LMFDB - Embedded newform 29.8.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [29,8,Mod(1,29)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(29, 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("29.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 29 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	29.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:	$9.05916573904$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - x^{6} - 616x^{5} + 1864x^{4} + 96785x^{3} - 257817x^{2} - 3929114x + 2682946 $ x^7 - x^6 - 616x^5 + 1864x^4 + 96785x^3 - 257817x^2 - 3929114*x + 2682946
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{4}\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$9.85813$ of defining polynomial
Character	$\chi$	$=$	29.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-10.8581 q^{2} +69.4472 q^{3} -10.1010 q^{4} -257.927 q^{5} -754.067 q^{6} -96.3589 q^{7} +1499.52 q^{8} +2635.91 q^{9} +O(q^{10})$	\(q-10.8581 q^{2} +69.4472 q^{3} -10.1010 q^{4} -257.927 q^{5} -754.067 q^{6} -96.3589 q^{7} +1499.52 q^{8} +2635.91 q^{9} +2800.60 q^{10} -6114.42 q^{11} -701.484 q^{12} -8992.21 q^{13} +1046.28 q^{14} -17912.3 q^{15} -14989.0 q^{16} +4816.57 q^{17} -28621.1 q^{18} -38743.8 q^{19} +2605.31 q^{20} -6691.86 q^{21} +66391.2 q^{22} -39696.3 q^{23} +104137. q^{24} -11598.8 q^{25} +97638.6 q^{26} +31175.6 q^{27} +973.319 q^{28} +24389.0 q^{29} +194494. q^{30} +162971. q^{31} -29185.3 q^{32} -424629. q^{33} -52299.0 q^{34} +24853.5 q^{35} -26625.3 q^{36} +53143.7 q^{37} +420685. q^{38} -624484. q^{39} -386766. q^{40} +780735. q^{41} +72661.1 q^{42} +81160.7 q^{43} +61761.5 q^{44} -679872. q^{45} +431027. q^{46} +1.28940e6 q^{47} -1.04095e6 q^{48} -814258. q^{49} +125941. q^{50} +334497. q^{51} +90830.0 q^{52} -1.13789e6 q^{53} -338509. q^{54} +1.57707e6 q^{55} -144492. q^{56} -2.69065e6 q^{57} -264819. q^{58} -615349. q^{59} +180931. q^{60} -1.21712e6 q^{61} -1.76956e6 q^{62} -253994. q^{63} +2.23550e6 q^{64} +2.31933e6 q^{65} +4.61068e6 q^{66} -2.76775e6 q^{67} -48652.0 q^{68} -2.75679e6 q^{69} -269863. q^{70} +4.31768e6 q^{71} +3.95260e6 q^{72} -2.39892e6 q^{73} -577041. q^{74} -805503. q^{75} +391350. q^{76} +589179. q^{77} +6.78073e6 q^{78} +3.99352e6 q^{79} +3.86608e6 q^{80} -3.59968e6 q^{81} -8.47732e6 q^{82} -1.91708e6 q^{83} +67594.2 q^{84} -1.24232e6 q^{85} -881253. q^{86} +1.69375e6 q^{87} -9.16868e6 q^{88} +9.76639e6 q^{89} +7.38214e6 q^{90} +866480. q^{91} +400971. q^{92} +1.13179e7 q^{93} -1.40005e7 q^{94} +9.99306e6 q^{95} -2.02684e6 q^{96} -5.60106e6 q^{97} +8.84132e6 q^{98} -1.61171e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 8 q^{2} - 82 q^{3} + 346 q^{4} - 320 q^{5} - 938 q^{6} - 1704 q^{7} + 2082 q^{8} + 4061 q^{9}+O(q^{10}) $ 7 * q - 8 * q^2 - 82 * q^3 + 346 * q^4 - 320 * q^5 - 938 * q^6 - 1704 * q^7 + 2082 * q^8 + 4061 * q^9	\( 7 q - 8 q^{2} - 82 q^{3} + 346 q^{4} - 320 q^{5} - 938 q^{6} - 1704 q^{7} + 2082 q^{8} + 4061 q^{9} - 14114 q^{10} - 14498 q^{11} - 42334 q^{12} - 9024 q^{13} - 45880 q^{14} - 24238 q^{15} - 3022 q^{16} - 54882 q^{17} + 17218 q^{18} - 100572 q^{19} - 86022 q^{20} + 34304 q^{21} + 9086 q^{22} + 55340 q^{23} - 138966 q^{24} + 125759 q^{25} + 257206 q^{26} - 176146 q^{27} - 41760 q^{28} + 170723 q^{29} + 1132178 q^{30} - 153330 q^{31} + 825478 q^{32} + 555898 q^{33} - 194256 q^{34} + 561160 q^{35} + 1939652 q^{36} - 457050 q^{37} + 617164 q^{38} - 1173662 q^{39} - 1151986 q^{40} - 864230 q^{41} + 2046224 q^{42} - 1590058 q^{43} - 1399966 q^{44} - 2268610 q^{45} + 1557900 q^{46} - 204750 q^{47} - 2501730 q^{48} - 1892625 q^{49} + 2115526 q^{50} - 2481996 q^{51} + 1469690 q^{52} - 2696092 q^{53} - 2918978 q^{54} - 2596662 q^{55} - 2818440 q^{56} - 96196 q^{57} - 195112 q^{58} + 1434256 q^{59} + 7687830 q^{60} - 5622798 q^{61} - 4660550 q^{62} - 5632816 q^{63} - 944442 q^{64} - 353086 q^{65} + 8421370 q^{66} - 5380324 q^{67} + 6393964 q^{68} - 2248580 q^{69} + 10805432 q^{70} + 4605140 q^{71} + 17475264 q^{72} + 3979266 q^{73} + 15124836 q^{74} - 2365120 q^{75} - 3893220 q^{76} + 8666288 q^{77} + 7790850 q^{78} - 6355522 q^{79} - 4424794 q^{80} + 6442139 q^{81} + 6831364 q^{82} + 3077704 q^{83} + 29008056 q^{84} + 5117008 q^{85} + 11620998 q^{86} - 1999898 q^{87} - 24708046 q^{88} + 743498 q^{89} - 38296444 q^{90} - 24167656 q^{91} + 11053132 q^{92} + 25723782 q^{93} - 29029210 q^{94} + 1137892 q^{95} - 34019010 q^{96} - 7924270 q^{97} + 19298152 q^{98} - 43451600 q^{99}+O(q^{100}) \) 7 * q - 8 * q^2 - 82 * q^3 + 346 * q^4 - 320 * q^5 - 938 * q^6 - 1704 * q^7 + 2082 * q^8 + 4061 * q^9 - 14114 * q^10 - 14498 * q^11 - 42334 * q^12 - 9024 * q^13 - 45880 * q^14 - 24238 * q^15 - 3022 * q^16 - 54882 * q^17 + 17218 * q^18 - 100572 * q^19 - 86022 * q^20 + 34304 * q^21 + 9086 * q^22 + 55340 * q^23 - 138966 * q^24 + 125759 * q^25 + 257206 * q^26 - 176146 * q^27 - 41760 * q^28 + 170723 * q^29 + 1132178 * q^30 - 153330 * q^31 + 825478 * q^32 + 555898 * q^33 - 194256 * q^34 + 561160 * q^35 + 1939652 * q^36 - 457050 * q^37 + 617164 * q^38 - 1173662 * q^39 - 1151986 * q^40 - 864230 * q^41 + 2046224 * q^42 - 1590058 * q^43 - 1399966 * q^44 - 2268610 * q^45 + 1557900 * q^46 - 204750 * q^47 - 2501730 * q^48 - 1892625 * q^49 + 2115526 * q^50 - 2481996 * q^51 + 1469690 * q^52 - 2696092 * q^53 - 2918978 * q^54 - 2596662 * q^55 - 2818440 * q^56 - 96196 * q^57 - 195112 * q^58 + 1434256 * q^59 + 7687830 * q^60 - 5622798 * q^61 - 4660550 * q^62 - 5632816 * q^63 - 944442 * q^64 - 353086 * q^65 + 8421370 * q^66 - 5380324 * q^67 + 6393964 * q^68 - 2248580 * q^69 + 10805432 * q^70 + 4605140 * q^71 + 17475264 * q^72 + 3979266 * q^73 + 15124836 * q^74 - 2365120 * q^75 - 3893220 * q^76 + 8666288 * q^77 + 7790850 * q^78 - 6355522 * q^79 - 4424794 * q^80 + 6442139 * q^81 + 6831364 * q^82 + 3077704 * q^83 + 29008056 * q^84 + 5117008 * q^85 + 11620998 * q^86 - 1999898 * q^87 - 24708046 * q^88 + 743498 * q^89 - 38296444 * q^90 - 24167656 * q^91 + 11053132 * q^92 + 25723782 * q^93 - 29029210 * q^94 + 1137892 * q^95 - 34019010 * q^96 - 7924270 * q^97 + 19298152 * q^98 - 43451600 * 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 $

$2$	−10.8581	−0.959732	−0.479866	−	0.877342i	$-0.659315\pi$
$2$	−10.8581	−0.959732	−0.479866	+	0.877342i	$0.659315\pi$
$3$	69.4472	1.48501	0.742506	−	0.669839i	$-0.233637\pi$
$3$	69.4472	1.48501	0.742506	+	0.669839i	$0.233637\pi$
$4$	−10.1010	−0.0789138
$5$	−257.927	−0.922787	−0.461393	−	0.887196i	$-0.652650\pi$
$5$	−257.927	−0.922787	−0.461393	+	0.887196i	$0.652650\pi$
$6$	−754.067	−1.42521
$7$	−96.3589	−0.106182	−0.0530908	−	0.998590i	$-0.516907\pi$
$7$	−96.3589	−0.106182	−0.0530908	+	0.998590i	$0.516907\pi$
$8$	1499.52	1.03547
$9$	2635.91	1.20526
$10$	2800.60	0.885628
$11$	−6114.42	−1.38510	−0.692549	−	0.721371i	$-0.743512\pi$
$11$	−6114.42	−1.38510	−0.692549	+	0.721371i	$0.743512\pi$
$12$	−701.484	−0.117188
$13$	−8992.21	−1.13518	−0.567590	−	0.823311i	$-0.692124\pi$
$13$	−8992.21	−1.13518	−0.567590	+	0.823311i	$0.692124\pi$
$14$	1046.28	0.101906
$15$	−17912.3	−1.37035
$16$	−14989.0	−0.914859
$17$	4816.57	0.237775	0.118888	−	0.992908i	$-0.462067\pi$
$17$	4816.57	0.237775	0.118888	+	0.992908i	$0.462067\pi$
$18$	−28621.1	−1.15673
$19$	−38743.8	−1.29588	−0.647940	−	0.761692i	$-0.724369\pi$
$19$	−38743.8	−1.29588	−0.647940	+	0.761692i	$0.724369\pi$
$20$	2605.31	0.0728206
$21$	−6691.86	−0.157681
$22$	66391.2	1.32932
$23$	−39696.3	−0.680303	−0.340151	−	0.940371i	$-0.610478\pi$
$23$	−39696.3	−0.680303	−0.340151	+	0.940371i	$0.610478\pi$
$24$	104137.	1.53768
$25$	−11598.8	−0.148465
$26$	97638.6	1.08947
$27$	31175.6	0.304819
$28$	973.319	0.00837919
$29$	24389.0	0.185695
$29$	24389.0	0.185695
$30$	194494.	1.31517
$31$	162971.	0.982525	0.491262	−	0.871012i	$-0.336536\pi$
$31$	162971.	0.982525	0.491262	+	0.871012i	$0.336536\pi$
$32$	−29185.3	−0.157449
$33$	−424629.	−2.05689
$34$	−52299.0	−0.228201
$35$	24853.5	0.0979829
$36$	−26625.3	−0.0951119
$37$	53143.7	0.172483	0.0862414	−	0.996274i	$-0.472514\pi$
$37$	53143.7	0.172483	0.0862414	+	0.996274i	$0.472514\pi$
$38$	420685.	1.24370
$39$	−624484.	−1.68576
$40$	−386766.	−0.955517
$41$	780735.	1.76913	0.884566	−	0.466415i	$-0.154455\pi$
$41$	780735.	1.76913	0.884566	+	0.466415i	$0.154455\pi$
$42$	72661.1	0.151331
$43$	81160.7	0.155670	0.0778352	−	0.996966i	$-0.475199\pi$
$43$	81160.7	0.155670	0.0778352	+	0.996966i	$0.475199\pi$
$44$	61761.5	0.109303
$45$	−679872.	−1.11220
$46$	431027.	0.652909
$47$	1.28940e6	1.81153	0.905767	−	0.423776i	$-0.139296\pi$
$47$	1.28940e6	1.81153	0.905767	+	0.423776i	$0.139296\pi$
$48$	−1.04095e6	−1.35858
$49$	−814258.	−0.988725
$50$	125941.	0.142486
$51$	334497.	0.353099
$52$	90830.0	0.0895814
$53$	−1.13789e6	−1.04987	−0.524934	−	0.851143i	$-0.675910\pi$
$53$	−1.13789e6	−1.04987	−0.524934	+	0.851143i	$0.675910\pi$
$54$	−338509.	−0.292544
$55$	1.57707e6	1.27815
$56$	−144492.	−0.109948
$57$	−2.69065e6	−1.92440
$58$	−264819.	−0.178218
$59$	−615349.	−0.390067	−0.195034	−	0.980797i	$-0.562482\pi$
$59$	−615349.	−0.390067	−0.195034	+	0.980797i	$0.562482\pi$
$60$	180931.	0.108140
$61$	−1.21712e6	−0.686562	−0.343281	−	0.939233i	$-0.611538\pi$
$61$	−1.21712e6	−0.686562	−0.343281	+	0.939233i	$0.611538\pi$
$62$	−1.76956e6	−0.942961
$63$	−253994.	−0.127977
$64$	2.23550e6	1.06597
$65$	2.31933e6	1.04753
$66$	4.61068e6	1.97406
$67$	−2.76775e6	−1.12426	−0.562128	−	0.827050i	$-0.690017\pi$
$67$	−2.76775e6	−1.12426	−0.562128	+	0.827050i	$0.690017\pi$
$68$	−48652.0	−0.0187638
$69$	−2.75679e6	−1.01026
$70$	−269863.	−0.0940374
$71$	4.31768e6	1.43168	0.715840	−	0.698264i	$-0.246044\pi$
$71$	4.31768e6	1.43168	0.715840	+	0.698264i	$0.246044\pi$
$72$	3.95260e6	1.24801
$73$	−2.39892e6	−0.721749	−0.360874	−	0.932614i	$-0.617522\pi$
$73$	−2.39892e6	−0.721749	−0.360874	+	0.932614i	$0.617522\pi$
$74$	−577041.	−0.165537
$75$	−805503.	−0.220472
$76$	391350.	0.102263
$77$	589179.	0.147072
$78$	6.78073e6	1.61788
$79$	3.99352e6	0.911299	0.455649	−	0.890159i	$-0.349407\pi$
$79$	3.99352e6	0.911299	0.455649	+	0.890159i	$0.349407\pi$
$80$	3.86608e6	0.844220
$81$	−3.59968e6	−0.752604
$82$	−8.47732e6	−1.69789
$83$	−1.91708e6	−0.368017	−0.184009	−	0.982925i	$-0.558907\pi$
$83$	−1.91708e6	−0.368017	−0.184009	+	0.982925i	$0.558907\pi$
$84$	67594.2	0.0124432
$85$	−1.24232e6	−0.219416
$86$	−881253.	−0.149402
$87$	1.69375e6	0.275760
$88$	−9.16868e6	−1.43423
$89$	9.76639e6	1.46848	0.734242	−	0.678888i	$-0.237538\pi$
$89$	9.76639e6	1.46848	0.734242	+	0.678888i	$0.237538\pi$
$90$	7.38214e6	1.06742
$91$	866480.	0.120535
$92$	400971.	0.0536853
$93$	1.13179e7	1.45906
$94$	−1.40005e7	−1.73859
$95$	9.99306e6	1.19582
$96$	−2.02684e6	−0.233814
$97$	−5.60106e6	−0.623117	−0.311558	−	0.950227i	$-0.600851\pi$
$97$	−5.60106e6	−0.623117	−0.311558	+	0.950227i	$0.600851\pi$
$98$	8.84132e6	0.948912
$99$	−1.61171e7	−1.66941
$100$	117159.	0.0117159
$101$	−2.49545e6	−0.241004	−0.120502	−	0.992713i	$-0.538450\pi$
$101$	−2.49545e6	−0.241004	−0.120502	+	0.992713i	$0.538450\pi$
$102$	−3.63202e6	−0.338881
$103$	−2.05815e7	−1.85586	−0.927931	−	0.372752i	$-0.878414\pi$
$103$	−2.05815e7	−1.85586	−0.927931	+	0.372752i	$0.878414\pi$
$104$	−1.34840e7	−1.17544
$105$	1.72601e6	0.145506
$106$	1.23553e7	1.00759
$107$	−9.05575e6	−0.714630	−0.357315	−	0.933984i	$-0.616308\pi$
$107$	−9.05575e6	−0.714630	−0.357315	+	0.933984i	$0.616308\pi$
$108$	−314904.	−0.0240544
$109$	−1.09720e7	−0.811510	−0.405755	−	0.913982i	$-0.632991\pi$
$109$	−1.09720e7	−0.811510	−0.405755	+	0.913982i	$0.632991\pi$
$110$	−1.71241e7	−1.22668
$111$	3.69068e6	0.256139
$112$	1.44433e6	0.0971411
$113$	−5.04191e6	−0.328716	−0.164358	−	0.986401i	$-0.552555\pi$
$113$	−5.04191e6	−0.328716	−0.164358	+	0.986401i	$0.552555\pi$
$114$	2.92154e7	1.84691
$115$	1.02387e7	0.627774
$116$	−246352.	−0.0146539
$117$	−2.37027e7	−1.36819
$118$	6.68154e6	0.374360
$119$	−464120.	−0.0252473
$120$	−2.68598e7	−1.41895
$121$	1.78989e7	0.918498
$122$	1.32157e7	0.658916
$123$	5.42198e7	2.62718
$124$	−1.64616e6	−0.0775348
$125$	2.31422e7	1.05979
$126$	2.75790e6	0.122823
$127$	2.86210e7	1.23986	0.619928	−	0.784659i	$-0.287162\pi$
$127$	2.86210e7	1.23986	0.619928	+	0.784659i	$0.287162\pi$
$128$	−2.05376e7	−0.865595
$129$	5.63638e6	0.231173
$130$	−2.51836e7	−1.00535
$131$	−2.22173e7	−0.863460	−0.431730	−	0.902003i	$-0.642097\pi$
$131$	−2.22173e7	−0.863460	−0.431730	+	0.902003i	$0.642097\pi$
$132$	4.28916e6	0.162317
$133$	3.73331e6	0.137598
$134$	3.00526e7	1.07899
$135$	−8.04102e6	−0.281283
$136$	7.22254e6	0.246209
$137$	1.91101e7	0.634952	0.317476	−	0.948266i	$-0.397165\pi$
$137$	1.91101e7	0.634952	0.317476	+	0.948266i	$0.397165\pi$
$138$	2.99336e7	0.969578
$139$	−4.44097e7	−1.40257	−0.701287	−	0.712879i	$-0.747391\pi$
$139$	−4.44097e7	−1.40257	−0.701287	+	0.712879i	$0.747391\pi$
$140$	−251045.	−0.00773220
$141$	8.95455e7	2.69015
$142$	−4.68819e7	−1.37403
$143$	5.49821e7	1.57234
$144$	−3.95098e7	−1.10265
$145$	−6.29058e6	−0.171357
$146$	2.60478e7	0.692686
$147$	−5.65479e7	−1.46827
$148$	−536803.	−0.0136113
$149$	−5.08092e7	−1.25832	−0.629159	−	0.777276i	$-0.716601\pi$
$149$	−5.08092e7	−1.25832	−0.629159	+	0.777276i	$0.716601\pi$
$150$	8.74626e6	0.211594
$151$	−1.28822e7	−0.304489	−0.152244	−	0.988343i	$-0.548650\pi$
$151$	−1.28822e7	−0.304489	−0.152244	+	0.988343i	$0.548650\pi$
$152$	−5.80970e7	−1.34184
$153$	1.26961e7	0.286582
$154$	−6.39738e6	−0.141150
$155$	−4.20345e7	−0.906661
$156$	6.30789e6	0.133029
$157$	−6.29602e7	−1.29843	−0.649213	−	0.760606i	$-0.724902\pi$
$157$	−6.29602e7	−1.29843	−0.649213	+	0.760606i	$0.724902\pi$
$158$	−4.33621e7	−0.874603
$159$	−7.90232e7	−1.55907
$160$	7.52768e6	0.145292
$161$	3.82509e6	0.0722356
$162$	3.90858e7	0.722298
$163$	8.35884e7	1.51178	0.755891	−	0.654697i	$-0.227204\pi$
$163$	8.35884e7	1.51178	0.755891	+	0.654697i	$0.227204\pi$
$164$	−7.88618e6	−0.139609
$165$	1.09523e8	1.89807
$166$	2.08160e7	0.353198
$167$	7.47971e7	1.24273	0.621366	−	0.783521i	$-0.286578\pi$
$167$	7.47971e7	1.24273	0.621366	+	0.783521i	$0.286578\pi$
$168$	−1.00346e7	−0.163274
$169$	1.81113e7	0.288634
$170$	1.34893e7	0.210581
$171$	−1.02125e8	−1.56188
$172$	−819801.	−0.0122845
$173$	1.27295e8	1.86918	0.934588	−	0.355732i	$-0.115768\pi$
$173$	1.27295e8	1.86918	0.934588	+	0.355732i	$0.115768\pi$
$174$	−1.83909e7	−0.264656
$175$	1.11765e6	0.0157642
$176$	9.16493e7	1.26717
$177$	−4.27343e7	−0.579255
$178$	−1.06045e8	−1.40935
$179$	−1.16244e8	−1.51490	−0.757452	−	0.652891i	$-0.773556\pi$
$179$	−1.16244e8	−1.51490	−0.757452	+	0.652891i	$0.773556\pi$
$180$	6.86736e6	0.0877680
$181$	1.44159e8	1.80704	0.903519	−	0.428548i	$-0.140975\pi$
$181$	1.44159e8	1.80704	0.903519	+	0.428548i	$0.140975\pi$
$182$	−9.40835e6	−0.115681
$183$	−8.45258e7	−1.01955
$184$	−5.95253e7	−0.704432
$185$	−1.37072e7	−0.159165
$186$	−1.22891e8	−1.40031
$187$	−2.94505e7	−0.329342
$188$	−1.30242e7	−0.142955
$189$	−3.00405e6	−0.0323661
$190$	−1.08506e8	−1.14767
$191$	−1.21483e8	−1.26153	−0.630765	−	0.775974i	$-0.717259\pi$
$191$	−1.21483e8	−1.26153	−0.630765	+	0.775974i	$0.717259\pi$
$192$	1.55249e8	1.58298
$193$	1.93410e7	0.193654	0.0968272	−	0.995301i	$-0.469131\pi$
$193$	1.93410e7	0.193654	0.0968272	+	0.995301i	$0.469131\pi$
$194$	6.08171e7	0.598025
$195$	1.61071e8	1.55559
$196$	8.22479e6	0.0780241
$197$	−2.40089e7	−0.223739	−0.111869	−	0.993723i	$-0.535684\pi$
$197$	−2.40089e7	−0.223739	−0.111869	+	0.993723i	$0.535684\pi$
$198$	1.75001e8	1.60219
$199$	−3.17720e7	−0.285798	−0.142899	−	0.989737i	$-0.545642\pi$
$199$	−3.17720e7	−0.285798	−0.142899	+	0.989737i	$0.545642\pi$
$200$	−1.73926e7	−0.153730
$201$	−1.92213e8	−1.66954
$202$	2.70959e7	0.231299
$203$	−2.35010e6	−0.0197174
$204$	−3.37875e6	−0.0278644
$205$	−2.01372e8	−1.63253
$206$	2.23476e8	1.78113
$207$	−1.04636e8	−0.819944
$208$	1.34785e8	1.03853
$209$	2.36896e8	1.79492
$210$	−1.87412e7	−0.139647
$211$	1.17802e8	0.863308	0.431654	−	0.902039i	$-0.357930\pi$
$211$	1.17802e8	0.863308	0.431654	+	0.902039i	$0.357930\pi$
$212$	1.14938e7	0.0828490
$213$	2.99851e8	2.12606
$214$	9.83285e7	0.685854
$215$	−2.09335e7	−0.143651
$216$	4.67484e7	0.315630
$217$	−1.57037e7	−0.104326
$218$	1.19136e8	0.778832
$219$	−1.66598e8	−1.07181
$220$	−1.59300e7	−0.100864
$221$	−4.33116e7	−0.269918
$222$	−4.00739e7	−0.245825
$223$	−1.33811e8	−0.808028	−0.404014	−	0.914753i	$-0.632385\pi$
$223$	−1.33811e8	−0.808028	−0.404014	+	0.914753i	$0.632385\pi$
$224$	2.81227e6	0.0167182
$225$	−3.05734e7	−0.178939
$226$	5.47457e7	0.315479
$227$	−3.22298e7	−0.182880	−0.0914401	−	0.995811i	$-0.529147\pi$
$227$	−3.22298e7	−0.182880	−0.0914401	+	0.995811i	$0.529147\pi$
$228$	2.71781e7	0.151862
$229$	−1.04189e8	−0.573320	−0.286660	−	0.958032i	$-0.592545\pi$
$229$	−1.04189e8	−0.573320	−0.286660	+	0.958032i	$0.592545\pi$
$230$	−1.11173e8	−0.602495
$231$	4.09168e7	0.218404
$232$	3.65718e7	0.192282
$233$	−3.53002e8	−1.82823	−0.914117	−	0.405451i	$-0.867114\pi$
$233$	−3.53002e8	−1.82823	−0.914117	+	0.405451i	$0.867114\pi$
$234$	2.57367e8	1.31310
$235$	−3.32572e8	−1.67166
$236$	6.21562e6	0.0307817
$237$	2.77338e8	1.35329
$238$	5.03947e6	0.0242307
$239$	−4.06680e7	−0.192690	−0.0963452	−	0.995348i	$-0.530715\pi$
$239$	−4.06680e7	−0.192690	−0.0963452	+	0.995348i	$0.530715\pi$
$240$	2.68488e8	1.25368
$241$	−6.53565e7	−0.300766	−0.150383	−	0.988628i	$-0.548051\pi$
$241$	−6.53565e7	−0.300766	−0.150383	+	0.988628i	$0.548051\pi$
$242$	−1.94349e8	−0.881512
$243$	−3.18169e8	−1.42244
$244$	1.22941e7	0.0541792
$245$	2.10019e8	0.912383
$246$	−5.88726e8	−2.52139
$247$	3.48392e8	1.47106
$248$	2.44378e8	1.01737
$249$	−1.33136e8	−0.546510
$250$	−2.51281e8	−1.01711
$251$	−4.56249e8	−1.82114	−0.910571	−	0.413352i	$-0.864358\pi$
$251$	−4.56249e8	−1.82114	−0.910571	+	0.413352i	$0.864358\pi$
$252$	2.56558e6	0.0100991
$253$	2.42720e8	0.942286
$254$	−3.10770e8	−1.18993
$255$	−8.62758e7	−0.325835
$256$	−6.31436e7	−0.235228
$257$	−4.56272e7	−0.167671	−0.0838354	−	0.996480i	$-0.526717\pi$
$257$	−4.56272e7	−0.167671	−0.0838354	+	0.996480i	$0.526717\pi$
$258$	−6.12006e7	−0.221864
$259$	−5.12087e6	−0.0183145
$260$	−2.34275e7	−0.0826645
$261$	6.42872e7	0.223812
$262$	2.41239e8	0.828690
$263$	5.61417e6	0.0190301	0.00951503	−	0.999955i	$-0.496971\pi$
$263$	5.61417e6	0.0190301	0.00951503	+	0.999955i	$0.496971\pi$
$264$	−6.36739e8	−2.12984
$265$	2.93492e8	0.968804
$266$	−4.05368e7	−0.132058
$267$	6.78248e8	2.18072
$268$	2.79570e7	0.0887194
$269$	4.01644e8	1.25808	0.629040	−	0.777373i	$-0.283448\pi$
$269$	4.01644e8	1.25808	0.629040	+	0.777373i	$0.283448\pi$
$270$	8.73105e7	0.269956
$271$	1.02086e8	0.311582	0.155791	−	0.987790i	$-0.450207\pi$
$271$	1.02086e8	0.311582	0.155791	+	0.987790i	$0.450207\pi$
$272$	−7.21958e7	−0.217531
$273$	6.01746e7	0.178996
$274$	−2.07500e8	−0.609384
$275$	7.09199e7	0.205638
$276$	2.78463e7	0.0797233
$277$	3.52104e8	0.995387	0.497693	−	0.867353i	$-0.334180\pi$
$277$	3.52104e8	0.995387	0.497693	+	0.867353i	$0.334180\pi$
$278$	4.82206e8	1.34610
$279$	4.29576e8	1.18420
$280$	3.72684e7	0.101458
$281$	−2.50686e8	−0.673996	−0.336998	−	0.941505i	$-0.609412\pi$
$281$	−2.50686e8	−0.673996	−0.336998	+	0.941505i	$0.609412\pi$
$282$	−9.72296e8	−2.58183
$283$	2.46045e8	0.645300	0.322650	−	0.946518i	$-0.395426\pi$
$283$	2.46045e8	0.645300	0.322650	+	0.946518i	$0.395426\pi$
$284$	−4.36127e7	−0.112979
$285$	6.93990e8	1.77581
$286$	−5.97003e8	−1.50902
$287$	−7.52308e7	−0.187849
$288$	−7.69299e7	−0.189767
$289$	−3.87139e8	−0.943463
$290$	6.83039e7	0.164457
$291$	−3.88978e8	−0.925336
$292$	2.42314e7	0.0569560
$293$	−3.55131e7	−0.0824806	−0.0412403	−	0.999149i	$-0.513131\pi$
$293$	−3.55131e7	−0.0824806	−0.0412403	+	0.999149i	$0.513131\pi$
$294$	6.14005e8	1.40915
$295$	1.58715e8	0.359949
$296$	7.96900e7	0.178601
$297$	−1.90621e8	−0.422204
$298$	5.51693e8	1.20765
$299$	3.56957e8	0.772266
$300$	8.13636e6	0.0173983
$301$	−7.82056e6	−0.0165293
$302$	1.39877e8	0.292228
$303$	−1.73302e8	−0.357893
$304$	5.80732e8	1.18555
$305$	3.13929e8	0.633551
$306$	−1.37855e8	−0.275042
$307$	6.24223e8	1.23128	0.615638	−	0.788029i	$-0.288898\pi$
$307$	6.24223e8	1.23128	0.615638	+	0.788029i	$0.288898\pi$
$308$	−5.95128e6	−0.0116060
$309$	−1.42932e9	−2.75598
$310$	4.56416e8	0.870152
$311$	−6.36181e7	−0.119928	−0.0599639	−	0.998201i	$-0.519099\pi$
$311$	−6.36181e7	−0.119928	−0.0599639	+	0.998201i	$0.519099\pi$
$312$	−9.36425e8	−1.74555
$313$	9.50815e8	1.75263	0.876316	−	0.481736i	$-0.159994\pi$
$313$	9.50815e8	1.75263	0.876316	+	0.481736i	$0.159994\pi$
$314$	6.83630e8	1.24614
$315$	6.55117e7	0.118095
$316$	−4.03384e7	−0.0719140
$317$	−5.52745e8	−0.974579	−0.487290	−	0.873240i	$-0.662014\pi$
$317$	−5.52745e8	−0.974579	−0.487290	+	0.873240i	$0.662014\pi$
$318$	8.58044e8	1.49629
$319$	−1.49125e8	−0.257206
$320$	−5.76594e8	−0.983661
$321$	−6.28896e8	−1.06123
$322$	−4.15333e7	−0.0693268
$323$	−1.86612e8	−0.308128
$324$	3.63602e7	0.0593908
$325$	1.04299e8	0.168534
$326$	−9.07614e8	−1.45091
$327$	−7.61976e8	−1.20510
$328$	1.17073e9	1.83188
$329$	−1.24246e8	−0.192351
$330$	−1.18922e9	−1.82164
$331$	−6.95661e8	−1.05439	−0.527193	−	0.849746i	$-0.676755\pi$
$331$	−6.95661e8	−1.05439	−0.527193	+	0.849746i	$0.676755\pi$
$332$	1.93644e7	0.0290416
$333$	1.40082e8	0.207887
$334$	−8.12157e8	−1.19269
$335$	7.13878e8	1.03745
$336$	1.00305e8	0.144256
$337$	2.20688e7	0.0314104	0.0157052	−	0.999877i	$-0.495001\pi$
$337$	2.20688e7	0.0314104	0.0157052	+	0.999877i	$0.495001\pi$
$338$	−1.96655e8	−0.277011
$339$	−3.50146e8	−0.488147
$340$	1.25487e7	0.0173149
$341$	−9.96471e8	−1.36089
$342$	1.10889e9	1.49898
$343$	1.57817e8	0.211166
$344$	1.21702e8	0.161192
$345$	7.11051e8	0.932253
$346$	−1.38219e9	−1.79391
$347$	3.47357e8	0.446295	0.223148	−	0.974785i	$-0.428367\pi$
$347$	3.47357e8	0.446295	0.223148	+	0.974785i	$0.428367\pi$
$348$	−1.71085e7	−0.0217613
$349$	9.94569e8	1.25241	0.626204	−	0.779659i	$-0.284608\pi$
$349$	9.94569e8	1.25241	0.626204	+	0.779659i	$0.284608\pi$
$350$	−1.21356e7	−0.0151294
$351$	−2.80338e8	−0.346024
$352$	1.78451e8	0.218082
$353$	−1.45500e9	−1.76056	−0.880279	−	0.474456i	$-0.842645\pi$
$353$	−1.45500e9	−1.76056	−0.880279	+	0.474456i	$0.842645\pi$
$354$	4.64014e8	0.555930
$355$	−1.11365e9	−1.32114
$356$	−9.86500e7	−0.115884
$357$	−3.22318e7	−0.0374926
$358$	1.26219e9	1.45390
$359$	4.53478e8	0.517280	0.258640	−	0.965974i	$-0.416726\pi$
$359$	4.53478e8	0.517280	0.258640	+	0.965974i	$0.416726\pi$
$360$	−1.01948e9	−1.15165
$361$	6.07209e8	0.679303
$362$	−1.56530e9	−1.73427
$363$	1.24303e9	1.36398
$364$	−8.75229e6	−0.00951189
$365$	6.18746e8	0.666020
$366$	9.17792e8	0.978499
$367$	−1.53020e9	−1.61591	−0.807957	−	0.589242i	$-0.799427\pi$
$367$	−1.53020e9	−1.61591	−0.807957	+	0.589242i	$0.799427\pi$
$368$	5.95009e8	0.622381
$369$	2.05795e9	2.13227
$370$	1.48834e8	0.152756
$371$	1.09646e8	0.111476
$372$	−1.14321e8	−0.115140
$373$	−6.89900e8	−0.688344	−0.344172	−	0.938907i	$-0.611840\pi$
$373$	−6.89900e8	−0.688344	−0.344172	+	0.938907i	$0.611840\pi$
$374$	3.19778e8	0.316080
$375$	1.60716e9	1.57380
$376$	1.93348e9	1.87579
$377$	−2.19311e8	−0.210798
$378$	3.26184e7	0.0310628
$379$	−1.02454e9	−0.966701	−0.483350	−	0.875427i	$-0.660580\pi$
$379$	−1.02454e9	−0.966701	−0.483350	+	0.875427i	$0.660580\pi$
$380$	−1.00940e8	−0.0943667
$381$	1.98765e9	1.84120
$382$	1.31908e9	1.21073
$383$	−2.06713e9	−1.88006	−0.940030	−	0.341092i	$-0.889203\pi$
$383$	−2.06713e9	−1.88006	−0.940030	+	0.341092i	$0.889203\pi$
$384$	−1.42628e9	−1.28542
$385$	−1.51965e8	−0.135716
$386$	−2.10007e8	−0.185856
$387$	2.13932e8	0.187624
$388$	5.65762e7	0.0491725
$389$	1.59282e9	1.37197	0.685984	−	0.727616i	$-0.259372\pi$
$389$	1.59282e9	1.37197	0.685984	+	0.727616i	$0.259372\pi$
$390$	−1.74893e9	−1.49295
$391$	−1.91200e8	−0.161759
$392$	−1.22099e9	−1.02379
$393$	−1.54293e9	−1.28225
$394$	2.60692e8	0.214729
$395$	−1.03003e9	−0.840934
$396$	1.62798e8	0.131739
$397$	−2.93498e8	−0.235417	−0.117709	−	0.993048i	$-0.537555\pi$
$397$	−2.93498e8	−0.235417	−0.117709	+	0.993048i	$0.537555\pi$
$398$	3.44985e8	0.274290
$399$	2.59268e8	0.204335
$400$	1.73855e8	0.135824
$401$	−7.79540e8	−0.603716	−0.301858	−	0.953353i	$-0.597607\pi$
$401$	−7.79540e8	−0.603716	−0.301858	+	0.953353i	$0.597607\pi$
$402$	2.08707e9	1.60231
$403$	−1.46547e9	−1.11534
$404$	2.52064e7	0.0190185
$405$	9.28454e8	0.694493
$406$	2.55177e7	0.0189234
$407$	−3.24943e8	−0.238906
$408$	5.01585e8	0.365623
$409$	−8.95080e8	−0.646890	−0.323445	−	0.946247i	$-0.604841\pi$
$409$	−8.95080e8	−0.646890	−0.323445	+	0.946247i	$0.604841\pi$
$410$	2.18653e9	1.56679
$411$	1.32714e9	0.942912
$412$	2.07893e8	0.146453
$413$	5.92944e7	0.0414179
$414$	1.13615e9	0.786927
$415$	4.94467e8	0.339601
$416$	2.62441e8	0.178733
$417$	−3.08413e9	−2.08284
$418$	−2.57224e9	−1.72264
$419$	7.12868e8	0.473435	0.236717	−	0.971579i	$-0.423928\pi$
$419$	7.12868e8	0.473435	0.236717	+	0.971579i	$0.423928\pi$
$420$	−1.74344e7	−0.0114824
$421$	9.68000e8	0.632249	0.316124	−	0.948718i	$-0.397618\pi$
$421$	9.68000e8	0.632249	0.316124	+	0.948718i	$0.397618\pi$
$422$	−1.27911e9	−0.828544
$423$	3.39875e9	2.18338
$424$	−1.70629e9	−1.08710
$425$	−5.58664e7	−0.0353012
$426$	−3.25582e9	−2.04045
$427$	1.17281e8	0.0729002
$428$	9.14718e7	0.0563942
$429$	3.81835e9	2.33494
$430$	2.27299e8	0.137866
$431$	2.42364e9	1.45814	0.729068	−	0.684441i	$-0.239954\pi$
$431$	2.42364e9	1.45814	0.729068	+	0.684441i	$0.239954\pi$
$432$	−4.67293e8	−0.278866
$433$	8.06568e8	0.477456	0.238728	−	0.971086i	$-0.423270\pi$
$433$	8.06568e8	0.477456	0.238728	+	0.971086i	$0.423270\pi$
$434$	1.70513e8	0.100125
$435$	−4.36863e8	−0.254468
$436$	1.10828e8	0.0640393
$437$	1.53798e9	0.881590
$438$	1.80895e9	1.02865
$439$	−2.11575e9	−1.19355	−0.596773	−	0.802410i	$-0.703551\pi$
$439$	−2.11575e9	−1.19355	−0.596773	+	0.802410i	$0.703551\pi$
$440$	2.36485e9	1.32348
$441$	−2.14631e9	−1.19167
$442$	4.70283e8	0.259049
$443$	2.24117e9	1.22479	0.612396	−	0.790551i	$-0.290206\pi$
$443$	2.24117e9	1.22479	0.612396	+	0.790551i	$0.290206\pi$
$444$	−3.72794e7	−0.0202129
$445$	−2.51901e9	−1.35510
$446$	1.45294e9	0.775490
$447$	−3.52856e9	−1.86862
$448$	−2.15410e8	−0.113186
$449$	−2.94807e9	−1.53701	−0.768503	−	0.639846i	$-0.778998\pi$
$449$	−2.94807e9	−1.53701	−0.768503	+	0.639846i	$0.778998\pi$
$450$	3.31970e8	0.171733
$451$	−4.77374e9	−2.45042
$452$	5.09281e7	0.0259402
$453$	−8.94633e8	−0.452170
$454$	3.49955e8	0.175516
$455$	−2.23488e8	−0.111228
$456$	−4.03467e9	−1.99265
$457$	7.86122e8	0.385286	0.192643	−	0.981269i	$-0.438294\pi$
$457$	7.86122e8	0.385286	0.192643	+	0.981269i	$0.438294\pi$
$458$	1.13130e9	0.550234
$459$	1.50160e8	0.0724784
$460$	−1.03421e8	−0.0495401
$461$	1.38634e9	0.659048	0.329524	−	0.944147i	$-0.393112\pi$
$461$	1.38634e9	0.659048	0.329524	+	0.944147i	$0.393112\pi$
$462$	−4.44280e8	−0.209609
$463$	−3.06256e9	−1.43401	−0.717004	−	0.697069i	$-0.754487\pi$
$463$	−3.06256e9	−1.43401	−0.717004	+	0.697069i	$0.754487\pi$
$464$	−3.65568e8	−0.169885
$465$	−2.91918e9	−1.34640
$466$	3.83294e9	1.75461
$467$	2.15117e9	0.977384	0.488692	−	0.872456i	$-0.337474\pi$
$467$	2.15117e9	0.977384	0.488692	+	0.872456i	$0.337474\pi$
$468$	2.39420e8	0.107969
$469$	2.66698e8	0.119375
$470$	3.61111e9	1.60435
$471$	−4.37241e9	−1.92818
$472$	−9.22728e8	−0.403902
$473$	−4.96250e8	−0.215619
$474$	−3.01138e9	−1.29880
$475$	4.49381e8	0.192392
$476$	4.68806e6	0.00199236
$477$	−2.99937e9	−1.26537
$478$	4.41579e8	0.184931
$479$	2.33213e8	0.0969569	0.0484784	−	0.998824i	$-0.484563\pi$
$479$	2.33213e8	0.0969569	0.0484784	+	0.998824i	$0.484563\pi$
$480$	5.22776e8	0.215760
$481$	−4.77879e8	−0.195799
$482$	7.09649e8	0.288655
$483$	2.65642e8	0.107271
$484$	−1.80797e8	−0.0724822
$485$	1.44466e9	0.575004
$486$	3.45472e9	1.36517
$487$	2.08417e9	0.817676	0.408838	−	0.912607i	$-0.365934\pi$
$487$	2.08417e9	0.817676	0.408838	+	0.912607i	$0.365934\pi$
$488$	−1.82510e9	−0.710914
$489$	5.80498e9	2.24502
$490$	−2.28041e9	−0.875643
$491$	2.31958e8	0.0884350	0.0442175	−	0.999022i	$-0.485921\pi$
$491$	2.31958e8	0.0884350	0.0442175	+	0.999022i	$0.485921\pi$
$492$	−5.47673e8	−0.207321
$493$	1.17471e8	0.0441538
$494$	−3.78289e9	−1.41182
$495$	4.15702e9	1.54051
$496$	−2.44278e9	−0.898871
$497$	−4.16047e8	−0.152018
$498$	1.44561e9	0.524503
$499$	9.76012e7	0.0351644	0.0175822	−	0.999845i	$-0.494403\pi$
$499$	9.76012e7	0.0351644	0.0175822	+	0.999845i	$0.494403\pi$
$500$	−2.33758e8	−0.0836319
$501$	5.19445e9	1.84547
$502$	4.95401e9	1.74781
$503$	1.94319e9	0.680813	0.340406	−	0.940278i	$-0.389435\pi$
$503$	1.94319e9	0.680813	0.340406	+	0.940278i	$0.389435\pi$
$504$	−3.80868e8	−0.132516
$505$	6.43642e8	0.222395
$506$	−2.63548e9	−0.904343
$507$	1.25778e9	0.428625
$508$	−2.89099e8	−0.0978417
$509$	−2.91549e9	−0.979938	−0.489969	−	0.871740i	$-0.662992\pi$
$509$	−2.91549e9	−0.979938	−0.489969	+	0.871740i	$0.662992\pi$
$510$	9.36794e8	0.312715
$511$	2.31158e8	0.0766364
$512$	3.31443e9	1.09135
$513$	−1.20786e9	−0.395008
$514$	4.95426e8	0.160919
$515$	5.30851e9	1.71257
$516$	−5.69329e7	−0.0182427
$517$	−7.88395e9	−2.50915
$518$	5.56031e7	0.0175770
$519$	8.84028e9	2.77575
$520$	3.47788e9	1.08468
$521$	3.10547e9	0.962044	0.481022	−	0.876708i	$-0.340266\pi$
$521$	3.10547e9	0.962044	0.481022	+	0.876708i	$0.340266\pi$
$522$	−6.98039e8	−0.214799
$523$	2.44858e9	0.748442	0.374221	−	0.927340i	$-0.377910\pi$
$523$	2.44858e9	0.748442	0.374221	+	0.927340i	$0.377910\pi$
$524$	2.24416e8	0.0681389
$525$	7.76175e7	0.0234100
$526$	−6.09594e7	−0.0182638
$527$	7.84960e8	0.233620
$528$	6.36478e9	1.88176
$529$	−1.82903e9	−0.537188
$530$	−3.18678e9	−0.929792
$531$	−1.62201e9	−0.470134
$532$	−3.77100e7	−0.0108584
$533$	−7.02053e9	−2.00828
$534$	−7.36451e9	−2.09290
$535$	2.33572e9	0.659451
$536$	−4.15030e9	−1.16413
$537$	−8.07282e9	−2.24965
$538$	−4.36110e9	−1.20742
$539$	4.97871e9	1.36948
$540$	8.12221e7	0.0221971
$541$	−5.75642e8	−0.156301	−0.0781505	−	0.996942i	$-0.524901\pi$
$541$	−5.75642e8	−0.156301	−0.0781505	+	0.996942i	$0.524901\pi$
$542$	−1.10846e9	−0.299036
$543$	1.00114e10	2.68347
$544$	−1.40573e8	−0.0374375
$545$	2.82998e9	0.748851
$546$	−6.53384e8	−0.171788
$547$	−4.72465e9	−1.23428	−0.617140	−	0.786853i	$-0.711709\pi$
$547$	−4.72465e9	−1.23428	−0.617140	+	0.786853i	$0.711709\pi$
$548$	−1.93031e8	−0.0501065
$549$	−3.20823e9	−0.827488
$550$	−7.70057e8	−0.197357
$551$	−9.44922e8	−0.240639
$552$	−4.13386e9	−1.04609
$553$	−3.84811e8	−0.0967631
$554$	−3.82319e9	−0.955305
$555$	−9.51925e8	−0.236362
$556$	4.48581e8	0.110683
$557$	−1.33845e8	−0.0328177	−0.0164089	−	0.999865i	$-0.505223\pi$
$557$	−1.33845e8	−0.0328177	−0.0164089	+	0.999865i	$0.505223\pi$
$558$	−4.66440e9	−1.13652
$559$	−7.29814e8	−0.176714
$560$	−3.72531e8	−0.0896405
$561$	−2.04526e9	−0.489077
$562$	2.72198e9	0.646856
$563$	−1.55604e9	−0.367485	−0.183743	−	0.982974i	$-0.558821\pi$
$563$	−1.55604e9	−0.367485	−0.183743	+	0.982974i	$0.558821\pi$
$564$	−9.04496e8	−0.212290
$565$	1.30044e9	0.303334
$566$	−2.67159e9	−0.619315
$567$	3.46861e8	0.0799126
$568$	6.47444e9	1.48246
$569$	3.07563e9	0.699908	0.349954	−	0.936767i	$-0.386197\pi$
$569$	3.07563e9	0.699908	0.349954	+	0.936767i	$0.386197\pi$
$570$	−7.53543e9	−1.70430
$571$	5.42605e9	1.21971	0.609856	−	0.792512i	$-0.291227\pi$
$571$	5.42605e9	1.21971	0.609856	+	0.792512i	$0.291227\pi$
$572$	−5.55373e8	−0.124079
$573$	−8.43663e9	−1.87339
$574$	8.16866e8	0.180285
$575$	4.60429e8	0.101001
$576$	5.89257e9	1.28477
$577$	−2.75088e9	−0.596151	−0.298075	−	0.954542i	$-0.596345\pi$
$577$	−2.75088e9	−0.596151	−0.298075	+	0.954542i	$0.596345\pi$
$578$	4.20361e9	0.905472
$579$	1.34317e9	0.287579
$580$	6.35409e7	0.0135224
$581$	1.84728e8	0.0390766
$582$	4.22357e9	0.888075
$583$	6.95753e9	1.45417
$584$	−3.59723e9	−0.747348
$585$	6.11355e9	1.26255
$586$	3.85606e8	0.0791593
$587$	1.67607e9	0.342027	0.171013	−	0.985269i	$-0.445296\pi$
$587$	1.67607e9	0.342027	0.171013	+	0.985269i	$0.445296\pi$
$588$	5.71189e8	0.115867
$589$	−6.31410e9	−1.27323
$590$	−1.72335e9	−0.345455
$591$	−1.66735e9	−0.332255
$592$	−7.96574e8	−0.157797
$593$	8.26130e9	1.62689	0.813443	−	0.581645i	$-0.197591\pi$
$593$	8.26130e9	1.62689	0.813443	+	0.581645i	$0.197591\pi$
$594$	2.06978e9	0.405203
$595$	1.19709e8	0.0232979
$596$	5.13222e8	0.0992987
$597$	−2.20648e9	−0.424414
$598$	−3.87589e9	−0.741169
$599$	−2.28824e9	−0.435019	−0.217509	−	0.976058i	$-0.569793\pi$
$599$	−2.28824e9	−0.435019	−0.217509	+	0.976058i	$0.569793\pi$
$600$	−1.20787e9	−0.228292
$601$	−2.06292e8	−0.0387633	−0.0193817	−	0.999812i	$-0.506170\pi$
$601$	−2.06292e8	−0.0387633	−0.0193817	+	0.999812i	$0.506170\pi$
$602$	8.49166e7	0.0158637
$603$	−7.29555e9	−1.35503
$604$	1.30123e8	0.0240284
$605$	−4.61661e9	−0.847578
$606$	1.88173e9	0.343482
$607$	3.67819e9	0.667535	0.333767	−	0.942655i	$-0.391680\pi$
$607$	3.67819e9	0.667535	0.333767	+	0.942655i	$0.391680\pi$
$608$	1.13075e9	0.204035
$609$	−1.63208e8	−0.0292806
$610$	−3.40868e9	−0.608039
$611$	−1.15946e10	−2.05642
$612$	−1.28242e8	−0.0226153
$613$	4.23307e9	0.742240	0.371120	−	0.928585i	$-0.378974\pi$
$613$	4.23307e9	0.742240	0.371120	+	0.928585i	$0.378974\pi$
$614$	−6.77790e9	−1.18170
$615$	−1.39847e10	−2.42433
$616$	8.83485e8	0.152288
$617$	8.84313e9	1.51568	0.757841	−	0.652439i	$-0.226254\pi$
$617$	8.84313e9	1.51568	0.757841	+	0.652439i	$0.226254\pi$
$618$	1.55198e10	2.64500
$619$	5.81708e9	0.985798	0.492899	−	0.870086i	$-0.335937\pi$
$619$	5.81708e9	0.985798	0.492899	+	0.870086i	$0.335937\pi$
$620$	4.24589e8	0.0715481
$621$	−1.23756e9	−0.207369
$622$	6.90774e8	0.115098
$623$	−9.41079e8	−0.155926
$624$	9.36041e9	1.54223
$625$	−5.06283e9	−0.829494
$626$	−1.03241e10	−1.68206
$627$	1.64517e10	2.66548
$628$	6.35959e8	0.102464
$629$	2.55970e8	0.0410122
$630$	−7.11335e8	−0.113340
$631$	−1.06337e10	−1.68492	−0.842462	−	0.538756i	$-0.818894\pi$
$631$	−1.06337e10	−1.68492	−0.842462	+	0.538756i	$0.818894\pi$
$632$	5.98835e9	0.943621
$633$	8.18105e9	1.28202
$634$	6.00177e9	0.935335
$635$	−7.38211e9	−1.14412
$636$	7.98211e8	0.123032
$637$	7.32198e9	1.12238
$638$	1.61921e9	0.246849
$639$	1.13810e10	1.72555
$640$	5.29719e9	0.798759
$641$	5.23495e9	0.785071	0.392536	−	0.919737i	$-0.371598\pi$
$641$	5.23495e9	0.785071	0.392536	+	0.919737i	$0.371598\pi$
$642$	6.82864e9	1.01850
$643$	−1.21953e10	−1.80907	−0.904536	−	0.426398i	$-0.859782\pi$
$643$	−1.21953e10	−1.80907	−0.904536	+	0.426398i	$0.859782\pi$
$644$	−3.86371e7	−0.00570038
$645$	−1.45377e9	−0.213323
$646$	2.02626e9	0.295720
$647$	1.96125e9	0.284687	0.142344	−	0.989817i	$-0.454536\pi$
$647$	1.96125e9	0.284687	0.142344	+	0.989817i	$0.454536\pi$
$648$	−5.39779e9	−0.779297
$649$	3.76250e9	0.540282
$650$	−1.13249e9	−0.161748
$651$	−1.09058e9	−0.154925
$652$	−8.44324e8	−0.119301
$653$	−5.92355e9	−0.832504	−0.416252	−	0.909249i	$-0.636657\pi$
$653$	−5.92355e9	−0.832504	−0.416252	+	0.909249i	$0.636657\pi$
$654$	8.27363e9	1.15658
$655$	5.73044e9	0.796789
$656$	−1.17025e10	−1.61851
$657$	−6.32335e9	−0.869898
$658$	1.34907e9	0.184606
$659$	−1.20388e10	−1.63864	−0.819320	−	0.573336i	$-0.805649\pi$
$659$	−1.20388e10	−1.63864	−0.819320	+	0.573336i	$0.805649\pi$
$660$	−1.10629e9	−0.149784
$661$	3.83588e9	0.516607	0.258303	−	0.966064i	$-0.416837\pi$
$661$	3.83588e9	0.516607	0.258303	+	0.966064i	$0.416837\pi$
$662$	7.55358e9	1.01193
$663$	−3.00787e9	−0.400831
$664$	−2.87470e9	−0.381070
$665$	−9.62921e8	−0.126974
$666$	−1.52103e9	−0.199516
$667$	−9.68152e8	−0.126329
$668$	−7.55523e8	−0.0980687
$669$	−9.29283e9	−1.19993
$670$	−7.75138e9	−0.995674
$671$	7.44200e9	0.950957
$672$	1.95304e8	0.0248267
$673$	6.92715e9	0.875996	0.437998	−	0.898976i	$-0.355688\pi$
$673$	6.92715e9	0.875996	0.437998	+	0.898976i	$0.355688\pi$
$674$	−2.39626e8	−0.0301456
$675$	−3.61599e8	−0.0452548
$676$	−1.82942e8	−0.0227772
$677$	−5.55286e9	−0.687791	−0.343896	−	0.939008i	$-0.611747\pi$
$677$	−5.55286e9	−0.687791	−0.343896	+	0.939008i	$0.611747\pi$
$678$	3.80193e9	0.468490
$679$	5.39713e8	0.0661635
$680$	−1.86289e9	−0.227198
$681$	−2.23827e9	−0.271580
$682$	1.08198e10	1.30609
$683$	−1.37064e9	−0.164608	−0.0823038	−	0.996607i	$-0.526228\pi$
$683$	−1.37064e9	−0.164608	−0.0823038	+	0.996607i	$0.526228\pi$
$684$	1.03156e9	0.123254
$685$	−4.92901e9	−0.585926
$686$	−1.71360e9	−0.202663
$687$	−7.23563e9	−0.851388
$688$	−1.21652e9	−0.142416
$689$	1.02321e10	1.19179
$690$	−7.72068e9	−0.894713
$691$	8.41608e9	0.970369	0.485184	−	0.874412i	$-0.338752\pi$
$691$	8.41608e9	0.970369	0.485184	+	0.874412i	$0.338752\pi$
$692$	−1.28580e9	−0.147504
$693$	1.55302e9	0.177260
$694$	−3.77164e9	−0.428324
$695$	1.14544e10	1.29428
$696$	2.53981e9	0.285541
$697$	3.76047e9	0.420656
$698$	−1.07992e10	−1.20198
$699$	−2.45150e10	−2.71495
$700$	−1.12893e7	−0.00124401
$701$	1.11440e10	1.22187	0.610937	−	0.791679i	$-0.290793\pi$
$701$	1.11440e10	1.22187	0.610937	+	0.791679i	$0.290793\pi$
$702$	3.04394e9	0.332091
$703$	−2.05899e9	−0.223517
$704$	−1.36688e10	−1.47647
$705$	−2.30962e10	−2.48244
$706$	1.57985e10	1.68967
$707$	2.40459e8	0.0255901
$708$	4.31657e8	0.0457112
$709$	4.06305e9	0.428144	0.214072	−	0.976818i	$-0.431327\pi$
$709$	4.06305e9	0.428144	0.214072	+	0.976818i	$0.431327\pi$
$710$	1.20921e10	1.26794
$711$	1.05266e10	1.09835
$712$	1.46449e10	1.52057
$713$	−6.46933e9	−0.668414
$714$	3.49977e8	0.0359829
$715$	−1.41814e10	−1.45093
$716$	1.17418e9	0.119547
$717$	−2.82428e9	−0.286148
$718$	−4.92393e9	−0.496450
$719$	−8.06855e9	−0.809551	−0.404776	−	0.914416i	$-0.632650\pi$
$719$	−8.06855e9	−0.809551	−0.404776	+	0.914416i	$0.632650\pi$
$720$	1.01906e10	1.01751
$721$	1.98321e9	0.197058
$722$	−6.59316e9	−0.651949
$723$	−4.53882e9	−0.446642
$724$	−1.45615e9	−0.142600
$725$	−2.82883e8	−0.0275692
$726$	−1.34970e10	−1.30906
$727$	−1.80363e9	−0.174092	−0.0870459	−	0.996204i	$-0.527743\pi$
$727$	−1.80363e9	−0.174092	−0.0870459	+	0.996204i	$0.527743\pi$
$728$	1.29930e9	0.124810
$729$	−1.42234e10	−1.35975
$730$	−6.71843e9	−0.639201
$731$	3.90916e8	0.0370146
$732$	8.53792e8	0.0804569
$733$	7.57269e9	0.710209	0.355104	−	0.934827i	$-0.384445\pi$
$733$	7.57269e9	0.710209	0.355104	+	0.934827i	$0.384445\pi$
$734$	1.66152e10	1.55084
$735$	1.45852e10	1.35490
$736$	1.15855e9	0.107113
$737$	1.69232e10	1.55721
$738$	−2.23455e10	−2.04641
$739$	−1.85526e10	−1.69102	−0.845509	−	0.533961i	$-0.820703\pi$
$739$	−1.85526e10	−1.69102	−0.845509	+	0.533961i	$0.820703\pi$
$740$	1.38456e8	0.0125603
$741$	2.41949e10	2.18454
$742$	−1.19055e9	−0.106988
$743$	6.62745e8	0.0592769	0.0296384	−	0.999561i	$-0.490564\pi$
$743$	6.62745e8	0.0592769	0.0296384	+	0.999561i	$0.490564\pi$
$744$	1.69713e10	1.51081
$745$	1.31051e10	1.16116
$746$	7.49103e9	0.660626
$747$	−5.05326e9	−0.443557
$748$	2.97479e8	0.0259896
$749$	8.72603e8	0.0758805
$750$	−1.74507e10	−1.51043
$751$	−9.30801e9	−0.801895	−0.400947	−	0.916101i	$-0.631319\pi$
$751$	−9.30801e9	−0.801895	−0.400947	+	0.916101i	$0.631319\pi$
$752$	−1.93269e10	−1.65730
$753$	−3.16852e10	−2.70442
$754$	2.38131e9	0.202309
$755$	3.32267e9	0.280978
$756$	3.03438e7	0.00255413
$757$	8.81928e9	0.738921	0.369460	−	0.929247i	$-0.379543\pi$
$757$	8.81928e9	0.738921	0.369460	+	0.929247i	$0.379543\pi$
$758$	1.11246e10	0.927774
$759$	1.68562e10	1.39931
$760$	1.49848e10	1.23823
$761$	1.82384e10	1.50017	0.750084	−	0.661342i	$-0.230013\pi$
$761$	1.82384e10	1.50017	0.750084	+	0.661342i	$0.230013\pi$
$762$	−2.15821e10	−1.76706
$763$	1.05725e9	0.0861674
$764$	1.22709e9	0.0995522
$765$	−3.27465e9	−0.264454
$766$	2.24452e10	1.80435
$767$	5.53335e9	0.442797
$768$	−4.38515e9	−0.349317
$769$	4.66330e9	0.369786	0.184893	−	0.982759i	$-0.440806\pi$
$769$	4.66330e9	0.369786	0.184893	+	0.982759i	$0.440806\pi$
$770$	1.65006e9	0.130251
$771$	−3.16868e9	−0.248993
$772$	−1.95362e8	−0.0152820
$773$	−1.38826e9	−0.108104	−0.0540522	−	0.998538i	$-0.517214\pi$
$773$	−1.38826e9	−0.108104	−0.0540522	+	0.998538i	$0.517214\pi$
$774$	−2.32291e9	−0.180069
$775$	−1.89026e9	−0.145870
$776$	−8.39890e9	−0.645218
$777$	−3.55630e8	−0.0271972
$778$	−1.72951e10	−1.31672
$779$	−3.02486e10	−2.29258
$780$	−1.62697e9	−0.122758
$781$	−2.64001e10	−1.98302
$782$	2.07607e9	0.155246
$783$	7.60342e8	0.0566034
$784$	1.22050e10	0.904544
$785$	1.62391e10	1.19817
$786$	1.67533e10	1.23062
$787$	−1.57582e10	−1.15238	−0.576188	−	0.817317i	$-0.695460\pi$
$787$	−1.57582e10	−1.15238	−0.576188	+	0.817317i	$0.695460\pi$
$788$	2.42514e8	0.0176561
$789$	3.89888e8	0.0282599
$790$	1.11843e10	0.807072
$791$	4.85833e8	0.0349035
$792$	−2.41678e10	−1.72862
$793$	1.09446e10	0.779372
$794$	3.18684e9	0.225937
$795$	2.03822e10	1.43869
$796$	3.20928e8	0.0225534
$797$	1.54806e8	0.0108314	0.00541569	−	0.999985i	$-0.498276\pi$
$797$	1.54806e8	0.0108314	0.00541569	+	0.999985i	$0.498276\pi$
$798$	−2.81517e9	−0.196107
$799$	6.21050e9	0.430738
$800$	3.38515e8	0.0233756
$801$	2.57433e10	1.76991
$802$	8.46434e9	0.579406
$803$	1.46680e10	0.999693
$804$	1.94153e9	0.131749
$805$	−9.86593e8	−0.0666580
$806$	1.59122e10	1.07043
$807$	2.78930e10	1.86826
$808$	−3.74197e9	−0.249552
$809$	2.69048e10	1.78653	0.893263	−	0.449535i	$-0.148410\pi$
$809$	2.69048e10	1.78653	0.893263	+	0.449535i	$0.148410\pi$
$810$	−1.00813e10	−0.666527
$811$	5.78780e9	0.381014	0.190507	−	0.981686i	$-0.438987\pi$
$811$	5.78780e9	0.381014	0.190507	+	0.981686i	$0.438987\pi$
$812$	2.37383e7	0.00155598
$813$	7.08957e9	0.462704
$814$	3.52827e9	0.229286
$815$	−2.15597e10	−1.39505
$816$	−5.01380e9	−0.323036
$817$	−3.14447e9	−0.201730
$818$	9.71890e9	0.620841
$819$	2.28396e9	0.145277
$820$	2.03406e9	0.128829
$821$	1.33206e9	0.0840087	0.0420043	−	0.999117i	$-0.486626\pi$
$821$	1.33206e9	0.0840087	0.0420043	+	0.999117i	$0.486626\pi$
$822$	−1.44103e10	−0.904943
$823$	−1.56878e10	−0.980987	−0.490494	−	0.871445i	$-0.663183\pi$
$823$	−1.56878e10	−0.980987	−0.490494	+	0.871445i	$0.663183\pi$
$824$	−3.08623e10	−1.92169
$825$	4.92518e9	0.305375
$826$	−6.43826e8	−0.0397501
$827$	1.59911e10	0.983126	0.491563	−	0.870842i	$-0.336426\pi$
$827$	1.59911e10	0.983126	0.491563	+	0.870842i	$0.336426\pi$
$828$	1.05692e9	0.0647049
$829$	−7.02888e9	−0.428495	−0.214247	−	0.976779i	$-0.568730\pi$
$829$	−7.02888e9	−0.428495	−0.214247	+	0.976779i	$0.568730\pi$
$830$	−5.36899e9	−0.325926
$831$	2.44526e10	1.47816
$832$	−2.01021e10	−1.21007
$833$	−3.92193e9	−0.235095
$834$	3.34879e10	1.99897
$835$	−1.92922e10	−1.14678
$836$	−2.39288e9	−0.141644
$837$	5.08071e9	0.299492
$838$	−7.74042e9	−0.454371
$839$	−5.49660e8	−0.0321312	−0.0160656	−	0.999871i	$-0.505114\pi$
$839$	−5.49660e8	−0.0321312	−0.0160656	+	0.999871i	$0.505114\pi$
$840$	2.58818e9	0.150667
$841$	5.94823e8	0.0344828
$842$	−1.05107e10	−0.606789
$843$	−1.74094e10	−1.00089
$844$	−1.18992e9	−0.0681269
$845$	−4.67140e9	−0.266347
$846$	−3.69041e10	−2.09546
$847$	−1.72472e9	−0.0975275
$848$	1.70559e10	0.960480
$849$	1.70871e10	0.958278
$850$	6.06605e8	0.0338797
$851$	−2.10961e9	−0.117341
$852$	−3.02878e9	−0.167776
$853$	1.82117e10	1.00468	0.502341	−	0.864670i	$-0.332472\pi$
$853$	1.82117e10	1.00468	0.502341	+	0.864670i	$0.332472\pi$
$854$	−1.27345e9	−0.0699647
$855$	2.63408e10	1.44128
$856$	−1.35793e10	−0.739977
$857$	−8.22318e9	−0.446279	−0.223140	−	0.974786i	$-0.571631\pi$
$857$	−8.22318e9	−0.446279	−0.223140	+	0.974786i	$0.571631\pi$
$858$	−4.14602e10	−2.24092
$859$	−2.53000e10	−1.36190	−0.680948	−	0.732331i	$-0.738432\pi$
$859$	−2.53000e10	−1.36190	−0.680948	+	0.732331i	$0.738432\pi$
$860$	2.11449e8	0.0113360
$861$	−5.22457e9	−0.278958
$862$	−2.63162e10	−1.39942
$863$	−1.33808e10	−0.708672	−0.354336	−	0.935118i	$-0.615293\pi$
$863$	−1.33808e10	−0.708672	−0.354336	+	0.935118i	$0.615293\pi$
$864$	−9.09870e8	−0.0479934
$865$	−3.28328e10	−1.72485
$866$	−8.75782e9	−0.458230
$867$	−2.68857e10	−1.40105
$868$	1.58622e8	0.00823276
$869$	−2.44180e10	−1.26224
$870$	4.74351e9	0.244221
$871$	2.48882e10	1.27623
$872$	−1.64527e10	−0.840293
$873$	−1.47639e10	−0.751020
$874$	−1.66996e10	−0.846091
$875$	−2.22995e9	−0.112530
$876$	1.68280e9	0.0845803
$877$	2.69766e10	1.35048	0.675242	−	0.737597i	$-0.264039\pi$
$877$	2.69766e10	1.35048	0.675242	+	0.737597i	$0.264039\pi$
$878$	2.29731e10	1.14548
$879$	−2.46628e9	−0.122485
$880$	−2.36388e10	−1.16933
$881$	−1.69852e9	−0.0836865	−0.0418433	−	0.999124i	$-0.513323\pi$
$881$	−1.69852e9	−0.0836865	−0.0418433	+	0.999124i	$0.513323\pi$
$882$	2.33049e10	1.14369
$883$	1.52571e10	0.745779	0.372890	−	0.927876i	$-0.378367\pi$
$883$	1.52571e10	0.745779	0.372890	+	0.927876i	$0.378367\pi$
$884$	4.37489e8	0.0213002
$885$	1.10223e10	0.534529
$886$	−2.43349e10	−1.17547
$887$	−8.66481e9	−0.416895	−0.208447	−	0.978034i	$-0.566841\pi$
$887$	−8.66481e9	−0.416895	−0.208447	+	0.978034i	$0.566841\pi$
$888$	5.53424e9	0.265224
$889$	−2.75789e9	−0.131650
$890$	2.73518e10	1.30053
$891$	2.20099e10	1.04243
$892$	1.35162e9	0.0637645
$893$	−4.99564e10	−2.34753
$894$	3.83135e10	1.79337
$895$	2.99824e10	1.39793
$896$	1.97898e9	0.0919102
$897$	2.47897e10	1.14683
$898$	3.20105e10	1.47511
$899$	3.97469e9	0.182450
$900$	3.08821e8	0.0141207
$901$	−5.48072e9	−0.249632
$902$	5.18339e10	2.35175
$903$	−5.43116e8	−0.0245462
$904$	−7.56043e9	−0.340375
$905$	−3.71825e10	−1.66751
$906$	9.71405e9	0.433962
$907$	−2.08445e10	−0.927612	−0.463806	−	0.885937i	$-0.653517\pi$
$907$	−2.08445e10	−0.927612	−0.463806	+	0.885937i	$0.653517\pi$
$908$	3.25552e8	0.0144318
$909$	−6.57777e9	−0.290473
$910$	2.42667e9	0.106749
$911$	−5.71524e9	−0.250449	−0.125225	−	0.992128i	$-0.539965\pi$
$911$	−5.71524e9	−0.250449	−0.125225	+	0.992128i	$0.539965\pi$
$912$	4.03302e10	1.76055
$913$	1.17219e10	0.509740
$914$	−8.53581e9	−0.369771
$915$	2.18015e10	0.940831
$916$	1.05241e9	0.0452429
$917$	2.14084e9	0.0916835
$918$	−1.63045e9	−0.0695599
$919$	4.82027e9	0.204865	0.102432	−	0.994740i	$-0.467337\pi$
$919$	4.82027e9	0.204865	0.102432	+	0.994740i	$0.467337\pi$
$920$	1.53532e10	0.650041
$921$	4.33505e10	1.82846
$922$	−1.50531e10	−0.632510
$923$	−3.88255e10	−1.62522
$924$	−4.13299e8	−0.0172351
$925$	−6.16403e8	−0.0256076
$926$	3.32537e10	1.37626
$927$	−5.42509e10	−2.23680
$928$	−7.11801e8	−0.0292375
$929$	−6.82808e9	−0.279411	−0.139705	−	0.990193i	$-0.544616\pi$
$929$	−6.82808e9	−0.279411	−0.139705	+	0.990193i	$0.544616\pi$
$930$	3.16968e10	1.29219
$931$	3.15474e10	1.28127
$932$	3.56566e9	0.144273
$933$	−4.41810e9	−0.178094
$934$	−2.33577e10	−0.938027
$935$	7.59608e9	0.303913
$936$	−3.55426e10	−1.41672
$937$	−3.09235e10	−1.22801	−0.614003	−	0.789304i	$-0.710442\pi$
$937$	−3.09235e10	−1.22801	−0.614003	+	0.789304i	$0.710442\pi$
$938$	−2.89584e9	−0.114568
$939$	6.60314e10	2.60268
$940$	3.35930e9	0.131917
$941$	4.26953e9	0.167038	0.0835192	−	0.996506i	$-0.473384\pi$
$941$	4.26953e9	0.167038	0.0835192	+	0.996506i	$0.473384\pi$
$942$	4.74762e10	1.85054
$943$	−3.09923e10	−1.20355
$944$	9.22350e9	0.356857
$945$	7.74825e8	0.0298670
$946$	5.38835e9	0.206936
$947$	−2.36297e9	−0.0904134	−0.0452067	−	0.998978i	$-0.514395\pi$
$947$	−2.36297e9	−0.0904134	−0.0452067	+	0.998978i	$0.514395\pi$
$948$	−2.80139e9	−0.106793
$949$	2.15716e10	0.819315
$950$	−4.87944e9	−0.184645
$951$	−3.83866e10	−1.44726
$952$	−6.95956e8	−0.0261428
$953$	1.63410e10	0.611581	0.305791	−	0.952099i	$-0.401079\pi$
$953$	1.63410e10	0.611581	0.305791	+	0.952099i	$0.401079\pi$
$954$	3.25676e10	1.21441
$955$	3.13336e10	1.16412
$956$	4.10786e8	0.0152059
$957$	−1.03563e10	−0.381955
$958$	−2.53226e9	−0.0930526
$959$	−1.84143e9	−0.0674202
$960$	−4.00428e10	−1.46075
$961$	−9.53174e8	−0.0346450
$962$	5.18888e9	0.187915
$963$	−2.38702e10	−0.861317
$964$	6.60164e8	0.0237346
$965$	−4.98855e9	−0.178702
$966$	−2.88437e9	−0.102951
$967$	9.44817e9	0.336012	0.168006	−	0.985786i	$-0.446267\pi$
$967$	9.44817e9	0.336012	0.168006	+	0.985786i	$0.446267\pi$
$968$	2.68398e10	0.951076
$969$	−1.29597e10	−0.457574
$970$	−1.56864e10	−0.551850
$971$	−4.99232e10	−1.74999	−0.874994	−	0.484134i	$-0.839135\pi$
$971$	−4.99232e10	−1.74999	−0.874994	+	0.484134i	$0.839135\pi$
$972$	3.21381e9	0.112251
$973$	4.27927e9	0.148928
$974$	−2.26302e10	−0.784750
$975$	7.24326e9	0.250275
$976$	1.82435e10	0.628108
$977$	7.92107e9	0.271740	0.135870	−	0.990727i	$-0.456617\pi$
$977$	7.92107e9	0.271740	0.135870	+	0.990727i	$0.456617\pi$
$978$	−6.30312e10	−2.15462
$979$	−5.97158e10	−2.03399
$980$	−2.12139e9	−0.0719996
$981$	−2.89213e10	−0.978083
$982$	−2.51863e9	−0.0848739
$983$	9.15508e9	0.307415	0.153707	−	0.988116i	$-0.450879\pi$
$983$	9.15508e9	0.307415	0.153707	+	0.988116i	$0.450879\pi$
$984$	8.13037e10	2.72037
$985$	6.19255e9	0.206463
$986$	−1.27552e9	−0.0423758
$987$	−8.62851e9	−0.285644
$988$	−3.51910e9	−0.116087
$989$	−3.22178e9	−0.105903
$990$	−4.51375e10	−1.47848
$991$	1.51105e10	0.493197	0.246599	−	0.969118i	$-0.420687\pi$
$991$	1.51105e10	0.493197	0.246599	+	0.969118i	$0.420687\pi$
$992$	−4.75635e9	−0.154697
$993$	−4.83117e10	−1.56578
$994$	4.51749e9	0.145897
$995$	8.19485e9	0.263731
$996$	1.34480e9	0.0431272
$997$	5.27378e10	1.68535	0.842673	−	0.538426i	$-0.180981\pi$
$997$	5.27378e10	1.68535	0.842673	+	0.538426i	$0.180981\pi$
$998$	−1.05977e9	−0.0337484
$999$	1.65679e9	0.0525760

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	29.8.a.a.1.3	✓	7
3.2	odd	2		261.8.a.b.1.5		7
4.3	odd	2		464.8.a.f.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
29.8.a.a.1.3	✓	7	1.1	even	1	trivial
261.8.a.b.1.5		7	3.2	odd	2
464.8.a.f.1.1		7	4.3	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:	\( N \)	\(=\)	\( 29 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	29.a (trivial)

\(f(q)\)	\(=\)	\(q-10.8581 q^{2} +69.4472 q^{3} -10.1010 q^{4} -257.927 q^{5} -754.067 q^{6} -96.3589 q^{7} +1499.52 q^{8} +2635.91 q^{9} +O(q^{10})\)	\(q-10.8581 q^{2} +69.4472 q^{3} -10.1010 q^{4} -257.927 q^{5} -754.067 q^{6} -96.3589 q^{7} +1499.52 q^{8} +2635.91 q^{9} +2800.60 q^{10} -6114.42 q^{11} -701.484 q^{12} -8992.21 q^{13} +1046.28 q^{14} -17912.3 q^{15} -14989.0 q^{16} +4816.57 q^{17} -28621.1 q^{18} -38743.8 q^{19} +2605.31 q^{20} -6691.86 q^{21} +66391.2 q^{22} -39696.3 q^{23} +104137. q^{24} -11598.8 q^{25} +97638.6 q^{26} +31175.6 q^{27} +973.319 q^{28} +24389.0 q^{29} +194494. q^{30} +162971. q^{31} -29185.3 q^{32} -424629. q^{33} -52299.0 q^{34} +24853.5 q^{35} -26625.3 q^{36} +53143.7 q^{37} +420685. q^{38} -624484. q^{39} -386766. q^{40} +780735. q^{41} +72661.1 q^{42} +81160.7 q^{43} +61761.5 q^{44} -679872. q^{45} +431027. q^{46} +1.28940e6 q^{47} -1.04095e6 q^{48} -814258. q^{49} +125941. q^{50} +334497. q^{51} +90830.0 q^{52} -1.13789e6 q^{53} -338509. q^{54} +1.57707e6 q^{55} -144492. q^{56} -2.69065e6 q^{57} -264819. q^{58} -615349. q^{59} +180931. q^{60} -1.21712e6 q^{61} -1.76956e6 q^{62} -253994. q^{63} +2.23550e6 q^{64} +2.31933e6 q^{65} +4.61068e6 q^{66} -2.76775e6 q^{67} -48652.0 q^{68} -2.75679e6 q^{69} -269863. q^{70} +4.31768e6 q^{71} +3.95260e6 q^{72} -2.39892e6 q^{73} -577041. q^{74} -805503. q^{75} +391350. q^{76} +589179. q^{77} +6.78073e6 q^{78} +3.99352e6 q^{79} +3.86608e6 q^{80} -3.59968e6 q^{81} -8.47732e6 q^{82} -1.91708e6 q^{83} +67594.2 q^{84} -1.24232e6 q^{85} -881253. q^{86} +1.69375e6 q^{87} -9.16868e6 q^{88} +9.76639e6 q^{89} +7.38214e6 q^{90} +866480. q^{91} +400971. q^{92} +1.13179e7 q^{93} -1.40005e7 q^{94} +9.99306e6 q^{95} -2.02684e6 q^{96} -5.60106e6 q^{97} +8.84132e6 q^{98} -1.61171e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 8 q^{2} - 82 q^{3} + 346 q^{4} - 320 q^{5} - 938 q^{6} - 1704 q^{7} + 2082 q^{8} + 4061 q^{9}+O(q^{10}) \) 7 * q - 8 * q^2 - 82 * q^3 + 346 * q^4 - 320 * q^5 - 938 * q^6 - 1704 * q^7 + 2082 * q^8 + 4061 * q^9	\( 7 q - 8 q^{2} - 82 q^{3} + 346 q^{4} - 320 q^{5} - 938 q^{6} - 1704 q^{7} + 2082 q^{8} + 4061 q^{9} - 14114 q^{10} - 14498 q^{11} - 42334 q^{12} - 9024 q^{13} - 45880 q^{14} - 24238 q^{15} - 3022 q^{16} - 54882 q^{17} + 17218 q^{18} - 100572 q^{19} - 86022 q^{20} + 34304 q^{21} + 9086 q^{22} + 55340 q^{23} - 138966 q^{24} + 125759 q^{25} + 257206 q^{26} - 176146 q^{27} - 41760 q^{28} + 170723 q^{29} + 1132178 q^{30} - 153330 q^{31} + 825478 q^{32} + 555898 q^{33} - 194256 q^{34} + 561160 q^{35} + 1939652 q^{36} - 457050 q^{37} + 617164 q^{38} - 1173662 q^{39} - 1151986 q^{40} - 864230 q^{41} + 2046224 q^{42} - 1590058 q^{43} - 1399966 q^{44} - 2268610 q^{45} + 1557900 q^{46} - 204750 q^{47} - 2501730 q^{48} - 1892625 q^{49} + 2115526 q^{50} - 2481996 q^{51} + 1469690 q^{52} - 2696092 q^{53} - 2918978 q^{54} - 2596662 q^{55} - 2818440 q^{56} - 96196 q^{57} - 195112 q^{58} + 1434256 q^{59} + 7687830 q^{60} - 5622798 q^{61} - 4660550 q^{62} - 5632816 q^{63} - 944442 q^{64} - 353086 q^{65} + 8421370 q^{66} - 5380324 q^{67} + 6393964 q^{68} - 2248580 q^{69} + 10805432 q^{70} + 4605140 q^{71} + 17475264 q^{72} + 3979266 q^{73} + 15124836 q^{74} - 2365120 q^{75} - 3893220 q^{76} + 8666288 q^{77} + 7790850 q^{78} - 6355522 q^{79} - 4424794 q^{80} + 6442139 q^{81} + 6831364 q^{82} + 3077704 q^{83} + 29008056 q^{84} + 5117008 q^{85} + 11620998 q^{86} - 1999898 q^{87} - 24708046 q^{88} + 743498 q^{89} - 38296444 q^{90} - 24167656 q^{91} + 11053132 q^{92} + 25723782 q^{93} - 29029210 q^{94} + 1137892 q^{95} - 34019010 q^{96} - 7924270 q^{97} + 19298152 q^{98} - 43451600 q^{99}+O(q^{100}) \) 7 * q - 8 * q^2 - 82 * q^3 + 346 * q^4 - 320 * q^5 - 938 * q^6 - 1704 * q^7 + 2082 * q^8 + 4061 * q^9 - 14114 * q^10 - 14498 * q^11 - 42334 * q^12 - 9024 * q^13 - 45880 * q^14 - 24238 * q^15 - 3022 * q^16 - 54882 * q^17 + 17218 * q^18 - 100572 * q^19 - 86022 * q^20 + 34304 * q^21 + 9086 * q^22 + 55340 * q^23 - 138966 * q^24 + 125759 * q^25 + 257206 * q^26 - 176146 * q^27 - 41760 * q^28 + 170723 * q^29 + 1132178 * q^30 - 153330 * q^31 + 825478 * q^32 + 555898 * q^33 - 194256 * q^34 + 561160 * q^35 + 1939652 * q^36 - 457050 * q^37 + 617164 * q^38 - 1173662 * q^39 - 1151986 * q^40 - 864230 * q^41 + 2046224 * q^42 - 1590058 * q^43 - 1399966 * q^44 - 2268610 * q^45 + 1557900 * q^46 - 204750 * q^47 - 2501730 * q^48 - 1892625 * q^49 + 2115526 * q^50 - 2481996 * q^51 + 1469690 * q^52 - 2696092 * q^53 - 2918978 * q^54 - 2596662 * q^55 - 2818440 * q^56 - 96196 * q^57 - 195112 * q^58 + 1434256 * q^59 + 7687830 * q^60 - 5622798 * q^61 - 4660550 * q^62 - 5632816 * q^63 - 944442 * q^64 - 353086 * q^65 + 8421370 * q^66 - 5380324 * q^67 + 6393964 * q^68 - 2248580 * q^69 + 10805432 * q^70 + 4605140 * q^71 + 17475264 * q^72 + 3979266 * q^73 + 15124836 * q^74 - 2365120 * q^75 - 3893220 * q^76 + 8666288 * q^77 + 7790850 * q^78 - 6355522 * q^79 - 4424794 * q^80 + 6442139 * q^81 + 6831364 * q^82 + 3077704 * q^83 + 29008056 * q^84 + 5117008 * q^85 + 11620998 * q^86 - 1999898 * q^87 - 24708046 * q^88 + 743498 * q^89 - 38296444 * q^90 - 24167656 * q^91 + 11053132 * q^92 + 25723782 * q^93 - 29029210 * q^94 + 1137892 * q^95 - 34019010 * q^96 - 7924270 * q^97 + 19298152 * q^98 - 43451600 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

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Groups

Database

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