LMFDB - Embedded newform 289.10.a.h.1.25

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.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:	$148.845356651$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.25
Character	$\chi$	$=$	289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+19.0528 q^{2} +138.351 q^{3} -148.990 q^{4} -952.816 q^{5} +2635.99 q^{6} -6303.69 q^{7} -12593.7 q^{8} -541.879 q^{9} +O(q^{10})$	\(q+19.0528 q^{2} +138.351 q^{3} -148.990 q^{4} -952.816 q^{5} +2635.99 q^{6} -6303.69 q^{7} -12593.7 q^{8} -541.879 q^{9} -18153.8 q^{10} -18156.0 q^{11} -20612.9 q^{12} -22499.5 q^{13} -120103. q^{14} -131823. q^{15} -163663. q^{16} -10324.3 q^{18} +167894. q^{19} +141960. q^{20} -872125. q^{21} -345924. q^{22} +237509. q^{23} -1.74236e6 q^{24} -1.04527e6 q^{25} -428680. q^{26} -2.79814e6 q^{27} +939185. q^{28} +7.21616e6 q^{29} -2.51161e6 q^{30} -7.65471e6 q^{31} +3.32974e6 q^{32} -2.51192e6 q^{33} +6.00626e6 q^{35} +80734.4 q^{36} -5.52951e6 q^{37} +3.19885e6 q^{38} -3.11284e6 q^{39} +1.19995e7 q^{40} -5.44258e6 q^{41} -1.66164e7 q^{42} +2.86100e7 q^{43} +2.70506e6 q^{44} +516311. q^{45} +4.52522e6 q^{46} +1.86290e7 q^{47} -2.26431e7 q^{48} -617083. q^{49} -1.99153e7 q^{50} +3.35220e6 q^{52} -3.78200e6 q^{53} -5.33125e7 q^{54} +1.72994e7 q^{55} +7.93869e7 q^{56} +2.32283e7 q^{57} +1.37488e8 q^{58} -9.03616e7 q^{59} +1.96403e7 q^{60} +6.48060e7 q^{61} -1.45844e8 q^{62} +3.41584e6 q^{63} +1.47237e8 q^{64} +2.14379e7 q^{65} -4.78591e7 q^{66} +3.00141e8 q^{67} +3.28597e7 q^{69} +1.14436e8 q^{70} +9.27324e7 q^{71} +6.82427e6 q^{72} +3.79969e8 q^{73} -1.05353e8 q^{74} -1.44614e8 q^{75} -2.50144e7 q^{76} +1.14450e8 q^{77} -5.93085e7 q^{78} -2.94778e8 q^{79} +1.55941e8 q^{80} -3.76461e8 q^{81} -1.03697e8 q^{82} -5.73331e8 q^{83} +1.29938e8 q^{84} +5.45101e8 q^{86} +9.98366e8 q^{87} +2.28652e8 q^{88} +3.06914e8 q^{89} +9.83718e6 q^{90} +1.41830e8 q^{91} -3.53864e7 q^{92} -1.05904e9 q^{93} +3.54936e8 q^{94} -1.59972e8 q^{95} +4.60674e8 q^{96} +2.52310e8 q^{97} -1.17572e7 q^{98} +9.83838e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) $ 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9} + 60000 q^{10} + 76902 q^{11} + 373248 q^{12} + 54216 q^{13} + 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} + 6439479 q^{20} - 138102 q^{21} + 267324 q^{22} + 4041462 q^{23} + 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} + 13281612 q^{27} + 18614784 q^{28} + 4005936 q^{29} + 22471686 q^{30} + 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} + 22076682 q^{37} - 27401376 q^{38} + 62736162 q^{39} - 12231630 q^{40} + 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} - 49578936 q^{44} + 129308238 q^{45} + 140524827 q^{46} - 118557912 q^{47} + 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} + 209848575 q^{54} - 365439924 q^{55} + 203095059 q^{56} - 4614108 q^{57} - 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} + 175597116 q^{61} + 720602571 q^{62} + 587415936 q^{63} + 853082511 q^{64} + 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} + 1308709542 q^{71} - 275337849 q^{72} + 494841342 q^{73} + 1545361890 q^{74} + 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} + 2270624538 q^{78} + 1980107868 q^{79} + 2897000199 q^{80} + 1598298840 q^{81} + 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} - 2705904618 q^{88} + 148394658 q^{89} + 117916215 q^{90} + 636340896 q^{91} - 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} + 4878626298 q^{95} - 8390096634 q^{96} - 891786822 q^{97} + 4285627647 q^{98} - 1476187998 q^{99}+O(q^{100}) \) 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9 + 60000 * q^10 + 76902 * q^11 + 373248 * q^12 + 54216 * q^13 + 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 + 6439479 * q^20 - 138102 * q^21 + 267324 * q^22 + 4041462 * q^23 + 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 + 13281612 * q^27 + 18614784 * q^28 + 4005936 * q^29 + 22471686 * q^30 + 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 + 22076682 * q^37 - 27401376 * q^38 + 62736162 * q^39 - 12231630 * q^40 + 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 - 49578936 * q^44 + 129308238 * q^45 + 140524827 * q^46 - 118557912 * q^47 + 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 + 209848575 * q^54 - 365439924 * q^55 + 203095059 * q^56 - 4614108 * q^57 - 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 + 175597116 * q^61 + 720602571 * q^62 + 587415936 * q^63 + 853082511 * q^64 + 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 + 1308709542 * q^71 - 275337849 * q^72 + 494841342 * q^73 + 1545361890 * q^74 + 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 + 2270624538 * q^78 + 1980107868 * q^79 + 2897000199 * q^80 + 1598298840 * q^81 + 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 - 2705904618 * q^88 + 148394658 * q^89 + 117916215 * q^90 + 636340896 * q^91 - 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 + 4878626298 * q^95 - 8390096634 * q^96 - 891786822 * q^97 + 4285627647 * q^98 - 1476187998 * 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 $

$2$	19.0528	0.842024	0.421012	−	0.907055i	$-0.361675\pi$
$2$	19.0528	0.842024	0.421012	+	0.907055i	$0.361675\pi$
$3$	138.351	0.986139	0.493069	−	0.869990i	$-0.335875\pi$
$3$	138.351	0.986139	0.493069	+	0.869990i	$0.335875\pi$
$4$	−148.990	−0.290995
$5$	−952.816	−0.681780	−0.340890	−	0.940103i	$-0.610728\pi$
$5$	−952.816	−0.681780	−0.340890	+	0.940103i	$0.610728\pi$
$6$	2635.99	0.830353
$7$	−6303.69	−0.992325	−0.496162	−	0.868230i	$-0.665258\pi$
$7$	−6303.69	−0.992325	−0.496162	+	0.868230i	$0.665258\pi$
$8$	−12593.7	−1.08705
$9$	−541.879	−0.0275303
$10$	−18153.8	−0.574075
$11$	−18156.0	−0.373899	−0.186949	−	0.982370i	$-0.559860\pi$
$11$	−18156.0	−0.373899	−0.186949	+	0.982370i	$0.559860\pi$
$12$	−20612.9	−0.286962
$13$	−22499.5	−0.218488	−0.109244	−	0.994015i	$-0.534843\pi$
$13$	−22499.5	−0.218488	−0.109244	+	0.994015i	$0.534843\pi$
$14$	−120103.	−0.835561
$15$	−131823.	−0.672329
$16$	−163663.	−0.624326
$17$	0	0
$17$	0	0
$18$	−10324.3	−0.0231812
$19$	167894.	0.295558	0.147779	−	0.989020i	$-0.452788\pi$
$19$	167894.	0.295558	0.147779	+	0.989020i	$0.452788\pi$
$20$	141960.	0.198395
$21$	−872125.	−0.978570
$22$	−345924.	−0.314832
$23$	237509.	0.176972	0.0884860	−	0.996077i	$-0.471797\pi$
$23$	237509.	0.176972	0.0884860	+	0.996077i	$0.471797\pi$
$24$	−1.74236e6	−1.07198
$25$	−1.04527e6	−0.535177
$26$	−428680.	−0.183973
$27$	−2.79814e6	−1.01329
$28$	939185.	0.288762
$29$	7.21616e6	1.89459	0.947295	−	0.320364i	$-0.103805\pi$
$29$	7.21616e6	1.89459	0.947295	+	0.320364i	$0.103805\pi$
$30$	−2.51161e6	−0.566117
$31$	−7.65471e6	−1.48868	−0.744339	−	0.667802i	$-0.767235\pi$
$31$	−7.65471e6	−1.48868	−0.744339	+	0.667802i	$0.767235\pi$
$32$	3.32974e6	0.561352
$33$	−2.51192e6	−0.368716
$34$	0	0
$35$	6.00626e6	0.676547
$36$	80734.4	0.00801119
$37$	−5.52951e6	−0.485042	−0.242521	−	0.970146i	$-0.577974\pi$
$37$	−5.52951e6	−0.485042	−0.242521	+	0.970146i	$0.577974\pi$
$38$	3.19885e6	0.248867
$39$	−3.11284e6	−0.215460
$40$	1.19995e7	0.741128
$41$	−5.44258e6	−0.300800	−0.150400	−	0.988625i	$-0.548056\pi$
$41$	−5.44258e6	−0.300800	−0.150400	+	0.988625i	$0.548056\pi$
$42$	−1.66164e7	−0.823979
$43$	2.86100e7	1.27617	0.638087	−	0.769964i	$-0.279726\pi$
$43$	2.86100e7	1.27617	0.638087	+	0.769964i	$0.279726\pi$
$44$	2.70506e6	0.108803
$45$	516311.	0.0187696
$46$	4.52522e6	0.149015
$47$	1.86290e7	0.556865	0.278432	−	0.960456i	$-0.410185\pi$
$47$	1.86290e7	0.556865	0.278432	+	0.960456i	$0.410185\pi$
$48$	−2.26431e7	−0.615672
$49$	−617083.	−0.0152919
$50$	−1.99153e7	−0.450632
$51$	0	0
$52$	3.35220e6	0.0635792
$53$	−3.78200e6	−0.0658386	−0.0329193	−	0.999458i	$-0.510480\pi$
$53$	−3.78200e6	−0.0658386	−0.0329193	+	0.999458i	$0.510480\pi$
$54$	−5.33125e7	−0.853212
$55$	1.72994e7	0.254917
$56$	7.93869e7	1.07871
$57$	2.32283e7	0.291461
$58$	1.37488e8	1.59529
$59$	−9.03616e7	−0.970845	−0.485422	−	0.874280i	$-0.661334\pi$
$59$	−9.03616e7	−0.970845	−0.485422	+	0.874280i	$0.661334\pi$
$60$	1.96403e7	0.195645
$61$	6.48060e7	0.599282	0.299641	−	0.954052i	$-0.403133\pi$
$61$	6.48060e7	0.599282	0.299641	+	0.954052i	$0.403133\pi$
$62$	−1.45844e8	−1.25350
$63$	3.41584e6	0.0273190
$64$	1.47237e8	1.09700
$65$	2.14379e7	0.148961
$66$	−4.78591e7	−0.310468
$67$	3.00141e8	1.81966	0.909828	−	0.414986i	$-0.136213\pi$
$67$	3.00141e8	1.81966	0.909828	+	0.414986i	$0.136213\pi$
$68$	0	0
$69$	3.28597e7	0.174519
$70$	1.14436e8	0.569669
$71$	9.27324e7	0.433081	0.216540	−	0.976274i	$-0.430523\pi$
$71$	9.27324e7	0.433081	0.216540	+	0.976274i	$0.430523\pi$
$72$	6.82427e6	0.0299268
$73$	3.79969e8	1.56601	0.783007	−	0.622013i	$-0.213685\pi$
$73$	3.79969e8	1.56601	0.783007	+	0.622013i	$0.213685\pi$
$74$	−1.05353e8	−0.408417
$75$	−1.44614e8	−0.527758
$76$	−2.50144e7	−0.0860061
$77$	1.14450e8	0.371029
$78$	−5.93085e7	−0.181422
$79$	−2.94778e8	−0.851477	−0.425738	−	0.904846i	$-0.639986\pi$
$79$	−2.94778e8	−0.851477	−0.425738	+	0.904846i	$0.639986\pi$
$80$	1.55941e8	0.425653
$81$	−3.76461e8	−0.971712
$82$	−1.03697e8	−0.253281
$83$	−5.73331e8	−1.32603	−0.663016	−	0.748605i	$-0.730724\pi$
$83$	−5.73331e8	−1.32603	−0.663016	+	0.748605i	$0.730724\pi$
$84$	1.29938e8	0.284759
$85$	0	0
$86$	5.45101e8	1.07457
$87$	9.98366e8	1.86833
$88$	2.28652e8	0.406447
$89$	3.06914e8	0.518516	0.259258	−	0.965808i	$-0.416522\pi$
$89$	3.06914e8	0.518516	0.259258	+	0.965808i	$0.416522\pi$
$90$	9.83718e6	0.0158044
$91$	1.41830e8	0.216811
$92$	−3.53864e7	−0.0514981
$93$	−1.05904e9	−1.46804
$94$	3.54936e8	0.468894
$95$	−1.59972e8	−0.201506
$96$	4.60674e8	0.553571
$97$	2.52310e8	0.289375	0.144688	−	0.989477i	$-0.453782\pi$
$97$	2.52310e8	0.289375	0.144688	+	0.989477i	$0.453782\pi$
$98$	−1.17572e7	−0.0128762
$99$	9.83838e6	0.0102935
$100$	1.55734e8	0.155734
$101$	2.30700e8	0.220598	0.110299	−	0.993898i	$-0.464819\pi$
$101$	2.30700e8	0.220598	0.110299	+	0.993898i	$0.464819\pi$
$102$	0	0
$103$	1.46432e9	1.28194	0.640971	−	0.767565i	$-0.278532\pi$
$103$	1.46432e9	1.28194	0.640971	+	0.767565i	$0.278532\pi$
$104$	2.83353e8	0.237508
$105$	8.30974e8	0.667169
$106$	−7.20579e7	−0.0554377
$107$	2.53090e9	1.86658	0.933292	−	0.359119i	$-0.116923\pi$
$107$	2.53090e9	1.86658	0.933292	+	0.359119i	$0.116923\pi$
$108$	4.16894e8	0.294862
$109$	3.53399e8	0.239798	0.119899	−	0.992786i	$-0.461743\pi$
$109$	3.53399e8	0.239798	0.119899	+	0.992786i	$0.461743\pi$
$110$	3.29602e8	0.214646
$111$	−7.65016e8	−0.478318
$112$	1.03168e9	0.619534
$113$	2.17428e9	1.25447	0.627237	−	0.778829i	$-0.284186\pi$
$113$	2.17428e9	1.25447	0.627237	+	0.778829i	$0.284186\pi$
$114$	4.42565e8	0.245417
$115$	−2.26302e8	−0.120656
$116$	−1.07513e9	−0.551317
$117$	1.21920e7	0.00601505
$118$	−1.72164e9	−0.817475
$119$	0	0
$120$	1.66015e9	0.730855
$121$	−2.02831e9	−0.860200
$122$	1.23474e9	0.504610
$123$	−7.52989e8	−0.296631
$124$	1.14047e9	0.433199
$125$	2.85692e9	1.04665
$126$	6.50814e7	0.0230032
$127$	−2.48006e9	−0.845951	−0.422975	−	0.906141i	$-0.639014\pi$
$127$	−2.48006e9	−0.845951	−0.422975	+	0.906141i	$0.639014\pi$
$128$	1.10045e9	0.362347
$129$	3.95823e9	1.25848
$130$	4.08453e8	0.125429
$131$	−6.16018e9	−1.82756	−0.913781	−	0.406207i	$-0.866851\pi$
$131$	−6.16018e9	−1.82756	−0.913781	+	0.406207i	$0.866851\pi$
$132$	3.74250e8	0.107295
$133$	−1.05835e9	−0.293290
$134$	5.71854e9	1.53219
$135$	2.66611e9	0.690839
$136$	0	0
$137$	−5.37708e9	−1.30408	−0.652039	−	0.758185i	$-0.726086\pi$
$137$	−5.37708e9	−1.30408	−0.652039	+	0.758185i	$0.726086\pi$
$138$	6.26070e8	0.146949
$139$	4.58306e9	1.04133	0.520665	−	0.853761i	$-0.325684\pi$
$139$	4.58306e9	1.04133	0.520665	+	0.853761i	$0.325684\pi$
$140$	−8.94870e8	−0.196872
$141$	2.57735e9	0.549146
$142$	1.76681e9	0.364664
$143$	4.08503e8	0.0816926
$144$	8.86857e7	0.0171879
$145$	−6.87567e9	−1.29169
$146$	7.23949e9	1.31862
$147$	−8.53744e7	−0.0150799
$148$	8.23840e8	0.141145
$149$	−1.11953e10	−1.86078	−0.930391	−	0.366568i	$-0.880533\pi$
$149$	−1.11953e10	−1.86078	−0.930391	+	0.366568i	$0.880533\pi$
$150$	−2.75531e9	−0.444385
$151$	−3.76917e8	−0.0589997	−0.0294998	−	0.999565i	$-0.509391\pi$
$151$	−3.76917e8	−0.0589997	−0.0294998	+	0.999565i	$0.509391\pi$
$152$	−2.11441e9	−0.321286
$153$	0	0
$154$	2.18060e9	0.312415
$155$	7.29353e9	1.01495
$156$	4.63782e8	0.0626979
$157$	−4.13371e9	−0.542990	−0.271495	−	0.962440i	$-0.587518\pi$
$157$	−4.13371e9	−0.542990	−0.271495	+	0.962440i	$0.587518\pi$
$158$	−5.61635e9	−0.716964
$159$	−5.23246e8	−0.0649260
$160$	−3.17263e9	−0.382718
$161$	−1.49718e9	−0.175614
$162$	−7.17265e9	−0.818205
$163$	6.28197e9	0.697030	0.348515	−	0.937303i	$-0.386686\pi$
$163$	6.28197e9	0.697030	0.348515	+	0.937303i	$0.386686\pi$
$164$	8.10889e8	0.0875314
$165$	2.39339e9	0.251383
$166$	−1.09236e10	−1.11655
$167$	9.32746e9	0.927982	0.463991	−	0.885840i	$-0.346417\pi$
$167$	9.32746e9	0.927982	0.463991	+	0.885840i	$0.346417\pi$
$168$	1.09833e10	1.06375
$169$	−1.00983e10	−0.952263
$170$	0	0
$171$	−9.09780e7	−0.00813680
$172$	−4.26259e9	−0.371361
$173$	1.14214e10	0.969418	0.484709	−	0.874675i	$-0.338925\pi$
$173$	1.14214e10	0.969418	0.484709	+	0.874675i	$0.338925\pi$
$174$	1.90217e10	1.57318
$175$	6.58904e9	0.531069
$176$	2.97148e9	0.233435
$177$	−1.25017e10	−0.957388
$178$	5.84758e9	0.436603
$179$	−1.60366e10	−1.16755	−0.583774	−	0.811916i	$-0.698425\pi$
$179$	−1.60366e10	−1.16755	−0.583774	+	0.811916i	$0.698425\pi$
$180$	−7.69250e7	−0.00546187
$181$	−2.25247e10	−1.55993	−0.779967	−	0.625821i	$-0.784764\pi$
$181$	−2.25247e10	−1.55993	−0.779967	+	0.625821i	$0.784764\pi$
$182$	2.70227e9	0.182560
$183$	8.96601e9	0.590975
$184$	−2.99112e9	−0.192377
$185$	5.26861e9	0.330691
$186$	−2.01777e10	−1.23613
$187$	0	0
$188$	−2.77553e9	−0.162045
$189$	1.76386e10	1.00551
$190$	−3.04791e9	−0.169672
$191$	−4.21446e9	−0.229135	−0.114568	−	0.993415i	$-0.536548\pi$
$191$	−4.21446e9	−0.229135	−0.114568	+	0.993415i	$0.536548\pi$
$192$	2.03704e10	1.08179
$193$	2.69959e10	1.40052	0.700261	−	0.713887i	$-0.253067\pi$
$193$	2.69959e10	1.40052	0.700261	+	0.713887i	$0.253067\pi$
$194$	4.80721e9	0.243661
$195$	2.96597e9	0.146896
$196$	9.19391e7	0.00444987
$197$	−1.53445e10	−0.725863	−0.362931	−	0.931816i	$-0.618224\pi$
$197$	−1.53445e10	−0.725863	−0.362931	+	0.931816i	$0.618224\pi$
$198$	1.87449e8	0.00866742
$199$	−3.17323e9	−0.143438	−0.0717188	−	0.997425i	$-0.522848\pi$
$199$	−3.17323e9	−0.143438	−0.0717188	+	0.997425i	$0.522848\pi$
$200$	1.31638e10	0.581763
$201$	4.15250e10	1.79443
$202$	4.39549e9	0.185749
$203$	−4.54884e10	−1.88005
$204$	0	0
$205$	5.18578e9	0.205079
$206$	2.78994e10	1.07943
$207$	−1.28701e8	−0.00487209
$208$	3.68235e9	0.136408
$209$	−3.04828e9	−0.110509
$210$	1.58324e10	0.561772
$211$	−2.21102e10	−0.767928	−0.383964	−	0.923348i	$-0.625441\pi$
$211$	−2.21102e10	−0.767928	−0.383964	+	0.923348i	$0.625441\pi$
$212$	5.63480e8	0.0191587
$213$	1.28297e10	0.427078
$214$	4.82207e10	1.57171
$215$	−2.72601e10	−0.870069
$216$	3.52390e10	1.10149
$217$	4.82529e10	1.47725
$218$	6.73324e9	0.201916
$219$	5.25693e10	1.54431
$220$	−2.57743e9	−0.0741796
$221$	0	0
$222$	−1.45757e10	−0.402756
$223$	4.57669e10	1.23931	0.619655	−	0.784874i	$-0.287272\pi$
$223$	4.57669e10	1.23931	0.619655	+	0.784874i	$0.287272\pi$
$224$	−2.09896e10	−0.557043
$225$	5.66408e8	0.0147336
$226$	4.14261e10	1.05630
$227$	3.70853e10	0.927012	0.463506	−	0.886094i	$-0.346591\pi$
$227$	3.70853e10	0.927012	0.463506	+	0.886094i	$0.346591\pi$
$228$	−3.46078e9	−0.0848139
$229$	7.15009e10	1.71811	0.859057	−	0.511880i	$-0.171051\pi$
$229$	7.15009e10	1.71811	0.859057	+	0.511880i	$0.171051\pi$
$230$	−4.31170e9	−0.101595
$231$	1.58343e10	0.365886
$232$	−9.08783e10	−2.05951
$233$	1.62179e10	0.360489	0.180245	−	0.983622i	$-0.442311\pi$
$233$	1.62179e10	0.360489	0.180245	+	0.983622i	$0.442311\pi$
$234$	2.32293e8	0.00506482
$235$	−1.77500e10	−0.379659
$236$	1.34629e10	0.282511
$237$	−4.07829e10	−0.839674
$238$	0	0
$239$	−1.01270e9	−0.0200765	−0.0100383	−	0.999950i	$-0.503195\pi$
$239$	−1.01270e9	−0.0200765	−0.0100383	+	0.999950i	$0.503195\pi$
$240$	2.15747e10	0.419753
$241$	−4.27071e10	−0.815499	−0.407749	−	0.913094i	$-0.633686\pi$
$241$	−4.27071e10	−0.815499	−0.407749	+	0.913094i	$0.633686\pi$
$242$	−3.86450e10	−0.724309
$243$	2.99188e9	0.0550448
$244$	−9.65543e9	−0.174388
$245$	5.87967e8	0.0104257
$246$	−1.43466e10	−0.249770
$247$	−3.77753e9	−0.0645760
$248$	9.64012e10	1.61827
$249$	−7.93211e10	−1.30765
$250$	5.44323e10	0.881306
$251$	−5.03694e10	−0.801005	−0.400503	−	0.916296i	$-0.631164\pi$
$251$	−5.03694e10	−0.801005	−0.400503	+	0.916296i	$0.631164\pi$
$252$	−5.08924e8	−0.00794970
$253$	−4.31222e9	−0.0661697
$254$	−4.72521e10	−0.712311
$255$	0	0
$256$	−5.44185e10	−0.791893
$257$	1.09809e11	1.57015	0.785074	−	0.619402i	$-0.212625\pi$
$257$	1.09809e11	1.57015	0.785074	+	0.619402i	$0.212625\pi$
$258$	7.54156e10	1.05967
$259$	3.48563e10	0.481319
$260$	−3.19403e9	−0.0433470
$261$	−3.91028e9	−0.0521586
$262$	−1.17369e11	−1.53885
$263$	−3.64718e10	−0.470064	−0.235032	−	0.971988i	$-0.575519\pi$
$263$	−3.64718e10	−0.470064	−0.235032	+	0.971988i	$0.575519\pi$
$264$	3.16344e10	0.400813
$265$	3.60355e9	0.0448874
$266$	−2.01645e10	−0.246957
$267$	4.24620e10	0.511328
$268$	−4.47180e10	−0.529512
$269$	1.15019e11	1.33932	0.669660	−	0.742668i	$-0.266440\pi$
$269$	1.15019e11	1.33932	0.669660	+	0.742668i	$0.266440\pi$
$270$	5.07970e10	0.581703
$271$	−9.61011e10	−1.08235	−0.541174	−	0.840911i	$-0.682020\pi$
$271$	−9.61011e10	−1.08235	−0.541174	+	0.840911i	$0.682020\pi$
$272$	0	0
$273$	1.96224e10	0.213806
$274$	−1.02449e11	−1.09807
$275$	1.89779e10	0.200102
$276$	−4.89576e9	−0.0507842
$277$	1.19097e11	1.21547	0.607733	−	0.794142i	$-0.292079\pi$
$277$	1.19097e11	1.21547	0.607733	+	0.794142i	$0.292079\pi$
$278$	8.73202e10	0.876825
$279$	4.14792e9	0.0409838
$280$	−7.56411e10	−0.735440
$281$	−1.10669e11	−1.05888	−0.529440	−	0.848347i	$-0.677598\pi$
$281$	−1.10669e11	−1.05888	−0.529440	+	0.848347i	$0.677598\pi$
$282$	4.91059e10	0.462394
$283$	5.83711e10	0.540952	0.270476	−	0.962727i	$-0.412819\pi$
$283$	5.83711e10	0.540952	0.270476	+	0.962727i	$0.412819\pi$
$284$	−1.38162e10	−0.126025
$285$	−2.21323e10	−0.198712
$286$	7.78313e9	0.0687871
$287$	3.43084e10	0.298491
$288$	−1.80431e9	−0.0154542
$289$	0	0
$290$	−1.31001e11	−1.08764
$291$	3.49074e10	0.285364
$292$	−5.66115e10	−0.455703
$293$	3.56947e10	0.282943	0.141472	−	0.989942i	$-0.454817\pi$
$293$	3.56947e10	0.282943	0.141472	+	0.989942i	$0.454817\pi$
$294$	−1.62662e9	−0.0126977
$295$	8.60980e10	0.661902
$296$	6.96371e10	0.527264
$297$	5.08032e10	0.378867
$298$	−2.13301e11	−1.56682
$299$	−5.34384e9	−0.0386663
$300$	2.15460e10	0.153575
$301$	−1.80349e11	−1.26638
$302$	−7.18134e9	−0.0496792
$303$	3.19177e10	0.217540
$304$	−2.74780e10	−0.184525
$305$	−6.17482e10	−0.408578
$306$	0	0
$307$	2.68418e11	1.72460	0.862300	−	0.506398i	$-0.169023\pi$
$307$	2.68418e11	1.72460	0.862300	+	0.506398i	$0.169023\pi$
$308$	−1.70519e10	−0.107968
$309$	2.02591e11	1.26417
$310$	1.38962e11	0.854613
$311$	6.58990e9	0.0399445	0.0199723	−	0.999801i	$-0.493642\pi$
$311$	6.58990e9	0.0399445	0.0199723	+	0.999801i	$0.493642\pi$
$312$	3.92023e10	0.234216
$313$	−6.23444e10	−0.367154	−0.183577	−	0.983005i	$-0.558768\pi$
$313$	−6.23444e10	−0.367154	−0.183577	+	0.983005i	$0.558768\pi$
$314$	−7.87589e10	−0.457210
$315$	−3.25466e9	−0.0186255
$316$	4.39188e10	0.247776
$317$	1.72442e11	0.959128	0.479564	−	0.877507i	$-0.340795\pi$
$317$	1.72442e11	0.959128	0.479564	+	0.877507i	$0.340795\pi$
$318$	−9.96931e9	−0.0546692
$319$	−1.31017e11	−0.708385
$320$	−1.40289e11	−0.747911
$321$	3.50153e11	1.84071
$322$	−2.85256e10	−0.147871
$323$	0	0
$324$	5.60888e10	0.282764
$325$	2.35180e10	0.116930
$326$	1.19689e11	0.586916
$327$	4.88932e10	0.236474
$328$	6.85424e10	0.326984
$329$	−1.17432e11	−0.552591
$330$	4.56009e10	0.211671
$331$	2.65135e11	1.21406	0.607031	−	0.794678i	$-0.292360\pi$
$331$	2.65135e11	1.21406	0.607031	+	0.794678i	$0.292360\pi$
$332$	8.54204e10	0.385869
$333$	2.99633e9	0.0133533
$334$	1.77715e11	0.781383
$335$	−2.85980e11	−1.24060
$336$	1.42735e11	0.610947
$337$	−1.55107e11	−0.655083	−0.327541	−	0.944837i	$-0.606220\pi$
$337$	−1.55107e11	−0.655083	−0.327541	+	0.944837i	$0.606220\pi$
$338$	−1.92401e11	−0.801828
$339$	3.00814e11	1.23709
$340$	0	0
$341$	1.38979e11	0.556615
$342$	−1.73339e9	−0.00685138
$343$	2.58267e11	1.00750
$344$	−3.60306e11	−1.38726
$345$	−3.13092e10	−0.118983
$346$	2.17610e11	0.816273
$347$	3.20294e11	1.18595	0.592974	−	0.805222i	$-0.297954\pi$
$347$	3.20294e11	1.18595	0.592974	+	0.805222i	$0.297954\pi$
$348$	−1.48746e11	−0.543675
$349$	−1.76652e11	−0.637388	−0.318694	−	0.947858i	$-0.603244\pi$
$349$	−1.76652e11	−0.637388	−0.318694	+	0.947858i	$0.603244\pi$
$350$	1.25540e11	0.447173
$351$	6.29569e10	0.221392
$352$	−6.04549e10	−0.209889
$353$	−3.04167e11	−1.04262	−0.521310	−	0.853367i	$-0.674556\pi$
$353$	−3.04167e11	−1.04262	−0.521310	+	0.853367i	$0.674556\pi$
$354$	−2.38192e11	−0.806143
$355$	−8.83569e10	−0.295266
$356$	−4.57270e10	−0.150886
$357$	0	0
$358$	−3.05543e11	−0.983104
$359$	2.40945e11	0.765585	0.382792	−	0.923834i	$-0.374962\pi$
$359$	2.40945e11	0.765585	0.382792	+	0.923834i	$0.374962\pi$
$360$	−6.50228e9	−0.0204035
$361$	−2.94499e11	−0.912645
$362$	−4.29160e11	−1.31350
$363$	−2.80619e11	−0.848276
$364$	−2.11312e10	−0.0630912
$365$	−3.62041e11	−1.06768
$366$	1.70828e11	0.497615
$367$	−2.39456e11	−0.689016	−0.344508	−	0.938783i	$-0.611954\pi$
$367$	−2.39456e11	−0.689016	−0.344508	+	0.938783i	$0.611954\pi$
$368$	−3.88715e10	−0.110488
$369$	2.94922e9	0.00828111
$370$	1.00382e11	0.278450
$371$	2.38406e10	0.0653333
$372$	1.57786e11	0.427194
$373$	6.75606e11	1.80719	0.903595	−	0.428387i	$-0.140918\pi$
$373$	6.75606e11	1.80719	0.903595	+	0.428387i	$0.140918\pi$
$374$	0	0
$375$	3.95258e11	1.03214
$376$	−2.34609e11	−0.605340
$377$	−1.62360e11	−0.413946
$378$	3.36066e11	0.846664
$379$	4.56297e11	1.13598	0.567990	−	0.823035i	$-0.307721\pi$
$379$	4.56297e11	1.13598	0.567990	+	0.823035i	$0.307721\pi$
$380$	2.38341e10	0.0586372
$381$	−3.43120e11	−0.834225
$382$	−8.02974e10	−0.192937
$383$	2.96911e11	0.705068	0.352534	−	0.935799i	$-0.385320\pi$
$383$	2.96911e11	0.705068	0.352534	+	0.935799i	$0.385320\pi$
$384$	1.52248e11	0.357324
$385$	−1.09050e11	−0.252960
$386$	5.14348e11	1.17927
$387$	−1.55031e10	−0.0351334
$388$	−3.75916e10	−0.0842069
$389$	−7.24841e11	−1.60498	−0.802490	−	0.596666i	$-0.796492\pi$
$389$	−7.24841e11	−1.60498	−0.802490	+	0.596666i	$0.796492\pi$
$390$	5.65101e10	0.123690
$391$	0	0
$392$	7.77138e9	0.0166231
$393$	−8.52269e11	−1.80223
$394$	−2.92356e11	−0.611194
$395$	2.80869e11	0.580519
$396$	−1.46582e9	−0.00299538
$397$	−5.66556e11	−1.14468	−0.572342	−	0.820015i	$-0.693965\pi$
$397$	−5.66556e11	−1.14468	−0.572342	+	0.820015i	$0.693965\pi$
$398$	−6.04590e10	−0.120778
$399$	−1.46424e11	−0.289224
$400$	1.71072e11	0.334125
$401$	−4.79278e11	−0.925630	−0.462815	−	0.886455i	$-0.653161\pi$
$401$	−4.79278e11	−0.925630	−0.462815	+	0.886455i	$0.653161\pi$
$402$	7.91169e11	1.51096
$403$	1.72227e11	0.325259
$404$	−3.43719e10	−0.0641930
$405$	3.58698e11	0.662493
$406$	−8.66683e11	−1.58305
$407$	1.00394e11	0.181357
$408$	0	0
$409$	−5.60817e11	−0.990983	−0.495491	−	0.868613i	$-0.665012\pi$
$409$	−5.60817e11	−0.990983	−0.495491	+	0.868613i	$0.665012\pi$
$410$	9.88038e10	0.172682
$411$	−7.43926e11	−1.28600
$412$	−2.18169e11	−0.373039
$413$	5.69612e11	0.963393
$414$	−2.45212e9	−0.00410242
$415$	5.46279e11	0.904061
$416$	−7.49175e10	−0.122649
$417$	6.34072e11	1.02690
$418$	−5.80784e10	−0.0930511
$419$	−5.48243e11	−0.868981	−0.434490	−	0.900676i	$-0.643071\pi$
$419$	−5.48243e11	−0.868981	−0.434490	+	0.900676i	$0.643071\pi$
$420$	−1.23807e11	−0.194143
$421$	2.99523e11	0.464687	0.232344	−	0.972634i	$-0.425361\pi$
$421$	2.99523e11	0.464687	0.232344	+	0.972634i	$0.425361\pi$
$422$	−4.21261e11	−0.646614
$423$	−1.00947e10	−0.0153307
$424$	4.76295e10	0.0715698
$425$	0	0
$426$	2.44441e11	0.359610
$427$	−4.08517e11	−0.594682
$428$	−3.77078e11	−0.543167
$429$	5.65169e10	0.0805602
$430$	−5.19381e11	−0.732619
$431$	−5.83808e11	−0.814934	−0.407467	−	0.913220i	$-0.633588\pi$
$431$	−5.83808e11	−0.814934	−0.407467	+	0.913220i	$0.633588\pi$
$432$	4.57953e11	0.632622
$433$	−6.11497e10	−0.0835986	−0.0417993	−	0.999126i	$-0.513309\pi$
$433$	−6.11497e10	−0.0835986	−0.0417993	+	0.999126i	$0.513309\pi$
$434$	9.19354e11	1.24388
$435$	−9.51259e11	−1.27379
$436$	−5.26528e10	−0.0697802
$437$	3.98762e10	0.0523055
$438$	1.00159e12	1.30034
$439$	6.65898e11	0.855692	0.427846	−	0.903852i	$-0.359273\pi$
$439$	6.65898e11	0.855692	0.427846	+	0.903852i	$0.359273\pi$
$440$	−2.17864e11	−0.277107
$441$	3.34384e8	0.000420991 0
$442$	0	0
$443$	1.00976e11	0.124567	0.0622833	−	0.998059i	$-0.480162\pi$
$443$	1.00976e11	0.124567	0.0622833	+	0.998059i	$0.480162\pi$
$444$	1.13979e11	0.139188
$445$	−2.92433e11	−0.353513
$446$	8.71990e11	1.04353
$447$	−1.54888e12	−1.83499
$448$	−9.28134e11	−1.08858
$449$	−1.05588e10	−0.0122604	−0.00613020	−	0.999981i	$-0.501951\pi$
$449$	−1.05588e10	−0.0122604	−0.00613020	+	0.999981i	$0.501951\pi$
$450$	1.07917e10	0.0124060
$451$	9.88158e10	0.112469
$452$	−3.23945e11	−0.365046
$453$	−5.21470e10	−0.0581819
$454$	7.06579e11	0.780566
$455$	−1.35138e11	−0.147818
$456$	−2.92531e11	−0.316833
$457$	−1.17320e11	−0.125819	−0.0629097	−	0.998019i	$-0.520038\pi$
$457$	−1.17320e11	−0.125819	−0.0629097	+	0.998019i	$0.520038\pi$
$458$	1.36230e12	1.44669
$459$	0	0
$460$	3.37167e10	0.0351103
$461$	−7.94505e10	−0.0819299	−0.0409650	−	0.999161i	$-0.513043\pi$
$461$	−7.94505e10	−0.0819299	−0.0409650	+	0.999161i	$0.513043\pi$
$462$	3.01689e11	0.308085
$463$	−1.60574e12	−1.62390	−0.811952	−	0.583724i	$-0.801595\pi$
$463$	−1.60574e12	−1.62390	−0.811952	+	0.583724i	$0.801595\pi$
$464$	−1.18102e12	−1.18284
$465$	1.00907e12	1.00088
$466$	3.08996e11	0.303541
$467$	1.78124e12	1.73299	0.866497	−	0.499182i	$-0.166366\pi$
$467$	1.78124e12	1.73299	0.866497	+	0.499182i	$0.166366\pi$
$468$	−1.81649e9	−0.00175035
$469$	−1.89200e12	−1.80569
$470$	−3.38188e11	−0.319682
$471$	−5.71905e11	−0.535463
$472$	1.13799e12	1.05536
$473$	−5.19444e11	−0.477160
$474$	−7.77030e11	−0.707026
$475$	−1.75494e11	−0.158176
$476$	0	0
$477$	2.04939e9	0.00181256
$478$	−1.92947e10	−0.0169049
$479$	−1.58006e12	−1.37140	−0.685698	−	0.727887i	$-0.740503\pi$
$479$	−1.58006e12	−1.37140	−0.685698	+	0.727887i	$0.740503\pi$
$480$	−4.38937e11	−0.377413
$481$	1.24411e11	0.105976
$482$	−8.13691e11	−0.686670
$483$	−2.07137e11	−0.173179
$484$	3.02197e11	0.250314
$485$	−2.40405e11	−0.197290
$486$	5.70038e10	0.0463490
$487$	8.30096e11	0.668726	0.334363	−	0.942444i	$-0.391479\pi$
$487$	8.30096e11	0.668726	0.334363	+	0.942444i	$0.391479\pi$
$488$	−8.16149e11	−0.651449
$489$	8.69119e11	0.687368
$490$	1.12024e10	0.00877870
$491$	6.34607e11	0.492763	0.246381	−	0.969173i	$-0.420758\pi$
$491$	6.34607e11	0.492763	0.246381	+	0.969173i	$0.420758\pi$
$492$	1.12188e11	0.0863182
$493$	0	0
$494$	−7.19726e10	−0.0543746
$495$	−9.37416e9	−0.00701793
$496$	1.25279e12	0.929421
$497$	−5.84556e11	−0.429757
$498$	−1.51129e12	−1.10107
$499$	−9.64233e11	−0.696193	−0.348096	−	0.937459i	$-0.613172\pi$
$499$	−9.64233e11	−0.696193	−0.348096	+	0.937459i	$0.613172\pi$
$500$	−4.25651e11	−0.304571
$501$	1.29047e12	0.915119
$502$	−9.59680e11	−0.674466
$503$	−5.67084e11	−0.394995	−0.197497	−	0.980303i	$-0.563281\pi$
$503$	−5.67084e11	−0.394995	−0.197497	+	0.980303i	$0.563281\pi$
$504$	−4.30181e10	−0.0296971
$505$	−2.19815e11	−0.150399
$506$	−8.21601e10	−0.0557164
$507$	−1.39711e12	−0.939063
$508$	3.69503e11	0.246168
$509$	1.44074e12	0.951383	0.475691	−	0.879612i	$-0.342198\pi$
$509$	1.44074e12	0.951383	0.475691	+	0.879612i	$0.342198\pi$
$510$	0	0
$511$	−2.39521e12	−1.55399
$512$	−1.60025e12	−1.02914
$513$	−4.69790e11	−0.299485
$514$	2.09218e12	1.32210
$515$	−1.39523e12	−0.874002
$516$	−5.89736e11	−0.366213
$517$	−3.38230e11	−0.208211
$518$	6.64112e11	0.405282
$519$	1.58016e12	0.955981
$520$	−2.69983e11	−0.161928
$521$	−1.42096e10	−0.00844914	−0.00422457	−	0.999991i	$-0.501345\pi$
$521$	−1.42096e10	−0.00844914	−0.00422457	+	0.999991i	$0.501345\pi$
$522$	−7.45020e10	−0.0439188
$523$	−2.07252e12	−1.21127	−0.605634	−	0.795743i	$-0.707081\pi$
$523$	−2.07252e12	−1.21127	−0.605634	+	0.795743i	$0.707081\pi$
$524$	9.17803e11	0.531812
$525$	9.11603e11	0.523708
$526$	−6.94891e11	−0.395805
$527$	0	0
$528$	4.11108e11	0.230199
$529$	−1.74474e12	−0.968681
$530$	6.86579e10	0.0377963
$531$	4.89650e10	0.0267276
$532$	1.57683e11	0.0853459
$533$	1.22456e11	0.0657213
$534$	8.09022e11	0.430551
$535$	−2.41148e12	−1.27260
$536$	−3.77990e12	−1.97806
$537$	−2.21869e12	−1.15136
$538$	2.19144e12	1.12774
$539$	1.12038e10	0.00571763
$540$	−3.97223e11	−0.201031
$541$	2.55255e12	1.28111	0.640554	−	0.767913i	$-0.278705\pi$
$541$	2.55255e12	1.28111	0.640554	+	0.767913i	$0.278705\pi$
$542$	−1.83100e12	−0.911363
$543$	−3.11633e12	−1.53831
$544$	0	0
$545$	−3.36724e11	−0.163489
$546$	3.73862e11	0.180030
$547$	−1.27039e12	−0.606730	−0.303365	−	0.952874i	$-0.598110\pi$
$547$	−1.27039e12	−0.606730	−0.303365	+	0.952874i	$0.598110\pi$
$548$	8.01129e11	0.379481
$549$	−3.51170e10	−0.0164984
$550$	3.61583e11	0.168491
$551$	1.21155e12	0.559961
$552$	−4.13826e11	−0.189711
$553$	1.85819e12	0.844941
$554$	2.26914e12	1.02345
$555$	7.28919e11	0.326108
$556$	−6.82828e11	−0.303022
$557$	−1.94959e12	−0.858215	−0.429107	−	0.903253i	$-0.641172\pi$
$557$	−1.94959e12	−0.858215	−0.429107	+	0.903253i	$0.641172\pi$
$558$	7.90297e10	0.0345093
$559$	−6.43712e11	−0.278829
$560$	−9.83004e11	−0.422386
$561$	0	0
$562$	−2.10856e12	−0.891603
$563$	−3.09690e12	−1.29909	−0.649545	−	0.760324i	$-0.725040\pi$
$563$	−3.09690e12	−1.29909	−0.649545	+	0.760324i	$0.725040\pi$
$564$	−3.83999e11	−0.159799
$565$	−2.07168e12	−0.855274
$566$	1.11213e12	0.455495
$567$	2.37309e12	0.964254
$568$	−1.16785e12	−0.470780
$569$	−1.67936e12	−0.671645	−0.335822	−	0.941925i	$-0.609014\pi$
$569$	−1.67936e12	−0.671645	−0.335822	+	0.941925i	$0.609014\pi$
$570$	−4.21683e11	−0.167321
$571$	4.88980e12	1.92499	0.962496	−	0.271297i	$-0.0874525\pi$
$571$	4.88980e12	1.92499	0.962496	+	0.271297i	$0.0874525\pi$
$572$	−6.08627e10	−0.0237722
$573$	−5.83076e11	−0.225959
$574$	6.53672e11	0.251337
$575$	−2.48260e11	−0.0947113
$576$	−7.97844e10	−0.0302007
$577$	2.47866e12	0.930949	0.465475	−	0.885061i	$-0.345884\pi$
$577$	2.47866e12	0.930949	0.465475	+	0.885061i	$0.345884\pi$
$578$	0	0
$579$	3.73492e12	1.38111
$580$	1.02440e12	0.375877
$581$	3.61410e12	1.31585
$582$	6.65085e11	0.240283
$583$	6.86662e10	0.0246170
$584$	−4.78523e12	−1.70233
$585$	−1.16168e10	−0.00410094
$586$	6.80085e11	0.238245
$587$	5.85645e11	0.203593	0.101796	−	0.994805i	$-0.467541\pi$
$587$	5.85645e11	0.203593	0.101796	+	0.994805i	$0.467541\pi$
$588$	1.27199e10	0.00438819
$589$	−1.28518e12	−0.439991
$590$	1.64041e12	0.557338
$591$	−2.12293e12	−0.715801
$592$	9.04978e11	0.302824
$593$	4.94064e12	1.64073	0.820365	−	0.571840i	$-0.193770\pi$
$593$	4.94064e12	1.64073	0.820365	+	0.571840i	$0.193770\pi$
$594$	9.67944e11	0.319015
$595$	0	0
$596$	1.66798e12	0.541479
$597$	−4.39021e11	−0.141449
$598$	−1.01815e11	−0.0325580
$599$	8.20879e11	0.260531	0.130265	−	0.991479i	$-0.458417\pi$
$599$	8.20879e11	0.260531	0.130265	+	0.991479i	$0.458417\pi$
$600$	1.82123e12	0.573699
$601$	2.83412e12	0.886101	0.443051	−	0.896497i	$-0.353896\pi$
$601$	2.83412e12	0.886101	0.443051	+	0.896497i	$0.353896\pi$
$602$	−3.43615e12	−1.06632
$603$	−1.62640e11	−0.0500957
$604$	5.61568e10	0.0171686
$605$	1.93260e12	0.586467
$606$	6.08122e11	0.183174
$607$	−5.35612e11	−0.160140	−0.0800702	−	0.996789i	$-0.525514\pi$
$607$	−5.35612e11	−0.160140	−0.0800702	+	0.996789i	$0.525514\pi$
$608$	5.59041e11	0.165912
$609$	−6.29339e12	−1.85399
$610$	−1.17648e12	−0.344033
$611$	−4.19144e11	−0.121669
$612$	0	0
$613$	−1.25611e12	−0.359298	−0.179649	−	0.983731i	$-0.557496\pi$
$613$	−1.25611e12	−0.359298	−0.179649	+	0.983731i	$0.557496\pi$
$614$	5.11411e12	1.45215
$615$	7.17460e11	0.202237
$616$	−1.44135e12	−0.403327
$617$	4.39177e12	1.21999	0.609996	−	0.792405i	$-0.291171\pi$
$617$	4.39177e12	1.21999	0.609996	+	0.792405i	$0.291171\pi$
$618$	3.85993e12	1.06446
$619$	2.69503e12	0.737830	0.368915	−	0.929463i	$-0.379729\pi$
$619$	2.69503e12	0.737830	0.368915	+	0.929463i	$0.379729\pi$
$620$	−1.08666e12	−0.295346
$621$	−6.64583e11	−0.179324
$622$	1.25556e11	0.0336342
$623$	−1.93469e12	−0.514536
$624$	5.09458e11	0.134517
$625$	−6.80578e11	−0.178409
$626$	−1.18784e12	−0.309152
$627$	−4.21734e11	−0.108977
$628$	6.15880e11	0.158008
$629$	0	0
$630$	−6.20106e10	−0.0156831
$631$	7.74703e12	1.94537	0.972687	−	0.232122i	$-0.0745669\pi$
$631$	7.74703e12	1.94537	0.972687	+	0.232122i	$0.0745669\pi$
$632$	3.71235e12	0.925597
$633$	−3.05897e12	−0.757284
$634$	3.28551e12	0.807609
$635$	2.36304e12	0.576752
$636$	7.79582e10	0.0188932
$637$	1.38841e10	0.00334110
$638$	−2.49624e12	−0.596477
$639$	−5.02497e10	−0.0119228
$640$	−1.04852e12	−0.247041
$641$	1.40190e12	0.327987	0.163994	−	0.986461i	$-0.447562\pi$
$641$	1.40190e12	0.327987	0.163994	+	0.986461i	$0.447562\pi$
$642$	6.67141e12	1.54992
$643$	1.34241e12	0.309695	0.154848	−	0.987938i	$-0.450511\pi$
$643$	1.34241e12	0.309695	0.154848	+	0.987938i	$0.450511\pi$
$644$	2.23065e11	0.0511028
$645$	−3.77147e12	−0.858009
$646$	0	0
$647$	2.03902e12	0.457458	0.228729	−	0.973490i	$-0.426543\pi$
$647$	2.03902e12	0.457458	0.228729	+	0.973490i	$0.426543\pi$
$648$	4.74105e12	1.05630
$649$	1.64061e12	0.362998
$650$	4.48085e11	0.0984578
$651$	6.67586e12	1.45678
$652$	−9.35948e11	−0.202833
$653$	−1.84441e11	−0.0396962	−0.0198481	−	0.999803i	$-0.506318\pi$
$653$	−1.84441e11	−0.0396962	−0.0198481	+	0.999803i	$0.506318\pi$
$654$	9.31554e11	0.199117
$655$	5.86951e12	1.24599
$656$	8.90752e11	0.187797
$657$	−2.05897e11	−0.0431128
$658$	−2.23741e12	−0.465295
$659$	−3.90936e12	−0.807461	−0.403731	−	0.914878i	$-0.632287\pi$
$659$	−3.90936e12	−0.807461	−0.403731	+	0.914878i	$0.632287\pi$
$660$	−3.56591e11	−0.0731514
$661$	1.24698e12	0.254070	0.127035	−	0.991898i	$-0.459454\pi$
$661$	1.24698e12	0.254070	0.127035	+	0.991898i	$0.459454\pi$
$662$	5.05157e12	1.02227
$663$	0	0
$664$	7.22037e12	1.44146
$665$	1.00841e12	0.199959
$666$	5.70885e10	0.0112438
$667$	1.71390e12	0.335289
$668$	−1.38970e12	−0.270039
$669$	6.33192e12	1.22213
$670$	−5.44872e12	−1.04462
$671$	−1.17662e12	−0.224071
$672$	−2.90395e12	−0.549322
$673$	7.46783e12	1.40322	0.701612	−	0.712559i	$-0.252464\pi$
$673$	7.46783e12	1.40322	0.701612	+	0.712559i	$0.252464\pi$
$674$	−2.95522e12	−0.551595
$675$	2.92480e12	0.542288
$676$	1.50454e12	0.277104
$677$	3.37053e12	0.616665	0.308332	−	0.951279i	$-0.400229\pi$
$677$	3.37053e12	0.616665	0.308332	+	0.951279i	$0.400229\pi$
$678$	5.73136e12	1.04166
$679$	−1.59048e12	−0.287154
$680$	0	0
$681$	5.13080e12	0.914162
$682$	2.64795e12	0.468683
$683$	2.41784e12	0.425142	0.212571	−	0.977146i	$-0.431816\pi$
$683$	2.41784e12	0.425142	0.212571	+	0.977146i	$0.431816\pi$
$684$	1.35548e10	0.00236777
$685$	5.12337e12	0.889094
$686$	4.92071e12	0.848338
$687$	9.89226e12	1.69430
$688$	−4.68241e12	−0.796748
$689$	8.50933e10	0.0143850
$690$	−5.96530e11	−0.100187
$691$	−5.96972e12	−0.996100	−0.498050	−	0.867148i	$-0.665950\pi$
$691$	−5.96972e12	−0.996100	−0.498050	+	0.867148i	$0.665950\pi$
$692$	−1.70167e12	−0.282096
$693$	−6.20181e10	−0.0102145
$694$	6.10250e12	0.998596
$695$	−4.36681e12	−0.709958
$696$	−1.25731e13	−2.03096
$697$	0	0
$698$	−3.36572e12	−0.536696
$699$	2.24377e12	0.355492
$700$	−9.81699e11	−0.154539
$701$	1.03450e13	1.61808	0.809042	−	0.587751i	$-0.199986\pi$
$701$	1.03450e13	1.61808	0.809042	+	0.587751i	$0.199986\pi$
$702$	1.19951e12	0.186417
$703$	−9.28369e11	−0.143358
$704$	−2.67323e12	−0.410166
$705$	−2.45574e12	−0.374397
$706$	−5.79524e12	−0.877911
$707$	−1.45426e12	−0.218905
$708$	1.86262e12	0.278595
$709$	8.01796e12	1.19167	0.595835	−	0.803107i	$-0.296821\pi$
$709$	8.01796e12	1.19167	0.595835	+	0.803107i	$0.296821\pi$
$710$	−1.68345e12	−0.248621
$711$	1.59734e11	0.0234414
$712$	−3.86519e12	−0.563652
$713$	−1.81806e12	−0.263454
$714$	0	0
$715$	−3.89228e11	−0.0556963
$716$	2.38929e12	0.339751
$717$	−1.40108e11	−0.0197982
$718$	4.59069e12	0.644641
$719$	6.72145e12	0.937957	0.468978	−	0.883210i	$-0.344622\pi$
$719$	6.72145e12	0.937957	0.468978	+	0.883210i	$0.344622\pi$
$720$	−8.45012e10	−0.0117183
$721$	−9.23062e12	−1.27210
$722$	−5.61105e12	−0.768469
$723$	−5.90859e12	−0.804195
$724$	3.35595e12	0.453934
$725$	−7.54281e12	−1.01394
$726$	−5.34659e12	−0.714269
$727$	−1.13938e13	−1.51274	−0.756369	−	0.654145i	$-0.773029\pi$
$727$	−1.13938e13	−1.51274	−0.756369	+	0.654145i	$0.773029\pi$
$728$	−1.78617e12	−0.235685
$729$	7.82381e12	1.02599
$730$	−6.89790e12	−0.899009
$731$	0	0
$732$	−1.33584e12	−0.171971
$733$	−1.29162e13	−1.65260	−0.826301	−	0.563228i	$-0.809559\pi$
$733$	−1.29162e13	−1.65260	−0.826301	+	0.563228i	$0.809559\pi$
$734$	−4.56232e12	−0.580168
$735$	8.13461e10	0.0102812
$736$	7.90842e11	0.0993435
$737$	−5.44938e12	−0.680367
$738$	5.61910e10	0.00697290
$739$	1.03277e13	1.27380	0.636902	−	0.770945i	$-0.280216\pi$
$739$	1.03277e13	1.27380	0.636902	+	0.770945i	$0.280216\pi$
$740$	−7.84968e11	−0.0962297
$741$	−5.22626e11	−0.0636809
$742$	4.54231e11	0.0550122
$743$	2.27020e12	0.273284	0.136642	−	0.990621i	$-0.456369\pi$
$743$	2.27020e12	0.273284	0.136642	+	0.990621i	$0.456369\pi$
$744$	1.33373e13	1.59584
$745$	1.06670e13	1.26864
$746$	1.28722e13	1.52170
$747$	3.10676e11	0.0365060
$748$	0	0
$749$	−1.59540e13	−1.85226
$750$	7.53079e12	0.869090
$751$	9.05954e12	1.03927	0.519633	−	0.854390i	$-0.326069\pi$
$751$	9.05954e12	1.03927	0.519633	+	0.854390i	$0.326069\pi$
$752$	−3.04889e12	−0.347665
$753$	−6.96869e12	−0.789902
$754$	−3.09342e12	−0.348552
$755$	3.59133e11	0.0402248
$756$	−2.62797e12	−0.292599
$757$	3.88407e12	0.429889	0.214944	−	0.976626i	$-0.431043\pi$
$757$	3.88407e12	0.429889	0.214944	+	0.976626i	$0.431043\pi$
$758$	8.69374e12	0.956523
$759$	−5.96602e11	−0.0652525
$760$	2.01464e12	0.219046
$761$	−6.01608e12	−0.650253	−0.325127	−	0.945670i	$-0.605407\pi$
$761$	−6.01608e12	−0.650253	−0.325127	+	0.945670i	$0.605407\pi$
$762$	−6.53740e12	−0.702438
$763$	−2.22772e12	−0.237957
$764$	6.27911e11	0.0666773
$765$	0	0
$766$	5.65699e12	0.593685
$767$	2.03309e12	0.212118
$768$	−7.52887e12	−0.780916
$769$	−3.71056e12	−0.382623	−0.191312	−	0.981529i	$-0.561274\pi$
$769$	−3.71056e12	−0.382623	−0.191312	+	0.981529i	$0.561274\pi$
$770$	−2.07771e12	−0.212998
$771$	1.51923e13	1.54838
$772$	−4.02211e12	−0.407545
$773$	7.74648e12	0.780363	0.390181	−	0.920738i	$-0.372412\pi$
$773$	7.74648e12	0.780363	0.390181	+	0.920738i	$0.372412\pi$
$774$	−2.95379e11	−0.0295832
$775$	8.00121e12	0.796706
$776$	−3.17752e12	−0.314565
$777$	4.82242e12	0.474647
$778$	−1.38103e13	−1.35143
$779$	−9.13775e11	−0.0889039
$780$	−4.41898e11	−0.0427461
$781$	−1.68365e12	−0.161928
$782$	0	0
$783$	−2.01918e13	−1.91976
$784$	1.00994e11	0.00954714
$785$	3.93866e12	0.370199
$786$	−1.62381e13	−1.51752
$787$	−1.47306e13	−1.36879	−0.684393	−	0.729114i	$-0.739933\pi$
$787$	−1.47306e13	−1.36879	−0.684393	+	0.729114i	$0.739933\pi$
$788$	2.28617e12	0.211223
$789$	−5.04593e12	−0.463548
$790$	5.35135e12	0.488811
$791$	−1.37060e13	−1.24484
$792$	−1.23902e11	−0.0111896
$793$	−1.45811e12	−0.130936
$794$	−1.07945e13	−0.963851
$795$	4.98557e11	0.0442652
$796$	4.72779e11	0.0417397
$797$	1.39364e12	0.122345	0.0611726	−	0.998127i	$-0.480516\pi$
$797$	1.39364e12	0.122345	0.0611726	+	0.998127i	$0.480516\pi$
$798$	−2.78979e12	−0.243534
$799$	0	0
$800$	−3.48046e12	−0.300422
$801$	−1.66310e11	−0.0142749
$802$	−9.13160e12	−0.779403
$803$	−6.89874e12	−0.585531
$804$	−6.18680e12	−0.522172
$805$	1.42654e12	0.119730
$806$	3.28142e12	0.273876
$807$	1.59131e13	1.32076
$808$	−2.90537e12	−0.239801
$809$	−1.50363e13	−1.23416	−0.617081	−	0.786899i	$-0.711685\pi$
$809$	−1.50363e13	−1.23416	−0.617081	+	0.786899i	$0.711685\pi$
$810$	6.83421e12	0.557835
$811$	−6.52258e12	−0.529451	−0.264725	−	0.964324i	$-0.585281\pi$
$811$	−6.52258e12	−0.529451	−0.264725	+	0.964324i	$0.585281\pi$
$812$	6.77731e12	0.547085
$813$	−1.32957e13	−1.06734
$814$	1.91279e12	0.152707
$815$	−5.98556e12	−0.475221
$816$	0	0
$817$	4.80343e12	0.377183
$818$	−1.06851e13	−0.834431
$819$	−7.68547e10	−0.00596888
$820$	−7.72628e11	−0.0596772
$821$	−4.89420e12	−0.375957	−0.187978	−	0.982173i	$-0.560193\pi$
$821$	−4.89420e12	−0.375957	−0.187978	+	0.982173i	$0.560193\pi$
$822$	−1.41739e13	−1.08284
$823$	2.23065e12	0.169485	0.0847425	−	0.996403i	$-0.472993\pi$
$823$	2.23065e12	0.169485	0.0847425	+	0.996403i	$0.472993\pi$
$824$	−1.84412e13	−1.39353
$825$	2.62562e12	0.197328
$826$	1.08527e13	0.811200
$827$	1.05655e12	0.0785446	0.0392723	−	0.999229i	$-0.487496\pi$
$827$	1.05655e12	0.0785446	0.0392723	+	0.999229i	$0.487496\pi$
$828$	1.91751e10	0.00141776
$829$	1.91993e13	1.41186	0.705928	−	0.708283i	$-0.250530\pi$
$829$	1.91993e13	1.41186	0.705928	+	0.708283i	$0.250530\pi$
$830$	1.04082e13	0.761241
$831$	1.64773e13	1.19862
$832$	−3.31275e12	−0.239681
$833$	0	0
$834$	1.20809e13	0.864672
$835$	−8.88736e12	−0.632679
$836$	4.54163e11	0.0321576
$837$	2.14189e13	1.50846
$838$	−1.04456e13	−0.731703
$839$	1.54194e13	1.07433	0.537166	−	0.843477i	$-0.319495\pi$
$839$	1.54194e13	1.07433	0.537166	+	0.843477i	$0.319495\pi$
$840$	−1.04651e13	−0.725245
$841$	3.75658e13	2.58947
$842$	5.70676e12	0.391278
$843$	−1.53112e13	−1.04420
$844$	3.29418e12	0.223464
$845$	9.62179e12	0.649233
$846$	−1.92332e11	−0.0129088
$847$	1.27858e13	0.853597
$848$	6.18975e11	0.0411048
$849$	8.07572e12	0.533454
$850$	0	0
$851$	−1.31331e12	−0.0858388
$852$	−1.91149e12	−0.124278
$853$	1.53610e13	0.993455	0.496727	−	0.867907i	$-0.334535\pi$
$853$	1.53610e13	0.993455	0.496727	+	0.867907i	$0.334535\pi$
$854$	−7.78341e12	−0.500737
$855$	8.66853e10	0.00554751
$856$	−3.18734e13	−2.02907
$857$	1.72627e13	1.09319	0.546595	−	0.837397i	$-0.315924\pi$
$857$	1.72627e13	1.09319	0.546595	+	0.837397i	$0.315924\pi$
$858$	1.07681e12	0.0678337
$859$	2.26812e13	1.42134	0.710669	−	0.703526i	$-0.248392\pi$
$859$	2.26812e13	1.42134	0.710669	+	0.703526i	$0.248392\pi$
$860$	4.06147e12	0.253186
$861$	4.74661e12	0.294354
$862$	−1.11232e13	−0.686194
$863$	6.94428e12	0.426166	0.213083	−	0.977034i	$-0.431650\pi$
$863$	6.94428e12	0.426166	0.213083	+	0.977034i	$0.431650\pi$
$864$	−9.31707e12	−0.568811
$865$	−1.08825e13	−0.660929
$866$	−1.16508e12	−0.0703920
$867$	0	0
$868$	−7.18918e12	−0.429874
$869$	5.35200e12	0.318366
$870$	−1.81242e13	−1.07256
$871$	−6.75304e12	−0.397574
$872$	−4.45060e12	−0.260672
$873$	−1.36721e11	−0.00796658
$874$	7.59755e11	0.0440425
$875$	−1.80091e13	−1.03862
$876$	−7.83228e12	−0.449386
$877$	−5.45893e12	−0.311608	−0.155804	−	0.987788i	$-0.549797\pi$
$877$	−5.45893e12	−0.311608	−0.155804	+	0.987788i	$0.549797\pi$
$878$	1.26872e13	0.720513
$879$	4.93841e12	0.279021
$880$	−2.83127e12	−0.159151
$881$	1.56062e13	0.872779	0.436390	−	0.899758i	$-0.356257\pi$
$881$	1.56062e13	0.872779	0.436390	+	0.899758i	$0.356257\pi$
$882$	6.37097e9	0.000354484 0
$883$	−8.94856e12	−0.495370	−0.247685	−	0.968841i	$-0.579670\pi$
$883$	−8.94856e12	−0.495370	−0.247685	+	0.968841i	$0.579670\pi$
$884$	0	0
$885$	1.19118e13	0.652727
$886$	1.92388e12	0.104888
$887$	−1.48899e12	−0.0807670	−0.0403835	−	0.999184i	$-0.512858\pi$
$887$	−1.48899e12	−0.0807670	−0.0403835	+	0.999184i	$0.512858\pi$
$888$	9.63440e12	0.519956
$889$	1.56335e13	0.839458
$890$	−5.57167e12	−0.297667
$891$	6.83505e12	0.363322
$892$	−6.81880e12	−0.360634
$893$	3.12769e12	0.164586
$894$	−2.95105e13	−1.54511
$895$	1.52800e13	0.796011
$896$	−6.93688e12	−0.359566
$897$	−7.39328e11	−0.0381304
$898$	−2.01174e11	−0.0103235
$899$	−5.52376e13	−2.82043
$900$	−8.43889e10	−0.00428740
$901$	0	0
$902$	1.88272e12	0.0947014
$903$	−2.49515e13	−1.24882
$904$	−2.73822e13	−1.36367
$905$	2.14619e13	1.06353
$906$	−9.93549e11	−0.0489905
$907$	3.88450e12	0.190591	0.0952954	−	0.995449i	$-0.469620\pi$
$907$	3.88450e12	0.190591	0.0952954	+	0.995449i	$0.469620\pi$
$908$	−5.52532e12	−0.269756
$909$	−1.25011e11	−0.00607313
$910$	−2.57476e12	−0.124466
$911$	−3.84104e13	−1.84764	−0.923818	−	0.382833i	$-0.874948\pi$
$911$	−3.84104e13	−1.84764	−0.923818	+	0.382833i	$0.874948\pi$
$912$	−3.80162e12	−0.181967
$913$	1.04094e13	0.495802
$914$	−2.23527e12	−0.105943
$915$	−8.54295e12	−0.402915
$916$	−1.06529e13	−0.499963
$917$	3.88318e13	1.81354
$918$	0	0
$919$	4.73291e12	0.218881	0.109441	−	0.993993i	$-0.465094\pi$
$919$	4.73291e12	0.218881	0.109441	+	0.993993i	$0.465094\pi$
$920$	2.84999e12	0.131159
$921$	3.71360e13	1.70069
$922$	−1.51376e12	−0.0689870
$923$	−2.08643e12	−0.0946231
$924$	−2.35915e12	−0.106471
$925$	5.77981e12	0.259583
$926$	−3.05939e13	−1.36737
$927$	−7.93484e11	−0.0352923
$928$	2.40279e13	1.06353
$929$	−1.52712e13	−0.672671	−0.336335	−	0.941742i	$-0.609188\pi$
$929$	−1.52712e13	−0.672671	−0.336335	+	0.941742i	$0.609188\pi$
$930$	1.92256e13	0.842767
$931$	−1.03604e11	−0.00451965
$932$	−2.41630e12	−0.104901
$933$	9.11723e11	0.0393908
$934$	3.39377e13	1.45922
$935$	0	0
$936$	−1.53543e11	−0.00653866
$937$	−2.13727e12	−0.0905797	−0.0452899	−	0.998974i	$-0.514421\pi$
$937$	−2.13727e12	−0.0905797	−0.0452899	+	0.998974i	$0.514421\pi$
$938$	−3.60479e13	−1.52043
$939$	−8.62543e12	−0.362064
$940$	2.64457e12	0.110479
$941$	−2.38440e12	−0.0991346	−0.0495673	−	0.998771i	$-0.515784\pi$
$941$	−2.38440e12	−0.0991346	−0.0495673	+	0.998771i	$0.515784\pi$
$942$	−1.08964e13	−0.450873
$943$	−1.29266e12	−0.0532332
$944$	1.47889e13	0.606124
$945$	−1.68064e13	−0.685536
$946$	−9.89689e12	−0.401780
$947$	−1.89384e13	−0.765189	−0.382595	−	0.923916i	$-0.624969\pi$
$947$	−1.89384e13	−0.765189	−0.382595	+	0.923916i	$0.624969\pi$
$948$	6.07623e12	0.244341
$949$	−8.54913e12	−0.342156
$950$	−3.34365e12	−0.133188
$951$	2.38576e13	0.945833
$952$	0	0
$953$	1.67573e13	0.658089	0.329045	−	0.944314i	$-0.393273\pi$
$953$	1.67573e13	0.658089	0.329045	+	0.944314i	$0.393273\pi$
$954$	3.90466e10	0.00152622
$955$	4.01560e12	0.156220
$956$	1.50881e11	0.00584217
$957$	−1.81264e13	−0.698566
$958$	−3.01045e13	−1.15475
$959$	3.38954e13	1.29407
$960$	−1.94092e13	−0.737544
$961$	3.21549e13	1.21616
$962$	2.37039e12	0.0892343
$963$	−1.37144e12	−0.0513876
$964$	6.36292e12	0.237306
$965$	−2.57221e13	−0.954847
$966$	−3.94655e12	−0.145821
$967$	−4.78486e13	−1.75975	−0.879873	−	0.475209i	$-0.842373\pi$
$967$	−4.78486e13	−1.75975	−0.879873	+	0.475209i	$0.842373\pi$
$968$	2.55439e13	0.935079
$969$	0	0
$970$	−4.58039e12	−0.166123
$971$	2.24909e13	0.811933	0.405966	−	0.913888i	$-0.366935\pi$
$971$	2.24909e13	0.811933	0.405966	+	0.913888i	$0.366935\pi$
$972$	−4.45760e11	−0.0160178
$973$	−2.88902e13	−1.03334
$974$	1.58157e13	0.563083
$975$	3.25375e12	0.115309
$976$	−1.06064e13	−0.374147
$977$	1.54105e13	0.541119	0.270559	−	0.962703i	$-0.412791\pi$
$977$	1.54105e13	0.541119	0.270559	+	0.962703i	$0.412791\pi$
$978$	1.65592e13	0.578780
$979$	−5.57235e12	−0.193872
$980$	−8.76010e10	−0.00303383
$981$	−1.91499e11	−0.00660171
$982$	1.20911e13	0.414918
$983$	−5.45274e13	−1.86262	−0.931309	−	0.364231i	$-0.881332\pi$
$983$	−5.45274e13	−1.86262	−0.931309	+	0.364231i	$0.881332\pi$
$984$	9.48294e12	0.322452
$985$	1.46205e13	0.494878
$986$	0	0
$987$	−1.62468e13	−0.544931
$988$	5.62813e11	0.0187913
$989$	6.79513e12	0.225847
$990$	−1.78604e11	−0.00590927
$991$	2.63091e12	0.0866510	0.0433255	−	0.999061i	$-0.486205\pi$
$991$	2.63091e12	0.0866510	0.0433255	+	0.999061i	$0.486205\pi$
$992$	−2.54882e13	−0.835672
$993$	3.66818e13	1.19723
$994$	−1.11374e13	−0.361865
$995$	3.02351e12	0.0977928
$996$	1.18180e13	0.380521
$997$	5.07497e13	1.62669	0.813345	−	0.581781i	$-0.197644\pi$
$997$	5.07497e13	1.62669	0.813345	+	0.581781i	$0.197644\pi$
$998$	−1.83714e13	−0.586211
$999$	1.54724e13	0.491487

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.h.1.25	yes	36
17.16	even	2		289.10.a.g.1.25	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.25	✓	36	17.16	even	2
289.10.a.h.1.25	yes	36	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q+19.0528 q^{2} +138.351 q^{3} -148.990 q^{4} -952.816 q^{5} +2635.99 q^{6} -6303.69 q^{7} -12593.7 q^{8} -541.879 q^{9} +O(q^{10})\)	\(q+19.0528 q^{2} +138.351 q^{3} -148.990 q^{4} -952.816 q^{5} +2635.99 q^{6} -6303.69 q^{7} -12593.7 q^{8} -541.879 q^{9} -18153.8 q^{10} -18156.0 q^{11} -20612.9 q^{12} -22499.5 q^{13} -120103. q^{14} -131823. q^{15} -163663. q^{16} -10324.3 q^{18} +167894. q^{19} +141960. q^{20} -872125. q^{21} -345924. q^{22} +237509. q^{23} -1.74236e6 q^{24} -1.04527e6 q^{25} -428680. q^{26} -2.79814e6 q^{27} +939185. q^{28} +7.21616e6 q^{29} -2.51161e6 q^{30} -7.65471e6 q^{31} +3.32974e6 q^{32} -2.51192e6 q^{33} +6.00626e6 q^{35} +80734.4 q^{36} -5.52951e6 q^{37} +3.19885e6 q^{38} -3.11284e6 q^{39} +1.19995e7 q^{40} -5.44258e6 q^{41} -1.66164e7 q^{42} +2.86100e7 q^{43} +2.70506e6 q^{44} +516311. q^{45} +4.52522e6 q^{46} +1.86290e7 q^{47} -2.26431e7 q^{48} -617083. q^{49} -1.99153e7 q^{50} +3.35220e6 q^{52} -3.78200e6 q^{53} -5.33125e7 q^{54} +1.72994e7 q^{55} +7.93869e7 q^{56} +2.32283e7 q^{57} +1.37488e8 q^{58} -9.03616e7 q^{59} +1.96403e7 q^{60} +6.48060e7 q^{61} -1.45844e8 q^{62} +3.41584e6 q^{63} +1.47237e8 q^{64} +2.14379e7 q^{65} -4.78591e7 q^{66} +3.00141e8 q^{67} +3.28597e7 q^{69} +1.14436e8 q^{70} +9.27324e7 q^{71} +6.82427e6 q^{72} +3.79969e8 q^{73} -1.05353e8 q^{74} -1.44614e8 q^{75} -2.50144e7 q^{76} +1.14450e8 q^{77} -5.93085e7 q^{78} -2.94778e8 q^{79} +1.55941e8 q^{80} -3.76461e8 q^{81} -1.03697e8 q^{82} -5.73331e8 q^{83} +1.29938e8 q^{84} +5.45101e8 q^{86} +9.98366e8 q^{87} +2.28652e8 q^{88} +3.06914e8 q^{89} +9.83718e6 q^{90} +1.41830e8 q^{91} -3.53864e7 q^{92} -1.05904e9 q^{93} +3.54936e8 q^{94} -1.59972e8 q^{95} +4.60674e8 q^{96} +2.52310e8 q^{97} -1.17572e7 q^{98} +9.83838e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9} + 60000 q^{10} + 76902 q^{11} + 373248 q^{12} + 54216 q^{13} + 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} + 6439479 q^{20} - 138102 q^{21} + 267324 q^{22} + 4041462 q^{23} + 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} + 13281612 q^{27} + 18614784 q^{28} + 4005936 q^{29} + 22471686 q^{30} + 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} + 22076682 q^{37} - 27401376 q^{38} + 62736162 q^{39} - 12231630 q^{40} + 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} - 49578936 q^{44} + 129308238 q^{45} + 140524827 q^{46} - 118557912 q^{47} + 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} + 209848575 q^{54} - 365439924 q^{55} + 203095059 q^{56} - 4614108 q^{57} - 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} + 175597116 q^{61} + 720602571 q^{62} + 587415936 q^{63} + 853082511 q^{64} + 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} + 1308709542 q^{71} - 275337849 q^{72} + 494841342 q^{73} + 1545361890 q^{74} + 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} + 2270624538 q^{78} + 1980107868 q^{79} + 2897000199 q^{80} + 1598298840 q^{81} + 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} - 2705904618 q^{88} + 148394658 q^{89} + 117916215 q^{90} + 636340896 q^{91} - 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} + 4878626298 q^{95} - 8390096634 q^{96} - 891786822 q^{97} + 4285627647 q^{98} - 1476187998 q^{99}+O(q^{100}) \) 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9 + 60000 * q^10 + 76902 * q^11 + 373248 * q^12 + 54216 * q^13 + 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 + 6439479 * q^20 - 138102 * q^21 + 267324 * q^22 + 4041462 * q^23 + 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 + 13281612 * q^27 + 18614784 * q^28 + 4005936 * q^29 + 22471686 * q^30 + 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 + 22076682 * q^37 - 27401376 * q^38 + 62736162 * q^39 - 12231630 * q^40 + 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 - 49578936 * q^44 + 129308238 * q^45 + 140524827 * q^46 - 118557912 * q^47 + 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 + 209848575 * q^54 - 365439924 * q^55 + 203095059 * q^56 - 4614108 * q^57 - 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 + 175597116 * q^61 + 720602571 * q^62 + 587415936 * q^63 + 853082511 * q^64 + 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 + 1308709542 * q^71 - 275337849 * q^72 + 494841342 * q^73 + 1545361890 * q^74 + 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 + 2270624538 * q^78 + 1980107868 * q^79 + 2897000199 * q^80 + 1598298840 * q^81 + 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 - 2705904618 * q^88 + 148394658 * q^89 + 117916215 * q^90 + 636340896 * q^91 - 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 + 4878626298 * q^95 - 8390096634 * q^96 - 891786822 * q^97 + 4285627647 * q^98 - 1476187998 * q^99

Introduction

L-functions

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