LMFDB - Embedded newform 308.3.r.a.57.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,3,Mod(29,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("308.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	308.r (of order $10$, degree $4$, 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:	$8.39239214230$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			57.2
Character	$\chi$	$=$	308.57
Dual form			308.3.r.a.281.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.23386 + 2.34954i) q^{3} +(-2.54199 - 7.82345i) q^{5} +(1.55513 - 2.14046i) q^{7} +(2.15638 - 6.63666i) q^{9} +O(q^{10})$	\(q+(-3.23386 + 2.34954i) q^{3} +(-2.54199 - 7.82345i) q^{5} +(1.55513 - 2.14046i) q^{7} +(2.15638 - 6.63666i) q^{9} +(3.85039 + 10.3041i) q^{11} +(4.32032 + 1.40376i) q^{13} +(26.6020 + 19.3274i) q^{15} +(-23.7294 + 7.71015i) q^{17} +(6.86447 + 9.44813i) q^{19} +10.5758i q^{21} +9.61699 q^{23} +(-34.5192 + 25.0797i) q^{25} +(-2.49739 - 7.68617i) q^{27} +(-22.3120 + 30.7098i) q^{29} +(-7.53575 + 23.1926i) q^{31} +(-36.6615 - 24.2754i) q^{33} +(-20.6989 - 6.72548i) q^{35} +(36.8254 + 26.7552i) q^{37} +(-17.2695 + 5.61120i) q^{39} +(5.08252 + 6.99549i) q^{41} +23.8528i q^{43} -57.4031 q^{45} +(-45.5886 + 33.1221i) q^{47} +(-2.16312 - 6.65740i) q^{49} +(58.6223 - 80.6866i) q^{51} +(-6.50291 + 20.0139i) q^{53} +(70.8260 - 56.3163i) q^{55} +(-44.3975 - 14.4256i) q^{57} +(46.1310 + 33.5161i) q^{59} +(44.7033 - 14.5250i) q^{61} +(-10.8520 - 14.9365i) q^{63} -37.3682i q^{65} +70.4803 q^{67} +(-31.1000 + 22.5955i) q^{69} +(35.2114 + 108.370i) q^{71} +(17.7274 - 24.3997i) q^{73} +(52.7047 - 162.208i) q^{75} +(28.0434 + 7.78267i) q^{77} +(-107.166 - 34.8204i) q^{79} +(76.9444 + 55.9034i) q^{81} +(70.4691 - 22.8968i) q^{83} +(120.640 + 166.047i) q^{85} -151.734i q^{87} -140.763 q^{89} +(9.72336 - 7.06444i) q^{91} +(-30.1224 - 92.7073i) q^{93} +(56.4676 - 77.7210i) q^{95} +(39.8011 - 122.495i) q^{97} +(76.6877 - 3.33412i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9}+O(q^{10}) $ 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9	$ 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9} - 10 q^{11} + 30 q^{13} + 24 q^{15} + 60 q^{19} - 132 q^{23} - 186 q^{25} - 110 q^{27} - 90 q^{29} - 26 q^{31} + 46 q^{33} + 82 q^{37} + 290 q^{39} - 336 q^{45} + 84 q^{47} + 84 q^{49} - 20 q^{51} + 58 q^{53} + 370 q^{55} - 20 q^{57} + 436 q^{59} + 160 q^{61} + 276 q^{67} - 118 q^{69} - 150 q^{71} - 320 q^{73} - 692 q^{75} + 28 q^{77} - 560 q^{79} + 122 q^{81} - 630 q^{83} + 220 q^{85} - 444 q^{89} - 126 q^{91} + 500 q^{93} + 440 q^{95} - 80 q^{97} + 1034 q^{99}+O(q^{100}) $ 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9 - 10 * q^11 + 30 * q^13 + 24 * q^15 + 60 * q^19 - 132 * q^23 - 186 * q^25 - 110 * q^27 - 90 * q^29 - 26 * q^31 + 46 * q^33 + 82 * q^37 + 290 * q^39 - 336 * q^45 + 84 * q^47 + 84 * q^49 - 20 * q^51 + 58 * q^53 + 370 * q^55 - 20 * q^57 + 436 * q^59 + 160 * q^61 + 276 * q^67 - 118 * q^69 - 150 * q^71 - 320 * q^73 - 692 * q^75 + 28 * q^77 - 560 * q^79 + 122 * q^81 - 630 * q^83 + 220 * q^85 - 444 * q^89 - 126 * q^91 + 500 * q^93 + 440 * q^95 - 80 * q^97 + 1034 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$	$1$

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
$3$	−3.23386	+	2.34954i	−1.07795	+	0.783179i	−0.977325	−	0.211745i	$-0.932086\pi$
$3$	−3.23386	+	2.34954i	−1.07795	+	0.783179i	−0.100629	+	0.994924i	$0.532086\pi$
$4$		0			0
$5$	−2.54199	−	7.82345i	−0.508399	−	1.56469i	−0.794981	−	0.606634i	$-0.792519\pi$
$5$	−2.54199	−	7.82345i	−0.508399	−	1.56469i	0.286582	−	0.958056i	$-0.407481\pi$
$6$		0			0
$7$	1.55513	−	2.14046i	0.222162	−	0.305780i
$7$	1.55513	−	2.14046i	0.222162	−	0.305780i
$8$		0			0
$9$	2.15638	−	6.63666i	0.239598	−	0.737406i
$10$		0			0
$11$	3.85039	+	10.3041i	0.350035	+	0.936737i
$11$	3.85039	+	10.3041i	0.350035	+	0.936737i
$12$		0			0
$13$	4.32032	+	1.40376i	0.332332	+	0.107981i	0.470430	−	0.882437i	$-0.344099\pi$
$13$	4.32032	+	1.40376i	0.332332	+	0.107981i	−0.138098	+	0.990419i	$0.544099\pi$
$14$		0			0
$15$	26.6020	+	19.3274i	1.77346	+	1.28850i
$16$		0			0
$17$	−23.7294	+	7.71015i	−1.39585	+	0.453538i	−0.907845	−	0.419305i	$-0.862274\pi$
$17$	−23.7294	+	7.71015i	−1.39585	+	0.453538i	−0.488001	+	0.872843i	$0.662274\pi$
$18$		0			0
$19$	6.86447	+	9.44813i	0.361288	+	0.497270i	0.950507	−	0.310703i	$-0.100564\pi$
$19$	6.86447	+	9.44813i	0.361288	+	0.497270i	−0.589219	+	0.807973i	$0.700564\pi$
$20$		0			0
$21$			10.5758i			0.503609i
$22$		0			0
$23$	9.61699			0.418130			0.209065	−	0.977902i	$-0.432958\pi$
$23$	9.61699			0.418130			0.209065	+	0.977902i	$0.432958\pi$
$24$		0			0
$25$	−34.5192	+	25.0797i	−1.38077	+	1.00319i
$26$		0			0
$27$	−2.49739	−	7.68617i	−0.0924958	−	0.284673i
$28$		0			0
$29$	−22.3120	+	30.7098i	−0.769378	+	1.05896i	0.226997	+	0.973895i	$0.427109\pi$
$29$	−22.3120	+	30.7098i	−0.769378	+	1.05896i	−0.996376	+	0.0850631i	$0.972891\pi$
$30$		0			0
$31$	−7.53575	+	23.1926i	−0.243089	+	0.748150i	0.752856	+	0.658185i	$0.228675\pi$
$31$	−7.53575	+	23.1926i	−0.243089	+	0.748150i	−0.995945	+	0.0899649i	$0.971325\pi$
$32$		0			0
$33$	−36.6615	−	24.2754i	−1.11095	−	0.735619i
$34$		0			0
$35$	−20.6989	−	6.72548i	−0.591397	−	0.192157i
$36$		0			0
$37$	36.8254	+	26.7552i	0.995282	+	0.723114i	0.961071	−	0.276300i	$-0.0891084\pi$
$37$	36.8254	+	26.7552i	0.995282	+	0.723114i	0.0342102	+	0.999415i	$0.489108\pi$
$38$		0			0
$39$	−17.2695	+	5.61120i	−0.442808	+	0.143877i
$40$		0			0
$41$	5.08252	+	6.99549i	0.123964	+	0.170622i	0.866488	−	0.499197i	$-0.166372\pi$
$41$	5.08252	+	6.99549i	0.123964	+	0.170622i	−0.742524	+	0.669819i	$0.766372\pi$
$42$		0			0
$43$			23.8528i			0.554715i	0.960767	+	0.277358i	$0.0894587\pi$
$43$			23.8528i			0.554715i	−0.960767	+	0.277358i	$0.910541\pi$
$44$		0			0
$45$	−57.4031			−1.27562
$46$		0			0
$47$	−45.5886	+	33.1221i	−0.969971	+	0.704725i	−0.955445	−	0.295169i	$-0.904624\pi$
$47$	−45.5886	+	33.1221i	−0.969971	+	0.704725i	−0.0145259	+	0.999894i	$0.504624\pi$
$48$		0			0
$49$	−2.16312	−	6.65740i	−0.0441453	−	0.135865i
$50$		0			0
$51$	58.6223	−	80.6866i	1.14946	−	1.58209i
$52$		0			0
$53$	−6.50291	+	20.0139i	−0.122697	+	0.377621i	−0.993474	−	0.114056i	$-0.963616\pi$
$53$	−6.50291	+	20.0139i	−0.122697	+	0.377621i	0.870778	+	0.491677i	$0.163616\pi$
$54$		0			0
$55$	70.8260	−	56.3163i	1.28775	−	1.02393i
$56$		0			0
$57$	−44.3975	−	14.4256i	−0.778904	−	0.253081i
$58$		0			0
$59$	46.1310	+	33.5161i	0.781881	+	0.568070i	0.905543	−	0.424254i	$-0.139464\pi$
$59$	46.1310	+	33.5161i	0.781881	+	0.568070i	−0.123662	+	0.992324i	$0.539464\pi$
$60$		0			0
$61$	44.7033	−	14.5250i	0.732841	−	0.238115i	0.0812596	−	0.996693i	$-0.474106\pi$
$61$	44.7033	−	14.5250i	0.732841	−	0.238115i	0.651582	+	0.758578i	$0.274106\pi$
$62$		0			0
$63$	−10.8520	−	14.9365i	−0.172254	−	0.237088i
$64$		0			0
$65$		−	37.3682i		−	0.574895i
$66$		0			0
$67$	70.4803			1.05194			0.525972	−	0.850502i	$-0.323701\pi$
$67$	70.4803			1.05194			0.525972	+	0.850502i	$0.323701\pi$
$68$		0			0
$69$	−31.1000	+	22.5955i	−0.450725	+	0.327471i
$70$		0			0
$71$	35.2114	+	108.370i	0.495936	+	1.52633i	0.815494	+	0.578766i	$0.196465\pi$
$71$	35.2114	+	108.370i	0.495936	+	1.52633i	−0.319558	+	0.947567i	$0.603535\pi$
$72$		0			0
$73$	17.7274	−	24.3997i	0.242842	−	0.334243i	−0.670147	−	0.742229i	$-0.733769\pi$
$73$	17.7274	−	24.3997i	0.242842	−	0.334243i	0.912988	+	0.407986i	$0.133769\pi$
$74$		0			0
$75$	52.7047	−	162.208i	0.702730	−	2.16278i
$76$		0			0
$77$	28.0434	+	7.78267i	0.364199	+	0.101074i
$78$		0			0
$79$	−107.166	−	34.8204i	−1.35653	−	0.440765i	−0.461649	−	0.887063i	$-0.652742\pi$
$79$	−107.166	−	34.8204i	−1.35653	−	0.440765i	−0.894884	+	0.446298i	$0.852742\pi$
$80$		0			0
$81$	76.9444	+	55.9034i	0.949931	+	0.690166i
$82$		0			0
$83$	70.4691	−	22.8968i	0.849026	−	0.275865i	0.147988	−	0.988989i	$-0.452720\pi$
$83$	70.4691	−	22.8968i	0.849026	−	0.275865i	0.701038	+	0.713124i	$0.252720\pi$
$84$		0			0
$85$	120.640	+	166.047i	1.41929	+	1.95349i
$86$		0			0
$87$		−	151.734i		−	1.74407i
$88$		0			0
$89$	−140.763			−1.58161			−0.790805	−	0.612068i	$-0.790338\pi$
$89$	−140.763			−1.58161			−0.790805	+	0.612068i	$0.790338\pi$
$90$		0			0
$91$	9.72336	−	7.06444i	0.106850	−	0.0776312i
$92$		0			0
$93$	−30.1224	−	92.7073i	−0.323897	−	0.996853i
$94$		0			0
$95$	56.4676	−	77.7210i	0.594396	−	0.818115i
$96$		0			0
$97$	39.8011	−	122.495i	0.410321	−	1.26284i	−0.506049	−	0.862505i	$-0.668894\pi$
$97$	39.8011	−	122.495i	0.410321	−	1.26284i	0.916370	−	0.400333i	$-0.131106\pi$
$98$		0			0
$99$	76.6877	−	3.33412i	0.774623	−	0.0336780i
$100$		0			0
$101$	−158.951	−	51.6463i	−1.57377	−	0.511349i	−0.613328	−	0.789828i	$-0.710170\pi$
$101$	−158.951	−	51.6463i	−1.57377	−	0.511349i	−0.960442	+	0.278479i	$0.910170\pi$
$102$		0			0
$103$	13.5819	+	9.86779i	0.131863	+	0.0958038i	0.651761	−	0.758424i	$-0.274030\pi$
$103$	13.5819	+	9.86779i	0.131863	+	0.0958038i	−0.519899	+	0.854228i	$0.674030\pi$
$104$		0			0
$105$	82.7392	−	26.8836i	0.787992	−	0.256034i
$106$		0			0
$107$	−59.3427	−	81.6783i	−0.554605	−	0.763348i	0.436023	−	0.899935i	$-0.356387\pi$
$107$	−59.3427	−	81.6783i	−0.554605	−	0.763348i	−0.990628	+	0.136587i	$0.956387\pi$
$108$		0			0
$109$			106.103i			0.973420i	0.873564	+	0.486710i	$0.161803\pi$
$109$			106.103i			0.973420i	−0.873564	+	0.486710i	$0.838197\pi$
$110$		0			0
$111$	−181.951			−1.63920
$112$		0			0
$113$	−129.400	+	94.0148i	−1.14514	+	0.831990i	−0.987826	−	0.155560i	$-0.950282\pi$
$113$	−129.400	+	94.0148i	−1.14514	+	0.831990i	−0.157309	+	0.987549i	$0.550282\pi$
$114$		0			0
$115$	−24.4463	−	75.2381i	−0.212577	−	0.654244i
$116$		0			0
$117$	18.6325	−	25.6455i	0.159252	−	0.219192i
$118$		0			0
$119$	−20.3991	+	62.7821i	−0.171421	+	0.527580i
$120$		0			0
$121$	−91.3491	+	79.3495i	−0.754951	+	0.655781i
$122$		0			0
$123$	−32.8723	−	10.6809i	−0.267255	−	0.0868363i
$124$		0			0
$125$	117.582	+	85.4281i	0.940654	+	0.683425i
$126$		0			0
$127$	−19.6437	+	6.38262i	−0.154675	+	0.0502569i	−0.385331	−	0.922778i	$-0.625913\pi$
$127$	−19.6437	+	6.38262i	−0.154675	+	0.0502569i	0.230656	+	0.973035i	$0.425913\pi$
$128$		0			0
$129$	−56.0430	−	77.1365i	−0.434442	−	0.597958i
$130$		0			0
$131$		−	168.199i		−	1.28396i	−0.766720	−	0.641982i	$-0.778113\pi$
$131$		−	168.199i		−	1.28396i	0.766720	−	0.641982i	$-0.221887\pi$
$132$		0			0
$133$	30.8985			0.232320
$134$		0			0
$135$	−53.7840	+	39.0764i	−0.398400	+	0.289455i
$136$		0			0
$137$	−66.7352	−	205.390i	−0.487118	−	1.49919i	−0.828890	−	0.559412i	$-0.811027\pi$
$137$	−66.7352	−	205.390i	−0.487118	−	1.49919i	0.341772	−	0.939783i	$-0.388973\pi$
$138$		0			0
$139$	−134.136	+	184.623i	−0.965010	+	1.32822i	−0.0204826	+	0.999790i	$0.506520\pi$
$139$	−134.136	+	184.623i	−0.965010	+	1.32822i	−0.944528	+	0.328432i	$0.893480\pi$
$140$		0			0
$141$	69.6057	−	214.224i	0.493658	−	1.51932i
$142$		0			0
$143$	2.17044	+	49.9221i	0.0151779	+	0.349105i
$144$		0			0
$145$	296.973	+	96.4925i	2.04809	+	0.665466i
$146$		0			0
$147$	22.6370	+	16.4468i	0.153993	+	0.111883i
$148$		0			0
$149$	−2.01801	+	0.655690i	−0.0135437	+	0.00440061i	−0.315781	−	0.948832i	$-0.602266\pi$
$149$	−2.01801	+	0.655690i	−0.0135437	+	0.00440061i	0.302237	+	0.953233i	$0.402266\pi$
$150$		0			0
$151$	155.030	+	213.381i	1.02669	+	1.41312i	0.907405	+	0.420257i	$0.138060\pi$
$151$	155.030	+	213.381i	1.02669	+	1.41312i	0.119284	+	0.992860i	$0.461940\pi$
$152$		0			0
$153$			174.110i			1.13797i
$154$		0			0
$155$	200.602			1.29421
$156$		0			0
$157$	147.235	−	106.973i	0.937804	−	0.681354i	−0.0100873	−	0.999949i	$-0.503211\pi$
$157$	147.235	−	106.973i	0.937804	−	0.681354i	0.947891	+	0.318595i	$0.103211\pi$
$158$		0			0
$159$	−25.9939	−	80.0011i	−0.163484	−	0.503151i
$160$		0			0
$161$	14.9557	−	20.5848i	0.0928926	−	0.127856i
$162$		0			0
$163$	−26.6375	+	81.9819i	−0.163420	+	0.502956i	−0.998916	−	0.0465403i	$-0.985180\pi$
$163$	−26.6375	+	81.9819i	−0.163420	+	0.502956i	0.835496	+	0.549496i	$0.185180\pi$
$164$		0			0
$165$	−96.7243	+	348.527i	−0.586208	+	2.11229i
$166$		0			0
$167$	−72.1562	−	23.4450i	−0.432073	−	0.140389i	0.0849023	−	0.996389i	$-0.472942\pi$
$167$	−72.1562	−	23.4450i	−0.432073	−	0.140389i	−0.516976	+	0.856000i	$0.672942\pi$
$168$		0			0
$169$	−120.029	−	87.2063i	−0.710232	−	0.516014i
$170$		0			0
$171$	77.5064	−	25.1834i	0.453254	−	0.147271i
$172$		0			0
$173$	185.147	+	254.833i	1.07022	+	1.47303i	0.869857	+	0.493303i	$0.164211\pi$
$173$	185.147	+	254.833i	1.07022	+	1.47303i	0.200359	+	0.979723i	$0.435789\pi$
$174$		0			0
$175$			112.889i			0.645081i
$176$		0			0
$177$	−227.929			−1.28773
$178$		0			0
$179$	271.455	−	197.224i	1.51651	−	1.10181i	0.553325	−	0.832965i	$-0.313359\pi$
$179$	271.455	−	197.224i	1.51651	−	1.10181i	0.963184	−	0.268843i	$-0.0866412\pi$
$180$		0			0
$181$	−1.15864	−	3.56593i	−0.00640133	−	0.0197013i	0.947805	−	0.318851i	$-0.103297\pi$
$181$	−1.15864	−	3.56593i	−0.00640133	−	0.0197013i	−0.954206	+	0.299150i	$0.903297\pi$
$182$		0			0
$183$	−110.437	+	152.004i	−0.603483	+	0.830623i
$184$		0			0
$185$	115.708	−	356.113i	0.625450	−	1.92494i
$186$		0			0
$187$	−170.813	−	214.823i	−0.913441	−	1.14879i
$188$		0			0
$189$	−20.3357	−	6.60746i	−0.107596	−	0.0349601i
$190$		0			0
$191$	12.3000	+	8.93644i	0.0643977	+	0.0467876i	0.619518	−	0.784982i	$-0.287328\pi$
$191$	12.3000	+	8.93644i	0.0643977	+	0.0467876i	−0.555121	+	0.831770i	$0.687328\pi$
$192$		0			0
$193$	−128.386	+	41.7152i	−0.665214	+	0.216141i	−0.622110	−	0.782930i	$-0.713724\pi$
$193$	−128.386	+	41.7152i	−0.665214	+	0.216141i	−0.0431033	+	0.999071i	$0.513724\pi$
$194$		0			0
$195$	87.7979	+	120.844i	0.450246	+	0.619710i
$196$		0			0
$197$		−	212.825i		−	1.08033i	−0.841559	−	0.540166i	$-0.818362\pi$
$197$		−	212.825i		−	1.08033i	0.841559	−	0.540166i	$-0.181638\pi$
$198$		0			0
$199$	7.60592			0.0382207			0.0191104	−	0.999817i	$-0.493917\pi$
$199$	7.60592			0.0382207			0.0191104	+	0.999817i	$0.493917\pi$
$200$		0			0
$201$	−227.924	+	165.596i	−1.13395	+	0.823862i
$202$		0			0
$203$	31.0349	+	95.5157i	0.152881	+	0.470521i
$204$		0			0
$205$	41.8091	−	57.5453i	0.203947	−	0.280709i
$206$		0			0
$207$	20.7379	−	63.8247i	0.100183	−	0.308332i
$208$		0			0
$209$	−70.9237	+	107.111i	−0.339348	+	0.512494i
$210$		0			0
$211$	−57.9020	−	18.8135i	−0.274417	−	0.0891636i	0.168576	−	0.985689i	$-0.446083\pi$
$211$	−57.9020	−	18.8135i	−0.274417	−	0.0891636i	−0.442993	+	0.896525i	$0.646083\pi$
$212$		0			0
$213$	−368.487	−	267.722i	−1.72999	−	1.25691i
$214$		0			0
$215$	186.611	−	60.6335i	0.867957	−	0.282016i
$216$		0			0
$217$	37.9238	+	52.1976i	0.174764	+	0.240542i
$218$		0			0
$219$			120.557i			0.550487i
$220$		0			0
$221$	−113.342			−0.512859
$222$		0			0
$223$	75.9850	−	55.2063i	0.340740	−	0.247562i	−0.404234	−	0.914656i	$-0.632462\pi$
$223$	75.9850	−	55.2063i	0.340740	−	0.247562i	0.744974	+	0.667094i	$0.232462\pi$
$224$		0			0
$225$	92.0087	+	283.174i	0.408927	+	1.25855i
$226$		0			0
$227$	−165.669	+	228.023i	−0.729818	+	1.00451i	0.269323	+	0.963050i	$0.413200\pi$
$227$	−165.669	+	228.023i	−0.729818	+	1.00451i	−0.999140	+	0.0414577i	$0.986800\pi$
$228$		0			0
$229$	−105.324	+	324.153i	−0.459929	+	1.41551i	0.405321	+	0.914174i	$0.367160\pi$
$229$	−105.324	+	324.153i	−0.459929	+	1.41551i	−0.865250	+	0.501341i	$0.832840\pi$
$230$		0			0
$231$	−108.974	+	40.7209i	−0.471749	+	0.176281i
$232$		0			0
$233$	−153.983	−	50.0322i	−0.660872	−	0.214730i	−0.0406703	−	0.999173i	$-0.512949\pi$
$233$	−153.983	−	50.0322i	−0.660872	−	0.214730i	−0.620202	+	0.784442i	$0.712949\pi$
$234$		0			0
$235$	375.015	+	272.464i	1.59581	+	1.15942i
$236$		0			0
$237$	428.372	−	139.187i	1.80748	−	0.587285i
$238$		0			0
$239$	183.980	+	253.226i	0.769789	+	1.05952i	0.996336	+	0.0855238i	$0.0272564\pi$
$239$	183.980	+	253.226i	0.769789	+	1.05952i	−0.226547	+	0.974000i	$0.572744\pi$
$240$		0			0
$241$			1.40070i			0.00581205i	0.999996	+	0.00290602i	$0.000925017\pi$
$241$			1.40070i			0.00581205i	−0.999996	+	0.00290602i	$0.999075\pi$
$242$		0			0
$243$	−307.439			−1.26518
$244$		0			0
$245$	−46.5852	+	33.8461i	−0.190144	+	0.138147i
$246$		0			0
$247$	16.3938	+	50.4550i	0.0663718	+	0.204271i
$248$		0			0
$249$	−174.090	+	239.615i	−0.699159	+	0.962309i
$250$		0			0
$251$	−119.100	+	366.552i	−0.474502	+	1.46037i	0.372126	+	0.928182i	$0.378629\pi$
$251$	−119.100	+	366.552i	−0.474502	+	1.46037i	−0.846628	+	0.532185i	$0.821371\pi$
$252$		0			0
$253$	37.0291	+	99.0945i	0.146360	+	0.391678i
$254$		0			0
$255$	−780.265	−	253.524i	−3.05986	−	0.994210i
$256$		0			0
$257$	−158.011	−	114.802i	−0.614828	−	0.446699i	0.236283	−	0.971684i	$-0.424071\pi$
$257$	−158.011	−	114.802i	−0.614828	−	0.446699i	−0.851111	+	0.524985i	$0.824071\pi$
$258$		0			0
$259$	114.537	−	37.2153i	0.442227	−	0.143688i
$260$		0			0
$261$	155.697	+	214.299i	0.596541	+	0.821069i
$262$		0			0
$263$		−	443.379i		−	1.68585i	−0.538029	−	0.842926i	$-0.680831\pi$
$263$		−	443.379i		−	1.68585i	0.538029	−	0.842926i	$-0.319169\pi$
$264$		0			0
$265$	173.108			0.653239
$266$		0			0
$267$	455.209	−	330.729i	1.70490	−	1.23868i
$268$		0			0
$269$	−74.8888	−	230.484i	−0.278397	−	0.856818i	−0.988301	−	0.152519i	$-0.951262\pi$
$269$	−74.8888	−	230.484i	−0.278397	−	0.856818i	0.709904	−	0.704299i	$-0.248738\pi$
$270$		0			0
$271$	−211.335	+	290.878i	−0.779834	+	1.07335i	0.215466	+	0.976511i	$0.430873\pi$
$271$	−211.335	+	290.878i	−0.779834	+	1.07335i	−0.995300	+	0.0968386i	$0.969127\pi$
$272$		0			0
$273$	−14.8458	+	45.6908i	−0.0543804	+	0.167366i
$274$		0			0
$275$	−391.336	−	259.123i	−1.42304	−	0.942266i
$276$		0			0
$277$	176.745	+	57.4280i	0.638070	+	0.207321i	0.610146	−	0.792289i	$-0.291111\pi$
$277$	176.745	+	57.4280i	0.638070	+	0.207321i	0.0279232	+	0.999610i	$0.491111\pi$
$278$		0			0
$279$	137.672	+	100.024i	0.493447	+	0.358510i
$280$		0			0
$281$	−257.295	+	83.6003i	−0.915642	+	0.297510i	−0.728678	−	0.684857i	$-0.759865\pi$
$281$	−257.295	+	83.6003i	−0.915642	+	0.297510i	−0.186964	+	0.982367i	$0.559865\pi$
$282$		0			0
$283$	38.6843	+	53.2443i	0.136694	+	0.188143i	0.871876	−	0.489727i	$-0.162903\pi$
$283$	38.6843	+	53.2443i	0.136694	+	0.188143i	−0.735182	+	0.677869i	$0.762903\pi$
$284$		0			0
$285$			384.012i			1.34741i
$286$		0			0
$287$	22.8775			0.0797127
$288$		0			0
$289$	269.832	−	196.044i	0.933673	−	0.678353i
$290$		0			0
$291$	159.096	+	489.647i	0.546722	+	1.68264i
$292$		0			0
$293$	−133.050	+	183.127i	−0.454095	+	0.625008i	−0.973271	−	0.229659i	$-0.926239\pi$
$293$	−133.050	+	183.127i	−0.454095	+	0.625008i	0.519176	+	0.854667i	$0.326239\pi$
$294$		0			0
$295$	144.947	−	446.101i	0.491346	−	1.51221i
$296$		0			0
$297$	69.5831	−	55.3280i	0.234287	−	0.186290i
$298$		0			0
$299$	41.5485	+	13.4999i	0.138958	+	0.0451503i
$300$		0			0
$301$	51.0558	+	37.0942i	0.169621	+	0.123237i
$302$		0			0
$303$	635.370	−	206.444i	2.09693	−	0.681334i
$304$		0			0
$305$	−227.271	−	312.812i	−0.745151	−	1.02561i
$306$		0			0
$307$			541.395i			1.76350i	0.471715	+	0.881751i	$0.343635\pi$
$307$			541.395i			1.76350i	−0.471715	+	0.881751i	$0.656365\pi$
$308$		0			0
$309$	−67.1066			−0.217173
$310$		0			0
$311$	55.3262	−	40.1968i	0.177898	−	0.129250i	−0.495273	−	0.868737i	$-0.664932\pi$
$311$	55.3262	−	40.1968i	0.177898	−	0.129250i	0.673171	+	0.739487i	$0.264932\pi$
$312$		0			0
$313$	−17.4323	−	53.6511i	−0.0556942	−	0.171409i	0.919340	−	0.393464i	$-0.128724\pi$
$313$	−17.4323	−	53.6511i	−0.0556942	−	0.171409i	−0.975034	+	0.222055i	$0.928724\pi$
$314$		0			0
$315$	−89.2694	+	122.869i	−0.283395	+	0.390060i
$316$		0			0
$317$	165.151	−	508.282i	0.520981	−	1.60341i	−0.251149	−	0.967948i	$-0.580808\pi$
$317$	165.151	−	508.282i	0.520981	−	1.60341i	0.772130	−	0.635465i	$-0.219192\pi$
$318$		0			0
$319$	−402.347	−	111.660i	−1.26127	−	0.350032i
$320$		0			0
$321$	383.812	+	124.708i	1.19568	+	0.388499i
$322$		0			0
$323$	−235.736	−	171.272i	−0.729833	−	0.530255i
$324$		0			0
$325$	−184.340	+	59.8957i	−0.567200	+	0.184294i
$326$		0			0
$327$	−249.292	−	343.122i	−0.762362	−	1.04930i
$328$		0			0
$329$			149.090i			0.453160i
$330$		0			0
$331$	379.213			1.14566			0.572829	−	0.819675i	$-0.305846\pi$
$331$	379.213			1.14566			0.572829	+	0.819675i	$0.305846\pi$
$332$		0			0
$333$	256.975	−	186.703i	0.771696	−	0.560670i
$334$		0			0
$335$	−179.160	−	551.399i	−0.534807	−	1.64597i
$336$		0			0
$337$	313.406	−	431.367i	0.929990	−	1.28002i	−0.0298741	−	0.999554i	$-0.509511\pi$
$337$	313.406	−	431.367i	0.929990	−	1.28002i	0.959864	−	0.280467i	$-0.0904894\pi$
$338$		0			0
$339$	197.571	−	608.062i	0.582806	−	1.79369i
$340$		0			0
$341$	−267.995	+	11.6515i	−0.785909	+	0.0341686i
$342$		0			0
$343$	−17.6138	−	5.72307i	−0.0513522	−	0.0166853i
$344$		0			0
$345$	255.831	+	185.872i	0.741538	+	0.538759i
$346$		0			0
$347$	−198.584	+	64.5239i	−0.572288	+	0.185948i	−0.580843	−	0.814016i	$-0.697277\pi$
$347$	−198.584	+	64.5239i	−0.572288	+	0.185948i	0.00855466	+	0.999963i	$0.497277\pi$
$348$		0			0
$349$	−287.539	−	395.763i	−0.823894	−	1.13399i	−0.989029	−	0.147721i	$-0.952806\pi$
$349$	−287.539	−	395.763i	−0.823894	−	1.13399i	0.165136	−	0.986271i	$-0.447194\pi$
$350$		0			0
$351$		−	36.7124i		−	0.104594i
$352$		0			0
$353$	380.439			1.07773			0.538866	−	0.842392i	$-0.318853\pi$
$353$	380.439			1.07773			0.538866	+	0.842392i	$0.318853\pi$
$354$		0			0
$355$	758.317	−	550.950i	2.13610	−	1.55197i
$356$		0			0
$357$	−81.5409	−	250.957i	−0.228406	−	0.702961i
$358$		0			0
$359$	−195.448	+	269.011i	−0.544424	+	0.749335i	−0.989242	−	0.146286i	$-0.953268\pi$
$359$	−195.448	+	269.011i	−0.544424	+	0.749335i	0.444819	+	0.895621i	$0.353268\pi$
$360$		0			0
$361$	69.4089	−	213.618i	0.192268	−	0.591741i
$362$		0			0
$363$	108.976	−	471.234i	0.300208	−	1.29816i
$364$		0			0
$365$	−235.953	−	76.6658i	−0.646447	−	0.210043i
$366$		0			0
$367$	−295.610	−	214.773i	−0.805476	−	0.585212i	0.107040	−	0.994255i	$-0.465863\pi$
$367$	−295.610	−	214.773i	−0.805476	−	0.585212i	−0.912515	+	0.409043i	$0.865863\pi$
$368$		0			0
$369$	57.3865	−	18.6460i	0.155519	−	0.0505312i
$370$		0			0
$371$	32.7260	+	45.0435i	0.0882103	+	0.121411i
$372$		0			0
$373$			234.864i			0.629661i	0.949148	+	0.314831i	$0.101948\pi$
$373$			234.864i			0.629661i	−0.949148	+	0.314831i	$0.898052\pi$
$374$		0			0
$375$	−580.960			−1.54923
$376$		0			0
$377$	−139.504	+	101.356i	−0.370037	+	0.268848i
$378$		0			0
$379$	134.606	+	414.276i	0.355162	+	1.09308i	0.955915	+	0.293642i	$0.0948674\pi$
$379$	134.606	+	414.276i	0.355162	+	1.09308i	−0.600753	+	0.799434i	$0.705133\pi$
$380$		0			0
$381$	48.5288	−	66.7941i	0.127372	−	0.175313i
$382$		0			0
$383$	−20.8863	+	64.2813i	−0.0545333	+	0.167836i	−0.974614	−	0.223894i	$-0.928123\pi$
$383$	−20.8863	+	64.2813i	−0.0545333	+	0.167836i	0.920080	+	0.391730i	$0.128123\pi$
$384$		0			0
$385$	−10.3987	−	239.179i	−0.0270096	−	0.621245i
$386$		0			0
$387$	158.303	+	51.4356i	0.409050	+	0.132909i
$388$		0			0
$389$	355.870	+	258.554i	0.914832	+	0.664664i	0.942232	−	0.334960i	$-0.108723\pi$
$389$	355.870	+	258.554i	0.914832	+	0.664664i	−0.0274003	+	0.999625i	$0.508723\pi$
$390$		0			0
$391$	−228.205	+	74.1484i	−0.583645	+	0.189638i
$392$		0			0
$393$	395.190	+	543.933i	1.00557	+	1.38405i
$394$		0			0
$395$			926.922i			2.34664i
$396$		0			0
$397$	−155.938			−0.392791			−0.196395	−	0.980525i	$-0.562924\pi$
$397$	−155.938			−0.392791			−0.196395	+	0.980525i	$0.562924\pi$
$398$		0			0
$399$	−99.9215	+	72.5972i	−0.250430	+	0.181948i
$400$		0			0
$401$	−112.209	−	345.344i	−0.279823	−	0.861207i	−0.987903	−	0.155075i	$-0.950438\pi$
$401$	−112.209	−	345.344i	−0.279823	−	0.861207i	0.708080	−	0.706133i	$-0.249562\pi$
$402$		0			0
$403$	−65.1137	+	89.6213i	−0.161572	+	0.222385i
$404$		0			0
$405$	241.765	−	744.077i	0.596951	−	1.83723i
$406$		0			0
$407$	−133.897	+	482.471i	−0.328984	+	1.18543i
$408$		0			0
$409$	597.631	+	194.182i	1.46120	+	0.474773i	0.928437	−	0.371490i	$-0.121153\pi$
$409$	597.631	+	194.182i	1.46120	+	0.474773i	0.532765	+	0.846263i	$0.321153\pi$
$410$		0			0
$411$	698.383	+	507.405i	1.69923	+	1.23456i
$412$		0			0
$413$	143.480	−	46.6194i	0.347409	−	0.112880i
$414$		0			0
$415$	−358.264	−	493.108i	−0.863287	−	1.18821i
$416$		0			0
$417$		−	912.204i		−	2.18754i
$418$		0			0
$419$	0.0845444			0.000201777			0.000100888	−	1.00000i	$-0.499968\pi$
$419$	0.0845444			0.000201777			0.000100888		1.00000i	$0.499968\pi$
$420$		0			0
$421$	283.970	−	206.316i	0.674512	−	0.490062i	−0.197021	−	0.980399i	$-0.563127\pi$
$421$	283.970	−	206.316i	0.674512	−	0.490062i	0.871533	+	0.490338i	$0.163127\pi$
$422$		0			0
$423$	121.513	+	373.980i	0.287266	+	0.884113i
$424$		0			0
$425$	625.752	−	861.274i	1.47236	−	2.02653i
$426$		0			0
$427$	38.4295	−	118.274i	0.0899989	−	0.276988i
$428$		0			0
$429$	−124.313	−	156.341i	−0.289773	−	0.364432i
$430$		0			0
$431$	379.691	+	123.369i	0.880953	+	0.286239i	0.714353	−	0.699786i	$-0.246721\pi$
$431$	379.691	+	123.369i	0.880953	+	0.286239i	0.166600	+	0.986025i	$0.446721\pi$
$432$		0			0
$433$	−55.6207	−	40.4108i	−0.128454	−	0.0933275i	0.521703	−	0.853127i	$-0.325297\pi$
$433$	−55.6207	−	40.4108i	−0.128454	−	0.0933275i	−0.650157	+	0.759800i	$0.725297\pi$
$434$		0			0
$435$	−1187.08	+	385.707i	−2.72893	+	0.886683i
$436$		0			0
$437$	66.0156	+	90.8626i	0.151065	+	0.207924i
$438$		0			0
$439$			140.190i			0.319340i	0.987170	+	0.159670i	$0.0510431\pi$
$439$			140.190i			0.319340i	−0.987170	+	0.159670i	$0.948957\pi$
$440$		0			0
$441$	−48.8474			−0.110765
$442$		0			0
$443$	−457.457	+	332.362i	−1.03263	+	0.750252i	−0.968834	−	0.247711i	$-0.920322\pi$
$443$	−457.457	+	332.362i	−1.03263	+	0.750252i	−0.0637992	+	0.997963i	$0.520322\pi$
$444$		0			0
$445$	357.819	+	1101.26i	0.804089	+	2.47473i
$446$		0			0
$447$	4.98539	−	6.86180i	0.0111530	−	0.0153508i
$448$		0			0
$449$	131.333	−	404.202i	0.292502	−	0.900228i	−0.691547	−	0.722331i	$-0.743071\pi$
$449$	131.333	−	404.202i	0.292502	−	0.900228i	0.984049	−	0.177897i	$-0.0569293\pi$
$450$		0			0
$451$	−52.5126	+	79.3061i	−0.116436	+	0.175845i
$452$		0			0
$453$	−1002.69	−	325.794i	−2.21345	−	0.719193i
$454$		0			0
$455$	−79.9850	−	58.1125i	−0.175791	−	0.127720i
$456$		0			0
$457$	−135.787	+	44.1199i	−0.297127	+	0.0965425i	−0.453787	−	0.891110i	$-0.649927\pi$
$457$	−135.787	+	44.1199i	−0.297127	+	0.0965425i	0.156660	+	0.987653i	$0.449927\pi$
$458$		0			0
$459$	118.523	+	163.133i	0.258220	+	0.355409i
$460$		0			0
$461$			756.300i			1.64056i	0.571959	+	0.820282i	$0.306184\pi$
$461$			756.300i			1.64056i	−0.571959	+	0.820282i	$0.693816\pi$
$462$		0			0
$463$	570.750			1.23272			0.616360	−	0.787464i	$-0.288607\pi$
$463$	570.750			1.23272			0.616360	+	0.787464i	$0.288607\pi$
$464$		0			0
$465$	−648.720	+	471.323i	−1.39510	+	1.01360i
$466$		0			0
$467$	−149.310	−	459.529i	−0.319722	−	0.984003i	−0.973767	−	0.227547i	$-0.926929\pi$
$467$	−149.310	−	459.529i	−0.319722	−	0.984003i	0.654045	−	0.756455i	$-0.273071\pi$
$468$		0			0
$469$	109.606	−	150.860i	0.233702	−	0.321663i
$470$		0			0
$471$	−224.802	+	691.869i	−0.477287	+	1.46894i
$472$		0			0
$473$	−245.781	+	91.8423i	−0.519622	+	0.194170i
$474$		0			0
$475$	−473.913	−	153.984i	−0.997711	−	0.324176i
$476$		0			0
$477$	118.803	+	86.3152i	0.249062	+	0.180954i
$478$		0			0
$479$	−349.615	+	113.597i	−0.729885	+	0.237154i	−0.650304	−	0.759674i	$-0.725358\pi$
$479$	−349.615	+	113.597i	−0.729885	+	0.237154i	−0.0795812	+	0.996828i	$0.525358\pi$
$480$		0			0
$481$	121.540	+	167.285i	0.252681	+	0.347786i
$482$		0			0
$483$			101.707i			0.210574i
$484$		0			0
$485$	−1059.51			−2.18456
$486$		0			0
$487$	−154.084	+	111.949i	−0.316394	+	0.229874i	−0.734635	−	0.678462i	$-0.762647\pi$
$487$	−154.084	+	111.949i	−0.316394	+	0.229874i	0.418241	+	0.908336i	$0.362647\pi$
$488$		0			0
$489$	−106.477	−	327.704i	−0.217745	−	0.670151i
$490$		0			0
$491$	−209.778	+	288.735i	−0.427246	+	0.588054i	−0.967318	−	0.253565i	$-0.918397\pi$
$491$	−209.778	+	288.735i	−0.427246	+	0.588054i	0.540072	+	0.841619i	$0.318397\pi$
$492$		0			0
$493$	292.672	−	900.753i	0.593656	−	1.82709i
$494$		0			0
$495$	−221.024	−	591.487i	−0.446513	−	1.19492i
$496$		0			0
$497$	286.719	+	93.1607i	0.576899	+	0.187446i
$498$		0			0
$499$	−115.869	−	84.1837i	−0.232202	−	0.168705i	0.465600	−	0.884995i	$-0.345839\pi$
$499$	−115.869	−	84.1837i	−0.232202	−	0.168705i	−0.697802	+	0.716290i	$0.745839\pi$
$500$		0			0
$501$	288.428	−	93.7160i	0.575705	−	0.187058i
$502$		0			0
$503$	293.916	+	404.541i	0.584326	+	0.804256i	0.994161	−	0.107903i	$-0.0344137\pi$
$503$	293.916	+	404.541i	0.584326	+	0.804256i	−0.409835	+	0.912160i	$0.634414\pi$
$504$		0			0
$505$			1374.83i			2.72243i
$506$		0			0
$507$	593.053			1.16973
$508$		0			0
$509$	503.893	−	366.100i	0.989967	−	0.719253i	0.0300529	−	0.999548i	$-0.490432\pi$
$509$	503.893	−	366.100i	0.989967	−	0.719253i	0.959914	+	0.280295i	$0.0904324\pi$
$510$		0			0
$511$	−24.6581	−	75.8897i	−0.0482545	−	0.148512i
$512$		0			0
$513$	55.4767	−	76.3571i	0.108142	−	0.148844i
$514$		0			0
$515$	42.6752	−	131.341i	0.0828645	−	0.255031i
$516$		0			0
$517$	−516.827	−	342.217i	−0.999666	−	0.661929i
$518$		0			0
$519$	−1197.48	−	389.086i	−2.30729	−	0.749683i
$520$		0			0
$521$	487.589	+	354.254i	0.935870	+	0.679950i	0.947423	−	0.319984i	$-0.103677\pi$
$521$	487.589	+	354.254i	0.935870	+	0.679950i	−0.0115526	+	0.999933i	$0.503677\pi$
$522$		0			0
$523$	241.749	−	78.5490i	0.462235	−	0.150189i	−0.0686361	−	0.997642i	$-0.521865\pi$
$523$	241.749	−	78.5490i	0.462235	−	0.150189i	0.530871	+	0.847452i	$0.321865\pi$
$524$		0			0
$525$	−265.238	−	365.068i	−0.505214	−	0.695368i
$526$		0			0
$527$		−	608.449i		−	1.15455i
$528$		0			0
$529$	−436.513			−0.825167
$530$		0			0
$531$	321.911	−	233.882i	0.606236	−	0.440456i
$532$		0			0
$533$	12.1381	+	37.3574i	0.0227733	+	0.0700889i
$534$		0			0
$535$	−488.157	+	671.891i	−0.912443	+	1.25587i
$536$		0			0
$537$	−414.464	+	1275.59i	−0.771813	+	2.37540i
$538$		0			0
$539$	60.2696	−	47.9225i	0.111818	−	0.0889101i
$540$		0			0
$541$	266.491	+	86.5883i	0.492591	+	0.160052i	0.544770	−	0.838585i	$-0.316617\pi$
$541$	266.491	+	86.5883i	0.492591	+	0.160052i	−0.0521797	+	0.998638i	$0.516617\pi$
$542$		0			0
$543$	12.1252	+	8.80945i	0.0223300	+	0.0162237i
$544$		0			0
$545$	830.090	−	269.712i	1.52310	−	0.494885i
$546$		0			0
$547$	−335.324	−	461.534i	−0.613023	−	0.843754i	0.383799	−	0.923417i	$-0.374616\pi$
$547$	−335.324	−	461.534i	−0.613023	−	0.843754i	−0.996822	+	0.0796626i	$0.974616\pi$
$548$		0			0
$549$		−	328.002i		−	0.597454i
$550$		0			0
$551$	−443.310			−0.804556
$552$		0			0
$553$	−241.189	+	175.234i	−0.436147	+	0.316879i
$554$		0			0
$555$	462.518	+	1423.48i	0.833365	+	2.56483i
$556$		0			0
$557$	401.771	−	552.990i	0.721312	−	0.992801i	−0.278167	−	0.960533i	$-0.589727\pi$
$557$	401.771	−	552.990i	0.721312	−	0.992801i	0.999479	−	0.0322683i	$-0.0102731\pi$
$558$		0			0
$559$	−33.4835	+	103.052i	−0.0598989	+	0.184350i
$560$		0			0
$561$	1057.12	+	293.375i	1.88435	+	0.522951i
$562$		0			0
$563$	641.084	+	208.301i	1.13869	+	0.369984i	0.816873	−	0.576817i	$-0.195705\pi$
$563$	641.084	+	208.301i	1.13869	+	0.369984i	0.321820	+	0.946801i	$0.395705\pi$
$564$		0			0
$565$	1064.45	+	773.372i	1.88399	+	1.36880i
$566$		0			0
$567$	239.318	−	77.7591i	0.422077	−	0.137141i
$568$		0			0
$569$	105.778	+	145.591i	0.185902	+	0.255872i	0.891788	−	0.452453i	$-0.149451\pi$
$569$	105.778	+	145.591i	0.185902	+	0.255872i	−0.705886	+	0.708325i	$0.749451\pi$
$570$		0			0
$571$		−	796.738i		−	1.39534i	−0.716420	−	0.697669i	$-0.754220\pi$
$571$		−	796.738i		−	1.39534i	0.716420	−	0.697669i	$-0.245780\pi$
$572$		0			0
$573$	−60.7729			−0.106061
$574$		0			0
$575$	−331.971	+	241.191i	−0.577341	+	0.419463i
$576$		0			0
$577$	283.170	+	871.508i	0.490763	+	1.51041i	0.823458	+	0.567378i	$0.192042\pi$
$577$	283.170	+	871.508i	0.490763	+	1.51041i	−0.332695	+	0.943034i	$0.607958\pi$
$578$		0			0
$579$	317.172	−	436.550i	0.547792	−	0.753972i
$580$		0			0
$581$	60.5792	−	186.444i	0.104267	−	0.320901i
$582$		0			0
$583$	−231.264	+	10.0546i	−0.396680	+	0.0172463i
$584$		0			0
$585$	−248.000	−	80.5800i	−0.423931	−	0.137744i
$586$		0			0
$587$	−484.724	−	352.172i	−0.825764	−	0.599953i	0.0925936	−	0.995704i	$-0.470484\pi$
$587$	−484.724	−	352.172i	−0.825764	−	0.599953i	−0.918358	+	0.395751i	$0.870484\pi$
$588$		0			0
$589$	−270.856	+	88.0065i	−0.459858	+	0.149417i
$590$		0			0
$591$	500.041	+	688.248i	0.846093	+	1.16455i
$592$		0			0
$593$			247.975i			0.418170i	0.977898	+	0.209085i	$0.0670485\pi$
$593$			247.975i			0.418170i	−0.977898	+	0.209085i	$0.932952\pi$
$594$		0			0
$595$	543.027			0.912650
$596$		0			0
$597$	−24.5965	+	17.8704i	−0.0412002	+	0.0299337i
$598$		0			0
$599$	165.685	+	509.927i	0.276603	+	0.851298i	0.988791	+	0.149308i	$0.0477047\pi$
$599$	165.685	+	509.927i	0.276603	+	0.851298i	−0.712187	+	0.701990i	$0.752295\pi$
$600$		0			0
$601$	−279.668	+	384.930i	−0.465337	+	0.640482i	−0.975605	−	0.219534i	$-0.929546\pi$
$601$	−279.668	+	384.930i	−0.465337	+	0.640482i	0.510268	+	0.860016i	$0.329546\pi$
$602$		0			0
$603$	151.982	−	467.754i	0.252044	−	0.775711i
$604$		0			0
$605$	852.996	+	512.959i	1.40991	+	0.847866i
$606$		0			0
$607$	184.448	+	59.9308i	0.303868	+	0.0987327i	0.456982	−	0.889476i	$-0.348930\pi$
$607$	184.448	+	59.9308i	0.303868	+	0.0987327i	−0.153114	+	0.988208i	$0.548930\pi$
$608$		0			0
$609$	−324.780	−	235.967i	−0.533301	−	0.387466i
$610$		0			0
$611$	−243.453	+	79.1027i	−0.398450	+	0.129464i
$612$		0			0
$613$	−318.458	−	438.319i	−0.519507	−	0.715040i	0.465979	−	0.884796i	$-0.345702\pi$
$613$	−318.458	−	438.319i	−0.519507	−	0.715040i	−0.985486	+	0.169756i	$0.945702\pi$
$614$		0			0
$615$			284.326i			0.462318i
$616$		0			0
$617$	−28.2446			−0.0457773			−0.0228887	−	0.999738i	$-0.507286\pi$
$617$	−28.2446			−0.0457773			−0.0228887	+	0.999738i	$0.507286\pi$
$618$		0			0
$619$	343.441	−	249.524i	0.554832	−	0.403109i	−0.274732	−	0.961521i	$-0.588589\pi$
$619$	343.441	−	249.524i	0.554832	−	0.403109i	0.829564	+	0.558412i	$0.188589\pi$
$620$		0			0
$621$	−24.0173	−	73.9178i	−0.0386753	−	0.119030i
$622$		0			0
$623$	−218.906	+	301.298i	−0.351374	+	0.483624i
$624$		0			0
$625$	39.8214	−	122.558i	0.0637143	−	0.196092i
$626$		0			0
$627$	−22.3044	−	513.021i	−0.0355732	−	0.818215i
$628$		0			0
$629$	−1080.13	−	350.956i	−1.71722	−	0.557959i
$630$		0			0
$631$	−833.744	−	605.751i	−1.32131	−	0.959985i	−0.999915	−	0.0130390i	$-0.995849\pi$
$631$	−833.744	−	605.751i	−1.32131	−	0.959985i	−0.321392	−	0.946946i	$-0.604151\pi$
$632$		0			0
$633$	231.450	−	75.2028i	0.365640	−	0.118804i
$634$		0			0
$635$	99.8683	+	137.457i	0.157273	+	0.216467i
$636$		0			0
$637$		−	31.7986i		−	0.0499193i
$638$		0			0
$639$	795.141			1.24435
$640$		0			0
$641$	17.5445	−	12.7468i	0.0273705	−	0.0198859i	−0.574016	−	0.818844i	$-0.694615\pi$
$641$	17.5445	−	12.7468i	0.0273705	−	0.0198859i	0.601386	+	0.798958i	$0.294615\pi$
$642$		0			0
$643$	−315.482	−	970.953i	−0.490640	−	1.51004i	−0.823642	−	0.567110i	$-0.808062\pi$
$643$	−315.482	−	970.953i	−0.490640	−	1.51004i	0.333002	−	0.942926i	$-0.391938\pi$
$644$		0			0
$645$	−461.013	+	634.530i	−0.714749	+	0.983767i
$646$		0			0
$647$	−265.571	+	817.343i	−0.410465	+	1.26328i	0.505780	+	0.862663i	$0.331205\pi$
$647$	−265.571	+	817.343i	−0.410465	+	1.26328i	−0.916245	+	0.400619i	$0.868795\pi$
$648$		0			0
$649$	−167.732	+	604.389i	−0.258446	+	0.931261i
$650$		0			0
$651$	−245.281	−	79.6965i	−0.376775	−	0.122422i
$652$		0			0
$653$	454.229	+	330.016i	0.695603	+	0.505385i	0.878497	−	0.477748i	$-0.158547\pi$
$653$	454.229	+	330.016i	0.695603	+	0.505385i	−0.182894	+	0.983133i	$0.558547\pi$
$654$		0			0
$655$	−1315.90	+	427.561i	−2.00900	+	0.652765i
$656$		0			0
$657$	−123.706	−	170.266i	−0.188288	−	0.259157i
$658$		0			0
$659$		−	872.376i		−	1.32379i	−0.749598	−	0.661894i	$-0.769753\pi$
$659$		−	872.376i		−	1.32379i	0.749598	−	0.661894i	$-0.230247\pi$
$660$		0			0
$661$	206.745			0.312776			0.156388	−	0.987696i	$-0.450015\pi$
$661$	206.745			0.312776			0.156388	+	0.987696i	$0.450015\pi$
$662$		0			0
$663$	366.532	−	266.301i	0.552838	−	0.401660i
$664$		0			0
$665$	−78.5438	−	241.733i	−0.118111	−	0.363508i
$666$		0			0
$667$	−214.574	+	295.336i	−0.321700	+	0.442782i
$668$		0			0
$669$	−116.016	+	357.059i	−0.173416	+	0.533721i
$670$		0			0
$671$	321.792	+	404.701i	0.479571	+	0.603131i
$672$		0			0
$673$	−384.974	−	125.086i	−0.572026	−	0.185863i	0.00869907	−	0.999962i	$-0.497231\pi$
$673$	−384.974	−	125.086i	−0.572026	−	0.185863i	−0.580725	+	0.814100i	$0.697231\pi$
$674$		0			0
$675$	278.974	+	202.687i	0.413296	+	0.300277i
$676$		0			0
$677$	−232.696	+	75.6077i	−0.343717	+	0.111680i	−0.475788	−	0.879560i	$-0.657837\pi$
$677$	−232.696	+	75.6077i	−0.343717	+	0.111680i	0.132071	+	0.991240i	$0.457837\pi$
$678$		0			0
$679$	−200.300	−	275.689i	−0.294992	−	0.406022i
$680$		0			0
$681$		−	1126.64i		−	1.65439i
$682$		0			0
$683$	−2.58367			−0.00378282			−0.00189141	−	0.999998i	$-0.500602\pi$
$683$	−2.58367			−0.00378282			−0.00189141	+	0.999998i	$0.500602\pi$
$684$		0			0
$685$	−1437.22	+	1044.20i	−2.09813	+	1.52438i
$686$		0			0
$687$	−421.007	−	1295.73i	−0.612820	−	1.88607i
$688$		0			0
$689$	−56.1894	+	77.3380i	−0.0815521	+	0.112247i
$690$		0			0
$691$	−34.4803	+	106.119i	−0.0498991	+	0.153574i	−0.972901	−	0.231221i	$-0.925728\pi$
$691$	−34.4803	+	106.119i	−0.0498991	+	0.153574i	0.923002	+	0.384795i	$0.125728\pi$
$692$		0			0
$693$	112.123	−	169.332i	0.161794	−	0.244346i
$694$		0			0
$695$	1785.36	+	580.099i	2.56887	+	0.834675i
$696$		0			0
$697$	−174.541	−	126.812i	−0.250418	−	0.181939i
$698$		0			0
$699$	615.513	−	199.992i	0.880562	−	0.286112i
$700$		0			0
$701$	655.272	+	901.905i	0.934768	+	1.28660i	0.957970	+	0.286867i	$0.0926139\pi$
$701$	655.272	+	901.905i	0.934768	+	1.28660i	−0.0232022	+	0.999731i	$0.507386\pi$
$702$		0			0
$703$			531.592i			0.756176i
$704$		0			0
$705$	−1852.91			−2.62824
$706$		0			0
$707$	−357.736	+	259.911i	−0.505992	+	0.367625i
$708$		0			0
$709$	−319.363	−	982.898i	−0.450442	−	1.38632i	−0.876404	−	0.481576i	$-0.840065\pi$
$709$	−319.363	−	982.898i	−0.450442	−	1.38632i	0.425963	−	0.904741i	$-0.359935\pi$
$710$		0			0
$711$	−462.182	+	636.139i	−0.650045	+	0.894710i
$712$		0			0
$713$	−72.4712	+	223.043i	−0.101643	+	0.312824i
$714$		0			0
$715$	385.045	−	143.882i	0.538525	−	0.201233i
$716$		0			0
$717$	−1189.93	−	386.632i	−1.65959	−	0.539235i
$718$		0			0
$719$	−321.521	−	233.599i	−0.447179	−	0.324894i	0.341302	−	0.939954i	$-0.389132\pi$
$719$	−321.521	−	233.599i	−0.447179	−	0.324894i	−0.788481	+	0.615059i	$0.789132\pi$
$720$		0			0
$721$	42.2432	−	13.7256i	0.0585897	−	0.0190370i
$722$		0			0
$723$	−3.29101	−	4.52968i	−0.00455188	−	0.00626512i
$724$		0			0
$725$		−	1619.66i		−	2.23401i
$726$		0			0
$727$	647.283			0.890347			0.445174	−	0.895444i	$-0.353142\pi$
$727$	647.283			0.890347			0.445174	+	0.895444i	$0.353142\pi$
$728$		0			0
$729$	301.717	−	219.210i	0.413878	−	0.300700i
$730$		0			0
$731$	−183.908	−	566.011i	−0.251584	−	0.774297i
$732$		0			0
$733$	16.1911	−	22.2852i	0.0220889	−	0.0304027i	−0.797830	−	0.602883i	$-0.794019\pi$
$733$	16.1911	−	22.2852i	0.0220889	−	0.0304027i	0.819919	+	0.572480i	$0.194019\pi$
$734$		0			0
$735$	71.1273	−	218.907i	0.0967718	−	0.297833i
$736$		0			0
$737$	271.376	+	726.236i	0.368218	+	0.985395i
$738$		0			0
$739$	1058.68	+	343.985i	1.43258	+	0.465474i	0.919576	−	0.392912i	$-0.128532\pi$
$739$	1058.68	+	343.985i	1.43258	+	0.465474i	0.513005	+	0.858386i	$0.328532\pi$
$740$		0			0
$741$	−171.561	−	124.647i	−0.231527	−	0.168214i
$742$		0			0
$743$	733.830	−	238.436i	0.987658	−	0.320910i	0.229735	−	0.973253i	$-0.426214\pi$
$743$	733.830	−	238.436i	0.987658	−	0.320910i	0.757923	+	0.652344i	$0.226214\pi$
$744$		0			0
$745$	10.2595	+	14.1210i	0.0137712	+	0.0189544i
$746$		0			0
$747$		−	517.054i		−	0.692173i
$748$		0			0
$749$	−267.115			−0.356629
$750$		0			0
$751$	−83.0883	+	60.3672i	−0.110637	+	0.0803824i	−0.641728	−	0.766932i	$-0.721782\pi$
$751$	−83.0883	+	60.3672i	−0.110637	+	0.0803824i	0.531091	+	0.847315i	$0.321782\pi$
$752$		0			0
$753$	−476.075	−	1465.21i	−0.632238	−	1.94583i
$754$		0			0
$755$	1275.29	−	1755.28i	1.68912	−	2.32488i
$756$		0			0
$757$	173.321	−	533.428i	0.228958	−	0.704661i	−0.768907	−	0.639360i	$-0.779199\pi$
$757$	173.321	−	533.428i	0.228958	−	0.704661i	0.997866	−	0.0653007i	$-0.0208007\pi$
$758$		0			0
$759$	−352.573	−	233.457i	−0.464523	−	0.307584i
$760$		0			0
$761$	1267.33	+	411.782i	1.66535	+	0.541106i	0.981983	−	0.188967i	$-0.0605139\pi$
$761$	1267.33	+	411.782i	1.66535	+	0.541106i	0.683369	+	0.730073i	$0.260514\pi$
$762$		0			0
$763$	227.108	+	165.004i	0.297652	+	0.216257i
$764$		0			0
$765$	1362.14	−	442.586i	1.78057	−	0.578544i
$766$		0			0
$767$	152.252	+	209.557i	0.198504	+	0.273217i
$768$		0			0
$769$			495.521i			0.644371i	0.946677	+	0.322185i	$0.104417\pi$
$769$			495.521i			0.644371i	−0.946677	+	0.322185i	$0.895583\pi$
$770$		0			0
$771$	780.716			1.01260
$772$		0			0
$773$	−947.242	+	688.212i	−1.22541	+	0.890313i	−0.996538	−	0.0831439i	$-0.973504\pi$
$773$	−947.242	+	688.212i	−1.22541	+	0.890313i	−0.228873	+	0.973456i	$0.573504\pi$
$774$		0			0
$775$	−321.536	−	989.586i	−0.414885	−	1.27689i
$776$		0			0
$777$	−282.958	+	389.458i	−0.364167	+	0.501233i
$778$		0			0
$779$	−31.2055	+	96.0406i	−0.0400584	+	0.123287i
$780$		0			0
$781$	−981.074	+	780.087i	−1.25618	+	0.998831i
$782$		0			0
$783$	291.762	+	94.7993i	0.372621	+	0.121072i
$784$		0			0
$785$	−1211.17	−	879.964i	−1.54289	−	1.12097i
$786$		0			0
$787$	528.900	−	171.850i	0.672046	−	0.218361i	0.0469363	−	0.998898i	$-0.485054\pi$
$787$	528.900	−	171.850i	0.672046	−	0.218361i	0.625110	+	0.780537i	$0.285054\pi$
$788$		0			0
$789$	1041.74	+	1433.83i	1.32033	+	1.81727i
$790$		0			0
$791$			423.181i			0.534996i
$792$		0			0
$793$	213.522			0.269259
$794$		0			0
$795$	−559.808	+	406.724i	−0.704161	+	0.511603i
$796$		0			0
$797$	−62.5388	−	192.475i	−0.0784678	−	0.241499i	0.904126	−	0.427266i	$-0.140523\pi$
$797$	−62.5388	−	192.475i	−0.0784678	−	0.241499i	−0.982594	+	0.185767i	$0.940523\pi$
$798$		0			0
$799$	826.414	−	1137.46i	1.03431	−	1.42361i
$800$		0			0
$801$	−303.539	+	934.198i	−0.378950	+	1.16629i
$802$		0			0
$803$	319.675	+	88.7170i	0.398101	+	0.110482i
$804$		0			0
$805$	−199.061	−	64.6789i	−0.247281	−	0.0803465i
$806$		0			0
$807$	783.711	+	569.399i	0.971141	+	0.705575i
$808$		0			0
$809$	868.887	−	282.318i	1.07403	−	0.348972i	0.281972	−	0.959423i	$-0.409012\pi$
$809$	868.887	−	282.318i	1.07403	−	0.348972i	0.792054	+	0.610451i	$0.209012\pi$
$810$		0			0
$811$	142.863	+	196.635i	0.176157	+	0.242460i	0.887961	−	0.459919i	$-0.152121\pi$
$811$	142.863	+	196.635i	0.176157	+	0.242460i	−0.711804	+	0.702378i	$0.752121\pi$
$812$		0			0
$813$		−	1437.20i		−	1.76777i
$814$		0			0
$815$	709.093			0.870053
$816$		0			0
$817$	−225.364	+	163.737i	−0.275843	+	0.200412i
$818$		0			0
$819$	−25.9170	−	79.7642i	−0.0316447	−	0.0973922i
$820$		0			0
$821$	−469.989	+	646.885i	−0.572460	+	0.787923i	−0.992843	−	0.119423i	$-0.961895\pi$
$821$	−469.989	+	646.885i	−0.572460	+	0.787923i	0.420384	+	0.907346i	$0.361895\pi$
$822$		0			0
$823$	24.0928	−	74.1500i	0.0292743	−	0.0900972i	−0.935352	−	0.353719i	$-0.884917\pi$
$823$	24.0928	−	74.1500i	0.0292743	−	0.0900972i	0.964626	+	0.263622i	$0.0849170\pi$
$824$		0			0
$825$	1874.35	−	81.4902i	2.27194	−	0.0987760i
$826$		0			0
$827$	−3.85548	−	1.25272i	−0.00466200	−	0.00151478i	0.306685	−	0.951811i	$-0.400780\pi$
$827$	−3.85548	−	1.25272i	−0.00466200	−	0.00151478i	−0.311347	+	0.950296i	$0.600780\pi$
$828$		0			0
$829$	−763.250	−	554.534i	−0.920688	−	0.668919i	0.0230075	−	0.999735i	$-0.492676\pi$
$829$	−763.250	−	554.534i	−0.920688	−	0.668919i	−0.943695	+	0.330817i	$0.892676\pi$
$830$		0			0
$831$	−706.499	+	229.555i	−0.850179	+	0.276240i
$832$		0			0
$833$	102.659	+	141.298i	0.123240	+	0.169625i
$834$		0			0
$835$			624.108i			0.747434i
$836$		0			0
$837$	197.082			0.235463
$838$		0			0
$839$	1251.76	−	909.460i	1.49197	−	1.08398i	0.518527	−	0.855062i	$-0.326481\pi$
$839$	1251.76	−	909.460i	1.49197	−	1.08398i	0.973445	−	0.228919i	$-0.0735193\pi$
$840$		0			0
$841$	−185.384	−	570.554i	−0.220433	−	0.678423i
$842$		0			0
$843$	635.635	−	874.877i	0.754016	−	1.03781i
$844$		0			0
$845$	−377.141	+	1160.72i	−0.446321	+	1.37363i
$846$		0			0
$847$	27.7843	+	318.928i	0.0328032	+	0.376538i
$848$		0			0
$849$	−250.199	−	81.2947i	−0.294699	−	0.0957534i
$850$		0			0
$851$	354.150	+	257.305i	0.416157	+	0.302356i
$852$		0			0
$853$	−57.3152	+	18.6229i	−0.0671925	+	0.0218322i	−0.342420	−	0.939547i	$-0.611247\pi$
$853$	−57.3152	+	18.6229i	−0.0671925	+	0.0218322i	0.275228	+	0.961379i	$0.411247\pi$
$854$		0			0
$855$	−394.042	−	542.352i	−0.460867	−	0.634330i
$856$		0			0
$857$		−	1284.46i		−	1.49879i	−0.662123	−	0.749395i	$-0.730345\pi$
$857$		−	1284.46i		−	1.49879i	0.662123	−	0.749395i	$-0.269655\pi$
$858$		0			0
$859$	102.785			0.119657			0.0598283	−	0.998209i	$-0.480945\pi$
$859$	102.785			0.119657			0.0598283	+	0.998209i	$0.480945\pi$
$860$		0			0
$861$	−73.9828	+	53.7516i	−0.0859266	+	0.0624293i
$862$		0			0
$863$	−67.5407	−	207.869i	−0.0782627	−	0.240868i	0.904269	−	0.426963i	$-0.140417\pi$
$863$	−67.5407	−	207.869i	−0.0782627	−	0.240868i	−0.982532	+	0.186095i	$0.940417\pi$
$864$		0			0
$865$	1523.03	−	2096.28i	1.76073	−	2.42344i
$866$		0			0
$867$	−411.985	+	1267.96i	−0.475184	+	1.46247i
$868$		0			0
$869$	−53.8381	−	1238.32i	−0.0619540	−	1.42500i
$870$		0			0
$871$	304.498	+	98.9373i	0.349595	+	0.113590i
$872$		0			0
$873$	−727.133	−	528.293i	−0.832912	−	0.605146i
$874$		0			0
$875$	365.711	−	118.827i	0.417955	−	0.135802i
$876$		0			0
$877$	−273.440	−	376.358i	−0.311790	−	0.429142i	0.624149	−	0.781306i	$-0.285446\pi$
$877$	−273.440	−	376.358i	−0.311790	−	0.429142i	−0.935938	+	0.352164i	$0.885446\pi$
$878$		0			0
$879$		−	904.814i		−	1.02937i
$880$		0			0
$881$	96.1025			0.109083			0.0545417	−	0.998511i	$-0.482630\pi$
$881$	96.1025			0.109083			0.0545417	+	0.998511i	$0.482630\pi$
$882$		0			0
$883$	313.790	−	227.982i	0.355368	−	0.258190i	−0.395749	−	0.918359i	$-0.629515\pi$
$883$	313.790	−	227.982i	0.355368	−	0.258190i	0.751118	+	0.660168i	$0.229515\pi$
$884$		0			0
$885$	579.393	+	1783.19i	0.654682	+	2.01490i
$886$		0			0
$887$	−424.317	+	584.022i	−0.478373	+	0.658424i	−0.978191	−	0.207706i	$-0.933400\pi$
$887$	−424.317	+	584.022i	−0.478373	+	0.658424i	0.499818	+	0.866130i	$0.333400\pi$
$888$		0			0
$889$	−16.8868	+	51.9723i	−0.0189953	+	0.0584615i
$890$		0			0
$891$	−279.769	+	1008.09i	−0.313994	+	1.13142i
$892$		0			0
$893$	−625.884	−	203.362i	−0.700878	−	0.227729i
$894$		0			0
$895$	−2233.01	−	1622.37i	−2.49498	−	1.81271i
$896$		0			0
$897$	−166.081	+	53.9629i	−0.185151	+	0.0601593i
$898$		0			0
$899$	−544.104	−	748.895i	−0.605232	−	0.833031i
$900$		0			0
$901$		−	525.056i		−	0.582748i
$902$		0			0
$903$	−252.262			−0.279360
$904$		0			0
$905$	−24.9526	+	18.1291i	−0.0275719	+	0.0200322i
$906$		0			0
$907$	15.5165	+	47.7548i	0.0171075	+	0.0526514i	0.959246	−	0.282573i	$-0.0911879\pi$
$907$	15.5165	+	47.7548i	0.0171075	+	0.0526514i	−0.942138	+	0.335224i	$0.891188\pi$
$908$		0			0
$909$	−685.517	+	943.533i	−0.754144	+	1.03799i
$910$		0			0
$911$	−7.28108	+	22.4089i	−0.00799241	+	0.0245981i	−0.954973	−	0.296692i	$-0.904116\pi$
$911$	−7.28108	+	22.4089i	−0.00799241	+	0.0245981i	0.946981	+	0.321290i	$0.104116\pi$
$912$		0			0
$913$	507.264	+	637.960i	0.555602	+	0.698751i
$914$		0			0
$915$	1469.93	+	477.608i	1.60648	+	0.521976i
$916$		0			0
$917$	−360.023	−	261.572i	−0.392610	−	0.285248i
$918$		0			0
$919$	309.931	−	100.703i	0.337248	−	0.109578i	−0.135497	−	0.990778i	$-0.543263\pi$
$919$	309.931	−	100.703i	0.337248	−	0.109578i	0.472745	+	0.881199i	$0.343263\pi$
$920$		0			0
$921$	−1272.03	−	1750.80i	−1.38114	−	1.90097i
$922$		0			0
$923$			517.620i			0.560802i
$924$		0			0
$925$	−1942.20			−2.09967
$926$		0			0
$927$	94.7768	−	68.8594i	0.102240	−	0.0742819i
$928$		0			0
$929$	209.421	+	644.531i	0.225426	+	0.693790i	0.998248	+	0.0591672i	$0.0188445\pi$
$929$	209.421	+	644.531i	0.225426	+	0.693790i	−0.772822	+	0.634623i	$0.781155\pi$
$930$		0			0
$931$	48.0513	−	66.1369i	0.0516126	−	0.0710386i
$932$		0			0
$933$	−84.4733	+	259.982i	−0.0905394	+	0.278652i
$934$		0			0
$935$	−1246.45	+	1882.43i	−1.33310	+	2.01329i
$936$		0			0
$937$	−294.694	−	95.7519i	−0.314508	−	0.102190i	0.147509	−	0.989061i	$-0.452874\pi$
$937$	−294.694	−	95.7519i	−0.314508	−	0.102190i	−0.462018	+	0.886871i	$0.652874\pi$
$938$		0			0
$939$	182.429	+	132.542i	0.194280	+	0.141153i
$940$		0			0
$941$	1289.05	−	418.838i	1.36987	−	0.445098i	0.470545	−	0.882376i	$-0.344057\pi$
$941$	1289.05	−	418.838i	1.36987	−	0.445098i	0.899327	+	0.437278i	$0.144057\pi$
$942$		0			0
$943$	48.8785	+	67.2755i	0.0518330	+	0.0713420i
$944$		0			0
$945$			175.891i			0.186128i
$946$		0			0
$947$	−785.957			−0.829944			−0.414972	−	0.909834i	$-0.636209\pi$
$947$	−785.957			−0.829944			−0.414972	+	0.909834i	$0.636209\pi$
$948$		0			0
$949$	110.840	−	80.5297i	0.116796	−	0.0848574i
$950$		0			0
$951$	660.153	+	2031.74i	0.694167	+	2.13643i
$952$		0			0
$953$	−582.263	+	801.417i	−0.610980	+	0.840941i	−0.996658	−	0.0816923i	$-0.973968\pi$
$953$	−582.263	+	801.417i	−0.610980	+	0.840941i	0.385678	+	0.922633i	$0.373968\pi$
$954$		0			0
$955$	38.6474	−	118.944i	0.0404685	−	0.124549i
$956$		0			0
$957$	1563.48	−	584.235i	1.63373	−	0.610486i
$958$		0			0
$959$	−543.410	−	176.565i	−0.566642	−	0.184113i
$960$		0			0
$961$	296.354	+	215.314i	0.308381	+	0.224052i
$962$		0			0
$963$	−670.036	+	217.708i	−0.695780	+	0.226073i
$964$		0			0
$965$	652.714	+	898.384i	0.676387	+	0.930967i
$966$		0			0
$967$			374.205i			0.386975i	0.981103	+	0.193487i	$0.0619799\pi$
$967$			374.205i			0.386975i	−0.981103	+	0.193487i	$0.938020\pi$
$968$		0			0
$969$	1164.75			1.20201
$970$		0			0
$971$	−904.574	+	657.211i	−0.931590	+	0.676840i	−0.946382	−	0.323051i	$-0.895291\pi$
$971$	−904.574	+	657.211i	−0.931590	+	0.676840i	0.0147919	+	0.999891i	$0.495291\pi$
$972$		0			0
$973$	186.578	+	574.227i	0.191755	+	0.590161i
$974$		0			0
$975$	455.403	−	626.808i	0.467080	−	0.642880i
$976$		0			0
$977$	−466.539	+	1435.86i	−0.477522	+	1.46966i	0.365003	+	0.931006i	$0.381068\pi$
$977$	−466.539	+	1435.86i	−0.477522	+	1.46966i	−0.842526	+	0.538656i	$0.818932\pi$
$978$		0			0
$979$	−541.993	−	1450.44i	−0.553619	−	1.48155i
$980$		0			0
$981$	704.167	+	228.798i	0.717806	+	0.233229i
$982$		0			0
$983$	177.978	+	129.309i	0.181056	+	0.131545i	0.674622	−	0.738163i	$-0.264307\pi$
$983$	177.978	+	129.309i	0.181056	+	0.131545i	−0.493566	+	0.869709i	$0.664307\pi$
$984$		0			0
$985$	−1665.03	+	541.000i	−1.69038	+	0.549239i
$986$		0			0
$987$	−350.292	−	482.136i	−0.354906	−	0.488486i
$988$		0			0
$989$			229.392i			0.231943i
$990$		0			0
$991$	−661.278			−0.667283			−0.333642	−	0.942700i	$-0.608278\pi$
$991$	−661.278			−0.667283			−0.333642	+	0.942700i	$0.608278\pi$
$992$		0			0
$993$	−1226.32	+	890.976i	−1.23497	+	0.897256i
$994$		0			0
$995$	−19.3342	−	59.5046i	−0.0194314	−	0.0598036i
$996$		0			0
$997$	−695.942	+	957.882i	−0.698036	+	0.960764i	0.301936	+	0.953328i	$0.402367\pi$
$997$	−695.942	+	957.882i	−0.698036	+	0.960764i	−0.999972	+	0.00743600i	$0.997633\pi$
$998$		0			0
$999$	113.678	−	349.864i	0.113792	−	0.350215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.3.r.a.57.2	✓	48
11.6	odd	10	inner	308.3.r.a.281.2	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.3.r.a.57.2	✓	48	1.1	even	1	trivial
308.3.r.a.281.2	yes	48	11.6	odd	10	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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	308.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-3.23386 + 2.34954i) q^{3} +(-2.54199 - 7.82345i) q^{5} +(1.55513 - 2.14046i) q^{7} +(2.15638 - 6.63666i) q^{9} +O(q^{10})\)	\(q+(-3.23386 + 2.34954i) q^{3} +(-2.54199 - 7.82345i) q^{5} +(1.55513 - 2.14046i) q^{7} +(2.15638 - 6.63666i) q^{9} +(3.85039 + 10.3041i) q^{11} +(4.32032 + 1.40376i) q^{13} +(26.6020 + 19.3274i) q^{15} +(-23.7294 + 7.71015i) q^{17} +(6.86447 + 9.44813i) q^{19} +10.5758i q^{21} +9.61699 q^{23} +(-34.5192 + 25.0797i) q^{25} +(-2.49739 - 7.68617i) q^{27} +(-22.3120 + 30.7098i) q^{29} +(-7.53575 + 23.1926i) q^{31} +(-36.6615 - 24.2754i) q^{33} +(-20.6989 - 6.72548i) q^{35} +(36.8254 + 26.7552i) q^{37} +(-17.2695 + 5.61120i) q^{39} +(5.08252 + 6.99549i) q^{41} +23.8528i q^{43} -57.4031 q^{45} +(-45.5886 + 33.1221i) q^{47} +(-2.16312 - 6.65740i) q^{49} +(58.6223 - 80.6866i) q^{51} +(-6.50291 + 20.0139i) q^{53} +(70.8260 - 56.3163i) q^{55} +(-44.3975 - 14.4256i) q^{57} +(46.1310 + 33.5161i) q^{59} +(44.7033 - 14.5250i) q^{61} +(-10.8520 - 14.9365i) q^{63} -37.3682i q^{65} +70.4803 q^{67} +(-31.1000 + 22.5955i) q^{69} +(35.2114 + 108.370i) q^{71} +(17.7274 - 24.3997i) q^{73} +(52.7047 - 162.208i) q^{75} +(28.0434 + 7.78267i) q^{77} +(-107.166 - 34.8204i) q^{79} +(76.9444 + 55.9034i) q^{81} +(70.4691 - 22.8968i) q^{83} +(120.640 + 166.047i) q^{85} -151.734i q^{87} -140.763 q^{89} +(9.72336 - 7.06444i) q^{91} +(-30.1224 - 92.7073i) q^{93} +(56.4676 - 77.7210i) q^{95} +(39.8011 - 122.495i) q^{97} +(76.6877 - 3.33412i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9}+O(q^{10}) \) 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9	\( 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9} - 10 q^{11} + 30 q^{13} + 24 q^{15} + 60 q^{19} - 132 q^{23} - 186 q^{25} - 110 q^{27} - 90 q^{29} - 26 q^{31} + 46 q^{33} + 82 q^{37} + 290 q^{39} - 336 q^{45} + 84 q^{47} + 84 q^{49} - 20 q^{51} + 58 q^{53} + 370 q^{55} - 20 q^{57} + 436 q^{59} + 160 q^{61} + 276 q^{67} - 118 q^{69} - 150 q^{71} - 320 q^{73} - 692 q^{75} + 28 q^{77} - 560 q^{79} + 122 q^{81} - 630 q^{83} + 220 q^{85} - 444 q^{89} - 126 q^{91} + 500 q^{93} + 440 q^{95} - 80 q^{97} + 1034 q^{99}+O(q^{100}) \) 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9 - 10 * q^11 + 30 * q^13 + 24 * q^15 + 60 * q^19 - 132 * q^23 - 186 * q^25 - 110 * q^27 - 90 * q^29 - 26 * q^31 + 46 * q^33 + 82 * q^37 + 290 * q^39 - 336 * q^45 + 84 * q^47 + 84 * q^49 - 20 * q^51 + 58 * q^53 + 370 * q^55 - 20 * q^57 + 436 * q^59 + 160 * q^61 + 276 * q^67 - 118 * q^69 - 150 * q^71 - 320 * q^73 - 692 * q^75 + 28 * q^77 - 560 * q^79 + 122 * q^81 - 630 * q^83 + 220 * q^85 - 444 * q^89 - 126 * q^91 + 500 * q^93 + 440 * q^95 - 80 * q^97 + 1034 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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