LMFDB - Embedded newform 289.10.a.g.1.20

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			1.20
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)

$f(q)$	$=$	$q+2.64758 q^{2} -62.7112 q^{3} -504.990 q^{4} -1957.56 q^{5} -166.033 q^{6} -4153.19 q^{7} -2692.56 q^{8} -15750.3 q^{9} +O(q^{10})$	\(q+2.64758 q^{2} -62.7112 q^{3} -504.990 q^{4} -1957.56 q^{5} -166.033 q^{6} -4153.19 q^{7} -2692.56 q^{8} -15750.3 q^{9} -5182.80 q^{10} -73075.6 q^{11} +31668.5 q^{12} -54341.7 q^{13} -10995.9 q^{14} +122761. q^{15} +251426. q^{16} -41700.2 q^{18} +811429. q^{19} +988551. q^{20} +260451. q^{21} -193473. q^{22} -163008. q^{23} +168854. q^{24} +1.87893e6 q^{25} -143874. q^{26} +2.22206e6 q^{27} +2.09732e6 q^{28} +5.42890e6 q^{29} +325020. q^{30} -946104. q^{31} +2.04426e6 q^{32} +4.58266e6 q^{33} +8.13013e6 q^{35} +7.95375e6 q^{36} -1.91041e7 q^{37} +2.14832e6 q^{38} +3.40783e6 q^{39} +5.27086e6 q^{40} -2.07663e7 q^{41} +689566. q^{42} -3.17001e7 q^{43} +3.69025e7 q^{44} +3.08322e7 q^{45} -431577. q^{46} +4.92240e7 q^{47} -1.57672e7 q^{48} -2.31046e7 q^{49} +4.97462e6 q^{50} +2.74420e7 q^{52} +6.39542e7 q^{53} +5.88309e6 q^{54} +1.43050e8 q^{55} +1.11827e7 q^{56} -5.08857e7 q^{57} +1.43734e7 q^{58} -1.75333e7 q^{59} -6.19932e7 q^{60} +1.01852e8 q^{61} -2.50489e6 q^{62} +6.54140e7 q^{63} -1.23318e8 q^{64} +1.06377e8 q^{65} +1.21329e7 q^{66} +5.10956e7 q^{67} +1.02224e7 q^{69} +2.15252e7 q^{70} +1.39323e8 q^{71} +4.24087e7 q^{72} -1.70150e8 q^{73} -5.05796e7 q^{74} -1.17830e8 q^{75} -4.09764e8 q^{76} +3.03497e8 q^{77} +9.02250e6 q^{78} +4.92862e8 q^{79} -4.92183e8 q^{80} +1.70665e8 q^{81} -5.49803e7 q^{82} +3.76175e8 q^{83} -1.31525e8 q^{84} -8.39284e7 q^{86} -3.40453e8 q^{87} +1.96761e8 q^{88} -8.85727e8 q^{89} +8.16308e7 q^{90} +2.25691e8 q^{91} +8.23176e7 q^{92} +5.93313e7 q^{93} +1.30325e8 q^{94} -1.58842e9 q^{95} -1.28198e8 q^{96} +1.16492e8 q^{97} -6.11713e7 q^{98} +1.15096e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	2.64758	0.117008	0.0585038	−	0.998287i	$-0.481367\pi$
$2$	2.64758	0.117008	0.0585038	+	0.998287i	$0.481367\pi$
$3$	−62.7112	−0.446992	−0.223496	−	0.974705i	$-0.571747\pi$
$3$	−62.7112	−0.446992	−0.223496	+	0.974705i	$0.571747\pi$
$4$	−504.990	−0.986309
$5$	−1957.56	−1.40072	−0.700359	−	0.713791i	$-0.746977\pi$
$5$	−1957.56	−1.40072	−0.700359	+	0.713791i	$0.746977\pi$
$6$	−166.033	−0.0523014
$7$	−4153.19	−0.653793	−0.326897	−	0.945060i	$-0.606003\pi$
$7$	−4153.19	−0.653793	−0.326897	+	0.945060i	$0.606003\pi$
$8$	−2692.56	−0.232413
$9$	−15750.3	−0.800199
$10$	−5182.80	−0.163895
$11$	−73075.6	−1.50489	−0.752446	−	0.658654i	$-0.771126\pi$
$11$	−73075.6	−1.50489	−0.752446	+	0.658654i	$0.771126\pi$
$12$	31668.5	0.440872
$13$	−54341.7	−0.527701	−0.263850	−	0.964564i	$-0.584993\pi$
$13$	−54341.7	−0.527701	−0.263850	+	0.964564i	$0.584993\pi$
$14$	−10995.9	−0.0764988
$15$	122761.	0.626109
$16$	251426.	0.959115
$17$	0	0
$17$	0	0
$18$	−41700.2	−0.0936293
$19$	811429.	1.42843	0.714216	−	0.699925i	$-0.246783\pi$
$19$	811429.	1.42843	0.714216	+	0.699925i	$0.246783\pi$
$20$	988551.	1.38154
$21$	260451.	0.292240
$22$	−193473.	−0.176084
$23$	−163008.	−0.121460	−0.0607301	−	0.998154i	$-0.519343\pi$
$23$	−163008.	−0.121460	−0.0607301	+	0.998154i	$0.519343\pi$
$24$	168854.	0.103887
$25$	1.87893e6	0.962012
$26$	−143874.	−0.0617450
$27$	2.22206e6	0.804674
$28$	2.09732e6	0.644843
$29$	5.42890e6	1.42535	0.712674	−	0.701496i	$-0.247484\pi$
$29$	5.42890e6	1.42535	0.712674	+	0.701496i	$0.247484\pi$
$30$	325020.	0.0732595
$31$	−946104.	−0.183997	−0.0919986	−	0.995759i	$-0.529326\pi$
$31$	−946104.	−0.183997	−0.0919986	+	0.995759i	$0.529326\pi$
$32$	2.04426e6	0.344637
$33$	4.58266e6	0.672674
$34$	0	0
$35$	8.13013e6	0.915781
$36$	7.95375e6	0.789243
$37$	−1.91041e7	−1.67579	−0.837893	−	0.545834i	$-0.816213\pi$
$37$	−1.91041e7	−1.67579	−0.837893	+	0.545834i	$0.816213\pi$
$38$	2.14832e6	0.167137
$39$	3.40783e6	0.235878
$40$	5.27086e6	0.325545
$41$	−2.07663e7	−1.14771	−0.573853	−	0.818958i	$-0.694552\pi$
$41$	−2.07663e7	−1.14771	−0.573853	+	0.818958i	$0.694552\pi$
$42$	689566.	0.0341943
$43$	−3.17001e7	−1.41401	−0.707004	−	0.707209i	$-0.749954\pi$
$43$	−3.17001e7	−1.41401	−0.707004	+	0.707209i	$0.749954\pi$
$44$	3.69025e7	1.48429
$45$	3.08322e7	1.12085
$46$	−431577.	−0.0142118
$47$	4.92240e7	1.47142	0.735710	−	0.677296i	$-0.236849\pi$
$47$	4.92240e7	1.47142	0.735710	+	0.677296i	$0.236849\pi$
$48$	−1.57672e7	−0.428716
$49$	−2.31046e7	−0.572554
$50$	4.97462e6	0.112563
$51$	0	0
$52$	2.74420e7	0.520476
$53$	6.39542e7	1.11334	0.556670	−	0.830734i	$-0.312079\pi$
$53$	6.39542e7	1.11334	0.556670	+	0.830734i	$0.312079\pi$
$54$	5.88309e6	0.0941529
$55$	1.43050e8	2.10793
$56$	1.11827e7	0.151950
$57$	−5.08857e7	−0.638497
$58$	1.43734e7	0.166776
$59$	−1.75333e7	−0.188378	−0.0941889	−	0.995554i	$-0.530026\pi$
$59$	−1.75333e7	−0.188378	−0.0941889	+	0.995554i	$0.530026\pi$
$60$	−6.19932e7	−0.617537
$61$	1.01852e8	0.941860	0.470930	−	0.882171i	$-0.343918\pi$
$61$	1.01852e8	0.941860	0.470930	+	0.882171i	$0.343918\pi$
$62$	−2.50489e6	−0.0215291
$63$	6.54140e7	0.523165
$64$	−1.23318e8	−0.918790
$65$	1.06377e8	0.739160
$66$	1.21329e7	0.0787080
$67$	5.10956e7	0.309775	0.154888	−	0.987932i	$-0.450498\pi$
$67$	5.10956e7	0.309775	0.154888	+	0.987932i	$0.450498\pi$
$68$	0	0
$69$	1.02224e7	0.0542917
$70$	2.15252e7	0.107153
$71$	1.39323e8	0.650671	0.325336	−	0.945599i	$-0.394523\pi$
$71$	1.39323e8	0.650671	0.325336	+	0.945599i	$0.394523\pi$
$72$	4.24087e7	0.185977
$73$	−1.70150e8	−0.701260	−0.350630	−	0.936514i	$-0.614033\pi$
$73$	−1.70150e8	−0.701260	−0.350630	+	0.936514i	$0.614033\pi$
$74$	−5.05796e7	−0.196080
$75$	−1.17830e8	−0.430011
$76$	−4.09764e8	−1.40888
$77$	3.03497e8	0.983889
$78$	9.02250e6	0.0275995
$79$	4.92862e8	1.42365	0.711825	−	0.702356i	$-0.247869\pi$
$79$	4.92862e8	1.42365	0.711825	+	0.702356i	$0.247869\pi$
$80$	−4.92183e8	−1.34345
$81$	1.70665e8	0.440516
$82$	−5.49803e7	−0.134290
$83$	3.76175e8	0.870039	0.435020	−	0.900421i	$-0.356741\pi$
$83$	3.76175e8	0.870039	0.435020	+	0.900421i	$0.356741\pi$
$84$	−1.31525e8	−0.288239
$85$	0	0
$86$	−8.39284e7	−0.165450
$87$	−3.40453e8	−0.637118
$88$	1.96761e8	0.349757
$89$	−8.85727e8	−1.49639	−0.748195	−	0.663479i	$-0.769079\pi$
$89$	−8.85727e8	−1.49639	−0.748195	+	0.663479i	$0.769079\pi$
$90$	8.16308e7	0.131148
$91$	2.25691e8	0.345007
$92$	8.23176e7	0.119797
$93$	5.93313e7	0.0822452
$94$	1.30325e8	0.172167
$95$	−1.58842e9	−2.00083
$96$	−1.28198e8	−0.154050
$97$	1.16492e8	0.133605	0.0668026	−	0.997766i	$-0.478720\pi$
$97$	1.16492e8	0.133605	0.0668026	+	0.997766i	$0.478720\pi$
$98$	−6.11713e7	−0.0669932
$99$	1.15096e9	1.20421
$100$	−9.48842e8	−0.948842
$101$	−5.35257e7	−0.0511819	−0.0255910	−	0.999672i	$-0.508147\pi$
$101$	−5.35257e7	−0.0511819	−0.0255910	+	0.999672i	$0.508147\pi$
$102$	0	0
$103$	−3.19474e8	−0.279684	−0.139842	−	0.990174i	$-0.544660\pi$
$103$	−3.19474e8	−0.279684	−0.139842	+	0.990174i	$0.544660\pi$
$104$	1.46318e8	0.122645
$105$	−5.09850e8	−0.409346
$106$	1.69324e8	0.130269
$107$	−1.63184e9	−1.20351	−0.601755	−	0.798681i	$-0.705532\pi$
$107$	−1.63184e9	−1.20351	−0.601755	+	0.798681i	$0.705532\pi$
$108$	−1.12212e9	−0.793657
$109$	8.10335e8	0.549852	0.274926	−	0.961465i	$-0.411347\pi$
$109$	8.10335e8	0.549852	0.274926	+	0.961465i	$0.411347\pi$
$110$	3.78737e8	0.246644
$111$	1.19804e9	0.749063
$112$	−1.04422e9	−0.627063
$113$	−1.89909e9	−1.09570	−0.547850	−	0.836576i	$-0.684554\pi$
$113$	−1.89909e9	−1.09570	−0.547850	+	0.836576i	$0.684554\pi$
$114$	−1.34724e8	−0.0747090
$115$	3.19099e8	0.170132
$116$	−2.74154e9	−1.40583
$117$	8.55898e8	0.422265
$118$	−4.64208e7	−0.0220416
$119$	0	0
$120$	−3.30542e8	−0.145516
$121$	2.98210e9	1.26470
$122$	2.69662e8	0.110205
$123$	1.30228e9	0.513015
$124$	4.77773e8	0.181478
$125$	1.45241e8	0.0532100
$126$	1.73189e8	0.0612142
$127$	3.55227e9	1.21168	0.605842	−	0.795585i	$-0.292836\pi$
$127$	3.55227e9	1.21168	0.605842	+	0.795585i	$0.292836\pi$
$128$	−1.37316e9	−0.452142
$129$	1.98795e9	0.632050
$130$	2.81642e8	0.0864874
$131$	−1.16394e9	−0.345312	−0.172656	−	0.984982i	$-0.555235\pi$
$131$	−1.16394e9	−0.345312	−0.172656	+	0.984982i	$0.555235\pi$
$132$	−2.31420e9	−0.663465
$133$	−3.37002e9	−0.933899
$134$	1.35280e8	0.0362460
$135$	−4.34983e9	−1.12712
$136$	0	0
$137$	6.06374e9	1.47061	0.735306	−	0.677735i	$-0.237038\pi$
$137$	6.06374e9	1.47061	0.735306	+	0.677735i	$0.237038\pi$
$138$	2.70647e7	0.00635254
$139$	−7.71758e9	−1.75353	−0.876767	−	0.480915i	$-0.840305\pi$
$139$	−7.71758e9	−1.75353	−0.876767	+	0.480915i	$0.840305\pi$
$140$	−4.10564e9	−0.903243
$141$	−3.08690e9	−0.657713
$142$	3.68870e8	0.0761335
$143$	3.97105e9	0.794133
$144$	−3.96004e9	−0.767483
$145$	−1.06274e10	−1.99651
$146$	−4.50486e8	−0.0820528
$147$	1.44892e9	0.255927
$148$	9.64738e9	1.65284
$149$	−2.01142e9	−0.334322	−0.167161	−	0.985930i	$-0.553460\pi$
$149$	−2.01142e9	−0.334322	−0.167161	+	0.985930i	$0.553460\pi$
$150$	−3.11964e8	−0.0503146
$151$	6.98565e9	1.09348	0.546740	−	0.837303i	$-0.315869\pi$
$151$	6.98565e9	1.09348	0.546740	+	0.837303i	$0.315869\pi$
$152$	−2.18482e9	−0.331986
$153$	0	0
$154$	8.03532e8	0.115122
$155$	1.85206e9	0.257728
$156$	−1.72092e9	−0.232648
$157$	9.93532e9	1.30507	0.652535	−	0.757759i	$-0.273706\pi$
$157$	9.93532e9	1.30507	0.652535	+	0.757759i	$0.273706\pi$
$158$	1.30489e9	0.166578
$159$	−4.01064e9	−0.497653
$160$	−4.00177e9	−0.482739
$161$	6.77004e8	0.0794099
$162$	4.51849e8	0.0515437
$163$	−4.23700e9	−0.470126	−0.235063	−	0.971980i	$-0.575530\pi$
$163$	−4.23700e9	−0.470126	−0.235063	+	0.971980i	$0.575530\pi$
$164$	1.04868e10	1.13199
$165$	−8.97084e9	−0.942227
$166$	9.95954e8	0.101801
$167$	9.26222e9	0.921491	0.460745	−	0.887532i	$-0.347582\pi$
$167$	9.26222e9	0.921491	0.460745	+	0.887532i	$0.347582\pi$
$168$	−7.01282e8	−0.0679205
$169$	−7.65148e9	−0.721532
$170$	0	0
$171$	−1.27803e10	−1.14303
$172$	1.60082e10	1.39465
$173$	6.09534e9	0.517357	0.258679	−	0.965963i	$-0.416713\pi$
$173$	6.09534e9	0.517357	0.258679	+	0.965963i	$0.416713\pi$
$174$	−9.01375e8	−0.0745477
$175$	−7.80355e9	−0.628957
$176$	−1.83731e10	−1.44336
$177$	1.09953e9	0.0842033
$178$	−2.34503e9	−0.175089
$179$	−1.48711e10	−1.08269	−0.541346	−	0.840800i	$-0.682085\pi$
$179$	−1.48711e10	−1.08269	−0.541346	+	0.840800i	$0.682085\pi$
$180$	−1.55700e10	−1.10551
$181$	7.88421e9	0.546015	0.273008	−	0.962012i	$-0.411982\pi$
$181$	7.88421e9	0.546015	0.273008	+	0.962012i	$0.411982\pi$
$182$	5.97535e8	0.0403685
$183$	−6.38727e9	−0.421003
$184$	4.38910e8	0.0282290
$185$	3.73975e10	2.34731
$186$	1.57084e8	0.00962331
$187$	0	0
$188$	−2.48577e10	−1.45128
$189$	−9.22866e9	−0.526090
$190$	−4.20548e9	−0.234112
$191$	1.18806e10	0.645933	0.322967	−	0.946410i	$-0.395320\pi$
$191$	1.18806e10	0.645933	0.322967	+	0.946410i	$0.395320\pi$
$192$	7.73341e9	0.410691
$193$	−2.37247e10	−1.23082	−0.615408	−	0.788209i	$-0.711009\pi$
$193$	−2.37247e10	−1.23082	−0.615408	+	0.788209i	$0.711009\pi$
$194$	3.08422e8	0.0156328
$195$	−6.67104e9	−0.330398
$196$	1.16676e10	0.564715
$197$	−4.00628e10	−1.89515	−0.947575	−	0.319534i	$-0.896474\pi$
$197$	−4.00628e10	−1.89515	−0.947575	+	0.319534i	$0.896474\pi$
$198$	3.04727e9	0.140902
$199$	−1.01005e10	−0.456569	−0.228284	−	0.973595i	$-0.573312\pi$
$199$	−1.01005e10	−0.456569	−0.228284	+	0.973595i	$0.573312\pi$
$200$	−5.05914e9	−0.223584
$201$	−3.20426e9	−0.138467
$202$	−1.41714e8	−0.00598867
$203$	−2.25472e10	−0.931883
$204$	0	0
$205$	4.06513e10	1.60761
$206$	−8.45833e8	−0.0327252
$207$	2.56743e9	0.0971923
$208$	−1.36629e10	−0.506126
$209$	−5.92957e10	−2.14964
$210$	−1.34987e9	−0.0478966
$211$	2.18033e10	0.757272	0.378636	−	0.925546i	$-0.376393\pi$
$211$	2.18033e10	0.757272	0.378636	+	0.925546i	$0.376393\pi$
$212$	−3.22963e10	−1.09810
$213$	−8.73714e9	−0.290845
$214$	−4.32042e9	−0.140820
$215$	6.20549e10	1.98063
$216$	−5.98305e9	−0.187017
$217$	3.92935e9	0.120296
$218$	2.14543e9	0.0643368
$219$	1.06703e10	0.313457
$220$	−7.22389e10	−2.07907
$221$	0	0
$222$	3.17191e9	0.0876460
$223$	6.76777e10	1.83262	0.916312	−	0.400464i	$-0.131151\pi$
$223$	6.76777e10	1.83262	0.916312	+	0.400464i	$0.131151\pi$
$224$	−8.49021e9	−0.225321
$225$	−2.95937e10	−0.769801
$226$	−5.02798e9	−0.128205
$227$	1.78509e10	0.446215	0.223107	−	0.974794i	$-0.428380\pi$
$227$	1.78509e10	0.446215	0.223107	+	0.974794i	$0.428380\pi$
$228$	2.56968e10	0.629756
$229$	6.47885e10	1.55682	0.778410	−	0.627757i	$-0.216027\pi$
$229$	6.47885e10	1.55682	0.778410	+	0.627757i	$0.216027\pi$
$230$	8.44840e8	0.0199067
$231$	−1.90326e10	−0.439790
$232$	−1.46177e10	−0.331270
$233$	−4.23546e10	−0.941454	−0.470727	−	0.882279i	$-0.656008\pi$
$233$	−4.23546e10	−0.941454	−0.470727	+	0.882279i	$0.656008\pi$
$234$	2.26606e9	0.0494083
$235$	−9.63592e10	−2.06105
$236$	8.85415e9	0.185799
$237$	−3.09080e10	−0.636360
$238$	0	0
$239$	−1.90315e10	−0.377297	−0.188649	−	0.982045i	$-0.560411\pi$
$239$	−1.90315e10	−0.377297	−0.188649	+	0.982045i	$0.560411\pi$
$240$	3.08654e10	0.600511
$241$	−5.40492e10	−1.03208	−0.516039	−	0.856565i	$-0.672594\pi$
$241$	−5.40492e10	−1.03208	−0.516039	+	0.856565i	$0.672594\pi$
$242$	7.89534e9	0.147980
$243$	−5.44395e10	−1.00158
$244$	−5.14344e10	−0.928965
$245$	4.52288e10	0.801987
$246$	3.44788e9	0.0600267
$247$	−4.40944e10	−0.753785
$248$	2.54744e9	0.0427634
$249$	−2.35904e10	−0.388900
$250$	3.84536e8	0.00622597
$251$	−1.87837e10	−0.298709	−0.149355	−	0.988784i	$-0.547720\pi$
$251$	−1.87837e10	−0.298709	−0.149355	+	0.988784i	$0.547720\pi$
$252$	−3.30334e10	−0.516002
$253$	1.19119e10	0.182785
$254$	9.40492e9	0.141776
$255$	0	0
$256$	5.95032e10	0.865886
$257$	1.37193e11	1.96170	0.980849	−	0.194769i	$-0.0623956\pi$
$257$	1.37193e11	1.96170	0.980849	+	0.194769i	$0.0623956\pi$
$258$	5.26325e9	0.0739546
$259$	7.93429e10	1.09562
$260$	−5.37195e10	−0.729041
$261$	−8.55068e10	−1.14056
$262$	−3.08164e9	−0.0404041
$263$	9.80468e10	1.26367	0.631833	−	0.775104i	$-0.282303\pi$
$263$	9.80468e10	1.26367	0.631833	+	0.775104i	$0.282303\pi$
$264$	−1.23391e10	−0.156338
$265$	−1.25194e11	−1.55948
$266$	−8.92239e9	−0.109273
$267$	5.55450e10	0.668874
$268$	−2.58028e10	−0.305534
$269$	5.66085e9	0.0659168	0.0329584	−	0.999457i	$-0.489507\pi$
$269$	5.66085e9	0.0659168	0.0329584	+	0.999457i	$0.489507\pi$
$270$	−1.15165e10	−0.131882
$271$	−1.95830e10	−0.220555	−0.110277	−	0.993901i	$-0.535174\pi$
$271$	−1.95830e10	−0.220555	−0.110277	+	0.993901i	$0.535174\pi$
$272$	0	0
$273$	−1.41534e10	−0.154215
$274$	1.60542e10	0.172073
$275$	−1.37304e11	−1.44772
$276$	−5.16223e9	−0.0535484
$277$	1.58344e10	0.161601	0.0808004	−	0.996730i	$-0.474252\pi$
$277$	1.58344e10	0.161601	0.0808004	+	0.996730i	$0.474252\pi$
$278$	−2.04329e10	−0.205177
$279$	1.49014e10	0.147234
$280$	−2.18909e10	−0.212840
$281$	−5.48078e10	−0.524401	−0.262201	−	0.965013i	$-0.584448\pi$
$281$	−5.48078e10	−0.524401	−0.262201	+	0.965013i	$0.584448\pi$
$282$	−8.17280e9	−0.0769573
$283$	1.85037e11	1.71482	0.857410	−	0.514633i	$-0.172072\pi$
$283$	1.85037e11	1.71482	0.857410	+	0.514633i	$0.172072\pi$
$284$	−7.03570e10	−0.641763
$285$	9.96120e10	0.894355
$286$	1.05137e10	0.0929196
$287$	8.62462e10	0.750363
$288$	−3.21978e10	−0.275778
$289$	0	0
$290$	−2.81369e10	−0.233607
$291$	−7.30536e9	−0.0597204
$292$	8.59241e10	0.691659
$293$	−4.24953e10	−0.336850	−0.168425	−	0.985714i	$-0.553868\pi$
$293$	−4.24953e10	−0.336850	−0.168425	+	0.985714i	$0.553868\pi$
$294$	3.83613e9	0.0299454
$295$	3.43226e10	0.263864
$296$	5.14390e10	0.389475
$297$	−1.62379e11	−1.21095
$298$	−5.32540e9	−0.0391182
$299$	8.85814e9	0.0640947
$300$	5.95030e10	0.424124
$301$	1.31656e11	0.924469
$302$	1.84951e10	0.127945
$303$	3.35666e9	0.0228779
$304$	2.04015e11	1.37003
$305$	−1.99382e11	−1.31928
$306$	0	0
$307$	−6.29686e10	−0.404577	−0.202289	−	0.979326i	$-0.564838\pi$
$307$	−6.29686e10	−0.404577	−0.202289	+	0.979326i	$0.564838\pi$
$308$	−1.53263e11	−0.970418
$309$	2.00346e10	0.125017
$310$	4.90347e9	0.0301562
$311$	−3.29544e10	−0.199752	−0.0998761	−	0.995000i	$-0.531845\pi$
$311$	−3.29544e10	−0.199752	−0.0998761	+	0.995000i	$0.531845\pi$
$312$	−9.17579e9	−0.0548211
$313$	−2.52444e11	−1.48667	−0.743336	−	0.668918i	$-0.766758\pi$
$313$	−2.52444e11	−1.48667	−0.743336	+	0.668918i	$0.766758\pi$
$314$	2.63046e10	0.152703
$315$	−1.28052e11	−0.732806
$316$	−2.48891e11	−1.40416
$317$	−9.07757e10	−0.504897	−0.252449	−	0.967610i	$-0.581236\pi$
$317$	−9.07757e10	−0.504897	−0.252449	+	0.967610i	$0.581236\pi$
$318$	−1.06185e10	−0.0582292
$319$	−3.96720e11	−2.14499
$320$	2.41403e11	1.28697
$321$	1.02334e11	0.537959
$322$	1.79242e9	0.00929156
$323$	0	0
$324$	−8.61842e10	−0.434485
$325$	−1.02104e11	−0.507655
$326$	−1.12178e10	−0.0550083
$327$	−5.08171e10	−0.245779
$328$	5.59145e10	0.266742
$329$	−2.04437e11	−0.962005
$330$	−2.37510e10	−0.110248
$331$	−3.94437e11	−1.80614	−0.903070	−	0.429493i	$-0.858692\pi$
$331$	−3.94437e11	−1.80614	−0.903070	+	0.429493i	$0.858692\pi$
$332$	−1.89965e11	−0.858128
$333$	3.00895e11	1.34096
$334$	2.45225e10	0.107821
$335$	−1.00023e11	−0.433908
$336$	6.54843e10	0.280292
$337$	8.92786e10	0.377062	0.188531	−	0.982067i	$-0.439627\pi$
$337$	8.92786e10	0.377062	0.188531	+	0.982067i	$0.439627\pi$
$338$	−2.02579e10	−0.0844247
$339$	1.19094e11	0.489769
$340$	0	0
$341$	6.91371e10	0.276896
$342$	−3.38368e10	−0.133743
$343$	2.63554e11	1.02813
$344$	8.53544e10	0.328634
$345$	−2.00111e10	−0.0760474
$346$	1.61379e10	0.0605347
$347$	4.33744e11	1.60602	0.803010	−	0.595965i	$-0.203230\pi$
$347$	4.33744e11	1.60602	0.803010	+	0.595965i	$0.203230\pi$
$348$	1.71925e11	0.628396
$349$	4.64877e11	1.67735	0.838676	−	0.544631i	$-0.183330\pi$
$349$	4.64877e11	1.67735	0.838676	+	0.544631i	$0.183330\pi$
$350$	−2.06605e10	−0.0735928
$351$	−1.20751e11	−0.424627
$352$	−1.49386e11	−0.518641
$353$	−1.39662e10	−0.0478731	−0.0239366	−	0.999713i	$-0.507620\pi$
$353$	−1.39662e10	−0.0478731	−0.0239366	+	0.999713i	$0.507620\pi$
$354$	2.91110e9	0.00985242
$355$	−2.72735e11	−0.911407
$356$	4.47284e11	1.47590
$357$	0	0
$358$	−3.93725e10	−0.126683
$359$	1.24630e11	0.396003	0.198002	−	0.980202i	$-0.436555\pi$
$359$	1.24630e11	0.396003	0.198002	+	0.980202i	$0.436555\pi$
$360$	−8.30177e10	−0.260501
$361$	3.35730e11	1.04042
$362$	2.08741e10	0.0638879
$363$	−1.87011e11	−0.565310
$364$	−1.13972e11	−0.340284
$365$	3.33080e11	0.982268
$366$	−1.69108e10	−0.0492606
$367$	−1.08338e9	−0.00311734	−0.00155867	−	0.999999i	$-0.500496\pi$
$367$	−1.08338e9	−0.00311734	−0.00155867	+	0.999999i	$0.500496\pi$
$368$	−4.09846e10	−0.116494
$369$	3.27075e11	0.918393
$370$	9.90128e10	0.274652
$371$	−2.65614e11	−0.727894
$372$	−2.99617e10	−0.0811192
$373$	−4.07410e11	−1.08979	−0.544895	−	0.838505i	$-0.683430\pi$
$373$	−4.07410e11	−1.08979	−0.544895	+	0.838505i	$0.683430\pi$
$374$	0	0
$375$	−9.10822e9	−0.0237844
$376$	−1.32539e11	−0.341978
$377$	−2.95015e11	−0.752157
$378$	−2.44336e10	−0.0615566
$379$	6.55713e11	1.63244	0.816220	−	0.577742i	$-0.196066\pi$
$379$	6.55713e11	1.63244	0.816220	+	0.577742i	$0.196066\pi$
$380$	8.02139e11	1.97344
$381$	−2.22767e11	−0.541613
$382$	3.14548e10	0.0755791
$383$	−2.37402e11	−0.563755	−0.281877	−	0.959450i	$-0.590957\pi$
$383$	−2.37402e11	−0.563755	−0.281877	+	0.959450i	$0.590957\pi$
$384$	8.61123e10	0.202104
$385$	−5.94114e11	−1.37815
$386$	−6.28131e10	−0.144015
$387$	4.99286e11	1.13149
$388$	−5.88274e10	−0.131776
$389$	−6.60328e11	−1.46213	−0.731066	−	0.682307i	$-0.760977\pi$
$389$	−6.60328e11	−1.46213	−0.731066	+	0.682307i	$0.760977\pi$
$390$	−1.76621e10	−0.0386591
$391$	0	0
$392$	6.22106e10	0.133069
$393$	7.29923e10	0.154351
$394$	−1.06069e11	−0.221747
$395$	−9.64809e11	−1.99413
$396$	−5.81225e11	−1.18773
$397$	5.84346e11	1.18063	0.590314	−	0.807174i	$-0.299004\pi$
$397$	5.84346e11	1.18063	0.590314	+	0.807174i	$0.299004\pi$
$398$	−2.67420e10	−0.0534220
$399$	2.11338e11	0.417445
$400$	4.72412e11	0.922681
$401$	7.67959e11	1.48316	0.741581	−	0.670863i	$-0.234076\pi$
$401$	7.67959e11	1.48316	0.741581	+	0.670863i	$0.234076\pi$
$402$	−8.48354e9	−0.0162017
$403$	5.14129e10	0.0970955
$404$	2.70300e10	0.0504812
$405$	−3.34088e11	−0.617039
$406$	−5.96956e10	−0.109037
$407$	1.39604e12	2.52188
$408$	0	0
$409$	1.00813e12	1.78140	0.890699	−	0.454594i	$-0.150216\pi$
$409$	1.00813e12	1.78140	0.890699	+	0.454594i	$0.150216\pi$
$410$	1.07627e11	0.188103
$411$	−3.80265e11	−0.657352
$412$	1.61331e11	0.275855
$413$	7.28191e10	0.123160
$414$	6.79747e9	0.0113722
$415$	−7.36387e11	−1.21868
$416$	−1.11089e11	−0.181865
$417$	4.83978e11	0.783815
$418$	−1.56990e11	−0.251524
$419$	2.58434e11	0.409626	0.204813	−	0.978801i	$-0.434341\pi$
$419$	2.58434e11	0.409626	0.204813	+	0.978801i	$0.434341\pi$
$420$	2.57469e11	0.403742
$421$	3.46983e11	0.538318	0.269159	−	0.963096i	$-0.413254\pi$
$421$	3.46983e11	0.538318	0.269159	+	0.963096i	$0.413254\pi$
$422$	5.77261e10	0.0886066
$423$	−7.75294e11	−1.17743
$424$	−1.72201e11	−0.258755
$425$	0	0
$426$	−2.31323e10	−0.0340310
$427$	−4.23012e11	−0.615782
$428$	8.24062e11	1.18703
$429$	−2.49029e11	−0.354971
$430$	1.64295e11	0.231748
$431$	8.62289e10	0.120366	0.0601832	−	0.998187i	$-0.480832\pi$
$431$	8.62289e10	0.120366	0.0601832	+	0.998187i	$0.480832\pi$
$432$	5.58685e11	0.771775
$433$	7.77469e11	1.06289	0.531444	−	0.847093i	$-0.321650\pi$
$433$	7.77469e11	1.06289	0.531444	+	0.847093i	$0.321650\pi$
$434$	1.04033e10	0.0140756
$435$	6.66458e11	0.892424
$436$	−4.09211e11	−0.542324
$437$	−1.32270e11	−0.173498
$438$	2.82505e10	0.0366769
$439$	1.06090e10	0.0136328	0.00681638	−	0.999977i	$-0.497830\pi$
$439$	1.06090e10	0.0136328	0.00681638	+	0.999977i	$0.497830\pi$
$440$	−3.85171e11	−0.489911
$441$	3.63905e11	0.458157
$442$	0	0
$443$	−9.16044e11	−1.13006	−0.565028	−	0.825072i	$-0.691135\pi$
$443$	−9.16044e11	−1.13006	−0.565028	+	0.825072i	$0.691135\pi$
$444$	−6.04999e11	−0.738807
$445$	1.73387e12	2.09602
$446$	1.79182e11	0.214431
$447$	1.26139e11	0.149439
$448$	5.12163e11	0.600699
$449$	−1.22897e11	−0.142703	−0.0713515	−	0.997451i	$-0.522731\pi$
$449$	−1.22897e11	−0.142703	−0.0713515	+	0.997451i	$0.522731\pi$
$450$	−7.83517e10	−0.0900725
$451$	1.51751e12	1.72718
$452$	9.59021e11	1.08070
$453$	−4.38078e11	−0.488776
$454$	4.72617e10	0.0522105
$455$	−4.41805e11	−0.483258
$456$	1.37013e11	0.148395
$457$	2.98540e11	0.320169	0.160085	−	0.987103i	$-0.448823\pi$
$457$	2.98540e11	0.320169	0.160085	+	0.987103i	$0.448823\pi$
$458$	1.71533e11	0.182160
$459$	0	0
$460$	−1.61142e11	−0.167802
$461$	−8.70582e11	−0.897751	−0.448875	−	0.893594i	$-0.648175\pi$
$461$	−8.70582e11	−0.897751	−0.448875	+	0.893594i	$0.648175\pi$
$462$	−5.03904e10	−0.0514588
$463$	6.99496e11	0.707409	0.353705	−	0.935357i	$-0.384922\pi$
$463$	6.99496e11	0.707409	0.353705	+	0.935357i	$0.384922\pi$
$464$	1.36497e12	1.36707
$465$	−1.16145e11	−0.115202
$466$	−1.12137e11	−0.110157
$467$	−1.26028e12	−1.22614	−0.613071	−	0.790028i	$-0.710066\pi$
$467$	−1.26028e12	−1.22614	−0.613071	+	0.790028i	$0.710066\pi$
$468$	−4.32220e11	−0.416484
$469$	−2.12210e11	−0.202529
$470$	−2.55119e11	−0.241158
$471$	−6.23056e11	−0.583355
$472$	4.72095e10	0.0437815
$473$	2.31650e12	2.12793
$474$	−8.18313e10	−0.0744589
$475$	1.52462e12	1.37417
$476$	0	0
$477$	−1.00730e12	−0.890893
$478$	−5.03875e10	−0.0441466
$479$	−3.89735e11	−0.338267	−0.169134	−	0.985593i	$-0.554097\pi$
$479$	−3.89735e11	−0.338267	−0.169134	+	0.985593i	$0.554097\pi$
$480$	2.50956e11	0.215780
$481$	1.03815e12	0.884314
$482$	−1.43100e11	−0.120761
$483$	−4.24557e10	−0.0354956
$484$	−1.50593e12	−1.24739
$485$	−2.28041e11	−0.187143
$486$	−1.44133e11	−0.117193
$487$	−1.53901e11	−0.123983	−0.0619915	−	0.998077i	$-0.519745\pi$
$487$	−1.53901e11	−0.123983	−0.0619915	+	0.998077i	$0.519745\pi$
$488$	−2.74243e11	−0.218901
$489$	2.65707e11	0.210142
$490$	1.19747e11	0.0938386
$491$	5.36570e11	0.416639	0.208320	−	0.978061i	$-0.433201\pi$
$491$	5.36570e11	0.416639	0.208320	+	0.978061i	$0.433201\pi$
$492$	−6.57637e11	−0.505992
$493$	0	0
$494$	−1.16743e11	−0.0881985
$495$	−2.25308e12	−1.68676
$496$	−2.37875e11	−0.176475
$497$	−5.78637e11	−0.425405
$498$	−6.24574e10	−0.0455043
$499$	1.60206e12	1.15671	0.578357	−	0.815784i	$-0.303694\pi$
$499$	1.60206e12	1.15671	0.578357	+	0.815784i	$0.303694\pi$
$500$	−7.33452e10	−0.0524815
$501$	−5.80845e11	−0.411899
$502$	−4.97312e10	−0.0349512
$503$	1.37869e12	0.960305	0.480153	−	0.877185i	$-0.340581\pi$
$503$	1.37869e12	0.960305	0.480153	+	0.877185i	$0.340581\pi$
$504$	−1.76131e11	−0.121590
$505$	1.04780e11	0.0716915
$506$	3.15378e10	0.0213872
$507$	4.79834e11	0.322519
$508$	−1.79386e12	−1.19510
$509$	2.44499e10	0.0161454	0.00807268	−	0.999967i	$-0.497430\pi$
$509$	2.44499e10	0.0161454	0.00807268	+	0.999967i	$0.497430\pi$
$510$	0	0
$511$	7.06665e11	0.458479
$512$	8.60596e11	0.553458
$513$	1.80305e12	1.14942
$514$	3.63229e11	0.229534
$515$	6.25391e11	0.391759
$516$	−1.00389e12	−0.623397
$517$	−3.59708e12	−2.21433
$518$	2.10067e11	0.128196
$519$	−3.82246e11	−0.231254
$520$	−2.86427e11	−0.171791
$521$	1.86370e12	1.10817	0.554085	−	0.832460i	$-0.313068\pi$
$521$	1.86370e12	1.10817	0.554085	+	0.832460i	$0.313068\pi$
$522$	−2.26386e11	−0.133454
$523$	−2.38491e11	−0.139384	−0.0696922	−	0.997569i	$-0.522202\pi$
$523$	−2.38491e11	−0.139384	−0.0696922	+	0.997569i	$0.522202\pi$
$524$	5.87781e11	0.340584
$525$	4.89370e11	0.281139
$526$	2.59587e11	0.147859
$527$	0	0
$528$	1.15220e12	0.645172
$529$	−1.77458e12	−0.985247
$530$	−3.31462e11	−0.182470
$531$	2.76155e11	0.150740
$532$	1.70183e12	0.921114
$533$	1.12847e12	0.605646
$534$	1.47060e11	0.0782633
$535$	3.19443e12	1.68578
$536$	−1.37578e11	−0.0719958
$537$	9.32586e11	0.483954
$538$	1.49875e10	0.00771277
$539$	1.68838e12	0.861632
$540$	2.19662e12	1.11169
$541$	−2.77186e12	−1.39118	−0.695589	−	0.718440i	$-0.744857\pi$
$541$	−2.77186e12	−1.39118	−0.695589	+	0.718440i	$0.744857\pi$
$542$	−5.18475e10	−0.0258066
$543$	−4.94428e11	−0.244064
$544$	0	0
$545$	−1.58628e12	−0.770187
$546$	−3.74721e10	−0.0180444
$547$	−3.03753e12	−1.45070	−0.725350	−	0.688381i	$-0.758322\pi$
$547$	−3.03753e12	−1.45070	−0.725350	+	0.688381i	$0.758322\pi$
$548$	−3.06213e12	−1.45048
$549$	−1.60420e12	−0.753675
$550$	−3.63523e11	−0.169395
$551$	4.40517e12	2.03601
$552$	−2.75246e10	−0.0126181
$553$	−2.04695e12	−0.930774
$554$	4.19229e10	0.0189085
$555$	−2.34524e12	−1.04923
$556$	3.89730e12	1.72953
$557$	−3.89518e12	−1.71467	−0.857333	−	0.514762i	$-0.827880\pi$
$557$	−3.89518e12	−1.71467	−0.857333	+	0.514762i	$0.827880\pi$
$558$	3.94527e10	0.0172275
$559$	1.72263e12	0.746173
$560$	2.04413e12	0.878339
$561$	0	0
$562$	−1.45108e11	−0.0613589
$563$	1.96578e12	0.824609	0.412305	−	0.911046i	$-0.364724\pi$
$563$	1.96578e12	0.824609	0.412305	+	0.911046i	$0.364724\pi$
$564$	1.55885e12	0.648708
$565$	3.71758e12	1.53477
$566$	4.89899e11	0.200647
$567$	−7.08804e11	−0.288007
$568$	−3.75137e11	−0.151225
$569$	2.20719e12	0.882744	0.441372	−	0.897324i	$-0.354492\pi$
$569$	2.20719e12	0.882744	0.441372	+	0.897324i	$0.354492\pi$
$570$	2.63731e11	0.104646
$571$	1.23698e12	0.486970	0.243485	−	0.969905i	$-0.421709\pi$
$571$	1.23698e12	0.486970	0.243485	+	0.969905i	$0.421709\pi$
$572$	−2.00534e12	−0.783261
$573$	−7.45045e11	−0.288727
$574$	2.28344e11	0.0877982
$575$	−3.06281e11	−0.116846
$576$	1.94229e12	0.735214
$577$	−9.00191e10	−0.0338099	−0.0169049	−	0.999857i	$-0.505381\pi$
$577$	−9.00191e10	−0.0338099	−0.0169049	+	0.999857i	$0.505381\pi$
$578$	0	0
$579$	1.48781e12	0.550164
$580$	5.36674e12	1.96918
$581$	−1.56233e12	−0.568826
$582$	−1.93415e10	−0.00698774
$583$	−4.67349e12	−1.67546
$584$	4.58140e11	0.162982
$585$	−1.67547e12	−0.591475
$586$	−1.12510e11	−0.0394141
$587$	4.18602e12	1.45522	0.727612	−	0.685989i	$-0.240630\pi$
$587$	4.18602e12	1.45522	0.727612	+	0.685989i	$0.240630\pi$
$588$	−7.31690e11	−0.252423
$589$	−7.67697e11	−0.262828
$590$	9.08717e10	0.0308741
$591$	2.51239e12	0.847116
$592$	−4.80327e12	−1.60727
$593$	−5.01785e12	−1.66637	−0.833185	−	0.552994i	$-0.813485\pi$
$593$	−5.01785e12	−1.66637	−0.833185	+	0.552994i	$0.813485\pi$
$594$	−4.29911e11	−0.141690
$595$	0	0
$596$	1.01575e12	0.329745
$597$	6.33417e11	0.204082
$598$	2.34526e10	0.00749956
$599$	−1.55548e12	−0.493679	−0.246840	−	0.969056i	$-0.579392\pi$
$599$	−1.55548e12	−0.493679	−0.246840	+	0.969056i	$0.579392\pi$
$600$	3.17264e11	0.0999403
$601$	5.68739e11	0.177819	0.0889094	−	0.996040i	$-0.471662\pi$
$601$	5.68739e11	0.177819	0.0889094	+	0.996040i	$0.471662\pi$
$602$	3.48571e11	0.108170
$603$	−8.04771e11	−0.247882
$604$	−3.52769e12	−1.07851
$605$	−5.83765e12	−1.77149
$606$	8.88703e9	0.00267689
$607$	−5.26859e12	−1.57524	−0.787618	−	0.616164i	$-0.788686\pi$
$607$	−5.26859e12	−1.57524	−0.787618	+	0.616164i	$0.788686\pi$
$608$	1.65878e12	0.492290
$609$	1.41396e12	0.416544
$610$	−5.27880e11	−0.154366
$611$	−2.67492e12	−0.776470
$612$	0	0
$613$	1.52329e12	0.435724	0.217862	−	0.975980i	$-0.430092\pi$
$613$	1.52329e12	0.435724	0.217862	+	0.975980i	$0.430092\pi$
$614$	−1.66714e11	−0.0473386
$615$	−2.54929e12	−0.718590
$616$	−8.17184e11	−0.228669
$617$	−2.76333e11	−0.0767625	−0.0383813	−	0.999263i	$-0.512220\pi$
$617$	−2.76333e11	−0.0767625	−0.0383813	+	0.999263i	$0.512220\pi$
$618$	5.30432e10	0.0146279
$619$	5.66715e12	1.55152	0.775759	−	0.631029i	$-0.217367\pi$
$619$	5.66715e12	1.55152	0.775759	+	0.631029i	$0.217367\pi$
$620$	−9.35272e11	−0.254200
$621$	−3.62215e11	−0.0977359
$622$	−8.72494e10	−0.0233725
$623$	3.67859e12	0.978330
$624$	8.56818e11	0.226234
$625$	−3.95410e12	−1.03654
$626$	−6.68365e11	−0.173952
$627$	3.71850e12	0.960869
$628$	−5.01724e12	−1.28720
$629$	0	0
$630$	−3.39028e11	−0.0857439
$631$	−3.55453e12	−0.892586	−0.446293	−	0.894887i	$-0.647256\pi$
$631$	−3.55453e12	−0.892586	−0.446293	+	0.894887i	$0.647256\pi$
$632$	−1.32706e12	−0.330875
$633$	−1.36731e12	−0.338494
$634$	−2.40336e11	−0.0590768
$635$	−6.95380e12	−1.69723
$636$	2.02534e12	0.490840
$637$	1.25554e12	0.302137
$638$	−1.05035e12	−0.250981
$639$	−2.19439e12	−0.520666
$640$	2.68804e12	0.633324
$641$	−6.59526e12	−1.54302	−0.771508	−	0.636219i	$-0.780497\pi$
$641$	−6.59526e12	−1.54302	−0.771508	+	0.636219i	$0.780497\pi$
$642$	2.70939e11	0.0629453
$643$	1.25758e12	0.290125	0.145063	−	0.989422i	$-0.453662\pi$
$643$	1.25758e12	0.290125	0.145063	+	0.989422i	$0.453662\pi$
$644$	−3.41881e11	−0.0783228
$645$	−3.89153e12	−0.885324
$646$	0	0
$647$	−1.68475e12	−0.377978	−0.188989	−	0.981979i	$-0.560521\pi$
$647$	−1.68475e12	−0.377978	−0.188989	+	0.981979i	$0.560521\pi$
$648$	−4.59526e11	−0.102382
$649$	1.28126e12	0.283488
$650$	−2.70329e11	−0.0593994
$651$	−2.46414e11	−0.0537714
$652$	2.13964e12	0.463690
$653$	−4.63150e12	−0.996810	−0.498405	−	0.866944i	$-0.666081\pi$
$653$	−4.63150e12	−0.996810	−0.498405	+	0.866944i	$0.666081\pi$
$654$	−1.34542e11	−0.0287580
$655$	2.27850e12	0.483685
$656$	−5.22118e12	−1.10078
$657$	2.67992e12	0.561147
$658$	−5.41262e11	−0.112562
$659$	−3.98192e12	−0.822447	−0.411223	−	0.911535i	$-0.634898\pi$
$659$	−3.98192e12	−0.822447	−0.411223	+	0.911535i	$0.634898\pi$
$660$	4.53019e12	0.929327
$661$	2.53278e12	0.516050	0.258025	−	0.966138i	$-0.416928\pi$
$661$	2.53278e12	0.516050	0.258025	+	0.966138i	$0.416928\pi$
$662$	−1.04430e12	−0.211332
$663$	0	0
$664$	−1.01288e12	−0.202209
$665$	6.59703e12	1.30813
$666$	7.96644e11	0.156903
$667$	−8.84955e11	−0.173123
$668$	−4.67733e12	−0.908875
$669$	−4.24415e12	−0.819168
$670$	−2.64818e11	−0.0507705
$671$	−7.44291e12	−1.41740
$672$	5.32431e11	0.100717
$673$	−3.73705e12	−0.702200	−0.351100	−	0.936338i	$-0.614192\pi$
$673$	−3.73705e12	−0.702200	−0.351100	+	0.936338i	$0.614192\pi$
$674$	2.36372e11	0.0441191
$675$	4.17510e12	0.774106
$676$	3.86393e12	0.711653
$677$	1.41128e12	0.258204	0.129102	−	0.991631i	$-0.458791\pi$
$677$	1.41128e12	0.258204	0.129102	+	0.991631i	$0.458791\pi$
$678$	3.15311e11	0.0573067
$679$	−4.83814e11	−0.0873502
$680$	0	0
$681$	−1.11945e12	−0.199454
$682$	1.83046e11	0.0323989
$683$	5.44425e11	0.0957293	0.0478646	−	0.998854i	$-0.484758\pi$
$683$	5.44425e11	0.0957293	0.0478646	+	0.998854i	$0.484758\pi$
$684$	6.45391e12	1.12738
$685$	−1.18702e13	−2.05991
$686$	6.97780e11	0.120298
$687$	−4.06296e12	−0.695885
$688$	−7.97023e12	−1.35620
$689$	−3.47538e12	−0.587510
$690$	−5.29809e10	−0.00889812
$691$	6.71997e12	1.12128	0.560642	−	0.828058i	$-0.310554\pi$
$691$	6.71997e12	1.12128	0.560642	+	0.828058i	$0.310554\pi$
$692$	−3.07809e12	−0.510274
$693$	−4.78017e12	−0.787306
$694$	1.14837e12	0.187917
$695$	1.51076e13	2.45621
$696$	9.16690e11	0.148075
$697$	0	0
$698$	1.23080e12	0.196263
$699$	2.65611e12	0.420822
$700$	3.94072e12	0.620346
$701$	1.89005e12	0.295625	0.147813	−	0.989015i	$-0.452777\pi$
$701$	1.89005e12	0.295625	0.147813	+	0.989015i	$0.452777\pi$
$702$	−3.19697e11	−0.0496846
$703$	−1.55016e13	−2.39375
$704$	9.01153e12	1.38268
$705$	6.04280e12	0.921270
$706$	−3.69766e10	−0.00560152
$707$	2.22303e11	0.0334624
$708$	−5.55254e11	−0.0830505
$709$	4.56043e12	0.677794	0.338897	−	0.940823i	$-0.389946\pi$
$709$	4.56043e12	0.677794	0.338897	+	0.940823i	$0.389946\pi$
$710$	−7.22086e11	−0.106642
$711$	−7.76273e12	−1.13920
$712$	2.38488e12	0.347781
$713$	1.54223e11	0.0223484
$714$	0	0
$715$	−7.77358e12	−1.11236
$716$	7.50977e12	1.06787
$717$	1.19349e12	0.168649
$718$	3.29969e11	0.0463354
$719$	7.71771e12	1.07698	0.538491	−	0.842631i	$-0.318995\pi$
$719$	7.71771e12	1.07698	0.538491	+	0.842631i	$0.318995\pi$
$720$	7.75203e12	1.07503
$721$	1.32684e12	0.182856
$722$	8.88872e11	0.121737
$723$	3.38949e12	0.461330
$724$	−3.98145e12	−0.538540
$725$	1.02005e13	1.37120
$726$	−4.95126e11	−0.0661456
$727$	8.85989e12	1.17631	0.588157	−	0.808747i	$-0.299854\pi$
$727$	8.85989e12	1.17631	0.588157	+	0.808747i	$0.299854\pi$
$728$	−6.07688e11	−0.0801843
$729$	5.47663e10	0.00718190
$730$	8.81854e11	0.114933
$731$	0	0
$732$	3.22551e12	0.415240
$733$	2.76655e12	0.353974	0.176987	−	0.984213i	$-0.443365\pi$
$733$	2.76655e12	0.353974	0.176987	+	0.984213i	$0.443365\pi$
$734$	−2.86834e9	−0.000364752 0
$735$	−2.83635e12	−0.358482
$736$	−3.33232e11	−0.0418597
$737$	−3.73384e12	−0.466178
$738$	8.65957e11	0.107459
$739$	3.07557e12	0.379338	0.189669	−	0.981848i	$-0.439259\pi$
$739$	3.07557e12	0.379338	0.189669	+	0.981848i	$0.439259\pi$
$740$	−1.88854e13	−2.31517
$741$	2.76521e12	0.336935
$742$	−7.03234e11	−0.0851691
$743$	3.96916e12	0.477803	0.238901	−	0.971044i	$-0.423213\pi$
$743$	3.96916e12	0.477803	0.238901	+	0.971044i	$0.423213\pi$
$744$	−1.59753e11	−0.0191149
$745$	3.93749e12	0.468291
$746$	−1.07865e12	−0.127514
$747$	−5.92488e12	−0.696204
$748$	0	0
$749$	6.77733e12	0.786847
$750$	−2.41147e10	−0.00278296
$751$	−1.22028e13	−1.39984	−0.699919	−	0.714222i	$-0.746781\pi$
$751$	−1.22028e13	−1.39984	−0.699919	+	0.714222i	$0.746781\pi$
$752$	1.23762e13	1.41126
$753$	1.17795e12	0.133520
$754$	−7.81077e11	−0.0880081
$755$	−1.36749e13	−1.53166
$756$	4.66038e12	0.518888
$757$	−1.03259e13	−1.14287	−0.571435	−	0.820647i	$-0.693613\pi$
$757$	−1.03259e13	−1.14287	−0.571435	+	0.820647i	$0.693613\pi$
$758$	1.73605e12	0.191008
$759$	−7.47011e11	−0.0817032
$760$	4.27693e12	0.465020
$761$	−1.04160e13	−1.12583	−0.562914	−	0.826516i	$-0.690320\pi$
$761$	−1.04160e13	−1.12583	−0.562914	+	0.826516i	$0.690320\pi$
$762$	−5.89794e11	−0.0633728
$763$	−3.36548e12	−0.359489
$764$	−5.99958e12	−0.637090
$765$	0	0
$766$	−6.28541e11	−0.0659636
$767$	9.52789e11	0.0994071
$768$	−3.73152e12	−0.387044
$769$	−1.00395e13	−1.03524	−0.517622	−	0.855610i	$-0.673183\pi$
$769$	−1.00395e13	−1.03524	−0.517622	+	0.855610i	$0.673183\pi$
$770$	−1.57296e12	−0.161254
$771$	−8.60352e12	−0.876863
$772$	1.19808e13	1.21397
$773$	5.92570e12	0.596942	0.298471	−	0.954419i	$-0.403523\pi$
$773$	5.92570e12	0.596942	0.298471	+	0.954419i	$0.403523\pi$
$774$	1.32190e12	0.132393
$775$	−1.77766e12	−0.177008
$776$	−3.13662e11	−0.0310516
$777$	−4.97569e12	−0.489732
$778$	−1.74827e12	−0.171080
$779$	−1.68504e13	−1.63942
$780$	3.36881e12	0.325875
$781$	−1.01811e13	−0.979190
$782$	0	0
$783$	1.20634e13	1.14694
$784$	−5.80911e12	−0.549145
$785$	−1.94490e13	−1.82803
$786$	1.93253e11	0.0180603
$787$	−2.24816e12	−0.208901	−0.104451	−	0.994530i	$-0.533308\pi$
$787$	−2.24816e12	−0.208901	−0.104451	+	0.994530i	$0.533308\pi$
$788$	2.02313e13	1.86920
$789$	−6.14863e12	−0.564848
$790$	−2.55441e12	−0.233329
$791$	7.88727e12	0.716362
$792$	−3.09904e12	−0.279875
$793$	−5.53482e12	−0.497020
$794$	1.54710e12	0.138142
$795$	7.85109e12	0.697072
$796$	5.10068e12	0.450318
$797$	−1.51847e13	−1.33305	−0.666523	−	0.745485i	$-0.732218\pi$
$797$	−1.51847e13	−1.33305	−0.666523	+	0.745485i	$0.732218\pi$
$798$	5.59534e11	0.0488442
$799$	0	0
$800$	3.84103e12	0.331545
$801$	1.39505e13	1.19741
$802$	2.03323e12	0.173541
$803$	1.24338e13	1.05532
$804$	1.61812e12	0.136571
$805$	−1.32528e12	−0.111231
$806$	1.36120e11	0.0113609
$807$	−3.54999e11	−0.0294643
$808$	1.44121e11	0.0118954
$809$	9.96291e12	0.817745	0.408873	−	0.912592i	$-0.365922\pi$
$809$	9.96291e12	0.817745	0.408873	+	0.912592i	$0.365922\pi$
$810$	−8.84523e11	−0.0721983
$811$	−1.30630e13	−1.06035	−0.530176	−	0.847887i	$-0.677874\pi$
$811$	−1.30630e13	−1.06035	−0.530176	+	0.847887i	$0.677874\pi$
$812$	1.13861e13	0.919125
$813$	1.22807e12	0.0985862
$814$	3.69614e12	0.295079
$815$	8.29420e12	0.658514
$816$	0	0
$817$	−2.57224e13	−2.01981
$818$	2.66910e12	0.208437
$819$	−3.55471e12	−0.276074
$820$	−2.05285e13	−1.58560
$821$	−3.57592e12	−0.274690	−0.137345	−	0.990523i	$-0.543857\pi$
$821$	−3.57592e12	−0.274690	−0.137345	+	0.990523i	$0.543857\pi$
$822$	−1.00678e12	−0.0769151
$823$	2.09663e13	1.59302	0.796512	−	0.604623i	$-0.206676\pi$
$823$	2.09663e13	1.59302	0.796512	+	0.604623i	$0.206676\pi$
$824$	8.60204e11	0.0650024
$825$	8.61050e12	0.647121
$826$	1.92794e11	0.0144107
$827$	−1.74701e13	−1.29873	−0.649366	−	0.760476i	$-0.724966\pi$
$827$	−1.74701e13	−1.29873	−0.649366	+	0.760476i	$0.724966\pi$
$828$	−1.29653e12	−0.0958617
$829$	−2.25587e13	−1.65890	−0.829448	−	0.558584i	$-0.811345\pi$
$829$	−2.25587e13	−1.65890	−0.829448	+	0.558584i	$0.811345\pi$
$830$	−1.94964e12	−0.142595
$831$	−9.92996e11	−0.0722342
$832$	6.70130e12	0.484846
$833$	0	0
$834$	1.28137e12	0.0917123
$835$	−1.81314e13	−1.29075
$836$	2.99438e13	2.12021
$837$	−2.10230e12	−0.148058
$838$	6.84225e11	0.0479293
$839$	−2.00947e12	−0.140008	−0.0700039	−	0.997547i	$-0.522301\pi$
$839$	−2.00947e12	−0.140008	−0.0700039	+	0.997547i	$0.522301\pi$
$840$	1.37280e12	0.0951375
$841$	1.49658e13	1.03162
$842$	9.18665e11	0.0629873
$843$	3.43706e12	0.234403
$844$	−1.10105e13	−0.746905
$845$	1.49783e13	1.01066
$846$	−2.05265e12	−0.137768
$847$	−1.23852e13	−0.826853
$848$	1.60798e13	1.06782
$849$	−1.16039e13	−0.766510
$850$	0	0
$851$	3.11412e12	0.203542
$852$	4.41217e12	0.286863
$853$	1.92491e13	1.24491	0.622457	−	0.782654i	$-0.286135\pi$
$853$	1.92491e13	1.24491	0.622457	+	0.782654i	$0.286135\pi$
$854$	−1.11996e12	−0.0720511
$855$	2.50182e13	1.60106
$856$	4.39382e12	0.279712
$857$	−1.66278e12	−0.105298	−0.0526492	−	0.998613i	$-0.516767\pi$
$857$	−1.66278e12	−0.105298	−0.0526492	+	0.998613i	$0.516767\pi$
$858$	−6.59325e11	−0.0415343
$859$	9.33148e12	0.584765	0.292382	−	0.956301i	$-0.405552\pi$
$859$	9.33148e12	0.584765	0.292382	+	0.956301i	$0.405552\pi$
$860$	−3.13371e13	−1.95351
$861$	−5.40860e12	−0.335406
$862$	2.28298e11	0.0140838
$863$	−1.24232e13	−0.762401	−0.381200	−	0.924492i	$-0.624489\pi$
$863$	−1.24232e13	−0.762401	−0.381200	+	0.924492i	$0.624489\pi$
$864$	4.54248e12	0.277320
$865$	−1.19320e13	−0.724672
$866$	2.05841e12	0.124366
$867$	0	0
$868$	−1.98428e12	−0.118649
$869$	−3.60162e13	−2.14244
$870$	1.76450e12	0.104420
$871$	−2.77662e12	−0.163469
$872$	−2.18188e12	−0.127793
$873$	−1.83479e12	−0.106911
$874$	−3.50194e11	−0.0203006
$875$	−6.03212e11	−0.0347884
$876$	−5.38840e12	−0.309166
$877$	1.23664e13	0.705903	0.352952	−	0.935642i	$-0.385178\pi$
$877$	1.23664e13	0.705903	0.352952	+	0.935642i	$0.385178\pi$
$878$	2.80881e10	0.00159514
$879$	2.66493e12	0.150569
$880$	3.59666e13	2.02175
$881$	2.42210e13	1.35457	0.677283	−	0.735723i	$-0.263157\pi$
$881$	2.42210e13	1.35457	0.677283	+	0.735723i	$0.263157\pi$
$882$	9.63467e11	0.0536078
$883$	2.87422e13	1.59110	0.795548	−	0.605891i	$-0.207183\pi$
$883$	2.87422e13	1.59110	0.795548	+	0.605891i	$0.207183\pi$
$884$	0	0
$885$	−2.15241e12	−0.117945
$886$	−2.42530e12	−0.132225
$887$	−5.52286e12	−0.299577	−0.149788	−	0.988718i	$-0.547859\pi$
$887$	−5.52286e12	−0.299577	−0.149788	+	0.988718i	$0.547859\pi$
$888$	−3.22580e12	−0.174092
$889$	−1.47533e13	−0.792191
$890$	4.59055e12	0.245250
$891$	−1.24714e13	−0.662929
$892$	−3.41766e13	−1.80753
$893$	3.99418e13	2.10182
$894$	3.33962e11	0.0174855
$895$	2.91112e13	1.51655
$896$	5.70298e12	0.295608
$897$	−5.55504e11	−0.0286498
$898$	−3.25380e11	−0.0166973
$899$	−5.13630e12	−0.262260
$900$	1.49445e13	0.759262
$901$	0	0
$902$	4.01772e12	0.202093
$903$	−8.25632e12	−0.413230
$904$	5.11341e12	0.254655
$905$	−1.54338e13	−0.764813
$906$	−1.15985e12	−0.0571905
$907$	1.32164e13	0.648458	0.324229	−	0.945979i	$-0.394895\pi$
$907$	1.32164e13	0.648458	0.324229	+	0.945979i	$0.394895\pi$
$908$	−9.01454e12	−0.440106
$909$	8.43047e11	0.0409557
$910$	−1.16971e12	−0.0565449
$911$	1.79264e13	0.862305	0.431152	−	0.902279i	$-0.358107\pi$
$911$	1.79264e13	0.862305	0.431152	+	0.902279i	$0.358107\pi$
$912$	−1.27940e13	−0.612392
$913$	−2.74892e13	−1.30932
$914$	7.90408e11	0.0374622
$915$	1.25035e13	0.589707
$916$	−3.27176e13	−1.53550
$917$	4.83408e12	0.225763
$918$	0	0
$919$	−1.17404e13	−0.542955	−0.271478	−	0.962445i	$-0.587512\pi$
$919$	−1.17404e13	−0.542955	−0.271478	+	0.962445i	$0.587512\pi$
$920$	−8.59194e11	−0.0395408
$921$	3.94884e12	0.180843
$922$	−2.30494e12	−0.105044
$923$	−7.57107e12	−0.343360
$924$	9.61130e12	0.433769
$925$	−3.58953e13	−1.61213
$926$	1.85197e12	0.0827722
$927$	5.03182e12	0.223803
$928$	1.10981e13	0.491227
$929$	−6.80294e12	−0.299658	−0.149829	−	0.988712i	$-0.547872\pi$
$929$	−6.80294e12	−0.299658	−0.149829	+	0.988712i	$0.547872\pi$
$930$	−3.07503e11	−0.0134796
$931$	−1.87478e13	−0.817855
$932$	2.13887e13	0.928565
$933$	2.06661e12	0.0892875
$934$	−3.33669e12	−0.143468
$935$	0	0
$936$	−2.30456e12	−0.0981401
$937$	1.18659e12	0.0502889	0.0251444	−	0.999684i	$-0.491995\pi$
$937$	1.18659e12	0.0502889	0.0251444	+	0.999684i	$0.491995\pi$
$938$	−5.61842e11	−0.0236974
$939$	1.58311e13	0.664530
$940$	4.86604e13	2.03283
$941$	2.04736e13	0.851219	0.425610	−	0.904907i	$-0.360060\pi$
$941$	2.04736e13	0.851219	0.425610	+	0.904907i	$0.360060\pi$
$942$	−1.64959e12	−0.0682569
$943$	3.38507e12	0.139401
$944$	−4.40833e12	−0.180676
$945$	1.80657e13	0.736904
$946$	6.13312e12	0.248984
$947$	−1.56711e11	−0.00633178	−0.00316589	−	0.999995i	$-0.501008\pi$
$947$	−1.56711e11	−0.00633178	−0.00316589	+	0.999995i	$0.501008\pi$
$948$	1.56082e13	0.627648
$949$	9.24624e12	0.370056
$950$	4.03655e12	0.160788
$951$	5.69265e12	0.225685
$952$	0	0
$953$	1.16177e13	0.456249	0.228124	−	0.973632i	$-0.426741\pi$
$953$	1.16177e13	0.456249	0.228124	+	0.973632i	$0.426741\pi$
$954$	−2.66690e12	−0.104241
$955$	−2.32570e13	−0.904771
$956$	9.61074e12	0.372132
$957$	2.48788e13	0.958795
$958$	−1.03186e12	−0.0395798
$959$	−2.51839e13	−0.961477
$960$	−1.51386e13	−0.575263
$961$	−2.55445e13	−0.966145
$962$	2.74858e12	0.103471
$963$	2.57019e13	0.963047
$964$	2.72943e13	1.01795
$965$	4.64426e13	1.72403
$966$	−1.12405e11	−0.00415325
$967$	−2.83183e13	−1.04147	−0.520736	−	0.853718i	$-0.674342\pi$
$967$	−2.83183e13	−1.04147	−0.520736	+	0.853718i	$0.674342\pi$
$968$	−8.02948e12	−0.293933
$969$	0	0
$970$	−6.03756e11	−0.0218972
$971$	−2.45044e13	−0.884623	−0.442311	−	0.896862i	$-0.645841\pi$
$971$	−2.45044e13	−0.884623	−0.442311	+	0.896862i	$0.645841\pi$
$972$	2.74914e13	0.987868
$973$	3.20526e13	1.14645
$974$	−4.07466e11	−0.0145070
$975$	6.40307e12	0.226917
$976$	2.56083e13	0.903352
$977$	1.92163e13	0.674753	0.337376	−	0.941370i	$-0.390461\pi$
$977$	1.92163e13	0.674753	0.337376	+	0.941370i	$0.390461\pi$
$978$	7.03481e11	0.0245883
$979$	6.47251e13	2.25191
$980$	−2.28401e13	−0.791007
$981$	−1.27630e13	−0.439990
$982$	1.42061e12	0.0487499
$983$	−4.13553e13	−1.41267	−0.706334	−	0.707878i	$-0.749653\pi$
$983$	−4.13553e13	−1.41267	−0.706334	+	0.707878i	$0.749653\pi$
$984$	−3.50646e12	−0.119232
$985$	7.84255e13	2.65457
$986$	0	0
$987$	1.28205e13	0.430008
$988$	2.22673e13	0.743465
$989$	5.16737e12	0.171746
$990$	−5.96522e12	−0.197364
$991$	−1.07977e12	−0.0355631	−0.0177816	−	0.999842i	$-0.505660\pi$
$991$	−1.07977e12	−0.0355631	−0.0177816	+	0.999842i	$0.505660\pi$
$992$	−1.93409e12	−0.0634122
$993$	2.47356e13	0.807329
$994$	−1.53199e12	−0.0497756
$995$	1.97725e13	0.639524
$996$	1.19129e13	0.383576
$997$	−3.60906e13	−1.15682	−0.578411	−	0.815746i	$-0.696327\pi$
$997$	−3.60906e13	−1.15682	−0.578411	+	0.815746i	$0.696327\pi$
$998$	4.24158e12	0.135344
$999$	−4.24505e13	−1.34846

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.g.1.20	✓	36
17.16	even	2		289.10.a.h.1.20	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.20	✓	36	1.1	even	1	trivial
289.10.a.h.1.20	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)

\(f(q)\)	\(=\)	\(q+2.64758 q^{2} -62.7112 q^{3} -504.990 q^{4} -1957.56 q^{5} -166.033 q^{6} -4153.19 q^{7} -2692.56 q^{8} -15750.3 q^{9} +O(q^{10})\)	\(q+2.64758 q^{2} -62.7112 q^{3} -504.990 q^{4} -1957.56 q^{5} -166.033 q^{6} -4153.19 q^{7} -2692.56 q^{8} -15750.3 q^{9} -5182.80 q^{10} -73075.6 q^{11} +31668.5 q^{12} -54341.7 q^{13} -10995.9 q^{14} +122761. q^{15} +251426. q^{16} -41700.2 q^{18} +811429. q^{19} +988551. q^{20} +260451. q^{21} -193473. q^{22} -163008. q^{23} +168854. q^{24} +1.87893e6 q^{25} -143874. q^{26} +2.22206e6 q^{27} +2.09732e6 q^{28} +5.42890e6 q^{29} +325020. q^{30} -946104. q^{31} +2.04426e6 q^{32} +4.58266e6 q^{33} +8.13013e6 q^{35} +7.95375e6 q^{36} -1.91041e7 q^{37} +2.14832e6 q^{38} +3.40783e6 q^{39} +5.27086e6 q^{40} -2.07663e7 q^{41} +689566. q^{42} -3.17001e7 q^{43} +3.69025e7 q^{44} +3.08322e7 q^{45} -431577. q^{46} +4.92240e7 q^{47} -1.57672e7 q^{48} -2.31046e7 q^{49} +4.97462e6 q^{50} +2.74420e7 q^{52} +6.39542e7 q^{53} +5.88309e6 q^{54} +1.43050e8 q^{55} +1.11827e7 q^{56} -5.08857e7 q^{57} +1.43734e7 q^{58} -1.75333e7 q^{59} -6.19932e7 q^{60} +1.01852e8 q^{61} -2.50489e6 q^{62} +6.54140e7 q^{63} -1.23318e8 q^{64} +1.06377e8 q^{65} +1.21329e7 q^{66} +5.10956e7 q^{67} +1.02224e7 q^{69} +2.15252e7 q^{70} +1.39323e8 q^{71} +4.24087e7 q^{72} -1.70150e8 q^{73} -5.05796e7 q^{74} -1.17830e8 q^{75} -4.09764e8 q^{76} +3.03497e8 q^{77} +9.02250e6 q^{78} +4.92862e8 q^{79} -4.92183e8 q^{80} +1.70665e8 q^{81} -5.49803e7 q^{82} +3.76175e8 q^{83} -1.31525e8 q^{84} -8.39284e7 q^{86} -3.40453e8 q^{87} +1.96761e8 q^{88} -8.85727e8 q^{89} +8.16308e7 q^{90} +2.25691e8 q^{91} +8.23176e7 q^{92} +5.93313e7 q^{93} +1.30325e8 q^{94} -1.58842e9 q^{95} -1.28198e8 q^{96} +1.16492e8 q^{97} -6.11713e7 q^{98} +1.15096e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 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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