LMFDB - Embedded newform 1020.3.bc.a.701.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1020,3,Mod(701,1020)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1020, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 0, 3]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("1020.701");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	1020.bc (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$27.7929869648$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$48$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			701.2
Character	$\chi$	$=$	1020.701
Dual form			1020.3.bc.a.761.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.99006 + 0.243979i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(8.18085 + 8.18085i) q^{7} +(8.88095 - 1.45903i) q^{9} +O(q^{10})$	\(q+(-2.99006 + 0.243979i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(8.18085 + 8.18085i) q^{7} +(8.88095 - 1.45903i) q^{9} +(0.320565 - 0.320565i) q^{11} +22.3498 q^{13} +(5.11347 + 4.34194i) q^{15} +(-9.86544 - 13.8446i) q^{17} +6.63468i q^{19} +(-26.4572 - 22.4653i) q^{21} +(-9.39551 + 9.39551i) q^{23} +5.00000i q^{25} +(-26.1986 + 6.52935i) q^{27} +(-15.7459 - 15.7459i) q^{29} +(5.68432 - 5.68432i) q^{31} +(-0.880299 + 1.03672i) q^{33} -25.8701i q^{35} +(35.8692 - 35.8692i) q^{37} +(-66.8273 + 5.45289i) q^{39} +(-10.8654 + 10.8654i) q^{41} +12.9695i q^{43} +(-16.3489 - 11.7351i) q^{45} +25.7996i q^{47} +84.8527i q^{49} +(32.8761 + 38.9893i) q^{51} +26.2935 q^{53} -1.01372 q^{55} +(-1.61873 - 19.8381i) q^{57} +94.0697 q^{59} +(38.7792 + 38.7792i) q^{61} +(84.5898 + 60.7176i) q^{63} +(-35.3381 - 35.3381i) q^{65} +31.1720 q^{67} +(25.8009 - 30.3855i) q^{69} +(50.4254 + 50.4254i) q^{71} +(-13.7243 + 13.7243i) q^{73} +(-1.21990 - 14.9503i) q^{75} +5.24500 q^{77} +(-110.980 - 110.980i) q^{79} +(76.7425 - 25.9151i) q^{81} +51.5381 q^{83} +(-6.29161 + 37.4889i) q^{85} +(50.9229 + 43.2396i) q^{87} -0.471386i q^{89} +(182.840 + 182.840i) q^{91} +(-15.6096 + 18.3833i) q^{93} +(10.4904 - 10.4904i) q^{95} +(27.5190 - 27.5190i) q^{97} +(2.37921 - 3.31464i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 8 q^{3}+O(q^{10}) $ 96 * q - 8 * q^3	$ 96 q - 8 q^{3} + 64 q^{21} + 100 q^{27} - 24 q^{31} + 40 q^{33} + 24 q^{37} - 52 q^{39} - 40 q^{45} - 4 q^{51} + 80 q^{55} + 192 q^{57} + 144 q^{61} + 28 q^{63} - 320 q^{67} + 208 q^{69} + 152 q^{73} - 40 q^{75} + 224 q^{79} + 488 q^{81} - 288 q^{91} + 80 q^{97} - 212 q^{99}+O(q^{100}) $ 96 * q - 8 * q^3 + 64 * q^21 + 100 * q^27 - 24 * q^31 + 40 * q^33 + 24 * q^37 - 52 * q^39 - 40 * q^45 - 4 * q^51 + 80 * q^55 + 192 * q^57 + 144 * q^61 + 28 * q^63 - 320 * q^67 + 208 * q^69 + 152 * q^73 - 40 * q^75 + 224 * q^79 + 488 * q^81 - 288 * q^91 + 80 * q^97 - 212 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1020\mathbb{Z}\right)^\times$.

$n$	$241$	$341$	$511$	$817$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$	$1$

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
$3$	−2.99006	+	0.243979i	−0.996688	+	0.0813265i
$3$	−2.99006	+	0.243979i	−0.996688	+	0.0813265i
$4$		0			0
$5$	−1.58114	−	1.58114i	−0.316228	−	0.316228i
$5$	−1.58114	−	1.58114i	−0.316228	−	0.316228i
$6$		0			0
$7$	8.18085	+	8.18085i	1.16869	+	1.16869i	0.982516	+	0.186177i	$0.0596097\pi$
$7$	8.18085	+	8.18085i	1.16869	+	1.16869i	0.186177	+	0.982516i	$0.440390\pi$
$8$		0			0
$9$	8.88095	−	1.45903i	0.986772	−	0.162114i
$10$		0			0
$11$	0.320565	−	0.320565i	0.0291423	−	0.0291423i	−0.692385	−	0.721528i	$-0.743440\pi$
$11$	0.320565	−	0.320565i	0.0291423	−	0.0291423i	0.721528	+	0.692385i	$0.243440\pi$
$12$		0			0
$13$	22.3498			1.71922			0.859608	−	0.510955i	$-0.170708\pi$
$13$	22.3498			1.71922			0.859608	+	0.510955i	$0.170708\pi$
$14$		0			0
$15$	5.11347	+	4.34194i	0.340898	+	0.289463i
$16$		0			0
$17$	−9.86544	−	13.8446i	−0.580320	−	0.814388i
$17$	−9.86544	−	13.8446i	−0.580320	−	0.814388i
$18$		0			0
$19$			6.63468i			0.349194i	0.984640	+	0.174597i	$0.0558622\pi$
$19$			6.63468i			0.349194i	−0.984640	+	0.174597i	$0.944138\pi$
$20$		0			0
$21$	−26.4572	−	22.4653i	−1.25987	−	1.06978i
$22$		0			0
$23$	−9.39551	+	9.39551i	−0.408501	+	0.408501i	−0.881215	−	0.472715i	$-0.843274\pi$
$23$	−9.39551	+	9.39551i	−0.408501	+	0.408501i	0.472715	+	0.881215i	$0.343274\pi$
$24$		0			0
$25$			5.00000i			0.200000i
$26$		0			0
$27$	−26.1986	+	6.52935i	−0.970319	+	0.241828i
$28$		0			0
$29$	−15.7459	−	15.7459i	−0.542962	−	0.542962i	0.381434	−	0.924396i	$-0.375430\pi$
$29$	−15.7459	−	15.7459i	−0.542962	−	0.542962i	−0.924396	+	0.381434i	$0.875430\pi$
$30$		0			0
$31$	5.68432	−	5.68432i	0.183365	−	0.183365i	−0.609455	−	0.792820i	$-0.708612\pi$
$31$	5.68432	−	5.68432i	0.183365	−	0.183365i	0.792820	+	0.609455i	$0.208612\pi$
$32$		0			0
$33$	−0.880299	+	1.03672i	−0.0266757	+	0.0314158i
$34$		0			0
$35$		−	25.8701i		−	0.739146i
$36$		0			0
$37$	35.8692	−	35.8692i	0.969438	−	0.969438i	−0.0301088	−	0.999547i	$-0.509585\pi$
$37$	35.8692	−	35.8692i	0.969438	−	0.969438i	0.999547	+	0.0301088i	$0.00958539\pi$
$38$		0			0
$39$	−66.8273	+	5.45289i	−1.71352	+	0.139818i
$40$		0			0
$41$	−10.8654	+	10.8654i	−0.265009	+	0.265009i	−0.827086	−	0.562076i	$-0.810003\pi$
$41$	−10.8654	+	10.8654i	−0.265009	+	0.265009i	0.562076	+	0.827086i	$0.310003\pi$
$42$		0			0
$43$			12.9695i			0.301616i	0.988563	+	0.150808i	$0.0481876\pi$
$43$			12.9695i			0.301616i	−0.988563	+	0.150808i	$0.951812\pi$
$44$		0			0
$45$	−16.3489	−	11.7351i	−0.363310	−	0.260780i
$46$		0			0
$47$			25.7996i			0.548927i	0.961598	+	0.274463i	$0.0885002\pi$
$47$			25.7996i			0.548927i	−0.961598	+	0.274463i	$0.911500\pi$
$48$		0			0
$49$			84.8527i			1.73169i
$50$		0			0
$51$	32.8761	+	38.9893i	0.644629	+	0.764495i
$52$		0			0
$53$	26.2935			0.496103			0.248052	−	0.968747i	$-0.420210\pi$
$53$	26.2935			0.496103			0.248052	+	0.968747i	$0.420210\pi$
$54$		0			0
$55$	−1.01372			−0.0184312
$56$		0			0
$57$	−1.61873	−	19.8381i	−0.0283987	−	0.348037i
$58$		0			0
$59$	94.0697			1.59440			0.797201	−	0.603715i	$-0.206313\pi$
$59$	94.0697			1.59440			0.797201	+	0.603715i	$0.206313\pi$
$60$		0			0
$61$	38.7792	+	38.7792i	0.635725	+	0.635725i	0.949498	−	0.313773i	$-0.101593\pi$
$61$	38.7792	+	38.7792i	0.635725	+	0.635725i	−0.313773	+	0.949498i	$0.601593\pi$
$62$		0			0
$63$	84.5898	+	60.7176i	1.34270	+	0.963772i
$64$		0			0
$65$	−35.3381	−	35.3381i	−0.543664	−	0.543664i
$66$		0			0
$67$	31.1720			0.465254			0.232627	−	0.972566i	$-0.425268\pi$
$67$	31.1720			0.465254			0.232627	+	0.972566i	$0.425268\pi$
$68$		0			0
$69$	25.8009	−	30.3855i	0.373926	−	0.440369i
$70$		0			0
$71$	50.4254	+	50.4254i	0.710218	+	0.710218i	0.966581	−	0.256363i	$-0.0825243\pi$
$71$	50.4254	+	50.4254i	0.710218	+	0.710218i	−0.256363	+	0.966581i	$0.582524\pi$
$72$		0			0
$73$	−13.7243	+	13.7243i	−0.188004	+	0.188004i	−0.794833	−	0.606829i	$-0.792441\pi$
$73$	−13.7243	+	13.7243i	−0.188004	+	0.188004i	0.606829	+	0.794833i	$0.292441\pi$
$74$		0			0
$75$	−1.21990	−	14.9503i	−0.0162653	−	0.199338i
$76$		0			0
$77$	5.24500			0.0681168
$78$		0			0
$79$	−110.980	−	110.980i	−1.40481	−	1.40481i	−0.783820	−	0.620989i	$-0.786731\pi$
$79$	−110.980	−	110.980i	−1.40481	−	1.40481i	−0.620989	−	0.783820i	$-0.713269\pi$
$80$		0			0
$81$	76.7425	−	25.9151i	0.947438	−	0.319940i
$82$		0			0
$83$	51.5381			0.620941			0.310471	−	0.950583i	$-0.399513\pi$
$83$	51.5381			0.620941			0.310471	+	0.950583i	$0.399513\pi$
$84$		0			0
$85$	−6.29161	+	37.4889i	−0.0740189	+	0.441046i
$86$		0			0
$87$	50.9229	+	43.2396i	0.585321	+	0.497006i
$88$		0			0
$89$		−	0.471386i		−	0.00529648i	−0.999996	−	0.00264824i	$-0.999157\pi$
$89$		−	0.471386i		−	0.00529648i	0.999996	−	0.00264824i	$-0.000842961\pi$
$90$		0			0
$91$	182.840	+	182.840i	2.00923	+	2.00923i
$92$		0			0
$93$	−15.6096	+	18.3833i	−0.167845	+	0.197670i
$94$		0			0
$95$	10.4904	−	10.4904i	0.110425	−	0.110425i
$96$		0			0
$97$	27.5190	−	27.5190i	0.283701	−	0.283701i	−0.550882	−	0.834583i	$-0.685709\pi$
$97$	27.5190	−	27.5190i	0.283701	−	0.283701i	0.834583	+	0.550882i	$0.185709\pi$
$98$		0			0
$99$	2.37921	−	3.31464i	0.0240324	−	0.0334812i
$100$		0			0
$101$			97.5400i			0.965743i	0.875691	+	0.482871i	$0.160406\pi$
$101$			97.5400i			0.965743i	−0.875691	+	0.482871i	$0.839594\pi$
$102$		0			0
$103$	8.40782			0.0816294			0.0408147	−	0.999167i	$-0.487005\pi$
$103$	8.40782			0.0816294			0.0408147	+	0.999167i	$0.487005\pi$
$104$		0			0
$105$	6.31178	+	77.3533i	0.0601122	+	0.736698i
$106$		0			0
$107$	7.11607	+	7.11607i	0.0665053	+	0.0665053i	0.739577	−	0.673072i	$-0.235026\pi$
$107$	7.11607	+	7.11607i	0.0665053	+	0.0665053i	−0.673072	+	0.739577i	$0.735026\pi$
$108$		0			0
$109$	14.5735	+	14.5735i	0.133702	+	0.133702i	0.770791	−	0.637089i	$-0.219861\pi$
$109$	14.5735	+	14.5735i	0.133702	+	0.133702i	−0.637089	+	0.770791i	$0.719861\pi$
$110$		0			0
$111$	−98.4998	+	116.002i	−0.887386	+	1.04507i
$112$		0			0
$113$	156.338	−	156.338i	1.38353	−	1.38353i	0.545257	−	0.838269i	$-0.316432\pi$
$113$	156.338	−	156.338i	1.38353	−	1.38353i	0.838269	−	0.545257i	$-0.183568\pi$
$114$		0			0
$115$	29.7112			0.258358
$116$		0			0
$117$	198.487	−	32.6090i	1.69647	−	0.278709i
$118$		0			0
$119$	32.5529	−	193.968i	0.273554	−	1.62999i
$120$		0			0
$121$			120.794i			0.998301i
$122$		0			0
$123$	29.8373	−	35.1391i	0.242579	−	0.285684i
$124$		0			0
$125$	7.90569	−	7.90569i	0.0632456	−	0.0632456i
$126$		0			0
$127$			81.0397i			0.638108i	0.947737	+	0.319054i	$0.103365\pi$
$127$			81.0397i			0.638108i	−0.947737	+	0.319054i	$0.896635\pi$
$128$		0			0
$129$	−3.16429	−	38.7796i	−0.0245294	−	0.300617i
$130$		0			0
$131$	128.500	+	128.500i	0.980913	+	0.980913i	0.999821	−	0.0189081i	$-0.00601901\pi$
$131$	128.500	+	128.500i	0.980913	+	0.980913i	−0.0189081	+	0.999821i	$0.506019\pi$
$132$		0			0
$133$	−54.2774	+	54.2774i	−0.408100	+	0.408100i
$134$		0			0
$135$	51.7475	+	31.0998i	0.383315	+	0.230369i
$136$		0			0
$137$		−	81.7240i		−	0.596526i	−0.954484	−	0.298263i	$-0.903593\pi$
$137$		−	81.7240i		−	0.596526i	0.954484	−	0.298263i	$-0.0964072\pi$
$138$		0			0
$139$	−105.486	+	105.486i	−0.758895	+	0.758895i	−0.976121	−	0.217227i	$-0.930299\pi$
$139$	−105.486	+	105.486i	−0.758895	+	0.758895i	0.217227	+	0.976121i	$0.430299\pi$
$140$		0			0
$141$	−6.29457	−	77.1423i	−0.0446423	−	0.547109i
$142$		0			0
$143$	7.16457	−	7.16457i	0.0501019	−	0.0501019i
$144$		0			0
$145$			49.7929i			0.343399i
$146$		0			0
$147$	−20.7023	−	253.715i	−0.140832	−	1.72595i
$148$		0			0
$149$			291.627i			1.95723i	0.205699	+	0.978615i	$0.434053\pi$
$149$			291.627i			1.95723i	−0.205699	+	0.978615i	$0.565947\pi$
$150$		0			0
$151$			138.217i			0.915347i	0.889120	+	0.457673i	$0.151317\pi$
$151$			138.217i			0.915347i	−0.889120	+	0.457673i	$0.848683\pi$
$152$		0			0
$153$	−107.814	−	108.559i	−0.704668	−	0.709538i
$154$		0			0
$155$	−17.9754			−0.115970
$156$		0			0
$157$	−78.8490			−0.502223			−0.251111	−	0.967958i	$-0.580796\pi$
$157$	−78.8490			−0.502223			−0.251111	+	0.967958i	$0.580796\pi$
$158$		0			0
$159$	−78.6191	+	6.41507i	−0.494460	+	0.0403463i
$160$		0			0
$161$	−153.727			−0.954824
$162$		0			0
$163$	145.366	+	145.366i	0.891814	+	0.891814i	0.994694	−	0.102879i	$-0.0328056\pi$
$163$	145.366	+	145.366i	0.891814	+	0.891814i	−0.102879	+	0.994694i	$0.532806\pi$
$164$		0			0
$165$	3.03108	−	0.247326i	0.0183702	−	0.00149895i
$166$		0			0
$167$	−48.8008	−	48.8008i	−0.292220	−	0.292220i	0.545737	−	0.837957i	$-0.316250\pi$
$167$	−48.8008	−	48.8008i	−0.292220	−	0.292220i	−0.837957	+	0.545737i	$0.816250\pi$
$168$		0			0
$169$	330.513			1.95570
$170$		0			0
$171$	9.68019	+	58.9223i	0.0566093	+	0.344575i
$172$		0			0
$173$	−57.2238	−	57.2238i	−0.330773	−	0.330773i	0.522107	−	0.852880i	$-0.325146\pi$
$173$	−57.2238	−	57.2238i	−0.330773	−	0.330773i	−0.852880	+	0.522107i	$0.825146\pi$
$174$		0			0
$175$	−40.9043	+	40.9043i	−0.233739	+	0.233739i
$176$		0			0
$177$	−281.274	+	22.9511i	−1.58912	+	0.129667i
$178$		0			0
$179$	250.310			1.39838			0.699189	−	0.714936i	$-0.253544\pi$
$179$	250.310			1.39838			0.699189	+	0.714936i	$0.253544\pi$
$180$		0			0
$181$	−147.582	−	147.582i	−0.815371	−	0.815371i	0.170062	−	0.985433i	$-0.445603\pi$
$181$	−147.582	−	147.582i	−0.815371	−	0.815371i	−0.985433	+	0.170062i	$0.945603\pi$
$182$		0			0
$183$	−125.414	−	106.491i	−0.685320	−	0.581918i
$184$		0			0
$185$	−113.428			−0.613126
$186$		0			0
$187$	−7.60062	−	1.27558i	−0.0406450	−	0.00682129i
$188$		0			0
$189$	−267.743	−	160.911i	−1.41663	−	0.851383i
$190$		0			0
$191$			278.975i			1.46060i	0.683125	+	0.730302i	$0.260621\pi$
$191$			278.975i			1.46060i	−0.683125	+	0.730302i	$0.739379\pi$
$192$		0			0
$193$	−226.399	−	226.399i	−1.17305	−	1.17305i	−0.981479	−	0.191571i	$-0.938642\pi$
$193$	−226.399	−	226.399i	−1.17305	−	1.17305i	−0.191571	−	0.981479i	$-0.561358\pi$
$194$		0			0
$195$	114.285	+	97.0414i	0.586077	+	0.497648i
$196$		0			0
$197$	−246.963	+	246.963i	−1.25362	+	1.25362i	−0.299535	+	0.954085i	$0.596832\pi$
$197$	−246.963	+	246.963i	−1.25362	+	1.25362i	−0.954085	+	0.299535i	$0.903168\pi$
$198$		0			0
$199$	136.868	−	136.868i	0.687778	−	0.687778i	−0.273963	−	0.961740i	$-0.588334\pi$
$199$	136.868	−	136.868i	0.687778	−	0.687778i	0.961740	+	0.273963i	$0.0883344\pi$
$200$		0			0
$201$	−93.2064	+	7.60534i	−0.463713	+	0.0378375i
$202$		0			0
$203$		−	257.630i		−	1.26911i
$204$		0			0
$205$	34.3594			0.167607
$206$		0			0
$207$	−69.7328	+	97.1494i	−0.336873	+	0.469321i
$208$		0			0
$209$	2.12685	+	2.12685i	0.0101763	+	0.0101763i
$210$		0			0
$211$	240.246	+	240.246i	1.13861	+	1.13861i	0.988700	+	0.149907i	$0.0478976\pi$
$211$	240.246	+	240.246i	1.13861	+	1.13861i	0.149907	+	0.988700i	$0.452102\pi$
$212$		0			0
$213$	−163.078	−	138.472i	−0.765624	−	0.650105i
$214$		0			0
$215$	20.5066	−	20.5066i	0.0953794	−	0.0953794i
$216$		0			0
$217$	93.0052			0.428595
$218$		0			0
$219$	37.6881	−	44.3850i	0.172092	−	0.202671i
$220$		0			0
$221$	−220.491	−	309.424i	−0.997695	−	1.40011i
$222$		0			0
$223$		−	206.836i		−	0.927518i	−0.885961	−	0.463759i	$-0.846500\pi$
$223$		−	206.836i		−	0.927518i	0.885961	−	0.463759i	$-0.153500\pi$
$224$		0			0
$225$	7.29514	+	44.4047i	0.0324228	+	0.197354i
$226$		0			0
$227$	219.495	−	219.495i	0.966938	−	0.966938i	−0.0325328	−	0.999471i	$-0.510357\pi$
$227$	219.495	−	219.495i	0.966938	−	0.966938i	0.999471	+	0.0325328i	$0.0103573\pi$
$228$		0			0
$229$		−	166.858i		−	0.728638i	−0.931274	−	0.364319i	$-0.881302\pi$
$229$		−	166.858i		−	0.728638i	0.931274	−	0.364319i	$-0.118698\pi$
$230$		0			0
$231$	−15.6829	+	1.27967i	−0.0678912	+	0.00553970i
$232$		0			0
$233$	110.717	+	110.717i	0.475180	+	0.475180i	0.903586	−	0.428406i	$-0.140925\pi$
$233$	110.717	+	110.717i	0.475180	+	0.475180i	−0.428406	+	0.903586i	$0.640925\pi$
$234$		0			0
$235$	40.7927	−	40.7927i	0.173586	−	0.173586i
$236$		0			0
$237$	358.913	+	304.760i	1.51440	+	1.28591i
$238$		0			0
$239$			29.1437i			0.121940i	0.998140	+	0.0609701i	$0.0194194\pi$
$239$			29.1437i			0.121940i	−0.998140	+	0.0609701i	$0.980581\pi$
$240$		0			0
$241$	−8.69655	+	8.69655i	−0.0360853	+	0.0360853i	−0.724919	−	0.688834i	$-0.758123\pi$
$241$	−8.69655	+	8.69655i	−0.0360853	+	0.0360853i	0.688834	+	0.724919i	$0.258123\pi$
$242$		0			0
$243$	−223.142	+	96.2114i	−0.918280	+	0.395932i
$244$		0			0
$245$	134.164	−	134.164i	0.547608	−	0.547608i
$246$		0			0
$247$			148.284i			0.600339i
$248$		0			0
$249$	−154.102	+	12.5742i	−0.618884	+	0.0504990i
$250$		0			0
$251$		−	167.411i		−	0.666976i	−0.942754	−	0.333488i	$-0.891774\pi$
$251$		−	167.411i		−	0.666976i	0.942754	−	0.333488i	$-0.108226\pi$
$252$		0			0
$253$			6.02375i			0.0238093i
$254$		0			0
$255$	9.66578	−	113.629i	0.0379050	−	0.445604i
$256$		0			0
$257$	−262.183			−1.02017			−0.510084	−	0.860125i	$-0.670386\pi$
$257$	−262.183			−1.02017			−0.510084	+	0.860125i	$0.670386\pi$
$258$		0			0
$259$	586.881			2.26595
$260$		0			0
$261$	−162.812	−	116.865i	−0.623802	−	0.447758i
$262$		0			0
$263$	−44.5924			−0.169553			−0.0847764	−	0.996400i	$-0.527018\pi$
$263$	−44.5924			−0.169553			−0.0847764	+	0.996400i	$0.527018\pi$
$264$		0			0
$265$	−41.5736	−	41.5736i	−0.156882	−	0.156882i
$266$		0			0
$267$	0.115009	+	1.40947i	0.000430744	+	0.00527893i
$268$		0			0
$269$	75.0566	+	75.0566i	0.279021	+	0.279021i	0.832718	−	0.553697i	$-0.186784\pi$
$269$	75.0566	+	75.0566i	0.279021	+	0.279021i	−0.553697	+	0.832718i	$0.686784\pi$
$270$		0			0
$271$	451.713			1.66684			0.833419	−	0.552641i	$-0.186380\pi$
$271$	451.713			1.66684			0.833419	+	0.552641i	$0.186380\pi$
$272$		0			0
$273$	−591.313	−	502.095i	−2.16598	−	1.83918i
$274$		0			0
$275$	1.60283	+	1.60283i	0.00582846	+	0.00582846i
$276$		0			0
$277$	116.662	−	116.662i	0.421161	−	0.421161i	−0.464442	−	0.885604i	$-0.653745\pi$
$277$	116.662	−	116.662i	0.421161	−	0.421161i	0.885604	+	0.464442i	$0.153745\pi$
$278$		0			0
$279$	42.1886	−	58.7758i	0.151214	−	0.210666i
$280$		0			0
$281$	−315.011			−1.12104			−0.560518	−	0.828142i	$-0.689398\pi$
$281$	−315.011			−1.12104			−0.560518	+	0.828142i	$0.689398\pi$
$282$		0			0
$283$	−67.4332	−	67.4332i	−0.238280	−	0.238280i	0.577858	−	0.816138i	$-0.303889\pi$
$283$	−67.4332	−	67.4332i	−0.238280	−	0.238280i	−0.816138	+	0.577858i	$0.803889\pi$
$284$		0			0
$285$	−28.8074	+	33.9262i	−0.101079	+	0.119039i
$286$		0			0
$287$	−177.776			−0.619429
$288$		0			0
$289$	−94.3461	+	273.166i	−0.326457	+	0.945212i
$290$		0			0
$291$	−75.5695	+	88.9977i	−0.259689	+	0.305834i
$292$		0			0
$293$		−	240.344i		−	0.820288i	−0.912021	−	0.410144i	$-0.865478\pi$
$293$		−	240.344i		−	0.820288i	0.912021	−	0.410144i	$-0.134522\pi$
$294$		0			0
$295$	−148.737	−	148.737i	−0.504194	−	0.504194i
$296$		0			0
$297$	−6.30529	+	10.4915i	−0.0212299	+	0.0353248i
$298$		0			0
$299$	−209.988	+	209.988i	−0.702300	+	0.702300i
$300$		0			0
$301$	−106.102	+	106.102i	−0.352497	+	0.352497i
$302$		0			0
$303$	−23.7978	−	291.651i	−0.0785405	−	0.962544i
$304$		0			0
$305$		−	122.631i		−	0.402068i
$306$		0			0
$307$	72.6066			0.236504			0.118252	−	0.992984i	$-0.462271\pi$
$307$	72.6066			0.236504			0.118252	+	0.992984i	$0.462271\pi$
$308$		0			0
$309$	−25.1399	+	2.05134i	−0.0813590	+	0.00663863i
$310$		0			0
$311$	241.226	+	241.226i	0.775648	+	0.775648i	0.979087	−	0.203440i	$-0.0652121\pi$
$311$	241.226	+	241.226i	0.775648	+	0.775648i	−0.203440	+	0.979087i	$0.565212\pi$
$312$		0			0
$313$	−338.823	−	338.823i	−1.08250	−	1.08250i	−0.996276	−	0.0862259i	$-0.972519\pi$
$313$	−338.823	−	338.823i	−1.08250	−	1.08250i	−0.0862259	−	0.996276i	$-0.527481\pi$
$314$		0			0
$315$	−37.7452	−	229.751i	−0.119826	−	0.729369i
$316$		0			0
$317$	−105.838	+	105.838i	−0.333875	+	0.333875i	−0.854056	−	0.520181i	$-0.825864\pi$
$317$	−105.838	+	105.838i	−0.333875	+	0.333875i	0.520181	+	0.854056i	$0.325864\pi$
$318$		0			0
$319$	−10.0952			−0.0316463
$320$		0			0
$321$	−23.0137	−	19.5413i	−0.0716937	−	0.0608764i
$322$		0			0
$323$	91.8546	−	65.4541i	0.284379	−	0.202644i
$324$		0			0
$325$			111.749i			0.343843i
$326$		0			0
$327$	−47.1314	−	40.0201i	−0.144133	−	0.122386i
$328$		0			0
$329$	−211.062	+	211.062i	−0.641527	+	0.641527i
$330$		0			0
$331$		−	115.894i		−	0.350133i	−0.984557	−	0.175067i	$-0.943986\pi$
$331$		−	115.894i		−	0.350133i	0.984557	−	0.175067i	$-0.0560140\pi$
$332$		0			0
$333$	266.218	−	370.887i	0.799454	−	1.11377i
$334$		0			0
$335$	−49.2873	−	49.2873i	−0.147126	−	0.147126i
$336$		0			0
$337$	453.684	−	453.684i	1.34624	−	1.34624i	0.456539	−	0.889704i	$-0.349089\pi$
$337$	453.684	−	453.684i	1.34624	−	1.34624i	0.889704	−	0.456539i	$-0.150911\pi$
$338$		0			0
$339$	−429.318	+	505.605i	−1.26643	+	1.49146i
$340$		0			0
$341$		−	3.64440i		−	0.0106874i
$342$		0			0
$343$	−293.305	+	293.305i	−0.855118	+	0.855118i
$344$		0			0
$345$	−88.8384	+	7.24893i	−0.257503	+	0.0210114i
$346$		0			0
$347$	−321.751	+	321.751i	−0.927237	+	0.927237i	−0.997527	−	0.0702899i	$-0.977608\pi$
$347$	−321.751	+	321.751i	−0.927237	+	0.927237i	0.0702899	+	0.997527i	$0.477608\pi$
$348$		0			0
$349$		−	281.871i		−	0.807654i	−0.914835	−	0.403827i	$-0.867680\pi$
$349$		−	281.871i		−	0.807654i	0.914835	−	0.403827i	$-0.132320\pi$
$350$		0			0
$351$	−585.534	+	145.930i	−1.66819	+	0.415754i
$352$		0			0
$353$			338.976i			0.960272i	0.877194	+	0.480136i	$0.159413\pi$
$353$			338.976i			0.960272i	−0.877194	+	0.480136i	$0.840587\pi$
$354$		0			0
$355$		−	159.459i		−	0.449181i
$356$		0			0
$357$	−50.0110	+	587.920i	−0.140087	+	1.64683i
$358$		0			0
$359$	−560.112			−1.56020			−0.780101	−	0.625654i	$-0.784832\pi$
$359$	−560.112			−1.56020			−0.780101	+	0.625654i	$0.784832\pi$
$360$		0			0
$361$	316.981			0.878064
$362$		0			0
$363$	−29.4714	−	361.183i	−0.0811884	−	0.994995i
$364$		0			0
$365$	43.4001			0.118904
$366$		0			0
$367$	−389.283	−	389.283i	−1.06072	−	1.06072i	−0.998034	−	0.0626826i	$-0.980034\pi$
$367$	−389.283	−	389.283i	−1.06072	−	1.06072i	−0.0626826	−	0.998034i	$-0.519966\pi$
$368$		0			0
$369$	−80.6420	+	112.348i	−0.218542	+	0.304466i
$370$		0			0
$371$	215.103	+	215.103i	0.579792	+	0.579792i
$372$		0			0
$373$	493.473			1.32298			0.661491	−	0.749953i	$-0.269924\pi$
$373$	493.473			1.32298			0.661491	+	0.749953i	$0.269924\pi$
$374$		0			0
$375$	−21.7097	+	25.5673i	−0.0578925	+	0.0681796i
$376$		0			0
$377$	−351.918	−	351.918i	−0.933469	−	0.933469i
$378$		0			0
$379$	30.0703	−	30.0703i	0.0793413	−	0.0793413i	−0.666322	−	0.745664i	$-0.732133\pi$
$379$	30.0703	−	30.0703i	0.0793413	−	0.0793413i	0.745664	+	0.666322i	$0.232133\pi$
$380$		0			0
$381$	−19.7720	−	242.314i	−0.0518951	−	0.635994i
$382$		0			0
$383$	19.6805			0.0513851			0.0256925	−	0.999670i	$-0.491821\pi$
$383$	19.6805			0.0513851			0.0256925	+	0.999670i	$0.491821\pi$
$384$		0			0
$385$	−8.29307	−	8.29307i	−0.0215404	−	0.0215404i
$386$		0			0
$387$	18.9229	+	115.181i	0.0488963	+	0.297626i
$388$		0			0
$389$	119.441			0.307045			0.153523	−	0.988145i	$-0.450938\pi$
$389$	119.441			0.307045			0.153523	+	0.988145i	$0.450938\pi$
$390$		0			0
$391$	222.768	+	37.3863i	0.569739	+	0.0956171i
$392$		0			0
$393$	−415.573	−	352.871i	−1.05744	−	0.897890i
$394$		0			0
$395$			350.949i			0.888479i
$396$		0			0
$397$	286.600	+	286.600i	0.721915	+	0.721915i	0.968995	−	0.247080i	$-0.0794711\pi$
$397$	286.600	+	286.600i	0.721915	+	0.721915i	−0.247080	+	0.968995i	$0.579471\pi$
$398$		0			0
$399$	149.050	−	175.535i	0.373559	−	0.439938i
$400$		0			0
$401$	−345.140	+	345.140i	−0.860699	+	0.860699i	−0.991419	−	0.130720i	$-0.958271\pi$
$401$	−345.140	+	345.140i	−0.860699	+	0.860699i	0.130720	+	0.991419i	$0.458271\pi$
$402$		0			0
$403$	127.043	−	127.043i	0.315244	−	0.315244i
$404$		0			0
$405$	−162.316	−	80.3651i	−0.400780	−	0.198432i
$406$		0			0
$407$		−	22.9969i		−	0.0565033i
$408$		0			0
$409$	−285.549			−0.698165			−0.349082	−	0.937092i	$-0.613507\pi$
$409$	−285.549			−0.698165			−0.349082	+	0.937092i	$0.613507\pi$
$410$		0			0
$411$	19.9390	+	244.360i	0.0485133	+	0.594550i
$412$		0			0
$413$	769.570	+	769.570i	1.86337	+	1.86337i
$414$		0			0
$415$	−81.4889	−	81.4889i	−0.196359	−	0.196359i
$416$		0			0
$417$	289.674	−	341.147i	0.694663	−	0.818099i
$418$		0			0
$419$	412.034	−	412.034i	0.983374	−	0.983374i	−0.0164896	−	0.999864i	$-0.505249\pi$
$419$	412.034	−	412.034i	0.983374	−	0.983374i	0.999864	+	0.0164896i	$0.00524905\pi$
$420$		0			0
$421$	−61.4425			−0.145944			−0.0729721	−	0.997334i	$-0.523248\pi$
$421$	−61.4425			−0.145944			−0.0729721	+	0.997334i	$0.523248\pi$
$422$		0			0
$423$	37.6423	+	229.125i	0.0889889	+	0.541666i
$424$		0			0
$425$	69.2230	−	49.3272i	0.162878	−	0.116064i
$426$		0			0
$427$			634.494i			1.48593i
$428$		0			0
$429$	−19.6745	+	23.1705i	−0.0458613	+	0.0540106i
$430$		0			0
$431$	−318.123	+	318.123i	−0.738104	+	0.738104i	−0.972211	−	0.234107i	$-0.924783\pi$
$431$	−318.123	+	318.123i	−0.738104	+	0.738104i	0.234107	+	0.972211i	$0.424783\pi$
$432$		0			0
$433$			347.586i			0.802739i	0.915916	+	0.401370i	$0.131466\pi$
$433$			347.586i			0.802739i	−0.915916	+	0.401370i	$0.868534\pi$
$434$		0			0
$435$	−12.1484	−	148.884i	−0.0279275	−	0.342262i
$436$		0			0
$437$	−62.3363	−	62.3363i	−0.142646	−	0.142646i
$438$		0			0
$439$	−536.592	+	536.592i	−1.22230	+	1.22230i	−0.255494	+	0.966811i	$0.582238\pi$
$439$	−536.592	+	536.592i	−1.22230	+	1.22230i	−0.966811	+	0.255494i	$0.917762\pi$
$440$		0			0
$441$	123.802	+	753.572i	0.280731	+	1.70878i
$442$		0			0
$443$		−	294.967i		−	0.665840i	−0.942955	−	0.332920i	$-0.891966\pi$
$443$		−	294.967i		−	0.665840i	0.942955	−	0.332920i	$-0.108034\pi$
$444$		0			0
$445$	−0.745327	+	0.745327i	−0.00167489	+	0.00167489i
$446$		0			0
$447$	−71.1511	−	871.984i	−0.159175	−	1.95075i
$448$		0			0
$449$	547.166	−	547.166i	1.21863	−	1.21863i	0.250521	−	0.968111i	$-0.419398\pi$
$449$	547.166	−	547.166i	1.21863	−	1.21863i	0.968111	−	0.250521i	$-0.0806020\pi$
$450$		0			0
$451$			6.96614i			0.0154460i
$452$		0			0
$453$	−33.7222	−	413.278i	−0.0744419	−	0.912315i
$454$		0			0
$455$		−	578.192i		−	1.27075i
$456$		0			0
$457$			74.0098i			0.161947i	0.996716	+	0.0809735i	$0.0258029\pi$
$457$			74.0098i			0.161947i	−0.996716	+	0.0809735i	$0.974197\pi$
$458$		0			0
$459$	348.857	+	298.294i	0.760038	+	0.649879i
$460$		0			0
$461$	518.651			1.12506			0.562528	−	0.826778i	$-0.309829\pi$
$461$	518.651			1.12506			0.562528	+	0.826778i	$0.309829\pi$
$462$		0			0
$463$	8.47775			0.0183105			0.00915523	−	0.999958i	$-0.497086\pi$
$463$	8.47775			0.0183105			0.00915523	+	0.999958i	$0.497086\pi$
$464$		0			0
$465$	53.7476	−	4.38563i	0.115586	−	0.00943146i
$466$		0			0
$467$	733.351			1.57035			0.785173	−	0.619277i	$-0.212574\pi$
$467$	733.351			1.57035			0.785173	+	0.619277i	$0.212574\pi$
$468$		0			0
$469$	255.014	+	255.014i	0.543740	+	0.543740i
$470$		0			0
$471$	235.763	−	19.2375i	0.500559	−	0.0408440i
$472$		0			0
$473$	4.15757	+	4.15757i	0.00878979	+	0.00878979i
$474$		0			0
$475$	−33.1734			−0.0698388
$476$		0			0
$477$	233.511	−	38.3629i	0.489541	−	0.0804254i
$478$		0			0
$479$	−487.200	−	487.200i	−1.01712	−	1.01712i	−0.999851	−	0.0172673i	$-0.994503\pi$
$479$	−487.200	−	487.200i	−1.01712	−	1.01712i	−0.0172673	−	0.999851i	$-0.505497\pi$
$480$		0			0
$481$	801.669	−	801.669i	1.66667	−	1.66667i
$482$		0			0
$483$	459.652	−	37.5061i	0.951661	−	0.0776525i
$484$		0			0
$485$	−87.0228			−0.179428
$486$		0			0
$487$	220.970	+	220.970i	0.453737	+	0.453737i	0.896593	−	0.442856i	$-0.146035\pi$
$487$	220.970	+	220.970i	0.453737	+	0.453737i	−0.442856	+	0.896593i	$0.646035\pi$
$488$		0			0
$489$	−470.119	−	399.186i	−0.961388	−	0.816332i
$490$		0			0
$491$	−747.670			−1.52275			−0.761375	−	0.648312i	$-0.775475\pi$
$491$	−747.670			−1.52275			−0.761375	+	0.648312i	$0.775475\pi$
$492$		0			0
$493$	−62.6555	+	373.336i	−0.127090	+	0.757274i
$494$		0			0
$495$	−9.00277	+	1.47904i	−0.0181874	+	0.00298796i
$496$		0			0
$497$			825.046i			1.66005i
$498$		0			0
$499$	−95.7577	−	95.7577i	−0.191899	−	0.191899i	0.604617	−	0.796516i	$-0.293326\pi$
$499$	−95.7577	−	95.7577i	−0.191899	−	0.191899i	−0.796516	+	0.604617i	$0.793326\pi$
$500$		0			0
$501$	157.824	+	134.011i	0.315017	+	0.267487i
$502$		0			0
$503$	254.991	−	254.991i	0.506939	−	0.506939i	−0.406646	−	0.913586i	$-0.633302\pi$
$503$	254.991	−	254.991i	0.506939	−	0.506939i	0.913586	+	0.406646i	$0.133302\pi$
$504$		0			0
$505$	154.224	−	154.224i	0.305395	−	0.305395i
$506$		0			0
$507$	−988.256	+	80.6385i	−1.94922	+	0.159050i
$508$		0			0
$509$		−	914.286i		−	1.79624i	−0.439751	−	0.898120i	$-0.644933\pi$
$509$		−	914.286i		−	1.79624i	0.439751	−	0.898120i	$-0.355067\pi$
$510$		0			0
$511$	−224.553			−0.439438
$512$		0			0
$513$	−43.3202	−	173.820i	−0.0844448	−	0.338829i
$514$		0			0
$515$	−13.2939	−	13.2939i	−0.0258135	−	0.0258135i
$516$		0			0
$517$	8.27045	+	8.27045i	0.0159970	+	0.0159970i
$518$		0			0
$519$	185.064	+	157.141i	0.356578	+	0.302777i
$520$		0			0
$521$	−507.849	+	507.849i	−0.974758	+	0.974758i	−0.999689	−	0.0249315i	$-0.992063\pi$
$521$	−507.849	+	507.849i	−0.974758	+	0.974758i	0.0249315	+	0.999689i	$0.492063\pi$
$522$		0			0
$523$	−826.929			−1.58113			−0.790564	−	0.612380i	$-0.790212\pi$
$523$	−826.929			−1.58113			−0.790564	+	0.612380i	$0.790212\pi$
$524$		0			0
$525$	112.326	−	132.286i	0.213955	−	0.251974i
$526$		0			0
$527$	−134.776	−	22.6188i	−0.255741	−	0.0429200i
$528$		0			0
$529$			352.449i			0.666254i
$530$		0			0
$531$	835.428	−	137.250i	1.57331	−	0.258475i
$532$		0			0
$533$	−242.839	+	242.839i	−0.455608	+	0.455608i
$534$		0			0
$535$		−	22.5030i		−	0.0420617i
$536$		0			0
$537$	−748.442	+	61.0705i	−1.39375	+	0.113725i
$538$		0			0
$539$	27.2008	+	27.2008i	0.0504654	+	0.0504654i
$540$		0			0
$541$	−260.997	+	260.997i	−0.482434	+	0.482434i	−0.905908	−	0.423474i	$-0.860810\pi$
$541$	−260.997	+	260.997i	−0.482434	+	0.482434i	0.423474	+	0.905908i	$0.360810\pi$
$542$		0			0
$543$	477.287	+	405.273i	0.878981	+	0.746359i
$544$		0			0
$545$		−	46.0855i		−	0.0845605i
$546$		0			0
$547$	−242.570	+	242.570i	−0.443456	+	0.443456i	−0.893172	−	0.449716i	$-0.851525\pi$
$547$	−242.570	+	242.570i	−0.443456	+	0.443456i	0.449716	+	0.893172i	$0.351525\pi$
$548$		0			0
$549$	400.976	+	287.816i	0.730375	+	0.524255i
$550$		0			0
$551$	104.469	−	104.469i	0.189599	−	0.189599i
$552$		0			0
$553$		−	1815.82i		−	3.28358i
$554$		0			0
$555$	339.158	−	27.6742i	0.611095	−	0.0498634i
$556$		0			0
$557$		−	135.656i		−	0.243547i	−0.992558	−	0.121774i	$-0.961142\pi$
$557$		−	135.656i		−	0.243547i	0.992558	−	0.121774i	$-0.0388582\pi$
$558$		0			0
$559$			289.866i			0.518543i
$560$		0			0
$561$	23.0375	+	1.95967i	0.0410651	+	0.00349318i
$562$		0			0
$563$	467.351			0.830108			0.415054	−	0.909797i	$-0.363763\pi$
$563$	467.351			0.830108			0.415054	+	0.909797i	$0.363763\pi$
$564$		0			0
$565$	−494.386			−0.875019
$566$		0			0
$567$	839.826	+	415.811i	1.48118	+	0.733353i
$568$		0			0
$569$	−1049.37			−1.84424			−0.922118	−	0.386910i	$-0.873543\pi$
$569$	−1049.37			−1.84424			−0.922118	+	0.386910i	$0.873543\pi$
$570$		0			0
$571$	−264.365	−	264.365i	−0.462987	−	0.462987i	0.436647	−	0.899633i	$-0.356166\pi$
$571$	−264.365	−	264.365i	−0.462987	−	0.462987i	−0.899633	+	0.436647i	$0.856166\pi$
$572$		0			0
$573$	−68.0643	−	834.154i	−0.118786	−	1.45577i
$574$		0			0
$575$	−46.9776	−	46.9776i	−0.0817001	−	0.0817001i
$576$		0			0
$577$	480.509			0.832771			0.416385	−	0.909188i	$-0.363297\pi$
$577$	480.509			0.832771			0.416385	+	0.909188i	$0.363297\pi$
$578$		0			0
$579$	732.183	+	621.710i	1.26456	+	1.07376i
$580$		0			0
$581$	421.626	+	421.626i	0.725690	+	0.725690i
$582$		0			0
$583$	8.42878	−	8.42878i	0.0144576	−	0.0144576i
$584$		0			0
$585$	−365.395	−	262.277i	−0.624608	−	0.448336i
$586$		0			0
$587$	779.817			1.32848			0.664240	−	0.747520i	$-0.268755\pi$
$587$	779.817			1.32848			0.664240	+	0.747520i	$0.268755\pi$
$588$		0			0
$589$	37.7137	+	37.7137i	0.0640300	+	0.0640300i
$590$		0			0
$591$	678.182	−	798.689i	1.14752	−	1.35142i
$592$		0			0
$593$	−310.567			−0.523721			−0.261861	−	0.965106i	$-0.584336\pi$
$593$	−310.567			−0.523721			−0.261861	+	0.965106i	$0.584336\pi$
$594$		0			0
$595$	−358.162	+	255.220i	−0.601952	+	0.428942i
$596$		0			0
$597$	−375.850	+	442.636i	−0.629565	+	0.741434i
$598$		0			0
$599$		−	575.782i		−	0.961239i	−0.876929	−	0.480619i	$-0.840412\pi$
$599$		−	575.782i		−	0.961239i	0.876929	−	0.480619i	$-0.159588\pi$
$600$		0			0
$601$	441.800	+	441.800i	0.735108	+	0.735108i	0.971627	−	0.236519i	$-0.0760065\pi$
$601$	441.800	+	441.800i	0.735108	+	0.735108i	−0.236519	+	0.971627i	$0.576006\pi$
$602$		0			0
$603$	276.837	−	45.4809i	0.459100	−	0.0754243i
$604$		0			0
$605$	190.993	−	190.993i	0.315691	−	0.315691i
$606$		0			0
$607$	33.3620	−	33.3620i	0.0549622	−	0.0549622i	−0.679091	−	0.734054i	$-0.737626\pi$
$607$	33.3620	−	33.3620i	0.0549622	−	0.0549622i	0.734054	+	0.679091i	$0.237626\pi$
$608$		0			0
$609$	62.8564	+	770.329i	0.103212	+	1.26491i
$610$		0			0
$611$			576.615i			0.943724i
$612$		0			0
$613$	−62.9346			−0.102667			−0.0513333	−	0.998682i	$-0.516347\pi$
$613$	−62.9346			−0.102667			−0.0513333	+	0.998682i	$0.516347\pi$
$614$		0			0
$615$	−102.737	+	8.38298i	−0.167052	+	0.0136309i
$616$		0			0
$617$	453.757	+	453.757i	0.735425	+	0.735425i	0.971689	−	0.236264i	$-0.0759230\pi$
$617$	453.757	+	453.757i	0.735425	+	0.735425i	−0.236264	+	0.971689i	$0.575923\pi$
$618$		0			0
$619$	−400.277	−	400.277i	−0.646650	−	0.646650i	0.305532	−	0.952182i	$-0.401166\pi$
$619$	−400.277	−	400.277i	−0.646650	−	0.646650i	−0.952182	+	0.305532i	$0.901166\pi$
$620$		0			0
$621$	184.803	−	307.496i	0.297589	−	0.495163i
$622$		0			0
$623$	3.85634	−	3.85634i	0.00618995	−	0.00618995i
$624$		0			0
$625$	−25.0000			−0.0400000
$626$		0			0
$627$	−6.87832	−	5.84051i	−0.0109702	−	0.00931500i
$628$		0			0
$629$	−850.460	−	142.729i	−1.35208	−	0.226915i
$630$		0			0
$631$		−	278.507i		−	0.441373i	−0.975345	−	0.220687i	$-0.929170\pi$
$631$		−	278.507i		−	0.441373i	0.975345	−	0.220687i	$-0.0708298\pi$
$632$		0			0
$633$	−776.966	−	659.736i	−1.22743	−	1.04224i
$634$		0			0
$635$	128.135	−	128.135i	0.201787	−	0.201787i
$636$		0			0
$637$			1896.44i			2.97714i
$638$		0			0
$639$	521.398	+	374.254i	0.815959	+	0.585686i
$640$		0			0
$641$	−6.33939	−	6.33939i	−0.00988985	−	0.00988985i	0.702145	−	0.712034i	$-0.252226\pi$
$641$	−6.33939	−	6.33939i	−0.00988985	−	0.00988985i	−0.712034	+	0.702145i	$0.752226\pi$
$642$		0			0
$643$	−883.342	+	883.342i	−1.37378	+	1.37378i	−0.519019	+	0.854763i	$0.673703\pi$
$643$	−883.342	+	883.342i	−1.37378	+	1.37378i	−0.854763	+	0.519019i	$0.826297\pi$
$644$		0			0
$645$	−56.3128	+	66.3191i	−0.0873066	+	0.102820i
$646$		0			0
$647$			237.513i			0.367098i	0.983011	+	0.183549i	$0.0587587\pi$
$647$			237.513i			0.367098i	−0.983011	+	0.183549i	$0.941241\pi$
$648$		0			0
$649$	30.1555	−	30.1555i	0.0464645	−	0.0464645i
$650$		0			0
$651$	−278.091	+	22.6914i	−0.427176	+	0.0348562i
$652$		0			0
$653$	615.515	−	615.515i	0.942596	−	0.942596i	−0.0558432	−	0.998440i	$-0.517785\pi$
$653$	615.515	−	615.515i	0.942596	−	0.942596i	0.998440	+	0.0558432i	$0.0177847\pi$
$654$		0			0
$655$		−	406.351i		−	0.620384i
$656$		0			0
$657$	−101.861	+	141.909i	−0.155039	+	0.215995i
$658$		0			0
$659$			675.130i			1.02448i	0.858843	+	0.512238i	$0.171184\pi$
$659$			675.130i			1.02448i	−0.858843	+	0.512238i	$0.828816\pi$
$660$		0			0
$661$		−	385.542i		−	0.583272i	−0.956529	−	0.291636i	$-0.905800\pi$
$661$		−	385.542i		−	0.583272i	0.956529	−	0.291636i	$-0.0941995\pi$
$662$		0			0
$663$	734.774	+	871.402i	1.10826	+	1.31433i
$664$		0			0
$665$	171.640			0.258105
$666$		0			0
$667$	295.882			0.443601
$668$		0			0
$669$	50.4639	+	618.454i	0.0754318	+	0.924445i
$670$		0			0
$671$	24.8625			0.0370530
$672$		0			0
$673$	−41.6775	−	41.6775i	−0.0619279	−	0.0619279i	0.675465	−	0.737392i	$-0.263943\pi$
$673$	−41.6775	−	41.6775i	−0.0619279	−	0.0619279i	−0.737392	+	0.675465i	$0.763943\pi$
$674$		0			0
$675$	−32.6468	−	130.993i	−0.0483656	−	0.194064i
$676$		0			0
$677$	89.9460	+	89.9460i	0.132860	+	0.132860i	0.770409	−	0.637550i	$-0.220052\pi$
$677$	89.9460	+	89.9460i	0.132860	+	0.132860i	−0.637550	+	0.770409i	$0.720052\pi$
$678$		0			0
$679$	450.258			0.663120
$680$		0			0
$681$	−602.751	+	709.856i	−0.885097	+	1.04237i
$682$		0			0
$683$	−589.757	−	589.757i	−0.863480	−	0.863480i	0.128261	−	0.991740i	$-0.459061\pi$
$683$	−589.757	−	589.757i	−0.863480	−	0.863480i	−0.991740	+	0.128261i	$0.959061\pi$
$684$		0			0
$685$	−129.217	+	129.217i	−0.188638	+	0.188638i
$686$		0			0
$687$	40.7100	+	498.916i	0.0592576	+	0.726225i
$688$		0			0
$689$	587.654			0.852908
$690$		0			0
$691$	−106.658	−	106.658i	−0.154353	−	0.154353i	0.625706	−	0.780059i	$-0.284811\pi$
$691$	−106.658	−	106.658i	−0.154353	−	0.154353i	−0.780059	+	0.625706i	$0.784811\pi$
$692$		0			0
$693$	46.5805	−	7.65260i	0.0672158	−	0.0110427i
$694$		0			0
$695$	333.577			0.479967
$696$		0			0
$697$	257.619	+	43.2351i	0.369611	+	0.0620303i
$698$		0			0
$699$	−358.063	−	304.038i	−0.512250	−	0.434961i
$700$		0			0
$701$		−	1143.41i		−	1.63111i	−0.578677	−	0.815557i	$-0.696431\pi$
$701$		−	1143.41i		−	1.63111i	0.578677	−	0.815557i	$-0.303569\pi$
$702$		0			0
$703$	237.981	+	237.981i	0.338522	+	0.338522i
$704$		0			0
$705$	−112.020	+	131.925i	−0.158894	+	0.187128i
$706$		0			0
$707$	−797.960	+	797.960i	−1.12866	+	1.12866i
$708$		0			0
$709$	−735.467	+	735.467i	−1.03733	+	1.03733i	−0.0380537	+	0.999276i	$0.512116\pi$
$709$	−735.467	+	735.467i	−1.03733	+	1.03733i	−0.999276	+	0.0380537i	$0.987884\pi$
$710$		0			0
$711$	−1147.53	−	823.684i	−1.61396	−	1.15849i
$712$		0			0
$713$			106.814i			0.149810i
$714$		0			0
$715$	−22.6564			−0.0316872
$716$		0			0
$717$	−7.11046	−	87.1414i	−0.00991696	−	0.121536i
$718$		0			0
$719$	−496.499	−	496.499i	−0.690541	−	0.690541i	0.271810	−	0.962351i	$-0.412378\pi$
$719$	−496.499	−	496.499i	−0.690541	−	0.690541i	−0.962351	+	0.271810i	$0.912378\pi$
$720$		0			0
$721$	68.7832	+	68.7832i	0.0953997	+	0.0953997i
$722$		0			0
$723$	23.8815	−	28.1250i	0.0330311	−	0.0389004i
$724$		0			0
$725$	78.7295	−	78.7295i	0.108592	−	0.108592i
$726$		0			0
$727$	437.583			0.601902			0.300951	−	0.953640i	$-0.402696\pi$
$727$	437.583			0.601902			0.300951	+	0.953640i	$0.402696\pi$
$728$		0			0
$729$	643.735	−	342.120i	0.883039	−	0.469301i
$730$		0			0
$731$	179.558	−	127.950i	0.245633	−	0.175034i
$732$		0			0
$733$		−	773.653i		−	1.05546i	−0.849412	−	0.527730i	$-0.823043\pi$
$733$		−	773.653i		−	1.05546i	0.849412	−	0.527730i	$-0.176957\pi$
$734$		0			0
$735$	−368.425	+	433.892i	−0.501259	+	0.590329i
$736$		0			0
$737$	9.99268	−	9.99268i	0.0135586	−	0.0135586i
$738$		0			0
$739$		−	804.284i		−	1.08834i	−0.838975	−	0.544170i	$-0.816845\pi$
$739$		−	804.284i		−	1.08834i	0.838975	−	0.544170i	$-0.183155\pi$
$740$		0			0
$741$	−36.1782	−	443.378i	−0.0488235	−	0.598351i
$742$		0			0
$743$	−906.421	−	906.421i	−1.21995	−	1.21995i	−0.967649	−	0.252299i	$-0.918813\pi$
$743$	−906.421	−	906.421i	−1.21995	−	1.21995i	−0.252299	−	0.967649i	$-0.581187\pi$
$744$		0			0
$745$	461.103	−	461.103i	0.618931	−	0.618931i
$746$		0			0
$747$	457.707	−	75.1956i	0.612727	−	0.100663i
$748$		0			0
$749$			116.431i			0.155449i
$750$		0			0
$751$	−653.617	+	653.617i	−0.870329	+	0.870329i	−0.992508	−	0.122179i	$-0.961012\pi$
$751$	−653.617	+	653.617i	−0.870329	+	0.870329i	0.122179	+	0.992508i	$0.461012\pi$
$752$		0			0
$753$	40.8448	+	500.569i	0.0542428	+	0.664766i
$754$		0			0
$755$	218.541	−	218.541i	0.289458	−	0.289458i
$756$		0			0
$757$			252.143i			0.333082i	0.986035	+	0.166541i	$0.0532597\pi$
$757$			252.143i			0.333082i	−0.986035	+	0.166541i	$0.946740\pi$
$758$		0			0
$759$	−1.46967	−	18.0114i	−0.00193633	−	0.0237304i
$760$		0			0
$761$			940.099i			1.23535i	0.786435	+	0.617673i	$0.211925\pi$
$761$			940.099i			1.23535i	−0.786435	+	0.617673i	$0.788075\pi$
$762$		0			0
$763$			238.447i			0.312513i
$764$		0			0
$765$	−1.17811	+	342.116i	−0.00154001	+	0.447211i
$766$		0			0
$767$	2102.44			2.74112
$768$		0			0
$769$	1252.88			1.62923			0.814617	−	0.579999i	$-0.196947\pi$
$769$	1252.88			1.62923			0.814617	+	0.579999i	$0.196947\pi$
$770$		0			0
$771$	783.943	−	63.9673i	1.01679	−	0.0829666i
$772$		0			0
$773$	552.155			0.714301			0.357150	−	0.934047i	$-0.383748\pi$
$773$	552.155			0.714301			0.357150	+	0.934047i	$0.383748\pi$
$774$		0			0
$775$	28.4216	+	28.4216i	0.0366731	+	0.0366731i
$776$		0			0
$777$	−1754.81	+	143.187i	−2.25844	+	0.184282i
$778$		0			0
$779$	−72.0884	−	72.0884i	−0.0925397	−	0.0925397i
$780$		0			0
$781$	32.3293			0.0413948
$782$		0			0
$783$	515.331	+	309.710i	0.658150	+	0.395543i
$784$		0			0
$785$	124.671	+	124.671i	0.158817	+	0.158817i
$786$		0			0
$787$	535.523	−	535.523i	0.680461	−	0.680461i	−0.279643	−	0.960104i	$-0.590216\pi$
$787$	535.523	−	535.523i	0.680461	−	0.680461i	0.960104	+	0.279643i	$0.0902162\pi$
$788$		0			0
$789$	133.334	−	10.8796i	0.168991	−	0.0137891i
$790$		0			0
$791$	2557.96			3.23383
$792$		0			0
$793$	866.707	+	866.707i	1.09295	+	1.09295i
$794$		0			0
$795$	134.451	+	114.165i	0.169121	+	0.143603i
$796$		0			0
$797$	−140.755			−0.176606			−0.0883028	−	0.996094i	$-0.528144\pi$
$797$	−140.755			−0.176606			−0.0883028	+	0.996094i	$0.528144\pi$
$798$		0			0
$799$	357.185	−	254.524i	0.447040	−	0.318553i
$800$		0			0
$801$	−0.687766	−	4.18636i	−0.000858634	−	0.00522641i
$802$		0			0
$803$			8.79908i			0.0109578i
$804$		0			0
$805$	243.063	+	243.063i	0.301942	+	0.301942i
$806$		0			0
$807$	−242.736	−	206.112i	−0.300788	−	0.255405i
$808$		0			0
$809$	711.471	−	711.471i	0.879445	−	0.879445i	−0.114032	−	0.993477i	$-0.536377\pi$
$809$	711.471	−	711.471i	0.879445	−	0.879445i	0.993477	+	0.114032i	$0.0363765\pi$
$810$		0			0
$811$	−545.429	+	545.429i	−0.672539	+	0.672539i	−0.958301	−	0.285762i	$-0.907753\pi$
$811$	−545.429	+	545.429i	−0.672539	+	0.672539i	0.285762	+	0.958301i	$0.407753\pi$
$812$		0			0
$813$	−1350.65	+	110.209i	−1.66132	+	0.135558i
$814$		0			0
$815$		−	459.687i		−	0.564033i
$816$		0			0
$817$	−86.0485			−0.105323
$818$		0			0
$819$	1890.57	+	1357.03i	2.30838	+	1.65693i
$820$		0			0
$821$	−261.920	−	261.920i	−0.319026	−	0.319026i	0.529367	−	0.848393i	$-0.322429\pi$
$821$	−261.920	−	261.920i	−0.319026	−	0.319026i	−0.848393	+	0.529367i	$0.822429\pi$
$822$		0			0
$823$	298.228	+	298.228i	0.362367	+	0.362367i	0.864684	−	0.502317i	$-0.167519\pi$
$823$	298.228	+	298.228i	0.362367	+	0.362367i	−0.502317	+	0.864684i	$0.667519\pi$
$824$		0			0
$825$	−5.18361	−	4.40150i	−0.00628316	−	0.00533515i
$826$		0			0
$827$	−151.654	+	151.654i	−0.183379	+	0.183379i	−0.792826	−	0.609448i	$-0.791391\pi$
$827$	−151.654	+	151.654i	−0.183379	+	0.183379i	0.609448	+	0.792826i	$0.291391\pi$
$828$		0			0
$829$	991.151			1.19560			0.597799	−	0.801646i	$-0.296042\pi$
$829$	991.151			1.19560			0.597799	+	0.801646i	$0.296042\pi$
$830$		0			0
$831$	−320.363	+	377.289i	−0.385515	+	0.454018i
$832$		0			0
$833$	1174.75	−	837.109i	1.41027	−	1.00493i
$834$		0			0
$835$			154.322i			0.184816i
$836$		0			0
$837$	−111.806	+	186.036i	−0.133580	+	0.222266i
$838$		0			0
$839$	−489.240	+	489.240i	−0.583123	+	0.583123i	−0.935760	−	0.352637i	$-0.885285\pi$
$839$	−489.240	+	489.240i	−0.583123	+	0.583123i	0.352637	+	0.935760i	$0.385285\pi$
$840$		0			0
$841$		−	345.133i		−	0.410384i
$842$		0			0
$843$	941.903	−	76.8562i	1.11732	−	0.0911699i
$844$		0			0
$845$	−522.588	−	522.588i	−0.618447	−	0.618447i
$846$		0			0
$847$	−988.202	+	988.202i	−1.16671	+	1.16671i
$848$		0			0
$849$	218.082	+	185.177i	0.256869	+	0.218112i
$850$		0			0
$851$			674.019i			0.792032i
$852$		0			0
$853$	69.7640	−	69.7640i	0.0817867	−	0.0817867i	−0.665030	−	0.746817i	$-0.731581\pi$
$853$	69.7640	−	69.7640i	0.0817867	−	0.0817867i	0.746817	+	0.665030i	$0.231581\pi$
$854$		0			0
$855$	77.8586	−	108.470i	0.0910627	−	0.126866i
$856$		0			0
$857$	1016.38	−	1016.38i	1.18597	−	1.18597i	0.207800	−	0.978171i	$-0.433370\pi$
$857$	1016.38	−	1016.38i	1.18597	−	1.18597i	0.978171	−	0.207800i	$-0.0666303\pi$
$858$		0			0
$859$		−	451.030i		−	0.525064i	−0.964923	−	0.262532i	$-0.915442\pi$
$859$		−	451.030i		−	0.525064i	0.964923	−	0.262532i	$-0.0845576\pi$
$860$		0			0
$861$	531.562	−	43.3738i	0.617378	−	0.0503760i
$862$		0			0
$863$			1034.82i			1.19910i	0.800338	+	0.599549i	$0.204653\pi$
$863$			1034.82i			1.19910i	−0.800338	+	0.599549i	$0.795347\pi$
$864$		0			0
$865$			180.957i			0.209199i
$866$		0			0
$867$	215.454	−	839.803i	0.248505	−	0.968631i
$868$		0			0
$869$	−71.1526			−0.0818787
$870$		0			0
$871$	696.689			0.799872
$872$		0			0
$873$	204.244	−	284.546i	0.233957	−	0.325941i
$874$		0			0
$875$	129.351			0.147829
$876$		0			0
$877$	−469.156	−	469.156i	−0.534956	−	0.534956i	0.387087	−	0.922043i	$-0.373481\pi$
$877$	−469.156	−	469.156i	−0.534956	−	0.534956i	−0.922043	+	0.387087i	$0.873481\pi$
$878$		0			0
$879$	58.6391	+	718.645i	0.0667112	+	0.817571i
$880$		0			0
$881$	−126.111	−	126.111i	−0.143145	−	0.143145i	0.631903	−	0.775048i	$-0.282274\pi$
$881$	−126.111	−	126.111i	−0.143145	−	0.143145i	−0.775048	+	0.631903i	$0.782274\pi$
$882$		0			0
$883$	−774.341			−0.876944			−0.438472	−	0.898745i	$-0.644480\pi$
$883$	−774.341			−0.876944			−0.438472	+	0.898745i	$0.644480\pi$
$884$		0			0
$885$	481.022	+	408.445i	0.543528	+	0.461519i
$886$		0			0
$887$	−64.8494	−	64.8494i	−0.0731109	−	0.0731109i	0.669606	−	0.742717i	$-0.266463\pi$
$887$	−64.8494	−	64.8494i	−0.0731109	−	0.0731109i	−0.742717	+	0.669606i	$0.766463\pi$
$888$		0			0
$889$	−662.974	+	662.974i	−0.745752	+	0.745752i
$890$		0			0
$891$	16.2935	−	32.9085i	0.0182868	−	0.0369343i
$892$		0			0
$893$	−171.172			−0.191682
$894$		0			0
$895$	−395.775	−	395.775i	−0.442206	−	0.442206i
$896$		0			0
$897$	576.644	−	679.110i	0.642858	−	0.757090i
$898$		0			0
$899$	−179.010			−0.199121
$900$		0			0
$901$	−259.397	−	364.023i	−0.287899	−	0.404021i
$902$		0			0
$903$	291.364	−	343.137i	0.322662	−	0.379996i
$904$		0			0
$905$			466.696i			0.515686i
$906$		0			0
$907$	−271.701	−	271.701i	−0.299560	−	0.299560i	0.541282	−	0.840841i	$-0.317939\pi$
$907$	−271.701	−	271.701i	−0.299560	−	0.299560i	−0.840841	+	0.541282i	$0.817939\pi$
$908$		0			0
$909$	142.314	+	866.248i	0.156561	+	0.952968i
$910$		0			0
$911$	−1008.71	+	1008.71i	−1.10725	+	1.10725i	−0.113743	+	0.993510i	$0.536284\pi$
$911$	−1008.71	+	1008.71i	−1.10725	+	1.10725i	−0.993510	+	0.113743i	$0.963716\pi$
$912$		0			0
$913$	16.5213	−	16.5213i	0.0180957	−	0.0180957i
$914$		0			0
$915$	29.9194	+	366.673i	0.0326988	+	0.400736i
$916$		0			0
$917$			2102.47i			2.29277i
$918$		0			0
$919$	−300.875			−0.327394			−0.163697	−	0.986511i	$-0.552342\pi$
$919$	−300.875			−0.327394			−0.163697	+	0.986511i	$0.552342\pi$
$920$		0			0
$921$	−217.098	+	17.7145i	−0.235720	+	0.0192340i
$922$		0			0
$923$	1127.00	+	1127.00i	1.22102	+	1.22102i
$924$		0			0
$925$	179.346	+	179.346i	0.193888	+	0.193888i
$926$		0			0
$927$	74.6694	−	12.2673i	0.0805496	−	0.0132333i
$928$		0			0
$929$	−196.773	+	196.773i	−0.211811	+	0.211811i	−0.805037	−	0.593225i	$-0.797854\pi$
$929$	−196.773	+	196.773i	−0.211811	+	0.211811i	0.593225	+	0.805037i	$0.297854\pi$
$930$		0			0
$931$	−562.971			−0.604694
$932$		0			0
$933$	−780.137	−	662.428i	−0.836159	−	0.709998i
$934$		0			0
$935$	10.0008	+	14.0345i	0.0106960	+	0.0150102i
$936$		0			0
$937$		−	1313.52i		−	1.40184i	−0.713240	−	0.700920i	$-0.752773\pi$
$937$		−	1313.52i		−	1.40184i	0.713240	−	0.700920i	$-0.247227\pi$
$938$		0			0
$939$	1095.77	+	930.436i	1.16695	+	0.990880i
$940$		0			0
$941$	−914.746	+	914.746i	−0.972100	+	0.972100i	−0.999621	−	0.0275210i	$-0.991239\pi$
$941$	−914.746	+	914.746i	−0.972100	+	0.972100i	0.0275210	+	0.999621i	$0.491239\pi$
$942$		0			0
$943$		−	204.172i		−	0.216513i
$944$		0			0
$945$	168.915	+	677.761i	0.178746	+	0.717208i
$946$		0			0
$947$	−329.076	−	329.076i	−0.347493	−	0.347493i	0.511682	−	0.859175i	$-0.329023\pi$
$947$	−329.076	−	329.076i	−0.347493	−	0.347493i	−0.859175	+	0.511682i	$0.829023\pi$
$948$		0			0
$949$	−306.735	+	306.735i	−0.323220	+	0.323220i
$950$		0			0
$951$	290.641	−	342.286i	0.305616	−	0.359922i
$952$		0			0
$953$		−	230.601i		−	0.241974i	−0.992654	−	0.120987i	$-0.961394\pi$
$953$		−	230.601i		−	0.241974i	0.992654	−	0.120987i	$-0.0386059\pi$
$954$		0			0
$955$	441.099	−	441.099i	0.461883	−	0.461883i
$956$		0			0
$957$	30.1852	−	2.46302i	0.0315415	−	0.00257369i
$958$		0			0
$959$	668.572	−	668.572i	0.697155	−	0.697155i
$960$		0			0
$961$			896.377i			0.932754i
$962$		0			0
$963$	73.5800	+	52.8149i	0.0764070	+	0.0548441i
$964$		0			0
$965$			715.935i			0.741902i
$966$		0			0
$967$		−	1384.46i		−	1.43171i	−0.698250	−	0.715854i	$-0.746038\pi$
$967$		−	1384.46i		−	1.43171i	0.698250	−	0.715854i	$-0.253962\pi$
$968$		0			0
$969$	−258.681	+	218.122i	−0.266957	+	0.225101i
$970$		0			0
$971$	509.395			0.524609			0.262304	−	0.964985i	$-0.415518\pi$
$971$	509.395			0.524609			0.262304	+	0.964985i	$0.415518\pi$
$972$		0			0
$973$	−1725.94			−1.77383
$974$		0			0
$975$	−27.2645	−	334.136i	−0.0279635	−	0.342704i
$976$		0			0
$977$	−476.569			−0.487789			−0.243894	−	0.969802i	$-0.578425\pi$
$977$	−476.569			−0.487789			−0.243894	+	0.969802i	$0.578425\pi$
$978$		0			0
$979$	−0.151110	−	0.151110i	−0.000154352	−	0.000154352i
$980$		0			0
$981$	150.690	+	108.163i	0.153608	+	0.110258i
$982$		0			0
$983$	−845.353	−	845.353i	−0.859973	−	0.859973i	0.131362	−	0.991334i	$-0.458065\pi$
$983$	−845.353	−	845.353i	−0.859973	−	0.859973i	−0.991334	+	0.131362i	$0.958065\pi$
$984$		0			0
$985$	780.966			0.792859
$986$		0			0
$987$	579.595	−	682.585i	0.587229	−	0.691575i
$988$		0			0
$989$	−121.855	−	121.855i	−0.123210	−	0.123210i
$990$		0			0
$991$	831.175	−	831.175i	0.838723	−	0.838723i	−0.149968	−	0.988691i	$-0.547917\pi$
$991$	831.175	−	831.175i	0.838723	−	0.838723i	0.988691	+	0.149968i	$0.0479169\pi$
$992$		0			0
$993$	28.2758	+	346.530i	0.0284751	+	0.348973i
$994$		0			0
$995$	−432.814			−0.434989
$996$		0			0
$997$	−46.2776	−	46.2776i	−0.0464169	−	0.0464169i	0.683517	−	0.729934i	$-0.260449\pi$
$997$	−46.2776	−	46.2776i	−0.0464169	−	0.0464169i	−0.729934	+	0.683517i	$0.760449\pi$
$998$		0			0
$999$	−705.521	+	1173.93i	−0.706227	+	1.17510i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1020.3.bc.a.701.2	✓	96
3.2	odd	2	inner	1020.3.bc.a.701.25	yes	96
17.13	even	4	inner	1020.3.bc.a.761.25	yes	96
51.47	odd	4	inner	1020.3.bc.a.761.2	yes	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1020.3.bc.a.701.2	✓	96	1.1	even	1	trivial
1020.3.bc.a.701.25	yes	96	3.2	odd	2	inner
1020.3.bc.a.761.2	yes	96	51.47	odd	4	inner
1020.3.bc.a.761.25	yes	96	17.13	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1020 = 2^{2} \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	1020.bc (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.99006 + 0.243979i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(8.18085 + 8.18085i) q^{7} +(8.88095 - 1.45903i) q^{9} +O(q^{10})\)	\(q+(-2.99006 + 0.243979i) q^{3} +(-1.58114 - 1.58114i) q^{5} +(8.18085 + 8.18085i) q^{7} +(8.88095 - 1.45903i) q^{9} +(0.320565 - 0.320565i) q^{11} +22.3498 q^{13} +(5.11347 + 4.34194i) q^{15} +(-9.86544 - 13.8446i) q^{17} +6.63468i q^{19} +(-26.4572 - 22.4653i) q^{21} +(-9.39551 + 9.39551i) q^{23} +5.00000i q^{25} +(-26.1986 + 6.52935i) q^{27} +(-15.7459 - 15.7459i) q^{29} +(5.68432 - 5.68432i) q^{31} +(-0.880299 + 1.03672i) q^{33} -25.8701i q^{35} +(35.8692 - 35.8692i) q^{37} +(-66.8273 + 5.45289i) q^{39} +(-10.8654 + 10.8654i) q^{41} +12.9695i q^{43} +(-16.3489 - 11.7351i) q^{45} +25.7996i q^{47} +84.8527i q^{49} +(32.8761 + 38.9893i) q^{51} +26.2935 q^{53} -1.01372 q^{55} +(-1.61873 - 19.8381i) q^{57} +94.0697 q^{59} +(38.7792 + 38.7792i) q^{61} +(84.5898 + 60.7176i) q^{63} +(-35.3381 - 35.3381i) q^{65} +31.1720 q^{67} +(25.8009 - 30.3855i) q^{69} +(50.4254 + 50.4254i) q^{71} +(-13.7243 + 13.7243i) q^{73} +(-1.21990 - 14.9503i) q^{75} +5.24500 q^{77} +(-110.980 - 110.980i) q^{79} +(76.7425 - 25.9151i) q^{81} +51.5381 q^{83} +(-6.29161 + 37.4889i) q^{85} +(50.9229 + 43.2396i) q^{87} -0.471386i q^{89} +(182.840 + 182.840i) q^{91} +(-15.6096 + 18.3833i) q^{93} +(10.4904 - 10.4904i) q^{95} +(27.5190 - 27.5190i) q^{97} +(2.37921 - 3.31464i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 8 q^{3}+O(q^{10}) \) 96 * q - 8 * q^3	\( 96 q - 8 q^{3} + 64 q^{21} + 100 q^{27} - 24 q^{31} + 40 q^{33} + 24 q^{37} - 52 q^{39} - 40 q^{45} - 4 q^{51} + 80 q^{55} + 192 q^{57} + 144 q^{61} + 28 q^{63} - 320 q^{67} + 208 q^{69} + 152 q^{73} - 40 q^{75} + 224 q^{79} + 488 q^{81} - 288 q^{91} + 80 q^{97} - 212 q^{99}+O(q^{100}) \) 96 * q - 8 * q^3 + 64 * q^21 + 100 * q^27 - 24 * q^31 + 40 * q^33 + 24 * q^37 - 52 * q^39 - 40 * q^45 - 4 * q^51 + 80 * q^55 + 192 * q^57 + 144 * q^61 + 28 * q^63 - 320 * q^67 + 208 * q^69 + 152 * q^73 - 40 * q^75 + 224 * q^79 + 488 * q^81 - 288 * q^91 + 80 * q^97 - 212 * q^99

Introduction

L-functions

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