LMFDB - Embedded newform 289.10.a.i.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.a (trivial)

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:	yes
Analytic conductor:	$148.845356651$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	no (minimal twist has level 17)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-31.9341 q^{2} +159.334 q^{3} +507.789 q^{4} -1397.46 q^{5} -5088.20 q^{6} +9976.78 q^{7} +134.480 q^{8} +5704.34 q^{9} +O(q^{10})$	\(q-31.9341 q^{2} +159.334 q^{3} +507.789 q^{4} -1397.46 q^{5} -5088.20 q^{6} +9976.78 q^{7} +134.480 q^{8} +5704.34 q^{9} +44626.6 q^{10} -50614.6 q^{11} +80908.1 q^{12} -76005.9 q^{13} -318600. q^{14} -222662. q^{15} -264282. q^{16} -182163. q^{18} -650626. q^{19} -709613. q^{20} +1.58964e6 q^{21} +1.61633e6 q^{22} +592123. q^{23} +21427.2 q^{24} -239.413 q^{25} +2.42718e6 q^{26} -2.22728e6 q^{27} +5.06610e6 q^{28} +3.53259e6 q^{29} +7.11053e6 q^{30} -3.41000e6 q^{31} +8.37077e6 q^{32} -8.06462e6 q^{33} -1.39421e7 q^{35} +2.89660e6 q^{36} -6.22732e6 q^{37} +2.07772e7 q^{38} -1.21103e7 q^{39} -187930. q^{40} +16809.2 q^{41} -5.07638e7 q^{42} +3.25305e7 q^{43} -2.57015e7 q^{44} -7.97157e6 q^{45} -1.89089e7 q^{46} -5.02215e7 q^{47} -4.21092e7 q^{48} +5.91825e7 q^{49} +7645.44 q^{50} -3.85949e7 q^{52} +1.56012e7 q^{53} +7.11261e7 q^{54} +7.07317e7 q^{55} +1.34168e6 q^{56} -1.03667e8 q^{57} -1.12810e8 q^{58} +1.62168e8 q^{59} -1.13066e8 q^{60} +1.55917e8 q^{61} +1.08895e8 q^{62} +5.69110e7 q^{63} -1.32001e8 q^{64} +1.06215e8 q^{65} +2.57537e8 q^{66} -2.74298e8 q^{67} +9.43453e7 q^{69} +4.45229e8 q^{70} +2.72244e8 q^{71} +767119. q^{72} -8.57367e6 q^{73} +1.98864e8 q^{74} -38146.6 q^{75} -3.30381e8 q^{76} -5.04970e8 q^{77} +3.86733e8 q^{78} +2.87273e8 q^{79} +3.69323e8 q^{80} -4.67160e8 q^{81} -536788. q^{82} -3.71797e8 q^{83} +8.07202e8 q^{84} -1.03883e9 q^{86} +5.62862e8 q^{87} -6.80664e6 q^{88} -4.29631e8 q^{89} +2.54565e8 q^{90} -7.58294e8 q^{91} +3.00673e8 q^{92} -5.43330e8 q^{93} +1.60378e9 q^{94} +9.09222e8 q^{95} +1.33375e9 q^{96} +1.01912e9 q^{97} -1.88994e9 q^{98} -2.88723e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) $ 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9	$ 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9} + 156200 q^{13} + 1207872 q^{15} + 3407880 q^{16} + 2193336 q^{18} + 1185568 q^{19} + 5198336 q^{21} + 13827692 q^{25} + 3618944 q^{26} - 9167544 q^{30} + 61884888 q^{32} + 1635208 q^{33} + 46992776 q^{35} + 156027320 q^{36} + 84813952 q^{38} - 4635776 q^{42} + 125448912 q^{43} + 164193176 q^{47} + 270850284 q^{49} - 226223888 q^{50} + 103553016 q^{52} + 426167208 q^{53} + 677761520 q^{55} + 375214512 q^{59} + 336918024 q^{60} + 190014416 q^{64} + 1377178928 q^{66} + 311910088 q^{67} + 533688136 q^{69} + 1477690280 q^{70} + 2757942680 q^{72} + 4047975520 q^{76} + 3440336432 q^{77} + 3266558756 q^{81} + 2072890608 q^{83} + 2630025952 q^{84} + 1538547296 q^{86} - 1010436256 q^{87} + 1873849184 q^{89} - 1998451624 q^{93} - 6880776704 q^{94} - 4667454128 q^{98}+O(q^{100}) $ 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9 + 156200 * q^13 + 1207872 * q^15 + 3407880 * q^16 + 2193336 * q^18 + 1185568 * q^19 + 5198336 * q^21 + 13827692 * q^25 + 3618944 * q^26 - 9167544 * q^30 + 61884888 * q^32 + 1635208 * q^33 + 46992776 * q^35 + 156027320 * q^36 + 84813952 * q^38 - 4635776 * q^42 + 125448912 * q^43 + 164193176 * q^47 + 270850284 * q^49 - 226223888 * q^50 + 103553016 * q^52 + 426167208 * q^53 + 677761520 * q^55 + 375214512 * q^59 + 336918024 * q^60 + 190014416 * q^64 + 1377178928 * q^66 + 311910088 * q^67 + 533688136 * q^69 + 1477690280 * q^70 + 2757942680 * q^72 + 4047975520 * q^76 + 3440336432 * q^77 + 3266558756 * q^81 + 2072890608 * q^83 + 2630025952 * q^84 + 1538547296 * q^86 - 1010436256 * q^87 + 1873849184 * q^89 - 1998451624 * q^93 - 6880776704 * q^94 - 4667454128 * q^98

Display 100 coefficients 10 coefficients

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 $

$2$	−31.9341	−1.41130	−0.705651	−	0.708559i	$-0.749345\pi$
$2$	−31.9341	−1.41130	−0.705651	+	0.708559i	$0.749345\pi$
$3$	159.334	1.13570	0.567849	−	0.823133i	$-0.307776\pi$
$3$	159.334	1.13570	0.567849	+	0.823133i	$0.307776\pi$
$4$	507.789	0.991775
$5$	−1397.46	−0.999939	−0.499969	−	0.866043i	$-0.666655\pi$
$5$	−1397.46	−0.999939	−0.499969	+	0.866043i	$0.666655\pi$
$6$	−5088.20	−1.60281
$7$	9976.78	1.57054	0.785270	−	0.619153i	$-0.212524\pi$
$7$	9976.78	1.57054	0.785270	+	0.619153i	$0.212524\pi$
$8$	134.480	0.0116079
$9$	5704.34	0.289811
$10$	44626.6	1.41122
$11$	−50614.6	−1.04234	−0.521169	−	0.853454i	$-0.674504\pi$
$11$	−50614.6	−1.04234	−0.521169	+	0.853454i	$0.674504\pi$
$12$	80908.1	1.12636
$13$	−76005.9	−0.738078	−0.369039	−	0.929414i	$-0.620313\pi$
$13$	−76005.9	−0.738078	−0.369039	+	0.929414i	$0.620313\pi$
$14$	−318600.	−2.21651
$15$	−222662.	−1.13563
$16$	−264282.	−1.00816
$17$	0	0
$17$	0	0
$18$	−182163.	−0.409011
$19$	−650626.	−1.14536	−0.572678	−	0.819781i	$-0.694095\pi$
$19$	−650626.	−1.14536	−0.572678	+	0.819781i	$0.694095\pi$
$20$	−709613.	−0.991714
$21$	1.58964e6	1.78366
$22$	1.61633e6	1.47105
$23$	592123.	0.441201	0.220600	−	0.975364i	$-0.429198\pi$
$23$	592123.	0.441201	0.220600	+	0.975364i	$0.429198\pi$
$24$	21427.2	0.0131830
$25$	−239.413	−0.000122579 0
$26$	2.42718e6	1.04165
$27$	−2.22728e6	−0.806561
$28$	5.06610e6	1.55762
$29$	3.53259e6	0.927475	0.463737	−	0.885973i	$-0.346508\pi$
$29$	3.53259e6	0.927475	0.463737	+	0.885973i	$0.346508\pi$
$30$	7.11053e6	1.60272
$31$	−3.41000e6	−0.663173	−0.331587	−	0.943425i	$-0.607584\pi$
$31$	−3.41000e6	−0.663173	−0.331587	+	0.943425i	$0.607584\pi$
$32$	8.37077e6	1.41121
$33$	−8.06462e6	−1.18378
$34$	0	0
$35$	−1.39421e7	−1.57044
$36$	2.89660e6	0.287427
$37$	−6.22732e6	−0.546253	−0.273126	−	0.961978i	$-0.588058\pi$
$37$	−6.22732e6	−0.546253	−0.273126	+	0.961978i	$0.588058\pi$
$38$	2.07772e7	1.61644
$39$	−1.21103e7	−0.838234
$40$	−187930.	−0.0116072
$41$	16809.2	0.000929011 0	0.000464505	−	1.00000i	$-0.499852\pi$
$41$	16809.2	0.000929011 0	0.000464505		1.00000i	$0.499852\pi$
$42$	−5.07638e7	−2.51728
$43$	3.25305e7	1.45105	0.725525	−	0.688196i	$-0.241597\pi$
$43$	3.25305e7	1.45105	0.725525	+	0.688196i	$0.241597\pi$
$44$	−2.57015e7	−1.03376
$45$	−7.97157e6	−0.289793
$46$	−1.89089e7	−0.622668
$47$	−5.02215e7	−1.50124	−0.750619	−	0.660736i	$-0.770244\pi$
$47$	−5.02215e7	−1.50124	−0.750619	+	0.660736i	$0.770244\pi$
$48$	−4.21092e7	−1.14496
$49$	5.91825e7	1.46660
$50$	7645.44	0.000172997 0
$51$	0	0
$52$	−3.85949e7	−0.732007
$53$	1.56012e7	0.271592	0.135796	−	0.990737i	$-0.456641\pi$
$53$	1.56012e7	0.271592	0.135796	+	0.990737i	$0.456641\pi$
$54$	7.11261e7	1.13830
$55$	7.07317e7	1.04227
$56$	1.34168e6	0.0182306
$57$	−1.03667e8	−1.30078
$58$	−1.12810e8	−1.30895
$59$	1.62168e8	1.74233	0.871165	−	0.490991i	$-0.163365\pi$
$59$	1.62168e8	1.74233	0.871165	+	0.490991i	$0.163365\pi$
$60$	−1.13066e8	−1.12629
$61$	1.55917e8	1.44181	0.720906	−	0.693033i	$-0.243726\pi$
$61$	1.55917e8	1.44181	0.720906	+	0.693033i	$0.243726\pi$
$62$	1.08895e8	0.935938
$63$	5.69110e7	0.455159
$64$	−1.32001e8	−0.983483
$65$	1.06215e8	0.738033
$66$	2.57537e8	1.67067
$67$	−2.74298e8	−1.66298	−0.831488	−	0.555542i	$-0.812511\pi$
$67$	−2.74298e8	−1.66298	−0.831488	+	0.555542i	$0.812511\pi$
$68$	0	0
$69$	9.43453e7	0.501071
$70$	4.45229e8	2.21637
$71$	2.72244e8	1.27144	0.635721	−	0.771919i	$-0.280703\pi$
$71$	2.72244e8	1.27144	0.635721	+	0.771919i	$0.280703\pi$
$72$	767119.	0.00336408
$73$	−8.57367e6	−0.0353357	−0.0176679	−	0.999844i	$-0.505624\pi$
$73$	−8.57367e6	−0.0353357	−0.0176679	+	0.999844i	$0.505624\pi$
$74$	1.98864e8	0.770928
$75$	−38146.6	−0.000139213 0
$76$	−3.30381e8	−1.13593
$77$	−5.04970e8	−1.63703
$78$	3.86733e8	1.18300
$79$	2.87273e8	0.829799	0.414899	−	0.909867i	$-0.363817\pi$
$79$	2.87273e8	0.829799	0.414899	+	0.909867i	$0.363817\pi$
$80$	3.69323e8	1.00810
$81$	−4.67160e8	−1.20582
$82$	−536788.	−0.00131112
$83$	−3.71797e8	−0.859913	−0.429956	−	0.902850i	$-0.641471\pi$
$83$	−3.71797e8	−0.859913	−0.429956	+	0.902850i	$0.641471\pi$
$84$	8.07202e8	1.76899
$85$	0	0
$86$	−1.03883e9	−2.04787
$87$	5.62862e8	1.05333
$88$	−6.80664e6	−0.0120993
$89$	−4.29631e8	−0.725839	−0.362919	−	0.931821i	$-0.618220\pi$
$89$	−4.29631e8	−0.725839	−0.362919	+	0.931821i	$0.618220\pi$
$90$	2.54565e8	0.408986
$91$	−7.58294e8	−1.15918
$92$	3.00673e8	0.437572
$93$	−5.43330e8	−0.753165
$94$	1.60378e9	2.11870
$95$	9.09222e8	1.14529
$96$	1.33375e9	1.60271
$97$	1.01912e9	1.16884	0.584418	−	0.811453i	$-0.301323\pi$
$97$	1.01912e9	1.16884	0.584418	+	0.811453i	$0.301323\pi$
$98$	−1.88994e9	−2.06981
$99$	−2.88723e8	−0.302081
$100$	−121571.	−0.000121571 0
$101$	−5.60377e8	−0.535838	−0.267919	−	0.963441i	$-0.586336\pi$
$101$	−5.60377e8	−0.535838	−0.267919	+	0.963441i	$0.586336\pi$
$102$	0	0
$103$	−1.44725e8	−0.126699	−0.0633497	−	0.997991i	$-0.520178\pi$
$103$	−1.44725e8	−0.126699	−0.0633497	+	0.997991i	$0.520178\pi$
$104$	−1.02213e7	−0.00856751
$105$	−2.22145e9	−1.78355
$106$	−4.98212e8	−0.383299
$107$	1.91158e9	1.40983	0.704914	−	0.709293i	$-0.250986\pi$
$107$	1.91158e9	1.40983	0.704914	+	0.709293i	$0.250986\pi$
$108$	−1.13099e9	−0.799927
$109$	−2.42408e9	−1.64485	−0.822426	−	0.568872i	$-0.807380\pi$
$109$	−2.42408e9	−1.64485	−0.822426	+	0.568872i	$0.807380\pi$
$110$	−2.25875e9	−1.47096
$111$	−9.92225e8	−0.620379
$112$	−2.63669e9	−1.58335
$113$	1.14662e9	0.661555	0.330777	−	0.943709i	$-0.392689\pi$
$113$	1.14662e9	0.661555	0.330777	+	0.943709i	$0.392689\pi$
$114$	3.31051e9	1.83579
$115$	−8.27466e8	−0.441174
$116$	1.79381e9	0.919846
$117$	−4.33564e8	−0.213903
$118$	−5.17869e9	−2.45895
$119$	0	0
$120$	−2.99436e7	−0.0131822
$121$	2.03886e8	0.0864676
$122$	−4.97907e9	−2.03483
$123$	2.67828e6	0.00105508
$124$	−1.73156e9	−0.657719
$125$	2.72974e9	1.00006
$126$	−1.81740e9	−0.642368
$127$	2.47510e9	0.844260	0.422130	−	0.906535i	$-0.361283\pi$
$127$	2.47510e9	0.844260	0.422130	+	0.906535i	$0.361283\pi$
$128$	−7.05038e7	−0.0232149
$129$	5.18321e9	1.64796
$130$	−3.39188e9	−1.04159
$131$	−2.01408e9	−0.597526	−0.298763	−	0.954327i	$-0.596574\pi$
$131$	−2.01408e9	−0.597526	−0.298763	+	0.954327i	$0.596574\pi$
$132$	−4.09513e9	−1.17404
$133$	−6.49115e9	−1.79883
$134$	8.75947e9	2.34696
$135$	3.11252e9	0.806511
$136$	0	0
$137$	2.91545e9	0.707070	0.353535	−	0.935421i	$-0.384979\pi$
$137$	2.91545e9	0.707070	0.353535	+	0.935421i	$0.384979\pi$
$138$	−3.01284e9	−0.707163
$139$	−7.52889e9	−1.71066	−0.855331	−	0.518081i	$-0.826647\pi$
$139$	−7.52889e9	−1.71066	−0.855331	+	0.518081i	$0.826647\pi$
$140$	−7.07965e9	−1.55753
$141$	−8.00200e9	−1.70495
$142$	−8.69389e9	−1.79439
$143$	3.84701e9	0.769326
$144$	−1.50756e9	−0.292175
$145$	−4.93664e9	−0.927418
$146$	2.73793e8	0.0498694
$147$	9.42979e9	1.66561
$148$	−3.16217e9	−0.541760
$149$	−8.08087e9	−1.34314	−0.671568	−	0.740943i	$-0.734379\pi$
$149$	−8.08087e9	−1.34314	−0.671568	+	0.740943i	$0.734379\pi$
$150$	1.21818e6	0.000196472 0
$151$	−3.19079e9	−0.499461	−0.249730	−	0.968315i	$-0.580342\pi$
$151$	−3.19079e9	−0.499461	−0.249730	+	0.968315i	$0.580342\pi$
$152$	−8.74961e7	−0.0132951
$153$	0	0
$154$	1.61258e10	2.31035
$155$	4.76533e9	0.663133
$156$	−6.14949e9	−0.831339
$157$	−2.16958e9	−0.284988	−0.142494	−	0.989796i	$-0.545512\pi$
$157$	−2.16958e9	−0.284988	−0.142494	+	0.989796i	$0.545512\pi$
$158$	−9.17381e9	−1.17110
$159$	2.48581e9	0.308447
$160$	−1.16978e10	−1.41112
$161$	5.90748e9	0.692924
$162$	1.49183e10	1.70178
$163$	1.61234e10	1.78900	0.894502	−	0.447064i	$-0.147530\pi$
$163$	1.61234e10	1.78900	0.894502	+	0.447064i	$0.147530\pi$
$164$	8.53554e6	0.000921370 0
$165$	1.12700e10	1.18371
$166$	1.18730e10	1.21360
$167$	1.11195e10	1.10627	0.553133	−	0.833093i	$-0.313432\pi$
$167$	1.11195e10	1.10627	0.553133	+	0.833093i	$0.313432\pi$
$168$	2.13775e8	0.0207045
$169$	−4.82760e9	−0.455241
$170$	0	0
$171$	−3.71139e9	−0.331936
$172$	1.65186e10	1.43912
$173$	1.48857e10	1.26346	0.631729	−	0.775189i	$-0.282346\pi$
$173$	1.48857e10	1.26346	0.631729	+	0.775189i	$0.282346\pi$
$174$	−1.79745e10	−1.48657
$175$	−2.38857e6	−0.000192516 0
$176$	1.33765e10	1.05084
$177$	2.58388e10	1.97876
$178$	1.37199e10	1.02438
$179$	1.45764e10	1.06124	0.530618	−	0.847611i	$-0.321960\pi$
$179$	1.45764e10	1.06124	0.530618	+	0.847611i	$0.321960\pi$
$180$	−4.04788e9	−0.287409
$181$	−2.90444e9	−0.201145	−0.100572	−	0.994930i	$-0.532067\pi$
$181$	−2.90444e9	−0.201145	−0.100572	+	0.994930i	$0.532067\pi$
$182$	2.42155e10	1.63596
$183$	2.48429e10	1.63746
$184$	7.96286e7	0.00512140
$185$	8.70242e9	0.546219
$186$	1.73508e10	1.06294
$187$	0	0
$188$	−2.55019e10	−1.48889
$189$	−2.22210e10	−1.26674
$190$	−2.90352e10	−1.61634
$191$	1.67129e10	0.908658	0.454329	−	0.890834i	$-0.349879\pi$
$191$	1.67129e10	0.908658	0.454329	+	0.890834i	$0.349879\pi$
$192$	−2.10322e10	−1.11694
$193$	1.00548e10	0.521635	0.260818	−	0.965388i	$-0.416008\pi$
$193$	1.00548e10	0.521635	0.260818	+	0.965388i	$0.416008\pi$
$194$	−3.25448e10	−1.64958
$195$	1.69237e10	0.838182
$196$	3.00522e10	1.45454
$197$	−6.48737e9	−0.306882	−0.153441	−	0.988158i	$-0.549035\pi$
$197$	−6.48737e9	−0.306882	−0.153441	+	0.988158i	$0.549035\pi$
$198$	9.22011e9	0.426327
$199$	−4.66693e8	−0.0210956	−0.0105478	−	0.999944i	$-0.503358\pi$
$199$	−4.66693e8	−0.0210956	−0.0105478	+	0.999944i	$0.503358\pi$
$200$	−32196.2	−1.42288e−6 0
$201$	−4.37050e10	−1.88864
$202$	1.78951e10	0.756230
$203$	3.52439e10	1.45664
$204$	0	0
$205$	−2.34902e7	−0.000928954 0
$206$	4.62165e9	0.178811
$207$	3.37767e9	0.127865
$208$	2.00870e10	0.744099
$209$	3.29312e10	1.19385
$210$	7.09402e10	2.51713
$211$	−1.06287e9	−0.0369156	−0.0184578	−	0.999830i	$-0.505876\pi$
$211$	−1.06287e9	−0.0369156	−0.0184578	+	0.999830i	$0.505876\pi$
$212$	7.92213e9	0.269359
$213$	4.33778e10	1.44397
$214$	−6.10447e10	−1.98969
$215$	−4.54599e10	−1.45096
$216$	−2.99524e8	−0.00936245
$217$	−3.40208e10	−1.04154
$218$	7.74108e10	2.32139
$219$	−1.36608e9	−0.0401307
$220$	3.59167e10	1.03370
$221$	0	0
$222$	3.16858e10	0.875542
$223$	−4.79547e10	−1.29855	−0.649276	−	0.760553i	$-0.724928\pi$
$223$	−4.79547e10	−1.29855	−0.649276	+	0.760553i	$0.724928\pi$
$224$	8.35134e10	2.21636
$225$	−1.36569e6	−3.55248e−5 0
$226$	−3.66163e10	−0.933654
$227$	2.10496e10	0.526171	0.263085	−	0.964773i	$-0.415260\pi$
$227$	2.10496e10	0.526171	0.263085	+	0.964773i	$0.415260\pi$
$228$	−5.26409e10	−1.29008
$229$	−1.60702e10	−0.386156	−0.193078	−	0.981183i	$-0.561847\pi$
$229$	−1.60702e10	−0.386156	−0.193078	+	0.981183i	$0.561847\pi$
$230$	2.64244e10	0.622630
$231$	−8.04590e10	−1.85918
$232$	4.75062e8	0.0107660
$233$	6.08238e10	1.35198	0.675992	−	0.736909i	$-0.263715\pi$
$233$	6.08238e10	1.35198	0.675992	+	0.736909i	$0.263715\pi$
$234$	1.38455e10	0.301882
$235$	7.01824e10	1.50115
$236$	8.23470e10	1.72800
$237$	4.57724e10	0.942401
$238$	0	0
$239$	4.66769e10	0.925362	0.462681	−	0.886525i	$-0.346887\pi$
$239$	4.66769e10	0.925362	0.462681	+	0.886525i	$0.346887\pi$
$240$	5.88458e10	1.14489
$241$	−9.83868e9	−0.187871	−0.0939356	−	0.995578i	$-0.529945\pi$
$241$	−9.83868e9	−0.187871	−0.0939356	+	0.995578i	$0.529945\pi$
$242$	−6.51093e9	−0.122032
$243$	−3.05950e10	−0.562887
$244$	7.91728e10	1.42995
$245$	−8.27050e10	−1.46651
$246$	−8.55287e7	−0.00148903
$247$	4.94514e10	0.845361
$248$	−4.58577e8	−0.00769803
$249$	−5.92399e10	−0.976601
$250$	−8.71720e10	−1.41139
$251$	5.71571e10	0.908947	0.454473	−	0.890760i	$-0.349827\pi$
$251$	5.71571e10	0.908947	0.454473	+	0.890760i	$0.349827\pi$
$252$	2.88988e10	0.451416
$253$	−2.99700e10	−0.459880
$254$	−7.90402e10	−1.19151
$255$	0	0
$256$	6.98359e10	1.01625
$257$	8.59864e10	1.22951	0.614753	−	0.788720i	$-0.289256\pi$
$257$	8.59864e10	1.22951	0.614753	+	0.788720i	$0.289256\pi$
$258$	−1.65521e11	−2.32576
$259$	−6.21286e10	−0.857912
$260$	5.39348e10	0.731962
$261$	2.01511e10	0.268792
$262$	6.43181e10	0.843290
$263$	2.61461e10	0.336982	0.168491	−	0.985703i	$-0.446111\pi$
$263$	2.61461e10	0.336982	0.168491	+	0.985703i	$0.446111\pi$
$264$	−1.08453e9	−0.0137412
$265$	−2.18021e10	−0.271576
$266$	2.07289e11	2.53869
$267$	−6.84548e10	−0.824334
$268$	−1.39285e11	−1.64930
$269$	−2.14758e10	−0.250072	−0.125036	−	0.992152i	$-0.539905\pi$
$269$	−2.14758e10	−0.250072	−0.125036	+	0.992152i	$0.539905\pi$
$270$	−9.93957e10	−1.13823
$271$	1.61241e11	1.81599	0.907997	−	0.418976i	$-0.137611\pi$
$271$	1.61241e11	1.81599	0.907997	+	0.418976i	$0.137611\pi$
$272$	0	0
$273$	−1.20822e11	−1.31648
$274$	−9.31023e10	−0.997890
$275$	1.21178e7	0.000127769 0
$276$	4.79075e10	0.496950
$277$	−4.74856e10	−0.484622	−0.242311	−	0.970199i	$-0.577905\pi$
$277$	−4.74856e10	−0.484622	−0.242311	+	0.970199i	$0.577905\pi$
$278$	2.40429e11	2.41426
$279$	−1.94518e10	−0.192195
$280$	−1.87493e9	−0.0182295
$281$	2.72583e9	0.0260808	0.0130404	−	0.999915i	$-0.495849\pi$
$281$	2.72583e9	0.0260808	0.0130404	+	0.999915i	$0.495849\pi$
$282$	2.55537e11	2.40620
$283$	4.24874e10	0.393751	0.196876	−	0.980428i	$-0.436921\pi$
$283$	4.24874e10	0.393751	0.196876	+	0.980428i	$0.436921\pi$
$284$	1.38243e11	1.26098
$285$	1.44870e11	1.30070
$286$	−1.22851e11	−1.08575
$287$	1.67702e8	0.00145905
$288$	4.77498e10	0.408983
$289$	0	0
$290$	1.57647e11	1.30887
$291$	1.62381e11	1.32744
$292$	−4.35361e9	−0.0350451
$293$	6.93631e9	0.0549825	0.0274912	−	0.999622i	$-0.491248\pi$
$293$	6.93631e9	0.0549825	0.0274912	+	0.999622i	$0.491248\pi$
$294$	−3.01132e11	−2.35068
$295$	−2.26622e11	−1.74222
$296$	−8.37450e8	−0.00634083
$297$	1.12733e11	0.840709
$298$	2.58056e11	1.89557
$299$	−4.50048e10	−0.325641
$300$	−1.93704e7	−0.000138068 0
$301$	3.24549e11	2.27893
$302$	1.01895e11	0.704891
$303$	−8.92871e10	−0.608551
$304$	1.71949e11	1.15470
$305$	−2.17887e11	−1.44172
$306$	0	0
$307$	1.64410e10	0.105635	0.0528173	−	0.998604i	$-0.483180\pi$
$307$	1.64410e10	0.105635	0.0528173	+	0.998604i	$0.483180\pi$
$308$	−2.56418e11	−1.62357
$309$	−2.30595e10	−0.143892
$310$	−1.52177e11	−0.935881
$311$	1.22476e11	0.742383	0.371191	−	0.928556i	$-0.378949\pi$
$311$	1.22476e11	0.742383	0.371191	+	0.928556i	$0.378949\pi$
$312$	−1.62860e9	−0.00973011
$313$	2.36493e11	1.39274	0.696368	−	0.717685i	$-0.254798\pi$
$313$	2.36493e11	1.39274	0.696368	+	0.717685i	$0.254798\pi$
$314$	6.92836e10	0.402204
$315$	−7.95306e10	−0.455132
$316$	1.45874e11	0.822974
$317$	−4.33607e10	−0.241173	−0.120587	−	0.992703i	$-0.538478\pi$
$317$	−4.33607e10	−0.241173	−0.120587	+	0.992703i	$0.538478\pi$
$318$	−7.93821e10	−0.435312
$319$	−1.78800e11	−0.966742
$320$	1.84466e11	0.983423
$321$	3.04580e11	1.60114
$322$	−1.88650e11	−0.977926
$323$	0	0
$324$	−2.37218e11	−1.19590
$325$	1.81968e7	9.04731e−5 0
$326$	−5.14885e11	−2.52483
$327$	−3.86238e11	−1.86806
$328$	2.26050e6	1.07838e−5 0
$329$	−5.01049e11	−2.35775
$330$	−3.59897e11	−1.67057
$331$	−1.69990e11	−0.778392	−0.389196	−	0.921155i	$-0.627247\pi$
$331$	−1.69990e11	−0.778392	−0.389196	+	0.921155i	$0.627247\pi$
$332$	−1.88794e11	−0.852840
$333$	−3.55228e10	−0.158310
$334$	−3.55090e11	−1.56128
$335$	3.83320e11	1.66287
$336$	−4.20114e11	−1.79821
$337$	1.02637e10	0.0433478	0.0216739	−	0.999765i	$-0.493100\pi$
$337$	1.02637e10	0.0433478	0.0216739	+	0.999765i	$0.493100\pi$
$338$	1.54165e11	0.642483
$339$	1.82695e11	0.751327
$340$	0	0
$341$	1.72596e11	0.691251
$342$	1.18520e11	0.468462
$343$	1.87852e11	0.732811
$344$	4.37469e9	0.0168436
$345$	−1.31844e11	−0.501040
$346$	−4.75361e11	−1.78312
$347$	1.50419e11	0.556957	0.278478	−	0.960443i	$-0.410170\pi$
$347$	1.50419e11	0.556957	0.278478	+	0.960443i	$0.410170\pi$
$348$	2.85815e11	1.04467
$349$	4.38444e11	1.58197	0.790987	−	0.611833i	$-0.209567\pi$
$349$	4.38444e11	1.58197	0.790987	+	0.611833i	$0.209567\pi$
$350$	7.62769e7	0.000271698 0
$351$	1.69286e11	0.595305
$352$	−4.23683e11	−1.47095
$353$	3.32465e10	0.113962	0.0569810	−	0.998375i	$-0.481853\pi$
$353$	3.32465e10	0.113962	0.0569810	+	0.998375i	$0.481853\pi$
$354$	−8.25141e11	−2.79263
$355$	−3.80450e11	−1.27136
$356$	−2.18162e11	−0.719869
$357$	0	0
$358$	−4.65485e11	−1.49773
$359$	2.04791e11	0.650707	0.325354	−	0.945592i	$-0.394517\pi$
$359$	2.04791e11	0.650707	0.325354	+	0.945592i	$0.394517\pi$
$360$	−1.07202e9	−0.00336388
$361$	1.00627e11	0.311839
$362$	9.27507e10	0.283876
$363$	3.24860e10	0.0982012
$364$	−3.85053e11	−1.14965
$365$	1.19813e10	0.0353336
$366$	−7.93335e11	−2.31096
$367$	3.19895e11	0.920472	0.460236	−	0.887797i	$-0.347765\pi$
$367$	3.19895e11	0.920472	0.460236	+	0.887797i	$0.347765\pi$
$368$	−1.56488e11	−0.444800
$369$	9.58857e7	0.000269237 0
$370$	−2.77904e11	−0.770881
$371$	1.55650e11	0.426547
$372$	−2.75897e11	−0.746970
$373$	−1.73495e11	−0.464084	−0.232042	−	0.972706i	$-0.574541\pi$
$373$	−1.73495e11	−0.464084	−0.232042	+	0.972706i	$0.574541\pi$
$374$	0	0
$375$	4.34941e11	1.13577
$376$	−6.75378e9	−0.0174262
$377$	−2.68498e11	−0.684549
$378$	7.09610e11	1.78775
$379$	1.34082e11	0.333807	0.166903	−	0.985973i	$-0.446623\pi$
$379$	1.34082e11	0.333807	0.166903	+	0.985973i	$0.446623\pi$
$380$	4.61693e11	1.13587
$381$	3.94368e11	0.958824
$382$	−5.33711e11	−1.28239
$383$	−5.78666e11	−1.37415	−0.687074	−	0.726588i	$-0.741105\pi$
$383$	−5.78666e11	−1.37415	−0.687074	+	0.726588i	$0.741105\pi$
$384$	−1.12337e10	−0.0263652
$385$	7.05674e11	1.63693
$386$	−3.21092e11	−0.736185
$387$	1.85565e11	0.420530
$388$	5.17499e11	1.15922
$389$	3.40387e11	0.753702	0.376851	−	0.926274i	$-0.377007\pi$
$389$	3.40387e11	0.753702	0.376851	+	0.926274i	$0.377007\pi$
$390$	−5.40442e11	−1.18293
$391$	0	0
$392$	7.95886e9	0.0170241
$393$	−3.20912e11	−0.678610
$394$	2.07169e11	0.433103
$395$	−4.01452e11	−0.829748
$396$	−1.46610e11	−0.299596
$397$	3.37985e11	0.682874	0.341437	−	0.939905i	$-0.389086\pi$
$397$	3.37985e11	0.682874	0.341437	+	0.939905i	$0.389086\pi$
$398$	1.49034e10	0.0297723
$399$	−1.03426e12	−2.04292
$400$	6.32726e7	0.000123579 0
$401$	6.78361e11	1.31012	0.655060	−	0.755577i	$-0.272643\pi$
$401$	6.78361e11	1.31012	0.655060	+	0.755577i	$0.272643\pi$
$402$	1.39568e12	2.66544
$403$	2.59180e11	0.489474
$404$	−2.84553e11	−0.531431
$405$	6.52835e11	1.20575
$406$	−1.12548e12	−2.05576
$407$	3.15193e11	0.569380
$408$	0	0
$409$	3.79922e11	0.671336	0.335668	−	0.941980i	$-0.391038\pi$
$409$	3.79922e11	0.671336	0.335668	+	0.941980i	$0.391038\pi$
$410$	7.50139e8	0.00131103
$411$	4.64530e11	0.803018
$412$	−7.34895e10	−0.125657
$413$	1.61791e12	2.73640
$414$	−1.07863e11	−0.180456
$415$	5.19570e11	0.859860
$416$	−6.36228e11	−1.04158
$417$	−1.19961e12	−1.94280
$418$	−1.05163e12	−1.68488
$419$	−6.30348e11	−0.999118	−0.499559	−	0.866280i	$-0.666505\pi$
$419$	−6.30348e11	−0.999118	−0.499559	+	0.866280i	$0.666505\pi$
$420$	−1.12803e12	−1.76888
$421$	3.36779e11	0.522488	0.261244	−	0.965273i	$-0.415867\pi$
$421$	3.36779e11	0.522488	0.261244	+	0.965273i	$0.415867\pi$
$422$	3.39419e10	0.0520990
$423$	−2.86481e11	−0.435075
$424$	2.09805e9	0.00315261
$425$	0	0
$426$	−1.38523e12	−2.03788
$427$	1.55555e12	2.26443
$428$	9.70680e11	1.39823
$429$	6.12959e11	0.873723
$430$	1.45172e12	2.04775
$431$	−2.07449e11	−0.289576	−0.144788	−	0.989463i	$-0.546250\pi$
$431$	−2.07449e11	−0.289576	−0.144788	+	0.989463i	$0.546250\pi$
$432$	5.88630e11	0.813140
$433$	6.52648e11	0.892243	0.446122	−	0.894972i	$-0.352805\pi$
$433$	6.52648e11	0.892243	0.446122	+	0.894972i	$0.352805\pi$
$434$	1.08643e12	1.46993
$435$	−7.86575e11	−1.05327
$436$	−1.23092e12	−1.63132
$437$	−3.85250e11	−0.505332
$438$	4.36245e10	0.0566366
$439$	−5.99383e11	−0.770218	−0.385109	−	0.922871i	$-0.625836\pi$
$439$	−5.99383e11	−0.770218	−0.385109	+	0.922871i	$0.625836\pi$
$440$	9.51199e9	0.0120986
$441$	3.37597e11	0.425036
$442$	0	0
$443$	1.38710e11	0.171117	0.0855583	−	0.996333i	$-0.472733\pi$
$443$	1.38710e11	0.171117	0.0855583	+	0.996333i	$0.472733\pi$
$444$	−5.03841e11	−0.615276
$445$	6.00390e11	0.725794
$446$	1.53139e12	1.83265
$447$	−1.28756e12	−1.52540
$448$	−1.31694e12	−1.54460
$449$	1.78071e11	0.206769	0.103385	−	0.994641i	$-0.467033\pi$
$449$	1.78071e11	0.206769	0.103385	+	0.994641i	$0.467033\pi$
$450$	4.36122e7	5.01362e−5 0
$451$	−8.50792e8	−0.000968343 0
$452$	5.82240e11	0.656114
$453$	−5.08401e11	−0.567237
$454$	−6.72199e11	−0.742586
$455$	1.05968e12	1.15911
$456$	−1.39411e10	−0.0150993
$457$	−1.62766e11	−0.174558	−0.0872790	−	0.996184i	$-0.527817\pi$
$457$	−1.62766e11	−0.174558	−0.0872790	+	0.996184i	$0.527817\pi$
$458$	5.13189e11	0.544983
$459$	0	0
$460$	−4.20178e11	−0.437545
$461$	−1.43453e12	−1.47930	−0.739648	−	0.672994i	$-0.765008\pi$
$461$	−1.43453e12	−1.47930	−0.739648	+	0.672994i	$0.765008\pi$
$462$	2.56939e12	2.62386
$463$	8.05823e11	0.814939	0.407470	−	0.913219i	$-0.366411\pi$
$463$	8.05823e11	0.814939	0.407470	+	0.913219i	$0.366411\pi$
$464$	−9.33601e11	−0.935040
$465$	7.59280e11	0.753119
$466$	−1.94235e12	−1.90806
$467$	9.22766e11	0.897771	0.448886	−	0.893589i	$-0.351821\pi$
$467$	9.22766e11	0.897771	0.448886	+	0.893589i	$0.351821\pi$
$468$	−2.20159e11	−0.212144
$469$	−2.73661e12	−2.61177
$470$	−2.24121e12	−2.11857
$471$	−3.45688e11	−0.323661
$472$	2.18083e10	0.0202247
$473$	−1.64652e12	−1.51248
$474$	−1.46170e12	−1.33001
$475$	1.55768e8	0.000140397 0
$476$	0	0
$477$	8.89948e10	0.0787104
$478$	−1.49059e12	−1.30597
$479$	−4.10737e11	−0.356496	−0.178248	−	0.983986i	$-0.557043\pi$
$479$	−4.10737e11	−0.356496	−0.178248	+	0.983986i	$0.557043\pi$
$480$	−1.86386e12	−1.60261
$481$	4.73313e11	0.403177
$482$	3.14190e11	0.265143
$483$	9.41262e11	0.786953
$484$	1.03531e11	0.0857565
$485$	−1.42418e12	−1.16876
$486$	9.77023e11	0.794405
$487$	−7.30098e11	−0.588167	−0.294083	−	0.955780i	$-0.595014\pi$
$487$	−7.30098e11	−0.588167	−0.294083	+	0.955780i	$0.595014\pi$
$488$	2.09677e10	0.0167364
$489$	2.56900e12	2.03177
$490$	2.64111e12	2.06969
$491$	2.19308e12	1.70289	0.851446	−	0.524442i	$-0.175726\pi$
$491$	2.19308e12	1.70289	0.851446	+	0.524442i	$0.175726\pi$
$492$	1.36000e9	0.00104640
$493$	0	0
$494$	−1.57919e12	−1.19306
$495$	4.03478e11	0.302062
$496$	9.01204e11	0.668583
$497$	2.71612e12	1.99685
$498$	1.89178e12	1.37828
$499$	−2.10713e12	−1.52138	−0.760691	−	0.649115i	$-0.775140\pi$
$499$	−2.10713e12	−1.52138	−0.760691	+	0.649115i	$0.775140\pi$
$500$	1.38613e12	0.991836
$501$	1.77171e12	1.25638
$502$	−1.82526e12	−1.28280
$503$	2.92024e11	0.203406	0.101703	−	0.994815i	$-0.467571\pi$
$503$	2.92024e11	0.203406	0.101703	+	0.994815i	$0.467571\pi$
$504$	7.65338e9	0.00528343
$505$	7.83102e11	0.535806
$506$	9.57067e11	0.649030
$507$	−7.69202e11	−0.517016
$508$	1.25683e12	0.837316
$509$	−3.27240e11	−0.216091	−0.108045	−	0.994146i	$-0.534459\pi$
$509$	−3.27240e11	−0.216091	−0.108045	+	0.994146i	$0.534459\pi$
$510$	0	0
$511$	−8.55376e10	−0.0554962
$512$	−2.19405e12	−1.41102
$513$	1.44912e12	0.923799
$514$	−2.74590e12	−1.73521
$515$	2.02246e11	0.126692
$516$	2.63198e12	1.63440
$517$	2.54194e12	1.56480
$518$	1.98402e12	1.21077
$519$	2.37179e12	1.43491
$520$	1.42838e10	0.00856698
$521$	−4.58716e11	−0.272756	−0.136378	−	0.990657i	$-0.543546\pi$
$521$	−4.58716e11	−0.272756	−0.136378	+	0.990657i	$0.543546\pi$
$522$	−6.43508e11	−0.379347
$523$	2.19925e11	0.128534	0.0642669	−	0.997933i	$-0.479529\pi$
$523$	2.19925e11	0.128534	0.0642669	+	0.997933i	$0.479529\pi$
$524$	−1.02273e12	−0.592612
$525$	−3.80580e8	−0.000218640 0
$526$	−8.34954e11	−0.475583
$527$	0	0
$528$	2.13134e12	1.19344
$529$	−1.45054e12	−0.805342
$530$	6.96230e11	0.383276
$531$	9.25060e11	0.504946
$532$	−3.29613e12	−1.78403
$533$	−1.27760e9	−0.000685682 0
$534$	2.18604e12	1.16338
$535$	−2.67135e12	−1.40974
$536$	−3.68876e10	−0.0193036
$537$	2.32252e12	1.20524
$538$	6.85812e11	0.352927
$539$	−2.99550e12	−1.52869
$540$	1.58050e12	0.799878
$541$	−1.58562e12	−0.795815	−0.397907	−	0.917426i	$-0.630263\pi$
$541$	−1.58562e12	−0.795815	−0.397907	+	0.917426i	$0.630263\pi$
$542$	−5.14910e12	−2.56292
$543$	−4.62776e11	−0.228440
$544$	0	0
$545$	3.38754e12	1.64475
$546$	3.85835e12	1.85795
$547$	−3.66475e12	−1.75025	−0.875127	−	0.483893i	$-0.839222\pi$
$547$	−3.66475e12	−1.75025	−0.875127	+	0.483893i	$0.839222\pi$
$548$	1.48043e12	0.701255
$549$	8.89403e11	0.417853
$550$	−3.86971e8	−0.000180321 0
$551$	−2.29839e12	−1.06229
$552$	1.26875e10	0.00581637
$553$	2.86606e12	1.30323
$554$	1.51641e12	0.683948
$555$	1.38659e12	0.620340
$556$	−3.82309e12	−1.69659
$557$	−1.44850e12	−0.637632	−0.318816	−	0.947817i	$-0.603285\pi$
$557$	−1.44850e12	−0.637632	−0.318816	+	0.947817i	$0.603285\pi$
$558$	6.21177e11	0.271245
$559$	−2.47251e12	−1.07099
$560$	3.68466e12	1.58326
$561$	0	0
$562$	−8.70470e10	−0.0368079
$563$	3.44734e12	1.44609	0.723046	−	0.690800i	$-0.242742\pi$
$563$	3.44734e12	1.44609	0.723046	+	0.690800i	$0.242742\pi$
$564$	−4.06332e12	−1.69093
$565$	−1.60235e12	−0.661514
$566$	−1.35680e12	−0.555702
$567$	−4.66075e12	−1.89379
$568$	3.66114e10	0.0147587
$569$	−2.93321e12	−1.17311	−0.586554	−	0.809910i	$-0.699516\pi$
$569$	−2.93321e12	−1.17311	−0.586554	+	0.809910i	$0.699516\pi$
$570$	−4.62630e12	−1.83568
$571$	−4.85517e12	−1.91136	−0.955678	−	0.294414i	$-0.904876\pi$
$571$	−4.85517e12	−1.91136	−0.955678	+	0.294414i	$0.904876\pi$
$572$	1.95347e12	0.762999
$573$	2.66293e12	1.03196
$574$	−5.35542e9	−0.00205916
$575$	−1.41762e8	−5.40821e−5 0
$576$	−7.52978e11	−0.285024
$577$	−3.14368e12	−1.18072	−0.590360	−	0.807140i	$-0.701014\pi$
$577$	−3.14368e12	−1.18072	−0.590360	+	0.807140i	$0.701014\pi$
$578$	0	0
$579$	1.60208e12	0.592420
$580$	−2.50677e12	−0.919790
$581$	−3.70934e12	−1.35053
$582$	−5.18549e12	−1.87343
$583$	−7.89650e11	−0.283091
$584$	−1.15299e9	−0.000410172 0
$585$	6.05887e11	0.213890
$586$	−2.21505e11	−0.0775969
$587$	5.29849e11	0.184196	0.0920981	−	0.995750i	$-0.470643\pi$
$587$	5.29849e11	0.184196	0.0920981	+	0.995750i	$0.470643\pi$
$588$	4.78834e12	1.65191
$589$	2.21864e12	0.759569
$590$	7.23699e12	2.45880
$591$	−1.03366e12	−0.348525
$592$	1.64577e12	0.550709
$593$	1.85102e12	0.614702	0.307351	−	0.951596i	$-0.400557\pi$
$593$	1.85102e12	0.614702	0.307351	+	0.951596i	$0.400557\pi$
$594$	−3.60002e12	−1.18649
$595$	0	0
$596$	−4.10338e12	−1.33209
$597$	−7.43601e10	−0.0239583
$598$	1.43719e12	0.459578
$599$	9.54735e11	0.303014	0.151507	−	0.988456i	$-0.451587\pi$
$599$	9.54735e11	0.303014	0.151507	+	0.988456i	$0.451587\pi$
$600$	−5.12995e6	−1.61597e−6 0
$601$	5.29994e12	1.65705	0.828526	−	0.559951i	$-0.189180\pi$
$601$	5.29994e12	1.65705	0.828526	+	0.559951i	$0.189180\pi$
$602$	−1.03642e13	−3.21626
$603$	−1.56469e12	−0.481948
$604$	−1.62025e12	−0.495353
$605$	−2.84922e11	−0.0864623
$606$	2.85131e12	0.858849
$607$	−2.76852e12	−0.827748	−0.413874	−	0.910334i	$-0.635825\pi$
$607$	−2.76852e12	−0.827748	−0.413874	+	0.910334i	$0.635825\pi$
$608$	−5.44624e12	−1.61633
$609$	5.61555e12	1.65430
$610$	6.95803e12	2.03471
$611$	3.81713e12	1.10803
$612$	0	0
$613$	6.26290e11	0.179144	0.0895722	−	0.995980i	$-0.471450\pi$
$613$	6.26290e11	0.179144	0.0895722	+	0.995980i	$0.471450\pi$
$614$	−5.25030e11	−0.149082
$615$	−3.74279e9	−0.00105501
$616$	−6.79083e10	−0.0190025
$617$	3.77388e12	1.04835	0.524173	−	0.851612i	$-0.324375\pi$
$617$	3.77388e12	1.04835	0.524173	+	0.851612i	$0.324375\pi$
$618$	7.36387e11	0.203076
$619$	1.48879e12	0.407592	0.203796	−	0.979013i	$-0.434672\pi$
$619$	1.48879e12	0.407592	0.203796	+	0.979013i	$0.434672\pi$
$620$	2.41978e12	0.657679
$621$	−1.31882e12	−0.355855
$622$	−3.91115e12	−1.04773
$623$	−4.28633e12	−1.13996
$624$	3.20055e12	0.845072
$625$	−3.81423e12	−0.999877
$626$	−7.55220e12	−1.96557
$627$	5.24705e12	1.35585
$628$	−1.10169e12	−0.282644
$629$	0	0
$630$	2.53974e12	0.642328
$631$	−8.19149e10	−0.0205698	−0.0102849	−	0.999947i	$-0.503274\pi$
$631$	−8.19149e10	−0.0205698	−0.0102849	+	0.999947i	$0.503274\pi$
$632$	3.86324e10	0.00963219
$633$	−1.69352e11	−0.0419249
$634$	1.38469e12	0.340368
$635$	−3.45885e12	−0.844208
$636$	1.26227e12	0.305910
$637$	−4.49822e12	−1.08246
$638$	5.70984e12	1.36437
$639$	1.55298e12	0.368477
$640$	9.85260e10	0.0232135
$641$	−8.71629e11	−0.203925	−0.101962	−	0.994788i	$-0.532512\pi$
$641$	−8.71629e11	−0.203925	−0.101962	+	0.994788i	$0.532512\pi$
$642$	−9.72650e12	−2.25969
$643$	−7.01475e11	−0.161831	−0.0809157	−	0.996721i	$-0.525784\pi$
$643$	−7.01475e11	−0.161831	−0.0809157	+	0.996721i	$0.525784\pi$
$644$	2.99975e12	0.687225
$645$	−7.24332e12	−1.64785
$646$	0	0
$647$	−6.30742e12	−1.41509	−0.707543	−	0.706671i	$-0.750196\pi$
$647$	−6.30742e12	−1.41509	−0.707543	+	0.706671i	$0.750196\pi$
$648$	−6.28236e10	−0.0139970
$649$	−8.20805e12	−1.81610
$650$	−5.81098e8	−0.000127685 0
$651$	−5.42068e12	−1.18288
$652$	8.18726e12	1.77429
$653$	2.08016e12	0.447701	0.223850	−	0.974624i	$-0.428137\pi$
$653$	2.08016e12	0.447701	0.223850	+	0.974624i	$0.428137\pi$
$654$	1.23342e13	2.63639
$655$	2.81460e12	0.597490
$656$	−4.44239e9	−0.000936589 0
$657$	−4.89072e10	−0.0102407
$658$	1.60006e13	3.32751
$659$	−1.77225e12	−0.366051	−0.183025	−	0.983108i	$-0.558589\pi$
$659$	−1.77225e12	−0.366051	−0.183025	+	0.983108i	$0.558589\pi$
$660$	5.72276e12	1.17397
$661$	−1.32844e12	−0.270666	−0.135333	−	0.990800i	$-0.543210\pi$
$661$	−1.32844e12	−0.270666	−0.135333	+	0.990800i	$0.543210\pi$
$662$	5.42849e12	1.09855
$663$	0	0
$664$	−4.99992e10	−0.00998175
$665$	9.07111e12	1.79872
$666$	1.13439e12	0.223423
$667$	2.09173e12	0.409203
$668$	5.64634e12	1.09717
$669$	−7.64081e12	−1.47476
$670$	−1.22410e13	−2.34682
$671$	−7.89166e12	−1.50286
$672$	1.33065e13	2.51711
$673$	7.10413e12	1.33488	0.667441	−	0.744662i	$-0.267389\pi$
$673$	7.10413e12	1.33488	0.667441	+	0.744662i	$0.267389\pi$
$674$	−3.27761e11	−0.0611769
$675$	5.33238e8	9.88677e−5 0
$676$	−2.45140e12	−0.451497
$677$	−1.12958e11	−0.0206665	−0.0103333	−	0.999947i	$-0.503289\pi$
$677$	−1.12958e11	−0.0206665	−0.0103333	+	0.999947i	$0.503289\pi$
$678$	−5.83422e12	−1.06035
$679$	1.01676e13	1.83570
$680$	0	0
$681$	3.35391e12	0.597571
$682$	−5.51170e12	−0.975564
$683$	3.35112e12	0.589246	0.294623	−	0.955614i	$-0.404806\pi$
$683$	3.35112e12	0.589246	0.294623	+	0.955614i	$0.404806\pi$
$684$	−1.88460e12	−0.329206
$685$	−4.07421e12	−0.707027
$686$	−5.99889e12	−1.03422
$687$	−2.56054e12	−0.438557
$688$	−8.59723e12	−1.46289
$689$	−1.18579e12	−0.200456
$690$	4.21031e12	0.707120
$691$	7.54720e12	1.25932	0.629658	−	0.776873i	$-0.283195\pi$
$691$	7.54720e12	1.25932	0.629658	+	0.776873i	$0.283195\pi$
$692$	7.55877e12	1.25307
$693$	−2.88052e12	−0.474430
$694$	−4.80351e12	−0.786034
$695$	1.05213e13	1.71056
$696$	7.56936e10	0.0122269
$697$	0	0
$698$	−1.40013e13	−2.23264
$699$	9.69130e12	1.53545
$700$	−1.21289e9	−0.000190932 0
$701$	1.61959e12	0.253323	0.126662	−	0.991946i	$-0.459574\pi$
$701$	1.61959e12	0.253323	0.126662	+	0.991946i	$0.459574\pi$
$702$	−5.40601e12	−0.840155
$703$	4.05166e12	0.625654
$704$	6.68117e12	1.02512
$705$	1.11824e13	1.70485
$706$	−1.06170e12	−0.160835
$707$	−5.59075e12	−0.841556
$708$	1.31207e13	1.96249
$709$	−1.71850e12	−0.255413	−0.127706	−	0.991812i	$-0.540761\pi$
$709$	−1.71850e12	−0.255413	−0.127706	+	0.991812i	$0.540761\pi$
$710$	1.21493e13	1.79428
$711$	1.63870e12	0.240485
$712$	−5.77767e10	−0.00842544
$713$	−2.01914e12	−0.292593
$714$	0	0
$715$	−5.37602e12	−0.769279
$716$	7.40174e12	1.05251
$717$	7.43723e12	1.05093
$718$	−6.53982e12	−0.918345
$719$	−1.34411e13	−1.87566	−0.937832	−	0.347089i	$-0.887170\pi$
$719$	−1.34411e13	−1.87566	−0.937832	+	0.347089i	$0.887170\pi$
$720$	2.10675e12	0.292157
$721$	−1.44388e12	−0.198987
$722$	−3.21342e12	−0.440099
$723$	−1.56764e12	−0.213365
$724$	−1.47484e12	−0.199490
$725$	−8.45747e8	−0.000113689 0
$726$	−1.03741e12	−0.138592
$727$	1.27527e13	1.69316	0.846579	−	0.532263i	$-0.178658\pi$
$727$	1.27527e13	1.69316	0.846579	+	0.532263i	$0.178658\pi$
$728$	−1.01975e11	−0.0134556
$729$	4.32028e12	0.566550
$730$	−3.82614e11	−0.0498663
$731$	0	0
$732$	1.26149e13	1.62400
$733$	1.14507e13	1.46509	0.732547	−	0.680717i	$-0.238332\pi$
$733$	1.14507e13	1.46509	0.732547	+	0.680717i	$0.238332\pi$
$734$	−1.02156e13	−1.29906
$735$	−1.31777e13	−1.66551
$736$	4.95653e12	0.622626
$737$	1.38835e13	1.73338
$738$	−3.06203e9	−0.000379975 0
$739$	1.27616e13	1.57400	0.787000	−	0.616953i	$-0.211633\pi$
$739$	1.27616e13	1.57400	0.787000	+	0.616953i	$0.211633\pi$
$740$	4.41899e12	0.541727
$741$	7.87930e12	0.960076
$742$	−4.97055e12	−0.601987
$743$	−4.54322e12	−0.546907	−0.273454	−	0.961885i	$-0.588166\pi$
$743$	−4.54322e12	−0.546907	−0.273454	+	0.961885i	$0.588166\pi$
$744$	−7.30669e10	−0.00874264
$745$	1.12927e13	1.34305
$746$	5.54041e12	0.654963
$747$	−2.12086e12	−0.249212
$748$	0	0
$749$	1.90714e13	2.21419
$750$	−1.38895e13	−1.60291
$751$	−8.88851e12	−1.01965	−0.509823	−	0.860279i	$-0.670289\pi$
$751$	−8.88851e12	−1.01965	−0.509823	+	0.860279i	$0.670289\pi$
$752$	1.32727e13	1.51348
$753$	9.10707e12	1.03229
$754$	8.57424e12	0.966105
$755$	4.45899e12	0.499430
$756$	−1.12836e13	−1.25632
$757$	6.29935e12	0.697211	0.348605	−	0.937270i	$-0.386655\pi$
$757$	6.29935e12	0.697211	0.348605	+	0.937270i	$0.386655\pi$
$758$	−4.28180e12	−0.471102
$759$	−4.77525e12	−0.522285
$760$	1.22272e11	0.0132943
$761$	2.40574e12	0.260026	0.130013	−	0.991512i	$-0.458498\pi$
$761$	2.40574e12	0.260026	0.130013	+	0.991512i	$0.458498\pi$
$762$	−1.25938e13	−1.35319
$763$	−2.41845e13	−2.58331
$764$	8.48660e12	0.901185
$765$	0	0
$766$	1.84792e13	1.93934
$767$	−1.23257e13	−1.28598
$768$	1.11272e13	1.15415
$769$	−1.51735e12	−0.156465	−0.0782326	−	0.996935i	$-0.524928\pi$
$769$	−1.51735e12	−0.156465	−0.0782326	+	0.996935i	$0.524928\pi$
$770$	−2.25351e13	−2.31021
$771$	1.37006e13	1.39635
$772$	5.10573e12	0.517345
$773$	1.39024e13	1.40050	0.700251	−	0.713897i	$-0.253072\pi$
$773$	1.39024e13	1.40050	0.700251	+	0.713897i	$0.253072\pi$
$774$	−5.92586e12	−0.593495
$775$	8.16398e8	8.12914e−5 0
$776$	1.37051e11	0.0135677
$777$	−9.89921e12	−0.974330
$778$	−1.08700e13	−1.06370
$779$	−1.09365e10	−0.00106405
$780$	8.59365e12	0.831289
$781$	−1.37795e13	−1.32527
$782$	0	0
$783$	−7.86805e12	−0.748065
$784$	−1.56409e13	−1.47856
$785$	3.03189e12	0.284971
$786$	1.02481e13	0.957723
$787$	1.50319e13	1.39678	0.698391	−	0.715716i	$-0.253900\pi$
$787$	1.50319e13	1.39678	0.698391	+	0.715716i	$0.253900\pi$
$788$	−3.29422e12	−0.304358
$789$	4.16597e12	0.382710
$790$	1.28200e13	1.17103
$791$	1.14396e13	1.03900
$792$	−3.88274e10	−0.00350651
$793$	−1.18506e13	−1.06417
$794$	−1.07933e13	−0.963741
$795$	−3.47381e12	−0.308428
$796$	−2.36982e11	−0.0209221
$797$	1.82924e13	1.60586	0.802930	−	0.596073i	$-0.203273\pi$
$797$	1.82924e13	1.60586	0.802930	+	0.596073i	$0.203273\pi$
$798$	3.30283e13	2.88319
$799$	0	0
$800$	−2.00407e9	−0.000172985 0
$801$	−2.45076e12	−0.210356
$802$	−2.16629e13	−1.84897
$803$	4.33953e11	0.0368317
$804$	−2.21929e13	−1.87311
$805$	−8.25545e12	−0.692882
$806$	−8.27670e12	−0.690796
$807$	−3.42183e12	−0.284006
$808$	−7.53594e10	−0.00621994
$809$	6.91099e11	0.0567246	0.0283623	−	0.999598i	$-0.490971\pi$
$809$	6.91099e11	0.0567246	0.0283623	+	0.999598i	$0.490971\pi$
$810$	−2.08477e13	−1.70167
$811$	−1.42607e13	−1.15757	−0.578785	−	0.815480i	$-0.696473\pi$
$811$	−1.42607e13	−1.15757	−0.578785	+	0.815480i	$0.696473\pi$
$812$	1.78964e13	1.44466
$813$	2.56912e13	2.06242
$814$	−1.00654e13	−0.803567
$815$	−2.25317e13	−1.78889
$816$	0	0
$817$	−2.11652e13	−1.66197
$818$	−1.21325e13	−0.947458
$819$	−4.32557e12	−0.335943
$820$	−1.19281e10	−0.000921313 0
$821$	4.35431e12	0.334484	0.167242	−	0.985916i	$-0.446514\pi$
$821$	4.35431e12	0.334484	0.167242	+	0.985916i	$0.446514\pi$
$822$	−1.48344e13	−1.13330
$823$	−1.25808e13	−0.955892	−0.477946	−	0.878389i	$-0.658619\pi$
$823$	−1.25808e13	−0.955892	−0.477946	+	0.878389i	$0.658619\pi$
$824$	−1.94625e10	−0.00147071
$825$	1.93077e9	0.000145107 0
$826$	−5.16666e13	−3.86189
$827$	−1.63352e13	−1.21437	−0.607183	−	0.794562i	$-0.707700\pi$
$827$	−1.63352e13	−1.21437	−0.607183	+	0.794562i	$0.707700\pi$
$828$	1.71514e12	0.126813
$829$	2.48744e13	1.82918	0.914591	−	0.404380i	$-0.132513\pi$
$829$	2.48744e13	1.82918	0.914591	+	0.404380i	$0.132513\pi$
$830$	−1.65920e13	−1.21352
$831$	−7.56607e12	−0.550384
$832$	1.00328e13	0.725887
$833$	0	0
$834$	3.83085e13	2.74187
$835$	−1.55390e13	−1.10620
$836$	1.67221e13	1.18403
$837$	7.59502e12	0.534890
$838$	2.01296e13	1.41006
$839$	1.61316e13	1.12396	0.561978	−	0.827152i	$-0.310040\pi$
$839$	1.61316e13	1.12396	0.561978	+	0.827152i	$0.310040\pi$
$840$	−2.98741e11	−0.0207032
$841$	−2.02796e12	−0.139791
$842$	−1.07548e13	−0.737388
$843$	4.34318e11	0.0296199
$844$	−5.39714e11	−0.0366119
$845$	6.74637e12	0.455213
$846$	9.14851e12	0.614022
$847$	2.03413e12	0.135801
$848$	−4.12313e12	−0.273808
$849$	6.76970e12	0.447182
$850$	0	0
$851$	−3.68734e12	−0.241007
$852$	2.20268e13	1.43210
$853$	1.29304e10	0.000836263 0	0.000418132	−	1.00000i	$-0.499867\pi$
$853$	1.29304e10	0.000836263 0	0.000418132		1.00000i	$0.499867\pi$
$854$	−4.96751e13	−3.19579
$855$	5.18651e12	0.331916
$856$	2.57069e11	0.0163651
$857$	1.42717e12	0.0903779	0.0451889	−	0.998978i	$-0.485611\pi$
$857$	1.42717e12	0.0903779	0.0451889	+	0.998978i	$0.485611\pi$
$858$	−1.95743e13	−1.23309
$859$	−9.05087e12	−0.567180	−0.283590	−	0.958946i	$-0.591526\pi$
$859$	−9.05087e12	−0.567180	−0.283590	+	0.958946i	$0.591526\pi$
$860$	−2.30840e13	−1.43903
$861$	2.67207e10	0.00165704
$862$	6.62469e12	0.408680
$863$	1.02844e13	0.631148	0.315574	−	0.948901i	$-0.397803\pi$
$863$	1.02844e13	0.631148	0.315574	+	0.948901i	$0.397803\pi$
$864$	−1.86440e13	−1.13822
$865$	−2.08021e13	−1.26338
$866$	−2.08417e13	−1.25923
$867$	0	0
$868$	−1.72754e13	−1.03297
$869$	−1.45402e13	−0.864931
$870$	2.51186e13	1.48648
$871$	2.08483e13	1.22741
$872$	−3.25989e11	−0.0190932
$873$	5.81342e12	0.338741
$874$	1.23026e13	0.713176
$875$	2.72340e13	1.57064
$876$	−6.93679e11	−0.0398006
$877$	−6.79965e12	−0.388140	−0.194070	−	0.980988i	$-0.562169\pi$
$877$	−6.79965e12	−0.388140	−0.194070	+	0.980988i	$0.562169\pi$
$878$	1.91408e13	1.08701
$879$	1.10519e12	0.0624435
$880$	−1.86931e13	−1.05078
$881$	3.08404e13	1.72476	0.862380	−	0.506262i	$-0.168973\pi$
$881$	3.08404e13	1.72476	0.862380	+	0.506262i	$0.168973\pi$
$882$	−1.07809e13	−0.599854
$883$	3.17104e13	1.75541	0.877706	−	0.479200i	$-0.159073\pi$
$883$	3.17104e13	1.75541	0.877706	+	0.479200i	$0.159073\pi$
$884$	0	0
$885$	−3.61087e13	−1.97864
$886$	−4.42960e12	−0.241497
$887$	−6.89150e12	−0.373816	−0.186908	−	0.982377i	$-0.559847\pi$
$887$	−6.89150e12	−0.373816	−0.186908	+	0.982377i	$0.559847\pi$
$888$	−1.33434e11	−0.00720127
$889$	2.46935e13	1.32594
$890$	−1.91729e13	−1.02432
$891$	2.36451e13	1.25687
$892$	−2.43508e13	−1.28787
$893$	3.26754e13	1.71945
$894$	4.11171e13	2.15280
$895$	−2.03699e13	−1.06117
$896$	−7.03401e11	−0.0364600
$897$	−7.17080e12	−0.369830
$898$	−5.68656e12	−0.291814
$899$	−1.20461e13	−0.615077
$900$	−6.93484e8	−3.52326e−5 0
$901$	0	0
$902$	2.71693e10	0.00136662
$903$	5.17118e13	2.58818
$904$	1.54197e11	0.00767924
$905$	4.05883e12	0.201132
$906$	1.62353e13	0.800543
$907$	2.11844e13	1.03940	0.519700	−	0.854349i	$-0.326044\pi$
$907$	2.11844e13	1.03940	0.519700	+	0.854349i	$0.326044\pi$
$908$	1.06887e13	0.521843
$909$	−3.19658e12	−0.155292
$910$	−3.38401e13	−1.63586
$911$	3.86760e13	1.86041	0.930206	−	0.367039i	$-0.119628\pi$
$911$	3.86760e13	1.86041	0.930206	+	0.367039i	$0.119628\pi$
$912$	2.73973e13	1.31139
$913$	1.88183e13	0.896319
$914$	5.19778e12	0.246354
$915$	−3.47168e13	−1.63736
$916$	−8.16029e12	−0.382980
$917$	−2.00941e13	−0.938439
$918$	0	0
$919$	3.05320e11	0.0141200	0.00706000	−	0.999975i	$-0.497753\pi$
$919$	3.05320e11	0.0141200	0.00706000	+	0.999975i	$0.497753\pi$
$920$	−1.11278e11	−0.00512109
$921$	2.61962e12	0.119969
$922$	4.58105e13	2.08774
$923$	−2.06922e13	−0.938423
$924$	−4.08562e13	−1.84388
$925$	1.49090e9	6.69593e−5 0
$926$	−2.57333e13	−1.15013
$927$	−8.25558e11	−0.0367188
$928$	2.95705e13	1.30886
$929$	1.17442e13	0.517313	0.258656	−	0.965969i	$-0.416720\pi$
$929$	1.17442e13	0.517313	0.258656	+	0.965969i	$0.416720\pi$
$930$	−2.42469e13	−1.06288
$931$	−3.85057e13	−1.67978
$932$	3.08856e13	1.34086
$933$	1.95145e13	0.843123
$934$	−2.94677e13	−1.26703
$935$	0	0
$936$	−5.83056e10	−0.00248296
$937$	−2.08580e13	−0.883983	−0.441991	−	0.897019i	$-0.645728\pi$
$937$	−2.08580e13	−0.883983	−0.441991	+	0.897019i	$0.645728\pi$
$938$	8.73913e13	3.68600
$939$	3.76814e13	1.58173
$940$	3.56378e13	1.48880
$941$	−3.69821e13	−1.53758	−0.768791	−	0.639500i	$-0.779141\pi$
$941$	−3.69821e13	−1.53758	−0.768791	+	0.639500i	$0.779141\pi$
$942$	1.10392e13	0.456783
$943$	9.95313e9	0.000409880 0
$944$	−4.28581e13	−1.75654
$945$	3.10529e13	1.26666
$946$	5.25801e13	2.13457
$947$	−3.26913e13	−1.32086	−0.660432	−	0.750886i	$-0.729627\pi$
$947$	−3.26913e13	−1.32086	−0.660432	+	0.750886i	$0.729627\pi$
$948$	2.32427e13	0.934650
$949$	6.51650e11	0.0260805
$950$	−4.97432e9	−0.000198143 0
$951$	−6.90883e12	−0.273900
$952$	0	0
$953$	−3.10457e13	−1.21922	−0.609612	−	0.792700i	$-0.708675\pi$
$953$	−3.10457e13	−1.21922	−0.609612	+	0.792700i	$0.708675\pi$
$954$	−2.84197e12	−0.111084
$955$	−2.33555e13	−0.908603
$956$	2.37020e13	0.917751
$957$	−2.84890e13	−1.09793
$958$	1.31165e13	0.503124
$959$	2.90868e13	1.11048
$960$	2.93916e13	1.11687
$961$	−1.48115e13	−0.560201
$962$	−1.51149e13	−0.569005
$963$	1.09043e13	0.408583
$964$	−4.99597e12	−0.186326
$965$	−1.40512e13	−0.521603
$966$	−3.00584e13	−1.11063
$967$	1.13694e13	0.418138	0.209069	−	0.977901i	$-0.432957\pi$
$967$	1.13694e13	0.418138	0.209069	+	0.977901i	$0.432957\pi$
$968$	2.74186e10	0.00100370
$969$	0	0
$970$	4.54799e13	1.64948
$971$	2.34437e13	0.846330	0.423165	−	0.906053i	$-0.360919\pi$
$971$	2.34437e13	0.846330	0.423165	+	0.906053i	$0.360919\pi$
$972$	−1.55358e13	−0.558258
$973$	−7.51141e13	−2.68667
$974$	2.33150e13	0.830082
$975$	2.89937e9	0.000102750 0
$976$	−4.12061e13	−1.45357
$977$	−8.22524e11	−0.0288817	−0.0144409	−	0.999896i	$-0.504597\pi$
$977$	−8.22524e11	−0.0288817	−0.0144409	+	0.999896i	$0.504597\pi$
$978$	−8.20388e13	−2.86744
$979$	2.17456e13	0.756569
$980$	−4.19967e13	−1.45445
$981$	−1.38278e13	−0.476696
$982$	−7.00340e13	−2.40330
$983$	2.37832e12	0.0812417	0.0406209	−	0.999175i	$-0.487066\pi$
$983$	2.37832e12	0.0812417	0.0406209	+	0.999175i	$0.487066\pi$
$984$	3.60175e8	1.22472e−5 0
$985$	9.06583e12	0.306863
$986$	0	0
$987$	−7.98342e13	−2.67770
$988$	2.51109e13	0.838408
$989$	1.92620e13	0.640205
$990$	−1.28847e13	−0.426301
$991$	−4.31408e11	−0.0142088	−0.00710439	−	0.999975i	$-0.502261\pi$
$991$	−4.31408e11	−0.0142088	−0.00710439	+	0.999975i	$0.502261\pi$
$992$	−2.85444e13	−0.935875
$993$	−2.70852e13	−0.884018
$994$	−8.67370e13	−2.81816
$995$	6.52184e11	0.0210943
$996$	−3.00814e13	−0.968569
$997$	−3.60987e13	−1.15708	−0.578539	−	0.815655i	$-0.696377\pi$
$997$	−3.60987e13	−1.15708	−0.578539	+	0.815655i	$0.696377\pi$
$998$	6.72892e13	2.14713
$999$	1.38700e13	0.440586

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.i.1.10		52
17.3	odd	16		17.10.d.a.9.3	yes	52
17.6	odd	16		17.10.d.a.2.3	✓	52
17.16	even	2	inner	289.10.a.i.1.9		52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.10.d.a.2.3	✓	52	17.6	odd	16
17.10.d.a.9.3	yes	52	17.3	odd	16
289.10.a.i.1.9		52	17.16	even	2	inner
289.10.a.i.1.10		52	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-31.9341 q^{2} +159.334 q^{3} +507.789 q^{4} -1397.46 q^{5} -5088.20 q^{6} +9976.78 q^{7} +134.480 q^{8} +5704.34 q^{9} +O(q^{10})\)	\(q-31.9341 q^{2} +159.334 q^{3} +507.789 q^{4} -1397.46 q^{5} -5088.20 q^{6} +9976.78 q^{7} +134.480 q^{8} +5704.34 q^{9} +44626.6 q^{10} -50614.6 q^{11} +80908.1 q^{12} -76005.9 q^{13} -318600. q^{14} -222662. q^{15} -264282. q^{16} -182163. q^{18} -650626. q^{19} -709613. q^{20} +1.58964e6 q^{21} +1.61633e6 q^{22} +592123. q^{23} +21427.2 q^{24} -239.413 q^{25} +2.42718e6 q^{26} -2.22728e6 q^{27} +5.06610e6 q^{28} +3.53259e6 q^{29} +7.11053e6 q^{30} -3.41000e6 q^{31} +8.37077e6 q^{32} -8.06462e6 q^{33} -1.39421e7 q^{35} +2.89660e6 q^{36} -6.22732e6 q^{37} +2.07772e7 q^{38} -1.21103e7 q^{39} -187930. q^{40} +16809.2 q^{41} -5.07638e7 q^{42} +3.25305e7 q^{43} -2.57015e7 q^{44} -7.97157e6 q^{45} -1.89089e7 q^{46} -5.02215e7 q^{47} -4.21092e7 q^{48} +5.91825e7 q^{49} +7645.44 q^{50} -3.85949e7 q^{52} +1.56012e7 q^{53} +7.11261e7 q^{54} +7.07317e7 q^{55} +1.34168e6 q^{56} -1.03667e8 q^{57} -1.12810e8 q^{58} +1.62168e8 q^{59} -1.13066e8 q^{60} +1.55917e8 q^{61} +1.08895e8 q^{62} +5.69110e7 q^{63} -1.32001e8 q^{64} +1.06215e8 q^{65} +2.57537e8 q^{66} -2.74298e8 q^{67} +9.43453e7 q^{69} +4.45229e8 q^{70} +2.72244e8 q^{71} +767119. q^{72} -8.57367e6 q^{73} +1.98864e8 q^{74} -38146.6 q^{75} -3.30381e8 q^{76} -5.04970e8 q^{77} +3.86733e8 q^{78} +2.87273e8 q^{79} +3.69323e8 q^{80} -4.67160e8 q^{81} -536788. q^{82} -3.71797e8 q^{83} +8.07202e8 q^{84} -1.03883e9 q^{86} +5.62862e8 q^{87} -6.80664e6 q^{88} -4.29631e8 q^{89} +2.54565e8 q^{90} -7.58294e8 q^{91} +3.00673e8 q^{92} -5.43330e8 q^{93} +1.60378e9 q^{94} +9.09222e8 q^{95} +1.33375e9 q^{96} +1.01912e9 q^{97} -1.88994e9 q^{98} -2.88723e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9}+O(q^{10}) \) 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9	\( 52 q + 64 q^{2} + 13312 q^{4} + 49152 q^{8} + 341172 q^{9} + 156200 q^{13} + 1207872 q^{15} + 3407880 q^{16} + 2193336 q^{18} + 1185568 q^{19} + 5198336 q^{21} + 13827692 q^{25} + 3618944 q^{26} - 9167544 q^{30} + 61884888 q^{32} + 1635208 q^{33} + 46992776 q^{35} + 156027320 q^{36} + 84813952 q^{38} - 4635776 q^{42} + 125448912 q^{43} + 164193176 q^{47} + 270850284 q^{49} - 226223888 q^{50} + 103553016 q^{52} + 426167208 q^{53} + 677761520 q^{55} + 375214512 q^{59} + 336918024 q^{60} + 190014416 q^{64} + 1377178928 q^{66} + 311910088 q^{67} + 533688136 q^{69} + 1477690280 q^{70} + 2757942680 q^{72} + 4047975520 q^{76} + 3440336432 q^{77} + 3266558756 q^{81} + 2072890608 q^{83} + 2630025952 q^{84} + 1538547296 q^{86} - 1010436256 q^{87} + 1873849184 q^{89} - 1998451624 q^{93} - 6880776704 q^{94} - 4667454128 q^{98}+O(q^{100}) \) 52 * q + 64 * q^2 + 13312 * q^4 + 49152 * q^8 + 341172 * q^9 + 156200 * q^13 + 1207872 * q^15 + 3407880 * q^16 + 2193336 * q^18 + 1185568 * q^19 + 5198336 * q^21 + 13827692 * q^25 + 3618944 * q^26 - 9167544 * q^30 + 61884888 * q^32 + 1635208 * q^33 + 46992776 * q^35 + 156027320 * q^36 + 84813952 * q^38 - 4635776 * q^42 + 125448912 * q^43 + 164193176 * q^47 + 270850284 * q^49 - 226223888 * q^50 + 103553016 * q^52 + 426167208 * q^53 + 677761520 * q^55 + 375214512 * q^59 + 336918024 * q^60 + 190014416 * q^64 + 1377178928 * q^66 + 311910088 * q^67 + 533688136 * q^69 + 1477690280 * q^70 + 2757942680 * q^72 + 4047975520 * q^76 + 3440336432 * q^77 + 3266558756 * q^81 + 2072890608 * q^83 + 2630025952 * q^84 + 1538547296 * q^86 - 1010436256 * q^87 + 1873849184 * q^89 - 1998451624 * q^93 - 6880776704 * q^94 - 4667454128 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more