LMFDB - Embedded newform 252.4.x.a.209.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(41,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5, 3]))

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

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

chi := DirichletCharacter("252.41");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.x (of order $6$, 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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			209.3
Character	$\chi$	$=$	252.209
Dual form			252.4.x.a.41.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-4.81916 - 1.94311i) q^{3} +(9.12012 + 15.7965i) q^{5} +(-9.48165 + 15.9091i) q^{7} +(19.4487 + 18.7283i) q^{9} +O(q^{10})$	\(q+(-4.81916 - 1.94311i) q^{3} +(9.12012 + 15.7965i) q^{5} +(-9.48165 + 15.9091i) q^{7} +(19.4487 + 18.7283i) q^{9} +(-49.3053 - 28.4664i) q^{11} +(9.36748 - 5.40831i) q^{13} +(-13.2570 - 93.8474i) q^{15} +65.2579 q^{17} -36.6039i q^{19} +(76.6067 - 58.2445i) q^{21} +(-70.2538 + 40.5611i) q^{23} +(-103.853 + 179.879i) q^{25} +(-57.3350 - 128.046i) q^{27} +(-233.584 - 134.860i) q^{29} +(-117.775 + 67.9976i) q^{31} +(182.297 + 232.990i) q^{33} +(-337.782 - 4.68434i) q^{35} -125.675 q^{37} +(-55.6523 + 7.86151i) q^{39} +(-117.524 - 203.557i) q^{41} +(22.6360 - 39.2067i) q^{43} +(-118.468 + 478.026i) q^{45} +(-241.097 + 417.592i) q^{47} +(-163.197 - 301.688i) q^{49} +(-314.488 - 126.803i) q^{51} +70.1770i q^{53} -1038.47i q^{55} +(-71.1255 + 176.400i) q^{57} +(176.673 + 306.007i) q^{59} +(512.605 + 295.953i) q^{61} +(-482.355 + 131.835i) q^{63} +(170.865 + 98.6490i) q^{65} +(-261.925 - 453.667i) q^{67} +(417.379 - 58.9595i) q^{69} +895.977i q^{71} -982.681i q^{73} +(850.011 - 665.069i) q^{75} +(920.369 - 514.492i) q^{77} +(510.195 - 883.684i) q^{79} +(27.5000 + 728.481i) q^{81} +(152.345 - 263.869i) q^{83} +(595.160 + 1030.85i) q^{85} +(863.632 + 1103.79i) q^{87} -1022.58 q^{89} +(-2.77785 + 200.308i) q^{91} +(699.705 - 98.8412i) q^{93} +(578.215 - 333.833i) q^{95} +(-677.719 - 391.281i) q^{97} +(-425.793 - 1477.04i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) $ 48 * q + 6 * q^7 + 60 * q^9	$ 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) $ 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−4.81916	−	1.94311i	−0.927448	−	0.373952i
$3$	−4.81916	−	1.94311i	−0.927448	−	0.373952i
$4$		0			0
$5$	9.12012	+	15.7965i	0.815729	+	1.41288i	0.908803	+	0.417225i	$0.136997\pi$
$5$	9.12012	+	15.7965i	0.815729	+	1.41288i	−0.0930747	+	0.995659i	$0.529670\pi$
$6$		0			0
$7$	−9.48165	+	15.9091i	−0.511961	+	0.859009i
$7$	−9.48165	+	15.9091i	−0.511961	+	0.859009i
$8$		0			0
$9$	19.4487	+	18.7283i	0.720320	+	0.693642i
$10$		0			0
$11$	−49.3053	−	28.4664i	−1.35146	−	0.780268i	−0.363009	−	0.931786i	$-0.618251\pi$
$11$	−49.3053	−	28.4664i	−1.35146	−	0.780268i	−0.988455	+	0.151518i	$0.951584\pi$
$12$		0			0
$13$	9.36748	−	5.40831i	0.199852	−	0.115384i	−0.396735	−	0.917933i	$-0.629857\pi$
$13$	9.36748	−	5.40831i	0.199852	−	0.115384i	0.596586	+	0.802549i	$0.296523\pi$
$14$		0			0
$15$	−13.2570	−	93.8474i	−0.228196	−	1.61542i
$16$		0			0
$17$	65.2579			0.931021			0.465511	−	0.885042i	$-0.345871\pi$
$17$	65.2579			0.931021			0.465511	+	0.885042i	$0.345871\pi$
$18$		0			0
$19$		−	36.6039i		−	0.441975i	−0.975277	−	0.220987i	$-0.929072\pi$
$19$		−	36.6039i		−	0.441975i	0.975277	−	0.220987i	$-0.0709280\pi$
$20$		0			0
$21$	76.6067	−	58.2445i	0.796045	−	0.605238i
$22$		0			0
$23$	−70.2538	+	40.5611i	−0.636910	+	0.367720i	−0.783423	−	0.621489i	$-0.786528\pi$
$23$	−70.2538	+	40.5611i	−0.636910	+	0.367720i	0.146513	+	0.989209i	$0.453195\pi$
$24$		0			0
$25$	−103.853	+	179.879i	−0.830827	+	1.43903i
$26$		0			0
$27$	−57.3350	−	128.046i	−0.408671	−	0.912682i
$28$		0			0
$29$	−233.584	−	134.860i	−1.49571	−	0.863546i	−0.495718	−	0.868484i	$-0.665095\pi$
$29$	−233.584	−	134.860i	−1.49571	−	0.863546i	−0.999988	+	0.00493734i	$0.998428\pi$
$30$		0			0
$31$	−117.775	+	67.9976i	−0.682357	+	0.393959i	−0.800743	−	0.599009i	$-0.795562\pi$
$31$	−117.775	+	67.9976i	−0.682357	+	0.393959i	0.118385	+	0.992968i	$0.462228\pi$
$32$		0			0
$33$	182.297	+	232.990i	0.961630	+	1.22904i
$34$		0			0
$35$	−337.782	−	4.68434i	−1.63130	−	0.0226228i
$36$		0			0
$37$	−125.675			−0.558400			−0.279200	−	0.960233i	$-0.590069\pi$
$37$	−125.675			−0.558400			−0.279200	+	0.960233i	$0.590069\pi$
$38$		0			0
$39$	−55.6523	+	7.86151i	−0.228500	+	0.0322782i
$40$		0			0
$41$	−117.524	−	203.557i	−0.447662	−	0.775374i	0.550571	−	0.834788i	$-0.314410\pi$
$41$	−117.524	−	203.557i	−0.447662	−	0.775374i	−0.998233	+	0.0594145i	$0.981077\pi$
$42$		0			0
$43$	22.6360	−	39.2067i	0.0802780	−	0.139046i	−0.823091	−	0.567909i	$-0.807753\pi$
$43$	22.6360	−	39.2067i	0.0802780	−	0.139046i	0.903369	+	0.428863i	$0.141086\pi$
$44$		0			0
$45$	−118.468	+	478.026i	−0.392449	+	1.58355i
$46$		0			0
$47$	−241.097	+	417.592i	−0.748246	+	1.29600i	0.200416	+	0.979711i	$0.435771\pi$
$47$	−241.097	+	417.592i	−0.748246	+	1.29600i	−0.948663	+	0.316290i	$0.897563\pi$
$48$		0			0
$49$	−163.197	−	301.688i	−0.475792	−	0.879558i
$50$		0			0
$51$	−314.488	−	126.803i	−0.863474	−	0.348157i
$52$		0			0
$53$			70.1770i			0.181878i	0.995856	+	0.0909392i	$0.0289869\pi$
$53$			70.1770i			0.181878i	−0.995856	+	0.0909392i	$0.971013\pi$
$54$		0			0
$55$		−	1038.47i		−	2.54595i
$56$		0			0
$57$	−71.1255	+	176.400i	−0.165277	+	0.409909i
$58$		0			0
$59$	176.673	+	306.007i	0.389845	+	0.675232i	0.992428	−	0.122824i	$-0.0391952\pi$
$59$	176.673	+	306.007i	0.389845	+	0.675232i	−0.602583	+	0.798056i	$0.705862\pi$
$60$		0			0
$61$	512.605	+	295.953i	1.07594	+	0.621194i	0.929798	−	0.368069i	$-0.119981\pi$
$61$	512.605	+	295.953i	1.07594	+	0.621194i	0.146142	+	0.989264i	$0.453314\pi$
$62$		0			0
$63$	−482.355	+	131.835i	−0.964620	+	0.263644i
$64$		0			0
$65$	170.865	+	98.6490i	0.326049	+	0.188245i
$66$		0			0
$67$	−261.925	−	453.667i	−0.477600	−	0.827228i	0.522070	−	0.852903i	$-0.325160\pi$
$67$	−261.925	−	453.667i	−0.477600	−	0.827228i	−0.999670	+	0.0256746i	$0.991827\pi$
$68$		0			0
$69$	417.379	−	58.9595i	0.728211	−	0.102868i
$70$		0			0
$71$			895.977i			1.49765i	0.662770	+	0.748823i	$0.269381\pi$
$71$			895.977i			1.49765i	−0.662770	+	0.748823i	$0.730619\pi$
$72$		0			0
$73$		−	982.681i		−	1.57554i	−0.615972	−	0.787768i	$-0.711237\pi$
$73$		−	982.681i		−	1.57554i	0.615972	−	0.787768i	$-0.288763\pi$
$74$		0			0
$75$	850.011	−	665.069i	1.30868	−	1.02394i
$76$		0			0
$77$	920.369	−	514.492i	1.36215	−	0.761453i
$78$		0			0
$79$	510.195	−	883.684i	0.726601	−	1.25851i	−0.231711	−	0.972785i	$-0.574432\pi$
$79$	510.195	−	883.684i	0.726601	−	1.25851i	0.958312	−	0.285725i	$-0.0922343\pi$
$80$		0			0
$81$	27.5000	+	728.481i	0.0377229	+	0.999288i
$82$		0			0
$83$	152.345	−	263.869i	0.201470	−	0.348957i	−0.747532	−	0.664226i	$-0.768761\pi$
$83$	152.345	−	263.869i	0.201470	−	0.348957i	0.949002	+	0.315269i	$0.102095\pi$
$84$		0			0
$85$	595.160	+	1030.85i	0.759461	+	1.31542i
$86$		0			0
$87$	863.632	+	1103.79i	1.06427	+	1.36022i
$88$		0			0
$89$	−1022.58			−1.21791			−0.608953	−	0.793206i	$-0.708410\pi$
$89$	−1022.58			−1.21791			−0.608953	+	0.793206i	$0.708410\pi$
$90$		0			0
$91$	−2.77785	+	200.308i	−0.00319998	+	0.230747i
$92$		0			0
$93$	699.705	−	98.8412i	0.780173	−	0.110208i
$94$		0			0
$95$	578.215	−	333.833i	0.624459	−	0.360532i
$96$		0			0
$97$	−677.719	−	391.281i	−0.709402	−	0.409573i	0.101438	−	0.994842i	$-0.467656\pi$
$97$	−677.719	−	391.281i	−0.709402	−	0.409573i	−0.810839	+	0.585269i	$0.800989\pi$
$98$		0			0
$99$	−425.793	−	1477.04i	−0.432261	−	1.49947i
$100$		0			0
$101$	−786.668	+	1362.55i	−0.775014	+	1.34236i	0.159773	+	0.987154i	$0.448924\pi$
$101$	−786.668	+	1362.55i	−0.775014	+	1.34236i	−0.934787	+	0.355209i	$0.884410\pi$
$102$		0			0
$103$	−597.068	+	344.717i	−0.571174	+	0.329767i	−0.757618	−	0.652698i	$-0.773637\pi$
$103$	−597.068	+	344.717i	−0.571174	+	0.329767i	0.186444	+	0.982466i	$0.440304\pi$
$104$		0			0
$105$	1618.72	+	678.921i	1.50449	+	0.631009i
$106$		0			0
$107$		−	627.635i		−	0.567063i	−0.958963	−	0.283532i	$-0.908494\pi$
$107$		−	627.635i		−	0.567063i	0.958963	−	0.283532i	$-0.0915061\pi$
$108$		0			0
$109$	−1110.51			−0.975851			−0.487925	−	0.872885i	$-0.662246\pi$
$109$	−1110.51			−0.975851			−0.487925	+	0.872885i	$0.662246\pi$
$110$		0			0
$111$	605.647	+	244.200i	0.517887	+	0.208814i
$112$		0			0
$113$	−1047.17	+	604.581i	−0.871762	+	0.503312i	−0.867933	−	0.496681i	$-0.834552\pi$
$113$	−1047.17	+	604.581i	−0.871762	+	0.503312i	−0.00382837	+	0.999993i	$0.501219\pi$
$114$		0			0
$115$	−1281.45	−	739.844i	−1.03909	−	0.599920i
$116$		0			0
$117$	283.473	+	70.2527i	0.223993	+	0.0555116i
$118$		0			0
$119$	−618.752	+	1038.19i	−0.476646	+	0.799755i
$120$		0			0
$121$	955.174	+	1654.41i	0.717636	+	1.24298i
$122$		0			0
$123$	170.832	+	1209.34i	0.125231	+	0.886523i
$124$		0			0
$125$	−1508.59			−1.07946
$126$		0			0
$127$	2687.40			1.87770			0.938850	−	0.344327i	$-0.111893\pi$
$127$	2687.40			1.87770			0.938850	+	0.344327i	$0.111893\pi$
$128$		0			0
$129$	−185.269	+	144.959i	−0.126450	+	0.0989375i
$130$		0			0
$131$	−74.0557	−	128.268i	−0.0493914	−	0.0855484i	0.840273	−	0.542164i	$-0.182395\pi$
$131$	−74.0557	−	128.268i	−0.0493914	−	0.0855484i	−0.889664	+	0.456616i	$0.849062\pi$
$132$		0			0
$133$	582.335	+	347.066i	0.379660	+	0.226274i
$134$		0			0
$135$	1499.77	−	2073.49i	0.956148	−	1.32191i
$136$		0			0
$137$	880.674	+	508.458i	0.549205	+	0.317084i	0.748801	−	0.662795i	$-0.230630\pi$
$137$	880.674	+	508.458i	0.549205	+	0.317084i	−0.199596	+	0.979878i	$0.563963\pi$
$138$		0			0
$139$	2221.28	−	1282.46i	1.35544	−	0.782566i	0.366438	−	0.930443i	$-0.380577\pi$
$139$	2221.28	−	1282.46i	1.35544	−	0.782566i	0.989006	+	0.147877i	$0.0472440\pi$
$140$		0			0
$141$	1973.31	−	1543.97i	1.17860	−	0.922166i
$142$		0			0
$143$	−615.821			−0.360123
$144$		0			0
$145$		−	4919.75i		−	2.81768i
$146$		0			0
$147$	200.258	+	1770.99i	0.112361	+	0.993667i
$148$		0			0
$149$	358.972	−	207.253i	0.197370	−	0.113952i	−0.398058	−	0.917360i	$-0.630316\pi$
$149$	358.972	−	207.253i	0.197370	−	0.113952i	0.595428	+	0.803409i	$0.296982\pi$
$150$		0			0
$151$	−949.812	+	1645.12i	−0.511885	+	0.886610i	0.488021	+	0.872832i	$0.337719\pi$
$151$	−949.812	+	1645.12i	−0.511885	+	0.886610i	−0.999905	+	0.0137779i	$0.995614\pi$
$152$		0			0
$153$	1269.18	+	1222.17i	0.670634	+	0.645795i
$154$		0			0
$155$	−2148.25	−	1240.29i	−1.11324	−	0.642728i
$156$		0			0
$157$	1833.97	−	1058.84i	0.932271	−	0.538247i	0.0447422	−	0.998999i	$-0.485753\pi$
$157$	1833.97	−	1058.84i	0.932271	−	0.538247i	0.887529	+	0.460751i	$0.152420\pi$
$158$		0			0
$159$	136.362	−	338.194i	0.0680137	−	0.168683i
$160$		0			0
$161$	20.8332	−	1502.26i	0.0101981	−	0.735370i
$162$		0			0
$163$	−62.3148			−0.0299440			−0.0149720	−	0.999888i	$-0.504766\pi$
$163$	−62.3148			−0.0299440			−0.0149720	+	0.999888i	$0.504766\pi$
$164$		0			0
$165$	−2017.86	+	5004.55i	−0.952061	+	2.36123i
$166$		0			0
$167$	504.850	+	874.426i	0.233931	+	0.405180i	0.958961	−	0.283536i	$-0.0915077\pi$
$167$	504.850	+	874.426i	0.233931	+	0.405180i	−0.725031	+	0.688717i	$0.758174\pi$
$168$		0			0
$169$	−1040.00	+	1801.33i	−0.473373	+	0.819906i
$170$		0			0
$171$	685.530	−	711.897i	0.306572	−	0.318363i
$172$		0			0
$173$	−234.008	+	405.315i	−0.102840	+	0.178124i	−0.912854	−	0.408287i	$-0.866126\pi$
$173$	−234.008	+	405.315i	−0.102840	+	0.178124i	0.810014	+	0.586411i	$0.199460\pi$
$174$		0			0
$175$	−1877.01	−	3357.76i	−0.810792	−	1.45042i
$176$		0			0
$177$	−256.811	−	1817.99i	−0.109057	−	0.772025i
$178$		0			0
$179$			2028.76i			0.847131i	0.905866	+	0.423565i	$0.139222\pi$
$179$			2028.76i			0.847131i	−0.905866	+	0.423565i	$0.860778\pi$
$180$		0			0
$181$			3998.62i			1.64207i	0.570876	+	0.821036i	$0.306604\pi$
$181$			3998.62i			1.64207i	−0.570876	+	0.821036i	$0.693396\pi$
$182$		0			0
$183$	−1895.26	−	2422.29i	−0.765582	−	0.978475i
$184$		0			0
$185$	−1146.17	−	1985.22i	−0.455503	−	0.788954i
$186$		0			0
$187$	−3217.56	−	1857.66i	−1.25824	−	0.726446i
$188$		0			0
$189$	2580.72	+	301.937i	0.993225	+	0.116205i
$190$		0			0
$191$	−1746.98	−	1008.62i	−0.661817	−	0.382100i	0.131152	−	0.991362i	$-0.458132\pi$
$191$	−1746.98	−	1008.62i	−0.661817	−	0.382100i	−0.792969	+	0.609262i	$0.791466\pi$
$192$		0			0
$193$	−582.965	−	1009.72i	−0.217423	−	0.376588i	0.736596	−	0.676333i	$-0.236432\pi$
$193$	−582.965	−	1009.72i	−0.217423	−	0.376588i	−0.954020	+	0.299745i	$0.903099\pi$
$194$		0			0
$195$	−631.741	−	807.415i	−0.231999	−	0.296514i
$196$		0			0
$197$			4449.56i			1.60923i	0.593799	+	0.804613i	$0.297627\pi$
$197$			4449.56i			1.60923i	−0.593799	+	0.804613i	$0.702373\pi$
$198$		0			0
$199$			5156.28i			1.83678i	0.395677	+	0.918390i	$0.370510\pi$
$199$			5156.28i			1.83678i	−0.395677	+	0.918390i	$0.629490\pi$
$200$		0			0
$201$	380.733	+	2695.25i	0.133606	+	0.945811i
$202$		0			0
$203$	4360.26	−	2437.41i	1.50754	−	0.842723i
$204$		0			0
$205$	2143.67	−	3712.94i	0.730342	−	1.26499i
$206$		0			0
$207$	−2125.98	−	526.878i	−0.713845	−	0.176911i
$208$		0			0
$209$	−1041.98	+	1804.77i	−0.344859	+	0.597313i
$210$		0			0
$211$	−354.558	−	614.113i	−0.115682	−	0.200366i	0.802370	−	0.596826i	$-0.203572\pi$
$211$	−354.558	−	614.113i	−0.115682	−	0.200366i	−0.918052	+	0.396460i	$0.870239\pi$
$212$		0			0
$213$	1740.98	−	4317.86i	0.560047	−	1.38899i
$214$		0			0
$215$	825.771			0.261940
$216$		0			0
$217$	34.9254	−	2518.42i	0.0109258	−	0.787842i
$218$		0			0
$219$	−1909.46	+	4735.70i	−0.589174	+	1.46123i
$220$		0			0
$221$	611.302	−	352.935i	0.186066	−	0.107425i
$222$		0			0
$223$	270.455	+	156.147i	0.0812153	+	0.0468897i	0.540058	−	0.841628i	$-0.318402\pi$
$223$	270.455	+	156.147i	0.0812153	+	0.0468897i	−0.458842	+	0.888518i	$0.651736\pi$
$224$		0			0
$225$	−5388.64	+	1553.41i	−1.59664	+	0.460270i
$226$		0			0
$227$	364.722	−	631.717i	0.106641	−	0.184707i	−0.807767	−	0.589502i	$-0.799324\pi$
$227$	364.722	−	631.717i	0.106641	−	0.184707i	0.914407	+	0.404795i	$0.132657\pi$
$228$		0			0
$229$	−1400.43	+	808.539i	−0.404118	+	0.233318i	−0.688259	−	0.725465i	$-0.741625\pi$
$229$	−1400.43	+	808.539i	−0.404118	+	0.233318i	0.284141	+	0.958782i	$0.408292\pi$
$230$		0			0
$231$	−5435.12	+	691.044i	−1.54807	+	0.196828i
$232$		0			0
$233$			2237.18i			0.629023i	0.949254	+	0.314511i	$0.101841\pi$
$233$			2237.18i			0.629023i	−0.949254	+	0.314511i	$0.898159\pi$
$234$		0			0
$235$	−8795.33			−2.44146
$236$		0			0
$237$	−4175.81	+	3267.25i	−1.14451	+	0.895489i
$238$		0			0
$239$	−4456.87	+	2573.17i	−1.20624	+	0.696422i	−0.961935	−	0.273278i	$-0.911892\pi$
$239$	−4456.87	+	2573.17i	−1.20624	+	0.696422i	−0.244302	+	0.969699i	$0.578559\pi$
$240$		0			0
$241$	−933.854	−	539.161i	−0.249605	−	0.144110i	0.369978	−	0.929040i	$-0.379365\pi$
$241$	−933.854	−	539.161i	−0.249605	−	0.144110i	−0.619583	+	0.784931i	$0.712698\pi$
$242$		0			0
$243$	1282.99	−	3564.10i	0.338699	−	0.940895i
$244$		0			0
$245$	3277.25	−	5329.38i	0.854595	−	1.38972i
$246$		0			0
$247$	−197.966	−	342.887i	−0.0509970	−	0.0883294i
$248$		0			0
$249$	−1246.90	+	975.605i	−0.317346	+	0.248299i
$250$		0			0
$251$	3429.17			0.862340			0.431170	−	0.902271i	$-0.358101\pi$
$251$	3429.17			0.862340			0.431170	+	0.902271i	$0.358101\pi$
$252$		0			0
$253$	4618.51			1.14768
$254$		0			0
$255$	−865.123	−	6124.28i	−0.212455	−	1.50399i
$256$		0			0
$257$	3394.82	+	5880.00i	0.823981	+	1.42718i	0.902695	+	0.430280i	$0.141585\pi$
$257$	3394.82	+	5880.00i	0.823981	+	1.42718i	−0.0787143	+	0.996897i	$0.525081\pi$
$258$		0			0
$259$	1191.60	−	1999.37i	0.285879	−	0.479670i
$260$		0			0
$261$	−2017.20	−	6997.48i	−0.478396	−	1.65951i
$262$		0			0
$263$	−6692.65	−	3864.00i	−1.56915	−	0.905949i	−0.996268	−	0.0863104i	$-0.972492\pi$
$263$	−6692.65	−	3864.00i	−1.56915	−	0.905949i	−0.572881	−	0.819638i	$-0.694174\pi$
$264$		0			0
$265$	−1108.55	+	640.023i	−0.256973	+	0.148363i
$266$		0			0
$267$	4928.00	+	1986.99i	1.12955	+	0.455438i
$268$		0			0
$269$	−2457.17			−0.556938			−0.278469	−	0.960445i	$-0.589827\pi$
$269$	−2457.17			−0.556938			−0.278469	+	0.960445i	$0.589827\pi$
$270$		0			0
$271$			6080.16i			1.36289i	0.731869	+	0.681446i	$0.238648\pi$
$271$			6080.16i			1.36289i	−0.731869	+	0.681446i	$0.761352\pi$
$272$		0			0
$273$	402.606	−	959.917i	0.0892559	−	0.212809i
$274$		0			0
$275$	10241.0	−	5912.67i	2.24566	−	1.29654i
$276$		0			0
$277$	−1092.78	+	1892.75i	−0.237036	+	0.410558i	−0.959862	−	0.280471i	$-0.909509\pi$
$277$	−1092.78	+	1892.75i	−0.237036	+	0.410558i	0.722827	+	0.691029i	$0.242843\pi$
$278$		0			0
$279$	−3564.05	−	883.272i	−0.764782	−	0.189535i
$280$		0			0
$281$	−2196.63	−	1268.23i	−0.466335	−	0.269239i	0.248369	−	0.968665i	$-0.420105\pi$
$281$	−2196.63	−	1268.23i	−0.466335	−	0.269239i	−0.714704	+	0.699427i	$0.753439\pi$
$282$		0			0
$283$	3627.22	−	2094.17i	0.761893	−	0.439879i	−0.0680823	−	0.997680i	$-0.521688\pi$
$283$	3627.22	−	2094.17i	0.761893	−	0.439879i	0.829975	+	0.557801i	$0.188355\pi$
$284$		0			0
$285$	−3435.19	+	485.258i	−0.713975	+	0.100857i
$286$		0			0
$287$	4352.73	+	60.3634i	0.895238	+	0.0124151i
$288$		0			0
$289$	−654.409			−0.133199
$290$		0			0
$291$	2505.74	+	3202.53i	0.504773	+	0.645140i
$292$		0			0
$293$	−3751.85	−	6498.40i	−0.748074	−	1.29570i	−0.948745	−	0.316043i	$-0.897646\pi$
$293$	−3751.85	−	6498.40i	−0.748074	−	1.29570i	0.200671	−	0.979659i	$-0.435688\pi$
$294$		0			0
$295$	−3222.56	+	5581.64i	−0.636016	+	1.10161i
$296$		0			0
$297$	−818.082	+	7945.45i	−0.159831	+	1.55233i
$298$		0			0
$299$	−438.734	+	759.909i	−0.0848583	+	0.146979i
$300$		0			0
$301$	409.115	+	731.861i	0.0783422	+	0.140145i
$302$		0			0
$303$	6438.66	−	5037.76i	1.22076	−	0.955155i
$304$		0			0
$305$			10796.5i			2.02690i
$306$		0			0
$307$			4315.01i			0.802184i	0.916038	+	0.401092i	$0.131369\pi$
$307$			4315.01i			0.802184i	−0.916038	+	0.401092i	$0.868631\pi$
$308$		0			0
$309$	3547.19	−	501.081i	0.653051	−	0.0922507i
$310$		0			0
$311$	2224.42	+	3852.80i	0.405579	+	0.702483i	0.994389	−	0.105788i	$-0.0337366\pi$
$311$	2224.42	+	3852.80i	0.405579	+	0.702483i	−0.588810	+	0.808272i	$0.700403\pi$
$312$		0			0
$313$	6535.19	+	3773.10i	1.18016	+	0.681367i	0.956052	−	0.293196i	$-0.0947190\pi$
$313$	6535.19	+	3773.10i	1.18016	+	0.681367i	0.224111	+	0.974564i	$0.428052\pi$
$314$		0			0
$315$	−6481.67	−	6417.19i	−1.15937	−	1.14783i
$316$		0			0
$317$	−7839.87	−	4526.35i	−1.38906	−	0.801973i	−0.395848	−	0.918316i	$-0.629549\pi$
$317$	−7839.87	−	4526.35i	−1.38906	−	0.801973i	−0.993209	+	0.116343i	$0.962883\pi$
$318$		0			0
$319$	7677.95	+	13298.6i	1.34759	+	2.33410i
$320$		0			0
$321$	−1219.56	+	3024.67i	−0.212054	+	0.525922i
$322$		0			0
$323$		−	2388.70i		−	0.411488i
$324$		0			0
$325$			2246.69i			0.383458i
$326$		0			0
$327$	5351.74	+	2157.85i	0.905051	+	0.364921i
$328$		0			0
$329$	−4357.50	−	7795.08i	−0.730203	−	1.30625i
$330$		0			0
$331$	3366.69	−	5831.27i	0.559063	−	0.968326i	−0.438512	−	0.898725i	$-0.644494\pi$
$331$	3366.69	−	5831.27i	0.559063	−	0.968326i	0.997575	−	0.0696003i	$-0.0221724\pi$
$332$		0			0
$333$	−2444.20	−	2353.68i	−0.402227	−	0.387329i
$334$		0			0
$335$	4777.58	−	8275.00i	0.779185	−	1.34959i
$336$		0			0
$337$	−1414.64	−	2450.22i	−0.228665	−	0.396060i	0.728747	−	0.684783i	$-0.240103\pi$
$337$	−1414.64	−	2450.22i	−0.228665	−	0.396060i	−0.957413	+	0.288723i	$0.906769\pi$
$338$		0			0
$339$	6221.23	−	878.818i	0.996728	−	0.140799i
$340$		0			0
$341$	7742.59			1.22957
$342$		0			0
$343$	6346.95	+	264.193i	0.999135	+	0.0415892i
$344$		0			0
$345$	4737.90	+	6055.42i	0.739363	+	0.944965i
$346$		0			0
$347$	−1635.49	+	944.250i	−0.253019	+	0.146081i	−0.621146	−	0.783695i	$-0.713333\pi$
$347$	−1635.49	+	944.250i	−0.253019	+	0.146081i	0.368127	+	0.929776i	$0.379999\pi$
$348$		0			0
$349$	8771.88	+	5064.44i	1.34541	+	0.776772i	0.987595	−	0.157021i	$-0.0501890\pi$
$349$	8771.88	+	5064.44i	1.34541	+	0.776772i	0.357814	+	0.933793i	$0.383522\pi$
$350$		0			0
$351$	−1229.60	−	889.379i	−0.186983	−	0.135247i
$352$		0			0
$353$	2939.16	−	5090.78i	0.443161	−	0.767577i	−0.554761	−	0.832010i	$-0.687190\pi$
$353$	2939.16	−	5090.78i	0.443161	−	0.767577i	0.997922	+	0.0644323i	$0.0205237\pi$
$354$		0			0
$355$	−14153.3	+	8171.42i	−2.11600	+	1.22167i
$356$		0			0
$357$	4999.19	−	3800.91i	0.741135	−	0.563489i
$358$		0			0
$359$			5020.49i			0.738081i	0.929413	+	0.369041i	$0.120314\pi$
$359$			5020.49i			0.738081i	−0.929413	+	0.369041i	$0.879686\pi$
$360$		0			0
$361$	5519.15			0.804658
$362$		0			0
$363$	−1388.44	−	9828.87i	−0.200755	−	1.42116i
$364$		0			0
$365$	15522.9	−	8962.17i	2.22605	−	1.28521i
$366$		0			0
$367$	−8074.26	−	4661.68i	−1.14843	−	0.663045i	−0.199924	−	0.979811i	$-0.564070\pi$
$367$	−8074.26	−	4661.68i	−1.14843	−	0.663045i	−0.948504	+	0.316766i	$0.897403\pi$
$368$		0			0
$369$	1526.61	−	6159.94i	0.215371	−	0.869035i
$370$		0			0
$371$	−1116.45	−	665.394i	−0.156235	−	0.0931146i
$372$		0			0
$373$	−510.522	−	884.250i	−0.0708682	−	0.122747i	0.828414	−	0.560116i	$-0.189244\pi$
$373$	−510.522	−	884.250i	−0.0708682	−	0.122747i	−0.899282	+	0.437369i	$0.855910\pi$
$374$		0			0
$375$	7270.14	+	2931.36i	1.00114	+	0.403666i
$376$		0			0
$377$	−2917.46			−0.398559
$378$		0			0
$379$	−8222.23			−1.11437			−0.557187	−	0.830387i	$-0.688119\pi$
$379$	−8222.23			−1.11437			−0.557187	+	0.830387i	$0.688119\pi$
$380$		0			0
$381$	−12951.0	−	5221.90i	−1.74147	−	0.702169i
$382$		0			0
$383$	1833.55	+	3175.80i	0.244621	+	0.423697i	0.962025	−	0.272961i	$-0.0880030\pi$
$383$	1833.55	+	3175.80i	0.244621	+	0.423697i	−0.717404	+	0.696658i	$0.754670\pi$
$384$		0			0
$385$	16521.1	+	9846.40i	2.18699	+	1.30343i
$386$		0			0
$387$	1174.51	−	338.583i	0.154274	−	0.0444732i
$388$		0			0
$389$	−1487.93	−	859.056i	−0.193936	−	0.111969i	0.399888	−	0.916564i	$-0.369049\pi$
$389$	−1487.93	−	859.056i	−0.193936	−	0.111969i	−0.593824	+	0.804595i	$0.702382\pi$
$390$		0			0
$391$	−4584.61	+	2646.93i	−0.592977	+	0.342355i
$392$		0			0
$393$	107.647	+	762.043i	0.0138170	+	0.0978117i
$394$		0			0
$395$	18612.2			2.37084
$396$		0			0
$397$		−	11666.0i		−	1.47481i	−0.675448	−	0.737407i	$-0.736050\pi$
$397$		−	11666.0i		−	1.47481i	0.675448	−	0.737407i	$-0.263950\pi$
$398$		0			0
$399$	−2131.98	−	2804.11i	−0.267500	−	0.351832i
$400$		0			0
$401$	2312.57	−	1335.16i	0.287990	−	0.166271i	−0.349045	−	0.937106i	$-0.613494\pi$
$401$	2312.57	−	1335.16i	0.287990	−	0.166271i	0.637035	+	0.770835i	$0.280161\pi$
$402$		0			0
$403$	−735.505	+	1273.93i	−0.0909134	+	0.157467i
$404$		0			0
$405$	−11256.7	+	7078.24i	−1.38111	+	0.868446i
$406$		0			0
$407$	6196.42	+	3577.51i	0.754657	+	0.435701i
$408$		0			0
$409$	−375.615	+	216.862i	−0.0454107	+	0.0262179i	−0.522533	−	0.852619i	$-0.675013\pi$
$409$	−375.615	+	216.862i	−0.0454107	+	0.0262179i	0.477123	+	0.878837i	$0.341680\pi$
$410$		0			0
$411$	−3256.12	−	4161.59i	−0.390785	−	0.499455i
$412$		0			0
$413$	−6543.43	−	90.7439i	−0.779615	−	0.0108117i
$414$		0			0
$415$	5557.62			0.657380
$416$		0			0
$417$	−13196.7	+	1864.18i	−1.54975	+	0.218919i
$418$		0			0
$419$	2916.15	+	5050.92i	0.340008	+	0.588911i	0.984434	−	0.175756i	$-0.0562369\pi$
$419$	2916.15	+	5050.92i	0.340008	+	0.588911i	−0.644426	+	0.764667i	$0.722904\pi$
$420$		0			0
$421$	5481.42	−	9494.10i	0.634556	−	1.09908i	−0.352053	−	0.935980i	$-0.614516\pi$
$421$	5481.42	−	9494.10i	0.634556	−	1.09908i	0.986609	−	0.163104i	$-0.0521505\pi$
$422$		0			0
$423$	−12509.8	+	3606.26i	−1.43794	+	0.414521i
$424$		0			0
$425$	−6777.25	+	11738.5i	−0.773517	+	1.33977i
$426$		0			0
$427$	−9568.67	+	5348.95i	−1.08445	+	0.606215i
$428$		0			0
$429$	2967.74	+	1196.61i	0.333995	+	0.134669i
$430$		0			0
$431$			9711.53i			1.08536i	0.839941	+	0.542678i	$0.182589\pi$
$431$			9711.53i			1.08536i	−0.839941	+	0.542678i	$0.817411\pi$
$432$		0			0
$433$			28.2134i			0.00313129i	0.999999	+	0.00156564i	$0.000498360\pi$
$433$			28.2134i			0.00313129i	−0.999999	+	0.00156564i	$0.999502\pi$
$434$		0			0
$435$	−9559.62	+	23709.1i	−1.05368	+	2.61325i
$436$		0			0
$437$	1484.69	+	2571.57i	0.162523	+	0.281498i
$438$		0			0
$439$	−5470.43	−	3158.35i	−0.594736	−	0.343371i	0.172232	−	0.985056i	$-0.444902\pi$
$439$	−5470.43	−	3158.35i	−0.594736	−	0.343371i	−0.766968	+	0.641685i	$0.778236\pi$
$440$		0			0
$441$	2476.16	−	8923.83i	0.267375	−	0.963593i
$442$		0			0
$443$	13946.4	+	8051.96i	1.49574	+	0.863567i	0.999988	−	0.00489651i	$-0.00155861\pi$
$443$	13946.4	+	8051.96i	1.49574	+	0.863567i	0.495754	+	0.868463i	$0.334892\pi$
$444$		0			0
$445$	−9326.09	−	16153.3i	−0.993481	−	1.72076i
$446$		0			0
$447$	−2132.66	+	301.262i	−0.225663	+	0.0318774i
$448$		0			0
$449$			2392.17i			0.251433i	0.992066	+	0.125717i	$0.0401230\pi$
$449$			2392.17i			0.251433i	−0.992066	+	0.125717i	$0.959877\pi$
$450$		0			0
$451$			13381.9i			1.39719i
$452$		0			0
$453$	7773.95	−	6082.52i	0.806296	−	0.630865i
$454$		0			0
$455$	−3189.50	+	1782.95i	−0.328628	+	0.183705i
$456$		0			0
$457$	−6222.62	+	10777.9i	−0.636940	+	1.10321i	0.349160	+	0.937063i	$0.386467\pi$
$457$	−6222.62	+	10777.9i	−0.636940	+	1.10321i	−0.986100	+	0.166150i	$0.946866\pi$
$458$		0			0
$459$	−3741.56	−	8355.99i	−0.380482	−	0.849726i
$460$		0			0
$461$	9386.24	−	16257.4i	0.948288	−	1.64248i	0.199257	−	0.979947i	$-0.436147\pi$
$461$	9386.24	−	16257.4i	0.948288	−	1.64248i	0.749031	−	0.662535i	$-0.230519\pi$
$462$		0			0
$463$	−3011.11	−	5215.40i	−0.302243	−	0.523499i	0.674401	−	0.738365i	$-0.264402\pi$
$463$	−3011.11	−	5215.40i	−0.302243	−	0.523499i	−0.976644	+	0.214866i	$0.931069\pi$
$464$		0			0
$465$	7942.75	+	10151.5i	0.792120	+	1.01239i
$466$		0			0
$467$	−8896.12			−0.881506			−0.440753	−	0.897628i	$-0.645289\pi$
$467$	−8896.12			−0.881506			−0.440753	+	0.897628i	$0.645289\pi$
$468$		0			0
$469$	9700.90	+	134.532i	0.955109	+	0.0132454i
$470$		0			0
$471$	−10895.6	+	1539.13i	−1.06591	+	0.150572i
$472$		0			0
$473$	−2232.15	+	1288.73i	−0.216986	+	0.125277i
$474$		0			0
$475$	6584.29	+	3801.44i	0.636017	+	0.367205i
$476$		0			0
$477$	−1314.30	+	1364.85i	−0.126158	+	0.131011i
$478$		0			0
$479$	−6.85714	+	11.8769i	−0.000654094	+	0.00113292i	−0.866352	−	0.499433i	$-0.833542\pi$
$479$	−6.85714	+	11.8769i	−0.000654094	+	0.00113292i	0.865698	+	0.500566i	$0.166875\pi$
$480$		0			0
$481$	−1177.25	+	679.688i	−0.111597	+	0.0644306i
$482$		0			0
$483$	−3019.45	+	7199.14i	−0.284451	+	0.678204i
$484$		0			0
$485$		−	14274.1i		−	1.33640i
$486$		0			0
$487$	14175.4			1.31899			0.659497	−	0.751708i	$-0.270770\pi$
$487$	14175.4			1.31899			0.659497	+	0.751708i	$0.270770\pi$
$488$		0			0
$489$	300.305	+	121.084i	0.0277715	+	0.0111976i
$490$		0			0
$491$	1949.66	−	1125.63i	0.179199	−	0.103461i	−0.407717	−	0.913108i	$-0.633675\pi$
$491$	1949.66	−	1125.63i	0.179199	−	0.103461i	0.586916	+	0.809648i	$0.300342\pi$
$492$		0			0
$493$	−15243.2	−	8800.67i	−1.39253	−	0.803980i
$494$		0			0
$495$	19448.8	−	20196.8i	1.76598	−	1.83390i
$496$		0			0
$497$	−14254.2	−	8495.34i	−1.28649	−	0.766736i
$498$		0			0
$499$	−3676.93	−	6368.63i	−0.329864	−	0.571340i	0.652621	−	0.757685i	$-0.273669\pi$
$499$	−3676.93	−	6368.63i	−0.329864	−	0.571340i	−0.982485	+	0.186344i	$0.940336\pi$
$500$		0			0
$501$	−733.849	−	5194.98i	−0.0654410	−	0.463263i
$502$		0			0
$503$	9876.83			0.875519			0.437759	−	0.899092i	$-0.355772\pi$
$503$	9876.83			0.875519			0.437759	+	0.899092i	$0.355772\pi$
$504$		0			0
$505$	−28698.0			−2.52880
$506$		0			0
$507$	8512.12	−	6660.08i	0.745634	−	0.583402i
$508$		0			0
$509$	−3653.69	−	6328.37i	−0.318167	−	0.551081i	0.661939	−	0.749558i	$-0.269734\pi$
$509$	−3653.69	−	6328.37i	−0.318167	−	0.551081i	−0.980106	+	0.198477i	$0.936401\pi$
$510$		0			0
$511$	15633.5	+	9317.43i	1.35340	+	0.806612i
$512$		0			0
$513$	−4686.98	+	2098.69i	−0.403382	+	0.180623i
$514$		0			0
$515$	−10890.7	−	6287.73i	−0.931845	−	0.538001i
$516$		0			0
$517$	23774.7	−	13726.3i	2.02246	−	1.16767i
$518$		0			0
$519$	1915.30	−	1498.57i	0.161989	−	0.126744i
$520$		0			0
$521$	−16702.5			−1.40451			−0.702256	−	0.711924i	$-0.747824\pi$
$521$	−16702.5			−1.40451			−0.702256	+	0.711924i	$0.747824\pi$
$522$		0			0
$523$		−	17735.9i		−	1.48286i	−0.671028	−	0.741432i	$-0.734147\pi$
$523$		−	17735.9i		−	1.48286i	0.671028	−	0.741432i	$-0.265853\pi$
$524$		0			0
$525$	2521.12	+	19828.8i	0.209582	+	1.64838i
$526$		0			0
$527$	−7685.77	+	4437.38i	−0.635289	+	0.366784i
$528$		0			0
$529$	−2793.10	+	4837.79i	−0.229564	+	0.397616i
$530$		0			0
$531$	−2294.94	+	9260.20i	−0.187555	+	0.756796i
$532$		0			0
$533$	−2201.80	−	1271.21i	−0.178932	−	0.103306i
$534$		0			0
$535$	9914.45	−	5724.11i	0.801194	−	0.462570i
$536$		0			0
$537$	3942.10	−	9776.91i	0.316786	−	0.785670i
$538$		0			0
$539$	−541.521	+	19520.5i	−0.0432745	+	1.55994i
$540$		0			0
$541$	−14759.1			−1.17291			−0.586454	−	0.809983i	$-0.699476\pi$
$541$	−14759.1			−1.17291			−0.586454	+	0.809983i	$0.699476\pi$
$542$		0			0
$543$	7769.76	−	19270.0i	0.614056	−	1.52294i
$544$		0			0
$545$	−10128.0	−	17542.2i	−0.796030	−	1.37876i
$546$		0			0
$547$	−1188.36	+	2058.30i	−0.0928897	+	0.160890i	−0.908726	−	0.417393i	$-0.862944\pi$
$547$	−1188.36	+	2058.30i	−0.0928897	+	0.160890i	0.815836	+	0.578283i	$0.196277\pi$
$548$		0			0
$549$	4426.78	+	15356.1i	0.344136	+	1.19378i
$550$		0			0
$551$	−4936.40	+	8550.10i	−0.381666	+	0.661064i
$552$		0			0
$553$	9221.10	+	16495.5i	0.709080	+	1.26846i
$554$		0			0
$555$	1666.07	+	11794.2i	0.127425	+	0.902050i
$556$		0			0
$557$			15.7702i			0.00119965i	1.00000		0.000599827i	$0.000190931\pi$
$557$			15.7702i			0.00119965i	−1.00000		0.000599827i	$0.999809\pi$
$558$		0			0
$559$		−	489.690i		−	0.0370513i
$560$		0			0
$561$	11896.3	+	15204.4i	0.895298	+	1.14426i
$562$		0			0
$563$	3299.49	+	5714.88i	0.246993	+	0.427804i	0.962690	−	0.270607i	$-0.0872243\pi$
$563$	3299.49	+	5714.88i	0.246993	+	0.427804i	−0.715697	+	0.698411i	$0.753891\pi$
$564$		0			0
$565$	−19100.6	−	11027.7i	−1.42224	−	0.821132i
$566$		0			0
$567$	−11850.2	−	6469.70i	−0.877710	−	0.479192i
$568$		0			0
$569$	−22038.3	−	12723.8i	−1.62371	−	0.937450i	−0.985915	−	0.167245i	$-0.946513\pi$
$569$	−22038.3	−	12723.8i	−1.62371	−	0.937450i	−0.637796	−	0.770205i	$-0.720154\pi$
$570$		0			0
$571$	10540.7	+	18257.0i	0.772527	+	1.33806i	0.936174	+	0.351538i	$0.114341\pi$
$571$	10540.7	+	18257.0i	0.772527	+	1.33806i	−0.163646	+	0.986519i	$0.552326\pi$
$572$		0			0
$573$	6459.12	+	8255.27i	0.470914	+	0.601865i
$574$		0			0
$575$		−	16849.6i		−	1.22205i
$576$		0			0
$577$			847.126i			0.0611201i	0.999533	+	0.0305601i	$0.00972908\pi$
$577$			847.126i			0.0611201i	−0.999533	+	0.0305601i	$0.990271\pi$
$578$		0			0
$579$	847.396	+	5998.79i	0.0608231	+	0.430572i
$580$		0			0
$581$	2753.43	+	4925.58i	0.196612	+	0.351717i
$582$		0			0
$583$	1997.69	−	3460.10i	0.141914	−	0.245802i
$584$		0			0
$585$	1475.57	+	5118.61i	0.104286	+	0.361758i
$586$		0			0
$587$	−9171.88	+	15886.2i	−0.644913	+	1.11702i	0.339408	+	0.940639i	$0.389773\pi$
$587$	−9171.88	+	15886.2i	−0.644913	+	1.11702i	−0.984322	+	0.176383i	$0.943560\pi$
$588$		0			0
$589$	2488.98	+	4311.04i	0.174120	+	0.301585i
$590$		0			0
$591$	8645.97	−	21443.1i	0.601773	−	1.49247i
$592$		0			0
$593$	−5722.96			−0.396314			−0.198157	−	0.980170i	$-0.563496\pi$
$593$	−5722.96			−0.396314			−0.198157	+	0.980170i	$0.563496\pi$
$594$		0			0
$595$	−22042.9	−	305.690i	−1.51878	−	0.0210623i
$596$		0			0
$597$	10019.2	−	24849.0i	0.686867	−	1.70352i
$598$		0			0
$599$	−8776.18	+	5066.93i	−0.598639	+	0.345625i	−0.768506	−	0.639842i	$-0.779000\pi$
$599$	−8776.18	+	5066.93i	−0.598639	+	0.345625i	0.169867	+	0.985467i	$0.445666\pi$
$600$		0			0
$601$	−6127.51	−	3537.72i	−0.415884	−	0.240111i	0.277431	−	0.960746i	$-0.410517\pi$
$601$	−6127.51	−	3537.72i	−0.415884	−	0.240111i	−0.693315	+	0.720635i	$0.743850\pi$
$602$		0			0
$603$	3402.34	−	13728.6i	0.229774	−	0.927153i
$604$		0			0
$605$	−17422.6	+	30176.8i	−1.17079	+	2.02787i
$606$		0			0
$607$	−11291.3	+	6519.01i	−0.755021	+	0.435912i	−0.827505	−	0.561458i	$-0.810241\pi$
$607$	−11291.3	+	6519.01i	−0.755021	+	0.435912i	0.0724839	+	0.997370i	$0.476907\pi$
$608$		0			0
$609$	−25748.9	+	3273.83i	−1.71330	+	0.217836i
$610$		0			0
$611$			5215.71i			0.345344i
$612$		0			0
$613$	5876.91			0.387220			0.193610	−	0.981079i	$-0.437980\pi$
$613$	5876.91			0.387220			0.193610	+	0.981079i	$0.437980\pi$
$614$		0			0
$615$	−17545.3	+	13727.9i	−1.15040	+	0.900099i
$616$		0			0
$617$	9655.60	−	5574.66i	0.630016	−	0.363740i	−0.150742	−	0.988573i	$-0.548166\pi$
$617$	9655.60	−	5574.66i	0.630016	−	0.363740i	0.780758	+	0.624833i	$0.214833\pi$
$618$		0			0
$619$	−15732.2	−	9083.00i	−1.02154	−	0.589785i	−0.106988	−	0.994260i	$-0.534121\pi$
$619$	−15732.2	−	9083.00i	−1.02154	−	0.589785i	−0.914549	+	0.404476i	$0.867454\pi$
$620$		0			0
$621$	9221.67	+	6670.13i	0.595898	+	0.431019i
$622$		0			0
$623$	9695.78	−	16268.4i	0.623520	−	1.04619i
$624$		0			0
$625$	−776.867	−	1345.57i	−0.0497195	−	0.0861167i
$626$		0			0
$627$	8528.35	−	6672.78i	0.543205	−	0.425016i
$628$		0			0
$629$	−8201.26			−0.519882
$630$		0			0
$631$	6044.76			0.381360			0.190680	−	0.981652i	$-0.438931\pi$
$631$	6044.76			0.381360			0.190680	+	0.981652i	$0.438931\pi$
$632$		0			0
$633$	515.385	+	3648.46i	0.0323613	+	0.229089i
$634$		0			0
$635$	24509.4	+	42451.5i	1.53169	+	2.65297i
$636$		0			0
$637$	−3160.37	−	1943.44i	−0.196575	−	0.120882i
$638$		0			0
$639$	−16780.1	+	17425.5i	−1.03883	+	1.07879i
$640$		0			0
$641$	3969.31	+	2291.68i	0.244584	+	0.141211i	0.617282	−	0.786742i	$-0.288234\pi$
$641$	3969.31	+	2291.68i	0.244584	+	0.141211i	−0.372698	+	0.927953i	$0.621567\pi$
$642$		0			0
$643$	6413.00	−	3702.55i	0.393319	−	0.227083i	−0.290278	−	0.956942i	$-0.593748\pi$
$643$	6413.00	−	3702.55i	0.393319	−	0.227083i	0.683597	+	0.729860i	$0.260415\pi$
$644$		0			0
$645$	−3979.53	−	1604.56i	−0.242936	−	0.0979530i
$646$		0			0
$647$	−21755.4			−1.32193			−0.660967	−	0.750415i	$-0.729854\pi$
$647$	−21755.4			−1.32193			−0.660967	+	0.750415i	$0.729854\pi$
$648$		0			0
$649$		−	20117.0i		−	1.21673i
$650$		0			0
$651$	−5061.89	+	12068.8i	−0.304748	+	0.726597i
$652$		0			0
$653$	−1656.32	+	956.276i	−0.0992599	+	0.0573078i	−0.548808	−	0.835948i	$-0.684918\pi$
$653$	−1656.32	+	956.276i	−0.0992599	+	0.0573078i	0.449548	+	0.893256i	$0.351585\pi$
$654$		0			0
$655$	1350.79	−	2339.64i	0.0805800	−	0.139569i
$656$		0			0
$657$	18404.0	−	19111.8i	1.09286	−	1.13489i
$658$		0			0
$659$	−1009.42	−	582.787i	−0.0596681	−	0.0344494i	0.469869	−	0.882736i	$-0.344301\pi$
$659$	−1009.42	−	582.787i	−0.0596681	−	0.0344494i	−0.529537	+	0.848287i	$0.677634\pi$
$660$		0			0
$661$	20327.5	−	11736.1i	1.19614	−	0.690593i	0.236449	−	0.971644i	$-0.424016\pi$
$661$	20327.5	−	11736.1i	1.19614	−	0.690593i	0.959693	+	0.281051i	$0.0906830\pi$
$662$		0			0
$663$	−3631.75	+	513.026i	−0.212738	+	0.0300517i
$664$		0			0
$665$	−171.465	+	12364.1i	−0.00999870	+	0.720994i
$666$		0			0
$667$	21880.2			1.27017
$668$		0			0
$669$	−999.956	−	1278.02i	−0.0577885	−	0.0738584i
$670$		0			0
$671$	−16849.4	−	29184.1i	−0.969396	−	1.67904i
$672$		0			0
$673$	12009.3	−	20800.7i	0.687850	−	1.19139i	−0.284682	−	0.958622i	$-0.591888\pi$
$673$	12009.3	−	20800.7i	0.687850	−	1.19139i	0.972532	−	0.232770i	$-0.0747788\pi$
$674$		0			0
$675$	28987.2	+	2984.59i	1.65292	+	0.170188i
$676$		0			0
$677$	−8076.04	+	13988.1i	−0.458475	+	0.794102i	−0.998881	−	0.0473029i	$-0.984937\pi$
$677$	−8076.04	+	13988.1i	−0.458475	+	0.794102i	0.540406	+	0.841405i	$0.318271\pi$
$678$		0			0
$679$	12650.8	−	7071.89i	0.715013	−	0.399697i
$680$		0			0
$681$	−2985.15	+	2335.65i	−0.167975	+	0.131428i
$682$		0			0
$683$		−	28554.3i		−	1.59970i	−0.600197	−	0.799852i	$-0.704911\pi$
$683$		−	28554.3i		−	1.59970i	0.600197	−	0.799852i	$-0.295089\pi$
$684$		0			0
$685$			18548.8i			1.03462i
$686$		0			0
$687$	8319.98	−	1175.29i	0.462048	−	0.0652695i
$688$		0			0
$689$	379.539	+	657.381i	0.0209859	+	0.0363487i
$690$		0			0
$691$	−29465.7	−	17012.0i	−1.62218	−	0.936567i	−0.986335	−	0.164753i	$-0.947317\pi$
$691$	−29465.7	−	17012.0i	−1.62218	−	0.936567i	−0.635848	−	0.771815i	$-0.719349\pi$
$692$		0			0
$693$	27535.5	+	7230.79i	1.50936	+	0.396356i
$694$		0			0
$695$	40516.7	+	23392.3i	2.21135	+	1.27672i
$696$		0			0
$697$	−7669.36	−	13283.7i	−0.416783	−	0.721889i
$698$		0			0
$699$	4347.08	−	10781.3i	0.235224	−	0.583386i
$700$		0			0
$701$			9879.92i			0.532325i	0.963928	+	0.266162i	$0.0857557\pi$
$701$			9879.92i			0.532325i	−0.963928	+	0.266162i	$0.914244\pi$
$702$		0			0
$703$			4600.19i			0.246799i
$704$		0			0
$705$	42386.1	+	17090.3i	2.26433	+	0.912990i
$706$		0			0
$707$	−14218.0	−	25434.4i	−0.756325	−	1.35298i
$708$		0			0
$709$	−16309.1	+	28248.1i	−0.863893	+	1.49631i	0.00424980	+	0.999991i	$0.498647\pi$
$709$	−16309.1	+	28248.1i	−0.863893	+	1.49631i	−0.868142	+	0.496315i	$0.834686\pi$
$710$		0			0
$711$	26472.5	−	7631.36i	1.39634	−	0.402529i
$712$		0			0
$713$	5516.11	−	9554.18i	0.289733	−	0.501833i
$714$		0			0
$715$	−5616.37	−	9727.83i	−0.293763	−	0.508812i
$716$		0			0
$717$	26478.3	−	3740.36i	1.37915	−	0.194820i
$718$		0			0
$719$	22467.8			1.16538			0.582689	−	0.812695i	$-0.302000\pi$
$719$	22467.8			1.16538			0.582689	+	0.812695i	$0.302000\pi$
$720$		0			0
$721$	177.056	−	12767.3i	0.00914550	−	0.659471i
$722$		0			0
$723$	3452.74	+	4412.88i	0.177606	+	0.226994i
$724$		0			0
$725$	48517.0	−	28011.3i	2.48534	−	1.43491i
$726$		0			0
$727$	9455.61	+	5459.20i	0.482378	+	0.278501i	0.721407	−	0.692511i	$-0.243496\pi$
$727$	9455.61	+	5459.20i	0.482378	+	0.278501i	−0.239029	+	0.971013i	$0.576829\pi$
$728$		0			0
$729$	−13108.4	+	14683.0i	−0.665975	+	0.745974i
$730$		0			0
$731$	1477.18	−	2558.54i	0.0747405	−	0.129454i
$732$		0			0
$733$	−10792.3	+	6230.94i	−0.543824	+	0.313977i	−0.746627	−	0.665243i	$-0.768328\pi$
$733$	−10792.3	+	6230.94i	−0.543824	+	0.313977i	0.202803	+	0.979219i	$0.434995\pi$
$734$		0			0
$735$	−26149.2	+	19315.1i	−1.31228	+	0.969316i
$736$		0			0
$737$			29824.3i			1.49062i
$738$		0			0
$739$	8019.93			0.399212			0.199606	−	0.979876i	$-0.436034\pi$
$739$	8019.93			0.399212			0.199606	+	0.979876i	$0.436034\pi$
$740$		0			0
$741$	287.762	+	2037.10i	0.0142662	+	0.100991i
$742$		0			0
$743$	−17310.5	+	9994.23i	−0.854725	+	0.493476i	−0.862242	−	0.506496i	$-0.830941\pi$
$743$	−17310.5	+	9994.23i	−0.854725	+	0.493476i	0.00751697	+	0.999972i	$0.497607\pi$
$744$		0			0
$745$	6547.74	+	3780.34i	0.322001	+	0.185907i
$746$		0			0
$747$	7904.73	−	2278.73i	0.387174	−	0.111612i
$748$		0			0
$749$	9985.09	+	5951.01i	0.487112	+	0.290314i
$750$		0			0
$751$	−5462.66	−	9461.60i	−0.265426	−	0.459732i	0.702249	−	0.711931i	$-0.252179\pi$
$751$	−5462.66	−	9461.60i	−0.265426	−	0.459732i	−0.967675	+	0.252200i	$0.918846\pi$
$752$		0			0
$753$	−16525.7	−	6663.26i	−0.799776	−	0.322473i
$754$		0			0
$755$	−34649.6			−1.67024
$756$		0			0
$757$	32902.1			1.57972			0.789859	−	0.613288i	$-0.210153\pi$
$757$	32902.1			1.57972			0.789859	+	0.613288i	$0.210153\pi$
$758$		0			0
$759$	−22257.4	−	8974.27i	−1.06441	−	0.429177i
$760$		0			0
$761$	13873.1	+	24028.9i	0.660839	+	1.14461i	0.980395	+	0.197040i	$0.0631329\pi$
$761$	13873.1	+	24028.9i	0.660839	+	1.14461i	−0.319556	+	0.947567i	$0.603534\pi$
$762$		0			0
$763$	10529.5	−	17667.2i	0.499597	−	0.838264i
$764$		0			0
$765$	−7730.98	+	31194.9i	−0.365378	+	1.47432i
$766$		0			0
$767$	3309.96	+	1911.01i	0.155822	+	0.0899641i
$768$		0			0
$769$	22748.3	−	13133.8i	1.06674	−	0.615885i	0.139454	−	0.990229i	$-0.455465\pi$
$769$	22748.3	−	13133.8i	1.06674	−	0.615885i	0.927290	+	0.374344i	$0.122132\pi$
$770$		0			0
$771$	−4934.71	−	34933.2i	−0.230505	−	1.63176i
$772$		0			0
$773$	−1419.67			−0.0660570			−0.0330285	−	0.999454i	$-0.510515\pi$
$773$	−1419.67			−0.0660570			−0.0330285	+	0.999454i	$0.510515\pi$
$774$		0			0
$775$		−	28247.1i		−	1.30925i
$776$		0			0
$777$	−9627.52	+	7319.86i	−0.444511	+	0.337965i
$778$		0			0
$779$	−7451.00	+	4301.84i	−0.342696	+	0.197855i
$780$		0			0
$781$	25505.3	−	44176.4i	1.16857	−	2.02402i
$782$		0			0
$783$	−3875.67	+	37641.6i	−0.176890	+	1.71801i
$784$		0			0
$785$	33452.0	+	19313.5i	1.52096	+	0.878127i
$786$		0			0
$787$	−11207.6	+	6470.69i	−0.507632	+	0.293082i	−0.731860	−	0.681455i	$-0.761347\pi$
$787$	−11207.6	+	6470.69i	−0.507632	+	0.293082i	0.224227	+	0.974537i	$0.428014\pi$
$788$		0			0
$789$	24744.8	+	31625.8i	1.11652	+	1.42701i
$790$		0			0
$791$	310.529	−	22391.9i	0.0139585	−	1.00653i
$792$		0			0
$793$	6402.42			0.286705
$794$		0			0
$795$	6585.93	−	930.336i	0.293810	−	0.0415039i
$796$		0			0
$797$	5013.20	+	8683.11i	0.222806	+	0.385912i	0.955659	−	0.294476i	$-0.0951450\pi$
$797$	5013.20	+	8683.11i	0.222806	+	0.385912i	−0.732853	+	0.680387i	$0.761812\pi$
$798$		0			0
$799$	−15733.5	+	27251.2i	−0.696633	+	1.20660i
$800$		0			0
$801$	−19887.9	−	19151.3i	−0.877283	−	0.844791i
$802$		0			0
$803$	−27973.4	+	48451.4i	−1.22934	+	2.12928i
$804$		0			0
$805$	23920.5	−	13371.7i	1.04731	−	0.585454i
$806$		0			0
$807$	11841.5	+	4774.55i	0.516531	+	0.208268i
$808$		0			0
$809$			17736.4i			0.770800i	0.922750	+	0.385400i	$0.125937\pi$
$809$			17736.4i			0.770800i	−0.922750	+	0.385400i	$0.874063\pi$
$810$		0			0
$811$		−	2438.23i		−	0.105571i	−0.998606	−	0.0527853i	$-0.983190\pi$
$811$		−	2438.23i		−	0.105571i	0.998606	−	0.0527853i	$-0.0168099\pi$
$812$		0			0
$813$	11814.4	−	29301.3i	0.509655	−	1.26401i
$814$		0			0
$815$	−568.319	−	984.357i	−0.0244262	−	0.0423074i
$816$		0			0
$817$	−1435.12	−	828.566i	−0.0614546	−	0.0354808i
$818$		0			0
$819$	−3805.45	+	3843.69i	−0.162360	+	0.163992i
$820$		0			0
$821$	−24719.7	−	14271.9i	−1.05082	−	0.606691i	−0.127941	−	0.991782i	$-0.540837\pi$
$821$	−24719.7	−	14271.9i	−1.05082	−	0.606691i	−0.922879	+	0.385091i	$0.874170\pi$
$822$		0			0
$823$	−16131.9	−	27941.3i	−0.683261	−	1.18344i	−0.973980	−	0.226635i	$-0.927228\pi$
$823$	−16131.9	−	27941.3i	−0.683261	−	1.18344i	0.290718	−	0.956809i	$-0.406106\pi$
$824$		0			0
$825$	−60842.2	+	8594.64i	−2.56758	+	0.362699i
$826$		0			0
$827$		−	28049.2i		−	1.17940i	−0.807622	−	0.589701i	$-0.799246\pi$
$827$		−	28049.2i		−	1.17940i	0.807622	−	0.589701i	$-0.200754\pi$
$828$		0			0
$829$		−	3574.94i		−	0.149774i	−0.997192	−	0.0748870i	$-0.976140\pi$
$829$		−	3574.94i		−	0.149774i	0.997192	−	0.0748870i	$-0.0238596\pi$
$830$		0			0
$831$	8944.12	−	6998.09i	0.373367	−	0.292131i
$832$		0			0
$833$	−10649.9	−	19687.5i	−0.442973	−	0.818887i
$834$		0			0
$835$	−9208.59	+	15949.7i	−0.381648	+	0.661034i
$836$		0			0
$837$	15459.5	+	11182.0i	0.638419	+	0.461775i
$838$		0			0
$839$	9245.81	−	16014.2i	0.380454	−	0.658966i	−0.610673	−	0.791883i	$-0.709101\pi$
$839$	9245.81	−	16014.2i	0.380454	−	0.658966i	0.991127	+	0.132917i	$0.0424344\pi$
$840$		0			0
$841$	24179.8	+	41880.7i	0.991424	+	1.71720i
$842$		0			0
$843$	8121.63	+	10380.1i	0.331819	+	0.424092i
$844$		0			0
$845$	−37939.7			−1.54458
$846$		0			0
$847$	−35376.7	−	490.602i	−1.43513	−	0.0199024i
$848$		0			0
$849$	−21549.3	+	3044.09i	−0.871109	+	0.123054i
$850$		0			0
$851$	8829.12	−	5097.50i	0.355650	−	0.205335i
$852$		0			0
$853$	16048.0	+	9265.31i	0.644165	+	0.371909i	0.786217	−	0.617950i	$-0.212037\pi$
$853$	16048.0	+	9265.31i	0.644165	+	0.371909i	−0.142052	+	0.989859i	$0.545370\pi$
$854$		0			0
$855$	17497.6	+	4336.40i	0.699890	+	0.173452i
$856$		0			0
$857$	2912.03	−	5043.79i	0.116071	−	0.201041i	−0.802136	−	0.597141i	$-0.796303\pi$
$857$	2912.03	−	5043.79i	0.116071	−	0.201041i	0.918207	+	0.396100i	$0.129637\pi$
$858$		0			0
$859$	−15711.1	+	9070.82i	−0.624047	+	0.360294i	−0.778443	−	0.627715i	$-0.783990\pi$
$859$	−15711.1	+	9070.82i	−0.624047	+	0.360294i	0.154396	+	0.988009i	$0.450657\pi$
$860$		0			0
$861$	−20859.2	−	8748.73i	−0.825645	−	0.346290i
$862$		0			0
$863$		−	30785.2i		−	1.21430i	−0.794587	−	0.607150i	$-0.792313\pi$
$863$		−	30785.2i		−	1.21430i	0.794587	−	0.607150i	$-0.207687\pi$
$864$		0			0
$865$	−8536.75			−0.335558
$866$		0			0
$867$	3153.70	+	1271.59i	0.123536	+	0.0498102i
$868$		0			0
$869$	−50310.6	+	29046.9i	−1.96395	+	1.13389i
$870$		0			0
$871$	−4907.15	−	2833.14i	−0.190898	−	0.110215i
$872$		0			0
$873$	−5852.68	−	20302.4i	−0.226900	−	0.787095i
$874$		0			0
$875$	14303.9	−	24000.3i	0.552641	−	0.927265i
$876$		0			0
$877$	7709.14	+	13352.6i	0.296829	+	0.514123i	0.975409	−	0.220404i	$-0.0707375\pi$
$877$	7709.14	+	13352.6i	0.296829	+	0.514123i	−0.678580	+	0.734527i	$0.737404\pi$
$878$		0			0
$879$	5453.69	+	38607.1i	0.209270	+	1.48144i
$880$		0			0
$881$	32547.9			1.24469			0.622343	−	0.782745i	$-0.286181\pi$
$881$	32547.9			1.24469			0.622343	+	0.782745i	$0.286181\pi$
$882$		0			0
$883$	8816.39			0.336008			0.168004	−	0.985786i	$-0.446268\pi$
$883$	8816.39			0.336008			0.168004	+	0.985786i	$0.446268\pi$
$884$		0			0
$885$	26375.8	−	20637.0i	1.00182	−	0.783849i
$886$		0			0
$887$	7698.51	+	13334.2i	0.291421	+	0.504756i	0.974146	−	0.225919i	$-0.0725386\pi$
$887$	7698.51	+	13334.2i	0.291421	+	0.504756i	−0.682725	+	0.730676i	$0.739205\pi$
$888$		0			0
$889$	−25480.9	+	42754.0i	−0.961308	+	1.61296i
$890$		0			0
$891$	19381.4	−	36700.8i	0.728731	−	1.37994i
$892$		0			0
$893$	15285.5	+	8825.10i	0.572800	+	0.330706i
$894$		0			0
$895$	−32047.3	+	18502.5i	−1.19690	+	0.691029i
$896$		0			0
$897$	3590.92	−	2809.62i	0.133665	−	0.104582i
$898$		0			0
$899$	36680.6			1.36081
$900$		0			0
$901$			4579.60i			0.169333i
$902$		0			0
$903$	−549.506	−	4321.91i	−0.0202507	−	0.159274i
$904$		0			0
$905$	−63164.3	+	36467.9i	−2.32006	+	1.33949i
$906$		0			0
$907$	−6029.71	+	10443.8i	−0.220742	+	0.382337i	−0.955034	−	0.296498i	$-0.904181\pi$
$907$	−6029.71	+	10443.8i	−0.220742	+	0.382337i	0.734291	+	0.678835i	$0.237515\pi$
$908$		0			0
$909$	−40817.9	+	11766.8i	−1.48938	+	0.429350i
$910$		0			0
$911$	−8661.13	−	5000.50i	−0.314990	−	0.181860i	0.334167	−	0.942514i	$-0.391545\pi$
$911$	−8661.13	−	5000.50i	−0.314990	−	0.181860i	−0.649157	+	0.760654i	$0.724878\pi$
$912$		0			0
$913$	−15022.8	+	8673.43i	−0.544559	+	0.314401i
$914$		0			0
$915$	20978.8	−	52030.1i	0.757964	−	1.87985i
$916$		0			0
$917$	2742.80	+	38.0369i	0.0987733	+	0.00136978i
$918$		0			0
$919$	−7722.40			−0.277191			−0.138596	−	0.990349i	$-0.544259\pi$
$919$	−7722.40			−0.277191			−0.138596	+	0.990349i	$0.544259\pi$
$920$		0			0
$921$	8384.53	−	20794.7i	0.299978	−	0.743984i
$922$		0			0
$923$	4845.73	+	8393.04i	0.172805	+	0.299307i
$924$		0			0
$925$	13051.7	−	22606.3i	0.463933	−	0.803556i
$926$		0			0
$927$	−18068.1	−	4477.79i	−0.640168	−	0.158652i
$928$		0			0
$929$	6779.53	−	11742.5i	0.239429	−	0.414702i	−0.721122	−	0.692808i	$-0.756373\pi$
$929$	6779.53	−	11742.5i	0.239429	−	0.414702i	0.960550	+	0.278106i	$0.0897066\pi$
$930$		0			0
$931$	−11043.0	+	5973.65i	−0.388742	+	0.210288i
$932$		0			0
$933$	−3233.41	−	22889.6i	−0.113459	−	0.803184i
$934$		0			0
$935$		−	67768.3i		−	2.37033i
$936$		0			0
$937$			28967.7i			1.00996i	0.863131	+	0.504980i	$0.168500\pi$
$937$			28967.7i			1.00996i	−0.863131	+	0.504980i	$0.831500\pi$
$938$		0			0
$939$	−24162.6	−	30881.8i	−0.839742	−	1.07326i
$940$		0			0
$941$	−10159.8	−	17597.2i	−0.351965	−	0.609621i	0.634629	−	0.772817i	$-0.281153\pi$
$941$	−10159.8	−	17597.2i	−0.351965	−	0.609621i	−0.986594	+	0.163196i	$0.947820\pi$
$942$		0			0
$943$	16513.0	+	9533.79i	0.570241	+	0.329229i
$944$		0			0
$945$	18766.9	+	43520.1i	0.646019	+	1.49810i
$946$		0			0
$947$	−8045.62	−	4645.14i	−0.276080	−	0.159395i	0.355568	−	0.934651i	$-0.384288\pi$
$947$	−8045.62	−	4645.14i	−0.276080	−	0.159395i	−0.631647	+	0.775256i	$0.717621\pi$
$948$		0			0
$949$	−5314.65	−	9205.24i	−0.181792	−	0.314873i
$950$		0			0
$951$	28986.4	+	37047.0i	0.988380	+	1.26323i
$952$		0			0
$953$		−	38803.4i		−	1.31896i	−0.751724	−	0.659478i	$-0.770777\pi$
$953$		−	38803.4i		−	1.31896i	0.751724	−	0.659478i	$-0.229223\pi$
$954$		0			0
$955$		−	36794.9i		−	1.24676i
$956$		0			0
$957$	−11160.7	−	79007.2i	−0.376983	−	2.66869i
$958$		0			0
$959$	−16439.3	+	9189.69i	−0.553549	+	0.309438i
$960$		0			0
$961$	−5648.15	+	9782.88i	−0.189592	+	0.328384i
$962$		0			0
$963$	11754.5	−	12206.7i	0.393339	−	0.408467i
$964$		0			0
$965$	10633.4	−	18417.6i	0.354717	−	0.614388i
$966$		0			0
$967$	−1327.12	−	2298.64i	−0.0441338	−	0.0764420i	0.843115	−	0.537734i	$-0.180719\pi$
$967$	−1327.12	−	2298.64i	−0.0441338	−	0.0764420i	−0.887248	+	0.461292i	$0.847386\pi$
$968$		0			0
$969$	−4641.50	+	11511.5i	−0.153877	+	0.381634i
$970$		0			0
$971$	9651.29			0.318975			0.159487	−	0.987200i	$-0.449016\pi$
$971$	9651.29			0.318975			0.159487	+	0.987200i	$0.449016\pi$
$972$		0			0
$973$	−658.704	+	47498.3i	−0.0217031	+	1.56498i
$974$		0			0
$975$	4365.56	−	10827.1i	0.143395	−	0.355637i
$976$		0			0
$977$	11836.4	−	6833.72i	0.387593	−	0.223777i	−0.293524	−	0.955952i	$-0.594828\pi$
$977$	11836.4	−	6833.72i	0.387593	−	0.223777i	0.681117	+	0.732175i	$0.261495\pi$
$978$		0			0
$979$	50418.8	+	29109.3i	1.64596	+	0.950293i
$980$		0			0
$981$	−21598.0	−	20798.0i	−0.702925	−	0.676891i
$982$		0			0
$983$	1350.47	−	2339.08i	0.0438181	−	0.0758952i	−0.843285	−	0.537467i	$-0.819381\pi$
$983$	1350.47	−	2339.08i	0.0438181	−	0.0758952i	0.887103	+	0.461572i	$0.152714\pi$
$984$		0			0
$985$	−70287.5	+	40580.5i	−2.27365	+	1.31269i
$986$		0			0
$987$	5852.81	+	46032.9i	0.188751	+	1.48454i
$988$		0			0
$989$			3672.56i			0.118079i
$990$		0			0
$991$	−50519.8			−1.61939			−0.809694	−	0.586852i	$-0.800367\pi$
$991$	−50519.8			−1.61939			−0.809694	+	0.586852i	$0.800367\pi$
$992$		0			0
$993$	−27555.4	+	21560.0i	−0.880609	+	0.689009i
$994$		0			0
$995$	−81451.3	+	47025.9i	−2.59516	+	1.49831i
$996$		0			0
$997$	−14397.0	−	8312.09i	−0.457329	−	0.264039i	0.253592	−	0.967311i	$-0.418388\pi$
$997$	−14397.0	−	8312.09i	−0.457329	−	0.264039i	−0.710920	+	0.703273i	$0.751721\pi$
$998$		0			0
$999$	7205.56	+	16092.1i	0.228202	+	0.509641i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.x.a.209.3	yes	48
3.2	odd	2		756.4.x.a.629.2		48
7.6	odd	2	inner	252.4.x.a.209.22	yes	48
9.2	odd	6		2268.4.f.a.1133.45		48
9.4	even	3		756.4.x.a.125.23		48
9.5	odd	6	inner	252.4.x.a.41.22	yes	48
9.7	even	3		2268.4.f.a.1133.4		48
21.20	even	2		756.4.x.a.629.23		48
63.13	odd	6		756.4.x.a.125.2		48
63.20	even	6		2268.4.f.a.1133.3		48
63.34	odd	6		2268.4.f.a.1133.46		48
63.41	even	6	inner	252.4.x.a.41.3	✓	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.x.a.41.3	✓	48	63.41	even	6	inner
252.4.x.a.41.22	yes	48	9.5	odd	6	inner
252.4.x.a.209.3	yes	48	1.1	even	1	trivial
252.4.x.a.209.22	yes	48	7.6	odd	2	inner
756.4.x.a.125.2		48	63.13	odd	6
756.4.x.a.125.23		48	9.4	even	3
756.4.x.a.629.2		48	3.2	odd	2
756.4.x.a.629.23		48	21.20	even	2
2268.4.f.a.1133.3		48	63.20	even	6
2268.4.f.a.1133.4		48	9.7	even	3
2268.4.f.a.1133.45		48	9.2	odd	6
2268.4.f.a.1133.46		48	63.34	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.x (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-4.81916 - 1.94311i) q^{3} +(9.12012 + 15.7965i) q^{5} +(-9.48165 + 15.9091i) q^{7} +(19.4487 + 18.7283i) q^{9} +O(q^{10})\)	\(q+(-4.81916 - 1.94311i) q^{3} +(9.12012 + 15.7965i) q^{5} +(-9.48165 + 15.9091i) q^{7} +(19.4487 + 18.7283i) q^{9} +(-49.3053 - 28.4664i) q^{11} +(9.36748 - 5.40831i) q^{13} +(-13.2570 - 93.8474i) q^{15} +65.2579 q^{17} -36.6039i q^{19} +(76.6067 - 58.2445i) q^{21} +(-70.2538 + 40.5611i) q^{23} +(-103.853 + 179.879i) q^{25} +(-57.3350 - 128.046i) q^{27} +(-233.584 - 134.860i) q^{29} +(-117.775 + 67.9976i) q^{31} +(182.297 + 232.990i) q^{33} +(-337.782 - 4.68434i) q^{35} -125.675 q^{37} +(-55.6523 + 7.86151i) q^{39} +(-117.524 - 203.557i) q^{41} +(22.6360 - 39.2067i) q^{43} +(-118.468 + 478.026i) q^{45} +(-241.097 + 417.592i) q^{47} +(-163.197 - 301.688i) q^{49} +(-314.488 - 126.803i) q^{51} +70.1770i q^{53} -1038.47i q^{55} +(-71.1255 + 176.400i) q^{57} +(176.673 + 306.007i) q^{59} +(512.605 + 295.953i) q^{61} +(-482.355 + 131.835i) q^{63} +(170.865 + 98.6490i) q^{65} +(-261.925 - 453.667i) q^{67} +(417.379 - 58.9595i) q^{69} +895.977i q^{71} -982.681i q^{73} +(850.011 - 665.069i) q^{75} +(920.369 - 514.492i) q^{77} +(510.195 - 883.684i) q^{79} +(27.5000 + 728.481i) q^{81} +(152.345 - 263.869i) q^{83} +(595.160 + 1030.85i) q^{85} +(863.632 + 1103.79i) q^{87} -1022.58 q^{89} +(-2.77785 + 200.308i) q^{91} +(699.705 - 98.8412i) q^{93} +(578.215 - 333.833i) q^{95} +(-677.719 - 391.281i) q^{97} +(-425.793 - 1477.04i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 6 q^{7} + 60 q^{9}+O(q^{10}) \) 48 * q + 6 * q^7 + 60 * q^9	\( 48 q + 6 q^{7} + 60 q^{9} - 12 q^{11} + 192 q^{15} - 72 q^{21} - 408 q^{23} - 600 q^{25} - 84 q^{29} + 336 q^{37} + 36 q^{39} + 84 q^{43} + 318 q^{49} - 1812 q^{51} - 852 q^{57} - 564 q^{63} + 2964 q^{65} - 588 q^{67} + 2400 q^{77} + 204 q^{79} + 1980 q^{81} - 360 q^{85} - 1080 q^{91} + 2496 q^{93} + 300 q^{95} - 4968 q^{99}+O(q^{100}) \) 48 * q + 6 * q^7 + 60 * q^9 - 12 * q^11 + 192 * q^15 - 72 * q^21 - 408 * q^23 - 600 * q^25 - 84 * q^29 + 336 * q^37 + 36 * q^39 + 84 * q^43 + 318 * q^49 - 1812 * q^51 - 852 * q^57 - 564 * q^63 + 2964 * q^65 - 588 * q^67 + 2400 * q^77 + 204 * q^79 + 1980 * q^81 - 360 * q^85 - 1080 * q^91 + 2496 * q^93 + 300 * q^95 - 4968 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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