LMFDB - Embedded newform 289.10.a.h.1.3

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			1.3
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)

$f(q)$	$=$	$q-38.3451 q^{2} -247.035 q^{3} +958.344 q^{4} +875.650 q^{5} +9472.58 q^{6} +7072.73 q^{7} -17115.1 q^{8} +41343.4 q^{9} +O(q^{10})$	\(q-38.3451 q^{2} -247.035 q^{3} +958.344 q^{4} +875.650 q^{5} +9472.58 q^{6} +7072.73 q^{7} -17115.1 q^{8} +41343.4 q^{9} -33576.9 q^{10} -55297.3 q^{11} -236745. q^{12} -179715. q^{13} -271204. q^{14} -216316. q^{15} +165608. q^{16} -1.58531e6 q^{18} -56519.2 q^{19} +839175. q^{20} -1.74721e6 q^{21} +2.12038e6 q^{22} -2.36581e6 q^{23} +4.22803e6 q^{24} -1.18636e6 q^{25} +6.89118e6 q^{26} -5.35087e6 q^{27} +6.77811e6 q^{28} +1.38770e6 q^{29} +8.29467e6 q^{30} -430357. q^{31} +2.41270e6 q^{32} +1.36604e7 q^{33} +6.19324e6 q^{35} +3.96212e7 q^{36} -1.73171e7 q^{37} +2.16723e6 q^{38} +4.43959e7 q^{39} -1.49868e7 q^{40} -2.41560e7 q^{41} +6.69970e7 q^{42} -3.24198e6 q^{43} -5.29939e7 q^{44} +3.62023e7 q^{45} +9.07170e7 q^{46} -4.13306e7 q^{47} -4.09109e7 q^{48} +9.66988e6 q^{49} +4.54911e7 q^{50} -1.72229e8 q^{52} +1.71427e7 q^{53} +2.05180e8 q^{54} -4.84211e7 q^{55} -1.21050e8 q^{56} +1.39622e7 q^{57} -5.32115e7 q^{58} -3.33334e7 q^{59} -2.07306e8 q^{60} -5.58769e7 q^{61} +1.65021e7 q^{62} +2.92410e8 q^{63} -1.77306e8 q^{64} -1.57367e8 q^{65} -5.23808e8 q^{66} -1.25537e8 q^{67} +5.84437e8 q^{69} -2.37480e8 q^{70} +6.66690e7 q^{71} -7.07596e8 q^{72} +2.13031e6 q^{73} +6.64026e8 q^{74} +2.93073e8 q^{75} -5.41649e7 q^{76} -3.91103e8 q^{77} -1.70236e9 q^{78} +3.27561e8 q^{79} +1.45014e8 q^{80} +5.08092e8 q^{81} +9.26263e8 q^{82} +2.63136e8 q^{83} -1.67443e9 q^{84} +1.24314e8 q^{86} -3.42811e8 q^{87} +9.46420e8 q^{88} +1.86798e8 q^{89} -1.38818e9 q^{90} -1.27107e9 q^{91} -2.26726e9 q^{92} +1.06313e8 q^{93} +1.58482e9 q^{94} -4.94911e7 q^{95} -5.96022e8 q^{96} +9.45632e7 q^{97} -3.70792e8 q^{98} -2.28618e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−38.3451	−1.69463	−0.847314	−	0.531092i	$-0.821782\pi$
$2$	−38.3451	−1.69463	−0.847314	+	0.531092i	$0.821782\pi$
$3$	−247.035	−1.76081	−0.880406	−	0.474220i	$-0.842730\pi$
$3$	−247.035	−1.76081	−0.880406	+	0.474220i	$0.842730\pi$
$4$	958.344	1.87177
$5$	875.650	0.626564	0.313282	−	0.949660i	$-0.398571\pi$
$5$	875.650	0.626564	0.313282	+	0.949660i	$0.398571\pi$
$6$	9472.58	2.98392
$7$	7072.73	1.11339	0.556693	−	0.830718i	$-0.312070\pi$
$7$	7072.73	1.11339	0.556693	+	0.830718i	$0.312070\pi$
$8$	−17115.1	−1.47732
$9$	41343.4	2.10046
$10$	−33576.9	−1.06179
$11$	−55297.3	−1.13877	−0.569386	−	0.822070i	$-0.692819\pi$
$11$	−55297.3	−1.13877	−0.569386	+	0.822070i	$0.692819\pi$
$12$	−236745.	−3.29583
$13$	−179715.	−1.74517	−0.872587	−	0.488458i	$-0.837559\pi$
$13$	−179715.	−1.74517	−0.872587	+	0.488458i	$0.837559\pi$
$14$	−271204.	−1.88678
$15$	−216316.	−1.10326
$16$	165608.	0.631743
$17$	0	0
$17$	0	0
$18$	−1.58531e6	−3.55950
$19$	−56519.2	−0.0994958	−0.0497479	−	0.998762i	$-0.515842\pi$
$19$	−56519.2	−0.0994958	−0.0497479	+	0.998762i	$0.515842\pi$
$20$	839175.	1.17278
$21$	−1.74721e6	−1.96046
$22$	2.12038e6	1.92980
$23$	−2.36581e6	−1.76280	−0.881402	−	0.472367i	$-0.843400\pi$
$23$	−2.36581e6	−1.76280	−0.881402	+	0.472367i	$0.843400\pi$
$24$	4.22803e6	2.60128
$25$	−1.18636e6	−0.607417
$26$	6.89118e6	2.95742
$27$	−5.35087e6	−1.93770
$28$	6.77811e6	2.08400
$29$	1.38770e6	0.364338	0.182169	−	0.983267i	$-0.441688\pi$
$29$	1.38770e6	0.364338	0.182169	+	0.983267i	$0.441688\pi$
$30$	8.29467e6	1.86962
$31$	−430357.	−0.0836953	−0.0418477	−	0.999124i	$-0.513324\pi$
$31$	−430357.	−0.0836953	−0.0418477	+	0.999124i	$0.513324\pi$
$32$	2.41270e6	0.406751
$33$	1.36604e7	2.00517
$34$	0	0
$35$	6.19324e6	0.697608
$36$	3.96212e7	3.93157
$37$	−1.73171e7	−1.51903	−0.759517	−	0.650487i	$-0.774565\pi$
$37$	−1.73171e7	−1.51903	−0.759517	+	0.650487i	$0.774565\pi$
$38$	2.16723e6	0.168608
$39$	4.43959e7	3.07292
$40$	−1.49868e7	−0.925636
$41$	−2.41560e7	−1.33505	−0.667525	−	0.744588i	$-0.732646\pi$
$41$	−2.41560e7	−1.33505	−0.667525	+	0.744588i	$0.732646\pi$
$42$	6.69970e7	3.32226
$43$	−3.24198e6	−0.144611	−0.0723057	−	0.997383i	$-0.523036\pi$
$43$	−3.24198e6	−0.144611	−0.0723057	+	0.997383i	$0.523036\pi$
$44$	−5.29939e7	−2.13152
$45$	3.62023e7	1.31607
$46$	9.07170e7	2.98730
$47$	−4.13306e7	−1.23547	−0.617734	−	0.786387i	$-0.711949\pi$
$47$	−4.13306e7	−1.23547	−0.617734	+	0.786387i	$0.711949\pi$
$48$	−4.09109e7	−1.11238
$49$	9.66988e6	0.239629
$50$	4.54911e7	1.02935
$51$	0	0
$52$	−1.72229e8	−3.26656
$53$	1.71427e7	0.298428	0.149214	−	0.988805i	$-0.452326\pi$
$53$	1.71427e7	0.298428	0.149214	+	0.988805i	$0.452326\pi$
$54$	2.05180e8	3.28369
$55$	−4.84211e7	−0.713515
$56$	−1.21050e8	−1.64483
$57$	1.39622e7	0.175194
$58$	−5.32115e7	−0.617418
$59$	−3.33334e7	−0.358135	−0.179067	−	0.983837i	$-0.557308\pi$
$59$	−3.33334e7	−0.358135	−0.179067	+	0.983837i	$0.557308\pi$
$60$	−2.07306e8	−2.06505
$61$	−5.58769e7	−0.516711	−0.258356	−	0.966050i	$-0.583181\pi$
$61$	−5.58769e7	−0.516711	−0.258356	+	0.966050i	$0.583181\pi$
$62$	1.65021e7	0.141832
$63$	2.92410e8	2.33862
$64$	−1.77306e8	−1.32103
$65$	−1.57367e8	−1.09346
$66$	−5.23808e8	−3.39801
$67$	−1.25537e8	−0.761086	−0.380543	−	0.924763i	$-0.624263\pi$
$67$	−1.25537e8	−0.761086	−0.380543	+	0.924763i	$0.624263\pi$
$68$	0	0
$69$	5.84437e8	3.10397
$70$	−2.37480e8	−1.18219
$71$	6.66690e7	0.311359	0.155680	−	0.987808i	$-0.450243\pi$
$71$	6.66690e7	0.311359	0.155680	+	0.987808i	$0.450243\pi$
$72$	−7.07596e8	−3.10305
$73$	2.13031e6	0.00877990	0.00438995	−	0.999990i	$-0.498603\pi$
$73$	2.13031e6	0.00877990	0.00438995	+	0.999990i	$0.498603\pi$
$74$	6.64026e8	2.57420
$75$	2.93073e8	1.06955
$76$	−5.41649e7	−0.186233
$77$	−3.91103e8	−1.26789
$78$	−1.70236e9	−5.20747
$79$	3.27561e8	0.946174	0.473087	−	0.881016i	$-0.343140\pi$
$79$	3.27561e8	0.946174	0.473087	+	0.881016i	$0.343140\pi$
$80$	1.45014e8	0.395827
$81$	5.08092e8	1.31147
$82$	9.26263e8	2.26241
$83$	2.63136e8	0.608595	0.304298	−	0.952577i	$-0.401578\pi$
$83$	2.63136e8	0.608595	0.304298	+	0.952577i	$0.401578\pi$
$84$	−1.67443e9	−3.66953
$85$	0	0
$86$	1.24314e8	0.245063
$87$	−3.42811e8	−0.641532
$88$	9.46420e8	1.68233
$89$	1.86798e8	0.315586	0.157793	−	0.987472i	$-0.449562\pi$
$89$	1.86798e8	0.315586	0.157793	+	0.987472i	$0.449562\pi$
$90$	−1.38818e9	−2.23026
$91$	−1.27107e9	−1.94305
$92$	−2.26726e9	−3.29956
$93$	1.06313e8	0.147372
$94$	1.58482e9	2.09366
$95$	−4.94911e7	−0.0623405
$96$	−5.96022e8	−0.716212
$97$	9.45632e7	0.108455	0.0542275	−	0.998529i	$-0.482730\pi$
$97$	9.45632e7	0.108455	0.0542275	+	0.998529i	$0.482730\pi$
$98$	−3.70792e8	−0.406082
$99$	−2.28618e9	−2.39195
$100$	−1.13694e9	−1.13694
$101$	−1.49062e9	−1.42535	−0.712673	−	0.701497i	$-0.752516\pi$
$101$	−1.49062e9	−1.42535	−0.712673	+	0.701497i	$0.752516\pi$
$102$	0	0
$103$	−1.81795e9	−1.59153	−0.795763	−	0.605609i	$-0.792930\pi$
$103$	−1.81795e9	−1.59153	−0.795763	+	0.605609i	$0.792930\pi$
$104$	3.07584e9	2.57818
$105$	−1.52995e9	−1.22836
$106$	−6.57340e8	−0.505724
$107$	−9.57357e8	−0.706069	−0.353034	−	0.935610i	$-0.614850\pi$
$107$	−9.57357e8	−0.706069	−0.353034	+	0.935610i	$0.614850\pi$
$108$	−5.12798e9	−3.62693
$109$	6.70544e8	0.454997	0.227498	−	0.973778i	$-0.426945\pi$
$109$	6.70544e8	0.454997	0.227498	+	0.973778i	$0.426945\pi$
$110$	1.85671e9	1.20914
$111$	4.27793e9	2.67473
$112$	1.17130e9	0.703373
$113$	1.13895e9	0.657132	0.328566	−	0.944481i	$-0.393435\pi$
$113$	1.13895e9	0.657132	0.328566	+	0.944481i	$0.393435\pi$
$114$	−5.35383e8	−0.296888
$115$	−2.07162e9	−1.10451
$116$	1.32990e9	0.681956
$117$	−7.43002e9	−3.66567
$118$	1.27817e9	0.606905
$119$	0	0
$120$	3.70228e9	1.62987
$121$	6.99848e8	0.296804
$122$	2.14260e9	0.875633
$123$	5.96738e9	2.35077
$124$	−4.12430e8	−0.156658
$125$	−2.74909e9	−1.00715
$126$	−1.12125e10	−3.96310
$127$	−1.48207e9	−0.505535	−0.252768	−	0.967527i	$-0.581341\pi$
$127$	−1.48207e9	−0.505535	−0.252768	+	0.967527i	$0.581341\pi$
$128$	5.56352e9	1.83191
$129$	8.00884e8	0.254634
$130$	6.03426e9	1.85302
$131$	3.68446e9	1.09308	0.546541	−	0.837432i	$-0.315944\pi$
$131$	3.68446e9	1.09308	0.546541	+	0.837432i	$0.315944\pi$
$132$	1.30914e10	3.75320
$133$	−3.99745e8	−0.110777
$134$	4.81371e9	1.28976
$135$	−4.68549e9	−1.21410
$136$	0	0
$137$	4.76832e9	1.15644	0.578220	−	0.815881i	$-0.303748\pi$
$137$	4.76832e9	1.15644	0.578220	+	0.815881i	$0.303748\pi$
$138$	−2.24103e10	−5.26007
$139$	−2.75609e9	−0.626220	−0.313110	−	0.949717i	$-0.601371\pi$
$139$	−2.75609e9	−0.626220	−0.313110	+	0.949717i	$0.601371\pi$
$140$	5.93525e9	1.30576
$141$	1.02101e10	2.17543
$142$	−2.55643e9	−0.527638
$143$	9.93775e9	1.98736
$144$	6.84677e9	1.32695
$145$	1.21514e9	0.228281
$146$	−8.16868e7	−0.0148787
$147$	−2.38880e9	−0.421941
$148$	−1.65957e10	−2.84328
$149$	−8.50459e9	−1.41356	−0.706781	−	0.707432i	$-0.749854\pi$
$149$	−8.50459e9	−1.41356	−0.706781	+	0.707432i	$0.749854\pi$
$150$	−1.12379e10	−1.81249
$151$	−4.69221e8	−0.0734482	−0.0367241	−	0.999325i	$-0.511692\pi$
$151$	−4.69221e8	−0.0734482	−0.0367241	+	0.999325i	$0.511692\pi$
$152$	9.67332e8	0.146987
$153$	0	0
$154$	1.49969e10	2.14861
$155$	−3.76842e8	−0.0524405
$156$	4.25465e10	5.75180
$157$	−9.71327e9	−1.27590	−0.637950	−	0.770077i	$-0.720218\pi$
$157$	−9.71327e9	−1.27590	−0.637950	+	0.770077i	$0.720218\pi$
$158$	−1.25604e10	−1.60341
$159$	−4.23486e9	−0.525475
$160$	2.11268e9	0.254856
$161$	−1.67327e10	−1.96268
$162$	−1.94828e10	−2.22246
$163$	−1.18283e10	−1.31244	−0.656218	−	0.754572i	$-0.727845\pi$
$163$	−1.18283e10	−1.31244	−0.656218	+	0.754572i	$0.727845\pi$
$164$	−2.31498e10	−2.49890
$165$	1.19617e10	1.25637
$166$	−1.00900e10	−1.03134
$167$	1.36543e10	1.35845	0.679226	−	0.733929i	$-0.262316\pi$
$167$	1.36543e10	1.35845	0.679226	+	0.733929i	$0.262316\pi$
$168$	2.99037e10	2.89623
$169$	2.16929e10	2.04563
$170$	0	0
$171$	−2.33669e9	−0.208987
$172$	−3.10694e9	−0.270679
$173$	3.18021e9	0.269928	0.134964	−	0.990850i	$-0.456908\pi$
$173$	3.18021e9	0.269928	0.134964	+	0.990850i	$0.456908\pi$
$174$	1.31451e10	1.08716
$175$	−8.39081e9	−0.676290
$176$	−9.15765e9	−0.719411
$177$	8.23453e9	0.630608
$178$	−7.16279e9	−0.534801
$179$	−6.21740e9	−0.452658	−0.226329	−	0.974051i	$-0.572672\pi$
$179$	−6.21740e9	−0.452658	−0.226329	+	0.974051i	$0.572672\pi$
$180$	3.46943e10	2.46338
$181$	5.79688e9	0.401458	0.200729	−	0.979647i	$-0.435669\pi$
$181$	5.79688e9	0.401458	0.200729	+	0.979647i	$0.435669\pi$
$182$	4.87394e10	3.29275
$183$	1.38035e10	0.909831
$184$	4.04910e10	2.60423
$185$	−1.51637e10	−0.951773
$186$	−4.07659e9	−0.249740
$187$	0	0
$188$	−3.96089e10	−2.31251
$189$	−3.78453e10	−2.15741
$190$	1.89774e9	0.105644
$191$	1.62977e10	0.886084	0.443042	−	0.896501i	$-0.353899\pi$
$191$	1.62977e10	0.886084	0.443042	+	0.896501i	$0.353899\pi$
$192$	4.38009e10	2.32609
$193$	−2.77841e10	−1.44141	−0.720707	−	0.693240i	$-0.756183\pi$
$193$	−2.77841e10	−1.44141	−0.720707	+	0.693240i	$0.756183\pi$
$194$	−3.62603e9	−0.183791
$195$	3.88753e10	1.92539
$196$	9.26707e9	0.448529
$197$	−3.12035e10	−1.47606	−0.738032	−	0.674766i	$-0.764245\pi$
$197$	−3.12035e10	−1.47606	−0.738032	+	0.674766i	$0.764245\pi$
$198$	8.76637e10	4.05346
$199$	−1.90992e10	−0.863330	−0.431665	−	0.902034i	$-0.642074\pi$
$199$	−1.90992e10	−0.863330	−0.431665	+	0.902034i	$0.642074\pi$
$200$	2.03047e10	0.897349
$201$	3.10120e10	1.34013
$202$	5.71579e10	2.41543
$203$	9.81483e9	0.405649
$204$	0	0
$205$	−2.11522e10	−0.836495
$206$	6.97093e10	2.69704
$207$	−9.78104e10	−3.70270
$208$	−2.97621e10	−1.10250
$209$	3.12536e9	0.113303
$210$	5.86659e10	2.08161
$211$	4.18494e10	1.45351	0.726755	−	0.686896i	$-0.241027\pi$
$211$	4.18494e10	1.45351	0.726755	+	0.686896i	$0.241027\pi$
$212$	1.64286e10	0.558587
$213$	−1.64696e10	−0.548245
$214$	3.67099e10	1.19652
$215$	−2.83884e9	−0.0906084
$216$	9.15807e10	2.86261
$217$	−3.04380e9	−0.0931852
$218$	−2.57121e10	−0.771050
$219$	−5.26261e8	−0.0154598
$220$	−4.64041e10	−1.33553
$221$	0	0
$222$	−1.64038e11	−4.53268
$223$	−1.10890e10	−0.300276	−0.150138	−	0.988665i	$-0.547972\pi$
$223$	−1.10890e10	−0.300276	−0.150138	+	0.988665i	$0.547972\pi$
$224$	1.70644e10	0.452871
$225$	−4.90482e10	−1.27586
$226$	−4.36732e10	−1.11359
$227$	4.43462e10	1.10851	0.554256	−	0.832346i	$-0.313003\pi$
$227$	4.43462e10	1.10851	0.554256	+	0.832346i	$0.313003\pi$
$228$	1.33806e10	0.327921
$229$	−9.70253e8	−0.0233145	−0.0116572	−	0.999932i	$-0.503711\pi$
$229$	−9.70253e8	−0.0233145	−0.0116572	+	0.999932i	$0.503711\pi$
$230$	7.94364e10	1.87173
$231$	9.66162e10	2.23252
$232$	−2.37506e10	−0.538244
$233$	−2.73732e10	−0.608448	−0.304224	−	0.952601i	$-0.598397\pi$
$233$	−2.73732e10	−0.608448	−0.304224	+	0.952601i	$0.598397\pi$
$234$	2.84904e11	6.21195
$235$	−3.61912e10	−0.774100
$236$	−3.19449e10	−0.670344
$237$	−8.09192e10	−1.66603
$238$	0	0
$239$	−5.26614e10	−1.04400	−0.522002	−	0.852944i	$-0.674815\pi$
$239$	−5.26614e10	−1.04400	−0.522002	+	0.852944i	$0.674815\pi$
$240$	−3.58236e10	−0.696978
$241$	4.93288e10	0.941941	0.470971	−	0.882149i	$-0.343904\pi$
$241$	4.93288e10	0.941941	0.470971	+	0.882149i	$0.343904\pi$
$242$	−2.68357e10	−0.502972
$243$	−2.01954e10	−0.371556
$244$	−5.35493e10	−0.967162
$245$	8.46743e9	0.150143
$246$	−2.28820e11	−3.98369
$247$	1.01573e10	0.173638
$248$	7.36560e9	0.123645
$249$	−6.50038e10	−1.07162
$250$	1.05414e11	1.70675
$251$	−2.44127e10	−0.388225	−0.194113	−	0.980979i	$-0.562183\pi$
$251$	−2.44127e10	−0.388225	−0.194113	+	0.980979i	$0.562183\pi$
$252$	2.80230e11	4.37736
$253$	1.30823e11	2.00743
$254$	5.68300e10	0.856695
$255$	0	0
$256$	−1.22553e11	−1.78338
$257$	1.14345e10	0.163500	0.0817502	−	0.996653i	$-0.473949\pi$
$257$	1.14345e10	0.163500	0.0817502	+	0.996653i	$0.473949\pi$
$258$	−3.07099e10	−0.431510
$259$	−1.22479e11	−1.69127
$260$	−1.50812e11	−2.04671
$261$	5.73722e10	0.765279
$262$	−1.41281e11	−1.85237
$263$	−1.47919e10	−0.190644	−0.0953218	−	0.995447i	$-0.530388\pi$
$263$	−1.47919e10	−0.190644	−0.0953218	+	0.995447i	$0.530388\pi$
$264$	−2.33799e11	−2.96227
$265$	1.50110e10	0.186984
$266$	1.53283e10	0.187726
$267$	−4.61458e10	−0.555688
$268$	−1.20307e11	−1.42458
$269$	1.08472e11	1.26309	0.631544	−	0.775340i	$-0.282421\pi$
$269$	1.08472e11	1.26309	0.631544	+	0.775340i	$0.282421\pi$
$270$	1.79666e11	2.05744
$271$	−1.24948e11	−1.40724	−0.703621	−	0.710575i	$-0.748435\pi$
$271$	−1.24948e11	−1.40724	−0.703621	+	0.710575i	$0.748435\pi$
$272$	0	0
$273$	3.14000e11	3.42135
$274$	−1.82842e11	−1.95974
$275$	6.56026e10	0.691710
$276$	5.60092e11	5.80990
$277$	−4.37655e10	−0.446656	−0.223328	−	0.974743i	$-0.571692\pi$
$277$	−4.37655e10	−0.446656	−0.223328	+	0.974743i	$0.571692\pi$
$278$	1.05682e11	1.06121
$279$	−1.77924e10	−0.175799
$280$	−1.05998e11	−1.03059
$281$	−9.36224e10	−0.895780	−0.447890	−	0.894089i	$-0.647824\pi$
$281$	−9.36224e10	−0.895780	−0.447890	+	0.894089i	$0.647824\pi$
$282$	−3.91507e11	−3.68654
$283$	3.44641e10	0.319395	0.159697	−	0.987166i	$-0.448948\pi$
$283$	3.44641e10	0.319395	0.159697	+	0.987166i	$0.448948\pi$
$284$	6.38919e10	0.582791
$285$	1.22260e10	0.109770
$286$	−3.81064e11	−3.36783
$287$	−1.70849e11	−1.48643
$288$	9.97492e10	0.854364
$289$	0	0
$290$	−4.65947e10	−0.386852
$291$	−2.33604e10	−0.190969
$292$	2.04157e9	0.0164339
$293$	−2.08082e11	−1.64942	−0.824709	−	0.565557i	$-0.808661\pi$
$293$	−2.08082e11	−1.64942	−0.824709	+	0.565557i	$0.808661\pi$
$294$	9.15987e10	0.715033
$295$	−2.91884e10	−0.224394
$296$	2.96384e11	2.24410
$297$	2.95889e11	2.20661
$298$	3.26109e11	2.39546
$299$	4.25171e11	3.07640
$300$	2.80865e11	2.00194
$301$	−2.29297e10	−0.161008
$302$	1.79923e10	0.124467
$303$	3.68235e11	2.50977
$304$	−9.36001e9	−0.0628557
$305$	−4.89286e10	−0.323753
$306$	0	0
$307$	−1.09580e11	−0.704060	−0.352030	−	0.935989i	$-0.614508\pi$
$307$	−1.09580e11	−0.704060	−0.352030	+	0.935989i	$0.614508\pi$
$308$	−3.74811e11	−2.37320
$309$	4.49097e11	2.80238
$310$	1.44500e10	0.0888672
$311$	1.65183e11	1.00125	0.500627	−	0.865663i	$-0.333103\pi$
$311$	1.65183e11	1.00125	0.500627	+	0.865663i	$0.333103\pi$
$312$	−7.59840e11	−4.53969
$313$	2.08573e11	1.22831	0.614156	−	0.789185i	$-0.289497\pi$
$313$	2.08573e11	1.22831	0.614156	+	0.789185i	$0.289497\pi$
$314$	3.72456e11	2.16218
$315$	2.56049e11	1.46530
$316$	3.13917e11	1.77102
$317$	−5.75119e10	−0.319883	−0.159941	−	0.987127i	$-0.551131\pi$
$317$	−5.75119e10	−0.319883	−0.159941	+	0.987127i	$0.551131\pi$
$318$	1.62386e11	0.890485
$319$	−7.67362e10	−0.414899
$320$	−1.55258e11	−0.827713
$321$	2.36501e11	1.24325
$322$	6.41617e11	3.32602
$323$	0	0
$324$	4.86927e11	2.45477
$325$	2.13207e11	1.06005
$326$	4.53557e11	2.22409
$327$	−1.65648e11	−0.801164
$328$	4.13432e11	1.97230
$329$	−2.92320e11	−1.37555
$330$	−4.58673e11	−2.12907
$331$	3.17672e11	1.45463	0.727316	−	0.686303i	$-0.240767\pi$
$331$	3.17672e11	1.45463	0.727316	+	0.686303i	$0.240767\pi$
$332$	2.52175e11	1.13915
$333$	−7.15947e11	−3.19067
$334$	−5.23574e11	−2.30207
$335$	−1.09926e11	−0.476869
$336$	−2.89352e11	−1.23851
$337$	−4.55316e11	−1.92300	−0.961498	−	0.274813i	$-0.911384\pi$
$337$	−4.55316e11	−1.92300	−0.961498	+	0.274813i	$0.911384\pi$
$338$	−8.31817e11	−3.46659
$339$	−2.81361e11	−1.15709
$340$	0	0
$341$	2.37976e10	0.0953100
$342$	8.96007e10	0.354155
$343$	−2.17018e11	−0.846587
$344$	5.54869e10	0.213637
$345$	5.11763e11	1.94484
$346$	−1.21945e11	−0.457428
$347$	−2.81867e10	−0.104367	−0.0521833	−	0.998638i	$-0.516618\pi$
$347$	−2.81867e10	−0.104367	−0.0521833	+	0.998638i	$0.516618\pi$
$348$	−3.28531e11	−1.20080
$349$	−2.63818e11	−0.951898	−0.475949	−	0.879473i	$-0.657895\pi$
$349$	−2.63818e11	−0.951898	−0.475949	+	0.879473i	$0.657895\pi$
$350$	3.21746e11	1.14606
$351$	9.61631e11	3.38163
$352$	−1.33416e11	−0.463197
$353$	−1.51848e10	−0.0520502	−0.0260251	−	0.999661i	$-0.508285\pi$
$353$	−1.51848e10	−0.0520502	−0.0260251	+	0.999661i	$0.508285\pi$
$354$	−3.15754e11	−1.06865
$355$	5.83788e10	0.195087
$356$	1.79017e11	0.590703
$357$	0	0
$358$	2.38407e11	0.767087
$359$	−1.10621e11	−0.351490	−0.175745	−	0.984436i	$-0.556233\pi$
$359$	−1.10621e11	−0.351490	−0.175745	+	0.984436i	$0.556233\pi$
$360$	−6.19607e11	−1.94426
$361$	−3.19493e11	−0.990101
$362$	−2.22282e11	−0.680323
$363$	−1.72887e11	−0.522616
$364$	−1.21813e12	−3.63694
$365$	1.86541e9	0.00550117
$366$	−5.29298e11	−1.54183
$367$	−1.63544e11	−0.470586	−0.235293	−	0.971925i	$-0.575605\pi$
$367$	−1.63544e11	−0.470586	−0.235293	+	0.971925i	$0.575605\pi$
$368$	−3.91795e11	−1.11364
$369$	−9.98690e11	−2.80422
$370$	5.81454e11	1.61290
$371$	1.21246e11	0.332265
$372$	1.01885e11	0.275845
$373$	−6.59311e11	−1.76360	−0.881801	−	0.471621i	$-0.843669\pi$
$373$	−6.59311e11	−1.76360	−0.881801	+	0.471621i	$0.843669\pi$
$374$	0	0
$375$	6.79122e11	1.77340
$376$	7.07378e11	1.82518
$377$	−2.49390e11	−0.635834
$378$	1.45118e12	3.65602
$379$	−6.18091e11	−1.53878	−0.769389	−	0.638781i	$-0.779439\pi$
$379$	−6.18091e11	−1.53878	−0.769389	+	0.638781i	$0.779439\pi$
$380$	−4.74295e10	−0.116687
$381$	3.66123e11	0.890153
$382$	−6.24935e11	−1.50158
$383$	6.31833e11	1.50040	0.750202	−	0.661209i	$-0.229956\pi$
$383$	6.31833e11	1.50040	0.750202	+	0.661209i	$0.229956\pi$
$384$	−1.37438e12	−3.22565
$385$	−3.42470e11	−0.794417
$386$	1.06538e12	2.44266
$387$	−1.34035e11	−0.303751
$388$	9.06241e10	0.203002
$389$	−1.82637e11	−0.404403	−0.202202	−	0.979344i	$-0.564810\pi$
$389$	−1.82637e11	−0.404403	−0.202202	+	0.979344i	$0.564810\pi$
$390$	−1.49067e12	−3.26281
$391$	0	0
$392$	−1.65501e11	−0.354008
$393$	−9.10191e11	−1.92471
$394$	1.19650e12	2.50138
$395$	2.86829e11	0.592839
$396$	−2.19095e12	−4.47717
$397$	2.05793e11	0.415790	0.207895	−	0.978151i	$-0.433339\pi$
$397$	2.05793e11	0.415790	0.207895	+	0.978151i	$0.433339\pi$
$398$	7.32361e11	1.46302
$399$	9.87511e10	0.195058
$400$	−1.96470e11	−0.383731
$401$	8.48355e11	1.63843	0.819215	−	0.573487i	$-0.194410\pi$
$401$	8.48355e11	1.63843	0.819215	+	0.573487i	$0.194410\pi$
$402$	−1.18916e12	−2.27102
$403$	7.73415e10	0.146063
$404$	−1.42853e12	−2.66791
$405$	4.44911e11	0.821723
$406$	−3.76350e11	−0.687425
$407$	9.57590e11	1.72983
$408$	0	0
$409$	−7.80687e11	−1.37950	−0.689750	−	0.724047i	$-0.742280\pi$
$409$	−7.80687e11	−1.37950	−0.689750	+	0.724047i	$0.742280\pi$
$410$	8.11083e11	1.41755
$411$	−1.17794e12	−2.03627
$412$	−1.74222e12	−2.97896
$413$	−2.35758e11	−0.398742
$414$	3.75055e12	6.27470
$415$	2.30415e11	0.381324
$416$	−4.33598e11	−0.709851
$417$	6.80851e11	1.10266
$418$	−1.19842e11	−0.192007
$419$	3.43347e11	0.544215	0.272108	−	0.962267i	$-0.412279\pi$
$419$	3.43347e11	0.544215	0.272108	+	0.962267i	$0.412279\pi$
$420$	−1.46622e12	−2.29920
$421$	4.68264e11	0.726477	0.363238	−	0.931696i	$-0.381671\pi$
$421$	4.68264e11	0.726477	0.363238	+	0.931696i	$0.381671\pi$
$422$	−1.60472e12	−2.46316
$423$	−1.70875e12	−2.59505
$424$	−2.93400e11	−0.440873
$425$	0	0
$426$	6.31528e11	0.929072
$427$	−3.95202e11	−0.575299
$428$	−9.17478e11	−1.32160
$429$	−2.45497e12	−3.49936
$430$	1.08856e11	0.153548
$431$	1.08014e12	1.50775	0.753877	−	0.657015i	$-0.228181\pi$
$431$	1.08014e12	1.50775	0.753877	+	0.657015i	$0.228181\pi$
$432$	−8.86145e11	−1.22413
$433$	−1.19984e12	−1.64031	−0.820157	−	0.572139i	$-0.806114\pi$
$433$	−1.19984e12	−1.64031	−0.820157	+	0.572139i	$0.806114\pi$
$434$	1.16715e11	0.157914
$435$	−3.00183e11	−0.401961
$436$	6.42612e11	0.851647
$437$	1.33714e11	0.175392
$438$	2.01795e10	0.0261986
$439$	1.20760e12	1.55178	0.775892	−	0.630865i	$-0.217300\pi$
$439$	1.20760e12	1.55178	0.775892	+	0.630865i	$0.217300\pi$
$440$	8.28733e11	1.05409
$441$	3.99785e11	0.503331
$442$	0	0
$443$	−7.07890e11	−0.873271	−0.436636	−	0.899638i	$-0.643830\pi$
$443$	−7.07890e11	−0.873271	−0.436636	+	0.899638i	$0.643830\pi$
$444$	4.09973e12	5.00648
$445$	1.63570e11	0.197735
$446$	4.25208e11	0.508856
$447$	2.10093e12	2.48902
$448$	−1.25404e12	−1.47082
$449$	−4.16466e11	−0.483583	−0.241791	−	0.970328i	$-0.577735\pi$
$449$	−4.16466e11	−0.483583	−0.241791	+	0.970328i	$0.577735\pi$
$450$	1.88076e12	2.16210
$451$	1.33576e12	1.52032
$452$	1.09151e12	1.23000
$453$	1.15914e11	0.129329
$454$	−1.70046e12	−1.87852
$455$	−1.11302e12	−1.21745
$456$	−2.38965e11	−0.258817
$457$	4.97073e11	0.533086	0.266543	−	0.963823i	$-0.414119\pi$
$457$	4.97073e11	0.533086	0.266543	+	0.963823i	$0.414119\pi$
$458$	3.72044e10	0.0395093
$459$	0	0
$460$	−1.98532e12	−2.06738
$461$	−9.75376e11	−1.00581	−0.502907	−	0.864340i	$-0.667736\pi$
$461$	−9.75376e11	−1.00581	−0.502907	+	0.864340i	$0.667736\pi$
$462$	−3.70475e12	−3.78330
$463$	1.43284e12	1.44905	0.724523	−	0.689251i	$-0.242060\pi$
$463$	1.43284e12	1.44905	0.724523	+	0.689251i	$0.242060\pi$
$464$	2.29814e11	0.230168
$465$	9.30933e10	0.0923379
$466$	1.04963e12	1.03109
$467$	1.42742e12	1.38876	0.694378	−	0.719610i	$-0.255680\pi$
$467$	1.42742e12	1.38876	0.694378	+	0.719610i	$0.255680\pi$
$468$	−7.12051e12	−6.86128
$469$	−8.87886e11	−0.847383
$470$	1.38775e12	1.31181
$471$	2.39952e12	2.24662
$472$	5.70505e11	0.529079
$473$	1.79273e11	0.164680
$474$	3.10285e12	2.82331
$475$	6.70522e10	0.0604355
$476$	0	0
$477$	7.08739e11	0.626835
$478$	2.01931e12	1.76920
$479$	3.08239e10	0.0267533	0.0133766	−	0.999911i	$-0.495742\pi$
$479$	3.08239e10	0.0267533	0.0133766	+	0.999911i	$0.495742\pi$
$480$	−5.21907e11	−0.448753
$481$	3.11214e12	2.65098
$482$	−1.89152e12	−1.59624
$483$	4.13357e12	3.45591
$484$	6.70695e11	0.555547
$485$	8.28043e10	0.0679540
$486$	7.74393e11	0.629649
$487$	−4.56397e11	−0.367674	−0.183837	−	0.982957i	$-0.558852\pi$
$487$	−4.56397e11	−0.367674	−0.183837	+	0.982957i	$0.558852\pi$
$488$	9.56338e11	0.763348
$489$	2.92200e12	2.31095
$490$	−3.24684e11	−0.254436
$491$	−1.49685e12	−1.16228	−0.581139	−	0.813804i	$-0.697393\pi$
$491$	−1.49685e12	−1.16228	−0.581139	+	0.813804i	$0.697393\pi$
$492$	5.71880e12	4.40010
$493$	0	0
$494$	−3.89484e11	−0.294251
$495$	−2.00189e12	−1.49871
$496$	−7.12703e10	−0.0528739
$497$	4.71532e11	0.346663
$498$	2.49257e12	1.81600
$499$	9.86104e11	0.711984	0.355992	−	0.934489i	$-0.384143\pi$
$499$	9.86104e11	0.711984	0.355992	+	0.934489i	$0.384143\pi$
$500$	−2.63458e12	−1.88515
$501$	−3.37309e12	−2.39198
$502$	9.36106e11	0.657897
$503$	−5.92003e11	−0.412352	−0.206176	−	0.978515i	$-0.566102\pi$
$503$	−5.92003e11	−0.412352	−0.206176	+	0.978515i	$0.566102\pi$
$504$	−5.00463e12	−3.45490
$505$	−1.30526e12	−0.893071
$506$	−5.01641e12	−3.40185
$507$	−5.35891e12	−3.60198
$508$	−1.42033e12	−0.946244
$509$	9.84420e11	0.650055	0.325028	−	0.945705i	$-0.394626\pi$
$509$	9.84420e11	0.650055	0.325028	+	0.945705i	$0.394626\pi$
$510$	0	0
$511$	1.50671e10	0.00977542
$512$	1.85077e12	1.19025
$513$	3.02427e11	0.192794
$514$	−4.38457e11	−0.277072
$515$	−1.59189e12	−0.997193
$516$	7.67522e11	0.476615
$517$	2.28547e12	1.40692
$518$	4.69647e12	2.86608
$519$	−7.85623e11	−0.475293
$520$	2.69336e12	1.61540
$521$	7.78676e11	0.463006	0.231503	−	0.972834i	$-0.425636\pi$
$521$	7.78676e11	0.463006	0.231503	+	0.972834i	$0.425636\pi$
$522$	−2.19994e12	−1.29686
$523$	−1.54298e12	−0.901786	−0.450893	−	0.892578i	$-0.648894\pi$
$523$	−1.54298e12	−0.901786	−0.450893	+	0.892578i	$0.648894\pi$
$524$	3.53098e12	2.04600
$525$	2.07283e12	1.19082
$526$	5.67195e11	0.323070
$527$	0	0
$528$	2.26226e12	1.26675
$529$	3.79589e12	2.10748
$530$	−5.75600e11	−0.316869
$531$	−1.37812e12	−0.752248
$532$	−3.83093e11	−0.207349
$533$	4.34119e12	2.32989
$534$	1.76946e12	0.941685
$535$	−8.38310e11	−0.442398
$536$	2.14857e12	1.12437
$537$	1.53592e12	0.797046
$538$	−4.15938e12	−2.14047
$539$	−5.34719e11	−0.272883
$540$	−4.49032e12	−2.27251
$541$	2.37260e12	1.19079	0.595397	−	0.803432i	$-0.296995\pi$
$541$	2.37260e12	1.19079	0.595397	+	0.803432i	$0.296995\pi$
$542$	4.79115e12	2.38475
$543$	−1.43203e12	−0.706893
$544$	0	0
$545$	5.87162e11	0.285085
$546$	−1.20404e13	−5.79792
$547$	1.52298e12	0.727364	0.363682	−	0.931523i	$-0.381520\pi$
$547$	1.52298e12	0.727364	0.363682	+	0.931523i	$0.381520\pi$
$548$	4.56969e12	2.16458
$549$	−2.31014e12	−1.08533
$550$	−2.51554e12	−1.17219
$551$	−7.84318e10	−0.0362502
$552$	−1.00027e13	−4.58555
$553$	2.31675e12	1.05346
$554$	1.67819e12	0.756916
$555$	3.74597e12	1.67589
$556$	−2.64128e12	−1.17214
$557$	9.15324e11	0.402927	0.201464	−	0.979496i	$-0.435430\pi$
$557$	9.15324e11	0.402927	0.201464	+	0.979496i	$0.435430\pi$
$558$	6.82251e11	0.297914
$559$	5.82632e11	0.252372
$560$	1.02565e12	0.440709
$561$	0	0
$562$	3.58996e12	1.51801
$563$	−3.29684e12	−1.38296	−0.691482	−	0.722394i	$-0.743042\pi$
$563$	−3.29684e12	−1.38296	−0.691482	+	0.722394i	$0.743042\pi$
$564$	9.78480e12	4.07189
$565$	9.97324e11	0.411736
$566$	−1.32153e12	−0.541255
$567$	3.59360e12	1.46018
$568$	−1.14105e12	−0.459977
$569$	2.75031e12	1.09996	0.549979	−	0.835178i	$-0.314636\pi$
$569$	2.75031e12	1.09996	0.549979	+	0.835178i	$0.314636\pi$
$570$	−4.68808e11	−0.186019
$571$	−1.83309e12	−0.721640	−0.360820	−	0.932635i	$-0.617503\pi$
$571$	−1.83309e12	−0.721640	−0.360820	+	0.932635i	$0.617503\pi$
$572$	9.52379e12	3.71987
$573$	−4.02610e12	−1.56023
$574$	6.55121e12	2.51894
$575$	2.80670e12	1.07076
$576$	−7.33044e12	−2.77478
$577$	−1.48112e12	−0.556288	−0.278144	−	0.960539i	$-0.589719\pi$
$577$	−1.48112e12	−0.556288	−0.278144	+	0.960539i	$0.589719\pi$
$578$	0	0
$579$	6.86365e12	2.53806
$580$	1.16452e12	0.427290
$581$	1.86109e12	0.677601
$582$	8.95758e11	0.323621
$583$	−9.47948e11	−0.339841
$584$	−3.64605e10	−0.0129707
$585$	−6.50610e12	−2.29678
$586$	7.97893e12	2.79515
$587$	−1.81141e12	−0.629716	−0.314858	−	0.949139i	$-0.601957\pi$
$587$	−1.81141e12	−0.629716	−0.314858	+	0.949139i	$0.601957\pi$
$588$	−2.28929e12	−0.789775
$589$	2.43234e10	0.00832734
$590$	1.11923e12	0.380265
$591$	7.70836e12	2.59907
$592$	−2.86784e12	−0.959638
$593$	−1.94583e12	−0.646188	−0.323094	−	0.946367i	$-0.604723\pi$
$593$	−1.94583e12	−0.646188	−0.323094	+	0.946367i	$0.604723\pi$
$594$	−1.13459e13	−3.73938
$595$	0	0
$596$	−8.15033e12	−2.64586
$597$	4.71818e12	1.52016
$598$	−1.63032e13	−5.21336
$599$	1.39777e12	0.443625	0.221812	−	0.975089i	$-0.428803\pi$
$599$	1.39777e12	0.443625	0.221812	+	0.975089i	$0.428803\pi$
$600$	−5.01597e12	−1.58006
$601$	−2.87702e12	−0.899513	−0.449756	−	0.893151i	$-0.648489\pi$
$601$	−2.87702e12	−0.899513	−0.449756	+	0.893151i	$0.648489\pi$
$602$	8.79240e11	0.272849
$603$	−5.19011e12	−1.59863
$604$	−4.49675e11	−0.137478
$605$	6.12822e11	0.185967
$606$	−1.41200e13	−4.25312
$607$	−1.04761e11	−0.0313221	−0.0156610	−	0.999877i	$-0.504985\pi$
$607$	−1.04761e11	−0.0313221	−0.0156610	+	0.999877i	$0.504985\pi$
$608$	−1.36364e11	−0.0404700
$609$	−2.42461e12	−0.714272
$610$	1.87617e12	0.548641
$611$	7.42772e12	2.15611
$612$	0	0
$613$	3.07681e12	0.880094	0.440047	−	0.897975i	$-0.354962\pi$
$613$	3.07681e12	0.880094	0.440047	+	0.897975i	$0.354962\pi$
$614$	4.20186e12	1.19312
$615$	5.22534e12	1.47291
$616$	6.69377e12	1.87309
$617$	−1.02089e12	−0.283593	−0.141797	−	0.989896i	$-0.545288\pi$
$617$	−1.02089e12	−0.283593	−0.141797	+	0.989896i	$0.545288\pi$
$618$	−1.72206e13	−4.74899
$619$	−4.26264e12	−1.16700	−0.583500	−	0.812113i	$-0.698317\pi$
$619$	−4.26264e12	−1.16700	−0.583500	+	0.812113i	$0.698317\pi$
$620$	−3.61145e11	−0.0981564
$621$	1.26591e13	3.41579
$622$	−6.33396e12	−1.69675
$623$	1.32117e12	0.351369
$624$	7.35229e12	1.94130
$625$	−9.01317e10	−0.0236275
$626$	−7.99774e12	−2.08153
$627$	−7.72074e11	−0.199506
$628$	−9.30865e12	−2.38819
$629$	0	0
$630$	−9.81823e12	−2.48314
$631$	2.55988e12	0.642818	0.321409	−	0.946940i	$-0.395844\pi$
$631$	2.55988e12	0.642818	0.321409	+	0.946940i	$0.395844\pi$
$632$	−5.60625e12	−1.39780
$633$	−1.03383e13	−2.55936
$634$	2.20530e12	0.542083
$635$	−1.29777e12	−0.316750
$636$	−4.05845e12	−0.983566
$637$	−1.73782e12	−0.418194
$638$	2.94245e12	0.703099
$639$	2.75632e12	0.653998
$640$	4.87170e12	1.14781
$641$	7.00235e12	1.63826	0.819130	−	0.573608i	$-0.194457\pi$
$641$	7.00235e12	1.63826	0.819130	+	0.573608i	$0.194457\pi$
$642$	−9.06864e12	−2.10686
$643$	3.17520e12	0.732523	0.366261	−	0.930512i	$-0.380638\pi$
$643$	3.17520e12	0.732523	0.366261	+	0.930512i	$0.380638\pi$
$644$	−1.60357e13	−3.67368
$645$	7.01294e11	0.159544
$646$	0	0
$647$	1.28689e12	0.288717	0.144359	−	0.989525i	$-0.453888\pi$
$647$	1.28689e12	0.288717	0.144359	+	0.989525i	$0.453888\pi$
$648$	−8.69605e12	−1.93747
$649$	1.84325e12	0.407834
$650$	−8.17543e12	−1.79639
$651$	7.51925e11	0.164082
$652$	−1.13356e13	−2.45657
$653$	−6.54997e12	−1.40971	−0.704856	−	0.709351i	$-0.748988\pi$
$653$	−6.54997e12	−1.40971	−0.704856	+	0.709351i	$0.748988\pi$
$654$	6.35178e12	1.35767
$655$	3.22630e12	0.684887
$656$	−4.00041e12	−0.843408
$657$	8.80741e10	0.0184418
$658$	1.12090e13	2.33105
$659$	4.44729e12	0.918567	0.459284	−	0.888290i	$-0.348106\pi$
$659$	4.44729e12	0.918567	0.459284	+	0.888290i	$0.348106\pi$
$660$	1.14634e13	2.35162
$661$	4.35836e12	0.888007	0.444004	−	0.896025i	$-0.353558\pi$
$661$	4.35836e12	0.888007	0.444004	+	0.896025i	$0.353558\pi$
$662$	−1.21812e13	−2.46506
$663$	0	0
$664$	−4.50360e12	−0.899090
$665$	−3.50037e11	−0.0694091
$666$	2.74531e13	5.40700
$667$	−3.28303e12	−0.642257
$668$	1.30855e13	2.54271
$669$	2.73937e12	0.528730
$670$	4.21513e12	0.808117
$671$	3.08984e12	0.588417
$672$	−4.21550e12	−0.797421
$673$	8.69544e12	1.63389	0.816946	−	0.576713i	$-0.195665\pi$
$673$	8.69544e12	1.63389	0.816946	+	0.576713i	$0.195665\pi$
$674$	1.74591e13	3.25876
$675$	6.34807e12	1.17700
$676$	2.07893e13	3.82895
$677$	−7.41727e12	−1.35705	−0.678524	−	0.734578i	$-0.737380\pi$
$677$	−7.41727e12	−1.35705	−0.678524	+	0.734578i	$0.737380\pi$
$678$	1.07888e13	1.96083
$679$	6.68820e11	0.120752
$680$	0	0
$681$	−1.09551e13	−1.95188
$682$	−9.12520e11	−0.161515
$683$	−2.91239e12	−0.512103	−0.256051	−	0.966663i	$-0.582422\pi$
$683$	−2.91239e12	−0.512103	−0.256051	+	0.966663i	$0.582422\pi$
$684$	−2.23936e12	−0.391175
$685$	4.17538e12	0.724584
$686$	8.32156e12	1.43465
$687$	2.39687e11	0.0410524
$688$	−5.36897e11	−0.0913572
$689$	−3.08080e12	−0.520808
$690$	−1.96236e13	−3.29577
$691$	3.84355e12	0.641330	0.320665	−	0.947193i	$-0.396094\pi$
$691$	3.84355e12	0.641330	0.320665	+	0.947193i	$0.396094\pi$
$692$	3.04773e12	0.505242
$693$	−1.61695e13	−2.66316
$694$	1.08082e12	0.176863
$695$	−2.41337e12	−0.392367
$696$	5.86725e12	0.947748
$697$	0	0
$698$	1.01161e13	1.61311
$699$	6.76214e12	1.07136
$700$	−8.04129e12	−1.26586
$701$	8.00517e12	1.25210	0.626051	−	0.779782i	$-0.284670\pi$
$701$	8.00517e12	1.25210	0.626051	+	0.779782i	$0.284670\pi$
$702$	−3.68738e13	−5.73061
$703$	9.78749e11	0.151138
$704$	9.80456e12	1.50436
$705$	8.94049e12	1.36305
$706$	5.82261e11	0.0882057
$707$	−1.05427e13	−1.58696
$708$	7.89152e12	1.18035
$709$	−1.29517e13	−1.92495	−0.962476	−	0.271367i	$-0.912524\pi$
$709$	−1.29517e13	−1.92495	−0.962476	+	0.271367i	$0.912524\pi$
$710$	−2.23854e12	−0.330599
$711$	1.35425e13	1.98740
$712$	−3.19707e12	−0.466222
$713$	1.01814e12	0.147538
$714$	0	0
$715$	8.70200e12	1.24521
$716$	−5.95841e12	−0.847270
$717$	1.30092e13	1.83830
$718$	4.24178e12	0.595646
$719$	9.90952e12	1.38284	0.691421	−	0.722452i	$-0.256985\pi$
$719$	9.90952e12	1.38284	0.691421	+	0.722452i	$0.256985\pi$
$720$	5.99538e12	0.831420
$721$	−1.28578e13	−1.77198
$722$	1.22510e13	1.67785
$723$	−1.21859e13	−1.65858
$724$	5.55540e12	0.751436
$725$	−1.64632e12	−0.221305
$726$	6.62936e12	0.885640
$727$	3.54774e12	0.471028	0.235514	−	0.971871i	$-0.424323\pi$
$727$	3.54774e12	0.471028	0.235514	+	0.971871i	$0.424323\pi$
$728$	2.17546e13	2.87051
$729$	−5.01181e12	−0.657235
$730$	−7.15291e10	−0.00932245
$731$	0	0
$732$	1.32286e13	1.70299
$733$	−1.45595e13	−1.86285	−0.931425	−	0.363935i	$-0.881433\pi$
$733$	−1.45595e13	−1.86285	−0.931425	+	0.363935i	$0.881433\pi$
$734$	6.27112e12	0.797468
$735$	−2.09175e12	−0.264373
$736$	−5.70798e12	−0.717022
$737$	6.94184e12	0.866704
$738$	3.82948e13	4.75211
$739$	−1.38078e13	−1.70304	−0.851522	−	0.524319i	$-0.824320\pi$
$739$	−1.38078e13	−1.70304	−0.851522	+	0.524319i	$0.824320\pi$
$740$	−1.45321e13	−1.78150
$741$	−2.50922e12	−0.305743
$742$	−4.64918e12	−0.563066
$743$	−3.03587e12	−0.365455	−0.182728	−	0.983164i	$-0.558493\pi$
$743$	−3.03587e12	−0.365455	−0.182728	+	0.983164i	$0.558493\pi$
$744$	−1.81956e12	−0.217715
$745$	−7.44705e12	−0.885688
$746$	2.52813e13	2.98865
$747$	1.08789e13	1.27833
$748$	0	0
$749$	−6.77113e12	−0.786127
$750$	−2.60410e13	−3.00526
$751$	−6.03816e12	−0.692668	−0.346334	−	0.938111i	$-0.612574\pi$
$751$	−6.03816e12	−0.692668	−0.346334	+	0.938111i	$0.612574\pi$
$752$	−6.84466e12	−0.780498
$753$	6.03079e12	0.683592
$754$	9.56290e12	1.07750
$755$	−4.10874e11	−0.0460200
$756$	−3.62688e13	−4.03817
$757$	−1.82580e12	−0.202079	−0.101040	−	0.994882i	$-0.532217\pi$
$757$	−1.82580e12	−0.202079	−0.101040	+	0.994882i	$0.532217\pi$
$758$	2.37007e13	2.60766
$759$	−3.23178e13	−3.53471
$760$	8.47045e11	0.0920969
$761$	5.83576e12	0.630763	0.315382	−	0.948965i	$-0.397867\pi$
$761$	5.83576e12	0.630763	0.315382	+	0.948965i	$0.397867\pi$
$762$	−1.40390e13	−1.50848
$763$	4.74258e12	0.506587
$764$	1.56188e13	1.65854
$765$	0	0
$766$	−2.42277e13	−2.54263
$767$	5.99052e12	0.625007
$768$	3.02748e13	3.14019
$769$	6.20247e12	0.639582	0.319791	−	0.947488i	$-0.396387\pi$
$769$	6.20247e12	0.639582	0.319791	+	0.947488i	$0.396387\pi$
$770$	1.31320e13	1.34624
$771$	−2.82473e12	−0.287894
$772$	−2.66267e13	−2.69799
$773$	1.11694e13	1.12518	0.562592	−	0.826735i	$-0.309804\pi$
$773$	1.11694e13	1.12518	0.562592	+	0.826735i	$0.309804\pi$
$774$	5.13956e12	0.514745
$775$	5.10559e11	0.0508380
$776$	−1.61846e12	−0.160223
$777$	3.02567e13	2.97801
$778$	7.00321e12	0.685313
$779$	1.36528e12	0.132832
$780$	3.72559e13	3.60387
$781$	−3.68662e12	−0.354567
$782$	0	0
$783$	−7.42541e12	−0.705980
$784$	1.60140e12	0.151384
$785$	−8.50543e12	−0.799434
$786$	3.49013e13	3.26168
$787$	−5.54415e12	−0.515168	−0.257584	−	0.966256i	$-0.582926\pi$
$787$	−5.54415e12	−0.515168	−0.257584	+	0.966256i	$0.582926\pi$
$788$	−2.99037e13	−2.76285
$789$	3.65411e12	0.335687
$790$	−1.09985e13	−1.00464
$791$	8.05550e12	0.731642
$792$	3.91282e13	3.53367
$793$	1.00419e13	0.901751
$794$	−7.89117e12	−0.704610
$795$	−3.70826e12	−0.329244
$796$	−1.83036e13	−1.61595
$797$	3.28819e12	0.288665	0.144333	−	0.989529i	$-0.453896\pi$
$797$	3.28819e12	0.288665	0.144333	+	0.989529i	$0.453896\pi$
$798$	−3.78662e12	−0.330551
$799$	0	0
$800$	−2.86234e12	−0.247067
$801$	7.72287e12	0.662876
$802$	−3.25302e13	−2.77653
$803$	−1.17800e11	−0.00999831
$804$	2.97201e13	2.50841
$805$	−1.46520e13	−1.22975
$806$	−2.96567e12	−0.247522
$807$	−2.67965e13	−2.22406
$808$	2.55121e13	2.10569
$809$	3.73326e12	0.306422	0.153211	−	0.988194i	$-0.451039\pi$
$809$	3.73326e12	0.306422	0.153211	+	0.988194i	$0.451039\pi$
$810$	−1.70601e13	−1.39252
$811$	−2.19138e12	−0.177879	−0.0889395	−	0.996037i	$-0.528348\pi$
$811$	−2.19138e12	−0.177879	−0.0889395	+	0.996037i	$0.528348\pi$
$812$	9.40599e12	0.759281
$813$	3.08666e13	2.47789
$814$	−3.67188e13	−2.93143
$815$	−1.03575e13	−0.822325
$816$	0	0
$817$	1.83234e11	0.0143882
$818$	2.99355e13	2.33774
$819$	−5.25505e13	−4.08131
$820$	−2.02711e13	−1.56572
$821$	1.53840e13	1.18175	0.590873	−	0.806765i	$-0.298784\pi$
$821$	1.53840e13	1.18175	0.590873	+	0.806765i	$0.298784\pi$
$822$	4.51683e13	3.45073
$823$	1.43392e13	1.08949	0.544747	−	0.838601i	$-0.316626\pi$
$823$	1.43392e13	1.08949	0.544747	+	0.838601i	$0.316626\pi$
$824$	3.11143e13	2.35119
$825$	−1.62062e13	−1.21797
$826$	9.04017e12	0.675720
$827$	−7.37627e12	−0.548355	−0.274178	−	0.961679i	$-0.588406\pi$
$827$	−7.37627e12	−0.548355	−0.274178	+	0.961679i	$0.588406\pi$
$828$	−9.37361e13	−6.93059
$829$	−1.99770e13	−1.46905	−0.734524	−	0.678583i	$-0.762594\pi$
$829$	−1.99770e13	−1.46905	−0.734524	+	0.678583i	$0.762594\pi$
$830$	−8.83528e12	−0.646203
$831$	1.08116e13	0.786477
$832$	3.18646e13	2.30544
$833$	0	0
$834$	−2.61073e13	−1.86859
$835$	1.19564e13	0.851158
$836$	2.99517e12	0.212077
$837$	2.30278e12	0.162177
$838$	−1.31657e13	−0.922243
$839$	−1.62969e13	−1.13547	−0.567734	−	0.823212i	$-0.692180\pi$
$839$	−1.62969e13	−1.13547	−0.567734	+	0.823212i	$0.692180\pi$
$840$	2.61852e13	1.81468
$841$	−1.25814e13	−0.867258
$842$	−1.79556e13	−1.23111
$843$	2.31280e13	1.57730
$844$	4.01061e13	2.72063
$845$	1.89954e13	1.28172
$846$	6.55220e13	4.39765
$847$	4.94983e12	0.330457
$848$	2.83897e12	0.188529
$849$	−8.51384e12	−0.562394
$850$	0	0
$851$	4.09689e13	2.67776
$852$	−1.57835e13	−1.02619
$853$	−2.73583e13	−1.76937	−0.884686	−	0.466188i	$-0.845627\pi$
$853$	−2.73583e13	−1.76937	−0.884686	+	0.466188i	$0.845627\pi$
$854$	1.51540e13	0.974918
$855$	−2.04613e12	−0.130944
$856$	1.63853e13	1.04309
$857$	−8.05643e12	−0.510187	−0.255093	−	0.966916i	$-0.582106\pi$
$857$	−8.05643e12	−0.510187	−0.255093	+	0.966916i	$0.582106\pi$
$858$	9.41361e13	5.93012
$859$	2.97873e13	1.86665	0.933324	−	0.359036i	$-0.116895\pi$
$859$	2.97873e13	1.86665	0.933324	+	0.359036i	$0.116895\pi$
$860$	−2.72059e12	−0.169598
$861$	4.22056e13	2.61732
$862$	−4.14179e13	−2.55508
$863$	1.30714e13	0.802183	0.401091	−	0.916038i	$-0.368631\pi$
$863$	1.30714e13	0.802183	0.401091	+	0.916038i	$0.368631\pi$
$864$	−1.29101e13	−0.788163
$865$	2.78475e12	0.169127
$866$	4.60078e13	2.77972
$867$	0	0
$868$	−2.91701e12	−0.174421
$869$	−1.81133e13	−1.07748
$870$	1.15105e13	0.681174
$871$	2.25608e13	1.32823
$872$	−1.14764e13	−0.672176
$873$	3.90956e12	0.227805
$874$	−5.12725e12	−0.297224
$875$	−1.94436e13	−1.12135
$876$	−5.04339e11	−0.0289371
$877$	2.52703e13	1.44249	0.721245	−	0.692680i	$-0.243570\pi$
$877$	2.52703e13	1.44249	0.721245	+	0.692680i	$0.243570\pi$
$878$	−4.63054e13	−2.62970
$879$	5.14036e13	2.90432
$880$	−8.01890e12	−0.450758
$881$	5.05069e12	0.282461	0.141231	−	0.989977i	$-0.454894\pi$
$881$	5.05069e12	0.282461	0.141231	+	0.989977i	$0.454894\pi$
$882$	−1.53298e13	−0.852958
$883$	−3.49182e13	−1.93299	−0.966493	−	0.256695i	$-0.917367\pi$
$883$	−3.49182e13	−1.93299	−0.966493	+	0.256695i	$0.917367\pi$
$884$	0	0
$885$	7.21057e12	0.395116
$886$	2.71441e13	1.47987
$887$	1.88815e13	1.02419	0.512095	−	0.858929i	$-0.328870\pi$
$887$	1.88815e13	1.02419	0.512095	+	0.858929i	$0.328870\pi$
$888$	−7.32173e13	−3.95144
$889$	−1.04823e13	−0.562856
$890$	−6.27210e12	−0.335087
$891$	−2.80961e13	−1.49347
$892$	−1.06271e13	−0.562046
$893$	2.33597e12	0.122924
$894$	−8.05604e13	−4.21796
$895$	−5.44427e12	−0.283619
$896$	3.93492e13	2.03963
$897$	−1.05032e14	−5.41696
$898$	1.59694e13	0.819494
$899$	−5.97207e11	−0.0304934
$900$	−4.70050e13	−2.38810
$901$	0	0
$902$	−5.12199e13	−2.57638
$903$	5.66443e12	0.283506
$904$	−1.94933e13	−0.970794
$905$	5.07604e12	0.251539
$906$	−4.44474e12	−0.219164
$907$	−1.79530e13	−0.880856	−0.440428	−	0.897788i	$-0.645173\pi$
$907$	−1.79530e13	−0.880856	−0.440428	+	0.897788i	$0.645173\pi$
$908$	4.24989e13	2.07487
$909$	−6.16272e13	−2.99388
$910$	4.26787e13	2.06312
$911$	−2.70781e12	−0.130252	−0.0651262	−	0.997877i	$-0.520745\pi$
$911$	−2.70781e12	−0.130252	−0.0651262	+	0.997877i	$0.520745\pi$
$912$	2.31225e12	0.110677
$913$	−1.45507e13	−0.693052
$914$	−1.90603e13	−0.903383
$915$	1.20871e13	0.570068
$916$	−9.29836e11	−0.0436392
$917$	2.60592e13	1.21702
$918$	0	0
$919$	−2.13588e13	−0.987773	−0.493886	−	0.869527i	$-0.664424\pi$
$919$	−2.13588e13	−0.987773	−0.493886	+	0.869527i	$0.664424\pi$
$920$	3.54560e13	1.63172
$921$	2.70702e13	1.23972
$922$	3.74009e13	1.70448
$923$	−1.19814e13	−0.543376
$924$	9.25916e13	4.17876
$925$	2.05443e13	0.922687
$926$	−5.49422e13	−2.45559
$927$	−7.51600e13	−3.34294
$928$	3.34811e12	0.148195
$929$	−3.90195e13	−1.71874	−0.859371	−	0.511353i	$-0.829144\pi$
$929$	−3.90195e13	−1.71874	−0.859371	+	0.511353i	$0.829144\pi$
$930$	−3.56967e12	−0.156478
$931$	−5.46534e11	−0.0238420
$932$	−2.62329e13	−1.13887
$933$	−4.08061e13	−1.76302
$934$	−5.47345e13	−2.35343
$935$	0	0
$936$	1.27165e14	5.41537
$937$	−9.65920e12	−0.409367	−0.204684	−	0.978828i	$-0.565617\pi$
$937$	−9.65920e12	−0.409367	−0.204684	+	0.978828i	$0.565617\pi$
$938$	3.40461e13	1.43600
$939$	−5.15248e13	−2.16283
$940$	−3.46836e13	−1.44893
$941$	5.33826e12	0.221946	0.110973	−	0.993823i	$-0.464603\pi$
$941$	5.33826e12	0.221946	0.110973	+	0.993823i	$0.464603\pi$
$942$	−9.20097e13	−3.80719
$943$	5.71484e13	2.35343
$944$	−5.52027e12	−0.226249
$945$	−3.31392e13	−1.35176
$946$	−6.87424e12	−0.279071
$947$	−2.92169e13	−1.18048	−0.590241	−	0.807227i	$-0.700967\pi$
$947$	−2.92169e13	−1.18048	−0.590241	+	0.807227i	$0.700967\pi$
$948$	−7.75484e13	−3.11843
$949$	−3.82848e11	−0.0153225
$950$	−2.57112e12	−0.102416
$951$	1.42075e13	0.563254
$952$	0	0
$953$	1.10222e13	0.432864	0.216432	−	0.976298i	$-0.430558\pi$
$953$	1.10222e13	0.432864	0.216432	+	0.976298i	$0.430558\pi$
$954$	−2.71766e13	−1.06225
$955$	1.42711e13	0.555189
$956$	−5.04678e13	−1.95413
$957$	1.89565e13	0.730559
$958$	−1.18194e12	−0.0453369
$959$	3.37250e13	1.28756
$960$	3.83543e13	1.45745
$961$	−2.62544e13	−0.992995
$962$	−1.19335e14	−4.49243
$963$	−3.95804e13	−1.48307
$964$	4.72740e13	1.76309
$965$	−2.43292e13	−0.903138
$966$	−1.58502e14	−5.85649
$967$	−8.21374e12	−0.302080	−0.151040	−	0.988528i	$-0.548262\pi$
$967$	−8.21374e12	−0.302080	−0.151040	+	0.988528i	$0.548262\pi$
$968$	−1.19780e13	−0.438474
$969$	0	0
$970$	−3.17514e12	−0.115157
$971$	3.39952e13	1.22724	0.613622	−	0.789600i	$-0.289712\pi$
$971$	3.39952e13	1.22724	0.613622	+	0.789600i	$0.289712\pi$
$972$	−1.93541e13	−0.695465
$973$	−1.94931e13	−0.697225
$974$	1.75006e13	0.623070
$975$	−5.26696e13	−1.86655
$976$	−9.25363e12	−0.326428
$977$	−2.44752e13	−0.859409	−0.429704	−	0.902970i	$-0.641382\pi$
$977$	−2.44752e13	−0.859409	−0.429704	+	0.902970i	$0.641382\pi$
$978$	−1.12044e14	−3.91621
$979$	−1.03294e13	−0.359381
$980$	8.11472e12	0.281032
$981$	2.77226e13	0.955702
$982$	5.73967e13	1.96963
$983$	2.23624e13	0.763884	0.381942	−	0.924186i	$-0.375255\pi$
$983$	2.23624e13	0.763884	0.381942	+	0.924186i	$0.375255\pi$
$984$	−1.02132e14	−3.47284
$985$	−2.73234e13	−0.924849
$986$	0	0
$987$	7.22133e13	2.42209
$988$	9.73423e12	0.325009
$989$	7.66991e12	0.254922
$990$	7.67627e13	2.53976
$991$	−3.63013e13	−1.19561	−0.597807	−	0.801640i	$-0.703961\pi$
$991$	−3.63013e13	−1.19561	−0.597807	+	0.801640i	$0.703961\pi$
$992$	−1.03832e12	−0.0340432
$993$	−7.84762e13	−2.56133
$994$	−1.80809e13	−0.587465
$995$	−1.67242e13	−0.540932
$996$	−6.22960e13	−2.00583
$997$	−4.17526e13	−1.33831	−0.669153	−	0.743125i	$-0.733343\pi$
$997$	−4.17526e13	−1.33831	−0.669153	+	0.743125i	$0.733343\pi$
$998$	−3.78122e13	−1.20655
$999$	9.26616e13	2.94344

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.h.1.3	yes	36
17.16	even	2		289.10.a.g.1.3	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.3	✓	36	17.16	even	2
289.10.a.h.1.3	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)

\(f(q)\)	\(=\)	\(q-38.3451 q^{2} -247.035 q^{3} +958.344 q^{4} +875.650 q^{5} +9472.58 q^{6} +7072.73 q^{7} -17115.1 q^{8} +41343.4 q^{9} +O(q^{10})\)	\(q-38.3451 q^{2} -247.035 q^{3} +958.344 q^{4} +875.650 q^{5} +9472.58 q^{6} +7072.73 q^{7} -17115.1 q^{8} +41343.4 q^{9} -33576.9 q^{10} -55297.3 q^{11} -236745. q^{12} -179715. q^{13} -271204. q^{14} -216316. q^{15} +165608. q^{16} -1.58531e6 q^{18} -56519.2 q^{19} +839175. q^{20} -1.74721e6 q^{21} +2.12038e6 q^{22} -2.36581e6 q^{23} +4.22803e6 q^{24} -1.18636e6 q^{25} +6.89118e6 q^{26} -5.35087e6 q^{27} +6.77811e6 q^{28} +1.38770e6 q^{29} +8.29467e6 q^{30} -430357. q^{31} +2.41270e6 q^{32} +1.36604e7 q^{33} +6.19324e6 q^{35} +3.96212e7 q^{36} -1.73171e7 q^{37} +2.16723e6 q^{38} +4.43959e7 q^{39} -1.49868e7 q^{40} -2.41560e7 q^{41} +6.69970e7 q^{42} -3.24198e6 q^{43} -5.29939e7 q^{44} +3.62023e7 q^{45} +9.07170e7 q^{46} -4.13306e7 q^{47} -4.09109e7 q^{48} +9.66988e6 q^{49} +4.54911e7 q^{50} -1.72229e8 q^{52} +1.71427e7 q^{53} +2.05180e8 q^{54} -4.84211e7 q^{55} -1.21050e8 q^{56} +1.39622e7 q^{57} -5.32115e7 q^{58} -3.33334e7 q^{59} -2.07306e8 q^{60} -5.58769e7 q^{61} +1.65021e7 q^{62} +2.92410e8 q^{63} -1.77306e8 q^{64} -1.57367e8 q^{65} -5.23808e8 q^{66} -1.25537e8 q^{67} +5.84437e8 q^{69} -2.37480e8 q^{70} +6.66690e7 q^{71} -7.07596e8 q^{72} +2.13031e6 q^{73} +6.64026e8 q^{74} +2.93073e8 q^{75} -5.41649e7 q^{76} -3.91103e8 q^{77} -1.70236e9 q^{78} +3.27561e8 q^{79} +1.45014e8 q^{80} +5.08092e8 q^{81} +9.26263e8 q^{82} +2.63136e8 q^{83} -1.67443e9 q^{84} +1.24314e8 q^{86} -3.42811e8 q^{87} +9.46420e8 q^{88} +1.86798e8 q^{89} -1.38818e9 q^{90} -1.27107e9 q^{91} -2.26726e9 q^{92} +1.06313e8 q^{93} +1.58482e9 q^{94} -4.94911e7 q^{95} -5.96022e8 q^{96} +9.45632e7 q^{97} -3.70792e8 q^{98} -2.28618e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 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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