LMFDB - Embedded newform 91.8.a.e.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [91,8,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, 8, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("91.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 91 = 7 \cdot 13 $
Weight:	$ k $	$=$	$ 8 $
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:	$28.4270373191$
Analytic rank:	$0$
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} - 6 x^{11} - 1243 x^{10} + 5598 x^{9} + 567554 x^{8} - 1739560 x^{7} - 117081910 x^{6} + \cdots + 59402280000 $ x^12 - 6x^11 - 1243x^10 + 5598x^9 + 567554x^8 - 1739560x^7 - 117081910x^6 + 186018392x^5 + 10752389517x^4 + 491049966x^3 - 344602049215x^2 - 835334324470*x + 59402280000
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Root			$-4.08138$ 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)

$f(q)$	$=$	$q+5.08138 q^{2} -25.2372 q^{3} -102.180 q^{4} +250.262 q^{5} -128.240 q^{6} +343.000 q^{7} -1169.63 q^{8} -1550.08 q^{9} +O(q^{10})$	\(q+5.08138 q^{2} -25.2372 q^{3} -102.180 q^{4} +250.262 q^{5} -128.240 q^{6} +343.000 q^{7} -1169.63 q^{8} -1550.08 q^{9} +1271.68 q^{10} +79.1782 q^{11} +2578.73 q^{12} +2197.00 q^{13} +1742.91 q^{14} -6315.91 q^{15} +7135.66 q^{16} -19865.7 q^{17} -7876.57 q^{18} +6411.64 q^{19} -25571.7 q^{20} -8656.36 q^{21} +402.335 q^{22} +108189. q^{23} +29518.2 q^{24} -15494.0 q^{25} +11163.8 q^{26} +94313.5 q^{27} -35047.6 q^{28} +249746. q^{29} -32093.5 q^{30} +60879.1 q^{31} +185972. q^{32} -1998.24 q^{33} -100945. q^{34} +85839.8 q^{35} +158387. q^{36} +182166. q^{37} +32580.0 q^{38} -55446.1 q^{39} -292714. q^{40} -89925.4 q^{41} -43986.2 q^{42} +346302. q^{43} -8090.40 q^{44} -387927. q^{45} +549751. q^{46} +631857. q^{47} -180084. q^{48} +117649. q^{49} -78730.7 q^{50} +501354. q^{51} -224489. q^{52} -861465. q^{53} +479243. q^{54} +19815.3 q^{55} -401183. q^{56} -161812. q^{57} +1.26906e6 q^{58} -157822. q^{59} +645357. q^{60} +2.00450e6 q^{61} +309350. q^{62} -531679. q^{63} +31628.0 q^{64} +549825. q^{65} -10153.8 q^{66} -999718. q^{67} +2.02987e6 q^{68} -2.73039e6 q^{69} +436185. q^{70} -315139. q^{71} +1.81302e6 q^{72} +3.40160e6 q^{73} +925657. q^{74} +391024. q^{75} -655139. q^{76} +27158.1 q^{77} -281743. q^{78} -646177. q^{79} +1.78578e6 q^{80} +1.00983e6 q^{81} -456945. q^{82} -8.03418e6 q^{83} +884503. q^{84} -4.97163e6 q^{85} +1.75969e6 q^{86} -6.30290e6 q^{87} -92609.2 q^{88} +3.26867e6 q^{89} -1.97120e6 q^{90} +753571. q^{91} -1.10547e7 q^{92} -1.53642e6 q^{93} +3.21070e6 q^{94} +1.60459e6 q^{95} -4.69340e6 q^{96} +3.88681e6 q^{97} +597819. q^{98} -122733. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9}+O(q^{10}) $ 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9} + 6668 q^{10} + 12168 q^{11} - 183 q^{12} + 26364 q^{13} + 2058 q^{14} - 28790 q^{15} + 85914 q^{16} + 82710 q^{17} - 44965 q^{18} - 10302 q^{19} + 141318 q^{20} + 28126 q^{21} - 97457 q^{22} + 98376 q^{23} - 519981 q^{24} + 272736 q^{25} + 13182 q^{26} + 306652 q^{27} + 338198 q^{28} + 350592 q^{29} + 231528 q^{30} + 55092 q^{31} + 114420 q^{32} + 609912 q^{33} + 812002 q^{34} + 351918 q^{35} + 1472143 q^{36} + 376310 q^{37} + 2825424 q^{38} + 180154 q^{39} + 2169290 q^{40} + 1387272 q^{41} + 105987 q^{42} + 568708 q^{43} + 3392031 q^{44} + 3556226 q^{45} - 1736829 q^{46} + 1359444 q^{47} + 4151249 q^{48} + 1411788 q^{49} + 3983712 q^{50} + 2709260 q^{51} + 2166242 q^{52} + 2061780 q^{53} + 2196651 q^{54} - 2112846 q^{55} + 78204 q^{56} + 2359902 q^{57} + 670268 q^{58} + 395964 q^{59} - 1052376 q^{60} + 444006 q^{61} + 2854353 q^{62} + 3739386 q^{63} + 12026858 q^{64} + 2254122 q^{65} - 4605681 q^{66} - 3094010 q^{67} + 4668954 q^{68} + 3839892 q^{69} + 2287124 q^{70} + 5694366 q^{71} - 9780585 q^{72} + 7052346 q^{73} - 4436259 q^{74} - 16288696 q^{75} - 3051830 q^{76} + 4173624 q^{77} + 678873 q^{78} + 4304160 q^{79} + 3807018 q^{80} - 6689556 q^{81} - 4733665 q^{82} + 2704554 q^{83} - 62769 q^{84} + 9301878 q^{85} + 1510998 q^{86} + 16231802 q^{87} - 70453923 q^{88} - 10986042 q^{89} - 12851300 q^{90} + 9042852 q^{91} - 16505451 q^{92} - 47230934 q^{93} - 24306151 q^{94} - 21839424 q^{95} - 86512741 q^{96} - 24462382 q^{97} + 705894 q^{98} + 11555078 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9 + 6668 * q^10 + 12168 * q^11 - 183 * q^12 + 26364 * q^13 + 2058 * q^14 - 28790 * q^15 + 85914 * q^16 + 82710 * q^17 - 44965 * q^18 - 10302 * q^19 + 141318 * q^20 + 28126 * q^21 - 97457 * q^22 + 98376 * q^23 - 519981 * q^24 + 272736 * q^25 + 13182 * q^26 + 306652 * q^27 + 338198 * q^28 + 350592 * q^29 + 231528 * q^30 + 55092 * q^31 + 114420 * q^32 + 609912 * q^33 + 812002 * q^34 + 351918 * q^35 + 1472143 * q^36 + 376310 * q^37 + 2825424 * q^38 + 180154 * q^39 + 2169290 * q^40 + 1387272 * q^41 + 105987 * q^42 + 568708 * q^43 + 3392031 * q^44 + 3556226 * q^45 - 1736829 * q^46 + 1359444 * q^47 + 4151249 * q^48 + 1411788 * q^49 + 3983712 * q^50 + 2709260 * q^51 + 2166242 * q^52 + 2061780 * q^53 + 2196651 * q^54 - 2112846 * q^55 + 78204 * q^56 + 2359902 * q^57 + 670268 * q^58 + 395964 * q^59 - 1052376 * q^60 + 444006 * q^61 + 2854353 * q^62 + 3739386 * q^63 + 12026858 * q^64 + 2254122 * q^65 - 4605681 * q^66 - 3094010 * q^67 + 4668954 * q^68 + 3839892 * q^69 + 2287124 * q^70 + 5694366 * q^71 - 9780585 * q^72 + 7052346 * q^73 - 4436259 * q^74 - 16288696 * q^75 - 3051830 * q^76 + 4173624 * q^77 + 678873 * q^78 + 4304160 * q^79 + 3807018 * q^80 - 6689556 * q^81 - 4733665 * q^82 + 2704554 * q^83 - 62769 * q^84 + 9301878 * q^85 + 1510998 * q^86 + 16231802 * q^87 - 70453923 * q^88 - 10986042 * q^89 - 12851300 * q^90 + 9042852 * q^91 - 16505451 * q^92 - 47230934 * q^93 - 24306151 * q^94 - 21839424 * q^95 - 86512741 * q^96 - 24462382 * q^97 + 705894 * q^98 + 11555078 * 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 $

$2$	5.08138	0.449135	0.224567	−	0.974459i	$-0.427903\pi$
$2$	5.08138	0.449135	0.224567	+	0.974459i	$0.427903\pi$
$3$	−25.2372	−0.539655	−0.269828	−	0.962909i	$-0.586967\pi$
$3$	−25.2372	−0.539655	−0.269828	+	0.962909i	$0.586967\pi$
$4$	−102.180	−0.798278
$5$	250.262	0.895364	0.447682	−	0.894193i	$-0.352250\pi$
$5$	250.262	0.895364	0.447682	+	0.894193i	$0.352250\pi$
$6$	−128.240	−0.242378
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	−1169.63	−0.807669
$9$	−1550.08	−0.708772
$10$	1271.68	0.402139
$11$	79.1782	0.0179362	0.00896812	−	0.999960i	$-0.497145\pi$
$11$	79.1782	0.0179362	0.00896812	+	0.999960i	$0.497145\pi$
$12$	2578.73	0.430795
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	1742.91	0.169757
$15$	−6315.91	−0.483188
$16$	7135.66	0.435526
$17$	−19865.7	−0.980692	−0.490346	−	0.871528i	$-0.663129\pi$
$17$	−19865.7	−0.980692	−0.490346	+	0.871528i	$0.663129\pi$
$18$	−7876.57	−0.318334
$19$	6411.64	0.214453	0.107226	−	0.994235i	$-0.465803\pi$
$19$	6411.64	0.214453	0.107226	+	0.994235i	$0.465803\pi$
$20$	−25571.7	−0.714750
$21$	−8656.36	−0.203971
$22$	402.335	0.00805579
$23$	108189.	1.85411	0.927057	−	0.374919i	$-0.122330\pi$
$23$	108189.	1.85411	0.927057	+	0.374919i	$0.122330\pi$
$24$	29518.2	0.435863
$25$	−15494.0	−0.198323
$26$	11163.8	0.124568
$27$	94313.5	0.922148
$28$	−35047.6	−0.301721
$29$	249746.	1.90154	0.950772	−	0.309892i	$-0.100293\pi$
$29$	249746.	1.90154	0.950772	+	0.309892i	$0.100293\pi$
$30$	−32093.5	−0.217017
$31$	60879.1	0.367030	0.183515	−	0.983017i	$-0.441252\pi$
$31$	60879.1	0.367030	0.183515	+	0.983017i	$0.441252\pi$
$32$	185972.	1.00328
$33$	−1998.24	−0.00967939
$34$	−100945.	−0.440463
$35$	85839.8	0.338416
$36$	158387.	0.565797
$37$	182166.	0.591238	0.295619	−	0.955306i	$-0.404474\pi$
$37$	182166.	0.591238	0.295619	+	0.955306i	$0.404474\pi$
$38$	32580.0	0.0963181
$39$	−55446.1	−0.149673
$40$	−292714.	−0.723158
$41$	−89925.4	−0.203769	−0.101885	−	0.994796i	$-0.532487\pi$
$41$	−89925.4	−0.203769	−0.101885	+	0.994796i	$0.532487\pi$
$42$	−43986.2	−0.0916103
$43$	346302.	0.664225	0.332112	−	0.943240i	$-0.392239\pi$
$43$	346302.	0.664225	0.332112	+	0.943240i	$0.392239\pi$
$44$	−8090.40	−0.0143181
$45$	−387927.	−0.634609
$46$	549751.	0.832747
$47$	631857.	0.887720	0.443860	−	0.896096i	$-0.353609\pi$
$47$	631857.	0.887720	0.443860	+	0.896096i	$0.353609\pi$
$48$	−180084.	−0.235034
$49$	117649.	0.142857
$50$	−78730.7	−0.0890736
$51$	501354.	0.529236
$52$	−224489.	−0.221402
$53$	−861465.	−0.794826	−0.397413	−	0.917640i	$-0.630092\pi$
$53$	−861465.	−0.794826	−0.397413	+	0.917640i	$0.630092\pi$
$54$	479243.	0.414169
$55$	19815.3	0.0160595
$56$	−401183.	−0.305270
$57$	−161812.	−0.115731
$58$	1.26906e6	0.854049
$59$	−157822.	−0.100042	−0.0500212	−	0.998748i	$-0.515929\pi$
$59$	−157822.	−0.100042	−0.0500212	+	0.998748i	$0.515929\pi$
$60$	645357.	0.385719
$61$	2.00450e6	1.13071	0.565354	−	0.824848i	$-0.308739\pi$
$61$	2.00450e6	1.13071	0.565354	+	0.824848i	$0.308739\pi$
$62$	309350.	0.164846
$63$	−531679.	−0.267891
$64$	31628.0	0.0150814
$65$	549825.	0.248329
$66$	−10153.8	−0.00434735
$67$	−999718.	−0.406084	−0.203042	−	0.979170i	$-0.565083\pi$
$67$	−999718.	−0.406084	−0.203042	+	0.979170i	$0.565083\pi$
$68$	2.02987e6	0.782864
$69$	−2.73039e6	−1.00058
$70$	436185.	0.151994
$71$	−315139.	−0.104496	−0.0522478	−	0.998634i	$-0.516639\pi$
$71$	−315139.	−0.104496	−0.0522478	+	0.998634i	$0.516639\pi$
$72$	1.81302e6	0.572453
$73$	3.40160e6	1.02342	0.511710	−	0.859158i	$-0.329012\pi$
$73$	3.40160e6	1.02342	0.511710	+	0.859158i	$0.329012\pi$
$74$	925657.	0.265545
$75$	391024.	0.107026
$76$	−655139.	−0.171193
$77$	27158.1	0.00677926
$78$	−281743.	−0.0672236
$79$	−646177.	−0.147454	−0.0737271	−	0.997278i	$-0.523489\pi$
$79$	−646177.	−0.147454	−0.0737271	+	0.997278i	$0.523489\pi$
$80$	1.78578e6	0.389954
$81$	1.00983e6	0.211130
$82$	−456945.	−0.0915199
$83$	−8.03418e6	−1.54230	−0.771149	−	0.636655i	$-0.780318\pi$
$83$	−8.03418e6	−1.54230	−0.771149	+	0.636655i	$0.780318\pi$
$84$	884503.	0.162825
$85$	−4.97163e6	−0.878076
$86$	1.75969e6	0.298326
$87$	−6.30290e6	−1.02618
$88$	−92609.2	−0.0144865
$89$	3.26867e6	0.491480	0.245740	−	0.969336i	$-0.420969\pi$
$89$	3.26867e6	0.491480	0.245740	+	0.969336i	$0.420969\pi$
$90$	−1.97120e6	−0.285025
$91$	753571.	0.104828
$92$	−1.10547e7	−1.48010
$93$	−1.53642e6	−0.198070
$94$	3.21070e6	0.398706
$95$	1.60459e6	0.192013
$96$	−4.69340e6	−0.541425
$97$	3.88681e6	0.432406	0.216203	−	0.976348i	$-0.430633\pi$
$97$	3.88681e6	0.432406	0.216203	+	0.976348i	$0.430633\pi$
$98$	597819.	0.0641621
$99$	−122733.	−0.0127127
$100$	1.58317e6	0.158317
$101$	−1.32661e7	−1.28120	−0.640601	−	0.767874i	$-0.721315\pi$
$101$	−1.32661e7	−1.28120	−0.640601	+	0.767874i	$0.721315\pi$
$102$	2.54757e6	0.237698
$103$	1.37517e7	1.24001	0.620006	−	0.784597i	$-0.287130\pi$
$103$	1.37517e7	1.24001	0.620006	+	0.784597i	$0.287130\pi$
$104$	−2.56968e6	−0.224007
$105$	−2.16636e6	−0.182628
$106$	−4.37743e6	−0.356984
$107$	−3.46186e6	−0.273191	−0.136595	−	0.990627i	$-0.543616\pi$
$107$	−3.46186e6	−0.273191	−0.136595	+	0.990627i	$0.543616\pi$
$108$	−9.63691e6	−0.736131
$109$	3.12654e6	0.231245	0.115622	−	0.993293i	$-0.463114\pi$
$109$	3.12654e6	0.231245	0.115622	+	0.993293i	$0.463114\pi$
$110$	100689.	0.00721286
$111$	−4.59737e6	−0.319065
$112$	2.44753e6	0.164613
$113$	4.84294e6	0.315744	0.157872	−	0.987460i	$-0.449537\pi$
$113$	4.84294e6	0.315744	0.157872	+	0.987460i	$0.449537\pi$
$114$	−822227.	−0.0519786
$115$	2.70756e7	1.66011
$116$	−2.55190e7	−1.51796
$117$	−3.40554e6	−0.196578
$118$	−801951.	−0.0449325
$119$	−6.81393e6	−0.370667
$120$	7.38727e6	0.390256
$121$	−1.94809e7	−0.999678
$122$	1.01856e7	0.507841
$123$	2.26946e6	0.109965
$124$	−6.22060e6	−0.292992
$125$	−2.34293e7	−1.07294
$126$	−2.70166e6	−0.120319
$127$	−3.32978e7	−1.44246	−0.721228	−	0.692697i	$-0.756422\pi$
$127$	−3.32978e7	−1.44246	−0.721228	+	0.692697i	$0.756422\pi$
$128$	−2.36436e7	−0.996505
$129$	−8.73968e6	−0.358452
$130$	2.79387e6	0.111533
$131$	−2.65056e7	−1.03012	−0.515061	−	0.857154i	$-0.672231\pi$
$131$	−2.65056e7	−1.03012	−0.515061	+	0.857154i	$0.672231\pi$
$132$	204179.	0.00772684
$133$	2.19919e6	0.0810555
$134$	−5.07995e6	−0.182386
$135$	2.36031e7	0.825659
$136$	2.32355e7	0.792074
$137$	4.90663e7	1.63028	0.815138	−	0.579267i	$-0.196661\pi$
$137$	4.90663e7	1.63028	0.815138	+	0.579267i	$0.196661\pi$
$138$	−1.38742e7	−0.449397
$139$	4.79488e7	1.51435	0.757174	−	0.653213i	$-0.226579\pi$
$139$	4.79488e7	1.51435	0.757174	+	0.653213i	$0.226579\pi$
$140$	−8.77108e6	−0.270150
$141$	−1.59463e7	−0.479063
$142$	−1.60134e6	−0.0469326
$143$	173955.	0.00497462
$144$	−1.10609e7	−0.308689
$145$	6.25020e7	1.70257
$146$	1.72848e7	0.459653
$147$	−2.96913e6	−0.0770936
$148$	−1.86137e7	−0.471972
$149$	7.72401e7	1.91289	0.956447	−	0.291907i	$-0.0942897\pi$
$149$	7.72401e7	1.91289	0.956447	+	0.291907i	$0.0942897\pi$
$150$	1.98694e6	0.0480691
$151$	−2.45116e7	−0.579364	−0.289682	−	0.957123i	$-0.593550\pi$
$151$	−2.45116e7	−0.579364	−0.289682	+	0.957123i	$0.593550\pi$
$152$	−7.49924e6	−0.173207
$153$	3.07935e7	0.695087
$154$	138001.	0.00304480
$155$	1.52357e7	0.328626
$156$	5.66546e6	0.119481
$157$	2.83667e7	0.585005	0.292503	−	0.956265i	$-0.405512\pi$
$157$	2.83667e7	0.585005	0.292503	+	0.956265i	$0.405512\pi$
$158$	−3.28347e6	−0.0662268
$159$	2.17409e7	0.428932
$160$	4.65416e7	0.898300
$161$	3.71089e7	0.700790
$162$	5.13131e6	0.0948257
$163$	−2.08358e7	−0.376837	−0.188419	−	0.982089i	$-0.560336\pi$
$163$	−2.08358e7	−0.376837	−0.188419	+	0.982089i	$0.560336\pi$
$164$	9.18854e6	0.162665
$165$	−500082.	−0.00866658
$166$	−4.08247e7	−0.692700
$167$	1.02968e8	1.71078	0.855391	−	0.517982i	$-0.173317\pi$
$167$	1.02968e8	1.71078	0.855391	+	0.517982i	$0.173317\pi$
$168$	1.01247e7	0.164741
$169$	4.82681e6	0.0769231
$170$	−2.52627e7	−0.394374
$171$	−9.93858e6	−0.151998
$172$	−3.53850e7	−0.530236
$173$	7.84611e7	1.15211	0.576054	−	0.817412i	$-0.304592\pi$
$173$	7.84611e7	1.15211	0.576054	+	0.817412i	$0.304592\pi$
$174$	−3.20274e7	−0.460892
$175$	−5.31443e6	−0.0749590
$176$	564989.	0.00781170
$177$	3.98297e6	0.0539885
$178$	1.66093e7	0.220741
$179$	−4.58627e7	−0.597688	−0.298844	−	0.954302i	$-0.596601\pi$
$179$	−4.58627e7	−0.597688	−0.298844	+	0.954302i	$0.596601\pi$
$180$	3.96382e7	0.506595
$181$	−4.79671e7	−0.601268	−0.300634	−	0.953740i	$-0.597198\pi$
$181$	−4.79671e7	−0.601268	−0.300634	+	0.953740i	$0.597198\pi$
$182$	3.82918e6	0.0470821
$183$	−5.05878e7	−0.610193
$184$	−1.26541e8	−1.49751
$185$	4.55893e7	0.529373
$186$	−7.80711e6	−0.0889601
$187$	−1.57293e6	−0.0175899
$188$	−6.45629e7	−0.708648
$189$	3.23495e7	0.348539
$190$	8.15352e6	0.0862398
$191$	−9.77001e7	−1.01456	−0.507281	−	0.861781i	$-0.669349\pi$
$191$	−9.77001e7	−1.01456	−0.507281	+	0.861781i	$0.669349\pi$
$192$	−798203.	−0.00813877
$193$	1.59457e8	1.59658	0.798292	−	0.602270i	$-0.205737\pi$
$193$	1.59457e8	1.59658	0.798292	+	0.602270i	$0.205737\pi$
$194$	1.97504e7	0.194209
$195$	−1.38760e7	−0.134012
$196$	−1.20213e7	−0.114040
$197$	1.18003e7	0.109967	0.0549833	−	0.998487i	$-0.482489\pi$
$197$	1.18003e7	0.109967	0.0549833	+	0.998487i	$0.482489\pi$
$198$	−623653.	−0.00570972
$199$	−2.19765e7	−0.197684	−0.0988422	−	0.995103i	$-0.531514\pi$
$199$	−2.19765e7	−0.197684	−0.0988422	+	0.995103i	$0.531514\pi$
$200$	1.81222e7	0.160179
$201$	2.52301e7	0.219145
$202$	−6.74100e7	−0.575432
$203$	8.56630e7	0.718716
$204$	−5.12282e7	−0.422477
$205$	−2.25049e7	−0.182448
$206$	6.98776e7	0.556933
$207$	−1.67702e8	−1.31414
$208$	1.56770e7	0.120793
$209$	507662.	0.00384647
$210$	−1.10081e7	−0.0820246
$211$	3.53463e7	0.259033	0.129517	−	0.991577i	$-0.458657\pi$
$211$	3.53463e7	0.259033	0.129517	+	0.991577i	$0.458657\pi$
$212$	8.80241e7	0.634492
$213$	7.95323e6	0.0563917
$214$	−1.75910e7	−0.122699
$215$	8.66661e7	0.594723
$216$	−1.10312e8	−0.744790
$217$	2.08815e7	0.138724
$218$	1.58872e7	0.103860
$219$	−8.58469e7	−0.552294
$220$	−2.02472e6	−0.0128199
$221$	−4.36449e7	−0.271995
$222$	−2.33610e7	−0.143303
$223$	−3.81868e7	−0.230593	−0.115297	−	0.993331i	$-0.536782\pi$
$223$	−3.81868e7	−0.230593	−0.115297	+	0.993331i	$0.536782\pi$
$224$	6.37882e7	0.379204
$225$	2.40170e7	0.140566
$226$	2.46088e7	0.141811
$227$	−1.30865e8	−0.742561	−0.371280	−	0.928521i	$-0.621081\pi$
$227$	−1.30865e8	−0.742561	−0.371280	+	0.928521i	$0.621081\pi$
$228$	1.65339e7	0.0923851
$229$	1.80392e8	0.992645	0.496322	−	0.868138i	$-0.334683\pi$
$229$	1.80392e8	0.992645	0.496322	+	0.868138i	$0.334683\pi$
$230$	1.37582e8	0.745612
$231$	−685395.	−0.00365847
$232$	−2.92111e8	−1.53582
$233$	−3.43754e8	−1.78034	−0.890169	−	0.455630i	$-0.849414\pi$
$233$	−3.43754e8	−1.78034	−0.890169	+	0.455630i	$0.849414\pi$
$234$	−1.73048e7	−0.0882900
$235$	1.58130e8	0.794833
$236$	1.61261e7	0.0798617
$237$	1.63077e7	0.0795744
$238$	−3.46242e7	−0.166479
$239$	1.55197e8	0.735346	0.367673	−	0.929955i	$-0.380155\pi$
$239$	1.55197e8	0.735346	0.367673	+	0.929955i	$0.380155\pi$
$240$	−4.50681e7	−0.210441
$241$	−1.44456e8	−0.664776	−0.332388	−	0.943143i	$-0.607854\pi$
$241$	−1.44456e8	−0.664776	−0.332388	+	0.943143i	$0.607854\pi$
$242$	−9.89898e7	−0.448990
$243$	−2.31749e8	−1.03609
$244$	−2.04819e8	−0.902620
$245$	2.94431e7	0.127909
$246$	1.15320e7	0.0493892
$247$	1.40864e7	0.0594785
$248$	−7.12060e7	−0.296439
$249$	2.02760e8	0.832310
$250$	−1.19053e8	−0.481893
$251$	−1.27311e8	−0.508168	−0.254084	−	0.967182i	$-0.581774\pi$
$251$	−1.27311e8	−0.508168	−0.254084	+	0.967182i	$0.581774\pi$
$252$	5.43267e7	0.213851
$253$	8.56623e6	0.0332559
$254$	−1.69199e8	−0.647857
$255$	1.25470e8	0.473859
$256$	−1.24191e8	−0.462646
$257$	2.52010e8	0.926086	0.463043	−	0.886336i	$-0.346757\pi$
$257$	2.52010e8	0.926086	0.463043	+	0.886336i	$0.346757\pi$
$258$	−4.44096e7	−0.160993
$259$	6.24831e7	0.223467
$260$	−5.61809e7	−0.198236
$261$	−3.87128e8	−1.34776
$262$	−1.34685e8	−0.462663
$263$	1.19269e8	0.404280	0.202140	−	0.979357i	$-0.435210\pi$
$263$	1.19269e8	0.404280	0.202140	+	0.979357i	$0.435210\pi$
$264$	2.33720e6	0.00781774
$265$	−2.15592e8	−0.711659
$266$	1.11749e7	0.0364048
$267$	−8.24919e7	−0.265230
$268$	1.02151e8	0.324168
$269$	8.10971e7	0.254023	0.127011	−	0.991901i	$-0.459462\pi$
$269$	8.10971e7	0.254023	0.127011	+	0.991901i	$0.459462\pi$
$270$	1.19936e8	0.370832
$271$	−6.68806e7	−0.204130	−0.102065	−	0.994778i	$-0.532545\pi$
$271$	−6.68806e7	−0.204130	−0.102065	+	0.994778i	$0.532545\pi$
$272$	−1.41755e8	−0.427117
$273$	−1.90180e7	−0.0565713
$274$	2.49324e8	0.732214
$275$	−1.22678e6	−0.00355716
$276$	2.78990e8	0.798744
$277$	4.93720e8	1.39573	0.697865	−	0.716230i	$-0.254134\pi$
$277$	4.93720e8	1.39573	0.697865	+	0.716230i	$0.254134\pi$
$278$	2.43646e8	0.680147
$279$	−9.43677e7	−0.260141
$280$	−1.00401e8	−0.273328
$281$	4.72884e8	1.27140	0.635701	−	0.771935i	$-0.280711\pi$
$281$	4.72884e8	1.27140	0.635701	+	0.771935i	$0.280711\pi$
$282$	−8.10291e7	−0.215164
$283$	−4.54591e7	−0.119225	−0.0596126	−	0.998222i	$-0.518987\pi$
$283$	−4.54591e7	−0.119225	−0.0596126	+	0.998222i	$0.518987\pi$
$284$	3.22008e7	0.0834166
$285$	−4.04953e7	−0.103621
$286$	883929.	0.00223427
$287$	−3.08444e7	−0.0770176
$288$	−2.88272e8	−0.711096
$289$	−1.56931e7	−0.0382442
$290$	3.17596e8	0.764685
$291$	−9.80921e7	−0.233350
$292$	−3.47574e8	−0.816973
$293$	−6.32640e8	−1.46933	−0.734666	−	0.678429i	$-0.762661\pi$
$293$	−6.32640e8	−1.46933	−0.734666	+	0.678429i	$0.762661\pi$
$294$	−1.50873e7	−0.0346254
$295$	−3.94967e7	−0.0895744
$296$	−2.13067e8	−0.477525
$297$	7.46758e6	0.0165399
$298$	3.92486e8	0.859147
$299$	2.37692e8	0.514239
$300$	−3.99547e7	−0.0854365
$301$	1.18781e8	0.251053
$302$	−1.24553e8	−0.260213
$303$	3.34798e8	0.691408
$304$	4.57512e7	0.0933997
$305$	5.01649e8	1.01240
$306$	1.56473e8	0.312188
$307$	7.75564e8	1.52980	0.764898	−	0.644151i	$-0.222789\pi$
$307$	7.75564e8	1.52980	0.764898	+	0.644151i	$0.222789\pi$
$308$	−2.77501e6	−0.00541174
$309$	−3.47054e8	−0.669180
$310$	7.74184e7	0.147597
$311$	3.83572e8	0.723078	0.361539	−	0.932357i	$-0.382251\pi$
$311$	3.83572e8	0.723078	0.361539	+	0.932357i	$0.382251\pi$
$312$	6.48514e7	0.120887
$313$	9.26958e8	1.70866	0.854329	−	0.519733i	$-0.173969\pi$
$313$	9.26958e8	1.70866	0.854329	+	0.519733i	$0.173969\pi$
$314$	1.44142e8	0.262746
$315$	−1.33059e8	−0.239860
$316$	6.60261e7	0.117709
$317$	−3.22691e8	−0.568957	−0.284479	−	0.958682i	$-0.591821\pi$
$317$	−3.22691e8	−0.568957	−0.284479	+	0.958682i	$0.591821\pi$
$318$	1.10474e8	0.192648
$319$	1.97745e7	0.0341065
$320$	7.91530e6	0.0135034
$321$	8.73675e7	0.147429
$322$	1.88564e8	0.314749
$323$	−1.27372e8	−0.210312
$324$	−1.03184e8	−0.168540
$325$	−3.40402e7	−0.0550048
$326$	−1.05875e8	−0.169251
$327$	−7.89052e7	−0.124792
$328$	1.05179e8	0.164578
$329$	2.16727e8	0.335527
$330$	−2.54111e6	−0.00389246
$331$	−1.10934e9	−1.68139	−0.840693	−	0.541512i	$-0.817852\pi$
$331$	−1.10934e9	−1.68139	−0.840693	+	0.541512i	$0.817852\pi$
$332$	8.20930e8	1.23118
$333$	−2.82373e8	−0.419053
$334$	5.23220e8	0.768372
$335$	−2.50191e8	−0.363593
$336$	−6.17688e7	−0.0888345
$337$	−1.09216e9	−1.55446	−0.777231	−	0.629216i	$-0.783376\pi$
$337$	−1.09216e9	−1.55446	−0.777231	+	0.629216i	$0.783376\pi$
$338$	2.45268e7	0.0345488
$339$	−1.22222e8	−0.170393
$340$	5.07999e8	0.700949
$341$	4.82030e6	0.00658315
$342$	−5.05017e7	−0.0682676
$343$	4.03536e7	0.0539949
$344$	−4.05045e8	−0.536474
$345$	−6.83313e8	−0.895886
$346$	3.98691e8	0.517451
$347$	7.78256e8	0.999929	0.499965	−	0.866046i	$-0.333346\pi$
$347$	7.78256e8	0.999929	0.499965	+	0.866046i	$0.333346\pi$
$348$	6.44027e8	0.819176
$349$	−1.03537e9	−1.30379	−0.651896	−	0.758309i	$-0.726026\pi$
$349$	−1.03537e9	−1.30379	−0.651896	+	0.758309i	$0.726026\pi$
$350$	−2.70046e7	−0.0336667
$351$	2.07207e8	0.255758
$352$	1.47249e7	0.0179950
$353$	9.16514e8	1.10899	0.554495	−	0.832187i	$-0.312911\pi$
$353$	9.16514e8	1.10899	0.554495	+	0.832187i	$0.312911\pi$
$354$	2.02390e7	0.0242481
$355$	−7.88674e7	−0.0935617
$356$	−3.33991e8	−0.392337
$357$	1.71964e8	0.200032
$358$	−2.33046e8	−0.268442
$359$	−1.26975e9	−1.44840	−0.724200	−	0.689589i	$-0.757791\pi$
$359$	−1.26975e9	−1.44840	−0.724200	+	0.689589i	$0.757791\pi$
$360$	4.53731e8	0.512554
$361$	−8.52763e8	−0.954010
$362$	−2.43739e8	−0.270050
$363$	4.91643e8	0.539482
$364$	−7.69996e7	−0.0836823
$365$	8.51292e8	0.916333
$366$	−2.57056e8	−0.274059
$367$	1.57507e8	0.166330	0.0831648	−	0.996536i	$-0.473497\pi$
$367$	1.57507e8	0.166330	0.0831648	+	0.996536i	$0.473497\pi$
$368$	7.72001e8	0.807515
$369$	1.39392e8	0.144426
$370$	2.31657e8	0.237760
$371$	−2.95482e8	−0.300416
$372$	1.56990e8	0.158115
$373$	−1.01070e9	−1.00841	−0.504207	−	0.863583i	$-0.668215\pi$
$373$	−1.01070e9	−1.00841	−0.504207	+	0.863583i	$0.668215\pi$
$374$	−7.99265e6	−0.00790024
$375$	5.91289e8	0.579015
$376$	−7.39038e8	−0.716984
$377$	5.48693e8	0.527393
$378$	1.64380e8	0.156541
$379$	8.65372e8	0.816518	0.408259	−	0.912866i	$-0.366136\pi$
$379$	8.65372e8	0.816518	0.408259	+	0.912866i	$0.366136\pi$
$380$	−1.63956e8	−0.153280
$381$	8.40343e8	0.778430
$382$	−4.96451e8	−0.455675
$383$	4.93362e8	0.448714	0.224357	−	0.974507i	$-0.427972\pi$
$383$	4.93362e8	0.448714	0.224357	+	0.974507i	$0.427972\pi$
$384$	5.96699e8	0.537769
$385$	6.79665e6	0.00606991
$386$	8.10259e8	0.717081
$387$	−5.36797e8	−0.470784
$388$	−3.97153e8	−0.345181
$389$	−9.07436e8	−0.781614	−0.390807	−	0.920473i	$-0.627804\pi$
$389$	−9.07436e8	−0.781614	−0.390807	+	0.920473i	$0.627804\pi$
$390$	−7.05095e7	−0.0601896
$391$	−2.14925e9	−1.81831
$392$	−1.37606e8	−0.115381
$393$	6.68927e8	0.555910
$394$	5.99618e7	0.0493899
$395$	−1.61714e8	−0.132025
$396$	1.25408e7	0.0101483
$397$	−1.06013e9	−0.850336	−0.425168	−	0.905115i	$-0.639785\pi$
$397$	−1.06013e9	−0.850336	−0.425168	+	0.905115i	$0.639785\pi$
$398$	−1.11671e8	−0.0887869
$399$	−5.55014e7	−0.0437420
$400$	−1.10560e8	−0.0863747
$401$	2.81346e8	0.217889	0.108945	−	0.994048i	$-0.465253\pi$
$401$	2.81346e8	0.217889	0.108945	+	0.994048i	$0.465253\pi$
$402$	1.28204e8	0.0984258
$403$	1.33751e8	0.101796
$404$	1.35552e9	1.02276
$405$	2.52721e8	0.189038
$406$	4.35286e8	0.322800
$407$	1.44236e7	0.0106046
$408$	−5.86399e8	−0.427447
$409$	2.45583e9	1.77487	0.887436	−	0.460932i	$-0.152485\pi$
$409$	2.45583e9	1.77487	0.887436	+	0.460932i	$0.152485\pi$
$410$	−1.14356e8	−0.0819437
$411$	−1.23829e9	−0.879787
$412$	−1.40514e9	−0.989875
$413$	−5.41328e7	−0.0378125
$414$	−8.52160e8	−0.590228
$415$	−2.01065e9	−1.38092
$416$	4.08580e8	0.278259
$417$	−1.21009e9	−0.817227
$418$	2.57962e6	0.00172759
$419$	1.12187e8	0.0745066	0.0372533	−	0.999306i	$-0.488139\pi$
$419$	1.12187e8	0.0745066	0.0372533	+	0.999306i	$0.488139\pi$
$420$	2.21357e8	0.145788
$421$	−1.09698e9	−0.716491	−0.358245	−	0.933627i	$-0.616625\pi$
$421$	−1.09698e9	−0.716491	−0.358245	+	0.933627i	$0.616625\pi$
$422$	1.79608e8	0.116341
$423$	−9.79431e8	−0.629191
$424$	1.00759e9	0.641956
$425$	3.07798e8	0.194493
$426$	4.04134e7	0.0253274
$427$	6.87542e8	0.427368
$428$	3.53731e8	0.218082
$429$	−4.39012e6	−0.00268458
$430$	4.40383e8	0.267111
$431$	−1.34997e9	−0.812184	−0.406092	−	0.913832i	$-0.633109\pi$
$431$	−1.34997e9	−0.812184	−0.406092	+	0.913832i	$0.633109\pi$
$432$	6.72989e8	0.401619
$433$	−2.79237e9	−1.65297	−0.826487	−	0.562956i	$-0.809664\pi$
$433$	−2.79237e9	−1.65297	−0.826487	+	0.562956i	$0.809664\pi$
$434$	1.06107e8	0.0623060
$435$	−1.57738e9	−0.918803
$436$	−3.19469e8	−0.184598
$437$	6.93670e8	0.397620
$438$	−4.36221e8	−0.248054
$439$	1.73244e9	0.977309	0.488654	−	0.872477i	$-0.337488\pi$
$439$	1.73244e9	0.977309	0.488654	+	0.872477i	$0.337488\pi$
$440$	−2.31766e7	−0.0129707
$441$	−1.82366e8	−0.101253
$442$	−2.21776e8	−0.122162
$443$	9.19646e8	0.502583	0.251291	−	0.967911i	$-0.419145\pi$
$443$	9.19646e8	0.502583	0.251291	+	0.967911i	$0.419145\pi$
$444$	4.69757e8	0.254702
$445$	8.18023e8	0.440053
$446$	−1.94042e8	−0.103567
$447$	−1.94932e9	−1.03230
$448$	1.08484e7	0.00570024
$449$	9.29747e8	0.484733	0.242367	−	0.970185i	$-0.422076\pi$
$449$	9.29747e8	0.484733	0.242367	+	0.970185i	$0.422076\pi$
$450$	1.22039e8	0.0631329
$451$	−7.12014e6	−0.00365486
$452$	−4.94850e8	−0.252051
$453$	6.18603e8	0.312657
$454$	−6.64973e8	−0.333510
$455$	1.88590e8	0.0938597
$456$	1.89260e8	0.0934720
$457$	−3.81360e8	−0.186908	−0.0934542	−	0.995624i	$-0.529791\pi$
$457$	−3.81360e8	−0.186908	−0.0934542	+	0.995624i	$0.529791\pi$
$458$	9.16642e8	0.445831
$459$	−1.87360e9	−0.904343
$460$	−2.76658e9	−1.32523
$461$	2.33633e9	1.11066	0.555330	−	0.831630i	$-0.312592\pi$
$461$	2.33633e9	1.11066	0.555330	+	0.831630i	$0.312592\pi$
$462$	−3.48275e6	−0.00164314
$463$	−3.70132e9	−1.73310	−0.866550	−	0.499090i	$-0.833668\pi$
$463$	−3.70132e9	−1.73310	−0.866550	+	0.499090i	$0.833668\pi$
$464$	1.78210e9	0.828171
$465$	−3.84507e8	−0.177345
$466$	−1.74675e9	−0.799612
$467$	−5.19950e8	−0.236239	−0.118120	−	0.992999i	$-0.537687\pi$
$467$	−5.19950e8	−0.236239	−0.118120	+	0.992999i	$0.537687\pi$
$468$	3.47976e8	0.156924
$469$	−3.42903e8	−0.153485
$470$	8.03517e8	0.356987
$471$	−7.15895e8	−0.315701
$472$	1.84593e8	0.0808012
$473$	2.74196e7	0.0119137
$474$	8.28656e7	0.0357396
$475$	−9.93417e7	−0.0425308
$476$	6.96245e8	0.295895
$477$	1.33534e9	0.563350
$478$	7.88617e8	0.330269
$479$	−1.76687e9	−0.734565	−0.367282	−	0.930110i	$-0.619712\pi$
$479$	−1.76687e9	−0.734565	−0.367282	+	0.930110i	$0.619712\pi$
$480$	−1.17458e9	−0.484772
$481$	4.00220e8	0.163980
$482$	−7.34035e8	−0.298574
$483$	−9.36524e8	−0.378185
$484$	1.99055e9	0.798021
$485$	9.72720e8	0.387161
$486$	−1.17760e9	−0.465342
$487$	2.04299e9	0.801521	0.400760	−	0.916183i	$-0.368746\pi$
$487$	2.04299e9	0.801521	0.400760	+	0.916183i	$0.368746\pi$
$488$	−2.34452e9	−0.913239
$489$	5.25837e8	0.203362
$490$	1.49611e8	0.0574485
$491$	3.47893e9	1.32636	0.663179	−	0.748461i	$-0.269207\pi$
$491$	3.47893e9	1.32636	0.663179	+	0.748461i	$0.269207\pi$
$492$	−2.31893e8	−0.0877829
$493$	−4.96138e9	−1.86483
$494$	7.15782e7	0.0267138
$495$	−3.07154e7	−0.0113825
$496$	4.34412e8	0.159851
$497$	−1.08093e8	−0.0394957
$498$	1.03030e9	0.373819
$499$	1.97195e9	0.710466	0.355233	−	0.934778i	$-0.384401\pi$
$499$	1.97195e9	0.710466	0.355233	+	0.934778i	$0.384401\pi$
$500$	2.39399e9	0.856501
$501$	−2.59862e9	−0.923233
$502$	−6.46914e8	−0.228236
$503$	2.02086e9	0.708025	0.354012	−	0.935241i	$-0.384817\pi$
$503$	2.02086e9	0.708025	0.354012	+	0.935241i	$0.384817\pi$
$504$	6.21867e8	0.216367
$505$	−3.31999e9	−1.14714
$506$	4.35283e7	0.0149364
$507$	−1.21815e8	−0.0415120
$508$	3.40236e9	1.15148
$509$	5.59050e9	1.87905	0.939525	−	0.342481i	$-0.111267\pi$
$509$	5.59050e9	1.87905	0.939525	+	0.342481i	$0.111267\pi$
$510$	6.37560e8	0.212826
$511$	1.16675e9	0.386816
$512$	2.39533e9	0.788715
$513$	6.04704e8	0.197757
$514$	1.28056e9	0.415937
$515$	3.44153e9	1.11026
$516$	8.93017e8	0.286145
$517$	5.00293e7	0.0159224
$518$	3.17500e8	0.100367
$519$	−1.98014e9	−0.621741
$520$	−6.43092e8	−0.200568
$521$	4.67025e7	0.0144680	0.00723400	−	0.999974i	$-0.497697\pi$
$521$	4.67025e7	0.0144680	0.00723400	+	0.999974i	$0.497697\pi$
$522$	−1.96714e9	−0.605326
$523$	6.32147e9	1.93224	0.966122	−	0.258086i	$-0.0830917\pi$
$523$	6.32147e9	1.93224	0.966122	+	0.258086i	$0.0830917\pi$
$524$	2.70833e9	0.822323
$525$	1.34121e8	0.0404520
$526$	6.06050e8	0.181576
$527$	−1.20940e9	−0.359944
$528$	−1.42587e7	−0.00421562
$529$	8.30009e9	2.43774
$530$	−1.09550e9	−0.319631
$531$	2.44637e8	0.0709073
$532$	−2.24713e8	−0.0647048
$533$	−1.97566e8	−0.0565155
$534$	−4.19173e8	−0.119124
$535$	−8.66371e8	−0.244605
$536$	1.16930e9	0.327981
$537$	1.15745e9	0.322545
$538$	4.12085e8	0.114090
$539$	9.31524e6	0.00256232
$540$	−2.41175e9	−0.659105
$541$	2.16904e9	0.588948	0.294474	−	0.955660i	$-0.404856\pi$
$541$	2.16904e9	0.588948	0.294474	+	0.955660i	$0.404856\pi$
$542$	−3.39845e8	−0.0916820
$543$	1.21055e9	0.324478
$544$	−3.69445e9	−0.983907
$545$	7.82455e8	0.207048
$546$	−9.66377e7	−0.0254081
$547$	−4.63439e9	−1.21070	−0.605351	−	0.795959i	$-0.706967\pi$
$547$	−4.63439e9	−1.21070	−0.605351	+	0.795959i	$0.706967\pi$
$548$	−5.01357e9	−1.30141
$549$	−3.10714e9	−0.801415
$550$	−6.23376e6	−0.00159765
$551$	1.60128e9	0.407791
$552$	3.19355e9	0.808140
$553$	−2.21639e8	−0.0557324
$554$	2.50878e9	0.626870
$555$	−1.15055e9	−0.285679
$556$	−4.89939e9	−1.20887
$557$	3.36947e9	0.826167	0.413084	−	0.910693i	$-0.364452\pi$
$557$	3.36947e9	0.826167	0.413084	+	0.910693i	$0.364452\pi$
$558$	−4.79518e8	−0.116838
$559$	7.60825e8	0.184223
$560$	6.12524e8	0.147389
$561$	3.96963e7	0.00949250
$562$	2.40291e9	0.571031
$563$	4.34631e9	1.02646	0.513229	−	0.858252i	$-0.328449\pi$
$563$	4.34631e9	1.02646	0.513229	+	0.858252i	$0.328449\pi$
$564$	1.62939e9	0.382426
$565$	1.21200e9	0.282706
$566$	−2.30995e8	−0.0535482
$567$	3.46371e8	0.0797996
$568$	3.68596e8	0.0843979
$569$	4.26627e9	0.970857	0.485429	−	0.874276i	$-0.338664\pi$
$569$	4.26627e9	0.970857	0.485429	+	0.874276i	$0.338664\pi$
$570$	−2.05772e8	−0.0465398
$571$	−5.43149e9	−1.22094	−0.610468	−	0.792041i	$-0.709019\pi$
$571$	−5.43149e9	−1.22094	−0.610468	+	0.792041i	$0.709019\pi$
$572$	−1.77746e7	−0.00397113
$573$	2.46568e9	0.547514
$574$	−1.56732e8	−0.0345913
$575$	−1.67628e9	−0.367713
$576$	−4.90261e7	−0.0106893
$577$	6.01348e9	1.30320	0.651599	−	0.758563i	$-0.274098\pi$
$577$	6.01348e9	1.30320	0.651599	+	0.758563i	$0.274098\pi$
$578$	−7.97424e7	−0.0171768
$579$	−4.02424e9	−0.861605
$580$	−6.38643e9	−1.35913
$581$	−2.75572e9	−0.582934
$582$	−4.98443e8	−0.104806
$583$	−6.82093e7	−0.0142562
$584$	−3.97862e9	−0.826584
$585$	−8.52276e8	−0.176009
$586$	−3.21468e9	−0.659928
$587$	−4.21371e9	−0.859866	−0.429933	−	0.902861i	$-0.641463\pi$
$587$	−4.21371e9	−0.859866	−0.429933	+	0.902861i	$0.641463\pi$
$588$	3.03384e8	0.0615422
$589$	3.90335e8	0.0787107
$590$	−2.00698e8	−0.0402310
$591$	−2.97806e8	−0.0593441
$592$	1.29988e9	0.257499
$593$	−3.07960e9	−0.606461	−0.303231	−	0.952917i	$-0.598065\pi$
$593$	−3.07960e9	−0.606461	−0.303231	+	0.952917i	$0.598065\pi$
$594$	3.79456e7	0.00742863
$595$	−1.70527e9	−0.331882
$596$	−7.89236e9	−1.52702
$597$	5.54625e8	0.106681
$598$	1.20780e9	0.230963
$599$	5.05994e8	0.0961948	0.0480974	−	0.998843i	$-0.484684\pi$
$599$	5.05994e8	0.0961948	0.0480974	+	0.998843i	$0.484684\pi$
$600$	−4.57353e8	−0.0864415
$601$	9.12497e9	1.71463	0.857315	−	0.514792i	$-0.172131\pi$
$601$	9.12497e9	1.71463	0.857315	+	0.514792i	$0.172131\pi$
$602$	6.03574e8	0.112757
$603$	1.54965e9	0.287821
$604$	2.50458e9	0.462494
$605$	−4.87533e9	−0.895076
$606$	1.70124e9	0.310535
$607$	−6.00486e9	−1.08979	−0.544894	−	0.838505i	$-0.683430\pi$
$607$	−6.00486e9	−1.08979	−0.544894	+	0.838505i	$0.683430\pi$
$608$	1.19238e9	0.215156
$609$	−2.16189e9	−0.387859
$610$	2.54907e9	0.454702
$611$	1.38819e9	0.246209
$612$	−3.14647e9	−0.554872
$613$	−6.37941e9	−1.11858	−0.559292	−	0.828971i	$-0.688927\pi$
$613$	−6.37941e9	−1.11858	−0.559292	+	0.828971i	$0.688927\pi$
$614$	3.94094e9	0.687085
$615$	5.67961e8	0.0984590
$616$	−3.17650e7	−0.00547540
$617$	8.45037e9	1.44836	0.724182	−	0.689609i	$-0.242217\pi$
$617$	8.45037e9	1.44836	0.724182	+	0.689609i	$0.242217\pi$
$618$	−1.76351e9	−0.300552
$619$	−9.26189e9	−1.56958	−0.784788	−	0.619764i	$-0.787228\pi$
$619$	−9.26189e9	−1.56958	−0.784788	+	0.619764i	$0.787228\pi$
$620$	−1.55678e9	−0.262335
$621$	1.02037e10	1.70977
$622$	1.94907e9	0.324759
$623$	1.12115e9	0.185762
$624$	−3.95644e8	−0.0651867
$625$	−4.65299e9	−0.762345
$626$	4.71023e9	0.767417
$627$	−1.28120e7	−0.00207577
$628$	−2.89849e9	−0.466997
$629$	−3.61886e9	−0.579822
$630$	−6.76123e8	−0.107729
$631$	−4.80371e9	−0.761156	−0.380578	−	0.924749i	$-0.624275\pi$
$631$	−4.80371e9	−0.761156	−0.380578	+	0.924749i	$0.624275\pi$
$632$	7.55788e8	0.119094
$633$	−8.92041e8	−0.139789
$634$	−1.63972e9	−0.255539
$635$	−8.33318e9	−1.29152
$636$	−2.22148e9	−0.342407
$637$	2.58475e8	0.0396214
$638$	1.00482e8	0.0153184
$639$	4.88492e8	0.0740636
$640$	−5.91710e9	−0.892235
$641$	3.90672e9	0.585881	0.292940	−	0.956131i	$-0.405366\pi$
$641$	3.90672e9	0.585881	0.292940	+	0.956131i	$0.405366\pi$
$642$	4.43947e8	0.0662154
$643$	2.35459e9	0.349282	0.174641	−	0.984632i	$-0.444124\pi$
$643$	2.35459e9	0.349282	0.174641	+	0.984632i	$0.444124\pi$
$644$	−3.79177e9	−0.559425
$645$	−2.18721e9	−0.320945
$646$	−6.47223e8	−0.0944584
$647$	1.09365e9	0.158750	0.0793750	−	0.996845i	$-0.474708\pi$
$647$	1.09365e9	0.158750	0.0793750	+	0.996845i	$0.474708\pi$
$648$	−1.18112e9	−0.170523
$649$	−1.24960e7	−0.00179439
$650$	−1.72971e8	−0.0247046
$651$	−5.26991e8	−0.0748634
$652$	2.12900e9	0.300821
$653$	−6.19178e8	−0.0870201	−0.0435100	−	0.999053i	$-0.513854\pi$
$653$	−6.19178e8	−0.0870201	−0.0435100	+	0.999053i	$0.513854\pi$
$654$	−4.00947e8	−0.0560486
$655$	−6.63335e9	−0.922334
$656$	−6.41677e8	−0.0887468
$657$	−5.27277e9	−0.725371
$658$	1.10127e9	0.150697
$659$	8.13367e9	1.10710	0.553551	−	0.832815i	$-0.313272\pi$
$659$	8.13367e9	1.10710	0.553551	+	0.832815i	$0.313272\pi$
$660$	5.10982e7	0.00691834
$661$	−3.23653e9	−0.435887	−0.217944	−	0.975961i	$-0.569935\pi$
$661$	−3.23653e9	−0.435887	−0.217944	+	0.975961i	$0.569935\pi$
$662$	−5.63699e9	−0.755169
$663$	1.10147e9	0.146784
$664$	9.39702e9	1.24567
$665$	5.50374e8	0.0725742
$666$	−1.43485e9	−0.188211
$667$	2.70199e10	3.52568
$668$	−1.05212e10	−1.36568
$669$	9.63728e8	0.124441
$670$	−1.27132e9	−0.163302
$671$	1.58712e8	0.0202807
$672$	−1.60984e9	−0.204639
$673$	−8.09061e9	−1.02313	−0.511563	−	0.859246i	$-0.670933\pi$
$673$	−8.09061e9	−1.02313	−0.511563	+	0.859246i	$0.670933\pi$
$674$	−5.54966e9	−0.698163
$675$	−1.46129e9	−0.182883
$676$	−4.93201e8	−0.0614060
$677$	5.86699e9	0.726700	0.363350	−	0.931653i	$-0.381633\pi$
$677$	5.86699e9	0.726700	0.363350	+	0.931653i	$0.381633\pi$
$678$	−6.21057e8	−0.0765293
$679$	1.33318e9	0.163434
$680$	5.81496e9	0.709195
$681$	3.30266e9	0.400727
$682$	2.44938e7	0.00295672
$683$	−1.37044e10	−1.64584	−0.822922	−	0.568155i	$-0.807658\pi$
$683$	−1.37044e10	−1.64584	−0.822922	+	0.568155i	$0.807658\pi$
$684$	1.01552e9	0.121337
$685$	1.22794e10	1.45969
$686$	2.05052e8	0.0242510
$687$	−4.55259e9	−0.535686
$688$	2.47109e9	0.289287
$689$	−1.89264e9	−0.220445
$690$	−3.47217e9	−0.402374
$691$	−1.60119e10	−1.84617	−0.923083	−	0.384600i	$-0.874339\pi$
$691$	−1.60119e10	−1.84617	−0.923083	+	0.384600i	$0.874339\pi$
$692$	−8.01712e9	−0.919702
$693$	−4.20974e7	−0.00480495
$694$	3.95461e9	0.449103
$695$	1.19998e10	1.35589
$696$	7.37205e9	0.828812
$697$	1.78643e9	0.199835
$698$	−5.26113e9	−0.585578
$699$	8.67539e9	0.960769
$700$	5.43026e8	0.0598381
$701$	−1.24919e10	−1.36967	−0.684834	−	0.728699i	$-0.740125\pi$
$701$	−1.24919e10	−1.36967	−0.684834	+	0.728699i	$0.740125\pi$
$702$	1.05290e9	0.114870
$703$	1.16799e9	0.126793
$704$	2.50425e6	0.000270504 0
$705$	−3.99075e9	−0.428936
$706$	4.65716e9	0.498086
$707$	−4.55026e9	−0.484249
$708$	−4.06979e8	−0.0430978
$709$	6.42382e9	0.676911	0.338455	−	0.940982i	$-0.390096\pi$
$709$	6.42382e9	0.676911	0.338455	+	0.940982i	$0.390096\pi$
$710$	−4.00755e8	−0.0420218
$711$	1.00163e9	0.104511
$712$	−3.82313e9	−0.396953
$713$	6.58646e9	0.680517
$714$	8.73817e8	0.0898414
$715$	4.35342e7	0.00445410
$716$	4.68623e9	0.477121
$717$	−3.91675e9	−0.396834
$718$	−6.45210e9	−0.650527
$719$	−5.20098e9	−0.521836	−0.260918	−	0.965361i	$-0.584025\pi$
$719$	−5.20098e9	−0.521836	−0.260918	+	0.965361i	$0.584025\pi$
$720$	−2.76811e9	−0.276389
$721$	4.71683e9	0.468681
$722$	−4.33321e9	−0.428479
$723$	3.64566e9	0.358750
$724$	4.90126e9	0.479979
$725$	−3.86956e9	−0.377119
$726$	2.49823e9	0.242300
$727$	−1.29835e10	−1.25321	−0.626603	−	0.779339i	$-0.715555\pi$
$727$	−1.29835e10	−1.25321	−0.626603	+	0.779339i	$0.715555\pi$
$728$	−8.81399e8	−0.0846667
$729$	3.64020e9	0.347999
$730$	4.32574e9	0.411557
$731$	−6.87952e9	−0.651399
$732$	5.16905e9	0.487104
$733$	−2.17698e9	−0.204169	−0.102085	−	0.994776i	$-0.532551\pi$
$733$	−2.17698e9	−0.204169	−0.102085	+	0.994776i	$0.532551\pi$
$734$	8.00355e8	0.0747044
$735$	−7.43060e8	−0.0690269
$736$	2.01201e10	1.86019
$737$	−7.91559e7	−0.00728362
$738$	7.08304e8	0.0648667
$739$	−3.15646e9	−0.287703	−0.143852	−	0.989599i	$-0.545949\pi$
$739$	−3.15646e9	−0.287703	−0.143852	+	0.989599i	$0.545949\pi$
$740$	−4.65830e9	−0.422587
$741$	−3.55500e8	−0.0320979
$742$	−1.50146e9	−0.134927
$743$	1.71071e10	1.53008	0.765042	−	0.643980i	$-0.222718\pi$
$743$	1.71071e10	1.53008	0.765042	+	0.643980i	$0.222718\pi$
$744$	1.79704e9	0.159975
$745$	1.93303e10	1.71274
$746$	−5.13572e9	−0.452914
$747$	1.24537e10	1.09314
$748$	1.60721e8	0.0140416
$749$	−1.18742e9	−0.103256
$750$	3.00456e9	0.260056
$751$	4.81930e9	0.415188	0.207594	−	0.978215i	$-0.433437\pi$
$751$	4.81930e9	0.415188	0.207594	+	0.978215i	$0.433437\pi$
$752$	4.50871e9	0.386625
$753$	3.21296e9	0.274235
$754$	2.78812e9	0.236871
$755$	−6.13431e9	−0.518742
$756$	−3.30546e9	−0.278231
$757$	−1.31139e9	−0.109875	−0.0549373	−	0.998490i	$-0.517496\pi$
$757$	−1.31139e9	−0.109875	−0.0549373	+	0.998490i	$0.517496\pi$
$758$	4.39728e9	0.366726
$759$	−2.16188e8	−0.0179467
$760$	−1.87678e9	−0.155083
$761$	7.59828e9	0.624984	0.312492	−	0.949920i	$-0.398836\pi$
$761$	7.59828e9	0.624984	0.312492	+	0.949920i	$0.398836\pi$
$762$	4.27010e9	0.349620
$763$	1.07240e9	0.0874023
$764$	9.98296e9	0.809902
$765$	7.70644e9	0.622356
$766$	2.50696e9	0.201533
$767$	−3.46734e8	−0.0277468
$768$	3.13422e9	0.249670
$769$	−5.74291e9	−0.455397	−0.227698	−	0.973732i	$-0.573120\pi$
$769$	−5.74291e9	−0.455397	−0.227698	+	0.973732i	$0.573120\pi$
$770$	3.45363e7	0.00272621
$771$	−6.36002e9	−0.499768
$772$	−1.62932e10	−1.27452
$773$	9.84863e9	0.766916	0.383458	−	0.923558i	$-0.374733\pi$
$773$	9.84863e9	0.766916	0.383458	+	0.923558i	$0.374733\pi$
$774$	−2.72767e9	−0.211445
$775$	−9.43258e8	−0.0727905
$776$	−4.54613e9	−0.349241
$777$	−1.57690e9	−0.120595
$778$	−4.61102e9	−0.351050
$779$	−5.76569e8	−0.0436989
$780$	1.41785e9	0.106979
$781$	−2.49522e7	−0.00187426
$782$	−1.09212e10	−0.816668
$783$	2.35545e10	1.75350
$784$	8.39503e8	0.0622180
$785$	7.09910e9	0.523793
$786$	3.39907e9	0.249679
$787$	−1.37136e10	−1.00286	−0.501429	−	0.865199i	$-0.667192\pi$
$787$	−1.37136e10	−1.00286	−0.501429	+	0.865199i	$0.667192\pi$
$788$	−1.20575e9	−0.0877840
$789$	−3.01001e9	−0.218172
$790$	−8.21728e8	−0.0592971
$791$	1.66113e9	0.119340
$792$	1.43552e8	0.0102677
$793$	4.40388e9	0.313602
$794$	−5.38690e9	−0.381915
$795$	5.44093e9	0.384050
$796$	2.24555e9	0.157807
$797$	1.65594e9	0.115862	0.0579308	−	0.998321i	$-0.481550\pi$
$797$	1.65594e9	0.115862	0.0579308	+	0.998321i	$0.481550\pi$
$798$	−2.82024e8	−0.0196461
$799$	−1.25523e10	−0.870580
$800$	−2.88144e9	−0.198973
$801$	−5.06671e9	−0.348347
$802$	1.42963e9	0.0978616
$803$	2.69333e8	0.0183563
$804$	−2.57800e9	−0.174939
$805$	9.28695e9	0.627462
$806$	6.79641e8	0.0457201
$807$	−2.04666e9	−0.137085
$808$	1.55164e10	1.03479
$809$	−4.41839e9	−0.293389	−0.146695	−	0.989182i	$-0.546863\pi$
$809$	−4.41839e9	−0.293389	−0.146695	+	0.989182i	$0.546863\pi$
$810$	1.28417e9	0.0849036
$811$	−1.42306e10	−0.936806	−0.468403	−	0.883515i	$-0.655170\pi$
$811$	−1.42306e10	−0.936806	−0.468403	+	0.883515i	$0.655170\pi$
$812$	−8.75301e9	−0.573735
$813$	1.68788e9	0.110160
$814$	7.32919e7	0.00476289
$815$	−5.21441e9	−0.337407
$816$	3.57749e9	0.230496
$817$	2.22036e9	0.142445
$818$	1.24790e10	0.797156
$819$	−1.16810e9	−0.0742995
$820$	2.29954e9	0.145644
$821$	−6.36868e9	−0.401650	−0.200825	−	0.979627i	$-0.564362\pi$
$821$	−6.36868e9	−0.401650	−0.200825	+	0.979627i	$0.564362\pi$
$822$	−6.29225e9	−0.395143
$823$	−1.52881e10	−0.955993	−0.477997	−	0.878362i	$-0.658637\pi$
$823$	−1.52881e10	−0.955993	−0.477997	+	0.878362i	$0.658637\pi$
$824$	−1.60844e10	−1.00152
$825$	3.09606e7	0.00191964
$826$	−2.75069e8	−0.0169829
$827$	−8.42914e7	−0.00518220	−0.00259110	−	0.999997i	$-0.500825\pi$
$827$	−8.42914e7	−0.00518220	−0.00259110	+	0.999997i	$0.500825\pi$
$828$	1.71358e10	1.04905
$829$	2.68377e9	0.163608	0.0818040	−	0.996648i	$-0.473932\pi$
$829$	2.68377e9	0.163608	0.0818040	+	0.996648i	$0.473932\pi$
$830$	−1.02169e10	−0.620219
$831$	−1.24601e10	−0.753213
$832$	6.94868e7	0.00418284
$833$	−2.33718e9	−0.140099
$834$	−6.14894e9	−0.367045
$835$	2.57690e10	1.53177
$836$	−5.18727e7	−0.00307056
$837$	5.74172e9	0.338456
$838$	5.70066e8	0.0334635
$839$	−1.82317e10	−1.06576	−0.532881	−	0.846190i	$-0.678891\pi$
$839$	−1.82317e10	−1.06576	−0.532881	+	0.846190i	$0.678891\pi$
$840$	2.53383e9	0.147503
$841$	4.51234e10	2.61587
$842$	−5.57416e9	−0.321801
$843$	−1.19343e10	−0.686119
$844$	−3.61167e9	−0.206780
$845$	1.20797e9	0.0688742
$846$	−4.97686e9	−0.282592
$847$	−6.68195e9	−0.377843
$848$	−6.14712e9	−0.346167
$849$	1.14726e9	0.0643406
$850$	1.56404e9	0.0873537
$851$	1.97084e10	1.09622
$852$	−8.12658e8	−0.0450162
$853$	2.15367e10	1.18811	0.594055	−	0.804424i	$-0.297526\pi$
$853$	2.15367e10	1.18811	0.594055	+	0.804424i	$0.297526\pi$
$854$	3.49366e9	0.191946
$855$	−2.48725e9	−0.136094
$856$	4.04909e9	0.220648
$857$	−1.59483e10	−0.865526	−0.432763	−	0.901508i	$-0.642461\pi$
$857$	−1.59483e10	−0.865526	−0.432763	+	0.901508i	$0.642461\pi$
$858$	−2.23079e7	−0.00120574
$859$	1.52450e10	0.820639	0.410319	−	0.911942i	$-0.365417\pi$
$859$	1.52450e10	0.820639	0.410319	+	0.911942i	$0.365417\pi$
$860$	−8.85551e9	−0.474754
$861$	7.78426e8	0.0415630
$862$	−6.85972e9	−0.364780
$863$	−2.76238e9	−0.146300	−0.0731502	−	0.997321i	$-0.523305\pi$
$863$	−2.76238e9	−0.146300	−0.0731502	+	0.997321i	$0.523305\pi$
$864$	1.75396e10	0.925172
$865$	1.96358e10	1.03156
$866$	−1.41891e10	−0.742408
$867$	3.96049e8	0.0206387
$868$	−2.13367e9	−0.110741
$869$	−5.11632e7	−0.00264477
$870$	−8.01524e9	−0.412666
$871$	−2.19638e9	−0.112627
$872$	−3.65690e9	−0.186769
$873$	−6.02488e9	−0.306478
$874$	3.52480e9	0.178585
$875$	−8.03624e9	−0.405531
$876$	8.77180e9	0.440884
$877$	−1.72192e10	−0.862016	−0.431008	−	0.902348i	$-0.641842\pi$
$877$	−1.72192e10	−0.862016	−0.431008	+	0.902348i	$0.641842\pi$
$878$	8.80317e9	0.438943
$879$	1.59661e10	0.792933
$880$	1.41395e8	0.00699431
$881$	9.29977e8	0.0458201	0.0229101	−	0.999738i	$-0.492707\pi$
$881$	9.29977e8	0.0458201	0.0229101	+	0.999738i	$0.492707\pi$
$882$	−9.26670e8	−0.0454763
$883$	−1.36965e10	−0.669494	−0.334747	−	0.942308i	$-0.608651\pi$
$883$	−1.36965e10	−0.669494	−0.334747	+	0.942308i	$0.608651\pi$
$884$	4.45962e9	0.217128
$885$	9.96786e8	0.0483393
$886$	4.67307e9	0.225727
$887$	−2.01674e10	−0.970327	−0.485163	−	0.874424i	$-0.661240\pi$
$887$	−2.01674e10	−0.970327	−0.485163	+	0.874424i	$0.661240\pi$
$888$	5.37722e9	0.257699
$889$	−1.14212e10	−0.545197
$890$	4.15668e9	0.197643
$891$	7.99563e7	0.00378687
$892$	3.90192e9	0.184078
$893$	4.05124e9	0.190374
$894$	−9.90525e9	−0.463643
$895$	−1.14777e10	−0.535148
$896$	−8.10977e9	−0.376644
$897$	−5.99867e9	−0.277512
$898$	4.72440e9	0.217711
$899$	1.52043e10	0.697924
$900$	−2.45404e9	−0.112210
$901$	1.71136e10	0.779479
$902$	−3.61801e7	−0.00164152
$903$	−2.99771e9	−0.135482
$904$	−5.66445e9	−0.255016
$905$	−1.20043e10	−0.538354
$906$	3.14336e9	0.140425
$907$	−1.69394e10	−0.753829	−0.376914	−	0.926248i	$-0.623015\pi$
$907$	−1.69394e10	−0.753829	−0.376914	+	0.926248i	$0.623015\pi$
$908$	1.33717e10	0.592770
$909$	2.05635e10	0.908080
$910$	9.58298e8	0.0421556
$911$	−4.37632e9	−0.191776	−0.0958881	−	0.995392i	$-0.530569\pi$
$911$	−4.37632e9	−0.191776	−0.0958881	+	0.995392i	$0.530569\pi$
$912$	−1.15463e9	−0.0504036
$913$	−6.36132e8	−0.0276630
$914$	−1.93784e9	−0.0839471
$915$	−1.26602e10	−0.546345
$916$	−1.84324e10	−0.792406
$917$	−9.09142e9	−0.389349
$918$	−9.52048e9	−0.406172
$919$	−2.89737e10	−1.23140	−0.615702	−	0.787979i	$-0.711127\pi$
$919$	−2.89737e10	−1.23140	−0.615702	+	0.787979i	$0.711127\pi$
$920$	−3.16685e10	−1.34082
$921$	−1.95731e10	−0.825563
$922$	1.18718e10	0.498836
$923$	−6.92361e8	−0.0289819
$924$	7.00334e7	0.00292047
$925$	−2.82248e9	−0.117256
$926$	−1.88078e10	−0.778395
$927$	−2.13163e10	−0.878886
$928$	4.64457e10	1.90778
$929$	8.50621e9	0.348082	0.174041	−	0.984738i	$-0.444318\pi$
$929$	8.50621e9	0.348082	0.174041	+	0.984738i	$0.444318\pi$
$930$	−1.95382e9	−0.0796517
$931$	7.54323e8	0.0306361
$932$	3.51247e10	1.42121
$933$	−9.68027e9	−0.390213
$934$	−2.64206e9	−0.106103
$935$	−3.93645e8	−0.0157494
$936$	3.98322e9	0.158770
$937$	−2.24557e10	−0.891741	−0.445870	−	0.895098i	$-0.647106\pi$
$937$	−2.24557e10	−0.891741	−0.445870	+	0.895098i	$0.647106\pi$
$938$	−1.74242e9	−0.0689355
$939$	−2.33938e10	−0.922086
$940$	−1.61576e10	−0.634498
$941$	−3.71711e9	−0.145426	−0.0727129	−	0.997353i	$-0.523166\pi$
$941$	−3.71711e9	−0.145426	−0.0727129	+	0.997353i	$0.523166\pi$
$942$	−3.63773e9	−0.141792
$943$	−9.72896e9	−0.377812
$944$	−1.12616e9	−0.0435711
$945$	8.09586e9	0.312070
$946$	1.39329e8	0.00535085
$947$	1.48219e10	0.567126	0.283563	−	0.958954i	$-0.408483\pi$
$947$	1.48219e10	0.567126	0.283563	+	0.958954i	$0.408483\pi$
$948$	−1.66631e9	−0.0635225
$949$	7.47332e9	0.283845
$950$	−5.04793e8	−0.0191021
$951$	8.14382e9	0.307041
$952$	7.96978e9	0.299376
$953$	−2.23056e10	−0.834811	−0.417405	−	0.908720i	$-0.637060\pi$
$953$	−2.23056e10	−0.834811	−0.417405	+	0.908720i	$0.637060\pi$
$954$	6.78538e9	0.253020
$955$	−2.44506e10	−0.908402
$956$	−1.58580e10	−0.587011
$957$	−4.99052e8	−0.0184058
$958$	−8.97813e9	−0.329918
$959$	1.68297e10	0.616186
$960$	−1.99760e8	−0.00728717
$961$	−2.38064e10	−0.865289
$962$	2.03367e9	0.0736491
$963$	5.36617e9	0.193630
$964$	1.47604e10	0.530676
$965$	3.99059e10	1.42952
$966$	−4.75884e9	−0.169856
$967$	−4.96874e10	−1.76707	−0.883534	−	0.468366i	$-0.844843\pi$
$967$	−4.96874e10	−1.76707	−0.883534	+	0.468366i	$0.844843\pi$
$968$	2.27854e10	0.807409
$969$	3.21450e9	0.113496
$970$	4.94276e9	0.173888
$971$	−3.96345e10	−1.38933	−0.694665	−	0.719333i	$-0.744448\pi$
$971$	−3.96345e10	−1.38933	−0.694665	+	0.719333i	$0.744448\pi$
$972$	2.36800e10	0.827084
$973$	1.64464e10	0.572370
$974$	1.03812e10	0.359991
$975$	8.59080e8	0.0296837
$976$	1.43034e10	0.492453
$977$	−2.94172e10	−1.00918	−0.504592	−	0.863358i	$-0.668357\pi$
$977$	−2.94172e10	−1.00918	−0.504592	+	0.863358i	$0.668357\pi$
$978$	2.67198e9	0.0913371
$979$	2.58807e8	0.00881530
$980$	−3.00848e9	−0.102107
$981$	−4.84641e9	−0.163900
$982$	1.76778e10	0.595713
$983$	−4.51735e10	−1.51686	−0.758432	−	0.651752i	$-0.774034\pi$
$983$	−4.51735e10	−1.51686	−0.758432	+	0.651752i	$0.774034\pi$
$984$	−2.65443e9	−0.0888155
$985$	2.95317e9	0.0984603
$986$	−2.52107e10	−0.837559
$987$	−5.46958e9	−0.181069
$988$	−1.43934e9	−0.0474804
$989$	3.74661e10	1.23155
$990$	−1.56077e8	−0.00511228
$991$	2.66926e10	0.871232	0.435616	−	0.900133i	$-0.356531\pi$
$991$	2.66926e10	0.871232	0.435616	+	0.900133i	$0.356531\pi$
$992$	1.13218e10	0.368234
$993$	2.79967e10	0.907369
$994$	−5.49260e8	−0.0177389
$995$	−5.49988e9	−0.177000
$996$	−2.07180e10	−0.664415
$997$	−4.73466e10	−1.51306	−0.756529	−	0.653960i	$-0.773107\pi$
$997$	−4.73466e10	−1.51306	−0.756529	+	0.653960i	$0.773107\pi$
$998$	1.00202e10	0.319095
$999$	1.71808e10	0.545209

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.e.1.8	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.e.1.8	✓	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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	91.a (trivial)

\(f(q)\)	\(=\)	\(q+5.08138 q^{2} -25.2372 q^{3} -102.180 q^{4} +250.262 q^{5} -128.240 q^{6} +343.000 q^{7} -1169.63 q^{8} -1550.08 q^{9} +O(q^{10})\)	\(q+5.08138 q^{2} -25.2372 q^{3} -102.180 q^{4} +250.262 q^{5} -128.240 q^{6} +343.000 q^{7} -1169.63 q^{8} -1550.08 q^{9} +1271.68 q^{10} +79.1782 q^{11} +2578.73 q^{12} +2197.00 q^{13} +1742.91 q^{14} -6315.91 q^{15} +7135.66 q^{16} -19865.7 q^{17} -7876.57 q^{18} +6411.64 q^{19} -25571.7 q^{20} -8656.36 q^{21} +402.335 q^{22} +108189. q^{23} +29518.2 q^{24} -15494.0 q^{25} +11163.8 q^{26} +94313.5 q^{27} -35047.6 q^{28} +249746. q^{29} -32093.5 q^{30} +60879.1 q^{31} +185972. q^{32} -1998.24 q^{33} -100945. q^{34} +85839.8 q^{35} +158387. q^{36} +182166. q^{37} +32580.0 q^{38} -55446.1 q^{39} -292714. q^{40} -89925.4 q^{41} -43986.2 q^{42} +346302. q^{43} -8090.40 q^{44} -387927. q^{45} +549751. q^{46} +631857. q^{47} -180084. q^{48} +117649. q^{49} -78730.7 q^{50} +501354. q^{51} -224489. q^{52} -861465. q^{53} +479243. q^{54} +19815.3 q^{55} -401183. q^{56} -161812. q^{57} +1.26906e6 q^{58} -157822. q^{59} +645357. q^{60} +2.00450e6 q^{61} +309350. q^{62} -531679. q^{63} +31628.0 q^{64} +549825. q^{65} -10153.8 q^{66} -999718. q^{67} +2.02987e6 q^{68} -2.73039e6 q^{69} +436185. q^{70} -315139. q^{71} +1.81302e6 q^{72} +3.40160e6 q^{73} +925657. q^{74} +391024. q^{75} -655139. q^{76} +27158.1 q^{77} -281743. q^{78} -646177. q^{79} +1.78578e6 q^{80} +1.00983e6 q^{81} -456945. q^{82} -8.03418e6 q^{83} +884503. q^{84} -4.97163e6 q^{85} +1.75969e6 q^{86} -6.30290e6 q^{87} -92609.2 q^{88} +3.26867e6 q^{89} -1.97120e6 q^{90} +753571. q^{91} -1.10547e7 q^{92} -1.53642e6 q^{93} +3.21070e6 q^{94} +1.60459e6 q^{95} -4.69340e6 q^{96} +3.88681e6 q^{97} +597819. q^{98} -122733. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9}+O(q^{10}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9} + 6668 q^{10} + 12168 q^{11} - 183 q^{12} + 26364 q^{13} + 2058 q^{14} - 28790 q^{15} + 85914 q^{16} + 82710 q^{17} - 44965 q^{18} - 10302 q^{19} + 141318 q^{20} + 28126 q^{21} - 97457 q^{22} + 98376 q^{23} - 519981 q^{24} + 272736 q^{25} + 13182 q^{26} + 306652 q^{27} + 338198 q^{28} + 350592 q^{29} + 231528 q^{30} + 55092 q^{31} + 114420 q^{32} + 609912 q^{33} + 812002 q^{34} + 351918 q^{35} + 1472143 q^{36} + 376310 q^{37} + 2825424 q^{38} + 180154 q^{39} + 2169290 q^{40} + 1387272 q^{41} + 105987 q^{42} + 568708 q^{43} + 3392031 q^{44} + 3556226 q^{45} - 1736829 q^{46} + 1359444 q^{47} + 4151249 q^{48} + 1411788 q^{49} + 3983712 q^{50} + 2709260 q^{51} + 2166242 q^{52} + 2061780 q^{53} + 2196651 q^{54} - 2112846 q^{55} + 78204 q^{56} + 2359902 q^{57} + 670268 q^{58} + 395964 q^{59} - 1052376 q^{60} + 444006 q^{61} + 2854353 q^{62} + 3739386 q^{63} + 12026858 q^{64} + 2254122 q^{65} - 4605681 q^{66} - 3094010 q^{67} + 4668954 q^{68} + 3839892 q^{69} + 2287124 q^{70} + 5694366 q^{71} - 9780585 q^{72} + 7052346 q^{73} - 4436259 q^{74} - 16288696 q^{75} - 3051830 q^{76} + 4173624 q^{77} + 678873 q^{78} + 4304160 q^{79} + 3807018 q^{80} - 6689556 q^{81} - 4733665 q^{82} + 2704554 q^{83} - 62769 q^{84} + 9301878 q^{85} + 1510998 q^{86} + 16231802 q^{87} - 70453923 q^{88} - 10986042 q^{89} - 12851300 q^{90} + 9042852 q^{91} - 16505451 q^{92} - 47230934 q^{93} - 24306151 q^{94} - 21839424 q^{95} - 86512741 q^{96} - 24462382 q^{97} + 705894 q^{98} + 11555078 q^{99}+O(q^{100}) \) 12 * q + 6 * q^2 + 82 * q^3 + 986 * q^4 + 1026 * q^5 + 309 * q^6 + 4116 * q^7 + 228 * q^8 + 10902 * q^9 + 6668 * q^10 + 12168 * q^11 - 183 * q^12 + 26364 * q^13 + 2058 * q^14 - 28790 * q^15 + 85914 * q^16 + 82710 * q^17 - 44965 * q^18 - 10302 * q^19 + 141318 * q^20 + 28126 * q^21 - 97457 * q^22 + 98376 * q^23 - 519981 * q^24 + 272736 * q^25 + 13182 * q^26 + 306652 * q^27 + 338198 * q^28 + 350592 * q^29 + 231528 * q^30 + 55092 * q^31 + 114420 * q^32 + 609912 * q^33 + 812002 * q^34 + 351918 * q^35 + 1472143 * q^36 + 376310 * q^37 + 2825424 * q^38 + 180154 * q^39 + 2169290 * q^40 + 1387272 * q^41 + 105987 * q^42 + 568708 * q^43 + 3392031 * q^44 + 3556226 * q^45 - 1736829 * q^46 + 1359444 * q^47 + 4151249 * q^48 + 1411788 * q^49 + 3983712 * q^50 + 2709260 * q^51 + 2166242 * q^52 + 2061780 * q^53 + 2196651 * q^54 - 2112846 * q^55 + 78204 * q^56 + 2359902 * q^57 + 670268 * q^58 + 395964 * q^59 - 1052376 * q^60 + 444006 * q^61 + 2854353 * q^62 + 3739386 * q^63 + 12026858 * q^64 + 2254122 * q^65 - 4605681 * q^66 - 3094010 * q^67 + 4668954 * q^68 + 3839892 * q^69 + 2287124 * q^70 + 5694366 * q^71 - 9780585 * q^72 + 7052346 * q^73 - 4436259 * q^74 - 16288696 * q^75 - 3051830 * q^76 + 4173624 * q^77 + 678873 * q^78 + 4304160 * q^79 + 3807018 * q^80 - 6689556 * q^81 - 4733665 * q^82 + 2704554 * q^83 - 62769 * q^84 + 9301878 * q^85 + 1510998 * q^86 + 16231802 * q^87 - 70453923 * q^88 - 10986042 * q^89 - 12851300 * q^90 + 9042852 * q^91 - 16505451 * q^92 - 47230934 * q^93 - 24306151 * q^94 - 21839424 * q^95 - 86512741 * q^96 - 24462382 * q^97 + 705894 * q^98 + 11555078 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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