LMFDB - Embedded newform 43.8.a.b.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,8,Mod(1,43)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("43.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	43.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:	$13.4325560958$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 3 x^{12} - 1279 x^{11} + 3765 x^{10} + 598742 x^{9} - 1518614 x^{8} - 124677082 x^{7} + \cdots + 1551032970660 $ x^13 - 3x^12 - 1279x^11 + 3765x^10 + 598742x^9 - 1518614x^8 - 124677082x^7 + 193428526x^6 + 11160446785x^5 + 1754605765x^4 - 349352939351x^3 - 481872751923x^2 + 2098464001560x + 1551032970660
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-16.1540$ of defining polynomial
Character	$\chi$	$=$	43.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-15.1540 q^{2} +48.8090 q^{3} +101.645 q^{4} +210.950 q^{5} -739.653 q^{6} +1100.87 q^{7} +399.390 q^{8} +195.321 q^{9} +O(q^{10})$	\(q-15.1540 q^{2} +48.8090 q^{3} +101.645 q^{4} +210.950 q^{5} -739.653 q^{6} +1100.87 q^{7} +399.390 q^{8} +195.321 q^{9} -3196.74 q^{10} -3136.09 q^{11} +4961.17 q^{12} -5743.36 q^{13} -16682.6 q^{14} +10296.3 q^{15} -19062.9 q^{16} +27231.5 q^{17} -2959.90 q^{18} +54685.6 q^{19} +21441.9 q^{20} +53732.2 q^{21} +47524.4 q^{22} +12024.9 q^{23} +19493.9 q^{24} -33625.2 q^{25} +87035.1 q^{26} -97211.9 q^{27} +111897. q^{28} +132127. q^{29} -156030. q^{30} +281517. q^{31} +237758. q^{32} -153070. q^{33} -412666. q^{34} +232228. q^{35} +19853.3 q^{36} -214511. q^{37} -828707. q^{38} -280328. q^{39} +84251.4 q^{40} +302212. q^{41} -814260. q^{42} -79507.0 q^{43} -318767. q^{44} +41202.9 q^{45} -182226. q^{46} +235041. q^{47} -930441. q^{48} +388365. q^{49} +509557. q^{50} +1.32914e6 q^{51} -583782. q^{52} +55032.5 q^{53} +1.47315e6 q^{54} -661558. q^{55} +439676. q^{56} +2.66915e6 q^{57} -2.00226e6 q^{58} +150144. q^{59} +1.04656e6 q^{60} -1.65598e6 q^{61} -4.26612e6 q^{62} +215022. q^{63} -1.16294e6 q^{64} -1.21156e6 q^{65} +2.31962e6 q^{66} +1.76796e6 q^{67} +2.76793e6 q^{68} +586923. q^{69} -3.51919e6 q^{70} +3.57159e6 q^{71} +78009.3 q^{72} -430044. q^{73} +3.25070e6 q^{74} -1.64121e6 q^{75} +5.55849e6 q^{76} -3.45242e6 q^{77} +4.24810e6 q^{78} -7.44014e6 q^{79} -4.02131e6 q^{80} -5.17199e6 q^{81} -4.57974e6 q^{82} +5.50388e6 q^{83} +5.46159e6 q^{84} +5.74447e6 q^{85} +1.20485e6 q^{86} +6.44900e6 q^{87} -1.25252e6 q^{88} -3.53700e6 q^{89} -624390. q^{90} -6.32268e6 q^{91} +1.22227e6 q^{92} +1.37406e7 q^{93} -3.56182e6 q^{94} +1.15359e7 q^{95} +1.16047e7 q^{96} -2.08749e6 q^{97} -5.88530e6 q^{98} -612544. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9}+O(q^{10}) $ 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9	\( 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9} + 4667 q^{10} + 1620 q^{11} - 19681 q^{12} + 13550 q^{13} + 44160 q^{14} + 31412 q^{15} + 114026 q^{16} + 110880 q^{17} + 159267 q^{18} + 105058 q^{19} + 167251 q^{20} + 129840 q^{21} + 201504 q^{22} + 160184 q^{23} + 161289 q^{24} + 270149 q^{25} + 272104 q^{26} + 252544 q^{27} + 208172 q^{28} + 285546 q^{29} + 107580 q^{30} - 99616 q^{31} + 200126 q^{32} + 531468 q^{33} - 80941 q^{34} - 187104 q^{35} - 608975 q^{36} + 176038 q^{37} + 652165 q^{38} - 794680 q^{39} - 895387 q^{40} - 410260 q^{41} - 3413218 q^{42} - 1033591 q^{43} - 2177076 q^{44} - 1051178 q^{45} - 3975765 q^{46} - 424556 q^{47} - 2360477 q^{48} - 1561359 q^{49} - 4063801 q^{50} - 2375738 q^{51} - 4172312 q^{52} + 3992458 q^{53} - 10438626 q^{54} + 406960 q^{55} + 1559556 q^{56} - 3116152 q^{57} - 4052005 q^{58} + 2248836 q^{59} - 2911436 q^{60} + 6210394 q^{61} + 885317 q^{62} + 11622368 q^{63} - 3096318 q^{64} + 5600420 q^{65} - 2174604 q^{66} - 1993648 q^{67} + 9327135 q^{68} + 13366240 q^{69} - 1105098 q^{70} + 4978064 q^{71} + 11370663 q^{72} + 8224814 q^{73} - 3613563 q^{74} + 27115592 q^{75} + 10687121 q^{76} + 17261892 q^{77} - 15226630 q^{78} + 6945708 q^{79} + 15822799 q^{80} + 35113185 q^{81} - 508449 q^{82} + 22937328 q^{83} - 14010106 q^{84} - 575532 q^{85} - 1272112 q^{86} + 9081380 q^{87} + 11202656 q^{88} + 9291302 q^{89} + 2841402 q^{90} + 25581108 q^{91} - 14388137 q^{92} + 25930480 q^{93} - 24645805 q^{94} + 30750464 q^{95} - 22461255 q^{96} + 10001852 q^{97} - 32304856 q^{98} + 5055452 q^{99}+O(q^{100}) \) 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9 + 4667 * q^10 + 1620 * q^11 - 19681 * q^12 + 13550 * q^13 + 44160 * q^14 + 31412 * q^15 + 114026 * q^16 + 110880 * q^17 + 159267 * q^18 + 105058 * q^19 + 167251 * q^20 + 129840 * q^21 + 201504 * q^22 + 160184 * q^23 + 161289 * q^24 + 270149 * q^25 + 272104 * q^26 + 252544 * q^27 + 208172 * q^28 + 285546 * q^29 + 107580 * q^30 - 99616 * q^31 + 200126 * q^32 + 531468 * q^33 - 80941 * q^34 - 187104 * q^35 - 608975 * q^36 + 176038 * q^37 + 652165 * q^38 - 794680 * q^39 - 895387 * q^40 - 410260 * q^41 - 3413218 * q^42 - 1033591 * q^43 - 2177076 * q^44 - 1051178 * q^45 - 3975765 * q^46 - 424556 * q^47 - 2360477 * q^48 - 1561359 * q^49 - 4063801 * q^50 - 2375738 * q^51 - 4172312 * q^52 + 3992458 * q^53 - 10438626 * q^54 + 406960 * q^55 + 1559556 * q^56 - 3116152 * q^57 - 4052005 * q^58 + 2248836 * q^59 - 2911436 * q^60 + 6210394 * q^61 + 885317 * q^62 + 11622368 * q^63 - 3096318 * q^64 + 5600420 * q^65 - 2174604 * q^66 - 1993648 * q^67 + 9327135 * q^68 + 13366240 * q^69 - 1105098 * q^70 + 4978064 * q^71 + 11370663 * q^72 + 8224814 * q^73 - 3613563 * q^74 + 27115592 * q^75 + 10687121 * q^76 + 17261892 * q^77 - 15226630 * q^78 + 6945708 * q^79 + 15822799 * q^80 + 35113185 * q^81 - 508449 * q^82 + 22937328 * q^83 - 14010106 * q^84 - 575532 * q^85 - 1272112 * q^86 + 9081380 * q^87 + 11202656 * q^88 + 9291302 * q^89 + 2841402 * q^90 + 25581108 * q^91 - 14388137 * q^92 + 25930480 * q^93 - 24645805 * q^94 + 30750464 * q^95 - 22461255 * q^96 + 10001852 * q^97 - 32304856 * q^98 + 5055452 * 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 $

$2$	−15.1540	−1.33944	−0.669720	−	0.742614i	$-0.733586\pi$
$2$	−15.1540	−1.33944	−0.669720	+	0.742614i	$0.733586\pi$
$3$	48.8090	1.04370	0.521850	−	0.853037i	$-0.325242\pi$
$3$	48.8090	1.04370	0.521850	+	0.853037i	$0.325242\pi$
$4$	101.645	0.794098
$5$	210.950	0.754717	0.377359	−	0.926067i	$-0.376832\pi$
$5$	210.950	0.754717	0.377359	+	0.926067i	$0.376832\pi$
$6$	−739.653	−1.39797
$7$	1100.87	1.21309	0.606543	−	0.795051i	$-0.292556\pi$
$7$	1100.87	1.21309	0.606543	+	0.795051i	$0.292556\pi$
$8$	399.390	0.275793
$9$	195.321	0.0893100
$10$	−3196.74	−1.01090
$11$	−3136.09	−0.710419	−0.355209	−	0.934787i	$-0.615590\pi$
$11$	−3136.09	−0.710419	−0.355209	+	0.934787i	$0.615590\pi$
$12$	4961.17	0.828801
$13$	−5743.36	−0.725044	−0.362522	−	0.931975i	$-0.618084\pi$
$13$	−5743.36	−0.725044	−0.362522	+	0.931975i	$0.618084\pi$
$14$	−16682.6	−1.62486
$15$	10296.3	0.787698
$16$	−19062.9	−1.16351
$17$	27231.5	1.34431	0.672155	−	0.740410i	$-0.265369\pi$
$17$	27231.5	1.34431	0.672155	+	0.740410i	$0.265369\pi$
$18$	−2959.90	−0.119625
$19$	54685.6	1.82909	0.914545	−	0.404484i	$-0.132549\pi$
$19$	54685.6	1.82909	0.914545	+	0.404484i	$0.132549\pi$
$20$	21441.9	0.599320
$21$	53732.2	1.26610
$22$	47524.4	0.951563
$23$	12024.9	0.206079	0.103040	−	0.994677i	$-0.467143\pi$
$23$	12024.9	0.206079	0.103040	+	0.994677i	$0.467143\pi$
$24$	19493.9	0.287845
$25$	−33625.2	−0.430402
$26$	87035.1	0.971153
$27$	−97211.9	−0.950487
$28$	111897.	0.963310
$29$	132127.	1.00600	0.503001	−	0.864286i	$-0.332229\pi$
$29$	132127.	1.00600	0.503001	+	0.864286i	$0.332229\pi$
$30$	−156030.	−1.05507
$31$	281517.	1.69722	0.848612	−	0.529016i	$-0.177439\pi$
$31$	281517.	1.69722	0.848612	+	0.529016i	$0.177439\pi$
$32$	237758.	1.28265
$33$	−153070.	−0.741464
$34$	−412666.	−1.80062
$35$	232228.	0.915537
$36$	19853.3	0.0709209
$37$	−214511.	−0.696215	−0.348107	−	0.937455i	$-0.613176\pi$
$37$	−214511.	−0.696215	−0.348107	+	0.937455i	$0.613176\pi$
$38$	−828707.	−2.44996
$39$	−280328.	−0.756729
$40$	84251.4	0.208145
$41$	302212.	0.684808	0.342404	−	0.939553i	$-0.388759\pi$
$41$	302212.	0.684808	0.342404	+	0.939553i	$0.388759\pi$
$42$	−814260.	−1.69586
$43$	−79507.0	−0.152499
$43$	−79507.0	−0.152499
$44$	−318767.	−0.564142
$45$	41202.9	0.0674038
$46$	−182226.	−0.276030
$47$	235041.	0.330218	0.165109	−	0.986275i	$-0.447202\pi$
$47$	235041.	0.330218	0.165109	+	0.986275i	$0.447202\pi$
$48$	−930441.	−1.21435
$49$	388365.	0.471578
$50$	509557.	0.576498
$51$	1.32914e6	1.40306
$52$	−583782.	−0.575757
$53$	55032.5	0.0507754	0.0253877	−	0.999678i	$-0.491918\pi$
$53$	55032.5	0.0507754	0.0253877	+	0.999678i	$0.491918\pi$
$54$	1.47315e6	1.27312
$55$	−661558.	−0.536165
$56$	439676.	0.334560
$57$	2.66915e6	1.90902
$58$	−2.00226e6	−1.34748
$59$	150144.	0.0951754	0.0475877	−	0.998867i	$-0.484847\pi$
$59$	150144.	0.0951754	0.0475877	+	0.998867i	$0.484847\pi$
$60$	1.04656e6	0.625510
$61$	−1.65598e6	−0.934113	−0.467057	−	0.884227i	$-0.654686\pi$
$61$	−1.65598e6	−0.934113	−0.467057	+	0.884227i	$0.654686\pi$
$62$	−4.26612e6	−2.27333
$63$	215022.	0.108341
$64$	−1.16294e6	−0.554531
$65$	−1.21156e6	−0.547203
$66$	2.31962e6	0.993146
$67$	1.76796e6	0.718144	0.359072	−	0.933310i	$-0.383093\pi$
$67$	1.76796e6	0.718144	0.359072	+	0.933310i	$0.383093\pi$
$68$	2.76793e6	1.06752
$69$	586923.	0.215085
$70$	−3.51919e6	−1.22631
$71$	3.57159e6	1.18429	0.592144	−	0.805832i	$-0.298282\pi$
$71$	3.57159e6	1.18429	0.592144	+	0.805832i	$0.298282\pi$
$72$	78009.3	0.0246310
$73$	−430044.	−0.129385	−0.0646923	−	0.997905i	$-0.520607\pi$
$73$	−430044.	−0.129385	−0.0646923	+	0.997905i	$0.520607\pi$
$74$	3.25070e6	0.932538
$75$	−1.64121e6	−0.449211
$76$	5.55849e6	1.45248
$77$	−3.45242e6	−0.861799
$78$	4.24810e6	1.01359
$79$	−7.44014e6	−1.69780	−0.848900	−	0.528554i	$-0.822734\pi$
$79$	−7.44014e6	−1.69780	−0.848900	+	0.528554i	$0.822734\pi$
$80$	−4.02131e6	−0.878118
$81$	−5.17199e6	−1.08133
$82$	−4.57974e6	−0.917259
$83$	5.50388e6	1.05656	0.528282	−	0.849069i	$-0.322837\pi$
$83$	5.50388e6	1.05656	0.528282	+	0.849069i	$0.322837\pi$
$84$	5.46159e6	1.00541
$85$	5.74447e6	1.01457
$86$	1.20485e6	0.204263
$87$	6.44900e6	1.04996
$88$	−1.25252e6	−0.195928
$89$	−3.53700e6	−0.531826	−0.265913	−	0.963997i	$-0.585673\pi$
$89$	−3.53700e6	−0.531826	−0.265913	+	0.963997i	$0.585673\pi$
$90$	−624390.	−0.0902833
$91$	−6.32268e6	−0.879541
$92$	1.22227e6	0.163647
$93$	1.37406e7	1.77139
$94$	−3.56182e6	−0.442308
$95$	1.15359e7	1.38045
$96$	1.16047e7	1.33871
$97$	−2.08749e6	−0.232233	−0.116117	−	0.993236i	$-0.537045\pi$
$97$	−2.08749e6	−0.232233	−0.116117	+	0.993236i	$0.537045\pi$
$98$	−5.88530e6	−0.631651
$99$	−612544.	−0.0634475
$100$	−3.41782e6	−0.341782
$101$	1.59947e7	1.54473	0.772364	−	0.635180i	$-0.219074\pi$
$101$	1.59947e7	1.54473	0.772364	+	0.635180i	$0.219074\pi$
$102$	−2.01418e7	−1.87931
$103$	−1.14391e7	−1.03148	−0.515739	−	0.856746i	$-0.672483\pi$
$103$	−1.14391e7	−1.03148	−0.515739	+	0.856746i	$0.672483\pi$
$104$	−2.29384e6	−0.199962
$105$	1.13348e7	0.955546
$106$	−833964.	−0.0680106
$107$	5.13105e6	0.404914	0.202457	−	0.979291i	$-0.435107\pi$
$107$	5.13105e6	0.404914	0.202457	+	0.979291i	$0.435107\pi$
$108$	−9.88107e6	−0.754781
$109$	−2.10496e7	−1.55687	−0.778433	−	0.627727i	$-0.783985\pi$
$109$	−2.10496e7	−1.55687	−0.778433	+	0.627727i	$0.783985\pi$
$110$	1.00253e7	0.718161
$111$	−1.04701e7	−0.726639
$112$	−2.09857e7	−1.41143
$113$	−1.44050e7	−0.939156	−0.469578	−	0.882891i	$-0.655594\pi$
$113$	−1.44050e7	−0.939156	−0.469578	+	0.882891i	$0.655594\pi$
$114$	−4.04484e7	−2.55702
$115$	2.53665e6	0.155531
$116$	1.34300e7	0.798865
$117$	−1.12180e6	−0.0647537
$118$	−2.27528e6	−0.127482
$119$	2.99782e7	1.63077
$120$	4.11223e6	0.217241
$121$	−9.65210e6	−0.495306
$122$	2.50947e7	1.25119
$123$	1.47507e7	0.714734
$124$	2.86147e7	1.34776
$125$	−2.35737e7	−1.07955
$126$	−3.25845e6	−0.145116
$127$	−2.66397e7	−1.15403	−0.577014	−	0.816734i	$-0.695782\pi$
$127$	−2.66397e7	−1.15403	−0.577014	+	0.816734i	$0.695782\pi$
$128$	−1.28098e7	−0.539893
$129$	−3.88066e6	−0.159163
$130$	1.83600e7	0.732946
$131$	−1.53052e7	−0.594825	−0.297413	−	0.954749i	$-0.596124\pi$
$131$	−1.53052e7	−0.594825	−0.297413	+	0.954749i	$0.596124\pi$
$132$	−1.55587e7	−0.588795
$133$	6.02015e7	2.21884
$134$	−2.67918e7	−0.961911
$135$	−2.05068e7	−0.717349
$136$	1.08760e7	0.370751
$137$	−2.88018e7	−0.956968	−0.478484	−	0.878096i	$-0.658814\pi$
$137$	−2.88018e7	−0.956968	−0.478484	+	0.878096i	$0.658814\pi$
$138$	−8.89425e6	−0.288093
$139$	2.41973e7	0.764213	0.382106	−	0.924118i	$-0.375199\pi$
$139$	2.41973e7	0.764213	0.382106	+	0.924118i	$0.375199\pi$
$140$	2.36047e7	0.727026
$141$	1.14721e7	0.344649
$142$	−5.41240e7	−1.58628
$143$	1.80117e7	0.515085
$144$	−3.72338e6	−0.103913
$145$	2.78722e7	0.759247
$146$	6.51690e6	0.173303
$147$	1.89557e7	0.492186
$148$	−2.18039e7	−0.552863
$149$	1.88108e7	0.465859	0.232929	−	0.972494i	$-0.425169\pi$
$149$	1.88108e7	0.465859	0.232929	+	0.972494i	$0.425169\pi$
$150$	2.48710e7	0.601691
$151$	−5.28673e7	−1.24959	−0.624796	−	0.780788i	$-0.714818\pi$
$151$	−5.28673e7	−1.24959	−0.624796	+	0.780788i	$0.714818\pi$
$152$	2.18409e7	0.504450
$153$	5.31887e6	0.120060
$154$	5.23181e7	1.15433
$155$	5.93860e7	1.28092
$156$	−2.84938e7	−0.600917
$157$	−5.80087e7	−1.19631	−0.598156	−	0.801380i	$-0.704100\pi$
$157$	−5.80087e7	−1.19631	−0.598156	+	0.801380i	$0.704100\pi$
$158$	1.12748e8	2.27410
$159$	2.68608e6	0.0529943
$160$	5.01549e7	0.968040
$161$	1.32378e7	0.249992
$162$	7.83764e7	1.44838
$163$	9.85826e7	1.78297	0.891484	−	0.453051i	$-0.149665\pi$
$163$	9.85826e7	1.78297	0.891484	+	0.453051i	$0.149665\pi$
$164$	3.07183e7	0.543805
$165$	−3.22900e7	−0.559595
$166$	−8.34059e7	−1.41520
$167$	3.30309e7	0.548798	0.274399	−	0.961616i	$-0.411521\pi$
$167$	3.30309e7	0.548798	0.274399	+	0.961616i	$0.411521\pi$
$168$	2.14601e7	0.349181
$169$	−2.97623e7	−0.474311
$170$	−8.70519e7	−1.35896
$171$	1.06812e7	0.163356
$172$	−8.08146e6	−0.121099
$173$	−9.21797e7	−1.35355	−0.676774	−	0.736191i	$-0.736623\pi$
$173$	−9.21797e7	−1.35355	−0.676774	+	0.736191i	$0.736623\pi$
$174$	−9.77283e7	−1.40636
$175$	−3.70168e7	−0.522115
$176$	5.97829e7	0.826576
$177$	7.32836e6	0.0993346
$178$	5.35998e7	0.712349
$179$	8.22086e7	1.07135	0.535675	−	0.844424i	$-0.320057\pi$
$179$	8.22086e7	1.07135	0.535675	+	0.844424i	$0.320057\pi$
$180$	4.18805e6	0.0535252
$181$	−4.53246e7	−0.568144	−0.284072	−	0.958803i	$-0.591686\pi$
$181$	−4.53246e7	−0.568144	−0.284072	+	0.958803i	$0.591686\pi$
$182$	9.58141e7	1.17809
$183$	−8.08266e7	−0.974934
$184$	4.80263e6	0.0568351
$185$	−4.52510e7	−0.525445
$186$	−2.08225e8	−2.37267
$187$	−8.54003e7	−0.955023
$188$	2.38907e7	0.262226
$189$	−1.07017e8	−1.15302
$190$	−1.74816e8	−1.84902
$191$	−1.21596e8	−1.26270	−0.631352	−	0.775496i	$-0.717500\pi$
$191$	−1.21596e8	−1.26270	−0.631352	+	0.775496i	$0.717500\pi$
$192$	−5.67617e7	−0.578764
$193$	1.40361e8	1.40538	0.702691	−	0.711495i	$-0.251981\pi$
$193$	1.40361e8	1.40538	0.702691	+	0.711495i	$0.251981\pi$
$194$	3.16339e7	0.311062
$195$	−5.91351e7	−0.571116
$196$	3.94752e7	0.374480
$197$	−5.68563e7	−0.529842	−0.264921	−	0.964270i	$-0.585346\pi$
$197$	−5.68563e7	−0.529842	−0.264921	+	0.964270i	$0.585346\pi$
$198$	9.28251e6	0.0849840
$199$	3.29464e7	0.296361	0.148181	−	0.988960i	$-0.452658\pi$
$199$	3.29464e7	0.296361	0.148181	+	0.988960i	$0.452658\pi$
$200$	−1.34296e7	−0.118702
$201$	8.62926e7	0.749527
$202$	−2.42385e8	−2.06907
$203$	1.45454e8	1.22037
$204$	1.35100e8	1.11417
$205$	6.37517e7	0.516836
$206$	1.73348e8	1.38160
$207$	2.34871e6	0.0184049
$208$	1.09485e8	0.843593
$209$	−1.71499e8	−1.29942
$210$	−1.71768e8	−1.27990
$211$	−2.35087e8	−1.72282	−0.861411	−	0.507908i	$-0.830419\pi$
$211$	−2.35087e8	−1.72282	−0.861411	+	0.507908i	$0.830419\pi$
$212$	5.59375e6	0.0403207
$213$	1.74326e8	1.23604
$214$	−7.77561e7	−0.542358
$215$	−1.67720e7	−0.115093
$216$	−3.88255e7	−0.262137
$217$	3.09913e8	2.05888
$218$	3.18986e8	2.08533
$219$	−2.09900e7	−0.135039
$220$	−6.72438e7	−0.425768
$221$	−1.56400e8	−0.974685
$222$	1.58664e8	0.973290
$223$	6.86931e7	0.414807	0.207404	−	0.978255i	$-0.433499\pi$
$223$	6.86931e7	0.414807	0.207404	+	0.978255i	$0.433499\pi$
$224$	2.61739e8	1.55597
$225$	−6.56770e6	−0.0384392
$226$	2.18293e8	1.25794
$227$	−3.33942e8	−1.89487	−0.947436	−	0.319945i	$-0.896336\pi$
$227$	−3.33942e8	−1.89487	−0.947436	+	0.319945i	$0.896336\pi$
$228$	2.71305e8	1.51595
$229$	3.08822e8	1.69935	0.849677	−	0.527303i	$-0.176797\pi$
$229$	3.08822e8	1.69935	0.849677	+	0.527303i	$0.176797\pi$
$230$	−3.84405e7	−0.208325
$231$	−1.68509e8	−0.899460
$232$	5.27703e7	0.277448
$233$	1.57739e8	0.816947	0.408473	−	0.912770i	$-0.366061\pi$
$233$	1.57739e8	0.816947	0.408473	+	0.912770i	$0.366061\pi$
$234$	1.69998e7	0.0867337
$235$	4.95819e7	0.249221
$236$	1.52613e7	0.0755787
$237$	−3.63146e8	−1.77199
$238$	−4.54291e8	−2.18431
$239$	−1.84694e8	−0.875105	−0.437553	−	0.899193i	$-0.644155\pi$
$239$	−1.84694e8	−0.875105	−0.437553	+	0.899193i	$0.644155\pi$
$240$	−1.96276e8	−0.916492
$241$	4.79565e7	0.220692	0.110346	−	0.993893i	$-0.464804\pi$
$241$	4.79565e7	0.220692	0.110346	+	0.993893i	$0.464804\pi$
$242$	1.46268e8	0.663432
$243$	−3.98371e7	−0.178101
$244$	−1.68321e8	−0.741778
$245$	8.19256e7	0.355908
$246$	−2.23532e8	−0.957343
$247$	−3.14079e8	−1.32617
$248$	1.12435e8	0.468082
$249$	2.68639e8	1.10274
$250$	3.57236e8	1.44599
$251$	−4.64988e8	−1.85602	−0.928012	−	0.372550i	$-0.878483\pi$
$251$	−4.64988e8	−1.85602	−0.928012	+	0.372550i	$0.878483\pi$
$252$	2.18559e7	0.0860332
$253$	−3.77112e7	−0.146402
$254$	4.03699e8	1.54575
$255$	2.80382e8	1.05891
$256$	3.42976e8	1.27768
$257$	2.59186e8	0.952456	0.476228	−	0.879322i	$-0.342004\pi$
$257$	2.59186e8	0.952456	0.476228	+	0.879322i	$0.342004\pi$
$258$	5.88076e7	0.213189
$259$	−2.36148e8	−0.844569
$260$	−1.23149e8	−0.434533
$261$	2.58072e7	0.0898460
$262$	2.31935e8	0.796732
$263$	−2.19827e8	−0.745137	−0.372569	−	0.928005i	$-0.621523\pi$
$263$	−2.19827e8	−0.745137	−0.372569	+	0.928005i	$0.621523\pi$
$264$	−6.11345e7	−0.204490
$265$	1.16091e7	0.0383211
$266$	−9.12296e8	−2.97201
$267$	−1.72637e8	−0.555067
$268$	1.79704e8	0.570277
$269$	5.19950e8	1.62865	0.814327	−	0.580407i	$-0.197107\pi$
$269$	5.19950e8	1.62865	0.814327	+	0.580407i	$0.197107\pi$
$270$	3.10761e8	0.960846
$271$	2.80890e8	0.857323	0.428661	−	0.903465i	$-0.358985\pi$
$271$	2.80890e8	0.857323	0.428661	+	0.903465i	$0.358985\pi$
$272$	−5.19110e8	−1.56411
$273$	−3.08604e8	−0.917977
$274$	4.36463e8	1.28180
$275$	1.05452e8	0.305766
$276$	5.96576e7	0.170798
$277$	2.46843e8	0.697818	0.348909	−	0.937157i	$-0.386552\pi$
$277$	2.46843e8	0.697818	0.348909	+	0.937157i	$0.386552\pi$
$278$	−3.66686e8	−1.02362
$279$	5.49862e7	0.151579
$280$	9.27495e7	0.252498
$281$	1.74389e8	0.468863	0.234432	−	0.972133i	$-0.424677\pi$
$281$	1.74389e8	0.468863	0.234432	+	0.972133i	$0.424677\pi$
$282$	−1.73849e8	−0.461636
$283$	−5.30249e8	−1.39068	−0.695341	−	0.718680i	$-0.744746\pi$
$283$	−5.30249e8	−1.39068	−0.695341	+	0.718680i	$0.744746\pi$
$284$	3.63033e8	0.940441
$285$	5.63057e8	1.44077
$286$	−2.72950e8	−0.689925
$287$	3.32696e8	0.830731
$288$	4.64390e7	0.114554
$289$	3.31214e8	0.807172
$290$	−4.22376e8	−1.01697
$291$	−1.01889e8	−0.242382
$292$	−4.37116e7	−0.102744
$293$	2.11533e8	0.491294	0.245647	−	0.969359i	$-0.421000\pi$
$293$	2.11533e8	0.491294	0.245647	+	0.969359i	$0.421000\pi$
$294$	−2.87256e8	−0.659254
$295$	3.16728e7	0.0718305
$296$	−8.56736e7	−0.192011
$297$	3.04865e8	0.675244
$298$	−2.85059e8	−0.623990
$299$	−6.90633e7	−0.149416
$300$	−1.66820e8	−0.356718
$301$	−8.75266e7	−0.184994
$302$	8.01153e8	1.67375
$303$	7.80687e8	1.61223
$304$	−1.04246e9	−2.12816
$305$	−3.49328e8	−0.704991
$306$	−8.06024e7	−0.160814
$307$	−3.83496e8	−0.756444	−0.378222	−	0.925715i	$-0.623464\pi$
$307$	−3.83496e8	−0.756444	−0.378222	+	0.925715i	$0.623464\pi$
$308$	−3.50920e8	−0.684353
$309$	−5.58330e8	−1.07655
$310$	−8.99937e8	−1.71572
$311$	2.71805e8	0.512386	0.256193	−	0.966626i	$-0.417532\pi$
$311$	2.71805e8	0.512386	0.256193	+	0.966626i	$0.417532\pi$
$312$	−1.11960e8	−0.208700
$313$	2.82814e8	0.521309	0.260655	−	0.965432i	$-0.416062\pi$
$313$	2.82814e8	0.521309	0.260655	+	0.965432i	$0.416062\pi$
$314$	8.79065e8	1.60239
$315$	4.53589e7	0.0817666
$316$	−7.56250e8	−1.34822
$317$	1.50905e8	0.266070	0.133035	−	0.991111i	$-0.457528\pi$
$317$	1.50905e8	0.266070	0.133035	+	0.991111i	$0.457528\pi$
$318$	−4.07050e7	−0.0709827
$319$	−4.14363e8	−0.714683
$320$	−2.45321e8	−0.418514
$321$	2.50442e8	0.422609
$322$	−2.00606e8	−0.334849
$323$	1.48917e9	2.45887
$324$	−5.25704e8	−0.858685
$325$	1.93122e8	0.312061
$326$	−1.49392e9	−2.38818
$327$	−1.02741e9	−1.62490
$328$	1.20701e8	0.188865
$329$	2.58749e8	0.400583
$330$	4.89324e8	0.749544
$331$	4.82795e8	0.731754	0.365877	−	0.930663i	$-0.380769\pi$
$331$	4.82795e8	0.731754	0.365877	+	0.930663i	$0.380769\pi$
$332$	5.59439e8	0.839015
$333$	−4.18985e7	−0.0621789
$334$	−5.00551e8	−0.735082
$335$	3.72952e8	0.541996
$336$	−1.02429e9	−1.47311
$337$	−5.19140e8	−0.738891	−0.369445	−	0.929252i	$-0.620452\pi$
$337$	−5.19140e8	−0.738891	−0.369445	+	0.929252i	$0.620452\pi$
$338$	4.51019e8	0.635311
$339$	−7.03092e8	−0.980197
$340$	5.83895e8	0.805672
$341$	−8.82863e8	−1.20574
$342$	−1.61864e8	−0.218805
$343$	−4.79073e8	−0.641021
$344$	−3.17543e7	−0.0420580
$345$	1.23811e8	0.162328
$346$	1.39689e9	1.81300
$347$	2.17439e8	0.279373	0.139686	−	0.990196i	$-0.455391\pi$
$347$	2.17439e8	0.279373	0.139686	+	0.990196i	$0.455391\pi$
$348$	6.55506e8	0.833775
$349$	−1.23345e8	−0.155322	−0.0776609	−	0.996980i	$-0.524745\pi$
$349$	−1.23345e8	−0.155322	−0.0776609	+	0.996980i	$0.524745\pi$
$350$	5.60954e8	0.699341
$351$	5.58323e8	0.689145
$352$	−7.45629e8	−0.911221
$353$	3.57356e8	0.432404	0.216202	−	0.976349i	$-0.430633\pi$
$353$	3.57356e8	0.432404	0.216202	+	0.976349i	$0.430633\pi$
$354$	−1.11054e8	−0.133053
$355$	7.53426e8	0.893802
$356$	−3.59517e8	−0.422322
$357$	1.46321e9	1.70203
$358$	−1.24579e9	−1.43501
$359$	−2.89591e8	−0.330335	−0.165168	−	0.986266i	$-0.552816\pi$
$359$	−2.89591e8	−0.330335	−0.165168	+	0.986266i	$0.552816\pi$
$360$	1.64561e7	0.0185895
$361$	2.09664e9	2.34557
$362$	6.86850e8	0.760995
$363$	−4.71110e8	−0.516950
$364$	−6.42666e8	−0.698442
$365$	−9.07177e7	−0.0976488
$366$	1.22485e9	1.30587
$367$	−8.92000e8	−0.941963	−0.470981	−	0.882143i	$-0.656100\pi$
$367$	−8.92000e8	−0.941963	−0.470981	+	0.882143i	$0.656100\pi$
$368$	−2.29229e8	−0.239774
$369$	5.90284e7	0.0611602
$370$	6.85735e8	0.703802
$371$	6.05834e7	0.0615950
$372$	1.39666e9	1.40666
$373$	1.71138e9	1.70752	0.853761	−	0.520665i	$-0.174316\pi$
$373$	1.71138e9	1.70752	0.853761	+	0.520665i	$0.174316\pi$
$374$	1.29416e9	1.27920
$375$	−1.15061e9	−1.12673
$376$	9.38732e7	0.0910718
$377$	−7.58854e8	−0.729396
$378$	1.62174e9	1.54440
$379$	4.74180e7	0.0447410	0.0223705	−	0.999750i	$-0.492879\pi$
$379$	4.74180e7	0.0447410	0.0223705	+	0.999750i	$0.492879\pi$
$380$	1.17256e9	1.09621
$381$	−1.30026e9	−1.20446
$382$	1.84267e9	1.69132
$383$	−3.02938e8	−0.275523	−0.137761	−	0.990465i	$-0.543991\pi$
$383$	−3.02938e8	−0.275523	−0.137761	+	0.990465i	$0.543991\pi$
$384$	−6.25234e8	−0.563486
$385$	−7.28287e8	−0.650414
$386$	−2.12703e9	−1.88243
$387$	−1.55294e7	−0.0136196
$388$	−2.12182e8	−0.184416
$389$	2.48110e8	0.213708	0.106854	−	0.994275i	$-0.465922\pi$
$389$	2.48110e8	0.213708	0.106854	+	0.994275i	$0.465922\pi$
$390$	8.96136e8	0.764976
$391$	3.27455e8	0.277034
$392$	1.55109e8	0.130058
$393$	−7.47032e8	−0.620819
$394$	8.61601e8	0.709691
$395$	−1.56950e9	−1.28136
$396$	−6.22618e7	−0.0503835
$397$	−1.17389e9	−0.941589	−0.470794	−	0.882243i	$-0.656033\pi$
$397$	−1.17389e9	−0.941589	−0.470794	+	0.882243i	$0.656033\pi$
$398$	−4.99270e8	−0.396958
$399$	2.93838e9	2.31581
$400$	6.40993e8	0.500776
$401$	−4.69179e8	−0.363357	−0.181679	−	0.983358i	$-0.558153\pi$
$401$	−4.69179e8	−0.363357	−0.181679	+	0.983358i	$0.558153\pi$
$402$	−1.30768e9	−1.00395
$403$	−1.61686e9	−1.23056
$404$	1.62578e9	1.22667
$405$	−1.09103e9	−0.816101
$406$	−2.20422e9	−1.63461
$407$	6.72726e8	0.494604
$408$	5.30846e8	0.386953
$409$	−2.36052e9	−1.70599	−0.852995	−	0.521918i	$-0.825217\pi$
$409$	−2.36052e9	−1.70599	−0.852995	+	0.521918i	$0.825217\pi$
$410$	−9.66094e8	−0.692271
$411$	−1.40579e9	−0.998788
$412$	−1.16272e9	−0.819096
$413$	1.65288e8	0.115456
$414$	−3.55925e7	−0.0246523
$415$	1.16104e9	0.797406
$416$	−1.36553e9	−0.929981
$417$	1.18104e9	0.797609
$418$	2.59890e9	1.74049
$419$	−2.55941e9	−1.69977	−0.849886	−	0.526967i	$-0.823329\pi$
$419$	−2.55941e9	−1.69977	−0.849886	+	0.526967i	$0.823329\pi$
$420$	1.15212e9	0.758798
$421$	−3.64111e7	−0.0237819	−0.0118909	−	0.999929i	$-0.503785\pi$
$421$	−3.64111e7	−0.0237819	−0.0118909	+	0.999929i	$0.503785\pi$
$422$	3.56252e9	2.30762
$423$	4.59084e7	0.0294918
$424$	2.19794e7	0.0140035
$425$	−9.15662e8	−0.578594
$426$	−2.64174e9	−1.65560
$427$	−1.82301e9	−1.13316
$428$	5.21543e8	0.321542
$429$	8.79134e8	0.537594
$430$	2.54163e8	0.154160
$431$	−1.88575e9	−1.13452	−0.567262	−	0.823538i	$-0.691997\pi$
$431$	−1.88575e9	−1.13452	−0.567262	+	0.823538i	$0.691997\pi$
$432$	1.85314e9	1.10590
$433$	−4.74195e8	−0.280705	−0.140352	−	0.990102i	$-0.544824\pi$
$433$	−4.74195e8	−0.280705	−0.140352	+	0.990102i	$0.544824\pi$
$434$	−4.69643e9	−2.75774
$435$	1.36041e9	0.792426
$436$	−2.13958e9	−1.23631
$437$	6.57588e8	0.376937
$438$	3.18083e8	0.180876
$439$	1.83494e9	1.03513	0.517565	−	0.855644i	$-0.326838\pi$
$439$	1.83494e9	1.03513	0.517565	+	0.855644i	$0.326838\pi$
$440$	−2.64220e8	−0.147870
$441$	7.58558e7	0.0421167
$442$	2.37009e9	1.30553
$443$	2.78161e9	1.52014	0.760070	−	0.649841i	$-0.225164\pi$
$443$	2.78161e9	1.52014	0.760070	+	0.649841i	$0.225164\pi$
$444$	−1.06423e9	−0.577023
$445$	−7.46129e8	−0.401378
$446$	−1.04098e9	−0.555609
$447$	9.18135e8	0.486217
$448$	−1.28024e9	−0.672694
$449$	−2.43689e9	−1.27050	−0.635250	−	0.772307i	$-0.719103\pi$
$449$	−2.43689e9	−1.27050	−0.635250	+	0.772307i	$0.719103\pi$
$450$	9.95271e7	0.0514870
$451$	−9.47766e8	−0.486500
$452$	−1.46419e9	−0.745782
$453$	−2.58040e9	−1.30420
$454$	5.06056e9	2.53807
$455$	−1.33377e9	−0.663805
$456$	1.06603e9	0.526494
$457$	3.65375e9	1.79074	0.895369	−	0.445324i	$-0.146912\pi$
$457$	3.65375e9	1.79074	0.895369	+	0.445324i	$0.146912\pi$
$458$	−4.67990e9	−2.27618
$459$	−2.64722e9	−1.27775
$460$	2.57837e8	0.123507
$461$	−1.07049e9	−0.508897	−0.254449	−	0.967086i	$-0.581894\pi$
$461$	−1.07049e9	−0.508897	−0.254449	+	0.967086i	$0.581894\pi$
$462$	2.55359e9	1.20477
$463$	3.98983e9	1.86819	0.934095	−	0.357025i	$-0.116209\pi$
$463$	3.98983e9	1.86819	0.934095	+	0.357025i	$0.116209\pi$
$464$	−2.51872e9	−1.17049
$465$	2.89857e9	1.33690
$466$	−2.39038e9	−1.09425
$467$	−3.19032e9	−1.44952	−0.724762	−	0.688999i	$-0.758050\pi$
$467$	−3.19032e9	−1.44952	−0.724762	+	0.688999i	$0.758050\pi$
$468$	−1.14025e8	−0.0514208
$469$	1.94629e9	0.871171
$470$	−7.51365e8	−0.333817
$471$	−2.83135e9	−1.24859
$472$	5.99659e7	0.0262487
$473$	2.49341e8	0.108338
$474$	5.50313e9	2.37348
$475$	−1.83881e9	−0.787244
$476$	3.04712e9	1.29499
$477$	1.07490e7	0.00453475
$478$	2.79886e9	1.17215
$479$	−2.57106e9	−1.06890	−0.534450	−	0.845200i	$-0.679481\pi$
$479$	−2.57106e9	−1.06890	−0.534450	+	0.845200i	$0.679481\pi$
$480$	2.44801e9	1.01034
$481$	1.23201e9	0.504787
$482$	−7.26734e8	−0.295604
$483$	6.46125e8	0.260916
$484$	−9.81084e8	−0.393321
$485$	−4.40356e8	−0.175270
$486$	6.03693e8	0.238555
$487$	2.60295e9	1.02121	0.510604	−	0.859816i	$-0.329422\pi$
$487$	2.60295e9	1.02121	0.510604	+	0.859816i	$0.329422\pi$
$488$	−6.61381e8	−0.257622
$489$	4.81172e9	1.86088
$490$	−1.24150e9	−0.476718
$491$	1.12697e9	0.429662	0.214831	−	0.976651i	$-0.431080\pi$
$491$	1.12697e9	0.429662	0.214831	+	0.976651i	$0.431080\pi$
$492$	1.49933e9	0.567569
$493$	3.59801e9	1.35238
$494$	4.75956e9	1.77633
$495$	−1.29216e8	−0.0478849
$496$	−5.36653e9	−1.97473
$497$	3.93184e9	1.43664
$498$	−4.07096e9	−1.47705
$499$	−4.16790e9	−1.50164	−0.750820	−	0.660507i	$-0.770341\pi$
$499$	−4.16790e9	−1.50164	−0.750820	+	0.660507i	$0.770341\pi$
$500$	−2.39614e9	−0.857268
$501$	1.61221e9	0.572781
$502$	7.04644e9	2.48603
$503$	4.24704e9	1.48799	0.743993	−	0.668187i	$-0.232930\pi$
$503$	4.24704e9	1.48799	0.743993	+	0.668187i	$0.232930\pi$
$504$	8.58779e7	0.0298796
$505$	3.37409e9	1.16583
$506$	5.71476e8	0.196097
$507$	−1.45267e9	−0.495038
$508$	−2.70778e9	−0.916412
$509$	4.51429e9	1.51732	0.758661	−	0.651486i	$-0.225854\pi$
$509$	4.51429e9	1.51732	0.758661	+	0.651486i	$0.225854\pi$
$510$	−4.24892e9	−1.41835
$511$	−4.73421e8	−0.156955
$512$	−3.55781e9	−1.17149
$513$	−5.31609e9	−1.73853
$514$	−3.92771e9	−1.27576
$515$	−2.41307e9	−0.778475
$516$	−3.94448e8	−0.126391
$517$	−7.37110e8	−0.234593
$518$	3.57859e9	1.13125
$519$	−4.49920e9	−1.41270
$520$	−4.83886e8	−0.150915
$521$	−1.82834e9	−0.566402	−0.283201	−	0.959061i	$-0.591396\pi$
$521$	−1.82834e9	−0.566402	−0.283201	+	0.959061i	$0.591396\pi$
$522$	−3.91083e8	−0.120343
$523$	−8.74437e8	−0.267284	−0.133642	−	0.991030i	$-0.542667\pi$
$523$	−8.74437e8	−0.267284	−0.133642	+	0.991030i	$0.542667\pi$
$524$	−1.55569e9	−0.472350
$525$	−1.80676e9	−0.544931
$526$	3.33127e9	0.998066
$527$	7.66612e9	2.28160
$528$	2.91795e9	0.862698
$529$	−3.26023e9	−0.957531
$530$	−1.75924e8	−0.0513288
$531$	2.93262e7	0.00850012
$532$	6.11916e9	1.76198
$533$	−1.73572e9	−0.496516
$534$	2.61615e9	0.743479
$535$	1.08239e9	0.305596
$536$	7.06108e8	0.198059
$537$	4.01252e9	1.11817
$538$	−7.87934e9	−2.18148
$539$	−1.21795e9	−0.335018
$540$	−2.08441e9	−0.569646
$541$	4.52769e9	1.22938	0.614690	−	0.788769i	$-0.289281\pi$
$541$	4.52769e9	1.22938	0.614690	+	0.788769i	$0.289281\pi$
$542$	−4.25662e9	−1.14833
$543$	−2.21225e9	−0.592972
$544$	6.47448e9	1.72429
$545$	−4.44041e9	−1.17499
$546$	4.67659e9	1.22958
$547$	2.38403e9	0.622811	0.311406	−	0.950277i	$-0.399200\pi$
$547$	2.38403e9	0.622811	0.311406	+	0.950277i	$0.399200\pi$
$548$	−2.92755e9	−0.759927
$549$	−3.23447e8	−0.0834257
$550$	−1.59802e9	−0.409555
$551$	7.22545e9	1.84007
$552$	2.34412e8	0.0593188
$553$	−8.19061e9	−2.05958
$554$	−3.74067e9	−0.934685
$555$	−2.20866e9	−0.548407
$556$	2.45952e9	0.606860
$557$	−2.04626e9	−0.501727	−0.250864	−	0.968022i	$-0.580715\pi$
$557$	−2.04626e9	−0.501727	−0.250864	+	0.968022i	$0.580715\pi$
$558$	−8.33262e8	−0.203031
$559$	4.56638e8	0.110568
$560$	−4.42693e9	−1.06523
$561$	−4.16831e9	−0.996758
$562$	−2.64269e9	−0.628014
$563$	3.85093e9	0.909465	0.454733	−	0.890628i	$-0.349735\pi$
$563$	3.85093e9	0.909465	0.454733	+	0.890628i	$0.349735\pi$
$564$	1.16608e9	0.273685
$565$	−3.03873e9	−0.708797
$566$	8.03541e9	1.86273
$567$	−5.69367e9	−1.31175
$568$	1.42646e9	0.326618
$569$	−1.30991e9	−0.298091	−0.149045	−	0.988830i	$-0.547620\pi$
$569$	−1.30991e9	−0.298091	−0.149045	+	0.988830i	$0.547620\pi$
$570$	−8.53258e9	−1.92983
$571$	3.44368e9	0.774098	0.387049	−	0.922059i	$-0.373494\pi$
$571$	3.44368e9	0.774098	0.387049	+	0.922059i	$0.373494\pi$
$572$	1.83079e9	0.409028
$573$	−5.93497e9	−1.31788
$574$	−5.04168e9	−1.11271
$575$	−4.04339e8	−0.0886969
$576$	−2.27146e8	−0.0495251
$577$	2.53520e9	0.549411	0.274706	−	0.961528i	$-0.411420\pi$
$577$	2.53520e9	0.549411	0.274706	+	0.961528i	$0.411420\pi$
$578$	−5.01922e9	−1.08116
$579$	6.85086e9	1.46680
$580$	2.83306e9	0.602917
$581$	6.05904e9	1.28170
$582$	1.54402e9	0.324656
$583$	−1.72587e8	−0.0360718
$584$	−1.71755e8	−0.0356833
$585$	−2.36643e8	−0.0488707
$586$	−3.20558e9	−0.658059
$587$	−7.98017e9	−1.62847	−0.814233	−	0.580539i	$-0.802842\pi$
$587$	−7.98017e9	−1.62847	−0.814233	+	0.580539i	$0.802842\pi$
$588$	1.92675e9	0.390845
$589$	1.53949e10	3.10437
$590$	−4.79970e8	−0.0962127
$591$	−2.77510e9	−0.552996
$592$	4.08920e9	0.810050
$593$	4.65675e8	0.0917047	0.0458523	−	0.998948i	$-0.485400\pi$
$593$	4.65675e8	0.0917047	0.0458523	+	0.998948i	$0.485400\pi$
$594$	−4.61994e9	−0.904448
$595$	6.32390e9	1.23077
$596$	1.91201e9	0.369938
$597$	1.60808e9	0.309312
$598$	1.04659e9	0.200134
$599$	6.41918e9	1.22035	0.610177	−	0.792265i	$-0.291098\pi$
$599$	6.41918e9	1.22035	0.610177	+	0.792265i	$0.291098\pi$
$600$	−6.55484e8	−0.123889
$601$	−5.93318e9	−1.11488	−0.557438	−	0.830219i	$-0.688216\pi$
$601$	−5.93318e9	−1.11488	−0.557438	+	0.830219i	$0.688216\pi$
$602$	1.32638e9	0.247788
$603$	3.45320e8	0.0641374
$604$	−5.37368e9	−0.992299
$605$	−2.03611e9	−0.373816
$606$	−1.18306e10	−2.15949
$607$	−8.51996e9	−1.54624	−0.773121	−	0.634259i	$-0.781305\pi$
$607$	−8.51996e9	−1.54624	−0.773121	+	0.634259i	$0.781305\pi$
$608$	1.30019e10	2.34609
$609$	7.09949e9	1.27370
$610$	5.29373e9	0.944293
$611$	−1.34993e9	−0.239423
$612$	5.40635e8	0.0953398
$613$	5.16503e9	0.905652	0.452826	−	0.891599i	$-0.350416\pi$
$613$	5.16503e9	0.905652	0.452826	+	0.891599i	$0.350416\pi$
$614$	5.81152e9	1.01321
$615$	3.11166e9	0.539422
$616$	−1.37886e9	−0.237678
$617$	−2.47374e9	−0.423991	−0.211995	−	0.977271i	$-0.567996\pi$
$617$	−2.47374e9	−0.423991	−0.211995	+	0.977271i	$0.567996\pi$
$618$	8.46094e9	1.44198
$619$	−5.19636e9	−0.880607	−0.440304	−	0.897849i	$-0.645129\pi$
$619$	−5.19636e9	−0.880607	−0.440304	+	0.897849i	$0.645129\pi$
$620$	6.03627e9	1.01718
$621$	−1.16896e9	−0.195876
$622$	−4.11895e9	−0.686309
$623$	−3.89376e9	−0.645151
$624$	5.34386e9	0.880459
$625$	−2.34590e9	−0.384352
$626$	−4.28577e9	−0.698263
$627$	−8.37070e9	−1.35620
$628$	−5.89627e9	−0.949989
$629$	−5.84144e9	−0.935929
$630$	−6.87371e8	−0.109521
$631$	4.50866e9	0.714405	0.357203	−	0.934027i	$-0.383731\pi$
$631$	4.50866e9	0.714405	0.357203	+	0.934027i	$0.383731\pi$
$632$	−2.97152e9	−0.468241
$633$	−1.14744e10	−1.79811
$634$	−2.28681e9	−0.356384
$635$	−5.61964e9	−0.870965
$636$	2.73026e8	0.0420827
$637$	−2.23052e9	−0.341915
$638$	6.27926e9	0.957274
$639$	6.97606e8	0.105769
$640$	−2.70223e9	−0.407466
$641$	−7.93187e8	−0.118952	−0.0594761	−	0.998230i	$-0.518943\pi$
$641$	−7.93187e8	−0.118952	−0.0594761	+	0.998230i	$0.518943\pi$
$642$	−3.79520e9	−0.566059
$643$	−1.11969e10	−1.66095	−0.830477	−	0.557053i	$-0.811932\pi$
$643$	−1.11969e10	−1.66095	−0.830477	+	0.557053i	$0.811932\pi$
$644$	1.34555e9	0.198518
$645$	−8.18624e8	−0.120123
$646$	−2.25669e10	−3.29350
$647$	1.19259e10	1.73111	0.865554	−	0.500815i	$-0.166966\pi$
$647$	1.19259e10	1.73111	0.865554	+	0.500815i	$0.166966\pi$
$648$	−2.06564e9	−0.298224
$649$	−4.70864e8	−0.0676144
$650$	−2.92657e9	−0.417986
$651$	1.51265e10	2.14885
$652$	1.00204e10	1.41585
$653$	−2.22608e9	−0.312857	−0.156428	−	0.987689i	$-0.549998\pi$
$653$	−2.22608e9	−0.312857	−0.156428	+	0.987689i	$0.549998\pi$
$654$	1.55694e10	2.17646
$655$	−3.22863e9	−0.448925
$656$	−5.76104e9	−0.796778
$657$	−8.39965e7	−0.0115553
$658$	−3.92109e9	−0.536557
$659$	−8.32960e7	−0.0113377	−0.00566885	−	0.999984i	$-0.501804\pi$
$659$	−8.32960e7	−0.0113377	−0.00566885	+	0.999984i	$0.501804\pi$
$660$	−3.28210e9	−0.444374
$661$	6.64097e9	0.894389	0.447194	−	0.894437i	$-0.352423\pi$
$661$	6.64097e9	0.894389	0.447194	+	0.894437i	$0.352423\pi$
$662$	−7.31629e9	−0.980140
$663$	−7.63374e9	−1.01728
$664$	2.19820e9	0.291392
$665$	1.26995e10	1.67460
$666$	6.34930e8	0.0832849
$667$	1.58881e9	0.207316
$668$	3.35741e9	0.435800
$669$	3.35284e9	0.432934
$670$	−5.65172e9	−0.725970
$671$	5.19329e9	0.663612
$672$	1.27752e10	1.62397
$673$	3.72281e9	0.470780	0.235390	−	0.971901i	$-0.424363\pi$
$673$	3.72281e9	0.470780	0.235390	+	0.971901i	$0.424363\pi$
$674$	7.86707e9	0.989699
$675$	3.26877e9	0.409092
$676$	−3.02518e9	−0.376649
$677$	1.49598e10	1.85296	0.926480	−	0.376343i	$-0.122819\pi$
$677$	1.49598e10	1.85296	0.926480	+	0.376343i	$0.122819\pi$
$678$	1.06547e10	1.31291
$679$	−2.29805e9	−0.281719
$680$	2.29429e9	0.279812
$681$	−1.62994e10	−1.97768
$682$	1.33789e10	1.61501
$683$	6.36282e9	0.764148	0.382074	−	0.924132i	$-0.375210\pi$
$683$	6.36282e9	0.764148	0.382074	+	0.924132i	$0.375210\pi$
$684$	1.08569e9	0.129721
$685$	−6.07573e9	−0.722240
$686$	7.25989e9	0.858609
$687$	1.50733e10	1.77362
$688$	1.51563e9	0.177433
$689$	−3.16071e8	−0.0368144
$690$	−1.87624e9	−0.217429
$691$	1.18625e10	1.36774	0.683870	−	0.729604i	$-0.260296\pi$
$691$	1.18625e10	1.36774	0.683870	+	0.729604i	$0.260296\pi$
$692$	−9.36957e9	−1.07485
$693$	−6.74330e8	−0.0769672
$694$	−3.29507e9	−0.374203
$695$	5.10441e9	0.576764
$696$	2.57567e9	0.289573
$697$	8.22969e9	0.920595
$698$	1.86917e9	0.208044
$699$	7.69909e9	0.852647
$700$	−3.76256e9	−0.414611
$701$	8.69584e9	0.953451	0.476725	−	0.879052i	$-0.341824\pi$
$701$	8.69584e9	0.953451	0.476725	+	0.879052i	$0.341824\pi$
$702$	−8.46085e9	−0.923069
$703$	−1.17306e10	−1.27344
$704$	3.64707e9	0.393949
$705$	2.42004e9	0.260112
$706$	−5.41539e9	−0.579179
$707$	1.76081e10	1.87389
$708$	7.44889e8	0.0788815
$709$	−6.50844e9	−0.685828	−0.342914	−	0.939367i	$-0.611414\pi$
$709$	−6.50844e9	−0.685828	−0.342914	+	0.939367i	$0.611414\pi$
$710$	−1.14174e10	−1.19719
$711$	−1.45322e9	−0.151630
$712$	−1.41264e9	−0.146674
$713$	3.38521e9	0.349762
$714$	−2.21735e10	−2.27977
$715$	3.79957e9	0.388743
$716$	8.35606e9	0.850758
$717$	−9.01474e9	−0.913348
$718$	4.38847e9	0.442464
$719$	−3.90453e9	−0.391757	−0.195879	−	0.980628i	$-0.562756\pi$
$719$	−3.90453e9	−0.391757	−0.195879	+	0.980628i	$0.562756\pi$
$720$	−7.85446e8	−0.0784247
$721$	−1.25929e10	−1.25127
$722$	−3.17725e10	−3.14175
$723$	2.34071e9	0.230337
$724$	−4.60700e9	−0.451163
$725$	−4.44280e9	−0.432986
$726$	7.13921e9	0.692424
$727$	−1.72837e10	−1.66827	−0.834133	−	0.551563i	$-0.814032\pi$
$727$	−1.72837e10	−1.66827	−0.834133	+	0.551563i	$0.814032\pi$
$728$	−2.52522e9	−0.242571
$729$	9.36672e9	0.895450
$730$	1.37474e9	0.130795
$731$	−2.16509e9	−0.205005
$732$	−8.21559e9	−0.774194
$733$	8.26113e9	0.774775	0.387387	−	0.921917i	$-0.373378\pi$
$733$	8.26113e9	0.774775	0.387387	+	0.921917i	$0.373378\pi$
$734$	1.35174e10	1.26170
$735$	3.99871e9	0.371462
$736$	2.85901e9	0.264328
$737$	−5.54450e9	−0.510183
$738$	−8.94518e8	−0.0819204
$739$	6.43474e9	0.586510	0.293255	−	0.956034i	$-0.405261\pi$
$739$	6.43474e9	0.586510	0.293255	+	0.956034i	$0.405261\pi$
$740$	−4.59952e9	−0.417255
$741$	−1.53299e10	−1.38413
$742$	−9.18083e8	−0.0825027
$743$	9.72354e9	0.869689	0.434844	−	0.900506i	$-0.356803\pi$
$743$	9.72354e9	0.869689	0.434844	+	0.900506i	$0.356803\pi$
$744$	5.48786e9	0.488537
$745$	3.96813e9	0.351592
$746$	−2.59344e10	−2.28712
$747$	1.07502e9	0.0943616
$748$	−8.68048e9	−0.758383
$749$	5.64860e9	0.491196
$750$	1.74364e10	1.50918
$751$	−1.14363e10	−0.985252	−0.492626	−	0.870241i	$-0.663963\pi$
$751$	−1.14363e10	−0.985252	−0.492626	+	0.870241i	$0.663963\pi$
$752$	−4.48056e9	−0.384211
$753$	−2.26956e10	−1.93713
$754$	1.14997e10	0.976982
$755$	−1.11524e10	−0.943088
$756$	−1.08777e10	−0.915614
$757$	−7.15016e9	−0.599073	−0.299537	−	0.954085i	$-0.596832\pi$
$757$	−7.15016e9	−0.599073	−0.299537	+	0.954085i	$0.596832\pi$
$758$	−7.18573e8	−0.0599278
$759$	−1.84065e9	−0.152800
$760$	4.60733e9	0.380717
$761$	3.88824e9	0.319821	0.159910	−	0.987132i	$-0.448879\pi$
$761$	3.88824e9	0.319821	0.159910	+	0.987132i	$0.448879\pi$
$762$	1.97042e10	1.61330
$763$	−2.31728e10	−1.88861
$764$	−1.23596e10	−1.00271
$765$	1.12202e9	0.0906116
$766$	4.59073e9	0.369046
$767$	−8.62330e8	−0.0690064
$768$	1.67403e10	1.33352
$769$	−1.58580e10	−1.25750	−0.628748	−	0.777609i	$-0.716432\pi$
$769$	−1.58580e10	−1.25750	−0.628748	+	0.777609i	$0.716432\pi$
$770$	1.10365e10	0.871191
$771$	1.26506e10	0.994079
$772$	1.42669e10	1.11601
$773$	−6.91144e9	−0.538196	−0.269098	−	0.963113i	$-0.586726\pi$
$773$	−6.91144e9	−0.538196	−0.269098	+	0.963113i	$0.586726\pi$
$774$	2.35333e8	0.0182427
$775$	−9.46606e9	−0.730488
$776$	−8.33725e8	−0.0640482
$777$	−1.15261e10	−0.881476
$778$	−3.75987e9	−0.286249
$779$	1.65267e10	1.25258
$780$	−6.01077e9	−0.453522
$781$	−1.12008e10	−0.841340
$782$	−4.96227e9	−0.371071
$783$	−1.28443e10	−0.956192
$784$	−7.40336e9	−0.548684
$785$	−1.22369e10	−0.902877
$786$	1.13205e10	0.831550
$787$	−8.31218e9	−0.607860	−0.303930	−	0.952694i	$-0.598299\pi$
$787$	−8.31218e9	−0.607860	−0.303930	+	0.952694i	$0.598299\pi$
$788$	−5.77913e9	−0.420747
$789$	−1.07296e10	−0.777700
$790$	2.37842e10	1.71630
$791$	−1.58580e10	−1.13928
$792$	−2.44644e8	−0.0174983
$793$	9.51087e9	0.677274
$794$	1.77892e10	1.26120
$795$	5.66628e8	0.0399957
$796$	3.34882e9	0.235340
$797$	2.22972e10	1.56008	0.780038	−	0.625733i	$-0.215200\pi$
$797$	2.22972e10	1.56008	0.780038	+	0.625733i	$0.215200\pi$
$798$	−4.45283e10	−3.10189
$799$	6.40051e9	0.443916
$800$	−7.99464e9	−0.552057
$801$	−6.90850e8	−0.0474974
$802$	7.10996e9	0.486695
$803$	1.34866e9	0.0919172
$804$	8.77118e9	0.595198
$805$	2.79251e9	0.188673
$806$	2.45019e10	1.64826
$807$	2.53783e10	1.69983
$808$	6.38814e9	0.426025
$809$	1.32718e10	0.881275	0.440638	−	0.897685i	$-0.354752\pi$
$809$	1.32718e10	0.881275	0.440638	+	0.897685i	$0.354752\pi$
$810$	1.65335e10	1.09312
$811$	4.23818e9	0.279002	0.139501	−	0.990222i	$-0.455450\pi$
$811$	4.23818e9	0.279002	0.139501	+	0.990222i	$0.455450\pi$
$812$	1.47847e10	0.969092
$813$	1.37100e10	0.894788
$814$	−1.01945e10	−0.662492
$815$	2.07960e10	1.34564
$816$	−2.53373e10	−1.63247
$817$	−4.34789e9	−0.278934
$818$	3.57714e10	2.28507
$819$	−1.23495e9	−0.0785518
$820$	6.48001e9	0.410419
$821$	−1.61244e10	−1.01691	−0.508455	−	0.861089i	$-0.669783\pi$
$821$	−1.61244e10	−1.01691	−0.508455	+	0.861089i	$0.669783\pi$
$822$	2.13033e10	1.33782
$823$	−1.67540e9	−0.104766	−0.0523829	−	0.998627i	$-0.516682\pi$
$823$	−1.67540e9	−0.104766	−0.0523829	+	0.998627i	$0.516682\pi$
$824$	−4.56865e9	−0.284474
$825$	5.14699e9	0.319128
$826$	−2.50478e9	−0.154646
$827$	−2.26903e10	−1.39499	−0.697496	−	0.716588i	$-0.745703\pi$
$827$	−2.26903e10	−1.39499	−0.697496	+	0.716588i	$0.745703\pi$
$828$	2.38734e8	0.0146153
$829$	−2.14017e10	−1.30469	−0.652345	−	0.757922i	$-0.726215\pi$
$829$	−2.14017e10	−1.30469	−0.652345	+	0.757922i	$0.726215\pi$
$830$	−1.75945e10	−1.06808
$831$	1.20482e10	0.728313
$832$	6.67916e9	0.402059
$833$	1.05758e10	0.633948
$834$	−1.78976e10	−1.06835
$835$	6.96786e9	0.414187
$836$	−1.74319e10	−1.03187
$837$	−2.73668e10	−1.61319
$838$	3.87854e10	2.27674
$839$	3.21757e10	1.88088	0.940439	−	0.339962i	$-0.110414\pi$
$839$	3.21757e10	1.88088	0.940439	+	0.339962i	$0.110414\pi$
$840$	4.52701e9	0.263533
$841$	2.07698e8	0.0120406
$842$	5.51774e8	0.0318544
$843$	8.51174e9	0.489353
$844$	−2.38953e10	−1.36809
$845$	−6.27835e9	−0.357970
$846$	−6.95698e8	−0.0395025
$847$	−1.06257e10	−0.600848
$848$	−1.04908e9	−0.0590775
$849$	−2.58810e10	−1.45145
$850$	1.38760e10	0.774992
$851$	−2.57947e9	−0.143475
$852$	1.77193e10	0.981539
$853$	−8.66660e9	−0.478109	−0.239055	−	0.971006i	$-0.576838\pi$
$853$	−8.66660e9	−0.478109	−0.239055	+	0.971006i	$0.576838\pi$
$854$	2.76259e10	1.51780
$855$	2.25320e9	0.123288
$856$	2.04929e9	0.111672
$857$	4.64158e9	0.251903	0.125951	−	0.992036i	$-0.459802\pi$
$857$	4.64158e9	0.251903	0.125951	+	0.992036i	$0.459802\pi$
$858$	−1.33224e10	−0.720075
$859$	1.96063e10	1.05541	0.527703	−	0.849429i	$-0.323053\pi$
$859$	1.96063e10	1.05541	0.527703	+	0.849429i	$0.323053\pi$
$860$	−1.70478e9	−0.0913954
$861$	1.62386e10	0.867034
$862$	2.85767e10	1.51963
$863$	2.94733e10	1.56096	0.780478	−	0.625183i	$-0.214976\pi$
$863$	2.94733e10	1.56096	0.780478	+	0.625183i	$0.214976\pi$
$864$	−2.31129e10	−1.21915
$865$	−1.94453e10	−1.02155
$866$	7.18597e9	0.375987
$867$	1.61662e10	0.842445
$868$	3.15010e10	1.63495
$869$	2.33330e10	1.20615
$870$	−2.06158e10	−1.06141
$871$	−1.01541e10	−0.520686
$872$	−8.40702e9	−0.429372
$873$	−4.07731e8	−0.0207407
$874$	−9.96511e9	−0.504885
$875$	−2.59515e10	−1.30959
$876$	−2.13352e9	−0.107234
$877$	−2.55789e9	−0.128051	−0.0640256	−	0.997948i	$-0.520394\pi$
$877$	−2.55789e9	−0.128051	−0.0640256	+	0.997948i	$0.520394\pi$
$878$	−2.78067e10	−1.38650
$879$	1.03247e10	0.512764
$880$	1.26112e10	0.623831
$881$	−2.66718e10	−1.31412	−0.657062	−	0.753837i	$-0.728201\pi$
$881$	−2.66718e10	−1.31412	−0.657062	+	0.753837i	$0.728201\pi$
$882$	−1.14952e9	−0.0564127
$883$	−4.99020e9	−0.243924	−0.121962	−	0.992535i	$-0.538919\pi$
$883$	−4.99020e9	−0.243924	−0.121962	+	0.992535i	$0.538919\pi$
$884$	−1.58972e10	−0.773996
$885$	1.54592e9	0.0749695
$886$	−4.21527e10	−2.03614
$887$	−2.25283e10	−1.08392	−0.541959	−	0.840405i	$-0.682317\pi$
$887$	−2.25283e10	−1.08392	−0.541959	+	0.840405i	$0.682317\pi$
$888$	−4.18164e9	−0.200402
$889$	−2.93268e10	−1.39994
$890$	1.13069e10	0.537622
$891$	1.62198e10	0.768199
$892$	6.98228e9	0.329398
$893$	1.28534e10	0.603999
$894$	−1.39134e10	−0.651258
$895$	1.73419e10	0.808567
$896$	−1.41019e10	−0.654937
$897$	−3.37091e9	−0.155946
$898$	3.69288e10	1.70176
$899$	3.71960e10	1.70741
$900$	−6.67571e8	−0.0305245
$901$	1.49861e9	0.0682579
$902$	1.43625e10	0.651638
$903$	−4.27209e9	−0.193078
$904$	−5.75321e9	−0.259012
$905$	−9.56121e9	−0.428788
$906$	3.91035e10	1.74690
$907$	2.20475e10	0.981145	0.490573	−	0.871400i	$-0.336788\pi$
$907$	2.20475e10	0.981145	0.490573	+	0.871400i	$0.336788\pi$
$908$	−3.39434e10	−1.50472
$909$	3.12411e9	0.137960
$910$	2.02120e10	0.889127
$911$	4.20990e9	0.184484	0.0922418	−	0.995737i	$-0.470597\pi$
$911$	4.20990e9	0.184484	0.0922418	+	0.995737i	$0.470597\pi$
$912$	−5.08817e10	−2.22116
$913$	−1.72607e10	−0.750602
$914$	−5.53690e10	−2.39859
$915$	−1.70504e10	−0.735800
$916$	3.13901e10	1.34945
$917$	−1.68490e10	−0.721574
$918$	4.01161e10	1.71147
$919$	−1.55285e10	−0.659972	−0.329986	−	0.943986i	$-0.607044\pi$
$919$	−1.55285e10	−0.659972	−0.329986	+	0.943986i	$0.607044\pi$
$920$	1.01311e9	0.0428944
$921$	−1.87181e10	−0.789501
$922$	1.62223e10	0.681637
$923$	−2.05129e10	−0.858661
$924$	−1.71281e10	−0.714260
$925$	7.21296e9	0.299652
$926$	−6.04620e10	−2.50233
$927$	−2.23429e9	−0.0921213
$928$	3.14142e10	1.29035
$929$	−2.69496e10	−1.10280	−0.551401	−	0.834240i	$-0.685907\pi$
$929$	−2.69496e10	−1.10280	−0.551401	+	0.834240i	$0.685907\pi$
$930$	−4.39251e10	−1.79070
$931$	2.12380e10	0.862560
$932$	1.60333e10	0.648736
$933$	1.32666e10	0.534777
$934$	4.83462e10	1.94155
$935$	−1.80152e10	−0.720772
$936$	−4.48036e8	−0.0178586
$937$	−1.04584e10	−0.415315	−0.207657	−	0.978202i	$-0.566584\pi$
$937$	−1.04584e10	−0.415315	−0.207657	+	0.978202i	$0.566584\pi$
$938$	−2.94942e10	−1.16688
$939$	1.38039e10	0.544091
$940$	5.03973e9	0.197906
$941$	2.29124e10	0.896412	0.448206	−	0.893930i	$-0.352063\pi$
$941$	2.29124e10	0.896412	0.448206	+	0.893930i	$0.352063\pi$
$942$	4.29063e10	1.67241
$943$	3.63407e9	0.141125
$944$	−2.86217e9	−0.110737
$945$	−2.25753e10	−0.870206
$946$	−3.77852e9	−0.145112
$947$	−2.22008e10	−0.849460	−0.424730	−	0.905320i	$-0.639631\pi$
$947$	−2.22008e10	−0.849460	−0.424730	+	0.905320i	$0.639631\pi$
$948$	−3.69118e10	−1.40714
$949$	2.46990e9	0.0938096
$950$	2.78654e10	1.05447
$951$	7.36551e9	0.277697
$952$	1.19730e10	0.449753
$953$	1.45448e10	0.544357	0.272178	−	0.962247i	$-0.412256\pi$
$953$	1.45448e10	0.544357	0.272178	+	0.962247i	$0.412256\pi$
$954$	−1.62891e8	−0.00607402
$955$	−2.56506e10	−0.952985
$956$	−1.87732e10	−0.694920
$957$	−2.02246e10	−0.745914
$958$	3.89619e10	1.43173
$959$	−3.17069e10	−1.16088
$960$	−1.19739e10	−0.436803
$961$	5.17393e10	1.88057
$962$	−1.86700e10	−0.676131
$963$	1.00220e9	0.0361629
$964$	4.87452e9	0.175252
$965$	2.96090e10	1.06067
$966$	−9.79139e9	−0.349482
$967$	−4.60488e10	−1.63767	−0.818833	−	0.574032i	$-0.805379\pi$
$967$	−4.60488e10	−1.63767	−0.818833	+	0.574032i	$0.805379\pi$
$968$	−3.85496e9	−0.136602
$969$	7.26848e10	2.56632
$970$	6.67317e9	0.234764
$971$	2.30696e10	0.808671	0.404335	−	0.914611i	$-0.367503\pi$
$971$	2.30696e10	0.808671	0.404335	+	0.914611i	$0.367503\pi$
$972$	−4.04923e9	−0.141430
$973$	2.66380e10	0.927056
$974$	−3.94451e10	−1.36785
$975$	9.42607e9	0.325698
$976$	3.15677e10	1.08685
$977$	5.54001e10	1.90055	0.950276	−	0.311408i	$-0.100801\pi$
$977$	5.54001e10	1.90055	0.950276	+	0.311408i	$0.100801\pi$
$978$	−7.29170e10	−2.49254
$979$	1.10923e10	0.377819
$980$	8.32729e9	0.282626
$981$	−4.11143e9	−0.139044
$982$	−1.70781e10	−0.575506
$983$	−3.63783e10	−1.22153	−0.610766	−	0.791811i	$-0.709139\pi$
$983$	−3.63783e10	−1.22153	−0.610766	+	0.791811i	$0.709139\pi$
$984$	5.89129e9	0.197118
$985$	−1.19938e10	−0.399881
$986$	−5.45244e10	−1.81143
$987$	1.26293e10	0.418089
$988$	−3.19244e10	−1.05311
$989$	−9.56063e8	−0.0314268
$990$	1.95814e9	0.0641389
$991$	1.33718e9	0.0436446	0.0218223	−	0.999762i	$-0.493053\pi$
$991$	1.33718e9	0.0436446	0.0218223	+	0.999762i	$0.493053\pi$
$992$	6.69328e10	2.17695
$993$	2.35648e10	0.763731
$994$	−5.95833e10	−1.92430
$995$	6.95003e9	0.223669
$996$	2.73057e10	0.875680
$997$	2.40234e10	0.767718	0.383859	−	0.923392i	$-0.374595\pi$
$997$	2.40234e10	0.767718	0.383859	+	0.923392i	$0.374595\pi$
$998$	6.31605e10	2.01135
$999$	2.08530e10	0.661743

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.a.b.1.3	✓	13
3.2	odd	2		387.8.a.d.1.11		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.b.1.3	✓	13	1.1	even	1	trivial
387.8.a.d.1.11		13	3.2	odd	2

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:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	43.a (trivial)

\(f(q)\)	\(=\)	\(q-15.1540 q^{2} +48.8090 q^{3} +101.645 q^{4} +210.950 q^{5} -739.653 q^{6} +1100.87 q^{7} +399.390 q^{8} +195.321 q^{9} +O(q^{10})\)	\(q-15.1540 q^{2} +48.8090 q^{3} +101.645 q^{4} +210.950 q^{5} -739.653 q^{6} +1100.87 q^{7} +399.390 q^{8} +195.321 q^{9} -3196.74 q^{10} -3136.09 q^{11} +4961.17 q^{12} -5743.36 q^{13} -16682.6 q^{14} +10296.3 q^{15} -19062.9 q^{16} +27231.5 q^{17} -2959.90 q^{18} +54685.6 q^{19} +21441.9 q^{20} +53732.2 q^{21} +47524.4 q^{22} +12024.9 q^{23} +19493.9 q^{24} -33625.2 q^{25} +87035.1 q^{26} -97211.9 q^{27} +111897. q^{28} +132127. q^{29} -156030. q^{30} +281517. q^{31} +237758. q^{32} -153070. q^{33} -412666. q^{34} +232228. q^{35} +19853.3 q^{36} -214511. q^{37} -828707. q^{38} -280328. q^{39} +84251.4 q^{40} +302212. q^{41} -814260. q^{42} -79507.0 q^{43} -318767. q^{44} +41202.9 q^{45} -182226. q^{46} +235041. q^{47} -930441. q^{48} +388365. q^{49} +509557. q^{50} +1.32914e6 q^{51} -583782. q^{52} +55032.5 q^{53} +1.47315e6 q^{54} -661558. q^{55} +439676. q^{56} +2.66915e6 q^{57} -2.00226e6 q^{58} +150144. q^{59} +1.04656e6 q^{60} -1.65598e6 q^{61} -4.26612e6 q^{62} +215022. q^{63} -1.16294e6 q^{64} -1.21156e6 q^{65} +2.31962e6 q^{66} +1.76796e6 q^{67} +2.76793e6 q^{68} +586923. q^{69} -3.51919e6 q^{70} +3.57159e6 q^{71} +78009.3 q^{72} -430044. q^{73} +3.25070e6 q^{74} -1.64121e6 q^{75} +5.55849e6 q^{76} -3.45242e6 q^{77} +4.24810e6 q^{78} -7.44014e6 q^{79} -4.02131e6 q^{80} -5.17199e6 q^{81} -4.57974e6 q^{82} +5.50388e6 q^{83} +5.46159e6 q^{84} +5.74447e6 q^{85} +1.20485e6 q^{86} +6.44900e6 q^{87} -1.25252e6 q^{88} -3.53700e6 q^{89} -624390. q^{90} -6.32268e6 q^{91} +1.22227e6 q^{92} +1.37406e7 q^{93} -3.56182e6 q^{94} +1.15359e7 q^{95} +1.16047e7 q^{96} -2.08749e6 q^{97} -5.88530e6 q^{98} -612544. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9}+O(q^{10}) \) 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9	\( 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9} + 4667 q^{10} + 1620 q^{11} - 19681 q^{12} + 13550 q^{13} + 44160 q^{14} + 31412 q^{15} + 114026 q^{16} + 110880 q^{17} + 159267 q^{18} + 105058 q^{19} + 167251 q^{20} + 129840 q^{21} + 201504 q^{22} + 160184 q^{23} + 161289 q^{24} + 270149 q^{25} + 272104 q^{26} + 252544 q^{27} + 208172 q^{28} + 285546 q^{29} + 107580 q^{30} - 99616 q^{31} + 200126 q^{32} + 531468 q^{33} - 80941 q^{34} - 187104 q^{35} - 608975 q^{36} + 176038 q^{37} + 652165 q^{38} - 794680 q^{39} - 895387 q^{40} - 410260 q^{41} - 3413218 q^{42} - 1033591 q^{43} - 2177076 q^{44} - 1051178 q^{45} - 3975765 q^{46} - 424556 q^{47} - 2360477 q^{48} - 1561359 q^{49} - 4063801 q^{50} - 2375738 q^{51} - 4172312 q^{52} + 3992458 q^{53} - 10438626 q^{54} + 406960 q^{55} + 1559556 q^{56} - 3116152 q^{57} - 4052005 q^{58} + 2248836 q^{59} - 2911436 q^{60} + 6210394 q^{61} + 885317 q^{62} + 11622368 q^{63} - 3096318 q^{64} + 5600420 q^{65} - 2174604 q^{66} - 1993648 q^{67} + 9327135 q^{68} + 13366240 q^{69} - 1105098 q^{70} + 4978064 q^{71} + 11370663 q^{72} + 8224814 q^{73} - 3613563 q^{74} + 27115592 q^{75} + 10687121 q^{76} + 17261892 q^{77} - 15226630 q^{78} + 6945708 q^{79} + 15822799 q^{80} + 35113185 q^{81} - 508449 q^{82} + 22937328 q^{83} - 14010106 q^{84} - 575532 q^{85} - 1272112 q^{86} + 9081380 q^{87} + 11202656 q^{88} + 9291302 q^{89} + 2841402 q^{90} + 25581108 q^{91} - 14388137 q^{92} + 25930480 q^{93} - 24645805 q^{94} + 30750464 q^{95} - 22461255 q^{96} + 10001852 q^{97} - 32304856 q^{98} + 5055452 q^{99}+O(q^{100}) \) 13 * q + 16 * q^2 + 94 * q^3 + 922 * q^4 + 998 * q^5 + 183 * q^6 + 1360 * q^7 + 3870 * q^8 + 10011 * q^9 + 4667 * q^10 + 1620 * q^11 - 19681 * q^12 + 13550 * q^13 + 44160 * q^14 + 31412 * q^15 + 114026 * q^16 + 110880 * q^17 + 159267 * q^18 + 105058 * q^19 + 167251 * q^20 + 129840 * q^21 + 201504 * q^22 + 160184 * q^23 + 161289 * q^24 + 270149 * q^25 + 272104 * q^26 + 252544 * q^27 + 208172 * q^28 + 285546 * q^29 + 107580 * q^30 - 99616 * q^31 + 200126 * q^32 + 531468 * q^33 - 80941 * q^34 - 187104 * q^35 - 608975 * q^36 + 176038 * q^37 + 652165 * q^38 - 794680 * q^39 - 895387 * q^40 - 410260 * q^41 - 3413218 * q^42 - 1033591 * q^43 - 2177076 * q^44 - 1051178 * q^45 - 3975765 * q^46 - 424556 * q^47 - 2360477 * q^48 - 1561359 * q^49 - 4063801 * q^50 - 2375738 * q^51 - 4172312 * q^52 + 3992458 * q^53 - 10438626 * q^54 + 406960 * q^55 + 1559556 * q^56 - 3116152 * q^57 - 4052005 * q^58 + 2248836 * q^59 - 2911436 * q^60 + 6210394 * q^61 + 885317 * q^62 + 11622368 * q^63 - 3096318 * q^64 + 5600420 * q^65 - 2174604 * q^66 - 1993648 * q^67 + 9327135 * q^68 + 13366240 * q^69 - 1105098 * q^70 + 4978064 * q^71 + 11370663 * q^72 + 8224814 * q^73 - 3613563 * q^74 + 27115592 * q^75 + 10687121 * q^76 + 17261892 * q^77 - 15226630 * q^78 + 6945708 * q^79 + 15822799 * q^80 + 35113185 * q^81 - 508449 * q^82 + 22937328 * q^83 - 14010106 * q^84 - 575532 * q^85 - 1272112 * q^86 + 9081380 * q^87 + 11202656 * q^88 + 9291302 * q^89 + 2841402 * q^90 + 25581108 * q^91 - 14388137 * q^92 + 25930480 * q^93 - 24645805 * q^94 + 30750464 * q^95 - 22461255 * q^96 + 10001852 * q^97 - 32304856 * q^98 + 5055452 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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