LMFDB - Embedded newform 91.8.a.d.1.9

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:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} - 3 x^{9} - 816 x^{8} + 2298 x^{7} + 213848 x^{6} - 507132 x^{5} - 19919976 x^{4} + \cdots - 7335224320 $ x^10 - 3x^9 - 816x^8 + 2298x^7 + 213848x^6 - 507132x^5 - 19919976x^4 + 24331248x^3 + 727257184x^2 - 56397312*x - 7335224320
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-17.8475$ 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)

$f(q)$	$=$	$q+17.8475 q^{2} +86.1795 q^{3} +190.532 q^{4} +250.298 q^{5} +1538.09 q^{6} -343.000 q^{7} +1116.04 q^{8} +5239.91 q^{9} +O(q^{10})$	\(q+17.8475 q^{2} +86.1795 q^{3} +190.532 q^{4} +250.298 q^{5} +1538.09 q^{6} -343.000 q^{7} +1116.04 q^{8} +5239.91 q^{9} +4467.19 q^{10} -5176.37 q^{11} +16419.9 q^{12} -2197.00 q^{13} -6121.68 q^{14} +21570.6 q^{15} -4469.66 q^{16} -8030.92 q^{17} +93519.0 q^{18} +16609.4 q^{19} +47689.9 q^{20} -29559.6 q^{21} -92385.0 q^{22} -63805.6 q^{23} +96179.5 q^{24} -15475.7 q^{25} -39210.9 q^{26} +263098. q^{27} -65352.5 q^{28} +107898. q^{29} +384980. q^{30} +91905.6 q^{31} -222625. q^{32} -446097. q^{33} -143331. q^{34} -85852.4 q^{35} +998370. q^{36} -502967. q^{37} +296436. q^{38} -189336. q^{39} +279342. q^{40} +348954. q^{41} -527563. q^{42} -48566.9 q^{43} -986263. q^{44} +1.31154e6 q^{45} -1.13877e6 q^{46} +926682. q^{47} -385193. q^{48} +117649. q^{49} -276201. q^{50} -692100. q^{51} -418599. q^{52} -389.092 q^{53} +4.69563e6 q^{54} -1.29564e6 q^{55} -382801. q^{56} +1.43139e6 q^{57} +1.92570e6 q^{58} -1.83950e6 q^{59} +4.10989e6 q^{60} +3.05118e6 q^{61} +1.64028e6 q^{62} -1.79729e6 q^{63} -3.40117e6 q^{64} -549906. q^{65} -7.96170e6 q^{66} +3.48168e6 q^{67} -1.53015e6 q^{68} -5.49873e6 q^{69} -1.53225e6 q^{70} +3.91686e6 q^{71} +5.84793e6 q^{72} +3.53303e6 q^{73} -8.97669e6 q^{74} -1.33369e6 q^{75} +3.16462e6 q^{76} +1.77549e6 q^{77} -3.37917e6 q^{78} -5.94106e6 q^{79} -1.11875e6 q^{80} +1.12140e7 q^{81} +6.22794e6 q^{82} -4.09684e6 q^{83} -5.63204e6 q^{84} -2.01013e6 q^{85} -866796. q^{86} +9.29857e6 q^{87} -5.77702e6 q^{88} +1.22553e7 q^{89} +2.34077e7 q^{90} +753571. q^{91} -1.21570e7 q^{92} +7.92038e6 q^{93} +1.65389e7 q^{94} +4.15731e6 q^{95} -1.91857e7 q^{96} -1.55200e7 q^{97} +2.09974e6 q^{98} -2.71237e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q - 3 q^{2} - 101 q^{3} + 361 q^{4} + 226 q^{5} + 1105 q^{6} - 3430 q^{7} + 291 q^{8} + 12247 q^{9}+O(q^{10}) $ 10 * q - 3 * q^2 - 101 * q^3 + 361 * q^4 + 226 * q^5 + 1105 * q^6 - 3430 * q^7 + 291 * q^8 + 12247 * q^9	\( 10 q - 3 q^{2} - 101 q^{3} + 361 q^{4} + 226 q^{5} + 1105 q^{6} - 3430 q^{7} + 291 q^{8} + 12247 q^{9} + 2548 q^{10} + 451 q^{11} - 16241 q^{12} - 21970 q^{13} + 1029 q^{14} + 27184 q^{15} + 11897 q^{16} - 8654 q^{17} + 159348 q^{18} + 10130 q^{19} - 82012 q^{20} + 34643 q^{21} - 57863 q^{22} - 52155 q^{23} - 49227 q^{24} + 47190 q^{25} + 6591 q^{26} - 155171 q^{27} - 123823 q^{28} + 520154 q^{29} + 1070236 q^{30} + 692605 q^{31} + 149835 q^{32} + 436053 q^{33} + 1059060 q^{34} - 77518 q^{35} + 2843742 q^{36} - 20511 q^{37} + 1905286 q^{38} + 221897 q^{39} + 636320 q^{40} + 355049 q^{41} - 379015 q^{42} + 1256772 q^{43} - 687913 q^{44} + 1259926 q^{45} + 4043075 q^{46} + 1260721 q^{47} + 1128551 q^{48} + 1176490 q^{49} + 609035 q^{50} + 1411976 q^{51} - 793117 q^{52} + 928854 q^{53} + 6642607 q^{54} + 3423196 q^{55} - 99813 q^{56} + 3014966 q^{57} + 1612588 q^{58} + 3144446 q^{59} + 7738848 q^{60} + 6322923 q^{61} + 6545331 q^{62} - 4200721 q^{63} - 6629943 q^{64} - 496522 q^{65} - 14343317 q^{66} + 3944507 q^{67} - 1787356 q^{68} - 148281 q^{69} - 873964 q^{70} + 6032248 q^{71} + 9760866 q^{72} + 1248533 q^{73} - 8263279 q^{74} + 1573413 q^{75} + 1788254 q^{76} - 154693 q^{77} - 2427685 q^{78} - 14947605 q^{79} - 9147616 q^{80} + 25716334 q^{81} - 6987095 q^{82} - 14177784 q^{83} + 5570663 q^{84} - 11788444 q^{85} + 8748840 q^{86} - 29484448 q^{87} - 15390723 q^{88} + 6734836 q^{89} + 5994972 q^{90} + 7535710 q^{91} - 24493215 q^{92} + 17307847 q^{93} - 22760149 q^{94} - 9329708 q^{95} - 36488483 q^{96} - 12365397 q^{97} - 352947 q^{98} - 43198042 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 - 101 * q^3 + 361 * q^4 + 226 * q^5 + 1105 * q^6 - 3430 * q^7 + 291 * q^8 + 12247 * q^9 + 2548 * q^10 + 451 * q^11 - 16241 * q^12 - 21970 * q^13 + 1029 * q^14 + 27184 * q^15 + 11897 * q^16 - 8654 * q^17 + 159348 * q^18 + 10130 * q^19 - 82012 * q^20 + 34643 * q^21 - 57863 * q^22 - 52155 * q^23 - 49227 * q^24 + 47190 * q^25 + 6591 * q^26 - 155171 * q^27 - 123823 * q^28 + 520154 * q^29 + 1070236 * q^30 + 692605 * q^31 + 149835 * q^32 + 436053 * q^33 + 1059060 * q^34 - 77518 * q^35 + 2843742 * q^36 - 20511 * q^37 + 1905286 * q^38 + 221897 * q^39 + 636320 * q^40 + 355049 * q^41 - 379015 * q^42 + 1256772 * q^43 - 687913 * q^44 + 1259926 * q^45 + 4043075 * q^46 + 1260721 * q^47 + 1128551 * q^48 + 1176490 * q^49 + 609035 * q^50 + 1411976 * q^51 - 793117 * q^52 + 928854 * q^53 + 6642607 * q^54 + 3423196 * q^55 - 99813 * q^56 + 3014966 * q^57 + 1612588 * q^58 + 3144446 * q^59 + 7738848 * q^60 + 6322923 * q^61 + 6545331 * q^62 - 4200721 * q^63 - 6629943 * q^64 - 496522 * q^65 - 14343317 * q^66 + 3944507 * q^67 - 1787356 * q^68 - 148281 * q^69 - 873964 * q^70 + 6032248 * q^71 + 9760866 * q^72 + 1248533 * q^73 - 8263279 * q^74 + 1573413 * q^75 + 1788254 * q^76 - 154693 * q^77 - 2427685 * q^78 - 14947605 * q^79 - 9147616 * q^80 + 25716334 * q^81 - 6987095 * q^82 - 14177784 * q^83 + 5570663 * q^84 - 11788444 * q^85 + 8748840 * q^86 - 29484448 * q^87 - 15390723 * q^88 + 6734836 * q^89 + 5994972 * q^90 + 7535710 * q^91 - 24493215 * q^92 + 17307847 * q^93 - 22760149 * q^94 - 9329708 * q^95 - 36488483 * q^96 - 12365397 * q^97 - 352947 * q^98 - 43198042 * 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 $

$2$	17.8475	1.57751	0.788754	−	0.614709i	$-0.210727\pi$
$2$	17.8475	1.57751	0.788754	+	0.614709i	$0.210727\pi$
$3$	86.1795	1.84281	0.921403	−	0.388609i	$-0.127044\pi$
$3$	86.1795	1.84281	0.921403	+	0.388609i	$0.127044\pi$
$4$	190.532	1.48853
$5$	250.298	0.895495	0.447748	−	0.894160i	$-0.352226\pi$
$5$	250.298	0.895495	0.447748	+	0.894160i	$0.352226\pi$
$6$	1538.09	2.90704
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	1116.04	0.770661
$9$	5239.91	2.39593
$10$	4467.19	1.41265
$11$	−5176.37	−1.17260	−0.586301	−	0.810093i	$-0.699416\pi$
$11$	−5176.37	−1.17260	−0.586301	+	0.810093i	$0.699416\pi$
$12$	16419.9	2.74307
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	−6121.68	−0.596242
$15$	21570.6	1.65022
$16$	−4469.66	−0.272807
$17$	−8030.92	−0.396455	−0.198228	−	0.980156i	$-0.563518\pi$
$17$	−8030.92	−0.396455	−0.198228	+	0.980156i	$0.563518\pi$
$18$	93519.0	3.77960
$19$	16609.4	0.555542	0.277771	−	0.960647i	$-0.410404\pi$
$19$	16609.4	0.555542	0.277771	+	0.960647i	$0.410404\pi$
$20$	47689.9	1.33297
$21$	−29559.6	−0.696515
$22$	−92385.0	−1.84979
$23$	−63805.6	−1.09348	−0.546740	−	0.837302i	$-0.684132\pi$
$23$	−63805.6	−1.09348	−0.546740	+	0.837302i	$0.684132\pi$
$24$	96179.5	1.42018
$25$	−15475.7	−0.198089
$26$	−39210.9	−0.437522
$27$	263098.	2.57243
$28$	−65352.5	−0.562612
$29$	107898.	0.821522	0.410761	−	0.911743i	$-0.365263\pi$
$29$	107898.	0.821522	0.410761	+	0.911743i	$0.365263\pi$
$30$	384980.	2.60324
$31$	91905.6	0.554085	0.277042	−	0.960858i	$-0.410646\pi$
$31$	91905.6	0.554085	0.277042	+	0.960858i	$0.410646\pi$
$32$	−222625.	−1.20102
$33$	−446097.	−2.16088
$34$	−143331.	−0.625411
$35$	−85852.4	−0.338465
$36$	998370.	3.56642
$37$	−502967.	−1.63243	−0.816213	−	0.577751i	$-0.803930\pi$
$37$	−502967.	−1.63243	−0.816213	+	0.577751i	$0.803930\pi$
$38$	296436.	0.876371
$39$	−189336.	−0.511102
$40$	279342.	0.690123
$41$	348954.	0.790723	0.395361	−	0.918526i	$-0.370619\pi$
$41$	348954.	0.790723	0.395361	+	0.918526i	$0.370619\pi$
$42$	−527563.	−1.09876
$43$	−48566.9	−0.0931538	−0.0465769	−	0.998915i	$-0.514831\pi$
$43$	−48566.9	−0.0931538	−0.0465769	+	0.998915i	$0.514831\pi$
$44$	−986263.	−1.74545
$45$	1.31154e6	2.14555
$46$	−1.13877e6	−1.72497
$47$	926682.	1.30193	0.650966	−	0.759107i	$-0.274364\pi$
$47$	926682.	1.30193	0.650966	+	0.759107i	$0.274364\pi$
$48$	−385193.	−0.502730
$49$	117649.	0.142857
$50$	−276201.	−0.312486
$51$	−692100.	−0.730590
$52$	−418599.	−0.412844
$53$	−389.092	−0.000358994 0	−0.000179497	−	1.00000i	$-0.500057\pi$
$53$	−389.092	−0.000358994 0	−0.000179497		1.00000i	$0.500057\pi$
$54$	4.69563e6	4.05804
$55$	−1.29564e6	−1.05006
$56$	−382801.	−0.291283
$57$	1.43139e6	1.02376
$58$	1.92570e6	1.29596
$59$	−1.83950e6	−1.16605	−0.583025	−	0.812454i	$-0.698131\pi$
$59$	−1.83950e6	−1.16605	−0.583025	+	0.812454i	$0.698131\pi$
$60$	4.10989e6	2.45641
$61$	3.05118e6	1.72113	0.860564	−	0.509342i	$-0.170111\pi$
$61$	3.05118e6	1.72113	0.860564	+	0.509342i	$0.170111\pi$
$62$	1.64028e6	0.874073
$63$	−1.79729e6	−0.905578
$64$	−3.40117e6	−1.62181
$65$	−549906.	−0.248366
$66$	−7.96170e6	−3.40880
$67$	3.48168e6	1.41425	0.707127	−	0.707087i	$-0.249991\pi$
$67$	3.48168e6	1.41425	0.707127	+	0.707087i	$0.249991\pi$
$68$	−1.53015e6	−0.590136
$69$	−5.49873e6	−2.01507
$70$	−1.53225e6	−0.533932
$71$	3.91686e6	1.29878	0.649388	−	0.760458i	$-0.275025\pi$
$71$	3.91686e6	1.29878	0.649388	+	0.760458i	$0.275025\pi$
$72$	5.84793e6	1.84645
$73$	3.53303e6	1.06296	0.531480	−	0.847071i	$-0.321636\pi$
$73$	3.53303e6	1.06296	0.531480	+	0.847071i	$0.321636\pi$
$74$	−8.97669e6	−2.57516
$75$	−1.33369e6	−0.365039
$76$	3.16462e6	0.826941
$77$	1.77549e6	0.443202
$78$	−3.37917e6	−0.806268
$79$	−5.94106e6	−1.35572	−0.677859	−	0.735192i	$-0.737092\pi$
$79$	−5.94106e6	−1.35572	−0.677859	+	0.735192i	$0.737092\pi$
$80$	−1.11875e6	−0.244297
$81$	1.12140e7	2.34456
$82$	6.22794e6	1.24737
$83$	−4.09684e6	−0.786459	−0.393230	−	0.919440i	$-0.628642\pi$
$83$	−4.09684e6	−0.786459	−0.393230	+	0.919440i	$0.628642\pi$
$84$	−5.63204e6	−1.03678
$85$	−2.01013e6	−0.355024
$86$	−866796.	−0.146951
$87$	9.29857e6	1.51391
$88$	−5.77702e6	−0.903679
$89$	1.22553e7	1.84272	0.921358	−	0.388715i	$-0.127081\pi$
$89$	1.22553e7	1.84272	0.921358	+	0.388715i	$0.127081\pi$
$90$	2.34077e7	3.38462
$91$	753571.	0.104828
$92$	−1.21570e7	−1.62768
$93$	7.92038e6	1.02107
$94$	1.65389e7	2.05381
$95$	4.15731e6	0.497485
$96$	−1.91857e7	−2.21324
$97$	−1.55200e7	−1.72660	−0.863300	−	0.504692i	$-0.831606\pi$
$97$	−1.55200e7	−1.72660	−0.863300	+	0.504692i	$0.831606\pi$
$98$	2.09974e6	0.225358
$99$	−2.71237e7	−2.80948
$100$	−2.94861e6	−0.294861
$101$	−1.06445e6	−0.102802	−0.0514009	−	0.998678i	$-0.516369\pi$
$101$	−1.06445e6	−0.102802	−0.0514009	+	0.998678i	$0.516369\pi$
$102$	−1.23522e7	−1.15251
$103$	−1.71761e7	−1.54879	−0.774397	−	0.632700i	$-0.781947\pi$
$103$	−1.71761e7	−1.54879	−0.774397	+	0.632700i	$0.781947\pi$
$104$	−2.45193e6	−0.213743
$105$	−7.39872e6	−0.623726
$106$	−6944.31	−0.000566315 0
$107$	−1.56628e7	−1.23602	−0.618011	−	0.786169i	$-0.712061\pi$
$107$	−1.56628e7	−1.23602	−0.618011	+	0.786169i	$0.712061\pi$
$108$	5.01286e7	3.82915
$109$	1.07254e6	0.0793270	0.0396635	−	0.999213i	$-0.487371\pi$
$109$	1.07254e6	0.0793270	0.0396635	+	0.999213i	$0.487371\pi$
$110$	−2.31238e7	−1.65648
$111$	−4.33455e7	−3.00824
$112$	1.53310e6	0.103111
$113$	1.91764e6	0.125024	0.0625118	−	0.998044i	$-0.480089\pi$
$113$	1.91764e6	0.125024	0.0625118	+	0.998044i	$0.480089\pi$
$114$	2.55467e7	1.61498
$115$	−1.59704e7	−0.979207
$116$	2.05580e7	1.22286
$117$	−1.15121e7	−0.664512
$118$	−3.28303e7	−1.83945
$119$	2.75460e6	0.149846
$120$	2.40736e7	1.27176
$121$	7.30761e6	0.374996
$122$	5.44558e7	2.71509
$123$	3.00727e7	1.45715
$124$	1.75110e7	0.824772
$125$	−2.34281e7	−1.07288
$126$	−3.20770e7	−1.42856
$127$	−3.08723e6	−0.133738	−0.0668692	−	0.997762i	$-0.521301\pi$
$127$	−3.08723e6	−0.133738	−0.0668692	+	0.997762i	$0.521301\pi$
$128$	−3.22063e7	−1.35739
$129$	−4.18547e6	−0.171664
$130$	−9.81442e6	−0.391799
$131$	−2.58455e7	−1.00447	−0.502233	−	0.864732i	$-0.667488\pi$
$131$	−2.58455e7	−1.00447	−0.502233	+	0.864732i	$0.667488\pi$
$132$	−8.49957e7	−3.21653
$133$	−5.69703e6	−0.209975
$134$	6.21392e7	2.23100
$135$	6.58530e7	2.30360
$136$	−8.96280e6	−0.305533
$137$	−3.61979e7	−1.20271	−0.601356	−	0.798981i	$-0.705373\pi$
$137$	−3.61979e7	−1.20271	−0.601356	+	0.798981i	$0.705373\pi$
$138$	−9.81384e7	−3.17879
$139$	413394.	0.0130561	0.00652803	−	0.999979i	$-0.497922\pi$
$139$	413394.	0.0130561	0.00652803	+	0.999979i	$0.497922\pi$
$140$	−1.63576e7	−0.503816
$141$	7.98610e7	2.39921
$142$	6.99060e7	2.04883
$143$	1.13725e7	0.325221
$144$	−2.34206e7	−0.653627
$145$	2.70066e7	0.735669
$146$	6.30555e7	1.67683
$147$	1.01389e7	0.263258
$148$	−9.58313e7	−2.42992
$149$	5.82484e7	1.44255	0.721277	−	0.692647i	$-0.243556\pi$
$149$	5.82484e7	1.44255	0.721277	+	0.692647i	$0.243556\pi$
$150$	−2.38029e7	−0.575851
$151$	6.20444e7	1.46650	0.733252	−	0.679957i	$-0.238002\pi$
$151$	6.20444e7	1.46650	0.733252	+	0.679957i	$0.238002\pi$
$152$	1.85367e7	0.428134
$153$	−4.20813e7	−0.949880
$154$	3.16881e7	0.699155
$155$	2.30038e7	0.496180
$156$	−3.60746e7	−0.760792
$157$	4.86375e6	0.100305	0.0501525	−	0.998742i	$-0.484029\pi$
$157$	4.86375e6	0.100305	0.0501525	+	0.998742i	$0.484029\pi$
$158$	−1.06033e8	−2.13865
$159$	−33531.8	−0.000661556 0
$160$	−5.57227e7	−1.07550
$161$	2.18853e7	0.413297
$162$	2.00141e8	3.69857
$163$	6.95645e7	1.25815	0.629073	−	0.777347i	$-0.283435\pi$
$163$	6.95645e7	1.25815	0.629073	+	0.777347i	$0.283435\pi$
$164$	6.64868e7	1.17702
$165$	−1.11657e8	−1.93506
$166$	−7.31183e7	−1.24065
$167$	5.12412e7	0.851357	0.425678	−	0.904875i	$-0.360035\pi$
$167$	5.12412e7	0.851357	0.425678	+	0.904875i	$0.360035\pi$
$168$	−3.29896e7	−0.536777
$169$	4.82681e6	0.0769231
$170$	−3.58757e7	−0.560052
$171$	8.70318e7	1.33104
$172$	−9.25354e6	−0.138662
$173$	−5.16057e7	−0.757768	−0.378884	−	0.925444i	$-0.623692\pi$
$173$	−5.16057e7	−0.757768	−0.378884	+	0.925444i	$0.623692\pi$
$174$	1.65956e8	2.38820
$175$	5.30815e6	0.0748704
$176$	2.31366e7	0.319894
$177$	−1.58527e8	−2.14880
$178$	2.18726e8	2.90690
$179$	7.23175e7	0.942448	0.471224	−	0.882014i	$-0.343812\pi$
$179$	7.23175e7	0.942448	0.471224	+	0.882014i	$0.343812\pi$
$180$	2.49890e8	3.19371
$181$	1.37277e8	1.72077	0.860386	−	0.509643i	$-0.170222\pi$
$181$	1.37277e8	1.72077	0.860386	+	0.509643i	$0.170222\pi$
$182$	1.34493e7	0.165368
$183$	2.62949e8	3.17170
$184$	−7.12094e7	−0.842703
$185$	−1.25892e8	−1.46183
$186$	1.41359e8	1.61075
$187$	4.15710e7	0.464884
$188$	1.76563e8	1.93797
$189$	−9.02426e7	−0.972289
$190$	7.41974e7	0.784786
$191$	4.39865e6	0.0456775	0.0228387	−	0.999739i	$-0.492730\pi$
$191$	4.39865e6	0.0456775	0.0228387	+	0.999739i	$0.492730\pi$
$192$	−2.93111e8	−2.98867
$193$	1.59769e7	0.159972	0.0799859	−	0.996796i	$-0.474512\pi$
$193$	1.59769e7	0.159972	0.0799859	+	0.996796i	$0.474512\pi$
$194$	−2.76993e8	−2.72372
$195$	−4.73906e7	−0.457690
$196$	2.24159e7	0.212647
$197$	−1.79076e8	−1.66881	−0.834404	−	0.551153i	$-0.814188\pi$
$197$	−1.79076e8	−1.66881	−0.834404	+	0.551153i	$0.814188\pi$
$198$	−4.84089e8	−4.43197
$199$	−7.48196e7	−0.673022	−0.336511	−	0.941679i	$-0.609247\pi$
$199$	−7.48196e7	−0.673022	−0.336511	+	0.941679i	$0.609247\pi$
$200$	−1.72714e7	−0.152659
$201$	3.00050e8	2.60620
$202$	−1.89978e7	−0.162171
$203$	−3.70089e7	−0.310506
$204$	−1.31867e8	−1.08751
$205$	8.73426e7	0.708088
$206$	−3.06550e8	−2.44324
$207$	−3.34335e8	−2.61991
$208$	9.81985e6	0.0756630
$209$	−8.59764e7	−0.651429
$210$	−1.32048e8	−0.983932
$211$	2.37163e8	1.73804	0.869019	−	0.494779i	$-0.164751\pi$
$211$	2.37163e8	1.73804	0.869019	+	0.494779i	$0.164751\pi$
$212$	−74134.5	−0.000534373 0
$213$	3.37553e8	2.39339
$214$	−2.79541e8	−1.94984
$215$	−1.21562e7	−0.0834188
$216$	2.93627e8	1.98248
$217$	−3.15236e7	−0.209424
$218$	1.91421e7	0.125139
$219$	3.04474e8	1.95883
$220$	−2.46860e8	−1.56305
$221$	1.76439e7	0.109957
$222$	−7.73606e8	−4.74553
$223$	−2.28677e8	−1.38088	−0.690441	−	0.723389i	$-0.742583\pi$
$223$	−2.28677e8	−1.38088	−0.690441	+	0.723389i	$0.742583\pi$
$224$	7.63603e7	0.453941
$225$	−8.10910e7	−0.474607
$226$	3.42250e7	0.197226
$227$	−3.55649e7	−0.201805	−0.100902	−	0.994896i	$-0.532173\pi$
$227$	−3.55649e7	−0.201805	−0.100902	+	0.994896i	$0.532173\pi$
$228$	2.72726e8	1.52389
$229$	1.61232e8	0.887214	0.443607	−	0.896221i	$-0.353699\pi$
$229$	1.61232e8	0.887214	0.443607	+	0.896221i	$0.353699\pi$
$230$	−2.85032e8	−1.54471
$231$	1.53011e8	0.816735
$232$	1.20418e8	0.633115
$233$	−1.70301e8	−0.882004	−0.441002	−	0.897506i	$-0.645377\pi$
$233$	−1.70301e8	−0.882004	−0.441002	+	0.897506i	$0.645377\pi$
$234$	−2.05461e8	−1.04827
$235$	2.31947e8	1.16587
$236$	−3.50483e8	−1.73570
$237$	−5.11998e8	−2.49832
$238$	4.91627e7	0.236383
$239$	1.90845e7	0.0904248	0.0452124	−	0.998977i	$-0.485604\pi$
$239$	1.90845e7	0.0904248	0.0452124	+	0.998977i	$0.485604\pi$
$240$	−9.64133e7	−0.450192
$241$	3.22849e8	1.48573	0.742866	−	0.669441i	$-0.233466\pi$
$241$	3.22849e8	1.48573	0.742866	+	0.669441i	$0.233466\pi$
$242$	1.30422e8	0.591559
$243$	3.91020e8	1.74814
$244$	5.81347e8	2.56195
$245$	2.94474e7	0.127928
$246$	5.36721e8	2.29866
$247$	−3.64909e7	−0.154080
$248$	1.02570e8	0.427012
$249$	−3.53064e8	−1.44929
$250$	−4.18132e8	−1.69248
$251$	1.10171e8	0.439753	0.219876	−	0.975528i	$-0.429435\pi$
$251$	1.10171e8	0.439753	0.219876	+	0.975528i	$0.429435\pi$
$252$	−3.42441e8	−1.34798
$253$	3.30281e8	1.28222
$254$	−5.50992e7	−0.210973
$255$	−1.73232e8	−0.654239
$256$	−1.39451e8	−0.519495
$257$	−1.46214e8	−0.537308	−0.268654	−	0.963237i	$-0.586579\pi$
$257$	−1.46214e8	−0.537308	−0.268654	+	0.963237i	$0.586579\pi$
$258$	−7.47000e7	−0.270802
$259$	1.72518e8	0.616999
$260$	−1.04775e8	−0.369700
$261$	5.65374e8	1.96831
$262$	−4.61277e8	−1.58455
$263$	1.86697e8	0.632837	0.316418	−	0.948620i	$-0.397520\pi$
$263$	1.86697e8	0.632837	0.316418	+	0.948620i	$0.397520\pi$
$264$	−4.97860e8	−1.66531
$265$	−97389.1	−0.000321477 0
$266$	−1.01677e8	−0.331237
$267$	1.05615e9	3.39577
$268$	6.63372e8	2.10516
$269$	2.76965e8	0.867544	0.433772	−	0.901023i	$-0.357182\pi$
$269$	2.76965e8	0.867544	0.433772	+	0.901023i	$0.357182\pi$
$270$	1.17531e9	3.63395
$271$	−5.53602e8	−1.68968	−0.844842	−	0.535016i	$-0.820306\pi$
$271$	−5.53602e8	−1.68968	−0.844842	+	0.535016i	$0.820306\pi$
$272$	3.58955e7	0.108156
$273$	6.49424e7	0.193179
$274$	−6.46041e8	−1.89729
$275$	8.01077e7	0.232279
$276$	−1.04768e9	−2.99950
$277$	4.99311e8	1.41154	0.705768	−	0.708443i	$-0.250602\pi$
$277$	4.99311e8	1.41154	0.705768	+	0.708443i	$0.250602\pi$
$278$	7.37803e6	0.0205960
$279$	4.81577e8	1.32755
$280$	−9.58144e7	−0.260842
$281$	−1.49319e8	−0.401462	−0.200731	−	0.979646i	$-0.564332\pi$
$281$	−1.49319e8	−0.401462	−0.200731	+	0.979646i	$0.564332\pi$
$282$	1.42532e9	3.78477
$283$	−6.30428e8	−1.65342	−0.826709	−	0.562630i	$-0.809790\pi$
$283$	−6.30428e8	−1.65342	−0.826709	+	0.562630i	$0.809790\pi$
$284$	7.46287e8	1.93327
$285$	3.58275e8	0.916768
$286$	2.02970e8	0.513039
$287$	−1.19691e8	−0.298865
$288$	−1.16653e9	−2.87755
$289$	−3.45843e8	−0.842823
$290$	4.82000e8	1.16052
$291$	−1.33751e9	−3.18179
$292$	6.73154e8	1.58225
$293$	9.43671e7	0.219171	0.109586	−	0.993977i	$-0.465048\pi$
$293$	9.43671e7	0.219171	0.109586	+	0.993977i	$0.465048\pi$
$294$	1.80954e8	0.415292
$295$	−4.60423e8	−1.04419
$296$	−5.61330e8	−1.25805
$297$	−1.36189e9	−3.01644
$298$	1.03959e9	2.27564
$299$	1.40181e8	0.303277
$300$	−2.54110e8	−0.543371
$301$	1.66584e7	0.0352088
$302$	1.10734e9	2.31342
$303$	−9.17339e7	−0.189444
$304$	−7.42385e7	−0.151555
$305$	7.63705e8	1.54126
$306$	−7.51044e8	−1.49844
$307$	1.56059e8	0.307826	0.153913	−	0.988084i	$-0.450812\pi$
$307$	1.56059e8	0.307826	0.153913	+	0.988084i	$0.450812\pi$
$308$	3.38288e8	0.659720
$309$	−1.48023e9	−2.85413
$310$	4.10560e8	0.782728
$311$	4.78053e8	0.901187	0.450593	−	0.892729i	$-0.351212\pi$
$311$	4.78053e8	0.901187	0.450593	+	0.892729i	$0.351212\pi$
$312$	−2.11306e8	−0.393887
$313$	9.05504e7	0.166911	0.0834555	−	0.996512i	$-0.473404\pi$
$313$	9.05504e7	0.166911	0.0834555	+	0.996512i	$0.473404\pi$
$314$	8.68057e7	0.158232
$315$	−4.49858e8	−0.810940
$316$	−1.13196e9	−2.01803
$317$	−3.47900e8	−0.613405	−0.306702	−	0.951806i	$-0.599226\pi$
$317$	−3.47900e8	−0.613405	−0.306702	+	0.951806i	$0.599226\pi$
$318$	−598457.	−0.00104361
$319$	−5.58518e8	−0.963319
$320$	−8.51308e8	−1.45232
$321$	−1.34981e9	−2.27775
$322$	3.90597e8	0.651979
$323$	−1.33389e8	−0.220247
$324$	2.13662e9	3.48996
$325$	3.40000e7	0.0549399
$326$	1.24155e9	1.98473
$327$	9.24310e7	0.146184
$328$	3.89445e8	0.609379
$329$	−3.17852e8	−0.492084
$330$	−1.99280e9	−3.05257
$331$	6.86417e8	1.04038	0.520188	−	0.854052i	$-0.325862\pi$
$331$	6.86417e8	1.04038	0.520188	+	0.854052i	$0.325862\pi$
$332$	−7.80580e8	−1.17067
$333$	−2.63550e9	−3.91118
$334$	9.14525e8	1.34302
$335$	8.71460e8	1.26646
$336$	1.32121e8	0.190014
$337$	8.00934e8	1.13997	0.569983	−	0.821656i	$-0.306950\pi$
$337$	8.00934e8	1.13997	0.569983	+	0.821656i	$0.306950\pi$
$338$	8.61463e7	0.121347
$339$	1.65261e8	0.230394
$340$	−3.82993e8	−0.528463
$341$	−4.75737e8	−0.649721
$342$	1.55330e9	2.09973
$343$	−4.03536e7	−0.0539949
$344$	−5.42024e7	−0.0717900
$345$	−1.37632e9	−1.80449
$346$	−9.21031e8	−1.19539
$347$	−1.26286e9	−1.62257	−0.811283	−	0.584653i	$-0.801231\pi$
$347$	−1.26286e9	−1.62257	−0.811283	+	0.584653i	$0.801231\pi$
$348$	1.77168e9	2.25350
$349$	9.59489e8	1.20823	0.604117	−	0.796896i	$-0.293526\pi$
$349$	9.59489e8	1.20823	0.604117	+	0.796896i	$0.293526\pi$
$350$	9.47371e7	0.118109
$351$	−5.78026e8	−0.713465
$352$	1.15239e9	1.40831
$353$	8.70288e8	1.05306	0.526528	−	0.850158i	$-0.323494\pi$
$353$	8.70288e8	1.05306	0.526528	+	0.850158i	$0.323494\pi$
$354$	−2.82930e9	−3.38975
$355$	9.80384e8	1.16305
$356$	2.33502e9	2.74294
$357$	2.37390e8	0.276137
$358$	1.29068e9	1.48672
$359$	7.00712e8	0.799299	0.399649	−	0.916668i	$-0.369132\pi$
$359$	7.00712e8	0.799299	0.399649	+	0.916668i	$0.369132\pi$
$360$	1.46373e9	1.65349
$361$	−6.17999e8	−0.691373
$362$	2.45005e9	2.71453
$363$	6.29766e8	0.691045
$364$	1.43579e8	0.156040
$365$	8.84311e8	0.951875
$366$	4.69297e9	5.00339
$367$	1.87850e8	0.198372	0.0991862	−	0.995069i	$-0.468376\pi$
$367$	1.87850e8	0.198372	0.0991862	+	0.995069i	$0.468376\pi$
$368$	2.85190e8	0.298309
$369$	1.82848e9	1.89452
$370$	−2.24685e9	−2.30605
$371$	133459.	0.000135687 0
$372$	1.50909e9	1.51990
$373$	−8.89098e8	−0.887092	−0.443546	−	0.896252i	$-0.646280\pi$
$373$	−8.89098e8	−0.887092	−0.443546	+	0.896252i	$0.646280\pi$
$374$	7.41937e8	0.733358
$375$	−2.01902e9	−1.97711
$376$	1.03421e9	1.00335
$377$	−2.37051e8	−0.227849
$378$	−1.61060e9	−1.53379
$379$	5.26798e8	0.497057	0.248529	−	0.968625i	$-0.420053\pi$
$379$	5.26798e8	0.497057	0.248529	+	0.968625i	$0.420053\pi$
$380$	7.92100e8	0.740522
$381$	−2.66056e8	−0.246454
$382$	7.85047e7	0.0720566
$383$	2.98233e7	0.0271244	0.0135622	−	0.999908i	$-0.495683\pi$
$383$	2.98233e7	0.0271244	0.0135622	+	0.999908i	$0.495683\pi$
$384$	−2.77552e9	−2.50141
$385$	4.44404e8	0.396885
$386$	2.85148e8	0.252357
$387$	−2.54486e8	−0.223190
$388$	−2.95706e9	−2.57010
$389$	6.10791e8	0.526101	0.263050	−	0.964782i	$-0.415271\pi$
$389$	6.10791e8	0.526101	0.263050	+	0.964782i	$0.415271\pi$
$390$	−8.45802e8	−0.722009
$391$	5.12417e8	0.433516
$392$	1.31301e8	0.110094
$393$	−2.22735e9	−1.85104
$394$	−3.19606e9	−2.63256
$395$	−1.48704e9	−1.21404
$396$	−5.16793e9	−4.18199
$397$	−6.43478e8	−0.516139	−0.258070	−	0.966126i	$-0.583086\pi$
$397$	−6.43478e8	−0.516139	−0.258070	+	0.966126i	$0.583086\pi$
$398$	−1.33534e9	−1.06170
$399$	−4.90967e8	−0.386943
$400$	6.91710e7	0.0540399
$401$	2.95105e8	0.228545	0.114272	−	0.993449i	$-0.463546\pi$
$401$	2.95105e8	0.228545	0.114272	+	0.993449i	$0.463546\pi$
$402$	5.35513e9	4.11129
$403$	−2.01917e8	−0.153675
$404$	−2.02812e8	−0.153024
$405$	2.80684e9	2.09955
$406$	−6.60515e8	−0.489826
$407$	2.60354e9	1.91419
$408$	−7.72410e8	−0.563037
$409$	−1.87486e9	−1.35499	−0.677496	−	0.735527i	$-0.736935\pi$
$409$	−1.87486e9	−1.35499	−0.677496	+	0.735527i	$0.736935\pi$
$410$	1.55884e9	1.11701
$411$	−3.11952e9	−2.21637
$412$	−3.27259e9	−2.30543
$413$	6.30947e8	0.440725
$414$	−5.96704e9	−4.13292
$415$	−1.02543e9	−0.704270
$416$	4.89107e8	0.333102
$417$	3.56261e7	0.0240598
$418$	−1.53446e9	−1.02763
$419$	−1.27027e9	−0.843620	−0.421810	−	0.906684i	$-0.638605\pi$
$419$	−1.27027e9	−0.843620	−0.421810	+	0.906684i	$0.638605\pi$
$420$	−1.40969e9	−0.928435
$421$	−1.90958e9	−1.24724	−0.623622	−	0.781726i	$-0.714340\pi$
$421$	−1.90958e9	−1.24724	−0.623622	+	0.781726i	$0.714340\pi$
$422$	4.23277e9	2.74177
$423$	4.85573e9	3.11934
$424$	−434241.	−0.000276663 0
$425$	1.24284e8	0.0785332
$426$	6.02447e9	3.77559
$427$	−1.04655e9	−0.650525
$428$	−2.98427e9	−1.83986
$429$	9.80075e8	0.599320
$430$	−2.16958e8	−0.131594
$431$	−8.14828e8	−0.490225	−0.245112	−	0.969495i	$-0.578825\pi$
$431$	−8.14828e8	−0.490225	−0.245112	+	0.969495i	$0.578825\pi$
$432$	−1.17596e9	−0.701777
$433$	−6.26784e8	−0.371031	−0.185516	−	0.982641i	$-0.559396\pi$
$433$	−6.26784e8	−0.371031	−0.185516	+	0.982641i	$0.559396\pi$
$434$	−5.62617e8	−0.330369
$435$	2.32742e9	1.35570
$436$	2.04353e8	0.118081
$437$	−1.05977e9	−0.607474
$438$	5.43410e9	3.09007
$439$	1.29938e9	0.733010	0.366505	−	0.930416i	$-0.380554\pi$
$439$	1.29938e9	0.733010	0.366505	+	0.930416i	$0.380554\pi$
$440$	−1.44598e9	−0.809240
$441$	6.16470e8	0.342276
$442$	3.14899e8	0.173458
$443$	−1.61363e9	−0.881844	−0.440922	−	0.897545i	$-0.645348\pi$
$443$	−1.61363e9	−0.881844	−0.440922	+	0.897545i	$0.645348\pi$
$444$	−8.25869e9	−4.47786
$445$	3.06748e9	1.65014
$446$	−4.08131e9	−2.17835
$447$	5.01982e9	2.65835
$448$	1.16660e9	0.612985
$449$	2.26557e9	1.18118	0.590588	−	0.806973i	$-0.298896\pi$
$449$	2.26557e9	1.18118	0.590588	+	0.806973i	$0.298896\pi$
$450$	−1.44727e9	−0.748696
$451$	−1.80631e9	−0.927203
$452$	3.65371e8	0.186102
$453$	5.34696e9	2.70248
$454$	−6.34743e8	−0.318348
$455$	1.88618e8	0.0938734
$456$	1.59748e9	0.788969
$457$	−1.44887e9	−0.710107	−0.355053	−	0.934846i	$-0.615537\pi$
$457$	−1.44887e9	−0.710107	−0.355053	+	0.934846i	$0.615537\pi$
$458$	2.87759e9	1.39959
$459$	−2.11292e9	−1.01985
$460$	−3.04288e9	−1.45758
$461$	2.76153e9	1.31279	0.656396	−	0.754417i	$-0.272080\pi$
$461$	2.76153e9	1.31279	0.656396	+	0.754417i	$0.272080\pi$
$462$	2.73086e9	1.28841
$463$	−4.17025e9	−1.95267	−0.976334	−	0.216267i	$-0.930612\pi$
$463$	−4.17025e9	−1.95267	−0.976334	+	0.216267i	$0.930612\pi$
$464$	−4.82267e8	−0.224117
$465$	1.98246e9	0.914364
$466$	−3.03943e9	−1.39137
$467$	−1.41332e9	−0.642145	−0.321072	−	0.947055i	$-0.604043\pi$
$467$	−1.41332e9	−0.642145	−0.321072	+	0.947055i	$0.604043\pi$
$468$	−2.19342e9	−0.989147
$469$	−1.19422e9	−0.534538
$470$	4.13967e9	1.83917
$471$	4.19156e8	0.184843
$472$	−2.05295e9	−0.898629
$473$	2.51400e8	0.109232
$474$	−9.13786e9	−3.94112
$475$	−2.57042e8	−0.110046
$476$	5.24840e8	0.223050
$477$	−2.03881e6	−0.000860125 0
$478$	3.40609e8	0.142646
$479$	3.36082e9	1.39724	0.698619	−	0.715494i	$-0.253798\pi$
$479$	3.36082e9	1.39724	0.698619	+	0.715494i	$0.253798\pi$
$480$	−4.80215e9	−1.98194
$481$	1.10502e9	0.452754
$482$	5.76204e9	2.34375
$483$	1.88607e9	0.761626
$484$	1.39233e9	0.558193
$485$	−3.88464e9	−1.54616
$486$	6.97871e9	2.75771
$487$	−1.03246e9	−0.405062	−0.202531	−	0.979276i	$-0.564917\pi$
$487$	−1.03246e9	−0.405062	−0.202531	+	0.979276i	$0.564917\pi$
$488$	3.40523e9	1.32641
$489$	5.99503e9	2.31852
$490$	5.25561e8	0.201807
$491$	1.23519e9	0.470920	0.235460	−	0.971884i	$-0.424340\pi$
$491$	1.23519e9	0.470920	0.235460	+	0.971884i	$0.424340\pi$
$492$	5.72980e9	2.16901
$493$	−8.66518e8	−0.325697
$494$	−6.51270e8	−0.243062
$495$	−6.78902e9	−2.51587
$496$	−4.10787e8	−0.151158
$497$	−1.34348e9	−0.490891
$498$	−6.30130e9	−2.28627
$499$	−3.03025e9	−1.09176	−0.545879	−	0.837864i	$-0.683804\pi$
$499$	−3.03025e9	−1.09176	−0.545879	+	0.837864i	$0.683804\pi$
$500$	−4.46380e9	−1.59702
$501$	4.41594e9	1.56889
$502$	1.96627e9	0.693713
$503$	1.02690e9	0.359784	0.179892	−	0.983686i	$-0.442425\pi$
$503$	1.02690e9	0.359784	0.179892	+	0.983686i	$0.442425\pi$
$504$	−2.00584e9	−0.697894
$505$	−2.66431e8	−0.0920586
$506$	5.89468e9	2.02271
$507$	4.15972e8	0.141754
$508$	−5.88216e8	−0.199074
$509$	−2.69975e9	−0.907425	−0.453713	−	0.891148i	$-0.649901\pi$
$509$	−2.69975e9	−0.907425	−0.453713	+	0.891148i	$0.649901\pi$
$510$	−3.09175e9	−1.03207
$511$	−1.21183e9	−0.401761
$512$	1.63356e9	0.537887
$513$	4.36990e9	1.42909
$514$	−2.60955e9	−0.847607
$515$	−4.29915e9	−1.38694
$516$	−7.97466e8	−0.255528
$517$	−4.79685e9	−1.52665
$518$	3.07900e9	0.973321
$519$	−4.44736e9	−1.39642
$520$	−6.13715e8	−0.191406
$521$	−4.12116e9	−1.27670	−0.638348	−	0.769748i	$-0.720382\pi$
$521$	−4.12116e9	−1.27670	−0.638348	+	0.769748i	$0.720382\pi$
$522$	1.00905e10	3.10503
$523$	−2.25266e9	−0.688557	−0.344278	−	0.938868i	$-0.611876\pi$
$523$	−2.25266e9	−0.688557	−0.344278	+	0.938868i	$0.611876\pi$
$524$	−4.92439e9	−1.49518
$525$	4.57454e8	0.137972
$526$	3.33206e9	0.998305
$527$	−7.38087e8	−0.219670
$528$	1.99390e9	0.589502
$529$	6.66325e8	0.195700
$530$	−1.73815e6	−0.000507133 0
$531$	−9.63879e9	−2.79378
$532$	−1.08547e9	−0.312554
$533$	−7.66651e8	−0.219307
$534$	1.88497e10	5.35685
$535$	−3.92038e9	−1.10685
$536$	3.88569e9	1.08991
$537$	6.23228e9	1.73675
$538$	4.94312e9	1.36856
$539$	−6.08994e8	−0.167515
$540$	1.25471e10	3.42898
$541$	2.44684e8	0.0664378	0.0332189	−	0.999448i	$-0.489424\pi$
$541$	2.44684e8	0.0664378	0.0332189	+	0.999448i	$0.489424\pi$
$542$	−9.88040e9	−2.66549
$543$	1.18305e10	3.17105
$544$	1.78788e9	0.476149
$545$	2.68455e8	0.0710369
$546$	1.15906e9	0.304741
$547$	1.15683e9	0.302213	0.151106	−	0.988518i	$-0.451716\pi$
$547$	1.15683e9	0.302213	0.151106	+	0.988518i	$0.451716\pi$
$548$	−6.89686e9	−1.79027
$549$	1.59879e10	4.12371
$550$	1.42972e9	0.366422
$551$	1.79212e9	0.456390
$552$	−6.13679e9	−1.55294
$553$	2.03778e9	0.512413
$554$	8.91144e9	2.22671
$555$	−1.08493e10	−2.69387
$556$	7.87648e7	0.0194344
$557$	6.92337e9	1.69756	0.848779	−	0.528748i	$-0.177338\pi$
$557$	6.92337e9	1.69756	0.848779	+	0.528748i	$0.177338\pi$
$558$	8.59493e9	2.09422
$559$	1.06701e8	0.0258362
$560$	3.83731e8	0.0923356
$561$	3.58257e9	0.856691
$562$	−2.66497e9	−0.633309
$563$	−3.81299e9	−0.900506	−0.450253	−	0.892901i	$-0.648666\pi$
$563$	−3.81299e9	−0.900506	−0.450253	+	0.892901i	$0.648666\pi$
$564$	1.52161e10	3.57129
$565$	4.79982e8	0.111958
$566$	−1.12515e10	−2.60828
$567$	−3.84639e9	−0.886162
$568$	4.37136e9	1.00092
$569$	−3.81583e9	−0.868354	−0.434177	−	0.900828i	$-0.642961\pi$
$569$	−3.81583e9	−0.868354	−0.434177	+	0.900828i	$0.642961\pi$
$570$	6.39430e9	1.44621
$571$	−5.54361e9	−1.24614	−0.623069	−	0.782166i	$-0.714115\pi$
$571$	−5.54361e9	−1.24614	−0.623069	+	0.782166i	$0.714115\pi$
$572$	2.16682e9	0.484102
$573$	3.79073e8	0.0841748
$574$	−2.13618e9	−0.471462
$575$	9.87434e8	0.216606
$576$	−1.78218e10	−3.88574
$577$	−2.02890e9	−0.439689	−0.219844	−	0.975535i	$-0.570555\pi$
$577$	−2.02890e9	−0.439689	−0.219844	+	0.975535i	$0.570555\pi$
$578$	−6.17242e9	−1.32956
$579$	1.37689e9	0.294797
$580$	5.14563e9	1.09507
$581$	1.40522e9	0.297254
$582$	−2.38711e10	−5.01929
$583$	2.01408e6	0.000420957 0
$584$	3.94299e9	0.819182
$585$	−2.88145e9	−0.595068
$586$	1.68421e9	0.345745
$587$	−1.20993e9	−0.246904	−0.123452	−	0.992351i	$-0.539397\pi$
$587$	−1.20993e9	−0.246904	−0.123452	+	0.992351i	$0.539397\pi$
$588$	1.93179e9	0.391868
$589$	1.52650e9	0.307817
$590$	−8.21739e9	−1.64722
$591$	−1.54327e10	−3.07529
$592$	2.24809e9	0.445337
$593$	3.71492e9	0.731574	0.365787	−	0.930699i	$-0.380800\pi$
$593$	3.71492e9	0.731574	0.365787	+	0.930699i	$0.380800\pi$
$594$	−2.43063e10	−4.75846
$595$	6.89473e8	0.134186
$596$	1.10982e10	2.14729
$597$	−6.44791e9	−1.24025
$598$	2.50187e9	0.478422
$599$	−2.65398e9	−0.504549	−0.252275	−	0.967656i	$-0.581179\pi$
$599$	−2.65398e9	−0.504549	−0.252275	+	0.967656i	$0.581179\pi$
$600$	−1.48844e9	−0.281321
$601$	4.32991e9	0.813614	0.406807	−	0.913514i	$-0.366642\pi$
$601$	4.32991e9	0.813614	0.406807	+	0.913514i	$0.366642\pi$
$602$	2.97311e8	0.0555422
$603$	1.82437e10	3.38846
$604$	1.18214e10	2.18294
$605$	1.82908e9	0.335807
$606$	−1.63722e9	−0.298849
$607$	1.19040e9	0.216039	0.108020	−	0.994149i	$-0.465549\pi$
$607$	1.19040e9	0.216039	0.108020	+	0.994149i	$0.465549\pi$
$608$	−3.69767e9	−0.667214
$609$	−3.18941e9	−0.572203
$610$	1.36302e10	2.43135
$611$	−2.03592e9	−0.361091
$612$	−8.01782e9	−1.41393
$613$	−2.60995e9	−0.457636	−0.228818	−	0.973469i	$-0.573486\pi$
$613$	−2.60995e9	−0.457636	−0.228818	+	0.973469i	$0.573486\pi$
$614$	2.78526e9	0.485597
$615$	7.52714e9	1.30487
$616$	1.98152e9	0.341559
$617$	1.04591e10	1.79266	0.896330	−	0.443387i	$-0.146223\pi$
$617$	1.04591e10	1.79266	0.896330	+	0.443387i	$0.146223\pi$
$618$	−2.64183e10	−4.50241
$619$	−6.89429e9	−1.16835	−0.584174	−	0.811628i	$-0.698581\pi$
$619$	−6.89429e9	−1.16835	−0.584174	+	0.811628i	$0.698581\pi$
$620$	4.38297e9	0.738580
$621$	−1.67871e10	−2.81291
$622$	8.53204e9	1.42163
$623$	−4.20356e9	−0.696481
$624$	8.46270e8	0.139432
$625$	−4.65498e9	−0.762672
$626$	1.61609e9	0.263303
$627$	−7.40941e9	−1.20046
$628$	9.26701e8	0.149307
$629$	4.03929e9	0.647184
$630$	−8.02883e9	−1.27926
$631$	−1.83912e9	−0.291412	−0.145706	−	0.989328i	$-0.546545\pi$
$631$	−1.83912e9	−0.291412	−0.145706	+	0.989328i	$0.546545\pi$
$632$	−6.63044e9	−1.04480
$633$	2.04386e10	3.20287
$634$	−6.20913e9	−0.967650
$635$	−7.72729e8	−0.119762
$636$	−6.38887e6	−0.000984746 0
$637$	−2.58475e8	−0.0396214
$638$	−9.96814e9	−1.51964
$639$	2.05240e10	3.11178
$640$	−8.06119e9	−1.21554
$641$	−2.61571e9	−0.392271	−0.196136	−	0.980577i	$-0.562839\pi$
$641$	−2.61571e9	−0.392271	−0.196136	+	0.980577i	$0.562839\pi$
$642$	−2.40907e10	−3.59317
$643$	5.37438e9	0.797241	0.398620	−	0.917116i	$-0.369489\pi$
$643$	5.37438e9	0.797241	0.398620	+	0.917116i	$0.369489\pi$
$644$	4.16985e9	0.615205
$645$	−1.04762e9	−0.153725
$646$	−2.38065e9	−0.347442
$647$	−1.40336e9	−0.203706	−0.101853	−	0.994799i	$-0.532477\pi$
$647$	−1.40336e9	−0.203706	−0.101853	+	0.994799i	$0.532477\pi$
$648$	1.25152e10	1.80686
$649$	9.52191e9	1.36731
$650$	6.06814e8	0.0866681
$651$	−2.71669e9	−0.385928
$652$	1.32543e10	1.87279
$653$	4.59220e9	0.645394	0.322697	−	0.946502i	$-0.395411\pi$
$653$	4.59220e9	0.645394	0.322697	+	0.946502i	$0.395411\pi$
$654$	1.64966e9	0.230607
$655$	−6.46909e9	−0.899495
$656$	−1.55971e9	−0.215714
$657$	1.85127e10	2.54678
$658$	−5.67285e9	−0.776266
$659$	1.28499e10	1.74904	0.874522	−	0.484987i	$-0.161176\pi$
$659$	1.28499e10	1.74904	0.874522	+	0.484987i	$0.161176\pi$
$660$	−2.12743e10	−2.88039
$661$	1.24324e8	0.0167436	0.00837179	−	0.999965i	$-0.497335\pi$
$661$	1.24324e8	0.0167436	0.00837179	+	0.999965i	$0.497335\pi$
$662$	1.22508e10	1.64120
$663$	1.52054e9	0.202629
$664$	−4.57223e9	−0.606094
$665$	−1.42596e9	−0.188032
$666$	−4.70370e10	−6.16992
$667$	−6.88448e9	−0.898319
$668$	9.76309e9	1.26727
$669$	−1.97073e10	−2.54470
$670$	1.55533e10	1.99785
$671$	−1.57940e10	−2.01820
$672$	6.58070e9	0.836526
$673$	4.47671e9	0.566117	0.283058	−	0.959103i	$-0.408651\pi$
$673$	4.47671e9	0.566117	0.283058	+	0.959103i	$0.408651\pi$
$674$	1.42946e10	1.79831
$675$	−4.07162e9	−0.509570
$676$	9.19661e8	0.114502
$677$	−1.41564e10	−1.75344	−0.876721	−	0.481000i	$-0.840274\pi$
$677$	−1.41564e10	−1.75344	−0.876721	+	0.481000i	$0.840274\pi$
$678$	2.94949e9	0.363449
$679$	5.32337e9	0.652593
$680$	−2.24337e9	−0.273603
$681$	−3.06496e9	−0.371887
$682$	−8.49071e9	−1.02494
$683$	8.74476e9	1.05021	0.525104	−	0.851038i	$-0.324026\pi$
$683$	8.74476e9	1.05021	0.525104	+	0.851038i	$0.324026\pi$
$684$	1.65823e10	1.98130
$685$	−9.06029e9	−1.07702
$686$	−7.20210e8	−0.0851774
$687$	1.38949e10	1.63496
$688$	2.17078e8	0.0254130
$689$	854835.	9.95669e−5 0
$690$	−2.45639e10	−2.84659
$691$	−1.24605e10	−1.43668	−0.718342	−	0.695690i	$-0.755099\pi$
$691$	−1.24605e10	−1.43668	−0.718342	+	0.695690i	$0.755099\pi$
$692$	−9.83254e9	−1.12796
$693$	9.30342e9	1.06188
$694$	−2.25389e10	−2.55961
$695$	1.03472e8	0.0116916
$696$	1.03775e10	1.16671
$697$	−2.80242e9	−0.313486
$698$	1.71244e10	1.90600
$699$	−1.46764e10	−1.62536
$700$	1.01137e9	0.111447
$701$	2.71944e9	0.298172	0.149086	−	0.988824i	$-0.452367\pi$
$701$	2.71944e9	0.298172	0.149086	+	0.988824i	$0.452367\pi$
$702$	−1.03163e10	−1.12550
$703$	−8.35399e9	−0.906881
$704$	1.76057e10	1.90173
$705$	1.99891e10	2.14848
$706$	1.55324e10	1.66120
$707$	3.65107e8	0.0388555
$708$	−3.02044e10	−3.19856
$709$	7.78563e9	0.820412	0.410206	−	0.911993i	$-0.365457\pi$
$709$	7.78563e9	0.820412	0.410206	+	0.911993i	$0.365457\pi$
$710$	1.74974e10	1.83472
$711$	−3.11306e10	−3.24821
$712$	1.36773e10	1.42011
$713$	−5.86409e9	−0.605881
$714$	4.23682e9	0.435608
$715$	2.84651e9	0.291234
$716$	1.37788e10	1.40286
$717$	1.64469e9	0.166635
$718$	1.25059e10	1.26090
$719$	3.25146e9	0.326233	0.163116	−	0.986607i	$-0.447845\pi$
$719$	3.25146e9	0.326233	0.163116	+	0.986607i	$0.447845\pi$
$720$	−5.86215e9	−0.585319
$721$	5.89140e9	0.585389
$722$	−1.10297e10	−1.09065
$723$	2.78230e10	2.73791
$724$	2.61557e10	2.56142
$725$	−1.66979e9	−0.162734
$726$	1.12397e10	1.09013
$727$	1.44076e10	1.39066	0.695329	−	0.718691i	$-0.255258\pi$
$727$	1.44076e10	1.39066	0.695329	+	0.718691i	$0.255258\pi$
$728$	8.41013e8	0.0807873
$729$	9.17291e9	0.876922
$730$	1.57827e10	1.50159
$731$	3.90037e8	0.0369313
$732$	5.01002e10	4.72118
$733$	−4.80128e9	−0.450291	−0.225146	−	0.974325i	$-0.572286\pi$
$733$	−4.80128e9	−0.450291	−0.225146	+	0.974325i	$0.572286\pi$
$734$	3.35265e9	0.312934
$735$	2.53776e9	0.235746
$736$	1.42047e10	1.31329
$737$	−1.80225e10	−1.65836
$738$	3.26338e10	2.98862
$739$	−1.31930e10	−1.20251	−0.601256	−	0.799056i	$-0.705333\pi$
$739$	−1.31930e10	−1.20251	−0.601256	+	0.799056i	$0.705333\pi$
$740$	−2.39864e10	−2.17598
$741$	−3.14477e9	−0.283939
$742$	2.38190e6	0.000214047 0
$743$	4.29855e9	0.384469	0.192234	−	0.981349i	$-0.438427\pi$
$743$	4.29855e9	0.384469	0.192234	+	0.981349i	$0.438427\pi$
$744$	8.83944e9	0.786900
$745$	1.45795e10	1.29180
$746$	−1.58681e10	−1.39939
$747$	−2.14671e10	−1.88430
$748$	7.92060e9	0.691994
$749$	5.37234e9	0.467173
$750$	−3.60344e10	−3.11891
$751$	−1.73238e10	−1.49247	−0.746233	−	0.665685i	$-0.768140\pi$
$751$	−1.73238e10	−1.49247	−0.746233	+	0.665685i	$0.768140\pi$
$752$	−4.14196e9	−0.355176
$753$	9.49446e9	0.810379
$754$	−4.23077e9	−0.359434
$755$	1.55296e10	1.31325
$756$	−1.71941e10	−1.44728
$757$	−1.32297e10	−1.10845	−0.554223	−	0.832368i	$-0.686985\pi$
$757$	−1.32297e10	−1.10845	−0.554223	+	0.832368i	$0.686985\pi$
$758$	9.40200e9	0.784112
$759$	2.84635e10	2.36288
$760$	4.63971e9	0.383392
$761$	−1.03170e9	−0.0848609	−0.0424304	−	0.999099i	$-0.513510\pi$
$761$	−1.03170e9	−0.0848609	−0.0424304	+	0.999099i	$0.513510\pi$
$762$	−4.74842e9	−0.388783
$763$	−3.67881e8	−0.0299828
$764$	8.38083e8	0.0679924
$765$	−1.05329e10	−0.850613
$766$	5.32270e8	0.0427889
$767$	4.04137e9	0.323404
$768$	−1.20178e10	−0.957329
$769$	−9.67541e9	−0.767233	−0.383617	−	0.923492i	$-0.625322\pi$
$769$	−9.67541e9	−0.767233	−0.383617	+	0.923492i	$0.625322\pi$
$770$	7.93148e9	0.626090
$771$	−1.26007e10	−0.990154
$772$	3.04412e9	0.238123
$773$	1.04562e10	0.814231	0.407115	−	0.913377i	$-0.366535\pi$
$773$	1.04562e10	0.814231	0.407115	+	0.913377i	$0.366535\pi$
$774$	−4.54193e9	−0.352084
$775$	−1.42230e9	−0.109758
$776$	−1.73209e10	−1.33062
$777$	1.48675e10	1.13701
$778$	1.09011e10	0.829928
$779$	5.79591e9	0.439279
$780$	−9.02942e9	−0.681285
$781$	−2.02751e10	−1.52295
$782$	9.14535e9	0.683875
$783$	2.83877e10	2.11331
$784$	−5.25852e8	−0.0389724
$785$	1.21739e9	0.0898227
$786$	−3.97526e10	−2.92003
$787$	1.11154e9	0.0812859	0.0406429	−	0.999174i	$-0.487059\pi$
$787$	1.11154e9	0.0812859	0.0406429	+	0.999174i	$0.487059\pi$
$788$	−3.41198e10	−2.48407
$789$	1.60894e10	1.16620
$790$	−2.65399e10	−1.91515
$791$	−6.57750e8	−0.0472545
$792$	−3.02710e10	−2.16516
$793$	−6.70344e9	−0.477355
$794$	−1.14844e10	−0.814214
$795$	−8.39295e6	−0.000592420 0
$796$	−1.42555e10	−1.00181
$797$	−2.33597e10	−1.63442	−0.817209	−	0.576341i	$-0.804480\pi$
$797$	−2.33597e10	−1.63442	−0.817209	+	0.576341i	$0.804480\pi$
$798$	−8.76252e9	−0.610406
$799$	−7.44211e9	−0.516157
$800$	3.44527e9	0.237907
$801$	6.42165e10	4.41502
$802$	5.26687e9	0.360531
$803$	−1.82882e10	−1.24643
$804$	5.71691e10	3.87940
$805$	5.47786e9	0.370105
$806$	−3.60370e9	−0.242424
$807$	2.38687e10	1.59872
$808$	−1.18797e9	−0.0792254
$809$	−1.36642e9	−0.0907329	−0.0453664	−	0.998970i	$-0.514446\pi$
$809$	−1.36642e9	−0.0907329	−0.0453664	+	0.998970i	$0.514446\pi$
$810$	5.00950e10	3.31205
$811$	−5.50245e9	−0.362229	−0.181114	−	0.983462i	$-0.557970\pi$
$811$	−5.50245e9	−0.362229	−0.181114	+	0.983462i	$0.557970\pi$
$812$	−7.05138e9	−0.462198
$813$	−4.77092e10	−3.11376
$814$	4.64666e10	3.01964
$815$	1.74119e10	1.12666
$816$	3.09346e9	0.199310
$817$	−8.06667e8	−0.0517508
$818$	−3.34614e10	−2.13751
$819$	3.94864e9	0.251162
$820$	1.66416e10	1.05401
$821$	1.85474e10	1.16972	0.584861	−	0.811134i	$-0.301149\pi$
$821$	1.85474e10	1.16972	0.584861	+	0.811134i	$0.301149\pi$
$822$	−5.56755e10	−3.49633
$823$	−8.31517e9	−0.519962	−0.259981	−	0.965614i	$-0.583716\pi$
$823$	−8.31517e9	−0.519962	−0.259981	+	0.965614i	$0.583716\pi$
$824$	−1.91691e10	−1.19360
$825$	6.90364e9	0.428045
$826$	1.12608e10	0.695247
$827$	−1.82500e10	−1.12200	−0.561000	−	0.827815i	$-0.689583\pi$
$827$	−1.82500e10	−1.12200	−0.561000	+	0.827815i	$0.689583\pi$
$828$	−6.37015e10	−3.89981
$829$	−2.98697e8	−0.0182092	−0.00910458	−	0.999959i	$-0.502898\pi$
$829$	−2.98697e8	−0.0182092	−0.00910458	+	0.999959i	$0.502898\pi$
$830$	−1.83014e10	−1.11099
$831$	4.30304e10	2.60119
$832$	7.47238e9	0.449808
$833$	−9.44829e8	−0.0566364
$834$	6.35835e8	0.0379545
$835$	1.28256e10	0.762386
$836$	−1.63813e10	−0.969673
$837$	2.41802e10	1.42535
$838$	−2.26711e10	−1.33082
$839$	−1.50288e10	−0.878530	−0.439265	−	0.898358i	$-0.644761\pi$
$839$	−1.50288e10	−0.878530	−0.439265	+	0.898358i	$0.644761\pi$
$840$	−8.25724e9	−0.480681
$841$	−5.60795e9	−0.325101
$842$	−3.40812e10	−1.96754
$843$	−1.28683e10	−0.739816
$844$	4.51872e10	2.58712
$845$	1.20814e9	0.0688842
$846$	8.66624e10	4.92079
$847$	−2.50651e9	−0.141735
$848$	1.73911e6	9.79359e−5 0
$849$	−5.43299e10	−3.04693
$850$	2.21815e9	0.123887
$851$	3.20921e10	1.78503
$852$	6.43147e10	3.56264
$853$	1.16836e10	0.644546	0.322273	−	0.946647i	$-0.395553\pi$
$853$	1.16836e10	0.644546	0.322273	+	0.946647i	$0.395553\pi$
$854$	−1.86783e10	−1.02621
$855$	2.17839e10	1.19194
$856$	−1.74803e10	−0.952555
$857$	−2.05782e10	−1.11680	−0.558400	−	0.829572i	$-0.688585\pi$
$857$	−2.05782e10	−1.11680	−0.558400	+	0.829572i	$0.688585\pi$
$858$	1.74918e10	0.945432
$859$	1.76894e10	0.952220	0.476110	−	0.879386i	$-0.342046\pi$
$859$	1.76894e10	0.952220	0.476110	+	0.879386i	$0.342046\pi$
$860$	−2.31615e9	−0.124171
$861$	−1.03149e10	−0.550750
$862$	−1.45426e10	−0.773334
$863$	−2.17789e9	−0.115345	−0.0576725	−	0.998336i	$-0.518368\pi$
$863$	−2.17789e9	−0.115345	−0.0576725	+	0.998336i	$0.518368\pi$
$864$	−5.85722e10	−3.08953
$865$	−1.29168e10	−0.678578
$866$	−1.11865e10	−0.585305
$867$	−2.98046e10	−1.55316
$868$	−6.00626e9	−0.311735
$869$	3.07531e10	1.58972
$870$	4.15385e10	2.13862
$871$	−7.64926e9	−0.392243
$872$	1.19699e9	0.0611342
$873$	−8.13235e10	−4.13682
$874$	−1.89143e10	−0.958295
$875$	8.03584e9	0.405511
$876$	5.80121e10	2.91578
$877$	3.17315e10	1.58852	0.794259	−	0.607579i	$-0.207859\pi$
$877$	3.17315e10	1.58852	0.794259	+	0.607579i	$0.207859\pi$
$878$	2.31906e10	1.15633
$879$	8.13251e9	0.403890
$880$	5.79106e9	0.286463
$881$	−2.65044e10	−1.30588	−0.652939	−	0.757410i	$-0.726464\pi$
$881$	−2.65044e10	−1.30588	−0.652939	+	0.757410i	$0.726464\pi$
$882$	1.10024e10	0.539943
$883$	−3.18551e10	−1.55710	−0.778550	−	0.627582i	$-0.784045\pi$
$883$	−3.18551e10	−1.55710	−0.778550	+	0.627582i	$0.784045\pi$
$884$	3.36173e9	0.163674
$885$	−3.96790e10	−1.92424
$886$	−2.87993e10	−1.39112
$887$	9.90979e8	0.0476795	0.0238398	−	0.999716i	$-0.492411\pi$
$887$	9.90979e8	0.0476795	0.0238398	+	0.999716i	$0.492411\pi$
$888$	−4.83751e10	−2.31834
$889$	1.05892e9	0.0505483
$890$	5.47467e10	2.60311
$891$	−5.80477e10	−2.74924
$892$	−4.35704e10	−2.05548
$893$	1.53916e10	0.723277
$894$	8.95910e10	4.19356
$895$	1.81009e10	0.843958
$896$	1.10468e10	0.513047
$897$	1.20807e10	0.558881
$898$	4.04346e10	1.86332
$899$	9.91641e9	0.455193
$900$	−1.54504e10	−0.706467
$901$	3.12477e6	0.000142325 0
$902$	−3.22381e10	−1.46267
$903$	1.43562e9	0.0648830
$904$	2.14016e9	0.0963509
$905$	3.43603e10	1.54094
$906$	9.54296e10	4.26319
$907$	−1.19006e10	−0.529593	−0.264796	−	0.964304i	$-0.585305\pi$
$907$	−1.19006e10	−0.529593	−0.264796	+	0.964304i	$0.585305\pi$
$908$	−6.77625e9	−0.300392
$909$	−5.57763e9	−0.246306
$910$	3.36635e9	0.148086
$911$	−5.35201e9	−0.234532	−0.117266	−	0.993101i	$-0.537413\pi$
$911$	−5.35201e9	−0.234532	−0.117266	+	0.993101i	$0.537413\pi$
$912$	−6.39784e9	−0.279287
$913$	2.12068e10	0.922204
$914$	−2.58587e10	−1.12020
$915$	6.58157e10	2.84025
$916$	3.07199e10	1.32064
$917$	8.86501e9	0.379653
$918$	−3.77102e10	−1.60883
$919$	3.18929e10	1.35547	0.677735	−	0.735307i	$-0.262962\pi$
$919$	3.18929e10	1.35547	0.677735	+	0.735307i	$0.262962\pi$
$920$	−1.78236e10	−0.754637
$921$	1.34491e10	0.567263
$922$	4.92862e10	2.07094
$923$	−8.60534e9	−0.360215
$924$	2.91535e10	1.21574
$925$	7.78375e9	0.323365
$926$	−7.44284e10	−3.08035
$927$	−9.00011e10	−3.71081
$928$	−2.40207e10	−0.986661
$929$	9.49324e9	0.388472	0.194236	−	0.980955i	$-0.437777\pi$
$929$	9.49324e9	0.388472	0.194236	+	0.980955i	$0.437777\pi$
$930$	3.53819e10	1.44242
$931$	1.95408e9	0.0793631
$932$	−3.24477e10	−1.31289
$933$	4.11984e10	1.66071
$934$	−2.52243e10	−1.01299
$935$	1.04052e10	0.416301
$936$	−1.28479e10	−0.512114
$937$	−8.84609e9	−0.351288	−0.175644	−	0.984454i	$-0.556201\pi$
$937$	−8.84609e9	−0.351288	−0.175644	+	0.984454i	$0.556201\pi$
$938$	−2.13137e10	−0.843237
$939$	7.80358e9	0.307585
$940$	4.41933e10	1.73544
$941$	−1.73569e10	−0.679062	−0.339531	−	0.940595i	$-0.610268\pi$
$941$	−1.73569e10	−0.679062	−0.339531	+	0.940595i	$0.610268\pi$
$942$	7.48087e9	0.291591
$943$	−2.22652e10	−0.864640
$944$	8.22193e9	0.318106
$945$	−2.25876e10	−0.870680
$946$	4.48685e9	0.172315
$947$	−1.74945e10	−0.669386	−0.334693	−	0.942327i	$-0.608633\pi$
$947$	−1.74945e10	−0.669386	−0.334693	+	0.942327i	$0.608633\pi$
$948$	−9.75519e10	−3.71883
$949$	−7.76206e9	−0.294812
$950$	−4.58754e9	−0.173599
$951$	−2.99818e10	−1.13039
$952$	3.07424e9	0.115480
$953$	2.60303e10	0.974213	0.487107	−	0.873342i	$-0.338052\pi$
$953$	2.60303e10	0.974213	0.487107	+	0.873342i	$0.338052\pi$
$954$	−3.63875e7	−0.00135685
$955$	1.10097e9	0.0409040
$956$	3.63620e9	0.134600
$957$	−4.81328e10	−1.77521
$958$	5.99820e10	2.20415
$959$	1.24159e10	0.454582
$960$	−7.33653e10	−2.67634
$961$	−1.90660e10	−0.692990
$962$	1.97218e10	0.714222
$963$	−8.20716e10	−2.96143
$964$	6.15131e10	2.21156
$965$	3.99901e9	0.143254
$966$	3.36615e10	1.20147
$967$	4.72415e10	1.68008	0.840042	−	0.542521i	$-0.182530\pi$
$967$	4.72415e10	1.68008	0.840042	+	0.542521i	$0.182530\pi$
$968$	8.15556e9	0.288995
$969$	−1.14954e10	−0.405873
$970$	−6.93310e10	−2.43908
$971$	−8.84569e9	−0.310073	−0.155037	−	0.987909i	$-0.549550\pi$
$971$	−8.84569e9	−0.310073	−0.155037	+	0.987909i	$0.549550\pi$
$972$	7.45017e10	2.60216
$973$	−1.41794e8	−0.00493473
$974$	−1.84268e10	−0.638989
$975$	2.93011e9	0.101244
$976$	−1.36377e10	−0.469535
$977$	2.67493e10	0.917658	0.458829	−	0.888525i	$-0.348269\pi$
$977$	2.67493e10	0.917658	0.458829	+	0.888525i	$0.348269\pi$
$978$	1.06996e11	3.65748
$979$	−6.34379e10	−2.16077
$980$	5.61066e9	0.190425
$981$	5.62001e9	0.190062
$982$	2.20449e10	0.742880
$983$	2.34413e10	0.787125	0.393562	−	0.919298i	$-0.371243\pi$
$983$	2.34413e10	0.787125	0.393562	+	0.919298i	$0.371243\pi$
$984$	3.35622e10	1.12297
$985$	−4.48226e10	−1.49441
$986$	−1.54651e10	−0.513789
$987$	−2.73923e10	−0.906815
$988$	−6.95268e9	−0.229352
$989$	3.09884e9	0.101862
$990$	−1.21167e11	−3.96881
$991$	−1.35669e10	−0.442816	−0.221408	−	0.975181i	$-0.571065\pi$
$991$	−1.35669e10	−0.442816	−0.221408	+	0.975181i	$0.571065\pi$
$992$	−2.04605e10	−0.665465
$993$	5.91551e10	1.91721
$994$	−2.39778e10	−0.774384
$995$	−1.87272e10	−0.602688
$996$	−6.72700e10	−2.15732
$997$	4.93893e10	1.57834	0.789169	−	0.614176i	$-0.210512\pi$
$997$	4.93893e10	1.57834	0.789169	+	0.614176i	$0.210512\pi$
$998$	−5.40822e10	−1.72226
$999$	−1.32330e11	−4.19931

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.d.1.9	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.8.a.d.1.9	✓	10	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)

\(f(q)\)	\(=\)	\(q+17.8475 q^{2} +86.1795 q^{3} +190.532 q^{4} +250.298 q^{5} +1538.09 q^{6} -343.000 q^{7} +1116.04 q^{8} +5239.91 q^{9} +O(q^{10})\)	\(q+17.8475 q^{2} +86.1795 q^{3} +190.532 q^{4} +250.298 q^{5} +1538.09 q^{6} -343.000 q^{7} +1116.04 q^{8} +5239.91 q^{9} +4467.19 q^{10} -5176.37 q^{11} +16419.9 q^{12} -2197.00 q^{13} -6121.68 q^{14} +21570.6 q^{15} -4469.66 q^{16} -8030.92 q^{17} +93519.0 q^{18} +16609.4 q^{19} +47689.9 q^{20} -29559.6 q^{21} -92385.0 q^{22} -63805.6 q^{23} +96179.5 q^{24} -15475.7 q^{25} -39210.9 q^{26} +263098. q^{27} -65352.5 q^{28} +107898. q^{29} +384980. q^{30} +91905.6 q^{31} -222625. q^{32} -446097. q^{33} -143331. q^{34} -85852.4 q^{35} +998370. q^{36} -502967. q^{37} +296436. q^{38} -189336. q^{39} +279342. q^{40} +348954. q^{41} -527563. q^{42} -48566.9 q^{43} -986263. q^{44} +1.31154e6 q^{45} -1.13877e6 q^{46} +926682. q^{47} -385193. q^{48} +117649. q^{49} -276201. q^{50} -692100. q^{51} -418599. q^{52} -389.092 q^{53} +4.69563e6 q^{54} -1.29564e6 q^{55} -382801. q^{56} +1.43139e6 q^{57} +1.92570e6 q^{58} -1.83950e6 q^{59} +4.10989e6 q^{60} +3.05118e6 q^{61} +1.64028e6 q^{62} -1.79729e6 q^{63} -3.40117e6 q^{64} -549906. q^{65} -7.96170e6 q^{66} +3.48168e6 q^{67} -1.53015e6 q^{68} -5.49873e6 q^{69} -1.53225e6 q^{70} +3.91686e6 q^{71} +5.84793e6 q^{72} +3.53303e6 q^{73} -8.97669e6 q^{74} -1.33369e6 q^{75} +3.16462e6 q^{76} +1.77549e6 q^{77} -3.37917e6 q^{78} -5.94106e6 q^{79} -1.11875e6 q^{80} +1.12140e7 q^{81} +6.22794e6 q^{82} -4.09684e6 q^{83} -5.63204e6 q^{84} -2.01013e6 q^{85} -866796. q^{86} +9.29857e6 q^{87} -5.77702e6 q^{88} +1.22553e7 q^{89} +2.34077e7 q^{90} +753571. q^{91} -1.21570e7 q^{92} +7.92038e6 q^{93} +1.65389e7 q^{94} +4.15731e6 q^{95} -1.91857e7 q^{96} -1.55200e7 q^{97} +2.09974e6 q^{98} -2.71237e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} - 101 q^{3} + 361 q^{4} + 226 q^{5} + 1105 q^{6} - 3430 q^{7} + 291 q^{8} + 12247 q^{9}+O(q^{10}) \) 10 * q - 3 * q^2 - 101 * q^3 + 361 * q^4 + 226 * q^5 + 1105 * q^6 - 3430 * q^7 + 291 * q^8 + 12247 * q^9	\( 10 q - 3 q^{2} - 101 q^{3} + 361 q^{4} + 226 q^{5} + 1105 q^{6} - 3430 q^{7} + 291 q^{8} + 12247 q^{9} + 2548 q^{10} + 451 q^{11} - 16241 q^{12} - 21970 q^{13} + 1029 q^{14} + 27184 q^{15} + 11897 q^{16} - 8654 q^{17} + 159348 q^{18} + 10130 q^{19} - 82012 q^{20} + 34643 q^{21} - 57863 q^{22} - 52155 q^{23} - 49227 q^{24} + 47190 q^{25} + 6591 q^{26} - 155171 q^{27} - 123823 q^{28} + 520154 q^{29} + 1070236 q^{30} + 692605 q^{31} + 149835 q^{32} + 436053 q^{33} + 1059060 q^{34} - 77518 q^{35} + 2843742 q^{36} - 20511 q^{37} + 1905286 q^{38} + 221897 q^{39} + 636320 q^{40} + 355049 q^{41} - 379015 q^{42} + 1256772 q^{43} - 687913 q^{44} + 1259926 q^{45} + 4043075 q^{46} + 1260721 q^{47} + 1128551 q^{48} + 1176490 q^{49} + 609035 q^{50} + 1411976 q^{51} - 793117 q^{52} + 928854 q^{53} + 6642607 q^{54} + 3423196 q^{55} - 99813 q^{56} + 3014966 q^{57} + 1612588 q^{58} + 3144446 q^{59} + 7738848 q^{60} + 6322923 q^{61} + 6545331 q^{62} - 4200721 q^{63} - 6629943 q^{64} - 496522 q^{65} - 14343317 q^{66} + 3944507 q^{67} - 1787356 q^{68} - 148281 q^{69} - 873964 q^{70} + 6032248 q^{71} + 9760866 q^{72} + 1248533 q^{73} - 8263279 q^{74} + 1573413 q^{75} + 1788254 q^{76} - 154693 q^{77} - 2427685 q^{78} - 14947605 q^{79} - 9147616 q^{80} + 25716334 q^{81} - 6987095 q^{82} - 14177784 q^{83} + 5570663 q^{84} - 11788444 q^{85} + 8748840 q^{86} - 29484448 q^{87} - 15390723 q^{88} + 6734836 q^{89} + 5994972 q^{90} + 7535710 q^{91} - 24493215 q^{92} + 17307847 q^{93} - 22760149 q^{94} - 9329708 q^{95} - 36488483 q^{96} - 12365397 q^{97} - 352947 q^{98} - 43198042 q^{99}+O(q^{100}) \) 10 * q - 3 * q^2 - 101 * q^3 + 361 * q^4 + 226 * q^5 + 1105 * q^6 - 3430 * q^7 + 291 * q^8 + 12247 * q^9 + 2548 * q^10 + 451 * q^11 - 16241 * q^12 - 21970 * q^13 + 1029 * q^14 + 27184 * q^15 + 11897 * q^16 - 8654 * q^17 + 159348 * q^18 + 10130 * q^19 - 82012 * q^20 + 34643 * q^21 - 57863 * q^22 - 52155 * q^23 - 49227 * q^24 + 47190 * q^25 + 6591 * q^26 - 155171 * q^27 - 123823 * q^28 + 520154 * q^29 + 1070236 * q^30 + 692605 * q^31 + 149835 * q^32 + 436053 * q^33 + 1059060 * q^34 - 77518 * q^35 + 2843742 * q^36 - 20511 * q^37 + 1905286 * q^38 + 221897 * q^39 + 636320 * q^40 + 355049 * q^41 - 379015 * q^42 + 1256772 * q^43 - 687913 * q^44 + 1259926 * q^45 + 4043075 * q^46 + 1260721 * q^47 + 1128551 * q^48 + 1176490 * q^49 + 609035 * q^50 + 1411976 * q^51 - 793117 * q^52 + 928854 * q^53 + 6642607 * q^54 + 3423196 * q^55 - 99813 * q^56 + 3014966 * q^57 + 1612588 * q^58 + 3144446 * q^59 + 7738848 * q^60 + 6322923 * q^61 + 6545331 * q^62 - 4200721 * q^63 - 6629943 * q^64 - 496522 * q^65 - 14343317 * q^66 + 3944507 * q^67 - 1787356 * q^68 - 148281 * q^69 - 873964 * q^70 + 6032248 * q^71 + 9760866 * q^72 + 1248533 * q^73 - 8263279 * q^74 + 1573413 * q^75 + 1788254 * q^76 - 154693 * q^77 - 2427685 * q^78 - 14947605 * q^79 - 9147616 * q^80 + 25716334 * q^81 - 6987095 * q^82 - 14177784 * q^83 + 5570663 * q^84 - 11788444 * q^85 + 8748840 * q^86 - 29484448 * q^87 - 15390723 * q^88 + 6734836 * q^89 + 5994972 * q^90 + 7535710 * q^91 - 24493215 * q^92 + 17307847 * q^93 - 22760149 * q^94 - 9329708 * q^95 - 36488483 * q^96 - 12365397 * q^97 - 352947 * q^98 - 43198042 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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