LMFDB - Embedded newform 91.8.a.d.1.3

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			1.3
Root			$9.01767$ 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)

$f(q)$	$=$	$q-9.01767 q^{2} -31.1400 q^{3} -46.6816 q^{4} +514.920 q^{5} +280.810 q^{6} -343.000 q^{7} +1575.22 q^{8} -1217.30 q^{9} +O(q^{10})$	\(q-9.01767 q^{2} -31.1400 q^{3} -46.6816 q^{4} +514.920 q^{5} +280.810 q^{6} -343.000 q^{7} +1575.22 q^{8} -1217.30 q^{9} -4643.38 q^{10} +7902.57 q^{11} +1453.67 q^{12} -2197.00 q^{13} +3093.06 q^{14} -16034.6 q^{15} -8229.58 q^{16} -34955.7 q^{17} +10977.2 q^{18} +4279.55 q^{19} -24037.3 q^{20} +10681.0 q^{21} -71262.8 q^{22} -85831.3 q^{23} -49052.4 q^{24} +187018. q^{25} +19811.8 q^{26} +106010. q^{27} +16011.8 q^{28} +187738. q^{29} +144595. q^{30} -67357.4 q^{31} -127417. q^{32} -246086. q^{33} +315219. q^{34} -176618. q^{35} +56825.6 q^{36} +362381. q^{37} -38591.5 q^{38} +68414.6 q^{39} +811113. q^{40} +269727. q^{41} -96317.9 q^{42} +547649. q^{43} -368905. q^{44} -626813. q^{45} +773998. q^{46} -219725. q^{47} +256269. q^{48} +117649. q^{49} -1.68646e6 q^{50} +1.08852e6 q^{51} +102560. q^{52} -330615. q^{53} -955962. q^{54} +4.06919e6 q^{55} -540301. q^{56} -133265. q^{57} -1.69296e6 q^{58} +1.83800e6 q^{59} +748522. q^{60} +548410. q^{61} +607406. q^{62} +417534. q^{63} +2.20239e6 q^{64} -1.13128e6 q^{65} +2.21912e6 q^{66} -2.38579e6 q^{67} +1.63179e6 q^{68} +2.67278e6 q^{69} +1.59268e6 q^{70} +3.21125e6 q^{71} -1.91752e6 q^{72} +2.72837e6 q^{73} -3.26783e6 q^{74} -5.82373e6 q^{75} -199776. q^{76} -2.71058e6 q^{77} -616940. q^{78} -4.79708e6 q^{79} -4.23758e6 q^{80} -638911. q^{81} -2.43231e6 q^{82} +377072. q^{83} -498607. q^{84} -1.79994e7 q^{85} -4.93852e6 q^{86} -5.84615e6 q^{87} +1.24483e7 q^{88} +2.51983e6 q^{89} +5.65239e6 q^{90} +753571. q^{91} +4.00674e6 q^{92} +2.09751e6 q^{93} +1.98141e6 q^{94} +2.20362e6 q^{95} +3.96775e6 q^{96} -3.17346e6 q^{97} -1.06092e6 q^{98} -9.61981e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−9.01767	−0.797057	−0.398529	−	0.917156i	$-0.630479\pi$
$2$	−9.01767	−0.797057	−0.398529	+	0.917156i	$0.630479\pi$
$3$	−31.1400	−0.665877	−0.332939	−	0.942949i	$-0.608040\pi$
$3$	−31.1400	−0.665877	−0.332939	+	0.942949i	$0.608040\pi$
$4$	−46.6816	−0.364700
$5$	514.920	1.84223	0.921117	−	0.389285i	$-0.127278\pi$
$5$	514.920	1.84223	0.921117	+	0.389285i	$0.127278\pi$
$6$	280.810	0.530742
$7$	−343.000	−0.377964
$7$	−343.000	−0.377964
$8$	1575.22	1.08774
$9$	−1217.30	−0.556608
$10$	−4643.38	−1.46837
$11$	7902.57	1.79017	0.895084	−	0.445897i	$-0.147115\pi$
$11$	7902.57	1.79017	0.895084	+	0.445897i	$0.147115\pi$
$12$	1453.67	0.242845
$13$	−2197.00	−0.277350
$13$	−2197.00	−0.277350
$14$	3093.06	0.301259
$15$	−16034.6	−1.22670
$16$	−8229.58	−0.502294
$17$	−34955.7	−1.72563	−0.862813	−	0.505523i	$-0.831300\pi$
$17$	−34955.7	−1.72563	−0.862813	+	0.505523i	$0.831300\pi$
$18$	10977.2	0.443648
$19$	4279.55	0.143140	0.0715698	−	0.997436i	$-0.477199\pi$
$19$	4279.55	0.143140	0.0715698	+	0.997436i	$0.477199\pi$
$20$	−24037.3	−0.671863
$21$	10681.0	0.251678
$22$	−71262.8	−1.42687
$23$	−85831.3	−1.47095	−0.735475	−	0.677552i	$-0.763041\pi$
$23$	−85831.3	−1.47095	−0.735475	+	0.677552i	$0.763041\pi$
$24$	−49052.4	−0.724304
$25$	187018.	2.39383
$26$	19811.8	0.221064
$27$	106010.	1.03651
$28$	16011.8	0.137844
$29$	187738.	1.42941	0.714707	−	0.699424i	$-0.246560\pi$
$29$	187738.	1.42941	0.714707	+	0.699424i	$0.246560\pi$
$30$	144595.	0.977751
$31$	−67357.4	−0.406087	−0.203044	−	0.979170i	$-0.565083\pi$
$31$	−67357.4	−0.406087	−0.203044	+	0.979170i	$0.565083\pi$
$32$	−127417.	−0.687387
$33$	−246086.	−1.19203
$34$	315219.	1.37542
$35$	−176618.	−0.696299
$36$	56825.6	0.202995
$37$	362381.	1.17614	0.588070	−	0.808810i	$-0.299888\pi$
$37$	362381.	1.17614	0.588070	+	0.808810i	$0.299888\pi$
$38$	−38591.5	−0.114090
$39$	68414.6	0.184681
$40$	811113.	2.00388
$41$	269727.	0.611196	0.305598	−	0.952161i	$-0.401144\pi$
$41$	269727.	0.611196	0.305598	+	0.952161i	$0.401144\pi$
$42$	−96317.9	−0.200602
$43$	547649.	1.05042	0.525210	−	0.850973i	$-0.323987\pi$
$43$	547649.	1.05042	0.525210	+	0.850973i	$0.323987\pi$
$44$	−368905.	−0.652875
$45$	−626813.	−1.02540
$46$	773998.	1.17243
$47$	−219725.	−0.308701	−0.154350	−	0.988016i	$-0.549328\pi$
$47$	−219725.	−0.308701	−0.154350	+	0.988016i	$0.549328\pi$
$48$	256269.	0.334466
$49$	117649.	0.142857
$50$	−1.68646e6	−1.90802
$51$	1.08852e6	1.14905
$52$	102560.	0.101150
$53$	−330615.	−0.305040	−0.152520	−	0.988300i	$-0.548739\pi$
$53$	−330615.	−0.305040	−0.152520	+	0.988300i	$0.548739\pi$
$54$	−955962.	−0.826157
$55$	4.06919e6	3.29791
$56$	−540301.	−0.411129
$57$	−133265.	−0.0953134
$58$	−1.69296e6	−1.13932
$59$	1.83800e6	1.16510	0.582549	−	0.812795i	$-0.302055\pi$
$59$	1.83800e6	1.16510	0.582549	+	0.812795i	$0.302055\pi$
$60$	748522.	0.447378
$61$	548410.	0.309350	0.154675	−	0.987965i	$-0.450567\pi$
$61$	548410.	0.309350	0.154675	+	0.987965i	$0.450567\pi$
$62$	607406.	0.323675
$63$	417534.	0.210378
$64$	2.20239e6	1.05018
$65$	−1.13128e6	−0.510944
$66$	2.21912e6	0.950118
$67$	−2.38579e6	−0.969103	−0.484551	−	0.874763i	$-0.661017\pi$
$67$	−2.38579e6	−0.969103	−0.484551	+	0.874763i	$0.661017\pi$
$68$	1.63179e6	0.629336
$69$	2.67278e6	0.979472
$70$	1.59268e6	0.554990
$71$	3.21125e6	1.06481	0.532403	−	0.846491i	$-0.321289\pi$
$71$	3.21125e6	1.06481	0.532403	+	0.846491i	$0.321289\pi$
$72$	−1.91752e6	−0.605446
$73$	2.72837e6	0.820867	0.410434	−	0.911890i	$-0.365377\pi$
$73$	2.72837e6	0.820867	0.410434	+	0.911890i	$0.365377\pi$
$74$	−3.26783e6	−0.937450
$75$	−5.82373e6	−1.59400
$76$	−199776.	−0.0522031
$77$	−2.71058e6	−0.676620
$78$	−616940.	−0.147201
$79$	−4.79708e6	−1.09467	−0.547334	−	0.836914i	$-0.684357\pi$
$79$	−4.79708e6	−1.09467	−0.547334	+	0.836914i	$0.684357\pi$
$80$	−4.23758e6	−0.925343
$81$	−638911.	−0.133580
$82$	−2.43231e6	−0.487158
$83$	377072.	0.0723853	0.0361927	−	0.999345i	$-0.488477\pi$
$83$	377072.	0.0723853	0.0361927	+	0.999345i	$0.488477\pi$
$84$	−498607.	−0.0917870
$85$	−1.79994e7	−3.17901
$86$	−4.93852e6	−0.837244
$87$	−5.84615e6	−0.951814
$88$	1.24483e7	1.94724
$89$	2.51983e6	0.378883	0.189442	−	0.981892i	$-0.439332\pi$
$89$	2.51983e6	0.378883	0.189442	+	0.981892i	$0.439332\pi$
$90$	5.65239e6	0.817304
$91$	753571.	0.104828
$92$	4.00674e6	0.536456
$93$	2.09751e6	0.270404
$94$	1.98141e6	0.246052
$95$	2.20362e6	0.263697
$96$	3.96775e6	0.457715
$97$	−3.17346e6	−0.353047	−0.176523	−	0.984296i	$-0.556485\pi$
$97$	−3.17346e6	−0.353047	−0.176523	+	0.984296i	$0.556485\pi$
$98$	−1.06092e6	−0.113865
$99$	−9.61981e6	−0.996422
$100$	−8.73029e6	−0.873029
$101$	4.77728e6	0.461377	0.230688	−	0.973028i	$-0.425902\pi$
$101$	4.77728e6	0.461377	0.230688	+	0.973028i	$0.425902\pi$
$102$	−9.81592e6	−0.915862
$103$	1.67244e7	1.50807	0.754035	−	0.656835i	$-0.228105\pi$
$103$	1.67244e7	1.50807	0.754035	+	0.656835i	$0.228105\pi$
$104$	−3.46076e6	−0.301686
$105$	5.49987e6	0.463650
$106$	2.98138e6	0.243134
$107$	−1.21147e6	−0.0956023	−0.0478012	−	0.998857i	$-0.515221\pi$
$107$	−1.21147e6	−0.0956023	−0.0478012	+	0.998857i	$0.515221\pi$
$108$	−4.94871e6	−0.378015
$109$	1.70268e7	1.25933	0.629666	−	0.776866i	$-0.283192\pi$
$109$	1.70268e7	1.25933	0.629666	+	0.776866i	$0.283192\pi$
$110$	−3.66946e7	−2.62862
$111$	−1.12845e7	−0.783165
$112$	2.82275e6	0.189849
$113$	1.84414e7	1.20232	0.601160	−	0.799128i	$-0.294705\pi$
$113$	1.84414e7	1.20232	0.601160	+	0.799128i	$0.294705\pi$
$114$	1.20174e6	0.0759702
$115$	−4.41962e7	−2.70984
$116$	−8.76389e6	−0.521308
$117$	2.67441e6	0.154375
$118$	−1.65745e7	−0.928650
$119$	1.19898e7	0.652225
$120$	−2.52581e7	−1.33434
$121$	4.29634e7	2.20470
$122$	−4.94538e6	−0.246570
$123$	−8.39929e6	−0.406982
$124$	3.14435e6	0.148100
$125$	5.60711e7	2.56776
$126$	−3.76519e6	−0.167683
$127$	2.76888e7	1.19947	0.599737	−	0.800197i	$-0.295272\pi$
$127$	2.76888e7	1.19947	0.599737	+	0.800197i	$0.295272\pi$
$128$	−3.55107e6	−0.149667
$129$	−1.70538e7	−0.699450
$130$	1.02015e7	0.407251
$131$	−4.61701e6	−0.179437	−0.0897183	−	0.995967i	$-0.528597\pi$
$131$	−4.61701e6	−0.179437	−0.0897183	+	0.995967i	$0.528597\pi$
$132$	1.14877e7	0.434734
$133$	−1.46788e6	−0.0541017
$134$	2.15142e7	0.772430
$135$	5.45866e7	1.90949
$136$	−5.50630e7	−1.87704
$137$	−3.51564e7	−1.16811	−0.584053	−	0.811715i	$-0.698534\pi$
$137$	−3.51564e7	−1.16811	−0.584053	+	0.811715i	$0.698534\pi$
$138$	−2.41023e7	−0.780695
$139$	−2.11162e7	−0.666905	−0.333452	−	0.942767i	$-0.608214\pi$
$139$	−2.11162e7	−0.666905	−0.333452	+	0.942767i	$0.608214\pi$
$140$	8.24480e6	0.253940
$141$	6.84225e6	0.205557
$142$	−2.89580e7	−0.848711
$143$	−1.73619e7	−0.496503
$144$	1.00179e7	0.279580
$145$	9.66699e7	2.63332
$146$	−2.46035e7	−0.654278
$147$	−3.66359e6	−0.0951253
$148$	−1.69165e7	−0.428938
$149$	9.29934e6	0.230303	0.115152	−	0.993348i	$-0.463265\pi$
$149$	9.29934e6	0.230303	0.115152	+	0.993348i	$0.463265\pi$
$150$	5.25165e7	1.27051
$151$	−2.14082e7	−0.506012	−0.253006	−	0.967465i	$-0.581419\pi$
$151$	−2.14082e7	−0.506012	−0.253006	+	0.967465i	$0.581419\pi$
$152$	6.74123e6	0.155699
$153$	4.25516e7	0.960497
$154$	2.44431e7	0.539305
$155$	−3.46837e7	−0.748108
$156$	−3.19370e6	−0.0673532
$157$	2.04932e7	0.422631	0.211316	−	0.977418i	$-0.432225\pi$
$157$	2.04932e7	0.422631	0.211316	+	0.977418i	$0.432225\pi$
$158$	4.32585e7	0.872512
$159$	1.02953e7	0.203119
$160$	−6.56094e7	−1.26633
$161$	2.94401e7	0.555967
$162$	5.76149e6	0.106471
$163$	1.02319e8	1.85054	0.925269	−	0.379312i	$-0.123839\pi$
$163$	1.02319e8	1.85054	0.925269	+	0.379312i	$0.123839\pi$
$164$	−1.25913e7	−0.222903
$165$	−1.26715e8	−2.19600
$166$	−3.40031e6	−0.0576952
$167$	−1.58677e7	−0.263637	−0.131818	−	0.991274i	$-0.542082\pi$
$167$	−1.58677e7	−0.263637	−0.131818	+	0.991274i	$0.542082\pi$
$168$	1.68250e7	0.273761
$169$	4.82681e6	0.0769231
$170$	1.62313e8	2.53385
$171$	−5.20949e6	−0.0796726
$172$	−2.55651e7	−0.383088
$173$	8.76128e7	1.28649	0.643245	−	0.765661i	$-0.277588\pi$
$173$	8.76128e7	1.28649	0.643245	+	0.765661i	$0.277588\pi$
$174$	5.27186e7	0.758650
$175$	−6.41471e7	−0.904782
$176$	−6.50348e7	−0.899190
$177$	−5.72352e7	−0.775813
$178$	−2.27230e7	−0.301992
$179$	−6.04897e7	−0.788308	−0.394154	−	0.919044i	$-0.628962\pi$
$179$	−6.04897e7	−0.788308	−0.394154	+	0.919044i	$0.628962\pi$
$180$	2.92606e7	0.373964
$181$	4.37548e7	0.548467	0.274234	−	0.961663i	$-0.411576\pi$
$181$	4.37548e7	0.548467	0.274234	+	0.961663i	$0.411576\pi$
$182$	−6.79546e6	−0.0835543
$183$	−1.70775e7	−0.205989
$184$	−1.35203e8	−1.60002
$185$	1.86597e8	2.16673
$186$	−1.89146e7	−0.215527
$187$	−2.76240e8	−3.08916
$188$	1.02571e7	0.112583
$189$	−3.63614e7	−0.391764
$190$	−1.98716e7	−0.210181
$191$	4.01352e7	0.416782	0.208391	−	0.978046i	$-0.433177\pi$
$191$	4.01352e7	0.416782	0.208391	+	0.978046i	$0.433177\pi$
$192$	−6.85823e7	−0.699291
$193$	1.01048e7	0.101176	0.0505879	−	0.998720i	$-0.483890\pi$
$193$	1.01048e7	0.101176	0.0505879	+	0.998720i	$0.483890\pi$
$194$	2.86172e7	0.281398
$195$	3.52280e7	0.340226
$196$	−5.49205e6	−0.0521000
$197$	6.75651e7	0.629638	0.314819	−	0.949152i	$-0.398056\pi$
$197$	6.75651e7	0.629638	0.314819	+	0.949152i	$0.398056\pi$
$198$	8.67482e7	0.794205
$199$	−4.44355e7	−0.399710	−0.199855	−	0.979826i	$-0.564047\pi$
$199$	−4.44355e7	−0.399710	−0.199855	+	0.979826i	$0.564047\pi$
$200$	2.94594e8	2.60387
$201$	7.42934e7	0.645303
$202$	−4.30799e7	−0.367744
$203$	−6.43940e7	−0.540268
$204$	−5.08139e7	−0.419060
$205$	1.38888e8	1.12597
$206$	−1.50816e8	−1.20202
$207$	1.04482e8	0.818742
$208$	1.80804e7	0.139311
$209$	3.38194e7	0.256244
$210$	−4.95960e7	−0.369555
$211$	2.33942e7	0.171443	0.0857216	−	0.996319i	$-0.472680\pi$
$211$	2.33942e7	0.171443	0.0857216	+	0.996319i	$0.472680\pi$
$212$	1.54336e7	0.111248
$213$	−9.99984e7	−0.709030
$214$	1.09246e7	0.0762005
$215$	2.81996e8	1.93512
$216$	1.66989e8	1.12746
$217$	2.31036e7	0.153486
$218$	−1.53542e8	−1.00376
$219$	−8.49613e7	−0.546597
$220$	−1.89957e8	−1.20275
$221$	7.67977e7	0.478603
$222$	1.01760e8	0.624227
$223$	−6.79456e7	−0.410293	−0.205147	−	0.978731i	$-0.565767\pi$
$223$	−6.79456e7	−0.410293	−0.205147	+	0.978731i	$0.565767\pi$
$224$	4.37039e7	0.259808
$225$	−2.27657e8	−1.33242
$226$	−1.66299e8	−0.958318
$227$	−1.80432e8	−1.02382	−0.511909	−	0.859040i	$-0.671062\pi$
$227$	−1.80432e8	−1.02382	−0.511909	+	0.859040i	$0.671062\pi$
$228$	6.22103e6	0.0347608
$229$	1.52915e6	0.00841447	0.00420724	−	0.999991i	$-0.498661\pi$
$229$	1.52915e6	0.00841447	0.00420724	+	0.999991i	$0.498661\pi$
$230$	3.98547e8	2.15989
$231$	8.44075e7	0.450546
$232$	2.95728e8	1.55484
$233$	−4.32721e7	−0.224111	−0.112055	−	0.993702i	$-0.535743\pi$
$233$	−4.32721e7	−0.224111	−0.112055	+	0.993702i	$0.535743\pi$
$234$	−2.41169e7	−0.123046
$235$	−1.13141e8	−0.568699
$236$	−8.58007e7	−0.424912
$237$	1.49381e8	0.728914
$238$	−1.08120e8	−0.519861
$239$	−2.80263e8	−1.32792	−0.663961	−	0.747767i	$-0.731126\pi$
$239$	−2.80263e8	−1.32792	−0.663961	+	0.747767i	$0.731126\pi$
$240$	1.31958e8	0.616165
$241$	2.18193e8	1.00411	0.502055	−	0.864836i	$-0.332578\pi$
$241$	2.18193e8	1.00411	0.502055	+	0.864836i	$0.332578\pi$
$242$	−3.87430e8	−1.75727
$243$	−2.11948e8	−0.947561
$244$	−2.56006e7	−0.112820
$245$	6.05798e7	0.263176
$246$	7.57420e7	0.324388
$247$	−9.40216e6	−0.0396998
$248$	−1.06103e8	−0.441719
$249$	−1.17420e7	−0.0481997
$250$	−5.05631e8	−2.04665
$251$	−1.76781e8	−0.705629	−0.352815	−	0.935693i	$-0.614775\pi$
$251$	−1.76781e8	−0.705629	−0.352815	+	0.935693i	$0.614775\pi$
$252$	−1.94912e7	−0.0767248
$253$	−6.78288e8	−2.63325
$254$	−2.49688e8	−0.956049
$255$	5.60501e8	2.11683
$256$	−2.49883e8	−0.930888
$257$	−4.06985e8	−1.49559	−0.747795	−	0.663930i	$-0.768887\pi$
$257$	−4.06985e8	−1.49559	−0.747795	+	0.663930i	$0.768887\pi$
$258$	1.53785e8	0.557502
$259$	−1.24297e8	−0.444539
$260$	5.28100e7	0.186341
$261$	−2.28533e8	−0.795623
$262$	4.16346e7	0.143021
$263$	−5.51482e7	−0.186933	−0.0934665	−	0.995622i	$-0.529795\pi$
$263$	−5.51482e7	−0.186933	−0.0934665	+	0.995622i	$0.529795\pi$
$264$	−3.87640e8	−1.29663
$265$	−1.70240e8	−0.561956
$266$	1.32369e7	0.0431221
$267$	−7.84674e7	−0.252290
$268$	1.11372e8	0.353432
$269$	1.13610e8	0.355863	0.177931	−	0.984043i	$-0.443059\pi$
$269$	1.13610e8	0.355863	0.177931	+	0.984043i	$0.443059\pi$
$270$	−4.92244e8	−1.52198
$271$	9.58876e7	0.292664	0.146332	−	0.989235i	$-0.453253\pi$
$271$	9.58876e7	0.292664	0.146332	+	0.989235i	$0.453253\pi$
$272$	2.87671e8	0.866771
$273$	−2.34662e7	−0.0698029
$274$	3.17029e8	0.931047
$275$	1.47792e9	4.28536
$276$	−1.24770e8	−0.357214
$277$	−2.90638e8	−0.821625	−0.410812	−	0.911720i	$-0.634755\pi$
$277$	−2.90638e8	−0.821625	−0.410812	+	0.911720i	$0.634755\pi$
$278$	1.90419e8	0.531561
$279$	8.19942e7	0.226031
$280$	−2.78212e8	−0.757395
$281$	2.68401e8	0.721626	0.360813	−	0.932638i	$-0.382499\pi$
$281$	2.68401e8	0.721626	0.360813	+	0.932638i	$0.382499\pi$
$282$	−6.17011e7	−0.163841
$283$	1.11096e8	0.291372	0.145686	−	0.989331i	$-0.453461\pi$
$283$	1.11096e8	0.291372	0.145686	+	0.989331i	$0.453461\pi$
$284$	−1.49906e8	−0.388335
$285$	−6.86208e7	−0.175590
$286$	1.56564e8	0.395742
$287$	−9.25163e7	−0.231010
$288$	1.55104e8	0.382605
$289$	8.11562e8	1.97779
$290$	−8.71737e8	−2.09890
$291$	9.88216e7	0.235086
$292$	−1.27365e8	−0.299370
$293$	−6.63546e7	−0.154111	−0.0770556	−	0.997027i	$-0.524552\pi$
$293$	−6.63546e7	−0.154111	−0.0770556	+	0.997027i	$0.524552\pi$
$294$	3.30370e7	0.0758203
$295$	9.46422e8	2.14639
$296$	5.70830e8	1.27934
$297$	8.37751e8	1.85553
$298$	−8.38584e7	−0.183565
$299$	1.88571e8	0.407968
$300$	2.71861e8	0.581330
$301$	−1.87844e8	−0.397021
$302$	1.93052e8	0.403320
$303$	−1.48764e8	−0.307220
$304$	−3.52189e7	−0.0718982
$305$	2.82387e8	0.569896
$306$	−3.83716e8	−0.765571
$307$	−5.08835e8	−1.00367	−0.501837	−	0.864962i	$-0.667342\pi$
$307$	−5.08835e8	−1.00367	−0.501837	+	0.864962i	$0.667342\pi$
$308$	1.26534e8	0.246763
$309$	−5.20799e8	−1.00419
$310$	3.12766e8	0.596284
$311$	−5.96814e8	−1.12506	−0.562532	−	0.826775i	$-0.690173\pi$
$311$	−5.96814e8	−1.12506	−0.562532	+	0.826775i	$0.690173\pi$
$312$	1.07768e8	0.200886
$313$	−8.32611e8	−1.53475	−0.767374	−	0.641200i	$-0.778437\pi$
$313$	−8.32611e8	−1.53475	−0.767374	+	0.641200i	$0.778437\pi$
$314$	−1.84801e8	−0.336861
$315$	2.14997e8	0.387565
$316$	2.23935e8	0.399225
$317$	4.80850e8	0.847818	0.423909	−	0.905705i	$-0.360658\pi$
$317$	4.80850e8	0.847818	0.423909	+	0.905705i	$0.360658\pi$
$318$	−9.28401e7	−0.161898
$319$	1.48361e9	2.55889
$320$	1.13405e9	1.93468
$321$	3.77251e7	0.0636594
$322$	−2.65481e8	−0.443137
$323$	−1.49594e8	−0.247006
$324$	2.98254e7	0.0487168
$325$	−4.10878e8	−0.663928
$326$	−9.22675e8	−1.47498
$327$	−5.30215e8	−0.838561
$328$	4.24879e8	0.664825
$329$	7.53658e7	0.116678
$330$	1.14267e9	1.75034
$331$	−1.30583e8	−0.197920	−0.0989600	−	0.995091i	$-0.531552\pi$
$331$	−1.30583e8	−0.197920	−0.0989600	+	0.995091i	$0.531552\pi$
$332$	−1.76023e7	−0.0263989
$333$	−4.41126e8	−0.654648
$334$	1.43090e8	0.210134
$335$	−1.22849e9	−1.78531
$336$	−8.79003e7	−0.126416
$337$	1.14071e9	1.62357	0.811783	−	0.583959i	$-0.198497\pi$
$337$	1.14071e9	1.62357	0.811783	+	0.583959i	$0.198497\pi$
$338$	−4.35266e7	−0.0613121
$339$	−5.74266e8	−0.800598
$340$	8.40241e8	1.15938
$341$	−5.32296e8	−0.726964
$342$	4.69775e7	0.0635036
$343$	−4.03536e7	−0.0539949
$344$	8.62669e8	1.14259
$345$	1.37627e9	1.80442
$346$	−7.90063e8	−1.02541
$347$	−6.42312e8	−0.825264	−0.412632	−	0.910898i	$-0.635390\pi$
$347$	−6.42312e8	−0.825264	−0.412632	+	0.910898i	$0.635390\pi$
$348$	2.72908e8	0.347127
$349$	1.21999e9	1.53627	0.768135	−	0.640288i	$-0.221185\pi$
$349$	1.21999e9	1.53627	0.768135	+	0.640288i	$0.221185\pi$
$350$	5.78457e8	0.721163
$351$	−2.32904e8	−0.287476
$352$	−1.00692e9	−1.23054
$353$	1.28799e9	1.55848	0.779242	−	0.626723i	$-0.215604\pi$
$353$	1.28799e9	1.55848	0.779242	+	0.626723i	$0.215604\pi$
$354$	5.16128e8	0.618367
$355$	1.65354e9	1.96162
$356$	−1.17630e8	−0.138179
$357$	−3.73362e8	−0.434302
$358$	5.45476e8	0.628326
$359$	8.76492e8	0.999810	0.499905	−	0.866080i	$-0.333368\pi$
$359$	8.76492e8	0.999810	0.499905	+	0.866080i	$0.333368\pi$
$360$	−9.87369e8	−1.11537
$361$	−8.75557e8	−0.979511
$362$	−3.94566e8	−0.437160
$363$	−1.33788e9	−1.46806
$364$	−3.51779e7	−0.0382310
$365$	1.40489e9	1.51223
$366$	1.53999e8	0.164185
$367$	−1.28931e9	−1.36152	−0.680762	−	0.732505i	$-0.738351\pi$
$367$	−1.28931e9	−1.36152	−0.680762	+	0.732505i	$0.738351\pi$
$368$	7.06355e8	0.738849
$369$	−3.28339e8	−0.340196
$370$	−1.68267e9	−1.72700
$371$	1.13401e8	0.115294
$372$	−9.79150e7	−0.0986164
$373$	−1.82655e9	−1.82243	−0.911213	−	0.411936i	$-0.864853\pi$
$373$	−1.82655e9	−1.82243	−0.911213	+	0.411936i	$0.864853\pi$
$374$	2.49104e9	2.46224
$375$	−1.74605e9	−1.70981
$376$	−3.46116e8	−0.335787
$377$	−4.12459e8	−0.396448
$378$	3.27895e8	0.312258
$379$	−1.15289e9	−1.08780	−0.543902	−	0.839149i	$-0.683054\pi$
$379$	−1.15289e9	−1.08780	−0.543902	+	0.839149i	$0.683054\pi$
$380$	−1.02869e8	−0.0961703
$381$	−8.62229e8	−0.798703
$382$	−3.61926e8	−0.332199
$383$	−1.69710e9	−1.54352	−0.771760	−	0.635914i	$-0.780623\pi$
$383$	−1.69710e9	−1.54352	−0.771760	+	0.635914i	$0.780623\pi$
$384$	1.10580e8	0.0996595
$385$	−1.39573e9	−1.24649
$386$	−9.11217e7	−0.0806429
$387$	−6.66654e8	−0.584672
$388$	1.48142e8	0.128756
$389$	1.69928e9	1.46367	0.731834	−	0.681483i	$-0.238665\pi$
$389$	1.69928e9	1.46367	0.731834	+	0.681483i	$0.238665\pi$
$390$	−3.17675e8	−0.271179
$391$	3.00029e9	2.53831
$392$	1.85323e8	0.155392
$393$	1.43774e8	0.119483
$394$	−6.09280e8	−0.501857
$395$	−2.47011e9	−2.01663
$396$	4.49068e8	0.363395
$397$	−3.01378e8	−0.241738	−0.120869	−	0.992668i	$-0.538568\pi$
$397$	−3.01378e8	−0.241738	−0.120869	+	0.992668i	$0.538568\pi$
$398$	4.00705e8	0.318591
$399$	4.57099e7	0.0360251
$400$	−1.53908e9	−1.20240
$401$	9.79289e8	0.758413	0.379206	−	0.925312i	$-0.376197\pi$
$401$	9.79289e8	0.758413	0.379206	+	0.925312i	$0.376197\pi$
$402$	−6.69953e8	−0.514343
$403$	1.47984e8	0.112628
$404$	−2.23011e8	−0.168264
$405$	−3.28988e8	−0.246086
$406$	5.80684e8	0.430624
$407$	2.86374e9	2.10549
$408$	1.71466e9	1.24988
$409$	−8.68674e8	−0.627806	−0.313903	−	0.949455i	$-0.601637\pi$
$409$	−8.68674e8	−0.627806	−0.313903	+	0.949455i	$0.601637\pi$
$410$	−1.25244e9	−0.897460
$411$	1.09477e9	0.777815
$412$	−7.80724e8	−0.549993
$413$	−6.30433e8	−0.440366
$414$	−9.42188e8	−0.652584
$415$	1.94162e8	0.133351
$416$	2.79934e8	0.190647
$417$	6.57558e8	0.444077
$418$	−3.04972e8	−0.204241
$419$	3.33007e7	0.0221159	0.0110579	−	0.999939i	$-0.496480\pi$
$419$	3.33007e7	0.0221159	0.0110579	+	0.999939i	$0.496480\pi$
$420$	−2.56743e8	−0.169093
$421$	2.32694e9	1.51984	0.759919	−	0.650017i	$-0.225238\pi$
$421$	2.32694e9	1.51984	0.759919	+	0.650017i	$0.225238\pi$
$422$	−2.10961e8	−0.136650
$423$	2.67472e8	0.171825
$424$	−5.20792e8	−0.331806
$425$	−6.53734e9	−4.13085
$426$	9.01752e8	0.565137
$427$	−1.88104e8	−0.116923
$428$	5.65532e7	0.0348662
$429$	5.40651e8	0.330610
$430$	−2.54294e9	−1.54240
$431$	−1.63497e9	−0.983648	−0.491824	−	0.870695i	$-0.663670\pi$
$431$	−1.63497e9	−0.983648	−0.491824	+	0.870695i	$0.663670\pi$
$432$	−8.72417e8	−0.520632
$433$	4.47022e8	0.264619	0.132310	−	0.991208i	$-0.457761\pi$
$433$	4.47022e8	0.264619	0.132310	+	0.991208i	$0.457761\pi$
$434$	−2.08340e8	−0.122337
$435$	−3.01030e9	−1.75347
$436$	−7.94839e8	−0.459279
$437$	−3.67319e8	−0.210551
$438$	7.66153e8	0.435669
$439$	2.87067e8	0.161941	0.0809705	−	0.996716i	$-0.474198\pi$
$439$	2.87067e8	0.161941	0.0809705	+	0.996716i	$0.474198\pi$
$440$	6.40988e9	3.58728
$441$	−1.43214e8	−0.0795154
$442$	−6.92536e8	−0.381474
$443$	1.29726e9	0.708949	0.354475	−	0.935066i	$-0.384660\pi$
$443$	1.29726e9	0.708949	0.354475	+	0.935066i	$0.384660\pi$
$444$	5.26780e8	0.285620
$445$	1.29751e9	0.697992
$446$	6.12711e8	0.327027
$447$	−2.89581e8	−0.153354
$448$	−7.55419e8	−0.396931
$449$	4.54129e8	0.236765	0.118382	−	0.992968i	$-0.462229\pi$
$449$	4.54129e8	0.236765	0.118382	+	0.992968i	$0.462229\pi$
$450$	2.05294e9	1.06202
$451$	2.13154e9	1.09414
$452$	−8.60876e8	−0.438487
$453$	6.66651e8	0.336942
$454$	1.62708e9	0.816041
$455$	3.88029e8	0.193119
$456$	−2.09922e8	−0.103677
$457$	−1.33326e9	−0.653444	−0.326722	−	0.945121i	$-0.605944\pi$
$457$	−1.33326e9	−0.653444	−0.326722	+	0.945121i	$0.605944\pi$
$458$	−1.37894e7	−0.00670681
$459$	−3.70565e9	−1.78863
$460$	2.06315e9	0.988277
$461$	−8.97736e8	−0.426771	−0.213386	−	0.976968i	$-0.568449\pi$
$461$	−8.97736e8	−0.426771	−0.213386	+	0.976968i	$0.568449\pi$
$462$	−7.61159e8	−0.359111
$463$	−2.63807e9	−1.23524	−0.617622	−	0.786475i	$-0.711904\pi$
$463$	−2.63807e9	−1.23524	−0.617622	+	0.786475i	$0.711904\pi$
$464$	−1.54500e9	−0.717986
$465$	1.08005e9	0.498148
$466$	3.90214e8	0.178629
$467$	3.53783e9	1.60742	0.803708	−	0.595024i	$-0.202857\pi$
$467$	3.53783e9	1.60742	0.803708	+	0.595024i	$0.202857\pi$
$468$	−1.24846e8	−0.0563006
$469$	8.18325e8	0.366286
$470$	1.02027e9	0.453286
$471$	−6.38159e8	−0.281421
$472$	2.89525e9	1.26733
$473$	4.32784e9	1.88043
$474$	−1.34707e9	−0.580986
$475$	8.00351e8	0.342652
$476$	−5.59703e8	−0.237867
$477$	4.02458e8	0.169788
$478$	2.52732e9	1.05843
$479$	8.27523e7	0.0344038	0.0172019	−	0.999852i	$-0.494524\pi$
$479$	8.27523e7	0.0344038	0.0172019	+	0.999852i	$0.494524\pi$
$480$	2.04308e9	0.843219
$481$	−7.96150e8	−0.326202
$482$	−1.96759e9	−0.800333
$483$	−9.16765e8	−0.370206
$484$	−2.00560e9	−0.804056
$485$	−1.63408e9	−0.650395
$486$	1.91128e9	0.755260
$487$	−1.23927e9	−0.486198	−0.243099	−	0.970001i	$-0.578164\pi$
$487$	−1.23927e9	−0.486198	−0.243099	+	0.970001i	$0.578164\pi$
$488$	8.63866e8	0.336494
$489$	−3.18620e9	−1.23223
$490$	−5.46289e8	−0.209767
$491$	−3.88535e9	−1.48131	−0.740653	−	0.671888i	$-0.765484\pi$
$491$	−3.88535e9	−1.48131	−0.740653	+	0.671888i	$0.765484\pi$
$492$	3.92093e8	0.148426
$493$	−6.56250e9	−2.46664
$494$	8.47856e7	0.0316430
$495$	−4.95343e9	−1.83564
$496$	5.54323e8	0.203975
$497$	−1.10146e9	−0.402459
$498$	1.05886e8	0.0384179
$499$	−9.68212e8	−0.348834	−0.174417	−	0.984672i	$-0.555804\pi$
$499$	−9.68212e8	−0.348834	−0.174417	+	0.984672i	$0.555804\pi$
$500$	−2.61749e9	−0.936462
$501$	4.94120e8	0.175550
$502$	1.59415e9	0.562427
$503$	4.42436e9	1.55011	0.775056	−	0.631893i	$-0.217722\pi$
$503$	4.42436e9	1.55011	0.775056	+	0.631893i	$0.217722\pi$
$504$	6.57709e8	0.228837
$505$	2.45992e9	0.849964
$506$	6.11657e9	2.09885
$507$	−1.50307e8	−0.0512213
$508$	−1.29256e9	−0.437448
$509$	−4.08592e9	−1.37334	−0.686670	−	0.726969i	$-0.740928\pi$
$509$	−4.08592e9	−1.37334	−0.686670	+	0.726969i	$0.740928\pi$
$510$	−5.05441e9	−1.68723
$511$	−9.35830e8	−0.310259
$512$	2.70790e9	0.891637
$513$	4.53674e8	0.148366
$514$	3.67006e9	1.19207
$515$	8.61175e9	2.77822
$516$	7.96098e8	0.255090
$517$	−1.73640e9	−0.552627
$518$	1.12087e9	0.354323
$519$	−2.72826e9	−0.856644
$520$	−1.78202e9	−0.555776
$521$	5.87480e9	1.81996	0.909979	−	0.414655i	$-0.136098\pi$
$521$	5.87480e9	1.81996	0.909979	+	0.414655i	$0.136098\pi$
$522$	2.06084e9	0.634157
$523$	3.16555e9	0.967595	0.483798	−	0.875180i	$-0.339257\pi$
$523$	3.16555e9	0.967595	0.483798	+	0.875180i	$0.339257\pi$
$524$	2.15529e8	0.0654405
$525$	1.99754e9	0.602474
$526$	4.97308e8	0.148996
$527$	2.35452e9	0.700754
$528$	2.02518e9	0.598750
$529$	3.96218e9	1.16370
$530$	1.53517e9	0.447911
$531$	−2.23740e9	−0.648503
$532$	6.85232e7	0.0197309
$533$	−5.92590e8	−0.169515
$534$	7.07593e8	0.201089
$535$	−6.23809e8	−0.176122
$536$	−3.75814e9	−1.05414
$537$	1.88365e9	0.524916
$538$	−1.02449e9	−0.283643
$539$	9.29729e8	0.255738
$540$	−2.54819e9	−0.696392
$541$	6.52591e8	0.177195	0.0885973	−	0.996068i	$-0.471762\pi$
$541$	6.52591e8	0.177195	0.0885973	+	0.996068i	$0.471762\pi$
$542$	−8.64683e8	−0.233270
$543$	−1.36252e9	−0.365212
$544$	4.45394e9	1.18617
$545$	8.76745e9	2.31999
$546$	2.11610e8	0.0556369
$547$	−6.25460e7	−0.0163397	−0.00816985	−	0.999967i	$-0.502601\pi$
$547$	−6.25460e7	−0.0163397	−0.00816985	+	0.999967i	$0.502601\pi$
$548$	1.64116e9	0.426008
$549$	−6.67579e8	−0.172187
$550$	−1.33274e10	−3.41567
$551$	8.03431e8	0.204606
$552$	4.21023e9	1.06541
$553$	1.64540e9	0.413745
$554$	2.62088e9	0.654882
$555$	−5.81063e9	−1.44277
$556$	9.85738e8	0.243220
$557$	−7.34644e9	−1.80129	−0.900645	−	0.434555i	$-0.856906\pi$
$557$	−7.34644e9	−1.80129	−0.900645	+	0.434555i	$0.856906\pi$
$558$	−7.39396e8	−0.180160
$559$	−1.20319e9	−0.291334
$560$	1.45349e9	0.349747
$561$	8.60211e9	2.05700
$562$	−2.42035e9	−0.575177
$563$	−5.82921e9	−1.37667	−0.688335	−	0.725393i	$-0.741658\pi$
$563$	−5.82921e9	−1.37667	−0.688335	+	0.725393i	$0.741658\pi$
$564$	−3.19407e8	−0.0749666
$565$	9.49587e9	2.21496
$566$	−1.00183e9	−0.232240
$567$	2.19146e8	0.0504886
$568$	5.05843e9	1.15824
$569$	3.46011e9	0.787403	0.393702	−	0.919238i	$-0.371194\pi$
$569$	3.46011e9	0.787403	0.393702	+	0.919238i	$0.371194\pi$
$570$	6.18800e8	0.139955
$571$	7.02380e9	1.57887	0.789434	−	0.613835i	$-0.210374\pi$
$571$	7.02380e9	1.57887	0.789434	+	0.613835i	$0.210374\pi$
$572$	8.10484e8	0.181075
$573$	−1.24981e9	−0.277525
$574$	8.34282e8	0.184128
$575$	−1.60520e10	−3.52120
$576$	−2.68097e9	−0.584538
$577$	−5.92260e9	−1.28350	−0.641752	−	0.766912i	$-0.721792\pi$
$577$	−5.92260e9	−1.28350	−0.641752	+	0.766912i	$0.721792\pi$
$578$	−7.31840e9	−1.57641
$579$	−3.14663e8	−0.0673707
$580$	−4.51271e9	−0.960371
$581$	−1.29336e8	−0.0273591
$582$	−8.91141e8	−0.187377
$583$	−2.61271e9	−0.546073
$584$	4.29778e9	0.892893
$585$	1.37711e9	0.284395
$586$	5.98364e8	0.122835
$587$	−3.29272e9	−0.671926	−0.335963	−	0.941875i	$-0.609062\pi$
$587$	−3.29272e9	−0.671926	−0.335963	+	0.941875i	$0.609062\pi$
$588$	1.71022e8	0.0346922
$589$	−2.88259e8	−0.0581272
$590$	−8.53452e9	−1.71079
$591$	−2.10398e9	−0.419261
$592$	−2.98224e9	−0.590768
$593$	2.43975e8	0.0480455	0.0240228	−	0.999711i	$-0.492353\pi$
$593$	2.43975e8	0.0480455	0.0240228	+	0.999711i	$0.492353\pi$
$594$	−7.55456e9	−1.47896
$595$	6.17379e9	1.20155
$596$	−4.34108e8	−0.0839917
$597$	1.38372e9	0.266157
$598$	−1.70047e9	−0.325174
$599$	1.55890e9	0.296363	0.148181	−	0.988960i	$-0.452658\pi$
$599$	1.55890e9	0.296363	0.148181	+	0.988960i	$0.452658\pi$
$600$	−9.17367e9	−1.73386
$601$	4.38860e9	0.824641	0.412320	−	0.911039i	$-0.364718\pi$
$601$	4.38860e9	0.824641	0.412320	+	0.911039i	$0.364718\pi$
$602$	1.69391e9	0.316449
$603$	2.90422e9	0.539410
$604$	9.99369e8	0.184543
$605$	2.21227e10	4.06158
$606$	1.34151e9	0.244872
$607$	5.88091e9	1.06729	0.533647	−	0.845707i	$-0.320821\pi$
$607$	5.88091e9	1.06729	0.533647	+	0.845707i	$0.320821\pi$
$608$	−5.45285e8	−0.0983924
$609$	2.00523e9	0.359752
$610$	−2.54647e9	−0.454239
$611$	4.82737e8	0.0856182
$612$	−1.98638e9	−0.350293
$613$	−6.80158e9	−1.19261	−0.596305	−	0.802758i	$-0.703365\pi$
$613$	−6.80158e9	−1.19261	−0.596305	+	0.802758i	$0.703365\pi$
$614$	4.58851e9	0.799985
$615$	−4.32496e9	−0.749756
$616$	−4.26977e9	−0.735989
$617$	−1.50540e9	−0.258021	−0.129011	−	0.991643i	$-0.541180\pi$
$617$	−1.50540e9	−0.258021	−0.129011	+	0.991643i	$0.541180\pi$
$618$	4.69639e9	0.800396
$619$	−4.85404e9	−0.822594	−0.411297	−	0.911501i	$-0.634924\pi$
$619$	−4.85404e9	−0.822594	−0.411297	+	0.911501i	$0.634924\pi$
$620$	1.61909e9	0.272835
$621$	−9.09896e9	−1.52465
$622$	5.38187e9	0.896740
$623$	−8.64301e8	−0.143204
$624$	−5.63023e8	−0.0927641
$625$	1.42614e10	2.33658
$626$	7.50821e9	1.22328
$627$	−1.05314e9	−0.170627
$628$	−9.56657e8	−0.154134
$629$	−1.26673e10	−2.02958
$630$	−1.93877e9	−0.308912
$631$	8.91451e9	1.41252	0.706260	−	0.707952i	$-0.250381\pi$
$631$	8.91451e9	1.41252	0.706260	+	0.707952i	$0.250381\pi$
$632$	−7.55646e9	−1.19072
$633$	−7.28496e8	−0.114160
$634$	−4.33615e9	−0.675759
$635$	1.42575e10	2.20971
$636$	−4.80604e8	−0.0740776
$637$	−2.58475e8	−0.0396214
$638$	−1.33787e10	−2.03958
$639$	−3.90906e9	−0.592679
$640$	−1.82852e9	−0.275721
$641$	1.13742e10	1.70575	0.852877	−	0.522111i	$-0.174855\pi$
$641$	1.13742e10	1.70575	0.852877	+	0.522111i	$0.174855\pi$
$642$	−3.40192e8	−0.0507402
$643$	4.72015e9	0.700193	0.350096	−	0.936714i	$-0.386149\pi$
$643$	4.72015e9	0.700193	0.350096	+	0.936714i	$0.386149\pi$
$644$	−1.37431e9	−0.202761
$645$	−8.78134e9	−1.28855
$646$	1.34899e9	0.196878
$647$	−1.24497e10	−1.80715	−0.903573	−	0.428435i	$-0.859065\pi$
$647$	−1.24497e10	−1.80715	−0.903573	+	0.428435i	$0.859065\pi$
$648$	−1.00643e9	−0.145301
$649$	1.45249e10	2.08572
$650$	3.70516e9	0.529189
$651$	−7.19445e8	−0.102203
$652$	−4.77640e9	−0.674891
$653$	2.60748e9	0.366459	0.183230	−	0.983070i	$-0.441345\pi$
$653$	2.60748e9	0.366459	0.183230	+	0.983070i	$0.441345\pi$
$654$	4.78130e9	0.668381
$655$	−2.37739e9	−0.330564
$656$	−2.21974e9	−0.307000
$657$	−3.32124e9	−0.456901
$658$	−6.79624e8	−0.0929990
$659$	5.67746e9	0.772779	0.386389	−	0.922336i	$-0.373722\pi$
$659$	5.67746e9	0.772779	0.386389	+	0.922336i	$0.373722\pi$
$660$	5.91524e9	0.800883
$661$	−8.65893e9	−1.16616	−0.583082	−	0.812414i	$-0.698153\pi$
$661$	−8.65893e9	−1.16616	−0.583082	+	0.812414i	$0.698153\pi$
$662$	1.17756e9	0.157753
$663$	−2.39148e9	−0.318691
$664$	5.93971e8	0.0787367
$665$	−7.55843e8	−0.0996680
$666$	3.97793e9	0.521792
$667$	−1.61138e10	−2.10260
$668$	7.40730e8	0.0961484
$669$	2.11583e9	0.273205
$670$	1.10781e10	1.42300
$671$	4.33384e9	0.553789
$672$	−1.36094e9	−0.173000
$673$	1.84941e9	0.233874	0.116937	−	0.993139i	$-0.462693\pi$
$673$	1.84941e9	0.233874	0.116937	+	0.993139i	$0.462693\pi$
$674$	−1.02865e10	−1.29407
$675$	1.98257e10	2.48123
$676$	−2.25323e8	−0.0280539
$677$	−6.57758e9	−0.814715	−0.407358	−	0.913269i	$-0.633550\pi$
$677$	−6.57758e9	−0.814715	−0.407358	+	0.913269i	$0.633550\pi$
$678$	5.17855e9	0.638122
$679$	1.08850e9	0.133439
$680$	−2.83530e10	−3.45795
$681$	5.61865e9	0.681737
$682$	4.80007e9	0.579432
$683$	9.94130e9	1.19391	0.596954	−	0.802275i	$-0.296377\pi$
$683$	9.94130e9	1.19391	0.596954	+	0.802275i	$0.296377\pi$
$684$	2.43188e8	0.0290566
$685$	−1.81027e10	−2.15193
$686$	3.63896e8	0.0430370
$687$	−4.76178e7	−0.00560300
$688$	−4.50692e9	−0.527619
$689$	7.26361e8	0.0846029
$690$	−1.24108e10	−1.43822
$691$	−2.42744e9	−0.279883	−0.139941	−	0.990160i	$-0.544691\pi$
$691$	−2.42744e9	−0.279883	−0.139941	+	0.990160i	$0.544691\pi$
$692$	−4.08991e9	−0.469183
$693$	3.29959e9	0.376612
$694$	5.79216e9	0.657782
$695$	−1.08732e10	−1.22859
$696$	−9.20897e9	−1.03533
$697$	−9.42849e9	−1.05470
$698$	−1.10015e10	−1.22449
$699$	1.34749e9	0.149230
$700$	2.99449e9	0.329974
$701$	1.34136e9	0.147073	0.0735364	−	0.997293i	$-0.476572\pi$
$701$	1.34136e9	0.147073	0.0735364	+	0.997293i	$0.476572\pi$
$702$	2.10025e9	0.229135
$703$	1.55082e9	0.168352
$704$	1.74045e10	1.88000
$705$	3.52321e9	0.378684
$706$	−1.16147e10	−1.24220
$707$	−1.63861e9	−0.174384
$708$	2.67183e9	0.282939
$709$	−1.44761e10	−1.52542	−0.762709	−	0.646741i	$-0.776131\pi$
$709$	−1.44761e10	−1.52542	−0.762709	+	0.646741i	$0.776131\pi$
$710$	−1.49111e10	−1.56352
$711$	5.83949e9	0.609300
$712$	3.96928e9	0.412128
$713$	5.78137e9	0.597334
$714$	3.36686e9	0.346163
$715$	−8.94002e9	−0.914676
$716$	2.82376e9	0.287496
$717$	8.72738e9	0.884233
$718$	−7.90392e9	−0.796905
$719$	−1.12009e10	−1.12383	−0.561915	−	0.827195i	$-0.689935\pi$
$719$	−1.12009e10	−1.12383	−0.561915	+	0.827195i	$0.689935\pi$
$720$	5.15841e9	0.515053
$721$	−5.73648e9	−0.569997
$722$	7.89549e9	0.780726
$723$	−6.79453e9	−0.668614
$724$	−2.04255e9	−0.200026
$725$	3.51103e10	3.42177
$726$	1.20646e10	1.17013
$727$	7.48529e9	0.722500	0.361250	−	0.932469i	$-0.382350\pi$
$727$	7.48529e9	0.722500	0.361250	+	0.932469i	$0.382350\pi$
$728$	1.18704e9	0.114027
$729$	7.99736e9	0.764540
$730$	−1.26688e10	−1.20533
$731$	−1.91435e10	−1.81263
$732$	7.97204e8	0.0751243
$733$	−1.41623e10	−1.32822	−0.664108	−	0.747636i	$-0.731189\pi$
$733$	−1.41623e10	−1.32822	−0.664108	+	0.747636i	$0.731189\pi$
$734$	1.16265e10	1.08521
$735$	−1.88646e9	−0.175243
$736$	1.09363e10	1.01111
$737$	−1.88538e10	−1.73486
$738$	2.96085e9	0.271156
$739$	6.27079e9	0.571566	0.285783	−	0.958294i	$-0.407746\pi$
$739$	6.27079e9	0.571566	0.285783	+	0.958294i	$0.407746\pi$
$740$	−8.71065e9	−0.790205
$741$	2.92783e8	0.0264352
$742$	−1.02261e9	−0.0918962
$743$	2.02771e10	1.81361	0.906806	−	0.421549i	$-0.138513\pi$
$743$	2.02771e10	1.81361	0.906806	+	0.421549i	$0.138513\pi$
$744$	3.30404e9	0.294130
$745$	4.78842e9	0.424273
$746$	1.64712e10	1.45258
$747$	−4.59010e8	−0.0402902
$748$	1.28953e10	1.12662
$749$	4.15533e8	0.0361343
$750$	1.57453e10	1.36282
$751$	−1.89816e10	−1.63528	−0.817641	−	0.575728i	$-0.804719\pi$
$751$	−1.89816e10	−1.63528	−0.817641	+	0.575728i	$0.804719\pi$
$752$	1.80825e9	0.155058
$753$	5.50495e9	0.469863
$754$	3.71942e9	0.315992
$755$	−1.10235e10	−0.932193
$756$	1.69741e9	0.142876
$757$	−2.21780e10	−1.85818	−0.929088	−	0.369859i	$-0.879406\pi$
$757$	−2.21780e10	−1.85818	−0.929088	+	0.369859i	$0.879406\pi$
$758$	1.03964e10	0.867042
$759$	2.11219e10	1.75342
$760$	3.47120e9	0.286835
$761$	1.84051e9	0.151388	0.0756941	−	0.997131i	$-0.475883\pi$
$761$	1.84051e9	0.151388	0.0756941	+	0.997131i	$0.475883\pi$
$762$	7.77529e9	0.636611
$763$	−5.84019e9	−0.475983
$764$	−1.87358e9	−0.152000
$765$	2.19107e10	1.76946
$766$	1.53039e10	1.23027
$767$	−4.03808e9	−0.323140
$768$	7.78136e9	0.619857
$769$	−1.36206e10	−1.08008	−0.540039	−	0.841640i	$-0.681591\pi$
$769$	−1.36206e10	−1.08008	−0.540039	+	0.841640i	$0.681591\pi$
$770$	1.25863e10	0.993526
$771$	1.26735e10	0.995879
$772$	−4.71708e8	−0.0368989
$773$	−7.27210e9	−0.566280	−0.283140	−	0.959079i	$-0.591376\pi$
$773$	−7.27210e9	−0.566280	−0.283140	+	0.959079i	$0.591376\pi$
$774$	6.01166e9	0.466017
$775$	−1.25970e10	−0.972102
$776$	−4.99891e9	−0.384024
$777$	3.87059e9	0.296008
$778$	−1.53236e10	−1.16663
$779$	1.15431e9	0.0874864
$780$	−1.64450e9	−0.124080
$781$	2.53771e10	1.90618
$782$	−2.70556e10	−2.02318
$783$	1.99020e10	1.48160
$784$	−9.68202e8	−0.0717562
$785$	1.05524e10	0.778586
$786$	−1.29650e9	−0.0952345
$787$	−1.79668e10	−1.31389	−0.656947	−	0.753937i	$-0.728152\pi$
$787$	−1.79668e10	−1.31389	−0.656947	+	0.753937i	$0.728152\pi$
$788$	−3.15405e9	−0.229629
$789$	1.71731e9	0.124474
$790$	2.22747e10	1.60737
$791$	−6.32541e9	−0.454435
$792$	−1.51533e10	−1.08385
$793$	−1.20486e9	−0.0857983
$794$	2.71773e9	0.192679
$795$	5.30128e9	0.374193
$796$	2.07432e9	0.145774
$797$	1.64795e10	1.15303	0.576515	−	0.817086i	$-0.304412\pi$
$797$	1.64795e10	1.15303	0.576515	+	0.817086i	$0.304412\pi$
$798$	−4.12197e8	−0.0287141
$799$	7.68065e9	0.532702
$800$	−2.38292e10	−1.64549
$801$	−3.06739e9	−0.210889
$802$	−8.83091e9	−0.604498
$803$	2.15611e10	1.46949
$804$	−3.46813e9	−0.235342
$805$	1.51593e10	1.02422
$806$	−1.33447e9	−0.0897712
$807$	−3.53781e9	−0.236961
$808$	7.52527e9	0.501860
$809$	−1.46761e10	−0.974522	−0.487261	−	0.873257i	$-0.662004\pi$
$809$	−1.46761e10	−0.974522	−0.487261	+	0.873257i	$0.662004\pi$
$810$	2.96671e9	0.196145
$811$	−1.50378e10	−0.989947	−0.494974	−	0.868908i	$-0.664822\pi$
$811$	−1.50378e10	−0.989947	−0.494974	+	0.868908i	$0.664822\pi$
$812$	3.00602e9	0.197036
$813$	−2.98594e9	−0.194879
$814$	−2.58242e10	−1.67819
$815$	5.26859e10	3.40912
$816$	−8.95806e9	−0.577163
$817$	2.34369e9	0.150357
$818$	7.83342e9	0.500397
$819$	−9.17323e8	−0.0583483
$820$	−6.48351e9	−0.410640
$821$	2.19601e10	1.38495	0.692473	−	0.721443i	$-0.256521\pi$
$821$	2.19601e10	1.38495	0.692473	+	0.721443i	$0.256521\pi$
$822$	−9.87227e9	−0.619963
$823$	−2.26640e10	−1.41722	−0.708610	−	0.705600i	$-0.750677\pi$
$823$	−2.26640e10	−1.41722	−0.708610	+	0.705600i	$0.750677\pi$
$824$	2.63447e10	1.64039
$825$	−4.60225e10	−2.85352
$826$	5.68504e9	0.350997
$827$	1.66495e10	1.02360	0.511802	−	0.859103i	$-0.328978\pi$
$827$	1.66495e10	1.02360	0.511802	+	0.859103i	$0.328978\pi$
$828$	−4.87741e9	−0.298595
$829$	2.55546e10	1.55786	0.778929	−	0.627112i	$-0.215763\pi$
$829$	2.55546e10	1.55786	0.778929	+	0.627112i	$0.215763\pi$
$830$	−1.75089e9	−0.106288
$831$	9.05047e9	0.547101
$832$	−4.83865e9	−0.291268
$833$	−4.11250e9	−0.246518
$834$	−5.92964e9	−0.353954
$835$	−8.17060e9	−0.485681
$836$	−1.57874e9	−0.0934523
$837$	−7.14055e9	−0.420913
$838$	−3.00295e8	−0.0176276
$839$	−1.79450e10	−1.04901	−0.524503	−	0.851409i	$-0.675749\pi$
$839$	−1.79450e10	−1.04901	−0.524503	+	0.851409i	$0.675749\pi$
$840$	8.66351e9	0.504332
$841$	1.79955e10	1.04323
$842$	−2.09836e10	−1.21140
$843$	−8.35801e9	−0.480514
$844$	−1.09208e9	−0.0625254
$845$	2.48542e9	0.141710
$846$	−2.41197e9	−0.136955
$847$	−1.47365e10	−0.833300
$848$	2.72082e9	0.153220
$849$	−3.45954e9	−0.194018
$850$	5.89516e10	3.29252
$851$	−3.11036e10	−1.73004
$852$	4.66809e9	0.258583
$853$	2.14748e10	1.18470	0.592348	−	0.805683i	$-0.298201\pi$
$853$	2.14748e10	1.18470	0.592348	+	0.805683i	$0.298201\pi$
$854$	1.69626e9	0.0931946
$855$	−2.68247e9	−0.146776
$856$	−1.90833e9	−0.103991
$857$	−1.27782e10	−0.693483	−0.346742	−	0.937961i	$-0.612712\pi$
$857$	−1.27782e10	−0.693483	−0.346742	+	0.937961i	$0.612712\pi$
$858$	−4.87541e9	−0.263515
$859$	2.68912e10	1.44755	0.723777	−	0.690034i	$-0.242404\pi$
$859$	2.68912e10	1.44755	0.723777	+	0.690034i	$0.242404\pi$
$860$	−1.31640e10	−0.705738
$861$	2.88096e9	0.153825
$862$	1.47436e10	0.784024
$863$	1.01035e9	0.0535097	0.0267549	−	0.999642i	$-0.491483\pi$
$863$	1.01035e9	0.0535097	0.0267549	+	0.999642i	$0.491483\pi$
$864$	−1.35074e10	−0.712483
$865$	4.51136e10	2.37001
$866$	−4.03110e9	−0.210917
$867$	−2.52720e10	−1.31696
$868$	−1.07851e9	−0.0559765
$869$	−3.79093e10	−1.95964
$870$	2.71459e10	1.39761
$871$	5.24157e9	0.268781
$872$	2.68210e10	1.36983
$873$	3.86306e9	0.196509
$874$	3.31236e9	0.167821
$875$	−1.92324e10	−0.970521
$876$	3.96613e9	0.199344
$877$	1.70486e9	0.0853473	0.0426736	−	0.999089i	$-0.486412\pi$
$877$	1.70486e9	0.0853473	0.0426736	+	0.999089i	$0.486412\pi$
$878$	−2.58867e9	−0.129076
$879$	2.06628e9	0.102619
$880$	−3.34877e10	−1.65652
$881$	−1.81646e10	−0.894973	−0.447486	−	0.894291i	$-0.647681\pi$
$881$	−1.81646e10	−0.894973	−0.447486	+	0.894291i	$0.647681\pi$
$882$	1.29146e9	0.0633783
$883$	−2.97037e7	−0.00145194	−0.000725970	−	1.00000i	$-0.500231\pi$
$883$	−2.97037e7	−0.00145194	−0.000725970		1.00000i	$0.500231\pi$
$884$	−3.58504e9	−0.174546
$885$	−2.94716e10	−1.42923
$886$	−1.16983e10	−0.565073
$887$	−1.68868e10	−0.812485	−0.406243	−	0.913765i	$-0.633161\pi$
$887$	−1.68868e10	−0.812485	−0.406243	+	0.913765i	$0.633161\pi$
$888$	−1.77756e10	−0.851882
$889$	−9.49725e9	−0.453359
$890$	−1.17005e10	−0.556340
$891$	−5.04904e9	−0.239131
$892$	3.17181e9	0.149634
$893$	−9.40325e8	−0.0441873
$894$	2.61135e9	0.122232
$895$	−3.11474e10	−1.45225
$896$	1.21802e9	0.0565686
$897$	−5.87211e9	−0.271657
$898$	−4.09518e9	−0.188715
$899$	−1.26455e10	−0.580467
$900$	1.06274e10	0.485935
$901$	1.15569e10	0.526385
$902$	−1.92215e10	−0.872095
$903$	5.84945e9	0.264367
$904$	2.90494e10	1.30782
$905$	2.25302e10	1.01041
$906$	−6.01164e9	−0.268562
$907$	1.20508e9	0.0536277	0.0268138	−	0.999640i	$-0.491464\pi$
$907$	1.20508e9	0.0536277	0.0268138	+	0.999640i	$0.491464\pi$
$908$	8.42285e9	0.373387
$909$	−5.81539e9	−0.256806
$910$	−3.49912e9	−0.153927
$911$	−1.57155e10	−0.688673	−0.344336	−	0.938846i	$-0.611896\pi$
$911$	−1.57155e10	−0.688673	−0.344336	+	0.938846i	$0.611896\pi$
$912$	1.09672e9	0.0478753
$913$	2.97983e9	0.129582
$914$	1.20229e10	0.520832
$915$	−8.79353e9	−0.379481
$916$	−7.13834e7	−0.00306876
$917$	1.58363e9	0.0678206
$918$	3.34163e10	1.42564
$919$	−1.73982e10	−0.739436	−0.369718	−	0.929144i	$-0.620546\pi$
$919$	−1.73982e10	−0.739436	−0.369718	+	0.929144i	$0.620546\pi$
$920$	−6.96189e10	−2.94761
$921$	1.58451e10	0.668323
$922$	8.09549e9	0.340161
$923$	−7.05512e9	−0.295324
$924$	−3.94028e9	−0.164314
$925$	6.77716e10	2.81548
$926$	2.37892e10	0.984560
$927$	−2.03587e10	−0.839403
$928$	−2.39209e10	−0.982561
$929$	−2.22751e10	−0.911515	−0.455758	−	0.890104i	$-0.650632\pi$
$929$	−2.22751e10	−0.911515	−0.455758	+	0.890104i	$0.650632\pi$
$930$	−9.73953e9	−0.397052
$931$	5.03484e8	0.0204485
$932$	2.02001e9	0.0817332
$933$	1.85848e10	0.749155
$934$	−3.19030e10	−1.28120
$935$	−1.42241e11	−5.69096
$936$	4.21279e9	0.167921
$937$	3.20843e10	1.27410	0.637050	−	0.770822i	$-0.280154\pi$
$937$	3.20843e10	1.27410	0.637050	+	0.770822i	$0.280154\pi$
$938$	−7.37938e9	−0.291951
$939$	2.59275e10	1.02195
$940$	5.28161e9	0.207405
$941$	9.25093e9	0.361928	0.180964	−	0.983490i	$-0.442078\pi$
$941$	9.25093e9	0.361928	0.180964	+	0.983490i	$0.442078\pi$
$942$	5.75471e9	0.224308
$943$	−2.31510e10	−0.899039
$944$	−1.51259e10	−0.585222
$945$	−1.87232e10	−0.721721
$946$	−3.90270e10	−1.49881
$947$	5.02352e10	1.92213	0.961065	−	0.276321i	$-0.0891154\pi$
$947$	5.02352e10	1.92213	0.961065	+	0.276321i	$0.0891154\pi$
$948$	−6.97335e9	−0.265835
$949$	−5.99422e9	−0.227668
$950$	−7.21730e9	−0.273113
$951$	−1.49737e10	−0.564542
$952$	1.88866e10	0.709454
$953$	−1.44437e10	−0.540572	−0.270286	−	0.962780i	$-0.587118\pi$
$953$	−1.44437e10	−0.540572	−0.270286	+	0.962780i	$0.587118\pi$
$954$	−3.62923e9	−0.135330
$955$	2.06664e10	0.767809
$956$	1.30831e10	0.484293
$957$	−4.61996e10	−1.70391
$958$	−7.46233e8	−0.0274218
$959$	1.20586e10	0.441503
$960$	−3.53144e10	−1.28826
$961$	−2.29756e10	−0.835093
$962$	7.17942e9	0.260002
$963$	1.47472e9	0.0532130
$964$	−1.01856e10	−0.366199
$965$	5.20316e9	0.186390
$966$	8.26709e9	0.295075
$967$	2.73676e10	0.973294	0.486647	−	0.873599i	$-0.338220\pi$
$967$	2.73676e10	0.973294	0.486647	+	0.873599i	$0.338220\pi$
$968$	6.76769e10	2.39815
$969$	4.65837e9	0.164475
$970$	1.47356e10	0.518402
$971$	−3.81575e10	−1.33756	−0.668778	−	0.743462i	$-0.733182\pi$
$971$	−3.81575e10	−1.33756	−0.668778	+	0.743462i	$0.733182\pi$
$972$	9.89407e9	0.345576
$973$	7.24285e9	0.252066
$974$	1.11753e10	0.387528
$975$	1.27947e10	0.442095
$976$	−4.51318e9	−0.155385
$977$	−3.87522e10	−1.32943	−0.664714	−	0.747098i	$-0.731447\pi$
$977$	−3.87522e10	−1.32943	−0.664714	+	0.747098i	$0.731447\pi$
$978$	2.87321e10	0.982158
$979$	1.99131e10	0.678265
$980$	−2.82797e9	−0.0959804
$981$	−2.07267e10	−0.700954
$982$	3.50368e10	1.18068
$983$	7.60016e9	0.255203	0.127601	−	0.991826i	$-0.459272\pi$
$983$	7.60016e9	0.255203	0.127601	+	0.991826i	$0.459272\pi$
$984$	−1.32307e10	−0.442692
$985$	3.47906e10	1.15994
$986$	5.91784e10	1.96605
$987$	−2.34689e9	−0.0776932
$988$	4.38908e8	0.0144785
$989$	−4.70054e10	−1.54512
$990$	4.46684e10	1.46311
$991$	−1.32601e9	−0.0432802	−0.0216401	−	0.999766i	$-0.506889\pi$
$991$	−1.32601e9	−0.0432802	−0.0216401	+	0.999766i	$0.506889\pi$
$992$	8.58245e9	0.279139
$993$	4.06636e9	0.131790
$994$	9.93260e9	0.320782
$995$	−2.28807e10	−0.736359
$996$	5.48136e8	0.0175784
$997$	4.39501e10	1.40452	0.702258	−	0.711922i	$-0.252175\pi$
$997$	4.39501e10	1.40452	0.702258	+	0.711922i	$0.252175\pi$
$998$	8.73101e9	0.278040
$999$	3.84159e10	1.21908

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	91.8.a.d.1.3	✓	10

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

\(f(q)\)	\(=\)	\(q-9.01767 q^{2} -31.1400 q^{3} -46.6816 q^{4} +514.920 q^{5} +280.810 q^{6} -343.000 q^{7} +1575.22 q^{8} -1217.30 q^{9} +O(q^{10})\)	\(q-9.01767 q^{2} -31.1400 q^{3} -46.6816 q^{4} +514.920 q^{5} +280.810 q^{6} -343.000 q^{7} +1575.22 q^{8} -1217.30 q^{9} -4643.38 q^{10} +7902.57 q^{11} +1453.67 q^{12} -2197.00 q^{13} +3093.06 q^{14} -16034.6 q^{15} -8229.58 q^{16} -34955.7 q^{17} +10977.2 q^{18} +4279.55 q^{19} -24037.3 q^{20} +10681.0 q^{21} -71262.8 q^{22} -85831.3 q^{23} -49052.4 q^{24} +187018. q^{25} +19811.8 q^{26} +106010. q^{27} +16011.8 q^{28} +187738. q^{29} +144595. q^{30} -67357.4 q^{31} -127417. q^{32} -246086. q^{33} +315219. q^{34} -176618. q^{35} +56825.6 q^{36} +362381. q^{37} -38591.5 q^{38} +68414.6 q^{39} +811113. q^{40} +269727. q^{41} -96317.9 q^{42} +547649. q^{43} -368905. q^{44} -626813. q^{45} +773998. q^{46} -219725. q^{47} +256269. q^{48} +117649. q^{49} -1.68646e6 q^{50} +1.08852e6 q^{51} +102560. q^{52} -330615. q^{53} -955962. q^{54} +4.06919e6 q^{55} -540301. q^{56} -133265. q^{57} -1.69296e6 q^{58} +1.83800e6 q^{59} +748522. q^{60} +548410. q^{61} +607406. q^{62} +417534. q^{63} +2.20239e6 q^{64} -1.13128e6 q^{65} +2.21912e6 q^{66} -2.38579e6 q^{67} +1.63179e6 q^{68} +2.67278e6 q^{69} +1.59268e6 q^{70} +3.21125e6 q^{71} -1.91752e6 q^{72} +2.72837e6 q^{73} -3.26783e6 q^{74} -5.82373e6 q^{75} -199776. q^{76} -2.71058e6 q^{77} -616940. q^{78} -4.79708e6 q^{79} -4.23758e6 q^{80} -638911. q^{81} -2.43231e6 q^{82} +377072. q^{83} -498607. q^{84} -1.79994e7 q^{85} -4.93852e6 q^{86} -5.84615e6 q^{87} +1.24483e7 q^{88} +2.51983e6 q^{89} +5.65239e6 q^{90} +753571. q^{91} +4.00674e6 q^{92} +2.09751e6 q^{93} +1.98141e6 q^{94} +2.20362e6 q^{95} +3.96775e6 q^{96} -3.17346e6 q^{97} -1.06092e6 q^{98} -9.61981e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q - 3 q^{2} - 101 q^{3} + 361 q^{4} + 226 q^{5} + 1105 q^{6} - 3430 q^{7} + 291 q^{8} + 12247 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

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