LMFDB - Embedded newform 210.10.a.j.1.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [210,10,Mod(1,210)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("210.1"); S:= CuspForms(chi, 10); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(210, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0])) N = Newforms(chi, 10, names="a")

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	210.a (trivial)

Newform invariants

comment:select newform

sage:traces = [2,32,-162,512,-1250,-2592,4802,8192,13122,-20000,-41964] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	yes
Analytic conductor:	$108.157525594$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{277}) $
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 69 $ x^2 - x - 69
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-7.82166$ of defining polynomial
Character	$\chi$	$=$	210.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+16.0000 q^{2} -81.0000 q^{3} +256.000 q^{4} -625.000 q^{5} -1296.00 q^{6} +2401.00 q^{7} +4096.00 q^{8} +6561.00 q^{9} -10000.0 q^{10} +16465.5 q^{11} -20736.0 q^{12} -80362.9 q^{13} +38416.0 q^{14} +50625.0 q^{15} +65536.0 q^{16} -359110. q^{17} +104976. q^{18} +786001. q^{19} -160000. q^{20} -194481. q^{21} +263447. q^{22} -1.23104e6 q^{23} -331776. q^{24} +390625. q^{25} -1.28581e6 q^{26} -531441. q^{27} +614656. q^{28} +172353. q^{29} +810000. q^{30} +4.27437e6 q^{31} +1.04858e6 q^{32} -1.33370e6 q^{33} -5.74577e6 q^{34} -1.50062e6 q^{35} +1.67962e6 q^{36} -1.75495e6 q^{37} +1.25760e7 q^{38} +6.50939e6 q^{39} -2.56000e6 q^{40} +3.44105e7 q^{41} -3.11170e6 q^{42} -1.28955e7 q^{43} +4.21516e6 q^{44} -4.10062e6 q^{45} -1.96966e7 q^{46} -3.10155e7 q^{47} -5.30842e6 q^{48} +5.76480e6 q^{49} +6.25000e6 q^{50} +2.90879e7 q^{51} -2.05729e7 q^{52} -4.58835e7 q^{53} -8.50306e6 q^{54} -1.02909e7 q^{55} +9.83450e6 q^{56} -6.36661e7 q^{57} +2.75764e6 q^{58} -2.43356e7 q^{59} +1.29600e7 q^{60} +6.17480e7 q^{61} +6.83899e7 q^{62} +1.57530e7 q^{63} +1.67772e7 q^{64} +5.02268e7 q^{65} -2.13392e7 q^{66} -2.71891e8 q^{67} -9.19323e7 q^{68} +9.97143e7 q^{69} -2.40100e7 q^{70} -4.21856e8 q^{71} +2.68739e7 q^{72} -4.28558e7 q^{73} -2.80792e7 q^{74} -3.16406e7 q^{75} +2.01216e8 q^{76} +3.95336e7 q^{77} +1.04150e8 q^{78} +4.53996e7 q^{79} -4.09600e7 q^{80} +4.30467e7 q^{81} +5.50569e8 q^{82} -2.31569e8 q^{83} -4.97871e7 q^{84} +2.24444e8 q^{85} -2.06327e8 q^{86} -1.39606e7 q^{87} +6.74425e7 q^{88} -3.96418e8 q^{89} -6.56100e7 q^{90} -1.92951e8 q^{91} -3.15146e8 q^{92} -3.46224e8 q^{93} -4.96248e8 q^{94} -4.91251e8 q^{95} -8.49347e7 q^{96} +2.38865e8 q^{97} +9.22368e7 q^{98} +1.08030e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 32 q^{2} - 162 q^{3} + 512 q^{4} - 1250 q^{5} - 2592 q^{6} + 4802 q^{7} + 8192 q^{8} + 13122 q^{9} - 20000 q^{10} - 41964 q^{11} - 41472 q^{12} - 67856 q^{13} + 76832 q^{14} + 101250 q^{15} + 131072 q^{16}+ \cdots - 275325804 q^{99}+O(q^{100}) $ 2 * q + 32 * q^2 - 162 * q^3 + 512 * q^4 - 1250 * q^5 - 2592 * q^6 + 4802 * q^7 + 8192 * q^8 + 13122 * q^9 - 20000 * q^10 - 41964 * q^11 - 41472 * q^12 - 67856 * q^13 + 76832 * q^14 + 101250 * q^15 + 131072 * q^16 + 96636 * q^17 + 209952 * q^18 + 664276 * q^19 - 320000 * q^20 - 388962 * q^21 - 671424 * q^22 + 246120 * q^23 - 663552 * q^24 + 781250 * q^25 - 1085696 * q^26 - 1062882 * q^27 + 1229312 * q^28 - 4304772 * q^29 + 1620000 * q^30 - 4366148 * q^31 + 2097152 * q^32 + 3399084 * q^33 + 1546176 * q^34 - 3001250 * q^35 + 3359232 * q^36 - 3575804 * q^37 + 10628416 * q^38 + 5496336 * q^39 - 5120000 * q^40 + 44782812 * q^41 - 6223392 * q^42 + 22063936 * q^43 - 10742784 * q^44 - 8201250 * q^45 + 3937920 * q^46 + 7082088 * q^47 - 10616832 * q^48 + 11529602 * q^49 + 12500000 * q^50 - 7827516 * q^51 - 17371136 * q^52 - 123069984 * q^53 - 17006112 * q^54 + 26227500 * q^55 + 19668992 * q^56 - 53806356 * q^57 - 68876352 * q^58 - 151552896 * q^59 + 25920000 * q^60 - 69217700 * q^61 - 69858368 * q^62 + 31505922 * q^63 + 33554432 * q^64 + 42410000 * q^65 + 54385344 * q^66 - 348097064 * q^67 + 24738816 * q^68 - 19935720 * q^69 - 48020000 * q^70 - 194772348 * q^71 + 53747712 * q^72 + 297178240 * q^73 - 57212864 * q^74 - 63281250 * q^75 + 170054656 * q^76 - 100755564 * q^77 + 87941376 * q^78 - 356059832 * q^79 - 81920000 * q^80 + 86093442 * q^81 + 716524992 * q^82 - 706246128 * q^83 - 99574272 * q^84 - 60397500 * q^85 + 353022976 * q^86 + 348686532 * q^87 - 171884544 * q^88 - 1122685860 * q^89 - 131220000 * q^90 - 162922256 * q^91 + 63006720 * q^92 + 353657988 * q^93 + 113313408 * q^94 - 415172500 * q^95 - 169869312 * q^96 - 939835400 * q^97 + 184473632 * q^98 - 275325804 * q^99

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 $

$2$	16.0000	0.707107
$2$	16.0000	0.707107
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	256.000	0.500000
$5$	−625.000	−0.447214
$5$	−625.000	−0.447214
$6$	−1296.00	−0.408248
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	4096.00	0.353553
$9$	6561.00	0.333333
$10$	−10000.0	−0.316228
$11$	16465.5	0.339084	0.169542	−	0.985523i	$-0.445771\pi$
$11$	16465.5	0.339084	0.169542	+	0.985523i	$0.445771\pi$
$12$	−20736.0	−0.288675
$13$	−80362.9	−0.780387	−0.390194	−	0.920733i	$-0.627592\pi$
$13$	−80362.9	−0.780387	−0.390194	+	0.920733i	$0.627592\pi$
$14$	38416.0	0.267261
$15$	50625.0	0.258199
$16$	65536.0	0.250000
$17$	−359110.	−1.04282	−0.521408	−	0.853307i	$-0.674593\pi$
$17$	−359110.	−1.04282	−0.521408	+	0.853307i	$0.674593\pi$
$18$	104976.	0.235702
$19$	786001.	1.38367	0.691834	−	0.722056i	$-0.256803\pi$
$19$	786001.	1.38367	0.691834	+	0.722056i	$0.256803\pi$
$20$	−160000.	−0.223607
$21$	−194481.	−0.218218
$22$	263447.	0.239768
$23$	−1.23104e6	−0.917270	−0.458635	−	0.888625i	$-0.651661\pi$
$23$	−1.23104e6	−0.917270	−0.458635	+	0.888625i	$0.651661\pi$
$24$	−331776.	−0.204124
$25$	390625.	0.200000
$26$	−1.28581e6	−0.551817
$27$	−531441.	−0.192450
$28$	614656.	0.188982
$29$	172353.	0.0452508	0.0226254	−	0.999744i	$-0.492797\pi$
$29$	172353.	0.0452508	0.0226254	+	0.999744i	$0.492797\pi$
$30$	810000.	0.182574
$31$	4.27437e6	0.831274	0.415637	−	0.909531i	$-0.363559\pi$
$31$	4.27437e6	0.831274	0.415637	+	0.909531i	$0.363559\pi$
$32$	1.04858e6	0.176777
$33$	−1.33370e6	−0.195770
$34$	−5.74577e6	−0.737383
$35$	−1.50062e6	−0.169031
$36$	1.67962e6	0.166667
$37$	−1.75495e6	−0.153942	−0.0769709	−	0.997033i	$-0.524525\pi$
$37$	−1.75495e6	−0.153942	−0.0769709	+	0.997033i	$0.524525\pi$
$38$	1.25760e7	0.978401
$39$	6.50939e6	0.450557
$40$	−2.56000e6	−0.158114
$41$	3.44105e7	1.90180	0.950899	−	0.309503i	$-0.100163\pi$
$41$	3.44105e7	1.90180	0.950899	+	0.309503i	$0.100163\pi$
$42$	−3.11170e6	−0.154303
$43$	−1.28955e7	−0.575213	−0.287607	−	0.957749i	$-0.592860\pi$
$43$	−1.28955e7	−0.575213	−0.287607	+	0.957749i	$0.592860\pi$
$44$	4.21516e6	0.169542
$45$	−4.10062e6	−0.149071
$46$	−1.96966e7	−0.648608
$47$	−3.10155e7	−0.927125	−0.463562	−	0.886064i	$-0.653429\pi$
$47$	−3.10155e7	−0.927125	−0.463562	+	0.886064i	$0.653429\pi$
$48$	−5.30842e6	−0.144338
$49$	5.76480e6	0.142857
$50$	6.25000e6	0.141421
$51$	2.90879e7	0.602070
$52$	−2.05729e7	−0.390194
$53$	−4.58835e7	−0.798757	−0.399378	−	0.916786i	$-0.630774\pi$
$53$	−4.58835e7	−0.798757	−0.399378	+	0.916786i	$0.630774\pi$
$54$	−8.50306e6	−0.136083
$55$	−1.02909e7	−0.151643
$56$	9.83450e6	0.133631
$57$	−6.36661e7	−0.798861
$58$	2.75764e6	0.0319972
$59$	−2.43356e7	−0.261462	−0.130731	−	0.991418i	$-0.541732\pi$
$59$	−2.43356e7	−0.261462	−0.130731	+	0.991418i	$0.541732\pi$
$60$	1.29600e7	0.129099
$61$	6.17480e7	0.571003	0.285502	−	0.958378i	$-0.407840\pi$
$61$	6.17480e7	0.571003	0.285502	+	0.958378i	$0.407840\pi$
$62$	6.83899e7	0.587799
$63$	1.57530e7	0.125988
$64$	1.67772e7	0.125000
$65$	5.02268e7	0.349000
$66$	−2.13392e7	−0.138430
$67$	−2.71891e8	−1.64838	−0.824192	−	0.566310i	$-0.808371\pi$
$67$	−2.71891e8	−1.64838	−0.824192	+	0.566310i	$0.808371\pi$
$68$	−9.19323e7	−0.521408
$69$	9.97143e7	0.529586
$70$	−2.40100e7	−0.119523
$71$	−4.21856e8	−1.97016	−0.985081	−	0.172089i	$-0.944948\pi$
$71$	−4.21856e8	−1.97016	−0.985081	+	0.172089i	$0.944948\pi$
$72$	2.68739e7	0.117851
$73$	−4.28558e7	−0.176627	−0.0883134	−	0.996093i	$-0.528148\pi$
$73$	−4.28558e7	−0.176627	−0.0883134	+	0.996093i	$0.528148\pi$
$74$	−2.80792e7	−0.108853
$75$	−3.16406e7	−0.115470
$76$	2.01216e8	0.691834
$77$	3.95336e7	0.128162
$78$	1.04150e8	0.318592
$79$	4.53996e7	0.131139	0.0655693	−	0.997848i	$-0.479114\pi$
$79$	4.53996e7	0.131139	0.0655693	+	0.997848i	$0.479114\pi$
$80$	−4.09600e7	−0.111803
$81$	4.30467e7	0.111111
$82$	5.50569e8	1.34477
$83$	−2.31569e8	−0.535585	−0.267792	−	0.963477i	$-0.586294\pi$
$83$	−2.31569e8	−0.535585	−0.267792	+	0.963477i	$0.586294\pi$
$84$	−4.97871e7	−0.109109
$85$	2.24444e8	0.466362
$86$	−2.06327e8	−0.406737
$87$	−1.39606e7	−0.0261256
$88$	6.74425e7	0.119884
$89$	−3.96418e8	−0.669728	−0.334864	−	0.942266i	$-0.608690\pi$
$89$	−3.96418e8	−0.669728	−0.334864	+	0.942266i	$0.608690\pi$
$90$	−6.56100e7	−0.105409
$91$	−1.92951e8	−0.294959
$92$	−3.15146e8	−0.458635
$93$	−3.46224e8	−0.479936
$94$	−4.96248e8	−0.655576
$95$	−4.91251e8	−0.618795
$96$	−8.49347e7	−0.102062
$97$	2.38865e8	0.273956	0.136978	−	0.990574i	$-0.456261\pi$
$97$	2.38865e8	0.273956	0.136978	+	0.990574i	$0.456261\pi$
$98$	9.22368e7	0.101015
$99$	1.08030e8	0.113028
$100$	1.00000e8	0.100000
$101$	7.00529e8	0.669854	0.334927	−	0.942244i	$-0.391288\pi$
$101$	7.00529e8	0.669854	0.334927	+	0.942244i	$0.391288\pi$
$102$	4.65407e8	0.425728
$103$	−2.03877e8	−0.178485	−0.0892424	−	0.996010i	$-0.528445\pi$
$103$	−2.03877e8	−0.178485	−0.0892424	+	0.996010i	$0.528445\pi$
$104$	−3.29166e8	−0.275909
$105$	1.21551e8	0.0975900
$106$	−7.34135e8	−0.564806
$107$	−2.17633e9	−1.60508	−0.802540	−	0.596598i	$-0.796519\pi$
$107$	−2.17633e9	−1.60508	−0.802540	+	0.596598i	$0.796519\pi$
$108$	−1.36049e8	−0.0962250
$109$	−2.75706e9	−1.87080	−0.935400	−	0.353591i	$-0.884961\pi$
$109$	−2.75706e9	−1.87080	−0.935400	+	0.353591i	$0.884961\pi$
$110$	−1.64655e8	−0.107228
$111$	1.42151e8	0.0888783
$112$	1.57352e8	0.0944911
$113$	2.74833e8	0.158568	0.0792841	−	0.996852i	$-0.474737\pi$
$113$	2.74833e8	0.158568	0.0792841	+	0.996852i	$0.474737\pi$
$114$	−1.01866e9	−0.564880
$115$	7.69400e8	0.410215
$116$	4.41222e7	0.0226254
$117$	−5.27261e8	−0.260129
$118$	−3.89370e8	−0.184881
$119$	−8.62224e8	−0.394148
$120$	2.07360e8	0.0912871
$121$	−2.08684e9	−0.885022
$122$	9.87967e8	0.403760
$123$	−2.78725e9	−1.09800
$124$	1.09424e9	0.415637
$125$	−2.44141e8	−0.0894427
$126$	2.52047e8	0.0890871
$127$	−1.29836e9	−0.442873	−0.221436	−	0.975175i	$-0.571075\pi$
$127$	−1.29836e9	−0.442873	−0.221436	+	0.975175i	$0.571075\pi$
$128$	2.68435e8	0.0883883
$129$	1.04453e9	0.332100
$130$	8.03629e8	0.246780
$131$	−2.60120e9	−0.771709	−0.385854	−	0.922560i	$-0.626093\pi$
$131$	−2.60120e9	−0.771709	−0.385854	+	0.922560i	$0.626093\pi$
$132$	−3.41428e8	−0.0978850
$133$	1.88719e9	0.522978
$134$	−4.35026e9	−1.16558
$135$	3.32151e8	0.0860663
$136$	−1.47092e9	−0.368691
$137$	−6.15574e8	−0.149292	−0.0746462	−	0.997210i	$-0.523783\pi$
$137$	−6.15574e8	−0.149292	−0.0746462	+	0.997210i	$0.523783\pi$
$138$	1.59543e9	0.374474
$139$	−4.65547e9	−1.05778	−0.528892	−	0.848689i	$-0.677392\pi$
$139$	−4.65547e9	−1.05778	−0.528892	+	0.848689i	$0.677392\pi$
$140$	−3.84160e8	−0.0845154
$141$	2.51225e9	0.535276
$142$	−6.74970e9	−1.39312
$143$	−1.32321e9	−0.264617
$144$	4.29982e8	0.0833333
$145$	−1.07720e8	−0.0202368
$146$	−6.85693e8	−0.124894
$147$	−4.66949e8	−0.0824786
$148$	−4.49267e8	−0.0769709
$149$	−2.25681e9	−0.375108	−0.187554	−	0.982254i	$-0.560056\pi$
$149$	−2.25681e9	−0.375108	−0.187554	+	0.982254i	$0.560056\pi$
$150$	−5.06250e8	−0.0816497
$151$	9.03962e9	1.41499	0.707496	−	0.706718i	$-0.249825\pi$
$151$	9.03962e9	1.41499	0.707496	+	0.706718i	$0.249825\pi$
$152$	3.21946e9	0.489201
$153$	−2.35612e9	−0.347605
$154$	6.32537e8	0.0906239
$155$	−2.67148e9	−0.371757
$156$	1.66640e9	0.225278
$157$	−4.92444e9	−0.646857	−0.323429	−	0.946253i	$-0.604836\pi$
$157$	−4.92444e9	−0.646857	−0.323429	+	0.946253i	$0.604836\pi$
$158$	7.26394e8	0.0927290
$159$	3.71656e9	0.461163
$160$	−6.55360e8	−0.0790569
$161$	−2.95573e9	−0.346695
$162$	6.88748e8	0.0785674
$163$	1.57017e10	1.74222	0.871111	−	0.491086i	$-0.163400\pi$
$163$	1.57017e10	1.74222	0.871111	+	0.491086i	$0.163400\pi$
$164$	8.80910e9	0.950899
$165$	8.33564e8	0.0875510
$166$	−3.70510e9	−0.378716
$167$	1.44317e10	1.43580	0.717901	−	0.696145i	$-0.245103\pi$
$167$	1.44317e10	1.43580	0.717901	+	0.696145i	$0.245103\pi$
$168$	−7.96594e8	−0.0771517
$169$	−4.14631e9	−0.390995
$170$	3.59110e9	0.329767
$171$	5.15695e9	0.461223
$172$	−3.30124e9	−0.287607
$173$	−1.49972e10	−1.27292	−0.636461	−	0.771309i	$-0.719602\pi$
$173$	−1.49972e10	−1.27292	−0.636461	+	0.771309i	$0.719602\pi$
$174$	−2.23369e8	−0.0184736
$175$	9.37891e8	0.0755929
$176$	1.07908e9	0.0847709
$177$	1.97118e9	0.150955
$178$	−6.34269e9	−0.473569
$179$	−5.01029e9	−0.364775	−0.182387	−	0.983227i	$-0.558382\pi$
$179$	−5.01029e9	−0.364775	−0.182387	+	0.983227i	$0.558382\pi$
$180$	−1.04976e9	−0.0745356
$181$	7.76895e9	0.538032	0.269016	−	0.963136i	$-0.413301\pi$
$181$	7.76895e9	0.538032	0.269016	+	0.963136i	$0.413301\pi$
$182$	−3.08722e9	−0.208567
$183$	−5.00159e9	−0.329669
$184$	−5.04234e9	−0.324304
$185$	1.09684e9	0.0688449
$186$	−5.53958e9	−0.339366
$187$	−5.91292e9	−0.353602
$188$	−7.93996e9	−0.463562
$189$	−1.27599e9	−0.0727393
$190$	−7.86001e9	−0.437554
$191$	−8.17803e9	−0.444630	−0.222315	−	0.974975i	$-0.571361\pi$
$191$	−8.17803e9	−0.444630	−0.222315	+	0.974975i	$0.571361\pi$
$192$	−1.35895e9	−0.0721688
$193$	−2.33346e10	−1.21058	−0.605288	−	0.796007i	$-0.706942\pi$
$193$	−2.33346e10	−1.21058	−0.605288	+	0.796007i	$0.706942\pi$
$194$	3.82185e9	0.193716
$195$	−4.06837e9	−0.201495
$196$	1.47579e9	0.0714286
$197$	1.27515e10	0.603202	0.301601	−	0.953434i	$-0.402479\pi$
$197$	1.27515e10	0.603202	0.301601	+	0.953434i	$0.402479\pi$
$198$	1.72848e9	0.0799228
$199$	−2.83841e10	−1.28303	−0.641514	−	0.767111i	$-0.721693\pi$
$199$	−2.83841e10	−1.28303	−0.641514	+	0.767111i	$0.721693\pi$
$200$	1.60000e9	0.0707107
$201$	2.20232e10	0.951695
$202$	1.12085e10	0.473658
$203$	4.13818e8	0.0171032
$204$	7.44651e9	0.301035
$205$	−2.15066e10	−0.850510
$206$	−3.26204e9	−0.126208
$207$	−8.07686e9	−0.305757
$208$	−5.26666e9	−0.195097
$209$	1.29419e10	0.469179
$210$	1.94481e9	0.0690066
$211$	−1.71378e9	−0.0595230	−0.0297615	−	0.999557i	$-0.509475\pi$
$211$	−1.71378e9	−0.0595230	−0.0297615	+	0.999557i	$0.509475\pi$
$212$	−1.17462e10	−0.399378
$213$	3.41704e10	1.13747
$214$	−3.48212e10	−1.13496
$215$	8.05966e9	0.257243
$216$	−2.17678e9	−0.0680414
$217$	1.02628e10	0.314192
$218$	−4.41130e10	−1.32286
$219$	3.47132e9	0.101976
$220$	−2.63447e9	−0.0758214
$221$	2.88591e10	0.813801
$222$	2.27441e9	0.0628465
$223$	−5.78570e10	−1.56669	−0.783347	−	0.621585i	$-0.786489\pi$
$223$	−5.78570e10	−1.56669	−0.783347	+	0.621585i	$0.786489\pi$
$224$	2.51763e9	0.0668153
$225$	2.56289e9	0.0666667
$226$	4.39733e9	0.112125
$227$	−2.21085e10	−0.552641	−0.276320	−	0.961066i	$-0.589115\pi$
$227$	−2.21085e10	−0.552641	−0.276320	+	0.961066i	$0.589115\pi$
$228$	−1.62985e10	−0.399431
$229$	−2.53301e9	−0.0608664	−0.0304332	−	0.999537i	$-0.509689\pi$
$229$	−2.53301e9	−0.0608664	−0.0304332	+	0.999537i	$0.509689\pi$
$230$	1.23104e10	0.290066
$231$	−3.20222e9	−0.0739941
$232$	7.05956e8	0.0159986
$233$	−4.88645e10	−1.08616	−0.543078	−	0.839682i	$-0.682741\pi$
$233$	−4.88645e10	−1.08616	−0.543078	+	0.839682i	$0.682741\pi$
$234$	−8.43617e9	−0.183939
$235$	1.93847e10	0.414623
$236$	−6.22992e9	−0.130731
$237$	−3.67737e9	−0.0757129
$238$	−1.37956e10	−0.278704
$239$	−3.12627e10	−0.619778	−0.309889	−	0.950773i	$-0.600292\pi$
$239$	−3.12627e10	−0.619778	−0.309889	+	0.950773i	$0.600292\pi$
$240$	3.31776e9	0.0645497
$241$	−7.31306e9	−0.139644	−0.0698220	−	0.997559i	$-0.522243\pi$
$241$	−7.31306e9	−0.139644	−0.0698220	+	0.997559i	$0.522243\pi$
$242$	−3.33894e10	−0.625805
$243$	−3.48678e9	−0.0641500
$244$	1.58075e10	0.285502
$245$	−3.60300e9	−0.0638877
$246$	−4.45961e10	−0.776405
$247$	−6.31653e10	−1.07980
$248$	1.75078e10	0.293900
$249$	1.87571e10	0.309220
$250$	−3.90625e9	−0.0632456
$251$	3.65618e9	0.0581428	0.0290714	−	0.999577i	$-0.490745\pi$
$251$	3.65618e9	0.0581428	0.0290714	+	0.999577i	$0.490745\pi$
$252$	4.03276e9	0.0629941
$253$	−2.02696e10	−0.311031
$254$	−2.07738e10	−0.313158
$255$	−1.81800e10	−0.269254
$256$	4.29497e9	0.0625000
$257$	−5.96250e10	−0.852569	−0.426285	−	0.904589i	$-0.640178\pi$
$257$	−5.96250e10	−0.852569	−0.426285	+	0.904589i	$0.640178\pi$
$258$	1.67125e10	0.234830
$259$	−4.21363e9	−0.0581845
$260$	1.28581e10	0.174500
$261$	1.13080e9	0.0150836
$262$	−4.16192e10	−0.545680
$263$	9.74709e10	1.25624	0.628122	−	0.778115i	$-0.283824\pi$
$263$	9.74709e10	1.25624	0.628122	+	0.778115i	$0.283824\pi$
$264$	−5.46285e9	−0.0692152
$265$	2.86772e10	0.357215
$266$	3.01950e10	0.369801
$267$	3.21099e10	0.386668
$268$	−6.96042e10	−0.824192
$269$	1.38129e11	1.60842	0.804208	−	0.594348i	$-0.202590\pi$
$269$	1.38129e11	1.60842	0.804208	+	0.594348i	$0.202590\pi$
$270$	5.31441e9	0.0608581
$271$	1.22829e11	1.38337	0.691685	−	0.722199i	$-0.256869\pi$
$271$	1.22829e11	1.38337	0.691685	+	0.722199i	$0.256869\pi$
$272$	−2.35347e10	−0.260704
$273$	1.56290e10	0.170294
$274$	−9.84919e9	−0.105566
$275$	6.43182e9	0.0678167
$276$	2.55269e10	0.264793
$277$	8.89605e10	0.907900	0.453950	−	0.891027i	$-0.350014\pi$
$277$	8.89605e10	0.907900	0.453950	+	0.891027i	$0.350014\pi$
$278$	−7.44876e10	−0.747967
$279$	2.80441e10	0.277091
$280$	−6.14656e9	−0.0597614
$281$	−8.61635e9	−0.0824413	−0.0412206	−	0.999150i	$-0.513125\pi$
$281$	−8.61635e9	−0.0824413	−0.0412206	+	0.999150i	$0.513125\pi$
$282$	4.01961e10	0.378497
$283$	1.27056e11	1.17748	0.588742	−	0.808321i	$-0.299623\pi$
$283$	1.27056e11	1.17748	0.588742	+	0.808321i	$0.299623\pi$
$284$	−1.07995e11	−0.985081
$285$	3.97913e10	0.357262
$286$	−2.11714e10	−0.187112
$287$	8.26197e10	0.718812
$288$	6.87971e9	0.0589256
$289$	1.03724e10	0.0874660
$290$	−1.72353e9	−0.0143096
$291$	−1.93481e10	−0.158168
$292$	−1.09711e10	−0.0883134
$293$	1.16742e11	0.925382	0.462691	−	0.886520i	$-0.346884\pi$
$293$	1.16742e11	0.925382	0.462691	+	0.886520i	$0.346884\pi$
$294$	−7.47118e9	−0.0583212
$295$	1.52098e10	0.116929
$296$	−7.18827e9	−0.0544266
$297$	−8.75042e9	−0.0652567
$298$	−3.61089e10	−0.265242
$299$	9.89299e10	0.715826
$300$	−8.10000e9	−0.0577350
$301$	−3.09620e10	−0.217410
$302$	1.44634e11	1.00055
$303$	−5.67429e10	−0.386740
$304$	5.15114e10	0.345917
$305$	−3.85925e10	−0.255360
$306$	−3.76980e10	−0.245794
$307$	1.99079e11	1.27909	0.639546	−	0.768752i	$-0.279122\pi$
$307$	1.99079e11	1.27909	0.639546	+	0.768752i	$0.279122\pi$
$308$	1.01206e10	0.0640808
$309$	1.65141e10	0.103048
$310$	−4.27437e10	−0.262872
$311$	7.65214e9	0.0463832	0.0231916	−	0.999731i	$-0.492617\pi$
$311$	7.65214e9	0.0463832	0.0231916	+	0.999731i	$0.492617\pi$
$312$	2.66625e10	0.159296
$313$	−1.22485e11	−0.721331	−0.360665	−	0.932695i	$-0.617450\pi$
$313$	−1.22485e11	−0.721331	−0.360665	+	0.932695i	$0.617450\pi$
$314$	−7.87911e10	−0.457397
$315$	−9.84560e9	−0.0563436
$316$	1.16223e10	0.0655693
$317$	2.69991e11	1.50170	0.750849	−	0.660474i	$-0.229644\pi$
$317$	2.69991e11	1.50170	0.750849	+	0.660474i	$0.229644\pi$
$318$	5.94650e10	0.326091
$319$	2.83786e9	0.0153438
$320$	−1.04858e10	−0.0559017
$321$	1.76282e11	0.926694
$322$	−4.72916e10	−0.245151
$323$	−2.82261e11	−1.44291
$324$	1.10200e10	0.0555556
$325$	−3.13917e10	−0.156077
$326$	2.51228e11	1.23194
$327$	2.23322e11	1.08011
$328$	1.40946e11	0.672387
$329$	−7.44682e10	−0.350420
$330$	1.33370e10	0.0619079
$331$	1.72789e11	0.791209	0.395604	−	0.918421i	$-0.370535\pi$
$331$	1.72789e11	0.791209	0.395604	+	0.918421i	$0.370535\pi$
$332$	−5.92816e10	−0.267792
$333$	−1.15142e10	−0.0513139
$334$	2.30908e11	1.01526
$335$	1.69932e11	0.737180
$336$	−1.27455e10	−0.0545545
$337$	2.07282e11	0.875442	0.437721	−	0.899111i	$-0.355786\pi$
$337$	2.07282e11	0.875442	0.437721	+	0.899111i	$0.355786\pi$
$338$	−6.63410e10	−0.276476
$339$	−2.22615e10	−0.0915494
$340$	5.74577e10	0.233181
$341$	7.03794e10	0.281871
$342$	8.25113e10	0.326134
$343$	1.38413e10	0.0539949
$344$	−5.28198e10	−0.203369
$345$	−6.23214e10	−0.236838
$346$	−2.39955e11	−0.900091
$347$	1.71821e11	0.636201	0.318100	−	0.948057i	$-0.396955\pi$
$347$	1.71821e11	0.636201	0.318100	+	0.948057i	$0.396955\pi$
$348$	−3.57390e9	−0.0130628
$349$	9.61604e10	0.346962	0.173481	−	0.984837i	$-0.444499\pi$
$349$	9.61604e10	0.346962	0.173481	+	0.984837i	$0.444499\pi$
$350$	1.50062e10	0.0534522
$351$	4.27081e10	0.150186
$352$	1.72653e10	0.0599421
$353$	−5.25913e11	−1.80272	−0.901358	−	0.433074i	$-0.857429\pi$
$353$	−5.25913e11	−1.80272	−0.901358	+	0.433074i	$0.857429\pi$
$354$	3.15390e10	0.106741
$355$	2.63660e11	0.881084
$356$	−1.01483e11	−0.334864
$357$	6.98401e10	0.227561
$358$	−8.01647e10	−0.257935
$359$	−8.21227e10	−0.260938	−0.130469	−	0.991452i	$-0.541648\pi$
$359$	−8.21227e10	−0.260938	−0.130469	+	0.991452i	$0.541648\pi$
$360$	−1.67962e10	−0.0527046
$361$	2.95110e11	0.914538
$362$	1.24303e11	0.380446
$363$	1.69034e11	0.510968
$364$	−4.93955e10	−0.147479
$365$	2.67849e10	0.0789899
$366$	−8.00254e10	−0.233111
$367$	4.57058e10	0.131515	0.0657573	−	0.997836i	$-0.479054\pi$
$367$	4.57058e10	0.131515	0.0657573	+	0.997836i	$0.479054\pi$
$368$	−8.06775e10	−0.229317
$369$	2.25768e11	0.633932
$370$	1.75495e10	0.0486807
$371$	−1.10166e11	−0.301902
$372$	−8.86333e10	−0.239968
$373$	5.39132e11	1.44213	0.721067	−	0.692865i	$-0.243652\pi$
$373$	5.39132e11	1.44213	0.721067	+	0.692865i	$0.243652\pi$
$374$	−9.46067e10	−0.250034
$375$	1.97754e10	0.0516398
$376$	−1.27039e11	−0.327788
$377$	−1.38507e10	−0.0353132
$378$	−2.04158e10	−0.0514344
$379$	−4.44075e11	−1.10555	−0.552777	−	0.833329i	$-0.686432\pi$
$379$	−4.44075e11	−1.10555	−0.552777	+	0.833329i	$0.686432\pi$
$380$	−1.25760e11	−0.309398
$381$	1.05167e11	0.255693
$382$	−1.30849e11	−0.314401
$383$	5.33160e11	1.26608	0.633042	−	0.774117i	$-0.281806\pi$
$383$	5.33160e11	1.26608	0.633042	+	0.774117i	$0.281806\pi$
$384$	−2.17433e10	−0.0510310
$385$	−2.47085e10	−0.0573156
$386$	−3.73353e11	−0.856006
$387$	−8.46071e10	−0.191738
$388$	6.11495e10	0.136978
$389$	−5.96135e11	−1.31999	−0.659996	−	0.751269i	$-0.729442\pi$
$389$	−5.96135e11	−1.31999	−0.659996	+	0.751269i	$0.729442\pi$
$390$	−6.50939e10	−0.142479
$391$	4.42079e11	0.956544
$392$	2.36126e10	0.0505076
$393$	2.10697e11	0.445546
$394$	2.04024e11	0.426528
$395$	−2.83748e10	−0.0586469
$396$	2.76557e10	0.0565139
$397$	3.14001e11	0.634416	0.317208	−	0.948356i	$-0.397255\pi$
$397$	3.14001e11	0.634416	0.317208	+	0.948356i	$0.397255\pi$
$398$	−4.54146e11	−0.907238
$399$	−1.52862e11	−0.301941
$400$	2.56000e10	0.0500000
$401$	−2.00223e11	−0.386691	−0.193346	−	0.981131i	$-0.561934\pi$
$401$	−2.00223e11	−0.386691	−0.193346	+	0.981131i	$0.561934\pi$
$402$	3.52371e11	0.672950
$403$	−3.43500e11	−0.648716
$404$	1.79336e11	0.334927
$405$	−2.69042e10	−0.0496904
$406$	6.62109e9	0.0120938
$407$	−2.88960e10	−0.0521991
$408$	1.19144e11	0.212864
$409$	−1.18269e10	−0.0208985	−0.0104493	−	0.999945i	$-0.503326\pi$
$409$	−1.18269e10	−0.0208985	−0.0104493	+	0.999945i	$0.503326\pi$
$410$	−3.44105e11	−0.601401
$411$	4.98615e10	0.0861940
$412$	−5.21926e10	−0.0892424
$413$	−5.84298e10	−0.0988233
$414$	−1.29230e11	−0.216203
$415$	1.44730e11	0.239521
$416$	−8.42666e10	−0.137954
$417$	3.77093e11	0.610712
$418$	2.07070e11	0.331760
$419$	2.84098e11	0.450303	0.225151	−	0.974324i	$-0.427712\pi$
$419$	2.84098e11	0.450303	0.225151	+	0.974324i	$0.427712\pi$
$420$	3.11170e10	0.0487950
$421$	−9.43850e11	−1.46431	−0.732156	−	0.681137i	$-0.761486\pi$
$421$	−9.43850e11	−1.46431	−0.732156	+	0.681137i	$0.761486\pi$
$422$	−2.74205e10	−0.0420891
$423$	−2.03493e11	−0.309042
$424$	−1.87939e11	−0.282403
$425$	−1.40277e11	−0.208563
$426$	5.46726e11	0.804316
$427$	1.48257e11	0.215819
$428$	−5.57139e11	−0.802540
$429$	1.07180e11	0.152776
$430$	1.28955e11	0.181898
$431$	−4.82696e11	−0.673792	−0.336896	−	0.941542i	$-0.609377\pi$
$431$	−4.82696e11	−0.673792	−0.336896	+	0.941542i	$0.609377\pi$
$432$	−3.48285e10	−0.0481125
$433$	−8.78885e11	−1.20154	−0.600768	−	0.799424i	$-0.705138\pi$
$433$	−8.78885e11	−1.20154	−0.600768	+	0.799424i	$0.705138\pi$
$434$	1.64204e11	0.222167
$435$	8.72535e9	0.0116837
$436$	−7.05808e11	−0.935400
$437$	−9.67599e11	−1.26920
$438$	5.55411e10	0.0721076
$439$	1.14719e12	1.47416	0.737080	−	0.675805i	$-0.236204\pi$
$439$	1.14719e12	1.47416	0.737080	+	0.675805i	$0.236204\pi$
$440$	−4.21516e10	−0.0536138
$441$	3.78229e10	0.0476190
$442$	4.61746e11	0.575444
$443$	−1.00077e12	−1.23457	−0.617286	−	0.786739i	$-0.711768\pi$
$443$	−1.00077e12	−1.23457	−0.617286	+	0.786739i	$0.711768\pi$
$444$	3.63906e10	0.0444392
$445$	2.47761e11	0.299512
$446$	−9.25712e11	−1.10782
$447$	1.82801e11	0.216569
$448$	4.02821e10	0.0472456
$449$	5.71267e11	0.663332	0.331666	−	0.943397i	$-0.392389\pi$
$449$	5.71267e11	0.663332	0.331666	+	0.943397i	$0.392389\pi$
$450$	4.10062e10	0.0471405
$451$	5.66586e11	0.644868
$452$	7.03573e10	0.0792841
$453$	−7.32209e11	−0.816946
$454$	−3.53736e11	−0.390776
$455$	1.20595e11	0.131910
$456$	−2.60776e11	−0.282440
$457$	1.71083e12	1.83478	0.917389	−	0.397992i	$-0.130293\pi$
$457$	1.71083e12	1.83478	0.917389	+	0.397992i	$0.130293\pi$
$458$	−4.05282e10	−0.0430390
$459$	1.90846e11	0.200690
$460$	1.96966e11	0.205108
$461$	−5.21862e11	−0.538147	−0.269074	−	0.963120i	$-0.586717\pi$
$461$	−5.21862e11	−0.538147	−0.269074	+	0.963120i	$0.586717\pi$
$462$	−5.12355e10	−0.0523217
$463$	1.56483e12	1.58253	0.791266	−	0.611472i	$-0.209422\pi$
$463$	1.56483e12	1.58253	0.791266	+	0.611472i	$0.209422\pi$
$464$	1.12953e10	0.0113127
$465$	2.16390e11	0.214634
$466$	−7.81832e11	−0.768028
$467$	5.43746e11	0.529017	0.264509	−	0.964383i	$-0.414790\pi$
$467$	5.43746e11	0.529017	0.264509	+	0.964383i	$0.414790\pi$
$468$	−1.34979e11	−0.130065
$469$	−6.52811e11	−0.623031
$470$	3.10155e11	0.293183
$471$	3.98880e11	0.373463
$472$	−9.96787e10	−0.0924407
$473$	−2.12330e11	−0.195045
$474$	−5.88379e10	−0.0535371
$475$	3.07032e11	0.276734
$476$	−2.20729e11	−0.197074
$477$	−3.01041e11	−0.266252
$478$	−5.00203e11	−0.438249
$479$	−1.02794e12	−0.892195	−0.446097	−	0.894984i	$-0.647186\pi$
$479$	−1.02794e12	−0.892195	−0.446097	+	0.894984i	$0.647186\pi$
$480$	5.30842e10	0.0456435
$481$	1.41033e11	0.120134
$482$	−1.17009e11	−0.0987433
$483$	2.39414e11	0.200165
$484$	−5.34230e11	−0.442511
$485$	−1.49291e11	−0.122517
$486$	−5.57886e10	−0.0453609
$487$	−1.75004e12	−1.40983	−0.704916	−	0.709291i	$-0.749015\pi$
$487$	−1.75004e12	−1.40983	−0.704916	+	0.709291i	$0.749015\pi$
$488$	2.52920e11	0.201880
$489$	−1.27184e12	−1.00587
$490$	−5.76480e10	−0.0451754
$491$	−8.44217e11	−0.655523	−0.327761	−	0.944761i	$-0.606294\pi$
$491$	−8.44217e11	−0.655523	−0.327761	+	0.944761i	$0.606294\pi$
$492$	−7.13537e11	−0.549002
$493$	−6.18936e10	−0.0471883
$494$	−1.01064e12	−0.763532
$495$	−6.75187e10	−0.0505476
$496$	2.80125e11	0.207818
$497$	−1.01288e12	−0.744652
$498$	3.00113e11	0.218652
$499$	9.71396e11	0.701364	0.350682	−	0.936495i	$-0.385950\pi$
$499$	9.71396e11	0.701364	0.350682	+	0.936495i	$0.385950\pi$
$500$	−6.25000e10	−0.0447214
$501$	−1.16897e12	−0.828960
$502$	5.84989e10	0.0411132
$503$	−3.96551e11	−0.276213	−0.138106	−	0.990417i	$-0.544102\pi$
$503$	−3.96551e11	−0.276213	−0.138106	+	0.990417i	$0.544102\pi$
$504$	6.45241e10	0.0445435
$505$	−4.37831e11	−0.299568
$506$	−3.24314e11	−0.219932
$507$	3.35851e11	0.225741
$508$	−3.32381e11	−0.221436
$509$	−1.27990e12	−0.845174	−0.422587	−	0.906322i	$-0.638878\pi$
$509$	−1.27990e12	−0.845174	−0.422587	+	0.906322i	$0.638878\pi$
$510$	−2.90879e11	−0.190391
$511$	−1.02897e11	−0.0667587
$512$	6.87195e10	0.0441942
$513$	−4.17713e11	−0.266287
$514$	−9.54001e11	−0.602857
$515$	1.27423e11	0.0798209
$516$	2.67400e11	0.166050
$517$	−5.10684e11	−0.314373
$518$	−6.74181e10	−0.0411427
$519$	1.21477e12	0.734921
$520$	2.05729e11	0.123390
$521$	−9.36174e11	−0.556656	−0.278328	−	0.960486i	$-0.589780\pi$
$521$	−9.36174e11	−0.556656	−0.278328	+	0.960486i	$0.589780\pi$
$522$	1.80929e10	0.0106657
$523$	−5.28396e11	−0.308818	−0.154409	−	0.988007i	$-0.549347\pi$
$523$	−5.28396e11	−0.308818	−0.154409	+	0.988007i	$0.549347\pi$
$524$	−6.65908e11	−0.385854
$525$	−7.59691e10	−0.0436436
$526$	1.55953e12	0.888299
$527$	−1.53497e12	−0.866866
$528$	−8.74055e10	−0.0489425
$529$	−2.85693e11	−0.158616
$530$	4.58835e11	0.252589
$531$	−1.59666e11	−0.0871539
$532$	4.83120e11	0.261489
$533$	−2.76533e12	−1.48414
$534$	5.13758e11	0.273415
$535$	1.36020e12	0.717814
$536$	−1.11367e12	−0.582792
$537$	4.05834e11	0.210603
$538$	2.21006e12	1.13732
$539$	9.49201e10	0.0484405
$540$	8.50306e10	0.0430331
$541$	4.91679e11	0.246771	0.123386	−	0.992359i	$-0.460625\pi$
$541$	4.91679e11	0.246771	0.123386	+	0.992359i	$0.460625\pi$
$542$	1.96526e12	0.978190
$543$	−6.29285e11	−0.310633
$544$	−3.76555e11	−0.184346
$545$	1.72316e12	0.836647
$546$	2.50065e11	0.120416
$547$	9.49541e11	0.453493	0.226746	−	0.973954i	$-0.427191\pi$
$547$	9.49541e11	0.453493	0.226746	+	0.973954i	$0.427191\pi$
$548$	−1.57587e11	−0.0746462
$549$	4.05128e11	0.190334
$550$	1.02909e11	0.0479537
$551$	1.35469e11	0.0626122
$552$	4.08430e11	0.187237
$553$	1.09004e11	0.0495657
$554$	1.42337e12	0.641982
$555$	−8.88443e10	−0.0397476
$556$	−1.19180e12	−0.528892
$557$	−2.65819e12	−1.17014	−0.585070	−	0.810983i	$-0.698933\pi$
$557$	−2.65819e12	−1.17014	−0.585070	+	0.810983i	$0.698933\pi$
$558$	4.48706e11	0.195933
$559$	1.03632e12	0.448889
$560$	−9.83450e10	−0.0422577
$561$	4.78946e11	0.204152
$562$	−1.37862e11	−0.0582948
$563$	−3.66144e12	−1.53590	−0.767951	−	0.640508i	$-0.778724\pi$
$563$	−3.66144e12	−1.53590	−0.767951	+	0.640508i	$0.778724\pi$
$564$	6.43137e11	0.267638
$565$	−1.71771e11	−0.0709139
$566$	2.03289e12	0.832607
$567$	1.03355e11	0.0419961
$568$	−1.72792e12	−0.696558
$569$	−2.43282e12	−0.972982	−0.486491	−	0.873686i	$-0.661723\pi$
$569$	−2.43282e12	−0.972982	−0.486491	+	0.873686i	$0.661723\pi$
$570$	6.36661e11	0.252622
$571$	−1.98949e12	−0.783211	−0.391606	−	0.920133i	$-0.628080\pi$
$571$	−1.98949e12	−0.783211	−0.391606	+	0.920133i	$0.628080\pi$
$572$	−3.38742e11	−0.132308
$573$	6.62421e11	0.256707
$574$	1.32192e12	0.508277
$575$	−4.80875e11	−0.183454
$576$	1.10075e11	0.0416667
$577$	−8.55311e10	−0.0321243	−0.0160621	−	0.999871i	$-0.505113\pi$
$577$	−8.55311e10	−0.0321243	−0.0160621	+	0.999871i	$0.505113\pi$
$578$	1.65958e11	0.0618478
$579$	1.89010e12	0.698926
$580$	−2.75764e10	−0.0101184
$581$	−5.55996e11	−0.202432
$582$	−3.09570e11	−0.111842
$583$	−7.55492e11	−0.270845
$584$	−1.75537e11	−0.0624470
$585$	3.29538e11	0.116333
$586$	1.86786e12	0.654344
$587$	−5.13204e12	−1.78410	−0.892050	−	0.451938i	$-0.850733\pi$
$587$	−5.13204e12	−1.78410	−0.892050	+	0.451938i	$0.850733\pi$
$588$	−1.19539e11	−0.0412393
$589$	3.35966e12	1.15021
$590$	2.43356e11	0.0826815
$591$	−1.03287e12	−0.348259
$592$	−1.15012e11	−0.0384854
$593$	4.11295e12	1.36586	0.682932	−	0.730482i	$-0.260705\pi$
$593$	4.11295e12	1.36586	0.682932	+	0.730482i	$0.260705\pi$
$594$	−1.40007e11	−0.0461434
$595$	5.38890e11	0.176268
$596$	−5.77743e11	−0.187554
$597$	2.29911e12	0.740757
$598$	1.58288e12	0.506165
$599$	2.01674e12	0.640073	0.320036	−	0.947405i	$-0.396305\pi$
$599$	2.01674e12	0.640073	0.320036	+	0.947405i	$0.396305\pi$
$600$	−1.29600e11	−0.0408248
$601$	−2.08999e12	−0.653444	−0.326722	−	0.945120i	$-0.605944\pi$
$601$	−2.08999e12	−0.653444	−0.326722	+	0.945120i	$0.605944\pi$
$602$	−4.95392e11	−0.153732
$603$	−1.78388e12	−0.549462
$604$	2.31414e12	0.707496
$605$	1.30427e12	0.395794
$606$	−9.07886e11	−0.273467
$607$	2.04365e12	0.611022	0.305511	−	0.952188i	$-0.401173\pi$
$607$	2.04365e12	0.611022	0.305511	+	0.952188i	$0.401173\pi$
$608$	8.24182e11	0.244600
$609$	−3.35193e10	−0.00987454
$610$	−6.17480e11	−0.180567
$611$	2.49249e12	0.723516
$612$	−6.03168e11	−0.173803
$613$	2.39808e12	0.685949	0.342974	−	0.939345i	$-0.388566\pi$
$613$	2.39808e12	0.685949	0.342974	+	0.939345i	$0.388566\pi$
$614$	3.18526e12	0.904455
$615$	1.74203e12	0.491042
$616$	1.61930e11	0.0453120
$617$	−2.48654e12	−0.690737	−0.345369	−	0.938467i	$-0.612246\pi$
$617$	−2.48654e12	−0.690737	−0.345369	+	0.938467i	$0.612246\pi$
$618$	2.64225e11	0.0728662
$619$	2.46630e12	0.675210	0.337605	−	0.941288i	$-0.390383\pi$
$619$	2.46630e12	0.675210	0.337605	+	0.941288i	$0.390383\pi$
$620$	−6.83899e11	−0.185878
$621$	6.54225e11	0.176529
$622$	1.22434e11	0.0327979
$623$	−9.51800e11	−0.253134
$624$	4.26599e11	0.112639
$625$	1.52588e11	0.0400000
$626$	−1.95976e12	−0.510058
$627$	−1.04829e12	−0.270881
$628$	−1.26066e12	−0.323429
$629$	6.30220e11	0.160533
$630$	−1.57530e11	−0.0398410
$631$	1.11136e12	0.279077	0.139538	−	0.990217i	$-0.455438\pi$
$631$	1.11136e12	0.279077	0.139538	+	0.990217i	$0.455438\pi$
$632$	1.85957e11	0.0463645
$633$	1.38816e11	0.0343656
$634$	4.31986e12	1.06186
$635$	8.11476e11	0.198059
$636$	9.51439e11	0.230581
$637$	−4.63276e11	−0.111484
$638$	4.54058e10	0.0108497
$639$	−2.76780e12	−0.656721
$640$	−1.67772e11	−0.0395285
$641$	−2.00691e12	−0.469535	−0.234767	−	0.972052i	$-0.575433\pi$
$641$	−2.00691e12	−0.469535	−0.234767	+	0.972052i	$0.575433\pi$
$642$	2.82052e12	0.655271
$643$	−3.48816e12	−0.804724	−0.402362	−	0.915481i	$-0.631811\pi$
$643$	−3.48816e12	−0.804724	−0.402362	+	0.915481i	$0.631811\pi$
$644$	−7.56666e11	−0.173348
$645$	−6.52833e11	−0.148519
$646$	−4.51618e12	−1.02029
$647$	5.65205e12	1.26805	0.634026	−	0.773312i	$-0.281401\pi$
$647$	5.65205e12	1.26805	0.634026	+	0.773312i	$0.281401\pi$
$648$	1.76319e11	0.0392837
$649$	−4.00697e11	−0.0886574
$650$	−5.02268e11	−0.110363
$651$	−8.31283e11	−0.181399
$652$	4.01965e12	0.871111
$653$	−5.75360e12	−1.23831	−0.619156	−	0.785268i	$-0.712525\pi$
$653$	−5.75360e12	−1.23831	−0.619156	+	0.785268i	$0.712525\pi$
$654$	3.57315e12	0.763751
$655$	1.62575e12	0.345119
$656$	2.25513e12	0.475449
$657$	−2.81177e11	−0.0588756
$658$	−1.19149e12	−0.247784
$659$	−4.08534e12	−0.843809	−0.421904	−	0.906640i	$-0.638638\pi$
$659$	−4.08534e12	−0.843809	−0.421904	+	0.906640i	$0.638638\pi$
$660$	2.13392e11	0.0437755
$661$	−4.66421e12	−0.950323	−0.475162	−	0.879899i	$-0.657610\pi$
$661$	−4.66421e12	−0.950323	−0.475162	+	0.879899i	$0.657610\pi$
$662$	2.76463e12	0.559469
$663$	−2.33759e12	−0.469848
$664$	−9.48505e11	−0.189358
$665$	−1.17949e12	−0.233883
$666$	−1.84227e11	−0.0362844
$667$	−2.12173e11	−0.0415072
$668$	3.69452e12	0.717901
$669$	4.68642e12	0.904531
$670$	2.71891e12	0.521265
$671$	1.01671e12	0.193618
$672$	−2.03928e11	−0.0385758
$673$	9.42094e12	1.77022	0.885109	−	0.465384i	$-0.154084\pi$
$673$	9.42094e12	1.77022	0.885109	+	0.465384i	$0.154084\pi$
$674$	3.31651e12	0.619031
$675$	−2.07594e11	−0.0384900
$676$	−1.06146e12	−0.195498
$677$	−3.58871e12	−0.656582	−0.328291	−	0.944577i	$-0.606473\pi$
$677$	−3.58871e12	−0.656582	−0.328291	+	0.944577i	$0.606473\pi$
$678$	−3.56184e11	−0.0647352
$679$	5.73516e11	0.103546
$680$	9.19323e11	0.164884
$681$	1.79079e12	0.319067
$682$	1.12607e12	0.199313
$683$	−8.80172e12	−1.54766	−0.773828	−	0.633395i	$-0.781661\pi$
$683$	−8.80172e12	−1.54766	−0.773828	+	0.633395i	$0.781661\pi$
$684$	1.32018e12	0.230611
$685$	3.84734e11	0.0667656
$686$	2.21461e11	0.0381802
$687$	2.05174e11	0.0351412
$688$	−8.45117e11	−0.143803
$689$	3.68733e12	0.623340
$690$	−9.97143e11	−0.167470
$691$	6.82500e12	1.13881	0.569405	−	0.822057i	$-0.307173\pi$
$691$	6.82500e12	1.13881	0.569405	+	0.822057i	$0.307173\pi$
$692$	−3.83927e12	−0.636461
$693$	2.59380e11	0.0427205
$694$	2.74914e12	0.449862
$695$	2.90967e12	0.473056
$696$	−5.71824e10	−0.00923679
$697$	−1.23572e13	−1.98323
$698$	1.53857e12	0.245339
$699$	3.95803e12	0.627092
$700$	2.40100e11	0.0377964
$701$	2.88392e12	0.451078	0.225539	−	0.974234i	$-0.427586\pi$
$701$	2.88392e12	0.451078	0.225539	+	0.974234i	$0.427586\pi$
$702$	6.83330e11	0.106197
$703$	−1.37939e12	−0.213004
$704$	2.76245e11	0.0423855
$705$	−1.57016e12	−0.239383
$706$	−8.41460e12	−1.27471
$707$	1.68197e12	0.253181
$708$	5.04623e11	0.0754775
$709$	4.19431e12	0.623379	0.311689	−	0.950184i	$-0.399105\pi$
$709$	4.19431e12	0.623379	0.311689	+	0.950184i	$0.399105\pi$
$710$	4.21856e12	0.623020
$711$	2.97867e11	0.0437128
$712$	−1.62373e12	−0.236785
$713$	−5.26192e12	−0.762502
$714$	1.11744e12	0.160910
$715$	8.27007e11	0.118340
$716$	−1.28264e12	−0.182387
$717$	2.53228e12	0.357829
$718$	−1.31396e12	−0.184511
$719$	2.13823e12	0.298384	0.149192	−	0.988808i	$-0.452333\pi$
$719$	2.13823e12	0.298384	0.149192	+	0.988808i	$0.452333\pi$
$720$	−2.68739e11	−0.0372678
$721$	−4.89510e11	−0.0674609
$722$	4.72176e12	0.646676
$723$	5.92358e11	0.0806235
$724$	1.98885e12	0.269016
$725$	6.73252e10	0.00905017
$726$	2.70454e12	0.361309
$727$	6.29192e12	0.835369	0.417684	−	0.908592i	$-0.362842\pi$
$727$	6.29192e12	0.835369	0.417684	+	0.908592i	$0.362842\pi$
$728$	−7.90328e11	−0.104284
$729$	2.82430e11	0.0370370
$730$	4.28558e11	0.0558543
$731$	4.63089e12	0.599842
$732$	−1.28041e12	−0.164834
$733$	4.01379e12	0.513554	0.256777	−	0.966471i	$-0.417339\pi$
$733$	4.01379e12	0.513554	0.256777	+	0.966471i	$0.417339\pi$
$734$	7.31293e11	0.0929949
$735$	2.91843e11	0.0368856
$736$	−1.29084e12	−0.162152
$737$	−4.47682e12	−0.558940
$738$	3.61228e12	0.448258
$739$	−7.70653e12	−0.950514	−0.475257	−	0.879847i	$-0.657645\pi$
$739$	−7.70653e12	−0.950514	−0.475257	+	0.879847i	$0.657645\pi$
$740$	2.80792e11	0.0344224
$741$	5.11639e12	0.623421
$742$	−1.76266e12	−0.213477
$743$	2.90006e12	0.349106	0.174553	−	0.984648i	$-0.444152\pi$
$743$	2.90006e12	0.349106	0.174553	+	0.984648i	$0.444152\pi$
$744$	−1.41813e12	−0.169683
$745$	1.41051e12	0.167753
$746$	8.62612e12	1.01974
$747$	−1.51932e12	−0.178528
$748$	−1.51371e12	−0.176801
$749$	−5.22536e12	−0.606663
$750$	3.16406e11	0.0365148
$751$	−4.29573e12	−0.492785	−0.246393	−	0.969170i	$-0.579245\pi$
$751$	−4.29573e12	−0.492785	−0.246393	+	0.969170i	$0.579245\pi$
$752$	−2.03263e12	−0.231781
$753$	−2.96151e11	−0.0335688
$754$	−2.21612e11	−0.0249702
$755$	−5.64976e12	−0.632803
$756$	−3.26653e11	−0.0363696
$757$	−4.74546e12	−0.525227	−0.262614	−	0.964901i	$-0.584584\pi$
$757$	−4.74546e12	−0.525227	−0.262614	+	0.964901i	$0.584584\pi$
$758$	−7.10520e12	−0.781744
$759$	1.64184e12	0.179574
$760$	−2.01216e12	−0.218777
$761$	4.56769e12	0.493703	0.246851	−	0.969053i	$-0.420604\pi$
$761$	4.56769e12	0.493703	0.246851	+	0.969053i	$0.420604\pi$
$762$	1.68268e12	0.180802
$763$	−6.61971e12	−0.707096
$764$	−2.09358e12	−0.222315
$765$	1.47258e12	0.155454
$766$	8.53055e12	0.895257
$767$	1.95568e12	0.204042
$768$	−3.47892e11	−0.0360844
$769$	8.64970e12	0.891933	0.445967	−	0.895050i	$-0.352860\pi$
$769$	8.64970e12	0.891933	0.445967	+	0.895050i	$0.352860\pi$
$770$	−3.95336e11	−0.0405282
$771$	4.82963e12	0.492231
$772$	−5.97365e12	−0.605288
$773$	−1.16271e13	−1.17128	−0.585642	−	0.810569i	$-0.699158\pi$
$773$	−1.16271e13	−1.17128	−0.585642	+	0.810569i	$0.699158\pi$
$774$	−1.35371e12	−0.135579
$775$	1.66967e12	0.166255
$776$	9.78393e11	0.0968580
$777$	3.41304e11	0.0335929
$778$	−9.53816e12	−0.933376
$779$	2.70467e13	2.63146
$780$	−1.04150e12	−0.100748
$781$	−6.94606e12	−0.668050
$782$	7.07327e12	0.676379
$783$	−9.15952e10	−0.00870853
$784$	3.77802e11	0.0357143
$785$	3.07778e12	0.289283
$786$	3.37116e12	0.315049
$787$	6.82487e12	0.634174	0.317087	−	0.948397i	$-0.397295\pi$
$787$	6.82487e12	0.634174	0.317087	+	0.948397i	$0.397295\pi$
$788$	3.26438e12	0.301601
$789$	−7.89514e12	−0.725293
$790$	−4.53996e11	−0.0414696
$791$	6.59875e11	0.0599332
$792$	4.42490e11	0.0399614
$793$	−4.96224e12	−0.445604
$794$	5.02402e12	0.448600
$795$	−2.32285e12	−0.206238
$796$	−7.26633e12	−0.641514
$797$	−6.86625e12	−0.602778	−0.301389	−	0.953501i	$-0.597450\pi$
$797$	−6.86625e12	−0.602778	−0.301389	+	0.953501i	$0.597450\pi$
$798$	−2.44580e12	−0.213505
$799$	1.11380e13	0.966821
$800$	4.09600e11	0.0353553
$801$	−2.60090e12	−0.223243
$802$	−3.20357e12	−0.273432
$803$	−7.05640e11	−0.0598913
$804$	5.63794e12	0.475848
$805$	1.84733e12	0.155047
$806$	−5.49600e12	−0.458711
$807$	−1.11884e13	−0.928619
$808$	2.86937e12	0.236829
$809$	1.91798e13	1.57426	0.787128	−	0.616789i	$-0.211567\pi$
$809$	1.91798e13	1.57426	0.787128	+	0.616789i	$0.211567\pi$
$810$	−4.30467e11	−0.0351364
$811$	−1.22840e13	−0.997114	−0.498557	−	0.866857i	$-0.666136\pi$
$811$	−1.22840e13	−0.997114	−0.498557	+	0.866857i	$0.666136\pi$
$812$	1.05938e11	0.00855160
$813$	−9.94913e12	−0.798689
$814$	−4.62337e11	−0.0369104
$815$	−9.81359e12	−0.779146
$816$	1.90631e12	0.150518
$817$	−1.01359e13	−0.795904
$818$	−1.89230e11	−0.0147775
$819$	−1.26595e12	−0.0983196
$820$	−5.50569e12	−0.425255
$821$	1.60413e13	1.23224	0.616119	−	0.787653i	$-0.288704\pi$
$821$	1.60413e13	1.23224	0.616119	+	0.787653i	$0.288704\pi$
$822$	7.97784e11	0.0609484
$823$	−5.46607e12	−0.415313	−0.207657	−	0.978202i	$-0.566584\pi$
$823$	−5.46607e12	−0.415313	−0.207657	+	0.978202i	$0.566584\pi$
$824$	−8.35082e11	−0.0631039
$825$	−5.20978e11	−0.0391540
$826$	−9.34877e11	−0.0698786
$827$	1.80145e12	0.133921	0.0669603	−	0.997756i	$-0.478670\pi$
$827$	1.80145e12	0.133921	0.0669603	+	0.997756i	$0.478670\pi$
$828$	−2.06767e12	−0.152878
$829$	2.58830e13	1.90335	0.951675	−	0.307108i	$-0.0993613\pi$
$829$	2.58830e13	1.90335	0.951675	+	0.307108i	$0.0993613\pi$
$830$	2.31569e12	0.169367
$831$	−7.20580e12	−0.524176
$832$	−1.34826e12	−0.0975484
$833$	−2.07020e12	−0.148974
$834$	6.03349e12	0.431839
$835$	−9.01983e12	−0.642110
$836$	3.31312e12	0.234590
$837$	−2.27157e12	−0.159979
$838$	4.54556e12	0.318412
$839$	9.23345e12	0.643332	0.321666	−	0.946853i	$-0.395757\pi$
$839$	9.23345e12	0.643332	0.321666	+	0.946853i	$0.395757\pi$
$840$	4.97871e11	0.0345033
$841$	−1.44774e13	−0.997952
$842$	−1.51016e13	−1.03543
$843$	6.97924e11	0.0475975
$844$	−4.38728e11	−0.0297615
$845$	2.59144e12	0.174858
$846$	−3.25588e12	−0.218525
$847$	−5.01049e12	−0.334507
$848$	−3.00702e12	−0.199689
$849$	−1.02915e13	−0.679821
$850$	−2.24444e12	−0.147477
$851$	2.16041e12	0.141206
$852$	8.74762e12	0.568737
$853$	−1.67712e13	−1.08466	−0.542329	−	0.840166i	$-0.682457\pi$
$853$	−1.67712e13	−1.08466	−0.542329	+	0.840166i	$0.682457\pi$
$854$	2.37211e12	0.152607
$855$	−3.22310e12	−0.206265
$856$	−8.91423e12	−0.567482
$857$	1.97980e13	1.25374	0.626871	−	0.779123i	$-0.284335\pi$
$857$	1.97980e13	1.25374	0.626871	+	0.779123i	$0.284335\pi$
$858$	1.71488e12	0.108029
$859$	1.52100e13	0.953150	0.476575	−	0.879134i	$-0.341878\pi$
$859$	1.52100e13	0.953150	0.476575	+	0.879134i	$0.341878\pi$
$860$	2.06327e12	0.128622
$861$	−6.69220e12	−0.415006
$862$	−7.72314e12	−0.476443
$863$	8.04292e12	0.493589	0.246794	−	0.969068i	$-0.420623\pi$
$863$	8.04292e12	0.493589	0.246794	+	0.969068i	$0.420623\pi$
$864$	−5.57256e11	−0.0340207
$865$	9.37322e12	0.569268
$866$	−1.40622e13	−0.849614
$867$	−8.40165e11	−0.0504985
$868$	2.62727e12	0.157096
$869$	7.47526e11	0.0444669
$870$	1.39606e11	0.00826164
$871$	2.18500e13	1.28638
$872$	−1.12929e13	−0.661428
$873$	1.56720e12	0.0913186
$874$	−1.54816e13	−0.897458
$875$	−5.86182e11	−0.0338062
$876$	8.88658e11	0.0509878
$877$	2.24883e13	1.28368	0.641841	−	0.766837i	$-0.278171\pi$
$877$	2.24883e13	1.28368	0.641841	+	0.766837i	$0.278171\pi$
$878$	1.83550e13	1.04239
$879$	−9.45606e12	−0.534269
$880$	−6.74425e11	−0.0379107
$881$	−2.10592e13	−1.17774	−0.588871	−	0.808227i	$-0.700427\pi$
$881$	−2.10592e13	−1.17774	−0.588871	+	0.808227i	$0.700427\pi$
$882$	6.05166e11	0.0336718
$883$	−2.71289e13	−1.50179	−0.750896	−	0.660421i	$-0.770378\pi$
$883$	−2.71289e13	−1.50179	−0.750896	+	0.660421i	$0.770378\pi$
$884$	7.38794e12	0.406900
$885$	−1.23199e12	−0.0675092
$886$	−1.60123e13	−0.872975
$887$	−2.69700e13	−1.46294	−0.731468	−	0.681876i	$-0.761164\pi$
$887$	−2.69700e13	−1.46294	−0.731468	+	0.681876i	$0.761164\pi$
$888$	5.82250e11	0.0314232
$889$	−3.11737e12	−0.167390
$890$	3.96418e12	0.211787
$891$	7.08784e11	0.0376760
$892$	−1.48114e13	−0.783347
$893$	−2.43782e13	−1.28283
$894$	2.92482e12	0.153137
$895$	3.13143e12	0.163132
$896$	6.44514e11	0.0334077
$897$	−8.01332e12	−0.413282
$898$	9.14028e12	0.469046
$899$	7.36698e11	0.0376158
$900$	6.56100e11	0.0333333
$901$	1.64772e13	0.832957
$902$	9.06537e12	0.455991
$903$	2.50792e12	0.125522
$904$	1.12572e12	0.0560623
$905$	−4.85559e12	−0.240615
$906$	−1.17153e13	−0.577668
$907$	2.11632e13	1.03836	0.519180	−	0.854665i	$-0.326237\pi$
$907$	2.11632e13	1.03836	0.519180	+	0.854665i	$0.326237\pi$
$908$	−5.65978e12	−0.276320
$909$	4.59617e12	0.223285
$910$	1.92951e12	0.0932741
$911$	−1.53168e13	−0.736774	−0.368387	−	0.929673i	$-0.620090\pi$
$911$	−1.53168e13	−0.736774	−0.368387	+	0.929673i	$0.620090\pi$
$912$	−4.17242e12	−0.199715
$913$	−3.81288e12	−0.181608
$914$	2.73732e13	1.29738
$915$	3.12599e12	0.147432
$916$	−6.48451e11	−0.0304332
$917$	−6.24549e12	−0.291678
$918$	3.05354e12	0.141909
$919$	1.79393e13	0.829630	0.414815	−	0.909906i	$-0.363846\pi$
$919$	1.79393e13	0.829630	0.414815	+	0.909906i	$0.363846\pi$
$920$	3.15146e12	0.145033
$921$	−1.61254e13	−0.738485
$922$	−8.34978e12	−0.380528
$923$	3.39016e13	1.53749
$924$	−8.19768e11	−0.0369971
$925$	−6.85527e11	−0.0307884
$926$	2.50373e13	1.11902
$927$	−1.33764e12	−0.0594950
$928$	1.80725e11	0.00799929
$929$	4.22683e13	1.86185	0.930924	−	0.365214i	$-0.119004\pi$
$929$	4.22683e13	1.86185	0.930924	+	0.365214i	$0.119004\pi$
$930$	3.46224e12	0.151769
$931$	4.53114e12	0.197667
$932$	−1.25093e13	−0.543078
$933$	−6.19823e11	−0.0267794
$934$	8.69993e12	0.374072
$935$	3.69557e12	0.158136
$936$	−2.15966e12	−0.0919695
$937$	3.14530e11	0.0133301	0.00666505	−	0.999978i	$-0.497878\pi$
$937$	3.14530e11	0.0133301	0.00666505	+	0.999978i	$0.497878\pi$
$938$	−1.04450e13	−0.440549
$939$	9.92131e12	0.416460
$940$	4.96248e12	0.207311
$941$	−4.81188e12	−0.200060	−0.100030	−	0.994984i	$-0.531894\pi$
$941$	−4.81188e12	−0.200060	−0.100030	+	0.994984i	$0.531894\pi$
$942$	6.38208e12	0.264078
$943$	−4.23608e13	−1.74446
$944$	−1.59486e12	−0.0653655
$945$	7.97494e11	0.0325300
$946$	−3.39728e12	−0.137918
$947$	−1.82929e13	−0.739106	−0.369553	−	0.929210i	$-0.620489\pi$
$947$	−1.82929e13	−0.739106	−0.369553	+	0.929210i	$0.620489\pi$
$948$	−9.41407e11	−0.0378564
$949$	3.44401e12	0.137837
$950$	4.91251e12	0.195680
$951$	−2.18693e13	−0.867006
$952$	−3.53167e12	−0.139352
$953$	−3.16121e13	−1.24147	−0.620734	−	0.784022i	$-0.713165\pi$
$953$	−3.16121e13	−1.24147	−0.620734	+	0.784022i	$0.713165\pi$
$954$	−4.81666e12	−0.188269
$955$	5.11127e12	0.198845
$956$	−8.00325e12	−0.309889
$957$	−2.29867e11	−0.00885876
$958$	−1.64471e13	−0.630877
$959$	−1.47799e12	−0.0564272
$960$	8.49347e11	0.0322749
$961$	−8.16941e12	−0.308984
$962$	2.25652e12	0.0849477
$963$	−1.42789e13	−0.535027
$964$	−1.87214e12	−0.0698220
$965$	1.45841e13	0.541386
$966$	3.83062e12	0.141538
$967$	2.17034e13	0.798195	0.399098	−	0.916908i	$-0.369323\pi$
$967$	2.17034e13	0.798195	0.399098	+	0.916908i	$0.369323\pi$
$968$	−8.54768e12	−0.312903
$969$	2.28632e13	0.833066
$970$	−2.38865e12	−0.0866324
$971$	2.54432e13	0.918514	0.459257	−	0.888304i	$-0.348116\pi$
$971$	2.54432e13	0.918514	0.459257	+	0.888304i	$0.348116\pi$
$972$	−8.92617e11	−0.0320750
$973$	−1.11778e13	−0.399805
$974$	−2.80006e13	−0.996902
$975$	2.54273e12	0.0901114
$976$	4.04671e12	0.142751
$977$	2.94855e13	1.03534	0.517670	−	0.855580i	$-0.326799\pi$
$977$	2.94855e13	1.03534	0.517670	+	0.855580i	$0.326799\pi$
$978$	−2.03495e13	−0.711259
$979$	−6.52721e12	−0.227094
$980$	−9.22368e11	−0.0319438
$981$	−1.80891e13	−0.623600
$982$	−1.35075e13	−0.463524
$983$	4.07203e13	1.39098	0.695488	−	0.718537i	$-0.255188\pi$
$983$	4.07203e13	1.39098	0.695488	+	0.718537i	$0.255188\pi$
$984$	−1.14166e13	−0.388203
$985$	−7.96968e12	−0.269760
$986$	−9.90297e11	−0.0333672
$987$	6.03192e12	0.202315
$988$	−1.61703e13	−0.539899
$989$	1.58748e13	0.527626
$990$	−1.08030e12	−0.0357426
$991$	−3.54803e13	−1.16857	−0.584286	−	0.811548i	$-0.698625\pi$
$991$	−3.54803e13	−1.16857	−0.584286	+	0.811548i	$0.698625\pi$
$992$	4.48200e12	0.146950
$993$	−1.39959e13	−0.456805
$994$	−1.62060e13	−0.526548
$995$	1.77401e13	0.573788
$996$	4.80181e12	0.154610
$997$	5.47044e12	0.175345	0.0876727	−	0.996149i	$-0.472057\pi$
$997$	5.47044e12	0.175345	0.0876727	+	0.996149i	$0.472057\pi$
$998$	1.55423e13	0.495939
$999$	9.32651e11	0.0296261

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.10.a.j.1.2	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.10.a.j.1.2	✓	2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	210.a (trivial)

\(f(q)\)	\(=\)	\(q+16.0000 q^{2} -81.0000 q^{3} +256.000 q^{4} -625.000 q^{5} -1296.00 q^{6} +2401.00 q^{7} +4096.00 q^{8} +6561.00 q^{9} -10000.0 q^{10} +16465.5 q^{11} -20736.0 q^{12} -80362.9 q^{13} +38416.0 q^{14} +50625.0 q^{15} +65536.0 q^{16} -359110. q^{17} +104976. q^{18} +786001. q^{19} -160000. q^{20} -194481. q^{21} +263447. q^{22} -1.23104e6 q^{23} -331776. q^{24} +390625. q^{25} -1.28581e6 q^{26} -531441. q^{27} +614656. q^{28} +172353. q^{29} +810000. q^{30} +4.27437e6 q^{31} +1.04858e6 q^{32} -1.33370e6 q^{33} -5.74577e6 q^{34} -1.50062e6 q^{35} +1.67962e6 q^{36} -1.75495e6 q^{37} +1.25760e7 q^{38} +6.50939e6 q^{39} -2.56000e6 q^{40} +3.44105e7 q^{41} -3.11170e6 q^{42} -1.28955e7 q^{43} +4.21516e6 q^{44} -4.10062e6 q^{45} -1.96966e7 q^{46} -3.10155e7 q^{47} -5.30842e6 q^{48} +5.76480e6 q^{49} +6.25000e6 q^{50} +2.90879e7 q^{51} -2.05729e7 q^{52} -4.58835e7 q^{53} -8.50306e6 q^{54} -1.02909e7 q^{55} +9.83450e6 q^{56} -6.36661e7 q^{57} +2.75764e6 q^{58} -2.43356e7 q^{59} +1.29600e7 q^{60} +6.17480e7 q^{61} +6.83899e7 q^{62} +1.57530e7 q^{63} +1.67772e7 q^{64} +5.02268e7 q^{65} -2.13392e7 q^{66} -2.71891e8 q^{67} -9.19323e7 q^{68} +9.97143e7 q^{69} -2.40100e7 q^{70} -4.21856e8 q^{71} +2.68739e7 q^{72} -4.28558e7 q^{73} -2.80792e7 q^{74} -3.16406e7 q^{75} +2.01216e8 q^{76} +3.95336e7 q^{77} +1.04150e8 q^{78} +4.53996e7 q^{79} -4.09600e7 q^{80} +4.30467e7 q^{81} +5.50569e8 q^{82} -2.31569e8 q^{83} -4.97871e7 q^{84} +2.24444e8 q^{85} -2.06327e8 q^{86} -1.39606e7 q^{87} +6.74425e7 q^{88} -3.96418e8 q^{89} -6.56100e7 q^{90} -1.92951e8 q^{91} -3.15146e8 q^{92} -3.46224e8 q^{93} -4.96248e8 q^{94} -4.91251e8 q^{95} -8.49347e7 q^{96} +2.38865e8 q^{97} +9.22368e7 q^{98} +1.08030e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 32 q^{2} - 162 q^{3} + 512 q^{4} - 1250 q^{5} - 2592 q^{6} + 4802 q^{7} + 8192 q^{8} + 13122 q^{9} - 20000 q^{10} - 41964 q^{11} - 41472 q^{12} - 67856 q^{13} + 76832 q^{14} + 101250 q^{15} + 131072 q^{16}+ \cdots - 275325804 q^{99}+O(q^{100}) \) 2 * q + 32 * q^2 - 162 * q^3 + 512 * q^4 - 1250 * q^5 - 2592 * q^6 + 4802 * q^7 + 8192 * q^8 + 13122 * q^9 - 20000 * q^10 - 41964 * q^11 - 41472 * q^12 - 67856 * q^13 + 76832 * q^14 + 101250 * q^15 + 131072 * q^16 + 96636 * q^17 + 209952 * q^18 + 664276 * q^19 - 320000 * q^20 - 388962 * q^21 - 671424 * q^22 + 246120 * q^23 - 663552 * q^24 + 781250 * q^25 - 1085696 * q^26 - 1062882 * q^27 + 1229312 * q^28 - 4304772 * q^29 + 1620000 * q^30 - 4366148 * q^31 + 2097152 * q^32 + 3399084 * q^33 + 1546176 * q^34 - 3001250 * q^35 + 3359232 * q^36 - 3575804 * q^37 + 10628416 * q^38 + 5496336 * q^39 - 5120000 * q^40 + 44782812 * q^41 - 6223392 * q^42 + 22063936 * q^43 - 10742784 * q^44 - 8201250 * q^45 + 3937920 * q^46 + 7082088 * q^47 - 10616832 * q^48 + 11529602 * q^49 + 12500000 * q^50 - 7827516 * q^51 - 17371136 * q^52 - 123069984 * q^53 - 17006112 * q^54 + 26227500 * q^55 + 19668992 * q^56 - 53806356 * q^57 - 68876352 * q^58 - 151552896 * q^59 + 25920000 * q^60 - 69217700 * q^61 - 69858368 * q^62 + 31505922 * q^63 + 33554432 * q^64 + 42410000 * q^65 + 54385344 * q^66 - 348097064 * q^67 + 24738816 * q^68 - 19935720 * q^69 - 48020000 * q^70 - 194772348 * q^71 + 53747712 * q^72 + 297178240 * q^73 - 57212864 * q^74 - 63281250 * q^75 + 170054656 * q^76 - 100755564 * q^77 + 87941376 * q^78 - 356059832 * q^79 - 81920000 * q^80 + 86093442 * q^81 + 716524992 * q^82 - 706246128 * q^83 - 99574272 * q^84 - 60397500 * q^85 + 353022976 * q^86 + 348686532 * q^87 - 171884544 * q^88 - 1122685860 * q^89 - 131220000 * q^90 - 162922256 * q^91 + 63006720 * q^92 + 353657988 * q^93 + 113313408 * q^94 - 415172500 * q^95 - 169869312 * q^96 - 939835400 * q^97 + 184473632 * q^98 - 275325804 * q^99

Introduction

L-functions

Modular forms

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