LMFDB - Embedded newform 289.10.a.h.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	yes
Analytic conductor:	$148.845356651$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-10.3896 q^{2} -121.426 q^{3} -404.056 q^{4} +1455.35 q^{5} +1261.57 q^{6} -5787.38 q^{7} +9517.45 q^{8} -4938.65 q^{9} +O(q^{10})$	\(q-10.3896 q^{2} -121.426 q^{3} -404.056 q^{4} +1455.35 q^{5} +1261.57 q^{6} -5787.38 q^{7} +9517.45 q^{8} -4938.65 q^{9} -15120.5 q^{10} -2333.01 q^{11} +49063.1 q^{12} +34111.1 q^{13} +60128.5 q^{14} -176718. q^{15} +107995. q^{16} +51310.5 q^{18} -247026. q^{19} -588043. q^{20} +702741. q^{21} +24239.0 q^{22} +666606. q^{23} -1.15567e6 q^{24} +164913. q^{25} -354400. q^{26} +2.98972e6 q^{27} +2.33843e6 q^{28} +2.98746e6 q^{29} +1.83602e6 q^{30} -7.53740e6 q^{31} -5.99495e6 q^{32} +283288. q^{33} -8.42266e6 q^{35} +1.99549e6 q^{36} +981789. q^{37} +2.56650e6 q^{38} -4.14198e6 q^{39} +1.38512e7 q^{40} -2.32449e7 q^{41} -7.30119e6 q^{42} +2.36383e7 q^{43} +942666. q^{44} -7.18745e6 q^{45} -6.92576e6 q^{46} +5.99211e7 q^{47} -1.31134e7 q^{48} -6.85981e6 q^{49} -1.71337e6 q^{50} -1.37828e7 q^{52} +5.88160e7 q^{53} -3.10619e7 q^{54} -3.39534e6 q^{55} -5.50811e7 q^{56} +2.99955e7 q^{57} -3.10385e7 q^{58} -1.19067e8 q^{59} +7.14039e7 q^{60} -1.73852e8 q^{61} +7.83105e7 q^{62} +2.85819e7 q^{63} +6.99189e6 q^{64} +4.96435e7 q^{65} -2.94325e6 q^{66} -2.80991e8 q^{67} -8.09435e7 q^{69} +8.75079e7 q^{70} -1.98936e7 q^{71} -4.70033e7 q^{72} -3.38604e8 q^{73} -1.02004e7 q^{74} -2.00247e7 q^{75} +9.98126e7 q^{76} +1.35020e7 q^{77} +4.30335e7 q^{78} -1.90781e8 q^{79} +1.57170e8 q^{80} -2.65823e8 q^{81} +2.41505e8 q^{82} -5.33966e8 q^{83} -2.83947e8 q^{84} -2.45592e8 q^{86} -3.62756e8 q^{87} -2.22043e7 q^{88} -7.82829e8 q^{89} +7.46747e7 q^{90} -1.97414e8 q^{91} -2.69346e8 q^{92} +9.15239e8 q^{93} -6.22555e8 q^{94} -3.59509e8 q^{95} +7.27945e8 q^{96} +1.10279e9 q^{97} +7.12705e7 q^{98} +1.15219e7 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−10.3896	−0.459159	−0.229580	−	0.973290i	$-0.573735\pi$
$2$	−10.3896	−0.459159	−0.229580	+	0.973290i	$0.573735\pi$
$3$	−121.426	−0.865500	−0.432750	−	0.901514i	$-0.642457\pi$
$3$	−121.426	−0.865500	−0.432750	+	0.901514i	$0.642457\pi$
$4$	−404.056	−0.789173
$5$	1455.35	1.04136	0.520681	−	0.853751i	$-0.325678\pi$
$5$	1455.35	1.04136	0.520681	+	0.853751i	$0.325678\pi$
$6$	1261.57	0.397402
$7$	−5787.38	−0.911048	−0.455524	−	0.890224i	$-0.650548\pi$
$7$	−5787.38	−0.911048	−0.455524	+	0.890224i	$0.650548\pi$
$8$	9517.45	0.821515
$9$	−4938.65	−0.250909
$10$	−15120.5	−0.478151
$11$	−2333.01	−0.0480451	−0.0240225	−	0.999711i	$-0.507647\pi$
$11$	−2333.01	−0.0480451	−0.0240225	+	0.999711i	$0.507647\pi$
$12$	49063.1	0.683029
$13$	34111.1	0.331246	0.165623	−	0.986189i	$-0.447037\pi$
$13$	34111.1	0.331246	0.165623	+	0.986189i	$0.447037\pi$
$14$	60128.5	0.418316
$15$	−176718.	−0.901299
$16$	107995.	0.411966
$17$	0	0
$17$	0	0
$18$	51310.5	0.115207
$19$	−247026.	−0.434862	−0.217431	−	0.976076i	$-0.569768\pi$
$19$	−247026.	−0.434862	−0.217431	+	0.976076i	$0.569768\pi$
$20$	−588043.	−0.821815
$21$	702741.	0.788512
$22$	24239.0	0.0220603
$23$	666606.	0.496700	0.248350	−	0.968670i	$-0.420112\pi$
$23$	666606.	0.496700	0.248350	+	0.968670i	$0.420112\pi$
$24$	−1.15567e6	−0.711022
$25$	164913.	0.0844352
$26$	−354400.	−0.152095
$27$	2.98972e6	1.08266
$28$	2.33843e6	0.718974
$29$	2.98746e6	0.784352	0.392176	−	0.919890i	$-0.371722\pi$
$29$	2.98746e6	0.784352	0.392176	+	0.919890i	$0.371722\pi$
$30$	1.83602e6	0.413840
$31$	−7.53740e6	−1.46586	−0.732932	−	0.680302i	$-0.761849\pi$
$31$	−7.53740e6	−1.46586	−0.732932	+	0.680302i	$0.761849\pi$
$32$	−5.99495e6	−1.01067
$33$	283288.	0.0415830
$34$	0	0
$35$	−8.42266e6	−0.948730
$36$	1.99549e6	0.198011
$37$	981789.	0.0861213	0.0430606	−	0.999072i	$-0.486289\pi$
$37$	981789.	0.0861213	0.0430606	+	0.999072i	$0.486289\pi$
$38$	2.56650e6	0.199671
$39$	−4.14198e6	−0.286693
$40$	1.38512e7	0.855495
$41$	−2.32449e7	−1.28470	−0.642349	−	0.766412i	$-0.722040\pi$
$41$	−2.32449e7	−1.28470	−0.642349	+	0.766412i	$0.722040\pi$
$42$	−7.30119e6	−0.362053
$43$	2.36383e7	1.05441	0.527203	−	0.849739i	$-0.323241\pi$
$43$	2.36383e7	1.05441	0.527203	+	0.849739i	$0.323241\pi$
$44$	942666.	0.0379159
$45$	−7.18745e6	−0.261288
$46$	−6.92576e6	−0.228064
$47$	5.99211e7	1.79118	0.895590	−	0.444881i	$-0.146754\pi$
$47$	5.99211e7	1.79118	0.895590	+	0.444881i	$0.146754\pi$
$48$	−1.31134e7	−0.356557
$49$	−6.85981e6	−0.169992
$50$	−1.71337e6	−0.0387692
$51$	0	0
$52$	−1.37828e7	−0.261410
$53$	5.88160e7	1.02389	0.511946	−	0.859017i	$-0.328925\pi$
$53$	5.88160e7	1.02389	0.511946	+	0.859017i	$0.328925\pi$
$54$	−3.10619e7	−0.497114
$55$	−3.39534e6	−0.0500323
$56$	−5.50811e7	−0.748439
$57$	2.99955e7	0.376374
$58$	−3.10385e7	−0.360142
$59$	−1.19067e8	−1.27926	−0.639629	−	0.768684i	$-0.720912\pi$
$59$	−1.19067e8	−1.27926	−0.639629	+	0.768684i	$0.720912\pi$
$60$	7.14039e7	0.711281
$61$	−1.73852e8	−1.60766	−0.803832	−	0.594857i	$-0.797209\pi$
$61$	−1.73852e8	−1.60766	−0.803832	+	0.594857i	$0.797209\pi$
$62$	7.83105e7	0.673065
$63$	2.85819e7	0.228590
$64$	6.99189e6	0.0520936
$65$	4.96435e7	0.344947
$66$	−2.94325e6	−0.0190932
$67$	−2.80991e8	−1.70355	−0.851776	−	0.523907i	$-0.824474\pi$
$67$	−2.80991e8	−1.70355	−0.851776	+	0.523907i	$0.824474\pi$
$68$	0	0
$69$	−8.09435e7	−0.429894
$70$	8.75079e7	0.435618
$71$	−1.98936e7	−0.0929073	−0.0464537	−	0.998920i	$-0.514792\pi$
$71$	−1.98936e7	−0.0929073	−0.0464537	+	0.998920i	$0.514792\pi$
$72$	−4.70033e7	−0.206126
$73$	−3.38604e8	−1.39553	−0.697764	−	0.716327i	$-0.745822\pi$
$73$	−3.38604e8	−1.39553	−0.697764	+	0.716327i	$0.745822\pi$
$74$	−1.02004e7	−0.0395434
$75$	−2.00247e7	−0.0730787
$76$	9.98126e7	0.343182
$77$	1.35020e7	0.0437713
$78$	4.30335e7	0.131638
$79$	−1.90781e8	−0.551078	−0.275539	−	0.961290i	$-0.588856\pi$
$79$	−1.90781e8	−0.551078	−0.275539	+	0.961290i	$0.588856\pi$
$80$	1.57170e8	0.429006
$81$	−2.65823e8	−0.686135
$82$	2.41505e8	0.589881
$83$	−5.33966e8	−1.23499	−0.617494	−	0.786576i	$-0.711852\pi$
$83$	−5.33966e8	−1.23499	−0.617494	+	0.786576i	$0.711852\pi$
$84$	−2.83947e8	−0.622272
$85$	0	0
$86$	−2.45592e8	−0.484141
$87$	−3.62756e8	−0.678856
$88$	−2.22043e7	−0.0394697
$89$	−7.82829e8	−1.32255	−0.661275	−	0.750144i	$-0.729984\pi$
$89$	−7.82829e8	−1.32255	−0.661275	+	0.750144i	$0.729984\pi$
$90$	7.46747e7	0.119973
$91$	−1.97414e8	−0.301781
$92$	−2.69346e8	−0.391982
$93$	9.15239e8	1.26871
$94$	−6.22555e8	−0.822437
$95$	−3.59509e8	−0.452849
$96$	7.27945e8	0.874738
$97$	1.10279e9	1.26479	0.632397	−	0.774645i	$-0.282071\pi$
$97$	1.10279e9	1.26479	0.632397	+	0.774645i	$0.282071\pi$
$98$	7.12705e7	0.0780536
$99$	1.15219e7	0.0120550
$100$	−6.66340e7	−0.0666340
$101$	−8.85019e8	−0.846265	−0.423132	−	0.906068i	$-0.639069\pi$
$101$	−8.85019e8	−0.846265	−0.423132	+	0.906068i	$0.639069\pi$
$102$	0	0
$103$	1.22210e9	1.06989	0.534947	−	0.844886i	$-0.320332\pi$
$103$	1.22210e9	1.06989	0.534947	+	0.844886i	$0.320332\pi$
$104$	3.24651e8	0.272124
$105$	1.02273e9	0.821126
$106$	−6.11075e8	−0.470130
$107$	4.24642e8	0.313181	0.156591	−	0.987664i	$-0.449950\pi$
$107$	4.24642e8	0.313181	0.156591	+	0.987664i	$0.449950\pi$
$108$	−1.20801e9	−0.854408
$109$	−625767.	−0.000424613 0	−0.000212307	−	1.00000i	$-0.500068\pi$
$109$	−625767.	−0.000424613 0	−0.000212307		1.00000i	$0.500068\pi$
$110$	3.52761e7	0.0229728
$111$	−1.19215e8	−0.0745380
$112$	−6.25006e8	−0.375321
$113$	4.92103e8	0.283925	0.141962	−	0.989872i	$-0.454659\pi$
$113$	4.92103e8	0.283925	0.141962	+	0.989872i	$0.454659\pi$
$114$	−3.11641e8	−0.172815
$115$	9.70143e8	0.517244
$116$	−1.20710e9	−0.618989
$117$	−1.68463e8	−0.0831127
$118$	1.23706e9	0.587383
$119$	0	0
$120$	−1.68190e9	−0.740431
$121$	−2.35250e9	−0.997692
$122$	1.80625e9	0.738173
$123$	2.82255e9	1.11191
$124$	3.04553e9	1.15682
$125$	−2.60247e9	−0.953435
$126$	−2.96954e8	−0.104959
$127$	−1.38264e9	−0.471620	−0.235810	−	0.971799i	$-0.575774\pi$
$127$	−1.38264e9	−0.471620	−0.235810	+	0.971799i	$0.575774\pi$
$128$	2.99677e9	0.986754
$129$	−2.87031e9	−0.912589
$130$	−5.15776e8	−0.158386
$131$	2.00175e9	0.593867	0.296934	−	0.954898i	$-0.404036\pi$
$131$	2.00175e9	0.593867	0.296934	+	0.954898i	$0.404036\pi$
$132$	−1.14464e8	−0.0328162
$133$	1.42964e9	0.396180
$134$	2.91938e9	0.782201
$135$	4.35108e9	1.12744
$136$	0	0
$137$	2.67902e9	0.649731	0.324865	−	0.945760i	$-0.394681\pi$
$137$	2.67902e9	0.649731	0.324865	+	0.945760i	$0.394681\pi$
$138$	8.40969e8	0.197390
$139$	6.25930e9	1.42219	0.711097	−	0.703094i	$-0.248199\pi$
$139$	6.25930e9	1.42219	0.711097	+	0.703094i	$0.248199\pi$
$140$	3.40323e9	0.748712
$141$	−7.27599e9	−1.55027
$142$	2.06686e8	0.0426593
$143$	−7.95814e7	−0.0159147
$144$	−5.33347e8	−0.103366
$145$	4.34779e9	0.816794
$146$	3.51795e9	0.640770
$147$	8.32961e8	0.147128
$148$	−3.96698e8	−0.0679645
$149$	4.42327e9	0.735200	0.367600	−	0.929984i	$-0.380180\pi$
$149$	4.42327e9	0.735200	0.367600	+	0.929984i	$0.380180\pi$
$150$	2.08049e8	0.0335548
$151$	3.63327e8	0.0568724	0.0284362	−	0.999596i	$-0.490947\pi$
$151$	3.63327e8	0.0568724	0.0284362	+	0.999596i	$0.490947\pi$
$152$	−2.35106e9	−0.357246
$153$	0	0
$154$	−1.40280e8	−0.0200980
$155$	−1.09695e10	−1.52650
$156$	1.67360e9	0.226251
$157$	7.98151e9	1.04842	0.524211	−	0.851588i	$-0.324360\pi$
$157$	7.98151e9	1.04842	0.524211	+	0.851588i	$0.324360\pi$
$158$	1.98213e9	0.253032
$159$	−7.14182e9	−0.886179
$160$	−8.72474e9	−1.05248
$161$	−3.85790e9	−0.452517
$162$	2.76179e9	0.315045
$163$	1.63762e10	1.81705	0.908527	−	0.417825i	$-0.137208\pi$
$163$	1.63762e10	1.81705	0.908527	+	0.417825i	$0.137208\pi$
$164$	9.39227e9	1.01385
$165$	4.12283e8	0.0433030
$166$	5.54769e9	0.567056
$167$	1.04216e10	1.03684	0.518418	−	0.855127i	$-0.326521\pi$
$167$	1.04216e10	1.03684	0.518418	+	0.855127i	$0.326521\pi$
$168$	6.68830e9	0.647774
$169$	−9.44093e9	−0.890276
$170$	0	0
$171$	1.21998e9	0.109111
$172$	−9.55121e9	−0.832109
$173$	−7.86202e8	−0.0667309	−0.0333654	−	0.999443i	$-0.510623\pi$
$173$	−7.86202e8	−0.0667309	−0.0333654	+	0.999443i	$0.510623\pi$
$174$	3.76889e9	0.311703
$175$	−9.54412e8	−0.0769245
$176$	−2.51952e8	−0.0197930
$177$	1.44579e10	1.10720
$178$	8.13327e9	0.607261
$179$	−5.72805e9	−0.417031	−0.208515	−	0.978019i	$-0.566863\pi$
$179$	−5.72805e9	−0.417031	−0.208515	+	0.978019i	$0.566863\pi$
$180$	2.90414e9	0.206201
$181$	−9.74370e9	−0.674793	−0.337396	−	0.941363i	$-0.609546\pi$
$181$	−9.74370e9	−0.674793	−0.337396	+	0.941363i	$0.609546\pi$
$182$	2.05105e9	0.138565
$183$	2.11102e10	1.39143
$184$	6.34439e9	0.408046
$185$	1.42884e9	0.0896834
$186$	−9.50895e9	−0.582538
$187$	0	0
$188$	−2.42115e10	−1.41355
$189$	−1.73026e10	−0.986357
$190$	3.73515e9	0.207930
$191$	−2.52142e10	−1.37087	−0.685434	−	0.728135i	$-0.740387\pi$
$191$	−2.52142e10	−1.37087	−0.685434	+	0.728135i	$0.740387\pi$
$192$	−8.48999e8	−0.0450870
$193$	−3.06794e10	−1.59162	−0.795810	−	0.605547i	$-0.792954\pi$
$193$	−3.06794e10	−1.59162	−0.795810	+	0.605547i	$0.792954\pi$
$194$	−1.14575e10	−0.580742
$195$	−6.02803e9	−0.298552
$196$	2.77175e9	0.134153
$197$	2.51918e9	0.119169	0.0595843	−	0.998223i	$-0.481022\pi$
$197$	2.51918e9	0.119169	0.0595843	+	0.998223i	$0.481022\pi$
$198$	−1.19708e8	−0.00553514
$199$	3.31066e10	1.49650	0.748248	−	0.663419i	$-0.230895\pi$
$199$	3.31066e10	1.49650	0.748248	+	0.663419i	$0.230895\pi$
$200$	1.56955e9	0.0693648
$201$	3.41197e10	1.47442
$202$	9.19498e9	0.388570
$203$	−1.72896e10	−0.714582
$204$	0	0
$205$	−3.38295e10	−1.33784
$206$	−1.26972e10	−0.491252
$207$	−3.29213e9	−0.124627
$208$	3.68381e9	0.136462
$209$	5.76314e8	0.0208930
$210$	−1.06258e10	−0.377028
$211$	3.71348e10	1.28976	0.644882	−	0.764282i	$-0.276907\pi$
$211$	3.71348e10	1.28976	0.644882	+	0.764282i	$0.276907\pi$
$212$	−2.37650e10	−0.808028
$213$	2.41560e9	0.0804113
$214$	−4.41185e9	−0.143800
$215$	3.44019e10	1.09802
$216$	2.84545e10	0.889424
$217$	4.36218e10	1.33547
$218$	6.50146e6	0.000194965 0
$219$	4.11154e10	1.20783
$220$	1.37191e9	0.0394841
$221$	0	0
$222$	1.23859e9	0.0342248
$223$	2.95004e10	0.798833	0.399416	−	0.916770i	$-0.369213\pi$
$223$	2.95004e10	0.798833	0.399416	+	0.916770i	$0.369213\pi$
$224$	3.46951e10	0.920772
$225$	−8.14445e8	−0.0211856
$226$	−5.11275e9	−0.130367
$227$	−1.59933e9	−0.0399781	−0.0199890	−	0.999800i	$-0.506363\pi$
$227$	−1.59933e9	−0.0399781	−0.0199890	+	0.999800i	$0.506363\pi$
$228$	−1.21199e10	−0.297024
$229$	4.03603e10	0.969827	0.484914	−	0.874562i	$-0.338851\pi$
$229$	4.03603e10	0.969827	0.484914	+	0.874562i	$0.338851\pi$
$230$	−1.00794e10	−0.237497
$231$	−1.63950e9	−0.0378841
$232$	2.84330e10	0.644357
$233$	8.88023e10	1.97389	0.986944	−	0.161061i	$-0.0514917\pi$
$233$	8.88023e10	1.97389	0.986944	+	0.161061i	$0.0514917\pi$
$234$	1.75026e9	0.0381620
$235$	8.72060e10	1.86527
$236$	4.81099e10	1.00956
$237$	2.31658e10	0.476958
$238$	0	0
$239$	−9.30238e10	−1.84418	−0.922090	−	0.386975i	$-0.873520\pi$
$239$	−9.30238e10	−1.84418	−0.922090	+	0.386975i	$0.873520\pi$
$240$	−1.90845e10	−0.371305
$241$	7.97680e10	1.52318	0.761592	−	0.648057i	$-0.224418\pi$
$241$	7.97680e10	1.52318	0.761592	+	0.648057i	$0.224418\pi$
$242$	2.44416e10	0.458099
$243$	−2.65687e10	−0.488812
$244$	7.02460e10	1.26872
$245$	−9.98340e9	−0.177024
$246$	−2.93251e10	−0.510542
$247$	−8.42634e9	−0.144046
$248$	−7.17368e10	−1.20423
$249$	6.48376e10	1.06888
$250$	2.70386e10	0.437778
$251$	4.47092e10	0.710993	0.355497	−	0.934678i	$-0.384312\pi$
$251$	4.47092e10	0.710993	0.355497	+	0.934678i	$0.384312\pi$
$252$	−1.15487e10	−0.180397
$253$	−1.55520e9	−0.0238640
$254$	1.43651e10	0.216549
$255$	0	0
$256$	−3.47151e10	−0.505171
$257$	−1.03452e11	−1.47925	−0.739624	−	0.673020i	$-0.764997\pi$
$257$	−1.03452e11	−1.47925	−0.739624	+	0.673020i	$0.764997\pi$
$258$	2.98213e10	0.419024
$259$	−5.68199e9	−0.0784606
$260$	−2.00588e10	−0.272223
$261$	−1.47540e10	−0.196801
$262$	−2.07974e10	−0.272680
$263$	8.72107e9	0.112401	0.0562003	−	0.998420i	$-0.482101\pi$
$263$	8.72107e9	0.112401	0.0562003	+	0.998420i	$0.482101\pi$
$264$	2.69618e9	0.0341611
$265$	8.55978e10	1.06624
$266$	−1.48533e10	−0.181910
$267$	9.50561e10	1.14467
$268$	1.13536e11	1.34440
$269$	−1.46865e10	−0.171014	−0.0855071	−	0.996338i	$-0.527251\pi$
$269$	−1.46865e10	−0.171014	−0.0855071	+	0.996338i	$0.527251\pi$
$270$	−4.52059e10	−0.517676
$271$	−2.26346e10	−0.254924	−0.127462	−	0.991843i	$-0.540683\pi$
$271$	−2.26346e10	−0.254924	−0.127462	+	0.991843i	$0.540683\pi$
$272$	0	0
$273$	2.39713e10	0.261191
$274$	−2.78339e10	−0.298330
$275$	−3.84742e8	−0.00405670
$276$	3.27057e10	0.339260
$277$	2.04552e10	0.208759	0.104380	−	0.994538i	$-0.466714\pi$
$277$	2.04552e10	0.208759	0.104380	+	0.994538i	$0.466714\pi$
$278$	−6.50315e10	−0.653014
$279$	3.72246e10	0.367799
$280$	−8.01622e10	−0.779397
$281$	5.58885e10	0.534741	0.267371	−	0.963594i	$-0.413845\pi$
$281$	5.58885e10	0.534741	0.267371	+	0.963594i	$0.413845\pi$
$282$	7.55946e10	0.711819
$283$	−3.87106e10	−0.358749	−0.179375	−	0.983781i	$-0.557407\pi$
$283$	−3.87106e10	−0.358749	−0.179375	+	0.983781i	$0.557407\pi$
$284$	8.03812e9	0.0733199
$285$	4.36539e10	0.391941
$286$	8.26818e8	0.00730740
$287$	1.34527e11	1.17042
$288$	2.96070e10	0.253587
$289$	0	0
$290$	−4.51718e10	−0.375039
$291$	−1.33908e11	−1.09468
$292$	1.36815e11	1.10131
$293$	−2.87885e10	−0.228200	−0.114100	−	0.993469i	$-0.536398\pi$
$293$	−2.87885e10	−0.228200	−0.114100	+	0.993469i	$0.536398\pi$
$294$	−8.65412e9	−0.0675554
$295$	−1.73284e11	−1.33217
$296$	9.34413e9	0.0707499
$297$	−6.97503e9	−0.0520166
$298$	−4.59560e10	−0.337574
$299$	2.27387e10	0.164530
$300$	8.09112e9	0.0576717
$301$	−1.36804e11	−0.960614
$302$	−3.77482e9	−0.0261135
$303$	1.07465e11	0.732442
$304$	−2.66775e10	−0.179149
$305$	−2.53015e11	−1.67416
$306$	0	0
$307$	8.97359e10	0.576558	0.288279	−	0.957546i	$-0.406917\pi$
$307$	8.97359e10	0.576558	0.288279	+	0.957546i	$0.406917\pi$
$308$	−5.45557e9	−0.0345431
$309$	−1.48396e11	−0.925993
$310$	1.13969e11	0.700905
$311$	1.85255e11	1.12292	0.561458	−	0.827505i	$-0.310241\pi$
$311$	1.85255e11	1.12292	0.561458	+	0.827505i	$0.310241\pi$
$312$	−3.94211e10	−0.235523
$313$	−7.32601e10	−0.431437	−0.215719	−	0.976456i	$-0.569209\pi$
$313$	−7.32601e10	−0.431437	−0.215719	+	0.976456i	$0.569209\pi$
$314$	−8.29246e10	−0.481393
$315$	4.15965e10	0.238045
$316$	7.70862e10	0.434896
$317$	6.70467e9	0.0372916	0.0186458	−	0.999826i	$-0.494065\pi$
$317$	6.70467e9	0.0372916	0.0186458	+	0.999826i	$0.494065\pi$
$318$	7.42005e10	0.406897
$319$	−6.96976e9	−0.0376842
$320$	1.01756e10	0.0542483
$321$	−5.15627e10	−0.271058
$322$	4.00820e10	0.207777
$323$	0	0
$324$	1.07407e11	0.541479
$325$	5.62535e9	0.0279688
$326$	−1.70142e11	−0.834318
$327$	7.59846e7	0.000367503 0
$328$	−2.21233e11	−1.05540
$329$	−3.46786e11	−1.63185
$330$	−4.28345e9	−0.0198830
$331$	3.70409e11	1.69612	0.848059	−	0.529902i	$-0.177771\pi$
$331$	3.70409e11	1.69612	0.848059	+	0.529902i	$0.177771\pi$
$332$	2.15753e11	0.974618
$333$	−4.84871e9	−0.0216086
$334$	−1.08276e11	−0.476073
$335$	−4.08939e11	−1.77401
$336$	7.58921e10	0.324840
$337$	2.14065e11	0.904087	0.452043	−	0.891996i	$-0.350695\pi$
$337$	2.14065e11	0.904087	0.452043	+	0.891996i	$0.350695\pi$
$338$	9.80874e10	0.408779
$339$	−5.97542e10	−0.245737
$340$	0	0
$341$	1.75848e10	0.0704276
$342$	−1.26750e10	−0.0500994
$343$	2.73242e11	1.06592
$344$	2.24976e11	0.866211
$345$	−1.17801e11	−0.447675
$346$	8.16832e9	0.0306401
$347$	−4.32305e10	−0.160069	−0.0800345	−	0.996792i	$-0.525503\pi$
$347$	−4.32305e10	−0.160069	−0.0800345	+	0.996792i	$0.525503\pi$
$348$	1.46574e11	0.535735
$349$	2.70051e11	0.974387	0.487194	−	0.873294i	$-0.338021\pi$
$349$	2.70051e11	0.974387	0.487194	+	0.873294i	$0.338021\pi$
$350$	9.91595e9	0.0353206
$351$	1.01982e11	0.358628
$352$	1.39863e10	0.0485579
$353$	−5.33235e11	−1.82781	−0.913907	−	0.405923i	$-0.866950\pi$
$353$	−5.33235e11	−1.82781	−0.913907	+	0.405923i	$0.866950\pi$
$354$	−1.50211e11	−0.508380
$355$	−2.89520e10	−0.0967502
$356$	3.16307e11	1.04372
$357$	0	0
$358$	5.95120e10	0.191483
$359$	−5.40222e10	−0.171651	−0.0858257	−	0.996310i	$-0.527353\pi$
$359$	−5.40222e10	−0.171651	−0.0858257	+	0.996310i	$0.527353\pi$
$360$	−6.84062e10	−0.214652
$361$	−2.61666e11	−0.810895
$362$	1.01233e11	0.309837
$363$	2.85656e11	0.863502
$364$	7.97664e10	0.238157
$365$	−4.92786e11	−1.45325
$366$	−2.19326e11	−0.638889
$367$	1.80940e10	0.0520640	0.0260320	−	0.999661i	$-0.491713\pi$
$367$	1.80940e10	0.0520640	0.0260320	+	0.999661i	$0.491713\pi$
$368$	7.19898e10	0.204624
$369$	1.14799e11	0.322343
$370$	−1.48451e10	−0.0411790
$371$	−3.40391e11	−0.932815
$372$	−3.69808e11	−1.00123
$373$	−2.44941e10	−0.0655196	−0.0327598	−	0.999463i	$-0.510430\pi$
$373$	−2.44941e10	−0.0655196	−0.0327598	+	0.999463i	$0.510430\pi$
$374$	0	0
$375$	3.16008e11	0.825198
$376$	5.70296e11	1.47148
$377$	1.01905e11	0.259813
$378$	1.79767e11	0.452895
$379$	6.10167e10	0.151905	0.0759526	−	0.997111i	$-0.475800\pi$
$379$	6.10167e10	0.151905	0.0759526	+	0.997111i	$0.475800\pi$
$380$	1.45262e11	0.357376
$381$	1.67889e11	0.408188
$382$	2.61965e11	0.629446
$383$	−2.92964e11	−0.695696	−0.347848	−	0.937551i	$-0.613087\pi$
$383$	−2.92964e11	−0.695696	−0.347848	+	0.937551i	$0.613087\pi$
$384$	−3.63887e11	−0.854036
$385$	1.96501e10	0.0455818
$386$	3.18746e11	0.730807
$387$	−1.16741e11	−0.264561
$388$	−4.45589e11	−0.998141
$389$	−4.44479e11	−0.984189	−0.492094	−	0.870542i	$-0.663769\pi$
$389$	−4.44479e11	−0.984189	−0.492094	+	0.870542i	$0.663769\pi$
$390$	6.26287e10	0.137083
$391$	0	0
$392$	−6.52878e10	−0.139651
$393$	−2.43065e11	−0.513992
$394$	−2.61733e10	−0.0547174
$395$	−2.77652e11	−0.573871
$396$	−4.65550e9	−0.00951344
$397$	8.73577e11	1.76500	0.882498	−	0.470316i	$-0.155860\pi$
$397$	8.73577e11	1.76500	0.882498	+	0.470316i	$0.155860\pi$
$398$	−3.43964e11	−0.687130
$399$	−1.73595e11	−0.342894
$400$	1.78097e10	0.0347845
$401$	−7.23977e11	−1.39822	−0.699109	−	0.715015i	$-0.746420\pi$
$401$	−7.23977e11	−1.39822	−0.699109	+	0.715015i	$0.746420\pi$
$402$	−3.54489e11	−0.676995
$403$	−2.57109e11	−0.485562
$404$	3.57598e11	0.667849
$405$	−3.86865e11	−0.714515
$406$	1.79631e11	0.328107
$407$	−2.29052e9	−0.00413770
$408$	0	0
$409$	5.85905e10	0.103531	0.0517657	−	0.998659i	$-0.483515\pi$
$409$	5.85905e10	0.103531	0.0517657	+	0.998659i	$0.483515\pi$
$410$	3.51474e11	0.614280
$411$	−3.25304e11	−0.562342
$412$	−4.93799e11	−0.844331
$413$	6.89087e11	1.16546
$414$	3.42039e10	0.0572235
$415$	−7.77107e11	−1.28607
$416$	−2.04494e11	−0.334781
$417$	−7.60043e11	−1.23091
$418$	−5.98766e9	−0.00959321
$419$	−2.55123e11	−0.404378	−0.202189	−	0.979347i	$-0.564805\pi$
$419$	−2.55123e11	−0.404378	−0.202189	+	0.979347i	$0.564805\pi$
$420$	−4.13242e11	−0.648011
$421$	−5.38001e11	−0.834668	−0.417334	−	0.908753i	$-0.637035\pi$
$421$	−5.38001e11	−0.834668	−0.417334	+	0.908753i	$0.637035\pi$
$422$	−3.85815e11	−0.592207
$423$	−2.95929e11	−0.449424
$424$	5.59779e11	0.841143
$425$	0	0
$426$	−2.50971e10	−0.0369216
$427$	1.00615e12	1.46466
$428$	−1.71579e11	−0.247154
$429$	9.66327e9	0.0137742
$430$	−3.57422e11	−0.504166
$431$	6.14842e11	0.858253	0.429127	−	0.903244i	$-0.358821\pi$
$431$	6.14842e11	0.858253	0.429127	+	0.903244i	$0.358821\pi$
$432$	3.22873e11	0.446021
$433$	4.79713e11	0.655822	0.327911	−	0.944709i	$-0.393655\pi$
$433$	4.79713e11	0.655822	0.327911	+	0.944709i	$0.393655\pi$
$434$	−4.53213e11	−0.613195
$435$	−5.27936e11	−0.706935
$436$	2.52845e8	0.000335093 0
$437$	−1.64669e11	−0.215996
$438$	−4.27172e11	−0.554587
$439$	−1.39973e11	−0.179867	−0.0899337	−	0.995948i	$-0.528666\pi$
$439$	−1.39973e11	−0.179867	−0.0899337	+	0.995948i	$0.528666\pi$
$440$	−3.23149e10	−0.0411023
$441$	3.38782e10	0.0426527
$442$	0	0
$443$	5.34602e11	0.659499	0.329749	−	0.944068i	$-0.393036\pi$
$443$	5.34602e11	0.659499	0.329749	+	0.944068i	$0.393036\pi$
$444$	4.81696e10	0.0588233
$445$	−1.13929e12	−1.37725
$446$	−3.06497e11	−0.366791
$447$	−5.37102e11	−0.636316
$448$	−4.04647e10	−0.0474598
$449$	1.58754e12	1.84339	0.921695	−	0.387914i	$-0.126804\pi$
$449$	1.58754e12	1.84339	0.921695	+	0.387914i	$0.126804\pi$
$450$	8.46175e9	0.00972756
$451$	5.42306e10	0.0617234
$452$	−1.98837e11	−0.224066
$453$	−4.41175e10	−0.0492231
$454$	1.66164e10	0.0183563
$455$	−2.87306e11	−0.314263
$456$	2.85481e11	0.309197
$457$	−1.56481e11	−0.167818	−0.0839092	−	0.996473i	$-0.526741\pi$
$457$	−1.56481e11	−0.167818	−0.0839092	+	0.996473i	$0.526741\pi$
$458$	−4.19327e11	−0.445305
$459$	0	0
$460$	−3.91993e11	−0.408195
$461$	1.32697e12	1.36838	0.684190	−	0.729304i	$-0.260156\pi$
$461$	1.32697e12	1.36838	0.684190	+	0.729304i	$0.260156\pi$
$462$	1.70337e10	0.0173948
$463$	−1.33241e12	−1.34748	−0.673739	−	0.738969i	$-0.735313\pi$
$463$	−1.33241e12	−1.34748	−0.673739	+	0.738969i	$0.735313\pi$
$464$	3.22629e11	0.323127
$465$	1.33199e12	1.32118
$466$	−9.22620e11	−0.906329
$467$	4.42532e10	0.0430545	0.0215273	−	0.999768i	$-0.493147\pi$
$467$	4.42532e10	0.0430545	0.0215273	+	0.999768i	$0.493147\pi$
$468$	6.80685e10	0.0655903
$469$	1.62620e12	1.55202
$470$	−9.06034e11	−0.856454
$471$	−9.69165e11	−0.907410
$472$	−1.13322e12	−1.05093
$473$	−5.51483e10	−0.0506590
$474$	−2.40683e11	−0.219000
$475$	−4.07377e10	−0.0367177
$476$	0	0
$477$	−2.90472e11	−0.256904
$478$	9.66479e11	0.846773
$479$	−1.73977e12	−1.51002	−0.755010	−	0.655713i	$-0.772368\pi$
$479$	−1.73977e12	−1.51002	−0.755010	+	0.655713i	$0.772368\pi$
$480$	1.05941e12	0.910919
$481$	3.34899e10	0.0285273
$482$	−8.28757e11	−0.699384
$483$	4.68451e11	0.391654
$484$	9.50545e11	0.787351
$485$	1.60494e12	1.31711
$486$	2.76038e11	0.224443
$487$	5.20901e11	0.419638	0.209819	−	0.977740i	$-0.432713\pi$
$487$	5.20901e11	0.419638	0.209819	+	0.977740i	$0.432713\pi$
$488$	−1.65463e12	−1.32072
$489$	−1.98850e12	−1.57266
$490$	1.03723e11	0.0812820
$491$	−4.74925e11	−0.368772	−0.184386	−	0.982854i	$-0.559030\pi$
$491$	−4.74925e11	−0.368772	−0.184386	+	0.982854i	$0.559030\pi$
$492$	−1.14047e12	−0.877486
$493$	0	0
$494$	8.75462e10	0.0661402
$495$	1.67684e10	0.0125536
$496$	−8.13998e11	−0.603887
$497$	1.15132e11	0.0846430
$498$	−6.73636e11	−0.490787
$499$	5.66987e10	0.0409375	0.0204687	−	0.999790i	$-0.493484\pi$
$499$	5.66987e10	0.0409375	0.0204687	+	0.999790i	$0.493484\pi$
$500$	1.05155e12	0.752425
$501$	−1.26546e12	−0.897382
$502$	−4.64511e11	−0.326459
$503$	−2.79705e10	−0.0194825	−0.00974125	−	0.999953i	$-0.503101\pi$
$503$	−2.79705e10	−0.0194825	−0.00974125	+	0.999953i	$0.503101\pi$
$504$	2.72026e11	0.187790
$505$	−1.28801e12	−0.881268
$506$	1.61578e10	0.0109574
$507$	1.14638e12	0.770534
$508$	5.58665e11	0.372190
$509$	2.28497e12	1.50887	0.754434	−	0.656376i	$-0.227911\pi$
$509$	2.28497e12	1.50887	0.754434	+	0.656376i	$0.227911\pi$
$510$	0	0
$511$	1.95963e12	1.27139
$512$	−1.17367e12	−0.754800
$513$	−7.38538e11	−0.470809
$514$	1.07483e12	0.679211
$515$	1.77859e12	1.11415
$516$	1.15977e12	0.720190
$517$	−1.39796e11	−0.0860573
$518$	5.90335e10	0.0360259
$519$	9.54657e10	0.0577556
$520$	4.72480e11	0.283379
$521$	−2.38544e12	−1.41840	−0.709199	−	0.705008i	$-0.750943\pi$
$521$	−2.38544e12	−1.41840	−0.709199	+	0.705008i	$0.750943\pi$
$522$	1.53288e11	0.0903631
$523$	2.62970e12	1.53691	0.768454	−	0.639905i	$-0.221026\pi$
$523$	2.62970e12	1.53691	0.768454	+	0.639905i	$0.221026\pi$
$524$	−8.08821e11	−0.468664
$525$	1.15891e11	0.0665782
$526$	−9.06083e10	−0.0516098
$527$	0	0
$528$	3.05936e10	0.0171308
$529$	−1.35679e12	−0.753289
$530$	−8.89326e11	−0.489575
$531$	5.88031e11	0.320978
$532$	−5.77653e11	−0.312655
$533$	−7.92910e11	−0.425551
$534$	−9.87594e11	−0.525585
$535$	6.18002e11	0.326135
$536$	−2.67431e12	−1.39949
$537$	6.95536e11	0.360940
$538$	1.52586e11	0.0785227
$539$	1.60040e10	0.00816729
$540$	−1.75808e12	−0.889748
$541$	−3.24028e12	−1.62628	−0.813140	−	0.582069i	$-0.802244\pi$
$541$	−3.24028e12	−1.62628	−0.813140	+	0.582069i	$0.802244\pi$
$542$	2.35164e11	0.117051
$543$	1.18314e12	0.584033
$544$	0	0
$545$	−9.10709e8	−0.000442176 0
$546$	−2.49051e11	−0.119928
$547$	1.35392e12	0.646621	0.323310	−	0.946293i	$-0.395204\pi$
$547$	1.35392e12	0.646621	0.323310	+	0.946293i	$0.395204\pi$
$548$	−1.08248e12	−0.512750
$549$	8.58593e11	0.403378
$550$	3.99731e9	0.00186267
$551$	−7.37980e11	−0.341085
$552$	−7.70376e11	−0.353164
$553$	1.10412e12	0.502058
$554$	−2.12521e11	−0.0958537
$555$	−1.73499e11	−0.0776210
$556$	−2.52911e12	−1.12236
$557$	3.86259e12	1.70032	0.850159	−	0.526526i	$-0.176506\pi$
$557$	3.86259e12	1.70032	0.850159	+	0.526526i	$0.176506\pi$
$558$	−3.86748e11	−0.168878
$559$	8.06328e11	0.349268
$560$	−9.09601e11	−0.390845
$561$	0	0
$562$	−5.80658e11	−0.245531
$563$	3.23036e12	1.35507	0.677536	−	0.735489i	$-0.263048\pi$
$563$	3.23036e12	1.35507	0.677536	+	0.735489i	$0.263048\pi$
$564$	2.93991e12	1.22343
$565$	7.16181e11	0.295668
$566$	4.02187e11	0.164723
$567$	1.53842e12	0.625102
$568$	−1.89336e11	−0.0763248
$569$	−2.61773e12	−1.04693	−0.523467	−	0.852046i	$-0.675362\pi$
$569$	−2.61773e12	−1.04693	−0.523467	+	0.852046i	$0.675362\pi$
$570$	−4.53546e11	−0.179963
$571$	7.43673e11	0.292765	0.146383	−	0.989228i	$-0.453237\pi$
$571$	7.43673e11	0.292765	0.146383	+	0.989228i	$0.453237\pi$
$572$	3.21554e10	0.0125595
$573$	3.06167e12	1.18649
$574$	−1.39768e12	−0.537410
$575$	1.09932e11	0.0419389
$576$	−3.45305e10	−0.0130708
$577$	1.94245e12	0.729556	0.364778	−	0.931094i	$-0.381145\pi$
$577$	1.94245e12	0.729556	0.364778	+	0.931094i	$0.381145\pi$
$578$	0	0
$579$	3.72529e12	1.37755
$580$	−1.75675e12	−0.644592
$581$	3.09027e12	1.12513
$582$	1.39125e12	0.502632
$583$	−1.37218e11	−0.0491930
$584$	−3.22264e12	−1.14645
$585$	−2.45172e11	−0.0865504
$586$	2.99101e11	0.104780
$587$	1.54986e12	0.538793	0.269396	−	0.963029i	$-0.413176\pi$
$587$	1.54986e12	0.538793	0.269396	+	0.963029i	$0.413176\pi$
$588$	−3.36563e11	−0.116110
$589$	1.86194e12	0.637450
$590$	1.80035e12	0.611678
$591$	−3.05895e11	−0.103140
$592$	1.06028e11	0.0354791
$593$	−2.14021e12	−0.710738	−0.355369	−	0.934726i	$-0.615645\pi$
$593$	−2.14021e12	−0.710738	−0.355369	+	0.934726i	$0.615645\pi$
$594$	7.24676e10	0.0238839
$595$	0	0
$596$	−1.78725e12	−0.580200
$597$	−4.02001e12	−1.29522
$598$	−2.36245e11	−0.0755454
$599$	1.00259e12	0.318201	0.159100	−	0.987262i	$-0.449141\pi$
$599$	1.00259e12	0.318201	0.159100	+	0.987262i	$0.449141\pi$
$600$	−1.90584e11	−0.0600353
$601$	−2.75646e11	−0.0861819	−0.0430909	−	0.999071i	$-0.513721\pi$
$601$	−2.75646e11	−0.0861819	−0.0430909	+	0.999071i	$0.513721\pi$
$602$	1.42134e12	0.441075
$603$	1.38771e12	0.427437
$604$	−1.46805e11	−0.0448821
$605$	−3.42371e12	−1.03896
$606$	−1.11651e12	−0.336308
$607$	3.23706e12	0.967835	0.483917	−	0.875114i	$-0.339214\pi$
$607$	3.23706e12	0.967835	0.483917	+	0.875114i	$0.339214\pi$
$608$	1.48091e12	0.439504
$609$	2.09941e12	0.618471
$610$	2.62872e12	0.768706
$611$	2.04397e12	0.593321
$612$	0	0
$613$	−4.13642e12	−1.18318	−0.591592	−	0.806238i	$-0.701500\pi$
$613$	−4.13642e12	−1.18318	−0.591592	+	0.806238i	$0.701500\pi$
$614$	−9.32319e11	−0.264732
$615$	4.10779e12	1.15790
$616$	1.28505e11	0.0359588
$617$	2.35389e11	0.0653887	0.0326944	−	0.999465i	$-0.489591\pi$
$617$	2.35389e11	0.0653887	0.0326944	+	0.999465i	$0.489591\pi$
$618$	1.54177e12	0.425178
$619$	−3.08679e12	−0.845081	−0.422541	−	0.906344i	$-0.638862\pi$
$619$	−3.08679e12	−0.845081	−0.422541	+	0.906344i	$0.638862\pi$
$620$	4.43231e12	1.20467
$621$	1.99296e12	0.537758
$622$	−1.92472e12	−0.515597
$623$	4.53053e12	1.20491
$624$	−4.47312e11	−0.118108
$625$	−4.10960e12	−1.07731
$626$	7.61142e11	0.198098
$627$	−6.99796e10	−0.0180829
$628$	−3.22498e12	−0.827387
$629$	0	0
$630$	−4.32171e11	−0.109301
$631$	1.50842e12	0.378783	0.189392	−	0.981902i	$-0.439348\pi$
$631$	1.50842e12	0.378783	0.189392	+	0.981902i	$0.439348\pi$
$632$	−1.81575e12	−0.452719
$633$	−4.50914e12	−1.11629
$634$	−6.96587e10	−0.0171228
$635$	−2.01222e12	−0.491128
$636$	2.88570e12	0.699349
$637$	−2.33995e11	−0.0563093
$638$	7.24129e10	0.0173031
$639$	9.82473e10	0.0233113
$640$	4.36135e12	1.02757
$641$	6.22573e12	1.45656	0.728281	−	0.685279i	$-0.240320\pi$
$641$	6.22573e12	1.45656	0.728281	+	0.685279i	$0.240320\pi$
$642$	5.35715e11	0.124459
$643$	7.75305e12	1.78864	0.894320	−	0.447428i	$-0.147660\pi$
$643$	7.75305e12	1.78864	0.894320	+	0.447428i	$0.147660\pi$
$644$	1.55881e12	0.357114
$645$	−4.17730e12	−0.950336
$646$	0	0
$647$	5.78109e11	0.129700	0.0648500	−	0.997895i	$-0.479343\pi$
$647$	5.78109e11	0.129700	0.0648500	+	0.997895i	$0.479343\pi$
$648$	−2.52995e12	−0.563670
$649$	2.77784e11	0.0614620
$650$	−5.84450e10	−0.0128421
$651$	−5.29684e12	−1.15585
$652$	−6.61690e12	−1.43397
$653$	−1.34041e12	−0.288488	−0.144244	−	0.989542i	$-0.546075\pi$
$653$	−1.34041e12	−0.288488	−0.144244	+	0.989542i	$0.546075\pi$
$654$	−7.89449e8	−0.000168742 0
$655$	2.91325e12	0.618431
$656$	−2.51033e12	−0.529253
$657$	1.67224e12	0.350151
$658$	3.60297e12	0.749279
$659$	7.95738e12	1.64356	0.821780	−	0.569805i	$-0.192981\pi$
$659$	7.95738e12	1.64356	0.821780	+	0.569805i	$0.192981\pi$
$660$	−1.66586e11	−0.0341735
$661$	−4.99569e12	−1.01786	−0.508931	−	0.860807i	$-0.669959\pi$
$661$	−4.99569e12	−1.01786	−0.508931	+	0.860807i	$0.669959\pi$
$662$	−3.84840e12	−0.778788
$663$	0	0
$664$	−5.08200e12	−1.01456
$665$	2.08062e12	0.412567
$666$	5.03761e10	0.00992180
$667$	1.99146e12	0.389587
$668$	−4.21091e12	−0.818243
$669$	−3.58212e12	−0.691390
$670$	4.24871e12	0.814555
$671$	4.05597e11	0.0772403
$672$	−4.21290e12	−0.796928
$673$	1.88855e12	0.354863	0.177431	−	0.984133i	$-0.443221\pi$
$673$	1.88855e12	0.354863	0.177431	+	0.984133i	$0.443221\pi$
$674$	−2.22404e12	−0.415120
$675$	4.93042e11	0.0914148
$676$	3.81467e12	0.702582
$677$	3.49370e12	0.639200	0.319600	−	0.947553i	$-0.396451\pi$
$677$	3.49370e12	0.639200	0.319600	+	0.947553i	$0.396451\pi$
$678$	6.20822e11	0.112832
$679$	−6.38226e12	−1.15229
$680$	0	0
$681$	1.94201e11	0.0346010
$682$	−1.82699e11	−0.0323375
$683$	1.11112e12	0.195375	0.0976875	−	0.995217i	$-0.468855\pi$
$683$	1.11112e12	0.195375	0.0976875	+	0.995217i	$0.468855\pi$
$684$	−4.92939e11	−0.0861075
$685$	3.89891e12	0.676605
$686$	−2.83887e12	−0.489426
$687$	−4.90080e12	−0.839386
$688$	2.55281e12	0.434380
$689$	2.00628e12	0.339160
$690$	1.22390e12	0.205554
$691$	1.27071e12	0.212030	0.106015	−	0.994365i	$-0.466191\pi$
$691$	1.27071e12	0.212030	0.106015	+	0.994365i	$0.466191\pi$
$692$	3.17670e11	0.0526622
$693$	−6.66816e10	−0.0109826
$694$	4.49147e11	0.0734971
$695$	9.10946e12	1.48102
$696$	−3.45251e12	−0.557691
$697$	0	0
$698$	−2.80572e12	−0.447399
$699$	−1.07829e13	−1.70840
$700$	3.85636e11	0.0607067
$701$	−7.14268e12	−1.11720	−0.558599	−	0.829438i	$-0.688661\pi$
$701$	−7.14268e12	−1.11720	−0.558599	+	0.829438i	$0.688661\pi$
$702$	−1.05956e12	−0.164667
$703$	−2.42528e11	−0.0374509
$704$	−1.63121e10	−0.00250284
$705$	−1.05891e13	−1.61439
$706$	5.54009e12	0.839258
$707$	5.12194e12	0.770987
$708$	−5.84180e12	−0.873770
$709$	4.09276e12	0.608287	0.304144	−	0.952626i	$-0.401630\pi$
$709$	4.09276e12	0.608287	0.304144	+	0.952626i	$0.401630\pi$
$710$	3.00800e11	0.0444237
$711$	9.42200e11	0.138271
$712$	−7.45054e12	−1.08649
$713$	−5.02447e12	−0.728094
$714$	0	0
$715$	−1.15819e11	−0.0165730
$716$	2.31445e12	0.329109
$717$	1.12955e13	1.59614
$718$	5.61269e11	0.0788154
$719$	3.19174e12	0.445397	0.222699	−	0.974887i	$-0.428513\pi$
$719$	3.19174e12	0.445397	0.222699	+	0.974887i	$0.428513\pi$
$720$	−7.76206e11	−0.107642
$721$	−7.07278e12	−0.974724
$722$	2.71860e12	0.372330
$723$	−9.68594e12	−1.31832
$724$	3.93701e12	0.532528
$725$	4.92669e11	0.0662269
$726$	−2.96785e12	−0.396485
$727$	1.43422e13	1.90419	0.952094	−	0.305806i	$-0.0989259\pi$
$727$	1.43422e13	1.90419	0.952094	+	0.305806i	$0.0989259\pi$
$728$	−1.87888e12	−0.247918
$729$	8.45833e12	1.10920
$730$	5.11985e12	0.667274
$731$	0	0
$732$	−8.52971e12	−1.09808
$733$	−6.30500e12	−0.806710	−0.403355	−	0.915044i	$-0.632156\pi$
$733$	−6.30500e12	−0.806710	−0.403355	+	0.915044i	$0.632156\pi$
$734$	−1.87989e11	−0.0239057
$735$	1.21225e12	0.153214
$736$	−3.99627e12	−0.502001
$737$	6.55553e11	0.0818472
$738$	−1.19271e12	−0.148007
$739$	−8.54398e12	−1.05381	−0.526903	−	0.849926i	$-0.676647\pi$
$739$	−8.54398e12	−1.05381	−0.526903	+	0.849926i	$0.676647\pi$
$740$	−5.77334e11	−0.0707757
$741$	1.02318e12	0.124672
$742$	3.53652e12	0.428311
$743$	8.28397e12	0.997215	0.498607	−	0.866828i	$-0.333845\pi$
$743$	8.28397e12	0.997215	0.498607	+	0.866828i	$0.333845\pi$
$744$	8.71074e12	1.04226
$745$	6.43740e12	0.765610
$746$	2.54483e11	0.0300839
$747$	2.63707e12	0.309870
$748$	0	0
$749$	−2.45757e12	−0.285323
$750$	−3.28320e12	−0.378897
$751$	−1.48068e13	−1.69857	−0.849284	−	0.527937i	$-0.822966\pi$
$751$	−1.48068e13	−1.69857	−0.849284	+	0.527937i	$0.822966\pi$
$752$	6.47115e12	0.737906
$753$	−5.42888e12	−0.615365
$754$	−1.05876e12	−0.119296
$755$	5.28767e11	0.0592247
$756$	6.99124e12	0.778406
$757$	1.52757e13	1.69072	0.845359	−	0.534199i	$-0.179387\pi$
$757$	1.52757e13	1.69072	0.845359	+	0.534199i	$0.179387\pi$
$758$	−6.33939e11	−0.0697487
$759$	1.88842e11	0.0206543
$760$	−3.42161e12	−0.372023
$761$	−8.91048e12	−0.963098	−0.481549	−	0.876419i	$-0.659926\pi$
$761$	−8.91048e12	−0.963098	−0.481549	+	0.876419i	$0.659926\pi$
$762$	−1.74430e12	−0.187423
$763$	3.62155e9	0.000386843 0
$764$	1.01880e13	1.08185
$765$	0	0
$766$	3.04377e12	0.319435
$767$	−4.06151e12	−0.423749
$768$	4.21532e12	0.437226
$769$	1.69319e13	1.74597	0.872986	−	0.487745i	$-0.162181\pi$
$769$	1.69319e13	1.74597	0.872986	+	0.487745i	$0.162181\pi$
$770$	−2.04156e11	−0.0209293
$771$	1.25618e13	1.28029
$772$	1.23962e13	1.25606
$773$	−8.71332e12	−0.877760	−0.438880	−	0.898546i	$-0.644625\pi$
$773$	−8.71332e12	−0.877760	−0.438880	+	0.898546i	$0.644625\pi$
$774$	1.21289e12	0.121475
$775$	−1.24301e12	−0.123771
$776$	1.04957e13	1.03905
$777$	6.89943e11	0.0679076
$778$	4.61796e12	0.451899
$779$	5.74211e12	0.558667
$780$	2.43566e12	0.235609
$781$	4.64118e10	0.00446374
$782$	0	0
$783$	8.93165e12	0.849188
$784$	−7.40821e11	−0.0700312
$785$	1.16159e13	1.09179
$786$	2.52535e12	0.236004
$787$	1.28811e13	1.19692	0.598460	−	0.801153i	$-0.295780\pi$
$787$	1.28811e13	1.19692	0.598460	+	0.801153i	$0.295780\pi$
$788$	−1.01789e12	−0.0940446
$789$	−1.05897e12	−0.0972828
$790$	2.88469e12	0.263498
$791$	−2.84799e12	−0.258669
$792$	1.09659e11	0.00990333
$793$	−5.93028e12	−0.532532
$794$	−9.07610e12	−0.810414
$795$	−1.03938e13	−0.922834
$796$	−1.33769e13	−1.18099
$797$	1.35922e13	1.19324	0.596620	−	0.802524i	$-0.296510\pi$
$797$	1.35922e13	1.19324	0.596620	+	0.802524i	$0.296510\pi$
$798$	1.80358e12	0.157443
$799$	0	0
$800$	−9.88643e11	−0.0853364
$801$	3.86612e12	0.331840
$802$	7.52182e12	0.642005
$803$	7.89964e11	0.0670483
$804$	−1.37863e13	−1.16358
$805$	−5.61459e12	−0.471234
$806$	2.67126e12	0.222950
$807$	1.78332e12	0.148013
$808$	−8.42312e12	−0.695219
$809$	2.22215e13	1.82391	0.911957	−	0.410287i	$-0.134571\pi$
$809$	2.22215e13	1.82391	0.911957	+	0.410287i	$0.134571\pi$
$810$	4.01936e12	0.328076
$811$	8.95583e12	0.726962	0.363481	−	0.931602i	$-0.381588\pi$
$811$	8.95583e12	0.726962	0.363481	+	0.931602i	$0.381588\pi$
$812$	6.98596e12	0.563928
$813$	2.74843e12	0.220637
$814$	2.37975e10	0.00189986
$815$	2.38330e13	1.89221
$816$	0	0
$817$	−5.83928e12	−0.458522
$818$	−6.08731e11	−0.0475374
$819$	9.74958e11	0.0757196
$820$	1.36690e13	1.05578
$821$	2.26555e13	1.74032	0.870160	−	0.492768i	$-0.164015\pi$
$821$	2.26555e13	1.74032	0.870160	+	0.492768i	$0.164015\pi$
$822$	3.37977e12	0.258205
$823$	8.51338e12	0.646849	0.323424	−	0.946254i	$-0.395166\pi$
$823$	8.51338e12	0.646849	0.323424	+	0.946254i	$0.395166\pi$
$824$	1.16313e13	0.878934
$825$	4.67178e10	0.00351107
$826$	−7.15933e12	−0.535134
$827$	6.30754e12	0.468905	0.234453	−	0.972128i	$-0.424670\pi$
$827$	6.30754e12	0.468905	0.234453	+	0.972128i	$0.424670\pi$
$828$	1.33021e12	0.0983519
$829$	−1.64758e13	−1.21158	−0.605790	−	0.795625i	$-0.707143\pi$
$829$	−1.64758e13	−1.21158	−0.605790	+	0.795625i	$0.707143\pi$
$830$	8.07382e12	0.590511
$831$	−2.48380e12	−0.180681
$832$	2.38501e11	0.0172558
$833$	0	0
$834$	7.89654e12	0.565184
$835$	1.51671e13	1.07972
$836$	−2.32863e11	−0.0164882
$837$	−2.25347e13	−1.58704
$838$	2.65063e12	0.185674
$839$	−7.27086e12	−0.506591	−0.253295	−	0.967389i	$-0.581514\pi$
$839$	−7.27086e12	−0.506591	−0.253295	+	0.967389i	$0.581514\pi$
$840$	9.73380e12	0.674568
$841$	−5.58224e12	−0.384793
$842$	5.58961e12	0.383245
$843$	−6.78633e12	−0.462819
$844$	−1.50046e13	−1.01785
$845$	−1.37398e13	−0.927100
$846$	3.07458e12	0.206357
$847$	1.36148e13	0.908945
$848$	6.35181e12	0.421809
$849$	4.70049e12	0.310497
$850$	0	0
$851$	6.54466e11	0.0427764
$852$	−9.76039e11	−0.0634584
$853$	−2.51770e13	−1.62830	−0.814148	−	0.580658i	$-0.802796\pi$
$853$	−2.51770e13	−1.62830	−0.814148	+	0.580658i	$0.802796\pi$
$854$	−1.04535e13	−0.672511
$855$	1.77549e12	0.113624
$856$	4.04151e12	0.257283
$857$	−1.61645e13	−1.02364	−0.511821	−	0.859092i	$-0.671029\pi$
$857$	−1.61645e13	−1.02364	−0.511821	+	0.859092i	$0.671029\pi$
$858$	−1.00397e11	−0.00632455
$859$	−6.12904e12	−0.384081	−0.192041	−	0.981387i	$-0.561511\pi$
$859$	−6.12904e12	−0.384081	−0.192041	+	0.981387i	$0.561511\pi$
$860$	−1.39003e13	−0.866527
$861$	−1.63352e13	−1.01300
$862$	−6.38795e12	−0.394075
$863$	−2.11554e13	−1.29829	−0.649147	−	0.760663i	$-0.724874\pi$
$863$	−2.11554e13	−1.29829	−0.649147	+	0.760663i	$0.724874\pi$
$864$	−1.79232e13	−1.09422
$865$	−1.14420e12	−0.0694910
$866$	−4.98402e12	−0.301127
$867$	0	0
$868$	−1.76257e13	−1.05392
$869$	4.45093e11	0.0264766
$870$	5.48504e12	0.324596
$871$	−9.58490e12	−0.564294
$872$	−5.95571e9	−0.000348826 0
$873$	−5.44629e12	−0.317349
$874$	1.71084e12	0.0991766
$875$	1.50615e13	0.868624
$876$	−1.66129e13	−0.953187
$877$	6.02432e12	0.343882	0.171941	−	0.985107i	$-0.444996\pi$
$877$	6.02432e12	0.343882	0.171941	+	0.985107i	$0.444996\pi$
$878$	1.45426e12	0.0825878
$879$	3.49568e12	0.197507
$880$	−3.66678e11	−0.0206116
$881$	−1.40880e13	−0.787877	−0.393939	−	0.919137i	$-0.628888\pi$
$881$	−1.40880e13	−0.787877	−0.393939	+	0.919137i	$0.628888\pi$
$882$	−3.51980e11	−0.0195844
$883$	−2.17863e13	−1.20604	−0.603019	−	0.797727i	$-0.706036\pi$
$883$	−2.17863e13	−1.20604	−0.603019	+	0.797727i	$0.706036\pi$
$884$	0	0
$885$	2.10413e13	1.15299
$886$	−5.55430e12	−0.302815
$887$	−2.02400e13	−1.09788	−0.548939	−	0.835862i	$-0.684968\pi$
$887$	−2.02400e13	−1.09788	−0.548939	+	0.835862i	$0.684968\pi$
$888$	−1.13462e12	−0.0612341
$889$	8.00187e12	0.429669
$890$	1.18367e13	0.632379
$891$	6.20166e11	0.0329654
$892$	−1.19198e13	−0.630417
$893$	−1.48021e13	−0.778917
$894$	5.58027e12	0.292170
$895$	−8.33630e12	−0.434280
$896$	−1.73435e13	−0.898980
$897$	−2.76107e12	−0.142401
$898$	−1.64939e13	−0.846410
$899$	−2.25177e13	−1.14975
$900$	3.29082e11	0.0167191
$901$	0	0
$902$	−5.63433e11	−0.0283409
$903$	1.66116e13	0.831412
$904$	4.68356e12	0.233248
$905$	−1.41805e13	−0.702704
$906$	4.58362e11	0.0226012
$907$	−5.58311e12	−0.273932	−0.136966	−	0.990576i	$-0.543735\pi$
$907$	−5.58311e12	−0.273932	−0.136966	+	0.990576i	$0.543735\pi$
$908$	6.46220e11	0.0315496
$909$	4.37080e12	0.212336
$910$	2.98499e12	0.144297
$911$	5.00192e12	0.240605	0.120302	−	0.992737i	$-0.461614\pi$
$911$	5.00192e12	0.240605	0.120302	+	0.992737i	$0.461614\pi$
$912$	3.23935e12	0.155053
$913$	1.24575e12	0.0593350
$914$	1.62578e12	0.0770554
$915$	3.07227e13	1.44899
$916$	−1.63078e13	−0.765361
$917$	−1.15849e13	−0.541041
$918$	0	0
$919$	4.12676e13	1.90849	0.954245	−	0.299027i	$-0.0966620\pi$
$919$	4.12676e13	1.90849	0.954245	+	0.299027i	$0.0966620\pi$
$920$	9.23329e12	0.424924
$921$	−1.08963e13	−0.499011
$922$	−1.37867e13	−0.628304
$923$	−6.78591e11	−0.0307752
$924$	6.62450e11	0.0298971
$925$	1.61909e11	0.00727167
$926$	1.38431e13	0.618707
$927$	−6.03554e12	−0.268446
$928$	−1.79097e13	−0.792723
$929$	3.84635e11	0.0169425	0.00847127	−	0.999964i	$-0.497303\pi$
$929$	3.84635e11	0.0169425	0.00847127	+	0.999964i	$0.497303\pi$
$930$	−1.38388e13	−0.606633
$931$	1.69455e12	0.0739233
$932$	−3.58812e13	−1.55774
$933$	−2.24948e13	−0.971884
$934$	−4.59772e11	−0.0197689
$935$	0	0
$936$	−1.60334e12	−0.0682784
$937$	1.61950e13	0.686360	0.343180	−	0.939270i	$-0.388496\pi$
$937$	1.61950e13	0.686360	0.343180	+	0.939270i	$0.388496\pi$
$938$	−1.68955e13	−0.712623
$939$	8.89570e12	0.373409
$940$	−3.52361e13	−1.47202
$941$	4.47189e13	1.85925	0.929625	−	0.368507i	$-0.120131\pi$
$941$	4.47189e13	1.85925	0.929625	+	0.368507i	$0.120131\pi$
$942$	1.00692e13	0.416646
$943$	−1.54952e13	−0.638109
$944$	−1.28586e13	−0.527011
$945$	−2.51814e13	−1.02715
$946$	5.72968e11	0.0232606
$947$	1.54921e13	0.625945	0.312972	−	0.949762i	$-0.398675\pi$
$947$	1.54921e13	0.625945	0.312972	+	0.949762i	$0.398675\pi$
$948$	−9.36030e12	−0.376402
$949$	−1.15501e13	−0.462263
$950$	4.23248e11	0.0168593
$951$	−8.14123e11	−0.0322759
$952$	0	0
$953$	−2.48096e13	−0.974321	−0.487160	−	0.873313i	$-0.661967\pi$
$953$	−2.48096e13	−0.974321	−0.487160	+	0.873313i	$0.661967\pi$
$954$	3.01788e12	0.117960
$955$	−3.66955e13	−1.42757
$956$	3.75869e13	1.45538
$957$	8.46312e11	0.0326157
$958$	1.80755e13	0.693340
$959$	−1.55045e13	−0.591936
$960$	−1.23559e12	−0.0469519
$961$	3.03728e13	1.14876
$962$	−3.47946e11	−0.0130986
$963$	−2.09716e12	−0.0785801
$964$	−3.22308e13	−1.20205
$965$	−4.46492e13	−1.65745
$966$	−4.86701e12	−0.179831
$967$	−4.72891e13	−1.73917	−0.869585	−	0.493784i	$-0.835613\pi$
$967$	−4.72891e13	−1.73917	−0.869585	+	0.493784i	$0.835613\pi$
$968$	−2.23898e13	−0.819619
$969$	0	0
$970$	−1.66747e13	−0.604763
$971$	2.61695e13	0.944733	0.472367	−	0.881402i	$-0.343400\pi$
$971$	2.61695e13	0.944733	0.472367	+	0.881402i	$0.343400\pi$
$972$	1.07353e13	0.385757
$973$	−3.62250e13	−1.29569
$974$	−5.41194e12	−0.192681
$975$	−6.83065e11	−0.0242070
$976$	−1.87751e13	−0.662303
$977$	−6.84591e12	−0.240384	−0.120192	−	0.992751i	$-0.538351\pi$
$977$	−6.84591e12	−0.240384	−0.120192	+	0.992751i	$0.538351\pi$
$978$	2.06597e13	0.722102
$979$	1.82635e12	0.0635420
$980$	4.03386e12	0.139702
$981$	3.09044e9	0.000106539 0
$982$	4.93428e12	0.169325
$983$	7.40291e11	0.0252878	0.0126439	−	0.999920i	$-0.495975\pi$
$983$	7.40291e11	0.0252878	0.0126439	+	0.999920i	$0.495975\pi$
$984$	2.68635e13	0.913448
$985$	3.66629e12	0.124098
$986$	0	0
$987$	4.21090e13	1.41237
$988$	3.40472e12	0.113678
$989$	1.57574e13	0.523723
$990$	−1.74216e11	−0.00576409
$991$	−3.36050e13	−1.10681	−0.553404	−	0.832913i	$-0.686671\pi$
$991$	−3.36050e13	−1.10681	−0.553404	+	0.832913i	$0.686671\pi$
$992$	4.51864e13	1.48151
$993$	−4.49774e13	−1.46799
$994$	−1.19617e12	−0.0388646
$995$	4.81816e13	1.55839
$996$	−2.61980e13	−0.843532
$997$	−1.42102e12	−0.0455482	−0.0227741	−	0.999741i	$-0.507250\pi$
$997$	−1.42102e12	−0.0455482	−0.0227741	+	0.999741i	$0.507250\pi$
$998$	−5.89076e11	−0.0187968
$999$	2.93527e12	0.0932402

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.h.1.15	yes	36
17.16	even	2		289.10.a.g.1.15	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.15	✓	36	17.16	even	2
289.10.a.h.1.15	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-10.3896 q^{2} -121.426 q^{3} -404.056 q^{4} +1455.35 q^{5} +1261.57 q^{6} -5787.38 q^{7} +9517.45 q^{8} -4938.65 q^{9} +O(q^{10})\)	\(q-10.3896 q^{2} -121.426 q^{3} -404.056 q^{4} +1455.35 q^{5} +1261.57 q^{6} -5787.38 q^{7} +9517.45 q^{8} -4938.65 q^{9} -15120.5 q^{10} -2333.01 q^{11} +49063.1 q^{12} +34111.1 q^{13} +60128.5 q^{14} -176718. q^{15} +107995. q^{16} +51310.5 q^{18} -247026. q^{19} -588043. q^{20} +702741. q^{21} +24239.0 q^{22} +666606. q^{23} -1.15567e6 q^{24} +164913. q^{25} -354400. q^{26} +2.98972e6 q^{27} +2.33843e6 q^{28} +2.98746e6 q^{29} +1.83602e6 q^{30} -7.53740e6 q^{31} -5.99495e6 q^{32} +283288. q^{33} -8.42266e6 q^{35} +1.99549e6 q^{36} +981789. q^{37} +2.56650e6 q^{38} -4.14198e6 q^{39} +1.38512e7 q^{40} -2.32449e7 q^{41} -7.30119e6 q^{42} +2.36383e7 q^{43} +942666. q^{44} -7.18745e6 q^{45} -6.92576e6 q^{46} +5.99211e7 q^{47} -1.31134e7 q^{48} -6.85981e6 q^{49} -1.71337e6 q^{50} -1.37828e7 q^{52} +5.88160e7 q^{53} -3.10619e7 q^{54} -3.39534e6 q^{55} -5.50811e7 q^{56} +2.99955e7 q^{57} -3.10385e7 q^{58} -1.19067e8 q^{59} +7.14039e7 q^{60} -1.73852e8 q^{61} +7.83105e7 q^{62} +2.85819e7 q^{63} +6.99189e6 q^{64} +4.96435e7 q^{65} -2.94325e6 q^{66} -2.80991e8 q^{67} -8.09435e7 q^{69} +8.75079e7 q^{70} -1.98936e7 q^{71} -4.70033e7 q^{72} -3.38604e8 q^{73} -1.02004e7 q^{74} -2.00247e7 q^{75} +9.98126e7 q^{76} +1.35020e7 q^{77} +4.30335e7 q^{78} -1.90781e8 q^{79} +1.57170e8 q^{80} -2.65823e8 q^{81} +2.41505e8 q^{82} -5.33966e8 q^{83} -2.83947e8 q^{84} -2.45592e8 q^{86} -3.62756e8 q^{87} -2.22043e7 q^{88} -7.82829e8 q^{89} +7.46747e7 q^{90} -1.97414e8 q^{91} -2.69346e8 q^{92} +9.15239e8 q^{93} -6.22555e8 q^{94} -3.59509e8 q^{95} +7.27945e8 q^{96} +1.10279e9 q^{97} +7.12705e7 q^{98} +1.15219e7 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9} + 60000 q^{10} + 76902 q^{11} + 373248 q^{12} + 54216 q^{13} + 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} + 6439479 q^{20} - 138102 q^{21} + 267324 q^{22} + 4041462 q^{23} + 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} + 13281612 q^{27} + 18614784 q^{28} + 4005936 q^{29} + 22471686 q^{30} + 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} + 22076682 q^{37} - 27401376 q^{38} + 62736162 q^{39} - 12231630 q^{40} + 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} - 49578936 q^{44} + 129308238 q^{45} + 140524827 q^{46} - 118557912 q^{47} + 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} + 209848575 q^{54} - 365439924 q^{55} + 203095059 q^{56} - 4614108 q^{57} - 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} + 175597116 q^{61} + 720602571 q^{62} + 587415936 q^{63} + 853082511 q^{64} + 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} + 1308709542 q^{71} - 275337849 q^{72} + 494841342 q^{73} + 1545361890 q^{74} + 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} + 2270624538 q^{78} + 1980107868 q^{79} + 2897000199 q^{80} + 1598298840 q^{81} + 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} - 2705904618 q^{88} + 148394658 q^{89} + 117916215 q^{90} + 636340896 q^{91} - 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} + 4878626298 q^{95} - 8390096634 q^{96} - 891786822 q^{97} + 4285627647 q^{98} - 1476187998 q^{99}+O(q^{100}) \) 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9 + 60000 * q^10 + 76902 * q^11 + 373248 * q^12 + 54216 * q^13 + 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 + 6439479 * q^20 - 138102 * q^21 + 267324 * q^22 + 4041462 * q^23 + 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 + 13281612 * q^27 + 18614784 * q^28 + 4005936 * q^29 + 22471686 * q^30 + 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 + 22076682 * q^37 - 27401376 * q^38 + 62736162 * q^39 - 12231630 * q^40 + 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 - 49578936 * q^44 + 129308238 * q^45 + 140524827 * q^46 - 118557912 * q^47 + 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 + 209848575 * q^54 - 365439924 * q^55 + 203095059 * q^56 - 4614108 * q^57 - 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 + 175597116 * q^61 + 720602571 * q^62 + 587415936 * q^63 + 853082511 * q^64 + 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 + 1308709542 * q^71 - 275337849 * q^72 + 494841342 * q^73 + 1545361890 * q^74 + 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 + 2270624538 * q^78 + 1980107868 * q^79 + 2897000199 * q^80 + 1598298840 * q^81 + 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 - 2705904618 * q^88 + 148394658 * q^89 + 117916215 * q^90 + 636340896 * q^91 - 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 + 4878626298 * q^95 - 8390096634 * q^96 - 891786822 * q^97 + 4285627647 * q^98 - 1476187998 * q^99

Introduction

L-functions

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