LMFDB - Embedded newform 91.8.a.e.1.5

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			1.5
Root			$10.5927$ 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)

$f(q)$	$=$	$q-9.59274 q^{2} +50.3591 q^{3} -35.9794 q^{4} +255.731 q^{5} -483.082 q^{6} +343.000 q^{7} +1573.01 q^{8} +349.039 q^{9} +O(q^{10})$	\(q-9.59274 q^{2} +50.3591 q^{3} -35.9794 q^{4} +255.731 q^{5} -483.082 q^{6} +343.000 q^{7} +1573.01 q^{8} +349.039 q^{9} -2453.16 q^{10} +2581.16 q^{11} -1811.89 q^{12} +2197.00 q^{13} -3290.31 q^{14} +12878.4 q^{15} -10484.1 q^{16} +2930.15 q^{17} -3348.23 q^{18} +21147.7 q^{19} -9201.06 q^{20} +17273.2 q^{21} -24760.4 q^{22} -17170.0 q^{23} +79215.4 q^{24} -12726.5 q^{25} -21075.2 q^{26} -92558.1 q^{27} -12340.9 q^{28} -93079.5 q^{29} -123539. q^{30} +203907. q^{31} -100774. q^{32} +129985. q^{33} -28108.2 q^{34} +87715.8 q^{35} -12558.2 q^{36} +108445. q^{37} -202864. q^{38} +110639. q^{39} +402268. q^{40} +568659. q^{41} -165697. q^{42} +788479. q^{43} -92868.6 q^{44} +89260.1 q^{45} +164707. q^{46} +640403. q^{47} -527971. q^{48} +117649. q^{49} +122082. q^{50} +147560. q^{51} -79046.8 q^{52} +82954.4 q^{53} +887885. q^{54} +660084. q^{55} +539543. q^{56} +1.06498e6 q^{57} +892887. q^{58} +192889. q^{59} -463357. q^{60} +2.44511e6 q^{61} -1.95603e6 q^{62} +119720. q^{63} +2.30867e6 q^{64} +561842. q^{65} -1.24691e6 q^{66} +4.16532e6 q^{67} -105425. q^{68} -864664. q^{69} -841435. q^{70} +3.47378e6 q^{71} +549042. q^{72} -4.77837e6 q^{73} -1.04028e6 q^{74} -640896. q^{75} -760881. q^{76} +885338. q^{77} -1.06133e6 q^{78} -7.65148e6 q^{79} -2.68112e6 q^{80} -5.42449e6 q^{81} -5.45500e6 q^{82} -4.92570e6 q^{83} -621478. q^{84} +749332. q^{85} -7.56367e6 q^{86} -4.68740e6 q^{87} +4.06020e6 q^{88} -5.29816e6 q^{89} -856248. q^{90} +753571. q^{91} +617765. q^{92} +1.02686e7 q^{93} -6.14322e6 q^{94} +5.40812e6 q^{95} -5.07489e6 q^{96} +5.37546e6 q^{97} -1.12858e6 q^{98} +900925. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.59274	−0.847886	−0.423943	−	0.905689i	$-0.639354\pi$
$2$	−9.59274	−0.847886	−0.423943	+	0.905689i	$0.639354\pi$
$3$	50.3591	1.07685	0.538423	−	0.842675i	$-0.319020\pi$
$3$	50.3591	1.07685	0.538423	+	0.842675i	$0.319020\pi$
$4$	−35.9794	−0.281089
$5$	255.731	0.914932	0.457466	−	0.889227i	$-0.348757\pi$
$5$	255.731	0.914932	0.457466	+	0.889227i	$0.348757\pi$
$6$	−483.082	−0.913043
$7$	343.000	0.377964
$7$	343.000	0.377964
$8$	1573.01	1.08622
$9$	349.039	0.159597
$10$	−2453.16	−0.775758
$11$	2581.16	0.584710	0.292355	−	0.956310i	$-0.405561\pi$
$11$	2581.16	0.584710	0.292355	+	0.956310i	$0.405561\pi$
$12$	−1811.89	−0.302690
$13$	2197.00	0.277350
$13$	2197.00	0.277350
$14$	−3290.31	−0.320471
$15$	12878.4	0.985241
$16$	−10484.1	−0.639900
$17$	2930.15	0.144650	0.0723251	−	0.997381i	$-0.476958\pi$
$17$	2930.15	0.144650	0.0723251	+	0.997381i	$0.476958\pi$
$18$	−3348.23	−0.135320
$19$	21147.7	0.707335	0.353667	−	0.935371i	$-0.384935\pi$
$19$	21147.7	0.707335	0.353667	+	0.935371i	$0.384935\pi$
$20$	−9201.06	−0.257177
$21$	17273.2	0.407009
$22$	−24760.4	−0.495768
$23$	−17170.0	−0.294254	−0.147127	−	0.989118i	$-0.547003\pi$
$23$	−17170.0	−0.294254	−0.147127	+	0.989118i	$0.547003\pi$
$24$	79215.4	1.16969
$25$	−12726.5	−0.162900
$26$	−21075.2	−0.235161
$27$	−92558.1	−0.904985
$28$	−12340.9	−0.106242
$29$	−93079.5	−0.708698	−0.354349	−	0.935113i	$-0.615298\pi$
$29$	−93079.5	−0.708698	−0.354349	+	0.935113i	$0.615298\pi$
$30$	−123539.	−0.835372
$31$	203907.	1.22933	0.614663	−	0.788790i	$-0.289292\pi$
$31$	203907.	1.22933	0.614663	+	0.788790i	$0.289292\pi$
$32$	−100774.	−0.543655
$33$	129985.	0.629643
$34$	−28108.2	−0.122647
$35$	87715.8	0.345812
$36$	−12558.2	−0.0448610
$37$	108445.	0.351967	0.175984	−	0.984393i	$-0.443689\pi$
$37$	108445.	0.351967	0.175984	+	0.984393i	$0.443689\pi$
$38$	−202864.	−0.599739
$39$	110639.	0.298663
$40$	402268.	0.993815
$41$	568659.	1.28857	0.644286	−	0.764785i	$-0.277155\pi$
$41$	568659.	1.28857	0.644286	+	0.764785i	$0.277155\pi$
$42$	−165697.	−0.345098
$43$	788479.	1.51234	0.756172	−	0.654373i	$-0.227067\pi$
$43$	788479.	1.51234	0.756172	+	0.654373i	$0.227067\pi$
$44$	−92868.6	−0.164356
$45$	89260.1	0.146020
$46$	164707.	0.249494
$47$	640403.	0.899727	0.449863	−	0.893097i	$-0.351473\pi$
$47$	640403.	0.899727	0.449863	+	0.893097i	$0.351473\pi$
$48$	−527971.	−0.689073
$49$	117649.	0.142857
$50$	122082.	0.138120
$51$	147560.	0.155766
$52$	−79046.8	−0.0779601
$53$	82954.4	0.0765374	0.0382687	−	0.999267i	$-0.487816\pi$
$53$	82954.4	0.0765374	0.0382687	+	0.999267i	$0.487816\pi$
$54$	887885.	0.767324
$55$	660084.	0.534970
$56$	539543.	0.410552
$57$	1.06498e6	0.761690
$58$	892887.	0.600895
$59$	192889.	0.122272	0.0611359	−	0.998129i	$-0.480528\pi$
$59$	192889.	0.122272	0.0611359	+	0.998129i	$0.480528\pi$
$60$	−463357.	−0.276940
$61$	2.44511e6	1.37925	0.689627	−	0.724165i	$-0.257774\pi$
$61$	2.44511e6	1.37925	0.689627	+	0.724165i	$0.257774\pi$
$62$	−1.95603e6	−1.04233
$63$	119720.	0.0603220
$64$	2.30867e6	1.10086
$65$	561842.	0.253756
$66$	−1.24691e6	−0.533865
$67$	4.16532e6	1.69195	0.845973	−	0.533226i	$-0.179021\pi$
$67$	4.16532e6	1.69195	0.845973	+	0.533226i	$0.179021\pi$
$68$	−105425.	−0.0406596
$69$	−864664.	−0.316866
$70$	−841435.	−0.293209
$71$	3.47378e6	1.15186	0.575928	−	0.817500i	$-0.304641\pi$
$71$	3.47378e6	1.15186	0.575928	+	0.817500i	$0.304641\pi$
$72$	549042.	0.173357
$73$	−4.77837e6	−1.43764	−0.718819	−	0.695197i	$-0.755317\pi$
$73$	−4.77837e6	−1.43764	−0.718819	+	0.695197i	$0.755317\pi$
$74$	−1.04028e6	−0.298428
$75$	−640896.	−0.175418
$76$	−760881.	−0.198824
$77$	885338.	0.221000
$78$	−1.06133e6	−0.253232
$79$	−7.65148e6	−1.74603	−0.873013	−	0.487696i	$-0.837837\pi$
$79$	−7.65148e6	−1.74603	−0.873013	+	0.487696i	$0.837837\pi$
$80$	−2.68112e6	−0.585465
$81$	−5.42449e6	−1.13413
$82$	−5.45500e6	−1.09256
$83$	−4.92570e6	−0.945573	−0.472786	−	0.881177i	$-0.656752\pi$
$83$	−4.92570e6	−0.945573	−0.472786	+	0.881177i	$0.656752\pi$
$84$	−621478.	−0.114406
$85$	749332.	0.132345
$86$	−7.56367e6	−1.28230
$87$	−4.68740e6	−0.763158
$88$	4.06020e6	0.635123
$89$	−5.29816e6	−0.796636	−0.398318	−	0.917247i	$-0.630406\pi$
$89$	−5.29816e6	−0.796636	−0.398318	+	0.917247i	$0.630406\pi$
$90$	−856248.	−0.123809
$91$	753571.	0.104828
$92$	617765.	0.0827115
$93$	1.02686e7	1.32380
$94$	−6.14322e6	−0.762866
$95$	5.40812e6	0.647163
$96$	−5.07489e6	−0.585433
$97$	5.37546e6	0.598018	0.299009	−	0.954250i	$-0.403344\pi$
$97$	5.37546e6	0.598018	0.299009	+	0.954250i	$0.403344\pi$
$98$	−1.12858e6	−0.121127
$99$	900925.	0.0933180
$100$	457893.	0.0457893
$101$	2.66268e6	0.257154	0.128577	−	0.991700i	$-0.458959\pi$
$101$	2.66268e6	0.257154	0.128577	+	0.991700i	$0.458959\pi$
$102$	−1.41550e6	−0.132072
$103$	−3.37971e6	−0.304754	−0.152377	−	0.988322i	$-0.548693\pi$
$103$	−3.37971e6	−0.304754	−0.152377	+	0.988322i	$0.548693\pi$
$104$	3.45591e6	0.301263
$105$	4.41729e6	0.372386
$106$	−795760.	−0.0648950
$107$	1.12679e7	0.889199	0.444599	−	0.895729i	$-0.353346\pi$
$107$	1.12679e7	0.889199	0.444599	+	0.895729i	$0.353346\pi$
$108$	3.33018e6	0.254381
$109$	−1.27866e6	−0.0945716	−0.0472858	−	0.998881i	$-0.515057\pi$
$109$	−1.27866e6	−0.0945716	−0.0472858	+	0.998881i	$0.515057\pi$
$110$	−6.33201e6	−0.453594
$111$	5.46117e6	0.379014
$112$	−3.59605e6	−0.241859
$113$	1.33359e7	0.869458	0.434729	−	0.900561i	$-0.356844\pi$
$113$	1.33359e7	0.869458	0.434729	+	0.900561i	$0.356844\pi$
$114$	−1.02160e7	−0.645827
$115$	−4.39090e6	−0.269222
$116$	3.34895e6	0.199207
$117$	766838.	0.0442642
$118$	−1.85034e6	−0.103673
$119$	1.00504e6	0.0546727
$120$	2.02579e7	1.07019
$121$	−1.28248e7	−0.658114
$122$	−2.34553e7	−1.16945
$123$	2.86372e7	1.38759
$124$	−7.33647e6	−0.345550
$125$	−2.32336e7	−1.06397
$126$	−1.14844e6	−0.0511462
$127$	−542790.	−0.0235136	−0.0117568	−	0.999931i	$-0.503742\pi$
$127$	−542790.	−0.0235136	−0.0117568	+	0.999931i	$0.503742\pi$
$128$	−9.24735e6	−0.389747
$129$	3.97071e7	1.62856
$130$	−5.38960e6	−0.215157
$131$	−2.56069e7	−0.995195	−0.497598	−	0.867408i	$-0.665784\pi$
$131$	−2.56069e7	−0.995195	−0.497598	+	0.867408i	$0.665784\pi$
$132$	−4.67678e6	−0.176986
$133$	7.25365e6	0.267347
$134$	−3.99568e7	−1.43458
$135$	−2.36700e7	−0.827999
$136$	4.60917e6	0.157122
$137$	2.79367e7	0.928223	0.464112	−	0.885777i	$-0.346374\pi$
$137$	2.79367e7	0.928223	0.464112	+	0.885777i	$0.346374\pi$
$138$	8.29449e6	0.268666
$139$	−1.40247e7	−0.442936	−0.221468	−	0.975168i	$-0.571085\pi$
$139$	−1.40247e7	−0.442936	−0.221468	+	0.975168i	$0.571085\pi$
$140$	−3.15596e6	−0.0972039
$141$	3.22501e7	0.968867
$142$	−3.33231e7	−0.976643
$143$	5.67081e6	0.162169
$144$	−3.65936e6	−0.102126
$145$	−2.38033e7	−0.648410
$146$	4.58376e7	1.21895
$147$	5.92470e6	0.153835
$148$	−3.90177e6	−0.0989341
$149$	−5.24708e7	−1.29947	−0.649734	−	0.760162i	$-0.725120\pi$
$149$	−5.24708e7	−1.29947	−0.649734	+	0.760162i	$0.725120\pi$
$150$	6.14795e6	0.148734
$151$	2.15427e7	0.509191	0.254596	−	0.967048i	$-0.418058\pi$
$151$	2.15427e7	0.509191	0.254596	+	0.967048i	$0.418058\pi$
$152$	3.32655e7	0.768319
$153$	1.02274e6	0.0230857
$154$	−8.49282e6	−0.187383
$155$	5.21455e7	1.12475
$156$	−3.98072e6	−0.0839510
$157$	2.98651e7	0.615906	0.307953	−	0.951402i	$-0.400356\pi$
$157$	2.98651e7	0.615906	0.307953	+	0.951402i	$0.400356\pi$
$158$	7.33987e7	1.48043
$159$	4.17751e6	0.0824190
$160$	−2.57711e7	−0.497408
$161$	−5.88930e6	−0.111217
$162$	5.20357e7	0.961610
$163$	−5.04574e7	−0.912575	−0.456288	−	0.889832i	$-0.650821\pi$
$163$	−5.04574e7	−0.912575	−0.456288	+	0.889832i	$0.650821\pi$
$164$	−2.04600e7	−0.362203
$165$	3.32412e7	0.576080
$166$	4.72510e7	0.801738
$167$	−3.22889e6	−0.0536470	−0.0268235	−	0.999640i	$-0.508539\pi$
$167$	−3.22889e6	−0.0536470	−0.0268235	+	0.999640i	$0.508539\pi$
$168$	2.71709e7	0.442101
$169$	4.82681e6	0.0769231
$170$	−7.18814e6	−0.112214
$171$	7.38135e6	0.112888
$172$	−2.83690e7	−0.425103
$173$	−8.18996e7	−1.20260	−0.601299	−	0.799024i	$-0.705350\pi$
$173$	−8.18996e7	−1.20260	−0.601299	+	0.799024i	$0.705350\pi$
$174$	4.49650e7	0.647071
$175$	−4.36520e6	−0.0615702
$176$	−2.70612e7	−0.374156
$177$	9.71373e6	0.131668
$178$	5.08238e7	0.675456
$179$	9.06789e7	1.18174	0.590868	−	0.806768i	$-0.298785\pi$
$179$	9.06789e7	1.18174	0.590868	+	0.806768i	$0.298785\pi$
$180$	−3.21152e6	−0.0410447
$181$	−4.70416e7	−0.589668	−0.294834	−	0.955549i	$-0.595264\pi$
$181$	−4.70416e7	−0.589668	−0.294834	+	0.955549i	$0.595264\pi$
$182$	−7.22881e6	−0.0888826
$183$	1.23134e8	1.48524
$184$	−2.70086e7	−0.319624
$185$	2.77327e7	0.322026
$186$	−9.85039e7	−1.12243
$187$	7.56320e6	0.0845785
$188$	−2.30413e7	−0.252903
$189$	−3.17474e7	−0.342052
$190$	−5.18787e7	−0.548721
$191$	3.45353e7	0.358630	0.179315	−	0.983792i	$-0.442612\pi$
$191$	3.45353e7	0.358630	0.179315	+	0.983792i	$0.442612\pi$
$192$	1.16262e8	1.18545
$193$	−1.73463e8	−1.73682	−0.868412	−	0.495843i	$-0.834859\pi$
$193$	−1.73463e8	−1.73682	−0.868412	+	0.495843i	$0.834859\pi$
$194$	−5.15654e7	−0.507051
$195$	2.82938e7	0.273257
$196$	−4.23294e6	−0.0401556
$197$	9.64533e7	0.898846	0.449423	−	0.893319i	$-0.351630\pi$
$197$	9.64533e7	0.898846	0.449423	+	0.893319i	$0.351630\pi$
$198$	−8.64233e6	−0.0791230
$199$	−8.24829e7	−0.741956	−0.370978	−	0.928642i	$-0.620978\pi$
$199$	−8.24829e7	−0.741956	−0.370978	+	0.928642i	$0.620978\pi$
$200$	−2.00190e7	−0.176944
$201$	2.09762e8	1.82196
$202$	−2.55424e7	−0.218037
$203$	−3.19263e7	−0.267863
$204$	−5.30912e6	−0.0437841
$205$	1.45424e8	1.17896
$206$	3.24207e7	0.258397
$207$	−5.99298e6	−0.0469620
$208$	−2.30336e7	−0.177476
$209$	5.45855e7	0.413586
$210$	−4.23739e7	−0.315741
$211$	−8.55662e6	−0.0627067	−0.0313533	−	0.999508i	$-0.509982\pi$
$211$	−8.55662e6	−0.0627067	−0.0313533	+	0.999508i	$0.509982\pi$
$212$	−2.98465e6	−0.0215138
$213$	1.74936e8	1.24037
$214$	−1.08090e8	−0.753939
$215$	2.01639e8	1.38369
$216$	−1.45595e8	−0.983010
$217$	6.99403e7	0.464642
$218$	1.22658e7	0.0801860
$219$	−2.40634e8	−1.54812
$220$	−2.37494e7	−0.150374
$221$	6.43755e6	0.0401188
$222$	−5.23876e7	−0.321361
$223$	−2.46144e8	−1.48635	−0.743177	−	0.669094i	$-0.766682\pi$
$223$	−2.46144e8	−1.48635	−0.743177	+	0.669094i	$0.766682\pi$
$224$	−3.45655e7	−0.205482
$225$	−4.44205e6	−0.0259983
$226$	−1.27928e8	−0.737201
$227$	1.78066e8	1.01039	0.505197	−	0.863004i	$-0.331420\pi$
$227$	1.78066e8	1.01039	0.505197	+	0.863004i	$0.331420\pi$
$228$	−3.83173e7	−0.214103
$229$	−2.76317e8	−1.52049	−0.760246	−	0.649636i	$-0.774921\pi$
$229$	−2.76317e8	−1.52049	−0.760246	+	0.649636i	$0.774921\pi$
$230$	4.21207e7	0.228270
$231$	4.45848e7	0.237983
$232$	−1.46415e8	−0.769800
$233$	5.58863e7	0.289440	0.144720	−	0.989473i	$-0.453772\pi$
$233$	5.58863e7	0.289440	0.144720	+	0.989473i	$0.453772\pi$
$234$	−7.35607e6	−0.0375310
$235$	1.63771e8	0.823189
$236$	−6.94004e6	−0.0343692
$237$	−3.85322e8	−1.88020
$238$	−9.64111e6	−0.0463562
$239$	1.28066e8	0.606794	0.303397	−	0.952864i	$-0.401879\pi$
$239$	1.28066e8	0.606794	0.303397	+	0.952864i	$0.401879\pi$
$240$	−1.35019e8	−0.630455
$241$	−6.44744e7	−0.296707	−0.148353	−	0.988934i	$-0.547397\pi$
$241$	−6.44744e7	−0.296707	−0.148353	+	0.988934i	$0.547397\pi$
$242$	1.23025e8	0.558006
$243$	−7.07478e7	−0.316294
$244$	−8.79737e7	−0.387693
$245$	3.00865e7	0.130705
$246$	−2.74709e8	−1.17652
$247$	4.64614e7	0.196179
$248$	3.20749e8	1.33532
$249$	−2.48054e8	−1.01824
$250$	2.22874e8	0.902129
$251$	−6.87480e7	−0.274411	−0.137206	−	0.990543i	$-0.543812\pi$
$251$	−6.87480e7	−0.274411	−0.137206	+	0.990543i	$0.543812\pi$
$252$	−4.30746e6	−0.0169559
$253$	−4.43185e7	−0.172053
$254$	5.20684e6	0.0199368
$255$	3.77357e7	0.142515
$256$	−2.06802e8	−0.770397
$257$	1.12481e8	0.413344	0.206672	−	0.978410i	$-0.433737\pi$
$257$	1.12481e8	0.413344	0.206672	+	0.978410i	$0.433737\pi$
$258$	−3.80900e8	−1.38083
$259$	3.71965e7	0.133031
$260$	−2.02147e7	−0.0713282
$261$	−3.24883e7	−0.113106
$262$	2.45641e8	0.843812
$263$	1.08966e8	0.369357	0.184678	−	0.982799i	$-0.440876\pi$
$263$	1.08966e8	0.369357	0.184678	+	0.982799i	$0.440876\pi$
$264$	2.04468e8	0.683929
$265$	2.12140e7	0.0700266
$266$	−6.95824e7	−0.226680
$267$	−2.66810e8	−0.857854
$268$	−1.49866e8	−0.475587
$269$	−6.77506e7	−0.212217	−0.106108	−	0.994355i	$-0.533839\pi$
$269$	−6.77506e7	−0.212217	−0.106108	+	0.994355i	$0.533839\pi$
$270$	2.27060e8	0.702049
$271$	5.74959e7	0.175487	0.0877434	−	0.996143i	$-0.472034\pi$
$271$	5.74959e7	0.175487	0.0877434	+	0.996143i	$0.472034\pi$
$272$	−3.07201e7	−0.0925617
$273$	3.79492e7	0.112884
$274$	−2.67989e8	−0.787028
$275$	−3.28492e7	−0.0952490
$276$	3.11101e7	0.0890676
$277$	1.27673e8	0.360927	0.180464	−	0.983582i	$-0.442240\pi$
$277$	1.27673e8	0.360927	0.180464	+	0.983582i	$0.442240\pi$
$278$	1.34535e8	0.375559
$279$	7.11716e7	0.196197
$280$	1.37978e8	0.375627
$281$	−4.20286e8	−1.12999	−0.564993	−	0.825096i	$-0.691121\pi$
$281$	−4.20286e8	−1.12999	−0.564993	+	0.825096i	$0.691121\pi$
$282$	−3.09367e8	−0.821489
$283$	4.95902e8	1.30060	0.650300	−	0.759677i	$-0.274643\pi$
$283$	4.95902e8	1.30060	0.650300	+	0.759677i	$0.274643\pi$
$284$	−1.24985e8	−0.323774
$285$	2.72348e8	0.696895
$286$	−5.43986e7	−0.137501
$287$	1.95050e8	0.487034
$288$	−3.51740e7	−0.0867658
$289$	−4.01753e8	−0.979076
$290$	2.28339e8	0.549778
$291$	2.70703e8	0.643973
$292$	1.71923e8	0.404105
$293$	1.95439e7	0.0453915	0.0226957	−	0.999742i	$-0.492775\pi$
$293$	1.95439e7	0.0453915	0.0226957	+	0.999742i	$0.492775\pi$
$294$	−5.68341e7	−0.130435
$295$	4.93278e7	0.111870
$296$	1.70585e8	0.382313
$297$	−2.38907e8	−0.529154
$298$	5.03338e8	1.10180
$299$	−3.77224e7	−0.0816113
$300$	2.30591e7	0.0493080
$301$	2.70448e8	0.571612
$302$	−2.06653e8	−0.431736
$303$	1.34090e8	0.276915
$304$	−2.21715e8	−0.452623
$305$	6.25292e8	1.26192
$306$	−9.81084e6	−0.0195741
$307$	−2.49035e8	−0.491220	−0.245610	−	0.969369i	$-0.578988\pi$
$307$	−2.49035e8	−0.491220	−0.245610	+	0.969369i	$0.578988\pi$
$308$	−3.18539e7	−0.0621206
$309$	−1.70199e8	−0.328173
$310$	−5.00218e8	−0.953660
$311$	−8.93074e7	−0.168355	−0.0841775	−	0.996451i	$-0.526826\pi$
$311$	−8.93074e7	−0.168355	−0.0841775	+	0.996451i	$0.526826\pi$
$312$	1.74036e8	0.324413
$313$	−4.27203e8	−0.787461	−0.393731	−	0.919226i	$-0.628816\pi$
$313$	−4.27203e8	−0.787461	−0.393731	+	0.919226i	$0.628816\pi$
$314$	−2.86488e8	−0.522218
$315$	3.06162e7	0.0551905
$316$	2.75296e8	0.490789
$317$	−9.12027e8	−1.60805	−0.804026	−	0.594594i	$-0.797313\pi$
$317$	−9.12027e8	−1.60805	−0.804026	+	0.594594i	$0.797313\pi$
$318$	−4.00737e7	−0.0698819
$319$	−2.40253e8	−0.414383
$320$	5.90398e8	1.00721
$321$	5.67440e8	0.957530
$322$	5.64945e7	0.0942998
$323$	6.19659e7	0.102316
$324$	1.95170e8	0.318790
$325$	−2.79602e7	−0.0451802
$326$	4.84025e8	0.773760
$327$	−6.43919e7	−0.101839
$328$	8.94507e8	1.39967
$329$	2.19658e8	0.340065
$330$	−3.18874e8	−0.488450
$331$	4.33628e8	0.657233	0.328616	−	0.944463i	$-0.393418\pi$
$331$	4.33628e8	0.657233	0.328616	+	0.944463i	$0.393418\pi$
$332$	1.77224e8	0.265790
$333$	3.78514e7	0.0561729
$334$	3.09739e7	0.0454865
$335$	1.06520e9	1.54801
$336$	−1.81094e8	−0.260445
$337$	1.02946e8	0.146522	0.0732612	−	0.997313i	$-0.476659\pi$
$337$	1.02946e8	0.146522	0.0732612	+	0.997313i	$0.476659\pi$
$338$	−4.63023e7	−0.0652220
$339$	6.71585e8	0.936272
$340$	−2.69605e7	−0.0372008
$341$	5.26318e8	0.718800
$342$	−7.08074e7	−0.0957166
$343$	4.03536e7	0.0539949
$344$	1.24029e9	1.64274
$345$	−2.21122e8	−0.289911
$346$	7.85641e8	1.01967
$347$	2.95663e8	0.379877	0.189939	−	0.981796i	$-0.439171\pi$
$347$	2.95663e8	0.379877	0.189939	+	0.981796i	$0.439171\pi$
$348$	1.68650e8	0.214516
$349$	5.28198e8	0.665132	0.332566	−	0.943080i	$-0.392086\pi$
$349$	5.28198e8	0.665132	0.332566	+	0.943080i	$0.392086\pi$
$350$	4.18742e7	0.0522045
$351$	−2.03350e8	−0.250998
$352$	−2.60114e8	−0.317881
$353$	2.36776e8	0.286501	0.143250	−	0.989686i	$-0.454245\pi$
$353$	2.36776e8	0.286501	0.143250	+	0.989686i	$0.454245\pi$
$354$	−9.31812e7	−0.111639
$355$	8.88354e8	1.05387
$356$	1.90624e8	0.223926
$357$	5.06131e7	0.0588740
$358$	−8.69859e8	−1.00198
$359$	−1.09643e9	−1.25069	−0.625347	−	0.780347i	$-0.715042\pi$
$359$	−1.09643e9	−1.25069	−0.625347	+	0.780347i	$0.715042\pi$
$360$	1.40407e8	0.158610
$361$	−4.46648e8	−0.499678
$362$	4.51258e8	0.499971
$363$	−6.45844e8	−0.708687
$364$	−2.71130e7	−0.0294661
$365$	−1.22198e9	−1.31534
$366$	−1.18119e9	−1.25932
$367$	−1.38313e9	−1.46060	−0.730302	−	0.683124i	$-0.760621\pi$
$367$	−1.38313e9	−1.46060	−0.730302	+	0.683124i	$0.760621\pi$
$368$	1.80012e8	0.188293
$369$	1.98484e8	0.205652
$370$	−2.66032e8	−0.273041
$371$	2.84534e7	0.0289284
$372$	−3.69458e8	−0.372104
$373$	3.87393e8	0.386520	0.193260	−	0.981148i	$-0.438094\pi$
$373$	3.87393e8	0.386520	0.193260	+	0.981148i	$0.438094\pi$
$374$	−7.25518e7	−0.0717129
$375$	−1.17002e9	−1.14574
$376$	1.00736e9	0.977299
$377$	−2.04496e8	−0.196557
$378$	3.04545e8	0.290021
$379$	−8.69794e8	−0.820690	−0.410345	−	0.911930i	$-0.634592\pi$
$379$	−8.69794e8	−0.820690	−0.410345	+	0.911930i	$0.634592\pi$
$380$	−1.94581e8	−0.181910
$381$	−2.73344e7	−0.0253205
$382$	−3.31288e8	−0.304077
$383$	1.44762e9	1.31661	0.658306	−	0.752750i	$-0.271273\pi$
$383$	1.44762e9	1.31661	0.658306	+	0.752750i	$0.271273\pi$
$384$	−4.65688e8	−0.419697
$385$	2.26409e8	0.202200
$386$	1.66398e9	1.47263
$387$	2.75210e8	0.241366
$388$	−1.93406e8	−0.168096
$389$	1.20585e9	1.03866	0.519328	−	0.854575i	$-0.326182\pi$
$389$	1.20585e9	1.03866	0.519328	+	0.854575i	$0.326182\pi$
$390$	−2.71415e8	−0.231690
$391$	−5.03107e7	−0.0425639
$392$	1.85063e8	0.155174
$393$	−1.28954e9	−1.07167
$394$	−9.25251e8	−0.762119
$395$	−1.95672e9	−1.59750
$396$	−3.24147e7	−0.0262307
$397$	−2.38600e9	−1.91383	−0.956914	−	0.290371i	$-0.906221\pi$
$397$	−2.38600e9	−1.91383	−0.956914	+	0.290371i	$0.906221\pi$
$398$	7.91237e8	0.629094
$399$	3.65287e8	0.287892
$400$	1.33426e8	0.104239
$401$	−1.01868e9	−0.788919	−0.394460	−	0.918913i	$-0.629068\pi$
$401$	−1.01868e9	−0.788919	−0.394460	+	0.918913i	$0.629068\pi$
$402$	−2.01219e9	−1.54482
$403$	4.47985e8	0.340954
$404$	−9.58015e7	−0.0722832
$405$	−1.38721e9	−1.03765
$406$	3.06260e8	0.227117
$407$	2.79913e8	0.205799
$408$	2.32113e8	0.169196
$409$	1.06801e9	0.771871	0.385936	−	0.922526i	$-0.373879\pi$
$409$	1.06801e9	0.771871	0.385936	+	0.922526i	$0.373879\pi$
$410$	−1.39501e9	−0.999620
$411$	1.40686e9	0.999553
$412$	1.21600e8	0.0856631
$413$	6.61610e7	0.0462144
$414$	5.74891e7	0.0398184
$415$	−1.25966e9	−0.865135
$416$	−2.21401e8	−0.150783
$417$	−7.06270e8	−0.476974
$418$	−5.23625e8	−0.350674
$419$	−9.84794e8	−0.654028	−0.327014	−	0.945020i	$-0.606042\pi$
$419$	−9.84794e8	−0.654028	−0.327014	+	0.945020i	$0.606042\pi$
$420$	−1.58931e8	−0.104674
$421$	−4.87733e7	−0.0318562	−0.0159281	−	0.999873i	$-0.505070\pi$
$421$	−4.87733e7	−0.0318562	−0.0159281	+	0.999873i	$0.505070\pi$
$422$	8.20814e7	0.0531681
$423$	2.23525e8	0.143594
$424$	1.30488e8	0.0831363
$425$	−3.72907e7	−0.0235635
$426$	−1.67812e9	−1.05169
$427$	8.38673e8	0.521309
$428$	−4.05412e8	−0.249944
$429$	2.85577e8	0.174631
$430$	−1.93427e9	−1.17321
$431$	1.73942e9	1.04649	0.523243	−	0.852183i	$-0.324722\pi$
$431$	1.73942e9	1.04649	0.523243	+	0.852183i	$0.324722\pi$
$432$	9.70390e8	0.579099
$433$	2.68764e9	1.59097	0.795487	−	0.605971i	$-0.207215\pi$
$433$	2.68764e9	1.59097	0.795487	+	0.605971i	$0.207215\pi$
$434$	−6.70919e8	−0.393963
$435$	−1.19871e9	−0.698238
$436$	4.60053e7	0.0265830
$437$	−3.63105e8	−0.208136
$438$	2.30834e9	1.31263
$439$	−3.53346e9	−1.99331	−0.996654	−	0.0817358i	$-0.973954\pi$
$439$	−3.53346e9	−1.99331	−0.996654	+	0.0817358i	$0.973954\pi$
$440$	1.03832e9	0.581094
$441$	4.10640e7	0.0227996
$442$	−6.17537e7	−0.0340161
$443$	−3.08727e9	−1.68718	−0.843591	−	0.536987i	$-0.819562\pi$
$443$	−3.08727e9	−1.68718	−0.843591	+	0.536987i	$0.819562\pi$
$444$	−1.96490e8	−0.106537
$445$	−1.35490e9	−0.728867
$446$	2.36120e9	1.26026
$447$	−2.64238e9	−1.39933
$448$	7.91872e8	0.416085
$449$	5.75588e8	0.300089	0.150044	−	0.988679i	$-0.452058\pi$
$449$	5.75588e8	0.300089	0.150044	+	0.988679i	$0.452058\pi$
$450$	4.26114e7	0.0220436
$451$	1.46780e9	0.753441
$452$	−4.79818e8	−0.244395
$453$	1.08487e9	0.548320
$454$	−1.70814e9	−0.856699
$455$	1.92712e8	0.0959109
$456$	1.67522e9	0.827361
$457$	4.07165e8	0.199556	0.0997779	−	0.995010i	$-0.468187\pi$
$457$	4.07165e8	0.199556	0.0997779	+	0.995010i	$0.468187\pi$
$458$	2.65064e9	1.28920
$459$	−2.71209e8	−0.130906
$460$	1.57982e8	0.0756754
$461$	2.06313e9	0.980785	0.490393	−	0.871502i	$-0.336853\pi$
$461$	2.06313e9	0.980785	0.490393	+	0.871502i	$0.336853\pi$
$462$	−4.27691e8	−0.201782
$463$	1.86283e9	0.872247	0.436124	−	0.899887i	$-0.356351\pi$
$463$	1.86283e9	0.872247	0.436124	+	0.899887i	$0.356351\pi$
$464$	9.75857e8	0.453496
$465$	2.62600e9	1.21118
$466$	−5.36102e8	−0.245413
$467$	−3.92325e9	−1.78253	−0.891266	−	0.453482i	$-0.850182\pi$
$467$	−3.92325e9	−1.78253	−0.891266	+	0.453482i	$0.850182\pi$
$468$	−2.75904e7	−0.0124422
$469$	1.42870e9	0.639495
$470$	−1.57101e9	−0.697970
$471$	1.50398e9	0.663236
$472$	3.03417e8	0.132814
$473$	2.03519e9	0.884283
$474$	3.69629e9	1.59420
$475$	−2.69136e8	−0.115224
$476$	−3.61608e7	−0.0153679
$477$	2.89543e7	0.0122151
$478$	−1.22850e9	−0.514492
$479$	1.38329e9	0.575095	0.287547	−	0.957766i	$-0.407160\pi$
$479$	1.38329e9	0.575095	0.287547	+	0.957766i	$0.407160\pi$
$480$	−1.29781e9	−0.535632
$481$	2.38253e8	0.0976181
$482$	6.18486e8	0.251574
$483$	−2.96580e8	−0.119764
$484$	4.61428e8	0.184989
$485$	1.37467e9	0.547146
$486$	6.78665e8	0.268181
$487$	2.73305e9	1.07225	0.536125	−	0.844139i	$-0.319888\pi$
$487$	2.73305e9	1.07225	0.536125	+	0.844139i	$0.319888\pi$
$488$	3.84619e9	1.49817
$489$	−2.54099e9	−0.982703
$490$	−2.88612e8	−0.110823
$491$	−1.52223e9	−0.580359	−0.290179	−	0.956972i	$-0.593715\pi$
$491$	−1.52223e9	−0.580359	−0.290179	+	0.956972i	$0.593715\pi$
$492$	−1.03035e9	−0.390037
$493$	−2.72737e8	−0.102513
$494$	−4.45692e8	−0.166338
$495$	2.30395e8	0.0853796
$496$	−2.13779e9	−0.786646
$497$	1.19151e9	0.435361
$498$	2.37952e9	0.863348
$499$	−1.68770e9	−0.608055	−0.304028	−	0.952663i	$-0.598332\pi$
$499$	−1.68770e9	−0.608055	−0.304028	+	0.952663i	$0.598332\pi$
$500$	8.35930e8	0.299071
$501$	−1.62604e8	−0.0577695
$502$	6.59481e8	0.232670
$503$	−2.30687e9	−0.808230	−0.404115	−	0.914708i	$-0.632420\pi$
$503$	−2.30687e9	−0.808230	−0.404115	+	0.914708i	$0.632420\pi$
$504$	1.88321e8	0.0655228
$505$	6.80930e8	0.235279
$506$	4.25135e8	0.145882
$507$	2.43074e8	0.0828343
$508$	1.95292e7	0.00660941
$509$	−4.07761e9	−1.37055	−0.685273	−	0.728287i	$-0.740317\pi$
$509$	−4.07761e9	−1.37055	−0.685273	+	0.728287i	$0.740317\pi$
$510$	−3.61988e8	−0.120837
$511$	−1.63898e9	−0.543376
$512$	3.16746e9	1.04296
$513$	−1.95739e9	−0.640127
$514$	−1.07900e9	−0.350469
$515$	−8.64299e8	−0.278829
$516$	−1.42864e9	−0.457771
$517$	1.65298e9	0.526080
$518$	−3.56816e8	−0.112795
$519$	−4.12439e9	−1.29501
$520$	8.83783e8	0.275635
$521$	5.21852e9	1.61665	0.808324	−	0.588737i	$-0.200375\pi$
$521$	5.21852e9	1.61665	0.808324	+	0.588737i	$0.200375\pi$
$522$	3.11652e8	0.0959010
$523$	−6.18898e9	−1.89175	−0.945874	−	0.324533i	$-0.894793\pi$
$523$	−6.18898e9	−1.89175	−0.945874	+	0.324533i	$0.894793\pi$
$524$	9.21323e8	0.279738
$525$	−2.19827e8	−0.0663016
$526$	−1.04528e9	−0.313172
$527$	5.97480e8	0.177822
$528$	−1.36278e9	−0.402908
$529$	−3.11002e9	−0.913415
$530$	−2.03501e8	−0.0593745
$531$	6.73258e7	0.0195142
$532$	−2.60982e8	−0.0751484
$533$	1.24934e9	0.357386
$534$	2.55944e9	0.727362
$535$	2.88155e9	0.813556
$536$	6.55209e9	1.83782
$537$	4.56651e9	1.27255
$538$	6.49913e8	0.179936
$539$	3.03671e8	0.0835300
$540$	8.51632e8	0.232742
$541$	4.69741e9	1.27546	0.637732	−	0.770258i	$-0.279873\pi$
$541$	4.69741e9	1.27546	0.637732	+	0.770258i	$0.279873\pi$
$542$	−5.51543e8	−0.148793
$543$	−2.36897e9	−0.634981
$544$	−2.95283e8	−0.0786399
$545$	−3.26992e8	−0.0865266
$546$	−3.64036e8	−0.0957129
$547$	−3.92149e9	−1.02446	−0.512230	−	0.858848i	$-0.671181\pi$
$547$	−3.92149e9	−1.02446	−0.512230	+	0.858848i	$0.671181\pi$
$548$	−1.00514e9	−0.260913
$549$	8.53438e8	0.220125
$550$	3.15114e8	0.0807603
$551$	−1.96842e9	−0.501287
$552$	−1.36013e9	−0.344185
$553$	−2.62446e9	−0.659936
$554$	−1.22473e9	−0.306025
$555$	1.39659e9	0.346772
$556$	5.04599e8	0.124504
$557$	−6.01806e9	−1.47558	−0.737791	−	0.675030i	$-0.764131\pi$
$557$	−6.01806e9	−1.47558	−0.737791	+	0.675030i	$0.764131\pi$
$558$	−6.82730e8	−0.166353
$559$	1.73229e9	0.419449
$560$	−9.19623e8	−0.221285
$561$	3.80876e8	0.0910780
$562$	4.03170e9	0.958099
$563$	5.67516e8	0.134029	0.0670145	−	0.997752i	$-0.478653\pi$
$563$	5.67516e8	0.134029	0.0670145	+	0.997752i	$0.478653\pi$
$564$	−1.16034e9	−0.272338
$565$	3.41041e9	0.795495
$566$	−4.75706e9	−1.10276
$567$	−1.86060e9	−0.428659
$568$	5.46430e9	1.25117
$569$	7.83634e9	1.78328	0.891641	−	0.452742i	$-0.149554\pi$
$569$	7.83634e9	1.78328	0.891641	+	0.452742i	$0.149554\pi$
$570$	−2.61256e9	−0.590887
$571$	−1.26314e9	−0.283938	−0.141969	−	0.989871i	$-0.545343\pi$
$571$	−1.26314e9	−0.283938	−0.141969	+	0.989871i	$0.545343\pi$
$572$	−2.04032e8	−0.0455841
$573$	1.73917e9	0.386189
$574$	−1.87106e9	−0.412950
$575$	2.18514e8	0.0479338
$576$	8.05813e8	0.175694
$577$	4.57842e9	0.992203	0.496102	−	0.868265i	$-0.334764\pi$
$577$	4.57842e9	0.992203	0.496102	+	0.868265i	$0.334764\pi$
$578$	3.85391e9	0.830145
$579$	−8.73543e9	−1.87029
$580$	8.56430e8	0.182261
$581$	−1.68952e9	−0.357393
$582$	−2.59678e9	−0.546016
$583$	2.14119e8	0.0447522
$584$	−7.51643e9	−1.56159
$585$	1.96104e8	0.0404988
$586$	−1.87479e8	−0.0384868
$587$	2.22324e9	0.453683	0.226841	−	0.973932i	$-0.427160\pi$
$587$	2.22324e9	0.453683	0.226841	+	0.973932i	$0.427160\pi$
$588$	−2.13167e8	−0.0432414
$589$	4.31217e9	0.869545
$590$	−4.73189e8	−0.0948533
$591$	4.85730e9	0.967919
$592$	−1.13695e9	−0.225224
$593$	7.87244e9	1.55031	0.775154	−	0.631772i	$-0.217672\pi$
$593$	7.87244e9	1.55031	0.775154	+	0.631772i	$0.217672\pi$
$594$	2.29177e9	0.448662
$595$	2.57021e8	0.0500218
$596$	1.88787e9	0.365266
$597$	−4.15377e9	−0.798972
$598$	3.61861e8	0.0691971
$599$	−4.20449e9	−0.799318	−0.399659	−	0.916664i	$-0.630871\pi$
$599$	−4.20449e9	−0.799318	−0.399659	+	0.916664i	$0.630871\pi$
$600$	−1.00814e9	−0.190542
$601$	6.72387e9	1.26345	0.631726	−	0.775192i	$-0.282347\pi$
$601$	6.72387e9	1.26345	0.631726	+	0.775192i	$0.282347\pi$
$602$	−2.59434e9	−0.484662
$603$	1.45386e9	0.270029
$604$	−7.75094e8	−0.143128
$605$	−3.27970e9	−0.602129
$606$	−1.28629e9	−0.234793
$607$	−6.31449e9	−1.14598	−0.572991	−	0.819562i	$-0.694217\pi$
$607$	−6.31449e9	−1.14598	−0.572991	+	0.819562i	$0.694217\pi$
$608$	−2.13114e9	−0.384546
$609$	−1.60778e9	−0.288447
$610$	−5.99826e9	−1.06997
$611$	1.40696e9	0.249539
$612$	−3.67975e7	−0.00648915
$613$	9.32575e9	1.63520	0.817602	−	0.575784i	$-0.195303\pi$
$613$	9.32575e9	1.63520	0.817602	+	0.575784i	$0.195303\pi$
$614$	2.38893e9	0.416499
$615$	7.32342e9	1.26955
$616$	1.39265e9	0.240054
$617$	2.95846e9	0.507069	0.253535	−	0.967326i	$-0.418407\pi$
$617$	2.95846e9	0.507069	0.253535	+	0.967326i	$0.418407\pi$
$618$	1.63268e9	0.278254
$619$	1.96622e9	0.333207	0.166603	−	0.986024i	$-0.446720\pi$
$619$	1.96622e9	0.333207	0.166603	+	0.986024i	$0.446720\pi$
$620$	−1.87616e9	−0.316155
$621$	1.58922e9	0.266295
$622$	8.56702e8	0.142746
$623$	−1.81727e9	−0.301100
$624$	−1.15995e9	−0.191115
$625$	−4.94729e9	−0.810564
$626$	4.09805e9	0.667677
$627$	2.74888e9	0.445368
$628$	−1.07453e9	−0.173125
$629$	3.17759e8	0.0509121
$630$	−2.93693e8	−0.0467953
$631$	−2.82147e9	−0.447067	−0.223533	−	0.974696i	$-0.571759\pi$
$631$	−2.82147e9	−0.447067	−0.223533	+	0.974696i	$0.571759\pi$
$632$	−1.20359e10	−1.89657
$633$	−4.30904e8	−0.0675254
$634$	8.74884e9	1.36345
$635$	−1.38808e8	−0.0215133
$636$	−1.50304e8	−0.0231671
$637$	2.58475e8	0.0396214
$638$	2.30469e9	0.351350
$639$	1.21248e9	0.183833
$640$	−2.36484e9	−0.356592
$641$	1.43892e9	0.215792	0.107896	−	0.994162i	$-0.465589\pi$
$641$	1.43892e9	0.215792	0.107896	+	0.994162i	$0.465589\pi$
$642$	−5.44330e9	−0.811877
$643$	−1.19689e10	−1.77547	−0.887737	−	0.460350i	$-0.847724\pi$
$643$	−1.19689e10	−1.77547	−0.887737	+	0.460350i	$0.847724\pi$
$644$	2.11893e8	0.0312620
$645$	1.01543e10	1.49002
$646$	−5.94423e8	−0.0867524
$647$	−9.94077e9	−1.44296	−0.721481	−	0.692434i	$-0.756538\pi$
$647$	−9.94077e9	−1.44296	−0.721481	+	0.692434i	$0.756538\pi$
$648$	−8.53278e9	−1.23191
$649$	4.97878e8	0.0714935
$650$	2.68215e8	0.0383077
$651$	3.52213e9	0.500348
$652$	1.81543e9	0.256515
$653$	9.63667e9	1.35435	0.677175	−	0.735822i	$-0.263204\pi$
$653$	9.63667e9	1.35435	0.677175	+	0.735822i	$0.263204\pi$
$654$	6.17695e8	0.0863479
$655$	−6.54850e9	−0.910536
$656$	−5.96189e9	−0.824557
$657$	−1.66784e9	−0.229443
$658$	−2.10712e9	−0.288336
$659$	1.14767e10	1.56213	0.781065	−	0.624450i	$-0.214677\pi$
$659$	1.14767e10	1.56213	0.781065	+	0.624450i	$0.214677\pi$
$660$	−1.19600e9	−0.161930
$661$	−9.41385e9	−1.26783	−0.633917	−	0.773401i	$-0.718554\pi$
$661$	−9.41385e9	−1.26783	−0.633917	+	0.773401i	$0.718554\pi$
$662$	−4.15968e9	−0.557259
$663$	3.24189e8	0.0432017
$664$	−7.74819e9	−1.02710
$665$	1.85499e9	0.244605
$666$	−3.63098e8	−0.0476282
$667$	1.59817e9	0.208537
$668$	1.16173e8	0.0150796
$669$	−1.23956e10	−1.60058
$670$	−1.02182e10	−1.31254
$671$	6.31123e9	0.806464
$672$	−1.74069e9	−0.221273
$673$	−1.98375e9	−0.250861	−0.125431	−	0.992102i	$-0.540031\pi$
$673$	−1.98375e9	−0.250861	−0.125431	+	0.992102i	$0.540031\pi$
$674$	−9.87532e8	−0.124234
$675$	1.17794e9	0.147422
$676$	−1.73666e8	−0.0216222
$677$	4.99973e9	0.619279	0.309639	−	0.950854i	$-0.399792\pi$
$677$	4.99973e9	0.619279	0.309639	+	0.950854i	$0.399792\pi$
$678$	−6.44234e9	−0.793852
$679$	1.84378e9	0.226030
$680$	1.17871e9	0.143756
$681$	8.96724e9	1.08804
$682$	−5.04883e9	−0.609460
$683$	−1.02974e10	−1.23667	−0.618334	−	0.785916i	$-0.712192\pi$
$683$	−1.02974e10	−1.23667	−0.618334	+	0.785916i	$0.712192\pi$
$684$	−2.65577e8	−0.0317317
$685$	7.14428e9	0.849261
$686$	−3.87102e8	−0.0457815
$687$	−1.39151e10	−1.63733
$688$	−8.26651e9	−0.967749
$689$	1.82251e8	0.0212277
$690$	2.12116e9	0.245811
$691$	4.38076e9	0.505099	0.252550	−	0.967584i	$-0.418731\pi$
$691$	4.38076e9	0.505099	0.252550	+	0.967584i	$0.418731\pi$
$692$	2.94670e9	0.338037
$693$	3.09017e8	0.0352709
$694$	−2.83621e9	−0.322093
$695$	−3.58655e9	−0.405256
$696$	−7.37333e9	−0.828956
$697$	1.66626e9	0.186392
$698$	−5.06686e9	−0.563956
$699$	2.81438e9	0.311683
$700$	1.57057e8	0.0173067
$701$	−5.61326e9	−0.615463	−0.307732	−	0.951473i	$-0.599570\pi$
$701$	−5.61326e9	−0.615463	−0.307732	+	0.951473i	$0.599570\pi$
$702$	1.95068e9	0.212817
$703$	2.29335e9	0.248958
$704$	5.95904e9	0.643683
$705$	8.24736e9	0.886448
$706$	−2.27133e9	−0.242920
$707$	9.13298e8	0.0971952
$708$	−3.49494e8	−0.0370104
$709$	5.90549e9	0.622292	0.311146	−	0.950362i	$-0.399287\pi$
$709$	5.90549e9	0.622292	0.311146	+	0.950362i	$0.399287\pi$
$710$	−8.52175e9	−0.893562
$711$	−2.67066e9	−0.278661
$712$	−8.33406e9	−0.865320
$713$	−3.50108e9	−0.361734
$714$	−4.85518e8	−0.0499185
$715$	1.45020e9	0.148374
$716$	−3.26257e9	−0.332173
$717$	6.44929e9	0.653424
$718$	1.05178e10	1.06045
$719$	1.46168e9	0.146656	0.0733282	−	0.997308i	$-0.476638\pi$
$719$	1.46168e9	0.146656	0.0733282	+	0.997308i	$0.476638\pi$
$720$	−9.35813e8	−0.0934384
$721$	−1.15924e9	−0.115186
$722$	4.28458e9	0.423670
$723$	−3.24687e9	−0.319508
$724$	1.69253e9	0.165749
$725$	1.18458e9	0.115447
$726$	6.19541e9	0.600886
$727$	2.64041e9	0.254859	0.127430	−	0.991848i	$-0.459327\pi$
$727$	2.64041e9	0.254859	0.127430	+	0.991848i	$0.459327\pi$
$728$	1.18538e9	0.113867
$729$	8.30056e9	0.793526
$730$	1.17221e10	1.11526
$731$	2.31037e9	0.218761
$732$	−4.43027e9	−0.417486
$733$	−2.02561e10	−1.89973	−0.949865	−	0.312660i	$-0.898780\pi$
$733$	−2.02561e10	−1.89973	−0.949865	+	0.312660i	$0.898780\pi$
$734$	1.32680e10	1.23843
$735$	1.51513e9	0.140749
$736$	1.73029e9	0.159973
$737$	1.07514e10	0.989298
$738$	−1.90400e9	−0.174370
$739$	3.39005e9	0.308995	0.154497	−	0.987993i	$-0.450624\pi$
$739$	3.39005e9	0.308995	0.154497	+	0.987993i	$0.450624\pi$
$740$	−9.97805e8	−0.0905180
$741$	2.33976e9	0.211255
$742$	−2.72946e8	−0.0245280
$743$	1.06366e10	0.951351	0.475676	−	0.879621i	$-0.342204\pi$
$743$	1.06366e10	0.951351	0.475676	+	0.879621i	$0.342204\pi$
$744$	1.61526e10	1.43793
$745$	−1.34184e10	−1.18892
$746$	−3.71616e9	−0.327725
$747$	−1.71926e9	−0.150911
$748$	−2.72119e8	−0.0237741
$749$	3.86488e9	0.336086
$750$	1.12237e10	0.971454
$751$	2.13371e10	1.83821	0.919105	−	0.394012i	$-0.128913\pi$
$751$	2.13371e10	1.83821	0.919105	+	0.394012i	$0.128913\pi$
$752$	−6.71406e9	−0.575735
$753$	−3.46209e9	−0.295499
$754$	1.96167e9	0.166658
$755$	5.50914e9	0.465875
$756$	1.14225e9	0.0961471
$757$	−2.55448e9	−0.214026	−0.107013	−	0.994258i	$-0.534129\pi$
$757$	−2.55448e9	−0.214026	−0.107013	+	0.994258i	$0.534129\pi$
$758$	8.34370e9	0.695851
$759$	−2.23184e9	−0.185275
$760$	8.50703e9	0.702960
$761$	−2.93006e9	−0.241007	−0.120504	−	0.992713i	$-0.538451\pi$
$761$	−2.93006e9	−0.241007	−0.120504	+	0.992713i	$0.538451\pi$
$762$	2.62212e8	0.0214689
$763$	−4.38579e8	−0.0357447
$764$	−1.24256e9	−0.100807
$765$	2.61546e8	0.0211219
$766$	−1.38866e10	−1.11634
$767$	4.23778e8	0.0339121
$768$	−1.04144e10	−0.829599
$769$	−1.78443e9	−0.141500	−0.0707500	−	0.997494i	$-0.522539\pi$
$769$	−1.78443e9	−0.141500	−0.0707500	+	0.997494i	$0.522539\pi$
$770$	−2.17188e9	−0.171442
$771$	5.66442e9	0.445108
$772$	6.24109e9	0.488202
$773$	4.06390e9	0.316457	0.158229	−	0.987402i	$-0.449422\pi$
$773$	4.06390e9	0.316457	0.158229	+	0.987402i	$0.449422\pi$
$774$	−2.64001e9	−0.204650
$775$	−2.59503e9	−0.200257
$776$	8.45566e9	0.649578
$777$	1.87318e9	0.143254
$778$	−1.15674e10	−0.880661
$779$	1.20258e10	0.911451
$780$	−1.01800e9	−0.0768094
$781$	8.96639e9	0.673502
$782$	4.82617e8	0.0360893
$783$	8.61526e9	0.641361
$784$	−1.23345e9	−0.0914143
$785$	7.63743e9	0.563512
$786$	1.23702e10	0.908656
$787$	−1.31725e10	−0.963293	−0.481646	−	0.876366i	$-0.659961\pi$
$787$	−1.31725e10	−0.963293	−0.481646	+	0.876366i	$0.659961\pi$
$788$	−3.47033e9	−0.252656
$789$	5.48743e9	0.397740
$790$	1.87703e10	1.35449
$791$	4.57422e9	0.328624
$792$	1.41716e9	0.101364
$793$	5.37191e9	0.382536
$794$	2.28882e10	1.62271
$795$	1.06832e9	0.0754078
$796$	2.96769e9	0.208556
$797$	−6.91244e8	−0.0483646	−0.0241823	−	0.999708i	$-0.507698\pi$
$797$	−6.91244e8	−0.0483646	−0.0241823	+	0.999708i	$0.507698\pi$
$798$	−3.50410e9	−0.244100
$799$	1.87648e9	0.130146
$800$	1.28250e9	0.0885612
$801$	−1.84926e9	−0.127141
$802$	9.77193e9	0.668914
$803$	−1.23337e10	−0.840602
$804$	−7.54710e9	−0.512134
$805$	−1.50608e9	−0.101756
$806$	−4.29740e9	−0.289090
$807$	−3.41186e9	−0.228525
$808$	4.18842e9	0.279325
$809$	−1.23420e10	−0.819530	−0.409765	−	0.912191i	$-0.634389\pi$
$809$	−1.23420e10	−0.819530	−0.409765	+	0.912191i	$0.634389\pi$
$810$	1.33072e10	0.879807
$811$	−2.28996e9	−0.150749	−0.0753747	−	0.997155i	$-0.524015\pi$
$811$	−2.28996e9	−0.150749	−0.0753747	+	0.997155i	$0.524015\pi$
$812$	1.14869e9	0.0752933
$813$	2.89544e9	0.188972
$814$	−2.68513e9	−0.174494
$815$	−1.29035e10	−0.834944
$816$	−1.54704e9	−0.0996747
$817$	1.66745e10	1.06973
$818$	−1.02452e10	−0.654459
$819$	2.63025e8	0.0167303
$820$	−5.23227e9	−0.331392
$821$	−2.74582e10	−1.73169	−0.865847	−	0.500308i	$-0.833220\pi$
$821$	−2.74582e10	−1.73169	−0.865847	+	0.500308i	$0.833220\pi$
$822$	−1.34957e10	−0.847508
$823$	1.25243e9	0.0783165	0.0391582	−	0.999233i	$-0.487532\pi$
$823$	1.25243e9	0.0783165	0.0391582	+	0.999233i	$0.487532\pi$
$824$	−5.31633e9	−0.331029
$825$	−1.65426e9	−0.102569
$826$	−6.34665e8	−0.0391845
$827$	−1.18078e10	−0.725939	−0.362969	−	0.931801i	$-0.618237\pi$
$827$	−1.18078e10	−0.725939	−0.362969	+	0.931801i	$0.618237\pi$
$828$	2.15624e8	0.0132005
$829$	−2.13259e10	−1.30007	−0.650036	−	0.759904i	$-0.725246\pi$
$829$	−2.13259e10	−1.30007	−0.650036	+	0.759904i	$0.725246\pi$
$830$	1.20836e10	0.733536
$831$	6.42949e9	0.388663
$832$	5.07214e9	0.305323
$833$	3.44730e8	0.0206643
$834$	6.77506e9	0.404419
$835$	−8.25728e8	−0.0490833
$836$	−1.96396e9	−0.116254
$837$	−1.88733e10	−1.11252
$838$	9.44687e9	0.554541
$839$	2.79317e10	1.63279	0.816395	−	0.577494i	$-0.195969\pi$
$839$	2.79317e10	1.63279	0.816395	+	0.577494i	$0.195969\pi$
$840$	6.94845e9	0.404492
$841$	−8.58608e9	−0.497747
$842$	4.67869e8	0.0270105
$843$	−2.11652e10	−1.21682
$844$	3.07862e8	0.0176262
$845$	1.23437e9	0.0703794
$846$	−2.14422e9	−0.121751
$847$	−4.39890e9	−0.248744
$848$	−8.69704e8	−0.0489763
$849$	2.49732e10	1.40055
$850$	3.57720e8	0.0199791
$851$	−1.86199e9	−0.103568
$852$	−6.29411e9	−0.348655
$853$	2.71120e10	1.49569	0.747843	−	0.663876i	$-0.231090\pi$
$853$	2.71120e10	1.49569	0.747843	+	0.663876i	$0.231090\pi$
$854$	−8.04517e9	−0.442011
$855$	1.88764e9	0.103285
$856$	1.77245e10	0.965864
$857$	−1.89625e10	−1.02911	−0.514556	−	0.857457i	$-0.672043\pi$
$857$	−1.89625e10	−1.02911	−0.514556	+	0.857457i	$0.672043\pi$
$858$	−2.73946e9	−0.148068
$859$	5.82829e9	0.313736	0.156868	−	0.987620i	$-0.449860\pi$
$859$	5.82829e9	0.313736	0.156868	+	0.987620i	$0.449860\pi$
$860$	−7.25484e9	−0.388941
$861$	9.82255e9	0.524461
$862$	−1.66858e10	−0.887301
$863$	−3.20815e10	−1.69909	−0.849545	−	0.527516i	$-0.823124\pi$
$863$	−3.20815e10	−1.69909	−0.849545	+	0.527516i	$0.823124\pi$
$864$	9.32745e9	0.492000
$865$	−2.09443e10	−1.10030
$866$	−2.57818e10	−1.34896
$867$	−2.02319e10	−1.05431
$868$	−2.51641e9	−0.130606
$869$	−1.97497e10	−1.02092
$870$	1.14990e10	0.592026
$871$	9.15120e9	0.469261
$872$	−2.01134e9	−0.102725
$873$	1.87624e9	0.0954419
$874$	3.48317e9	0.176476
$875$	−7.96912e9	−0.402144
$876$	8.65788e9	0.435158
$877$	−1.24151e10	−0.621515	−0.310757	−	0.950489i	$-0.600583\pi$
$877$	−1.24151e10	−0.621515	−0.310757	+	0.950489i	$0.600583\pi$
$878$	3.38956e10	1.69010
$879$	9.84212e8	0.0488796
$880$	−6.92039e9	−0.342327
$881$	8.84588e9	0.435838	0.217919	−	0.975967i	$-0.430073\pi$
$881$	8.84588e9	0.435838	0.217919	+	0.975967i	$0.430073\pi$
$882$	−3.93916e8	−0.0193314
$883$	−2.84140e10	−1.38890	−0.694449	−	0.719542i	$-0.744352\pi$
$883$	−2.84140e10	−1.38890	−0.694449	+	0.719542i	$0.744352\pi$
$884$	−2.31619e8	−0.0112769
$885$	2.48410e9	0.120467
$886$	2.96154e10	1.43054
$887$	−8.27315e8	−0.0398051	−0.0199025	−	0.999802i	$-0.506336\pi$
$887$	−8.27315e8	−0.0398051	−0.0199025	+	0.999802i	$0.506336\pi$
$888$	8.59049e9	0.411692
$889$	−1.86177e8	−0.00888729
$890$	1.29972e10	0.617997
$891$	−1.40015e10	−0.663135
$892$	8.85612e9	0.417798
$893$	1.35430e10	0.636408
$894$	2.53477e10	1.18647
$895$	2.31894e10	1.08121
$896$	−3.17184e9	−0.147310
$897$	−1.89967e9	−0.0878828
$898$	−5.52147e9	−0.254441
$899$	−1.89796e10	−0.871221
$900$	1.59822e8	0.00730783
$901$	2.43069e8	0.0110712
$902$	−1.40802e10	−0.638832
$903$	1.36195e10	0.615538
$904$	2.09776e10	0.944420
$905$	−1.20300e10	−0.539506
$906$	−1.04069e10	−0.464913
$907$	−4.17403e10	−1.85751	−0.928753	−	0.370699i	$-0.879118\pi$
$907$	−4.17403e10	−1.85751	−0.928753	+	0.370699i	$0.879118\pi$
$908$	−6.40671e9	−0.284011
$909$	9.29377e8	0.0410410
$910$	−1.84863e9	−0.0813215
$911$	−3.21554e10	−1.40909	−0.704547	−	0.709657i	$-0.748850\pi$
$911$	−3.21554e10	−1.40909	−0.704547	+	0.709657i	$0.748850\pi$
$912$	−1.11654e10	−0.487405
$913$	−1.27140e10	−0.552886
$914$	−3.90583e9	−0.169201
$915$	3.14891e10	1.35890
$916$	9.94173e9	0.427394
$917$	−8.78318e9	−0.376148
$918$	2.60164e9	0.110994
$919$	3.25496e10	1.38338	0.691690	−	0.722195i	$-0.256867\pi$
$919$	3.25496e10	1.38338	0.691690	+	0.722195i	$0.256867\pi$
$920$	−6.90693e9	−0.292434
$921$	−1.25412e10	−0.528968
$922$	−1.97911e10	−0.831594
$923$	7.63190e9	0.319467
$924$	−1.60414e9	−0.0668943
$925$	−1.38012e9	−0.0573353
$926$	−1.78696e10	−0.739567
$927$	−1.17965e9	−0.0486379
$928$	9.38000e9	0.385288
$929$	2.95871e10	1.21073	0.605365	−	0.795948i	$-0.293027\pi$
$929$	2.95871e10	1.21073	0.605365	+	0.795948i	$0.293027\pi$
$930$	−2.51905e10	−1.02694
$931$	2.48800e9	0.101048
$932$	−2.01075e9	−0.0813586
$933$	−4.49744e9	−0.181292
$934$	3.76347e10	1.51138
$935$	1.93415e9	0.0773836
$936$	1.20624e9	0.0480806
$937$	1.81202e10	0.719573	0.359786	−	0.933035i	$-0.382850\pi$
$937$	1.81202e10	0.719573	0.359786	+	0.933035i	$0.382850\pi$
$938$	−1.37052e10	−0.542219
$939$	−2.15136e10	−0.847974
$940$	−5.89238e9	−0.231389
$941$	1.03402e10	0.404544	0.202272	−	0.979329i	$-0.435167\pi$
$941$	1.03402e10	0.404544	0.202272	+	0.979329i	$0.435167\pi$
$942$	−1.44273e10	−0.562349
$943$	−9.76386e9	−0.379167
$944$	−2.02227e9	−0.0782417
$945$	−8.11881e9	−0.312954
$946$	−1.95231e10	−0.749771
$947$	−3.10070e10	−1.18641	−0.593205	−	0.805051i	$-0.702138\pi$
$947$	−3.10070e10	−1.18641	−0.593205	+	0.805051i	$0.702138\pi$
$948$	1.38637e10	0.528504
$949$	−1.04981e10	−0.398729
$950$	2.58175e9	0.0976972
$951$	−4.59289e10	−1.73163
$952$	1.58094e9	0.0593864
$953$	−3.14767e10	−1.17805	−0.589026	−	0.808114i	$-0.700489\pi$
$953$	−3.14767e10	−1.17805	−0.589026	+	0.808114i	$0.700489\pi$
$954$	−2.77751e8	−0.0103571
$955$	8.83175e9	0.328122
$956$	−4.60774e9	−0.170563
$957$	−1.20989e10	−0.446227
$958$	−1.32695e10	−0.487615
$959$	9.58227e9	0.350835
$960$	2.97319e10	1.08461
$961$	1.40656e10	0.511244
$962$	−2.28550e9	−0.0827690
$963$	3.93292e9	0.141913
$964$	2.31975e9	0.0834011
$965$	−4.43599e10	−1.58908
$966$	2.84501e9	0.101546
$967$	1.15875e10	0.412094	0.206047	−	0.978542i	$-0.433940\pi$
$967$	1.15875e10	0.412094	0.206047	+	0.978542i	$0.433940\pi$
$968$	−2.01735e10	−0.714855
$969$	3.12055e9	0.110179
$970$	−1.31869e10	−0.463918
$971$	−2.13089e10	−0.746955	−0.373477	−	0.927639i	$-0.621835\pi$
$971$	−2.13089e10	−0.746955	−0.373477	+	0.927639i	$0.621835\pi$
$972$	2.54546e9	0.0889068
$973$	−4.81046e9	−0.167414
$974$	−2.62174e10	−0.909146
$975$	−1.40805e9	−0.0486521
$976$	−2.56348e10	−0.882585
$977$	−1.26958e10	−0.435541	−0.217770	−	0.976000i	$-0.569878\pi$
$977$	−1.26958e10	−0.435541	−0.217770	+	0.976000i	$0.569878\pi$
$978$	2.43751e10	0.833220
$979$	−1.36754e10	−0.465801
$980$	−1.08250e9	−0.0367396
$981$	−4.46300e8	−0.0150933
$982$	1.46024e10	0.492078
$983$	4.72623e10	1.58700	0.793500	−	0.608570i	$-0.208256\pi$
$983$	4.72623e10	1.58700	0.793500	+	0.608570i	$0.208256\pi$
$984$	4.50466e10	1.50723
$985$	2.46661e10	0.822383
$986$	2.61630e9	0.0869196
$987$	1.10618e10	0.366197
$988$	−1.67165e9	−0.0551439
$989$	−1.35382e10	−0.445013
$990$	−2.21011e9	−0.0723922
$991$	−1.40624e10	−0.458989	−0.229495	−	0.973310i	$-0.573707\pi$
$991$	−1.40624e10	−0.458989	−0.229495	+	0.973310i	$0.573707\pi$
$992$	−2.05486e10	−0.668330
$993$	2.18371e10	0.707739
$994$	−1.14298e10	−0.369136
$995$	−2.10935e10	−0.678839
$996$	8.92483e9	0.286215
$997$	2.64671e10	0.845809	0.422905	−	0.906174i	$-0.361010\pi$
$997$	2.64671e10	0.845809	0.422905	+	0.906174i	$0.361010\pi$
$998$	1.61896e10	0.515562
$999$	−1.00374e10	−0.318525

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.e.1.5	✓	12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.e.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-9.59274 q^{2} +50.3591 q^{3} -35.9794 q^{4} +255.731 q^{5} -483.082 q^{6} +343.000 q^{7} +1573.01 q^{8} +349.039 q^{9} +O(q^{10})\)	\(q-9.59274 q^{2} +50.3591 q^{3} -35.9794 q^{4} +255.731 q^{5} -483.082 q^{6} +343.000 q^{7} +1573.01 q^{8} +349.039 q^{9} -2453.16 q^{10} +2581.16 q^{11} -1811.89 q^{12} +2197.00 q^{13} -3290.31 q^{14} +12878.4 q^{15} -10484.1 q^{16} +2930.15 q^{17} -3348.23 q^{18} +21147.7 q^{19} -9201.06 q^{20} +17273.2 q^{21} -24760.4 q^{22} -17170.0 q^{23} +79215.4 q^{24} -12726.5 q^{25} -21075.2 q^{26} -92558.1 q^{27} -12340.9 q^{28} -93079.5 q^{29} -123539. q^{30} +203907. q^{31} -100774. q^{32} +129985. q^{33} -28108.2 q^{34} +87715.8 q^{35} -12558.2 q^{36} +108445. q^{37} -202864. q^{38} +110639. q^{39} +402268. q^{40} +568659. q^{41} -165697. q^{42} +788479. q^{43} -92868.6 q^{44} +89260.1 q^{45} +164707. q^{46} +640403. q^{47} -527971. q^{48} +117649. q^{49} +122082. q^{50} +147560. q^{51} -79046.8 q^{52} +82954.4 q^{53} +887885. q^{54} +660084. q^{55} +539543. q^{56} +1.06498e6 q^{57} +892887. q^{58} +192889. q^{59} -463357. q^{60} +2.44511e6 q^{61} -1.95603e6 q^{62} +119720. q^{63} +2.30867e6 q^{64} +561842. q^{65} -1.24691e6 q^{66} +4.16532e6 q^{67} -105425. q^{68} -864664. q^{69} -841435. q^{70} +3.47378e6 q^{71} +549042. q^{72} -4.77837e6 q^{73} -1.04028e6 q^{74} -640896. q^{75} -760881. q^{76} +885338. q^{77} -1.06133e6 q^{78} -7.65148e6 q^{79} -2.68112e6 q^{80} -5.42449e6 q^{81} -5.45500e6 q^{82} -4.92570e6 q^{83} -621478. q^{84} +749332. q^{85} -7.56367e6 q^{86} -4.68740e6 q^{87} +4.06020e6 q^{88} -5.29816e6 q^{89} -856248. q^{90} +753571. q^{91} +617765. q^{92} +1.02686e7 q^{93} -6.14322e6 q^{94} +5.40812e6 q^{95} -5.07489e6 q^{96} +5.37546e6 q^{97} -1.12858e6 q^{98} +900925. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{2} + 82 q^{3} + 986 q^{4} + 1026 q^{5} + 309 q^{6} + 4116 q^{7} + 228 q^{8} + 10902 q^{9}+O(q^{10}) \) 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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