LMFDB - Embedded newform 33.8.a.d.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,8,Mod(1,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("33.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	33.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:	$10.3087058410$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.115512.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 70x - 194 $ x^3 - x^2 - 70*x - 194
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-5.30133$ of defining polynomial
Character	$\chi$	$=$	33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+17.9120 q^{2} -27.0000 q^{3} +192.840 q^{4} +84.6717 q^{5} -483.624 q^{6} +1679.06 q^{7} +1161.42 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+17.9120 q^{2} -27.0000 q^{3} +192.840 q^{4} +84.6717 q^{5} -483.624 q^{6} +1679.06 q^{7} +1161.42 q^{8} +729.000 q^{9} +1516.64 q^{10} -1331.00 q^{11} -5206.68 q^{12} +14614.0 q^{13} +30075.3 q^{14} -2286.14 q^{15} -3880.24 q^{16} -28806.7 q^{17} +13057.9 q^{18} -20668.0 q^{19} +16328.1 q^{20} -45334.6 q^{21} -23840.9 q^{22} +24408.1 q^{23} -31358.2 q^{24} -70955.7 q^{25} +261766. q^{26} -19683.0 q^{27} +323790. q^{28} +44808.9 q^{29} -40949.3 q^{30} -79797.2 q^{31} -218164. q^{32} +35937.0 q^{33} -515985. q^{34} +142169. q^{35} +140580. q^{36} +114809. q^{37} -370205. q^{38} -394578. q^{39} +98339.1 q^{40} -124871. q^{41} -812033. q^{42} -182014. q^{43} -256670. q^{44} +61725.7 q^{45} +437198. q^{46} -1.17849e6 q^{47} +104767. q^{48} +1.99569e6 q^{49} -1.27096e6 q^{50} +777780. q^{51} +2.81817e6 q^{52} -1.08629e6 q^{53} -352562. q^{54} -112698. q^{55} +1.95008e6 q^{56} +558035. q^{57} +802617. q^{58} +1.64390e6 q^{59} -440859. q^{60} +470621. q^{61} -1.42933e6 q^{62} +1.22403e6 q^{63} -3.41109e6 q^{64} +1.23739e6 q^{65} +643704. q^{66} +2.85835e6 q^{67} -5.55508e6 q^{68} -659019. q^{69} +2.54653e6 q^{70} +5.01261e6 q^{71} +846672. q^{72} -2.89295e6 q^{73} +2.05646e6 q^{74} +1.91580e6 q^{75} -3.98561e6 q^{76} -2.23483e6 q^{77} -7.06769e6 q^{78} -530006. q^{79} -328547. q^{80} +531441. q^{81} -2.23670e6 q^{82} -3.43217e6 q^{83} -8.74232e6 q^{84} -2.43911e6 q^{85} -3.26023e6 q^{86} -1.20984e6 q^{87} -1.54584e6 q^{88} -1.84475e6 q^{89} +1.10563e6 q^{90} +2.45378e7 q^{91} +4.70686e6 q^{92} +2.15453e6 q^{93} -2.11091e7 q^{94} -1.74999e6 q^{95} +5.89043e6 q^{96} +1.81707e6 q^{97} +3.57469e7 q^{98} -970299. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 9 q^{2} - 81 q^{3} - 15 q^{4} - 444 q^{5} - 243 q^{6} + 1614 q^{7} + 3153 q^{8} + 2187 q^{9}+O(q^{10}) $ 3 * q + 9 * q^2 - 81 * q^3 - 15 * q^4 - 444 * q^5 - 243 * q^6 + 1614 * q^7 + 3153 * q^8 + 2187 * q^9	\( 3 q + 9 q^{2} - 81 q^{3} - 15 q^{4} - 444 q^{5} - 243 q^{6} + 1614 q^{7} + 3153 q^{8} + 2187 q^{9} + 2880 q^{10} - 3993 q^{11} + 405 q^{12} + 20772 q^{13} + 36258 q^{14} + 11988 q^{15} + 12225 q^{16} - 14538 q^{17} + 6561 q^{18} + 24492 q^{19} + 80112 q^{20} - 43578 q^{21} - 11979 q^{22} + 35094 q^{23} - 85131 q^{24} + 29121 q^{25} + 203832 q^{26} - 59049 q^{27} + 278034 q^{28} - 179862 q^{29} - 77760 q^{30} + 288888 q^{31} - 519567 q^{32} + 107811 q^{33} - 491586 q^{34} - 532872 q^{35} - 10935 q^{36} + 107562 q^{37} - 686328 q^{38} - 560844 q^{39} - 237360 q^{40} - 135198 q^{41} - 978966 q^{42} + 193536 q^{43} + 19965 q^{44} - 323676 q^{45} + 16422 q^{46} - 591486 q^{47} - 330075 q^{48} + 4461159 q^{49} - 1192245 q^{50} + 392526 q^{51} + 2449992 q^{52} + 79044 q^{53} - 177147 q^{54} + 590964 q^{55} + 752658 q^{56} - 661284 q^{57} + 2289930 q^{58} + 2532768 q^{59} - 2163024 q^{60} + 6678792 q^{61} - 2660808 q^{62} + 1176606 q^{63} - 3966303 q^{64} + 3191832 q^{65} + 323433 q^{66} + 7150356 q^{67} - 7821954 q^{68} - 947538 q^{69} + 4029120 q^{70} + 1390398 q^{71} + 2298537 q^{72} - 6429114 q^{73} + 2507478 q^{74} - 786267 q^{75} - 7654728 q^{76} - 2148234 q^{77} - 5503464 q^{78} + 6873186 q^{79} - 7556016 q^{80} + 1594323 q^{81} - 1774590 q^{82} + 6505596 q^{83} - 7506918 q^{84} - 16546032 q^{85} - 6519468 q^{86} + 4856274 q^{87} - 4196643 q^{88} - 8842962 q^{89} + 2099520 q^{90} + 3066648 q^{91} + 6921990 q^{92} - 7799976 q^{93} - 24038238 q^{94} - 190968 q^{95} + 14028309 q^{96} - 1764774 q^{97} + 24377397 q^{98} - 2910897 q^{99}+O(q^{100}) \) 3 * q + 9 * q^2 - 81 * q^3 - 15 * q^4 - 444 * q^5 - 243 * q^6 + 1614 * q^7 + 3153 * q^8 + 2187 * q^9 + 2880 * q^10 - 3993 * q^11 + 405 * q^12 + 20772 * q^13 + 36258 * q^14 + 11988 * q^15 + 12225 * q^16 - 14538 * q^17 + 6561 * q^18 + 24492 * q^19 + 80112 * q^20 - 43578 * q^21 - 11979 * q^22 + 35094 * q^23 - 85131 * q^24 + 29121 * q^25 + 203832 * q^26 - 59049 * q^27 + 278034 * q^28 - 179862 * q^29 - 77760 * q^30 + 288888 * q^31 - 519567 * q^32 + 107811 * q^33 - 491586 * q^34 - 532872 * q^35 - 10935 * q^36 + 107562 * q^37 - 686328 * q^38 - 560844 * q^39 - 237360 * q^40 - 135198 * q^41 - 978966 * q^42 + 193536 * q^43 + 19965 * q^44 - 323676 * q^45 + 16422 * q^46 - 591486 * q^47 - 330075 * q^48 + 4461159 * q^49 - 1192245 * q^50 + 392526 * q^51 + 2449992 * q^52 + 79044 * q^53 - 177147 * q^54 + 590964 * q^55 + 752658 * q^56 - 661284 * q^57 + 2289930 * q^58 + 2532768 * q^59 - 2163024 * q^60 + 6678792 * q^61 - 2660808 * q^62 + 1176606 * q^63 - 3966303 * q^64 + 3191832 * q^65 + 323433 * q^66 + 7150356 * q^67 - 7821954 * q^68 - 947538 * q^69 + 4029120 * q^70 + 1390398 * q^71 + 2298537 * q^72 - 6429114 * q^73 + 2507478 * q^74 - 786267 * q^75 - 7654728 * q^76 - 2148234 * q^77 - 5503464 * q^78 + 6873186 * q^79 - 7556016 * q^80 + 1594323 * q^81 - 1774590 * q^82 + 6505596 * q^83 - 7506918 * q^84 - 16546032 * q^85 - 6519468 * q^86 + 4856274 * q^87 - 4196643 * q^88 - 8842962 * q^89 + 2099520 * q^90 + 3066648 * q^91 + 6921990 * q^92 - 7799976 * q^93 - 24038238 * q^94 - 190968 * q^95 + 14028309 * q^96 - 1764774 * q^97 + 24377397 * q^98 - 2910897 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	17.9120	1.58321	0.791606	−	0.611031i	$-0.209245\pi$
$2$	17.9120	1.58321	0.791606	+	0.611031i	$0.209245\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	192.840	1.50656
$5$	84.6717	0.302931	0.151465	−	0.988463i	$-0.451601\pi$
$5$	84.6717	0.302931	0.151465	+	0.988463i	$0.451601\pi$
$6$	−483.624	−0.914068
$7$	1679.06	1.85022	0.925109	−	0.379703i	$-0.123974\pi$
$7$	1679.06	1.85022	0.925109	+	0.379703i	$0.123974\pi$
$8$	1161.42	0.801997
$9$	729.000	0.333333
$10$	1516.64	0.479604
$11$	−1331.00	−0.301511
$11$	−1331.00	−0.301511
$12$	−5206.68	−0.869814
$13$	14614.0	1.84488	0.922439	−	0.386143i	$-0.126193\pi$
$13$	14614.0	1.84488	0.922439	+	0.386143i	$0.126193\pi$
$14$	30075.3	2.92929
$15$	−2286.14	−0.174897
$16$	−3880.24	−0.236831
$17$	−28806.7	−1.42207	−0.711036	−	0.703156i	$-0.751774\pi$
$17$	−28806.7	−1.42207	−0.711036	+	0.703156i	$0.751774\pi$
$18$	13057.9	0.527738
$19$	−20668.0	−0.691289	−0.345645	−	0.938365i	$-0.612340\pi$
$19$	−20668.0	−0.691289	−0.345645	+	0.938365i	$0.612340\pi$
$20$	16328.1	0.456384
$21$	−45334.6	−1.06822
$22$	−23840.9	−0.477357
$23$	24408.1	0.418299	0.209149	−	0.977884i	$-0.432930\pi$
$23$	24408.1	0.418299	0.209149	+	0.977884i	$0.432930\pi$
$24$	−31358.2	−0.463033
$25$	−70955.7	−0.908233
$26$	261766.	2.92083
$27$	−19683.0	−0.192450
$28$	323790.	2.78747
$29$	44808.9	0.341170	0.170585	−	0.985343i	$-0.445434\pi$
$29$	44808.9	0.341170	0.170585	+	0.985343i	$0.445434\pi$
$30$	−40949.3	−0.276899
$31$	−79797.2	−0.481085	−0.240543	−	0.970639i	$-0.577325\pi$
$31$	−79797.2	−0.481085	−0.240543	+	0.970639i	$0.577325\pi$
$32$	−218164.	−1.17695
$33$	35937.0	0.174078
$34$	−515985.	−2.25144
$35$	142169.	0.560488
$36$	140580.	0.502188
$37$	114809.	0.372624	0.186312	−	0.982491i	$-0.440346\pi$
$37$	114809.	0.372624	0.186312	+	0.982491i	$0.440346\pi$
$38$	−370205.	−1.09446
$39$	−394578.	−1.06514
$40$	98339.1	0.242950
$41$	−124871.	−0.282956	−0.141478	−	0.989941i	$-0.545186\pi$
$41$	−124871.	−0.282956	−0.141478	+	0.989941i	$0.545186\pi$
$42$	−812033.	−1.69122
$43$	−182014.	−0.349112	−0.174556	−	0.984647i	$-0.555849\pi$
$43$	−182014.	−0.349112	−0.174556	+	0.984647i	$0.555849\pi$
$44$	−256670.	−0.454246
$45$	61725.7	0.100977
$46$	437198.	0.662256
$47$	−1.17849e6	−1.65570	−0.827851	−	0.560948i	$-0.810437\pi$
$47$	−1.17849e6	−1.65570	−0.827851	+	0.560948i	$0.810437\pi$
$48$	104767.	0.136735
$49$	1.99569e6	2.42330
$50$	−1.27096e6	−1.43793
$51$	777780.	0.821034
$52$	2.81817e6	2.77942
$53$	−1.08629e6	−1.00226	−0.501131	−	0.865371i	$-0.667082\pi$
$53$	−1.08629e6	−1.00226	−0.501131	+	0.865371i	$0.667082\pi$
$54$	−352562.	−0.304689
$55$	−112698.	−0.0913371
$56$	1.95008e6	1.48387
$57$	558035.	0.399116
$58$	802617.	0.540145
$59$	1.64390e6	1.04206	0.521031	−	0.853538i	$-0.325548\pi$
$59$	1.64390e6	1.04206	0.521031	+	0.853538i	$0.325548\pi$
$60$	−440859.	−0.263494
$61$	470621.	0.265471	0.132735	−	0.991151i	$-0.457624\pi$
$61$	470621.	0.265471	0.132735	+	0.991151i	$0.457624\pi$
$62$	−1.42933e6	−0.761660
$63$	1.22403e6	0.616739
$64$	−3.41109e6	−1.62653
$65$	1.23739e6	0.558870
$66$	643704.	0.275602
$67$	2.85835e6	1.16106	0.580528	−	0.814240i	$-0.302846\pi$
$67$	2.85835e6	1.16106	0.580528	+	0.814240i	$0.302846\pi$
$68$	−5.55508e6	−2.14244
$69$	−659019.	−0.241505
$70$	2.54653e6	0.887371
$71$	5.01261e6	1.66211	0.831056	−	0.556189i	$-0.187737\pi$
$71$	5.01261e6	1.66211	0.831056	+	0.556189i	$0.187737\pi$
$72$	846672.	0.267332
$73$	−2.89295e6	−0.870384	−0.435192	−	0.900338i	$-0.643320\pi$
$73$	−2.89295e6	−0.870384	−0.435192	+	0.900338i	$0.643320\pi$
$74$	2.05646e6	0.589943
$75$	1.91580e6	0.524369
$76$	−3.98561e6	−1.04147
$77$	−2.23483e6	−0.557861
$78$	−7.06769e6	−1.68634
$79$	−530006.	−0.120944	−0.0604722	−	0.998170i	$-0.519261\pi$
$79$	−530006.	−0.120944	−0.0604722	+	0.998170i	$0.519261\pi$
$80$	−328547.	−0.0717435
$81$	531441.	0.111111
$82$	−2.23670e6	−0.447980
$83$	−3.43217e6	−0.658864	−0.329432	−	0.944179i	$-0.606857\pi$
$83$	−3.43217e6	−0.658864	−0.329432	+	0.944179i	$0.606857\pi$
$84$	−8.74232e6	−1.60935
$85$	−2.43911e6	−0.430789
$86$	−3.26023e6	−0.552719
$87$	−1.20984e6	−0.196975
$88$	−1.54584e6	−0.241811
$89$	−1.84475e6	−0.277378	−0.138689	−	0.990336i	$-0.544289\pi$
$89$	−1.84475e6	−0.277378	−0.138689	+	0.990336i	$0.544289\pi$
$90$	1.10563e6	0.159868
$91$	2.45378e7	3.41342
$92$	4.70686e6	0.630194
$93$	2.15453e6	0.277755
$94$	−2.11091e7	−2.62133
$95$	−1.74999e6	−0.209413
$96$	5.89043e6	0.679513
$97$	1.81707e6	0.202148	0.101074	−	0.994879i	$-0.467772\pi$
$97$	1.81707e6	0.202148	0.101074	+	0.994879i	$0.467772\pi$
$98$	3.57469e7	3.83660
$99$	−970299.	−0.100504
$100$	−1.36831e7	−1.36831
$101$	−6.54808e6	−0.632396	−0.316198	−	0.948693i	$-0.602406\pi$
$101$	−6.54808e6	−0.632396	−0.316198	+	0.948693i	$0.602406\pi$
$102$	1.39316e7	1.29987
$103$	1.65984e6	0.149670	0.0748350	−	0.997196i	$-0.476157\pi$
$103$	1.65984e6	0.149670	0.0748350	+	0.997196i	$0.476157\pi$
$104$	1.69729e7	1.47959
$105$	−3.83856e6	−0.323598
$106$	−1.94577e7	−1.58679
$107$	−1.21374e7	−0.957819	−0.478909	−	0.877864i	$-0.658968\pi$
$107$	−1.21374e7	−0.957819	−0.478909	+	0.877864i	$0.658968\pi$
$108$	−3.79567e6	−0.289938
$109$	−1.55927e7	−1.15326	−0.576632	−	0.817004i	$-0.695633\pi$
$109$	−1.55927e7	−1.15326	−0.576632	+	0.817004i	$0.695633\pi$
$110$	−2.01865e6	−0.144606
$111$	−3.09985e6	−0.215135
$112$	−6.51515e6	−0.438189
$113$	1.90097e7	1.23937	0.619684	−	0.784851i	$-0.287261\pi$
$113$	1.90097e7	1.23937	0.619684	+	0.784851i	$0.287261\pi$
$114$	9.99552e6	0.631886
$115$	2.06668e6	0.126716
$116$	8.64094e6	0.513994
$117$	1.06536e7	0.614959
$118$	2.94455e7	1.64980
$119$	−4.83681e7	−2.63114
$120$	−2.65515e6	−0.140267
$121$	1.77156e6	0.0909091
$122$	8.42977e6	0.420297
$123$	3.37153e6	0.163365
$124$	−1.53881e7	−0.724785
$125$	−1.26229e7	−0.578063
$126$	2.19249e7	0.976429
$127$	3.78164e7	1.63820	0.819101	−	0.573649i	$-0.194473\pi$
$127$	3.78164e7	1.63820	0.819101	+	0.573649i	$0.194473\pi$
$128$	−3.31744e7	−1.39820
$129$	4.91437e6	0.201560
$130$	2.21642e7	0.884811
$131$	3.18728e6	0.123871	0.0619356	−	0.998080i	$-0.480273\pi$
$131$	3.18728e6	0.123871	0.0619356	+	0.998080i	$0.480273\pi$
$132$	6.93009e6	0.262259
$133$	−3.47027e7	−1.27904
$134$	5.11988e7	1.83820
$135$	−1.66659e6	−0.0582991
$136$	−3.34565e7	−1.14050
$137$	−1.19898e7	−0.398374	−0.199187	−	0.979962i	$-0.563830\pi$
$137$	−1.19898e7	−0.398374	−0.199187	+	0.979962i	$0.563830\pi$
$138$	−1.18044e7	−0.382354
$139$	−3.72434e7	−1.17625	−0.588123	−	0.808772i	$-0.700133\pi$
$139$	−3.72434e7	−1.17625	−0.588123	+	0.808772i	$0.700133\pi$
$140$	2.74158e7	0.844410
$141$	3.18192e7	0.955920
$142$	8.97860e7	2.63148
$143$	−1.94512e7	−0.556252
$144$	−2.82870e6	−0.0789437
$145$	3.79404e6	0.103351
$146$	−5.18186e7	−1.37800
$147$	−5.38837e7	−1.39909
$148$	2.21398e7	0.561381
$149$	−2.57274e7	−0.637153	−0.318577	−	0.947897i	$-0.603205\pi$
$149$	−2.57274e7	−0.637153	−0.318577	+	0.947897i	$0.603205\pi$
$150$	3.43159e7	0.830187
$151$	6.21116e7	1.46809	0.734046	−	0.679100i	$-0.237630\pi$
$151$	6.21116e7	1.46809	0.734046	+	0.679100i	$0.237630\pi$
$152$	−2.40041e7	−0.554412
$153$	−2.10000e7	−0.474024
$154$	−4.00302e7	−0.883213
$155$	−6.75657e6	−0.145736
$156$	−7.60905e7	−1.60470
$157$	−9.21174e7	−1.89973	−0.949867	−	0.312655i	$-0.898782\pi$
$157$	−9.21174e7	−1.89973	−0.949867	+	0.312655i	$0.898782\pi$
$158$	−9.49347e6	−0.191481
$159$	2.93299e7	0.578656
$160$	−1.84723e7	−0.356535
$161$	4.09827e7	0.773944
$162$	9.51918e6	0.175913
$163$	4.45131e7	0.805066	0.402533	−	0.915405i	$-0.368130\pi$
$163$	4.45131e7	0.805066	0.402533	+	0.915405i	$0.368130\pi$
$164$	−2.40802e7	−0.426292
$165$	3.04285e6	0.0527335
$166$	−6.14771e7	−1.04312
$167$	9.92107e7	1.64835	0.824177	−	0.566332i	$-0.191638\pi$
$167$	9.92107e7	1.64835	0.824177	+	0.566332i	$0.191638\pi$
$168$	−5.26523e7	−0.856712
$169$	1.50821e8	2.40357
$170$	−4.36893e7	−0.682031
$171$	−1.50669e7	−0.230430
$172$	−3.50996e7	−0.525959
$173$	−1.10605e8	−1.62411	−0.812053	−	0.583584i	$-0.801650\pi$
$173$	−1.10605e8	−1.62411	−0.812053	+	0.583584i	$0.801650\pi$
$174$	−2.16707e7	−0.311853
$175$	−1.19139e8	−1.68043
$176$	5.16460e6	0.0714073
$177$	−4.43853e7	−0.601634
$178$	−3.30431e7	−0.439148
$179$	−1.72547e7	−0.224866	−0.112433	−	0.993659i	$-0.535864\pi$
$179$	−1.72547e7	−0.224866	−0.112433	+	0.993659i	$0.535864\pi$
$180$	1.19032e7	0.152128
$181$	−6.38371e6	−0.0800199	−0.0400100	−	0.999199i	$-0.512739\pi$
$181$	−6.38371e6	−0.0800199	−0.0400100	+	0.999199i	$0.512739\pi$
$182$	4.39521e8	5.40418
$183$	−1.27068e7	−0.153270
$184$	2.83480e7	0.335474
$185$	9.72110e6	0.112879
$186$	3.85919e7	0.439745
$187$	3.83417e7	0.428771
$188$	−2.27260e8	−2.49442
$189$	−3.30489e7	−0.356074
$190$	−3.13459e7	−0.331545
$191$	5.28928e7	0.549263	0.274631	−	0.961550i	$-0.411444\pi$
$191$	5.28928e7	0.549263	0.274631	+	0.961550i	$0.411444\pi$
$192$	9.20993e7	0.939079
$193$	7.37840e7	0.738774	0.369387	−	0.929276i	$-0.379568\pi$
$193$	7.37840e7	0.738774	0.369387	+	0.929276i	$0.379568\pi$
$194$	3.25474e7	0.320044
$195$	−3.34096e7	−0.322664
$196$	3.84850e8	3.65086
$197$	1.54444e8	1.43926	0.719632	−	0.694355i	$-0.244310\pi$
$197$	1.54444e8	1.43926	0.719632	+	0.694355i	$0.244310\pi$
$198$	−1.73800e7	−0.159119
$199$	1.71708e8	1.54456	0.772282	−	0.635280i	$-0.219115\pi$
$199$	1.71708e8	1.54456	0.772282	+	0.635280i	$0.219115\pi$
$200$	−8.24090e7	−0.728400
$201$	−7.71754e7	−0.670336
$202$	−1.17289e8	−1.00122
$203$	7.52367e7	0.631239
$204$	1.49987e8	1.23694
$205$	−1.05731e7	−0.0857162
$206$	2.97310e7	0.236960
$207$	1.77935e7	0.139433
$208$	−5.67059e7	−0.436925
$209$	2.75090e7	0.208432
$210$	−6.87563e7	−0.512324
$211$	1.74167e8	1.27638	0.638188	−	0.769881i	$-0.279684\pi$
$211$	1.74167e8	1.27638	0.638188	+	0.769881i	$0.279684\pi$
$212$	−2.09481e8	−1.50997
$213$	−1.35341e8	−0.959620
$214$	−2.17406e8	−1.51643
$215$	−1.54114e7	−0.105757
$216$	−2.28601e7	−0.154344
$217$	−1.33984e8	−0.890112
$218$	−2.79297e8	−1.82586
$219$	7.81097e7	0.502517
$220$	−2.17327e7	−0.137605
$221$	−4.20981e8	−2.62355
$222$	−5.55245e7	−0.340604
$223$	−3.30551e7	−0.199605	−0.0998024	−	0.995007i	$-0.531821\pi$
$223$	−3.30551e7	−0.199605	−0.0998024	+	0.995007i	$0.531821\pi$
$224$	−3.66310e8	−2.17761
$225$	−5.17267e7	−0.302744
$226$	3.40502e8	1.96218
$227$	−2.39768e7	−0.136051	−0.0680254	−	0.997684i	$-0.521670\pi$
$227$	−2.39768e7	−0.136051	−0.0680254	+	0.997684i	$0.521670\pi$
$228$	1.07611e8	0.601294
$229$	5.27005e7	0.289995	0.144997	−	0.989432i	$-0.453683\pi$
$229$	5.27005e7	0.289995	0.144997	+	0.989432i	$0.453683\pi$
$230$	3.70183e7	0.200618
$231$	6.03403e7	0.322081
$232$	5.20417e7	0.273617
$233$	−1.28749e8	−0.666805	−0.333403	−	0.942785i	$-0.608197\pi$
$233$	−1.28749e8	−0.666805	−0.333403	+	0.942785i	$0.608197\pi$
$234$	1.90828e8	0.973611
$235$	−9.97846e7	−0.501563
$236$	3.17010e8	1.56993
$237$	1.43102e7	0.0698273
$238$	−8.66369e8	−4.16566
$239$	2.07063e8	0.981093	0.490547	−	0.871415i	$-0.336797\pi$
$239$	2.07063e8	0.981093	0.490547	+	0.871415i	$0.336797\pi$
$240$	8.87077e6	0.0414211
$241$	1.42333e8	0.655005	0.327503	−	0.944850i	$-0.393793\pi$
$241$	1.42333e8	0.655005	0.327503	+	0.944850i	$0.393793\pi$
$242$	3.17322e7	0.143928
$243$	−1.43489e7	−0.0641500
$244$	9.07546e7	0.399949
$245$	1.68979e8	0.734093
$246$	6.03908e7	0.258642
$247$	−3.02042e8	−1.27534
$248$	−9.26777e7	−0.385829
$249$	9.26686e7	0.380395
$250$	−2.26102e8	−0.915196
$251$	1.95278e8	0.779464	0.389732	−	0.920928i	$-0.372568\pi$
$251$	1.95278e8	0.779464	0.389732	+	0.920928i	$0.372568\pi$
$252$	2.36043e8	0.929156
$253$	−3.24872e7	−0.126122
$254$	6.77368e8	2.59362
$255$	6.58560e7	0.248716
$256$	−1.57601e8	−0.587110
$257$	1.26071e8	0.463285	0.231643	−	0.972801i	$-0.425590\pi$
$257$	1.26071e8	0.463285	0.231643	+	0.972801i	$0.425590\pi$
$258$	8.80263e7	0.319112
$259$	1.92771e8	0.689435
$260$	2.38619e8	0.841973
$261$	3.26657e7	0.113723
$262$	5.70905e7	0.196114
$263$	3.01855e7	0.102318	0.0511592	−	0.998691i	$-0.483708\pi$
$263$	3.01855e7	0.102318	0.0511592	+	0.998691i	$0.483708\pi$
$264$	4.17378e7	0.139610
$265$	−9.19783e7	−0.303616
$266$	−6.21595e8	−2.02499
$267$	4.98081e7	0.160144
$268$	5.51204e8	1.74920
$269$	−1.24498e8	−0.389967	−0.194984	−	0.980807i	$-0.562465\pi$
$269$	−1.24498e8	−0.389967	−0.194984	+	0.980807i	$0.562465\pi$
$270$	−2.98520e7	−0.0922998
$271$	−6.31118e8	−1.92627	−0.963136	−	0.269014i	$-0.913302\pi$
$271$	−6.31118e8	−1.92627	−0.963136	+	0.269014i	$0.913302\pi$
$272$	1.11777e8	0.336791
$273$	−6.62520e8	−1.97074
$274$	−2.14762e8	−0.630710
$275$	9.44420e7	0.273843
$276$	−1.27085e8	−0.363843
$277$	4.21993e8	1.19296	0.596480	−	0.802628i	$-0.296566\pi$
$277$	4.21993e8	1.19296	0.596480	+	0.802628i	$0.296566\pi$
$278$	−6.67105e8	−1.86225
$279$	−5.81722e7	−0.160362
$280$	1.65117e8	0.449509
$281$	8.82276e7	0.237210	0.118605	−	0.992942i	$-0.462158\pi$
$281$	8.82276e7	0.237210	0.118605	+	0.992942i	$0.462158\pi$
$282$	5.69945e8	1.51343
$283$	5.13265e8	1.34614	0.673069	−	0.739580i	$-0.264976\pi$
$283$	5.13265e8	1.34614	0.673069	+	0.739580i	$0.264976\pi$
$284$	9.66633e8	2.50408
$285$	4.72498e7	0.120905
$286$	−3.48411e8	−0.880665
$287$	−2.09666e8	−0.523531
$288$	−1.59042e8	−0.392317
$289$	4.19484e8	1.02229
$290$	6.79590e7	0.163627
$291$	−4.90609e7	−0.116710
$292$	−5.57877e8	−1.31129
$293$	5.48004e8	1.27276	0.636381	−	0.771375i	$-0.280431\pi$
$293$	5.48004e8	1.27276	0.636381	+	0.771375i	$0.280431\pi$
$294$	−9.65166e8	−2.21506
$295$	1.39192e8	0.315672
$296$	1.33341e8	0.298843
$297$	2.61981e7	0.0580259
$298$	−4.60829e8	−1.00875
$299$	3.56700e8	0.771711
$300$	3.69444e8	0.789994
$301$	−3.05612e8	−0.645933
$302$	1.11254e9	2.32430
$303$	1.76798e8	0.365114
$304$	8.01967e7	0.163719
$305$	3.98483e7	0.0804193
$306$	−3.76153e8	−0.750481
$307$	2.02567e8	0.399562	0.199781	−	0.979841i	$-0.435977\pi$
$307$	2.02567e8	0.399562	0.199781	+	0.979841i	$0.435977\pi$
$308$	−4.30964e8	−0.840453
$309$	−4.48156e7	−0.0864121
$310$	−1.21024e8	−0.230730
$311$	3.03524e8	0.572179	0.286089	−	0.958203i	$-0.407645\pi$
$311$	3.03524e8	0.572179	0.286089	+	0.958203i	$0.407645\pi$
$312$	−4.58269e8	−0.854239
$313$	5.20257e6	0.00958987	0.00479494	−	0.999989i	$-0.498474\pi$
$313$	5.20257e6	0.00958987	0.00479494	+	0.999989i	$0.498474\pi$
$314$	−1.65001e9	−3.00768
$315$	1.03641e8	0.186829
$316$	−1.02206e8	−0.182210
$317$	−1.00853e9	−1.77821	−0.889104	−	0.457705i	$-0.848672\pi$
$317$	−1.00853e9	−1.77821	−0.889104	+	0.457705i	$0.848672\pi$
$318$	5.25357e8	0.916136
$319$	−5.96406e7	−0.102867
$320$	−2.88823e8	−0.492727
$321$	3.27710e8	0.552997
$322$	7.34082e8	1.22532
$323$	5.95375e8	0.983063
$324$	1.02483e8	0.167396
$325$	−1.03695e9	−1.67558
$326$	7.97320e8	1.27459
$327$	4.21003e8	0.665837
$328$	−1.45028e8	−0.226930
$329$	−1.97875e9	−3.06341
$330$	5.45035e7	0.0834883
$331$	4.78969e8	0.725954	0.362977	−	0.931798i	$-0.381760\pi$
$331$	4.78969e8	0.725954	0.362977	+	0.931798i	$0.381760\pi$
$332$	−6.61860e8	−0.992619
$333$	8.36959e7	0.124208
$334$	1.77706e9	2.60970
$335$	2.42021e8	0.351720
$336$	1.75909e8	0.252989
$337$	−2.29982e8	−0.327333	−0.163667	−	0.986516i	$-0.552332\pi$
$337$	−2.29982e8	−0.327333	−0.163667	+	0.986516i	$0.552332\pi$
$338$	2.70150e9	3.80537
$339$	−5.13262e8	−0.715550
$340$	−4.70358e8	−0.649011
$341$	1.06210e8	0.145053
$342$	−2.69879e8	−0.364819
$343$	1.96811e9	2.63342
$344$	−2.11394e8	−0.279987
$345$	−5.58003e7	−0.0731593
$346$	−1.98116e9	−2.57130
$347$	−6.33227e8	−0.813591	−0.406796	−	0.913519i	$-0.633354\pi$
$347$	−6.33227e8	−0.813591	−0.406796	+	0.913519i	$0.633354\pi$
$348$	−2.33305e8	−0.296755
$349$	−5.37194e8	−0.676460	−0.338230	−	0.941063i	$-0.609828\pi$
$349$	−5.37194e8	−0.676460	−0.338230	+	0.941063i	$0.609828\pi$
$350$	−2.13401e9	−2.66048
$351$	−2.87648e8	−0.355047
$352$	2.90376e8	0.354864
$353$	−1.56430e9	−1.89282	−0.946408	−	0.322975i	$-0.895317\pi$
$353$	−1.56430e9	−1.89282	−0.946408	+	0.322975i	$0.895317\pi$
$354$	−7.95030e8	−0.952515
$355$	4.24427e8	0.503505
$356$	−3.55741e8	−0.417887
$357$	1.30594e9	1.51909
$358$	−3.09067e8	−0.356010
$359$	−3.09660e8	−0.353227	−0.176613	−	0.984280i	$-0.556514\pi$
$359$	−3.09660e8	−0.353227	−0.176613	+	0.984280i	$0.556514\pi$
$360$	7.16892e7	0.0809832
$361$	−4.66707e8	−0.522119
$362$	−1.14345e8	−0.126689
$363$	−4.78321e7	−0.0524864
$364$	4.73187e9	5.14254
$365$	−2.44951e8	−0.263666
$366$	−2.27604e8	−0.242659
$367$	−2.61453e8	−0.276098	−0.138049	−	0.990425i	$-0.544083\pi$
$367$	−2.61453e8	−0.276098	−0.138049	+	0.990425i	$0.544083\pi$
$368$	−9.47094e7	−0.0990662
$369$	−9.10313e7	−0.0943188
$370$	1.74124e8	0.178712
$371$	−1.82395e9	−1.85440
$372$	4.15479e8	0.418455
$373$	1.64951e8	0.164579	0.0822897	−	0.996608i	$-0.473777\pi$
$373$	1.64951e8	0.164579	0.0822897	+	0.996608i	$0.473777\pi$
$374$	6.86776e8	0.678835
$375$	3.40819e8	0.333745
$376$	−1.36871e9	−1.32787
$377$	6.54837e8	0.629417
$378$	−5.91972e8	−0.563742
$379$	−1.26692e9	−1.19540	−0.597699	−	0.801721i	$-0.703918\pi$
$379$	−1.26692e9	−1.19540	−0.597699	+	0.801721i	$0.703918\pi$
$380$	−3.37468e8	−0.315494
$381$	−1.02104e9	−0.945817
$382$	9.47417e8	0.869600
$383$	1.71179e9	1.55688	0.778441	−	0.627718i	$-0.216011\pi$
$383$	1.71179e9	1.55688	0.778441	+	0.627718i	$0.216011\pi$
$384$	8.95709e8	0.807249
$385$	−1.89227e8	−0.168993
$386$	1.32162e9	1.16964
$387$	−1.32688e8	−0.116371
$388$	3.50404e8	0.304549
$389$	−1.32730e9	−1.14326	−0.571630	−	0.820512i	$-0.693689\pi$
$389$	−1.32730e9	−1.14326	−0.571630	+	0.820512i	$0.693689\pi$
$390$	−5.98433e8	−0.510846
$391$	−7.03116e8	−0.594851
$392$	2.31783e9	1.94348
$393$	−8.60565e7	−0.0715170
$394$	2.76641e9	2.27866
$395$	−4.48765e7	−0.0366378
$396$	−1.87113e8	−0.151415
$397$	−1.24222e9	−0.996397	−0.498199	−	0.867063i	$-0.666005\pi$
$397$	−1.24222e9	−0.996397	−0.498199	+	0.867063i	$0.666005\pi$
$398$	3.07564e9	2.44537
$399$	9.36973e8	0.738451
$400$	2.75325e8	0.215098
$401$	9.25894e8	0.717061	0.358530	−	0.933518i	$-0.383278\pi$
$401$	9.25894e8	0.717061	0.358530	+	0.933518i	$0.383278\pi$
$402$	−1.38237e9	−1.06128
$403$	−1.16616e9	−0.887543
$404$	−1.26273e9	−0.952744
$405$	4.49980e7	0.0336590
$406$	1.34764e9	0.999385
$407$	−1.52811e8	−0.112350
$408$	9.03325e8	0.658466
$409$	5.85741e8	0.423325	0.211663	−	0.977343i	$-0.432112\pi$
$409$	5.85741e8	0.423325	0.211663	+	0.977343i	$0.432112\pi$
$410$	−1.89385e8	−0.135707
$411$	3.23725e8	0.230001
$412$	3.20083e8	0.225487
$413$	2.76020e9	1.92804
$414$	3.18718e8	0.220752
$415$	−2.90608e8	−0.199590
$416$	−3.18825e9	−2.17133
$417$	1.00557e9	0.679106
$418$	4.92742e8	0.329992
$419$	−2.56026e8	−0.170033	−0.0850167	−	0.996380i	$-0.527094\pi$
$419$	−2.56026e8	−0.170033	−0.0850167	+	0.996380i	$0.527094\pi$
$420$	−7.40228e8	−0.487520
$421$	6.64580e8	0.434070	0.217035	−	0.976164i	$-0.430361\pi$
$421$	6.64580e8	0.434070	0.217035	+	0.976164i	$0.430361\pi$
$422$	3.11969e9	2.02077
$423$	−8.59117e8	−0.551901
$424$	−1.26164e9	−0.803811
$425$	2.04400e9	1.29157
$426$	−2.42422e9	−1.51928
$427$	7.90200e8	0.491179
$428$	−2.34058e9	−1.44301
$429$	5.25184e8	0.321152
$430$	−2.76050e8	−0.167436
$431$	−3.54271e8	−0.213140	−0.106570	−	0.994305i	$-0.533987\pi$
$431$	−3.54271e8	−0.213140	−0.106570	+	0.994305i	$0.533987\pi$
$432$	7.63748e7	0.0455782
$433$	−1.77346e9	−1.04981	−0.524907	−	0.851159i	$-0.675900\pi$
$433$	−1.77346e9	−1.04981	−0.524907	+	0.851159i	$0.675900\pi$
$434$	−2.39993e9	−1.40924
$435$	−1.02439e8	−0.0596697
$436$	−3.00690e9	−1.73746
$437$	−5.04466e8	−0.289166
$438$	1.39910e9	0.795591
$439$	−2.65420e9	−1.49729	−0.748647	−	0.662969i	$-0.769296\pi$
$439$	−2.65420e9	−1.49729	−0.748647	+	0.662969i	$0.769296\pi$
$440$	−1.30889e8	−0.0732521
$441$	1.45486e9	0.807768
$442$	−7.54061e9	−4.15364
$443$	1.94908e9	1.06517	0.532583	−	0.846378i	$-0.321221\pi$
$443$	1.94908e9	1.06517	0.532583	+	0.846378i	$0.321221\pi$
$444$	−5.97775e8	−0.324114
$445$	−1.56198e8	−0.0840263
$446$	−5.92083e8	−0.316017
$447$	6.94639e8	0.367860
$448$	−5.72741e9	−3.00944
$449$	−9.24726e8	−0.482115	−0.241058	−	0.970511i	$-0.577494\pi$
$449$	−9.24726e8	−0.482115	−0.241058	+	0.970511i	$0.577494\pi$
$450$	−9.26529e8	−0.479309
$451$	1.66204e8	0.0853146
$452$	3.66583e9	1.86719
$453$	−1.67701e9	−0.847603
$454$	−4.29473e8	−0.215397
$455$	2.07766e9	1.03403
$456$	6.48110e8	0.320090
$457$	3.00088e9	1.47076	0.735379	−	0.677656i	$-0.237004\pi$
$457$	3.00088e9	1.47076	0.735379	+	0.677656i	$0.237004\pi$
$458$	9.43971e8	0.459124
$459$	5.67001e8	0.273678
$460$	3.98538e8	0.190905
$461$	1.87779e9	0.892678	0.446339	−	0.894864i	$-0.352728\pi$
$461$	1.87779e9	0.892678	0.446339	+	0.894864i	$0.352728\pi$
$462$	1.08082e9	0.509923
$463$	−1.16774e9	−0.546778	−0.273389	−	0.961904i	$-0.588145\pi$
$463$	−1.16774e9	−0.546778	−0.273389	+	0.961904i	$0.588145\pi$
$464$	−1.73869e8	−0.0807997
$465$	1.82427e8	0.0841404
$466$	−2.30616e9	−1.05569
$467$	−4.01912e9	−1.82609	−0.913043	−	0.407863i	$-0.866274\pi$
$467$	−4.01912e9	−1.82609	−0.913043	+	0.407863i	$0.866274\pi$
$468$	2.05444e9	0.926475
$469$	4.79933e9	2.14821
$470$	−1.78734e9	−0.794082
$471$	2.48717e9	1.09681
$472$	1.90925e9	0.835730
$473$	2.42260e8	0.105261
$474$	2.56324e8	0.110552
$475$	1.46651e9	0.627852
$476$	−9.32730e9	−3.96398
$477$	−7.91907e8	−0.334087
$478$	3.70892e9	1.55328
$479$	3.87806e8	0.161228	0.0806139	−	0.996745i	$-0.474312\pi$
$479$	3.87806e8	0.161228	0.0806139	+	0.996745i	$0.474312\pi$
$480$	4.98753e8	0.205845
$481$	1.67782e9	0.687446
$482$	2.54946e9	1.03701
$483$	−1.10653e9	−0.446837
$484$	3.41628e8	0.136960
$485$	1.53854e8	0.0612370
$486$	−2.57018e8	−0.101563
$487$	−2.76181e8	−0.108353	−0.0541766	−	0.998531i	$-0.517253\pi$
$487$	−2.76181e8	−0.108353	−0.0541766	+	0.998531i	$0.517253\pi$
$488$	5.46587e8	0.212907
$489$	−1.20185e9	−0.464805
$490$	3.02675e9	1.16223
$491$	1.75761e9	0.670098	0.335049	−	0.942201i	$-0.391247\pi$
$491$	1.75761e9	0.670098	0.335049	+	0.942201i	$0.391247\pi$
$492$	6.50166e8	0.246120
$493$	−1.29079e9	−0.485168
$494$	−5.41017e9	−2.01914
$495$	−8.21569e7	−0.0304457
$496$	3.09633e8	0.113936
$497$	8.41647e9	3.07527
$498$	1.65988e9	0.602246
$499$	−5.78797e8	−0.208533	−0.104266	−	0.994549i	$-0.533249\pi$
$499$	−5.78797e8	−0.208533	−0.104266	+	0.994549i	$0.533249\pi$
$500$	−2.43420e9	−0.870888
$501$	−2.67869e9	−0.951678
$502$	3.49783e9	1.23406
$503$	1.78609e9	0.625772	0.312886	−	0.949791i	$-0.398704\pi$
$503$	1.78609e9	0.625772	0.312886	+	0.949791i	$0.398704\pi$
$504$	1.42161e9	0.494623
$505$	−5.54437e8	−0.191572
$506$	−5.81911e8	−0.199678
$507$	−4.07216e9	−1.38770
$508$	7.29252e9	2.46805
$509$	−1.97986e9	−0.665459	−0.332730	−	0.943022i	$-0.607970\pi$
$509$	−1.97986e9	−0.665459	−0.332730	+	0.943022i	$0.607970\pi$
$510$	1.17961e9	0.393771
$511$	−4.85743e9	−1.61040
$512$	1.42337e9	0.468677
$513$	4.06807e8	0.133039
$514$	2.25818e9	0.733479
$515$	1.40541e8	0.0453397
$516$	9.47688e8	0.303663
$517$	1.56857e9	0.499213
$518$	3.45292e9	1.09152
$519$	2.98634e9	0.937677
$520$	1.43713e9	0.448212
$521$	−3.74479e9	−1.16010	−0.580051	−	0.814580i	$-0.696967\pi$
$521$	−3.74479e9	−1.16010	−0.580051	+	0.814580i	$0.696967\pi$
$522$	5.85108e8	0.180048
$523$	3.97812e8	0.121597	0.0607984	−	0.998150i	$-0.480635\pi$
$523$	3.97812e8	0.121597	0.0607984	+	0.998150i	$0.480635\pi$
$524$	6.14634e8	0.186620
$525$	3.21675e9	0.970196
$526$	5.40683e8	0.161992
$527$	2.29869e9	0.684138
$528$	−1.39444e8	−0.0412270
$529$	−2.80907e9	−0.825026
$530$	−1.64752e9	−0.480689
$531$	1.19840e9	0.347354
$532$	−6.69207e9	−1.92695
$533$	−1.82487e9	−0.522020
$534$	8.92164e8	0.253542
$535$	−1.02770e9	−0.290153
$536$	3.31973e9	0.931164
$537$	4.65878e8	0.129826
$538$	−2.23000e9	−0.617401
$539$	−2.65627e9	−0.730653
$540$	−3.21386e8	−0.0878312
$541$	−3.75208e9	−1.01878	−0.509391	−	0.860535i	$-0.670129\pi$
$541$	−3.75208e9	−1.01878	−0.509391	+	0.860535i	$0.670129\pi$
$542$	−1.13046e10	−3.04970
$543$	1.72360e8	0.0461995
$544$	6.28458e9	1.67371
$545$	−1.32026e9	−0.349359
$546$	−1.18671e10	−3.12010
$547$	−1.88842e9	−0.493335	−0.246667	−	0.969100i	$-0.579336\pi$
$547$	−1.88842e9	−0.493335	−0.246667	+	0.969100i	$0.579336\pi$
$548$	−2.31212e9	−0.600175
$549$	3.43083e8	0.0884903
$550$	1.69165e9	0.433551
$551$	−9.26108e8	−0.235847
$552$	−7.65395e8	−0.193686
$553$	−8.89911e8	−0.223774
$554$	7.55874e9	1.88871
$555$	−2.62470e8	−0.0651709
$556$	−7.18203e9	−1.77209
$557$	−5.58269e8	−0.136883	−0.0684416	−	0.997655i	$-0.521803\pi$
$557$	−5.58269e8	−0.136883	−0.0684416	+	0.997655i	$0.521803\pi$
$558$	−1.04198e9	−0.253887
$559$	−2.65995e9	−0.644069
$560$	−5.51649e8	−0.132741
$561$	−1.03522e9	−0.247551
$562$	1.58033e9	0.375553
$563$	2.10337e9	0.496747	0.248374	−	0.968664i	$-0.420104\pi$
$563$	2.10337e9	0.496747	0.248374	+	0.968664i	$0.420104\pi$
$564$	6.13601e9	1.44015
$565$	1.60958e9	0.375443
$566$	9.19361e9	2.13122
$567$	8.92321e8	0.205580
$568$	5.82173e9	1.33301
$569$	5.17228e9	1.17704	0.588518	−	0.808484i	$-0.299712\pi$
$569$	5.17228e9	1.17704	0.588518	+	0.808484i	$0.299712\pi$
$570$	8.46338e8	0.191418
$571$	−2.45037e9	−0.550814	−0.275407	−	0.961328i	$-0.588813\pi$
$571$	−2.45037e9	−0.550814	−0.275407	+	0.961328i	$0.588813\pi$
$572$	−3.75098e9	−0.838028
$573$	−1.42811e9	−0.317117
$574$	−3.75555e9	−0.828861
$575$	−1.73189e9	−0.379913
$576$	−2.48668e9	−0.542178
$577$	4.18992e9	0.908011	0.454005	−	0.890999i	$-0.349995\pi$
$577$	4.18992e9	0.908011	0.454005	+	0.890999i	$0.349995\pi$
$578$	7.51381e9	1.61850
$579$	−1.99217e9	−0.426531
$580$	7.31644e8	0.155705
$581$	−5.76281e9	−1.21904
$582$	−8.78779e8	−0.184778
$583$	1.44586e9	0.302193
$584$	−3.35992e9	−0.698045
$585$	9.02060e8	0.186290
$586$	9.81585e9	2.01505
$587$	3.46463e9	0.707007	0.353503	−	0.935433i	$-0.384990\pi$
$587$	3.46463e9	0.707007	0.353503	+	0.935433i	$0.384990\pi$
$588$	−1.03909e10	−2.10782
$589$	1.64925e9	0.332569
$590$	2.49321e9	0.499777
$591$	−4.17000e9	−0.830960
$592$	−4.45488e8	−0.0882490
$593$	1.28200e9	0.252462	0.126231	−	0.992001i	$-0.459712\pi$
$593$	1.28200e9	0.252462	0.126231	+	0.992001i	$0.459712\pi$
$594$	4.69260e8	0.0918673
$595$	−4.09541e9	−0.797054
$596$	−4.96127e9	−0.959911
$597$	−4.63613e9	−0.891755
$598$	6.38922e9	1.22178
$599$	6.40800e9	1.21823	0.609114	−	0.793083i	$-0.291525\pi$
$599$	6.40800e9	1.21823	0.609114	+	0.793083i	$0.291525\pi$
$600$	2.22504e9	0.420542
$601$	3.72569e9	0.700077	0.350039	−	0.936735i	$-0.386168\pi$
$601$	3.72569e9	0.700077	0.350039	+	0.936735i	$0.386168\pi$
$602$	−5.47412e9	−1.02265
$603$	2.08374e9	0.387019
$604$	1.19776e10	2.21177
$605$	1.50001e8	0.0275392
$606$	3.16681e9	0.578053
$607$	−5.51998e9	−1.00179	−0.500895	−	0.865508i	$-0.666996\pi$
$607$	−5.51998e9	−1.00179	−0.500895	+	0.865508i	$0.666996\pi$
$608$	4.50901e9	0.813614
$609$	−2.03139e9	−0.364446
$610$	7.13763e8	0.127321
$611$	−1.72224e10	−3.05457
$612$	−4.04965e9	−0.714147
$613$	−7.49019e9	−1.31335	−0.656676	−	0.754173i	$-0.728038\pi$
$613$	−7.49019e9	−1.31335	−0.656676	+	0.754173i	$0.728038\pi$
$614$	3.62838e9	0.632592
$615$	2.85473e8	0.0494883
$616$	−2.59556e9	−0.447403
$617$	2.10268e9	0.360392	0.180196	−	0.983631i	$-0.442327\pi$
$617$	2.10268e9	0.360392	0.180196	+	0.983631i	$0.442327\pi$
$618$	−8.02737e8	−0.136809
$619$	−9.42831e8	−0.159778	−0.0798889	−	0.996804i	$-0.525457\pi$
$619$	−9.42831e8	−0.159778	−0.0798889	+	0.996804i	$0.525457\pi$
$620$	−1.30294e9	−0.219560
$621$	−4.80425e8	−0.0805017
$622$	5.43672e9	0.905880
$623$	−3.09744e9	−0.513209
$624$	1.53106e9	0.252259
$625$	4.47461e9	0.733120
$626$	9.31885e7	0.0151828
$627$	−7.42744e8	−0.120338
$628$	−1.77639e10	−2.86207
$629$	−3.30727e9	−0.529898
$630$	1.85642e9	0.295790
$631$	−1.11126e10	−1.76081	−0.880405	−	0.474223i	$-0.842729\pi$
$631$	−1.11126e10	−1.76081	−0.880405	+	0.474223i	$0.842729\pi$
$632$	−6.15557e8	−0.0969971
$633$	−4.70252e9	−0.736916
$634$	−1.80648e10	−2.81528
$635$	3.20198e9	0.496262
$636$	5.65598e9	0.871782
$637$	2.91651e10	4.47070
$638$	−1.06828e9	−0.162860
$639$	3.65420e9	0.554037
$640$	−2.80893e9	−0.423557
$641$	8.00380e9	1.20031	0.600154	−	0.799884i	$-0.295106\pi$
$641$	8.00380e9	1.20031	0.600154	+	0.799884i	$0.295106\pi$
$642$	5.86995e9	0.875512
$643$	2.72761e9	0.404617	0.202308	−	0.979322i	$-0.435156\pi$
$643$	2.72761e9	0.404617	0.202308	+	0.979322i	$0.435156\pi$
$644$	7.90310e9	1.16600
$645$	4.16109e8	0.0610587
$646$	1.06644e10	1.55640
$647$	8.76207e9	1.27187	0.635934	−	0.771744i	$-0.280615\pi$
$647$	8.76207e9	1.27187	0.635934	+	0.771744i	$0.280615\pi$
$648$	6.17224e8	0.0891108
$649$	−2.18803e9	−0.314193
$650$	−1.85738e10	−2.65280
$651$	3.61757e9	0.513906
$652$	8.58392e9	1.21288
$653$	−6.26088e9	−0.879912	−0.439956	−	0.898019i	$-0.645006\pi$
$653$	−6.26088e9	−0.879912	−0.439956	+	0.898019i	$0.645006\pi$
$654$	7.54101e9	1.05416
$655$	2.69872e8	0.0375244
$656$	4.84531e8	0.0670129
$657$	−2.10896e9	−0.290128
$658$	−3.54434e10	−4.85003
$659$	−1.06118e10	−1.44441	−0.722205	−	0.691679i	$-0.756871\pi$
$659$	−1.06118e10	−1.44441	−0.722205	+	0.691679i	$0.756871\pi$
$660$	5.86783e8	0.0794463
$661$	5.77805e9	0.778173	0.389087	−	0.921201i	$-0.372791\pi$
$661$	5.77805e9	0.778173	0.389087	+	0.921201i	$0.372791\pi$
$662$	8.57929e9	1.14934
$663$	1.13665e10	1.51471
$664$	−3.98618e9	−0.528407
$665$	−2.93834e9	−0.387459
$666$	1.49916e9	0.196648
$667$	1.09370e9	0.142711
$668$	1.91318e10	2.48335
$669$	8.92487e8	0.115242
$670$	4.33509e9	0.556847
$671$	−6.26397e8	−0.0800425
$672$	9.89038e9	1.25725
$673$	4.20986e9	0.532371	0.266186	−	0.963922i	$-0.414237\pi$
$673$	4.20986e9	0.532371	0.266186	+	0.963922i	$0.414237\pi$
$674$	−4.11945e9	−0.518238
$675$	1.39662e9	0.174790
$676$	2.90843e10	3.62114
$677$	−4.91057e9	−0.608235	−0.304118	−	0.952634i	$-0.598362\pi$
$677$	−4.91057e9	−0.608235	−0.304118	+	0.952634i	$0.598362\pi$
$678$	−9.19355e9	−1.13287
$679$	3.05097e9	0.374019
$680$	−2.83282e9	−0.345492
$681$	6.47374e8	0.0785490
$682$	1.90244e9	0.229649
$683$	9.00588e9	1.08157	0.540784	−	0.841162i	$-0.318128\pi$
$683$	9.00588e9	1.08157	0.540784	+	0.841162i	$0.318128\pi$
$684$	−2.90551e9	−0.347157
$685$	−1.01520e9	−0.120680
$686$	3.52528e10	4.16926
$687$	−1.42291e9	−0.167429
$688$	7.06258e8	0.0826806
$689$	−1.58751e10	−1.84905
$690$	−9.99495e8	−0.115827
$691$	2.67573e9	0.308510	0.154255	−	0.988031i	$-0.450702\pi$
$691$	2.67573e9	0.308510	0.154255	+	0.988031i	$0.450702\pi$
$692$	−2.13291e10	−2.44682
$693$	−1.62919e9	−0.185954
$694$	−1.13424e10	−1.28809
$695$	−3.15347e9	−0.356321
$696$	−1.40513e9	−0.157973
$697$	3.59713e9	0.402384
$698$	−9.62222e9	−1.07098
$699$	3.47623e9	0.384980
$700$	−2.29747e10	−2.53167
$701$	1.46686e10	1.60833	0.804166	−	0.594405i	$-0.202613\pi$
$701$	1.46686e10	1.60833	0.804166	+	0.594405i	$0.202613\pi$
$702$	−5.15234e9	−0.562115
$703$	−2.37287e9	−0.257591
$704$	4.54016e9	0.490418
$705$	2.69418e9	0.289578
$706$	−2.80197e10	−2.99673
$707$	−1.09946e10	−1.17007
$708$	−8.55926e9	−0.906400
$709$	4.70273e9	0.495551	0.247775	−	0.968817i	$-0.420300\pi$
$709$	4.70273e9	0.495551	0.247775	+	0.968817i	$0.420300\pi$
$710$	7.60234e9	0.797155
$711$	−3.86374e8	−0.0403148
$712$	−2.14252e9	−0.222456
$713$	−1.94770e9	−0.201237
$714$	2.33920e10	2.40504
$715$	−1.64697e9	−0.168506
$716$	−3.32741e9	−0.338774
$717$	−5.59071e9	−0.566434
$718$	−5.54662e9	−0.559234
$719$	−1.44754e10	−1.45238	−0.726190	−	0.687494i	$-0.758711\pi$
$719$	−1.44754e10	−1.45238	−0.726190	+	0.687494i	$0.758711\pi$
$720$	−2.39511e8	−0.0239145
$721$	2.78696e9	0.276922
$722$	−8.35967e9	−0.826625
$723$	−3.84298e9	−0.378167
$724$	−1.23103e9	−0.120555
$725$	−3.17944e9	−0.309862
$726$	−8.56770e8	−0.0830971
$727$	8.12115e9	0.783875	0.391938	−	0.919992i	$-0.371805\pi$
$727$	8.12115e9	0.783875	0.391938	+	0.919992i	$0.371805\pi$
$728$	2.84986e10	2.73756
$729$	3.87420e8	0.0370370
$730$	−4.38757e9	−0.417440
$731$	5.24321e9	0.496462
$732$	−2.45037e9	−0.230910
$733$	1.58815e10	1.48945	0.744726	−	0.667370i	$-0.232580\pi$
$733$	1.58815e10	1.48945	0.744726	+	0.667370i	$0.232580\pi$
$734$	−4.68316e9	−0.437122
$735$	−4.56243e9	−0.423829
$736$	−5.32497e9	−0.492317
$737$	−3.80446e9	−0.350072
$738$	−1.63055e9	−0.149327
$739$	1.54228e9	0.140575	0.0702874	−	0.997527i	$-0.477608\pi$
$739$	1.54228e9	0.140575	0.0702874	+	0.997527i	$0.477608\pi$
$740$	1.87462e9	0.170060
$741$	8.15512e9	0.736320
$742$	−3.26706e10	−2.93591
$743$	−8.45656e8	−0.0756367	−0.0378184	−	0.999285i	$-0.512041\pi$
$743$	−8.45656e8	−0.0756367	−0.0378184	+	0.999285i	$0.512041\pi$
$744$	2.50230e9	0.222758
$745$	−2.17838e9	−0.193013
$746$	2.95461e9	0.260564
$747$	−2.50205e9	−0.219621
$748$	7.39381e9	0.645970
$749$	−2.03794e10	−1.77217
$750$	6.10475e9	0.528389
$751$	−1.19584e10	−1.03023	−0.515115	−	0.857121i	$-0.672251\pi$
$751$	−1.19584e10	−1.03023	−0.515115	+	0.857121i	$0.672251\pi$
$752$	4.57282e9	0.392122
$753$	−5.27251e9	−0.450023
$754$	1.17294e10	0.996501
$755$	5.25909e9	0.444730
$756$	−6.37315e9	−0.536449
$757$	1.64003e10	1.37409	0.687045	−	0.726615i	$-0.258908\pi$
$757$	1.64003e10	1.37409	0.687045	+	0.726615i	$0.258908\pi$
$758$	−2.26931e10	−1.89257
$759$	8.77154e8	0.0728165
$760$	−2.03247e9	−0.167948
$761$	1.45875e10	1.19987	0.599937	−	0.800047i	$-0.295192\pi$
$761$	1.45875e10	1.19987	0.599937	+	0.800047i	$0.295192\pi$
$762$	−1.82889e10	−1.49743
$763$	−2.61811e10	−2.13379
$764$	1.01999e10	0.827499
$765$	−1.77811e9	−0.143596
$766$	3.06617e10	2.46487
$767$	2.40240e10	1.92248
$768$	4.25523e9	0.338968
$769$	−2.48714e10	−1.97223	−0.986117	−	0.166054i	$-0.946897\pi$
$769$	−2.48714e10	−1.97223	−0.986117	+	0.166054i	$0.946897\pi$
$770$	−3.38943e9	−0.267553
$771$	−3.40391e9	−0.267478
$772$	1.42285e10	1.11301
$773$	2.94099e9	0.229015	0.114508	−	0.993422i	$-0.463471\pi$
$773$	2.94099e9	0.229015	0.114508	+	0.993422i	$0.463471\pi$
$774$	−2.37671e9	−0.184240
$775$	5.66207e9	0.436937
$776$	2.11037e9	0.162122
$777$	−5.20483e9	−0.398046
$778$	−2.37746e10	−1.81002
$779$	2.58084e9	0.195605
$780$	−6.44271e9	−0.486114
$781$	−6.67179e9	−0.501145
$782$	−1.25942e10	−0.941776
$783$	−8.81973e8	−0.0656582
$784$	−7.74378e9	−0.573914
$785$	−7.79974e9	−0.575488
$786$	−1.54144e9	−0.113227
$787$	3.41977e9	0.250084	0.125042	−	0.992151i	$-0.460093\pi$
$787$	3.41977e9	0.250084	0.125042	+	0.992151i	$0.460093\pi$
$788$	2.97831e10	2.16834
$789$	−8.15009e8	−0.0590735
$790$	−8.03829e8	−0.0580055
$791$	3.19184e10	2.29310
$792$	−1.12692e9	−0.0806037
$793$	6.87766e9	0.489762
$794$	−2.22507e10	−1.57751
$795$	2.48341e9	0.175293
$796$	3.31123e10	2.32698
$797$	1.09396e10	0.765419	0.382709	−	0.923869i	$-0.374991\pi$
$797$	1.09396e10	0.765419	0.382709	+	0.923869i	$0.374991\pi$
$798$	1.67831e10	1.16913
$799$	3.39483e10	2.35453
$800$	1.54800e10	1.06895
$801$	−1.34482e9	−0.0924592
$802$	1.65846e10	1.13526
$803$	3.85052e9	0.262431
$804$	−1.48825e10	−1.00990
$805$	3.47007e9	0.234451
$806$	−2.08882e10	−1.40517
$807$	3.36144e9	0.225148
$808$	−7.60504e9	−0.507180
$809$	9.62137e9	0.638877	0.319438	−	0.947607i	$-0.396506\pi$
$809$	9.62137e9	0.638877	0.319438	+	0.947607i	$0.396506\pi$
$810$	8.06005e8	0.0532893
$811$	−2.08135e10	−1.37016	−0.685080	−	0.728468i	$-0.740233\pi$
$811$	−2.08135e10	−1.37016	−0.685080	+	0.728468i	$0.740233\pi$
$812$	1.45086e10	0.951001
$813$	1.70402e10	1.11213
$814$	−2.73715e9	−0.177875
$815$	3.76901e9	0.243879
$816$	−3.01797e9	−0.194446
$817$	3.76185e9	0.241337
$818$	1.04918e10	0.670214
$819$	1.78880e10	1.13781
$820$	−2.03891e9	−0.129137
$821$	1.07357e10	0.677064	0.338532	−	0.940955i	$-0.390070\pi$
$821$	1.07357e10	0.677064	0.338532	+	0.940955i	$0.390070\pi$
$822$	5.79857e9	0.364141
$823$	1.39671e10	0.873388	0.436694	−	0.899610i	$-0.356149\pi$
$823$	1.39671e10	0.873388	0.436694	+	0.899610i	$0.356149\pi$
$824$	1.92776e9	0.120035
$825$	−2.54993e9	−0.158103
$826$	4.94408e10	3.05250
$827$	−3.06795e10	−1.88616	−0.943081	−	0.332564i	$-0.892086\pi$
$827$	−3.06795e10	−1.88616	−0.943081	+	0.332564i	$0.892086\pi$
$828$	3.43130e9	0.210065
$829$	−1.51733e9	−0.0924995	−0.0462497	−	0.998930i	$-0.514727\pi$
$829$	−1.51733e9	−0.0924995	−0.0462497	+	0.998930i	$0.514727\pi$
$830$	−5.20537e9	−0.315994
$831$	−1.13938e10	−0.688756
$832$	−4.98496e10	−3.00075
$833$	−5.74893e10	−3.44611
$834$	1.80118e10	1.07517
$835$	8.40034e9	0.499338
$836$	5.30485e9	0.314015
$837$	1.57065e9	0.0925849
$838$	−4.58593e9	−0.269199
$839$	−3.27713e10	−1.91570	−0.957848	−	0.287276i	$-0.907250\pi$
$839$	−3.27713e10	−1.91570	−0.957848	+	0.287276i	$0.907250\pi$
$840$	−4.45816e9	−0.259524
$841$	−1.52420e10	−0.883603
$842$	1.19040e10	0.687226
$843$	−2.38215e9	−0.136953
$844$	3.35865e10	1.92294
$845$	1.27703e10	0.728117
$846$	−1.53885e10	−0.873777
$847$	2.97455e9	0.168202
$848$	4.21508e9	0.237367
$849$	−1.38582e10	−0.777193
$850$	3.66121e10	2.04483
$851$	2.80228e9	0.155868
$852$	−2.60991e10	−1.44573
$853$	−9.71082e9	−0.535716	−0.267858	−	0.963458i	$-0.586316\pi$
$853$	−9.71082e9	−0.535716	−0.267858	+	0.963458i	$0.586316\pi$
$854$	1.41541e10	0.777641
$855$	−1.27574e9	−0.0698043
$856$	−1.40966e10	−0.768168
$857$	−2.20307e10	−1.19562	−0.597812	−	0.801636i	$-0.703963\pi$
$857$	−2.20307e10	−1.19562	−0.597812	+	0.801636i	$0.703963\pi$
$858$	9.40709e9	0.508452
$859$	−2.00371e10	−1.07860	−0.539298	−	0.842115i	$-0.681310\pi$
$859$	−2.00371e10	−1.07860	−0.539298	+	0.842115i	$0.681310\pi$
$860$	−2.97194e9	−0.159329
$861$	5.66099e9	0.302261
$862$	−6.34570e9	−0.337446
$863$	−2.67107e9	−0.141465	−0.0707323	−	0.997495i	$-0.522534\pi$
$863$	−2.67107e9	−0.141465	−0.0707323	+	0.997495i	$0.522534\pi$
$864$	4.29412e9	0.226504
$865$	−9.36513e9	−0.491991
$866$	−3.17662e10	−1.66208
$867$	−1.13261e10	−0.590218
$868$	−2.58375e10	−1.34101
$869$	7.05438e8	0.0364661
$870$	−1.83489e9	−0.0944698
$871$	4.17719e10	2.14201
$872$	−1.81096e10	−0.924914
$873$	1.32464e9	0.0673828
$874$	−9.03600e9	−0.457811
$875$	−2.11946e10	−1.06954
$876$	1.50627e10	0.757073
$877$	−1.74553e10	−0.873832	−0.436916	−	0.899502i	$-0.643929\pi$
$877$	−1.74553e10	−0.873832	−0.436916	+	0.899502i	$0.643929\pi$
$878$	−4.75420e10	−2.37054
$879$	−1.47961e10	−0.734829
$880$	4.37296e8	0.0216315
$881$	3.48759e10	1.71834	0.859171	−	0.511689i	$-0.170980\pi$
$881$	3.48759e10	1.71834	0.859171	+	0.511689i	$0.170980\pi$
$882$	2.60595e10	1.27887
$883$	−1.18476e10	−0.579121	−0.289561	−	0.957160i	$-0.593509\pi$
$883$	−1.18476e10	−0.579121	−0.289561	+	0.957160i	$0.593509\pi$
$884$	−8.11819e10	−3.95254
$885$	−3.75818e9	−0.182254
$886$	3.49120e10	1.68639
$887$	2.64987e10	1.27494	0.637472	−	0.770473i	$-0.279980\pi$
$887$	2.64987e10	1.27494	0.637472	+	0.770473i	$0.279980\pi$
$888$	−3.60021e9	−0.172537
$889$	6.34960e10	3.03103
$890$	−2.79782e9	−0.133031
$891$	−7.07348e8	−0.0335013
$892$	−6.37434e9	−0.300717
$893$	2.43569e10	1.14457
$894$	1.24424e10	0.582401
$895$	−1.46099e9	−0.0681187
$896$	−5.57018e10	−2.58697
$897$	−9.63091e9	−0.445547
$898$	−1.65637e10	−0.763291
$899$	−3.57562e9	−0.164132
$900$	−9.97498e9	−0.456103
$901$	3.12924e10	1.42529
$902$	2.97704e9	0.135071
$903$	8.25152e9	0.372930
$904$	2.20782e10	0.993970
$905$	−5.40520e8	−0.0242405
$906$	−3.00387e10	−1.34194
$907$	−4.98476e9	−0.221829	−0.110915	−	0.993830i	$-0.535378\pi$
$907$	−4.98476e9	−0.221829	−0.110915	+	0.993830i	$0.535378\pi$
$908$	−4.62369e9	−0.204969
$909$	−4.77355e9	−0.210799
$910$	3.72150e10	1.63709
$911$	1.45013e10	0.635465	0.317733	−	0.948180i	$-0.397079\pi$
$911$	1.45013e10	0.635465	0.317733	+	0.948180i	$0.397079\pi$
$912$	−2.16531e9	−0.0945231
$913$	4.56822e9	0.198655
$914$	5.37517e10	2.32852
$915$	−1.07590e9	−0.0464301
$916$	1.01628e10	0.436896
$917$	5.35162e9	0.229189
$918$	1.01561e10	0.433290
$919$	−2.19450e10	−0.932678	−0.466339	−	0.884606i	$-0.654427\pi$
$919$	−2.19450e10	−0.932678	−0.466339	+	0.884606i	$0.654427\pi$
$920$	2.40027e9	0.101626
$921$	−5.46931e9	−0.230687
$922$	3.36351e10	1.41330
$923$	7.32544e10	3.06639
$924$	1.16360e10	0.485236
$925$	−8.14637e9	−0.338429
$926$	−2.09165e10	−0.865666
$927$	1.21002e9	0.0498900
$928$	−9.77569e9	−0.401540
$929$	1.43781e10	0.588365	0.294182	−	0.955749i	$-0.404953\pi$
$929$	1.43781e10	0.588365	0.294182	+	0.955749i	$0.404953\pi$
$930$	3.26764e9	0.133212
$931$	−4.12469e10	−1.67520
$932$	−2.48280e10	−1.00458
$933$	−8.19515e9	−0.330347
$934$	−7.19904e10	−2.89108
$935$	3.24645e9	0.129888
$936$	1.23733e10	0.493195
$937$	−1.51530e10	−0.601741	−0.300871	−	0.953665i	$-0.597277\pi$
$937$	−1.51530e10	−0.601741	−0.300871	+	0.953665i	$0.597277\pi$
$938$	8.59657e10	3.40107
$939$	−1.40469e8	−0.00553672
$940$	−1.92425e10	−0.755637
$941$	−2.22919e10	−0.872134	−0.436067	−	0.899914i	$-0.643629\pi$
$941$	−2.22919e10	−0.872134	−0.436067	+	0.899914i	$0.643629\pi$
$942$	4.45502e10	1.73649
$943$	−3.04788e9	−0.118360
$944$	−6.37873e9	−0.246793
$945$	−2.79831e9	−0.107866
$946$	4.33937e9	0.166651
$947$	1.63897e9	0.0627115	0.0313557	−	0.999508i	$-0.490018\pi$
$947$	1.63897e9	0.0627115	0.0313557	+	0.999508i	$0.490018\pi$
$948$	2.75957e9	0.105199
$949$	−4.22776e10	−1.60575
$950$	2.62681e10	0.994023
$951$	2.72304e10	1.02665
$952$	−5.61754e10	−2.11017
$953$	−2.30180e10	−0.861475	−0.430738	−	0.902477i	$-0.641747\pi$
$953$	−2.30180e10	−0.861475	−0.430738	+	0.902477i	$0.641747\pi$
$954$	−1.41846e10	−0.528931
$955$	4.47853e9	0.166389
$956$	3.99301e10	1.47808
$957$	1.61030e9	0.0593901
$958$	6.94638e9	0.255258
$959$	−2.01316e10	−0.737078
$960$	7.79821e9	0.284476
$961$	−2.11450e10	−0.768557
$962$	3.00532e10	1.08837
$963$	−8.84818e9	−0.319273
$964$	2.74474e10	0.986806
$965$	6.24742e9	0.223797
$966$	−1.98202e10	−0.707438
$967$	−1.59030e10	−0.565571	−0.282785	−	0.959183i	$-0.591258\pi$
$967$	−1.59030e10	−0.565571	−0.282785	+	0.959183i	$0.591258\pi$
$968$	2.05752e9	0.0729088
$969$	−1.60751e10	−0.567572
$970$	2.75584e9	0.0969512
$971$	2.99324e10	1.04924	0.524619	−	0.851337i	$-0.324208\pi$
$971$	2.99324e10	1.04924	0.524619	+	0.851337i	$0.324208\pi$
$972$	−2.76704e9	−0.0966461
$973$	−6.25339e10	−2.17631
$974$	−4.94695e9	−0.171546
$975$	2.79976e10	0.967396
$976$	−1.82612e9	−0.0628718
$977$	−3.39606e10	−1.16505	−0.582524	−	0.812813i	$-0.697935\pi$
$977$	−3.39606e10	−1.16505	−0.582524	+	0.812813i	$0.697935\pi$
$978$	−2.15276e10	−0.735886
$979$	2.45536e9	0.0836325
$980$	3.25859e10	1.10596
$981$	−1.13671e10	−0.384421
$982$	3.14824e10	1.06091
$983$	3.34888e10	1.12451	0.562254	−	0.826965i	$-0.309934\pi$
$983$	3.34888e10	1.12451	0.562254	+	0.826965i	$0.309934\pi$
$984$	3.91575e9	0.131018
$985$	1.30771e10	0.435998
$986$	−2.31207e10	−0.768125
$987$	5.34262e10	1.76866
$988$	−5.82457e10	−1.92139
$989$	−4.44262e9	−0.146033
$990$	−1.47160e9	−0.0482020
$991$	−1.14251e10	−0.372907	−0.186453	−	0.982464i	$-0.559699\pi$
$991$	−1.14251e10	−0.372907	−0.186453	+	0.982464i	$0.559699\pi$
$992$	1.74089e10	0.566214
$993$	−1.29322e10	−0.419130
$994$	1.50756e11	4.86880
$995$	1.45389e10	0.467896
$996$	1.78702e10	0.573089
$997$	−2.07985e10	−0.664659	−0.332329	−	0.943163i	$-0.607835\pi$
$997$	−2.07985e10	−0.664659	−0.332329	+	0.943163i	$0.607835\pi$
$998$	−1.03674e10	−0.330152
$999$	−2.25979e9	−0.0717115

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.8.a.d.1.3	✓	3
3.2	odd	2		99.8.a.e.1.1		3
4.3	odd	2		528.8.a.o.1.3		3
11.10	odd	2		363.8.a.e.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.a.d.1.3	✓	3	1.1	even	1	trivial
99.8.a.e.1.1		3	3.2	odd	2
363.8.a.e.1.1		3	11.10	odd	2
528.8.a.o.1.3		3	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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	33.a (trivial)

\(f(q)\)	\(=\)	\(q+17.9120 q^{2} -27.0000 q^{3} +192.840 q^{4} +84.6717 q^{5} -483.624 q^{6} +1679.06 q^{7} +1161.42 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+17.9120 q^{2} -27.0000 q^{3} +192.840 q^{4} +84.6717 q^{5} -483.624 q^{6} +1679.06 q^{7} +1161.42 q^{8} +729.000 q^{9} +1516.64 q^{10} -1331.00 q^{11} -5206.68 q^{12} +14614.0 q^{13} +30075.3 q^{14} -2286.14 q^{15} -3880.24 q^{16} -28806.7 q^{17} +13057.9 q^{18} -20668.0 q^{19} +16328.1 q^{20} -45334.6 q^{21} -23840.9 q^{22} +24408.1 q^{23} -31358.2 q^{24} -70955.7 q^{25} +261766. q^{26} -19683.0 q^{27} +323790. q^{28} +44808.9 q^{29} -40949.3 q^{30} -79797.2 q^{31} -218164. q^{32} +35937.0 q^{33} -515985. q^{34} +142169. q^{35} +140580. q^{36} +114809. q^{37} -370205. q^{38} -394578. q^{39} +98339.1 q^{40} -124871. q^{41} -812033. q^{42} -182014. q^{43} -256670. q^{44} +61725.7 q^{45} +437198. q^{46} -1.17849e6 q^{47} +104767. q^{48} +1.99569e6 q^{49} -1.27096e6 q^{50} +777780. q^{51} +2.81817e6 q^{52} -1.08629e6 q^{53} -352562. q^{54} -112698. q^{55} +1.95008e6 q^{56} +558035. q^{57} +802617. q^{58} +1.64390e6 q^{59} -440859. q^{60} +470621. q^{61} -1.42933e6 q^{62} +1.22403e6 q^{63} -3.41109e6 q^{64} +1.23739e6 q^{65} +643704. q^{66} +2.85835e6 q^{67} -5.55508e6 q^{68} -659019. q^{69} +2.54653e6 q^{70} +5.01261e6 q^{71} +846672. q^{72} -2.89295e6 q^{73} +2.05646e6 q^{74} +1.91580e6 q^{75} -3.98561e6 q^{76} -2.23483e6 q^{77} -7.06769e6 q^{78} -530006. q^{79} -328547. q^{80} +531441. q^{81} -2.23670e6 q^{82} -3.43217e6 q^{83} -8.74232e6 q^{84} -2.43911e6 q^{85} -3.26023e6 q^{86} -1.20984e6 q^{87} -1.54584e6 q^{88} -1.84475e6 q^{89} +1.10563e6 q^{90} +2.45378e7 q^{91} +4.70686e6 q^{92} +2.15453e6 q^{93} -2.11091e7 q^{94} -1.74999e6 q^{95} +5.89043e6 q^{96} +1.81707e6 q^{97} +3.57469e7 q^{98} -970299. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 9 q^{2} - 81 q^{3} - 15 q^{4} - 444 q^{5} - 243 q^{6} + 1614 q^{7} + 3153 q^{8} + 2187 q^{9}+O(q^{10}) \) 3 * q + 9 * q^2 - 81 * q^3 - 15 * q^4 - 444 * q^5 - 243 * q^6 + 1614 * q^7 + 3153 * q^8 + 2187 * q^9	\( 3 q + 9 q^{2} - 81 q^{3} - 15 q^{4} - 444 q^{5} - 243 q^{6} + 1614 q^{7} + 3153 q^{8} + 2187 q^{9} + 2880 q^{10} - 3993 q^{11} + 405 q^{12} + 20772 q^{13} + 36258 q^{14} + 11988 q^{15} + 12225 q^{16} - 14538 q^{17} + 6561 q^{18} + 24492 q^{19} + 80112 q^{20} - 43578 q^{21} - 11979 q^{22} + 35094 q^{23} - 85131 q^{24} + 29121 q^{25} + 203832 q^{26} - 59049 q^{27} + 278034 q^{28} - 179862 q^{29} - 77760 q^{30} + 288888 q^{31} - 519567 q^{32} + 107811 q^{33} - 491586 q^{34} - 532872 q^{35} - 10935 q^{36} + 107562 q^{37} - 686328 q^{38} - 560844 q^{39} - 237360 q^{40} - 135198 q^{41} - 978966 q^{42} + 193536 q^{43} + 19965 q^{44} - 323676 q^{45} + 16422 q^{46} - 591486 q^{47} - 330075 q^{48} + 4461159 q^{49} - 1192245 q^{50} + 392526 q^{51} + 2449992 q^{52} + 79044 q^{53} - 177147 q^{54} + 590964 q^{55} + 752658 q^{56} - 661284 q^{57} + 2289930 q^{58} + 2532768 q^{59} - 2163024 q^{60} + 6678792 q^{61} - 2660808 q^{62} + 1176606 q^{63} - 3966303 q^{64} + 3191832 q^{65} + 323433 q^{66} + 7150356 q^{67} - 7821954 q^{68} - 947538 q^{69} + 4029120 q^{70} + 1390398 q^{71} + 2298537 q^{72} - 6429114 q^{73} + 2507478 q^{74} - 786267 q^{75} - 7654728 q^{76} - 2148234 q^{77} - 5503464 q^{78} + 6873186 q^{79} - 7556016 q^{80} + 1594323 q^{81} - 1774590 q^{82} + 6505596 q^{83} - 7506918 q^{84} - 16546032 q^{85} - 6519468 q^{86} + 4856274 q^{87} - 4196643 q^{88} - 8842962 q^{89} + 2099520 q^{90} + 3066648 q^{91} + 6921990 q^{92} - 7799976 q^{93} - 24038238 q^{94} - 190968 q^{95} + 14028309 q^{96} - 1764774 q^{97} + 24377397 q^{98} - 2910897 q^{99}+O(q^{100}) \) 3 * q + 9 * q^2 - 81 * q^3 - 15 * q^4 - 444 * q^5 - 243 * q^6 + 1614 * q^7 + 3153 * q^8 + 2187 * q^9 + 2880 * q^10 - 3993 * q^11 + 405 * q^12 + 20772 * q^13 + 36258 * q^14 + 11988 * q^15 + 12225 * q^16 - 14538 * q^17 + 6561 * q^18 + 24492 * q^19 + 80112 * q^20 - 43578 * q^21 - 11979 * q^22 + 35094 * q^23 - 85131 * q^24 + 29121 * q^25 + 203832 * q^26 - 59049 * q^27 + 278034 * q^28 - 179862 * q^29 - 77760 * q^30 + 288888 * q^31 - 519567 * q^32 + 107811 * q^33 - 491586 * q^34 - 532872 * q^35 - 10935 * q^36 + 107562 * q^37 - 686328 * q^38 - 560844 * q^39 - 237360 * q^40 - 135198 * q^41 - 978966 * q^42 + 193536 * q^43 + 19965 * q^44 - 323676 * q^45 + 16422 * q^46 - 591486 * q^47 - 330075 * q^48 + 4461159 * q^49 - 1192245 * q^50 + 392526 * q^51 + 2449992 * q^52 + 79044 * q^53 - 177147 * q^54 + 590964 * q^55 + 752658 * q^56 - 661284 * q^57 + 2289930 * q^58 + 2532768 * q^59 - 2163024 * q^60 + 6678792 * q^61 - 2660808 * q^62 + 1176606 * q^63 - 3966303 * q^64 + 3191832 * q^65 + 323433 * q^66 + 7150356 * q^67 - 7821954 * q^68 - 947538 * q^69 + 4029120 * q^70 + 1390398 * q^71 + 2298537 * q^72 - 6429114 * q^73 + 2507478 * q^74 - 786267 * q^75 - 7654728 * q^76 - 2148234 * q^77 - 5503464 * q^78 + 6873186 * q^79 - 7556016 * q^80 + 1594323 * q^81 - 1774590 * q^82 + 6505596 * q^83 - 7506918 * q^84 - 16546032 * q^85 - 6519468 * q^86 + 4856274 * q^87 - 4196643 * q^88 - 8842962 * q^89 + 2099520 * q^90 + 3066648 * q^91 + 6921990 * q^92 - 7799976 * q^93 - 24038238 * q^94 - 190968 * q^95 + 14028309 * q^96 - 1764774 * q^97 + 24377397 * q^98 - 2910897 * q^99

Introduction

L-functions

Modular forms

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