LMFDB - Embedded newform 289.10.a.h.1.28

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			1.28
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)

$f(q)$	$=$	$q+28.5023 q^{2} -173.222 q^{3} +300.380 q^{4} +1462.89 q^{5} -4937.21 q^{6} -2705.62 q^{7} -6031.66 q^{8} +10322.7 q^{9} +O(q^{10})$	\(q+28.5023 q^{2} -173.222 q^{3} +300.380 q^{4} +1462.89 q^{5} -4937.21 q^{6} -2705.62 q^{7} -6031.66 q^{8} +10322.7 q^{9} +41695.6 q^{10} -45163.0 q^{11} -52032.2 q^{12} -57896.3 q^{13} -77116.3 q^{14} -253403. q^{15} -325710. q^{16} +294221. q^{18} +323804. q^{19} +439421. q^{20} +468671. q^{21} -1.28725e6 q^{22} -2.17545e6 q^{23} +1.04481e6 q^{24} +186908. q^{25} -1.65018e6 q^{26} +1.62140e6 q^{27} -812712. q^{28} +2.98380e6 q^{29} -7.22257e6 q^{30} +9.05752e6 q^{31} -6.19528e6 q^{32} +7.82320e6 q^{33} -3.95801e6 q^{35} +3.10073e6 q^{36} +1.28689e7 q^{37} +9.22914e6 q^{38} +1.00289e7 q^{39} -8.82363e6 q^{40} -2.91740e7 q^{41} +1.33582e7 q^{42} -2.54101e7 q^{43} -1.35660e7 q^{44} +1.51009e7 q^{45} -6.20053e7 q^{46} -2.66571e7 q^{47} +5.64201e7 q^{48} -3.30332e7 q^{49} +5.32729e6 q^{50} -1.73909e7 q^{52} -1.32615e7 q^{53} +4.62137e7 q^{54} -6.60682e7 q^{55} +1.63194e7 q^{56} -5.60898e7 q^{57} +8.50452e7 q^{58} +5.04039e7 q^{59} -7.61172e7 q^{60} +1.10036e8 q^{61} +2.58160e8 q^{62} -2.79293e7 q^{63} -9.81574e6 q^{64} -8.46956e7 q^{65} +2.22979e8 q^{66} -1.13093e8 q^{67} +3.76835e8 q^{69} -1.12812e8 q^{70} +3.38574e8 q^{71} -6.22631e7 q^{72} -2.36539e8 q^{73} +3.66794e8 q^{74} -3.23764e7 q^{75} +9.72640e7 q^{76} +1.22194e8 q^{77} +2.85846e8 q^{78} +5.61145e8 q^{79} -4.76477e8 q^{80} -4.84044e8 q^{81} -8.31527e8 q^{82} +2.95912e8 q^{83} +1.40779e8 q^{84} -7.24245e8 q^{86} -5.16859e8 q^{87} +2.72408e8 q^{88} -1.78872e8 q^{89} +4.30411e8 q^{90} +1.56645e8 q^{91} -6.53461e8 q^{92} -1.56896e9 q^{93} -7.59787e8 q^{94} +4.73687e8 q^{95} +1.07316e9 q^{96} +9.76224e7 q^{97} -9.41522e8 q^{98} -4.66204e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	28.5023	1.25963	0.629817	−	0.776743i	$-0.283130\pi$
$2$	28.5023	1.25963	0.629817	+	0.776743i	$0.283130\pi$
$3$	−173.222	−1.23469	−0.617343	−	0.786694i	$-0.711791\pi$
$3$	−173.222	−1.23469	−0.617343	+	0.786694i	$0.711791\pi$
$4$	300.380	0.586679
$5$	1462.89	1.04676	0.523378	−	0.852101i	$-0.324672\pi$
$5$	1462.89	1.04676	0.523378	+	0.852101i	$0.324672\pi$
$6$	−4937.21	−1.55525
$7$	−2705.62	−0.425917	−0.212959	−	0.977061i	$-0.568310\pi$
$7$	−2705.62	−0.425917	−0.212959	+	0.977061i	$0.568310\pi$
$8$	−6031.66	−0.520633
$9$	10322.7	0.524448
$10$	41695.6	1.31853
$11$	−45163.0	−0.930069	−0.465035	−	0.885292i	$-0.653958\pi$
$11$	−45163.0	−0.930069	−0.465035	+	0.885292i	$0.653958\pi$
$12$	−52032.2	−0.724364
$13$	−57896.3	−0.562219	−0.281110	−	0.959676i	$-0.590702\pi$
$13$	−57896.3	−0.562219	−0.281110	+	0.959676i	$0.590702\pi$
$14$	−77116.3	−0.536500
$15$	−253403.	−1.29241
$16$	−325710.	−1.24249
$17$	0	0
$17$	0	0
$18$	294221.	0.660613
$19$	323804.	0.570021	0.285010	−	0.958524i	$-0.408003\pi$
$19$	323804.	0.570021	0.285010	+	0.958524i	$0.408003\pi$
$20$	439421.	0.614109
$21$	468671.	0.525874
$22$	−1.28725e6	−1.17155
$23$	−2.17545e6	−1.62097	−0.810483	−	0.585763i	$-0.800795\pi$
$23$	−2.17545e6	−1.62097	−0.810483	+	0.585763i	$0.800795\pi$
$24$	1.04481e6	0.642819
$25$	186908.	0.0956967
$26$	−1.65018e6	−0.708190
$27$	1.62140e6	0.587157
$28$	−812712.	−0.249877
$29$	2.98380e6	0.783392	0.391696	−	0.920095i	$-0.371888\pi$
$29$	2.98380e6	0.783392	0.391696	+	0.920095i	$0.371888\pi$
$30$	−7.22257e6	−1.62797
$31$	9.05752e6	1.76150	0.880748	−	0.473584i	$-0.157040\pi$
$31$	9.05752e6	1.76150	0.880748	+	0.473584i	$0.157040\pi$
$32$	−6.19528e6	−1.04445
$33$	7.82320e6	1.14834
$34$	0	0
$35$	−3.95801e6	−0.445831
$36$	3.10073e6	0.307683
$37$	1.28689e7	1.12885	0.564423	−	0.825486i	$-0.309099\pi$
$37$	1.28689e7	1.12885	0.564423	+	0.825486i	$0.309099\pi$
$38$	9.22914e6	0.718018
$39$	1.00289e7	0.694164
$40$	−8.82363e6	−0.544976
$41$	−2.91740e7	−1.61239	−0.806194	−	0.591652i	$-0.798476\pi$
$41$	−2.91740e7	−1.61239	−0.806194	+	0.591652i	$0.798476\pi$
$42$	1.33582e7	0.662409
$43$	−2.54101e7	−1.13344	−0.566719	−	0.823911i	$-0.691788\pi$
$43$	−2.54101e7	−1.13344	−0.566719	+	0.823911i	$0.691788\pi$
$44$	−1.35660e7	−0.545652
$45$	1.51009e7	0.548969
$46$	−6.20053e7	−2.04182
$47$	−2.66571e7	−0.796842	−0.398421	−	0.917203i	$-0.630442\pi$
$47$	−2.66571e7	−0.796842	−0.398421	+	0.917203i	$0.630442\pi$
$48$	5.64201e7	1.53408
$49$	−3.30332e7	−0.818594
$50$	5.32729e6	0.120543
$51$	0	0
$52$	−1.73909e7	−0.329842
$53$	−1.32615e7	−0.230861	−0.115430	−	0.993316i	$-0.536825\pi$
$53$	−1.32615e7	−0.230861	−0.115430	+	0.993316i	$0.536825\pi$
$54$	4.62137e7	0.739603
$55$	−6.60682e7	−0.973555
$56$	1.63194e7	0.221747
$57$	−5.60898e7	−0.703796
$58$	8.50452e7	0.986788
$59$	5.04039e7	0.541539	0.270770	−	0.962644i	$-0.412722\pi$
$59$	5.04039e7	0.541539	0.270770	+	0.962644i	$0.412722\pi$
$60$	−7.61172e7	−0.758232
$61$	1.10036e8	1.01754	0.508768	−	0.860904i	$-0.330101\pi$
$61$	1.10036e8	1.01754	0.508768	+	0.860904i	$0.330101\pi$
$62$	2.58160e8	2.21884
$63$	−2.79293e7	−0.223372
$64$	−9.81574e6	−0.0731330
$65$	−8.46956e7	−0.588506
$66$	2.22979e8	1.44649
$67$	−1.13093e8	−0.685646	−0.342823	−	0.939400i	$-0.611383\pi$
$67$	−1.13093e8	−0.685646	−0.342823	+	0.939400i	$0.611383\pi$
$68$	0	0
$69$	3.76835e8	2.00138
$70$	−1.12812e8	−0.561584
$71$	3.38574e8	1.58121	0.790607	−	0.612324i	$-0.209765\pi$
$71$	3.38574e8	1.58121	0.790607	+	0.612324i	$0.209765\pi$
$72$	−6.22631e7	−0.273045
$73$	−2.36539e8	−0.974877	−0.487438	−	0.873157i	$-0.662069\pi$
$73$	−2.36539e8	−0.974877	−0.487438	+	0.873157i	$0.662069\pi$
$74$	3.66794e8	1.42193
$75$	−3.23764e7	−0.118155
$76$	9.72640e7	0.334419
$77$	1.22194e8	0.396133
$78$	2.85846e8	0.874393
$79$	5.61145e8	1.62089	0.810444	−	0.585816i	$-0.199226\pi$
$79$	5.61145e8	1.62089	0.810444	+	0.585816i	$0.199226\pi$
$80$	−4.76477e8	−1.30058
$81$	−4.84044e8	−1.24940
$82$	−8.31527e8	−2.03102
$83$	2.95912e8	0.684403	0.342201	−	0.939627i	$-0.388827\pi$
$83$	2.95912e8	0.684403	0.342201	+	0.939627i	$0.388827\pi$
$84$	1.40779e8	0.308519
$85$	0	0
$86$	−7.24245e8	−1.42772
$87$	−5.16859e8	−0.967243
$88$	2.72408e8	0.484225
$89$	−1.78872e8	−0.302195	−0.151098	−	0.988519i	$-0.548281\pi$
$89$	−1.78872e8	−0.302195	−0.151098	+	0.988519i	$0.548281\pi$
$90$	4.30411e8	0.691500
$91$	1.56645e8	0.239459
$92$	−6.53461e8	−0.950986
$93$	−1.56896e9	−2.17489
$94$	−7.59787e8	−1.00373
$95$	4.73687e8	0.596672
$96$	1.07316e9	1.28956
$97$	9.76224e7	0.111964	0.0559818	−	0.998432i	$-0.482171\pi$
$97$	9.76224e7	0.111964	0.0559818	+	0.998432i	$0.482171\pi$
$98$	−9.41522e8	−1.03113
$99$	−4.66204e8	−0.487773
$100$	5.61433e7	0.0561433
$101$	7.74498e8	0.740583	0.370292	−	0.928916i	$-0.379258\pi$
$101$	7.74498e8	0.740583	0.370292	+	0.928916i	$0.379258\pi$
$102$	0	0
$103$	1.22734e9	1.07448	0.537240	−	0.843429i	$-0.319467\pi$
$103$	1.22734e9	1.07448	0.537240	+	0.843429i	$0.319467\pi$
$104$	3.49211e8	0.292710
$105$	6.85612e8	0.550461
$106$	−3.77982e8	−0.290800
$107$	2.30141e9	1.69733	0.848665	−	0.528930i	$-0.177407\pi$
$107$	2.30141e9	1.69733	0.848665	+	0.528930i	$0.177407\pi$
$108$	4.87037e8	0.344473
$109$	2.60083e9	1.76479	0.882393	−	0.470513i	$-0.155931\pi$
$109$	2.60083e9	1.76479	0.882393	+	0.470513i	$0.155931\pi$
$110$	−1.88309e9	−1.22632
$111$	−2.22918e9	−1.39377
$112$	8.81248e8	0.529197
$113$	−1.75376e9	−1.01185	−0.505925	−	0.862577i	$-0.668849\pi$
$113$	−1.75376e9	−1.01185	−0.505925	+	0.862577i	$0.668849\pi$
$114$	−1.59869e9	−0.886526
$115$	−3.18243e9	−1.69675
$116$	8.96274e8	0.459600
$117$	−5.97647e8	−0.294855
$118$	1.43662e9	0.682141
$119$	0	0
$120$	1.52844e9	0.672874
$121$	−3.18255e8	−0.134971
$122$	3.13627e9	1.28172
$123$	5.05357e9	1.99079
$124$	2.72070e9	1.03343
$125$	−2.58377e9	−0.946584
$126$	−7.96049e8	−0.281367
$127$	−1.62086e9	−0.552877	−0.276438	−	0.961032i	$-0.589154\pi$
$127$	−1.62086e9	−0.552877	−0.276438	+	0.961032i	$0.589154\pi$
$128$	2.89221e9	0.952325
$129$	4.40158e9	1.39944
$130$	−2.41402e9	−0.741302
$131$	−1.04453e9	−0.309884	−0.154942	−	0.987924i	$-0.549519\pi$
$131$	−1.04453e9	−0.309884	−0.154942	+	0.987924i	$0.549519\pi$
$132$	2.34993e9	0.673709
$133$	−8.76089e8	−0.242782
$134$	−3.22342e9	−0.863664
$135$	2.37193e9	0.614610
$136$	0	0
$137$	6.19321e9	1.50201	0.751005	−	0.660296i	$-0.229569\pi$
$137$	6.19321e9	1.50201	0.751005	+	0.660296i	$0.229569\pi$
$138$	1.07406e10	2.52101
$139$	2.59074e9	0.588649	0.294325	−	0.955706i	$-0.404905\pi$
$139$	2.59074e9	0.588649	0.294325	+	0.955706i	$0.404905\pi$
$140$	−1.18890e9	−0.261560
$141$	4.61758e9	0.983849
$142$	9.65012e9	1.99175
$143$	2.61477e9	0.522903
$144$	−3.36222e9	−0.651620
$145$	4.36496e9	0.820020
$146$	−6.74190e9	−1.22799
$147$	5.72207e9	1.01071
$148$	3.86556e9	0.662270
$149$	4.82673e9	0.802259	0.401130	−	0.916021i	$-0.368618\pi$
$149$	4.82673e9	0.802259	0.401130	+	0.916021i	$0.368618\pi$
$150$	−9.22802e8	−0.148833
$151$	6.24839e9	0.978075	0.489037	−	0.872263i	$-0.337348\pi$
$151$	6.24839e9	0.978075	0.489037	+	0.872263i	$0.337348\pi$
$152$	−1.95307e9	−0.296772
$153$	0	0
$154$	3.48280e9	0.498982
$155$	1.32501e10	1.84386
$156$	3.01247e9	0.407251
$157$	−3.18687e9	−0.418616	−0.209308	−	0.977850i	$-0.567121\pi$
$157$	−3.18687e9	−0.418616	−0.209308	+	0.977850i	$0.567121\pi$
$158$	1.59939e10	2.04173
$159$	2.29717e9	0.285040
$160$	−9.06298e9	−1.09328
$161$	5.88593e9	0.690397
$162$	−1.37964e10	−1.57379
$163$	1.22687e10	1.36130	0.680650	−	0.732609i	$-0.261698\pi$
$163$	1.22687e10	1.36130	0.680650	+	0.732609i	$0.261698\pi$
$164$	−8.76329e9	−0.945954
$165$	1.14444e10	1.20203
$166$	8.43418e9	0.862097
$167$	−6.15276e9	−0.612133	−0.306066	−	0.952010i	$-0.599013\pi$
$167$	−6.15276e9	−0.612133	−0.306066	+	0.952010i	$0.599013\pi$
$168$	−2.82687e9	−0.273788
$169$	−7.25252e9	−0.683910
$170$	0	0
$171$	3.34253e9	0.298946
$172$	−7.63267e9	−0.664965
$173$	−1.18129e10	−1.00265	−0.501323	−	0.865260i	$-0.667153\pi$
$173$	−1.18129e10	−1.00265	−0.501323	+	0.865260i	$0.667153\pi$
$174$	−1.47317e10	−1.21837
$175$	−5.05701e8	−0.0407589
$176$	1.47100e10	1.15560
$177$	−8.73104e9	−0.668630
$178$	−5.09826e9	−0.380655
$179$	2.62945e10	1.91437	0.957184	−	0.289479i	$-0.0934822\pi$
$179$	2.62945e10	1.91437	0.957184	+	0.289479i	$0.0934822\pi$
$180$	4.53602e9	0.322069
$181$	−1.32577e10	−0.918154	−0.459077	−	0.888397i	$-0.651820\pi$
$181$	−1.32577e10	−0.918154	−0.459077	+	0.888397i	$0.651820\pi$
$182$	4.46474e9	0.301631
$183$	−1.90606e10	−1.25634
$184$	1.31216e10	0.843929
$185$	1.88258e10	1.18163
$186$	−4.47189e10	−2.73957
$187$	0	0
$188$	−8.00724e9	−0.467490
$189$	−4.38690e9	−0.250080
$190$	1.35012e10	0.751589
$191$	1.65717e10	0.900983	0.450492	−	0.892781i	$-0.351249\pi$
$191$	1.65717e10	0.900983	0.450492	+	0.892781i	$0.351249\pi$
$192$	1.70030e9	0.0902962
$193$	−1.44377e10	−0.749016	−0.374508	−	0.927224i	$-0.622188\pi$
$193$	−1.44377e10	−0.749016	−0.374508	+	0.927224i	$0.622188\pi$
$194$	2.78246e9	0.141033
$195$	1.46711e10	0.726620
$196$	−9.92251e9	−0.480252
$197$	2.61363e10	1.23636	0.618181	−	0.786036i	$-0.287870\pi$
$197$	2.61363e10	1.23636	0.618181	+	0.786036i	$0.287870\pi$
$198$	−1.32879e10	−0.614416
$199$	6.06022e8	0.0273936	0.0136968	−	0.999906i	$-0.495640\pi$
$199$	6.06022e8	0.0273936	0.0136968	+	0.999906i	$0.495640\pi$
$200$	−1.12736e9	−0.0498229
$201$	1.95902e10	0.846558
$202$	2.20749e10	0.932864
$203$	−8.07303e9	−0.333660
$204$	0	0
$205$	−4.26783e10	−1.68777
$206$	3.49821e10	1.35345
$207$	−2.24565e10	−0.850112
$208$	1.88574e10	0.698550
$209$	−1.46239e10	−0.530159
$210$	1.95415e10	0.693380
$211$	−2.06432e10	−0.716979	−0.358490	−	0.933534i	$-0.616708\pi$
$211$	−2.06432e10	−0.716979	−0.358490	+	0.933534i	$0.616708\pi$
$212$	−3.98347e9	−0.135441
$213$	−5.86482e10	−1.95230
$214$	6.55953e10	2.13802
$215$	−3.71720e10	−1.18643
$216$	−9.77976e9	−0.305693
$217$	−2.45062e10	−0.750252
$218$	7.41294e10	2.22298
$219$	4.09736e10	1.20367
$220$	−1.98455e10	−0.571164
$221$	0	0
$222$	−6.35366e10	−1.75564
$223$	−4.43950e10	−1.20216	−0.601080	−	0.799189i	$-0.705263\pi$
$223$	−4.43950e10	−1.20216	−0.601080	+	0.799189i	$0.705263\pi$
$224$	1.67621e10	0.444847
$225$	1.92939e9	0.0501880
$226$	−4.99860e10	−1.27456
$227$	3.23612e10	0.808924	0.404462	−	0.914555i	$-0.367459\pi$
$227$	3.23612e10	0.808924	0.404462	+	0.914555i	$0.367459\pi$
$228$	−1.68482e10	−0.412902
$229$	5.05693e10	1.21514	0.607571	−	0.794265i	$-0.292144\pi$
$229$	5.05693e10	1.21514	0.607571	+	0.794265i	$0.292144\pi$
$230$	−9.07066e10	−2.13729
$231$	−2.11666e10	−0.489099
$232$	−1.79973e10	−0.407860
$233$	1.71501e10	0.381211	0.190606	−	0.981667i	$-0.438955\pi$
$233$	1.71501e10	0.381211	0.190606	+	0.981667i	$0.438955\pi$
$234$	−1.70343e10	−0.371409
$235$	−3.89962e10	−0.834098
$236$	1.51403e10	0.317710
$237$	−9.72024e10	−2.00129
$238$	0	0
$239$	−1.56762e10	−0.310779	−0.155389	−	0.987853i	$-0.549663\pi$
$239$	−1.56762e10	−0.310779	−0.155389	+	0.987853i	$0.549663\pi$
$240$	8.25361e10	1.60581
$241$	−7.80137e9	−0.148968	−0.0744842	−	0.997222i	$-0.523731\pi$
$241$	−7.80137e9	−0.148968	−0.0744842	+	0.997222i	$0.523731\pi$
$242$	−9.07099e9	−0.170014
$243$	5.19328e10	0.955462
$244$	3.30525e10	0.596967
$245$	−4.83238e10	−0.856868
$246$	1.44038e11	2.50767
$247$	−1.87470e10	−0.320476
$248$	−5.46319e10	−0.917094
$249$	−5.12584e10	−0.845022
$250$	−7.36434e10	−1.19235
$251$	9.23115e10	1.46799	0.733996	−	0.679153i	$-0.237653\pi$
$251$	9.23115e10	1.46799	0.733996	+	0.679153i	$0.237653\pi$
$252$	−8.38940e9	−0.131047
$253$	9.82497e10	1.50761
$254$	−4.61982e10	−0.696423
$255$	0	0
$256$	8.74603e10	1.27271
$257$	−9.75670e9	−0.139510	−0.0697548	−	0.997564i	$-0.522222\pi$
$257$	−9.75670e9	−0.139510	−0.0697548	+	0.997564i	$0.522222\pi$
$258$	1.25455e11	1.76278
$259$	−3.48184e10	−0.480795
$260$	−2.54408e10	−0.345264
$261$	3.08010e10	0.410849
$262$	−2.97714e10	−0.390340
$263$	−1.15838e11	−1.49296	−0.746482	−	0.665406i	$-0.768259\pi$
$263$	−1.15838e11	−1.49296	−0.746482	+	0.665406i	$0.768259\pi$
$264$	−4.71869e10	−0.597866
$265$	−1.94000e10	−0.241654
$266$	−2.49705e10	−0.305816
$267$	3.09845e10	0.373116
$268$	−3.39709e10	−0.402254
$269$	5.41725e10	0.630802	0.315401	−	0.948958i	$-0.397861\pi$
$269$	5.41725e10	0.630802	0.315401	+	0.948958i	$0.397861\pi$
$270$	6.76053e10	0.774183
$271$	−1.20057e11	−1.35215	−0.676073	−	0.736834i	$-0.736320\pi$
$271$	−1.20057e11	−1.35215	−0.676073	+	0.736834i	$0.736320\pi$
$272$	0	0
$273$	−2.71343e10	−0.295656
$274$	1.76520e11	1.89198
$275$	−8.44130e9	−0.0890046
$276$	1.13193e11	1.17417
$277$	−2.71263e10	−0.276842	−0.138421	−	0.990373i	$-0.544203\pi$
$277$	−2.71263e10	−0.276842	−0.138421	+	0.990373i	$0.544203\pi$
$278$	7.38418e10	0.741483
$279$	9.34982e10	0.923814
$280$	2.38734e10	0.232115
$281$	7.42502e10	0.710427	0.355213	−	0.934785i	$-0.384408\pi$
$281$	7.42502e10	0.710427	0.355213	+	0.934785i	$0.384408\pi$
$282$	1.31612e11	1.23929
$283$	5.06373e10	0.469279	0.234640	−	0.972082i	$-0.424609\pi$
$283$	5.06373e10	0.469279	0.234640	+	0.972082i	$0.424609\pi$
$284$	1.01701e11	0.927664
$285$	−8.20529e10	−0.736702
$286$	7.45268e10	0.658666
$287$	7.89338e10	0.686744
$288$	−6.39521e10	−0.547758
$289$	0	0
$290$	1.24411e11	1.03293
$291$	−1.69103e10	−0.138240
$292$	−7.10515e10	−0.571940
$293$	−1.70721e11	−1.35326	−0.676632	−	0.736321i	$-0.736561\pi$
$293$	−1.70721e11	−1.35326	−0.676632	+	0.736321i	$0.736561\pi$
$294$	1.63092e11	1.27312
$295$	7.37351e10	0.566859
$296$	−7.76210e10	−0.587715
$297$	−7.32274e10	−0.546097
$298$	1.37573e11	1.01055
$299$	1.25950e11	0.911338
$300$	−9.72522e9	−0.0693193
$301$	6.87500e10	0.482751
$302$	1.78093e11	1.23202
$303$	−1.34160e11	−0.914387
$304$	−1.05466e11	−0.708243
$305$	1.60970e11	1.06511
$306$	0	0
$307$	1.23971e11	0.796522	0.398261	−	0.917272i	$-0.369614\pi$
$307$	1.23971e11	0.796522	0.398261	+	0.917272i	$0.369614\pi$
$308$	3.67045e10	0.232403
$309$	−2.12602e11	−1.32665
$310$	3.77658e11	2.32258
$311$	3.00821e11	1.82342	0.911709	−	0.410836i	$-0.134763\pi$
$311$	3.00821e11	1.82342	0.911709	+	0.410836i	$0.134763\pi$
$312$	−6.04908e10	−0.361405
$313$	−1.54699e11	−0.911040	−0.455520	−	0.890225i	$-0.650547\pi$
$313$	−1.54699e11	−0.911040	−0.455520	+	0.890225i	$0.650547\pi$
$314$	−9.08330e10	−0.527303
$315$	−4.08574e10	−0.233815
$316$	1.68556e11	0.950941
$317$	−5.39434e10	−0.300035	−0.150017	−	0.988683i	$-0.547933\pi$
$317$	−5.39434e10	−0.300035	−0.150017	+	0.988683i	$0.547933\pi$
$318$	6.54746e10	0.359046
$319$	−1.34757e11	−0.728609
$320$	−1.43593e10	−0.0765523
$321$	−3.98653e11	−2.09567
$322$	1.67763e11	0.869648
$323$	0	0
$324$	−1.45397e11	−0.732998
$325$	−1.08213e10	−0.0538025
$326$	3.49685e11	1.71474
$327$	−4.50519e11	−2.17896
$328$	1.75968e11	0.839463
$329$	7.21238e10	0.339389
$330$	3.26193e11	1.51412
$331$	−3.15316e11	−1.44384	−0.721921	−	0.691975i	$-0.756741\pi$
$331$	−3.15316e11	−1.44384	−0.721921	+	0.691975i	$0.756741\pi$
$332$	8.88861e10	0.401525
$333$	1.32842e11	0.592021
$334$	−1.75368e11	−0.771064
$335$	−1.65442e11	−0.717704
$336$	−1.52651e11	−0.653391
$337$	−1.09713e10	−0.0463367	−0.0231684	−	0.999732i	$-0.507375\pi$
$337$	−1.09713e10	−0.0463367	−0.0231684	+	0.999732i	$0.507375\pi$
$338$	−2.06713e11	−0.861476
$339$	3.03788e11	1.24932
$340$	0	0
$341$	−4.09065e11	−1.63831
$342$	9.52698e10	0.376563
$343$	1.98557e11	0.774571
$344$	1.53265e11	0.590106
$345$	5.51266e11	2.09496
$346$	−3.36693e11	−1.26297
$347$	−7.01283e10	−0.259663	−0.129832	−	0.991536i	$-0.541444\pi$
$347$	−7.01283e10	−0.259663	−0.129832	+	0.991536i	$0.541444\pi$
$348$	−1.55254e11	−0.567461
$349$	3.76499e11	1.35847	0.679234	−	0.733922i	$-0.262312\pi$
$349$	3.76499e11	1.35847	0.679234	+	0.733922i	$0.262312\pi$
$350$	−1.44136e10	−0.0513413
$351$	−9.38732e10	−0.330111
$352$	2.79797e11	0.971407
$353$	−3.15575e11	−1.08172	−0.540862	−	0.841112i	$-0.681902\pi$
$353$	−3.15575e11	−1.08172	−0.540862	+	0.841112i	$0.681902\pi$
$354$	−2.48854e11	−0.842230
$355$	4.95294e11	1.65514
$356$	−5.37295e10	−0.177292
$357$	0	0
$358$	7.49452e11	2.41140
$359$	−2.05111e11	−0.651723	−0.325861	−	0.945418i	$-0.605654\pi$
$359$	−2.05111e11	−0.651723	−0.325861	+	0.945418i	$0.605654\pi$
$360$	−9.10838e10	−0.285812
$361$	−2.17839e11	−0.675077
$362$	−3.77875e11	−1.15654
$363$	5.51286e10	0.166647
$364$	4.70530e10	0.140485
$365$	−3.46029e11	−1.02046
$366$	−5.43270e11	−1.58252
$367$	−1.30843e11	−0.376489	−0.188245	−	0.982122i	$-0.560280\pi$
$367$	−1.30843e11	−0.376489	−0.188245	+	0.982122i	$0.560280\pi$
$368$	7.08567e11	2.01403
$369$	−3.01155e11	−0.845614
$370$	5.36577e11	1.48842
$371$	3.58804e10	0.0983275
$372$	−4.71283e11	−1.27596
$373$	4.08317e11	1.09221	0.546107	−	0.837715i	$-0.316109\pi$
$373$	4.08317e11	1.09221	0.546107	+	0.837715i	$0.316109\pi$
$374$	0	0
$375$	4.47565e11	1.16873
$376$	1.60786e11	0.414862
$377$	−1.72751e11	−0.440438
$378$	−1.25037e11	−0.315010
$379$	−6.78686e11	−1.68963	−0.844817	−	0.535055i	$-0.820291\pi$
$379$	−6.78686e11	−1.68963	−0.844817	+	0.535055i	$0.820291\pi$
$380$	1.42286e11	0.350055
$381$	2.80768e11	0.682629
$382$	4.72331e11	1.13491
$383$	3.43718e11	0.816221	0.408111	−	0.912932i	$-0.366188\pi$
$383$	3.43718e11	0.816221	0.408111	+	0.912932i	$0.366188\pi$
$384$	−5.00993e11	−1.17582
$385$	1.78755e11	0.414654
$386$	−4.11508e11	−0.943487
$387$	−2.62301e11	−0.594430
$388$	2.93238e10	0.0656867
$389$	3.94284e11	0.873044	0.436522	−	0.899694i	$-0.356210\pi$
$389$	3.94284e11	0.873044	0.436522	+	0.899694i	$0.356210\pi$
$390$	4.18160e11	0.915275
$391$	0	0
$392$	1.99245e11	0.426188
$393$	1.80935e11	0.382609
$394$	7.44943e11	1.55736
$395$	8.20890e11	1.69667
$396$	−1.40038e11	−0.286166
$397$	2.30296e9	0.00465295	0.00232648	−	0.999997i	$-0.499259\pi$
$397$	2.30296e9	0.00465295	0.00232648	+	0.999997i	$0.499259\pi$
$398$	1.72730e10	0.0345059
$399$	1.51757e11	0.299759
$400$	−6.08778e10	−0.118902
$401$	−5.69424e11	−1.09973	−0.549865	−	0.835253i	$-0.685321\pi$
$401$	−5.69424e11	−1.09973	−0.549865	+	0.835253i	$0.685321\pi$
$402$	5.58365e11	1.06635
$403$	−5.24397e11	−0.990347
$404$	2.32643e11	0.434485
$405$	−7.08101e11	−1.30782
$406$	−2.30100e11	−0.420290
$407$	−5.81199e11	−1.04990
$408$	0	0
$409$	3.66217e11	0.647118	0.323559	−	0.946208i	$-0.395121\pi$
$409$	3.66217e11	0.647118	0.323559	+	0.946208i	$0.395121\pi$
$410$	−1.21643e12	−2.12598
$411$	−1.07280e12	−1.85451
$412$	3.68669e11	0.630375
$413$	−1.36374e11	−0.230651
$414$	−6.40063e11	−1.07083
$415$	4.32886e11	0.716402
$416$	3.58683e11	0.587207
$417$	−4.48771e11	−0.726796
$418$	−4.16815e11	−0.667806
$419$	6.26394e11	0.992852	0.496426	−	0.868079i	$-0.334645\pi$
$419$	6.26394e11	0.992852	0.496426	+	0.868079i	$0.334645\pi$
$420$	2.05944e11	0.322944
$421$	−5.86511e11	−0.909927	−0.454963	−	0.890510i	$-0.650348\pi$
$421$	−5.86511e11	−0.909927	−0.454963	+	0.890510i	$0.650348\pi$
$422$	−5.88379e11	−0.903132
$423$	−2.75173e11	−0.417902
$424$	7.99886e10	0.120194
$425$	0	0
$426$	−1.67161e12	−2.45919
$427$	−2.97715e11	−0.433386
$428$	6.91296e11	0.995788
$429$	−4.52934e11	−0.645620
$430$	−1.05949e12	−1.49447
$431$	1.97901e11	0.276249	0.138125	−	0.990415i	$-0.455893\pi$
$431$	1.97901e11	0.276249	0.138125	+	0.990415i	$0.455893\pi$
$432$	−5.28108e11	−0.729535
$433$	1.60613e11	0.219576	0.109788	−	0.993955i	$-0.464983\pi$
$433$	1.60613e11	0.219576	0.109788	+	0.993955i	$0.464983\pi$
$434$	−6.98482e11	−0.945043
$435$	−7.56106e11	−1.01247
$436$	7.81235e11	1.03536
$437$	−7.04418e11	−0.923984
$438$	1.16784e12	1.51618
$439$	1.14252e12	1.46816	0.734078	−	0.679065i	$-0.237615\pi$
$439$	1.14252e12	1.46816	0.734078	+	0.679065i	$0.237615\pi$
$440$	3.98501e11	0.506865
$441$	−3.40993e11	−0.429310
$442$	0	0
$443$	−5.38672e11	−0.664520	−0.332260	−	0.943188i	$-0.607811\pi$
$443$	−5.38672e11	−0.664520	−0.332260	+	0.943188i	$0.607811\pi$
$444$	−6.69599e11	−0.817695
$445$	−2.61669e11	−0.316324
$446$	−1.26536e12	−1.51428
$447$	−8.36094e11	−0.990538
$448$	2.65576e10	0.0311486
$449$	3.13597e11	0.364136	0.182068	−	0.983286i	$-0.441721\pi$
$449$	3.13597e11	0.364136	0.182068	+	0.983286i	$0.441721\pi$
$450$	5.49921e10	0.0632185
$451$	1.31759e12	1.49963
$452$	−5.26793e11	−0.593631
$453$	−1.08236e12	−1.20761
$454$	9.22367e11	1.01895
$455$	2.29154e11	0.250655
$456$	3.38315e11	0.366420
$457$	−2.44031e11	−0.261711	−0.130856	−	0.991401i	$-0.541772\pi$
$457$	−2.44031e11	−0.261711	−0.130856	+	0.991401i	$0.541772\pi$
$458$	1.44134e12	1.53064
$459$	0	0
$460$	−9.55938e11	−0.995450
$461$	−1.41045e12	−1.45447	−0.727235	−	0.686388i	$-0.759195\pi$
$461$	−1.41045e12	−1.45447	−0.727235	+	0.686388i	$0.759195\pi$
$462$	−6.03296e11	−0.616086
$463$	−6.57436e11	−0.664873	−0.332437	−	0.943126i	$-0.607871\pi$
$463$	−6.57436e11	−0.664873	−0.332437	+	0.943126i	$0.607871\pi$
$464$	−9.71856e11	−0.973355
$465$	−2.29521e12	−2.27658
$466$	4.88817e11	0.480187
$467$	7.29178e11	0.709427	0.354714	−	0.934975i	$-0.384578\pi$
$467$	7.29178e11	0.709427	0.354714	+	0.934975i	$0.384578\pi$
$468$	−1.79521e11	−0.172985
$469$	3.05987e11	0.292029
$470$	−1.11148e12	−1.05066
$471$	5.52034e11	0.516859
$472$	−3.04019e11	−0.281943
$473$	1.14759e12	1.05418
$474$	−2.77049e12	−2.52089
$475$	6.05214e10	0.0545491
$476$	0	0
$477$	−1.36894e11	−0.121074
$478$	−4.46808e11	−0.391467
$479$	−1.63616e12	−1.42009	−0.710044	−	0.704157i	$-0.751325\pi$
$479$	−1.63616e12	−1.42009	−0.710044	+	0.704157i	$0.751325\pi$
$480$	1.56990e12	1.34986
$481$	−7.45063e11	−0.634659
$482$	−2.22357e11	−0.187646
$483$	−1.01957e12	−0.852423
$484$	−9.55973e10	−0.0791847
$485$	1.42810e11	0.117198
$486$	1.48020e12	1.20353
$487$	−6.40767e11	−0.516202	−0.258101	−	0.966118i	$-0.583097\pi$
$487$	−6.40767e11	−0.516202	−0.258101	+	0.966118i	$0.583097\pi$
$488$	−6.63699e11	−0.529763
$489$	−2.12520e12	−1.68078
$490$	−1.37734e12	−1.07934
$491$	1.71959e12	1.33523	0.667617	−	0.744505i	$-0.267314\pi$
$491$	1.71959e12	1.33523	0.667617	+	0.744505i	$0.267314\pi$
$492$	1.51799e12	1.16796
$493$	0	0
$494$	−5.34333e11	−0.403683
$495$	−6.82003e11	−0.510579
$496$	−2.95013e12	−2.18864
$497$	−9.16051e11	−0.673466
$498$	−1.46098e12	−1.06442
$499$	−2.47929e12	−1.79009	−0.895045	−	0.445975i	$-0.852857\pi$
$499$	−2.47929e12	−1.79009	−0.895045	+	0.445975i	$0.852857\pi$
$500$	−7.76113e11	−0.555341
$501$	1.06579e12	0.755792
$502$	2.63109e12	1.84913
$503$	−1.47785e12	−1.02938	−0.514689	−	0.857377i	$-0.672093\pi$
$503$	−1.47785e12	−1.02938	−0.514689	+	0.857377i	$0.672093\pi$
$504$	1.68460e11	0.116295
$505$	1.13300e12	0.775210
$506$	2.80034e12	1.89904
$507$	1.25629e12	0.844413
$508$	−4.86873e11	−0.324361
$509$	−1.05268e12	−0.695127	−0.347564	−	0.937656i	$-0.612991\pi$
$509$	−1.05268e12	−0.695127	−0.347564	+	0.937656i	$0.612991\pi$
$510$	0	0
$511$	6.39984e11	0.415217
$512$	1.01200e12	0.650830
$513$	5.25016e11	0.334691
$514$	−2.78088e11	−0.175731
$515$	1.79546e12	1.12472
$516$	1.32214e12	0.821022
$517$	1.20391e12	0.741118
$518$	−9.92404e11	−0.605626
$519$	2.04624e12	1.23795
$520$	5.10855e11	0.306396
$521$	3.56580e11	0.212025	0.106013	−	0.994365i	$-0.466192\pi$
$521$	3.56580e11	0.212025	0.106013	+	0.994365i	$0.466192\pi$
$522$	8.77897e11	0.517519
$523$	1.08984e12	0.636951	0.318476	−	0.947931i	$-0.396829\pi$
$523$	1.08984e12	0.636951	0.318476	+	0.947931i	$0.396829\pi$
$524$	−3.13755e11	−0.181802
$525$	8.75983e10	0.0503244
$526$	−3.30164e12	−1.88059
$527$	0	0
$528$	−2.54810e12	−1.42680
$529$	2.93143e12	1.62753
$530$	−5.52944e11	−0.304396
$531$	5.20305e11	0.284009
$532$	−2.63159e11	−0.142435
$533$	1.68907e12	0.906515
$534$	8.83129e11	0.469990
$535$	3.36669e12	1.77669
$536$	6.82140e11	0.356970
$537$	−4.55477e12	−2.36364
$538$	1.54404e12	0.794580
$539$	1.49188e12	0.761350
$540$	7.12478e11	0.360578
$541$	−1.83215e12	−0.919546	−0.459773	−	0.888036i	$-0.652069\pi$
$541$	−1.83215e12	−0.919546	−0.459773	+	0.888036i	$0.652069\pi$
$542$	−3.42188e12	−1.70321
$543$	2.29652e12	1.13363
$544$	0	0
$545$	3.80471e12	1.84730
$546$	−7.73390e11	−0.372419
$547$	1.24502e12	0.594609	0.297305	−	0.954783i	$-0.403912\pi$
$547$	1.24502e12	0.594609	0.297305	+	0.954783i	$0.403912\pi$
$548$	1.86031e12	0.881198
$549$	1.13587e12	0.533645
$550$	−2.40596e11	−0.112113
$551$	9.66167e11	0.446550
$552$	−2.27294e12	−1.04199
$553$	−1.51824e12	−0.690364
$554$	−7.73161e11	−0.348719
$555$	−3.26103e12	−1.45894
$556$	7.78204e11	0.345348
$557$	3.48794e12	1.53540	0.767698	−	0.640812i	$-0.221402\pi$
$557$	3.48794e12	1.53540	0.767698	+	0.640812i	$0.221402\pi$
$558$	2.66491e12	1.16367
$559$	1.47115e12	0.637241
$560$	1.28916e12	0.553939
$561$	0	0
$562$	2.11630e12	0.894878
$563$	−3.26487e11	−0.136955	−0.0684775	−	0.997653i	$-0.521814\pi$
$563$	−3.26487e11	−0.136955	−0.0684775	+	0.997653i	$0.521814\pi$
$564$	1.38703e12	0.577203
$565$	−2.56554e12	−1.05916
$566$	1.44328e12	0.591120
$567$	1.30964e12	0.532142
$568$	−2.04216e12	−0.823233
$569$	−4.62696e11	−0.185051	−0.0925254	−	0.995710i	$-0.529494\pi$
$569$	−4.62696e11	−0.185051	−0.0925254	+	0.995710i	$0.529494\pi$
$570$	−2.33869e12	−0.927976
$571$	−1.24733e11	−0.0491044	−0.0245522	−	0.999699i	$-0.507816\pi$
$571$	−1.24733e11	−0.0491044	−0.0245522	+	0.999699i	$0.507816\pi$
$572$	7.85423e11	0.306776
$573$	−2.87057e12	−1.11243
$574$	2.24979e12	0.865046
$575$	−4.06608e11	−0.155121
$576$	−1.01325e11	−0.0383545
$577$	6.12818e11	0.230166	0.115083	−	0.993356i	$-0.463287\pi$
$577$	6.12818e11	0.230166	0.115083	+	0.993356i	$0.463287\pi$
$578$	0	0
$579$	2.50093e12	0.924800
$580$	1.31115e12	0.481089
$581$	−8.00626e11	−0.291499
$582$	−4.81982e11	−0.174132
$583$	5.98926e11	0.214716
$584$	1.42672e12	0.507553
$585$	−8.74289e11	−0.308641
$586$	−4.86594e12	−1.70462
$587$	−1.18091e12	−0.410529	−0.205264	−	0.978707i	$-0.565805\pi$
$587$	−1.18091e12	−0.410529	−0.205264	+	0.978707i	$0.565805\pi$
$588$	1.71879e12	0.592960
$589$	2.93286e12	1.00409
$590$	2.10162e12	0.714035
$591$	−4.52737e12	−1.52652
$592$	−4.19154e12	−1.40258
$593$	−3.63746e10	−0.0120796	−0.00603979	−	0.999982i	$-0.501923\pi$
$593$	−3.63746e10	−0.0120796	−0.00603979	+	0.999982i	$0.501923\pi$
$594$	−2.08715e12	−0.687882
$595$	0	0
$596$	1.44985e12	0.470669
$597$	−1.04976e11	−0.0338225
$598$	3.58987e12	1.14795
$599$	4.00830e12	1.27215	0.636077	−	0.771625i	$-0.280556\pi$
$599$	4.00830e12	1.27215	0.636077	+	0.771625i	$0.280556\pi$
$600$	1.95284e11	0.0615156
$601$	4.29519e12	1.34291	0.671456	−	0.741044i	$-0.265669\pi$
$601$	4.29519e12	1.34291	0.671456	+	0.741044i	$0.265669\pi$
$602$	1.95953e12	0.608090
$603$	−1.16743e12	−0.359586
$604$	1.87689e12	0.573816
$605$	−4.65570e11	−0.141282
$606$	−3.82386e12	−1.15179
$607$	−4.27985e12	−1.27961	−0.639807	−	0.768535i	$-0.720986\pi$
$607$	−4.27985e12	−1.27961	−0.639807	+	0.768535i	$0.720986\pi$
$608$	−2.00605e12	−0.595355
$609$	1.39842e12	0.411966
$610$	4.58800e12	1.34165
$611$	1.54335e12	0.448000
$612$	0	0
$613$	−1.59171e12	−0.455293	−0.227647	−	0.973744i	$-0.573103\pi$
$613$	−1.59171e12	−0.455293	−0.227647	+	0.973744i	$0.573103\pi$
$614$	3.53346e12	1.00333
$615$	7.39280e12	2.08387
$616$	−7.37031e11	−0.206240
$617$	5.66989e12	1.57504	0.787519	−	0.616290i	$-0.211365\pi$
$617$	5.66989e12	1.57504	0.787519	+	0.616290i	$0.211365\pi$
$618$	−6.05965e12	−1.67109
$619$	−6.99348e11	−0.191463	−0.0957316	−	0.995407i	$-0.530519\pi$
$619$	−6.99348e11	−0.191463	−0.0957316	+	0.995407i	$0.530519\pi$
$620$	3.98007e12	1.08175
$621$	−3.52728e12	−0.951761
$622$	8.57408e12	2.29684
$623$	4.83959e11	0.128710
$624$	−3.26651e12	−0.862489
$625$	−4.14482e12	−1.08654
$626$	−4.40927e12	−1.14758
$627$	2.53318e12	0.654579
$628$	−9.57270e11	−0.245593
$629$	0	0
$630$	−1.16453e12	−0.294522
$631$	1.12865e12	0.283417	0.141708	−	0.989908i	$-0.454740\pi$
$631$	1.12865e12	0.283417	0.141708	+	0.989908i	$0.454740\pi$
$632$	−3.38463e12	−0.843888
$633$	3.57585e12	0.885244
$634$	−1.53751e12	−0.377934
$635$	−2.37113e12	−0.578727
$636$	6.90023e11	0.167227
$637$	1.91250e12	0.460229
$638$	−3.84089e12	−0.917781
$639$	3.49500e12	0.829265
$640$	4.23097e12	0.996851
$641$	−1.79395e12	−0.419711	−0.209855	−	0.977732i	$-0.567299\pi$
$641$	−1.79395e12	−0.419711	−0.209855	+	0.977732i	$0.567299\pi$
$642$	−1.13625e13	−2.63978
$643$	5.27160e12	1.21617	0.608083	−	0.793873i	$-0.291939\pi$
$643$	5.27160e12	1.21617	0.608083	+	0.793873i	$0.291939\pi$
$644$	1.76801e12	0.405041
$645$	6.43900e12	1.46487
$646$	0	0
$647$	−1.48582e12	−0.333347	−0.166674	−	0.986012i	$-0.553303\pi$
$647$	−1.48582e12	−0.333347	−0.166674	+	0.986012i	$0.553303\pi$
$648$	2.91959e12	0.650481
$649$	−2.27639e12	−0.503669
$650$	−3.08431e11	−0.0677715
$651$	4.24500e12	0.926325
$652$	3.68526e12	0.798646
$653$	5.84380e12	1.25773	0.628863	−	0.777516i	$-0.283521\pi$
$653$	5.84380e12	1.25773	0.628863	+	0.777516i	$0.283521\pi$
$654$	−1.28408e13	−2.74469
$655$	−1.52802e12	−0.324373
$656$	9.50229e12	2.00337
$657$	−2.44172e12	−0.511272
$658$	2.05569e12	0.427506
$659$	−3.45631e12	−0.713885	−0.356943	−	0.934126i	$-0.616181\pi$
$659$	−3.45631e12	−0.713885	−0.356943	+	0.934126i	$0.616181\pi$
$660$	3.43768e12	0.705208
$661$	−6.00332e12	−1.22316	−0.611582	−	0.791181i	$-0.709467\pi$
$661$	−6.00332e12	−1.22316	−0.611582	+	0.791181i	$0.709467\pi$
$662$	−8.98722e12	−1.81871
$663$	0	0
$664$	−1.78484e12	−0.356323
$665$	−1.28162e12	−0.254133
$666$	3.78631e12	0.745730
$667$	−6.49111e12	−1.26985
$668$	−1.84816e12	−0.359125
$669$	7.69017e12	1.48429
$670$	−4.71549e12	−0.904045
$671$	−4.96954e12	−0.946379
$672$	−2.90355e12	−0.549247
$673$	−4.90600e12	−0.921849	−0.460925	−	0.887439i	$-0.652482\pi$
$673$	−4.90600e12	−0.921849	−0.460925	+	0.887439i	$0.652482\pi$
$674$	−3.12708e11	−0.0583673
$675$	3.03053e11	0.0561890
$676$	−2.17851e12	−0.401235
$677$	−6.76575e12	−1.23785	−0.618923	−	0.785451i	$-0.712431\pi$
$677$	−6.76575e12	−1.23785	−0.618923	+	0.785451i	$0.712431\pi$
$678$	8.65866e12	1.57368
$679$	−2.64129e11	−0.0476872
$680$	0	0
$681$	−5.60565e12	−0.998767
$682$	−1.16593e13	−2.06368
$683$	9.99306e12	1.75714	0.878568	−	0.477618i	$-0.158500\pi$
$683$	9.99306e12	1.75714	0.878568	+	0.477618i	$0.158500\pi$
$684$	1.00403e12	0.175385
$685$	9.05995e12	1.57224
$686$	5.65932e12	0.975676
$687$	−8.75969e12	−1.50032
$688$	8.27633e12	1.40828
$689$	7.67789e11	0.129794
$690$	1.57123e13	2.63888
$691$	7.48255e12	1.24853	0.624264	−	0.781213i	$-0.285399\pi$
$691$	7.48255e12	1.24853	0.624264	+	0.781213i	$0.285399\pi$
$692$	−3.54834e12	−0.588231
$693$	1.26137e12	0.207751
$694$	−1.99882e12	−0.327081
$695$	3.78995e12	0.616172
$696$	3.11752e12	0.503579
$697$	0	0
$698$	1.07311e13	1.71117
$699$	−2.97077e12	−0.470676
$700$	−1.51902e11	−0.0239124
$701$	−2.73381e12	−0.427599	−0.213800	−	0.976878i	$-0.568584\pi$
$701$	−2.73381e12	−0.427599	−0.213800	+	0.976878i	$0.568584\pi$
$702$	−2.67560e12	−0.415819
$703$	4.16701e12	0.643465
$704$	4.43308e11	0.0680187
$705$	6.75499e12	1.02985
$706$	−8.99460e12	−1.36258
$707$	−2.09549e12	−0.315427
$708$	−2.62263e12	−0.392271
$709$	4.63155e12	0.688364	0.344182	−	0.938903i	$-0.388156\pi$
$709$	4.63155e12	0.688364	0.344182	+	0.938903i	$0.388156\pi$
$710$	1.41170e13	2.08488
$711$	5.79254e12	0.850072
$712$	1.07890e12	0.157333
$713$	−1.97042e13	−2.85533
$714$	0	0
$715$	3.82510e12	0.547351
$716$	7.89832e12	1.12312
$717$	2.71546e12	0.383714
$718$	−5.84612e12	−0.820932
$719$	8.31957e10	0.0116097	0.00580485	−	0.999983i	$-0.498152\pi$
$719$	8.31957e10	0.0116097	0.00580485	+	0.999983i	$0.498152\pi$
$720$	−4.91854e12	−0.682087
$721$	−3.32072e12	−0.457640
$722$	−6.20890e12	−0.850350
$723$	1.35137e12	0.183929
$724$	−3.98235e12	−0.538662
$725$	5.57696e11	0.0749681
$726$	1.57129e12	0.209914
$727$	6.97498e10	0.00926058	0.00463029	−	0.999989i	$-0.498526\pi$
$727$	6.97498e10	0.00926058	0.00463029	+	0.999989i	$0.498526\pi$
$728$	−9.44831e11	−0.124670
$729$	5.31559e11	0.0697072
$730$	−9.86262e12	−1.28540
$731$	0	0
$732$	−5.72541e12	−0.737066
$733$	1.35099e13	1.72856	0.864278	−	0.503014i	$-0.167776\pi$
$733$	1.35099e13	1.72856	0.864278	+	0.503014i	$0.167776\pi$
$734$	−3.72932e12	−0.474239
$735$	8.37073e12	1.05796
$736$	1.34775e13	1.69301
$737$	5.10763e12	0.637699
$738$	−8.58361e12	−1.06516
$739$	8.62113e12	1.06332	0.531660	−	0.846958i	$-0.321568\pi$
$739$	8.62113e12	1.06332	0.531660	+	0.846958i	$0.321568\pi$
$740$	5.65487e12	0.693235
$741$	3.24739e12	0.395688
$742$	1.02267e12	0.123857
$743$	6.08624e12	0.732654	0.366327	−	0.930486i	$-0.380615\pi$
$743$	6.08624e12	0.732654	0.366327	+	0.930486i	$0.380615\pi$
$744$	9.46343e12	1.13232
$745$	7.06095e12	0.839769
$746$	1.16380e13	1.37579
$747$	3.05462e12	0.358934
$748$	0	0
$749$	−6.22673e12	−0.722922
$750$	1.27566e13	1.47218
$751$	4.96208e12	0.569225	0.284613	−	0.958643i	$-0.408135\pi$
$751$	4.96208e12	0.569225	0.284613	+	0.958643i	$0.408135\pi$
$752$	8.68249e12	0.990065
$753$	−1.59903e13	−1.81251
$754$	−4.92380e12	−0.554791
$755$	9.14068e12	1.02381
$756$	−1.31773e12	−0.146717
$757$	1.25361e13	1.38749	0.693746	−	0.720219i	$-0.255959\pi$
$757$	1.25361e13	1.38749	0.693746	+	0.720219i	$0.255959\pi$
$758$	−1.93441e13	−2.12832
$759$	−1.70190e13	−1.86142
$760$	−2.85712e12	−0.310647
$761$	−1.38427e13	−1.49620	−0.748102	−	0.663584i	$-0.769035\pi$
$761$	−1.38427e13	−1.49620	−0.748102	+	0.663584i	$0.769035\pi$
$762$	8.00252e12	0.859863
$763$	−7.03684e12	−0.751653
$764$	4.97780e12	0.528588
$765$	0	0
$766$	9.79675e12	1.02814
$767$	−2.91820e12	−0.304464
$768$	−1.51500e13	−1.57140
$769$	−1.11058e13	−1.14520	−0.572598	−	0.819837i	$-0.694064\pi$
$769$	−1.11058e13	−1.14520	−0.572598	+	0.819837i	$0.694064\pi$
$770$	5.09493e12	0.522312
$771$	1.69007e12	0.172250
$772$	−4.33680e12	−0.439432
$773$	9.23656e12	0.930470	0.465235	−	0.885187i	$-0.345970\pi$
$773$	9.23656e12	0.930470	0.465235	+	0.885187i	$0.345970\pi$
$774$	−7.47618e12	−0.748765
$775$	1.69292e12	0.168570
$776$	−5.88825e11	−0.0582920
$777$	6.03130e12	0.593630
$778$	1.12380e13	1.09972
$779$	−9.44666e12	−0.919094
$780$	4.40690e12	0.426292
$781$	−1.52910e13	−1.47064
$782$	0	0
$783$	4.83795e12	0.459974
$784$	1.07593e13	1.01709
$785$	−4.66202e12	−0.438188
$786$	5.15705e12	0.481948
$787$	−9.46933e12	−0.879900	−0.439950	−	0.898022i	$-0.645004\pi$
$787$	−9.46933e12	−0.879900	−0.439950	+	0.898022i	$0.645004\pi$
$788$	7.85080e12	0.725347
$789$	2.00656e13	1.84334
$790$	2.33972e13	2.13719
$791$	4.74499e12	0.430964
$792$	2.81199e12	0.253951
$793$	−6.37066e12	−0.572078
$794$	6.56395e10	0.00586102
$795$	3.36049e12	0.298367
$796$	1.82037e11	0.0160713
$797$	−5.94914e12	−0.522266	−0.261133	−	0.965303i	$-0.584096\pi$
$797$	−5.94914e12	−0.522266	−0.261133	+	0.965303i	$0.584096\pi$
$798$	4.32543e12	0.377587
$799$	0	0
$800$	−1.15795e12	−0.0999500
$801$	−1.84645e12	−0.158486
$802$	−1.62299e13	−1.38526
$803$	1.06828e13	0.906703
$804$	5.88449e12	0.496657
$805$	8.61045e12	0.722677
$806$	−1.49465e13	−1.24748
$807$	−9.38384e12	−0.778843
$808$	−4.67151e12	−0.385572
$809$	2.92616e12	0.240176	0.120088	−	0.992763i	$-0.461682\pi$
$809$	2.92616e12	0.240176	0.120088	+	0.992763i	$0.461682\pi$
$810$	−2.01825e13	−1.64737
$811$	1.70693e13	1.38555	0.692774	−	0.721155i	$-0.256388\pi$
$811$	1.70693e13	1.38555	0.692774	+	0.721155i	$0.256388\pi$
$812$	−2.42497e12	−0.195751
$813$	2.07964e13	1.66948
$814$	−1.65655e13	−1.32250
$815$	1.79477e13	1.42495
$816$	0	0
$817$	−8.22788e12	−0.646083
$818$	1.04380e13	0.815132
$819$	1.61700e12	0.125584
$820$	−1.28197e13	−0.990182
$821$	−2.36190e13	−1.81433	−0.907166	−	0.420772i	$-0.861759\pi$
$821$	−2.36190e13	−1.81433	−0.907166	+	0.420772i	$0.861759\pi$
$822$	−3.05771e13	−2.33601
$823$	−8.07533e12	−0.613566	−0.306783	−	0.951779i	$-0.599253\pi$
$823$	−8.07533e12	−0.613566	−0.306783	+	0.951779i	$0.599253\pi$
$824$	−7.40292e12	−0.559410
$825$	1.46222e12	0.109893
$826$	−3.88696e12	−0.290536
$827$	−2.36419e13	−1.75755	−0.878774	−	0.477239i	$-0.841638\pi$
$827$	−2.36419e13	−1.75755	−0.878774	+	0.477239i	$0.841638\pi$
$828$	−6.74549e12	−0.498743
$829$	1.99403e13	1.46635	0.733173	−	0.680042i	$-0.238038\pi$
$829$	1.99403e13	1.46635	0.733173	+	0.680042i	$0.238038\pi$
$830$	1.23382e13	0.902405
$831$	4.69886e12	0.341812
$832$	5.68295e11	0.0411167
$833$	0	0
$834$	−1.27910e13	−0.915498
$835$	−9.00078e12	−0.640753
$836$	−4.39273e12	−0.311033
$837$	1.46859e13	1.03427
$838$	1.78537e13	1.25063
$839$	5.03307e11	0.0350675	0.0175337	−	0.999846i	$-0.494419\pi$
$839$	5.03307e11	0.0350675	0.0175337	+	0.999846i	$0.494419\pi$
$840$	−4.13538e12	−0.286589
$841$	−5.60406e12	−0.386296
$842$	−1.67169e13	−1.14617
$843$	−1.28617e13	−0.877154
$844$	−6.20081e12	−0.420637
$845$	−1.06096e13	−0.715886
$846$	−7.84307e12	−0.526404
$847$	8.61076e11	0.0574866
$848$	4.31939e12	0.286841
$849$	−8.77147e12	−0.579412
$850$	0	0
$851$	−2.79957e13	−1.82982
$852$	−1.76167e13	−1.14537
$853$	1.68280e13	1.08833	0.544167	−	0.838977i	$-0.316846\pi$
$853$	1.68280e13	1.08833	0.544167	+	0.838977i	$0.316846\pi$
$854$	−8.48555e12	−0.545908
$855$	4.88974e12	0.312924
$856$	−1.38813e13	−0.883687
$857$	2.00682e13	1.27085	0.635425	−	0.772163i	$-0.280825\pi$
$857$	2.00682e13	1.27085	0.635425	+	0.772163i	$0.280825\pi$
$858$	−1.29097e13	−0.813246
$859$	2.05798e13	1.28965	0.644826	−	0.764329i	$-0.276930\pi$
$859$	2.05798e13	1.28965	0.644826	+	0.764329i	$0.276930\pi$
$860$	−1.11657e13	−0.696055
$861$	−1.36730e13	−0.847912
$862$	5.64064e12	0.347973
$863$	−5.58574e11	−0.0342793	−0.0171397	−	0.999853i	$-0.505456\pi$
$863$	−5.58574e11	−0.0342793	−0.0171397	+	0.999853i	$0.505456\pi$
$864$	−1.00450e13	−0.613253
$865$	−1.72808e13	−1.04952
$866$	4.57783e12	0.276585
$867$	0	0
$868$	−7.36116e12	−0.440157
$869$	−2.53430e13	−1.50754
$870$	−2.15507e13	−1.27534
$871$	6.54768e12	0.385483
$872$	−1.56873e13	−0.918806
$873$	1.00773e12	0.0587191
$874$	−2.00775e13	−1.16388
$875$	6.99070e12	0.403167
$876$	1.23076e13	0.706166
$877$	1.61009e13	0.919076	0.459538	−	0.888158i	$-0.348015\pi$
$877$	1.61009e13	0.919076	0.459538	+	0.888158i	$0.348015\pi$
$878$	3.25643e13	1.84934
$879$	2.95726e13	1.67086
$880$	2.15191e13	1.20963
$881$	−3.38486e13	−1.89299	−0.946496	−	0.322715i	$-0.895404\pi$
$881$	−3.38486e13	−1.89299	−0.946496	+	0.322715i	$0.895404\pi$
$882$	−9.71907e12	−0.540774
$883$	6.37789e12	0.353064	0.176532	−	0.984295i	$-0.443512\pi$
$883$	6.37789e12	0.353064	0.176532	+	0.984295i	$0.443512\pi$
$884$	0	0
$885$	−1.27725e13	−0.699892
$886$	−1.53534e13	−0.837052
$887$	−1.11778e13	−0.606315	−0.303158	−	0.952940i	$-0.598041\pi$
$887$	−1.11778e13	−0.606315	−0.303158	+	0.952940i	$0.598041\pi$
$888$	1.34456e13	0.725643
$889$	4.38542e12	0.235480
$890$	−7.45817e12	−0.398453
$891$	2.18609e13	1.16203
$892$	−1.33354e13	−0.705282
$893$	−8.63166e12	−0.454216
$894$	−2.38306e13	−1.24772
$895$	3.84658e13	2.00388
$896$	−7.82522e12	−0.405612
$897$	−2.18173e13	−1.12522
$898$	8.93824e12	0.458678
$899$	2.70259e13	1.37994
$900$	5.79551e11	0.0294442
$901$	0	0
$902$	3.75542e13	1.88899
$903$	−1.19090e13	−0.596046
$904$	1.05781e13	0.526803
$905$	−1.93945e13	−0.961082
$906$	−3.08496e13	−1.52115
$907$	1.99609e13	0.979373	0.489686	−	0.871899i	$-0.337111\pi$
$907$	1.99609e13	0.979373	0.489686	+	0.871899i	$0.337111\pi$
$908$	9.72064e12	0.474579
$909$	7.99492e12	0.388398
$910$	6.53141e12	0.315733
$911$	2.62947e13	1.26484	0.632420	−	0.774626i	$-0.282062\pi$
$911$	2.62947e13	1.26484	0.632420	+	0.774626i	$0.282062\pi$
$912$	1.82690e13	0.874457
$913$	−1.33643e13	−0.636542
$914$	−6.95544e12	−0.329660
$915$	−2.78834e13	−1.31508
$916$	1.51900e13	0.712898
$917$	2.82609e12	0.131985
$918$	0	0
$919$	1.48727e13	0.687812	0.343906	−	0.939004i	$-0.388250\pi$
$919$	1.48727e13	0.687812	0.343906	+	0.939004i	$0.388250\pi$
$920$	1.91954e13	0.883387
$921$	−2.14745e13	−0.983454
$922$	−4.02012e13	−1.83210
$923$	−1.96021e13	−0.888988
$924$	−6.35801e12	−0.286944
$925$	2.40530e12	0.108027
$926$	−1.87384e13	−0.837497
$927$	1.26695e13	0.563509
$928$	−1.84855e13	−0.818211
$929$	3.16348e13	1.39346	0.696730	−	0.717333i	$-0.254638\pi$
$929$	3.16348e13	1.39346	0.696730	+	0.717333i	$0.254638\pi$
$930$	−6.54186e13	−2.86766
$931$	−1.06963e13	−0.466616
$932$	5.15155e12	0.223649
$933$	−5.21087e13	−2.25135
$934$	2.07832e13	0.893619
$935$	0	0
$936$	3.60480e12	0.153511
$937$	−2.25664e13	−0.956390	−0.478195	−	0.878254i	$-0.658709\pi$
$937$	−2.25664e13	−0.956390	−0.478195	+	0.878254i	$0.658709\pi$
$938$	8.72133e12	0.367849
$939$	2.67972e13	1.12485
$940$	−1.17137e13	−0.489348
$941$	2.88841e13	1.20090	0.600448	−	0.799664i	$-0.294989\pi$
$941$	2.88841e13	1.20090	0.600448	+	0.799664i	$0.294989\pi$
$942$	1.57342e13	0.651053
$943$	6.34667e13	2.61362
$944$	−1.64171e13	−0.672855
$945$	−6.41753e12	−0.261773
$946$	3.27091e13	1.32788
$947$	1.70699e13	0.689695	0.344847	−	0.938659i	$-0.387931\pi$
$947$	1.70699e13	0.689695	0.344847	+	0.938659i	$0.387931\pi$
$948$	−2.91976e13	−1.17411
$949$	1.36947e13	0.548094
$950$	1.72500e12	0.0687119
$951$	9.34416e12	0.370449
$952$	0	0
$953$	4.06332e13	1.59574	0.797872	−	0.602827i	$-0.205959\pi$
$953$	4.06332e13	1.59574	0.797872	+	0.602827i	$0.205959\pi$
$954$	−3.90180e12	−0.152509
$955$	2.42425e13	0.943109
$956$	−4.70882e12	−0.182327
$957$	2.33429e13	0.899603
$958$	−4.66342e13	−1.78879
$959$	−1.67564e13	−0.639732
$960$	2.48734e12	0.0945180
$961$	5.55991e13	2.10287
$962$	−2.12360e13	−0.799438
$963$	2.37568e13	0.890162
$964$	−2.34337e12	−0.0873966
$965$	−2.11208e13	−0.784037
$966$	−2.90601e13	−1.07374
$967$	3.75260e13	1.38011	0.690055	−	0.723757i	$-0.257586\pi$
$967$	3.75260e13	1.38011	0.690055	+	0.723757i	$0.257586\pi$
$968$	1.91961e12	0.0702705
$969$	0	0
$970$	4.07042e12	0.147627
$971$	−2.63924e13	−0.952778	−0.476389	−	0.879235i	$-0.658055\pi$
$971$	−2.63924e13	−0.952778	−0.476389	+	0.879235i	$0.658055\pi$
$972$	1.55996e13	0.560549
$973$	−7.00954e12	−0.250716
$974$	−1.82633e13	−0.650226
$975$	1.87448e12	0.0664292
$976$	−3.58398e13	−1.26427
$977$	−4.44812e13	−1.56189	−0.780947	−	0.624598i	$-0.785263\pi$
$977$	−4.44812e13	−1.56189	−0.780947	+	0.624598i	$0.785263\pi$
$978$	−6.05731e13	−2.11716
$979$	8.07839e12	0.281062
$980$	−1.45155e13	−0.502706
$981$	2.68476e13	0.925539
$982$	4.90121e13	1.68191
$983$	−3.61778e13	−1.23581	−0.617904	−	0.786254i	$-0.712018\pi$
$983$	−3.61778e13	−1.23581	−0.617904	+	0.786254i	$0.712018\pi$
$984$	−3.04815e13	−1.03647
$985$	3.82344e13	1.29417
$986$	0	0
$987$	−1.24934e13	−0.419038
$988$	−5.63122e12	−0.188017
$989$	5.52784e13	1.83727
$990$	−1.94386e13	−0.643143
$991$	1.90887e13	0.628701	0.314351	−	0.949307i	$-0.398213\pi$
$991$	1.90887e13	0.628701	0.314351	+	0.949307i	$0.398213\pi$
$992$	−5.61139e13	−1.83979
$993$	5.46195e13	1.78269
$994$	−2.61095e13	−0.848321
$995$	8.86540e11	0.0286744
$996$	−1.53970e13	−0.495757
$997$	5.48487e13	1.75808	0.879039	−	0.476749i	$-0.158185\pi$
$997$	5.48487e13	1.75808	0.879039	+	0.476749i	$0.158185\pi$
$998$	−7.06654e13	−2.25486
$999$	2.08657e13	0.662809

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.h.1.28	yes	36
17.16	even	2		289.10.a.g.1.28	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.28	✓	36	17.16	even	2
289.10.a.h.1.28	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)

\(f(q)\)	\(=\)	\(q+28.5023 q^{2} -173.222 q^{3} +300.380 q^{4} +1462.89 q^{5} -4937.21 q^{6} -2705.62 q^{7} -6031.66 q^{8} +10322.7 q^{9} +O(q^{10})\)	\(q+28.5023 q^{2} -173.222 q^{3} +300.380 q^{4} +1462.89 q^{5} -4937.21 q^{6} -2705.62 q^{7} -6031.66 q^{8} +10322.7 q^{9} +41695.6 q^{10} -45163.0 q^{11} -52032.2 q^{12} -57896.3 q^{13} -77116.3 q^{14} -253403. q^{15} -325710. q^{16} +294221. q^{18} +323804. q^{19} +439421. q^{20} +468671. q^{21} -1.28725e6 q^{22} -2.17545e6 q^{23} +1.04481e6 q^{24} +186908. q^{25} -1.65018e6 q^{26} +1.62140e6 q^{27} -812712. q^{28} +2.98380e6 q^{29} -7.22257e6 q^{30} +9.05752e6 q^{31} -6.19528e6 q^{32} +7.82320e6 q^{33} -3.95801e6 q^{35} +3.10073e6 q^{36} +1.28689e7 q^{37} +9.22914e6 q^{38} +1.00289e7 q^{39} -8.82363e6 q^{40} -2.91740e7 q^{41} +1.33582e7 q^{42} -2.54101e7 q^{43} -1.35660e7 q^{44} +1.51009e7 q^{45} -6.20053e7 q^{46} -2.66571e7 q^{47} +5.64201e7 q^{48} -3.30332e7 q^{49} +5.32729e6 q^{50} -1.73909e7 q^{52} -1.32615e7 q^{53} +4.62137e7 q^{54} -6.60682e7 q^{55} +1.63194e7 q^{56} -5.60898e7 q^{57} +8.50452e7 q^{58} +5.04039e7 q^{59} -7.61172e7 q^{60} +1.10036e8 q^{61} +2.58160e8 q^{62} -2.79293e7 q^{63} -9.81574e6 q^{64} -8.46956e7 q^{65} +2.22979e8 q^{66} -1.13093e8 q^{67} +3.76835e8 q^{69} -1.12812e8 q^{70} +3.38574e8 q^{71} -6.22631e7 q^{72} -2.36539e8 q^{73} +3.66794e8 q^{74} -3.23764e7 q^{75} +9.72640e7 q^{76} +1.22194e8 q^{77} +2.85846e8 q^{78} +5.61145e8 q^{79} -4.76477e8 q^{80} -4.84044e8 q^{81} -8.31527e8 q^{82} +2.95912e8 q^{83} +1.40779e8 q^{84} -7.24245e8 q^{86} -5.16859e8 q^{87} +2.72408e8 q^{88} -1.78872e8 q^{89} +4.30411e8 q^{90} +1.56645e8 q^{91} -6.53461e8 q^{92} -1.56896e9 q^{93} -7.59787e8 q^{94} +4.73687e8 q^{95} +1.07316e9 q^{96} +9.76224e7 q^{97} -9.41522e8 q^{98} -4.66204e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 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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