LMFDB - Embedded newform 33.8.a.c.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{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			1.1
Root			$-4.42443$ 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)

$f(q)$	$=$	$q-14.2733 q^{2} -27.0000 q^{3} +75.7267 q^{4} +109.826 q^{5} +385.379 q^{6} +411.478 q^{7} +746.112 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-14.2733 q^{2} -27.0000 q^{3} +75.7267 q^{4} +109.826 q^{5} +385.379 q^{6} +411.478 q^{7} +746.112 q^{8} +729.000 q^{9} -1567.58 q^{10} +1331.00 q^{11} -2044.62 q^{12} -7184.38 q^{13} -5873.14 q^{14} -2965.30 q^{15} -20342.5 q^{16} -7787.19 q^{17} -10405.2 q^{18} -27944.2 q^{19} +8316.76 q^{20} -11109.9 q^{21} -18997.7 q^{22} +23452.2 q^{23} -20145.0 q^{24} -66063.2 q^{25} +102545. q^{26} -19683.0 q^{27} +31159.9 q^{28} +75081.3 q^{29} +42324.6 q^{30} -26738.3 q^{31} +194852. q^{32} -35937.0 q^{33} +111149. q^{34} +45191.0 q^{35} +55204.8 q^{36} -56543.1 q^{37} +398856. q^{38} +193978. q^{39} +81942.5 q^{40} -61025.9 q^{41} +158575. q^{42} -745444. q^{43} +100792. q^{44} +80063.2 q^{45} -334741. q^{46} -1.22101e6 q^{47} +549247. q^{48} -654229. q^{49} +942940. q^{50} +210254. q^{51} -544050. q^{52} -682893. q^{53} +280941. q^{54} +146178. q^{55} +307009. q^{56} +754494. q^{57} -1.07166e6 q^{58} -664718. q^{59} -224553. q^{60} +2.01979e6 q^{61} +381643. q^{62} +299967. q^{63} -177338. q^{64} -789032. q^{65} +512939. q^{66} -1.66531e6 q^{67} -589698. q^{68} -633210. q^{69} -645024. q^{70} -2.80056e6 q^{71} +543915. q^{72} -968685. q^{73} +807057. q^{74} +1.78371e6 q^{75} -2.11613e6 q^{76} +547677. q^{77} -2.76871e6 q^{78} -125746. q^{79} -2.23413e6 q^{80} +531441. q^{81} +871040. q^{82} +8.19771e6 q^{83} -841317. q^{84} -855236. q^{85} +1.06399e7 q^{86} -2.02719e6 q^{87} +993075. q^{88} +4.48340e6 q^{89} -1.14276e6 q^{90} -2.95622e6 q^{91} +1.77596e6 q^{92} +721934. q^{93} +1.74278e7 q^{94} -3.06900e6 q^{95} -5.26100e6 q^{96} +1.20638e7 q^{97} +9.33800e6 q^{98} +970299. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−14.2733	−1.26159	−0.630796	−	0.775949i	$-0.717272\pi$
$2$	−14.2733	−1.26159	−0.630796	+	0.775949i	$0.717272\pi$
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	75.7267	0.591615
$5$	109.826	0.392925	0.196463	−	0.980511i	$-0.437055\pi$
$5$	109.826	0.392925	0.196463	+	0.980511i	$0.437055\pi$
$6$	385.379	0.728381
$7$	411.478	0.453423	0.226711	−	0.973962i	$-0.427203\pi$
$7$	411.478	0.453423	0.226711	+	0.973962i	$0.427203\pi$
$8$	746.112	0.515215
$9$	729.000	0.333333
$10$	−1567.58	−0.495712
$11$	1331.00	0.301511
$11$	1331.00	0.301511
$12$	−2044.62	−0.341569
$13$	−7184.38	−0.906959	−0.453480	−	0.891267i	$-0.649818\pi$
$13$	−7184.38	−0.906959	−0.453480	+	0.891267i	$0.649818\pi$
$14$	−5873.14	−0.572035
$15$	−2965.30	−0.226856
$16$	−20342.5	−1.24161
$17$	−7787.19	−0.384423	−0.192212	−	0.981354i	$-0.561566\pi$
$17$	−7787.19	−0.384423	−0.192212	+	0.981354i	$0.561566\pi$
$18$	−10405.2	−0.420531
$19$	−27944.2	−0.934662	−0.467331	−	0.884082i	$-0.654784\pi$
$19$	−27944.2	−0.934662	−0.467331	+	0.884082i	$0.654784\pi$
$20$	8316.76	0.232461
$21$	−11109.9	−0.261784
$22$	−18997.7	−0.380384
$23$	23452.2	0.401917	0.200959	−	0.979600i	$-0.435594\pi$
$23$	23452.2	0.401917	0.200959	+	0.979600i	$0.435594\pi$
$24$	−20145.0	−0.297460
$25$	−66063.2	−0.845610
$26$	102545.	1.14421
$27$	−19683.0	−0.192450
$28$	31159.9	0.268252
$29$	75081.3	0.571661	0.285831	−	0.958280i	$-0.407731\pi$
$29$	75081.3	0.571661	0.285831	+	0.958280i	$0.407731\pi$
$30$	42324.6	0.286199
$31$	−26738.3	−0.161201	−0.0806005	−	0.996746i	$-0.525684\pi$
$31$	−26738.3	−0.161201	−0.0806005	+	0.996746i	$0.525684\pi$
$32$	194852.	1.05119
$33$	−35937.0	−0.174078
$34$	111149.	0.484985
$35$	45191.0	0.178161
$36$	55204.8	0.197205
$37$	−56543.1	−0.183516	−0.0917580	−	0.995781i	$-0.529249\pi$
$37$	−56543.1	−0.183516	−0.0917580	+	0.995781i	$0.529249\pi$
$38$	398856.	1.17916
$39$	193978.	0.523633
$40$	81942.5	0.202441
$41$	−61025.9	−0.138284	−0.0691418	−	0.997607i	$-0.522026\pi$
$41$	−61025.9	−0.138284	−0.0691418	+	0.997607i	$0.522026\pi$
$42$	158575.	0.330265
$43$	−745444.	−1.42980	−0.714900	−	0.699227i	$-0.753528\pi$
$43$	−745444.	−1.42980	−0.714900	+	0.699227i	$0.753528\pi$
$44$	100792.	0.178379
$45$	80063.2	0.130975
$46$	−334741.	−0.507056
$47$	−1.22101e6	−1.71544	−0.857722	−	0.514114i	$-0.828121\pi$
$47$	−1.22101e6	−1.71544	−0.857722	+	0.514114i	$0.828121\pi$
$48$	549247.	0.716842
$49$	−654229.	−0.794408
$50$	942940.	1.06681
$51$	210254.	0.221947
$52$	−544050.	−0.536571
$53$	−682893.	−0.630068	−0.315034	−	0.949080i	$-0.602016\pi$
$53$	−682893.	−0.630068	−0.315034	+	0.949080i	$0.602016\pi$
$54$	280941.	0.242794
$55$	146178.	0.118471
$56$	307009.	0.233611
$57$	754494.	0.539627
$58$	−1.07166e6	−0.721203
$59$	−664718.	−0.421362	−0.210681	−	0.977555i	$-0.567568\pi$
$59$	−664718.	−0.421362	−0.210681	+	0.977555i	$0.567568\pi$
$60$	−224553.	−0.134211
$61$	2.01979e6	1.13933	0.569667	−	0.821875i	$-0.307072\pi$
$61$	2.01979e6	1.13933	0.569667	+	0.821875i	$0.307072\pi$
$62$	381643.	0.203370
$63$	299967.	0.151141
$64$	−177338.	−0.0845613
$65$	−789032.	−0.356367
$66$	512939.	0.219615
$67$	−1.66531e6	−0.676448	−0.338224	−	0.941066i	$-0.609826\pi$
$67$	−1.66531e6	−0.676448	−0.338224	+	0.941066i	$0.609826\pi$
$68$	−589698.	−0.227431
$69$	−633210.	−0.232047
$70$	−645024.	−0.224767
$71$	−2.80056e6	−0.928625	−0.464312	−	0.885672i	$-0.653698\pi$
$71$	−2.80056e6	−0.928625	−0.464312	+	0.885672i	$0.653698\pi$
$72$	543915.	0.171738
$73$	−968685.	−0.291442	−0.145721	−	0.989326i	$-0.546550\pi$
$73$	−968685.	−0.291442	−0.145721	+	0.989326i	$0.546550\pi$
$74$	807057.	0.231522
$75$	1.78371e6	0.488213
$76$	−2.11613e6	−0.552960
$77$	547677.	0.136712
$78$	−2.76871e6	−0.660612
$79$	−125746.	−0.0286945	−0.0143472	−	0.999897i	$-0.504567\pi$
$79$	−125746.	−0.0286945	−0.0143472	+	0.999897i	$0.504567\pi$
$80$	−2.23413e6	−0.487859
$81$	531441.	0.111111
$82$	871040.	0.174458
$83$	8.19771e6	1.57369	0.786845	−	0.617150i	$-0.211713\pi$
$83$	8.19771e6	1.57369	0.786845	+	0.617150i	$0.211713\pi$
$84$	−841317.	−0.154875
$85$	−855236.	−0.151050
$86$	1.06399e7	1.80383
$87$	−2.02719e6	−0.330049
$88$	993075.	0.155343
$89$	4.48340e6	0.674128	0.337064	−	0.941482i	$-0.390566\pi$
$89$	4.48340e6	0.674128	0.337064	+	0.941482i	$0.390566\pi$
$90$	−1.14276e6	−0.165237
$91$	−2.95622e6	−0.411236
$92$	1.77596e6	0.237780
$93$	721934.	0.0930694
$94$	1.74278e7	2.16419
$95$	−3.06900e6	−0.367253
$96$	−5.26100e6	−0.606902
$97$	1.20638e7	1.34209	0.671047	−	0.741415i	$-0.265845\pi$
$97$	1.20638e7	1.34209	0.671047	+	0.741415i	$0.265845\pi$
$98$	9.33800e6	1.00222
$99$	970299.	0.100504
$100$	−5.00275e6	−0.500275
$101$	783507.	0.0756690	0.0378345	−	0.999284i	$-0.487954\pi$
$101$	783507.	0.0756690	0.0378345	+	0.999284i	$0.487954\pi$
$102$	−3.00102e6	−0.280006
$103$	−1.59309e7	−1.43651	−0.718257	−	0.695778i	$-0.755060\pi$
$103$	−1.59309e7	−1.43651	−0.718257	+	0.695778i	$0.755060\pi$
$104$	−5.36035e6	−0.467279
$105$	−1.22016e6	−0.102862
$106$	9.74713e6	0.794889
$107$	−2.20825e7	−1.74263	−0.871315	−	0.490725i	$-0.836732\pi$
$107$	−2.20825e7	−1.74263	−0.871315	+	0.490725i	$0.836732\pi$
$108$	−1.49053e6	−0.113856
$109$	9.31486e6	0.688944	0.344472	−	0.938797i	$-0.388058\pi$
$109$	9.31486e6	0.688944	0.344472	+	0.938797i	$0.388058\pi$
$110$	−2.08645e6	−0.149463
$111$	1.52667e6	0.105953
$112$	−8.37049e6	−0.562973
$113$	−2.94478e7	−1.91990	−0.959951	−	0.280169i	$-0.909609\pi$
$113$	−2.94478e7	−1.91990	−0.959951	+	0.280169i	$0.909609\pi$
$114$	−1.07691e7	−0.680790
$115$	2.57567e6	0.157924
$116$	5.68566e6	0.338203
$117$	−5.23742e6	−0.302320
$118$	9.48771e6	0.531587
$119$	−3.20426e6	−0.174306
$120$	−2.21245e6	−0.116880
$121$	1.77156e6	0.0909091
$122$	−2.88290e7	−1.43738
$123$	1.64770e6	0.0798381
$124$	−2.02480e6	−0.0953689
$125$	−1.58356e7	−0.725187
$126$	−4.28152e6	−0.190678
$127$	1.10860e7	0.480243	0.240121	−	0.970743i	$-0.422813\pi$
$127$	1.10860e7	0.480243	0.240121	+	0.970743i	$0.422813\pi$
$128$	−2.24098e7	−0.944504
$129$	2.01270e7	0.825496
$130$	1.12621e7	0.449590
$131$	1.42408e7	0.553460	0.276730	−	0.960948i	$-0.410749\pi$
$131$	1.42408e7	0.553460	0.276730	+	0.960948i	$0.410749\pi$
$132$	−2.72139e6	−0.102987
$133$	−1.14984e7	−0.423797
$134$	2.37695e7	0.853401
$135$	−2.16171e6	−0.0756185
$136$	−5.81011e6	−0.198061
$137$	1.95861e7	0.650769	0.325385	−	0.945582i	$-0.394506\pi$
$137$	1.95861e7	0.650769	0.325385	+	0.945582i	$0.394506\pi$
$138$	9.03799e6	0.292749
$139$	8.73161e6	0.275767	0.137884	−	0.990448i	$-0.455970\pi$
$139$	8.73161e6	0.275767	0.137884	+	0.990448i	$0.455970\pi$
$140$	3.42217e6	0.105403
$141$	3.29673e7	0.990412
$142$	3.99731e7	1.17155
$143$	−9.56242e6	−0.273459
$144$	−1.48297e7	−0.413869
$145$	8.24588e6	0.224620
$146$	1.38263e7	0.367681
$147$	1.76642e7	0.458651
$148$	−4.28183e6	−0.108571
$149$	4.90830e7	1.21557	0.607784	−	0.794102i	$-0.292059\pi$
$149$	4.90830e7	1.21557	0.607784	+	0.794102i	$0.292059\pi$
$150$	−2.54594e7	−0.615926
$151$	4.13384e7	0.977089	0.488545	−	0.872539i	$-0.337528\pi$
$151$	4.13384e7	0.977089	0.488545	+	0.872539i	$0.337528\pi$
$152$	−2.08495e7	−0.481552
$153$	−5.67686e6	−0.128141
$154$	−7.81715e6	−0.172475
$155$	−2.93656e6	−0.0633400
$156$	1.46893e7	0.309789
$157$	−3.84652e7	−0.793267	−0.396633	−	0.917977i	$-0.629822\pi$
$157$	−3.84652e7	−0.793267	−0.396633	+	0.917977i	$0.629822\pi$
$158$	1.79480e6	0.0362007
$159$	1.84381e7	0.363770
$160$	2.13998e7	0.413038
$161$	9.65008e6	0.182239
$162$	−7.58541e6	−0.140177
$163$	−6.83002e7	−1.23528	−0.617640	−	0.786461i	$-0.711911\pi$
$163$	−6.83002e7	−1.23528	−0.617640	+	0.786461i	$0.711911\pi$
$164$	−4.62129e6	−0.0818106
$165$	−3.94682e6	−0.0683995
$166$	−1.17008e8	−1.98536
$167$	5.98051e7	0.993644	0.496822	−	0.867852i	$-0.334500\pi$
$167$	5.98051e7	0.993644	0.496822	+	0.867852i	$0.334500\pi$
$168$	−8.28923e6	−0.134875
$169$	−1.11331e7	−0.177425
$170$	1.22070e7	0.190563
$171$	−2.03713e7	−0.311554
$172$	−5.64500e7	−0.845891
$173$	7.01056e7	1.02942	0.514709	−	0.857365i	$-0.327900\pi$
$173$	7.01056e7	1.02942	0.514709	+	0.857365i	$0.327900\pi$
$174$	2.89347e7	0.416387
$175$	−2.71836e7	−0.383419
$176$	−2.70758e7	−0.374359
$177$	1.79474e7	0.243273
$178$	−6.39928e7	−0.850474
$179$	2.22947e7	0.290547	0.145274	−	0.989392i	$-0.453594\pi$
$179$	2.22947e7	0.290547	0.145274	+	0.989392i	$0.453594\pi$
$180$	6.06292e6	0.0774869
$181$	1.44491e8	1.81120	0.905599	−	0.424136i	$-0.139422\pi$
$181$	1.44491e8	1.81120	0.905599	+	0.424136i	$0.139422\pi$
$182$	4.21949e7	0.518812
$183$	−5.45343e7	−0.657795
$184$	1.74980e7	0.207074
$185$	−6.20991e6	−0.0721081
$186$	−1.03044e7	−0.117416
$187$	−1.03648e7	−0.115908
$188$	−9.24630e7	−1.01488
$189$	−8.09912e6	−0.0872613
$190$	4.38048e7	0.463323
$191$	1.11105e8	1.15376	0.576880	−	0.816829i	$-0.304270\pi$
$191$	1.11105e8	1.15376	0.576880	+	0.816829i	$0.304270\pi$
$192$	4.78812e6	0.0488215
$193$	−1.49792e8	−1.49982	−0.749909	−	0.661541i	$-0.769903\pi$
$193$	−1.49792e8	−1.49982	−0.749909	+	0.661541i	$0.769903\pi$
$194$	−1.72190e8	−1.69318
$195$	2.13039e7	0.205749
$196$	−4.95426e7	−0.469983
$197$	8.55203e7	0.796962	0.398481	−	0.917177i	$-0.369538\pi$
$197$	8.55203e7	0.796962	0.398481	+	0.917177i	$0.369538\pi$
$198$	−1.38494e7	−0.126795
$199$	−1.92493e8	−1.73152	−0.865762	−	0.500455i	$-0.833166\pi$
$199$	−1.92493e8	−1.73152	−0.865762	+	0.500455i	$0.833166\pi$
$200$	−4.92906e7	−0.435671
$201$	4.49635e7	0.390547
$202$	−1.11832e7	−0.0954635
$203$	3.08943e7	0.259204
$204$	1.59219e7	0.131307
$205$	−6.70223e6	−0.0543351
$206$	2.27386e8	1.81230
$207$	1.70967e7	0.133972
$208$	1.46148e8	1.12609
$209$	−3.71938e7	−0.281811
$210$	1.74156e7	0.129769
$211$	−2.50165e8	−1.83332	−0.916661	−	0.399666i	$-0.869126\pi$
$211$	−2.50165e8	−1.83332	−0.916661	+	0.399666i	$0.869126\pi$
$212$	−5.17133e7	−0.372758
$213$	7.56150e7	0.536142
$214$	3.15190e8	2.19849
$215$	−8.18691e7	−0.561805
$216$	−1.46857e7	−0.0991533
$217$	−1.10022e7	−0.0730922
$218$	−1.32954e8	−0.869166
$219$	2.61545e7	0.168264
$220$	1.10696e7	0.0700895
$221$	5.59462e7	0.348656
$222$	−2.17905e7	−0.133670
$223$	−1.42950e7	−0.0863209	−0.0431605	−	0.999068i	$-0.513743\pi$
$223$	−1.42950e7	−0.0863209	−0.0431605	+	0.999068i	$0.513743\pi$
$224$	8.01772e7	0.476632
$225$	−4.81601e7	−0.281870
$226$	4.20317e8	2.42213
$227$	−3.07304e8	−1.74372	−0.871861	−	0.489753i	$-0.837087\pi$
$227$	−3.07304e8	−1.74372	−0.871861	+	0.489753i	$0.837087\pi$
$228$	5.71354e7	0.319252
$229$	−2.46226e8	−1.35491	−0.677453	−	0.735566i	$-0.736916\pi$
$229$	−2.46226e8	−1.35491	−0.677453	+	0.735566i	$0.736916\pi$
$230$	−3.67632e7	−0.199235
$231$	−1.47873e7	−0.0789308
$232$	5.60190e7	0.294529
$233$	5.60107e6	0.0290085	0.0145043	−	0.999895i	$-0.495383\pi$
$233$	5.60107e6	0.0290085	0.0145043	+	0.999895i	$0.495383\pi$
$234$	7.47551e7	0.381404
$235$	−1.34099e8	−0.674042
$236$	−5.03369e7	−0.249284
$237$	3.39513e6	0.0165668
$238$	4.57353e7	0.219904
$239$	−1.33278e8	−0.631489	−0.315744	−	0.948844i	$-0.602254\pi$
$239$	−1.33278e8	−0.631489	−0.315744	+	0.948844i	$0.602254\pi$
$240$	6.03216e7	0.281665
$241$	3.93129e8	1.80915	0.904577	−	0.426310i	$-0.140187\pi$
$241$	3.93129e8	1.80915	0.904577	+	0.426310i	$0.140187\pi$
$242$	−2.52860e7	−0.114690
$243$	−1.43489e7	−0.0641500
$244$	1.52952e8	0.674048
$245$	−7.18513e7	−0.312143
$246$	−2.35181e7	−0.100723
$247$	2.00762e8	0.847701
$248$	−1.99497e7	−0.0830532
$249$	−2.21338e8	−0.908571
$250$	2.26026e8	0.914890
$251$	4.51565e8	1.80245	0.901224	−	0.433354i	$-0.142670\pi$
$251$	4.51565e8	1.80245	0.901224	+	0.433354i	$0.142670\pi$
$252$	2.27156e7	0.0894173
$253$	3.12149e7	0.121183
$254$	−1.58233e8	−0.605871
$255$	2.30914e7	0.0872086
$256$	3.42561e8	1.27614
$257$	1.01340e8	0.372406	0.186203	−	0.982511i	$-0.440382\pi$
$257$	1.01340e8	0.372406	0.186203	+	0.982511i	$0.440382\pi$
$258$	−2.87278e8	−1.04144
$259$	−2.32663e7	−0.0832104
$260$	−5.97508e7	−0.210832
$261$	5.47343e7	0.190554
$262$	−2.03264e8	−0.698241
$263$	−2.83914e8	−0.962368	−0.481184	−	0.876620i	$-0.659793\pi$
$263$	−2.83914e8	−0.962368	−0.481184	+	0.876620i	$0.659793\pi$
$264$	−2.68130e7	−0.0896875
$265$	−7.49995e7	−0.247570
$266$	1.64121e8	0.534659
$267$	−1.21052e8	−0.389208
$268$	−1.26109e8	−0.400197
$269$	1.50225e8	0.470553	0.235276	−	0.971929i	$-0.424400\pi$
$269$	1.50225e8	0.470553	0.235276	+	0.971929i	$0.424400\pi$
$270$	3.08546e7	0.0953998
$271$	2.16496e8	0.660780	0.330390	−	0.943845i	$-0.392820\pi$
$271$	2.16496e8	0.660780	0.330390	+	0.943845i	$0.392820\pi$
$272$	1.58411e8	0.477302
$273$	7.98178e7	0.237427
$274$	−2.79559e8	−0.821005
$275$	−8.79302e7	−0.254961
$276$	−4.79509e7	−0.137283
$277$	−6.86265e7	−0.194005	−0.0970025	−	0.995284i	$-0.530925\pi$
$277$	−6.86265e7	−0.194005	−0.0970025	+	0.995284i	$0.530925\pi$
$278$	−1.24629e8	−0.347906
$279$	−1.94922e7	−0.0537337
$280$	3.37175e7	0.0917915
$281$	1.28535e8	0.345580	0.172790	−	0.984959i	$-0.444722\pi$
$281$	1.28535e8	0.345580	0.172790	+	0.984959i	$0.444722\pi$
$282$	−4.70551e8	−1.24950
$283$	−7.20456e8	−1.88953	−0.944767	−	0.327742i	$-0.893712\pi$
$283$	−7.20456e8	−1.88953	−0.944767	+	0.327742i	$0.893712\pi$
$284$	−2.12077e8	−0.549388
$285$	8.28631e7	0.212033
$286$	1.36487e8	0.344993
$287$	−2.51108e7	−0.0627010
$288$	1.42047e8	0.350395
$289$	−3.49698e8	−0.852219
$290$	−1.17696e8	−0.283379
$291$	−3.25723e8	−0.774858
$292$	−7.33553e7	−0.172422
$293$	3.73086e8	0.866508	0.433254	−	0.901272i	$-0.357365\pi$
$293$	3.73086e8	0.866508	0.433254	+	0.901272i	$0.357365\pi$
$294$	−2.52126e8	−0.578631
$295$	−7.30033e7	−0.165564
$296$	−4.21875e7	−0.0945503
$297$	−2.61981e7	−0.0580259
$298$	−7.00576e8	−1.53355
$299$	−1.68490e8	−0.364523
$300$	1.35074e8	0.288834
$301$	−3.06734e8	−0.648304
$302$	−5.90035e8	−1.23269
$303$	−2.11547e7	−0.0436875
$304$	5.68455e8	1.16048
$305$	2.21825e8	0.447674
$306$	8.10275e7	0.161662
$307$	5.81869e8	1.14773	0.573866	−	0.818949i	$-0.305443\pi$
$307$	5.81869e8	1.14773	0.573866	+	0.818949i	$0.305443\pi$
$308$	4.14738e7	0.0808810
$309$	4.30134e8	0.829372
$310$	4.19144e7	0.0799092
$311$	−6.36311e8	−1.19952	−0.599761	−	0.800179i	$-0.704738\pi$
$311$	−6.36311e8	−1.19952	−0.599761	+	0.800179i	$0.704738\pi$
$312$	1.44730e8	0.269784
$313$	4.35135e8	0.802082	0.401041	−	0.916060i	$-0.368648\pi$
$313$	4.35135e8	0.802082	0.401041	+	0.916060i	$0.368648\pi$
$314$	5.49025e8	1.00078
$315$	3.29442e7	0.0593871
$316$	−9.52231e6	−0.0169761
$317$	1.09605e9	1.93251	0.966255	−	0.257587i	$-0.0829273\pi$
$317$	1.09605e9	1.93251	0.966255	+	0.257587i	$0.0829273\pi$
$318$	−2.63173e8	−0.458929
$319$	9.99332e7	0.172362
$320$	−1.94763e7	−0.0332263
$321$	5.96227e8	1.00611
$322$	−1.37738e8	−0.229911
$323$	2.17607e8	0.359306
$324$	4.02443e7	0.0657350
$325$	4.74624e8	0.766934
$326$	9.74868e8	1.55842
$327$	−2.51501e8	−0.397762
$328$	−4.55321e7	−0.0712458
$329$	−5.02419e8	−0.777822
$330$	5.63341e7	0.0862923
$331$	8.09770e8	1.22734	0.613668	−	0.789564i	$-0.289693\pi$
$331$	8.09770e8	1.22734	0.613668	+	0.789564i	$0.289693\pi$
$332$	6.20786e8	0.931019
$333$	−4.12200e7	−0.0611720
$334$	−8.53616e8	−1.25357
$335$	−1.82895e8	−0.265794
$336$	2.26003e8	0.325033
$337$	1.12369e9	1.59934	0.799671	−	0.600439i	$-0.205007\pi$
$337$	1.12369e9	1.59934	0.799671	+	0.600439i	$0.205007\pi$
$338$	1.58906e8	0.223837
$339$	7.95092e8	1.10846
$340$	−6.47642e7	−0.0893633
$341$	−3.55887e7	−0.0486039
$342$	2.90766e8	0.393054
$343$	−6.08071e8	−0.813626
$344$	−5.56184e8	−0.736655
$345$	−6.95430e7	−0.0911772
$346$	−1.00064e9	−1.29871
$347$	−1.24026e9	−1.59353	−0.796765	−	0.604289i	$-0.793457\pi$
$347$	−1.24026e9	−1.59353	−0.796765	+	0.604289i	$0.793457\pi$
$348$	−1.53513e8	−0.195262
$349$	−2.75407e8	−0.346806	−0.173403	−	0.984851i	$-0.555476\pi$
$349$	−2.75407e8	−0.346806	−0.173403	+	0.984851i	$0.555476\pi$
$350$	3.87999e8	0.483718
$351$	1.41410e8	0.174544
$352$	2.59348e8	0.316944
$353$	5.05448e8	0.611596	0.305798	−	0.952096i	$-0.401077\pi$
$353$	5.05448e8	0.611596	0.305798	+	0.952096i	$0.401077\pi$
$354$	−2.56168e8	−0.306912
$355$	−3.07574e8	−0.364880
$356$	3.39513e8	0.398824
$357$	8.65150e7	0.100636
$358$	−3.18219e8	−0.366552
$359$	2.98025e8	0.339956	0.169978	−	0.985448i	$-0.445630\pi$
$359$	2.98025e8	0.339956	0.169978	+	0.985448i	$0.445630\pi$
$360$	5.97361e7	0.0674804
$361$	−1.12991e8	−0.126407
$362$	−2.06236e9	−2.28499
$363$	−4.78321e7	−0.0524864
$364$	−2.23865e8	−0.243294
$365$	−1.06387e8	−0.114515
$366$	7.78383e8	0.829869
$367$	−9.50573e8	−1.00382	−0.501908	−	0.864921i	$-0.667368\pi$
$367$	−9.50573e8	−1.00382	−0.501908	+	0.864921i	$0.667368\pi$
$368$	−4.77077e8	−0.499023
$369$	−4.44879e7	−0.0460945
$370$	8.86358e7	0.0909710
$371$	−2.80996e8	−0.285687
$372$	5.46697e7	0.0550613
$373$	6.72457e8	0.670940	0.335470	−	0.942051i	$-0.391105\pi$
$373$	6.72457e8	0.670940	0.335470	+	0.942051i	$0.391105\pi$
$374$	1.47939e8	0.146229
$375$	4.27562e8	0.418687
$376$	−9.11009e8	−0.883823
$377$	−5.39413e8	−0.518473
$378$	1.15601e8	0.110088
$379$	2.16611e8	0.204382	0.102191	−	0.994765i	$-0.467415\pi$
$379$	2.16611e8	0.204382	0.102191	+	0.994765i	$0.467415\pi$
$380$	−2.32406e8	−0.217272
$381$	−2.99321e8	−0.277268
$382$	−1.58583e9	−1.45558
$383$	−5.24528e8	−0.477060	−0.238530	−	0.971135i	$-0.576665\pi$
$383$	−5.24528e8	−0.477060	−0.238530	+	0.971135i	$0.576665\pi$
$384$	6.05066e8	0.545310
$385$	6.01492e7	0.0537177
$386$	2.13803e9	1.89216
$387$	−5.43429e8	−0.476600
$388$	9.13552e8	0.794003
$389$	−3.59005e8	−0.309227	−0.154613	−	0.987975i	$-0.549413\pi$
$389$	−3.59005e8	−0.309227	−0.154613	+	0.987975i	$0.549413\pi$
$390$	−3.04076e8	−0.259571
$391$	−1.82627e8	−0.154506
$392$	−4.88128e8	−0.409291
$393$	−3.84503e8	−0.319540
$394$	−1.22066e9	−1.00544
$395$	−1.38101e7	−0.0112748
$396$	7.34776e7	0.0594595
$397$	2.47540e8	0.198554	0.0992769	−	0.995060i	$-0.468347\pi$
$397$	2.47540e8	0.198554	0.0992769	+	0.995060i	$0.468347\pi$
$398$	2.74750e9	2.18448
$399$	3.10458e8	0.244679
$400$	1.34389e9	1.04991
$401$	−1.22586e8	−0.0949373	−0.0474687	−	0.998873i	$-0.515115\pi$
$401$	−1.22586e8	−0.0949373	−0.0474687	+	0.998873i	$0.515115\pi$
$402$	−6.41776e8	−0.492711
$403$	1.92098e8	0.146203
$404$	5.93324e7	0.0447669
$405$	5.83660e7	0.0436584
$406$	−4.40963e8	−0.327010
$407$	−7.52589e7	−0.0553322
$408$	1.56873e8	0.114350
$409$	−9.02182e8	−0.652023	−0.326011	−	0.945366i	$-0.605705\pi$
$409$	−9.02182e8	−0.652023	−0.326011	+	0.945366i	$0.605705\pi$
$410$	9.56629e7	0.0685488
$411$	−5.28826e8	−0.375722
$412$	−1.20639e9	−0.849863
$413$	−2.73517e8	−0.191055
$414$	−2.44026e8	−0.169019
$415$	9.00322e8	0.618343
$416$	−1.39989e9	−0.953383
$417$	−2.35754e8	−0.159214
$418$	5.30877e8	0.355531
$419$	2.87496e8	0.190934	0.0954669	−	0.995433i	$-0.469566\pi$
$419$	2.87496e8	0.190934	0.0954669	+	0.995433i	$0.469566\pi$
$420$	−9.23985e7	−0.0608544
$421$	1.74385e9	1.13900	0.569498	−	0.821993i	$-0.307138\pi$
$421$	1.74385e9	1.13900	0.569498	+	0.821993i	$0.307138\pi$
$422$	3.57068e9	2.31290
$423$	−8.90116e8	−0.571815
$424$	−5.09515e8	−0.324621
$425$	5.14447e8	0.325072
$426$	−1.07928e9	−0.676392
$427$	8.31099e8	0.516601
$428$	−1.67224e9	−1.03097
$429$	2.58185e8	0.157881
$430$	1.16854e9	0.708769
$431$	1.38175e8	0.0831302	0.0415651	−	0.999136i	$-0.486766\pi$
$431$	1.38175e8	0.0831302	0.0415651	+	0.999136i	$0.486766\pi$
$432$	4.00401e8	0.238947
$433$	−6.13716e7	−0.0363295	−0.0181648	−	0.999835i	$-0.505782\pi$
$433$	−6.13716e7	−0.0363295	−0.0181648	+	0.999835i	$0.505782\pi$
$434$	1.57038e8	0.0922126
$435$	−2.22639e8	−0.129685
$436$	7.05384e8	0.407589
$437$	−6.55355e8	−0.375657
$438$	−3.73311e8	−0.212281
$439$	2.31684e8	0.130698	0.0653491	−	0.997862i	$-0.479184\pi$
$439$	2.31684e8	0.130698	0.0653491	+	0.997862i	$0.479184\pi$
$440$	1.09065e8	0.0610383
$441$	−4.76933e8	−0.264803
$442$	−7.98536e8	−0.439862
$443$	5.84990e8	0.319695	0.159847	−	0.987142i	$-0.448900\pi$
$443$	5.84990e8	0.319695	0.159847	+	0.987142i	$0.448900\pi$
$444$	1.15609e8	0.0626834
$445$	4.92394e8	0.264882
$446$	2.04036e8	0.108902
$447$	−1.32524e9	−0.701809
$448$	−7.29707e7	−0.0383420
$449$	−1.51251e9	−0.788565	−0.394282	−	0.918989i	$-0.629007\pi$
$449$	−1.51251e9	−0.788565	−0.394282	+	0.918989i	$0.629007\pi$
$450$	6.87403e8	0.355605
$451$	−8.12255e7	−0.0416941
$452$	−2.22999e9	−1.13584
$453$	−1.11614e9	−0.564123
$454$	4.38624e9	2.19987
$455$	−3.24669e8	−0.161585
$456$	5.62937e8	0.278024
$457$	−3.45890e9	−1.69524	−0.847620	−	0.530603i	$-0.821966\pi$
$457$	−3.45890e9	−1.69524	−0.847620	+	0.530603i	$0.821966\pi$
$458$	3.51445e9	1.70934
$459$	1.53275e8	0.0739823
$460$	1.95047e8	0.0934300
$461$	9.30194e8	0.442202	0.221101	−	0.975251i	$-0.429035\pi$
$461$	9.30194e8	0.442202	0.221101	+	0.975251i	$0.429035\pi$
$462$	2.11063e8	0.0995785
$463$	3.87855e9	1.81608	0.908041	−	0.418882i	$-0.137578\pi$
$463$	3.87855e9	1.81608	0.908041	+	0.418882i	$0.137578\pi$
$464$	−1.52734e9	−0.709778
$465$	7.92871e7	0.0365693
$466$	−7.99457e7	−0.0365969
$467$	5.14096e8	0.233580	0.116790	−	0.993157i	$-0.462740\pi$
$467$	5.14096e8	0.233580	0.116790	+	0.993157i	$0.462740\pi$
$468$	−3.96612e8	−0.178857
$469$	−6.85240e8	−0.306717
$470$	1.91403e9	0.850366
$471$	1.03856e9	0.457993
$472$	−4.95954e8	−0.217092
$473$	−9.92186e8	−0.431101
$474$	−4.84597e7	−0.0209005
$475$	1.84609e9	0.790359
$476$	−2.42648e8	−0.103122
$477$	−4.97829e8	−0.210023
$478$	1.90231e9	0.796682
$479$	−3.48082e9	−1.44713	−0.723565	−	0.690256i	$-0.757498\pi$
$479$	−3.48082e9	−1.44713	−0.723565	+	0.690256i	$0.757498\pi$
$480$	−5.77795e8	−0.238467
$481$	4.06228e8	0.166442
$482$	−5.61124e9	−2.28241
$483$	−2.60552e8	−0.105216
$484$	1.34154e8	0.0537832
$485$	1.32492e9	0.527343
$486$	2.04806e8	0.0809312
$487$	6.67664e8	0.261943	0.130972	−	0.991386i	$-0.458190\pi$
$487$	6.67664e8	0.261943	0.130972	+	0.991386i	$0.458190\pi$
$488$	1.50699e9	0.587003
$489$	1.84410e9	0.713189
$490$	1.02555e9	0.393797
$491$	3.17436e9	1.21024	0.605119	−	0.796135i	$-0.293126\pi$
$491$	3.17436e9	1.21024	0.605119	+	0.796135i	$0.293126\pi$
$492$	1.24775e8	0.0472334
$493$	−5.84672e8	−0.219760
$494$	−2.86554e9	−1.06945
$495$	1.06564e8	0.0394905
$496$	5.43923e8	0.200148
$497$	−1.15237e9	−0.421060
$498$	3.15922e9	1.14625
$499$	2.00061e9	0.720794	0.360397	−	0.932799i	$-0.382641\pi$
$499$	2.00061e9	0.720794	0.360397	+	0.932799i	$0.382641\pi$
$500$	−1.19918e9	−0.429031
$501$	−1.61474e9	−0.573681
$502$	−6.44532e9	−2.27395
$503$	2.90222e9	1.01682	0.508408	−	0.861116i	$-0.330234\pi$
$503$	2.90222e9	1.01682	0.508408	+	0.861116i	$0.330234\pi$
$504$	2.23809e8	0.0778702
$505$	8.60495e7	0.0297323
$506$	−4.45540e8	−0.152883
$507$	3.00595e8	0.102436
$508$	8.39505e8	0.284119
$509$	−5.24891e9	−1.76424	−0.882118	−	0.471028i	$-0.843883\pi$
$509$	−5.24891e9	−1.76424	−0.882118	+	0.471028i	$0.843883\pi$
$510$	−3.29590e8	−0.110022
$511$	−3.98593e8	−0.132147
$512$	−2.02102e9	−0.665465
$513$	5.50026e8	0.179876
$514$	−1.44646e9	−0.469825
$515$	−1.74963e9	−0.564443
$516$	1.52415e9	0.488376
$517$	−1.62516e9	−0.517226
$518$	3.32086e8	0.104978
$519$	−1.89285e9	−0.594334
$520$	−5.88706e8	−0.183606
$521$	7.43243e8	0.230249	0.115125	−	0.993351i	$-0.463273\pi$
$521$	7.43243e8	0.230249	0.115125	+	0.993351i	$0.463273\pi$
$522$	−7.81238e8	−0.240401
$523$	−2.82158e9	−0.862456	−0.431228	−	0.902243i	$-0.641920\pi$
$523$	−2.82158e9	−0.862456	−0.431228	+	0.902243i	$0.641920\pi$
$524$	1.07841e9	0.327435
$525$	7.33957e8	0.221367
$526$	4.05238e9	1.21412
$527$	2.08216e8	0.0619694
$528$	7.31048e8	0.216136
$529$	−2.85482e9	−0.838462
$530$	1.07049e9	0.312332
$531$	−4.84579e8	−0.140454
$532$	−8.70739e8	−0.250725
$533$	4.38434e8	0.125418
$534$	1.72781e9	0.491022
$535$	−2.42523e9	−0.684723
$536$	−1.24251e9	−0.348516
$537$	−6.01958e8	−0.167748
$538$	−2.14420e9	−0.593646
$539$	−8.70779e8	−0.239523
$540$	−1.63699e8	−0.0447371
$541$	−4.89997e7	−0.0133046	−0.00665232	−	0.999978i	$-0.502118\pi$
$541$	−4.89997e7	−0.0133046	−0.00665232	+	0.999978i	$0.502118\pi$
$542$	−3.09010e9	−0.833634
$543$	−3.90126e9	−1.04570
$544$	−1.51735e9	−0.404100
$545$	1.02301e9	0.270704
$546$	−1.13926e9	−0.299537
$547$	2.87944e9	0.752233	0.376116	−	0.926572i	$-0.377259\pi$
$547$	2.87944e9	0.752233	0.376116	+	0.926572i	$0.377259\pi$
$548$	1.48319e9	0.385005
$549$	1.47243e9	0.379778
$550$	1.25505e9	0.321657
$551$	−2.09809e9	−0.534310
$552$	−4.72446e8	−0.119554
$553$	−5.17416e7	−0.0130107
$554$	9.79526e8	0.244755
$555$	1.67668e8	0.0416316
$556$	6.61216e8	0.163148
$557$	6.23189e9	1.52801	0.764006	−	0.645209i	$-0.223230\pi$
$557$	6.23189e9	1.52801	0.764006	+	0.645209i	$0.223230\pi$
$558$	2.78218e8	0.0677900
$559$	5.35556e9	1.29677
$560$	−9.19297e8	−0.221206
$561$	2.79848e8	0.0669195
$562$	−1.83461e9	−0.435981
$563$	5.80197e9	1.37024	0.685119	−	0.728431i	$-0.259750\pi$
$563$	5.80197e9	1.37024	0.685119	+	0.728431i	$0.259750\pi$
$564$	2.49650e9	0.585943
$565$	−3.23414e9	−0.754378
$566$	1.02833e10	2.38382
$567$	2.18676e8	0.0503803
$568$	−2.08953e9	−0.478442
$569$	1.31916e9	0.300195	0.150097	−	0.988671i	$-0.452041\pi$
$569$	1.31916e9	0.300195	0.150097	+	0.988671i	$0.452041\pi$
$570$	−1.18273e9	−0.267500
$571$	1.99889e9	0.449328	0.224664	−	0.974436i	$-0.427872\pi$
$571$	1.99889e9	0.449328	0.224664	+	0.974436i	$0.427872\pi$
$572$	−7.24130e8	−0.161782
$573$	−2.99983e9	−0.666124
$574$	3.58414e8	0.0791030
$575$	−1.54933e9	−0.339865
$576$	−1.29279e8	−0.0281871
$577$	−6.30790e9	−1.36700	−0.683501	−	0.729949i	$-0.739544\pi$
$577$	−6.30790e9	−1.36700	−0.683501	+	0.729949i	$0.739544\pi$
$578$	4.99134e9	1.07515
$579$	4.04439e9	0.865920
$580$	6.24433e8	0.132889
$581$	3.37318e9	0.713548
$582$	4.64913e9	0.977555
$583$	−9.08931e8	−0.189973
$584$	−7.22747e8	−0.150156
$585$	−5.75205e8	−0.118789
$586$	−5.32517e9	−1.09318
$587$	3.94396e8	0.0804820	0.0402410	−	0.999190i	$-0.487187\pi$
$587$	3.94396e8	0.0804820	0.0402410	+	0.999190i	$0.487187\pi$
$588$	1.33765e9	0.271345
$589$	7.47181e8	0.150668
$590$	1.04200e9	0.208874
$591$	−2.30905e9	−0.460126
$592$	1.15023e9	0.227855
$593$	3.67822e9	0.724347	0.362173	−	0.932111i	$-0.382035\pi$
$593$	3.67822e9	0.724347	0.362173	+	0.932111i	$0.382035\pi$
$594$	3.73933e8	0.0732050
$595$	−3.51911e8	−0.0684894
$596$	3.71690e9	0.719149
$597$	5.19730e9	0.999696
$598$	2.40490e9	0.459879
$599$	−2.06900e9	−0.393338	−0.196669	−	0.980470i	$-0.563012\pi$
$599$	−2.06900e9	−0.393338	−0.196669	+	0.980470i	$0.563012\pi$
$600$	1.33084e9	0.251535
$601$	−5.77788e9	−1.08570	−0.542848	−	0.839831i	$-0.682654\pi$
$601$	−5.77788e9	−1.08570	−0.542848	+	0.839831i	$0.682654\pi$
$602$	4.37810e9	0.817896
$603$	−1.21401e9	−0.225483
$604$	3.13042e9	0.578061
$605$	1.94563e8	0.0357205
$606$	3.01947e8	0.0551159
$607$	3.36148e9	0.610057	0.305028	−	0.952343i	$-0.401334\pi$
$607$	3.36148e9	0.610057	0.305028	+	0.952343i	$0.401334\pi$
$608$	−5.44499e9	−0.982504
$609$	−8.34146e8	−0.149652
$610$	−3.16618e9	−0.564782
$611$	8.77220e9	1.55584
$612$	−4.29890e8	−0.0758102
$613$	−9.04578e9	−1.58611	−0.793057	−	0.609147i	$-0.791512\pi$
$613$	−9.04578e9	−1.58611	−0.793057	+	0.609147i	$0.791512\pi$
$614$	−8.30518e9	−1.44797
$615$	1.80960e8	0.0313704
$616$	4.08628e8	0.0704362
$617$	−4.01028e9	−0.687348	−0.343674	−	0.939089i	$-0.611672\pi$
$617$	−4.01028e9	−0.687348	−0.343674	+	0.939089i	$0.611672\pi$
$618$	−6.13943e9	−1.04633
$619$	7.53237e9	1.27648	0.638240	−	0.769837i	$-0.279663\pi$
$619$	7.53237e9	1.27648	0.638240	+	0.769837i	$0.279663\pi$
$620$	−2.22376e8	−0.0374729
$621$	−4.61610e8	−0.0773490
$622$	9.08225e9	1.51331
$623$	1.84482e9	0.305665
$624$	−3.94600e9	−0.650147
$625$	3.42203e9	0.560665
$626$	−6.21081e9	−1.01190
$627$	1.00423e9	0.162704
$628$	−2.91284e9	−0.469308
$629$	4.40312e8	0.0705478
$630$	−4.70222e8	−0.0749224
$631$	−3.42569e9	−0.542807	−0.271403	−	0.962466i	$-0.587488\pi$
$631$	−3.42569e9	−0.542807	−0.271403	+	0.962466i	$0.587488\pi$
$632$	−9.38203e7	−0.0147838
$633$	6.75447e9	1.05847
$634$	−1.56442e10	−2.43804
$635$	1.21753e9	0.188700
$636$	1.39626e9	0.215212
$637$	4.70023e9	0.720495
$638$	−1.42637e9	−0.217451
$639$	−2.04161e9	−0.309542
$640$	−2.46118e9	−0.371120
$641$	−7.65541e9	−1.14806	−0.574031	−	0.818834i	$-0.694621\pi$
$641$	−7.65541e9	−1.14806	−0.574031	+	0.818834i	$0.694621\pi$
$642$	−8.51013e9	−1.26930
$643$	−1.53294e9	−0.227398	−0.113699	−	0.993515i	$-0.536270\pi$
$643$	−1.53294e9	−0.227398	−0.113699	+	0.993515i	$0.536270\pi$
$644$	7.30769e8	0.107815
$645$	2.21047e9	0.324358
$646$	−3.10597e9	−0.453297
$647$	3.86179e9	0.560562	0.280281	−	0.959918i	$-0.409572\pi$
$647$	3.86179e9	0.560562	0.280281	+	0.959918i	$0.409572\pi$
$648$	3.96514e8	0.0572462
$649$	−8.84739e8	−0.127045
$650$	−6.77444e9	−0.967557
$651$	2.97060e8	0.0421998
$652$	−5.17215e9	−0.730810
$653$	−1.09632e10	−1.54078	−0.770388	−	0.637575i	$-0.779937\pi$
$653$	−1.09632e10	−1.54078	−0.770388	+	0.637575i	$0.779937\pi$
$654$	3.58975e9	0.501813
$655$	1.56402e9	0.217469
$656$	1.24142e9	0.171694
$657$	−7.06171e8	−0.0971474
$658$	7.17116e9	0.981294
$659$	−7.96853e9	−1.08462	−0.542312	−	0.840177i	$-0.682451\pi$
$659$	−7.96853e9	−1.08462	−0.542312	+	0.840177i	$0.682451\pi$
$660$	−2.98880e8	−0.0404662
$661$	−3.59159e9	−0.483706	−0.241853	−	0.970313i	$-0.577755\pi$
$661$	−3.59159e9	−0.483706	−0.241853	+	0.970313i	$0.577755\pi$
$662$	−1.15581e10	−1.54840
$663$	−1.51055e9	−0.201297
$664$	6.11641e9	0.810790
$665$	−1.26283e9	−0.166521
$666$	5.88344e8	0.0771741
$667$	1.76082e9	0.229761
$668$	4.52885e9	0.587855
$669$	3.85964e8	0.0498374
$670$	2.61051e9	0.335323
$671$	2.68834e9	0.343522
$672$	−2.16479e9	−0.275184
$673$	8.88634e9	1.12375	0.561875	−	0.827222i	$-0.310080\pi$
$673$	8.88634e9	1.12375	0.561875	+	0.827222i	$0.310080\pi$
$674$	−1.60387e10	−2.01772
$675$	1.30032e9	0.162738
$676$	−8.43075e8	−0.104967
$677$	8.62914e9	1.06883	0.534413	−	0.845223i	$-0.320533\pi$
$677$	8.62914e9	1.06883	0.534413	+	0.845223i	$0.320533\pi$
$678$	−1.13486e10	−1.39842
$679$	4.96399e9	0.608536
$680$	−6.38102e8	−0.0778231
$681$	8.29720e9	1.00674
$682$	5.07967e8	0.0613183
$683$	−1.16919e10	−1.40415	−0.702074	−	0.712104i	$-0.747742\pi$
$683$	−1.16919e10	−1.40415	−0.702074	+	0.712104i	$0.747742\pi$
$684$	−1.54266e9	−0.184320
$685$	2.15107e9	0.255704
$686$	8.67917e9	1.02646
$687$	6.64809e9	0.782255
$688$	1.51642e10	1.77525
$689$	4.90617e9	0.571446
$690$	9.92607e8	0.115028
$691$	1.17768e10	1.35786	0.678931	−	0.734202i	$-0.262443\pi$
$691$	1.17768e10	1.35786	0.678931	+	0.734202i	$0.262443\pi$
$692$	5.30887e9	0.609019
$693$	3.99257e8	0.0455707
$694$	1.77026e10	2.01038
$695$	9.58958e8	0.108356
$696$	−1.51251e9	−0.170046
$697$	4.75220e8	0.0531594
$698$	3.93097e9	0.437528
$699$	−1.51229e8	−0.0167481
$700$	−2.05852e9	−0.226836
$701$	6.87866e8	0.0754208	0.0377104	−	0.999289i	$-0.487994\pi$
$701$	6.87866e8	0.0754208	0.0377104	+	0.999289i	$0.487994\pi$
$702$	−2.01839e9	−0.220204
$703$	1.58006e9	0.171525
$704$	−2.36037e8	−0.0254962
$705$	3.62066e9	0.389158
$706$	−7.21440e9	−0.771585
$707$	3.22396e8	0.0343101
$708$	1.35910e9	0.143924
$709$	−1.12319e9	−0.118357	−0.0591784	−	0.998247i	$-0.518848\pi$
$709$	−1.12319e9	−0.118357	−0.0591784	+	0.998247i	$0.518848\pi$
$710$	4.39009e9	0.460330
$711$	−9.16686e7	−0.00956482
$712$	3.34512e9	0.347321
$713$	−6.27073e8	−0.0647895
$714$	−1.23485e9	−0.126961
$715$	−1.05020e9	−0.107449
$716$	1.68831e9	0.171892
$717$	3.59851e9	0.364590
$718$	−4.25380e9	−0.428885
$719$	−8.52118e9	−0.854966	−0.427483	−	0.904023i	$-0.640600\pi$
$719$	−8.52118e9	−0.854966	−0.427483	+	0.904023i	$0.640600\pi$
$720$	−1.62868e9	−0.162620
$721$	−6.55521e9	−0.651349
$722$	1.61276e9	0.159474
$723$	−1.06145e10	−1.04452
$724$	1.09418e10	1.07153
$725$	−4.96011e9	−0.483402
$726$	6.82722e8	0.0662164
$727$	−2.01807e9	−0.194790	−0.0973948	−	0.995246i	$-0.531051\pi$
$727$	−2.01807e9	−0.194790	−0.0973948	+	0.995246i	$0.531051\pi$
$728$	−2.20567e9	−0.211875
$729$	3.87420e8	0.0370370
$730$	1.51849e9	0.144471
$731$	5.80491e9	0.549648
$732$	−4.12970e9	−0.389162
$733$	−2.06270e10	−1.93451	−0.967256	−	0.253801i	$-0.918319\pi$
$733$	−2.06270e10	−1.93451	−0.967256	+	0.253801i	$0.918319\pi$
$734$	1.35678e10	1.26641
$735$	1.93999e9	0.180216
$736$	4.56971e9	0.422490
$737$	−2.21653e9	−0.203957
$738$	6.34988e8	0.0581525
$739$	2.77599e9	0.253025	0.126512	−	0.991965i	$-0.459622\pi$
$739$	2.77599e9	0.253025	0.126512	+	0.991965i	$0.459622\pi$
$740$	−4.70256e8	−0.0426602
$741$	−5.42058e9	−0.489420
$742$	4.01073e9	0.360421
$743$	−1.24982e10	−1.11786	−0.558930	−	0.829215i	$-0.688788\pi$
$743$	−1.24982e10	−1.11786	−0.558930	+	0.829215i	$0.688788\pi$
$744$	5.38643e8	0.0479508
$745$	5.39059e9	0.477628
$746$	−9.59817e9	−0.846453
$747$	5.97613e9	0.524564
$748$	−7.84889e8	−0.0685729
$749$	−9.08646e9	−0.790148
$750$	−6.10271e9	−0.528212
$751$	−4.87365e9	−0.419870	−0.209935	−	0.977715i	$-0.567325\pi$
$751$	−4.87365e9	−0.419870	−0.209935	+	0.977715i	$0.567325\pi$
$752$	2.48384e10	2.12991
$753$	−1.21923e10	−1.04064
$754$	7.69919e9	0.654102
$755$	4.54003e9	0.383923
$756$	−6.13320e8	−0.0516251
$757$	−2.10232e10	−1.76142	−0.880709	−	0.473657i	$-0.842934\pi$
$757$	−2.10232e10	−1.76142	−0.880709	+	0.473657i	$0.842934\pi$
$758$	−3.09175e9	−0.257847
$759$	−8.42803e8	−0.0699648
$760$	−2.28982e9	−0.189214
$761$	1.49529e10	1.22992	0.614962	−	0.788557i	$-0.289172\pi$
$761$	1.49529e10	1.22992	0.614962	+	0.788557i	$0.289172\pi$
$762$	4.27230e9	0.349800
$763$	3.83286e9	0.312383
$764$	8.41360e9	0.682582
$765$	−6.23467e8	−0.0503499
$766$	7.48673e9	0.601855
$767$	4.77559e9	0.382158
$768$	−9.24916e9	−0.736780
$769$	−9.62801e9	−0.763474	−0.381737	−	0.924271i	$-0.624674\pi$
$769$	−9.62801e9	−0.763474	−0.381737	+	0.924271i	$0.624674\pi$
$770$	−8.58527e8	−0.0677698
$771$	−2.73619e9	−0.215009
$772$	−1.13433e10	−0.887314
$773$	5.59033e9	0.435321	0.217660	−	0.976025i	$-0.430157\pi$
$773$	5.59033e9	0.435321	0.217660	+	0.976025i	$0.430157\pi$
$774$	7.75651e9	0.601275
$775$	1.76642e9	0.136313
$776$	9.00094e9	0.691468
$777$	6.28189e8	0.0480415
$778$	5.12418e9	0.390118
$779$	1.70532e9	0.129248
$780$	1.61327e9	0.121724
$781$	−3.72754e9	−0.279991
$782$	2.60669e9	0.194924
$783$	−1.47782e9	−0.110016
$784$	1.33086e10	0.986342
$785$	−4.22448e9	−0.311695
$786$	5.48812e9	0.403130
$787$	−1.24501e10	−0.910463	−0.455231	−	0.890373i	$-0.650443\pi$
$787$	−1.24501e10	−0.910463	−0.455231	+	0.890373i	$0.650443\pi$
$788$	6.47617e9	0.471494
$789$	7.66567e9	0.555623
$790$	1.97116e8	0.0142242
$791$	−1.21171e10	−0.870527
$792$	7.23951e8	0.0517811
$793$	−1.45109e10	−1.03333
$794$	−3.53321e9	−0.250494
$795$	2.02499e9	0.142934
$796$	−1.45768e10	−1.02440
$797$	1.92241e10	1.34506	0.672531	−	0.740069i	$-0.265207\pi$
$797$	1.92241e10	1.34506	0.672531	+	0.740069i	$0.265207\pi$
$798$	−4.43125e9	−0.308686
$799$	9.50823e9	0.659457
$800$	−1.28725e10	−0.888893
$801$	3.26840e9	0.224709
$802$	1.74971e9	0.119772
$803$	−1.28932e9	−0.0878731
$804$	3.40494e9	0.231054
$805$	1.05983e9	0.0716062
$806$	−2.74187e9	−0.184448
$807$	−4.05607e9	−0.271674
$808$	5.84584e8	0.0389859
$809$	−1.88593e10	−1.25229	−0.626145	−	0.779707i	$-0.715368\pi$
$809$	−1.88593e10	−1.25229	−0.626145	+	0.779707i	$0.715368\pi$
$810$	−8.33075e8	−0.0550791
$811$	−1.89368e9	−0.124662	−0.0623310	−	0.998056i	$-0.519853\pi$
$811$	−1.89368e9	−0.124662	−0.0623310	+	0.998056i	$0.519853\pi$
$812$	2.33952e9	0.153349
$813$	−5.84538e9	−0.381501
$814$	1.07419e9	0.0698066
$815$	−7.50113e9	−0.485373
$816$	−4.27709e9	−0.275571
$817$	2.08309e10	1.33638
$818$	1.28771e10	0.822587
$819$	−2.15508e9	−0.137079
$820$	−5.07538e8	−0.0321455
$821$	−5.18430e9	−0.326956	−0.163478	−	0.986547i	$-0.552271\pi$
$821$	−5.18430e9	−0.326956	−0.163478	+	0.986547i	$0.552271\pi$
$822$	7.54808e9	0.474008
$823$	−2.56326e10	−1.60285	−0.801426	−	0.598094i	$-0.795925\pi$
$823$	−2.56326e10	−1.60285	−0.801426	+	0.598094i	$0.795925\pi$
$824$	−1.18862e10	−0.740114
$825$	2.37411e9	0.147202
$826$	3.90398e9	0.241034
$827$	1.33869e10	0.823023	0.411512	−	0.911405i	$-0.365001\pi$
$827$	1.33869e10	0.823023	0.411512	+	0.911405i	$0.365001\pi$
$828$	1.29468e9	0.0792601
$829$	−9.05194e9	−0.551824	−0.275912	−	0.961183i	$-0.588980\pi$
$829$	−9.05194e9	−0.551824	−0.275912	+	0.961183i	$0.588980\pi$
$830$	−1.28506e10	−0.780097
$831$	1.85292e9	0.112009
$832$	1.27406e9	0.0766937
$833$	5.09461e9	0.305389
$834$	3.36498e9	0.200863
$835$	6.56816e9	0.390428
$836$	−2.81656e9	−0.166724
$837$	5.26290e8	0.0310231
$838$	−4.10352e9	−0.240881
$839$	6.29681e9	0.368089	0.184045	−	0.982918i	$-0.441081\pi$
$839$	6.29681e9	0.368089	0.184045	+	0.982918i	$0.441081\pi$
$840$	−9.10373e8	−0.0529959
$841$	−1.16127e10	−0.673204
$842$	−2.48905e10	−1.43695
$843$	−3.47044e9	−0.199520
$844$	−1.89442e10	−1.08462
$845$	−1.22271e9	−0.0697146
$846$	1.27049e10	0.721397
$847$	7.28958e8	0.0412203
$848$	1.38917e10	0.782297
$849$	1.94523e10	1.09092
$850$	−7.34285e9	−0.410108
$851$	−1.32606e9	−0.0737583
$852$	5.72608e9	0.317189
$853$	−2.00556e10	−1.10641	−0.553203	−	0.833046i	$-0.686595\pi$
$853$	−2.00556e10	−1.10641	−0.553203	+	0.833046i	$0.686595\pi$
$854$	−1.18625e10	−0.651739
$855$	−2.23730e9	−0.122418
$856$	−1.64760e10	−0.897829
$857$	2.82992e10	1.53582	0.767911	−	0.640556i	$-0.221296\pi$
$857$	2.82992e10	1.53582	0.767911	+	0.640556i	$0.221296\pi$
$858$	−3.68515e9	−0.199182
$859$	1.65258e9	0.0889583	0.0444792	−	0.999010i	$-0.485837\pi$
$859$	1.65258e9	0.0889583	0.0444792	+	0.999010i	$0.485837\pi$
$860$	−6.19968e9	−0.332372
$861$	6.77992e8	0.0362004
$862$	−1.97221e9	−0.104876
$863$	−3.01008e10	−1.59419	−0.797096	−	0.603852i	$-0.793632\pi$
$863$	−3.01008e10	−1.59419	−0.797096	+	0.603852i	$0.793632\pi$
$864$	−3.83527e9	−0.202301
$865$	7.69942e9	0.404484
$866$	8.75974e8	0.0458330
$867$	9.44185e9	0.492029
$868$	−8.33162e8	−0.0432424
$869$	−1.67367e8	−0.00865171
$870$	3.17779e9	0.163609
$871$	1.19643e10	0.613511
$872$	6.94993e9	0.354954
$873$	8.79451e9	0.447365
$874$	9.35407e9	0.473926
$875$	−6.51601e9	−0.328816
$876$	1.98059e9	0.0995477
$877$	6.73121e9	0.336972	0.168486	−	0.985704i	$-0.446112\pi$
$877$	6.73121e9	0.336972	0.168486	+	0.985704i	$0.446112\pi$
$878$	−3.30689e9	−0.164888
$879$	−1.00733e10	−0.500278
$880$	−2.97363e9	−0.147095
$881$	2.35379e10	1.15972	0.579858	−	0.814717i	$-0.303108\pi$
$881$	2.35379e10	1.15972	0.579858	+	0.814717i	$0.303108\pi$
$882$	6.80740e9	0.334073
$883$	3.53909e10	1.72993	0.864965	−	0.501832i	$-0.167340\pi$
$883$	3.53909e10	1.72993	0.864965	+	0.501832i	$0.167340\pi$
$884$	4.23662e9	0.206270
$885$	1.97109e9	0.0955883
$886$	−8.34973e9	−0.403324
$887$	−1.40193e9	−0.0674516	−0.0337258	−	0.999431i	$-0.510737\pi$
$887$	−1.40193e9	−0.0674516	−0.0337258	+	0.999431i	$0.510737\pi$
$888$	1.13906e9	0.0545886
$889$	4.56164e9	0.217753
$890$	−7.02808e9	−0.334173
$891$	7.07348e8	0.0335013
$892$	−1.08251e9	−0.0510687
$893$	3.41202e10	1.60336
$894$	1.89156e10	0.885397
$895$	2.44854e9	0.114163
$896$	−9.22116e9	−0.428260
$897$	4.54923e9	0.210457
$898$	2.15886e10	0.994847
$899$	−2.00754e9	−0.0921523
$900$	−3.64701e9	−0.166758
$901$	5.31782e9	0.242213
$902$	1.15935e9	0.0526009
$903$	8.28181e9	0.374299
$904$	−2.19714e10	−0.989163
$905$	1.58689e10	0.711666
$906$	1.59309e10	0.711693
$907$	4.09603e10	1.82280	0.911398	−	0.411526i	$-0.135004\pi$
$907$	4.09603e10	1.82280	0.911398	+	0.411526i	$0.135004\pi$
$908$	−2.32711e10	−1.03161
$909$	5.71177e8	0.0252230
$910$	4.63410e9	0.203855
$911$	−3.25987e9	−0.142852	−0.0714259	−	0.997446i	$-0.522755\pi$
$911$	−3.25987e9	−0.142852	−0.0714259	+	0.997446i	$0.522755\pi$
$912$	−1.53483e10	−0.670005
$913$	1.09112e10	0.474486
$914$	4.93699e10	2.13870
$915$	−5.98928e9	−0.258465
$916$	−1.86459e10	−0.801583
$917$	5.85980e9	0.250952
$918$	−2.18774e9	−0.0933355
$919$	−4.07468e10	−1.73177	−0.865883	−	0.500246i	$-0.833243\pi$
$919$	−4.07468e10	−1.73177	−0.865883	+	0.500246i	$0.833243\pi$
$920$	1.92173e9	0.0813647
$921$	−1.57105e10	−0.662644
$922$	−1.32769e10	−0.557878
$923$	2.01203e10	0.842225
$924$	−1.11979e9	−0.0466966
$925$	3.73542e9	0.155183
$926$	−5.53596e10	−2.29115
$927$	−1.16136e10	−0.478838
$928$	1.46297e10	0.600922
$929$	−5.45800e9	−0.223346	−0.111673	−	0.993745i	$-0.535621\pi$
$929$	−5.45800e9	−0.223346	−0.111673	+	0.993745i	$0.535621\pi$
$930$	−1.13169e9	−0.0461356
$931$	1.82819e10	0.742503
$932$	4.24151e8	0.0171619
$933$	1.71804e10	0.692544
$934$	−7.33783e9	−0.294682
$935$	−1.13832e9	−0.0455432
$936$	−3.90770e9	−0.155760
$937$	1.14895e9	0.0456259	0.0228129	−	0.999740i	$-0.492738\pi$
$937$	1.14895e9	0.0456259	0.0228129	+	0.999740i	$0.492738\pi$
$938$	9.78063e9	0.386952
$939$	−1.17486e10	−0.463082
$940$	−1.01548e10	−0.398773
$941$	3.27671e10	1.28196	0.640979	−	0.767558i	$-0.278528\pi$
$941$	3.27671e10	1.28196	0.640979	+	0.767558i	$0.278528\pi$
$942$	−1.48237e10	−0.577800
$943$	−1.43119e9	−0.0555786
$944$	1.35220e10	0.523166
$945$	−8.89494e8	−0.0342872
$946$	1.41618e10	0.543874
$947$	−8.21655e9	−0.314387	−0.157194	−	0.987568i	$-0.550245\pi$
$947$	−8.21655e9	−0.314387	−0.157194	+	0.987568i	$0.550245\pi$
$948$	2.57102e8	0.00980114
$949$	6.95941e9	0.264326
$950$	−2.63497e10	−0.997111
$951$	−2.95933e10	−1.11574
$952$	−2.39073e9	−0.0898053
$953$	−8.78033e9	−0.328614	−0.164307	−	0.986409i	$-0.552539\pi$
$953$	−8.78033e9	−0.328614	−0.164307	+	0.986409i	$0.552539\pi$
$954$	7.10566e9	0.264963
$955$	1.22022e10	0.453342
$956$	−1.00927e10	−0.373598
$957$	−2.69820e9	−0.0995134
$958$	4.96828e10	1.82569
$959$	8.05927e9	0.295074
$960$	5.25861e8	0.0191832
$961$	−2.67977e10	−0.974014
$962$	−5.79821e9	−0.209981
$963$	−1.60981e10	−0.580876
$964$	2.97704e10	1.07032
$965$	−1.64511e10	−0.589317
$966$	3.71894e9	0.132739
$967$	−1.59560e10	−0.567456	−0.283728	−	0.958905i	$-0.591571\pi$
$967$	−1.59560e10	−0.567456	−0.283728	+	0.958905i	$0.591571\pi$
$968$	1.32178e9	0.0468378
$969$	−5.87539e9	−0.207445
$970$	−1.89109e10	−0.665292
$971$	−1.62710e10	−0.570356	−0.285178	−	0.958475i	$-0.592053\pi$
$971$	−1.62710e10	−0.570356	−0.285178	+	0.958475i	$0.592053\pi$
$972$	−1.08660e9	−0.0379521
$973$	3.59287e9	0.125039
$974$	−9.52976e9	−0.330465
$975$	−1.28148e10	−0.442789
$976$	−4.10875e10	−1.41461
$977$	6.21190e9	0.213105	0.106552	−	0.994307i	$-0.466019\pi$
$977$	6.21190e9	0.213105	0.106552	+	0.994307i	$0.466019\pi$
$978$	−2.63214e10	−0.899753
$979$	5.96740e9	0.203257
$980$	−5.44107e9	−0.184668
$981$	6.79054e9	0.229648
$982$	−4.53085e10	−1.52683
$983$	−2.45158e10	−0.823208	−0.411604	−	0.911363i	$-0.635031\pi$
$983$	−2.45158e10	−0.823208	−0.411604	+	0.911363i	$0.635031\pi$
$984$	1.22937e9	0.0411338
$985$	9.39235e9	0.313147
$986$	8.34520e9	0.277247
$987$	1.35653e10	0.449076
$988$	1.52031e10	0.501512
$989$	−1.74823e10	−0.574662
$990$	−1.52102e9	−0.0498209
$991$	−5.05367e10	−1.64949	−0.824744	−	0.565506i	$-0.808681\pi$
$991$	−5.05367e10	−1.64949	−0.824744	+	0.565506i	$0.808681\pi$
$992$	−5.21000e9	−0.169452
$993$	−2.18638e10	−0.708603
$994$	1.64481e10	0.531206
$995$	−2.11407e10	−0.680360
$996$	−1.67612e10	−0.537524
$997$	5.30325e10	1.69476	0.847382	−	0.530985i	$-0.178178\pi$
$997$	5.30325e10	1.69476	0.847382	+	0.530985i	$0.178178\pi$
$998$	−2.85553e10	−0.909348
$999$	1.11294e9	0.0353177

Twists

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

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

\(f(q)\)	\(=\)	\(q-14.2733 q^{2} -27.0000 q^{3} +75.7267 q^{4} +109.826 q^{5} +385.379 q^{6} +411.478 q^{7} +746.112 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-14.2733 q^{2} -27.0000 q^{3} +75.7267 q^{4} +109.826 q^{5} +385.379 q^{6} +411.478 q^{7} +746.112 q^{8} +729.000 q^{9} -1567.58 q^{10} +1331.00 q^{11} -2044.62 q^{12} -7184.38 q^{13} -5873.14 q^{14} -2965.30 q^{15} -20342.5 q^{16} -7787.19 q^{17} -10405.2 q^{18} -27944.2 q^{19} +8316.76 q^{20} -11109.9 q^{21} -18997.7 q^{22} +23452.2 q^{23} -20145.0 q^{24} -66063.2 q^{25} +102545. q^{26} -19683.0 q^{27} +31159.9 q^{28} +75081.3 q^{29} +42324.6 q^{30} -26738.3 q^{31} +194852. q^{32} -35937.0 q^{33} +111149. q^{34} +45191.0 q^{35} +55204.8 q^{36} -56543.1 q^{37} +398856. q^{38} +193978. q^{39} +81942.5 q^{40} -61025.9 q^{41} +158575. q^{42} -745444. q^{43} +100792. q^{44} +80063.2 q^{45} -334741. q^{46} -1.22101e6 q^{47} +549247. q^{48} -654229. q^{49} +942940. q^{50} +210254. q^{51} -544050. q^{52} -682893. q^{53} +280941. q^{54} +146178. q^{55} +307009. q^{56} +754494. q^{57} -1.07166e6 q^{58} -664718. q^{59} -224553. q^{60} +2.01979e6 q^{61} +381643. q^{62} +299967. q^{63} -177338. q^{64} -789032. q^{65} +512939. q^{66} -1.66531e6 q^{67} -589698. q^{68} -633210. q^{69} -645024. q^{70} -2.80056e6 q^{71} +543915. q^{72} -968685. q^{73} +807057. q^{74} +1.78371e6 q^{75} -2.11613e6 q^{76} +547677. q^{77} -2.76871e6 q^{78} -125746. q^{79} -2.23413e6 q^{80} +531441. q^{81} +871040. q^{82} +8.19771e6 q^{83} -841317. q^{84} -855236. q^{85} +1.06399e7 q^{86} -2.02719e6 q^{87} +993075. q^{88} +4.48340e6 q^{89} -1.14276e6 q^{90} -2.95622e6 q^{91} +1.77596e6 q^{92} +721934. q^{93} +1.74278e7 q^{94} -3.06900e6 q^{95} -5.26100e6 q^{96} +1.20638e7 q^{97} +9.33800e6 q^{98} +970299. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - 54 q^{3} + 181 q^{4} - 194 q^{5} - 27 q^{6} - 418 q^{7} + 399 q^{8} + 1458 q^{9}+O(q^{10}) \) 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

Varieties

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Groups

Database

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