LMFDB - Embedded newform 43.8.a.b.1.5

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			1.5
Root			$-4.99525$ 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)

$f(q)$	$=$	$q-3.99525 q^{2} +84.4924 q^{3} -112.038 q^{4} -383.451 q^{5} -337.568 q^{6} +1003.83 q^{7} +959.011 q^{8} +4951.96 q^{9} +O(q^{10})$	\(q-3.99525 q^{2} +84.4924 q^{3} -112.038 q^{4} -383.451 q^{5} -337.568 q^{6} +1003.83 q^{7} +959.011 q^{8} +4951.96 q^{9} +1531.98 q^{10} +1620.93 q^{11} -9466.36 q^{12} +7962.52 q^{13} -4010.57 q^{14} -32398.7 q^{15} +10509.4 q^{16} +36412.1 q^{17} -19784.3 q^{18} -40353.3 q^{19} +42961.1 q^{20} +84816.3 q^{21} -6476.03 q^{22} +13321.7 q^{23} +81029.1 q^{24} +68909.7 q^{25} -31812.2 q^{26} +233618. q^{27} -112468. q^{28} +119451. q^{29} +129441. q^{30} -103590. q^{31} -164741. q^{32} +136956. q^{33} -145476. q^{34} -384921. q^{35} -554808. q^{36} +191874. q^{37} +161221. q^{38} +672772. q^{39} -367734. q^{40} -240868. q^{41} -338862. q^{42} -79507.0 q^{43} -181606. q^{44} -1.89884e6 q^{45} -53223.7 q^{46} +502478. q^{47} +887962. q^{48} +184140. q^{49} -275311. q^{50} +3.07655e6 q^{51} -892105. q^{52} +1.09942e6 q^{53} -933363. q^{54} -621548. q^{55} +962688. q^{56} -3.40954e6 q^{57} -477236. q^{58} -2.43199e6 q^{59} +3.62988e6 q^{60} -620335. q^{61} +413868. q^{62} +4.97095e6 q^{63} -687019. q^{64} -3.05324e6 q^{65} -547175. q^{66} -4.73308e6 q^{67} -4.07954e6 q^{68} +1.12559e6 q^{69} +1.53786e6 q^{70} -2.81874e6 q^{71} +4.74899e6 q^{72} +2.78345e6 q^{73} -766582. q^{74} +5.82235e6 q^{75} +4.52110e6 q^{76} +1.62715e6 q^{77} -2.68789e6 q^{78} +6.00989e6 q^{79} -4.02983e6 q^{80} +8.90902e6 q^{81} +962329. q^{82} +4.68609e6 q^{83} -9.50265e6 q^{84} -1.39623e7 q^{85} +317650. q^{86} +1.00927e7 q^{87} +1.55449e6 q^{88} +2.94676e6 q^{89} +7.58632e6 q^{90} +7.99305e6 q^{91} -1.49254e6 q^{92} -8.75257e6 q^{93} -2.00753e6 q^{94} +1.54735e7 q^{95} -1.39194e7 q^{96} -1.41877e7 q^{97} -735685. q^{98} +8.02680e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−3.99525	−0.353133	−0.176567	−	0.984289i	$-0.556499\pi$
$2$	−3.99525	−0.353133	−0.176567	+	0.984289i	$0.556499\pi$
$3$	84.4924	1.80673	0.903365	−	0.428873i	$-0.141089\pi$
$3$	84.4924	1.80673	0.903365	+	0.428873i	$0.141089\pi$
$4$	−112.038	−0.875297
$5$	−383.451	−1.37188	−0.685938	−	0.727660i	$-0.740608\pi$
$5$	−383.451	−1.37188	−0.685938	+	0.727660i	$0.740608\pi$
$6$	−337.568	−0.638016
$7$	1003.83	1.10616	0.553081	−	0.833127i	$-0.313452\pi$
$7$	1003.83	1.10616	0.553081	+	0.833127i	$0.313452\pi$
$8$	959.011	0.662230
$9$	4951.96	2.26427
$10$	1531.98	0.484455
$11$	1620.93	0.367190	0.183595	−	0.983002i	$-0.441227\pi$
$11$	1620.93	0.367190	0.183595	+	0.983002i	$0.441227\pi$
$12$	−9466.36	−1.58142
$13$	7962.52	1.00519	0.502596	−	0.864522i	$-0.332378\pi$
$13$	7962.52	1.00519	0.502596	+	0.864522i	$0.332378\pi$
$14$	−4010.57	−0.390623
$15$	−32398.7	−2.47861
$16$	10509.4	0.641441
$17$	36412.1	1.79753	0.898763	−	0.438435i	$-0.144467\pi$
$17$	36412.1	1.79753	0.898763	+	0.438435i	$0.144467\pi$
$18$	−19784.3	−0.799590
$19$	−40353.3	−1.34971	−0.674856	−	0.737950i	$-0.735794\pi$
$19$	−40353.3	−1.34971	−0.674856	+	0.737950i	$0.735794\pi$
$20$	42961.1	1.20080
$21$	84816.3	1.99854
$22$	−6476.03	−0.129667
$23$	13321.7	0.228304	0.114152	−	0.993463i	$-0.463585\pi$
$23$	13321.7	0.228304	0.114152	+	0.993463i	$0.463585\pi$
$24$	81029.1	1.19647
$25$	68909.7	0.882044
$26$	−31812.2	−0.354967
$27$	233618.	2.28420
$28$	−112468.	−0.968220
$29$	119451.	0.909487	0.454743	−	0.890623i	$-0.349731\pi$
$29$	119451.	0.909487	0.454743	+	0.890623i	$0.349731\pi$
$30$	129441.	0.875280
$31$	−103590.	−0.624529	−0.312264	−	0.949995i	$-0.601087\pi$
$31$	−103590.	−0.624529	−0.312264	+	0.949995i	$0.601087\pi$
$32$	−164741.	−0.888744
$33$	136956.	0.663413
$34$	−145476.	−0.634766
$35$	−384921.	−1.51752
$36$	−554808.	−1.98191
$37$	191874.	0.622743	0.311372	−	0.950288i	$-0.399212\pi$
$37$	191874.	0.622743	0.311372	+	0.950288i	$0.399212\pi$
$38$	161221.	0.476628
$39$	672772.	1.81611
$40$	−367734.	−0.908497
$41$	−240868.	−0.545804	−0.272902	−	0.962042i	$-0.587983\pi$
$41$	−240868.	−0.545804	−0.272902	+	0.962042i	$0.587983\pi$
$42$	−338862.	−0.705750
$43$	−79507.0	−0.152499
$43$	−79507.0	−0.152499
$44$	−181606.	−0.321400
$45$	−1.89884e6	−3.10630
$46$	−53223.7	−0.0806218
$47$	502478.	0.705951	0.352976	−	0.935632i	$-0.385170\pi$
$47$	502478.	0.705951	0.352976	+	0.935632i	$0.385170\pi$
$48$	887962.	1.15891
$49$	184140.	0.223595
$50$	−275311.	−0.311479
$51$	3.07655e6	3.24764
$52$	−892105.	−0.879841
$53$	1.09942e6	1.01437	0.507187	−	0.861836i	$-0.330685\pi$
$53$	1.09942e6	1.01437	0.507187	+	0.861836i	$0.330685\pi$
$54$	−933363.	−0.806626
$55$	−621548.	−0.503739
$56$	962688.	0.732534
$57$	−3.40954e6	−2.43856
$58$	−477236.	−0.321170
$59$	−2.43199e6	−1.54163	−0.770813	−	0.637061i	$-0.780150\pi$
$59$	−2.43199e6	−1.54163	−0.770813	+	0.637061i	$0.780150\pi$
$60$	3.62988e6	2.16952
$61$	−620335.	−0.349923	−0.174961	−	0.984575i	$-0.555980\pi$
$61$	−620335.	−0.349923	−0.174961	+	0.984575i	$0.555980\pi$
$62$	413868.	0.220542
$63$	4.97095e6	2.50465
$64$	−687019.	−0.327596
$65$	−3.05324e6	−1.37900
$66$	−547175.	−0.234273
$67$	−4.73308e6	−1.92257	−0.961285	−	0.275555i	$-0.911138\pi$
$67$	−4.73308e6	−1.92257	−0.961285	+	0.275555i	$0.911138\pi$
$68$	−4.07954e6	−1.57337
$69$	1.12559e6	0.412484
$70$	1.53786e6	0.535886
$71$	−2.81874e6	−0.934655	−0.467327	−	0.884084i	$-0.654783\pi$
$71$	−2.81874e6	−0.934655	−0.467327	+	0.884084i	$0.654783\pi$
$72$	4.74899e6	1.49947
$73$	2.78345e6	0.837440	0.418720	−	0.908115i	$-0.362479\pi$
$73$	2.78345e6	0.837440	0.418720	+	0.908115i	$0.362479\pi$
$74$	−766582.	−0.219911
$75$	5.82235e6	1.59362
$76$	4.52110e6	1.18140
$77$	1.62715e6	0.406172
$78$	−2.68789e6	−0.641329
$79$	6.00989e6	1.37142	0.685712	−	0.727873i	$-0.259491\pi$
$79$	6.00989e6	1.37142	0.685712	+	0.727873i	$0.259491\pi$
$80$	−4.02983e6	−0.879978
$81$	8.90902e6	1.86265
$82$	962329.	0.192741
$83$	4.68609e6	0.899574	0.449787	−	0.893136i	$-0.351500\pi$
$83$	4.68609e6	0.899574	0.449787	+	0.893136i	$0.351500\pi$
$84$	−9.50265e6	−1.74931
$85$	−1.39623e7	−2.46598
$86$	317650.	0.0538523
$87$	1.00927e7	1.64320
$88$	1.55449e6	0.243164
$89$	2.94676e6	0.443077	0.221539	−	0.975152i	$-0.428892\pi$
$89$	2.94676e6	0.443077	0.221539	+	0.975152i	$0.428892\pi$
$90$	7.58632e6	1.09694
$91$	7.99305e6	1.11191
$92$	−1.49254e6	−0.199834
$93$	−8.75257e6	−1.12835
$94$	−2.00753e6	−0.249295
$95$	1.54735e7	1.85164
$96$	−1.39194e7	−1.60572
$97$	−1.41877e7	−1.57838	−0.789192	−	0.614147i	$-0.789500\pi$
$97$	−1.41877e7	−1.57838	−0.789192	+	0.614147i	$0.789500\pi$
$98$	−735685.	−0.0789588
$99$	8.02680e6	0.831418
$100$	−7.72051e6	−0.772051
$101$	1.46728e7	1.41706	0.708531	−	0.705680i	$-0.249358\pi$
$101$	1.46728e7	1.41706	0.708531	+	0.705680i	$0.249358\pi$
$102$	−1.22916e7	−1.14685
$103$	−1.29765e7	−1.17011	−0.585057	−	0.810992i	$-0.698928\pi$
$103$	−1.29765e7	−1.17011	−0.585057	+	0.810992i	$0.698928\pi$
$104$	7.63615e6	0.665668
$105$	−3.25229e7	−2.74174
$106$	−4.39246e6	−0.358209
$107$	−1.57757e7	−1.24493	−0.622464	−	0.782648i	$-0.713868\pi$
$107$	−1.57757e7	−1.24493	−0.622464	+	0.782648i	$0.713868\pi$
$108$	−2.61741e7	−1.99935
$109$	1.93156e7	1.42861	0.714307	−	0.699833i	$-0.246742\pi$
$109$	1.93156e7	1.42861	0.714307	+	0.699833i	$0.246742\pi$
$110$	2.48324e6	0.177887
$111$	1.62119e7	1.12513
$112$	1.05497e7	0.709538
$113$	−2.22839e6	−0.145283	−0.0726417	−	0.997358i	$-0.523143\pi$
$113$	−2.22839e6	−0.145283	−0.0726417	+	0.997358i	$0.523143\pi$
$114$	1.36220e7	0.861138
$115$	−5.10824e6	−0.313205
$116$	−1.33830e7	−0.796071
$117$	3.94301e7	2.27603
$118$	9.71639e6	0.544400
$119$	3.65518e7	1.98835
$120$	−3.10707e7	−1.64141
$121$	−1.68597e7	−0.865172
$122$	2.47839e6	0.123569
$123$	−2.03515e7	−0.986119
$124$	1.16060e7	0.546648
$125$	3.53361e6	0.161821
$126$	−1.98602e7	−0.884476
$127$	−3.40735e7	−1.47606	−0.738028	−	0.674770i	$-0.764243\pi$
$127$	−3.40735e7	−1.47606	−0.738028	+	0.674770i	$0.764243\pi$
$128$	2.38317e7	1.00443
$129$	−6.71774e6	−0.275524
$130$	1.21984e7	0.486970
$131$	3.55332e7	1.38097	0.690487	−	0.723345i	$-0.257396\pi$
$131$	3.55332e7	1.38097	0.690487	+	0.723345i	$0.257396\pi$
$132$	−1.53443e7	−0.580683
$133$	−4.05080e7	−1.49300
$134$	1.89098e7	0.678924
$135$	−8.95812e7	−3.13364
$136$	3.49197e7	1.19037
$137$	−3.77219e7	−1.25335	−0.626674	−	0.779281i	$-0.715584\pi$
$137$	−3.77219e7	−1.25335	−0.626674	+	0.779281i	$0.715584\pi$
$138$	−4.49699e6	−0.145662
$139$	1.44974e7	0.457867	0.228934	−	0.973442i	$-0.426476\pi$
$139$	1.44974e7	0.457867	0.228934	+	0.973442i	$0.426476\pi$
$140$	4.31258e7	1.32828
$141$	4.24556e7	1.27546
$142$	1.12616e7	0.330058
$143$	1.29067e7	0.369096
$144$	5.20420e7	1.45240
$145$	−4.58036e7	−1.24770
$146$	−1.11206e7	−0.295728
$147$	1.55584e7	0.403976
$148$	−2.14971e7	−0.545085
$149$	2.17133e7	0.537743	0.268871	−	0.963176i	$-0.413349\pi$
$149$	2.17133e7	0.537743	0.268871	+	0.963176i	$0.413349\pi$
$150$	−2.32617e7	−0.562759
$151$	−1.73559e7	−0.410231	−0.205115	−	0.978738i	$-0.565757\pi$
$151$	−1.73559e7	−0.410231	−0.205115	+	0.978738i	$0.565757\pi$
$152$	−3.86992e7	−0.893819
$153$	1.80312e8	4.07009
$154$	−6.50086e6	−0.143433
$155$	3.97217e7	0.856776
$156$	−7.53761e7	−1.58963
$157$	−2.86214e6	−0.0590258	−0.0295129	−	0.999564i	$-0.509396\pi$
$157$	−2.86214e6	−0.0590258	−0.0295129	+	0.999564i	$0.509396\pi$
$158$	−2.40110e7	−0.484296
$159$	9.28927e7	1.83270
$160$	6.31701e7	1.21925
$161$	1.33728e7	0.252541
$162$	−3.55937e7	−0.657766
$163$	2.66759e7	0.482461	0.241231	−	0.970468i	$-0.422449\pi$
$163$	2.66759e7	0.482461	0.241231	+	0.970468i	$0.422449\pi$
$164$	2.69864e7	0.477740
$165$	−5.25161e7	−0.910120
$166$	−1.87221e7	−0.317670
$167$	−4.84714e7	−0.805337	−0.402669	−	0.915346i	$-0.631917\pi$
$167$	−4.84714e7	−0.805337	−0.402669	+	0.915346i	$0.631917\pi$
$168$	8.13398e7	1.32349
$169$	653231.	0.0104103
$170$	5.57827e7	0.870821
$171$	−1.99828e8	−3.05611
$172$	8.90781e6	0.133482
$173$	1.18312e8	1.73726	0.868632	−	0.495458i	$-0.165000\pi$
$173$	1.18312e8	1.73726	0.868632	+	0.495458i	$0.165000\pi$
$174$	−4.03228e7	−0.580267
$175$	6.91739e7	0.975684
$176$	1.70350e7	0.235531
$177$	−2.05484e8	−2.78530
$178$	−1.17730e7	−0.156465
$179$	−3.21297e7	−0.418718	−0.209359	−	0.977839i	$-0.567138\pi$
$179$	−3.21297e7	−0.418718	−0.209359	+	0.977839i	$0.567138\pi$
$180$	2.12742e8	2.71894
$181$	−1.19731e8	−1.50083	−0.750413	−	0.660969i	$-0.770145\pi$
$181$	−1.19731e8	−1.50083	−0.750413	+	0.660969i	$0.770145\pi$
$182$	−3.19342e7	−0.392651
$183$	−5.24136e7	−0.632216
$184$	1.27757e7	0.151190
$185$	−7.35741e7	−0.854327
$186$	3.49687e7	0.398459
$187$	5.90216e7	0.660033
$188$	−5.62967e7	−0.617917
$189$	2.34514e8	2.52669
$190$	−6.18205e7	−0.653875
$191$	−2.39670e7	−0.248884	−0.124442	−	0.992227i	$-0.539714\pi$
$191$	−2.39670e7	−0.248884	−0.124442	+	0.992227i	$0.539714\pi$
$192$	−5.80479e7	−0.591878
$193$	5.81894e7	0.582631	0.291315	−	0.956627i	$-0.405907\pi$
$193$	5.81894e7	0.582631	0.291315	+	0.956627i	$0.405907\pi$
$194$	5.66836e7	0.557380
$195$	−2.57975e8	−2.49148
$196$	−2.06307e7	−0.195712
$197$	−1.66210e6	−0.0154890	−0.00774452	−	0.999970i	$-0.502465\pi$
$197$	−1.66210e6	−0.0154890	−0.00774452	+	0.999970i	$0.502465\pi$
$198$	−3.20690e7	−0.293601
$199$	2.39093e7	0.215070	0.107535	−	0.994201i	$-0.465704\pi$
$199$	2.39093e7	0.215070	0.107535	+	0.994201i	$0.465704\pi$
$200$	6.60852e7	0.584116
$201$	−3.99909e8	−3.47357
$202$	−5.86216e7	−0.500412
$203$	1.19909e8	1.00604
$204$	−3.44690e8	−2.84265
$205$	9.23612e7	0.748775
$206$	5.18444e7	0.413206
$207$	6.59688e7	0.516943
$208$	8.36811e7	0.644772
$209$	−6.54099e7	−0.495600
$210$	1.29937e8	0.968201
$211$	−1.89004e7	−0.138510	−0.0692550	−	0.997599i	$-0.522062\pi$
$211$	−1.89004e7	−0.138510	−0.0692550	+	0.997599i	$0.522062\pi$
$212$	−1.23177e8	−0.887879
$213$	−2.38162e8	−1.68867
$214$	6.30277e7	0.439626
$215$	3.04870e7	0.209209
$216$	2.24043e8	1.51266
$217$	−1.03987e8	−0.690830
$218$	−7.71705e7	−0.504491
$219$	2.35180e8	1.51303
$220$	6.96370e7	0.440921
$221$	2.89933e8	1.80686
$222$	−6.47704e7	−0.397320
$223$	−2.65364e8	−1.60241	−0.801207	−	0.598387i	$-0.795808\pi$
$223$	−2.65364e8	−1.60241	−0.801207	+	0.598387i	$0.795808\pi$
$224$	−1.65373e8	−0.983095
$225$	3.41238e8	1.99719
$226$	8.90296e6	0.0513044
$227$	2.54830e8	1.44597	0.722986	−	0.690862i	$-0.242769\pi$
$227$	2.54830e8	1.44597	0.722986	+	0.690862i	$0.242769\pi$
$228$	3.81998e8	2.13447
$229$	−1.45333e8	−0.799727	−0.399863	−	0.916575i	$-0.630942\pi$
$229$	−1.45333e8	−0.799727	−0.399863	+	0.916575i	$0.630942\pi$
$230$	2.04087e7	0.110603
$231$	1.37482e8	0.733842
$232$	1.14555e8	0.602289
$233$	6.81068e7	0.352732	0.176366	−	0.984325i	$-0.443566\pi$
$233$	6.81068e7	0.352732	0.176366	+	0.984325i	$0.443566\pi$
$234$	−1.57533e8	−0.803741
$235$	−1.92676e8	−0.968478
$236$	2.72475e8	1.34938
$237$	5.07790e8	2.47779
$238$	−1.46033e8	−0.702154
$239$	−2.19022e8	−1.03776	−0.518878	−	0.854848i	$-0.673650\pi$
$239$	−2.19022e8	−1.03776	−0.518878	+	0.854848i	$0.673650\pi$
$240$	−3.40490e8	−1.58988
$241$	1.44105e7	0.0663160	0.0331580	−	0.999450i	$-0.489444\pi$
$241$	1.44105e7	0.0663160	0.0331580	+	0.999450i	$0.489444\pi$
$242$	6.73589e7	0.305521
$243$	2.41821e8	1.08112
$244$	6.95011e7	0.306286
$245$	−7.06087e7	−0.306745
$246$	8.13095e7	0.348232
$247$	−3.21314e8	−1.35672
$248$	−9.93441e7	−0.413581
$249$	3.95939e8	1.62529
$250$	−1.41177e7	−0.0571442
$251$	−2.09847e8	−0.837615	−0.418808	−	0.908075i	$-0.637552\pi$
$251$	−2.09847e8	−0.837615	−0.418808	+	0.908075i	$0.637552\pi$
$252$	−5.56935e8	−2.19231
$253$	2.15937e7	0.0838309
$254$	1.36132e8	0.521245
$255$	−1.17971e9	−4.45536
$256$	−7.27492e6	−0.0271012
$257$	−2.67717e8	−0.983808	−0.491904	−	0.870649i	$-0.663699\pi$
$257$	−2.67717e8	−0.983808	−0.491904	+	0.870649i	$0.663699\pi$
$258$	2.68390e7	0.0972966
$259$	1.92609e8	0.688855
$260$	3.42079e8	1.20703
$261$	5.91516e8	2.05932
$262$	−1.41964e8	−0.487668
$263$	−1.00008e8	−0.338993	−0.169497	−	0.985531i	$-0.554214\pi$
$263$	−1.00008e8	−0.338993	−0.169497	+	0.985531i	$0.554214\pi$
$264$	1.31343e8	0.439332
$265$	−4.21574e8	−1.39160
$266$	1.61839e8	0.527228
$267$	2.48979e8	0.800521
$268$	5.30285e8	1.68282
$269$	8.77731e7	0.274934	0.137467	−	0.990506i	$-0.456104\pi$
$269$	8.77731e7	0.274934	0.137467	+	0.990506i	$0.456104\pi$
$270$	3.57899e8	1.10659
$271$	−2.14577e8	−0.654924	−0.327462	−	0.944864i	$-0.606193\pi$
$271$	−2.14577e8	−0.654924	−0.327462	+	0.944864i	$0.606193\pi$
$272$	3.82669e8	1.15301
$273$	6.75352e8	2.00891
$274$	1.50708e8	0.442599
$275$	1.11698e8	0.323878
$276$	−1.26108e8	−0.361046
$277$	−3.67563e8	−1.03909	−0.519544	−	0.854443i	$-0.673898\pi$
$277$	−3.67563e8	−1.03909	−0.519544	+	0.854443i	$0.673898\pi$
$278$	−5.79208e7	−0.161688
$279$	−5.12974e8	−1.41410
$280$	−3.69144e8	−1.00495
$281$	−3.86156e8	−1.03822	−0.519111	−	0.854707i	$-0.673737\pi$
$281$	−3.86156e8	−1.03822	−0.519111	+	0.854707i	$0.673737\pi$
$282$	−1.69621e8	−0.450409
$283$	2.07849e7	0.0545125	0.0272562	−	0.999628i	$-0.491323\pi$
$283$	2.07849e7	0.0545125	0.0272562	+	0.999628i	$0.491323\pi$
$284$	3.15806e8	0.818100
$285$	1.30739e9	3.34541
$286$	−5.15655e7	−0.130340
$287$	−2.41792e8	−0.603747
$288$	−8.15791e8	−2.01236
$289$	9.15506e8	2.23110
$290$	1.82997e8	0.440606
$291$	−1.19876e9	−2.85171
$292$	−3.11852e8	−0.733008
$293$	9.72174e7	0.225791	0.112896	−	0.993607i	$-0.463987\pi$
$293$	9.72174e7	0.225791	0.112896	+	0.993607i	$0.463987\pi$
$294$	−6.21598e7	−0.142657
$295$	9.32548e8	2.11492
$296$	1.84009e8	0.412399
$297$	3.78680e8	0.838734
$298$	−8.67501e7	−0.189895
$299$	1.06075e8	0.229489
$300$	−6.52324e8	−1.39489
$301$	−7.98118e7	−0.168688
$302$	6.93412e7	0.144866
$303$	1.23974e9	2.56025
$304$	−4.24088e8	−0.865761
$305$	2.37868e8	0.480051
$306$	−7.20389e8	−1.43728
$307$	−8.13750e8	−1.60512	−0.802558	−	0.596573i	$-0.796528\pi$
$307$	−8.13750e8	−1.60512	−0.802558	+	0.596573i	$0.796528\pi$
$308$	−1.82302e8	−0.355521
$309$	−1.09642e9	−2.11408
$310$	−1.58698e8	−0.302556
$311$	−4.77734e7	−0.0900585	−0.0450293	−	0.998986i	$-0.514338\pi$
$311$	−4.77734e7	−0.0900585	−0.0450293	+	0.998986i	$0.514338\pi$
$312$	6.45196e8	1.20268
$313$	4.14127e7	0.0763357	0.0381679	−	0.999271i	$-0.487848\pi$
$313$	4.14127e7	0.0763357	0.0381679	+	0.999271i	$0.487848\pi$
$314$	1.14349e7	0.0208440
$315$	−1.90612e9	−3.43607
$316$	−6.73336e8	−1.20040
$317$	1.29531e8	0.228385	0.114192	−	0.993459i	$-0.463572\pi$
$317$	1.29531e8	0.228385	0.114192	+	0.993459i	$0.463572\pi$
$318$	−3.71129e8	−0.647188
$319$	1.93622e8	0.333954
$320$	2.63438e8	0.449422
$321$	−1.33292e9	−2.24925
$322$	−5.34277e7	−0.0891808
$323$	−1.46935e9	−2.42614
$324$	−9.98149e8	−1.63038
$325$	5.48695e8	0.886624
$326$	−1.06577e8	−0.170373
$327$	1.63202e9	2.58112
$328$	−2.30995e8	−0.361447
$329$	5.04405e8	0.780897
$330$	2.09815e8	0.321394
$331$	1.06545e9	1.61486	0.807431	−	0.589962i	$-0.200857\pi$
$331$	1.06545e9	1.61486	0.807431	+	0.589962i	$0.200857\pi$
$332$	−5.25020e8	−0.787395
$333$	9.50151e8	1.41006
$334$	1.93655e8	0.284391
$335$	1.81491e9	2.63753
$336$	8.91367e8	1.28194
$337$	−2.29211e8	−0.326235	−0.163118	−	0.986607i	$-0.552155\pi$
$337$	−2.29211e8	−0.326235	−0.163118	+	0.986607i	$0.552155\pi$
$338$	−2.60982e6	−0.00367622
$339$	−1.88282e8	−0.262488
$340$	1.56431e9	2.15847
$341$	−1.67913e8	−0.229321
$342$	7.98362e8	1.07922
$343$	−6.41855e8	−0.858830
$344$	−7.62481e7	−0.100989
$345$	−4.31607e8	−0.565877
$346$	−4.72684e8	−0.613486
$347$	−5.28413e8	−0.678923	−0.339461	−	0.940620i	$-0.610245\pi$
$347$	−5.28413e8	−0.678923	−0.339461	+	0.940620i	$0.610245\pi$
$348$	−1.13076e9	−1.43828
$349$	−4.51049e6	−0.00567982	−0.00283991	−	0.999996i	$-0.500904\pi$
$349$	−4.51049e6	−0.00567982	−0.00283991	+	0.999996i	$0.500904\pi$
$350$	−2.76367e8	−0.344547
$351$	1.86019e9	2.29606
$352$	−2.67034e8	−0.326338
$353$	2.41469e8	0.292179	0.146090	−	0.989271i	$-0.453331\pi$
$353$	2.41469e8	0.292179	0.146090	+	0.989271i	$0.453331\pi$
$354$	8.20961e8	0.983583
$355$	1.08085e9	1.28223
$356$	−3.30149e8	−0.387824
$357$	3.08834e9	3.59242
$358$	1.28366e8	0.147863
$359$	−7.82115e8	−0.892154	−0.446077	−	0.894995i	$-0.647179\pi$
$359$	−7.82115e8	−0.892154	−0.446077	+	0.894995i	$0.647179\pi$
$360$	−1.82100e9	−2.05708
$361$	7.34514e8	0.821722
$362$	4.78353e8	0.529992
$363$	−1.42452e9	−1.56313
$364$	−8.95525e8	−0.973247
$365$	−1.06732e9	−1.14886
$366$	2.09405e8	0.223256
$367$	−2.09454e8	−0.221186	−0.110593	−	0.993866i	$-0.535275\pi$
$367$	−2.09454e8	−0.221186	−0.110593	+	0.993866i	$0.535275\pi$
$368$	1.40003e8	0.146444
$369$	−1.19277e9	−1.23585
$370$	2.93947e8	0.301691
$371$	1.10364e9	1.12206
$372$	9.80621e8	0.987645
$373$	7.65743e8	0.764015	0.382008	−	0.924159i	$-0.375233\pi$
$373$	7.65743e8	0.764015	0.382008	+	0.924159i	$0.375233\pi$
$374$	−2.35806e8	−0.233080
$375$	2.98563e8	0.292366
$376$	4.81882e8	0.467502
$377$	9.51130e8	0.914208
$378$	−9.36941e8	−0.892259
$379$	5.91930e8	0.558513	0.279257	−	0.960217i	$-0.409912\pi$
$379$	5.91930e8	0.558513	0.279257	+	0.960217i	$0.409912\pi$
$380$	−1.73362e9	−1.62073
$381$	−2.87895e9	−2.66684
$382$	9.57543e7	0.0878894
$383$	1.93100e9	1.75625	0.878125	−	0.478432i	$-0.158795\pi$
$383$	1.93100e9	1.75625	0.878125	+	0.478432i	$0.158795\pi$
$384$	2.01359e9	1.81473
$385$	−6.23932e8	−0.557217
$386$	−2.32481e8	−0.205746
$387$	−3.93716e8	−0.345298
$388$	1.58957e9	1.38155
$389$	−2.18340e8	−0.188066	−0.0940330	−	0.995569i	$-0.529976\pi$
$389$	−2.18340e8	−0.188066	−0.0940330	+	0.995569i	$0.529976\pi$
$390$	1.03068e9	0.879824
$391$	4.85073e8	0.410382
$392$	1.76592e8	0.148071
$393$	3.00229e9	2.49505
$394$	6.64048e6	0.00546969
$395$	−2.30450e9	−1.88142
$396$	−8.99306e8	−0.727737
$397$	1.18371e9	0.949464	0.474732	−	0.880130i	$-0.342545\pi$
$397$	1.18371e9	0.949464	0.474732	+	0.880130i	$0.342545\pi$
$398$	−9.55235e7	−0.0759485
$399$	−3.42262e9	−2.69745
$400$	7.24198e8	0.565780
$401$	−1.56318e9	−1.21061	−0.605304	−	0.795994i	$-0.706948\pi$
$401$	−1.56318e9	−1.21061	−0.605304	+	0.795994i	$0.706948\pi$
$402$	1.59774e9	1.22663
$403$	−8.24838e8	−0.627771
$404$	−1.64391e9	−1.24035
$405$	−3.41617e9	−2.55533
$406$	−4.79066e8	−0.355266
$407$	3.11014e8	0.228665
$408$	2.95044e9	2.15069
$409$	−2.43312e8	−0.175846	−0.0879230	−	0.996127i	$-0.528023\pi$
$409$	−2.43312e8	−0.175846	−0.0879230	+	0.996127i	$0.528023\pi$
$410$	−3.69006e8	−0.264417
$411$	−3.18721e9	−2.26446
$412$	1.45386e9	1.02420
$413$	−2.44131e9	−1.70529
$414$	−2.63562e8	−0.182550
$415$	−1.79689e9	−1.23410
$416$	−1.31175e9	−0.893358
$417$	1.22492e9	0.827242
$418$	2.61329e8	0.175013
$419$	−8.76950e8	−0.582406	−0.291203	−	0.956661i	$-0.594056\pi$
$419$	−8.76950e8	−0.582406	−0.291203	+	0.956661i	$0.594056\pi$
$420$	3.64380e9	2.39984
$421$	4.62306e7	0.0301955	0.0150977	−	0.999886i	$-0.495194\pi$
$421$	4.62306e7	0.0301955	0.0150977	+	0.999886i	$0.495194\pi$
$422$	7.55116e7	0.0489125
$423$	2.48825e9	1.59847
$424$	1.05436e9	0.671749
$425$	2.50915e9	1.58550
$426$	9.51517e8	0.596325
$427$	−6.22714e8	−0.387071
$428$	1.76747e9	1.08968
$429$	1.09052e9	0.666857
$430$	−1.21803e8	−0.0738787
$431$	2.41795e9	1.45471	0.727355	−	0.686261i	$-0.240749\pi$
$431$	2.41795e9	1.45471	0.727355	+	0.686261i	$0.240749\pi$
$432$	2.45518e9	1.46518
$433$	−2.05635e9	−1.21728	−0.608638	−	0.793448i	$-0.708284\pi$
$433$	−2.05635e9	−1.21728	−0.608638	+	0.793448i	$0.708284\pi$
$434$	4.15455e8	0.243955
$435$	−3.87005e9	−2.25426
$436$	−2.16408e9	−1.25046
$437$	−5.37576e8	−0.308145
$438$	−9.39604e8	−0.534300
$439$	−3.96658e8	−0.223764	−0.111882	−	0.993722i	$-0.535688\pi$
$439$	−3.96658e8	−0.223764	−0.111882	+	0.993722i	$0.535688\pi$
$440$	−5.96072e8	−0.333591
$441$	9.11854e8	0.506280
$442$	−1.15835e9	−0.638062
$443$	−2.23365e9	−1.22068	−0.610340	−	0.792139i	$-0.708967\pi$
$443$	−2.23365e9	−1.22068	−0.610340	+	0.792139i	$0.708967\pi$
$444$	−1.81634e9	−0.984822
$445$	−1.12994e9	−0.607847
$446$	1.06019e9	0.565866
$447$	1.83461e9	0.971556
$448$	−6.89653e8	−0.362375
$449$	−1.08951e9	−0.568027	−0.284014	−	0.958820i	$-0.591666\pi$
$449$	−1.08951e9	−0.568027	−0.284014	+	0.958820i	$0.591666\pi$
$450$	−1.36333e9	−0.705274
$451$	−3.90432e8	−0.200413
$452$	2.49664e8	0.127166
$453$	−1.46644e9	−0.741176
$454$	−1.01811e9	−0.510621
$455$	−3.06494e9	−1.52540
$456$	−3.26979e9	−1.61489
$457$	9.19833e8	0.450819	0.225410	−	0.974264i	$-0.427628\pi$
$457$	9.19833e8	0.450819	0.225410	+	0.974264i	$0.427628\pi$
$458$	5.80643e8	0.282410
$459$	8.50654e9	4.10590
$460$	5.72317e8	0.274147
$461$	3.88554e8	0.184713	0.0923567	−	0.995726i	$-0.470560\pi$
$461$	3.88554e8	0.184713	0.0923567	+	0.995726i	$0.470560\pi$
$462$	−5.49273e8	−0.259144
$463$	1.15813e7	0.00542279	0.00271140	−	0.999996i	$-0.499137\pi$
$463$	1.15813e7	0.00542279	0.00271140	+	0.999996i	$0.499137\pi$
$464$	1.25535e9	0.583382
$465$	3.35618e9	1.54796
$466$	−2.72104e8	−0.124561
$467$	−1.80641e9	−0.820742	−0.410371	−	0.911919i	$-0.634601\pi$
$467$	−1.80641e9	−0.820742	−0.410371	+	0.911919i	$0.634601\pi$
$468$	−4.41767e9	−1.99220
$469$	−4.75123e9	−2.12667
$470$	7.69788e8	0.342002
$471$	−2.41829e8	−0.106644
$472$	−2.33230e9	−1.02091
$473$	−1.28876e8	−0.0559959
$474$	−2.02875e9	−0.874991
$475$	−2.78073e9	−1.19051
$476$	−4.09519e9	−1.74040
$477$	5.44429e9	2.29682
$478$	8.75047e8	0.366466
$479$	4.53886e8	0.188700	0.0943500	−	0.995539i	$-0.469923\pi$
$479$	4.53886e8	0.188700	0.0943500	+	0.995539i	$0.469923\pi$
$480$	5.33739e9	2.20285
$481$	1.52780e9	0.625976
$482$	−5.75734e7	−0.0234184
$483$	1.12990e9	0.456274
$484$	1.88893e9	0.757282
$485$	5.44031e9	2.16535
$486$	−9.66136e8	−0.381778
$487$	3.04275e9	1.19375	0.596877	−	0.802333i	$-0.296408\pi$
$487$	3.04275e9	1.19375	0.596877	+	0.802333i	$0.296408\pi$
$488$	−5.94909e8	−0.231729
$489$	2.25391e9	0.871677
$490$	2.82099e8	0.108322
$491$	6.19673e8	0.236253	0.118126	−	0.992999i	$-0.462311\pi$
$491$	6.19673e8	0.236253	0.118126	+	0.992999i	$0.462311\pi$
$492$	2.28015e9	0.863147
$493$	4.34946e9	1.63483
$494$	1.28373e9	0.479103
$495$	−3.07788e9	−1.14060
$496$	−1.08867e9	−0.400598
$497$	−2.82955e9	−1.03388
$498$	−1.58187e9	−0.573943
$499$	4.07486e9	1.46812	0.734059	−	0.679086i	$-0.237624\pi$
$499$	4.07486e9	1.46812	0.734059	+	0.679086i	$0.237624\pi$
$500$	−3.95899e8	−0.141641
$501$	−4.09546e9	−1.45503
$502$	8.38390e8	0.295790
$503$	−3.44575e8	−0.120725	−0.0603623	−	0.998177i	$-0.519226\pi$
$503$	−3.44575e8	−0.120725	−0.0603623	+	0.998177i	$0.519226\pi$
$504$	4.76720e9	1.65866
$505$	−5.62631e9	−1.94403
$506$	−8.62720e7	−0.0296035
$507$	5.51930e7	0.0188086
$508$	3.81752e9	1.29199
$509$	5.78650e8	0.194493	0.0972464	−	0.995260i	$-0.468997\pi$
$509$	5.78650e8	0.194493	0.0972464	+	0.995260i	$0.468997\pi$
$510$	4.71322e9	1.57334
$511$	2.79412e9	0.926344
$512$	−3.02139e9	−0.994859
$513$	−9.42726e9	−3.08301
$514$	1.06960e9	0.347415
$515$	4.97586e9	1.60525
$516$	7.52642e8	0.241165
$517$	8.14484e8	0.259218
$518$	−7.69521e8	−0.243258
$519$	9.99642e9	3.13877
$520$	−2.92809e9	−0.913214
$521$	3.77073e9	1.16814	0.584068	−	0.811705i	$-0.301460\pi$
$521$	3.77073e9	1.16814	0.584068	+	0.811705i	$0.301460\pi$
$522$	−2.36325e9	−0.727216
$523$	5.11275e8	0.156278	0.0781391	−	0.996942i	$-0.475102\pi$
$523$	5.11275e8	0.156278	0.0781391	+	0.996942i	$0.475102\pi$
$524$	−3.98107e9	−1.20876
$525$	5.84467e9	1.76280
$526$	3.99558e8	0.119710
$527$	−3.77194e9	−1.12261
$528$	1.43933e9	0.425540
$529$	−3.22736e9	−0.947877
$530$	1.68429e9	0.491419
$531$	−1.20431e10	−3.49066
$532$	4.53843e9	1.30682
$533$	−1.91792e9	−0.548637
$534$	−9.94731e8	−0.282691
$535$	6.04920e9	1.70789
$536$	−4.53908e9	−1.27318
$537$	−2.71472e9	−0.756510
$538$	−3.50675e8	−0.0970884
$539$	2.98479e8	0.0821018
$540$	1.00365e10	2.74286
$541$	4.17611e9	1.13392	0.566959	−	0.823746i	$-0.308120\pi$
$541$	4.17611e9	1.13392	0.566959	+	0.823746i	$0.308120\pi$
$542$	8.57289e8	0.231276
$543$	−1.01163e10	−2.71159
$544$	−5.99857e9	−1.59754
$545$	−7.40657e9	−1.95988
$546$	−2.69820e9	−0.709414
$547$	1.14489e9	0.299093	0.149547	−	0.988755i	$-0.452219\pi$
$547$	1.14489e9	0.299093	0.149547	+	0.988755i	$0.452219\pi$
$548$	4.22629e9	1.09705
$549$	−3.07188e9	−0.792320
$550$	−4.46261e8	−0.114372
$551$	−4.82023e9	−1.22754
$552$	1.07945e9	0.273159
$553$	6.03294e9	1.51702
$554$	1.46851e9	0.366937
$555$	−6.21645e9	−1.54354
$556$	−1.62426e9	−0.400770
$557$	−5.14104e9	−1.26054	−0.630271	−	0.776375i	$-0.717056\pi$
$557$	−5.14104e9	−1.26054	−0.630271	+	0.776375i	$0.717056\pi$
$558$	2.04946e9	0.499367
$559$	−6.33076e8	−0.153290
$560$	−4.04528e9	−0.973399
$561$	4.98688e9	1.19250
$562$	1.54279e9	0.366631
$563$	−9.25393e8	−0.218548	−0.109274	−	0.994012i	$-0.534853\pi$
$563$	−9.25393e8	−0.218548	−0.109274	+	0.994012i	$0.534853\pi$
$564$	−4.75664e9	−1.11641
$565$	8.54478e8	0.199311
$566$	−8.30409e7	−0.0192502
$567$	8.94318e9	2.06040
$568$	−2.70321e9	−0.618956
$569$	3.80230e9	0.865273	0.432637	−	0.901568i	$-0.357583\pi$
$569$	3.80230e9	0.865273	0.432637	+	0.901568i	$0.357583\pi$
$570$	−5.22336e9	−1.18138
$571$	3.02988e9	0.681082	0.340541	−	0.940230i	$-0.389390\pi$
$571$	3.02988e9	0.681082	0.340541	+	0.940230i	$0.389390\pi$
$572$	−1.44604e9	−0.323069
$573$	−2.02503e9	−0.449667
$574$	9.66019e8	0.213203
$575$	9.17998e8	0.201374
$576$	−3.40209e9	−0.741767
$577$	4.05303e9	0.878344	0.439172	−	0.898403i	$-0.355272\pi$
$577$	4.05303e9	0.878344	0.439172	+	0.898403i	$0.355272\pi$
$578$	−3.65767e9	−0.787875
$579$	4.91656e9	1.05266
$580$	5.13174e9	1.09211
$581$	4.70406e9	0.995075
$582$	4.78933e9	1.00703
$583$	1.78209e9	0.372468
$584$	2.66936e9	0.554578
$585$	−1.51195e10	−3.12243
$586$	−3.88407e8	−0.0797344
$587$	1.99299e9	0.406697	0.203348	−	0.979106i	$-0.434818\pi$
$587$	1.99299e9	0.406697	0.203348	+	0.979106i	$0.434818\pi$
$588$	−1.74314e9	−0.353598
$589$	4.18020e9	0.842933
$590$	−3.72576e9	−0.746849
$591$	−1.40434e8	−0.0279845
$592$	2.01647e9	0.399453
$593$	6.10682e9	1.20261	0.601303	−	0.799021i	$-0.294648\pi$
$593$	6.10682e9	1.20261	0.601303	+	0.799021i	$0.294648\pi$
$594$	−1.51292e9	−0.296185
$595$	−1.40158e10	−2.72778
$596$	−2.43272e9	−0.470684
$597$	2.02015e9	0.388574
$598$	−4.23795e8	−0.0810403
$599$	6.06702e9	1.15340	0.576702	−	0.816954i	$-0.304339\pi$
$599$	6.06702e9	1.15340	0.576702	+	0.816954i	$0.304339\pi$
$600$	5.58369e9	1.05534
$601$	−3.62416e9	−0.681000	−0.340500	−	0.940245i	$-0.610596\pi$
$601$	−3.62416e9	−0.681000	−0.340500	+	0.940245i	$0.610596\pi$
$602$	3.18868e8	0.0595694
$603$	−2.34380e10	−4.35322
$604$	1.94452e9	0.359074
$605$	6.46489e9	1.18691
$606$	−4.95308e9	−0.904109
$607$	6.80418e9	1.23485	0.617427	−	0.786629i	$-0.288175\pi$
$607$	6.80418e9	1.23485	0.617427	+	0.786629i	$0.288175\pi$
$608$	6.64784e9	1.19955
$609$	1.01314e10	1.81764
$610$	−9.50343e8	−0.169522
$611$	4.00099e9	0.709616
$612$	−2.02017e10	−3.56253
$613$	−5.90679e9	−1.03571	−0.517857	−	0.855467i	$-0.673270\pi$
$613$	−5.90679e9	−1.03571	−0.517857	+	0.855467i	$0.673270\pi$
$614$	3.25113e9	0.566820
$615$	7.80382e9	1.35283
$616$	1.56045e9	0.268979
$617$	−3.23829e9	−0.555031	−0.277516	−	0.960721i	$-0.589511\pi$
$617$	−3.23829e9	−0.555031	−0.277516	+	0.960721i	$0.589511\pi$
$618$	4.38046e9	0.746552
$619$	−3.39944e9	−0.576090	−0.288045	−	0.957617i	$-0.593005\pi$
$619$	−3.39944e9	−0.576090	−0.288045	+	0.957617i	$0.593005\pi$
$620$	−4.45034e9	−0.749933
$621$	3.11220e9	0.521492
$622$	1.90867e8	0.0318027
$623$	2.95806e9	0.490115
$624$	7.07042e9	1.16493
$625$	−6.73854e9	−1.10404
$626$	−1.65454e8	−0.0269567
$627$	−5.52664e9	−0.895416
$628$	3.20668e8	0.0516651
$629$	6.98653e9	1.11940
$630$	7.61540e9	1.21339
$631$	1.54777e9	0.245247	0.122623	−	0.992453i	$-0.460869\pi$
$631$	1.54777e9	0.245247	0.122623	+	0.992453i	$0.460869\pi$
$632$	5.76356e9	0.908198
$633$	−1.59694e9	−0.250250
$634$	−5.17509e8	−0.0806503
$635$	1.30655e10	2.02497
$636$	−1.04075e10	−1.60416
$637$	1.46622e9	0.224756
$638$	−7.73567e8	−0.117930
$639$	−1.39583e10	−2.11631
$640$	−9.13827e9	−1.37795
$641$	−7.31802e9	−1.09747	−0.548733	−	0.835998i	$-0.684889\pi$
$641$	−7.31802e9	−1.09747	−0.548733	+	0.835998i	$0.684889\pi$
$642$	5.32536e9	0.794285
$643$	−1.05084e10	−1.55883	−0.779413	−	0.626511i	$-0.784482\pi$
$643$	−1.05084e10	−1.55883	−0.779413	+	0.626511i	$0.784482\pi$
$644$	−1.49826e9	−0.221049
$645$	2.57592e9	0.377984
$646$	5.87041e9	0.856751
$647$	−1.82079e9	−0.264299	−0.132150	−	0.991230i	$-0.542188\pi$
$647$	−1.82079e9	−0.264299	−0.132150	+	0.991230i	$0.542188\pi$
$648$	8.54385e9	1.23351
$649$	−3.94209e9	−0.566070
$650$	−2.19217e9	−0.313096
$651$	−8.78613e9	−1.24814
$652$	−2.98872e9	−0.422297
$653$	1.05192e10	1.47838	0.739190	−	0.673497i	$-0.235208\pi$
$653$	1.05192e10	1.47838	0.739190	+	0.673497i	$0.235208\pi$
$654$	−6.52032e9	−0.911479
$655$	−1.36253e10	−1.89452
$656$	−2.53138e9	−0.350101
$657$	1.37835e10	1.89619
$658$	−2.01522e9	−0.275761
$659$	7.91936e9	1.07793	0.538965	−	0.842328i	$-0.318815\pi$
$659$	7.91936e9	1.07793	0.538965	+	0.842328i	$0.318815\pi$
$660$	5.88380e9	0.796625
$661$	1.09291e10	1.47191	0.735954	−	0.677031i	$-0.236734\pi$
$661$	1.09291e10	1.47191	0.735954	+	0.677031i	$0.236734\pi$
$662$	−4.25674e9	−0.570262
$663$	2.44971e10	3.26450
$664$	4.49401e9	0.595725
$665$	1.55328e10	2.04821
$666$	−3.79609e9	−0.497939
$667$	1.59129e9	0.207640
$668$	5.43064e9	0.704909
$669$	−2.24212e10	−2.89513
$670$	−7.25100e9	−0.931399
$671$	−1.00552e9	−0.128488
$672$	−1.39727e10	−1.77619
$673$	8.76741e9	1.10871	0.554356	−	0.832280i	$-0.312965\pi$
$673$	8.76741e9	1.10871	0.554356	+	0.832280i	$0.312965\pi$
$674$	9.15754e8	0.115204
$675$	1.60986e10	2.01476
$676$	−7.31866e7	−0.00911210
$677$	−3.98192e8	−0.0493211	−0.0246605	−	0.999696i	$-0.507850\pi$
$677$	−3.98192e8	−0.0493211	−0.0246605	+	0.999696i	$0.507850\pi$
$678$	7.52232e8	0.0926932
$679$	−1.42421e10	−1.74595
$680$	−1.33900e10	−1.63305
$681$	2.15312e10	2.61248
$682$	6.70852e8	0.0809807
$683$	4.45535e9	0.535068	0.267534	−	0.963548i	$-0.413791\pi$
$683$	4.45535e9	0.535068	0.267534	+	0.963548i	$0.413791\pi$
$684$	2.23883e10	2.67501
$685$	1.44645e10	1.71944
$686$	2.56437e9	0.303281
$687$	−1.22796e10	−1.44489
$688$	−8.35569e8	−0.0978189
$689$	8.75416e9	1.01964
$690$	1.72438e9	0.199830
$691$	−1.49029e10	−1.71829	−0.859146	−	0.511730i	$-0.829005\pi$
$691$	−1.49029e10	−1.71829	−0.859146	+	0.511730i	$0.829005\pi$
$692$	−1.32554e10	−1.52062
$693$	8.05757e9	0.919683
$694$	2.11114e9	0.239750
$695$	−5.55906e9	−0.628137
$696$	9.67900e9	1.08817
$697$	−8.77054e9	−0.981096
$698$	1.80205e7	0.00200573
$699$	5.75451e9	0.637291
$700$	−7.75011e9	−0.854013
$701$	4.40614e9	0.483109	0.241555	−	0.970387i	$-0.422343\pi$
$701$	4.40614e9	0.483109	0.241555	+	0.970387i	$0.422343\pi$
$702$	−7.43192e9	−0.810814
$703$	−7.74272e9	−0.840524
$704$	−1.11361e9	−0.120290
$705$	−1.62796e10	−1.74978
$706$	−9.64727e8	−0.103178
$707$	1.47291e10	1.56750
$708$	2.30221e10	2.43797
$709$	−7.42152e9	−0.782043	−0.391022	−	0.920381i	$-0.627878\pi$
$709$	−7.42152e9	−0.782043	−0.391022	+	0.920381i	$0.627878\pi$
$710$	−4.31826e9	−0.452798
$711$	2.97608e10	3.10528
$712$	2.82597e9	0.293419
$713$	−1.38000e9	−0.142582
$714$	−1.23387e10	−1.26860
$715$	−4.94909e9	−0.506354
$716$	3.59975e9	0.366503
$717$	−1.85057e10	−1.87494
$718$	3.12474e9	0.315049
$719$	−7.84543e9	−0.787165	−0.393582	−	0.919289i	$-0.628764\pi$
$719$	−7.84543e9	−0.787165	−0.393582	+	0.919289i	$0.628764\pi$
$720$	−1.99556e10	−1.99251
$721$	−1.30263e10	−1.29434
$722$	−2.93456e9	−0.290177
$723$	1.21757e9	0.119815
$724$	1.34144e10	1.31367
$725$	8.23132e9	0.802207
$726$	5.69131e9	0.551994
$727$	1.92504e10	1.85810	0.929052	−	0.369949i	$-0.120625\pi$
$727$	1.92504e10	1.85810	0.929052	+	0.369949i	$0.120625\pi$
$728$	7.66543e9	0.736337
$729$	9.48025e8	0.0906303
$730$	4.26420e9	0.405702
$731$	−2.89502e9	−0.274120
$732$	5.87232e9	0.553376
$733$	−1.25342e10	−1.17553	−0.587766	−	0.809031i	$-0.699992\pi$
$733$	−1.25342e10	−1.17553	−0.587766	+	0.809031i	$0.699992\pi$
$734$	8.36820e8	0.0781081
$735$	−5.96590e9	−0.554204
$736$	−2.19464e9	−0.202904
$737$	−7.67201e9	−0.705948
$738$	4.76542e9	0.436419
$739$	3.51649e9	0.320519	0.160259	−	0.987075i	$-0.448767\pi$
$739$	3.51649e9	0.320519	0.160259	+	0.987075i	$0.448767\pi$
$740$	8.24310e9	0.747789
$741$	−2.71486e10	−2.45122
$742$	−4.40930e9	−0.396238
$743$	3.44470e9	0.308099	0.154050	−	0.988063i	$-0.450768\pi$
$743$	3.44470e9	0.308099	0.154050	+	0.988063i	$0.450768\pi$
$744$	−8.39382e9	−0.747230
$745$	−8.32600e9	−0.737716
$746$	−3.05933e9	−0.269799
$747$	2.32053e10	2.03688
$748$	−6.61267e9	−0.577725
$749$	−1.58362e10	−1.37709
$750$	−1.19283e9	−0.103244
$751$	5.87692e9	0.506302	0.253151	−	0.967427i	$-0.418533\pi$
$751$	5.87692e9	0.506302	0.253151	+	0.967427i	$0.418533\pi$
$752$	5.28073e9	0.452826
$753$	−1.77305e10	−1.51334
$754$	−3.80000e9	−0.322837
$755$	6.65514e9	0.562786
$756$	−2.62745e10	−2.21161
$757$	−8.53566e9	−0.715157	−0.357579	−	0.933883i	$-0.616398\pi$
$757$	−8.53566e9	−0.715157	−0.357579	+	0.933883i	$0.616398\pi$
$758$	−2.36491e9	−0.197230
$759$	1.82450e9	0.151460
$760$	1.48393e10	1.22621
$761$	1.24999e10	1.02815	0.514077	−	0.857744i	$-0.328134\pi$
$761$	1.24999e10	1.02815	0.514077	+	0.857744i	$0.328134\pi$
$762$	1.15021e10	0.941749
$763$	1.93896e10	1.58028
$764$	2.68522e9	0.217848
$765$	−6.91407e10	−5.58365
$766$	−7.71482e9	−0.620190
$767$	−1.93647e10	−1.54963
$768$	−6.14676e8	−0.0489646
$769$	−9.50817e9	−0.753971	−0.376985	−	0.926219i	$-0.623039\pi$
$769$	−9.50817e9	−0.753971	−0.376985	+	0.926219i	$0.623039\pi$
$770$	2.49276e9	0.196772
$771$	−2.26201e10	−1.77747
$772$	−6.51943e9	−0.509975
$773$	−1.06727e10	−0.831089	−0.415544	−	0.909573i	$-0.636409\pi$
$773$	−1.06727e10	−0.831089	−0.415544	+	0.909573i	$0.636409\pi$
$774$	1.57299e9	0.121936
$775$	−7.13836e9	−0.550862
$776$	−1.36062e10	−1.04525
$777$	1.62740e10	1.24457
$778$	8.72323e8	0.0664123
$779$	9.71982e9	0.736677
$780$	2.89030e10	2.18078
$781$	−4.56899e9	−0.343196
$782$	−1.93799e9	−0.144920
$783$	2.79059e10	2.07745
$784$	1.93520e9	0.143423
$785$	1.09749e9	0.0809760
$786$	−1.19949e10	−0.881084
$787$	2.51180e10	1.83685	0.918425	−	0.395596i	$-0.129462\pi$
$787$	2.51180e10	1.83685	0.918425	+	0.395596i	$0.129462\pi$
$788$	1.86218e8	0.0135575
$789$	−8.44994e9	−0.612469
$790$	9.20705e9	0.664394
$791$	−2.23693e9	−0.160707
$792$	7.69779e9	0.550590
$793$	−4.93943e9	−0.351739
$794$	−4.72921e9	−0.335287
$795$	−3.56198e10	−2.51424
$796$	−2.67875e9	−0.188250
$797$	1.35480e10	0.947917	0.473959	−	0.880547i	$-0.342825\pi$
$797$	1.35480e10	0.947917	0.473959	+	0.880547i	$0.342825\pi$
$798$	1.36742e10	0.952559
$799$	1.82963e10	1.26897
$800$	−1.13523e10	−0.783912
$801$	1.45922e10	1.00325
$802$	6.24529e9	0.427506
$803$	4.51179e9	0.307499
$804$	4.48051e10	3.04040
$805$	−5.12782e9	−0.346455
$806$	3.29543e9	0.221687
$807$	7.41616e9	0.496732
$808$	1.40714e10	0.938421
$809$	1.21582e10	0.807328	0.403664	−	0.914907i	$-0.367736\pi$
$809$	1.21582e10	0.807328	0.403664	+	0.914907i	$0.367736\pi$
$810$	1.36485e10	0.902373
$811$	2.69149e10	1.77182	0.885911	−	0.463855i	$-0.153534\pi$
$811$	2.69149e10	1.77182	0.885911	+	0.463855i	$0.153534\pi$
$812$	−1.34343e10	−0.880583
$813$	−1.81301e10	−1.18327
$814$	−1.24258e9	−0.0807492
$815$	−1.02289e10	−0.661877
$816$	3.23326e10	2.08317
$817$	3.20837e9	0.205829
$818$	9.72093e8	0.0620971
$819$	3.95813e10	2.51766
$820$	−1.03480e10	−0.655400
$821$	−1.50522e10	−0.949292	−0.474646	−	0.880177i	$-0.657424\pi$
$821$	−1.50522e10	−0.949292	−0.474646	+	0.880177i	$0.657424\pi$
$822$	1.27337e10	0.799657
$823$	−1.95484e10	−1.22240	−0.611198	−	0.791478i	$-0.709312\pi$
$823$	−1.95484e10	−1.22240	−0.611198	+	0.791478i	$0.709312\pi$
$824$	−1.24446e10	−0.774885
$825$	9.43763e9	0.585159
$826$	9.75364e9	0.602194
$827$	−2.07950e9	−0.127847	−0.0639233	−	0.997955i	$-0.520361\pi$
$827$	−2.07950e9	−0.127847	−0.0639233	+	0.997955i	$0.520361\pi$
$828$	−7.39101e9	−0.452478
$829$	2.13263e10	1.30009	0.650047	−	0.759894i	$-0.274749\pi$
$829$	2.13263e10	1.30009	0.650047	+	0.759894i	$0.274749\pi$
$830$	7.17900e9	0.435804
$831$	−3.10563e10	−1.87735
$832$	−5.47040e9	−0.329297
$833$	6.70493e9	0.401918
$834$	−4.89387e9	−0.292127
$835$	1.85864e10	1.10482
$836$	7.32840e9	0.433797
$837$	−2.42005e10	−1.42655
$838$	3.50363e9	0.205667
$839$	−1.08997e10	−0.637161	−0.318580	−	0.947896i	$-0.603206\pi$
$839$	−1.08997e10	−0.637161	−0.318580	+	0.947896i	$0.603206\pi$
$840$	−3.11898e10	−1.81566
$841$	−2.98137e9	−0.172834
$842$	−1.84703e8	−0.0106630
$843$	−3.26272e10	−1.87579
$844$	2.11756e9	0.121237
$845$	−2.50482e8	−0.0142816
$846$	−9.94119e9	−0.564472
$847$	−1.69244e10	−0.957020
$848$	1.15542e10	0.650662
$849$	1.75617e9	0.0984893
$850$	−1.00247e10	−0.559892
$851$	2.55609e9	0.142175
$852$	2.66832e10	1.47809
$853$	−2.05206e10	−1.13206	−0.566028	−	0.824386i	$-0.691521\pi$
$853$	−2.05206e10	−1.13206	−0.566028	+	0.824386i	$0.691521\pi$
$854$	2.48790e9	0.136688
$855$	7.66242e10	4.19261
$856$	−1.51290e10	−0.824429
$857$	−2.27910e10	−1.23689	−0.618443	−	0.785830i	$-0.712236\pi$
$857$	−2.27910e10	−1.23689	−0.618443	+	0.785830i	$0.712236\pi$
$858$	−4.35689e9	−0.235489
$859$	−5.82236e9	−0.313418	−0.156709	−	0.987645i	$-0.550088\pi$
$859$	−5.82236e9	−0.313418	−0.156709	+	0.987645i	$0.550088\pi$
$860$	−3.41571e9	−0.183120
$861$	−2.04296e10	−1.09081
$862$	−9.66030e9	−0.513707
$863$	1.77088e10	0.937891	0.468945	−	0.883227i	$-0.344634\pi$
$863$	1.77088e10	0.937891	0.468945	+	0.883227i	$0.344634\pi$
$864$	−3.84865e10	−2.03007
$865$	−4.53667e10	−2.38331
$866$	8.21562e9	0.429861
$867$	7.73533e10	4.03099
$868$	1.16505e10	0.604681
$869$	9.74163e9	0.503573
$870$	1.54618e10	0.796055
$871$	−3.76873e10	−1.93255
$872$	1.85238e10	0.946070
$873$	−7.02572e10	−3.57389
$874$	2.14775e9	0.108816
$875$	3.54716e9	0.179000
$876$	−2.63491e10	−1.32435
$877$	2.41157e10	1.20726	0.603630	−	0.797264i	$-0.293720\pi$
$877$	2.41157e10	1.20726	0.603630	+	0.797264i	$0.293720\pi$
$878$	1.58475e9	0.0790185
$879$	8.21413e9	0.407944
$880$	−6.53209e9	−0.323119
$881$	2.64320e10	1.30231	0.651155	−	0.758945i	$-0.274285\pi$
$881$	2.64320e10	1.30231	0.651155	+	0.758945i	$0.274285\pi$
$882$	−3.64308e9	−0.178784
$883$	2.34325e10	1.14540	0.572699	−	0.819766i	$-0.305896\pi$
$883$	2.34325e10	1.14540	0.572699	+	0.819766i	$0.305896\pi$
$884$	−3.24835e10	−1.58154
$885$	7.87932e10	3.82109
$886$	8.92398e9	0.431063
$887$	−2.01156e10	−0.967832	−0.483916	−	0.875114i	$-0.660786\pi$
$887$	−2.01156e10	−0.967832	−0.483916	+	0.875114i	$0.660786\pi$
$888$	1.55473e10	0.745094
$889$	−3.42041e10	−1.63276
$890$	4.51438e9	0.214651
$891$	1.44409e10	0.683948
$892$	2.97308e10	1.40259
$893$	−2.02766e10	−0.952831
$894$	−7.32973e9	−0.343089
$895$	1.23202e10	0.574429
$896$	2.39230e10	1.11106
$897$	8.96250e9	0.414625
$898$	4.35286e9	0.200589
$899$	−1.23739e10	−0.568000
$900$	−3.82317e10	−1.74813
$901$	4.00323e10	1.82336
$902$	1.55987e9	0.0707727
$903$	−6.74349e9	−0.304774
$904$	−2.13705e9	−0.0962110
$905$	4.59108e10	2.05895
$906$	5.85880e9	0.261734
$907$	−2.12612e10	−0.946156	−0.473078	−	0.881021i	$-0.656857\pi$
$907$	−2.12612e10	−0.946156	−0.473078	+	0.881021i	$0.656857\pi$
$908$	−2.85506e10	−1.26566
$909$	7.26593e10	3.20861
$910$	1.22452e10	0.538668
$911$	5.63102e9	0.246759	0.123379	−	0.992360i	$-0.460627\pi$
$911$	5.63102e9	0.246759	0.123379	+	0.992360i	$0.460627\pi$
$912$	−3.58322e10	−1.56420
$913$	7.59583e9	0.330315
$914$	−3.67496e9	−0.159199
$915$	2.00981e10	0.867322
$916$	1.62829e10	0.699998
$917$	3.56695e10	1.52758
$918$	−3.39857e10	−1.44993
$919$	−1.37242e10	−0.583286	−0.291643	−	0.956527i	$-0.594202\pi$
$919$	−1.37242e10	−0.583286	−0.291643	+	0.956527i	$0.594202\pi$
$920$	−4.89886e9	−0.207414
$921$	−6.87557e10	−2.90001
$922$	−1.55237e9	−0.0652285
$923$	−2.24443e10	−0.939507
$924$	−1.54032e10	−0.642330
$925$	1.32220e10	0.549287
$926$	−4.62701e7	−0.00191497
$927$	−6.42593e10	−2.64946
$928$	−1.96785e10	−0.808301
$929$	1.80192e10	0.737363	0.368682	−	0.929556i	$-0.379809\pi$
$929$	1.80192e10	0.737363	0.368682	+	0.929556i	$0.379809\pi$
$930$	−1.34088e10	−0.546637
$931$	−7.43065e9	−0.301789
$932$	−7.63055e9	−0.308745
$933$	−4.03649e9	−0.162711
$934$	7.21705e9	0.289831
$935$	−2.26319e10	−0.905484
$936$	3.78139e10	1.50725
$937$	1.76207e10	0.699736	0.349868	−	0.936799i	$-0.386227\pi$
$937$	1.76207e10	0.699736	0.349868	+	0.936799i	$0.386227\pi$
$938$	1.89823e10	0.751000
$939$	3.49905e9	0.137918
$940$	2.15870e10	0.847706
$941$	−3.45116e9	−0.135021	−0.0675105	−	0.997719i	$-0.521506\pi$
$941$	−3.45116e9	−0.135021	−0.0675105	+	0.997719i	$0.521506\pi$
$942$	9.66166e8	0.0376594
$943$	−3.20879e9	−0.124609
$944$	−2.55587e10	−0.988863
$945$	−8.99246e10	−3.46631
$946$	5.14890e8	0.0197740
$947$	5.63093e9	0.215454	0.107727	−	0.994181i	$-0.465643\pi$
$947$	5.63093e9	0.215454	0.107727	+	0.994181i	$0.465643\pi$
$948$	−5.68918e10	−2.16880
$949$	2.21633e10	0.841787
$950$	1.11097e10	0.420407
$951$	1.09444e10	0.412629
$952$	3.50535e10	1.31675
$953$	4.39854e10	1.64620	0.823101	−	0.567896i	$-0.192242\pi$
$953$	4.39854e10	1.64620	0.823101	+	0.567896i	$0.192242\pi$
$954$	−2.17513e10	−0.811084
$955$	9.19019e9	0.341439
$956$	2.45388e10	0.908344
$957$	1.63596e10	0.603365
$958$	−1.81339e9	−0.0666363
$959$	−3.78666e10	−1.38641
$960$	2.22585e10	0.811983
$961$	−1.67817e10	−0.609964
$962$	−6.10393e9	−0.221053
$963$	−7.81205e10	−2.81886
$964$	−1.61452e9	−0.0580462
$965$	−2.23128e10	−0.799298
$966$	−4.51424e9	−0.161126
$967$	3.74348e10	1.33132	0.665660	−	0.746255i	$-0.268150\pi$
$967$	3.74348e10	1.33132	0.665660	+	0.746255i	$0.268150\pi$
$968$	−1.61687e10	−0.572942
$969$	−1.24149e11	−4.38338
$970$	−2.17354e10	−0.764656
$971$	3.42358e9	0.120009	0.0600044	−	0.998198i	$-0.480889\pi$
$971$	3.42358e9	0.120009	0.0600044	+	0.998198i	$0.480889\pi$
$972$	−2.70932e10	−0.946298
$973$	1.45530e10	0.506475
$974$	−1.21565e10	−0.421554
$975$	4.63606e10	1.60189
$976$	−6.51934e9	−0.224455
$977$	−5.03847e10	−1.72849	−0.864247	−	0.503068i	$-0.832205\pi$
$977$	−5.03847e10	−1.72849	−0.864247	+	0.503068i	$0.832205\pi$
$978$	−9.00493e9	−0.307818
$979$	4.77650e9	0.162693
$980$	7.91086e9	0.268493
$981$	9.56500e10	3.23477
$982$	−2.47575e9	−0.0834288
$983$	−3.95623e10	−1.32845	−0.664224	−	0.747534i	$-0.731238\pi$
$983$	−3.95623e10	−1.32845	−0.664224	+	0.747534i	$0.731238\pi$
$984$	−1.95174e10	−0.653038
$985$	6.37332e8	0.0212490
$986$	−1.73772e10	−0.577311
$987$	4.26184e10	1.41087
$988$	3.59993e10	1.18753
$989$	−1.05917e9	−0.0348160
$990$	1.22969e10	0.402785
$991$	1.79657e10	0.586388	0.293194	−	0.956053i	$-0.405282\pi$
$991$	1.79657e10	0.586388	0.293194	+	0.956053i	$0.405282\pi$
$992$	1.70655e10	0.555046
$993$	9.00225e10	2.91762
$994$	1.13048e10	0.365097
$995$	−9.16804e9	−0.295050
$996$	−4.43602e10	−1.42261
$997$	1.97079e9	0.0629807	0.0314904	−	0.999504i	$-0.489975\pi$
$997$	1.97079e9	0.0629807	0.0314904	+	0.999504i	$0.489975\pi$
$998$	−1.62801e10	−0.518441
$999$	4.48252e10	1.42247

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.8.a.b.1.5	✓	13
3.2	odd	2		387.8.a.d.1.9		13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.8.a.b.1.5	✓	13	1.1	even	1	trivial
387.8.a.d.1.9		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)

\(f(q)\)	\(=\)	\(q-3.99525 q^{2} +84.4924 q^{3} -112.038 q^{4} -383.451 q^{5} -337.568 q^{6} +1003.83 q^{7} +959.011 q^{8} +4951.96 q^{9} +O(q^{10})\)	\(q-3.99525 q^{2} +84.4924 q^{3} -112.038 q^{4} -383.451 q^{5} -337.568 q^{6} +1003.83 q^{7} +959.011 q^{8} +4951.96 q^{9} +1531.98 q^{10} +1620.93 q^{11} -9466.36 q^{12} +7962.52 q^{13} -4010.57 q^{14} -32398.7 q^{15} +10509.4 q^{16} +36412.1 q^{17} -19784.3 q^{18} -40353.3 q^{19} +42961.1 q^{20} +84816.3 q^{21} -6476.03 q^{22} +13321.7 q^{23} +81029.1 q^{24} +68909.7 q^{25} -31812.2 q^{26} +233618. q^{27} -112468. q^{28} +119451. q^{29} +129441. q^{30} -103590. q^{31} -164741. q^{32} +136956. q^{33} -145476. q^{34} -384921. q^{35} -554808. q^{36} +191874. q^{37} +161221. q^{38} +672772. q^{39} -367734. q^{40} -240868. q^{41} -338862. q^{42} -79507.0 q^{43} -181606. q^{44} -1.89884e6 q^{45} -53223.7 q^{46} +502478. q^{47} +887962. q^{48} +184140. q^{49} -275311. q^{50} +3.07655e6 q^{51} -892105. q^{52} +1.09942e6 q^{53} -933363. q^{54} -621548. q^{55} +962688. q^{56} -3.40954e6 q^{57} -477236. q^{58} -2.43199e6 q^{59} +3.62988e6 q^{60} -620335. q^{61} +413868. q^{62} +4.97095e6 q^{63} -687019. q^{64} -3.05324e6 q^{65} -547175. q^{66} -4.73308e6 q^{67} -4.07954e6 q^{68} +1.12559e6 q^{69} +1.53786e6 q^{70} -2.81874e6 q^{71} +4.74899e6 q^{72} +2.78345e6 q^{73} -766582. q^{74} +5.82235e6 q^{75} +4.52110e6 q^{76} +1.62715e6 q^{77} -2.68789e6 q^{78} +6.00989e6 q^{79} -4.02983e6 q^{80} +8.90902e6 q^{81} +962329. q^{82} +4.68609e6 q^{83} -9.50265e6 q^{84} -1.39623e7 q^{85} +317650. q^{86} +1.00927e7 q^{87} +1.55449e6 q^{88} +2.94676e6 q^{89} +7.58632e6 q^{90} +7.99305e6 q^{91} -1.49254e6 q^{92} -8.75257e6 q^{93} -2.00753e6 q^{94} +1.54735e7 q^{95} -1.39194e7 q^{96} -1.41877e7 q^{97} -735685. q^{98} +8.02680e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 16 q^{2} + 94 q^{3} + 922 q^{4} + 998 q^{5} + 183 q^{6} + 1360 q^{7} + 3870 q^{8} + 10011 q^{9}+O(q^{10}) \) 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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