LMFDB - Embedded newform 33.8.a.b.1.1

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{177}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 44 $ x^2 - x - 44
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$7.15207$ 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)

$f(q)$	$=$	$q-16.1521 q^{2} +27.0000 q^{3} +132.889 q^{4} -269.779 q^{5} -436.106 q^{6} +941.418 q^{7} -78.9720 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-16.1521 q^{2} +27.0000 q^{3} +132.889 q^{4} -269.779 q^{5} -436.106 q^{6} +941.418 q^{7} -78.9720 q^{8} +729.000 q^{9} +4357.48 q^{10} -1331.00 q^{11} +3588.01 q^{12} -494.485 q^{13} -15205.9 q^{14} -7284.02 q^{15} -15734.3 q^{16} -37797.5 q^{17} -11774.9 q^{18} -13322.4 q^{19} -35850.7 q^{20} +25418.3 q^{21} +21498.4 q^{22} -3235.41 q^{23} -2132.24 q^{24} -5344.53 q^{25} +7986.95 q^{26} +19683.0 q^{27} +125104. q^{28} -190198. q^{29} +117652. q^{30} +5370.40 q^{31} +264249. q^{32} -35937.0 q^{33} +610507. q^{34} -253974. q^{35} +96876.3 q^{36} -18819.6 q^{37} +215185. q^{38} -13351.1 q^{39} +21304.9 q^{40} -722656. q^{41} -410558. q^{42} +349819. q^{43} -176876. q^{44} -196669. q^{45} +52258.6 q^{46} +766610. q^{47} -424825. q^{48} +62725.6 q^{49} +86325.2 q^{50} -1.02053e6 q^{51} -65711.7 q^{52} -253491. q^{53} -317921. q^{54} +359075. q^{55} -74345.7 q^{56} -359706. q^{57} +3.07209e6 q^{58} +2.51185e6 q^{59} -967968. q^{60} -2.43883e6 q^{61} -86743.0 q^{62} +686294. q^{63} -2.25419e6 q^{64} +133401. q^{65} +580457. q^{66} -2.24986e6 q^{67} -5.02288e6 q^{68} -87356.2 q^{69} +4.10221e6 q^{70} -425851. q^{71} -57570.6 q^{72} -4.57520e6 q^{73} +303975. q^{74} -144302. q^{75} -1.77041e6 q^{76} -1.25303e6 q^{77} +215648. q^{78} +3.87265e6 q^{79} +4.24477e6 q^{80} +531441. q^{81} +1.16724e7 q^{82} -7.25736e6 q^{83} +3.37782e6 q^{84} +1.01969e7 q^{85} -5.65030e6 q^{86} -5.13534e6 q^{87} +105112. q^{88} +1.05242e7 q^{89} +3.17660e6 q^{90} -465517. q^{91} -429952. q^{92} +145001. q^{93} -1.23823e7 q^{94} +3.59411e6 q^{95} +7.13473e6 q^{96} -8.33350e6 q^{97} -1.01315e6 q^{98} -970299. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 19 q^{2} + 54 q^{3} + 13 q^{4} - 34 q^{5} - 513 q^{6} - 166 q^{7} + 627 q^{8} + 1458 q^{9}+O(q^{10}) $ 2 * q - 19 * q^2 + 54 * q^3 + 13 * q^4 - 34 * q^5 - 513 * q^6 - 166 * q^7 + 627 * q^8 + 1458 * q^9	\( 2 q - 19 q^{2} + 54 q^{3} + 13 q^{4} - 34 q^{5} - 513 q^{6} - 166 q^{7} + 627 q^{8} + 1458 q^{9} + 3686 q^{10} - 2662 q^{11} + 351 q^{12} - 12670 q^{13} - 12052 q^{14} - 918 q^{15} - 2399 q^{16} - 62344 q^{17} - 13851 q^{18} - 37980 q^{19} - 64118 q^{20} - 4482 q^{21} + 25289 q^{22} - 90686 q^{23} + 16929 q^{24} - 27878 q^{25} + 42662 q^{26} + 39366 q^{27} + 257872 q^{28} + 13992 q^{29} + 99522 q^{30} + 245000 q^{31} + 135907 q^{32} - 71874 q^{33} + 680414 q^{34} - 515080 q^{35} + 9477 q^{36} + 327852 q^{37} + 285408 q^{38} - 342090 q^{39} + 187758 q^{40} - 275932 q^{41} - 325404 q^{42} - 244104 q^{43} - 17303 q^{44} - 24786 q^{45} + 301312 q^{46} + 536926 q^{47} - 64773 q^{48} + 465558 q^{49} + 150499 q^{50} - 1683288 q^{51} + 1394002 q^{52} - 1821882 q^{53} - 373977 q^{54} + 45254 q^{55} - 856152 q^{56} - 1025460 q^{57} + 2490570 q^{58} + 2502028 q^{59} - 1731186 q^{60} - 2191098 q^{61} - 769192 q^{62} - 121014 q^{63} - 3595591 q^{64} - 2737324 q^{65} + 682803 q^{66} + 1674784 q^{67} - 2080010 q^{68} - 2448522 q^{69} + 4845824 q^{70} - 368310 q^{71} + 457083 q^{72} - 3336604 q^{73} - 683322 q^{74} - 752706 q^{75} + 1185768 q^{76} + 220946 q^{77} + 1151874 q^{78} - 1682618 q^{79} + 7388938 q^{80} + 1062882 q^{81} + 10400150 q^{82} - 8376504 q^{83} + 6962544 q^{84} + 4409396 q^{85} - 3958848 q^{86} + 377784 q^{87} - 834537 q^{88} + 9027204 q^{89} + 2687094 q^{90} + 13017872 q^{91} + 10054436 q^{92} + 6615000 q^{93} - 11728208 q^{94} - 2219616 q^{95} + 3669489 q^{96} - 16703552 q^{97} - 2160387 q^{98} - 1940598 q^{99}+O(q^{100}) \) 2 * q - 19 * q^2 + 54 * q^3 + 13 * q^4 - 34 * q^5 - 513 * q^6 - 166 * q^7 + 627 * q^8 + 1458 * q^9 + 3686 * q^10 - 2662 * q^11 + 351 * q^12 - 12670 * q^13 - 12052 * q^14 - 918 * q^15 - 2399 * q^16 - 62344 * q^17 - 13851 * q^18 - 37980 * q^19 - 64118 * q^20 - 4482 * q^21 + 25289 * q^22 - 90686 * q^23 + 16929 * q^24 - 27878 * q^25 + 42662 * q^26 + 39366 * q^27 + 257872 * q^28 + 13992 * q^29 + 99522 * q^30 + 245000 * q^31 + 135907 * q^32 - 71874 * q^33 + 680414 * q^34 - 515080 * q^35 + 9477 * q^36 + 327852 * q^37 + 285408 * q^38 - 342090 * q^39 + 187758 * q^40 - 275932 * q^41 - 325404 * q^42 - 244104 * q^43 - 17303 * q^44 - 24786 * q^45 + 301312 * q^46 + 536926 * q^47 - 64773 * q^48 + 465558 * q^49 + 150499 * q^50 - 1683288 * q^51 + 1394002 * q^52 - 1821882 * q^53 - 373977 * q^54 + 45254 * q^55 - 856152 * q^56 - 1025460 * q^57 + 2490570 * q^58 + 2502028 * q^59 - 1731186 * q^60 - 2191098 * q^61 - 769192 * q^62 - 121014 * q^63 - 3595591 * q^64 - 2737324 * q^65 + 682803 * q^66 + 1674784 * q^67 - 2080010 * q^68 - 2448522 * q^69 + 4845824 * q^70 - 368310 * q^71 + 457083 * q^72 - 3336604 * q^73 - 683322 * q^74 - 752706 * q^75 + 1185768 * q^76 + 220946 * q^77 + 1151874 * q^78 - 1682618 * q^79 + 7388938 * q^80 + 1062882 * q^81 + 10400150 * q^82 - 8376504 * q^83 + 6962544 * q^84 + 4409396 * q^85 - 3958848 * q^86 + 377784 * q^87 - 834537 * q^88 + 9027204 * q^89 + 2687094 * q^90 + 13017872 * q^91 + 10054436 * q^92 + 6615000 * q^93 - 11728208 * q^94 - 2219616 * q^95 + 3669489 * q^96 - 16703552 * q^97 - 2160387 * 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 $

$2$	−16.1521	−1.42765	−0.713827	−	0.700322i	$-0.753040\pi$
$2$	−16.1521	−1.42765	−0.713827	+	0.700322i	$0.753040\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	132.889	1.03820
$5$	−269.779	−0.965189	−0.482595	−	0.875844i	$-0.660306\pi$
$5$	−269.779	−0.965189	−0.482595	+	0.875844i	$0.660306\pi$
$6$	−436.106	−0.824257
$7$	941.418	1.03738	0.518692	−	0.854961i	$-0.326419\pi$
$7$	941.418	1.03738	0.518692	+	0.854961i	$0.326419\pi$
$8$	−78.9720	−0.0545328
$9$	729.000	0.333333
$10$	4357.48	1.37796
$11$	−1331.00	−0.301511
$11$	−1331.00	−0.301511
$12$	3588.01	0.599404
$13$	−494.485	−0.0624240	−0.0312120	−	0.999513i	$-0.509937\pi$
$13$	−494.485	−0.0624240	−0.0312120	+	0.999513i	$0.509937\pi$
$14$	−15205.9	−1.48103
$15$	−7284.02	−0.557252
$16$	−15734.3	−0.960343
$17$	−37797.5	−1.86591	−0.932956	−	0.359989i	$-0.882780\pi$
$17$	−37797.5	−1.86591	−0.932956	+	0.359989i	$0.882780\pi$
$18$	−11774.9	−0.475885
$19$	−13322.4	−0.445601	−0.222800	−	0.974864i	$-0.571520\pi$
$19$	−13322.4	−0.445601	−0.222800	+	0.974864i	$0.571520\pi$
$20$	−35850.7	−1.00206
$21$	25418.3	0.598934
$22$	21498.4	0.430454
$23$	−3235.41	−0.0554476	−0.0277238	−	0.999616i	$-0.508826\pi$
$23$	−3235.41	−0.0554476	−0.0277238	+	0.999616i	$0.508826\pi$
$24$	−2132.24	−0.0314845
$25$	−5344.53	−0.0684100
$26$	7986.95	0.0891198
$27$	19683.0	0.192450
$28$	125104.	1.07701
$29$	−190198.	−1.44815	−0.724074	−	0.689723i	$-0.757732\pi$
$29$	−190198.	−1.44815	−0.724074	+	0.689723i	$0.757732\pi$
$30$	117652.	0.795564
$31$	5370.40	0.0323773	0.0161886	−	0.999869i	$-0.494847\pi$
$31$	5370.40	0.0323773	0.0161886	+	0.999869i	$0.494847\pi$
$32$	264249.	1.42557
$33$	−35937.0	−0.174078
$34$	610507.	2.66388
$35$	−253974.	−1.00127
$36$	96876.3	0.346066
$37$	−18819.6	−0.0610807	−0.0305404	−	0.999534i	$-0.509723\pi$
$37$	−18819.6	−0.0610807	−0.0305404	+	0.999534i	$0.509723\pi$
$38$	215185.	0.636164
$39$	−13351.1	−0.0360405
$40$	21304.9	0.0526345
$41$	−722656.	−1.63753	−0.818763	−	0.574132i	$-0.805340\pi$
$41$	−722656.	−1.63753	−0.818763	+	0.574132i	$0.805340\pi$
$42$	−410558.	−0.855071
$43$	349819.	0.670971	0.335486	−	0.942045i	$-0.391100\pi$
$43$	349819.	0.670971	0.335486	+	0.942045i	$0.391100\pi$
$44$	−176876.	−0.313028
$45$	−196669.	−0.321730
$46$	52258.6	0.0791600
$47$	766610.	1.07704	0.538520	−	0.842613i	$-0.318984\pi$
$47$	766610.	1.07704	0.538520	+	0.842613i	$0.318984\pi$
$48$	−424825.	−0.554455
$49$	62725.6	0.0761655
$50$	86325.2	0.0976658
$51$	−1.02053e6	−1.07729
$52$	−65711.7	−0.0648084
$53$	−253491.	−0.233882	−0.116941	−	0.993139i	$-0.537309\pi$
$53$	−253491.	−0.233882	−0.116941	+	0.993139i	$0.537309\pi$
$54$	−317921.	−0.274752
$55$	359075.	0.291015
$56$	−74345.7	−0.0565715
$57$	−359706.	−0.257268
$58$	3.07209e6	2.06745
$59$	2.51185e6	1.59225	0.796125	−	0.605133i	$-0.206880\pi$
$59$	2.51185e6	1.59225	0.796125	+	0.605133i	$0.206880\pi$
$60$	−967968.	−0.578538
$61$	−2.43883e6	−1.37571	−0.687855	−	0.725848i	$-0.741447\pi$
$61$	−2.43883e6	−1.37571	−0.687855	+	0.725848i	$0.741447\pi$
$62$	−86743.0	−0.0462236
$63$	686294.	0.345795
$64$	−2.25419e6	−1.07488
$65$	133401.	0.0602509
$66$	580457.	0.248523
$67$	−2.24986e6	−0.913889	−0.456945	−	0.889495i	$-0.651056\pi$
$67$	−2.24986e6	−0.913889	−0.456945	+	0.889495i	$0.651056\pi$
$68$	−5.02288e6	−1.93719
$69$	−87356.2	−0.0320127
$70$	4.10221e6	1.42947
$71$	−425851.	−0.141206	−0.0706031	−	0.997504i	$-0.522492\pi$
$71$	−425851.	−0.141206	−0.0706031	+	0.997504i	$0.522492\pi$
$72$	−57570.6	−0.0181776
$73$	−4.57520e6	−1.37651	−0.688256	−	0.725467i	$-0.741624\pi$
$73$	−4.57520e6	−1.37651	−0.688256	+	0.725467i	$0.741624\pi$
$74$	303975.	0.0872022
$75$	−144302.	−0.0394965
$76$	−1.77041e6	−0.462622
$77$	−1.25303e6	−0.312783
$78$	215648.	0.0514534
$79$	3.87265e6	0.883718	0.441859	−	0.897085i	$-0.354319\pi$
$79$	3.87265e6	0.883718	0.441859	+	0.897085i	$0.354319\pi$
$80$	4.24477e6	0.926913
$81$	531441.	0.111111
$82$	1.16724e7	2.33782
$83$	−7.25736e6	−1.39317	−0.696587	−	0.717473i	$-0.745299\pi$
$83$	−7.25736e6	−1.39317	−0.696587	+	0.717473i	$0.745299\pi$
$84$	3.37782e6	0.621812
$85$	1.01969e7	1.80096
$86$	−5.65030e6	−0.957915
$87$	−5.13534e6	−0.836088
$88$	105112.	0.0164423
$89$	1.05242e7	1.58243	0.791214	−	0.611539i	$-0.209449\pi$
$89$	1.05242e7	1.58243	0.791214	+	0.611539i	$0.209449\pi$
$90$	3.17660e6	0.459319
$91$	−465517.	−0.0647576
$92$	−429952.	−0.0575655
$93$	145001.	0.0186930
$94$	−1.23823e7	−1.53764
$95$	3.59411e6	0.430089
$96$	7.13473e6	0.823054
$97$	−8.33350e6	−0.927099	−0.463550	−	0.886071i	$-0.653424\pi$
$97$	−8.33350e6	−0.927099	−0.463550	+	0.886071i	$0.653424\pi$
$98$	−1.01315e6	−0.108738
$99$	−970299.	−0.100504
$100$	−710231.	−0.0710231
$101$	3.58521e6	0.346250	0.173125	−	0.984900i	$-0.444614\pi$
$101$	3.58521e6	0.346250	0.173125	+	0.984900i	$0.444614\pi$
$102$	1.64837e7	1.53799
$103$	2.71347e6	0.244678	0.122339	−	0.992488i	$-0.460960\pi$
$103$	2.71347e6	0.244678	0.122339	+	0.992488i	$0.460960\pi$
$104$	39050.4	0.00340415
$105$	−6.85731e6	−0.578084
$106$	4.09440e6	0.333902
$107$	1.55536e7	1.22740	0.613702	−	0.789538i	$-0.289680\pi$
$107$	1.55536e7	1.22740	0.613702	+	0.789538i	$0.289680\pi$
$108$	2.61566e6	0.199801
$109$	−1.40840e7	−1.04167	−0.520837	−	0.853656i	$-0.674380\pi$
$109$	−1.40840e7	−1.04167	−0.520837	+	0.853656i	$0.674380\pi$
$110$	−5.79981e6	−0.415470
$111$	−508129.	−0.0352650
$112$	−1.48125e7	−0.996245
$113$	−9.23989e6	−0.602410	−0.301205	−	0.953559i	$-0.597389\pi$
$113$	−9.23989e6	−0.602410	−0.301205	+	0.953559i	$0.597389\pi$
$114$	5.80999e6	0.367290
$115$	872845.	0.0535174
$116$	−2.52753e7	−1.50346
$117$	−360479.	−0.0208080
$118$	−4.05715e7	−2.27318
$119$	−3.55832e7	−1.93567
$120$	575234.	0.0303885
$121$	1.77156e6	0.0909091
$122$	3.93921e7	1.96404
$123$	−1.95117e7	−0.945426
$124$	713668.	0.0336140
$125$	2.25183e7	1.03122
$126$	−1.10851e7	−0.493675
$127$	−3.88279e7	−1.68202	−0.841010	−	0.541019i	$-0.818039\pi$
$127$	−3.88279e7	−1.68202	−0.841010	+	0.541019i	$0.818039\pi$
$128$	2.58587e6	0.108986
$129$	9.44511e6	0.387385
$130$	−2.15471e6	−0.0860175
$131$	4.69251e7	1.82371	0.911855	−	0.410513i	$-0.134650\pi$
$131$	4.69251e7	1.82371	0.911855	+	0.410513i	$0.134650\pi$
$132$	−4.77564e6	−0.180727
$133$	−1.25420e7	−0.462259
$134$	3.63399e7	1.30472
$135$	−5.31005e6	−0.185751
$136$	2.98494e6	0.101754
$137$	−1.89428e7	−0.629393	−0.314697	−	0.949192i	$-0.601903\pi$
$137$	−1.89428e7	−0.629393	−0.314697	+	0.949192i	$0.601903\pi$
$138$	1.41098e6	0.0457030
$139$	5.52030e7	1.74346	0.871728	−	0.489989i	$-0.162999\pi$
$139$	5.52030e7	1.74346	0.871728	+	0.489989i	$0.162999\pi$
$140$	−3.37505e7	−1.03952
$141$	2.06985e7	0.621829
$142$	6.87838e6	0.201594
$143$	658159.	0.0188215
$144$	−1.14703e7	−0.320114
$145$	5.13113e7	1.39774
$146$	7.38990e7	1.96518
$147$	1.69359e6	0.0439742
$148$	−2.50092e6	−0.0634139
$149$	3.62425e7	0.897564	0.448782	−	0.893641i	$-0.351858\pi$
$149$	3.62425e7	0.897564	0.448782	+	0.893641i	$0.351858\pi$
$150$	2.33078e6	0.0563874
$151$	−6.76465e6	−0.159892	−0.0799458	−	0.996799i	$-0.525475\pi$
$151$	−6.76465e6	−0.159892	−0.0799458	+	0.996799i	$0.525475\pi$
$152$	1.05210e6	0.0242999
$153$	−2.75543e7	−0.621971
$154$	2.02390e7	0.446546
$155$	−1.44882e6	−0.0312502
$156$	−1.77422e6	−0.0374171
$157$	7.49380e7	1.54544	0.772722	−	0.634744i	$-0.218894\pi$
$157$	7.49380e7	1.54544	0.772722	+	0.634744i	$0.218894\pi$
$158$	−6.25513e7	−1.26164
$159$	−6.84425e6	−0.135032
$160$	−7.12888e7	−1.37595
$161$	−3.04588e6	−0.0575204
$162$	−8.58387e6	−0.158628
$163$	1.45225e7	0.262655	0.131328	−	0.991339i	$-0.458076\pi$
$163$	1.45225e7	0.262655	0.131328	+	0.991339i	$0.458076\pi$
$164$	−9.60333e7	−1.70008
$165$	9.69503e6	0.168018
$166$	1.17221e8	1.98897
$167$	3.86641e7	0.642392	0.321196	−	0.947013i	$-0.395915\pi$
$167$	3.86641e7	0.642392	0.321196	+	0.947013i	$0.395915\pi$
$168$	−2.00733e6	−0.0326616
$169$	−6.25040e7	−0.996103
$170$	−1.64702e8	−2.57115
$171$	−9.71206e6	−0.148534
$172$	4.64872e7	0.696601
$173$	−1.07747e8	−1.58214	−0.791069	−	0.611727i	$-0.790475\pi$
$173$	−1.07747e8	−1.58214	−0.791069	+	0.611727i	$0.790475\pi$
$174$	8.29464e7	1.19365
$175$	−5.03144e6	−0.0709674
$176$	2.09423e7	0.289554
$177$	6.78199e7	0.919286
$178$	−1.69988e8	−2.25916
$179$	−7.21236e7	−0.939922	−0.469961	−	0.882687i	$-0.655732\pi$
$179$	−7.21236e7	−0.939922	−0.469961	+	0.882687i	$0.655732\pi$
$180$	−2.61351e7	−0.334019
$181$	1.40112e8	1.75630	0.878151	−	0.478384i	$-0.158777\pi$
$181$	1.40112e8	1.75630	0.878151	+	0.478384i	$0.158777\pi$
$182$	7.51906e6	0.0924515
$183$	−6.58483e7	−0.794266
$184$	255507.	0.00302371
$185$	5.07712e6	0.0589545
$186$	−2.34206e6	−0.0266872
$187$	5.03084e7	0.562594
$188$	1.01874e8	1.11818
$189$	1.85299e7	0.199645
$190$	−5.80523e7	−0.614019
$191$	6.81775e7	0.707985	0.353993	−	0.935248i	$-0.384824\pi$
$191$	6.81775e7	0.707985	0.353993	+	0.935248i	$0.384824\pi$
$192$	−6.08631e7	−0.620582
$193$	1.46685e8	1.46870	0.734352	−	0.678769i	$-0.237486\pi$
$193$	1.46685e8	1.46870	0.734352	+	0.678769i	$0.237486\pi$
$194$	1.34603e8	1.32358
$195$	3.60184e6	0.0347859
$196$	8.33555e6	0.0790748
$197$	−1.09852e8	−1.02371	−0.511853	−	0.859073i	$-0.671041\pi$
$197$	−1.09852e8	−1.02371	−0.511853	+	0.859073i	$0.671041\pi$
$198$	1.56723e7	0.143485
$199$	−3.69783e7	−0.332630	−0.166315	−	0.986073i	$-0.553187\pi$
$199$	−3.69783e7	−0.332630	−0.166315	+	0.986073i	$0.553187\pi$
$200$	422068.	0.00373059
$201$	−6.07462e7	−0.527634
$202$	−5.79085e7	−0.494325
$203$	−1.79056e8	−1.50228
$204$	−1.35618e8	−1.11843
$205$	1.94957e8	1.58052
$206$	−4.38282e7	−0.349316
$207$	−2.35862e6	−0.0184825
$208$	7.78036e6	0.0599484
$209$	1.77322e7	0.134354
$210$	1.10760e8	0.825305
$211$	6.65043e6	0.0487373	0.0243686	−	0.999703i	$-0.492242\pi$
$211$	6.65043e6	0.0487373	0.0243686	+	0.999703i	$0.492242\pi$
$212$	−3.36862e7	−0.242815
$213$	−1.14980e7	−0.0815254
$214$	−2.51223e8	−1.75231
$215$	−9.43737e7	−0.647614
$216$	−1.55441e6	−0.0104948
$217$	5.05579e6	0.0335877
$218$	2.27485e8	1.48715
$219$	−1.23530e8	−0.794730
$220$	4.77173e7	0.302132
$221$	1.86903e7	0.116478
$222$	8.20733e6	0.0503462
$223$	−2.26359e8	−1.36688	−0.683442	−	0.730005i	$-0.739518\pi$
$223$	−2.26359e8	−1.36688	−0.683442	+	0.730005i	$0.739518\pi$
$224$	2.48769e8	1.47887
$225$	−3.89616e6	−0.0228033
$226$	1.49243e8	0.860034
$227$	2.68565e7	0.152391	0.0761956	−	0.997093i	$-0.475723\pi$
$227$	2.68565e7	0.152391	0.0761956	+	0.997093i	$0.475723\pi$
$228$	−4.78011e7	−0.267095
$229$	−6.97765e7	−0.383959	−0.191980	−	0.981399i	$-0.561491\pi$
$229$	−6.97765e7	−0.383959	−0.191980	+	0.981399i	$0.561491\pi$
$230$	−1.40983e7	−0.0764043
$231$	−3.38318e7	−0.180585
$232$	1.50203e7	0.0789716
$233$	1.46171e8	0.757036	0.378518	−	0.925594i	$-0.376434\pi$
$233$	1.46171e8	0.757036	0.378518	+	0.925594i	$0.376434\pi$
$234$	5.82249e6	0.0297066
$235$	−2.06815e8	−1.03955
$236$	3.33798e8	1.65307
$237$	1.04562e8	0.510215
$238$	5.74743e8	2.76347
$239$	−2.37847e8	−1.12695	−0.563475	−	0.826133i	$-0.690536\pi$
$239$	−2.37847e8	−1.12695	−0.563475	+	0.826133i	$0.690536\pi$
$240$	1.14609e8	0.535153
$241$	−1.14347e8	−0.526216	−0.263108	−	0.964766i	$-0.584748\pi$
$241$	−1.14347e8	−0.526216	−0.263108	+	0.964766i	$0.584748\pi$
$242$	−2.86144e7	−0.129787
$243$	1.43489e7	0.0641500
$244$	−3.24094e8	−1.42826
$245$	−1.69220e7	−0.0735141
$246$	3.15155e8	1.34974
$247$	6.58774e6	0.0278162
$248$	−424111.	−0.00176563
$249$	−1.95949e8	−0.804349
$250$	−3.63717e8	−1.47222
$251$	4.25659e7	0.169904	0.0849520	−	0.996385i	$-0.472926\pi$
$251$	4.25659e7	0.169904	0.0849520	+	0.996385i	$0.472926\pi$
$252$	9.12011e7	0.359003
$253$	4.30634e6	0.0167181
$254$	6.27151e8	2.40134
$255$	2.75317e8	1.03978
$256$	2.46769e8	0.919286
$257$	3.16681e8	1.16374	0.581870	−	0.813282i	$-0.302321\pi$
$257$	3.16681e8	1.16374	0.581870	+	0.813282i	$0.302321\pi$
$258$	−1.52558e8	−0.553053
$259$	−1.77171e7	−0.0633642
$260$	1.77276e7	0.0625524
$261$	−1.38654e8	−0.482716
$262$	−7.57937e8	−2.60363
$263$	−5.47643e8	−1.85632	−0.928159	−	0.372183i	$-0.878609\pi$
$263$	−5.47643e8	−1.85632	−0.928159	+	0.372183i	$0.878609\pi$
$264$	2.83802e6	0.00949295
$265$	6.83863e7	0.225740
$266$	2.02579e8	0.659947
$267$	2.84153e8	0.913615
$268$	−2.98982e8	−0.948797
$269$	−3.25584e8	−1.01983	−0.509917	−	0.860223i	$-0.670324\pi$
$269$	−3.25584e8	−1.01983	−0.509917	+	0.860223i	$0.670324\pi$
$270$	8.57683e7	0.265188
$271$	1.69008e8	0.515840	0.257920	−	0.966166i	$-0.416963\pi$
$271$	1.69008e8	0.515840	0.257920	+	0.966166i	$0.416963\pi$
$272$	5.94715e8	1.79192
$273$	−1.25690e7	−0.0373878
$274$	3.05965e8	0.898556
$275$	7.11357e6	0.0206264
$276$	−1.16087e7	−0.0332355
$277$	−1.00530e8	−0.284195	−0.142097	−	0.989853i	$-0.545385\pi$
$277$	−1.00530e8	−0.284195	−0.142097	+	0.989853i	$0.545385\pi$
$278$	−8.91643e8	−2.48905
$279$	3.91502e6	0.0107924
$280$	2.00569e7	0.0546022
$281$	−1.39087e8	−0.373952	−0.186976	−	0.982365i	$-0.559869\pi$
$281$	−1.39087e8	−0.373952	−0.186976	+	0.982365i	$0.559869\pi$
$282$	−3.34323e8	−0.887757
$283$	−3.98925e7	−0.104626	−0.0523129	−	0.998631i	$-0.516659\pi$
$283$	−3.98925e7	−0.104626	−0.0523129	+	0.998631i	$0.516659\pi$
$284$	−5.65911e7	−0.146600
$285$	9.70409e7	0.248312
$286$	−1.06306e7	−0.0268706
$287$	−6.80322e8	−1.69874
$288$	1.92638e8	0.475191
$289$	1.01831e9	2.48163
$290$	−8.28784e8	−1.99548
$291$	−2.25004e8	−0.535261
$292$	−6.07995e8	−1.42909
$293$	−5.98076e8	−1.38905	−0.694527	−	0.719466i	$-0.744387\pi$
$293$	−5.98076e8	−1.38905	−0.694527	+	0.719466i	$0.744387\pi$
$294$	−2.73550e7	−0.0627799
$295$	−6.77642e8	−1.53682
$296$	1.48622e6	0.00333091
$297$	−2.61981e7	−0.0580259
$298$	−5.85391e8	−1.28141
$299$	1.59986e6	0.00346126
$300$	−1.91762e7	−0.0410052
$301$	3.29326e8	0.696055
$302$	1.09263e8	0.228270
$303$	9.68005e7	0.199907
$304$	2.09619e8	0.427930
$305$	6.57943e8	1.32782
$306$	4.45060e8	0.887960
$307$	4.73935e8	0.934834	0.467417	−	0.884037i	$-0.345185\pi$
$307$	4.73935e8	0.934834	0.467417	+	0.884037i	$0.345185\pi$
$308$	−1.66514e8	−0.324731
$309$	7.32637e7	0.141265
$310$	2.34014e7	0.0446145
$311$	9.40946e8	1.77379	0.886897	−	0.461967i	$-0.152856\pi$
$311$	9.40946e8	1.77379	0.886897	+	0.461967i	$0.152856\pi$
$312$	1.05436e6	0.00196539
$313$	7.85930e8	1.44870	0.724350	−	0.689432i	$-0.242140\pi$
$313$	7.85930e8	1.44870	0.724350	+	0.689432i	$0.242140\pi$
$314$	−1.21040e9	−2.20636
$315$	−1.85147e8	−0.333757
$316$	5.14634e8	0.917474
$317$	9.32750e8	1.64459	0.822295	−	0.569061i	$-0.192693\pi$
$317$	9.32750e8	1.64459	0.822295	+	0.569061i	$0.192693\pi$
$318$	1.10549e8	0.192779
$319$	2.53153e8	0.436633
$320$	6.08131e8	1.03746
$321$	4.19947e8	0.708642
$322$	4.91972e7	0.0821193
$323$	5.03554e8	0.831453
$324$	7.06228e7	0.115355
$325$	2.64279e6	0.00427042
$326$	−2.34569e8	−0.374981
$327$	−3.80267e8	−0.601411
$328$	5.70696e7	0.0892989
$329$	7.21700e8	1.11730
$330$	−1.56595e8	−0.239871
$331$	−4.26957e8	−0.647122	−0.323561	−	0.946207i	$-0.604880\pi$
$331$	−4.26957e8	−0.647122	−0.323561	+	0.946207i	$0.604880\pi$
$332$	−9.64425e8	−1.44639
$333$	−1.37195e7	−0.0203602
$334$	−6.24505e8	−0.917114
$335$	6.06964e8	0.882076
$336$	−3.99938e8	−0.575182
$337$	−6.52544e8	−0.928764	−0.464382	−	0.885635i	$-0.653723\pi$
$337$	−6.52544e8	−0.928764	−0.464382	+	0.885635i	$0.653723\pi$
$338$	1.00957e9	1.42209
$339$	−2.49477e8	−0.347802
$340$	1.35506e9	1.86975
$341$	−7.14800e6	−0.00976212
$342$	1.56870e8	0.212055
$343$	−7.16248e8	−0.958371
$344$	−2.76259e7	−0.0365900
$345$	2.35668e7	0.0308983
$346$	1.74034e9	2.25875
$347$	1.60286e7	0.0205940	0.0102970	−	0.999947i	$-0.496722\pi$
$347$	1.60286e7	0.0205940	0.0102970	+	0.999947i	$0.496722\pi$
$348$	−6.82432e8	−0.868025
$349$	−2.05119e8	−0.258296	−0.129148	−	0.991625i	$-0.541224\pi$
$349$	−2.05119e8	−0.258296	−0.129148	+	0.991625i	$0.541224\pi$
$350$	8.12681e7	0.101317
$351$	−9.73295e6	−0.0120135
$352$	−3.51716e8	−0.429826
$353$	−8.74453e8	−1.05810	−0.529048	−	0.848592i	$-0.677451\pi$
$353$	−8.74453e8	−1.05810	−0.529048	+	0.848592i	$0.677451\pi$
$354$	−1.09543e9	−1.31242
$355$	1.14886e8	0.136291
$356$	1.39855e9	1.64287
$357$	−9.60747e8	−1.11756
$358$	1.16494e9	1.34188
$359$	3.18774e8	0.363623	0.181812	−	0.983333i	$-0.441804\pi$
$359$	3.18774e8	0.363623	0.181812	+	0.983333i	$0.441804\pi$
$360$	1.55313e7	0.0175448
$361$	−7.16384e8	−0.801440
$362$	−2.26309e9	−2.50739
$363$	4.78321e7	0.0524864
$364$	−6.18622e7	−0.0672312
$365$	1.23429e9	1.32860
$366$	1.06359e9	1.13394
$367$	−9.04506e8	−0.955169	−0.477584	−	0.878586i	$-0.658488\pi$
$367$	−9.04506e8	−0.955169	−0.477584	+	0.878586i	$0.658488\pi$
$368$	5.09069e7	0.0532487
$369$	−5.26816e8	−0.545842
$370$	−8.20060e7	−0.0841666
$371$	−2.38641e8	−0.242625
$372$	1.92690e7	0.0194071
$373$	−5.80057e7	−0.0578749	−0.0289374	−	0.999581i	$-0.509212\pi$
$373$	−5.80057e7	−0.0578749	−0.0289374	+	0.999581i	$0.509212\pi$
$374$	−8.12585e8	−0.803190
$375$	6.07994e8	0.595374
$376$	−6.05407e7	−0.0587340
$377$	9.40500e7	0.0903991
$378$	−2.99297e8	−0.285024
$379$	1.04052e9	0.981778	0.490889	−	0.871222i	$-0.336672\pi$
$379$	1.04052e9	0.981778	0.490889	+	0.871222i	$0.336672\pi$
$380$	4.77618e8	0.446518
$381$	−1.04835e9	−0.971115
$382$	−1.10121e9	−1.01076
$383$	−1.32127e9	−1.20170	−0.600850	−	0.799362i	$-0.705171\pi$
$383$	−1.32127e9	−1.20170	−0.600850	+	0.799362i	$0.705171\pi$
$384$	6.98184e7	0.0629232
$385$	3.38040e8	0.301895
$386$	−2.36926e9	−2.09680
$387$	2.55018e8	0.223657
$388$	−1.10743e9	−0.962512
$389$	8.54262e8	0.735813	0.367907	−	0.929863i	$-0.380075\pi$
$389$	8.54262e8	0.735813	0.367907	+	0.929863i	$0.380075\pi$
$390$	−5.81771e7	−0.0496622
$391$	1.22290e8	0.103460
$392$	−4.95356e6	−0.00415352
$393$	1.26698e9	1.05292
$394$	1.77433e9	1.46150
$395$	−1.04476e9	−0.852955
$396$	−1.28942e8	−0.104343
$397$	−2.12795e9	−1.70685	−0.853423	−	0.521219i	$-0.825477\pi$
$397$	−2.12795e9	−1.70685	−0.853423	+	0.521219i	$0.825477\pi$
$398$	5.97276e8	0.474880
$399$	−3.38634e8	−0.266886
$400$	8.40922e7	0.0656971
$401$	−6.65496e8	−0.515395	−0.257698	−	0.966226i	$-0.582964\pi$
$401$	−6.65496e8	−0.515395	−0.257698	+	0.966226i	$0.582964\pi$
$402$	9.81177e8	0.753279
$403$	−2.65558e6	−0.00202112
$404$	4.76435e8	0.359475
$405$	−1.43371e8	−0.107243
$406$	2.89212e9	2.14474
$407$	2.50489e7	0.0184165
$408$	8.05934e7	0.0587474
$409$	4.67414e8	0.337808	0.168904	−	0.985632i	$-0.445977\pi$
$409$	4.67414e8	0.337808	0.168904	+	0.985632i	$0.445977\pi$
$410$	−3.14896e9	−2.25644
$411$	−5.11456e8	−0.363380
$412$	3.60591e8	0.254024
$413$	2.36470e9	1.65177
$414$	3.80965e7	0.0263867
$415$	1.95788e9	1.34468
$416$	−1.30667e8	−0.0889898
$417$	1.49048e9	1.00659
$418$	−2.86411e8	−0.191811
$419$	1.39394e8	0.0925751	0.0462875	−	0.998928i	$-0.485261\pi$
$419$	1.39394e8	0.0925751	0.0462875	+	0.998928i	$0.485261\pi$
$420$	−9.11263e8	−0.600166
$421$	−1.06298e9	−0.694285	−0.347142	−	0.937812i	$-0.612848\pi$
$421$	−1.06298e9	−0.694285	−0.347142	+	0.937812i	$0.612848\pi$
$422$	−1.07418e8	−0.0695800
$423$	5.58858e8	0.359013
$424$	2.00187e7	0.0127542
$425$	2.02010e8	0.127647
$426$	1.85716e8	0.116390
$427$	−2.29596e9	−1.42714
$428$	2.06691e9	1.27429
$429$	1.77703e7	0.0108666
$430$	1.52433e9	0.924569
$431$	9.93068e8	0.597460	0.298730	−	0.954338i	$-0.403437\pi$
$431$	9.93068e8	0.597460	0.298730	+	0.954338i	$0.403437\pi$
$432$	−3.09698e8	−0.184818
$433$	1.53717e9	0.909946	0.454973	−	0.890505i	$-0.349649\pi$
$433$	1.53717e9	0.909946	0.454973	+	0.890505i	$0.349649\pi$
$434$	−8.16615e7	−0.0479516
$435$	1.38541e9	0.806983
$436$	−1.87161e9	−1.08146
$437$	4.31036e7	0.0247075
$438$	1.99527e9	1.13460
$439$	−3.02801e9	−1.70817	−0.854085	−	0.520133i	$-0.825882\pi$
$439$	−3.02801e9	−1.70817	−0.854085	+	0.520133i	$0.825882\pi$
$440$	−2.83569e7	−0.0158699
$441$	4.57269e7	0.0253885
$442$	−3.01887e8	−0.166290
$443$	−9.36755e8	−0.511933	−0.255966	−	0.966686i	$-0.582394\pi$
$443$	−9.36755e8	−0.511933	−0.255966	+	0.966686i	$0.582394\pi$
$444$	−6.75249e7	−0.0366120
$445$	−2.83920e9	−1.52734
$446$	3.65617e9	1.95144
$447$	9.78546e8	0.518209
$448$	−2.12213e9	−1.11506
$449$	−2.70066e9	−1.40801	−0.704007	−	0.710193i	$-0.748608\pi$
$449$	−2.70066e9	−1.40801	−0.704007	+	0.710193i	$0.748608\pi$
$450$	6.29311e7	0.0325553
$451$	9.61855e8	0.493733
$452$	−1.22788e9	−0.625421
$453$	−1.82645e8	−0.0923135
$454$	−4.33789e8	−0.217562
$455$	1.25587e8	0.0625033
$456$	2.84067e7	0.0140295
$457$	2.09600e9	1.02727	0.513636	−	0.858008i	$-0.328298\pi$
$457$	2.09600e9	1.02727	0.513636	+	0.858008i	$0.328298\pi$
$458$	1.12703e9	0.548161
$459$	−7.43967e8	−0.359095
$460$	1.15992e8	0.0555616
$461$	−1.31874e9	−0.626913	−0.313456	−	0.949603i	$-0.601487\pi$
$461$	−1.31874e9	−0.626913	−0.313456	+	0.949603i	$0.601487\pi$
$462$	5.46453e8	0.257814
$463$	−5.89762e8	−0.276149	−0.138074	−	0.990422i	$-0.544091\pi$
$463$	−5.89762e8	−0.276149	−0.138074	+	0.990422i	$0.544091\pi$
$464$	2.99262e9	1.39072
$465$	−3.91181e7	−0.0180423
$466$	−2.36097e9	−1.08079
$467$	−1.44373e9	−0.655958	−0.327979	−	0.944685i	$-0.606367\pi$
$467$	−1.44373e9	−0.655958	−0.327979	+	0.944685i	$0.606367\pi$
$468$	−4.79039e7	−0.0216028
$469$	−2.11806e9	−0.948054
$470$	3.34049e9	1.48411
$471$	2.02333e9	0.892263
$472$	−1.98366e8	−0.0868299
$473$	−4.65609e8	−0.202305
$474$	−1.68889e9	−0.728410
$475$	7.12022e7	0.0304835
$476$	−4.72863e9	−2.00961
$477$	−1.84795e8	−0.0779606
$478$	3.84172e9	1.60889
$479$	3.23211e9	1.34373	0.671865	−	0.740674i	$-0.265494\pi$
$479$	3.23211e9	1.34373	0.671865	+	0.740674i	$0.265494\pi$
$480$	−1.92480e9	−0.794403
$481$	9.30600e6	0.00381290
$482$	1.84694e9	0.751254
$483$	−8.22387e7	−0.0332094
$484$	2.35421e8	0.0943816
$485$	2.24820e9	0.894826
$486$	−2.31765e8	−0.0915841
$487$	1.96799e9	0.772097	0.386049	−	0.922478i	$-0.373840\pi$
$487$	1.96799e9	0.772097	0.386049	+	0.922478i	$0.373840\pi$
$488$	1.92599e8	0.0750213
$489$	3.92108e8	0.151644
$490$	2.73325e8	0.104953
$491$	2.95682e9	1.12730	0.563651	−	0.826013i	$-0.309396\pi$
$491$	2.95682e9	1.12730	0.563651	+	0.826013i	$0.309396\pi$
$492$	−2.59290e9	−0.981539
$493$	7.18900e9	2.70212
$494$	−1.06406e8	−0.0397119
$495$	2.61766e8	0.0970052
$496$	−8.44993e7	−0.0310933
$497$	−4.00904e8	−0.146485
$498$	3.16498e9	1.14833
$499$	−8.93127e8	−0.321782	−0.160891	−	0.986972i	$-0.551437\pi$
$499$	−8.93127e8	−0.321782	−0.160891	+	0.986972i	$0.551437\pi$
$500$	2.99244e9	1.07061
$501$	1.04393e9	0.370885
$502$	−6.87527e8	−0.242564
$503$	−2.21703e9	−0.776753	−0.388376	−	0.921501i	$-0.626964\pi$
$503$	−2.21703e9	−0.776753	−0.388376	+	0.921501i	$0.626964\pi$
$504$	−5.41980e7	−0.0188572
$505$	−9.67211e8	−0.334196
$506$	−6.95562e7	−0.0238676
$507$	−1.68761e9	−0.575100
$508$	−5.15982e9	−1.74627
$509$	−3.13384e9	−1.05333	−0.526665	−	0.850073i	$-0.676558\pi$
$509$	−3.13384e9	−1.05333	−0.526665	+	0.850073i	$0.676558\pi$
$510$	−4.44695e9	−1.48445
$511$	−4.30718e9	−1.42797
$512$	−4.31682e9	−1.42141
$513$	−2.62226e8	−0.0857559
$514$	−5.11505e9	−1.66142
$515$	−7.32036e8	−0.236161
$516$	1.25515e9	0.402183
$517$	−1.02036e9	−0.324740
$518$	2.86168e8	0.0904621
$519$	−2.90917e9	−0.913448
$520$	−1.05350e7	−0.00328565
$521$	−3.68152e9	−1.14050	−0.570250	−	0.821471i	$-0.693154\pi$
$521$	−3.68152e9	−1.14050	−0.570250	+	0.821471i	$0.693154\pi$
$522$	2.23955e9	0.689151
$523$	−2.56743e9	−0.784769	−0.392385	−	0.919801i	$-0.628350\pi$
$523$	−2.56743e9	−0.784769	−0.392385	+	0.919801i	$0.628350\pi$
$524$	6.23584e9	1.89337
$525$	−1.35849e8	−0.0409731
$526$	8.84557e9	2.65018
$527$	−2.02987e8	−0.0604132
$528$	5.65442e8	0.167174
$529$	−3.39436e9	−0.996926
$530$	−1.10458e9	−0.322279
$531$	1.83114e9	0.530750
$532$	−1.66670e9	−0.479916
$533$	3.57343e8	0.102221
$534$	−4.58966e9	−1.30433
$535$	−4.19603e9	−1.18468
$536$	1.77676e8	0.0498370
$537$	−1.94734e9	−0.542664
$538$	5.25885e9	1.45597
$539$	−8.34877e7	−0.0229648
$540$	−7.05649e8	−0.192846
$541$	4.04285e8	0.109773	0.0548867	−	0.998493i	$-0.482520\pi$
$541$	4.04285e8	0.109773	0.0548867	+	0.998493i	$0.482520\pi$
$542$	−2.72983e9	−0.736442
$543$	3.78301e9	1.01400
$544$	−9.98795e9	−2.65999
$545$	3.79955e9	1.00541
$546$	2.03015e8	0.0533769
$547$	4.51504e9	1.17952	0.589761	−	0.807578i	$-0.299222\pi$
$547$	4.51504e9	1.17952	0.589761	+	0.807578i	$0.299222\pi$
$548$	−2.51730e9	−0.653435
$549$	−1.77791e9	−0.458570
$550$	−1.14899e8	−0.0294473
$551$	2.53390e9	0.645296
$552$	6.89869e6	0.00174574
$553$	3.64579e9	0.916755
$554$	1.62377e9	0.405732
$555$	1.37082e8	0.0340374
$556$	7.33589e9	1.81005
$557$	−5.11346e9	−1.25378	−0.626891	−	0.779107i	$-0.715673\pi$
$557$	−5.11346e9	−1.25378	−0.626891	+	0.779107i	$0.715673\pi$
$558$	−6.32357e7	−0.0154079
$559$	−1.72980e8	−0.0418847
$560$	3.99610e9	0.961565
$561$	1.35833e9	0.324814
$562$	2.24655e9	0.533874
$563$	−1.11554e9	−0.263455	−0.131728	−	0.991286i	$-0.542052\pi$
$563$	−1.11554e9	−0.263455	−0.131728	+	0.991286i	$0.542052\pi$
$564$	2.75060e9	0.645582
$565$	2.49272e9	0.581440
$566$	6.44347e8	0.149370
$567$	5.00308e8	0.115265
$568$	3.36303e7	0.00770037
$569$	−2.04157e9	−0.464592	−0.232296	−	0.972645i	$-0.574624\pi$
$569$	−2.04157e9	−0.464592	−0.232296	+	0.972645i	$0.574624\pi$
$570$	−1.56741e9	−0.354504
$571$	−3.20960e9	−0.721481	−0.360740	−	0.932666i	$-0.617476\pi$
$571$	−3.20960e9	−0.721481	−0.360740	+	0.932666i	$0.617476\pi$
$572$	8.74623e7	0.0195405
$573$	1.84079e9	0.408756
$574$	1.09886e10	2.42522
$575$	1.72918e7	0.00379317
$576$	−1.64330e9	−0.358293
$577$	3.42730e9	0.742741	0.371370	−	0.928485i	$-0.378888\pi$
$577$	3.42730e9	0.742741	0.371370	+	0.928485i	$0.378888\pi$
$578$	−1.64478e10	−3.54291
$579$	3.96049e9	0.847957
$580$	6.81872e9	1.45113
$581$	−6.83221e9	−1.44526
$582$	3.63429e9	0.764168
$583$	3.37396e8	0.0705180
$584$	3.61313e8	0.0750651
$585$	9.72496e7	0.0200836
$586$	9.66016e9	1.98309
$587$	8.35946e9	1.70586	0.852932	−	0.522021i	$-0.174822\pi$
$587$	8.35946e9	1.70586	0.852932	+	0.522021i	$0.174822\pi$
$588$	2.25060e8	0.0456539
$589$	−7.15468e7	−0.0144274
$590$	1.09453e10	2.19405
$591$	−2.96600e9	−0.591037
$592$	2.96113e8	0.0586585
$593$	−8.12059e9	−1.59918	−0.799588	−	0.600549i	$-0.794949\pi$
$593$	−8.12059e9	−1.59918	−0.799588	+	0.600549i	$0.794949\pi$
$594$	4.23153e8	0.0828409
$595$	9.59959e9	1.86829
$596$	4.81623e9	0.931849
$597$	−9.98414e8	−0.192044
$598$	−2.58411e7	−0.00494148
$599$	6.41597e9	1.21974	0.609872	−	0.792500i	$-0.291221\pi$
$599$	6.41597e9	1.21974	0.609872	+	0.792500i	$0.291221\pi$
$600$	1.13958e7	0.00215386
$601$	2.70488e8	0.0508262	0.0254131	−	0.999677i	$-0.491910\pi$
$601$	2.70488e8	0.0508262	0.0254131	+	0.999677i	$0.491910\pi$
$602$	−5.31930e9	−0.993726
$603$	−1.64015e9	−0.304630
$604$	−8.98949e8	−0.165999
$605$	−4.77929e8	−0.0877445
$606$	−1.56353e9	−0.285399
$607$	1.90836e8	0.0346338	0.0173169	−	0.999850i	$-0.494488\pi$
$607$	1.90836e8	0.0346338	0.0173169	+	0.999850i	$0.494488\pi$
$608$	−3.52045e9	−0.635236
$609$	−4.83451e9	−0.867344
$610$	−1.06271e10	−1.89567
$611$	−3.79077e8	−0.0672331
$612$	−3.66168e9	−0.645729
$613$	2.99655e9	0.525424	0.262712	−	0.964874i	$-0.415383\pi$
$613$	2.99655e9	0.525424	0.262712	+	0.964874i	$0.415383\pi$
$614$	−7.65503e9	−1.33462
$615$	5.26384e9	0.912515
$616$	9.89541e7	0.0170569
$617$	−5.07771e9	−0.870302	−0.435151	−	0.900358i	$-0.643305\pi$
$617$	−5.07771e9	−0.870302	−0.435151	+	0.900358i	$0.643305\pi$
$618$	−1.18336e9	−0.201677
$619$	3.44385e9	0.583615	0.291808	−	0.956477i	$-0.405743\pi$
$619$	3.44385e9	0.583615	0.291808	+	0.956477i	$0.405743\pi$
$620$	−1.92532e8	−0.0324439
$621$	−6.36826e7	−0.0106709
$622$	−1.51982e10	−2.53237
$623$	9.90767e9	1.64159
$624$	2.10070e8	0.0346112
$625$	−5.65741e9	−0.926910
$626$	−1.26944e10	−2.06824
$627$	4.78768e8	0.0775692
$628$	9.95846e9	1.60448
$629$	7.11333e8	0.113971
$630$	2.99051e9	0.476490
$631$	4.35206e9	0.689592	0.344796	−	0.938678i	$-0.387948\pi$
$631$	4.35206e9	0.689592	0.344796	+	0.938678i	$0.387948\pi$
$632$	−3.05831e8	−0.0481916
$633$	1.79562e8	0.0281385
$634$	−1.50658e10	−2.34791
$635$	1.04749e10	1.62347
$636$	−9.09527e8	−0.140190
$637$	−3.10168e7	−0.00475455
$638$	−4.08895e9	−0.623361
$639$	−3.10446e8	−0.0470687
$640$	−6.97611e8	−0.105192
$641$	−4.77613e9	−0.716264	−0.358132	−	0.933671i	$-0.616586\pi$
$641$	−4.77613e9	−0.716264	−0.358132	+	0.933671i	$0.616586\pi$
$642$	−6.78301e9	−1.01170
$643$	3.33799e9	0.495161	0.247581	−	0.968867i	$-0.420364\pi$
$643$	3.33799e9	0.495161	0.247581	+	0.968867i	$0.420364\pi$
$644$	−4.04765e8	−0.0597175
$645$	−2.54809e9	−0.373900
$646$	−8.13344e9	−1.18703
$647$	−1.35612e9	−0.196849	−0.0984244	−	0.995145i	$-0.531380\pi$
$647$	−1.35612e9	−0.196849	−0.0984244	+	0.995145i	$0.531380\pi$
$648$	−4.19689e7	−0.00605920
$649$	−3.34327e9	−0.480081
$650$	−4.26865e7	−0.00609669
$651$	1.36506e8	0.0193919
$652$	1.92989e9	0.272688
$653$	2.60069e9	0.365504	0.182752	−	0.983159i	$-0.441500\pi$
$653$	2.60069e9	0.365504	0.182752	+	0.983159i	$0.441500\pi$
$654$	6.14210e9	0.858608
$655$	−1.26594e10	−1.76022
$656$	1.13705e10	1.57259
$657$	−3.33532e9	−0.458838
$658$	−1.16570e10	−1.59512
$659$	4.22761e9	0.575435	0.287718	−	0.957715i	$-0.407104\pi$
$659$	4.22761e9	0.575435	0.287718	+	0.957715i	$0.407104\pi$
$660$	1.28837e9	0.174436
$661$	9.80160e9	1.32005	0.660027	−	0.751242i	$-0.270545\pi$
$661$	9.80160e9	1.32005	0.660027	+	0.751242i	$0.270545\pi$
$662$	6.89624e9	0.923867
$663$	5.04637e8	0.0672484
$664$	5.73128e8	0.0759737
$665$	3.38356e9	0.446168
$666$	2.21598e8	0.0290674
$667$	6.15369e8	0.0802962
$668$	5.13804e9	0.666930
$669$	−6.11170e9	−0.789170
$670$	−9.80372e9	−1.25930
$671$	3.24608e9	0.414792
$672$	6.71677e9	0.853823
$673$	−1.20950e10	−1.52951	−0.764756	−	0.644320i	$-0.777141\pi$
$673$	−1.20950e10	−1.52951	−0.764756	+	0.644320i	$0.777141\pi$
$674$	1.05399e10	1.32595
$675$	−1.05196e8	−0.0131655
$676$	−8.30611e9	−1.03415
$677$	7.17956e8	0.0889278	0.0444639	−	0.999011i	$-0.485842\pi$
$677$	7.17956e8	0.0889278	0.0444639	+	0.999011i	$0.485842\pi$
$678$	4.02957e9	0.496541
$679$	−7.84531e9	−0.961758
$680$	−8.05273e8	−0.0982114
$681$	7.25127e8	0.0879831
$682$	1.15455e8	0.0139369
$683$	1.25624e9	0.150869	0.0754344	−	0.997151i	$-0.475966\pi$
$683$	1.25624e9	0.150869	0.0754344	+	0.997151i	$0.475966\pi$
$684$	−1.29063e9	−0.154207
$685$	5.11036e9	0.607484
$686$	1.15689e10	1.36822
$687$	−1.88397e9	−0.221679
$688$	−5.50415e9	−0.644363
$689$	1.25347e8	0.0145998
$690$	−3.80653e8	−0.0441121
$691$	7.52575e9	0.867714	0.433857	−	0.900982i	$-0.357152\pi$
$691$	7.52575e9	0.867714	0.433857	+	0.900982i	$0.357152\pi$
$692$	−1.43184e10	−1.64257
$693$	−9.13457e8	−0.104261
$694$	−2.58894e8	−0.0294012
$695$	−1.48926e10	−1.68277
$696$	4.05548e8	0.0455943
$697$	2.73146e10	3.05548
$698$	3.31310e9	0.368757
$699$	3.94663e9	0.437075
$700$	−6.68624e8	−0.0736782
$701$	5.32937e9	0.584336	0.292168	−	0.956367i	$-0.405623\pi$
$701$	5.32937e9	0.584336	0.292168	+	0.956367i	$0.405623\pi$
$702$	1.57207e8	0.0171511
$703$	2.50723e8	0.0272176
$704$	3.00032e9	0.324089
$705$	−5.58400e9	−0.600183
$706$	1.41242e10	1.51060
$707$	3.37518e9	0.359194
$708$	9.01253e9	0.954400
$709$	−2.69688e9	−0.284184	−0.142092	−	0.989853i	$-0.545383\pi$
$709$	−2.69688e9	−0.284184	−0.142092	+	0.989853i	$0.545383\pi$
$710$	−1.85564e9	−0.194576
$711$	2.82316e9	0.294573
$712$	−8.31117e8	−0.0862943
$713$	−1.73755e7	−0.00179524
$714$	1.55181e10	1.59549
$715$	−1.77557e8	−0.0181663
$716$	−9.58445e9	−0.975824
$717$	−6.42186e9	−0.650645
$718$	−5.14885e9	−0.519129
$719$	7.06919e9	0.709282	0.354641	−	0.935003i	$-0.384603\pi$
$719$	7.06919e9	0.709282	0.354641	+	0.935003i	$0.384603\pi$
$720$	3.09444e9	0.308971
$721$	2.55451e9	0.253825
$722$	1.15711e10	1.14418
$723$	−3.08736e9	−0.303811
$724$	1.86193e10	1.82339
$725$	1.01652e9	0.0990677
$726$	−7.72588e8	−0.0749324
$727$	2.93968e9	0.283746	0.141873	−	0.989885i	$-0.454688\pi$
$727$	2.93968e9	0.283746	0.141873	+	0.989885i	$0.454688\pi$
$728$	3.67628e7	0.00353142
$729$	3.87420e8	0.0370370
$730$	−1.99364e10	−1.89678
$731$	−1.32223e10	−1.25197
$732$	−8.75054e9	−0.824605
$733$	−1.31189e10	−1.23036	−0.615181	−	0.788386i	$-0.710917\pi$
$733$	−1.31189e10	−1.23036	−0.615181	+	0.788386i	$0.710917\pi$
$734$	1.46096e10	1.36365
$735$	−4.56894e8	−0.0424434
$736$	−8.54956e8	−0.0790445
$737$	2.99456e9	0.275548
$738$	8.50917e9	0.779274
$739$	−1.64503e10	−1.49940	−0.749701	−	0.661777i	$-0.769803\pi$
$739$	−1.64503e10	−1.49940	−0.749701	+	0.661777i	$0.769803\pi$
$740$	6.74695e8	0.0612064
$741$	1.77869e8	0.0160597
$742$	3.85454e9	0.346385
$743$	−1.47546e10	−1.31968	−0.659838	−	0.751408i	$-0.729375\pi$
$743$	−1.47546e10	−1.31968	−0.659838	+	0.751408i	$0.729375\pi$
$744$	−1.14510e7	−0.00101938
$745$	−9.77744e9	−0.866319
$746$	9.36913e8	0.0826253
$747$	−5.29061e9	−0.464391
$748$	6.68545e9	0.584084
$749$	1.46424e10	1.27329
$750$	−9.82036e9	−0.849988
$751$	−3.17761e9	−0.273754	−0.136877	−	0.990588i	$-0.543706\pi$
$751$	−3.17761e9	−0.273754	−0.136877	+	0.990588i	$0.543706\pi$
$752$	−1.20620e10	−1.03433
$753$	1.14928e9	0.0980941
$754$	−1.51910e9	−0.129059
$755$	1.82496e9	0.154326
$756$	2.46243e9	0.207271
$757$	−5.96410e8	−0.0499700	−0.0249850	−	0.999688i	$-0.507954\pi$
$757$	−5.96410e8	−0.0499700	−0.0249850	+	0.999688i	$0.507954\pi$
$758$	−1.68066e10	−1.40164
$759$	1.16271e8	0.00965218
$760$	−2.83834e8	−0.0234540
$761$	−1.29261e10	−1.06322	−0.531609	−	0.846990i	$-0.678413\pi$
$761$	−1.29261e10	−1.06322	−0.531609	+	0.846990i	$0.678413\pi$
$762$	1.69331e10	1.38642
$763$	−1.32589e10	−1.08062
$764$	9.06006e9	0.735029
$765$	7.43357e9	0.600320
$766$	2.13412e10	1.71561
$767$	−1.24207e9	−0.0993945
$768$	6.66276e9	0.530750
$769$	2.12256e10	1.68313	0.841566	−	0.540154i	$-0.181634\pi$
$769$	2.12256e10	1.68313	0.841566	+	0.540154i	$0.181634\pi$
$770$	−5.46005e9	−0.431001
$771$	8.55038e9	0.671885
$772$	1.94928e10	1.52481
$773$	−1.41888e10	−1.10488	−0.552442	−	0.833551i	$-0.686304\pi$
$773$	−1.41888e10	−1.10488	−0.552442	+	0.833551i	$0.686304\pi$
$774$	−4.11907e9	−0.319305
$775$	−2.87022e7	−0.00221493
$776$	6.58113e8	0.0505573
$777$	−4.78362e8	−0.0365833
$778$	−1.37981e10	−1.05049
$779$	9.62754e9	0.729683
$780$	4.78646e8	0.0361146
$781$	5.66808e8	0.0425753
$782$	−1.97524e9	−0.147706
$783$	−3.74366e9	−0.278696
$784$	−9.86941e8	−0.0731450
$785$	−2.02167e10	−1.49165
$786$	−2.04643e10	−1.50320
$787$	2.08224e10	1.52272	0.761358	−	0.648331i	$-0.224533\pi$
$787$	2.08224e10	1.52272	0.761358	+	0.648331i	$0.224533\pi$
$788$	−1.45981e10	−1.06281
$789$	−1.47864e10	−1.07175
$790$	1.68750e10	1.21772
$791$	−8.69860e9	−0.624931
$792$	7.66264e7	0.00548076
$793$	1.20596e9	0.0858772
$794$	3.43708e10	2.43679
$795$	1.84643e9	0.130331
$796$	−4.91402e9	−0.345335
$797$	7.34091e9	0.513625	0.256812	−	0.966461i	$-0.417328\pi$
$797$	7.34091e9	0.513625	0.256812	+	0.966461i	$0.417328\pi$
$798$	5.46963e9	0.381020
$799$	−2.89759e10	−2.00966
$800$	−1.41229e9	−0.0975233
$801$	7.67214e9	0.527476
$802$	1.07491e10	0.735806
$803$	6.08959e9	0.415034
$804$	−8.07252e9	−0.547788
$805$	8.21713e8	0.0555181
$806$	4.28931e7	0.00288546
$807$	−8.79076e9	−0.588802
$808$	−2.83131e8	−0.0188820
$809$	1.66982e10	1.10879	0.554396	−	0.832253i	$-0.312949\pi$
$809$	1.66982e10	1.10879	0.554396	+	0.832253i	$0.312949\pi$
$810$	2.31574e9	0.153106
$811$	−6.51741e9	−0.429044	−0.214522	−	0.976719i	$-0.568819\pi$
$811$	−6.51741e9	−0.429044	−0.214522	+	0.976719i	$0.568819\pi$
$812$	−2.37946e10	−1.55967
$813$	4.56322e9	0.297821
$814$	−4.04591e8	−0.0262924
$815$	−3.91787e9	−0.253512
$816$	1.60573e10	1.03456
$817$	−4.66044e9	−0.298985
$818$	−7.54970e9	−0.482273
$819$	−3.39362e8	−0.0215859
$820$	2.59077e10	1.64089
$821$	−1.18606e10	−0.748004	−0.374002	−	0.927428i	$-0.622015\pi$
$821$	−1.18606e10	−0.748004	−0.374002	+	0.927428i	$0.622015\pi$
$822$	8.26107e9	0.518782
$823$	−1.25746e10	−0.786312	−0.393156	−	0.919472i	$-0.628617\pi$
$823$	−1.25746e10	−0.786312	−0.393156	+	0.919472i	$0.628617\pi$
$824$	−2.14288e8	−0.0133430
$825$	1.92066e8	0.0119086
$826$	−3.81948e10	−2.35816
$827$	9.40698e9	0.578337	0.289168	−	0.957278i	$-0.406621\pi$
$827$	9.40698e9	0.578337	0.289168	+	0.957278i	$0.406621\pi$
$828$	−3.13435e8	−0.0191885
$829$	1.41629e10	0.863397	0.431698	−	0.902018i	$-0.357914\pi$
$829$	1.41629e10	0.863397	0.431698	+	0.902018i	$0.357914\pi$
$830$	−3.16238e10	−1.91973
$831$	−2.71431e9	−0.164080
$832$	1.11466e9	0.0670983
$833$	−2.37087e9	−0.142118
$834$	−2.40744e10	−1.43706
$835$	−1.04307e10	−0.620030
$836$	2.35641e9	0.139486
$837$	1.05706e8	0.00623101
$838$	−2.25150e9	−0.132165
$839$	−2.87491e10	−1.68058	−0.840288	−	0.542141i	$-0.817614\pi$
$839$	−2.87491e10	−1.68058	−0.840288	+	0.542141i	$0.817614\pi$
$840$	5.41535e8	0.0315246
$841$	1.89254e10	1.09713
$842$	1.71693e10	0.991198
$843$	−3.75536e9	−0.215901
$844$	8.83771e8	0.0505989
$845$	1.68622e10	0.961428
$846$	−9.02672e9	−0.512547
$847$	1.66778e9	0.0943076
$848$	3.98849e9	0.224607
$849$	−1.07710e9	−0.0604057
$850$	−3.26287e9	−0.182236
$851$	6.08892e7	0.00338678
$852$	−1.52796e9	−0.0846395
$853$	−1.16952e10	−0.645185	−0.322593	−	0.946538i	$-0.604554\pi$
$853$	−1.16952e10	−0.645185	−0.322593	+	0.946538i	$0.604554\pi$
$854$	3.70845e10	2.03746
$855$	2.62010e9	0.143363
$856$	−1.22830e9	−0.0669338
$857$	2.19293e10	1.19012	0.595061	−	0.803680i	$-0.297128\pi$
$857$	2.19293e10	1.19012	0.595061	+	0.803680i	$0.297128\pi$
$858$	−2.87027e8	−0.0155138
$859$	3.01068e10	1.62065	0.810323	−	0.585984i	$-0.199292\pi$
$859$	3.01068e10	1.62065	0.810323	+	0.585984i	$0.199292\pi$
$860$	−1.25413e10	−0.672351
$861$	−1.83687e10	−0.980770
$862$	−1.60401e10	−0.852966
$863$	−8.99179e9	−0.476221	−0.238110	−	0.971238i	$-0.576528\pi$
$863$	−8.99179e9	−0.476221	−0.238110	+	0.971238i	$0.576528\pi$
$864$	5.20122e9	0.274351
$865$	2.90679e10	1.52706
$866$	−2.48285e10	−1.29909
$867$	2.74943e10	1.43277
$868$	6.71860e8	0.0348707
$869$	−5.15450e9	−0.266451
$870$	−2.23772e10	−1.15209
$871$	1.11252e9	0.0570486
$872$	1.11224e9	0.0568055
$873$	−6.07512e9	−0.309033
$874$	−6.96212e8	−0.0352738
$875$	2.11991e10	1.06977
$876$	−1.64159e10	−0.825087
$877$	2.83846e10	1.42097	0.710483	−	0.703715i	$-0.248477\pi$
$877$	2.83846e10	1.42097	0.710483	+	0.703715i	$0.248477\pi$
$878$	4.89086e10	2.43868
$879$	−1.61480e10	−0.801971
$880$	−5.64979e9	−0.279475
$881$	2.39358e9	0.117932	0.0589661	−	0.998260i	$-0.481220\pi$
$881$	2.39358e9	0.117932	0.0589661	+	0.998260i	$0.481220\pi$
$882$	−7.38584e8	−0.0362460
$883$	8.31976e7	0.00406676	0.00203338	−	0.999998i	$-0.499353\pi$
$883$	8.31976e7	0.00406676	0.00203338	+	0.999998i	$0.499353\pi$
$884$	2.48374e9	0.120927
$885$	−1.82963e10	−0.887285
$886$	1.51305e10	0.730863
$887$	−2.65449e10	−1.27717	−0.638585	−	0.769552i	$-0.720480\pi$
$887$	−2.65449e10	−1.27717	−0.638585	+	0.769552i	$0.720480\pi$
$888$	4.01280e7	0.00192310
$889$	−3.65533e10	−1.74490
$890$	4.58590e10	2.18052
$891$	−7.07348e8	−0.0335013
$892$	−3.00807e10	−1.41909
$893$	−1.02131e10	−0.479930
$894$	−1.58055e10	−0.739824
$895$	1.94574e10	0.907202
$896$	2.43438e9	0.113060
$897$	4.31963e7	0.00199836
$898$	4.36212e10	2.01016
$899$	−1.02144e9	−0.0468871
$900$	−5.17758e8	−0.0236744
$901$	9.58130e9	0.436403
$902$	−1.55360e10	−0.704880
$903$	8.89180e9	0.401867
$904$	7.29693e8	0.0328511
$905$	−3.77991e10	−1.69516
$906$	2.95010e9	0.131792
$907$	2.73757e10	1.21826	0.609129	−	0.793071i	$-0.291519\pi$
$907$	2.73757e10	1.21826	0.609129	+	0.793071i	$0.291519\pi$
$908$	3.56895e9	0.158212
$909$	2.61361e9	0.115417
$910$	−2.02848e9	−0.0892332
$911$	2.12356e10	0.930573	0.465286	−	0.885160i	$-0.345951\pi$
$911$	2.12356e10	0.930573	0.465286	+	0.885160i	$0.345951\pi$
$912$	5.65971e9	0.247065
$913$	9.65954e9	0.420058
$914$	−3.38548e10	−1.46659
$915$	1.77645e10	0.766617
$916$	−9.27255e9	−0.398625
$917$	4.41762e10	1.89189
$918$	1.20166e10	0.512664
$919$	−1.70856e10	−0.726148	−0.363074	−	0.931760i	$-0.618273\pi$
$919$	−1.70856e10	−0.726148	−0.363074	+	0.931760i	$0.618273\pi$
$920$	−6.89303e7	−0.00291845
$921$	1.27962e10	0.539726
$922$	2.13004e10	0.895015
$923$	2.10577e8	0.00881465
$924$	−4.49588e9	−0.187483
$925$	1.00582e8	0.00417853
$926$	9.52587e9	0.394245
$927$	1.97812e9	0.0815593
$928$	−5.02597e10	−2.06444
$929$	1.92047e10	0.785873	0.392937	−	0.919566i	$-0.371459\pi$
$929$	1.92047e10	0.785873	0.392937	+	0.919566i	$0.371459\pi$
$930$	6.31838e8	0.0257582
$931$	−8.35657e8	−0.0339394
$932$	1.94246e10	0.785953
$933$	2.54055e10	1.02410
$934$	2.33192e10	0.936481
$935$	−1.35721e10	−0.543010
$936$	2.84678e7	0.00113472
$937$	1.27664e10	0.506967	0.253483	−	0.967340i	$-0.418424\pi$
$937$	1.27664e10	0.506967	0.253483	+	0.967340i	$0.418424\pi$
$938$	3.42110e10	1.35349
$939$	2.12201e10	0.836407
$940$	−2.74835e10	−1.07926
$941$	1.63894e10	0.641208	0.320604	−	0.947213i	$-0.396114\pi$
$941$	1.63894e10	0.641208	0.320604	+	0.947213i	$0.396114\pi$
$942$	−3.26809e10	−1.27384
$943$	2.33809e9	0.0907968
$944$	−3.95221e10	−1.52911
$945$	−4.99898e9	−0.192695
$946$	7.52055e9	0.288822
$947$	1.60375e10	0.613636	0.306818	−	0.951768i	$-0.400736\pi$
$947$	1.60375e10	0.613636	0.306818	+	0.951768i	$0.400736\pi$
$948$	1.38951e10	0.529704
$949$	2.26237e9	0.0859274
$950$	−1.15006e9	−0.0435200
$951$	2.51842e10	0.949505
$952$	2.81008e9	0.105557
$953$	6.76173e9	0.253065	0.126533	−	0.991962i	$-0.459615\pi$
$953$	6.76173e9	0.253065	0.126533	+	0.991962i	$0.459615\pi$
$954$	2.98482e9	0.111301
$955$	−1.83928e10	−0.683340
$956$	−3.16073e10	−1.17000
$957$	6.83514e9	0.252090
$958$	−5.22053e10	−1.91838
$959$	−1.78331e10	−0.652923
$960$	1.64195e10	0.598979
$961$	−2.74838e10	−0.998952
$962$	−1.50311e8	−0.00544350
$963$	1.13386e10	0.409135
$964$	−1.51954e10	−0.546316
$965$	−3.95724e10	−1.41758
$966$	1.32833e9	0.0474116
$967$	−4.73091e10	−1.68249	−0.841244	−	0.540656i	$-0.818176\pi$
$967$	−4.73091e10	−1.68249	−0.841244	+	0.540656i	$0.818176\pi$
$968$	−1.39904e8	−0.00495753
$969$	1.35960e10	0.480039
$970$	−3.63131e10	−1.27750
$971$	−1.37661e10	−0.482553	−0.241277	−	0.970456i	$-0.577566\pi$
$971$	−1.37661e10	−0.482553	−0.241277	+	0.970456i	$0.577566\pi$
$972$	1.90682e9	0.0666004
$973$	5.19692e10	1.80863
$974$	−3.17871e10	−1.10229
$975$	7.13553e7	0.00246553
$976$	3.83732e10	1.32115
$977$	−3.45342e10	−1.18473	−0.592364	−	0.805670i	$-0.701805\pi$
$977$	−3.45342e10	−1.18473	−0.592364	+	0.805670i	$0.701805\pi$
$978$	−6.33336e9	−0.216495
$979$	−1.40077e10	−0.477120
$980$	−2.24875e9	−0.0763221
$981$	−1.02672e10	−0.347225
$982$	−4.77588e10	−1.60940
$983$	1.27156e9	0.0426972	0.0213486	−	0.999772i	$-0.493204\pi$
$983$	1.27156e9	0.0426972	0.0213486	+	0.999772i	$0.493204\pi$
$984$	1.54088e9	0.0515568
$985$	2.96357e10	0.988071
$986$	−1.16117e11	−3.85769
$987$	1.94859e10	0.645076
$988$	8.75441e8	0.0288787
$989$	−1.13181e9	−0.0372037
$990$	−4.22806e9	−0.138490
$991$	−4.82056e10	−1.57340	−0.786700	−	0.617335i	$-0.788212\pi$
$991$	−4.82056e10	−1.57340	−0.786700	+	0.617335i	$0.788212\pi$
$992$	1.41912e9	0.0461561
$993$	−1.15278e10	−0.373616
$994$	6.47543e9	0.209130
$995$	9.97595e9	0.321051
$996$	−2.60395e10	−0.835073
$997$	1.86779e10	0.596892	0.298446	−	0.954427i	$-0.403532\pi$
$997$	1.86779e10	0.596892	0.298446	+	0.954427i	$0.403532\pi$
$998$	1.44258e10	0.459393
$999$	−3.70426e8	−0.0117550

Twists

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

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

\(f(q)\)	\(=\)	\(q-16.1521 q^{2} +27.0000 q^{3} +132.889 q^{4} -269.779 q^{5} -436.106 q^{6} +941.418 q^{7} -78.9720 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-16.1521 q^{2} +27.0000 q^{3} +132.889 q^{4} -269.779 q^{5} -436.106 q^{6} +941.418 q^{7} -78.9720 q^{8} +729.000 q^{9} +4357.48 q^{10} -1331.00 q^{11} +3588.01 q^{12} -494.485 q^{13} -15205.9 q^{14} -7284.02 q^{15} -15734.3 q^{16} -37797.5 q^{17} -11774.9 q^{18} -13322.4 q^{19} -35850.7 q^{20} +25418.3 q^{21} +21498.4 q^{22} -3235.41 q^{23} -2132.24 q^{24} -5344.53 q^{25} +7986.95 q^{26} +19683.0 q^{27} +125104. q^{28} -190198. q^{29} +117652. q^{30} +5370.40 q^{31} +264249. q^{32} -35937.0 q^{33} +610507. q^{34} -253974. q^{35} +96876.3 q^{36} -18819.6 q^{37} +215185. q^{38} -13351.1 q^{39} +21304.9 q^{40} -722656. q^{41} -410558. q^{42} +349819. q^{43} -176876. q^{44} -196669. q^{45} +52258.6 q^{46} +766610. q^{47} -424825. q^{48} +62725.6 q^{49} +86325.2 q^{50} -1.02053e6 q^{51} -65711.7 q^{52} -253491. q^{53} -317921. q^{54} +359075. q^{55} -74345.7 q^{56} -359706. q^{57} +3.07209e6 q^{58} +2.51185e6 q^{59} -967968. q^{60} -2.43883e6 q^{61} -86743.0 q^{62} +686294. q^{63} -2.25419e6 q^{64} +133401. q^{65} +580457. q^{66} -2.24986e6 q^{67} -5.02288e6 q^{68} -87356.2 q^{69} +4.10221e6 q^{70} -425851. q^{71} -57570.6 q^{72} -4.57520e6 q^{73} +303975. q^{74} -144302. q^{75} -1.77041e6 q^{76} -1.25303e6 q^{77} +215648. q^{78} +3.87265e6 q^{79} +4.24477e6 q^{80} +531441. q^{81} +1.16724e7 q^{82} -7.25736e6 q^{83} +3.37782e6 q^{84} +1.01969e7 q^{85} -5.65030e6 q^{86} -5.13534e6 q^{87} +105112. q^{88} +1.05242e7 q^{89} +3.17660e6 q^{90} -465517. q^{91} -429952. q^{92} +145001. q^{93} -1.23823e7 q^{94} +3.59411e6 q^{95} +7.13473e6 q^{96} -8.33350e6 q^{97} -1.01315e6 q^{98} -970299. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 19 q^{2} + 54 q^{3} + 13 q^{4} - 34 q^{5} - 513 q^{6} - 166 q^{7} + 627 q^{8} + 1458 q^{9}+O(q^{10}) \) 2 * q - 19 * q^2 + 54 * q^3 + 13 * q^4 - 34 * q^5 - 513 * q^6 - 166 * q^7 + 627 * q^8 + 1458 * q^9	\( 2 q - 19 q^{2} + 54 q^{3} + 13 q^{4} - 34 q^{5} - 513 q^{6} - 166 q^{7} + 627 q^{8} + 1458 q^{9} + 3686 q^{10} - 2662 q^{11} + 351 q^{12} - 12670 q^{13} - 12052 q^{14} - 918 q^{15} - 2399 q^{16} - 62344 q^{17} - 13851 q^{18} - 37980 q^{19} - 64118 q^{20} - 4482 q^{21} + 25289 q^{22} - 90686 q^{23} + 16929 q^{24} - 27878 q^{25} + 42662 q^{26} + 39366 q^{27} + 257872 q^{28} + 13992 q^{29} + 99522 q^{30} + 245000 q^{31} + 135907 q^{32} - 71874 q^{33} + 680414 q^{34} - 515080 q^{35} + 9477 q^{36} + 327852 q^{37} + 285408 q^{38} - 342090 q^{39} + 187758 q^{40} - 275932 q^{41} - 325404 q^{42} - 244104 q^{43} - 17303 q^{44} - 24786 q^{45} + 301312 q^{46} + 536926 q^{47} - 64773 q^{48} + 465558 q^{49} + 150499 q^{50} - 1683288 q^{51} + 1394002 q^{52} - 1821882 q^{53} - 373977 q^{54} + 45254 q^{55} - 856152 q^{56} - 1025460 q^{57} + 2490570 q^{58} + 2502028 q^{59} - 1731186 q^{60} - 2191098 q^{61} - 769192 q^{62} - 121014 q^{63} - 3595591 q^{64} - 2737324 q^{65} + 682803 q^{66} + 1674784 q^{67} - 2080010 q^{68} - 2448522 q^{69} + 4845824 q^{70} - 368310 q^{71} + 457083 q^{72} - 3336604 q^{73} - 683322 q^{74} - 752706 q^{75} + 1185768 q^{76} + 220946 q^{77} + 1151874 q^{78} - 1682618 q^{79} + 7388938 q^{80} + 1062882 q^{81} + 10400150 q^{82} - 8376504 q^{83} + 6962544 q^{84} + 4409396 q^{85} - 3958848 q^{86} + 377784 q^{87} - 834537 q^{88} + 9027204 q^{89} + 2687094 q^{90} + 13017872 q^{91} + 10054436 q^{92} + 6615000 q^{93} - 11728208 q^{94} - 2219616 q^{95} + 3669489 q^{96} - 16703552 q^{97} - 2160387 q^{98} - 1940598 q^{99}+O(q^{100}) \) 2 * q - 19 * q^2 + 54 * q^3 + 13 * q^4 - 34 * q^5 - 513 * q^6 - 166 * q^7 + 627 * q^8 + 1458 * q^9 + 3686 * q^10 - 2662 * q^11 + 351 * q^12 - 12670 * q^13 - 12052 * q^14 - 918 * q^15 - 2399 * q^16 - 62344 * q^17 - 13851 * q^18 - 37980 * q^19 - 64118 * q^20 - 4482 * q^21 + 25289 * q^22 - 90686 * q^23 + 16929 * q^24 - 27878 * q^25 + 42662 * q^26 + 39366 * q^27 + 257872 * q^28 + 13992 * q^29 + 99522 * q^30 + 245000 * q^31 + 135907 * q^32 - 71874 * q^33 + 680414 * q^34 - 515080 * q^35 + 9477 * q^36 + 327852 * q^37 + 285408 * q^38 - 342090 * q^39 + 187758 * q^40 - 275932 * q^41 - 325404 * q^42 - 244104 * q^43 - 17303 * q^44 - 24786 * q^45 + 301312 * q^46 + 536926 * q^47 - 64773 * q^48 + 465558 * q^49 + 150499 * q^50 - 1683288 * q^51 + 1394002 * q^52 - 1821882 * q^53 - 373977 * q^54 + 45254 * q^55 - 856152 * q^56 - 1025460 * q^57 + 2490570 * q^58 + 2502028 * q^59 - 1731186 * q^60 - 2191098 * q^61 - 769192 * q^62 - 121014 * q^63 - 3595591 * q^64 - 2737324 * q^65 + 682803 * q^66 + 1674784 * q^67 - 2080010 * q^68 - 2448522 * q^69 + 4845824 * q^70 - 368310 * q^71 + 457083 * q^72 - 3336604 * q^73 - 683322 * q^74 - 752706 * q^75 + 1185768 * q^76 + 220946 * q^77 + 1151874 * q^78 - 1682618 * q^79 + 7388938 * q^80 + 1062882 * q^81 + 10400150 * q^82 - 8376504 * q^83 + 6962544 * q^84 + 4409396 * q^85 - 3958848 * q^86 + 377784 * q^87 - 834537 * q^88 + 9027204 * q^89 + 2687094 * q^90 + 13017872 * q^91 + 10054436 * q^92 + 6615000 * q^93 - 11728208 * q^94 - 2219616 * q^95 + 3669489 * q^96 - 16703552 * q^97 - 2160387 * q^98 - 1940598 * q^99

Introduction

L-functions

Modular forms

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