LMFDB - Embedded newform 252.4.x.a.41.3

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			41.3
Character	$\chi$	$=$	252.41
Dual form			252.4.x.a.209.3

$q$-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 $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$-1$	$1$

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	−0.0930747	−	0.995659i	$-0.529670\pi$
$5$	9.12012	−	15.7965i	0.815729	−	1.41288i	0.908803	−	0.417225i	$-0.136997\pi$
$6$		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	−0.988455	−	0.151518i	$-0.951584\pi$
$11$	−49.3053	+	28.4664i	−1.35146	+	0.780268i	−0.363009	+	0.931786i	$0.618251\pi$
$12$		0			0
$13$	9.36748	+	5.40831i	0.199852	+	0.115384i	0.596586	−	0.802549i	$-0.296523\pi$
$13$	9.36748	+	5.40831i	0.199852	+	0.115384i	−0.396735	+	0.917933i	$0.629857\pi$
$14$		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	$0.0709280\pi$
$19$			36.6039i			0.441975i	−0.975277	+	0.220987i	$0.929072\pi$
$20$		0			0
$21$	76.6067	+	58.2445i	0.796045	+	0.605238i
$22$		0			0
$23$	−70.2538	−	40.5611i	−0.636910	−	0.367720i	0.146513	−	0.989209i	$-0.453195\pi$
$23$	−70.2538	−	40.5611i	−0.636910	−	0.367720i	−0.783423	+	0.621489i	$0.786528\pi$
$24$		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	−0.999988	−	0.00493734i	$-0.998428\pi$
$29$	−233.584	+	134.860i	−1.49571	+	0.863546i	−0.495718	+	0.868484i	$0.665095\pi$
$30$		0			0
$31$	−117.775	−	67.9976i	−0.682357	−	0.393959i	0.118385	−	0.992968i	$-0.462228\pi$
$31$	−117.775	−	67.9976i	−0.682357	−	0.393959i	−0.800743	+	0.599009i	$0.795562\pi$
$32$		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	−0.998233	−	0.0594145i	$-0.981077\pi$
$41$	−117.524	+	203.557i	−0.447662	+	0.775374i	0.550571	+	0.834788i	$0.314410\pi$
$42$		0			0
$43$	22.6360	+	39.2067i	0.0802780	+	0.139046i	0.903369	−	0.428863i	$-0.141086\pi$
$43$	22.6360	+	39.2067i	0.0802780	+	0.139046i	−0.823091	+	0.567909i	$0.807753\pi$
$44$		0			0
$45$	−118.468	−	478.026i	−0.392449	−	1.58355i
$46$		0			0
$47$	−241.097	−	417.592i	−0.748246	−	1.29600i	−0.948663	−	0.316290i	$-0.897563\pi$
$47$	−241.097	−	417.592i	−0.748246	−	1.29600i	0.200416	−	0.979711i	$-0.435771\pi$
$48$		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	$-0.971013\pi$
$53$		−	70.1770i		−	0.181878i	0.995856	−	0.0909392i	$-0.0289869\pi$
$54$		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	−0.602583	−	0.798056i	$-0.705862\pi$
$59$	176.673	−	306.007i	0.389845	−	0.675232i	0.992428	+	0.122824i	$0.0391952\pi$
$60$		0			0
$61$	512.605	−	295.953i	1.07594	−	0.621194i	0.146142	−	0.989264i	$-0.453314\pi$
$61$	512.605	−	295.953i	1.07594	−	0.621194i	0.929798	+	0.368069i	$0.119981\pi$
$62$		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	−0.999670	−	0.0256746i	$-0.991827\pi$
$67$	−261.925	+	453.667i	−0.477600	+	0.827228i	0.522070	+	0.852903i	$0.325160\pi$
$68$		0			0
$69$	417.379	+	58.9595i	0.728211	+	0.102868i
$70$		0			0
$71$		−	895.977i		−	1.49765i	−0.662770	−	0.748823i	$-0.730619\pi$
$71$		−	895.977i		−	1.49765i	0.662770	−	0.748823i	$-0.269381\pi$
$72$		0			0
$73$			982.681i			1.57554i	0.615972	+	0.787768i	$0.288763\pi$
$73$			982.681i			1.57554i	−0.615972	+	0.787768i	$0.711237\pi$
$74$		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	0.958312	+	0.285725i	$0.0922343\pi$
$79$	510.195	+	883.684i	0.726601	+	1.25851i	−0.231711	+	0.972785i	$0.574432\pi$
$80$		0			0
$81$	27.5000	−	728.481i	0.0377229	−	0.999288i
$82$		0			0
$83$	152.345	+	263.869i	0.201470	+	0.348957i	0.949002	−	0.315269i	$-0.102095\pi$
$83$	152.345	+	263.869i	0.201470	+	0.348957i	−0.747532	+	0.664226i	$0.768761\pi$
$84$		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	−0.810839	−	0.585269i	$-0.800989\pi$
$97$	−677.719	+	391.281i	−0.709402	+	0.409573i	0.101438	+	0.994842i	$0.467656\pi$
$98$		0			0
$99$	−425.793	+	1477.04i	−0.432261	+	1.49947i
$100$		0			0
$101$	−786.668	−	1362.55i	−0.775014	−	1.34236i	−0.934787	−	0.355209i	$-0.884410\pi$
$101$	−786.668	−	1362.55i	−0.775014	−	1.34236i	0.159773	−	0.987154i	$-0.448924\pi$
$102$		0			0
$103$	−597.068	−	344.717i	−0.571174	−	0.329767i	0.186444	−	0.982466i	$-0.440304\pi$
$103$	−597.068	−	344.717i	−0.571174	−	0.329767i	−0.757618	+	0.652698i	$0.773637\pi$
$104$		0			0
$105$	1618.72	−	678.921i	1.50449	−	0.631009i
$106$		0			0
$107$			627.635i			0.567063i	0.958963	+	0.283532i	$0.0915061\pi$
$107$			627.635i			0.567063i	−0.958963	+	0.283532i	$0.908494\pi$
$108$		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	−0.00382837	−	0.999993i	$-0.501219\pi$
$113$	−1047.17	−	604.581i	−0.871762	−	0.503312i	−0.867933	+	0.496681i	$0.834552\pi$
$114$		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	−0.889664	−	0.456616i	$-0.849062\pi$
$131$	−74.0557	+	128.268i	−0.0493914	+	0.0855484i	0.840273	+	0.542164i	$0.182395\pi$
$132$		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	−0.199596	−	0.979878i	$-0.563963\pi$
$137$	880.674	−	508.458i	0.549205	−	0.317084i	0.748801	+	0.662795i	$0.230630\pi$
$138$		0			0
$139$	2221.28	+	1282.46i	1.35544	+	0.782566i	0.989006	−	0.147877i	$-0.0472440\pi$
$139$	2221.28	+	1282.46i	1.35544	+	0.782566i	0.366438	+	0.930443i	$0.380577\pi$
$140$		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	0.595428	−	0.803409i	$-0.296982\pi$
$149$	358.972	+	207.253i	0.197370	+	0.113952i	−0.398058	+	0.917360i	$0.630316\pi$
$150$		0			0
$151$	−949.812	−	1645.12i	−0.511885	−	0.886610i	−0.999905	−	0.0137779i	$-0.995614\pi$
$151$	−949.812	−	1645.12i	−0.511885	−	0.886610i	0.488021	−	0.872832i	$-0.337719\pi$
$152$		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	0.887529	−	0.460751i	$-0.152420\pi$
$157$	1833.97	+	1058.84i	0.932271	+	0.538247i	0.0447422	+	0.998999i	$0.485753\pi$
$158$		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	−0.725031	−	0.688717i	$-0.758174\pi$
$167$	504.850	−	874.426i	0.233931	−	0.405180i	0.958961	+	0.283536i	$0.0915077\pi$
$168$		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	0.810014	−	0.586411i	$-0.199460\pi$
$173$	−234.008	−	405.315i	−0.102840	−	0.178124i	−0.912854	+	0.408287i	$0.866126\pi$
$174$		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	$-0.860778\pi$
$179$		−	2028.76i		−	0.847131i	0.905866	−	0.423565i	$-0.139222\pi$
$180$		0			0
$181$		−	3998.62i		−	1.64207i	−0.570876	−	0.821036i	$-0.693396\pi$
$181$		−	3998.62i		−	1.64207i	0.570876	−	0.821036i	$-0.306604\pi$
$182$		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	−0.792969	−	0.609262i	$-0.791466\pi$
$191$	−1746.98	+	1008.62i	−0.661817	+	0.382100i	0.131152	+	0.991362i	$0.458132\pi$
$192$		0			0
$193$	−582.965	+	1009.72i	−0.217423	+	0.376588i	−0.954020	−	0.299745i	$-0.903099\pi$
$193$	−582.965	+	1009.72i	−0.217423	+	0.376588i	0.736596	+	0.676333i	$0.236432\pi$
$194$		0			0
$195$	−631.741	+	807.415i	−0.231999	+	0.296514i
$196$		0			0
$197$		−	4449.56i		−	1.60923i	−0.593799	−	0.804613i	$-0.702373\pi$
$197$		−	4449.56i		−	1.60923i	0.593799	−	0.804613i	$-0.297627\pi$
$198$		0			0
$199$		−	5156.28i		−	1.83678i	−0.395677	−	0.918390i	$-0.629490\pi$
$199$		−	5156.28i		−	1.83678i	0.395677	−	0.918390i	$-0.370510\pi$
$200$		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	−0.918052	−	0.396460i	$-0.870239\pi$
$211$	−354.558	+	614.113i	−0.115682	+	0.200366i	0.802370	+	0.596826i	$0.203572\pi$
$212$		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	−0.458842	−	0.888518i	$-0.651736\pi$
$223$	270.455	−	156.147i	0.0812153	−	0.0468897i	0.540058	+	0.841628i	$0.318402\pi$
$224$		0			0
$225$	−5388.64	−	1553.41i	−1.59664	−	0.460270i
$226$		0			0
$227$	364.722	+	631.717i	0.106641	+	0.184707i	0.914407	−	0.404795i	$-0.132657\pi$
$227$	364.722	+	631.717i	0.106641	+	0.184707i	−0.807767	+	0.589502i	$0.799324\pi$
$228$		0			0
$229$	−1400.43	−	808.539i	−0.404118	−	0.233318i	0.284141	−	0.958782i	$-0.408292\pi$
$229$	−1400.43	−	808.539i	−0.404118	−	0.233318i	−0.688259	+	0.725465i	$0.741625\pi$
$230$		0			0
$231$	−5435.12	−	691.044i	−1.54807	−	0.196828i
$232$		0			0
$233$		−	2237.18i		−	0.629023i	−0.949254	−	0.314511i	$-0.898159\pi$
$233$		−	2237.18i		−	0.629023i	0.949254	−	0.314511i	$-0.101841\pi$
$234$		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	−0.244302	−	0.969699i	$-0.578559\pi$
$239$	−4456.87	−	2573.17i	−1.20624	−	0.696422i	−0.961935	+	0.273278i	$0.911892\pi$
$240$		0			0
$241$	−933.854	+	539.161i	−0.249605	+	0.144110i	−0.619583	−	0.784931i	$-0.712698\pi$
$241$	−933.854	+	539.161i	−0.249605	+	0.144110i	0.369978	+	0.929040i	$0.379365\pi$
$242$		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	−0.0787143	−	0.996897i	$-0.525081\pi$
$257$	3394.82	−	5880.00i	0.823981	−	1.42718i	0.902695	−	0.430280i	$-0.141585\pi$
$258$		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	−0.572881	+	0.819638i	$0.694174\pi$
$263$	−6692.65	+	3864.00i	−1.56915	+	0.905949i	−0.996268	+	0.0863104i	$0.972492\pi$
$264$		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	$-0.761352\pi$
$271$		−	6080.16i		−	1.36289i	0.731869	−	0.681446i	$-0.238648\pi$
$272$		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	0.722827	−	0.691029i	$-0.242843\pi$
$277$	−1092.78	−	1892.75i	−0.237036	−	0.410558i	−0.959862	+	0.280471i	$0.909509\pi$
$278$		0			0
$279$	−3564.05	+	883.272i	−0.764782	+	0.189535i
$280$		0			0
$281$	−2196.63	+	1268.23i	−0.466335	+	0.269239i	−0.714704	−	0.699427i	$-0.753439\pi$
$281$	−2196.63	+	1268.23i	−0.466335	+	0.269239i	0.248369	+	0.968665i	$0.420105\pi$
$282$		0			0
$283$	3627.22	+	2094.17i	0.761893	+	0.439879i	0.829975	−	0.557801i	$-0.188355\pi$
$283$	3627.22	+	2094.17i	0.761893	+	0.439879i	−0.0680823	+	0.997680i	$0.521688\pi$
$284$		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	0.200671	+	0.979659i	$0.435688\pi$
$293$	−3751.85	+	6498.40i	−0.748074	+	1.29570i	−0.948745	+	0.316043i	$0.897646\pi$
$294$		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	$-0.868631\pi$
$307$		−	4315.01i		−	0.802184i	0.916038	−	0.401092i	$-0.131369\pi$
$308$		0			0
$309$	3547.19	+	501.081i	0.653051	+	0.0922507i
$310$		0			0
$311$	2224.42	−	3852.80i	0.405579	−	0.702483i	−0.588810	−	0.808272i	$-0.700403\pi$
$311$	2224.42	−	3852.80i	0.405579	−	0.702483i	0.994389	+	0.105788i	$0.0337366\pi$
$312$		0			0
$313$	6535.19	−	3773.10i	1.18016	−	0.681367i	0.224111	−	0.974564i	$-0.428052\pi$
$313$	6535.19	−	3773.10i	1.18016	−	0.681367i	0.956052	+	0.293196i	$0.0947190\pi$
$314$		0			0
$315$	−6481.67	+	6417.19i	−1.15937	+	1.14783i
$316$		0			0
$317$	−7839.87	+	4526.35i	−1.38906	+	0.801973i	−0.993209	−	0.116343i	$-0.962883\pi$
$317$	−7839.87	+	4526.35i	−1.38906	+	0.801973i	−0.395848	+	0.918316i	$0.629549\pi$
$318$		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	0.997575	+	0.0696003i	$0.0221724\pi$
$331$	3366.69	+	5831.27i	0.559063	+	0.968326i	−0.438512	+	0.898725i	$0.644494\pi$
$332$		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	−0.957413	−	0.288723i	$-0.906769\pi$
$337$	−1414.64	+	2450.22i	−0.228665	+	0.396060i	0.728747	+	0.684783i	$0.240103\pi$
$338$		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	0.368127	−	0.929776i	$-0.379999\pi$
$347$	−1635.49	−	944.250i	−0.253019	−	0.146081i	−0.621146	+	0.783695i	$0.713333\pi$
$348$		0			0
$349$	8771.88	−	5064.44i	1.34541	−	0.776772i	0.357814	−	0.933793i	$-0.383522\pi$
$349$	8771.88	−	5064.44i	1.34541	−	0.776772i	0.987595	+	0.157021i	$0.0501890\pi$
$350$		0			0
$351$	−1229.60	+	889.379i	−0.186983	+	0.135247i
$352$		0			0
$353$	2939.16	+	5090.78i	0.443161	+	0.767577i	0.997922	−	0.0644323i	$-0.0205237\pi$
$353$	2939.16	+	5090.78i	0.443161	+	0.767577i	−0.554761	+	0.832010i	$0.687190\pi$
$354$		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	$-0.879686\pi$
$359$		−	5020.49i		−	0.738081i	0.929413	−	0.369041i	$-0.120314\pi$
$360$		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	−0.948504	−	0.316766i	$-0.897403\pi$
$367$	−8074.26	+	4661.68i	−1.14843	+	0.663045i	−0.199924	+	0.979811i	$0.564070\pi$
$368$		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	−0.899282	−	0.437369i	$-0.855910\pi$
$373$	−510.522	+	884.250i	−0.0708682	+	0.122747i	0.828414	+	0.560116i	$0.189244\pi$
$374$		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	−0.717404	−	0.696658i	$-0.754670\pi$
$383$	1833.55	−	3175.80i	0.244621	−	0.423697i	0.962025	+	0.272961i	$0.0880030\pi$
$384$		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	−0.593824	−	0.804595i	$-0.702382\pi$
$389$	−1487.93	+	859.056i	−0.193936	+	0.111969i	0.399888	+	0.916564i	$0.369049\pi$
$390$		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	$0.263950\pi$
$397$			11666.0i			1.47481i	−0.675448	+	0.737407i	$0.736050\pi$
$398$		0			0
$399$	−2131.98	+	2804.11i	−0.267500	+	0.351832i
$400$		0			0
$401$	2312.57	+	1335.16i	0.287990	+	0.166271i	0.637035	−	0.770835i	$-0.280161\pi$
$401$	2312.57	+	1335.16i	0.287990	+	0.166271i	−0.349045	+	0.937106i	$0.613494\pi$
$402$		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	0.477123	−	0.878837i	$-0.341680\pi$
$409$	−375.615	−	216.862i	−0.0454107	−	0.0262179i	−0.522533	+	0.852619i	$0.675013\pi$
$410$		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	−0.644426	−	0.764667i	$-0.722904\pi$
$419$	2916.15	−	5050.92i	0.340008	−	0.588911i	0.984434	+	0.175756i	$0.0562369\pi$
$420$		0			0
$421$	5481.42	+	9494.10i	0.634556	+	1.09908i	0.986609	+	0.163104i	$0.0521505\pi$
$421$	5481.42	+	9494.10i	0.634556	+	1.09908i	−0.352053	+	0.935980i	$0.614516\pi$
$422$		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	$-0.817411\pi$
$431$		−	9711.53i		−	1.08536i	0.839941	−	0.542678i	$-0.182589\pi$
$432$		0			0
$433$		−	28.2134i		−	0.00313129i	−0.999999	−	0.00156564i	$-0.999502\pi$
$433$		−	28.2134i		−	0.00313129i	0.999999	−	0.00156564i	$-0.000498360\pi$
$434$		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	−0.766968	−	0.641685i	$-0.778236\pi$
$439$	−5470.43	+	3158.35i	−0.594736	+	0.343371i	0.172232	+	0.985056i	$0.444902\pi$
$440$		0			0
$441$	2476.16	+	8923.83i	0.267375	+	0.963593i
$442$		0			0
$443$	13946.4	−	8051.96i	1.49574	−	0.863567i	0.495754	−	0.868463i	$-0.334892\pi$
$443$	13946.4	−	8051.96i	1.49574	−	0.863567i	0.999988	+	0.00489651i	$0.00155861\pi$
$444$		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	$-0.959877\pi$
$449$		−	2392.17i		−	0.251433i	0.992066	−	0.125717i	$-0.0401230\pi$
$450$		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	−0.986100	−	0.166150i	$-0.946866\pi$
$457$	−6222.62	−	10777.9i	−0.636940	−	1.10321i	0.349160	−	0.937063i	$-0.386467\pi$
$458$		0			0
$459$	−3741.56	+	8355.99i	−0.380482	+	0.849726i
$460$		0			0
$461$	9386.24	+	16257.4i	0.948288	+	1.64248i	0.749031	+	0.662535i	$0.230519\pi$
$461$	9386.24	+	16257.4i	0.948288	+	1.64248i	0.199257	+	0.979947i	$0.436147\pi$
$462$		0			0
$463$	−3011.11	+	5215.40i	−0.302243	+	0.523499i	−0.976644	−	0.214866i	$-0.931069\pi$
$463$	−3011.11	+	5215.40i	−0.302243	+	0.523499i	0.674401	+	0.738365i	$0.264402\pi$
$464$		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	0.865698	−	0.500566i	$-0.166875\pi$
$479$	−6.85714	−	11.8769i	−0.000654094	−	0.00113292i	−0.866352	+	0.499433i	$0.833542\pi$
$480$		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	0.586916	−	0.809648i	$-0.300342\pi$
$491$	1949.66	+	1125.63i	0.179199	+	0.103461i	−0.407717	+	0.913108i	$0.633675\pi$
$492$		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	−0.982485	−	0.186344i	$-0.940336\pi$
$499$	−3676.93	+	6368.63i	−0.329864	+	0.571340i	0.652621	+	0.757685i	$0.273669\pi$
$500$		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	−0.980106	−	0.198477i	$-0.936401\pi$
$509$	−3653.69	+	6328.37i	−0.318167	+	0.551081i	0.661939	+	0.749558i	$0.269734\pi$
$510$		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	$0.265853\pi$
$523$			17735.9i			1.48286i	−0.671028	+	0.741432i	$0.734147\pi$
$524$		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	0.815836	−	0.578283i	$-0.196277\pi$
$547$	−1188.36	−	2058.30i	−0.0928897	−	0.160890i	−0.908726	+	0.417393i	$0.862944\pi$
$548$		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	$-0.999809\pi$
$557$		−	15.7702i		−	0.00119965i	1.00000		0.000599827i	$-0.000190931\pi$
$558$		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	−0.715697	−	0.698411i	$-0.753891\pi$
$563$	3299.49	−	5714.88i	0.246993	−	0.427804i	0.962690	+	0.270607i	$0.0872243\pi$
$564$		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	−0.637796	+	0.770205i	$0.720154\pi$
$569$	−22038.3	+	12723.8i	−1.62371	+	0.937450i	−0.985915	+	0.167245i	$0.946513\pi$
$570$		0			0
$571$	10540.7	−	18257.0i	0.772527	−	1.33806i	−0.163646	−	0.986519i	$-0.552326\pi$
$571$	10540.7	−	18257.0i	0.772527	−	1.33806i	0.936174	−	0.351538i	$-0.114341\pi$
$572$		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	$-0.990271\pi$
$577$		−	847.126i		−	0.0611201i	0.999533	−	0.0305601i	$-0.00972908\pi$
$578$		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	−0.984322	−	0.176383i	$-0.943560\pi$
$587$	−9171.88	−	15886.2i	−0.644913	−	1.11702i	0.339408	−	0.940639i	$-0.389773\pi$
$588$		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	0.169867	−	0.985467i	$-0.445666\pi$
$599$	−8776.18	−	5066.93i	−0.598639	−	0.345625i	−0.768506	+	0.639842i	$0.779000\pi$
$600$		0			0
$601$	−6127.51	+	3537.72i	−0.415884	+	0.240111i	−0.693315	−	0.720635i	$-0.743850\pi$
$601$	−6127.51	+	3537.72i	−0.415884	+	0.240111i	0.277431	+	0.960746i	$0.410517\pi$
$602$		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	0.0724839	−	0.997370i	$-0.476907\pi$
$607$	−11291.3	−	6519.01i	−0.755021	−	0.435912i	−0.827505	+	0.561458i	$0.810241\pi$
$608$		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	0.780758	−	0.624833i	$-0.214833\pi$
$617$	9655.60	+	5574.66i	0.630016	+	0.363740i	−0.150742	+	0.988573i	$0.548166\pi$
$618$		0			0
$619$	−15732.2	+	9083.00i	−1.02154	+	0.589785i	−0.914549	−	0.404476i	$-0.867454\pi$
$619$	−15732.2	+	9083.00i	−1.02154	+	0.589785i	−0.106988	+	0.994260i	$0.534121\pi$
$620$		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	−0.372698	−	0.927953i	$-0.621567\pi$
$641$	3969.31	−	2291.68i	0.244584	−	0.141211i	0.617282	+	0.786742i	$0.288234\pi$
$642$		0			0
$643$	6413.00	+	3702.55i	0.393319	+	0.227083i	0.683597	−	0.729860i	$-0.260415\pi$
$643$	6413.00	+	3702.55i	0.393319	+	0.227083i	−0.290278	+	0.956942i	$0.593748\pi$
$644$		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	0.449548	−	0.893256i	$-0.351585\pi$
$653$	−1656.32	−	956.276i	−0.0992599	−	0.0573078i	−0.548808	+	0.835948i	$0.684918\pi$
$654$		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	−0.529537	−	0.848287i	$-0.677634\pi$
$659$	−1009.42	+	582.787i	−0.0596681	+	0.0344494i	0.469869	+	0.882736i	$0.344301\pi$
$660$		0			0
$661$	20327.5	+	11736.1i	1.19614	+	0.690593i	0.959693	−	0.281051i	$-0.0906830\pi$
$661$	20327.5	+	11736.1i	1.19614	+	0.690593i	0.236449	+	0.971644i	$0.424016\pi$
$662$		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	0.972532	+	0.232770i	$0.0747788\pi$
$673$	12009.3	+	20800.7i	0.687850	+	1.19139i	−0.284682	+	0.958622i	$0.591888\pi$
$674$		0			0
$675$	28987.2	−	2984.59i	1.65292	−	0.170188i
$676$		0			0
$677$	−8076.04	−	13988.1i	−0.458475	−	0.794102i	0.540406	−	0.841405i	$-0.318271\pi$
$677$	−8076.04	−	13988.1i	−0.458475	−	0.794102i	−0.998881	+	0.0473029i	$0.984937\pi$
$678$		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	$0.295089\pi$
$683$			28554.3i			1.59970i	−0.600197	+	0.799852i	$0.704911\pi$
$684$		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	−0.635848	+	0.771815i	$0.719349\pi$
$691$	−29465.7	+	17012.0i	−1.62218	+	0.936567i	−0.986335	+	0.164753i	$0.947317\pi$
$692$		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	$-0.914244\pi$
$701$		−	9879.92i		−	0.532325i	0.963928	−	0.266162i	$-0.0857557\pi$
$702$		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	−0.868142	−	0.496315i	$-0.834686\pi$
$709$	−16309.1	−	28248.1i	−0.863893	−	1.49631i	0.00424980	−	0.999991i	$-0.498647\pi$
$710$		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	−0.239029	−	0.971013i	$-0.576829\pi$
$727$	9455.61	−	5459.20i	0.482378	−	0.278501i	0.721407	+	0.692511i	$0.243496\pi$
$728$		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	0.202803	−	0.979219i	$-0.434995\pi$
$733$	−10792.3	−	6230.94i	−0.543824	−	0.313977i	−0.746627	+	0.665243i	$0.768328\pi$
$734$		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	0.00751697	−	0.999972i	$-0.497607\pi$
$743$	−17310.5	−	9994.23i	−0.854725	−	0.493476i	−0.862242	+	0.506496i	$0.830941\pi$
$744$		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	−0.967675	−	0.252200i	$-0.918846\pi$
$751$	−5462.66	+	9461.60i	−0.265426	+	0.459732i	0.702249	+	0.711931i	$0.252179\pi$
$752$		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	−0.319556	−	0.947567i	$-0.603534\pi$
$761$	13873.1	−	24028.9i	0.660839	−	1.14461i	0.980395	−	0.197040i	$-0.0631329\pi$
$762$		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	0.927290	−	0.374344i	$-0.122132\pi$
$769$	22748.3	+	13133.8i	1.06674	+	0.615885i	0.139454	+	0.990229i	$0.455465\pi$
$770$		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	0.224227	−	0.974537i	$-0.428014\pi$
$787$	−11207.6	−	6470.69i	−0.507632	−	0.293082i	−0.731860	+	0.681455i	$0.761347\pi$
$788$		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	−0.732853	−	0.680387i	$-0.761812\pi$
$797$	5013.20	−	8683.11i	0.222806	−	0.385912i	0.955659	+	0.294476i	$0.0951450\pi$
$798$		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	$-0.874063\pi$
$809$		−	17736.4i		−	0.770800i	0.922750	−	0.385400i	$-0.125937\pi$
$810$		0			0
$811$			2438.23i			0.105571i	0.998606	+	0.0527853i	$0.0168099\pi$
$811$			2438.23i			0.105571i	−0.998606	+	0.0527853i	$0.983190\pi$
$812$		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	−0.922879	−	0.385091i	$-0.874170\pi$
$821$	−24719.7	+	14271.9i	−1.05082	+	0.606691i	−0.127941	+	0.991782i	$0.540837\pi$
$822$		0			0
$823$	−16131.9	+	27941.3i	−0.683261	+	1.18344i	0.290718	+	0.956809i	$0.406106\pi$
$823$	−16131.9	+	27941.3i	−0.683261	+	1.18344i	−0.973980	+	0.226635i	$0.927228\pi$
$824$		0			0
$825$	−60842.2	−	8594.64i	−2.56758	−	0.362699i
$826$		0			0
$827$			28049.2i			1.17940i	0.807622	+	0.589701i	$0.200754\pi$
$827$			28049.2i			1.17940i	−0.807622	+	0.589701i	$0.799246\pi$
$828$		0			0
$829$			3574.94i			0.149774i	0.997192	+	0.0748870i	$0.0238596\pi$
$829$			3574.94i			0.149774i	−0.997192	+	0.0748870i	$0.976140\pi$
$830$		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	0.991127	−	0.132917i	$-0.0424344\pi$
$839$	9245.81	+	16014.2i	0.380454	+	0.658966i	−0.610673	+	0.791883i	$0.709101\pi$
$840$		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	−0.142052	−	0.989859i	$-0.545370\pi$
$853$	16048.0	−	9265.31i	0.644165	−	0.371909i	0.786217	+	0.617950i	$0.212037\pi$
$854$		0			0
$855$	17497.6	−	4336.40i	0.699890	−	0.173452i
$856$		0			0
$857$	2912.03	+	5043.79i	0.116071	+	0.201041i	0.918207	−	0.396100i	$-0.129637\pi$
$857$	2912.03	+	5043.79i	0.116071	+	0.201041i	−0.802136	+	0.597141i	$0.796303\pi$
$858$		0			0
$859$	−15711.1	−	9070.82i	−0.624047	−	0.360294i	0.154396	−	0.988009i	$-0.450657\pi$
$859$	−15711.1	−	9070.82i	−0.624047	−	0.360294i	−0.778443	+	0.627715i	$0.783990\pi$
$860$		0			0
$861$	−20859.2	+	8748.73i	−0.825645	+	0.346290i
$862$		0			0
$863$			30785.2i			1.21430i	0.794587	+	0.607150i	$0.207687\pi$
$863$			30785.2i			1.21430i	−0.794587	+	0.607150i	$0.792313\pi$
$864$		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	−0.678580	−	0.734527i	$-0.737404\pi$
$877$	7709.14	−	13352.6i	0.296829	−	0.514123i	0.975409	+	0.220404i	$0.0707375\pi$
$878$		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	−0.682725	−	0.730676i	$-0.739205\pi$
$887$	7698.51	−	13334.2i	0.291421	−	0.504756i	0.974146	+	0.225919i	$0.0725386\pi$
$888$		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	0.734291	−	0.678835i	$-0.237515\pi$
$907$	−6029.71	−	10443.8i	−0.220742	−	0.382337i	−0.955034	+	0.296498i	$0.904181\pi$
$908$		0			0
$909$	−40817.9	−	11766.8i	−1.48938	−	0.429350i
$910$		0			0
$911$	−8661.13	+	5000.50i	−0.314990	+	0.181860i	−0.649157	−	0.760654i	$-0.724878\pi$
$911$	−8661.13	+	5000.50i	−0.314990	+	0.181860i	0.334167	+	0.942514i	$0.391545\pi$
$912$		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	0.960550	−	0.278106i	$-0.0897066\pi$
$929$	6779.53	+	11742.5i	0.239429	+	0.414702i	−0.721122	+	0.692808i	$0.756373\pi$
$930$		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	$-0.831500\pi$
$937$		−	28967.7i		−	1.00996i	0.863131	−	0.504980i	$-0.168500\pi$
$938$		0			0
$939$	−24162.6	+	30881.8i	−0.839742	+	1.07326i
$940$		0			0
$941$	−10159.8	+	17597.2i	−0.351965	+	0.609621i	−0.986594	−	0.163196i	$-0.947820\pi$
$941$	−10159.8	+	17597.2i	−0.351965	+	0.609621i	0.634629	+	0.772817i	$0.281153\pi$
$942$		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	−0.631647	−	0.775256i	$-0.717621\pi$
$947$	−8045.62	+	4645.14i	−0.276080	+	0.159395i	0.355568	+	0.934651i	$0.384288\pi$
$948$		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	$0.229223\pi$
$953$			38803.4i			1.31896i	−0.751724	+	0.659478i	$0.770777\pi$
$954$		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	−0.887248	−	0.461292i	$-0.847386\pi$
$967$	−1327.12	+	2298.64i	−0.0441338	+	0.0764420i	0.843115	+	0.537734i	$0.180719\pi$
$968$		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	0.681117	−	0.732175i	$-0.261495\pi$
$977$	11836.4	+	6833.72i	0.387593	+	0.223777i	−0.293524	+	0.955952i	$0.594828\pi$
$978$		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	0.887103	−	0.461572i	$-0.152714\pi$
$983$	1350.47	+	2339.08i	0.0438181	+	0.0758952i	−0.843285	+	0.537467i	$0.819381\pi$
$984$		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	−0.710920	−	0.703273i	$-0.751721\pi$
$997$	−14397.0	+	8312.09i	−0.457329	+	0.264039i	0.253592	+	0.967311i	$0.418388\pi$
$998$		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.41.3	✓	48
3.2	odd	2		756.4.x.a.125.2		48
7.6	odd	2	inner	252.4.x.a.41.22	yes	48
9.2	odd	6	inner	252.4.x.a.209.22	yes	48
9.4	even	3		2268.4.f.a.1133.3		48
9.5	odd	6		2268.4.f.a.1133.46		48
9.7	even	3		756.4.x.a.629.23		48
21.20	even	2		756.4.x.a.125.23		48
63.13	odd	6		2268.4.f.a.1133.45		48
63.20	even	6	inner	252.4.x.a.209.3	yes	48
63.34	odd	6		756.4.x.a.629.2		48
63.41	even	6		2268.4.f.a.1133.4		48

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