.99974
$750$		0			0
$751$	32593.6			1.58370			0.791849	−	0.610716i	$-0.209118\pi$
$751$	32593.6			1.58370			0.791849	+	0.610716i	$0.209118\pi$
$752$	14167.1	+	14167.1i	0.686996	+	0.686996i
$753$		0			0
$754$		−	69799.3i		−	3.37127i
$755$	14284.7	+	24205.1i	0.688574	+	1.16677i
$756$		0			0
$757$	−8386.27	+	8386.27i	−0.402648	+	0.402648i	−0.879165	−	0.476517i	$-0.841899\pi$
$757$	−8386.27	+	8386.27i	−0.402648	+	0.402648i	0.476517	+	0.879165i	$0.341899\pi$
$758$	22835.3	−	22835.3i	1.09422	−	1.09422i
$759$		0			0
$760$	−5328.95	+	20675.6i	−0.254344	+	0.986818i
$761$		−	25999.1i		−	1.23846i	−0.785211	−	0.619229i	$-0.787445\pi$
$761$		−	25999.1i		−	1.23846i	0.785211	−	0.619229i	$-0.212555\pi$
$762$		0			0
$763$	−197.545	−	197.545i	−0.00937300	−	0.00937300i
$764$	15849.1			0.750523
$765$		0			0
$766$	−4048.82			−0.190979
$767$	8632.26	+	8632.26i	0.406379	+	0.406379i
$768$		0			0
$769$			7248.73i			0.339917i	0.985451	+	0.169958i	$0.0543633\pi$
$769$			7248.73i			0.339917i	−0.985451	+	0.169958i	$0.945637\pi$
$770$	15137.2	−	8933.25i	0.708450	−	0.418094i
$771$		0			0
$772$	27861.8	−	27861.8i	1.29892	−	1.29892i
$773$	−3230.09	+	3230.09i	−0.150296	+	0.150296i	−0.778250	−	0.627955i	$-0.783892\pi$
$773$	−3230.09	+	3230.09i	−0.150296	+	0.150296i	0.627955	+	0.778250i	$0.283892\pi$
$774$		0			0
$775$	−7563.98	+	13698.8i	−0.350589	+	0.634937i
$776$		−	91289.9i		−	4.22309i
$777$		0			0
$778$	−54018.6	−	54018.6i	−2.48928	−	2.48928i
$779$	1773.99			0.0815917
$780$		0			0
$781$	−7412.90			−0.339634
$782$	4980.81	+	4980.81i	0.227766	+	0.227766i
$783$		0			0
$784$			97548.8i			4.44373i
$785$	−37815.7	−	9746.66i	−1.71936	−	0.443150i
$786$		0			0
$787$	−1331.78	+	1331.78i	−0.0603213	+	0.0603213i	−0.736624	−	0.676303i	$-0.763581\pi$
$787$	−1331.78	+	1331.78i	−0.0603213	+	0.0603213i	0.676303	+	0.736624i	$0.263581\pi$
$788$	52378.3	−	52378.3i	2.36789	−	2.36789i
$789$		0			0
$790$	−53284.5	−	13733.6i	−2.39972	−	0.618506i
$791$		−	46235.5i		−	2.07831i
$792$		0			0
$793$	33086.9	+	33086.9i	1.48165	+	1.48165i
$794$	10878.5			0.486226
$795$		0			0
$796$	−107235.			−4.77494
$797$	16069.0	+	16069.0i	0.714168	+	0.714168i	0.967404	−	0.253236i	$-0.0814950\pi$
$797$	16069.0	+	16069.0i	0.714168	+	0.714168i	−0.253236	+	0.967404i	$0.581495\pi$
$798$		0			0
$799$		−	3989.42i		−	0.176640i
$800$	−62079.3	+	17911.4i	−2.74354	+	0.791580i
$801$		0			0
$802$	−34379.8	+	34379.8i	−1.51371	+	1.51371i
$803$	−1891.04	+	1891.04i	−0.0831048	+	0.0831048i
$804$		0			0
$805$	9293.85	−	5484.79i	0.406913	−	0.240141i
$806$			35376.2i			1.54600i
$807$		0			0
$808$	46754.2	+	46754.2i	2.03565	+	2.03565i
$809$	−2050.85			−0.0891273			−0.0445637	−	0.999007i	$-0.514190\pi$
$809$	−2050.85			−0.0891273			−0.0445637	+	0.999007i	$0.514190\pi$
$810$		0			0
$811$	9209.80			0.398767			0.199383	−	0.979922i	$-0.436106\pi$
$811$	9209.80			0.398767			0.199383	+	0.979922i	$0.436106\pi$
$812$	−104379.	−	104379.i	−4.51107	−	4.51107i
$813$		0			0
$814$		−	5847.09i		−	0.251770i
$815$	−8464.84	+	32842.4i	−0.363816	+	1.41156i
$816$		0			0
$817$	−3511.02	+	3511.02i	−0.150349	+	0.150349i
$818$	4219.53	−	4219.53i	0.180357	−	0.180357i
$819$		0			0
$820$	7402.16	+	12542.8i	0.315237	+	0.534162i
$821$			41268.0i			1.75428i	0.480234	+	0.877141i	$0.340552\pi$
$821$			41268.0i			1.75428i	−0.480234	+	0.877141i	$0.659448\pi$
$822$		0			0
$823$	25253.2	+	25253.2i	1.06959	+	1.06959i	0.997390	+	0.0721962i	$0.0230008\pi$
$823$	25253.2	+	25253.2i	1.06959	+	1.06959i	0.0721962	+	0.997390i	$0.476999\pi$
$824$	−57081.8			−2.41328
$825$		0			0
$826$	35809.9			1.50846
$827$	−25655.4	−	25655.4i	−1.07875	−	1.07875i	−0.996622	−	0.0821261i	$-0.973829\pi$
$827$	−25655.4	−	25655.4i	−1.07875	−	1.07875i	−0.0821261	−	0.996622i	$-0.526171\pi$
$828$		0			0
$829$		−	20318.4i		−	0.851253i	−0.904899	−	0.425626i	$-0.860054\pi$
$829$		−	20318.4i		−	0.851253i	0.904899	−	0.425626i	$-0.139946\pi$
$830$	17067.2	+	28919.9i	0.713747	+	1.20943i
$831$		0			0
$832$	−44203.7	+	44203.7i	−1.84193	+	1.84193i
$833$	13734.7	−	13734.7i	0.571285	−	0.571285i
$834$		0			0
$835$	3221.08	−	12497.4i	0.133497	−	0.517951i
$836$		−	5908.73i		−	0.244447i
$837$		0			0
$838$	−27170.6	−	27170.6i	−1.12004	−	1.12004i
$839$	29925.6			1.23140			0.615701	−	0.787980i	$-0.288873\pi$
$839$	29925.6			1.23140			0.615701	+	0.787980i	$0.288873\pi$
$840$		0			0
$841$	36620.6			1.50152
$842$	−48292.9	−	48292.9i	−1.97658	−	1.97658i
$843$		0			0
$844$		−	6770.33i		−	0.276119i
$845$	5664.56	−	3342.95i	0.230612	−	0.136096i
$846$		0			0
$847$	25102.9	−	25102.9i	1.01835	−	1.01835i
$848$	29396.5	−	29396.5i	1.19042	−	1.19042i
$849$		0			0
$850$	23088.3	+	12748.5i	0.931674	+	0.514436i
$851$		−	3589.96i		−	0.144609i
$852$		0			0
$853$	1868.97	+	1868.97i	0.0750202	+	0.0750202i	0.743621	−	0.668601i	$-0.233107\pi$
$853$	1868.97	+	1868.97i	0.0750202	+	0.0750202i	−0.668601	+	0.743621i	$0.733107\pi$
$854$	137257.			5.49982
$855$		0			0
$856$	96186.0			3.84062
$857$	18501.3	+	18501.3i	0.737446	+	0.737446i	0.972083	−	0.234637i	$-0.0753903\pi$
$857$	18501.3	+	18501.3i	0.737446	+	0.737446i	−0.234637	+	0.972083i	$0.575390\pi$
$858$		0			0
$859$		−	3849.58i		−	0.152906i	−0.997073	−	0.0764529i	$-0.975641\pi$
$859$		−	3849.58i		−	0.152906i	0.997073	−	0.0764529i	$-0.0243595\pi$
$860$	−39474.3	−	10174.2i	−1.56519	−	0.403414i
$861$		0			0
$862$	−61685.1	+	61685.1i	−2.43736	+	2.43736i
$863$	18649.4	−	18649.4i	0.735613	−	0.735613i	−0.236113	−	0.971726i	$-0.575874\pi$
$863$	18649.4	−	18649.4i	0.735613	−	0.735613i	0.971726	+	0.236113i	$0.0758736\pi$
$864$		0			0
$865$	14673.6	+	3781.99i	0.576783	+	0.148661i
$866$			17523.7i			0.687619i
$867$		0			0
$868$	52902.2	+	52902.2i	2.06868	+	2.06868i
$869$	9334.20			0.364374
$870$		0			0
$871$	−32746.8			−1.27392
$872$	−463.534	−	463.534i	−0.0180014	−	0.0180014i
$873$		0			0
$874$		−	5031.88i		−	0.194744i
$875$	27741.5	−	29378.2i	1.07181	−	1.13504i
$876$		0			0
$877$	−15382.2	+	15382.2i	−0.592269	+	0.592269i	−0.938244	−	0.345974i	$-0.887548\pi$
$877$	−15382.2	+	15382.2i	−0.592269	+	0.592269i	0.345974	+	0.938244i	$0.387548\pi$
$878$	−49257.3	+	49257.3i	−1.89334	+	1.89334i
$879$		0			0
$880$	19350.2	−	11419.5i	0.741243	−	0.437446i
$881$			49097.1i			1.87755i	0.344527	+	0.938776i	$0.388039\pi$
$881$			49097.1i			1.87755i	−0.344527	+	0.938776i	$0.611961\pi$
$882$		0			0
$883$	−27399.0	−	27399.0i	−1.04422	−	1.04422i	−0.998976	−	0.0452491i	$-0.985592\pi$
$883$	−27399.0	−	27399.0i	−1.04422	−	1.04422i	−0.0452491	−	0.998976i	$-0.514408\pi$
$884$	42986.7			1.63552
$885$		0			0
$886$	−12698.3			−0.481499
$887$	26231.0	+	26231.0i	0.992953	+	0.992953i	0.999975	−	0.00702257i	$-0.00223537\pi$
$887$	26231.0	+	26231.0i	0.992953	+	0.992953i	−0.00702257	+	0.999975i	$0.502235\pi$
$888$		0			0
$889$			37239.9i			1.40493i
$890$	−20764.8	+	80564.7i	−0.782066	+	3.03431i
$891$		0			0
$892$	−74500.4	+	74500.4i	−2.79648	+	2.79648i
$893$	−2015.16	+	2015.16i	−0.0755149	+	0.0755149i
$894$		0			0
$895$	−17947.9	−	30412.3i	−0.670314	−	1.13583i
$896$			63816.9i			2.37943i
$897$		0			0
$898$	−22513.7	−	22513.7i	−0.836627	−	0.836627i
$899$	−30921.3			−1.14715
$900$		0			0
$901$	−8277.97			−0.306081
$902$	−2423.06	−	2423.06i	−0.0894448	−	0.0894448i
$903$		0			0
$904$		−	108491.i		−	3.99153i
$905$	−7729.45	−	13097.4i	−0.283907	−	0.481074i
$906$		0			0
$907$	32035.1	−	32035.1i	1.17277	−	1.17277i	0.191230	−	0.981545i	$-0.438752\pi$
$907$	32035.1	−	32035.1i	1.17277	−	1.17277i	0.981545	−	0.191230i	$-0.0612475\pi$
$908$	45640.3	−	45640.3i	1.66809	−	1.66809i
$909$		0			0
$910$	22798.6	−	88455.5i	0.830513	−	3.22228i
$911$		−	43587.6i		−	1.58521i	−0.609738	−	0.792603i	$-0.708725\pi$
$911$		−	43587.6i		−	1.58521i	0.609738	−	0.792603i	$-0.291275\pi$
$912$		0			0
$913$	−4027.93	−	4027.93i	−0.146008	−	0.146008i
$914$	−83113.9			−3.00784
$915$		0			0
$916$	−26098.9			−0.941409
$917$	1422.21	+	1422.21i	0.0512167	+	0.0512167i
$918$		0			0
$919$			22984.0i			0.824997i	0.910958	+	0.412498i	$0.135344\pi$
$919$			22984.0i			0.824997i	−0.910958	+	0.412498i	$0.864656\pi$
$920$	21807.8	−	12869.9i	0.781502	−	0.461205i
$921$		0			0
$922$	38710.4	−	38710.4i	1.38271	−	1.38271i
$923$	−27241.4	+	27241.4i	−0.971463	+	0.971463i
$924$		0			0
$925$	−3726.26	−	12914.9i	−0.132453	−	0.459068i
$926$			51149.9i			1.81522i
$927$		0			0
$928$	−90278.6	−	90278.6i	−3.19347	−	3.19347i
$929$	−26522.8			−0.936691			−0.468345	−	0.883545i	$-0.655150\pi$
$929$	−26522.8			−0.936691			−0.468345	+	0.883545i	$0.655150\pi$
$930$		0			0
$931$	−13875.6			−0.488457
$932$	67259.7	+	67259.7i	2.36391	+	2.36391i
$933$		0			0
$934$			92929.2i			3.25561i
$935$	−4332.33	−	1116.62i	−0.151532	−	0.0390561i
$936$		0			0
$937$	−4731.11	+	4731.11i	−0.164950	+	0.164950i	−0.784756	−	0.619805i	$-0.787212\pi$
$937$	−4731.11	+	4731.11i	−0.164950	+	0.164950i	0.619805	+	0.784756i	$0.287212\pi$
$938$	−67923.0	+	67923.0i	−2.36436	+	2.36436i
$939$		0			0
$940$	−22656.4	−	5839.49i	−0.786139	−	0.202620i
$941$		−	16766.8i		−	0.580851i	−0.956898	−	0.290426i	$-0.906203\pi$
$941$		−	16766.8i		−	0.580851i	0.956898	−	0.290426i	$-0.0937969\pi$
$942$		0			0
$943$	−1487.70	−	1487.70i	−0.0513745	−	0.0513745i
$944$	45776.5			1.57828
$945$		0			0
$946$	9591.28			0.329640
$947$	−10328.0	−	10328.0i	−0.354398	−	0.354398i	0.507345	−	0.861743i	$-0.330627\pi$
$947$	−10328.0	−	10328.0i	−0.354398	−	0.354398i	−0.861743	+	0.507345i	$0.830627\pi$
$948$		0			0
$949$			13898.6i			0.475413i
$950$	−5222.92	−	18102.2i	−0.178372	−	0.618223i
$951$		0			0
$952$	54654.1	−	54654.1i	1.86066	−	1.86066i
$953$	−9306.59	+	9306.59i	−0.316338	+	0.316338i	−0.847359	−	0.531021i	$-0.821809\pi$
$953$	−9306.59	+	9306.59i	−0.316338	+	0.316338i	0.531021	+	0.847359i	$0.321809\pi$
$954$		0			0
$955$	−7382.84	+	4357.00i	−0.250160	+	0.147633i
$956$			7124.05i			0.241013i
$957$		0			0
$958$	4886.29	+	4886.29i	0.164790	+	0.164790i
$959$	−61523.3			−2.07163
$960$		0			0
$961$	−14119.2			−0.473942
$962$	−21487.2	−	21487.2i	−0.720142	−	0.720142i
$963$		0			0
$964$		−	5339.80i		−	0.178406i
$965$	−5319.26	+	20638.0i	−0.177444	+	0.688456i
$966$		0			0
$967$	−11687.1	+	11687.1i	−0.388658	+	0.388658i	−0.874208	−	0.485551i	$-0.838619\pi$
$967$	−11687.1	+	11687.1i	−0.388658	+	0.388658i	0.485551	+	0.874208i	$0.338619\pi$
$968$	58903.3	−	58903.3i	1.95581	−	1.95581i
$969$		0			0
$970$	40941.8	+	69375.0i	1.35522	+	2.29639i
$971$		−	4178.22i		−	0.138090i	−0.997614	−	0.0690450i	$-0.978005\pi$
$971$		−	4178.22i		−	0.138090i	0.997614	−	0.0690450i	$-0.0219952\pi$
$972$		0			0
$973$	−19294.7	−	19294.7i	−0.635724	−	0.635724i
$974$	23322.2			0.767241
$975$		0			0
$976$	175458.			5.75439
$977$	−2867.31	−	2867.31i	−0.0938928	−	0.0938928i	0.658600	−	0.752493i	$-0.271149\pi$
$977$	−2867.31	−	2867.31i	−0.0938928	−	0.0938928i	−0.752493	+	0.658600i	$0.771149\pi$
$978$		0			0
$979$		−	14113.0i		−	0.460730i
$980$	−57897.2	−	98105.5i	−1.88720	−	3.19782i
$981$		0			0
$982$	−1198.68	+	1198.68i	−0.0389526	+	0.0389526i
$983$	2681.51	−	2681.51i	0.0870058	−	0.0870058i	−0.662264	−	0.749270i	$-0.730404\pi$
$983$	2681.51	−	2681.51i	0.0870058	−	0.0870058i	0.749270	+	0.662264i	$0.230404\pi$
$984$		0			0
$985$	−9999.84	+	38798.0i	−0.323474	+	1.25503i
$986$			52115.6i			1.68326i
$987$		0			0
$988$	−21713.8	−	21713.8i	−0.699197	−	0.699197i
$989$	5888.80			0.189336
$990$		0			0
$991$	−18422.7			−0.590532			−0.295266	−	0.955415i	$-0.595408\pi$
$991$	−18422.7			−0.590532			−0.295266	+	0.955415i	$0.595408\pi$
$992$	45755.6	+	45755.6i	1.46446	+	1.46446i
$993$		0			0
$994$			113007.i			3.60602i
$995$	49952.5	−	29479.6i	1.59156	−	0.939261i
$996$		0			0
$997$	35155.9	−	35155.9i	1.11675	−	1.11675i	0.124535	−	0.992215i	$-0.460256\pi$
$997$	35155.9	−	35155.9i	1.11675	−	1.11675i	0.992215	−	0.124535i	$-0.0397438\pi$
$998$	−2070.08	+	2070.08i	−0.0656585	+	0.0656585i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	135.4.f.b.53.1	✓	24
3.2	odd	2	inner	135.4.f.b.53.12	yes	24
5.2	odd	4	inner	135.4.f.b.107.12	yes	24
15.2	even	4	inner	135.4.f.b.107.1	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
135.4.f.b.53.1	✓	24	1.1	even	1	trivial
135.4.f.b.53.12	yes	24	3.2	odd	2	inner
135.4.f.b.107.1	yes	24	15.2	even	4	inner
135.4.f.b.107.12	yes	24	5.2	odd	4	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:	\( N \)	\(=\)	\( 135 = 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	135.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.78617 - 3.78617i) q^{2} +20.6702i q^{4} +(-5.68236 - 9.62864i) q^{5} +(20.4442 - 20.4442i) q^{7} +(47.9717 - 47.9717i) q^{8} +O(q^{10})\)	\(q+(-3.78617 - 3.78617i) q^{2} +20.6702i q^{4} +(-5.68236 - 9.62864i) q^{5} +(20.4442 - 20.4442i) q^{7} +(47.9717 - 47.9717i) q^{8} +(-14.9413 + 57.9701i) q^{10} -10.1550i q^{11} +(-37.3182 - 37.3182i) q^{13} -154.810 q^{14} -197.897 q^{16} +(27.8636 + 27.8636i) q^{17} -28.1493i q^{19} +(199.026 - 117.456i) q^{20} +(-38.4487 + 38.4487i) q^{22} +(-23.6065 + 23.6065i) q^{23} +(-60.4215 + 109.427i) q^{25} +282.587i q^{26} +(422.586 + 422.586i) q^{28} -247.001 q^{29} +125.187 q^{31} +(365.498 + 365.498i) q^{32} -210.993i q^{34} +(-313.021 - 80.6783i) q^{35} +(-76.0376 + 76.0376i) q^{37} +(-106.578 + 106.578i) q^{38} +(-734.496 - 189.310i) q^{40} +63.0208i q^{41} +(-124.728 - 124.728i) q^{43} +209.907 q^{44} +178.757 q^{46} +(-71.5882 - 71.5882i) q^{47} -492.927i q^{49} +(643.076 - 185.543i) q^{50} +(771.377 - 771.377i) q^{52} +(-148.544 + 148.544i) q^{53} +(-97.7790 + 57.7045i) q^{55} -1961.48i q^{56} +(935.190 + 935.190i) q^{58} -231.315 q^{59} -886.615 q^{61} +(-473.980 - 473.980i) q^{62} -1184.51i q^{64} +(-147.268 + 571.380i) q^{65} +(438.750 - 438.750i) q^{67} +(-575.948 + 575.948i) q^{68} +(879.689 + 1490.61i) q^{70} -729.974i q^{71} +(-186.217 - 186.217i) q^{73} +575.784 q^{74} +581.854 q^{76} +(-207.611 - 207.611i) q^{77} +919.171i q^{79} +(1124.52 + 1905.48i) q^{80} +(238.608 - 238.608i) q^{82} +(396.645 - 396.645i) q^{83} +(109.958 - 426.620i) q^{85} +944.487i q^{86} +(-487.154 - 487.154i) q^{88} +1389.76 q^{89} -1525.88 q^{91} +(-487.952 - 487.952i) q^{92} +542.091i q^{94} +(-271.040 + 159.955i) q^{95} +(951.496 - 951.496i) q^{97} +(-1866.31 + 1866.31i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{7}+O(q^{10}) \) 24 * q + 12 * q^7	\( 24 q + 12 q^{7} - 120 q^{10} - 72 q^{13} - 612 q^{16} - 552 q^{22} + 144 q^{25} + 1008 q^{28} + 456 q^{31} + 360 q^{37} - 1092 q^{40} - 1848 q^{43} + 732 q^{46} + 2868 q^{52} - 2052 q^{55} + 2424 q^{58} - 2544 q^{61} - 1776 q^{67} + 7332 q^{70} + 4236 q^{73} + 5844 q^{76} + 1188 q^{82} - 48 q^{85} - 8472 q^{88} - 7056 q^{91} + 2916 q^{97}+O(q^{100}) \) 24 * q + 12 * q^7 - 120 * q^10 - 72 * q^13 - 612 * q^16 - 552 * q^22 + 144 * q^25 + 1008 * q^28 + 456 * q^31 + 360 * q^37 - 1092 * q^40 - 1848 * q^43 + 732 * q^46 + 2868 * q^52 - 2052 * q^55 + 2424 * q^58 - 2544 * q^61 - 1776 * q^67 + 7332 * q^70 + 4236 * q^73 + 5844 * q^76 + 1188 * q^82 - 48 * q^85 - 8472 * q^88 - 7056 * q^91 + 2916 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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