LMFDB - Embedded newform 289.10.a.h.1.7

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			1.7
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)

$f(q)$	$=$	$q-32.5443 q^{2} -213.342 q^{3} +547.129 q^{4} +2406.57 q^{5} +6943.04 q^{6} +8347.75 q^{7} -1143.25 q^{8} +25831.6 q^{9} +O(q^{10})$	\(q-32.5443 q^{2} -213.342 q^{3} +547.129 q^{4} +2406.57 q^{5} +6943.04 q^{6} +8347.75 q^{7} -1143.25 q^{8} +25831.6 q^{9} -78320.2 q^{10} -29406.6 q^{11} -116725. q^{12} +114840. q^{13} -271671. q^{14} -513422. q^{15} -242924. q^{16} -840671. q^{18} +79151.9 q^{19} +1.31671e6 q^{20} -1.78092e6 q^{21} +957015. q^{22} +2.58010e6 q^{23} +243903. q^{24} +3.83848e6 q^{25} -3.73739e6 q^{26} -1.31176e6 q^{27} +4.56730e6 q^{28} +569151. q^{29} +1.67090e7 q^{30} -3.28465e6 q^{31} +8.49112e6 q^{32} +6.27364e6 q^{33} +2.00895e7 q^{35} +1.41332e7 q^{36} +1.35898e7 q^{37} -2.57594e6 q^{38} -2.45002e7 q^{39} -2.75132e6 q^{40} -5.82076e6 q^{41} +5.79588e7 q^{42} +4.20879e7 q^{43} -1.60892e7 q^{44} +6.21657e7 q^{45} -8.39674e7 q^{46} -2.37790e7 q^{47} +5.18258e7 q^{48} +2.93314e7 q^{49} -1.24920e8 q^{50} +6.28325e7 q^{52} +4.78987e7 q^{53} +4.26902e7 q^{54} -7.07691e7 q^{55} -9.54357e6 q^{56} -1.68864e7 q^{57} -1.85226e7 q^{58} +1.36738e8 q^{59} -2.80908e8 q^{60} -8.58524e7 q^{61} +1.06896e8 q^{62} +2.15636e8 q^{63} -1.51960e8 q^{64} +2.76372e8 q^{65} -2.04171e8 q^{66} +1.38932e8 q^{67} -5.50442e8 q^{69} -6.53798e8 q^{70} +1.34182e7 q^{71} -2.95320e7 q^{72} -1.85812e8 q^{73} -4.42269e8 q^{74} -8.18906e8 q^{75} +4.33063e7 q^{76} -2.45479e8 q^{77} +7.97342e8 q^{78} +9.57070e7 q^{79} -5.84614e8 q^{80} -2.28592e8 q^{81} +1.89432e8 q^{82} +6.11352e8 q^{83} -9.74395e8 q^{84} -1.36972e9 q^{86} -1.21424e8 q^{87} +3.36191e7 q^{88} +3.05565e8 q^{89} -2.02314e9 q^{90} +9.58659e8 q^{91} +1.41165e9 q^{92} +7.00752e8 q^{93} +7.73870e8 q^{94} +1.90485e8 q^{95} -1.81151e9 q^{96} +4.08368e8 q^{97} -9.54568e8 q^{98} -7.59619e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−32.5443	−1.43827	−0.719133	−	0.694872i	$-0.755461\pi$
$2$	−32.5443	−1.43827	−0.719133	+	0.694872i	$0.755461\pi$
$3$	−213.342	−1.52065	−0.760326	−	0.649542i	$-0.774961\pi$
$3$	−213.342	−1.52065	−0.760326	+	0.649542i	$0.774961\pi$
$4$	547.129	1.06861
$5$	2406.57	1.72200	0.861002	−	0.508601i	$-0.169837\pi$
$5$	2406.57	1.72200	0.861002	+	0.508601i	$0.169837\pi$
$6$	6943.04	2.18710
$7$	8347.75	1.31410	0.657050	−	0.753847i	$-0.271804\pi$
$7$	8347.75	1.31410	0.657050	+	0.753847i	$0.271804\pi$
$8$	−1143.25	−0.0986817
$9$	25831.6	1.31238
$10$	−78320.2	−2.47670
$11$	−29406.6	−0.605588	−0.302794	−	0.953056i	$-0.597919\pi$
$11$	−29406.6	−0.605588	−0.302794	+	0.953056i	$0.597919\pi$
$12$	−116725.	−1.62499
$13$	114840.	1.11519	0.557596	−	0.830113i	$-0.311724\pi$
$13$	114840.	1.11519	0.557596	+	0.830113i	$0.311724\pi$
$14$	−271671.	−1.89003
$15$	−513422.	−2.61857
$16$	−242924.	−0.926681
$17$	0	0
$17$	0	0
$18$	−840671.	−1.88756
$19$	79151.9	0.139338	0.0696691	−	0.997570i	$-0.477806\pi$
$19$	79151.9	0.139338	0.0696691	+	0.997570i	$0.477806\pi$
$20$	1.31671e6	1.84015
$21$	−1.78092e6	−1.99829
$22$	957015.	0.870997
$23$	2.58010e6	1.92248	0.961239	−	0.275718i	$-0.0889156\pi$
$23$	2.58010e6	1.92248	0.961239	+	0.275718i	$0.0889156\pi$
$24$	243903.	0.150060
$25$	3.83848e6	1.96530
$26$	−3.73739e6	−1.60394
$27$	−1.31176e6	−0.475025
$28$	4.56730e6	1.40426
$29$	569151.	0.149430	0.0747148	−	0.997205i	$-0.476195\pi$
$29$	569151.	0.149430	0.0747148	+	0.997205i	$0.476195\pi$
$30$	1.67090e7	3.76620
$31$	−3.28465e6	−0.638795	−0.319397	−	0.947621i	$-0.603480\pi$
$31$	−3.28465e6	−0.638795	−0.319397	+	0.947621i	$0.603480\pi$
$32$	8.49112e6	1.43150
$33$	6.27364e6	0.920888
$34$	0	0
$35$	2.00895e7	2.26289
$36$	1.41332e7	1.40243
$37$	1.35898e7	1.19208	0.596038	−	0.802956i	$-0.296741\pi$
$37$	1.35898e7	1.19208	0.596038	+	0.802956i	$0.296741\pi$
$38$	−2.57594e6	−0.200406
$39$	−2.45002e7	−1.69582
$40$	−2.75132e6	−0.169930
$41$	−5.82076e6	−0.321701	−0.160851	−	0.986979i	$-0.551424\pi$
$41$	−5.82076e6	−0.321701	−0.160851	+	0.986979i	$0.551424\pi$
$42$	5.79588e7	2.87407
$43$	4.20879e7	1.87737	0.938684	−	0.344779i	$-0.112046\pi$
$43$	4.20879e7	1.87737	0.938684	+	0.344779i	$0.112046\pi$
$44$	−1.60892e7	−0.647138
$45$	6.21657e7	2.25993
$46$	−8.39674e7	−2.76504
$47$	−2.37790e7	−0.710810	−0.355405	−	0.934712i	$-0.615657\pi$
$47$	−2.37790e7	−0.710810	−0.355405	+	0.934712i	$0.615657\pi$
$48$	5.18258e7	1.40916
$49$	2.93314e7	0.726859
$50$	−1.24920e8	−2.82662
$51$	0	0
$52$	6.28325e7	1.19171
$53$	4.78987e7	0.833839	0.416920	−	0.908943i	$-0.363110\pi$
$53$	4.78987e7	0.833839	0.416920	+	0.908943i	$0.363110\pi$
$54$	4.26902e7	0.683213
$55$	−7.07691e7	−1.04283
$56$	−9.54357e6	−0.129678
$57$	−1.68864e7	−0.211885
$58$	−1.85226e7	−0.214920
$59$	1.36738e8	1.46911	0.734555	−	0.678549i	$-0.237391\pi$
$59$	1.36738e8	1.46911	0.734555	+	0.678549i	$0.237391\pi$
$60$	−2.80908e8	−2.79823
$61$	−8.58524e7	−0.793905	−0.396952	−	0.917839i	$-0.629932\pi$
$61$	−8.58524e7	−0.793905	−0.396952	+	0.917839i	$0.629932\pi$
$62$	1.06896e8	0.918757
$63$	2.15636e8	1.72460
$64$	−1.51960e8	−1.13219
$65$	2.76372e8	1.92036
$66$	−2.04171e8	−1.32448
$67$	1.38932e8	0.842296	0.421148	−	0.906992i	$-0.361627\pi$
$67$	1.38932e8	0.842296	0.421148	+	0.906992i	$0.361627\pi$
$68$	0	0
$69$	−5.50442e8	−2.92342
$70$	−6.53798e8	−3.25463
$71$	1.34182e7	0.0626659	0.0313330	−	0.999509i	$-0.490025\pi$
$71$	1.34182e7	0.0626659	0.0313330	+	0.999509i	$0.490025\pi$
$72$	−2.95320e7	−0.129508
$73$	−1.85812e8	−0.765809	−0.382904	−	0.923788i	$-0.625076\pi$
$73$	−1.85812e8	−0.765809	−0.382904	+	0.923788i	$0.625076\pi$
$74$	−4.42269e8	−1.71452
$75$	−8.18906e8	−2.98854
$76$	4.33063e7	0.148898
$77$	−2.45479e8	−0.795803
$78$	7.97342e8	2.43904
$79$	9.57070e7	0.276453	0.138227	−	0.990401i	$-0.455860\pi$
$79$	9.57070e7	0.276453	0.138227	+	0.990401i	$0.455860\pi$
$80$	−5.84614e8	−1.59575
$81$	−2.28592e8	−0.590035
$82$	1.89432e8	0.462692
$83$	6.11352e8	1.41397	0.706985	−	0.707229i	$-0.250055\pi$
$83$	6.11352e8	1.41397	0.706985	+	0.707229i	$0.250055\pi$
$84$	−9.74395e8	−2.13539
$85$	0	0
$86$	−1.36972e9	−2.70016
$87$	−1.21424e8	−0.227231
$88$	3.36191e7	0.0597604
$89$	3.05565e8	0.516237	0.258118	−	0.966113i	$-0.416898\pi$
$89$	3.05565e8	0.516237	0.258118	+	0.966113i	$0.416898\pi$
$90$	−2.02314e9	−3.25038
$91$	9.58659e8	1.46547
$92$	1.41165e9	2.05438
$93$	7.00752e8	0.971384
$94$	7.73870e8	1.02233
$95$	1.90485e8	0.239941
$96$	−1.81151e9	−2.17681
$97$	4.08368e8	0.468359	0.234179	−	0.972193i	$-0.424760\pi$
$97$	4.08368e8	0.468359	0.234179	+	0.972193i	$0.424760\pi$
$98$	−9.54568e8	−1.04542
$99$	−7.59619e8	−0.794763
$100$	2.10014e9	2.10014
$101$	−3.77148e8	−0.360633	−0.180317	−	0.983609i	$-0.557712\pi$
$101$	−3.77148e8	−0.360633	−0.180317	+	0.983609i	$0.557712\pi$
$102$	0	0
$103$	1.64827e8	0.144298	0.0721492	−	0.997394i	$-0.477014\pi$
$103$	1.64827e8	0.144298	0.0721492	+	0.997394i	$0.477014\pi$
$104$	−1.31291e8	−0.110049
$105$	−4.28592e9	−3.44106
$106$	−1.55883e9	−1.19928
$107$	−3.09454e8	−0.228228	−0.114114	−	0.993468i	$-0.536403\pi$
$107$	−3.09454e8	−0.228228	−0.114114	+	0.993468i	$0.536403\pi$
$108$	−7.17701e8	−0.507617
$109$	6.81315e8	0.462305	0.231152	−	0.972918i	$-0.425750\pi$
$109$	6.81315e8	0.462305	0.231152	+	0.972918i	$0.425750\pi$
$110$	2.30313e9	1.49986
$111$	−2.89926e9	−1.81273
$112$	−2.02787e9	−1.21775
$113$	8.86461e8	0.511454	0.255727	−	0.966749i	$-0.417685\pi$
$113$	8.86461e8	0.511454	0.255727	+	0.966749i	$0.417685\pi$
$114$	5.49555e8	0.304747
$115$	6.20920e9	3.31051
$116$	3.11399e8	0.159682
$117$	2.96651e9	1.46356
$118$	−4.45003e9	−2.11297
$119$	0	0
$120$	5.86970e8	0.258405
$121$	−1.49320e9	−0.633263
$122$	2.79400e9	1.14185
$123$	1.24181e9	0.489195
$124$	−1.79713e9	−0.682623
$125$	4.53724e9	1.66225
$126$	−7.01772e9	−2.48044
$127$	2.43262e9	0.829770	0.414885	−	0.909874i	$-0.363822\pi$
$127$	2.43262e9	0.829770	0.414885	+	0.909874i	$0.363822\pi$
$128$	5.97982e8	0.196899
$129$	−8.97910e9	−2.85482
$130$	−8.99432e9	−2.76200
$131$	2.50008e9	0.741710	0.370855	−	0.928691i	$-0.379065\pi$
$131$	2.50008e9	0.741710	0.370855	+	0.928691i	$0.379065\pi$
$132$	3.43249e9	0.984072
$133$	6.60741e8	0.183104
$134$	−4.52143e9	−1.21145
$135$	−3.15684e9	−0.817995
$136$	0	0
$137$	−5.99822e9	−1.45472	−0.727361	−	0.686255i	$-0.759253\pi$
$137$	−5.99822e9	−1.45472	−0.727361	+	0.686255i	$0.759253\pi$
$138$	1.79137e10	4.20466
$139$	1.99556e9	0.453417	0.226708	−	0.973963i	$-0.427204\pi$
$139$	1.99556e9	0.453417	0.226708	+	0.973963i	$0.427204\pi$
$140$	1.09915e10	2.41815
$141$	5.07305e9	1.08089
$142$	−4.36685e8	−0.0901303
$143$	−3.37706e9	−0.675346
$144$	−6.27512e9	−1.21616
$145$	1.36971e9	0.257319
$146$	6.04711e9	1.10144
$147$	−6.25760e9	−1.10530
$148$	7.43535e9	1.27387
$149$	−2.73561e8	−0.0454690	−0.0227345	−	0.999742i	$-0.507237\pi$
$149$	−2.73561e8	−0.0454690	−0.0227345	+	0.999742i	$0.507237\pi$
$150$	2.66507e10	4.29831
$151$	−8.80058e9	−1.37757	−0.688787	−	0.724964i	$-0.741856\pi$
$151$	−8.80058e9	−1.37757	−0.688787	+	0.724964i	$0.741856\pi$
$152$	−9.04905e7	−0.0137501
$153$	0	0
$154$	7.98892e9	1.14458
$155$	−7.90475e9	−1.10001
$156$	−1.34048e10	−1.81217
$157$	−9.26065e9	−1.21645	−0.608223	−	0.793766i	$-0.708117\pi$
$157$	−9.26065e9	−1.21645	−0.608223	+	0.793766i	$0.708117\pi$
$158$	−3.11471e9	−0.397614
$159$	−1.02188e10	−1.26798
$160$	2.04345e10	2.46504
$161$	2.15380e10	2.52633
$162$	7.43934e9	0.848627
$163$	1.62020e10	1.79773	0.898866	−	0.438223i	$-0.144392\pi$
$163$	1.62020e10	1.79773	0.898866	+	0.438223i	$0.144392\pi$
$164$	−3.18471e9	−0.343773
$165$	1.50980e10	1.58577
$166$	−1.98960e10	−2.03367
$167$	−1.25587e10	−1.24945	−0.624727	−	0.780843i	$-0.714790\pi$
$167$	−1.25587e10	−1.24945	−0.624727	+	0.780843i	$0.714790\pi$
$168$	2.03604e9	0.197194
$169$	2.58381e9	0.243652
$170$	0	0
$171$	2.04462e9	0.182865
$172$	2.30275e10	2.00618
$173$	9.75223e9	0.827745	0.413873	−	0.910335i	$-0.364176\pi$
$173$	9.75223e9	0.827745	0.413873	+	0.910335i	$0.364176\pi$
$174$	3.95164e9	0.326818
$175$	3.20426e10	2.58260
$176$	7.14356e9	0.561187
$177$	−2.91718e10	−2.23401
$178$	−9.94440e9	−0.742486
$179$	−9.31876e9	−0.678453	−0.339226	−	0.940705i	$-0.610165\pi$
$179$	−9.31876e9	−0.678453	−0.339226	+	0.940705i	$0.610165\pi$
$180$	3.40127e10	2.41499
$181$	−2.61754e10	−1.81276	−0.906380	−	0.422464i	$-0.861165\pi$
$181$	−2.61754e10	−1.81276	−0.906380	+	0.422464i	$0.861165\pi$
$182$	−3.11988e10	−2.10774
$183$	1.83159e10	1.20725
$184$	−2.94970e9	−0.189713
$185$	3.27048e10	2.05276
$186$	−2.28055e10	−1.39711
$187$	0	0
$188$	−1.30102e10	−0.759579
$189$	−1.09502e10	−0.624230
$190$	−6.19919e9	−0.345099
$191$	−3.30724e10	−1.79811	−0.899054	−	0.437838i	$-0.855744\pi$
$191$	−3.30724e10	−1.79811	−0.899054	+	0.437838i	$0.855744\pi$
$192$	3.24194e10	1.72167
$193$	2.13626e9	0.110827	0.0554136	−	0.998463i	$-0.482352\pi$
$193$	2.13626e9	0.110827	0.0554136	+	0.998463i	$0.482352\pi$
$194$	−1.32900e10	−0.673625
$195$	−5.89616e10	−2.92021
$196$	1.60481e10	0.776730
$197$	1.08284e10	0.512230	0.256115	−	0.966646i	$-0.417557\pi$
$197$	1.08284e10	0.512230	0.256115	+	0.966646i	$0.417557\pi$
$198$	2.47213e10	1.14308
$199$	9.25080e9	0.418158	0.209079	−	0.977899i	$-0.432953\pi$
$199$	9.25080e9	0.418158	0.209079	+	0.977899i	$0.432953\pi$
$200$	−4.38834e9	−0.193939
$201$	−2.96399e10	−1.28084
$202$	1.22740e10	0.518687
$203$	4.75114e9	0.196366
$204$	0	0
$205$	−1.40081e10	−0.553971
$206$	−5.36418e9	−0.207540
$207$	6.66482e10	2.52303
$208$	−2.78975e10	−1.03343
$209$	−2.32759e9	−0.0843815
$210$	1.39482e11	4.94917
$211$	1.62289e10	0.563662	0.281831	−	0.959464i	$-0.409058\pi$
$211$	1.62289e10	0.563662	0.281831	+	0.959464i	$0.409058\pi$
$212$	2.62068e10	0.891050
$213$	−2.86266e9	−0.0952931
$214$	1.00709e10	0.328252
$215$	1.01288e11	3.23284
$216$	1.49967e9	0.0468763
$217$	−2.74194e10	−0.839440
$218$	−2.21729e10	−0.664918
$219$	3.96414e10	1.16453
$220$	−3.87198e10	−1.11437
$221$	0	0
$222$	9.43543e10	2.60719
$223$	−1.75738e9	−0.0475876	−0.0237938	−	0.999717i	$-0.507575\pi$
$223$	−1.75738e9	−0.0475876	−0.0237938	+	0.999717i	$0.507575\pi$
$224$	7.08818e10	1.88113
$225$	9.91541e10	2.57922
$226$	−2.88492e10	−0.735607
$227$	−1.96458e10	−0.491082	−0.245541	−	0.969386i	$-0.578966\pi$
$227$	−1.96458e10	−0.491082	−0.245541	+	0.969386i	$0.578966\pi$
$228$	−9.23904e9	−0.226423
$229$	−1.37016e10	−0.329240	−0.164620	−	0.986357i	$-0.552640\pi$
$229$	−1.37016e10	−0.329240	−0.164620	+	0.986357i	$0.552640\pi$
$230$	−2.02074e11	−4.76140
$231$	5.23708e10	1.21014
$232$	−6.50683e8	−0.0147460
$233$	5.64303e9	0.125433	0.0627164	−	0.998031i	$-0.480024\pi$
$233$	5.64303e9	0.125433	0.0627164	+	0.998031i	$0.480024\pi$
$234$	−9.65430e10	−2.10499
$235$	−5.72259e10	−1.22402
$236$	7.48132e10	1.56991
$237$	−2.04183e10	−0.420389
$238$	0	0
$239$	3.17941e10	0.630312	0.315156	−	0.949040i	$-0.397943\pi$
$239$	3.17941e10	0.630312	0.315156	+	0.949040i	$0.397943\pi$
$240$	1.24723e11	2.42658
$241$	−6.89080e10	−1.31581	−0.657905	−	0.753101i	$-0.728557\pi$
$241$	−6.89080e10	−1.31581	−0.657905	+	0.753101i	$0.728557\pi$
$242$	4.85951e10	0.910802
$243$	7.45874e10	1.37226
$244$	−4.69724e10	−0.848376
$245$	7.05881e10	1.25165
$246$	−4.04138e10	−0.703594
$247$	9.08983e9	0.155389
$248$	3.75518e9	0.0630373
$249$	−1.30427e11	−2.15016
$250$	−1.47661e11	−2.39076
$251$	−1.03534e11	−1.64646	−0.823232	−	0.567705i	$-0.807831\pi$
$251$	−1.03534e11	−1.64646	−0.823232	+	0.567705i	$0.807831\pi$
$252$	1.17981e11	1.84293
$253$	−7.58719e10	−1.16423
$254$	−7.91678e10	−1.19343
$255$	0	0
$256$	5.83428e10	0.849000
$257$	−4.04963e10	−0.579051	−0.289525	−	0.957170i	$-0.593497\pi$
$257$	−4.04963e10	−0.579051	−0.289525	+	0.957170i	$0.593497\pi$
$258$	2.92218e11	4.10600
$259$	1.13444e11	1.56651
$260$	1.51211e11	2.05212
$261$	1.47021e10	0.196109
$262$	−8.13634e10	−1.06678
$263$	−1.21938e10	−0.157159	−0.0785794	−	0.996908i	$-0.525038\pi$
$263$	−1.21938e10	−0.157159	−0.0785794	+	0.996908i	$0.525038\pi$
$264$	−7.17234e9	−0.0908748
$265$	1.15272e11	1.43587
$266$	−2.15033e10	−0.263353
$267$	−6.51898e10	−0.785017
$268$	7.60136e10	0.900087
$269$	7.36710e10	0.857850	0.428925	−	0.903340i	$-0.358892\pi$
$269$	7.36710e10	0.857850	0.428925	+	0.903340i	$0.358892\pi$
$270$	1.02737e11	1.17650
$271$	9.33641e10	1.05152	0.525761	−	0.850632i	$-0.323781\pi$
$271$	9.33641e10	1.05152	0.525761	+	0.850632i	$0.323781\pi$
$272$	0	0
$273$	−2.04522e11	−2.22847
$274$	1.95208e11	2.09228
$275$	−1.12876e11	−1.19016
$276$	−3.01163e11	−3.12400
$277$	−1.30118e11	−1.32794	−0.663972	−	0.747757i	$-0.731131\pi$
$277$	−1.30118e11	−1.32794	−0.663972	+	0.747757i	$0.731131\pi$
$278$	−6.49439e10	−0.652134
$279$	−8.48478e10	−0.838343
$280$	−2.29673e10	−0.223305
$281$	−1.06116e11	−1.01532	−0.507661	−	0.861557i	$-0.669490\pi$
$281$	−1.06116e11	−1.01532	−0.507661	+	0.861557i	$0.669490\pi$
$282$	−1.65099e11	−1.55461
$283$	5.53369e10	0.512833	0.256416	−	0.966566i	$-0.417458\pi$
$283$	5.53369e10	0.512833	0.256416	+	0.966566i	$0.417458\pi$
$284$	7.34149e9	0.0669655
$285$	−4.06384e10	−0.364867
$286$	1.09904e11	0.971328
$287$	−4.85903e10	−0.422747
$288$	2.19339e11	1.87867
$289$	0	0
$290$	−4.45761e10	−0.370093
$291$	−8.71219e10	−0.712211
$292$	−1.01663e11	−0.818352
$293$	−3.36671e10	−0.266871	−0.133436	−	0.991057i	$-0.542601\pi$
$293$	−3.36671e10	−0.266871	−0.133436	+	0.991057i	$0.542601\pi$
$294$	2.03649e11	1.58972
$295$	3.29070e11	2.52981
$296$	−1.55365e10	−0.117636
$297$	3.85743e10	0.287669
$298$	8.90284e9	0.0653966
$299$	2.96300e11	2.14393
$300$	−4.48047e11	−3.19358
$301$	3.51340e11	2.46705
$302$	2.86408e11	1.98132
$303$	8.04613e10	0.548397
$304$	−1.92279e10	−0.129122
$305$	−2.06610e11	−1.36711
$306$	0	0
$307$	9.76052e10	0.627120	0.313560	−	0.949568i	$-0.398478\pi$
$307$	9.76052e10	0.627120	0.313560	+	0.949568i	$0.398478\pi$
$308$	−1.34309e11	−0.850404
$309$	−3.51645e10	−0.219428
$310$	2.57254e11	1.58210
$311$	1.53666e11	0.931443	0.465721	−	0.884931i	$-0.345795\pi$
$311$	1.53666e11	0.931443	0.465721	+	0.884931i	$0.345795\pi$
$312$	2.80099e10	0.167346
$313$	2.24848e11	1.32416	0.662079	−	0.749434i	$-0.269674\pi$
$313$	2.24848e11	1.32416	0.662079	+	0.749434i	$0.269674\pi$
$314$	3.01381e11	1.74957
$315$	5.18944e11	2.96977
$316$	5.23641e10	0.295421
$317$	3.30628e10	0.183897	0.0919483	−	0.995764i	$-0.470691\pi$
$317$	3.30628e10	0.183897	0.0919483	+	0.995764i	$0.470691\pi$
$318$	3.32563e11	1.82369
$319$	−1.67368e10	−0.0904928
$320$	−3.65704e11	−1.94964
$321$	6.60193e10	0.347055
$322$	−7.00939e11	−3.63353
$323$	0	0
$324$	−1.25069e11	−0.630518
$325$	4.40812e11	2.19168
$326$	−5.27283e11	−2.58562
$327$	−1.45353e11	−0.703005
$328$	6.65459e9	0.0317460
$329$	−1.98501e11	−0.934075
$330$	−4.91353e11	−2.28077
$331$	4.07516e10	0.186603	0.0933016	−	0.995638i	$-0.470258\pi$
$331$	4.07516e10	0.186603	0.0933016	+	0.995638i	$0.470258\pi$
$332$	3.34489e11	1.51098
$333$	3.51045e11	1.56446
$334$	4.08714e11	1.79705
$335$	3.34350e11	1.45044
$336$	4.32629e11	1.85178
$337$	−4.53568e11	−1.91562	−0.957808	−	0.287410i	$-0.907206\pi$
$337$	−4.53568e11	−1.91562	−0.957808	+	0.287410i	$0.907206\pi$
$338$	−8.40880e10	−0.350436
$339$	−1.89119e11	−0.777744
$340$	0	0
$341$	9.65902e10	0.386846
$342$	−6.65407e10	−0.263009
$343$	−9.20108e10	−0.358935
$344$	−4.81170e10	−0.185262
$345$	−1.32468e12	−5.03414
$346$	−3.17379e11	−1.19052
$347$	−2.42308e10	−0.0897191	−0.0448596	−	0.998993i	$-0.514284\pi$
$347$	−2.42308e10	−0.0897191	−0.0448596	+	0.998993i	$0.514284\pi$
$348$	−6.64344e10	−0.242821
$349$	2.69343e11	0.971833	0.485917	−	0.874005i	$-0.338486\pi$
$349$	2.69343e11	0.971833	0.485917	+	0.874005i	$0.338486\pi$
$350$	−1.04280e12	−3.71447
$351$	−1.50643e11	−0.529744
$352$	−2.49695e11	−0.866897
$353$	2.67498e11	0.916926	0.458463	−	0.888713i	$-0.348400\pi$
$353$	2.67498e11	0.916926	0.458463	+	0.888713i	$0.348400\pi$
$354$	9.49376e11	3.21310
$355$	3.22919e10	0.107911
$356$	1.67184e11	0.551657
$357$	0	0
$358$	3.03272e11	0.975796
$359$	−4.36037e11	−1.38547	−0.692736	−	0.721191i	$-0.743595\pi$
$359$	−4.36037e11	−1.38547	−0.692736	+	0.721191i	$0.743595\pi$
$360$	−7.10710e10	−0.223013
$361$	−3.16423e11	−0.980585
$362$	8.51860e11	2.60723
$363$	3.18562e11	0.962973
$364$	5.24510e11	1.56602
$365$	−4.47170e11	−1.31873
$366$	−5.96077e11	−1.73635
$367$	−3.31532e11	−0.953955	−0.476977	−	0.878916i	$-0.658268\pi$
$367$	−3.31532e11	−0.953955	−0.476977	+	0.878916i	$0.658268\pi$
$368$	−6.26768e11	−1.78152
$369$	−1.50360e11	−0.422195
$370$	−1.06435e12	−2.95242
$371$	3.99847e11	1.09575
$372$	3.83402e11	1.03803
$373$	−8.47512e10	−0.226702	−0.113351	−	0.993555i	$-0.536159\pi$
$373$	−8.47512e10	−0.226702	−0.113351	+	0.993555i	$0.536159\pi$
$374$	0	0
$375$	−9.67981e11	−2.52770
$376$	2.71854e10	0.0701439
$377$	6.53615e10	0.166643
$378$	3.56367e11	0.897810
$379$	−4.47024e11	−1.11290	−0.556448	−	0.830883i	$-0.687836\pi$
$379$	−4.47024e11	−1.11290	−0.556448	+	0.830883i	$0.687836\pi$
$380$	1.04220e11	0.256404
$381$	−5.18979e11	−1.26179
$382$	1.07632e12	2.58616
$383$	−3.74823e11	−0.890085	−0.445042	−	0.895510i	$-0.646811\pi$
$383$	−3.74823e11	−0.890085	−0.445042	+	0.895510i	$0.646811\pi$
$384$	−1.27574e11	−0.299414
$385$	−5.90763e11	−1.37038
$386$	−6.95230e10	−0.159399
$387$	1.08720e12	2.46382
$388$	2.23430e11	0.500494
$389$	−6.71762e11	−1.48745	−0.743725	−	0.668486i	$-0.766943\pi$
$389$	−6.71762e11	−1.48745	−0.743725	+	0.668486i	$0.766943\pi$
$390$	1.91886e12	4.20004
$391$	0	0
$392$	−3.35331e10	−0.0717276
$393$	−5.33372e11	−1.12788
$394$	−3.52401e11	−0.736723
$395$	2.30326e11	0.476054
$396$	−4.15610e11	−0.849293
$397$	−2.67081e11	−0.539618	−0.269809	−	0.962914i	$-0.586961\pi$
$397$	−2.67081e11	−0.539618	−0.269809	+	0.962914i	$0.586961\pi$
$398$	−3.01061e11	−0.601423
$399$	−1.40963e11	−0.278438
$400$	−9.32457e11	−1.82121
$401$	−3.41629e11	−0.659790	−0.329895	−	0.944018i	$-0.607013\pi$
$401$	−3.41629e11	−0.659790	−0.329895	+	0.944018i	$0.607013\pi$
$402$	9.64609e11	1.84219
$403$	−3.77210e11	−0.712378
$404$	−2.06349e11	−0.385377
$405$	−5.50123e11	−1.01604
$406$	−1.54622e11	−0.282426
$407$	−3.99628e11	−0.721907
$408$	0	0
$409$	−2.79471e11	−0.493835	−0.246918	−	0.969036i	$-0.579418\pi$
$409$	−2.79471e11	−0.493835	−0.246918	+	0.969036i	$0.579418\pi$
$410$	4.55883e11	0.796758
$411$	1.27967e12	2.21213
$412$	9.01818e10	0.154199
$413$	1.14145e12	1.93056
$414$	−2.16902e12	−3.62878
$415$	1.47127e12	2.43486
$416$	9.75123e11	1.59639
$417$	−4.25735e11	−0.689489
$418$	7.57496e10	0.121363
$419$	7.29751e11	1.15668	0.578338	−	0.815798i	$-0.303702\pi$
$419$	7.29751e11	1.15668	0.578338	+	0.815798i	$0.303702\pi$
$420$	−2.34495e12	−3.67716
$421$	−1.03145e12	−1.60021	−0.800105	−	0.599859i	$-0.795223\pi$
$421$	−1.03145e12	−1.60021	−0.800105	+	0.599859i	$0.795223\pi$
$422$	−5.28159e11	−0.810697
$423$	−6.14250e11	−0.932854
$424$	−5.47602e10	−0.0822846
$425$	0	0
$426$	9.31631e10	0.137057
$427$	−7.16675e11	−1.04327
$428$	−1.69311e11	−0.243887
$429$	7.20467e11	1.02697
$430$	−3.29633e12	−4.64968
$431$	1.03111e12	1.43932	0.719659	−	0.694328i	$-0.244298\pi$
$431$	1.03111e12	1.43932	0.719659	+	0.694328i	$0.244298\pi$
$432$	3.18657e11	0.440197
$433$	−2.66222e11	−0.363956	−0.181978	−	0.983303i	$-0.558250\pi$
$433$	−2.66222e11	−0.363956	−0.181978	+	0.983303i	$0.558250\pi$
$434$	8.92345e11	1.20734
$435$	−2.92215e11	−0.391292
$436$	3.72767e11	0.494024
$437$	2.04220e11	0.267875
$438$	−1.29010e12	−1.67490
$439$	−6.24076e11	−0.801950	−0.400975	−	0.916089i	$-0.631329\pi$
$439$	−6.24076e11	−0.801950	−0.400975	+	0.916089i	$0.631329\pi$
$440$	8.09068e10	0.102908
$441$	7.57677e11	0.953917
$442$	0	0
$443$	−7.32431e11	−0.903545	−0.451773	−	0.892133i	$-0.649208\pi$
$443$	−7.32431e11	−0.903545	−0.451773	+	0.892133i	$0.649208\pi$
$444$	−1.58627e12	−1.93711
$445$	7.35366e11	0.888962
$446$	5.71926e10	0.0684436
$447$	5.83619e10	0.0691426
$448$	−1.26853e12	−1.48781
$449$	1.38765e12	1.61128	0.805642	−	0.592402i	$-0.201820\pi$
$449$	1.38765e12	1.61128	0.805642	+	0.592402i	$0.201820\pi$
$450$	−3.22690e12	−3.70961
$451$	1.71169e11	0.194818
$452$	4.85009e11	0.546546
$453$	1.87753e12	2.09481
$454$	6.39359e11	0.706307
$455$	2.30708e12	2.52355
$456$	1.93054e10	0.0209092
$457$	−1.37587e10	−0.0147555	−0.00737774	−	0.999973i	$-0.502348\pi$
$457$	−1.37587e10	−0.0147555	−0.00737774	+	0.999973i	$0.502348\pi$
$458$	4.45910e11	0.473535
$459$	0	0
$460$	3.39723e12	3.53765
$461$	6.11926e11	0.631022	0.315511	−	0.948922i	$-0.397824\pi$
$461$	6.11926e11	0.631022	0.315511	+	0.948922i	$0.397824\pi$
$462$	−1.70437e12	−1.74050
$463$	−3.86495e11	−0.390867	−0.195434	−	0.980717i	$-0.562611\pi$
$463$	−3.86495e11	−0.390867	−0.195434	+	0.980717i	$0.562611\pi$
$464$	−1.38260e11	−0.138474
$465$	1.68641e12	1.67273
$466$	−1.83648e11	−0.180406
$467$	9.78281e10	0.0951783	0.0475891	−	0.998867i	$-0.484846\pi$
$467$	9.78281e10	0.0951783	0.0475891	+	0.998867i	$0.484846\pi$
$468$	1.62307e12	1.56397
$469$	1.15977e12	1.10686
$470$	1.86238e12	1.76046
$471$	1.97568e12	1.84979
$472$	−1.56325e11	−0.144974
$473$	−1.23766e12	−1.13691
$474$	6.64498e11	0.604632
$475$	3.03823e11	0.273841
$476$	0	0
$477$	1.23730e12	1.09432
$478$	−1.03471e12	−0.906557
$479$	5.72522e11	0.496916	0.248458	−	0.968643i	$-0.420076\pi$
$479$	5.72522e11	0.496916	0.248458	+	0.968643i	$0.420076\pi$
$480$	−4.35953e12	−3.74847
$481$	1.56065e12	1.32939
$482$	2.24256e12	1.89249
$483$	−4.59496e12	−3.84166
$484$	−8.16974e11	−0.676712
$485$	9.82768e11	0.806516
$486$	−2.42739e12	−1.97368
$487$	6.80061e11	0.547858	0.273929	−	0.961750i	$-0.411677\pi$
$487$	6.80061e11	0.547858	0.273929	+	0.961750i	$0.411677\pi$
$488$	9.81508e10	0.0783438
$489$	−3.45656e12	−2.73373
$490$	−2.29724e12	−1.80021
$491$	−1.01894e12	−0.791190	−0.395595	−	0.918425i	$-0.629462\pi$
$491$	−1.01894e12	−0.791190	−0.395595	+	0.918425i	$0.629462\pi$
$492$	6.79431e11	0.522760
$493$	0	0
$494$	−2.95822e11	−0.223491
$495$	−1.82808e12	−1.36859
$496$	7.97920e11	0.591959
$497$	1.12012e11	0.0823493
$498$	4.24465e12	3.09250
$499$	−1.19473e12	−0.862615	−0.431308	−	0.902205i	$-0.641948\pi$
$499$	−1.19473e12	−0.862615	−0.431308	+	0.902205i	$0.641948\pi$
$500$	2.48245e12	1.77630
$501$	2.67929e12	1.89999
$502$	3.36945e12	2.36806
$503$	−1.03906e12	−0.723745	−0.361872	−	0.932228i	$-0.617862\pi$
$503$	−1.03906e12	−0.723745	−0.361872	+	0.932228i	$0.617862\pi$
$504$	−2.46526e11	−0.170187
$505$	−9.07635e11	−0.621012
$506$	2.46919e12	1.67447
$507$	−5.51233e11	−0.370510
$508$	1.33096e12	0.886701
$509$	1.35492e12	0.894713	0.447357	−	0.894356i	$-0.352365\pi$
$509$	1.35492e12	0.894713	0.447357	+	0.894356i	$0.352365\pi$
$510$	0	0
$511$	−1.55111e12	−1.00635
$512$	−2.20489e12	−1.41799
$513$	−1.03828e11	−0.0661891
$514$	1.31792e12	0.832830
$515$	3.96669e11	0.248482
$516$	−4.91273e12	−3.05070
$517$	6.99259e11	0.430458
$518$	−3.69195e12	−2.25305
$519$	−2.08056e12	−1.25871
$520$	−3.15962e11	−0.189505
$521$	2.04235e12	1.21439	0.607197	−	0.794551i	$-0.292294\pi$
$521$	2.04235e12	1.21439	0.607197	+	0.794551i	$0.292294\pi$
$522$	−4.78469e11	−0.282057
$523$	2.71255e12	1.58533	0.792665	−	0.609657i	$-0.208693\pi$
$523$	2.71255e12	1.58533	0.792665	+	0.609657i	$0.208693\pi$
$524$	1.36787e12	0.792599
$525$	−6.83603e12	−3.92724
$526$	3.96839e11	0.226036
$527$	0	0
$528$	−1.52402e12	−0.853370
$529$	4.85576e12	2.69592
$530$	−3.75144e12	−2.06517
$531$	3.53216e12	1.92803
$532$	3.61510e11	0.195667
$533$	−6.68458e11	−0.358758
$534$	2.12155e12	1.12906
$535$	−7.44723e11	−0.393009
$536$	−1.58834e11	−0.0831192
$537$	1.98808e12	1.03169
$538$	−2.39757e12	−1.23382
$539$	−8.62535e11	−0.440177
$540$	−1.72720e12	−0.874119
$541$	−4.82877e11	−0.242353	−0.121176	−	0.992631i	$-0.538667\pi$
$541$	−4.82877e11	−0.242353	−0.121176	+	0.992631i	$0.538667\pi$
$542$	−3.03847e12	−1.51237
$543$	5.58431e12	2.75658
$544$	0	0
$545$	1.63963e12	0.796091
$546$	6.65601e12	3.20514
$547$	1.06963e12	0.510845	0.255422	−	0.966830i	$-0.417786\pi$
$547$	1.06963e12	0.510845	0.255422	+	0.966830i	$0.417786\pi$
$548$	−3.28180e12	−1.55453
$549$	−2.21771e12	−1.04191
$550$	3.67348e12	1.71177
$551$	4.50494e10	0.0208213
$552$	6.29294e11	0.288488
$553$	7.98939e11	0.363287
$554$	4.23461e12	1.90994
$555$	−6.97728e12	−3.12153
$556$	1.09183e12	0.484526
$557$	8.49296e11	0.373861	0.186931	−	0.982373i	$-0.440146\pi$
$557$	8.49296e11	0.373861	0.186931	+	0.982373i	$0.440146\pi$
$558$	2.76131e12	1.20576
$559$	4.83339e12	2.09362
$560$	−4.88022e12	−2.09697
$561$	0	0
$562$	3.45347e12	1.46030
$563$	−2.02291e12	−0.848571	−0.424285	−	0.905529i	$-0.639475\pi$
$563$	−2.02291e12	−0.848571	−0.424285	+	0.905529i	$0.639475\pi$
$564$	2.77561e12	1.15506
$565$	2.13333e12	0.880726
$566$	−1.80090e12	−0.737590
$567$	−1.90823e12	−0.775365
$568$	−1.53404e10	−0.00618398
$569$	3.08353e12	1.23323	0.616614	−	0.787266i	$-0.288504\pi$
$569$	3.08353e12	1.23323	0.616614	+	0.787266i	$0.288504\pi$
$570$	1.32255e12	0.524776
$571$	−1.70922e12	−0.672878	−0.336439	−	0.941705i	$-0.609223\pi$
$571$	−1.70922e12	−0.672878	−0.336439	+	0.941705i	$0.609223\pi$
$572$	−1.84769e12	−0.721683
$573$	7.05572e12	2.73430
$574$	1.58134e12	0.608024
$575$	9.90365e12	3.77824
$576$	−3.92538e12	−1.48587
$577$	1.85610e12	0.697123	0.348561	−	0.937286i	$-0.386670\pi$
$577$	1.85610e12	0.697123	0.348561	+	0.937286i	$0.386670\pi$
$578$	0	0
$579$	−4.55753e11	−0.168530
$580$	7.49406e11	0.274974
$581$	5.10342e12	1.85810
$582$	2.83532e12	1.02435
$583$	−1.40854e12	−0.504963
$584$	2.12429e11	0.0755713
$585$	7.13913e12	2.52025
$586$	1.09567e12	0.383832
$587$	−3.27838e12	−1.13969	−0.569846	−	0.821751i	$-0.692997\pi$
$587$	−3.27838e12	−1.13969	−0.569846	+	0.821751i	$0.692997\pi$
$588$	−3.42372e12	−1.18114
$589$	−2.59986e11	−0.0890085
$590$	−1.07093e13	−3.63855
$591$	−2.31014e12	−0.778923
$592$	−3.30128e12	−1.10467
$593$	4.48451e12	1.48925	0.744626	−	0.667481i	$-0.232628\pi$
$593$	4.48451e12	1.48925	0.744626	+	0.667481i	$0.232628\pi$
$594$	−1.25537e12	−0.413745
$595$	0	0
$596$	−1.49673e11	−0.0485887
$597$	−1.97358e12	−0.635873
$598$	−9.64285e12	−3.08354
$599$	4.59065e12	1.45698	0.728489	−	0.685057i	$-0.240223\pi$
$599$	4.59065e12	1.45698	0.728489	+	0.685057i	$0.240223\pi$
$600$	9.36215e11	0.294914
$601$	−9.24328e11	−0.288995	−0.144498	−	0.989505i	$-0.546157\pi$
$601$	−9.24328e11	−0.288995	−0.144498	+	0.989505i	$0.546157\pi$
$602$	−1.14341e13	−3.54828
$603$	3.58883e12	1.10541
$604$	−4.81505e12	−1.47209
$605$	−3.59350e12	−1.09048
$606$	−2.61855e12	−0.788742
$607$	1.75024e12	0.523297	0.261648	−	0.965163i	$-0.415734\pi$
$607$	1.75024e12	0.523297	0.261648	+	0.965163i	$0.415734\pi$
$608$	6.72089e11	0.199462
$609$	−1.01361e12	−0.298604
$610$	6.72398e12	1.96627
$611$	−2.73079e12	−0.792689
$612$	0	0
$613$	−2.24701e12	−0.642736	−0.321368	−	0.946954i	$-0.604143\pi$
$613$	−2.24701e12	−0.642736	−0.321368	+	0.946954i	$0.604143\pi$
$614$	−3.17649e12	−0.901965
$615$	2.98851e12	0.842397
$616$	2.80644e11	0.0785312
$617$	−1.84453e12	−0.512393	−0.256196	−	0.966625i	$-0.582469\pi$
$617$	−1.84453e12	−0.512393	−0.256196	+	0.966625i	$0.582469\pi$
$618$	1.14440e12	0.315595
$619$	−1.72585e12	−0.472491	−0.236246	−	0.971693i	$-0.575917\pi$
$619$	−1.72585e12	−0.472491	−0.236246	+	0.971693i	$0.575917\pi$
$620$	−4.32492e12	−1.17548
$621$	−3.38446e12	−0.913225
$622$	−5.00095e12	−1.33966
$623$	2.55078e12	0.678387
$624$	5.95169e12	1.57148
$625$	3.42217e12	0.897102
$626$	−7.31752e12	−1.90449
$627$	4.96571e11	0.128315
$628$	−5.06677e12	−1.29991
$629$	0	0
$630$	−1.68887e13	−4.27132
$631$	1.74383e12	0.437898	0.218949	−	0.975736i	$-0.429737\pi$
$631$	1.74383e12	0.437898	0.218949	+	0.975736i	$0.429737\pi$
$632$	−1.09417e11	−0.0272809
$633$	−3.46231e12	−0.857134
$634$	−1.07601e12	−0.264492
$635$	5.85428e12	1.42887
$636$	−5.59099e12	−1.35498
$637$	3.36843e12	0.810587
$638$	5.44686e11	0.130153
$639$	3.46614e11	0.0822417
$640$	1.43909e12	0.339061
$641$	−3.54167e12	−0.828603	−0.414302	−	0.910140i	$-0.635974\pi$
$641$	−3.54167e12	−0.828603	−0.414302	+	0.910140i	$0.635974\pi$
$642$	−2.14855e12	−0.499158
$643$	−6.73053e12	−1.55274	−0.776372	−	0.630275i	$-0.782942\pi$
$643$	−6.73053e12	−1.55274	−0.776372	+	0.630275i	$0.782942\pi$
$644$	1.17841e13	2.69966
$645$	−2.16089e13	−4.91602
$646$	0	0
$647$	8.11471e12	1.82055	0.910277	−	0.414000i	$-0.135869\pi$
$647$	8.11471e12	1.82055	0.910277	+	0.414000i	$0.135869\pi$
$648$	2.61337e11	0.0582256
$649$	−4.02099e12	−0.889675
$650$	−1.43459e13	−3.15223
$651$	5.84971e12	1.27650
$652$	8.86460e12	1.92108
$653$	7.02546e12	1.51205	0.756024	−	0.654544i	$-0.227139\pi$
$653$	7.02546e12	1.51205	0.756024	+	0.654544i	$0.227139\pi$
$654$	4.73040e12	1.01111
$655$	6.01664e12	1.27723
$656$	1.41400e12	0.298114
$657$	−4.79982e12	−1.00503
$658$	6.46008e12	1.34345
$659$	−1.06157e12	−0.219263	−0.109631	−	0.993972i	$-0.534967\pi$
$659$	−1.06157e12	−0.219263	−0.109631	+	0.993972i	$0.534967\pi$
$660$	8.26055e12	1.69458
$661$	−3.21945e12	−0.655956	−0.327978	−	0.944685i	$-0.606367\pi$
$661$	−3.21945e12	−0.655956	−0.327978	+	0.944685i	$0.606367\pi$
$662$	−1.32623e12	−0.268385
$663$	0	0
$664$	−6.98929e11	−0.139533
$665$	1.59012e12	0.315307
$666$	−1.14245e13	−2.25011
$667$	1.46847e12	0.287275
$668$	−6.87123e12	−1.33518
$669$	3.74922e11	0.0723641
$670$	−1.08812e13	−2.08612
$671$	2.52462e12	0.480779
$672$	−1.51220e13	−2.86054
$673$	4.50498e12	0.846496	0.423248	−	0.906014i	$-0.360890\pi$
$673$	4.50498e12	0.846496	0.423248	+	0.906014i	$0.360890\pi$
$674$	1.47611e13	2.75517
$675$	−5.03515e12	−0.933566
$676$	1.41368e12	0.260369
$677$	8.94321e12	1.63623	0.818115	−	0.575055i	$-0.195019\pi$
$677$	8.94321e12	1.63623	0.818115	+	0.575055i	$0.195019\pi$
$678$	6.15474e12	1.11860
$679$	3.40895e12	0.615471
$680$	0	0
$681$	4.19127e12	0.746765
$682$	−3.14346e12	−0.556388
$683$	8.23905e12	1.44872	0.724359	−	0.689423i	$-0.242136\pi$
$683$	8.23905e12	1.44872	0.724359	+	0.689423i	$0.242136\pi$
$684$	1.11867e12	0.195412
$685$	−1.44352e13	−2.50504
$686$	2.99443e12	0.516244
$687$	2.92313e12	0.500660
$688$	−1.02242e13	−1.73972
$689$	5.50070e12	0.929890
$690$	4.31108e13	7.24044
$691$	−4.03124e12	−0.672647	−0.336323	−	0.941747i	$-0.609184\pi$
$691$	−4.03124e12	−0.672647	−0.336323	+	0.941747i	$0.609184\pi$
$692$	5.33573e12	0.884538
$693$	−6.34111e12	−1.04440
$694$	7.88573e11	0.129040
$695$	4.80246e12	0.780786
$696$	1.38818e11	0.0224235
$697$	0	0
$698$	−8.76558e12	−1.39776
$699$	−1.20389e12	−0.190740
$700$	1.75315e13	2.75980
$701$	5.69408e12	0.890620	0.445310	−	0.895377i	$-0.353094\pi$
$701$	5.69408e12	0.890620	0.445310	+	0.895377i	$0.353094\pi$
$702$	4.90255e12	0.761913
$703$	1.07566e12	0.166102
$704$	4.46863e12	0.685642
$705$	1.22087e13	1.86130
$706$	−8.70553e12	−1.31878
$707$	−3.14834e12	−0.473908
$708$	−1.59608e13	−2.38728
$709$	−3.52243e12	−0.523522	−0.261761	−	0.965133i	$-0.584303\pi$
$709$	−3.52243e12	−0.523522	−0.261761	+	0.965133i	$0.584303\pi$
$710$	−1.05092e12	−0.155205
$711$	2.47227e12	0.362813
$712$	−3.49338e11	−0.0509431
$713$	−8.47472e12	−1.22807
$714$	0	0
$715$	−8.12715e12	−1.16295
$716$	−5.09857e12	−0.725002
$717$	−6.78300e12	−0.958485
$718$	1.41905e13	1.99268
$719$	−1.46742e12	−0.204774	−0.102387	−	0.994745i	$-0.532648\pi$
$719$	−1.46742e12	−0.204774	−0.102387	+	0.994745i	$0.532648\pi$
$720$	−1.51015e13	−2.09423
$721$	1.37594e12	0.189623
$722$	1.02977e13	1.41034
$723$	1.47009e13	2.00089
$724$	−1.43213e13	−1.93714
$725$	2.18467e12	0.293674
$726$	−1.03674e13	−1.38501
$727$	−7.00907e12	−0.930584	−0.465292	−	0.885157i	$-0.654051\pi$
$727$	−7.00907e12	−0.930584	−0.465292	+	0.885157i	$0.654051\pi$
$728$	−1.09599e12	−0.144615
$729$	−1.14132e13	−1.49670
$730$	1.45528e13	1.89668
$731$	0	0
$732$	1.00212e13	1.29008
$733$	8.15509e11	0.104342	0.0521712	−	0.998638i	$-0.483386\pi$
$733$	8.15509e11	0.104342	0.0521712	+	0.998638i	$0.483386\pi$
$734$	1.07895e13	1.37204
$735$	−1.50594e13	−1.90333
$736$	2.19079e13	2.75202
$737$	−4.08551e12	−0.510084
$738$	4.89335e12	0.607229
$739$	−6.04363e12	−0.745415	−0.372707	−	0.927949i	$-0.621570\pi$
$739$	−6.04363e12	−0.745415	−0.372707	+	0.927949i	$0.621570\pi$
$740$	1.78937e13	2.19360
$741$	−1.93924e12	−0.236292
$742$	−1.30127e13	−1.57598
$743$	1.48814e13	1.79140	0.895701	−	0.444656i	$-0.146674\pi$
$743$	1.48814e13	1.79140	0.895701	+	0.444656i	$0.146674\pi$
$744$	−8.01135e11	−0.0958578
$745$	−6.58345e11	−0.0782979
$746$	2.75817e12	0.326059
$747$	1.57922e13	1.85567
$748$	0	0
$749$	−2.58324e12	−0.299914
$750$	3.15022e13	3.63551
$751$	1.61093e13	1.84798	0.923989	−	0.382418i	$-0.124909\pi$
$751$	1.61093e13	1.84798	0.923989	+	0.382418i	$0.124909\pi$
$752$	5.77649e12	0.658694
$753$	2.20882e13	2.50370
$754$	−2.12714e12	−0.239677
$755$	−2.11792e13	−2.37219
$756$	−5.99119e12	−0.667060
$757$	−1.73403e13	−1.91922	−0.959608	−	0.281339i	$-0.909221\pi$
$757$	−1.73403e13	−1.91922	−0.959608	+	0.281339i	$0.909221\pi$
$758$	1.45481e13	1.60064
$759$	1.61866e13	1.77039
$760$	−2.17772e11	−0.0236778
$761$	−6.34332e11	−0.0685624	−0.0342812	−	0.999412i	$-0.510914\pi$
$761$	−6.34332e11	−0.0685624	−0.0342812	+	0.999412i	$0.510914\pi$
$762$	1.68898e13	1.81479
$763$	5.68745e12	0.607515
$764$	−1.80949e13	−1.92148
$765$	0	0
$766$	1.21983e13	1.28018
$767$	1.57030e13	1.63834
$768$	−1.24469e13	−1.29103
$769$	−1.70009e13	−1.75309	−0.876546	−	0.481319i	$-0.840158\pi$
$769$	−1.70009e13	−1.75309	−0.876546	+	0.481319i	$0.840158\pi$
$770$	1.92259e13	1.97097
$771$	8.63955e12	0.880535
$772$	1.16881e12	0.118431
$773$	−1.40716e13	−1.41754	−0.708770	−	0.705440i	$-0.750750\pi$
$773$	−1.40716e13	−1.41754	−0.708770	+	0.705440i	$0.750750\pi$
$774$	−3.53821e13	−3.54364
$775$	−1.26080e13	−1.25542
$776$	−4.66867e11	−0.0462184
$777$	−2.42023e13	−2.38211
$778$	2.18620e13	2.13935
$779$	−4.60725e11	−0.0448253
$780$	−3.22596e13	−3.12057
$781$	−3.94583e11	−0.0379497
$782$	0	0
$783$	−7.46588e11	−0.0709828
$784$	−7.12529e12	−0.673566
$785$	−2.22864e13	−2.09473
$786$	1.73582e13	1.62220
$787$	7.48035e12	0.695081	0.347541	−	0.937665i	$-0.387017\pi$
$787$	7.48035e12	0.695081	0.347541	+	0.937665i	$0.387017\pi$
$788$	5.92451e12	0.547375
$789$	2.60145e12	0.238984
$790$	−7.49579e12	−0.684693
$791$	7.39996e12	0.672102
$792$	8.68435e11	0.0784285
$793$	−9.85932e12	−0.885356
$794$	8.69196e12	0.776114
$795$	−2.45923e13	−2.18347
$796$	5.06138e12	0.446849
$797$	−9.27081e12	−0.813870	−0.406935	−	0.913457i	$-0.633402\pi$
$797$	−9.27081e12	−0.813870	−0.406935	+	0.913457i	$0.633402\pi$
$798$	4.58755e12	0.400468
$799$	0	0
$800$	3.25930e13	2.81332
$801$	7.89325e12	0.677500
$802$	1.11181e13	0.948953
$803$	5.46408e12	0.463764
$804$	−1.62169e13	−1.36872
$805$	5.18329e13	4.35035
$806$	1.22760e13	1.02459
$807$	−1.57171e13	−1.30449
$808$	4.31175e11	0.0355879
$809$	−2.34872e13	−1.92781	−0.963903	−	0.266254i	$-0.914214\pi$
$809$	−2.34872e13	−1.92781	−0.963903	+	0.266254i	$0.914214\pi$
$810$	1.79033e13	1.46134
$811$	−2.76399e11	−0.0224358	−0.0112179	−	0.999937i	$-0.503571\pi$
$811$	−2.76399e11	−0.0224358	−0.0112179	+	0.999937i	$0.503571\pi$
$812$	2.59948e12	0.209838
$813$	−1.99185e13	−1.59900
$814$	1.30056e13	1.03829
$815$	3.89914e13	3.09570
$816$	0	0
$817$	3.33134e12	0.261589
$818$	9.09518e12	0.710267
$819$	2.47637e13	1.92326
$820$	−7.66424e12	−0.591979
$821$	9.26634e12	0.711810	0.355905	−	0.934522i	$-0.384173\pi$
$821$	9.26634e12	0.711810	0.355905	+	0.934522i	$0.384173\pi$
$822$	−4.16459e13	−3.18163
$823$	5.87654e12	0.446501	0.223250	−	0.974761i	$-0.428333\pi$
$823$	5.87654e12	0.446501	0.223250	+	0.974761i	$0.428333\pi$
$824$	−1.88439e11	−0.0142396
$825$	2.40812e13	1.80982
$826$	−3.71477e13	−2.77666
$827$	−1.65281e13	−1.22871	−0.614353	−	0.789031i	$-0.710583\pi$
$827$	−1.65281e13	−1.22871	−0.614353	+	0.789031i	$0.710583\pi$
$828$	3.64651e13	2.69613
$829$	3.30054e12	0.242711	0.121356	−	0.992609i	$-0.461276\pi$
$829$	3.30054e12	0.242711	0.121356	+	0.992609i	$0.461276\pi$
$830$	−4.78812e13	−3.50198
$831$	2.77597e13	2.01934
$832$	−1.74512e13	−1.26261
$833$	0	0
$834$	1.38552e13	0.991669
$835$	−3.02234e13	−2.15157
$836$	−1.27349e12	−0.0901711
$837$	4.30866e12	0.303443
$838$	−2.37492e13	−1.66361
$839$	−1.38522e12	−0.0965136	−0.0482568	−	0.998835i	$-0.515367\pi$
$839$	−1.38522e12	−0.0965136	−0.0482568	+	0.998835i	$0.515367\pi$
$840$	4.89988e12	0.339570
$841$	−1.41832e13	−0.977671
$842$	3.35677e13	2.30153
$843$	2.26390e13	1.54395
$844$	8.87933e12	0.602336
$845$	6.21812e12	0.419569
$846$	1.99903e13	1.34169
$847$	−1.24649e13	−0.832171
$848$	−1.16357e13	−0.772703
$849$	−1.18057e13	−0.779840
$850$	0	0
$851$	3.50629e13	2.29174
$852$	−1.56624e12	−0.101831
$853$	−2.07349e13	−1.34101	−0.670503	−	0.741907i	$-0.733922\pi$
$853$	−2.07349e13	−1.34101	−0.670503	+	0.741907i	$0.733922\pi$
$854$	2.33237e13	1.50050
$855$	4.92054e12	0.314894
$856$	3.53783e11	0.0225219
$857$	2.00968e13	1.27266	0.636331	−	0.771416i	$-0.280451\pi$
$857$	2.00968e13	1.27266	0.636331	+	0.771416i	$0.280451\pi$
$858$	−2.34471e13	−1.47705
$859$	6.44106e12	0.403635	0.201817	−	0.979423i	$-0.435315\pi$
$859$	6.44106e12	0.403635	0.201817	+	0.979423i	$0.435315\pi$
$860$	5.54175e13	3.45465
$861$	1.03663e13	0.642852
$862$	−3.35567e13	−2.07012
$863$	1.26986e13	0.779302	0.389651	−	0.920963i	$-0.372596\pi$
$863$	1.26986e13	0.779302	0.389651	+	0.920963i	$0.372596\pi$
$864$	−1.11383e13	−0.679997
$865$	2.34695e13	1.42538
$866$	8.66400e12	0.523465
$867$	0	0
$868$	−1.50020e13	−0.897035
$869$	−2.81441e12	−0.167417
$870$	9.50992e12	0.562782
$871$	1.59550e13	0.939322
$872$	−7.78913e11	−0.0456210
$873$	1.05488e13	0.614666
$874$	−6.64618e12	−0.385275
$875$	3.78757e13	2.18436
$876$	2.16889e13	1.24443
$877$	−1.81273e13	−1.03475	−0.517375	−	0.855759i	$-0.673091\pi$
$877$	−1.81273e13	−1.03475	−0.517375	+	0.855759i	$0.673091\pi$
$878$	2.03101e13	1.15342
$879$	7.18260e12	0.405818
$880$	1.71915e13	0.966366
$881$	3.52517e13	1.97146	0.985731	−	0.168327i	$-0.0538363\pi$
$881$	3.52517e13	1.97146	0.985731	+	0.168327i	$0.0538363\pi$
$882$	−2.46580e13	−1.37199
$883$	−2.08656e13	−1.15507	−0.577534	−	0.816367i	$-0.695985\pi$
$883$	−2.08656e13	−1.15507	−0.577534	+	0.816367i	$0.695985\pi$
$884$	0	0
$885$	−7.02042e13	−3.84697
$886$	2.38364e13	1.29954
$887$	2.84618e12	0.154386	0.0771928	−	0.997016i	$-0.475404\pi$
$887$	2.84618e12	0.154386	0.0771928	+	0.997016i	$0.475404\pi$
$888$	3.31458e12	0.178883
$889$	2.03069e13	1.09040
$890$	−2.39319e13	−1.27856
$891$	6.72209e12	0.357318
$892$	−9.61513e11	−0.0508526
$893$	−1.88215e12	−0.0990429
$894$	−1.89935e12	−0.0994455
$895$	−2.24263e13	−1.16830
$896$	4.99180e12	0.258745
$897$	−6.32130e13	−3.26017
$898$	−4.51601e13	−2.31746
$899$	−1.86946e12	−0.0954549
$900$	5.42501e13	2.75619
$901$	0	0
$902$	−5.57056e12	−0.280201
$903$	−7.49553e13	−3.75152
$904$	−1.01345e12	−0.0504711
$905$	−6.29931e13	−3.12158
$906$	−6.11028e13	−3.01290
$907$	−1.72640e13	−0.847050	−0.423525	−	0.905884i	$-0.639207\pi$
$907$	−1.72640e13	−0.847050	−0.423525	+	0.905884i	$0.639207\pi$
$908$	−1.07488e13	−0.524776
$909$	−9.74234e12	−0.473289
$910$	−7.50823e13	−3.62954
$911$	6.01739e12	0.289451	0.144726	−	0.989472i	$-0.453770\pi$
$911$	6.01739e12	0.289451	0.144726	+	0.989472i	$0.453770\pi$
$912$	4.10211e12	0.196350
$913$	−1.79778e13	−0.856283
$914$	4.47765e11	0.0212223
$915$	4.40786e13	2.07889
$916$	−7.49657e12	−0.351830
$917$	2.08701e13	0.974681
$918$	0	0
$919$	−3.37780e13	−1.56212	−0.781059	−	0.624457i	$-0.785320\pi$
$919$	−3.37780e13	−1.56212	−0.781059	+	0.624457i	$0.785320\pi$
$920$	−7.09867e12	−0.326687
$921$	−2.08232e13	−0.953631
$922$	−1.99147e13	−0.907578
$923$	1.54095e12	0.0698845
$924$	2.86536e13	1.29317
$925$	5.21639e13	2.34279
$926$	1.25782e13	0.562171
$927$	4.25776e12	0.189375
$928$	4.83273e12	0.213908
$929$	1.10689e12	0.0487565	0.0243783	−	0.999703i	$-0.492239\pi$
$929$	1.10689e12	0.0487565	0.0243783	+	0.999703i	$0.492239\pi$
$930$	−5.48830e13	−2.40583
$931$	2.32163e12	0.101279
$932$	3.08747e12	0.134039
$933$	−3.27834e13	−1.41640
$934$	−3.18374e12	−0.136892
$935$	0	0
$936$	−3.39147e12	−0.144426
$937$	−1.67042e13	−0.707942	−0.353971	−	0.935256i	$-0.615169\pi$
$937$	−1.67042e13	−0.707942	−0.353971	+	0.935256i	$0.615169\pi$
$938$	−3.77438e13	−1.59196
$939$	−4.79695e13	−2.01358
$940$	−3.13100e13	−1.30800
$941$	−2.56263e13	−1.06545	−0.532725	−	0.846289i	$-0.678832\pi$
$941$	−2.56263e13	−1.06545	−0.532725	+	0.846289i	$0.678832\pi$
$942$	−6.42971e13	−2.66049
$943$	−1.50181e13	−0.618463
$944$	−3.32169e13	−1.36140
$945$	−2.63525e13	−1.07493
$946$	4.02788e13	1.63518
$947$	3.58181e13	1.44720	0.723599	−	0.690220i	$-0.242486\pi$
$947$	3.58181e13	1.44720	0.723599	+	0.690220i	$0.242486\pi$
$948$	−1.11714e13	−0.449233
$949$	−2.13387e13	−0.854023
$950$	−9.88769e12	−0.393857
$951$	−7.05368e12	−0.279643
$952$	0	0
$953$	2.09829e12	0.0824037	0.0412018	−	0.999151i	$-0.486881\pi$
$953$	2.09829e12	0.0824037	0.0412018	+	0.999151i	$0.486881\pi$
$954$	−4.02671e13	−1.57392
$955$	−7.95912e13	−3.09635
$956$	1.73955e13	0.673559
$957$	3.57065e12	0.137608
$958$	−1.86323e13	−0.714697
$959$	−5.00717e13	−1.91165
$960$	7.80198e13	2.96472
$961$	−1.56507e13	−0.591941
$962$	−5.07903e13	−1.91202
$963$	−7.99369e12	−0.299522
$964$	−3.77016e13	−1.40609
$965$	5.14107e12	0.190845
$966$	1.49540e14	5.52534
$967$	1.14380e13	0.420660	0.210330	−	0.977631i	$-0.432546\pi$
$967$	1.14380e13	0.420660	0.210330	+	0.977631i	$0.432546\pi$
$968$	1.70710e12	0.0624915
$969$	0	0
$970$	−3.19835e13	−1.15999
$971$	2.93654e13	1.06011	0.530054	−	0.847964i	$-0.322172\pi$
$971$	2.93654e13	1.06011	0.530054	+	0.847964i	$0.322172\pi$
$972$	4.08089e13	1.46642
$973$	1.66584e13	0.595835
$974$	−2.21321e13	−0.787966
$975$	−9.40435e13	−3.33279
$976$	2.08556e13	0.735696
$977$	2.99752e13	1.05253	0.526267	−	0.850319i	$-0.323591\pi$
$977$	2.99752e13	1.05253	0.526267	+	0.850319i	$0.323591\pi$
$978$	1.12491e14	3.93183
$979$	−8.98563e12	−0.312627
$980$	3.86208e13	1.33753
$981$	1.75995e13	0.606721
$982$	3.31606e13	1.13794
$983$	−3.61112e13	−1.23353	−0.616767	−	0.787145i	$-0.711558\pi$
$983$	−3.61112e13	−1.23353	−0.616767	+	0.787145i	$0.711558\pi$
$984$	−1.41970e12	−0.0482746
$985$	2.60593e13	0.882062
$986$	0	0
$987$	4.23486e13	1.42040
$988$	4.97331e12	0.166050
$989$	1.08591e14	3.60920
$990$	5.94935e13	1.96839
$991$	−1.15766e13	−0.381285	−0.190642	−	0.981660i	$-0.561057\pi$
$991$	−1.15766e13	−0.381285	−0.190642	+	0.981660i	$0.561057\pi$
$992$	−2.78904e13	−0.914432
$993$	−8.69402e12	−0.283759
$994$	−3.64534e12	−0.118440
$995$	2.22627e13	0.720070
$996$	−7.13603e13	−2.29768
$997$	−2.93056e13	−0.939339	−0.469669	−	0.882842i	$-0.655627\pi$
$997$	−2.93056e13	−0.939339	−0.469669	+	0.882842i	$0.655627\pi$
$998$	3.88816e13	1.24067
$999$	−1.78265e13	−0.566266

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.h.1.7	yes	36
17.16	even	2		289.10.a.g.1.7	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.7	✓	36	17.16	even	2
289.10.a.h.1.7	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)

\(f(q)\)	\(=\)	\(q-32.5443 q^{2} -213.342 q^{3} +547.129 q^{4} +2406.57 q^{5} +6943.04 q^{6} +8347.75 q^{7} -1143.25 q^{8} +25831.6 q^{9} +O(q^{10})\)	\(q-32.5443 q^{2} -213.342 q^{3} +547.129 q^{4} +2406.57 q^{5} +6943.04 q^{6} +8347.75 q^{7} -1143.25 q^{8} +25831.6 q^{9} -78320.2 q^{10} -29406.6 q^{11} -116725. q^{12} +114840. q^{13} -271671. q^{14} -513422. q^{15} -242924. q^{16} -840671. q^{18} +79151.9 q^{19} +1.31671e6 q^{20} -1.78092e6 q^{21} +957015. q^{22} +2.58010e6 q^{23} +243903. q^{24} +3.83848e6 q^{25} -3.73739e6 q^{26} -1.31176e6 q^{27} +4.56730e6 q^{28} +569151. q^{29} +1.67090e7 q^{30} -3.28465e6 q^{31} +8.49112e6 q^{32} +6.27364e6 q^{33} +2.00895e7 q^{35} +1.41332e7 q^{36} +1.35898e7 q^{37} -2.57594e6 q^{38} -2.45002e7 q^{39} -2.75132e6 q^{40} -5.82076e6 q^{41} +5.79588e7 q^{42} +4.20879e7 q^{43} -1.60892e7 q^{44} +6.21657e7 q^{45} -8.39674e7 q^{46} -2.37790e7 q^{47} +5.18258e7 q^{48} +2.93314e7 q^{49} -1.24920e8 q^{50} +6.28325e7 q^{52} +4.78987e7 q^{53} +4.26902e7 q^{54} -7.07691e7 q^{55} -9.54357e6 q^{56} -1.68864e7 q^{57} -1.85226e7 q^{58} +1.36738e8 q^{59} -2.80908e8 q^{60} -8.58524e7 q^{61} +1.06896e8 q^{62} +2.15636e8 q^{63} -1.51960e8 q^{64} +2.76372e8 q^{65} -2.04171e8 q^{66} +1.38932e8 q^{67} -5.50442e8 q^{69} -6.53798e8 q^{70} +1.34182e7 q^{71} -2.95320e7 q^{72} -1.85812e8 q^{73} -4.42269e8 q^{74} -8.18906e8 q^{75} +4.33063e7 q^{76} -2.45479e8 q^{77} +7.97342e8 q^{78} +9.57070e7 q^{79} -5.84614e8 q^{80} -2.28592e8 q^{81} +1.89432e8 q^{82} +6.11352e8 q^{83} -9.74395e8 q^{84} -1.36972e9 q^{86} -1.21424e8 q^{87} +3.36191e7 q^{88} +3.05565e8 q^{89} -2.02314e9 q^{90} +9.58659e8 q^{91} +1.41165e9 q^{92} +7.00752e8 q^{93} +7.73870e8 q^{94} +1.90485e8 q^{95} -1.81151e9 q^{96} +4.08368e8 q^{97} -9.54568e8 q^{98} -7.59619e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9} + 60000 q^{10} + 76902 q^{11} + 373248 q^{12} + 54216 q^{13} + 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} + 6439479 q^{20} - 138102 q^{21} + 267324 q^{22} + 4041462 q^{23} + 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} + 13281612 q^{27} + 18614784 q^{28} + 4005936 q^{29} + 22471686 q^{30} + 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} + 22076682 q^{37} - 27401376 q^{38} + 62736162 q^{39} - 12231630 q^{40} + 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} - 49578936 q^{44} + 129308238 q^{45} + 140524827 q^{46} - 118557912 q^{47} + 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} + 209848575 q^{54} - 365439924 q^{55} + 203095059 q^{56} - 4614108 q^{57} - 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} + 175597116 q^{61} + 720602571 q^{62} + 587415936 q^{63} + 853082511 q^{64} + 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} + 1308709542 q^{71} - 275337849 q^{72} + 494841342 q^{73} + 1545361890 q^{74} + 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} + 2270624538 q^{78} + 1980107868 q^{79} + 2897000199 q^{80} + 1598298840 q^{81} + 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} - 2705904618 q^{88} + 148394658 q^{89} + 117916215 q^{90} + 636340896 q^{91} - 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} + 4878626298 q^{95} - 8390096634 q^{96} - 891786822 q^{97} + 4285627647 q^{98} - 1476187998 q^{99}+O(q^{100}) \) 36 * q + 486 * q^3 + 9216 * q^4 + 3750 * q^5 + 11061 * q^6 + 29040 * q^7 + 24837 * q^8 + 236196 * q^9 + 60000 * q^10 + 76902 * q^11 + 373248 * q^12 + 54216 * q^13 + 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 + 6439479 * q^20 - 138102 * q^21 + 267324 * q^22 + 4041462 * q^23 + 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 + 13281612 * q^27 + 18614784 * q^28 + 4005936 * q^29 + 22471686 * q^30 + 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 + 22076682 * q^37 - 27401376 * q^38 + 62736162 * q^39 - 12231630 * q^40 + 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 - 49578936 * q^44 + 129308238 * q^45 + 140524827 * q^46 - 118557912 * q^47 + 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 + 209848575 * q^54 - 365439924 * q^55 + 203095059 * q^56 - 4614108 * q^57 - 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 + 175597116 * q^61 + 720602571 * q^62 + 587415936 * q^63 + 853082511 * q^64 + 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 + 1308709542 * q^71 - 275337849 * q^72 + 494841342 * q^73 + 1545361890 * q^74 + 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 + 2270624538 * q^78 + 1980107868 * q^79 + 2897000199 * q^80 + 1598298840 * q^81 + 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 - 2705904618 * q^88 + 148394658 * q^89 + 117916215 * q^90 + 636340896 * q^91 - 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 + 4878626298 * q^95 - 8390096634 * q^96 - 891786822 * q^97 + 4285627647 * q^98 - 1476187998 * q^99

Introduction

L-functions

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