LMFDB - Embedded newform 289.10.a.g.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:	$1$
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	$-0.943568\pi$
$3$	−276.194	−1.96865	−0.984326	+	0.176360i	$0.943568\pi$
$4$	−248.524	−0.485398
$5$	1638.38	1.17233	0.586166	−	0.810191i	$-0.300637\pi$
$5$	1638.38	1.17233	0.586166	+	0.810191i	$0.300637\pi$
$6$	4483.17	1.41223
$7$	−8498.12	−1.33777	−0.668886	−	0.743365i	$-0.733228\pi$
$7$	−8498.12	−1.33777	−0.668886	+	0.743365i	$0.733228\pi$
$8$	12344.8	1.06556
$9$	56600.2	2.87559
$10$	−26594.2	−0.840982
$11$	−46186.5	−0.951147	−0.475573	−	0.879676i	$-0.657759\pi$
$11$	−46186.5	−0.951147	−0.475573	+	0.879676i	$0.657759\pi$
$12$	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	$-0.662110\pi$
$23$	−1.30866e6	−0.975104	−0.487552	+	0.873094i	$0.662110\pi$
$24$	−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	$-0.635555\pi$
$29$	−3.14687e6	−0.826205	−0.413103	+	0.910684i	$0.635555\pi$
$30$	7.34516e6	1.65560
$31$	−3.13731e6	−0.610141	−0.305070	−	0.952330i	$-0.598680\pi$
$31$	−3.13731e6	−0.610141	−0.305070	+	0.952330i	$0.598680\pi$
$32$	−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	$-0.399564\pi$
$37$	7.07531e6	0.620637	0.310318	+	0.950633i	$0.399564\pi$
$38$	−3.12213e6	−0.242898
$39$	−1.30061e7	−0.900234
$40$	2.02255e7	1.24919
$41$	−3.58972e6	−0.198396	−0.0991980	−	0.995068i	$-0.531628\pi$
$41$	−3.58972e6	−0.198396	−0.0991980	+	0.995068i	$0.531628\pi$
$42$	−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	$-0.323622\pi$
$61$	1.13803e8	1.05237	0.526185	+	0.850370i	$0.323622\pi$
$62$	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	$-0.439811\pi$
$71$	8.04952e7	0.375930	0.187965	+	0.982176i	$0.439811\pi$
$72$	6.98717e8	3.06412
$73$	2.91761e8	1.20247	0.601236	−	0.799071i	$-0.294675\pi$
$73$	2.91761e8	1.20247	0.601236	+	0.799071i	$0.294675\pi$
$74$	−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	$-0.226989\pi$
$79$	5.23679e8	1.51267	0.756333	+	0.654187i	$0.226989\pi$
$80$	−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	$-0.520327\pi$
$97$	−1.11282e8	−0.127630	−0.0638151	+	0.997962i	$0.520327\pi$
$98$	−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	$-0.400844\pi$
$107$	8.31146e8	0.612986	0.306493	+	0.951873i	$0.400844\pi$
$108$	2.53402e9	1.79227
$109$	−1.16494e9	−0.790470	−0.395235	−	0.918580i	$-0.629337\pi$
$109$	−1.16494e9	−0.790470	−0.395235	+	0.918580i	$0.629337\pi$
$110$	1.22829e9	0.799897
$111$	−1.95416e9	−1.22182
$112$	6.21518e8	0.373227
$113$	1.30540e9	0.753164	0.376582	−	0.926383i	$-0.377099\pi$
$113$	1.30540e9	0.753164	0.376582	+	0.926383i	$0.377099\pi$
$114$	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	$-0.682346\pi$
$131$	−3.65407e9	−1.08407	−0.542034	+	0.840357i	$0.682346\pi$
$132$	−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	$-0.891166\pi$
$139$	−8.29279e9	−1.88423	−0.942115	+	0.335289i	$0.891166\pi$
$140$	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	$-0.277047\pi$
$163$	1.16179e10	1.28909	0.644545	+	0.764567i	$0.277047\pi$
$164$	8.92130e8	0.0963010
$165$	2.08999e10	2.19517
$166$	5.09095e9	0.520370
$167$	3.47032e9	0.345259	0.172630	−	0.984987i	$-0.444774\pi$
$167$	3.47032e9	0.345259	0.172630	+	0.984987i	$0.444774\pi$
$168$	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	$-0.501843\pi$
$173$	−1.36446e8	−0.0115812	−0.00579061	+	0.999983i	$0.501843\pi$
$174$	−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	$-0.442476\pi$
$181$	5.19059e9	0.359471	0.179735	+	0.983715i	$0.442476\pi$
$182$	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	$-0.333434\pi$
$193$	1.92651e10	0.999455	0.499727	+	0.866183i	$0.333434\pi$
$194$	1.80633e9	0.0915565
$195$	−2.13090e10	−1.05537
$196$	−7.91907e9	−0.383285
$197$	−7.46589e9	−0.353170	−0.176585	−	0.984285i	$-0.556505\pi$
$197$	−7.46589e9	−0.353170	−0.176585	+	0.984285i	$0.556505\pi$
$198$	4.24330e10	1.96205
$199$	2.74384e10	1.24028	0.620140	−	0.784491i	$-0.287076\pi$
$199$	2.74384e10	1.24028	0.620140	+	0.784491i	$0.287076\pi$
$200$	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	$-0.570420\pi$
$211$	−1.26357e10	−0.438863	−0.219432	+	0.975628i	$0.570420\pi$
$212$	−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	$-0.480317\pi$
$227$	4.94426e9	0.123591	0.0617953	+	0.998089i	$0.480317\pi$
$228$	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	$-0.808838\pi$
$233$	−7.42331e10	−1.65005	−0.825023	+	0.565099i	$0.808838\pi$
$234$	−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	$-0.586335\pi$
$241$	−2.80613e10	−0.535835	−0.267918	+	0.963442i	$0.586335\pi$
$242$	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	$-0.550332\pi$
$269$	−2.70459e10	−0.314931	−0.157466	+	0.987524i	$0.550332\pi$
$270$	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	$-0.230315\pi$
$277$	1.46871e11	1.49891	0.749456	+	0.662055i	$0.230315\pi$
$278$	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	$-0.624448\pi$
$283$	−8.22402e10	−0.762159	−0.381079	+	0.924542i	$0.624448\pi$
$284$	−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	$-0.404342\pi$
$311$	9.76715e10	0.592033	0.296017	+	0.955183i	$0.404342\pi$
$312$	−1.60557e11	−0.959255
$313$	2.36302e11	1.39161	0.695805	−	0.718230i	$-0.255048\pi$
$313$	2.36302e11	1.39161	0.695805	+	0.718230i	$0.255048\pi$
$314$	6.20935e10	0.360464
$315$	−7.88055e11	−4.50982
$316$	−1.30147e11	−0.734245
$317$	4.50722e10	0.250693	0.125346	−	0.992113i	$-0.459996\pi$
$317$	4.50722e10	0.250693	0.125346	+	0.992113i	$0.459996\pi$
$318$	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	$-0.609650\pi$
$337$	−1.59919e11	−0.675408	−0.337704	+	0.941252i	$0.609650\pi$
$338$	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	$-0.191104\pi$
$347$	4.45690e11	1.65025	0.825127	+	0.564948i	$0.191104\pi$
$348$	−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	$-0.317897\pi$
$367$	3.76306e11	1.08279	0.541394	+	0.840769i	$0.317897\pi$
$368$	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	$-0.888794\pi$
$379$	−7.54823e11	−1.87918	−0.939590	+	0.342301i	$0.888794\pi$
$380$	−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	$-0.562619\pi$
$397$	−1.93481e11	−0.390913	−0.195457	+	0.980712i	$0.562619\pi$
$398$	−4.45379e11	−0.889725
$399$	4.51458e11	0.891741
$400$	−5.34755e10	−0.104444
$401$	−2.79164e11	−0.539150	−0.269575	−	0.962979i	$-0.586883\pi$
$401$	−2.79164e11	−0.539150	−0.269575	+	0.962979i	$0.586883\pi$
$402$	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	$-0.627560\pi$
$419$	−4.92234e11	−0.780205	−0.390103	+	0.920771i	$0.627560\pi$
$420$	−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	$-0.476619\pi$
$431$	1.05149e11	0.146777	0.0733884	+	0.997303i	$0.476619\pi$
$432$	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	$-0.711303\pi$
$439$	−9.58953e11	−1.23227	−0.616137	+	0.787639i	$0.711303\pi$
$440$	−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	$-0.640391\pi$
$449$	−7.35282e11	−0.853779	−0.426889	+	0.904304i	$0.640391\pi$
$450$	−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	$-0.500113\pi$
$479$	−8.19136e8	−0.000710962 0	−0.000355481		1.00000i	$0.500113\pi$
$480$	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	$-0.193229\pi$
$487$	2.03907e12	1.64267	0.821336	+	0.570444i	$0.193229\pi$
$488$	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	$-0.349149\pi$
$499$	1.26416e12	0.912742	0.456371	+	0.889790i	$0.349149\pi$
$500$	4.97548e11	0.356017
$501$	−9.58482e11	−0.679695
$502$	−1.06049e12	−0.745313
$503$	−4.72983e11	−0.329450	−0.164725	−	0.986340i	$-0.552674\pi$
$503$	−4.72983e11	−0.329450	−0.164725	+	0.986340i	$0.552674\pi$
$504$	−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	$-0.551395\pi$
$521$	−5.40736e11	−0.321525	−0.160763	+	0.986993i	$0.551395\pi$
$522$	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	$-0.307131\pi$
$541$	2.26946e12	1.13903	0.569514	+	0.821982i	$0.307131\pi$
$542$	−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	$-0.427613\pi$
$547$	9.44132e11	0.450910	0.225455	+	0.974254i	$0.427613\pi$
$548$	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	$-0.581689\pi$
$571$	−1.28951e12	−0.507649	−0.253824	+	0.967250i	$0.581689\pi$
$572$	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	$-0.105284\pi$
$601$	6.05010e12	1.89159	0.945796	+	0.324761i	$0.105284\pi$
$602$	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	$-0.388643\pi$
$607$	2.29272e12	0.685492	0.342746	+	0.939428i	$0.388643\pi$
$608$	−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	$-0.744063\pi$
$617$	−4.99510e12	−1.38759	−0.693795	+	0.720172i	$0.744063\pi$
$618$	5.87342e12	1.61973
$619$	−6.13894e12	−1.68068	−0.840341	−	0.542058i	$-0.817645\pi$
$619$	−6.13894e12	−1.68068	−0.840341	+	0.542058i	$0.817645\pi$
$620$	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	$-0.617228\pi$
$641$	−3.07759e12	−0.720029	−0.360014	+	0.932947i	$0.617228\pi$
$642$	3.72617e12	0.865676
$643$	−1.79981e12	−0.415219	−0.207609	−	0.978212i	$-0.566568\pi$
$643$	−1.79981e12	−0.415219	−0.207609	+	0.978212i	$0.566568\pi$
$644$	−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	$-0.652416\pi$
$653$	−4.28149e12	−0.921480	−0.460740	+	0.887535i	$0.652416\pi$
$654$	−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	$-0.482109\pi$
$673$	5.97945e11	0.112355	0.0561776	+	0.998421i	$0.482109\pi$
$674$	2.59580e12	0.484509
$675$	−7.45533e12	−1.38229
$676$	2.08437e12	0.383896
$677$	−1.85086e12	−0.338630	−0.169315	−	0.985562i	$-0.554156\pi$
$677$	−1.85086e12	−0.338630	−0.169315	+	0.985562i	$0.554156\pi$
$678$	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	$-0.587861\pi$
$683$	−3.09984e12	−0.545062	−0.272531	+	0.962147i	$0.587861\pi$
$684$	−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	$-0.445421\pi$
$691$	2.04515e12	0.341250	0.170625	+	0.985336i	$0.445421\pi$
$692$	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	$-0.505442\pi$
$709$	−2.30053e11	−0.0341917	−0.0170958	+	0.999854i	$0.505442\pi$
$710$	−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	$-0.565407\pi$
$719$	−2.92429e12	−0.408076	−0.204038	+	0.978963i	$0.565407\pi$
$720$	−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	$-0.323694\pi$
$743$	8.73895e12	1.05199	0.525993	+	0.850489i	$0.323694\pi$
$744$	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	$-0.473641\pi$
$751$	1.44210e12	0.165430	0.0827152	+	0.996573i	$0.473641\pi$
$752$	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	$-0.201333\pi$
$787$	1.73599e13	1.61310	0.806549	+	0.591167i	$0.201333\pi$
$788$	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	$-0.541859\pi$
$809$	−3.19512e12	−0.262252	−0.131126	+	0.991366i	$0.541859\pi$
$810$	−4.52660e13	−3.69479
$811$	−1.04002e13	−0.844204	−0.422102	−	0.906548i	$-0.638708\pi$
$811$	−1.04002e13	−0.844204	−0.422102	+	0.906548i	$0.638708\pi$
$812$	−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	$-0.564437\pi$
$821$	−5.23470e12	−0.402112	−0.201056	+	0.979580i	$0.564437\pi$
$822$	−8.56014e12	−0.653970
$823$	−2.49083e13	−1.89254	−0.946271	−	0.323375i	$-0.895183\pi$
$823$	−2.49083e13	−1.89254	−0.946271	+	0.323375i	$0.895183\pi$
$824$	1.61730e13	1.22213
$825$	9.32724e12	0.700987
$826$	−8.88539e12	−0.664150
$827$	−5.31180e12	−0.394882	−0.197441	−	0.980315i	$-0.563263\pi$
$827$	−5.31180e12	−0.394882	−0.197441	+	0.980315i	$0.563263\pi$
$828$	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	$-0.404163\pi$
$839$	8.51253e12	0.593103	0.296551	+	0.955017i	$0.404163\pi$
$840$	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	$-0.815443\pi$
$853$	−2.58704e13	−1.67314	−0.836571	+	0.547858i	$0.815443\pi$
$854$	1.56981e13	1.00992
$855$	1.78367e13	1.14147
$856$	1.02603e13	0.653174
$857$	1.63312e13	1.03420	0.517100	−	0.855925i	$-0.327012\pi$
$857$	1.63312e13	1.03420	0.517100	+	0.855925i	$0.327012\pi$
$858$	−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	$-0.521203\pi$
$877$	−2.33213e12	−0.133123	−0.0665617	+	0.997782i	$0.521203\pi$
$878$	1.55657e13	0.883981
$879$	4.76059e12	0.268974
$880$	5.53428e12	0.311092
$881$	−1.99931e13	−1.11812	−0.559061	−	0.829127i	$-0.688838\pi$
$881$	−1.99931e13	−1.11812	−0.559061	+	0.829127i	$0.688838\pi$
$882$	−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	$-0.502578\pi$
$887$	−2.98647e11	−0.0161995	−0.00809975	+	0.999967i	$0.502578\pi$
$888$	−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	$-0.650368\pi$
$907$	−1.85478e13	−0.910041	−0.455020	+	0.890481i	$0.650368\pi$
$908$	−1.22877e12	−0.0599906
$909$	4.75049e13	2.30781
$910$	1.06424e13	0.514464
$911$	−2.65224e13	−1.27580	−0.637898	−	0.770121i	$-0.720196\pi$
$911$	−2.65224e13	−1.27580	−0.637898	+	0.770121i	$0.720196\pi$
$912$	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	$-0.793043\pi$
$929$	−3.61411e13	−1.59195	−0.795977	+	0.605326i	$0.793043\pi$
$930$	−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	$-0.391724\pi$
$941$	1.60493e13	0.667273	0.333636	+	0.942702i	$0.391724\pi$
$942$	−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	$-0.423071\pi$
$947$	1.18470e13	0.478667	0.239334	+	0.970937i	$0.423071\pi$
$948$	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	$-0.717001\pi$
$983$	−3.68939e13	−1.26027	−0.630136	+	0.776485i	$0.717001\pi$
$984$	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	$-0.232027\pi$
$991$	4.52933e13	1.49177	0.745885	+	0.666074i	$0.232027\pi$
$992$	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	$-0.344161\pi$
$997$	2.93423e13	0.940515	0.470257	+	0.882529i	$0.344161\pi$
$998$	−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.g.1.13	✓	36
17.16	even	2		289.10.a.h.1.13	yes	36

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
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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