LMFDB - Embedded newform 289.10.a.h.1.13

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			1.13
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)

$f(q)$	$=$	$q-16.2320 q^{2} +276.194 q^{3} -248.524 q^{4} -1638.38 q^{5} -4483.17 q^{6} +8498.12 q^{7} +12344.8 q^{8} +56600.2 q^{9} +O(q^{10})$	\(q-16.2320 q^{2} +276.194 q^{3} -248.524 q^{4} -1638.38 q^{5} -4483.17 q^{6} +8498.12 q^{7} +12344.8 q^{8} +56600.2 q^{9} +26594.2 q^{10} +46186.5 q^{11} -68640.8 q^{12} +47090.3 q^{13} -137941. q^{14} -452512. q^{15} -73135.9 q^{16} -918732. q^{18} +192344. q^{19} +407177. q^{20} +2.34713e6 q^{21} -749697. q^{22} +1.30866e6 q^{23} +3.40956e6 q^{24} +731179. q^{25} -764368. q^{26} +1.01963e7 q^{27} -2.11198e6 q^{28} +3.14687e6 q^{29} +7.34516e6 q^{30} +3.13731e6 q^{31} -5.13339e6 q^{32} +1.27564e7 q^{33} -1.39232e7 q^{35} -1.40665e7 q^{36} -7.07531e6 q^{37} -3.12213e6 q^{38} +1.30061e7 q^{39} -2.02255e7 q^{40} +3.58972e6 q^{41} -3.80985e7 q^{42} +2.56336e7 q^{43} -1.14784e7 q^{44} -9.27329e7 q^{45} -2.12421e7 q^{46} -4.61978e7 q^{47} -2.01997e7 q^{48} +3.18645e7 q^{49} -1.18685e7 q^{50} -1.17031e7 q^{52} +7.23226e7 q^{53} -1.65506e8 q^{54} -7.56712e7 q^{55} +1.04907e8 q^{56} +5.31244e7 q^{57} -5.10799e7 q^{58} -6.44143e7 q^{59} +1.12460e8 q^{60} -1.13803e8 q^{61} -5.09247e7 q^{62} +4.80995e8 q^{63} +1.20771e8 q^{64} -7.71521e7 q^{65} -2.07062e8 q^{66} +3.92655e7 q^{67} +3.61444e8 q^{69} +2.26001e8 q^{70} -8.04952e7 q^{71} +6.98717e8 q^{72} -2.91761e8 q^{73} +1.14846e8 q^{74} +2.01947e8 q^{75} -4.78021e7 q^{76} +3.92498e8 q^{77} -2.11114e8 q^{78} -5.23679e8 q^{79} +1.19825e8 q^{80} +1.70210e9 q^{81} -5.82682e7 q^{82} -3.13638e8 q^{83} -5.83318e8 q^{84} -4.16084e8 q^{86} +8.69147e8 q^{87} +5.70162e8 q^{88} -6.56594e8 q^{89} +1.50524e9 q^{90} +4.00179e8 q^{91} -3.25232e8 q^{92} +8.66507e8 q^{93} +7.49881e8 q^{94} -3.15134e8 q^{95} -1.41781e9 q^{96} +1.11282e8 q^{97} -5.17223e8 q^{98} +2.61416e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−16.2320	−0.717358	−0.358679	−	0.933461i	$-0.616773\pi$
$2$	−16.2320	−0.717358	−0.358679	+	0.933461i	$0.616773\pi$
$3$	276.194	1.96865	0.984326	−	0.176360i	$-0.0564324\pi$
$3$	276.194	1.96865	0.984326	+	0.176360i	$0.0564324\pi$
$4$	−248.524	−0.485398
$5$	−1638.38	−1.17233	−0.586166	−	0.810191i	$-0.699363\pi$
$5$	−1638.38	−1.17233	−0.586166	+	0.810191i	$0.699363\pi$
$6$	−4483.17	−1.41223
$7$	8498.12	1.33777	0.668886	−	0.743365i	$-0.266772\pi$
$7$	8498.12	1.33777	0.668886	+	0.743365i	$0.266772\pi$
$8$	12344.8	1.06556
$9$	56600.2	2.87559
$10$	26594.2	0.840982
$11$	46186.5	0.951147	0.475573	−	0.879676i	$-0.342241\pi$
$11$	46186.5	0.951147	0.475573	+	0.879676i	$0.342241\pi$
$12$	−68640.8	−0.955579
$13$	47090.3	0.457285	0.228642	−	0.973510i	$-0.426571\pi$
$13$	47090.3	0.457285	0.228642	+	0.973510i	$0.426571\pi$
$14$	−137941.	−0.959661
$15$	−452512.	−2.30791
$16$	−73135.9	−0.278991
$17$	0	0
$17$	0	0
$18$	−918732.	−2.06283
$19$	192344.	0.338601	0.169301	−	0.985564i	$-0.445849\pi$
$19$	192344.	0.338601	0.169301	+	0.985564i	$0.445849\pi$
$20$	407177.	0.569048
$21$	2.34713e6	2.63360
$22$	−749697.	−0.682313
$23$	1.30866e6	0.975104	0.487552	−	0.873094i	$-0.337890\pi$
$23$	1.30866e6	0.975104	0.487552	+	0.873094i	$0.337890\pi$
$24$	3.40956e6	2.09772
$25$	731179.	0.374364
$26$	−764368.	−0.328037
$27$	1.01963e7	3.69238
$28$	−2.11198e6	−0.649351
$29$	3.14687e6	0.826205	0.413103	−	0.910684i	$-0.364445\pi$
$29$	3.14687e6	0.826205	0.413103	+	0.910684i	$0.364445\pi$
$30$	7.34516e6	1.65560
$31$	3.13731e6	0.610141	0.305070	−	0.952330i	$-0.401320\pi$
$31$	3.13731e6	0.610141	0.305070	+	0.952330i	$0.401320\pi$
$32$	−5.13339e6	−0.865425
$33$	1.27564e7	1.87248
$34$	0	0
$35$	−1.39232e7	−1.56831
$36$	−1.40665e7	−1.39580
$37$	−7.07531e6	−0.620637	−0.310318	−	0.950633i	$-0.600436\pi$
$37$	−7.07531e6	−0.620637	−0.310318	+	0.950633i	$0.600436\pi$
$38$	−3.12213e6	−0.242898
$39$	1.30061e7	0.900234
$40$	−2.02255e7	−1.24919
$41$	3.58972e6	0.198396	0.0991980	−	0.995068i	$-0.468372\pi$
$41$	3.58972e6	0.198396	0.0991980	+	0.995068i	$0.468372\pi$
$42$	−3.80985e7	−1.88924
$43$	2.56336e7	1.14341	0.571705	−	0.820460i	$-0.306282\pi$
$43$	2.56336e7	1.14341	0.571705	+	0.820460i	$0.306282\pi$
$44$	−1.14784e7	−0.461684
$45$	−9.27329e7	−3.37115
$46$	−2.12421e7	−0.699498
$47$	−4.61978e7	−1.38096	−0.690480	−	0.723351i	$-0.742601\pi$
$47$	−4.61978e7	−1.38096	−0.690480	+	0.723351i	$0.742601\pi$
$48$	−2.01997e7	−0.549237
$49$	3.18645e7	0.789631
$50$	−1.18685e7	−0.268553
$51$	0	0
$52$	−1.17031e7	−0.221965
$53$	7.23226e7	1.25902	0.629510	−	0.776993i	$-0.283256\pi$
$53$	7.23226e7	1.25902	0.629510	+	0.776993i	$0.283256\pi$
$54$	−1.65506e8	−2.64876
$55$	−7.56712e7	−1.11506
$56$	1.04907e8	1.42548
$57$	5.31244e7	0.666587
$58$	−5.10799e7	−0.592685
$59$	−6.44143e7	−0.692067	−0.346034	−	0.938222i	$-0.612472\pi$
$59$	−6.44143e7	−0.692067	−0.346034	+	0.938222i	$0.612472\pi$
$60$	1.12460e8	1.12026
$61$	−1.13803e8	−1.05237	−0.526185	−	0.850370i	$-0.676378\pi$
$61$	−1.13803e8	−1.05237	−0.526185	+	0.850370i	$0.676378\pi$
$62$	−5.09247e7	−0.437689
$63$	4.80995e8	3.84688
$64$	1.20771e8	0.899811
$65$	−7.71521e7	−0.536090
$66$	−2.07062e8	−1.34324
$67$	3.92655e7	0.238053	0.119027	−	0.992891i	$-0.462023\pi$
$67$	3.92655e7	0.238053	0.119027	+	0.992891i	$0.462023\pi$
$68$	0	0
$69$	3.61444e8	1.91964
$70$	2.26001e8	1.12504
$71$	−8.04952e7	−0.375930	−0.187965	−	0.982176i	$-0.560189\pi$
$71$	−8.04952e7	−0.375930	−0.187965	+	0.982176i	$0.560189\pi$
$72$	6.98717e8	3.06412
$73$	−2.91761e8	−1.20247	−0.601236	−	0.799071i	$-0.705325\pi$
$73$	−2.91761e8	−1.20247	−0.601236	+	0.799071i	$0.705325\pi$
$74$	1.14846e8	0.445219
$75$	2.01947e8	0.736992
$76$	−4.78021e7	−0.164356
$77$	3.92498e8	1.27242
$78$	−2.11114e8	−0.645790
$79$	−5.23679e8	−1.51267	−0.756333	−	0.654187i	$-0.773011\pi$
$79$	−5.23679e8	−1.51267	−0.756333	+	0.654187i	$0.773011\pi$
$80$	1.19825e8	0.327071
$81$	1.70210e9	4.39342
$82$	−5.82682e7	−0.142321
$83$	−3.13638e8	−0.725398	−0.362699	−	0.931906i	$-0.618145\pi$
$83$	−3.13638e8	−0.725398	−0.362699	+	0.931906i	$0.618145\pi$
$84$	−5.83318e8	−1.27835
$85$	0	0
$86$	−4.16084e8	−0.820234
$87$	8.69147e8	1.62651
$88$	5.70162e8	1.01351
$89$	−6.56594e8	−1.10928	−0.554641	−	0.832090i	$-0.687144\pi$
$89$	−6.56594e8	−1.10928	−0.554641	+	0.832090i	$0.687144\pi$
$90$	1.50524e9	2.41832
$91$	4.00179e8	0.611742
$92$	−3.25232e8	−0.473313
$93$	8.66507e8	1.20115
$94$	7.49881e8	0.990643
$95$	−3.15134e8	−0.396953
$96$	−1.41781e9	−1.70372
$97$	1.11282e8	0.127630	0.0638151	−	0.997962i	$-0.479673\pi$
$97$	1.11282e8	0.127630	0.0638151	+	0.997962i	$0.479673\pi$
$98$	−5.17223e8	−0.566448
$99$	2.61416e9	2.73511
$100$	−1.81715e8	−0.181715
$101$	8.39306e8	0.802554	0.401277	−	0.915957i	$-0.368566\pi$
$101$	8.39306e8	0.802554	0.401277	+	0.915957i	$0.368566\pi$
$102$	0	0
$103$	1.31010e9	1.14693	0.573467	−	0.819229i	$-0.305598\pi$
$103$	1.31010e9	1.14693	0.573467	+	0.819229i	$0.305598\pi$
$104$	5.81320e8	0.487265
$105$	−3.84550e9	−3.08746
$106$	−1.17394e9	−0.903167
$107$	−8.31146e8	−0.612986	−0.306493	−	0.951873i	$-0.599156\pi$
$107$	−8.31146e8	−0.612986	−0.306493	+	0.951873i	$0.599156\pi$
$108$	−2.53402e9	−1.79227
$109$	1.16494e9	0.790470	0.395235	−	0.918580i	$-0.370663\pi$
$109$	1.16494e9	0.790470	0.395235	+	0.918580i	$0.370663\pi$
$110$	1.22829e9	0.799897
$111$	−1.95416e9	−1.22182
$112$	−6.21518e8	−0.373227
$113$	−1.30540e9	−0.753164	−0.376582	−	0.926383i	$-0.622901\pi$
$113$	−1.30540e9	−0.753164	−0.376582	+	0.926383i	$0.622901\pi$
$114$	−8.62313e8	−0.478182
$115$	−2.14408e9	−1.14315
$116$	−7.82072e8	−0.401038
$117$	2.66532e9	1.31496
$118$	1.04557e9	0.496460
$119$	0	0
$120$	−5.58617e9	−2.45923
$121$	−2.24759e8	−0.0953197
$122$	1.84724e9	0.754925
$123$	9.91459e8	0.390573
$124$	−7.79696e8	−0.296161
$125$	2.00202e9	0.733454
$126$	−7.80750e9	−2.75959
$127$	1.36724e9	0.466367	0.233184	−	0.972433i	$-0.425086\pi$
$127$	1.36724e9	0.466367	0.233184	+	0.972433i	$0.425086\pi$
$128$	6.67953e8	0.219939
$129$	7.07985e9	2.25097
$130$	1.25233e9	0.384568
$131$	3.65407e9	1.08407	0.542034	−	0.840357i	$-0.317654\pi$
$131$	3.65407e9	1.08407	0.542034	+	0.840357i	$0.317654\pi$
$132$	−3.17027e9	−0.908896
$133$	1.63457e9	0.452971
$134$	−6.37355e8	−0.170769
$135$	−1.67055e10	−4.32870
$136$	0	0
$137$	−1.90939e9	−0.463077	−0.231538	−	0.972826i	$-0.574376\pi$
$137$	−1.90939e9	−0.463077	−0.231538	+	0.972826i	$0.574376\pi$
$138$	−5.86694e9	−1.37707
$139$	8.29279e9	1.88423	0.942115	−	0.335289i	$-0.108834\pi$
$139$	8.29279e9	1.88423	0.942115	+	0.335289i	$0.108834\pi$
$140$	3.46024e9	0.761255
$141$	−1.27596e10	−2.71863
$142$	1.30659e9	0.269677
$143$	2.17494e9	0.434945
$144$	−4.13951e9	−0.802265
$145$	−5.15579e9	−0.968587
$146$	4.73586e9	0.862603
$147$	8.80078e9	1.55451
$148$	1.75838e9	0.301256
$149$	1.38793e9	0.230690	0.115345	−	0.993326i	$-0.463203\pi$
$149$	1.38793e9	0.230690	0.115345	+	0.993326i	$0.463203\pi$
$150$	−3.27800e9	−0.528687
$151$	7.05930e9	1.10501	0.552504	−	0.833510i	$-0.313672\pi$
$151$	7.05930e9	1.10501	0.552504	+	0.833510i	$0.313672\pi$
$152$	2.37445e9	0.360800
$153$	0	0
$154$	−6.37101e9	−0.912778
$155$	−5.14012e9	−0.715288
$156$	−3.23232e9	−0.436972
$157$	−3.82538e9	−0.502489	−0.251244	−	0.967924i	$-0.580840\pi$
$157$	−3.82538e9	−0.502489	−0.251244	+	0.967924i	$0.580840\pi$
$158$	8.50033e9	1.08512
$159$	1.99751e10	2.47857
$160$	8.41047e9	1.01457
$161$	1.11211e10	1.30447
$162$	−2.76284e10	−3.15165
$163$	−1.16179e10	−1.28909	−0.644545	−	0.764567i	$-0.722953\pi$
$163$	−1.16179e10	−1.28909	−0.644545	+	0.764567i	$0.722953\pi$
$164$	−8.92130e8	−0.0963010
$165$	−2.08999e10	−2.19517
$166$	5.09095e9	0.520370
$167$	−3.47032e9	−0.345259	−0.172630	−	0.984987i	$-0.555226\pi$
$167$	−3.47032e9	−0.345259	−0.172630	+	0.984987i	$0.555226\pi$
$168$	2.89748e10	2.80627
$169$	−8.38700e9	−0.790891
$170$	0	0
$171$	1.08867e10	0.973677
$172$	−6.37056e9	−0.555008
$173$	1.36446e8	0.0115812	0.00579061	−	0.999983i	$-0.498157\pi$
$173$	1.36446e8	0.0115812	0.00579061	+	0.999983i	$0.498157\pi$
$174$	−1.41080e10	−1.16679
$175$	6.21365e9	0.500813
$176$	−3.37789e9	−0.265362
$177$	−1.77909e10	−1.36244
$178$	1.06578e10	0.795752
$179$	1.66738e10	1.21394	0.606969	−	0.794726i	$-0.292385\pi$
$179$	1.66738e10	1.21394	0.606969	+	0.794726i	$0.292385\pi$
$180$	2.30463e10	1.63635
$181$	−5.19059e9	−0.359471	−0.179735	−	0.983715i	$-0.557524\pi$
$181$	−5.19059e9	−0.359471	−0.179735	+	0.983715i	$0.557524\pi$
$182$	−6.49570e9	−0.438838
$183$	−3.14316e10	−2.07175
$184$	1.61551e10	1.03903
$185$	1.15921e10	0.727593
$186$	−1.40651e10	−0.861657
$187$	0	0
$188$	1.14813e10	0.670315
$189$	8.66495e10	4.93956
$190$	5.11524e9	0.284757
$191$	2.87746e10	1.56444	0.782220	−	0.623003i	$-0.214087\pi$
$191$	2.87746e10	1.56444	0.782220	+	0.623003i	$0.214087\pi$
$192$	3.33561e10	1.77141
$193$	−1.92651e10	−0.999455	−0.499727	−	0.866183i	$-0.666566\pi$
$193$	−1.92651e10	−0.999455	−0.499727	+	0.866183i	$0.666566\pi$
$194$	−1.80633e9	−0.0915565
$195$	−2.13090e10	−1.05537
$196$	−7.91907e9	−0.383285
$197$	7.46589e9	0.353170	0.176585	−	0.984285i	$-0.443495\pi$
$197$	7.46589e9	0.353170	0.176585	+	0.984285i	$0.443495\pi$
$198$	−4.24330e10	−1.96205
$199$	−2.74384e10	−1.24028	−0.620140	−	0.784491i	$-0.712924\pi$
$199$	−2.74384e10	−1.24028	−0.620140	+	0.784491i	$0.712924\pi$
$200$	9.02625e9	0.398908
$201$	1.08449e10	0.468644
$202$	−1.36236e10	−0.575719
$203$	2.67425e10	1.10527
$204$	0	0
$205$	−5.88134e9	−0.232586
$206$	−2.12655e10	−0.822762
$207$	7.40703e10	2.80400
$208$	−3.44400e9	−0.127579
$209$	8.88371e9	0.322059
$210$	6.24201e10	2.21481
$211$	1.26357e10	0.438863	0.219432	−	0.975628i	$-0.429580\pi$
$211$	1.26357e10	0.438863	0.219432	+	0.975628i	$0.429580\pi$
$212$	−1.79739e10	−0.611125
$213$	−2.22323e10	−0.740076
$214$	1.34911e10	0.439730
$215$	−4.19977e10	−1.34046
$216$	1.25871e11	3.93446
$217$	2.66613e10	0.816228
$218$	−1.89093e10	−0.567050
$219$	−8.05828e10	−2.36725
$220$	1.88061e10	0.541248
$221$	0	0
$222$	3.17198e10	0.876480
$223$	5.64536e10	1.52869	0.764346	−	0.644806i	$-0.223062\pi$
$223$	5.64536e10	1.52869	0.764346	+	0.644806i	$0.223062\pi$
$224$	−4.36242e10	−1.15774
$225$	4.13849e10	1.07652
$226$	2.11892e10	0.540288
$227$	−4.94426e9	−0.123591	−0.0617953	−	0.998089i	$-0.519683\pi$
$227$	−4.94426e9	−0.123591	−0.0617953	+	0.998089i	$0.519683\pi$
$228$	−1.32027e10	−0.323560
$229$	−5.68904e10	−1.36703	−0.683516	−	0.729935i	$-0.739550\pi$
$229$	−5.68904e10	−1.36703	−0.683516	+	0.729935i	$0.739550\pi$
$230$	3.48027e10	0.820045
$231$	1.08406e11	2.50494
$232$	3.88474e10	0.880373
$233$	7.42331e10	1.65005	0.825023	−	0.565099i	$-0.191162\pi$
$233$	7.42331e10	1.65005	0.825023	+	0.565099i	$0.191162\pi$
$234$	−4.32634e10	−0.943299
$235$	7.56898e10	1.61895
$236$	1.60085e10	0.335928
$237$	−1.44637e11	−2.97791
$238$	0	0
$239$	4.47275e10	0.886715	0.443357	−	0.896345i	$-0.353787\pi$
$239$	4.47275e10	0.886715	0.443357	+	0.896345i	$0.353787\pi$
$240$	3.30949e10	0.643888
$241$	2.80613e10	0.535835	0.267918	−	0.963442i	$-0.413665\pi$
$241$	2.80613e10	0.535835	0.267918	+	0.963442i	$0.413665\pi$
$242$	3.64827e9	0.0683783
$243$	2.69416e11	4.95673
$244$	2.82826e10	0.510817
$245$	−5.22063e10	−0.925711
$246$	−1.60933e10	−0.280180
$247$	9.05756e9	0.154837
$248$	3.87294e10	0.650143
$249$	−8.66248e10	−1.42806
$250$	−3.24967e10	−0.526149
$251$	6.53333e10	1.03897	0.519485	−	0.854480i	$-0.326124\pi$
$251$	6.53333e10	1.03897	0.519485	+	0.854480i	$0.326124\pi$
$252$	−1.19539e11	−1.86727
$253$	6.04423e10	0.927467
$254$	−2.21930e10	−0.334552
$255$	0	0
$256$	−7.26767e10	−1.05759
$257$	4.29846e10	0.614630	0.307315	−	0.951608i	$-0.400569\pi$
$257$	4.29846e10	0.614630	0.307315	+	0.951608i	$0.400569\pi$
$258$	−1.14920e11	−1.61475
$259$	−6.01268e10	−0.830270
$260$	1.91741e10	0.260217
$261$	1.78114e11	2.37583
$262$	−5.93127e10	−0.777664
$263$	2.22590e10	0.286882	0.143441	−	0.989659i	$-0.454183\pi$
$263$	2.22590e10	0.286882	0.143441	+	0.989659i	$0.454183\pi$
$264$	1.57475e11	1.99524
$265$	−1.18492e11	−1.47599
$266$	−2.65322e10	−0.324942
$267$	−1.81347e11	−2.18379
$268$	−9.75840e9	−0.115551
$269$	2.70459e10	0.314931	0.157466	−	0.987524i	$-0.449668\pi$
$269$	2.70459e10	0.314931	0.157466	+	0.987524i	$0.449668\pi$
$270$	2.71163e11	3.10522
$271$	1.20580e11	1.35805	0.679023	−	0.734117i	$-0.262404\pi$
$271$	1.20580e11	1.35805	0.679023	+	0.734117i	$0.262404\pi$
$272$	0	0
$273$	1.10527e11	1.20431
$274$	3.09932e10	0.332192
$275$	3.37706e10	0.356075
$276$	−8.98273e10	−0.931788
$277$	−1.46871e11	−1.49891	−0.749456	−	0.662055i	$-0.769685\pi$
$277$	−1.46871e11	−1.49891	−0.749456	+	0.662055i	$0.769685\pi$
$278$	−1.34608e11	−1.35167
$279$	1.77572e11	1.75451
$280$	−1.71879e11	−1.67113
$281$	−1.74963e11	−1.67404	−0.837022	−	0.547169i	$-0.815705\pi$
$281$	−1.74963e11	−1.67404	−0.837022	+	0.547169i	$0.815705\pi$
$282$	2.07113e11	1.95023
$283$	8.22402e10	0.762159	0.381079	−	0.924542i	$-0.375552\pi$
$283$	8.22402e10	0.762159	0.381079	+	0.924542i	$0.375552\pi$
$284$	2.00050e10	0.182476
$285$	−8.70382e10	−0.781462
$286$	−3.53035e10	−0.312011
$287$	3.05059e10	0.265408
$288$	−2.90551e11	−2.48861
$289$	0	0
$290$	8.36885e10	0.694824
$291$	3.07355e10	0.251259
$292$	7.25096e10	0.583677
$293$	−1.72364e10	−0.136629	−0.0683144	−	0.997664i	$-0.521762\pi$
$293$	−1.72364e10	−0.136629	−0.0683144	+	0.997664i	$0.521762\pi$
$294$	−1.42854e11	−1.11514
$295$	1.05535e11	0.811333
$296$	−8.73432e10	−0.661327
$297$	4.70932e11	3.51199
$298$	−2.25287e10	−0.165487
$299$	6.16251e10	0.445900
$300$	−5.01887e10	−0.357734
$301$	2.17838e11	1.52962
$302$	−1.14586e11	−0.792687
$303$	2.31811e11	1.57995
$304$	−1.40673e10	−0.0944668
$305$	1.86453e11	1.23373
$306$	0	0
$307$	−2.56161e11	−1.64585	−0.822925	−	0.568150i	$-0.807659\pi$
$307$	−2.56161e11	−1.64585	−0.822925	+	0.568150i	$0.807659\pi$
$308$	−9.75451e10	−0.617628
$309$	3.61843e11	2.25791
$310$	8.34342e10	0.513117
$311$	−9.76715e10	−0.592033	−0.296017	−	0.955183i	$-0.595658\pi$
$311$	−9.76715e10	−0.592033	−0.296017	+	0.955183i	$0.595658\pi$
$312$	1.60557e11	0.959255
$313$	−2.36302e11	−1.39161	−0.695805	−	0.718230i	$-0.744952\pi$
$313$	−2.36302e11	−1.39161	−0.695805	+	0.718230i	$0.744952\pi$
$314$	6.20935e10	0.360464
$315$	−7.88055e11	−4.50982
$316$	1.30147e11	0.734245
$317$	−4.50722e10	−0.250693	−0.125346	−	0.992113i	$-0.540004\pi$
$317$	−4.50722e10	−0.250693	−0.125346	+	0.992113i	$0.540004\pi$
$318$	−3.24234e11	−1.77802
$319$	1.45343e11	0.785843
$320$	−1.97869e11	−1.05488
$321$	−2.29558e11	−1.20676
$322$	−1.80518e11	−0.935769
$323$	0	0
$324$	−4.23012e11	−2.13255
$325$	3.44315e10	0.171191
$326$	1.88581e11	0.924738
$327$	3.21750e11	1.55616
$328$	4.43143e10	0.211403
$329$	−3.92595e11	−1.84741
$330$	3.39247e11	1.57472
$331$	−5.28894e10	−0.242183	−0.121091	−	0.992641i	$-0.538639\pi$
$331$	−5.28894e10	−0.242183	−0.121091	+	0.992641i	$0.538639\pi$
$332$	7.79463e10	0.352107
$333$	−4.00464e11	−1.78470
$334$	5.63301e10	0.247674
$335$	−6.43319e10	−0.279078
$336$	−1.71660e11	−0.734753
$337$	1.59919e11	0.675408	0.337704	−	0.941252i	$-0.390350\pi$
$337$	1.59919e11	0.675408	0.337704	+	0.941252i	$0.390350\pi$
$338$	1.36137e11	0.567352
$339$	−3.60543e11	−1.48272
$340$	0	0
$341$	1.44901e11	0.580333
$342$	−1.76713e11	−0.698475
$343$	−7.21417e10	−0.281425
$344$	3.16441e11	1.21837
$345$	−5.92184e11	−2.25046
$346$	−2.21479e9	−0.00830789
$347$	−4.45690e11	−1.65025	−0.825127	−	0.564948i	$-0.808896\pi$
$347$	−4.45690e11	−1.65025	−0.825127	+	0.564948i	$0.808896\pi$
$348$	−2.16004e11	−0.789504
$349$	−2.71132e10	−0.0978286	−0.0489143	−	0.998803i	$-0.515576\pi$
$349$	−2.71132e10	−0.0978286	−0.0489143	+	0.998803i	$0.515576\pi$
$350$	−1.00860e11	−0.359262
$351$	4.80148e11	1.68847
$352$	−2.37093e11	−0.823146
$353$	−3.52177e11	−1.20719	−0.603594	−	0.797292i	$-0.706265\pi$
$353$	−3.52177e11	−1.20719	−0.603594	+	0.797292i	$0.706265\pi$
$354$	2.88780e11	0.977357
$355$	1.31882e11	0.440715
$356$	1.63179e11	0.538442
$357$	0	0
$358$	−2.70649e11	−0.870828
$359$	−3.28144e11	−1.04265	−0.521326	−	0.853358i	$-0.674562\pi$
$359$	−3.28144e11	−1.04265	−0.521326	+	0.853358i	$0.674562\pi$
$360$	−1.14477e12	−3.59216
$361$	−2.85691e11	−0.885349
$362$	8.42535e10	0.257869
$363$	−6.20771e10	−0.187651
$364$	−9.94540e10	−0.296938
$365$	4.78018e11	1.40970
$366$	5.10197e11	1.48618
$367$	−3.76306e11	−1.08279	−0.541394	−	0.840769i	$-0.682103\pi$
$367$	−3.76306e11	−1.08279	−0.541394	+	0.840769i	$0.682103\pi$
$368$	−9.57099e10	−0.272046
$369$	2.03179e11	0.570505
$370$	−1.88162e11	−0.521944
$371$	6.14606e11	1.68428
$372$	−2.15347e11	−0.583037
$373$	2.49099e11	0.666319	0.333159	−	0.942871i	$-0.391885\pi$
$373$	2.49099e11	0.666319	0.333159	+	0.942871i	$0.391885\pi$
$374$	0	0
$375$	5.52945e11	1.44391
$376$	−5.70302e11	−1.47150
$377$	1.48187e11	0.377811
$378$	−1.40649e12	−3.54343
$379$	7.54823e11	1.87918	0.939590	−	0.342301i	$-0.111206\pi$
$379$	7.54823e11	1.87918	0.939590	+	0.342301i	$0.111206\pi$
$380$	7.83183e10	0.192680
$381$	3.77624e11	0.918114
$382$	−4.67068e11	−1.12226
$383$	5.92227e11	1.40635	0.703176	−	0.711016i	$-0.251765\pi$
$383$	5.92227e11	1.40635	0.703176	+	0.711016i	$0.251765\pi$
$384$	1.84485e11	0.432982
$385$	−6.43063e11	−1.49170
$386$	3.12710e11	0.716967
$387$	1.45087e12	3.28797
$388$	−2.76563e10	−0.0619514
$389$	8.71873e11	1.93055	0.965273	−	0.261243i	$-0.0841322\pi$
$389$	8.71873e11	1.93055	0.965273	+	0.261243i	$0.0841322\pi$
$390$	3.45886e11	0.757081
$391$	0	0
$392$	3.93360e11	0.841401
$393$	1.00923e12	2.13415
$394$	−1.21186e11	−0.253349
$395$	8.57987e11	1.77335
$396$	−6.49681e11	−1.32761
$397$	1.93481e11	0.390913	0.195457	−	0.980712i	$-0.437381\pi$
$397$	1.93481e11	0.390913	0.195457	+	0.980712i	$0.437381\pi$
$398$	4.45379e11	0.889725
$399$	4.51458e11	0.891741
$400$	−5.34755e10	−0.104444
$401$	2.79164e11	0.539150	0.269575	−	0.962979i	$-0.413117\pi$
$401$	2.79164e11	0.539150	0.269575	+	0.962979i	$0.413117\pi$
$402$	−1.76034e11	−0.336185
$403$	1.47737e11	0.279008
$404$	−2.08587e11	−0.389558
$405$	−2.78869e12	−5.15055
$406$	−4.34083e11	−0.792877
$407$	−3.26783e11	−0.590317
$408$	0	0
$409$	−4.08871e11	−0.722490	−0.361245	−	0.932471i	$-0.617648\pi$
$409$	−4.08871e11	−0.722490	−0.361245	+	0.932471i	$0.617648\pi$
$410$	9.54656e10	0.166848
$411$	−5.27363e11	−0.911637
$412$	−3.25592e11	−0.556719
$413$	−5.47401e11	−0.925828
$414$	−1.20231e12	−2.01147
$415$	5.13859e11	0.850408
$416$	−2.41733e11	−0.395746
$417$	2.29042e12	3.70939
$418$	−1.44200e11	−0.231032
$419$	4.92234e11	0.780205	0.390103	−	0.920771i	$-0.372440\pi$
$419$	4.92234e11	0.780205	0.390103	+	0.920771i	$0.372440\pi$
$420$	9.55699e11	1.49865
$421$	7.95456e11	1.23409	0.617045	−	0.786928i	$-0.288330\pi$
$421$	7.95456e11	1.23409	0.617045	+	0.786928i	$0.288330\pi$
$422$	−2.05103e11	−0.314822
$423$	−2.61481e12	−3.97107
$424$	8.92807e11	1.34156
$425$	0	0
$426$	3.60874e11	0.530899
$427$	−9.67109e11	−1.40783
$428$	2.06559e11	0.297542
$429$	6.00705e11	0.856255
$430$	6.81705e11	0.961587
$431$	−1.05149e11	−0.146777	−0.0733884	−	0.997303i	$-0.523381\pi$
$431$	−1.05149e11	−0.146777	−0.0733884	+	0.997303i	$0.523381\pi$
$432$	−7.45717e11	−1.03014
$433$	−2.40019e11	−0.328134	−0.164067	−	0.986449i	$-0.552461\pi$
$433$	−2.40019e11	−0.328134	−0.164067	+	0.986449i	$0.552461\pi$
$434$	−4.32764e11	−0.585528
$435$	−1.42400e12	−1.90681
$436$	−2.89516e11	−0.383692
$437$	2.51713e11	0.330171
$438$	1.30802e12	1.69816
$439$	9.58953e11	1.23227	0.616137	−	0.787639i	$-0.288697\pi$
$439$	9.58953e11	1.23227	0.616137	+	0.787639i	$0.288697\pi$
$440$	−9.34145e11	−1.18817
$441$	1.80354e12	2.27065
$442$	0	0
$443$	−1.36741e12	−1.68688	−0.843439	−	0.537225i	$-0.819472\pi$
$443$	−1.36741e12	−1.68688	−0.843439	+	0.537225i	$0.819472\pi$
$444$	4.85654e11	0.593067
$445$	1.07575e12	1.30045
$446$	−9.16353e11	−1.09662
$447$	3.83337e11	0.454147
$448$	1.02632e12	1.20374
$449$	7.35282e11	0.853779	0.426889	−	0.904304i	$-0.359609\pi$
$449$	7.35282e11	0.853779	0.426889	+	0.904304i	$0.359609\pi$
$450$	−6.71758e11	−0.772247
$451$	1.65796e11	0.188704
$452$	3.24422e11	0.365584
$453$	1.94974e12	2.17538
$454$	8.02551e10	0.0886587
$455$	−6.55648e11	−0.717165
$456$	6.55809e11	0.710290
$457$	−1.16538e12	−1.24981	−0.624904	−	0.780702i	$-0.714862\pi$
$457$	−1.16538e12	−1.24981	−0.624904	+	0.780702i	$0.714862\pi$
$458$	9.23442e11	0.980652
$459$	0	0
$460$	5.32856e11	0.554880
$461$	1.00400e12	1.03533	0.517665	−	0.855583i	$-0.326801\pi$
$461$	1.00400e12	1.03533	0.517665	+	0.855583i	$0.326801\pi$
$462$	−1.75964e12	−1.79694
$463$	7.44078e11	0.752496	0.376248	−	0.926519i	$-0.377214\pi$
$463$	7.44078e11	0.752496	0.376248	+	0.926519i	$0.377214\pi$
$464$	−2.30149e11	−0.230504
$465$	−1.41967e12	−1.40815
$466$	−1.20495e12	−1.18367
$467$	−8.92235e11	−0.868067	−0.434034	−	0.900897i	$-0.642910\pi$
$467$	−8.92235e11	−0.868067	−0.434034	+	0.900897i	$0.642910\pi$
$468$	−6.62396e11	−0.638280
$469$	3.33683e11	0.318461
$470$	−1.22859e12	−1.16136
$471$	−1.05655e12	−0.989226
$472$	−7.95181e11	−0.737441
$473$	1.18393e12	1.08755
$474$	2.34774e12	2.13623
$475$	1.40638e11	0.126760
$476$	0	0
$477$	4.09347e12	3.62042
$478$	−7.26015e11	−0.636092
$479$	8.19136e8	0.000710962 0	0.000355481	−	1.00000i	$-0.499887\pi$
$479$	8.19136e8	0.000710962 0	0.000355481		1.00000i	$0.499887\pi$
$480$	2.32292e12	1.99733
$481$	−3.33179e11	−0.283808
$482$	−4.55490e11	−0.384386
$483$	3.07159e12	2.56804
$484$	5.58579e10	0.0462679
$485$	−1.82323e11	−0.149625
$486$	−4.37315e12	−3.55575
$487$	−2.03907e12	−1.64267	−0.821336	−	0.570444i	$-0.806771\pi$
$487$	−2.03907e12	−1.64267	−0.821336	+	0.570444i	$0.806771\pi$
$488$	−1.40487e12	−1.12136
$489$	−3.20879e12	−2.53777
$490$	8.47410e11	0.664066
$491$	−6.01145e11	−0.466780	−0.233390	−	0.972383i	$-0.574982\pi$
$491$	−6.01145e11	−0.466780	−0.233390	+	0.972383i	$0.574982\pi$
$492$	−2.46401e11	−0.189583
$493$	0	0
$494$	−1.47022e11	−0.111074
$495$	−4.28300e12	−3.20645
$496$	−2.29450e11	−0.170224
$497$	−6.84058e11	−0.502909
$498$	1.40609e12	1.02443
$499$	−1.26416e12	−0.912742	−0.456371	−	0.889790i	$-0.650851\pi$
$499$	−1.26416e12	−0.912742	−0.456371	+	0.889790i	$0.650851\pi$
$500$	−4.97548e11	−0.356017
$501$	−9.58482e11	−0.679695
$502$	−1.06049e12	−0.745313
$503$	4.72983e11	0.329450	0.164725	−	0.986340i	$-0.447326\pi$
$503$	4.72983e11	0.329450	0.164725	+	0.986340i	$0.447326\pi$
$504$	5.93779e12	4.09909
$505$	−1.37511e12	−0.940860
$506$	−9.81096e11	−0.665326
$507$	−2.31644e12	−1.55699
$508$	−3.39791e11	−0.226373
$509$	7.50257e11	0.495427	0.247714	−	0.968833i	$-0.420321\pi$
$509$	7.50257e11	0.495427	0.247714	+	0.968833i	$0.420321\pi$
$510$	0	0
$511$	−2.47942e12	−1.60863
$512$	8.37693e11	0.538729
$513$	1.96120e12	1.25024
$514$	−6.97724e11	−0.440910
$515$	−2.14645e12	−1.34459
$516$	−1.75951e12	−1.09262
$517$	−2.13371e12	−1.31350
$518$	9.75976e11	0.595601
$519$	3.76857e10	0.0227994
$520$	−9.52426e11	−0.571237
$521$	5.40736e11	0.321525	0.160763	−	0.986993i	$-0.448605\pi$
$521$	5.40736e11	0.321525	0.160763	+	0.986993i	$0.448605\pi$
$522$	−2.89113e12	−1.70432
$523$	6.61335e11	0.386513	0.193256	−	0.981148i	$-0.438095\pi$
$523$	6.61335e11	0.386513	0.193256	+	0.981148i	$0.438095\pi$
$524$	−9.08123e11	−0.526204
$525$	1.71617e12	0.985926
$526$	−3.61306e11	−0.205797
$527$	0	0
$528$	−9.32953e11	−0.522405
$529$	−8.85673e10	−0.0491726
$530$	1.92336e12	1.05881
$531$	−3.64586e12	−1.99010
$532$	−4.06228e11	−0.219871
$533$	1.69041e11	0.0907235
$534$	2.94362e12	1.56656
$535$	1.36174e12	0.718623
$536$	4.84724e11	0.253660
$537$	4.60521e12	2.38982
$538$	−4.39008e11	−0.225919
$539$	1.47171e12	0.751055
$540$	4.15171e12	2.10114
$541$	−2.26946e12	−1.13903	−0.569514	−	0.821982i	$-0.692869\pi$
$541$	−2.26946e12	−1.13903	−0.569514	+	0.821982i	$0.692869\pi$
$542$	−1.95725e12	−0.974205
$543$	−1.43361e12	−0.707672
$544$	0	0
$545$	−1.90862e12	−0.926694
$546$	−1.79407e12	−0.863919
$547$	−9.44132e11	−0.450910	−0.225455	−	0.974254i	$-0.572387\pi$
$547$	−9.44132e11	−0.450910	−0.225455	+	0.974254i	$0.572387\pi$
$548$	4.74530e11	0.224776
$549$	−6.44125e12	−3.02618
$550$	−5.48163e11	−0.255433
$551$	6.05283e11	0.279754
$552$	4.46194e12	2.04549
$553$	−4.45029e12	−2.02360
$554$	2.38400e12	1.07526
$555$	3.20166e12	1.43238
$556$	−2.06095e12	−0.914601
$557$	−2.30243e12	−1.01354	−0.506768	−	0.862083i	$-0.669160\pi$
$557$	−2.30243e12	−1.01354	−0.506768	+	0.862083i	$0.669160\pi$
$558$	−2.88235e12	−1.25861
$559$	1.20710e12	0.522864
$560$	1.01829e12	0.437546
$561$	0	0
$562$	2.83999e12	1.20089
$563$	1.68590e12	0.707201	0.353601	−	0.935396i	$-0.384957\pi$
$563$	1.68590e12	0.707201	0.353601	+	0.935396i	$0.384957\pi$
$564$	3.17106e12	1.31962
$565$	2.13874e12	0.882959
$566$	−1.33492e12	−0.546740
$567$	1.44647e13	5.87739
$568$	−9.93696e11	−0.400577
$569$	−4.88221e12	−1.95259	−0.976295	−	0.216443i	$-0.930554\pi$
$569$	−4.88221e12	−1.95259	−0.976295	+	0.216443i	$0.930554\pi$
$570$	1.41280e12	0.560588
$571$	1.28951e12	0.507649	0.253824	−	0.967250i	$-0.418311\pi$
$571$	1.28951e12	0.507649	0.253824	+	0.967250i	$0.418311\pi$
$572$	−5.40523e11	−0.211121
$573$	7.94737e12	3.07984
$574$	−4.95170e11	−0.190393
$575$	9.56864e11	0.365044
$576$	6.83564e12	2.58749
$577$	3.35989e12	1.26193	0.630963	−	0.775813i	$-0.282660\pi$
$577$	3.35989e12	1.26193	0.630963	+	0.775813i	$0.282660\pi$
$578$	0	0
$579$	−5.32090e12	−1.96758
$580$	1.28133e12	0.470150
$581$	−2.66533e12	−0.970417
$582$	−4.98898e11	−0.180243
$583$	3.34032e12	1.19751
$584$	−3.60173e12	−1.28131
$585$	−4.36682e12	−1.54157
$586$	2.79780e11	0.0980117
$587$	1.98787e11	0.0691059	0.0345530	−	0.999403i	$-0.488999\pi$
$587$	1.98787e11	0.0691059	0.0345530	+	0.999403i	$0.488999\pi$
$588$	−2.18720e12	−0.754555
$589$	6.03444e11	0.206594
$590$	−1.71305e12	−0.582016
$591$	2.06204e12	0.695269
$592$	5.17459e11	0.173152
$593$	−1.77542e12	−0.589598	−0.294799	−	0.955559i	$-0.595253\pi$
$593$	−1.77542e12	−0.589598	−0.294799	+	0.955559i	$0.595253\pi$
$594$	−7.64414e12	−2.51936
$595$	0	0
$596$	−3.44932e11	−0.111976
$597$	−7.57832e12	−2.44168
$598$	−1.00030e12	−0.319870
$599$	−5.82261e12	−1.84798	−0.923990	−	0.382418i	$-0.875092\pi$
$599$	−5.82261e12	−1.84798	−0.923990	+	0.382418i	$0.875092\pi$
$600$	2.49300e12	0.785310
$601$	−6.05010e12	−1.89159	−0.945796	−	0.324761i	$-0.894716\pi$
$601$	−6.05010e12	−1.89159	−0.945796	+	0.324761i	$0.894716\pi$
$602$	−3.53593e12	−1.09728
$603$	2.22243e12	0.684543
$604$	−1.75440e12	−0.536369
$605$	3.68241e11	0.111746
$606$	−3.76275e12	−1.13339
$607$	−2.29272e12	−0.685492	−0.342746	−	0.939428i	$-0.611357\pi$
$607$	−2.29272e12	−0.685492	−0.342746	+	0.939428i	$0.611357\pi$
$608$	−9.87379e11	−0.293034
$609$	7.38612e12	2.17590
$610$	−3.02649e12	−0.885024
$611$	−2.17547e12	−0.631492
$612$	0	0
$613$	−2.58028e12	−0.738064	−0.369032	−	0.929417i	$-0.620311\pi$
$613$	−2.58028e12	−0.738064	−0.369032	+	0.929417i	$0.620311\pi$
$614$	4.15799e12	1.18066
$615$	−1.62439e12	−0.457881
$616$	4.84531e12	1.35584
$617$	4.99510e12	1.38759	0.693795	−	0.720172i	$-0.255937\pi$
$617$	4.99510e12	1.38759	0.693795	+	0.720172i	$0.255937\pi$
$618$	−5.87342e12	−1.61973
$619$	6.13894e12	1.68068	0.840341	−	0.542058i	$-0.182355\pi$
$619$	6.13894e12	1.68068	0.840341	+	0.542058i	$0.182355\pi$
$620$	1.27744e12	0.347199
$621$	1.33435e13	3.60045
$622$	1.58540e12	0.424700
$623$	−5.57981e12	−1.48396
$624$	−9.51212e11	−0.251158
$625$	−4.70816e12	−1.23422
$626$	3.83564e12	0.998283
$627$	2.45363e12	0.634022
$628$	9.50698e11	0.243907
$629$	0	0
$630$	1.27917e13	3.23516
$631$	1.08545e11	0.0272569	0.0136284	−	0.999907i	$-0.495662\pi$
$631$	1.08545e11	0.0272569	0.0136284	+	0.999907i	$0.495662\pi$
$632$	−6.46470e12	−1.61184
$633$	3.48991e12	0.863969
$634$	7.31610e11	0.179837
$635$	−2.24006e12	−0.546737
$636$	−4.96428e12	−1.20309
$637$	1.50051e12	0.361086
$638$	−2.35920e12	−0.563730
$639$	−4.55604e12	−1.08102
$640$	−1.09436e12	−0.257841
$641$	3.07759e12	0.720029	0.360014	−	0.932947i	$-0.382772\pi$
$641$	3.07759e12	0.720029	0.360014	+	0.932947i	$0.382772\pi$
$642$	3.72617e12	0.865676
$643$	1.79981e12	0.415219	0.207609	−	0.978212i	$-0.433432\pi$
$643$	1.79981e12	0.415219	0.207609	+	0.978212i	$0.433432\pi$
$644$	−2.76386e12	−0.633185
$645$	−1.15995e13	−2.63889
$646$	0	0
$647$	−1.16719e12	−0.261861	−0.130931	−	0.991392i	$-0.541797\pi$
$647$	−1.16719e12	−0.261861	−0.130931	+	0.991392i	$0.541797\pi$
$648$	2.10121e13	4.68146
$649$	−2.97507e12	−0.658258
$650$	−5.58890e11	−0.122805
$651$	7.36368e12	1.60687
$652$	2.88732e12	0.625721
$653$	4.28149e12	0.921480	0.460740	−	0.887535i	$-0.347584\pi$
$653$	4.28149e12	0.921480	0.460740	+	0.887535i	$0.347584\pi$
$654$	−5.22264e12	−1.11632
$655$	−5.98678e12	−1.27089
$656$	−2.62537e11	−0.0553508
$657$	−1.65138e13	−3.45781
$658$	6.37258e12	1.32525
$659$	−2.61751e12	−0.540636	−0.270318	−	0.962771i	$-0.587129\pi$
$659$	−2.61751e12	−0.540636	−0.270318	+	0.962771i	$0.587129\pi$
$660$	5.19413e12	1.06553
$661$	−6.71780e11	−0.136874	−0.0684369	−	0.997655i	$-0.521801\pi$
$661$	−6.71780e11	−0.136874	−0.0684369	+	0.997655i	$0.521801\pi$
$662$	8.58499e11	0.173732
$663$	0	0
$664$	−3.87179e12	−0.772957
$665$	−2.67805e12	−0.531032
$666$	6.50031e12	1.28027
$667$	4.11818e12	0.805636
$668$	8.62456e11	0.167588
$669$	1.55922e13	3.00946
$670$	1.04423e12	0.200199
$671$	−5.25614e12	−1.00096
$672$	−1.20487e13	−2.27919
$673$	−5.97945e11	−0.112355	−0.0561776	−	0.998421i	$-0.517891\pi$
$673$	−5.97945e11	−0.112355	−0.0561776	+	0.998421i	$0.517891\pi$
$674$	−2.59580e12	−0.484509
$675$	7.45533e12	1.38229
$676$	2.08437e12	0.383896
$677$	1.85086e12	0.338630	0.169315	−	0.985562i	$-0.445844\pi$
$677$	1.85086e12	0.338630	0.169315	+	0.985562i	$0.445844\pi$
$678$	5.85232e12	1.06364
$679$	9.45691e11	0.170740
$680$	0	0
$681$	−1.36558e12	−0.243307
$682$	−2.35203e12	−0.416307
$683$	3.09984e12	0.545062	0.272531	−	0.962147i	$-0.412139\pi$
$683$	3.09984e12	0.545062	0.272531	+	0.962147i	$0.412139\pi$
$684$	−2.70561e12	−0.472621
$685$	3.12832e12	0.542880
$686$	1.17100e12	0.201883
$687$	−1.57128e13	−2.69121
$688$	−1.87474e12	−0.319001
$689$	3.40569e12	0.575730
$690$	9.61230e12	1.61438
$691$	−2.04515e12	−0.341250	−0.170625	−	0.985336i	$-0.554579\pi$
$691$	−2.04515e12	−0.341250	−0.170625	+	0.985336i	$0.554579\pi$
$692$	−3.39102e10	−0.00562150
$693$	2.22155e13	3.65895
$694$	7.23443e12	1.18382
$695$	−1.35868e13	−2.20895
$696$	1.07294e13	1.73315
$697$	0	0
$698$	4.40100e11	0.0701781
$699$	2.05027e13	3.24836
$700$	−1.54424e12	−0.243093
$701$	5.75738e12	0.900521	0.450261	−	0.892897i	$-0.351331\pi$
$701$	5.75738e12	0.900521	0.450261	+	0.892897i	$0.351331\pi$
$702$	−7.79374e12	−1.21124
$703$	−1.36090e12	−0.210148
$704$	5.57797e12	0.855852
$705$	2.09051e13	3.18714
$706$	5.71652e12	0.865986
$707$	7.13253e12	1.07363
$708$	4.42145e12	0.661325
$709$	2.30053e11	0.0341917	0.0170958	−	0.999854i	$-0.494558\pi$
$709$	2.30053e11	0.0341917	0.0170958	+	0.999854i	$0.494558\pi$
$710$	−2.14070e12	−0.316151
$711$	−2.96403e13	−4.34980
$712$	−8.10551e12	−1.18201
$713$	4.10567e12	0.594950
$714$	0	0
$715$	−3.56338e12	−0.509900
$716$	−4.14384e12	−0.589242
$717$	1.23535e13	1.74563
$718$	5.32642e12	0.747955
$719$	2.92429e12	0.408076	0.204038	−	0.978963i	$-0.434593\pi$
$719$	2.92429e12	0.408076	0.204038	+	0.978963i	$0.434593\pi$
$720$	6.78211e12	0.940521
$721$	1.11334e13	1.53433
$722$	4.63733e12	0.635112
$723$	7.75037e12	1.05487
$724$	1.28998e12	0.174486
$725$	2.30093e12	0.309301
$726$	1.00763e12	0.134613
$727$	−1.35766e13	−1.80255	−0.901276	−	0.433246i	$-0.857368\pi$
$727$	−1.35766e13	−1.80255	−0.901276	+	0.433246i	$0.857368\pi$
$728$	4.94013e12	0.651849
$729$	4.09087e13	5.36465
$730$	−7.75916e12	−1.01126
$731$	0	0
$732$	7.81150e12	1.00562
$733$	1.01336e12	0.129656	0.0648282	−	0.997896i	$-0.479350\pi$
$733$	1.01336e12	0.129656	0.0648282	+	0.997896i	$0.479350\pi$
$734$	6.10818e12	0.776747
$735$	−1.44191e13	−1.82240
$736$	−6.71785e12	−0.843879
$737$	1.81353e12	0.226424
$738$	−3.29799e12	−0.409256
$739$	−7.79008e12	−0.960820	−0.480410	−	0.877044i	$-0.659512\pi$
$739$	−7.79008e12	−0.960820	−0.480410	+	0.877044i	$0.659512\pi$
$740$	−2.88090e12	−0.353172
$741$	2.50165e12	0.304820
$742$	−9.97626e12	−1.20823
$743$	−8.73895e12	−1.05199	−0.525993	−	0.850489i	$-0.676306\pi$
$743$	−8.73895e12	−1.05199	−0.525993	+	0.850489i	$0.676306\pi$
$744$	1.06968e13	1.27990
$745$	−2.27396e12	−0.270445
$746$	−4.04336e12	−0.477989
$747$	−1.77519e13	−2.08595
$748$	0	0
$749$	−7.06318e12	−0.820035
$750$	−8.97538e12	−1.03580
$751$	−1.44210e12	−0.165430	−0.0827152	−	0.996573i	$-0.526359\pi$
$751$	−1.44210e12	−0.165430	−0.0827152	+	0.996573i	$0.526359\pi$
$752$	3.37872e12	0.385276
$753$	1.80447e13	2.04537
$754$	−2.40537e12	−0.271026
$755$	−1.15659e13	−1.29544
$756$	−2.15344e13	−2.39765
$757$	−2.38384e12	−0.263843	−0.131921	−	0.991260i	$-0.542115\pi$
$757$	−2.38384e12	−0.263843	−0.131921	+	0.991260i	$0.542115\pi$
$758$	−1.22522e13	−1.34805
$759$	1.66938e13	1.82586
$760$	−3.89026e12	−0.422978
$761$	−1.06430e13	−1.15035	−0.575177	−	0.818029i	$-0.695067\pi$
$761$	−1.06430e13	−1.15035	−0.575177	+	0.818029i	$0.695067\pi$
$762$	−6.12957e12	−0.658616
$763$	9.89983e12	1.05747
$764$	−7.15116e12	−0.759375
$765$	0	0
$766$	−9.61301e12	−1.00886
$767$	−3.03329e12	−0.316472
$768$	−2.00729e13	−2.08202
$769$	3.67087e12	0.378530	0.189265	−	0.981926i	$-0.439390\pi$
$769$	3.67087e12	0.378530	0.189265	+	0.981926i	$0.439390\pi$
$770$	1.04382e13	1.07008
$771$	1.18721e13	1.20999
$772$	4.78783e12	0.485133
$773$	3.56580e12	0.359211	0.179605	−	0.983739i	$-0.442518\pi$
$773$	3.56580e12	0.359211	0.179605	+	0.983739i	$0.442518\pi$
$774$	−2.35504e13	−2.35865
$775$	2.29394e12	0.228415
$776$	1.37376e12	0.135998
$777$	−1.66067e13	−1.63451
$778$	−1.41522e13	−1.38489
$779$	6.90462e11	0.0671771
$780$	5.29578e12	0.512276
$781$	−3.71779e12	−0.357565
$782$	0	0
$783$	3.20865e13	3.05066
$784$	−2.33044e12	−0.220300
$785$	6.26745e12	0.589084
$786$	−1.63818e13	−1.53095
$787$	−1.73599e13	−1.61310	−0.806549	−	0.591167i	$-0.798667\pi$
$787$	−1.73599e13	−1.61310	−0.806549	+	0.591167i	$0.798667\pi$
$788$	−1.85545e12	−0.171428
$789$	6.14779e12	0.564771
$790$	−1.39268e13	−1.27213
$791$	−1.10934e13	−1.00756
$792$	3.22713e13	2.91442
$793$	−5.35900e12	−0.481232
$794$	−3.14057e12	−0.280425
$795$	−3.27268e13	−2.90571
$796$	6.81909e12	0.602029
$797$	3.92379e12	0.344464	0.172232	−	0.985056i	$-0.444902\pi$
$797$	3.92379e12	0.344464	0.172232	+	0.985056i	$0.444902\pi$
$798$	−7.32804e12	−0.639698
$799$	0	0
$800$	−3.75343e12	−0.323984
$801$	−3.71633e13	−3.18984
$802$	−4.53138e12	−0.386764
$803$	−1.34754e13	−1.14373
$804$	−2.69521e12	−0.227479
$805$	−1.82207e13	−1.52927
$806$	−2.39806e12	−0.200149
$807$	7.46992e12	0.619990
$808$	1.03611e13	0.855171
$809$	3.19512e12	0.262252	0.131126	−	0.991366i	$-0.458141\pi$
$809$	3.19512e12	0.262252	0.131126	+	0.991366i	$0.458141\pi$
$810$	4.52660e13	3.69479
$811$	1.04002e13	0.844204	0.422102	−	0.906548i	$-0.361292\pi$
$811$	1.04002e13	0.844204	0.422102	+	0.906548i	$0.361292\pi$
$812$	−6.64614e12	−0.536497
$813$	3.33036e13	2.67352
$814$	5.30433e12	0.423468
$815$	1.90346e13	1.51124
$816$	0	0
$817$	4.93048e12	0.387160
$818$	6.63678e12	0.518284
$819$	2.26502e13	1.75912
$820$	1.46165e12	0.112897
$821$	5.23470e12	0.402112	0.201056	−	0.979580i	$-0.435563\pi$
$821$	5.23470e12	0.402112	0.201056	+	0.979580i	$0.435563\pi$
$822$	8.56014e12	0.653970
$823$	2.49083e13	1.89254	0.946271	−	0.323375i	$-0.104817\pi$
$823$	2.49083e13	1.89254	0.946271	+	0.323375i	$0.104817\pi$
$824$	1.61730e13	1.22213
$825$	9.32724e12	0.700987
$826$	8.88539e12	0.664150
$827$	5.31180e12	0.394882	0.197441	−	0.980315i	$-0.436737\pi$
$827$	5.31180e12	0.394882	0.197441	+	0.980315i	$0.436737\pi$
$828$	−1.84082e13	−1.36105
$829$	−1.03173e13	−0.758700	−0.379350	−	0.925253i	$-0.623852\pi$
$829$	−1.03173e13	−0.758700	−0.379350	+	0.925253i	$0.623852\pi$
$830$	−8.34094e12	−0.610047
$831$	−4.05648e13	−2.95083
$832$	5.68713e12	0.411470
$833$	0	0
$834$	−3.71780e13	−2.66096
$835$	5.68572e12	0.404759
$836$	−2.20781e12	−0.156327
$837$	3.19890e13	2.25287
$838$	−7.98993e12	−0.559686
$839$	−8.51253e12	−0.593103	−0.296551	−	0.955017i	$-0.595837\pi$
$839$	−8.51253e12	−0.593103	−0.296551	+	0.955017i	$0.595837\pi$
$840$	−4.74719e13	−3.28988
$841$	−4.60435e12	−0.317385
$842$	−1.29118e13	−0.885285
$843$	−4.83237e13	−3.29561
$844$	−3.14028e12	−0.213023
$845$	1.37411e13	0.927187
$846$	4.24434e13	2.84868
$847$	−1.91003e12	−0.127516
$848$	−5.28938e12	−0.351256
$849$	2.27143e13	1.50042
$850$	0	0
$851$	−9.25916e12	−0.605185
$852$	5.52525e12	0.359231
$853$	2.58704e13	1.67314	0.836571	−	0.547858i	$-0.184557\pi$
$853$	2.58704e13	1.67314	0.836571	+	0.547858i	$0.184557\pi$
$854$	1.56981e13	1.00992
$855$	−1.78367e13	−1.14147
$856$	−1.02603e13	−0.653174
$857$	−1.63312e13	−1.03420	−0.517100	−	0.855925i	$-0.672988\pi$
$857$	−1.63312e13	−1.03420	−0.517100	+	0.855925i	$0.672988\pi$
$858$	−9.75061e12	−0.614241
$859$	−1.45571e13	−0.912235	−0.456118	−	0.889919i	$-0.650760\pi$
$859$	−1.45571e13	−0.912235	−0.456118	+	0.889919i	$0.650760\pi$
$860$	1.04374e13	0.650654
$861$	8.42554e12	0.522497
$862$	1.70677e12	0.105291
$863$	−1.08493e13	−0.665817	−0.332909	−	0.942959i	$-0.608030\pi$
$863$	−1.08493e13	−0.665817	−0.332909	+	0.942959i	$0.608030\pi$
$864$	−5.23417e13	−3.19548
$865$	−2.23552e11	−0.0135771
$866$	3.89598e12	0.235389
$867$	0	0
$868$	−6.62595e12	−0.396195
$869$	−2.41869e13	−1.43877
$870$	2.31143e13	1.36787
$871$	1.84902e12	0.108858
$872$	1.43810e13	0.842294
$873$	6.29860e12	0.367012
$874$	−4.08579e12	−0.236851
$875$	1.70134e13	0.981193
$876$	2.00267e13	1.14906
$877$	2.33213e12	0.133123	0.0665617	−	0.997782i	$-0.478797\pi$
$877$	2.33213e12	0.133123	0.0665617	+	0.997782i	$0.478797\pi$
$878$	−1.55657e13	−0.883981
$879$	−4.76059e12	−0.268974
$880$	5.53428e12	0.311092
$881$	1.99931e13	1.11812	0.559061	−	0.829127i	$-0.311162\pi$
$881$	1.99931e13	1.11812	0.559061	+	0.829127i	$0.311162\pi$
$882$	−2.92749e13	−1.62887
$883$	1.20279e13	0.665834	0.332917	−	0.942956i	$-0.391967\pi$
$883$	1.20279e13	0.665834	0.332917	+	0.942956i	$0.391967\pi$
$884$	0	0
$885$	2.91483e13	1.59723
$886$	2.21958e13	1.21009
$887$	2.98647e11	0.0161995	0.00809975	−	0.999967i	$-0.497422\pi$
$887$	2.98647e11	0.0161995	0.00809975	+	0.999967i	$0.497422\pi$
$888$	−2.41237e13	−1.30192
$889$	1.16190e13	0.623892
$890$	−1.74616e13	−0.932886
$891$	7.86140e13	4.17879
$892$	−1.40301e13	−0.742023
$893$	−8.88590e12	−0.467595
$894$	−6.22231e12	−0.325786
$895$	−2.73181e13	−1.42314
$896$	5.67635e12	0.294227
$897$	1.70205e13	0.877822
$898$	−1.19351e13	−0.612465
$899$	9.87271e12	0.504101
$900$	−1.02851e13	−0.522538
$901$	0	0
$902$	−2.69120e12	−0.135368
$903$	6.01654e13	3.01129
$904$	−1.61149e13	−0.802543
$905$	8.50419e12	0.421419
$906$	−3.16481e13	−1.56052
$907$	1.85478e13	0.910041	0.455020	−	0.890481i	$-0.349632\pi$
$907$	1.85478e13	0.910041	0.455020	+	0.890481i	$0.349632\pi$
$908$	1.22877e12	0.0599906
$909$	4.75049e13	2.30781
$910$	1.06424e13	0.514464
$911$	2.65224e13	1.27580	0.637898	−	0.770121i	$-0.279804\pi$
$911$	2.65224e13	1.27580	0.637898	+	0.770121i	$0.279804\pi$
$912$	−3.88530e12	−0.185972
$913$	−1.44858e13	−0.689960
$914$	1.89163e13	0.896559
$915$	5.14971e13	2.42878
$916$	1.41386e13	0.663555
$917$	3.10528e13	1.45023
$918$	0	0
$919$	2.29442e13	1.06109	0.530546	−	0.847656i	$-0.321987\pi$
$919$	2.29442e13	1.06109	0.530546	+	0.847656i	$0.321987\pi$
$920$	−2.64683e13	−1.21809
$921$	−7.07502e13	−3.24010
$922$	−1.62969e13	−0.742702
$923$	−3.79055e12	−0.171907
$924$	−2.69414e13	−1.21589
$925$	−5.17332e12	−0.232344
$926$	−1.20778e13	−0.539809
$927$	7.41521e13	3.29811
$928$	−1.61541e13	−0.715019
$929$	3.61411e13	1.59195	0.795977	−	0.605326i	$-0.206957\pi$
$929$	3.61411e13	1.59195	0.795977	+	0.605326i	$0.206957\pi$
$930$	2.30440e13	1.01015
$931$	6.12895e12	0.267370
$932$	−1.84487e13	−0.800928
$933$	−2.69763e13	−1.16551
$934$	1.44827e13	0.622715
$935$	0	0
$936$	3.29028e13	1.40117
$937$	1.16635e13	0.494313	0.247156	−	0.968976i	$-0.420504\pi$
$937$	1.16635e13	0.494313	0.247156	+	0.968976i	$0.420504\pi$
$938$	−5.41632e12	−0.228450
$939$	−6.52652e13	−2.73960
$940$	−1.88107e13	−0.785832
$941$	−1.60493e13	−0.667273	−0.333636	−	0.942702i	$-0.608276\pi$
$941$	−1.60493e13	−0.667273	−0.333636	+	0.942702i	$0.608276\pi$
$942$	1.71498e13	0.709629
$943$	4.69771e12	0.193457
$944$	4.71100e12	0.193081
$945$	−1.41965e14	−5.79080
$946$	−1.92174e13	−0.780163
$947$	−1.18470e13	−0.478667	−0.239334	−	0.970937i	$-0.576929\pi$
$947$	−1.18470e13	−0.478667	−0.239334	+	0.970937i	$0.576929\pi$
$948$	3.59457e13	1.44547
$949$	−1.37391e13	−0.549872
$950$	−2.28283e12	−0.0909323
$951$	−1.24487e13	−0.493527
$952$	0	0
$953$	4.20395e13	1.65097	0.825485	−	0.564424i	$-0.190902\pi$
$953$	4.20395e13	1.65097	0.825485	+	0.564424i	$0.190902\pi$
$954$	−6.64450e13	−2.59714
$955$	−4.71438e13	−1.83404
$956$	−1.11158e13	−0.430409
$957$	4.01428e13	1.54705
$958$	−1.32962e10	−0.000510014 0
$959$	−1.62263e13	−0.619491
$960$	−5.46502e13	−2.07669
$961$	−1.65969e13	−0.627728
$962$	5.40814e12	0.203592
$963$	−4.70430e13	−1.76269
$964$	−6.97390e12	−0.260093
$965$	3.15636e13	1.17169
$966$	−4.98579e13	−1.84220
$967$	−9.82534e12	−0.361350	−0.180675	−	0.983543i	$-0.557828\pi$
$967$	−9.82534e12	−0.361350	−0.180675	+	0.983543i	$0.557828\pi$
$968$	−2.77460e12	−0.101569
$969$	0	0
$970$	2.95946e12	0.107335
$971$	−1.13310e13	−0.409053	−0.204527	−	0.978861i	$-0.565566\pi$
$971$	−1.13310e13	−0.409053	−0.204527	+	0.978861i	$0.565566\pi$
$972$	−6.69562e13	−2.40598
$973$	7.04732e13	2.52067
$974$	3.30980e13	1.17838
$975$	9.50977e12	0.337015
$976$	8.32306e12	0.293602
$977$	−3.63787e13	−1.27738	−0.638692	−	0.769463i	$-0.720524\pi$
$977$	−3.63787e13	−1.27738	−0.638692	+	0.769463i	$0.720524\pi$
$978$	5.20850e13	1.82049
$979$	−3.03257e13	−1.05509
$980$	1.29745e13	0.449338
$981$	6.59360e13	2.27307
$982$	9.75776e12	0.334848
$983$	3.68939e13	1.26027	0.630136	−	0.776485i	$-0.282999\pi$
$983$	3.68939e13	1.26027	0.630136	+	0.776485i	$0.282999\pi$
$984$	1.22394e13	0.416179
$985$	−1.22320e13	−0.414033
$986$	0	0
$987$	−1.08432e14	−3.63690
$988$	−2.25102e12	−0.0751576
$989$	3.35456e13	1.11494
$990$	6.95215e13	2.30018
$991$	−4.52933e13	−1.49177	−0.745885	−	0.666074i	$-0.767973\pi$
$991$	−4.52933e13	−1.49177	−0.745885	+	0.666074i	$0.767973\pi$
$992$	−1.61050e13	−0.528031
$993$	−1.46078e13	−0.476773
$994$	1.11036e13	0.360765
$995$	4.49546e13	1.45402
$996$	2.15283e13	0.693175
$997$	−2.93423e13	−0.940515	−0.470257	−	0.882529i	$-0.655839\pi$
$997$	−2.93423e13	−0.940515	−0.470257	+	0.882529i	$0.655839\pi$
$998$	2.05197e13	0.654763
$999$	−7.21421e13	−2.29163

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.h.1.13	yes	36
17.16	even	2		289.10.a.g.1.13	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.13	✓	36	17.16	even	2
289.10.a.h.1.13	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)

\(f(q)\)	\(=\)	\(q-16.2320 q^{2} +276.194 q^{3} -248.524 q^{4} -1638.38 q^{5} -4483.17 q^{6} +8498.12 q^{7} +12344.8 q^{8} +56600.2 q^{9} +O(q^{10})\)	\(q-16.2320 q^{2} +276.194 q^{3} -248.524 q^{4} -1638.38 q^{5} -4483.17 q^{6} +8498.12 q^{7} +12344.8 q^{8} +56600.2 q^{9} +26594.2 q^{10} +46186.5 q^{11} -68640.8 q^{12} +47090.3 q^{13} -137941. q^{14} -452512. q^{15} -73135.9 q^{16} -918732. q^{18} +192344. q^{19} +407177. q^{20} +2.34713e6 q^{21} -749697. q^{22} +1.30866e6 q^{23} +3.40956e6 q^{24} +731179. q^{25} -764368. q^{26} +1.01963e7 q^{27} -2.11198e6 q^{28} +3.14687e6 q^{29} +7.34516e6 q^{30} +3.13731e6 q^{31} -5.13339e6 q^{32} +1.27564e7 q^{33} -1.39232e7 q^{35} -1.40665e7 q^{36} -7.07531e6 q^{37} -3.12213e6 q^{38} +1.30061e7 q^{39} -2.02255e7 q^{40} +3.58972e6 q^{41} -3.80985e7 q^{42} +2.56336e7 q^{43} -1.14784e7 q^{44} -9.27329e7 q^{45} -2.12421e7 q^{46} -4.61978e7 q^{47} -2.01997e7 q^{48} +3.18645e7 q^{49} -1.18685e7 q^{50} -1.17031e7 q^{52} +7.23226e7 q^{53} -1.65506e8 q^{54} -7.56712e7 q^{55} +1.04907e8 q^{56} +5.31244e7 q^{57} -5.10799e7 q^{58} -6.44143e7 q^{59} +1.12460e8 q^{60} -1.13803e8 q^{61} -5.09247e7 q^{62} +4.80995e8 q^{63} +1.20771e8 q^{64} -7.71521e7 q^{65} -2.07062e8 q^{66} +3.92655e7 q^{67} +3.61444e8 q^{69} +2.26001e8 q^{70} -8.04952e7 q^{71} +6.98717e8 q^{72} -2.91761e8 q^{73} +1.14846e8 q^{74} +2.01947e8 q^{75} -4.78021e7 q^{76} +3.92498e8 q^{77} -2.11114e8 q^{78} -5.23679e8 q^{79} +1.19825e8 q^{80} +1.70210e9 q^{81} -5.82682e7 q^{82} -3.13638e8 q^{83} -5.83318e8 q^{84} -4.16084e8 q^{86} +8.69147e8 q^{87} +5.70162e8 q^{88} -6.56594e8 q^{89} +1.50524e9 q^{90} +4.00179e8 q^{91} -3.25232e8 q^{92} +8.66507e8 q^{93} +7.49881e8 q^{94} -3.15134e8 q^{95} -1.41781e9 q^{96} +1.11282e8 q^{97} -5.17223e8 q^{98} +2.61416e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 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

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