LMFDB - Embedded newform 289.10.a.h.1.22

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			1.22
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)

$f(q)$	$=$	$q+10.7250 q^{2} +53.3726 q^{3} -396.975 q^{4} -85.7107 q^{5} +572.419 q^{6} +4510.26 q^{7} -9748.72 q^{8} -16834.4 q^{9} +O(q^{10})$	\(q+10.7250 q^{2} +53.3726 q^{3} -396.975 q^{4} -85.7107 q^{5} +572.419 q^{6} +4510.26 q^{7} -9748.72 q^{8} -16834.4 q^{9} -919.244 q^{10} -31525.7 q^{11} -21187.6 q^{12} -6484.90 q^{13} +48372.4 q^{14} -4574.61 q^{15} +98696.8 q^{16} -180548. q^{18} +508379. q^{19} +34025.1 q^{20} +240725. q^{21} -338112. q^{22} -1.78877e6 q^{23} -520315. q^{24} -1.94578e6 q^{25} -69550.3 q^{26} -1.94903e6 q^{27} -1.79046e6 q^{28} -1.55740e6 q^{29} -49062.5 q^{30} +2.05480e6 q^{31} +6.04986e6 q^{32} -1.68261e6 q^{33} -386578. q^{35} +6.68283e6 q^{36} -7.61805e6 q^{37} +5.45235e6 q^{38} -346116. q^{39} +835570. q^{40} +5.31174e6 q^{41} +2.58176e6 q^{42} +2.91537e7 q^{43} +1.25149e7 q^{44} +1.44289e6 q^{45} -1.91844e7 q^{46} +1.71037e7 q^{47} +5.26771e6 q^{48} -2.00111e7 q^{49} -2.08684e7 q^{50} +2.57435e6 q^{52} -4.87721e7 q^{53} -2.09032e7 q^{54} +2.70209e6 q^{55} -4.39693e7 q^{56} +2.71336e7 q^{57} -1.67030e7 q^{58} -1.48825e7 q^{59} +1.81601e6 q^{60} +1.92173e8 q^{61} +2.20376e7 q^{62} -7.59274e7 q^{63} +1.43517e7 q^{64} +555826. q^{65} -1.80459e7 q^{66} +3.41459e7 q^{67} -9.54712e7 q^{69} -4.14603e6 q^{70} -1.63417e8 q^{71} +1.64113e8 q^{72} +8.46020e7 q^{73} -8.17032e7 q^{74} -1.03851e8 q^{75} -2.01814e8 q^{76} -1.42189e8 q^{77} -3.71208e6 q^{78} -3.66702e8 q^{79} -8.45938e6 q^{80} +2.27326e8 q^{81} +5.69682e7 q^{82} +5.02953e8 q^{83} -9.55618e7 q^{84} +3.12672e8 q^{86} -8.31223e7 q^{87} +3.07335e8 q^{88} +8.00609e7 q^{89} +1.54749e7 q^{90} -2.92486e7 q^{91} +7.10096e8 q^{92} +1.09670e8 q^{93} +1.83437e8 q^{94} -4.35736e7 q^{95} +3.22897e8 q^{96} +1.90554e8 q^{97} -2.14618e8 q^{98} +5.30715e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	10.7250	0.473980	0.236990	−	0.971512i	$-0.423839\pi$
$2$	10.7250	0.473980	0.236990	+	0.971512i	$0.423839\pi$
$3$	53.3726	0.380428	0.190214	−	0.981743i	$-0.439082\pi$
$3$	53.3726	0.380428	0.190214	+	0.981743i	$0.439082\pi$
$4$	−396.975	−0.775343
$5$	−85.7107	−0.0613296	−0.0306648	−	0.999530i	$-0.509762\pi$
$5$	−85.7107	−0.0613296	−0.0306648	+	0.999530i	$0.509762\pi$
$6$	572.419	0.180316
$7$	4510.26	0.710004	0.355002	−	0.934866i	$-0.384480\pi$
$7$	4510.26	0.710004	0.355002	+	0.934866i	$0.384480\pi$
$8$	−9748.72	−0.841478
$9$	−16834.4	−0.855274
$10$	−919.244	−0.0290690
$11$	−31525.7	−0.649229	−0.324614	−	0.945846i	$-0.605234\pi$
$11$	−31525.7	−0.649229	−0.324614	+	0.945846i	$0.605234\pi$
$12$	−21187.6	−0.294962
$13$	−6484.90	−0.0629736	−0.0314868	−	0.999504i	$-0.510024\pi$
$13$	−6484.90	−0.0629736	−0.0314868	+	0.999504i	$0.510024\pi$
$14$	48372.4	0.336528
$15$	−4574.61	−0.0233315
$16$	98696.8	0.376499
$17$	0	0
$17$	0	0
$18$	−180548.	−0.405383
$19$	508379.	0.894946	0.447473	−	0.894297i	$-0.352324\pi$
$19$	508379.	0.894946	0.447473	+	0.894297i	$0.352324\pi$
$20$	34025.1	0.0475515
$21$	240725.	0.270106
$22$	−338112.	−0.307722
$23$	−1.78877e6	−1.33284	−0.666420	−	0.745576i	$-0.732174\pi$
$23$	−1.78877e6	−1.33284	−0.666420	+	0.745576i	$0.732174\pi$
$24$	−520315.	−0.320122
$25$	−1.94578e6	−0.996239
$26$	−69550.3	−0.0298483
$27$	−1.94903e6	−0.705799
$28$	−1.79046e6	−0.550496
$29$	−1.55740e6	−0.408891	−0.204446	−	0.978878i	$-0.565539\pi$
$29$	−1.55740e6	−0.408891	−0.204446	+	0.978878i	$0.565539\pi$
$30$	−49062.5	−0.0110587
$31$	2.05480e6	0.399615	0.199807	−	0.979835i	$-0.435968\pi$
$31$	2.05480e6	0.399615	0.199807	+	0.979835i	$0.435968\pi$
$32$	6.04986e6	1.01993
$33$	−1.68261e6	−0.246985
$34$	0	0
$35$	−386578.	−0.0435443
$36$	6.68283e6	0.663130
$37$	−7.61805e6	−0.668245	−0.334123	−	0.942530i	$-0.608440\pi$
$37$	−7.61805e6	−0.668245	−0.334123	+	0.942530i	$0.608440\pi$
$38$	5.45235e6	0.424187
$39$	−346116.	−0.0239569
$40$	835570.	0.0516075
$41$	5.31174e6	0.293569	0.146784	−	0.989169i	$-0.453108\pi$
$41$	5.31174e6	0.293569	0.146784	+	0.989169i	$0.453108\pi$
$42$	2.58176e6	0.128025
$43$	2.91537e7	1.30042	0.650212	−	0.759753i	$-0.274680\pi$
$43$	2.91537e7	1.30042	0.650212	+	0.759753i	$0.274680\pi$
$44$	1.25149e7	0.503375
$45$	1.44289e6	0.0524536
$46$	−1.91844e7	−0.631740
$47$	1.71037e7	0.511271	0.255635	−	0.966773i	$-0.417715\pi$
$47$	1.71037e7	0.511271	0.255635	+	0.966773i	$0.417715\pi$
$48$	5.26771e6	0.143231
$49$	−2.00111e7	−0.495895
$50$	−2.08684e7	−0.472198
$51$	0	0
$52$	2.57435e6	0.0488261
$53$	−4.87721e7	−0.849043	−0.424522	−	0.905418i	$-0.639558\pi$
$53$	−4.87721e7	−0.849043	−0.424522	+	0.905418i	$0.639558\pi$
$54$	−2.09032e7	−0.334535
$55$	2.70209e6	0.0398169
$56$	−4.39693e7	−0.597452
$57$	2.71336e7	0.340463
$58$	−1.67030e7	−0.193806
$59$	−1.48825e7	−0.159898	−0.0799488	−	0.996799i	$-0.525476\pi$
$59$	−1.48825e7	−0.159898	−0.0799488	+	0.996799i	$0.525476\pi$
$60$	1.81601e6	0.0180899
$61$	1.92173e8	1.77708	0.888541	−	0.458797i	$-0.151719\pi$
$61$	1.92173e8	1.77708	0.888541	+	0.458797i	$0.151719\pi$
$62$	2.20376e7	0.189410
$63$	−7.59274e7	−0.607248
$64$	1.43517e7	0.106929
$65$	555826.	0.00386215
$66$	−1.80459e7	−0.117066
$67$	3.41459e7	0.207015	0.103508	−	0.994629i	$-0.466993\pi$
$67$	3.41459e7	0.207015	0.103508	+	0.994629i	$0.466993\pi$
$68$	0	0
$69$	−9.54712e7	−0.507051
$70$	−4.14603e6	−0.0206391
$71$	−1.63417e8	−0.763196	−0.381598	−	0.924328i	$-0.624626\pi$
$71$	−1.63417e8	−0.763196	−0.381598	+	0.924328i	$0.624626\pi$
$72$	1.64113e8	0.719694
$73$	8.46020e7	0.348681	0.174340	−	0.984685i	$-0.444221\pi$
$73$	8.46020e7	0.348681	0.174340	+	0.984685i	$0.444221\pi$
$74$	−8.17032e7	−0.316735
$75$	−1.03851e8	−0.378998
$76$	−2.01814e8	−0.693890
$77$	−1.42189e8	−0.460955
$78$	−3.71208e6	−0.0113551
$79$	−3.66702e8	−1.05923	−0.529617	−	0.848237i	$-0.677664\pi$
$79$	−3.66702e8	−1.05923	−0.529617	+	0.848237i	$0.677664\pi$
$80$	−8.45938e6	−0.0230905
$81$	2.27326e8	0.586768
$82$	5.69682e7	0.139146
$83$	5.02953e8	1.16326	0.581629	−	0.813454i	$-0.302415\pi$
$83$	5.02953e8	1.16326	0.581629	+	0.813454i	$0.302415\pi$
$84$	−9.55618e7	−0.209424
$85$	0	0
$86$	3.12672e8	0.616375
$87$	−8.31223e7	−0.155554
$88$	3.07335e8	0.546311
$89$	8.00609e7	0.135259	0.0676293	−	0.997711i	$-0.478456\pi$
$89$	8.00609e7	0.135259	0.0676293	+	0.997711i	$0.478456\pi$
$90$	1.54749e7	0.0248620
$91$	−2.92486e7	−0.0447115
$92$	7.10096e8	1.03341
$93$	1.09670e8	0.152025
$94$	1.83437e8	0.242332
$95$	−4.35736e7	−0.0548867
$96$	3.22897e8	0.388011
$97$	1.90554e8	0.218547	0.109274	−	0.994012i	$-0.465148\pi$
$97$	1.90554e8	0.218547	0.109274	+	0.994012i	$0.465148\pi$
$98$	−2.14618e8	−0.235044
$99$	5.30715e8	0.555268
$100$	7.72426e8	0.772426
$101$	1.48512e9	1.42009	0.710043	−	0.704158i	$-0.248675\pi$
$101$	1.48512e9	1.42009	0.710043	+	0.704158i	$0.248675\pi$
$102$	0	0
$103$	−1.36804e9	−1.19766	−0.598829	−	0.800877i	$-0.704367\pi$
$103$	−1.36804e9	−1.19766	−0.598829	+	0.800877i	$0.704367\pi$
$104$	6.32195e7	0.0529909
$105$	−2.06327e7	−0.0165655
$106$	−5.23078e8	−0.402430
$107$	1.07471e9	0.792619	0.396309	−	0.918117i	$-0.370291\pi$
$107$	1.07471e9	0.792619	0.396309	+	0.918117i	$0.370291\pi$
$108$	7.73716e8	0.547236
$109$	1.15724e9	0.785245	0.392623	−	0.919700i	$-0.371568\pi$
$109$	1.15724e9	0.785245	0.392623	+	0.919700i	$0.371568\pi$
$110$	2.89798e7	0.0188725
$111$	−4.06595e8	−0.254220
$112$	4.45149e8	0.267315
$113$	1.48036e9	0.854109	0.427055	−	0.904226i	$-0.359551\pi$
$113$	1.48036e9	0.854109	0.427055	+	0.904226i	$0.359551\pi$
$114$	2.91006e8	0.161373
$115$	1.53316e8	0.0817426
$116$	6.18248e8	0.317031
$117$	1.09169e8	0.0538597
$118$	−1.59614e8	−0.0757883
$119$	0	0
$120$	4.45966e7	0.0196330
$121$	−1.36408e9	−0.578502
$122$	2.06104e9	0.842302
$123$	2.83502e8	0.111682
$124$	−8.15704e8	−0.309838
$125$	3.34178e8	0.122429
$126$	−8.14318e8	−0.287824
$127$	1.39247e9	0.474975	0.237487	−	0.971391i	$-0.423676\pi$
$127$	1.39247e9	0.474975	0.237487	+	0.971391i	$0.423676\pi$
$128$	−2.94361e9	−0.969249
$129$	1.55601e9	0.494718
$130$	5.96121e6	0.00183058
$131$	5.23614e9	1.55342	0.776712	−	0.629856i	$-0.216886\pi$
$131$	5.23614e9	1.55342	0.776712	+	0.629856i	$0.216886\pi$
$132$	6.67955e8	0.191498
$133$	2.29293e9	0.635415
$134$	3.66214e8	0.0981212
$135$	1.67053e8	0.0432864
$136$	0	0
$137$	−4.92226e9	−1.19377	−0.596887	−	0.802325i	$-0.703596\pi$
$137$	−4.92226e9	−1.19377	−0.596887	+	0.802325i	$0.703596\pi$
$138$	−1.02392e9	−0.240332
$139$	−2.60255e9	−0.591333	−0.295667	−	0.955291i	$-0.595542\pi$
$139$	−2.60255e9	−0.591333	−0.295667	+	0.955291i	$0.595542\pi$
$140$	1.53462e8	0.0337617
$141$	9.12872e8	0.194502
$142$	−1.75264e9	−0.361740
$143$	2.04441e8	0.0408843
$144$	−1.66150e9	−0.322009
$145$	1.33486e8	0.0250771
$146$	9.07352e8	0.165268
$147$	−1.06805e9	−0.188652
$148$	3.02418e9	0.518119
$149$	9.01492e9	1.49839	0.749193	−	0.662352i	$-0.230442\pi$
$149$	9.01492e9	1.49839	0.749193	+	0.662352i	$0.230442\pi$
$150$	−1.11380e9	−0.179637
$151$	7.98640e9	1.25013	0.625064	−	0.780573i	$-0.285073\pi$
$151$	7.98640e9	1.25013	0.625064	+	0.780573i	$0.285073\pi$
$152$	−4.95605e9	−0.753077
$153$	0	0
$154$	−1.52497e9	−0.218484
$155$	−1.76118e8	−0.0245082
$156$	1.37400e8	0.0185748
$157$	−1.80627e9	−0.237266	−0.118633	−	0.992938i	$-0.537851\pi$
$157$	−1.80627e9	−0.237266	−0.118633	+	0.992938i	$0.537851\pi$
$158$	−3.93286e9	−0.502056
$159$	−2.60309e9	−0.323000
$160$	−5.18538e8	−0.0625520
$161$	−8.06781e9	−0.946322
$162$	2.43806e9	0.278117
$163$	−6.70881e8	−0.0744392	−0.0372196	−	0.999307i	$-0.511850\pi$
$163$	−6.70881e8	−0.0744392	−0.0372196	+	0.999307i	$0.511850\pi$
$164$	−2.10863e9	−0.227616
$165$	1.44218e8	0.0151475
$166$	5.39415e9	0.551362
$167$	1.10815e10	1.10248	0.551242	−	0.834345i	$-0.314154\pi$
$167$	1.10815e10	1.10248	0.551242	+	0.834345i	$0.314154\pi$
$168$	−2.34676e9	−0.227288
$169$	−1.05624e10	−0.996034
$170$	0	0
$171$	−8.55824e9	−0.765424
$172$	−1.15733e10	−1.00827
$173$	1.48057e10	1.25667	0.628337	−	0.777941i	$-0.283736\pi$
$173$	1.48057e10	1.25667	0.628337	+	0.777941i	$0.283736\pi$
$174$	−8.91483e8	−0.0737295
$175$	−8.77597e9	−0.707333
$176$	−3.11149e9	−0.244434
$177$	−7.94318e8	−0.0608296
$178$	8.58649e8	0.0641100
$179$	1.92425e10	1.40095	0.700476	−	0.713676i	$-0.252971\pi$
$179$	1.92425e10	1.40095	0.700476	+	0.713676i	$0.252971\pi$
$180$	−5.72790e8	−0.0406695
$181$	2.28736e10	1.58410	0.792048	−	0.610459i	$-0.209015\pi$
$181$	2.28736e10	1.58410	0.792048	+	0.610459i	$0.209015\pi$
$182$	−3.13690e8	−0.0211924
$183$	1.02568e10	0.676053
$184$	1.74382e10	1.12156
$185$	6.52949e8	0.0409832
$186$	1.17621e9	0.0720568
$187$	0	0
$188$	−6.78977e9	−0.396410
$189$	−8.79063e9	−0.501120
$190$	−4.67325e8	−0.0260152
$191$	1.88324e10	1.02390	0.511948	−	0.859017i	$-0.328924\pi$
$191$	1.88324e10	1.02390	0.511948	+	0.859017i	$0.328924\pi$
$192$	7.65989e8	0.0406787
$193$	−2.59035e10	−1.34385	−0.671924	−	0.740620i	$-0.734532\pi$
$193$	−2.59035e10	−1.34385	−0.671924	+	0.740620i	$0.734532\pi$
$194$	2.04368e9	0.103587
$195$	2.96659e7	0.00146927
$196$	7.94393e9	0.384488
$197$	1.18331e10	0.559757	0.279879	−	0.960035i	$-0.409706\pi$
$197$	1.18331e10	0.559757	0.279879	+	0.960035i	$0.409706\pi$
$198$	5.69189e9	0.263186
$199$	3.42416e10	1.54780	0.773901	−	0.633307i	$-0.218303\pi$
$199$	3.42416e10	1.54780	0.773901	+	0.633307i	$0.218303\pi$
$200$	1.89688e10	0.838313
$201$	1.82246e9	0.0787545
$202$	1.59278e10	0.673093
$203$	−7.02426e9	−0.290314
$204$	0	0
$205$	−4.55273e8	−0.0180045
$206$	−1.46722e10	−0.567666
$207$	3.01127e10	1.13994
$208$	−6.40039e8	−0.0237095
$209$	−1.60270e10	−0.581025
$210$	−2.21285e8	−0.00785171
$211$	−1.80185e10	−0.625819	−0.312910	−	0.949783i	$-0.601304\pi$
$211$	−1.80185e10	−0.625819	−0.312910	+	0.949783i	$0.601304\pi$
$212$	1.93613e10	0.658299
$213$	−8.72202e9	−0.290341
$214$	1.15262e10	0.375686
$215$	−2.49878e9	−0.0797545
$216$	1.90005e10	0.593914
$217$	9.26768e9	0.283728
$218$	1.24114e10	0.372191
$219$	4.51543e9	0.132648
$220$	−1.07266e9	−0.0308718
$221$	0	0
$222$	−4.36072e9	−0.120495
$223$	−6.99529e10	−1.89424	−0.947118	−	0.320886i	$-0.896019\pi$
$223$	−6.99529e10	−1.89424	−0.947118	+	0.320886i	$0.896019\pi$
$224$	2.72865e10	0.724155
$225$	3.27559e10	0.852057
$226$	1.58768e10	0.404831
$227$	−7.03288e10	−1.75799	−0.878996	−	0.476830i	$-0.841786\pi$
$227$	−7.03288e10	−1.75799	−0.878996	+	0.476830i	$0.841786\pi$
$228$	−1.07714e10	−0.263975
$229$	−5.34700e9	−0.128485	−0.0642423	−	0.997934i	$-0.520463\pi$
$229$	−5.34700e9	−0.128485	−0.0642423	+	0.997934i	$0.520463\pi$
$230$	1.64431e9	0.0387444
$231$	−7.58901e9	−0.175360
$232$	1.51826e10	0.344073
$233$	6.84853e10	1.52228	0.761142	−	0.648585i	$-0.224639\pi$
$233$	6.84853e10	1.52228	0.761142	+	0.648585i	$0.224639\pi$
$234$	1.17083e9	0.0255284
$235$	−1.46597e9	−0.0313560
$236$	5.90799e9	0.123975
$237$	−1.95719e10	−0.402963
$238$	0	0
$239$	−2.52056e9	−0.0499696	−0.0249848	−	0.999688i	$-0.507954\pi$
$239$	−2.52056e9	−0.0499696	−0.0249848	+	0.999688i	$0.507954\pi$
$240$	−4.51499e8	−0.00878429
$241$	9.69476e10	1.85123	0.925615	−	0.378468i	$-0.123549\pi$
$241$	9.69476e10	1.85123	0.925615	+	0.378468i	$0.123549\pi$
$242$	−1.46297e10	−0.274199
$243$	5.04957e10	0.929022
$244$	−7.62879e10	−1.37785
$245$	1.71517e9	0.0304130
$246$	3.04054e9	0.0529350
$247$	−3.29679e9	−0.0563580
$248$	−2.00316e10	−0.336267
$249$	2.68439e10	0.442537
$250$	3.58404e9	0.0580287
$251$	1.22305e11	1.94496	0.972481	−	0.232984i	$-0.0748489\pi$
$251$	1.22305e11	1.94496	0.972481	+	0.232984i	$0.0748489\pi$
$252$	3.01413e10	0.470825
$253$	5.63921e10	0.865318
$254$	1.49342e10	0.225129
$255$	0	0
$256$	−3.89181e10	−0.566334
$257$	−7.99606e10	−1.14334	−0.571672	−	0.820482i	$-0.693705\pi$
$257$	−7.99606e10	−1.14334	−0.571672	+	0.820482i	$0.693705\pi$
$258$	1.66881e10	0.234487
$259$	−3.43594e10	−0.474457
$260$	−2.20649e8	−0.00299449
$261$	2.62178e10	0.349714
$262$	5.61573e10	0.736293
$263$	−3.97042e10	−0.511723	−0.255862	−	0.966713i	$-0.582359\pi$
$263$	−3.97042e10	−0.511723	−0.255862	+	0.966713i	$0.582359\pi$
$264$	1.64033e10	0.207832
$265$	4.18029e9	0.0520715
$266$	2.45915e10	0.301174
$267$	4.27306e9	0.0514563
$268$	−1.35551e10	−0.160508
$269$	1.12054e11	1.30479	0.652395	−	0.757879i	$-0.273765\pi$
$269$	1.12054e11	1.30479	0.652395	+	0.757879i	$0.273765\pi$
$270$	1.79163e9	0.0205169
$271$	8.52215e9	0.0959815	0.0479907	−	0.998848i	$-0.484718\pi$
$271$	8.52215e9	0.0959815	0.0479907	+	0.998848i	$0.484718\pi$
$272$	0	0
$273$	−1.56108e9	−0.0170095
$274$	−5.27911e10	−0.565826
$275$	6.13420e10	0.646787
$276$	3.78997e10	0.393138
$277$	−1.24828e11	−1.27395	−0.636977	−	0.770883i	$-0.719815\pi$
$277$	−1.24828e11	−1.27395	−0.636977	+	0.770883i	$0.719815\pi$
$278$	−2.79122e10	−0.280280
$279$	−3.45912e10	−0.341780
$280$	3.76864e9	0.0366415
$281$	3.96570e10	0.379438	0.189719	−	0.981838i	$-0.439242\pi$
$281$	3.96570e10	0.379438	0.189719	+	0.981838i	$0.439242\pi$
$282$	9.79051e9	0.0921901
$283$	7.61061e10	0.705311	0.352655	−	0.935753i	$-0.385279\pi$
$283$	7.61061e10	0.705311	0.352655	+	0.935753i	$0.385279\pi$
$284$	6.48727e10	0.591738
$285$	−2.32564e9	−0.0208805
$286$	2.19262e9	0.0193783
$287$	2.39574e10	0.208435
$288$	−1.01846e11	−0.872320
$289$	0	0
$290$	1.43163e9	0.0118861
$291$	1.01704e10	0.0831416
$292$	−3.35849e10	−0.270347
$293$	7.22311e10	0.572558	0.286279	−	0.958146i	$-0.407582\pi$
$293$	7.22311e10	0.572558	0.286279	+	0.958146i	$0.407582\pi$
$294$	−1.14548e10	−0.0894176
$295$	1.27559e9	0.00980646
$296$	7.42662e10	0.562314
$297$	6.14445e10	0.458225
$298$	9.66846e10	0.710206
$299$	1.16000e10	0.0839338
$300$	4.12264e10	0.293853
$301$	1.31491e11	0.923306
$302$	8.56538e10	0.592537
$303$	7.92647e10	0.540241
$304$	5.01754e10	0.336946
$305$	−1.64713e10	−0.108988
$306$	0	0
$307$	−2.11970e11	−1.36192	−0.680962	−	0.732319i	$-0.738438\pi$
$307$	−2.11970e11	−1.36192	−0.680962	+	0.732319i	$0.738438\pi$
$308$	5.64456e10	0.357398
$309$	−7.30161e10	−0.455623
$310$	−1.88886e9	−0.0116164
$311$	−2.52341e10	−0.152956	−0.0764778	−	0.997071i	$-0.524367\pi$
$311$	−2.52341e10	−0.152956	−0.0764778	+	0.997071i	$0.524367\pi$
$312$	3.37419e9	0.0201592
$313$	−1.99311e11	−1.17377	−0.586885	−	0.809671i	$-0.699646\pi$
$313$	−1.99311e11	−1.17377	−0.586885	+	0.809671i	$0.699646\pi$
$314$	−1.93722e10	−0.112459
$315$	6.50779e9	0.0372423
$316$	1.45572e11	0.821269
$317$	−2.14588e11	−1.19355	−0.596774	−	0.802410i	$-0.703551\pi$
$317$	−2.14588e11	−1.19355	−0.596774	+	0.802410i	$0.703551\pi$
$318$	−2.79181e10	−0.153096
$319$	4.90980e10	0.265464
$320$	−1.23010e9	−0.00655789
$321$	5.73601e10	0.301535
$322$	−8.65268e10	−0.448538
$323$	0	0
$324$	−9.02428e10	−0.454946
$325$	1.26182e10	0.0627367
$326$	−7.19517e9	−0.0352827
$327$	6.17651e10	0.298730
$328$	−5.17827e10	−0.247031
$329$	7.71424e10	0.363004
$330$	1.54673e9	0.00717962
$331$	−2.28406e11	−1.04588	−0.522940	−	0.852370i	$-0.675165\pi$
$331$	−2.28406e11	−1.04588	−0.522940	+	0.852370i	$0.675165\pi$
$332$	−1.99660e11	−0.901924
$333$	1.28245e11	0.571533
$334$	1.18848e11	0.522556
$335$	−2.92667e9	−0.0126962
$336$	2.37588e10	0.101694
$337$	−3.98649e10	−0.168367	−0.0841834	−	0.996450i	$-0.526828\pi$
$337$	−3.98649e10	−0.168367	−0.0841834	+	0.996450i	$0.526828\pi$
$338$	−1.13282e11	−0.472101
$339$	7.90105e10	0.324927
$340$	0	0
$341$	−6.47789e10	−0.259441
$342$	−9.17868e10	−0.362796
$343$	−2.72261e11	−1.06209
$344$	−2.84211e11	−1.09428
$345$	8.18290e9	0.0310972
$346$	1.58791e11	0.595639
$347$	2.09902e11	0.777202	0.388601	−	0.921406i	$-0.372959\pi$
$347$	2.09902e11	0.777202	0.388601	+	0.921406i	$0.372959\pi$
$348$	3.29975e10	0.120608
$349$	−1.18382e11	−0.427143	−0.213571	−	0.976927i	$-0.568510\pi$
$349$	−1.18382e11	−0.427143	−0.213571	+	0.976927i	$0.568510\pi$
$350$	−9.41219e10	−0.335262
$351$	1.26393e10	0.0444467
$352$	−1.90726e11	−0.662168
$353$	1.27894e11	0.438395	0.219197	−	0.975681i	$-0.429656\pi$
$353$	1.27894e11	0.438395	0.219197	+	0.975681i	$0.429656\pi$
$354$	−8.51903e9	−0.0288320
$355$	1.40066e10	0.0468065
$356$	−3.17822e10	−0.104872
$357$	0	0
$358$	2.06375e11	0.664024
$359$	3.73004e11	1.18519	0.592596	−	0.805500i	$-0.298103\pi$
$359$	3.73004e11	1.18519	0.592596	+	0.805500i	$0.298103\pi$
$360$	−1.40663e10	−0.0441386
$361$	−6.42380e10	−0.199072
$362$	2.45319e11	0.750830
$363$	−7.28044e10	−0.220079
$364$	1.16110e10	0.0346667
$365$	−7.25130e9	−0.0213844
$366$	1.10003e11	0.320436
$367$	−1.77243e11	−0.510003	−0.255002	−	0.966941i	$-0.582076\pi$
$367$	−1.77243e11	−0.510003	−0.255002	+	0.966941i	$0.582076\pi$
$368$	−1.76546e11	−0.501813
$369$	−8.94198e10	−0.251082
$370$	7.00284e9	0.0194253
$371$	−2.19975e11	−0.602824
$372$	−4.35363e10	−0.117871
$373$	3.59334e11	0.961189	0.480595	−	0.876943i	$-0.340421\pi$
$373$	3.59334e11	0.961189	0.480595	+	0.876943i	$0.340421\pi$
$374$	0	0
$375$	1.78360e10	0.0465753
$376$	−1.66740e11	−0.430223
$377$	1.00996e10	0.0257494
$378$	−9.42791e10	−0.237521
$379$	3.22981e11	0.804081	0.402041	−	0.915622i	$-0.368301\pi$
$379$	3.22981e11	0.804081	0.402041	+	0.915622i	$0.368301\pi$
$380$	1.72976e10	0.0425560
$381$	7.43200e10	0.180694
$382$	2.01977e11	0.485306
$383$	−1.00894e11	−0.239591	−0.119796	−	0.992799i	$-0.538224\pi$
$383$	−1.00894e11	−0.239591	−0.119796	+	0.992799i	$0.538224\pi$
$384$	−1.57108e11	−0.368730
$385$	1.21871e10	0.0282702
$386$	−2.77814e11	−0.636958
$387$	−4.90783e11	−1.11222
$388$	−7.56453e10	−0.169449
$389$	1.56379e11	0.346263	0.173131	−	0.984899i	$-0.444611\pi$
$389$	1.56379e11	0.346263	0.173131	+	0.984899i	$0.444611\pi$
$390$	3.18165e8	0.000696405 0
$391$	0	0
$392$	1.95083e11	0.417284
$393$	2.79466e11	0.590967
$394$	1.26909e11	0.265314
$395$	3.14303e10	0.0649624
$396$	−2.10681e11	−0.430523
$397$	7.86417e11	1.58890	0.794448	−	0.607332i	$-0.207760\pi$
$397$	7.86417e11	1.58890	0.794448	+	0.607332i	$0.207760\pi$
$398$	3.67240e11	0.733628
$399$	1.22379e11	0.241730
$400$	−1.92042e11	−0.375082
$401$	1.63679e11	0.316114	0.158057	−	0.987430i	$-0.449477\pi$
$401$	1.63679e11	0.316114	0.158057	+	0.987430i	$0.449477\pi$
$402$	1.95458e10	0.0373281
$403$	−1.33252e10	−0.0251652
$404$	−5.89555e11	−1.10105
$405$	−1.94843e10	−0.0359863
$406$	−7.53349e10	−0.137603
$407$	2.40164e11	0.433844
$408$	0	0
$409$	5.24910e11	0.927534	0.463767	−	0.885957i	$-0.346497\pi$
$409$	5.24910e11	0.927534	0.463767	+	0.885957i	$0.346497\pi$
$410$	−4.88279e9	−0.00853376
$411$	−2.62714e11	−0.454146
$412$	5.43080e11	0.928595
$413$	−6.71240e10	−0.113528
$414$	3.22958e11	0.540311
$415$	−4.31085e10	−0.0713422
$416$	−3.92328e10	−0.0642287
$417$	−1.38905e11	−0.224960
$418$	−1.71889e11	−0.275394
$419$	−4.60592e11	−0.730052	−0.365026	−	0.930997i	$-0.618940\pi$
$419$	−4.60592e11	−0.730052	−0.365026	+	0.930997i	$0.618940\pi$
$420$	8.19067e9	0.0128439
$421$	−1.28301e12	−1.99050	−0.995249	−	0.0973671i	$-0.968958\pi$
$421$	−1.28301e12	−1.99050	−0.995249	+	0.0973671i	$0.968958\pi$
$422$	−1.93248e11	−0.296626
$423$	−2.87931e11	−0.437277
$424$	4.75465e11	0.714451
$425$	0	0
$426$	−9.35433e10	−0.137616
$427$	8.66750e11	1.26174
$428$	−4.26633e11	−0.614551
$429$	1.09116e10	0.0155535
$430$	−2.67993e10	−0.0378021
$431$	−6.90653e11	−0.964079	−0.482039	−	0.876150i	$-0.660104\pi$
$431$	−6.90653e11	−0.964079	−0.482039	+	0.876150i	$0.660104\pi$
$432$	−1.92363e11	−0.265732
$433$	4.81087e11	0.657701	0.328850	−	0.944382i	$-0.393339\pi$
$433$	4.81087e11	0.657701	0.328850	+	0.944382i	$0.393339\pi$
$434$	9.93954e10	0.134482
$435$	7.12447e9	0.00954006
$436$	−4.59397e11	−0.608834
$437$	−9.09372e11	−1.19282
$438$	4.84278e10	0.0628726
$439$	−9.71396e11	−1.24826	−0.624131	−	0.781320i	$-0.714547\pi$
$439$	−9.71396e11	−1.24826	−0.624131	+	0.781320i	$0.714547\pi$
$440$	−2.63419e10	−0.0335051
$441$	3.36875e11	0.424126
$442$	0	0
$443$	1.18504e12	1.46189	0.730946	−	0.682435i	$-0.239079\pi$
$443$	1.18504e12	1.46189	0.730946	+	0.682435i	$0.239079\pi$
$444$	1.61408e11	0.197107
$445$	−6.86208e9	−0.00829536
$446$	−7.50242e11	−0.897831
$447$	4.81150e11	0.570029
$448$	6.47300e10	0.0759198
$449$	−1.07515e12	−1.24842	−0.624208	−	0.781258i	$-0.714578\pi$
$449$	−1.07515e12	−1.24842	−0.624208	+	0.781258i	$0.714578\pi$
$450$	3.51306e11	0.403858
$451$	−1.67456e11	−0.190593
$452$	−5.87665e11	−0.662227
$453$	4.26255e11	0.475585
$454$	−7.54273e11	−0.833253
$455$	2.50692e9	0.00274214
$456$	−2.64517e11	−0.286492
$457$	−1.74356e12	−1.86988	−0.934941	−	0.354803i	$-0.884548\pi$
$457$	−1.74356e12	−1.86988	−0.934941	+	0.354803i	$0.884548\pi$
$458$	−5.73464e10	−0.0608992
$459$	0	0
$460$	−6.08629e10	−0.0633785
$461$	5.00512e11	0.516131	0.258066	−	0.966127i	$-0.416915\pi$
$461$	5.00512e11	0.516131	0.258066	+	0.966127i	$0.416915\pi$
$462$	−8.13918e10	−0.0831174
$463$	2.96663e11	0.300019	0.150009	−	0.988685i	$-0.452070\pi$
$463$	2.96663e11	0.300019	0.150009	+	0.988685i	$0.452070\pi$
$464$	−1.53710e11	−0.153947
$465$	−9.39990e9	−0.00932362
$466$	7.34502e11	0.721533
$467$	−1.49213e12	−1.45171	−0.725854	−	0.687848i	$-0.758555\pi$
$467$	−1.49213e12	−1.45171	−0.725854	+	0.687848i	$0.758555\pi$
$468$	−4.33375e10	−0.0417597
$469$	1.54007e11	0.146982
$470$	−1.57225e10	−0.0148621
$471$	−9.64055e10	−0.0902626
$472$	1.45085e11	0.134550
$473$	−9.19089e11	−0.844272
$474$	−2.09907e11	−0.190996
$475$	−9.89194e11	−0.891580
$476$	0	0
$477$	8.21047e11	0.726165
$478$	−2.70328e10	−0.0236846
$479$	−1.59309e12	−1.38271	−0.691355	−	0.722515i	$-0.742986\pi$
$479$	−1.59309e12	−1.38271	−0.691355	+	0.722515i	$0.742986\pi$
$480$	−2.76758e10	−0.0237965
$481$	4.94023e10	0.0420818
$482$	1.03976e12	0.877446
$483$	−4.30600e11	−0.360008
$484$	5.41505e11	0.448537
$485$	−1.63325e10	−0.0134034
$486$	5.41564e11	0.440338
$487$	−1.59961e12	−1.28865	−0.644324	−	0.764752i	$-0.722861\pi$
$487$	−1.59961e12	−1.28865	−0.644324	+	0.764752i	$0.722861\pi$
$488$	−1.87344e12	−1.49538
$489$	−3.58067e10	−0.0283188
$490$	1.83951e10	0.0144152
$491$	−5.94395e10	−0.0461539	−0.0230769	−	0.999734i	$-0.507346\pi$
$491$	−5.94395e10	−0.0461539	−0.0230769	+	0.999734i	$0.507346\pi$
$492$	−1.12543e11	−0.0865917
$493$	0	0
$494$	−3.53579e10	−0.0267126
$495$	−4.54880e10	−0.0340544
$496$	2.02802e11	0.150454
$497$	−7.37056e11	−0.541872
$498$	2.87900e11	0.209754
$499$	6.12547e11	0.442269	0.221135	−	0.975243i	$-0.429024\pi$
$499$	6.12547e11	0.442269	0.221135	+	0.975243i	$0.429024\pi$
$500$	−1.32660e11	−0.0949241
$501$	5.91446e11	0.419417
$502$	1.31171e12	0.921874
$503$	−1.79381e12	−1.24945	−0.624726	−	0.780844i	$-0.714789\pi$
$503$	−1.79381e12	−1.24945	−0.624726	+	0.780844i	$0.714789\pi$
$504$	7.40195e11	0.510986
$505$	−1.27291e11	−0.0870934
$506$	6.04803e11	0.410144
$507$	−5.63746e11	−0.378920
$508$	−5.52778e11	−0.368268
$509$	−7.83948e11	−0.517675	−0.258837	−	0.965921i	$-0.583339\pi$
$509$	−7.83948e11	−0.517675	−0.258837	+	0.965921i	$0.583339\pi$
$510$	0	0
$511$	3.81577e11	0.247565
$512$	1.08973e12	0.700817
$513$	−9.90846e11	−0.631652
$514$	−8.57573e11	−0.541923
$515$	1.17256e11	0.0734519
$516$	−6.17697e11	−0.383576
$517$	−5.39208e11	−0.331932
$518$	−3.68503e11	−0.224883
$519$	7.90222e11	0.478075
$520$	−5.41859e9	−0.00324991
$521$	−9.27420e11	−0.551451	−0.275725	−	0.961236i	$-0.588918\pi$
$521$	−9.27420e11	−0.551451	−0.275725	+	0.961236i	$0.588918\pi$
$522$	2.81184e11	0.165758
$523$	−2.22342e12	−1.29946	−0.649731	−	0.760164i	$-0.725118\pi$
$523$	−2.22342e12	−1.29946	−0.649731	+	0.760164i	$0.725118\pi$
$524$	−2.07862e12	−1.20444
$525$	−4.68397e11	−0.269090
$526$	−4.25825e11	−0.242547
$527$	0	0
$528$	−1.66068e11	−0.0929895
$529$	1.39853e12	0.776465
$530$	4.48334e10	0.0246809
$531$	2.50537e11	0.136756
$532$	−9.10235e11	−0.492664
$533$	−3.44461e10	−0.0184871
$534$	4.58284e10	0.0243893
$535$	−9.21142e10	−0.0486110
$536$	−3.32879e11	−0.174199
$537$	1.02702e12	0.532962
$538$	1.20177e12	0.618445
$539$	6.30865e11	0.321949
$540$	−6.63158e10	−0.0335618
$541$	2.88963e12	1.45029	0.725145	−	0.688597i	$-0.241773\pi$
$541$	2.88963e12	1.45029	0.725145	+	0.688597i	$0.241773\pi$
$542$	9.13997e10	0.0454934
$543$	1.22083e12	0.602635
$544$	0	0
$545$	−9.91881e10	−0.0481588
$546$	−1.67425e10	−0.00806218
$547$	7.62225e11	0.364032	0.182016	−	0.983296i	$-0.441738\pi$
$547$	7.62225e11	0.364032	0.182016	+	0.983296i	$0.441738\pi$
$548$	1.95402e12	0.925584
$549$	−3.23511e12	−1.51989
$550$	6.57890e11	0.306564
$551$	−7.91748e11	−0.365936
$552$	9.30722e11	0.426672
$553$	−1.65392e12	−0.752060
$554$	−1.33878e12	−0.603829
$555$	3.48496e10	0.0155912
$556$	1.03315e12	0.458486
$557$	−1.15854e12	−0.509991	−0.254996	−	0.966942i	$-0.582074\pi$
$557$	−1.15854e12	−0.509991	−0.254996	+	0.966942i	$0.582074\pi$
$558$	−3.70989e11	−0.161997
$559$	−1.89059e11	−0.0818924
$560$	−3.81540e10	−0.0163943
$561$	0	0
$562$	4.25319e11	0.179846
$563$	−1.68046e12	−0.704919	−0.352460	−	0.935827i	$-0.614655\pi$
$563$	−1.68046e12	−0.704919	−0.352460	+	0.935827i	$0.614655\pi$
$564$	−3.62388e11	−0.150806
$565$	−1.26882e11	−0.0523822
$566$	8.16235e11	0.334304
$567$	1.02530e12	0.416608
$568$	1.59311e12	0.642212
$569$	−9.26592e11	−0.370581	−0.185291	−	0.982684i	$-0.559323\pi$
$569$	−9.26592e11	−0.370581	−0.185291	+	0.982684i	$0.559323\pi$
$570$	−2.49424e10	−0.00989693
$571$	2.85270e11	0.112304	0.0561518	−	0.998422i	$-0.482117\pi$
$571$	2.85270e11	0.112304	0.0561518	+	0.998422i	$0.482117\pi$
$572$	−8.11581e10	−0.0316993
$573$	1.00514e12	0.389519
$574$	2.56942e11	0.0987941
$575$	3.48054e12	1.32783
$576$	−2.41602e11	−0.0914533
$577$	8.48052e11	0.318516	0.159258	−	0.987237i	$-0.449090\pi$
$577$	8.48052e11	0.318516	0.159258	+	0.987237i	$0.449090\pi$
$578$	0	0
$579$	−1.38254e12	−0.511238
$580$	−5.29905e10	−0.0194434
$581$	2.26845e12	0.825918
$582$	1.09077e11	0.0394075
$583$	1.53757e12	0.551223
$584$	−8.24761e11	−0.293407
$585$	−9.35697e9	−0.00330319
$586$	7.74675e11	0.271381
$587$	−1.26388e12	−0.439373	−0.219686	−	0.975571i	$-0.570503\pi$
$587$	−1.26388e12	−0.439373	−0.219686	+	0.975571i	$0.570503\pi$
$588$	4.23988e11	0.146270
$589$	1.04462e12	0.357634
$590$	1.36806e10	0.00464807
$591$	6.31563e11	0.212948
$592$	−7.51877e11	−0.251593
$593$	5.10144e12	1.69413	0.847065	−	0.531489i	$-0.178367\pi$
$593$	5.10144e12	1.69413	0.847065	+	0.531489i	$0.178367\pi$
$594$	6.58989e11	0.217190
$595$	0	0
$596$	−3.57870e12	−1.16176
$597$	1.82756e12	0.588828
$598$	1.24409e11	0.0397830
$599$	−3.14052e12	−0.996738	−0.498369	−	0.866965i	$-0.666067\pi$
$599$	−3.14052e12	−0.996738	−0.498369	+	0.866965i	$0.666067\pi$
$600$	1.01242e12	0.318918
$601$	−1.47610e12	−0.461509	−0.230754	−	0.973012i	$-0.574119\pi$
$601$	−1.47610e12	−0.461509	−0.230754	+	0.973012i	$0.574119\pi$
$602$	1.41023e12	0.437629
$603$	−5.74825e11	−0.177055
$604$	−3.17040e12	−0.969278
$605$	1.16916e11	0.0354793
$606$	8.50110e11	0.256064
$607$	1.75134e12	0.523627	0.261814	−	0.965118i	$-0.415679\pi$
$607$	1.75134e12	0.523627	0.261814	+	0.965118i	$0.415679\pi$
$608$	3.07563e12	0.912783
$609$	−3.74903e11	−0.110444
$610$	−1.76654e11	−0.0516581
$611$	−1.10916e11	−0.0321965
$612$	0	0
$613$	1.53717e12	0.439694	0.219847	−	0.975534i	$-0.429444\pi$
$613$	1.53717e12	0.439694	0.219847	+	0.975534i	$0.429444\pi$
$614$	−2.27337e12	−0.645525
$615$	−2.42991e10	−0.00684941
$616$	1.38616e12	0.387883
$617$	6.14608e12	1.70732	0.853659	−	0.520832i	$-0.174378\pi$
$617$	6.14608e12	1.70732	0.853659	+	0.520832i	$0.174378\pi$
$618$	−7.83094e11	−0.215956
$619$	1.18984e12	0.325748	0.162874	−	0.986647i	$-0.447924\pi$
$619$	1.18984e12	0.325748	0.162874	+	0.986647i	$0.447924\pi$
$620$	6.99146e10	0.0190023
$621$	3.48635e12	0.940718
$622$	−2.70634e11	−0.0724979
$623$	3.61096e11	0.0960342
$624$	−3.41606e10	−0.00901976
$625$	3.77171e12	0.988730
$626$	−2.13761e12	−0.556344
$627$	−8.55404e11	−0.221038
$628$	7.17045e11	0.183962
$629$	0	0
$630$	6.97958e10	0.0176521
$631$	−7.35552e12	−1.84706	−0.923531	−	0.383524i	$-0.874710\pi$
$631$	−7.35552e12	−1.84706	−0.923531	+	0.383524i	$0.874710\pi$
$632$	3.57488e12	0.891321
$633$	−9.61698e11	−0.238079
$634$	−2.30145e12	−0.565718
$635$	−1.19350e11	−0.0291300
$636$	1.03336e12	0.250436
$637$	1.29770e11	0.0312283
$638$	5.26574e11	0.125825
$639$	2.75103e12	0.652741
$640$	2.52299e11	0.0594436
$641$	4.43828e12	1.03837	0.519186	−	0.854661i	$-0.326235\pi$
$641$	4.43828e12	1.03837	0.519186	+	0.854661i	$0.326235\pi$
$642$	6.15185e11	0.142922
$643$	4.13998e12	0.955099	0.477550	−	0.878605i	$-0.341525\pi$
$643$	4.13998e12	0.955099	0.477550	+	0.878605i	$0.341525\pi$
$644$	3.20272e12	0.733724
$645$	−1.33367e11	−0.0303409
$646$	0	0
$647$	−8.23149e11	−0.184675	−0.0923377	−	0.995728i	$-0.529434\pi$
$647$	−8.23149e11	−0.184675	−0.0923377	+	0.995728i	$0.529434\pi$
$648$	−2.21614e12	−0.493752
$649$	4.69181e11	0.103810
$650$	1.35329e11	0.0297360
$651$	4.94640e11	0.107938
$652$	2.66323e11	0.0577159
$653$	7.00981e10	0.0150868	0.00754339	−	0.999972i	$-0.497599\pi$
$653$	7.00981e10	0.0150868	0.00754339	+	0.999972i	$0.497599\pi$
$654$	6.62428e11	0.141592
$655$	−4.48793e11	−0.0952709
$656$	5.24252e11	0.110528
$657$	−1.42422e12	−0.298217
$658$	8.27349e11	0.172057
$659$	2.88785e12	0.596472	0.298236	−	0.954492i	$-0.403602\pi$
$659$	2.88785e12	0.596472	0.298236	+	0.954492i	$0.403602\pi$
$660$	−5.72509e10	−0.0117445
$661$	5.63361e12	1.14784	0.573919	−	0.818912i	$-0.305422\pi$
$661$	5.63361e12	1.14784	0.573919	+	0.818912i	$0.305422\pi$
$662$	−2.44964e12	−0.495726
$663$	0	0
$664$	−4.90315e12	−0.978856
$665$	−1.96528e11	−0.0389698
$666$	1.37542e12	0.270895
$667$	2.78582e12	0.544987
$668$	−4.39906e12	−0.854803
$669$	−3.73357e12	−0.720621
$670$	−3.13885e10	−0.00601774
$671$	−6.05838e12	−1.15373
$672$	1.45635e12	0.275489
$673$	7.23222e12	1.35895	0.679475	−	0.733699i	$-0.262208\pi$
$673$	7.23222e12	1.35895	0.679475	+	0.733699i	$0.262208\pi$
$674$	−4.27549e11	−0.0798025
$675$	3.79238e12	0.703144
$676$	4.19303e12	0.772268
$677$	7.50966e12	1.37395	0.686975	−	0.726681i	$-0.258938\pi$
$677$	7.50966e12	1.37395	0.686975	+	0.726681i	$0.258938\pi$
$678$	8.47384e11	0.154009
$679$	8.59449e11	0.155169
$680$	0	0
$681$	−3.75363e12	−0.668790
$682$	−6.94751e11	−0.122970
$683$	−1.37129e12	−0.241121	−0.120560	−	0.992706i	$-0.538469\pi$
$683$	−1.37129e12	−0.241121	−0.120560	+	0.992706i	$0.538469\pi$
$684$	3.39741e12	0.593466
$685$	4.21891e11	0.0732138
$686$	−2.91999e12	−0.503410
$687$	−2.85384e11	−0.0488792
$688$	2.87737e12	0.489608
$689$	3.16282e11	0.0534673
$690$	8.77613e10	0.0147395
$691$	6.89373e12	1.15028	0.575140	−	0.818055i	$-0.304948\pi$
$691$	6.89373e12	1.15028	0.575140	+	0.818055i	$0.304948\pi$
$692$	−5.87752e12	−0.974353
$693$	2.39366e12	0.394243
$694$	2.25119e12	0.368378
$695$	2.23066e11	0.0362662
$696$	8.10336e11	0.130895
$697$	0	0
$698$	−1.26965e12	−0.202457
$699$	3.65524e12	0.579120
$700$	3.48385e12	0.548426
$701$	4.32595e12	0.676629	0.338315	−	0.941033i	$-0.390143\pi$
$701$	4.32595e12	0.676629	0.338315	+	0.941033i	$0.390143\pi$
$702$	1.35555e11	0.0210669
$703$	−3.87286e12	−0.598043
$704$	−4.52448e11	−0.0694212
$705$	−7.82429e10	−0.0119287
$706$	1.37166e12	0.207791
$707$	6.69827e12	1.00827
$708$	3.15325e11	0.0471638
$709$	8.57015e12	1.27374	0.636870	−	0.770971i	$-0.280229\pi$
$709$	8.57015e12	1.27374	0.636870	+	0.770971i	$0.280229\pi$
$710$	1.50220e11	0.0221854
$711$	6.17320e12	0.905935
$712$	−7.80491e11	−0.113817
$713$	−3.67555e12	−0.532623
$714$	0	0
$715$	−1.75228e10	−0.00250742
$716$	−7.63880e12	−1.08622
$717$	−1.34529e11	−0.0190099
$718$	4.00045e12	0.561758
$719$	−6.91965e12	−0.965615	−0.482807	−	0.875727i	$-0.660383\pi$
$719$	−6.91965e12	−0.965615	−0.482807	+	0.875727i	$0.660383\pi$
$720$	1.42408e11	0.0197487
$721$	−6.17024e12	−0.850341
$722$	−6.88949e11	−0.0943561
$723$	5.17435e12	0.704260
$724$	−9.08027e12	−1.22822
$725$	3.03035e12	0.407353
$726$	−7.80824e11	−0.104313
$727$	−2.79887e12	−0.371602	−0.185801	−	0.982587i	$-0.559488\pi$
$727$	−2.79887e12	−0.371602	−0.185801	+	0.982587i	$0.559488\pi$
$728$	2.85137e11	0.0376237
$729$	−1.77937e12	−0.233341
$730$	−7.77699e10	−0.0101358
$731$	0	0
$732$	−4.07168e12	−0.524172
$733$	−6.24246e12	−0.798707	−0.399354	−	0.916797i	$-0.630765\pi$
$733$	−6.24246e12	−0.798707	−0.399354	+	0.916797i	$0.630765\pi$
$734$	−1.90093e12	−0.241732
$735$	9.15431e10	0.0115700
$736$	−1.08218e13	−1.35941
$737$	−1.07647e12	−0.134400
$738$	−9.59023e11	−0.119008
$739$	−4.03767e12	−0.498002	−0.249001	−	0.968503i	$-0.580102\pi$
$739$	−4.03767e12	−0.498002	−0.249001	+	0.968503i	$0.580102\pi$
$740$	−2.59204e11	−0.0317760
$741$	−1.75958e11	−0.0214402
$742$	−2.35922e12	−0.285727
$743$	2.86891e12	0.345356	0.172678	−	0.984978i	$-0.444758\pi$
$743$	2.86891e12	0.345356	0.172678	+	0.984978i	$0.444758\pi$
$744$	−1.06914e12	−0.127925
$745$	−7.72675e11	−0.0918954
$746$	3.85384e12	0.455585
$747$	−8.46690e12	−0.994905
$748$	0	0
$749$	4.84723e12	0.562762
$750$	1.91290e11	0.0220758
$751$	1.28197e13	1.47061	0.735307	−	0.677734i	$-0.237038\pi$
$751$	1.28197e13	1.47061	0.735307	+	0.677734i	$0.237038\pi$
$752$	1.68809e12	0.192493
$753$	6.52772e12	0.739919
$754$	1.08317e11	0.0122047
$755$	−6.84520e11	−0.0766699
$756$	3.48966e12	0.388540
$757$	7.97188e12	0.882327	0.441163	−	0.897427i	$-0.354566\pi$
$757$	7.97188e12	0.882327	0.441163	+	0.897427i	$0.354566\pi$
$758$	3.46395e12	0.381119
$759$	3.00980e12	0.329192
$760$	4.24787e11	0.0461859
$761$	1.58619e13	1.71444	0.857222	−	0.514948i	$-0.172189\pi$
$761$	1.58619e13	1.71444	0.857222	+	0.514948i	$0.172189\pi$
$762$	7.97079e11	0.0856454
$763$	5.21947e12	0.557527
$764$	−7.47600e12	−0.793870
$765$	0	0
$766$	−1.08208e12	−0.113561
$767$	9.65116e10	0.0100693
$768$	−2.07716e12	−0.215449
$769$	−1.90312e13	−1.96244	−0.981221	−	0.192885i	$-0.938216\pi$
$769$	−1.90312e13	−1.96244	−0.981221	+	0.192885i	$0.938216\pi$
$770$	1.30707e11	0.0133995
$771$	−4.26771e12	−0.434961
$772$	1.02830e13	1.04194
$773$	−3.15285e12	−0.317611	−0.158805	−	0.987310i	$-0.550764\pi$
$773$	−3.15285e12	−0.317611	−0.158805	+	0.987310i	$0.550764\pi$
$774$	−5.26363e12	−0.527170
$775$	−3.99818e12	−0.398112
$776$	−1.85766e12	−0.183903
$777$	−1.83385e12	−0.180497
$778$	1.67716e12	0.164122
$779$	2.70038e12	0.262728
$780$	−1.17766e10	−0.00113919
$781$	5.15185e12	0.495488
$782$	0	0
$783$	3.03541e12	0.288595
$784$	−1.97504e12	−0.186704
$785$	1.54817e11	0.0145514
$786$	2.99726e12	0.280107
$787$	1.38558e13	1.28749	0.643745	−	0.765240i	$-0.277380\pi$
$787$	1.38558e13	1.28749	0.643745	+	0.765240i	$0.277380\pi$
$788$	−4.69744e12	−0.434004
$789$	−2.11912e12	−0.194674
$790$	3.37089e11	0.0307909
$791$	6.67680e12	0.606421
$792$	−5.17379e12	−0.467246
$793$	−1.24622e12	−0.111909
$794$	8.43428e12	0.753106
$795$	2.23113e11	0.0198095
$796$	−1.35931e13	−1.20008
$797$	−1.66687e13	−1.46332	−0.731662	−	0.681668i	$-0.761255\pi$
$797$	−1.66687e13	−1.46332	−0.731662	+	0.681668i	$0.761255\pi$
$798$	1.31251e12	0.114575
$799$	0	0
$800$	−1.17717e13	−1.01609
$801$	−1.34777e12	−0.115683
$802$	1.75545e12	0.149832
$803$	−2.66714e12	−0.226373
$804$	−7.23472e11	−0.0610617
$805$	6.91498e11	0.0580376
$806$	−1.42912e11	−0.0119278
$807$	5.98059e12	0.496379
$808$	−1.44780e13	−1.19497
$809$	−1.04805e13	−0.860231	−0.430115	−	0.902774i	$-0.641527\pi$
$809$	−1.04805e13	−0.860231	−0.430115	+	0.902774i	$0.641527\pi$
$810$	−2.08968e11	−0.0170568
$811$	1.18989e13	0.965860	0.482930	−	0.875659i	$-0.339573\pi$
$811$	1.18989e13	0.965860	0.482930	+	0.875659i	$0.339573\pi$
$812$	2.78846e12	0.225093
$813$	4.54850e11	0.0365141
$814$	2.57575e12	0.205634
$815$	5.75017e10	0.00456533
$816$	0	0
$817$	1.48211e13	1.16381
$818$	5.62964e12	0.439633
$819$	4.92382e11	0.0382406
$820$	1.80732e11	0.0139596
$821$	2.38314e12	0.183065	0.0915324	−	0.995802i	$-0.470823\pi$
$821$	2.38314e12	0.183065	0.0915324	+	0.995802i	$0.470823\pi$
$822$	−2.81760e12	−0.215256
$823$	−1.35076e13	−1.02631	−0.513155	−	0.858296i	$-0.671523\pi$
$823$	−1.35076e13	−1.02631	−0.513155	+	0.858296i	$0.671523\pi$
$824$	1.33367e13	1.00780
$825$	3.27399e12	0.246056
$826$	−7.19902e11	−0.0538100
$827$	1.30268e12	0.0968417	0.0484208	−	0.998827i	$-0.484581\pi$
$827$	1.30268e12	0.0968417	0.0484208	+	0.998827i	$0.484581\pi$
$828$	−1.19540e13	−0.883847
$829$	−1.65695e13	−1.21847	−0.609234	−	0.792991i	$-0.708523\pi$
$829$	−1.65695e13	−1.21847	−0.609234	+	0.792991i	$0.708523\pi$
$830$	−4.62337e11	−0.0338148
$831$	−6.66241e12	−0.484649
$832$	−9.30695e10	−0.00673368
$833$	0	0
$834$	−1.48975e12	−0.106627
$835$	−9.49800e11	−0.0676150
$836$	6.36233e12	0.450493
$837$	−4.00486e12	−0.282048
$838$	−4.93983e12	−0.346030
$839$	1.58393e13	1.10359	0.551794	−	0.833981i	$-0.313944\pi$
$839$	1.58393e13	1.10359	0.551794	+	0.833981i	$0.313944\pi$
$840$	2.01142e11	0.0139395
$841$	−1.20817e13	−0.832808
$842$	−1.37603e13	−0.943457
$843$	2.11660e12	0.144349
$844$	7.15292e12	0.485224
$845$	9.05315e11	0.0610864
$846$	−3.08804e12	−0.207261
$847$	−6.15235e12	−0.410739
$848$	−4.81365e12	−0.319664
$849$	4.06198e12	0.268320
$850$	0	0
$851$	1.36269e13	0.890665
$852$	3.46243e12	0.225114
$853$	1.78273e12	0.115296	0.0576481	−	0.998337i	$-0.481640\pi$
$853$	1.78273e12	0.115296	0.0576481	+	0.998337i	$0.481640\pi$
$854$	9.29585e12	0.598038
$855$	7.33533e11	0.0469432
$856$	−1.04770e13	−0.666971
$857$	4.16362e12	0.263668	0.131834	−	0.991272i	$-0.457913\pi$
$857$	4.16362e12	0.263668	0.131834	+	0.991272i	$0.457913\pi$
$858$	1.17026e11	0.00737207
$859$	−3.08310e11	−0.0193205	−0.00966026	−	0.999953i	$-0.503075\pi$
$859$	−3.08310e11	−0.0193205	−0.00966026	+	0.999953i	$0.503075\pi$
$860$	9.91955e11	0.0618370
$861$	1.27867e12	0.0792946
$862$	−7.40723e12	−0.456954
$863$	−2.48841e13	−1.52712	−0.763562	−	0.645735i	$-0.776551\pi$
$863$	−2.48841e13	−1.52712	−0.763562	+	0.645735i	$0.776551\pi$
$864$	−1.17914e13	−0.719866
$865$	−1.26901e12	−0.0770714
$866$	5.15964e12	0.311737
$867$	0	0
$868$	−3.67904e12	−0.219986
$869$	1.15605e13	0.687685
$870$	7.64097e10	0.00452180
$871$	−2.21433e11	−0.0130365
$872$	−1.12816e13	−0.660766
$873$	−3.20786e12	−0.186918
$874$	−9.75297e12	−0.565374
$875$	1.50723e12	0.0869247
$876$	−1.79252e12	−0.102848
$877$	−1.78295e13	−1.01775	−0.508874	−	0.860841i	$-0.669938\pi$
$877$	−1.78295e13	−1.01775	−0.508874	+	0.860841i	$0.669938\pi$
$878$	−1.04182e13	−0.591652
$879$	3.85516e12	0.217818
$880$	2.66688e11	0.0149910
$881$	1.94178e13	1.08595	0.542974	−	0.839749i	$-0.317298\pi$
$881$	1.94178e13	1.08595	0.542974	+	0.839749i	$0.317298\pi$
$882$	3.61297e12	0.201027
$883$	1.76231e13	0.975574	0.487787	−	0.872963i	$-0.337804\pi$
$883$	1.76231e13	0.975574	0.487787	+	0.872963i	$0.337804\pi$
$884$	0	0
$885$	6.80816e10	0.00373066
$886$	1.27095e13	0.692908
$887$	−2.04207e13	−1.10768	−0.553841	−	0.832622i	$-0.686839\pi$
$887$	−2.04207e13	−1.10768	−0.553841	+	0.832622i	$0.686839\pi$
$888$	3.96378e12	0.213920
$889$	6.28043e12	0.337234
$890$	−7.35954e10	−0.00393184
$891$	−7.16661e12	−0.380947
$892$	2.77696e13	1.46868
$893$	8.69519e12	0.457560
$894$	5.16031e12	0.270182
$895$	−1.64929e12	−0.0859198
$896$	−1.32764e13	−0.688170
$897$	6.19121e11	0.0319308
$898$	−1.15309e13	−0.591725
$899$	−3.20013e12	−0.163399
$900$	−1.30033e13	−0.660636
$901$	0	0
$902$	−1.79596e12	−0.0903374
$903$	7.01800e12	0.351252
$904$	−1.44316e13	−0.718714
$905$	−1.96052e12	−0.0971520
$906$	4.57157e12	0.225418
$907$	3.48284e13	1.70884	0.854418	−	0.519587i	$-0.173914\pi$
$907$	3.48284e13	1.70884	0.854418	+	0.519587i	$0.173914\pi$
$908$	2.79188e13	1.36305
$909$	−2.50010e13	−1.21456
$910$	2.68866e10	0.00129972
$911$	2.39979e13	1.15436	0.577179	−	0.816618i	$-0.304154\pi$
$911$	2.39979e13	1.15436	0.577179	+	0.816618i	$0.304154\pi$
$912$	2.67800e12	0.128184
$913$	−1.58560e13	−0.755221
$914$	−1.86996e13	−0.886288
$915$	−8.79115e11	−0.0414621
$916$	2.12263e12	0.0996195
$917$	2.36164e13	1.10294
$918$	0	0
$919$	1.68855e13	0.780896	0.390448	−	0.920625i	$-0.372320\pi$
$919$	1.68855e13	0.780896	0.390448	+	0.920625i	$0.372320\pi$
$920$	−1.49464e12	−0.0687846
$921$	−1.13134e13	−0.518114
$922$	5.36796e12	0.244636
$923$	1.05975e12	0.0480612
$924$	3.01265e12	0.135964
$925$	1.48230e13	0.665732
$926$	3.18169e12	0.142203
$927$	2.30301e13	1.02433
$928$	−9.42203e12	−0.417041
$929$	−2.44294e13	−1.07607	−0.538037	−	0.842921i	$-0.680834\pi$
$929$	−2.44294e13	−1.07607	−0.538037	+	0.842921i	$0.680834\pi$
$930$	−1.00813e11	−0.00441922
$931$	−1.01733e13	−0.443799
$932$	−2.71870e13	−1.18029
$933$	−1.34681e12	−0.0581886
$934$	−1.60030e13	−0.688082
$935$	0	0
$936$	−1.06426e12	−0.0453217
$937$	7.06840e12	0.299566	0.149783	−	0.988719i	$-0.452142\pi$
$937$	7.06840e12	0.299566	0.149783	+	0.988719i	$0.452142\pi$
$938$	1.65172e12	0.0696665
$939$	−1.06378e13	−0.446535
$940$	5.81956e11	0.0243117
$941$	3.45639e13	1.43704	0.718521	−	0.695506i	$-0.244820\pi$
$941$	3.45639e13	1.43704	0.718521	+	0.695506i	$0.244820\pi$
$942$	−1.03394e12	−0.0427827
$943$	−9.50146e12	−0.391280
$944$	−1.46886e12	−0.0602012
$945$	7.53451e11	0.0307335
$946$	−9.85719e12	−0.400169
$947$	−3.93920e13	−1.59160	−0.795799	−	0.605560i	$-0.792949\pi$
$947$	−3.93920e13	−1.59160	−0.795799	+	0.605560i	$0.792949\pi$
$948$	7.76955e12	0.312434
$949$	−5.48636e11	−0.0219577
$950$	−1.06091e13	−0.422591
$951$	−1.14531e13	−0.454059
$952$	0	0
$953$	3.51103e13	1.37885	0.689425	−	0.724357i	$-0.257863\pi$
$953$	3.51103e13	1.37885	0.689425	+	0.724357i	$0.257863\pi$
$954$	8.80569e12	0.344188
$955$	−1.61414e12	−0.0627951
$956$	1.00060e12	0.0387435
$957$	2.62049e12	0.100990
$958$	−1.70858e13	−0.655377
$959$	−2.22007e13	−0.847585
$960$	−6.56535e10	−0.00249481
$961$	−2.22174e13	−0.840308
$962$	5.29837e11	0.0199460
$963$	−1.80921e13	−0.677906
$964$	−3.84858e13	−1.43534
$965$	2.22021e12	0.0824177
$966$	−4.61817e12	−0.170637
$967$	−1.93513e12	−0.0711690	−0.0355845	−	0.999367i	$-0.511329\pi$
$967$	−1.93513e12	−0.0711690	−0.0355845	+	0.999367i	$0.511329\pi$
$968$	1.32980e13	0.486797
$969$	0	0
$970$	−1.75166e11	−0.00635296
$971$	1.69806e13	0.613010	0.306505	−	0.951869i	$-0.400840\pi$
$971$	1.69806e13	0.613010	0.306505	+	0.951869i	$0.400840\pi$
$972$	−2.00456e13	−0.720311
$973$	−1.17382e13	−0.419849
$974$	−1.71558e13	−0.610794
$975$	6.73466e11	0.0238668
$976$	1.89668e13	0.669069
$977$	−1.76777e13	−0.620726	−0.310363	−	0.950618i	$-0.600451\pi$
$977$	−1.76777e13	−0.620726	−0.310363	+	0.950618i	$0.600451\pi$
$978$	−3.84025e11	−0.0134226
$979$	−2.52397e12	−0.0878138
$980$	−6.80880e11	−0.0235805
$981$	−1.94814e13	−0.671600
$982$	−6.37486e11	−0.0218760
$983$	−5.81116e12	−0.198505	−0.0992527	−	0.995062i	$-0.531645\pi$
$983$	−5.81116e12	−0.198505	−0.0992527	+	0.995062i	$0.531645\pi$
$984$	−2.76378e12	−0.0939778
$985$	−1.01422e12	−0.0343297
$986$	0	0
$987$	4.11729e12	0.138097
$988$	1.30875e12	0.0436967
$989$	−5.21491e13	−1.73326
$990$	−4.87856e11	−0.0161411
$991$	5.41563e13	1.78368	0.891841	−	0.452348i	$-0.149414\pi$
$991$	5.41563e13	1.78368	0.891841	+	0.452348i	$0.149414\pi$
$992$	1.24312e13	0.407579
$993$	−1.21906e13	−0.397882
$994$	−7.90489e12	−0.256837
$995$	−2.93487e12	−0.0949261
$996$	−1.06564e13	−0.343117
$997$	9.07988e11	0.0291040	0.0145520	−	0.999894i	$-0.495368\pi$
$997$	9.07988e11	0.0291040	0.0145520	+	0.999894i	$0.495368\pi$
$998$	6.56954e12	0.209627
$999$	1.48478e13	0.471647

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.h.1.22	yes	36
17.16	even	2		289.10.a.g.1.22	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.22	✓	36	17.16	even	2
289.10.a.h.1.22	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)

\(f(q)\)	\(=\)	\(q+10.7250 q^{2} +53.3726 q^{3} -396.975 q^{4} -85.7107 q^{5} +572.419 q^{6} +4510.26 q^{7} -9748.72 q^{8} -16834.4 q^{9} +O(q^{10})\)	\(q+10.7250 q^{2} +53.3726 q^{3} -396.975 q^{4} -85.7107 q^{5} +572.419 q^{6} +4510.26 q^{7} -9748.72 q^{8} -16834.4 q^{9} -919.244 q^{10} -31525.7 q^{11} -21187.6 q^{12} -6484.90 q^{13} +48372.4 q^{14} -4574.61 q^{15} +98696.8 q^{16} -180548. q^{18} +508379. q^{19} +34025.1 q^{20} +240725. q^{21} -338112. q^{22} -1.78877e6 q^{23} -520315. q^{24} -1.94578e6 q^{25} -69550.3 q^{26} -1.94903e6 q^{27} -1.79046e6 q^{28} -1.55740e6 q^{29} -49062.5 q^{30} +2.05480e6 q^{31} +6.04986e6 q^{32} -1.68261e6 q^{33} -386578. q^{35} +6.68283e6 q^{36} -7.61805e6 q^{37} +5.45235e6 q^{38} -346116. q^{39} +835570. q^{40} +5.31174e6 q^{41} +2.58176e6 q^{42} +2.91537e7 q^{43} +1.25149e7 q^{44} +1.44289e6 q^{45} -1.91844e7 q^{46} +1.71037e7 q^{47} +5.26771e6 q^{48} -2.00111e7 q^{49} -2.08684e7 q^{50} +2.57435e6 q^{52} -4.87721e7 q^{53} -2.09032e7 q^{54} +2.70209e6 q^{55} -4.39693e7 q^{56} +2.71336e7 q^{57} -1.67030e7 q^{58} -1.48825e7 q^{59} +1.81601e6 q^{60} +1.92173e8 q^{61} +2.20376e7 q^{62} -7.59274e7 q^{63} +1.43517e7 q^{64} +555826. q^{65} -1.80459e7 q^{66} +3.41459e7 q^{67} -9.54712e7 q^{69} -4.14603e6 q^{70} -1.63417e8 q^{71} +1.64113e8 q^{72} +8.46020e7 q^{73} -8.17032e7 q^{74} -1.03851e8 q^{75} -2.01814e8 q^{76} -1.42189e8 q^{77} -3.71208e6 q^{78} -3.66702e8 q^{79} -8.45938e6 q^{80} +2.27326e8 q^{81} +5.69682e7 q^{82} +5.02953e8 q^{83} -9.55618e7 q^{84} +3.12672e8 q^{86} -8.31223e7 q^{87} +3.07335e8 q^{88} +8.00609e7 q^{89} +1.54749e7 q^{90} -2.92486e7 q^{91} +7.10096e8 q^{92} +1.09670e8 q^{93} +1.83437e8 q^{94} -4.35736e7 q^{95} +3.22897e8 q^{96} +1.90554e8 q^{97} -2.14618e8 q^{98} +5.30715e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 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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