LMFDB - Embedded newform 91.10.a.a.1.4

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			1.4
Root			$-22.2119$ 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)

$f(q)$	$=$	$q-24.2119 q^{2} +6.29566 q^{3} +74.2177 q^{4} +2011.41 q^{5} -152.430 q^{6} +2401.00 q^{7} +10599.6 q^{8} -19643.4 q^{9} +O(q^{10})$	\(q-24.2119 q^{2} +6.29566 q^{3} +74.2177 q^{4} +2011.41 q^{5} -152.430 q^{6} +2401.00 q^{7} +10599.6 q^{8} -19643.4 q^{9} -48700.2 q^{10} -30042.8 q^{11} +467.250 q^{12} +28561.0 q^{13} -58132.8 q^{14} +12663.2 q^{15} -294635. q^{16} -576543. q^{17} +475604. q^{18} +282669. q^{19} +149282. q^{20} +15115.9 q^{21} +727393. q^{22} +1.75925e6 q^{23} +66731.3 q^{24} +2.09265e6 q^{25} -691517. q^{26} -247586. q^{27} +178197. q^{28} -28745.8 q^{29} -306600. q^{30} -6.18815e6 q^{31} +1.70671e6 q^{32} -189139. q^{33} +1.39592e7 q^{34} +4.82940e6 q^{35} -1.45788e6 q^{36} -4.71914e6 q^{37} -6.84397e6 q^{38} +179810. q^{39} +2.13201e7 q^{40} +3.07403e7 q^{41} -365985. q^{42} +1.13424e7 q^{43} -2.22970e6 q^{44} -3.95109e7 q^{45} -4.25948e7 q^{46} -3.74184e7 q^{47} -1.85492e6 q^{48} +5.76480e6 q^{49} -5.06672e7 q^{50} -3.62972e6 q^{51} +2.11973e6 q^{52} +3.09065e7 q^{53} +5.99453e6 q^{54} -6.04284e7 q^{55} +2.54495e7 q^{56} +1.77959e6 q^{57} +695991. q^{58} -3.11616e7 q^{59} +939831. q^{60} -1.96023e8 q^{61} +1.49827e8 q^{62} -4.71637e7 q^{63} +1.09530e8 q^{64} +5.74479e7 q^{65} +4.57943e6 q^{66} -2.53265e8 q^{67} -4.27897e7 q^{68} +1.10756e7 q^{69} -1.16929e8 q^{70} -3.89974e8 q^{71} -2.08211e8 q^{72} -1.45469e8 q^{73} +1.14260e8 q^{74} +1.31746e7 q^{75} +2.09791e7 q^{76} -7.21327e7 q^{77} -4.35356e6 q^{78} -1.55125e8 q^{79} -5.92633e8 q^{80} +3.85082e8 q^{81} -7.44283e8 q^{82} -2.55020e8 q^{83} +1.12187e6 q^{84} -1.15967e9 q^{85} -2.74622e8 q^{86} -180974. q^{87} -3.18440e8 q^{88} +8.80255e8 q^{89} +9.56635e8 q^{90} +6.85750e7 q^{91} +1.30567e8 q^{92} -3.89585e7 q^{93} +9.05973e8 q^{94} +5.68564e8 q^{95} +1.07449e7 q^{96} +1.53722e8 q^{97} -1.39577e8 q^{98} +5.90141e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−24.2119	−1.07003	−0.535013	−	0.844844i	$-0.679693\pi$
$2$	−24.2119	−1.07003	−0.535013	+	0.844844i	$0.679693\pi$
$3$	6.29566	0.0448741	0.0224371	−	0.999748i	$-0.492857\pi$
$3$	6.29566	0.0448741	0.0224371	+	0.999748i	$0.492857\pi$
$4$	74.2177	0.144956
$5$	2011.41	1.43925	0.719625	−	0.694363i	$-0.244314\pi$
$5$	2011.41	1.43925	0.719625	+	0.694363i	$0.244314\pi$
$6$	−152.430	−0.0480165
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	10599.6	0.914919
$9$	−19643.4	−0.997986
$10$	−48700.2	−1.54003
$11$	−30042.8	−0.618690	−0.309345	−	0.950950i	$-0.600110\pi$
$11$	−30042.8	−0.618690	−0.309345	+	0.950950i	$0.600110\pi$
$12$	467.250	0.00650479
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	−58132.8	−0.404432
$15$	12663.2	0.0645850
$16$	−294635.	−1.12394
$17$	−576543.	−1.67422	−0.837108	−	0.547037i	$-0.815756\pi$
$17$	−576543.	−1.67422	−0.837108	+	0.547037i	$0.815756\pi$
$18$	475604.	1.06787
$19$	282669.	0.497608	0.248804	−	0.968554i	$-0.419962\pi$
$19$	282669.	0.497608	0.248804	+	0.968554i	$0.419962\pi$
$20$	149282.	0.208628
$21$	15115.9	0.0169608
$22$	727393.	0.662014
$23$	1.75925e6	1.31085	0.655423	−	0.755262i	$-0.272491\pi$
$23$	1.75925e6	1.31085	0.655423	+	0.755262i	$0.272491\pi$
$24$	66731.3	0.0410562
$25$	2.09265e6	1.07144
$26$	−691517.	−0.296772
$27$	−247586.	−0.0896579
$28$	178197.	0.0547884
$29$	−28745.8	−0.00754715	−0.00377358	−	0.999993i	$-0.501201\pi$
$29$	−28745.8	−0.00754715	−0.00377358	+	0.999993i	$0.501201\pi$
$30$	−306600.	−0.0691077
$31$	−6.18815e6	−1.20347	−0.601733	−	0.798698i	$-0.705523\pi$
$31$	−6.18815e6	−1.20347	−0.601733	+	0.798698i	$0.705523\pi$
$32$	1.70671e6	0.287731
$33$	−189139.	−0.0277632
$34$	1.39592e7	1.79146
$35$	4.82940e6	0.543985
$36$	−1.45788e6	−0.144664
$37$	−4.71914e6	−0.413957	−0.206979	−	0.978345i	$-0.566363\pi$
$37$	−4.71914e6	−0.413957	−0.206979	+	0.978345i	$0.566363\pi$
$38$	−6.84397e6	−0.532454
$39$	179810.	0.0124458
$40$	2.13201e7	1.31680
$41$	3.07403e7	1.69895	0.849476	−	0.527628i	$-0.176918\pi$
$41$	3.07403e7	1.69895	0.849476	+	0.527628i	$0.176918\pi$
$42$	−365985.	−0.0181485
$43$	1.13424e7	0.505939	0.252969	−	0.967474i	$-0.418593\pi$
$43$	1.13424e7	0.505939	0.252969	+	0.967474i	$0.418593\pi$
$44$	−2.22970e6	−0.0896830
$45$	−3.95109e7	−1.43635
$46$	−4.25948e7	−1.40264
$47$	−3.74184e7	−1.11852	−0.559262	−	0.828991i	$-0.688915\pi$
$47$	−3.74184e7	−1.11852	−0.559262	+	0.828991i	$0.688915\pi$
$48$	−1.85492e6	−0.0504360
$49$	5.76480e6	0.142857
$50$	−5.06672e7	−1.14647
$51$	−3.62972e6	−0.0751290
$52$	2.11973e6	0.0402037
$53$	3.09065e7	0.538033	0.269016	−	0.963136i	$-0.413301\pi$
$53$	3.09065e7	0.538033	0.269016	+	0.963136i	$0.413301\pi$
$54$	5.99453e6	0.0959363
$55$	−6.04284e7	−0.890449
$56$	2.54495e7	0.345807
$57$	1.77959e6	0.0223297
$58$	695991.	0.00807565
$59$	−3.11616e7	−0.334800	−0.167400	−	0.985889i	$-0.553537\pi$
$59$	−3.11616e7	−0.334800	−0.167400	+	0.985889i	$0.553537\pi$
$60$	939831.	0.00936201
$61$	−1.96023e8	−1.81268	−0.906342	−	0.422545i	$-0.861137\pi$
$61$	−1.96023e8	−1.81268	−0.906342	+	0.422545i	$0.861137\pi$
$62$	1.49827e8	1.28774
$63$	−4.71637e7	−0.377203
$64$	1.09530e8	0.816065
$65$	5.74479e7	0.399176
$66$	4.57943e6	0.0297073
$67$	−2.53265e8	−1.53546	−0.767731	−	0.640773i	$-0.778614\pi$
$67$	−2.53265e8	−1.53546	−0.767731	+	0.640773i	$0.778614\pi$
$68$	−4.27897e7	−0.242688
$69$	1.10756e7	0.0588230
$70$	−1.16929e8	−0.582078
$71$	−3.89974e8	−1.82127	−0.910633	−	0.413216i	$-0.864406\pi$
$71$	−3.89974e8	−1.82127	−0.910633	+	0.413216i	$0.864406\pi$
$72$	−2.08211e8	−0.913077
$73$	−1.45469e8	−0.599540	−0.299770	−	0.954012i	$-0.596910\pi$
$73$	−1.45469e8	−0.599540	−0.299770	+	0.954012i	$0.596910\pi$
$74$	1.14260e8	0.442945
$75$	1.31746e7	0.0480798
$76$	2.09791e7	0.0721315
$77$	−7.21327e7	−0.233843
$78$	−4.35356e6	−0.0133174
$79$	−1.55125e8	−0.448085	−0.224042	−	0.974579i	$-0.571925\pi$
$79$	−1.55125e8	−0.448085	−0.224042	+	0.974579i	$0.571925\pi$
$80$	−5.92633e8	−1.61764
$81$	3.85082e8	0.993963
$82$	−7.44283e8	−1.81792
$83$	−2.55020e8	−0.589825	−0.294913	−	0.955524i	$-0.595291\pi$
$83$	−2.55020e8	−0.589825	−0.294913	+	0.955524i	$0.595291\pi$
$84$	1.12187e6	0.00245858
$85$	−1.15967e9	−2.40961
$86$	−2.74622e8	−0.541368
$87$	−180974.	−0.000338672 0
$88$	−3.18440e8	−0.566051
$89$	8.80255e8	1.48715	0.743573	−	0.668655i	$-0.233130\pi$
$89$	8.80255e8	1.48715	0.743573	+	0.668655i	$0.233130\pi$
$90$	9.56635e8	1.53693
$91$	6.85750e7	0.104828
$92$	1.30567e8	0.190015
$93$	−3.89585e7	−0.0540044
$94$	9.05973e8	1.19685
$95$	5.68564e8	0.716182
$96$	1.07449e7	0.0129117
$97$	1.53722e8	0.176304	0.0881522	−	0.996107i	$-0.471904\pi$
$97$	1.53722e8	0.176304	0.0881522	+	0.996107i	$0.471904\pi$
$98$	−1.39577e8	−0.152861
$99$	5.90141e8	0.617444
$100$	1.55312e8	0.155312
$101$	−8.47811e7	−0.0810687	−0.0405343	−	0.999178i	$-0.512906\pi$
$101$	−8.47811e7	−0.0810687	−0.0405343	+	0.999178i	$0.512906\pi$
$102$	8.78826e7	0.0803900
$103$	−7.58258e8	−0.663818	−0.331909	−	0.943311i	$-0.607693\pi$
$103$	−7.58258e8	−0.663818	−0.331909	+	0.943311i	$0.607693\pi$
$104$	3.02734e8	0.253753
$105$	3.04043e7	0.0244108
$106$	−7.48306e8	−0.575709
$107$	3.33641e8	0.246066	0.123033	−	0.992403i	$-0.460738\pi$
$107$	3.33641e8	0.246066	0.123033	+	0.992403i	$0.460738\pi$
$108$	−1.83752e7	−0.0129965
$109$	1.41941e9	0.963135	0.481568	−	0.876409i	$-0.340068\pi$
$109$	1.41941e9	0.963135	0.481568	+	0.876409i	$0.340068\pi$
$110$	1.46309e9	0.952803
$111$	−2.97101e7	−0.0185760
$112$	−7.07419e8	−0.424811
$113$	−1.52248e9	−0.878412	−0.439206	−	0.898386i	$-0.644740\pi$
$113$	−1.52248e9	−0.878412	−0.439206	+	0.898386i	$0.644740\pi$
$114$	−4.30873e7	−0.0238934
$115$	3.53857e9	1.88663
$116$	−2.13345e6	−0.00109401
$117$	−5.61034e8	−0.276792
$118$	7.54482e8	0.358245
$119$	−1.38428e9	−0.632794
$120$	1.34224e8	0.0590901
$121$	−1.45538e9	−0.617223
$122$	4.74609e9	1.93962
$123$	1.93531e8	0.0762390
$124$	−4.59270e8	−0.174450
$125$	2.80647e8	0.102817
$126$	1.14192e9	0.403618
$127$	1.69398e8	0.0577820	0.0288910	−	0.999583i	$-0.490802\pi$
$127$	1.69398e8	0.0577820	0.0288910	+	0.999583i	$0.490802\pi$
$128$	−3.52578e9	−1.16094
$129$	7.14081e7	0.0227036
$130$	−1.39093e9	−0.427129
$131$	1.11398e9	0.330487	0.165244	−	0.986253i	$-0.447159\pi$
$131$	1.11398e9	0.330487	0.165244	+	0.986253i	$0.447159\pi$
$132$	−1.40375e7	−0.00402445
$133$	6.78689e8	0.188078
$134$	6.13204e9	1.64298
$135$	−4.97997e8	−0.129040
$136$	−6.11110e9	−1.53177
$137$	−3.16000e9	−0.766380	−0.383190	−	0.923669i	$-0.625175\pi$
$137$	−3.16000e9	−0.766380	−0.383190	+	0.923669i	$0.625175\pi$
$138$	−2.68162e8	−0.0629422
$139$	1.38977e9	0.315773	0.157887	−	0.987457i	$-0.449532\pi$
$139$	1.38977e9	0.315773	0.157887	+	0.987457i	$0.449532\pi$
$140$	3.58427e8	0.0788541
$141$	−2.35574e8	−0.0501928
$142$	9.44203e9	1.94880
$143$	−8.58051e8	−0.171594
$144$	5.78763e9	1.12168
$145$	−5.78196e7	−0.0108622
$146$	3.52209e9	0.641523
$147$	3.62933e7	0.00641059
$148$	−3.50244e8	−0.0600057
$149$	−9.59418e9	−1.59466	−0.797332	−	0.603540i	$-0.793756\pi$
$149$	−9.59418e9	−1.59466	−0.797332	+	0.603540i	$0.793756\pi$
$150$	−3.18983e8	−0.0514467
$151$	4.88287e9	0.764326	0.382163	−	0.924095i	$-0.375179\pi$
$151$	4.88287e9	0.764326	0.382163	+	0.924095i	$0.375179\pi$
$152$	2.99617e9	0.455271
$153$	1.13252e10	1.67085
$154$	1.74647e9	0.250218
$155$	−1.24469e10	−1.73209
$156$	1.33451e7	0.00180410
$157$	−1.28335e10	−1.68576	−0.842882	−	0.538098i	$-0.819143\pi$
$157$	−1.28335e10	−1.68576	−0.842882	+	0.538098i	$0.819143\pi$
$158$	3.75588e9	0.479463
$159$	1.94577e8	0.0241437
$160$	3.43291e9	0.414116
$161$	4.22395e9	0.495453
$162$	−9.32357e9	−1.06357
$163$	−4.22651e9	−0.468962	−0.234481	−	0.972121i	$-0.575339\pi$
$163$	−4.22651e9	−0.468962	−0.234481	+	0.972121i	$0.575339\pi$
$164$	2.28148e9	0.246274
$165$	−3.80437e8	−0.0399581
$166$	6.17454e9	0.631129
$167$	−1.66408e10	−1.65558	−0.827791	−	0.561037i	$-0.810403\pi$
$167$	−1.66408e10	−1.65558	−0.827791	+	0.561037i	$0.810403\pi$
$168$	1.60222e8	0.0155178
$169$	8.15731e8	0.0769231
$170$	2.80777e10	2.57835
$171$	−5.55258e9	−0.496606
$172$	8.41809e8	0.0733391
$173$	8.89469e9	0.754959	0.377480	−	0.926018i	$-0.376791\pi$
$173$	8.89469e9	0.754959	0.377480	+	0.926018i	$0.376791\pi$
$174$	4.38173e6	0.000362388 0
$175$	5.02446e9	0.404965
$176$	8.85166e9	0.695373
$177$	−1.96183e8	−0.0150238
$178$	−2.13127e10	−1.59129
$179$	−2.13424e10	−1.55383	−0.776916	−	0.629604i	$-0.783217\pi$
$179$	−2.13424e10	−1.55383	−0.776916	+	0.629604i	$0.783217\pi$
$180$	−2.93241e9	−0.208208
$181$	−1.27540e9	−0.0883268	−0.0441634	−	0.999024i	$-0.514062\pi$
$181$	−1.27540e9	−0.0883268	−0.0441634	+	0.999024i	$0.514062\pi$
$182$	−1.66033e9	−0.112169
$183$	−1.23409e9	−0.0813426
$184$	1.86472e10	1.19932
$185$	−9.49214e9	−0.595788
$186$	9.43262e8	0.0577862
$187$	1.73210e10	1.03582
$188$	−2.77711e9	−0.162137
$189$	−5.94453e8	−0.0338875
$190$	−1.37660e10	−0.766334
$191$	6.83481e9	0.371601	0.185800	−	0.982588i	$-0.440512\pi$
$191$	6.83481e9	0.371601	0.185800	+	0.982588i	$0.440512\pi$
$192$	6.89566e8	0.0366202
$193$	−3.40888e10	−1.76850	−0.884248	−	0.467018i	$-0.845329\pi$
$193$	−3.40888e10	−1.76850	−0.884248	+	0.467018i	$0.845329\pi$
$194$	−3.72190e9	−0.188650
$195$	3.61673e8	0.0179127
$196$	4.27850e8	0.0207081
$197$	2.78745e8	0.0131859	0.00659295	−	0.999978i	$-0.497901\pi$
$197$	2.78745e8	0.0131859	0.00659295	+	0.999978i	$0.497901\pi$
$198$	−1.42885e10	−0.660681
$199$	1.97894e10	0.894528	0.447264	−	0.894402i	$-0.352399\pi$
$199$	1.97894e10	0.894528	0.447264	+	0.894402i	$0.352399\pi$
$200$	2.21812e10	0.980279
$201$	−1.59447e9	−0.0689025
$202$	2.05272e9	0.0867456
$203$	−6.90186e7	−0.00285256
$204$	−2.69390e8	−0.0108904
$205$	6.18314e10	2.44521
$206$	1.83589e10	0.710303
$207$	−3.45575e10	−1.30821
$208$	−8.41508e9	−0.311726
$209$	−8.49217e9	−0.307865
$210$	−7.36146e8	−0.0261203
$211$	1.12980e10	0.392403	0.196201	−	0.980564i	$-0.437139\pi$
$211$	1.12980e10	0.392403	0.196201	+	0.980564i	$0.437139\pi$
$212$	2.29381e9	0.0779913
$213$	−2.45515e9	−0.0817277
$214$	−8.07809e9	−0.263297
$215$	2.28143e10	0.728172
$216$	−2.62430e9	−0.0820297
$217$	−1.48578e10	−0.454867
$218$	−3.43665e10	−1.03058
$219$	−9.15825e8	−0.0269038
$220$	−4.48485e9	−0.129076
$221$	−1.64666e10	−0.464344
$222$	7.19340e8	0.0198768
$223$	3.00947e10	0.814927	0.407464	−	0.913221i	$-0.366413\pi$
$223$	3.00947e10	0.814927	0.407464	+	0.913221i	$0.366413\pi$
$224$	4.09782e9	0.108752
$225$	−4.11067e10	−1.06928
$226$	3.68621e10	0.939924
$227$	4.82417e9	0.120589	0.0602943	−	0.998181i	$-0.480796\pi$
$227$	4.82417e9	0.120589	0.0602943	+	0.998181i	$0.480796\pi$
$228$	1.32077e8	0.00323684
$229$	5.42517e9	0.130363	0.0651814	−	0.997873i	$-0.479237\pi$
$229$	5.42517e9	0.130363	0.0651814	+	0.997873i	$0.479237\pi$
$230$	−8.56756e10	−2.01875
$231$	−4.54123e8	−0.0104935
$232$	−3.04693e8	−0.00690504
$233$	−7.74224e10	−1.72094	−0.860469	−	0.509504i	$-0.829829\pi$
$233$	−7.74224e10	−1.72094	−0.860469	+	0.509504i	$0.829829\pi$
$234$	1.35837e10	0.296174
$235$	−7.52639e10	−1.60983
$236$	−2.31274e9	−0.0485314
$237$	−9.76616e8	−0.0201074
$238$	3.35161e10	0.677107
$239$	−2.04264e10	−0.404950	−0.202475	−	0.979287i	$-0.564898\pi$
$239$	−2.04264e10	−0.404950	−0.202475	+	0.979287i	$0.564898\pi$
$240$	−3.73102e9	−0.0725900
$241$	−6.20364e10	−1.18460	−0.592298	−	0.805719i	$-0.701779\pi$
$241$	−6.20364e10	−1.18460	−0.592298	+	0.805719i	$0.701779\pi$
$242$	3.52376e10	0.660445
$243$	7.29757e9	0.134261
$244$	−1.45484e10	−0.262760
$245$	1.15954e10	0.205607
$246$	−4.68575e9	−0.0815777
$247$	8.07332e9	0.138012
$248$	−6.55917e10	−1.10107
$249$	−1.60552e9	−0.0264679
$250$	−6.79500e9	−0.110017
$251$	4.99797e10	0.794807	0.397404	−	0.917644i	$-0.369911\pi$
$251$	4.99797e10	0.794807	0.397404	+	0.917644i	$0.369911\pi$
$252$	−3.50038e9	−0.0546780
$253$	−5.28526e10	−0.811006
$254$	−4.10146e9	−0.0618283
$255$	−7.30087e9	−0.108129
$256$	2.92864e10	0.426173
$257$	−6.64363e10	−0.949962	−0.474981	−	0.879996i	$-0.657545\pi$
$257$	−6.64363e10	−0.949962	−0.474981	+	0.879996i	$0.657545\pi$
$258$	−1.72893e9	−0.0242934
$259$	−1.13307e10	−0.156461
$260$	4.26365e9	0.0578631
$261$	5.64664e8	0.00753196
$262$	−2.69715e10	−0.353630
$263$	3.84218e10	0.495196	0.247598	−	0.968863i	$-0.420359\pi$
$263$	3.84218e10	0.495196	0.247598	+	0.968863i	$0.420359\pi$
$264$	−2.00479e9	−0.0254010
$265$	6.21657e10	0.774363
$266$	−1.64324e10	−0.201249
$267$	5.54179e9	0.0667344
$268$	−1.87968e10	−0.222575
$269$	−1.40719e11	−1.63857	−0.819287	−	0.573384i	$-0.805630\pi$
$269$	−1.40719e11	−1.63857	−0.819287	+	0.573384i	$0.805630\pi$
$270$	1.20575e10	0.138076
$271$	1.54656e11	1.74182	0.870912	−	0.491440i	$-0.163529\pi$
$271$	1.54656e11	1.74182	0.870912	+	0.491440i	$0.163529\pi$
$272$	1.69870e11	1.88173
$273$	4.31725e8	0.00470409
$274$	7.65097e10	0.820047
$275$	−6.28691e10	−0.662888
$276$	8.22007e8	0.00852677
$277$	3.62631e10	0.370089	0.185044	−	0.982730i	$-0.440757\pi$
$277$	3.62631e10	0.370089	0.185044	+	0.982730i	$0.440757\pi$
$278$	−3.36489e10	−0.337885
$279$	1.21556e11	1.20104
$280$	5.11895e10	0.497702
$281$	−1.13196e11	−1.08306	−0.541531	−	0.840680i	$-0.682155\pi$
$281$	−1.13196e11	−1.08306	−0.541531	+	0.840680i	$0.682155\pi$
$282$	5.70370e9	0.0537076
$283$	1.31351e11	1.21729	0.608647	−	0.793441i	$-0.291713\pi$
$283$	1.31351e11	1.21729	0.608647	+	0.793441i	$0.291713\pi$
$284$	−2.89430e10	−0.264004
$285$	3.57949e9	0.0321380
$286$	2.07751e10	0.183610
$287$	7.38075e10	0.642143
$288$	−3.35256e10	−0.287151
$289$	2.13814e11	1.80300
$290$	1.39992e9	0.0116229
$291$	9.67782e8	0.00791150
$292$	−1.07964e10	−0.0869071
$293$	1.04899e11	0.831508	0.415754	−	0.909477i	$-0.363518\pi$
$293$	1.04899e11	0.831508	0.415754	+	0.909477i	$0.363518\pi$
$294$	−8.78730e8	−0.00685950
$295$	−6.26787e10	−0.481860
$296$	−5.00208e10	−0.378737
$297$	7.43816e9	0.0554704
$298$	2.32294e11	1.70633
$299$	5.02458e10	0.363563
$300$	9.77791e8	0.00696948
$301$	2.72332e10	0.191227
$302$	−1.18224e11	−0.817849
$303$	−5.33754e8	−0.00363789
$304$	−8.32843e10	−0.559284
$305$	−3.94282e11	−2.60890
$306$	−2.74206e11	−1.78785
$307$	1.47584e11	0.948236	0.474118	−	0.880461i	$-0.342767\pi$
$307$	1.47584e11	0.948236	0.474118	+	0.880461i	$0.342767\pi$
$308$	−5.35352e9	−0.0338970
$309$	−4.77374e9	−0.0297883
$310$	3.01364e11	1.85338
$311$	1.19975e10	0.0727227	0.0363613	−	0.999339i	$-0.488423\pi$
$311$	1.19975e10	0.0727227	0.0363613	+	0.999339i	$0.488423\pi$
$312$	1.90591e9	0.0113869
$313$	1.15683e11	0.681269	0.340635	−	0.940196i	$-0.389358\pi$
$313$	1.15683e11	0.681269	0.340635	+	0.940196i	$0.389358\pi$
$314$	3.10724e11	1.80381
$315$	−9.48657e10	−0.542890
$316$	−1.15130e10	−0.0649528
$317$	4.25724e10	0.236789	0.118395	−	0.992967i	$-0.462225\pi$
$317$	4.25724e10	0.236789	0.118395	+	0.992967i	$0.462225\pi$
$318$	−4.71109e9	−0.0258344
$319$	8.63603e8	0.00466935
$320$	2.20311e11	1.17452
$321$	2.10049e9	0.0110420
$322$	−1.02270e11	−0.530148
$323$	−1.62971e11	−0.833104
$324$	2.85799e10	0.144081
$325$	5.97682e10	0.297163
$326$	1.02332e11	0.501802
$327$	8.93610e9	0.0432198
$328$	3.25834e11	1.55440
$329$	−8.98417e10	−0.422762
$330$	9.21111e9	0.0427562
$331$	1.41353e11	0.647259	0.323629	−	0.946184i	$-0.395097\pi$
$331$	1.41353e11	0.647259	0.323629	+	0.946184i	$0.395097\pi$
$332$	−1.89270e10	−0.0854990
$333$	9.26999e10	0.413124
$334$	4.02907e11	1.77152
$335$	−5.09421e11	−2.20991
$336$	−4.45367e9	−0.0190630
$337$	−2.51597e11	−1.06260	−0.531302	−	0.847182i	$-0.678297\pi$
$337$	−2.51597e11	−1.06260	−0.531302	+	0.847182i	$0.678297\pi$
$338$	−1.97504e10	−0.0823097
$339$	−9.58501e9	−0.0394180
$340$	−8.60677e10	−0.349289
$341$	1.85909e11	0.744571
$342$	1.34439e11	0.531382
$343$	1.38413e10	0.0539949
$344$	1.20225e11	0.462893
$345$	2.22776e10	0.0846610
$346$	−2.15358e11	−0.807826
$347$	4.63528e11	1.71630	0.858151	−	0.513398i	$-0.171614\pi$
$347$	4.63528e11	1.71630	0.858151	+	0.513398i	$0.171614\pi$
$348$	−1.34315e7	−4.90927e−5 0
$349$	−1.00354e11	−0.362092	−0.181046	−	0.983475i	$-0.557948\pi$
$349$	−1.00354e11	−0.362092	−0.181046	+	0.983475i	$0.557948\pi$
$350$	−1.21652e11	−0.433324
$351$	−7.07129e9	−0.0248666
$352$	−5.12744e10	−0.178016
$353$	1.87907e11	0.644104	0.322052	−	0.946722i	$-0.395627\pi$
$353$	1.87907e11	0.644104	0.322052	+	0.946722i	$0.395627\pi$
$354$	4.74996e9	0.0160759
$355$	−7.84399e11	−2.62126
$356$	6.53305e10	0.215571
$357$	−8.71496e9	−0.0283961
$358$	5.16740e11	1.66264
$359$	4.90223e11	1.55764	0.778822	−	0.627244i	$-0.215817\pi$
$359$	4.90223e11	1.55764	0.778822	+	0.627244i	$0.215817\pi$
$360$	−4.18798e11	−1.31415
$361$	−2.42786e11	−0.752386
$362$	3.08799e10	0.0945120
$363$	−9.16258e9	−0.0276973
$364$	5.08947e9	0.0151956
$365$	−2.92598e11	−0.862887
$366$	2.98798e10	0.0870387
$367$	−3.42258e9	−0.00984820	−0.00492410	−	0.999988i	$-0.501567\pi$
$367$	−3.42258e9	−0.00984820	−0.00492410	+	0.999988i	$0.501567\pi$
$368$	−5.18336e11	−1.47332
$369$	−6.03843e11	−1.69553
$370$	2.29823e11	0.637508
$371$	7.42065e10	0.203357
$372$	−2.89141e9	−0.00782829
$373$	1.85283e11	0.495616	0.247808	−	0.968809i	$-0.420290\pi$
$373$	1.85283e11	0.495616	0.247808	+	0.968809i	$0.420290\pi$
$374$	−4.19374e11	−1.10836
$375$	1.76686e9	0.00461382
$376$	−3.96619e11	−1.02336
$377$	−8.21008e8	−0.00209320
$378$	1.43929e10	0.0362605
$379$	−1.06955e11	−0.266272	−0.133136	−	0.991098i	$-0.542505\pi$
$379$	−1.06955e11	−0.266272	−0.133136	+	0.991098i	$0.542505\pi$
$380$	4.21975e10	0.103815
$381$	1.06648e9	0.00259292
$382$	−1.65484e11	−0.397623
$383$	−6.69645e11	−1.59019	−0.795097	−	0.606482i	$-0.792580\pi$
$383$	−6.69645e11	−1.59019	−0.795097	+	0.606482i	$0.792580\pi$
$384$	−2.21971e10	−0.0520962
$385$	−1.45089e11	−0.336558
$386$	8.25356e11	1.89234
$387$	−2.22803e11	−0.504920
$388$	1.14089e10	0.0255564
$389$	−4.35983e11	−0.965376	−0.482688	−	0.875792i	$-0.660339\pi$
$389$	−4.35983e11	−0.965376	−0.482688	+	0.875792i	$0.660339\pi$
$390$	−8.75680e9	−0.0191670
$391$	−1.01428e12	−2.19464
$392$	6.11043e10	0.130703
$393$	7.01322e9	0.0148303
$394$	−6.74897e9	−0.0141093
$395$	−3.12021e11	−0.644906
$396$	4.37989e10	0.0895024
$397$	9.25523e11	1.86995	0.934975	−	0.354713i	$-0.115421\pi$
$397$	9.25523e11	1.86995	0.934975	+	0.354713i	$0.115421\pi$
$398$	−4.79140e11	−0.957168
$399$	4.27280e9	0.00843984
$400$	−6.16569e11	−1.20424
$401$	1.01599e12	1.96218	0.981088	−	0.193562i	$-0.0620041\pi$
$401$	1.01599e12	1.96218	0.981088	+	0.193562i	$0.0620041\pi$
$402$	3.86053e10	0.0737275
$403$	−1.76740e11	−0.333781
$404$	−6.29226e9	−0.0117514
$405$	7.74558e11	1.43056
$406$	1.67107e9	0.00305231
$407$	1.41776e11	0.256111
$408$	−3.84734e10	−0.0687370
$409$	−5.69331e11	−1.00603	−0.503014	−	0.864279i	$-0.667775\pi$
$409$	−5.69331e11	−1.00603	−0.503014	+	0.864279i	$0.667775\pi$
$410$	−1.49706e12	−2.61644
$411$	−1.98943e10	−0.0343906
$412$	−5.62761e10	−0.0962247
$413$	−7.48189e10	−0.126542
$414$	8.36704e11	1.39981
$415$	−5.12951e11	−0.848906
$416$	4.87455e10	0.0798021
$417$	8.74950e9	0.0141700
$418$	2.05612e11	0.329424
$419$	−9.48916e11	−1.50406	−0.752029	−	0.659130i	$-0.770925\pi$
$419$	−9.48916e11	−1.50406	−0.752029	+	0.659130i	$0.770925\pi$
$420$	2.25653e9	0.00353851
$421$	4.56911e11	0.708863	0.354431	−	0.935082i	$-0.384674\pi$
$421$	4.56911e11	0.708863	0.354431	+	0.935082i	$0.384674\pi$
$422$	−2.73547e11	−0.419881
$423$	7.35024e11	1.11627
$424$	3.27595e11	0.492256
$425$	−1.20650e12	−1.79382
$426$	5.94439e10	0.0874508
$427$	−4.70651e11	−0.685130
$428$	2.47620e10	0.0356689
$429$	−5.40200e9	−0.00770011
$430$	−5.52378e11	−0.779163
$431$	1.20269e11	0.167882	0.0839410	−	0.996471i	$-0.473249\pi$
$431$	1.20269e11	0.167882	0.0839410	+	0.996471i	$0.473249\pi$
$432$	7.29474e10	0.100770
$433$	1.29563e12	1.77128	0.885639	−	0.464374i	$-0.153721\pi$
$433$	1.29563e12	1.77128	0.885639	+	0.464374i	$0.153721\pi$
$434$	3.59735e11	0.486720
$435$	−3.64013e8	−0.000487433 0
$436$	1.05345e11	0.139613
$437$	4.97285e11	0.652287
$438$	2.21739e10	0.0287878
$439$	1.55250e11	0.199499	0.0997493	−	0.995013i	$-0.468196\pi$
$439$	1.55250e11	0.199499	0.0997493	+	0.995013i	$0.468196\pi$
$440$	−6.40514e11	−0.814688
$441$	−1.13240e11	−0.142569
$442$	3.98689e11	0.496860
$443$	1.44640e12	1.78432	0.892160	−	0.451720i	$-0.149190\pi$
$443$	1.44640e12	1.78432	0.892160	+	0.451720i	$0.149190\pi$
$444$	−2.20502e9	−0.00269270
$445$	1.77056e12	2.14037
$446$	−7.28652e11	−0.871994
$447$	−6.04017e10	−0.0715592
$448$	2.62982e11	0.308443
$449$	6.38236e11	0.741093	0.370546	−	0.928814i	$-0.379170\pi$
$449$	6.38236e11	0.741093	0.370546	+	0.928814i	$0.379170\pi$
$450$	9.95273e11	1.14416
$451$	−9.23524e11	−1.05112
$452$	−1.12995e11	−0.127331
$453$	3.07409e10	0.0342985
$454$	−1.16802e11	−0.129033
$455$	1.37932e11	0.150874
$456$	1.88629e10	0.0204299
$457$	−8.32269e10	−0.0892567	−0.0446284	−	0.999004i	$-0.514210\pi$
$457$	−8.32269e10	−0.0892567	−0.0446284	+	0.999004i	$0.514210\pi$
$458$	−1.31354e11	−0.139492
$459$	1.42744e11	0.150107
$460$	2.62624e11	0.273479
$461$	−1.79458e12	−1.85058	−0.925292	−	0.379254i	$-0.876181\pi$
$461$	−1.79458e12	−1.85058	−0.925292	+	0.379254i	$0.876181\pi$
$462$	1.09952e10	0.0112283
$463$	1.55403e12	1.57161	0.785806	−	0.618473i	$-0.212248\pi$
$463$	1.55403e12	1.57161	0.785806	+	0.618473i	$0.212248\pi$
$464$	8.46952e9	0.00848258
$465$	−7.83617e10	−0.0777258
$466$	1.87455e12	1.84145
$467$	1.55205e11	0.151001	0.0755003	−	0.997146i	$-0.475945\pi$
$467$	1.55205e11	0.151001	0.0755003	+	0.997146i	$0.475945\pi$
$468$	−4.16386e10	−0.0401227
$469$	−6.08090e11	−0.580350
$470$	1.82228e12	1.72257
$471$	−8.07955e10	−0.0756472
$472$	−3.30299e11	−0.306315
$473$	−3.40758e11	−0.313019
$474$	2.36458e10	0.0215155
$475$	5.91529e11	0.533156
$476$	−1.02738e11	−0.0917276
$477$	−6.07108e11	−0.536949
$478$	4.94562e11	0.433307
$479$	1.67162e11	0.145086	0.0725432	−	0.997365i	$-0.476888\pi$
$479$	1.67162e11	0.145086	0.0725432	+	0.997365i	$0.476888\pi$
$480$	2.16124e10	0.0185831
$481$	−1.34783e11	−0.114811
$482$	1.50202e12	1.26755
$483$	2.65926e10	0.0222330
$484$	−1.08015e11	−0.0894704
$485$	3.09198e11	0.253746
$486$	−1.76688e11	−0.143663
$487$	−2.29324e12	−1.84743	−0.923717	−	0.383076i	$-0.874865\pi$
$487$	−2.29324e12	−1.84743	−0.923717	+	0.383076i	$0.874865\pi$
$488$	−2.07775e12	−1.65846
$489$	−2.66087e10	−0.0210443
$490$	−2.80747e11	−0.220005
$491$	−8.75896e10	−0.0680121	−0.0340060	−	0.999422i	$-0.510827\pi$
$491$	−8.75896e10	−0.0680121	−0.0340060	+	0.999422i	$0.510827\pi$
$492$	1.43634e10	0.0110513
$493$	1.65732e10	0.0126356
$494$	−1.95471e11	−0.147676
$495$	1.18702e12	0.888655
$496$	1.82325e12	1.35263
$497$	−9.36328e11	−0.688374
$498$	3.88728e10	0.0283213
$499$	−4.13751e11	−0.298735	−0.149368	−	0.988782i	$-0.547724\pi$
$499$	−4.13751e11	−0.298735	−0.149368	+	0.988782i	$0.547724\pi$
$500$	2.08290e10	0.0149040
$501$	−1.04765e11	−0.0742928
$502$	−1.21010e12	−0.850465
$503$	−1.87574e12	−1.30652	−0.653260	−	0.757134i	$-0.726599\pi$
$503$	−1.87574e12	−1.30652	−0.653260	+	0.757134i	$0.726599\pi$
$504$	−4.99914e11	−0.345111
$505$	−1.70530e11	−0.116678
$506$	1.27966e12	0.867798
$507$	5.13557e9	0.00345186
$508$	1.25724e10	0.00837587
$509$	−8.08683e11	−0.534009	−0.267004	−	0.963695i	$-0.586034\pi$
$509$	−8.08683e11	−0.534009	−0.267004	+	0.963695i	$0.586034\pi$
$510$	1.76768e11	0.115701
$511$	−3.49271e11	−0.226605
$512$	1.09612e12	0.704925
$513$	−6.99848e10	−0.0446145
$514$	1.60855e12	1.01648
$515$	−1.52517e12	−0.955400
$516$	5.29974e9	0.00329103
$517$	1.12415e12	0.692019
$518$	2.74337e11	0.167418
$519$	5.59980e10	0.0338781
$520$	6.08923e11	0.365214
$521$	−2.14661e12	−1.27639	−0.638195	−	0.769874i	$-0.720319\pi$
$521$	−2.14661e12	−1.27639	−0.638195	+	0.769874i	$0.720319\pi$
$522$	−1.36716e10	−0.00805939
$523$	6.45639e11	0.377339	0.188670	−	0.982041i	$-0.439582\pi$
$523$	6.45639e11	0.377339	0.188670	+	0.982041i	$0.439582\pi$
$524$	8.26767e10	0.0479063
$525$	3.16323e10	0.0181725
$526$	−9.30266e11	−0.529872
$527$	3.56774e12	2.01486
$528$	5.57271e10	0.0312042
$529$	1.29379e12	0.718315
$530$	−1.50515e12	−0.828589
$531$	6.12118e11	0.334126
$532$	5.03707e10	0.0272631
$533$	8.77974e11	0.471204
$534$	−1.34177e11	−0.0714075
$535$	6.71089e11	0.354151
$536$	−2.68450e12	−1.40482
$537$	−1.34364e11	−0.0697269
$538$	3.40707e12	1.75332
$539$	−1.73191e11	−0.0883842
$540$	−3.69601e10	−0.0187052
$541$	1.62332e12	0.814733	0.407366	−	0.913265i	$-0.366447\pi$
$541$	1.62332e12	0.814733	0.407366	+	0.913265i	$0.366447\pi$
$542$	−3.74451e12	−1.86380
$543$	−8.02948e9	−0.00396359
$544$	−9.83995e11	−0.481723
$545$	2.85501e12	1.38619
$546$	−1.04529e10	−0.00503350
$547$	1.50699e12	0.719725	0.359863	−	0.933005i	$-0.382824\pi$
$547$	1.50699e12	0.719725	0.359863	+	0.933005i	$0.382824\pi$
$548$	−2.34528e11	−0.111092
$549$	3.85055e12	1.80903
$550$	1.52218e12	0.709307
$551$	−8.12555e9	−0.00375552
$552$	1.17397e11	0.0538183
$553$	−3.72456e11	−0.169360
$554$	−8.77999e11	−0.396005
$555$	−5.97593e10	−0.0267354
$556$	1.03145e11	0.0457733
$557$	3.20939e12	1.41278	0.706388	−	0.707824i	$-0.250323\pi$
$557$	3.20939e12	1.41278	0.706388	+	0.707824i	$0.250323\pi$
$558$	−2.94311e12	−1.28515
$559$	3.23951e11	0.140322
$560$	−1.42291e12	−0.611409
$561$	1.09047e11	0.0464815
$562$	2.74070e12	1.15891
$563$	2.95439e12	1.23931	0.619654	−	0.784875i	$-0.287273\pi$
$563$	2.95439e12	1.23931	0.619654	+	0.784875i	$0.287273\pi$
$564$	−1.74838e10	−0.00727576
$565$	−3.06233e12	−1.26425
$566$	−3.18027e12	−1.30254
$567$	9.24581e11	0.375683
$568$	−4.13355e12	−1.66631
$569$	−1.52799e12	−0.611103	−0.305551	−	0.952176i	$-0.598841\pi$
$569$	−1.52799e12	−0.611103	−0.305551	+	0.952176i	$0.598841\pi$
$570$	−8.66664e10	−0.0343885
$571$	−2.58983e12	−1.01955	−0.509776	−	0.860307i	$-0.670272\pi$
$571$	−2.58983e12	−1.01955	−0.509776	+	0.860307i	$0.670272\pi$
$572$	−6.36826e10	−0.0248736
$573$	4.30297e10	0.0166753
$574$	−1.78702e12	−0.687110
$575$	3.68149e12	1.40449
$576$	−2.15154e12	−0.814421
$577$	9.80075e11	0.368102	0.184051	−	0.982917i	$-0.441079\pi$
$577$	9.80075e11	0.368102	0.184051	+	0.982917i	$0.441079\pi$
$578$	−5.17685e12	−1.92926
$579$	−2.14612e11	−0.0793597
$580$	−4.29124e9	−0.00157455
$581$	−6.12304e11	−0.222933
$582$	−2.34319e10	−0.00846551
$583$	−9.28517e11	−0.332875
$584$	−1.54191e12	−0.548530
$585$	−1.12847e12	−0.398372
$586$	−2.53980e12	−0.889735
$587$	−5.81451e11	−0.202135	−0.101067	−	0.994880i	$-0.532226\pi$
$587$	−5.81451e11	−0.202135	−0.101067	+	0.994880i	$0.532226\pi$
$588$	2.69360e9	0.000929256 0
$589$	−1.74920e12	−0.598854
$590$	1.51757e12	0.515603
$591$	1.75489e9	0.000591706 0
$592$	1.39043e12	0.465265
$593$	−1.04203e12	−0.346046	−0.173023	−	0.984918i	$-0.555353\pi$
$593$	−1.04203e12	−0.346046	−0.173023	+	0.984918i	$0.555353\pi$
$594$	−1.80092e11	−0.0593548
$595$	−2.78436e12	−0.910749
$596$	−7.12057e11	−0.231157
$597$	1.24587e11	0.0401411
$598$	−1.21655e12	−0.389022
$599$	5.43809e12	1.72594	0.862970	−	0.505256i	$-0.168602\pi$
$599$	5.43809e12	1.72594	0.862970	+	0.505256i	$0.168602\pi$
$600$	1.39645e11	0.0439892
$601$	3.95819e12	1.23755	0.618774	−	0.785569i	$-0.287630\pi$
$601$	3.95819e12	1.23755	0.618774	+	0.785569i	$0.287630\pi$
$602$	−6.59368e11	−0.204618
$603$	4.97498e12	1.53237
$604$	3.62395e11	0.110794
$605$	−2.92737e12	−0.888338
$606$	1.29232e10	0.00389263
$607$	3.05579e12	0.913640	0.456820	−	0.889559i	$-0.348988\pi$
$607$	3.05579e12	0.913640	0.456820	+	0.889559i	$0.348988\pi$
$608$	4.82436e11	0.143177
$609$	−4.34518e8	−0.000128006 0
$610$	9.54634e12	2.79160
$611$	−1.06871e12	−0.310223
$612$	8.40533e11	0.242200
$613$	−1.18677e12	−0.339466	−0.169733	−	0.985490i	$-0.554290\pi$
$613$	−1.18677e12	−0.339466	−0.169733	+	0.985490i	$0.554290\pi$
$614$	−3.57329e12	−1.01464
$615$	3.89270e11	0.109727
$616$	−7.64574e11	−0.213947
$617$	6.94626e11	0.192960	0.0964801	−	0.995335i	$-0.469242\pi$
$617$	6.94626e11	0.192960	0.0964801	+	0.995335i	$0.469242\pi$
$618$	1.15581e11	0.0318742
$619$	2.54412e12	0.696515	0.348257	−	0.937399i	$-0.386774\pi$
$619$	2.54412e12	0.696515	0.348257	+	0.937399i	$0.386774\pi$
$620$	−9.23782e11	−0.251077
$621$	−4.35564e11	−0.117528
$622$	−2.90483e11	−0.0778152
$623$	2.11349e12	0.562088
$624$	−5.29785e10	−0.0139884
$625$	−3.52272e12	−0.923459
$626$	−2.80090e12	−0.728976
$627$	−5.34638e10	−0.0138152
$628$	−9.52473e11	−0.244362
$629$	2.72079e12	0.693054
$630$	2.29688e12	0.580906
$631$	−4.10571e12	−1.03099	−0.515497	−	0.856891i	$-0.672393\pi$
$631$	−4.10571e12	−1.03099	−0.515497	+	0.856891i	$0.672393\pi$
$632$	−1.64426e12	−0.409962
$633$	7.11287e10	0.0176087
$634$	−1.03076e12	−0.253371
$635$	3.40730e11	0.0831627
$636$	1.44411e10	0.00349979
$637$	1.64648e11	0.0396214
$638$	−2.09095e10	−0.00499632
$639$	7.66041e12	1.81760
$640$	−7.09179e12	−1.67088
$641$	2.93476e12	0.686612	0.343306	−	0.939224i	$-0.388453\pi$
$641$	2.93476e12	0.686612	0.343306	+	0.939224i	$0.388453\pi$
$642$	−5.08569e10	−0.0118152
$643$	−6.69969e12	−1.54563	−0.772815	−	0.634632i	$-0.781152\pi$
$643$	−6.69969e12	−1.54563	−0.772815	+	0.634632i	$0.781152\pi$
$644$	3.13492e11	0.0718191
$645$	1.43631e11	0.0326761
$646$	3.94584e12	0.891443
$647$	−6.23009e12	−1.39774	−0.698868	−	0.715250i	$-0.746313\pi$
$647$	−6.23009e12	−1.39774	−0.698868	+	0.715250i	$0.746313\pi$
$648$	4.08169e12	0.909396
$649$	9.36180e11	0.207137
$650$	−1.44710e12	−0.317973
$651$	−9.35395e10	−0.0204118
$652$	−3.13682e11	−0.0679791
$653$	−4.42425e12	−0.952206	−0.476103	−	0.879390i	$-0.657951\pi$
$653$	−4.42425e12	−0.952206	−0.476103	+	0.879390i	$0.657951\pi$
$654$	−2.16360e11	−0.0462464
$655$	2.24066e12	0.475654
$656$	−9.05718e12	−1.90953
$657$	2.85750e12	0.598332
$658$	2.17524e12	0.452367
$659$	−1.19733e12	−0.247304	−0.123652	−	0.992326i	$-0.539461\pi$
$659$	−1.19733e12	−0.247304	−0.123652	+	0.992326i	$0.539461\pi$
$660$	−2.82351e10	−0.00579218
$661$	−8.59424e12	−1.75106	−0.875530	−	0.483164i	$-0.839487\pi$
$661$	−8.59424e12	−1.75106	−0.875530	+	0.483164i	$0.839487\pi$
$662$	−3.42242e12	−0.692584
$663$	−1.03668e11	−0.0208370
$664$	−2.70310e12	−0.539643
$665$	1.36512e12	0.270691
$666$	−2.24444e12	−0.442053
$667$	−5.05709e10	−0.00989315
$668$	−1.23504e12	−0.239987
$669$	1.89466e11	0.0365691
$670$	1.23341e13	2.36466
$671$	5.88907e12	1.12149
$672$	2.57985e10	0.00488015
$673$	−4.63034e11	−0.0870051	−0.0435026	−	0.999053i	$-0.513852\pi$
$673$	−4.63034e11	−0.0870051	−0.0435026	+	0.999053i	$0.513852\pi$
$674$	6.09166e12	1.13701
$675$	−5.18111e11	−0.0960629
$676$	6.05416e10	0.0111505
$677$	4.72455e12	0.864393	0.432196	−	0.901780i	$-0.357739\pi$
$677$	4.72455e12	0.864393	0.432196	+	0.901780i	$0.357739\pi$
$678$	2.32072e11	0.0421783
$679$	3.69086e11	0.0666368
$680$	−1.22919e13	−2.20460
$681$	3.03714e10	0.00541131
$682$	−4.50122e12	−0.796711
$683$	−1.89286e12	−0.332832	−0.166416	−	0.986056i	$-0.553219\pi$
$683$	−1.89286e12	−0.332832	−0.166416	+	0.986056i	$0.553219\pi$
$684$	−4.12099e11	−0.0719862
$685$	−6.35606e12	−1.10301
$686$	−3.35124e11	−0.0577760
$687$	3.41551e10	0.00584992
$688$	−3.34188e12	−0.568647
$689$	8.82721e11	0.149223
$690$	−5.39385e11	−0.0905895
$691$	9.50737e12	1.58639	0.793193	−	0.608970i	$-0.208417\pi$
$691$	9.50737e12	1.58639	0.793193	+	0.608970i	$0.208417\pi$
$692$	6.60143e11	0.109436
$693$	1.41693e12	0.233372
$694$	−1.12229e13	−1.83649
$695$	2.79539e12	0.454476
$696$	−1.91824e9	−0.000309857 0
$697$	−1.77231e13	−2.84441
$698$	2.42976e12	0.387448
$699$	−4.87425e11	−0.0772255
$700$	3.72904e11	0.0587023
$701$	3.69030e12	0.577205	0.288603	−	0.957449i	$-0.406809\pi$
$701$	3.69030e12	0.577205	0.288603	+	0.957449i	$0.406809\pi$
$702$	1.71210e11	0.0266079
$703$	−1.33396e12	−0.205988
$704$	−3.29060e12	−0.504891
$705$	−4.73836e11	−0.0722399
$706$	−4.54958e12	−0.689208
$707$	−2.03560e11	−0.0306411
$708$	−1.45602e10	−0.00217780
$709$	9.02589e12	1.34147	0.670737	−	0.741695i	$-0.265978\pi$
$709$	9.02589e12	1.34147	0.670737	+	0.741695i	$0.265978\pi$
$710$	1.89918e13	2.80481
$711$	3.04718e12	0.447183
$712$	9.33031e12	1.36062
$713$	−1.08865e13	−1.57756
$714$	2.11006e11	0.0303846
$715$	−1.72589e12	−0.246966
$716$	−1.58398e12	−0.225238
$717$	−1.28598e11	−0.0181718
$718$	−1.18692e13	−1.66672
$719$	−5.57596e12	−0.778108	−0.389054	−	0.921215i	$-0.627198\pi$
$719$	−5.57596e12	−0.778108	−0.389054	+	0.921215i	$0.627198\pi$
$720$	1.16413e13	1.61438
$721$	−1.82058e12	−0.250900
$722$	5.87831e12	0.805073
$723$	−3.90560e11	−0.0531577
$724$	−9.46571e10	−0.0128035
$725$	−6.01549e10	−0.00808631
$726$	2.21844e11	0.0296369
$727$	5.66814e12	0.752551	0.376276	−	0.926508i	$-0.377205\pi$
$727$	5.66814e12	0.752551	0.376276	+	0.926508i	$0.377205\pi$
$728$	7.26864e11	0.0959096
$729$	−7.53362e12	−0.987938
$730$	7.08437e12	0.923312
$731$	−6.53940e12	−0.847051
$732$	−9.15915e10	−0.0117911
$733$	−2.25858e12	−0.288980	−0.144490	−	0.989506i	$-0.546154\pi$
$733$	−2.25858e12	−0.288980	−0.144490	+	0.989506i	$0.546154\pi$
$734$	8.28673e10	0.0105378
$735$	7.30007e10	0.00922643
$736$	3.00253e12	0.377170
$737$	7.60879e12	0.949974
$738$	1.46202e13	1.81426
$739$	1.34627e13	1.66047	0.830235	−	0.557413i	$-0.188206\pi$
$739$	1.34627e13	1.66047	0.830235	+	0.557413i	$0.188206\pi$
$740$	−7.04485e11	−0.0863632
$741$	5.08269e10	0.00619315
$742$	−1.79668e12	−0.217598
$743$	−1.23724e13	−1.48938	−0.744688	−	0.667413i	$-0.767402\pi$
$743$	−1.23724e13	−1.48938	−0.744688	+	0.667413i	$0.767402\pi$
$744$	−4.12943e11	−0.0494097
$745$	−1.92978e13	−2.29512
$746$	−4.48605e12	−0.530322
$747$	5.00946e12	0.588638
$748$	1.28552e12	0.150149
$749$	8.01071e11	0.0930043
$750$	−4.27790e10	−0.00493691
$751$	−4.20252e12	−0.482092	−0.241046	−	0.970514i	$-0.577490\pi$
$751$	−4.20252e12	−0.482092	−0.241046	+	0.970514i	$0.577490\pi$
$752$	1.10248e13	1.25716
$753$	3.14655e11	0.0356663
$754$	1.98782e10	0.00223978
$755$	9.82146e12	1.10006
$756$	−4.41189e10	−0.00491221
$757$	1.32766e13	1.46946	0.734728	−	0.678361i	$-0.237310\pi$
$757$	1.32766e13	1.46946	0.734728	+	0.678361i	$0.237310\pi$
$758$	2.58959e12	0.284918
$759$	−3.32742e11	−0.0363932
$760$	6.02653e12	0.655249
$761$	3.70152e11	0.0400083	0.0200041	−	0.999800i	$-0.493632\pi$
$761$	3.70152e11	0.0400083	0.0200041	+	0.999800i	$0.493632\pi$
$762$	−2.58214e10	−0.00277449
$763$	3.40799e12	0.364031
$764$	5.07264e11	0.0538659
$765$	2.27797e13	2.40476
$766$	1.62134e13	1.70155
$767$	−8.90005e11	−0.0928568
$768$	1.84377e11	0.0191241
$769$	−1.57793e13	−1.62712	−0.813558	−	0.581484i	$-0.802472\pi$
$769$	−1.57793e13	−1.62712	−0.813558	+	0.581484i	$0.802472\pi$
$770$	3.51287e12	0.360126
$771$	−4.18261e11	−0.0426287
$772$	−2.52999e12	−0.256355
$773$	3.76505e12	0.379283	0.189642	−	0.981853i	$-0.439267\pi$
$773$	3.76505e12	0.379283	0.189642	+	0.981853i	$0.439267\pi$
$774$	5.39450e12	0.540278
$775$	−1.29497e13	−1.28944
$776$	1.62938e12	0.161304
$777$	−7.13341e10	−0.00702105
$778$	1.05560e13	1.03298
$779$	8.68934e12	0.845412
$780$	2.68425e10	0.00259656
$781$	1.17159e13	1.12680
$782$	2.45577e13	2.34832
$783$	7.11704e9	0.000676662 0
$784$	−1.69851e12	−0.160563
$785$	−2.58135e13	−2.42624
$786$	−1.69804e11	−0.0158688
$787$	1.18260e13	1.09889	0.549444	−	0.835531i	$-0.314840\pi$
$787$	1.18260e13	1.09889	0.549444	+	0.835531i	$0.314840\pi$
$788$	2.06878e10	0.00191138
$789$	2.41891e11	0.0222215
$790$	7.55462e12	0.690066
$791$	−3.65547e12	−0.332008
$792$	6.25523e12	0.564911
$793$	−5.59861e12	−0.502748
$794$	−2.24087e13	−2.00090
$795$	3.91375e11	0.0347489
$796$	1.46872e12	0.129668
$797$	−6.28239e12	−0.551521	−0.275761	−	0.961226i	$-0.588930\pi$
$797$	−6.28239e12	−0.551521	−0.275761	+	0.961226i	$0.588930\pi$
$798$	−1.03453e11	−0.00903085
$799$	2.15733e13	1.87265
$800$	3.57156e12	0.308285
$801$	−1.72912e13	−1.48415
$802$	−2.45990e13	−2.09958
$803$	4.37029e12	0.370929
$804$	−1.18338e11	−0.00998785
$805$	8.49610e12	0.713080
$806$	4.27921e12	0.357155
$807$	−8.85917e11	−0.0735296
$808$	−8.98642e11	−0.0741713
$809$	3.18104e12	0.261097	0.130548	−	0.991442i	$-0.458326\pi$
$809$	3.18104e12	0.261097	0.130548	+	0.991442i	$0.458326\pi$
$810$	−1.87535e13	−1.53074
$811$	1.45353e13	1.17986	0.589929	−	0.807455i	$-0.299156\pi$
$811$	1.45353e13	1.17986	0.589929	+	0.807455i	$0.299156\pi$
$812$	−5.12240e9	−0.000413496 0
$813$	9.73660e11	0.0781628
$814$	−3.43267e12	−0.274046
$815$	−8.50126e12	−0.674954
$816$	1.06944e12	0.0844408
$817$	3.20616e12	0.251759
$818$	1.37846e13	1.07648
$819$	−1.34704e12	−0.104617
$820$	4.58899e12	0.354449
$821$	−2.29827e13	−1.76545	−0.882726	−	0.469888i	$-0.844294\pi$
$821$	−2.29827e13	−1.76545	−0.882726	+	0.469888i	$0.844294\pi$
$822$	4.81679e11	0.0367989
$823$	1.19282e13	0.906309	0.453154	−	0.891432i	$-0.350299\pi$
$823$	1.19282e13	0.906309	0.453154	+	0.891432i	$0.350299\pi$
$824$	−8.03719e12	−0.607340
$825$	−3.95803e11	−0.0297465
$826$	1.81151e12	0.135404
$827$	−1.61714e13	−1.20219	−0.601094	−	0.799178i	$-0.705268\pi$
$827$	−1.61714e13	−1.20219	−0.601094	+	0.799178i	$0.705268\pi$
$828$	−2.56478e12	−0.189633
$829$	−1.82619e13	−1.34292	−0.671462	−	0.741039i	$-0.734333\pi$
$829$	−1.82619e13	−1.34292	−0.671462	+	0.741039i	$0.734333\pi$
$830$	1.24195e13	0.908352
$831$	2.28300e11	0.0166074
$832$	3.12830e12	0.226336
$833$	−3.32366e12	−0.239174
$834$	−2.11842e11	−0.0151623
$835$	−3.34715e13	−2.38279
$836$	−6.30269e11	−0.0446270
$837$	1.53210e12	0.107900
$838$	2.29751e13	1.60938
$839$	1.51573e13	1.05607	0.528035	−	0.849222i	$-0.322929\pi$
$839$	1.51573e13	1.05607	0.528035	+	0.849222i	$0.322929\pi$
$840$	3.22272e11	0.0223340
$841$	−1.45063e13	−0.999943
$842$	−1.10627e13	−0.758502
$843$	−7.12646e11	−0.0486015
$844$	8.38514e11	0.0568813
$845$	1.64077e12	0.110711
$846$	−1.77964e13	−1.19444
$847$	−3.49437e12	−0.233288
$848$	−9.10615e12	−0.604718
$849$	8.26943e11	0.0546250
$850$	2.92118e13	1.91943
$851$	−8.30214e12	−0.542634
$852$	−1.82215e11	−0.0118470
$853$	2.16876e13	1.40262	0.701312	−	0.712854i	$-0.252598\pi$
$853$	2.16876e13	1.40262	0.701312	+	0.712854i	$0.252598\pi$
$854$	1.13954e13	0.733107
$855$	−1.11685e13	−0.714740
$856$	3.53644e12	0.225131
$857$	1.19059e13	0.753961	0.376981	−	0.926221i	$-0.376962\pi$
$857$	1.19059e13	0.753961	0.376981	+	0.926221i	$0.376962\pi$
$858$	1.30793e11	0.00823932
$859$	2.06615e13	1.29477	0.647386	−	0.762162i	$-0.275862\pi$
$859$	2.06615e13	1.29477	0.647386	+	0.762162i	$0.275862\pi$
$860$	1.69322e12	0.105553
$861$	4.64667e11	0.0288156
$862$	−2.91193e12	−0.179638
$863$	−2.69412e13	−1.65336	−0.826682	−	0.562670i	$-0.809774\pi$
$863$	−2.69412e13	−1.65336	−0.826682	+	0.562670i	$0.809774\pi$
$864$	−4.22558e11	−0.0257973
$865$	1.78909e13	1.08657
$866$	−3.13698e13	−1.89531
$867$	1.34610e12	0.0809081
$868$	−1.10271e12	−0.0659359
$869$	4.66039e12	0.277226
$870$	8.81346e9	0.000521566 0
$871$	−7.23351e12	−0.425860
$872$	1.50451e13	0.881191
$873$	−3.01962e12	−0.175949
$874$	−1.20402e13	−0.697964
$875$	6.73833e11	0.0388612
$876$	−6.79704e10	−0.00389988
$877$	2.18247e12	0.124580	0.0622902	−	0.998058i	$-0.480160\pi$
$877$	2.18247e12	0.124580	0.0622902	+	0.998058i	$0.480160\pi$
$878$	−3.75889e12	−0.213469
$879$	6.60408e11	0.0373132
$880$	1.78043e13	1.00081
$881$	−1.17134e13	−0.655077	−0.327538	−	0.944838i	$-0.606219\pi$
$881$	−1.17134e13	−0.655077	−0.327538	+	0.944838i	$0.606219\pi$
$882$	2.74176e12	0.152553
$883$	1.38647e13	0.767517	0.383759	−	0.923433i	$-0.374629\pi$
$883$	1.38647e13	0.767517	0.383759	+	0.923433i	$0.374629\pi$
$884$	−1.22212e12	−0.0673097
$885$	−3.94604e11	−0.0216231
$886$	−3.50202e13	−1.90927
$887$	−2.07690e13	−1.12657	−0.563286	−	0.826262i	$-0.690463\pi$
$887$	−2.07690e13	−1.12657	−0.563286	+	0.826262i	$0.690463\pi$
$888$	−3.14914e11	−0.0169955
$889$	4.06726e11	0.0218395
$890$	−4.28686e13	−2.29026
$891$	−1.15689e13	−0.614955
$892$	2.23356e12	0.118129
$893$	−1.05770e13	−0.556587
$894$	1.46244e12	0.0765702
$895$	−4.29283e13	−2.23635
$896$	−8.46540e12	−0.438795
$897$	3.16331e11	0.0163146
$898$	−1.54529e13	−0.792989
$899$	1.77883e11	0.00908274
$900$	−3.05085e12	−0.154999
$901$	−1.78189e13	−0.900783
$902$	2.23603e13	1.12473
$903$	1.71451e11	0.00858114
$904$	−1.61376e13	−0.803676
$905$	−2.56535e12	−0.127124
$906$	−7.44297e11	−0.0367003
$907$	1.25577e13	0.616138	0.308069	−	0.951364i	$-0.400317\pi$
$907$	1.25577e13	0.616138	0.308069	+	0.951364i	$0.400317\pi$
$908$	3.58039e11	0.0174801
$909$	1.66539e12	0.0809054
$910$	−3.33961e12	−0.161439
$911$	−1.91027e12	−0.0918888	−0.0459444	−	0.998944i	$-0.514630\pi$
$911$	−1.91027e12	−0.0918888	−0.0459444	+	0.998944i	$0.514630\pi$
$912$	−5.24330e11	−0.0250974
$913$	7.66152e12	0.364919
$914$	2.01509e12	0.0955071
$915$	−2.48227e12	−0.117072
$916$	4.02644e11	0.0188969
$917$	2.67466e12	0.124913
$918$	−3.45610e12	−0.160618
$919$	−6.24982e12	−0.289033	−0.144517	−	0.989502i	$-0.546163\pi$
$919$	−6.24982e12	−0.289033	−0.144517	+	0.989502i	$0.546163\pi$
$920$	3.75073e13	1.72612
$921$	9.29139e11	0.0425513
$922$	4.34503e13	1.98017
$923$	−1.11381e13	−0.505128
$924$	−3.37040e10	−0.00152110
$925$	−9.87553e12	−0.443529
$926$	−3.76261e13	−1.68167
$927$	1.48947e13	0.662482
$928$	−4.90609e10	−0.00217155
$929$	−3.02983e13	−1.33459	−0.667293	−	0.744795i	$-0.732547\pi$
$929$	−3.02983e13	−1.33459	−0.667293	+	0.744795i	$0.732547\pi$
$930$	1.89729e12	0.0831687
$931$	1.62953e12	0.0710869
$932$	−5.74611e12	−0.249461
$933$	7.55324e10	0.00326337
$934$	−3.75780e12	−0.161575
$935$	3.48396e13	1.49080
$936$	−5.94671e12	−0.253242
$937$	6.44264e12	0.273046	0.136523	−	0.990637i	$-0.456407\pi$
$937$	6.44264e12	0.273046	0.136523	+	0.990637i	$0.456407\pi$
$938$	1.47230e13	0.620990
$939$	7.28299e11	0.0305714
$940$	−5.58591e12	−0.233356
$941$	−3.76681e12	−0.156610	−0.0783052	−	0.996929i	$-0.524951\pi$
$941$	−3.76681e12	−0.156610	−0.0783052	+	0.996929i	$0.524951\pi$
$942$	1.95621e12	0.0809445
$943$	5.40798e13	2.22706
$944$	9.18129e12	0.376296
$945$	−1.19569e12	−0.0487725
$946$	8.25041e12	0.334939
$947$	−3.85590e13	−1.55794	−0.778969	−	0.627062i	$-0.784257\pi$
$947$	−3.85590e13	−1.55794	−0.778969	+	0.627062i	$0.784257\pi$
$948$	−7.24822e10	−0.00291470
$949$	−4.15474e12	−0.166282
$950$	−1.43220e13	−0.570491
$951$	2.68022e11	0.0106257
$952$	−1.46728e13	−0.578956
$953$	−3.84061e13	−1.50828	−0.754140	−	0.656713i	$-0.771946\pi$
$953$	−3.84061e13	−1.50828	−0.754140	+	0.656713i	$0.771946\pi$
$954$	1.46993e13	0.574550
$955$	1.37476e13	0.534826
$956$	−1.51600e12	−0.0587000
$957$	5.43695e9	0.000209533 0
$958$	−4.04731e12	−0.155246
$959$	−7.58716e12	−0.289665
$960$	1.38700e12	0.0527056
$961$	1.18536e13	0.448329
$962$	3.26337e12	0.122851
$963$	−6.55383e12	−0.245571
$964$	−4.60420e12	−0.171715
$965$	−6.85667e13	−2.54531
$966$	−6.43858e11	−0.0237899
$967$	1.79148e13	0.658859	0.329430	−	0.944180i	$-0.393144\pi$
$967$	1.79148e13	0.658859	0.329430	+	0.944180i	$0.393144\pi$
$968$	−1.54264e13	−0.564709
$969$	−1.02601e12	−0.0373848
$970$	−7.48628e12	−0.271515
$971$	3.22379e13	1.16381	0.581903	−	0.813258i	$-0.302308\pi$
$971$	3.22379e13	1.16381	0.581903	+	0.813258i	$0.302308\pi$
$972$	5.41609e11	0.0194620
$973$	3.33683e12	0.119351
$974$	5.55237e13	1.97680
$975$	3.76281e11	0.0133349
$976$	5.77552e13	2.03736
$977$	7.62010e12	0.267569	0.133784	−	0.991010i	$-0.457287\pi$
$977$	7.62010e12	0.267569	0.133784	+	0.991010i	$0.457287\pi$
$978$	6.44248e11	0.0225179
$979$	−2.64453e13	−0.920082
$980$	8.60583e11	0.0298041
$981$	−2.78819e13	−0.961196
$982$	2.12071e12	0.0727747
$983$	2.22466e13	0.759928	0.379964	−	0.925001i	$-0.375936\pi$
$983$	2.22466e13	0.759928	0.379964	+	0.925001i	$0.375936\pi$
$984$	2.05134e12	0.0697525
$985$	5.60672e11	0.0189778
$986$	−4.01269e11	−0.0135204
$987$	−5.65613e11	−0.0189711
$988$	5.99183e11	0.0200057
$989$	1.99541e13	0.663207
$990$	−2.87400e13	−0.950885
$991$	1.18711e13	0.390985	0.195493	−	0.980705i	$-0.437369\pi$
$991$	1.18711e13	0.390985	0.195493	+	0.980705i	$0.437369\pi$
$992$	−1.05614e13	−0.346274
$993$	8.89908e11	0.0290452
$994$	2.26703e13	0.736578
$995$	3.98046e13	1.28745
$996$	−1.19158e11	−0.00383669
$997$	−1.63112e13	−0.522828	−0.261414	−	0.965227i	$-0.584189\pi$
$997$	−1.63112e13	−0.522828	−0.261414	+	0.965227i	$0.584189\pi$
$998$	1.00177e13	0.319654
$999$	1.16839e12	0.0371145

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.a.1.4	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.a.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-24.2119 q^{2} +6.29566 q^{3} +74.2177 q^{4} +2011.41 q^{5} -152.430 q^{6} +2401.00 q^{7} +10599.6 q^{8} -19643.4 q^{9} +O(q^{10})\)	\(q-24.2119 q^{2} +6.29566 q^{3} +74.2177 q^{4} +2011.41 q^{5} -152.430 q^{6} +2401.00 q^{7} +10599.6 q^{8} -19643.4 q^{9} -48700.2 q^{10} -30042.8 q^{11} +467.250 q^{12} +28561.0 q^{13} -58132.8 q^{14} +12663.2 q^{15} -294635. q^{16} -576543. q^{17} +475604. q^{18} +282669. q^{19} +149282. q^{20} +15115.9 q^{21} +727393. q^{22} +1.75925e6 q^{23} +66731.3 q^{24} +2.09265e6 q^{25} -691517. q^{26} -247586. q^{27} +178197. q^{28} -28745.8 q^{29} -306600. q^{30} -6.18815e6 q^{31} +1.70671e6 q^{32} -189139. q^{33} +1.39592e7 q^{34} +4.82940e6 q^{35} -1.45788e6 q^{36} -4.71914e6 q^{37} -6.84397e6 q^{38} +179810. q^{39} +2.13201e7 q^{40} +3.07403e7 q^{41} -365985. q^{42} +1.13424e7 q^{43} -2.22970e6 q^{44} -3.95109e7 q^{45} -4.25948e7 q^{46} -3.74184e7 q^{47} -1.85492e6 q^{48} +5.76480e6 q^{49} -5.06672e7 q^{50} -3.62972e6 q^{51} +2.11973e6 q^{52} +3.09065e7 q^{53} +5.99453e6 q^{54} -6.04284e7 q^{55} +2.54495e7 q^{56} +1.77959e6 q^{57} +695991. q^{58} -3.11616e7 q^{59} +939831. q^{60} -1.96023e8 q^{61} +1.49827e8 q^{62} -4.71637e7 q^{63} +1.09530e8 q^{64} +5.74479e7 q^{65} +4.57943e6 q^{66} -2.53265e8 q^{67} -4.27897e7 q^{68} +1.10756e7 q^{69} -1.16929e8 q^{70} -3.89974e8 q^{71} -2.08211e8 q^{72} -1.45469e8 q^{73} +1.14260e8 q^{74} +1.31746e7 q^{75} +2.09791e7 q^{76} -7.21327e7 q^{77} -4.35356e6 q^{78} -1.55125e8 q^{79} -5.92633e8 q^{80} +3.85082e8 q^{81} -7.44283e8 q^{82} -2.55020e8 q^{83} +1.12187e6 q^{84} -1.15967e9 q^{85} -2.74622e8 q^{86} -180974. q^{87} -3.18440e8 q^{88} +8.80255e8 q^{89} +9.56635e8 q^{90} +6.85750e7 q^{91} +1.30567e8 q^{92} -3.89585e7 q^{93} +9.05973e8 q^{94} +5.68564e8 q^{95} +1.07449e7 q^{96} +1.53722e8 q^{97} -1.39577e8 q^{98} +5.90141e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 21 q^{2} - 323 q^{3} + 2945 q^{4} - 5202 q^{5} - 9897 q^{6} + 28812 q^{7} - 25431 q^{8} + 78519 q^{9}+O(q^{10}) \) 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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