LMFDB - Embedded newform 289.10.a.g.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

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

Embedding invariants

Embedding label			1.12
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)

$f(q)$	$=$	$q-20.0534 q^{2} +107.002 q^{3} -109.862 q^{4} +2675.64 q^{5} -2145.75 q^{6} -1982.25 q^{7} +12470.4 q^{8} -8233.60 q^{9} +O(q^{10})$	\(q-20.0534 q^{2} +107.002 q^{3} -109.862 q^{4} +2675.64 q^{5} -2145.75 q^{6} -1982.25 q^{7} +12470.4 q^{8} -8233.60 q^{9} -53655.7 q^{10} -37670.6 q^{11} -11755.5 q^{12} -25139.4 q^{13} +39750.8 q^{14} +286299. q^{15} -193825. q^{16} +165111. q^{18} +623741. q^{19} -293952. q^{20} -212104. q^{21} +755422. q^{22} +88926.9 q^{23} +1.33436e6 q^{24} +5.20595e6 q^{25} +504130. q^{26} -2.98713e6 q^{27} +217774. q^{28} -116951. q^{29} -5.74126e6 q^{30} -8.85431e6 q^{31} -2.49802e6 q^{32} -4.03082e6 q^{33} -5.30379e6 q^{35} +904560. q^{36} +1.75902e7 q^{37} -1.25081e7 q^{38} -2.68996e6 q^{39} +3.33664e7 q^{40} -2.89173e7 q^{41} +4.25341e6 q^{42} -4.22052e6 q^{43} +4.13857e6 q^{44} -2.20302e7 q^{45} -1.78328e6 q^{46} -3.58857e7 q^{47} -2.07396e7 q^{48} -3.64243e7 q^{49} -1.04397e8 q^{50} +2.76187e6 q^{52} -1.03300e7 q^{53} +5.99020e7 q^{54} -1.00793e8 q^{55} -2.47195e7 q^{56} +6.67414e7 q^{57} +2.34527e6 q^{58} +6.28093e7 q^{59} -3.14534e7 q^{60} +1.06527e8 q^{61} +1.77559e8 q^{62} +1.63210e7 q^{63} +1.49332e8 q^{64} -6.72641e7 q^{65} +8.08316e7 q^{66} -9.64274e7 q^{67} +9.51535e6 q^{69} +1.06359e8 q^{70} -2.78873e8 q^{71} -1.02677e8 q^{72} +3.95597e8 q^{73} -3.52744e8 q^{74} +5.57046e8 q^{75} -6.85255e7 q^{76} +7.46724e7 q^{77} +5.39428e7 q^{78} -5.96898e8 q^{79} -5.18606e8 q^{80} -1.57567e8 q^{81} +5.79890e8 q^{82} -7.90776e8 q^{83} +2.33022e7 q^{84} +8.46356e7 q^{86} -1.25140e7 q^{87} -4.69768e8 q^{88} +8.30223e8 q^{89} +4.41779e8 q^{90} +4.98325e7 q^{91} -9.76970e6 q^{92} -9.47428e8 q^{93} +7.19629e8 q^{94} +1.66891e9 q^{95} -2.67293e8 q^{96} -2.87280e8 q^{97} +7.30430e8 q^{98} +3.10164e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−20.0534	−0.886242	−0.443121	−	0.896462i	$-0.646129\pi$
$2$	−20.0534	−0.886242	−0.443121	+	0.896462i	$0.646129\pi$
$3$	107.002	0.762686	0.381343	−	0.924434i	$-0.375462\pi$
$3$	107.002	0.762686	0.381343	+	0.924434i	$0.375462\pi$
$4$	−109.862	−0.214575
$5$	2675.64	1.91454	0.957268	−	0.289204i	$-0.0933905\pi$
$5$	2675.64	1.91454	0.957268	+	0.289204i	$0.0933905\pi$
$6$	−2145.75	−0.675925
$7$	−1982.25	−0.312045	−0.156022	−	0.987754i	$-0.549867\pi$
$7$	−1982.25	−0.312045	−0.156022	+	0.987754i	$0.549867\pi$
$8$	12470.4	1.07641
$9$	−8233.60	−0.418310
$10$	−53655.7	−1.69674
$11$	−37670.6	−0.775774	−0.387887	−	0.921707i	$-0.626795\pi$
$11$	−37670.6	−0.775774	−0.387887	+	0.921707i	$0.626795\pi$
$12$	−11755.5	−0.163653
$13$	−25139.4	−0.244124	−0.122062	−	0.992523i	$-0.538951\pi$
$13$	−25139.4	−0.244124	−0.122062	+	0.992523i	$0.538951\pi$
$14$	39750.8	0.276547
$15$	286299.	1.46019
$16$	−193825.	−0.739383
$17$	0	0
$17$	0	0
$18$	165111.	0.370724
$19$	623741.	1.09803	0.549013	−	0.835814i	$-0.315004\pi$
$19$	623741.	1.09803	0.549013	+	0.835814i	$0.315004\pi$
$20$	−293952.	−0.410810
$21$	−212104.	−0.237992
$22$	755422.	0.687523
$23$	88926.9	0.0662610	0.0331305	−	0.999451i	$-0.489452\pi$
$23$	88926.9	0.0662610	0.0331305	+	0.999451i	$0.489452\pi$
$24$	1.33436e6	0.820961
$25$	5.20595e6	2.66544
$26$	504130.	0.216353
$27$	−2.98713e6	−1.08173
$28$	217774.	0.0669569
$29$	−116951.	−0.0307053	−0.0153527	−	0.999882i	$-0.504887\pi$
$29$	−116951.	−0.0307053	−0.0153527	+	0.999882i	$0.504887\pi$
$30$	−5.74126e6	−1.29408
$31$	−8.85431e6	−1.72198	−0.860988	−	0.508625i	$-0.830154\pi$
$31$	−8.85431e6	−1.72198	−0.860988	+	0.508625i	$0.830154\pi$
$32$	−2.49802e6	−0.421135
$33$	−4.03082e6	−0.591672
$34$	0	0
$35$	−5.30379e6	−0.597421
$36$	904560.	0.0897587
$37$	1.75902e7	1.54299	0.771496	−	0.636234i	$-0.219509\pi$
$37$	1.75902e7	1.54299	0.771496	+	0.636234i	$0.219509\pi$
$38$	−1.25081e7	−0.973118
$39$	−2.68996e6	−0.186190
$40$	3.33664e7	2.06082
$41$	−2.89173e7	−1.59820	−0.799100	−	0.601199i	$-0.794690\pi$
$41$	−2.89173e7	−1.59820	−0.799100	+	0.601199i	$0.794690\pi$
$42$	4.25341e6	0.210919
$43$	−4.22052e6	−0.188260	−0.0941299	−	0.995560i	$-0.530007\pi$
$43$	−4.22052e6	−0.188260	−0.0941299	+	0.995560i	$0.530007\pi$
$44$	4.13857e6	0.166461
$45$	−2.20302e7	−0.800869
$46$	−1.78328e6	−0.0587233
$47$	−3.58857e7	−1.07271	−0.536353	−	0.843994i	$-0.680199\pi$
$47$	−3.58857e7	−1.07271	−0.536353	+	0.843994i	$0.680199\pi$
$48$	−2.07396e7	−0.563917
$49$	−3.64243e7	−0.902628
$50$	−1.04397e8	−2.36223
$51$	0	0
$52$	2.76187e6	0.0523827
$53$	−1.03300e7	−0.179829	−0.0899147	−	0.995949i	$-0.528659\pi$
$53$	−1.03300e7	−0.179829	−0.0899147	+	0.995949i	$0.528659\pi$
$54$	5.99020e7	0.958671
$55$	−1.00793e8	−1.48525
$56$	−2.47195e7	−0.335887
$57$	6.67414e7	0.837450
$58$	2.34527e6	0.0272124
$59$	6.28093e7	0.674823	0.337412	−	0.941357i	$-0.390449\pi$
$59$	6.28093e7	0.674823	0.337412	+	0.941357i	$0.390449\pi$
$60$	−3.14534e7	−0.313319
$61$	1.06527e8	0.985089	0.492545	−	0.870287i	$-0.336067\pi$
$61$	1.06527e8	0.985089	0.492545	+	0.870287i	$0.336067\pi$
$62$	1.77559e8	1.52609
$63$	1.63210e7	0.130531
$64$	1.49332e8	1.11261
$65$	−6.72641e7	−0.467383
$66$	8.08316e7	0.524365
$67$	−9.64274e7	−0.584607	−0.292303	−	0.956326i	$-0.594422\pi$
$67$	−9.64274e7	−0.584607	−0.292303	+	0.956326i	$0.594422\pi$
$68$	0	0
$69$	9.51535e6	0.0505363
$70$	1.06359e8	0.529460
$71$	−2.78873e8	−1.30240	−0.651199	−	0.758907i	$-0.725734\pi$
$71$	−2.78873e8	−1.30240	−0.651199	+	0.758907i	$0.725734\pi$
$72$	−1.02677e8	−0.450272
$73$	3.95597e8	1.63042	0.815212	−	0.579163i	$-0.196621\pi$
$73$	3.95597e8	1.63042	0.815212	+	0.579163i	$0.196621\pi$
$74$	−3.52744e8	−1.36747
$75$	5.57046e8	2.03290
$76$	−6.85255e7	−0.235609
$77$	7.46724e7	0.242076
$78$	5.39428e7	0.165009
$79$	−5.96898e8	−1.72416	−0.862082	−	0.506769i	$-0.830840\pi$
$79$	−5.96898e8	−1.72416	−0.862082	+	0.506769i	$0.830840\pi$
$80$	−5.18606e8	−1.41558
$81$	−1.57567e8	−0.406707
$82$	5.79890e8	1.41639
$83$	−7.90776e8	−1.82895	−0.914475	−	0.404642i	$-0.867396\pi$
$83$	−7.90776e8	−1.82895	−0.914475	+	0.404642i	$0.867396\pi$
$84$	2.33022e7	0.0510671
$85$	0	0
$86$	8.46356e7	0.166844
$87$	−1.25140e7	−0.0234185
$88$	−4.69768e8	−0.835049
$89$	8.30223e8	1.40262	0.701309	−	0.712857i	$-0.252599\pi$
$89$	8.30223e8	1.40262	0.701309	+	0.712857i	$0.252599\pi$
$90$	4.41779e8	0.709764
$91$	4.98325e7	0.0761775
$92$	−9.76970e6	−0.0142179
$93$	−9.47428e8	−1.31333
$94$	7.19629e8	0.950678
$95$	1.66891e9	2.10221
$96$	−2.67293e8	−0.321193
$97$	−2.87280e8	−0.329483	−0.164741	−	0.986337i	$-0.552679\pi$
$97$	−2.87280e8	−0.329483	−0.164741	+	0.986337i	$0.552679\pi$
$98$	7.30430e8	0.799947
$99$	3.10164e8	0.324514
$100$	−5.71936e8	−0.571936
$101$	3.45867e8	0.330721	0.165361	−	0.986233i	$-0.447121\pi$
$101$	3.45867e8	0.330721	0.165361	+	0.986233i	$0.447121\pi$
$102$	0	0
$103$	−6.59446e8	−0.577313	−0.288657	−	0.957433i	$-0.593209\pi$
$103$	−6.59446e8	−0.577313	−0.288657	+	0.957433i	$0.593209\pi$
$104$	−3.13499e8	−0.262776
$105$	−5.67516e8	−0.455644
$106$	2.07152e8	0.159372
$107$	−1.09750e9	−0.809429	−0.404715	−	0.914443i	$-0.632629\pi$
$107$	−1.09750e9	−0.809429	−0.404715	+	0.914443i	$0.632629\pi$
$108$	3.28172e8	0.232111
$109$	1.47757e9	1.00260	0.501302	−	0.865273i	$-0.332855\pi$
$109$	1.47757e9	1.00260	0.501302	+	0.865273i	$0.332855\pi$
$110$	2.02124e9	1.31629
$111$	1.88219e9	1.17682
$112$	3.84209e8	0.230721
$113$	−2.63247e8	−0.151884	−0.0759418	−	0.997112i	$-0.524196\pi$
$113$	−2.63247e8	−0.151884	−0.0759418	+	0.997112i	$0.524196\pi$
$114$	−1.33839e9	−0.742183
$115$	2.37937e8	0.126859
$116$	1.28485e7	0.00658858
$117$	2.06988e8	0.102119
$118$	−1.25954e9	−0.598057
$119$	0	0
$120$	3.57027e9	1.57176
$121$	−9.38876e8	−0.398175
$122$	−2.13623e9	−0.873028
$123$	−3.09421e9	−1.21892
$124$	9.72753e8	0.369492
$125$	8.70339e9	3.18855
$126$	−3.27292e8	−0.115683
$127$	1.75497e9	0.598624	0.299312	−	0.954155i	$-0.403243\pi$
$127$	1.75497e9	0.598624	0.299312	+	0.954155i	$0.403243\pi$
$128$	−1.71563e9	−0.564908
$129$	−4.51603e8	−0.143583
$130$	1.34887e9	0.414215
$131$	3.38174e9	1.00327	0.501637	−	0.865078i	$-0.332731\pi$
$131$	3.38174e9	1.00327	0.501637	+	0.865078i	$0.332731\pi$
$132$	4.42835e8	0.126958
$133$	−1.23641e9	−0.342634
$134$	1.93370e9	0.518103
$135$	−7.99249e9	−2.07100
$136$	0	0
$137$	1.32160e9	0.320521	0.160261	−	0.987075i	$-0.448766\pi$
$137$	1.32160e9	0.320521	0.160261	+	0.987075i	$0.448766\pi$
$138$	−1.90815e8	−0.0447874
$139$	−2.93386e9	−0.666612	−0.333306	−	0.942819i	$-0.608164\pi$
$139$	−2.93386e9	−0.666612	−0.333306	+	0.942819i	$0.608164\pi$
$140$	5.82686e8	0.128191
$141$	−3.83984e9	−0.818138
$142$	5.59234e9	1.15424
$143$	9.47015e8	0.189385
$144$	1.59588e9	0.309291
$145$	−3.12920e8	−0.0587864
$146$	−7.93306e9	−1.44495
$147$	−3.89747e9	−0.688422
$148$	−1.93250e9	−0.331087
$149$	−8.15943e9	−1.35619	−0.678097	−	0.734972i	$-0.737195\pi$
$149$	−8.15943e9	−1.35619	−0.678097	+	0.734972i	$0.737195\pi$
$150$	−1.11707e10	−1.80164
$151$	−4.41970e9	−0.691825	−0.345912	−	0.938267i	$-0.612431\pi$
$151$	−4.41970e9	−0.691825	−0.345912	+	0.938267i	$0.612431\pi$
$152$	7.77832e9	1.18192
$153$	0	0
$154$	−1.49743e9	−0.214538
$155$	−2.36910e10	−3.29678
$156$	2.95525e8	0.0399516
$157$	1.30118e10	1.70918	0.854590	−	0.519304i	$-0.173809\pi$
$157$	1.30118e10	1.70918	0.854590	+	0.519304i	$0.173809\pi$
$158$	1.19698e10	1.52803
$159$	−1.10533e9	−0.137153
$160$	−6.68381e9	−0.806277
$161$	−1.76275e8	−0.0206764
$162$	3.15974e9	0.360441
$163$	3.28470e9	0.364461	0.182231	−	0.983256i	$-0.441668\pi$
$163$	3.28470e9	0.364461	0.182231	+	0.983256i	$0.441668\pi$
$164$	3.17692e9	0.342933
$165$	−1.07850e10	−1.13278
$166$	1.58577e10	1.62089
$167$	2.91128e9	0.289641	0.144820	−	0.989458i	$-0.453740\pi$
$167$	2.91128e9	0.289641	0.144820	+	0.989458i	$0.453740\pi$
$168$	−2.64503e9	−0.256177
$169$	−9.97251e9	−0.940404
$170$	0	0
$171$	−5.13563e9	−0.459316
$172$	4.63675e8	0.0403957
$173$	−5.10510e9	−0.433308	−0.216654	−	0.976248i	$-0.569514\pi$
$173$	−5.10510e9	−0.433308	−0.216654	+	0.976248i	$0.569514\pi$
$174$	2.50948e8	0.0207545
$175$	−1.03195e10	−0.831738
$176$	7.30149e9	0.573594
$177$	6.72072e9	0.514678
$178$	−1.66488e10	−1.24306
$179$	1.56901e10	1.14232	0.571158	−	0.820840i	$-0.306494\pi$
$179$	1.56901e10	1.14232	0.571158	+	0.820840i	$0.306494\pi$
$180$	2.42028e9	0.171846
$181$	−1.38232e10	−0.957317	−0.478659	−	0.878001i	$-0.658877\pi$
$181$	−1.38232e10	−0.957317	−0.478659	+	0.878001i	$0.658877\pi$
$182$	−9.99310e8	−0.0675117
$183$	1.13986e10	0.751314
$184$	1.10896e9	0.0713238
$185$	4.70652e10	2.95411
$186$	1.89991e10	1.16393
$187$	0	0
$188$	3.94248e9	0.230175
$189$	5.92123e9	0.337547
$190$	−3.34672e10	−1.86307
$191$	8.25387e9	0.448753	0.224376	−	0.974503i	$-0.427965\pi$
$191$	8.25387e9	0.448753	0.224376	+	0.974503i	$0.427965\pi$
$192$	1.59788e10	0.848573
$193$	−2.79430e10	−1.44966	−0.724828	−	0.688929i	$-0.758081\pi$
$193$	−2.79430e10	−1.44966	−0.724828	+	0.688929i	$0.758081\pi$
$194$	5.76093e9	0.292001
$195$	−7.19738e9	−0.356467
$196$	4.00165e9	0.193681
$197$	−3.02715e10	−1.43198	−0.715988	−	0.698113i	$-0.754024\pi$
$197$	−3.02715e10	−1.43198	−0.715988	+	0.698113i	$0.754024\pi$
$198$	−6.21984e9	−0.287598
$199$	−2.62292e10	−1.18562	−0.592810	−	0.805342i	$-0.701982\pi$
$199$	−2.62292e10	−1.18562	−0.592810	+	0.805342i	$0.701982\pi$
$200$	6.49204e10	2.86910
$201$	−1.03179e10	−0.445871
$202$	−6.93579e9	−0.293099
$203$	2.31826e8	0.00958144
$204$	0	0
$205$	−7.73725e10	−3.05981
$206$	1.32241e10	0.511640
$207$	−7.32188e8	−0.0277176
$208$	4.87264e9	0.180501
$209$	−2.34967e10	−0.851820
$210$	1.13806e10	0.403811
$211$	1.09711e9	0.0381048	0.0190524	−	0.999818i	$-0.493935\pi$
$211$	1.09711e9	0.0381048	0.0190524	+	0.999818i	$0.493935\pi$
$212$	1.13488e9	0.0385868
$213$	−2.98399e10	−0.993320
$214$	2.20086e10	0.717350
$215$	−1.12926e10	−0.360430
$216$	−3.72508e10	−1.16438
$217$	1.75514e10	0.537334
$218$	−2.96303e10	−0.888549
$219$	4.23297e10	1.24350
$220$	1.10733e10	0.318696
$221$	0	0
$222$	−3.77442e10	−1.04295
$223$	−4.13547e10	−1.11983	−0.559916	−	0.828549i	$-0.689167\pi$
$223$	−4.13547e10	−1.11983	−0.559916	+	0.828549i	$0.689167\pi$
$224$	4.95170e9	0.131413
$225$	−4.28637e10	−1.11498
$226$	5.27900e9	0.134606
$227$	4.74605e10	1.18636	0.593180	−	0.805070i	$-0.297872\pi$
$227$	4.74605e10	1.18636	0.593180	+	0.805070i	$0.297872\pi$
$228$	−7.33236e9	−0.179695
$229$	−2.55438e10	−0.613799	−0.306899	−	0.951742i	$-0.599291\pi$
$229$	−2.55438e10	−0.613799	−0.306899	+	0.951742i	$0.599291\pi$
$230$	−4.77144e9	−0.112428
$231$	7.99009e9	0.184628
$232$	−1.45843e9	−0.0330514
$233$	−2.41242e10	−0.536229	−0.268115	−	0.963387i	$-0.586401\pi$
$233$	−2.41242e10	−0.536229	−0.268115	+	0.963387i	$0.586401\pi$
$234$	−4.15080e9	−0.0905025
$235$	−9.60173e10	−2.05373
$236$	−6.90037e9	−0.144800
$237$	−6.38693e10	−1.31500
$238$	0	0
$239$	−2.43035e10	−0.481814	−0.240907	−	0.970548i	$-0.577445\pi$
$239$	−2.43035e10	−0.481814	−0.240907	+	0.970548i	$0.577445\pi$
$240$	−5.54919e10	−1.07964
$241$	3.87672e10	0.740266	0.370133	−	0.928979i	$-0.379312\pi$
$241$	3.87672e10	0.740266	0.370133	+	0.928979i	$0.379312\pi$
$242$	1.88276e10	0.352880
$243$	4.19357e10	0.771536
$244$	−1.17033e10	−0.211375
$245$	−9.74585e10	−1.72811
$246$	6.20493e10	1.08026
$247$	−1.56805e10	−0.268054
$248$	−1.10417e11	−1.85355
$249$	−8.46145e10	−1.39491
$250$	−1.74532e11	−2.82583
$251$	−2.65809e10	−0.422705	−0.211353	−	0.977410i	$-0.567787\pi$
$251$	−2.65809e10	−0.422705	−0.211353	+	0.977410i	$0.567787\pi$
$252$	−1.79306e9	−0.0280087
$253$	−3.34993e9	−0.0514035
$254$	−3.51932e10	−0.530526
$255$	0	0
$256$	−4.20539e10	−0.611965
$257$	−5.92099e10	−0.846633	−0.423317	−	0.905982i	$-0.639134\pi$
$257$	−5.92099e10	−0.846633	−0.423317	+	0.905982i	$0.639134\pi$
$258$	9.05617e9	0.127249
$259$	−3.48682e10	−0.481483
$260$	7.38978e9	0.100289
$261$	9.62929e8	0.0128443
$262$	−6.78153e10	−0.889144
$263$	1.23170e10	0.158746	0.0793731	−	0.996845i	$-0.474708\pi$
$263$	1.23170e10	0.158746	0.0793731	+	0.996845i	$0.474708\pi$
$264$	−5.02661e10	−0.636880
$265$	−2.76395e10	−0.344290
$266$	2.47942e10	0.303656
$267$	8.88354e10	1.06976
$268$	1.05937e10	0.125442
$269$	−1.58343e11	−1.84379	−0.921897	−	0.387435i	$-0.873361\pi$
$269$	−1.58343e11	−1.84379	−0.921897	+	0.387435i	$0.873361\pi$
$270$	1.60276e11	1.83541
$271$	−1.08239e11	−1.21905	−0.609524	−	0.792767i	$-0.708640\pi$
$271$	−1.08239e11	−1.21905	−0.609524	+	0.792767i	$0.708640\pi$
$272$	0	0
$273$	5.33218e9	0.0580995
$274$	−2.65025e10	−0.284060
$275$	−1.96111e11	−2.06778
$276$	−1.04538e9	−0.0108438
$277$	−5.35501e10	−0.546515	−0.273257	−	0.961941i	$-0.588101\pi$
$277$	−5.35501e10	−0.546515	−0.273257	+	0.961941i	$0.588101\pi$
$278$	5.88338e10	0.590779
$279$	7.29028e10	0.720320
$280$	−6.61406e10	−0.643068
$281$	2.49764e10	0.238974	0.119487	−	0.992836i	$-0.461875\pi$
$281$	2.49764e10	0.238974	0.119487	+	0.992836i	$0.461875\pi$
$282$	7.70017e10	0.725069
$283$	8.45073e10	0.783169	0.391585	−	0.920142i	$-0.371927\pi$
$283$	8.45073e10	0.783169	0.391585	+	0.920142i	$0.371927\pi$
$284$	3.06376e10	0.279461
$285$	1.78576e11	1.60333
$286$	−1.89909e10	−0.167841
$287$	5.73213e10	0.498710
$288$	2.05677e10	0.176165
$289$	0	0
$290$	6.27510e9	0.0520990
$291$	−3.07395e10	−0.251292
$292$	−4.34612e10	−0.349847
$293$	−1.26184e11	−1.00023	−0.500116	−	0.865958i	$-0.666709\pi$
$293$	−1.26184e11	−1.00023	−0.500116	+	0.865958i	$0.666709\pi$
$294$	7.81574e10	0.610109
$295$	1.68055e11	1.29197
$296$	2.19358e11	1.66089
$297$	1.12527e11	0.839174
$298$	1.63624e11	1.20192
$299$	−2.23557e9	−0.0161759
$300$	−6.11983e10	−0.436208
$301$	8.36611e9	0.0587455
$302$	8.86298e10	0.613124
$303$	3.70084e10	0.252237
$304$	−1.20896e11	−0.811863
$305$	2.85028e11	1.88599
$306$	0	0
$307$	3.13729e10	0.201573	0.100786	−	0.994908i	$-0.467864\pi$
$307$	3.13729e10	0.201573	0.100786	+	0.994908i	$0.467864\pi$
$308$	−8.20367e9	−0.0519434
$309$	−7.05620e10	−0.440309
$310$	4.75084e11	2.92175
$311$	1.11315e11	0.674735	0.337368	−	0.941373i	$-0.390463\pi$
$311$	1.11315e11	0.674735	0.337368	+	0.941373i	$0.390463\pi$
$312$	−3.35450e10	−0.200416
$313$	−1.05855e11	−0.623394	−0.311697	−	0.950181i	$-0.600897\pi$
$313$	−1.05855e11	−0.623394	−0.311697	+	0.950181i	$0.600897\pi$
$314$	−2.60930e11	−1.51475
$315$	4.36693e10	0.249907
$316$	6.55765e10	0.369962
$317$	−1.05802e11	−0.588474	−0.294237	−	0.955733i	$-0.595065\pi$
$317$	−1.05802e11	−0.588474	−0.294237	+	0.955733i	$0.595065\pi$
$318$	2.21657e10	0.121551
$319$	4.40562e9	0.0238204
$320$	3.99559e11	2.13013
$321$	−1.17435e11	−0.617340
$322$	3.53491e9	0.0183243
$323$	0	0
$324$	1.73106e10	0.0872689
$325$	−1.30874e11	−0.650698
$326$	−6.58693e10	−0.323001
$327$	1.58103e11	0.764671
$328$	−3.60612e11	−1.72031
$329$	7.11344e10	0.334732
$330$	2.16277e11	1.00391
$331$	−1.63950e11	−0.750733	−0.375367	−	0.926876i	$-0.622483\pi$
$331$	−1.63950e11	−0.750733	−0.375367	+	0.926876i	$0.622483\pi$
$332$	8.68763e10	0.392446
$333$	−1.44831e11	−0.645449
$334$	−5.83810e10	−0.256692
$335$	−2.58005e11	−1.11925
$336$	4.11111e10	0.175967
$337$	1.50386e11	0.635144	0.317572	−	0.948234i	$-0.397132\pi$
$337$	1.50386e11	0.635144	0.317572	+	0.948234i	$0.397132\pi$
$338$	1.99982e11	0.833426
$339$	−2.81680e10	−0.115840
$340$	0	0
$341$	3.33547e11	1.33586
$342$	1.02987e11	0.407065
$343$	1.52193e11	0.593705
$344$	−5.26317e10	−0.202644
$345$	2.54597e10	0.0967536
$346$	1.02374e11	0.384016
$347$	−2.37865e10	−0.0880741	−0.0440370	−	0.999030i	$-0.514022\pi$
$347$	−2.37865e10	−0.0880741	−0.0440370	+	0.999030i	$0.514022\pi$
$348$	1.37482e9	0.00502502
$349$	4.04400e11	1.45914	0.729570	−	0.683907i	$-0.239720\pi$
$349$	4.04400e11	1.45914	0.729570	+	0.683907i	$0.239720\pi$
$350$	2.06940e11	0.737122
$351$	7.50946e10	0.264075
$352$	9.41018e10	0.326705
$353$	4.98816e10	0.170984	0.0854918	−	0.996339i	$-0.472754\pi$
$353$	4.98816e10	0.170984	0.0854918	+	0.996339i	$0.472754\pi$
$354$	−1.34773e11	−0.456130
$355$	−7.46164e11	−2.49349
$356$	−9.12100e10	−0.300966
$357$	0	0
$358$	−3.14639e11	−1.01237
$359$	1.03719e11	0.329559	0.164779	−	0.986330i	$-0.447309\pi$
$359$	1.03719e11	0.329559	0.164779	+	0.986330i	$0.447309\pi$
$360$	−2.74726e11	−0.862061
$361$	6.63648e10	0.205663
$362$	2.77202e11	0.848415
$363$	−1.00462e11	−0.303683
$364$	−5.47471e9	−0.0163457
$365$	1.05848e12	3.12150
$366$	−2.28580e11	−0.665846
$367$	4.35557e10	0.125328	0.0626640	−	0.998035i	$-0.480040\pi$
$367$	4.35557e10	0.125328	0.0626640	+	0.998035i	$0.480040\pi$
$368$	−1.72362e10	−0.0489923
$369$	2.38094e11	0.668543
$370$	−9.43816e11	−2.61806
$371$	2.04767e10	0.0561148
$372$	1.04086e11	0.281806
$373$	−2.49530e11	−0.667473	−0.333737	−	0.942666i	$-0.608310\pi$
$373$	−2.49530e11	−0.667473	−0.333737	+	0.942666i	$0.608310\pi$
$374$	0	0
$375$	9.31280e11	2.43186
$376$	−4.47510e11	−1.15467
$377$	2.94008e9	0.00749590
$378$	−1.18741e11	−0.299148
$379$	1.02770e11	0.255852	0.127926	−	0.991784i	$-0.459168\pi$
$379$	1.02770e11	0.255852	0.127926	+	0.991784i	$0.459168\pi$
$380$	−1.83350e11	−0.451081
$381$	1.87786e11	0.456562
$382$	−1.65518e11	−0.397704
$383$	1.80024e10	0.0427499	0.0213749	−	0.999772i	$-0.493196\pi$
$383$	1.80024e10	0.0427499	0.0213749	+	0.999772i	$0.493196\pi$
$384$	−1.83575e11	−0.430847
$385$	1.99797e11	0.463463
$386$	5.60352e11	1.28475
$387$	3.47500e10	0.0787509
$388$	3.15612e10	0.0706985
$389$	−8.51136e9	−0.0188463	−0.00942314	−	0.999956i	$-0.503000\pi$
$389$	−8.51136e9	−0.0188463	−0.00942314	+	0.999956i	$0.503000\pi$
$390$	1.44332e11	0.315916
$391$	0	0
$392$	−4.54227e11	−0.971595
$393$	3.61853e11	0.765183
$394$	6.07046e11	1.26908
$395$	−1.59709e12	−3.30097
$396$	−3.40753e10	−0.0696324
$397$	4.11624e11	0.831655	0.415828	−	0.909443i	$-0.363492\pi$
$397$	4.11624e11	0.831655	0.415828	+	0.909443i	$0.363492\pi$
$398$	5.25984e11	1.05075
$399$	−1.32298e11	−0.261322
$400$	−1.00904e12	−1.97079
$401$	5.74069e11	1.10870	0.554350	−	0.832284i	$-0.312967\pi$
$401$	5.74069e11	1.10870	0.554350	+	0.832284i	$0.312967\pi$
$402$	2.06909e11	0.395150
$403$	2.22592e11	0.420375
$404$	−3.79976e10	−0.0709644
$405$	−4.21592e11	−0.778654
$406$	−4.64890e9	−0.00849148
$407$	−6.62634e11	−1.19701
$408$	0	0
$409$	3.72832e11	0.658806	0.329403	−	0.944189i	$-0.393152\pi$
$409$	3.72832e11	0.658806	0.329403	+	0.944189i	$0.393152\pi$
$410$	1.55158e12	2.71173
$411$	1.41414e11	0.244457
$412$	7.24481e10	0.123877
$413$	−1.24504e11	−0.210575
$414$	1.46828e10	0.0245645
$415$	−2.11583e12	−3.50159
$416$	6.27987e10	0.102809
$417$	−3.13929e11	−0.508415
$418$	4.71187e11	0.754919
$419$	5.40188e11	0.856214	0.428107	−	0.903728i	$-0.359181\pi$
$419$	5.40188e11	0.856214	0.428107	+	0.903728i	$0.359181\pi$
$420$	6.23485e10	0.0977697
$421$	−6.79434e11	−1.05409	−0.527045	−	0.849837i	$-0.676700\pi$
$421$	−6.79434e11	−1.05409	−0.527045	+	0.849837i	$0.676700\pi$
$422$	−2.20008e10	−0.0337701
$423$	2.95468e11	0.448724
$424$	−1.28820e11	−0.193570
$425$	0	0
$426$	5.98391e11	0.880323
$427$	−2.11163e11	−0.307392
$428$	1.20574e11	0.173683
$429$	1.01332e11	0.144441
$430$	2.26455e11	0.319428
$431$	−1.12689e12	−1.57302	−0.786511	−	0.617577i	$-0.788114\pi$
$431$	−1.12689e12	−1.57302	−0.786511	+	0.617577i	$0.788114\pi$
$432$	5.78980e11	0.799810
$433$	−1.10436e12	−1.50979	−0.754893	−	0.655848i	$-0.772311\pi$
$433$	−1.10436e12	−1.50979	−0.754893	+	0.655848i	$0.772311\pi$
$434$	−3.51966e11	−0.476208
$435$	−3.34830e10	−0.0448356
$436$	−1.62329e11	−0.215133
$437$	5.54673e10	0.0727563
$438$	−8.48853e11	−1.10204
$439$	1.12796e12	1.44945	0.724725	−	0.689038i	$-0.241967\pi$
$439$	1.12796e12	1.44945	0.724725	+	0.689038i	$0.241967\pi$
$440$	−1.25693e12	−1.59873
$441$	2.99903e11	0.377578
$442$	0	0
$443$	−1.35306e12	−1.66917	−0.834587	−	0.550877i	$-0.814294\pi$
$443$	−1.35306e12	−1.66917	−0.834587	+	0.550877i	$0.814294\pi$
$444$	−2.06781e11	−0.252515
$445$	2.22138e12	2.68536
$446$	8.29302e11	0.992443
$447$	−8.73075e11	−1.03435
$448$	−2.96013e11	−0.347184
$449$	4.41678e11	0.512859	0.256429	−	0.966563i	$-0.417454\pi$
$449$	4.41678e11	0.512859	0.256429	+	0.966563i	$0.417454\pi$
$450$	8.59561e11	0.988144
$451$	1.08933e12	1.23984
$452$	2.89209e10	0.0325904
$453$	−4.72916e11	−0.527645
$454$	−9.51744e11	−1.05140
$455$	1.33334e11	0.145844
$456$	8.32295e11	0.901437
$457$	−5.10055e11	−0.547008	−0.273504	−	0.961871i	$-0.588183\pi$
$457$	−5.10055e11	−0.547008	−0.273504	+	0.961871i	$0.588183\pi$
$458$	5.12239e11	0.543974
$459$	0	0
$460$	−2.61402e10	−0.0272207
$461$	1.40177e12	1.44551	0.722755	−	0.691104i	$-0.242875\pi$
$461$	1.40177e12	1.44551	0.722755	+	0.691104i	$0.242875\pi$
$462$	−1.60228e11	−0.163625
$463$	−8.12639e8	−0.000821832 0	−0.000410916	−	1.00000i	$-0.500131\pi$
$463$	−8.12639e8	−0.000821832 0	−0.000410916		1.00000i	$0.500131\pi$
$464$	2.26681e10	0.0227030
$465$	−2.53498e12	−2.51441
$466$	4.83771e11	0.475229
$467$	−5.50598e11	−0.535684	−0.267842	−	0.963463i	$-0.586311\pi$
$467$	−5.50598e11	−0.535684	−0.267842	+	0.963463i	$0.586311\pi$
$468$	−2.27401e10	−0.0219122
$469$	1.91143e11	0.182424
$470$	1.92547e12	1.82011
$471$	1.39228e12	1.30357
$472$	7.83260e11	0.726385
$473$	1.58989e11	0.146047
$474$	1.28079e12	1.16540
$475$	3.24716e12	2.92673
$476$	0	0
$477$	8.50534e10	0.0752244
$478$	4.87368e11	0.427004
$479$	−4.11777e11	−0.357398	−0.178699	−	0.983904i	$-0.557189\pi$
$479$	−4.11777e11	−0.357398	−0.178699	+	0.983904i	$0.557189\pi$
$480$	−7.15180e11	−0.614936
$481$	−4.42208e11	−0.376681
$482$	−7.77413e11	−0.656055
$483$	−1.88618e10	−0.0157696
$484$	1.03147e11	0.0854382
$485$	−7.68659e11	−0.630806
$486$	−8.40953e11	−0.683768
$487$	−1.25805e12	−1.01349	−0.506743	−	0.862097i	$-0.669151\pi$
$487$	−1.25805e12	−1.01349	−0.506743	+	0.862097i	$0.669151\pi$
$488$	1.32844e12	1.06036
$489$	3.51469e11	0.277969
$490$	1.95437e12	1.53153
$491$	5.36226e11	0.416372	0.208186	−	0.978089i	$-0.433244\pi$
$491$	5.36226e11	0.416372	0.208186	+	0.978089i	$0.433244\pi$
$492$	3.39936e11	0.261550
$493$	0	0
$494$	3.14446e11	0.237561
$495$	8.29889e11	0.621293
$496$	1.71619e12	1.27320
$497$	5.52795e11	0.406406
$498$	1.69681e12	1.23623
$499$	−1.36830e12	−0.987935	−0.493967	−	0.869480i	$-0.664454\pi$
$499$	−1.36830e12	−0.987935	−0.493967	+	0.869480i	$0.664454\pi$
$500$	−9.56173e11	−0.684182
$501$	3.11512e11	0.220905
$502$	5.33036e11	0.374619
$503$	−2.29853e12	−1.60101	−0.800507	−	0.599324i	$-0.795436\pi$
$503$	−2.29853e12	−1.60101	−0.800507	+	0.599324i	$0.795436\pi$
$504$	2.03530e11	0.140505
$505$	9.25416e11	0.633178
$506$	6.71773e10	0.0455560
$507$	−1.06708e12	−0.717233
$508$	−1.92805e11	−0.128449
$509$	−1.11229e11	−0.0734491	−0.0367246	−	0.999325i	$-0.511692\pi$
$509$	−1.11229e11	−0.0734491	−0.0367246	+	0.999325i	$0.511692\pi$
$510$	0	0
$511$	−7.84172e11	−0.508765
$512$	1.72172e12	1.10726
$513$	−1.86319e12	−1.18776
$514$	1.18736e12	0.750322
$515$	−1.76444e12	−1.10529
$516$	4.96141e10	0.0308093
$517$	1.35183e12	0.832177
$518$	6.99225e11	0.426710
$519$	−5.46255e11	−0.330478
$520$	−8.38812e11	−0.503095
$521$	−2.42441e12	−1.44157	−0.720785	−	0.693159i	$-0.756218\pi$
$521$	−2.42441e12	−1.44157	−0.720785	+	0.693159i	$0.756218\pi$
$522$	−1.93100e10	−0.0113832
$523$	−2.27833e12	−1.33156	−0.665778	−	0.746150i	$-0.731900\pi$
$523$	−2.27833e12	−1.33156	−0.665778	+	0.746150i	$0.731900\pi$
$524$	−3.71525e11	−0.215277
$525$	−1.10420e12	−0.634355
$526$	−2.46997e11	−0.140688
$527$	0	0
$528$	7.81274e11	0.437472
$529$	−1.79324e12	−0.995609
$530$	5.54266e11	0.305124
$531$	−5.17147e11	−0.282285
$532$	1.35835e11	0.0735204
$533$	7.26964e11	0.390158
$534$	−1.78145e12	−0.948064
$535$	−2.93653e12	−1.54968
$536$	−1.20249e12	−0.629275
$537$	1.67887e12	0.871229
$538$	3.17530e12	1.63405
$539$	1.37212e12	0.700235
$540$	8.78072e11	0.444384
$541$	−4.55216e11	−0.228470	−0.114235	−	0.993454i	$-0.536442\pi$
$541$	−4.55216e11	−0.228470	−0.114235	+	0.993454i	$0.536442\pi$
$542$	2.17055e12	1.08037
$543$	−1.47911e12	−0.730133
$544$	0	0
$545$	3.95345e12	1.91952
$546$	−1.06928e11	−0.0514903
$547$	1.30843e12	0.624897	0.312449	−	0.949935i	$-0.398851\pi$
$547$	1.30843e12	0.624897	0.312449	+	0.949935i	$0.398851\pi$
$548$	−1.45194e11	−0.0687757
$549$	−8.77100e11	−0.412073
$550$	3.93269e12	1.83256
$551$	−7.29472e10	−0.0337153
$552$	1.18661e11	0.0543977
$553$	1.18320e12	0.538016
$554$	1.07386e12	0.484344
$555$	5.03607e12	2.25306
$556$	3.22320e11	0.143038
$557$	−1.03372e12	−0.455045	−0.227523	−	0.973773i	$-0.573063\pi$
$557$	−1.03372e12	−0.455045	−0.227523	+	0.973773i	$0.573063\pi$
$558$	−1.46195e12	−0.638378
$559$	1.06101e11	0.0459586
$560$	1.02801e12	0.441723
$561$	0	0
$562$	−5.00861e11	−0.211789
$563$	−4.14096e12	−1.73705	−0.868526	−	0.495643i	$-0.834932\pi$
$563$	−4.14096e12	−1.73705	−0.868526	+	0.495643i	$0.834932\pi$
$564$	4.21853e11	0.175552
$565$	−7.04356e11	−0.290787
$566$	−1.69466e12	−0.694078
$567$	3.12336e11	0.126911
$568$	−3.47767e12	−1.40191
$569$	1.09427e12	0.437641	0.218821	−	0.975765i	$-0.429779\pi$
$569$	1.09427e12	0.437641	0.218821	+	0.975765i	$0.429779\pi$
$570$	−3.58106e12	−1.42094
$571$	9.36336e11	0.368612	0.184306	−	0.982869i	$-0.440996\pi$
$571$	9.36336e11	0.368612	0.184306	+	0.982869i	$0.440996\pi$
$572$	−1.04041e11	−0.0406371
$573$	8.83179e11	0.342258
$574$	−1.14949e12	−0.441978
$575$	4.62949e11	0.176615
$576$	−1.22954e12	−0.465416
$577$	−3.33902e12	−1.25409	−0.627044	−	0.778984i	$-0.715735\pi$
$577$	−3.33902e12	−1.25409	−0.627044	+	0.778984i	$0.715735\pi$
$578$	0	0
$579$	−2.98995e12	−1.10563
$580$	3.43780e10	0.0126141
$581$	1.56751e12	0.570714
$582$	6.16430e11	0.222705
$583$	3.89138e11	0.139507
$584$	4.93327e12	1.75500
$585$	5.53825e11	0.195511
$586$	2.53042e12	0.886448
$587$	3.96101e12	1.37700	0.688501	−	0.725236i	$-0.258269\pi$
$587$	3.96101e12	1.37700	0.688501	+	0.725236i	$0.258269\pi$
$588$	4.28184e11	0.147718
$589$	−5.52279e12	−1.89078
$590$	−3.37008e12	−1.14500
$591$	−3.23911e12	−1.09215
$592$	−3.40943e12	−1.14086
$593$	3.43524e12	1.14080	0.570401	−	0.821366i	$-0.306788\pi$
$593$	3.43524e12	1.14080	0.570401	+	0.821366i	$0.306788\pi$
$594$	−2.25654e12	−0.743712
$595$	0	0
$596$	8.96413e11	0.291005
$597$	−2.80657e12	−0.904256
$598$	4.48307e10	0.0143357
$599$	−2.49343e12	−0.791364	−0.395682	−	0.918388i	$-0.629492\pi$
$599$	−2.49343e12	−0.791364	−0.395682	+	0.918388i	$0.629492\pi$
$600$	6.94661e12	2.18823
$601$	−3.17215e12	−0.991789	−0.495894	−	0.868383i	$-0.665160\pi$
$601$	−3.17215e12	−0.991789	−0.495894	+	0.868383i	$0.665160\pi$
$602$	−1.67769e11	−0.0520627
$603$	7.93944e11	0.244547
$604$	4.85557e11	0.148448
$605$	−2.51210e12	−0.762320
$606$	−7.42143e11	−0.223543
$607$	−4.31465e12	−1.29002	−0.645010	−	0.764174i	$-0.723147\pi$
$607$	−4.31465e12	−1.29002	−0.645010	+	0.764174i	$0.723147\pi$
$608$	−1.55812e12	−0.462417
$609$	2.48059e10	0.00730763
$610$	−5.71578e12	−1.67144
$611$	9.02144e11	0.261873
$612$	0	0
$613$	3.26850e12	0.934924	0.467462	−	0.884013i	$-0.345168\pi$
$613$	3.26850e12	0.934924	0.467462	+	0.884013i	$0.345168\pi$
$614$	−6.29132e11	−0.178642
$615$	−8.27900e12	−2.33367
$616$	9.31198e11	0.260573
$617$	−5.06880e12	−1.40806	−0.704031	−	0.710169i	$-0.748619\pi$
$617$	−5.06880e12	−1.40806	−0.704031	+	0.710169i	$0.748619\pi$
$618$	1.41501e12	0.390220
$619$	7.06562e12	1.93438	0.967191	−	0.254049i	$-0.0817626\pi$
$619$	7.06562e12	1.93438	0.967191	+	0.254049i	$0.0817626\pi$
$620$	2.60274e12	0.707406
$621$	−2.65636e11	−0.0716762
$622$	−2.23225e12	−0.597979
$623$	−1.64571e12	−0.437680
$624$	5.21382e11	0.137666
$625$	1.31193e13	3.43915
$626$	2.12276e12	0.552479
$627$	−2.51419e12	−0.649671
$628$	−1.42950e12	−0.366746
$629$	0	0
$630$	−8.75716e11	−0.221478
$631$	7.16033e12	1.79805	0.899023	−	0.437902i	$-0.144278\pi$
$631$	7.16033e12	1.79805	0.899023	+	0.437902i	$0.144278\pi$
$632$	−7.44358e12	−1.85590
$633$	1.17393e11	0.0290620
$634$	2.12169e12	0.521530
$635$	4.69569e12	1.14609
$636$	1.21434e11	0.0294296
$637$	9.15685e11	0.220353
$638$	−8.83475e10	−0.0211106
$639$	2.29613e12	0.544806
$640$	−4.59040e12	−1.08154
$641$	−2.36539e11	−0.0553404	−0.0276702	−	0.999617i	$-0.508809\pi$
$641$	−2.36539e11	−0.0553404	−0.0276702	+	0.999617i	$0.508809\pi$
$642$	2.35497e12	0.547113
$643$	2.08306e12	0.480566	0.240283	−	0.970703i	$-0.422760\pi$
$643$	2.08306e12	0.480566	0.240283	+	0.970703i	$0.422760\pi$
$644$	1.93660e10	0.00443663
$645$	−1.20833e12	−0.274895
$646$	0	0
$647$	−2.70502e12	−0.606877	−0.303439	−	0.952851i	$-0.598135\pi$
$647$	−2.70502e12	−0.606877	−0.303439	+	0.952851i	$0.598135\pi$
$648$	−1.96492e12	−0.437782
$649$	−2.36606e12	−0.523510
$650$	2.62447e12	0.576676
$651$	1.87804e12	0.409817
$652$	−3.60864e11	−0.0782040
$653$	5.39287e12	1.16067	0.580337	−	0.814376i	$-0.302921\pi$
$653$	5.39287e12	1.16067	0.580337	+	0.814376i	$0.302921\pi$
$654$	−3.17050e12	−0.677684
$655$	9.04834e12	1.92080
$656$	5.60490e12	1.18168
$657$	−3.25719e12	−0.682022
$658$	−1.42648e12	−0.296654
$659$	1.48113e12	0.305921	0.152960	−	0.988232i	$-0.451119\pi$
$659$	1.48113e12	0.305921	0.152960	+	0.988232i	$0.451119\pi$
$660$	1.18487e12	0.243065
$661$	4.29716e12	0.875539	0.437769	−	0.899087i	$-0.355769\pi$
$661$	4.29716e12	0.875539	0.437769	+	0.899087i	$0.355769\pi$
$662$	3.28775e12	0.665332
$663$	0	0
$664$	−9.86131e12	−1.96870
$665$	−3.30819e12	−0.655984
$666$	2.90435e12	0.572024
$667$	−1.04001e10	−0.00203457
$668$	−3.19839e11	−0.0621495
$669$	−4.42503e12	−0.854081
$670$	5.17388e12	0.991927
$671$	−4.01293e12	−0.764206
$672$	5.29841e11	0.100227
$673$	4.96387e12	0.932723	0.466361	−	0.884594i	$-0.345565\pi$
$673$	4.96387e12	0.932723	0.466361	+	0.884594i	$0.345565\pi$
$674$	−3.01574e12	−0.562892
$675$	−1.55508e13	−2.88328
$676$	1.09560e12	0.201787
$677$	−6.78832e12	−1.24198	−0.620988	−	0.783820i	$-0.713269\pi$
$677$	−6.78832e12	−1.24198	−0.620988	+	0.783820i	$0.713269\pi$
$678$	5.64863e11	0.102662
$679$	5.69460e11	0.102813
$680$	0	0
$681$	5.07837e12	0.904820
$682$	−6.68874e12	−1.18390
$683$	−2.03815e12	−0.358379	−0.179190	−	0.983815i	$-0.557348\pi$
$683$	−2.03815e12	−0.358379	−0.179190	+	0.983815i	$0.557348\pi$
$684$	5.64211e11	0.0985574
$685$	3.53613e12	0.613650
$686$	−3.05198e12	−0.526167
$687$	−2.73324e12	−0.468136
$688$	8.18041e11	0.139196
$689$	2.59691e11	0.0439006
$690$	−5.10553e11	−0.0857471
$691$	7.41249e12	1.23684	0.618419	−	0.785848i	$-0.287773\pi$
$691$	7.41249e12	1.23684	0.618419	+	0.785848i	$0.287773\pi$
$692$	5.60857e11	0.0929769
$693$	−6.14823e11	−0.101263
$694$	4.77000e11	0.0780550
$695$	−7.84997e12	−1.27625
$696$	−1.56055e11	−0.0252079
$697$	0	0
$698$	−8.10959e12	−1.29315
$699$	−2.58133e12	−0.408975
$700$	1.13372e12	0.178470
$701$	8.92468e12	1.39592	0.697962	−	0.716135i	$-0.254090\pi$
$701$	8.92468e12	1.39592	0.697962	+	0.716135i	$0.254090\pi$
$702$	−1.50590e12	−0.234034
$703$	1.09717e13	1.69425
$704$	−5.62542e12	−0.863134
$705$	−1.02740e13	−1.56635
$706$	−1.00030e12	−0.151533
$707$	−6.85593e11	−0.103200
$708$	−7.38352e11	−0.110437
$709$	−4.22575e12	−0.628053	−0.314026	−	0.949414i	$-0.601678\pi$
$709$	−4.22575e12	−0.628053	−0.314026	+	0.949414i	$0.601678\pi$
$710$	1.49631e13	2.20983
$711$	4.91462e12	0.721235
$712$	1.03532e13	1.50979
$713$	−7.87386e11	−0.114100
$714$	0	0
$715$	2.53388e12	0.362584
$716$	−1.72375e12	−0.245112
$717$	−2.60052e12	−0.367472
$718$	−2.07991e12	−0.292069
$719$	3.96748e12	0.553649	0.276825	−	0.960920i	$-0.410718\pi$
$719$	3.96748e12	0.553649	0.276825	+	0.960920i	$0.410718\pi$
$720$	4.27000e12	0.592149
$721$	1.30719e12	0.180148
$722$	−1.33084e12	−0.182267
$723$	4.14817e12	0.564591
$724$	1.51865e12	0.205416
$725$	−6.08842e11	−0.0818434
$726$	2.01459e12	0.269136
$727$	4.61627e12	0.612895	0.306447	−	0.951888i	$-0.400860\pi$
$727$	4.61627e12	0.612895	0.306447	+	0.951888i	$0.400860\pi$
$728$	6.21433e11	0.0819980
$729$	7.58858e12	0.995146
$730$	−2.12260e13	−2.76641
$731$	0	0
$732$	−1.25227e12	−0.161213
$733$	8.49490e12	1.08690	0.543451	−	0.839441i	$-0.317117\pi$
$733$	8.49490e12	1.08690	0.543451	+	0.839441i	$0.317117\pi$
$734$	−8.73439e11	−0.111071
$735$	−1.04282e13	−1.31801
$736$	−2.22141e11	−0.0279048
$737$	3.63247e12	0.453523
$738$	−4.77458e12	−0.592491
$739$	3.33909e12	0.411839	0.205920	−	0.978569i	$-0.433981\pi$
$739$	3.33909e12	0.411839	0.205920	+	0.978569i	$0.433981\pi$
$740$	−5.17068e12	−0.633877
$741$	−1.67784e12	−0.204441
$742$	−4.10627e11	−0.0497313
$743$	−5.88526e12	−0.708461	−0.354231	−	0.935158i	$-0.615257\pi$
$743$	−5.88526e12	−0.708461	−0.354231	+	0.935158i	$0.615257\pi$
$744$	−1.18148e13	−1.41367
$745$	−2.18317e13	−2.59648
$746$	5.00393e12	0.591543
$747$	6.51093e12	0.765068
$748$	0	0
$749$	2.17552e12	0.252578
$750$	−1.86753e13	−2.15522
$751$	−9.96514e12	−1.14315	−0.571576	−	0.820549i	$-0.693668\pi$
$751$	−9.96514e12	−1.14315	−0.571576	+	0.820549i	$0.693668\pi$
$752$	6.95554e12	0.793141
$753$	−2.84420e12	−0.322391
$754$	−5.89586e10	−0.00664318
$755$	−1.18255e13	−1.32452
$756$	−6.50519e11	−0.0724289
$757$	−1.18200e13	−1.30823	−0.654116	−	0.756394i	$-0.726959\pi$
$757$	−1.18200e13	−1.30823	−0.654116	+	0.756394i	$0.726959\pi$
$758$	−2.06088e12	−0.226747
$759$	−3.58449e11	−0.0392048
$760$	2.08120e13	2.26284
$761$	−5.90382e12	−0.638120	−0.319060	−	0.947735i	$-0.603367\pi$
$761$	−5.90382e12	−0.638120	−0.319060	+	0.947735i	$0.603367\pi$
$762$	−3.76574e12	−0.404625
$763$	−2.92891e12	−0.312857
$764$	−9.06788e11	−0.0962909
$765$	0	0
$766$	−3.61008e11	−0.0378868
$767$	−1.57899e12	−0.164740
$768$	−4.49985e12	−0.466737
$769$	−1.02640e12	−0.105839	−0.0529196	−	0.998599i	$-0.516853\pi$
$769$	−1.02640e12	−0.105839	−0.0529196	+	0.998599i	$0.516853\pi$
$770$	−4.00660e12	−0.410741
$771$	−6.33557e12	−0.645715
$772$	3.06988e12	0.311059
$773$	9.17802e12	0.924573	0.462286	−	0.886731i	$-0.347029\pi$
$773$	9.17802e12	0.924573	0.462286	+	0.886731i	$0.347029\pi$
$774$	−6.96855e11	−0.0697924
$775$	−4.60951e13	−4.58983
$776$	−3.58250e12	−0.354657
$777$	−3.73097e12	−0.367220
$778$	1.70682e11	0.0167024
$779$	−1.80369e13	−1.75487
$780$	7.90720e11	0.0764887
$781$	1.05053e13	1.01037
$782$	0	0
$783$	3.49348e11	0.0332147
$784$	7.05994e12	0.667388
$785$	3.48148e13	3.27228
$786$	−7.25637e12	−0.678138
$787$	4.74889e12	0.441271	0.220636	−	0.975356i	$-0.429187\pi$
$787$	4.74889e12	0.441271	0.220636	+	0.975356i	$0.429187\pi$
$788$	3.32569e12	0.307266
$789$	1.31794e12	0.121074
$790$	3.20270e13	2.92546
$791$	5.21822e11	0.0473945
$792$	3.86788e12	0.349309
$793$	−2.67803e12	−0.240484
$794$	−8.25445e12	−0.737048
$795$	−2.95748e12	−0.262585
$796$	2.88159e12	0.254404
$797$	7.41306e12	0.650781	0.325390	−	0.945580i	$-0.394504\pi$
$797$	7.41306e12	0.650781	0.325390	+	0.945580i	$0.394504\pi$
$798$	2.65302e12	0.231594
$799$	0	0
$800$	−1.30046e13	−1.12251
$801$	−6.83572e12	−0.586729
$802$	−1.15120e13	−0.982577
$803$	−1.49024e13	−1.26484
$804$	1.13355e12	0.0956727
$805$	−4.71650e11	−0.0395857
$806$	−4.46372e12	−0.372554
$807$	−1.69430e13	−1.40624
$808$	4.31311e12	0.355991
$809$	8.29607e12	0.680933	0.340466	−	0.940257i	$-0.389415\pi$
$809$	8.29607e12	0.680933	0.340466	+	0.940257i	$0.389415\pi$
$810$	8.45434e12	0.690077
$811$	1.69807e13	1.37836	0.689178	−	0.724592i	$-0.257972\pi$
$811$	1.69807e13	1.37836	0.689178	+	0.724592i	$0.257972\pi$
$812$	−2.54689e10	−0.00205593
$813$	−1.15818e13	−0.929751
$814$	1.32880e13	1.06084
$815$	8.78868e12	0.697773
$816$	0	0
$817$	−2.63251e12	−0.206714
$818$	−7.47653e12	−0.583862
$819$	−4.10301e11	−0.0318658
$820$	8.50031e12	0.656557
$821$	−1.43912e13	−1.10549	−0.552743	−	0.833352i	$-0.686419\pi$
$821$	−1.43912e13	−1.10549	−0.552743	+	0.833352i	$0.686419\pi$
$822$	−2.83582e12	−0.216648
$823$	−2.53247e12	−0.192418	−0.0962089	−	0.995361i	$-0.530672\pi$
$823$	−2.53247e12	−0.192418	−0.0962089	+	0.995361i	$0.530672\pi$
$824$	−8.22358e12	−0.621424
$825$	−2.09842e13	−1.57707
$826$	2.49672e12	0.186621
$827$	3.93590e12	0.292597	0.146298	−	0.989241i	$-0.453264\pi$
$827$	3.93590e12	0.292597	0.146298	+	0.989241i	$0.453264\pi$
$828$	8.04398e10	0.00594750
$829$	1.55976e13	1.14700	0.573500	−	0.819205i	$-0.305585\pi$
$829$	1.55976e13	1.14700	0.573500	+	0.819205i	$0.305585\pi$
$830$	4.24296e13	3.10326
$831$	−5.72997e12	−0.416819
$832$	−3.75412e12	−0.271614
$833$	0	0
$834$	6.29533e12	0.450579
$835$	7.78955e12	0.554527
$836$	2.58139e12	0.182779
$837$	2.64490e13	1.86270
$838$	−1.08326e13	−0.758813
$839$	5.06030e12	0.352571	0.176286	−	0.984339i	$-0.443592\pi$
$839$	5.06030e12	0.352571	0.176286	+	0.984339i	$0.443592\pi$
$840$	−7.07717e12	−0.490459
$841$	−1.44935e13	−0.999057
$842$	1.36249e13	0.934180
$843$	2.67252e12	0.182262
$844$	−1.20531e11	−0.00817631
$845$	−2.66829e13	−1.80044
$846$	−5.92513e12	−0.397678
$847$	1.86109e12	0.124248
$848$	2.00222e12	0.132963
$849$	9.04245e12	0.597312
$850$	0	0
$851$	1.56425e12	0.102240
$852$	3.27828e12	0.213141
$853$	1.69134e13	1.09386	0.546929	−	0.837179i	$-0.315797\pi$
$853$	1.69134e13	1.09386	0.546929	+	0.837179i	$0.315797\pi$
$854$	4.23453e12	0.272424
$855$	−1.37411e13	−0.879376
$856$	−1.36863e13	−0.871275
$857$	−4.73778e12	−0.300028	−0.150014	−	0.988684i	$-0.547932\pi$
$857$	−4.73778e12	−0.300028	−0.150014	+	0.988684i	$0.547932\pi$
$858$	−2.03206e12	−0.128010
$859$	2.24036e13	1.40394	0.701969	−	0.712208i	$-0.252305\pi$
$859$	2.24036e13	1.40394	0.701969	+	0.712208i	$0.252305\pi$
$860$	1.24063e12	0.0773391
$861$	6.13349e12	0.380359
$862$	2.25980e13	1.39408
$863$	−2.34169e13	−1.43708	−0.718541	−	0.695485i	$-0.755190\pi$
$863$	−2.34169e13	−1.43708	−0.718541	+	0.695485i	$0.755190\pi$
$864$	7.46190e12	0.455552
$865$	−1.36594e13	−0.829583
$866$	2.21461e13	1.33804
$867$	0	0
$868$	−1.92824e12	−0.115298
$869$	2.24855e13	1.33756
$870$	6.71447e11	0.0397352
$871$	2.42413e12	0.142716
$872$	1.84259e13	1.07921
$873$	2.36535e12	0.137826
$874$	−1.11231e12	−0.0644798
$875$	−1.72523e13	−0.994971
$876$	−4.65043e12	−0.266824
$877$	2.82044e12	0.160997	0.0804986	−	0.996755i	$-0.474349\pi$
$877$	2.82044e12	0.160997	0.0804986	+	0.996755i	$0.474349\pi$
$878$	−2.26194e13	−1.28456
$879$	−1.35020e13	−0.762863
$880$	1.95362e13	1.09817
$881$	1.48809e13	0.832218	0.416109	−	0.909315i	$-0.363394\pi$
$881$	1.48809e13	0.832218	0.416109	+	0.909315i	$0.363394\pi$
$882$	−6.01407e12	−0.334626
$883$	−2.31573e12	−0.128193	−0.0640966	−	0.997944i	$-0.520417\pi$
$883$	−2.31573e12	−0.128193	−0.0640966	+	0.997944i	$0.520417\pi$
$884$	0	0
$885$	1.79822e13	0.985370
$886$	2.71335e13	1.47929
$887$	−9.47146e12	−0.513760	−0.256880	−	0.966443i	$-0.582695\pi$
$887$	−9.47146e12	−0.513760	−0.256880	+	0.966443i	$0.582695\pi$
$888$	2.34717e13	1.26674
$889$	−3.47880e12	−0.186798
$890$	−4.45462e13	−2.37988
$891$	5.93562e12	0.315512
$892$	4.54332e12	0.240288
$893$	−2.23834e13	−1.17786
$894$	1.75081e13	0.916685
$895$	4.19811e13	2.18701
$896$	3.40080e12	0.176277
$897$	−2.39210e11	−0.0123371
$898$	−8.85714e12	−0.454517
$899$	1.03552e12	0.0528738
$900$	4.70909e12	0.239247
$901$	0	0
$902$	−2.18448e13	−1.09880
$903$	8.95190e11	0.0448044
$904$	−3.28281e12	−0.163489
$905$	−3.69860e13	−1.83282
$906$	9.48356e12	0.467621
$907$	−7.59597e12	−0.372692	−0.186346	−	0.982484i	$-0.559665\pi$
$907$	−7.59597e12	−0.372692	−0.186346	+	0.982484i	$0.559665\pi$
$908$	−5.21412e12	−0.254563
$909$	−2.84772e12	−0.138344
$910$	−2.67380e12	−0.129254
$911$	2.28116e13	1.09729	0.548647	−	0.836054i	$-0.315143\pi$
$911$	2.28116e13	1.09729	0.548647	+	0.836054i	$0.315143\pi$
$912$	−1.29362e13	−0.619196
$913$	2.97890e13	1.41885
$914$	1.02283e13	0.484782
$915$	3.04986e13	1.43842
$916$	2.80630e12	0.131706
$917$	−6.70345e12	−0.313067
$918$	0	0
$919$	1.37159e13	0.634315	0.317158	−	0.948373i	$-0.397272\pi$
$919$	1.37159e13	0.634315	0.317158	+	0.948373i	$0.397272\pi$
$920$	2.96717e12	0.136552
$921$	3.35696e12	0.153737
$922$	−2.81101e13	−1.28107
$923$	7.01069e12	0.317946
$924$	−8.77809e11	−0.0396165
$925$	9.15738e13	4.11276
$926$	1.62962e10	0.000728342 0
$927$	5.42961e12	0.241496
$928$	2.92146e11	0.0129311
$929$	−3.39205e12	−0.149414	−0.0747070	−	0.997206i	$-0.523802\pi$
$929$	−3.39205e12	−0.149414	−0.0747070	+	0.997206i	$0.523802\pi$
$930$	5.08349e13	2.22838
$931$	−2.27193e13	−0.991110
$932$	2.65033e12	0.115061
$933$	1.19110e13	0.514611
$934$	1.10414e13	0.474746
$935$	0	0
$936$	2.58123e12	0.109922
$937$	3.08488e12	0.130740	0.0653702	−	0.997861i	$-0.479177\pi$
$937$	3.08488e12	0.130740	0.0653702	+	0.997861i	$0.479177\pi$
$938$	−3.83306e12	−0.161671
$939$	−1.13267e13	−0.475454
$940$	1.05487e13	0.440679
$941$	−1.10199e13	−0.458167	−0.229084	−	0.973407i	$-0.573573\pi$
$941$	−1.10199e13	−0.458167	−0.229084	+	0.973407i	$0.573573\pi$
$942$	−2.79200e13	−1.15528
$943$	−2.57153e12	−0.105898
$944$	−1.21740e13	−0.498953
$945$	1.58431e13	0.646245
$946$	−3.18827e12	−0.129433
$947$	−2.51700e13	−1.01697	−0.508485	−	0.861071i	$-0.669794\pi$
$947$	−2.51700e13	−1.01697	−0.508485	+	0.861071i	$0.669794\pi$
$948$	7.01681e12	0.282165
$949$	−9.94508e12	−0.398025
$950$	−6.51165e13	−2.59379
$951$	−1.13210e13	−0.448821
$952$	0	0
$953$	4.52926e13	1.77873	0.889364	−	0.457200i	$-0.151148\pi$
$953$	4.52926e13	1.77873	0.889364	+	0.457200i	$0.151148\pi$
$954$	−1.70561e12	−0.0666671
$955$	2.20844e13	0.859153
$956$	2.67004e12	0.103385
$957$	4.71409e11	0.0181675
$958$	8.25752e12	0.316741
$959$	−2.61974e12	−0.100017
$960$	4.27536e13	1.62462
$961$	5.19592e13	1.96520
$962$	8.86776e12	0.333831
$963$	9.03640e12	0.338592
$964$	−4.25905e12	−0.158842
$965$	−7.47655e13	−2.77542
$966$	3.78242e11	0.0139757
$967$	−2.02193e13	−0.743614	−0.371807	−	0.928310i	$-0.621262\pi$
$967$	−2.02193e13	−0.743614	−0.371807	+	0.928310i	$0.621262\pi$
$968$	−1.17082e13	−0.428599
$969$	0	0
$970$	1.54142e13	0.559047
$971$	3.04494e13	1.09924	0.549620	−	0.835415i	$-0.314772\pi$
$971$	3.04494e13	1.09924	0.549620	+	0.835415i	$0.314772\pi$
$972$	−4.60715e12	−0.165552
$973$	5.81564e12	0.208013
$974$	2.52281e13	0.898193
$975$	−1.40038e13	−0.496278
$976$	−2.06476e13	−0.728358
$977$	3.69433e13	1.29721	0.648604	−	0.761126i	$-0.275353\pi$
$977$	3.69433e13	1.29721	0.648604	+	0.761126i	$0.275353\pi$
$978$	−7.04814e12	−0.246348
$979$	−3.12750e13	−1.08811
$980$	1.07070e13	0.370809
$981$	−1.21657e13	−0.419399
$982$	−1.07531e13	−0.369006
$983$	−5.15287e13	−1.76018	−0.880092	−	0.474803i	$-0.842519\pi$
$983$	−5.15287e13	−1.76018	−0.880092	+	0.474803i	$0.842519\pi$
$984$	−3.85861e13	−1.31206
$985$	−8.09957e13	−2.74157
$986$	0	0
$987$	7.61151e12	0.255296
$988$	1.72269e12	0.0575176
$989$	−3.75317e11	−0.0124743
$990$	−1.66421e13	−0.550616
$991$	2.98474e13	0.983049	0.491524	−	0.870864i	$-0.336440\pi$
$991$	2.98474e13	0.983049	0.491524	+	0.870864i	$0.336440\pi$
$992$	2.21182e13	0.725184
$993$	−1.75430e13	−0.572574
$994$	−1.10854e13	−0.360175
$995$	−7.01799e13	−2.26991
$996$	9.29593e12	0.299313
$997$	−3.49991e13	−1.12183	−0.560917	−	0.827872i	$-0.689551\pi$
$997$	−3.49991e13	−1.12183	−0.560917	+	0.827872i	$0.689551\pi$
$998$	2.74390e13	0.875550
$999$	−5.25443e13	−1.66909

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.g.1.12	✓	36
17.16	even	2		289.10.a.h.1.12	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.12	✓	36	1.1	even	1	trivial
289.10.a.h.1.12	yes	36	17.16	even	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-20.0534 q^{2} +107.002 q^{3} -109.862 q^{4} +2675.64 q^{5} -2145.75 q^{6} -1982.25 q^{7} +12470.4 q^{8} -8233.60 q^{9} +O(q^{10})\)	\(q-20.0534 q^{2} +107.002 q^{3} -109.862 q^{4} +2675.64 q^{5} -2145.75 q^{6} -1982.25 q^{7} +12470.4 q^{8} -8233.60 q^{9} -53655.7 q^{10} -37670.6 q^{11} -11755.5 q^{12} -25139.4 q^{13} +39750.8 q^{14} +286299. q^{15} -193825. q^{16} +165111. q^{18} +623741. q^{19} -293952. q^{20} -212104. q^{21} +755422. q^{22} +88926.9 q^{23} +1.33436e6 q^{24} +5.20595e6 q^{25} +504130. q^{26} -2.98713e6 q^{27} +217774. q^{28} -116951. q^{29} -5.74126e6 q^{30} -8.85431e6 q^{31} -2.49802e6 q^{32} -4.03082e6 q^{33} -5.30379e6 q^{35} +904560. q^{36} +1.75902e7 q^{37} -1.25081e7 q^{38} -2.68996e6 q^{39} +3.33664e7 q^{40} -2.89173e7 q^{41} +4.25341e6 q^{42} -4.22052e6 q^{43} +4.13857e6 q^{44} -2.20302e7 q^{45} -1.78328e6 q^{46} -3.58857e7 q^{47} -2.07396e7 q^{48} -3.64243e7 q^{49} -1.04397e8 q^{50} +2.76187e6 q^{52} -1.03300e7 q^{53} +5.99020e7 q^{54} -1.00793e8 q^{55} -2.47195e7 q^{56} +6.67414e7 q^{57} +2.34527e6 q^{58} +6.28093e7 q^{59} -3.14534e7 q^{60} +1.06527e8 q^{61} +1.77559e8 q^{62} +1.63210e7 q^{63} +1.49332e8 q^{64} -6.72641e7 q^{65} +8.08316e7 q^{66} -9.64274e7 q^{67} +9.51535e6 q^{69} +1.06359e8 q^{70} -2.78873e8 q^{71} -1.02677e8 q^{72} +3.95597e8 q^{73} -3.52744e8 q^{74} +5.57046e8 q^{75} -6.85255e7 q^{76} +7.46724e7 q^{77} +5.39428e7 q^{78} -5.96898e8 q^{79} -5.18606e8 q^{80} -1.57567e8 q^{81} +5.79890e8 q^{82} -7.90776e8 q^{83} +2.33022e7 q^{84} +8.46356e7 q^{86} -1.25140e7 q^{87} -4.69768e8 q^{88} +8.30223e8 q^{89} +4.41779e8 q^{90} +4.98325e7 q^{91} -9.76970e6 q^{92} -9.47428e8 q^{93} +7.19629e8 q^{94} +1.66891e9 q^{95} -2.67293e8 q^{96} -2.87280e8 q^{97} +7.30430e8 q^{98} +3.10164e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 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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