LMFDB - Embedded newform 289.10.a.g.1.19

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			1.19
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)

$f(q)$	$=$	$q-0.561663 q^{2} +191.593 q^{3} -511.685 q^{4} +819.697 q^{5} -107.611 q^{6} +1085.21 q^{7} +574.966 q^{8} +17024.9 q^{9} +O(q^{10})$	\(q-0.561663 q^{2} +191.593 q^{3} -511.685 q^{4} +819.697 q^{5} -107.611 q^{6} +1085.21 q^{7} +574.966 q^{8} +17024.9 q^{9} -460.393 q^{10} -48291.1 q^{11} -98035.2 q^{12} -107794. q^{13} -609.525 q^{14} +157048. q^{15} +261660. q^{16} -9562.26 q^{18} +872306. q^{19} -419426. q^{20} +207920. q^{21} +27123.3 q^{22} +1.91838e6 q^{23} +110159. q^{24} -1.28122e6 q^{25} +60543.9 q^{26} -509272. q^{27} -555288. q^{28} +476986. q^{29} -88208.1 q^{30} -11704.8 q^{31} -441347. q^{32} -9.25225e6 q^{33} +889547. q^{35} -8.71138e6 q^{36} -3.41910e6 q^{37} -489942. q^{38} -2.06526e7 q^{39} +471297. q^{40} +6.67947e6 q^{41} -116781. q^{42} -2.97683e7 q^{43} +2.47098e7 q^{44} +1.39553e7 q^{45} -1.07748e6 q^{46} -4.42148e7 q^{47} +5.01322e7 q^{48} -3.91759e7 q^{49} +719615. q^{50} +5.51565e7 q^{52} +4.59898e7 q^{53} +286039. q^{54} -3.95841e7 q^{55} +623961. q^{56} +1.67128e8 q^{57} -267905. q^{58} +2.34565e6 q^{59} -8.03591e7 q^{60} +1.31038e8 q^{61} +6574.13 q^{62} +1.84757e7 q^{63} -1.33722e8 q^{64} -8.83584e7 q^{65} +5.19664e6 q^{66} -1.30959e8 q^{67} +3.67548e8 q^{69} -499625. q^{70} -1.91474e8 q^{71} +9.78873e6 q^{72} -3.50083e8 q^{73} +1.92038e6 q^{74} -2.45473e8 q^{75} -4.46346e8 q^{76} -5.24062e7 q^{77} +1.15998e7 q^{78} +4.60211e8 q^{79} +2.14481e8 q^{80} -4.32674e8 q^{81} -3.75161e6 q^{82} -8.12815e8 q^{83} -1.06389e8 q^{84} +1.67198e7 q^{86} +9.13873e7 q^{87} -2.77657e7 q^{88} -6.40777e8 q^{89} -7.83815e6 q^{90} -1.16980e8 q^{91} -9.81604e8 q^{92} -2.24255e6 q^{93} +2.48338e7 q^{94} +7.15027e8 q^{95} -8.45590e7 q^{96} +2.77833e8 q^{97} +2.20037e7 q^{98} -8.22152e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−0.561663	−0.0248222	−0.0124111	−	0.999923i	$-0.503951\pi$
$2$	−0.561663	−0.0248222	−0.0124111	+	0.999923i	$0.503951\pi$
$3$	191.593	1.36563	0.682817	−	0.730590i	$-0.260755\pi$
$3$	191.593	1.36563	0.682817	+	0.730590i	$0.260755\pi$
$4$	−511.685	−0.999384
$5$	819.697	0.586527	0.293264	−	0.956032i	$-0.405259\pi$
$5$	819.697	0.586527	0.293264	+	0.956032i	$0.405259\pi$
$6$	−107.611	−0.0338981
$7$	1085.21	0.170834	0.0854170	−	0.996345i	$-0.472778\pi$
$7$	1085.21	0.170834	0.0854170	+	0.996345i	$0.472778\pi$
$8$	574.966	0.0496292
$9$	17024.9	0.864955
$10$	−460.393	−0.0145589
$11$	−48291.1	−0.994490	−0.497245	−	0.867610i	$-0.665655\pi$
$11$	−48291.1	−0.994490	−0.497245	+	0.867610i	$0.665655\pi$
$12$	−98035.2	−1.36479
$13$	−107794.	−1.04677	−0.523383	−	0.852098i	$-0.675330\pi$
$13$	−107794.	−1.04677	−0.523383	+	0.852098i	$0.675330\pi$
$14$	−609.525	−0.00424048
$15$	157048.	0.800981
$16$	261660.	0.998152
$17$	0	0
$17$	0	0
$18$	−9562.26	−0.0214701
$19$	872306.	1.53560	0.767799	−	0.640690i	$-0.221352\pi$
$19$	872306.	1.53560	0.767799	+	0.640690i	$0.221352\pi$
$20$	−419426.	−0.586166
$21$	207920.	0.233297
$22$	27123.3	0.0246854
$23$	1.91838e6	1.42942	0.714708	−	0.699423i	$-0.246559\pi$
$23$	1.91838e6	1.42942	0.714708	+	0.699423i	$0.246559\pi$
$24$	110159.	0.0677752
$25$	−1.28122e6	−0.655986
$26$	60543.9	0.0259831
$27$	−509272.	−0.184422
$28$	−555288.	−0.170729
$29$	476986.	0.125232	0.0626159	−	0.998038i	$-0.480056\pi$
$29$	476986.	0.125232	0.0626159	+	0.998038i	$0.480056\pi$
$30$	−88208.1	−0.0198821
$31$	−11704.8	−0.00227633	−0.00113817	−	0.999999i	$-0.500362\pi$
$31$	−11704.8	−0.00227633	−0.00113817	+	0.999999i	$0.500362\pi$
$32$	−441347.	−0.0744055
$33$	−9.25225e6	−1.35811
$34$	0	0
$35$	889547.	0.100199
$36$	−8.71138e6	−0.864422
$37$	−3.41910e6	−0.299919	−0.149960	−	0.988692i	$-0.547914\pi$
$37$	−3.41910e6	−0.299919	−0.149960	+	0.988692i	$0.547914\pi$
$38$	−489942.	−0.0381170
$39$	−2.06526e7	−1.42950
$40$	471297.	0.0291089
$41$	6.67947e6	0.369160	0.184580	−	0.982817i	$-0.440908\pi$
$41$	6.67947e6	0.369160	0.184580	+	0.982817i	$0.440908\pi$
$42$	−116781.	−0.00579094
$43$	−2.97683e7	−1.32784	−0.663921	−	0.747803i	$-0.731109\pi$
$43$	−2.97683e7	−1.32784	−0.663921	+	0.747803i	$0.731109\pi$
$44$	2.47098e7	0.993877
$45$	1.39553e7	0.507320
$46$	−1.07748e6	−0.0354813
$47$	−4.42148e7	−1.32168	−0.660841	−	0.750526i	$-0.729800\pi$
$47$	−4.42148e7	−1.32168	−0.660841	+	0.750526i	$0.729800\pi$
$48$	5.01322e7	1.36311
$49$	−3.91759e7	−0.970816
$50$	719615.	0.0162830
$51$	0	0
$52$	5.51565e7	1.04612
$53$	4.59898e7	0.800609	0.400304	−	0.916382i	$-0.368904\pi$
$53$	4.59898e7	0.800609	0.400304	+	0.916382i	$0.368904\pi$
$54$	286039.	0.00457777
$55$	−3.95841e7	−0.583295
$56$	623961.	0.00847835
$57$	1.67128e8	2.09707
$58$	−267905.	−0.00310853
$59$	2.34565e6	0.0252017	0.0126008	−	0.999921i	$-0.495989\pi$
$59$	2.34565e6	0.0252017	0.0126008	+	0.999921i	$0.495989\pi$
$60$	−8.03591e7	−0.800488
$61$	1.31038e8	1.21175	0.605877	−	0.795559i	$-0.292823\pi$
$61$	1.31038e8	1.21175	0.605877	+	0.795559i	$0.292823\pi$
$62$	6574.13	5.65036e−5 0
$63$	1.84757e7	0.147764
$64$	−1.33722e8	−0.996305
$65$	−8.83584e7	−0.613957
$66$	5.19664e6	0.0337113
$67$	−1.30959e8	−0.793962	−0.396981	−	0.917827i	$-0.629942\pi$
$67$	−1.30959e8	−0.793962	−0.396981	+	0.917827i	$0.629942\pi$
$68$	0	0
$69$	3.67548e8	1.95206
$70$	−499625.	−0.00248716
$71$	−1.91474e8	−0.894227	−0.447114	−	0.894477i	$-0.647548\pi$
$71$	−1.91474e8	−0.894227	−0.447114	+	0.894477i	$0.647548\pi$
$72$	9.78873e6	0.0429270
$73$	−3.50083e8	−1.44284	−0.721421	−	0.692497i	$-0.756511\pi$
$73$	−3.50083e8	−1.44284	−0.721421	+	0.692497i	$0.756511\pi$
$74$	1.92038e6	0.00744466
$75$	−2.45473e8	−0.895836
$76$	−4.46346e8	−1.53465
$77$	−5.24062e7	−0.169893
$78$	1.15998e7	0.0354833
$79$	4.60211e8	1.32934	0.664669	−	0.747138i	$-0.268573\pi$
$79$	4.60211e8	1.32934	0.664669	+	0.747138i	$0.268573\pi$
$80$	2.14481e8	0.585443
$81$	−4.32674e8	−1.11681
$82$	−3.75161e6	−0.00916337
$83$	−8.12815e8	−1.87992	−0.939962	−	0.341280i	$-0.889139\pi$
$83$	−8.12815e8	−1.87992	−0.939962	+	0.341280i	$0.889139\pi$
$84$	−1.06389e8	−0.233153
$85$	0	0
$86$	1.67198e7	0.0329600
$87$	9.13873e7	0.171021
$88$	−2.77657e7	−0.0493557
$89$	−6.40777e8	−1.08256	−0.541280	−	0.840842i	$-0.682060\pi$
$89$	−6.40777e8	−1.08256	−0.541280	+	0.840842i	$0.682060\pi$
$90$	−7.83815e6	−0.0125928
$91$	−1.16980e8	−0.178823
$92$	−9.81604e8	−1.42854
$93$	−2.24255e6	−0.00310863
$94$	2.48338e7	0.0328071
$95$	7.15027e8	0.900671
$96$	−8.45590e7	−0.101611
$97$	2.77833e8	0.318648	0.159324	−	0.987226i	$-0.449068\pi$
$97$	2.77833e8	0.318648	0.159324	+	0.987226i	$0.449068\pi$
$98$	2.20037e7	0.0240978
$99$	−8.22152e8	−0.860189
$100$	6.55582e8	0.655582
$101$	1.68691e9	1.61304	0.806522	−	0.591204i	$-0.201347\pi$
$101$	1.68691e9	1.61304	0.806522	+	0.591204i	$0.201347\pi$
$102$	0	0
$103$	2.74439e8	0.240259	0.120129	−	0.992758i	$-0.461669\pi$
$103$	2.74439e8	0.240259	0.120129	+	0.992758i	$0.461669\pi$
$104$	−6.19778e7	−0.0519501
$105$	1.70431e8	0.136835
$106$	−2.58308e7	−0.0198729
$107$	1.26641e9	0.934002	0.467001	−	0.884257i	$-0.345334\pi$
$107$	1.26641e9	0.934002	0.467001	+	0.884257i	$0.345334\pi$
$108$	2.60587e8	0.184309
$109$	−6.82388e8	−0.463033	−0.231517	−	0.972831i	$-0.574369\pi$
$109$	−6.82388e8	−0.463033	−0.231517	+	0.972831i	$0.574369\pi$
$110$	2.22329e7	0.0144787
$111$	−6.55076e8	−0.409580
$112$	2.83957e8	0.170518
$113$	−2.35663e9	−1.35968	−0.679842	−	0.733359i	$-0.737952\pi$
$113$	−2.35663e9	−1.35968	−0.679842	+	0.733359i	$0.737952\pi$
$114$	−9.38695e7	−0.0520538
$115$	1.57249e9	0.838392
$116$	−2.44067e8	−0.125155
$117$	−1.83518e9	−0.905405
$118$	−1.31747e6	−0.000625562 0
$119$	0	0
$120$	9.02973e7	0.0397520
$121$	−2.59142e7	−0.0109902
$122$	−7.35994e7	−0.0300784
$123$	1.27974e9	0.504137
$124$	5.98915e6	0.00227493
$125$	−2.65118e9	−0.971281
$126$	−1.03771e7	−0.00366782
$127$	−1.95160e9	−0.665693	−0.332846	−	0.942981i	$-0.608009\pi$
$127$	−1.95160e9	−0.665693	−0.332846	+	0.942981i	$0.608009\pi$
$128$	3.01076e8	0.0991360
$129$	−5.70340e9	−1.81334
$130$	4.96276e7	0.0152398
$131$	−3.45384e9	−1.02466	−0.512331	−	0.858788i	$-0.671218\pi$
$131$	−3.45384e9	−1.02466	−0.512331	+	0.858788i	$0.671218\pi$
$132$	4.73423e9	1.35727
$133$	9.46639e8	0.262333
$134$	7.35550e7	0.0197079
$135$	−4.17449e8	−0.108169
$136$	0	0
$137$	−6.90720e9	−1.67517	−0.837586	−	0.546306i	$-0.816034\pi$
$137$	−6.90720e9	−1.67517	−0.837586	+	0.546306i	$0.816034\pi$
$138$	−2.06438e8	−0.0484544
$139$	4.01418e9	0.912075	0.456038	−	0.889960i	$-0.349268\pi$
$139$	4.01418e9	0.912075	0.456038	+	0.889960i	$0.349268\pi$
$140$	−4.55167e8	−0.100137
$141$	−8.47124e9	−1.80493
$142$	1.07544e8	0.0221967
$143$	5.20549e9	1.04100
$144$	4.45473e9	0.863356
$145$	3.90984e8	0.0734519
$146$	1.96629e8	0.0358145
$147$	−7.50583e9	−1.32578
$148$	1.74950e9	0.299734
$149$	6.40738e9	1.06498	0.532491	−	0.846436i	$-0.321256\pi$
$149$	6.40738e9	1.06498	0.532491	+	0.846436i	$0.321256\pi$
$150$	1.37873e8	0.0222366
$151$	1.00847e10	1.57858	0.789291	−	0.614019i	$-0.210448\pi$
$151$	1.00847e10	1.57858	0.789291	+	0.614019i	$0.210448\pi$
$152$	5.01546e8	0.0762105
$153$	0	0
$154$	2.94346e7	0.00421712
$155$	−9.59436e6	−0.00133513
$156$	1.05676e10	1.42862
$157$	−1.00244e10	−1.31677	−0.658384	−	0.752682i	$-0.728760\pi$
$157$	−1.00244e10	−1.31677	−0.658384	+	0.752682i	$0.728760\pi$
$158$	−2.58483e8	−0.0329971
$159$	8.81133e9	1.09334
$160$	−3.61771e8	−0.0436409
$161$	2.08185e9	0.244193
$162$	2.43017e8	0.0277217
$163$	−1.21030e10	−1.34292	−0.671458	−	0.741042i	$-0.734332\pi$
$163$	−1.21030e10	−1.34292	−0.671458	+	0.741042i	$0.734332\pi$
$164$	−3.41778e9	−0.368933
$165$	−7.58404e9	−0.796568
$166$	4.56528e8	0.0466639
$167$	1.68715e10	1.67853	0.839265	−	0.543723i	$-0.182986\pi$
$167$	1.68715e10	1.67853	0.839265	+	0.543723i	$0.182986\pi$
$168$	1.19547e8	0.0115783
$169$	1.01505e9	0.0957185
$170$	0	0
$171$	1.48509e10	1.32822
$172$	1.52320e10	1.32702
$173$	5.48179e9	0.465280	0.232640	−	0.972563i	$-0.425264\pi$
$173$	5.48179e9	0.465280	0.232640	+	0.972563i	$0.425264\pi$
$174$	−5.13288e7	−0.00424512
$175$	−1.39040e9	−0.112065
$176$	−1.26358e10	−0.992652
$177$	4.49411e8	0.0344163
$178$	3.59901e8	0.0268715
$179$	−2.39604e10	−1.74443	−0.872217	−	0.489118i	$-0.837319\pi$
$179$	−2.39604e10	−1.74443	−0.872217	+	0.489118i	$0.837319\pi$
$180$	−7.14069e9	−0.507007
$181$	−1.12778e10	−0.781037	−0.390518	−	0.920595i	$-0.627704\pi$
$181$	−1.12778e10	−0.781037	−0.390518	+	0.920595i	$0.627704\pi$
$182$	6.57031e7	0.00443879
$183$	2.51060e10	1.65481
$184$	1.10300e9	0.0709407
$185$	−2.80263e9	−0.175911
$186$	1.25956e6	7.71632e−5 0
$187$	0	0
$188$	2.26240e10	1.32087
$189$	−5.52670e8	−0.0315056
$190$	−4.01604e8	−0.0223566
$191$	−2.75406e10	−1.49735	−0.748674	−	0.662939i	$-0.769309\pi$
$191$	−2.75406e10	−1.49735	−0.748674	+	0.662939i	$0.769309\pi$
$192$	−2.56202e10	−1.36059
$193$	−4.05941e9	−0.210598	−0.105299	−	0.994441i	$-0.533580\pi$
$193$	−4.05941e9	−0.210598	−0.105299	+	0.994441i	$0.533580\pi$
$194$	−1.56049e8	−0.00790956
$195$	−1.69289e10	−0.838440
$196$	2.00457e10	0.970218
$197$	1.28333e10	0.607071	0.303536	−	0.952820i	$-0.401833\pi$
$197$	1.28333e10	0.607071	0.303536	+	0.952820i	$0.401833\pi$
$198$	4.61772e8	0.0213518
$199$	3.32562e9	0.150326	0.0751629	−	0.997171i	$-0.476052\pi$
$199$	3.32562e9	0.150326	0.0751629	+	0.997171i	$0.476052\pi$
$200$	−7.36659e8	−0.0325560
$201$	−2.50909e10	−1.08426
$202$	−9.47476e8	−0.0400393
$203$	5.17633e8	0.0213939
$204$	0	0
$205$	5.47514e9	0.216522
$206$	−1.54142e8	−0.00596375
$207$	3.26602e10	1.23638
$208$	−2.82053e10	−1.04483
$209$	−4.21247e10	−1.52714
$210$	−9.57248e7	−0.00339655
$211$	−5.54278e10	−1.92511	−0.962557	−	0.271078i	$-0.912620\pi$
$211$	−5.54278e10	−1.92511	−0.962557	+	0.271078i	$0.912620\pi$
$212$	−2.35323e10	−0.800116
$213$	−3.66851e10	−1.22119
$214$	−7.11296e8	−0.0231840
$215$	−2.44010e10	−0.778815
$216$	−2.92814e8	−0.00915272
$217$	−1.27022e7	−0.000388875 0
$218$	3.83272e8	0.0114935
$219$	−6.70736e10	−1.97039
$220$	2.02546e10	0.582936
$221$	0	0
$222$	3.67932e8	0.0101667
$223$	3.94370e9	0.106790	0.0533951	−	0.998573i	$-0.482996\pi$
$223$	3.94370e9	0.106790	0.0533951	+	0.998573i	$0.482996\pi$
$224$	−4.78956e8	−0.0127110
$225$	−2.18127e10	−0.567398
$226$	1.32363e9	0.0337504
$227$	7.53067e10	1.88242	0.941212	−	0.337817i	$-0.109689\pi$
$227$	7.53067e10	1.88242	0.941212	+	0.337817i	$0.109689\pi$
$228$	−8.55167e10	−2.09577
$229$	−4.18732e10	−1.00618	−0.503091	−	0.864234i	$-0.667804\pi$
$229$	−4.18732e10	−1.00618	−0.503091	+	0.864234i	$0.667804\pi$
$230$	−8.83208e8	−0.0208107
$231$	−1.00407e10	−0.232011
$232$	2.74251e8	0.00621515
$233$	7.83446e9	0.174144	0.0870718	−	0.996202i	$-0.472249\pi$
$233$	7.83446e9	0.174144	0.0870718	+	0.996202i	$0.472249\pi$
$234$	1.03075e9	0.0224742
$235$	−3.62427e10	−0.775202
$236$	−1.20023e9	−0.0251862
$237$	8.81733e10	1.81539
$238$	0	0
$239$	1.99505e10	0.395516	0.197758	−	0.980251i	$-0.436634\pi$
$239$	1.99505e10	0.395516	0.197758	+	0.980251i	$0.436634\pi$
$240$	4.10932e10	0.799501
$241$	−9.79058e9	−0.186953	−0.0934763	−	0.995622i	$-0.529798\pi$
$241$	−9.79058e9	−0.186953	−0.0934763	+	0.995622i	$0.529798\pi$
$242$	1.45550e7	0.000272800 0
$243$	−7.28734e10	−1.34073
$244$	−6.70503e10	−1.21101
$245$	−3.21124e10	−0.569410
$246$	−7.18783e8	−0.0125138
$247$	−9.40294e10	−1.60741
$248$	−6.72984e6	−0.000112972 0
$249$	−1.55730e11	−2.56729
$250$	1.48907e9	0.0241093
$251$	4.99029e10	0.793587	0.396793	−	0.917908i	$-0.370123\pi$
$251$	4.99029e10	0.793587	0.396793	+	0.917908i	$0.370123\pi$
$252$	−9.45372e9	−0.147673
$253$	−9.26406e10	−1.42154
$254$	1.09614e9	0.0165240
$255$	0	0
$256$	6.82965e10	0.993844
$257$	−4.15019e10	−0.593429	−0.296715	−	0.954966i	$-0.595891\pi$
$257$	−4.15019e10	−0.593429	−0.296715	+	0.954966i	$0.595891\pi$
$258$	3.20339e9	0.0450112
$259$	−3.71046e9	−0.0512364
$260$	4.52116e10	0.613578
$261$	8.12065e9	0.108320
$262$	1.93989e9	0.0254344
$263$	−4.28114e10	−0.551770	−0.275885	−	0.961191i	$-0.588971\pi$
$263$	−4.28114e10	−0.551770	−0.275885	+	0.961191i	$0.588971\pi$
$264$	−5.31972e9	−0.0674018
$265$	3.76977e10	0.469579
$266$	−5.31692e8	−0.00651168
$267$	−1.22768e11	−1.47838
$268$	6.70098e10	0.793473
$269$	−9.09356e9	−0.105889	−0.0529443	−	0.998597i	$-0.516861\pi$
$269$	−9.09356e9	−0.105889	−0.0529443	+	0.998597i	$0.516861\pi$
$270$	2.34466e8	0.00268499
$271$	−6.01033e10	−0.676919	−0.338459	−	0.940981i	$-0.609906\pi$
$271$	−6.01033e10	−0.676919	−0.338459	+	0.940981i	$0.609906\pi$
$272$	0	0
$273$	−2.24125e10	−0.244207
$274$	3.87951e9	0.0415815
$275$	6.18717e10	0.652371
$276$	−1.88069e11	−1.95086
$277$	−1.16062e11	−1.18449	−0.592245	−	0.805758i	$-0.701758\pi$
$277$	−1.16062e11	−1.18449	−0.592245	+	0.805758i	$0.701758\pi$
$278$	−2.25462e9	−0.0226397
$279$	−1.99273e8	−0.00196892
$280$	5.11459e8	0.00497278
$281$	−1.64638e10	−0.157526	−0.0787628	−	0.996893i	$-0.525097\pi$
$281$	−1.64638e10	−0.157526	−0.0787628	+	0.996893i	$0.525097\pi$
$282$	4.75798e9	0.0448024
$283$	−2.94955e10	−0.273349	−0.136674	−	0.990616i	$-0.543641\pi$
$283$	−2.94955e10	−0.273349	−0.136674	+	0.990616i	$0.543641\pi$
$284$	9.79744e10	0.893676
$285$	1.36994e11	1.22999
$286$	−2.92373e9	−0.0258399
$287$	7.24866e9	0.0630651
$288$	−7.51389e9	−0.0643574
$289$	0	0
$290$	−2.19601e8	−0.00182324
$291$	5.32310e10	0.435157
$292$	1.79132e11	1.44195
$293$	6.57753e10	0.521385	0.260693	−	0.965422i	$-0.416049\pi$
$293$	6.57753e10	0.521385	0.260693	+	0.965422i	$0.416049\pi$
$294$	4.21575e9	0.0329088
$295$	1.92272e9	0.0147815
$296$	−1.96587e9	−0.0148847
$297$	2.45933e10	0.183406
$298$	−3.59878e9	−0.0264352
$299$	−2.06790e11	−1.49626
$300$	1.25605e11	0.895284
$301$	−3.23050e10	−0.226841
$302$	−5.66421e9	−0.0391839
$303$	3.23201e11	2.20283
$304$	2.28247e11	1.53276
$305$	1.07412e11	0.710726
$306$	0	0
$307$	−1.32282e11	−0.849922	−0.424961	−	0.905212i	$-0.639712\pi$
$307$	−1.32282e11	−0.849922	−0.424961	+	0.905212i	$0.639712\pi$
$308$	2.68155e10	0.169788
$309$	5.25807e10	0.328105
$310$	5.38880e6	3.31409e−5 0
$311$	−1.82289e11	−1.10494	−0.552469	−	0.833533i	$-0.686314\pi$
$311$	−1.82289e11	−1.10494	−0.552469	+	0.833533i	$0.686314\pi$
$312$	−1.18745e10	−0.0709448
$313$	2.01875e11	1.18887	0.594433	−	0.804145i	$-0.297377\pi$
$313$	2.01875e11	1.18887	0.594433	+	0.804145i	$0.297377\pi$
$314$	5.63032e9	0.0326851
$315$	1.51445e10	0.0866675
$316$	−2.35483e11	−1.32852
$317$	−2.34059e11	−1.30184	−0.650922	−	0.759145i	$-0.725618\pi$
$317$	−2.34059e11	−1.30184	−0.650922	+	0.759145i	$0.725618\pi$
$318$	−4.94900e9	−0.0271391
$319$	−2.30342e10	−0.124542
$320$	−1.09611e11	−0.584360
$321$	2.42636e11	1.27550
$322$	−1.16930e9	−0.00606141
$323$	0	0
$324$	2.21393e11	1.11612
$325$	1.38108e11	0.686663
$326$	6.79781e9	0.0333342
$327$	−1.30741e11	−0.632334
$328$	3.84047e9	0.0183211
$329$	−4.79825e10	−0.225788
$330$	4.25967e9	0.0197726
$331$	3.53670e11	1.61947	0.809733	−	0.586799i	$-0.199612\pi$
$331$	3.53670e11	1.61947	0.809733	+	0.586799i	$0.199612\pi$
$332$	4.15905e11	1.87876
$333$	−5.82099e10	−0.259417
$334$	−9.47608e9	−0.0416648
$335$	−1.07347e11	−0.465680
$336$	5.44042e10	0.232866
$337$	−1.79455e10	−0.0757918	−0.0378959	−	0.999282i	$-0.512066\pi$
$337$	−1.79455e10	−0.0757918	−0.0378959	+	0.999282i	$0.512066\pi$
$338$	−5.70114e8	−0.00237595
$339$	−4.51513e11	−1.85683
$340$	0	0
$341$	5.65237e8	0.00226379
$342$	−8.34122e9	−0.0329695
$343$	−8.63066e10	−0.336682
$344$	−1.71158e10	−0.0658996
$345$	3.01278e11	1.14494
$346$	−3.07892e9	−0.0115493
$347$	2.92641e11	1.08356	0.541780	−	0.840520i	$-0.317751\pi$
$347$	2.92641e11	1.08356	0.541780	+	0.840520i	$0.317751\pi$
$348$	−4.67615e10	−0.170915
$349$	−3.69601e11	−1.33358	−0.666790	−	0.745245i	$-0.732332\pi$
$349$	−3.69601e11	−1.33358	−0.666790	+	0.745245i	$0.732332\pi$
$350$	7.80937e8	0.00278170
$351$	5.48965e10	0.193047
$352$	2.13131e10	0.0739955
$353$	2.48893e11	0.853151	0.426575	−	0.904452i	$-0.359720\pi$
$353$	2.48893e11	0.853151	0.426575	+	0.904452i	$0.359720\pi$
$354$	−2.52417e8	−0.000854289 0
$355$	−1.56951e11	−0.524489
$356$	3.27876e11	1.08189
$357$	0	0
$358$	1.34576e10	0.0433007
$359$	−1.11262e11	−0.353525	−0.176763	−	0.984254i	$-0.556562\pi$
$359$	−1.11262e11	−0.353525	−0.176763	+	0.984254i	$0.556562\pi$
$360$	8.02379e9	0.0251778
$361$	4.38230e11	1.35806
$362$	6.33433e9	0.0193871
$363$	−4.96498e9	−0.0150085
$364$	5.98567e10	0.178713
$365$	−2.86962e11	−0.846266
$366$	−1.41011e10	−0.0410761
$367$	4.78209e11	1.37601	0.688004	−	0.725707i	$-0.258487\pi$
$367$	4.78209e11	1.37601	0.688004	+	0.725707i	$0.258487\pi$
$368$	5.01962e11	1.42677
$369$	1.13717e11	0.319307
$370$	1.57413e9	0.00436650
$371$	4.99088e10	0.136771
$372$	1.14748e9	0.00310672
$373$	−2.01183e9	−0.00538147	−0.00269073	−	0.999996i	$-0.500856\pi$
$373$	−2.01183e9	−0.00538147	−0.00269073	+	0.999996i	$0.500856\pi$
$374$	0	0
$375$	−5.07948e11	−1.32641
$376$	−2.54220e10	−0.0655939
$377$	−5.14163e10	−0.131088
$378$	3.10414e8	0.000782039 0
$379$	2.36032e11	0.587617	0.293809	−	0.955864i	$-0.405077\pi$
$379$	2.36032e11	0.587617	0.293809	+	0.955864i	$0.405077\pi$
$380$	−3.65868e11	−0.900116
$381$	−3.73913e11	−0.909092
$382$	1.54685e10	0.0371675
$383$	2.18959e11	0.519959	0.259979	−	0.965614i	$-0.416284\pi$
$383$	2.18959e11	0.519959	0.259979	+	0.965614i	$0.416284\pi$
$384$	5.76841e10	0.135383
$385$	−4.29572e10	−0.0996467
$386$	2.28002e9	0.00522752
$387$	−5.06803e11	−1.14852
$388$	−1.42163e11	−0.318452
$389$	−3.26424e11	−0.722785	−0.361393	−	0.932414i	$-0.617699\pi$
$389$	−3.26424e11	−0.722785	−0.361393	+	0.932414i	$0.617699\pi$
$390$	9.50831e9	0.0208119
$391$	0	0
$392$	−2.25248e10	−0.0481808
$393$	−6.61731e11	−1.39931
$394$	−7.20797e9	−0.0150689
$395$	3.77234e11	0.779693
$396$	4.20682e11	0.859659
$397$	5.53429e11	1.11816	0.559081	−	0.829113i	$-0.311154\pi$
$397$	5.53429e11	1.11816	0.559081	+	0.829113i	$0.311154\pi$
$398$	−1.86788e9	−0.00373142
$399$	1.81370e11	0.358250
$400$	−3.35244e11	−0.654773
$401$	6.02853e11	1.16429	0.582146	−	0.813084i	$-0.302213\pi$
$401$	6.02853e11	1.16429	0.582146	+	0.813084i	$0.302213\pi$
$402$	1.40926e10	0.0269138
$403$	1.26170e9	0.00238278
$404$	−8.63167e11	−1.61205
$405$	−3.54662e11	−0.655038
$406$	−2.90735e8	−0.000531044 0
$407$	1.65112e11	0.298267
$408$	0	0
$409$	−4.44389e11	−0.785251	−0.392626	−	0.919698i	$-0.628433\pi$
$409$	−4.44389e11	−0.785251	−0.392626	+	0.919698i	$0.628433\pi$
$410$	−3.07518e9	−0.00537457
$411$	−1.32337e12	−2.28767
$412$	−1.40426e11	−0.240110
$413$	2.54554e9	0.00430531
$414$	−1.83440e10	−0.0306897
$415$	−6.66262e11	−1.10263
$416$	4.75745e10	0.0778851
$417$	7.69090e11	1.24556
$418$	2.36599e10	0.0379069
$419$	4.80215e10	0.0761154	0.0380577	−	0.999276i	$-0.487883\pi$
$419$	4.80215e10	0.0761154	0.0380577	+	0.999276i	$0.487883\pi$
$420$	−8.72069e10	−0.136751
$421$	−1.06241e12	−1.64825	−0.824125	−	0.566408i	$-0.808333\pi$
$421$	−1.06241e12	−1.64825	−0.824125	+	0.566408i	$0.808333\pi$
$422$	3.11317e10	0.0477856
$423$	−7.52752e11	−1.14320
$424$	2.64426e10	0.0397335
$425$	0	0
$426$	2.06047e10	0.0303126
$427$	1.42205e11	0.207009
$428$	−6.48003e11	−0.933426
$429$	9.97337e11	1.42162
$430$	1.37051e10	0.0193319
$431$	4.85426e11	0.677603	0.338802	−	0.940858i	$-0.389978\pi$
$431$	4.85426e11	0.677603	0.338802	+	0.940858i	$0.389978\pi$
$432$	−1.33256e11	−0.184081
$433$	−4.47519e11	−0.611809	−0.305905	−	0.952062i	$-0.598959\pi$
$433$	−4.47519e11	−0.611809	−0.305905	+	0.952062i	$0.598959\pi$
$434$	7.13435e6	9.65274e−6 0
$435$	7.49099e10	0.100308
$436$	3.49167e11	0.462748
$437$	1.67341e12	2.19501
$438$	3.76727e10	0.0489095
$439$	−1.06264e12	−1.36551	−0.682756	−	0.730646i	$-0.739219\pi$
$439$	−1.06264e12	−1.36551	−0.682756	+	0.730646i	$0.739219\pi$
$440$	−2.27595e10	−0.0289485
$441$	−6.66966e11	−0.839712
$442$	0	0
$443$	9.71271e11	1.19818	0.599092	−	0.800680i	$-0.295528\pi$
$443$	9.71271e11	1.19818	0.599092	+	0.800680i	$0.295528\pi$
$444$	3.35192e11	0.409327
$445$	−5.25243e11	−0.634951
$446$	−2.21503e9	−0.00265077
$447$	1.22761e12	1.45437
$448$	−1.45117e11	−0.170203
$449$	1.32225e12	1.53535	0.767673	−	0.640842i	$-0.221415\pi$
$449$	1.32225e12	1.53535	0.767673	+	0.640842i	$0.221415\pi$
$450$	1.22514e10	0.0140841
$451$	−3.22559e11	−0.367126
$452$	1.20585e12	1.35885
$453$	1.93216e12	2.15576
$454$	−4.22970e10	−0.0467259
$455$	−9.58878e10	−0.104885
$456$	9.60927e10	0.104076
$457$	6.63489e11	0.711559	0.355780	−	0.934570i	$-0.384215\pi$
$457$	6.63489e11	0.711559	0.355780	+	0.934570i	$0.384215\pi$
$458$	2.35186e10	0.0249756
$459$	0	0
$460$	−8.04618e11	−0.837875
$461$	−5.21820e11	−0.538105	−0.269052	−	0.963126i	$-0.586710\pi$
$461$	−5.21820e11	−0.538105	−0.269052	+	0.963126i	$0.586710\pi$
$462$	5.63947e9	0.00575903
$463$	7.05702e11	0.713686	0.356843	−	0.934164i	$-0.383853\pi$
$463$	7.05702e11	0.713686	0.356843	+	0.934164i	$0.383853\pi$
$464$	1.24808e11	0.125000
$465$	−1.83821e9	−0.00182330
$466$	−4.40033e9	−0.00432263
$467$	−4.78900e10	−0.0465928	−0.0232964	−	0.999729i	$-0.507416\pi$
$467$	−4.78900e10	−0.0465928	−0.0232964	+	0.999729i	$0.507416\pi$
$468$	9.39035e11	0.904847
$469$	−1.42119e11	−0.135636
$470$	2.03562e10	0.0192422
$471$	−1.92060e12	−1.79822
$472$	1.34867e9	0.00125074
$473$	1.43755e12	1.32052
$474$	−4.95236e10	−0.0450620
$475$	−1.11762e12	−1.00733
$476$	0	0
$477$	7.82973e11	0.692490
$478$	−1.12055e10	−0.00981758
$479$	1.02694e12	0.891325	0.445662	−	0.895201i	$-0.352968\pi$
$479$	1.02694e12	0.891325	0.445662	+	0.895201i	$0.352968\pi$
$480$	−6.93127e10	−0.0595974
$481$	3.68559e11	0.313945
$482$	5.49900e9	0.00464058
$483$	3.98868e11	0.333478
$484$	1.32599e10	0.0109834
$485$	2.27739e11	0.186896
$486$	4.09303e10	0.0332799
$487$	1.58420e12	1.27623	0.638117	−	0.769939i	$-0.279713\pi$
$487$	1.58420e12	1.27623	0.638117	+	0.769939i	$0.279713\pi$
$488$	7.53425e10	0.0601383
$489$	−2.31885e12	−1.83393
$490$	1.80363e10	0.0141340
$491$	1.84598e12	1.43338	0.716689	−	0.697393i	$-0.245657\pi$
$491$	1.84598e12	1.43338	0.716689	+	0.697393i	$0.245657\pi$
$492$	−6.54823e11	−0.503827
$493$	0	0
$494$	5.28128e10	0.0398995
$495$	−6.73915e11	−0.504524
$496$	−3.06267e9	−0.00227212
$497$	−2.07791e11	−0.152764
$498$	8.74675e10	0.0637257
$499$	−2.56834e12	−1.85438	−0.927192	−	0.374587i	$-0.877784\pi$
$499$	−2.56834e12	−1.85438	−0.927192	+	0.374587i	$0.877784\pi$
$500$	1.35657e12	0.970682
$501$	3.23246e12	2.29226
$502$	−2.80286e10	−0.0196986
$503$	2.19698e11	0.153028	0.0765139	−	0.997069i	$-0.475621\pi$
$503$	2.19698e11	0.153028	0.0765139	+	0.997069i	$0.475621\pi$
$504$	1.06229e10	0.00733339
$505$	1.38276e12	0.946094
$506$	5.20328e10	0.0352858
$507$	1.94476e11	0.130716
$508$	9.98603e11	0.665282
$509$	1.18957e12	0.785523	0.392762	−	0.919640i	$-0.371520\pi$
$509$	1.18957e12	0.785523	0.392762	+	0.919640i	$0.371520\pi$
$510$	0	0
$511$	−3.79916e11	−0.246486
$512$	−1.92511e11	−0.123805
$513$	−4.44241e11	−0.283198
$514$	2.33101e10	0.0147302
$515$	2.24957e11	0.140918
$516$	2.91834e12	1.81223
$517$	2.13518e12	1.31440
$518$	2.08403e9	0.00127180
$519$	1.05027e12	0.635403
$520$	−5.08030e10	−0.0304701
$521$	−1.42213e12	−0.845611	−0.422805	−	0.906221i	$-0.638955\pi$
$521$	−1.42213e12	−0.845611	−0.422805	+	0.906221i	$0.638955\pi$
$522$	−4.56107e9	−0.00268874
$523$	1.87654e12	1.09673	0.548365	−	0.836239i	$-0.315250\pi$
$523$	1.87654e12	1.09673	0.548365	+	0.836239i	$0.315250\pi$
$524$	1.76727e12	1.02403
$525$	−2.66391e11	−0.153039
$526$	2.40456e10	0.0136962
$527$	0	0
$528$	−2.42094e12	−1.35560
$529$	1.87902e12	1.04323
$530$	−2.11734e10	−0.0116560
$531$	3.99345e10	0.0217983
$532$	−4.84381e11	−0.262171
$533$	−7.20007e11	−0.386424
$534$	6.89545e10	0.0366967
$535$	1.03807e12	0.547818
$536$	−7.52971e10	−0.0394037
$537$	−4.59064e12	−2.38226
$538$	5.10752e9	0.00262839
$539$	1.89185e12	0.965466
$540$	2.13602e11	0.108102
$541$	−1.39571e11	−0.0700501	−0.0350251	−	0.999386i	$-0.511151\pi$
$541$	−1.39571e11	−0.0700501	−0.0350251	+	0.999386i	$0.511151\pi$
$542$	3.37578e10	0.0168026
$543$	−2.16075e12	−1.06661
$544$	0	0
$545$	−5.59351e11	−0.271582
$546$	1.25883e10	0.00606176
$547$	−2.15413e12	−1.02879	−0.514396	−	0.857552i	$-0.671984\pi$
$547$	−2.15413e12	−1.02879	−0.514396	+	0.857552i	$0.671984\pi$
$548$	3.53431e12	1.67414
$549$	2.23092e12	1.04811
$550$	−3.47510e10	−0.0161933
$551$	4.16078e11	0.192306
$552$	2.11327e11	0.0968790
$553$	4.99428e11	0.227096
$554$	6.51877e10	0.0294017
$555$	−5.36964e11	−0.240230
$556$	−2.05400e12	−0.911513
$557$	2.19665e12	0.966967	0.483484	−	0.875353i	$-0.339371\pi$
$557$	2.19665e12	0.966967	0.483484	+	0.875353i	$0.339371\pi$
$558$	1.11924e8	4.88731e−5 0
$559$	3.20885e12	1.38994
$560$	2.32758e11	0.100014
$561$	0	0
$562$	9.24709e9	0.00391013
$563$	−2.37997e12	−0.998351	−0.499176	−	0.866501i	$-0.666364\pi$
$563$	−2.37997e12	−0.998351	−0.499176	+	0.866501i	$0.666364\pi$
$564$	4.33460e12	1.80382
$565$	−1.93172e12	−0.797492
$566$	1.65665e10	0.00678512
$567$	−4.69544e11	−0.190789
$568$	−1.10091e11	−0.0443797
$569$	−3.68803e12	−1.47499	−0.737496	−	0.675351i	$-0.763992\pi$
$569$	−3.68803e12	−1.47499	−0.737496	+	0.675351i	$0.763992\pi$
$570$	−7.69445e10	−0.0305310
$571$	−1.37282e11	−0.0540446	−0.0270223	−	0.999635i	$-0.508603\pi$
$571$	−1.37282e11	−0.0540446	−0.0270223	+	0.999635i	$0.508603\pi$
$572$	−2.66357e12	−1.04036
$573$	−5.27658e12	−2.04483
$574$	−4.07130e9	−0.00156542
$575$	−2.45787e12	−0.937677
$576$	−2.27660e12	−0.861759
$577$	1.13535e12	0.426421	0.213211	−	0.977006i	$-0.431608\pi$
$577$	1.13535e12	0.426421	0.213211	+	0.977006i	$0.431608\pi$
$578$	0	0
$579$	−7.77755e11	−0.287600
$580$	−2.00061e11	−0.0734067
$581$	−8.82078e11	−0.321155
$582$	−2.98978e10	−0.0108016
$583$	−2.22090e12	−0.796197
$584$	−2.01286e11	−0.0716070
$585$	−1.50429e12	−0.531045
$586$	−3.69436e10	−0.0129419
$587$	1.87198e12	0.650775	0.325387	−	0.945581i	$-0.394505\pi$
$587$	1.87198e12	0.650775	0.325387	+	0.945581i	$0.394505\pi$
$588$	3.84062e12	1.32496
$589$	−1.02101e10	−0.00349553
$590$	−1.07992e9	−0.000366909 0
$591$	2.45877e12	0.829037
$592$	−8.94641e11	−0.299365
$593$	−1.38472e12	−0.459849	−0.229924	−	0.973208i	$-0.573848\pi$
$593$	−1.38472e12	−0.459849	−0.229924	+	0.973208i	$0.573848\pi$
$594$	−1.38132e10	−0.00455254
$595$	0	0
$596$	−3.27855e12	−1.06433
$597$	6.37165e11	0.205290
$598$	1.16146e11	0.0371406
$599$	1.12797e12	0.357994	0.178997	−	0.983850i	$-0.442715\pi$
$599$	1.12797e12	0.357994	0.178997	+	0.983850i	$0.442715\pi$
$600$	−1.41139e11	−0.0444596
$601$	−1.59905e12	−0.499950	−0.249975	−	0.968252i	$-0.580422\pi$
$601$	−1.59905e12	−0.499950	−0.249975	+	0.968252i	$0.580422\pi$
$602$	1.81445e10	0.00563069
$603$	−2.22957e12	−0.686741
$604$	−5.16019e12	−1.57761
$605$	−2.12418e10	−0.00644603
$606$	−1.81530e11	−0.0546791
$607$	6.28574e12	1.87935	0.939675	−	0.342070i	$-0.111128\pi$
$607$	6.28574e12	1.87935	0.939675	+	0.342070i	$0.111128\pi$
$608$	−3.84990e11	−0.114257
$609$	9.91748e10	0.0292162
$610$	−6.03292e10	−0.0176418
$611$	4.76609e12	1.38349
$612$	0	0
$613$	4.11174e12	1.17612	0.588062	−	0.808816i	$-0.299891\pi$
$613$	4.11174e12	1.17612	0.588062	+	0.808816i	$0.299891\pi$
$614$	7.42980e10	0.0210969
$615$	1.04900e12	0.295690
$616$	−3.01318e10	−0.00843163
$617$	−1.45708e12	−0.404763	−0.202382	−	0.979307i	$-0.564868\pi$
$617$	−1.45708e12	−0.404763	−0.202382	+	0.979307i	$0.564868\pi$
$618$	−2.95326e10	−0.00814430
$619$	−5.12989e12	−1.40443	−0.702215	−	0.711965i	$-0.747805\pi$
$619$	−5.12989e12	−1.40443	−0.702215	+	0.711965i	$0.747805\pi$
$620$	4.90929e9	0.00133431
$621$	−9.76977e11	−0.263616
$622$	1.02385e11	0.0274270
$623$	−6.95381e11	−0.184938
$624$	−5.40395e12	−1.42686
$625$	3.29220e11	0.0863031
$626$	−1.13386e11	−0.0295103
$627$	−8.07079e12	−2.08551
$628$	5.12932e12	1.31596
$629$	0	0
$630$	−8.50608e9	−0.00215128
$631$	2.41230e12	0.605758	0.302879	−	0.953029i	$-0.402052\pi$
$631$	2.41230e12	0.605758	0.302879	+	0.953029i	$0.402052\pi$
$632$	2.64606e11	0.0659739
$633$	−1.06196e13	−2.62900
$634$	1.31462e11	0.0323147
$635$	−1.59972e12	−0.390447
$636$	−4.50862e12	−1.09266
$637$	4.22293e12	1.01622
$638$	1.29375e10	0.00309141
$639$	−3.25983e12	−0.773466
$640$	2.46791e11	0.0581460
$641$	7.11788e12	1.66529	0.832644	−	0.553808i	$-0.186826\pi$
$641$	7.11788e12	1.66529	0.832644	+	0.553808i	$0.186826\pi$
$642$	−1.36279e11	−0.0316608
$643$	−1.35629e12	−0.312898	−0.156449	−	0.987686i	$-0.550005\pi$
$643$	−1.35629e12	−0.312898	−0.156449	+	0.987686i	$0.550005\pi$
$644$	−1.06525e12	−0.244043
$645$	−4.67506e12	−1.06358
$646$	0	0
$647$	6.77234e12	1.51939	0.759696	−	0.650279i	$-0.225348\pi$
$647$	6.77234e12	1.51939	0.759696	+	0.650279i	$0.225348\pi$
$648$	−2.48773e11	−0.0554262
$649$	−1.13274e11	−0.0250628
$650$	−7.75702e10	−0.0170445
$651$	−2.43365e9	−0.000531060 0
$652$	6.19292e12	1.34209
$653$	−3.75856e12	−0.808932	−0.404466	−	0.914553i	$-0.632543\pi$
$653$	−3.75856e12	−0.808932	−0.404466	+	0.914553i	$0.632543\pi$
$654$	7.34323e10	0.0156959
$655$	−2.83110e12	−0.600993
$656$	1.74775e12	0.368478
$657$	−5.96014e12	−1.24799
$658$	2.69500e10	0.00560457
$659$	−5.81223e11	−0.120049	−0.0600245	−	0.998197i	$-0.519118\pi$
$659$	−5.81223e11	−0.120049	−0.0600245	+	0.998197i	$0.519118\pi$
$660$	3.88063e12	0.796077
$661$	2.62625e11	0.0535093	0.0267547	−	0.999642i	$-0.491483\pi$
$661$	2.62625e11	0.0535093	0.0267547	+	0.999642i	$0.491483\pi$
$662$	−1.98643e11	−0.0401987
$663$	0	0
$664$	−4.67340e11	−0.0932990
$665$	7.75957e11	0.153865
$666$	3.26943e10	0.00643930
$667$	9.15040e11	0.179009
$668$	−8.63287e12	−1.67750
$669$	7.55585e11	0.145836
$670$	6.02928e10	0.0115592
$671$	−6.32799e12	−1.20508
$672$	−9.17647e10	−0.0173586
$673$	−1.29413e11	−0.0243171	−0.0121585	−	0.999926i	$-0.503870\pi$
$673$	−1.29413e11	−0.0243171	−0.0121585	+	0.999926i	$0.503870\pi$
$674$	1.00793e10	0.00188132
$675$	6.52491e11	0.120978
$676$	−5.19384e11	−0.0956595
$677$	−7.30256e12	−1.33606	−0.668030	−	0.744134i	$-0.732862\pi$
$677$	−7.30256e12	−1.33606	−0.668030	+	0.744134i	$0.732862\pi$
$678$	2.53598e11	0.0460906
$679$	3.01509e11	0.0544360
$680$	0	0
$681$	1.44282e13	2.57070
$682$	−3.17472e8	−5.61922e−5 0
$683$	4.16386e12	0.732155	0.366077	−	0.930584i	$-0.380701\pi$
$683$	4.16386e12	0.732155	0.366077	+	0.930584i	$0.380701\pi$
$684$	−7.59899e12	−1.32741
$685$	−5.66181e12	−0.982534
$686$	4.84752e10	0.00835721
$687$	−8.02261e12	−1.37407
$688$	−7.78916e12	−1.32539
$689$	−4.95743e12	−0.838050
$690$	−1.69217e11	−0.0284199
$691$	2.56802e12	0.428497	0.214249	−	0.976779i	$-0.431270\pi$
$691$	2.56802e12	0.428497	0.214249	+	0.976779i	$0.431270\pi$
$692$	−2.80495e12	−0.464994
$693$	−8.92211e11	−0.146950
$694$	−1.64366e11	−0.0268964
$695$	3.29041e12	0.534957
$696$	5.25445e10	0.00848762
$697$	0	0
$698$	2.07591e11	0.0331024
$699$	1.50103e12	0.237816
$700$	7.11447e11	0.111996
$701$	−7.09539e11	−0.110980	−0.0554901	−	0.998459i	$-0.517672\pi$
$701$	−7.09539e11	−0.110980	−0.0554901	+	0.998459i	$0.517672\pi$
$702$	−3.08333e10	−0.00479185
$703$	−2.98250e12	−0.460556
$704$	6.45758e12	0.990815
$705$	−6.94385e12	−1.05864
$706$	−1.39794e11	−0.0211771
$707$	1.83066e12	0.275563
$708$	−2.29957e11	−0.0343951
$709$	−7.62898e12	−1.13386	−0.566929	−	0.823767i	$-0.691869\pi$
$709$	−7.62898e12	−1.13386	−0.566929	+	0.823767i	$0.691869\pi$
$710$	8.81534e10	0.0130190
$711$	7.83505e12	1.14982
$712$	−3.68425e11	−0.0537265
$713$	−2.24542e10	−0.00325382
$714$	0	0
$715$	4.26693e12	0.610574
$716$	1.22601e13	1.74336
$717$	3.82238e12	0.540129
$718$	6.24915e10	0.00877528
$719$	−1.27543e13	−1.77982	−0.889912	−	0.456132i	$-0.849235\pi$
$719$	−1.27543e13	−1.77982	−0.889912	+	0.456132i	$0.849235\pi$
$720$	3.65153e12	0.506382
$721$	2.97826e11	0.0410443
$722$	−2.46138e11	−0.0337102
$723$	−1.87581e12	−0.255309
$724$	5.77068e12	0.780555
$725$	−6.11125e11	−0.0821503
$726$	2.78865e9	0.000372545 0
$727$	1.32065e13	1.75341	0.876706	−	0.481027i	$-0.159736\pi$
$727$	1.32065e13	1.75341	0.876706	+	0.481027i	$0.159736\pi$
$728$	−6.72593e10	−0.00887485
$729$	−5.44571e12	−0.714135
$730$	1.61176e11	0.0210062
$731$	0	0
$732$	−1.28464e13	−1.65379
$733$	−3.68770e12	−0.471832	−0.235916	−	0.971773i	$-0.575809\pi$
$733$	−3.68770e12	−0.471832	−0.235916	+	0.971773i	$0.575809\pi$
$734$	−2.68592e11	−0.0341556
$735$	−6.15251e12	−0.777605
$736$	−8.46670e11	−0.106356
$737$	6.32417e12	0.789587
$738$	−6.38708e10	−0.00792590
$739$	8.56654e12	1.05659	0.528294	−	0.849062i	$-0.322832\pi$
$739$	8.56654e12	1.05659	0.528294	+	0.849062i	$0.322832\pi$
$740$	1.43406e12	0.175802
$741$	−1.80154e13	−2.19514
$742$	−2.80319e10	−0.00339497
$743$	2.43702e12	0.293366	0.146683	−	0.989184i	$-0.453140\pi$
$743$	2.43702e12	0.293366	0.146683	+	0.989184i	$0.453140\pi$
$744$	−1.28939e9	−0.000154279 0
$745$	5.25210e12	0.624641
$746$	1.12997e9	0.000133580 0
$747$	−1.38381e13	−1.62605
$748$	0	0
$749$	1.37433e12	0.159559
$750$	2.85296e11	0.0329245
$751$	3.48665e12	0.399971	0.199986	−	0.979799i	$-0.435910\pi$
$751$	3.48665e12	0.399971	0.199986	+	0.979799i	$0.435910\pi$
$752$	−1.15692e13	−1.31924
$753$	9.56106e12	1.08375
$754$	2.88786e10	0.00325391
$755$	8.26640e12	0.925881
$756$	2.82793e11	0.0314862
$757$	−5.04037e12	−0.557868	−0.278934	−	0.960310i	$-0.589981\pi$
$757$	−5.04037e12	−0.557868	−0.278934	+	0.960310i	$0.589981\pi$
$758$	−1.32570e11	−0.0145860
$759$	−1.77493e13	−1.94130
$760$	4.11116e11	0.0446995
$761$	3.98658e12	0.430893	0.215447	−	0.976516i	$-0.430879\pi$
$761$	3.98658e12	0.430893	0.215447	+	0.976516i	$0.430879\pi$
$762$	2.10013e11	0.0225657
$763$	−7.40538e11	−0.0791019
$764$	1.40921e13	1.49642
$765$	0	0
$766$	−1.22981e11	−0.0129065
$767$	−2.52847e11	−0.0263803
$768$	1.30851e13	1.35723
$769$	1.13185e13	1.16713	0.583567	−	0.812065i	$-0.301656\pi$
$769$	1.13185e13	1.16713	0.583567	+	0.812065i	$0.301656\pi$
$770$	2.41275e10	0.00247345
$771$	−7.95148e12	−0.810407
$772$	2.07714e12	0.210469
$773$	1.89037e13	1.90431	0.952157	−	0.305610i	$-0.0988603\pi$
$773$	1.89037e13	1.90431	0.952157	+	0.305610i	$0.0988603\pi$
$774$	2.84652e11	0.0285089
$775$	1.49964e10	0.00149324
$776$	1.59745e11	0.0158142
$777$	−7.10898e11	−0.0699702
$778$	1.83340e11	0.0179411
$779$	5.82654e12	0.566882
$780$	8.66223e12	0.837923
$781$	9.24651e12	0.889300
$782$	0	0
$783$	−2.42916e11	−0.0230955
$784$	−1.02508e13	−0.969022
$785$	−8.21695e12	−0.772320
$786$	3.71670e11	0.0347341
$787$	−1.40103e13	−1.30185	−0.650926	−	0.759141i	$-0.725619\pi$
$787$	−1.40103e13	−1.30185	−0.650926	+	0.759141i	$0.725619\pi$
$788$	−6.56659e12	−0.606697
$789$	−8.20236e12	−0.753516
$790$	−2.11878e11	−0.0193537
$791$	−2.55745e12	−0.232280
$792$	−4.72709e11	−0.0426904
$793$	−1.41251e13	−1.26842
$794$	−3.10841e11	−0.0277553
$795$	7.22262e12	0.641273
$796$	−1.70167e12	−0.150233
$797$	1.51222e13	1.32756	0.663779	−	0.747929i	$-0.268952\pi$
$797$	1.51222e13	1.32756	0.663779	+	0.747929i	$0.268952\pi$
$798$	−1.01869e11	−0.00889257
$799$	0	0
$800$	5.65463e11	0.0488089
$801$	−1.09092e13	−0.936366
$802$	−3.38600e11	−0.0289003
$803$	1.69059e13	1.43489
$804$	1.28386e13	1.08359
$805$	1.70649e12	0.143226
$806$	−7.08652e8	−5.91460e−5 0
$807$	−1.74226e12	−0.144605
$808$	9.69916e11	0.0800540
$809$	−1.21574e13	−0.997866	−0.498933	−	0.866640i	$-0.666275\pi$
$809$	−1.21574e13	−0.997866	−0.498933	+	0.866640i	$0.666275\pi$
$810$	1.99200e11	0.0162595
$811$	1.74499e12	0.141644	0.0708222	−	0.997489i	$-0.477438\pi$
$811$	1.74499e12	0.141644	0.0708222	+	0.997489i	$0.477438\pi$
$812$	−2.64865e11	−0.0213807
$813$	−1.15154e13	−0.924423
$814$	−9.27374e10	−0.00740364
$815$	−9.92079e12	−0.787657
$816$	0	0
$817$	−2.59671e13	−2.03903
$818$	2.49597e11	0.0194917
$819$	−1.99157e12	−0.154674
$820$	−2.80154e12	−0.216389
$821$	1.53608e13	1.17997	0.589983	−	0.807416i	$-0.299135\pi$
$821$	1.53608e13	1.17997	0.589983	+	0.807416i	$0.299135\pi$
$822$	7.43288e11	0.0567851
$823$	9.62758e12	0.731506	0.365753	−	0.930712i	$-0.380811\pi$
$823$	9.62758e12	0.731506	0.365753	+	0.930712i	$0.380811\pi$
$824$	1.57793e11	0.0119238
$825$	1.18542e13	0.890900
$826$	−1.42973e9	−0.000106867 0
$827$	2.95089e12	0.219370	0.109685	−	0.993966i	$-0.465016\pi$
$827$	2.95089e12	0.219370	0.109685	+	0.993966i	$0.465016\pi$
$828$	−1.67117e13	−1.23562
$829$	1.75845e13	1.29311	0.646554	−	0.762868i	$-0.276209\pi$
$829$	1.75845e13	1.29311	0.646554	+	0.762868i	$0.276209\pi$
$830$	3.74214e11	0.0273696
$831$	−2.22367e13	−1.61758
$832$	1.44144e13	1.04290
$833$	0	0
$834$	−4.31969e11	−0.0309176
$835$	1.38295e13	0.984503
$836$	2.15545e13	1.52620
$837$	5.96092e9	0.000419806 0
$838$	−2.69719e10	−0.00188935
$839$	−1.82710e13	−1.27302	−0.636509	−	0.771269i	$-0.719622\pi$
$839$	−1.82710e13	−1.27302	−0.636509	+	0.771269i	$0.719622\pi$
$840$	9.79920e10	0.00679100
$841$	−1.42796e13	−0.984317
$842$	5.96717e11	0.0409132
$843$	−3.15435e12	−0.215122
$844$	2.83616e13	1.92393
$845$	8.32031e11	0.0561415
$846$	4.22793e11	0.0283766
$847$	−2.81225e10	−0.00187749
$848$	1.20337e13	0.799129
$849$	−5.65113e12	−0.373294
$850$	0	0
$851$	−6.55913e12	−0.428709
$852$	1.87712e13	1.22043
$853$	−2.21213e13	−1.43067	−0.715337	−	0.698780i	$-0.753727\pi$
$853$	−2.21213e13	−1.43067	−0.715337	+	0.698780i	$0.753727\pi$
$854$	−7.98711e10	−0.00513842
$855$	1.21733e13	0.779039
$856$	7.28143e11	0.0463537
$857$	3.03667e12	0.192302	0.0961511	−	0.995367i	$-0.469347\pi$
$857$	3.03667e12	0.192302	0.0961511	+	0.995367i	$0.469347\pi$
$858$	−5.60167e11	−0.0352878
$859$	1.80675e13	1.13221	0.566107	−	0.824332i	$-0.308449\pi$
$859$	1.80675e13	1.13221	0.566107	+	0.824332i	$0.308449\pi$
$860$	1.24856e13	0.778335
$861$	1.38879e12	0.0861238
$862$	−2.72646e11	−0.0168196
$863$	−4.21555e12	−0.258705	−0.129353	−	0.991599i	$-0.541290\pi$
$863$	−4.21555e12	−0.258705	−0.129353	+	0.991599i	$0.541290\pi$
$864$	2.24766e11	0.0137220
$865$	4.49340e12	0.272900
$866$	2.51355e11	0.0151865
$867$	0	0
$868$	6.49951e9	0.000388635 0
$869$	−2.22241e13	−1.32201
$870$	−4.20741e10	−0.00248988
$871$	1.41166e13	0.831092
$872$	−3.92350e11	−0.0229800
$873$	4.73009e12	0.275616
$874$	−9.39894e11	−0.0544850
$875$	−2.87710e12	−0.165928
$876$	3.43205e13	1.96918
$877$	1.83513e12	0.104754	0.0523768	−	0.998627i	$-0.483320\pi$
$877$	1.83513e12	0.104754	0.0523768	+	0.998627i	$0.483320\pi$
$878$	5.96845e11	0.0338951
$879$	1.26021e13	0.712021
$880$	−1.03576e13	−0.582217
$881$	−2.66113e13	−1.48825	−0.744124	−	0.668042i	$-0.767133\pi$
$881$	−2.66113e13	−1.48825	−0.744124	+	0.668042i	$0.767133\pi$
$882$	3.74610e11	0.0208435
$883$	−1.48033e13	−0.819472	−0.409736	−	0.912204i	$-0.634379\pi$
$883$	−1.48033e13	−0.819472	−0.409736	+	0.912204i	$0.634379\pi$
$884$	0	0
$885$	3.68381e11	0.0201861
$886$	−5.45527e11	−0.0297416
$887$	−2.12459e13	−1.15244	−0.576221	−	0.817294i	$-0.695473\pi$
$887$	−2.12459e13	−1.15244	−0.576221	+	0.817294i	$0.695473\pi$
$888$	−3.76646e11	−0.0203271
$889$	−2.11790e12	−0.113723
$890$	2.95009e11	0.0157609
$891$	2.08943e13	1.11065
$892$	−2.01793e12	−0.106724
$893$	−3.85688e13	−2.02957
$894$	−6.89502e11	−0.0361008
$895$	−1.96402e13	−1.02316
$896$	3.26732e11	0.0169358
$897$	−3.96195e13	−2.04335
$898$	−7.42660e11	−0.0381107
$899$	−5.58302e9	−0.000285069 0
$900$	1.11612e13	0.567048
$901$	0	0
$902$	1.81169e11	0.00911288
$903$	−6.18942e12	−0.309781
$904$	−1.35498e12	−0.0674799
$905$	−9.24439e12	−0.458099
$906$	−1.08522e12	−0.0535109
$907$	6.95909e12	0.341444	0.170722	−	0.985319i	$-0.445390\pi$
$907$	6.95909e12	0.341444	0.170722	+	0.985319i	$0.445390\pi$
$908$	−3.85333e13	−1.88126
$909$	2.87195e13	1.39521
$910$	5.38566e10	0.00260347
$911$	3.30588e13	1.59021	0.795105	−	0.606472i	$-0.207416\pi$
$911$	3.30588e13	1.59021	0.795105	+	0.606472i	$0.207416\pi$
$912$	4.37306e13	2.09319
$913$	3.92517e13	1.86956
$914$	−3.72657e11	−0.0176625
$915$	2.05793e13	0.970592
$916$	2.14259e13	1.00556
$917$	−3.74815e12	−0.175047
$918$	0	0
$919$	3.72968e13	1.72485	0.862425	−	0.506185i	$-0.168945\pi$
$919$	3.72968e13	1.72485	0.862425	+	0.506185i	$0.168945\pi$
$920$	9.04126e11	0.0416087
$921$	−2.53444e13	−1.16068
$922$	2.93087e11	0.0133570
$923$	2.06398e13	0.936046
$924$	5.13766e12	0.231868
$925$	4.38063e12	0.196743
$926$	−3.96367e11	−0.0177153
$927$	4.67230e12	0.207813
$928$	−2.10516e11	−0.00931794
$929$	1.89331e13	0.833971	0.416986	−	0.908913i	$-0.363087\pi$
$929$	1.89331e13	0.833971	0.416986	+	0.908913i	$0.363087\pi$
$930$	1.03246e9	4.52583e−5 0
$931$	−3.41734e13	−1.49078
$932$	−4.00877e12	−0.174036
$933$	−3.49252e13	−1.50894
$934$	2.68980e10	0.00115654
$935$	0	0
$936$	−1.05517e12	−0.0449345
$937$	−1.85059e13	−0.784300	−0.392150	−	0.919901i	$-0.628269\pi$
$937$	−1.85059e13	−0.784300	−0.392150	+	0.919901i	$0.628269\pi$
$938$	7.98229e10	0.00336678
$939$	3.86778e13	1.62355
$940$	1.85448e13	0.774725
$941$	9.74771e12	0.405274	0.202637	−	0.979254i	$-0.435049\pi$
$941$	9.74771e12	0.405274	0.202637	+	0.979254i	$0.435049\pi$
$942$	1.07873e12	0.0446359
$943$	1.28137e13	0.527683
$944$	6.13763e11	0.0251551
$945$	−4.53022e11	−0.0184789
$946$	−8.07416e11	−0.0327784
$947$	−1.19050e13	−0.481009	−0.240504	−	0.970648i	$-0.577313\pi$
$947$	−1.19050e13	−0.481009	−0.240504	+	0.970648i	$0.577313\pi$
$948$	−4.51169e13	−1.81427
$949$	3.77369e13	1.51032
$950$	6.27724e11	0.0250042
$951$	−4.48441e13	−1.77784
$952$	0	0
$953$	5.94643e12	0.233527	0.116764	−	0.993160i	$-0.462748\pi$
$953$	5.94643e12	0.233527	0.116764	+	0.993160i	$0.462748\pi$
$954$	−4.39767e11	−0.0171892
$955$	−2.25749e13	−0.878235
$956$	−1.02084e13	−0.395272
$957$	−4.41320e12	−0.170079
$958$	−5.76795e11	−0.0221247
$959$	−7.49579e12	−0.286176
$960$	−2.10008e13	−0.798022
$961$	−2.64395e13	−0.999995
$962$	−2.07006e11	−0.00779282
$963$	2.15605e13	0.807869
$964$	5.00969e12	0.186837
$965$	−3.32749e12	−0.123522
$966$	−2.24029e11	−0.00827767
$967$	−1.78714e13	−0.657262	−0.328631	−	0.944458i	$-0.606587\pi$
$967$	−1.78714e13	−0.657262	−0.328631	+	0.944458i	$0.606587\pi$
$968$	−1.48998e10	−0.000545432 0
$969$	0	0
$970$	−1.27913e11	−0.00463917
$971$	−7.79284e12	−0.281326	−0.140663	−	0.990058i	$-0.544923\pi$
$971$	−7.79284e12	−0.281326	−0.140663	+	0.990058i	$0.544923\pi$
$972$	3.72882e13	1.33990
$973$	4.35625e12	0.155814
$974$	−8.89788e11	−0.0316790
$975$	2.64605e13	0.937731
$976$	3.42874e13	1.20951
$977$	−3.49964e12	−0.122885	−0.0614424	−	0.998111i	$-0.519570\pi$
$977$	−3.49964e12	−0.122885	−0.0614424	+	0.998111i	$0.519570\pi$
$978$	1.30241e12	0.0455223
$979$	3.09439e13	1.07659
$980$	1.64314e13	0.569059
$981$	−1.16176e13	−0.400503
$982$	−1.03682e12	−0.0355796
$983$	−1.22347e13	−0.417930	−0.208965	−	0.977923i	$-0.567009\pi$
$983$	−1.22347e13	−0.417930	−0.208965	+	0.977923i	$0.567009\pi$
$984$	7.35807e11	0.0250199
$985$	1.05194e13	0.356064
$986$	0	0
$987$	−9.19312e12	−0.308344
$988$	4.81134e13	1.60642
$989$	−5.71069e13	−1.89804
$990$	3.78513e11	0.0125234
$991$	−4.06704e12	−0.133951	−0.0669756	−	0.997755i	$-0.521335\pi$
$991$	−4.06704e12	−0.133951	−0.0669756	+	0.997755i	$0.521335\pi$
$992$	5.16586e9	0.000169372 0
$993$	6.77607e13	2.21160
$994$	1.16708e11	0.00379195
$995$	2.72600e12	0.0881702
$996$	7.96845e13	2.56570
$997$	4.00990e13	1.28530	0.642650	−	0.766160i	$-0.277835\pi$
$997$	4.00990e13	1.28530	0.642650	+	0.766160i	$0.277835\pi$
$998$	1.44254e12	0.0460299
$999$	1.74125e12	0.0553118

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.g.1.19	✓	36
17.16	even	2		289.10.a.h.1.19	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.19	✓	36	1.1	even	1	trivial
289.10.a.h.1.19	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)

\(f(q)\)	\(=\)	\(q-0.561663 q^{2} +191.593 q^{3} -511.685 q^{4} +819.697 q^{5} -107.611 q^{6} +1085.21 q^{7} +574.966 q^{8} +17024.9 q^{9} +O(q^{10})\)	\(q-0.561663 q^{2} +191.593 q^{3} -511.685 q^{4} +819.697 q^{5} -107.611 q^{6} +1085.21 q^{7} +574.966 q^{8} +17024.9 q^{9} -460.393 q^{10} -48291.1 q^{11} -98035.2 q^{12} -107794. q^{13} -609.525 q^{14} +157048. q^{15} +261660. q^{16} -9562.26 q^{18} +872306. q^{19} -419426. q^{20} +207920. q^{21} +27123.3 q^{22} +1.91838e6 q^{23} +110159. q^{24} -1.28122e6 q^{25} +60543.9 q^{26} -509272. q^{27} -555288. q^{28} +476986. q^{29} -88208.1 q^{30} -11704.8 q^{31} -441347. q^{32} -9.25225e6 q^{33} +889547. q^{35} -8.71138e6 q^{36} -3.41910e6 q^{37} -489942. q^{38} -2.06526e7 q^{39} +471297. q^{40} +6.67947e6 q^{41} -116781. q^{42} -2.97683e7 q^{43} +2.47098e7 q^{44} +1.39553e7 q^{45} -1.07748e6 q^{46} -4.42148e7 q^{47} +5.01322e7 q^{48} -3.91759e7 q^{49} +719615. q^{50} +5.51565e7 q^{52} +4.59898e7 q^{53} +286039. q^{54} -3.95841e7 q^{55} +623961. q^{56} +1.67128e8 q^{57} -267905. q^{58} +2.34565e6 q^{59} -8.03591e7 q^{60} +1.31038e8 q^{61} +6574.13 q^{62} +1.84757e7 q^{63} -1.33722e8 q^{64} -8.83584e7 q^{65} +5.19664e6 q^{66} -1.30959e8 q^{67} +3.67548e8 q^{69} -499625. q^{70} -1.91474e8 q^{71} +9.78873e6 q^{72} -3.50083e8 q^{73} +1.92038e6 q^{74} -2.45473e8 q^{75} -4.46346e8 q^{76} -5.24062e7 q^{77} +1.15998e7 q^{78} +4.60211e8 q^{79} +2.14481e8 q^{80} -4.32674e8 q^{81} -3.75161e6 q^{82} -8.12815e8 q^{83} -1.06389e8 q^{84} +1.67198e7 q^{86} +9.13873e7 q^{87} -2.77657e7 q^{88} -6.40777e8 q^{89} -7.83815e6 q^{90} -1.16980e8 q^{91} -9.81604e8 q^{92} -2.24255e6 q^{93} +2.48338e7 q^{94} +7.15027e8 q^{95} -8.45590e7 q^{96} +2.77833e8 q^{97} +2.20037e7 q^{98} -8.22152e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 36 * q - 486 * q^3 + 9216 * q^4 - 3750 * q^5 - 11061 * q^6 - 29040 * q^7 + 24837 * q^8 + 236196 * q^9	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9} - 60000 q^{10} - 76902 q^{11} - 373248 q^{12} + 54216 q^{13} - 17373 q^{14} - 34122 q^{15} + 2359296 q^{16} - 1779435 q^{18} - 245058 q^{19} - 6439479 q^{20} - 138102 q^{21} - 267324 q^{22} - 4041462 q^{23} - 7653888 q^{24} + 16582356 q^{25} + 15822744 q^{26} - 13281612 q^{27} - 18614784 q^{28} - 4005936 q^{29} + 22471686 q^{30} - 21257064 q^{31} - 30922641 q^{32} + 35736474 q^{33} - 9039642 q^{35} + 39076761 q^{36} - 22076682 q^{37} - 27401376 q^{38} - 62736162 q^{39} + 12231630 q^{40} - 59641782 q^{41} + 150001536 q^{42} - 47951586 q^{43} + 49578936 q^{44} - 129308238 q^{45} - 140524827 q^{46} - 118557912 q^{47} - 407719119 q^{48} + 99849138 q^{49} + 435669051 q^{50} - 105017607 q^{52} + 13698846 q^{53} - 209848575 q^{54} - 365439924 q^{55} - 203095059 q^{56} + 4614108 q^{57} + 179071413 q^{58} + 343015128 q^{59} + 427179186 q^{60} - 175597116 q^{61} - 720602571 q^{62} - 587415936 q^{63} + 853082511 q^{64} - 393820182 q^{65} - 494661978 q^{66} + 502776528 q^{67} - 469106598 q^{69} - 1062525966 q^{70} - 1308709542 q^{71} - 275337849 q^{72} - 494841342 q^{73} - 1545361890 q^{74} - 1824677616 q^{75} + 242064891 q^{76} - 792768144 q^{77} - 2270624538 q^{78} - 1980107868 q^{79} - 2897000199 q^{80} + 1598298840 q^{81} - 898743654 q^{82} + 275294520 q^{83} - 2144532369 q^{84} - 2880848046 q^{86} + 1088458710 q^{87} + 2705904618 q^{88} + 148394658 q^{89} - 117916215 q^{90} - 636340896 q^{91} + 3458472327 q^{92} - 628345524 q^{93} - 200245965 q^{94} - 4878626298 q^{95} + 8390096634 q^{96} + 891786822 q^{97} + 4285627647 q^{98} + 1476187998 q^{99}+O(q^{100}) \) 36 * q - 486 * q^3 + 9216 * q^4 - 3750 * q^5 - 11061 * q^6 - 29040 * q^7 + 24837 * q^8 + 236196 * q^9 - 60000 * q^10 - 76902 * q^11 - 373248 * q^12 + 54216 * q^13 - 17373 * q^14 - 34122 * q^15 + 2359296 * q^16 - 1779435 * q^18 - 245058 * q^19 - 6439479 * q^20 - 138102 * q^21 - 267324 * q^22 - 4041462 * q^23 - 7653888 * q^24 + 16582356 * q^25 + 15822744 * q^26 - 13281612 * q^27 - 18614784 * q^28 - 4005936 * q^29 + 22471686 * q^30 - 21257064 * q^31 - 30922641 * q^32 + 35736474 * q^33 - 9039642 * q^35 + 39076761 * q^36 - 22076682 * q^37 - 27401376 * q^38 - 62736162 * q^39 + 12231630 * q^40 - 59641782 * q^41 + 150001536 * q^42 - 47951586 * q^43 + 49578936 * q^44 - 129308238 * q^45 - 140524827 * q^46 - 118557912 * q^47 - 407719119 * q^48 + 99849138 * q^49 + 435669051 * q^50 - 105017607 * q^52 + 13698846 * q^53 - 209848575 * q^54 - 365439924 * q^55 - 203095059 * q^56 + 4614108 * q^57 + 179071413 * q^58 + 343015128 * q^59 + 427179186 * q^60 - 175597116 * q^61 - 720602571 * q^62 - 587415936 * q^63 + 853082511 * q^64 - 393820182 * q^65 - 494661978 * q^66 + 502776528 * q^67 - 469106598 * q^69 - 1062525966 * q^70 - 1308709542 * q^71 - 275337849 * q^72 - 494841342 * q^73 - 1545361890 * q^74 - 1824677616 * q^75 + 242064891 * q^76 - 792768144 * q^77 - 2270624538 * q^78 - 1980107868 * q^79 - 2897000199 * q^80 + 1598298840 * q^81 - 898743654 * q^82 + 275294520 * q^83 - 2144532369 * q^84 - 2880848046 * q^86 + 1088458710 * q^87 + 2705904618 * q^88 + 148394658 * q^89 - 117916215 * q^90 - 636340896 * q^91 + 3458472327 * q^92 - 628345524 * q^93 - 200245965 * q^94 - 4878626298 * q^95 + 8390096634 * q^96 + 891786822 * q^97 + 4285627647 * q^98 + 1476187998 * q^99

Introduction

L-functions

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