LMFDB - Embedded newform 33.14.a.c.1.2

Error: no document with id 239787625 found in table mf_hecke_traces.

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [33,14,Mod(1,33)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("33.1"); S:= CuspForms(chi, 14); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(33, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 14, names="a")

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 14 $
Character orbit:	$[\chi]$	$=$	33.a (trivial)

Newform invariants

comment:select newform

sage:traces = [4,41] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$35.3862065541$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 28008x^{2} - 426124x + 63795376 $ x^4 - x^3 - 28008x^2 - 426124x + 63795376
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{3}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-60.8281$ 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)

$f(q)$	$=$	\(q-50.8281 q^{2} +729.000 q^{3} -5608.51 q^{4} +40325.0 q^{5} -37053.7 q^{6} +161391. q^{7} +701453. q^{8} +531441. q^{9} -2.04964e6 q^{10} -1.77156e6 q^{11} -4.08860e6 q^{12} +1.00855e7 q^{13} -8.20318e6 q^{14} +2.93969e7 q^{15} +1.02914e7 q^{16} -5.44308e7 q^{17} -2.70121e7 q^{18} +3.35823e7 q^{19} -2.26163e8 q^{20} +1.17654e8 q^{21} +9.00451e7 q^{22} -5.77067e7 q^{23} +5.11359e8 q^{24} +4.05404e8 q^{25} -5.12626e8 q^{26} +3.87420e8 q^{27} -9.05161e8 q^{28} -1.42770e9 q^{29} -1.49419e9 q^{30} -3.95227e8 q^{31} -6.26940e9 q^{32} -1.29147e9 q^{33} +2.76661e9 q^{34} +6.50808e9 q^{35} -2.98059e9 q^{36} +2.97526e10 q^{37} -1.70692e9 q^{38} +7.35233e9 q^{39} +2.82861e10 q^{40} +4.78825e10 q^{41} -5.98012e9 q^{42} +5.25504e10 q^{43} +9.93581e9 q^{44} +2.14304e10 q^{45} +2.93312e9 q^{46} +7.82524e10 q^{47} +7.50240e9 q^{48} -7.08421e10 q^{49} -2.06059e10 q^{50} -3.96800e10 q^{51} -5.65646e10 q^{52} +1.39229e11 q^{53} -1.96918e10 q^{54} -7.14382e10 q^{55} +1.13208e11 q^{56} +2.44815e10 q^{57} +7.25673e10 q^{58} +4.00667e11 q^{59} -1.64873e11 q^{60} +8.48232e9 q^{61} +2.00887e10 q^{62} +8.57696e10 q^{63} +2.34355e11 q^{64} +4.06698e11 q^{65} +6.56428e10 q^{66} -2.54018e11 q^{67} +3.05275e11 q^{68} -4.20682e10 q^{69} -3.30793e11 q^{70} -9.45197e11 q^{71} +3.72781e11 q^{72} -1.26364e12 q^{73} -1.51227e12 q^{74} +2.95540e11 q^{75} -1.88346e11 q^{76} -2.85913e11 q^{77} -3.73705e11 q^{78} +1.73956e12 q^{79} +4.14999e11 q^{80} +2.82430e11 q^{81} -2.43377e12 q^{82} +3.01003e12 q^{83} -6.59862e11 q^{84} -2.19492e12 q^{85} -2.67104e12 q^{86} -1.04079e12 q^{87} -1.24267e12 q^{88} +2.47839e11 q^{89} -1.08926e12 q^{90} +1.62771e12 q^{91} +3.23648e11 q^{92} -2.88121e11 q^{93} -3.97742e12 q^{94} +1.35421e12 q^{95} -4.57039e12 q^{96} -1.01179e13 q^{97} +3.60077e12 q^{98} -9.41480e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 41 q^{2} + 2916 q^{3} + 23669 q^{4} - 38422 q^{5} + 29889 q^{6} + 41998 q^{7} + 2375463 q^{8} + 2125764 q^{9} - 5866868 q^{10} - 7086244 q^{11} + 17254701 q^{12} + 50891230 q^{13} + 51438518 q^{14}+ \cdots - 3765920597604 q^{99}+O(q^{100}) $ 4 * q + 41 * q^2 + 2916 * q^3 + 23669 * q^4 - 38422 * q^5 + 29889 * q^6 + 41998 * q^7 + 2375463 * q^8 + 2125764 * q^9 - 5866868 * q^10 - 7086244 * q^11 + 17254701 * q^12 + 50891230 * q^13 + 51438518 * q^14 - 28009638 * q^15 + 285120977 * q^16 + 192739820 * q^17 + 21789081 * q^18 - 183220188 * q^19 - 898094912 * q^20 + 30616542 * q^21 - 72634001 * q^22 - 14728250 * q^23 + 1731712527 * q^24 - 1100820808 * q^25 + 4093863728 * q^26 + 1549681956 * q^27 - 7107233974 * q^28 - 548077356 * q^29 - 4276946772 * q^30 - 681968600 * q^31 + 39383025007 * q^32 - 5165871876 * q^33 + 19950148786 * q^34 + 5394617384 * q^35 + 12578677029 * q^36 - 5154946872 * q^37 + 18554908452 * q^38 + 37099706670 * q^39 - 15687175464 * q^40 + 51238857992 * q^41 + 37498679622 * q^42 + 74347734480 * q^43 - 41931077309 * q^44 - 20419026102 * q^45 + 166685861450 * q^46 + 274474225690 * q^47 + 207853192233 * q^48 - 153177492648 * q^49 - 149839157 * q^50 + 140507328780 * q^51 + 898475423084 * q^52 + 213982590882 * q^53 + 15884240049 * q^54 + 68066916742 * q^55 - 15495316938 * q^56 - 133567517052 * q^57 - 366985322898 * q^58 + 1321318473964 * q^59 - 654711190848 * q^60 - 103045963950 * q^61 - 1085044917496 * q^62 + 22319459118 * q^63 + 2752080303457 * q^64 - 592303463140 * q^65 - 52950186729 * q^66 + 564819557912 * q^67 + 475206163858 * q^68 - 10736894250 * q^69 - 1630864907696 * q^70 + 755239009806 * q^71 + 1262418432183 * q^72 + 1553343364552 * q^73 - 1161503492586 * q^74 - 802498369032 * q^75 - 4781019846036 * q^76 - 74402018878 * q^77 + 2984426657712 * q^78 - 409630665982 * q^79 - 7292238669896 * q^80 + 1129718145924 * q^81 - 14121959211962 * q^82 - 2873448789168 * q^83 - 5181173567046 * q^84 - 9861359797412 * q^85 - 5038703996808 * q^86 - 399548392524 * q^87 - 4208277607743 * q^88 - 2345798585688 * q^89 - 3117894196788 * q^90 - 4061579957120 * q^91 - 4480747709890 * q^92 - 497155109400 * q^93 - 21071642578954 * q^94 + 5118679925808 * q^95 + 28710225230103 * q^96 - 325787932204 * q^97 - 19699761224547 * q^98 - 3765920597604 * q^99

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 $

$2$	−50.8281	−0.561576	−0.280788	−	0.959770i	$-0.590596\pi$
$2$	−50.8281	−0.561576	−0.280788	+	0.959770i	$0.590596\pi$
$3$	729.000	0.577350
$3$	729.000	0.577350
$4$	−5608.51	−0.684632
$5$	40325.0	1.15417	0.577085	−	0.816684i	$-0.304190\pi$
$5$	40325.0	1.15417	0.577085	+	0.816684i	$0.304190\pi$
$6$	−37053.7	−0.324226
$7$	161391.	0.518491	0.259245	−	0.965811i	$-0.416526\pi$
$7$	161391.	0.518491	0.259245	+	0.965811i	$0.416526\pi$
$8$	701453.	0.946049
$9$	531441.	0.333333
$10$	−2.04964e6	−0.648154
$11$	−1.77156e6	−0.301511
$11$	−1.77156e6	−0.301511
$12$	−4.08860e6	−0.395273
$13$	1.00855e7	0.579516	0.289758	−	0.957100i	$-0.406425\pi$
$13$	1.00855e7	0.579516	0.289758	+	0.957100i	$0.406425\pi$
$14$	−8.20318e6	−0.291172
$15$	2.93969e7	0.666360
$16$	1.02914e7	0.153353
$17$	−5.44308e7	−0.546923	−0.273462	−	0.961883i	$-0.588169\pi$
$17$	−5.44308e7	−0.546923	−0.273462	+	0.961883i	$0.588169\pi$
$18$	−2.70121e7	−0.187192
$19$	3.35823e7	0.163761	0.0818807	−	0.996642i	$-0.473907\pi$
$19$	3.35823e7	0.163761	0.0818807	+	0.996642i	$0.473907\pi$
$20$	−2.26163e8	−0.790181
$21$	1.17654e8	0.299351
$22$	9.00451e7	0.169322
$23$	−5.77067e7	−0.0812821	−0.0406411	−	0.999174i	$-0.512940\pi$
$23$	−5.77067e7	−0.0812821	−0.0406411	+	0.999174i	$0.512940\pi$
$24$	5.11359e8	0.546202
$25$	4.05404e8	0.332107
$26$	−5.12626e8	−0.325442
$27$	3.87420e8	0.192450
$28$	−9.05161e8	−0.354976
$29$	−1.42770e9	−0.445708	−0.222854	−	0.974852i	$-0.571537\pi$
$29$	−1.42770e9	−0.445708	−0.222854	+	0.974852i	$0.571537\pi$
$30$	−1.49419e9	−0.374212
$31$	−3.95227e8	−0.0799827	−0.0399914	−	0.999200i	$-0.512733\pi$
$31$	−3.95227e8	−0.0799827	−0.0399914	+	0.999200i	$0.512733\pi$
$32$	−6.26940e9	−1.03217
$33$	−1.29147e9	−0.174078
$34$	2.76661e9	0.307139
$35$	6.50808e9	0.598426
$36$	−2.98059e9	−0.228211
$37$	2.97526e10	1.90640	0.953200	−	0.302339i	$-0.0977675\pi$
$37$	2.97526e10	1.90640	0.953200	+	0.302339i	$0.0977675\pi$
$38$	−1.70692e9	−0.0919646
$39$	7.35233e9	0.334584
$40$	2.82861e10	1.09190
$41$	4.78825e10	1.57428	0.787139	−	0.616776i	$-0.211561\pi$
$41$	4.78825e10	1.57428	0.787139	+	0.616776i	$0.211561\pi$
$42$	−5.98012e9	−0.168108
$43$	5.25504e10	1.26774	0.633871	−	0.773439i	$-0.281465\pi$
$43$	5.25504e10	1.26774	0.633871	+	0.773439i	$0.281465\pi$
$44$	9.93581e9	0.206424
$45$	2.14304e10	0.384723
$46$	2.93312e9	0.0456461
$47$	7.82524e10	1.05892	0.529458	−	0.848336i	$-0.322395\pi$
$47$	7.82524e10	1.05892	0.529458	+	0.848336i	$0.322395\pi$
$48$	7.50240e9	0.0885385
$49$	−7.08421e10	−0.731167
$50$	−2.06059e10	−0.186504
$51$	−3.96800e10	−0.315766
$52$	−5.65646e10	−0.396755
$53$	1.39229e11	0.862850	0.431425	−	0.902149i	$-0.358011\pi$
$53$	1.39229e11	0.862850	0.431425	+	0.902149i	$0.358011\pi$
$54$	−1.96918e10	−0.108075
$55$	−7.14382e10	−0.347995
$56$	1.13208e11	0.490518
$57$	2.44815e10	0.0945477
$58$	7.25673e10	0.250299
$59$	4.00667e11	1.23665	0.618324	−	0.785923i	$-0.287812\pi$
$59$	4.00667e11	1.23665	0.618324	+	0.785923i	$0.287812\pi$
$60$	−1.64873e11	−0.456211
$61$	8.48232e9	0.0210800	0.0105400	−	0.999944i	$-0.496645\pi$
$61$	8.48232e9	0.0210800	0.0105400	+	0.999944i	$0.496645\pi$
$62$	2.00887e10	0.0449164
$63$	8.57696e10	0.172830
$64$	2.34355e11	0.426288
$65$	4.06698e11	0.668860
$66$	6.56428e10	0.0977579
$67$	−2.54018e11	−0.343067	−0.171533	−	0.985178i	$-0.554872\pi$
$67$	−2.54018e11	−0.343067	−0.171533	+	0.985178i	$0.554872\pi$
$68$	3.05275e11	0.374441
$69$	−4.20682e10	−0.0469283
$70$	−3.30793e11	−0.336062
$71$	−9.45197e11	−0.875675	−0.437838	−	0.899054i	$-0.644255\pi$
$71$	−9.45197e11	−0.875675	−0.437838	+	0.899054i	$0.644255\pi$
$72$	3.72781e11	0.315350
$73$	−1.26364e12	−0.977297	−0.488648	−	0.872481i	$-0.662510\pi$
$73$	−1.26364e12	−0.977297	−0.488648	+	0.872481i	$0.662510\pi$
$74$	−1.51227e12	−1.07059
$75$	2.95540e11	0.191742
$76$	−1.88346e11	−0.112116
$77$	−2.85913e11	−0.156331
$78$	−3.73705e11	−0.187894
$79$	1.73956e12	0.805127	0.402563	−	0.915392i	$-0.368119\pi$
$79$	1.73956e12	0.805127	0.402563	+	0.915392i	$0.368119\pi$
$80$	4.14999e11	0.176996
$81$	2.82430e11	0.111111
$82$	−2.43377e12	−0.884077
$83$	3.01003e12	1.01056	0.505281	−	0.862955i	$-0.331389\pi$
$83$	3.01003e12	1.01056	0.505281	+	0.862955i	$0.331389\pi$
$84$	−6.59862e11	−0.204945
$85$	−2.19492e12	−0.631242
$86$	−2.67104e12	−0.711934
$87$	−1.04079e12	−0.257329
$88$	−1.24267e12	−0.285245
$89$	2.47839e11	0.0528609	0.0264304	−	0.999651i	$-0.491586\pi$
$89$	2.47839e11	0.0528609	0.0264304	+	0.999651i	$0.491586\pi$
$90$	−1.08926e12	−0.216051
$91$	1.62771e12	0.300474
$92$	3.23648e11	0.0556484
$93$	−2.88121e11	−0.0461780
$94$	−3.97742e12	−0.594663
$95$	1.35421e12	0.189008
$96$	−4.57039e12	−0.595923
$97$	−1.01179e13	−1.23332	−0.616659	−	0.787230i	$-0.711514\pi$
$97$	−1.01179e13	−1.23332	−0.616659	+	0.787230i	$0.711514\pi$
$98$	3.60077e12	0.410606
$99$	−9.41480e11	−0.100504
$100$	−2.27371e12	−0.227371
$101$	3.89127e12	0.364756	0.182378	−	0.983229i	$-0.441621\pi$
$101$	3.89127e12	0.364756	0.182378	+	0.983229i	$0.441621\pi$
$102$	2.01686e12	0.177327
$103$	−6.01807e12	−0.496610	−0.248305	−	0.968682i	$-0.579873\pi$
$103$	−6.01807e12	−0.496610	−0.248305	+	0.968682i	$0.579873\pi$
$104$	7.07450e12	0.548251
$105$	4.74439e12	0.345502
$106$	−7.07672e12	−0.484556
$107$	−1.78982e13	−1.15296	−0.576480	−	0.817111i	$-0.695574\pi$
$107$	−1.78982e13	−1.15296	−0.576480	+	0.817111i	$0.695574\pi$
$108$	−2.17285e12	−0.131758
$109$	2.38534e13	1.36232	0.681158	−	0.732136i	$-0.261477\pi$
$109$	2.38534e13	1.36232	0.681158	+	0.732136i	$0.261477\pi$
$110$	3.63107e12	0.195426
$111$	2.16897e13	1.10066
$112$	1.66093e12	0.0795122
$113$	1.74936e13	0.790439	0.395219	−	0.918587i	$-0.370669\pi$
$113$	1.74936e13	0.790439	0.395219	+	0.918587i	$0.370669\pi$
$114$	−1.24435e12	−0.0530958
$115$	−2.32702e12	−0.0938134
$116$	8.00726e12	0.305146
$117$	5.35985e12	0.193172
$118$	−2.03652e13	−0.694472
$119$	−8.78462e12	−0.283575
$120$	2.06206e13	0.630410
$121$	3.13843e12	0.0909091
$122$	−4.31140e11	−0.0118380
$123$	3.49063e13	0.908910
$124$	2.21664e12	0.0547587
$125$	−3.28769e13	−0.770862
$126$	−4.35951e12	−0.0970574
$127$	9.69545e12	0.205043	0.102521	−	0.994731i	$-0.467309\pi$
$127$	9.69545e12	0.205043	0.102521	+	0.994731i	$0.467309\pi$
$128$	3.94471e13	0.792775
$129$	3.83092e13	0.731931
$130$	−2.06717e13	−0.375616
$131$	1.03655e14	1.79196	0.895978	−	0.444098i	$-0.146476\pi$
$131$	1.03655e14	1.79196	0.895978	+	0.444098i	$0.146476\pi$
$132$	7.24321e12	0.119179
$133$	5.41987e12	0.0849088
$134$	1.29113e13	0.192658
$135$	1.56227e13	0.222120
$136$	−3.81806e13	−0.517417
$137$	−1.70943e13	−0.220886	−0.110443	−	0.993882i	$-0.535227\pi$
$137$	−1.70943e13	−0.220886	−0.110443	+	0.993882i	$0.535227\pi$
$138$	2.13824e12	0.0263538
$139$	−6.71135e13	−0.789249	−0.394624	−	0.918843i	$-0.629125\pi$
$139$	−6.71135e13	−0.789249	−0.394624	+	0.918843i	$0.629125\pi$
$140$	−3.65006e13	−0.409702
$141$	5.70460e13	0.611366
$142$	4.80425e13	0.491758
$143$	−1.78671e13	−0.174731
$144$	5.46925e12	0.0511177
$145$	−5.75720e13	−0.514422
$146$	6.42286e13	0.548827
$147$	−5.16439e13	−0.422140
$148$	−1.66868e14	−1.30518
$149$	2.58976e13	0.193887	0.0969435	−	0.995290i	$-0.469093\pi$
$149$	2.58976e13	0.193887	0.0969435	+	0.995290i	$0.469093\pi$
$150$	−1.50217e13	−0.107678
$151$	−9.34481e12	−0.0641535	−0.0320767	−	0.999485i	$-0.510212\pi$
$151$	−9.34481e12	−0.0641535	−0.0320767	+	0.999485i	$0.510212\pi$
$152$	2.35564e13	0.154926
$153$	−2.89267e13	−0.182308
$154$	1.45324e13	0.0877917
$155$	−1.59376e13	−0.0923136
$156$	−4.12356e13	−0.229067
$157$	−2.90880e14	−1.55012	−0.775061	−	0.631886i	$-0.782281\pi$
$157$	−2.90880e14	−1.55012	−0.775061	+	0.631886i	$0.782281\pi$
$158$	−8.84187e13	−0.452140
$159$	1.01498e14	0.498167
$160$	−2.52813e14	−1.19130
$161$	−9.31332e12	−0.0421441
$162$	−1.43554e13	−0.0623974
$163$	2.47872e14	1.03516	0.517580	−	0.855635i	$-0.326833\pi$
$163$	2.47872e14	1.03516	0.517580	+	0.855635i	$0.326833\pi$
$164$	−2.68549e14	−1.07780
$165$	−5.20785e13	−0.200915
$166$	−1.52994e14	−0.567508
$167$	4.57504e13	0.163207	0.0816034	−	0.996665i	$-0.473996\pi$
$167$	4.57504e13	0.163207	0.0816034	+	0.996665i	$0.473996\pi$
$168$	8.25286e13	0.283201
$169$	−2.01158e14	−0.664161
$170$	1.11564e14	0.354491
$171$	1.78470e13	0.0545872
$172$	−2.94729e14	−0.867937
$173$	−6.05688e13	−0.171771	−0.0858854	−	0.996305i	$-0.527372\pi$
$173$	−6.05688e13	−0.171771	−0.0858854	+	0.996305i	$0.527372\pi$
$174$	5.29015e13	0.144510
$175$	6.54285e13	0.172195
$176$	−1.82318e13	−0.0462377
$177$	2.92087e14	0.713979
$178$	−1.25972e13	−0.0296854
$179$	6.12761e14	1.39234	0.696172	−	0.717875i	$-0.254885\pi$
$179$	6.12761e14	1.39234	0.696172	+	0.717875i	$0.254885\pi$
$180$	−1.20192e14	−0.263394
$181$	−1.61023e14	−0.340390	−0.170195	−	0.985410i	$-0.554440\pi$
$181$	−1.61023e14	−0.340390	−0.170195	+	0.985410i	$0.554440\pi$
$182$	−8.27331e13	−0.168739
$183$	6.18361e12	0.0121705
$184$	−4.04785e13	−0.0768969
$185$	1.19978e15	2.20031
$186$	1.46446e13	0.0259325
$187$	9.64274e13	0.164904
$188$	−4.38879e14	−0.724968
$189$	6.25261e13	0.0997836
$190$	−6.88317e13	−0.106143
$191$	4.59444e13	0.0684724	0.0342362	−	0.999414i	$-0.489100\pi$
$191$	4.59444e13	0.0684724	0.0342362	+	0.999414i	$0.489100\pi$
$192$	1.70844e14	0.246118
$193$	−5.94745e14	−0.828340	−0.414170	−	0.910200i	$-0.635928\pi$
$193$	−5.94745e14	−0.828340	−0.414170	+	0.910200i	$0.635928\pi$
$194$	5.14275e14	0.692602
$195$	2.96483e14	0.386166
$196$	3.97318e14	0.500580
$197$	−3.87638e14	−0.472494	−0.236247	−	0.971693i	$-0.575917\pi$
$197$	−3.87638e14	−0.472494	−0.236247	+	0.971693i	$0.575917\pi$
$198$	4.78536e13	0.0564405
$199$	−7.15122e14	−0.816273	−0.408136	−	0.912921i	$-0.633821\pi$
$199$	−7.15122e14	−0.816273	−0.408136	+	0.912921i	$0.633821\pi$
$200$	2.84372e14	0.314190
$201$	−1.85179e14	−0.198070
$202$	−1.97786e14	−0.204838
$203$	−2.30417e14	−0.231095
$204$	2.22546e14	0.216184
$205$	1.93086e15	1.81698
$206$	3.05887e14	0.278884
$207$	−3.06677e13	−0.0270940
$208$	1.03793e14	0.0888706
$209$	−5.94931e13	−0.0493759
$210$	−2.41148e14	−0.194026
$211$	1.07694e15	0.840148	0.420074	−	0.907490i	$-0.362004\pi$
$211$	1.07694e15	0.840148	0.420074	+	0.907490i	$0.362004\pi$
$212$	−7.80864e14	−0.590735
$213$	−6.89048e14	−0.505571
$214$	9.09730e14	0.647475
$215$	2.11910e15	1.46319
$216$	2.71757e14	0.182067
$217$	−6.37860e13	−0.0414703
$218$	−1.21242e15	−0.765044
$219$	−9.21197e14	−0.564243
$220$	4.00662e14	0.238249
$221$	−5.48961e14	−0.316951
$222$	−1.10244e15	−0.618105
$223$	−1.91496e15	−1.04274	−0.521372	−	0.853329i	$-0.674580\pi$
$223$	−1.91496e15	−1.04274	−0.521372	+	0.853329i	$0.674580\pi$
$224$	−1.01182e15	−0.535170
$225$	2.15448e14	0.110702
$226$	−8.89164e14	−0.443892
$227$	3.38641e14	0.164275	0.0821375	−	0.996621i	$-0.473825\pi$
$227$	3.38641e14	0.164275	0.0821375	+	0.996621i	$0.473825\pi$
$228$	−1.37305e14	−0.0647304
$229$	2.23378e15	1.02355	0.511775	−	0.859120i	$-0.328988\pi$
$229$	2.23378e15	1.02355	0.511775	+	0.859120i	$0.328988\pi$
$230$	1.18278e14	0.0526834
$231$	−2.08431e14	−0.0902577
$232$	−1.00146e15	−0.421661
$233$	2.42044e15	0.991015	0.495508	−	0.868604i	$-0.334982\pi$
$233$	2.42044e15	0.991015	0.495508	+	0.868604i	$0.334982\pi$
$234$	−2.72431e14	−0.108481
$235$	3.15553e15	1.22217
$236$	−2.24715e15	−0.846649
$237$	1.26814e15	0.464840
$238$	4.46505e14	0.159249
$239$	−8.59607e14	−0.298341	−0.149171	−	0.988811i	$-0.547660\pi$
$239$	−8.59607e14	−0.298341	−0.149171	+	0.988811i	$0.547660\pi$
$240$	3.02534e14	0.102188
$241$	3.86032e15	1.26915	0.634575	−	0.772862i	$-0.281175\pi$
$241$	3.86032e15	1.26915	0.634575	+	0.772862i	$0.281175\pi$
$242$	−1.59520e14	−0.0510524
$243$	2.05891e14	0.0641500
$244$	−4.75731e13	−0.0144320
$245$	−2.85671e15	−0.843891
$246$	−1.77422e15	−0.510422
$247$	3.38694e14	0.0949024
$248$	−2.77234e14	−0.0756676
$249$	2.19431e15	0.583448
$250$	1.67107e15	0.432898
$251$	−5.11575e15	−1.29131	−0.645655	−	0.763629i	$-0.723416\pi$
$251$	−5.11575e15	−1.29131	−0.645655	+	0.763629i	$0.723416\pi$
$252$	−4.81039e14	−0.118325
$253$	1.02231e14	0.0245075
$254$	−4.92801e14	−0.115147
$255$	−1.60010e15	−0.364448
$256$	−3.92485e15	−0.871492
$257$	−5.04066e15	−1.09124	−0.545622	−	0.838031i	$-0.683707\pi$
$257$	−5.04066e15	−1.09124	−0.545622	+	0.838031i	$0.683707\pi$
$258$	−1.94719e15	−0.411035
$259$	4.80180e15	0.988452
$260$	−2.28097e15	−0.457923
$261$	−7.58738e14	−0.148569
$262$	−5.26859e15	−1.00632
$263$	−6.88032e15	−1.28202	−0.641012	−	0.767531i	$-0.721485\pi$
$263$	−6.88032e15	−1.28202	−0.641012	+	0.767531i	$0.721485\pi$
$264$	−9.05904e14	−0.164686
$265$	5.61440e15	0.995875
$266$	−2.75481e14	−0.0476828
$267$	1.80674e14	0.0305192
$268$	1.42466e15	0.234874
$269$	−7.02139e15	−1.12988	−0.564941	−	0.825131i	$-0.691101\pi$
$269$	−7.02139e15	−1.12988	−0.564941	+	0.825131i	$0.691101\pi$
$270$	−7.94074e14	−0.124737
$271$	−6.42148e15	−0.984769	−0.492385	−	0.870378i	$-0.663875\pi$
$271$	−6.42148e15	−0.984769	−0.492385	+	0.870378i	$0.663875\pi$
$272$	−5.60166e14	−0.0838724
$273$	1.18660e15	0.173479
$274$	8.68872e14	0.124044
$275$	−7.18198e14	−0.100134
$276$	2.35940e14	0.0321286
$277$	9.12510e15	1.21372	0.606861	−	0.794808i	$-0.292428\pi$
$277$	9.12510e15	1.21372	0.606861	+	0.794808i	$0.292428\pi$
$278$	3.41125e15	0.443223
$279$	−2.10040e14	−0.0266609
$280$	4.56512e15	0.566141
$281$	1.24217e16	1.50519	0.752594	−	0.658485i	$-0.228803\pi$
$281$	1.24217e16	1.50519	0.752594	+	0.658485i	$0.228803\pi$
$282$	−2.89954e15	−0.343329
$283$	−1.43393e16	−1.65926	−0.829632	−	0.558311i	$-0.811450\pi$
$283$	−1.43393e16	−1.65926	−0.829632	+	0.558311i	$0.811450\pi$
$284$	5.30114e15	0.599515
$285$	9.87216e14	0.109124
$286$	9.08149e14	0.0981246
$287$	7.72778e15	0.816249
$288$	−3.33181e15	−0.344056
$289$	−6.94187e15	−0.700875
$290$	2.92628e15	0.288887
$291$	−7.37597e15	−0.712057
$292$	7.08716e15	0.669089
$293$	4.83453e15	0.446390	0.223195	−	0.974774i	$-0.428351\pi$
$293$	4.83453e15	0.446390	0.223195	+	0.974774i	$0.428351\pi$
$294$	2.62496e15	0.237064
$295$	1.61569e16	1.42730
$296$	2.08701e16	1.80355
$297$	−6.86339e14	−0.0580259
$298$	−1.31633e15	−0.108882
$299$	−5.82000e14	−0.0471043
$300$	−1.65754e15	−0.131273
$301$	8.48114e15	0.657313
$302$	4.74979e14	0.0360271
$303$	2.83673e15	0.210592
$304$	3.45607e14	0.0251133
$305$	3.42050e14	0.0243299
$306$	1.47029e15	0.102380
$307$	−1.45721e16	−0.993397	−0.496699	−	0.867923i	$-0.665455\pi$
$307$	−1.45721e16	−0.993397	−0.496699	+	0.867923i	$0.665455\pi$
$308$	1.60355e15	0.107029
$309$	−4.38717e15	−0.286718
$310$	8.10075e14	0.0518411
$311$	−1.87327e16	−1.17397	−0.586985	−	0.809598i	$-0.699685\pi$
$311$	−1.87327e16	−1.17397	−0.586985	+	0.809598i	$0.699685\pi$
$312$	5.15731e15	0.316533
$313$	2.64002e16	1.58697	0.793485	−	0.608590i	$-0.208265\pi$
$313$	2.64002e16	1.58697	0.793485	+	0.608590i	$0.208265\pi$
$314$	1.47849e16	0.870512
$315$	3.45866e15	0.199475
$316$	−9.75636e15	−0.551216
$317$	−1.88635e16	−1.04409	−0.522043	−	0.852919i	$-0.674830\pi$
$317$	−1.88635e16	−1.04409	−0.522043	+	0.852919i	$0.674830\pi$
$318$	−5.15893e15	−0.279759
$319$	2.52926e15	0.134386
$320$	9.45035e15	0.492009
$321$	−1.30478e16	−0.665662
$322$	4.73378e14	0.0236671
$323$	−1.82791e15	−0.0895650
$324$	−1.58401e15	−0.0760702
$325$	4.08870e15	0.192461
$326$	−1.25989e16	−0.581322
$327$	1.73891e16	0.786534
$328$	3.35873e16	1.48934
$329$	1.26292e16	0.549039
$330$	2.64705e15	0.112829
$331$	−3.39689e16	−1.41971	−0.709855	−	0.704348i	$-0.751239\pi$
$331$	−3.39689e16	−1.41971	−0.709855	+	0.704348i	$0.751239\pi$
$332$	−1.68818e16	−0.691863
$333$	1.58118e16	0.635467
$334$	−2.32541e15	−0.0916530
$335$	−1.02433e16	−0.395957
$336$	1.21082e15	0.0459064
$337$	−3.27545e16	−1.21808	−0.609042	−	0.793138i	$-0.708446\pi$
$337$	−3.27545e16	−1.21808	−0.609042	+	0.793138i	$0.708446\pi$
$338$	1.02245e16	0.372977
$339$	1.27528e16	0.456360
$340$	1.23102e16	0.432169
$341$	7.00170e14	0.0241157
$342$	−9.07129e14	−0.0306549
$343$	−2.70702e16	−0.897595
$344$	3.68616e16	1.19935
$345$	−1.69640e15	−0.0541632
$346$	3.07860e15	0.0964624
$347$	3.01513e16	0.927180	0.463590	−	0.886050i	$-0.346561\pi$
$347$	3.01513e16	0.927180	0.463590	+	0.886050i	$0.346561\pi$
$348$	5.83730e15	0.176176
$349$	−1.67039e16	−0.494825	−0.247413	−	0.968910i	$-0.579580\pi$
$349$	−1.67039e16	−0.494825	−0.247413	+	0.968910i	$0.579580\pi$
$350$	−3.32560e15	−0.0967004
$351$	3.90733e15	0.111528
$352$	1.11066e16	0.311211
$353$	−6.76688e16	−1.86146	−0.930728	−	0.365711i	$-0.880826\pi$
$353$	−6.76688e16	−1.86146	−0.930728	+	0.365711i	$0.880826\pi$
$354$	−1.48462e16	−0.400954
$355$	−3.81151e16	−1.01068
$356$	−1.39001e15	−0.0361902
$357$	−6.40399e15	−0.163722
$358$	−3.11455e16	−0.781907
$359$	2.06740e16	0.509694	0.254847	−	0.966981i	$-0.417975\pi$
$359$	2.06740e16	0.509694	0.254847	+	0.966981i	$0.417975\pi$
$360$	1.50324e16	0.363967
$361$	−4.09252e16	−0.973182
$362$	8.18449e15	0.191155
$363$	2.28791e15	0.0524864
$364$	−9.12899e15	−0.205714
$365$	−5.09565e16	−1.12797
$366$	−3.14301e14	−0.00683469
$367$	−7.62996e16	−1.63002	−0.815010	−	0.579446i	$-0.803269\pi$
$367$	−7.62996e16	−1.63002	−0.815010	+	0.579446i	$0.803269\pi$
$368$	−5.93880e14	−0.0124649
$369$	2.54467e16	0.524759
$370$	−6.09823e16	−1.23564
$371$	2.24702e16	0.447380
$372$	1.61593e15	0.0316150
$373$	−9.18470e16	−1.76587	−0.882933	−	0.469499i	$-0.844434\pi$
$373$	−9.18470e16	−1.76587	−0.882933	+	0.469499i	$0.844434\pi$
$374$	−4.90122e15	−0.0926060
$375$	−2.39673e16	−0.445057
$376$	5.48904e16	1.00179
$377$	−1.43991e16	−0.258295
$378$	−3.17808e15	−0.0560361
$379$	9.64183e16	1.67111	0.835554	−	0.549408i	$-0.185147\pi$
$379$	9.64183e16	1.67111	0.835554	+	0.549408i	$0.185147\pi$
$380$	−7.59507e15	−0.129401
$381$	7.06799e15	0.118381
$382$	−2.33527e15	−0.0384525
$383$	6.12788e16	0.992015	0.496007	−	0.868318i	$-0.334799\pi$
$383$	6.12788e16	0.992015	0.496007	+	0.868318i	$0.334799\pi$
$384$	2.87569e16	0.457709
$385$	−1.15295e16	−0.180432
$386$	3.02298e16	0.465176
$387$	2.79274e16	0.422581
$388$	5.67464e16	0.844369
$389$	3.60725e16	0.527842	0.263921	−	0.964544i	$-0.414984\pi$
$389$	3.60725e16	0.527842	0.263921	+	0.964544i	$0.414984\pi$
$390$	−1.50696e16	−0.216862
$391$	3.14102e15	0.0444551
$392$	−4.96924e16	−0.691720
$393$	7.55646e16	1.03459
$394$	1.97029e16	0.265341
$395$	7.01480e16	0.929253
$396$	5.28030e15	0.0688081
$397$	−2.35211e16	−0.301523	−0.150761	−	0.988570i	$-0.548172\pi$
$397$	−2.35211e16	−0.301523	−0.150761	+	0.988570i	$0.548172\pi$
$398$	3.63483e16	0.458399
$399$	3.95108e15	0.0490221
$400$	4.17216e15	0.0509297
$401$	−1.66325e16	−0.199765	−0.0998824	−	0.994999i	$-0.531847\pi$
$401$	−1.66325e16	−0.199765	−0.0998824	+	0.994999i	$0.531847\pi$
$402$	9.41230e15	0.111231
$403$	−3.98607e15	−0.0463513
$404$	−2.18242e16	−0.249724
$405$	1.13890e16	0.128241
$406$	1.17117e16	0.129778
$407$	−5.27086e16	−0.574802
$408$	−2.78337e16	−0.298731
$409$	4.34909e16	0.459406	0.229703	−	0.973261i	$-0.426224\pi$
$409$	4.34909e16	0.459406	0.229703	+	0.973261i	$0.426224\pi$
$410$	−9.81420e16	−1.02037
$411$	−1.24618e16	−0.127529
$412$	3.37524e16	0.339995
$413$	6.46640e16	0.641191
$414$	1.55878e15	0.0152154
$415$	1.21379e17	1.16636
$416$	−6.32300e16	−0.598158
$417$	−4.89258e16	−0.455673
$418$	3.02392e15	0.0277284
$419$	4.23191e16	0.382072	0.191036	−	0.981583i	$-0.438815\pi$
$419$	4.23191e16	0.382072	0.191036	+	0.981583i	$0.438815\pi$
$420$	−2.66090e16	−0.236542
$421$	−9.41086e16	−0.823750	−0.411875	−	0.911240i	$-0.635126\pi$
$421$	−9.41086e16	−0.823750	−0.411875	+	0.911240i	$0.635126\pi$
$422$	−5.47388e16	−0.471807
$423$	4.15866e16	0.352972
$424$	9.76623e16	0.816299
$425$	−2.20665e16	−0.181637
$426$	3.50230e16	0.283917
$427$	1.36897e15	0.0109298
$428$	1.00382e17	0.789353
$429$	−1.30251e16	−0.100881
$430$	−1.07710e17	−0.821693
$431$	1.77811e17	1.33615	0.668077	−	0.744092i	$-0.267118\pi$
$431$	1.77811e17	1.33615	0.668077	+	0.744092i	$0.267118\pi$
$432$	3.98708e15	0.0295128
$433$	2.17293e17	1.58444	0.792218	−	0.610239i	$-0.208926\pi$
$433$	2.17293e17	1.58444	0.792218	+	0.610239i	$0.208926\pi$
$434$	3.24212e15	0.0232887
$435$	−4.19700e16	−0.297002
$436$	−1.33782e17	−0.932685
$437$	−1.93792e15	−0.0133109
$438$	4.68227e16	0.316865
$439$	1.38182e17	0.921368	0.460684	−	0.887564i	$-0.347604\pi$
$439$	1.38182e17	0.921368	0.460684	+	0.887564i	$0.347604\pi$
$440$	−5.01106e16	−0.329221
$441$	−3.76484e16	−0.243722
$442$	2.79027e16	0.177992
$443$	2.38504e15	0.0149924	0.00749620	−	0.999972i	$-0.497614\pi$
$443$	2.38504e15	0.0149924	0.00749620	+	0.999972i	$0.497614\pi$
$444$	−1.21647e17	−0.753548
$445$	9.99410e15	0.0610104
$446$	9.73337e16	0.585581
$447$	1.88793e16	0.111941
$448$	3.78226e16	0.221027
$449$	−1.62508e17	−0.935993	−0.467997	−	0.883730i	$-0.655024\pi$
$449$	−1.62508e17	−0.935993	−0.467997	+	0.883730i	$0.655024\pi$
$450$	−1.09508e16	−0.0621678
$451$	−8.48267e16	−0.474663
$452$	−9.81127e16	−0.541160
$453$	−6.81236e15	−0.0370390
$454$	−1.72125e16	−0.0922530
$455$	6.56372e16	0.346798
$456$	1.71726e16	0.0894468
$457$	−1.35196e17	−0.694237	−0.347119	−	0.937821i	$-0.612840\pi$
$457$	−1.35196e17	−0.694237	−0.347119	+	0.937821i	$0.612840\pi$
$458$	−1.13539e17	−0.574801
$459$	−2.10876e16	−0.105255
$460$	1.30511e16	0.0642276
$461$	2.61048e17	1.26667	0.633337	−	0.773876i	$-0.281685\pi$
$461$	2.61048e17	1.26667	0.633337	+	0.773876i	$0.281685\pi$
$462$	1.05941e16	0.0506866
$463$	−2.68515e17	−1.26675	−0.633376	−	0.773844i	$-0.718331\pi$
$463$	−2.68515e17	−1.26675	−0.633376	+	0.773844i	$0.718331\pi$
$464$	−1.46930e16	−0.0683506
$465$	−1.16185e16	−0.0532973
$466$	−1.23026e17	−0.556531
$467$	2.63618e17	1.17602	0.588011	−	0.808853i	$-0.299911\pi$
$467$	2.63618e17	1.17602	0.588011	+	0.808853i	$0.299911\pi$
$468$	−3.00607e16	−0.132252
$469$	−4.09961e16	−0.177877
$470$	−1.60390e17	−0.686341
$471$	−2.12051e17	−0.894963
$472$	2.81049e17	1.16993
$473$	−9.30962e16	−0.382239
$474$	−6.44572e16	−0.261043
$475$	1.36144e16	0.0543864
$476$	4.92686e16	0.194144
$477$	7.39918e16	0.287617
$478$	4.36922e16	0.167541
$479$	1.28995e16	0.0487967	0.0243984	−	0.999702i	$-0.492233\pi$
$479$	1.28995e16	0.0487967	0.0243984	+	0.999702i	$0.492233\pi$
$480$	−1.84301e17	−0.687796
$481$	3.00070e17	1.10479
$482$	−1.96213e17	−0.712724
$483$	−6.78941e15	−0.0243319
$484$	−1.76019e16	−0.0622393
$485$	−4.08006e17	−1.42346
$486$	−1.04651e16	−0.0360251
$487$	−1.21187e17	−0.411640	−0.205820	−	0.978590i	$-0.565986\pi$
$487$	−1.21187e17	−0.411640	−0.205820	+	0.978590i	$0.565986\pi$
$488$	5.94995e15	0.0199427
$489$	1.80699e17	0.597650
$490$	1.45201e17	0.473909
$491$	1.87480e16	0.0603844	0.0301922	−	0.999544i	$-0.490388\pi$
$491$	1.87480e16	0.0603844	0.0301922	+	0.999544i	$0.490388\pi$
$492$	−1.95772e17	−0.622269
$493$	7.77108e16	0.243768
$494$	−1.72152e16	−0.0532949
$495$	−3.79652e16	−0.115998
$496$	−4.06743e15	−0.0122656
$497$	−1.52546e17	−0.454030
$498$	−1.11533e17	−0.327651
$499$	−3.02024e16	−0.0875766	−0.0437883	−	0.999041i	$-0.513943\pi$
$499$	−3.02024e16	−0.0875766	−0.0437883	+	0.999041i	$0.513943\pi$
$500$	1.84391e17	0.527757
$501$	3.33521e16	0.0942275
$502$	2.60024e17	0.725169
$503$	3.61031e17	0.993921	0.496961	−	0.867773i	$-0.334449\pi$
$503$	3.61031e17	0.993921	0.496961	+	0.867773i	$0.334449\pi$
$504$	6.01634e16	0.163506
$505$	1.56915e17	0.420990
$506$	−5.19620e15	−0.0137628
$507$	−1.46644e17	−0.383454
$508$	−5.43770e16	−0.140379
$509$	−3.96957e17	−1.01176	−0.505881	−	0.862603i	$-0.668832\pi$
$509$	−3.96957e17	−1.01176	−0.505881	+	0.862603i	$0.668832\pi$
$510$	8.13299e16	0.204665
$511$	−2.03941e17	−0.506720
$512$	−1.23658e17	−0.303366
$513$	1.30105e16	0.0315159
$514$	2.56207e17	0.612817
$515$	−2.42679e17	−0.573172
$516$	−2.14858e17	−0.501104
$517$	−1.38629e17	−0.319275
$518$	−2.44066e17	−0.555091
$519$	−4.41547e16	−0.0991719
$520$	2.85280e17	0.632774
$521$	−4.50995e17	−0.987931	−0.493965	−	0.869482i	$-0.664453\pi$
$521$	−4.50995e17	−0.987931	−0.493965	+	0.869482i	$0.664453\pi$
$522$	3.85652e16	0.0834329
$523$	6.59136e17	1.40836	0.704180	−	0.710021i	$-0.251315\pi$
$523$	6.59136e17	1.40836	0.704180	+	0.710021i	$0.251315\pi$
$524$	−5.81351e17	−1.22683
$525$	4.76974e16	0.0994166
$526$	3.49713e17	0.719954
$527$	2.15125e16	0.0437444
$528$	−1.32910e16	−0.0266954
$529$	−5.00706e17	−0.993393
$530$	−2.85369e17	−0.559260
$531$	2.12931e17	0.412216
$532$	−3.03974e16	−0.0581313
$533$	4.82918e17	0.912319
$534$	−9.18334e15	−0.0171389
$535$	−7.21744e17	−1.33071
$536$	−1.78182e17	−0.324558
$537$	4.46703e17	0.803870
$538$	3.56884e17	0.634515
$539$	1.25501e17	0.220455
$540$	−8.76202e16	−0.152070
$541$	−4.61819e17	−0.791934	−0.395967	−	0.918265i	$-0.629591\pi$
$541$	−4.61819e17	−0.791934	−0.395967	+	0.918265i	$0.629591\pi$
$542$	3.26391e17	0.553023
$543$	−1.17386e17	−0.196524
$544$	3.41248e17	0.564517
$545$	9.61889e17	1.57234
$546$	−6.03125e16	−0.0974215
$547$	1.14325e18	1.82483	0.912416	−	0.409264i	$-0.134215\pi$
$547$	1.14325e18	1.82483	0.912416	+	0.409264i	$0.134215\pi$
$548$	9.58736e16	0.151226
$549$	4.50785e15	0.00702667
$550$	3.65046e16	0.0562329
$551$	−4.79454e16	−0.0729897
$552$	−2.95089e16	−0.0443965
$553$	2.80749e17	0.417451
$554$	−4.63811e17	−0.681598
$555$	8.74636e17	1.27035
$556$	3.76407e17	0.540345
$557$	−8.21907e17	−1.16618	−0.583088	−	0.812409i	$-0.698156\pi$
$557$	−8.21907e17	−1.16618	−0.583088	+	0.812409i	$0.698156\pi$
$558$	1.06759e16	0.0149721
$559$	5.29997e17	0.734677
$560$	6.69770e16	0.0917706
$561$	7.02956e16	0.0952072
$562$	−6.31372e17	−0.845277
$563$	1.16556e18	1.54252	0.771260	−	0.636521i	$-0.219627\pi$
$563$	1.16556e18	1.54252	0.771260	+	0.636521i	$0.219627\pi$
$564$	−3.19943e17	−0.418561
$565$	7.05428e17	0.912300
$566$	7.28838e17	0.931803
$567$	4.55815e16	0.0576101
$568$	−6.63011e17	−0.828432
$569$	1.01972e18	1.25966	0.629828	−	0.776735i	$-0.283126\pi$
$569$	1.01972e18	1.25966	0.629828	+	0.776735i	$0.283126\pi$
$570$	−5.01783e16	−0.0612815
$571$	−4.09487e17	−0.494431	−0.247216	−	0.968961i	$-0.579516\pi$
$571$	−4.09487e17	−0.494431	−0.247216	+	0.968961i	$0.579516\pi$
$572$	1.00208e17	0.119626
$573$	3.34935e16	0.0395326
$574$	−3.92788e17	−0.458386
$575$	−2.33945e16	−0.0269944
$576$	1.24546e17	0.142096
$577$	−1.14413e18	−1.29072	−0.645360	−	0.763879i	$-0.723293\pi$
$577$	−1.14413e18	−1.29072	−0.645360	+	0.763879i	$0.723293\pi$
$578$	3.52842e17	0.393595
$579$	−4.33569e17	−0.478242
$580$	3.22893e17	0.352190
$581$	4.85790e17	0.523967
$582$	3.74906e17	0.399874
$583$	−2.46652e17	−0.260159
$584$	−8.86388e17	−0.924571
$585$	2.16136e17	0.222953
$586$	−2.45730e17	−0.250682
$587$	8.95116e17	0.903091	0.451546	−	0.892248i	$-0.350873\pi$
$587$	8.95116e17	0.903091	0.451546	+	0.892248i	$0.350873\pi$
$588$	2.89645e17	0.289010
$589$	−1.32726e16	−0.0130981
$590$	−8.21225e17	−0.801538
$591$	−2.82588e17	−0.272795
$592$	3.06195e17	0.292353
$593$	1.07087e18	1.01130	0.505652	−	0.862737i	$-0.331252\pi$
$593$	1.07087e18	1.01130	0.505652	+	0.862737i	$0.331252\pi$
$594$	3.48853e16	0.0325860
$595$	−3.54240e17	−0.327293
$596$	−1.45247e17	−0.132741
$597$	−5.21324e17	−0.471275
$598$	2.95820e16	0.0264527
$599$	−1.90802e17	−0.168775	−0.0843874	−	0.996433i	$-0.526893\pi$
$599$	−1.90802e17	−0.168775	−0.0843874	+	0.996433i	$0.526893\pi$
$600$	2.07307e17	0.181398
$601$	−2.23338e18	−1.93321	−0.966604	−	0.256274i	$-0.917505\pi$
$601$	−2.23338e18	−1.93321	−0.966604	+	0.256274i	$0.917505\pi$
$602$	−4.31080e17	−0.369131
$603$	−1.34996e17	−0.114356
$604$	5.24104e16	0.0439215
$605$	1.26557e17	0.104924
$606$	−1.44186e17	−0.118263
$607$	−2.02012e18	−1.63927	−0.819637	−	0.572883i	$-0.805825\pi$
$607$	−2.02012e18	−1.63927	−0.819637	+	0.572883i	$0.805825\pi$
$608$	−2.10541e17	−0.169029
$609$	−1.67974e17	−0.133423
$610$	−1.73857e16	−0.0136631
$611$	7.89215e17	0.613659
$612$	1.62236e17	0.124814
$613$	−6.43787e17	−0.490060	−0.245030	−	0.969516i	$-0.578798\pi$
$613$	−6.43787e17	−0.490060	−0.245030	+	0.969516i	$0.578798\pi$
$614$	7.40672e17	0.557868
$615$	1.40760e18	1.04904
$616$	−2.00555e17	−0.147897
$617$	−2.34190e18	−1.70889	−0.854446	−	0.519540i	$-0.826103\pi$
$617$	−2.34190e18	−1.70889	−0.854446	+	0.519540i	$0.826103\pi$
$618$	2.22992e17	0.161014
$619$	−9.74689e17	−0.696429	−0.348214	−	0.937415i	$-0.613212\pi$
$619$	−9.74689e17	−0.696429	−0.348214	+	0.937415i	$0.613212\pi$
$620$	8.93859e16	0.0632009
$621$	−2.23567e16	−0.0156428
$622$	9.52145e17	0.659273
$623$	3.99989e16	0.0274079
$624$	7.56654e16	0.0513095
$625$	−1.82064e18	−1.22181
$626$	−1.34187e18	−0.891204
$627$	−4.33704e16	−0.0285072
$628$	1.63140e18	1.06126
$629$	−1.61946e18	−1.04266
$630$	−1.75797e17	−0.112021
$631$	−3.15158e18	−1.98764	−0.993819	−	0.111010i	$-0.964592\pi$
$631$	−3.15158e18	−1.98764	−0.993819	+	0.111010i	$0.964592\pi$
$632$	1.22022e18	0.761690
$633$	7.85089e17	0.485060
$634$	9.58794e17	0.586334
$635$	3.90969e17	0.236654
$636$	−5.69250e17	−0.341061
$637$	−7.14477e17	−0.423723
$638$	−1.28557e17	−0.0754679
$639$	−5.02316e17	−0.291892
$640$	1.59070e18	0.914997
$641$	−2.55544e18	−1.45508	−0.727542	−	0.686063i	$-0.759338\pi$
$641$	−2.55544e18	−1.45508	−0.727542	+	0.686063i	$0.759338\pi$
$642$	6.63193e17	0.373820
$643$	−8.03329e17	−0.448252	−0.224126	−	0.974560i	$-0.571953\pi$
$643$	−8.03329e17	−0.448252	−0.224126	+	0.974560i	$0.571953\pi$
$644$	5.22338e16	0.0288532
$645$	1.54482e18	0.844773
$646$	9.29091e16	0.0502976
$647$	1.30317e18	0.698431	0.349215	−	0.937042i	$-0.386448\pi$
$647$	1.30317e18	0.698431	0.349215	+	0.937042i	$0.386448\pi$
$648$	1.98111e17	0.105117
$649$	−7.09807e17	−0.372863
$650$	−2.07821e17	−0.108082
$651$	−4.65000e16	−0.0239429
$652$	−1.39019e18	−0.708704
$653$	2.59971e17	0.131217	0.0656084	−	0.997845i	$-0.479101\pi$
$653$	2.59971e17	0.131217	0.0656084	+	0.997845i	$0.479101\pi$
$654$	−8.83856e17	−0.441699
$655$	4.17990e18	2.06822
$656$	4.92775e17	0.241420
$657$	−6.71553e17	−0.325766
$658$	−6.41919e17	−0.308327
$659$	2.40811e18	1.14530	0.572652	−	0.819799i	$-0.305915\pi$
$659$	2.40811e18	1.14530	0.572652	+	0.819799i	$0.305915\pi$
$660$	2.92082e17	0.137553
$661$	−1.24778e18	−0.581874	−0.290937	−	0.956742i	$-0.593967\pi$
$661$	−1.24778e18	−0.581874	−0.290937	+	0.956742i	$0.593967\pi$
$662$	1.72657e18	0.797275
$663$	−4.00193e17	−0.182992
$664$	2.11139e18	0.956041
$665$	2.18556e17	0.0979992
$666$	−8.03682e17	−0.356863
$667$	8.23878e16	0.0362281
$668$	−2.56592e17	−0.111737
$669$	−1.39601e18	−0.602029
$670$	5.20646e17	0.222360
$671$	−1.50269e16	−0.00635586
$672$	−7.37618e17	−0.308981
$673$	6.64659e17	0.275741	0.137870	−	0.990450i	$-0.455974\pi$
$673$	6.64659e17	0.275741	0.137870	+	0.990450i	$0.455974\pi$
$674$	1.66485e18	0.684047
$675$	1.57062e17	0.0639141
$676$	1.12820e18	0.454706
$677$	2.77653e18	1.10835	0.554174	−	0.832401i	$-0.313034\pi$
$677$	2.77653e18	1.10835	0.554174	+	0.832401i	$0.313034\pi$
$678$	−6.48201e17	−0.256281
$679$	−1.63294e18	−0.639464
$680$	−1.53964e18	−0.597187
$681$	2.46869e17	0.0948443
$682$	−3.55883e16	−0.0135428
$683$	1.08769e18	0.409986	0.204993	−	0.978763i	$-0.434283\pi$
$683$	1.08769e18	0.409986	0.204993	+	0.978763i	$0.434283\pi$
$684$	−1.00095e17	−0.0373721
$685$	−6.89329e17	−0.254940
$686$	1.37593e18	0.504068
$687$	1.62842e18	0.590947
$688$	5.40815e17	0.194412
$689$	1.40419e18	0.500035
$690$	8.62248e16	0.0304168
$691$	3.26378e18	1.14055	0.570273	−	0.821455i	$-0.306837\pi$
$691$	3.26378e18	1.14055	0.570273	+	0.821455i	$0.306837\pi$
$692$	3.39701e17	0.117600
$693$	−1.51946e17	−0.0521103
$694$	−1.53253e18	−0.520682
$695$	−2.70635e18	−0.910927
$696$	−7.30068e17	−0.243446
$697$	−2.60628e18	−0.861010
$698$	8.49025e17	0.277882
$699$	1.76450e18	0.572163
$700$	−3.66956e17	−0.117890
$701$	−1.91850e18	−0.610654	−0.305327	−	0.952248i	$-0.598766\pi$
$701$	−1.91850e18	−0.610654	−0.305327	+	0.952248i	$0.598766\pi$
$702$	−1.98602e17	−0.0626314
$703$	9.99161e17	0.312195
$704$	−4.15173e17	−0.128531
$705$	2.30038e18	0.705620
$706$	3.43948e18	1.04535
$707$	6.28015e17	0.189123
$708$	−1.63817e18	−0.488813
$709$	2.80441e17	0.0829165	0.0414583	−	0.999140i	$-0.486800\pi$
$709$	2.80441e17	0.0829165	0.0414583	+	0.999140i	$0.486800\pi$
$710$	1.93732e18	0.567572
$711$	9.24476e17	0.268376
$712$	1.73847e17	0.0500090
$713$	2.28073e16	0.00650117
$714$	3.25502e17	0.0919424
$715$	−7.20490e17	−0.201669
$716$	−3.43667e18	−0.953243
$717$	−6.26653e17	−0.172247
$718$	−1.05082e18	−0.286232
$719$	−4.26107e18	−1.15022	−0.575110	−	0.818076i	$-0.695041\pi$
$719$	−4.26107e18	−1.15022	−0.575110	+	0.818076i	$0.695041\pi$
$720$	2.20548e17	0.0589985
$721$	−9.71260e17	−0.257488
$722$	2.08015e18	0.546516
$723$	2.81417e18	0.732744
$724$	9.03099e17	0.233042
$725$	−5.78796e17	−0.148023
$726$	−1.16290e17	−0.0294751
$727$	4.58389e18	1.15149	0.575745	−	0.817629i	$-0.304712\pi$
$727$	4.58389e18	1.15149	0.575745	+	0.817629i	$0.304712\pi$
$728$	1.14176e18	0.284263
$729$	1.50095e17	0.0370370
$730$	2.59002e18	0.633439
$731$	−2.86036e18	−0.693358
$732$	−3.46808e16	−0.00833234
$733$	−2.51601e18	−0.599151	−0.299575	−	0.954073i	$-0.596845\pi$
$733$	−2.51601e18	−0.599151	−0.299575	+	0.954073i	$0.596845\pi$
$734$	3.87816e18	0.915381
$735$	−2.08254e18	−0.487221
$736$	3.61786e17	0.0838969
$737$	4.50008e17	0.103438
$738$	−1.29341e18	−0.294692
$739$	8.62679e18	1.94832	0.974160	−	0.225859i	$-0.0725190\pi$
$739$	8.62679e18	1.94832	0.974160	+	0.225859i	$0.0725190\pi$
$740$	−6.72895e18	−1.50640
$741$	2.46908e17	0.0547919
$742$	−1.14212e18	−0.251238
$743$	−7.52533e18	−1.64096	−0.820481	−	0.571674i	$-0.806294\pi$
$743$	−7.52533e18	−1.64096	−0.820481	+	0.571674i	$0.806294\pi$
$744$	−2.02103e17	−0.0436867
$745$	1.04432e18	0.223778
$746$	4.66841e18	0.991668
$747$	1.59965e18	0.336854
$748$	−5.40814e17	−0.112898
$749$	−2.88860e18	−0.597799
$750$	1.21821e18	0.249934
$751$	5.74109e17	0.116771	0.0583854	−	0.998294i	$-0.481405\pi$
$751$	5.74109e17	0.116771	0.0583854	+	0.998294i	$0.481405\pi$
$752$	8.05324e17	0.162388
$753$	−3.72938e18	−0.745538
$754$	7.31877e17	0.145052
$755$	−3.76829e17	−0.0740440
$756$	−3.50678e17	−0.0683151
$757$	6.00586e18	1.15998	0.579992	−	0.814622i	$-0.303056\pi$
$757$	6.00586e18	1.15998	0.579992	+	0.814622i	$0.303056\pi$
$758$	−4.90076e18	−0.938455
$759$	7.45263e16	0.0141494
$760$	9.49912e17	0.178811
$761$	−9.37486e18	−1.74970	−0.874852	−	0.484390i	$-0.839041\pi$
$761$	−9.37486e18	−1.74970	−0.874852	+	0.484390i	$0.839041\pi$
$762$	−3.59252e17	−0.0664802
$763$	3.84972e18	0.706349
$764$	−2.57679e17	−0.0468784
$765$	−1.16647e18	−0.210414
$766$	−3.11468e18	−0.557092
$767$	4.04093e18	0.716657
$768$	−2.86122e18	−0.503156
$769$	−5.81923e18	−1.01472	−0.507358	−	0.861735i	$-0.669378\pi$
$769$	−5.81923e18	−1.01472	−0.507358	+	0.861735i	$0.669378\pi$
$770$	5.86021e17	0.101327
$771$	−3.67464e18	−0.630030
$772$	3.33563e18	0.567108
$773$	5.96862e18	1.00625	0.503127	−	0.864213i	$-0.332183\pi$
$773$	5.96862e18	1.00625	0.503127	+	0.864213i	$0.332183\pi$
$774$	−1.41950e18	−0.237311
$775$	−1.60227e17	−0.0265628
$776$	−7.09725e18	−1.16678
$777$	3.50051e18	0.570683
$778$	−1.83350e18	−0.296423
$779$	1.60800e18	0.257806
$780$	−1.66283e18	−0.264382
$781$	1.67447e18	0.264026
$782$	−1.59652e17	−0.0249649
$783$	−5.53120e17	−0.0857765
$784$	−7.29061e17	−0.112127
$785$	−1.17297e19	−1.78910
$786$	−3.84080e18	−0.580999
$787$	−6.41219e18	−0.961990	−0.480995	−	0.876723i	$-0.659724\pi$
$787$	−6.41219e18	−0.961990	−0.480995	+	0.876723i	$0.659724\pi$
$788$	2.17407e18	0.323485
$789$	−5.01575e18	−0.740177
$790$	−3.56549e18	−0.521846
$791$	2.82330e18	0.409835
$792$	−6.60404e17	−0.0950815
$793$	8.55484e16	0.0122162
$794$	1.19553e18	0.169328
$795$	4.09289e18	0.574969
$796$	4.01077e18	0.558847
$797$	5.53258e18	0.764625	0.382313	−	0.924033i	$-0.375128\pi$
$797$	5.53258e18	0.764625	0.382313	+	0.924033i	$0.375128\pi$
$798$	−2.00826e17	−0.0275297
$799$	−4.25934e18	−0.579146
$800$	−2.54164e18	−0.342791
$801$	1.31712e17	0.0176203
$802$	8.45397e17	0.112183
$803$	2.23862e18	0.294666
$804$	1.03858e18	0.135605
$805$	−3.75560e17	−0.0486414
$806$	2.02604e17	0.0260298
$807$	−5.11859e18	−0.652338
$808$	2.72954e18	0.345077
$809$	3.66138e18	0.459176	0.229588	−	0.973288i	$-0.426262\pi$
$809$	3.66138e18	0.459176	0.229588	+	0.973288i	$0.426262\pi$
$810$	−5.78880e17	−0.0720171
$811$	1.41941e18	0.175176	0.0875878	−	0.996157i	$-0.472084\pi$
$811$	1.41941e18	0.175176	0.0875878	+	0.996157i	$0.472084\pi$
$812$	1.29230e18	0.158215
$813$	−4.68126e18	−0.568557
$814$	2.67908e18	0.322795
$815$	9.99544e18	1.19475
$816$	−4.08361e17	−0.0484238
$817$	1.76476e18	0.207607
$818$	−2.21056e18	−0.257992
$819$	8.65029e17	0.100158
$820$	−1.08292e19	−1.24397
$821$	3.72995e18	0.425082	0.212541	−	0.977152i	$-0.431826\pi$
$821$	3.72995e18	0.425082	0.212541	+	0.977152i	$0.431826\pi$
$822$	6.33408e17	0.0716171
$823$	1.37777e19	1.54553	0.772763	−	0.634694i	$-0.218874\pi$
$823$	1.37777e19	1.54553	0.772763	+	0.634694i	$0.218874\pi$
$824$	−4.22140e18	−0.469817
$825$	−5.23567e17	−0.0578124
$826$	−3.28675e18	−0.360077
$827$	−9.68527e17	−0.105275	−0.0526376	−	0.998614i	$-0.516763\pi$
$827$	−9.68527e17	−0.105275	−0.0526376	+	0.998614i	$0.516763\pi$
$828$	1.72000e17	0.0185495
$829$	1.27866e19	1.36821	0.684103	−	0.729385i	$-0.260194\pi$
$829$	1.27866e19	1.36821	0.684103	+	0.729385i	$0.260194\pi$
$830$	−6.16948e18	−0.655000
$831$	6.65220e18	0.700743
$832$	2.36358e18	0.247041
$833$	3.85599e18	0.399892
$834$	2.48680e18	0.255895
$835$	1.84489e18	0.188368
$836$	3.33667e17	0.0338044
$837$	−1.53119e17	−0.0153927
$838$	−2.15100e18	−0.214563
$839$	1.70005e19	1.68271	0.841355	−	0.540484i	$-0.181759\pi$
$839$	1.70005e19	1.68271	0.841355	+	0.540484i	$0.181759\pi$
$840$	3.32797e18	0.326862
$841$	−8.22230e18	−0.801345
$842$	4.78336e18	0.462599
$843$	9.05543e18	0.869020
$844$	−6.04003e18	−0.575192
$845$	−8.11170e18	−0.766555
$846$	−2.11376e18	−0.198221
$847$	5.06513e17	0.0471355
$848$	1.43285e18	0.132321
$849$	−1.04533e19	−0.957976
$850$	1.12160e18	0.102003
$851$	−1.71693e18	−0.154956
$852$	3.86453e18	0.346130
$853$	−1.61107e19	−1.43201	−0.716005	−	0.698095i	$-0.754031\pi$
$853$	−1.61107e19	−1.43201	−0.716005	+	0.698095i	$0.754031\pi$
$854$	−6.95820e16	−0.00613791
$855$	7.19681e17	0.0630028
$856$	−1.25547e19	−1.09076
$857$	1.09844e19	0.947113	0.473556	−	0.880763i	$-0.342970\pi$
$857$	1.09844e19	0.947113	0.473556	+	0.880763i	$0.342970\pi$
$858$	6.62041e17	0.0566523
$859$	9.69824e18	0.823640	0.411820	−	0.911265i	$-0.364893\pi$
$859$	9.69824e18	0.823640	0.411820	+	0.911265i	$0.364893\pi$
$860$	−1.18850e19	−1.00175
$861$	5.63355e18	0.471262
$862$	−9.03780e18	−0.750353
$863$	7.07808e18	0.583238	0.291619	−	0.956535i	$-0.405806\pi$
$863$	7.07808e18	0.583238	0.291619	+	0.956535i	$0.405806\pi$
$864$	−2.42889e18	−0.198641
$865$	−2.44244e18	−0.198253
$866$	−1.10446e19	−0.889781
$867$	−5.06062e18	−0.404650
$868$	3.57744e17	0.0283919
$869$	−3.08174e18	−0.242755
$870$	2.13326e18	0.166789
$871$	−2.56190e18	−0.198813
$872$	1.67320e19	1.28882
$873$	−5.37708e18	−0.411106
$874$	9.85008e16	0.00747508
$875$	−5.30603e18	−0.399685
$876$	5.16654e18	0.386299
$877$	−1.28865e19	−0.956398	−0.478199	−	0.878252i	$-0.658710\pi$
$877$	−1.28865e19	−0.956398	−0.478199	+	0.878252i	$0.658710\pi$
$878$	−7.02354e18	−0.517418
$879$	3.52437e18	0.257723
$880$	−7.35196e17	−0.0533662
$881$	1.82623e19	1.31586	0.657932	−	0.753077i	$-0.271431\pi$
$881$	1.82623e19	1.31586	0.657932	+	0.753077i	$0.271431\pi$
$882$	1.91359e18	0.136869
$883$	1.25385e19	0.890228	0.445114	−	0.895474i	$-0.353163\pi$
$883$	1.25385e19	0.890228	0.445114	+	0.895474i	$0.353163\pi$
$884$	3.07885e18	0.216995
$885$	1.17784e19	0.824053
$886$	−1.21227e17	−0.00841937
$887$	6.75580e18	0.465772	0.232886	−	0.972504i	$-0.425183\pi$
$887$	6.75580e18	0.465772	0.232886	+	0.972504i	$0.425183\pi$
$888$	1.52143e19	1.04128
$889$	1.56476e18	0.106313
$890$	−5.07981e17	−0.0342620
$891$	−5.00341e17	−0.0335013
$892$	1.07401e19	0.713896
$893$	2.62790e18	0.173410
$894$	−9.59601e17	−0.0628632
$895$	2.47096e19	1.60700
$896$	6.36639e18	0.411047
$897$	−4.24278e17	−0.0271957
$898$	8.25996e18	0.525632
$899$	5.64266e17	0.0356489
$900$	−1.20834e18	−0.0757904
$901$	−7.57832e18	−0.471913
$902$	4.31158e18	0.266559
$903$	6.18275e18	0.379500
$904$	1.22709e19	0.747794
$905$	−6.49326e18	−0.392868
$906$	3.46259e17	0.0208002
$907$	−1.12737e19	−0.672388	−0.336194	−	0.941793i	$-0.609140\pi$
$907$	−1.12737e19	−0.672388	−0.336194	+	0.941793i	$0.609140\pi$
$908$	−1.89927e18	−0.112468
$909$	2.06798e18	0.121585
$910$	−3.33622e18	−0.194753
$911$	−1.78217e19	−1.03295	−0.516474	−	0.856303i	$-0.672756\pi$
$911$	−1.78217e19	−1.03295	−0.516474	+	0.856303i	$0.672756\pi$
$912$	2.51948e17	0.0144992
$913$	−5.33245e18	−0.304696
$914$	6.87174e18	0.389867
$915$	2.49354e17	0.0140469
$916$	−1.25281e19	−0.700755
$917$	1.67290e19	0.929113
$918$	1.07184e18	0.0591090
$919$	−1.37092e19	−0.750693	−0.375346	−	0.926885i	$-0.622476\pi$
$919$	−1.37092e19	−0.750693	−0.375346	+	0.926885i	$0.622476\pi$
$920$	−1.63230e18	−0.0887521
$921$	−1.06231e19	−0.573538
$922$	−1.32686e19	−0.711334
$923$	−9.53278e18	−0.507468
$924$	1.16899e18	0.0617933
$925$	1.20618e19	0.633129
$926$	1.36481e19	0.711378
$927$	−3.19825e18	−0.165537
$928$	8.95082e18	0.460045
$929$	−2.64762e19	−1.35131	−0.675653	−	0.737220i	$-0.736138\pi$
$929$	−2.64762e19	−1.35131	−0.675653	+	0.737220i	$0.736138\pi$
$930$	5.90545e17	0.0299305
$931$	−2.37904e18	−0.119737
$932$	−1.35750e19	−0.678481
$933$	−1.36561e19	−0.677791
$934$	−1.33992e19	−0.660426
$935$	3.88844e18	0.190327
$936$	3.75968e18	0.182750
$937$	−1.29501e19	−0.625124	−0.312562	−	0.949897i	$-0.601187\pi$
$937$	−1.29501e19	−0.625124	−0.312562	+	0.949897i	$0.601187\pi$
$938$	2.08376e18	0.0998914
$939$	1.92457e19	0.916237
$940$	−1.76978e19	−0.836736
$941$	−2.82844e19	−1.32805	−0.664024	−	0.747711i	$-0.731153\pi$
$941$	−2.82844e19	−1.32805	−0.664024	+	0.747711i	$0.731153\pi$
$942$	1.07782e19	0.502590
$943$	−2.76314e18	−0.127961
$944$	4.12341e18	0.189644
$945$	2.52136e18	0.115167
$946$	4.73190e18	0.214656
$947$	1.92431e19	0.866963	0.433482	−	0.901162i	$-0.357285\pi$
$947$	1.92431e19	0.866963	0.433482	+	0.901162i	$0.357285\pi$
$948$	−7.11238e18	−0.318245
$949$	−1.27445e19	−0.566359
$950$	−6.91994e17	−0.0305421
$951$	−1.37515e19	−0.602804
$952$	−6.16200e18	−0.268276
$953$	1.39412e18	0.0602833	0.0301416	−	0.999546i	$-0.490404\pi$
$953$	1.39412e18	0.0602833	0.0301416	+	0.999546i	$0.490404\pi$
$954$	−3.76086e18	−0.161519
$955$	1.85271e18	0.0790288
$956$	4.82111e18	0.204254
$957$	1.84383e18	0.0775877
$958$	−6.55655e17	−0.0274031
$959$	−2.75887e18	−0.114527
$960$	6.88931e18	0.284062
$961$	−2.42613e19	−0.993603
$962$	−1.52520e19	−0.620424
$963$	−9.51182e18	−0.384320
$964$	−2.16506e19	−0.868900
$965$	−2.39831e19	−0.956044
$966$	3.45093e17	0.0136642
$967$	−2.12119e19	−0.834272	−0.417136	−	0.908844i	$-0.636966\pi$
$967$	−2.12119e19	−0.834272	−0.417136	+	0.908844i	$0.636966\pi$
$968$	2.20146e18	0.0860045
$969$	−1.33255e18	−0.0517104
$970$	2.07381e19	0.799380
$971$	1.34015e19	0.513132	0.256566	−	0.966527i	$-0.417409\pi$
$971$	1.34015e19	0.513132	0.256566	+	0.966527i	$0.417409\pi$
$972$	−1.15474e18	−0.0439192
$973$	−1.08315e19	−0.409218
$974$	6.15970e18	0.231167
$975$	2.98066e18	0.111118
$976$	8.72945e16	0.00323268
$977$	−2.97354e19	−1.09385	−0.546926	−	0.837181i	$-0.684202\pi$
$977$	−2.97354e19	−1.09385	−0.546926	+	0.837181i	$0.684202\pi$
$978$	−9.18456e18	−0.335626
$979$	−4.39061e17	−0.0159381
$980$	1.60219e19	0.577755
$981$	1.26767e19	0.454105
$982$	−9.52924e17	−0.0339104
$983$	2.23524e19	0.790182	0.395091	−	0.918642i	$-0.370713\pi$
$983$	2.23524e19	0.790182	0.395091	+	0.918642i	$0.370713\pi$
$984$	2.44852e19	0.859874
$985$	−1.56315e19	−0.545338
$986$	−3.94989e18	−0.136894
$987$	9.20670e18	0.316988
$988$	−1.89957e18	−0.0649732
$989$	−3.03251e18	−0.103045
$990$	1.92970e18	0.0651419
$991$	4.17080e19	1.39875	0.699377	−	0.714753i	$-0.253461\pi$
$991$	4.17080e19	1.39875	0.699377	+	0.714753i	$0.253461\pi$
$992$	2.47784e18	0.0825557
$993$	−2.47633e19	−0.819669
$994$	7.75362e18	0.254972
$995$	−2.88373e19	−0.942117
$996$	−1.23068e19	−0.399447
$997$	3.97661e19	1.28231	0.641157	−	0.767410i	$-0.278455\pi$
$997$	3.97661e19	1.28231	0.641157	+	0.767410i	$0.278455\pi$
$998$	1.53513e18	0.0491810
$999$	1.15268e19	0.366887

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.14.a.c.1.2	✓	4
3.2	odd	2		99.14.a.b.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.14.a.c.1.2	✓	4	1.1	even	1	trivial
99.14.a.b.1.3		4	3.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 14 \)
Character orbit:	\([\chi]\)	\(=\)	33.a (trivial)

\(f(q)\)	\(=\)	\(q-50.8281 q^{2} +729.000 q^{3} -5608.51 q^{4} +40325.0 q^{5} -37053.7 q^{6} +161391. q^{7} +701453. q^{8} +531441. q^{9} -2.04964e6 q^{10} -1.77156e6 q^{11} -4.08860e6 q^{12} +1.00855e7 q^{13} -8.20318e6 q^{14} +2.93969e7 q^{15} +1.02914e7 q^{16} -5.44308e7 q^{17} -2.70121e7 q^{18} +3.35823e7 q^{19} -2.26163e8 q^{20} +1.17654e8 q^{21} +9.00451e7 q^{22} -5.77067e7 q^{23} +5.11359e8 q^{24} +4.05404e8 q^{25} -5.12626e8 q^{26} +3.87420e8 q^{27} -9.05161e8 q^{28} -1.42770e9 q^{29} -1.49419e9 q^{30} -3.95227e8 q^{31} -6.26940e9 q^{32} -1.29147e9 q^{33} +2.76661e9 q^{34} +6.50808e9 q^{35} -2.98059e9 q^{36} +2.97526e10 q^{37} -1.70692e9 q^{38} +7.35233e9 q^{39} +2.82861e10 q^{40} +4.78825e10 q^{41} -5.98012e9 q^{42} +5.25504e10 q^{43} +9.93581e9 q^{44} +2.14304e10 q^{45} +2.93312e9 q^{46} +7.82524e10 q^{47} +7.50240e9 q^{48} -7.08421e10 q^{49} -2.06059e10 q^{50} -3.96800e10 q^{51} -5.65646e10 q^{52} +1.39229e11 q^{53} -1.96918e10 q^{54} -7.14382e10 q^{55} +1.13208e11 q^{56} +2.44815e10 q^{57} +7.25673e10 q^{58} +4.00667e11 q^{59} -1.64873e11 q^{60} +8.48232e9 q^{61} +2.00887e10 q^{62} +8.57696e10 q^{63} +2.34355e11 q^{64} +4.06698e11 q^{65} +6.56428e10 q^{66} -2.54018e11 q^{67} +3.05275e11 q^{68} -4.20682e10 q^{69} -3.30793e11 q^{70} -9.45197e11 q^{71} +3.72781e11 q^{72} -1.26364e12 q^{73} -1.51227e12 q^{74} +2.95540e11 q^{75} -1.88346e11 q^{76} -2.85913e11 q^{77} -3.73705e11 q^{78} +1.73956e12 q^{79} +4.14999e11 q^{80} +2.82430e11 q^{81} -2.43377e12 q^{82} +3.01003e12 q^{83} -6.59862e11 q^{84} -2.19492e12 q^{85} -2.67104e12 q^{86} -1.04079e12 q^{87} -1.24267e12 q^{88} +2.47839e11 q^{89} -1.08926e12 q^{90} +1.62771e12 q^{91} +3.23648e11 q^{92} -2.88121e11 q^{93} -3.97742e12 q^{94} +1.35421e12 q^{95} -4.57039e12 q^{96} -1.01179e13 q^{97} +3.60077e12 q^{98} -9.41480e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 41 q^{2} + 2916 q^{3} + 23669 q^{4} - 38422 q^{5} + 29889 q^{6} + 41998 q^{7} + 2375463 q^{8} + 2125764 q^{9} - 5866868 q^{10} - 7086244 q^{11} + 17254701 q^{12} + 50891230 q^{13} + 51438518 q^{14}+ \cdots - 3765920597604 q^{99}+O(q^{100}) \) 4 * q + 41 * q^2 + 2916 * q^3 + 23669 * q^4 - 38422 * q^5 + 29889 * q^6 + 41998 * q^7 + 2375463 * q^8 + 2125764 * q^9 - 5866868 * q^10 - 7086244 * q^11 + 17254701 * q^12 + 50891230 * q^13 + 51438518 * q^14 - 28009638 * q^15 + 285120977 * q^16 + 192739820 * q^17 + 21789081 * q^18 - 183220188 * q^19 - 898094912 * q^20 + 30616542 * q^21 - 72634001 * q^22 - 14728250 * q^23 + 1731712527 * q^24 - 1100820808 * q^25 + 4093863728 * q^26 + 1549681956 * q^27 - 7107233974 * q^28 - 548077356 * q^29 - 4276946772 * q^30 - 681968600 * q^31 + 39383025007 * q^32 - 5165871876 * q^33 + 19950148786 * q^34 + 5394617384 * q^35 + 12578677029 * q^36 - 5154946872 * q^37 + 18554908452 * q^38 + 37099706670 * q^39 - 15687175464 * q^40 + 51238857992 * q^41 + 37498679622 * q^42 + 74347734480 * q^43 - 41931077309 * q^44 - 20419026102 * q^45 + 166685861450 * q^46 + 274474225690 * q^47 + 207853192233 * q^48 - 153177492648 * q^49 - 149839157 * q^50 + 140507328780 * q^51 + 898475423084 * q^52 + 213982590882 * q^53 + 15884240049 * q^54 + 68066916742 * q^55 - 15495316938 * q^56 - 133567517052 * q^57 - 366985322898 * q^58 + 1321318473964 * q^59 - 654711190848 * q^60 - 103045963950 * q^61 - 1085044917496 * q^62 + 22319459118 * q^63 + 2752080303457 * q^64 - 592303463140 * q^65 - 52950186729 * q^66 + 564819557912 * q^67 + 475206163858 * q^68 - 10736894250 * q^69 - 1630864907696 * q^70 + 755239009806 * q^71 + 1262418432183 * q^72 + 1553343364552 * q^73 - 1161503492586 * q^74 - 802498369032 * q^75 - 4781019846036 * q^76 - 74402018878 * q^77 + 2984426657712 * q^78 - 409630665982 * q^79 - 7292238669896 * q^80 + 1129718145924 * q^81 - 14121959211962 * q^82 - 2873448789168 * q^83 - 5181173567046 * q^84 - 9861359797412 * q^85 - 5038703996808 * q^86 - 399548392524 * q^87 - 4208277607743 * q^88 - 2345798585688 * q^89 - 3117894196788 * q^90 - 4061579957120 * q^91 - 4480747709890 * q^92 - 497155109400 * q^93 - 21071642578954 * q^94 + 5118679925808 * q^95 + 28710225230103 * q^96 - 325787932204 * q^97 - 19699761224547 * q^98 - 3765920597604 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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