LMFDB - Embedded newform 289.10.a.g.1.6

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			1.6
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)

$f(q)$	$=$	$q-33.0540 q^{2} +199.787 q^{3} +580.568 q^{4} -108.765 q^{5} -6603.77 q^{6} +1478.44 q^{7} -2266.45 q^{8} +20231.9 q^{9} +O(q^{10})$	\(q-33.0540 q^{2} +199.787 q^{3} +580.568 q^{4} -108.765 q^{5} -6603.77 q^{6} +1478.44 q^{7} -2266.45 q^{8} +20231.9 q^{9} +3595.11 q^{10} +82128.1 q^{11} +115990. q^{12} +23617.4 q^{13} -48868.3 q^{14} -21729.8 q^{15} -222336. q^{16} -668745. q^{18} -539058. q^{19} -63145.3 q^{20} +295373. q^{21} -2.71466e6 q^{22} -960277. q^{23} -452808. q^{24} -1.94130e6 q^{25} -780651. q^{26} +109662. q^{27} +858334. q^{28} +6.36845e6 q^{29} +718256. q^{30} -5.33710e6 q^{31} +8.50951e6 q^{32} +1.64081e7 q^{33} -160802. q^{35} +1.17460e7 q^{36} -2.03822e7 q^{37} +1.78180e7 q^{38} +4.71846e6 q^{39} +246510. q^{40} -3.70567e6 q^{41} -9.76326e6 q^{42} -3.16986e7 q^{43} +4.76809e7 q^{44} -2.20051e6 q^{45} +3.17410e7 q^{46} +3.24736e7 q^{47} -4.44198e7 q^{48} -3.81678e7 q^{49} +6.41676e7 q^{50} +1.37115e7 q^{52} -3.44852e7 q^{53} -3.62476e6 q^{54} -8.93263e6 q^{55} -3.35081e6 q^{56} -1.07697e8 q^{57} -2.10503e8 q^{58} -8.66911e7 q^{59} -1.26156e7 q^{60} -2.76467e7 q^{61} +1.76413e8 q^{62} +2.99116e7 q^{63} -1.67438e8 q^{64} -2.56874e6 q^{65} -5.42355e8 q^{66} -8.41005e7 q^{67} -1.91851e8 q^{69} +5.31514e6 q^{70} -1.01356e8 q^{71} -4.58546e7 q^{72} +3.67214e8 q^{73} +6.73712e8 q^{74} -3.87846e8 q^{75} -3.12960e8 q^{76} +1.21421e8 q^{77} -1.55964e8 q^{78} -1.40097e8 q^{79} +2.41822e7 q^{80} -3.76315e8 q^{81} +1.22487e8 q^{82} -7.40629e8 q^{83} +1.71484e8 q^{84} +1.04777e9 q^{86} +1.27233e9 q^{87} -1.86139e8 q^{88} -2.04859e8 q^{89} +7.27358e7 q^{90} +3.49169e7 q^{91} -5.57506e8 q^{92} -1.06628e9 q^{93} -1.07338e9 q^{94} +5.86304e7 q^{95} +1.70009e9 q^{96} +7.98484e8 q^{97} +1.26160e9 q^{98} +1.66161e9 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−33.0540	−1.46080	−0.730398	−	0.683022i	$-0.760665\pi$
$2$	−33.0540	−1.46080	−0.730398	+	0.683022i	$0.760665\pi$
$3$	199.787	1.42404	0.712019	−	0.702160i	$-0.247781\pi$
$3$	199.787	1.42404	0.712019	+	0.702160i	$0.247781\pi$
$4$	580.568	1.13392
$5$	−108.765	−0.0778256	−0.0389128	−	0.999243i	$-0.512389\pi$
$5$	−108.765	−0.0778256	−0.0389128	+	0.999243i	$0.512389\pi$
$6$	−6603.77	−2.08023
$7$	1478.44	0.232735	0.116368	−	0.993206i	$-0.462875\pi$
$7$	1478.44	0.232735	0.116368	+	0.993206i	$0.462875\pi$
$8$	−2266.45	−0.195633
$9$	20231.9	1.02789
$10$	3595.11	0.113687
$11$	82128.1	1.69131	0.845657	−	0.533726i	$-0.179209\pi$
$11$	82128.1	1.69131	0.845657	+	0.533726i	$0.179209\pi$
$12$	115990.	1.61475
$13$	23617.4	0.229344	0.114672	−	0.993403i	$-0.463418\pi$
$13$	23617.4	0.229344	0.114672	+	0.993403i	$0.463418\pi$
$14$	−48868.3	−0.339978
$15$	−21729.8	−0.110827
$16$	−222336.	−0.848143
$17$	0	0
$17$	0	0
$18$	−668745.	−1.50153
$19$	−539058.	−0.948952	−0.474476	−	0.880268i	$-0.657362\pi$
$19$	−539058.	−0.948952	−0.474476	+	0.880268i	$0.657362\pi$
$20$	−63145.3	−0.0882482
$21$	295373.	0.331424
$22$	−2.71466e6	−2.47066
$23$	−960277.	−0.715519	−0.357760	−	0.933814i	$-0.616459\pi$
$23$	−960277.	−0.715519	−0.357760	+	0.933814i	$0.616459\pi$
$24$	−452808.	−0.278589
$25$	−1.94130e6	−0.993943
$26$	−780651.	−0.335025
$27$	109662.	0.0397116
$28$	858334.	0.263903
$29$	6.36845e6	1.67203	0.836013	−	0.548710i	$-0.184881\pi$
$29$	6.36845e6	1.67203	0.836013	+	0.548710i	$0.184881\pi$
$30$	718256.	0.161895
$31$	−5.33710e6	−1.03795	−0.518977	−	0.854788i	$-0.673687\pi$
$31$	−5.33710e6	−1.03795	−0.518977	+	0.854788i	$0.673687\pi$
$32$	8.50951e6	1.43460
$33$	1.64081e7	2.40850
$34$	0	0
$35$	−160802.	−0.0181127
$36$	1.17460e7	1.16554
$37$	−2.03822e7	−1.78790	−0.893948	−	0.448171i	$-0.852076\pi$
$37$	−2.03822e7	−1.78790	−0.893948	+	0.448171i	$0.852076\pi$
$38$	1.78180e7	1.38622
$39$	4.71846e6	0.326595
$40$	246510.	0.0152252
$41$	−3.70567e6	−0.204804	−0.102402	−	0.994743i	$-0.532653\pi$
$41$	−3.70567e6	−0.204804	−0.102402	+	0.994743i	$0.532653\pi$
$42$	−9.76326e6	−0.484142
$43$	−3.16986e7	−1.41394	−0.706972	−	0.707242i	$-0.749939\pi$
$43$	−3.16986e7	−1.41394	−0.706972	+	0.707242i	$0.749939\pi$
$44$	4.76809e7	1.91782
$45$	−2.20051e6	−0.0799959
$46$	3.17410e7	1.04523
$47$	3.24736e7	0.970711	0.485356	−	0.874317i	$-0.338690\pi$
$47$	3.24736e7	0.970711	0.485356	+	0.874317i	$0.338690\pi$
$48$	−4.44198e7	−1.20779
$49$	−3.81678e7	−0.945834
$50$	6.41676e7	1.45195
$51$	0	0
$52$	1.37115e7	0.260058
$53$	−3.44852e7	−0.600332	−0.300166	−	0.953887i	$-0.597042\pi$
$53$	−3.44852e7	−0.600332	−0.300166	+	0.953887i	$0.597042\pi$
$54$	−3.62476e6	−0.0580106
$55$	−8.93263e6	−0.131628
$56$	−3.35081e6	−0.0455306
$57$	−1.07697e8	−1.35134
$58$	−2.10503e8	−2.44249
$59$	−8.66911e7	−0.931409	−0.465704	−	0.884940i	$-0.654199\pi$
$59$	−8.66911e7	−0.931409	−0.465704	+	0.884940i	$0.654199\pi$
$60$	−1.26156e7	−0.125669
$61$	−2.76467e7	−0.255658	−0.127829	−	0.991796i	$-0.540801\pi$
$61$	−2.76467e7	−0.255658	−0.127829	+	0.991796i	$0.540801\pi$
$62$	1.76413e8	1.51624
$63$	2.99116e7	0.239225
$64$	−1.67438e8	−1.24751
$65$	−2.56874e6	−0.0178488
$66$	−5.42355e8	−3.51832
$67$	−8.41005e7	−0.509873	−0.254936	−	0.966958i	$-0.582055\pi$
$67$	−8.41005e7	−0.509873	−0.254936	+	0.966958i	$0.582055\pi$
$68$	0	0
$69$	−1.91851e8	−1.01893
$70$	5.31514e6	0.0264590
$71$	−1.01356e8	−0.473354	−0.236677	−	0.971588i	$-0.576058\pi$
$71$	−1.01356e8	−0.473354	−0.236677	+	0.971588i	$0.576058\pi$
$72$	−4.58546e7	−0.201088
$73$	3.67214e8	1.51345	0.756723	−	0.653736i	$-0.226799\pi$
$73$	3.67214e8	1.51345	0.756723	+	0.653736i	$0.226799\pi$
$74$	6.73712e8	2.61175
$75$	−3.87846e8	−1.41541
$76$	−3.12960e8	−1.07604
$77$	1.21421e8	0.393628
$78$	−1.55964e8	−0.477088
$79$	−1.40097e8	−0.404676	−0.202338	−	0.979316i	$-0.564854\pi$
$79$	−1.40097e8	−0.404676	−0.202338	+	0.979316i	$0.564854\pi$
$80$	2.41822e7	0.0660072
$81$	−3.76315e8	−0.971336
$82$	1.22487e8	0.299177
$83$	−7.40629e8	−1.71297	−0.856484	−	0.516173i	$-0.827356\pi$
$83$	−7.40629e8	−1.71297	−0.856484	+	0.516173i	$0.827356\pi$
$84$	1.71484e8	0.375809
$85$	0	0
$86$	1.04777e9	2.06548
$87$	1.27233e9	2.38103
$88$	−1.86139e8	−0.330877
$89$	−2.04859e8	−0.346099	−0.173049	−	0.984913i	$-0.555362\pi$
$89$	−2.04859e8	−0.346099	−0.173049	+	0.984913i	$0.555362\pi$
$90$	7.27358e7	0.116858
$91$	3.49169e7	0.0533764
$92$	−5.57506e8	−0.811343
$93$	−1.06628e9	−1.47809
$94$	−1.07338e9	−1.41801
$95$	5.86304e7	0.0738528
$96$	1.70009e9	2.04292
$97$	7.98484e8	0.915784	0.457892	−	0.889008i	$-0.348605\pi$
$97$	7.98484e8	0.915784	0.457892	+	0.889008i	$0.348605\pi$
$98$	1.26160e9	1.38167
$99$	1.66161e9	1.73848
$100$	−1.12705e9	−1.12705
$101$	−3.07991e8	−0.294504	−0.147252	−	0.989099i	$-0.547043\pi$
$101$	−3.07991e8	−0.294504	−0.147252	+	0.989099i	$0.547043\pi$
$102$	0	0
$103$	−6.64656e8	−0.581875	−0.290937	−	0.956742i	$-0.593967\pi$
$103$	−6.64656e8	−0.581875	−0.290937	+	0.956742i	$0.593967\pi$
$104$	−5.35278e7	−0.0448672
$105$	−3.21261e7	−0.0257933
$106$	1.13987e9	0.876961
$107$	−1.44876e9	−1.06849	−0.534245	−	0.845330i	$-0.679404\pi$
$107$	−1.44876e9	−1.06849	−0.534245	+	0.845330i	$0.679404\pi$
$108$	6.36661e7	0.0450299
$109$	2.45299e9	1.66447	0.832235	−	0.554423i	$-0.187061\pi$
$109$	2.45299e9	1.66447	0.832235	+	0.554423i	$0.187061\pi$
$110$	2.95259e8	0.192281
$111$	−4.07209e9	−2.54603
$112$	−3.28709e8	−0.197393
$113$	3.00054e9	1.73120	0.865598	−	0.500740i	$-0.166939\pi$
$113$	3.00054e9	1.73120	0.865598	+	0.500740i	$0.166939\pi$
$114$	3.55981e9	1.97404
$115$	1.04444e8	0.0556857
$116$	3.69732e9	1.89595
$117$	4.77825e8	0.235740
$118$	2.86549e9	1.36060
$119$	0	0
$120$	4.92495e7	0.0216813
$121$	4.38707e9	1.86055
$122$	9.13835e8	0.373464
$123$	−7.40345e8	−0.291649
$124$	−3.09855e9	−1.17696
$125$	4.23575e8	0.155180
$126$	−9.88698e8	−0.349459
$127$	1.22338e9	0.417297	0.208649	−	0.977991i	$-0.433094\pi$
$127$	1.22338e9	0.417297	0.208649	+	0.977991i	$0.433094\pi$
$128$	1.17762e9	0.387757
$129$	−6.33297e9	−2.01351
$130$	8.49072e7	0.0260735
$131$	1.89291e9	0.561576	0.280788	−	0.959770i	$-0.409404\pi$
$131$	1.89291e9	0.561576	0.280788	+	0.959770i	$0.409404\pi$
$132$	9.52604e9	2.73105
$133$	−7.96964e8	−0.220854
$134$	2.77986e9	0.744820
$135$	−1.19273e7	−0.00309058
$136$	0	0
$137$	−1.42855e9	−0.346461	−0.173230	−	0.984881i	$-0.555421\pi$
$137$	−1.42855e9	−0.346461	−0.173230	+	0.984881i	$0.555421\pi$
$138$	6.34145e9	1.48844
$139$	4.86338e9	1.10502	0.552512	−	0.833505i	$-0.313669\pi$
$139$	4.86338e9	1.10502	0.552512	+	0.833505i	$0.313669\pi$
$140$	−9.33563e7	−0.0205384
$141$	6.48781e9	1.38233
$142$	3.35021e9	0.691473
$143$	1.93965e9	0.387893
$144$	−4.49827e9	−0.871795
$145$	−6.92662e8	−0.130126
$146$	−1.21379e10	−2.21083
$147$	−7.62544e9	−1.34690
$148$	−1.18332e10	−2.02734
$149$	3.73603e8	0.0620972	0.0310486	−	0.999518i	$-0.490115\pi$
$149$	3.73603e8	0.0620972	0.0310486	+	0.999518i	$0.490115\pi$
$150$	1.28199e10	2.06763
$151$	−1.22330e10	−1.91486	−0.957429	−	0.288670i	$-0.906787\pi$
$151$	−1.22330e10	−1.91486	−0.957429	+	0.288670i	$0.906787\pi$
$152$	1.22175e9	0.185646
$153$	0	0
$154$	−4.01346e9	−0.575010
$155$	5.80488e8	0.0807794
$156$	2.73939e9	0.370333
$157$	7.26890e9	0.954818	0.477409	−	0.878681i	$-0.341576\pi$
$157$	7.26890e9	0.954818	0.477409	+	0.878681i	$0.341576\pi$
$158$	4.63078e9	0.591149
$159$	−6.88970e9	−0.854895
$160$	−9.25533e8	−0.111648
$161$	−1.41971e9	−0.166526
$162$	1.24387e10	1.41892
$163$	−3.62816e9	−0.402571	−0.201285	−	0.979533i	$-0.564512\pi$
$163$	−3.62816e9	−0.402571	−0.201285	+	0.979533i	$0.564512\pi$
$164$	−2.15139e9	−0.232232
$165$	−1.78462e9	−0.187443
$166$	2.44808e10	2.50230
$167$	−1.50076e10	−1.49309	−0.746546	−	0.665334i	$-0.768289\pi$
$167$	−1.50076e10	−1.49309	−0.746546	+	0.665334i	$0.768289\pi$
$168$	−6.69448e8	−0.0648374
$169$	−1.00467e10	−0.947401
$170$	0	0
$171$	−1.09062e10	−0.975415
$172$	−1.84032e10	−1.60330
$173$	2.29866e10	1.95105	0.975523	−	0.219899i	$-0.0705728\pi$
$173$	2.29866e10	1.95105	0.975523	+	0.219899i	$0.0705728\pi$
$174$	−4.20558e10	−3.47820
$175$	−2.87008e9	−0.231325
$176$	−1.82600e10	−1.43448
$177$	−1.73198e10	−1.32636
$178$	6.77141e9	0.505579
$179$	−1.02963e10	−0.749625	−0.374812	−	0.927101i	$-0.622293\pi$
$179$	−1.02963e10	−0.749625	−0.374812	+	0.927101i	$0.622293\pi$
$180$	−1.27755e9	−0.0907091
$181$	−1.97780e10	−1.36971	−0.684857	−	0.728678i	$-0.740135\pi$
$181$	−1.97780e10	−1.36971	−0.684857	+	0.728678i	$0.740135\pi$
$182$	−1.15414e9	−0.0779720
$183$	−5.52346e9	−0.364067
$184$	2.17642e9	0.139979
$185$	2.21686e9	0.139144
$186$	3.52450e10	2.15918
$187$	0	0
$188$	1.88531e10	1.10071
$189$	1.62128e8	0.00924229
$190$	−1.93797e9	−0.107884
$191$	1.03563e10	0.563057	0.281529	−	0.959553i	$-0.409159\pi$
$191$	1.03563e10	0.563057	0.281529	+	0.959553i	$0.409159\pi$
$192$	−3.34519e10	−1.77650
$193$	1.76983e10	0.918173	0.459086	−	0.888392i	$-0.348177\pi$
$193$	1.76983e10	0.918173	0.459086	+	0.888392i	$0.348177\pi$
$194$	−2.63931e10	−1.33777
$195$	−5.13201e8	−0.0254174
$196$	−2.21590e10	−1.07250
$197$	1.40731e10	0.665721	0.332860	−	0.942976i	$-0.391986\pi$
$197$	1.40731e10	0.665721	0.332860	+	0.942976i	$0.391986\pi$
$198$	−5.49228e10	−2.53956
$199$	−9.51240e8	−0.0429983	−0.0214992	−	0.999769i	$-0.506844\pi$
$199$	−9.51240e8	−0.0429983	−0.0214992	+	0.999769i	$0.506844\pi$
$200$	4.39985e9	0.194448
$201$	−1.68022e10	−0.726079
$202$	1.01803e10	0.430211
$203$	9.41536e9	0.389139
$204$	0	0
$205$	4.03046e8	0.0159390
$206$	2.19696e10	0.850000
$207$	−1.94282e10	−0.735473
$208$	−5.25099e9	−0.194516
$209$	−4.42718e10	−1.60498
$210$	1.06190e9	0.0376787
$211$	2.33273e10	0.810201	0.405101	−	0.914272i	$-0.367236\pi$
$211$	2.33273e10	0.810201	0.405101	+	0.914272i	$0.367236\pi$
$212$	−2.00210e10	−0.680729
$213$	−2.02496e10	−0.674074
$214$	4.78875e10	1.56085
$215$	3.44769e9	0.110041
$216$	−2.48543e8	−0.00776890
$217$	−7.89057e9	−0.241568
$218$	−8.10811e10	−2.43145
$219$	7.33647e10	2.15520
$220$	−5.18600e9	−0.149255
$221$	0	0
$222$	1.34599e11	3.71923
$223$	−2.38061e10	−0.644638	−0.322319	−	0.946631i	$-0.604462\pi$
$223$	−2.38061e10	−0.644638	−0.322319	+	0.946631i	$0.604462\pi$
$224$	1.25808e10	0.333881
$225$	−3.92761e10	−1.02166
$226$	−9.91799e10	−2.52892
$227$	1.43719e10	0.359251	0.179626	−	0.983735i	$-0.442511\pi$
$227$	1.43719e10	0.359251	0.179626	+	0.983735i	$0.442511\pi$
$228$	−6.25254e10	−1.53232
$229$	−5.55766e10	−1.33546	−0.667732	−	0.744402i	$-0.732735\pi$
$229$	−5.55766e10	−1.33546	−0.667732	+	0.744402i	$0.732735\pi$
$230$	−3.45230e9	−0.0813454
$231$	2.42584e10	0.560542
$232$	−1.44338e10	−0.327103
$233$	−4.77598e10	−1.06160	−0.530800	−	0.847497i	$-0.678108\pi$
$233$	−4.77598e10	−1.06160	−0.530800	+	0.847497i	$0.678108\pi$
$234$	−1.57940e10	−0.344367
$235$	−3.53198e9	−0.0755462
$236$	−5.03301e10	−1.05614
$237$	−2.79896e10	−0.576274
$238$	0	0
$239$	8.16620e9	0.161894	0.0809468	−	0.996718i	$-0.474206\pi$
$239$	8.16620e9	0.161894	0.0809468	+	0.996718i	$0.474206\pi$
$240$	4.83130e9	0.0939969
$241$	1.30949e10	0.250049	0.125025	−	0.992154i	$-0.460099\pi$
$241$	1.30949e10	0.250049	0.125025	+	0.992154i	$0.460099\pi$
$242$	−1.45010e11	−2.71788
$243$	−7.73414e10	−1.42293
$244$	−1.60508e10	−0.289896
$245$	4.15131e9	0.0736101
$246$	2.44714e10	0.426040
$247$	−1.27312e10	−0.217637
$248$	1.20963e10	0.203058
$249$	−1.47968e11	−2.43933
$250$	−1.40009e10	−0.226686
$251$	4.05239e9	0.0644435	0.0322217	−	0.999481i	$-0.489742\pi$
$251$	4.05239e9	0.0644435	0.0322217	+	0.999481i	$0.489742\pi$
$252$	1.73657e10	0.271263
$253$	−7.88657e10	−1.21017
$254$	−4.04377e10	−0.609586
$255$	0	0
$256$	4.68030e10	0.681074
$257$	−1.03270e11	−1.47664	−0.738322	−	0.674448i	$-0.764382\pi$
$257$	−1.03270e11	−1.47664	−0.738322	+	0.674448i	$0.764382\pi$
$258$	2.09330e11	2.94133
$259$	−3.01337e10	−0.416106
$260$	−1.49133e9	−0.0202392
$261$	1.28846e11	1.71865
$262$	−6.25682e10	−0.820348
$263$	4.00733e10	0.516480	0.258240	−	0.966081i	$-0.416857\pi$
$263$	4.00733e10	0.516480	0.258240	+	0.966081i	$0.416857\pi$
$264$	−3.71882e10	−0.471181
$265$	3.75077e9	0.0467212
$266$	2.63429e10	0.322623
$267$	−4.09282e10	−0.492858
$268$	−4.88260e10	−0.578156
$269$	1.37028e11	1.59560	0.797799	−	0.602924i	$-0.205998\pi$
$269$	1.37028e11	1.59560	0.797799	+	0.602924i	$0.205998\pi$
$270$	3.94245e8	0.00451471
$271$	−4.28730e10	−0.482861	−0.241431	−	0.970418i	$-0.577617\pi$
$271$	−4.28730e10	−0.482861	−0.241431	+	0.970418i	$0.577617\pi$
$272$	0	0
$273$	6.97594e9	0.0760100
$274$	4.72195e10	0.506108
$275$	−1.59435e11	−1.68107
$276$	−1.11383e11	−1.15538
$277$	3.59363e10	0.366753	0.183377	−	0.983043i	$-0.441297\pi$
$277$	3.59363e10	0.366753	0.183377	+	0.983043i	$0.441297\pi$
$278$	−1.60754e11	−1.61421
$279$	−1.07980e11	−1.06690
$280$	3.64449e8	0.00354345
$281$	6.81885e10	0.652429	0.326214	−	0.945296i	$-0.394227\pi$
$281$	6.81885e10	0.652429	0.326214	+	0.945296i	$0.394227\pi$
$282$	−2.14448e11	−2.01930
$283$	−5.87965e10	−0.544895	−0.272448	−	0.962171i	$-0.587833\pi$
$283$	−5.87965e10	−0.544895	−0.272448	+	0.962171i	$0.587833\pi$
$284$	−5.88439e10	−0.536746
$285$	1.17136e10	0.105169
$286$	−6.41133e10	−0.566632
$287$	−5.47860e9	−0.0476652
$288$	1.72163e11	1.47460
$289$	0	0
$290$	2.28953e10	0.190088
$291$	1.59527e11	1.30411
$292$	2.13193e11	1.71613
$293$	9.24412e10	0.732760	0.366380	−	0.930465i	$-0.380597\pi$
$293$	9.24412e10	0.732760	0.366380	+	0.930465i	$0.380597\pi$
$294$	2.52051e11	1.96755
$295$	9.42892e9	0.0724875
$296$	4.61952e10	0.349771
$297$	9.00630e9	0.0671649
$298$	−1.23491e10	−0.0907112
$299$	−2.26793e10	−0.164100
$300$	−2.25171e11	−1.60497
$301$	−4.68644e10	−0.329074
$302$	4.04350e11	2.79721
$303$	−6.15326e10	−0.419386
$304$	1.19852e11	0.804847
$305$	3.00698e9	0.0198967
$306$	0	0
$307$	−2.31914e11	−1.49006	−0.745032	−	0.667029i	$-0.767566\pi$
$307$	−2.31914e11	−1.49006	−0.745032	+	0.667029i	$0.767566\pi$
$308$	7.04933e10	0.446344
$309$	−1.32790e11	−0.828612
$310$	−1.91875e10	−0.118002
$311$	−3.18428e11	−1.93014	−0.965071	−	0.261989i	$-0.915622\pi$
$311$	−3.18428e11	−1.93014	−0.965071	+	0.261989i	$0.915622\pi$
$312$	−1.06942e10	−0.0638927
$313$	1.68213e11	0.990629	0.495315	−	0.868714i	$-0.335053\pi$
$313$	1.68213e11	0.990629	0.495315	+	0.868714i	$0.335053\pi$
$314$	−2.40266e11	−1.39479
$315$	−3.25332e9	−0.0186179
$316$	−8.13360e10	−0.458871
$317$	1.71014e11	0.951187	0.475594	−	0.879665i	$-0.342233\pi$
$317$	1.71014e11	0.951187	0.475594	+	0.879665i	$0.342233\pi$
$318$	2.27732e11	1.24883
$319$	5.23029e11	2.82792
$320$	1.82113e10	0.0970880
$321$	−2.89444e11	−1.52157
$322$	4.69271e10	0.243261
$323$	0	0
$324$	−2.18477e11	−1.10142
$325$	−4.58484e10	−0.227955
$326$	1.19925e11	0.588073
$327$	4.90075e11	2.37027
$328$	8.39873e9	0.0400665
$329$	4.80102e10	0.225919
$330$	5.89890e10	0.273816
$331$	−2.35952e11	−1.08043	−0.540215	−	0.841527i	$-0.681657\pi$
$331$	−2.35952e11	−1.08043	−0.540215	+	0.841527i	$0.681657\pi$
$332$	−4.29986e11	−1.94237
$333$	−4.12370e11	−1.83775
$334$	4.96061e11	2.18110
$335$	9.14715e9	0.0396812
$336$	−6.56719e10	−0.281095
$337$	1.03556e11	0.437364	0.218682	−	0.975796i	$-0.429824\pi$
$337$	1.03556e11	0.437364	0.218682	+	0.975796i	$0.429824\pi$
$338$	3.32084e11	1.38396
$339$	5.99469e11	2.46529
$340$	0	0
$341$	−4.38326e11	−1.75551
$342$	3.60493e11	1.42488
$343$	−1.16089e11	−0.452864
$344$	7.18434e10	0.276614
$345$	2.08666e10	0.0792986
$346$	−7.59800e11	−2.85008
$347$	−4.83654e10	−0.179082	−0.0895411	−	0.995983i	$-0.528540\pi$
$347$	−4.83654e10	−0.179082	−0.0895411	+	0.995983i	$0.528540\pi$
$348$	7.38677e11	2.69990
$349$	3.17902e11	1.14704	0.573520	−	0.819191i	$-0.305577\pi$
$349$	3.17902e11	1.14704	0.573520	+	0.819191i	$0.305577\pi$
$350$	9.48678e10	0.337919
$351$	2.58993e9	0.00910763
$352$	6.98869e11	2.42635
$353$	−1.59102e11	−0.545368	−0.272684	−	0.962104i	$-0.587911\pi$
$353$	−1.59102e11	−0.545368	−0.272684	+	0.962104i	$0.587911\pi$
$354$	5.72488e11	1.93754
$355$	1.10239e10	0.0368390
$356$	−1.18935e11	−0.392449
$357$	0	0
$358$	3.40335e11	1.09505
$359$	−6.73256e10	−0.213922	−0.106961	−	0.994263i	$-0.534112\pi$
$359$	−6.73256e10	−0.213922	−0.106961	+	0.994263i	$0.534112\pi$
$360$	4.98736e9	0.0156498
$361$	−3.21040e10	−0.0994895
$362$	6.53744e11	2.00087
$363$	8.76480e11	2.64949
$364$	2.02716e10	0.0605247
$365$	−3.99399e10	−0.117785
$366$	1.82572e11	0.531827
$367$	−8.98916e10	−0.258655	−0.129328	−	0.991602i	$-0.541282\pi$
$367$	−8.98916e10	−0.258655	−0.129328	+	0.991602i	$0.541282\pi$
$368$	2.13504e11	0.606862
$369$	−7.49727e10	−0.210516
$370$	−7.32760e10	−0.203261
$371$	−5.09842e10	−0.139718
$372$	−6.19051e11	−1.67603
$373$	−4.15763e11	−1.11213	−0.556065	−	0.831139i	$-0.687690\pi$
$373$	−4.15763e11	−1.11213	−0.556065	+	0.831139i	$0.687690\pi$
$374$	0	0
$375$	8.46248e10	0.220982
$376$	−7.35999e10	−0.189903
$377$	1.50406e11	0.383469
$378$	−5.35898e9	−0.0135011
$379$	−2.18793e11	−0.544699	−0.272350	−	0.962198i	$-0.587801\pi$
$379$	−2.18793e11	−0.544699	−0.272350	+	0.962198i	$0.587801\pi$
$380$	3.40390e10	0.0837433
$381$	2.44416e11	0.594247
$382$	−3.42316e11	−0.822511
$383$	−7.68723e11	−1.82547	−0.912736	−	0.408549i	$-0.866035\pi$
$383$	−7.68723e11	−1.82547	−0.912736	+	0.408549i	$0.866035\pi$
$384$	2.35273e11	0.552181
$385$	−1.32063e10	−0.0306344
$386$	−5.85001e11	−1.34126
$387$	−6.41323e11	−1.45337
$388$	4.63574e11	1.03843
$389$	−3.53345e11	−0.782394	−0.391197	−	0.920307i	$-0.627939\pi$
$389$	−3.53345e11	−0.782394	−0.391197	+	0.920307i	$0.627939\pi$
$390$	1.69634e10	0.0371297
$391$	0	0
$392$	8.65056e10	0.185036
$393$	3.78179e11	0.799706
$394$	−4.65173e11	−0.972481
$395$	1.52376e10	0.0314942
$396$	9.64676e11	1.97130
$397$	3.01014e11	0.608176	0.304088	−	0.952644i	$-0.401648\pi$
$397$	3.01014e11	0.608176	0.304088	+	0.952644i	$0.401648\pi$
$398$	3.14423e10	0.0628117
$399$	−1.59223e11	−0.314505
$400$	4.31619e11	0.843006
$401$	−2.94871e11	−0.569486	−0.284743	−	0.958604i	$-0.591908\pi$
$401$	−2.94871e11	−0.569486	−0.284743	+	0.958604i	$0.591908\pi$
$402$	5.55380e11	1.06065
$403$	−1.26049e11	−0.238048
$404$	−1.78810e11	−0.333945
$405$	4.09298e10	0.0755948
$406$	−3.11215e11	−0.568452
$407$	−1.67395e12	−3.02390
$408$	0	0
$409$	5.44264e11	0.961733	0.480867	−	0.876794i	$-0.340322\pi$
$409$	5.44264e11	0.961733	0.480867	+	0.876794i	$0.340322\pi$
$410$	−1.33223e10	−0.0232837
$411$	−2.85407e11	−0.493374
$412$	−3.85878e11	−0.659801
$413$	−1.28167e11	−0.216771
$414$	6.42181e11	1.07437
$415$	8.05543e10	0.133313
$416$	2.00973e11	0.329016
$417$	9.71641e11	1.57360
$418$	1.46336e12	2.34454
$419$	7.83707e11	1.24220	0.621099	−	0.783732i	$-0.286686\pi$
$419$	7.83707e11	1.24220	0.621099	+	0.783732i	$0.286686\pi$
$420$	−1.86514e10	−0.0292475
$421$	−8.34641e11	−1.29488	−0.647441	−	0.762115i	$-0.724161\pi$
$421$	−8.34641e11	−1.29488	−0.647441	+	0.762115i	$0.724161\pi$
$422$	−7.71060e11	−1.18354
$423$	6.57002e11	0.997781
$424$	7.81590e10	0.117445
$425$	0	0
$426$	6.69330e11	0.984684
$427$	−4.08739e10	−0.0595005
$428$	−8.41106e11	−1.21159
$429$	3.87518e11	0.552375
$430$	−1.13960e11	−0.160747
$431$	−5.21428e11	−0.727858	−0.363929	−	0.931427i	$-0.618565\pi$
$431$	−5.21428e11	−0.727858	−0.363929	+	0.931427i	$0.618565\pi$
$432$	−2.43817e10	−0.0336811
$433$	−1.09566e12	−1.49790	−0.748948	−	0.662629i	$-0.769441\pi$
$433$	−1.09566e12	−1.49790	−0.748948	+	0.662629i	$0.769441\pi$
$434$	2.60815e11	0.352882
$435$	−1.38385e11	−0.185305
$436$	1.42413e12	1.88738
$437$	5.17645e11	0.678994
$438$	−2.42500e12	−3.14831
$439$	−5.78364e11	−0.743208	−0.371604	−	0.928391i	$-0.621192\pi$
$439$	−5.78364e11	−0.743208	−0.371604	+	0.928391i	$0.621192\pi$
$440$	2.02454e10	0.0257507
$441$	−7.72207e11	−0.972211
$442$	0	0
$443$	−1.28456e12	−1.58466	−0.792332	−	0.610091i	$-0.791133\pi$
$443$	−1.28456e12	−1.58466	−0.792332	+	0.610091i	$0.791133\pi$
$444$	−2.36413e12	−2.88700
$445$	2.22814e10	0.0269354
$446$	7.86886e11	0.941684
$447$	7.46410e10	0.0884288
$448$	−2.47546e11	−0.290339
$449$	−8.37005e11	−0.971895	−0.485948	−	0.873988i	$-0.661525\pi$
$449$	−8.37005e11	−0.971895	−0.485948	+	0.873988i	$0.661525\pi$
$450$	1.29823e12	1.49244
$451$	−3.04339e11	−0.346389
$452$	1.74202e12	1.96304
$453$	−2.44399e12	−2.72683
$454$	−4.75049e11	−0.524792
$455$	−3.79772e9	−0.00415405
$456$	2.44090e11	0.264367
$457$	1.06355e12	1.14061	0.570304	−	0.821434i	$-0.306825\pi$
$457$	1.06355e12	1.14061	0.570304	+	0.821434i	$0.306825\pi$
$458$	1.83703e12	1.95084
$459$	0	0
$460$	6.06369e10	0.0631433
$461$	2.92562e10	0.0301691	0.0150846	−	0.999886i	$-0.495198\pi$
$461$	2.92562e10	0.0301691	0.0150846	+	0.999886i	$0.495198\pi$
$462$	−8.01837e11	−0.818837
$463$	8.91918e11	0.902008	0.451004	−	0.892522i	$-0.351066\pi$
$463$	8.91918e11	0.902008	0.451004	+	0.892522i	$0.351066\pi$
$464$	−1.41593e12	−1.41812
$465$	1.15974e11	0.115033
$466$	1.57865e12	1.55078
$467$	1.16802e12	1.13638	0.568190	−	0.822898i	$-0.307644\pi$
$467$	1.16802e12	1.13638	0.568190	+	0.822898i	$0.307644\pi$
$468$	2.77410e11	0.267310
$469$	−1.24337e11	−0.118665
$470$	1.16746e11	0.110358
$471$	1.45223e12	1.35970
$472$	1.96481e11	0.182214
$473$	−2.60334e12	−2.39142
$474$	9.25169e11	0.841819
$475$	1.04647e12	0.943205
$476$	0	0
$477$	−6.97701e11	−0.617073
$478$	−2.69926e11	−0.236493
$479$	−1.54953e12	−1.34490	−0.672452	−	0.740141i	$-0.734759\pi$
$479$	−1.54953e12	−1.34490	−0.672452	+	0.740141i	$0.734759\pi$
$480$	−1.84910e11	−0.158991
$481$	−4.81374e11	−0.410043
$482$	−4.32839e11	−0.365271
$483$	−2.83640e11	−0.237140
$484$	2.54699e12	2.10971
$485$	−8.68468e10	−0.0712715
$486$	2.55645e12	2.07861
$487$	−5.43663e11	−0.437975	−0.218988	−	0.975728i	$-0.570275\pi$
$487$	−5.43663e11	−0.437975	−0.218988	+	0.975728i	$0.570275\pi$
$488$	6.26600e10	0.0500151
$489$	−7.24859e11	−0.573276
$490$	−1.37217e11	−0.107529
$491$	1.97444e12	1.53312	0.766561	−	0.642171i	$-0.221966\pi$
$491$	1.97444e12	1.53312	0.766561	+	0.642171i	$0.221966\pi$
$492$	−4.29821e11	−0.330708
$493$	0	0
$494$	4.20816e11	0.317922
$495$	−1.80724e11	−0.135298
$496$	1.18663e12	0.880333
$497$	−1.49848e11	−0.110166
$498$	4.89094e12	3.56337
$499$	−7.59393e11	−0.548295	−0.274147	−	0.961688i	$-0.588396\pi$
$499$	−7.59393e11	−0.548295	−0.274147	+	0.961688i	$0.588396\pi$
$500$	2.45914e11	0.175962
$501$	−2.99832e12	−2.12622
$502$	−1.33948e11	−0.0941387
$503$	−6.63986e11	−0.462490	−0.231245	−	0.972895i	$-0.574280\pi$
$503$	−6.63986e11	−0.462490	−0.231245	+	0.972895i	$0.574280\pi$
$504$	−6.77932e10	−0.0468003
$505$	3.34985e10	0.0229200
$506$	2.60683e12	1.76781
$507$	−2.00720e12	−1.34914
$508$	7.10257e11	0.473182
$509$	3.72373e11	0.245894	0.122947	−	0.992413i	$-0.460765\pi$
$509$	3.72373e11	0.245894	0.122947	+	0.992413i	$0.460765\pi$
$510$	0	0
$511$	5.42903e11	0.352232
$512$	−2.14997e12	−1.38267
$513$	−5.91140e10	−0.0376845
$514$	3.41349e12	2.15707
$515$	7.22911e10	0.0452848
$516$	−3.67672e12	−2.28316
$517$	2.66699e12	1.64178
$518$	9.96041e11	0.607846
$519$	4.59243e12	2.77836
$520$	5.82193e9	0.00349182
$521$	1.83776e12	1.09275	0.546374	−	0.837541i	$-0.316008\pi$
$521$	1.83776e12	1.09275	0.546374	+	0.837541i	$0.316008\pi$
$522$	−4.25887e12	−2.51060
$523$	−1.35808e12	−0.793720	−0.396860	−	0.917879i	$-0.629900\pi$
$523$	−1.35808e12	−0.793720	−0.396860	+	0.917879i	$0.629900\pi$
$524$	1.09896e12	0.636784
$525$	−5.73406e11	−0.329416
$526$	−1.32458e12	−0.754472
$527$	0	0
$528$	−3.64811e12	−2.04275
$529$	−8.79021e11	−0.488032
$530$	−1.23978e11	−0.0682501
$531$	−1.75392e12	−0.957383
$532$	−4.62692e11	−0.250432
$533$	−8.75184e10	−0.0469707
$534$	1.35284e12	0.719965
$535$	1.57574e11	0.0831559
$536$	1.90610e11	0.0997478
$537$	−2.05708e12	−1.06750
$538$	−4.52932e12	−2.33084
$539$	−3.13465e12	−1.59970
$540$	−6.92461e9	−0.00350448
$541$	−3.20356e11	−0.160785	−0.0803925	−	0.996763i	$-0.525617\pi$
$541$	−3.20356e11	−0.160785	−0.0803925	+	0.996763i	$0.525617\pi$
$542$	1.41713e12	0.705362
$543$	−3.95140e12	−1.95053
$544$	0	0
$545$	−2.66798e11	−0.129538
$546$	−2.30583e11	−0.111035
$547$	6.22782e11	0.297436	0.148718	−	0.988880i	$-0.452485\pi$
$547$	6.22782e11	0.297436	0.148718	+	0.988880i	$0.452485\pi$
$548$	−8.29373e11	−0.392860
$549$	−5.59345e11	−0.262787
$550$	5.26996e12	2.45570
$551$	−3.43297e12	−1.58667
$552$	4.34821e11	0.199336
$553$	−2.07125e11	−0.0941823
$554$	−1.18784e12	−0.535751
$555$	4.42899e11	0.198147
$556$	2.82353e12	1.25301
$557$	6.56343e11	0.288923	0.144462	−	0.989510i	$-0.453855\pi$
$557$	6.56343e11	0.288923	0.144462	+	0.989510i	$0.453855\pi$
$558$	3.56916e12	1.55852
$559$	−7.48639e11	−0.324279
$560$	3.57519e10	0.0153622
$561$	0	0
$562$	−2.25391e12	−0.953064
$563$	4.16855e12	1.74863	0.874313	−	0.485362i	$-0.161312\pi$
$563$	4.16855e12	1.74863	0.874313	+	0.485362i	$0.161312\pi$
$564$	3.76661e12	1.56746
$565$	−3.26352e11	−0.134731
$566$	1.94346e12	0.795980
$567$	−5.56359e11	−0.226064
$568$	2.29718e11	0.0926035
$569$	3.85025e12	1.53987	0.769935	−	0.638122i	$-0.220289\pi$
$569$	3.85025e12	1.53987	0.769935	+	0.638122i	$0.220289\pi$
$570$	−3.87182e11	−0.153631
$571$	−3.98793e12	−1.56995	−0.784973	−	0.619530i	$-0.787323\pi$
$571$	−3.98793e12	−1.56995	−0.784973	+	0.619530i	$0.787323\pi$
$572$	1.12610e12	0.439840
$573$	2.06905e12	0.801815
$574$	1.81090e11	0.0696290
$575$	1.86418e12	0.711185
$576$	−3.38758e12	−1.28230
$577$	1.61359e12	0.606042	0.303021	−	0.952984i	$-0.402005\pi$
$577$	1.61359e12	0.606042	0.303021	+	0.952984i	$0.402005\pi$
$578$	0	0
$579$	3.53590e12	1.30751
$580$	−4.02138e11	−0.147553
$581$	−1.09497e12	−0.398668
$582$	−5.27300e12	−1.90504
$583$	−2.83220e12	−1.01535
$584$	−8.32274e11	−0.296080
$585$	−5.19705e10	−0.0183466
$586$	−3.05555e12	−1.07041
$587$	2.68902e12	0.934809	0.467405	−	0.884043i	$-0.345189\pi$
$587$	2.68902e12	0.934809	0.467405	+	0.884043i	$0.345189\pi$
$588$	−4.42709e12	−1.52729
$589$	2.87701e12	0.984969
$590$	−3.11664e11	−0.105889
$591$	2.81163e12	0.948012
$592$	4.53168e12	1.51639
$593$	1.62650e12	0.540141	0.270071	−	0.962840i	$-0.412953\pi$
$593$	1.62650e12	0.540141	0.270071	+	0.962840i	$0.412953\pi$
$594$	−2.97694e11	−0.0981141
$595$	0	0
$596$	2.16902e11	0.0704134
$597$	−1.90046e11	−0.0612313
$598$	7.49641e11	0.239717
$599$	2.52469e12	0.801286	0.400643	−	0.916234i	$-0.368787\pi$
$599$	2.52469e12	0.801286	0.400643	+	0.916234i	$0.368787\pi$
$600$	8.79034e11	0.276901
$601$	5.30235e11	0.165781	0.0828903	−	0.996559i	$-0.473585\pi$
$601$	5.30235e11	0.165781	0.0828903	+	0.996559i	$0.473585\pi$
$602$	1.54906e12	0.480710
$603$	−1.70151e12	−0.524091
$604$	−7.10209e12	−2.17130
$605$	−4.77158e11	−0.144798
$606$	2.03390e12	0.612637
$607$	4.14892e12	1.24047	0.620234	−	0.784416i	$-0.287037\pi$
$607$	4.14892e12	1.24047	0.620234	+	0.784416i	$0.287037\pi$
$608$	−4.58712e12	−1.36136
$609$	1.88107e12	0.554149
$610$	−9.93929e10	−0.0290651
$611$	7.66943e11	0.222627
$612$	0	0
$613$	4.35661e12	1.24617	0.623084	−	0.782155i	$-0.285879\pi$
$613$	4.35661e12	1.24617	0.623084	+	0.782155i	$0.285879\pi$
$614$	7.66570e12	2.17668
$615$	8.05233e10	0.0226978
$616$	−2.75195e11	−0.0770066
$617$	−6.33871e11	−0.176083	−0.0880416	−	0.996117i	$-0.528061\pi$
$617$	−6.33871e11	−0.176083	−0.0880416	+	0.996117i	$0.528061\pi$
$618$	4.38923e12	1.21043
$619$	2.92858e12	0.801770	0.400885	−	0.916128i	$-0.368703\pi$
$619$	2.92858e12	0.801770	0.400885	+	0.916128i	$0.368703\pi$
$620$	3.37013e11	0.0915975
$621$	−1.05306e11	−0.0284144
$622$	1.05253e13	2.81954
$623$	−3.02871e11	−0.0805493
$624$	−1.04908e12	−0.276999
$625$	3.74552e12	0.981866
$626$	−5.56013e12	−1.44711
$627$	−8.84493e12	−2.28555
$628$	4.22009e12	1.08269
$629$	0	0
$630$	1.07535e11	0.0271969
$631$	1.86510e12	0.468348	0.234174	−	0.972195i	$-0.424761\pi$
$631$	1.86510e12	0.468348	0.234174	+	0.972195i	$0.424761\pi$
$632$	3.17524e11	0.0791679
$633$	4.66049e12	1.15376
$634$	−5.65271e12	−1.38949
$635$	−1.33061e11	−0.0324764
$636$	−3.99994e12	−0.969385
$637$	−9.01426e11	−0.216921
$638$	−1.72882e13	−4.13101
$639$	−2.05062e12	−0.486554
$640$	−1.28083e11	−0.0301774
$641$	4.47273e12	1.04643	0.523216	−	0.852200i	$-0.324732\pi$
$641$	4.47273e12	1.04643	0.523216	+	0.852200i	$0.324732\pi$
$642$	9.56730e12	2.22270
$643$	6.50740e12	1.50127	0.750634	−	0.660718i	$-0.229748\pi$
$643$	6.50740e12	1.50127	0.750634	+	0.660718i	$0.229748\pi$
$644$	−8.24238e11	−0.188828
$645$	6.88803e11	0.156703
$646$	0	0
$647$	4.43814e12	0.995708	0.497854	−	0.867261i	$-0.334121\pi$
$647$	4.43814e12	0.995708	0.497854	+	0.867261i	$0.334121\pi$
$648$	8.52901e11	0.190025
$649$	−7.11977e12	−1.57531
$650$	1.51547e12	0.332995
$651$	−1.57643e12	−0.344002
$652$	−2.10639e12	−0.456484
$653$	−4.32967e12	−0.931848	−0.465924	−	0.884825i	$-0.654278\pi$
$653$	−4.32967e12	−0.931848	−0.465924	+	0.884825i	$0.654278\pi$
$654$	−1.61990e13	−3.46248
$655$	−2.05881e11	−0.0437050
$656$	8.23902e11	0.173703
$657$	7.42944e12	1.55565
$658$	−1.58693e12	−0.330021
$659$	4.54367e12	0.938475	0.469238	−	0.883072i	$-0.344529\pi$
$659$	4.54367e12	0.938475	0.469238	+	0.883072i	$0.344529\pi$
$660$	−1.03610e12	−0.212546
$661$	6.91408e12	1.40873	0.704365	−	0.709838i	$-0.251232\pi$
$661$	6.91408e12	1.40873	0.704365	+	0.709838i	$0.251232\pi$
$662$	7.79915e12	1.57829
$663$	0	0
$664$	1.67860e12	0.335113
$665$	8.66814e10	0.0171881
$666$	1.36305e13	2.68458
$667$	−6.11548e12	−1.19637
$668$	−8.71292e12	−1.69305
$669$	−4.75615e12	−0.917990
$670$	−3.02350e11	−0.0579660
$671$	−2.27057e12	−0.432398
$672$	2.51348e12	0.475459
$673$	−5.42906e12	−1.02013	−0.510066	−	0.860135i	$-0.670379\pi$
$673$	−5.42906e12	−1.02013	−0.510066	+	0.860135i	$0.670379\pi$
$674$	−3.42296e12	−0.638898
$675$	−2.12886e11	−0.0394711
$676$	−5.83280e12	−1.07428
$677$	−4.96708e12	−0.908766	−0.454383	−	0.890806i	$-0.650140\pi$
$677$	−4.96708e12	−0.908766	−0.454383	+	0.890806i	$0.650140\pi$
$678$	−1.98149e13	−3.60128
$679$	1.18051e12	0.213135
$680$	0	0
$681$	2.87132e12	0.511587
$682$	1.44884e13	2.56444
$683$	−5.99267e12	−1.05372	−0.526862	−	0.849951i	$-0.676632\pi$
$683$	−5.99267e12	−1.05372	−0.526862	+	0.849951i	$0.676632\pi$
$684$	−6.33177e12	−1.10605
$685$	1.55376e11	0.0269635
$686$	3.83721e12	0.661541
$687$	−1.11035e13	−1.90175
$688$	7.04772e12	1.19923
$689$	−8.14451e11	−0.137682
$690$	−6.89725e11	−0.115839
$691$	−1.36510e12	−0.227778	−0.113889	−	0.993493i	$-0.536331\pi$
$691$	−1.36510e12	−0.227778	−0.113889	+	0.993493i	$0.536331\pi$
$692$	1.33453e13	2.21233
$693$	2.45658e12	0.404605
$694$	1.59867e12	0.261602
$695$	−5.28964e11	−0.0859992
$696$	−2.88369e12	−0.465807
$697$	0	0
$698$	−1.05079e13	−1.67559
$699$	−9.54179e12	−1.51176
$700$	−1.66628e12	−0.262305
$701$	−6.05370e12	−0.946869	−0.473435	−	0.880829i	$-0.656986\pi$
$701$	−6.05370e12	−0.946869	−0.473435	+	0.880829i	$0.656986\pi$
$702$	−8.56075e10	−0.0133044
$703$	1.09872e13	1.69663
$704$	−1.37513e13	−2.10993
$705$	−7.05644e11	−0.107581
$706$	5.25896e12	0.796671
$707$	−4.55345e11	−0.0685415
$708$	−1.00553e13	−1.50399
$709$	4.47272e12	0.664758	0.332379	−	0.943146i	$-0.392149\pi$
$709$	4.47272e12	0.664758	0.332379	+	0.943146i	$0.392149\pi$
$710$	−3.64385e11	−0.0538143
$711$	−2.83443e12	−0.415961
$712$	4.64303e11	0.0677083
$713$	5.12510e12	0.742676
$714$	0	0
$715$	−2.10966e11	−0.0301880
$716$	−5.97772e12	−0.850016
$717$	1.63150e12	0.230543
$718$	2.22538e12	0.312496
$719$	1.23980e13	1.73010	0.865050	−	0.501686i	$-0.167287\pi$
$719$	1.23980e13	1.73010	0.865050	+	0.501686i	$0.167287\pi$
$720$	4.89252e11	0.0678479
$721$	−9.82652e11	−0.135423
$722$	1.06117e12	0.145334
$723$	2.61619e12	0.356080
$724$	−1.14825e13	−1.55315
$725$	−1.23630e13	−1.66190
$726$	−2.89712e13	−3.87036
$727$	−6.14698e12	−0.816125	−0.408063	−	0.912954i	$-0.633795\pi$
$727$	−6.14698e12	−0.816125	−0.408063	+	0.912954i	$0.633795\pi$
$728$	−7.91375e10	−0.0104422
$729$	−8.04481e12	−1.05497
$730$	1.32017e12	0.172059
$731$	0	0
$732$	−3.20674e12	−0.412823
$733$	−5.25486e12	−0.672347	−0.336173	−	0.941800i	$-0.609133\pi$
$733$	−5.25486e12	−0.672347	−0.336173	+	0.941800i	$0.609133\pi$
$734$	2.97128e12	0.377843
$735$	8.29378e11	0.104824
$736$	−8.17148e12	−1.02648
$737$	−6.90701e12	−0.862355
$738$	2.47815e12	0.307520
$739$	−1.24520e12	−0.153581	−0.0767907	−	0.997047i	$-0.524467\pi$
$739$	−1.24520e12	−0.153581	−0.0767907	+	0.997047i	$0.524467\pi$
$740$	1.28704e12	0.157779
$741$	−2.54352e12	−0.309923
$742$	1.68523e12	0.204100
$743$	−8.09895e12	−0.974943	−0.487471	−	0.873139i	$-0.662081\pi$
$743$	−8.09895e12	−0.974943	−0.487471	+	0.873139i	$0.662081\pi$
$744$	2.41668e12	0.289162
$745$	−4.06348e10	−0.00483275
$746$	1.37426e13	1.62459
$747$	−1.49843e13	−1.76074
$748$	0	0
$749$	−2.14191e12	−0.248675
$750$	−2.79719e12	−0.322810
$751$	1.09947e13	1.26125	0.630627	−	0.776086i	$-0.282798\pi$
$751$	1.09947e13	1.26125	0.630627	+	0.776086i	$0.282798\pi$
$752$	−7.22004e12	−0.823302
$753$	8.09615e11	0.0917700
$754$	−4.97154e12	−0.560170
$755$	1.33052e12	0.149025
$756$	9.41263e10	0.0104800
$757$	−9.44013e12	−1.04483	−0.522416	−	0.852691i	$-0.674969\pi$
$757$	−9.44013e12	−1.04483	−0.522416	+	0.852691i	$0.674969\pi$
$758$	7.23199e12	0.795694
$759$	−1.57563e13	−1.72333
$760$	−1.32883e11	−0.0144480
$761$	1.19815e13	1.29504	0.647518	−	0.762050i	$-0.275807\pi$
$761$	1.19815e13	1.29504	0.647518	+	0.762050i	$0.275807\pi$
$762$	−8.07893e12	−0.868073
$763$	3.62659e12	0.387380
$764$	6.01251e12	0.638463
$765$	0	0
$766$	2.54094e13	2.66664
$767$	−2.04742e12	−0.213613
$768$	9.35064e12	0.969876
$769$	−1.26588e13	−1.30535	−0.652673	−	0.757640i	$-0.726352\pi$
$769$	−1.26588e13	−1.30535	−0.652673	+	0.757640i	$0.726352\pi$
$770$	4.36522e11	0.0447505
$771$	−2.06321e13	−2.10280
$772$	1.02751e13	1.04114
$773$	−1.64501e12	−0.165715	−0.0828574	−	0.996561i	$-0.526405\pi$
$773$	−1.64501e12	−0.165715	−0.0828574	+	0.996561i	$0.526405\pi$
$774$	2.11983e13	2.12308
$775$	1.03609e13	1.03167
$776$	−1.80973e12	−0.179157
$777$	−6.02033e12	−0.592551
$778$	1.16795e13	1.14292
$779$	1.99757e12	0.194350
$780$	−2.97948e11	−0.0288214
$781$	−8.32415e12	−0.800590
$782$	0	0
$783$	6.98375e11	0.0663989
$784$	8.48606e12	0.802203
$785$	−7.90599e11	−0.0743093
$786$	−1.25003e13	−1.16821
$787$	2.05349e12	0.190812	0.0954060	−	0.995438i	$-0.469585\pi$
$787$	2.05349e12	0.190812	0.0954060	+	0.995438i	$0.469585\pi$
$788$	8.17040e12	0.754875
$789$	8.00612e12	0.735488
$790$	−5.03664e11	−0.0460065
$791$	4.43611e12	0.402910
$792$	−3.76595e12	−0.340104
$793$	−6.52944e11	−0.0586336
$794$	−9.94971e12	−0.888420
$795$	7.49355e11	0.0665328
$796$	−5.52260e11	−0.0487567
$797$	3.95127e12	0.346876	0.173438	−	0.984845i	$-0.444512\pi$
$797$	3.95127e12	0.346876	0.173438	+	0.984845i	$0.444512\pi$
$798$	5.26296e12	0.459428
$799$	0	0
$800$	−1.65195e13	−1.42591
$801$	−4.14469e12	−0.355750
$802$	9.74669e12	0.831902
$803$	3.01586e13	2.55971
$804$	−9.75482e12	−0.823317
$805$	1.54414e11	0.0129600
$806$	4.16641e12	0.347740
$807$	2.73764e13	2.27219
$808$	6.98047e11	0.0576147
$809$	−5.18664e11	−0.0425714	−0.0212857	−	0.999773i	$-0.506776\pi$
$809$	−5.18664e11	−0.0425714	−0.0212857	+	0.999773i	$0.506776\pi$
$810$	−1.35289e12	−0.110429
$811$	2.06846e13	1.67901	0.839506	−	0.543350i	$-0.182844\pi$
$811$	2.06846e13	1.67901	0.839506	+	0.543350i	$0.182844\pi$
$812$	5.46626e12	0.441253
$813$	−8.56548e12	−0.687613
$814$	5.53307e13	4.41729
$815$	3.94615e11	0.0313303
$816$	0	0
$817$	1.70874e13	1.34176
$818$	−1.79901e13	−1.40489
$819$	7.06435e11	0.0548649
$820$	2.33996e11	0.0180736
$821$	−1.09345e13	−0.839952	−0.419976	−	0.907535i	$-0.637962\pi$
$821$	−1.09345e13	−0.839952	−0.419976	+	0.907535i	$0.637962\pi$
$822$	9.43384e12	0.720718
$823$	2.58366e13	1.96307	0.981537	−	0.191270i	$-0.0612606\pi$
$823$	2.58366e13	1.96307	0.981537	+	0.191270i	$0.0612606\pi$
$824$	1.50641e12	0.113834
$825$	−3.18530e13	−2.39391
$826$	4.23644e12	0.316659
$827$	−1.70530e13	−1.26773	−0.633866	−	0.773443i	$-0.718533\pi$
$827$	−1.70530e13	−1.26773	−0.633866	+	0.773443i	$0.718533\pi$
$828$	−1.12794e13	−0.833969
$829$	−2.05890e13	−1.51405	−0.757023	−	0.653388i	$-0.773347\pi$
$829$	−2.05890e13	−1.51405	−0.757023	+	0.653388i	$0.773347\pi$
$830$	−2.66264e12	−0.194743
$831$	7.17960e12	0.522271
$832$	−3.95444e12	−0.286108
$833$	0	0
$834$	−3.21167e13	−2.29870
$835$	1.63229e12	0.116201
$836$	−2.57028e13	−1.81992
$837$	−5.85276e11	−0.0412188
$838$	−2.59047e13	−1.81460
$839$	−1.36702e13	−0.952459	−0.476230	−	0.879321i	$-0.657997\pi$
$839$	−1.36702e13	−0.952459	−0.476230	+	0.879321i	$0.657997\pi$
$840$	7.28123e10	0.00504601
$841$	2.60500e13	1.79567
$842$	2.75882e13	1.89156
$843$	1.36232e13	0.929084
$844$	1.35431e13	0.918705
$845$	1.09273e12	0.0737321
$846$	−2.17166e13	−1.45755
$847$	6.48601e12	0.433014
$848$	7.66728e12	0.509167
$849$	−1.17468e13	−0.775952
$850$	0	0
$851$	1.95725e13	1.27927
$852$	−1.17563e13	−0.764347
$853$	−1.37513e13	−0.889348	−0.444674	−	0.895692i	$-0.646680\pi$
$853$	−1.37513e13	−0.889348	−0.444674	+	0.895692i	$0.646680\pi$
$854$	1.35105e12	0.0869181
$855$	1.18620e12	0.0759123
$856$	3.28356e12	0.209032
$857$	1.76873e13	1.12008	0.560038	−	0.828467i	$-0.310787\pi$
$857$	1.76873e13	1.12008	0.560038	+	0.828467i	$0.310787\pi$
$858$	−1.28090e13	−0.806906
$859$	−1.77011e13	−1.10925	−0.554627	−	0.832099i	$-0.687139\pi$
$859$	−1.77011e13	−1.10925	−0.554627	+	0.832099i	$0.687139\pi$
$860$	2.00162e12	0.124778
$861$	−1.09455e12	−0.0678770
$862$	1.72353e13	1.06325
$863$	−1.00533e12	−0.0616965	−0.0308483	−	0.999524i	$-0.509821\pi$
$863$	−1.00533e12	−0.0616965	−0.0308483	+	0.999524i	$0.509821\pi$
$864$	9.33167e11	0.0569701
$865$	−2.50013e12	−0.151841
$866$	3.62161e13	2.18812
$867$	0	0
$868$	−4.58101e12	−0.273919
$869$	−1.15059e13	−0.684435
$870$	4.57418e12	0.270693
$871$	−1.98624e12	−0.116936
$872$	−5.55958e12	−0.325625
$873$	1.61548e13	0.941323
$874$	−1.71103e13	−0.991870
$875$	6.26229e11	0.0361158
$876$	4.25932e13	2.44383
$877$	−1.95904e13	−1.11827	−0.559134	−	0.829077i	$-0.688866\pi$
$877$	−1.95904e13	−1.11827	−0.559134	+	0.829077i	$0.688866\pi$
$878$	1.91172e13	1.08568
$879$	1.84686e13	1.04348
$880$	1.98604e12	0.111639
$881$	−1.82837e13	−1.02252	−0.511260	−	0.859426i	$-0.670821\pi$
$881$	−1.82837e13	−1.02252	−0.511260	+	0.859426i	$0.670821\pi$
$882$	2.55246e13	1.42020
$883$	−2.47667e13	−1.37102	−0.685512	−	0.728061i	$-0.740422\pi$
$883$	−2.47667e13	−1.37102	−0.685512	+	0.728061i	$0.740422\pi$
$884$	0	0
$885$	1.88378e12	0.103225
$886$	4.24598e13	2.31487
$887$	1.60579e13	0.871030	0.435515	−	0.900181i	$-0.356566\pi$
$887$	1.60579e13	0.871030	0.435515	+	0.900181i	$0.356566\pi$
$888$	9.22920e12	0.498088
$889$	1.80869e12	0.0971196
$890$	−7.36490e11	−0.0393470
$891$	−3.09060e13	−1.64283
$892$	−1.38210e13	−0.730969
$893$	−1.75052e13	−0.921159
$894$	−2.46719e12	−0.129176
$895$	1.11988e12	0.0583400
$896$	1.74103e12	0.0902446
$897$	−4.53103e12	−0.233685
$898$	2.76664e13	1.41974
$899$	−3.39891e13	−1.73548
$900$	−2.28024e13	−1.15848
$901$	0	0
$902$	1.00596e13	0.506003
$903$	−9.36290e12	−0.468614
$904$	−6.80058e12	−0.338679
$905$	2.15115e12	0.106599
$906$	8.07838e13	3.98334
$907$	−1.25253e13	−0.614547	−0.307273	−	0.951621i	$-0.599417\pi$
$907$	−1.25253e13	−0.614547	−0.307273	+	0.951621i	$0.599417\pi$
$908$	8.34387e12	0.407363
$909$	−6.23124e12	−0.302717
$910$	1.25530e11	0.00606822
$911$	1.02944e13	0.495185	0.247593	−	0.968864i	$-0.420361\pi$
$911$	1.02944e13	0.495185	0.247593	+	0.968864i	$0.420361\pi$
$912$	2.39448e13	1.14613
$913$	−6.08264e13	−2.89717
$914$	−3.51547e13	−1.66619
$915$	6.00757e11	0.0283337
$916$	−3.22660e13	−1.51431
$917$	2.79855e12	0.130698
$918$	0	0
$919$	−7.39445e12	−0.341968	−0.170984	−	0.985274i	$-0.554695\pi$
$919$	−7.39445e12	−0.341968	−0.170984	+	0.985274i	$0.554695\pi$
$920$	−2.36718e11	−0.0108940
$921$	−4.63335e13	−2.12191
$922$	−9.67033e11	−0.0440709
$923$	−2.39376e12	−0.108561
$924$	1.40836e13	0.635611
$925$	3.95678e13	1.77707
$926$	−2.94815e13	−1.31765
$927$	−1.34472e13	−0.598101
$928$	5.41924e13	2.39868
$929$	−9.16655e12	−0.403771	−0.201886	−	0.979409i	$-0.564707\pi$
$929$	−9.16655e12	−0.403771	−0.201886	+	0.979409i	$0.564707\pi$
$930$	−3.83341e12	−0.168040
$931$	2.05747e13	0.897552
$932$	−2.77278e13	−1.20377
$933$	−6.36178e13	−2.74860
$934$	−3.86077e13	−1.66002
$935$	0	0
$936$	−1.08297e12	−0.0461184
$937$	−4.03344e13	−1.70941	−0.854706	−	0.519112i	$-0.826263\pi$
$937$	−4.03344e13	−1.70941	−0.854706	+	0.519112i	$0.826263\pi$
$938$	4.10985e12	0.173346
$939$	3.36069e13	1.41069
$940$	−2.05055e12	−0.0856635
$941$	−1.80297e13	−0.749609	−0.374804	−	0.927104i	$-0.622290\pi$
$941$	−1.80297e13	−0.749609	−0.374804	+	0.927104i	$0.622290\pi$
$942$	−4.80021e13	−1.98624
$943$	3.55847e12	0.146541
$944$	1.92745e13	0.789967
$945$	−1.76338e10	−0.000719287 0
$946$	8.60510e13	3.49338
$947$	3.85278e13	1.55668	0.778339	−	0.627844i	$-0.216062\pi$
$947$	3.85278e13	1.55668	0.778339	+	0.627844i	$0.216062\pi$
$948$	−1.62499e13	−0.653450
$949$	8.67266e12	0.347100
$950$	−3.45901e13	−1.37783
$951$	3.41665e13	1.35453
$952$	0	0
$953$	−4.24042e13	−1.66530	−0.832648	−	0.553803i	$-0.813176\pi$
$953$	−4.24042e13	−1.66530	−0.832648	+	0.553803i	$0.813176\pi$
$954$	2.30618e13	0.901417
$955$	−1.12639e12	−0.0438203
$956$	4.74104e12	0.183575
$957$	1.04494e14	4.02707
$958$	5.12183e13	1.96463
$959$	−2.11203e12	−0.0806336
$960$	3.63838e12	0.138257
$961$	2.04505e12	0.0773477
$962$	1.59113e13	0.598989
$963$	−2.93112e13	−1.09829
$964$	7.60249e12	0.283536
$965$	−1.92495e12	−0.0714573
$966$	9.37543e12	0.346413
$967$	−3.95530e12	−0.145466	−0.0727328	−	0.997351i	$-0.523172\pi$
$967$	−3.95530e12	−0.145466	−0.0727328	+	0.997351i	$0.523172\pi$
$968$	−9.94309e12	−0.363984
$969$	0	0
$970$	2.87063e12	0.104113
$971$	2.88879e13	1.04287	0.521434	−	0.853292i	$-0.325397\pi$
$971$	2.88879e13	1.04287	0.521434	+	0.853292i	$0.325397\pi$
$972$	−4.49020e13	−1.61349
$973$	7.19021e12	0.257178
$974$	1.79702e13	0.639792
$975$	−9.15992e12	−0.324617
$976$	6.14685e12	0.216834
$977$	6.86810e12	0.241163	0.120582	−	0.992703i	$-0.461524\pi$
$977$	6.86810e12	0.241163	0.120582	+	0.992703i	$0.461524\pi$
$978$	2.39595e13	0.837439
$979$	−1.68247e13	−0.585362
$980$	2.41012e12	0.0834682
$981$	4.96286e13	1.71089
$982$	−6.52631e13	−2.23958
$983$	2.43295e13	0.831079	0.415539	−	0.909575i	$-0.363593\pi$
$983$	2.43295e13	0.831079	0.415539	+	0.909575i	$0.363593\pi$
$984$	1.67796e12	0.0570562
$985$	−1.53066e12	−0.0518101
$986$	0	0
$987$	9.59182e12	0.321717
$988$	−7.39131e12	−0.246783
$989$	3.04394e13	1.01170
$990$	5.97365e12	0.197643
$991$	−2.94849e13	−0.971109	−0.485554	−	0.874206i	$-0.661382\pi$
$991$	−2.94849e13	−0.971109	−0.485554	+	0.874206i	$0.661382\pi$
$992$	−4.54161e13	−1.48904
$993$	−4.71401e13	−1.53858
$994$	4.95308e12	0.160930
$995$	1.03461e11	0.00334637
$996$	−8.59056e13	−2.76602
$997$	3.59823e13	1.15335	0.576674	−	0.816974i	$-0.304350\pi$
$997$	3.59823e13	1.15335	0.576674	+	0.816974i	$0.304350\pi$
$998$	2.51010e13	0.800946
$999$	−2.23514e12	−0.0710003

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.g.1.6	✓	36
17.16	even	2		289.10.a.h.1.6	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.6	✓	36	1.1	even	1	trivial
289.10.a.h.1.6	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)

\(f(q)\)	\(=\)	\(q-33.0540 q^{2} +199.787 q^{3} +580.568 q^{4} -108.765 q^{5} -6603.77 q^{6} +1478.44 q^{7} -2266.45 q^{8} +20231.9 q^{9} +O(q^{10})\)	\(q-33.0540 q^{2} +199.787 q^{3} +580.568 q^{4} -108.765 q^{5} -6603.77 q^{6} +1478.44 q^{7} -2266.45 q^{8} +20231.9 q^{9} +3595.11 q^{10} +82128.1 q^{11} +115990. q^{12} +23617.4 q^{13} -48868.3 q^{14} -21729.8 q^{15} -222336. q^{16} -668745. q^{18} -539058. q^{19} -63145.3 q^{20} +295373. q^{21} -2.71466e6 q^{22} -960277. q^{23} -452808. q^{24} -1.94130e6 q^{25} -780651. q^{26} +109662. q^{27} +858334. q^{28} +6.36845e6 q^{29} +718256. q^{30} -5.33710e6 q^{31} +8.50951e6 q^{32} +1.64081e7 q^{33} -160802. q^{35} +1.17460e7 q^{36} -2.03822e7 q^{37} +1.78180e7 q^{38} +4.71846e6 q^{39} +246510. q^{40} -3.70567e6 q^{41} -9.76326e6 q^{42} -3.16986e7 q^{43} +4.76809e7 q^{44} -2.20051e6 q^{45} +3.17410e7 q^{46} +3.24736e7 q^{47} -4.44198e7 q^{48} -3.81678e7 q^{49} +6.41676e7 q^{50} +1.37115e7 q^{52} -3.44852e7 q^{53} -3.62476e6 q^{54} -8.93263e6 q^{55} -3.35081e6 q^{56} -1.07697e8 q^{57} -2.10503e8 q^{58} -8.66911e7 q^{59} -1.26156e7 q^{60} -2.76467e7 q^{61} +1.76413e8 q^{62} +2.99116e7 q^{63} -1.67438e8 q^{64} -2.56874e6 q^{65} -5.42355e8 q^{66} -8.41005e7 q^{67} -1.91851e8 q^{69} +5.31514e6 q^{70} -1.01356e8 q^{71} -4.58546e7 q^{72} +3.67214e8 q^{73} +6.73712e8 q^{74} -3.87846e8 q^{75} -3.12960e8 q^{76} +1.21421e8 q^{77} -1.55964e8 q^{78} -1.40097e8 q^{79} +2.41822e7 q^{80} -3.76315e8 q^{81} +1.22487e8 q^{82} -7.40629e8 q^{83} +1.71484e8 q^{84} +1.04777e9 q^{86} +1.27233e9 q^{87} -1.86139e8 q^{88} -2.04859e8 q^{89} +7.27358e7 q^{90} +3.49169e7 q^{91} -5.57506e8 q^{92} -1.06628e9 q^{93} -1.07338e9 q^{94} +5.86304e7 q^{95} +1.70009e9 q^{96} +7.98484e8 q^{97} +1.26160e9 q^{98} +1.66161e9 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 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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