LMFDB - Embedded newform 91.10.a.a.1.1

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			1.1
Root			$-37.6810$ 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)

$f(q)$	$=$	$q-39.6810 q^{2} -201.837 q^{3} +1062.58 q^{4} +764.411 q^{5} +8009.09 q^{6} +2401.00 q^{7} -21847.5 q^{8} +21055.2 q^{9} +O(q^{10})$	\(q-39.6810 q^{2} -201.837 q^{3} +1062.58 q^{4} +764.411 q^{5} +8009.09 q^{6} +2401.00 q^{7} -21847.5 q^{8} +21055.2 q^{9} -30332.6 q^{10} -87028.8 q^{11} -214468. q^{12} +28561.0 q^{13} -95274.0 q^{14} -154286. q^{15} +322890. q^{16} -46185.1 q^{17} -835490. q^{18} +504454. q^{19} +812247. q^{20} -484611. q^{21} +3.45339e6 q^{22} -599831. q^{23} +4.40964e6 q^{24} -1.36880e6 q^{25} -1.13333e6 q^{26} -276959. q^{27} +2.55125e6 q^{28} +2.58941e6 q^{29} +6.12224e6 q^{30} +3.96298e6 q^{31} -1.62665e6 q^{32} +1.75656e7 q^{33} +1.83267e6 q^{34} +1.83535e6 q^{35} +2.23728e7 q^{36} -6.19845e6 q^{37} -2.00172e7 q^{38} -5.76467e6 q^{39} -1.67005e7 q^{40} -1.66091e7 q^{41} +1.92298e7 q^{42} +3.31849e7 q^{43} -9.24750e7 q^{44} +1.60948e7 q^{45} +2.38019e7 q^{46} +2.64372e7 q^{47} -6.51711e7 q^{48} +5.76480e6 q^{49} +5.43153e7 q^{50} +9.32186e6 q^{51} +3.03483e7 q^{52} -3.90874e7 q^{53} +1.09900e7 q^{54} -6.65258e7 q^{55} -5.24559e7 q^{56} -1.01817e8 q^{57} -1.02750e8 q^{58} +4.81308e7 q^{59} -1.63942e8 q^{60} +1.43492e8 q^{61} -1.57255e8 q^{62} +5.05535e7 q^{63} -1.00773e8 q^{64} +2.18323e7 q^{65} -6.97022e8 q^{66} -1.77854e7 q^{67} -4.90753e7 q^{68} +1.21068e8 q^{69} -7.28285e7 q^{70} -8.31277e7 q^{71} -4.60003e8 q^{72} +2.29798e8 q^{73} +2.45960e8 q^{74} +2.76275e8 q^{75} +5.36022e8 q^{76} -2.08956e8 q^{77} +2.28748e8 q^{78} -2.99993e8 q^{79} +2.46820e8 q^{80} -3.58529e8 q^{81} +6.59064e8 q^{82} +8.34408e8 q^{83} -5.14937e8 q^{84} -3.53044e7 q^{85} -1.31681e9 q^{86} -5.22638e8 q^{87} +1.90136e9 q^{88} -2.13503e8 q^{89} -6.38658e8 q^{90} +6.85750e7 q^{91} -6.37368e8 q^{92} -7.99875e8 q^{93} -1.04906e9 q^{94} +3.85610e8 q^{95} +3.28318e8 q^{96} -1.36917e9 q^{97} -2.28753e8 q^{98} -1.83241e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−39.6810	−1.75367	−0.876834	−	0.480794i	$-0.840349\pi$
$2$	−39.6810	−1.75367	−0.876834	+	0.480794i	$0.840349\pi$
$3$	−201.837	−1.43865	−0.719325	−	0.694674i	$-0.755549\pi$
$3$	−201.837	−1.43865	−0.719325	+	0.694674i	$0.755549\pi$
$4$	1062.58	2.07535
$5$	764.411	0.546968	0.273484	−	0.961877i	$-0.411824\pi$
$5$	764.411	0.546968	0.273484	+	0.961877i	$0.411824\pi$
$6$	8009.09	2.52291
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	−21847.5	−1.88581
$9$	21055.2	1.06971
$10$	−30332.6	−0.959200
$11$	−87028.8	−1.79224	−0.896120	−	0.443812i	$-0.853626\pi$
$11$	−87028.8	−1.79224	−0.896120	+	0.443812i	$0.853626\pi$
$12$	−214468.	−2.98570
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	−95274.0	−0.662824
$15$	−154286.	−0.786896
$16$	322890.	1.23173
$17$	−46185.1	−0.134116	−0.0670581	−	0.997749i	$-0.521361\pi$
$17$	−46185.1	−0.134116	−0.0670581	+	0.997749i	$0.521361\pi$
$18$	−835490.	−1.87592
$19$	504454.	0.888035	0.444017	−	0.896018i	$-0.353553\pi$
$19$	504454.	0.888035	0.444017	+	0.896018i	$0.353553\pi$
$20$	812247.	1.13515
$21$	−484611.	−0.543759
$22$	3.45339e6	3.14299
$23$	−599831.	−0.446945	−0.223472	−	0.974710i	$-0.571739\pi$
$23$	−599831.	−0.446945	−0.223472	+	0.974710i	$0.571739\pi$
$24$	4.40964e6	2.71301
$25$	−1.36880e6	−0.700826
$26$	−1.13333e6	−0.486380
$27$	−276959.	−0.100295
$28$	2.55125e6	0.784408
$29$	2.58941e6	0.679844	0.339922	−	0.940454i	$-0.389599\pi$
$29$	2.58941e6	0.679844	0.339922	+	0.940454i	$0.389599\pi$
$30$	6.12224e6	1.37995
$31$	3.96298e6	0.770715	0.385357	−	0.922767i	$-0.374078\pi$
$31$	3.96298e6	0.770715	0.385357	+	0.922767i	$0.374078\pi$
$32$	−1.62665e6	−0.274232
$33$	1.75656e7	2.57841
$34$	1.83267e6	0.235195
$35$	1.83535e6	0.206734
$36$	2.23728e7	2.22003
$37$	−6.19845e6	−0.543720	−0.271860	−	0.962337i	$-0.587639\pi$
$37$	−6.19845e6	−0.543720	−0.271860	+	0.962337i	$0.587639\pi$
$38$	−2.00172e7	−1.55732
$39$	−5.76467e6	−0.399010
$40$	−1.67005e7	−1.03148
$41$	−1.66091e7	−0.917948	−0.458974	−	0.888450i	$-0.651783\pi$
$41$	−1.66091e7	−0.917948	−0.458974	+	0.888450i	$0.651783\pi$
$42$	1.92298e7	0.953572
$43$	3.31849e7	1.48024	0.740121	−	0.672474i	$-0.234768\pi$
$43$	3.31849e7	1.48024	0.740121	+	0.672474i	$0.234768\pi$
$44$	−9.24750e7	−3.71952
$45$	1.60948e7	0.585100
$46$	2.38019e7	0.783792
$47$	2.64372e7	0.790271	0.395135	−	0.918623i	$-0.370698\pi$
$47$	2.64372e7	0.790271	0.395135	+	0.918623i	$0.370698\pi$
$48$	−6.51711e7	−1.77202
$49$	5.76480e6	0.142857
$50$	5.43153e7	1.22902
$51$	9.32186e6	0.192946
$52$	3.03483e7	0.575598
$53$	−3.90874e7	−0.680448	−0.340224	−	0.940344i	$-0.610503\pi$
$53$	−3.90874e7	−0.680448	−0.340224	+	0.940344i	$0.610503\pi$
$54$	1.09900e7	0.175884
$55$	−6.65258e7	−0.980298
$56$	−5.24559e7	−0.712767
$57$	−1.01817e8	−1.27757
$58$	−1.02750e8	−1.19222
$59$	4.81308e7	0.517117	0.258558	−	0.965996i	$-0.416753\pi$
$59$	4.81308e7	0.517117	0.258558	+	0.965996i	$0.416753\pi$
$60$	−1.63942e8	−1.63308
$61$	1.43492e8	1.32692	0.663458	−	0.748214i	$-0.269088\pi$
$61$	1.43492e8	1.32692	0.663458	+	0.748214i	$0.269088\pi$
$62$	−1.57255e8	−1.35158
$63$	5.05535e7	0.404314
$64$	−1.00773e8	−0.750814
$65$	2.18323e7	0.151702
$66$	−6.97022e8	−4.52167
$67$	−1.77854e7	−0.107827	−0.0539133	−	0.998546i	$-0.517169\pi$
$67$	−1.77854e7	−0.107827	−0.0539133	+	0.998546i	$0.517169\pi$
$68$	−4.90753e7	−0.278338
$69$	1.21068e8	0.642997
$70$	−7.28285e7	−0.362544
$71$	−8.31277e7	−0.388225	−0.194112	−	0.980979i	$-0.562183\pi$
$71$	−8.31277e7	−0.388225	−0.194112	+	0.980979i	$0.562183\pi$
$72$	−4.60003e8	−2.01727
$73$	2.29798e8	0.947095	0.473547	−	0.880768i	$-0.342973\pi$
$73$	2.29798e8	0.947095	0.473547	+	0.880768i	$0.342973\pi$
$74$	2.45960e8	0.953504
$75$	2.76275e8	1.00824
$76$	5.36022e8	1.84298
$77$	−2.08956e8	−0.677403
$78$	2.28748e8	0.699730
$79$	−2.99993e8	−0.866540	−0.433270	−	0.901264i	$-0.642640\pi$
$79$	−2.99993e8	−0.866540	−0.433270	+	0.901264i	$0.642640\pi$
$80$	2.46820e8	0.673715
$81$	−3.58529e8	−0.925425
$82$	6.59064e8	1.60978
$83$	8.34408e8	1.92987	0.964933	−	0.262497i	$-0.0845461\pi$
$83$	8.34408e8	1.92987	0.964933	+	0.262497i	$0.0845461\pi$
$84$	−5.14937e8	−1.12849
$85$	−3.53044e7	−0.0733573
$86$	−1.31681e9	−2.59585
$87$	−5.22638e8	−0.978057
$88$	1.90136e9	3.37982
$89$	−2.13503e8	−0.360702	−0.180351	−	0.983602i	$-0.557723\pi$
$89$	−2.13503e8	−0.360702	−0.180351	+	0.983602i	$0.557723\pi$
$90$	−6.38658e8	−1.02607
$91$	6.85750e7	0.104828
$92$	−6.37368e8	−0.927566
$93$	−7.99875e8	−1.10879
$94$	−1.04906e9	−1.38587
$95$	3.85610e8	0.485727
$96$	3.28318e8	0.394524
$97$	−1.36917e9	−1.57031	−0.785155	−	0.619300i	$-0.787417\pi$
$97$	−1.36917e9	−1.57031	−0.785155	+	0.619300i	$0.787417\pi$
$98$	−2.28753e8	−0.250524
$99$	−1.83241e9	−1.91719
$100$	−1.45446e9	−1.45446
$101$	−1.06790e9	−1.02114	−0.510571	−	0.859836i	$-0.670566\pi$
$101$	−1.06790e9	−1.02114	−0.510571	+	0.859836i	$0.670566\pi$
$102$	−3.69900e8	−0.338364
$103$	1.98007e9	1.73346	0.866728	−	0.498782i	$-0.166219\pi$
$103$	1.98007e9	1.73346	0.866728	+	0.498782i	$0.166219\pi$
$104$	−6.23987e8	−0.523028
$105$	−3.70442e8	−0.297419
$106$	1.55102e9	1.19328
$107$	2.70735e9	1.99672	0.998362	−	0.0572160i	$-0.0182224\pi$
$107$	2.70735e9	1.99672	0.998362	+	0.0572160i	$0.0182224\pi$
$108$	−2.94291e8	−0.208147
$109$	−8.51469e8	−0.577763	−0.288882	−	0.957365i	$-0.593283\pi$
$109$	−8.51469e8	−0.577763	−0.288882	+	0.957365i	$0.593283\pi$
$110$	2.63981e9	1.71912
$111$	1.25108e9	0.782223
$112$	7.75258e8	0.465549
$113$	−1.97004e9	−1.13664	−0.568318	−	0.822809i	$-0.692406\pi$
$113$	−1.97004e9	−1.13664	−0.568318	+	0.822809i	$0.692406\pi$
$114$	4.04021e9	2.24044
$115$	−4.58517e8	−0.244464
$116$	2.75145e9	1.41091
$117$	6.01357e8	0.296685
$118$	−1.90988e9	−0.906851
$119$	−1.10890e8	−0.0506912
$120$	3.37077e9	1.48393
$121$	5.21607e9	2.21212
$122$	−5.69390e9	−2.32697
$123$	3.35233e9	1.32061
$124$	4.21097e9	1.59950
$125$	−2.53932e9	−0.930297
$126$	−2.00601e9	−0.709033
$127$	1.62686e9	0.554923	0.277462	−	0.960737i	$-0.410507\pi$
$127$	1.62686e9	0.554923	0.277462	+	0.960737i	$0.410507\pi$
$128$	4.83159e9	1.59091
$129$	−6.69794e9	−2.12955
$130$	−8.66328e8	−0.266034
$131$	−2.20493e9	−0.654146	−0.327073	−	0.944999i	$-0.606062\pi$
$131$	−2.20493e9	−0.654146	−0.327073	+	0.944999i	$0.606062\pi$
$132$	1.86649e10	5.35109
$133$	1.21119e9	0.335646
$134$	7.05740e8	0.189092
$135$	−2.11711e8	−0.0548581
$136$	1.00903e9	0.252917
$137$	4.32814e9	1.04969	0.524843	−	0.851199i	$-0.324124\pi$
$137$	4.32814e9	1.04969	0.524843	+	0.851199i	$0.324124\pi$
$138$	−4.80410e9	−1.12760
$139$	−2.38823e9	−0.542637	−0.271318	−	0.962490i	$-0.587460\pi$
$139$	−2.38823e9	−0.542637	−0.271318	+	0.962490i	$0.587460\pi$
$140$	1.95021e9	0.429046
$141$	−5.33602e9	−1.13692
$142$	3.29859e9	0.680817
$143$	−2.48563e9	−0.497078
$144$	6.79850e9	1.31760
$145$	1.97937e9	0.371853
$146$	−9.11861e9	−1.66089
$147$	−1.16355e9	−0.205521
$148$	−6.58634e9	−1.12841
$149$	−6.32030e9	−1.05051	−0.525254	−	0.850945i	$-0.676030\pi$
$149$	−6.32030e9	−1.05051	−0.525254	+	0.850945i	$0.676030\pi$
$150$	−1.09628e10	−1.76812
$151$	−7.50622e9	−1.17497	−0.587483	−	0.809237i	$-0.699881\pi$
$151$	−7.50622e9	−1.17497	−0.587483	+	0.809237i	$0.699881\pi$
$152$	−1.10211e10	−1.67466
$153$	−9.72436e8	−0.143466
$154$	8.29159e9	1.18794
$155$	3.02934e9	0.421556
$156$	−6.12541e9	−0.828085
$157$	−9.47459e8	−0.124455	−0.0622274	−	0.998062i	$-0.519820\pi$
$157$	−9.47459e8	−0.124455	−0.0622274	+	0.998062i	$0.519820\pi$
$158$	1.19040e10	1.51962
$159$	7.88928e9	0.978927
$160$	−1.24343e9	−0.149996
$161$	−1.44019e9	−0.168929
$162$	1.42268e10	1.62289
$163$	−1.13452e10	−1.25883	−0.629417	−	0.777067i	$-0.716706\pi$
$163$	−1.13452e10	−1.25883	−0.629417	+	0.777067i	$0.716706\pi$
$164$	−1.76485e10	−1.90506
$165$	1.34274e10	1.41031
$166$	−3.31101e10	−3.38434
$167$	−1.09555e10	−1.08995	−0.544975	−	0.838453i	$-0.683461\pi$
$167$	−1.09555e10	−1.08995	−0.544975	+	0.838453i	$0.683461\pi$
$168$	1.05875e10	1.02542
$169$	8.15731e8	0.0769231
$170$	1.40091e9	0.128644
$171$	1.06214e10	0.949944
$172$	3.52616e10	3.07202
$173$	−1.16926e10	−0.992436	−0.496218	−	0.868198i	$-0.665278\pi$
$173$	−1.16926e10	−0.992436	−0.496218	+	0.868198i	$0.665278\pi$
$174$	2.07388e10	1.71519
$175$	−3.28649e9	−0.264887
$176$	−2.81007e10	−2.20755
$177$	−9.71457e9	−0.743950
$178$	8.47201e9	0.632552
$179$	−2.27115e10	−1.65351	−0.826756	−	0.562561i	$-0.809816\pi$
$179$	−2.27115e10	−1.65351	−0.826756	+	0.562561i	$0.809816\pi$
$180$	1.71020e10	1.21429
$181$	−1.64962e10	−1.14243	−0.571216	−	0.820800i	$-0.693528\pi$
$181$	−1.64962e10	−1.14243	−0.571216	+	0.820800i	$0.693528\pi$
$182$	−2.72112e9	−0.183834
$183$	−2.89620e10	−1.90897
$184$	1.31048e10	0.842850
$185$	−4.73816e9	−0.297397
$186$	3.17398e10	1.94445
$187$	4.01943e9	0.240369
$188$	2.80917e10	1.64009
$189$	−6.64979e8	−0.0379079
$190$	−1.53014e10	−0.851803
$191$	−7.64027e9	−0.415392	−0.207696	−	0.978193i	$-0.566597\pi$
$191$	−7.64027e9	−0.415392	−0.207696	+	0.978193i	$0.566597\pi$
$192$	2.03396e10	1.08016
$193$	1.38071e10	0.716301	0.358151	−	0.933664i	$-0.383407\pi$
$193$	1.38071e10	0.716301	0.358151	+	0.933664i	$0.383407\pi$
$194$	5.43301e10	2.75380
$195$	−4.40658e9	−0.218246
$196$	6.12556e9	0.296478
$197$	−2.81607e10	−1.33213	−0.666064	−	0.745895i	$-0.732022\pi$
$197$	−2.81607e10	−1.33213	−0.666064	+	0.745895i	$0.732022\pi$
$198$	7.27118e10	3.36211
$199$	−2.65123e9	−0.119842	−0.0599209	−	0.998203i	$-0.519085\pi$
$199$	−2.65123e9	−0.119842	−0.0599209	+	0.998203i	$0.519085\pi$
$200$	2.99049e10	1.32162
$201$	3.58974e9	0.155125
$202$	4.23755e10	1.79074
$203$	6.21716e9	0.256957
$204$	9.90521e9	0.400431
$205$	−1.26962e10	−0.502088
$206$	−7.85710e10	−3.03990
$207$	−1.26296e10	−0.478103
$208$	9.22205e9	0.341619
$209$	−4.39020e10	−1.59157
$210$	1.46995e10	0.521573
$211$	5.04101e10	1.75084	0.875421	−	0.483362i	$-0.160584\pi$
$211$	5.04101e10	1.75084	0.875421	+	0.483362i	$0.160584\pi$
$212$	−4.15334e10	−1.41217
$213$	1.67783e10	0.558520
$214$	−1.07430e11	−3.50159
$215$	2.53669e10	0.809645
$216$	6.05087e9	0.189137
$217$	9.51510e9	0.291303
$218$	3.37871e10	1.01320
$219$	−4.63817e10	−1.36254
$220$	−7.06889e10	−2.03446
$221$	−1.31909e9	−0.0371972
$222$	−4.96439e10	−1.37176
$223$	6.29895e8	0.0170568	0.00852838	−	0.999964i	$-0.497285\pi$
$223$	6.29895e8	0.0170568	0.00852838	+	0.999964i	$0.497285\pi$
$224$	−3.90558e9	−0.103650
$225$	−2.88204e10	−0.749684
$226$	7.81729e10	1.99328
$227$	−5.51412e10	−1.37835	−0.689175	−	0.724595i	$-0.742027\pi$
$227$	−5.51412e10	−1.37835	−0.689175	+	0.724595i	$0.742027\pi$
$228$	−1.08189e11	−2.65141
$229$	2.46673e10	0.592737	0.296369	−	0.955074i	$-0.404224\pi$
$229$	2.46673e10	0.592737	0.296369	+	0.955074i	$0.404224\pi$
$230$	1.81944e10	0.428709
$231$	4.21751e10	0.974546
$232$	−5.65720e10	−1.28205
$233$	2.87752e10	0.639613	0.319806	−	0.947483i	$-0.396382\pi$
$233$	2.87752e10	0.639613	0.319806	+	0.947483i	$0.396382\pi$
$234$	−2.38624e10	−0.520288
$235$	2.02089e10	0.432253
$236$	5.11427e10	1.07320
$237$	6.05496e10	1.24665
$238$	4.40024e9	0.0888955
$239$	−2.14647e10	−0.425534	−0.212767	−	0.977103i	$-0.568248\pi$
$239$	−2.14647e10	−0.425534	−0.212767	+	0.977103i	$0.568248\pi$
$240$	−4.98175e10	−0.969240
$241$	5.95005e10	1.13617	0.568086	−	0.822969i	$-0.307684\pi$
$241$	5.95005e10	1.13617	0.568086	+	0.822969i	$0.307684\pi$
$242$	−2.06979e11	−3.87933
$243$	7.78158e10	1.43166
$244$	1.52471e11	2.75381
$245$	4.40668e9	0.0781383
$246$	−1.33024e11	−2.31590
$247$	1.44077e10	0.246297
$248$	−8.65811e10	−1.45342
$249$	−1.68414e11	−2.77640
$250$	1.00763e11	1.63143
$251$	−9.95398e10	−1.58294	−0.791471	−	0.611207i	$-0.790684\pi$
$251$	−9.95398e10	−1.58294	−0.791471	+	0.611207i	$0.790684\pi$
$252$	5.37171e10	0.839093
$253$	5.22026e10	0.801032
$254$	−6.45553e10	−0.973151
$255$	7.12573e9	0.105536
$256$	−1.40127e11	−2.03911
$257$	4.89105e9	0.0699364	0.0349682	−	0.999388i	$-0.488867\pi$
$257$	4.89105e9	0.0699364	0.0349682	+	0.999388i	$0.488867\pi$
$258$	2.65781e11	3.73452
$259$	−1.48825e10	−0.205507
$260$	2.31986e10	0.314834
$261$	5.45204e10	0.727239
$262$	8.74939e10	1.14716
$263$	−1.03933e10	−0.133953	−0.0669767	−	0.997755i	$-0.521335\pi$
$263$	−1.03933e10	−0.133953	−0.0669767	+	0.997755i	$0.521335\pi$
$264$	−3.83765e11	−4.86237
$265$	−2.98788e10	−0.372183
$266$	−4.80613e10	−0.588611
$267$	4.30928e10	0.518925
$268$	−1.88983e10	−0.223778
$269$	−1.23860e11	−1.44227	−0.721135	−	0.692795i	$-0.756379\pi$
$269$	−1.23860e11	−1.44227	−0.721135	+	0.692795i	$0.756379\pi$
$270$	8.40089e9	0.0962029
$271$	1.04040e11	1.17176	0.585880	−	0.810398i	$-0.300749\pi$
$271$	1.04040e11	1.17176	0.585880	+	0.810398i	$0.300749\pi$
$272$	−1.49127e10	−0.165194
$273$	−1.38410e10	−0.150812
$274$	−1.71745e11	−1.84080
$275$	1.19125e11	1.25605
$276$	1.28644e11	1.33444
$277$	−1.11720e11	−1.14017	−0.570087	−	0.821584i	$-0.693090\pi$
$277$	−1.11720e11	−1.14017	−0.570087	+	0.821584i	$0.693090\pi$
$278$	9.47672e10	0.951605
$279$	8.34412e10	0.824445
$280$	−4.00978e10	−0.389861
$281$	8.46126e10	0.809574	0.404787	−	0.914411i	$-0.367346\pi$
$281$	8.46126e10	0.809574	0.404787	+	0.914411i	$0.367346\pi$
$282$	2.11738e11	1.99378
$283$	−9.70546e9	−0.0899450	−0.0449725	−	0.998988i	$-0.514320\pi$
$283$	−9.70546e9	−0.0899450	−0.0449725	+	0.998988i	$0.514320\pi$
$284$	−8.83298e10	−0.805702
$285$	−7.78304e10	−0.698791
$286$	9.86322e10	0.871709
$287$	−3.98784e10	−0.346952
$288$	−3.42494e10	−0.293350
$289$	−1.16455e11	−0.982013
$290$	−7.85433e10	−0.652106
$291$	2.76350e11	2.25913
$292$	2.44178e11	1.96555
$293$	1.53609e11	1.21762	0.608809	−	0.793317i	$-0.291648\pi$
$293$	1.53609e11	1.21762	0.608809	+	0.793317i	$0.291648\pi$
$294$	4.61708e10	0.360416
$295$	3.67917e10	0.282846
$296$	1.35421e11	1.02535
$297$	2.41035e10	0.179753
$298$	2.50796e11	1.84224
$299$	−1.71318e10	−0.123960
$300$	2.93564e11	2.09246
$301$	7.96770e10	0.559479
$302$	2.97854e11	2.06050
$303$	2.15543e11	1.46907
$304$	1.62883e11	1.09382
$305$	1.09687e11	0.725780
$306$	3.85872e10	0.251592
$307$	1.44131e11	0.926048	0.463024	−	0.886346i	$-0.346764\pi$
$307$	1.44131e11	0.926048	0.463024	+	0.886346i	$0.346764\pi$
$308$	−2.22033e11	−1.40585
$309$	−3.99651e11	−2.49384
$310$	−1.20207e11	−0.739270
$311$	−2.59353e11	−1.57206	−0.786030	−	0.618188i	$-0.787867\pi$
$311$	−2.59353e11	−1.57206	−0.786030	+	0.618188i	$0.787867\pi$
$312$	1.25944e11	0.752455
$313$	1.49010e11	0.877538	0.438769	−	0.898600i	$-0.355415\pi$
$313$	1.49010e11	0.877538	0.438769	+	0.898600i	$0.355415\pi$
$314$	3.75961e10	0.218252
$315$	3.86437e10	0.221147
$316$	−3.18766e11	−1.79837
$317$	3.08871e11	1.71795	0.858976	−	0.512016i	$-0.171101\pi$
$317$	3.08871e11	1.71795	0.858976	+	0.512016i	$0.171101\pi$
$318$	−3.13054e11	−1.71671
$319$	−2.25353e11	−1.21844
$320$	−7.70316e10	−0.410671
$321$	−5.46444e11	−2.87259
$322$	5.71483e10	0.296246
$323$	−2.32982e10	−0.119100
$324$	−3.80965e11	−1.92058
$325$	−3.90943e10	−0.194374
$326$	4.50189e11	2.20758
$327$	1.71858e11	0.831199
$328$	3.62867e11	1.73107
$329$	6.34758e10	0.298694
$330$	−5.32811e11	−2.47321
$331$	2.79598e11	1.28029	0.640144	−	0.768255i	$-0.278875\pi$
$331$	2.79598e11	1.28029	0.640144	+	0.768255i	$0.278875\pi$
$332$	8.86624e11	4.00515
$333$	−1.30510e11	−0.581625
$334$	4.34723e11	1.91141
$335$	−1.35953e10	−0.0589777
$336$	−1.56476e11	−0.669762
$337$	−1.24066e11	−0.523984	−0.261992	−	0.965070i	$-0.584379\pi$
$337$	−1.24066e11	−0.523984	−0.261992	+	0.965070i	$0.584379\pi$
$338$	−3.23690e10	−0.134897
$339$	3.97626e11	1.63522
$340$	−3.75137e10	−0.152242
$341$	−3.44893e11	−1.38131
$342$	−4.21466e11	−1.66589
$343$	1.38413e10	0.0539949
$344$	−7.25007e11	−2.79145
$345$	9.25458e10	0.351699
$346$	4.63972e11	1.74040
$347$	−4.24443e11	−1.57158	−0.785791	−	0.618492i	$-0.787744\pi$
$347$	−4.24443e11	−1.57158	−0.785791	+	0.618492i	$0.787744\pi$
$348$	−5.55344e11	−2.02981
$349$	−2.73427e11	−0.986568	−0.493284	−	0.869868i	$-0.664204\pi$
$349$	−2.73427e11	−0.986568	−0.493284	+	0.869868i	$0.664204\pi$
$350$	1.30411e11	0.464524
$351$	−7.91024e9	−0.0278168
$352$	1.41565e11	0.491490
$353$	1.64625e11	0.564301	0.282151	−	0.959370i	$-0.408952\pi$
$353$	1.64625e11	0.564301	0.282151	+	0.959370i	$0.408952\pi$
$354$	3.85484e11	1.30464
$355$	−6.35437e10	−0.212347
$356$	−2.26864e11	−0.748584
$357$	2.23818e10	0.0729269
$358$	9.01214e11	2.89971
$359$	3.73577e11	1.18701	0.593507	−	0.804829i	$-0.297743\pi$
$359$	3.73577e11	1.18701	0.593507	+	0.804829i	$0.297743\pi$
$360$	−3.51632e11	−1.10338
$361$	−6.82143e10	−0.211394
$362$	6.54585e11	2.00344
$363$	−1.05280e12	−3.18247
$364$	7.28663e10	0.217556
$365$	1.75660e11	0.518030
$366$	1.14924e12	3.34769
$367$	−2.58080e11	−0.742604	−0.371302	−	0.928512i	$-0.621088\pi$
$367$	−2.58080e11	−0.742604	−0.371302	+	0.928512i	$0.621088\pi$
$368$	−1.93679e11	−0.550513
$369$	−3.49707e11	−0.981942
$370$	1.88015e11	0.521536
$371$	−9.38488e10	−0.257185
$372$	−8.49931e11	−2.30112
$373$	−5.05371e11	−1.35182	−0.675912	−	0.736982i	$-0.736250\pi$
$373$	−5.05371e11	−1.35182	−0.675912	+	0.736982i	$0.736250\pi$
$374$	−1.59495e11	−0.421526
$375$	5.12528e11	1.33837
$376$	−5.77588e11	−1.49030
$377$	7.39560e10	0.188555
$378$	2.63870e10	0.0664779
$379$	−7.39437e10	−0.184088	−0.0920438	−	0.995755i	$-0.529340\pi$
$379$	−7.39437e10	−0.184088	−0.0920438	+	0.995755i	$0.529340\pi$
$380$	4.09741e11	1.00805
$381$	−3.28360e11	−0.798341
$382$	3.03173e11	0.728460
$383$	−1.19857e10	−0.0284623	−0.0142312	−	0.999899i	$-0.504530\pi$
$383$	−1.19857e10	−0.0284623	−0.0142312	+	0.999899i	$0.504530\pi$
$384$	−9.75195e11	−2.28876
$385$	−1.59728e11	−0.370518
$386$	−5.47880e11	−1.25615
$387$	6.98715e11	1.58344
$388$	−1.45485e12	−3.25894
$389$	−2.82555e11	−0.625647	−0.312823	−	0.949811i	$-0.601275\pi$
$389$	−2.82555e11	−0.625647	−0.312823	+	0.949811i	$0.601275\pi$
$390$	1.74857e11	0.382730
$391$	2.77032e10	0.0599425
$392$	−1.25947e11	−0.269401
$393$	4.45038e11	0.941088
$394$	1.11745e12	2.33611
$395$	−2.29318e11	−0.473970
$396$	−1.94708e12	−3.97883
$397$	−5.51391e11	−1.11404	−0.557022	−	0.830497i	$-0.688056\pi$
$397$	−5.51391e11	−1.11404	−0.557022	+	0.830497i	$0.688056\pi$
$398$	1.05203e11	0.210163
$399$	−2.44464e11	−0.482877
$400$	−4.41971e11	−0.863226
$401$	−8.56723e11	−1.65459	−0.827296	−	0.561767i	$-0.810122\pi$
$401$	−8.56723e11	−1.65459	−0.827296	+	0.561767i	$0.810122\pi$
$402$	−1.42444e11	−0.272037
$403$	1.13187e11	0.213758
$404$	−1.13473e12	−2.11923
$405$	−2.74063e11	−0.506178
$406$	−2.46703e11	−0.450617
$407$	5.39444e11	0.974476
$408$	−2.03659e11	−0.363859
$409$	−4.41170e11	−0.779563	−0.389782	−	0.920907i	$-0.627450\pi$
$409$	−4.41170e11	−0.779563	−0.389782	+	0.920907i	$0.627450\pi$
$410$	5.03796e11	0.880496
$411$	−8.73580e11	−1.51013
$412$	2.10398e12	3.59753
$413$	1.15562e11	0.195452
$414$	5.01153e11	0.838434
$415$	6.37831e11	1.05557
$416$	−4.64587e10	−0.0760584
$417$	4.82033e11	0.780665
$418$	1.74207e12	2.79109
$419$	−1.04353e12	−1.65402	−0.827009	−	0.562189i	$-0.809959\pi$
$419$	−1.04353e12	−1.65402	−0.827009	+	0.562189i	$0.809959\pi$
$420$	−3.93624e11	−0.617248
$421$	−4.64177e11	−0.720135	−0.360068	−	0.932926i	$-0.617246\pi$
$421$	−4.64177e11	−0.720135	−0.360068	+	0.932926i	$0.617246\pi$
$422$	−2.00032e12	−3.07039
$423$	5.56641e11	0.845364
$424$	8.53962e11	1.28319
$425$	6.32182e10	0.0939922
$426$	−6.65777e11	−0.979458
$427$	3.44524e11	0.501527
$428$	2.87678e12	4.14390
$429$	5.01692e11	0.715121
$430$	−1.00658e12	−1.41985
$431$	1.03602e12	1.44617	0.723086	−	0.690758i	$-0.242723\pi$
$431$	1.03602e12	1.44617	0.723086	+	0.690758i	$0.242723\pi$
$432$	−8.94273e10	−0.123536
$433$	2.95265e11	0.403661	0.201830	−	0.979420i	$-0.435311\pi$
$433$	2.95265e11	0.403661	0.201830	+	0.979420i	$0.435311\pi$
$434$	−3.77568e11	−0.510848
$435$	−3.99510e11	−0.534966
$436$	−9.04753e11	−1.19906
$437$	−3.02587e11	−0.396902
$438$	1.84047e12	2.38944
$439$	1.60114e11	0.205750	0.102875	−	0.994694i	$-0.467196\pi$
$439$	1.60114e11	0.205750	0.102875	+	0.994694i	$0.467196\pi$
$440$	1.45342e12	1.84865
$441$	1.21379e11	0.152816
$442$	5.23428e10	0.0652314
$443$	−6.60319e11	−0.814586	−0.407293	−	0.913297i	$-0.633527\pi$
$443$	−6.60319e11	−0.814586	−0.407293	+	0.913297i	$0.633527\pi$
$444$	1.32937e12	1.62339
$445$	−1.63204e11	−0.197293
$446$	−2.49948e10	−0.0299119
$447$	1.27567e12	1.51131
$448$	−2.41955e11	−0.283781
$449$	1.17755e12	1.36732	0.683661	−	0.729800i	$-0.260387\pi$
$449$	1.17755e12	1.36732	0.683661	+	0.729800i	$0.260387\pi$
$450$	1.14362e12	1.31470
$451$	1.44547e12	1.64518
$452$	−2.09332e12	−2.35892
$453$	1.51503e12	1.69036
$454$	2.18805e12	2.41717
$455$	5.24195e10	0.0573378
$456$	2.22446e12	2.40925
$457$	4.73878e11	0.508210	0.254105	−	0.967177i	$-0.418219\pi$
$457$	4.73878e11	0.508210	0.254105	+	0.967177i	$0.418219\pi$
$458$	−9.78823e11	−1.03946
$459$	1.27914e10	0.0134512
$460$	−4.87211e11	−0.507349
$461$	−7.86748e11	−0.811300	−0.405650	−	0.914028i	$-0.632955\pi$
$461$	−7.86748e11	−0.811300	−0.405650	+	0.914028i	$0.632955\pi$
$462$	−1.67355e12	−1.70903
$463$	−1.98673e11	−0.200921	−0.100461	−	0.994941i	$-0.532032\pi$
$463$	−1.98673e11	−0.200921	−0.100461	+	0.994941i	$0.532032\pi$
$464$	8.36092e11	0.837381
$465$	−6.11433e11	−0.606472
$466$	−1.14183e12	−1.12167
$467$	−4.02028e11	−0.391138	−0.195569	−	0.980690i	$-0.562655\pi$
$467$	−4.02028e11	−0.391138	−0.195569	+	0.980690i	$0.562655\pi$
$468$	6.38990e11	0.615726
$469$	−4.27026e10	−0.0407546
$470$	−8.01910e11	−0.758028
$471$	1.91232e11	0.179047
$472$	−1.05154e12	−0.975182
$473$	−2.88804e12	−2.65295
$474$	−2.40267e12	−2.18621
$475$	−6.90496e11	−0.622358
$476$	−1.17830e11	−0.105202
$477$	−8.22992e11	−0.727885
$478$	8.51740e11	0.746245
$479$	−4.03884e11	−0.350548	−0.175274	−	0.984520i	$-0.556081\pi$
$479$	−4.03884e11	−0.350548	−0.175274	+	0.984520i	$0.556081\pi$
$480$	2.50970e11	0.215792
$481$	−1.77034e11	−0.150801
$482$	−2.36104e12	−1.99247
$483$	2.90685e11	0.243030
$484$	5.54249e12	4.59093
$485$	−1.04661e12	−0.858909
$486$	−3.08780e12	−2.51065
$487$	−1.32903e12	−1.07067	−0.535335	−	0.844640i	$-0.679815\pi$
$487$	−1.32903e12	−1.07067	−0.535335	+	0.844640i	$0.679815\pi$
$488$	−3.13494e12	−2.50230
$489$	2.28989e12	1.81102
$490$	−1.74861e11	−0.137029
$491$	−1.73030e12	−1.34355	−0.671777	−	0.740753i	$-0.734469\pi$
$491$	−1.73030e12	−1.34355	−0.671777	+	0.740753i	$0.734469\pi$
$492$	3.56211e12	2.74072
$493$	−1.19592e11	−0.0911781
$494$	−5.71711e11	−0.431922
$495$	−1.40071e12	−1.04864
$496$	1.27960e12	0.949309
$497$	−1.99590e11	−0.146735
$498$	6.68285e12	4.86888
$499$	−1.01113e12	−0.730051	−0.365026	−	0.930998i	$-0.618940\pi$
$499$	−1.01113e12	−0.730051	−0.365026	+	0.930998i	$0.618940\pi$
$500$	−2.69822e12	−1.93069
$501$	2.21122e12	1.56806
$502$	3.94984e12	2.77595
$503$	−1.40816e12	−0.980835	−0.490418	−	0.871488i	$-0.663156\pi$
$503$	−1.40816e12	−0.980835	−0.490418	+	0.871488i	$0.663156\pi$
$504$	−1.10447e12	−0.762458
$505$	−8.16318e11	−0.558532
$506$	−2.07145e12	−1.40474
$507$	−1.64645e11	−0.110665
$508$	1.72867e12	1.15166
$509$	5.65749e11	0.373589	0.186794	−	0.982399i	$-0.440190\pi$
$509$	5.65749e11	0.373589	0.186794	+	0.982399i	$0.440190\pi$
$510$	−2.82756e11	−0.185074
$511$	5.51745e11	0.357968
$512$	3.08659e12	1.98502
$513$	−1.39713e11	−0.0890654
$514$	−1.94082e11	−0.122645
$515$	1.51359e12	0.948145
$516$	−7.11709e12	−4.41956
$517$	−2.30080e12	−1.41635
$518$	5.90551e11	0.360391
$519$	2.35999e12	1.42777
$520$	−4.76982e11	−0.286080
$521$	2.40433e12	1.42963	0.714816	−	0.699312i	$-0.246510\pi$
$521$	2.40433e12	1.42963	0.714816	+	0.699312i	$0.246510\pi$
$522$	−2.16342e12	−1.27533
$523$	−2.71200e12	−1.58501	−0.792505	−	0.609865i	$-0.791224\pi$
$523$	−2.71200e12	−1.58501	−0.792505	+	0.609865i	$0.791224\pi$
$524$	−2.34292e12	−1.35758
$525$	6.63336e11	0.381080
$526$	4.12417e11	0.234910
$527$	−1.83030e11	−0.103365
$528$	5.67176e12	3.17589
$529$	−1.44136e12	−0.800241
$530$	1.18562e12	0.652686
$531$	1.01340e12	0.553168
$532$	1.28699e12	0.696582
$533$	−4.74372e11	−0.254593
$534$	−1.70997e12	−0.910021
$535$	2.06953e12	1.09214
$536$	3.88566e11	0.203340
$537$	4.58402e12	2.37882
$538$	4.91489e12	2.52926
$539$	−5.01704e11	−0.256034
$540$	−2.24959e11	−0.113850
$541$	−1.85773e12	−0.932382	−0.466191	−	0.884684i	$-0.654374\pi$
$541$	−1.85773e12	−0.932382	−0.466191	+	0.884684i	$0.654374\pi$
$542$	−4.12841e12	−2.05488
$543$	3.32954e12	1.64356
$544$	7.51268e10	0.0367790
$545$	−6.50873e11	−0.316018
$546$	5.49223e11	0.264473
$547$	3.11372e11	0.148709	0.0743543	−	0.997232i	$-0.476310\pi$
$547$	3.11372e11	0.148709	0.0743543	+	0.997232i	$0.476310\pi$
$548$	4.59899e12	2.17846
$549$	3.02125e12	1.41942
$550$	−4.72700e12	−2.20269
$551$	1.30623e12	0.603725
$552$	−2.64504e12	−1.21257
$553$	−7.20282e11	−0.327521
$554$	4.43315e12	1.99949
$555$	9.56337e11	0.427851
$556$	−2.53768e12	−1.12616
$557$	1.34798e12	0.593382	0.296691	−	0.954974i	$-0.404117\pi$
$557$	1.34798e12	0.593382	0.296691	+	0.954974i	$0.404117\pi$
$558$	−3.31103e12	−1.44580
$559$	9.47794e11	0.410545
$560$	5.92616e11	0.254640
$561$	−8.11271e11	−0.345806
$562$	−3.35751e12	−1.41972
$563$	2.32125e12	0.973718	0.486859	−	0.873481i	$-0.338143\pi$
$563$	2.32125e12	0.973718	0.486859	+	0.873481i	$0.338143\pi$
$564$	−5.66994e12	−2.35951
$565$	−1.50592e12	−0.621703
$566$	3.85122e11	0.157734
$567$	−8.60827e11	−0.349778
$568$	1.81613e12	0.732116
$569$	1.44089e12	0.576268	0.288134	−	0.957590i	$-0.406965\pi$
$569$	1.44089e12	0.576268	0.288134	+	0.957590i	$0.406965\pi$
$570$	3.08838e12	1.22545
$571$	−1.18856e12	−0.467906	−0.233953	−	0.972248i	$-0.575166\pi$
$571$	−1.18856e12	−0.467906	−0.233953	+	0.972248i	$0.575166\pi$
$572$	−2.64118e12	−1.03161
$573$	1.54209e12	0.597604
$574$	1.58241e12	0.608438
$575$	8.21049e11	0.313230
$576$	−2.12178e12	−0.803156
$577$	7.32215e11	0.275009	0.137505	−	0.990501i	$-0.456092\pi$
$577$	7.32215e11	0.275009	0.137505	+	0.990501i	$0.456092\pi$
$578$	4.62104e12	1.72212
$579$	−2.78679e12	−1.03051
$580$	2.10324e12	0.771724
$581$	2.00341e12	0.729421
$582$	−1.09658e13	−3.96176
$583$	3.40173e12	1.21953
$584$	−5.02051e12	−1.78604
$585$	4.59684e11	0.162277
$586$	−6.09533e12	−2.13530
$587$	1.83141e12	0.636669	0.318334	−	0.947978i	$-0.396877\pi$
$587$	1.83141e12	0.636669	0.318334	+	0.947978i	$0.396877\pi$
$588$	−1.23636e12	−0.426529
$589$	1.99914e12	0.684422
$590$	−1.45993e12	−0.496019
$591$	5.68388e12	1.91647
$592$	−2.00141e12	−0.669714
$593$	1.13605e12	0.377270	0.188635	−	0.982047i	$-0.439594\pi$
$593$	1.13605e12	0.377270	0.188635	+	0.982047i	$0.439594\pi$
$594$	−9.56448e11	−0.315226
$595$	−8.47658e10	−0.0277265
$596$	−6.71582e12	−2.18017
$597$	5.35116e11	0.172410
$598$	6.79805e11	0.217385
$599$	5.79013e12	1.83767	0.918836	−	0.394640i	$-0.129131\pi$
$599$	5.79013e12	1.83767	0.918836	+	0.394640i	$0.129131\pi$
$600$	−6.03591e12	−1.90135
$601$	−4.77276e11	−0.149222	−0.0746112	−	0.997213i	$-0.523772\pi$
$601$	−4.77276e11	−0.149222	−0.0746112	+	0.997213i	$0.523772\pi$
$602$	−3.16166e12	−0.981139
$603$	−3.74474e11	−0.115344
$604$	−7.97595e12	−2.43846
$605$	3.98722e12	1.20996
$606$	−8.55294e12	−2.57625
$607$	−5.55565e12	−1.66106	−0.830531	−	0.556972i	$-0.811963\pi$
$607$	−5.55565e12	−1.66106	−0.830531	+	0.556972i	$0.811963\pi$
$608$	−8.20568e11	−0.243528
$609$	−1.25485e12	−0.369671
$610$	−4.35248e12	−1.27278
$611$	7.55074e11	0.219182
$612$	−1.03329e12	−0.297742
$613$	3.19190e12	0.913014	0.456507	−	0.889720i	$-0.349100\pi$
$613$	3.19190e12	0.913014	0.456507	+	0.889720i	$0.349100\pi$
$614$	−5.71924e12	−1.62398
$615$	2.56256e12	0.722329
$616$	4.56517e12	1.27745
$617$	−2.54892e12	−0.708064	−0.354032	−	0.935233i	$-0.615190\pi$
$617$	−2.54892e12	−0.708064	−0.354032	+	0.935233i	$0.615190\pi$
$618$	1.58585e13	4.37336
$619$	−3.56626e12	−0.976348	−0.488174	−	0.872746i	$-0.662337\pi$
$619$	−3.56626e12	−0.976348	−0.488174	+	0.872746i	$0.662337\pi$
$620$	3.21891e12	0.874877
$621$	1.66129e11	0.0448263
$622$	1.02914e13	2.75687
$623$	−5.12621e11	−0.136333
$624$	−1.86135e12	−0.491471
$625$	7.32357e11	0.191983
$626$	−5.91286e12	−1.53891
$627$	8.86105e12	2.28971
$628$	−1.00675e12	−0.258287
$629$	2.86276e11	0.0729217
$630$	−1.53342e12	−0.387818
$631$	6.93158e12	1.74060	0.870302	−	0.492518i	$-0.163924\pi$
$631$	6.93158e12	1.74060	0.870302	+	0.492518i	$0.163924\pi$
$632$	6.55409e12	1.63413
$633$	−1.01746e13	−2.51885
$634$	−1.22563e13	−3.01272
$635$	1.24359e12	0.303525
$636$	8.38298e12	2.03162
$637$	1.64648e11	0.0396214
$638$	8.94222e12	2.13674
$639$	−1.75027e12	−0.415290
$640$	3.69332e12	0.870177
$641$	6.87093e12	1.60751	0.803756	−	0.594959i	$-0.202832\pi$
$641$	6.87093e12	1.60751	0.803756	+	0.594959i	$0.202832\pi$
$642$	2.16834e13	5.03756
$643$	2.96454e12	0.683924	0.341962	−	0.939714i	$-0.388909\pi$
$643$	2.96454e12	0.683924	0.341962	+	0.939714i	$0.388909\pi$
$644$	−1.53032e12	−0.350587
$645$	−5.11998e12	−1.16480
$646$	9.24496e11	0.208862
$647$	−3.09024e12	−0.693302	−0.346651	−	0.937994i	$-0.612681\pi$
$647$	−3.09024e12	−0.693302	−0.346651	+	0.937994i	$0.612681\pi$
$648$	7.83296e12	1.74517
$649$	−4.18877e12	−0.926798
$650$	1.55130e12	0.340868
$651$	−1.92050e12	−0.419083
$652$	−1.20552e13	−2.61252
$653$	−1.34253e12	−0.288944	−0.144472	−	0.989509i	$-0.546148\pi$
$653$	−1.34253e12	−0.288944	−0.144472	+	0.989509i	$0.546148\pi$
$654$	−6.81949e12	−1.45765
$655$	−1.68548e12	−0.357797
$656$	−5.36290e12	−1.13066
$657$	4.83844e12	1.01312
$658$	−2.51878e12	−0.523810
$659$	5.64054e12	1.16503	0.582514	−	0.812821i	$-0.302069\pi$
$659$	5.64054e12	1.16503	0.582514	+	0.812821i	$0.302069\pi$
$660$	1.42676e13	2.92688
$661$	−7.62722e12	−1.55403	−0.777015	−	0.629482i	$-0.783267\pi$
$661$	−7.62722e12	−1.55403	−0.777015	+	0.629482i	$0.783267\pi$
$662$	−1.10947e13	−2.24520
$663$	2.66242e11	0.0535137
$664$	−1.82297e13	−3.63935
$665$	9.25849e11	0.183587
$666$	5.17874e12	1.01998
$667$	−1.55321e12	−0.303852
$668$	−1.16410e13	−2.26203
$669$	−1.27136e11	−0.0245387
$670$	5.39475e11	0.103427
$671$	−1.24879e13	−2.37815
$672$	7.88291e11	0.149116
$673$	−6.65404e12	−1.25031	−0.625154	−	0.780501i	$-0.714964\pi$
$673$	−6.65404e12	−1.25031	−0.625154	+	0.780501i	$0.714964\pi$
$674$	4.92305e12	0.918893
$675$	3.79102e11	0.0702893
$676$	8.66778e11	0.159642
$677$	3.62414e11	0.0663065	0.0331532	−	0.999450i	$-0.489445\pi$
$677$	3.62414e11	0.0663065	0.0331532	+	0.999450i	$0.489445\pi$
$678$	−1.57782e13	−2.86763
$679$	−3.28738e12	−0.593521
$680$	7.71312e11	0.138338
$681$	1.11295e13	1.98296
$682$	1.36857e13	2.42235
$683$	7.87971e12	1.38553	0.692767	−	0.721162i	$-0.256392\pi$
$683$	7.87971e12	1.38553	0.692767	+	0.721162i	$0.256392\pi$
$684$	1.12860e13	1.97147
$685$	3.30848e12	0.574144
$686$	−5.49236e11	−0.0946891
$687$	−4.97878e12	−0.852741
$688$	1.07151e13	1.82325
$689$	−1.11637e12	−0.188722
$690$	−3.67231e12	−0.616763
$691$	−3.59867e11	−0.0600469	−0.0300235	−	0.999549i	$-0.509558\pi$
$691$	−3.59867e11	−0.0600469	−0.0300235	+	0.999549i	$0.509558\pi$
$692$	−1.24243e13	−2.05965
$693$	−4.39961e12	−0.724628
$694$	1.68423e13	2.75603
$695$	−1.82559e12	−0.296805
$696$	1.14183e13	1.84443
$697$	7.67091e11	0.123112
$698$	1.08499e13	1.73011
$699$	−5.80791e12	−0.920179
$700$	−3.49216e12	−0.549734
$701$	−9.48905e12	−1.48420	−0.742099	−	0.670291i	$-0.766169\pi$
$701$	−9.48905e12	−1.48420	−0.742099	+	0.670291i	$0.766169\pi$
$702$	3.13886e11	0.0487815
$703$	−3.12683e12	−0.482842
$704$	8.77011e12	1.34564
$705$	−4.07891e12	−0.621861
$706$	−6.53250e12	−0.989596
$707$	−2.56404e12	−0.385955
$708$	−1.03225e13	−1.54396
$709$	−1.69854e11	−0.0252446	−0.0126223	−	0.999920i	$-0.504018\pi$
$709$	−1.69854e11	−0.0252446	−0.0126223	+	0.999920i	$0.504018\pi$
$710$	2.52148e12	0.372385
$711$	−6.31640e12	−0.926951
$712$	4.66451e12	0.680215
$713$	−2.37712e12	−0.344467
$714$	−8.88131e11	−0.127889
$715$	−1.90004e12	−0.271886
$716$	−2.41328e13	−3.43161
$717$	4.33237e12	0.612195
$718$	−1.48239e13	−2.08163
$719$	9.92019e12	1.38433	0.692166	−	0.721739i	$-0.256657\pi$
$719$	9.92019e12	1.38433	0.692166	+	0.721739i	$0.256657\pi$
$720$	5.19685e12	0.720682
$721$	4.75414e12	0.655185
$722$	2.70681e12	0.370715
$723$	−1.20094e13	−1.63455
$724$	−1.75285e13	−2.37094
$725$	−3.54438e12	−0.476452
$726$	4.17760e13	5.58100
$727$	−9.34395e11	−0.124058	−0.0620291	−	0.998074i	$-0.519757\pi$
$727$	−9.34395e11	−0.124058	−0.0620291	+	0.998074i	$0.519757\pi$
$728$	−1.49819e12	−0.197686
$729$	−8.64918e12	−1.13423
$730$	−6.97036e12	−0.908453
$731$	−1.53265e12	−0.198524
$732$	−3.07744e13	−3.96177
$733$	−4.07900e12	−0.521899	−0.260949	−	0.965352i	$-0.584036\pi$
$733$	−4.07900e12	−0.521899	−0.260949	+	0.965352i	$0.584036\pi$
$734$	1.02409e13	1.30228
$735$	−8.89431e11	−0.112414
$736$	9.75714e11	0.122567
$737$	1.54784e12	0.193251
$738$	1.38767e13	1.72200
$739$	3.37654e12	0.416458	0.208229	−	0.978080i	$-0.433230\pi$
$739$	3.37654e12	0.416458	0.208229	+	0.978080i	$0.433230\pi$
$740$	−5.03467e12	−0.617203
$741$	−2.90801e12	−0.354335
$742$	3.72401e12	0.451017
$743$	−8.79058e12	−1.05820	−0.529100	−	0.848560i	$-0.677470\pi$
$743$	−8.79058e12	−1.05820	−0.529100	+	0.848560i	$0.677470\pi$
$744$	1.74753e13	2.09096
$745$	−4.83131e12	−0.574594
$746$	2.00536e13	2.37065
$747$	1.75686e13	2.06441
$748$	4.27097e12	0.498849
$749$	6.50036e12	0.754691
$750$	−2.03376e13	−2.34706
$751$	1.49673e13	1.71697	0.858484	−	0.512840i	$-0.171406\pi$
$751$	1.49673e13	1.71697	0.858484	+	0.512840i	$0.171406\pi$
$752$	8.53631e12	0.973397
$753$	2.00908e13	2.27730
$754$	−2.93465e12	−0.330662
$755$	−5.73784e12	−0.642668
$756$	−7.06593e11	−0.0786722
$757$	−1.55150e13	−1.71720	−0.858598	−	0.512650i	$-0.828664\pi$
$757$	−1.55150e13	−1.71720	−0.858598	+	0.512650i	$0.828664\pi$
$758$	2.93416e12	0.322828
$759$	−1.05364e13	−1.15240
$760$	−8.42461e12	−0.915986
$761$	−1.49750e13	−1.61859	−0.809294	−	0.587404i	$-0.800150\pi$
$761$	−1.49750e13	−1.61859	−0.809294	+	0.587404i	$0.800150\pi$
$762$	1.30297e13	1.40002
$763$	−2.04438e12	−0.218374
$764$	−8.11839e12	−0.862084
$765$	−7.43340e11	−0.0784714
$766$	4.75606e11	0.0499135
$767$	1.37466e12	0.143422
$768$	2.82828e13	2.93357
$769$	1.66756e13	1.71954	0.859769	−	0.510683i	$-0.170607\pi$
$769$	1.66756e13	1.71954	0.859769	+	0.510683i	$0.170607\pi$
$770$	6.33818e12	0.649765
$771$	−9.87195e11	−0.100614
$772$	1.46712e13	1.48658
$773$	3.21304e12	0.323674	0.161837	−	0.986817i	$-0.448258\pi$
$773$	3.21304e12	0.323674	0.161837	+	0.986817i	$0.448258\pi$
$774$	−2.77257e13	−2.77682
$775$	−5.42452e12	−0.540137
$776$	2.99130e13	2.96130
$777$	3.00383e12	0.295652
$778$	1.12120e13	1.09718
$779$	−8.37851e12	−0.815170
$780$	−4.68233e12	−0.452936
$781$	7.23451e12	0.695792
$782$	−1.09929e12	−0.105119
$783$	−7.17160e11	−0.0681849
$784$	1.86139e12	0.175961
$785$	−7.24248e11	−0.0680728
$786$	−1.76595e13	−1.65036
$787$	−1.41868e11	−0.0131826	−0.00659128	−	0.999978i	$-0.502098\pi$
$787$	−1.41868e11	−0.0131826	−0.00659128	+	0.999978i	$0.502098\pi$
$788$	−2.99230e13	−2.76463
$789$	2.09776e12	0.192712
$790$	9.09955e12	0.831185
$791$	−4.73006e12	−0.429608
$792$	4.00336e13	3.61544
$793$	4.09827e12	0.368020
$794$	2.18797e13	1.95366
$795$	6.03065e12	0.535442
$796$	−2.81714e12	−0.248714
$797$	9.50720e12	0.834623	0.417311	−	0.908764i	$-0.362972\pi$
$797$	9.50720e12	0.834623	0.417311	+	0.908764i	$0.362972\pi$
$798$	9.70055e12	0.846805
$799$	−1.22101e12	−0.105988
$800$	2.22656e12	0.192189
$801$	−4.49535e12	−0.385849
$802$	3.39956e13	2.90160
$803$	−1.99991e13	−1.69742
$804$	3.81439e12	0.321938
$805$	−1.10090e12	−0.0923988
$806$	−4.49135e12	−0.374860
$807$	2.49996e13	2.07492
$808$	2.33310e13	1.92567
$809$	1.98831e13	1.63198	0.815990	−	0.578066i	$-0.196192\pi$
$809$	1.98831e13	1.63198	0.815990	+	0.578066i	$0.196192\pi$
$810$	1.08751e13	0.887668
$811$	−4.24777e12	−0.344800	−0.172400	−	0.985027i	$-0.555152\pi$
$811$	−4.24777e12	−0.344800	−0.172400	+	0.985027i	$0.555152\pi$
$812$	6.60623e12	0.533275
$813$	−2.09991e13	−1.68575
$814$	−2.14056e13	−1.70891
$815$	−8.67241e12	−0.688542
$816$	3.00993e12	0.237657
$817$	1.67402e13	1.31451
$818$	1.75061e13	1.36709
$819$	1.44386e12	0.112137
$820$	−1.34907e13	−1.04201
$821$	−1.55168e13	−1.19195	−0.595974	−	0.803003i	$-0.703234\pi$
$821$	−1.55168e13	−1.19195	−0.595974	+	0.803003i	$0.703234\pi$
$822$	3.46645e13	2.64827
$823$	−1.21234e13	−0.921136	−0.460568	−	0.887624i	$-0.652354\pi$
$823$	−1.21234e13	−0.921136	−0.460568	+	0.887624i	$0.652354\pi$
$824$	−4.32595e13	−3.26896
$825$	−2.40439e13	−1.80701
$826$	−4.58561e12	−0.342758
$827$	1.41174e13	1.04950	0.524748	−	0.851257i	$-0.324159\pi$
$827$	1.41174e13	1.04950	0.524748	+	0.851257i	$0.324159\pi$
$828$	−1.34199e13	−0.992231
$829$	8.72820e12	0.641844	0.320922	−	0.947106i	$-0.396007\pi$
$829$	8.72820e12	0.641844	0.320922	+	0.947106i	$0.396007\pi$
$830$	−2.53097e13	−1.85113
$831$	2.25492e13	1.64031
$832$	−2.87816e12	−0.208238
$833$	−2.66248e11	−0.0191595
$834$	−1.91275e13	−1.36903
$835$	−8.37447e12	−0.596167
$836$	−4.66494e13	−3.30307
$837$	−1.09758e12	−0.0772988
$838$	4.14081e13	2.90060
$839$	1.74217e13	1.21384	0.606922	−	0.794762i	$-0.292404\pi$
$839$	1.74217e13	1.21384	0.606922	+	0.794762i	$0.292404\pi$
$840$	8.09323e12	0.560874
$841$	−7.80213e12	−0.537813
$842$	1.84190e13	1.26288
$843$	−1.70780e13	−1.16469
$844$	5.35647e13	3.63361
$845$	6.23554e11	0.0420745
$846$	−2.20881e13	−1.48249
$847$	1.25238e13	0.836104
$848$	−1.26209e13	−0.838126
$849$	1.95892e12	0.129399
$850$	−2.50856e12	−0.164831
$851$	3.71802e12	0.243013
$852$	1.78282e13	1.15912
$853$	1.67487e12	0.108320	0.0541602	−	0.998532i	$-0.482752\pi$
$853$	1.67487e12	0.108320	0.0541602	+	0.998532i	$0.482752\pi$
$854$	−1.36710e13	−0.879511
$855$	8.11909e12	0.519589
$856$	−5.91489e13	−3.76543
$857$	2.04783e13	1.29682	0.648412	−	0.761290i	$-0.275434\pi$
$857$	2.04783e13	1.29682	0.648412	+	0.761290i	$0.275434\pi$
$858$	−1.99076e13	−1.25408
$859$	−2.22613e13	−1.39502	−0.697510	−	0.716575i	$-0.745709\pi$
$859$	−2.22613e13	−1.39502	−0.697510	+	0.716575i	$0.745709\pi$
$860$	2.69543e13	1.68030
$861$	8.04894e12	0.499142
$862$	−4.11102e13	−2.53610
$863$	−1.70230e13	−1.04469	−0.522345	−	0.852734i	$-0.674943\pi$
$863$	−1.70230e13	−1.04469	−0.522345	+	0.852734i	$0.674943\pi$
$864$	4.50515e11	0.0275041
$865$	−8.93793e12	−0.542831
$866$	−1.17164e13	−0.707887
$867$	2.35049e13	1.41277
$868$	1.01105e13	0.604555
$869$	2.61080e13	1.55305
$870$	1.58529e13	0.938153
$871$	−5.07968e11	−0.0299057
$872$	1.86025e13	1.08955
$873$	−2.88282e13	−1.67978
$874$	1.20069e13	0.696035
$875$	−6.09690e12	−0.351619
$876$	−4.92843e13	−2.82774
$877$	−5.12343e12	−0.292458	−0.146229	−	0.989251i	$-0.546714\pi$
$877$	−5.12343e12	−0.292458	−0.146229	+	0.989251i	$0.546714\pi$
$878$	−6.35349e12	−0.360817
$879$	−3.10039e13	−1.75173
$880$	−2.14805e13	−1.20746
$881$	−2.66945e13	−1.49290	−0.746450	−	0.665441i	$-0.768243\pi$
$881$	−2.66945e13	−1.49290	−0.746450	+	0.665441i	$0.768243\pi$
$882$	−4.81644e12	−0.267989
$883$	−5.33946e12	−0.295579	−0.147790	−	0.989019i	$-0.547216\pi$
$883$	−5.33946e12	−0.295579	−0.147790	+	0.989019i	$0.547216\pi$
$884$	−1.40164e12	−0.0771971
$885$	−7.42593e12	−0.406917
$886$	2.62021e13	1.42851
$887$	−3.02361e13	−1.64010	−0.820048	−	0.572295i	$-0.806053\pi$
$887$	−3.02361e13	−1.64010	−0.820048	+	0.572295i	$0.806053\pi$
$888$	−2.73329e13	−1.47512
$889$	3.90609e12	0.209741
$890$	6.47610e12	0.345986
$891$	3.12023e13	1.65858
$892$	6.69313e11	0.0353987
$893$	1.33364e13	0.701788
$894$	−5.06198e13	−2.65034
$895$	−1.73609e13	−0.904418
$896$	1.16007e13	0.601307
$897$	3.45783e12	0.178335
$898$	−4.67263e13	−2.39783
$899$	1.02617e13	0.523966
$900$	−3.06239e13	−1.55586
$901$	1.80525e12	0.0912592
$902$	−5.73576e13	−2.88510
$903$	−1.60818e13	−0.804894
$904$	4.30404e13	2.14347
$905$	−1.26099e13	−0.624873
$906$	−6.01180e13	−2.96434
$907$	2.31549e13	1.13608	0.568040	−	0.823001i	$-0.307702\pi$
$907$	2.31549e13	1.13608	0.568040	+	0.823001i	$0.307702\pi$
$908$	−5.85918e13	−2.86056
$909$	−2.24849e13	−1.09233
$910$	−2.08005e12	−0.100551
$911$	7.59486e11	0.0365332	0.0182666	−	0.999833i	$-0.494185\pi$
$911$	7.59486e11	0.0365332	0.0182666	+	0.999833i	$0.494185\pi$
$912$	−3.28758e13	−1.57362
$913$	−7.26176e13	−3.45878
$914$	−1.88039e13	−0.891232
$915$	−2.21389e13	−1.04414
$916$	2.62110e13	1.23014
$917$	−5.29405e12	−0.247244
$918$	−5.07575e11	−0.0235889
$919$	2.94594e13	1.36240	0.681199	−	0.732098i	$-0.261459\pi$
$919$	2.94594e13	1.36240	0.681199	+	0.732098i	$0.261459\pi$
$920$	1.00175e13	0.461012
$921$	−2.90909e13	−1.33226
$922$	3.12189e13	1.42275
$923$	−2.37421e12	−0.107674
$924$	4.48144e13	2.02252
$925$	8.48444e12	0.381053
$926$	7.88355e12	0.352349
$927$	4.16907e13	1.85430
$928$	−4.21205e12	−0.186435
$929$	−8.83235e12	−0.389050	−0.194525	−	0.980898i	$-0.562317\pi$
$929$	−8.83235e12	−0.389050	−0.194525	+	0.980898i	$0.562317\pi$
$930$	2.42623e13	1.06355
$931$	2.90807e12	0.126862
$932$	3.05760e13	1.32742
$933$	5.23470e13	2.26165
$934$	1.59529e13	0.685926
$935$	3.07250e12	0.131474
$936$	−1.31382e13	−0.559491
$937$	−2.01513e13	−0.854033	−0.427017	−	0.904244i	$-0.640435\pi$
$937$	−2.01513e13	−0.854033	−0.427017	+	0.904244i	$0.640435\pi$
$938$	1.69448e12	0.0714701
$939$	−3.00757e13	−1.26247
$940$	2.14736e13	0.897076
$941$	1.48474e13	0.617302	0.308651	−	0.951175i	$-0.400122\pi$
$941$	1.48474e13	0.617302	0.308651	+	0.951175i	$0.400122\pi$
$942$	−7.58828e12	−0.313989
$943$	9.96264e12	0.410272
$944$	1.55409e13	0.636946
$945$	−5.08318e11	−0.0207344
$946$	1.14600e14	4.65239
$947$	1.67021e12	0.0674832	0.0337416	−	0.999431i	$-0.489258\pi$
$947$	1.67021e12	0.0674832	0.0337416	+	0.999431i	$0.489258\pi$
$948$	6.43387e13	2.58723
$949$	6.56326e12	0.262677
$950$	2.73996e13	1.09141
$951$	−6.23417e13	−2.47153
$952$	2.42268e12	0.0955937
$953$	1.48456e13	0.583014	0.291507	−	0.956569i	$-0.405843\pi$
$953$	1.48456e13	0.583014	0.291507	+	0.956569i	$0.405843\pi$
$954$	3.26571e13	1.27647
$955$	−5.84030e12	−0.227206
$956$	−2.28079e13	−0.883132
$957$	4.54846e13	1.75291
$958$	1.60265e13	0.614744
$959$	1.03919e13	0.396744
$960$	1.55478e13	0.590812
$961$	−1.07345e13	−0.405999
$962$	7.02487e12	0.264454
$963$	5.70039e13	2.13592
$964$	6.32240e13	2.35795
$965$	1.05543e13	0.391794
$966$	−1.15346e13	−0.426194
$967$	3.82621e13	1.40718	0.703590	−	0.710607i	$-0.251579\pi$
$967$	3.82621e13	1.40718	0.703590	+	0.710607i	$0.251579\pi$
$968$	−1.13958e14	−4.17164
$969$	4.70244e12	0.171343
$970$	4.15305e13	1.50624
$971$	−4.68778e12	−0.169231	−0.0846156	−	0.996414i	$-0.526966\pi$
$971$	−4.68778e12	−0.169231	−0.0846156	+	0.996414i	$0.526966\pi$
$972$	8.26854e13	2.97119
$973$	−5.73414e12	−0.205097
$974$	5.27374e13	1.87760
$975$	7.89068e12	0.279636
$976$	4.63320e13	1.63440
$977$	−2.05720e13	−0.722355	−0.361177	−	0.932497i	$-0.617625\pi$
$977$	−2.05720e13	−0.722355	−0.361177	+	0.932497i	$0.617625\pi$
$978$	−9.08649e13	−3.17593
$979$	1.85809e13	0.646465
$980$	4.68244e12	0.162164
$981$	−1.79278e13	−0.618042
$982$	6.86600e13	2.35615
$983$	−1.66354e13	−0.568255	−0.284128	−	0.958787i	$-0.591704\pi$
$983$	−1.66354e13	−0.568255	−0.284128	+	0.958787i	$0.591704\pi$
$984$	−7.32400e13	−2.49041
$985$	−2.15264e13	−0.728632
$986$	4.74552e12	0.159896
$987$	−1.28118e13	−0.429717
$988$	1.53093e13	0.511151
$989$	−1.99053e13	−0.661586
$990$	5.55817e13	1.83896
$991$	2.83299e13	0.933067	0.466534	−	0.884503i	$-0.345503\pi$
$991$	2.83299e13	0.933067	0.466534	+	0.884503i	$0.345503\pi$
$992$	−6.44636e12	−0.211355
$993$	−5.64332e13	−1.84189
$994$	7.91991e12	0.257325
$995$	−2.02663e12	−0.0655496
$996$	−1.78954e14	−5.76200
$997$	1.89205e13	0.606463	0.303232	−	0.952917i	$-0.401934\pi$
$997$	1.89205e13	0.606463	0.303232	+	0.952917i	$0.401934\pi$
$998$	4.01225e13	1.28027
$999$	1.71672e12	0.0545324

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.a.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-39.6810 q^{2} -201.837 q^{3} +1062.58 q^{4} +764.411 q^{5} +8009.09 q^{6} +2401.00 q^{7} -21847.5 q^{8} +21055.2 q^{9} +O(q^{10})\)	\(q-39.6810 q^{2} -201.837 q^{3} +1062.58 q^{4} +764.411 q^{5} +8009.09 q^{6} +2401.00 q^{7} -21847.5 q^{8} +21055.2 q^{9} -30332.6 q^{10} -87028.8 q^{11} -214468. q^{12} +28561.0 q^{13} -95274.0 q^{14} -154286. q^{15} +322890. q^{16} -46185.1 q^{17} -835490. q^{18} +504454. q^{19} +812247. q^{20} -484611. q^{21} +3.45339e6 q^{22} -599831. q^{23} +4.40964e6 q^{24} -1.36880e6 q^{25} -1.13333e6 q^{26} -276959. q^{27} +2.55125e6 q^{28} +2.58941e6 q^{29} +6.12224e6 q^{30} +3.96298e6 q^{31} -1.62665e6 q^{32} +1.75656e7 q^{33} +1.83267e6 q^{34} +1.83535e6 q^{35} +2.23728e7 q^{36} -6.19845e6 q^{37} -2.00172e7 q^{38} -5.76467e6 q^{39} -1.67005e7 q^{40} -1.66091e7 q^{41} +1.92298e7 q^{42} +3.31849e7 q^{43} -9.24750e7 q^{44} +1.60948e7 q^{45} +2.38019e7 q^{46} +2.64372e7 q^{47} -6.51711e7 q^{48} +5.76480e6 q^{49} +5.43153e7 q^{50} +9.32186e6 q^{51} +3.03483e7 q^{52} -3.90874e7 q^{53} +1.09900e7 q^{54} -6.65258e7 q^{55} -5.24559e7 q^{56} -1.01817e8 q^{57} -1.02750e8 q^{58} +4.81308e7 q^{59} -1.63942e8 q^{60} +1.43492e8 q^{61} -1.57255e8 q^{62} +5.05535e7 q^{63} -1.00773e8 q^{64} +2.18323e7 q^{65} -6.97022e8 q^{66} -1.77854e7 q^{67} -4.90753e7 q^{68} +1.21068e8 q^{69} -7.28285e7 q^{70} -8.31277e7 q^{71} -4.60003e8 q^{72} +2.29798e8 q^{73} +2.45960e8 q^{74} +2.76275e8 q^{75} +5.36022e8 q^{76} -2.08956e8 q^{77} +2.28748e8 q^{78} -2.99993e8 q^{79} +2.46820e8 q^{80} -3.58529e8 q^{81} +6.59064e8 q^{82} +8.34408e8 q^{83} -5.14937e8 q^{84} -3.53044e7 q^{85} -1.31681e9 q^{86} -5.22638e8 q^{87} +1.90136e9 q^{88} -2.13503e8 q^{89} -6.38658e8 q^{90} +6.85750e7 q^{91} -6.37368e8 q^{92} -7.99875e8 q^{93} -1.04906e9 q^{94} +3.85610e8 q^{95} +3.28318e8 q^{96} -1.36917e9 q^{97} -2.28753e8 q^{98} -1.83241e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 21 q^{2} - 323 q^{3} + 2945 q^{4} - 5202 q^{5} - 9897 q^{6} + 28812 q^{7} - 25431 q^{8} + 78519 q^{9}+O(q^{10}) \) 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

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more