LMFDB - Embedded newform 91.10.a.a.1.2

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			1.2
Root			$-35.8265$ 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)

$f(q)$	$=$	$q-37.8265 q^{2} +32.9997 q^{3} +918.841 q^{4} -2427.98 q^{5} -1248.26 q^{6} +2401.00 q^{7} -15389.3 q^{8} -18594.0 q^{9} +O(q^{10})$	\(q-37.8265 q^{2} +32.9997 q^{3} +918.841 q^{4} -2427.98 q^{5} -1248.26 q^{6} +2401.00 q^{7} -15389.3 q^{8} -18594.0 q^{9} +91841.7 q^{10} +38536.0 q^{11} +30321.5 q^{12} +28561.0 q^{13} -90821.3 q^{14} -80122.4 q^{15} +111678. q^{16} -187269. q^{17} +703346. q^{18} -109656. q^{19} -2.23092e6 q^{20} +79232.2 q^{21} -1.45768e6 q^{22} +599698. q^{23} -507844. q^{24} +3.94194e6 q^{25} -1.08036e6 q^{26} -1.26313e6 q^{27} +2.20614e6 q^{28} +1.91020e6 q^{29} +3.03075e6 q^{30} +9.83738e6 q^{31} +3.65496e6 q^{32} +1.27167e6 q^{33} +7.08374e6 q^{34} -5.82957e6 q^{35} -1.70849e7 q^{36} -6.01821e6 q^{37} +4.14790e6 q^{38} +942504. q^{39} +3.73650e7 q^{40} -2.93333e6 q^{41} -2.99707e6 q^{42} +3.42326e7 q^{43} +3.54084e7 q^{44} +4.51458e7 q^{45} -2.26844e7 q^{46} +4.06316e7 q^{47} +3.68534e6 q^{48} +5.76480e6 q^{49} -1.49110e8 q^{50} -6.17983e6 q^{51} +2.62430e7 q^{52} -1.10955e8 q^{53} +4.77797e7 q^{54} -9.35644e7 q^{55} -3.69498e7 q^{56} -3.61861e6 q^{57} -7.22562e7 q^{58} -3.51298e7 q^{59} -7.36197e7 q^{60} -4.03761e7 q^{61} -3.72113e8 q^{62} -4.46442e7 q^{63} -1.95433e8 q^{64} -6.93454e7 q^{65} -4.81029e7 q^{66} +9.71041e7 q^{67} -1.72071e8 q^{68} +1.97898e7 q^{69} +2.20512e8 q^{70} -3.17659e8 q^{71} +2.86150e8 q^{72} +1.93918e6 q^{73} +2.27648e8 q^{74} +1.30083e8 q^{75} -1.00756e8 q^{76} +9.25248e7 q^{77} -3.56516e7 q^{78} +2.55882e8 q^{79} -2.71151e8 q^{80} +3.24303e8 q^{81} +1.10957e8 q^{82} -6.62526e8 q^{83} +7.28018e7 q^{84} +4.54685e8 q^{85} -1.29490e9 q^{86} +6.30361e7 q^{87} -5.93043e8 q^{88} -1.50214e7 q^{89} -1.70771e9 q^{90} +6.85750e7 q^{91} +5.51027e8 q^{92} +3.24630e8 q^{93} -1.53695e9 q^{94} +2.66242e8 q^{95} +1.20613e8 q^{96} +7.63478e8 q^{97} -2.18062e8 q^{98} -7.16539e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−37.8265	−1.67171	−0.835855	−	0.548951i	$-0.815027\pi$
$2$	−37.8265	−1.67171	−0.835855	+	0.548951i	$0.815027\pi$
$3$	32.9997	0.235214	0.117607	−	0.993060i	$-0.462478\pi$
$3$	32.9997	0.235214	0.117607	+	0.993060i	$0.462478\pi$
$4$	918.841	1.79461
$5$	−2427.98	−1.73732	−0.868659	−	0.495411i	$-0.835018\pi$
$5$	−2427.98	−1.73732	−0.868659	+	0.495411i	$0.835018\pi$
$6$	−1248.26	−0.393210
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	−15389.3	−1.32836
$9$	−18594.0	−0.944674
$10$	91841.7	2.90429
$11$	38536.0	0.793595	0.396798	−	0.917906i	$-0.370121\pi$
$11$	38536.0	0.793595	0.396798	+	0.917906i	$0.370121\pi$
$12$	30321.5	0.422118
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	−90821.3	−0.631847
$15$	−80122.4	−0.408642
$16$	111678.	0.426018
$17$	−187269.	−0.543809	−0.271905	−	0.962324i	$-0.587654\pi$
$17$	−187269.	−0.543809	−0.271905	+	0.962324i	$0.587654\pi$
$18$	703346.	1.57922
$19$	−109656.	−0.193037	−0.0965186	−	0.995331i	$-0.530771\pi$
$19$	−109656.	−0.193037	−0.0965186	+	0.995331i	$0.530771\pi$
$20$	−2.23092e6	−3.11781
$21$	79232.2	0.0889027
$22$	−1.45768e6	−1.32666
$23$	599698.	0.446845	0.223423	−	0.974722i	$-0.428277\pi$
$23$	599698.	0.446845	0.223423	+	0.974722i	$0.428277\pi$
$24$	−507844.	−0.312449
$25$	3.94194e6	2.01827
$26$	−1.08036e6	−0.463649
$27$	−1.26313e6	−0.457416
$28$	2.20614e6	0.678299
$29$	1.91020e6	0.501520	0.250760	−	0.968049i	$-0.419319\pi$
$29$	1.91020e6	0.501520	0.250760	+	0.968049i	$0.419319\pi$
$30$	3.03075e6	0.683131
$31$	9.83738e6	1.91316	0.956582	−	0.291465i	$-0.0941427\pi$
$31$	9.83738e6	1.91316	0.956582	+	0.291465i	$0.0941427\pi$
$32$	3.65496e6	0.616181
$33$	1.27167e6	0.186665
$34$	7.08374e6	0.909091
$35$	−5.82957e6	−0.656644
$36$	−1.70849e7	−1.69532
$37$	−6.01821e6	−0.527910	−0.263955	−	0.964535i	$-0.585027\pi$
$37$	−6.01821e6	−0.527910	−0.263955	+	0.964535i	$0.585027\pi$
$38$	4.14790e6	0.322702
$39$	942504.	0.0652368
$40$	3.73650e7	2.30778
$41$	−2.93333e6	−0.162119	−0.0810593	−	0.996709i	$-0.525830\pi$
$41$	−2.93333e6	−0.162119	−0.0810593	+	0.996709i	$0.525830\pi$
$42$	−2.99707e6	−0.148619
$43$	3.42326e7	1.52697	0.763487	−	0.645824i	$-0.223486\pi$
$43$	3.42326e7	1.52697	0.763487	+	0.645824i	$0.223486\pi$
$44$	3.54084e7	1.42420
$45$	4.51458e7	1.64120
$46$	−2.26844e7	−0.746996
$47$	4.06316e7	1.21457	0.607287	−	0.794483i	$-0.292258\pi$
$47$	4.06316e7	1.21457	0.607287	+	0.794483i	$0.292258\pi$
$48$	3.68534e6	0.100206
$49$	5.76480e6	0.142857
$50$	−1.49110e8	−3.37397
$51$	−6.17983e6	−0.127912
$52$	2.62430e7	0.497736
$53$	−1.10955e8	−1.93155	−0.965776	−	0.259376i	$-0.916483\pi$
$53$	−1.10955e8	−1.93155	−0.965776	+	0.259376i	$0.916483\pi$
$54$	4.77797e7	0.764666
$55$	−9.35644e7	−1.37873
$56$	−3.69498e7	−0.502072
$57$	−3.61861e6	−0.0454051
$58$	−7.22562e7	−0.838396
$59$	−3.51298e7	−0.377435	−0.188717	−	0.982031i	$-0.560433\pi$
$59$	−3.51298e7	−0.377435	−0.188717	+	0.982031i	$0.560433\pi$
$60$	−7.36197e7	−0.733354
$61$	−4.03761e7	−0.373371	−0.186685	−	0.982420i	$-0.559774\pi$
$61$	−4.03761e7	−0.373371	−0.186685	+	0.982420i	$0.559774\pi$
$62$	−3.72113e8	−3.19825
$63$	−4.46442e7	−0.357053
$64$	−1.95433e8	−1.45609
$65$	−6.93454e7	−0.481845
$66$	−4.81029e7	−0.312050
$67$	9.71041e7	0.588710	0.294355	−	0.955696i	$-0.404895\pi$
$67$	9.71041e7	0.588710	0.294355	+	0.955696i	$0.404895\pi$
$68$	−1.72071e8	−0.975926
$69$	1.97898e7	0.105105
$70$	2.20512e8	1.09772
$71$	−3.17659e8	−1.48354	−0.741768	−	0.670657i	$-0.766012\pi$
$71$	−3.17659e8	−1.48354	−0.741768	+	0.670657i	$0.766012\pi$
$72$	2.86150e8	1.25487
$73$	1.93918e6	0.00799220	0.00399610	−	0.999992i	$-0.498728\pi$
$73$	1.93918e6	0.00799220	0.00399610	+	0.999992i	$0.498728\pi$
$74$	2.27648e8	0.882512
$75$	1.30083e8	0.474727
$76$	−1.00756e8	−0.346427
$77$	9.25248e7	0.299951
$78$	−3.56516e7	−0.109057
$79$	2.55882e8	0.739124	0.369562	−	0.929206i	$-0.379508\pi$
$79$	2.55882e8	0.739124	0.369562	+	0.929206i	$0.379508\pi$
$80$	−2.71151e8	−0.740128
$81$	3.24303e8	0.837083
$82$	1.10957e8	0.271015
$83$	−6.62526e8	−1.53233	−0.766164	−	0.642645i	$-0.777837\pi$
$83$	−6.62526e8	−1.53233	−0.766164	+	0.642645i	$0.777837\pi$
$84$	7.28018e7	0.159546
$85$	4.54685e8	0.944770
$86$	−1.29490e9	−2.55266
$87$	6.30361e7	0.117965
$88$	−5.93043e8	−1.05418
$89$	−1.50214e7	−0.0253779	−0.0126889	−	0.999919i	$-0.504039\pi$
$89$	−1.50214e7	−0.0253779	−0.0126889	+	0.999919i	$0.504039\pi$
$90$	−1.70771e9	−2.74361
$91$	6.85750e7	0.104828
$92$	5.51027e8	0.801914
$93$	3.24630e8	0.450004
$94$	−1.53695e9	−2.03041
$95$	2.66242e8	0.335367
$96$	1.20613e8	0.144935
$97$	7.63478e8	0.875636	0.437818	−	0.899064i	$-0.355751\pi$
$97$	7.63478e8	0.875636	0.437818	+	0.899064i	$0.355751\pi$
$98$	−2.18062e8	−0.238816
$99$	−7.16539e8	−0.749689
$100$	3.62202e9	3.62202
$101$	−1.81478e9	−1.73531	−0.867655	−	0.497167i	$-0.834374\pi$
$101$	−1.81478e9	−1.73531	−0.867655	+	0.497167i	$0.834374\pi$
$102$	2.33761e8	0.213831
$103$	−1.54586e9	−1.35332	−0.676662	−	0.736294i	$-0.736574\pi$
$103$	−1.54586e9	−1.35332	−0.676662	+	0.736294i	$0.736574\pi$
$104$	−4.39535e8	−0.368420
$105$	−1.92374e8	−0.154452
$106$	4.19705e9	3.22899
$107$	−1.24455e9	−0.917881	−0.458941	−	0.888467i	$-0.651771\pi$
$107$	−1.24455e9	−0.917881	−0.458941	+	0.888467i	$0.651771\pi$
$108$	−1.16061e9	−0.820883
$109$	2.12104e9	1.43923	0.719615	−	0.694374i	$-0.244318\pi$
$109$	2.12104e9	1.43923	0.719615	+	0.694374i	$0.244318\pi$
$110$	3.53921e9	2.30483
$111$	−1.98599e8	−0.124172
$112$	2.68139e8	0.161020
$113$	−2.03847e8	−0.117612	−0.0588060	−	0.998269i	$-0.518729\pi$
$113$	−2.03847e8	−0.117612	−0.0588060	+	0.998269i	$0.518729\pi$
$114$	1.36879e8	0.0759042
$115$	−1.45605e9	−0.776313
$116$	1.75517e9	0.900034
$117$	−5.31064e8	−0.262005
$118$	1.32884e9	0.630961
$119$	−4.49634e8	−0.205541
$120$	1.23303e9	0.542823
$121$	−8.72927e8	−0.370206
$122$	1.52728e9	0.624167
$123$	−9.67988e7	−0.0381327
$124$	9.03899e9	3.43338
$125$	−4.82879e9	−1.76906
$126$	1.68873e9	0.596889
$127$	−4.46639e9	−1.52349	−0.761746	−	0.647876i	$-0.775657\pi$
$127$	−4.46639e9	−1.52349	−0.761746	+	0.647876i	$0.775657\pi$
$128$	5.52121e9	1.81798
$129$	1.12966e9	0.359166
$130$	2.62309e9	0.805505
$131$	−1.88424e9	−0.559005	−0.279502	−	0.960145i	$-0.590170\pi$
$131$	−1.88424e9	−0.559005	−0.279502	+	0.960145i	$0.590170\pi$
$132$	1.16847e9	0.334991
$133$	−2.63284e8	−0.0729612
$134$	−3.67311e9	−0.984151
$135$	3.06685e9	0.794676
$136$	2.88195e9	0.722374
$137$	1.19271e9	0.289263	0.144631	−	0.989486i	$-0.453800\pi$
$137$	1.19271e9	0.289263	0.144631	+	0.989486i	$0.453800\pi$
$138$	−7.48580e8	−0.175704
$139$	−5.91993e9	−1.34509	−0.672543	−	0.740058i	$-0.734798\pi$
$139$	−5.91993e9	−1.34509	−0.672543	+	0.740058i	$0.734798\pi$
$140$	−5.35645e9	−1.17842
$141$	1.34083e9	0.285685
$142$	1.20159e10	2.48004
$143$	1.10063e9	0.220104
$144$	−2.07654e9	−0.402448
$145$	−4.63793e9	−0.871300
$146$	−7.33525e7	−0.0133606
$147$	1.90237e8	0.0336021
$148$	−5.52978e9	−0.947393
$149$	6.45915e9	1.07359	0.536794	−	0.843714i	$-0.319635\pi$
$149$	6.45915e9	1.07359	0.536794	+	0.843714i	$0.319635\pi$
$150$	−4.92057e9	−0.793605
$151$	2.95041e9	0.461835	0.230917	−	0.972973i	$-0.425827\pi$
$151$	2.95041e9	0.461835	0.230917	+	0.972973i	$0.425827\pi$
$152$	1.68753e9	0.256423
$153$	3.48209e9	0.513723
$154$	−3.49989e9	−0.501431
$155$	−2.38849e10	−3.32377
$156$	8.66011e8	0.117075
$157$	−8.18461e9	−1.07510	−0.537551	−	0.843231i	$-0.680650\pi$
$157$	−8.18461e9	−1.07510	−0.537551	+	0.843231i	$0.680650\pi$
$158$	−9.67910e9	−1.23560
$159$	−3.66149e9	−0.454329
$160$	−8.87416e9	−1.07050
$161$	1.43987e9	0.168892
$162$	−1.22672e10	−1.39936
$163$	−2.70691e9	−0.300351	−0.150175	−	0.988659i	$-0.547984\pi$
$163$	−2.70691e9	−0.300351	−0.150175	+	0.988659i	$0.547984\pi$
$164$	−2.69526e9	−0.290940
$165$	−3.08759e9	−0.324297
$166$	2.50610e10	2.56161
$167$	1.00308e10	0.997959	0.498979	−	0.866614i	$-0.333708\pi$
$167$	1.00308e10	0.997959	0.498979	+	0.866614i	$0.333708\pi$
$168$	−1.21933e9	−0.118095
$169$	8.15731e8	0.0769231
$170$	−1.71991e10	−1.57938
$171$	2.03894e9	0.182357
$172$	3.14543e10	2.74032
$173$	1.40569e10	1.19311	0.596556	−	0.802571i	$-0.296535\pi$
$173$	1.40569e10	1.19311	0.596556	+	0.802571i	$0.296535\pi$
$174$	−2.38443e9	−0.197203
$175$	9.46460e9	0.762836
$176$	4.30362e9	0.338086
$177$	−1.15927e9	−0.0887782
$178$	5.68206e8	0.0424244
$179$	−8.96605e9	−0.652773	−0.326387	−	0.945236i	$-0.605831\pi$
$179$	−8.96605e9	−0.652773	−0.326387	+	0.945236i	$0.605831\pi$
$180$	4.14818e10	2.94531
$181$	1.33482e10	0.924422	0.462211	−	0.886770i	$-0.347056\pi$
$181$	1.33482e10	0.924422	0.462211	+	0.886770i	$0.347056\pi$
$182$	−2.59395e9	−0.175243
$183$	−1.33240e9	−0.0878222
$184$	−9.22896e9	−0.593571
$185$	1.46121e10	0.917147
$186$	−1.22796e10	−0.752275
$187$	−7.21661e9	−0.431565
$188$	3.73340e10	2.17969
$189$	−3.03277e9	−0.172887
$190$	−1.00710e10	−0.560636
$191$	−1.17556e10	−0.639139	−0.319569	−	0.947563i	$-0.603538\pi$
$191$	−1.17556e10	−0.639139	−0.319569	+	0.947563i	$0.603538\pi$
$192$	−6.44924e9	−0.342494
$193$	2.07058e10	1.07420	0.537099	−	0.843520i	$-0.319520\pi$
$193$	2.07058e10	1.07420	0.537099	+	0.843520i	$0.319520\pi$
$194$	−2.88797e10	−1.46381
$195$	−2.28838e9	−0.113337
$196$	5.29693e9	0.256373
$197$	−7.32118e9	−0.346324	−0.173162	−	0.984893i	$-0.555398\pi$
$197$	−7.32118e9	−0.346324	−0.173162	+	0.984893i	$0.555398\pi$
$198$	2.71041e10	1.25326
$199$	−2.27663e10	−1.02909	−0.514546	−	0.857463i	$-0.672040\pi$
$199$	−2.27663e10	−1.02909	−0.514546	+	0.857463i	$0.672040\pi$
$200$	−6.06639e10	−2.68099
$201$	3.20440e9	0.138473
$202$	6.86466e10	2.90093
$203$	4.58640e9	0.189557
$204$	−5.67828e9	−0.229552
$205$	7.12204e9	0.281652
$206$	5.84743e10	2.26236
$207$	−1.11508e10	−0.422123
$208$	3.18964e9	0.118156
$209$	−4.22570e9	−0.153193
$210$	7.27682e9	0.258199
$211$	1.63637e10	0.568343	0.284171	−	0.958773i	$-0.408282\pi$
$211$	1.63637e10	0.568343	0.284171	+	0.958773i	$0.408282\pi$
$212$	−1.01950e11	−3.46639
$213$	−1.04826e10	−0.348949
$214$	4.70770e10	1.53443
$215$	−8.31158e10	−2.65284
$216$	1.94387e10	0.607612
$217$	2.36196e10	0.723108
$218$	−8.02315e10	−2.40597
$219$	6.39925e7	0.00187988
$220$	−8.59708e10	−2.47428
$221$	−5.34860e9	−0.150826
$222$	7.51230e9	0.207579
$223$	1.35777e10	0.367667	0.183834	−	0.982957i	$-0.441149\pi$
$223$	1.35777e10	0.367667	0.183834	+	0.982957i	$0.441149\pi$
$224$	8.77557e9	0.232894
$225$	−7.32965e10	−1.90661
$226$	7.71081e9	0.196613
$227$	7.52071e9	0.187993	0.0939966	−	0.995573i	$-0.470036\pi$
$227$	7.52071e9	0.187993	0.0939966	+	0.995573i	$0.470036\pi$
$228$	−3.32493e9	−0.0814846
$229$	−4.84088e10	−1.16323	−0.581614	−	0.813465i	$-0.697578\pi$
$229$	−4.84088e10	−1.16323	−0.581614	+	0.813465i	$0.697578\pi$
$230$	5.50773e10	1.29777
$231$	3.05329e9	0.0705528
$232$	−2.93968e10	−0.666199
$233$	8.15887e10	1.81355	0.906773	−	0.421620i	$-0.138538\pi$
$233$	8.15887e10	1.81355	0.906773	+	0.421620i	$0.138538\pi$
$234$	2.00883e10	0.437997
$235$	−9.86526e10	−2.11010
$236$	−3.22787e10	−0.677349
$237$	8.44401e9	0.173853
$238$	1.70081e10	0.343604
$239$	4.53407e10	0.898871	0.449436	−	0.893313i	$-0.351625\pi$
$239$	4.53407e10	0.898871	0.449436	+	0.893313i	$0.351625\pi$
$240$	−8.94791e9	−0.174089
$241$	−7.77958e10	−1.48552	−0.742761	−	0.669556i	$-0.766484\pi$
$241$	−7.77958e10	−1.48552	−0.742761	+	0.669556i	$0.766484\pi$
$242$	3.30197e10	0.618877
$243$	3.55641e10	0.654310
$244$	−3.70992e10	−0.670055
$245$	−1.39968e10	−0.248188
$246$	3.66156e9	0.0637467
$247$	−3.13188e9	−0.0535389
$248$	−1.51391e11	−2.54137
$249$	−2.18631e10	−0.360426
$250$	1.82656e11	2.95736
$251$	2.00266e10	0.318475	0.159238	−	0.987240i	$-0.449096\pi$
$251$	2.00266e10	0.318475	0.159238	+	0.987240i	$0.449096\pi$
$252$	−4.10210e10	−0.640772
$253$	2.31099e10	0.354614
$254$	1.68948e11	2.54683
$255$	1.50045e10	0.222223
$256$	−1.08786e11	−1.58305
$257$	−8.67825e10	−1.24089	−0.620445	−	0.784250i	$-0.713048\pi$
$257$	−8.67825e10	−1.24089	−0.620445	+	0.784250i	$0.713048\pi$
$258$	−4.27312e10	−0.600421
$259$	−1.44497e10	−0.199531
$260$	−6.37174e10	−0.864725
$261$	−3.55184e10	−0.473773
$262$	7.12742e10	0.934494
$263$	2.98699e10	0.384975	0.192487	−	0.981299i	$-0.438345\pi$
$263$	2.98699e10	0.384975	0.192487	+	0.981299i	$0.438345\pi$
$264$	−1.95702e10	−0.247958
$265$	2.69397e11	3.35572
$266$	9.95910e9	0.121970
$267$	−4.95701e8	−0.00596924
$268$	8.92232e10	1.05650
$269$	6.90189e10	0.803679	0.401839	−	0.915710i	$-0.368371\pi$
$269$	6.90189e10	0.803679	0.401839	+	0.915710i	$0.368371\pi$
$270$	−1.16008e11	−1.32847
$271$	−5.45891e10	−0.614814	−0.307407	−	0.951578i	$-0.599461\pi$
$271$	−5.45891e10	−0.614814	−0.307407	+	0.951578i	$0.599461\pi$
$272$	−2.09139e10	−0.231672
$273$	2.26295e9	0.0246572
$274$	−4.51160e10	−0.483563
$275$	1.51906e11	1.60169
$276$	1.81837e10	0.188622
$277$	−3.93625e10	−0.401720	−0.200860	−	0.979620i	$-0.564374\pi$
$277$	−3.93625e10	−0.401720	−0.200860	+	0.979620i	$0.564374\pi$
$278$	2.23930e11	2.24859
$279$	−1.82917e11	−1.80732
$280$	8.97133e10	0.872259
$281$	−1.41844e11	−1.35716	−0.678582	−	0.734525i	$-0.737405\pi$
$281$	−1.41844e11	−1.35716	−0.678582	+	0.734525i	$0.737405\pi$
$282$	−5.07189e10	−0.477583
$283$	1.78445e9	0.0165374	0.00826869	−	0.999966i	$-0.497368\pi$
$283$	1.78445e9	0.0165374	0.00826869	+	0.999966i	$0.497368\pi$
$284$	−2.91878e11	−2.66237
$285$	8.78590e9	0.0788832
$286$	−4.16328e10	−0.367949
$287$	−7.04292e9	−0.0612751
$288$	−6.79605e10	−0.582090
$289$	−8.35181e10	−0.704271
$290$	1.75436e11	1.45656
$291$	2.51945e10	0.205962
$292$	1.78180e9	0.0143429
$293$	1.72454e11	1.36700	0.683502	−	0.729948i	$-0.260456\pi$
$293$	1.72454e11	1.36700	0.683502	+	0.729948i	$0.260456\pi$
$294$	−7.19598e9	−0.0561729
$295$	8.52944e10	0.655725
$296$	9.26164e10	0.701253
$297$	−4.86759e10	−0.363003
$298$	−2.44327e11	−1.79473
$299$	1.71280e10	0.123933
$300$	1.19525e11	0.851950
$301$	8.21924e10	0.577142
$302$	−1.11604e11	−0.772054
$303$	−5.98870e10	−0.408170
$304$	−1.22462e10	−0.0822373
$305$	9.80322e10	0.648663
$306$	−1.31715e11	−0.858795
$307$	−1.82140e11	−1.17026	−0.585129	−	0.810940i	$-0.698956\pi$
$307$	−1.82140e11	−1.17026	−0.585129	+	0.810940i	$0.698956\pi$
$308$	8.50156e10	0.538295
$309$	−5.10128e10	−0.318321
$310$	9.03482e11	5.55638
$311$	−1.87477e11	−1.13639	−0.568194	−	0.822895i	$-0.692358\pi$
$311$	−1.87477e11	−1.13639	−0.568194	+	0.822895i	$0.692358\pi$
$312$	−1.45045e10	−0.0866578
$313$	2.91361e10	0.171586	0.0857930	−	0.996313i	$-0.472658\pi$
$313$	2.91361e10	0.171586	0.0857930	+	0.996313i	$0.472658\pi$
$314$	3.09595e11	1.79726
$315$	1.08395e11	0.620315
$316$	2.35115e11	1.32644
$317$	7.68072e10	0.427204	0.213602	−	0.976921i	$-0.431480\pi$
$317$	7.68072e10	0.427204	0.213602	+	0.976921i	$0.431480\pi$
$318$	1.38501e11	0.759506
$319$	7.36115e10	0.398004
$320$	4.74508e11	2.52970
$321$	−4.10699e10	−0.215899
$322$	−5.44654e10	−0.282338
$323$	2.05352e10	0.104975
$324$	2.97983e11	1.50224
$325$	1.12586e11	0.559768
$326$	1.02393e11	0.502099
$327$	6.99937e10	0.338528
$328$	4.51420e10	0.215352
$329$	9.75565e10	0.459066
$330$	1.16793e11	0.542130
$331$	−4.32748e11	−1.98157	−0.990784	−	0.135452i	$-0.956751\pi$
$331$	−4.32748e11	−1.98157	−0.990784	+	0.135452i	$0.956751\pi$
$332$	−6.08756e11	−2.74993
$333$	1.11903e11	0.498703
$334$	−3.79431e11	−1.66830
$335$	−2.35766e11	−1.02278
$336$	8.84850e9	0.0378741
$337$	2.09548e10	0.0885010	0.0442505	−	0.999020i	$-0.485910\pi$
$337$	2.09548e10	0.0885010	0.0442505	+	0.999020i	$0.485910\pi$
$338$	−3.08562e10	−0.128593
$339$	−6.72689e9	−0.0276640
$340$	4.17784e11	1.69549
$341$	3.79093e11	1.51828
$342$	−7.71261e10	−0.304848
$343$	1.38413e10	0.0539949
$344$	−5.26817e11	−2.02837
$345$	−4.80492e10	−0.182600
$346$	−5.31722e11	−1.99454
$347$	4.16346e11	1.54160	0.770801	−	0.637076i	$-0.219856\pi$
$347$	4.16346e11	1.54160	0.770801	+	0.637076i	$0.219856\pi$
$348$	5.79201e10	0.211701
$349$	3.93666e11	1.42041	0.710204	−	0.703996i	$-0.248603\pi$
$349$	3.93666e11	1.42041	0.710204	+	0.703996i	$0.248603\pi$
$350$	−3.58012e11	−1.27524
$351$	−3.60762e10	−0.126864
$352$	1.40848e11	0.488998
$353$	−5.47569e11	−1.87695	−0.938474	−	0.345349i	$-0.887761\pi$
$353$	−5.47569e11	−1.87695	−0.938474	+	0.345349i	$0.887761\pi$
$354$	4.38512e10	0.148411
$355$	7.71267e11	2.57737
$356$	−1.38023e10	−0.0455434
$357$	−1.48378e10	−0.0483461
$358$	3.39154e11	1.09125
$359$	−4.62717e11	−1.47025	−0.735124	−	0.677932i	$-0.762876\pi$
$359$	−4.62717e11	−1.47025	−0.735124	+	0.677932i	$0.762876\pi$
$360$	−6.94765e11	−2.18010
$361$	−3.10663e11	−0.962737
$362$	−5.04917e11	−1.54537
$363$	−2.88063e10	−0.0870779
$364$	6.30095e10	0.188126
$365$	−4.70829e9	−0.0138850
$366$	5.03999e10	0.146813
$367$	−1.23136e10	−0.0354313	−0.0177156	−	0.999843i	$-0.505639\pi$
$367$	−1.23136e10	−0.0354313	−0.0177156	+	0.999843i	$0.505639\pi$
$368$	6.69731e10	0.190364
$369$	5.45423e10	0.153149
$370$	−5.52723e11	−1.53320
$371$	−2.66404e11	−0.730058
$372$	2.98284e11	0.807581
$373$	−4.88330e11	−1.30624	−0.653122	−	0.757253i	$-0.726541\pi$
$373$	−4.88330e11	−1.30624	−0.653122	+	0.757253i	$0.726541\pi$
$374$	2.72979e11	0.721450
$375$	−1.59349e11	−0.416109
$376$	−6.25294e11	−1.61339
$377$	5.45573e10	0.139097
$378$	1.14719e11	0.289016
$379$	4.62229e11	1.15075	0.575374	−	0.817890i	$-0.304856\pi$
$379$	4.62229e11	1.15075	0.575374	+	0.817890i	$0.304856\pi$
$380$	2.44634e11	0.601853
$381$	−1.47389e11	−0.358347
$382$	4.44673e11	1.06845
$383$	−2.34025e11	−0.555734	−0.277867	−	0.960620i	$-0.589627\pi$
$383$	−2.34025e11	−0.555734	−0.277867	+	0.960620i	$0.589627\pi$
$384$	1.82198e11	0.427616
$385$	−2.24648e11	−0.521110
$386$	−7.83227e11	−1.79574
$387$	−6.36521e11	−1.44249
$388$	7.01515e11	1.57143
$389$	2.33383e11	0.516768	0.258384	−	0.966042i	$-0.416810\pi$
$389$	2.33383e11	0.516768	0.258384	+	0.966042i	$0.416810\pi$
$390$	8.65612e10	0.189466
$391$	−1.12305e11	−0.242999
$392$	−8.87165e10	−0.189765
$393$	−6.21793e10	−0.131486
$394$	2.76934e11	0.578953
$395$	−6.21274e11	−1.28409
$396$	−6.58385e11	−1.34540
$397$	−2.06380e11	−0.416976	−0.208488	−	0.978025i	$-0.566854\pi$
$397$	−2.06380e11	−0.416976	−0.208488	+	0.978025i	$0.566854\pi$
$398$	8.61170e11	1.72034
$399$	−8.68828e9	−0.0171615
$400$	4.40228e11	0.859820
$401$	−4.59933e11	−0.888269	−0.444135	−	0.895960i	$-0.646489\pi$
$401$	−4.59933e11	−0.888269	−0.444135	+	0.895960i	$0.646489\pi$
$402$	−1.21211e11	−0.231487
$403$	2.80966e11	0.530616
$404$	−1.66749e12	−3.11421
$405$	−7.87400e11	−1.45428
$406$	−1.73487e11	−0.316884
$407$	−2.31918e11	−0.418947
$408$	9.51035e10	0.169913
$409$	−5.62917e11	−0.994695	−0.497347	−	0.867552i	$-0.665693\pi$
$409$	−5.62917e11	−0.994695	−0.497347	+	0.867552i	$0.665693\pi$
$410$	−2.69402e11	−0.470840
$411$	3.93590e10	0.0680387
$412$	−1.42040e12	−2.42869
$413$	−8.43468e10	−0.142657
$414$	4.21795e11	0.705667
$415$	1.60860e12	2.66214
$416$	1.04389e11	0.170898
$417$	−1.95356e11	−0.316384
$418$	1.59843e11	0.256095
$419$	1.87181e11	0.296687	0.148343	−	0.988936i	$-0.452606\pi$
$419$	1.87181e11	0.296687	0.148343	+	0.988936i	$0.452606\pi$
$420$	−1.76761e11	−0.277182
$421$	−2.66341e11	−0.413208	−0.206604	−	0.978425i	$-0.566241\pi$
$421$	−2.66341e11	−0.413208	−0.206604	+	0.978425i	$0.566241\pi$
$422$	−6.18981e11	−0.950104
$423$	−7.55505e11	−1.14738
$424$	1.70753e12	2.56579
$425$	−7.38205e11	−1.09756
$426$	3.96521e11	0.583341
$427$	−9.69430e10	−0.141121
$428$	−1.14355e12	−1.64724
$429$	3.63203e10	0.0517716
$430$	3.14398e12	4.43477
$431$	1.65717e10	0.0231324	0.0115662	−	0.999933i	$-0.496318\pi$
$431$	1.65717e10	0.0231324	0.0115662	+	0.999933i	$0.496318\pi$
$432$	−1.41064e11	−0.194867
$433$	1.23308e12	1.68576	0.842878	−	0.538105i	$-0.180860\pi$
$433$	1.23308e12	1.68576	0.842878	+	0.538105i	$0.180860\pi$
$434$	−8.93444e11	−1.20883
$435$	−1.53050e11	−0.204942
$436$	1.94890e12	2.58286
$437$	−6.57604e10	−0.0862578
$438$	−2.42061e9	−0.00314261
$439$	1.00390e11	0.129004	0.0645018	−	0.997918i	$-0.479454\pi$
$439$	1.00390e11	0.129004	0.0645018	+	0.997918i	$0.479454\pi$
$440$	1.43989e12	1.83144
$441$	−1.07191e11	−0.134953
$442$	2.02319e11	0.252136
$443$	5.39889e11	0.666021	0.333010	−	0.942923i	$-0.391936\pi$
$443$	5.39889e11	0.666021	0.333010	+	0.942923i	$0.391936\pi$
$444$	−1.82481e11	−0.222840
$445$	3.64715e10	0.0440894
$446$	−5.13597e11	−0.614633
$447$	2.13150e11	0.252523
$448$	−4.69236e11	−0.550351
$449$	−3.83225e11	−0.444985	−0.222493	−	0.974934i	$-0.571419\pi$
$449$	−3.83225e11	−0.444985	−0.222493	+	0.974934i	$0.571419\pi$
$450$	2.77255e12	3.18730
$451$	−1.13039e11	−0.128657
$452$	−1.87303e11	−0.211068
$453$	9.73627e10	0.108630
$454$	−2.84482e11	−0.314270
$455$	−1.66498e11	−0.182120
$456$	5.56881e10	0.0603143
$457$	8.64714e11	0.927363	0.463681	−	0.886002i	$-0.346528\pi$
$457$	8.64714e11	0.927363	0.463681	+	0.886002i	$0.346528\pi$
$458$	1.83113e12	1.94458
$459$	2.36545e11	0.248747
$460$	−1.33788e12	−1.39318
$461$	−1.69137e12	−1.74415	−0.872075	−	0.489373i	$-0.837226\pi$
$461$	−1.69137e12	−1.74415	−0.872075	+	0.489373i	$0.837226\pi$
$462$	−1.15495e11	−0.117944
$463$	1.16394e12	1.17710	0.588552	−	0.808459i	$-0.299698\pi$
$463$	1.16394e12	1.17710	0.588552	+	0.808459i	$0.299698\pi$
$464$	2.13328e11	0.213657
$465$	−7.88195e11	−0.781799
$466$	−3.08621e12	−3.03172
$467$	−2.92923e11	−0.284988	−0.142494	−	0.989796i	$-0.545512\pi$
$467$	−2.92923e11	−0.284988	−0.142494	+	0.989796i	$0.545512\pi$
$468$	−4.87963e11	−0.470198
$469$	2.33147e11	0.222511
$470$	3.73168e12	3.52747
$471$	−2.70090e11	−0.252880
$472$	5.40625e11	0.501369
$473$	1.31919e12	1.21180
$474$	−3.19407e11	−0.290631
$475$	−4.32257e11	−0.389602
$476$	−4.13142e11	−0.368865
$477$	2.06310e12	1.82469
$478$	−1.71508e12	−1.50265
$479$	9.83590e11	0.853698	0.426849	−	0.904323i	$-0.359624\pi$
$479$	9.83590e11	0.853698	0.426849	+	0.904323i	$0.359624\pi$
$480$	−2.92844e11	−0.251797
$481$	−1.71886e11	−0.146416
$482$	2.94274e12	2.48336
$483$	4.75154e10	0.0397258
$484$	−8.02081e11	−0.664376
$485$	−1.85371e12	−1.52126
$486$	−1.34526e12	−1.09382
$487$	−1.98477e12	−1.59893	−0.799464	−	0.600714i	$-0.794883\pi$
$487$	−1.98477e12	−1.59893	−0.799464	+	0.600714i	$0.794883\pi$
$488$	6.21362e11	0.495970
$489$	−8.93270e10	−0.0706469
$490$	5.29449e11	0.414899
$491$	−1.34044e12	−1.04083	−0.520416	−	0.853913i	$-0.674223\pi$
$491$	−1.34044e12	−1.04083	−0.520416	+	0.853913i	$0.674223\pi$
$492$	−8.89427e10	−0.0684333
$493$	−3.57723e11	−0.272731
$494$	1.18468e11	0.0895014
$495$	1.73974e12	1.30245
$496$	1.09862e12	0.815041
$497$	−7.62698e11	−0.560724
$498$	8.27005e11	0.602527
$499$	8.16247e11	0.589344	0.294672	−	0.955598i	$-0.404790\pi$
$499$	8.16247e11	0.589344	0.294672	+	0.955598i	$0.404790\pi$
$500$	−4.43689e12	−3.17478
$501$	3.31014e11	0.234734
$502$	−7.57536e11	−0.532398
$503$	2.58243e12	1.79876	0.899380	−	0.437168i	$-0.144019\pi$
$503$	2.58243e12	1.79876	0.899380	+	0.437168i	$0.144019\pi$
$504$	6.87046e11	0.474295
$505$	4.40623e12	3.01478
$506$	−8.74167e11	−0.592812
$507$	2.69188e10	0.0180934
$508$	−4.10390e12	−2.73407
$509$	−1.50530e12	−0.994018	−0.497009	−	0.867745i	$-0.665568\pi$
$509$	−1.50530e12	−0.994018	−0.497009	+	0.867745i	$0.665568\pi$
$510$	−5.67566e11	−0.371493
$511$	4.65598e9	0.00302077
$512$	1.28813e12	0.828408
$513$	1.38510e11	0.0882982
$514$	3.28267e12	2.07441
$515$	3.75330e12	2.35115
$516$	1.03798e12	0.644564
$517$	1.56578e12	0.963880
$518$	5.46582e11	0.333558
$519$	4.63873e11	0.280637
$520$	1.06718e12	0.640063
$521$	−1.92587e12	−1.14513	−0.572567	−	0.819858i	$-0.694053\pi$
$521$	−1.92587e12	−1.14513	−0.572567	+	0.819858i	$0.694053\pi$
$522$	1.34353e12	0.792011
$523$	−3.01269e12	−1.76075	−0.880374	−	0.474280i	$-0.842708\pi$
$523$	−3.01269e12	−1.76075	−0.880374	+	0.474280i	$0.842708\pi$
$524$	−1.73132e12	−1.00320
$525$	3.12329e11	0.179430
$526$	−1.12987e12	−0.643566
$527$	−1.84224e12	−1.04040
$528$	1.42018e11	0.0795227
$529$	−1.44151e12	−0.800329
$530$	−1.01903e13	−5.60979
$531$	6.53205e11	0.356553
$532$	−2.41916e11	−0.130937
$533$	−8.37787e10	−0.0449636
$534$	1.87506e10	0.00997883
$535$	3.02174e12	1.59465
$536$	−1.49437e12	−0.782017
$537$	−2.95877e11	−0.153542
$538$	−2.61074e12	−1.34352
$539$	2.22152e11	0.113371
$540$	2.81794e12	1.42613
$541$	6.80680e10	0.0341630	0.0170815	−	0.999854i	$-0.494563\pi$
$541$	6.80680e10	0.0341630	0.0170815	+	0.999854i	$0.494563\pi$
$542$	2.06491e12	1.02779
$543$	4.40488e11	0.217437
$544$	−6.84463e11	−0.335085
$545$	−5.14984e12	−2.50040
$546$	−8.55994e10	−0.0412196
$547$	7.82289e11	0.373615	0.186807	−	0.982397i	$-0.440186\pi$
$547$	7.82289e11	0.373615	0.186807	+	0.982397i	$0.440186\pi$
$548$	1.09591e12	0.519114
$549$	7.50754e11	0.352714
$550$	−5.74608e12	−2.67756
$551$	−2.09465e11	−0.0968121
$552$	−3.04553e11	−0.139616
$553$	6.14372e11	0.279363
$554$	1.48894e12	0.671559
$555$	4.82194e11	0.215726
$556$	−5.43947e12	−2.41391
$557$	−2.05884e12	−0.906305	−0.453152	−	0.891433i	$-0.649701\pi$
$557$	−2.05884e12	−0.906305	−0.453152	+	0.891433i	$0.649701\pi$
$558$	6.91908e12	3.02131
$559$	9.77717e11	0.423506
$560$	−6.51035e11	−0.279742
$561$	−2.38146e11	−0.101510
$562$	5.36545e12	2.26878
$563$	1.66481e11	0.0698356	0.0349178	−	0.999390i	$-0.488883\pi$
$563$	1.66481e11	0.0698356	0.0349178	+	0.999390i	$0.488883\pi$
$564$	1.23201e12	0.512694
$565$	4.94936e11	0.204329
$566$	−6.74996e10	−0.0276457
$567$	7.78652e11	0.316388
$568$	4.88856e12	1.97067
$569$	2.32174e12	0.928557	0.464279	−	0.885689i	$-0.346314\pi$
$569$	2.32174e12	0.928557	0.464279	+	0.885689i	$0.346314\pi$
$570$	−3.32339e11	−0.131870
$571$	4.50517e12	1.77357	0.886786	−	0.462180i	$-0.152933\pi$
$571$	4.50517e12	1.77357	0.886786	+	0.462180i	$0.152933\pi$
$572$	1.01130e12	0.395001
$573$	−3.87931e11	−0.150335
$574$	2.66409e11	0.102434
$575$	2.36397e12	0.901856
$576$	3.63389e12	1.37553
$577$	2.63619e12	0.990115	0.495058	−	0.868860i	$-0.335147\pi$
$577$	2.63619e12	0.990115	0.495058	+	0.868860i	$0.335147\pi$
$578$	3.15919e12	1.17734
$579$	6.83284e11	0.252667
$580$	−4.26152e12	−1.56365
$581$	−1.59073e12	−0.579165
$582$	−9.53020e11	−0.344309
$583$	−4.27577e12	−1.53287
$584$	−2.98428e10	−0.0106165
$585$	1.28941e12	0.455187
$586$	−6.52334e12	−2.28523
$587$	9.93841e11	0.345498	0.172749	−	0.984966i	$-0.444735\pi$
$587$	9.93841e11	0.345498	0.172749	+	0.984966i	$0.444735\pi$
$588$	1.74797e11	0.0603026
$589$	−1.07873e12	−0.369312
$590$	−3.22638e12	−1.09618
$591$	−2.41597e11	−0.0814605
$592$	−6.72102e11	−0.224899
$593$	3.68590e12	1.22405	0.612023	−	0.790840i	$-0.290356\pi$
$593$	3.68590e12	1.22405	0.612023	+	0.790840i	$0.290356\pi$
$594$	1.84124e12	0.606835
$595$	1.09170e12	0.357089
$596$	5.93493e12	1.92667
$597$	−7.51282e11	−0.242057
$598$	−6.47891e11	−0.207179
$599$	−4.70229e12	−1.49241	−0.746206	−	0.665716i	$-0.768126\pi$
$599$	−4.70229e12	−1.49241	−0.746206	+	0.665716i	$0.768126\pi$
$600$	−2.00189e12	−0.630608
$601$	4.24671e11	0.132775	0.0663877	−	0.997794i	$-0.478853\pi$
$601$	4.24671e11	0.132775	0.0663877	+	0.997794i	$0.478853\pi$
$602$	−3.10905e12	−0.964813
$603$	−1.80556e12	−0.556139
$604$	2.71096e12	0.828814
$605$	2.11945e12	0.643166
$606$	2.26531e12	0.682341
$607$	−3.16983e12	−0.947735	−0.473868	−	0.880596i	$-0.657142\pi$
$607$	−3.16983e12	−0.947735	−0.473868	+	0.880596i	$0.657142\pi$
$608$	−4.00788e11	−0.118946
$609$	1.51350e11	0.0445865
$610$	−3.70821e12	−1.08438
$611$	1.16048e12	0.336862
$612$	3.19949e12	0.921932
$613$	4.79240e12	1.37082	0.685410	−	0.728157i	$-0.259623\pi$
$613$	4.79240e12	1.37082	0.685410	+	0.728157i	$0.259623\pi$
$614$	6.88970e12	1.95633
$615$	2.35025e11	0.0662485
$616$	−1.42390e12	−0.398442
$617$	2.79264e12	0.775767	0.387884	−	0.921708i	$-0.373206\pi$
$617$	2.79264e12	0.775767	0.387884	+	0.921708i	$0.373206\pi$
$618$	1.92963e12	0.532141
$619$	−6.02914e12	−1.65062	−0.825310	−	0.564680i	$-0.809000\pi$
$619$	−6.02914e12	−1.65062	−0.825310	+	0.564680i	$0.809000\pi$
$620$	−2.19464e13	−5.96488
$621$	−7.57496e11	−0.204394
$622$	7.09159e12	1.89971
$623$	−3.60663e10	−0.00959193
$624$	1.05257e11	0.0277920
$625$	4.02509e12	1.05515
$626$	−1.10212e12	−0.286842
$627$	−1.39447e11	−0.0360333
$628$	−7.52036e12	−1.92939
$629$	1.12703e12	0.287082
$630$	−4.10020e12	−1.03699
$631$	−7.23665e12	−1.81721	−0.908606	−	0.417654i	$-0.862853\pi$
$631$	−7.23665e12	−1.81721	−0.908606	+	0.417654i	$0.862853\pi$
$632$	−3.93785e12	−0.981822
$633$	5.39997e11	0.133682
$634$	−2.90534e12	−0.714161
$635$	1.08443e13	2.64679
$636$	−3.36433e12	−0.815344
$637$	1.64648e11	0.0396214
$638$	−2.78446e12	−0.665347
$639$	5.90655e12	1.40146
$640$	−1.34054e13	−3.15841
$641$	5.22035e11	0.122135	0.0610673	−	0.998134i	$-0.480550\pi$
$641$	5.22035e11	0.122135	0.0610673	+	0.998134i	$0.480550\pi$
$642$	1.55353e12	0.360920
$643$	−7.19567e12	−1.66005	−0.830026	−	0.557724i	$-0.811675\pi$
$643$	−7.19567e12	−1.66005	−0.830026	+	0.557724i	$0.811675\pi$
$644$	1.32302e12	0.303095
$645$	−2.74280e12	−0.623986
$646$	−7.76774e11	−0.175488
$647$	6.24024e12	1.40001	0.700007	−	0.714136i	$-0.253180\pi$
$647$	6.24024e12	1.40001	0.700007	+	0.714136i	$0.253180\pi$
$648$	−4.99082e12	−1.11195
$649$	−1.35376e12	−0.299531
$650$	−4.25872e12	−0.935770
$651$	7.79438e11	0.170085
$652$	−2.48722e12	−0.539013
$653$	7.84804e12	1.68909	0.844543	−	0.535488i	$-0.179872\pi$
$653$	7.84804e12	1.68909	0.844543	+	0.535488i	$0.179872\pi$
$654$	−2.64761e12	−0.565920
$655$	4.57489e12	0.971169
$656$	−3.27588e11	−0.0690654
$657$	−3.60572e10	−0.00755002
$658$	−3.69022e12	−0.767424
$659$	−1.05598e12	−0.218108	−0.109054	−	0.994036i	$-0.534782\pi$
$659$	−1.05598e12	−0.218108	−0.109054	+	0.994036i	$0.534782\pi$
$660$	−2.83701e12	−0.581986
$661$	5.88556e12	1.19917	0.599586	−	0.800311i	$-0.295332\pi$
$661$	5.88556e12	1.19917	0.599586	+	0.800311i	$0.295332\pi$
$662$	1.63693e13	3.31260
$663$	−1.76502e11	−0.0354764
$664$	1.01958e13	2.03548
$665$	6.39247e11	0.126757
$666$	−4.23289e12	−0.833686
$667$	1.14555e12	0.224102
$668$	9.21673e12	1.79095
$669$	4.48060e11	0.0864807
$670$	8.91821e12	1.70978
$671$	−1.55593e12	−0.296305
$672$	2.89591e11	0.0547801
$673$	7.23246e12	1.35900	0.679498	−	0.733677i	$-0.262198\pi$
$673$	7.23246e12	1.35900	0.679498	+	0.733677i	$0.262198\pi$
$674$	−7.92644e11	−0.147948
$675$	−4.97918e12	−0.923189
$676$	7.49527e11	0.138047
$677$	−9.20487e12	−1.68410	−0.842051	−	0.539398i	$-0.818652\pi$
$677$	−9.20487e12	−1.68410	−0.842051	+	0.539398i	$0.818652\pi$
$678$	2.54454e11	0.0462462
$679$	1.83311e12	0.330959
$680$	−6.99731e12	−1.25499
$681$	2.48181e11	0.0442187
$682$	−1.43397e13	−2.53812
$683$	5.85392e12	1.02933	0.514664	−	0.857392i	$-0.327917\pi$
$683$	5.85392e12	1.02933	0.514664	+	0.857392i	$0.327917\pi$
$684$	1.87347e12	0.327260
$685$	−2.89587e12	−0.502541
$686$	−5.23567e11	−0.0902638
$687$	−1.59747e12	−0.273608
$688$	3.82303e12	0.650518
$689$	−3.16899e12	−0.535716
$690$	1.81753e12	0.305254
$691$	−5.99081e12	−0.999619	−0.499810	−	0.866135i	$-0.666597\pi$
$691$	−5.99081e12	−0.999619	−0.499810	+	0.866135i	$0.666597\pi$
$692$	1.29160e13	2.14117
$693$	−1.72041e12	−0.283356
$694$	−1.57489e13	−2.57711
$695$	1.43734e13	2.33684
$696$	−9.70084e11	−0.156700
$697$	5.49322e11	0.0881616
$698$	−1.48910e13	−2.37451
$699$	2.69240e12	0.426572
$700$	8.69646e12	1.36899
$701$	−8.32407e12	−1.30198	−0.650990	−	0.759086i	$-0.725646\pi$
$701$	−8.32407e12	−1.30198	−0.650990	+	0.759086i	$0.725646\pi$
$702$	1.36464e12	0.212080
$703$	6.59933e11	0.101906
$704$	−7.53122e12	−1.15555
$705$	−3.25550e12	−0.496326
$706$	2.07126e13	3.13771
$707$	−4.35728e12	−0.655885
$708$	−1.06519e12	−0.159322
$709$	−1.01539e13	−1.50913	−0.754563	−	0.656227i	$-0.772151\pi$
$709$	−1.01539e13	−1.50913	−0.754563	+	0.656227i	$0.772151\pi$
$710$	−2.91743e13	−4.30862
$711$	−4.75787e12	−0.698231
$712$	2.31169e11	0.0337109
$713$	5.89946e12	0.854888
$714$	5.61260e11	0.0808206
$715$	−2.67229e12	−0.382390
$716$	−8.23837e12	−1.17147
$717$	1.49623e12	0.211427
$718$	1.75030e13	2.45783
$719$	1.65891e12	0.231495	0.115748	−	0.993279i	$-0.463074\pi$
$719$	1.65891e12	0.231495	0.115748	+	0.993279i	$0.463074\pi$
$720$	5.04180e12	0.699180
$721$	−3.71160e12	−0.511508
$722$	1.17513e13	1.60942
$723$	−2.56723e12	−0.349416
$724$	1.22649e13	1.65898
$725$	7.52991e12	1.01221
$726$	1.08964e12	0.145569
$727$	−3.35563e12	−0.445522	−0.222761	−	0.974873i	$-0.571507\pi$
$727$	−3.35563e12	−0.445522	−0.222761	+	0.974873i	$0.571507\pi$
$728$	−1.05532e12	−0.139250
$729$	−5.20966e12	−0.683180
$730$	1.78098e11	0.0232117
$731$	−6.41071e12	−0.830382
$732$	−1.22426e12	−0.157607
$733$	3.50033e12	0.447858	0.223929	−	0.974605i	$-0.428112\pi$
$733$	3.50033e12	0.447858	0.223929	+	0.974605i	$0.428112\pi$
$734$	4.65779e11	0.0592308
$735$	−4.61890e11	−0.0583775
$736$	2.19187e12	0.275338
$737$	3.74200e12	0.467197
$738$	−2.06314e12	−0.256021
$739$	−2.83109e12	−0.349183	−0.174592	−	0.984641i	$-0.555861\pi$
$739$	−2.83109e12	−0.349183	−0.174592	+	0.984641i	$0.555861\pi$
$740$	1.34262e13	1.64592
$741$	−1.03351e11	−0.0125931
$742$	1.00771e13	1.22045
$743$	−1.13531e13	−1.36667	−0.683335	−	0.730105i	$-0.739471\pi$
$743$	−1.13531e13	−1.36667	−0.683335	+	0.730105i	$0.739471\pi$
$744$	−4.99585e12	−0.597766
$745$	−1.56827e13	−1.86516
$746$	1.84718e13	2.18366
$747$	1.23190e13	1.44755
$748$	−6.63091e12	−0.774491
$749$	−2.98817e12	−0.346926
$750$	6.02759e12	0.695614
$751$	4.74099e11	0.0543863	0.0271931	−	0.999630i	$-0.491343\pi$
$751$	4.74099e11	0.0543863	0.0271931	+	0.999630i	$0.491343\pi$
$752$	4.53766e12	0.517430
$753$	6.60872e11	0.0749100
$754$	−2.06371e12	−0.232529
$755$	−7.16353e12	−0.802354
$756$	−2.78664e12	−0.310265
$757$	−9.72131e12	−1.07595	−0.537976	−	0.842960i	$-0.680811\pi$
$757$	−9.72131e12	−1.07595	−0.537976	+	0.842960i	$0.680811\pi$
$758$	−1.74845e13	−1.92372
$759$	7.62621e11	0.0834105
$760$	−4.09729e12	−0.445487
$761$	1.21142e13	1.30937	0.654685	−	0.755902i	$-0.272801\pi$
$761$	1.21142e13	1.30937	0.654685	+	0.755902i	$0.272801\pi$
$762$	5.57522e12	0.599052
$763$	5.09262e12	0.543978
$764$	−1.08015e13	−1.14701
$765$	−8.45443e12	−0.892499
$766$	8.85232e12	0.929026
$767$	−1.00334e12	−0.104682
$768$	−3.58990e12	−0.372355
$769$	3.73032e12	0.384660	0.192330	−	0.981330i	$-0.438396\pi$
$769$	3.73032e12	0.384660	0.192330	+	0.981330i	$0.438396\pi$
$770$	8.49764e12	0.871144
$771$	−2.86379e12	−0.291875
$772$	1.90253e13	1.92777
$773$	−2.49728e12	−0.251570	−0.125785	−	0.992058i	$-0.540145\pi$
$773$	−2.49728e12	−0.251570	−0.125785	+	0.992058i	$0.540145\pi$
$774$	2.40773e13	2.41143
$775$	3.87784e13	3.86129
$776$	−1.17494e13	−1.16316
$777$	−4.76836e11	−0.0469326
$778$	−8.82804e12	−0.863885
$779$	3.21657e11	0.0312949
$780$	−2.10265e12	−0.203396
$781$	−1.22413e13	−1.17733
$782$	4.24810e12	0.406223
$783$	−2.41283e12	−0.229403
$784$	6.43801e11	0.0608597
$785$	1.98720e13	1.86779
$786$	2.35202e12	0.219806
$787$	−4.16341e11	−0.0386868	−0.0193434	−	0.999813i	$-0.506158\pi$
$787$	−4.16341e11	−0.0386868	−0.0193434	+	0.999813i	$0.506158\pi$
$788$	−6.72700e12	−0.621517
$789$	9.85695e11	0.0905516
$790$	2.35006e13	2.14663
$791$	−4.89437e11	−0.0444531
$792$	1.10271e13	0.995856
$793$	−1.15318e12	−0.103554
$794$	7.80664e12	0.697063
$795$	8.89000e12	0.789314
$796$	−2.09186e13	−1.84682
$797$	−1.41842e13	−1.24521	−0.622607	−	0.782535i	$-0.713926\pi$
$797$	−1.41842e13	−1.24521	−0.622607	+	0.782535i	$0.713926\pi$
$798$	3.28647e11	0.0286891
$799$	−7.60906e12	−0.660496
$800$	1.44076e13	1.24362
$801$	2.79308e11	0.0239738
$802$	1.73976e13	1.48493
$803$	7.47284e10	0.00634257
$804$	2.94434e12	0.248505
$805$	−3.49598e12	−0.293419
$806$	−1.06279e13	−0.887035
$807$	2.27760e12	0.189037
$808$	2.79282e13	2.30511
$809$	7.88321e12	0.647045	0.323523	−	0.946220i	$-0.395133\pi$
$809$	7.88321e12	0.647045	0.323523	+	0.946220i	$0.395133\pi$
$810$	2.97846e13	2.43113
$811$	−6.02618e12	−0.489157	−0.244579	−	0.969629i	$-0.578650\pi$
$811$	−6.02618e12	−0.489157	−0.244579	+	0.969629i	$0.578650\pi$
$812$	4.21417e12	0.340181
$813$	−1.80142e12	−0.144613
$814$	8.77262e12	0.700357
$815$	6.57230e12	0.521805
$816$	−6.90151e11	−0.0544927
$817$	−3.75380e12	−0.294763
$818$	2.12932e13	1.66284
$819$	−1.27508e12	−0.0990288
$820$	6.54402e12	0.505455
$821$	−4.85583e12	−0.373009	−0.186504	−	0.982454i	$-0.559716\pi$
$821$	−4.85583e12	−0.373009	−0.186504	+	0.982454i	$0.559716\pi$
$822$	−1.48881e12	−0.113741
$823$	−1.33705e13	−1.01589	−0.507946	−	0.861389i	$-0.669595\pi$
$823$	−1.33705e13	−1.01589	−0.507946	+	0.861389i	$0.669595\pi$
$824$	2.37897e13	1.79770
$825$	5.01286e12	0.376741
$826$	3.19054e12	0.238481
$827$	2.10835e12	0.156735	0.0783677	−	0.996925i	$-0.475029\pi$
$827$	2.10835e12	0.156735	0.0783677	+	0.996925i	$0.475029\pi$
$828$	−1.02458e13	−0.757547
$829$	1.09881e13	0.808032	0.404016	−	0.914752i	$-0.367614\pi$
$829$	1.09881e13	0.808032	0.404016	+	0.914752i	$0.367614\pi$
$830$	−6.08475e13	−4.45032
$831$	−1.29895e12	−0.0944904
$832$	−5.58177e12	−0.403847
$833$	−1.07957e12	−0.0776870
$834$	7.38962e12	0.528901
$835$	−2.43546e13	−1.73377
$836$	−3.88274e12	−0.274923
$837$	−1.24259e13	−0.875110
$838$	−7.08038e12	−0.495974
$839$	−1.80392e13	−1.25686	−0.628431	−	0.777866i	$-0.716302\pi$
$839$	−1.80392e13	−1.25686	−0.628431	+	0.777866i	$0.716302\pi$
$840$	2.96051e12	0.205168
$841$	−1.08583e13	−0.748477
$842$	1.00747e13	0.690764
$843$	−4.68080e12	−0.319224
$844$	1.50356e13	1.01995
$845$	−1.98057e12	−0.133640
$846$	2.85781e13	1.91808
$847$	−2.09590e12	−0.139925
$848$	−1.23913e13	−0.822876
$849$	5.88864e10	0.00388983
$850$	2.79237e13	1.83479
$851$	−3.60911e12	−0.235894
$852$	−9.63187e12	−0.626228
$853$	−1.67337e13	−1.08223	−0.541116	−	0.840948i	$-0.681998\pi$
$853$	−1.67337e13	−1.08223	−0.541116	+	0.840948i	$0.681998\pi$
$854$	3.66701e12	0.235913
$855$	−4.95051e12	−0.316812
$856$	1.91529e13	1.21928
$857$	−1.39355e13	−0.882487	−0.441243	−	0.897387i	$-0.645462\pi$
$857$	−1.39355e13	−0.882487	−0.441243	+	0.897387i	$0.645462\pi$
$858$	−1.37387e12	−0.0865470
$859$	−7.59876e12	−0.476183	−0.238091	−	0.971243i	$-0.576522\pi$
$859$	−7.59876e12	−0.476183	−0.238091	+	0.971243i	$0.576522\pi$
$860$	−7.63702e13	−4.76081
$861$	−2.32414e11	−0.0144128
$862$	−6.26850e11	−0.0386706
$863$	−2.41467e12	−0.148187	−0.0740934	−	0.997251i	$-0.523606\pi$
$863$	−2.41467e12	−0.148187	−0.0740934	+	0.997251i	$0.523606\pi$
$864$	−4.61669e12	−0.281851
$865$	−3.41298e13	−2.07282
$866$	−4.66429e13	−2.81809
$867$	−2.75607e12	−0.165655
$868$	2.17026e13	1.29770
$869$	9.86065e12	0.586565
$870$	5.78934e12	0.342604
$871$	2.77339e12	0.163279
$872$	−3.26415e13	−1.91181
$873$	−1.41961e13	−0.827191
$874$	2.48748e12	0.144198
$875$	−1.15939e13	−0.668643
$876$	5.87989e10	0.00337366
$877$	−1.98971e13	−1.13578	−0.567888	−	0.823106i	$-0.692239\pi$
$877$	−1.98971e13	−1.13578	−0.567888	+	0.823106i	$0.692239\pi$
$878$	−3.79741e12	−0.215656
$879$	5.69094e12	0.321539
$880$	−1.04491e13	−0.587362
$881$	−9.20036e12	−0.514533	−0.257266	−	0.966340i	$-0.582822\pi$
$881$	−9.20036e12	−0.514533	−0.257266	+	0.966340i	$0.582822\pi$
$882$	4.05465e12	0.225603
$883$	−2.39231e13	−1.32432	−0.662162	−	0.749361i	$-0.730361\pi$
$883$	−2.39231e13	−1.32432	−0.662162	+	0.749361i	$0.730361\pi$
$884$	−4.91451e12	−0.270673
$885$	2.81469e12	0.154236
$886$	−2.04221e13	−1.11339
$887$	−1.94162e13	−1.05320	−0.526598	−	0.850115i	$-0.676533\pi$
$887$	−1.94162e13	−1.05320	−0.526598	+	0.850115i	$0.676533\pi$
$888$	3.05631e12	0.164945
$889$	−1.07238e13	−0.575826
$890$	−1.37959e12	−0.0737046
$891$	1.24973e13	0.664306
$892$	1.24758e13	0.659820
$893$	−4.45550e12	−0.234458
$894$	−8.06271e12	−0.422145
$895$	2.17693e13	1.13407
$896$	1.32564e13	0.687133
$897$	5.65218e11	0.0291507
$898$	1.44961e13	0.743886
$899$	1.87914e13	0.959490
$900$	−6.73478e13	−3.42162
$901$	2.07785e13	1.05040
$902$	4.27585e12	0.215076
$903$	2.71232e12	0.135752
$904$	3.13707e12	0.156231
$905$	−3.24092e13	−1.60602
$906$	−3.68289e12	−0.181598
$907$	2.75418e13	1.35133	0.675663	−	0.737211i	$-0.263857\pi$
$907$	2.75418e13	1.35133	0.675663	+	0.737211i	$0.263857\pi$
$908$	6.91033e12	0.337375
$909$	3.37440e13	1.63930
$910$	6.29804e12	0.304452
$911$	2.26747e13	1.09071	0.545354	−	0.838206i	$-0.316395\pi$
$911$	2.26747e13	1.09071	0.545354	+	0.838206i	$0.316395\pi$
$912$	−4.04119e11	−0.0193434
$913$	−2.55311e13	−1.21605
$914$	−3.27091e13	−1.55028
$915$	3.23503e12	0.152575
$916$	−4.44800e13	−2.08754
$917$	−4.52406e12	−0.211284
$918$	−8.94768e12	−0.415832
$919$	1.07689e13	0.498024	0.249012	−	0.968500i	$-0.419894\pi$
$919$	1.07689e13	0.498024	0.249012	+	0.968500i	$0.419894\pi$
$920$	2.24077e13	1.03122
$921$	−6.01055e12	−0.275262
$922$	6.39784e13	2.91571
$923$	−9.07265e12	−0.411459
$924$	2.80549e12	0.126615
$925$	−2.37234e13	−1.06547
$926$	−4.40276e13	−1.96778
$927$	2.87437e13	1.27845
$928$	6.98172e12	0.309027
$929$	3.44561e13	1.51773	0.758867	−	0.651246i	$-0.225753\pi$
$929$	3.44561e13	1.51773	0.758867	+	0.651246i	$0.225753\pi$
$930$	2.98146e13	1.30694
$931$	−6.32145e11	−0.0275767
$932$	7.49670e13	3.25461
$933$	−6.18668e12	−0.267295
$934$	1.10802e13	0.476417
$935$	1.75217e13	0.749765
$936$	8.17273e12	0.348037
$937$	1.12966e13	0.478764	0.239382	−	0.970925i	$-0.423055\pi$
$937$	1.12966e13	0.478764	0.239382	+	0.970925i	$0.423055\pi$
$938$	−8.81913e12	−0.371974
$939$	9.61482e11	0.0403595
$940$	−9.06460e13	−3.78681
$941$	−4.40804e13	−1.83270	−0.916352	−	0.400373i	$-0.868881\pi$
$941$	−4.40804e13	−1.83270	−0.916352	+	0.400373i	$0.868881\pi$
$942$	1.02165e13	0.422741
$943$	−1.75911e12	−0.0724420
$944$	−3.92323e12	−0.160794
$945$	7.36350e12	0.300359
$946$	−4.99001e13	−2.02578
$947$	2.80960e13	1.13519	0.567597	−	0.823307i	$-0.307873\pi$
$947$	2.80960e13	1.13519	0.567597	+	0.823307i	$0.307873\pi$
$948$	7.75870e12	0.311998
$949$	5.53851e10	0.00221664
$950$	1.63508e13	0.651301
$951$	2.53461e12	0.100485
$952$	6.91957e12	0.273032
$953$	1.22439e13	0.480841	0.240420	−	0.970669i	$-0.422715\pi$
$953$	1.22439e13	0.480841	0.240420	+	0.970669i	$0.422715\pi$
$954$	−7.80399e13	−3.05035
$955$	2.85423e13	1.11039
$956$	4.16609e13	1.61312
$957$	2.42916e12	0.0936164
$958$	−3.72057e13	−1.42714
$959$	2.86370e12	0.109331
$960$	1.56586e13	0.595021
$961$	7.03345e13	2.66019
$962$	6.50184e12	0.244765
$963$	2.31413e13	0.867099
$964$	−7.14819e13	−2.66594
$965$	−5.02732e13	−1.86622
$966$	−1.79734e12	−0.0664099
$967$	3.18431e12	0.117111	0.0585553	−	0.998284i	$-0.481351\pi$
$967$	3.18431e12	0.117111	0.0585553	+	0.998284i	$0.481351\pi$
$968$	1.34338e13	0.491767
$969$	6.77655e11	0.0246917
$970$	7.01191e13	2.54310
$971$	1.16608e13	0.420961	0.210480	−	0.977598i	$-0.432497\pi$
$971$	1.16608e13	0.420961	0.210480	+	0.977598i	$0.432497\pi$
$972$	3.26777e13	1.17423
$973$	−1.42138e13	−0.508395
$974$	7.50766e13	2.67294
$975$	3.71529e12	0.131666
$976$	−4.50912e12	−0.159063
$977$	4.88625e13	1.71574	0.857868	−	0.513870i	$-0.171789\pi$
$977$	4.88625e13	1.71574	0.857868	+	0.513870i	$0.171789\pi$
$978$	3.37893e12	0.118101
$979$	−5.78863e11	−0.0201397
$980$	−1.28608e13	−0.445401
$981$	−3.94387e13	−1.35960
$982$	5.07041e13	1.73997
$983$	−2.12652e13	−0.726404	−0.363202	−	0.931710i	$-0.618317\pi$
$983$	−2.12652e13	−0.726404	−0.363202	+	0.931710i	$0.618317\pi$
$984$	1.48967e12	0.0506538
$985$	1.77756e13	0.601675
$986$	1.35314e13	0.455928
$987$	3.21933e12	0.107979
$988$	−2.87770e12	−0.0960815
$989$	2.05292e13	0.682321
$990$	−6.58081e13	−2.17731
$991$	3.63511e13	1.19725	0.598627	−	0.801028i	$-0.295713\pi$
$991$	3.63511e13	1.19725	0.598627	+	0.801028i	$0.295713\pi$
$992$	3.59553e13	1.17885
$993$	−1.42805e13	−0.466093
$994$	2.88502e13	0.937367
$995$	5.52761e13	1.78786
$996$	−2.00888e13	−0.646824
$997$	−4.50181e13	−1.44297	−0.721487	−	0.692428i	$-0.756541\pi$
$997$	−4.50181e13	−1.44297	−0.721487	+	0.692428i	$0.756541\pi$
$998$	−3.08757e13	−0.985212
$999$	7.60178e12	0.241474

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.a.1.2	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.a.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-37.8265 q^{2} +32.9997 q^{3} +918.841 q^{4} -2427.98 q^{5} -1248.26 q^{6} +2401.00 q^{7} -15389.3 q^{8} -18594.0 q^{9} +O(q^{10})\)	\(q-37.8265 q^{2} +32.9997 q^{3} +918.841 q^{4} -2427.98 q^{5} -1248.26 q^{6} +2401.00 q^{7} -15389.3 q^{8} -18594.0 q^{9} +91841.7 q^{10} +38536.0 q^{11} +30321.5 q^{12} +28561.0 q^{13} -90821.3 q^{14} -80122.4 q^{15} +111678. q^{16} -187269. q^{17} +703346. q^{18} -109656. q^{19} -2.23092e6 q^{20} +79232.2 q^{21} -1.45768e6 q^{22} +599698. q^{23} -507844. q^{24} +3.94194e6 q^{25} -1.08036e6 q^{26} -1.26313e6 q^{27} +2.20614e6 q^{28} +1.91020e6 q^{29} +3.03075e6 q^{30} +9.83738e6 q^{31} +3.65496e6 q^{32} +1.27167e6 q^{33} +7.08374e6 q^{34} -5.82957e6 q^{35} -1.70849e7 q^{36} -6.01821e6 q^{37} +4.14790e6 q^{38} +942504. q^{39} +3.73650e7 q^{40} -2.93333e6 q^{41} -2.99707e6 q^{42} +3.42326e7 q^{43} +3.54084e7 q^{44} +4.51458e7 q^{45} -2.26844e7 q^{46} +4.06316e7 q^{47} +3.68534e6 q^{48} +5.76480e6 q^{49} -1.49110e8 q^{50} -6.17983e6 q^{51} +2.62430e7 q^{52} -1.10955e8 q^{53} +4.77797e7 q^{54} -9.35644e7 q^{55} -3.69498e7 q^{56} -3.61861e6 q^{57} -7.22562e7 q^{58} -3.51298e7 q^{59} -7.36197e7 q^{60} -4.03761e7 q^{61} -3.72113e8 q^{62} -4.46442e7 q^{63} -1.95433e8 q^{64} -6.93454e7 q^{65} -4.81029e7 q^{66} +9.71041e7 q^{67} -1.72071e8 q^{68} +1.97898e7 q^{69} +2.20512e8 q^{70} -3.17659e8 q^{71} +2.86150e8 q^{72} +1.93918e6 q^{73} +2.27648e8 q^{74} +1.30083e8 q^{75} -1.00756e8 q^{76} +9.25248e7 q^{77} -3.56516e7 q^{78} +2.55882e8 q^{79} -2.71151e8 q^{80} +3.24303e8 q^{81} +1.10957e8 q^{82} -6.62526e8 q^{83} +7.28018e7 q^{84} +4.54685e8 q^{85} -1.29490e9 q^{86} +6.30361e7 q^{87} -5.93043e8 q^{88} -1.50214e7 q^{89} -1.70771e9 q^{90} +6.85750e7 q^{91} +5.51027e8 q^{92} +3.24630e8 q^{93} -1.53695e9 q^{94} +2.66242e8 q^{95} +1.20613e8 q^{96} +7.63478e8 q^{97} -2.18062e8 q^{98} -7.16539e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 21 q^{2} - 323 q^{3} + 2945 q^{4} - 5202 q^{5} - 9897 q^{6} + 28812 q^{7} - 25431 q^{8} + 78519 q^{9}+O(q^{10}) \) 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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