LMFDB - Embedded newform 354.4.c.a.353.8

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			353.8
Character	$\chi$	$=$	354.353
Dual form			354.4.c.a.353.7

$q$-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	$-0.688257\pi$
$5$		−	18.5626i		−	1.66029i	0.557546	−	0.830146i	$-0.311743\pi$
$6$	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	$-0.233392\pi$
$11$	54.2151			1.48604			0.743022	+	0.669267i	$0.233392\pi$
$12$	−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	$0.0204192\pi$
$17$			8.98656i			0.128209i	−0.997943	+	0.0641047i	$0.979581\pi$
$18$	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	$-0.358905\pi$
$23$	94.6163			0.857777			0.428888	+	0.903357i	$0.358905\pi$
$24$	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	$0.0594134\pi$
$29$			57.9611i			0.371141i	−0.982631	+	0.185571i	$0.940587\pi$
$30$	−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	$-0.794320\pi$
$41$		−	316.150i		−	1.20425i	0.798401	−	0.602126i	$-0.205680\pi$
$42$	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	$-0.428599\pi$
$47$	143.346			0.444875			0.222438	+	0.974947i	$0.428599\pi$
$48$	−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	$-0.621604\pi$
$53$		−	716.060i		−	1.85582i	0.372805	−	0.927910i	$-0.378396\pi$
$54$	−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	$0.00383423\pi$
$71$			14.4123i			0.0240906i	−0.999927	+	0.0120453i	$0.996166\pi$
$72$	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	$-0.755439\pi$
$83$	−1087.50			−1.43817			−0.719085	+	0.694922i	$0.755439\pi$
$84$	−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	$-0.786846\pi$
$89$	−1316.60			−1.56809			−0.784044	+	0.620705i	$0.786846\pi$
$90$	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	$-0.275064\pi$
$101$	1318.12			1.29859			0.649294	+	0.760537i	$0.275064\pi$
$102$	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	$-0.965113\pi$
$107$		−	242.129i		−	0.218761i	0.994000	−	0.109381i	$-0.0348867\pi$
$108$	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	$-0.806323\pi$
$113$	−1971.26			−1.64106			−0.820532	+	0.571601i	$0.806323\pi$
$114$	−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	$-0.431590\pi$
$131$	639.528			0.426533			0.213266	+	0.976994i	$0.431590\pi$
$132$	−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	$0.0822147\pi$
$137$			819.164i			0.510846i	−0.966829	+	0.255423i	$0.917785\pi$
$138$	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	$-0.169397\pi$
$149$	3134.50			1.72341			0.861705	+	0.507410i	$0.169397\pi$
$150$	−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	$-0.766662\pi$
$167$		−	2888.17i		−	1.33828i	0.743135	−	0.669142i	$-0.233338\pi$
$168$	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	$-0.658053\pi$
$173$	−2167.99			−0.952771			−0.476385	+	0.879237i	$0.658053\pi$
$174$	431.082	+	420.705i	0.187817	+	0.183296i
$175$	−2034.62			−0.878872
$176$	867.442			0.371511
$177$	−883.284	+	2182.90i	−0.375094	+	0.926987i
$178$	2633.21			1.10881
$179$	−3362.66			−1.40412			−0.702059	−	0.712119i	$-0.747736\pi$
$179$	−3362.66			−1.40412			−0.702059	+	0.712119i	$0.747736\pi$
$180$	−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	$-0.685228\pi$
$191$	−2901.64			−1.09924			−0.549621	+	0.835414i	$0.685228\pi$
$192$	−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	$-0.820315\pi$
$197$		−	2958.53i		−	1.06998i	0.844858	−	0.534991i	$-0.179685\pi$
$198$	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	$-0.461302\pi$
$227$	829.549			0.242551			0.121276	+	0.992619i	$0.461302\pi$
$228$	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	$-0.372333\pi$
$233$	2777.07			0.780823			0.390411	+	0.920641i	$0.372333\pi$
$234$	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	$0.0204818\pi$
$239$			475.166i			0.128602i	−0.997931	+	0.0643012i	$0.979518\pi$
$240$	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	$-0.976502\pi$
$251$		−	586.570i		−	0.147506i	0.997277	−	0.0737529i	$-0.0234976\pi$
$252$	−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	$-0.621266\pi$
$257$		−	7649.27i		−	1.85661i	0.371821	−	0.928304i	$-0.378734\pi$
$258$	−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	$0.158008\pi$
$263$			4062.63i			0.952518i	−0.879305	+	0.476259i	$0.841992\pi$
$264$	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	$-0.282415\pi$
$269$	5572.80			1.26312			0.631560	+	0.775327i	$0.282415\pi$
$270$	−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	$0.303645\pi$
$281$			7684.53i			1.63139i	−0.578482	+	0.815695i	$0.696355\pi$
$282$	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	$-0.911947\pi$
$293$		−	2739.50i		−	0.546223i	0.961982	−	0.273112i	$-0.0880528\pi$
$294$	−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	$-0.712329\pi$
$311$		−	8617.85i		−	1.57130i	0.618673	−	0.785649i	$-0.287671\pi$
$312$	−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	$0.219931\pi$
$317$			7193.38i			1.27451i	−0.770652	+	0.637256i	$0.780069\pi$
$318$	−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	$-0.270639\pi$
$347$	8529.80			1.31961			0.659804	+	0.751438i	$0.270639\pi$
$348$	−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	$-0.245323\pi$
$353$	9516.24			1.43484			0.717419	+	0.696641i	$0.245323\pi$
$354$	1766.57	−	4365.80i	0.265232	−	0.655479i
$355$	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	$-0.994341\pi$
$359$		−	241.857i		−	0.0355563i	0.999842	−	0.0177781i	$-0.00565925\pi$
$360$	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	$-0.898334\pi$
$383$		−	4707.02i		−	0.627983i	0.949426	−	0.313991i	$-0.101666\pi$
$384$	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	$-0.772231\pi$
$389$		−	10066.6i		−	1.31208i	0.754727	−	0.656039i	$-0.227769\pi$
$390$	−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	$-0.825509\pi$
$401$	−13706.8			−1.70695			−0.853475	+	0.521134i	$0.825509\pi$
$402$	−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	$-0.453258\pi$
$419$	2509.86			0.292636			0.146318	+	0.989238i	$0.453258\pi$
$420$	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	$-0.444784\pi$
$431$	3088.71			0.345192			0.172596	+	0.984993i	$0.444784\pi$
$432$	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	$-0.0624290\pi$
$443$	18290.6			1.96166			0.980829	+	0.194872i	$0.0624290\pi$
$444$	−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	$-0.921198\pi$
$449$		−	4662.73i		−	0.490084i	0.969512	−	0.245042i	$-0.0788018\pi$
$450$	−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	$0.356139\pi$
$461$			17808.6i			1.79919i	−0.436722	+	0.899597i	$0.643861\pi$
$462$	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	$-0.276252\pi$
$467$	13047.9			1.29290			0.646452	+	0.762955i	$0.276252\pi$
$468$	−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	$0.147442\pi$
$479$			9368.32i			0.893632i	−0.894626	+	0.446816i	$0.852558\pi$
$480$	−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	$0.293825\pi$
$491$			17352.5i			1.59492i	−0.603369	+	0.797462i	$0.706175\pi$
$492$	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	$-0.550839\pi$
$503$	−3588.26			−0.318077			−0.159038	+	0.987272i	$0.550839\pi$
$504$	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	$-0.370435\pi$
$509$	9092.54			0.791787			0.395893	+	0.918296i	$0.370435\pi$
$510$	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	$0.183070\pi$
$521$			12937.2i			1.08789i	−0.839121	+	0.543944i	$0.816930\pi$
$522$	−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
$531$	−4911.97	−	11206.9i	−0.401434	−	0.915888i
$532$	−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	$0.136375\pi$
$557$			10922.6i			0.830893i	−0.909618	+	0.415446i	$0.863625\pi$
$558$	−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	$-0.423293\pi$
$563$	6376.23			0.477311			0.238655	+	0.971104i	$0.423293\pi$
$564$	−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	$-0.472734\pi$
$569$	2322.37			0.171105			0.0855526	+	0.996334i	$0.472734\pi$
$570$	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	$-0.320255\pi$
$587$	15221.7			1.07030			0.535150	+	0.844757i	$0.320255\pi$
$588$	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	$-0.966188\pi$
$593$		−	3062.08i		−	0.212048i	0.994364	−	0.106024i	$-0.0338121\pi$
$594$	−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	$-0.814405\pi$
$599$		−	16143.3i		−	1.10117i	0.834780	−	0.550583i	$-0.185595\pi$
$600$	−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	$-0.840255\pi$
$617$		−	14745.1i		−	0.962102i	0.876693	−	0.481051i	$-0.159745\pi$
$618$	−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	$-0.945865\pi$
$641$		−	5493.48i		−	0.338501i	0.985573	−	0.169251i	$-0.0541347\pi$
$642$	−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	$-0.947047\pi$
$647$		−	5450.32i		−	0.331181i	0.986195	−	0.165591i	$-0.0529530\pi$
$648$	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	$0.150137\pi$
$653$			15164.0i			0.908749i	−0.890811	+	0.454375i	$0.849863\pi$
$654$	−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	$-0.325798\pi$
$659$	17606.1			1.04072			0.520360	+	0.853947i	$0.325798\pi$
$660$	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	$0.0504849\pi$
$677$			5564.20i			0.315878i	−0.987449	+	0.157939i	$0.949515\pi$
$678$	−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	$-0.602290\pi$
$683$	−11275.7			−0.631703			−0.315852	+	0.948809i	$0.602290\pi$
$684$	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	$-0.350562\pi$
$701$	16793.7			0.904833			0.452416	+	0.891807i	$0.350562\pi$
$702$	−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
$708$	−3533.13	+	8731.59i	−0.187547	+	0.463493i
$709$	−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	$-0.513422\pi$
$719$	−1625.41			−0.0843081			−0.0421540	+	0.999111i	$0.513422\pi$
$720$	−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	$-0.768814\pi$
$743$		−	26899.8i		−	1.32821i	0.747641	−	0.664103i	$-0.231186\pi$
$744$	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	$-0.758850\pi$
$761$		−	28851.9i		−	1.37435i	0.726491	−	0.687176i	$-0.241150\pi$
$762$	−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	$-0.669630\pi$
$773$	−21837.2			−1.01608			−0.508040	+	0.861333i	$0.669630\pi$
$774$	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	$-0.404773\pi$
$797$	13262.6			0.589441			0.294720	+	0.955584i	$0.404773\pi$
$798$	−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	$-0.370249\pi$
$809$	18244.0			0.792860			0.396430	+	0.918065i	$0.370249\pi$
$810$	−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	$-0.517986\pi$
$821$	−2657.07			−0.112950			−0.0564752	+	0.998404i	$0.517986\pi$
$822$	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	$-0.761398\pi$
$827$		−	32408.0i		−	1.36268i	0.731967	−	0.681340i	$-0.238602\pi$
$828$	−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	$-0.281944\pi$
$839$	30752.1			1.26541			0.632705	+	0.774393i	$0.281944\pi$
$840$	−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	$-0.470031\pi$
$857$	4717.24			0.188026			0.0940128	+	0.995571i	$0.470031\pi$
$858$	−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	$-0.303361\pi$
$863$	29368.5			1.15842			0.579210	+	0.815178i	$0.303361\pi$
$864$	−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	$-0.659736\pi$
$881$	−25157.2			−0.962053			−0.481026	+	0.876706i	$0.659736\pi$
$882$	−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
$885$	40520.3	+	16396.1i	1.53907	+	0.622766i
$886$	−36581.3			−1.38710
$887$	4627.33			0.175164			0.0875820	−	0.996157i	$-0.472086\pi$
$887$	4627.33			0.175164			0.0875820	+	0.996157i	$0.472086\pi$
$888$	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	$-0.893909\pi$
$911$		−	17991.4i		−	0.654317i	0.944970	−	0.327158i	$-0.106091\pi$
$912$	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	$-0.299582\pi$
$929$	33346.9			1.17769			0.588847	+	0.808245i	$0.299582\pi$
$930$	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	$-0.464739\pi$
$941$	6382.16			0.221097			0.110549	+	0.993871i	$0.464739\pi$
$942$	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	$0.123512\pi$
$947$			22052.6i			0.756719i	−0.925659	+	0.378360i	$0.876488\pi$
$948$	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	$0.197755\pi$
$953$			34248.4i			1.16413i	−0.813143	+	0.582064i	$0.802245\pi$
$954$	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	$0.105739\pi$
$971$			19734.5i			0.652225i	−0.945331	+	0.326113i	$0.894261\pi$
$972$	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	$-0.446793\pi$
$977$	10161.6			0.332752			0.166376	+	0.986062i	$0.446793\pi$
$978$	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	$-0.298661\pi$
$983$	36440.4			1.18237			0.591184	+	0.806537i	$0.298661\pi$
$984$	−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.a.353.8	yes	30
3.2	odd	2		354.4.c.b.353.7	yes	30
59.58	odd	2		354.4.c.b.353.8	yes	30
177.176	even	2	inner	354.4.c.a.353.7	✓	30

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

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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