LMFDB - Embedded newform 91.10.a.a.1.3

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			1.3
Root			$-33.9466$ 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)

$f(q)$	$=$	$q-35.9466 q^{2} +230.724 q^{3} +780.160 q^{4} +434.116 q^{5} -8293.74 q^{6} +2401.00 q^{7} -9639.45 q^{8} +33550.4 q^{9} +O(q^{10})$	\(q-35.9466 q^{2} +230.724 q^{3} +780.160 q^{4} +434.116 q^{5} -8293.74 q^{6} +2401.00 q^{7} -9639.45 q^{8} +33550.4 q^{9} -15605.0 q^{10} -37127.2 q^{11} +180001. q^{12} +28561.0 q^{13} -86307.9 q^{14} +100161. q^{15} -52936.3 q^{16} -546796. q^{17} -1.20603e6 q^{18} -902942. q^{19} +338680. q^{20} +553968. q^{21} +1.33460e6 q^{22} -1.65189e6 q^{23} -2.22405e6 q^{24} -1.76467e6 q^{25} -1.02667e6 q^{26} +3.19955e6 q^{27} +1.87316e6 q^{28} -2.15158e6 q^{29} -3.60045e6 q^{30} +2.15325e6 q^{31} +6.83828e6 q^{32} -8.56612e6 q^{33} +1.96555e7 q^{34} +1.04231e6 q^{35} +2.61747e7 q^{36} +1.55393e7 q^{37} +3.24577e7 q^{38} +6.58970e6 q^{39} -4.18464e6 q^{40} -2.64886e6 q^{41} -1.99133e7 q^{42} -3.32538e7 q^{43} -2.89651e7 q^{44} +1.45648e7 q^{45} +5.93799e7 q^{46} -4.58283e6 q^{47} -1.22137e7 q^{48} +5.76480e6 q^{49} +6.34339e7 q^{50} -1.26159e8 q^{51} +2.22821e7 q^{52} +1.52908e7 q^{53} -1.15013e8 q^{54} -1.61175e7 q^{55} -2.31443e7 q^{56} -2.08330e8 q^{57} +7.73421e7 q^{58} -1.05493e8 q^{59} +7.81416e7 q^{60} +515476. q^{61} -7.74022e7 q^{62} +8.05546e7 q^{63} -2.18710e8 q^{64} +1.23988e7 q^{65} +3.07923e8 q^{66} +2.84354e8 q^{67} -4.26589e8 q^{68} -3.81130e8 q^{69} -3.74677e7 q^{70} +3.30668e8 q^{71} -3.23408e8 q^{72} -1.87286e8 q^{73} -5.58584e8 q^{74} -4.07151e8 q^{75} -7.04439e8 q^{76} -8.91423e7 q^{77} -2.36877e8 q^{78} +4.60455e8 q^{79} -2.29805e7 q^{80} +7.78381e7 q^{81} +9.52175e7 q^{82} -1.63544e8 q^{83} +4.32183e8 q^{84} -2.37373e8 q^{85} +1.19536e9 q^{86} -4.96421e8 q^{87} +3.57885e8 q^{88} -8.24421e8 q^{89} -5.23555e8 q^{90} +6.85750e7 q^{91} -1.28874e9 q^{92} +4.96806e8 q^{93} +1.64737e8 q^{94} -3.91982e8 q^{95} +1.57775e9 q^{96} -6.27004e8 q^{97} -2.07225e8 q^{98} -1.24563e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−35.9466	−1.58863	−0.794316	−	0.607505i	$-0.792170\pi$
$2$	−35.9466	−1.58863	−0.794316	+	0.607505i	$0.792170\pi$
$3$	230.724	1.64455	0.822274	−	0.569092i	$-0.192705\pi$
$3$	230.724	1.64455	0.822274	+	0.569092i	$0.192705\pi$
$4$	780.160	1.52375
$5$	434.116	0.310628	0.155314	−	0.987865i	$-0.450361\pi$
$5$	434.116	0.310628	0.155314	+	0.987865i	$0.450361\pi$
$6$	−8293.74	−2.61258
$7$	2401.00	0.377964
$7$	2401.00	0.377964
$8$	−9639.45	−0.832046
$9$	33550.4	1.70454
$10$	−15605.0	−0.493474
$11$	−37127.2	−0.764583	−0.382292	−	0.924042i	$-0.624865\pi$
$11$	−37127.2	−0.764583	−0.382292	+	0.924042i	$0.624865\pi$
$12$	180001.	2.50588
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	−86307.9	−0.600446
$15$	100161.	0.510843
$16$	−52936.3	−0.201936
$17$	−546796.	−1.58784	−0.793918	−	0.608025i	$-0.791962\pi$
$17$	−546796.	−1.58784	−0.793918	+	0.608025i	$0.791962\pi$
$18$	−1.20603e6	−2.70788
$19$	−902942.	−1.58953	−0.794765	−	0.606917i	$-0.792406\pi$
$19$	−902942.	−1.58953	−0.794765	+	0.606917i	$0.792406\pi$
$20$	338680.	0.473320
$21$	553968.	0.621581
$22$	1.33460e6	1.21464
$23$	−1.65189e6	−1.23085	−0.615426	−	0.788194i	$-0.711016\pi$
$23$	−1.65189e6	−1.23085	−0.615426	+	0.788194i	$0.711016\pi$
$24$	−2.22405e6	−1.36834
$25$	−1.76467e6	−0.903510
$26$	−1.02667e6	−0.440607
$27$	3.19955e6	1.15865
$28$	1.87316e6	0.575923
$29$	−2.15158e6	−0.564894	−0.282447	−	0.959283i	$-0.591146\pi$
$29$	−2.15158e6	−0.564894	−0.282447	+	0.959283i	$0.591146\pi$
$30$	−3.60045e6	−0.811542
$31$	2.15325e6	0.418762	0.209381	−	0.977834i	$-0.432855\pi$
$31$	2.15325e6	0.418762	0.209381	+	0.977834i	$0.432855\pi$
$32$	6.83828e6	1.15285
$33$	−8.56612e6	−1.25739
$34$	1.96555e7	2.52249
$35$	1.04231e6	0.117407
$36$	2.61747e7	2.59729
$37$	1.55393e7	1.36308	0.681542	−	0.731779i	$-0.261310\pi$
$37$	1.55393e7	1.36308	0.681542	+	0.731779i	$0.261310\pi$
$38$	3.24577e7	2.52518
$39$	6.58970e6	0.456116
$40$	−4.18464e6	−0.258457
$41$	−2.64886e6	−0.146397	−0.0731983	−	0.997317i	$-0.523321\pi$
$41$	−2.64886e6	−0.146397	−0.0731983	+	0.997317i	$0.523321\pi$
$42$	−1.99133e7	−0.987463
$43$	−3.32538e7	−1.48331	−0.741656	−	0.670780i	$-0.765959\pi$
$43$	−3.32538e7	−1.48331	−0.741656	+	0.670780i	$0.765959\pi$
$44$	−2.89651e7	−1.16503
$45$	1.45648e7	0.529478
$46$	5.93799e7	1.95537
$47$	−4.58283e6	−0.136991	−0.0684956	−	0.997651i	$-0.521820\pi$
$47$	−4.58283e6	−0.136991	−0.0684956	+	0.997651i	$0.521820\pi$
$48$	−1.22137e7	−0.332094
$49$	5.76480e6	0.142857
$50$	6.34339e7	1.43534
$51$	−1.26159e8	−2.61127
$52$	2.22821e7	0.422612
$53$	1.52908e7	0.266188	0.133094	−	0.991103i	$-0.457509\pi$
$53$	1.52908e7	0.266188	0.133094	+	0.991103i	$0.457509\pi$
$54$	−1.15013e8	−1.84066
$55$	−1.61175e7	−0.237501
$56$	−2.31443e7	−0.314484
$57$	−2.08330e8	−2.61406
$58$	7.73421e7	0.897408
$59$	−1.05493e8	−1.13342	−0.566710	−	0.823917i	$-0.691784\pi$
$59$	−1.05493e8	−1.13342	−0.566710	+	0.823917i	$0.691784\pi$
$60$	7.81416e7	0.778398
$61$	515476.	0.00476677	0.00238338	−	0.999997i	$-0.499241\pi$
$61$	515476.	0.00476677	0.00238338	+	0.999997i	$0.499241\pi$
$62$	−7.74022e7	−0.665258
$63$	8.05546e7	0.644255
$64$	−2.18710e8	−1.62951
$65$	1.23988e7	0.0861528
$66$	3.07923e8	1.99754
$67$	2.84354e8	1.72394	0.861972	−	0.506956i	$-0.169229\pi$
$67$	2.84354e8	1.72394	0.861972	+	0.506956i	$0.169229\pi$
$68$	−4.26589e8	−2.41946
$69$	−3.81130e8	−2.02420
$70$	−3.74677e7	−0.186516
$71$	3.30668e8	1.54429	0.772147	−	0.635444i	$-0.219183\pi$
$71$	3.30668e8	1.54429	0.772147	+	0.635444i	$0.219183\pi$
$72$	−3.23408e8	−1.41825
$73$	−1.87286e8	−0.771885	−0.385943	−	0.922523i	$-0.626124\pi$
$73$	−1.87286e8	−0.771885	−0.385943	+	0.922523i	$0.626124\pi$
$74$	−5.58584e8	−2.16544
$75$	−4.07151e8	−1.48587
$76$	−7.04439e8	−2.42205
$77$	−8.91423e7	−0.288985
$78$	−2.36877e8	−0.724600
$79$	4.60455e8	1.33004	0.665020	−	0.746825i	$-0.268423\pi$
$79$	4.60455e8	1.33004	0.665020	+	0.746825i	$0.268423\pi$
$80$	−2.29805e7	−0.0627271
$81$	7.78381e7	0.200914
$82$	9.52175e7	0.232570
$83$	−1.63544e8	−0.378253	−0.189127	−	0.981953i	$-0.560566\pi$
$83$	−1.63544e8	−0.378253	−0.189127	+	0.981953i	$0.560566\pi$
$84$	4.32183e8	0.947134
$85$	−2.37373e8	−0.493227
$86$	1.19536e9	2.35644
$87$	−4.96421e8	−0.928995
$88$	3.57885e8	0.636168
$89$	−8.24421e8	−1.39282	−0.696408	−	0.717646i	$-0.745220\pi$
$89$	−8.24421e8	−1.39282	−0.696408	+	0.717646i	$0.745220\pi$
$90$	−5.23555e8	−0.841146
$91$	6.85750e7	0.104828
$92$	−1.28874e9	−1.87551
$93$	4.96806e8	0.688674
$94$	1.64737e8	0.217629
$95$	−3.91982e8	−0.493753
$96$	1.57775e9	1.89591
$97$	−6.27004e8	−0.719113	−0.359557	−	0.933123i	$-0.617072\pi$
$97$	−6.27004e8	−0.719113	−0.359557	+	0.933123i	$0.617072\pi$
$98$	−2.07225e8	−0.226947
$99$	−1.24563e9	−1.30326
$100$	−1.37672e9	−1.37672
$101$	8.53911e8	0.816520	0.408260	−	0.912866i	$-0.366136\pi$
$101$	8.53911e8	0.816520	0.408260	+	0.912866i	$0.366136\pi$
$102$	4.53499e9	4.14835
$103$	−6.22026e8	−0.544554	−0.272277	−	0.962219i	$-0.587777\pi$
$103$	−6.22026e8	−0.544554	−0.272277	+	0.962219i	$0.587777\pi$
$104$	−2.75312e8	−0.230768
$105$	2.40486e8	0.193081
$106$	−5.49652e8	−0.422874
$107$	3.72891e8	0.275014	0.137507	−	0.990501i	$-0.456091\pi$
$107$	3.72891e8	0.275014	0.137507	+	0.990501i	$0.456091\pi$
$108$	2.49616e9	1.76549
$109$	1.62826e9	1.10485	0.552427	−	0.833562i	$-0.313702\pi$
$109$	1.62826e9	1.10485	0.552427	+	0.833562i	$0.313702\pi$
$110$	5.79370e8	0.377302
$111$	3.58528e9	2.24166
$112$	−1.27100e8	−0.0763247
$113$	−2.54267e9	−1.46702	−0.733511	−	0.679678i	$-0.762120\pi$
$113$	−2.54267e9	−1.46702	−0.733511	+	0.679678i	$0.762120\pi$
$114$	7.48877e9	4.15278
$115$	−7.17113e8	−0.382338
$116$	−1.67858e9	−0.860757
$117$	9.58234e8	0.472754
$118$	3.79213e9	1.80059
$119$	−1.31286e9	−0.600146
$120$	−9.65496e8	−0.425045
$121$	−9.79521e8	−0.415413
$122$	−1.85296e7	−0.00757264
$123$	−6.11154e8	−0.240756
$124$	1.67988e9	0.638089
$125$	−1.61396e9	−0.591284
$126$	−2.89567e9	−1.02348
$127$	−2.88641e9	−0.984559	−0.492279	−	0.870437i	$-0.663836\pi$
$127$	−2.88641e9	−0.984559	−0.492279	+	0.870437i	$0.663836\pi$
$128$	4.36068e9	1.43585
$129$	−7.67243e9	−2.43938
$130$	−4.45695e8	−0.136865
$131$	−2.81188e9	−0.834210	−0.417105	−	0.908858i	$-0.636955\pi$
$131$	−2.81188e9	−0.834210	−0.417105	+	0.908858i	$0.636955\pi$
$132$	−6.68294e9	−1.91595
$133$	−2.16796e9	−0.600786
$134$	−1.02216e10	−2.73871
$135$	1.38898e9	0.359909
$136$	5.27082e9	1.32115
$137$	3.31457e9	0.803867	0.401934	−	0.915669i	$-0.368338\pi$
$137$	3.31457e9	0.803867	0.401934	+	0.915669i	$0.368338\pi$
$138$	1.37004e10	3.21570
$139$	5.32393e9	1.20967	0.604833	−	0.796352i	$-0.293240\pi$
$139$	5.32393e9	1.20967	0.604833	+	0.796352i	$0.293240\pi$
$140$	8.13171e8	0.178898
$141$	−1.05737e9	−0.225289
$142$	−1.18864e10	−2.45332
$143$	−1.06039e9	−0.212057
$144$	−1.77604e9	−0.344208
$145$	−9.34037e8	−0.175472
$146$	6.73231e9	1.22624
$147$	1.33008e9	0.234935
$148$	1.21231e10	2.07700
$149$	−3.15502e9	−0.524402	−0.262201	−	0.965013i	$-0.584448\pi$
$149$	−3.15502e9	−0.524402	−0.262201	+	0.965013i	$0.584448\pi$
$150$	1.46357e10	2.36049
$151$	−1.66845e9	−0.261166	−0.130583	−	0.991437i	$-0.541685\pi$
$151$	−1.66845e9	−0.261166	−0.130583	+	0.991437i	$0.541685\pi$
$152$	8.70386e9	1.32256
$153$	−1.83453e10	−2.70653
$154$	3.20437e9	0.459091
$155$	9.34762e8	0.130079
$156$	5.14102e9	0.695006
$157$	3.85793e9	0.506765	0.253382	−	0.967366i	$-0.418457\pi$
$157$	3.85793e9	0.506765	0.253382	+	0.967366i	$0.418457\pi$
$158$	−1.65518e10	−2.11294
$159$	3.52795e9	0.437759
$160$	2.96861e9	0.358107
$161$	−3.96619e9	−0.465219
$162$	−2.79802e9	−0.319178
$163$	1.14839e10	1.27422	0.637111	−	0.770772i	$-0.280129\pi$
$163$	1.14839e10	1.27422	0.637111	+	0.770772i	$0.280129\pi$
$164$	−2.06653e9	−0.223072
$165$	−3.71869e9	−0.390582
$166$	5.87885e9	0.600905
$167$	−1.49406e10	−1.48643	−0.743213	−	0.669055i	$-0.766699\pi$
$167$	−1.49406e10	−1.48643	−0.743213	+	0.669055i	$0.766699\pi$
$168$	−5.33994e9	−0.517184
$169$	8.15731e8	0.0769231
$170$	8.53277e9	0.783556
$171$	−3.02941e10	−2.70942
$172$	−2.59433e10	−2.26020
$173$	5.46601e9	0.463941	0.231971	−	0.972723i	$-0.425483\pi$
$173$	5.46601e9	0.463941	0.231971	+	0.972723i	$0.425483\pi$
$174$	1.78447e10	1.47583
$175$	−4.23697e9	−0.341495
$176$	1.96538e9	0.154397
$177$	−2.43398e10	−1.86396
$178$	2.96351e10	2.21267
$179$	2.22364e10	1.61892	0.809461	−	0.587173i	$-0.199759\pi$
$179$	2.22364e10	1.61892	0.809461	+	0.587173i	$0.199759\pi$
$180$	1.13629e10	0.806792
$181$	−4.21143e9	−0.291659	−0.145830	−	0.989310i	$-0.546585\pi$
$181$	−4.21143e9	−0.291659	−0.145830	+	0.989310i	$0.546585\pi$
$182$	−2.46504e9	−0.166534
$183$	1.18932e8	0.00783918
$184$	1.59233e10	1.02413
$185$	6.74585e9	0.423413
$186$	−1.78585e10	−1.09405
$187$	2.03010e10	1.21403
$188$	−3.57534e9	−0.208740
$189$	7.68211e9	0.437928
$190$	1.40904e10	0.784392
$191$	1.11392e10	0.605627	0.302813	−	0.953050i	$-0.402074\pi$
$191$	1.11392e10	0.605627	0.302813	+	0.953050i	$0.402074\pi$
$192$	−5.04615e10	−2.67981
$193$	2.91759e10	1.51362	0.756808	−	0.653637i	$-0.226758\pi$
$193$	2.91759e10	1.51362	0.756808	+	0.653637i	$0.226758\pi$
$194$	2.25387e10	1.14241
$195$	2.86070e9	0.141682
$196$	4.49747e9	0.217679
$197$	−2.66926e10	−1.26268	−0.631338	−	0.775507i	$-0.717494\pi$
$197$	−2.66926e10	−1.26268	−0.631338	+	0.775507i	$0.717494\pi$
$198$	4.47763e10	2.07040
$199$	2.08728e10	0.943501	0.471751	−	0.881732i	$-0.343622\pi$
$199$	2.08728e10	0.943501	0.471751	+	0.881732i	$0.343622\pi$
$200$	1.70104e10	0.751761
$201$	6.56073e10	2.83511
$202$	−3.06952e10	−1.29715
$203$	−5.16595e9	−0.213510
$204$	−9.84241e10	−3.97893
$205$	−1.14991e9	−0.0454750
$206$	2.23597e10	0.865095
$207$	−5.54217e10	−2.09804
$208$	−1.51191e9	−0.0560070
$209$	3.35237e10	1.21533
$210$	−8.64468e9	−0.306734
$211$	−2.72187e10	−0.945358	−0.472679	−	0.881235i	$-0.656713\pi$
$211$	−2.72187e10	−0.945358	−0.472679	+	0.881235i	$0.656713\pi$
$212$	1.19293e10	0.405604
$213$	7.62931e10	2.53967
$214$	−1.34042e10	−0.436896
$215$	−1.44360e10	−0.460759
$216$	−3.08419e10	−0.964048
$217$	5.16996e9	0.158277
$218$	−5.85305e10	−1.75520
$219$	−4.32114e10	−1.26940
$220$	−1.25742e10	−0.361893
$221$	−1.56171e10	−0.440386
$222$	−1.28879e11	−3.56117
$223$	3.81531e10	1.03314	0.516569	−	0.856246i	$-0.327209\pi$
$223$	3.81531e10	1.03314	0.516569	+	0.856246i	$0.327209\pi$
$224$	1.64187e10	0.435735
$225$	−5.92054e10	−1.54007
$226$	9.14003e10	2.33056
$227$	−2.63924e10	−0.659726	−0.329863	−	0.944029i	$-0.607002\pi$
$227$	−2.63924e10	−0.659726	−0.329863	+	0.944029i	$0.607002\pi$
$228$	−1.62531e11	−3.98317
$229$	5.14334e10	1.23591	0.617953	−	0.786215i	$-0.287962\pi$
$229$	5.14334e10	1.23591	0.617953	+	0.786215i	$0.287962\pi$
$230$	2.57778e10	0.607394
$231$	−2.05673e10	−0.475250
$232$	2.07400e10	0.470017
$233$	−6.10637e10	−1.35732	−0.678659	−	0.734454i	$-0.737438\pi$
$233$	−6.10637e10	−1.35732	−0.678659	+	0.734454i	$0.737438\pi$
$234$	−3.44453e10	−0.751032
$235$	−1.98948e9	−0.0425534
$236$	−8.23016e10	−1.72705
$237$	1.06238e11	2.18732
$238$	4.71928e10	0.953410
$239$	−7.41233e10	−1.46948	−0.734741	−	0.678348i	$-0.762696\pi$
$239$	−7.41233e10	−1.46948	−0.734741	+	0.678348i	$0.762696\pi$
$240$	−5.30216e9	−0.103158
$241$	2.24805e10	0.429269	0.214634	−	0.976694i	$-0.431144\pi$
$241$	2.24805e10	0.429269	0.214634	+	0.976694i	$0.431144\pi$
$242$	3.52105e10	0.659938
$243$	−4.50176e10	−0.828236
$244$	4.02154e8	0.00726336
$245$	2.50259e9	0.0443755
$246$	2.19689e10	0.382473
$247$	−2.57889e10	−0.440856
$248$	−2.07562e10	−0.348429
$249$	−3.77334e10	−0.622056
$250$	5.80162e10	0.939333
$251$	−2.53210e10	−0.402669	−0.201335	−	0.979523i	$-0.564528\pi$
$251$	−2.53210e10	−0.402669	−0.201335	+	0.979523i	$0.564528\pi$
$252$	6.28455e10	0.981684
$253$	6.13300e10	0.941089
$254$	1.03757e11	1.56410
$255$	−5.47677e10	−0.811136
$256$	−4.47722e10	−0.651522
$257$	−7.30610e10	−1.04469	−0.522344	−	0.852735i	$-0.674942\pi$
$257$	−7.30610e10	−1.04469	−0.522344	+	0.852735i	$0.674942\pi$
$258$	2.75798e11	3.87527
$259$	3.73098e10	0.515198
$260$	9.67305e9	0.131275
$261$	−7.21865e10	−0.962883
$262$	1.01077e11	1.32525
$263$	1.14086e11	1.47038	0.735191	−	0.677860i	$-0.237093\pi$
$263$	1.14086e11	1.47038	0.735191	+	0.677860i	$0.237093\pi$
$264$	8.25726e10	1.04621
$265$	6.63798e9	0.0826855
$266$	7.79310e10	0.954427
$267$	−1.90213e11	−2.29055
$268$	2.21842e11	2.62686
$269$	−1.48238e10	−0.172613	−0.0863067	−	0.996269i	$-0.527506\pi$
$269$	−1.48238e10	−0.172613	−0.0863067	+	0.996269i	$0.527506\pi$
$270$	−4.99290e10	−0.571763
$271$	−2.59065e10	−0.291775	−0.145887	−	0.989301i	$-0.546604\pi$
$271$	−2.59065e10	−0.291775	−0.145887	+	0.989301i	$0.546604\pi$
$272$	2.89454e10	0.320641
$273$	1.58219e10	0.172395
$274$	−1.19148e11	−1.27705
$275$	6.55171e10	0.690809
$276$	−2.97343e11	−3.08437
$277$	−3.70344e10	−0.377961	−0.188980	−	0.981981i	$-0.560518\pi$
$277$	−3.70344e10	−0.377961	−0.188980	+	0.981981i	$0.560518\pi$
$278$	−1.91377e11	−1.92171
$279$	7.22426e10	0.713796
$280$	−1.00473e10	−0.0976876
$281$	−8.33411e10	−0.797408	−0.398704	−	0.917080i	$-0.630540\pi$
$281$	−8.33411e10	−0.797408	−0.398704	+	0.917080i	$0.630540\pi$
$282$	3.80088e10	0.357901
$283$	−1.02296e11	−0.948026	−0.474013	−	0.880518i	$-0.657195\pi$
$283$	−1.02296e11	−0.948026	−0.474013	+	0.880518i	$0.657195\pi$
$284$	2.57974e11	2.35312
$285$	−9.04396e10	−0.812001
$286$	3.81174e10	0.336881
$287$	−6.35991e9	−0.0553327
$288$	2.29427e11	1.96507
$289$	1.80399e11	1.52122
$290$	3.35755e10	0.278760
$291$	−1.44665e11	−1.18262
$292$	−1.46113e11	−1.17616
$293$	4.44571e10	0.352400	0.176200	−	0.984354i	$-0.443619\pi$
$293$	4.44571e10	0.352400	0.176200	+	0.984354i	$0.443619\pi$
$294$	−4.78118e10	−0.373226
$295$	−4.57964e10	−0.352072
$296$	−1.49790e11	−1.13415
$297$	−1.18790e11	−0.885883
$298$	1.13412e11	0.833081
$299$	−4.71797e10	−0.341377
$300$	−3.17643e11	−2.26409
$301$	−7.98423e10	−0.560639
$302$	5.99752e10	0.414897
$303$	1.97018e11	1.34281
$304$	4.77985e10	0.320984
$305$	2.23776e8	0.00148069
$306$	6.59450e11	4.29968
$307$	4.96403e10	0.318942	0.159471	−	0.987203i	$-0.449021\pi$
$307$	4.96403e10	0.318942	0.159471	+	0.987203i	$0.449021\pi$
$308$	−6.95453e10	−0.440341
$309$	−1.43516e11	−0.895545
$310$	−3.36015e10	−0.206648
$311$	1.63025e10	0.0988170	0.0494085	−	0.998779i	$-0.484266\pi$
$311$	1.63025e10	0.0988170	0.0494085	+	0.998779i	$0.484266\pi$
$312$	−6.35211e10	−0.379509
$313$	3.07617e10	0.181159	0.0905797	−	0.995889i	$-0.471128\pi$
$313$	3.07617e10	0.181159	0.0905797	+	0.995889i	$0.471128\pi$
$314$	−1.38680e11	−0.805062
$315$	3.49701e10	0.200124
$316$	3.59228e11	2.02665
$317$	6.00070e9	0.0333761	0.0166880	−	0.999861i	$-0.494688\pi$
$317$	6.00070e9	0.0333761	0.0166880	+	0.999861i	$0.494688\pi$
$318$	−1.26818e11	−0.695437
$319$	7.98821e10	0.431908
$320$	−9.49455e10	−0.506173
$321$	8.60349e10	0.452274
$322$	1.42571e11	0.739061
$323$	4.93726e11	2.52391
$324$	6.07262e10	0.306142
$325$	−5.04007e10	−0.250589
$326$	−4.12808e11	−2.02427
$327$	3.75678e11	1.81698
$328$	2.55335e10	0.121809
$329$	−1.10034e10	−0.0517778
$330$	1.33674e11	0.620491
$331$	−2.75688e11	−1.26238	−0.631192	−	0.775627i	$-0.717434\pi$
$331$	−2.75688e11	−1.26238	−0.631192	+	0.775627i	$0.717434\pi$
$332$	−1.27590e11	−0.576364
$333$	5.21349e11	2.32343
$334$	5.37064e11	2.36138
$335$	1.23443e11	0.535506
$336$	−2.93250e10	−0.125520
$337$	−1.39653e11	−0.589815	−0.294907	−	0.955526i	$-0.595289\pi$
$337$	−1.39653e11	−0.589815	−0.294907	+	0.955526i	$0.595289\pi$
$338$	−2.93228e10	−0.122202
$339$	−5.86654e11	−2.41259
$340$	−1.85189e11	−0.751555
$341$	−7.99442e10	−0.320178
$342$	1.08897e12	4.30426
$343$	1.38413e10	0.0539949
$344$	3.20548e11	1.23418
$345$	−1.65455e11	−0.628773
$346$	−1.96485e11	−0.737031
$347$	−4.96372e11	−1.83791	−0.918955	−	0.394363i	$-0.870965\pi$
$347$	−4.96372e11	−1.83791	−0.918955	+	0.394363i	$0.870965\pi$
$348$	−3.87288e11	−1.41556
$349$	4.34232e11	1.56678	0.783388	−	0.621533i	$-0.213490\pi$
$349$	4.34232e11	1.56678	0.783388	+	0.621533i	$0.213490\pi$
$350$	1.52305e11	0.542509
$351$	9.13823e10	0.321351
$352$	−2.53886e11	−0.881448
$353$	5.55167e11	1.90299	0.951496	−	0.307660i	$-0.0995458\pi$
$353$	5.55167e11	1.90299	0.951496	+	0.307660i	$0.0995458\pi$
$354$	8.74934e11	2.96115
$355$	1.43549e11	0.479702
$356$	−6.43180e11	−2.12230
$357$	−3.02908e11	−0.986968
$358$	−7.99324e11	−2.57187
$359$	1.82924e11	0.581227	0.290613	−	0.956841i	$-0.406141\pi$
$359$	1.82924e11	0.581227	0.290613	+	0.956841i	$0.406141\pi$
$360$	−1.40397e11	−0.440550
$361$	4.92617e11	1.52661
$362$	1.51387e11	0.463339
$363$	−2.25999e11	−0.683166
$364$	5.34994e10	0.159732
$365$	−8.13040e10	−0.239770
$366$	−4.27522e9	−0.0124536
$367$	−1.84215e11	−0.530064	−0.265032	−	0.964240i	$-0.585383\pi$
$367$	−1.84215e11	−0.530064	−0.265032	+	0.964240i	$0.585383\pi$
$368$	8.74451e10	0.248554
$369$	−8.88703e10	−0.249539
$370$	−2.42491e11	−0.672647
$371$	3.67132e10	0.100610
$372$	3.87588e11	1.04937
$373$	4.08286e10	0.109213	0.0546065	−	0.998508i	$-0.482610\pi$
$373$	4.08286e10	0.109213	0.0546065	+	0.998508i	$0.482610\pi$
$374$	−7.29753e11	−1.92865
$375$	−3.72378e11	−0.972396
$376$	4.41759e10	0.113983
$377$	−6.14513e10	−0.156673
$378$	−2.76146e11	−0.695706
$379$	−1.76701e11	−0.439908	−0.219954	−	0.975510i	$-0.570591\pi$
$379$	−1.76701e11	−0.439908	−0.219954	+	0.975510i	$0.570591\pi$
$380$	−3.05809e11	−0.752357
$381$	−6.65964e11	−1.61915
$382$	−4.00418e11	−0.962117
$383$	−7.60004e11	−1.80477	−0.902384	−	0.430932i	$-0.858185\pi$
$383$	−7.60004e11	−1.80477	−0.902384	+	0.430932i	$0.858185\pi$
$384$	1.00611e12	2.36132
$385$	−3.86982e10	−0.0897670
$386$	−1.04877e12	−2.40458
$387$	−1.11568e12	−2.52836
$388$	−4.89163e11	−1.09575
$389$	3.59913e10	0.0796938	0.0398469	−	0.999206i	$-0.487313\pi$
$389$	3.59913e10	0.0796938	0.0398469	+	0.999206i	$0.487313\pi$
$390$	−1.02832e11	−0.225081
$391$	9.03248e11	1.95439
$392$	−5.55695e10	−0.118864
$393$	−6.48766e11	−1.37190
$394$	9.59508e11	2.00593
$395$	1.99891e11	0.413148
$396$	−9.71793e11	−1.98584
$397$	−5.85617e11	−1.18319	−0.591597	−	0.806234i	$-0.701502\pi$
$397$	−5.85617e11	−1.18319	−0.591597	+	0.806234i	$0.701502\pi$
$398$	−7.50308e11	−1.49888
$399$	−5.00201e11	−0.988021
$400$	9.34151e10	0.182451
$401$	9.17734e10	0.177242	0.0886211	−	0.996065i	$-0.471754\pi$
$401$	9.17734e10	0.177242	0.0886211	+	0.996065i	$0.471754\pi$
$402$	−2.35836e12	−4.50394
$403$	6.14990e10	0.116144
$404$	6.66187e11	1.24417
$405$	3.37908e10	0.0624095
$406$	1.85698e11	0.339188
$407$	−5.76929e11	−1.04219
$408$	1.21610e12	2.17270
$409$	3.83284e11	0.677276	0.338638	−	0.940917i	$-0.390034\pi$
$409$	3.83284e11	0.677276	0.338638	+	0.940917i	$0.390034\pi$
$410$	4.13355e10	0.0722430
$411$	7.64749e11	1.32200
$412$	−4.85279e11	−0.829764
$413$	−2.53289e11	−0.428392
$414$	1.99222e12	3.33301
$415$	−7.09971e10	−0.117496
$416$	1.95308e11	0.319742
$417$	1.22836e12	1.98935
$418$	−1.20506e12	−1.93071
$419$	−1.50550e11	−0.238625	−0.119313	−	0.992857i	$-0.538069\pi$
$419$	−1.50550e11	−0.238625	−0.119313	+	0.992857i	$0.538069\pi$
$420$	1.87618e11	0.294207
$421$	1.08971e12	1.69061	0.845303	−	0.534287i	$-0.179420\pi$
$421$	1.08971e12	1.69061	0.845303	+	0.534287i	$0.179420\pi$
$422$	9.78421e11	1.50183
$423$	−1.53756e11	−0.233507
$424$	−1.47395e11	−0.221480
$425$	9.64914e11	1.43463
$426$	−2.74248e12	−4.03459
$427$	1.23766e9	0.00180167
$428$	2.90915e11	0.419053
$429$	−2.44657e11	−0.348738
$430$	5.18926e11	0.731976
$431$	−4.54924e11	−0.635025	−0.317512	−	0.948254i	$-0.602848\pi$
$431$	−4.54924e11	−0.635025	−0.317512	+	0.948254i	$0.602848\pi$
$432$	−1.69372e11	−0.233973
$433$	−8.89329e11	−1.21581	−0.607906	−	0.794009i	$-0.707990\pi$
$433$	−8.89329e11	−1.21581	−0.607906	+	0.794009i	$0.707990\pi$
$434$	−1.85843e11	−0.251444
$435$	−2.15504e11	−0.288572
$436$	1.27030e12	1.68352
$437$	1.49156e12	1.95648
$438$	1.55330e12	2.01661
$439$	−1.19486e12	−1.53541	−0.767707	−	0.640801i	$-0.778602\pi$
$439$	−1.19486e12	−1.53541	−0.767707	+	0.640801i	$0.778602\pi$
$440$	1.55364e11	0.197612
$441$	1.93412e11	0.243506
$442$	5.61380e11	0.699612
$443$	7.07379e11	0.872640	0.436320	−	0.899791i	$-0.356282\pi$
$443$	7.07379e11	0.872640	0.436320	+	0.899791i	$0.356282\pi$
$444$	2.79709e12	3.41573
$445$	−3.57895e11	−0.432648
$446$	−1.37148e12	−1.64128
$447$	−7.27938e11	−0.862404
$448$	−5.25122e11	−0.615898
$449$	−1.52186e12	−1.76712	−0.883558	−	0.468322i	$-0.844859\pi$
$449$	−1.52186e12	−1.76712	−0.883558	+	0.468322i	$0.844859\pi$
$450$	2.12823e12	2.44660
$451$	9.83446e10	0.111932
$452$	−1.98369e12	−2.23537
$453$	−3.84951e11	−0.429500
$454$	9.48719e11	1.04806
$455$	2.97695e10	0.0325627
$456$	2.00819e12	2.17502
$457$	4.30973e11	0.462197	0.231098	−	0.972930i	$-0.425768\pi$
$457$	4.30973e11	0.462197	0.231098	+	0.972930i	$0.425768\pi$
$458$	−1.84886e12	−1.96340
$459$	−1.74950e12	−1.83974
$460$	−5.59463e11	−0.582587
$461$	−3.63737e11	−0.375088	−0.187544	−	0.982256i	$-0.560053\pi$
$461$	−3.63737e11	−0.375088	−0.187544	+	0.982256i	$0.560053\pi$
$462$	7.39323e11	0.754997
$463$	1.70614e12	1.72544	0.862721	−	0.505681i	$-0.168759\pi$
$463$	1.70614e12	1.72544	0.862721	+	0.505681i	$0.168759\pi$
$464$	1.13897e11	0.114072
$465$	2.15672e11	0.213922
$466$	2.19503e12	2.15628
$467$	−8.23780e11	−0.801466	−0.400733	−	0.916195i	$-0.631245\pi$
$467$	−8.23780e11	−0.801466	−0.400733	+	0.916195i	$0.631245\pi$
$468$	7.47576e11	0.720359
$469$	6.82735e11	0.651590
$470$	7.15151e10	0.0676017
$471$	8.90117e11	0.833399
$472$	1.01690e12	0.943057
$473$	1.23462e12	1.13412
$474$	−3.81889e12	−3.47484
$475$	1.59339e12	1.43616
$476$	−1.02424e12	−0.914472
$477$	5.13012e11	0.453728
$478$	2.66448e12	2.33447
$479$	1.33355e12	1.15744	0.578722	−	0.815525i	$-0.303552\pi$
$479$	1.33355e12	1.15744	0.578722	+	0.815525i	$0.303552\pi$
$480$	6.84929e11	0.588925
$481$	4.43817e11	0.378052
$482$	−8.08098e11	−0.681950
$483$	−9.15094e11	−0.765074
$484$	−7.64183e11	−0.632985
$485$	−2.72193e11	−0.223377
$486$	1.61823e12	1.31576
$487$	−3.46476e11	−0.279121	−0.139560	−	0.990214i	$-0.544569\pi$
$487$	−3.46476e11	−0.279121	−0.139560	+	0.990214i	$0.544569\pi$
$488$	−4.96890e9	−0.00396617
$489$	2.64961e12	2.09552
$490$	−8.99598e10	−0.0704963
$491$	2.15900e12	1.67643	0.838216	−	0.545338i	$-0.183599\pi$
$491$	2.15900e12	1.67643	0.838216	+	0.545338i	$0.183599\pi$
$492$	−4.76798e11	−0.366853
$493$	1.17648e12	0.896958
$494$	9.27025e11	0.700358
$495$	−5.40750e11	−0.404830
$496$	−1.13985e11	−0.0845632
$497$	7.93935e11	0.583689
$498$	1.35639e12	0.988218
$499$	−1.08273e12	−0.781749	−0.390875	−	0.920444i	$-0.627827\pi$
$499$	−1.08273e12	−0.781749	−0.390875	+	0.920444i	$0.627827\pi$
$500$	−1.25914e12	−0.900969
$501$	−3.44715e12	−2.44450
$502$	9.10203e11	0.639693
$503$	−2.04294e12	−1.42298	−0.711492	−	0.702694i	$-0.751980\pi$
$503$	−2.04294e12	−1.42298	−0.711492	+	0.702694i	$0.751980\pi$
$504$	−7.76502e11	−0.536050
$505$	3.70697e11	0.253634
$506$	−2.20461e12	−1.49504
$507$	1.88208e11	0.126504
$508$	−2.25186e12	−1.50022
$509$	−2.96107e12	−1.95533	−0.977663	−	0.210178i	$-0.932596\pi$
$509$	−2.96107e12	−1.95533	−0.977663	+	0.210178i	$0.932596\pi$
$510$	1.96871e12	1.28860
$511$	−4.49674e11	−0.291745
$512$	−6.23255e11	−0.400822
$513$	−2.88901e12	−1.84171
$514$	2.62629e12	1.65962
$515$	−2.70032e11	−0.169154
$516$	−5.98572e12	−3.71700
$517$	1.70147e11	0.104741
$518$	−1.34116e12	−0.818459
$519$	1.26114e12	0.762974
$520$	−1.19518e11	−0.0716831
$521$	−5.60548e11	−0.333306	−0.166653	−	0.986016i	$-0.553296\pi$
$521$	−5.60548e11	−0.333306	−0.166653	+	0.986016i	$0.553296\pi$
$522$	2.59486e12	1.52967
$523$	2.85263e12	1.66720	0.833599	−	0.552370i	$-0.186276\pi$
$523$	2.85263e12	1.66720	0.833599	+	0.552370i	$0.186276\pi$
$524$	−2.19371e12	−1.27113
$525$	−9.77569e11	−0.561604
$526$	−4.10099e12	−2.33589
$527$	−1.17739e12	−0.664925
$528$	4.53459e11	0.253913
$529$	9.27591e11	0.514998
$530$	−2.38613e11	−0.131357
$531$	−3.53935e12	−1.93196
$532$	−1.69136e12	−0.915448
$533$	−7.56540e10	−0.0406031
$534$	6.83753e12	3.63884
$535$	1.61878e11	0.0854273
$536$	−2.74102e12	−1.43440
$537$	5.13047e12	2.66240
$538$	5.32866e11	0.274219
$539$	−2.14031e11	−0.109226
$540$	1.08362e12	0.548411
$541$	−3.07722e12	−1.54444	−0.772220	−	0.635355i	$-0.780854\pi$
$541$	−3.07722e12	−1.54444	−0.772220	+	0.635355i	$0.780854\pi$
$542$	9.31253e11	0.463522
$543$	−9.71676e11	−0.479648
$544$	−3.73915e12	−1.83053
$545$	7.06855e11	0.343199
$546$	−5.68743e11	−0.273873
$547$	−2.99830e12	−1.43196	−0.715982	−	0.698119i	$-0.754021\pi$
$547$	−2.99830e12	−1.43196	−0.715982	+	0.698119i	$0.754021\pi$
$548$	2.58589e12	1.22489
$549$	1.72944e10	0.00812514
$550$	−2.35512e12	−1.09744
$551$	1.94275e12	0.897915
$552$	3.67389e12	1.68422
$553$	1.10555e12	0.502708
$554$	1.33126e12	0.600440
$555$	1.55643e12	0.696323
$556$	4.15351e12	1.84323
$557$	2.77410e12	1.22116	0.610581	−	0.791954i	$-0.290936\pi$
$557$	2.77410e12	1.22116	0.610581	+	0.791954i	$0.290936\pi$
$558$	−2.59688e12	−1.13396
$559$	−9.49761e11	−0.411397
$560$	−5.51763e10	−0.0237086
$561$	4.68392e12	1.99653
$562$	2.99583e12	1.26679
$563$	−6.92492e11	−0.290487	−0.145244	−	0.989396i	$-0.546397\pi$
$563$	−6.92492e11	−0.290487	−0.145244	+	0.989396i	$0.546397\pi$
$564$	−8.24915e11	−0.343284
$565$	−1.10381e12	−0.455699
$566$	3.67720e12	1.50606
$567$	1.86889e11	0.0759383
$568$	−3.18746e12	−1.28492
$569$	4.26105e11	0.170417	0.0852083	−	0.996363i	$-0.472844\pi$
$569$	4.26105e11	0.170417	0.0852083	+	0.996363i	$0.472844\pi$
$570$	3.25100e12	1.28997
$571$	−3.57448e12	−1.40718	−0.703591	−	0.710605i	$-0.748421\pi$
$571$	−3.57448e12	−1.40718	−0.703591	+	0.710605i	$0.748421\pi$
$572$	−8.27273e11	−0.323122
$573$	2.57008e12	0.995982
$574$	2.28617e11	0.0879033
$575$	2.91504e12	1.11209
$576$	−7.33780e12	−2.77757
$577$	−3.13230e12	−1.17645	−0.588224	−	0.808698i	$-0.700173\pi$
$577$	−3.13230e12	−1.17645	−0.588224	+	0.808698i	$0.700173\pi$
$578$	−6.48472e12	−2.41666
$579$	6.73156e12	2.48922
$580$	−7.28698e11	−0.267375
$581$	−3.92669e11	−0.142966
$582$	5.20021e12	1.87874
$583$	−5.67703e11	−0.203523
$584$	1.80533e12	0.642244
$585$	4.15985e11	0.146851
$586$	−1.59808e12	−0.559834
$587$	7.18927e11	0.249927	0.124963	−	0.992161i	$-0.460119\pi$
$587$	7.18927e11	0.249927	0.124963	+	0.992161i	$0.460119\pi$
$588$	1.03767e12	0.357983
$589$	−1.94426e12	−0.665635
$590$	1.64623e12	0.559313
$591$	−6.15861e12	−2.07653
$592$	−8.22592e11	−0.275256
$593$	4.09447e12	1.35973	0.679864	−	0.733339i	$-0.262039\pi$
$593$	4.09447e12	1.35973	0.679864	+	0.733339i	$0.262039\pi$
$594$	4.27010e12	1.40734
$595$	−5.69933e11	−0.186422
$596$	−2.46142e12	−0.799057
$597$	4.81586e12	1.55163
$598$	1.69595e12	0.542322
$599$	−9.86003e11	−0.312938	−0.156469	−	0.987683i	$-0.550011\pi$
$599$	−9.86003e11	−0.312938	−0.156469	+	0.987683i	$0.550011\pi$
$600$	3.92471e12	1.23631
$601$	3.62685e12	1.13395	0.566976	−	0.823735i	$-0.308113\pi$
$601$	3.62685e12	1.13395	0.566976	+	0.823735i	$0.308113\pi$
$602$	2.87006e12	0.890650
$603$	9.54021e12	2.93853
$604$	−1.30166e12	−0.397952
$605$	−4.25226e11	−0.129039
$606$	−7.08212e12	−2.13322
$607$	3.76025e12	1.12426	0.562131	−	0.827048i	$-0.309982\pi$
$607$	3.76025e12	1.12426	0.562131	+	0.827048i	$0.309982\pi$
$608$	−6.17457e12	−1.83249
$609$	−1.19191e12	−0.351127
$610$	−8.04401e9	−0.00235228
$611$	−1.30890e11	−0.0379945
$612$	−1.43122e13	−4.12407
$613$	−2.13878e12	−0.611780	−0.305890	−	0.952067i	$-0.598954\pi$
$613$	−2.13878e12	−0.611780	−0.305890	+	0.952067i	$0.598954\pi$
$614$	−1.78440e12	−0.506681
$615$	−2.65312e11	−0.0747858
$616$	8.59283e11	0.240449
$617$	2.69179e12	0.747752	0.373876	−	0.927479i	$-0.378028\pi$
$617$	2.69179e12	0.747752	0.373876	+	0.927479i	$0.378028\pi$
$618$	5.15892e12	1.42269
$619$	−7.17858e11	−0.196531	−0.0982654	−	0.995160i	$-0.531329\pi$
$619$	−7.17858e11	−0.196531	−0.0982654	+	0.995160i	$0.531329\pi$
$620$	7.29264e11	0.198208
$621$	−5.28530e12	−1.42613
$622$	−5.86019e11	−0.156984
$623$	−1.97943e12	−0.526435
$624$	−3.48835e11	−0.0921062
$625$	2.74597e12	0.719840
$626$	−1.10578e12	−0.287796
$627$	7.73471e12	1.99867
$628$	3.00981e12	0.772183
$629$	−8.49682e12	−2.16435
$630$	−1.25706e12	−0.317923
$631$	−4.59827e12	−1.15468	−0.577341	−	0.816503i	$-0.695910\pi$
$631$	−4.59827e12	−1.15468	−0.577341	+	0.816503i	$0.695910\pi$
$632$	−4.43853e12	−1.10665
$633$	−6.28000e12	−1.55469
$634$	−2.15705e11	−0.0530223
$635$	−1.25304e12	−0.305832
$636$	2.75236e12	0.667035
$637$	1.64648e11	0.0396214
$638$	−2.87149e12	−0.686143
$639$	1.10941e13	2.63231
$640$	1.89304e12	0.446016
$641$	−5.40351e12	−1.26420	−0.632099	−	0.774888i	$-0.717806\pi$
$641$	−5.40351e12	−1.26420	−0.632099	+	0.774888i	$0.717806\pi$
$642$	−3.09266e12	−0.718497
$643$	2.49434e12	0.575449	0.287724	−	0.957713i	$-0.407101\pi$
$643$	2.49434e12	0.575449	0.287724	+	0.957713i	$0.407101\pi$
$644$	−3.09426e12	−0.708877
$645$	−3.33073e12	−0.757741
$646$	−1.77478e13	−4.00957
$647$	7.00912e12	1.57251	0.786257	−	0.617900i	$-0.212016\pi$
$647$	7.00912e12	1.57251	0.786257	+	0.617900i	$0.212016\pi$
$648$	−7.50316e11	−0.167169
$649$	3.91667e12	0.866594
$650$	1.81173e12	0.398093
$651$	1.19283e12	0.260294
$652$	8.95928e12	1.94160
$653$	6.91176e12	1.48758	0.743788	−	0.668416i	$-0.233027\pi$
$653$	6.91176e12	1.48758	0.743788	+	0.668416i	$0.233027\pi$
$654$	−1.35044e13	−2.88652
$655$	−1.22068e12	−0.259129
$656$	1.40221e11	0.0295628
$657$	−6.28353e12	−1.31571
$658$	3.95534e11	0.0822559
$659$	2.27667e12	0.470236	0.235118	−	0.971967i	$-0.424452\pi$
$659$	2.27667e12	0.470236	0.235118	+	0.971967i	$0.424452\pi$
$660$	−2.90118e12	−0.595150
$661$	2.29883e12	0.468383	0.234191	−	0.972190i	$-0.424756\pi$
$661$	2.29883e12	0.468383	0.234191	+	0.972190i	$0.424756\pi$
$662$	9.91004e12	2.00546
$663$	−3.60323e12	−0.724237
$664$	1.57647e12	0.314724
$665$	−9.41149e11	−0.186621
$666$	−1.87407e13	−3.69108
$667$	3.55418e12	0.695301
$668$	−1.16560e13	−2.26494
$669$	8.80283e12	1.69905
$670$	−4.43736e12	−0.850722
$671$	−1.91382e10	−0.00364459
$672$	3.78819e12	0.716588
$673$	−5.78650e12	−1.08730	−0.543649	−	0.839313i	$-0.682958\pi$
$673$	−5.78650e12	−1.08730	−0.543649	+	0.839313i	$0.682958\pi$
$674$	5.02005e12	0.936998
$675$	−5.64614e12	−1.04685
$676$	6.36400e11	0.117212
$677$	8.97926e12	1.64283	0.821413	−	0.570334i	$-0.193186\pi$
$677$	8.97926e12	1.64283	0.821413	+	0.570334i	$0.193186\pi$
$678$	2.10882e13	3.83271
$679$	−1.50544e12	−0.271799
$680$	2.28815e12	0.410387
$681$	−6.08936e12	−1.08495
$682$	2.87372e12	0.508645
$683$	1.01954e13	1.79272	0.896358	−	0.443331i	$-0.146203\pi$
$683$	1.01954e13	1.79272	0.896358	+	0.443331i	$0.146203\pi$
$684$	−2.36342e13	−4.12847
$685$	1.43891e12	0.249704
$686$	−4.97548e11	−0.0857780
$687$	1.18669e13	2.03251
$688$	1.76033e12	0.299534
$689$	4.36720e11	0.0738272
$690$	5.94755e12	0.998889
$691$	2.79110e12	0.465720	0.232860	−	0.972510i	$-0.425192\pi$
$691$	2.79110e12	0.465720	0.232860	+	0.972510i	$0.425192\pi$
$692$	4.26436e12	0.706930
$693$	−2.99076e12	−0.492587
$694$	1.78429e13	2.91976
$695$	2.31120e12	0.375757
$696$	4.78522e12	0.772966
$697$	1.44839e12	0.232454
$698$	−1.56092e13	−2.48903
$699$	−1.40888e13	−2.23217
$700$	−3.30551e12	−0.520352
$701$	−2.22264e12	−0.347647	−0.173824	−	0.984777i	$-0.555612\pi$
$701$	−2.22264e12	−0.347647	−0.173824	+	0.984777i	$0.555612\pi$
$702$	−3.28488e12	−0.510509
$703$	−1.40311e13	−2.16666
$704$	8.12007e12	1.24590
$705$	−4.59020e11	−0.0699811
$706$	−1.99564e13	−3.02315
$707$	2.05024e12	0.308615
$708$	−1.89889e13	−2.84021
$709$	−6.86568e12	−1.02041	−0.510206	−	0.860052i	$-0.670431\pi$
$709$	−6.86568e12	−1.02041	−0.510206	+	0.860052i	$0.670431\pi$
$710$	−5.16009e12	−0.762069
$711$	1.54485e13	2.26711
$712$	7.94696e12	1.15889
$713$	−3.55694e12	−0.515434
$714$	1.08885e13	1.56793
$715$	−4.60332e11	−0.0658710
$716$	1.73480e13	2.46683
$717$	−1.71020e13	−2.41663
$718$	−6.57550e12	−0.923355
$719$	1.08604e13	1.51553	0.757766	−	0.652526i	$-0.226291\pi$
$719$	1.08604e13	1.51553	0.757766	+	0.652526i	$0.226291\pi$
$720$	−7.71007e11	−0.106921
$721$	−1.49348e12	−0.205822
$722$	−1.77079e13	−2.42521
$723$	5.18679e12	0.705953
$724$	−3.28559e12	−0.444416
$725$	3.79683e12	0.510387
$726$	8.12389e12	1.08530
$727$	1.18416e13	1.57220	0.786098	−	0.618102i	$-0.212098\pi$
$727$	1.18416e13	1.57220	0.786098	+	0.618102i	$0.212098\pi$
$728$	−6.61025e11	−0.0872221
$729$	−1.19187e13	−1.56299
$730$	2.92260e12	0.380905
$731$	1.81830e13	2.35526
$732$	9.27864e10	0.0119449
$733$	5.16125e12	0.660369	0.330184	−	0.943916i	$-0.392889\pi$
$733$	5.16125e12	0.660369	0.330184	+	0.943916i	$0.392889\pi$
$734$	6.62192e12	0.842077
$735$	5.77408e11	0.0729776
$736$	−1.12961e13	−1.41899
$737$	−1.05573e13	−1.31810
$738$	3.19459e12	0.396425
$739$	−9.11730e12	−1.12452	−0.562259	−	0.826961i	$-0.690068\pi$
$739$	−9.11730e12	−1.12452	−0.562259	+	0.826961i	$0.690068\pi$
$740$	5.26284e12	0.645175
$741$	−5.95012e12	−0.725010
$742$	−1.31971e12	−0.159832
$743$	−1.58640e12	−0.190969	−0.0954843	−	0.995431i	$-0.530440\pi$
$743$	−1.58640e12	−0.190969	−0.0954843	+	0.995431i	$0.530440\pi$
$744$	−4.78894e12	−0.573008
$745$	−1.36965e12	−0.162894
$746$	−1.46765e12	−0.173499
$747$	−5.48697e12	−0.644748
$748$	1.58380e13	1.84988
$749$	8.95312e11	0.103946
$750$	1.33857e13	1.54478
$751$	1.04973e13	1.20420	0.602100	−	0.798420i	$-0.294331\pi$
$751$	1.04973e13	1.20420	0.602100	+	0.798420i	$0.294331\pi$
$752$	2.42598e11	0.0276635
$753$	−5.84215e12	−0.662209
$754$	2.20897e12	0.248896
$755$	−7.24302e11	−0.0811257
$756$	5.99328e12	0.667292
$757$	5.39506e12	0.597125	0.298562	−	0.954390i	$-0.403493\pi$
$757$	5.39506e12	0.597125	0.298562	+	0.954390i	$0.403493\pi$
$758$	6.35179e12	0.698851
$759$	1.41503e13	1.54767
$760$	3.77849e12	0.410825
$761$	3.08992e12	0.333977	0.166988	−	0.985959i	$-0.446596\pi$
$761$	3.08992e12	0.333977	0.166988	+	0.985959i	$0.446596\pi$
$762$	2.39392e13	2.57224
$763$	3.90945e12	0.417595
$764$	8.69038e12	0.922823
$765$	−7.96398e12	−0.840724
$766$	2.73196e13	2.86711
$767$	−3.01299e12	−0.314354
$768$	−1.03300e13	−1.07146
$769$	−1.64177e13	−1.69295	−0.846473	−	0.532432i	$-0.821278\pi$
$769$	−1.64177e13	−1.69295	−0.846473	+	0.532432i	$0.821278\pi$
$770$	1.39107e12	0.142607
$771$	−1.68569e13	−1.71804
$772$	2.27618e13	2.30637
$773$	−1.51411e13	−1.52528	−0.762640	−	0.646823i	$-0.776097\pi$
$773$	−1.51411e13	−1.52528	−0.762640	+	0.646823i	$0.776097\pi$
$774$	4.01049e13	4.01664
$775$	−3.79977e12	−0.378356
$776$	6.04397e12	0.598335
$777$	8.60825e12	0.847267
$778$	−1.29377e12	−0.126604
$779$	2.39177e12	0.232702
$780$	2.23180e12	0.215889
$781$	−1.22768e13	−1.18074
$782$	−3.24687e13	−3.10481
$783$	−6.88408e12	−0.654513
$784$	−3.05167e11	−0.0288480
$785$	1.67479e12	0.157416
$786$	2.33210e13	2.17944
$787$	−1.10748e13	−1.02908	−0.514542	−	0.857465i	$-0.672038\pi$
$787$	−1.10748e13	−1.02908	−0.514542	+	0.857465i	$0.672038\pi$
$788$	−2.08245e13	−1.92400
$789$	2.63223e13	2.41811
$790$	−7.18540e12	−0.656341
$791$	−6.10494e12	−0.554482
$792$	1.20072e13	1.08437
$793$	1.47225e10	0.00132206
$794$	2.10509e13	1.87966
$795$	1.53154e12	0.135980
$796$	1.62841e13	1.43766
$797$	−1.41284e13	−1.24032	−0.620158	−	0.784477i	$-0.712931\pi$
$797$	−1.41284e13	−1.24032	−0.620158	+	0.784477i	$0.712931\pi$
$798$	1.79805e13	1.56960
$799$	2.50587e12	0.217520
$800$	−1.20673e13	−1.04161
$801$	−2.76597e13	−2.37411
$802$	−3.29894e12	−0.281573
$803$	6.95340e12	0.590171
$804$	5.11842e13	4.32000
$805$	−1.72179e12	−0.144510
$806$	−2.21068e12	−0.184510
$807$	−3.42020e12	−0.283871
$808$	−8.23123e12	−0.679382
$809$	−1.45772e13	−1.19648	−0.598239	−	0.801317i	$-0.704133\pi$
$809$	−1.45772e13	−1.19648	−0.598239	+	0.801317i	$0.704133\pi$
$810$	−1.21467e12	−0.0991457
$811$	8.28702e12	0.672674	0.336337	−	0.941742i	$-0.390812\pi$
$811$	8.28702e12	0.672674	0.336337	+	0.941742i	$0.390812\pi$
$812$	−4.03026e12	−0.325335
$813$	−5.97725e12	−0.479838
$814$	2.07387e13	1.65566
$815$	4.98535e12	0.395810
$816$	6.67839e12	0.527310
$817$	3.00262e13	2.35777
$818$	−1.37778e13	−1.07594
$819$	2.30072e12	0.178684
$820$	−8.97116e11	−0.0692925
$821$	−1.34592e13	−1.03389	−0.516944	−	0.856019i	$-0.672931\pi$
$821$	−1.34592e13	−1.03389	−0.516944	+	0.856019i	$0.672931\pi$
$822$	−2.74902e13	−2.10017
$823$	−1.12252e13	−0.852892	−0.426446	−	0.904513i	$-0.640235\pi$
$823$	−1.12252e13	−0.852892	−0.426446	+	0.904513i	$0.640235\pi$
$824$	5.99598e12	0.453094
$825$	1.51164e13	1.13607
$826$	9.10490e12	0.680558
$827$	1.18754e13	0.882821	0.441411	−	0.897305i	$-0.354478\pi$
$827$	1.18754e13	0.882821	0.441411	+	0.897305i	$0.354478\pi$
$828$	−4.32378e13	−3.19688
$829$	1.79748e13	1.32181	0.660903	−	0.750471i	$-0.270173\pi$
$829$	1.79748e13	1.32181	0.660903	+	0.750471i	$0.270173\pi$
$830$	2.55211e12	0.186658
$831$	−8.54472e12	−0.621574
$832$	−6.24657e12	−0.451946
$833$	−3.15217e12	−0.226834
$834$	−4.41553e13	−3.16035
$835$	−6.48595e12	−0.461726
$836$	2.61538e13	1.85186
$837$	6.88943e12	0.485198
$838$	5.41175e12	0.379088
$839$	−1.21225e13	−0.844623	−0.422312	−	0.906451i	$-0.638781\pi$
$839$	−1.21225e13	−0.844623	−0.422312	+	0.906451i	$0.638781\pi$
$840$	−2.31816e12	−0.160652
$841$	−9.87785e12	−0.680895
$842$	−3.91715e13	−2.68575
$843$	−1.92288e13	−1.31138
$844$	−2.12349e13	−1.44049
$845$	3.54122e11	0.0238945
$846$	5.52700e12	0.370957
$847$	−2.35183e12	−0.157011
$848$	−8.09438e11	−0.0537529
$849$	−2.36021e13	−1.55907
$850$	−3.46854e13	−2.27909
$851$	−2.56692e13	−1.67776
$852$	5.95208e13	3.86982
$853$	−1.99327e13	−1.28913	−0.644564	−	0.764550i	$-0.722961\pi$
$853$	−1.99327e13	−1.28913	−0.644564	+	0.764550i	$0.722961\pi$
$854$	−4.44896e10	−0.00286219
$855$	−1.31512e13	−0.841622
$856$	−3.59447e12	−0.228824
$857$	−1.82579e13	−1.15621	−0.578107	−	0.815961i	$-0.696208\pi$
$857$	−1.82579e13	−1.15621	−0.578107	+	0.815961i	$0.696208\pi$
$858$	8.79459e12	0.554017
$859$	−6.62180e12	−0.414961	−0.207480	−	0.978239i	$-0.566526\pi$
$859$	−6.62180e12	−0.414961	−0.207480	+	0.978239i	$0.566526\pi$
$860$	−1.12624e13	−0.702082
$861$	−1.46738e12	−0.0909974
$862$	1.63530e13	1.00882
$863$	2.17631e12	0.133559	0.0667794	−	0.997768i	$-0.478728\pi$
$863$	2.17631e12	0.133559	0.0667794	+	0.997768i	$0.478728\pi$
$864$	2.18794e13	1.33574
$865$	2.37288e12	0.144113
$866$	3.19684e13	1.93148
$867$	4.16222e13	2.50172
$868$	4.03339e12	0.241175
$869$	−1.70954e13	−1.01693
$870$	7.74666e12	0.458435
$871$	8.12144e12	0.478136
$872$	−1.56955e13	−0.919288
$873$	−2.10363e13	−1.22576
$874$	−5.36166e13	−3.10812
$875$	−3.87511e12	−0.223484
$876$	−3.37118e13	−1.93425
$877$	−1.95150e12	−0.111396	−0.0556981	−	0.998448i	$-0.517738\pi$
$877$	−1.95150e12	−0.111396	−0.0556981	+	0.998448i	$0.517738\pi$
$878$	4.29511e13	2.43921
$879$	1.02573e13	0.579539
$880$	8.53202e11	0.0479601
$881$	−1.04264e12	−0.0583102	−0.0291551	−	0.999575i	$-0.509282\pi$
$881$	−1.04264e12	−0.0583102	−0.0291551	+	0.999575i	$0.509282\pi$
$882$	−6.95249e12	−0.386841
$883$	1.82714e13	1.01146	0.505730	−	0.862692i	$-0.331223\pi$
$883$	1.82714e13	1.01146	0.505730	+	0.862692i	$0.331223\pi$
$884$	−1.21838e13	−0.671039
$885$	−1.05663e13	−0.579000
$886$	−2.54279e13	−1.38630
$887$	−2.54434e13	−1.38012	−0.690062	−	0.723750i	$-0.742417\pi$
$887$	−2.54434e13	−1.38012	−0.690062	+	0.723750i	$0.742417\pi$
$888$	−3.45601e13	−1.86516
$889$	−6.93028e12	−0.372128
$890$	1.28651e13	0.687319
$891$	−2.88991e12	−0.153615
$892$	2.97656e13	1.57424
$893$	4.13803e12	0.217752
$894$	2.61669e13	1.37004
$895$	9.65319e12	0.502883
$896$	1.04700e13	0.542700
$897$	−1.08855e13	−0.561411
$898$	5.47056e13	2.80730
$899$	−4.63290e12	−0.236556
$900$	−4.61897e13	−2.34668
$901$	−8.36095e12	−0.422663
$902$	−3.53516e12	−0.177819
$903$	−1.84215e13	−0.921999
$904$	2.45099e13	1.22063
$905$	−1.82825e12	−0.0905976
$906$	1.38377e13	0.682318
$907$	2.68870e13	1.31920	0.659598	−	0.751618i	$-0.270726\pi$
$907$	2.68870e13	1.31920	0.659598	+	0.751618i	$0.270726\pi$
$908$	−2.05903e13	−1.00526
$909$	2.86491e13	1.39179
$910$	−1.07011e12	−0.0517301
$911$	1.32637e13	0.638015	0.319008	−	0.947752i	$-0.396650\pi$
$911$	1.32637e13	0.638015	0.319008	+	0.947752i	$0.396650\pi$
$912$	1.10282e13	0.527873
$913$	6.07192e12	0.289206
$914$	−1.54920e13	−0.734260
$915$	5.16305e10	0.00243507
$916$	4.01263e13	1.88321
$917$	−6.75131e12	−0.315302
$918$	6.28887e13	2.92267
$919$	−2.84043e13	−1.31360	−0.656801	−	0.754064i	$-0.728091\pi$
$919$	−2.84043e13	−1.31360	−0.656801	+	0.754064i	$0.728091\pi$
$920$	6.91257e12	0.318123
$921$	1.14532e13	0.524515
$922$	1.30751e13	0.595877
$923$	9.44422e12	0.428310
$924$	−1.60457e13	−0.724162
$925$	−2.74216e13	−1.23156
$926$	−6.13300e13	−2.74109
$927$	−2.08692e13	−0.928213
$928$	−1.47131e13	−0.651236
$929$	−1.41616e12	−0.0623796	−0.0311898	−	0.999513i	$-0.509930\pi$
$929$	−1.41616e12	−0.0623796	−0.0311898	+	0.999513i	$0.509930\pi$
$930$	−7.75267e12	−0.339843
$931$	−5.20528e12	−0.227076
$932$	−4.76394e13	−2.06821
$933$	3.76137e12	0.162509
$934$	2.96121e13	1.27323
$935$	8.81300e12	0.377113
$936$	−9.23685e12	−0.393353
$937$	1.36000e13	0.576381	0.288191	−	0.957573i	$-0.406946\pi$
$937$	1.36000e13	0.576381	0.288191	+	0.957573i	$0.406946\pi$
$938$	−2.45420e13	−1.03514
$939$	7.09746e12	0.297926
$940$	−1.55211e12	−0.0648407
$941$	1.71397e13	0.712606	0.356303	−	0.934370i	$-0.384037\pi$
$941$	1.71397e13	0.712606	0.356303	+	0.934370i	$0.384037\pi$
$942$	−3.19967e13	−1.32396
$943$	4.37562e12	0.180193
$944$	5.58443e12	0.228878
$945$	3.33493e12	0.136033
$946$	−4.43803e13	−1.80169
$947$	1.72767e13	0.698050	0.349025	−	0.937113i	$-0.386513\pi$
$947$	1.72767e13	0.698050	0.349025	+	0.937113i	$0.386513\pi$
$948$	8.28825e13	3.33292
$949$	−5.34908e12	−0.214082
$950$	−5.72771e13	−2.28152
$951$	1.38450e12	0.0548886
$952$	1.26552e13	0.499348
$953$	2.53499e13	0.995540	0.497770	−	0.867309i	$-0.334152\pi$
$953$	2.53499e13	0.995540	0.497770	+	0.867309i	$0.334152\pi$
$954$	−1.84411e13	−0.720806
$955$	4.83572e12	0.188125
$956$	−5.78280e13	−2.23912
$957$	1.84307e13	0.710294
$958$	−4.79367e13	−1.83875
$959$	7.95828e12	0.303833
$960$	−2.19062e13	−0.832427
$961$	−2.18031e13	−0.824638
$962$	−1.59537e13	−0.600585
$963$	1.25107e13	0.468773
$964$	1.75384e13	0.654098
$965$	1.26657e13	0.470172
$966$	3.28945e13	1.21542
$967$	9.19232e12	0.338069	0.169035	−	0.985610i	$-0.445935\pi$
$967$	9.19232e12	0.338069	0.169035	+	0.985610i	$0.445935\pi$
$968$	9.44204e12	0.345642
$969$	1.13914e14	4.15070
$970$	9.78441e12	0.354864
$971$	−2.88697e13	−1.04221	−0.521106	−	0.853492i	$-0.674480\pi$
$971$	−2.88697e13	−1.04221	−0.521106	+	0.853492i	$0.674480\pi$
$972$	−3.51209e13	−1.26202
$973$	1.27827e13	0.457211
$974$	1.24546e13	0.443420
$975$	−1.16286e13	−0.412105
$976$	−2.72874e10	−0.000962582 0
$977$	−1.03809e13	−0.364511	−0.182255	−	0.983251i	$-0.558340\pi$
$977$	−1.03809e13	−0.364511	−0.182255	+	0.983251i	$0.558340\pi$
$978$	−9.52445e13	−3.32901
$979$	3.06084e13	1.06492
$980$	1.95242e12	0.0676172
$981$	5.46288e13	1.88327
$982$	−7.76088e13	−2.66323
$983$	−7.46537e12	−0.255012	−0.127506	−	0.991838i	$-0.540697\pi$
$983$	−7.46537e12	−0.255012	−0.127506	+	0.991838i	$0.540697\pi$
$984$	5.89119e12	0.200320
$985$	−1.15877e13	−0.392223
$986$	−4.22904e13	−1.42494
$987$	−2.53874e12	−0.0851512
$988$	−2.01195e13	−0.671755
$989$	5.49316e13	1.82574
$990$	1.94381e13	0.643126
$991$	1.19731e13	0.394345	0.197173	−	0.980369i	$-0.436824\pi$
$991$	1.19731e13	0.394345	0.197173	+	0.980369i	$0.436824\pi$
$992$	1.47245e13	0.482769
$993$	−6.36077e13	−2.07605
$994$	−2.85393e13	−0.927266
$995$	9.06124e12	0.293078
$996$	−2.94381e13	−0.947858
$997$	3.43494e12	0.110101	0.0550504	−	0.998484i	$-0.482468\pi$
$997$	3.43494e12	0.110101	0.0550504	+	0.998484i	$0.482468\pi$
$998$	3.89205e13	1.24191
$999$	4.97186e13	1.57934

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.a.1.3	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.a.1.3	✓	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)

\(f(q)\)	\(=\)	\(q-35.9466 q^{2} +230.724 q^{3} +780.160 q^{4} +434.116 q^{5} -8293.74 q^{6} +2401.00 q^{7} -9639.45 q^{8} +33550.4 q^{9} +O(q^{10})\)	\(q-35.9466 q^{2} +230.724 q^{3} +780.160 q^{4} +434.116 q^{5} -8293.74 q^{6} +2401.00 q^{7} -9639.45 q^{8} +33550.4 q^{9} -15605.0 q^{10} -37127.2 q^{11} +180001. q^{12} +28561.0 q^{13} -86307.9 q^{14} +100161. q^{15} -52936.3 q^{16} -546796. q^{17} -1.20603e6 q^{18} -902942. q^{19} +338680. q^{20} +553968. q^{21} +1.33460e6 q^{22} -1.65189e6 q^{23} -2.22405e6 q^{24} -1.76467e6 q^{25} -1.02667e6 q^{26} +3.19955e6 q^{27} +1.87316e6 q^{28} -2.15158e6 q^{29} -3.60045e6 q^{30} +2.15325e6 q^{31} +6.83828e6 q^{32} -8.56612e6 q^{33} +1.96555e7 q^{34} +1.04231e6 q^{35} +2.61747e7 q^{36} +1.55393e7 q^{37} +3.24577e7 q^{38} +6.58970e6 q^{39} -4.18464e6 q^{40} -2.64886e6 q^{41} -1.99133e7 q^{42} -3.32538e7 q^{43} -2.89651e7 q^{44} +1.45648e7 q^{45} +5.93799e7 q^{46} -4.58283e6 q^{47} -1.22137e7 q^{48} +5.76480e6 q^{49} +6.34339e7 q^{50} -1.26159e8 q^{51} +2.22821e7 q^{52} +1.52908e7 q^{53} -1.15013e8 q^{54} -1.61175e7 q^{55} -2.31443e7 q^{56} -2.08330e8 q^{57} +7.73421e7 q^{58} -1.05493e8 q^{59} +7.81416e7 q^{60} +515476. q^{61} -7.74022e7 q^{62} +8.05546e7 q^{63} -2.18710e8 q^{64} +1.23988e7 q^{65} +3.07923e8 q^{66} +2.84354e8 q^{67} -4.26589e8 q^{68} -3.81130e8 q^{69} -3.74677e7 q^{70} +3.30668e8 q^{71} -3.23408e8 q^{72} -1.87286e8 q^{73} -5.58584e8 q^{74} -4.07151e8 q^{75} -7.04439e8 q^{76} -8.91423e7 q^{77} -2.36877e8 q^{78} +4.60455e8 q^{79} -2.29805e7 q^{80} +7.78381e7 q^{81} +9.52175e7 q^{82} -1.63544e8 q^{83} +4.32183e8 q^{84} -2.37373e8 q^{85} +1.19536e9 q^{86} -4.96421e8 q^{87} +3.57885e8 q^{88} -8.24421e8 q^{89} -5.23555e8 q^{90} +6.85750e7 q^{91} -1.28874e9 q^{92} +4.96806e8 q^{93} +1.64737e8 q^{94} -3.91982e8 q^{95} +1.57775e9 q^{96} -6.27004e8 q^{97} -2.07225e8 q^{98} -1.24563e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 21 q^{2} - 323 q^{3} + 2945 q^{4} - 5202 q^{5} - 9897 q^{6} + 28812 q^{7} - 25431 q^{8} + 78519 q^{9}+O(q^{10}) \) 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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