LMFDB - Embedded newform 211.10.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [211,10,Mod(1,211)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(211, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("211.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 211 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	211.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:	$108.672561431$
Analytic rank:	$0$
Dimension:	$82$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	211.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-39.1065 q^{2} -17.2889 q^{3} +1017.32 q^{4} +2451.89 q^{5} +676.107 q^{6} +9796.00 q^{7} -19761.4 q^{8} -19384.1 q^{9} +O(q^{10})$	\(q-39.1065 q^{2} -17.2889 q^{3} +1017.32 q^{4} +2451.89 q^{5} +676.107 q^{6} +9796.00 q^{7} -19761.4 q^{8} -19384.1 q^{9} -95884.8 q^{10} +66296.2 q^{11} -17588.3 q^{12} -9579.51 q^{13} -383088. q^{14} -42390.3 q^{15} +251930. q^{16} -562067. q^{17} +758045. q^{18} -710048. q^{19} +2.49436e6 q^{20} -169362. q^{21} -2.59261e6 q^{22} -2.17794e6 q^{23} +341652. q^{24} +4.05862e6 q^{25} +374622. q^{26} +675425. q^{27} +9.96568e6 q^{28} +5.08394e6 q^{29} +1.65774e6 q^{30} +3.05666e6 q^{31} +265701. q^{32} -1.14618e6 q^{33} +2.19805e7 q^{34} +2.40187e7 q^{35} -1.97199e7 q^{36} -1.08329e7 q^{37} +2.77675e7 q^{38} +165619. q^{39} -4.84526e7 q^{40} +7.78873e6 q^{41} +6.62315e6 q^{42} +1.97240e6 q^{43} +6.74445e7 q^{44} -4.75276e7 q^{45} +8.51719e7 q^{46} +1.22375e7 q^{47} -4.35559e6 q^{48} +5.56079e7 q^{49} -1.58719e8 q^{50} +9.71749e6 q^{51} -9.74544e6 q^{52} -2.06448e7 q^{53} -2.64136e7 q^{54} +1.62551e8 q^{55} -1.93582e8 q^{56} +1.22759e7 q^{57} -1.98815e8 q^{58} -1.14334e8 q^{59} -4.31246e7 q^{60} +6.69345e7 q^{61} -1.19535e8 q^{62} -1.89887e8 q^{63} -1.39379e8 q^{64} -2.34879e7 q^{65} +4.48233e7 q^{66} +1.87723e8 q^{67} -5.71803e8 q^{68} +3.76542e7 q^{69} -9.39287e8 q^{70} +3.32978e8 q^{71} +3.83056e8 q^{72} +2.02133e8 q^{73} +4.23638e8 q^{74} -7.01689e7 q^{75} -7.22347e8 q^{76} +6.49437e8 q^{77} -6.47678e6 q^{78} +2.25060e8 q^{79} +6.17704e8 q^{80} +3.69860e8 q^{81} -3.04590e8 q^{82} +6.15203e8 q^{83} -1.72295e8 q^{84} -1.37812e9 q^{85} -7.71338e7 q^{86} -8.78956e7 q^{87} -1.31010e9 q^{88} -5.24525e8 q^{89} +1.85864e9 q^{90} -9.38409e7 q^{91} -2.21567e9 q^{92} -5.28462e7 q^{93} -4.78565e8 q^{94} -1.74096e9 q^{95} -4.59367e6 q^{96} -1.18430e9 q^{97} -2.17463e9 q^{98} -1.28509e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 82 q + 48 q^{2} + 331 q^{3} + 22272 q^{4} + 11249 q^{5} + 9392 q^{6} + 6632 q^{7} + 36864 q^{8} + 630129 q^{9}+O(q^{10}) $ 82 * q + 48 * q^2 + 331 * q^3 + 22272 * q^4 + 11249 * q^5 + 9392 * q^6 + 6632 * q^7 + 36864 * q^8 + 630129 * q^9	\( 82 q + 48 q^{2} + 331 q^{3} + 22272 q^{4} + 11249 q^{5} + 9392 q^{6} + 6632 q^{7} + 36864 q^{8} + 630129 q^{9} + 73920 q^{10} + 255733 q^{11} + 262929 q^{12} + 291015 q^{13} + 599651 q^{14} + 151566 q^{15} + 6088388 q^{16} + 1450152 q^{17} + 1803076 q^{18} + 1658423 q^{19} + 5677520 q^{20} + 4437026 q^{21} + 402001 q^{22} + 4279922 q^{23} + 8660330 q^{24} + 36692027 q^{25} + 14084490 q^{26} + 11692912 q^{27} + 1686063 q^{28} + 28121309 q^{29} + 22795315 q^{30} + 8118600 q^{31} + 13477081 q^{32} + 17174434 q^{33} + 19372534 q^{34} + 37542780 q^{35} + 215622860 q^{36} + 50413779 q^{37} + 58031367 q^{38} + 23234242 q^{39} + 58731852 q^{40} + 103434140 q^{41} + 15334009 q^{42} + 34281571 q^{43} + 183086279 q^{44} + 235979107 q^{45} + 149265183 q^{46} + 93000602 q^{47} + 114303721 q^{48} + 570480578 q^{49} + 222019553 q^{50} + 77929810 q^{51} + 79999859 q^{52} + 407531048 q^{53} + 1321436783 q^{54} + 449488153 q^{55} + 756123028 q^{56} + 335002024 q^{57} + 481532629 q^{58} + 570753278 q^{59} - 244569748 q^{60} + 694734563 q^{61} - 73212918 q^{62} - 540500692 q^{63} + 194355770 q^{64} + 53860661 q^{65} - 737702157 q^{66} - 162897225 q^{67} - 1298035011 q^{68} + 602016364 q^{69} - 3064991165 q^{70} + 323986036 q^{71} - 1711822491 q^{72} - 1077391483 q^{73} - 683958107 q^{74} - 1166367949 q^{75} - 478318455 q^{76} + 1584572500 q^{77} - 5134824150 q^{78} + 342296112 q^{79} + 1441041507 q^{80} + 5540929446 q^{81} - 1240907573 q^{82} + 1202053700 q^{83} - 1781018244 q^{84} + 312682194 q^{85} - 305650461 q^{86} + 1589558614 q^{87} + 1034360734 q^{88} + 3298871808 q^{89} + 1695581030 q^{90} + 1989076496 q^{91} + 3997408364 q^{92} + 2435977176 q^{93} + 2258199495 q^{94} + 4724645555 q^{95} + 9729772859 q^{96} + 2626833632 q^{97} + 7407181902 q^{98} + 6900390127 q^{99}+O(q^{100}) \) 82 * q + 48 * q^2 + 331 * q^3 + 22272 * q^4 + 11249 * q^5 + 9392 * q^6 + 6632 * q^7 + 36864 * q^8 + 630129 * q^9 + 73920 * q^10 + 255733 * q^11 + 262929 * q^12 + 291015 * q^13 + 599651 * q^14 + 151566 * q^15 + 6088388 * q^16 + 1450152 * q^17 + 1803076 * q^18 + 1658423 * q^19 + 5677520 * q^20 + 4437026 * q^21 + 402001 * q^22 + 4279922 * q^23 + 8660330 * q^24 + 36692027 * q^25 + 14084490 * q^26 + 11692912 * q^27 + 1686063 * q^28 + 28121309 * q^29 + 22795315 * q^30 + 8118600 * q^31 + 13477081 * q^32 + 17174434 * q^33 + 19372534 * q^34 + 37542780 * q^35 + 215622860 * q^36 + 50413779 * q^37 + 58031367 * q^38 + 23234242 * q^39 + 58731852 * q^40 + 103434140 * q^41 + 15334009 * q^42 + 34281571 * q^43 + 183086279 * q^44 + 235979107 * q^45 + 149265183 * q^46 + 93000602 * q^47 + 114303721 * q^48 + 570480578 * q^49 + 222019553 * q^50 + 77929810 * q^51 + 79999859 * q^52 + 407531048 * q^53 + 1321436783 * q^54 + 449488153 * q^55 + 756123028 * q^56 + 335002024 * q^57 + 481532629 * q^58 + 570753278 * q^59 - 244569748 * q^60 + 694734563 * q^61 - 73212918 * q^62 - 540500692 * q^63 + 194355770 * q^64 + 53860661 * q^65 - 737702157 * q^66 - 162897225 * q^67 - 1298035011 * q^68 + 602016364 * q^69 - 3064991165 * q^70 + 323986036 * q^71 - 1711822491 * q^72 - 1077391483 * q^73 - 683958107 * q^74 - 1166367949 * q^75 - 478318455 * q^76 + 1584572500 * q^77 - 5134824150 * q^78 + 342296112 * q^79 + 1441041507 * q^80 + 5540929446 * q^81 - 1240907573 * q^82 + 1202053700 * q^83 - 1781018244 * q^84 + 312682194 * q^85 - 305650461 * q^86 + 1589558614 * q^87 + 1034360734 * q^88 + 3298871808 * q^89 + 1695581030 * q^90 + 1989076496 * q^91 + 3997408364 * q^92 + 2435977176 * q^93 + 2258199495 * q^94 + 4724645555 * q^95 + 9729772859 * q^96 + 2626833632 * q^97 + 7407181902 * q^98 + 6900390127 * 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 $

$2$	−39.1065	−1.72828	−0.864141	−	0.503250i	$-0.832137\pi$
$2$	−39.1065	−1.72828	−0.864141	+	0.503250i	$0.832137\pi$
$3$	−17.2889	−0.123231	−0.0616156	−	0.998100i	$-0.519625\pi$
$3$	−17.2889	−0.123231	−0.0616156	+	0.998100i	$0.519625\pi$
$4$	1017.32	1.98696
$5$	2451.89	1.75443	0.877213	−	0.480101i	$-0.159400\pi$
$5$	2451.89	1.75443	0.877213	+	0.480101i	$0.159400\pi$
$6$	676.107	0.212978
$7$	9796.00	1.54208	0.771041	−	0.636786i	$-0.219736\pi$
$7$	9796.00	1.54208	0.771041	+	0.636786i	$0.219736\pi$
$8$	−19761.4	−1.70574
$9$	−19384.1	−0.984814
$10$	−95884.8	−3.03214
$11$	66296.2	1.36528	0.682639	−	0.730756i	$-0.260832\pi$
$11$	66296.2	1.36528	0.682639	+	0.730756i	$0.260832\pi$
$12$	−17588.3	−0.244855
$13$	−9579.51	−0.0930247	−0.0465124	−	0.998918i	$-0.514811\pi$
$13$	−9579.51	−0.0930247	−0.0465124	+	0.998918i	$0.514811\pi$
$14$	−383088.	−2.66515
$15$	−42390.3	−0.216200
$16$	251930.	0.961038
$17$	−562067.	−1.63218	−0.816090	−	0.577925i	$-0.803862\pi$
$17$	−562067.	−1.63218	−0.816090	+	0.577925i	$0.803862\pi$
$18$	758045.	1.70204
$19$	−710048.	−1.24996	−0.624981	−	0.780640i	$-0.714893\pi$
$19$	−710048.	−1.24996	−0.624981	+	0.780640i	$0.714893\pi$
$20$	2.49436e6	3.48597
$21$	−169362.	−0.190033
$22$	−2.59261e6	−2.35959
$23$	−2.17794e6	−1.62282	−0.811412	−	0.584474i	$-0.801301\pi$
$23$	−2.17794e6	−1.62282	−0.811412	+	0.584474i	$0.801301\pi$
$24$	341652.	0.210200
$25$	4.05862e6	2.07801
$26$	374622.	0.160773
$27$	675425.	0.244591
$28$	9.96568e6	3.06405
$29$	5.08394e6	1.33478	0.667390	−	0.744708i	$-0.267411\pi$
$29$	5.08394e6	1.33478	0.667390	+	0.744708i	$0.267411\pi$
$30$	1.65774e6	0.373655
$31$	3.05666e6	0.594456	0.297228	−	0.954807i	$-0.403938\pi$
$31$	3.05666e6	0.594456	0.297228	+	0.954807i	$0.403938\pi$
$32$	265701.	0.0447939
$33$	−1.14618e6	−0.168245
$34$	2.19805e7	2.82086
$35$	2.40187e7	2.70547
$36$	−1.97199e7	−1.95678
$37$	−1.08329e7	−0.950250	−0.475125	−	0.879918i	$-0.657597\pi$
$37$	−1.08329e7	−0.950250	−0.475125	+	0.879918i	$0.657597\pi$
$38$	2.77675e7	2.16028
$39$	165619.	0.0114635
$40$	−4.84526e7	−2.99259
$41$	7.78873e6	0.430466	0.215233	−	0.976563i	$-0.430949\pi$
$41$	7.78873e6	0.430466	0.215233	+	0.976563i	$0.430949\pi$
$42$	6.62315e6	0.328430
$43$	1.97240e6	0.0879807	0.0439904	−	0.999032i	$-0.485993\pi$
$43$	1.97240e6	0.0879807	0.0439904	+	0.999032i	$0.485993\pi$
$44$	6.74445e7	2.71275
$45$	−4.75276e7	−1.72778
$46$	8.51719e7	2.80470
$47$	1.22375e7	0.365806	0.182903	−	0.983131i	$-0.441451\pi$
$47$	1.22375e7	0.365806	0.182903	+	0.983131i	$0.441451\pi$
$48$	−4.35559e6	−0.118430
$49$	5.56079e7	1.37802
$50$	−1.58719e8	−3.59139
$51$	9.71749e6	0.201135
$52$	−9.74544e6	−0.184836
$53$	−2.06448e7	−0.359392	−0.179696	−	0.983722i	$-0.557511\pi$
$53$	−2.06448e7	−0.359392	−0.179696	+	0.983722i	$0.557511\pi$
$54$	−2.64136e7	−0.422722
$55$	1.62551e8	2.39528
$56$	−1.93582e8	−2.63039
$57$	1.22759e7	0.154034
$58$	−1.98815e8	−2.30688
$59$	−1.14334e8	−1.22841	−0.614204	−	0.789147i	$-0.710523\pi$
$59$	−1.14334e8	−1.22841	−0.614204	+	0.789147i	$0.710523\pi$
$60$	−4.31246e7	−0.429580
$61$	6.69345e7	0.618964	0.309482	−	0.950905i	$-0.399844\pi$
$61$	6.69345e7	0.618964	0.309482	+	0.950905i	$0.399844\pi$
$62$	−1.19535e8	−1.02739
$63$	−1.89887e8	−1.51866
$64$	−1.39379e8	−1.03845
$65$	−2.34879e7	−0.163205
$66$	4.48233e7	0.290774
$67$	1.87723e8	1.13810	0.569051	−	0.822302i	$-0.307311\pi$
$67$	1.87723e8	1.13810	0.569051	+	0.822302i	$0.307311\pi$
$68$	−5.71803e8	−3.24307
$69$	3.76542e7	0.199983
$70$	−9.39287e8	−4.67581
$71$	3.32978e8	1.55508	0.777539	−	0.628834i	$-0.216468\pi$
$71$	3.32978e8	1.55508	0.777539	+	0.628834i	$0.216468\pi$
$72$	3.83056e8	1.67983
$73$	2.02133e8	0.833074	0.416537	−	0.909119i	$-0.363244\pi$
$73$	2.02133e8	0.833074	0.416537	+	0.909119i	$0.363244\pi$
$74$	4.23638e8	1.64230
$75$	−7.01689e7	−0.256076
$76$	−7.22347e8	−2.48362
$77$	6.49437e8	2.10537
$78$	−6.47678e6	−0.0198122
$79$	2.25060e8	0.650094	0.325047	−	0.945698i	$-0.394620\pi$
$79$	2.25060e8	0.650094	0.325047	+	0.945698i	$0.394620\pi$
$80$	6.17704e8	1.68607
$81$	3.69860e8	0.954673
$82$	−3.04590e8	−0.743967
$83$	6.15203e8	1.42288	0.711438	−	0.702749i	$-0.248044\pi$
$83$	6.15203e8	1.42288	0.711438	+	0.702749i	$0.248044\pi$
$84$	−1.72295e8	−0.377586
$85$	−1.37812e9	−2.86354
$86$	−7.71338e7	−0.152055
$87$	−8.78956e7	−0.164487
$88$	−1.31010e9	−2.32881
$89$	−5.24525e8	−0.886157	−0.443079	−	0.896483i	$-0.646114\pi$
$89$	−5.24525e8	−0.886157	−0.443079	+	0.896483i	$0.646114\pi$
$90$	1.85864e9	2.98610
$91$	−9.38409e7	−0.143452
$92$	−2.21567e9	−3.22448
$93$	−5.28462e7	−0.0732555
$94$	−4.78565e8	−0.632216
$95$	−1.74096e9	−2.19297
$96$	−4.59367e6	−0.00552001
$97$	−1.18430e9	−1.35828	−0.679138	−	0.734011i	$-0.737646\pi$
$97$	−1.18430e9	−1.35828	−0.679138	+	0.734011i	$0.737646\pi$
$98$	−2.17463e9	−2.38160
$99$	−1.28509e9	−1.34455
$100$	4.12892e9	4.12892
$101$	1.46261e9	1.39857	0.699284	−	0.714844i	$-0.253502\pi$
$101$	1.46261e9	1.39857	0.699284	+	0.714844i	$0.253502\pi$
$102$	−3.80018e8	−0.347619
$103$	1.89995e9	1.66331	0.831656	−	0.555292i	$-0.187393\pi$
$103$	1.89995e9	1.66331	0.831656	+	0.555292i	$0.187393\pi$
$104$	1.89304e8	0.158676
$105$	−4.15255e8	−0.333398
$106$	8.07346e8	0.621131
$107$	1.40954e9	1.03956	0.519782	−	0.854299i	$-0.326013\pi$
$107$	1.40954e9	1.03956	0.519782	+	0.854299i	$0.326013\pi$
$108$	6.87125e8	0.485992
$109$	2.04167e9	1.38537	0.692686	−	0.721239i	$-0.256427\pi$
$109$	2.04167e9	1.38537	0.692686	+	0.721239i	$0.256427\pi$
$110$	−6.35679e9	−4.13972
$111$	1.87289e8	0.117100
$112$	2.46791e9	1.48200
$113$	6.75490e7	0.0389732	0.0194866	−	0.999810i	$-0.493797\pi$
$113$	6.75490e7	0.0389732	0.0194866	+	0.999810i	$0.493797\pi$
$114$	−4.80069e8	−0.266214
$115$	−5.34007e9	−2.84713
$116$	5.17200e9	2.65215
$117$	1.85690e8	0.0916121
$118$	4.47122e9	2.12304
$119$	−5.50601e9	−2.51695
$120$	8.37691e8	0.368781
$121$	2.03723e9	0.863985
$122$	−2.61758e9	−1.06974
$123$	−1.34658e8	−0.0530469
$124$	3.10961e9	1.18116
$125$	5.16243e9	1.89130
$126$	7.42581e9	2.62468
$127$	9.67781e8	0.330111	0.165056	−	0.986284i	$-0.447220\pi$
$127$	9.67781e8	0.330111	0.165056	+	0.986284i	$0.447220\pi$
$128$	5.31459e9	1.74995
$129$	−3.41006e7	−0.0108420
$130$	9.18530e8	0.282064
$131$	6.06350e9	1.79888	0.899441	−	0.437042i	$-0.143974\pi$
$131$	6.06350e9	1.79888	0.899441	+	0.437042i	$0.143974\pi$
$132$	−1.16604e9	−0.334295
$133$	−6.95563e9	−1.92754
$134$	−7.34120e9	−1.96696
$135$	1.65607e9	0.429117
$136$	1.11072e10	2.78407
$137$	5.36693e9	1.30162	0.650809	−	0.759241i	$-0.274430\pi$
$137$	5.36693e9	1.30162	0.650809	+	0.759241i	$0.274430\pi$
$138$	−1.47252e9	−0.345626
$139$	−2.36074e9	−0.536392	−0.268196	−	0.963364i	$-0.586427\pi$
$139$	−2.36074e9	−0.536392	−0.268196	+	0.963364i	$0.586427\pi$
$140$	2.44347e10	5.37565
$141$	−2.11572e8	−0.0450787
$142$	−1.30216e10	−2.68761
$143$	−6.35085e8	−0.127005
$144$	−4.88344e9	−0.946443
$145$	1.24653e10	2.34177
$146$	−7.90470e9	−1.43979
$147$	−9.61398e8	−0.169815
$148$	−1.10206e10	−1.88810
$149$	−2.49442e8	−0.0414601	−0.0207301	−	0.999785i	$-0.506599\pi$
$149$	−2.49442e8	−0.0414601	−0.0207301	+	0.999785i	$0.506599\pi$
$150$	2.74406e9	0.442571
$151$	1.76028e9	0.275541	0.137770	−	0.990464i	$-0.456006\pi$
$151$	1.76028e9	0.275541	0.137770	+	0.990464i	$0.456006\pi$
$152$	1.40315e10	2.13211
$153$	1.08952e10	1.60739
$154$	−2.53972e10	−3.63867
$155$	7.49458e9	1.04293
$156$	1.68488e8	0.0227776
$157$	1.04340e10	1.37058	0.685290	−	0.728271i	$-0.259676\pi$
$157$	1.04340e10	1.37058	0.685290	+	0.728271i	$0.259676\pi$
$158$	−8.80132e9	−1.12355
$159$	3.56925e8	0.0442884
$160$	6.51469e8	0.0785876
$161$	−2.13351e10	−2.50253
$162$	−1.44639e10	−1.64994
$163$	1.35894e10	1.50784	0.753920	−	0.656966i	$-0.228160\pi$
$163$	1.35894e10	1.50784	0.753920	+	0.656966i	$0.228160\pi$
$164$	7.92364e9	0.855318
$165$	−2.81031e9	−0.295173
$166$	−2.40585e10	−2.45913
$167$	−1.18741e10	−1.18134	−0.590671	−	0.806912i	$-0.701137\pi$
$167$	−1.18741e10	−1.18134	−0.590671	+	0.806912i	$0.701137\pi$
$168$	3.34682e9	0.324146
$169$	−1.05127e10	−0.991346
$170$	5.38937e10	4.94900
$171$	1.37636e10	1.23098
$172$	2.00657e9	0.174814
$173$	4.08244e9	0.346507	0.173254	−	0.984877i	$-0.444572\pi$
$173$	4.08244e9	0.346507	0.173254	+	0.984877i	$0.444572\pi$
$174$	3.43729e9	0.284279
$175$	3.97582e10	3.20447
$176$	1.67020e10	1.31208
$177$	1.97671e9	0.151378
$178$	2.05123e10	1.53153
$179$	1.01567e10	0.739459	0.369730	−	0.929139i	$-0.379450\pi$
$179$	1.01567e10	0.739459	0.369730	+	0.929139i	$0.379450\pi$
$180$	−4.83508e10	−3.43303
$181$	−1.77100e9	−0.122649	−0.0613246	−	0.998118i	$-0.519532\pi$
$181$	−1.77100e9	−0.122649	−0.0613246	+	0.998118i	$0.519532\pi$
$182$	3.66979e9	0.247925
$183$	−1.15722e9	−0.0762757
$184$	4.30392e10	2.76811
$185$	−2.65611e10	−1.66714
$186$	2.06663e9	0.126606
$187$	−3.72629e10	−2.22838
$188$	1.24494e10	0.726841
$189$	6.61647e9	0.377179
$190$	6.80828e10	3.79006
$191$	5.24803e9	0.285329	0.142665	−	0.989771i	$-0.454433\pi$
$191$	5.24803e9	0.285329	0.142665	+	0.989771i	$0.454433\pi$
$192$	2.40970e9	0.127970
$193$	−2.45286e10	−1.27252	−0.636261	−	0.771474i	$-0.719520\pi$
$193$	−2.45286e10	−1.27252	−0.636261	+	0.771474i	$0.719520\pi$
$194$	4.63137e10	2.34748
$195$	4.06079e8	0.0201120
$196$	5.65712e10	2.73806
$197$	−2.48985e10	−1.17781	−0.588906	−	0.808202i	$-0.700441\pi$
$197$	−2.48985e10	−1.17781	−0.588906	+	0.808202i	$0.700441\pi$
$198$	5.02555e10	2.32375
$199$	−2.72265e10	−1.23070	−0.615351	−	0.788253i	$-0.710986\pi$
$199$	−2.72265e10	−1.23070	−0.615351	+	0.788253i	$0.710986\pi$
$200$	−8.02039e10	−3.54454
$201$	−3.24552e9	−0.140250
$202$	−5.71978e10	−2.41712
$203$	4.98023e10	2.05834
$204$	9.88582e9	0.399647
$205$	1.90971e10	0.755222
$206$	−7.43003e10	−2.87467
$207$	4.22175e10	1.59818
$208$	−2.41337e9	−0.0894003
$209$	−4.70735e10	−1.70655
$210$	1.62392e10	0.576206
$211$	1.98212e9	0.0688428
$211$	1.98212e9	0.0688428
$212$	−2.10024e10	−0.714097
$213$	−5.75680e9	−0.191634
$214$	−5.51223e10	−1.79666
$215$	4.83611e9	0.154356
$216$	−1.33473e10	−0.417208
$217$	2.99430e10	0.916699
$218$	−7.98427e10	−2.39431
$219$	−3.49464e9	−0.102661
$220$	1.65366e11	4.75932
$221$	5.38433e9	0.151833
$222$	−7.32422e9	−0.202382
$223$	5.84486e10	1.58271	0.791356	−	0.611355i	$-0.209375\pi$
$223$	5.84486e10	1.58271	0.791356	+	0.611355i	$0.209375\pi$
$224$	2.60281e9	0.0690759
$225$	−7.86727e10	−2.04646
$226$	−2.64161e9	−0.0673566
$227$	1.33982e10	0.334910	0.167455	−	0.985880i	$-0.446445\pi$
$227$	1.33982e10	0.334910	0.167455	+	0.985880i	$0.446445\pi$
$228$	1.24886e10	0.306059
$229$	3.29598e10	0.792000	0.396000	−	0.918250i	$-0.370398\pi$
$229$	3.29598e10	0.792000	0.396000	+	0.918250i	$0.370398\pi$
$230$	2.08832e11	4.92064
$231$	−1.12280e10	−0.259447
$232$	−1.00466e11	−2.27678
$233$	−2.69217e10	−0.598412	−0.299206	−	0.954188i	$-0.596722\pi$
$233$	−2.69217e10	−0.598412	−0.299206	+	0.954188i	$0.596722\pi$
$234$	−7.26170e9	−0.158331
$235$	3.00049e10	0.641780
$236$	−1.16315e11	−2.44079
$237$	−3.89103e9	−0.0801119
$238$	2.15321e11	4.35000
$239$	4.63481e10	0.918843	0.459422	−	0.888218i	$-0.348057\pi$
$239$	4.63481e10	0.918843	0.459422	+	0.888218i	$0.348057\pi$
$240$	−1.06794e10	−0.207776
$241$	−7.49790e10	−1.43174	−0.715868	−	0.698235i	$-0.753969\pi$
$241$	−7.49790e10	−1.43174	−0.715868	+	0.698235i	$0.753969\pi$
$242$	−7.96691e10	−1.49321
$243$	−1.96889e10	−0.362236
$244$	6.80939e10	1.22985
$245$	1.36344e11	2.41763
$246$	5.26602e9	0.0916799
$247$	6.80191e9	0.116277
$248$	−6.04038e10	−1.01399
$249$	−1.06362e10	−0.175343
$250$	−2.01885e11	−3.26869
$251$	6.44283e10	1.02458	0.512289	−	0.858813i	$-0.328798\pi$
$251$	6.44283e10	1.02458	0.512289	+	0.858813i	$0.328798\pi$
$252$	−1.93176e11	−3.01752
$253$	−1.44389e11	−2.21561
$254$	−3.78466e10	−0.570525
$255$	2.38262e10	0.352877
$256$	−1.36473e11	−1.98595
$257$	−1.00165e11	−1.43224	−0.716120	−	0.697977i	$-0.754084\pi$
$257$	−1.00165e11	−1.43224	−0.716120	+	0.697977i	$0.754084\pi$
$258$	1.33356e9	0.0187380
$259$	−1.06119e11	−1.46536
$260$	−2.38947e10	−0.324281
$261$	−9.85477e10	−1.31451
$262$	−2.37123e11	−3.10897
$263$	1.02440e11	1.32028	0.660142	−	0.751140i	$-0.270496\pi$
$263$	1.02440e11	1.32028	0.660142	+	0.751140i	$0.270496\pi$
$264$	2.26502e10	0.286982
$265$	−5.06187e10	−0.630528
$266$	2.72011e11	3.33134
$267$	9.06843e9	0.109202
$268$	1.90975e11	2.26136
$269$	7.08421e10	0.824909	0.412455	−	0.910978i	$-0.364672\pi$
$269$	7.08421e10	0.824909	0.412455	+	0.910978i	$0.364672\pi$
$270$	−6.47630e10	−0.741635
$271$	−1.67685e10	−0.188857	−0.0944284	−	0.995532i	$-0.530102\pi$
$271$	−1.67685e10	−0.188857	−0.0944284	+	0.995532i	$0.530102\pi$
$272$	−1.41602e11	−1.56859
$273$	1.62240e9	0.0176777
$274$	−2.09882e11	−2.24956
$275$	2.69071e11	2.83707
$276$	3.83064e10	0.397357
$277$	−2.22177e10	−0.226746	−0.113373	−	0.993552i	$-0.536166\pi$
$277$	−2.22177e10	−0.226746	−0.113373	+	0.993552i	$0.536166\pi$
$278$	9.23205e10	0.927036
$279$	−5.92506e10	−0.585428
$280$	−4.74642e11	−4.61482
$281$	6.15320e10	0.588739	0.294370	−	0.955692i	$-0.404890\pi$
$281$	6.15320e10	0.588739	0.294370	+	0.955692i	$0.404890\pi$
$282$	8.27384e9	0.0779087
$283$	−3.78663e10	−0.350925	−0.175463	−	0.984486i	$-0.556142\pi$
$283$	−3.78663e10	−0.350925	−0.175463	+	0.984486i	$0.556142\pi$
$284$	3.38745e11	3.08987
$285$	3.00992e10	0.270242
$286$	2.48360e10	0.219500
$287$	7.62984e10	0.663814
$288$	−5.15038e9	−0.0441137
$289$	1.97331e11	1.66401
$290$	−4.87473e11	−4.04724
$291$	2.04751e10	0.167382
$292$	2.05634e11	1.65528
$293$	−5.60895e10	−0.444608	−0.222304	−	0.974977i	$-0.571358\pi$
$293$	−5.60895e10	−0.444608	−0.222304	+	0.974977i	$0.571358\pi$
$294$	3.75969e10	0.293487
$295$	−2.80335e11	−2.15515
$296$	2.14073e11	1.62088
$297$	4.47781e10	0.333935
$298$	9.75480e9	0.0716548
$299$	2.08637e10	0.150963
$300$	−7.13843e10	−0.508812
$301$	1.93216e10	0.135673
$302$	−6.88385e10	−0.476212
$303$	−2.52869e10	−0.172347
$304$	−1.78883e11	−1.20126
$305$	1.64116e11	1.08593
$306$	−4.26072e11	−2.77803
$307$	−2.65575e11	−1.70633	−0.853167	−	0.521638i	$-0.825321\pi$
$307$	−2.65575e11	−1.70633	−0.853167	+	0.521638i	$0.825321\pi$
$308$	6.60686e11	4.18328
$309$	−3.28479e10	−0.204972
$310$	−2.93087e11	−1.80247
$311$	7.73440e10	0.468819	0.234409	−	0.972138i	$-0.424684\pi$
$311$	7.73440e10	0.468819	0.234409	+	0.972138i	$0.424684\pi$
$312$	−3.27286e9	−0.0195538
$313$	−9.91925e10	−0.584156	−0.292078	−	0.956394i	$-0.594347\pi$
$313$	−9.91925e10	−0.584156	−0.292078	+	0.956394i	$0.594347\pi$
$314$	−4.08039e11	−2.36875
$315$	−4.65580e11	−2.66438
$316$	2.28958e11	1.29171
$317$	1.67613e11	0.932269	0.466134	−	0.884714i	$-0.345646\pi$
$317$	1.67613e11	0.932269	0.466134	+	0.884714i	$0.345646\pi$
$318$	−1.39581e10	−0.0765427
$319$	3.37046e11	1.82235
$320$	−3.41741e11	−1.82189
$321$	−2.43694e10	−0.128107
$322$	8.34344e11	4.32507
$323$	3.99094e11	2.04016
$324$	3.76266e11	1.89689
$325$	−3.88796e10	−0.193307
$326$	−5.31434e11	−2.60597
$327$	−3.52982e10	−0.170721
$328$	−1.53916e11	−0.734262
$329$	1.19878e11	0.564103
$330$	1.09902e11	0.510143
$331$	−2.37907e11	−1.08939	−0.544693	−	0.838636i	$-0.683354\pi$
$331$	−2.37907e11	−1.08939	−0.544693	+	0.838636i	$0.683354\pi$
$332$	6.25859e11	2.82719
$333$	2.09986e11	0.935819
$334$	4.64354e11	2.04169
$335$	4.60276e11	1.99672
$336$	−4.26673e10	−0.182628
$337$	−3.29304e10	−0.139079	−0.0695396	−	0.997579i	$-0.522153\pi$
$337$	−3.29304e10	−0.139079	−0.0695396	+	0.997579i	$0.522153\pi$
$338$	4.11117e11	1.71333
$339$	−1.16785e9	−0.00480271
$340$	−1.40200e12	−5.68973
$341$	2.02645e11	0.811597
$342$	−5.38248e11	−2.12748
$343$	1.49431e11	0.582933
$344$	−3.89774e10	−0.150072
$345$	9.23238e10	0.350855
$346$	−1.59650e11	−0.598862
$347$	−3.52460e11	−1.30505	−0.652525	−	0.757767i	$-0.726290\pi$
$347$	−3.52460e11	−1.30505	−0.652525	+	0.757767i	$0.726290\pi$
$348$	−8.94181e10	−0.326828
$349$	−2.82138e11	−1.01800	−0.508999	−	0.860767i	$-0.669984\pi$
$349$	−2.82138e11	−1.01800	−0.508999	+	0.860767i	$0.669984\pi$
$350$	−1.55481e12	−5.53822
$351$	−6.47025e9	−0.0227530
$352$	1.76150e10	0.0611562
$353$	4.55238e10	0.156046	0.0780229	−	0.996952i	$-0.475139\pi$
$353$	4.55238e10	0.156046	0.0780229	+	0.996952i	$0.475139\pi$
$354$	−7.73023e10	−0.261624
$355$	8.16423e11	2.72827
$356$	−5.33610e11	−1.76076
$357$	9.51925e10	0.310167
$358$	−3.97194e11	−1.27799
$359$	2.79771e11	0.888952	0.444476	−	0.895791i	$-0.353390\pi$
$359$	2.79771e11	0.888952	0.444476	+	0.895791i	$0.353390\pi$
$360$	9.39210e11	2.94715
$361$	1.81480e11	0.562403
$362$	6.92576e10	0.211972
$363$	−3.52214e10	−0.106470
$364$	−9.54663e10	−0.285032
$365$	4.95606e11	1.46157
$366$	4.52549e10	0.131826
$367$	−1.52120e11	−0.437713	−0.218856	−	0.975757i	$-0.570233\pi$
$367$	−1.52120e11	−0.437713	−0.218856	+	0.975757i	$0.570233\pi$
$368$	−5.48690e11	−1.55960
$369$	−1.50977e11	−0.423929
$370$	1.03871e12	2.88129
$371$	−2.02236e11	−0.554213
$372$	−5.37615e10	−0.145555
$373$	5.32343e11	1.42397	0.711987	−	0.702193i	$-0.247796\pi$
$373$	5.32343e11	1.42397	0.711987	+	0.702193i	$0.247796\pi$
$374$	1.45722e12	3.85127
$375$	−8.92526e10	−0.233067
$376$	−2.41829e11	−0.623969
$377$	−4.87017e10	−0.124168
$378$	−2.58747e11	−0.651872
$379$	−5.78561e11	−1.44037	−0.720183	−	0.693784i	$-0.755942\pi$
$379$	−5.78561e11	−1.44037	−0.720183	+	0.693784i	$0.755942\pi$
$380$	−1.77111e12	−4.35733
$381$	−1.67318e10	−0.0406800
$382$	−2.05232e11	−0.493129
$383$	4.18788e11	0.994488	0.497244	−	0.867611i	$-0.334345\pi$
$383$	4.18788e11	0.994488	0.497244	+	0.867611i	$0.334345\pi$
$384$	−9.18832e10	−0.215648
$385$	1.59235e12	3.69372
$386$	9.59230e11	2.19928
$387$	−3.82332e10	−0.0866446
$388$	−1.20481e12	−2.69883
$389$	−2.61425e11	−0.578860	−0.289430	−	0.957199i	$-0.593466\pi$
$389$	−2.61425e11	−0.578860	−0.289430	+	0.957199i	$0.593466\pi$
$390$	−1.58803e10	−0.0347591
$391$	1.22415e12	2.64874
$392$	−1.09889e12	−2.35053
$393$	−1.04831e11	−0.221678
$394$	9.73696e11	2.03559
$395$	5.51822e11	1.14054
$396$	−1.30735e12	−2.67155
$397$	−2.19850e11	−0.444189	−0.222095	−	0.975025i	$-0.571289\pi$
$397$	−2.19850e11	−0.444189	−0.222095	+	0.975025i	$0.571289\pi$
$398$	1.06473e12	2.12700
$399$	1.20255e11	0.237533
$400$	1.02249e12	1.99705
$401$	4.37941e11	0.845796	0.422898	−	0.906177i	$-0.361013\pi$
$401$	4.37941e11	0.845796	0.422898	+	0.906177i	$0.361013\pi$
$402$	1.26921e11	0.242391
$403$	−2.92813e10	−0.0552991
$404$	1.48795e12	2.77889
$405$	9.06854e11	1.67490
$406$	−1.94760e12	−3.55739
$407$	−7.18181e11	−1.29736
$408$	−1.92031e11	−0.343084
$409$	4.00110e11	0.707008	0.353504	−	0.935433i	$-0.384990\pi$
$409$	4.00110e11	0.707008	0.353504	+	0.935433i	$0.384990\pi$
$410$	−7.46820e11	−1.30524
$411$	−9.27882e10	−0.160400
$412$	1.93285e12	3.30493
$413$	−1.12002e12	−1.89431
$414$	−1.65098e12	−2.76211
$415$	1.50841e12	2.49633
$416$	−2.54529e9	−0.00416694
$417$	4.08146e10	0.0661002
$418$	1.84088e12	2.94939
$419$	−2.36072e11	−0.374180	−0.187090	−	0.982343i	$-0.559906\pi$
$419$	−2.36072e11	−0.374180	−0.187090	+	0.982343i	$0.559906\pi$
$420$	−4.22448e11	−0.662448
$421$	−6.63000e11	−1.02859	−0.514297	−	0.857612i	$-0.671947\pi$
$421$	−6.63000e11	−1.02859	−0.514297	+	0.857612i	$0.671947\pi$
$422$	−7.75138e10	−0.118980
$423$	−2.37212e11	−0.360251
$424$	4.07969e11	0.613029
$425$	−2.28122e12	−3.39169
$426$	2.25129e11	0.331198
$427$	6.55690e11	0.954494
$428$	1.43396e12	2.06557
$429$	1.09799e10	0.0156509
$430$	−1.89123e11	−0.266770
$431$	−2.34327e11	−0.327095	−0.163548	−	0.986535i	$-0.552294\pi$
$431$	−2.34327e11	−0.327095	−0.163548	+	0.986535i	$0.552294\pi$
$432$	1.70160e11	0.235061
$433$	−6.29227e11	−0.860224	−0.430112	−	0.902775i	$-0.641526\pi$
$433$	−6.29227e11	−0.860224	−0.430112	+	0.902775i	$0.641526\pi$
$434$	−1.17097e12	−1.58431
$435$	−2.15510e11	−0.288580
$436$	2.07704e12	2.75267
$437$	1.54645e12	2.02847
$438$	1.36663e11	0.177426
$439$	−9.14797e10	−0.117553	−0.0587766	−	0.998271i	$-0.518720\pi$
$439$	−9.14797e10	−0.117553	−0.0587766	+	0.998271i	$0.518720\pi$
$440$	−3.21222e12	−4.08572
$441$	−1.07791e12	−1.35709
$442$	−2.10562e11	−0.262410
$443$	1.56286e11	0.192799	0.0963993	−	0.995343i	$-0.469267\pi$
$443$	1.56286e11	0.192799	0.0963993	+	0.995343i	$0.469267\pi$
$444$	1.90533e11	0.232673
$445$	−1.28607e12	−1.55470
$446$	−2.28572e12	−2.73537
$447$	4.31256e9	0.00510918
$448$	−1.36536e12	−1.60138
$449$	4.68358e11	0.543838	0.271919	−	0.962320i	$-0.412342\pi$
$449$	4.68358e11	0.543838	0.271919	+	0.962320i	$0.412342\pi$
$450$	3.07662e12	3.53685
$451$	5.16363e11	0.587706
$452$	6.87191e10	0.0774380
$453$	−3.04332e10	−0.0339552
$454$	−5.23955e11	−0.578819
$455$	−2.30087e11	−0.251676
$456$	−2.42589e11	−0.262742
$457$	−7.70086e11	−0.825879	−0.412940	−	0.910758i	$-0.635498\pi$
$457$	−7.70086e11	−0.825879	−0.412940	+	0.910758i	$0.635498\pi$
$458$	−1.28894e12	−1.36880
$459$	−3.79634e11	−0.399216
$460$	−5.43257e12	−5.65712
$461$	7.51157e11	0.774599	0.387299	−	0.921954i	$-0.373408\pi$
$461$	7.51157e11	0.774599	0.387299	+	0.921954i	$0.373408\pi$
$462$	4.39089e11	0.448398
$463$	1.41152e12	1.42749	0.713743	−	0.700408i	$-0.246999\pi$
$463$	1.41152e12	1.42749	0.713743	+	0.700408i	$0.246999\pi$
$464$	1.28080e12	1.28277
$465$	−1.29573e11	−0.128521
$466$	1.05281e12	1.03422
$467$	−8.87544e11	−0.863503	−0.431752	−	0.901993i	$-0.642104\pi$
$467$	−8.87544e11	−0.863503	−0.431752	+	0.901993i	$0.642104\pi$
$468$	1.88907e11	0.182029
$469$	1.83893e12	1.75505
$470$	−1.17339e12	−1.10918
$471$	−1.80393e11	−0.168898
$472$	2.25940e12	2.09534
$473$	1.30763e11	0.120118
$474$	1.52165e11	0.138456
$475$	−2.88182e12	−2.59744
$476$	−5.60138e12	−5.00108
$477$	4.00180e11	0.353935
$478$	−1.81251e12	−1.58802
$479$	7.65867e11	0.664727	0.332364	−	0.943151i	$-0.392154\pi$
$479$	7.65867e11	0.664727	0.332364	+	0.943151i	$0.392154\pi$
$480$	−1.12632e10	−0.00968445
$481$	1.03774e11	0.0883967
$482$	2.93217e12	2.47444
$483$	3.68860e11	0.308390
$484$	2.07252e12	1.71670
$485$	−2.90376e12	−2.38299
$486$	7.69963e11	0.626046
$487$	−1.49355e12	−1.20321	−0.601604	−	0.798795i	$-0.705471\pi$
$487$	−1.49355e12	−1.20321	−0.601604	+	0.798795i	$0.705471\pi$
$488$	−1.32272e12	−1.05579
$489$	−2.34945e11	−0.185813
$490$	−5.33196e12	−4.17834
$491$	−3.53912e11	−0.274807	−0.137404	−	0.990515i	$-0.543876\pi$
$491$	−3.53912e11	−0.274807	−0.137404	+	0.990515i	$0.543876\pi$
$492$	−1.36991e11	−0.105402
$493$	−2.85752e12	−2.17860
$494$	−2.65999e11	−0.200960
$495$	−3.15090e12	−2.35891
$496$	7.70065e11	0.571294
$497$	3.26185e12	2.39806
$498$	4.15943e11	0.303041
$499$	−8.68732e11	−0.627239	−0.313620	−	0.949549i	$-0.601542\pi$
$499$	−8.68732e11	−0.627239	−0.313620	+	0.949549i	$0.601542\pi$
$500$	5.25185e12	3.75792
$501$	2.05289e11	0.145578
$502$	−2.51957e12	−1.77076
$503$	−1.94856e12	−1.35725	−0.678623	−	0.734486i	$-0.737423\pi$
$503$	−1.94856e12	−1.35725	−0.678623	+	0.734486i	$0.737423\pi$
$504$	3.75242e12	2.59044
$505$	3.58616e12	2.45368
$506$	5.64657e12	3.82919
$507$	1.81753e11	0.122165
$508$	9.84544e11	0.655916
$509$	2.03032e12	1.34071	0.670354	−	0.742041i	$-0.266142\pi$
$509$	2.03032e12	1.34071	0.670354	+	0.742041i	$0.266142\pi$
$510$	−9.31760e11	−0.609871
$511$	1.98009e12	1.28467
$512$	2.61592e12	1.68233
$513$	−4.79585e11	−0.305729
$514$	3.91709e12	2.47531
$515$	4.65845e12	2.91816
$516$	−3.46913e10	−0.0215425
$517$	8.11297e11	0.499427
$518$	4.14996e12	2.53256
$519$	−7.05807e10	−0.0427005
$520$	4.64153e11	0.278385
$521$	2.75603e12	1.63875	0.819377	−	0.573255i	$-0.194320\pi$
$521$	2.75603e12	1.63875	0.819377	+	0.573255i	$0.194320\pi$
$522$	3.85386e12	2.27184
$523$	−1.17835e12	−0.688679	−0.344340	−	0.938845i	$-0.611897\pi$
$523$	−1.17835e12	−0.688679	−0.344340	+	0.938845i	$0.611897\pi$
$524$	6.16853e12	3.57430
$525$	−6.87374e11	−0.394890
$526$	−4.00606e12	−2.28182
$527$	−1.71805e12	−0.970258
$528$	−2.88759e11	−0.161690
$529$	2.94229e12	1.63356
$530$	1.97952e12	1.08973
$531$	2.21627e12	1.20975
$532$	−7.07611e12	−3.82994
$533$	−7.46122e10	−0.0400440
$534$	−3.54635e11	−0.188732
$535$	3.45604e12	1.82384
$536$	−3.70967e12	−1.94130
$537$	−1.75598e11	−0.0911244
$538$	−2.77039e12	−1.42568
$539$	3.68659e12	1.88138
$540$	1.68475e12	0.852637
$541$	−8.83085e11	−0.443215	−0.221608	−	0.975136i	$-0.571130\pi$
$541$	−8.83085e11	−0.443215	−0.221608	+	0.975136i	$0.571130\pi$
$542$	6.55759e11	0.326398
$543$	3.06185e10	0.0151142
$544$	−1.49342e11	−0.0731117
$545$	5.00595e12	2.43054
$546$	−6.34465e10	−0.0305521
$547$	−1.47494e12	−0.704421	−0.352211	−	0.935921i	$-0.614570\pi$
$547$	−1.47494e12	−0.704421	−0.352211	+	0.935921i	$0.614570\pi$
$548$	5.45990e12	2.58626
$549$	−1.29746e12	−0.609565
$550$	−1.05224e13	−4.90325
$551$	−3.60984e12	−1.66842
$552$	−7.44098e11	−0.341118
$553$	2.20469e12	1.00250
$554$	8.68857e11	0.391881
$555$	4.59211e11	0.205444
$556$	−2.40164e12	−1.06579
$557$	−2.32545e12	−1.02367	−0.511834	−	0.859084i	$-0.671034\pi$
$557$	−2.32545e12	−1.02367	−0.511834	+	0.859084i	$0.671034\pi$
$558$	2.31709e12	1.01178
$559$	−1.88947e10	−0.00818438
$560$	6.05103e12	2.60006
$561$	6.44233e11	0.274606
$562$	−2.40631e12	−1.01751
$563$	−1.39770e11	−0.0586309	−0.0293154	−	0.999570i	$-0.509333\pi$
$563$	−1.39770e11	−0.0586309	−0.0293154	+	0.999570i	$0.509333\pi$
$564$	−2.15237e11	−0.0895695
$565$	1.65622e11	0.0683756
$566$	1.48082e12	0.606497
$567$	3.62315e12	1.47218
$568$	−6.58009e12	−2.65256
$569$	1.63993e11	0.0655875	0.0327938	−	0.999462i	$-0.489560\pi$
$569$	1.63993e11	0.0655875	0.0327938	+	0.999462i	$0.489560\pi$
$570$	−1.17707e12	−0.467054
$571$	−2.23780e12	−0.880966	−0.440483	−	0.897761i	$-0.645193\pi$
$571$	−2.23780e12	−0.880966	−0.440483	+	0.897761i	$0.645193\pi$
$572$	−6.46085e11	−0.252353
$573$	−9.07325e10	−0.0351615
$574$	−2.98376e12	−1.14726
$575$	−8.83945e12	−3.37225
$576$	2.70173e12	1.02268
$577$	1.22959e12	0.461817	0.230909	−	0.972975i	$-0.425830\pi$
$577$	1.22959e12	0.461817	0.230909	+	0.972975i	$0.425830\pi$
$578$	−7.71695e12	−2.87588
$579$	4.24072e11	0.156814
$580$	1.26812e13	4.65300
$581$	6.02653e12	2.19419
$582$	−8.00712e11	−0.289283
$583$	−1.36867e12	−0.490671
$584$	−3.99442e12	−1.42100
$585$	4.55291e11	0.160727
$586$	2.19347e12	0.768408
$587$	3.70574e12	1.28826	0.644130	−	0.764916i	$-0.277220\pi$
$587$	3.70574e12	1.28826	0.644130	+	0.764916i	$0.277220\pi$
$588$	−9.78051e11	−0.337414
$589$	−2.17037e12	−0.743046
$590$	1.09629e13	3.72471
$591$	4.30467e11	0.145143
$592$	−2.72914e12	−0.913226
$593$	−8.21988e11	−0.272973	−0.136486	−	0.990642i	$-0.543581\pi$
$593$	−8.21988e11	−0.272973	−0.136486	+	0.990642i	$0.543581\pi$
$594$	−1.75112e12	−0.577133
$595$	−1.35001e13	−4.41581
$596$	−2.53762e11	−0.0823794
$597$	4.70715e11	0.151661
$598$	−8.15905e11	−0.260906
$599$	−4.02406e12	−1.27716	−0.638578	−	0.769557i	$-0.720477\pi$
$599$	−4.02406e12	−1.27716	−0.638578	+	0.769557i	$0.720477\pi$
$600$	1.38663e12	0.436799
$601$	−3.90035e11	−0.121946	−0.0609731	−	0.998139i	$-0.519420\pi$
$601$	−3.90035e11	−0.121946	−0.0609731	+	0.998139i	$0.519420\pi$
$602$	−7.55603e11	−0.234482
$603$	−3.63884e12	−1.12082
$604$	1.79077e12	0.547487
$605$	4.99506e12	1.51580
$606$	9.88884e11	0.297864
$607$	−9.45124e11	−0.282579	−0.141289	−	0.989968i	$-0.545125\pi$
$607$	−9.45124e11	−0.282579	−0.141289	+	0.989968i	$0.545125\pi$
$608$	−1.88661e11	−0.0559906
$609$	−8.61025e11	−0.253652
$610$	−6.41800e12	−1.87679
$611$	−1.17229e11	−0.0340290
$612$	1.10839e13	3.19382
$613$	3.26028e12	0.932572	0.466286	−	0.884634i	$-0.345592\pi$
$613$	3.26028e12	0.932572	0.466286	+	0.884634i	$0.345592\pi$
$614$	1.03857e13	2.94903
$615$	−3.30167e11	−0.0930669
$616$	−1.28338e13	−3.59121
$617$	2.45288e11	0.0681387	0.0340694	−	0.999419i	$-0.489153\pi$
$617$	2.45288e11	0.0681387	0.0340694	+	0.999419i	$0.489153\pi$
$618$	1.28457e12	0.354249
$619$	5.74877e12	1.57386	0.786932	−	0.617040i	$-0.211668\pi$
$619$	5.74877e12	1.57386	0.786932	+	0.617040i	$0.211668\pi$
$620$	7.62440e12	2.07225
$621$	−1.47104e12	−0.396928
$622$	−3.02466e12	−0.810250
$623$	−5.13824e12	−1.36653
$624$	4.17244e10	0.0110169
$625$	4.73071e12	1.24013
$626$	3.87907e12	1.00959
$627$	8.13846e11	0.210300
$628$	1.06148e13	2.72328
$629$	6.08883e12	1.55098
$630$	1.82072e13	4.60481
$631$	−8.32758e11	−0.209116	−0.104558	−	0.994519i	$-0.533343\pi$
$631$	−8.32758e11	−0.209116	−0.104558	+	0.994519i	$0.533343\pi$
$632$	−4.44749e12	−1.10889
$633$	−3.42686e10	−0.00848359
$634$	−6.55477e12	−1.61122
$635$	2.37289e12	0.579156
$636$	3.63107e11	0.0879990
$637$	−5.32697e11	−0.128190
$638$	−1.31807e13	−3.14953
$639$	−6.45447e12	−1.53146
$640$	1.30308e13	3.07015
$641$	5.89472e12	1.37912	0.689560	−	0.724228i	$-0.257804\pi$
$641$	5.89472e12	1.37912	0.689560	+	0.724228i	$0.257804\pi$
$642$	9.53002e11	0.221404
$643$	8.29500e11	0.191367	0.0956834	−	0.995412i	$-0.469496\pi$
$643$	8.29500e11	0.191367	0.0956834	+	0.995412i	$0.469496\pi$
$644$	−2.17047e13	−4.97241
$645$	−8.36107e10	−0.0190214
$646$	−1.56072e13	−3.52597
$647$	2.24666e12	0.504043	0.252021	−	0.967722i	$-0.418905\pi$
$647$	2.24666e12	0.504043	0.252021	+	0.967722i	$0.418905\pi$
$648$	−7.30894e12	−1.62842
$649$	−7.57993e12	−1.67712
$650$	1.52045e12	0.334088
$651$	−5.17681e11	−0.112966
$652$	1.38248e13	2.99601
$653$	−2.18191e12	−0.469600	−0.234800	−	0.972044i	$-0.575444\pi$
$653$	−2.18191e12	−0.469600	−0.234800	+	0.972044i	$0.575444\pi$
$654$	1.38039e12	0.295054
$655$	1.48670e13	3.15601
$656$	1.96222e12	0.413694
$657$	−3.91816e12	−0.820423
$658$	−4.68802e12	−0.974929
$659$	−2.90826e12	−0.600688	−0.300344	−	0.953831i	$-0.597101\pi$
$659$	−2.90826e12	−0.600688	−0.300344	+	0.953831i	$0.597101\pi$
$660$	−2.85899e12	−0.586496
$661$	−2.88454e12	−0.587719	−0.293860	−	0.955849i	$-0.594940\pi$
$661$	−2.88454e12	−0.587719	−0.293860	+	0.955849i	$0.594940\pi$
$662$	9.30373e12	1.88276
$663$	−9.30889e10	−0.0187106
$664$	−1.21573e13	−2.42705
$665$	−1.70544e13	−3.38173
$666$	−8.21184e12	−1.61736
$667$	−1.10726e13	−2.16611
$668$	−1.20798e13	−2.34728
$669$	−1.01051e12	−0.195040
$670$	−1.79998e13	−3.45089
$671$	4.43750e12	0.845059
$672$	−4.49996e10	−0.00851230
$673$	−3.27544e12	−0.615463	−0.307731	−	0.951473i	$-0.599570\pi$
$673$	−3.27544e12	−0.615463	−0.307731	+	0.951473i	$0.599570\pi$
$674$	1.28779e12	0.240368
$675$	2.74130e12	0.508263
$676$	−1.06948e13	−1.96976
$677$	−3.13203e12	−0.573030	−0.286515	−	0.958076i	$-0.592497\pi$
$677$	−3.13203e12	−0.573030	−0.286515	+	0.958076i	$0.592497\pi$
$678$	4.56704e10	0.00830044
$679$	−1.16014e13	−2.09457
$680$	2.72336e13	4.88445
$681$	−2.31639e11	−0.0412714
$682$	−7.92474e12	−1.40267
$683$	−1.05810e13	−1.86052	−0.930262	−	0.366896i	$-0.880421\pi$
$683$	−1.05810e13	−1.86052	−0.930262	+	0.366896i	$0.880421\pi$
$684$	1.40020e13	2.44590
$685$	1.31591e13	2.28359
$686$	−5.84375e12	−1.00747
$687$	−5.69838e11	−0.0975991
$688$	4.96908e11	0.0845528
$689$	1.97767e11	0.0334324
$690$	−3.61046e12	−0.606376
$691$	7.67931e12	1.28136	0.640680	−	0.767808i	$-0.278653\pi$
$691$	7.67931e12	1.28136	0.640680	+	0.767808i	$0.278653\pi$
$692$	4.15315e12	0.688494
$693$	−1.25887e13	−2.07340
$694$	1.37835e13	2.25549
$695$	−5.78828e12	−0.941061
$696$	1.73694e12	0.280571
$697$	−4.37779e12	−0.702598
$698$	1.10334e13	1.75939
$699$	4.65445e11	0.0737431
$700$	4.04469e13	6.36713
$701$	8.75891e12	1.37000	0.684998	−	0.728545i	$-0.259803\pi$
$701$	8.75891e12	1.37000	0.684998	+	0.728545i	$0.259803\pi$
$702$	2.53029e11	0.0393236
$703$	7.69189e12	1.18778
$704$	−9.24029e12	−1.41778
$705$	−5.18750e11	−0.0790874
$706$	−1.78028e12	−0.269691
$707$	1.43278e13	2.15671
$708$	2.01095e12	0.300782
$709$	−1.07452e13	−1.59700	−0.798500	−	0.601995i	$-0.794373\pi$
$709$	−1.07452e13	−1.59700	−0.798500	+	0.601995i	$0.794373\pi$
$710$	−3.19275e13	−4.71522
$711$	−4.36258e12	−0.640222
$712$	1.03653e13	1.51155
$713$	−6.65724e12	−0.964697
$714$	−3.72265e12	−0.536056
$715$	−1.55716e12	−0.222820
$716$	1.03326e13	1.46927
$717$	−8.01306e11	−0.113230
$718$	−1.09409e13	−1.53636
$719$	1.12130e12	0.156474	0.0782368	−	0.996935i	$-0.475071\pi$
$719$	1.12130e12	0.156474	0.0782368	+	0.996935i	$0.475071\pi$
$720$	−1.19736e13	−1.66047
$721$	1.86119e13	2.56496
$722$	−7.09707e12	−0.971990
$723$	1.29630e12	0.176435
$724$	−1.80167e12	−0.243698
$725$	2.06338e13	2.77369
$726$	1.37739e12	0.184010
$727$	−3.60906e12	−0.479170	−0.239585	−	0.970875i	$-0.577011\pi$
$727$	−3.60906e12	−0.479170	−0.239585	+	0.970875i	$0.577011\pi$
$728$	1.85442e12	0.244691
$729$	−6.93955e12	−0.910034
$730$	−1.93814e13	−2.52600
$731$	−1.10862e12	−0.143600
$732$	−1.17727e12	−0.151556
$733$	−5.23171e12	−0.669385	−0.334692	−	0.942327i	$-0.608632\pi$
$733$	−5.23171e12	−0.669385	−0.334692	+	0.942327i	$0.608632\pi$
$734$	5.94889e12	0.756491
$735$	−2.35724e12	−0.297927
$736$	−5.78683e11	−0.0726927
$737$	1.24453e13	1.55383
$738$	5.90421e12	0.732669
$739$	−1.21367e13	−1.49693	−0.748463	−	0.663176i	$-0.769208\pi$
$739$	−1.21367e13	−1.49693	−0.748463	+	0.663176i	$0.769208\pi$
$740$	−2.70212e13	−3.31254
$741$	−1.17597e11	−0.0143290
$742$	7.90876e12	0.957835
$743$	−2.69383e12	−0.324280	−0.162140	−	0.986768i	$-0.551840\pi$
$743$	−2.69383e12	−0.324280	−0.162140	+	0.986768i	$0.551840\pi$
$744$	1.04431e12	0.124955
$745$	−6.11602e11	−0.0727388
$746$	−2.08181e13	−2.46103
$747$	−1.19252e13	−1.40127
$748$	−3.79083e13	−4.42769
$749$	1.38079e13	1.60309
$750$	3.49036e12	0.402805
$751$	−1.66962e13	−1.91531	−0.957654	−	0.287923i	$-0.907035\pi$
$751$	−1.66962e13	−1.91531	−0.957654	+	0.287923i	$0.907035\pi$
$752$	3.08299e12	0.351554
$753$	−1.11389e12	−0.126260
$754$	1.90456e12	0.214596
$755$	4.31601e12	0.483416
$756$	6.73107e12	0.749439
$757$	−1.28404e13	−1.42117	−0.710585	−	0.703612i	$-0.751569\pi$
$757$	−1.28404e13	−1.42117	−0.710585	+	0.703612i	$0.751569\pi$
$758$	2.26255e13	2.48936
$759$	2.49633e12	0.273032
$760$	3.44037e13	3.74062
$761$	4.93199e12	0.533078	0.266539	−	0.963824i	$-0.414120\pi$
$761$	4.93199e12	0.533078	0.266539	+	0.963824i	$0.414120\pi$
$762$	6.54324e11	0.0703065
$763$	2.00002e13	2.13636
$764$	5.33893e12	0.566936
$765$	2.67137e13	2.82005
$766$	−1.63773e13	−1.71875
$767$	1.09527e12	0.114272
$768$	2.35947e12	0.244730
$769$	1.14024e13	1.17578	0.587892	−	0.808940i	$-0.299958\pi$
$769$	1.14024e13	1.17578	0.587892	+	0.808940i	$0.299958\pi$
$770$	−6.22711e13	−6.38379
$771$	1.73173e12	0.176497
$772$	−2.49535e13	−2.52845
$773$	1.58119e12	0.159286	0.0796429	−	0.996823i	$-0.474622\pi$
$773$	1.58119e12	0.159286	0.0796429	+	0.996823i	$0.474622\pi$
$774$	1.49517e12	0.149746
$775$	1.24058e13	1.23529
$776$	2.34033e13	2.31686
$777$	1.83468e12	0.180578
$778$	1.02234e13	1.00043
$779$	−5.53037e12	−0.538066
$780$	4.13112e11	0.0399616
$781$	2.20751e13	2.12312
$782$	−4.78723e13	−4.57777
$783$	3.43383e12	0.326475
$784$	1.40093e13	1.32433
$785$	2.55831e13	2.40458
$786$	4.09958e12	0.383123
$787$	−1.41046e12	−0.131061	−0.0655305	−	0.997851i	$-0.520874\pi$
$787$	−1.41046e12	−0.131061	−0.0655305	+	0.997851i	$0.520874\pi$
$788$	−2.53298e13	−2.34026
$789$	−1.77107e12	−0.162700
$790$	−2.15798e13	−1.97118
$791$	6.61710e11	0.0600999
$792$	2.53952e13	2.29344
$793$	−6.41200e11	−0.0575790
$794$	8.59755e12	0.767684
$795$	8.75139e11	0.0777007
$796$	−2.76981e13	−2.44535
$797$	−1.00612e13	−0.883254	−0.441627	−	0.897199i	$-0.645599\pi$
$797$	−1.00612e13	−0.883254	−0.441627	+	0.897199i	$0.645599\pi$
$798$	−4.70275e12	−0.410524
$799$	−6.87828e12	−0.597061
$800$	1.07838e12	0.0930823
$801$	1.01674e13	0.872700
$802$	−1.71263e13	−1.46177
$803$	1.34006e13	1.13738
$804$	−3.30173e12	−0.278670
$805$	−5.23113e13	−4.39050
$806$	1.14509e12	0.0955723
$807$	−1.22478e12	−0.101655
$808$	−2.89033e13	−2.38559
$809$	2.08330e13	1.70995	0.854973	−	0.518672i	$-0.173573\pi$
$809$	2.08330e13	1.70995	0.854973	+	0.518672i	$0.173573\pi$
$810$	−3.54639e13	−2.89470
$811$	−7.75040e12	−0.629116	−0.314558	−	0.949238i	$-0.601856\pi$
$811$	−7.75040e12	−0.629116	−0.314558	+	0.949238i	$0.601856\pi$
$812$	5.06649e13	4.08983
$813$	2.89908e11	0.0232731
$814$	2.80856e13	2.24220
$815$	3.33196e13	2.64540
$816$	2.44813e12	0.193299
$817$	−1.40050e12	−0.109972
$818$	−1.56469e13	−1.22191
$819$	1.81902e12	0.141273
$820$	1.94279e13	1.50059
$821$	−2.29893e13	−1.76597	−0.882983	−	0.469405i	$-0.844468\pi$
$821$	−2.29893e13	−1.76597	−0.882983	+	0.469405i	$0.844468\pi$
$822$	3.62862e12	0.277216
$823$	2.34721e13	1.78342	0.891708	−	0.452612i	$-0.149508\pi$
$823$	2.34721e13	1.78342	0.891708	+	0.452612i	$0.149508\pi$
$824$	−3.75455e13	−2.83717
$825$	−4.65193e12	−0.349615
$826$	4.38001e13	3.27390
$827$	−1.52851e13	−1.13630	−0.568150	−	0.822925i	$-0.692341\pi$
$827$	−1.52851e13	−1.13630	−0.568150	+	0.822925i	$0.692341\pi$
$828$	4.29488e13	3.17551
$829$	−4.12646e12	−0.303447	−0.151723	−	0.988423i	$-0.548482\pi$
$829$	−4.12646e12	−0.303447	−0.151723	+	0.988423i	$0.548482\pi$
$830$	−5.89886e13	−4.31436
$831$	3.84119e11	0.0279422
$832$	1.33518e12	0.0966019
$833$	−3.12554e13	−2.24917
$834$	−1.59612e12	−0.114240
$835$	−2.91139e13	−2.07258
$836$	−4.78888e13	−3.39083
$837$	2.06455e12	0.145399
$838$	9.23195e12	0.646689
$839$	8.77162e11	0.0611155	0.0305577	−	0.999533i	$-0.490272\pi$
$839$	8.77162e11	0.0611155	0.0305577	+	0.999533i	$0.490272\pi$
$840$	8.20601e12	0.568690
$841$	1.13393e13	0.781638
$842$	2.59276e13	1.77770
$843$	−1.06382e12	−0.0725510
$844$	2.01645e12	0.136788
$845$	−2.57760e13	−1.73924
$846$	9.27655e12	0.622615
$847$	1.99567e13	1.33234
$848$	−5.20105e12	−0.345390
$849$	6.54666e11	0.0432449
$850$	8.92105e13	5.86180
$851$	2.35935e13	1.54209
$852$	−5.85652e12	−0.380769
$853$	8.26622e12	0.534609	0.267305	−	0.963612i	$-0.413867\pi$
$853$	8.26622e12	0.534609	0.267305	+	0.963612i	$0.413867\pi$
$854$	−2.56418e13	−1.64963
$855$	3.37469e13	2.15966
$856$	−2.78545e13	−1.77322
$857$	−2.80318e13	−1.77516	−0.887580	−	0.460654i	$-0.847615\pi$
$857$	−2.80318e13	−1.77516	−0.887580	+	0.460654i	$0.847615\pi$
$858$	−4.29386e11	−0.0270492
$859$	−5.96424e12	−0.373754	−0.186877	−	0.982383i	$-0.559837\pi$
$859$	−5.96424e12	−0.373754	−0.186877	+	0.982383i	$0.559837\pi$
$860$	4.91987e12	0.306698
$861$	−1.31911e12	−0.0818026
$862$	9.16371e12	0.565313
$863$	−1.55949e13	−0.957050	−0.478525	−	0.878074i	$-0.658828\pi$
$863$	−1.55949e13	−0.957050	−0.478525	+	0.878074i	$0.658828\pi$
$864$	1.79461e11	0.0109562
$865$	1.00097e13	0.607921
$866$	2.46069e13	1.48671
$867$	−3.41163e12	−0.205058
$868$	3.04617e13	1.82144
$869$	1.49206e13	0.887560
$870$	8.42785e12	0.498747
$871$	−1.79830e12	−0.105872
$872$	−4.03462e13	−2.36308
$873$	2.29565e13	1.33765
$874$	−6.04761e13	−3.50576
$875$	5.05712e13	2.91653
$876$	−3.55517e12	−0.203982
$877$	−1.88559e13	−1.07634	−0.538168	−	0.842837i	$-0.680884\pi$
$877$	−1.88559e13	−1.07634	−0.538168	+	0.842837i	$0.680884\pi$
$878$	3.57745e12	0.203165
$879$	9.69724e11	0.0547896
$880$	4.09514e13	2.30196
$881$	2.95083e13	1.65026	0.825130	−	0.564943i	$-0.191102\pi$
$881$	2.95083e13	1.65026	0.825130	+	0.564943i	$0.191102\pi$
$882$	4.21533e13	2.34543
$883$	9.10640e11	0.0504108	0.0252054	−	0.999682i	$-0.491976\pi$
$883$	9.10640e11	0.0504108	0.0252054	+	0.999682i	$0.491976\pi$
$884$	5.47759e12	0.301686
$885$	4.84667e12	0.265582
$886$	−6.11181e12	−0.333210
$887$	2.72363e13	1.47738	0.738690	−	0.674046i	$-0.235445\pi$
$887$	2.72363e13	1.47738	0.738690	+	0.674046i	$0.235445\pi$
$888$	−3.70108e12	−0.199743
$889$	9.48038e12	0.509058
$890$	5.02939e13	2.68696
$891$	2.45203e13	1.30339
$892$	5.94610e13	3.14478
$893$	−8.68919e12	−0.457244
$894$	−1.68649e11	−0.00883010
$895$	2.49031e13	1.29733
$896$	5.20617e13	2.69856
$897$	−3.60709e11	−0.0186033
$898$	−1.83159e13	−0.939905
$899$	1.55399e13	0.793468
$900$	−8.00354e13	−4.06622
$901$	1.16037e13	0.586593
$902$	−2.01932e13	−1.01572
$903$	−3.34049e11	−0.0167192
$904$	−1.33486e12	−0.0664780
$905$	−4.34228e12	−0.215179
$906$	1.19014e12	0.0586841
$907$	−2.92798e13	−1.43660	−0.718299	−	0.695735i	$-0.755079\pi$
$907$	−2.92798e13	−1.43660	−0.718299	+	0.695735i	$0.755079\pi$
$908$	1.36302e13	0.665452
$909$	−2.83514e13	−1.37733
$910$	8.99791e12	0.434966
$911$	−3.70164e13	−1.78058	−0.890290	−	0.455394i	$-0.849499\pi$
$911$	−3.70164e13	−1.78058	−0.890290	+	0.455394i	$0.849499\pi$
$912$	3.09268e12	0.148033
$913$	4.07856e13	1.94262
$914$	3.01154e13	1.42735
$915$	−2.83737e12	−0.133820
$916$	3.35307e13	1.57367
$917$	5.93981e13	2.77402
$918$	1.48462e13	0.689958
$919$	5.73808e12	0.265367	0.132683	−	0.991158i	$-0.457641\pi$
$919$	5.73808e12	0.265367	0.132683	+	0.991158i	$0.457641\pi$
$920$	1.05527e14	4.85645
$921$	4.59148e12	0.210274
$922$	−2.93752e13	−1.33872
$923$	−3.18976e12	−0.144661
$924$	−1.14225e13	−0.515511
$925$	−4.39667e13	−1.97463
$926$	−5.51996e13	−2.46710
$927$	−3.68287e13	−1.63805
$928$	1.35081e12	0.0597900
$929$	−1.49825e13	−0.659954	−0.329977	−	0.943989i	$-0.607041\pi$
$929$	−1.49825e13	−0.659954	−0.329977	+	0.943989i	$0.607041\pi$
$930$	5.06714e12	0.222121
$931$	−3.94843e13	−1.72247
$932$	−2.73880e13	−1.18902
$933$	−1.33719e12	−0.0577731
$934$	3.47088e13	1.49238
$935$	−9.13643e13	−3.90953
$936$	−3.66949e12	−0.156266
$937$	1.07426e13	0.455283	0.227642	−	0.973745i	$-0.426899\pi$
$937$	1.07426e13	0.455283	0.227642	+	0.973745i	$0.426899\pi$
$938$	−7.19144e13	−3.03321
$939$	1.71492e12	0.0719863
$940$	3.05246e13	1.27519
$941$	2.02239e13	0.840839	0.420419	−	0.907330i	$-0.361883\pi$
$941$	2.02239e13	0.840839	0.420419	+	0.907330i	$0.361883\pi$
$942$	7.05453e12	0.291903
$943$	−1.69634e13	−0.698571
$944$	−2.88043e13	−1.18055
$945$	1.62228e13	0.661734
$946$	−5.11368e12	−0.207598
$947$	3.97192e13	1.60482	0.802408	−	0.596776i	$-0.203552\pi$
$947$	3.97192e13	1.60482	0.802408	+	0.596776i	$0.203552\pi$
$948$	−3.95843e12	−0.159179
$949$	−1.93633e12	−0.0774964
$950$	1.12698e14	4.48910
$951$	−2.89784e12	−0.114885
$952$	1.08806e14	4.29326
$953$	2.45154e13	0.962766	0.481383	−	0.876510i	$-0.340135\pi$
$953$	2.45154e13	0.962766	0.481383	+	0.876510i	$0.340135\pi$
$954$	−1.56497e13	−0.611699
$955$	1.28676e13	0.500589
$956$	4.71509e13	1.82570
$957$	−5.82714e12	−0.224570
$958$	−2.99504e13	−1.14884
$959$	5.25745e13	2.00720
$960$	5.90832e12	0.224514
$961$	−1.70965e13	−0.646623
$962$	−4.05825e12	−0.152774
$963$	−2.73227e13	−1.02378
$964$	−7.62778e13	−2.84480
$965$	−6.01414e13	−2.23255
$966$	−1.44248e13	−0.532984
$967$	3.84204e13	1.41300	0.706500	−	0.707713i	$-0.250273\pi$
$967$	3.84204e13	1.41300	0.706500	+	0.707713i	$0.250273\pi$
$968$	−4.02585e13	−1.47373
$969$	−6.89989e12	−0.251411
$970$	1.13556e14	4.11848
$971$	−2.16062e13	−0.779993	−0.389997	−	0.920816i	$-0.627524\pi$
$971$	−2.16062e13	−0.779993	−0.389997	+	0.920816i	$0.627524\pi$
$972$	−2.00299e13	−0.719748
$973$	−2.31258e13	−0.827160
$974$	5.84077e13	2.07948
$975$	6.72184e11	0.0238214
$976$	1.68628e13	0.594848
$977$	−8.02443e12	−0.281766	−0.140883	−	0.990026i	$-0.544994\pi$
$977$	−8.02443e12	−0.281766	−0.140883	+	0.990026i	$0.544994\pi$
$978$	9.18788e12	0.321137
$979$	−3.47740e13	−1.20985
$980$	1.38706e14	4.80372
$981$	−3.95760e13	−1.36433
$982$	1.38403e13	0.474944
$983$	−3.78430e13	−1.29269	−0.646346	−	0.763045i	$-0.723704\pi$
$983$	−3.78430e13	−1.29269	−0.646346	+	0.763045i	$0.723704\pi$
$984$	2.66103e12	0.0904840
$985$	−6.10484e13	−2.06638
$986$	1.11748e14	3.76523
$987$	−2.07256e12	−0.0695151
$988$	6.91973e12	0.231038
$989$	−4.29578e12	−0.142777
$990$	1.23221e14	4.07685
$991$	1.62752e13	0.536036	0.268018	−	0.963414i	$-0.413631\pi$
$991$	1.62752e13	0.536036	0.268018	+	0.963414i	$0.413631\pi$
$992$	8.12159e11	0.0266280
$993$	4.11314e12	0.134246
$994$	−1.27560e14	−4.14452
$995$	−6.67562e13	−2.15918
$996$	−1.08204e13	−0.348398
$997$	−2.80852e13	−0.900220	−0.450110	−	0.892973i	$-0.648615\pi$
$997$	−2.80852e13	−0.900220	−0.450110	+	0.892973i	$0.648615\pi$
$998$	3.39731e13	1.08405
$999$	−7.31683e12	−0.232423

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	211.10.a.b.1.7	✓	82

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
211.10.a.b.1.7	✓	82	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 211 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	211.a (trivial)

\(f(q)\)	\(=\)	\(q-39.1065 q^{2} -17.2889 q^{3} +1017.32 q^{4} +2451.89 q^{5} +676.107 q^{6} +9796.00 q^{7} -19761.4 q^{8} -19384.1 q^{9} +O(q^{10})\)	\(q-39.1065 q^{2} -17.2889 q^{3} +1017.32 q^{4} +2451.89 q^{5} +676.107 q^{6} +9796.00 q^{7} -19761.4 q^{8} -19384.1 q^{9} -95884.8 q^{10} +66296.2 q^{11} -17588.3 q^{12} -9579.51 q^{13} -383088. q^{14} -42390.3 q^{15} +251930. q^{16} -562067. q^{17} +758045. q^{18} -710048. q^{19} +2.49436e6 q^{20} -169362. q^{21} -2.59261e6 q^{22} -2.17794e6 q^{23} +341652. q^{24} +4.05862e6 q^{25} +374622. q^{26} +675425. q^{27} +9.96568e6 q^{28} +5.08394e6 q^{29} +1.65774e6 q^{30} +3.05666e6 q^{31} +265701. q^{32} -1.14618e6 q^{33} +2.19805e7 q^{34} +2.40187e7 q^{35} -1.97199e7 q^{36} -1.08329e7 q^{37} +2.77675e7 q^{38} +165619. q^{39} -4.84526e7 q^{40} +7.78873e6 q^{41} +6.62315e6 q^{42} +1.97240e6 q^{43} +6.74445e7 q^{44} -4.75276e7 q^{45} +8.51719e7 q^{46} +1.22375e7 q^{47} -4.35559e6 q^{48} +5.56079e7 q^{49} -1.58719e8 q^{50} +9.71749e6 q^{51} -9.74544e6 q^{52} -2.06448e7 q^{53} -2.64136e7 q^{54} +1.62551e8 q^{55} -1.93582e8 q^{56} +1.22759e7 q^{57} -1.98815e8 q^{58} -1.14334e8 q^{59} -4.31246e7 q^{60} +6.69345e7 q^{61} -1.19535e8 q^{62} -1.89887e8 q^{63} -1.39379e8 q^{64} -2.34879e7 q^{65} +4.48233e7 q^{66} +1.87723e8 q^{67} -5.71803e8 q^{68} +3.76542e7 q^{69} -9.39287e8 q^{70} +3.32978e8 q^{71} +3.83056e8 q^{72} +2.02133e8 q^{73} +4.23638e8 q^{74} -7.01689e7 q^{75} -7.22347e8 q^{76} +6.49437e8 q^{77} -6.47678e6 q^{78} +2.25060e8 q^{79} +6.17704e8 q^{80} +3.69860e8 q^{81} -3.04590e8 q^{82} +6.15203e8 q^{83} -1.72295e8 q^{84} -1.37812e9 q^{85} -7.71338e7 q^{86} -8.78956e7 q^{87} -1.31010e9 q^{88} -5.24525e8 q^{89} +1.85864e9 q^{90} -9.38409e7 q^{91} -2.21567e9 q^{92} -5.28462e7 q^{93} -4.78565e8 q^{94} -1.74096e9 q^{95} -4.59367e6 q^{96} -1.18430e9 q^{97} -2.17463e9 q^{98} -1.28509e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 82 q + 48 q^{2} + 331 q^{3} + 22272 q^{4} + 11249 q^{5} + 9392 q^{6} + 6632 q^{7} + 36864 q^{8} + 630129 q^{9}+O(q^{10}) \) 82 * q + 48 * q^2 + 331 * q^3 + 22272 * q^4 + 11249 * q^5 + 9392 * q^6 + 6632 * q^7 + 36864 * q^8 + 630129 * q^9	\( 82 q + 48 q^{2} + 331 q^{3} + 22272 q^{4} + 11249 q^{5} + 9392 q^{6} + 6632 q^{7} + 36864 q^{8} + 630129 q^{9} + 73920 q^{10} + 255733 q^{11} + 262929 q^{12} + 291015 q^{13} + 599651 q^{14} + 151566 q^{15} + 6088388 q^{16} + 1450152 q^{17} + 1803076 q^{18} + 1658423 q^{19} + 5677520 q^{20} + 4437026 q^{21} + 402001 q^{22} + 4279922 q^{23} + 8660330 q^{24} + 36692027 q^{25} + 14084490 q^{26} + 11692912 q^{27} + 1686063 q^{28} + 28121309 q^{29} + 22795315 q^{30} + 8118600 q^{31} + 13477081 q^{32} + 17174434 q^{33} + 19372534 q^{34} + 37542780 q^{35} + 215622860 q^{36} + 50413779 q^{37} + 58031367 q^{38} + 23234242 q^{39} + 58731852 q^{40} + 103434140 q^{41} + 15334009 q^{42} + 34281571 q^{43} + 183086279 q^{44} + 235979107 q^{45} + 149265183 q^{46} + 93000602 q^{47} + 114303721 q^{48} + 570480578 q^{49} + 222019553 q^{50} + 77929810 q^{51} + 79999859 q^{52} + 407531048 q^{53} + 1321436783 q^{54} + 449488153 q^{55} + 756123028 q^{56} + 335002024 q^{57} + 481532629 q^{58} + 570753278 q^{59} - 244569748 q^{60} + 694734563 q^{61} - 73212918 q^{62} - 540500692 q^{63} + 194355770 q^{64} + 53860661 q^{65} - 737702157 q^{66} - 162897225 q^{67} - 1298035011 q^{68} + 602016364 q^{69} - 3064991165 q^{70} + 323986036 q^{71} - 1711822491 q^{72} - 1077391483 q^{73} - 683958107 q^{74} - 1166367949 q^{75} - 478318455 q^{76} + 1584572500 q^{77} - 5134824150 q^{78} + 342296112 q^{79} + 1441041507 q^{80} + 5540929446 q^{81} - 1240907573 q^{82} + 1202053700 q^{83} - 1781018244 q^{84} + 312682194 q^{85} - 305650461 q^{86} + 1589558614 q^{87} + 1034360734 q^{88} + 3298871808 q^{89} + 1695581030 q^{90} + 1989076496 q^{91} + 3997408364 q^{92} + 2435977176 q^{93} + 2258199495 q^{94} + 4724645555 q^{95} + 9729772859 q^{96} + 2626833632 q^{97} + 7407181902 q^{98} + 6900390127 q^{99}+O(q^{100}) \) 82 * q + 48 * q^2 + 331 * q^3 + 22272 * q^4 + 11249 * q^5 + 9392 * q^6 + 6632 * q^7 + 36864 * q^8 + 630129 * q^9 + 73920 * q^10 + 255733 * q^11 + 262929 * q^12 + 291015 * q^13 + 599651 * q^14 + 151566 * q^15 + 6088388 * q^16 + 1450152 * q^17 + 1803076 * q^18 + 1658423 * q^19 + 5677520 * q^20 + 4437026 * q^21 + 402001 * q^22 + 4279922 * q^23 + 8660330 * q^24 + 36692027 * q^25 + 14084490 * q^26 + 11692912 * q^27 + 1686063 * q^28 + 28121309 * q^29 + 22795315 * q^30 + 8118600 * q^31 + 13477081 * q^32 + 17174434 * q^33 + 19372534 * q^34 + 37542780 * q^35 + 215622860 * q^36 + 50413779 * q^37 + 58031367 * q^38 + 23234242 * q^39 + 58731852 * q^40 + 103434140 * q^41 + 15334009 * q^42 + 34281571 * q^43 + 183086279 * q^44 + 235979107 * q^45 + 149265183 * q^46 + 93000602 * q^47 + 114303721 * q^48 + 570480578 * q^49 + 222019553 * q^50 + 77929810 * q^51 + 79999859 * q^52 + 407531048 * q^53 + 1321436783 * q^54 + 449488153 * q^55 + 756123028 * q^56 + 335002024 * q^57 + 481532629 * q^58 + 570753278 * q^59 - 244569748 * q^60 + 694734563 * q^61 - 73212918 * q^62 - 540500692 * q^63 + 194355770 * q^64 + 53860661 * q^65 - 737702157 * q^66 - 162897225 * q^67 - 1298035011 * q^68 + 602016364 * q^69 - 3064991165 * q^70 + 323986036 * q^71 - 1711822491 * q^72 - 1077391483 * q^73 - 683958107 * q^74 - 1166367949 * q^75 - 478318455 * q^76 + 1584572500 * q^77 - 5134824150 * q^78 + 342296112 * q^79 + 1441041507 * q^80 + 5540929446 * q^81 - 1240907573 * q^82 + 1202053700 * q^83 - 1781018244 * q^84 + 312682194 * q^85 - 305650461 * q^86 + 1589558614 * q^87 + 1034360734 * q^88 + 3298871808 * q^89 + 1695581030 * q^90 + 1989076496 * q^91 + 3997408364 * q^92 + 2435977176 * q^93 + 2258199495 * q^94 + 4724645555 * q^95 + 9729772859 * q^96 + 2626833632 * q^97 + 7407181902 * q^98 + 6900390127 * q^99

Introduction

L-functions

Modular forms

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