LMFDB - Embedded newform 354.4.c.b.353.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,4,Mod(353,354)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("354.353");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	354.c (of order $2$, degree $1$, 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:	$20.8866761420$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			353.7
Character	$\chi$	$=$	354.353
Dual form			354.4.c.b.353.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +(-3.62921 - 3.71872i) q^{3} +4.00000 q^{4} +18.5626i q^{5} +(-7.25841 - 7.43744i) q^{6} +9.26632 q^{7} +8.00000 q^{8} +(-0.657741 + 26.9920i) q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +(-3.62921 - 3.71872i) q^{3} +4.00000 q^{4} +18.5626i q^{5} +(-7.25841 - 7.43744i) q^{6} +9.26632 q^{7} +8.00000 q^{8} +(-0.657741 + 26.9920i) q^{9} +37.1253i q^{10} -54.2151 q^{11} +(-14.5168 - 14.8749i) q^{12} -34.8767i q^{13} +18.5326 q^{14} +(69.0292 - 67.3676i) q^{15} +16.0000 q^{16} -8.98656i q^{17} +(-1.31548 + 53.9840i) q^{18} -123.132 q^{19} +74.2505i q^{20} +(-33.6294 - 34.4588i) q^{21} -108.430 q^{22} -94.6163 q^{23} +(-29.0336 - 29.7498i) q^{24} -219.571 q^{25} -69.7535i q^{26} +(102.763 - 95.5135i) q^{27} +37.0653 q^{28} -57.9611i q^{29} +(138.058 - 134.735i) q^{30} +8.78061i q^{31} +32.0000 q^{32} +(196.758 + 201.611i) q^{33} -17.9731i q^{34} +172.007i q^{35} +(-2.63096 + 107.968i) q^{36} +124.314i q^{37} -246.264 q^{38} +(-129.697 + 126.575i) q^{39} +148.501i q^{40} +316.150i q^{41} +(-67.2587 - 68.9177i) q^{42} -249.805i q^{43} -216.861 q^{44} +(-501.042 - 12.2094i) q^{45} -189.233 q^{46} -143.346 q^{47} +(-58.0673 - 59.4995i) q^{48} -257.135 q^{49} -439.142 q^{50} +(-33.4185 + 32.6141i) q^{51} -139.507i q^{52} +716.060i q^{53} +(205.525 - 191.027i) q^{54} -1006.38i q^{55} +74.1306 q^{56} +(446.872 + 457.894i) q^{57} -115.922i q^{58} +(-419.378 + 171.759i) q^{59} +(276.117 - 269.470i) q^{60} +583.044i q^{61} +17.5612i q^{62} +(-6.09484 + 250.116i) q^{63} +64.0000 q^{64} +647.404 q^{65} +(393.516 + 403.222i) q^{66} -11.7588i q^{67} -35.9462i q^{68} +(343.382 + 351.852i) q^{69} +344.014i q^{70} -14.4123i q^{71} +(-5.26193 + 215.936i) q^{72} -1141.82i q^{73} +248.628i q^{74} +(796.869 + 816.524i) q^{75} -492.528 q^{76} -502.375 q^{77} +(-259.394 + 253.150i) q^{78} -491.309 q^{79} +297.002i q^{80} +(-728.135 - 35.5075i) q^{81} +632.300i q^{82} +1087.50 q^{83} +(-134.517 - 137.835i) q^{84} +166.814 q^{85} -499.610i q^{86} +(-215.541 + 210.353i) q^{87} -433.721 q^{88} +1316.60 q^{89} +(-1002.08 - 24.4188i) q^{90} -323.179i q^{91} -378.465 q^{92} +(32.6526 - 31.8666i) q^{93} -286.692 q^{94} -2285.66i q^{95} +(-116.135 - 118.999i) q^{96} +823.374i q^{97} -514.271 q^{98} +(35.6595 - 1463.37i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 60 q^{2} + 5 q^{3} + 120 q^{4} + 10 q^{6} + 6 q^{7} + 240 q^{8} + 27 q^{9}+O(q^{10}) $ 30 * q + 60 * q^2 + 5 * q^3 + 120 * q^4 + 10 * q^6 + 6 * q^7 + 240 * q^8 + 27 * q^9	$ 30 q + 60 q^{2} + 5 q^{3} + 120 q^{4} + 10 q^{6} + 6 q^{7} + 240 q^{8} + 27 q^{9} + 60 q^{11} + 20 q^{12} + 12 q^{14} + 20 q^{15} + 480 q^{16} + 54 q^{18} + 90 q^{19} + 132 q^{21} + 120 q^{22} - 24 q^{23} + 40 q^{24} - 1080 q^{25} - 55 q^{27} + 24 q^{28} + 40 q^{30} + 960 q^{32} - 336 q^{33} + 108 q^{36} + 180 q^{38} - 652 q^{39} + 264 q^{42} + 240 q^{44} - 878 q^{45} - 48 q^{46} - 792 q^{47} + 80 q^{48} + 2016 q^{49} - 2160 q^{50} + 650 q^{51} - 110 q^{54} + 48 q^{56} + 846 q^{57} + 480 q^{59} + 80 q^{60} + 887 q^{63} + 1920 q^{64} + 1416 q^{65} - 672 q^{66} + 590 q^{69} + 216 q^{72} - 952 q^{75} + 360 q^{76} - 864 q^{77} - 1304 q^{78} + 738 q^{79} - 1217 q^{81} - 876 q^{83} + 528 q^{84} + 1176 q^{85} + 534 q^{87} + 480 q^{88} + 300 q^{89} - 1756 q^{90} - 96 q^{92} - 1684 q^{93} - 1584 q^{94} + 160 q^{96} + 4032 q^{98} - 730 q^{99}+O(q^{100}) $ 30 * q + 60 * q^2 + 5 * q^3 + 120 * q^4 + 10 * q^6 + 6 * q^7 + 240 * q^8 + 27 * q^9 + 60 * q^11 + 20 * q^12 + 12 * q^14 + 20 * q^15 + 480 * q^16 + 54 * q^18 + 90 * q^19 + 132 * q^21 + 120 * q^22 - 24 * q^23 + 40 * q^24 - 1080 * q^25 - 55 * q^27 + 24 * q^28 + 40 * q^30 + 960 * q^32 - 336 * q^33 + 108 * q^36 + 180 * q^38 - 652 * q^39 + 264 * q^42 + 240 * q^44 - 878 * q^45 - 48 * q^46 - 792 * q^47 + 80 * q^48 + 2016 * q^49 - 2160 * q^50 + 650 * q^51 - 110 * q^54 + 48 * q^56 + 846 * q^57 + 480 * q^59 + 80 * q^60 + 887 * q^63 + 1920 * q^64 + 1416 * q^65 - 672 * q^66 + 590 * q^69 + 216 * q^72 - 952 * q^75 + 360 * q^76 - 864 * q^77 - 1304 * q^78 + 738 * q^79 - 1217 * q^81 - 876 * q^83 + 528 * q^84 + 1176 * q^85 + 534 * q^87 + 480 * q^88 + 300 * q^89 - 1756 * q^90 - 96 * q^92 - 1684 * q^93 - 1584 * q^94 + 160 * q^96 + 4032 * q^98 - 730 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/354\mathbb{Z}\right)^\times$.

$n$	$61$	$119$
$\chi(n)$	$-1$	$-1$

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 $

$2$	2.00000			0.707107
$2$	2.00000			0.707107
$3$	−3.62921	−	3.71872i	−0.698441	−	0.715668i
$3$	−3.62921	−	3.71872i	−0.698441	−	0.715668i
$4$	4.00000			0.500000
$5$			18.5626i			1.66029i	0.557546	+	0.830146i	$0.311743\pi$
$5$			18.5626i			1.66029i	−0.557546	+	0.830146i	$0.688257\pi$
$6$	−7.25841	−	7.43744i	−0.493872	−	0.506054i
$7$	9.26632			0.500334			0.250167	−	0.968203i	$-0.419514\pi$
$7$	9.26632			0.500334			0.250167	+	0.968203i	$0.419514\pi$
$8$	8.00000			0.353553
$9$	−0.657741	+	26.9920i	−0.0243608	+	0.999703i
$10$			37.1253i			1.17400i
$11$	−54.2151			−1.48604			−0.743022	−	0.669267i	$-0.766608\pi$
$11$	−54.2151			−1.48604			−0.743022	+	0.669267i	$0.766608\pi$
$12$	−14.5168	−	14.8749i	−0.349220	−	0.357834i
$13$		−	34.8767i		−	0.744082i	−0.928216	−	0.372041i	$-0.878658\pi$
$13$		−	34.8767i		−	0.744082i	0.928216	−	0.372041i	$-0.121342\pi$
$14$	18.5326			0.353790
$15$	69.0292	−	67.3676i	1.18822	−	1.15962i
$16$	16.0000			0.250000
$17$		−	8.98656i		−	0.128209i	−0.997943	−	0.0641047i	$-0.979581\pi$
$17$		−	8.98656i		−	0.128209i	0.997943	−	0.0641047i	$-0.0204192\pi$
$18$	−1.31548	+	53.9840i	−0.0172257	+	0.706897i
$19$	−123.132			−1.48676			−0.743380	−	0.668869i	$-0.766779\pi$
$19$	−123.132			−1.48676			−0.743380	+	0.668869i	$0.766779\pi$
$20$			74.2505i			0.830146i
$21$	−33.6294	−	34.4588i	−0.349454	−	0.358073i
$22$	−108.430			−1.05079
$23$	−94.6163			−0.857777			−0.428888	−	0.903357i	$-0.641095\pi$
$23$	−94.6163			−0.857777			−0.428888	+	0.903357i	$0.641095\pi$
$24$	−29.0336	−	29.7498i	−0.246936	−	0.253027i
$25$	−219.571			−1.75657
$26$		−	69.7535i		−	0.526145i
$27$	102.763	−	95.5135i	0.732470	−	0.680799i
$28$	37.0653			0.250167
$29$		−	57.9611i		−	0.371141i	−0.982631	−	0.185571i	$-0.940587\pi$
$29$		−	57.9611i		−	0.371141i	0.982631	−	0.185571i	$-0.0594134\pi$
$30$	138.058	−	134.735i	0.840197	−	0.819972i
$31$			8.78061i			0.0508724i	0.999676	+	0.0254362i	$0.00809747\pi$
$31$			8.78061i			0.0508724i	−0.999676	+	0.0254362i	$0.991903\pi$
$32$	32.0000			0.176777
$33$	196.758	+	201.611i	1.03791	+	1.06351i
$34$		−	17.9731i		−	0.0906577i
$35$			172.007i			0.830701i
$36$	−2.63096	+	107.968i	−0.0121804	+	0.499852i
$37$			124.314i			0.552354i	0.961107	+	0.276177i	$0.0890676\pi$
$37$			124.314i			0.552354i	−0.961107	+	0.276177i	$0.910932\pi$
$38$	−246.264			−1.05130
$39$	−129.697	+	126.575i	−0.532516	+	0.519697i
$40$			148.501i			0.587002i
$41$			316.150i			1.20425i	0.798401	+	0.602126i	$0.205680\pi$
$41$			316.150i			1.20425i	−0.798401	+	0.602126i	$0.794320\pi$
$42$	−67.2587	−	68.9177i	−0.247101	−	0.253196i
$43$		−	249.805i		−	0.885927i	−0.896540	−	0.442964i	$-0.853927\pi$
$43$		−	249.805i		−	0.885927i	0.896540	−	0.442964i	$-0.146073\pi$
$44$	−216.861			−0.743022
$45$	−501.042	−	12.2094i	−1.65980	−	0.0404460i
$46$	−189.233			−0.606540
$47$	−143.346			−0.444875			−0.222438	−	0.974947i	$-0.571401\pi$
$47$	−143.346			−0.444875			−0.222438	+	0.974947i	$0.571401\pi$
$48$	−58.0673	−	59.4995i	−0.174610	−	0.178917i
$49$	−257.135			−0.749666
$50$	−439.142			−1.24208
$51$	−33.4185	+	32.6141i	−0.0917553	+	0.0895467i
$52$		−	139.507i		−	0.372041i
$53$			716.060i			1.85582i	0.372805	+	0.927910i	$0.378396\pi$
$53$			716.060i			1.85582i	−0.372805	+	0.927910i	$0.621604\pi$
$54$	205.525	−	191.027i	0.517934	−	0.481398i
$55$		−	1006.38i		−	2.46727i
$56$	74.1306			0.176895
$57$	446.872	+	457.894i	1.03841	+	1.06403i
$58$		−	115.922i		−	0.262437i
$59$	−419.378	+	171.759i	−0.925396	+	0.379003i
$59$	−419.378	+	171.759i	−0.925396	+	0.379003i
$60$	276.117	−	269.470i	0.594109	−	0.579808i
$61$			583.044i			1.22379i	0.790939	+	0.611895i	$0.209593\pi$
$61$			583.044i			1.22379i	−0.790939	+	0.611895i	$0.790407\pi$
$62$			17.5612i			0.0359722i
$63$	−6.09484	+	250.116i	−0.0121885	+	0.500186i
$64$	64.0000			0.125000
$65$	647.404			1.23539
$66$	393.516	+	403.222i	0.733916	+	0.752018i
$67$		−	11.7588i		−	0.0214412i	−0.999943	−	0.0107206i	$-0.996587\pi$
$67$		−	11.7588i		−	0.0214412i	0.999943	−	0.0107206i	$-0.00341254\pi$
$68$		−	35.9462i		−	0.0641047i
$69$	343.382	+	351.852i	0.599106	+	0.613883i
$70$			344.014i			0.587394i
$71$		−	14.4123i		−	0.0240906i	−0.999927	−	0.0120453i	$-0.996166\pi$
$71$		−	14.4123i		−	0.0240906i	0.999927	−	0.0120453i	$-0.00383423\pi$
$72$	−5.26193	+	215.936i	−0.00861283	+	0.353448i
$73$		−	1141.82i		−	1.83068i	−0.402686	−	0.915338i	$-0.631923\pi$
$73$		−	1141.82i		−	1.83068i	0.402686	−	0.915338i	$-0.368077\pi$
$74$			248.628i			0.390573i
$75$	796.869	+	816.524i	1.22686	+	1.25712i
$76$	−492.528			−0.743380
$77$	−502.375			−0.743518
$78$	−259.394	+	253.150i	−0.376545	+	0.367481i
$79$	−491.309			−0.699703			−0.349852	−	0.936805i	$-0.613768\pi$
$79$	−491.309			−0.699703			−0.349852	+	0.936805i	$0.613768\pi$
$80$			297.002i			0.415073i
$81$	−728.135	−	35.5075i	−0.998813	−	0.0487071i
$82$			632.300i			0.851535i
$83$	1087.50			1.43817			0.719085	−	0.694922i	$-0.244561\pi$
$83$	1087.50			1.43817			0.719085	+	0.694922i	$0.244561\pi$
$84$	−134.517	−	137.835i	−0.174727	−	0.179037i
$85$	166.814			0.212865
$86$		−	499.610i		−	0.626445i
$87$	−215.541	+	210.353i	−0.265614	+	0.259220i
$88$	−433.721			−0.525396
$89$	1316.60			1.56809			0.784044	−	0.620705i	$-0.213154\pi$
$89$	1316.60			1.56809			0.784044	+	0.620705i	$0.213154\pi$
$90$	−1002.08	−	24.4188i	−1.17366	−	0.0285996i
$91$		−	323.179i		−	0.372290i
$92$	−378.465			−0.428888
$93$	32.6526	−	31.8666i	0.0364077	−	0.0355314i
$94$	−286.692			−0.314574
$95$		−	2285.66i		−	2.46846i
$96$	−116.135	−	118.999i	−0.123468	−	0.126513i
$97$			823.374i			0.861865i	0.902384	+	0.430933i	$0.141815\pi$
$97$			823.374i			0.861865i	−0.902384	+	0.430933i	$0.858185\pi$
$98$	−514.271			−0.530094
$99$	35.6595	−	1463.37i	0.0362012	−	1.48560i
$100$	−878.285			−0.878285
$101$	−1318.12			−1.29859			−0.649294	−	0.760537i	$-0.724936\pi$
$101$	−1318.12			−1.29859			−0.649294	+	0.760537i	$0.724936\pi$
$102$	−66.8370	+	65.2281i	−0.0648808	+	0.0633191i
$103$		−	1243.68i		−	1.18974i	−0.803821	−	0.594871i	$-0.797203\pi$
$103$		−	1243.68i		−	1.18974i	0.803821	−	0.594871i	$-0.202797\pi$
$104$		−	279.014i		−	0.263073i
$105$	639.647	−	624.250i	0.594506	−	0.580195i
$106$			1432.12i			1.31226i
$107$			242.129i			0.218761i	0.994000	+	0.109381i	$0.0348867\pi$
$107$			242.129i			0.218761i	−0.994000	+	0.109381i	$0.965113\pi$
$108$	411.051	−	382.054i	0.366235	−	0.340400i
$109$		−	176.929i		−	0.155474i	−0.996974	−	0.0777372i	$-0.975230\pi$
$109$		−	176.929i		−	0.155474i	0.996974	−	0.0777372i	$-0.0247695\pi$
$110$		−	2012.75i		−	1.74462i
$111$	462.289	−	451.161i	0.395302	−	0.385787i
$112$	148.261			0.125084
$113$	1971.26			1.64106			0.820532	−	0.571601i	$-0.193677\pi$
$113$	1971.26			1.64106			0.820532	+	0.571601i	$0.193677\pi$
$114$	893.743	+	915.787i	0.734269	+	0.752380i
$115$		−	1756.33i		−	1.42416i
$116$		−	231.844i		−	0.185571i
$117$	941.392	+	22.9399i	0.743861	+	0.0181264i
$118$	−838.756	+	343.519i	−0.654354	+	0.267995i
$119$		−	83.2723i		−	0.0641476i
$120$	552.234	−	538.941i	0.420098	−	0.409986i
$121$	1608.28			1.20833
$122$			1166.09i			0.865350i
$123$	1175.67	−	1147.37i	0.861845	−	0.841099i
$124$			35.1225i			0.0254362i
$125$		−	1755.49i		−	1.25613i
$126$	−12.1897	+	500.233i	−0.00861859	+	0.353685i
$127$	−55.7928			−0.0389828			−0.0194914	−	0.999810i	$-0.506205\pi$
$127$	−55.7928			−0.0389828			−0.0194914	+	0.999810i	$0.506205\pi$
$128$	128.000			0.0883883
$129$	−928.954	+	906.593i	−0.634030	+	0.618768i
$130$	1294.81			0.873555
$131$	−639.528			−0.426533			−0.213266	−	0.976994i	$-0.568410\pi$
$131$	−639.528			−0.426533			−0.213266	+	0.976994i	$0.568410\pi$
$132$	787.031	+	806.443i	0.518957	+	0.531757i
$133$	−1140.98			−0.743877
$134$		−	23.5175i		−	0.0151612i
$135$	1772.98	+	1907.55i	1.13033	+	1.21611i
$136$		−	71.8924i		−	0.0453289i
$137$		−	819.164i		−	0.510846i	−0.966829	−	0.255423i	$-0.917785\pi$
$137$		−	819.164i		−	0.510846i	0.966829	−	0.255423i	$-0.0822147\pi$
$138$	686.764	+	703.703i	0.423632	+	0.434081i
$139$	−1329.14			−0.811054			−0.405527	−	0.914083i	$-0.632912\pi$
$139$	−1329.14			−0.811054			−0.405527	+	0.914083i	$0.632912\pi$
$140$			688.029i			0.415350i
$141$	520.231	+	533.063i	0.310719	+	0.318383i
$142$		−	28.8247i		−	0.0170346i
$143$			1890.85i			1.10574i
$144$	−10.5239	+	431.872i	−0.00609019	+	0.249926i
$145$	1075.91			0.616203
$146$		−	2283.63i		−	1.29448i
$147$	933.197	+	956.214i	0.523597	+	0.536512i
$148$			497.256i			0.276177i
$149$	−3134.50			−1.72341			−0.861705	−	0.507410i	$-0.830603\pi$
$149$	−3134.50			−1.72341			−0.861705	+	0.507410i	$0.830603\pi$
$150$	1593.74	+	1633.05i	0.867521	+	0.888918i
$151$			971.652i			0.523655i	0.965115	+	0.261828i	$0.0843252\pi$
$151$			971.652i			0.523655i	−0.965115	+	0.261828i	$0.915675\pi$
$152$	−985.057			−0.525649
$153$	242.565	+	5.91083i	0.128171	+	0.00312328i
$154$	−1004.75			−0.525747
$155$	−162.991			−0.0844631
$156$	−518.787	+	506.299i	−0.266258	+	0.259849i
$157$			1224.22i			0.622317i	0.950358	+	0.311158i	$0.100717\pi$
$157$			1224.22i			0.622317i	−0.950358	+	0.311158i	$0.899283\pi$
$158$	−982.618			−0.494765
$159$	2662.83	−	2598.73i	1.32815	−	1.29618i
$160$			594.004i			0.293501i
$161$	−876.745			−0.429175
$162$	−1456.27	−	71.0149i	−0.706268	−	0.0344411i
$163$	1710.53			0.821959			0.410980	−	0.911645i	$-0.365187\pi$
$163$	1710.53			0.821959			0.410980	+	0.911645i	$0.365187\pi$
$164$			1264.60i			0.602126i
$165$	−3742.43	+	3652.34i	−1.76574	+	1.72324i
$166$	2174.99			1.01694
$167$			2888.17i			1.33828i	0.743135	+	0.669142i	$0.233338\pi$
$167$			2888.17i			1.33828i	−0.743135	+	0.669142i	$0.766662\pi$
$168$	−269.035	−	275.671i	−0.123551	−	0.126598i
$169$	980.613			0.446342
$170$	333.628			0.150518
$171$	80.9890	−	3323.58i	0.0362186	−	1.48632i
$172$		−	999.219i		−	0.442964i
$173$	2167.99			0.952771			0.476385	−	0.879237i	$-0.341947\pi$
$173$	2167.99			0.952771			0.476385	+	0.879237i	$0.341947\pi$
$174$	−431.082	+	420.705i	−0.187817	+	0.183296i
$175$	−2034.62			−0.878872
$176$	−867.442			−0.371511
$177$	2160.73	+	936.199i	0.917574	+	0.397565i
$178$	2633.21			1.10881
$179$	3362.66			1.40412			0.702059	−	0.712119i	$-0.252264\pi$
$179$	3362.66			1.40412			0.702059	+	0.712119i	$0.252264\pi$
$180$	−2004.17	−	48.8376i	−0.829900	−	0.0202230i
$181$	−4336.44			−1.78080			−0.890400	−	0.455179i	$-0.849575\pi$
$181$	−4336.44			−1.78080			−0.890400	+	0.455179i	$0.849575\pi$
$182$		−	646.358i		−	0.263249i
$183$	2168.18	−	2115.99i	0.875827	−	0.854745i
$184$	−756.931			−0.303270
$185$	−2307.60			−0.917069
$186$	65.3053	−	63.7333i	0.0257442	−	0.0251245i
$187$			487.207i			0.190525i
$188$	−573.383			−0.222438
$189$	952.232	−	885.059i	0.366480	−	0.340627i
$190$		−	4571.31i		−	1.74546i
$191$	2901.64			1.09924			0.549621	−	0.835414i	$-0.314772\pi$
$191$	2901.64			1.09924			0.549621	+	0.835414i	$0.314772\pi$
$192$	−232.269	−	237.998i	−0.0873051	−	0.0894585i
$193$	1743.29			0.650179			0.325089	−	0.945683i	$-0.394606\pi$
$193$	1743.29			0.650179			0.325089	+	0.945683i	$0.394606\pi$
$194$			1646.75i			0.609431i
$195$	−2349.56	−	2407.51i	−0.862849	−	0.884131i
$196$	−1028.54			−0.374833
$197$			2958.53i			1.06998i	0.844858	+	0.534991i	$0.179685\pi$
$197$			2958.53i			1.06998i	−0.844858	+	0.534991i	$0.820315\pi$
$198$	71.3190	−	2926.75i	0.0255981	−	1.05048i
$199$	−1306.74			−0.465490			−0.232745	−	0.972538i	$-0.574771\pi$
$199$	−1306.74			−0.465490			−0.232745	+	0.972538i	$0.574771\pi$
$200$	−1756.57			−0.621041
$201$	−43.7275	+	42.6749i	−0.0153448	+	0.0149754i
$202$	−2636.23			−0.918241
$203$		−	537.086i		−	0.185695i
$204$	−133.674	+	130.456i	−0.0458777	+	0.0447733i
$205$	−5868.58			−1.99941
$206$		−	2487.36i		−	0.841274i
$207$	62.2330	−	2553.88i	0.0208961	−	0.857522i
$208$		−	558.028i		−	0.186021i
$209$	6675.62			2.20939
$210$	1279.29	−	1248.50i	0.420379	−	0.410260i
$211$			5584.81i			1.82215i	0.412238	+	0.911076i	$0.364747\pi$
$211$			5584.81i			1.82215i	−0.412238	+	0.911076i	$0.635253\pi$
$212$			2864.24i			0.927910i
$213$	−53.5954	+	52.3053i	−0.0172408	+	0.0168258i
$214$			484.257i			0.154688i
$215$	4637.03			1.47090
$216$	822.102	−	764.108i	0.258967	−	0.240699i
$217$			81.3640i			0.0254532i
$218$		−	353.858i		−	0.109937i
$219$	−4246.09	+	4143.88i	−1.31016	+	1.27862i
$220$		−	4025.50i		−	1.23363i
$221$	−313.422			−0.0953983
$222$	924.578	−	902.323i	0.279521	−	0.272792i
$223$	625.862			0.187941			0.0939704	−	0.995575i	$-0.470044\pi$
$223$	625.862			0.187941			0.0939704	+	0.995575i	$0.470044\pi$
$224$	296.522			0.0884474
$225$	144.421	−	5926.66i	0.0427914	−	1.75605i
$226$	3942.51			1.16041
$227$	−829.549			−0.242551			−0.121276	−	0.992619i	$-0.538698\pi$
$227$	−829.549			−0.242551			−0.121276	+	0.992619i	$0.538698\pi$
$228$	1787.49	+	1831.57i	0.519207	+	0.532013i
$229$		−	832.505i		−	0.240233i	−0.992760	−	0.120117i	$-0.961673\pi$
$229$		−	832.505i		−	0.240233i	0.992760	−	0.120117i	$-0.0383269\pi$
$230$		−	3512.66i		−	1.00703i
$231$	1823.22	+	1868.19i	0.519304	+	0.532112i
$232$		−	463.689i		−	0.131218i
$233$	−2777.07			−0.780823			−0.390411	−	0.920641i	$-0.627667\pi$
$233$	−2777.07			−0.780823			−0.390411	+	0.920641i	$0.627667\pi$
$234$	1882.78	+	45.8797i	0.525989	+	0.0128173i
$235$		−	2660.87i		−	0.738623i
$236$	−1677.51	+	687.037i	−0.462698	+	0.189501i
$237$	1783.06	+	1827.04i	0.488701	+	0.500755i
$238$		−	166.545i		−	0.0453592i
$239$		−	475.166i		−	0.128602i	−0.997931	−	0.0643012i	$-0.979518\pi$
$239$		−	475.166i		−	0.128602i	0.997931	−	0.0643012i	$-0.0204818\pi$
$240$	1104.47	−	1077.88i	0.297054	−	0.289904i
$241$	−785.860			−0.210049			−0.105024	−	0.994470i	$-0.533492\pi$
$241$	−785.860			−0.210049			−0.105024	+	0.994470i	$0.533492\pi$
$242$	3216.56			0.854415
$243$	2510.51	+	2836.59i	0.662754	+	0.748837i
$244$			2332.18i			0.611895i
$245$		−	4773.11i		−	1.24466i
$246$	2351.35	−	2294.75i	0.609416	−	0.594747i
$247$			4294.45i			1.10627i
$248$			70.2449i			0.0179861i
$249$	−3946.74	−	4044.09i	−1.00448	−	1.02925i
$250$		−	3510.98i		−	0.888216i
$251$			586.570i			0.147506i	0.997277	+	0.0737529i	$0.0234976\pi$
$251$			586.570i			0.147506i	−0.997277	+	0.0737529i	$0.976502\pi$
$252$	−24.3794	+	1000.47i	−0.00609426	+	0.250093i
$253$	5129.64			1.27469
$254$	−111.586			−0.0275650
$255$	−605.403	−	620.335i	−0.148674	−	0.152341i
$256$	256.000			0.0625000
$257$			7649.27i			1.85661i	0.371821	+	0.928304i	$0.378734\pi$
$257$			7649.27i			1.85661i	−0.371821	+	0.928304i	$0.621266\pi$
$258$	−1857.91	+	1813.19i	−0.448327	+	0.437535i
$259$			1151.93i			0.276362i
$260$	2589.62			0.617697
$261$	1564.48	+	38.1234i	0.371031	+	0.00904129i
$262$	−1279.06			−0.301604
$263$		−	4062.63i		−	0.952518i	−0.879305	−	0.476259i	$-0.841992\pi$
$263$		−	4062.63i		−	0.952518i	0.879305	−	0.476259i	$-0.158008\pi$
$264$	1574.06	+	1612.89i	0.366958	+	0.376009i
$265$	−13292.0			−3.08120
$266$	−2281.96			−0.526000
$267$	−4778.23	−	4896.08i	−1.09522	−	1.12223i
$268$		−	47.0350i		−	0.0107206i
$269$	−5572.80			−1.26312			−0.631560	−	0.775327i	$-0.717585\pi$
$269$	−5572.80			−1.26312			−0.631560	+	0.775327i	$0.717585\pi$
$270$	3545.96	+	3815.09i	0.799261	+	0.859922i
$271$	3046.98			0.682992			0.341496	−	0.939883i	$-0.389066\pi$
$271$	3046.98			0.682992			0.341496	+	0.939883i	$0.389066\pi$
$272$		−	143.785i		−	0.0320524i
$273$	−1201.81	+	1172.88i	−0.266436	+	0.260022i
$274$		−	1638.33i		−	0.361223i
$275$	11904.1			2.61034
$276$	1373.53	+	1407.41i	0.299553	+	0.306942i
$277$	5927.99			1.28584			0.642921	−	0.765932i	$-0.277722\pi$
$277$	5927.99			1.28584			0.642921	+	0.765932i	$0.277722\pi$
$278$	−2658.29			−0.573502
$279$	−237.006	−	5.77537i	−0.0508573	−	0.00123929i
$280$			1376.06i			0.293697i
$281$		−	7684.53i		−	1.63139i	−0.578482	−	0.815695i	$-0.696355\pi$
$281$		−	7684.53i		−	1.63139i	0.578482	−	0.815695i	$-0.303645\pi$
$282$	1040.46	+	1066.13i	0.219711	+	0.225131i
$283$		−	4035.27i		−	0.847603i	−0.905755	−	0.423802i	$-0.860695\pi$
$283$		−	4035.27i		−	0.847603i	0.905755	−	0.423802i	$-0.139305\pi$
$284$		−	57.6494i		−	0.0120453i
$285$	−8499.71	+	8295.11i	−1.76659	+	1.72407i
$286$			3781.69i			0.781875i
$287$			2929.55i			0.602529i
$288$	−21.0477	+	863.744i	−0.00430642	+	0.176724i
$289$	4832.24			0.983562
$290$	2151.82			0.435721
$291$	3061.90	−	2988.19i	0.616809	−	0.601962i
$292$		−	4567.26i		−	0.915338i
$293$			2739.50i			0.546223i	0.961982	+	0.273112i	$0.0880528\pi$
$293$			2739.50i			0.546223i	−0.961982	+	0.273112i	$0.911947\pi$
$294$	1866.39	+	1912.43i	0.370239	+	0.379371i
$295$	−3188.30	−	7784.75i	−0.629255	−	1.53643i
$296$			994.513i			0.195287i
$297$	−5571.29	+	5178.28i	−1.08848	+	1.01170i
$298$	−6269.00			−1.21863
$299$			3299.91i			0.638256i
$300$	3187.48	+	3266.09i	0.613430	+	0.628560i
$301$		−	2314.77i		−	0.443260i
$302$			1943.30i			0.370280i
$303$	4783.71	+	4901.70i	0.906987	+	0.929358i
$304$	−1970.11			−0.371690
$305$	−10822.8			−2.03185
$306$	485.130	+	11.8217i	0.0906308	+	0.00220849i
$307$	−3546.52			−0.659317			−0.329659	−	0.944100i	$-0.606934\pi$
$307$	−3546.52			−0.659317			−0.329659	+	0.944100i	$0.606934\pi$
$308$	−2009.50			−0.371759
$309$	−4624.89	+	4513.57i	−0.851460	+	0.830964i
$310$	−325.983			−0.0597244
$311$			8617.85i			1.57130i	0.618673	+	0.785649i	$0.287671\pi$
$311$			8617.85i			1.57130i	−0.618673	+	0.785649i	$0.712329\pi$
$312$	−1037.57	+	1012.60i	−0.188273	+	0.183741i
$313$		−	2505.69i		−	0.452491i	−0.974070	−	0.226246i	$-0.927355\pi$
$313$		−	2505.69i		−	0.452491i	0.974070	−	0.226246i	$-0.0726452\pi$
$314$			2448.45i			0.440044i
$315$	−4642.82	−	113.136i	−0.830454	−	0.0202365i
$316$	−1965.24			−0.349852
$317$		−	7193.38i		−	1.27451i	−0.770652	−	0.637256i	$-0.780069\pi$
$317$		−	7193.38i		−	1.27451i	0.770652	−	0.637256i	$-0.219931\pi$
$318$	5325.65	−	5197.46i	0.939144	−	0.916538i
$319$			3142.37i			0.551532i
$320$			1188.01i			0.207537i
$321$	900.408	−	878.734i	0.156560	−	0.152792i
$322$	−1753.49			−0.303473
$323$			1106.53i			0.190617i
$324$	−2912.54	−	142.030i	−0.499407	−	0.0243535i
$325$			7657.93i			1.30703i
$326$	3421.07			0.581213
$327$	−657.949	+	642.111i	−0.111268	+	0.108590i
$328$			2529.20i			0.425768i
$329$	−1328.29			−0.222586
$330$	−7484.85	+	7304.69i	−1.24857	+	1.21851i
$331$	−199.972			−0.0332068			−0.0166034	−	0.999862i	$-0.505285\pi$
$331$	−199.972			−0.0332068			−0.0166034	+	0.999862i	$0.505285\pi$
$332$	4349.98			0.719085
$333$	−3355.48	−	81.7665i	−0.552190	−	0.0134558i
$334$			5776.34i			0.946309i
$335$	218.273			0.0355987
$336$	−538.070	−	551.341i	−0.0873635	−	0.0895183i
$337$		−	10530.6i		−	1.70220i	−0.525007	−	0.851098i	$-0.675937\pi$
$337$		−	10530.6i		−	1.70220i	0.525007	−	0.851098i	$-0.324063\pi$
$338$	1961.23			0.315611
$339$	−7154.09	−	7330.55i	−1.14619	−	1.17446i
$340$	667.256			0.106433
$341$		−	476.042i		−	0.0755986i
$342$	161.978	−	6647.16i	0.0256104	−	1.05099i
$343$	−5561.05			−0.875418
$344$		−	1998.44i		−	0.313223i
$345$	−6531.29	+	6374.07i	−1.01923	+	0.994692i
$346$	4335.98			0.673711
$347$	−8529.80			−1.31961			−0.659804	−	0.751438i	$-0.729361\pi$
$347$	−8529.80			−1.31961			−0.659804	+	0.751438i	$0.729361\pi$
$348$	−862.164	+	841.410i	−0.132807	+	0.129610i
$349$		−	2668.60i		−	0.409303i	−0.978835	−	0.204651i	$-0.934394\pi$
$349$		−	2668.60i		−	0.409303i	0.978835	−	0.204651i	$-0.0656061\pi$
$350$	−4069.23			−0.621456
$351$	−3331.20	−	3584.03i	−0.506571	−	0.545018i
$352$	−1734.88			−0.262698
$353$	−9516.24			−1.43484			−0.717419	−	0.696641i	$-0.754677\pi$
$353$	−9516.24			−1.43484			−0.717419	+	0.696641i	$0.754677\pi$
$354$	4321.47	+	1872.40i	0.648823	+	0.281121i
$355$	267.531			0.0399974
$356$	5266.42			0.784044
$357$	−309.666	+	302.212i	−0.0459083	+	0.0448033i
$358$	6725.32			0.992861
$359$			241.857i			0.0355563i	0.999842	+	0.0177781i	$0.00565925\pi$
$359$			241.857i			0.0355563i	−0.999842	+	0.0177781i	$0.994341\pi$
$360$	−4008.34	−	97.6752i	−0.586828	−	0.0142998i
$361$	8302.51			1.21045
$362$	−8672.87			−1.25922
$363$	−5836.78	−	5980.74i	−0.843944	−	0.864759i
$364$		−	1292.72i		−	0.186145i
$365$	21195.1			3.03946
$366$	4336.36	−	4231.98i	0.619303	−	0.604396i
$367$			6578.98i			0.935749i	0.883795	+	0.467875i	$0.154980\pi$
$367$			6578.98i			0.935749i	−0.883795	+	0.467875i	$0.845020\pi$
$368$	−1513.86			−0.214444
$369$	−8533.52	−	207.945i	−1.20390	−	0.0293365i
$370$	−4615.19			−0.648466
$371$			6635.24i			0.928530i
$372$	130.611	−	127.467i	0.0182039	−	0.0177657i
$373$	−8671.15			−1.20369			−0.601843	−	0.798614i	$-0.705567\pi$
$373$	−8671.15			−1.20369			−0.601843	+	0.798614i	$0.705567\pi$
$374$			974.415i			0.134721i
$375$	−6528.17	+	6371.03i	−0.898969	+	0.877330i
$376$	−1146.77			−0.157287
$377$	−2021.49			−0.276160
$378$	1904.46	−	1770.12i	0.259140	−	0.240860i
$379$	6216.31			0.842507			0.421254	−	0.906943i	$-0.361590\pi$
$379$	6216.31			0.842507			0.421254	+	0.906943i	$0.361590\pi$
$380$		−	9142.62i		−	1.23423i
$381$	202.484	+	207.478i	0.0272272	+	0.0278987i
$382$	5803.28			0.777282
$383$			4707.02i			0.627983i	0.949426	+	0.313991i	$0.101666\pi$
$383$			4707.02i			0.627983i	−0.949426	+	0.313991i	$0.898334\pi$
$384$	−464.538	−	475.996i	−0.0617340	−	0.0632567i
$385$		−	9325.40i		−	1.23446i
$386$	3486.57			0.459746
$387$	6742.73	+	164.307i	0.885665	+	0.0215819i
$388$			3293.49i			0.430933i
$389$			10066.6i			1.31208i	0.754727	+	0.656039i	$0.227769\pi$
$389$			10066.6i			1.31208i	−0.754727	+	0.656039i	$0.772231\pi$
$390$	−4699.12	−	4815.03i	−0.610127	−	0.625175i
$391$			850.275i			0.109975i
$392$	−2057.08			−0.265047
$393$	2320.98	+	2378.22i	0.297908	+	0.305256i
$394$			5917.05i			0.756591i
$395$		−	9119.99i		−	1.16171i
$396$	142.638	−	5853.50i	0.0181006	−	0.742801i
$397$			4219.41i			0.533416i	0.963777	+	0.266708i	$0.0859359\pi$
$397$			4219.41i			0.533416i	−0.963777	+	0.266708i	$0.914064\pi$
$398$	−2613.48			−0.329151
$399$	4140.85	+	4242.99i	0.519554	+	0.532369i
$400$	−3513.14			−0.439142
$401$	13706.8			1.70695			0.853475	−	0.521134i	$-0.174491\pi$
$401$	13706.8			1.70695			0.853475	+	0.521134i	$0.174491\pi$
$402$	−87.4550	+	85.3499i	−0.0108504	+	0.0105892i
$403$	306.239			0.0378533
$404$	−5272.46			−0.649294
$405$	659.112	−	13516.1i	0.0808680	−	1.65832i
$406$		−	1074.17i		−	0.131306i
$407$		−	6739.70i		−	0.820822i
$408$	−267.348	+	260.912i	−0.0324404	+	0.0316595i
$409$			3252.45i			0.393212i	0.980483	+	0.196606i	$0.0629919\pi$
$409$			3252.45i			0.393212i	−0.980483	+	0.196606i	$0.937008\pi$
$410$	−11737.2			−1.41380
$411$	−3046.24	+	2972.91i	−0.365596	+	0.356796i
$412$		−	4974.72i		−	0.594871i
$413$	−3886.09	+	1591.58i	−0.463007	+	0.189628i
$414$	124.466	−	5107.77i	0.0147758	−	0.606360i
$415$			20186.8i			2.38778i
$416$		−	1116.06i		−	0.131536i
$417$	4823.74	+	4942.71i	0.566473	+	0.580445i
$418$	13351.2			1.56227
$419$	−2509.86			−0.292636			−0.146318	−	0.989238i	$-0.546742\pi$
$419$	−2509.86			−0.292636			−0.146318	+	0.989238i	$0.546742\pi$
$420$	2558.59	−	2497.00i	0.297253	−	0.290098i
$421$			6602.50i			0.764338i	0.924092	+	0.382169i	$0.124823\pi$
$421$			6602.50i			0.764338i	−0.924092	+	0.382169i	$0.875177\pi$
$422$			11169.6i			1.28846i
$423$	94.2844	−	3869.19i	0.0108375	−	0.444743i
$424$			5728.48i			0.656131i
$425$			1973.19i			0.225209i
$426$	−107.191	+	104.611i	−0.0121911	+	0.0118977i
$427$			5402.68i			0.612304i
$428$			968.514i			0.109381i
$429$	7031.53	−	6862.27i	0.791341	−	0.772293i
$430$	9274.07			1.04008
$431$	−3088.71			−0.345192			−0.172596	−	0.984993i	$-0.555216\pi$
$431$	−3088.71			−0.345192			−0.172596	+	0.984993i	$0.555216\pi$
$432$	1644.20	−	1528.22i	0.183117	−	0.170200i
$433$	9731.72			1.08008			0.540042	−	0.841638i	$-0.318408\pi$
$433$	9731.72			1.08008			0.540042	+	0.841638i	$0.318408\pi$
$434$			162.728i			0.0179981i
$435$	−3904.70	−	4001.01i	−0.430381	−	0.440997i
$436$		−	707.715i		−	0.0777372i
$437$	11650.3			1.27531
$438$	−8492.18	+	8287.76i	−0.926420	+	0.904120i
$439$	4657.33			0.506338			0.253169	−	0.967422i	$-0.418527\pi$
$439$	4657.33			0.506338			0.253169	+	0.967422i	$0.418527\pi$
$440$		−	8051.00i		−	0.872310i
$441$	169.128	−	6940.59i	0.0182624	−	0.749443i
$442$	−626.844			−0.0674568
$443$	−18290.6			−1.96166			−0.980829	−	0.194872i	$-0.937571\pi$
$443$	−18290.6			−1.96166			−0.980829	+	0.194872i	$0.937571\pi$
$444$	1849.16	−	1804.65i	0.197651	−	0.192893i
$445$			24439.6i			2.60348i
$446$	1251.72			0.132894
$447$	11375.7	+	11656.3i	1.20370	+	1.23339i
$448$	593.044			0.0625418
$449$			4662.73i			0.490084i	0.969512	+	0.245042i	$0.0788018\pi$
$449$			4662.73i			0.490084i	−0.969512	+	0.245042i	$0.921198\pi$
$450$	288.842	−	11853.3i	0.0302581	−	1.24171i
$451$		−	17140.1i		−	1.78957i
$452$	7885.02			0.820532
$453$	3613.30	−	3526.32i	0.374763	−	0.365742i
$454$	−1659.10			−0.171509
$455$	5999.05			0.618110
$456$	3574.97	+	3663.15i	0.367135	+	0.376190i
$457$		−	5158.85i		−	0.528055i	−0.964515	−	0.264027i	$-0.914949\pi$
$457$		−	5158.85i		−	0.528055i	0.964515	−	0.264027i	$-0.0850509\pi$
$458$		−	1665.01i		−	0.169871i
$459$	−858.337	−	923.483i	−0.0872849	−	0.0939095i
$460$		−	7025.31i		−	0.712080i
$461$		−	17808.6i		−	1.79919i	−0.436722	−	0.899597i	$-0.643861\pi$
$461$		−	17808.6i		−	1.79919i	0.436722	−	0.899597i	$-0.356139\pi$
$462$	3646.44	+	3736.38i	0.367203	+	0.376260i
$463$			105.508i			0.0105905i	0.999986	+	0.00529523i	$0.00168553\pi$
$463$			105.508i			0.0105905i	−0.999986	+	0.00529523i	$0.998314\pi$
$464$		−	927.377i		−	0.0927853i
$465$	591.529	+	606.119i	0.0589925	+	0.0604475i
$466$	−5554.13			−0.552125
$467$	−13047.9			−1.29290			−0.646452	−	0.762955i	$-0.723748\pi$
$467$	−13047.9			−1.29290			−0.646452	+	0.762955i	$0.723748\pi$
$468$	3765.57	+	91.7594i	0.371931	+	0.00906321i
$469$		−	108.960i		−	0.0107278i
$470$		−	5321.75i		−	0.522285i
$471$	4552.55	−	4442.96i	0.445372	−	0.434651i
$472$	−3355.02	+	1374.07i	−0.327177	+	0.133998i
$473$			13543.2i			1.31653i
$474$	3566.12	+	3654.08i	0.345564	+	0.354087i
$475$	27036.3			2.61160
$476$		−	333.089i		−	0.0320738i
$477$	−19327.9	−	470.982i	−1.85527	−	0.0452092i
$478$		−	950.333i		−	0.0909356i
$479$		−	9368.32i		−	0.893632i	−0.894626	−	0.446816i	$-0.852558\pi$
$479$		−	9368.32i		−	0.893632i	0.894626	−	0.446816i	$-0.147442\pi$
$480$	2208.93	−	2155.76i	0.210049	−	0.204993i
$481$	4335.67			0.410997
$482$	−1571.72			−0.148527
$483$	3181.89	+	3260.37i	0.299753	+	0.307147i
$484$	6433.12			0.604163
$485$	−15284.0			−1.43095
$486$	5021.02	+	5673.18i	0.468638	+	0.529508i
$487$	4407.08			0.410070			0.205035	−	0.978755i	$-0.434269\pi$
$487$	4407.08			0.410070			0.205035	+	0.978755i	$0.434269\pi$
$488$			4664.36i			0.432675i
$489$	−6207.88	−	6360.99i	−0.574090	−	0.588250i
$490$		−	9546.22i		−	0.880110i
$491$		−	17352.5i		−	1.59492i	−0.603369	−	0.797462i	$-0.706175\pi$
$491$		−	17352.5i		−	1.59492i	0.603369	−	0.797462i	$-0.293825\pi$
$492$	4702.69	−	4589.49i	0.430922	−	0.420550i
$493$	−520.870			−0.0475838
$494$			8588.89i			0.782252i
$495$	27164.1	+	661.934i	2.46653	+	0.0601045i
$496$			140.490i			0.0127181i
$497$		−	133.549i		−	0.0120533i
$498$	−7893.49	−	8088.18i	−0.710272	−	0.727791i
$499$	17240.5			1.54667			0.773337	−	0.633996i	$-0.218586\pi$
$499$	17240.5			1.54667			0.773337	+	0.633996i	$0.218586\pi$
$500$		−	7021.96i		−	0.628063i
$501$	10740.3	−	10481.8i	0.957766	−	0.934712i
$502$			1173.14i			0.104302i
$503$	3588.26			0.318077			0.159038	−	0.987272i	$-0.449161\pi$
$503$	3588.26			0.318077			0.159038	+	0.987272i	$0.449161\pi$
$504$	−48.7587	+	2000.93i	−0.00430930	+	0.176842i
$505$		−	24467.7i		−	2.15604i
$506$	10259.3			0.901345
$507$	−3558.85	−	3646.62i	−0.311743	−	0.319433i
$508$	−223.171			−0.0194914
$509$	−9092.54			−0.791787			−0.395893	−	0.918296i	$-0.629565\pi$
$509$	−9092.54			−0.791787			−0.395893	+	0.918296i	$0.629565\pi$
$510$	−1210.81	−	1240.67i	−0.105128	−	0.107721i
$511$		−	10580.4i		−	0.915950i
$512$	512.000			0.0441942
$513$	−12653.4	+	11760.8i	−1.08901	+	1.01219i
$514$			15298.5i			1.31282i
$515$	23086.0			1.97532
$516$	−3715.82	+	3626.37i	−0.317015	+	0.309384i
$517$	7771.51			0.661104
$518$			2303.87i			0.195417i
$519$	−7868.09	−	8062.15i	−0.665454	−	0.681867i
$520$	5179.23			0.436778
$521$		−	12937.2i		−	1.08789i	−0.839121	−	0.543944i	$-0.816930\pi$
$521$		−	12937.2i		−	1.08789i	0.839121	−	0.543944i	$-0.183070\pi$
$522$	3128.97	+	76.2467i	0.262359	+	0.00639316i
$523$	1999.10			0.167141			0.0835704	−	0.996502i	$-0.473368\pi$
$523$	1999.10			0.167141			0.0835704	+	0.996502i	$0.473368\pi$
$524$	−2558.11			−0.213266
$525$	7384.04	+	7566.17i	0.613840	+	0.628980i
$526$		−	8125.25i		−	0.673532i
$527$	78.9075			0.00652232
$528$	3148.13	+	3225.77i	0.259478	+	0.265878i
$529$	−3214.75			−0.264219
$530$	−26583.9			−2.17874
$531$	−4360.28	−	11432.8i	−0.356347	−	0.934354i
$532$	−4563.92			−0.371938
$533$	11026.3			0.896063
$534$	−9556.46	−	9792.17i	−0.774435	−	0.793536i
$535$	−4494.54			−0.363208
$536$		−	94.0701i		−	0.00758061i
$537$	−12203.8	−	12504.8i	−0.980693	−	1.00488i
$538$	−11145.6			−0.893161
$539$	13940.6			1.11404
$540$	7091.93	+	7630.18i	0.565163	+	0.608057i
$541$			9649.39i			0.766839i	0.923574	+	0.383419i	$0.125254\pi$
$541$			9649.39i			0.766839i	−0.923574	+	0.383419i	$0.874746\pi$
$542$	6093.96			0.482948
$543$	15737.8	+	16126.0i	1.24378	+	1.27446i
$544$		−	287.570i		−	0.0226644i
$545$	3284.26			0.258133
$546$	−2403.62	+	2345.77i	−0.188399	+	0.183864i
$547$	−4789.64			−0.374388			−0.187194	−	0.982323i	$-0.559939\pi$
$547$	−4789.64			−0.374388			−0.187194	+	0.982323i	$0.559939\pi$
$548$		−	3276.65i		−	0.255423i
$549$	−15737.5	−	383.492i	−1.22343	−	0.0298125i
$550$	23808.2			1.84579
$551$			7136.87i			0.551798i
$552$	2747.06	+	2814.81i	0.211816	+	0.217041i
$553$	−4552.63			−0.350086
$554$	11856.0			0.909228
$555$	8374.74	+	8581.30i	0.640519	+	0.656317i
$556$	−5316.58			−0.405527
$557$		−	10922.6i		−	0.830893i	−0.909618	−	0.415446i	$-0.863625\pi$
$557$		−	10922.6i		−	0.830893i	0.909618	−	0.415446i	$-0.136375\pi$
$558$	−474.012	−	11.5507i	−0.0359616	−	0.000876311i
$559$	−8712.38			−0.659203
$560$			2752.12i			0.207675i
$561$	1811.79	−	1768.18i	0.136352	−	0.133070i
$562$		−	15369.1i		−	1.15357i
$563$	−6376.23			−0.477311			−0.238655	−	0.971104i	$-0.576707\pi$
$563$	−6376.23			−0.477311			−0.238655	+	0.971104i	$0.576707\pi$
$564$	2080.92	+	2132.25i	0.155359	+	0.159191i
$565$			36591.7i			2.72464i
$566$		−	8070.53i		−	0.599346i
$567$	−6747.13	−	329.024i	−0.499740	−	0.0243698i
$568$		−	115.299i		−	0.00851730i
$569$	−2322.37			−0.171105			−0.0855526	−	0.996334i	$-0.527266\pi$
$569$	−2322.37			−0.171105			−0.0855526	+	0.996334i	$0.527266\pi$
$570$	−16999.4	+	16590.2i	−1.24917	+	1.21910i
$571$		−	4310.97i		−	0.315952i	−0.987443	−	0.157976i	$-0.949503\pi$
$571$		−	4310.97i		−	0.315952i	0.987443	−	0.157976i	$-0.0504969\pi$
$572$			7563.39i			0.552869i
$573$	−10530.6	−	10790.4i	−0.767756	−	0.786692i
$574$			5859.10i			0.426052i
$575$	20775.0			1.50674
$576$	−42.0954	+	1727.49i	−0.00304510	+	0.124963i
$577$	−12321.9			−0.889024			−0.444512	−	0.895773i	$-0.646623\pi$
$577$	−12321.9			−0.889024			−0.444512	+	0.895773i	$0.646623\pi$
$578$	9664.48			0.695484
$579$	−6326.75	−	6482.79i	−0.454112	−	0.465312i
$580$	4303.64			0.308102
$581$	10077.1			0.719566
$582$	6123.79	−	5976.38i	0.436150	−	0.425651i
$583$		−	38821.3i		−	2.75783i
$584$		−	9134.52i		−	0.647242i
$585$	−425.824	+	17474.7i	−0.0300951	+	1.23503i
$586$			5479.00i			0.386238i
$587$	−15221.7			−1.07030			−0.535150	−	0.844757i	$-0.679745\pi$
$587$	−15221.7			−1.07030			−0.535150	+	0.844757i	$0.679745\pi$
$588$	3732.79	+	3824.86i	0.261799	+	0.268256i
$589$		−	1081.18i		−	0.0756351i
$590$	−6376.61	−	15569.5i	−0.444951	−	1.08642i
$591$	11001.9	−	10737.1i	0.765751	−	0.747319i
$592$			1989.03i			0.138089i
$593$			3062.08i			0.212048i	0.994364	+	0.106024i	$0.0338121\pi$
$593$			3062.08i			0.212048i	−0.994364	+	0.106024i	$0.966188\pi$
$594$	−11142.6	+	10356.6i	−0.769673	+	0.715378i
$595$	1545.75			0.106504
$596$	−12538.0			−0.861705
$597$	4742.44	+	4859.41i	0.325117	+	0.333136i
$598$			6599.82i			0.451315i
$599$			16143.3i			1.10117i	0.834780	+	0.550583i	$0.185595\pi$
$599$			16143.3i			1.10117i	−0.834780	+	0.550583i	$0.814405\pi$
$600$	6374.95	+	6532.19i	0.433760	+	0.444459i
$601$			18045.1i			1.22475i	0.790568	+	0.612375i	$0.209786\pi$
$601$			18045.1i			1.22475i	−0.790568	+	0.612375i	$0.790214\pi$
$602$		−	4629.54i		−	0.313432i
$603$	317.392	+	7.73422i	0.0214348	+	0.000522324i
$604$			3886.61i			0.261828i
$605$			29853.9i			2.00617i
$606$	9567.42	+	9803.40i	0.641337	+	0.657155i
$607$	−5069.05			−0.338956			−0.169478	−	0.985534i	$-0.554208\pi$
$607$	−5069.05			−0.338956			−0.169478	+	0.985534i	$0.554208\pi$
$608$	−3940.23			−0.262824
$609$	−1997.27	+	1949.19i	−0.132896	+	0.129697i
$610$	−21645.7			−1.43673
$611$			4999.43i			0.331024i
$612$	970.260	+	23.6433i	0.0640857	+	0.00156164i
$613$			11631.3i			0.766368i	0.923672	+	0.383184i	$0.125173\pi$
$613$			11631.3i			0.766368i	−0.923672	+	0.383184i	$0.874827\pi$
$614$	−7093.04			−0.466208
$615$	21298.3	+	21823.6i	1.39647	+	1.43091i
$616$	−4019.00			−0.262873
$617$			14745.1i			0.962102i	0.876693	+	0.481051i	$0.159745\pi$
$617$			14745.1i			0.962102i	−0.876693	+	0.481051i	$0.840255\pi$
$618$	−9249.79	+	9027.13i	−0.602073	+	0.587580i
$619$	17357.2			1.12705			0.563526	−	0.826098i	$-0.309445\pi$
$619$	17357.2			1.12705			0.563526	+	0.826098i	$0.309445\pi$
$620$	−651.965			−0.0422315
$621$	−9723.03	+	9037.14i	−0.628296	+	0.583974i
$622$			17235.7i			1.11107i
$623$	12200.1			0.784568
$624$	−2075.15	+	2025.20i	−0.133129	+	0.129924i
$625$	5140.11			0.328967
$626$		−	5011.37i		−	0.319960i
$627$	−24227.2	−	24824.8i	−1.54313	−	1.58119i
$628$			4896.90i			0.311158i
$629$	1117.16			0.0708170
$630$	−9285.63	−	226.272i	−0.587220	−	0.0143094i
$631$	21200.9			1.33755			0.668777	−	0.743463i	$-0.266818\pi$
$631$	21200.9			1.33755			0.668777	+	0.743463i	$0.266818\pi$
$632$	−3930.47			−0.247383
$633$	20768.3	−	20268.4i	1.30406	−	1.27267i
$634$		−	14386.8i		−	0.901216i
$635$		−	1035.66i		−	0.0647228i
$636$	10651.3	−	10394.9i	0.664075	−	0.648090i
$637$			8968.04i			0.557813i
$638$			6284.73i			0.389992i
$639$	389.018	+	9.47959i	0.0240834	+	0.000586865i
$640$			2376.02i			0.146750i
$641$			5493.48i			0.338501i	0.985573	+	0.169251i	$0.0541347\pi$
$641$			5493.48i			0.338501i	−0.985573	+	0.169251i	$0.945865\pi$
$642$	1800.82	−	1757.47i	0.110705	−	0.108040i
$643$	−9544.92			−0.585404			−0.292702	−	0.956204i	$-0.594554\pi$
$643$	−9544.92			−0.585404			−0.292702	+	0.956204i	$0.594554\pi$
$644$	−3506.98			−0.214588
$645$	−16828.8	−	17243.8i	−1.02734	−	1.05267i
$646$			2213.07i			0.134786i
$647$			5450.32i			0.331181i	0.986195	+	0.165591i	$0.0529530\pi$
$647$			5450.32i			0.331181i	−0.986195	+	0.165591i	$0.947047\pi$
$648$	−5825.08	−	284.060i	−0.353134	−	0.0172206i
$649$	22736.6	−	9311.95i	1.37518	−	0.563214i
$650$			15315.9i			0.924211i
$651$	302.570	−	295.287i	0.0182160	−	0.0177776i
$652$	6842.13			0.410980
$653$		−	15164.0i		−	0.908749i	−0.890811	−	0.454375i	$-0.849863\pi$
$653$		−	15164.0i		−	0.908749i	0.890811	−	0.454375i	$-0.150137\pi$
$654$	−1315.90	+	1284.22i	−0.0786784	+	0.0767845i
$655$		−	11871.3i		−	0.708169i
$656$			5058.40i			0.301063i
$657$	30819.9	+	751.019i	1.83013	+	0.0445967i
$658$	−2656.58			−0.157392
$659$	−17606.1			−1.04072			−0.520360	−	0.853947i	$-0.674202\pi$
$659$	−17606.1			−1.04072			−0.520360	+	0.853947i	$0.674202\pi$
$660$	−14969.7	+	14609.4i	−0.882871	+	0.861620i
$661$	−8936.66			−0.525863			−0.262932	−	0.964814i	$-0.584689\pi$
$661$	−8936.66			−0.525863			−0.262932	+	0.964814i	$0.584689\pi$
$662$	−399.944			−0.0234808
$663$	1137.47	+	1165.53i	0.0666301	+	0.0682735i
$664$	8699.96			0.508470
$665$		−	21179.6i		−	1.23505i
$666$	−6710.97	−	163.533i	−0.390458	−	0.00951467i
$667$			5484.06i			0.318357i
$668$			11552.7i			0.669142i
$669$	−2271.38	−	2327.40i	−0.131266	−	0.134503i
$670$	436.547			0.0251721
$671$		−	31609.8i		−	1.81861i
$672$	−1076.14	−	1102.68i	−0.0617753	−	0.0632990i
$673$			19811.2i			1.13472i	0.823471	+	0.567358i	$0.192034\pi$
$673$			19811.2i			1.13472i	−0.823471	+	0.567358i	$0.807966\pi$
$674$		−	21061.3i		−	1.20363i
$675$	−22563.7	+	20972.0i	−1.28663	+	1.19587i
$676$	3922.45			0.223171
$677$		−	5564.20i		−	0.315878i	−0.987449	−	0.157939i	$-0.949515\pi$
$677$		−	5564.20i		−	0.315878i	0.987449	−	0.157939i	$-0.0504849\pi$
$678$	−14308.2	−	14661.1i	−0.810476	−	0.830466i
$679$			7629.64i			0.431221i
$680$	1334.51			0.0752592
$681$	3010.60	+	3084.86i	0.169408	+	0.173586i
$682$		−	952.084i		−	0.0534563i
$683$	11275.7			0.631703			0.315852	−	0.948809i	$-0.397710\pi$
$683$	11275.7			0.631703			0.315852	+	0.948809i	$0.397710\pi$
$684$	323.956	−	13294.3i	0.0181093	−	0.743159i
$685$	15205.8			0.848153
$686$	−11122.1			−0.619014
$687$	−3095.85	+	3021.33i	−0.171927	+	0.167789i
$688$		−	3996.88i		−	0.221482i
$689$	24973.8			1.38088
$690$	−13062.6	+	12748.1i	−0.720701	+	0.703353i
$691$			4333.14i			0.238553i	0.992861	+	0.119277i	$0.0380576\pi$
$691$			4333.14i			0.238553i	−0.992861	+	0.119277i	$0.961942\pi$
$692$	8671.97			0.476385
$693$	330.432	−	13560.1i	0.0181127	−	0.743298i
$694$	−17059.6			−0.933103
$695$		−	24672.4i		−	1.34659i
$696$	−1724.33	+	1682.82i	−0.0939087	+	0.0916482i
$697$	2841.10			0.154397
$698$		−	5337.19i		−	0.289421i
$699$	10078.5	+	10327.1i	0.545358	+	0.558810i
$700$	−8138.47			−0.439436
$701$	−16793.7			−0.904833			−0.452416	−	0.891807i	$-0.649438\pi$
$701$	−16793.7			−0.904833			−0.452416	+	0.891807i	$0.649438\pi$
$702$	−6662.40	−	7168.06i	−0.358199	−	0.385386i
$703$		−	15307.1i		−	0.821218i
$704$	−3469.77			−0.185755
$705$	−9895.04	+	9656.86i	−0.528608	+	0.515884i
$706$	−19032.5			−1.01458
$707$	−12214.1			−0.649728
$708$	8642.93	+	3744.79i	0.458787	+	0.198782i
$709$	−32248.4			−1.70820			−0.854101	−	0.520107i	$-0.825892\pi$
$709$	−32248.4			−1.70820			−0.854101	+	0.520107i	$0.825892\pi$
$710$	535.062			0.0282824
$711$	323.154	−	13261.4i	0.0170453	−	0.699496i
$712$	10532.8			0.554403
$713$		−	830.790i		−	0.0436372i
$714$	−619.333	+	604.424i	−0.0324621	+	0.0316807i
$715$	−35099.1			−1.83585
$716$	13450.6			0.702059
$717$	−1767.01	+	1724.48i	−0.0920366	+	0.0898211i
$718$			483.713i			0.0251421i
$719$	1625.41			0.0843081			0.0421540	−	0.999111i	$-0.486578\pi$
$719$	1625.41			0.0843081			0.0421540	+	0.999111i	$0.486578\pi$
$720$	−8016.68	−	195.350i	−0.414950	−	0.0101115i
$721$		−	11524.3i		−	0.595268i
$722$	16605.0			0.855921
$723$	2852.05	+	2922.39i	0.146706	+	0.150325i
$724$	−17345.7			−0.890400
$725$			12726.6i			0.651936i
$726$	−11673.6	−	11961.5i	−0.596758	−	0.611477i
$727$	−34310.7			−1.75036			−0.875181	−	0.483796i	$-0.839258\pi$
$727$	−34310.7			−1.75036			−0.875181	+	0.483796i	$0.839258\pi$
$728$		−	2585.43i		−	0.131624i
$729$	1437.34	−	19630.4i	0.0730245	−	0.997330i
$730$	42390.2			2.14922
$731$	−2244.89			−0.113584
$732$	8672.71	−	8463.95i	0.437914	−	0.427373i
$733$	−25140.2			−1.26682			−0.633408	−	0.773818i	$-0.718344\pi$
$733$	−25140.2			−1.26682			−0.633408	+	0.773818i	$0.718344\pi$
$734$			13158.0i			0.661675i
$735$	−17749.8	+	17322.6i	−0.890766	+	0.869324i
$736$	−3027.72			−0.151635
$737$			637.503i			0.0318626i
$738$	−17067.0	−	415.890i	−0.851282	−	0.0207441i
$739$			16873.5i			0.839919i	0.907543	+	0.419960i	$0.137956\pi$
$739$			16873.5i			0.839919i	−0.907543	+	0.419960i	$0.862044\pi$
$740$	−9230.38			−0.458535
$741$	15969.8	−	15585.4i	0.791723	−	0.772665i
$742$			13270.5i			0.656570i
$743$			26899.8i			1.32821i	0.747641	+	0.664103i	$0.231186\pi$
$743$			26899.8i			1.32821i	−0.747641	+	0.664103i	$0.768814\pi$
$744$	261.221	−	254.933i	0.0128721	−	0.0125622i
$745$		−	58184.5i		−	2.86136i
$746$	−17342.3			−0.851135
$747$	−715.290	+	29353.7i	−0.0350349	+	1.43774i
$748$			1948.83i			0.0952624i
$749$			2243.64i			0.109454i
$750$	−13056.3	+	12742.1i	−0.635667	+	0.620366i
$751$		−	29779.8i		−	1.44698i	−0.690337	−	0.723488i	$-0.742538\pi$
$751$		−	29779.8i		−	1.44698i	0.690337	−	0.723488i	$-0.257462\pi$
$752$	−2293.53			−0.111219
$753$	2181.29	−	2128.78i	0.105565	−	0.103024i
$754$	−4042.99			−0.195274
$755$	−18036.4			−0.869420
$756$	3808.93	−	3540.23i	0.183240	−	0.170314i
$757$	1790.21			0.0859527			0.0429764	−	0.999076i	$-0.486316\pi$
$757$	1790.21			0.0859527			0.0429764	+	0.999076i	$0.486316\pi$
$758$	12432.6			0.595743
$759$	−18616.5	−	19075.7i	−0.890298	−	0.912257i
$760$		−	18285.2i		−	0.872731i
$761$			28851.9i			1.37435i	0.726491	+	0.687176i	$0.241150\pi$
$761$			28851.9i			1.37435i	−0.726491	+	0.687176i	$0.758850\pi$
$762$	404.967	+	414.956i	0.0192525	+	0.0197274i
$763$		−	1639.48i		−	0.0777892i
$764$	11606.6			0.549621
$765$	−109.720	+	4502.64i	−0.00518556	+	0.212802i
$766$			9414.04i			0.444051i
$767$	5990.40	+	14626.5i	0.282009	+	0.688570i
$768$	−929.077	−	951.992i	−0.0436526	−	0.0447292i
$769$			20797.2i			0.975251i	0.873053	+	0.487625i	$0.162137\pi$
$769$			20797.2i			0.975251i	−0.873053	+	0.487625i	$0.837863\pi$
$770$		−	18650.8i		−	0.872893i
$771$	28445.5	−	27760.8i	1.32872	−	1.29673i
$772$	6973.15			0.325089
$773$	21837.2			1.01608			0.508040	−	0.861333i	$-0.330370\pi$
$773$	21837.2			1.01608			0.508040	+	0.861333i	$0.330370\pi$
$774$	13485.5	+	328.614i	0.626259	+	0.0152607i
$775$		−	1927.97i		−	0.0893609i
$776$			6586.99i			0.304715i
$777$	4283.72	−	4180.60i	0.197783	−	0.193022i
$778$			20133.3i			0.927779i
$779$		−	38928.2i		−	1.79043i
$780$	−9398.25	−	9630.05i	−0.431425	−	0.442066i
$781$			781.367i			0.0357996i
$782$			1700.55i			0.0777641i
$783$	−5536.06	−	5956.24i	−0.252673	−	0.271850i
$784$	−4114.17			−0.187416
$785$	−22724.8			−1.03323
$786$	4641.95	+	4756.45i	0.210653	+	0.215848i
$787$	−1115.20			−0.0505116			−0.0252558	−	0.999681i	$-0.508040\pi$
$787$	−1115.20			−0.0505116			−0.0252558	+	0.999681i	$0.508040\pi$
$788$			11834.1i			0.534991i
$789$	−15107.8	+	14744.1i	−0.681687	+	0.665278i
$790$		−	18240.0i		−	0.821454i
$791$	18266.3			0.821080
$792$	285.276	−	11707.0i	0.0127990	−	0.525240i
$793$	20334.7			0.910600
$794$			8438.82i			0.377182i
$795$	48239.2	+	49429.1i	2.15204	+	2.20512i
$796$	−5226.97			−0.232745
$797$	−13262.6			−0.589441			−0.294720	−	0.955584i	$-0.595227\pi$
$797$	−13262.6			−0.589441			−0.294720	+	0.955584i	$0.595227\pi$
$798$	8281.71	+	8485.98i	0.367380	+	0.376442i
$799$			1288.18i			0.0570372i
$800$	−7026.28			−0.310521
$801$	−865.985	+	35537.8i	−0.0381998	+	1.56762i
$802$	27413.7			1.20700
$803$			61903.7i			2.72046i
$804$	−174.910	+	170.700i	−0.00767239	+	0.00748771i
$805$		−	16274.7i		−	0.712556i
$806$	612.478			0.0267663
$807$	20224.8	+	20723.7i	0.882215	+	0.903975i
$808$	−10544.9			−0.459120
$809$	−18244.0			−0.792860			−0.396430	−	0.918065i	$-0.629751\pi$
$809$	−18244.0			−0.792860			−0.396430	+	0.918065i	$0.629751\pi$
$810$	1318.22	−	27032.2i	0.0571823	−	1.17261i
$811$		−	43932.9i		−	1.90221i	−0.308867	−	0.951105i	$-0.599950\pi$
$811$		−	43932.9i		−	1.90221i	0.308867	−	0.951105i	$-0.400050\pi$
$812$		−	2148.34i		−	0.0928474i
$813$	−11058.1	−	11330.9i	−0.477030	−	0.488795i
$814$		−	13479.4i		−	0.580409i
$815$			31752.0i			1.36469i
$816$	−534.696	+	521.825i	−0.0229388	+	0.0223867i
$817$			30759.0i			1.31716i
$818$			6504.91i			0.278043i
$819$	8723.24	+	212.568i	0.372179	+	0.00906927i
$820$	−23474.3			−0.999705
$821$	2657.07			0.112950			0.0564752	−	0.998404i	$-0.482014\pi$
$821$	2657.07			0.112950			0.0564752	+	0.998404i	$0.482014\pi$
$822$	−6092.48	+	5945.83i	−0.258515	+	0.252293i
$823$		−	40814.8i		−	1.72869i	−0.502896	−	0.864347i	$-0.667732\pi$
$823$		−	40814.8i		−	1.72869i	0.502896	−	0.864347i	$-0.332268\pi$
$824$		−	9949.43i		−	0.420637i
$825$	−43202.4	−	44267.9i	−1.82317	−	1.86814i
$826$	−7772.18	+	3183.15i	−0.327395	+	0.134087i
$827$			32408.0i			1.36268i	0.731967	+	0.681340i	$0.238602\pi$
$827$			32408.0i			1.36268i	−0.731967	+	0.681340i	$0.761398\pi$
$828$	248.932	−	10215.5i	0.0104481	−	0.428761i
$829$	2127.63			0.0891381			0.0445691	−	0.999006i	$-0.485809\pi$
$829$	2127.63			0.0891381			0.0445691	+	0.999006i	$0.485809\pi$
$830$			40373.5i			1.68842i
$831$	−21513.9	−	22044.5i	−0.898085	−	0.920236i
$832$		−	2232.11i		−	0.0930103i
$833$			2310.76i			0.0961142i
$834$	9647.47	+	9885.42i	0.400557	+	0.410437i
$835$	−53612.0			−2.22194
$836$	26702.5			1.10469
$837$	838.667	+	902.320i	0.0346339	+	0.0372625i
$838$	−5019.71			−0.206925
$839$	−30752.1			−1.26541			−0.632705	−	0.774393i	$-0.718056\pi$
$839$	−30752.1			−1.26541			−0.632705	+	0.774393i	$0.718056\pi$
$840$	5117.17	−	4994.00i	0.210190	−	0.205130i
$841$	21029.5			0.862254
$842$			13205.0i			0.540469i
$843$	−28576.6	+	27888.7i	−1.16753	+	1.13943i
$844$			22339.2i			0.911076i
$845$			18202.8i			0.741058i
$846$	188.569	−	7738.37i	0.00766327	−	0.314481i
$847$	14902.8			0.604566
$848$			11457.0i			0.463955i
$849$	−15006.0	+	14644.8i	−0.606602	+	0.592001i
$850$			3946.38i			0.159247i
$851$		−	11762.1i		−	0.473797i
$852$	−214.382	+	209.221i	−0.00862042	+	0.00841292i
$853$	−30954.1			−1.24250			−0.621248	−	0.783614i	$-0.713374\pi$
$853$	−30954.1			−1.24250			−0.621248	+	0.783614i	$0.713374\pi$
$854$			10805.4i			0.432964i
$855$	61694.4	+	1503.37i	2.46772	+	0.0601335i
$856$			1937.03i			0.0773438i
$857$	−4717.24			−0.188026			−0.0940128	−	0.995571i	$-0.529969\pi$
$857$	−4717.24			−0.188026			−0.0940128	+	0.995571i	$0.529969\pi$
$858$	14063.1	−	13724.5i	0.559563	−	0.546093i
$859$			30456.2i			1.20972i	0.796330	+	0.604862i	$0.206772\pi$
$859$			30456.2i			1.20972i	−0.796330	+	0.604862i	$0.793228\pi$
$860$	18548.1			0.735449
$861$	10894.2	−	10631.9i	0.431210	−	0.420831i
$862$	−6177.42			−0.244088
$863$	−29368.5			−1.15842			−0.579210	−	0.815178i	$-0.696639\pi$
$863$	−29368.5			−1.15842			−0.579210	+	0.815178i	$0.696639\pi$
$864$	3288.41	−	3056.43i	0.129484	−	0.120349i
$865$			40243.6i			1.58188i
$866$	19463.4			0.763735
$867$	−17537.2	−	17969.7i	−0.686960	−	0.703904i
$868$			325.456i			0.0127266i
$869$	26636.4			1.03979
$870$	−7809.39	−	8002.01i	−0.304326	−	0.311832i
$871$	−410.107			−0.0159540
$872$		−	1415.43i		−	0.0549685i
$873$	−22224.5	−	541.567i	−0.861609	−	0.0209957i
$874$	23300.6			0.901779
$875$		−	16266.9i		−	0.628483i
$876$	−16984.4	+	16575.5i	−0.655078	+	0.639309i
$877$	24310.7			0.936049			0.468024	−	0.883716i	$-0.344966\pi$
$877$	24310.7			0.936049			0.468024	+	0.883716i	$0.344966\pi$
$878$	9314.67			0.358035
$879$	10187.4	−	9942.21i	0.390914	−	0.381505i
$880$		−	16102.0i		−	0.616817i
$881$	25157.2			0.962053			0.481026	−	0.876706i	$-0.340264\pi$
$881$	25157.2			0.962053			0.481026	+	0.876706i	$0.340264\pi$
$882$	338.257	−	13881.2i	0.0129135	−	0.529936i
$883$	20299.3			0.773642			0.386821	−	0.922155i	$-0.373573\pi$
$883$	20299.3			0.773642			0.386821	+	0.922155i	$0.373573\pi$
$884$	−1253.69			−0.0476992
$885$	−17378.3	+	40108.9i	−0.660074	+	1.52344i
$886$	−36581.3			−1.38710
$887$	−4627.33			−0.175164			−0.0875820	−	0.996157i	$-0.527914\pi$
$887$	−4627.33			−0.175164			−0.0875820	+	0.996157i	$0.527914\pi$
$888$	3698.31	−	3609.29i	0.139760	−	0.136396i
$889$	−516.994			−0.0195044
$890$			48879.3i			1.84094i
$891$	39475.9	+	1925.04i	1.48428	+	0.0723809i
$892$	2503.45			0.0939704
$893$	17650.5			0.661422
$894$	22751.5	+	23312.6i	0.851144	+	0.872138i
$895$			62419.8i			2.33125i
$896$	1186.09			0.0442237
$897$	12271.4	−	11976.0i	0.456780	−	0.445784i
$898$			9325.45i			0.346542i
$899$	508.934			0.0188809
$900$	577.684	−	23706.7i	0.0213957	−	0.878024i
$901$	6434.91			0.237933
$902$		−	34280.2i		−	1.26542i
$903$	−8607.98	+	8400.78i	−0.317227	+	0.309591i
$904$	15770.0			0.580204
$905$		−	80495.7i		−	2.95665i
$906$	7226.60	−	7052.65i	0.264998	−	0.258619i
$907$	49579.7			1.81507			0.907534	−	0.419979i	$-0.137962\pi$
$907$	49579.7			1.81507			0.907534	+	0.419979i	$0.137962\pi$
$908$	−3318.20			−0.121276
$909$	866.979	−	35578.6i	0.0316346	−	1.29820i
$910$	11998.1			0.437070
$911$			17991.4i			0.654317i	0.944970	+	0.327158i	$0.106091\pi$
$911$			17991.4i			0.654317i	−0.944970	+	0.327158i	$0.893909\pi$
$912$	7149.95	+	7326.30i	0.259603	+	0.266007i
$913$	−58958.7			−2.13718
$914$		−	10317.7i		−	0.373391i
$915$	39278.3	+	40247.1i	1.41913	+	1.45413i
$916$		−	3330.02i		−	0.120117i
$917$	−5926.07			−0.213409
$918$	−1716.67	−	1846.97i	−0.0617197	−	0.0664041i
$919$		−	45993.3i		−	1.65090i	−0.564474	−	0.825451i	$-0.690921\pi$
$919$		−	45993.3i		−	1.65090i	0.564474	−	0.825451i	$-0.309079\pi$
$920$		−	14050.6i		−	0.503517i
$921$	12871.0	+	13188.5i	0.460494	+	0.471852i
$922$		−	35617.1i		−	1.27222i
$923$	−502.655			−0.0179254
$924$	7292.88	+	7472.76i	0.259652	+	0.266056i
$925$		−	27295.8i		−	0.970249i
$926$			211.016i			0.00748859i
$927$	33569.4	+	818.019i	1.18939	+	0.0289830i
$928$		−	1854.75i		−	0.0656091i
$929$	−33346.9			−1.17769			−0.588847	−	0.808245i	$-0.700418\pi$
$929$	−33346.9			−1.17769			−0.588847	+	0.808245i	$0.700418\pi$
$930$	1183.06	+	1212.24i	0.0417140	+	0.0427428i
$931$	31661.6			1.11457
$932$	−11108.3			−0.390411
$933$	32047.4	−	31275.9i	1.12453	−	1.09746i
$934$	−26095.9			−0.914221
$935$	−9043.85			−0.316327
$936$	7531.14	+	183.519i	0.262995	+	0.00640866i
$937$		−	49726.7i		−	1.73372i	−0.498548	−	0.866862i	$-0.666133\pi$
$937$		−	49726.7i		−	1.73372i	0.498548	−	0.866862i	$-0.333867\pi$
$938$		−	217.921i		−	0.00758568i
$939$	−9317.94	+	9093.65i	−0.323833	+	0.316038i
$940$		−	10643.5i		−	0.369311i
$941$	−6382.16			−0.221097			−0.110549	−	0.993871i	$-0.535261\pi$
$941$	−6382.16			−0.221097			−0.110549	+	0.993871i	$0.535261\pi$
$942$	9105.09	−	8885.92i	0.314926	−	0.307345i
$943$		−	29913.0i		−	1.03298i
$944$	−6710.04	+	2748.15i	−0.231349	+	0.0947507i
$945$	16429.0	+	17675.9i	0.565541	+	0.608463i
$946$			27086.4i			0.930925i
$947$		−	22052.6i		−	0.756719i	−0.925659	−	0.378360i	$-0.876488\pi$
$947$		−	22052.6i		−	0.756719i	0.925659	−	0.378360i	$-0.123512\pi$
$948$	7132.24	+	7308.16i	0.244351	+	0.250378i
$949$	−39822.8			−1.36217
$950$	54072.5			1.84668
$951$	−26750.2	+	26106.2i	−0.912127	+	0.890172i
$952$		−	666.178i		−	0.0226796i
$953$		−	34248.4i		−	1.16413i	−0.813143	−	0.582064i	$-0.802245\pi$
$953$		−	34248.4i		−	1.16413i	0.813143	−	0.582064i	$-0.197755\pi$
$954$	−38655.8	−	941.964i	−1.31187	−	0.0319677i
$955$			53862.1i			1.82506i
$956$		−	1900.67i		−	0.0643012i
$957$	11685.6	−	11404.3i	0.394714	−	0.385213i
$958$		−	18736.6i		−	0.631893i
$959$		−	7590.63i		−	0.255594i
$960$	4417.87	−	4311.53i	0.148527	−	0.144952i
$961$	29713.9			0.997412
$962$	8671.34			0.290619
$963$	−6535.53	−	159.258i	−0.218696	−	0.00532919i
$964$	−3143.44			−0.105024
$965$			32360.0i			1.07949i
$966$	6363.78	+	6520.74i	0.211958	+	0.217186i
$967$			20182.5i			0.671174i	0.942009	+	0.335587i	$0.108935\pi$
$967$			20182.5i			0.671174i	−0.942009	+	0.335587i	$0.891065\pi$
$968$	12866.2			0.427207
$969$	4114.89	−	4015.84i	0.136418	−	0.133134i
$970$	−30568.0			−1.01183
$971$		−	19734.5i		−	0.652225i	−0.945331	−	0.326113i	$-0.894261\pi$
$971$		−	19734.5i		−	0.652225i	0.945331	−	0.326113i	$-0.105739\pi$
$972$	10042.0	+	11346.4i	0.331377	+	0.374419i
$973$	−12316.3			−0.405798
$974$	8814.16			0.289963
$975$	28477.7	−	27792.2i	0.935401	−	0.912884i
$976$			9328.71i			0.305948i
$977$	−10161.6			−0.332752			−0.166376	−	0.986062i	$-0.553207\pi$
$977$	−10161.6			−0.332752			−0.166376	+	0.986062i	$0.553207\pi$
$978$	−12415.8	−	12722.0i	−0.405943	−	0.415955i
$979$	−71379.9			−2.33025
$980$		−	19092.4i		−	0.622332i
$981$	4775.66	+	116.373i	0.155428	+	0.00378748i
$982$		−	34705.0i		−	1.12778i
$983$	−36440.4			−1.18237			−0.591184	−	0.806537i	$-0.701339\pi$
$983$	−36440.4			−1.18237			−0.591184	+	0.806537i	$0.701339\pi$
$984$	9405.39	−	9178.99i	0.304708	−	0.297373i
$985$	−54918.0			−1.77648
$986$	−1041.74			−0.0336468
$987$	4820.63	+	4939.53i	0.155463	+	0.159298i
$988$			17177.8i			0.553136i
$989$			23635.6i			0.759928i
$990$	54328.1	+	1323.87i	1.74410	+	0.0425003i
$991$		−	20201.3i		−	0.647544i	−0.946135	−	0.323772i	$-0.895049\pi$
$991$		−	20201.3i		−	0.647544i	0.946135	−	0.323772i	$-0.104951\pi$
$992$			280.980i			0.00899306i
$993$	725.740	+	743.640i	0.0231930	+	0.0237651i
$994$		−	267.099i		−	0.00852299i
$995$		−	24256.6i		−	0.772849i
$996$	−15787.0	−	16176.4i	−0.502238	−	0.514626i
$997$	37363.4			1.18687			0.593436	−	0.804881i	$-0.297771\pi$
$997$	37363.4			1.18687			0.593436	+	0.804881i	$0.297771\pi$
$998$	34481.0			1.09366
$999$	11873.7	+	12774.8i	0.376042	+	0.404583i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.4.c.b.353.7	yes	30
3.2	odd	2		354.4.c.a.353.8	yes	30
59.58	odd	2		354.4.c.a.353.7	✓	30
177.176	even	2	inner	354.4.c.b.353.8	yes	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.4.c.a.353.7	✓	30	59.58	odd	2
354.4.c.a.353.8	yes	30	3.2	odd	2
354.4.c.b.353.7	yes	30	1.1	even	1	trivial
354.4.c.b.353.8	yes	30	177.176	even	2	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:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	354.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +(-3.62921 - 3.71872i) q^{3} +4.00000 q^{4} +18.5626i q^{5} +(-7.25841 - 7.43744i) q^{6} +9.26632 q^{7} +8.00000 q^{8} +(-0.657741 + 26.9920i) q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +(-3.62921 - 3.71872i) q^{3} +4.00000 q^{4} +18.5626i q^{5} +(-7.25841 - 7.43744i) q^{6} +9.26632 q^{7} +8.00000 q^{8} +(-0.657741 + 26.9920i) q^{9} +37.1253i q^{10} -54.2151 q^{11} +(-14.5168 - 14.8749i) q^{12} -34.8767i q^{13} +18.5326 q^{14} +(69.0292 - 67.3676i) q^{15} +16.0000 q^{16} -8.98656i q^{17} +(-1.31548 + 53.9840i) q^{18} -123.132 q^{19} +74.2505i q^{20} +(-33.6294 - 34.4588i) q^{21} -108.430 q^{22} -94.6163 q^{23} +(-29.0336 - 29.7498i) q^{24} -219.571 q^{25} -69.7535i q^{26} +(102.763 - 95.5135i) q^{27} +37.0653 q^{28} -57.9611i q^{29} +(138.058 - 134.735i) q^{30} +8.78061i q^{31} +32.0000 q^{32} +(196.758 + 201.611i) q^{33} -17.9731i q^{34} +172.007i q^{35} +(-2.63096 + 107.968i) q^{36} +124.314i q^{37} -246.264 q^{38} +(-129.697 + 126.575i) q^{39} +148.501i q^{40} +316.150i q^{41} +(-67.2587 - 68.9177i) q^{42} -249.805i q^{43} -216.861 q^{44} +(-501.042 - 12.2094i) q^{45} -189.233 q^{46} -143.346 q^{47} +(-58.0673 - 59.4995i) q^{48} -257.135 q^{49} -439.142 q^{50} +(-33.4185 + 32.6141i) q^{51} -139.507i q^{52} +716.060i q^{53} +(205.525 - 191.027i) q^{54} -1006.38i q^{55} +74.1306 q^{56} +(446.872 + 457.894i) q^{57} -115.922i q^{58} +(-419.378 + 171.759i) q^{59} +(276.117 - 269.470i) q^{60} +583.044i q^{61} +17.5612i q^{62} +(-6.09484 + 250.116i) q^{63} +64.0000 q^{64} +647.404 q^{65} +(393.516 + 403.222i) q^{66} -11.7588i q^{67} -35.9462i q^{68} +(343.382 + 351.852i) q^{69} +344.014i q^{70} -14.4123i q^{71} +(-5.26193 + 215.936i) q^{72} -1141.82i q^{73} +248.628i q^{74} +(796.869 + 816.524i) q^{75} -492.528 q^{76} -502.375 q^{77} +(-259.394 + 253.150i) q^{78} -491.309 q^{79} +297.002i q^{80} +(-728.135 - 35.5075i) q^{81} +632.300i q^{82} +1087.50 q^{83} +(-134.517 - 137.835i) q^{84} +166.814 q^{85} -499.610i q^{86} +(-215.541 + 210.353i) q^{87} -433.721 q^{88} +1316.60 q^{89} +(-1002.08 - 24.4188i) q^{90} -323.179i q^{91} -378.465 q^{92} +(32.6526 - 31.8666i) q^{93} -286.692 q^{94} -2285.66i q^{95} +(-116.135 - 118.999i) q^{96} +823.374i q^{97} -514.271 q^{98} +(35.6595 - 1463.37i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 60 q^{2} + 5 q^{3} + 120 q^{4} + 10 q^{6} + 6 q^{7} + 240 q^{8} + 27 q^{9}+O(q^{10}) \) 30 * q + 60 * q^2 + 5 * q^3 + 120 * q^4 + 10 * q^6 + 6 * q^7 + 240 * q^8 + 27 * q^9	\( 30 q + 60 q^{2} + 5 q^{3} + 120 q^{4} + 10 q^{6} + 6 q^{7} + 240 q^{8} + 27 q^{9} + 60 q^{11} + 20 q^{12} + 12 q^{14} + 20 q^{15} + 480 q^{16} + 54 q^{18} + 90 q^{19} + 132 q^{21} + 120 q^{22} - 24 q^{23} + 40 q^{24} - 1080 q^{25} - 55 q^{27} + 24 q^{28} + 40 q^{30} + 960 q^{32} - 336 q^{33} + 108 q^{36} + 180 q^{38} - 652 q^{39} + 264 q^{42} + 240 q^{44} - 878 q^{45} - 48 q^{46} - 792 q^{47} + 80 q^{48} + 2016 q^{49} - 2160 q^{50} + 650 q^{51} - 110 q^{54} + 48 q^{56} + 846 q^{57} + 480 q^{59} + 80 q^{60} + 887 q^{63} + 1920 q^{64} + 1416 q^{65} - 672 q^{66} + 590 q^{69} + 216 q^{72} - 952 q^{75} + 360 q^{76} - 864 q^{77} - 1304 q^{78} + 738 q^{79} - 1217 q^{81} - 876 q^{83} + 528 q^{84} + 1176 q^{85} + 534 q^{87} + 480 q^{88} + 300 q^{89} - 1756 q^{90} - 96 q^{92} - 1684 q^{93} - 1584 q^{94} + 160 q^{96} + 4032 q^{98} - 730 q^{99}+O(q^{100}) \) 30 * q + 60 * q^2 + 5 * q^3 + 120 * q^4 + 10 * q^6 + 6 * q^7 + 240 * q^8 + 27 * q^9 + 60 * q^11 + 20 * q^12 + 12 * q^14 + 20 * q^15 + 480 * q^16 + 54 * q^18 + 90 * q^19 + 132 * q^21 + 120 * q^22 - 24 * q^23 + 40 * q^24 - 1080 * q^25 - 55 * q^27 + 24 * q^28 + 40 * q^30 + 960 * q^32 - 336 * q^33 + 108 * q^36 + 180 * q^38 - 652 * q^39 + 264 * q^42 + 240 * q^44 - 878 * q^45 - 48 * q^46 - 792 * q^47 + 80 * q^48 + 2016 * q^49 - 2160 * q^50 + 650 * q^51 - 110 * q^54 + 48 * q^56 + 846 * q^57 + 480 * q^59 + 80 * q^60 + 887 * q^63 + 1920 * q^64 + 1416 * q^65 - 672 * q^66 + 590 * q^69 + 216 * q^72 - 952 * q^75 + 360 * q^76 - 864 * q^77 - 1304 * q^78 + 738 * q^79 - 1217 * q^81 - 876 * q^83 + 528 * q^84 + 1176 * q^85 + 534 * q^87 + 480 * q^88 + 300 * q^89 - 1756 * q^90 - 96 * q^92 - 1684 * q^93 - 1584 * q^94 + 160 * q^96 + 4032 * q^98 - 730 * q^99

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