LMFDB - Embedded newform 21.10.a.b.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,10,Mod(1,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("21.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	21.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:	$10.8157525594$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{2353}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 588 $ x^2 - x - 588
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-23.7539$ of defining polynomial
Character	$\chi$	$=$	21.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+28.7539 q^{2} -81.0000 q^{3} +314.785 q^{4} -1112.77 q^{5} -2329.06 q^{6} -2401.00 q^{7} -5670.70 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+28.7539 q^{2} -81.0000 q^{3} +314.785 q^{4} -1112.77 q^{5} -2329.06 q^{6} -2401.00 q^{7} -5670.70 q^{8} +6561.00 q^{9} -31996.5 q^{10} -86212.6 q^{11} -25497.6 q^{12} +45883.4 q^{13} -69038.0 q^{14} +90134.4 q^{15} -324224. q^{16} +434720. q^{17} +188654. q^{18} -103627. q^{19} -350283. q^{20} +194481. q^{21} -2.47895e6 q^{22} -1.15745e6 q^{23} +459327. q^{24} -714867. q^{25} +1.31933e6 q^{26} -531441. q^{27} -755798. q^{28} +5.46099e6 q^{29} +2.59171e6 q^{30} +4.80298e6 q^{31} -6.41931e6 q^{32} +6.98322e6 q^{33} +1.24999e7 q^{34} +2.67176e6 q^{35} +2.06530e6 q^{36} -5.59947e6 q^{37} -2.97967e6 q^{38} -3.71656e6 q^{39} +6.31019e6 q^{40} -1.48886e7 q^{41} +5.59208e6 q^{42} +2.34211e7 q^{43} -2.71384e7 q^{44} -7.30089e6 q^{45} -3.32811e7 q^{46} -4.12205e7 q^{47} +2.62622e7 q^{48} +5.76480e6 q^{49} -2.05552e7 q^{50} -3.52123e7 q^{51} +1.44434e7 q^{52} -1.07141e8 q^{53} -1.52810e7 q^{54} +9.59349e7 q^{55} +1.36153e7 q^{56} +8.39378e6 q^{57} +1.57025e8 q^{58} -4.07986e7 q^{59} +2.83729e7 q^{60} -8.35090e7 q^{61} +1.38104e8 q^{62} -1.57530e7 q^{63} -1.85770e7 q^{64} -5.10577e7 q^{65} +2.00795e8 q^{66} -2.31112e8 q^{67} +1.36843e8 q^{68} +9.37533e7 q^{69} +7.68235e7 q^{70} -1.02926e8 q^{71} -3.72055e7 q^{72} +4.32488e7 q^{73} -1.61007e8 q^{74} +5.79042e7 q^{75} -3.26202e7 q^{76} +2.06997e8 q^{77} -1.06865e8 q^{78} +6.54101e6 q^{79} +3.60787e8 q^{80} +4.30467e7 q^{81} -4.28105e8 q^{82} -2.58155e8 q^{83} +6.12197e7 q^{84} -4.83744e8 q^{85} +6.73446e8 q^{86} -4.42341e8 q^{87} +4.88886e8 q^{88} +5.67430e8 q^{89} -2.09929e8 q^{90} -1.10166e8 q^{91} -3.64347e8 q^{92} -3.89041e8 q^{93} -1.18525e9 q^{94} +1.15313e8 q^{95} +5.19964e8 q^{96} +1.44367e9 q^{97} +1.65760e8 q^{98} -5.65641e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 9 q^{2} - 162 q^{3} + 193 q^{4} + 1170 q^{5} - 729 q^{6} - 4802 q^{7} + 6849 q^{8} + 13122 q^{9}+O(q^{10}) $ 2 * q + 9 * q^2 - 162 * q^3 + 193 * q^4 + 1170 * q^5 - 729 * q^6 - 4802 * q^7 + 6849 * q^8 + 13122 * q^9	\( 2 q + 9 q^{2} - 162 q^{3} + 193 q^{4} + 1170 q^{5} - 729 q^{6} - 4802 q^{7} + 6849 q^{8} + 13122 q^{9} - 77090 q^{10} - 145746 q^{11} - 15633 q^{12} + 86528 q^{13} - 21609 q^{14} - 94770 q^{15} - 509183 q^{16} - 229842 q^{17} + 59049 q^{18} - 221224 q^{19} - 628290 q^{20} + 388962 q^{21} - 1302932 q^{22} - 2035782 q^{23} - 554769 q^{24} + 2543050 q^{25} + 516438 q^{26} - 1062882 q^{27} - 463393 q^{28} + 9756252 q^{29} + 6244290 q^{30} + 204000 q^{31} - 9175743 q^{32} + 11805426 q^{33} + 25627554 q^{34} - 2809170 q^{35} + 1266273 q^{36} - 13959816 q^{37} - 656676 q^{38} - 7008768 q^{39} + 34889790 q^{40} - 42362550 q^{41} + 1750329 q^{42} - 4763912 q^{43} - 19888164 q^{44} + 7676370 q^{45} - 15930600 q^{46} - 48278484 q^{47} + 41243823 q^{48} + 11529602 q^{49} - 84911625 q^{50} + 18617202 q^{51} + 9493510 q^{52} - 108980352 q^{53} - 4782969 q^{54} - 39966160 q^{55} - 16444449 q^{56} + 17919144 q^{57} + 72176782 q^{58} - 188376804 q^{59} + 50891490 q^{60} + 19722092 q^{61} + 228951936 q^{62} - 31505922 q^{63} + 130572161 q^{64} + 41724540 q^{65} + 105537492 q^{66} + 70274396 q^{67} + 217776834 q^{68} + 164898342 q^{69} + 185093090 q^{70} - 382044186 q^{71} + 44936289 q^{72} + 191785896 q^{73} + 4142502 q^{74} - 205987050 q^{75} - 18298628 q^{76} + 349936146 q^{77} - 41831478 q^{78} - 72592148 q^{79} - 61430850 q^{80} + 86093442 q^{81} + 114611450 q^{82} + 187994232 q^{83} + 37534833 q^{84} - 2000786580 q^{85} + 1230207804 q^{86} - 790256412 q^{87} - 256454052 q^{88} + 42930954 q^{89} - 505787490 q^{90} - 207753728 q^{91} - 257379192 q^{92} - 16524000 q^{93} - 1045824480 q^{94} - 153134280 q^{95} + 743235183 q^{96} + 1726854096 q^{97} + 51883209 q^{98} - 956239506 q^{99}+O(q^{100}) \) 2 * q + 9 * q^2 - 162 * q^3 + 193 * q^4 + 1170 * q^5 - 729 * q^6 - 4802 * q^7 + 6849 * q^8 + 13122 * q^9 - 77090 * q^10 - 145746 * q^11 - 15633 * q^12 + 86528 * q^13 - 21609 * q^14 - 94770 * q^15 - 509183 * q^16 - 229842 * q^17 + 59049 * q^18 - 221224 * q^19 - 628290 * q^20 + 388962 * q^21 - 1302932 * q^22 - 2035782 * q^23 - 554769 * q^24 + 2543050 * q^25 + 516438 * q^26 - 1062882 * q^27 - 463393 * q^28 + 9756252 * q^29 + 6244290 * q^30 + 204000 * q^31 - 9175743 * q^32 + 11805426 * q^33 + 25627554 * q^34 - 2809170 * q^35 + 1266273 * q^36 - 13959816 * q^37 - 656676 * q^38 - 7008768 * q^39 + 34889790 * q^40 - 42362550 * q^41 + 1750329 * q^42 - 4763912 * q^43 - 19888164 * q^44 + 7676370 * q^45 - 15930600 * q^46 - 48278484 * q^47 + 41243823 * q^48 + 11529602 * q^49 - 84911625 * q^50 + 18617202 * q^51 + 9493510 * q^52 - 108980352 * q^53 - 4782969 * q^54 - 39966160 * q^55 - 16444449 * q^56 + 17919144 * q^57 + 72176782 * q^58 - 188376804 * q^59 + 50891490 * q^60 + 19722092 * q^61 + 228951936 * q^62 - 31505922 * q^63 + 130572161 * q^64 + 41724540 * q^65 + 105537492 * q^66 + 70274396 * q^67 + 217776834 * q^68 + 164898342 * q^69 + 185093090 * q^70 - 382044186 * q^71 + 44936289 * q^72 + 191785896 * q^73 + 4142502 * q^74 - 205987050 * q^75 - 18298628 * q^76 + 349936146 * q^77 - 41831478 * q^78 - 72592148 * q^79 - 61430850 * q^80 + 86093442 * q^81 + 114611450 * q^82 + 187994232 * q^83 + 37534833 * q^84 - 2000786580 * q^85 + 1230207804 * q^86 - 790256412 * q^87 - 256454052 * q^88 + 42930954 * q^89 - 505787490 * q^90 - 207753728 * q^91 - 257379192 * q^92 - 16524000 * q^93 - 1045824480 * q^94 - 153134280 * q^95 + 743235183 * q^96 + 1726854096 * q^97 + 51883209 * q^98 - 956239506 * q^99

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 $

$2$	28.7539	1.27075	0.635377	−	0.772202i	$-0.280845\pi$
$2$	28.7539	1.27075	0.635377	+	0.772202i	$0.280845\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	314.785	0.614814
$5$	−1112.77	−0.796234	−0.398117	−	0.917335i	$-0.630336\pi$
$5$	−1112.77	−0.796234	−0.398117	+	0.917335i	$0.630336\pi$
$6$	−2329.06	−0.733670
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	−5670.70	−0.489476
$9$	6561.00	0.333333
$10$	−31996.5	−1.01182
$11$	−86212.6	−1.77543	−0.887715	−	0.460392i	$-0.847709\pi$
$11$	−86212.6	−1.77543	−0.887715	+	0.460392i	$0.847709\pi$
$12$	−25497.6	−0.354963
$13$	45883.4	0.445565	0.222782	−	0.974868i	$-0.428486\pi$
$13$	45883.4	0.445565	0.222782	+	0.974868i	$0.428486\pi$
$14$	−69038.0	−0.480300
$15$	90134.4	0.459706
$16$	−324224.	−1.23682
$17$	434720.	1.26238	0.631189	−	0.775629i	$-0.282567\pi$
$17$	434720.	1.26238	0.631189	+	0.775629i	$0.282567\pi$
$18$	188654.	0.423584
$19$	−103627.	−0.182424	−0.0912118	−	0.995832i	$-0.529074\pi$
$19$	−103627.	−0.182424	−0.0912118	+	0.995832i	$0.529074\pi$
$20$	−350283.	−0.489536
$21$	194481.	0.218218
$22$	−2.47895e6	−2.25613
$23$	−1.15745e6	−0.862435	−0.431217	−	0.902248i	$-0.641916\pi$
$23$	−1.15745e6	−0.862435	−0.431217	+	0.902248i	$0.641916\pi$
$24$	459327.	0.282599
$25$	−714867.	−0.366012
$26$	1.31933e6	0.566203
$27$	−531441.	−0.192450
$28$	−755798.	−0.232378
$29$	5.46099e6	1.43377	0.716887	−	0.697189i	$-0.245566\pi$
$29$	5.46099e6	1.43377	0.716887	+	0.697189i	$0.245566\pi$
$30$	2.59171e6	0.584173
$31$	4.80298e6	0.934078	0.467039	−	0.884237i	$-0.345321\pi$
$31$	4.80298e6	0.934078	0.467039	+	0.884237i	$0.345321\pi$
$32$	−6.41931e6	−1.08221
$33$	6.98322e6	1.02505
$34$	1.24999e7	1.60417
$35$	2.67176e6	0.300948
$36$	2.06530e6	0.204938
$37$	−5.59947e6	−0.491179	−0.245589	−	0.969374i	$-0.578981\pi$
$37$	−5.59947e6	−0.491179	−0.245589	+	0.969374i	$0.578981\pi$
$38$	−2.97967e6	−0.231816
$39$	−3.71656e6	−0.257247
$40$	6.31019e6	0.389738
$41$	−1.48886e7	−0.822862	−0.411431	−	0.911441i	$-0.634971\pi$
$41$	−1.48886e7	−0.822862	−0.411431	+	0.911441i	$0.634971\pi$
$42$	5.59208e6	0.277301
$43$	2.34211e7	1.04472	0.522358	−	0.852726i	$-0.325052\pi$
$43$	2.34211e7	1.04472	0.522358	+	0.852726i	$0.325052\pi$
$44$	−2.71384e7	−1.09156
$45$	−7.30089e6	−0.265411
$46$	−3.32811e7	−1.09594
$47$	−4.12205e7	−1.23218	−0.616088	−	0.787678i	$-0.711283\pi$
$47$	−4.12205e7	−1.23218	−0.616088	+	0.787678i	$0.711283\pi$
$48$	2.62622e7	0.714077
$49$	5.76480e6	0.142857
$50$	−2.05552e7	−0.465111
$51$	−3.52123e7	−0.728835
$52$	1.44434e7	0.273939
$53$	−1.07141e8	−1.86516	−0.932579	−	0.360966i	$-0.882447\pi$
$53$	−1.07141e8	−1.86516	−0.932579	+	0.360966i	$0.882447\pi$
$54$	−1.52810e7	−0.244557
$55$	9.59349e7	1.41366
$56$	1.36153e7	0.185005
$57$	8.39378e6	0.105322
$58$	1.57025e8	1.82197
$59$	−4.07986e7	−0.438340	−0.219170	−	0.975687i	$-0.570335\pi$
$59$	−4.07986e7	−0.438340	−0.219170	+	0.975687i	$0.570335\pi$
$60$	2.83729e7	0.282634
$61$	−8.35090e7	−0.772234	−0.386117	−	0.922450i	$-0.626184\pi$
$61$	−8.35090e7	−0.772234	−0.386117	+	0.922450i	$0.626184\pi$
$62$	1.38104e8	1.18698
$63$	−1.57530e7	−0.125988
$64$	−1.85770e7	−0.138409
$65$	−5.10577e7	−0.354774
$66$	2.00795e8	1.30258
$67$	−2.31112e8	−1.40115	−0.700576	−	0.713578i	$-0.747074\pi$
$67$	−2.31112e8	−1.40115	−0.700576	+	0.713578i	$0.747074\pi$
$68$	1.36843e8	0.776128
$69$	9.37533e7	0.497927
$70$	7.68235e7	0.382431
$71$	−1.02926e8	−0.480687	−0.240344	−	0.970688i	$-0.577260\pi$
$71$	−1.02926e8	−0.480687	−0.240344	+	0.970688i	$0.577260\pi$
$72$	−3.72055e7	−0.163159
$73$	4.32488e7	0.178246	0.0891232	−	0.996021i	$-0.471594\pi$
$73$	4.32488e7	0.178246	0.0891232	+	0.996021i	$0.471594\pi$
$74$	−1.61007e8	−0.624167
$75$	5.79042e7	0.211317
$76$	−3.26202e7	−0.112157
$77$	2.06997e8	0.671050
$78$	−1.06865e8	−0.326897
$79$	6.54101e6	0.0188939	0.00944697	−	0.999955i	$-0.496993\pi$
$79$	6.54101e6	0.0188939	0.00944697	+	0.999955i	$0.496993\pi$
$80$	3.60787e8	0.984796
$81$	4.30467e7	0.111111
$82$	−4.28105e8	−1.04565
$83$	−2.58155e8	−0.597075	−0.298538	−	0.954398i	$-0.596499\pi$
$83$	−2.58155e8	−0.597075	−0.298538	+	0.954398i	$0.596499\pi$
$84$	6.12197e7	0.134163
$85$	−4.83744e8	−1.00515
$86$	6.73446e8	1.32758
$87$	−4.42341e8	−0.827790
$88$	4.88886e8	0.869031
$89$	5.67430e8	0.958643	0.479322	−	0.877639i	$-0.340883\pi$
$89$	5.67430e8	0.958643	0.479322	+	0.877639i	$0.340883\pi$
$90$	−2.09929e8	−0.337272
$91$	−1.10166e8	−0.168408
$92$	−3.64347e8	−0.530237
$93$	−3.89041e8	−0.539290
$94$	−1.18525e9	−1.56579
$95$	1.15313e8	0.145252
$96$	5.19964e8	0.624817
$97$	1.44367e9	1.65575	0.827876	−	0.560911i	$-0.189549\pi$
$97$	1.44367e9	1.65575	0.827876	+	0.560911i	$0.189549\pi$
$98$	1.65760e8	0.181536
$99$	−5.65641e8	−0.591810
$100$	−2.25029e8	−0.225029
$101$	−1.65369e9	−1.58128	−0.790639	−	0.612283i	$-0.790251\pi$
$101$	−1.65369e9	−1.58128	−0.790639	+	0.612283i	$0.790251\pi$
$102$	−1.01249e9	−0.926169
$103$	8.61899e8	0.754552	0.377276	−	0.926101i	$-0.376861\pi$
$103$	8.61899e8	0.754552	0.377276	+	0.926101i	$0.376861\pi$
$104$	−2.60191e8	−0.218093
$105$	−2.16413e8	−0.173752
$106$	−3.08073e9	−2.37016
$107$	−2.39211e8	−0.176422	−0.0882111	−	0.996102i	$-0.528115\pi$
$107$	−2.39211e8	−0.176422	−0.0882111	+	0.996102i	$0.528115\pi$
$108$	−1.67290e8	−0.118321
$109$	1.80618e9	1.22558	0.612791	−	0.790245i	$-0.290047\pi$
$109$	1.80618e9	1.22558	0.612791	+	0.790245i	$0.290047\pi$
$110$	2.75850e9	1.79641
$111$	4.53557e8	0.283582
$112$	7.78463e8	0.467473
$113$	8.59829e8	0.496089	0.248044	−	0.968749i	$-0.420212\pi$
$113$	8.59829e8	0.496089	0.248044	+	0.968749i	$0.420212\pi$
$114$	2.41354e8	0.133839
$115$	1.28797e9	0.686700
$116$	1.71904e9	0.881505
$117$	3.01041e8	0.148522
$118$	−1.17312e9	−0.557022
$119$	−1.04376e9	−0.477134
$120$	−5.11125e8	−0.225015
$121$	5.07467e9	2.15216
$122$	−2.40121e9	−0.981319
$123$	1.20598e9	0.475079
$124$	1.51191e9	0.574284
$125$	2.96886e9	1.08766
$126$	−4.52959e8	−0.160100
$127$	−3.24389e9	−1.10650	−0.553248	−	0.833017i	$-0.686612\pi$
$127$	−3.24389e9	−1.10650	−0.553248	+	0.833017i	$0.686612\pi$
$128$	2.75252e9	0.906330
$129$	−1.89711e9	−0.603167
$130$	−1.46811e9	−0.450830
$131$	2.69277e9	0.798874	0.399437	−	0.916761i	$-0.369206\pi$
$131$	2.69277e9	0.798874	0.399437	+	0.916761i	$0.369206\pi$
$132$	2.19821e9	0.630212
$133$	2.48808e8	0.0689497
$134$	−6.64536e9	−1.78052
$135$	5.91372e8	0.153235
$136$	−2.46517e9	−0.617904
$137$	−6.41294e9	−1.55530	−0.777651	−	0.628696i	$-0.783589\pi$
$137$	−6.41294e9	−1.55530	−0.777651	+	0.628696i	$0.783589\pi$
$138$	2.69577e9	0.632742
$139$	−7.65454e9	−1.73921	−0.869606	−	0.493746i	$-0.835627\pi$
$139$	−7.65454e9	−1.73921	−0.869606	+	0.493746i	$0.835627\pi$
$140$	8.41030e8	0.185027
$141$	3.33886e9	0.711397
$142$	−2.95952e9	−0.610835
$143$	−3.95573e9	−0.791069
$144$	−2.12724e9	−0.412273
$145$	−6.07683e9	−1.14162
$146$	1.24357e9	0.226507
$147$	−4.66949e8	−0.0824786
$148$	−1.76263e9	−0.301984
$149$	−5.30168e9	−0.881202	−0.440601	−	0.897703i	$-0.645235\pi$
$149$	−5.30168e9	−0.881202	−0.440601	+	0.897703i	$0.645235\pi$
$150$	1.66497e9	0.268532
$151$	6.15013e9	0.962693	0.481347	−	0.876530i	$-0.340148\pi$
$151$	6.15013e9	0.962693	0.481347	+	0.876530i	$0.340148\pi$
$152$	5.87637e8	0.0892921
$153$	2.85220e9	0.420793
$154$	5.95195e9	0.852739
$155$	−5.34462e9	−0.743745
$156$	−1.16992e9	−0.158159
$157$	1.28865e10	1.69272	0.846360	−	0.532611i	$-0.178789\pi$
$157$	1.28865e10	1.69272	0.846360	+	0.532611i	$0.178789\pi$
$158$	1.88079e8	0.0240095
$159$	8.67845e9	1.07685
$160$	7.14321e9	0.861695
$161$	2.77903e9	0.325970
$162$	1.23776e9	0.141195
$163$	8.69437e9	0.964704	0.482352	−	0.875977i	$-0.339783\pi$
$163$	8.69437e9	0.964704	0.482352	+	0.875977i	$0.339783\pi$
$164$	−4.68671e9	−0.505907
$165$	−7.77072e9	−0.816176
$166$	−7.42296e9	−0.758736
$167$	1.56185e10	1.55388	0.776938	−	0.629577i	$-0.216772\pi$
$167$	1.56185e10	1.55388	0.776938	+	0.629577i	$0.216772\pi$
$168$	−1.10284e9	−0.106812
$169$	−8.49921e9	−0.801472
$170$	−1.39095e10	−1.27730
$171$	−6.79896e8	−0.0608079
$172$	7.37259e9	0.642306
$173$	−1.63273e10	−1.38582	−0.692908	−	0.721026i	$-0.743671\pi$
$173$	−1.63273e10	−1.38582	−0.692908	+	0.721026i	$0.743671\pi$
$174$	−1.27190e10	−1.05192
$175$	1.71639e9	0.138339
$176$	2.79522e10	2.19588
$177$	3.30468e9	0.253076
$178$	1.63158e10	1.21820
$179$	−1.02362e10	−0.745246	−0.372623	−	0.927983i	$-0.621542\pi$
$179$	−1.02362e10	−0.745246	−0.372623	+	0.927983i	$0.621542\pi$
$180$	−2.29821e9	−0.163179
$181$	2.11503e10	1.46475	0.732373	−	0.680904i	$-0.238413\pi$
$181$	2.11503e10	1.46475	0.732373	+	0.680904i	$0.238413\pi$
$182$	−3.16770e9	−0.214005
$183$	6.76423e9	0.445849
$184$	6.56354e9	0.422141
$185$	6.23093e9	0.391093
$186$	−1.11864e10	−0.685305
$187$	−3.74784e10	−2.24127
$188$	−1.29756e10	−0.757559
$189$	1.27599e9	0.0727393
$190$	3.31569e9	0.184579
$191$	−1.23634e8	−0.00672181	−0.00336090	−	0.999994i	$-0.501070\pi$
$191$	−1.23634e8	−0.00672181	−0.00336090	+	0.999994i	$0.501070\pi$
$192$	1.50473e9	0.0799106
$193$	−1.26726e10	−0.657445	−0.328722	−	0.944427i	$-0.606618\pi$
$193$	−1.26726e10	−0.657445	−0.328722	+	0.944427i	$0.606618\pi$
$194$	4.15111e10	2.10405
$195$	4.13568e9	0.204829
$196$	1.81467e9	0.0878306
$197$	9.10309e9	0.430617	0.215308	−	0.976546i	$-0.430924\pi$
$197$	9.10309e9	0.430617	0.215308	+	0.976546i	$0.430924\pi$
$198$	−1.62644e10	−0.752045
$199$	−2.09809e10	−0.948388	−0.474194	−	0.880420i	$-0.657261\pi$
$199$	−2.09809e10	−0.948388	−0.474194	+	0.880420i	$0.657261\pi$
$200$	4.05379e9	0.179154
$201$	1.87201e10	0.808956
$202$	−4.75500e10	−2.00941
$203$	−1.31118e10	−0.541916
$204$	−1.10843e10	−0.448098
$205$	1.65676e10	0.655190
$206$	2.47829e10	0.958849
$207$	−7.59401e9	−0.287478
$208$	−1.48765e10	−0.551082
$209$	8.93395e9	0.323881
$210$	−6.22270e9	−0.220797
$211$	1.91584e10	0.665408	0.332704	−	0.943031i	$-0.392039\pi$
$211$	1.91584e10	0.665408	0.332704	+	0.943031i	$0.392039\pi$
$212$	−3.37265e10	−1.14673
$213$	8.33701e9	0.277525
$214$	−6.87823e9	−0.224189
$215$	−2.60623e10	−0.831838
$216$	3.01364e9	0.0941998
$217$	−1.15320e10	−0.353048
$218$	5.19348e10	1.55741
$219$	−3.50315e9	−0.102911
$220$	3.01988e10	0.869137
$221$	1.99464e10	0.562471
$222$	1.30415e10	0.360363
$223$	−5.41094e10	−1.46521	−0.732607	−	0.680652i	$-0.761697\pi$
$223$	−5.41094e10	−1.46521	−0.732607	+	0.680652i	$0.761697\pi$
$224$	1.54128e10	0.409038
$225$	−4.69024e9	−0.122004
$226$	2.47234e10	0.630406
$227$	−7.97167e10	−1.99266	−0.996330	−	0.0855990i	$-0.972720\pi$
$227$	−7.97167e10	−1.99266	−0.996330	+	0.0855990i	$0.972720\pi$
$228$	2.64223e9	0.0647537
$229$	−4.88686e10	−1.17428	−0.587139	−	0.809486i	$-0.699746\pi$
$229$	−4.88686e10	−1.17428	−0.587139	+	0.809486i	$0.699746\pi$
$230$	3.70342e10	0.872626
$231$	−1.67667e10	−0.387431
$232$	−3.09677e10	−0.701799
$233$	1.56363e10	0.347562	0.173781	−	0.984784i	$-0.444402\pi$
$233$	1.56363e10	0.347562	0.173781	+	0.984784i	$0.444402\pi$
$234$	8.65610e9	0.188734
$235$	4.58689e10	0.981100
$236$	−1.28428e10	−0.269497
$237$	−5.29822e8	−0.0109084
$238$	−3.00122e10	−0.606320
$239$	4.73934e10	0.939566	0.469783	−	0.882782i	$-0.344332\pi$
$239$	4.73934e10	0.939566	0.469783	+	0.882782i	$0.344332\pi$
$240$	−2.92238e10	−0.568572
$241$	1.86639e10	0.356391	0.178195	−	0.983995i	$-0.442974\pi$
$241$	1.86639e10	0.356391	0.178195	+	0.983995i	$0.442974\pi$
$242$	1.45916e11	2.73486
$243$	−3.48678e9	−0.0641500
$244$	−2.62874e10	−0.474780
$245$	−6.41490e9	−0.113748
$246$	3.46765e10	0.603709
$247$	−4.75476e9	−0.0812815
$248$	−2.72363e10	−0.457209
$249$	2.09106e10	0.344722
$250$	8.53663e10	1.38215
$251$	−9.18400e10	−1.46050	−0.730248	−	0.683182i	$-0.760595\pi$
$251$	−9.18400e10	−1.46050	−0.730248	+	0.683182i	$0.760595\pi$
$252$	−4.95879e9	−0.0774593
$253$	9.97866e10	1.53119
$254$	−9.32745e10	−1.40608
$255$	3.91832e10	0.580323
$256$	8.86571e10	1.29013
$257$	7.37968e10	1.05521	0.527605	−	0.849490i	$-0.323090\pi$
$257$	7.37968e10	1.05521	0.527605	+	0.849490i	$0.323090\pi$
$258$	−5.45491e10	−0.766477
$259$	1.34443e10	0.185648
$260$	−1.60722e10	−0.218120
$261$	3.58296e10	0.477925
$262$	7.74275e10	1.01517
$263$	−9.72936e10	−1.25396	−0.626979	−	0.779036i	$-0.715709\pi$
$263$	−9.72936e10	−1.25396	−0.626979	+	0.779036i	$0.715709\pi$
$264$	−3.95998e10	−0.501736
$265$	1.19224e11	1.48510
$266$	7.15420e9	0.0876180
$267$	−4.59618e10	−0.553473
$268$	−7.27505e10	−0.861448
$269$	−7.91665e10	−0.921842	−0.460921	−	0.887441i	$-0.652481\pi$
$269$	−7.91665e10	−0.921842	−0.460921	+	0.887441i	$0.652481\pi$
$270$	1.70042e10	0.194724
$271$	−2.72065e10	−0.306416	−0.153208	−	0.988194i	$-0.548960\pi$
$271$	−2.72065e10	−0.306416	−0.153208	+	0.988194i	$0.548960\pi$
$272$	−1.40947e11	−1.56133
$273$	8.92345e9	0.0972302
$274$	−1.84397e11	−1.97640
$275$	6.16305e10	0.649829
$276$	2.95121e10	0.306132
$277$	−1.58031e10	−0.161282	−0.0806408	−	0.996743i	$-0.525697\pi$
$277$	−1.58031e10	−0.161282	−0.0806408	+	0.996743i	$0.525697\pi$
$278$	−2.20098e11	−2.21011
$279$	3.15124e10	0.311359
$280$	−1.51508e10	−0.147307
$281$	2.76239e10	0.264305	0.132153	−	0.991229i	$-0.457811\pi$
$281$	2.76239e10	0.264305	0.132153	+	0.991229i	$0.457811\pi$
$282$	9.60051e10	0.904010
$283$	7.05864e10	0.654157	0.327078	−	0.944997i	$-0.393936\pi$
$283$	7.05864e10	0.654157	0.327078	+	0.944997i	$0.393936\pi$
$284$	−3.23995e10	−0.295533
$285$	−9.34035e9	−0.0838612
$286$	−1.13743e11	−1.00525
$287$	3.57476e10	0.311012
$288$	−4.21171e10	−0.360738
$289$	7.03937e10	0.593599
$290$	−1.74732e11	−1.45072
$291$	−1.16937e11	−0.955949
$292$	1.36141e10	0.109588
$293$	9.09393e10	0.720854	0.360427	−	0.932787i	$-0.382631\pi$
$293$	9.09393e10	0.720854	0.360427	+	0.932787i	$0.382631\pi$
$294$	−1.34266e10	−0.104810
$295$	4.53994e10	0.349021
$296$	3.17529e10	0.240420
$297$	4.58169e10	0.341682
$298$	−1.52444e11	−1.11979
$299$	−5.31077e10	−0.384270
$300$	1.82274e10	0.129921
$301$	−5.62339e10	−0.394866
$302$	1.76840e11	1.22335
$303$	1.33949e11	0.912951
$304$	3.35984e10	0.225625
$305$	9.29263e10	0.614879
$306$	8.20117e10	0.534724
$307$	1.24793e11	0.801802	0.400901	−	0.916121i	$-0.368697\pi$
$307$	1.24793e11	0.801802	0.400901	+	0.916121i	$0.368697\pi$
$308$	6.51594e10	0.412571
$309$	−6.98138e10	−0.435641
$310$	−1.53678e11	−0.945116
$311$	3.38953e9	0.0205455	0.0102728	−	0.999947i	$-0.496730\pi$
$311$	3.38953e9	0.0205455	0.0102728	+	0.999947i	$0.496730\pi$
$312$	2.10755e10	0.125916
$313$	2.64656e11	1.55859	0.779297	−	0.626655i	$-0.215577\pi$
$313$	2.64656e11	1.55859	0.779297	+	0.626655i	$0.215577\pi$
$314$	3.70536e11	2.15103
$315$	1.75294e10	0.100316
$316$	2.05901e9	0.0116163
$317$	1.96528e9	0.0109310	0.00546548	−	0.999985i	$-0.498260\pi$
$317$	1.96528e9	0.0109310	0.00546548	+	0.999985i	$0.498260\pi$
$318$	2.49539e11	1.36841
$319$	−4.70807e11	−2.54557
$320$	2.06719e10	0.110206
$321$	1.93761e10	0.101857
$322$	7.99079e10	0.414227
$323$	−4.50487e10	−0.230288
$324$	1.35505e10	0.0683127
$325$	−3.28005e10	−0.163082
$326$	2.49997e11	1.22590
$327$	−1.46301e11	−0.707591
$328$	8.44288e10	0.402771
$329$	9.89703e10	0.465718
$330$	−2.23438e11	−1.03716
$331$	−2.01624e11	−0.923244	−0.461622	−	0.887077i	$-0.652732\pi$
$331$	−2.01624e11	−0.923244	−0.461622	+	0.887077i	$0.652732\pi$
$332$	−8.12633e10	−0.367090
$333$	−3.67382e10	−0.163726
$334$	4.49094e11	1.97459
$335$	2.57174e11	1.11565
$336$	−6.30555e10	−0.269896
$337$	9.86566e10	0.416669	0.208335	−	0.978058i	$-0.433196\pi$
$337$	9.86566e10	0.416669	0.208335	+	0.978058i	$0.433196\pi$
$338$	−2.44385e11	−1.01847
$339$	−6.96462e10	−0.286417
$340$	−1.52275e11	−0.617979
$341$	−4.14078e11	−1.65839
$342$	−1.95496e10	−0.0772718
$343$	−1.38413e10	−0.0539949
$344$	−1.32814e11	−0.511364
$345$	−1.04326e11	−0.396466
$346$	−4.69472e11	−1.76103
$347$	−2.40715e11	−0.891292	−0.445646	−	0.895209i	$-0.647026\pi$
$347$	−2.40715e11	−0.891292	−0.445646	+	0.895209i	$0.647026\pi$
$348$	−1.39242e11	−0.508937
$349$	−3.14712e10	−0.113553	−0.0567766	−	0.998387i	$-0.518082\pi$
$349$	−3.14712e10	−0.113553	−0.0567766	+	0.998387i	$0.518082\pi$
$350$	4.93530e10	0.175795
$351$	−2.43843e10	−0.0857489
$352$	5.53425e11	1.92140
$353$	2.01856e9	0.00691918	0.00345959	−	0.999994i	$-0.498899\pi$
$353$	2.01856e9	0.00691918	0.00345959	+	0.999994i	$0.498899\pi$
$354$	9.50224e10	0.321597
$355$	1.14533e11	0.382739
$356$	1.78618e11	0.589387
$357$	8.45448e10	0.275474
$358$	−2.94330e11	−0.947024
$359$	7.60801e9	0.0241739	0.0120869	−	0.999927i	$-0.496153\pi$
$359$	7.60801e9	0.0241739	0.0120869	+	0.999927i	$0.496153\pi$
$360$	4.14011e10	0.129913
$361$	−3.11949e11	−0.966722
$362$	6.08152e11	1.86133
$363$	−4.11048e11	−1.24255
$364$	−3.46786e10	−0.103539
$365$	−4.81260e10	−0.141926
$366$	1.94498e11	0.566565
$367$	4.35640e11	1.25352	0.626758	−	0.779214i	$-0.284381\pi$
$367$	4.35640e11	1.25352	0.626758	+	0.779214i	$0.284381\pi$
$368$	3.75273e11	1.06667
$369$	−9.76842e10	−0.274287
$370$	1.79163e11	0.496983
$371$	2.57246e11	0.704964
$372$	−1.22464e11	−0.331563
$373$	−2.27528e11	−0.608618	−0.304309	−	0.952573i	$-0.598426\pi$
$373$	−2.27528e11	−0.608618	−0.304309	+	0.952573i	$0.598426\pi$
$374$	−1.07765e12	−2.84810
$375$	−2.40478e11	−0.627964
$376$	2.33749e11	0.603121
$377$	2.50569e11	0.638839
$378$	3.66896e10	0.0924337
$379$	−3.89140e11	−0.968790	−0.484395	−	0.874849i	$-0.660960\pi$
$379$	−3.89140e11	−0.968790	−0.484395	+	0.874849i	$0.660960\pi$
$380$	3.62988e10	0.0893029
$381$	2.62755e11	0.638836
$382$	−3.55494e9	−0.00854176
$383$	7.31390e10	0.173682	0.0868410	−	0.996222i	$-0.472323\pi$
$383$	7.31390e10	0.173682	0.0868410	+	0.996222i	$0.472323\pi$
$384$	−2.22954e11	−0.523270
$385$	−2.30340e11	−0.534313
$386$	−3.64388e11	−0.835450
$387$	1.53666e11	0.348239
$388$	4.54446e11	1.01798
$389$	7.87807e11	1.74440	0.872201	−	0.489148i	$-0.162692\pi$
$389$	7.87807e11	1.74440	0.872201	+	0.489148i	$0.162692\pi$
$390$	1.18917e11	0.260287
$391$	−5.03166e11	−1.08872
$392$	−3.26905e10	−0.0699252
$393$	−2.18114e11	−0.461230
$394$	2.61749e11	0.547208
$395$	−7.27864e9	−0.0150440
$396$	−1.78055e11	−0.363853
$397$	1.25453e11	0.253468	0.126734	−	0.991937i	$-0.459550\pi$
$397$	1.25453e11	0.253468	0.126734	+	0.991937i	$0.459550\pi$
$398$	−6.03283e11	−1.20517
$399$	−2.01535e10	−0.0398081
$400$	2.31777e11	0.452690
$401$	−3.72727e11	−0.719848	−0.359924	−	0.932982i	$-0.617197\pi$
$401$	−3.72727e11	−0.719848	−0.359924	+	0.932982i	$0.617197\pi$
$402$	5.38274e11	1.02798
$403$	2.20377e11	0.416192
$404$	−5.20557e11	−0.972192
$405$	−4.79011e10	−0.0884704
$406$	−3.77016e11	−0.688641
$407$	4.82745e11	0.872054
$408$	1.99679e11	0.356747
$409$	−4.49696e11	−0.794629	−0.397314	−	0.917683i	$-0.630058\pi$
$409$	−4.49696e11	−0.794629	−0.397314	+	0.917683i	$0.630058\pi$
$410$	4.76383e11	0.832585
$411$	5.19448e11	0.897954
$412$	2.71313e11	0.463909
$413$	9.79573e10	0.165677
$414$	−2.18357e11	−0.365314
$415$	2.87267e11	0.475412
$416$	−2.94540e11	−0.482196
$417$	6.20018e11	1.00413
$418$	2.56885e11	0.411572
$419$	1.74140e11	0.276017	0.138008	−	0.990431i	$-0.455930\pi$
$419$	1.74140e11	0.276017	0.138008	+	0.990431i	$0.455930\pi$
$420$	−6.81234e10	−0.106825
$421$	−5.75644e11	−0.893068	−0.446534	−	0.894767i	$-0.647342\pi$
$421$	−5.75644e11	−0.893068	−0.446534	+	0.894767i	$0.647342\pi$
$422$	5.50878e11	0.845569
$423$	−2.70447e11	−0.410725
$424$	6.07566e11	0.912951
$425$	−3.10767e11	−0.462045
$426$	2.39721e11	0.352666
$427$	2.00505e11	0.291877
$428$	−7.52999e10	−0.108467
$429$	3.20414e11	0.456724
$430$	−7.49391e11	−1.05706
$431$	1.60316e10	0.0223783	0.0111892	−	0.999937i	$-0.496438\pi$
$431$	1.60316e10	0.0223783	0.0111892	+	0.999937i	$0.496438\pi$
$432$	1.72306e11	0.238026
$433$	9.39390e11	1.28425	0.642126	−	0.766599i	$-0.278052\pi$
$433$	9.39390e11	1.28425	0.642126	+	0.766599i	$0.278052\pi$
$434$	−3.31588e11	−0.448637
$435$	4.92224e11	0.659114
$436$	5.68559e11	0.753506
$437$	1.19943e11	0.157328
$438$	−1.00729e11	−0.130774
$439$	−1.02287e12	−1.31440	−0.657202	−	0.753715i	$-0.728260\pi$
$439$	−1.02287e12	−1.31440	−0.657202	+	0.753715i	$0.728260\pi$
$440$	−5.44018e11	−0.691952
$441$	3.78229e10	0.0476190
$442$	5.73537e11	0.714762
$443$	−3.08809e11	−0.380954	−0.190477	−	0.981692i	$-0.561003\pi$
$443$	−3.08809e11	−0.380954	−0.190477	+	0.981692i	$0.561003\pi$
$444$	1.42773e11	0.174350
$445$	−6.31419e11	−0.763304
$446$	−1.55585e12	−1.86192
$447$	4.29436e11	0.508762
$448$	4.46033e10	0.0523138
$449$	9.78577e11	1.13628	0.568141	−	0.822931i	$-0.307663\pi$
$449$	9.78577e11	1.13628	0.568141	+	0.822931i	$0.307663\pi$
$450$	−1.34863e11	−0.155037
$451$	1.28359e12	1.46093
$452$	2.70661e11	0.305002
$453$	−4.98160e11	−0.555811
$454$	−2.29216e12	−2.53218
$455$	1.22590e11	0.134092
$456$	−4.75986e10	−0.0515528
$457$	−1.36675e12	−1.46578	−0.732888	−	0.680350i	$-0.761828\pi$
$457$	−1.36675e12	−1.46578	−0.732888	+	0.680350i	$0.761828\pi$
$458$	−1.40516e12	−1.49222
$459$	−2.31028e11	−0.242945
$460$	4.05435e11	0.422193
$461$	−2.05041e11	−0.211440	−0.105720	−	0.994396i	$-0.533715\pi$
$461$	−2.05041e11	−0.211440	−0.105720	+	0.994396i	$0.533715\pi$
$462$	−4.82108e11	−0.492329
$463$	−3.62358e11	−0.366458	−0.183229	−	0.983070i	$-0.558655\pi$
$463$	−3.62358e11	−0.366458	−0.183229	+	0.983070i	$0.558655\pi$
$464$	−1.77059e12	−1.77332
$465$	4.32914e11	0.429401
$466$	4.49604e11	0.441665
$467$	1.95057e12	1.89773	0.948866	−	0.315678i	$-0.102232\pi$
$467$	1.95057e12	1.89773	0.948866	+	0.315678i	$0.102232\pi$
$468$	9.47632e10	0.0913131
$469$	5.54899e11	0.529586
$470$	1.31891e12	1.24674
$471$	−1.04380e12	−0.977293
$472$	2.31356e11	0.214557
$473$	−2.01919e12	−1.85482
$474$	−1.52344e10	−0.0138619
$475$	7.40794e10	0.0667692
$476$	−3.28561e11	−0.293349
$477$	−7.02954e11	−0.621719
$478$	1.36274e12	1.19396
$479$	2.72138e11	0.236200	0.118100	−	0.993002i	$-0.462320\pi$
$479$	2.72138e11	0.236200	0.118100	+	0.993002i	$0.462320\pi$
$480$	−5.78600e11	−0.497500
$481$	−2.56923e11	−0.218852
$482$	5.36660e11	0.452885
$483$	−2.25102e11	−0.188199
$484$	1.59743e12	1.32318
$485$	−1.60647e12	−1.31837
$486$	−1.00259e11	−0.0815189
$487$	1.38708e12	1.11743	0.558717	−	0.829358i	$-0.311294\pi$
$487$	1.38708e12	1.11743	0.558717	+	0.829358i	$0.311294\pi$
$488$	4.73554e11	0.377990
$489$	−7.04244e11	−0.556972
$490$	−1.84453e11	−0.144545
$491$	1.34583e12	1.04501	0.522507	−	0.852635i	$-0.324997\pi$
$491$	1.34583e12	1.04501	0.522507	+	0.852635i	$0.324997\pi$
$492$	3.79623e11	0.292085
$493$	2.37400e12	1.80997
$494$	−1.36718e11	−0.103289
$495$	6.29429e11	0.471219
$496$	−1.55724e12	−1.15528
$497$	2.47125e11	0.181683
$498$	6.01259e11	0.438056
$499$	−1.73869e12	−1.25537	−0.627683	−	0.778469i	$-0.715997\pi$
$499$	−1.73869e12	−1.25537	−0.627683	+	0.778469i	$0.715997\pi$
$500$	9.34553e11	0.668712
$501$	−1.26510e12	−0.897131
$502$	−2.64076e12	−1.85593
$503$	2.79599e11	0.194751	0.0973756	−	0.995248i	$-0.468955\pi$
$503$	2.79599e11	0.194751	0.0973756	+	0.995248i	$0.468955\pi$
$504$	8.93303e10	0.0616682
$505$	1.84018e12	1.25907
$506$	2.86925e12	1.94577
$507$	6.88436e11	0.462730
$508$	−1.02113e12	−0.680289
$509$	−1.90203e12	−1.25599	−0.627996	−	0.778217i	$-0.716124\pi$
$509$	−1.90203e12	−1.25599	−0.627996	+	0.778217i	$0.716124\pi$
$510$	1.12667e12	0.737447
$511$	−1.03840e11	−0.0673708
$512$	1.13994e12	0.733108
$513$	5.50716e10	0.0351075
$514$	2.12194e12	1.34091
$515$	−9.59096e11	−0.600799
$516$	−5.97180e11	−0.370836
$517$	3.55372e12	2.18764
$518$	3.86577e11	0.235913
$519$	1.32251e12	0.800101
$520$	2.89533e11	0.173653
$521$	1.65149e12	0.981986	0.490993	−	0.871163i	$-0.336634\pi$
$521$	1.65149e12	0.981986	0.490993	+	0.871163i	$0.336634\pi$
$522$	1.03024e12	0.607324
$523$	−2.12410e12	−1.24141	−0.620707	−	0.784043i	$-0.713154\pi$
$523$	−2.12410e12	−1.24141	−0.620707	+	0.784043i	$0.713154\pi$
$524$	8.47643e11	0.491159
$525$	−1.39028e11	−0.0798703
$526$	−2.79757e12	−1.59347
$527$	2.08795e12	1.17916
$528$	−2.26413e12	−1.26779
$529$	−4.61467e11	−0.256207
$530$	3.42814e12	1.88720
$531$	−2.67679e11	−0.146113
$532$	7.83210e10	0.0423912
$533$	−6.83140e11	−0.366638
$534$	−1.32158e12	−0.703327
$535$	2.66187e11	0.140473
$536$	1.31057e12	0.685831
$537$	8.29132e11	0.430268
$538$	−2.27634e12	−1.17143
$539$	−4.96999e11	−0.253633
$540$	1.86155e11	0.0942112
$541$	−2.50527e12	−1.25738	−0.628690	−	0.777656i	$-0.716408\pi$
$541$	−2.50527e12	−1.25738	−0.628690	+	0.777656i	$0.716408\pi$
$542$	−7.82292e11	−0.389379
$543$	−1.71317e12	−0.845671
$544$	−2.79060e12	−1.36616
$545$	−2.00987e12	−0.975851
$546$	2.56584e11	0.123556
$547$	−2.92513e12	−1.39702	−0.698510	−	0.715600i	$-0.746153\pi$
$547$	−2.92513e12	−1.39702	−0.698510	+	0.715600i	$0.746153\pi$
$548$	−2.01870e12	−0.956221
$549$	−5.47902e11	−0.257411
$550$	1.77212e12	0.825772
$551$	−5.65906e11	−0.261554
$552$	−5.31647e11	−0.243723
$553$	−1.57050e10	−0.00714124
$554$	−4.54402e11	−0.204949
$555$	−5.04705e11	−0.225798
$556$	−2.40953e12	−1.06929
$557$	−1.82074e12	−0.801494	−0.400747	−	0.916189i	$-0.631249\pi$
$557$	−1.82074e12	−0.801494	−0.400747	+	0.916189i	$0.631249\pi$
$558$	9.06102e11	0.395661
$559$	1.07464e12	0.465489
$560$	−8.66250e11	−0.372218
$561$	3.03575e12	1.29400
$562$	7.94293e11	0.335867
$563$	2.14833e12	0.901183	0.450591	−	0.892730i	$-0.351213\pi$
$563$	2.14833e12	0.901183	0.450591	+	0.892730i	$0.351213\pi$
$564$	1.05102e12	0.437377
$565$	−9.56793e11	−0.395003
$566$	2.02963e12	0.831272
$567$	−1.03355e11	−0.0419961
$568$	5.83662e11	0.235285
$569$	−1.41128e12	−0.564425	−0.282213	−	0.959352i	$-0.591068\pi$
$569$	−1.41128e12	−0.564425	−0.282213	+	0.959352i	$0.591068\pi$
$570$	−2.68571e11	−0.106567
$571$	9.82803e11	0.386905	0.193452	−	0.981110i	$-0.438032\pi$
$571$	9.82803e11	0.386905	0.193452	+	0.981110i	$0.438032\pi$
$572$	−1.24520e12	−0.486360
$573$	1.00143e10	0.00388084
$574$	1.02788e12	0.395220
$575$	8.27421e11	0.315661
$576$	−1.21884e11	−0.0461364
$577$	−3.98319e12	−1.49603	−0.748015	−	0.663682i	$-0.768993\pi$
$577$	−3.98319e12	−1.49603	−0.748015	+	0.663682i	$0.768993\pi$
$578$	2.02409e12	0.754318
$579$	1.02648e12	0.379576
$580$	−1.91290e12	−0.701884
$581$	6.19830e11	0.225673
$582$	−3.36240e12	−1.21478
$583$	9.23694e12	3.31146
$584$	−2.45251e11	−0.0872474
$585$	−3.34990e11	−0.118258
$586$	2.61486e12	0.916028
$587$	−2.16495e12	−0.752622	−0.376311	−	0.926493i	$-0.622808\pi$
$587$	−2.16495e12	−0.752622	−0.376311	+	0.926493i	$0.622808\pi$
$588$	−1.46988e11	−0.0507090
$589$	−4.97718e11	−0.170398
$590$	1.30541e12	0.443519
$591$	−7.37350e11	−0.248617
$592$	1.81549e12	0.607499
$593$	−3.86048e9	−0.00128202	−0.000641010	−	1.00000i	$-0.500204\pi$
$593$	−3.86048e9	−0.00128202	−0.000641010		1.00000i	$0.500204\pi$
$594$	1.31741e12	0.434193
$595$	1.16147e12	0.379910
$596$	−1.66889e12	−0.541775
$597$	1.69946e12	0.547552
$598$	−1.52705e12	−0.488313
$599$	−5.42634e11	−0.172221	−0.0861105	−	0.996286i	$-0.527444\pi$
$599$	−5.42634e11	−0.172221	−0.0861105	+	0.996286i	$0.527444\pi$
$600$	−3.28357e11	−0.103435
$601$	−2.46767e11	−0.0771529	−0.0385764	−	0.999256i	$-0.512282\pi$
$601$	−2.46767e11	−0.0771529	−0.0385764	+	0.999256i	$0.512282\pi$
$602$	−1.61694e12	−0.501777
$603$	−1.51632e12	−0.467051
$604$	1.93597e12	0.591877
$605$	−5.64694e12	−1.71362
$606$	3.85155e12	1.16014
$607$	1.30882e12	0.391320	0.195660	−	0.980672i	$-0.437315\pi$
$607$	1.30882e12	0.391320	0.195660	+	0.980672i	$0.437315\pi$
$608$	6.65213e11	0.197421
$609$	1.06206e12	0.312875
$610$	2.67199e12	0.781359
$611$	−1.89134e12	−0.549014
$612$	8.97829e11	0.258709
$613$	2.70764e12	0.774494	0.387247	−	0.921976i	$-0.373426\pi$
$613$	2.70764e12	0.774494	0.387247	+	0.921976i	$0.373426\pi$
$614$	3.58828e12	1.01889
$615$	−1.34198e12	−0.378274
$616$	−1.17382e12	−0.328463
$617$	−5.71904e12	−1.58869	−0.794347	−	0.607464i	$-0.792187\pi$
$617$	−5.71904e12	−1.58869	−0.794347	+	0.607464i	$0.792187\pi$
$618$	−2.00742e12	−0.553592
$619$	6.69715e11	0.183350	0.0916752	−	0.995789i	$-0.470778\pi$
$619$	6.69715e11	0.183350	0.0916752	+	0.995789i	$0.470778\pi$
$620$	−1.68240e12	−0.457265
$621$	6.15115e11	0.165976
$622$	9.74620e10	0.0261083
$623$	−1.36240e12	−0.362333
$624$	1.20500e12	0.318167
$625$	−1.90744e12	−0.500024
$626$	7.60989e12	1.98059
$627$	−7.23650e11	−0.186993
$628$	4.05646e12	1.04071
$629$	−2.43420e12	−0.620053
$630$	5.04039e11	0.127477
$631$	−7.64799e11	−0.192050	−0.0960252	−	0.995379i	$-0.530613\pi$
$631$	−7.64799e11	−0.192050	−0.0960252	+	0.995379i	$0.530613\pi$
$632$	−3.70921e10	−0.00924814
$633$	−1.55183e12	−0.384173
$634$	5.65095e10	0.0138906
$635$	3.60971e12	0.881029
$636$	2.73184e12	0.662062
$637$	2.64509e11	0.0636521
$638$	−1.35375e13	−3.23479
$639$	−6.75297e11	−0.160229
$640$	−3.06293e12	−0.721651
$641$	1.59438e12	0.373020	0.186510	−	0.982453i	$-0.440282\pi$
$641$	1.59438e12	0.373020	0.186510	+	0.982453i	$0.440282\pi$
$642$	5.57137e11	0.129436
$643$	3.20400e12	0.739169	0.369584	−	0.929197i	$-0.379500\pi$
$643$	3.20400e12	0.739169	0.369584	+	0.929197i	$0.379500\pi$
$644$	8.74797e11	0.200411
$645$	2.11104e12	0.480262
$646$	−1.29532e12	−0.292639
$647$	3.76896e12	0.845575	0.422787	−	0.906229i	$-0.361052\pi$
$647$	3.76896e12	0.845575	0.422787	+	0.906229i	$0.361052\pi$
$648$	−2.44105e11	−0.0543863
$649$	3.51735e12	0.778242
$650$	−9.43142e11	−0.207237
$651$	9.34089e11	0.203833
$652$	2.73686e12	0.593114
$653$	5.09659e12	1.09691	0.548454	−	0.836181i	$-0.315217\pi$
$653$	5.09659e12	1.09691	0.548454	+	0.836181i	$0.315217\pi$
$654$	−4.20672e12	−0.899173
$655$	−2.99644e12	−0.636091
$656$	4.82725e12	1.01773
$657$	2.83755e11	0.0594155
$658$	2.84578e12	0.591813
$659$	−6.39776e12	−1.32143	−0.660714	−	0.750637i	$-0.729747\pi$
$659$	−6.39776e12	−1.32143	−0.660714	+	0.750637i	$0.729747\pi$
$660$	−2.44611e12	−0.501796
$661$	−2.04808e12	−0.417293	−0.208647	−	0.977991i	$-0.566906\pi$
$661$	−2.04808e12	−0.417293	−0.208647	+	0.977991i	$0.566906\pi$
$662$	−5.79747e12	−1.17321
$663$	−1.61566e12	−0.324743
$664$	1.46392e12	0.292254
$665$	−2.76866e11	−0.0549001
$666$	−1.05636e12	−0.208056
$667$	−6.32082e12	−1.23654
$668$	4.91648e12	0.955345
$669$	4.38286e12	0.845941
$670$	7.39476e12	1.41771
$671$	7.19953e12	1.37105
$672$	−1.24843e12	−0.236158
$673$	−1.59877e12	−0.300413	−0.150207	−	0.988655i	$-0.547994\pi$
$673$	−1.59877e12	−0.300413	−0.150207	+	0.988655i	$0.547994\pi$
$674$	2.83676e12	0.529484
$675$	3.79909e11	0.0704390
$676$	−2.67542e12	−0.492756
$677$	−5.68551e12	−1.04021	−0.520105	−	0.854103i	$-0.674107\pi$
$677$	−5.68551e12	−1.04021	−0.520105	+	0.854103i	$0.674107\pi$
$678$	−2.00260e12	−0.363965
$679$	−3.46625e12	−0.625816
$680$	2.74317e12	0.491996
$681$	6.45705e12	1.15046
$682$	−1.19063e13	−2.10741
$683$	−3.03397e12	−0.533480	−0.266740	−	0.963768i	$-0.585947\pi$
$683$	−3.03397e12	−0.533480	−0.266740	+	0.963768i	$0.585947\pi$
$684$	−2.14021e11	−0.0373855
$685$	7.13613e12	1.23838
$686$	−3.97991e11	−0.0686142
$687$	3.95836e12	0.677969
$688$	−7.59368e12	−1.29212
$689$	−4.91601e12	−0.831048
$690$	−2.99977e12	−0.503811
$691$	−1.04034e13	−1.73590	−0.867952	−	0.496648i	$-0.834564\pi$
$691$	−1.04034e13	−1.73590	−0.867952	+	0.496648i	$0.834564\pi$
$692$	−5.13957e12	−0.852019
$693$	1.35810e12	0.223683
$694$	−6.92148e12	−1.13261
$695$	8.51775e12	1.38482
$696$	2.50838e12	0.405184
$697$	−6.47238e12	−1.03876
$698$	−9.04920e11	−0.144298
$699$	−1.26654e12	−0.200665
$700$	5.40295e11	0.0850530
$701$	1.10158e13	1.72301	0.861503	−	0.507753i	$-0.169524\pi$
$701$	1.10158e13	1.72301	0.861503	+	0.507753i	$0.169524\pi$
$702$	−7.01144e11	−0.108966
$703$	5.80256e11	0.0896026
$704$	1.60157e12	0.245736
$705$	−3.71538e12	−0.566438
$706$	5.80413e10	0.00879258
$707$	3.97051e12	0.597667
$708$	1.04026e12	0.155594
$709$	−1.66735e12	−0.247810	−0.123905	−	0.992294i	$-0.539542\pi$
$709$	−1.66735e12	−0.247810	−0.123905	+	0.992294i	$0.539542\pi$
$710$	3.29327e12	0.486367
$711$	4.29155e10	0.00629798
$712$	−3.21772e12	−0.469233
$713$	−5.55920e12	−0.805581
$714$	2.43099e12	0.350059
$715$	4.40182e12	0.629876
$716$	−3.22220e12	−0.458188
$717$	−3.83887e12	−0.542459
$718$	2.18760e11	0.0307190
$719$	−4.76181e12	−0.664496	−0.332248	−	0.943192i	$-0.607807\pi$
$719$	−4.76181e12	−0.664496	−0.332248	+	0.943192i	$0.607807\pi$
$720$	2.36713e12	0.328265
$721$	−2.06942e12	−0.285194
$722$	−8.96974e12	−1.22846
$723$	−1.51178e12	−0.205762
$724$	6.65778e12	0.900546
$725$	−3.90388e12	−0.524778
$726$	−1.18192e13	−1.57897
$727$	1.11951e13	1.48636	0.743181	−	0.669091i	$-0.233316\pi$
$727$	1.11951e13	1.48636	0.743181	+	0.669091i	$0.233316\pi$
$728$	6.24719e11	0.0824315
$729$	2.82430e11	0.0370370
$730$	−1.38381e12	−0.180353
$731$	1.01816e13	1.31883
$732$	2.12928e12	0.274114
$733$	1.43593e13	1.83723	0.918617	−	0.395148i	$-0.129307\pi$
$733$	1.43593e13	1.83723	0.918617	+	0.395148i	$0.129307\pi$
$734$	1.25263e13	1.59291
$735$	5.19607e11	0.0656723
$736$	7.43001e12	0.933339
$737$	1.99248e13	2.48765
$738$	−2.80880e12	−0.348551
$739$	−3.96122e12	−0.488572	−0.244286	−	0.969703i	$-0.578554\pi$
$739$	−3.96122e12	−0.488572	−0.244286	+	0.969703i	$0.578554\pi$
$740$	1.96140e12	0.240450
$741$	3.85135e11	0.0469279
$742$	7.39683e12	0.895835
$743$	1.29119e13	1.55432	0.777160	−	0.629303i	$-0.216660\pi$
$743$	1.29119e13	1.55432	0.777160	+	0.629303i	$0.216660\pi$
$744$	2.20614e12	0.263970
$745$	5.89955e12	0.701643
$746$	−6.54231e12	−0.773404
$747$	−1.69376e12	−0.199025
$748$	−1.17976e13	−1.37796
$749$	5.74345e11	0.0666814
$750$	−6.91467e12	−0.797987
$751$	−7.43150e12	−0.852504	−0.426252	−	0.904604i	$-0.640166\pi$
$751$	−7.43150e12	−0.852504	−0.426252	+	0.904604i	$0.640166\pi$
$752$	1.33647e13	1.52398
$753$	7.43904e12	0.843217
$754$	7.20483e12	0.811807
$755$	−6.84368e12	−0.766529
$756$	4.01662e11	0.0447211
$757$	6.81890e12	0.754715	0.377358	−	0.926068i	$-0.376833\pi$
$757$	6.81890e12	0.754715	0.377358	+	0.926068i	$0.376833\pi$
$758$	−1.11893e13	−1.23109
$759$	−8.08272e12	−0.884035
$760$	−6.53905e11	−0.0710974
$761$	−1.28538e12	−0.138931	−0.0694656	−	0.997584i	$-0.522129\pi$
$761$	−1.28538e12	−0.138931	−0.0694656	+	0.997584i	$0.522129\pi$
$762$	7.55523e12	0.811803
$763$	−4.33665e12	−0.463227
$764$	−3.89180e10	−0.00413266
$765$	−3.17384e12	−0.335049
$766$	2.10303e12	0.220707
$767$	−1.87198e12	−0.195309
$768$	−7.18123e12	−0.744857
$769$	−5.36609e10	−0.00553336	−0.00276668	−	0.999996i	$-0.500881\pi$
$769$	−5.36609e10	−0.00553336	−0.00276668	+	0.999996i	$0.500881\pi$
$770$	−6.62315e12	−0.678979
$771$	−5.97754e12	−0.609225
$772$	−3.98916e12	−0.404206
$773$	7.89274e12	0.795097	0.397549	−	0.917581i	$-0.369861\pi$
$773$	7.89274e12	0.795097	0.397549	+	0.917581i	$0.369861\pi$
$774$	4.41848e12	0.442526
$775$	−3.43349e12	−0.341884
$776$	−8.18662e12	−0.810452
$777$	−1.08899e12	−0.107184
$778$	2.26525e13	2.21670
$779$	1.54286e12	0.150109
$780$	1.30185e12	0.125932
$781$	8.87352e12	0.853427
$782$	−1.44680e13	−1.38349
$783$	−2.90220e12	−0.275930
$784$	−1.86909e12	−0.176688
$785$	−1.43397e13	−1.34780
$786$	−6.27163e12	−0.586110
$787$	−1.98582e13	−1.84524	−0.922621	−	0.385707i	$-0.873958\pi$
$787$	−1.98582e13	−1.84524	−0.922621	+	0.385707i	$0.873958\pi$
$788$	2.86551e12	0.264749
$789$	7.88078e12	0.723973
$790$	−2.09289e11	−0.0191172
$791$	−2.06445e12	−0.187504
$792$	3.20758e12	0.289677
$793$	−3.83168e12	−0.344080
$794$	3.60726e12	0.322096
$795$	−9.65712e12	−0.857424
$796$	−6.60448e12	−0.583082
$797$	−1.22047e13	−1.07144	−0.535718	−	0.844397i	$-0.679959\pi$
$797$	−1.22047e13	−1.07144	−0.535718	+	0.844397i	$0.679959\pi$
$798$	−5.79490e11	−0.0505863
$799$	−1.79194e13	−1.55547
$800$	4.58895e12	0.396103
$801$	3.72291e12	0.319548
$802$	−1.07173e13	−0.914749
$803$	−3.72859e12	−0.316464
$804$	5.89279e12	0.497357
$805$	−3.09243e12	−0.259548
$806$	6.33670e12	0.528878
$807$	6.41249e12	0.532226
$808$	9.37759e12	0.773998
$809$	1.29102e13	1.05966	0.529828	−	0.848105i	$-0.322257\pi$
$809$	1.29102e13	1.05966	0.529828	+	0.848105i	$0.322257\pi$
$810$	−1.37734e12	−0.112424
$811$	−1.04776e13	−0.850487	−0.425243	−	0.905079i	$-0.639812\pi$
$811$	−1.04776e13	−0.850487	−0.425243	+	0.905079i	$0.639812\pi$
$812$	−4.12741e12	−0.333177
$813$	2.20373e12	0.176909
$814$	1.38808e13	1.10817
$815$	−9.67484e12	−0.768130
$816$	1.14167e13	0.901435
$817$	−2.42705e12	−0.190581
$818$	−1.29305e13	−1.00978
$819$	−7.22800e11	−0.0561359
$820$	5.21523e12	0.402820
$821$	−1.63508e13	−1.25601	−0.628007	−	0.778207i	$-0.716129\pi$
$821$	−1.63508e13	−1.25601	−0.628007	+	0.778207i	$0.716129\pi$
$822$	1.49361e13	1.14108
$823$	1.08350e13	0.823248	0.411624	−	0.911354i	$-0.364962\pi$
$823$	1.08350e13	0.823248	0.411624	+	0.911354i	$0.364962\pi$
$824$	−4.88757e12	−0.369335
$825$	−4.99207e12	−0.375179
$826$	2.81665e12	0.210534
$827$	−1.43795e13	−1.06898	−0.534488	−	0.845176i	$-0.679496\pi$
$827$	−1.43795e13	−1.06898	−0.534488	+	0.845176i	$0.679496\pi$
$828$	−2.39048e12	−0.176746
$829$	5.67182e12	0.417088	0.208544	−	0.978013i	$-0.433128\pi$
$829$	5.67182e12	0.417088	0.208544	+	0.978013i	$0.433128\pi$
$830$	8.26005e12	0.604131
$831$	1.28006e12	0.0931159
$832$	−8.52375e11	−0.0616702
$833$	2.50607e12	0.180340
$834$	1.78279e13	1.27601
$835$	−1.73799e13	−1.23725
$836$	2.81227e12	0.199126
$837$	−2.55250e12	−0.179763
$838$	5.00720e12	0.350749
$839$	2.95303e11	0.0205749	0.0102875	−	0.999947i	$-0.496725\pi$
$839$	2.95303e11	0.0205749	0.0102875	+	0.999947i	$0.496725\pi$
$840$	1.22721e12	0.0850477
$841$	1.53153e13	1.05571
$842$	−1.65520e13	−1.13487
$843$	−2.23753e12	−0.152597
$844$	6.03077e12	0.409102
$845$	9.45767e12	0.638159
$846$	−7.77641e12	−0.521930
$847$	−1.21843e13	−0.813438
$848$	3.47378e13	2.30686
$849$	−5.71750e12	−0.377678
$850$	−8.93575e12	−0.587146
$851$	6.48110e12	0.423609
$852$	2.62436e12	0.170626
$853$	−1.31135e12	−0.0848103	−0.0424051	−	0.999100i	$-0.513502\pi$
$853$	−1.31135e12	−0.0848103	−0.0424051	+	0.999100i	$0.513502\pi$
$854$	5.76529e12	0.370904
$855$	7.56568e11	0.0484173
$856$	1.35649e12	0.0863545
$857$	−1.16774e13	−0.739488	−0.369744	−	0.929134i	$-0.620555\pi$
$857$	−1.16774e13	−0.739488	−0.369744	+	0.929134i	$0.620555\pi$
$858$	9.21314e12	0.580384
$859$	2.25789e13	1.41493	0.707463	−	0.706750i	$-0.249840\pi$
$859$	2.25789e13	1.41493	0.707463	+	0.706750i	$0.249840\pi$
$860$	−8.20400e12	−0.511426
$861$	−2.89555e12	−0.179563
$862$	4.60969e11	0.0284374
$863$	2.05141e13	1.25894	0.629469	−	0.777025i	$-0.283272\pi$
$863$	2.05141e13	1.25894	0.629469	+	0.777025i	$0.283272\pi$
$864$	3.41148e12	0.208272
$865$	1.81685e13	1.10343
$866$	2.70111e13	1.63197
$867$	−5.70189e12	−0.342715
$868$	−3.63008e12	−0.217059
$869$	−5.63917e11	−0.0335449
$870$	1.41533e13	0.837572
$871$	−1.06042e13	−0.624304
$872$	−1.02423e13	−0.599894
$873$	9.47192e12	0.551917
$874$	3.44882e12	0.199926
$875$	−7.12824e12	−0.411099
$876$	−1.10274e12	−0.0632709
$877$	1.11033e13	0.633805	0.316902	−	0.948458i	$-0.397357\pi$
$877$	1.11033e13	0.633805	0.316902	+	0.948458i	$0.397357\pi$
$878$	−2.94114e13	−1.67028
$879$	−7.36608e12	−0.416185
$880$	−3.11044e13	−1.74844
$881$	1.63535e12	0.0914573	0.0457286	−	0.998954i	$-0.485439\pi$
$881$	1.63535e12	0.0914573	0.0457286	+	0.998954i	$0.485439\pi$
$882$	1.08755e12	0.0605121
$883$	−2.07153e12	−0.114675	−0.0573375	−	0.998355i	$-0.518261\pi$
$883$	−2.07153e12	−0.114675	−0.0573375	+	0.998355i	$0.518261\pi$
$884$	6.27884e12	0.345815
$885$	−3.67735e12	−0.201507
$886$	−8.87944e12	−0.484099
$887$	7.09293e12	0.384742	0.192371	−	0.981322i	$-0.438382\pi$
$887$	7.09293e12	0.384742	0.192371	+	0.981322i	$0.438382\pi$
$888$	−2.57199e12	−0.138807
$889$	7.78859e12	0.418216
$890$	−1.81557e13	−0.969971
$891$	−3.71117e12	−0.197270
$892$	−1.70328e13	−0.900834
$893$	4.27155e12	0.224778
$894$	1.23479e13	0.646511
$895$	1.13905e13	0.593390
$896$	−6.60881e12	−0.342561
$897$	4.30172e12	0.221859
$898$	2.81379e13	1.44394
$899$	2.62291e13	1.33926
$900$	−1.47642e12	−0.0750097
$901$	−4.65765e13	−2.35454
$902$	3.69081e13	1.85649
$903$	4.55495e12	0.227976
$904$	−4.87583e12	−0.242824
$905$	−2.35354e13	−1.16628
$906$	−1.43240e13	−0.706299
$907$	3.99737e13	1.96129	0.980645	−	0.195796i	$-0.0627289\pi$
$907$	3.99737e13	1.96129	0.980645	+	0.195796i	$0.0627289\pi$
$908$	−2.50936e13	−1.22511
$909$	−1.08499e13	−0.527093
$910$	3.52492e12	0.170398
$911$	7.01330e12	0.337357	0.168679	−	0.985671i	$-0.446050\pi$
$911$	7.01330e12	0.337357	0.168679	+	0.985671i	$0.446050\pi$
$912$	−2.72147e12	−0.130265
$913$	2.22562e13	1.06007
$914$	−3.92994e13	−1.86264
$915$	−7.52703e12	−0.355000
$916$	−1.53831e13	−0.721962
$917$	−6.46534e12	−0.301946
$918$	−6.64295e12	−0.308723
$919$	6.54102e12	0.302500	0.151250	−	0.988496i	$-0.451670\pi$
$919$	6.54102e12	0.302500	0.151250	+	0.988496i	$0.451670\pi$
$920$	−7.30371e12	−0.336123
$921$	−1.01082e13	−0.462921
$922$	−5.89573e12	−0.268688
$923$	−4.72260e12	−0.214177
$924$	−5.27791e12	−0.238198
$925$	4.00288e12	0.179777
$926$	−1.04192e13	−0.465677
$927$	5.65492e12	0.251517
$928$	−3.50558e13	−1.55165
$929$	7.02626e12	0.309495	0.154748	−	0.987954i	$-0.450544\pi$
$929$	7.02626e12	0.309495	0.154748	+	0.987954i	$0.450544\pi$
$930$	1.24479e13	0.545663
$931$	−5.97388e11	−0.0260605
$932$	4.92206e12	0.213686
$933$	−2.74552e11	−0.0118620
$934$	5.60864e13	2.41155
$935$	4.17048e13	1.78457
$936$	−1.70711e12	−0.0726978
$937$	−3.67954e12	−0.155943	−0.0779713	−	0.996956i	$-0.524844\pi$
$937$	−3.67954e12	−0.155943	−0.0779713	+	0.996956i	$0.524844\pi$
$938$	1.59555e13	0.672973
$939$	−2.14372e13	−0.899854
$940$	1.44388e13	0.603194
$941$	−1.35072e13	−0.561579	−0.280789	−	0.959769i	$-0.590596\pi$
$941$	−1.35072e13	−0.561579	−0.280789	+	0.959769i	$0.590596\pi$
$942$	−3.00134e13	−1.24190
$943$	1.72328e13	0.709664
$944$	1.32279e13	0.542146
$945$	−1.41988e12	−0.0579175
$946$	−5.80595e13	−2.35702
$947$	−1.46126e12	−0.0590407	−0.0295204	−	0.999564i	$-0.509398\pi$
$947$	−1.46126e12	−0.0590407	−0.0295204	+	0.999564i	$0.509398\pi$
$948$	−1.66780e11	−0.00670665
$949$	1.98440e12	0.0794203
$950$	2.13007e12	0.0848472
$951$	−1.59188e11	−0.00631099
$952$	5.91887e12	0.233546
$953$	−1.41223e13	−0.554611	−0.277305	−	0.960782i	$-0.589441\pi$
$953$	−1.41223e13	−0.554611	−0.277305	+	0.960782i	$0.589441\pi$
$954$	−2.02127e13	−0.790052
$955$	1.37576e11	0.00535213
$956$	1.49187e13	0.577658
$957$	3.81353e13	1.46968
$958$	7.82502e12	0.300151
$959$	1.53975e13	0.587849
$960$	−1.67442e12	−0.0636275
$961$	−3.37099e12	−0.127498
$962$	−7.38753e12	−0.278107
$963$	−1.56946e12	−0.0588074
$964$	5.87512e12	0.219114
$965$	1.41017e13	0.523480
$966$	−6.47254e12	−0.239154
$967$	−2.08026e13	−0.765067	−0.382533	−	0.923942i	$-0.624948\pi$
$967$	−2.08026e13	−0.765067	−0.382533	+	0.923942i	$0.624948\pi$
$968$	−2.87769e13	−1.05343
$969$	3.64894e12	0.132957
$970$	−4.61923e13	−1.67532
$971$	−1.01098e13	−0.364969	−0.182484	−	0.983209i	$-0.558414\pi$
$971$	−1.01098e13	−0.364969	−0.182484	+	0.983209i	$0.558414\pi$
$972$	−1.09759e12	−0.0394403
$973$	1.83786e13	0.657361
$974$	3.98840e13	1.41998
$975$	2.65684e12	0.0941554
$976$	2.70756e13	0.955113
$977$	9.14311e12	0.321047	0.160523	−	0.987032i	$-0.448682\pi$
$977$	9.14311e12	0.321047	0.160523	+	0.987032i	$0.448682\pi$
$978$	−2.02497e13	−0.707774
$979$	−4.89196e13	−1.70200
$980$	−2.01931e12	−0.0699337
$981$	1.18504e13	0.408528
$982$	3.86977e13	1.32795
$983$	−4.31288e12	−0.147325	−0.0736626	−	0.997283i	$-0.523469\pi$
$983$	−4.31288e12	−0.147325	−0.0736626	+	0.997283i	$0.523469\pi$
$984$	−6.83874e12	−0.232540
$985$	−1.01297e13	−0.342872
$986$	6.82618e13	2.30002
$987$	−8.01660e12	−0.268883
$988$	−1.49672e12	−0.0499730
$989$	−2.71086e13	−0.900999
$990$	1.80985e13	0.598804
$991$	−3.36774e13	−1.10919	−0.554596	−	0.832120i	$-0.687127\pi$
$991$	−3.36774e13	−1.10919	−0.554596	+	0.832120i	$0.687127\pi$
$992$	−3.08318e13	−1.01087
$993$	1.63315e13	0.533035
$994$	7.10581e12	0.230874
$995$	2.33470e13	0.755139
$996$	6.58233e12	0.211940
$997$	−4.05656e12	−0.130026	−0.0650129	−	0.997884i	$-0.520709\pi$
$997$	−4.05656e12	−0.130026	−0.0650129	+	0.997884i	$0.520709\pi$
$998$	−4.99941e13	−1.59526
$999$	2.97579e12	0.0945274

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.10.a.b.1.2	✓	2
3.2	odd	2		63.10.a.c.1.1		2
4.3	odd	2		336.10.a.m.1.1		2
7.6	odd	2		147.10.a.d.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.10.a.b.1.2	✓	2	1.1	even	1	trivial
63.10.a.c.1.1		2	3.2	odd	2
147.10.a.d.1.2		2	7.6	odd	2
336.10.a.m.1.1		2	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	21.a (trivial)

\(f(q)\)	\(=\)	\(q+28.7539 q^{2} -81.0000 q^{3} +314.785 q^{4} -1112.77 q^{5} -2329.06 q^{6} -2401.00 q^{7} -5670.70 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+28.7539 q^{2} -81.0000 q^{3} +314.785 q^{4} -1112.77 q^{5} -2329.06 q^{6} -2401.00 q^{7} -5670.70 q^{8} +6561.00 q^{9} -31996.5 q^{10} -86212.6 q^{11} -25497.6 q^{12} +45883.4 q^{13} -69038.0 q^{14} +90134.4 q^{15} -324224. q^{16} +434720. q^{17} +188654. q^{18} -103627. q^{19} -350283. q^{20} +194481. q^{21} -2.47895e6 q^{22} -1.15745e6 q^{23} +459327. q^{24} -714867. q^{25} +1.31933e6 q^{26} -531441. q^{27} -755798. q^{28} +5.46099e6 q^{29} +2.59171e6 q^{30} +4.80298e6 q^{31} -6.41931e6 q^{32} +6.98322e6 q^{33} +1.24999e7 q^{34} +2.67176e6 q^{35} +2.06530e6 q^{36} -5.59947e6 q^{37} -2.97967e6 q^{38} -3.71656e6 q^{39} +6.31019e6 q^{40} -1.48886e7 q^{41} +5.59208e6 q^{42} +2.34211e7 q^{43} -2.71384e7 q^{44} -7.30089e6 q^{45} -3.32811e7 q^{46} -4.12205e7 q^{47} +2.62622e7 q^{48} +5.76480e6 q^{49} -2.05552e7 q^{50} -3.52123e7 q^{51} +1.44434e7 q^{52} -1.07141e8 q^{53} -1.52810e7 q^{54} +9.59349e7 q^{55} +1.36153e7 q^{56} +8.39378e6 q^{57} +1.57025e8 q^{58} -4.07986e7 q^{59} +2.83729e7 q^{60} -8.35090e7 q^{61} +1.38104e8 q^{62} -1.57530e7 q^{63} -1.85770e7 q^{64} -5.10577e7 q^{65} +2.00795e8 q^{66} -2.31112e8 q^{67} +1.36843e8 q^{68} +9.37533e7 q^{69} +7.68235e7 q^{70} -1.02926e8 q^{71} -3.72055e7 q^{72} +4.32488e7 q^{73} -1.61007e8 q^{74} +5.79042e7 q^{75} -3.26202e7 q^{76} +2.06997e8 q^{77} -1.06865e8 q^{78} +6.54101e6 q^{79} +3.60787e8 q^{80} +4.30467e7 q^{81} -4.28105e8 q^{82} -2.58155e8 q^{83} +6.12197e7 q^{84} -4.83744e8 q^{85} +6.73446e8 q^{86} -4.42341e8 q^{87} +4.88886e8 q^{88} +5.67430e8 q^{89} -2.09929e8 q^{90} -1.10166e8 q^{91} -3.64347e8 q^{92} -3.89041e8 q^{93} -1.18525e9 q^{94} +1.15313e8 q^{95} +5.19964e8 q^{96} +1.44367e9 q^{97} +1.65760e8 q^{98} -5.65641e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 9 q^{2} - 162 q^{3} + 193 q^{4} + 1170 q^{5} - 729 q^{6} - 4802 q^{7} + 6849 q^{8} + 13122 q^{9}+O(q^{10}) \) 2 * q + 9 * q^2 - 162 * q^3 + 193 * q^4 + 1170 * q^5 - 729 * q^6 - 4802 * q^7 + 6849 * q^8 + 13122 * q^9	\( 2 q + 9 q^{2} - 162 q^{3} + 193 q^{4} + 1170 q^{5} - 729 q^{6} - 4802 q^{7} + 6849 q^{8} + 13122 q^{9} - 77090 q^{10} - 145746 q^{11} - 15633 q^{12} + 86528 q^{13} - 21609 q^{14} - 94770 q^{15} - 509183 q^{16} - 229842 q^{17} + 59049 q^{18} - 221224 q^{19} - 628290 q^{20} + 388962 q^{21} - 1302932 q^{22} - 2035782 q^{23} - 554769 q^{24} + 2543050 q^{25} + 516438 q^{26} - 1062882 q^{27} - 463393 q^{28} + 9756252 q^{29} + 6244290 q^{30} + 204000 q^{31} - 9175743 q^{32} + 11805426 q^{33} + 25627554 q^{34} - 2809170 q^{35} + 1266273 q^{36} - 13959816 q^{37} - 656676 q^{38} - 7008768 q^{39} + 34889790 q^{40} - 42362550 q^{41} + 1750329 q^{42} - 4763912 q^{43} - 19888164 q^{44} + 7676370 q^{45} - 15930600 q^{46} - 48278484 q^{47} + 41243823 q^{48} + 11529602 q^{49} - 84911625 q^{50} + 18617202 q^{51} + 9493510 q^{52} - 108980352 q^{53} - 4782969 q^{54} - 39966160 q^{55} - 16444449 q^{56} + 17919144 q^{57} + 72176782 q^{58} - 188376804 q^{59} + 50891490 q^{60} + 19722092 q^{61} + 228951936 q^{62} - 31505922 q^{63} + 130572161 q^{64} + 41724540 q^{65} + 105537492 q^{66} + 70274396 q^{67} + 217776834 q^{68} + 164898342 q^{69} + 185093090 q^{70} - 382044186 q^{71} + 44936289 q^{72} + 191785896 q^{73} + 4142502 q^{74} - 205987050 q^{75} - 18298628 q^{76} + 349936146 q^{77} - 41831478 q^{78} - 72592148 q^{79} - 61430850 q^{80} + 86093442 q^{81} + 114611450 q^{82} + 187994232 q^{83} + 37534833 q^{84} - 2000786580 q^{85} + 1230207804 q^{86} - 790256412 q^{87} - 256454052 q^{88} + 42930954 q^{89} - 505787490 q^{90} - 207753728 q^{91} - 257379192 q^{92} - 16524000 q^{93} - 1045824480 q^{94} - 153134280 q^{95} + 743235183 q^{96} + 1726854096 q^{97} + 51883209 q^{98} - 956239506 q^{99}+O(q^{100}) \) 2 * q + 9 * q^2 - 162 * q^3 + 193 * q^4 + 1170 * q^5 - 729 * q^6 - 4802 * q^7 + 6849 * q^8 + 13122 * q^9 - 77090 * q^10 - 145746 * q^11 - 15633 * q^12 + 86528 * q^13 - 21609 * q^14 - 94770 * q^15 - 509183 * q^16 - 229842 * q^17 + 59049 * q^18 - 221224 * q^19 - 628290 * q^20 + 388962 * q^21 - 1302932 * q^22 - 2035782 * q^23 - 554769 * q^24 + 2543050 * q^25 + 516438 * q^26 - 1062882 * q^27 - 463393 * q^28 + 9756252 * q^29 + 6244290 * q^30 + 204000 * q^31 - 9175743 * q^32 + 11805426 * q^33 + 25627554 * q^34 - 2809170 * q^35 + 1266273 * q^36 - 13959816 * q^37 - 656676 * q^38 - 7008768 * q^39 + 34889790 * q^40 - 42362550 * q^41 + 1750329 * q^42 - 4763912 * q^43 - 19888164 * q^44 + 7676370 * q^45 - 15930600 * q^46 - 48278484 * q^47 + 41243823 * q^48 + 11529602 * q^49 - 84911625 * q^50 + 18617202 * q^51 + 9493510 * q^52 - 108980352 * q^53 - 4782969 * q^54 - 39966160 * q^55 - 16444449 * q^56 + 17919144 * q^57 + 72176782 * q^58 - 188376804 * q^59 + 50891490 * q^60 + 19722092 * q^61 + 228951936 * q^62 - 31505922 * q^63 + 130572161 * q^64 + 41724540 * q^65 + 105537492 * q^66 + 70274396 * q^67 + 217776834 * q^68 + 164898342 * q^69 + 185093090 * q^70 - 382044186 * q^71 + 44936289 * q^72 + 191785896 * q^73 + 4142502 * q^74 - 205987050 * q^75 - 18298628 * q^76 + 349936146 * q^77 - 41831478 * q^78 - 72592148 * q^79 - 61430850 * q^80 + 86093442 * q^81 + 114611450 * q^82 + 187994232 * q^83 + 37534833 * q^84 - 2000786580 * q^85 + 1230207804 * q^86 - 790256412 * q^87 - 256454052 * q^88 + 42930954 * q^89 - 505787490 * q^90 - 207753728 * q^91 - 257379192 * q^92 - 16524000 * q^93 - 1045824480 * q^94 - 153134280 * q^95 + 743235183 * q^96 + 1726854096 * q^97 + 51883209 * q^98 - 956239506 * q^99

Introduction

L-functions

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