LMFDB - Embedded newform 289.10.a.g.1.11

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			1.11
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)

$f(q)$	$=$	$q-21.2323 q^{2} -64.4551 q^{3} -61.1895 q^{4} -398.305 q^{5} +1368.53 q^{6} +3851.88 q^{7} +12170.1 q^{8} -15528.5 q^{9} +O(q^{10})$	\(q-21.2323 q^{2} -64.4551 q^{3} -61.1895 q^{4} -398.305 q^{5} +1368.53 q^{6} +3851.88 q^{7} +12170.1 q^{8} -15528.5 q^{9} +8456.93 q^{10} +57855.9 q^{11} +3943.98 q^{12} +18882.5 q^{13} -81784.2 q^{14} +25672.8 q^{15} -227071. q^{16} +329707. q^{18} -786629. q^{19} +24372.1 q^{20} -248273. q^{21} -1.22841e6 q^{22} +821658. q^{23} -784427. q^{24} -1.79448e6 q^{25} -400918. q^{26} +2.26956e6 q^{27} -235694. q^{28} +1.71388e6 q^{29} -545093. q^{30} -7.63150e6 q^{31} -1.40987e6 q^{32} -3.72911e6 q^{33} -1.53422e6 q^{35} +950183. q^{36} +8.29440e6 q^{37} +1.67020e7 q^{38} -1.21707e6 q^{39} -4.84742e6 q^{40} +9.40014e6 q^{41} +5.27141e6 q^{42} -1.23821e6 q^{43} -3.54017e6 q^{44} +6.18509e6 q^{45} -1.74457e7 q^{46} -5.62823e6 q^{47} +1.46359e7 q^{48} -2.55167e7 q^{49} +3.81009e7 q^{50} -1.15541e6 q^{52} +5.02821e7 q^{53} -4.81881e7 q^{54} -2.30443e7 q^{55} +4.68778e7 q^{56} +5.07023e7 q^{57} -3.63896e7 q^{58} +3.74512e7 q^{59} -1.57091e6 q^{60} +5.48296e7 q^{61} +1.62034e8 q^{62} -5.98140e7 q^{63} +1.46195e8 q^{64} -7.52098e6 q^{65} +7.91775e7 q^{66} -1.56686e8 q^{67} -5.29601e7 q^{69} +3.25751e7 q^{70} +2.37280e8 q^{71} -1.88984e8 q^{72} -4.12331e7 q^{73} -1.76109e8 q^{74} +1.15663e8 q^{75} +4.81335e7 q^{76} +2.22854e8 q^{77} +2.58412e7 q^{78} +1.46264e8 q^{79} +9.04435e7 q^{80} +1.59363e8 q^{81} -1.99586e8 q^{82} +8.36517e7 q^{83} +1.51917e7 q^{84} +2.62900e7 q^{86} -1.10468e8 q^{87} +7.04114e8 q^{88} +9.53686e8 q^{89} -1.31324e8 q^{90} +7.27329e7 q^{91} -5.02768e7 q^{92} +4.91889e8 q^{93} +1.19500e8 q^{94} +3.13318e8 q^{95} +9.08734e7 q^{96} -1.21808e9 q^{97} +5.41777e8 q^{98} -8.98417e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−21.2323	−0.938344	−0.469172	−	0.883107i	$-0.655448\pi$
$2$	−21.2323	−0.938344	−0.469172	+	0.883107i	$0.655448\pi$
$3$	−64.4551	−0.459422	−0.229711	−	0.973259i	$-0.573778\pi$
$3$	−64.4551	−0.459422	−0.229711	+	0.973259i	$0.573778\pi$
$4$	−61.1895	−0.119511
$5$	−398.305	−0.285004	−0.142502	−	0.989795i	$-0.545515\pi$
$5$	−398.305	−0.285004	−0.142502	+	0.989795i	$0.545515\pi$
$6$	1368.53	0.431096
$7$	3851.88	0.606361	0.303180	−	0.952933i	$-0.401952\pi$
$7$	3851.88	0.606361	0.303180	+	0.952933i	$0.401952\pi$
$8$	12170.1	1.05049
$9$	−15528.5	−0.788931
$10$	8456.93	0.267432
$11$	57855.9	1.19146	0.595731	−	0.803184i	$-0.296862\pi$
$11$	57855.9	1.19146	0.595731	+	0.803184i	$0.296862\pi$
$12$	3943.98	0.0549059
$13$	18882.5	0.183364	0.0916819	−	0.995788i	$-0.470776\pi$
$13$	18882.5	0.183364	0.0916819	+	0.995788i	$0.470776\pi$
$14$	−81784.2	−0.568975
$15$	25672.8	0.130937
$16$	−227071.	−0.866206
$17$	0	0
$17$	0	0
$18$	329707.	0.740289
$19$	−786629.	−1.38477	−0.692387	−	0.721526i	$-0.743441\pi$
$19$	−786629.	−1.38477	−0.692387	+	0.721526i	$0.743441\pi$
$20$	24372.1	0.0340610
$21$	−248273.	−0.278576
$22$	−1.22841e6	−1.11800
$23$	821658.	0.612232	0.306116	−	0.951994i	$-0.400971\pi$
$23$	821658.	0.612232	0.306116	+	0.951994i	$0.400971\pi$
$24$	−784427.	−0.482617
$25$	−1.79448e6	−0.918773
$26$	−400918.	−0.172058
$27$	2.26956e6	0.821875
$28$	−235694.	−0.0724666
$29$	1.71388e6	0.449975	0.224988	−	0.974362i	$-0.427766\pi$
$29$	1.71388e6	0.449975	0.224988	+	0.974362i	$0.427766\pi$
$30$	−545093.	−0.122864
$31$	−7.63150e6	−1.48416	−0.742082	−	0.670309i	$-0.766162\pi$
$31$	−7.63150e6	−1.48416	−0.742082	+	0.670309i	$0.766162\pi$
$32$	−1.40987e6	−0.237687
$33$	−3.72911e6	−0.547384
$34$	0	0
$35$	−1.53422e6	−0.172815
$36$	950183.	0.0942858
$37$	8.29440e6	0.727574	0.363787	−	0.931482i	$-0.381484\pi$
$37$	8.29440e6	0.727574	0.363787	+	0.931482i	$0.381484\pi$
$38$	1.67020e7	1.29939
$39$	−1.21707e6	−0.0842414
$40$	−4.84742e6	−0.299393
$41$	9.40014e6	0.519525	0.259763	−	0.965672i	$-0.416356\pi$
$41$	9.40014e6	0.519525	0.259763	+	0.965672i	$0.416356\pi$
$42$	5.27141e6	0.261400
$43$	−1.23821e6	−0.0552314	−0.0276157	−	0.999619i	$-0.508791\pi$
$43$	−1.23821e6	−0.0552314	−0.0276157	+	0.999619i	$0.508791\pi$
$44$	−3.54017e6	−0.142393
$45$	6.18509e6	0.224848
$46$	−1.74457e7	−0.574484
$47$	−5.62823e6	−0.168241	−0.0841204	−	0.996456i	$-0.526808\pi$
$47$	−5.62823e6	−0.168241	−0.0841204	+	0.996456i	$0.526808\pi$
$48$	1.46359e7	0.397954
$49$	−2.55167e7	−0.632326
$50$	3.81009e7	0.862125
$51$	0	0
$52$	−1.15541e6	−0.0219139
$53$	5.02821e7	0.875330	0.437665	−	0.899138i	$-0.355806\pi$
$53$	5.02821e7	0.875330	0.437665	+	0.899138i	$0.355806\pi$
$54$	−4.81881e7	−0.771201
$55$	−2.30443e7	−0.339571
$56$	4.68778e7	0.636974
$57$	5.07023e7	0.636196
$58$	−3.63896e7	−0.422232
$59$	3.74512e7	0.402376	0.201188	−	0.979553i	$-0.435520\pi$
$59$	3.74512e7	0.402376	0.201188	+	0.979553i	$0.435520\pi$
$60$	−1.57091e6	−0.0156484
$61$	5.48296e7	0.507026	0.253513	−	0.967332i	$-0.418414\pi$
$61$	5.48296e7	0.507026	0.253513	+	0.967332i	$0.418414\pi$
$62$	1.62034e8	1.39266
$63$	−5.98140e7	−0.478377
$64$	1.46195e8	1.08924
$65$	−7.52098e6	−0.0522594
$66$	7.91775e7	0.513635
$67$	−1.56686e8	−0.949934	−0.474967	−	0.880004i	$-0.657540\pi$
$67$	−1.56686e8	−0.949934	−0.474967	+	0.880004i	$0.657540\pi$
$68$	0	0
$69$	−5.29601e7	−0.281273
$70$	3.25751e7	0.162160
$71$	2.37280e8	1.10815	0.554074	−	0.832467i	$-0.313072\pi$
$71$	2.37280e8	1.10815	0.554074	+	0.832467i	$0.313072\pi$
$72$	−1.88984e8	−0.828761
$73$	−4.12331e7	−0.169939	−0.0849696	−	0.996384i	$-0.527079\pi$
$73$	−4.12331e7	−0.169939	−0.0849696	+	0.996384i	$0.527079\pi$
$74$	−1.76109e8	−0.682715
$75$	1.15663e8	0.422105
$76$	4.81335e7	0.165495
$77$	2.22854e8	0.722456
$78$	2.58412e7	0.0790474
$79$	1.46264e8	0.422489	0.211244	−	0.977433i	$-0.432248\pi$
$79$	1.46264e8	0.422489	0.211244	+	0.977433i	$0.432248\pi$
$80$	9.04435e7	0.246872
$81$	1.59363e8	0.411344
$82$	−1.99586e8	−0.487493
$83$	8.36517e7	0.193474	0.0967371	−	0.995310i	$-0.469159\pi$
$83$	8.36517e7	0.193474	0.0967371	+	0.995310i	$0.469159\pi$
$84$	1.51917e7	0.0332928
$85$	0	0
$86$	2.62900e7	0.0518260
$87$	−1.10468e8	−0.206729
$88$	7.04114e8	1.25161
$89$	9.53686e8	1.61120	0.805602	−	0.592458i	$-0.201842\pi$
$89$	9.53686e8	1.61120	0.805602	+	0.592458i	$0.201842\pi$
$90$	−1.31324e8	−0.210985
$91$	7.27329e7	0.111185
$92$	−5.02768e7	−0.0731682
$93$	4.91889e8	0.681858
$94$	1.19500e8	0.157868
$95$	3.13318e8	0.394666
$96$	9.08734e7	0.109198
$97$	−1.21808e9	−1.39702	−0.698509	−	0.715601i	$-0.746153\pi$
$97$	−1.21808e9	−1.39702	−0.698509	+	0.715601i	$0.746153\pi$
$98$	5.41777e8	0.593340
$99$	−8.98417e8	−0.939982
$100$	1.09803e8	0.109803
$101$	−1.85970e9	−1.77826	−0.889132	−	0.457652i	$-0.848691\pi$
$101$	−1.85970e9	−1.77826	−0.889132	+	0.457652i	$0.848691\pi$
$102$	0	0
$103$	−1.82228e9	−1.59532	−0.797660	−	0.603107i	$-0.793929\pi$
$103$	−1.82228e9	−1.59532	−0.797660	+	0.603107i	$0.793929\pi$
$104$	2.29802e8	0.192621
$105$	9.88885e7	0.0793951
$106$	−1.06760e9	−0.821360
$107$	1.89558e9	1.39802	0.699012	−	0.715109i	$-0.253623\pi$
$107$	1.89558e9	1.39802	0.699012	+	0.715109i	$0.253623\pi$
$108$	−1.38873e8	−0.0982228
$109$	1.15703e9	0.785104	0.392552	−	0.919730i	$-0.371592\pi$
$109$	1.15703e9	0.785104	0.392552	+	0.919730i	$0.371592\pi$
$110$	4.89283e8	0.318635
$111$	−5.34617e8	−0.334264
$112$	−8.74649e8	−0.525234
$113$	3.34864e9	1.93204	0.966018	−	0.258473i	$-0.0832194\pi$
$113$	3.34864e9	1.93204	0.966018	+	0.258473i	$0.0832194\pi$
$114$	−1.07653e9	−0.596971
$115$	−3.27270e8	−0.174488
$116$	−1.04871e8	−0.0537769
$117$	−2.93217e8	−0.144661
$118$	−7.95176e8	−0.377567
$119$	0	0
$120$	3.12441e8	0.137548
$121$	9.89355e8	0.419583
$122$	−1.16416e9	−0.475765
$123$	−6.05887e8	−0.238681
$124$	4.66967e8	0.177374
$125$	1.49269e9	0.546858
$126$	1.26999e9	0.448882
$127$	3.51461e9	1.19884	0.599418	−	0.800436i	$-0.295399\pi$
$127$	3.51461e9	1.19884	0.599418	+	0.800436i	$0.295399\pi$
$128$	−2.38220e9	−0.784393
$129$	7.98089e7	0.0253745
$130$	1.59688e8	0.0490373
$131$	2.53404e9	0.751783	0.375892	−	0.926664i	$-0.377337\pi$
$131$	2.53404e9	0.751783	0.375892	+	0.926664i	$0.377337\pi$
$132$	2.28182e8	0.0654183
$133$	−3.03000e9	−0.839673
$134$	3.32680e9	0.891364
$135$	−9.03979e8	−0.234237
$136$	0	0
$137$	−3.06420e9	−0.743146	−0.371573	−	0.928404i	$-0.621181\pi$
$137$	−3.06420e9	−0.743146	−0.371573	+	0.928404i	$0.621181\pi$
$138$	1.12446e9	0.263931
$139$	3.98153e9	0.904655	0.452327	−	0.891852i	$-0.350594\pi$
$139$	3.98153e9	0.904655	0.452327	+	0.891852i	$0.350594\pi$
$140$	9.38782e7	0.0206533
$141$	3.62768e8	0.0772935
$142$	−5.03799e9	−1.03982
$143$	1.09246e9	0.218471
$144$	3.52608e9	0.683377
$145$	−6.82646e8	−0.128245
$146$	8.75474e8	0.159461
$147$	1.64468e9	0.290505
$148$	−5.07530e8	−0.0869529
$149$	1.25034e9	0.207822	0.103911	−	0.994587i	$-0.466864\pi$
$149$	1.25034e9	0.207822	0.103911	+	0.994587i	$0.466864\pi$
$150$	−2.45580e9	−0.396079
$151$	1.16543e10	1.82427	0.912137	−	0.409885i	$-0.134431\pi$
$151$	1.16543e10	1.82427	0.912137	+	0.409885i	$0.134431\pi$
$152$	−9.57338e9	−1.45469
$153$	0	0
$154$	−4.73170e9	−0.677912
$155$	3.03966e9	0.422993
$156$	7.44720e7	0.0100677
$157$	4.36782e9	0.573742	0.286871	−	0.957969i	$-0.407385\pi$
$157$	4.36782e9	0.573742	0.286871	+	0.957969i	$0.407385\pi$
$158$	−3.10552e9	−0.396440
$159$	−3.24094e9	−0.402146
$160$	5.61559e8	0.0677416
$161$	3.16492e9	0.371233
$162$	−3.38364e9	−0.385982
$163$	−1.39760e10	−1.55073	−0.775367	−	0.631511i	$-0.782435\pi$
$163$	−1.39760e10	−1.55073	−0.775367	+	0.631511i	$0.782435\pi$
$164$	−5.75189e8	−0.0620889
$165$	1.48532e9	0.156007
$166$	−1.77612e9	−0.181545
$167$	−4.41364e9	−0.439109	−0.219555	−	0.975600i	$-0.570460\pi$
$167$	−4.41364e9	−0.439109	−0.219555	+	0.975600i	$0.570460\pi$
$168$	−3.02152e9	−0.292640
$169$	−1.02480e10	−0.966378
$170$	0	0
$171$	1.22152e10	1.09249
$172$	7.57653e7	0.00660074
$173$	−1.72782e10	−1.46653	−0.733267	−	0.679941i	$-0.762006\pi$
$173$	−1.72782e10	−1.46653	−0.733267	+	0.679941i	$0.762006\pi$
$174$	2.34549e9	0.193983
$175$	−6.91211e9	−0.557108
$176$	−1.31374e10	−1.03205
$177$	−2.41392e9	−0.184860
$178$	−2.02489e10	−1.51186
$179$	−1.48464e10	−1.08089	−0.540445	−	0.841379i	$-0.681744\pi$
$179$	−1.48464e10	−1.08089	−0.540445	+	0.841379i	$0.681744\pi$
$180$	−3.78463e8	−0.0268718
$181$	4.63118e9	0.320729	0.160364	−	0.987058i	$-0.448733\pi$
$181$	4.63118e9	0.320729	0.160364	+	0.987058i	$0.448733\pi$
$182$	−1.54429e9	−0.104329
$183$	−3.53405e9	−0.232939
$184$	9.99968e9	0.643141
$185$	−3.30370e9	−0.207361
$186$	−1.04439e10	−0.639817
$187$	0	0
$188$	3.44388e8	0.0201066
$189$	8.74208e9	0.498353
$190$	−6.65247e9	−0.370332
$191$	−5.36986e9	−0.291953	−0.145977	−	0.989288i	$-0.546632\pi$
$191$	−5.36986e9	−0.291953	−0.145977	+	0.989288i	$0.546632\pi$
$192$	−9.42302e9	−0.500420
$193$	−6.19209e9	−0.321240	−0.160620	−	0.987016i	$-0.551349\pi$
$193$	−6.19209e9	−0.321240	−0.160620	+	0.987016i	$0.551349\pi$
$194$	2.58626e10	1.31088
$195$	4.84766e8	0.0240091
$196$	1.56135e9	0.0755698
$197$	−2.78857e10	−1.31912	−0.659558	−	0.751653i	$-0.729257\pi$
$197$	−2.78857e10	−1.31912	−0.659558	+	0.751653i	$0.729257\pi$
$198$	1.90755e10	0.882026
$199$	−3.10537e10	−1.40370	−0.701851	−	0.712324i	$-0.747643\pi$
$199$	−3.10537e10	−1.40370	−0.701851	+	0.712324i	$0.747643\pi$
$200$	−2.18390e10	−0.965158
$201$	1.00992e10	0.436420
$202$	3.94856e10	1.66862
$203$	6.60164e9	0.272847
$204$	0	0
$205$	−3.74412e9	−0.148067
$206$	3.86912e10	1.49696
$207$	−1.27591e10	−0.483009
$208$	−4.28766e9	−0.158831
$209$	−4.55111e10	−1.64991
$210$	−2.09963e9	−0.0744999
$211$	−5.99281e9	−0.208142	−0.104071	−	0.994570i	$-0.533187\pi$
$211$	−5.99281e9	−0.208142	−0.104071	+	0.994570i	$0.533187\pi$
$212$	−3.07673e9	−0.104611
$213$	−1.52939e10	−0.509108
$214$	−4.02475e10	−1.31183
$215$	4.93185e8	0.0157412
$216$	2.76209e10	0.863368
$217$	−2.93956e10	−0.899940
$218$	−2.45665e10	−0.736698
$219$	2.65769e9	0.0780738
$220$	1.41007e9	0.0405824
$221$	0	0
$222$	1.13511e10	0.313654
$223$	5.94964e10	1.61109	0.805544	−	0.592536i	$-0.201873\pi$
$223$	5.94964e10	1.61109	0.805544	+	0.592536i	$0.201873\pi$
$224$	−5.43065e9	−0.144124
$225$	2.78656e10	0.724849
$226$	−7.10993e10	−1.81291
$227$	−7.39599e10	−1.84876	−0.924379	−	0.381475i	$-0.875416\pi$
$227$	−7.39599e10	−1.84876	−0.924379	+	0.381475i	$0.875416\pi$
$228$	−3.10245e9	−0.0760322
$229$	−4.92124e10	−1.18254	−0.591269	−	0.806474i	$-0.701373\pi$
$229$	−4.92124e10	−1.18254	−0.591269	+	0.806474i	$0.701373\pi$
$230$	6.94870e9	0.163730
$231$	−1.43641e10	−0.331912
$232$	2.08581e10	0.472693
$233$	4.09686e10	0.910646	0.455323	−	0.890326i	$-0.349524\pi$
$233$	4.09686e10	0.910646	0.455323	+	0.890326i	$0.349524\pi$
$234$	6.22567e9	0.135742
$235$	2.24175e9	0.0479493
$236$	−2.29162e9	−0.0480883
$237$	−9.42746e9	−0.194101
$238$	0	0
$239$	8.62890e10	1.71066	0.855332	−	0.518080i	$-0.173353\pi$
$239$	8.62890e10	1.71066	0.855332	+	0.518080i	$0.173353\pi$
$240$	−5.82955e9	−0.113419
$241$	−6.30098e10	−1.20318	−0.601591	−	0.798804i	$-0.705466\pi$
$241$	−6.30098e10	−1.20318	−0.601591	+	0.798804i	$0.705466\pi$
$242$	−2.10063e10	−0.393713
$243$	−5.49436e10	−1.01086
$244$	−3.35499e9	−0.0605951
$245$	1.01634e10	0.180216
$246$	1.28644e10	0.223965
$247$	−1.48535e10	−0.253918
$248$	−9.28763e10	−1.55909
$249$	−5.39178e9	−0.0888864
$250$	−3.16932e10	−0.513141
$251$	3.24383e10	0.515854	0.257927	−	0.966164i	$-0.416961\pi$
$251$	3.24383e10	0.515854	0.257927	+	0.966164i	$0.416961\pi$
$252$	3.65999e9	0.0571712
$253$	4.75377e10	0.729451
$254$	−7.46232e10	−1.12492
$255$	0	0
$256$	−2.42722e10	−0.353207
$257$	2.45445e10	0.350958	0.175479	−	0.984483i	$-0.443853\pi$
$257$	2.45445e10	0.350958	0.175479	+	0.984483i	$0.443853\pi$
$258$	−1.69453e9	−0.0238100
$259$	3.19490e10	0.441172
$260$	4.60205e8	0.00624556
$261$	−2.66140e10	−0.355000
$262$	−5.38035e10	−0.705431
$263$	−1.95967e10	−0.252570	−0.126285	−	0.991994i	$-0.540305\pi$
$263$	−1.95967e10	−0.252570	−0.126285	+	0.991994i	$0.540305\pi$
$264$	−4.53837e10	−0.575019
$265$	−2.00276e10	−0.249472
$266$	6.43339e10	0.787902
$267$	−6.14700e10	−0.740222
$268$	9.58753e9	0.113527
$269$	−3.80419e10	−0.442973	−0.221486	−	0.975163i	$-0.571091\pi$
$269$	−3.80419e10	−0.442973	−0.221486	+	0.975163i	$0.571091\pi$
$270$	1.91935e10	0.219795
$271$	−1.13318e11	−1.27625	−0.638125	−	0.769933i	$-0.720290\pi$
$271$	−1.13318e11	−1.27625	−0.638125	+	0.769933i	$0.720290\pi$
$272$	0	0
$273$	−4.68801e9	−0.0510807
$274$	6.50599e10	0.697326
$275$	−1.03821e11	−1.09468
$276$	3.24060e9	0.0336151
$277$	−6.42382e10	−0.655594	−0.327797	−	0.944748i	$-0.606306\pi$
$277$	−6.42382e10	−0.655594	−0.327797	+	0.944748i	$0.606306\pi$
$278$	−8.45369e10	−0.848877
$279$	1.18506e11	1.17090
$280$	−1.86717e10	−0.181540
$281$	−6.78724e10	−0.649404	−0.324702	−	0.945816i	$-0.605264\pi$
$281$	−6.78724e10	−0.649404	−0.324702	+	0.945816i	$0.605264\pi$
$282$	−7.70240e9	−0.0725279
$283$	−4.27495e10	−0.396180	−0.198090	−	0.980184i	$-0.563474\pi$
$283$	−4.27495e10	−0.396180	−0.198090	+	0.980184i	$0.563474\pi$
$284$	−1.45190e10	−0.132436
$285$	−2.01950e10	−0.181318
$286$	−2.31955e10	−0.205001
$287$	3.62082e10	0.315020
$288$	2.18932e10	0.187518
$289$	0	0
$290$	1.44941e10	0.120338
$291$	7.85114e10	0.641821
$292$	2.52303e9	0.0203096
$293$	3.38660e10	0.268448	0.134224	−	0.990951i	$-0.457146\pi$
$293$	3.38660e10	0.268448	0.134224	+	0.990951i	$0.457146\pi$
$294$	−3.49203e10	−0.272593
$295$	−1.49170e10	−0.114679
$296$	1.00944e11	0.764306
$297$	1.31308e11	0.979233
$298$	−2.65476e10	−0.195008
$299$	1.55149e10	0.112261
$300$	−7.07738e9	−0.0504460
$301$	−4.76943e9	−0.0334901
$302$	−2.47448e11	−1.71180
$303$	1.19867e11	0.816973
$304$	1.78621e11	1.19950
$305$	−2.18389e10	−0.144504
$306$	0	0
$307$	−1.43665e11	−0.923056	−0.461528	−	0.887126i	$-0.652699\pi$
$307$	−1.43665e11	−0.923056	−0.461528	+	0.887126i	$0.652699\pi$
$308$	−1.36363e10	−0.0863413
$309$	1.17455e11	0.732926
$310$	−6.45391e10	−0.396913
$311$	2.41669e11	1.46487	0.732436	−	0.680836i	$-0.238383\pi$
$311$	2.41669e11	1.46487	0.732436	+	0.680836i	$0.238383\pi$
$312$	−1.48119e10	−0.0884944
$313$	3.00713e10	0.177093	0.0885467	−	0.996072i	$-0.471778\pi$
$313$	3.00713e10	0.177093	0.0885467	+	0.996072i	$0.471778\pi$
$314$	−9.27390e10	−0.538367
$315$	2.38242e10	0.136339
$316$	−8.94981e9	−0.0504919
$317$	2.08347e11	1.15883	0.579417	−	0.815031i	$-0.303280\pi$
$317$	2.08347e11	1.15883	0.579417	+	0.815031i	$0.303280\pi$
$318$	6.88125e10	0.377351
$319$	9.91579e10	0.536129
$320$	−5.82302e10	−0.310437
$321$	−1.22180e11	−0.642284
$322$	−6.71986e10	−0.348345
$323$	0	0
$324$	−9.75135e9	−0.0491600
$325$	−3.38842e10	−0.168470
$326$	2.96742e11	1.45512
$327$	−7.45768e10	−0.360694
$328$	1.14401e11	0.545754
$329$	−2.16792e10	−0.102015
$330$	−3.15368e10	−0.146388
$331$	3.16856e11	1.45090	0.725448	−	0.688277i	$-0.241633\pi$
$331$	3.16856e11	1.45090	0.725448	+	0.688277i	$0.241633\pi$
$332$	−5.11860e9	−0.0231223
$333$	−1.28800e11	−0.574006
$334$	9.37116e10	0.412035
$335$	6.24088e10	0.270735
$336$	5.63756e10	0.241304
$337$	−4.30379e11	−1.81768	−0.908838	−	0.417149i	$-0.863029\pi$
$337$	−4.30379e11	−1.81768	−0.908838	+	0.417149i	$0.863029\pi$
$338$	2.17588e11	0.906795
$339$	−2.15837e11	−0.887620
$340$	0	0
$341$	−4.41527e11	−1.76833
$342$	−2.59357e11	−1.02513
$343$	−2.53724e11	−0.989779
$344$	−1.50692e10	−0.0580198
$345$	2.10943e10	0.0801638
$346$	3.66857e11	1.37611
$347$	−1.95226e11	−0.722863	−0.361431	−	0.932399i	$-0.617712\pi$
$347$	−1.95226e11	−0.722863	−0.361431	+	0.932399i	$0.617712\pi$
$348$	6.75949e9	0.0247063
$349$	−1.86031e11	−0.671230	−0.335615	−	0.941999i	$-0.608944\pi$
$349$	−1.86031e11	−0.671230	−0.335615	+	0.941999i	$0.608944\pi$
$350$	1.46760e11	0.522759
$351$	4.28550e10	0.150702
$352$	−8.15693e10	−0.283195
$353$	4.03261e11	1.38229	0.691146	−	0.722715i	$-0.257106\pi$
$353$	4.03261e11	1.38229	0.691146	+	0.722715i	$0.257106\pi$
$354$	5.12532e10	0.173463
$355$	−9.45097e10	−0.315827
$356$	−5.83556e10	−0.192556
$357$	0	0
$358$	3.15222e11	1.01425
$359$	−8.31340e10	−0.264152	−0.132076	−	0.991240i	$-0.542164\pi$
$359$	−8.31340e10	−0.264152	−0.132076	+	0.991240i	$0.542164\pi$
$360$	7.52734e10	0.236200
$361$	2.96098e11	0.917600
$362$	−9.83305e10	−0.300954
$363$	−6.37690e10	−0.192766
$364$	−4.45049e9	−0.0132878
$365$	1.64234e10	0.0484333
$366$	7.50359e10	0.218577
$367$	1.69270e11	0.487059	0.243530	−	0.969893i	$-0.421695\pi$
$367$	1.69270e11	0.487059	0.243530	+	0.969893i	$0.421695\pi$
$368$	−1.86575e11	−0.530319
$369$	−1.45970e11	−0.409870
$370$	7.01452e10	0.194576
$371$	1.93680e11	0.530766
$372$	−3.00985e10	−0.0814894
$373$	3.17477e11	0.849223	0.424612	−	0.905376i	$-0.360411\pi$
$373$	3.17477e11	0.849223	0.424612	+	0.905376i	$0.360411\pi$
$374$	0	0
$375$	−9.62115e10	−0.251239
$376$	−6.84963e10	−0.176735
$377$	3.23622e10	0.0825092
$378$	−1.85614e11	−0.467626
$379$	6.44843e11	1.60538	0.802690	−	0.596397i	$-0.203401\pi$
$379$	6.44843e11	1.60538	0.802690	+	0.596397i	$0.203401\pi$
$380$	−1.91718e10	−0.0471668
$381$	−2.26534e11	−0.550772
$382$	1.14015e11	0.273952
$383$	4.18939e11	0.994846	0.497423	−	0.867508i	$-0.334280\pi$
$383$	4.18939e11	0.994846	0.497423	+	0.867508i	$0.334280\pi$
$384$	1.53545e11	0.360368
$385$	−8.87637e10	−0.205903
$386$	1.31472e11	0.301433
$387$	1.92276e10	0.0435737
$388$	7.45336e10	0.166959
$389$	−7.48004e11	−1.65627	−0.828134	−	0.560530i	$-0.810598\pi$
$389$	−7.48004e11	−1.65627	−0.828134	+	0.560530i	$0.810598\pi$
$390$	−1.02927e10	−0.0225288
$391$	0	0
$392$	−3.10541e11	−0.664250
$393$	−1.63332e11	−0.345386
$394$	5.92077e11	1.23779
$395$	−5.82576e10	−0.120411
$396$	5.49737e10	0.112338
$397$	6.24540e9	0.0126184	0.00630918	−	0.999980i	$-0.497992\pi$
$397$	6.24540e9	0.0126184	0.00630918	+	0.999980i	$0.497992\pi$
$398$	6.59342e11	1.31715
$399$	1.95299e11	0.385764
$400$	4.07474e11	0.795847
$401$	5.27612e11	1.01898	0.509489	−	0.860477i	$-0.329834\pi$
$401$	5.27612e11	1.01898	0.509489	+	0.860477i	$0.329834\pi$
$402$	−2.14429e11	−0.409513
$403$	−1.44102e11	−0.272142
$404$	1.13794e11	0.212522
$405$	−6.34751e10	−0.117235
$406$	−1.40168e11	−0.256025
$407$	4.79880e11	0.866877
$408$	0	0
$409$	3.85068e11	0.680429	0.340214	−	0.940348i	$-0.389500\pi$
$409$	3.85068e11	0.680429	0.340214	+	0.940348i	$0.389500\pi$
$410$	7.94963e10	0.138938
$411$	1.97503e11	0.341418
$412$	1.11504e11	0.190658
$413$	1.44258e11	0.243985
$414$	2.70906e11	0.453228
$415$	−3.33189e10	−0.0551409
$416$	−2.66218e10	−0.0435831
$417$	−2.56630e11	−0.415618
$418$	9.66306e11	1.54818
$419$	−2.72620e11	−0.432110	−0.216055	−	0.976381i	$-0.569319\pi$
$419$	−2.72620e11	−0.432110	−0.216055	+	0.976381i	$0.569319\pi$
$420$	−6.05094e9	−0.00948857
$421$	−3.26170e11	−0.506028	−0.253014	−	0.967463i	$-0.581422\pi$
$421$	−3.26170e11	−0.506028	−0.253014	+	0.967463i	$0.581422\pi$
$422$	1.27241e11	0.195309
$423$	8.73981e10	0.132730
$424$	6.11939e11	0.919522
$425$	0	0
$426$	3.24725e11	0.477718
$427$	2.11197e11	0.307441
$428$	−1.15990e11	−0.167079
$429$	−7.04148e10	−0.100370
$430$	−1.04714e10	−0.0147706
$431$	8.94389e11	1.24847	0.624236	−	0.781236i	$-0.285410\pi$
$431$	8.94389e11	1.24847	0.624236	+	0.781236i	$0.285410\pi$
$432$	−5.15352e11	−0.711913
$433$	−6.57153e11	−0.898403	−0.449202	−	0.893430i	$-0.648291\pi$
$433$	−6.57153e11	−0.898403	−0.449202	+	0.893430i	$0.648291\pi$
$434$	6.24136e11	0.844453
$435$	4.40000e10	0.0589185
$436$	−7.07984e10	−0.0938284
$437$	−6.46340e11	−0.847803
$438$	−5.64288e10	−0.0732601
$439$	7.30710e11	0.938976	0.469488	−	0.882939i	$-0.344439\pi$
$439$	7.30710e11	0.938976	0.469488	+	0.882939i	$0.344439\pi$
$440$	−2.80452e11	−0.356715
$441$	3.96236e11	0.498862
$442$	0	0
$443$	8.53914e11	1.05341	0.526705	−	0.850048i	$-0.323427\pi$
$443$	8.53914e11	1.05341	0.526705	+	0.850048i	$0.323427\pi$
$444$	3.27129e10	0.0399481
$445$	−3.79858e11	−0.459199
$446$	−1.26325e12	−1.51175
$447$	−8.05910e10	−0.0954778
$448$	5.63125e11	0.660471
$449$	−7.82728e11	−0.908871	−0.454435	−	0.890780i	$-0.650159\pi$
$449$	−7.82728e11	−0.908871	−0.454435	+	0.890780i	$0.650159\pi$
$450$	−5.91651e11	−0.680157
$451$	5.43853e11	0.618995
$452$	−2.04902e11	−0.230899
$453$	−7.51180e11	−0.838112
$454$	1.57034e12	1.73477
$455$	−2.89699e10	−0.0316881
$456$	6.17054e11	0.668315
$457$	−1.29347e12	−1.38718	−0.693590	−	0.720370i	$-0.743972\pi$
$457$	−1.29347e12	−1.38718	−0.693590	+	0.720370i	$0.743972\pi$
$458$	1.04489e12	1.10963
$459$	0	0
$460$	2.00255e10	0.0208532
$461$	−1.76880e12	−1.82400	−0.912000	−	0.410191i	$-0.865462\pi$
$461$	−1.76880e12	−1.82400	−0.912000	+	0.410191i	$0.865462\pi$
$462$	3.04982e11	0.311448
$463$	1.10120e12	1.11366	0.556829	−	0.830627i	$-0.312018\pi$
$463$	1.10120e12	1.11366	0.556829	+	0.830627i	$0.312018\pi$
$464$	−3.89172e11	−0.389772
$465$	−1.95922e11	−0.194332
$466$	−8.69858e11	−0.854499
$467$	−5.83654e11	−0.567845	−0.283922	−	0.958847i	$-0.591636\pi$
$467$	−5.83654e11	−0.567845	−0.283922	+	0.958847i	$0.591636\pi$
$468$	1.79418e10	0.0172886
$469$	−6.03535e11	−0.576003
$470$	−4.75975e10	−0.0449929
$471$	−2.81529e11	−0.263590
$472$	4.55786e11	0.422690
$473$	−7.16376e10	−0.0658061
$474$	2.00167e11	0.182133
$475$	1.41159e12	1.27229
$476$	0	0
$477$	−7.80807e11	−0.690575
$478$	−1.83211e12	−1.60519
$479$	−9.68349e11	−0.840470	−0.420235	−	0.907415i	$-0.638052\pi$
$479$	−9.68349e11	−0.840470	−0.420235	+	0.907415i	$0.638052\pi$
$480$	−3.61953e10	−0.0311220
$481$	1.56619e11	0.133411
$482$	1.33784e12	1.12900
$483$	−2.03996e11	−0.170553
$484$	−6.05381e10	−0.0501447
$485$	4.85166e11	0.398156
$486$	1.16658e12	0.948530
$487$	−7.26481e11	−0.585254	−0.292627	−	0.956227i	$-0.594529\pi$
$487$	−7.26481e11	−0.585254	−0.292627	+	0.956227i	$0.594529\pi$
$488$	6.67283e11	0.532624
$489$	9.00822e11	0.712441
$490$	−2.15793e11	−0.169104
$491$	−1.63273e12	−1.26779	−0.633897	−	0.773418i	$-0.718545\pi$
$491$	−1.63273e12	−1.26779	−0.633897	+	0.773418i	$0.718545\pi$
$492$	3.70739e10	0.0285250
$493$	0	0
$494$	3.15374e11	0.238262
$495$	3.57844e11	0.267899
$496$	1.73289e12	1.28559
$497$	9.13972e11	0.671938
$498$	1.14480e11	0.0834060
$499$	−1.74280e12	−1.25833	−0.629165	−	0.777272i	$-0.716603\pi$
$499$	−1.74280e12	−1.25833	−0.629165	+	0.777272i	$0.716603\pi$
$500$	−9.13369e10	−0.0653554
$501$	2.84481e11	0.201736
$502$	−6.88741e11	−0.484049
$503$	−4.24077e11	−0.295385	−0.147692	−	0.989033i	$-0.547185\pi$
$503$	−4.24077e11	−0.295385	−0.147692	+	0.989033i	$0.547185\pi$
$504$	−7.27944e11	−0.502528
$505$	7.40727e11	0.506812
$506$	−1.00934e12	−0.684476
$507$	6.60533e11	0.443975
$508$	−2.15057e11	−0.143274
$509$	1.03436e12	0.683030	0.341515	−	0.939876i	$-0.389060\pi$
$509$	1.03436e12	0.683030	0.341515	+	0.939876i	$0.389060\pi$
$510$	0	0
$511$	−1.58825e11	−0.103044
$512$	1.73504e12	1.11582
$513$	−1.78531e12	−1.13811
$514$	−5.21136e11	−0.329319
$515$	7.25824e11	0.454673
$516$	−4.88347e9	−0.00303253
$517$	−3.25626e11	−0.200453
$518$	−6.78351e11	−0.413971
$519$	1.11367e12	0.673758
$520$	−9.15313e10	−0.0548978
$521$	−2.77034e12	−1.64726	−0.823631	−	0.567126i	$-0.808055\pi$
$521$	−2.77034e12	−1.64726	−0.823631	+	0.567126i	$0.808055\pi$
$522$	5.65076e11	0.333112
$523$	−1.80710e12	−1.05615	−0.528073	−	0.849199i	$-0.677085\pi$
$523$	−1.80710e12	−1.05615	−0.528073	+	0.849199i	$0.677085\pi$
$524$	−1.55057e11	−0.0898462
$525$	4.45521e11	0.255948
$526$	4.16083e11	0.236998
$527$	0	0
$528$	8.46772e11	0.474148
$529$	−1.12603e12	−0.625172
$530$	4.25232e11	0.234091
$531$	−5.81563e11	−0.317447
$532$	1.85404e11	0.100350
$533$	1.77498e11	0.0952622
$534$	1.30515e12	0.694583
$535$	−7.55019e11	−0.398443
$536$	−1.90689e12	−0.997892
$537$	9.56924e11	0.496585
$538$	8.07717e11	0.415661
$539$	−1.47629e12	−0.753393
$540$	5.53140e10	0.0279939
$541$	3.71654e12	1.86531	0.932654	−	0.360772i	$-0.117487\pi$
$541$	3.71654e12	1.86531	0.932654	+	0.360772i	$0.117487\pi$
$542$	2.40599e12	1.19756
$543$	−2.98503e11	−0.147350
$544$	0	0
$545$	−4.60853e11	−0.223758
$546$	9.95373e10	0.0479312
$547$	−3.59458e11	−0.171674	−0.0858372	−	0.996309i	$-0.527357\pi$
$547$	−3.59458e11	−0.171674	−0.0858372	+	0.996309i	$0.527357\pi$
$548$	1.87497e11	0.0888139
$549$	−8.51423e11	−0.400009
$550$	2.20436e12	1.02719
$551$	−1.34819e12	−0.623114
$552$	−6.44531e11	−0.295473
$553$	5.63390e11	0.256181
$554$	1.36393e12	0.615172
$555$	2.12940e11	0.0952664
$556$	−2.43628e11	−0.108116
$557$	7.21729e10	0.0317706	0.0158853	−	0.999874i	$-0.494943\pi$
$557$	7.21729e10	0.0317706	0.0158853	+	0.999874i	$0.494943\pi$
$558$	−2.51615e12	−1.09871
$559$	−2.33804e10	−0.0101274
$560$	3.48377e11	0.149694
$561$	0	0
$562$	1.44109e12	0.609364
$563$	−9.06094e11	−0.380089	−0.190045	−	0.981775i	$-0.560863\pi$
$563$	−9.06094e11	−0.380089	−0.190045	+	0.981775i	$0.560863\pi$
$564$	−2.21976e10	−0.00923740
$565$	−1.33378e12	−0.550638
$566$	9.07670e11	0.371753
$567$	6.13847e11	0.249423
$568$	2.88773e12	1.16409
$569$	4.41941e12	1.76750	0.883749	−	0.467962i	$-0.155012\pi$
$569$	4.41941e12	1.76750	0.883749	+	0.467962i	$0.155012\pi$
$570$	4.28786e11	0.170139
$571$	−6.14608e10	−0.0241956	−0.0120978	−	0.999927i	$-0.503851\pi$
$571$	−6.14608e10	−0.0241956	−0.0120978	+	0.999927i	$0.503851\pi$
$572$	−6.68472e10	−0.0261096
$573$	3.46115e11	0.134130
$574$	−7.68782e11	−0.295597
$575$	−1.47445e12	−0.562502
$576$	−2.27020e12	−0.859334
$577$	−4.50208e12	−1.69092	−0.845459	−	0.534041i	$-0.820673\pi$
$577$	−4.50208e12	−1.69092	−0.845459	+	0.534041i	$0.820673\pi$
$578$	0	0
$579$	3.99112e11	0.147585
$580$	4.17708e10	0.0153266
$581$	3.22216e11	0.117315
$582$	−1.66698e12	−0.602249
$583$	2.90911e12	1.04292
$584$	−5.01813e11	−0.178519
$585$	1.16790e11	0.0412291
$586$	−7.19054e11	−0.251896
$587$	−1.77497e12	−0.617048	−0.308524	−	0.951216i	$-0.599835\pi$
$587$	−1.77497e12	−0.617048	−0.308524	+	0.951216i	$0.599835\pi$
$588$	−1.00637e11	−0.0347184
$589$	6.00316e12	2.05523
$590$	3.16723e11	0.107608
$591$	1.79738e12	0.606031
$592$	−1.88342e12	−0.630229
$593$	2.40742e12	0.799476	0.399738	−	0.916629i	$-0.369101\pi$
$593$	2.40742e12	0.799476	0.399738	+	0.916629i	$0.369101\pi$
$594$	−2.78796e12	−0.918857
$595$	0	0
$596$	−7.65078e10	−0.0248369
$597$	2.00157e12	0.644891
$598$	−3.29418e11	−0.105340
$599$	1.95233e12	0.619629	0.309814	−	0.950797i	$-0.399733\pi$
$599$	1.95233e12	0.619629	0.309814	+	0.950797i	$0.399733\pi$
$600$	1.40764e12	0.443415
$601$	−3.26884e12	−1.02202	−0.511010	−	0.859575i	$-0.670728\pi$
$601$	−3.26884e12	−1.02202	−0.511010	+	0.859575i	$0.670728\pi$
$602$	1.01266e11	0.0314253
$603$	2.43310e12	0.749432
$604$	−7.13121e11	−0.218020
$605$	−3.94065e11	−0.119583
$606$	−2.54505e12	−0.766602
$607$	−1.38191e12	−0.413171	−0.206586	−	0.978429i	$-0.566235\pi$
$607$	−1.38191e12	−0.413171	−0.206586	+	0.978429i	$0.566235\pi$
$608$	1.10905e12	0.329142
$609$	−4.25510e11	−0.125352
$610$	4.63690e11	0.135595
$611$	−1.06275e11	−0.0308493
$612$	0	0
$613$	−5.58587e12	−1.59779	−0.798893	−	0.601473i	$-0.794581\pi$
$613$	−5.58587e12	−1.59779	−0.798893	+	0.601473i	$0.794581\pi$
$614$	3.05034e12	0.866144
$615$	2.41328e11	0.0680251
$616$	2.71216e12	0.758930
$617$	−5.10855e12	−1.41911	−0.709553	−	0.704652i	$-0.751103\pi$
$617$	−5.10855e12	−1.41911	−0.709553	+	0.704652i	$0.751103\pi$
$618$	−2.49385e12	−0.687736
$619$	−1.71845e12	−0.470466	−0.235233	−	0.971939i	$-0.575585\pi$
$619$	−1.71845e12	−0.470466	−0.235233	+	0.971939i	$0.575585\pi$
$620$	−1.85995e11	−0.0505522
$621$	1.86481e12	0.503178
$622$	−5.13119e12	−1.37455
$623$	3.67348e12	0.976971
$624$	2.76362e11	0.0729704
$625$	2.91029e12	0.762916
$626$	−6.38482e11	−0.166175
$627$	2.93343e12	0.758004
$628$	−2.67265e11	−0.0685683
$629$	0	0
$630$	−5.05843e11	−0.127933
$631$	−1.38543e12	−0.347899	−0.173950	−	0.984755i	$-0.555653\pi$
$631$	−1.38543e12	−0.347899	−0.173950	+	0.984755i	$0.555653\pi$
$632$	1.78005e12	0.443818
$633$	3.86267e11	0.0956250
$634$	−4.42369e12	−1.08738
$635$	−1.39989e12	−0.341673
$636$	1.98311e11	0.0480607
$637$	−4.81817e11	−0.115946
$638$	−2.10535e12	−0.503073
$639$	−3.68461e12	−0.874253
$640$	9.48844e11	0.223555
$641$	−2.91632e12	−0.682299	−0.341149	−	0.940009i	$-0.610816\pi$
$641$	−2.91632e12	−0.682299	−0.341149	+	0.940009i	$0.610816\pi$
$642$	2.59416e12	0.602683
$643$	−6.28300e12	−1.44950	−0.724749	−	0.689013i	$-0.758044\pi$
$643$	−6.28300e12	−1.44950	−0.724749	+	0.689013i	$0.758044\pi$
$644$	−1.93660e11	−0.0443664
$645$	−3.17883e10	−0.00723183
$646$	0	0
$647$	−6.41096e12	−1.43832	−0.719158	−	0.694847i	$-0.755472\pi$
$647$	−6.41096e12	−1.43832	−0.719158	+	0.694847i	$0.755472\pi$
$648$	1.93947e12	0.432111
$649$	2.16677e12	0.479416
$650$	7.19439e11	0.158083
$651$	1.89470e12	0.413452
$652$	8.55182e11	0.185329
$653$	4.86499e12	1.04706	0.523531	−	0.852007i	$-0.324614\pi$
$653$	4.86499e12	1.04706	0.523531	+	0.852007i	$0.324614\pi$
$654$	1.58344e12	0.338455
$655$	−1.00932e12	−0.214261
$656$	−2.13450e12	−0.450016
$657$	6.40290e11	0.134070
$658$	4.60300e11	0.0957248
$659$	−3.83458e12	−0.792016	−0.396008	−	0.918247i	$-0.629605\pi$
$659$	−3.83458e12	−0.792016	−0.396008	+	0.918247i	$0.629605\pi$
$660$	−9.08861e10	−0.0186445
$661$	8.14305e11	0.165913	0.0829565	−	0.996553i	$-0.473564\pi$
$661$	8.14305e11	0.165913	0.0829565	+	0.996553i	$0.473564\pi$
$662$	−6.72758e12	−1.36144
$663$	0	0
$664$	1.01805e12	0.203242
$665$	1.20686e12	0.239310
$666$	2.73472e12	0.538615
$667$	1.40822e12	0.275489
$668$	2.70068e11	0.0524782
$669$	−3.83485e12	−0.740169
$670$	−1.32508e12	−0.254042
$671$	3.17221e12	0.604103
$672$	3.50033e11	0.0662137
$673$	4.30358e12	0.808652	0.404326	−	0.914615i	$-0.367506\pi$
$673$	4.30358e12	0.808652	0.404326	+	0.914615i	$0.367506\pi$
$674$	9.13794e12	1.70561
$675$	−4.07268e12	−0.755116
$676$	6.27067e11	0.115492
$677$	1.91909e11	0.0351113	0.0175556	−	0.999846i	$-0.494412\pi$
$677$	1.91909e11	0.0351113	0.0175556	+	0.999846i	$0.494412\pi$
$678$	4.58272e12	0.832893
$679$	−4.69188e12	−0.847097
$680$	0	0
$681$	4.76710e12	0.849361
$682$	9.37463e12	1.65930
$683$	−4.03721e12	−0.709886	−0.354943	−	0.934888i	$-0.615500\pi$
$683$	−4.03721e12	−0.709886	−0.354943	+	0.934888i	$0.615500\pi$
$684$	−7.47442e11	−0.130564
$685$	1.22048e12	0.211799
$686$	5.38715e12	0.928753
$687$	3.17199e12	0.543284
$688$	2.81161e11	0.0478418
$689$	9.49449e11	0.160504
$690$	−4.47880e11	−0.0752212
$691$	8.05343e12	1.34379	0.671893	−	0.740649i	$-0.265482\pi$
$691$	8.05343e12	1.34379	0.671893	+	0.740649i	$0.265482\pi$
$692$	1.05725e12	0.175267
$693$	−3.46059e12	−0.569968
$694$	4.14510e12	0.678294
$695$	−1.58586e12	−0.257830
$696$	−1.34441e12	−0.217166
$697$	0	0
$698$	3.94987e12	0.629845
$699$	−2.64064e12	−0.418371
$700$	4.22948e11	0.0665804
$701$	−7.33234e12	−1.14686	−0.573432	−	0.819254i	$-0.694388\pi$
$701$	−7.33234e12	−1.14686	−0.573432	+	0.819254i	$0.694388\pi$
$702$	−9.09910e11	−0.141410
$703$	−6.52462e12	−1.00753
$704$	8.45824e12	1.29779
$705$	−1.44492e11	−0.0220290
$706$	−8.56215e12	−1.29706
$707$	−7.16332e12	−1.07827
$708$	1.47707e11	0.0220928
$709$	−7.00566e12	−1.04122	−0.520608	−	0.853796i	$-0.674295\pi$
$709$	−7.00566e12	−1.04122	−0.520608	+	0.853796i	$0.674295\pi$
$710$	2.00666e12	0.296354
$711$	−2.27126e12	−0.333315
$712$	1.16065e13	1.69255
$713$	−6.27048e12	−0.908653
$714$	0	0
$715$	−4.35133e11	−0.0622651
$716$	9.08441e11	0.129178
$717$	−5.56177e12	−0.785917
$718$	1.76513e12	0.247865
$719$	−9.87945e12	−1.37865	−0.689323	−	0.724454i	$-0.742092\pi$
$719$	−9.87945e12	−1.37865	−0.689323	+	0.724454i	$0.742092\pi$
$720$	−1.40445e12	−0.194765
$721$	−7.01920e12	−0.967340
$722$	−6.28685e12	−0.861024
$723$	4.06131e12	0.552769
$724$	−2.83379e11	−0.0383305
$725$	−3.07552e12	−0.413425
$726$	1.35396e12	0.180880
$727$	−1.06391e13	−1.41253	−0.706266	−	0.707947i	$-0.749622\pi$
$727$	−1.06391e13	−1.41253	−0.706266	+	0.707947i	$0.749622\pi$
$728$	8.85169e11	0.116798
$729$	4.04654e11	0.0530652
$730$	−3.48706e11	−0.0454471
$731$	0	0
$732$	2.16247e11	0.0278387
$733$	6.87663e12	0.879849	0.439924	−	0.898035i	$-0.355005\pi$
$733$	6.87663e12	0.879849	0.439924	+	0.898035i	$0.355005\pi$
$734$	−3.59398e12	−0.457029
$735$	−6.55084e11	−0.0827950
$736$	−1.15843e12	−0.145519
$737$	−9.06520e12	−1.13181
$738$	3.09929e12	0.384599
$739$	−9.11004e12	−1.12362	−0.561811	−	0.827265i	$-0.689895\pi$
$739$	−9.11004e12	−1.12362	−0.561811	+	0.827265i	$0.689895\pi$
$740$	2.02152e11	0.0247819
$741$	9.57385e11	0.116655
$742$	−4.11228e12	−0.498041
$743$	5.65338e12	0.680548	0.340274	−	0.940326i	$-0.389480\pi$
$743$	5.65338e12	0.680548	0.340274	+	0.940326i	$0.389480\pi$
$744$	5.98636e12	0.716282
$745$	−4.98018e11	−0.0592300
$746$	−6.74076e12	−0.796863
$747$	−1.29899e12	−0.152638
$748$	0	0
$749$	7.30154e12	0.847708
$750$	2.04279e12	0.235748
$751$	−5.02019e12	−0.575891	−0.287945	−	0.957647i	$-0.592972\pi$
$751$	−5.02019e12	−0.575891	−0.287945	+	0.957647i	$0.592972\pi$
$752$	1.27801e12	0.145731
$753$	−2.09082e12	−0.236995
$754$	−6.87125e11	−0.0774220
$755$	−4.64197e12	−0.519925
$756$	−5.34923e11	−0.0595585
$757$	−1.11047e13	−1.22907	−0.614536	−	0.788889i	$-0.710657\pi$
$757$	−1.11047e13	−1.22907	−0.614536	+	0.788889i	$0.710657\pi$
$758$	−1.36915e13	−1.50640
$759$	−3.06405e12	−0.335126
$760$	3.81313e12	0.414591
$761$	−1.20295e13	−1.30022	−0.650108	−	0.759841i	$-0.725277\pi$
$761$	−1.20295e13	−1.30022	−0.650108	+	0.759841i	$0.725277\pi$
$762$	4.80985e12	0.516814
$763$	4.45676e12	0.476056
$764$	3.28579e11	0.0348915
$765$	0	0
$766$	−8.89503e12	−0.933508
$767$	7.07172e11	0.0737812
$768$	1.56447e12	0.162271
$769$	1.19597e13	1.23325	0.616624	−	0.787258i	$-0.288500\pi$
$769$	1.19597e13	1.23325	0.616624	+	0.787258i	$0.288500\pi$
$770$	1.88466e12	0.193208
$771$	−1.58202e12	−0.161238
$772$	3.78891e11	0.0383916
$773$	1.28955e13	1.29907	0.649533	−	0.760333i	$-0.274964\pi$
$773$	1.28955e13	1.29907	0.649533	+	0.760333i	$0.274964\pi$
$774$	−4.08245e11	−0.0408872
$775$	1.36946e13	1.36361
$776$	−1.48242e13	−1.46755
$777$	−2.05928e12	−0.202684
$778$	1.58818e13	1.55415
$779$	−7.39442e12	−0.719425
$780$	−2.96626e10	−0.00286935
$781$	1.37280e13	1.32032
$782$	0	0
$783$	3.88975e12	0.369823
$784$	5.79409e12	0.547725
$785$	−1.73973e12	−0.163519
$786$	3.46791e12	0.324091
$787$	−1.19313e13	−1.10867	−0.554335	−	0.832293i	$-0.687027\pi$
$787$	−1.19313e13	−1.10867	−0.554335	+	0.832293i	$0.687027\pi$
$788$	1.70631e12	0.157649
$789$	1.26311e12	0.116036
$790$	1.23694e12	0.112987
$791$	1.28985e13	1.17151
$792$	−1.09339e13	−0.987438
$793$	1.03532e12	0.0929703
$794$	−1.32604e11	−0.0118404
$795$	1.29088e12	0.114613
$796$	1.90016e12	0.167757
$797$	3.92641e12	0.344693	0.172347	−	0.985036i	$-0.444865\pi$
$797$	3.92641e12	0.344693	0.172347	+	0.985036i	$0.444865\pi$
$798$	−4.14665e12	−0.361980
$799$	0	0
$800$	2.52998e12	0.218380
$801$	−1.48093e13	−1.27113
$802$	−1.12024e13	−0.956153
$803$	−2.38558e12	−0.202476
$804$	−6.17965e11	−0.0521569
$805$	−1.26061e12	−0.105803
$806$	3.05961e12	0.255363
$807$	2.45200e12	0.203511
$808$	−2.26328e13	−1.86804
$809$	−1.18171e13	−0.969937	−0.484969	−	0.874532i	$-0.661169\pi$
$809$	−1.18171e13	−0.969937	−0.484969	+	0.874532i	$0.661169\pi$
$810$	1.34772e12	0.110006
$811$	2.28011e13	1.85081	0.925406	−	0.378976i	$-0.123724\pi$
$811$	2.28011e13	1.85081	0.925406	+	0.378976i	$0.123724\pi$
$812$	−4.03951e11	−0.0326082
$813$	7.30390e12	0.586337
$814$	−1.01889e13	−0.813429
$815$	5.56669e12	0.441965
$816$	0	0
$817$	9.74011e11	0.0764830
$818$	−8.17588e12	−0.638476
$819$	−1.12944e12	−0.0877171
$820$	2.29101e11	0.0176956
$821$	−6.28999e12	−0.483176	−0.241588	−	0.970379i	$-0.577668\pi$
$821$	−6.28999e12	−0.483176	−0.241588	+	0.970379i	$0.577668\pi$
$822$	−4.19345e12	−0.320367
$823$	−1.47598e13	−1.12146	−0.560728	−	0.828000i	$-0.689479\pi$
$823$	−1.47598e13	−1.12146	−0.560728	+	0.828000i	$0.689479\pi$
$824$	−2.21774e13	−1.67586
$825$	6.69180e12	0.502922
$826$	−3.06292e12	−0.228942
$827$	−1.16508e12	−0.0866122	−0.0433061	−	0.999062i	$-0.513789\pi$
$827$	−1.16508e12	−0.0866122	−0.0433061	+	0.999062i	$0.513789\pi$
$828$	7.80726e11	0.0577247
$829$	−2.10717e13	−1.54955	−0.774774	−	0.632238i	$-0.782137\pi$
$829$	−2.10717e13	−1.54955	−0.774774	+	0.632238i	$0.782137\pi$
$830$	7.07437e11	0.0517411
$831$	4.14048e12	0.301194
$832$	2.76052e12	0.199727
$833$	0	0
$834$	5.44884e12	0.389993
$835$	1.75797e12	0.125148
$836$	2.78480e12	0.197182
$837$	−1.73202e13	−1.21980
$838$	5.78835e12	0.405468
$839$	−1.60286e11	−0.0111678	−0.00558388	−	0.999984i	$-0.501777\pi$
$839$	−1.60286e11	−0.0111678	−0.00558388	+	0.999984i	$0.501777\pi$
$840$	1.20349e12	0.0834035
$841$	−1.15698e13	−0.797522
$842$	6.92534e12	0.474828
$843$	4.37473e12	0.298351
$844$	3.66697e11	0.0248752
$845$	4.08181e12	0.275421
$846$	−1.85566e12	−0.124547
$847$	3.81087e12	0.254419
$848$	−1.14176e13	−0.758216
$849$	2.75542e12	0.182014
$850$	0	0
$851$	6.81516e12	0.445444
$852$	9.35826e11	0.0608439
$853$	−8.02673e12	−0.519120	−0.259560	−	0.965727i	$-0.583578\pi$
$853$	−8.02673e12	−0.519120	−0.259560	+	0.965727i	$0.583578\pi$
$854$	−4.48419e12	−0.288485
$855$	−4.86538e12	−0.311364
$856$	2.30694e13	1.46861
$857$	−1.46074e13	−0.925040	−0.462520	−	0.886609i	$-0.653055\pi$
$857$	−1.46074e13	−0.925040	−0.462520	+	0.886609i	$0.653055\pi$
$858$	1.49507e12	0.0941820
$859$	9.67406e12	0.606233	0.303117	−	0.952953i	$-0.401973\pi$
$859$	9.67406e12	0.606233	0.303117	+	0.952953i	$0.401973\pi$
$860$	−3.01777e10	−0.00188124
$861$	−2.33380e12	−0.144727
$862$	−1.89899e13	−1.17150
$863$	−1.28618e13	−0.789318	−0.394659	−	0.918828i	$-0.629137\pi$
$863$	−1.28618e13	−0.789318	−0.394659	+	0.918828i	$0.629137\pi$
$864$	−3.19979e12	−0.195348
$865$	6.88201e12	0.417968
$866$	1.39529e13	0.843011
$867$	0	0
$868$	1.79870e12	0.107552
$869$	8.46222e12	0.503379
$870$	−9.34222e11	−0.0552858
$871$	−2.95862e12	−0.174183
$872$	1.40813e13	0.824741
$873$	1.89150e13	1.10215
$874$	1.37233e13	0.795530
$875$	5.74965e12	0.331593
$876$	−1.62623e11	−0.00933066
$877$	3.18137e13	1.81600	0.908000	−	0.418970i	$-0.137609\pi$
$877$	3.18137e13	1.81600	0.908000	+	0.418970i	$0.137609\pi$
$878$	−1.55146e13	−0.881082
$879$	−2.18284e12	−0.123331
$880$	5.23269e12	0.294139
$881$	3.55268e12	0.198685	0.0993425	−	0.995053i	$-0.468326\pi$
$881$	3.55268e12	0.198685	0.0993425	+	0.995053i	$0.468326\pi$
$882$	−8.41301e12	−0.468104
$883$	6.90201e12	0.382079	0.191039	−	0.981582i	$-0.438814\pi$
$883$	6.90201e12	0.382079	0.191039	+	0.981582i	$0.438814\pi$
$884$	0	0
$885$	9.61478e11	0.0526859
$886$	−1.81306e13	−0.988461
$887$	−2.48053e11	−0.0134551	−0.00672756	−	0.999977i	$-0.502141\pi$
$887$	−2.48053e11	−0.0134551	−0.00672756	+	0.999977i	$0.502141\pi$
$888$	−6.50635e12	−0.351139
$889$	1.35378e13	0.726928
$890$	8.06526e12	0.430887
$891$	9.22009e12	0.490101
$892$	−3.64056e12	−0.192542
$893$	4.42733e12	0.232975
$894$	1.71113e12	0.0895911
$895$	5.91338e12	0.308058
$896$	−9.17595e12	−0.475626
$897$	−1.00002e12	−0.0515752
$898$	1.66191e13	0.852833
$899$	−1.30795e13	−0.667838
$900$	−1.70508e12	−0.0866272
$901$	0	0
$902$	−1.15473e13	−0.580830
$903$	3.07414e11	0.0153861
$904$	4.07534e13	2.02958
$905$	−1.84462e12	−0.0914089
$906$	1.59493e13	0.786437
$907$	−2.41672e13	−1.18575	−0.592876	−	0.805294i	$-0.702008\pi$
$907$	−2.41672e13	−1.18575	−0.592876	+	0.805294i	$0.702008\pi$
$908$	4.52557e12	0.220946
$909$	2.88784e13	1.40293
$910$	6.15097e11	0.0297343
$911$	3.01501e13	1.45029	0.725146	−	0.688595i	$-0.241772\pi$
$911$	3.01501e13	1.45029	0.725146	+	0.688595i	$0.241772\pi$
$912$	−1.15130e13	−0.551077
$913$	4.83974e12	0.230517
$914$	2.74633e13	1.30165
$915$	1.40763e12	0.0663885
$916$	3.01128e12	0.141326
$917$	9.76081e12	0.455852
$918$	0	0
$919$	−1.09318e13	−0.505558	−0.252779	−	0.967524i	$-0.581345\pi$
$919$	−1.09318e13	−0.505558	−0.252779	+	0.967524i	$0.581345\pi$
$920$	−3.98292e12	−0.183298
$921$	9.25994e12	0.424072
$922$	3.75557e13	1.71154
$923$	4.48043e12	0.203194
$924$	8.78930e11	0.0396671
$925$	−1.48841e13	−0.668475
$926$	−2.33810e13	−1.04499
$927$	2.82974e13	1.25860
$928$	−2.41635e12	−0.106953
$929$	9.34286e12	0.411537	0.205769	−	0.978601i	$-0.434031\pi$
$929$	9.34286e12	0.411537	0.205769	+	0.978601i	$0.434031\pi$
$930$	4.15987e12	0.182350
$931$	2.00722e13	0.875629
$932$	−2.50685e12	−0.108832
$933$	−1.55768e13	−0.672994
$934$	1.23923e13	0.532834
$935$	0	0
$936$	−3.56849e12	−0.151965
$937$	−3.26873e13	−1.38532	−0.692660	−	0.721264i	$-0.743561\pi$
$937$	−3.26873e13	−1.38532	−0.692660	+	0.721264i	$0.743561\pi$
$938$	1.28144e13	0.540489
$939$	−1.93825e12	−0.0813606
$940$	−1.37172e11	−0.00573045
$941$	6.47375e12	0.269155	0.134578	−	0.990903i	$-0.457032\pi$
$941$	6.47375e12	0.269155	0.134578	+	0.990903i	$0.457032\pi$
$942$	5.97750e12	0.247338
$943$	7.72370e12	0.318070
$944$	−8.50408e12	−0.348541
$945$	−3.48202e12	−0.142032
$946$	1.52103e12	0.0617487
$947$	−1.29609e13	−0.523674	−0.261837	−	0.965112i	$-0.584328\pi$
$947$	−1.29609e13	−0.523674	−0.261837	+	0.965112i	$0.584328\pi$
$948$	5.76861e11	0.0231971
$949$	−7.78583e11	−0.0311607
$950$	−2.99713e13	−1.19385
$951$	−1.34290e13	−0.532394
$952$	0	0
$953$	7.79031e12	0.305940	0.152970	−	0.988231i	$-0.451116\pi$
$953$	7.79031e12	0.305940	0.152970	+	0.988231i	$0.451116\pi$
$954$	1.65783e13	0.647997
$955$	2.13884e12	0.0832077
$956$	−5.27998e12	−0.204443
$957$	−6.39123e12	−0.246309
$958$	2.05603e13	0.788650
$959$	−1.18029e13	−0.450615
$960$	3.75324e12	0.142622
$961$	3.18001e13	1.20275
$962$	−3.32538e12	−0.125185
$963$	−2.94356e13	−1.10295
$964$	3.85554e12	0.143793
$965$	2.46634e12	0.0915545
$966$	4.33130e12	0.160037
$967$	1.11152e13	0.408789	0.204395	−	0.978889i	$-0.434477\pi$
$967$	1.11152e13	0.408789	0.204395	+	0.978889i	$0.434477\pi$
$968$	1.20406e13	0.440766
$969$	0	0
$970$	−1.03012e13	−0.373607
$971$	−2.99153e13	−1.07996	−0.539979	−	0.841678i	$-0.681568\pi$
$971$	−2.99153e13	−1.07996	−0.539979	+	0.841678i	$0.681568\pi$
$972$	3.36197e12	0.120808
$973$	1.53363e13	0.548547
$974$	1.54249e13	0.549169
$975$	2.18401e12	0.0773987
$976$	−1.24502e13	−0.439189
$977$	3.43150e13	1.20492	0.602460	−	0.798149i	$-0.294187\pi$
$977$	3.43150e13	1.20492	0.602460	+	0.798149i	$0.294187\pi$
$978$	−1.91265e13	−0.668515
$979$	5.51763e13	1.91969
$980$	−6.21894e11	−0.0215377
$981$	−1.79671e13	−0.619393
$982$	3.46667e13	1.18963
$983$	−3.36007e13	−1.14778	−0.573888	−	0.818934i	$-0.694566\pi$
$983$	−3.36007e13	−1.14778	−0.573888	+	0.818934i	$0.694566\pi$
$984$	−7.37372e12	−0.250732
$985$	1.11070e13	0.375953
$986$	0	0
$987$	1.39734e12	0.0468678
$988$	9.08878e11	0.0303459
$989$	−1.01738e12	−0.0338144
$990$	−7.59785e12	−0.251381
$991$	5.72727e13	1.88633	0.943163	−	0.332332i	$-0.107835\pi$
$991$	5.72727e13	1.88633	0.943163	+	0.332332i	$0.107835\pi$
$992$	1.07594e13	0.352766
$993$	−2.04230e13	−0.666573
$994$	−1.94057e13	−0.630509
$995$	1.23689e13	0.400060
$996$	3.29920e11	0.0106229
$997$	6.10726e13	1.95757	0.978786	−	0.204883i	$-0.0656814\pi$
$997$	6.10726e13	1.95757	0.978786	+	0.204883i	$0.0656814\pi$
$998$	3.70036e13	1.18075
$999$	1.88247e13	0.597975

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.g.1.11	✓	36
17.16	even	2		289.10.a.h.1.11	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.11	✓	36	1.1	even	1	trivial
289.10.a.h.1.11	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)

\(f(q)\)	\(=\)	\(q-21.2323 q^{2} -64.4551 q^{3} -61.1895 q^{4} -398.305 q^{5} +1368.53 q^{6} +3851.88 q^{7} +12170.1 q^{8} -15528.5 q^{9} +O(q^{10})\)	\(q-21.2323 q^{2} -64.4551 q^{3} -61.1895 q^{4} -398.305 q^{5} +1368.53 q^{6} +3851.88 q^{7} +12170.1 q^{8} -15528.5 q^{9} +8456.93 q^{10} +57855.9 q^{11} +3943.98 q^{12} +18882.5 q^{13} -81784.2 q^{14} +25672.8 q^{15} -227071. q^{16} +329707. q^{18} -786629. q^{19} +24372.1 q^{20} -248273. q^{21} -1.22841e6 q^{22} +821658. q^{23} -784427. q^{24} -1.79448e6 q^{25} -400918. q^{26} +2.26956e6 q^{27} -235694. q^{28} +1.71388e6 q^{29} -545093. q^{30} -7.63150e6 q^{31} -1.40987e6 q^{32} -3.72911e6 q^{33} -1.53422e6 q^{35} +950183. q^{36} +8.29440e6 q^{37} +1.67020e7 q^{38} -1.21707e6 q^{39} -4.84742e6 q^{40} +9.40014e6 q^{41} +5.27141e6 q^{42} -1.23821e6 q^{43} -3.54017e6 q^{44} +6.18509e6 q^{45} -1.74457e7 q^{46} -5.62823e6 q^{47} +1.46359e7 q^{48} -2.55167e7 q^{49} +3.81009e7 q^{50} -1.15541e6 q^{52} +5.02821e7 q^{53} -4.81881e7 q^{54} -2.30443e7 q^{55} +4.68778e7 q^{56} +5.07023e7 q^{57} -3.63896e7 q^{58} +3.74512e7 q^{59} -1.57091e6 q^{60} +5.48296e7 q^{61} +1.62034e8 q^{62} -5.98140e7 q^{63} +1.46195e8 q^{64} -7.52098e6 q^{65} +7.91775e7 q^{66} -1.56686e8 q^{67} -5.29601e7 q^{69} +3.25751e7 q^{70} +2.37280e8 q^{71} -1.88984e8 q^{72} -4.12331e7 q^{73} -1.76109e8 q^{74} +1.15663e8 q^{75} +4.81335e7 q^{76} +2.22854e8 q^{77} +2.58412e7 q^{78} +1.46264e8 q^{79} +9.04435e7 q^{80} +1.59363e8 q^{81} -1.99586e8 q^{82} +8.36517e7 q^{83} +1.51917e7 q^{84} +2.62900e7 q^{86} -1.10468e8 q^{87} +7.04114e8 q^{88} +9.53686e8 q^{89} -1.31324e8 q^{90} +7.27329e7 q^{91} -5.02768e7 q^{92} +4.91889e8 q^{93} +1.19500e8 q^{94} +3.13318e8 q^{95} +9.08734e7 q^{96} -1.21808e9 q^{97} +5.41777e8 q^{98} -8.98417e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 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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