LMFDB - Embedded newform 33.8.a.c.1.2

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:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{97}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 24 $ x^2 - x - 24
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$5.42443$ 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)

$f(q)$	$=$	$q+15.2733 q^{2} -27.0000 q^{3} +105.273 q^{4} -303.826 q^{5} -412.379 q^{6} -829.478 q^{7} -347.112 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+15.2733 q^{2} -27.0000 q^{3} +105.273 q^{4} -303.826 q^{5} -412.379 q^{6} -829.478 q^{7} -347.112 q^{8} +729.000 q^{9} -4640.42 q^{10} +1331.00 q^{11} -2842.38 q^{12} -6061.62 q^{13} -12668.9 q^{14} +8203.30 q^{15} -18776.5 q^{16} -2468.81 q^{17} +11134.2 q^{18} +42140.2 q^{19} -31984.8 q^{20} +22395.9 q^{21} +20328.7 q^{22} -37118.2 q^{23} +9372.01 q^{24} +14185.2 q^{25} -92580.8 q^{26} -19683.0 q^{27} -87321.9 q^{28} -59769.3 q^{29} +125291. q^{30} -21301.7 q^{31} -242349. q^{32} -35937.0 q^{33} -37706.8 q^{34} +252017. q^{35} +76744.2 q^{36} +330635. q^{37} +643620. q^{38} +163664. q^{39} +105462. q^{40} +816862. q^{41} +342059. q^{42} -958652. q^{43} +140119. q^{44} -221489. q^{45} -566917. q^{46} +38915.5 q^{47} +506966. q^{48} -135509. q^{49} +216655. q^{50} +66657.8 q^{51} -638126. q^{52} -1.47350e6 q^{53} -300624. q^{54} -404392. q^{55} +287921. q^{56} -1.13779e6 q^{57} -912873. q^{58} +1.59205e6 q^{59} +863589. q^{60} -3.08178e6 q^{61} -325347. q^{62} -604689. q^{63} -1.29807e6 q^{64} +1.84168e6 q^{65} -548876. q^{66} -1.59464e6 q^{67} -259900. q^{68} +1.00219e6 q^{69} +3.84913e6 q^{70} -2.69496e6 q^{71} -253044. q^{72} -4.48213e6 q^{73} +5.04989e6 q^{74} -383002. q^{75} +4.43624e6 q^{76} -1.10404e6 q^{77} +2.49968e6 q^{78} -1.41084e6 q^{79} +5.70479e6 q^{80} +531441. q^{81} +1.24762e7 q^{82} +653174. q^{83} +2.35769e6 q^{84} +750088. q^{85} -1.46418e7 q^{86} +1.61377e6 q^{87} -462006. q^{88} +2.32673e6 q^{89} -3.38287e6 q^{90} +5.02798e6 q^{91} -3.90756e6 q^{92} +575146. q^{93} +594367. q^{94} -1.28033e7 q^{95} +6.54342e6 q^{96} -2.16642e6 q^{97} -2.06967e6 q^{98} +970299. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - 54 q^{3} + 181 q^{4} - 194 q^{5} - 27 q^{6} - 418 q^{7} + 399 q^{8} + 1458 q^{9}+O(q^{10}) $ 2 * q + q^2 - 54 * q^3 + 181 * q^4 - 194 * q^5 - 27 * q^6 - 418 * q^7 + 399 * q^8 + 1458 * q^9	\( 2 q + q^{2} - 54 q^{3} + 181 q^{4} - 194 q^{5} - 27 q^{6} - 418 q^{7} + 399 q^{8} + 1458 q^{9} - 6208 q^{10} + 2662 q^{11} - 4887 q^{12} - 13246 q^{13} - 18542 q^{14} + 5238 q^{15} - 39119 q^{16} - 10256 q^{17} + 729 q^{18} + 14196 q^{19} - 23668 q^{20} + 11286 q^{21} + 1331 q^{22} - 13666 q^{23} - 10773 q^{24} - 51878 q^{25} + 9964 q^{26} - 39366 q^{27} - 56162 q^{28} + 15312 q^{29} + 167616 q^{30} - 48040 q^{31} - 47497 q^{32} - 71874 q^{33} + 73442 q^{34} + 297208 q^{35} + 131949 q^{36} + 274092 q^{37} + 1042476 q^{38} + 357642 q^{39} + 187404 q^{40} + 755836 q^{41} + 500634 q^{42} - 1704096 q^{43} + 240911 q^{44} - 141426 q^{45} - 901658 q^{46} - 1182094 q^{47} + 1056213 q^{48} - 789738 q^{49} + 1159595 q^{50} + 276912 q^{51} - 1182176 q^{52} - 2156394 q^{53} - 19683 q^{54} - 258214 q^{55} + 594930 q^{56} - 383292 q^{57} - 1984530 q^{58} + 927332 q^{59} + 639036 q^{60} - 1061994 q^{61} + 56296 q^{62} - 304722 q^{63} - 1475407 q^{64} + 1052644 q^{65} - 35937 q^{66} - 3259952 q^{67} - 849598 q^{68} + 368982 q^{69} + 3204104 q^{70} - 5495514 q^{71} + 290871 q^{72} - 5450812 q^{73} + 5856942 q^{74} + 1400706 q^{75} + 2320116 q^{76} - 556358 q^{77} - 269028 q^{78} - 1536590 q^{79} + 3470660 q^{80} + 1062882 q^{81} + 13347206 q^{82} + 8850888 q^{83} + 1516374 q^{84} - 105148 q^{85} - 4001832 q^{86} - 413424 q^{87} + 531069 q^{88} + 6810132 q^{89} - 4525632 q^{90} + 2071760 q^{91} - 2131598 q^{92} + 1297080 q^{93} + 18022186 q^{94} - 15872304 q^{95} + 1282419 q^{96} + 9897376 q^{97} + 7268325 q^{98} + 1940598 q^{99}+O(q^{100}) \) 2 * q + q^2 - 54 * q^3 + 181 * q^4 - 194 * q^5 - 27 * q^6 - 418 * q^7 + 399 * q^8 + 1458 * q^9 - 6208 * q^10 + 2662 * q^11 - 4887 * q^12 - 13246 * q^13 - 18542 * q^14 + 5238 * q^15 - 39119 * q^16 - 10256 * q^17 + 729 * q^18 + 14196 * q^19 - 23668 * q^20 + 11286 * q^21 + 1331 * q^22 - 13666 * q^23 - 10773 * q^24 - 51878 * q^25 + 9964 * q^26 - 39366 * q^27 - 56162 * q^28 + 15312 * q^29 + 167616 * q^30 - 48040 * q^31 - 47497 * q^32 - 71874 * q^33 + 73442 * q^34 + 297208 * q^35 + 131949 * q^36 + 274092 * q^37 + 1042476 * q^38 + 357642 * q^39 + 187404 * q^40 + 755836 * q^41 + 500634 * q^42 - 1704096 * q^43 + 240911 * q^44 - 141426 * q^45 - 901658 * q^46 - 1182094 * q^47 + 1056213 * q^48 - 789738 * q^49 + 1159595 * q^50 + 276912 * q^51 - 1182176 * q^52 - 2156394 * q^53 - 19683 * q^54 - 258214 * q^55 + 594930 * q^56 - 383292 * q^57 - 1984530 * q^58 + 927332 * q^59 + 639036 * q^60 - 1061994 * q^61 + 56296 * q^62 - 304722 * q^63 - 1475407 * q^64 + 1052644 * q^65 - 35937 * q^66 - 3259952 * q^67 - 849598 * q^68 + 368982 * q^69 + 3204104 * q^70 - 5495514 * q^71 + 290871 * q^72 - 5450812 * q^73 + 5856942 * q^74 + 1400706 * q^75 + 2320116 * q^76 - 556358 * q^77 - 269028 * q^78 - 1536590 * q^79 + 3470660 * q^80 + 1062882 * q^81 + 13347206 * q^82 + 8850888 * q^83 + 1516374 * q^84 - 105148 * q^85 - 4001832 * q^86 - 413424 * q^87 + 531069 * q^88 + 6810132 * q^89 - 4525632 * q^90 + 2071760 * q^91 - 2131598 * q^92 + 1297080 * q^93 + 18022186 * q^94 - 15872304 * q^95 + 1282419 * q^96 + 9897376 * q^97 + 7268325 * q^98 + 1940598 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	15.2733	1.34998	0.674990	−	0.737827i	$-0.264148\pi$
$2$	15.2733	1.34998	0.674990	+	0.737827i	$0.264148\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	105.273	0.822448
$5$	−303.826	−1.08700	−0.543500	−	0.839409i	$-0.682901\pi$
$5$	−303.826	−1.08700	−0.543500	+	0.839409i	$0.682901\pi$
$6$	−412.379	−0.779412
$7$	−829.478	−0.914033	−0.457016	−	0.889458i	$-0.651082\pi$
$7$	−829.478	−0.914033	−0.457016	+	0.889458i	$0.651082\pi$
$8$	−347.112	−0.239692
$9$	729.000	0.333333
$10$	−4640.42	−1.46743
$11$	1331.00	0.301511
$11$	1331.00	0.301511
$12$	−2842.38	−0.474840
$13$	−6061.62	−0.765221	−0.382610	−	0.923910i	$-0.624975\pi$
$13$	−6061.62	−0.765221	−0.382610	+	0.923910i	$0.624975\pi$
$14$	−12668.9	−1.23393
$15$	8203.30	0.627580
$16$	−18776.5	−1.14603
$17$	−2468.81	−0.121875	−0.0609377	−	0.998142i	$-0.519409\pi$
$17$	−2468.81	−0.121875	−0.0609377	+	0.998142i	$0.519409\pi$
$18$	11134.2	0.449994
$19$	42140.2	1.40948	0.704741	−	0.709465i	$-0.251063\pi$
$19$	42140.2	1.40948	0.704741	+	0.709465i	$0.251063\pi$
$20$	−31984.8	−0.894001
$21$	22395.9	0.527717
$22$	20328.7	0.407034
$23$	−37118.2	−0.636121	−0.318061	−	0.948070i	$-0.603032\pi$
$23$	−37118.2	−0.636121	−0.318061	+	0.948070i	$0.603032\pi$
$24$	9372.01	0.138386
$25$	14185.2	0.181571
$26$	−92580.8	−1.03303
$27$	−19683.0	−0.192450
$28$	−87321.9	−0.751744
$29$	−59769.3	−0.455077	−0.227539	−	0.973769i	$-0.573068\pi$
$29$	−59769.3	−0.455077	−0.227539	+	0.973769i	$0.573068\pi$
$30$	125291.	0.847221
$31$	−21301.7	−0.128425	−0.0642124	−	0.997936i	$-0.520454\pi$
$31$	−21301.7	−0.128425	−0.0642124	+	0.997936i	$0.520454\pi$
$32$	−242349.	−1.30742
$33$	−35937.0	−0.174078
$34$	−37706.8	−0.164529
$35$	252017.	0.993554
$36$	76744.2	0.274149
$37$	330635.	1.07311	0.536553	−	0.843866i	$-0.319726\pi$
$37$	330635.	1.07311	0.536553	+	0.843866i	$0.319726\pi$
$38$	643620.	1.90277
$39$	163664.	0.441800
$40$	105462.	0.260546
$41$	816862.	1.85099	0.925497	−	0.378754i	$-0.123647\pi$
$41$	816862.	1.85099	0.925497	+	0.378754i	$0.123647\pi$
$42$	342059.	0.712408
$43$	−958652.	−1.83874	−0.919372	−	0.393389i	$-0.871303\pi$
$43$	−958652.	−1.83874	−0.919372	+	0.393389i	$0.871303\pi$
$44$	140119.	0.247977
$45$	−221489.	−0.362334
$46$	−566917.	−0.858751
$47$	38915.5	0.0546739	0.0273369	−	0.999626i	$-0.491297\pi$
$47$	38915.5	0.0546739	0.0273369	+	0.999626i	$0.491297\pi$
$48$	506966.	0.661659
$49$	−135509.	−0.164544
$50$	216655.	0.245118
$51$	66657.8	0.0703648
$52$	−638126.	−0.629354
$53$	−1.47350e6	−1.35952	−0.679759	−	0.733436i	$-0.737916\pi$
$53$	−1.47350e6	−1.35952	−0.679759	+	0.733436i	$0.737916\pi$
$54$	−300624.	−0.259804
$55$	−404392.	−0.327743
$56$	287921.	0.219087
$57$	−1.13779e6	−0.813764
$58$	−912873.	−0.614345
$59$	1.59205e6	1.00919	0.504597	−	0.863355i	$-0.331641\pi$
$59$	1.59205e6	1.00919	0.504597	+	0.863355i	$0.331641\pi$
$60$	863589.	0.516152
$61$	−3.08178e6	−1.73839	−0.869196	−	0.494468i	$-0.835363\pi$
$61$	−3.08178e6	−1.73839	−0.869196	+	0.494468i	$0.835363\pi$
$62$	−325347.	−0.173371
$63$	−604689.	−0.304678
$64$	−1.29807e6	−0.618968
$65$	1.84168e6	0.831795
$66$	−548876.	−0.235001
$67$	−1.59464e6	−0.647739	−0.323870	−	0.946102i	$-0.604984\pi$
$67$	−1.59464e6	−0.647739	−0.323870	+	0.946102i	$0.604984\pi$
$68$	−259900.	−0.100236
$69$	1.00219e6	0.367265
$70$	3.84913e6	1.34128
$71$	−2.69496e6	−0.893609	−0.446805	−	0.894632i	$-0.647438\pi$
$71$	−2.69496e6	−0.893609	−0.446805	+	0.894632i	$0.647438\pi$
$72$	−253044.	−0.0798975
$73$	−4.48213e6	−1.34851	−0.674255	−	0.738499i	$-0.735535\pi$
$73$	−4.48213e6	−1.34851	−0.674255	+	0.738499i	$0.735535\pi$
$74$	5.04989e6	1.44867
$75$	−383002.	−0.104830
$76$	4.43624e6	1.15922
$77$	−1.10404e6	−0.275591
$78$	2.49968e6	0.596422
$79$	−1.41084e6	−0.321947	−0.160973	−	0.986959i	$-0.551463\pi$
$79$	−1.41084e6	−0.321947	−0.160973	+	0.986959i	$0.551463\pi$
$80$	5.70479e6	1.24573
$81$	531441.	0.111111
$82$	1.24762e7	2.49881
$83$	653174.	0.125388	0.0626939	−	0.998033i	$-0.480031\pi$
$83$	653174.	0.125388	0.0626939	+	0.998033i	$0.480031\pi$
$84$	2.35769e6	0.434020
$85$	750088.	0.132479
$86$	−1.46418e7	−2.48227
$87$	1.61377e6	0.262739
$88$	−462006.	−0.0722700
$89$	2.32673e6	0.349850	0.174925	−	0.984582i	$-0.444032\pi$
$89$	2.32673e6	0.349850	0.174925	+	0.984582i	$0.444032\pi$
$90$	−3.38287e6	−0.489143
$91$	5.02798e6	0.699437
$92$	−3.90756e6	−0.523176
$93$	575146.	0.0741460
$94$	594367.	0.0738087
$95$	−1.28033e7	−1.53211
$96$	6.54342e6	0.754841
$97$	−2.16642e6	−0.241014	−0.120507	−	0.992712i	$-0.538452\pi$
$97$	−2.16642e6	−0.241014	−0.120507	+	0.992712i	$0.538452\pi$
$98$	−2.06967e6	−0.222131
$99$	970299.	0.100504
$100$	1.49333e6	0.149333
$101$	6.34311e6	0.612600	0.306300	−	0.951935i	$-0.400909\pi$
$101$	6.34311e6	0.612600	0.306300	+	0.951935i	$0.400909\pi$
$102$	1.01808e6	0.0949911
$103$	5.53067e6	0.498709	0.249355	−	0.968412i	$-0.419782\pi$
$103$	5.53067e6	0.498709	0.249355	+	0.968412i	$0.419782\pi$
$104$	2.10406e6	0.183418
$105$	−6.80446e6	−0.573629
$106$	−2.25052e7	−1.83532
$107$	−1.24836e7	−0.985141	−0.492570	−	0.870273i	$-0.663943\pi$
$107$	−1.24836e7	−0.985141	−0.492570	+	0.870273i	$0.663943\pi$
$108$	−2.07209e6	−0.158280
$109$	1.15577e7	0.854831	0.427416	−	0.904055i	$-0.359424\pi$
$109$	1.15577e7	0.854831	0.427416	+	0.904055i	$0.359424\pi$
$110$	−6.17640e6	−0.442447
$111$	−8.92715e6	−0.619559
$112$	1.55747e7	1.04751
$113$	2.91312e7	1.89926	0.949629	−	0.313378i	$-0.101461\pi$
$113$	2.91312e7	1.89926	0.949629	+	0.313378i	$0.101461\pi$
$114$	−1.73777e7	−1.09857
$115$	1.12775e7	0.691464
$116$	−6.29211e6	−0.374277
$117$	−4.41892e6	−0.255074
$118$	2.43158e7	1.36239
$119$	2.04782e6	0.111398
$120$	−2.84746e6	−0.150426
$121$	1.77156e6	0.0909091
$122$	−4.70689e7	−2.34679
$123$	−2.20553e7	−1.06867
$124$	−2.24250e6	−0.105623
$125$	1.94266e7	0.889633
$126$	−9.23560e6	−0.411309
$127$	−4.29589e7	−1.86097	−0.930487	−	0.366326i	$-0.880616\pi$
$127$	−4.29589e7	−1.86097	−0.930487	+	0.366326i	$0.880616\pi$
$128$	1.11949e7	0.471828
$129$	2.58836e7	1.06160
$130$	2.81285e7	1.12291
$131$	3.87619e7	1.50645	0.753226	−	0.657761i	$-0.228496\pi$
$131$	3.87619e7	1.50645	0.753226	+	0.657761i	$0.228496\pi$
$132$	−3.78321e6	−0.143170
$133$	−3.49544e7	−1.28831
$134$	−2.43554e7	−0.874436
$135$	5.98021e6	0.209193
$136$	856952.	0.0292126
$137$	2.16108e7	0.718040	0.359020	−	0.933330i	$-0.383111\pi$
$137$	2.16108e7	0.718040	0.359020	+	0.933330i	$0.383111\pi$
$138$	1.53068e7	0.495800
$139$	−1.06241e7	−0.335537	−0.167769	−	0.985826i	$-0.553656\pi$
$139$	−1.06241e7	−0.335537	−0.167769	+	0.985826i	$0.553656\pi$
$140$	2.65307e7	0.817146
$141$	−1.05072e6	−0.0315660
$142$	−4.11609e7	−1.20636
$143$	−8.06801e6	−0.230723
$144$	−1.36881e7	−0.382009
$145$	1.81595e7	0.494669
$146$	−6.84568e7	−1.82046
$147$	3.65875e6	0.0949996
$148$	3.48070e7	0.882574
$149$	6.36303e7	1.57584	0.787920	−	0.615777i	$-0.211158\pi$
$149$	6.36303e7	1.57584	0.787920	+	0.615777i	$0.211158\pi$
$150$	−5.84969e6	−0.141519
$151$	−1.42528e7	−0.336885	−0.168443	−	0.985711i	$-0.553874\pi$
$151$	−1.42528e7	−0.336885	−0.168443	+	0.985711i	$0.553874\pi$
$152$	−1.46274e7	−0.337842
$153$	−1.79976e6	−0.0406251
$154$	−1.68622e7	−0.372043
$155$	6.47202e6	0.139598
$156$	1.72294e7	0.363358
$157$	−1.42133e7	−0.293119	−0.146560	−	0.989202i	$-0.546820\pi$
$157$	−1.42133e7	−0.293119	−0.146560	+	0.989202i	$0.546820\pi$
$158$	−2.15482e7	−0.434622
$159$	3.97845e7	0.784918
$160$	7.36319e7	1.42117
$161$	3.07888e7	0.581436
$162$	8.11685e6	0.149998
$163$	8.04737e7	1.45545	0.727725	−	0.685869i	$-0.240578\pi$
$163$	8.04737e7	1.45545	0.727725	+	0.685869i	$0.240578\pi$
$164$	8.59937e7	1.52235
$165$	1.09186e7	0.189223
$166$	9.97611e6	0.169271
$167$	7.01073e6	0.116481	0.0582406	−	0.998303i	$-0.481451\pi$
$167$	7.01073e6	0.116481	0.0582406	+	0.998303i	$0.481451\pi$
$168$	−7.77388e6	−0.126490
$169$	−2.60053e7	−0.414438
$170$	1.14563e7	0.178844
$171$	3.07202e7	0.469827
$172$	−1.00920e8	−1.51227
$173$	−1.81447e7	−0.266433	−0.133216	−	0.991087i	$-0.542531\pi$
$173$	−1.81447e7	−0.266433	−0.133216	+	0.991087i	$0.542531\pi$
$174$	2.46476e7	0.354692
$175$	−1.17664e7	−0.165962
$176$	−2.49915e7	−0.345540
$177$	−4.29853e7	−0.582658
$178$	3.55369e7	0.472291
$179$	−1.16784e8	−1.52195	−0.760973	−	0.648784i	$-0.775278\pi$
$179$	−1.16784e8	−1.52195	−0.760973	+	0.648784i	$0.775278\pi$
$180$	−2.33169e7	−0.298000
$181$	−9.11199e7	−1.14219	−0.571095	−	0.820884i	$-0.693481\pi$
$181$	−9.11199e7	−1.14219	−0.571095	+	0.820884i	$0.693481\pi$
$182$	7.67937e7	0.944226
$183$	8.32081e7	1.00366
$184$	1.28842e7	0.152473
$185$	−1.00456e8	−1.16647
$186$	8.78437e6	0.100096
$187$	−3.28598e6	−0.0367468
$188$	4.09676e6	0.0449664
$189$	1.63266e7	0.175906
$190$	−1.95548e8	−2.06832
$191$	−1.82885e8	−1.89916	−0.949581	−	0.313522i	$-0.898491\pi$
$191$	−1.82885e8	−1.89916	−0.949581	+	0.313522i	$0.898491\pi$
$192$	3.50479e7	0.357361
$193$	1.32994e8	1.33163	0.665814	−	0.746118i	$-0.268084\pi$
$193$	1.32994e8	1.33163	0.665814	+	0.746118i	$0.268084\pi$
$194$	−3.30884e7	−0.325364
$195$	−4.97253e7	−0.480237
$196$	−1.42655e7	−0.135329
$197$	−2.82339e7	−0.263111	−0.131555	−	0.991309i	$-0.541997\pi$
$197$	−2.82339e7	−0.263111	−0.131555	+	0.991309i	$0.541997\pi$
$198$	1.48197e7	0.135678
$199$	−1.99071e8	−1.79070	−0.895350	−	0.445362i	$-0.853075\pi$
$199$	−1.99071e8	−1.79070	−0.895350	+	0.445362i	$0.853075\pi$
$200$	−4.92386e6	−0.0435212
$201$	4.30552e7	0.373973
$202$	9.68801e7	0.826999
$203$	4.95773e7	0.415955
$204$	7.01729e6	0.0578714
$205$	−2.48184e8	−2.01203
$206$	8.44715e7	0.673248
$207$	−2.70592e7	−0.212040
$208$	1.13816e8	0.876964
$209$	5.60887e7	0.424975
$210$	−1.03926e8	−0.774388
$211$	3.80016e7	0.278493	0.139246	−	0.990258i	$-0.455532\pi$
$211$	3.80016e7	0.278493	0.139246	+	0.990258i	$0.455532\pi$
$212$	−1.55120e8	−1.11813
$213$	7.27638e7	0.515926
$214$	−1.90666e8	−1.32992
$215$	2.91263e8	1.99872
$216$	6.83220e6	0.0461288
$217$	1.76693e7	0.117384
$218$	1.76525e8	1.15401
$219$	1.21017e8	0.778563
$220$	−4.25717e7	−0.269552
$221$	1.49650e7	0.0932616
$222$	−1.36347e8	−0.836392
$223$	1.14601e8	0.692022	0.346011	−	0.938230i	$-0.387536\pi$
$223$	1.14601e8	0.692022	0.346011	+	0.938230i	$0.387536\pi$
$224$	2.01023e8	1.19503
$225$	1.03410e7	0.0605237
$226$	4.44929e8	2.56396
$227$	−9.29427e7	−0.527381	−0.263691	−	0.964607i	$-0.584940\pi$
$227$	−9.29427e7	−0.527381	−0.263691	+	0.964607i	$0.584940\pi$
$228$	−1.19779e8	−0.669279
$229$	3.51772e8	1.93569	0.967847	−	0.251541i	$-0.0809374\pi$
$229$	3.51772e8	1.93569	0.967847	+	0.251541i	$0.0809374\pi$
$230$	1.72244e8	0.933464
$231$	2.98090e7	0.159113
$232$	2.07466e7	0.109079
$233$	1.90315e8	0.985661	0.492831	−	0.870125i	$-0.335962\pi$
$233$	1.90315e8	0.985661	0.492831	+	0.870125i	$0.335962\pi$
$234$	−6.74914e7	−0.344344
$235$	−1.18235e7	−0.0594306
$236$	1.67600e8	0.830009
$237$	3.80928e7	0.185876
$238$	3.12770e7	0.150385
$239$	−2.00720e8	−0.951038	−0.475519	−	0.879705i	$-0.657740\pi$
$239$	−2.00720e8	−0.951038	−0.475519	+	0.879705i	$0.657740\pi$
$240$	−1.54029e8	−0.719224
$241$	−2.08229e8	−0.958258	−0.479129	−	0.877745i	$-0.659047\pi$
$241$	−2.08229e8	−0.958258	−0.479129	+	0.877745i	$0.659047\pi$
$242$	2.70576e7	0.122726
$243$	−1.43489e7	−0.0641500
$244$	−3.24429e8	−1.42974
$245$	4.11712e7	0.178860
$246$	−3.36856e8	−1.44269
$247$	−2.55438e8	−1.07856
$248$	7.39407e6	0.0307824
$249$	−1.76357e7	−0.0723927
$250$	2.96707e8	1.20099
$251$	−4.78103e7	−0.190837	−0.0954186	−	0.995437i	$-0.530419\pi$
$251$	−4.78103e7	−0.190837	−0.0954186	+	0.995437i	$0.530419\pi$
$252$	−6.36577e7	−0.250581
$253$	−4.94044e7	−0.191798
$254$	−6.56124e8	−2.51228
$255$	−2.02524e7	−0.0764866
$256$	3.37135e8	1.25593
$257$	−2.02303e8	−0.743425	−0.371712	−	0.928348i	$-0.621229\pi$
$257$	−2.02303e8	−0.743425	−0.371712	+	0.928348i	$0.621229\pi$
$258$	3.95328e8	1.43314
$259$	−2.74255e8	−0.980855
$260$	1.93879e8	0.684108
$261$	−4.35718e7	−0.151692
$262$	5.92022e8	2.03368
$263$	−4.06426e8	−1.37764	−0.688822	−	0.724931i	$-0.741872\pi$
$263$	−4.06426e8	−1.37764	−0.688822	+	0.724931i	$0.741872\pi$
$264$	1.24741e7	0.0417251
$265$	4.47688e8	1.47780
$266$	−5.33869e8	−1.73920
$267$	−6.28218e7	−0.201986
$268$	−1.67873e8	−0.532732
$269$	5.29696e8	1.65918	0.829590	−	0.558373i	$-0.188574\pi$
$269$	5.29696e8	1.65918	0.829590	+	0.558373i	$0.188574\pi$
$270$	9.13374e7	0.282407
$271$	−4.79694e8	−1.46410	−0.732051	−	0.681249i	$-0.761437\pi$
$271$	−4.79694e8	−1.46410	−0.732051	+	0.681249i	$0.761437\pi$
$272$	4.63556e7	0.139673
$273$	−1.35755e8	−0.403820
$274$	3.30068e8	0.969340
$275$	1.88806e7	0.0547458
$276$	1.05504e8	0.302056
$277$	5.74020e8	1.62274	0.811369	−	0.584535i	$-0.198723\pi$
$277$	5.74020e8	1.62274	0.811369	+	0.584535i	$0.198723\pi$
$278$	−1.62265e8	−0.452969
$279$	−1.55290e7	−0.0428082
$280$	−8.74780e7	−0.238147
$281$	−5.08869e8	−1.36815	−0.684075	−	0.729412i	$-0.739794\pi$
$281$	−5.08869e8	−1.36815	−0.684075	+	0.729412i	$0.739794\pi$
$282$	−1.60479e7	−0.0426135
$283$	1.55996e8	0.409130	0.204565	−	0.978853i	$-0.434422\pi$
$283$	1.55996e8	0.409130	0.204565	+	0.978853i	$0.434422\pi$
$284$	−2.83707e8	−0.734947
$285$	3.45689e8	0.884563
$286$	−1.23225e8	−0.311471
$287$	−6.77569e8	−1.69187
$288$	−1.76672e8	−0.435808
$289$	−4.04244e8	−0.985146
$290$	2.77355e8	0.667794
$291$	5.84934e7	0.139149
$292$	−4.71848e8	−1.10908
$293$	3.31026e8	0.768821	0.384411	−	0.923162i	$-0.374405\pi$
$293$	3.31026e8	0.768821	0.384411	+	0.923162i	$0.374405\pi$
$294$	5.58811e7	0.128248
$295$	−4.83706e8	−1.09699
$296$	−1.14767e8	−0.257216
$297$	−2.61981e7	−0.0580259
$298$	9.71845e8	2.12735
$299$	2.24996e8	0.486773
$300$	−4.03198e7	−0.0862173
$301$	7.95181e8	1.68067
$302$	−2.17688e8	−0.454788
$303$	−1.71264e8	−0.353685
$304$	−7.91247e8	−1.61530
$305$	9.36326e8	1.88963
$306$	−2.74883e7	−0.0548432
$307$	−1.59688e8	−0.314983	−0.157491	−	0.987520i	$-0.550341\pi$
$307$	−1.59688e8	−0.314983	−0.157491	+	0.987520i	$0.550341\pi$
$308$	−1.16225e8	−0.226659
$309$	−1.49328e8	−0.287930
$310$	9.88489e7	0.188454
$311$	3.51157e8	0.661973	0.330986	−	0.943636i	$-0.392619\pi$
$311$	3.51157e8	0.661973	0.330986	+	0.943636i	$0.392619\pi$
$312$	−5.68095e7	−0.105896
$313$	−5.46772e8	−1.00786	−0.503931	−	0.863744i	$-0.668114\pi$
$313$	−5.46772e8	−1.00786	−0.503931	+	0.863744i	$0.668114\pi$
$314$	−2.17083e8	−0.395706
$315$	1.83720e8	0.331185
$316$	−1.48524e8	−0.264784
$317$	−6.18068e8	−1.08975	−0.544877	−	0.838516i	$-0.683424\pi$
$317$	−6.18068e8	−1.08975	−0.544877	+	0.838516i	$0.683424\pi$
$318$	6.07640e8	1.05962
$319$	−7.95529e7	−0.137211
$320$	3.94387e8	0.672818
$321$	3.37058e8	0.568771
$322$	4.70246e8	0.784927
$323$	−1.04036e8	−0.171781
$324$	5.59465e7	0.0913831
$325$	−8.59855e7	−0.138942
$326$	1.22910e9	1.96483
$327$	−3.12059e8	−0.493537
$328$	−2.83542e8	−0.443669
$329$	−3.22795e7	−0.0499737
$330$	1.66763e8	0.255447
$331$	−6.84846e8	−1.03799	−0.518997	−	0.854776i	$-0.673694\pi$
$331$	−6.84846e8	−1.03799	−0.518997	+	0.854776i	$0.673694\pi$
$332$	6.87618e7	0.103125
$333$	2.41033e8	0.357702
$334$	1.07077e8	0.157247
$335$	4.84493e8	0.704093
$336$	−4.20517e8	−0.604778
$337$	1.19934e6	0.00170701	0.000853507	−	1.00000i	$-0.499728\pi$
$337$	1.19934e6	0.00170701	0.000853507		1.00000i	$0.499728\pi$
$338$	−3.97187e8	−0.559483
$339$	−7.86542e8	−1.09654
$340$	7.89643e7	0.108957
$341$	−2.83526e7	−0.0387215
$342$	4.69199e8	0.634258
$343$	7.95513e8	1.06443
$344$	3.32759e8	0.440733
$345$	−3.04492e8	−0.399217
$346$	−2.77129e8	−0.359679
$347$	−2.08559e8	−0.267964	−0.133982	−	0.990984i	$-0.542776\pi$
$347$	−2.08559e8	−0.267964	−0.133982	+	0.990984i	$0.542776\pi$
$348$	1.69887e8	0.216089
$349$	1.13428e7	0.0142834	0.00714172	−	0.999974i	$-0.497727\pi$
$349$	1.13428e7	0.0142834	0.00714172	+	0.999974i	$0.497727\pi$
$350$	−1.79711e8	−0.224045
$351$	1.19311e8	0.147267
$352$	−3.22566e8	−0.394203
$353$	5.47130e8	0.662032	0.331016	−	0.943625i	$-0.392609\pi$
$353$	5.47130e8	0.662032	0.331016	+	0.943625i	$0.392609\pi$
$354$	−6.56527e8	−0.786577
$355$	8.18798e8	0.971354
$356$	2.44943e8	0.287733
$357$	−5.52912e7	−0.0643157
$358$	−1.78368e9	−2.05460
$359$	1.04623e9	1.19343	0.596715	−	0.802453i	$-0.296472\pi$
$359$	1.04623e9	1.19343	0.596715	+	0.802453i	$0.296472\pi$
$360$	7.68815e7	0.0868486
$361$	8.81928e8	0.986638
$362$	−1.39170e9	−1.54193
$363$	−4.78321e7	−0.0524864
$364$	5.29312e8	0.575250
$365$	1.36179e9	1.46583
$366$	1.27086e9	1.35492
$367$	4.80538e8	0.507453	0.253727	−	0.967276i	$-0.418344\pi$
$367$	4.80538e8	0.507453	0.253727	+	0.967276i	$0.418344\pi$
$368$	6.96951e8	0.729013
$369$	5.95492e8	0.616998
$370$	−1.53429e9	−1.57471
$371$	1.22224e9	1.24264
$372$	6.05475e7	0.0609812
$373$	−1.45793e9	−1.45464	−0.727320	−	0.686298i	$-0.759235\pi$
$373$	−1.45793e9	−1.45464	−0.727320	+	0.686298i	$0.759235\pi$
$374$	−5.01878e7	−0.0496075
$375$	−5.24517e8	−0.513630
$376$	−1.35080e7	−0.0131049
$377$	3.62298e8	0.348234
$378$	2.49361e8	0.237469
$379$	−1.16963e8	−0.110359	−0.0551797	−	0.998476i	$-0.517573\pi$
$379$	−1.16963e8	−0.110359	−0.0551797	+	0.998476i	$0.517573\pi$
$380$	−1.34785e9	−1.26008
$381$	1.15989e9	1.07443
$382$	−2.79326e9	−2.56383
$383$	−1.54022e9	−1.40084	−0.700418	−	0.713732i	$-0.747003\pi$
$383$	−1.54022e9	−1.40084	−0.700418	+	0.713732i	$0.747003\pi$
$384$	−3.02261e8	−0.272410
$385$	3.35435e8	0.299568
$386$	2.03126e9	1.79767
$387$	−6.98857e8	−0.612915
$388$	−2.28066e8	−0.198221
$389$	6.82704e8	0.588043	0.294022	−	0.955799i	$-0.405006\pi$
$389$	6.82704e8	0.588043	0.294022	+	0.955799i	$0.405006\pi$
$390$	−7.59468e8	−0.648311
$391$	9.16378e7	0.0775276
$392$	4.70368e7	0.0394400
$393$	−1.04657e9	−0.869751
$394$	−4.31224e8	−0.355195
$395$	4.28651e8	0.349957
$396$	1.02147e8	0.0826591
$397$	−4.39437e8	−0.352476	−0.176238	−	0.984348i	$-0.556393\pi$
$397$	−4.39437e8	−0.352476	−0.176238	+	0.984348i	$0.556393\pi$
$398$	−3.04047e9	−2.41741
$399$	9.43769e8	0.743807
$400$	−2.66350e8	−0.208086
$401$	−1.92220e9	−1.48865	−0.744326	−	0.667816i	$-0.767229\pi$
$401$	−1.92220e9	−1.48865	−0.744326	+	0.667816i	$0.767229\pi$
$402$	6.57595e8	0.504856
$403$	1.29123e8	0.0982732
$404$	6.67760e8	0.503832
$405$	−1.61466e8	−0.120778
$406$	7.57208e8	0.561532
$407$	4.40075e8	0.323554
$408$	−2.31377e7	−0.0168659
$409$	−5.70106e8	−0.412026	−0.206013	−	0.978549i	$-0.566049\pi$
$409$	−5.70106e8	−0.412026	−0.206013	+	0.978549i	$0.566049\pi$
$410$	−3.79058e9	−2.71621
$411$	−5.83492e8	−0.414561
$412$	5.82232e8	0.410162
$413$	−1.32057e9	−0.922436
$414$	−4.13283e8	−0.286250
$415$	−1.98451e8	−0.136297
$416$	1.46903e9	1.00047
$417$	2.86851e8	0.193723
$418$	8.56658e8	0.573708
$419$	−1.12807e9	−0.749179	−0.374589	−	0.927191i	$-0.622216\pi$
$419$	−1.12807e9	−0.749179	−0.374589	+	0.927191i	$0.622216\pi$
$420$	−7.16328e8	−0.471780
$421$	2.91413e9	1.90336	0.951681	−	0.307089i	$-0.0993549\pi$
$421$	2.91413e9	1.90336	0.951681	+	0.307089i	$0.0993549\pi$
$422$	5.80410e8	0.375960
$423$	2.83694e7	0.0182246
$424$	5.11469e8	0.325866
$425$	−3.50207e7	−0.0221291
$426$	1.11134e9	0.696489
$427$	2.55627e9	1.58895
$428$	−1.31419e9	−0.810226
$429$	2.17836e8	0.133208
$430$	4.44855e9	2.69823
$431$	8.77990e8	0.528225	0.264113	−	0.964492i	$-0.414921\pi$
$431$	8.77990e8	0.528225	0.264113	+	0.964492i	$0.414921\pi$
$432$	3.69578e8	0.220553
$433$	−7.45894e8	−0.441539	−0.220770	−	0.975326i	$-0.570857\pi$
$433$	−7.45894e8	−0.441539	−0.220770	+	0.975326i	$0.570857\pi$
$434$	2.69868e8	0.158467
$435$	−4.90305e8	−0.285597
$436$	1.21672e9	0.703054
$437$	−1.56417e9	−0.896601
$438$	1.84833e9	1.05104
$439$	3.31044e8	0.186749	0.0933747	−	0.995631i	$-0.470235\pi$
$439$	3.31044e8	0.186749	0.0933747	+	0.995631i	$0.470235\pi$
$440$	1.40369e8	0.0785575
$441$	−9.87862e7	−0.0548480
$442$	2.28564e8	0.125901
$443$	−1.92657e9	−1.05286	−0.526432	−	0.850217i	$-0.676470\pi$
$443$	−1.92657e9	−1.05286	−0.526432	+	0.850217i	$0.676470\pi$
$444$	−9.39790e8	−0.509554
$445$	−7.06922e8	−0.380287
$446$	1.75033e9	0.934217
$447$	−1.71802e9	−0.909812
$448$	1.07672e9	0.565757
$449$	3.35149e8	0.174733	0.0873667	−	0.996176i	$-0.472155\pi$
$449$	3.35149e8	0.174733	0.0873667	+	0.996176i	$0.472155\pi$
$450$	1.57942e8	0.0817058
$451$	1.08724e9	0.558096
$452$	3.06674e9	1.56204
$453$	3.84826e8	0.194501
$454$	−1.41954e9	−0.711955
$455$	−1.52763e9	−0.760288
$456$	3.94939e8	0.195053
$457$	−9.81385e8	−0.480986	−0.240493	−	0.970651i	$-0.577309\pi$
$457$	−9.81385e8	−0.480986	−0.240493	+	0.970651i	$0.577309\pi$
$458$	5.37271e9	2.61315
$459$	4.85936e7	0.0234549
$460$	1.18722e9	0.568693
$461$	−7.99148e8	−0.379904	−0.189952	−	0.981793i	$-0.560833\pi$
$461$	−7.99148e8	−0.379904	−0.189952	+	0.981793i	$0.560833\pi$
$462$	4.55281e8	0.214799
$463$	−1.01685e9	−0.476128	−0.238064	−	0.971249i	$-0.576513\pi$
$463$	−1.01685e9	−0.476128	−0.238064	+	0.971249i	$0.576513\pi$
$464$	1.12226e9	0.521531
$465$	−1.74744e8	−0.0805968
$466$	2.90674e9	1.33062
$467$	−2.83923e9	−1.29000	−0.645002	−	0.764181i	$-0.723143\pi$
$467$	−2.83923e9	−1.29000	−0.645002	+	0.764181i	$0.723143\pi$
$468$	−4.65194e8	−0.209785
$469$	1.32272e9	0.592055
$470$	−1.80584e8	−0.0802301
$471$	3.83758e8	0.169233
$472$	−5.52619e8	−0.241896
$473$	−1.27597e9	−0.554402
$474$	5.81802e8	0.250929
$475$	5.97770e8	0.255921
$476$	2.15581e8	0.0916191
$477$	−1.07418e9	−0.453172
$478$	−3.06565e9	−1.28388
$479$	3.24833e9	1.35047	0.675236	−	0.737602i	$-0.264042\pi$
$479$	3.24833e9	1.35047	0.675236	+	0.737602i	$0.264042\pi$
$480$	−1.98806e9	−0.820513
$481$	−2.00418e9	−0.821163
$482$	−3.18035e9	−1.29363
$483$	−8.31297e8	−0.335692
$484$	1.86498e8	0.0747680
$485$	6.58215e8	0.261982
$486$	−2.19155e8	−0.0866013
$487$	−6.55732e8	−0.257262	−0.128631	−	0.991693i	$-0.541058\pi$
$487$	−6.55732e8	−0.257262	−0.128631	+	0.991693i	$0.541058\pi$
$488$	1.06972e9	0.416679
$489$	−2.17279e9	−0.840304
$490$	6.28820e8	0.241457
$491$	9.37028e8	0.357246	0.178623	−	0.983918i	$-0.442836\pi$
$491$	9.37028e8	0.357246	0.178623	+	0.983918i	$0.442836\pi$
$492$	−2.32183e9	−0.878927
$493$	1.47559e8	0.0554627
$494$	−3.90138e9	−1.45604
$495$	−2.94802e8	−0.109248
$496$	3.99972e8	0.147178
$497$	2.23541e9	0.816788
$498$	−2.69355e8	−0.0977288
$499$	−5.07602e9	−1.82882	−0.914411	−	0.404786i	$-0.867346\pi$
$499$	−5.07602e9	−1.82882	−0.914411	+	0.404786i	$0.867346\pi$
$500$	2.04510e9	0.731676
$501$	−1.89290e8	−0.0672504
$502$	−7.30220e8	−0.257627
$503$	−3.30955e9	−1.15953	−0.579763	−	0.814785i	$-0.696855\pi$
$503$	−3.30955e9	−1.15953	−0.579763	+	0.814785i	$0.696855\pi$
$504$	2.09895e8	0.0730289
$505$	−1.92720e9	−0.665897
$506$	−7.54567e8	−0.258923
$507$	7.02144e8	0.239276
$508$	−4.52242e9	−1.53055
$509$	−5.09686e8	−0.171313	−0.0856566	−	0.996325i	$-0.527299\pi$
$509$	−5.09686e8	−0.171313	−0.0856566	+	0.996325i	$0.527299\pi$
$510$	−3.09320e8	−0.103255
$511$	3.71783e9	1.23258
$512$	3.71622e9	1.22365
$513$	−8.29446e8	−0.271255
$514$	−3.08984e9	−1.00361
$515$	−1.68036e9	−0.542097
$516$	2.72485e9	0.873110
$517$	5.17965e7	0.0164848
$518$	−4.18877e9	−1.32413
$519$	4.89906e8	0.153825
$520$	−6.39267e8	−0.199375
$521$	4.24284e9	1.31439	0.657196	−	0.753720i	$-0.271742\pi$
$521$	4.24284e9	1.31439	0.657196	+	0.753720i	$0.271742\pi$
$522$	−6.65485e8	−0.204782
$523$	4.77407e9	1.45926	0.729630	−	0.683843i	$-0.239692\pi$
$523$	4.77407e9	1.45926	0.729630	+	0.683843i	$0.239692\pi$
$524$	4.08059e9	1.23898
$525$	3.17691e8	0.0958182
$526$	−6.20747e9	−1.85979
$527$	5.25899e7	0.0156518
$528$	6.74772e8	0.199498
$529$	−2.02706e9	−0.595350
$530$	6.83766e9	1.99500
$531$	1.16060e9	0.336398
$532$	−3.67976e9	−1.05957
$533$	−4.95150e9	−1.41642
$534$	−9.59496e8	−0.272677
$535$	3.79286e9	1.07085
$536$	5.53517e8	0.155258
$537$	3.15318e9	0.878696
$538$	8.09019e9	2.23986
$539$	−1.80363e8	−0.0496119
$540$	6.29556e8	0.172051
$541$	3.10457e9	0.842967	0.421483	−	0.906836i	$-0.361510\pi$
$541$	3.10457e9	0.842967	0.421483	+	0.906836i	$0.361510\pi$
$542$	−7.32650e9	−1.97651
$543$	2.46024e9	0.659443
$544$	5.98313e8	0.159343
$545$	−3.51154e9	−0.929202
$546$	−2.07343e9	−0.545149
$547$	5.81117e9	1.51813	0.759063	−	0.651017i	$-0.225658\pi$
$547$	5.81117e9	1.51813	0.759063	+	0.651017i	$0.225658\pi$
$548$	2.27504e9	0.590550
$549$	−2.24662e9	−0.579464
$550$	2.88368e8	0.0739057
$551$	−2.51869e9	−0.641423
$552$	−3.47873e8	−0.0880306
$553$	1.17026e9	0.294270
$554$	8.76718e9	2.19066
$555$	2.71230e9	0.673461
$556$	−1.11844e9	−0.275962
$557$	−4.69891e8	−0.115214	−0.0576068	−	0.998339i	$-0.518347\pi$
$557$	−4.69891e8	−0.115214	−0.0576068	+	0.998339i	$0.518347\pi$
$558$	−2.37178e8	−0.0577903
$559$	5.81098e9	1.40705
$560$	−4.73200e9	−1.13864
$561$	8.87216e7	0.0212158
$562$	−7.77209e9	−1.84697
$563$	4.00223e9	0.945199	0.472599	−	0.881277i	$-0.343316\pi$
$563$	4.00223e9	0.945199	0.472599	+	0.881277i	$0.343316\pi$
$564$	−1.10613e8	−0.0259614
$565$	−8.85082e9	−2.06449
$566$	2.38258e9	0.552318
$567$	−4.40819e8	−0.101559
$568$	9.35451e8	0.214191
$569$	1.36018e9	0.309530	0.154765	−	0.987951i	$-0.450538\pi$
$569$	1.36018e9	0.309530	0.154765	+	0.987951i	$0.450538\pi$
$570$	5.27981e9	1.19414
$571$	5.92967e9	1.33292	0.666461	−	0.745540i	$-0.267808\pi$
$571$	5.92967e9	1.33292	0.666461	+	0.745540i	$0.267808\pi$
$572$	−8.49346e8	−0.189757
$573$	4.93790e9	1.09648
$574$	−1.03487e10	−2.28399
$575$	−5.26531e8	−0.115501
$576$	−9.46292e8	−0.206323
$577$	−5.08690e9	−1.10240	−0.551199	−	0.834374i	$-0.685829\pi$
$577$	−5.08690e9	−1.10240	−0.551199	+	0.834374i	$0.685829\pi$
$578$	−6.17413e9	−1.32993
$579$	−3.59085e9	−0.768816
$580$	1.91171e9	0.406840
$581$	−5.41793e8	−0.114609
$582$	8.93387e8	0.187849
$583$	−1.96123e9	−0.409910
$584$	1.55580e9	0.323228
$585$	1.34258e9	0.277265
$586$	5.05585e9	1.03789
$587$	−3.07480e9	−0.627456	−0.313728	−	0.949513i	$-0.601578\pi$
$587$	−3.07480e9	−0.627456	−0.313728	+	0.949513i	$0.601578\pi$
$588$	3.85168e8	0.0781322
$589$	−8.97659e8	−0.181012
$590$	−7.38778e9	−1.48092
$591$	7.62315e8	0.151907
$592$	−6.20818e9	−1.22981
$593$	4.96104e9	0.976970	0.488485	−	0.872572i	$-0.337550\pi$
$593$	4.96104e9	0.976970	0.488485	+	0.872572i	$0.337550\pi$
$594$	−4.00131e8	−0.0783338
$595$	−6.22182e8	−0.121090
$596$	6.69858e9	1.29605
$597$	5.37493e9	1.03386
$598$	3.43644e9	0.657134
$599$	4.34257e9	0.825568	0.412784	−	0.910829i	$-0.364557\pi$
$599$	4.34257e9	0.825568	0.412784	+	0.910829i	$0.364557\pi$
$600$	1.32944e8	0.0251270
$601$	1.77668e9	0.333848	0.166924	−	0.985970i	$-0.446617\pi$
$601$	1.77668e9	0.333848	0.166924	+	0.985970i	$0.446617\pi$
$602$	1.21450e10	2.26888
$603$	−1.16249e9	−0.215913
$604$	−1.50044e9	−0.277070
$605$	−5.38246e8	−0.0988183
$606$	−2.61576e9	−0.477468
$607$	−8.76418e9	−1.59056	−0.795282	−	0.606240i	$-0.792677\pi$
$607$	−8.76418e9	−1.59056	−0.795282	+	0.606240i	$0.792677\pi$
$608$	−1.02126e10	−1.84279
$609$	−1.33859e9	−0.240152
$610$	1.43008e10	2.55097
$611$	−2.35891e8	−0.0418376
$612$	−1.89467e8	−0.0334120
$613$	−1.13075e9	−0.198269	−0.0991346	−	0.995074i	$-0.531607\pi$
$613$	−1.13075e9	−0.198269	−0.0991346	+	0.995074i	$0.531607\pi$
$614$	−2.43895e9	−0.425221
$615$	6.70097e9	1.16165
$616$	3.83223e8	0.0660571
$617$	2.36299e7	0.00405008	0.00202504	−	0.999998i	$-0.499355\pi$
$617$	2.36299e7	0.00405008	0.00202504	+	0.999998i	$0.499355\pi$
$618$	−2.28073e9	−0.388700
$619$	5.90610e9	1.00088	0.500442	−	0.865770i	$-0.333171\pi$
$619$	5.90610e9	1.00088	0.500442	+	0.865770i	$0.333171\pi$
$620$	6.81330e8	0.114812
$621$	7.30598e8	0.122422
$622$	5.36332e9	0.893650
$623$	−1.92997e9	−0.319774
$624$	−3.07303e9	−0.506315
$625$	−7.01052e9	−1.14860
$626$	−8.35101e9	−1.36059
$627$	−1.51439e9	−0.245359
$628$	−1.49628e9	−0.241075
$629$	−8.16275e8	−0.130785
$630$	2.80601e9	0.447093
$631$	−3.87609e9	−0.614173	−0.307087	−	0.951682i	$-0.599354\pi$
$631$	−3.87609e9	−0.614173	−0.307087	+	0.951682i	$0.599354\pi$
$632$	4.89720e8	0.0771682
$633$	−1.02604e9	−0.160788
$634$	−9.43992e9	−1.47115
$635$	1.30520e10	2.02288
$636$	4.18825e9	0.645554
$637$	8.21404e8	0.125913
$638$	−1.21503e9	−0.185232
$639$	−1.96462e9	−0.297870
$640$	−3.40129e9	−0.512878
$641$	4.60264e9	0.690246	0.345123	−	0.938558i	$-0.387837\pi$
$641$	4.60264e9	0.690246	0.345123	+	0.938558i	$0.387837\pi$
$642$	5.14799e9	0.767830
$643$	1.10814e10	1.64383	0.821917	−	0.569607i	$-0.192905\pi$
$643$	1.10814e10	1.64383	0.821917	+	0.569607i	$0.192905\pi$
$644$	3.24123e9	0.478200
$645$	−7.86411e9	−1.15396
$646$	−1.58897e9	−0.231901
$647$	3.95562e9	0.574183	0.287091	−	0.957903i	$-0.407312\pi$
$647$	3.95562e9	0.574183	0.287091	+	0.957903i	$0.407312\pi$
$648$	−1.84469e8	−0.0266325
$649$	2.11902e9	0.304283
$650$	−1.31328e9	−0.187569
$651$	−4.77071e8	−0.0677719
$652$	8.47173e9	1.19703
$653$	−3.72327e9	−0.523274	−0.261637	−	0.965166i	$-0.584262\pi$
$653$	−3.72327e9	−0.523274	−0.261637	+	0.965166i	$0.584262\pi$
$654$	−4.76617e9	−0.666265
$655$	−1.17769e10	−1.63752
$656$	−1.53378e10	−2.12129
$657$	−3.26747e9	−0.449503
$658$	−4.93015e8	−0.0674636
$659$	−2.45031e9	−0.333520	−0.166760	−	0.985998i	$-0.553330\pi$
$659$	−2.45031e9	−0.333520	−0.166760	+	0.985998i	$0.553330\pi$
$660$	1.14944e9	0.155626
$661$	−4.82392e9	−0.649673	−0.324836	−	0.945770i	$-0.605309\pi$
$661$	−4.82392e9	−0.649673	−0.324836	+	0.945770i	$0.605309\pi$
$662$	−1.04599e10	−1.40127
$663$	−4.04054e8	−0.0538446
$664$	−2.26724e8	−0.0300545
$665$	1.06201e10	1.40040
$666$	3.68137e9	0.482891
$667$	2.21853e9	0.289484
$668$	7.38043e8	0.0957996
$669$	−3.09422e9	−0.399539
$670$	7.39979e9	0.950513
$671$	−4.10185e9	−0.524145
$672$	−5.42762e9	−0.689949
$673$	−2.17377e9	−0.274891	−0.137446	−	0.990509i	$-0.543889\pi$
$673$	−2.17377e9	−0.274891	−0.137446	+	0.990509i	$0.543889\pi$
$674$	1.83178e7	0.00230444
$675$	−2.79208e8	−0.0349434
$676$	−2.73767e9	−0.340853
$677$	−4.71648e9	−0.584194	−0.292097	−	0.956389i	$-0.594353\pi$
$677$	−4.71648e9	−0.584194	−0.292097	+	0.956389i	$0.594353\pi$
$678$	−1.20131e10	−1.48030
$679$	1.79700e9	0.220295
$680$	−2.60364e8	−0.0317541
$681$	2.50945e9	0.304484
$682$	−4.33037e8	−0.0522733
$683$	−6.72757e9	−0.807953	−0.403976	−	0.914769i	$-0.632372\pi$
$683$	−6.72757e9	−0.807953	−0.403976	+	0.914769i	$0.632372\pi$
$684$	3.23402e9	0.386408
$685$	−6.56592e9	−0.780510
$686$	1.21501e10	1.43696
$687$	−9.49783e9	−1.11757
$688$	1.80001e10	2.10725
$689$	8.93179e9	1.04033
$690$	−4.65060e9	−0.538935
$691$	−4.98106e9	−0.574313	−0.287157	−	0.957884i	$-0.592710\pi$
$691$	−4.98106e9	−0.574313	−0.287157	+	0.957884i	$0.592710\pi$
$692$	−1.91015e9	−0.219127
$693$	−8.04842e8	−0.0918637
$694$	−3.18538e9	−0.361746
$695$	3.22788e9	0.364729
$696$	−5.60158e8	−0.0629765
$697$	−2.01668e9	−0.225591
$698$	1.73242e8	0.0192824
$699$	−5.13851e9	−0.569072
$700$	−1.23868e9	−0.136495
$701$	4.43468e9	0.486238	0.243119	−	0.969996i	$-0.421829\pi$
$701$	4.43468e9	0.486238	0.243119	+	0.969996i	$0.421829\pi$
$702$	1.82227e9	0.198807
$703$	1.39330e10	1.51252
$704$	−1.72773e9	−0.186626
$705$	3.19236e8	0.0343123
$706$	8.35647e9	0.893730
$707$	−5.26147e9	−0.559937
$708$	−4.52521e9	−0.479206
$709$	−4.96472e9	−0.523158	−0.261579	−	0.965182i	$-0.584243\pi$
$709$	−4.96472e9	−0.523158	−0.261579	+	0.965182i	$0.584243\pi$
$710$	1.25057e10	1.31131
$711$	−1.02851e9	−0.107316
$712$	−8.07636e8	−0.0838563
$713$	7.90682e8	0.0816937
$714$	−8.44478e8	−0.0868250
$715$	2.45127e9	0.250796
$716$	−1.22943e10	−1.25172
$717$	5.41944e9	0.549082
$718$	1.59794e10	1.61111
$719$	7.62145e9	0.764692	0.382346	−	0.924019i	$-0.375116\pi$
$719$	7.62145e9	0.764692	0.382346	+	0.924019i	$0.375116\pi$
$720$	4.15879e9	0.415244
$721$	−4.58757e9	−0.455837
$722$	1.34699e10	1.33194
$723$	5.62219e9	0.553250
$724$	−9.59249e9	−0.939391
$725$	−8.47842e8	−0.0826289
$726$	−7.30554e8	−0.0708556
$727$	−9.67350e9	−0.933712	−0.466856	−	0.884333i	$-0.654613\pi$
$727$	−9.67350e9	−0.933712	−0.466856	+	0.884333i	$0.654613\pi$
$728$	−1.74527e9	−0.167650
$729$	3.87420e8	0.0370370
$730$	2.07990e10	1.97884
$731$	2.36673e9	0.224098
$732$	8.75959e9	0.825458
$733$	6.37101e9	0.597509	0.298755	−	0.954330i	$-0.403429\pi$
$733$	6.37101e9	0.597509	0.298755	+	0.954330i	$0.403429\pi$
$734$	7.33939e9	0.685052
$735$	−1.11162e9	−0.103265
$736$	8.99556e9	0.831679
$737$	−2.12246e9	−0.195301
$738$	9.09512e9	0.832936
$739$	1.16634e10	1.06309	0.531544	−	0.847031i	$-0.321612\pi$
$739$	1.16634e10	1.06309	0.531544	+	0.847031i	$0.321612\pi$
$740$	−1.05753e10	−0.959359
$741$	6.89682e9	0.622709
$742$	1.86676e10	1.67754
$743$	−1.87781e9	−0.167955	−0.0839773	−	0.996468i	$-0.526762\pi$
$743$	−1.87781e9	−0.167955	−0.0839773	+	0.996468i	$0.526762\pi$
$744$	−1.99640e8	−0.0177722
$745$	−1.93326e10	−1.71294
$746$	−2.22674e10	−1.96374
$747$	4.76164e8	0.0417960
$748$	−3.45926e8	−0.0302223
$749$	1.03549e10	0.900451
$750$	−8.01110e9	−0.693390
$751$	−1.89594e10	−1.63337	−0.816684	−	0.577085i	$-0.804190\pi$
$751$	−1.89594e10	−1.63337	−0.816684	+	0.577085i	$0.804190\pi$
$752$	−7.30697e8	−0.0626578
$753$	1.29088e9	0.110180
$754$	5.53349e9	0.470110
$755$	4.33038e9	0.366194
$756$	1.71876e9	0.144673
$757$	2.13638e9	0.178996	0.0894980	−	0.995987i	$-0.471474\pi$
$757$	2.13638e9	0.178996	0.0894980	+	0.995987i	$0.471474\pi$
$758$	−1.78640e9	−0.148983
$759$	1.33392e9	0.110735
$760$	4.44417e9	0.367235
$761$	−8.14245e9	−0.669744	−0.334872	−	0.942264i	$-0.608693\pi$
$761$	−8.14245e9	−0.669744	−0.334872	+	0.942264i	$0.608693\pi$
$762$	1.77153e10	1.45046
$763$	−9.58690e9	−0.781344
$764$	−1.92529e10	−1.56196
$765$	5.46814e8	0.0441596
$766$	−2.35242e10	−1.89110
$767$	−9.65039e9	−0.772256
$768$	−9.10265e9	−0.725110
$769$	3.93260e9	0.311844	0.155922	−	0.987769i	$-0.450165\pi$
$769$	3.93260e9	0.311844	0.155922	+	0.987769i	$0.450165\pi$
$770$	5.12319e9	0.404411
$771$	5.46219e9	0.429216
$772$	1.40008e10	1.09519
$773$	−2.04769e10	−1.59455	−0.797273	−	0.603619i	$-0.793725\pi$
$773$	−2.04769e10	−1.59455	−0.797273	+	0.603619i	$0.793725\pi$
$774$	−1.06738e10	−0.827423
$775$	−3.02170e8	−0.0233182
$776$	7.51990e8	0.0577692
$777$	7.40487e9	0.566297
$778$	1.04271e10	0.793847
$779$	3.44228e10	2.60894
$780$	−5.23474e9	−0.394970
$781$	−3.58699e9	−0.269433
$782$	1.39961e9	0.104661
$783$	1.17644e9	0.0875796
$784$	2.54439e9	0.188572
$785$	4.31836e9	0.318621
$786$	−1.59846e10	−1.17415
$787$	2.33821e10	1.70991	0.854954	−	0.518704i	$-0.173585\pi$
$787$	2.33821e10	1.70991	0.854954	+	0.518704i	$0.173585\pi$
$788$	−2.97227e9	−0.216395
$789$	1.09735e10	0.795383
$790$	6.54691e9	0.472435
$791$	−2.41637e10	−1.73598
$792$	−3.36802e8	−0.0240900
$793$	1.86806e10	1.33025
$794$	−6.71165e9	−0.475836
$795$	−1.20876e10	−0.853206
$796$	−2.09569e10	−1.47276
$797$	5.55295e9	0.388526	0.194263	−	0.980950i	$-0.437769\pi$
$797$	5.55295e9	0.388526	0.194263	+	0.980950i	$0.437769\pi$
$798$	1.44145e10	1.00413
$799$	−9.60749e7	−0.00666340
$800$	−3.43778e9	−0.237390
$801$	1.69619e9	0.116617
$802$	−2.93583e10	−2.00965
$803$	−5.96571e9	−0.406591
$804$	4.53257e9	0.307573
$805$	−9.35443e9	−0.632021
$806$	1.97213e9	0.132667
$807$	−1.43018e10	−0.957928
$808$	−2.20177e9	−0.146836
$809$	−1.91933e10	−1.27447	−0.637237	−	0.770668i	$-0.719923\pi$
$809$	−1.91933e10	−1.27447	−0.637237	+	0.770668i	$0.719923\pi$
$810$	−2.46611e9	−0.163048
$811$	−1.30956e9	−0.0862091	−0.0431045	−	0.999071i	$-0.513725\pi$
$811$	−1.30956e9	−0.0862091	−0.0431045	+	0.999071i	$0.513725\pi$
$812$	5.21917e9	0.342102
$813$	1.29517e10	0.845300
$814$	6.72140e9	0.436791
$815$	−2.44500e10	−1.58208
$816$	−1.25160e9	−0.0806400
$817$	−4.03978e10	−2.59168
$818$	−8.70740e9	−0.556227
$819$	3.66539e9	0.233146
$820$	−2.61271e10	−1.65479
$821$	1.43007e10	0.901896	0.450948	−	0.892550i	$-0.351086\pi$
$821$	1.43007e10	0.901896	0.450948	+	0.892550i	$0.351086\pi$
$822$	−8.91183e9	−0.559649
$823$	2.08892e10	1.30624	0.653120	−	0.757254i	$-0.273460\pi$
$823$	2.08892e10	1.30624	0.653120	+	0.757254i	$0.273460\pi$
$824$	−1.91976e9	−0.119537
$825$	−5.09775e8	−0.0316075
$826$	−2.01694e10	−1.24527
$827$	1.31770e10	0.810116	0.405058	−	0.914291i	$-0.367251\pi$
$827$	1.31770e10	0.810116	0.405058	+	0.914291i	$0.367251\pi$
$828$	−2.84861e9	−0.174392
$829$	−1.77646e10	−1.08296	−0.541481	−	0.840713i	$-0.682136\pi$
$829$	−1.77646e10	−1.08296	−0.541481	+	0.840713i	$0.682136\pi$
$830$	−3.03100e9	−0.183998
$831$	−1.54986e10	−0.936888
$832$	7.86839e9	0.473647
$833$	3.34546e8	0.0200539
$834$	4.38116e9	0.261522
$835$	−2.13004e9	−0.126615
$836$	5.90464e9	0.349519
$837$	4.19282e8	0.0247153
$838$	−1.72293e10	−1.01138
$839$	1.05490e10	0.616659	0.308329	−	0.951280i	$-0.400230\pi$
$839$	1.05490e10	0.616659	0.308329	+	0.951280i	$0.400230\pi$
$840$	2.36191e9	0.137494
$841$	−1.36775e10	−0.792905
$842$	4.45083e10	2.56950
$843$	1.37394e10	0.789901
$844$	4.00056e9	0.229046
$845$	7.90110e9	0.450494
$846$	4.33294e8	0.0246029
$847$	−1.46947e9	−0.0830939
$848$	2.76672e10	1.55804
$849$	−4.21190e9	−0.236212
$850$	−5.34881e8	−0.0298738
$851$	−1.22726e10	−0.682626
$852$	7.66009e9	0.424322
$853$	6.93413e8	0.0382534	0.0191267	−	0.999817i	$-0.493911\pi$
$853$	6.93413e8	0.0382534	0.0191267	+	0.999817i	$0.493911\pi$
$854$	3.90427e10	2.14505
$855$	−9.33361e9	−0.510703
$856$	4.33322e9	0.236131
$857$	2.42332e10	1.31516	0.657578	−	0.753387i	$-0.271581\pi$
$857$	2.42332e10	1.31516	0.657578	+	0.753387i	$0.271581\pi$
$858$	3.32708e9	0.179828
$859$	1.50069e10	0.807823	0.403911	−	0.914798i	$-0.367650\pi$
$859$	1.50069e10	0.807823	0.403911	+	0.914798i	$0.367650\pi$
$860$	3.06623e10	1.64384
$861$	1.82944e10	0.976801
$862$	1.34098e10	0.713094
$863$	4.48430e9	0.237496	0.118748	−	0.992924i	$-0.462112\pi$
$863$	4.48430e9	0.237496	0.118748	+	0.992924i	$0.462112\pi$
$864$	4.77015e9	0.251614
$865$	5.51282e9	0.289613
$866$	−1.13922e10	−0.596069
$867$	1.09146e10	0.568775
$868$	1.86011e9	0.0965425
$869$	−1.87783e9	−0.0970706
$870$	−7.48858e9	−0.385551
$871$	9.66608e9	0.495664
$872$	−4.01183e9	−0.204897
$873$	−1.57932e9	−0.0803380
$874$	−2.38900e10	−1.21039
$875$	−1.61139e10	−0.813154
$876$	1.27399e10	0.640327
$877$	−2.15250e10	−1.07757	−0.538784	−	0.842444i	$-0.681116\pi$
$877$	−2.15250e10	−1.07757	−0.538784	+	0.842444i	$0.681116\pi$
$878$	5.05612e9	0.252108
$879$	−8.93770e9	−0.443879
$880$	7.59308e9	0.375603
$881$	1.89298e10	0.932676	0.466338	−	0.884607i	$-0.345573\pi$
$881$	1.89298e10	0.932676	0.466338	+	0.884607i	$0.345573\pi$
$882$	−1.50879e9	−0.0740438
$883$	7.30415e9	0.357032	0.178516	−	0.983937i	$-0.442870\pi$
$883$	7.30415e9	0.357032	0.178516	+	0.983937i	$0.442870\pi$
$884$	1.57541e9	0.0767028
$885$	1.30601e10	0.633350
$886$	−2.94251e10	−1.42134
$887$	−2.12379e10	−1.02183	−0.510915	−	0.859631i	$-0.670693\pi$
$887$	−2.12379e10	−1.02183	−0.510915	+	0.859631i	$0.670693\pi$
$888$	3.09872e9	0.148503
$889$	3.56335e10	1.70099
$890$	−1.07970e10	−0.513380
$891$	7.07348e8	0.0335013
$892$	1.20644e10	0.569152
$893$	1.63991e9	0.0770618
$894$	−2.62398e10	−1.22823
$895$	3.54821e10	1.65436
$896$	−9.28590e9	−0.431267
$897$	−6.07490e9	−0.281039
$898$	5.11883e9	0.235887
$899$	1.27319e9	0.0584432
$900$	1.08864e9	0.0497776
$901$	3.63779e9	0.165692
$902$	1.66058e10	0.753419
$903$	−2.14699e10	−0.970337
$904$	−1.01118e10	−0.455237
$905$	2.76846e10	1.24156
$906$	5.87756e9	0.262572
$907$	−3.80530e10	−1.69341	−0.846707	−	0.532059i	$-0.821419\pi$
$907$	−3.80530e10	−1.69341	−0.846707	+	0.532059i	$0.821419\pi$
$908$	−9.78439e9	−0.433744
$909$	4.62413e9	0.204200
$910$	−2.33319e10	−1.02637
$911$	−3.43756e10	−1.50638	−0.753192	−	0.657800i	$-0.771487\pi$
$911$	−3.43756e10	−1.50638	−0.753192	+	0.657800i	$0.771487\pi$
$912$	2.13637e10	0.932597
$913$	8.69374e8	0.0378059
$914$	−1.49890e10	−0.649322
$915$	−2.52808e10	−1.09098
$916$	3.70321e10	1.59201
$917$	−3.21521e10	−1.37695
$918$	7.42183e8	0.0316637
$919$	−9.00499e9	−0.382718	−0.191359	−	0.981520i	$-0.561289\pi$
$919$	−9.00499e9	−0.382718	−0.191359	+	0.981520i	$0.561289\pi$
$920$	−3.91455e9	−0.165739
$921$	4.31156e9	0.181855
$922$	−1.22056e10	−0.512863
$923$	1.63358e10	0.683808
$924$	3.13809e9	0.130862
$925$	4.69014e9	0.194845
$926$	−1.55307e10	−0.642764
$927$	4.03186e9	0.166236
$928$	1.44850e10	0.594978
$929$	−1.39486e10	−0.570788	−0.285394	−	0.958410i	$-0.592125\pi$
$929$	−1.39486e10	−0.570788	−0.285394	+	0.958410i	$0.592125\pi$
$930$	−2.66892e9	−0.108804
$931$	−5.71039e9	−0.231922
$932$	2.00351e10	0.810655
$933$	−9.48124e9	−0.382190
$934$	−4.33643e10	−1.74148
$935$	9.98367e8	0.0399438
$936$	1.53386e9	0.0611392
$937$	3.54170e10	1.40645	0.703223	−	0.710970i	$-0.251744\pi$
$937$	3.54170e10	1.40645	0.703223	+	0.710970i	$0.251744\pi$
$938$	2.02022e10	0.799263
$939$	1.47629e10	0.581890
$940$	−1.24470e9	−0.0488785
$941$	2.25006e10	0.880299	0.440150	−	0.897924i	$-0.354925\pi$
$941$	2.25006e10	0.880299	0.440150	+	0.897924i	$0.354925\pi$
$942$	5.86124e9	0.228461
$943$	−3.03205e10	−1.17746
$944$	−2.98931e10	−1.15656
$945$	−4.96045e9	−0.191210
$946$	−1.94882e10	−0.748432
$947$	1.92828e10	0.737810	0.368905	−	0.929467i	$-0.379733\pi$
$947$	1.92828e10	0.737810	0.368905	+	0.929467i	$0.379733\pi$
$948$	4.01015e9	0.152873
$949$	2.71689e10	1.03191
$950$	9.12991e9	0.345489
$951$	1.66878e10	0.629170
$952$	−7.10823e8	−0.0267013
$953$	1.08950e10	0.407759	0.203879	−	0.978996i	$-0.434645\pi$
$953$	1.08950e10	0.407759	0.203879	+	0.978996i	$0.434645\pi$
$954$	−1.64063e10	−0.611774
$955$	5.55653e10	2.06439
$956$	−2.11304e10	−0.782179
$957$	2.14793e9	0.0792188
$958$	4.96126e10	1.82311
$959$	−1.79257e10	−0.656312
$960$	−1.06485e10	−0.388452
$961$	−2.70589e10	−0.983507
$962$	−3.06105e10	−1.10855
$963$	−9.10058e9	−0.328380
$964$	−2.19210e10	−0.788117
$965$	−4.04072e10	−1.44748
$966$	−1.26966e10	−0.453178
$967$	−1.35695e10	−0.482584	−0.241292	−	0.970453i	$-0.577571\pi$
$967$	−1.35695e10	−0.482584	−0.241292	+	0.970453i	$0.577571\pi$
$968$	−6.14929e8	−0.0217902
$969$	2.80898e9	0.0991779
$970$	1.00531e10	0.353671
$971$	−4.33843e9	−0.152078	−0.0760388	−	0.997105i	$-0.524227\pi$
$971$	−4.33843e9	−0.152078	−0.0760388	+	0.997105i	$0.524227\pi$
$972$	−1.51056e9	−0.0527600
$973$	8.81247e9	0.306692
$974$	−1.00152e10	−0.347298
$975$	2.32161e9	0.0802182
$976$	5.78651e10	1.99224
$977$	−3.90981e10	−1.34130	−0.670648	−	0.741776i	$-0.733984\pi$
$977$	−3.90981e10	−1.34130	−0.670648	+	0.741776i	$0.733984\pi$
$978$	−3.31856e10	−1.13439
$979$	3.09688e9	0.105484
$980$	4.33423e9	0.147103
$981$	8.42560e9	0.284944
$982$	1.43115e10	0.482275
$983$	−3.05704e10	−1.02651	−0.513257	−	0.858235i	$-0.671561\pi$
$983$	−3.05704e10	−1.02651	−0.513257	+	0.858235i	$0.671561\pi$
$984$	7.65564e9	0.256153
$985$	8.57819e9	0.286002
$986$	2.25371e9	0.0748736
$987$	8.71548e8	0.0288523
$988$	−2.68908e10	−0.887062
$989$	3.55835e10	1.16966
$990$	−4.50260e9	−0.147482
$991$	3.59751e10	1.17421	0.587103	−	0.809512i	$-0.300268\pi$
$991$	3.59751e10	1.17421	0.587103	+	0.809512i	$0.300268\pi$
$992$	5.16245e9	0.167905
$993$	1.84908e10	0.599286
$994$	3.41420e10	1.10265
$995$	6.04831e10	1.94649
$996$	−1.85657e9	−0.0595392
$997$	2.97463e10	0.950604	0.475302	−	0.879823i	$-0.342339\pi$
$997$	2.97463e10	0.950604	0.475302	+	0.879823i	$0.342339\pi$
$998$	−7.75275e10	−2.46888
$999$	−6.50789e9	−0.206520

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.8.a.c.1.2	✓	2
3.2	odd	2		99.8.a.b.1.1		2
4.3	odd	2		528.8.a.h.1.1		2
11.10	odd	2		363.8.a.c.1.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.a.c.1.2	✓	2	1.1	even	1	trivial
99.8.a.b.1.1		2	3.2	odd	2
363.8.a.c.1.1		2	11.10	odd	2
528.8.a.h.1.1		2	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)

\(f(q)\)	\(=\)	\(q+15.2733 q^{2} -27.0000 q^{3} +105.273 q^{4} -303.826 q^{5} -412.379 q^{6} -829.478 q^{7} -347.112 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+15.2733 q^{2} -27.0000 q^{3} +105.273 q^{4} -303.826 q^{5} -412.379 q^{6} -829.478 q^{7} -347.112 q^{8} +729.000 q^{9} -4640.42 q^{10} +1331.00 q^{11} -2842.38 q^{12} -6061.62 q^{13} -12668.9 q^{14} +8203.30 q^{15} -18776.5 q^{16} -2468.81 q^{17} +11134.2 q^{18} +42140.2 q^{19} -31984.8 q^{20} +22395.9 q^{21} +20328.7 q^{22} -37118.2 q^{23} +9372.01 q^{24} +14185.2 q^{25} -92580.8 q^{26} -19683.0 q^{27} -87321.9 q^{28} -59769.3 q^{29} +125291. q^{30} -21301.7 q^{31} -242349. q^{32} -35937.0 q^{33} -37706.8 q^{34} +252017. q^{35} +76744.2 q^{36} +330635. q^{37} +643620. q^{38} +163664. q^{39} +105462. q^{40} +816862. q^{41} +342059. q^{42} -958652. q^{43} +140119. q^{44} -221489. q^{45} -566917. q^{46} +38915.5 q^{47} +506966. q^{48} -135509. q^{49} +216655. q^{50} +66657.8 q^{51} -638126. q^{52} -1.47350e6 q^{53} -300624. q^{54} -404392. q^{55} +287921. q^{56} -1.13779e6 q^{57} -912873. q^{58} +1.59205e6 q^{59} +863589. q^{60} -3.08178e6 q^{61} -325347. q^{62} -604689. q^{63} -1.29807e6 q^{64} +1.84168e6 q^{65} -548876. q^{66} -1.59464e6 q^{67} -259900. q^{68} +1.00219e6 q^{69} +3.84913e6 q^{70} -2.69496e6 q^{71} -253044. q^{72} -4.48213e6 q^{73} +5.04989e6 q^{74} -383002. q^{75} +4.43624e6 q^{76} -1.10404e6 q^{77} +2.49968e6 q^{78} -1.41084e6 q^{79} +5.70479e6 q^{80} +531441. q^{81} +1.24762e7 q^{82} +653174. q^{83} +2.35769e6 q^{84} +750088. q^{85} -1.46418e7 q^{86} +1.61377e6 q^{87} -462006. q^{88} +2.32673e6 q^{89} -3.38287e6 q^{90} +5.02798e6 q^{91} -3.90756e6 q^{92} +575146. q^{93} +594367. q^{94} -1.28033e7 q^{95} +6.54342e6 q^{96} -2.16642e6 q^{97} -2.06967e6 q^{98} +970299. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 54 q^{3} + 181 q^{4} - 194 q^{5} - 27 q^{6} - 418 q^{7} + 399 q^{8} + 1458 q^{9}+O(q^{10}) \) 2 * q + q^2 - 54 * q^3 + 181 * q^4 - 194 * q^5 - 27 * q^6 - 418 * q^7 + 399 * q^8 + 1458 * q^9	\( 2 q + q^{2} - 54 q^{3} + 181 q^{4} - 194 q^{5} - 27 q^{6} - 418 q^{7} + 399 q^{8} + 1458 q^{9} - 6208 q^{10} + 2662 q^{11} - 4887 q^{12} - 13246 q^{13} - 18542 q^{14} + 5238 q^{15} - 39119 q^{16} - 10256 q^{17} + 729 q^{18} + 14196 q^{19} - 23668 q^{20} + 11286 q^{21} + 1331 q^{22} - 13666 q^{23} - 10773 q^{24} - 51878 q^{25} + 9964 q^{26} - 39366 q^{27} - 56162 q^{28} + 15312 q^{29} + 167616 q^{30} - 48040 q^{31} - 47497 q^{32} - 71874 q^{33} + 73442 q^{34} + 297208 q^{35} + 131949 q^{36} + 274092 q^{37} + 1042476 q^{38} + 357642 q^{39} + 187404 q^{40} + 755836 q^{41} + 500634 q^{42} - 1704096 q^{43} + 240911 q^{44} - 141426 q^{45} - 901658 q^{46} - 1182094 q^{47} + 1056213 q^{48} - 789738 q^{49} + 1159595 q^{50} + 276912 q^{51} - 1182176 q^{52} - 2156394 q^{53} - 19683 q^{54} - 258214 q^{55} + 594930 q^{56} - 383292 q^{57} - 1984530 q^{58} + 927332 q^{59} + 639036 q^{60} - 1061994 q^{61} + 56296 q^{62} - 304722 q^{63} - 1475407 q^{64} + 1052644 q^{65} - 35937 q^{66} - 3259952 q^{67} - 849598 q^{68} + 368982 q^{69} + 3204104 q^{70} - 5495514 q^{71} + 290871 q^{72} - 5450812 q^{73} + 5856942 q^{74} + 1400706 q^{75} + 2320116 q^{76} - 556358 q^{77} - 269028 q^{78} - 1536590 q^{79} + 3470660 q^{80} + 1062882 q^{81} + 13347206 q^{82} + 8850888 q^{83} + 1516374 q^{84} - 105148 q^{85} - 4001832 q^{86} - 413424 q^{87} + 531069 q^{88} + 6810132 q^{89} - 4525632 q^{90} + 2071760 q^{91} - 2131598 q^{92} + 1297080 q^{93} + 18022186 q^{94} - 15872304 q^{95} + 1282419 q^{96} + 9897376 q^{97} + 7268325 q^{98} + 1940598 q^{99}+O(q^{100}) \) 2 * q + q^2 - 54 * q^3 + 181 * q^4 - 194 * q^5 - 27 * q^6 - 418 * q^7 + 399 * q^8 + 1458 * q^9 - 6208 * q^10 + 2662 * q^11 - 4887 * q^12 - 13246 * q^13 - 18542 * q^14 + 5238 * q^15 - 39119 * q^16 - 10256 * q^17 + 729 * q^18 + 14196 * q^19 - 23668 * q^20 + 11286 * q^21 + 1331 * q^22 - 13666 * q^23 - 10773 * q^24 - 51878 * q^25 + 9964 * q^26 - 39366 * q^27 - 56162 * q^28 + 15312 * q^29 + 167616 * q^30 - 48040 * q^31 - 47497 * q^32 - 71874 * q^33 + 73442 * q^34 + 297208 * q^35 + 131949 * q^36 + 274092 * q^37 + 1042476 * q^38 + 357642 * q^39 + 187404 * q^40 + 755836 * q^41 + 500634 * q^42 - 1704096 * q^43 + 240911 * q^44 - 141426 * q^45 - 901658 * q^46 - 1182094 * q^47 + 1056213 * q^48 - 789738 * q^49 + 1159595 * q^50 + 276912 * q^51 - 1182176 * q^52 - 2156394 * q^53 - 19683 * q^54 - 258214 * q^55 + 594930 * q^56 - 383292 * q^57 - 1984530 * q^58 + 927332 * q^59 + 639036 * q^60 - 1061994 * q^61 + 56296 * q^62 - 304722 * q^63 - 1475407 * q^64 + 1052644 * q^65 - 35937 * q^66 - 3259952 * q^67 - 849598 * q^68 + 368982 * q^69 + 3204104 * q^70 - 5495514 * q^71 + 290871 * q^72 - 5450812 * q^73 + 5856942 * q^74 + 1400706 * q^75 + 2320116 * q^76 - 556358 * q^77 - 269028 * q^78 - 1536590 * q^79 + 3470660 * q^80 + 1062882 * q^81 + 13347206 * q^82 + 8850888 * q^83 + 1516374 * q^84 - 105148 * q^85 - 4001832 * q^86 - 413424 * q^87 + 531069 * q^88 + 6810132 * q^89 - 4525632 * q^90 + 2071760 * q^91 - 2131598 * q^92 + 1297080 * q^93 + 18022186 * q^94 - 15872304 * q^95 + 1282419 * q^96 + 9897376 * q^97 + 7268325 * q^98 + 1940598 * q^99

Introduction

L-functions

Modular forms

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Database

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