LMFDB - Embedded newform 91.10.a.a.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,10,Mod(1,91)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(91, 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("91.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	91.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:	$46.8682610909$
Analytic rank:	$1$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} - 4522 x^{10} + 11094 x^{9} + 7471016 x^{8} - 18339296 x^{7} - 5497728352 x^{6} + \cdots + 170905444356096 $ x^12 - 3x^11 - 4522x^10 + 11094x^9 + 7471016x^8 - 18339296x^7 - 5497728352x^6 + 13724467264x^5 + 1698856105344x^4 - 3404524011264x^3 - 154369782114304x^2 + 70325953652224*x + 170905444356096
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{9}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-0.857959$ of defining polynomial
Character	$\chi$	$=$	91.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.85796 q^{2} +143.668 q^{3} -503.832 q^{4} -15.3125 q^{5} -410.598 q^{6} +2401.00 q^{7} +2903.21 q^{8} +957.575 q^{9} +O(q^{10})$	\(q-2.85796 q^{2} +143.668 q^{3} -503.832 q^{4} -15.3125 q^{5} -410.598 q^{6} +2401.00 q^{7} +2903.21 q^{8} +957.575 q^{9} +43.7625 q^{10} -2617.92 q^{11} -72384.7 q^{12} +28561.0 q^{13} -6861.96 q^{14} -2199.92 q^{15} +249665. q^{16} +86313.3 q^{17} -2736.71 q^{18} -90449.5 q^{19} +7714.92 q^{20} +344948. q^{21} +7481.92 q^{22} -855540. q^{23} +417099. q^{24} -1.95289e6 q^{25} -81626.2 q^{26} -2.69025e6 q^{27} -1.20970e6 q^{28} +1.60148e6 q^{29} +6287.28 q^{30} -2.47079e6 q^{31} -2.19997e6 q^{32} -376112. q^{33} -246680. q^{34} -36765.3 q^{35} -482457. q^{36} +1.00763e6 q^{37} +258501. q^{38} +4.10331e6 q^{39} -44455.3 q^{40} -3.12371e7 q^{41} -985846. q^{42} +1.84833e7 q^{43} +1.31899e6 q^{44} -14662.9 q^{45} +2.44510e6 q^{46} +2.65637e6 q^{47} +3.58689e7 q^{48} +5.76480e6 q^{49} +5.58128e6 q^{50} +1.24005e7 q^{51} -1.43899e7 q^{52} -6.38851e7 q^{53} +7.68862e6 q^{54} +40086.9 q^{55} +6.97060e6 q^{56} -1.29947e7 q^{57} -4.57696e6 q^{58} -1.84110e7 q^{59} +1.10839e6 q^{60} -9.45649e7 q^{61} +7.06143e6 q^{62} +2.29914e6 q^{63} -1.21541e8 q^{64} -437340. q^{65} +1.07491e6 q^{66} -1.40600e8 q^{67} -4.34874e7 q^{68} -1.22914e8 q^{69} +105074. q^{70} -2.69191e8 q^{71} +2.78004e6 q^{72} -1.26381e8 q^{73} -2.87978e6 q^{74} -2.80568e8 q^{75} +4.55713e7 q^{76} -6.28563e6 q^{77} -1.17271e7 q^{78} -4.38026e8 q^{79} -3.82299e6 q^{80} -4.05351e8 q^{81} +8.92745e7 q^{82} -3.83977e7 q^{83} -1.73796e8 q^{84} -1.32167e6 q^{85} -5.28244e7 q^{86} +2.30082e8 q^{87} -7.60037e6 q^{88} -2.45390e8 q^{89} +41905.8 q^{90} +6.85750e7 q^{91} +4.31048e8 q^{92} -3.54975e8 q^{93} -7.59181e6 q^{94} +1.38501e6 q^{95} -3.16066e8 q^{96} +4.47528e8 q^{97} -1.64756e7 q^{98} -2.50686e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 21 q^{2} - 323 q^{3} + 2945 q^{4} - 5202 q^{5} - 9897 q^{6} + 28812 q^{7} - 25431 q^{8} + 78519 q^{9}+O(q^{10}) $ 12 * q - 21 * q^2 - 323 * q^3 + 2945 * q^4 - 5202 * q^5 - 9897 * q^6 + 28812 * q^7 - 25431 * q^8 + 78519 * q^9	\( 12 q - 21 q^{2} - 323 q^{3} + 2945 q^{4} - 5202 q^{5} - 9897 q^{6} + 28812 q^{7} - 25431 q^{8} + 78519 q^{9} - 65812 q^{10} - 80061 q^{11} - 184395 q^{12} + 342732 q^{13} - 50421 q^{14} + 160096 q^{15} + 385497 q^{16} - 1493598 q^{17} + 1520858 q^{18} - 109038 q^{19} - 622260 q^{20} - 775523 q^{21} + 4636975 q^{22} - 3367443 q^{23} - 5963895 q^{24} - 51480 q^{25} - 599781 q^{26} - 8158937 q^{27} + 7070945 q^{28} - 13333098 q^{29} + 2915424 q^{30} - 3954765 q^{31} + 4389297 q^{32} - 5790219 q^{33} + 14879968 q^{34} - 12490002 q^{35} + 80697058 q^{36} + 580535 q^{37} - 19134246 q^{38} - 9225203 q^{39} + 12365024 q^{40} - 27018171 q^{41} - 23762697 q^{42} + 31237588 q^{43} - 125053839 q^{44} - 62765470 q^{45} - 114008121 q^{46} - 21983709 q^{47} - 309724207 q^{48} + 69177612 q^{49} - 131331747 q^{50} - 176522692 q^{51} + 84112145 q^{52} - 196548234 q^{53} - 456152547 q^{54} - 309055872 q^{55} - 61059831 q^{56} - 274411494 q^{57} - 521980612 q^{58} - 215907906 q^{59} - 177006648 q^{60} - 218340705 q^{61} - 673289997 q^{62} + 188524119 q^{63} - 386667247 q^{64} - 148574322 q^{65} - 777397365 q^{66} + 14544775 q^{67} - 1246637448 q^{68} - 65252625 q^{69} - 158014612 q^{70} - 552451776 q^{71} + 369379470 q^{72} - 349395159 q^{73} + 73591023 q^{74} + 329300747 q^{75} - 1036299002 q^{76} - 192226461 q^{77} - 282668217 q^{78} + 962249727 q^{79} - 1494536184 q^{80} + 874458108 q^{81} - 1417698067 q^{82} - 2032575912 q^{83} - 442732395 q^{84} - 411671064 q^{85} - 2139249420 q^{86} - 759642172 q^{87} + 558651957 q^{88} - 280821684 q^{89} - 5764700804 q^{90} + 822899532 q^{91} - 4491569571 q^{92} - 1729557923 q^{93} - 1591372165 q^{94} - 1282463328 q^{95} - 2148993055 q^{96} - 2115165937 q^{97} - 121060821 q^{98} - 3595669198 q^{99}+O(q^{100}) \) 12 * q - 21 * q^2 - 323 * q^3 + 2945 * q^4 - 5202 * q^5 - 9897 * q^6 + 28812 * q^7 - 25431 * q^8 + 78519 * q^9 - 65812 * q^10 - 80061 * q^11 - 184395 * q^12 + 342732 * q^13 - 50421 * q^14 + 160096 * q^15 + 385497 * q^16 - 1493598 * q^17 + 1520858 * q^18 - 109038 * q^19 - 622260 * q^20 - 775523 * q^21 + 4636975 * q^22 - 3367443 * q^23 - 5963895 * q^24 - 51480 * q^25 - 599781 * q^26 - 8158937 * q^27 + 7070945 * q^28 - 13333098 * q^29 + 2915424 * q^30 - 3954765 * q^31 + 4389297 * q^32 - 5790219 * q^33 + 14879968 * q^34 - 12490002 * q^35 + 80697058 * q^36 + 580535 * q^37 - 19134246 * q^38 - 9225203 * q^39 + 12365024 * q^40 - 27018171 * q^41 - 23762697 * q^42 + 31237588 * q^43 - 125053839 * q^44 - 62765470 * q^45 - 114008121 * q^46 - 21983709 * q^47 - 309724207 * q^48 + 69177612 * q^49 - 131331747 * q^50 - 176522692 * q^51 + 84112145 * q^52 - 196548234 * q^53 - 456152547 * q^54 - 309055872 * q^55 - 61059831 * q^56 - 274411494 * q^57 - 521980612 * q^58 - 215907906 * q^59 - 177006648 * q^60 - 218340705 * q^61 - 673289997 * q^62 + 188524119 * q^63 - 386667247 * q^64 - 148574322 * q^65 - 777397365 * q^66 + 14544775 * q^67 - 1246637448 * q^68 - 65252625 * q^69 - 158014612 * q^70 - 552451776 * q^71 + 369379470 * q^72 - 349395159 * q^73 + 73591023 * q^74 + 329300747 * q^75 - 1036299002 * q^76 - 192226461 * q^77 - 282668217 * q^78 + 962249727 * q^79 - 1494536184 * q^80 + 874458108 * q^81 - 1417698067 * q^82 - 2032575912 * q^83 - 442732395 * q^84 - 411671064 * q^85 - 2139249420 * q^86 - 759642172 * q^87 + 558651957 * q^88 - 280821684 * q^89 - 5764700804 * q^90 + 822899532 * q^91 - 4491569571 * q^92 - 1729557923 * q^93 - 1591372165 * q^94 - 1282463328 * q^95 - 2148993055 * q^96 - 2115165937 * q^97 - 121060821 * q^98 - 3595669198 * 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 $

$2$	−2.85796	−0.126305	−0.0631526	−	0.998004i	$-0.520115\pi$
$2$	−2.85796	−0.126305	−0.0631526	+	0.998004i	$0.520115\pi$
$3$	143.668	1.02404	0.512018	−	0.858975i	$-0.328898\pi$
$3$	143.668	1.02404	0.512018	+	0.858975i	$0.328898\pi$
$4$	−503.832	−0.984047
$5$	−15.3125	−0.0109567	−0.00547836	−	0.999985i	$-0.501744\pi$
$5$	−15.3125	−0.0109567	−0.00547836	+	0.999985i	$0.501744\pi$
$6$	−410.598	−0.129341
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	2903.21	0.250595
$9$	957.575	0.0486498
$10$	43.7625	0.00138389
$11$	−2617.92	−0.0539125	−0.0269563	−	0.999637i	$-0.508581\pi$
$11$	−2617.92	−0.0539125	−0.0269563	+	0.999637i	$0.508581\pi$
$12$	−72384.7	−1.00770
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	−6861.96	−0.0477389
$15$	−2199.92	−0.0112201
$16$	249665.	0.952396
$17$	86313.3	0.250644	0.125322	−	0.992116i	$-0.460004\pi$
$17$	86313.3	0.250644	0.125322	+	0.992116i	$0.460004\pi$
$18$	−2736.71	−0.00614473
$19$	−90449.5	−0.159226	−0.0796131	−	0.996826i	$-0.525368\pi$
$19$	−90449.5	−0.159226	−0.0796131	+	0.996826i	$0.525368\pi$
$20$	7714.92	0.0107819
$21$	344948.	0.387049
$22$	7481.92	0.00680943
$23$	−855540.	−0.637477	−0.318739	−	0.947843i	$-0.603259\pi$
$23$	−855540.	−0.637477	−0.318739	+	0.947843i	$0.603259\pi$
$24$	417099.	0.256619
$25$	−1.95289e6	−0.999880
$26$	−81626.2	−0.0350307
$27$	−2.69025e6	−0.974217
$28$	−1.20970e6	−0.371935
$29$	1.60148e6	0.420466	0.210233	−	0.977651i	$-0.432578\pi$
$29$	1.60148e6	0.420466	0.210233	+	0.977651i	$0.432578\pi$
$30$	6287.28	0.00141715
$31$	−2.47079e6	−0.480517	−0.240259	−	0.970709i	$-0.577232\pi$
$31$	−2.47079e6	−0.480517	−0.240259	+	0.970709i	$0.577232\pi$
$32$	−2.19997e6	−0.370888
$33$	−376112.	−0.0552084
$34$	−246680.	−0.0316576
$35$	−36765.3	−0.00414125
$36$	−482457.	−0.0478737
$37$	1.00763e6	0.0883884	0.0441942	−	0.999023i	$-0.485928\pi$
$37$	1.00763e6	0.0883884	0.0441942	+	0.999023i	$0.485928\pi$
$38$	258501.	0.0201111
$39$	4.10331e6	0.284017
$40$	−44455.3	−0.00274570
$41$	−3.12371e7	−1.72641	−0.863205	−	0.504854i	$-0.831546\pi$
$41$	−3.12371e7	−1.72641	−0.863205	+	0.504854i	$0.831546\pi$
$42$	−985846.	−0.0488863
$43$	1.84833e7	0.824462	0.412231	−	0.911079i	$-0.364750\pi$
$43$	1.84833e7	0.824462	0.412231	+	0.911079i	$0.364750\pi$
$44$	1.31899e6	0.0530525
$45$	−14662.9	−0.000533043 0
$46$	2.44510e6	0.0805167
$47$	2.65637e6	0.0794052	0.0397026	−	0.999212i	$-0.487359\pi$
$47$	2.65637e6	0.0794052	0.0397026	+	0.999212i	$0.487359\pi$
$48$	3.58689e7	0.975287
$49$	5.76480e6	0.142857
$50$	5.58128e6	0.126290
$51$	1.24005e7	0.256669
$52$	−1.43899e7	−0.272926
$53$	−6.38851e7	−1.11214	−0.556068	−	0.831137i	$-0.687691\pi$
$53$	−6.38851e7	−1.11214	−0.556068	+	0.831137i	$0.687691\pi$
$54$	7.68862e6	0.123049
$55$	40086.9	0.000590705 0
$56$	6.97060e6	0.0947161
$57$	−1.29947e7	−0.163053
$58$	−4.57696e6	−0.0531070
$59$	−1.84110e7	−0.197808	−0.0989040	−	0.995097i	$-0.531534\pi$
$59$	−1.84110e7	−0.197808	−0.0989040	+	0.995097i	$0.531534\pi$
$60$	1.10839e6	0.0110411
$61$	−9.45649e7	−0.874471	−0.437236	−	0.899347i	$-0.644042\pi$
$61$	−9.45649e7	−0.874471	−0.437236	+	0.899347i	$0.644042\pi$
$62$	7.06143e6	0.0606918
$63$	2.29914e6	0.0183879
$64$	−1.21541e8	−0.905550
$65$	−437340.	−0.00303885
$66$	1.07491e6	0.00697310
$67$	−1.40600e8	−0.852408	−0.426204	−	0.904627i	$-0.640149\pi$
$67$	−1.40600e8	−0.852408	−0.426204	+	0.904627i	$0.640149\pi$
$68$	−4.34874e7	−0.246645
$69$	−1.22914e8	−0.652800
$70$	105074.	0.000523061 0
$71$	−2.69191e8	−1.25718	−0.628590	−	0.777737i	$-0.716368\pi$
$71$	−2.69191e8	−1.25718	−0.628590	+	0.777737i	$0.716368\pi$
$72$	2.78004e6	0.0121914
$73$	−1.26381e8	−0.520869	−0.260435	−	0.965492i	$-0.583866\pi$
$73$	−1.26381e8	−0.520869	−0.260435	+	0.965492i	$0.583866\pi$
$74$	−2.87978e6	−0.0111639
$75$	−2.80568e8	−1.02391
$76$	4.55713e7	0.156686
$77$	−6.28563e6	−0.0203770
$78$	−1.17271e7	−0.0358727
$79$	−4.38026e8	−1.26526	−0.632628	−	0.774456i	$-0.718024\pi$
$79$	−4.38026e8	−1.26526	−0.632628	+	0.774456i	$0.718024\pi$
$80$	−3.82299e6	−0.0104351
$81$	−4.05351e8	−1.04628
$82$	8.92745e7	0.218054
$83$	−3.83977e7	−0.0888084	−0.0444042	−	0.999014i	$-0.514139\pi$
$83$	−3.83977e7	−0.0888084	−0.0444042	+	0.999014i	$0.514139\pi$
$84$	−1.73796e8	−0.380875
$85$	−1.32167e6	−0.00274624
$86$	−5.28244e7	−0.104134
$87$	2.30082e8	0.430572
$88$	−7.60037e6	−0.0135102
$89$	−2.45390e8	−0.414574	−0.207287	−	0.978280i	$-0.566463\pi$
$89$	−2.45390e8	−0.414574	−0.207287	+	0.978280i	$0.566463\pi$
$90$	41905.8	6.73261e−5 0
$91$	6.85750e7	0.104828
$92$	4.31048e8	0.627308
$93$	−3.54975e8	−0.492067
$94$	−7.59181e6	−0.0100293
$95$	1.38501e6	0.00174460
$96$	−3.16066e8	−0.379802
$97$	4.47528e8	0.513272	0.256636	−	0.966508i	$-0.417386\pi$
$97$	4.47528e8	0.513272	0.256636	+	0.966508i	$0.417386\pi$
$98$	−1.64756e7	−0.0180436
$99$	−2.50686e6	−0.00262284
$100$	9.83929e8	0.983929
$101$	1.39090e9	1.32999	0.664995	−	0.746848i	$-0.268434\pi$
$101$	1.39090e9	1.32999	0.664995	+	0.746848i	$0.268434\pi$
$102$	−3.54401e7	−0.0324186
$103$	−1.82795e8	−0.160028	−0.0800140	−	0.996794i	$-0.525497\pi$
$103$	−1.82795e8	−0.160028	−0.0800140	+	0.996794i	$0.525497\pi$
$104$	8.29185e7	0.0695026
$105$	−5.28200e6	−0.00424079
$106$	1.82581e8	0.140468
$107$	9.74520e8	0.718727	0.359363	−	0.933198i	$-0.382994\pi$
$107$	9.74520e8	0.718727	0.359363	+	0.933198i	$0.382994\pi$
$108$	1.35543e9	0.958675
$109$	−5.98386e8	−0.406034	−0.203017	−	0.979175i	$-0.565075\pi$
$109$	−5.98386e8	−0.406034	−0.203017	+	0.979175i	$0.565075\pi$
$110$	−114567.	−7.46091e−5 0
$111$	1.44765e8	0.0905129
$112$	5.99445e8	0.359972
$113$	−4.67968e8	−0.270000	−0.135000	−	0.990846i	$-0.543103\pi$
$113$	−4.67968e8	−0.270000	−0.135000	+	0.990846i	$0.543103\pi$
$114$	3.71384e7	0.0205945
$115$	1.31004e7	0.00698466
$116$	−8.06877e8	−0.413758
$117$	2.73493e7	0.0134930
$118$	5.26179e7	0.0249842
$119$	2.07238e8	0.0947345
$120$	−6.38682e6	−0.00281170
$121$	−2.35109e9	−0.997093
$122$	2.70263e8	0.110450
$123$	−4.48779e9	−1.76791
$124$	1.24487e9	0.472851
$125$	5.98108e7	0.0219121
$126$	−6.57084e6	−0.00232249
$127$	−6.49754e8	−0.221632	−0.110816	−	0.993841i	$-0.535346\pi$
$127$	−6.49754e8	−0.221632	−0.110816	+	0.993841i	$0.535346\pi$
$128$	1.47375e9	0.485263
$129$	2.65546e9	0.844279
$130$	1.24990e6	0.000383822 0
$131$	3.34637e9	0.992782	0.496391	−	0.868099i	$-0.334658\pi$
$131$	3.34637e9	0.992782	0.496391	+	0.868099i	$0.334658\pi$
$132$	1.89498e8	0.0543276
$133$	−2.17169e8	−0.0601819
$134$	4.01828e8	0.107664
$135$	4.11944e7	0.0106742
$136$	2.50585e8	0.0628102
$137$	−4.28524e9	−1.03928	−0.519640	−	0.854386i	$-0.673934\pi$
$137$	−4.28524e9	−1.03928	−0.519640	+	0.854386i	$0.673934\pi$
$138$	3.51283e8	0.0824520
$139$	9.12782e8	0.207396	0.103698	−	0.994609i	$-0.466932\pi$
$139$	9.12782e8	0.207396	0.103698	+	0.994609i	$0.466932\pi$
$140$	1.85235e7	0.00407519
$141$	3.81637e8	0.0813138
$142$	7.69336e8	0.158788
$143$	−7.47705e7	−0.0149526
$144$	2.39073e8	0.0463339
$145$	−2.45226e7	−0.00460692
$146$	3.61191e8	0.0657884
$147$	8.28219e8	0.146291
$148$	−5.07678e8	−0.0869783
$149$	1.02262e10	1.69972	0.849859	−	0.527010i	$-0.176687\pi$
$149$	1.02262e10	1.69972	0.849859	+	0.527010i	$0.176687\pi$
$150$	8.01853e8	0.129325
$151$	2.84718e9	0.445675	0.222838	−	0.974856i	$-0.428468\pi$
$151$	2.84718e9	0.445675	0.222838	+	0.974856i	$0.428468\pi$
$152$	−2.62593e8	−0.0399014
$153$	8.26514e7	0.0121938
$154$	1.79641e7	0.00257372
$155$	3.78340e7	0.00526489
$156$	−2.06738e9	−0.279486
$157$	1.42852e10	1.87645	0.938224	−	0.346029i	$-0.112470\pi$
$157$	1.42852e10	1.87645	0.938224	+	0.346029i	$0.112470\pi$
$158$	1.25186e9	0.159808
$159$	−9.17826e9	−1.13887
$160$	3.36871e7	0.00406372
$161$	−2.05415e9	−0.240944
$162$	1.15848e9	0.132151
$163$	2.93151e9	0.325272	0.162636	−	0.986686i	$-0.448000\pi$
$163$	2.93151e9	0.325272	0.162636	+	0.986686i	$0.448000\pi$
$164$	1.57383e10	1.69887
$165$	5.75922e6	0.000604903 0
$166$	1.09739e8	0.0112170
$167$	1.14737e10	1.14151	0.570753	−	0.821121i	$-0.306651\pi$
$167$	1.14737e10	1.14151	0.570753	+	0.821121i	$0.306651\pi$
$168$	1.00145e9	0.0969927
$169$	8.15731e8	0.0769231
$170$	3.77728e6	0.000346864 0
$171$	−8.66121e7	−0.00774633
$172$	−9.31246e9	−0.811310
$173$	1.26545e10	1.07408	0.537042	−	0.843555i	$-0.319542\pi$
$173$	1.26545e10	1.07408	0.537042	+	0.843555i	$0.319542\pi$
$174$	−6.57564e8	−0.0543834
$175$	−4.68889e9	−0.377919
$176$	−6.53603e8	−0.0513461
$177$	−2.64508e9	−0.202563
$178$	7.01315e8	0.0523628
$179$	−1.03113e10	−0.750715	−0.375358	−	0.926880i	$-0.622480\pi$
$179$	−1.03113e10	−0.750715	−0.375358	+	0.926880i	$0.622480\pi$
$180$	7.38762e6	0.000524539 0
$181$	−8.02667e9	−0.555881	−0.277940	−	0.960598i	$-0.589652\pi$
$181$	−8.02667e9	−0.555881	−0.277940	+	0.960598i	$0.589652\pi$
$182$	−1.95984e8	−0.0132404
$183$	−1.35860e10	−0.895490
$184$	−2.48381e9	−0.159749
$185$	−1.54294e7	−0.000968447 0
$186$	1.01450e9	0.0621506
$187$	−2.25961e8	−0.0135129
$188$	−1.33837e9	−0.0781385
$189$	−6.45929e9	−0.368219
$190$	−3.95829e6	−0.000220352 0
$191$	3.21002e9	0.174525	0.0872626	−	0.996185i	$-0.472188\pi$
$191$	3.21002e9	0.174525	0.0872626	+	0.996185i	$0.472188\pi$
$192$	−1.74616e10	−0.927316
$193$	−4.45146e9	−0.230938	−0.115469	−	0.993311i	$-0.536837\pi$
$193$	−4.45146e9	−0.230938	−0.115469	+	0.993311i	$0.536837\pi$
$194$	−1.27902e9	−0.0648289
$195$	−6.28319e7	−0.00311189
$196$	−2.90449e9	−0.140578
$197$	−1.25795e10	−0.595064	−0.297532	−	0.954712i	$-0.596164\pi$
$197$	−1.25795e10	−0.595064	−0.297532	+	0.954712i	$0.596164\pi$
$198$	7.16450e6	0.000331278 0
$199$	1.73373e10	0.783685	0.391843	−	0.920032i	$-0.371838\pi$
$199$	1.73373e10	0.783685	0.391843	+	0.920032i	$0.371838\pi$
$200$	−5.66964e9	−0.250565
$201$	−2.01997e10	−0.872897
$202$	−3.97512e9	−0.167985
$203$	3.84515e9	0.158921
$204$	−6.24776e9	−0.252574
$205$	4.78318e8	0.0189158
$206$	5.22420e8	0.0202124
$207$	−8.19243e8	−0.0310132
$208$	7.13068e9	0.264147
$209$	2.36790e8	0.00858429
$210$	1.50958e7	0.000535634 0
$211$	−3.20449e10	−1.11298	−0.556490	−	0.830854i	$-0.687852\pi$
$211$	−3.20449e10	−1.11298	−0.556490	+	0.830854i	$0.687852\pi$
$212$	3.21873e10	1.09439
$213$	−3.86742e10	−1.28740
$214$	−2.78514e9	−0.0907789
$215$	−2.83025e8	−0.00903341
$216$	−7.81035e9	−0.244134
$217$	−5.93238e9	−0.181618
$218$	1.71016e9	0.0512842
$219$	−1.81569e10	−0.533389
$220$	−2.01971e7	−0.000581281 0
$221$	2.46519e9	0.0695161
$222$	−4.13733e8	−0.0114322
$223$	−4.67025e10	−1.26464	−0.632322	−	0.774705i	$-0.717898\pi$
$223$	−4.67025e10	−1.26464	−0.632322	+	0.774705i	$0.717898\pi$
$224$	−5.28214e9	−0.140182
$225$	−1.87004e9	−0.0486440
$226$	1.33743e9	0.0341023
$227$	−3.63837e10	−0.909475	−0.454737	−	0.890626i	$-0.650267\pi$
$227$	−3.63837e10	−0.909475	−0.454737	+	0.890626i	$0.650267\pi$
$228$	6.54716e9	0.160452
$229$	4.58774e10	1.10240	0.551200	−	0.834373i	$-0.314170\pi$
$229$	4.58774e10	1.10240	0.551200	+	0.834373i	$0.314170\pi$
$230$	−3.74405e7	−0.000882199 0
$231$	−9.03046e8	−0.0208668
$232$	4.64943e9	0.105367
$233$	4.92733e10	1.09524	0.547621	−	0.836727i	$-0.315534\pi$
$233$	4.92733e10	1.09524	0.547621	+	0.836727i	$0.315534\pi$
$234$	−7.81632e7	−0.00170424
$235$	−4.06757e7	−0.000870021 0
$236$	9.27606e9	0.194652
$237$	−6.29305e10	−1.29567
$238$	−5.92278e8	−0.0119655
$239$	−2.13419e10	−0.423100	−0.211550	−	0.977367i	$-0.567851\pi$
$239$	−2.13419e10	−0.423100	−0.211550	+	0.977367i	$0.567851\pi$
$240$	−5.49242e8	−0.0106860
$241$	3.43411e10	0.655748	0.327874	−	0.944721i	$-0.393668\pi$
$241$	3.43411e10	0.655748	0.327874	+	0.944721i	$0.393668\pi$
$242$	6.71933e9	0.125938
$243$	−5.28397e9	−0.0972147
$244$	4.76448e10	0.860521
$245$	−8.82734e7	−0.00156525
$246$	1.28259e10	0.223296
$247$	−2.58333e9	−0.0441614
$248$	−7.17322e9	−0.120415
$249$	−5.51653e9	−0.0909430
$250$	−1.70937e8	−0.00276762
$251$	2.49984e10	0.397539	0.198769	−	0.980046i	$-0.436305\pi$
$251$	2.49984e10	0.397539	0.198769	+	0.980046i	$0.436305\pi$
$252$	−1.15838e9	−0.0180946
$253$	2.23974e9	0.0343680
$254$	1.85697e9	0.0279933
$255$	−1.89882e8	−0.00281225
$256$	5.80171e10	0.844259
$257$	−7.08375e10	−1.01289	−0.506447	−	0.862271i	$-0.669042\pi$
$257$	−7.08375e10	−1.01289	−0.506447	+	0.862271i	$0.669042\pi$
$258$	−7.58920e9	−0.106637
$259$	2.41933e9	0.0334077
$260$	2.20346e8	0.00299037
$261$	1.53354e9	0.0204556
$262$	−9.56380e9	−0.125393
$263$	−7.08775e10	−0.913498	−0.456749	−	0.889596i	$-0.650986\pi$
$263$	−7.08775e10	−0.913498	−0.456749	+	0.889596i	$0.650986\pi$
$264$	−1.09193e9	−0.0138350
$265$	9.78239e8	0.0121854
$266$	6.20661e8	0.00760128
$267$	−3.52548e10	−0.424538
$268$	7.08386e10	0.838810
$269$	−6.78221e10	−0.789743	−0.394871	−	0.918736i	$-0.629211\pi$
$269$	−6.78221e10	−0.789743	−0.394871	+	0.918736i	$0.629211\pi$
$270$	−1.17732e8	−0.00134821
$271$	2.64639e10	0.298052	0.149026	−	0.988833i	$-0.452386\pi$
$271$	2.64639e10	0.298052	0.149026	+	0.988833i	$0.452386\pi$
$272$	2.15494e10	0.238712
$273$	9.85205e9	0.107348
$274$	1.22470e10	0.131266
$275$	5.11252e9	0.0539061
$276$	6.19280e10	0.642386
$277$	1.07161e11	1.09365	0.546826	−	0.837247i	$-0.315836\pi$
$277$	1.07161e11	1.09365	0.546826	+	0.837247i	$0.315836\pi$
$278$	−2.60869e9	−0.0261952
$279$	−2.36597e9	−0.0233771
$280$	−1.06737e8	−0.00103778
$281$	9.81760e10	0.939349	0.469674	−	0.882840i	$-0.344371\pi$
$281$	9.81760e10	0.939349	0.469674	+	0.882840i	$0.344371\pi$
$282$	−1.09070e9	−0.0102704
$283$	−1.67457e11	−1.55191	−0.775953	−	0.630791i	$-0.782731\pi$
$283$	−1.67457e11	−1.55191	−0.775953	+	0.630791i	$0.782731\pi$
$284$	1.35627e11	1.23712
$285$	1.98981e8	0.00178653
$286$	2.13691e8	0.00188860
$287$	−7.50004e10	−0.652522
$288$	−2.10664e9	−0.0180436
$289$	−1.11138e11	−0.937178
$290$	7.00847e7	0.000581878 0
$291$	6.42956e10	0.525609
$292$	6.36747e10	0.512560
$293$	−1.39998e10	−0.110973	−0.0554866	−	0.998459i	$-0.517671\pi$
$293$	−1.39998e10	−0.110973	−0.0554866	+	0.998459i	$0.517671\pi$
$294$	−2.36702e9	−0.0184773
$295$	2.81919e8	0.00216733
$296$	2.92537e9	0.0221497
$297$	7.04287e9	0.0525225
$298$	−2.92261e10	−0.214683
$299$	−2.44351e10	−0.176804
$300$	1.41359e11	1.00758
$301$	4.43783e10	0.311617
$302$	−8.13712e9	−0.0562911
$303$	1.99828e11	1.36196
$304$	−2.25820e10	−0.151646
$305$	1.44802e9	0.00958134
$306$	−2.36214e8	−0.00154014
$307$	2.48086e11	1.59397	0.796985	−	0.603999i	$-0.206427\pi$
$307$	2.48086e11	1.59397	0.796985	+	0.603999i	$0.206427\pi$
$308$	3.16690e9	0.0200519
$309$	−2.62618e10	−0.163874
$310$	−1.08128e8	−0.000664983 0
$311$	−1.67737e11	−1.01673	−0.508367	−	0.861141i	$-0.669751\pi$
$311$	−1.67737e11	−1.01673	−0.508367	+	0.861141i	$0.669751\pi$
$312$	1.19128e10	0.0711732
$313$	−1.10406e11	−0.650196	−0.325098	−	0.945680i	$-0.605397\pi$
$313$	−1.10406e11	−0.650196	−0.325098	+	0.945680i	$0.605397\pi$
$314$	−4.08264e10	−0.237005
$315$	−3.52055e7	−0.000201471 0
$316$	2.20692e11	1.24507
$317$	−7.89060e10	−0.438877	−0.219439	−	0.975626i	$-0.570423\pi$
$317$	−7.89060e10	−0.438877	−0.219439	+	0.975626i	$0.570423\pi$
$318$	2.62311e10	0.143845
$319$	−4.19255e9	−0.0226684
$320$	1.86109e9	0.00992187
$321$	1.40008e11	0.736002
$322$	5.87068e9	0.0304324
$323$	−7.80699e9	−0.0399091
$324$	2.04229e11	1.02959
$325$	−5.57765e10	−0.277317
$326$	−8.37813e9	−0.0410836
$327$	−8.59691e10	−0.415793
$328$	−9.06879e10	−0.432630
$329$	6.37796e9	0.0300123
$330$	−1.64596e7	−7.64024e−5 0
$331$	8.20817e10	0.375855	0.187928	−	0.982183i	$-0.439823\pi$
$331$	8.20817e10	0.375855	0.187928	+	0.982183i	$0.439823\pi$
$332$	1.93460e10	0.0873916
$333$	9.64885e8	0.00430008
$334$	−3.27913e10	−0.144178
$335$	2.15293e9	0.00933960
$336$	8.61212e10	0.368624
$337$	2.83816e11	1.19868	0.599338	−	0.800496i	$-0.295431\pi$
$337$	2.83816e11	1.19868	0.599338	+	0.800496i	$0.295431\pi$
$338$	−2.33133e9	−0.00971578
$339$	−6.72321e10	−0.276489
$340$	6.65900e8	0.00270243
$341$	6.46835e9	0.0259059
$342$	2.47534e8	0.000978402 0
$343$	1.38413e10	0.0539949
$344$	5.36608e10	0.206606
$345$	1.88212e9	0.00715255
$346$	−3.61661e10	−0.135662
$347$	−3.38226e11	−1.25234	−0.626172	−	0.779685i	$-0.715379\pi$
$347$	−3.38226e11	−1.25234	−0.626172	+	0.779685i	$0.715379\pi$
$348$	−1.15923e11	−0.423703
$349$	5.12708e11	1.84993	0.924966	−	0.380049i	$-0.124093\pi$
$349$	5.12708e11	1.84993	0.924966	+	0.380049i	$0.124093\pi$
$350$	1.34007e10	0.0477331
$351$	−7.68362e10	−0.270199
$352$	5.75936e9	0.0199955
$353$	−4.34925e11	−1.49083	−0.745414	−	0.666601i	$-0.767748\pi$
$353$	−4.34925e11	−1.49083	−0.745414	+	0.666601i	$0.767748\pi$
$354$	7.55953e9	0.0255847
$355$	4.12198e9	0.0137746
$356$	1.23635e11	0.407960
$357$	2.97735e10	0.0970116
$358$	2.94693e10	0.0948192
$359$	7.29872e10	0.231911	0.115956	−	0.993254i	$-0.463007\pi$
$359$	7.29872e10	0.231911	0.115956	+	0.993254i	$0.463007\pi$
$360$	−4.25693e7	−0.000133578 0
$361$	−3.14507e11	−0.974647
$362$	2.29399e10	0.0702106
$363$	−3.37778e11	−1.02106
$364$	−3.45503e10	−0.103156
$365$	1.93521e9	0.00570702
$366$	3.88282e10	0.113105
$367$	−1.94125e11	−0.558577	−0.279289	−	0.960207i	$-0.590099\pi$
$367$	−1.94125e11	−0.558577	−0.279289	+	0.960207i	$0.590099\pi$
$368$	−2.13598e11	−0.607131
$369$	−2.99119e10	−0.0839896
$370$	4.40965e7	0.000122320 0
$371$	−1.53388e11	−0.420348
$372$	1.78848e11	0.484217
$373$	9.78363e10	0.261704	0.130852	−	0.991402i	$-0.458229\pi$
$373$	9.78363e10	0.261704	0.130852	+	0.991402i	$0.458229\pi$
$374$	6.45789e8	0.00170674
$375$	8.59292e9	0.0224388
$376$	7.71200e9	0.0198986
$377$	4.57399e10	0.116616
$378$	1.84604e10	0.0465080
$379$	2.10996e11	0.525287	0.262644	−	0.964893i	$-0.415406\pi$
$379$	2.10996e11	0.525287	0.262644	+	0.964893i	$0.415406\pi$
$380$	−6.97811e8	−0.00171677
$381$	−9.33491e10	−0.226959
$382$	−9.17411e9	−0.0220434
$383$	−3.68029e11	−0.873951	−0.436976	−	0.899473i	$-0.643950\pi$
$383$	−3.68029e11	−0.873951	−0.436976	+	0.899473i	$0.643950\pi$
$384$	2.11730e11	0.496927
$385$	9.62487e7	0.000223265 0
$386$	1.27221e10	0.0291686
$387$	1.76991e10	0.0401100
$388$	−2.25479e11	−0.505084
$389$	−3.34352e11	−0.740339	−0.370170	−	0.928964i	$-0.620700\pi$
$389$	−3.34352e11	−0.740339	−0.370170	+	0.928964i	$0.620700\pi$
$390$	1.79571e8	0.000393048 0
$391$	−7.38444e10	−0.159780
$392$	1.67364e10	0.0357993
$393$	4.80768e11	1.01664
$394$	3.59516e10	0.0751597
$395$	6.70727e9	0.0138631
$396$	1.26303e9	0.00258099
$397$	−4.55124e11	−0.919544	−0.459772	−	0.888037i	$-0.652069\pi$
$397$	−4.55124e11	−0.919544	−0.459772	+	0.888037i	$0.652069\pi$
$398$	−4.95492e10	−0.0989835
$399$	−3.12003e10	−0.0616284
$400$	−4.87568e11	−0.952281
$401$	4.86374e11	0.939335	0.469668	−	0.882843i	$-0.344374\pi$
$401$	4.86374e11	0.939335	0.469668	+	0.882843i	$0.344374\pi$
$402$	5.77299e10	0.110251
$403$	−7.05683e10	−0.133271
$404$	−7.00778e11	−1.30877
$405$	6.20694e9	0.0114638
$406$	−1.09893e10	−0.0200725
$407$	−2.63791e9	−0.00476524
$408$	3.60011e10	0.0643199
$409$	−2.38979e11	−0.422285	−0.211142	−	0.977455i	$-0.567718\pi$
$409$	−2.38979e11	−0.422285	−0.211142	+	0.977455i	$0.567718\pi$
$410$	−1.36701e9	−0.00238916
$411$	−6.15653e11	−1.06426
$412$	9.20978e10	0.157475
$413$	−4.42049e10	−0.0747644
$414$	2.34136e9	0.00391712
$415$	5.87964e8	0.000973049 0
$416$	−6.28334e10	−0.102866
$417$	1.31138e11	0.212381
$418$	−6.76735e8	−0.00108424
$419$	1.39300e11	0.220794	0.110397	−	0.993888i	$-0.464788\pi$
$419$	1.39300e11	0.220794	0.110397	+	0.993888i	$0.464788\pi$
$420$	2.66124e9	0.00417314
$421$	−1.04165e11	−0.161604	−0.0808019	−	0.996730i	$-0.525748\pi$
$421$	−1.04165e11	−0.161604	−0.0808019	+	0.996730i	$0.525748\pi$
$422$	9.15830e10	0.140575
$423$	2.54368e9	0.00386305
$424$	−1.85472e11	−0.278696
$425$	−1.68560e11	−0.250614
$426$	1.10529e11	0.162605
$427$	−2.27050e11	−0.330519
$428$	−4.90994e11	−0.707261
$429$	−1.07421e10	−0.0153121
$430$	8.08873e8	0.00114097
$431$	−1.10468e12	−1.54202	−0.771010	−	0.636823i	$-0.780248\pi$
$431$	−1.10468e12	−1.54202	−0.771010	+	0.636823i	$0.780248\pi$
$432$	−6.71661e11	−0.927840
$433$	−3.53626e11	−0.483447	−0.241724	−	0.970345i	$-0.577713\pi$
$433$	−3.53626e11	−0.483447	−0.241724	+	0.970345i	$0.577713\pi$
$434$	1.69545e10	0.0229393
$435$	−3.52312e9	−0.00471766
$436$	3.01486e11	0.399556
$437$	7.73831e10	0.101503
$438$	5.18918e10	0.0673697
$439$	6.43978e11	0.827524	0.413762	−	0.910385i	$-0.364214\pi$
$439$	6.43978e11	0.827524	0.413762	+	0.910385i	$0.364214\pi$
$440$	1.16381e8	0.000148028 0
$441$	5.52023e9	0.00694998
$442$	−7.04542e9	−0.00878025
$443$	−6.41849e11	−0.791802	−0.395901	−	0.918293i	$-0.629568\pi$
$443$	−6.41849e11	−0.791802	−0.395901	+	0.918293i	$0.629568\pi$
$444$	−7.29373e10	−0.0890689
$445$	3.75753e9	0.00454237
$446$	1.33474e11	0.159731
$447$	1.46918e12	1.74057
$448$	−2.91820e11	−0.342266
$449$	1.25397e12	1.45606	0.728029	−	0.685546i	$-0.240437\pi$
$449$	1.25397e12	1.45606	0.728029	+	0.685546i	$0.240437\pi$
$450$	5.34449e9	0.00614399
$451$	8.17764e10	0.0930751
$452$	2.35777e11	0.265692
$453$	4.09049e11	0.456388
$454$	1.03983e11	0.114871
$455$	−1.05005e9	−0.00114858
$456$	−3.77264e10	−0.0408604
$457$	1.25906e12	1.35028	0.675141	−	0.737689i	$-0.264083\pi$
$457$	1.25906e12	1.35028	0.675141	+	0.737689i	$0.264083\pi$
$458$	−1.31116e11	−0.139239
$459$	−2.32204e11	−0.244182
$460$	−6.60042e9	−0.00687324
$461$	4.43884e11	0.457737	0.228868	−	0.973457i	$-0.426497\pi$
$461$	4.43884e11	0.457737	0.228868	+	0.973457i	$0.426497\pi$
$462$	2.58087e9	0.00263559
$463$	−1.26115e12	−1.27542	−0.637710	−	0.770277i	$-0.720118\pi$
$463$	−1.26115e12	−1.27542	−0.637710	+	0.770277i	$0.720118\pi$
$464$	3.99833e11	0.400450
$465$	5.43555e9	0.00539144
$466$	−1.40821e11	−0.138335
$467$	1.85885e11	0.180850	0.0904249	−	0.995903i	$-0.471178\pi$
$467$	1.85885e11	0.180850	0.0904249	+	0.995903i	$0.471178\pi$
$468$	−1.37795e10	−0.0132778
$469$	−3.37580e11	−0.322180
$470$	1.16250e8	0.000109888 0
$471$	2.05232e12	1.92155
$472$	−5.34510e10	−0.0495698
$473$	−4.83878e10	−0.0444489
$474$	1.79853e11	0.163649
$475$	1.76638e11	0.159207
$476$	−1.04413e11	−0.0932232
$477$	−6.11747e10	−0.0541052
$478$	6.09943e10	0.0534396
$479$	1.51780e11	0.131736	0.0658680	−	0.997828i	$-0.479018\pi$
$479$	1.51780e11	0.131736	0.0658680	+	0.997828i	$0.479018\pi$
$480$	4.83976e9	0.00416139
$481$	2.87790e10	0.0245145
$482$	−9.81453e10	−0.0828243
$483$	−2.95116e11	−0.246735
$484$	1.18456e12	0.981187
$485$	−6.85277e9	−0.00562378
$486$	1.51014e10	0.0122787
$487$	−7.60064e10	−0.0612308	−0.0306154	−	0.999531i	$-0.509747\pi$
$487$	−7.60064e10	−0.0612308	−0.0306154	+	0.999531i	$0.509747\pi$
$488$	−2.74541e11	−0.219138
$489$	4.21165e11	0.333091
$490$	2.52282e8	0.000197699 0
$491$	−7.25712e11	−0.563505	−0.281752	−	0.959487i	$-0.590916\pi$
$491$	−7.25712e11	−0.563505	−0.281752	+	0.959487i	$0.590916\pi$
$492$	2.26109e12	1.73970
$493$	1.38229e11	0.105387
$494$	7.38304e9	0.00557782
$495$	3.83862e7	2.87377e−5 0
$496$	−6.16870e11	−0.457642
$497$	−6.46327e11	−0.475170
$498$	1.57660e10	0.0114866
$499$	2.70447e12	1.95268	0.976338	−	0.216251i	$-0.0693828\pi$
$499$	2.70447e12	1.95268	0.976338	+	0.216251i	$0.0693828\pi$
$500$	−3.01346e10	−0.0215626
$501$	1.64840e12	1.16894
$502$	−7.14443e10	−0.0502112
$503$	−7.93395e11	−0.552629	−0.276314	−	0.961067i	$-0.589113\pi$
$503$	−7.93395e11	−0.552629	−0.276314	+	0.961067i	$0.589113\pi$
$504$	6.67487e9	0.00460793
$505$	−2.12981e10	−0.0145723
$506$	−6.40108e9	−0.00434086
$507$	1.17195e11	0.0787720
$508$	3.27367e11	0.218096
$509$	1.61881e12	1.06897	0.534487	−	0.845177i	$-0.320505\pi$
$509$	1.61881e12	1.06897	0.534487	+	0.845177i	$0.320505\pi$
$510$	5.42675e8	0.000355201 0
$511$	−3.03441e11	−0.196870
$512$	−9.20368e11	−0.591898
$513$	2.43332e11	0.155121
$514$	2.02451e11	0.127934
$515$	2.79904e9	0.00175338
$516$	−1.33791e12	−0.830810
$517$	−6.95418e9	−0.00428094
$518$	−6.91434e9	−0.00421956
$519$	1.81805e12	1.09990
$520$	−1.26969e9	−0.000761521 0
$521$	−3.78680e11	−0.225166	−0.112583	−	0.993642i	$-0.535912\pi$
$521$	−3.78680e11	−0.225166	−0.112583	+	0.993642i	$0.535912\pi$
$522$	−4.38278e9	−0.00258365
$523$	−6.27715e11	−0.366864	−0.183432	−	0.983032i	$-0.558721\pi$
$523$	−6.27715e11	−0.366864	−0.183432	+	0.983032i	$0.558721\pi$
$524$	−1.68601e12	−0.976944
$525$	−6.73645e11	−0.387003
$526$	2.02565e11	0.115380
$527$	−2.13262e11	−0.120439
$528$	−9.39020e10	−0.0525802
$529$	−1.06920e12	−0.593623
$530$	−2.79577e9	−0.00153907
$531$	−1.76299e10	−0.00962333
$532$	1.09417e11	0.0592218
$533$	−8.92164e11	−0.478820
$534$	1.00757e11	0.0536214
$535$	−1.49223e10	−0.00787489
$536$	−4.08190e11	−0.213610
$537$	−1.48141e12	−0.768760
$538$	1.93833e11	0.0997486
$539$	−1.50918e10	−0.00770179
$540$	−2.07551e10	−0.0105039
$541$	1.45230e12	0.728902	0.364451	−	0.931223i	$-0.381257\pi$
$541$	1.45230e12	0.728902	0.364451	+	0.931223i	$0.381257\pi$
$542$	−7.56328e10	−0.0376456
$543$	−1.15318e12	−0.569242
$544$	−1.89887e11	−0.0929608
$545$	9.16278e9	0.00444880
$546$	−2.81567e10	−0.0135586
$547$	2.61898e12	1.25080	0.625402	−	0.780302i	$-0.284935\pi$
$547$	2.61898e12	1.25080	0.625402	+	0.780302i	$0.284935\pi$
$548$	2.15904e12	1.02270
$549$	−9.05529e10	−0.0425429
$550$	−1.46114e10	−0.00680861
$551$	−1.44853e11	−0.0669492
$552$	−3.56844e11	−0.163589
$553$	−1.05170e12	−0.478222
$554$	−3.06263e11	−0.138134
$555$	−2.21671e9	−0.000991724 0
$556$	−4.59889e11	−0.204088
$557$	−1.64364e12	−0.723533	−0.361767	−	0.932269i	$-0.617826\pi$
$557$	−1.64364e12	−0.723533	−0.361767	+	0.932269i	$0.617826\pi$
$558$	6.76185e9	0.00295265
$559$	5.27901e11	0.228665
$560$	−9.17900e9	−0.00394411
$561$	−3.24635e10	−0.0138377
$562$	−2.80583e11	−0.118645
$563$	−3.36157e12	−1.41011	−0.705056	−	0.709151i	$-0.749078\pi$
$563$	−3.36157e12	−1.41011	−0.705056	+	0.709151i	$0.749078\pi$
$564$	−1.92281e11	−0.0800166
$565$	7.16575e9	0.00295831
$566$	4.78587e11	0.196014
$567$	−9.73249e11	−0.395458
$568$	−7.81517e11	−0.315044
$569$	3.54649e12	1.41838	0.709192	−	0.705015i	$-0.249060\pi$
$569$	3.54649e12	1.41838	0.709192	+	0.705015i	$0.249060\pi$
$570$	−5.68681e8	−0.000225648 0
$571$	1.25130e12	0.492604	0.246302	−	0.969193i	$-0.420785\pi$
$571$	1.25130e12	0.492604	0.246302	+	0.969193i	$0.420785\pi$
$572$	3.76718e10	0.0147141
$573$	4.61178e11	0.178720
$574$	2.14348e11	0.0824168
$575$	1.67078e12	0.637401
$576$	−1.16385e11	−0.0440549
$577$	9.21167e11	0.345977	0.172989	−	0.984924i	$-0.444658\pi$
$577$	9.21167e11	0.345977	0.172989	+	0.984924i	$0.444658\pi$
$578$	3.17628e11	0.118370
$579$	−6.39534e11	−0.236488
$580$	1.23553e10	0.00453343
$581$	−9.21929e10	−0.0335664
$582$	−1.83754e11	−0.0663872
$583$	1.67246e11	0.0599581
$584$	−3.66910e11	−0.130527
$585$	−4.18786e8	−0.000147839 0
$586$	4.00109e10	0.0140165
$587$	3.24374e12	1.12765	0.563826	−	0.825894i	$-0.309329\pi$
$587$	3.24374e12	1.12765	0.563826	+	0.825894i	$0.309329\pi$
$588$	−4.17283e11	−0.143957
$589$	2.23482e11	0.0765110
$590$	−8.05712e8	−0.000273745 0
$591$	−1.80727e12	−0.609367
$592$	2.51571e11	0.0841807
$593$	−1.00916e12	−0.335130	−0.167565	−	0.985861i	$-0.553590\pi$
$593$	−1.00916e12	−0.335130	−0.167565	+	0.985861i	$0.553590\pi$
$594$	−2.01282e10	−0.00663386
$595$	−3.17333e9	−0.00103798
$596$	−5.15230e12	−1.67260
$597$	2.49081e12	0.802522
$598$	6.98344e10	0.0223313
$599$	−1.04975e12	−0.333170	−0.166585	−	0.986027i	$-0.553274\pi$
$599$	−1.04975e12	−0.333170	−0.166585	+	0.986027i	$0.553274\pi$
$600$	−8.14548e11	−0.256588
$601$	8.80068e11	0.275157	0.137579	−	0.990491i	$-0.456068\pi$
$601$	8.80068e11	0.275157	0.137579	+	0.990491i	$0.456068\pi$
$602$	−1.26831e11	−0.0393589
$603$	−1.34635e11	−0.0414695
$604$	−1.43450e12	−0.438565
$605$	3.60011e10	0.0109249
$606$	−5.71099e11	−0.172022
$607$	2.70896e12	0.809942	0.404971	−	0.914329i	$-0.367282\pi$
$607$	2.70896e12	0.809942	0.404971	+	0.914329i	$0.367282\pi$
$608$	1.98986e11	0.0590551
$609$	5.52426e11	0.162741
$610$	−4.13839e9	−0.00121017
$611$	7.58687e10	0.0220230
$612$	−4.16424e10	−0.0119993
$613$	1.95586e12	0.559455	0.279727	−	0.960079i	$-0.409756\pi$
$613$	1.95586e12	0.559455	0.279727	+	0.960079i	$0.409756\pi$
$614$	−7.09021e11	−0.201327
$615$	6.87192e10	0.0193705
$616$	−1.82485e10	−0.00510639
$617$	−4.94329e12	−1.37320	−0.686599	−	0.727037i	$-0.740897\pi$
$617$	−4.94329e12	−1.37320	−0.686599	+	0.727037i	$0.740897\pi$
$618$	7.50552e10	0.0206982
$619$	−1.57550e12	−0.431332	−0.215666	−	0.976467i	$-0.569192\pi$
$619$	−1.57550e12	−0.431332	−0.215666	+	0.976467i	$0.569192\pi$
$620$	−1.90620e10	−0.00518090
$621$	2.30161e12	0.621041
$622$	4.79385e11	0.128419
$623$	−5.89181e11	−0.156694
$624$	1.02445e12	0.270496
$625$	3.81332e12	0.999640
$626$	3.15537e11	0.0821231
$627$	3.40192e10	0.00879063
$628$	−7.19732e12	−1.84651
$629$	8.69722e10	0.0221540
$630$	1.00616e8	2.54469e−5 0
$631$	7.29862e12	1.83277	0.916386	−	0.400295i	$-0.131092\pi$
$631$	7.29862e12	1.83277	0.916386	+	0.400295i	$0.131092\pi$
$632$	−1.27168e12	−0.317067
$633$	−4.60383e12	−1.13973
$634$	2.25510e11	0.0554325
$635$	9.94935e9	0.00242836
$636$	4.62430e12	1.12070
$637$	1.64648e11	0.0396214
$638$	1.19821e10	0.00286313
$639$	−2.57770e11	−0.0611616
$640$	−2.25667e10	−0.00531690
$641$	−5.11451e12	−1.19658	−0.598292	−	0.801278i	$-0.704154\pi$
$641$	−5.11451e12	−1.19658	−0.598292	+	0.801278i	$0.704154\pi$
$642$	−4.00136e11	−0.0929608
$643$	−2.13356e12	−0.492216	−0.246108	−	0.969242i	$-0.579152\pi$
$643$	−2.13356e12	−0.492216	−0.246108	+	0.969242i	$0.579152\pi$
$644$	1.03495e12	0.237100
$645$	−4.06617e10	−0.00925053
$646$	2.23120e10	0.00504073
$647$	−1.64637e12	−0.369368	−0.184684	−	0.982798i	$-0.559126\pi$
$647$	−1.64637e12	−0.369368	−0.184684	+	0.982798i	$0.559126\pi$
$648$	−1.17682e12	−0.262194
$649$	4.81986e10	0.0106643
$650$	1.59407e11	0.0350265
$651$	−8.52294e11	−0.185984
$652$	−1.47699e12	−0.320083
$653$	−7.65775e12	−1.64813	−0.824066	−	0.566494i	$-0.808299\pi$
$653$	−7.65775e12	−1.64813	−0.824066	+	0.566494i	$0.808299\pi$
$654$	2.45696e11	0.0525168
$655$	−5.12413e10	−0.0108776
$656$	−7.79881e12	−1.64422
$657$	−1.21019e11	−0.0253402
$658$	−1.82279e10	−0.00379071
$659$	7.62072e11	0.157402	0.0787012	−	0.996898i	$-0.474923\pi$
$659$	7.62072e11	0.157402	0.0787012	+	0.996898i	$0.474923\pi$
$660$	−2.90168e9	−0.000595253 0
$661$	−3.40869e12	−0.694513	−0.347257	−	0.937770i	$-0.612887\pi$
$661$	−3.40869e12	−0.694513	−0.347257	+	0.937770i	$0.612887\pi$
$662$	−2.34586e11	−0.0474724
$663$	3.54170e11	0.0711870
$664$	−1.11476e11	−0.0222550
$665$	3.32540e9	0.000659396 0
$666$	−2.75760e9	−0.000543122 0
$667$	−1.37013e12	−0.268037
$668$	−5.78081e12	−1.12330
$669$	−6.70967e12	−1.29504
$670$	−6.15299e9	−0.00117964
$671$	2.47564e11	0.0471450
$672$	−7.58875e11	−0.143552
$673$	1.78459e12	0.335328	0.167664	−	0.985844i	$-0.446378\pi$
$673$	1.78459e12	0.335328	0.167664	+	0.985844i	$0.446378\pi$
$674$	−8.11133e11	−0.151399
$675$	5.25376e12	0.974100
$676$	−4.10991e11	−0.0756959
$677$	−2.42571e12	−0.443803	−0.221902	−	0.975069i	$-0.571226\pi$
$677$	−2.42571e12	−0.443803	−0.221902	+	0.975069i	$0.571226\pi$
$678$	1.92147e11	0.0349220
$679$	1.07452e12	0.193999
$680$	−3.83708e9	−0.000688194 0
$681$	−5.22719e12	−0.931335
$682$	−1.84863e10	−0.00327205
$683$	2.67882e12	0.471033	0.235516	−	0.971870i	$-0.424322\pi$
$683$	2.67882e12	0.471033	0.235516	+	0.971870i	$0.424322\pi$
$684$	4.36380e10	0.00762276
$685$	6.56176e10	0.0113871
$686$	−3.95578e10	−0.00681984
$687$	6.59113e12	1.12890
$688$	4.61462e12	0.785214
$689$	−1.82462e12	−0.308451
$690$	−5.37901e9	−0.000903404 0
$691$	5.77069e11	0.0962890	0.0481445	−	0.998840i	$-0.484669\pi$
$691$	5.77069e11	0.0962890	0.0481445	+	0.998840i	$0.484669\pi$
$692$	−6.37576e12	−1.05695
$693$	−6.01896e9	−0.000991339 0
$694$	9.66635e11	0.158178
$695$	−1.39770e10	−0.00227238
$696$	6.67975e11	0.107899
$697$	−2.69618e12	−0.432714
$698$	−1.46530e12	−0.233656
$699$	7.07901e12	1.12157
$700$	2.36241e12	0.371890
$701$	4.67001e12	0.730443	0.365222	−	0.930921i	$-0.380993\pi$
$701$	4.67001e12	0.730443	0.365222	+	0.930921i	$0.380993\pi$
$702$	2.19595e11	0.0341275
$703$	−9.11400e10	−0.0140738
$704$	3.18185e11	0.0488205
$705$	−5.84381e9	−0.000890933 0
$706$	1.24300e12	0.188299
$707$	3.33954e12	0.502689
$708$	1.33268e12	0.199331
$709$	3.32880e12	0.494743	0.247372	−	0.968921i	$-0.420433\pi$
$709$	3.32880e12	0.494743	0.247372	+	0.968921i	$0.420433\pi$
$710$	−1.17805e10	−0.00173980
$711$	−4.19443e11	−0.0615545
$712$	−7.12418e11	−0.103890
$713$	2.11386e12	0.306319
$714$	−8.50916e10	−0.0122531
$715$	1.14492e9	0.000163832 0
$716$	5.19517e12	0.738739
$717$	−3.06615e12	−0.433269
$718$	−2.08594e11	−0.0292916
$719$	−7.15618e11	−0.0998623	−0.0499311	−	0.998753i	$-0.515900\pi$
$719$	−7.15618e11	−0.0998623	−0.0499311	+	0.998753i	$0.515900\pi$
$720$	−3.66080e9	−0.000507668 0
$721$	−4.38890e11	−0.0604849
$722$	8.98847e11	0.123103
$723$	4.93372e12	0.671510
$724$	4.04409e12	0.547013
$725$	−3.12751e12	−0.420415
$726$	9.65355e11	0.128965
$727$	8.28829e12	1.10042	0.550212	−	0.835025i	$-0.314547\pi$
$727$	8.28829e12	1.10042	0.550212	+	0.835025i	$0.314547\pi$
$728$	1.99087e11	0.0262695
$729$	7.21939e12	0.946732
$730$	−5.53074e9	−0.000720826 0
$731$	1.59535e12	0.206647
$732$	6.84505e12	0.881205
$733$	7.87930e12	1.00814	0.504069	−	0.863664i	$-0.331836\pi$
$733$	7.87930e12	1.00814	0.504069	+	0.863664i	$0.331836\pi$
$734$	5.54800e11	0.0705512
$735$	−1.26821e10	−0.00160287
$736$	1.88216e12	0.236433
$737$	3.68079e11	0.0459555
$738$	8.54870e10	0.0106083
$739$	9.31945e12	1.14945	0.574725	−	0.818346i	$-0.305109\pi$
$739$	9.31945e12	1.14945	0.574725	+	0.818346i	$0.305109\pi$
$740$	7.77382e9	0.000952997 0
$741$	−3.71142e11	−0.0452229
$742$	4.38377e11	0.0530921
$743$	3.17339e12	0.382009	0.191004	−	0.981589i	$-0.438826\pi$
$743$	3.17339e12	0.382009	0.191004	+	0.981589i	$0.438826\pi$
$744$	−1.03056e12	−0.123310
$745$	−1.56589e11	−0.0186233
$746$	−2.79612e11	−0.0330546
$747$	−3.67687e10	−0.00432051
$748$	1.13847e11	0.0132973
$749$	2.33982e12	0.271653
$750$	−2.45582e10	−0.00283414
$751$	−3.64334e12	−0.417946	−0.208973	−	0.977921i	$-0.567012\pi$
$751$	−3.64334e12	−0.417946	−0.208973	+	0.977921i	$0.567012\pi$
$752$	6.63203e11	0.0756252
$753$	3.59147e12	0.407094
$754$	−1.30723e11	−0.0147292
$755$	−4.35974e10	−0.00488314
$756$	3.25440e12	0.362345
$757$	−6.03038e12	−0.667441	−0.333721	−	0.942672i	$-0.608304\pi$
$757$	−6.03038e12	−0.667441	−0.333721	+	0.942672i	$0.608304\pi$
$758$	−6.03017e11	−0.0663465
$759$	3.21779e11	0.0351941
$760$	4.02096e9	0.000437188 0
$761$	−2.97715e11	−0.0321788	−0.0160894	−	0.999871i	$-0.505122\pi$
$761$	−2.97715e11	−0.0321788	−0.0160894	+	0.999871i	$0.505122\pi$
$762$	2.66788e11	0.0286661
$763$	−1.43672e12	−0.153466
$764$	−1.61731e12	−0.171741
$765$	−1.26560e9	−0.000133604 0
$766$	1.05181e12	0.110385
$767$	−5.25837e11	−0.0548621
$768$	8.33521e12	0.864552
$769$	1.20527e13	1.24284	0.621418	−	0.783479i	$-0.286557\pi$
$769$	1.20527e13	1.24284	0.621418	+	0.783479i	$0.286557\pi$
$770$	−2.75075e8	−2.81996e−5 0
$771$	−1.01771e13	−1.03724
$772$	2.24279e12	0.227253
$773$	−1.72502e13	−1.73775	−0.868876	−	0.495030i	$-0.835157\pi$
$773$	−1.72502e13	−1.73775	−0.868876	+	0.495030i	$0.835157\pi$
$774$	−5.05833e10	−0.00506609
$775$	4.82519e12	0.480459
$776$	1.29927e12	0.128624
$777$	3.47581e11	0.0342106
$778$	9.55564e11	0.0935087
$779$	2.82538e12	0.274890
$780$	3.16567e10	0.00306225
$781$	7.04721e11	0.0677778
$782$	2.11044e11	0.0201810
$783$	−4.30838e12	−0.409625
$784$	1.43927e12	0.136057
$785$	−2.18741e11	−0.0205597
$786$	−1.37402e12	−0.128407
$787$	1.33731e13	1.24264	0.621320	−	0.783557i	$-0.286597\pi$
$787$	1.33731e13	1.24264	0.621320	+	0.783557i	$0.286597\pi$
$788$	6.33793e12	0.585571
$789$	−1.01829e13	−0.935455
$790$	−1.91691e10	−0.00175098
$791$	−1.12359e12	−0.102050
$792$	−7.27792e9	−0.000657271 0
$793$	−2.70087e12	−0.242535
$794$	1.30073e12	0.116143
$795$	1.40542e11	0.0124783
$796$	−8.73507e12	−0.771183
$797$	−4.33914e12	−0.380926	−0.190463	−	0.981694i	$-0.560999\pi$
$797$	−4.33914e12	−0.380926	−0.190463	+	0.981694i	$0.560999\pi$
$798$	8.91692e10	0.00778399
$799$	2.29280e11	0.0199024
$800$	4.29631e12	0.370843
$801$	−2.34979e11	−0.0201689
$802$	−1.39004e12	−0.118643
$803$	3.30855e11	0.0280814
$804$	1.01773e13	0.858971
$805$	3.14542e10	0.00263995
$806$	2.01681e11	0.0168329
$807$	−9.74388e12	−0.808725
$808$	4.03806e12	0.333289
$809$	−1.12260e13	−0.921421	−0.460710	−	0.887551i	$-0.652405\pi$
$809$	−1.12260e13	−0.921421	−0.460710	+	0.887551i	$0.652405\pi$
$810$	−1.77392e10	−0.00144794
$811$	−1.10314e13	−0.895439	−0.447720	−	0.894174i	$-0.647764\pi$
$811$	−1.10314e13	−0.895439	−0.447720	+	0.894174i	$0.647764\pi$
$812$	−1.93731e12	−0.156386
$813$	3.80203e12	0.305216
$814$	7.53903e9	0.000601874 0
$815$	−4.48887e10	−0.00356392
$816$	3.09596e12	0.244450
$817$	−1.67180e12	−0.131276
$818$	6.82993e11	0.0533367
$819$	6.56657e10	0.00509989
$820$	−2.40992e11	−0.0186140
$821$	−2.22237e13	−1.70715	−0.853576	−	0.520969i	$-0.825571\pi$
$821$	−2.22237e13	−1.70715	−0.853576	+	0.520969i	$0.825571\pi$
$822$	1.75951e12	0.134421
$823$	−3.71507e12	−0.282272	−0.141136	−	0.989990i	$-0.545076\pi$
$823$	−3.71507e12	−0.282272	−0.141136	+	0.989990i	$0.545076\pi$
$824$	−5.30691e11	−0.0401023
$825$	7.34507e11	0.0552018
$826$	1.26336e11	0.00944313
$827$	−8.46104e12	−0.628997	−0.314499	−	0.949258i	$-0.601836\pi$
$827$	−8.46104e12	−0.628997	−0.314499	+	0.949258i	$0.601836\pi$
$828$	4.12761e11	0.0305184
$829$	−7.73805e12	−0.569031	−0.284516	−	0.958671i	$-0.591833\pi$
$829$	−7.73805e12	−0.569031	−0.284516	+	0.958671i	$0.591833\pi$
$830$	−1.68038e9	−0.000122901 0
$831$	1.53957e13	1.11994
$832$	−3.47133e12	−0.251155
$833$	4.97579e11	0.0358063
$834$	−3.74787e11	−0.0268248
$835$	−1.75691e11	−0.0125072
$836$	−1.19302e11	−0.00844735
$837$	6.64705e12	0.468128
$838$	−3.98113e11	−0.0278874
$839$	3.66210e12	0.255153	0.127577	−	0.991829i	$-0.459280\pi$
$839$	3.66210e12	0.255153	0.127577	+	0.991829i	$0.459280\pi$
$840$	−1.53348e10	−0.00106272
$841$	−1.19424e13	−0.823209
$842$	2.97699e11	0.0204114
$843$	1.41048e13	0.961927
$844$	1.61452e13	1.09523
$845$	−1.24909e10	−0.000842825 0
$846$	−7.26973e9	−0.000487923 0
$847$	−5.64498e12	−0.376866
$848$	−1.59498e13	−1.05919
$849$	−2.40583e13	−1.58921
$850$	4.81739e11	0.0316538
$851$	−8.62071e11	−0.0563456
$852$	1.94853e13	1.26686
$853$	−2.33183e13	−1.50809	−0.754043	−	0.656825i	$-0.771899\pi$
$853$	−2.33183e13	−1.50809	−0.754043	+	0.656825i	$0.771899\pi$
$854$	6.48900e11	0.0417463
$855$	1.32625e9	8.48744e−5 0
$856$	2.82923e12	0.180110
$857$	4.14264e12	0.262340	0.131170	−	0.991360i	$-0.458127\pi$
$857$	4.14264e12	0.262340	0.131170	+	0.991360i	$0.458127\pi$
$858$	3.07006e10	0.00193399
$859$	7.00855e12	0.439197	0.219598	−	0.975590i	$-0.429525\pi$
$859$	7.00855e12	0.439197	0.219598	+	0.975590i	$0.429525\pi$
$860$	1.42597e11	0.00888930
$861$	−1.07752e13	−0.668206
$862$	3.15714e12	0.194765
$863$	2.00687e13	1.23160	0.615800	−	0.787902i	$-0.288833\pi$
$863$	2.00687e13	1.23160	0.615800	+	0.787902i	$0.288833\pi$
$864$	5.91848e12	0.361325
$865$	−1.93772e11	−0.0117684
$866$	1.01065e12	0.0610619
$867$	−1.59670e13	−0.959704
$868$	2.98892e12	0.178721
$869$	1.14672e12	0.0682131
$870$	1.00689e10	0.000595864 0
$871$	−4.01567e12	−0.236415
$872$	−1.73724e12	−0.101750
$873$	4.28542e11	0.0249706
$874$	−2.21158e11	−0.0128204
$875$	1.43606e11	0.00828201
$876$	9.14804e12	0.524880
$877$	−1.46130e12	−0.0834142	−0.0417071	−	0.999130i	$-0.513280\pi$
$877$	−1.46130e12	−0.0834142	−0.0417071	+	0.999130i	$0.513280\pi$
$878$	−1.84046e12	−0.104521
$879$	−2.01133e12	−0.113641
$880$	1.00083e10	0.000562585 0
$881$	−2.41994e13	−1.35336	−0.676681	−	0.736276i	$-0.736582\pi$
$881$	−2.41994e13	−1.35336	−0.676681	+	0.736276i	$0.736582\pi$
$882$	−1.57766e10	−0.000877818 0
$883$	4.59585e12	0.254415	0.127207	−	0.991876i	$-0.459399\pi$
$883$	4.59585e12	0.254415	0.127207	+	0.991876i	$0.459399\pi$
$884$	−1.24204e12	−0.0684071
$885$	4.05027e10	0.00221942
$886$	1.83438e12	0.100009
$887$	1.20937e13	0.655999	0.327999	−	0.944678i	$-0.393626\pi$
$887$	1.20937e13	0.655999	0.327999	+	0.944678i	$0.393626\pi$
$888$	4.20283e11	0.0226821
$889$	−1.56006e12	−0.0837690
$890$	−1.07389e10	−0.000573725 0
$891$	1.06118e12	0.0564078
$892$	2.35302e13	1.24447
$893$	−2.40268e11	−0.0126434
$894$	−4.19887e12	−0.219843
$895$	1.57892e11	0.00822538
$896$	3.53846e12	0.183412
$897$	−3.51054e12	−0.181054
$898$	−3.58380e12	−0.183908
$899$	−3.95693e12	−0.202041
$900$	9.42186e11	0.0478680
$901$	−5.51413e12	−0.278750
$902$	−2.33714e11	−0.0117559
$903$	6.37576e12	0.319108
$904$	−1.35861e12	−0.0676606
$905$	1.22908e11	0.00609063
$906$	−1.16905e12	−0.0576441
$907$	2.56987e11	0.0126089	0.00630446	−	0.999980i	$-0.497993\pi$
$907$	2.56987e11	0.0126089	0.00630446	+	0.999980i	$0.497993\pi$
$908$	1.83313e13	0.894966
$909$	1.33189e12	0.0647038
$910$	3.00101e9	0.000145071 0
$911$	−3.43373e13	−1.65171	−0.825853	−	0.563885i	$-0.809306\pi$
$911$	−3.43373e13	−1.65171	−0.825853	+	0.563885i	$0.809306\pi$
$912$	−3.24432e12	−0.155291
$913$	1.00522e11	0.00478788
$914$	−3.59835e12	−0.170547
$915$	2.08035e11	0.00981164
$916$	−2.31145e13	−1.08481
$917$	8.03465e12	0.375236
$918$	6.63630e11	0.0308414
$919$	−2.98053e13	−1.37840	−0.689198	−	0.724573i	$-0.742037\pi$
$919$	−2.98053e13	−1.37840	−0.689198	+	0.724573i	$0.742037\pi$
$920$	3.80333e10	0.00175032
$921$	3.56421e13	1.63228
$922$	−1.26860e12	−0.0578145
$923$	−7.68836e12	−0.348679
$924$	4.54984e11	0.0205339
$925$	−1.96780e12	−0.0883777
$926$	3.60432e12	0.161092
$927$	−1.75040e11	−0.00778534
$928$	−3.52321e12	−0.155946
$929$	−4.65926e12	−0.205232	−0.102616	−	0.994721i	$-0.532721\pi$
$929$	−4.65926e12	−0.205232	−0.102616	+	0.994721i	$0.532721\pi$
$930$	−1.55346e10	−0.000680967 0
$931$	−5.21423e11	−0.0227466
$932$	−2.48255e13	−1.07777
$933$	−2.40985e13	−1.04117
$934$	−5.31251e11	−0.0228423
$935$	3.46003e9	0.000148057 0
$936$	7.94007e10	0.00338129
$937$	−4.08252e13	−1.73022	−0.865108	−	0.501585i	$-0.832750\pi$
$937$	−4.08252e13	−1.73022	−0.865108	+	0.501585i	$0.832750\pi$
$938$	9.64789e11	0.0406930
$939$	−1.58619e13	−0.665824
$940$	2.04937e10	0.000856141 0
$941$	2.07456e13	0.862526	0.431263	−	0.902226i	$-0.358068\pi$
$941$	2.07456e13	0.862526	0.431263	+	0.902226i	$0.358068\pi$
$942$	−5.86546e12	−0.242702
$943$	2.67246e13	1.10055
$944$	−4.59658e12	−0.188391
$945$	9.89078e10	0.00403448
$946$	1.38290e11	0.00561412
$947$	1.68721e13	0.681700	0.340850	−	0.940118i	$-0.389285\pi$
$947$	1.68721e13	0.681700	0.340850	+	0.940118i	$0.389285\pi$
$948$	3.17064e13	1.27500
$949$	−3.60956e12	−0.144463
$950$	−5.04824e11	−0.0201087
$951$	−1.13363e13	−0.449426
$952$	6.01655e11	0.0237400
$953$	−1.38338e13	−0.543280	−0.271640	−	0.962399i	$-0.587566\pi$
$953$	−1.38338e13	−0.543280	−0.271640	+	0.962399i	$0.587566\pi$
$954$	1.74835e11	0.00683377
$955$	−4.91534e10	−0.00191222
$956$	1.07527e13	0.416350
$957$	−6.02336e11	−0.0232132
$958$	−4.33780e11	−0.0166389
$959$	−1.02889e13	−0.392811
$960$	2.67380e11	0.0101603
$961$	−2.03348e13	−0.769103
$962$	−8.22493e10	−0.00309631
$963$	9.33176e11	0.0349659
$964$	−1.73021e13	−0.645287
$965$	6.81629e10	0.00253032
$966$	8.43430e11	0.0311639
$967$	2.30154e13	0.846448	0.423224	−	0.906025i	$-0.360898\pi$
$967$	2.30154e13	0.846448	0.423224	+	0.906025i	$0.360898\pi$
$968$	−6.82571e12	−0.249867
$969$	−1.12162e12	−0.0408684
$970$	1.95849e10	0.000710313 0
$971$	2.99062e13	1.07963	0.539814	−	0.841784i	$-0.318495\pi$
$971$	2.99062e13	1.07963	0.539814	+	0.841784i	$0.318495\pi$
$972$	2.66223e12	0.0956638
$973$	2.19159e12	0.0783884
$974$	2.17223e11	0.00773377
$975$	−8.01331e12	−0.283982
$976$	−2.36095e13	−0.832843
$977$	−3.16873e13	−1.11265	−0.556326	−	0.830964i	$-0.687789\pi$
$977$	−3.16873e13	−1.11265	−0.556326	+	0.830964i	$0.687789\pi$
$978$	−1.20367e12	−0.0420711
$979$	6.42412e11	0.0223507
$980$	4.44750e10	0.00154028
$981$	−5.72999e11	−0.0197535
$982$	2.07406e12	0.0711736
$983$	1.11886e13	0.382194	0.191097	−	0.981571i	$-0.438795\pi$
$983$	1.11886e13	0.382194	0.191097	+	0.981571i	$0.438795\pi$
$984$	−1.30290e13	−0.443029
$985$	1.92623e11	0.00651995
$986$	−3.95053e11	−0.0133109
$987$	9.16310e11	0.0307337
$988$	1.30156e12	0.0434569
$989$	−1.58132e13	−0.525576
$990$	−1.09706e8	−3.62972e−6 0
$991$	−2.37751e13	−0.783052	−0.391526	−	0.920167i	$-0.628053\pi$
$991$	−2.37751e13	−0.783052	−0.391526	+	0.920167i	$0.628053\pi$
$992$	5.43568e12	0.178218
$993$	1.17925e13	0.384889
$994$	1.84718e12	0.0600164
$995$	−2.65477e11	−0.00858662
$996$	2.77941e12	0.0894922
$997$	4.78551e13	1.53391	0.766956	−	0.641700i	$-0.221770\pi$
$997$	4.78551e13	1.53391	0.766956	+	0.641700i	$0.221770\pi$
$998$	−7.72927e12	−0.246633
$999$	−2.71079e12	−0.0861094

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.a.1.6	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.a.1.6	✓	12	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:	\( N \)	\(=\)	\( 91 = 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	91.a (trivial)

\(f(q)\)	\(=\)	\(q-2.85796 q^{2} +143.668 q^{3} -503.832 q^{4} -15.3125 q^{5} -410.598 q^{6} +2401.00 q^{7} +2903.21 q^{8} +957.575 q^{9} +O(q^{10})\)	\(q-2.85796 q^{2} +143.668 q^{3} -503.832 q^{4} -15.3125 q^{5} -410.598 q^{6} +2401.00 q^{7} +2903.21 q^{8} +957.575 q^{9} +43.7625 q^{10} -2617.92 q^{11} -72384.7 q^{12} +28561.0 q^{13} -6861.96 q^{14} -2199.92 q^{15} +249665. q^{16} +86313.3 q^{17} -2736.71 q^{18} -90449.5 q^{19} +7714.92 q^{20} +344948. q^{21} +7481.92 q^{22} -855540. q^{23} +417099. q^{24} -1.95289e6 q^{25} -81626.2 q^{26} -2.69025e6 q^{27} -1.20970e6 q^{28} +1.60148e6 q^{29} +6287.28 q^{30} -2.47079e6 q^{31} -2.19997e6 q^{32} -376112. q^{33} -246680. q^{34} -36765.3 q^{35} -482457. q^{36} +1.00763e6 q^{37} +258501. q^{38} +4.10331e6 q^{39} -44455.3 q^{40} -3.12371e7 q^{41} -985846. q^{42} +1.84833e7 q^{43} +1.31899e6 q^{44} -14662.9 q^{45} +2.44510e6 q^{46} +2.65637e6 q^{47} +3.58689e7 q^{48} +5.76480e6 q^{49} +5.58128e6 q^{50} +1.24005e7 q^{51} -1.43899e7 q^{52} -6.38851e7 q^{53} +7.68862e6 q^{54} +40086.9 q^{55} +6.97060e6 q^{56} -1.29947e7 q^{57} -4.57696e6 q^{58} -1.84110e7 q^{59} +1.10839e6 q^{60} -9.45649e7 q^{61} +7.06143e6 q^{62} +2.29914e6 q^{63} -1.21541e8 q^{64} -437340. q^{65} +1.07491e6 q^{66} -1.40600e8 q^{67} -4.34874e7 q^{68} -1.22914e8 q^{69} +105074. q^{70} -2.69191e8 q^{71} +2.78004e6 q^{72} -1.26381e8 q^{73} -2.87978e6 q^{74} -2.80568e8 q^{75} +4.55713e7 q^{76} -6.28563e6 q^{77} -1.17271e7 q^{78} -4.38026e8 q^{79} -3.82299e6 q^{80} -4.05351e8 q^{81} +8.92745e7 q^{82} -3.83977e7 q^{83} -1.73796e8 q^{84} -1.32167e6 q^{85} -5.28244e7 q^{86} +2.30082e8 q^{87} -7.60037e6 q^{88} -2.45390e8 q^{89} +41905.8 q^{90} +6.85750e7 q^{91} +4.31048e8 q^{92} -3.54975e8 q^{93} -7.59181e6 q^{94} +1.38501e6 q^{95} -3.16066e8 q^{96} +4.47528e8 q^{97} -1.64756e7 q^{98} -2.50686e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 21 q^{2} - 323 q^{3} + 2945 q^{4} - 5202 q^{5} - 9897 q^{6} + 28812 q^{7} - 25431 q^{8} + 78519 q^{9}+O(q^{10}) \) 12 * q - 21 * q^2 - 323 * q^3 + 2945 * q^4 - 5202 * q^5 - 9897 * q^6 + 28812 * q^7 - 25431 * q^8 + 78519 * q^9	\( 12 q - 21 q^{2} - 323 q^{3} + 2945 q^{4} - 5202 q^{5} - 9897 q^{6} + 28812 q^{7} - 25431 q^{8} + 78519 q^{9} - 65812 q^{10} - 80061 q^{11} - 184395 q^{12} + 342732 q^{13} - 50421 q^{14} + 160096 q^{15} + 385497 q^{16} - 1493598 q^{17} + 1520858 q^{18} - 109038 q^{19} - 622260 q^{20} - 775523 q^{21} + 4636975 q^{22} - 3367443 q^{23} - 5963895 q^{24} - 51480 q^{25} - 599781 q^{26} - 8158937 q^{27} + 7070945 q^{28} - 13333098 q^{29} + 2915424 q^{30} - 3954765 q^{31} + 4389297 q^{32} - 5790219 q^{33} + 14879968 q^{34} - 12490002 q^{35} + 80697058 q^{36} + 580535 q^{37} - 19134246 q^{38} - 9225203 q^{39} + 12365024 q^{40} - 27018171 q^{41} - 23762697 q^{42} + 31237588 q^{43} - 125053839 q^{44} - 62765470 q^{45} - 114008121 q^{46} - 21983709 q^{47} - 309724207 q^{48} + 69177612 q^{49} - 131331747 q^{50} - 176522692 q^{51} + 84112145 q^{52} - 196548234 q^{53} - 456152547 q^{54} - 309055872 q^{55} - 61059831 q^{56} - 274411494 q^{57} - 521980612 q^{58} - 215907906 q^{59} - 177006648 q^{60} - 218340705 q^{61} - 673289997 q^{62} + 188524119 q^{63} - 386667247 q^{64} - 148574322 q^{65} - 777397365 q^{66} + 14544775 q^{67} - 1246637448 q^{68} - 65252625 q^{69} - 158014612 q^{70} - 552451776 q^{71} + 369379470 q^{72} - 349395159 q^{73} + 73591023 q^{74} + 329300747 q^{75} - 1036299002 q^{76} - 192226461 q^{77} - 282668217 q^{78} + 962249727 q^{79} - 1494536184 q^{80} + 874458108 q^{81} - 1417698067 q^{82} - 2032575912 q^{83} - 442732395 q^{84} - 411671064 q^{85} - 2139249420 q^{86} - 759642172 q^{87} + 558651957 q^{88} - 280821684 q^{89} - 5764700804 q^{90} + 822899532 q^{91} - 4491569571 q^{92} - 1729557923 q^{93} - 1591372165 q^{94} - 1282463328 q^{95} - 2148993055 q^{96} - 2115165937 q^{97} - 121060821 q^{98} - 3595669198 q^{99}+O(q^{100}) \) 12 * q - 21 * q^2 - 323 * q^3 + 2945 * q^4 - 5202 * q^5 - 9897 * q^6 + 28812 * q^7 - 25431 * q^8 + 78519 * q^9 - 65812 * q^10 - 80061 * q^11 - 184395 * q^12 + 342732 * q^13 - 50421 * q^14 + 160096 * q^15 + 385497 * q^16 - 1493598 * q^17 + 1520858 * q^18 - 109038 * q^19 - 622260 * q^20 - 775523 * q^21 + 4636975 * q^22 - 3367443 * q^23 - 5963895 * q^24 - 51480 * q^25 - 599781 * q^26 - 8158937 * q^27 + 7070945 * q^28 - 13333098 * q^29 + 2915424 * q^30 - 3954765 * q^31 + 4389297 * q^32 - 5790219 * q^33 + 14879968 * q^34 - 12490002 * q^35 + 80697058 * q^36 + 580535 * q^37 - 19134246 * q^38 - 9225203 * q^39 + 12365024 * q^40 - 27018171 * q^41 - 23762697 * q^42 + 31237588 * q^43 - 125053839 * q^44 - 62765470 * q^45 - 114008121 * q^46 - 21983709 * q^47 - 309724207 * q^48 + 69177612 * q^49 - 131331747 * q^50 - 176522692 * q^51 + 84112145 * q^52 - 196548234 * q^53 - 456152547 * q^54 - 309055872 * q^55 - 61059831 * q^56 - 274411494 * q^57 - 521980612 * q^58 - 215907906 * q^59 - 177006648 * q^60 - 218340705 * q^61 - 673289997 * q^62 + 188524119 * q^63 - 386667247 * q^64 - 148574322 * q^65 - 777397365 * q^66 + 14544775 * q^67 - 1246637448 * q^68 - 65252625 * q^69 - 158014612 * q^70 - 552451776 * q^71 + 369379470 * q^72 - 349395159 * q^73 + 73591023 * q^74 + 329300747 * q^75 - 1036299002 * q^76 - 192226461 * q^77 - 282668217 * q^78 + 962249727 * q^79 - 1494536184 * q^80 + 874458108 * q^81 - 1417698067 * q^82 - 2032575912 * q^83 - 442732395 * q^84 - 411671064 * q^85 - 2139249420 * q^86 - 759642172 * q^87 + 558651957 * q^88 - 280821684 * q^89 - 5764700804 * q^90 + 822899532 * q^91 - 4491569571 * q^92 - 1729557923 * q^93 - 1591372165 * q^94 - 1282463328 * q^95 - 2148993055 * q^96 - 2115165937 * q^97 - 121060821 * q^98 - 3595669198 * q^99

Introduction

L-functions

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