LMFDB - Embedded newform 91.10.a.d.1.15

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:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 7 x^{14} - 7002 x^{13} + 56252 x^{12} + 19365525 x^{11} - 172593791 x^{10} + \cdots + 15\!\cdots\!80 $ x^15 - 7x^14 - 7002x^13 + 56252x^12 + 19365525x^11 - 172593791x^10 - 26814463634x^9 + 254652735184x^8 + 19468686934379x^7 - 187275922162581x^6 - 7114485342885046x^5 + 65109704629514532x^4 + 1131832063959701151x^3 - 8977247355614269573x^2 - 47004259937698392062x + 152144189066892720880
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{13}\cdot 3^{6} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Root			$44.2074$ 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)

$f(q)$	$=$	$q+45.2074 q^{2} +261.874 q^{3} +1531.71 q^{4} -1682.03 q^{5} +11838.6 q^{6} -2401.00 q^{7} +46098.2 q^{8} +48894.9 q^{9} +O(q^{10})$	\(q+45.2074 q^{2} +261.874 q^{3} +1531.71 q^{4} -1682.03 q^{5} +11838.6 q^{6} -2401.00 q^{7} +46098.2 q^{8} +48894.9 q^{9} -76040.1 q^{10} -2595.99 q^{11} +401114. q^{12} +28561.0 q^{13} -108543. q^{14} -440479. q^{15} +1.29975e6 q^{16} -274656. q^{17} +2.21041e6 q^{18} -711453. q^{19} -2.57637e6 q^{20} -628759. q^{21} -117358. q^{22} +484103. q^{23} +1.20719e7 q^{24} +876094. q^{25} +1.29117e6 q^{26} +7.64984e6 q^{27} -3.67763e6 q^{28} +91376.3 q^{29} -1.99129e7 q^{30} -1.75488e6 q^{31} +3.51558e7 q^{32} -679822. q^{33} -1.24165e7 q^{34} +4.03855e6 q^{35} +7.48926e7 q^{36} -1.89306e6 q^{37} -3.21629e7 q^{38} +7.47938e6 q^{39} -7.75385e7 q^{40} +876544. q^{41} -2.84245e7 q^{42} -2.10803e7 q^{43} -3.97629e6 q^{44} -8.22426e7 q^{45} +2.18850e7 q^{46} -4.96753e7 q^{47} +3.40369e8 q^{48} +5.76480e6 q^{49} +3.96059e7 q^{50} -7.19253e7 q^{51} +4.37471e7 q^{52} +6.13159e7 q^{53} +3.45829e8 q^{54} +4.36653e6 q^{55} -1.10682e8 q^{56} -1.86311e8 q^{57} +4.13088e6 q^{58} -7.47874e7 q^{59} -6.74685e8 q^{60} +8.72517e7 q^{61} -7.93335e7 q^{62} -1.17397e8 q^{63} +9.23831e8 q^{64} -4.80404e7 q^{65} -3.07329e7 q^{66} -9.76501e7 q^{67} -4.20693e8 q^{68} +1.26774e8 q^{69} +1.82572e8 q^{70} -2.83745e8 q^{71} +2.25397e9 q^{72} +6.66323e7 q^{73} -8.55804e7 q^{74} +2.29426e8 q^{75} -1.08974e9 q^{76} +6.23297e6 q^{77} +3.38123e8 q^{78} -1.40119e8 q^{79} -2.18621e9 q^{80} +1.04089e9 q^{81} +3.96263e7 q^{82} -4.69517e8 q^{83} -9.63074e8 q^{84} +4.61979e8 q^{85} -9.52984e8 q^{86} +2.39291e7 q^{87} -1.19670e8 q^{88} +5.07175e8 q^{89} -3.71797e9 q^{90} -6.85750e7 q^{91} +7.41504e8 q^{92} -4.59557e8 q^{93} -2.24569e9 q^{94} +1.19668e9 q^{95} +9.20638e9 q^{96} +1.03248e9 q^{97} +2.60611e8 q^{98} -1.26931e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 22 q^{2} + q^{3} + 6402 q^{4} + 1694 q^{5} + 4189 q^{6} - 36015 q^{7} - 1704 q^{8} + 160366 q^{9}+O(q^{10}) $ 15 * q + 22 * q^2 + q^3 + 6402 * q^4 + 1694 * q^5 + 4189 * q^6 - 36015 * q^7 - 1704 * q^8 + 160366 * q^9	\( 15 q + 22 q^{2} + q^{3} + 6402 q^{4} + 1694 q^{5} + 4189 q^{6} - 36015 q^{7} - 1704 q^{8} + 160366 q^{9} - 69748 q^{10} + 23441 q^{11} + 64437 q^{12} + 428415 q^{13} - 52822 q^{14} - 68316 q^{15} + 2694730 q^{16} + 606640 q^{17} + 1242207 q^{18} + 1762528 q^{19} + 43054 q^{20} - 2401 q^{21} + 119431 q^{22} + 3649531 q^{23} + 15986883 q^{24} + 9120575 q^{25} + 628342 q^{26} - 5957633 q^{27} - 15371202 q^{28} + 18072234 q^{29} - 58091296 q^{30} - 1096937 q^{31} + 6565744 q^{32} - 18425617 q^{33} - 46741622 q^{34} - 4067294 q^{35} + 132788567 q^{36} - 34982109 q^{37} - 2819104 q^{38} + 28561 q^{39} + 2107274 q^{40} + 59341985 q^{41} - 10057789 q^{42} + 38829122 q^{43} + 202791507 q^{44} + 2955478 q^{45} + 165169119 q^{46} + 18734035 q^{47} + 340656557 q^{48} + 86472015 q^{49} + 220443888 q^{50} + 93517168 q^{51} + 182847522 q^{52} + 332415086 q^{53} + 567466451 q^{54} - 120908856 q^{55} + 4091304 q^{56} + 62932402 q^{57} + 180863580 q^{58} + 28220174 q^{59} + 467078152 q^{60} + 404536605 q^{61} + 4283245 q^{62} - 385038766 q^{63} + 1276533074 q^{64} + 48382334 q^{65} + 1696546059 q^{66} + 746448213 q^{67} + 492702034 q^{68} + 453755667 q^{69} + 167464948 q^{70} + 81316200 q^{71} + 1255645679 q^{72} + 12687907 q^{73} + 1350657501 q^{74} - 164589481 q^{75} + 679560842 q^{76} - 56281841 q^{77} + 119642029 q^{78} + 1896008477 q^{79} - 1458560390 q^{80} + 3853340295 q^{81} + 410985635 q^{82} - 753815178 q^{83} - 154713237 q^{84} - 259541636 q^{85} - 1842794378 q^{86} + 1391390932 q^{87} + 288708813 q^{88} + 1109816012 q^{89} + 1196058116 q^{90} - 1028624415 q^{91} + 2409710277 q^{92} + 3345736043 q^{93} - 1423358651 q^{94} + 4615875678 q^{95} + 11615772371 q^{96} + 1054179205 q^{97} + 126825622 q^{98} - 2512222258 q^{99}+O(q^{100}) \) 15 * q + 22 * q^2 + q^3 + 6402 * q^4 + 1694 * q^5 + 4189 * q^6 - 36015 * q^7 - 1704 * q^8 + 160366 * q^9 - 69748 * q^10 + 23441 * q^11 + 64437 * q^12 + 428415 * q^13 - 52822 * q^14 - 68316 * q^15 + 2694730 * q^16 + 606640 * q^17 + 1242207 * q^18 + 1762528 * q^19 + 43054 * q^20 - 2401 * q^21 + 119431 * q^22 + 3649531 * q^23 + 15986883 * q^24 + 9120575 * q^25 + 628342 * q^26 - 5957633 * q^27 - 15371202 * q^28 + 18072234 * q^29 - 58091296 * q^30 - 1096937 * q^31 + 6565744 * q^32 - 18425617 * q^33 - 46741622 * q^34 - 4067294 * q^35 + 132788567 * q^36 - 34982109 * q^37 - 2819104 * q^38 + 28561 * q^39 + 2107274 * q^40 + 59341985 * q^41 - 10057789 * q^42 + 38829122 * q^43 + 202791507 * q^44 + 2955478 * q^45 + 165169119 * q^46 + 18734035 * q^47 + 340656557 * q^48 + 86472015 * q^49 + 220443888 * q^50 + 93517168 * q^51 + 182847522 * q^52 + 332415086 * q^53 + 567466451 * q^54 - 120908856 * q^55 + 4091304 * q^56 + 62932402 * q^57 + 180863580 * q^58 + 28220174 * q^59 + 467078152 * q^60 + 404536605 * q^61 + 4283245 * q^62 - 385038766 * q^63 + 1276533074 * q^64 + 48382334 * q^65 + 1696546059 * q^66 + 746448213 * q^67 + 492702034 * q^68 + 453755667 * q^69 + 167464948 * q^70 + 81316200 * q^71 + 1255645679 * q^72 + 12687907 * q^73 + 1350657501 * q^74 - 164589481 * q^75 + 679560842 * q^76 - 56281841 * q^77 + 119642029 * q^78 + 1896008477 * q^79 - 1458560390 * q^80 + 3853340295 * q^81 + 410985635 * q^82 - 753815178 * q^83 - 154713237 * q^84 - 259541636 * q^85 - 1842794378 * q^86 + 1391390932 * q^87 + 288708813 * q^88 + 1109816012 * q^89 + 1196058116 * q^90 - 1028624415 * q^91 + 2409710277 * q^92 + 3345736043 * q^93 - 1423358651 * q^94 + 4615875678 * q^95 + 11615772371 * q^96 + 1054179205 * q^97 + 126825622 * q^98 - 2512222258 * 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 $

$2$	45.2074	1.99790	0.998951	−	0.0457897i	$-0.0145804\pi$
$2$	45.2074	1.99790	0.998951	+	0.0457897i	$0.0145804\pi$
$3$	261.874	1.86658	0.933290	−	0.359124i	$-0.116925\pi$
$3$	261.874	1.86658	0.933290	+	0.359124i	$0.116925\pi$
$4$	1531.71	2.99161
$5$	−1682.03	−1.20356	−0.601781	−	0.798661i	$-0.705542\pi$
$5$	−1682.03	−1.20356	−0.601781	+	0.798661i	$0.705542\pi$
$6$	11838.6	3.72924
$7$	−2401.00	−0.377964
$7$	−2401.00	−0.377964
$8$	46098.2	3.97905
$9$	48894.9	2.48412
$10$	−76040.1	−2.40460
$11$	−2595.99	−0.0534608	−0.0267304	−	0.999643i	$-0.508510\pi$
$11$	−2595.99	−0.0534608	−0.0267304	+	0.999643i	$0.508510\pi$
$12$	401114.	5.58408
$13$	28561.0	0.277350
$13$	28561.0	0.277350
$14$	−108543.	−0.755136
$15$	−440479.	−2.24654
$16$	1.29975e6	4.95814
$17$	−274656.	−0.797571	−0.398785	−	0.917044i	$-0.630568\pi$
$17$	−274656.	−0.797571	−0.398785	+	0.917044i	$0.630568\pi$
$18$	2.21041e6	4.96303
$19$	−711453.	−1.25243	−0.626217	−	0.779649i	$-0.715398\pi$
$19$	−711453.	−1.25243	−0.626217	+	0.779649i	$0.715398\pi$
$20$	−2.57637e6	−3.60059
$21$	−628759.	−0.705501
$22$	−117358.	−0.106810
$23$	484103.	0.360714	0.180357	−	0.983601i	$-0.442275\pi$
$23$	484103.	0.360714	0.180357	+	0.983601i	$0.442275\pi$
$24$	1.20719e7	7.42721
$25$	876094.	0.448560
$26$	1.29117e6	0.554118
$27$	7.64984e6	2.77023
$28$	−3.67763e6	−1.13072
$29$	91376.3	0.0239907	0.0119953	−	0.999928i	$-0.496182\pi$
$29$	91376.3	0.0239907	0.0119953	+	0.999928i	$0.496182\pi$
$30$	−1.99129e7	−4.48837
$31$	−1.75488e6	−0.341287	−0.170643	−	0.985333i	$-0.554585\pi$
$31$	−1.75488e6	−0.341287	−0.170643	+	0.985333i	$0.554585\pi$
$32$	3.51558e7	5.92682
$33$	−679822.	−0.0997889
$34$	−1.24165e7	−1.59347
$35$	4.03855e6	0.454903
$36$	7.48926e7	7.43152
$37$	−1.89306e6	−0.166057	−0.0830286	−	0.996547i	$-0.526459\pi$
$37$	−1.89306e6	−0.166057	−0.0830286	+	0.996547i	$0.526459\pi$
$38$	−3.21629e7	−2.50224
$39$	7.47938e6	0.517696
$40$	−7.75385e7	−4.78903
$41$	876544.	0.0484447	0.0242224	−	0.999707i	$-0.492289\pi$
$41$	876544.	0.0484447	0.0242224	+	0.999707i	$0.492289\pi$
$42$	−2.84245e7	−1.40952
$43$	−2.10803e7	−0.940304	−0.470152	−	0.882585i	$-0.655801\pi$
$43$	−2.10803e7	−0.940304	−0.470152	+	0.882585i	$0.655801\pi$
$44$	−3.97629e6	−0.159934
$45$	−8.22426e7	−2.98979
$46$	2.18850e7	0.720671
$47$	−4.96753e7	−1.48491	−0.742456	−	0.669895i	$-0.766339\pi$
$47$	−4.96753e7	−1.48491	−0.742456	+	0.669895i	$0.766339\pi$
$48$	3.40369e8	9.25476
$49$	5.76480e6	0.142857
$50$	3.96059e7	0.896179
$51$	−7.19253e7	−1.48873
$52$	4.37471e7	0.829724
$53$	6.13159e7	1.06741	0.533705	−	0.845671i	$-0.320799\pi$
$53$	6.13159e7	1.06741	0.533705	+	0.845671i	$0.320799\pi$
$54$	3.45829e8	5.53464
$55$	4.36653e6	0.0643434
$56$	−1.10682e8	−1.50394
$57$	−1.86311e8	−2.33777
$58$	4.13088e6	0.0479310
$59$	−7.47874e7	−0.803516	−0.401758	−	0.915746i	$-0.631601\pi$
$59$	−7.47874e7	−0.803516	−0.401758	+	0.915746i	$0.631601\pi$
$60$	−6.74685e8	−6.72079
$61$	8.72517e7	0.806844	0.403422	−	0.915014i	$-0.367821\pi$
$61$	8.72517e7	0.806844	0.403422	+	0.915014i	$0.367821\pi$
$62$	−7.93335e7	−0.681858
$63$	−1.17397e8	−0.938909
$64$	9.23831e8	6.88308
$65$	−4.80404e7	−0.333808
$66$	−3.07329e7	−0.199368
$67$	−9.76501e7	−0.592020	−0.296010	−	0.955185i	$-0.595656\pi$
$67$	−9.76501e7	−0.592020	−0.296010	+	0.955185i	$0.595656\pi$
$68$	−4.20693e8	−2.38602
$69$	1.26774e8	0.673301
$70$	1.82572e8	0.908853
$71$	−2.83745e8	−1.32515	−0.662575	−	0.748995i	$-0.730537\pi$
$71$	−2.83745e8	−1.32515	−0.662575	+	0.748995i	$0.730537\pi$
$72$	2.25397e9	9.88443
$73$	6.66323e7	0.274620	0.137310	−	0.990528i	$-0.456154\pi$
$73$	6.66323e7	0.274620	0.137310	+	0.990528i	$0.456154\pi$
$74$	−8.55804e7	−0.331766
$75$	2.29426e8	0.837273
$76$	−1.08974e9	−3.74680
$77$	6.23297e6	0.0202063
$78$	3.38123e8	1.03431
$79$	−1.40119e8	−0.404738	−0.202369	−	0.979309i	$-0.564864\pi$
$79$	−1.40119e8	−0.404738	−0.202369	+	0.979309i	$0.564864\pi$
$80$	−2.18621e9	−5.96742
$81$	1.04089e9	2.68673
$82$	3.96263e7	0.0967878
$83$	−4.69517e8	−1.08593	−0.542963	−	0.839757i	$-0.682698\pi$
$83$	−4.69517e8	−1.08593	−0.542963	+	0.839757i	$0.682698\pi$
$84$	−9.63074e8	−2.11059
$85$	4.61979e8	0.959925
$86$	−9.52984e8	−1.87864
$87$	2.39291e7	0.0447805
$88$	−1.19670e8	−0.212723
$89$	5.07175e8	0.856846	0.428423	−	0.903578i	$-0.359069\pi$
$89$	5.07175e8	0.856846	0.428423	+	0.903578i	$0.359069\pi$
$90$	−3.71797e9	−5.97331
$91$	−6.85750e7	−0.104828
$92$	7.41504e8	1.07912
$93$	−4.59557e8	−0.637039
$94$	−2.24569e9	−2.96671
$95$	1.19668e9	1.50738
$96$	9.20638e9	11.0629
$97$	1.03248e9	1.18416	0.592079	−	0.805880i	$-0.298307\pi$
$97$	1.03248e9	1.18416	0.592079	+	0.805880i	$0.298307\pi$
$98$	2.60611e8	0.285415
$99$	−1.26931e8	−0.132803
$100$	1.34192e9	1.34192
$101$	9.69160e8	0.926722	0.463361	−	0.886170i	$-0.346643\pi$
$101$	9.69160e8	0.926722	0.463361	+	0.886170i	$0.346643\pi$
$102$	−3.25155e9	−2.97434
$103$	4.63907e8	0.406129	0.203064	−	0.979165i	$-0.434910\pi$
$103$	4.63907e8	0.406129	0.203064	+	0.979165i	$0.434910\pi$
$104$	1.31661e9	1.10359
$105$	1.05759e9	0.849114
$106$	2.77193e9	2.13258
$107$	−6.37122e8	−0.469889	−0.234945	−	0.972009i	$-0.575491\pi$
$107$	−6.37122e8	−0.469889	−0.234945	+	0.972009i	$0.575491\pi$
$108$	1.17173e10	8.28745
$109$	9.76071e8	0.662311	0.331156	−	0.943576i	$-0.392562\pi$
$109$	9.76071e8	0.662311	0.331156	+	0.943576i	$0.392562\pi$
$110$	1.97399e8	0.128552
$111$	−4.95744e8	−0.309959
$112$	−3.12069e9	−1.87400
$113$	6.57879e7	0.0379571	0.0189785	−	0.999820i	$-0.493959\pi$
$113$	6.57879e7	0.0379571	0.0189785	+	0.999820i	$0.493959\pi$
$114$	−8.42262e9	−4.67063
$115$	−8.14275e8	−0.434141
$116$	1.39962e8	0.0717708
$117$	1.39649e9	0.688971
$118$	−3.38094e9	−1.60535
$119$	6.59450e8	0.301453
$120$	−2.03053e10	−8.93910
$121$	−2.35121e9	−0.997142
$122$	3.94442e9	1.61200
$123$	2.29544e8	0.0904259
$124$	−2.68796e9	−1.02100
$125$	1.81160e9	0.663692
$126$	−5.30720e9	−1.87585
$127$	1.64027e9	0.559496	0.279748	−	0.960073i	$-0.409749\pi$
$127$	1.64027e9	0.559496	0.279748	+	0.960073i	$0.409749\pi$
$128$	2.37642e10	7.82489
$129$	−5.52038e9	−1.75515
$130$	−2.17178e9	−0.666916
$131$	−7.84143e8	−0.232635	−0.116317	−	0.993212i	$-0.537109\pi$
$131$	−7.84143e8	−0.232635	−0.116317	+	0.993212i	$0.537109\pi$
$132$	−1.04129e9	−0.298530
$133$	1.70820e9	0.473375
$134$	−4.41450e9	−1.18280
$135$	−1.28672e10	−3.33414
$136$	−1.26612e10	−3.17357
$137$	−1.80298e9	−0.437268	−0.218634	−	0.975807i	$-0.570160\pi$
$137$	−1.80298e9	−0.437268	−0.218634	+	0.975807i	$0.570160\pi$
$138$	5.73112e9	1.34519
$139$	−6.62583e9	−1.50547	−0.752737	−	0.658321i	$-0.771267\pi$
$139$	−6.62583e9	−1.50547	−0.752737	+	0.658321i	$0.771267\pi$
$140$	6.18587e9	1.36090
$141$	−1.30087e10	−2.77170
$142$	−1.28274e10	−2.64752
$143$	−7.41440e7	−0.0148274
$144$	6.35510e10	12.3166
$145$	−1.53698e8	−0.0288743
$146$	3.01227e9	0.548663
$147$	1.50965e9	0.266654
$148$	−2.89962e9	−0.496779
$149$	4.26920e9	0.709592	0.354796	−	0.934944i	$-0.384550\pi$
$149$	4.26920e9	0.709592	0.354796	+	0.934944i	$0.384550\pi$
$150$	1.03718e10	1.67279
$151$	−3.07576e9	−0.481455	−0.240728	−	0.970593i	$-0.577386\pi$
$151$	−3.07576e9	−0.481455	−0.240728	+	0.970593i	$0.577386\pi$
$152$	−3.27967e10	−4.98349
$153$	−1.34293e10	−1.98126
$154$	2.81776e8	0.0403702
$155$	2.95176e9	0.410760
$156$	1.14562e10	1.54875
$157$	3.47791e9	0.456846	0.228423	−	0.973562i	$-0.426643\pi$
$157$	3.47791e9	0.456846	0.228423	+	0.973562i	$0.426643\pi$
$158$	−6.33439e9	−0.808627
$159$	1.60570e10	1.99241
$160$	−5.91330e10	−7.13330
$161$	−1.16233e9	−0.136337
$162$	4.70561e10	5.36782
$163$	1.52669e10	1.69397	0.846986	−	0.531616i	$-0.178415\pi$
$163$	1.52669e10	1.69397	0.846986	+	0.531616i	$0.178415\pi$
$164$	1.34261e9	0.144928
$165$	1.14348e9	0.120102
$166$	−2.12256e10	−2.16957
$167$	7.90083e9	0.786047	0.393024	−	0.919528i	$-0.371429\pi$
$167$	7.90083e9	0.786047	0.393024	+	0.919528i	$0.371429\pi$
$168$	−2.89847e10	−2.80722
$169$	8.15731e8	0.0769231
$170$	2.08849e10	1.91784
$171$	−3.47864e10	−3.11119
$172$	−3.22888e10	−2.81303
$173$	2.21843e10	1.88295	0.941473	−	0.337089i	$-0.109442\pi$
$173$	2.21843e10	1.88295	0.941473	+	0.337089i	$0.109442\pi$
$174$	1.08177e9	0.0894671
$175$	−2.10350e9	−0.169540
$176$	−3.37413e9	−0.265066
$177$	−1.95849e10	−1.49983
$178$	2.29281e10	1.71190
$179$	−2.58031e10	−1.87860	−0.939298	−	0.343101i	$-0.888523\pi$
$179$	−2.58031e10	−1.87860	−0.939298	+	0.343101i	$0.888523\pi$
$180$	−1.25972e11	−8.94430
$181$	3.01621e9	0.208885	0.104443	−	0.994531i	$-0.466694\pi$
$181$	3.01621e9	0.208885	0.104443	+	0.994531i	$0.466694\pi$
$182$	−3.10009e9	−0.209437
$183$	2.28489e10	1.50604
$184$	2.23163e10	1.43530
$185$	3.18419e9	0.199860
$186$	−2.07754e10	−1.27274
$187$	7.13004e8	0.0426388
$188$	−7.60880e10	−4.44228
$189$	−1.83673e10	−1.04705
$190$	5.40989e10	3.01160
$191$	2.89600e10	1.57452	0.787260	−	0.616621i	$-0.211499\pi$
$191$	2.89600e10	1.57452	0.787260	+	0.616621i	$0.211499\pi$
$192$	2.41927e11	12.8478
$193$	2.57591e10	1.33636	0.668178	−	0.744001i	$-0.267074\pi$
$193$	2.57591e10	1.33636	0.668178	+	0.744001i	$0.267074\pi$
$194$	4.66758e10	2.36583
$195$	−1.25805e10	−0.623079
$196$	8.82998e9	0.427373
$197$	−1.73585e10	−0.821136	−0.410568	−	0.911830i	$-0.634670\pi$
$197$	−1.73585e10	−0.821136	−0.410568	+	0.911830i	$0.634670\pi$
$198$	−5.73820e9	−0.265328
$199$	−3.57974e10	−1.61813	−0.809063	−	0.587722i	$-0.800025\pi$
$199$	−3.57974e10	−1.61813	−0.809063	+	0.587722i	$0.800025\pi$
$200$	4.03864e10	1.78484
$201$	−2.55720e10	−1.10505
$202$	4.38132e10	1.85150
$203$	−2.19395e8	−0.00906763
$204$	−1.10168e11	−4.45370
$205$	−1.47437e9	−0.0583062
$206$	2.09720e10	0.811405
$207$	2.36702e10	0.896056
$208$	3.71220e10	1.37514
$209$	1.84692e9	0.0669561
$210$	4.78109e10	1.69645
$211$	1.43405e10	0.498075	0.249037	−	0.968494i	$-0.419886\pi$
$211$	1.43405e10	0.498075	0.249037	+	0.968494i	$0.419886\pi$
$212$	9.39179e10	3.19328
$213$	−7.43053e10	−2.47350
$214$	−2.88026e10	−0.938793
$215$	3.54576e10	1.13171
$216$	3.52644e11	11.0229
$217$	4.21347e9	0.128994
$218$	4.41256e10	1.32323
$219$	1.74493e10	0.512600
$220$	6.68823e9	0.192491
$221$	−7.84446e9	−0.221206
$222$	−2.24113e10	−0.619268
$223$	−2.20695e10	−0.597614	−0.298807	−	0.954314i	$-0.596589\pi$
$223$	−2.20695e10	−0.597614	−0.298807	+	0.954314i	$0.596589\pi$
$224$	−8.44091e10	−2.24013
$225$	4.28365e10	1.11428
$226$	2.97410e9	0.0758345
$227$	−5.09543e10	−1.27369	−0.636846	−	0.770991i	$-0.719761\pi$
$227$	−5.09543e10	−1.27369	−0.636846	+	0.770991i	$0.719761\pi$
$228$	−2.85373e11	−6.99370
$229$	−3.52149e10	−0.846188	−0.423094	−	0.906086i	$-0.639056\pi$
$229$	−3.52149e10	−0.846188	−0.423094	+	0.906086i	$0.639056\pi$
$230$	−3.68112e10	−0.867372
$231$	1.63225e9	0.0377167
$232$	4.21229e9	0.0954601
$233$	7.56261e10	1.68101	0.840505	−	0.541804i	$-0.182259\pi$
$233$	7.56261e10	1.68101	0.840505	+	0.541804i	$0.182259\pi$
$234$	6.31315e10	1.37650
$235$	8.35553e10	1.78718
$236$	−1.14552e11	−2.40381
$237$	−3.66934e10	−0.755476
$238$	2.98120e10	0.602274
$239$	8.66138e10	1.71710	0.858551	−	0.512727i	$-0.171365\pi$
$239$	8.66138e10	1.71710	0.858551	+	0.512727i	$0.171365\pi$
$240$	−5.72511e11	−11.1387
$241$	4.92398e10	0.940242	0.470121	−	0.882602i	$-0.344210\pi$
$241$	4.92398e10	0.940242	0.470121	+	0.882602i	$0.344210\pi$
$242$	−1.06292e11	−1.99219
$243$	1.22011e11	2.24477
$244$	1.33644e11	2.41377
$245$	−9.69656e9	−0.171937
$246$	1.03771e10	0.180662
$247$	−2.03198e10	−0.347363
$248$	−8.08968e10	−1.35800
$249$	−1.22954e11	−2.02697
$250$	8.18975e10	1.32599
$251$	5.65486e10	0.899271	0.449635	−	0.893212i	$-0.351554\pi$
$251$	5.65486e10	0.899271	0.449635	+	0.893212i	$0.351554\pi$
$252$	−1.79817e11	−2.80885
$253$	−1.25673e9	−0.0192841
$254$	7.41521e10	1.11782
$255$	1.20980e11	1.79178
$256$	6.01315e11	8.75029
$257$	−7.66768e10	−1.09639	−0.548195	−	0.836351i	$-0.684685\pi$
$257$	−7.66768e10	−1.09639	−0.548195	+	0.836351i	$0.684685\pi$
$258$	−2.49562e11	−3.50662
$259$	4.54525e9	0.0627637
$260$	−7.35838e10	−0.998624
$261$	4.46784e9	0.0595957
$262$	−3.54490e10	−0.464781
$263$	4.21938e10	0.543811	0.271905	−	0.962324i	$-0.412346\pi$
$263$	4.21938e10	0.543811	0.271905	+	0.962324i	$0.412346\pi$
$264$	−3.13386e10	−0.397065
$265$	−1.03135e11	−1.28469
$266$	7.72231e10	0.945758
$267$	1.32816e11	1.59937
$268$	−1.49571e11	−1.77109
$269$	1.16160e11	1.35261	0.676305	−	0.736622i	$-0.263580\pi$
$269$	1.16160e11	1.35261	0.676305	+	0.736622i	$0.263580\pi$
$270$	−5.81694e11	−6.66128
$271$	1.02536e11	1.15482	0.577409	−	0.816455i	$-0.304064\pi$
$271$	1.02536e11	1.15482	0.577409	+	0.816455i	$0.304064\pi$
$272$	−3.56983e11	−3.95446
$273$	−1.79580e10	−0.195671
$274$	−8.15079e10	−0.873619
$275$	−2.27433e9	−0.0239804
$276$	1.94180e11	2.01426
$277$	−1.35902e11	−1.38697	−0.693485	−	0.720471i	$-0.743926\pi$
$277$	−1.35902e11	−1.38697	−0.693485	+	0.720471i	$0.743926\pi$
$278$	−2.99536e11	−3.00779
$279$	−8.58047e10	−0.847798
$280$	1.86170e11	1.81008
$281$	1.12881e11	1.08005	0.540024	−	0.841650i	$-0.318415\pi$
$281$	1.12881e11	1.08005	0.540024	+	0.841650i	$0.318415\pi$
$282$	−5.88088e11	−5.53760
$283$	−5.04927e10	−0.467939	−0.233970	−	0.972244i	$-0.575172\pi$
$283$	−5.04927e10	−0.467939	−0.233970	+	0.972244i	$0.575172\pi$
$284$	−4.34613e11	−3.96434
$285$	3.13380e11	2.81365
$286$	−3.35186e9	−0.0296236
$287$	−2.10458e9	−0.0183104
$288$	1.71894e12	14.7229
$289$	−4.31519e10	−0.363881
$290$	−6.94826e9	−0.0576879
$291$	2.70380e11	2.21033
$292$	1.02061e11	0.821556
$293$	−2.23609e10	−0.177249	−0.0886247	−	0.996065i	$-0.528247\pi$
$293$	−2.23609e10	−0.177249	−0.0886247	+	0.996065i	$0.528247\pi$
$294$	6.82473e10	0.532749
$295$	1.25795e11	0.967081
$296$	−8.72669e10	−0.660749
$297$	−1.98589e10	−0.148099
$298$	1.92999e11	1.41769
$299$	1.38265e10	0.100044
$300$	3.51413e11	2.50480
$301$	5.06138e10	0.355402
$302$	−1.39047e11	−0.961900
$303$	2.53798e11	1.72980
$304$	−9.24707e11	−6.20974
$305$	−1.46760e11	−0.971086
$306$	−6.07103e11	−3.95837
$307$	−8.25323e10	−0.530275	−0.265138	−	0.964211i	$-0.585417\pi$
$307$	−8.25323e10	−0.530275	−0.265138	+	0.964211i	$0.585417\pi$
$308$	9.54708e9	0.0604494
$309$	1.21485e11	0.758071
$310$	1.33441e11	0.820658
$311$	−1.05045e11	−0.636727	−0.318363	−	0.947969i	$-0.603133\pi$
$311$	−1.05045e11	−0.636727	−0.318363	+	0.947969i	$0.603133\pi$
$312$	3.44786e11	2.05994
$313$	−3.69433e8	−0.00217564	−0.00108782	−	0.999999i	$-0.500346\pi$
$313$	−3.69433e8	−0.00217564	−0.00108782	+	0.999999i	$0.500346\pi$
$314$	1.57227e11	0.912735
$315$	1.97465e11	1.13003
$316$	−2.14621e11	−1.21082
$317$	7.24188e10	0.402796	0.201398	−	0.979510i	$-0.435452\pi$
$317$	7.24188e10	0.402796	0.201398	+	0.979510i	$0.435452\pi$
$318$	7.25896e11	3.98063
$319$	−2.37212e8	−0.00128256
$320$	−1.55391e12	−8.28421
$321$	−1.66846e11	−0.877086
$322$	−5.25460e10	−0.272388
$323$	1.95405e11	0.998905
$324$	1.59434e12	8.03765
$325$	2.50221e10	0.124408
$326$	6.90175e11	3.38439
$327$	2.55607e11	1.23626
$328$	4.04071e10	0.192764
$329$	1.19270e11	0.561244
$330$	5.16937e10	0.239952
$331$	8.09811e10	0.370815	0.185408	−	0.982662i	$-0.440639\pi$
$331$	8.09811e10	0.370815	0.185408	+	0.982662i	$0.440639\pi$
$332$	−7.19163e11	−3.24867
$333$	−9.25612e10	−0.412506
$334$	3.57176e11	1.57045
$335$	1.64250e11	0.712532
$336$	−8.17227e11	−3.49797
$337$	−3.03081e11	−1.28004	−0.640021	−	0.768357i	$-0.721075\pi$
$337$	−3.03081e11	−1.28004	−0.640021	+	0.768357i	$0.721075\pi$
$338$	3.68770e10	0.153685
$339$	1.72281e10	0.0708499
$340$	7.07617e11	2.87173
$341$	4.55565e9	0.0182455
$342$	−1.57260e12	−6.21586
$343$	−1.38413e10	−0.0539949
$344$	−9.71764e11	−3.74152
$345$	−2.13237e11	−0.810359
$346$	1.00289e12	3.76194
$347$	1.08960e11	0.403445	0.201722	−	0.979443i	$-0.435346\pi$
$347$	1.08960e11	0.403445	0.201722	+	0.979443i	$0.435346\pi$
$348$	3.66523e10	0.133966
$349$	−2.12380e11	−0.766299	−0.383150	−	0.923686i	$-0.625161\pi$
$349$	−2.12380e11	−0.766299	−0.383150	+	0.923686i	$0.625161\pi$
$350$	−9.50938e10	−0.338724
$351$	2.18487e11	0.768323
$352$	−9.12640e10	−0.316853
$353$	−3.45226e10	−0.118336	−0.0591681	−	0.998248i	$-0.518845\pi$
$353$	−3.45226e10	−0.118336	−0.0591681	+	0.998248i	$0.518845\pi$
$354$	−8.85380e11	−2.99651
$355$	4.77267e11	1.59490
$356$	7.76843e11	2.56335
$357$	1.72693e11	0.562687
$358$	−1.16649e12	−3.75325
$359$	−1.37513e11	−0.436938	−0.218469	−	0.975844i	$-0.570106\pi$
$359$	−1.37513e11	−0.436938	−0.218469	+	0.975844i	$0.570106\pi$
$360$	−3.79124e12	−11.8965
$361$	1.83477e11	0.568590
$362$	1.36355e11	0.417332
$363$	−6.15720e11	−1.86124
$364$	−1.05037e11	−0.313606
$365$	−1.12077e11	−0.330522
$366$	1.03294e12	3.00892
$367$	3.55821e11	1.02384	0.511922	−	0.859032i	$-0.328934\pi$
$367$	3.55821e11	1.02384	0.511922	+	0.859032i	$0.328934\pi$
$368$	6.29211e11	1.78847
$369$	4.28586e10	0.120342
$370$	1.43949e11	0.399301
$371$	−1.47219e11	−0.403443
$372$	−7.03906e11	−1.90578
$373$	3.72574e11	0.996604	0.498302	−	0.867003i	$-0.333957\pi$
$373$	3.72574e11	0.996604	0.498302	+	0.867003i	$0.333957\pi$
$374$	3.22331e10	0.0851882
$375$	4.74410e11	1.23883
$376$	−2.28994e12	−5.90853
$377$	2.60980e9	0.00665382
$378$	−8.30336e11	−2.09190
$379$	−2.02319e11	−0.503687	−0.251843	−	0.967768i	$-0.581037\pi$
$379$	−2.02319e11	−0.503687	−0.251843	+	0.967768i	$0.581037\pi$
$380$	1.83297e12	4.50950
$381$	4.29543e11	1.04434
$382$	1.30920e12	3.14574
$383$	−6.90455e11	−1.63961	−0.819806	−	0.572641i	$-0.805919\pi$
$383$	−6.90455e11	−1.63961	−0.819806	+	0.572641i	$0.805919\pi$
$384$	6.22322e12	14.6058
$385$	−1.04840e10	−0.0243195
$386$	1.16450e12	2.66991
$387$	−1.03072e12	−2.33583
$388$	1.58146e12	3.54255
$389$	3.01848e11	0.668368	0.334184	−	0.942508i	$-0.391539\pi$
$389$	3.01848e11	0.668368	0.334184	+	0.942508i	$0.391539\pi$
$390$	−5.68733e11	−1.24485
$391$	−1.32962e11	−0.287695
$392$	2.65747e11	0.568435
$393$	−2.05347e11	−0.434231
$394$	−7.84734e11	−1.64055
$395$	2.35684e11	0.487127
$396$	−1.94420e11	−0.397295
$397$	−2.45625e11	−0.496267	−0.248133	−	0.968726i	$-0.579817\pi$
$397$	−2.45625e11	−0.496267	−0.248133	+	0.968726i	$0.579817\pi$
$398$	−1.61830e12	−3.23286
$399$	4.47332e11	0.883593
$400$	1.13870e12	2.22402
$401$	7.28484e11	1.40692	0.703461	−	0.710733i	$-0.251637\pi$
$401$	7.28484e11	1.40692	0.703461	+	0.710733i	$0.251637\pi$
$402$	−1.15604e12	−2.20778
$403$	−5.01211e10	−0.0946560
$404$	1.48447e12	2.77239
$405$	−1.75081e12	−3.23364
$406$	−9.91825e9	−0.0181162
$407$	4.91437e9	0.00887755
$408$	−3.31563e12	−5.92373
$409$	−4.19341e11	−0.740990	−0.370495	−	0.928834i	$-0.620812\pi$
$409$	−4.19341e11	−0.740990	−0.370495	+	0.928834i	$0.620812\pi$
$410$	−6.66525e10	−0.116490
$411$	−4.72153e11	−0.816196
$412$	7.10569e11	1.21498
$413$	1.79565e11	0.303700
$414$	1.07007e12	1.79023
$415$	7.89742e11	1.30698
$416$	1.00408e12	1.64381
$417$	−1.73513e12	−2.81009
$418$	8.34945e10	0.133772
$419$	−2.20280e11	−0.349149	−0.174575	−	0.984644i	$-0.555855\pi$
$419$	−2.20280e11	−0.349149	−0.174575	+	0.984644i	$0.555855\pi$
$420$	1.61992e12	2.54022
$421$	2.15733e11	0.334694	0.167347	−	0.985898i	$-0.446480\pi$
$421$	2.15733e11	0.334694	0.167347	+	0.985898i	$0.446480\pi$
$422$	6.48298e11	0.995105
$423$	−2.42887e12	−3.68870
$424$	2.82655e12	4.24728
$425$	−2.40625e11	−0.357758
$426$	−3.35915e12	−4.94181
$427$	−2.09491e11	−0.304958
$428$	−9.75884e11	−1.40573
$429$	−1.94164e10	−0.0276765
$430$	1.60295e12	2.26105
$431$	−1.25472e12	−1.75145	−0.875725	−	0.482810i	$-0.839616\pi$
$431$	−1.25472e12	−1.75145	−0.875725	+	0.482810i	$0.839616\pi$
$432$	9.94284e12	13.7352
$433$	5.20770e11	0.711951	0.355975	−	0.934495i	$-0.384149\pi$
$433$	5.20770e11	0.711951	0.355975	+	0.934495i	$0.384149\pi$
$434$	1.90480e11	0.257718
$435$	−4.02494e10	−0.0538961
$436$	1.49505e12	1.98138
$437$	−3.44417e11	−0.451770
$438$	7.88835e11	1.02412
$439$	2.09689e11	0.269455	0.134727	−	0.990883i	$-0.456984\pi$
$439$	2.09689e11	0.269455	0.134727	+	0.990883i	$0.456984\pi$
$440$	2.01289e11	0.256025
$441$	2.81869e11	0.354874
$442$	−3.54627e11	−0.441949
$443$	−9.71744e11	−1.19877	−0.599384	−	0.800462i	$-0.704588\pi$
$443$	−9.71744e11	−1.19877	−0.599384	+	0.800462i	$0.704588\pi$
$444$	−7.59334e11	−0.927277
$445$	−8.53083e11	−1.03127
$446$	−9.97704e11	−1.19397
$447$	1.11799e12	1.32451
$448$	−2.21812e12	−2.60156
$449$	−6.32166e11	−0.734044	−0.367022	−	0.930212i	$-0.619623\pi$
$449$	−6.32166e11	−0.734044	−0.367022	+	0.930212i	$0.619623\pi$
$450$	1.93653e12	2.22622
$451$	−2.27550e9	−0.00258990
$452$	1.00768e11	0.113553
$453$	−8.05461e11	−0.898674
$454$	−2.30351e12	−2.54471
$455$	1.15345e11	0.126168
$456$	−8.58860e12	−9.30209
$457$	−1.03580e12	−1.11084	−0.555421	−	0.831569i	$-0.687443\pi$
$457$	−1.03580e12	−1.11084	−0.555421	+	0.831569i	$0.687443\pi$
$458$	−1.59197e12	−1.69060
$459$	−2.10108e12	−2.20945
$460$	−1.24723e12	−1.29878
$461$	1.04641e12	1.07907	0.539535	−	0.841963i	$-0.318600\pi$
$461$	1.04641e12	1.07907	0.539535	+	0.841963i	$0.318600\pi$
$462$	7.37898e10	0.0753542
$463$	8.03470e11	0.812560	0.406280	−	0.913749i	$-0.366826\pi$
$463$	8.03470e11	0.812560	0.406280	+	0.913749i	$0.366826\pi$
$464$	1.18766e11	0.118949
$465$	7.72988e11	0.766716
$466$	3.41886e12	3.35849
$467$	1.80235e12	1.75353	0.876767	−	0.480915i	$-0.159695\pi$
$467$	1.80235e12	1.75353	0.876767	+	0.480915i	$0.159695\pi$
$468$	2.13901e12	2.06113
$469$	2.34458e11	0.223762
$470$	3.77732e12	3.57061
$471$	9.10774e11	0.852740
$472$	−3.44757e12	−3.19723
$473$	5.47242e10	0.0502695
$474$	−1.65881e12	−1.50937
$475$	−6.23299e11	−0.561792
$476$	1.01008e12	0.901832
$477$	2.99803e12	2.65158
$478$	3.91558e12	3.43060
$479$	−9.88425e11	−0.857895	−0.428947	−	0.903330i	$-0.641115\pi$
$479$	−9.88425e11	−0.857895	−0.428947	+	0.903330i	$0.641115\pi$
$480$	−1.54854e13	−13.3149
$481$	−5.40678e10	−0.0460560
$482$	2.22600e12	1.87851
$483$	−3.04384e11	−0.254484
$484$	−3.60136e12	−2.98306
$485$	−1.73667e12	−1.42521
$486$	5.51580e12	4.48483
$487$	−1.07338e12	−0.864713	−0.432357	−	0.901703i	$-0.642318\pi$
$487$	−1.07338e12	−0.864713	−0.432357	+	0.901703i	$0.642318\pi$
$488$	4.02215e12	3.21047
$489$	3.99800e12	3.16193
$490$	−4.38356e11	−0.343514
$491$	1.75084e11	0.135950	0.0679751	−	0.997687i	$-0.478346\pi$
$491$	1.75084e11	0.135950	0.0679751	+	0.997687i	$0.478346\pi$
$492$	3.51594e11	0.270519
$493$	−2.50971e10	−0.0191343
$494$	−9.18604e11	−0.693997
$495$	2.13501e11	0.159837
$496$	−2.28090e12	−1.69215
$497$	6.81271e11	0.500860
$498$	−5.55844e12	−4.04968
$499$	1.93587e12	1.39773	0.698865	−	0.715254i	$-0.253689\pi$
$499$	1.93587e12	1.39773	0.698865	+	0.715254i	$0.253689\pi$
$500$	2.77483e12	1.98551
$501$	2.06902e12	1.46722
$502$	2.55641e12	1.79665
$503$	2.19735e12	1.53053	0.765267	−	0.643713i	$-0.222607\pi$
$503$	2.19735e12	1.53053	0.765267	+	0.643713i	$0.222607\pi$
$504$	−5.41178e12	−3.73596
$505$	−1.63015e12	−1.11537
$506$	−5.68133e10	−0.0385277
$507$	2.13619e11	0.143583
$508$	2.51240e12	1.67380
$509$	1.85414e12	1.22437	0.612185	−	0.790714i	$-0.290291\pi$
$509$	1.85414e12	1.22437	0.612185	+	0.790714i	$0.290291\pi$
$510$	5.46920e12	3.57980
$511$	−1.59984e11	−0.103797
$512$	1.50166e13	9.65733
$513$	−5.44250e12	−3.46953
$514$	−3.46636e12	−2.19048
$515$	−7.80305e11	−0.488801
$516$	−8.45559e12	−5.25074
$517$	1.28957e11	0.0793846
$518$	2.05479e11	0.125396
$519$	5.80948e12	3.51467
$520$	−2.21458e12	−1.32824
$521$	−1.32945e12	−0.790502	−0.395251	−	0.918573i	$-0.629342\pi$
$521$	−1.32945e12	−0.790502	−0.395251	+	0.918573i	$0.629342\pi$
$522$	2.01979e11	0.119066
$523$	1.03974e12	0.607669	0.303834	−	0.952725i	$-0.401733\pi$
$523$	1.03974e12	0.607669	0.303834	+	0.952725i	$0.401733\pi$
$524$	−1.20108e12	−0.695953
$525$	−5.50852e11	−0.316460
$526$	1.90747e12	1.08648
$527$	4.81989e11	0.272201
$528$	−8.83595e11	−0.494767
$529$	−1.56680e12	−0.869886
$530$	−4.66246e12	−2.56669
$531$	−3.65672e12	−1.99603
$532$	2.61646e12	1.41616
$533$	2.50350e10	0.0134361
$534$	6.00426e12	3.19539
$535$	1.07166e12	0.565541
$536$	−4.50150e12	−2.35567
$537$	−6.75716e12	−3.50655
$538$	5.25130e12	2.70238
$539$	−1.49654e10	−0.00763726
$540$	−1.97088e13	−9.97445
$541$	1.02665e12	0.515268	0.257634	−	0.966243i	$-0.417057\pi$
$541$	1.02665e12	0.515268	0.257634	+	0.966243i	$0.417057\pi$
$542$	4.63537e12	2.30721
$543$	7.89867e11	0.389901
$544$	−9.65576e12	−4.72706
$545$	−1.64178e12	−0.797132
$546$	−8.11833e11	−0.390931
$547$	−1.25282e12	−0.598338	−0.299169	−	0.954200i	$-0.596709\pi$
$547$	−1.25282e12	−0.598338	−0.299169	+	0.954200i	$0.596709\pi$
$548$	−2.76163e12	−1.30814
$549$	4.26616e12	2.00430
$550$	−1.02816e11	−0.0479105
$551$	−6.50099e10	−0.0300467
$552$	5.84406e12	2.67910
$553$	3.36425e11	0.152977
$554$	−6.14378e12	−2.77103
$555$	8.33855e11	0.373055
$556$	−1.01488e13	−4.50380
$557$	6.91893e11	0.304572	0.152286	−	0.988336i	$-0.451336\pi$
$557$	6.91893e11	0.304572	0.152286	+	0.988336i	$0.451336\pi$
$558$	−3.87900e12	−1.69382
$559$	−6.02074e11	−0.260794
$560$	5.24909e12	2.25547
$561$	1.86717e11	0.0795887
$562$	5.10306e12	2.15783
$563$	1.79625e12	0.753491	0.376746	−	0.926317i	$-0.377043\pi$
$563$	1.79625e12	0.753491	0.376746	+	0.926317i	$0.377043\pi$
$564$	−1.99255e13	−8.29187
$565$	−1.10657e11	−0.0456837
$566$	−2.28264e12	−0.934897
$567$	−2.49919e12	−1.01549
$568$	−1.30801e13	−5.27284
$569$	−4.22188e12	−1.68850	−0.844250	−	0.535950i	$-0.819954\pi$
$569$	−4.22188e12	−1.68850	−0.844250	+	0.535950i	$0.819954\pi$
$570$	1.41671e13	5.62139
$571$	3.75727e12	1.47914	0.739570	−	0.673079i	$-0.235029\pi$
$571$	3.75727e12	1.47914	0.739570	+	0.673079i	$0.235029\pi$
$572$	−1.13567e11	−0.0443577
$573$	7.58386e12	2.93897
$574$	−9.51426e10	−0.0365824
$575$	4.24120e11	0.161802
$576$	4.51706e13	17.0984
$577$	−3.94794e12	−1.48279	−0.741395	−	0.671069i	$-0.765835\pi$
$577$	−3.94794e12	−1.48279	−0.741395	+	0.671069i	$0.765835\pi$
$578$	−1.95078e12	−0.726998
$579$	6.74563e12	2.49442
$580$	−2.35419e11	−0.0863806
$581$	1.12731e12	0.410442
$582$	1.22232e13	4.41602
$583$	−1.59175e11	−0.0570647
$584$	3.07163e12	1.09273
$585$	−2.34893e12	−0.829219
$586$	−1.01088e12	−0.354127
$587$	−2.20022e12	−0.764882	−0.382441	−	0.923980i	$-0.624917\pi$
$587$	−2.20022e12	−0.764882	−0.382441	+	0.923980i	$0.624917\pi$
$588$	2.31234e12	0.797726
$589$	1.24851e12	0.427439
$590$	5.68684e12	1.93213
$591$	−4.54575e12	−1.53272
$592$	−2.46050e12	−0.823334
$593$	4.17452e12	1.38631	0.693155	−	0.720789i	$-0.256220\pi$
$593$	4.17452e12	1.38631	0.693155	+	0.720789i	$0.256220\pi$
$594$	−8.97768e11	−0.295887
$595$	−1.10921e12	−0.362818
$596$	6.53916e12	2.12282
$597$	−9.37439e12	−3.02036
$598$	6.25058e11	0.199878
$599$	3.38075e12	1.07298	0.536490	−	0.843907i	$-0.319750\pi$
$599$	3.38075e12	1.07298	0.536490	+	0.843907i	$0.319750\pi$
$600$	1.05761e13	3.33155
$601$	2.81793e12	0.881040	0.440520	−	0.897743i	$-0.354794\pi$
$601$	2.81793e12	0.881040	0.440520	+	0.897743i	$0.354794\pi$
$602$	2.28812e12	0.710058
$603$	−4.77459e12	−1.47065
$604$	−4.71116e12	−1.44033
$605$	3.95480e12	1.20012
$606$	1.14735e13	3.45597
$607$	4.53398e12	1.35560	0.677799	−	0.735247i	$-0.262934\pi$
$607$	4.53398e12	1.35560	0.677799	+	0.735247i	$0.262934\pi$
$608$	−2.50117e13	−7.42295
$609$	−5.74537e10	−0.0169254
$610$	−6.63462e12	−1.94014
$611$	−1.41878e12	−0.411840
$612$	−2.05697e13	−5.92717
$613$	1.62925e12	0.466031	0.233015	−	0.972473i	$-0.425141\pi$
$613$	1.62925e12	0.466031	0.233015	+	0.972473i	$0.425141\pi$
$614$	−3.73107e12	−1.05944
$615$	−3.86100e11	−0.108833
$616$	2.87329e11	0.0804018
$617$	7.18643e11	0.199632	0.0998159	−	0.995006i	$-0.468175\pi$
$617$	7.18643e11	0.199632	0.0998159	+	0.995006i	$0.468175\pi$
$618$	5.49202e12	1.51455
$619$	2.52780e12	0.692046	0.346023	−	0.938226i	$-0.387532\pi$
$619$	2.52780e12	0.692046	0.346023	+	0.938226i	$0.387532\pi$
$620$	4.52122e12	1.22883
$621$	3.70331e12	0.999259
$622$	−4.74880e12	−1.27212
$623$	−1.21773e12	−0.323858
$624$	9.72129e12	2.56681
$625$	−4.75828e12	−1.24735
$626$	−1.67011e10	−0.00434671
$627$	4.83661e11	0.124979
$628$	5.32714e12	1.36671
$629$	5.19942e11	0.132442
$630$	8.92685e12	2.25770
$631$	−6.16803e12	−1.54887	−0.774433	−	0.632656i	$-0.781965\pi$
$631$	−6.16803e12	−1.54887	−0.774433	+	0.632656i	$0.781965\pi$
$632$	−6.45922e12	−1.61047
$633$	3.75541e12	0.929696
$634$	3.27387e12	0.804747
$635$	−2.75897e12	−0.673388
$636$	2.45946e13	5.96051
$637$	1.64648e11	0.0396214
$638$	−1.07237e10	−0.00256243
$639$	−1.38737e13	−3.29183
$640$	−3.99721e13	−9.41774
$641$	−2.59505e12	−0.607134	−0.303567	−	0.952810i	$-0.598178\pi$
$641$	−2.59505e12	−0.607134	−0.303567	+	0.952810i	$0.598178\pi$
$642$	−7.54265e12	−1.75233
$643$	−3.02915e12	−0.698829	−0.349414	−	0.936968i	$-0.613619\pi$
$643$	−3.02915e12	−0.698829	−0.349414	+	0.936968i	$0.613619\pi$
$644$	−1.78035e12	−0.407868
$645$	9.28543e12	2.11243
$646$	8.83374e12	1.99571
$647$	−7.67500e12	−1.72191	−0.860953	−	0.508685i	$-0.830132\pi$
$647$	−7.67500e12	−1.72191	−0.860953	+	0.508685i	$0.830132\pi$
$648$	4.79834e13	10.6906
$649$	1.94147e11	0.0429566
$650$	1.13118e12	0.248555
$651$	1.10340e12	0.240778
$652$	2.33844e13	5.06771
$653$	−1.76412e10	−0.00379681	−0.00189841	−	0.999998i	$-0.500604\pi$
$653$	−1.76412e10	−0.00379681	−0.00189841	+	0.999998i	$0.500604\pi$
$654$	1.15553e13	2.46992
$655$	1.31895e12	0.279990
$656$	1.13928e12	0.240196
$657$	3.25798e12	0.682188
$658$	5.39190e12	1.12131
$659$	−3.70692e11	−0.0765647	−0.0382824	−	0.999267i	$-0.512189\pi$
$659$	−3.70692e11	−0.0765647	−0.0382824	+	0.999267i	$0.512189\pi$
$660$	1.75147e12	0.359299
$661$	−2.21014e12	−0.450312	−0.225156	−	0.974323i	$-0.572289\pi$
$661$	−2.21014e12	−0.450312	−0.225156	+	0.974323i	$0.572289\pi$
$662$	3.66094e12	0.740853
$663$	−2.05426e12	−0.412899
$664$	−2.16439e13	−4.32095
$665$	−2.87324e12	−0.569736
$666$	−4.18445e12	−0.824146
$667$	4.42356e10	0.00865377
$668$	1.21017e13	2.35155
$669$	−5.77942e12	−1.11549
$670$	7.42532e12	1.42357
$671$	−2.26504e11	−0.0431346
$672$	−2.21045e13	−4.18138
$673$	−8.03897e11	−0.151054	−0.0755271	−	0.997144i	$-0.524064\pi$
$673$	−8.03897e11	−0.151054	−0.0755271	+	0.997144i	$0.524064\pi$
$674$	−1.37015e13	−2.55740
$675$	6.70198e12	1.24261
$676$	1.24946e12	0.230124
$677$	6.36924e12	1.16530	0.582651	−	0.812723i	$-0.302016\pi$
$677$	6.36924e12	1.16530	0.582651	+	0.812723i	$0.302016\pi$
$678$	7.78838e11	0.141551
$679$	−2.47899e12	−0.447570
$680$	2.12964e13	3.81959
$681$	−1.33436e13	−2.37745
$682$	2.05949e11	0.0364527
$683$	−9.17059e12	−1.61252	−0.806258	−	0.591564i	$-0.798511\pi$
$683$	−9.17059e12	−1.61252	−0.806258	+	0.591564i	$0.798511\pi$
$684$	−5.32826e13	−9.30749
$685$	3.03266e12	0.526279
$686$	−6.25728e11	−0.107877
$687$	−9.22186e12	−1.57948
$688$	−2.73990e13	−4.66216
$689$	1.75124e12	0.296046
$690$	−9.63990e12	−1.61902
$691$	−9.89171e11	−0.165052	−0.0825259	−	0.996589i	$-0.526299\pi$
$691$	−9.89171e11	−0.165052	−0.0825259	+	0.996589i	$0.526299\pi$
$692$	3.39798e13	5.63305
$693$	3.04761e11	0.0501948
$694$	4.92579e12	0.806044
$695$	1.11448e13	1.81193
$696$	1.10309e12	0.178184
$697$	−2.40748e11	−0.0386381
$698$	−9.60112e12	−1.53099
$699$	1.98045e13	3.13774
$700$	−3.22195e12	−0.507198
$701$	−2.67256e12	−0.418020	−0.209010	−	0.977914i	$-0.567024\pi$
$701$	−2.67256e12	−0.418020	−0.209010	+	0.977914i	$0.567024\pi$
$702$	9.87722e12	1.53503
$703$	1.34683e12	0.207976
$704$	−2.39825e12	−0.367975
$705$	2.18810e13	3.33592
$706$	−1.56068e12	−0.236424
$707$	−2.32695e12	−0.350268
$708$	−2.99983e13	−4.48690
$709$	1.12088e12	0.166592	0.0832958	−	0.996525i	$-0.473455\pi$
$709$	1.12088e12	0.166592	0.0832958	+	0.996525i	$0.473455\pi$
$710$	2.15760e13	3.18645
$711$	−6.85109e12	−1.00542
$712$	2.33799e13	3.40943
$713$	−8.49543e11	−0.123107
$714$	7.80698e12	1.12419
$715$	1.24712e11	0.0178456
$716$	−3.95228e13	−5.62003
$717$	2.26819e13	3.20511
$718$	−6.21662e12	−0.872960
$719$	1.46742e11	0.0204774	0.0102387	−	0.999948i	$-0.496741\pi$
$719$	1.46742e11	0.0204774	0.0102387	+	0.999948i	$0.496741\pi$
$720$	−1.06895e14	−14.8238
$721$	−1.11384e12	−0.153502
$722$	8.29451e12	1.13599
$723$	1.28946e13	1.75504
$724$	4.61995e12	0.624904
$725$	8.00542e10	0.0107613
$726$	−2.78351e13	−3.71859
$727$	5.22926e12	0.694281	0.347140	−	0.937813i	$-0.387153\pi$
$727$	5.22926e12	0.694281	0.347140	+	0.937813i	$0.387153\pi$
$728$	−3.16118e12	−0.417118
$729$	1.14636e13	1.50331
$730$	−5.06672e12	−0.660350
$731$	5.78983e12	0.749959
$732$	3.49979e13	4.50549
$733$	−7.19786e12	−0.920949	−0.460474	−	0.887673i	$-0.652321\pi$
$733$	−7.19786e12	−0.920949	−0.460474	+	0.887673i	$0.652321\pi$
$734$	1.60857e13	2.04554
$735$	−2.53928e12	−0.320935
$736$	1.70190e13	2.13789
$737$	2.53499e11	0.0316499
$738$	1.93752e12	0.240432
$739$	−1.36449e13	−1.68295	−0.841476	−	0.540294i	$-0.818313\pi$
$739$	−1.36449e13	−1.68295	−0.841476	+	0.540294i	$0.818313\pi$
$740$	4.87724e12	0.597904
$741$	−5.32122e12	−0.648380
$742$	−6.65540e12	−0.806040
$743$	−1.41892e13	−1.70807	−0.854037	−	0.520212i	$-0.825853\pi$
$743$	−1.41892e13	−1.70807	−0.854037	+	0.520212i	$0.825853\pi$
$744$	−2.11848e13	−2.53481
$745$	−7.18092e12	−0.854037
$746$	1.68431e13	1.99112
$747$	−2.29570e13	−2.69757
$748$	1.09211e12	0.127559
$749$	1.52973e12	0.177602
$750$	2.14468e13	2.47507
$751$	−1.55340e13	−1.78199	−0.890994	−	0.454015i	$-0.849991\pi$
$751$	−1.55340e13	−1.78199	−0.890994	+	0.454015i	$0.849991\pi$
$752$	−6.45653e13	−7.36239
$753$	1.48086e13	1.67856
$754$	1.17982e11	0.0132937
$755$	5.17351e12	0.579461
$756$	−2.81332e13	−3.13236
$757$	−1.29205e13	−1.43004	−0.715018	−	0.699106i	$-0.753581\pi$
$757$	−1.29205e13	−1.43004	−0.715018	+	0.699106i	$0.753581\pi$
$758$	−9.14631e12	−1.00632
$759$	−3.29104e11	−0.0359952
$760$	5.51650e13	5.99794
$761$	−6.46670e12	−0.698959	−0.349480	−	0.936944i	$-0.613642\pi$
$761$	−6.46670e12	−0.698959	−0.349480	+	0.936944i	$0.613642\pi$
$762$	1.94185e13	2.08650
$763$	−2.34355e12	−0.250330
$764$	4.43582e13	4.71035
$765$	2.25884e13	2.38457
$766$	−3.12137e13	−3.27578
$767$	−2.13600e12	−0.222855
$768$	1.57469e14	16.3331
$769$	6.70081e11	0.0690970	0.0345485	−	0.999403i	$-0.489001\pi$
$769$	6.70081e11	0.0690970	0.0345485	+	0.999403i	$0.489001\pi$
$770$	−4.73955e11	−0.0485880
$771$	−2.00796e13	−2.04650
$772$	3.94553e13	3.99786
$773$	−1.51145e13	−1.52260	−0.761301	−	0.648399i	$-0.775439\pi$
$773$	−1.51145e13	−1.52260	−0.761301	+	0.648399i	$0.775439\pi$
$774$	−4.65961e13	−4.66676
$775$	−1.53744e12	−0.153088
$776$	4.75956e13	4.71183
$777$	1.19028e12	0.117153
$778$	1.36458e13	1.33533
$779$	−6.23620e11	−0.0606738
$780$	−1.92697e13	−1.86401
$781$	7.36598e11	0.0708436
$782$	−6.01086e12	−0.574786
$783$	6.99014e11	0.0664596
$784$	7.49278e12	0.708305
$785$	−5.84995e12	−0.549843
$786$	−9.28318e12	−0.867551
$787$	−1.94696e13	−1.80913	−0.904566	−	0.426333i	$-0.859805\pi$
$787$	−1.94696e13	−1.80913	−0.904566	+	0.426333i	$0.859805\pi$
$788$	−2.65882e13	−2.45652
$789$	1.10495e13	1.01507
$790$	1.06546e13	0.973232
$791$	−1.57957e11	−0.0143464
$792$	−5.85128e12	−0.528430
$793$	2.49200e12	0.223778
$794$	−1.11041e13	−0.991493
$795$	−2.70084e13	−2.39798
$796$	−5.48310e13	−4.84081
$797$	−7.57997e11	−0.0665434	−0.0332717	−	0.999446i	$-0.510593\pi$
$797$	−7.57997e11	−0.0665434	−0.0332717	+	0.999446i	$0.510593\pi$
$798$	2.02227e13	1.76533
$799$	1.36436e13	1.18432
$800$	3.07998e13	2.65854
$801$	2.47983e13	2.12851
$802$	3.29328e13	2.81089
$803$	−1.72977e11	−0.0146814
$804$	−3.91688e13	−3.30589
$805$	1.95508e12	0.164090
$806$	−2.26584e12	−0.189113
$807$	3.04193e13	2.52475
$808$	4.46766e13	3.68747
$809$	−1.57679e13	−1.29421	−0.647104	−	0.762402i	$-0.724020\pi$
$809$	−1.57679e13	−1.29421	−0.647104	+	0.762402i	$0.724020\pi$
$810$	−7.91496e13	−6.46050
$811$	2.37637e12	0.192895	0.0964474	−	0.995338i	$-0.469252\pi$
$811$	2.37637e12	0.192895	0.0964474	+	0.995338i	$0.469252\pi$
$812$	−3.36048e11	−0.0271268
$813$	2.68514e13	2.15556
$814$	2.22166e11	0.0177365
$815$	−2.56793e13	−2.03880
$816$	−9.34846e13	−7.38132
$817$	1.49976e13	1.17767
$818$	−1.89573e13	−1.48043
$819$	−3.35297e12	−0.260406
$820$	−2.25830e12	−0.174430
$821$	7.18504e12	0.551931	0.275966	−	0.961167i	$-0.411002\pi$
$821$	7.18504e12	0.551931	0.275966	+	0.961167i	$0.411002\pi$
$822$	−2.13448e13	−1.63068
$823$	1.79968e13	1.36740	0.683700	−	0.729763i	$-0.260370\pi$
$823$	1.79968e13	1.36740	0.683700	+	0.729763i	$0.260370\pi$
$824$	2.13853e13	1.61601
$825$	−5.95588e11	−0.0447613
$826$	8.11764e12	0.606764
$827$	2.04189e13	1.51795	0.758977	−	0.651118i	$-0.225700\pi$
$827$	2.04189e13	1.51795	0.758977	+	0.651118i	$0.225700\pi$
$828$	3.62558e13	2.68065
$829$	−5.99725e12	−0.441018	−0.220509	−	0.975385i	$-0.570772\pi$
$829$	−5.99725e12	−0.441018	−0.220509	+	0.975385i	$0.570772\pi$
$830$	3.57021e13	2.61122
$831$	−3.55892e13	−2.58889
$832$	2.63855e13	1.90902
$833$	−1.58334e12	−0.113939
$834$	−7.84407e13	−5.61428
$835$	−1.32894e13	−0.946056
$836$	2.82894e12	0.200307
$837$	−1.34245e13	−0.945442
$838$	−9.95826e12	−0.697566
$839$	9.11365e12	0.634985	0.317493	−	0.948261i	$-0.397159\pi$
$839$	9.11365e12	0.634985	0.317493	+	0.948261i	$0.397159\pi$
$840$	4.87530e13	3.37866
$841$	−1.44988e13	−0.999424
$842$	9.75273e12	0.668686
$843$	2.95606e13	2.01600
$844$	2.19655e13	1.49005
$845$	−1.37208e12	−0.0925816
$846$	−1.09803e14	−7.36965
$847$	5.64525e12	0.376884
$848$	7.96950e13	5.29237
$849$	−1.32227e13	−0.873446
$850$	−1.08780e13	−0.714766
$851$	−9.16439e11	−0.0598991
$852$	−1.13814e14	−7.39975
$853$	−1.51814e13	−0.981841	−0.490921	−	0.871204i	$-0.663340\pi$
$853$	−1.51814e13	−0.981841	−0.490921	+	0.871204i	$0.663340\pi$
$854$	−9.47055e12	−0.609277
$855$	5.85117e13	3.74451
$856$	−2.93702e13	−1.86971
$857$	1.27654e13	0.808389	0.404195	−	0.914673i	$-0.367552\pi$
$857$	1.27654e13	0.808389	0.404195	+	0.914673i	$0.367552\pi$
$858$	−8.77764e11	−0.0552949
$859$	−1.49424e13	−0.936378	−0.468189	−	0.883628i	$-0.655093\pi$
$859$	−1.49424e13	−0.936378	−0.468189	+	0.883628i	$0.655093\pi$
$860$	5.43107e13	3.38565
$861$	−5.51135e11	−0.0341778
$862$	−5.67224e13	−3.49923
$863$	1.15937e13	0.711496	0.355748	−	0.934582i	$-0.384226\pi$
$863$	1.15937e13	0.711496	0.355748	+	0.934582i	$0.384226\pi$
$864$	2.68936e14	16.4186
$865$	−3.73146e13	−2.26624
$866$	2.35426e13	1.42241
$867$	−1.13003e13	−0.679212
$868$	6.45379e12	0.385901
$869$	3.63746e11	0.0216376
$870$	−1.81957e12	−0.107679
$871$	−2.78898e12	−0.164197
$872$	4.49951e13	2.63537
$873$	5.04832e13	2.94159
$874$	−1.55702e13	−0.902592
$875$	−4.34964e12	−0.250852
$876$	2.67271e13	1.53350
$877$	−2.13772e13	−1.22026	−0.610130	−	0.792302i	$-0.708883\pi$
$877$	−2.13772e13	−1.22026	−0.610130	+	0.792302i	$0.708883\pi$
$878$	9.47950e12	0.538344
$879$	−5.85573e12	−0.330850
$880$	5.67537e12	0.319023
$881$	8.56434e12	0.478963	0.239482	−	0.970901i	$-0.423023\pi$
$881$	8.56434e12	0.478963	0.239482	+	0.970901i	$0.423023\pi$
$882$	1.27426e13	0.709004
$883$	8.23945e12	0.456116	0.228058	−	0.973648i	$-0.426762\pi$
$883$	8.23945e12	0.456116	0.228058	+	0.973648i	$0.426762\pi$
$884$	−1.20154e13	−0.661764
$885$	3.29423e13	1.80513
$886$	−4.39300e13	−2.39502
$887$	−1.43874e13	−0.780413	−0.390207	−	0.920727i	$-0.627596\pi$
$887$	−1.43874e13	−0.780413	−0.390207	+	0.920727i	$0.627596\pi$
$888$	−2.28529e13	−1.23334
$889$	−3.93828e12	−0.211470
$890$	−3.85656e13	−2.06037
$891$	−2.70215e12	−0.143635
$892$	−3.38040e13	−1.78783
$893$	3.53416e13	1.85975
$894$	5.05415e13	2.64624
$895$	4.34016e13	2.26101
$896$	−5.70578e13	−2.95753
$897$	3.62079e12	0.186740
$898$	−2.85785e13	−1.46655
$899$	−1.60354e11	−0.00818771
$900$	6.56130e13	3.33349
$901$	−1.68408e13	−0.851336
$902$	−1.02869e11	−0.00517436
$903$	1.32544e13	0.663386
$904$	3.03270e12	0.151033
$905$	−5.07335e12	−0.251406
$906$	−3.64128e13	−1.79546
$907$	−3.37696e13	−1.65689	−0.828444	−	0.560072i	$-0.810774\pi$
$907$	−3.37696e13	−1.65689	−0.828444	+	0.560072i	$0.810774\pi$
$908$	−7.80470e13	−3.81039
$909$	4.73870e13	2.30209
$910$	5.21444e12	0.252070
$911$	−2.79828e12	−0.134604	−0.0673020	−	0.997733i	$-0.521439\pi$
$911$	−2.79828e12	−0.134604	−0.0673020	+	0.997733i	$0.521439\pi$
$912$	−2.42157e14	−11.5910
$913$	1.21886e12	0.0580545
$914$	−4.68258e13	−2.21936
$915$	−3.84326e13	−1.81261
$916$	−5.39389e13	−2.53147
$917$	1.88273e12	0.0879276
$918$	−9.49841e13	−4.41427
$919$	1.23660e11	0.00571885	0.00285942	−	0.999996i	$-0.499090\pi$
$919$	1.23660e11	0.00571885	0.00285942	+	0.999996i	$0.499090\pi$
$920$	−3.75366e13	−1.72747
$921$	−2.16131e13	−0.989801
$922$	4.73057e13	2.15588
$923$	−8.10403e12	−0.367531
$924$	2.50013e12	0.112834
$925$	−1.65850e12	−0.0744866
$926$	3.63228e13	1.62342
$927$	2.26827e13	1.00887
$928$	3.21241e12	0.142189
$929$	3.56389e13	1.56984	0.784918	−	0.619600i	$-0.212705\pi$
$929$	3.56389e13	1.56984	0.784918	+	0.619600i	$0.212705\pi$
$930$	3.49448e13	1.53182
$931$	−4.10138e12	−0.178919
$932$	1.15837e14	5.02893
$933$	−2.75085e13	−1.18850
$934$	8.14797e13	3.50339
$935$	−1.19929e12	−0.0513184
$936$	6.43756e13	2.74145
$937$	−2.61283e12	−0.110735	−0.0553673	−	0.998466i	$-0.517633\pi$
$937$	−2.61283e12	−0.110735	−0.0553673	+	0.998466i	$0.517633\pi$
$938$	1.05992e13	0.447055
$939$	−9.67448e10	−0.00406100
$940$	1.27982e14	5.34656
$941$	3.25111e13	1.35169	0.675847	−	0.737042i	$-0.263778\pi$
$941$	3.25111e13	1.35169	0.675847	+	0.737042i	$0.263778\pi$
$942$	4.11737e13	1.70369
$943$	4.24338e11	0.0174747
$944$	−9.72046e13	−3.98394
$945$	3.08943e13	1.26019
$946$	2.47394e12	0.100433
$947$	−4.43944e12	−0.179371	−0.0896856	−	0.995970i	$-0.528586\pi$
$947$	−4.43944e12	−0.179371	−0.0896856	+	0.995970i	$0.528586\pi$
$948$	−5.62035e13	−2.26009
$949$	1.90308e12	0.0761658
$950$	−2.81777e13	−1.12241
$951$	1.89646e13	0.751850
$952$	3.03994e13	1.19950
$953$	−6.47621e12	−0.254333	−0.127167	−	0.991881i	$-0.540588\pi$
$953$	−6.47621e12	−0.254333	−0.127167	+	0.991881i	$0.540588\pi$
$954$	1.35533e14	5.29759
$955$	−4.87115e13	−1.89503
$956$	1.32667e14	5.13691
$957$	−6.21196e10	−0.00239400
$958$	−4.46841e13	−1.71399
$959$	4.32895e12	0.165272
$960$	−4.06928e14	−15.4631
$961$	−2.33600e13	−0.883523
$962$	−2.44426e12	−0.0920153
$963$	−3.11520e13	−1.16726
$964$	7.54209e13	2.81284
$965$	−4.33275e13	−1.60839
$966$	−1.37604e13	−0.508434
$967$	2.29870e13	0.845401	0.422700	−	0.906269i	$-0.361082\pi$
$967$	2.29870e13	0.845401	0.422700	+	0.906269i	$0.361082\pi$
$968$	−1.08387e14	−3.96768
$969$	5.11714e13	1.86453
$970$	−7.85101e13	−2.84743
$971$	−4.02348e13	−1.45250	−0.726248	−	0.687432i	$-0.758738\pi$
$971$	−4.02348e13	−1.45250	−0.726248	+	0.687432i	$0.758738\pi$
$972$	1.86885e14	6.71548
$973$	1.59086e13	0.569016
$974$	−4.85246e13	−1.72761
$975$	6.55264e12	0.232218
$976$	1.13405e14	4.00044
$977$	−4.04036e13	−1.41871	−0.709356	−	0.704851i	$-0.751014\pi$
$977$	−4.04036e13	−1.41871	−0.709356	+	0.704851i	$0.751014\pi$
$978$	1.80739e14	6.31723
$979$	−1.31662e12	−0.0458077
$980$	−1.48523e13	−0.514370
$981$	4.77249e13	1.64526
$982$	7.91509e12	0.271615
$983$	4.21025e13	1.43819	0.719096	−	0.694911i	$-0.244556\pi$
$983$	4.21025e13	1.43819	0.719096	+	0.694911i	$0.244556\pi$
$984$	1.05816e13	0.359809
$985$	2.91975e13	0.988288
$986$	−1.13457e12	−0.0382284
$987$	3.12338e13	1.04761
$988$	−3.11240e13	−1.03917
$989$	−1.02050e13	−0.339181
$990$	9.65182e12	0.319338
$991$	−3.81192e13	−1.25549	−0.627744	−	0.778420i	$-0.716022\pi$
$991$	−3.81192e13	−1.25549	−0.627744	+	0.778420i	$0.716022\pi$
$992$	−6.16942e13	−2.02275
$993$	2.12068e13	0.692156
$994$	3.07985e13	1.00067
$995$	6.02122e13	1.94751
$996$	−1.88330e14	−6.06390
$997$	−2.69721e12	−0.0864543	−0.0432272	−	0.999065i	$-0.513764\pi$
$997$	−2.69721e12	−0.0864543	−0.0432272	+	0.999065i	$0.513764\pi$
$998$	8.75155e13	2.79253
$999$	−1.44816e13	−0.460016

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.10.a.d.1.15	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.10.a.d.1.15	✓	15	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)

\(f(q)\)	\(=\)	\(q+45.2074 q^{2} +261.874 q^{3} +1531.71 q^{4} -1682.03 q^{5} +11838.6 q^{6} -2401.00 q^{7} +46098.2 q^{8} +48894.9 q^{9} +O(q^{10})\)	\(q+45.2074 q^{2} +261.874 q^{3} +1531.71 q^{4} -1682.03 q^{5} +11838.6 q^{6} -2401.00 q^{7} +46098.2 q^{8} +48894.9 q^{9} -76040.1 q^{10} -2595.99 q^{11} +401114. q^{12} +28561.0 q^{13} -108543. q^{14} -440479. q^{15} +1.29975e6 q^{16} -274656. q^{17} +2.21041e6 q^{18} -711453. q^{19} -2.57637e6 q^{20} -628759. q^{21} -117358. q^{22} +484103. q^{23} +1.20719e7 q^{24} +876094. q^{25} +1.29117e6 q^{26} +7.64984e6 q^{27} -3.67763e6 q^{28} +91376.3 q^{29} -1.99129e7 q^{30} -1.75488e6 q^{31} +3.51558e7 q^{32} -679822. q^{33} -1.24165e7 q^{34} +4.03855e6 q^{35} +7.48926e7 q^{36} -1.89306e6 q^{37} -3.21629e7 q^{38} +7.47938e6 q^{39} -7.75385e7 q^{40} +876544. q^{41} -2.84245e7 q^{42} -2.10803e7 q^{43} -3.97629e6 q^{44} -8.22426e7 q^{45} +2.18850e7 q^{46} -4.96753e7 q^{47} +3.40369e8 q^{48} +5.76480e6 q^{49} +3.96059e7 q^{50} -7.19253e7 q^{51} +4.37471e7 q^{52} +6.13159e7 q^{53} +3.45829e8 q^{54} +4.36653e6 q^{55} -1.10682e8 q^{56} -1.86311e8 q^{57} +4.13088e6 q^{58} -7.47874e7 q^{59} -6.74685e8 q^{60} +8.72517e7 q^{61} -7.93335e7 q^{62} -1.17397e8 q^{63} +9.23831e8 q^{64} -4.80404e7 q^{65} -3.07329e7 q^{66} -9.76501e7 q^{67} -4.20693e8 q^{68} +1.26774e8 q^{69} +1.82572e8 q^{70} -2.83745e8 q^{71} +2.25397e9 q^{72} +6.66323e7 q^{73} -8.55804e7 q^{74} +2.29426e8 q^{75} -1.08974e9 q^{76} +6.23297e6 q^{77} +3.38123e8 q^{78} -1.40119e8 q^{79} -2.18621e9 q^{80} +1.04089e9 q^{81} +3.96263e7 q^{82} -4.69517e8 q^{83} -9.63074e8 q^{84} +4.61979e8 q^{85} -9.52984e8 q^{86} +2.39291e7 q^{87} -1.19670e8 q^{88} +5.07175e8 q^{89} -3.71797e9 q^{90} -6.85750e7 q^{91} +7.41504e8 q^{92} -4.59557e8 q^{93} -2.24569e9 q^{94} +1.19668e9 q^{95} +9.20638e9 q^{96} +1.03248e9 q^{97} +2.60611e8 q^{98} -1.26931e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 22 q^{2} + q^{3} + 6402 q^{4} + 1694 q^{5} + 4189 q^{6} - 36015 q^{7} - 1704 q^{8} + 160366 q^{9}+O(q^{10}) \) 15 * q + 22 * q^2 + q^3 + 6402 * q^4 + 1694 * q^5 + 4189 * q^6 - 36015 * q^7 - 1704 * q^8 + 160366 * q^9	\( 15 q + 22 q^{2} + q^{3} + 6402 q^{4} + 1694 q^{5} + 4189 q^{6} - 36015 q^{7} - 1704 q^{8} + 160366 q^{9} - 69748 q^{10} + 23441 q^{11} + 64437 q^{12} + 428415 q^{13} - 52822 q^{14} - 68316 q^{15} + 2694730 q^{16} + 606640 q^{17} + 1242207 q^{18} + 1762528 q^{19} + 43054 q^{20} - 2401 q^{21} + 119431 q^{22} + 3649531 q^{23} + 15986883 q^{24} + 9120575 q^{25} + 628342 q^{26} - 5957633 q^{27} - 15371202 q^{28} + 18072234 q^{29} - 58091296 q^{30} - 1096937 q^{31} + 6565744 q^{32} - 18425617 q^{33} - 46741622 q^{34} - 4067294 q^{35} + 132788567 q^{36} - 34982109 q^{37} - 2819104 q^{38} + 28561 q^{39} + 2107274 q^{40} + 59341985 q^{41} - 10057789 q^{42} + 38829122 q^{43} + 202791507 q^{44} + 2955478 q^{45} + 165169119 q^{46} + 18734035 q^{47} + 340656557 q^{48} + 86472015 q^{49} + 220443888 q^{50} + 93517168 q^{51} + 182847522 q^{52} + 332415086 q^{53} + 567466451 q^{54} - 120908856 q^{55} + 4091304 q^{56} + 62932402 q^{57} + 180863580 q^{58} + 28220174 q^{59} + 467078152 q^{60} + 404536605 q^{61} + 4283245 q^{62} - 385038766 q^{63} + 1276533074 q^{64} + 48382334 q^{65} + 1696546059 q^{66} + 746448213 q^{67} + 492702034 q^{68} + 453755667 q^{69} + 167464948 q^{70} + 81316200 q^{71} + 1255645679 q^{72} + 12687907 q^{73} + 1350657501 q^{74} - 164589481 q^{75} + 679560842 q^{76} - 56281841 q^{77} + 119642029 q^{78} + 1896008477 q^{79} - 1458560390 q^{80} + 3853340295 q^{81} + 410985635 q^{82} - 753815178 q^{83} - 154713237 q^{84} - 259541636 q^{85} - 1842794378 q^{86} + 1391390932 q^{87} + 288708813 q^{88} + 1109816012 q^{89} + 1196058116 q^{90} - 1028624415 q^{91} + 2409710277 q^{92} + 3345736043 q^{93} - 1423358651 q^{94} + 4615875678 q^{95} + 11615772371 q^{96} + 1054179205 q^{97} + 126825622 q^{98} - 2512222258 q^{99}+O(q^{100}) \) 15 * q + 22 * q^2 + q^3 + 6402 * q^4 + 1694 * q^5 + 4189 * q^6 - 36015 * q^7 - 1704 * q^8 + 160366 * q^9 - 69748 * q^10 + 23441 * q^11 + 64437 * q^12 + 428415 * q^13 - 52822 * q^14 - 68316 * q^15 + 2694730 * q^16 + 606640 * q^17 + 1242207 * q^18 + 1762528 * q^19 + 43054 * q^20 - 2401 * q^21 + 119431 * q^22 + 3649531 * q^23 + 15986883 * q^24 + 9120575 * q^25 + 628342 * q^26 - 5957633 * q^27 - 15371202 * q^28 + 18072234 * q^29 - 58091296 * q^30 - 1096937 * q^31 + 6565744 * q^32 - 18425617 * q^33 - 46741622 * q^34 - 4067294 * q^35 + 132788567 * q^36 - 34982109 * q^37 - 2819104 * q^38 + 28561 * q^39 + 2107274 * q^40 + 59341985 * q^41 - 10057789 * q^42 + 38829122 * q^43 + 202791507 * q^44 + 2955478 * q^45 + 165169119 * q^46 + 18734035 * q^47 + 340656557 * q^48 + 86472015 * q^49 + 220443888 * q^50 + 93517168 * q^51 + 182847522 * q^52 + 332415086 * q^53 + 567466451 * q^54 - 120908856 * q^55 + 4091304 * q^56 + 62932402 * q^57 + 180863580 * q^58 + 28220174 * q^59 + 467078152 * q^60 + 404536605 * q^61 + 4283245 * q^62 - 385038766 * q^63 + 1276533074 * q^64 + 48382334 * q^65 + 1696546059 * q^66 + 746448213 * q^67 + 492702034 * q^68 + 453755667 * q^69 + 167464948 * q^70 + 81316200 * q^71 + 1255645679 * q^72 + 12687907 * q^73 + 1350657501 * q^74 - 164589481 * q^75 + 679560842 * q^76 - 56281841 * q^77 + 119642029 * q^78 + 1896008477 * q^79 - 1458560390 * q^80 + 3853340295 * q^81 + 410985635 * q^82 - 753815178 * q^83 - 154713237 * q^84 - 259541636 * q^85 - 1842794378 * q^86 + 1391390932 * q^87 + 288708813 * q^88 + 1109816012 * q^89 + 1196058116 * q^90 - 1028624415 * q^91 + 2409710277 * q^92 + 3345736043 * q^93 - 1423358651 * q^94 + 4615875678 * q^95 + 11615772371 * q^96 + 1054179205 * q^97 + 126825622 * q^98 - 2512222258 * q^99

Introduction

L-functions

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