LMFDB - Embedded newform 289.10.a.g.1.31

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			1.31
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)

$f(q)$	$=$	$q+35.6294 q^{2} -0.238037 q^{3} +757.456 q^{4} +2006.11 q^{5} -8.48114 q^{6} -3110.91 q^{7} +8745.46 q^{8} -19682.9 q^{9} +O(q^{10})$	\(q+35.6294 q^{2} -0.238037 q^{3} +757.456 q^{4} +2006.11 q^{5} -8.48114 q^{6} -3110.91 q^{7} +8745.46 q^{8} -19682.9 q^{9} +71476.4 q^{10} +21988.6 q^{11} -180.303 q^{12} -170282. q^{13} -110840. q^{14} -477.528 q^{15} -76221.9 q^{16} -701292. q^{18} +578915. q^{19} +1.51954e6 q^{20} +740.514 q^{21} +783440. q^{22} -1.14210e6 q^{23} -2081.75 q^{24} +2.07134e6 q^{25} -6.06707e6 q^{26} +9370.57 q^{27} -2.35638e6 q^{28} -2.04445e6 q^{29} -17014.1 q^{30} -6.36010e6 q^{31} -7.19342e6 q^{32} -5234.10 q^{33} -6.24082e6 q^{35} -1.49090e7 q^{36} -1.74773e7 q^{37} +2.06264e7 q^{38} +40533.6 q^{39} +1.75443e7 q^{40} -8.92910e6 q^{41} +26384.1 q^{42} +2.23811e7 q^{43} +1.66554e7 q^{44} -3.94861e7 q^{45} -4.06922e7 q^{46} +5.29083e7 q^{47} +18143.7 q^{48} -3.06758e7 q^{49} +7.38005e7 q^{50} -1.28981e8 q^{52} -4.96802e7 q^{53} +333868. q^{54} +4.41114e7 q^{55} -2.72064e7 q^{56} -137804. q^{57} -7.28426e7 q^{58} -1.25066e8 q^{59} -361707. q^{60} +7.55780e7 q^{61} -2.26607e8 q^{62} +6.12319e7 q^{63} -2.17272e8 q^{64} -3.41605e8 q^{65} -186488. q^{66} -5.66451e7 q^{67} +271862. q^{69} -2.22357e8 q^{70} +9.81048e6 q^{71} -1.72136e8 q^{72} +4.37401e8 q^{73} -6.22707e8 q^{74} -493056. q^{75} +4.38503e8 q^{76} -6.84045e7 q^{77} +1.44419e6 q^{78} -1.18121e8 q^{79} -1.52909e8 q^{80} +3.87417e8 q^{81} -3.18139e8 q^{82} +7.42977e8 q^{83} +560907. q^{84} +7.97425e8 q^{86} +486656. q^{87} +1.92300e8 q^{88} -6.40009e8 q^{89} -1.40687e9 q^{90} +5.29734e8 q^{91} -8.65088e8 q^{92} +1.51394e6 q^{93} +1.88509e9 q^{94} +1.16137e9 q^{95} +1.71230e6 q^{96} -1.49842e9 q^{97} -1.09296e9 q^{98} -4.32800e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	35.6294	1.57461	0.787307	−	0.616562i	$-0.211475\pi$
$2$	35.6294	1.57461	0.787307	+	0.616562i	$0.211475\pi$
$3$	−0.238037	−0.00169668	−0.000848340	−	1.00000i	$-0.500270\pi$
$3$	−0.238037	−0.00169668	−0.000848340		1.00000i	$0.500270\pi$
$4$	757.456	1.47941
$5$	2006.11	1.43545	0.717726	−	0.696325i	$-0.245183\pi$
$5$	2006.11	1.43545	0.717726	+	0.696325i	$0.245183\pi$
$6$	−8.48114	−0.00267161
$7$	−3110.91	−0.489719	−0.244859	−	0.969559i	$-0.578742\pi$
$7$	−3110.91	−0.489719	−0.244859	+	0.969559i	$0.578742\pi$
$8$	8745.46	0.754879
$9$	−19682.9	−0.999997
$10$	71476.4	2.26028
$11$	21988.6	0.452824	0.226412	−	0.974032i	$-0.427300\pi$
$11$	21988.6	0.452824	0.226412	+	0.974032i	$0.427300\pi$
$12$	−180.303	−0.00251008
$13$	−170282.	−1.65358	−0.826789	−	0.562512i	$-0.809835\pi$
$13$	−170282.	−1.65358	−0.826789	+	0.562512i	$0.809835\pi$
$14$	−110840.	−0.771118
$15$	−477.528	−0.00243550
$16$	−76221.9	−0.290763
$17$	0	0
$17$	0	0
$18$	−701292.	−1.57461
$19$	578915.	1.01912	0.509558	−	0.860436i	$-0.329809\pi$
$19$	578915.	1.01912	0.509558	+	0.860436i	$0.329809\pi$
$20$	1.51954e6	2.12362
$21$	740.514	0.000830896 0
$22$	783440.	0.713023
$23$	−1.14210e6	−0.850996	−0.425498	−	0.904959i	$-0.639901\pi$
$23$	−1.14210e6	−0.850996	−0.425498	+	0.904959i	$0.639901\pi$
$24$	−2081.75	−0.00128079
$25$	2.07134e6	1.06052
$26$	−6.06707e6	−2.60375
$27$	9370.57	0.00339335
$28$	−2.35638e6	−0.724493
$29$	−2.04445e6	−0.536767	−0.268384	−	0.963312i	$-0.586489\pi$
$29$	−2.04445e6	−0.536767	−0.268384	+	0.963312i	$0.586489\pi$
$30$	−17014.1	−0.00383497
$31$	−6.36010e6	−1.23691	−0.618453	−	0.785822i	$-0.712240\pi$
$31$	−6.36010e6	−1.23691	−0.618453	+	0.785822i	$0.712240\pi$
$32$	−7.19342e6	−1.21272
$33$	−5234.10	−0.000768298 0
$34$	0	0
$35$	−6.24082e6	−0.702968
$36$	−1.49090e7	−1.47940
$37$	−1.74773e7	−1.53309	−0.766544	−	0.642192i	$-0.778025\pi$
$37$	−1.74773e7	−1.53309	−0.766544	+	0.642192i	$0.778025\pi$
$38$	2.06264e7	1.60471
$39$	40533.6	0.00280559
$40$	1.75443e7	1.08359
$41$	−8.92910e6	−0.493492	−0.246746	−	0.969080i	$-0.579361\pi$
$41$	−8.92910e6	−0.493492	−0.246746	+	0.969080i	$0.579361\pi$
$42$	26384.1	0.00130834
$43$	2.23811e7	0.998327	0.499163	−	0.866508i	$-0.333641\pi$
$43$	2.23811e7	0.998327	0.499163	+	0.866508i	$0.333641\pi$
$44$	1.66554e7	0.669911
$45$	−3.94861e7	−1.43545
$46$	−4.06922e7	−1.33999
$47$	5.29083e7	1.58155	0.790776	−	0.612106i	$-0.209678\pi$
$47$	5.29083e7	1.58155	0.790776	+	0.612106i	$0.209678\pi$
$48$	18143.7	0.000493332 0
$49$	−3.06758e7	−0.760176
$50$	7.38005e7	1.66992
$51$	0	0
$52$	−1.28981e8	−2.44631
$53$	−4.96802e7	−0.864853	−0.432427	−	0.901669i	$-0.642343\pi$
$53$	−4.96802e7	−0.864853	−0.432427	+	0.901669i	$0.642343\pi$
$54$	333868.	0.00534322
$55$	4.41114e7	0.650008
$56$	−2.72064e7	−0.369679
$57$	−137804.	−0.00172911
$58$	−7.28426e7	−0.845201
$59$	−1.25066e8	−1.34371	−0.671853	−	0.740684i	$-0.734501\pi$
$59$	−1.25066e8	−1.34371	−0.671853	+	0.740684i	$0.734501\pi$
$60$	−361707.	−0.00360310
$61$	7.55780e7	0.698893	0.349447	−	0.936956i	$-0.386370\pi$
$61$	7.55780e7	0.698893	0.349447	+	0.936956i	$0.386370\pi$
$62$	−2.26607e8	−1.94765
$63$	6.12319e7	0.489717
$64$	−2.17272e8	−1.61880
$65$	−3.41605e8	−2.37363
$66$	−186488.	−0.00120977
$67$	−5.66451e7	−0.343420	−0.171710	−	0.985148i	$-0.554929\pi$
$67$	−5.66451e7	−0.343420	−0.171710	+	0.985148i	$0.554929\pi$
$68$	0	0
$69$	271862.	0.00144387
$70$	−2.22357e8	−1.10690
$71$	9.81048e6	0.0458171	0.0229085	−	0.999738i	$-0.492707\pi$
$71$	9.81048e6	0.0458171	0.0229085	+	0.999738i	$0.492707\pi$
$72$	−1.72136e8	−0.754877
$73$	4.37401e8	1.80271	0.901357	−	0.433078i	$-0.142572\pi$
$73$	4.37401e8	1.80271	0.901357	+	0.433078i	$0.142572\pi$
$74$	−6.22707e8	−2.41402
$75$	−493056.	−0.00179937
$76$	4.38503e8	1.50769
$77$	−6.84045e7	−0.221757
$78$	1.44419e6	0.00441772
$79$	−1.18121e8	−0.341196	−0.170598	−	0.985341i	$-0.554570\pi$
$79$	−1.18121e8	−0.341196	−0.170598	+	0.985341i	$0.554570\pi$
$80$	−1.52909e8	−0.417377
$81$	3.87417e8	0.999991
$82$	−3.18139e8	−0.777060
$83$	7.42977e8	1.71840	0.859199	−	0.511641i	$-0.170962\pi$
$83$	7.42977e8	1.71840	0.859199	+	0.511641i	$0.170962\pi$
$84$	560907.	0.00122923
$85$	0	0
$86$	7.97425e8	1.57198
$87$	486656.	0.000910722 0
$88$	1.92300e8	0.341828
$89$	−6.40009e8	−1.08126	−0.540631	−	0.841260i	$-0.681814\pi$
$89$	−6.40009e8	−1.08126	−0.540631	+	0.841260i	$0.681814\pi$
$90$	−1.40687e9	−2.26028
$91$	5.29734e8	0.809788
$92$	−8.65088e8	−1.25897
$93$	1.51394e6	0.00209863
$94$	1.88509e9	2.49033
$95$	1.16137e9	1.46289
$96$	1.71230e6	0.00205760
$97$	−1.49842e9	−1.71855	−0.859274	−	0.511516i	$-0.829084\pi$
$97$	−1.49842e9	−1.71855	−0.859274	+	0.511516i	$0.829084\pi$
$98$	−1.09296e9	−1.19698
$99$	−4.32800e8	−0.452823
$100$	1.56895e9	1.56895
$101$	1.10300e7	0.0105470	0.00527352	−	0.999986i	$-0.498321\pi$
$101$	1.10300e7	0.0105470	0.00527352	+	0.999986i	$0.498321\pi$
$102$	0	0
$103$	2.12633e9	1.86150	0.930748	−	0.365660i	$-0.119157\pi$
$103$	2.12633e9	1.86150	0.930748	+	0.365660i	$0.119157\pi$
$104$	−1.48920e9	−1.24825
$105$	1.48555e6	0.00119271
$106$	−1.77008e9	−1.36181
$107$	−1.24966e9	−0.921651	−0.460825	−	0.887491i	$-0.652447\pi$
$107$	−1.24966e9	−0.921651	−0.460825	+	0.887491i	$0.652447\pi$
$108$	7.09779e6	0.00502015
$109$	2.38971e9	1.62153	0.810766	−	0.585371i	$-0.199051\pi$
$109$	2.38971e9	1.62153	0.810766	+	0.585371i	$0.199051\pi$
$110$	1.57166e9	1.02351
$111$	4.16026e6	0.00260116
$112$	2.37120e8	0.142392
$113$	−1.78971e9	−1.03260	−0.516298	−	0.856409i	$-0.672690\pi$
$113$	−1.78971e9	−1.03260	−0.516298	+	0.856409i	$0.672690\pi$
$114$	−4.90986e6	−0.00272268
$115$	−2.29117e9	−1.22156
$116$	−1.54858e9	−0.794097
$117$	3.35166e9	1.65357
$118$	−4.45602e9	−2.11582
$119$	0	0
$120$	−4.17620e6	−0.00183851
$121$	−1.87445e9	−0.794950
$122$	2.69280e9	1.10049
$123$	2.12546e6	0.000837298 0
$124$	−4.81750e9	−1.82989
$125$	2.37144e8	0.0868796
$126$	2.18166e9	0.771115
$127$	−1.30529e9	−0.445235	−0.222618	−	0.974906i	$-0.571460\pi$
$127$	−1.30529e9	−0.445235	−0.222618	+	0.974906i	$0.571460\pi$
$128$	−4.05824e9	−1.33626
$129$	−5.32753e6	−0.00169384
$130$	−1.21712e10	−3.73755
$131$	−6.34853e8	−0.188344	−0.0941722	−	0.995556i	$-0.530020\pi$
$131$	−6.34853e8	−0.188344	−0.0941722	+	0.995556i	$0.530020\pi$
$132$	−3.96460e6	−0.00113662
$133$	−1.80096e9	−0.499080
$134$	−2.01823e9	−0.540754
$135$	1.87984e7	0.00487100
$136$	0	0
$137$	1.67526e9	0.406293	0.203147	−	0.979148i	$-0.434883\pi$
$137$	1.67526e9	0.406293	0.203147	+	0.979148i	$0.434883\pi$
$138$	9.68628e6	0.00227353
$139$	3.13923e8	0.0713273	0.0356637	−	0.999364i	$-0.488645\pi$
$139$	3.13923e8	0.0713273	0.0356637	+	0.999364i	$0.488645\pi$
$140$	−4.72715e9	−1.03998
$141$	−1.25942e7	−0.00268338
$142$	3.49542e8	0.0721442
$143$	−3.74427e9	−0.748781
$144$	1.50027e9	0.290763
$145$	−4.10139e9	−0.770504
$146$	1.55843e10	2.83858
$147$	7.30200e6	0.00128977
$148$	−1.32383e10	−2.26806
$149$	1.88570e8	0.0313426	0.0156713	−	0.999877i	$-0.495011\pi$
$149$	1.88570e8	0.0313426	0.0156713	+	0.999877i	$0.495011\pi$
$150$	−1.75673e7	−0.00283331
$151$	2.87194e9	0.449551	0.224775	−	0.974411i	$-0.427835\pi$
$151$	2.87194e9	0.449551	0.224775	+	0.974411i	$0.427835\pi$
$152$	5.06288e9	0.769310
$153$	0	0
$154$	−2.43721e9	−0.349181
$155$	−1.27590e10	−1.77552
$156$	3.07024e7	0.00415061
$157$	−1.23729e9	−0.162526	−0.0812630	−	0.996693i	$-0.525895\pi$
$157$	−1.23729e9	−0.162526	−0.0812630	+	0.996693i	$0.525895\pi$
$158$	−4.20857e9	−0.537251
$159$	1.18258e7	0.00146738
$160$	−1.44308e10	−1.74080
$161$	3.55296e9	0.416749
$162$	1.38035e10	1.57460
$163$	−1.52441e10	−1.69144	−0.845722	−	0.533624i	$-0.820830\pi$
$163$	−1.52441e10	−1.69144	−0.845722	+	0.533624i	$0.820830\pi$
$164$	−6.76340e9	−0.730076
$165$	−1.05002e7	−0.00110285
$166$	2.64718e10	2.70581
$167$	−7.98265e9	−0.794187	−0.397094	−	0.917778i	$-0.629981\pi$
$167$	−7.98265e9	−0.794187	−0.397094	+	0.917778i	$0.629981\pi$
$168$	6.47613e6	0.000627226 0
$169$	1.83916e10	1.73432
$170$	0	0
$171$	−1.13948e10	−1.01911
$172$	1.69527e10	1.47693
$173$	−6.70354e9	−0.568980	−0.284490	−	0.958679i	$-0.591824\pi$
$173$	−6.70354e9	−0.568980	−0.284490	+	0.958679i	$0.591824\pi$
$174$	1.73393e7	0.00143403
$175$	−6.44375e9	−0.519359
$176$	−1.67601e9	−0.131665
$177$	2.97703e7	0.00227984
$178$	−2.28031e10	−1.70257
$179$	−6.50426e9	−0.473543	−0.236771	−	0.971565i	$-0.576089\pi$
$179$	−6.50426e9	−0.473543	−0.236771	+	0.971565i	$0.576089\pi$
$180$	−2.99090e10	−2.12361
$181$	1.61582e9	0.111902	0.0559510	−	0.998434i	$-0.482181\pi$
$181$	1.61582e9	0.111902	0.0559510	+	0.998434i	$0.482181\pi$
$182$	1.88741e10	1.27510
$183$	−1.79904e7	−0.00118580
$184$	−9.98816e9	−0.642399
$185$	−3.50614e10	−2.20068
$186$	5.39409e7	0.00330453
$187$	0	0
$188$	4.00757e10	2.33976
$189$	−2.91510e7	−0.00166179
$190$	4.13788e10	2.30349
$191$	−3.04910e10	−1.65776	−0.828879	−	0.559428i	$-0.811021\pi$
$191$	−3.04910e10	−1.65776	−0.828879	+	0.559428i	$0.811021\pi$
$192$	5.17188e7	0.00274658
$193$	−2.89268e10	−1.50070	−0.750349	−	0.661042i	$-0.770114\pi$
$193$	−2.89268e10	−1.50070	−0.750349	+	0.661042i	$0.770114\pi$
$194$	−5.33879e10	−2.70605
$195$	8.13147e7	0.00402729
$196$	−2.32356e10	−1.12461
$197$	2.47919e9	0.117277	0.0586383	−	0.998279i	$-0.481324\pi$
$197$	2.47919e9	0.117277	0.0586383	+	0.998279i	$0.481324\pi$
$198$	−1.54204e10	−0.713021
$199$	2.36696e10	1.06992	0.534960	−	0.844877i	$-0.320327\pi$
$199$	2.36696e10	1.06992	0.534960	+	0.844877i	$0.320327\pi$
$200$	1.81148e10	0.800568
$201$	1.34837e7	0.000582674 0
$202$	3.92994e8	0.0166075
$203$	6.36011e9	0.262865
$204$	0	0
$205$	−1.79127e10	−0.708385
$206$	7.57598e10	2.93114
$207$	2.24798e10	0.850994
$208$	1.29792e10	0.480800
$209$	1.27295e10	0.461481
$210$	5.29293e7	0.00187806
$211$	5.06744e10	1.76002	0.880009	−	0.474956i	$-0.157536\pi$
$211$	5.06744e10	1.76002	0.880009	+	0.474956i	$0.157536\pi$
$212$	−3.76306e10	−1.27947
$213$	−2.33526e6	−7.77369e−5 0
$214$	−4.45248e10	−1.45124
$215$	4.48988e10	1.43305
$216$	8.19499e7	0.00256157
$217$	1.97857e10	0.605736
$218$	8.51439e10	2.55328
$219$	−1.04118e8	−0.00305863
$220$	3.34124e10	0.961626
$221$	0	0
$222$	1.48228e8	0.00409582
$223$	1.86341e10	0.504588	0.252294	−	0.967651i	$-0.418815\pi$
$223$	1.86341e10	0.504588	0.252294	+	0.967651i	$0.418815\pi$
$224$	2.23781e10	0.593891
$225$	−4.07700e10	−1.06052
$226$	−6.37665e10	−1.62594
$227$	6.75910e10	1.68956	0.844778	−	0.535118i	$-0.179733\pi$
$227$	6.75910e10	1.68956	0.844778	+	0.535118i	$0.179733\pi$
$228$	−1.04380e8	−0.00255806
$229$	−4.65557e9	−0.111870	−0.0559349	−	0.998434i	$-0.517814\pi$
$229$	−4.65557e9	−0.111870	−0.0559349	+	0.998434i	$0.517814\pi$
$230$	−8.16330e10	−1.92349
$231$	1.62828e7	0.000376250 0
$232$	−1.78797e10	−0.405194
$233$	−3.07788e10	−0.684148	−0.342074	−	0.939673i	$-0.611129\pi$
$233$	−3.07788e10	−0.684148	−0.342074	+	0.939673i	$0.611129\pi$
$234$	1.19418e11	2.60374
$235$	1.06140e11	2.27024
$236$	−9.47318e10	−1.98789
$237$	2.81171e7	0.000578900 0
$238$	0	0
$239$	7.55716e10	1.49819	0.749097	−	0.662460i	$-0.230487\pi$
$239$	7.55716e10	1.49819	0.749097	+	0.662460i	$0.230487\pi$
$240$	3.63981e7	0.000708155 0
$241$	−2.68306e10	−0.512335	−0.256167	−	0.966632i	$-0.582460\pi$
$241$	−2.68306e10	−0.512335	−0.256167	+	0.966632i	$0.582460\pi$
$242$	−6.67856e10	−1.25174
$243$	−2.76661e8	−0.00509002
$244$	5.72470e10	1.03395
$245$	−6.15390e10	−1.09120
$246$	7.57290e7	0.00131842
$247$	−9.85791e10	−1.68519
$248$	−5.56220e10	−0.933714
$249$	−1.76856e8	−0.00291557
$250$	8.44932e9	0.136802
$251$	4.14790e10	0.659624	0.329812	−	0.944047i	$-0.393015\pi$
$251$	4.14790e10	0.659624	0.329812	+	0.944047i	$0.393015\pi$
$252$	4.63805e10	0.724491
$253$	−2.51131e10	−0.385352
$254$	−4.65066e10	−0.701073
$255$	0	0
$256$	−3.33495e10	−0.485299
$257$	4.82861e10	0.690435	0.345217	−	0.938523i	$-0.387805\pi$
$257$	4.82861e10	0.690435	0.345217	+	0.938523i	$0.387805\pi$
$258$	−1.89817e8	−0.00266714
$259$	5.43704e10	0.750782
$260$	−2.58750e11	−3.51157
$261$	4.02408e10	0.536766
$262$	−2.26195e10	−0.296569
$263$	−2.55822e10	−0.329714	−0.164857	−	0.986317i	$-0.552716\pi$
$263$	−2.55822e10	−0.329714	−0.164857	+	0.986317i	$0.552716\pi$
$264$	−4.57746e7	−0.000579972 0
$265$	−9.96638e10	−1.24146
$266$	−6.41670e10	−0.785859
$267$	1.52346e8	0.00183455
$268$	−4.29062e10	−0.508058
$269$	−6.96548e10	−0.811083	−0.405542	−	0.914077i	$-0.632917\pi$
$269$	−6.96548e10	−0.811083	−0.405542	+	0.914077i	$0.632917\pi$
$270$	6.69775e8	0.00766994
$271$	−5.29874e10	−0.596775	−0.298387	−	0.954445i	$-0.596449\pi$
$271$	−5.29874e10	−0.596775	−0.298387	+	0.954445i	$0.596449\pi$
$272$	0	0
$273$	−1.26097e8	−0.00137395
$274$	5.96886e10	0.639755
$275$	4.55457e10	0.480231
$276$	2.05923e8	0.00213607
$277$	1.49045e11	1.52110	0.760552	−	0.649277i	$-0.224928\pi$
$277$	1.49045e11	1.52110	0.760552	+	0.649277i	$0.224928\pi$
$278$	1.11849e10	0.112313
$279$	1.25186e11	1.23690
$280$	−5.45788e10	−0.530656
$281$	−2.16237e10	−0.206896	−0.103448	−	0.994635i	$-0.532987\pi$
$281$	−2.16237e10	−0.206896	−0.103448	+	0.994635i	$0.532987\pi$
$282$	−4.48722e8	−0.00422529
$283$	−1.51427e11	−1.40335	−0.701675	−	0.712498i	$-0.747564\pi$
$283$	−1.51427e11	−1.40335	−0.701675	+	0.712498i	$0.747564\pi$
$284$	7.43100e9	0.0677821
$285$	−2.76448e8	−0.00248206
$286$	−1.33406e11	−1.17904
$287$	2.77777e10	0.241673
$288$	1.41588e11	1.21272
$289$	0	0
$290$	−1.46130e11	−1.21325
$291$	3.56681e8	0.00291582
$292$	3.31312e11	2.66695
$293$	4.42128e10	0.350464	0.175232	−	0.984527i	$-0.443932\pi$
$293$	4.42128e10	0.350464	0.175232	+	0.984527i	$0.443932\pi$
$294$	2.60166e8	0.00203089
$295$	−2.50895e11	−1.92883
$296$	−1.52847e11	−1.15730
$297$	2.06045e8	0.00153659
$298$	6.71865e9	0.0493525
$299$	1.94479e11	1.40719
$300$	−3.73468e8	−0.00266200
$301$	−6.96256e10	−0.488899
$302$	1.02325e11	0.707868
$303$	−2.62556e6	−1.78950e−5 0
$304$	−4.41260e10	−0.296322
$305$	1.51617e11	1.00323
$306$	0	0
$307$	2.29583e11	1.47509	0.737543	−	0.675300i	$-0.235986\pi$
$307$	2.29583e11	1.47509	0.737543	+	0.675300i	$0.235986\pi$
$308$	−5.18134e10	−0.328068
$309$	−5.06145e8	−0.00315836
$310$	−4.54597e11	−2.79576
$311$	4.73812e10	0.287200	0.143600	−	0.989636i	$-0.454132\pi$
$311$	4.73812e10	0.287200	0.143600	+	0.989636i	$0.454132\pi$
$312$	3.54485e8	0.00211788
$313$	−2.62450e11	−1.54560	−0.772801	−	0.634648i	$-0.781145\pi$
$313$	−2.62450e11	−1.54560	−0.772801	+	0.634648i	$0.781145\pi$
$314$	−4.40839e10	−0.255916
$315$	1.22838e11	0.702966
$316$	−8.94711e10	−0.504767
$317$	−9.07698e10	−0.504864	−0.252432	−	0.967615i	$-0.581230\pi$
$317$	−9.07698e10	−0.504864	−0.252432	+	0.967615i	$0.581230\pi$
$318$	4.21345e8	0.00231055
$319$	−4.49546e10	−0.243061
$320$	−4.35870e11	−2.32371
$321$	2.97467e8	0.00156375
$322$	1.26590e11	0.656218
$323$	0	0
$324$	2.93451e11	1.47939
$325$	−3.52712e11	−1.75366
$326$	−5.43138e11	−2.66337
$327$	−5.68840e8	−0.00275122
$328$	−7.80891e10	−0.372527
$329$	−1.64593e11	−0.774515
$330$	−3.74115e8	−0.00173657
$331$	1.53040e11	0.700775	0.350387	−	0.936605i	$-0.386050\pi$
$331$	1.53040e11	0.700775	0.350387	+	0.936605i	$0.386050\pi$
$332$	5.62772e11	2.54221
$333$	3.44005e11	1.53308
$334$	−2.84417e11	−1.25054
$335$	−1.13636e11	−0.492963
$336$	−5.64434e7	−0.000241594 0
$337$	−4.73479e10	−0.199971	−0.0999854	−	0.994989i	$-0.531880\pi$
$337$	−4.73479e10	−0.199971	−0.0999854	+	0.994989i	$0.531880\pi$
$338$	6.55282e11	2.73088
$339$	4.26019e8	0.00175198
$340$	0	0
$341$	−1.39850e11	−0.560101
$342$	−4.05989e11	−1.60471
$343$	2.20966e11	0.861991
$344$	1.95733e11	0.753616
$345$	5.45384e8	0.00207260
$346$	−2.38843e11	−0.895923
$347$	−1.71966e11	−0.636736	−0.318368	−	0.947967i	$-0.603135\pi$
$347$	−1.71966e11	−0.636736	−0.318368	+	0.947967i	$0.603135\pi$
$348$	3.68621e8	0.00134733
$349$	−9.37822e10	−0.338381	−0.169191	−	0.985583i	$-0.554115\pi$
$349$	−9.37822e10	−0.338381	−0.169191	+	0.985583i	$0.554115\pi$
$350$	−2.29587e11	−0.817789
$351$	−1.59564e9	−0.00561118
$352$	−1.58173e11	−0.549149
$353$	3.21525e11	1.10212	0.551059	−	0.834466i	$-0.314224\pi$
$353$	3.21525e11	1.10212	0.551059	+	0.834466i	$0.314224\pi$
$354$	1.06070e9	0.00358986
$355$	1.96809e10	0.0657683
$356$	−4.84778e11	−1.59963
$357$	0	0
$358$	−2.31743e11	−0.745647
$359$	−2.50132e10	−0.0794776	−0.0397388	−	0.999210i	$-0.512653\pi$
$359$	−2.50132e10	−0.0794776	−0.0397388	+	0.999210i	$0.512653\pi$
$360$	−3.45324e11	−1.08359
$361$	1.24551e10	0.0385981
$362$	5.75706e10	0.176202
$363$	4.46190e8	0.00134878
$364$	4.01250e11	1.19801
$365$	8.77472e11	2.58771
$366$	−6.40987e8	−0.00186717
$367$	5.32399e11	1.53193	0.765967	−	0.642880i	$-0.222260\pi$
$367$	5.32399e11	1.53193	0.765967	+	0.642880i	$0.222260\pi$
$368$	8.70528e10	0.247439
$369$	1.75751e11	0.493491
$370$	−1.24922e12	−3.46521
$371$	1.54551e11	0.423535
$372$	1.14675e9	0.00310473
$373$	−3.56768e11	−0.954325	−0.477163	−	0.878815i	$-0.658335\pi$
$373$	−3.56768e11	−0.954325	−0.477163	+	0.878815i	$0.658335\pi$
$374$	0	0
$375$	−5.64493e7	−0.000147407 0
$376$	4.62707e11	1.19388
$377$	3.48134e11	0.887586
$378$	−1.03863e9	−0.00261667
$379$	−2.85881e11	−0.711720	−0.355860	−	0.934539i	$-0.615812\pi$
$379$	−2.85881e11	−0.711720	−0.355860	+	0.934539i	$0.615812\pi$
$380$	8.79683e11	2.16421
$381$	3.10707e8	0.000755421 0
$382$	−1.08638e12	−2.61033
$383$	−3.68259e11	−0.874498	−0.437249	−	0.899340i	$-0.644047\pi$
$383$	−3.68259e11	−0.874498	−0.437249	+	0.899340i	$0.644047\pi$
$384$	9.66012e8	0.00226721
$385$	−1.37227e11	−0.318321
$386$	−1.03065e12	−2.36302
$387$	−4.40525e11	−0.998324
$388$	−1.13499e12	−2.54243
$389$	3.24891e11	0.719391	0.359696	−	0.933070i	$-0.382881\pi$
$389$	3.24891e11	0.719391	0.359696	+	0.933070i	$0.382881\pi$
$390$	2.89720e9	0.00634143
$391$	0	0
$392$	−2.68274e11	−0.573841
$393$	1.51119e8	0.000319560 0
$394$	8.83321e10	0.184665
$395$	−2.36962e11	−0.489770
$396$	−3.27827e11	−0.669909
$397$	−1.08653e11	−0.219525	−0.109763	−	0.993958i	$-0.535009\pi$
$397$	−1.08653e11	−0.219525	−0.109763	+	0.993958i	$0.535009\pi$
$398$	8.43333e11	1.68471
$399$	4.28695e8	0.000846779 0
$400$	−1.57881e11	−0.308362
$401$	1.67993e11	0.324446	0.162223	−	0.986754i	$-0.448134\pi$
$401$	1.67993e11	0.324446	0.162223	+	0.986754i	$0.448134\pi$
$402$	4.80415e8	0.000917486 0
$403$	1.08301e12	2.04532
$404$	8.35477e9	0.0156034
$405$	7.77200e11	1.43544
$406$	2.26607e11	0.413911
$407$	−3.84301e11	−0.694220
$408$	0	0
$409$	3.07465e11	0.543302	0.271651	−	0.962396i	$-0.412430\pi$
$409$	3.07465e11	0.543302	0.271651	+	0.962396i	$0.412430\pi$
$410$	−6.38220e11	−1.11543
$411$	−3.98775e8	−0.000689349 0
$412$	1.61060e12	2.75391
$413$	3.89069e11	0.658038
$414$	8.00943e11	1.33999
$415$	1.49049e12	2.46668
$416$	1.22491e12	2.00533
$417$	−7.47254e7	−0.000121020 0
$418$	4.53545e11	0.726654
$419$	4.23303e11	0.670947	0.335473	−	0.942050i	$-0.391104\pi$
$419$	4.23303e11	0.670947	0.335473	+	0.942050i	$0.391104\pi$
$420$	1.12524e9	0.00176450
$421$	−1.49913e11	−0.232578	−0.116289	−	0.993215i	$-0.537100\pi$
$421$	−1.49913e11	−0.232578	−0.116289	+	0.993215i	$0.537100\pi$
$422$	1.80550e12	2.77135
$423$	−1.04139e12	−1.58155
$424$	−4.34476e11	−0.652860
$425$	0	0
$426$	−8.32040e7	−0.000122406 0
$427$	−2.35116e11	−0.342261
$428$	−9.46566e11	−1.36350
$429$	8.91276e8	0.00127044
$430$	1.59972e12	2.25650
$431$	−1.13823e12	−1.58885	−0.794427	−	0.607360i	$-0.792229\pi$
$431$	−1.13823e12	−1.58885	−0.794427	+	0.607360i	$0.792229\pi$
$432$	−7.14243e8	−0.000986663 0
$433$	9.00628e11	1.23126	0.615630	−	0.788035i	$-0.288902\pi$
$433$	9.00628e11	1.23126	0.615630	+	0.788035i	$0.288902\pi$
$434$	7.04954e11	0.953800
$435$	9.76284e8	0.00130730
$436$	1.81010e12	2.39890
$437$	−6.61177e11	−0.867264
$438$	−3.70966e9	−0.00481615
$439$	2.15467e11	0.276879	0.138440	−	0.990371i	$-0.455791\pi$
$439$	2.15467e11	0.276879	0.138440	+	0.990371i	$0.455791\pi$
$440$	3.85774e11	0.490678
$441$	6.03791e11	0.760173
$442$	0	0
$443$	3.47695e11	0.428925	0.214462	−	0.976732i	$-0.431200\pi$
$443$	3.47695e11	0.428925	0.214462	+	0.976732i	$0.431200\pi$
$444$	3.15121e9	0.00384817
$445$	−1.28393e12	−1.55210
$446$	6.63923e11	0.794531
$447$	−4.48868e7	−5.31783e−5 0
$448$	6.75913e11	0.792757
$449$	−1.08563e12	−1.26059	−0.630296	−	0.776355i	$-0.717066\pi$
$449$	−1.08563e12	−1.26059	−0.630296	+	0.776355i	$0.717066\pi$
$450$	−1.45261e12	−1.66991
$451$	−1.96338e11	−0.223465
$452$	−1.35563e12	−1.52763
$453$	−6.83629e8	−0.000762743 0
$454$	2.40823e12	2.66040
$455$	1.06270e12	1.16241
$456$	−1.20515e9	−0.00130527
$457$	−8.91105e11	−0.955666	−0.477833	−	0.878451i	$-0.658578\pi$
$457$	−8.91105e11	−0.955666	−0.477833	+	0.878451i	$0.658578\pi$
$458$	−1.65875e11	−0.176152
$459$	0	0
$460$	−1.73546e12	−1.80719
$461$	7.21170e11	0.743675	0.371838	−	0.928298i	$-0.378728\pi$
$461$	7.21170e11	0.743675	0.371838	+	0.928298i	$0.378728\pi$
$462$	5.80148e8	0.000592448 0
$463$	2.47341e11	0.250139	0.125069	−	0.992148i	$-0.460085\pi$
$463$	2.47341e11	0.250139	0.125069	+	0.992148i	$0.460085\pi$
$464$	1.55832e11	0.156072
$465$	3.03713e9	0.00301249
$466$	−1.09663e12	−1.07727
$467$	3.73549e10	0.0363431	0.0181715	−	0.999835i	$-0.494215\pi$
$467$	3.73549e10	0.0363431	0.0181715	+	0.999835i	$0.494215\pi$
$468$	2.53873e12	2.44631
$469$	1.76218e11	0.168179
$470$	3.78169e12	3.57475
$471$	2.94521e8	0.000275754 0
$472$	−1.09376e12	−1.01434
$473$	4.92128e11	0.452067
$474$	1.00180e9	0.000911543 0
$475$	1.19913e12	1.08080
$476$	0	0
$477$	9.77853e11	0.864851
$478$	2.69257e12	2.35908
$479$	1.56185e11	0.135560	0.0677798	−	0.997700i	$-0.478408\pi$
$479$	1.56185e11	0.135560	0.0677798	+	0.997700i	$0.478408\pi$
$480$	3.43506e9	0.00295358
$481$	2.97608e12	2.53508
$482$	−9.55959e11	−0.806729
$483$	−8.45739e8	−0.000707089 0
$484$	−1.41981e12	−1.17605
$485$	−3.00600e12	−2.46689
$486$	−9.85726e9	−0.00801481
$487$	−7.04881e11	−0.567853	−0.283926	−	0.958846i	$-0.591637\pi$
$487$	−7.04881e11	−0.567853	−0.283926	+	0.958846i	$0.591637\pi$
$488$	6.60964e11	0.527580
$489$	3.62867e9	0.00286984
$490$	−2.19260e12	−1.71821
$491$	2.70124e11	0.209747	0.104874	−	0.994486i	$-0.466556\pi$
$491$	2.70124e11	0.209747	0.104874	+	0.994486i	$0.466556\pi$
$492$	1.60994e9	0.00123870
$493$	0	0
$494$	−3.51232e12	−2.65352
$495$	−8.68242e11	−0.650006
$496$	4.84779e11	0.359647
$497$	−3.05195e10	−0.0224375
$498$	−6.30129e9	−0.00459090
$499$	−1.68888e12	−1.21940	−0.609699	−	0.792633i	$-0.708710\pi$
$499$	−1.68888e12	−1.21940	−0.609699	+	0.792633i	$0.708710\pi$
$500$	1.79626e11	0.128530
$501$	1.90017e9	0.00134748
$502$	1.47787e12	1.03865
$503$	−4.85829e11	−0.338398	−0.169199	−	0.985582i	$-0.554118\pi$
$503$	−4.85829e11	−0.338398	−0.169199	+	0.985582i	$0.554118\pi$
$504$	5.35501e11	0.369678
$505$	2.21274e10	0.0151398
$506$	−8.94764e11	−0.606780
$507$	−4.37789e9	−0.00294259
$508$	−9.88698e11	−0.658684
$509$	4.99864e11	0.330082	0.165041	−	0.986287i	$-0.447224\pi$
$509$	4.99864e11	0.330082	0.165041	+	0.986287i	$0.447224\pi$
$510$	0	0
$511$	−1.36072e12	−0.882823
$512$	8.89593e11	0.572106
$513$	5.42477e9	0.00345822
$514$	1.72040e12	1.08717
$515$	4.26563e12	2.67209
$516$	−4.03537e9	−0.00250588
$517$	1.16338e12	0.716165
$518$	1.93719e12	1.18219
$519$	1.59569e9	0.000965376 0
$520$	−2.98749e12	−1.79181
$521$	2.25253e12	1.33937	0.669687	−	0.742644i	$-0.266428\pi$
$521$	2.25253e12	1.33937	0.669687	+	0.742644i	$0.266428\pi$
$522$	1.43376e12	0.845198
$523$	1.33630e12	0.780990	0.390495	−	0.920605i	$-0.372304\pi$
$523$	1.33630e12	0.780990	0.390495	+	0.920605i	$0.372304\pi$
$524$	−4.80873e11	−0.278638
$525$	1.53385e9	0.000881185 0
$526$	−9.11481e11	−0.519172
$527$	0	0
$528$	3.98953e8	0.000223393 0
$529$	−4.96768e11	−0.275806
$530$	−3.55097e12	−1.95481
$531$	2.46166e12	1.34370
$532$	−1.36414e12	−0.738343
$533$	1.52047e12	0.816028
$534$	5.42800e9	0.00288871
$535$	−2.50696e12	−1.32299
$536$	−4.95387e11	−0.259241
$537$	1.54826e9	0.000803451 0
$538$	−2.48176e12	−1.27714
$539$	−6.74517e11	−0.344226
$540$	1.42389e10	0.00720618
$541$	1.60577e12	0.805928	0.402964	−	0.915216i	$-0.367980\pi$
$541$	1.60577e12	0.805928	0.402964	+	0.915216i	$0.367980\pi$
$542$	−1.88791e12	−0.939689
$543$	−3.84625e8	−0.000189862 0
$544$	0	0
$545$	4.79400e12	2.32763
$546$	−4.49275e9	−0.00216344
$547$	2.50244e12	1.19515	0.597573	−	0.801815i	$-0.296132\pi$
$547$	2.50244e12	1.19515	0.597573	+	0.801815i	$0.296132\pi$
$548$	1.26894e12	0.601073
$549$	−1.48760e12	−0.698891
$550$	1.62277e12	0.756178
$551$	−1.18356e12	−0.547028
$552$	2.37756e9	0.00108995
$553$	3.67463e11	0.167090
$554$	5.31040e12	2.39515
$555$	8.34592e9	0.00373384
$556$	2.37783e11	0.105522
$557$	3.78565e10	0.0166645	0.00833225	−	0.999965i	$-0.497348\pi$
$557$	3.78565e10	0.0166645	0.00833225	+	0.999965i	$0.497348\pi$
$558$	4.46029e12	1.94764
$559$	−3.81110e12	−1.65081
$560$	4.75687e11	0.204397
$561$	0	0
$562$	−7.70440e11	−0.325781
$563$	−3.79841e12	−1.59336	−0.796681	−	0.604400i	$-0.793413\pi$
$563$	−3.79841e12	−1.59336	−0.796681	+	0.604400i	$0.793413\pi$
$564$	−9.53952e9	−0.00396982
$565$	−3.59035e12	−1.48224
$566$	−5.39527e12	−2.20973
$567$	−1.20522e12	−0.489715
$568$	8.57971e10	0.0345864
$569$	4.15125e12	1.66025	0.830126	−	0.557575i	$-0.188268\pi$
$569$	4.15125e12	1.66025	0.830126	+	0.557575i	$0.188268\pi$
$570$	−9.84970e9	−0.00390828
$571$	2.49821e12	0.983483	0.491741	−	0.870741i	$-0.336361\pi$
$571$	2.49821e12	0.983483	0.491741	+	0.870741i	$0.336361\pi$
$572$	−2.83612e12	−1.10775
$573$	7.25800e9	0.00281268
$574$	9.89702e11	0.380541
$575$	−2.36567e12	−0.902502
$576$	4.27655e12	1.61880
$577$	9.96726e11	0.374356	0.187178	−	0.982326i	$-0.440066\pi$
$577$	9.96726e11	0.374356	0.187178	+	0.982326i	$0.440066\pi$
$578$	0	0
$579$	6.88567e9	0.00254620
$580$	−3.10662e12	−1.13989
$581$	−2.31134e12	−0.841532
$582$	1.27083e10	0.00459129
$583$	−1.09240e12	−0.391627
$584$	3.82527e12	1.36083
$585$	6.72378e12	2.37363
$586$	1.57528e12	0.551845
$587$	−3.55291e12	−1.23513	−0.617566	−	0.786519i	$-0.711881\pi$
$587$	−3.55291e12	−1.23513	−0.617566	+	0.786519i	$0.711881\pi$
$588$	5.53094e9	0.00190810
$589$	−3.68196e12	−1.26055
$590$	−8.93925e12	−3.03716
$591$	−5.90140e8	−0.000198981 0
$592$	1.33215e12	0.445766
$593$	4.25252e12	1.41221	0.706107	−	0.708105i	$-0.250450\pi$
$593$	4.25252e12	1.41221	0.706107	+	0.708105i	$0.250450\pi$
$594$	7.34128e9	0.00241954
$595$	0	0
$596$	1.42834e11	0.0463684
$597$	−5.63424e9	−0.00181531
$598$	6.92917e12	2.21578
$599$	−4.95143e12	−1.57149	−0.785743	−	0.618554i	$-0.787719\pi$
$599$	−4.95143e12	−1.57149	−0.785743	+	0.618554i	$0.787719\pi$
$600$	−4.31200e9	−0.00135831
$601$	1.76825e12	0.552850	0.276425	−	0.961035i	$-0.410850\pi$
$601$	1.76825e12	0.552850	0.276425	+	0.961035i	$0.410850\pi$
$602$	−2.48072e12	−0.769827
$603$	1.11494e12	0.343419
$604$	2.17537e12	0.665068
$605$	−3.76035e12	−1.14111
$606$	−9.35473e7	−2.81776e−5 0
$607$	−2.04371e11	−0.0611042	−0.0305521	−	0.999533i	$-0.509727\pi$
$607$	−2.04371e11	−0.0611042	−0.0305521	+	0.999533i	$0.509727\pi$
$608$	−4.16438e12	−1.23590
$609$	−1.51395e9	−0.000445997 0
$610$	5.40204e12	1.57970
$611$	−9.00935e12	−2.61522
$612$	0	0
$613$	−1.76517e12	−0.504911	−0.252455	−	0.967609i	$-0.581238\pi$
$613$	−1.76517e12	−0.504911	−0.252455	+	0.967609i	$0.581238\pi$
$614$	8.17992e12	2.32269
$615$	4.26390e9	0.00120190
$616$	−5.98229e11	−0.167399
$617$	−4.51327e12	−1.25374	−0.626872	−	0.779123i	$-0.715665\pi$
$617$	−4.51327e12	−1.25374	−0.626872	+	0.779123i	$0.715665\pi$
$618$	−1.80337e10	−0.00497320
$619$	2.40683e10	0.00658926	0.00329463	−	0.999995i	$-0.498951\pi$
$619$	2.40683e10	0.00658926	0.00329463	+	0.999995i	$0.498951\pi$
$620$	−9.66441e12	−2.62671
$621$	−1.07021e10	−0.00288773
$622$	1.68816e12	0.452228
$623$	1.99101e12	0.529514
$624$	−3.08955e9	−0.000815764 0
$625$	−3.56984e12	−0.935813
$626$	−9.35096e12	−2.43373
$627$	−3.03010e9	−0.000782985 0
$628$	−9.37192e11	−0.240442
$629$	0	0
$630$	4.37664e12	1.10690
$631$	−5.35424e12	−1.34451	−0.672257	−	0.740318i	$-0.734675\pi$
$631$	−5.35424e12	−1.34451	−0.672257	+	0.740318i	$0.734675\pi$
$632$	−1.03302e12	−0.257562
$633$	−1.20624e10	−0.00298619
$634$	−3.23408e12	−0.794966
$635$	−2.61854e12	−0.639114
$636$	8.95749e9	0.00217085
$637$	5.22355e12	1.25701
$638$	−1.60171e12	−0.382727
$639$	−1.93099e11	−0.0458170
$640$	−8.14125e12	−1.91814
$641$	6.68364e12	1.56369	0.781847	−	0.623470i	$-0.214278\pi$
$641$	6.68364e12	1.56369	0.781847	+	0.623470i	$0.214278\pi$
$642$	1.05986e10	0.00246229
$643$	−4.42198e12	−1.02016	−0.510079	−	0.860128i	$-0.670384\pi$
$643$	−4.42198e12	−1.02016	−0.510079	+	0.860128i	$0.670384\pi$
$644$	2.69121e12	0.616541
$645$	−1.06876e10	−0.00243143
$646$	0	0
$647$	7.65641e12	1.71773	0.858867	−	0.512198i	$-0.171169\pi$
$647$	7.65641e12	1.71773	0.858867	+	0.512198i	$0.171169\pi$
$648$	3.38814e12	0.754873
$649$	−2.75002e12	−0.608463
$650$	−1.25669e13	−2.76134
$651$	−4.70975e9	−0.00102774
$652$	−1.15467e13	−2.50233
$653$	−8.87094e12	−1.90924	−0.954620	−	0.297826i	$-0.903738\pi$
$653$	−8.87094e12	−1.90924	−0.954620	+	0.297826i	$0.903738\pi$
$654$	−2.02674e10	−0.00433210
$655$	−1.27358e12	−0.270359
$656$	6.80593e11	0.143490
$657$	−8.60933e12	−1.80271
$658$	−5.86436e12	−1.21956
$659$	2.06299e12	0.426101	0.213051	−	0.977041i	$-0.431660\pi$
$659$	2.06299e12	0.426101	0.213051	+	0.977041i	$0.431660\pi$
$660$	−7.95341e9	−0.00163157
$661$	1.41824e11	0.0288965	0.0144482	−	0.999896i	$-0.495401\pi$
$661$	1.41824e11	0.0288965	0.0144482	+	0.999896i	$0.495401\pi$
$662$	5.45272e12	1.10345
$663$	0	0
$664$	6.49767e12	1.29718
$665$	−3.61291e12	−0.716406
$666$	1.22567e13	2.41401
$667$	2.33496e12	0.456787
$668$	−6.04650e12	−1.17493
$669$	−4.43562e9	−0.000856124 0
$670$	−4.04879e12	−0.776226
$671$	1.66185e12	0.316476
$672$	−5.32683e9	−0.00100764
$673$	−9.81683e11	−0.184460	−0.0922302	−	0.995738i	$-0.529400\pi$
$673$	−9.81683e11	−0.184460	−0.0922302	+	0.995738i	$0.529400\pi$
$674$	−1.68698e12	−0.314877
$675$	1.94096e10	0.00359873
$676$	1.39308e13	2.56577
$677$	2.20727e12	0.403837	0.201919	−	0.979402i	$-0.435282\pi$
$677$	2.20727e12	0.403837	0.201919	+	0.979402i	$0.435282\pi$
$678$	1.51788e10	0.00275870
$679$	4.66146e12	0.841605
$680$	0	0
$681$	−1.60892e10	−0.00286663
$682$	−4.98276e12	−0.881942
$683$	3.00134e11	0.0527742	0.0263871	−	0.999652i	$-0.491600\pi$
$683$	3.00134e11	0.0527742	0.0263871	+	0.999652i	$0.491600\pi$
$684$	−8.63103e12	−1.50768
$685$	3.36075e12	0.583215
$686$	7.87291e12	1.35730
$687$	1.10820e9	0.000189807 0
$688$	−1.70593e12	−0.290277
$689$	8.45967e12	1.43010
$690$	1.94317e10	0.00326355
$691$	7.77169e10	0.0129677	0.00648387	−	0.999979i	$-0.497936\pi$
$691$	7.77169e10	0.0129677	0.00648387	+	0.999979i	$0.497936\pi$
$692$	−5.07764e12	−0.841752
$693$	1.34640e12	0.221756
$694$	−6.12704e12	−1.00261
$695$	6.29762e11	0.102387
$696$	4.25603e9	0.000687485 0
$697$	0	0
$698$	−3.34141e12	−0.532819
$699$	7.32651e9	0.00116078
$700$	−4.88086e12	−0.768342
$701$	5.48906e12	0.858552	0.429276	−	0.903173i	$-0.358769\pi$
$701$	5.48906e12	0.858552	0.429276	+	0.903173i	$0.358769\pi$
$702$	−5.68519e10	−0.00883543
$703$	−1.01179e13	−1.56240
$704$	−4.77749e12	−0.733032
$705$	−2.52652e10	−0.00385187
$706$	1.14557e13	1.73541
$707$	−3.43135e10	−0.00516509
$708$	2.25497e10	0.00337281
$709$	2.18350e12	0.324523	0.162262	−	0.986748i	$-0.448121\pi$
$709$	2.18350e12	0.324523	0.162262	+	0.986748i	$0.448121\pi$
$710$	7.01217e11	0.103560
$711$	2.32496e12	0.341195
$712$	−5.59717e12	−0.816222
$713$	7.26385e12	1.05260
$714$	0	0
$715$	−7.51139e12	−1.07484
$716$	−4.92669e12	−0.700562
$717$	−1.79889e10	−0.00254196
$718$	−8.91207e11	−0.125146
$719$	−6.20764e12	−0.866257	−0.433128	−	0.901332i	$-0.642590\pi$
$719$	−6.20764e12	−0.866257	−0.433128	+	0.901332i	$0.642590\pi$
$720$	3.00970e12	0.417376
$721$	−6.61482e12	−0.911610
$722$	4.43769e11	0.0607771
$723$	6.38669e9	0.000869267 0
$724$	1.22391e12	0.165549
$725$	−4.23475e12	−0.569255
$726$	1.58975e10	0.00212380
$727$	8.67792e12	1.15215	0.576077	−	0.817395i	$-0.304583\pi$
$727$	8.67792e12	1.15215	0.576077	+	0.817395i	$0.304583\pi$
$728$	4.63276e12	0.611292
$729$	−7.62547e12	−0.999983
$730$	3.12638e13	4.07464
$731$	0	0
$732$	−1.36269e10	−0.00175428
$733$	6.34487e12	0.811811	0.405905	−	0.913915i	$-0.366956\pi$
$733$	6.34487e12	0.811811	0.405905	+	0.913915i	$0.366956\pi$
$734$	1.89691e13	2.41220
$735$	1.46486e10	0.00185141
$736$	8.21558e12	1.03202
$737$	−1.24554e12	−0.155509
$738$	6.26191e12	0.777057
$739$	−1.28807e13	−1.58869	−0.794344	−	0.607468i	$-0.792185\pi$
$739$	−1.28807e13	−1.58869	−0.794344	+	0.607468i	$0.792185\pi$
$740$	−2.65574e13	−3.25569
$741$	2.34655e10	0.00285922
$742$	5.50656e12	0.666903
$743$	−1.97478e12	−0.237722	−0.118861	−	0.992911i	$-0.537924\pi$
$743$	−1.97478e12	−0.237722	−0.118861	+	0.992911i	$0.537924\pi$
$744$	1.32401e10	0.00158421
$745$	3.78292e11	0.0449908
$746$	−1.27114e13	−1.50269
$747$	−1.46240e13	−1.71839
$748$	0	0
$749$	3.88760e12	0.451350
$750$	−2.01125e9	−0.000232109 0
$751$	−1.19872e13	−1.37512	−0.687558	−	0.726129i	$-0.741317\pi$
$751$	−1.19872e13	−1.37512	−0.687558	+	0.726129i	$0.741317\pi$
$752$	−4.03277e12	−0.459857
$753$	−9.87356e9	−0.00111917
$754$	1.24038e13	1.39761
$755$	5.76141e12	0.645309
$756$	−2.20806e10	−0.00245846
$757$	−9.64713e12	−1.06774	−0.533871	−	0.845566i	$-0.679263\pi$
$757$	−9.64713e12	−1.06774	−0.533871	+	0.845566i	$0.679263\pi$
$758$	−1.01858e13	−1.12068
$759$	5.97785e9	0.000653818 0
$760$	1.01567e13	1.10431
$761$	−4.48077e12	−0.484308	−0.242154	−	0.970238i	$-0.577854\pi$
$761$	−4.48077e12	−0.484308	−0.242154	+	0.970238i	$0.577854\pi$
$762$	1.10703e10	0.00118950
$763$	−7.43417e12	−0.794094
$764$	−2.30956e13	−2.45250
$765$	0	0
$766$	−1.31209e13	−1.37700
$767$	2.12965e13	2.22192
$768$	7.93844e9	0.000823397 0
$769$	1.58699e13	1.63646	0.818230	−	0.574891i	$-0.194956\pi$
$769$	1.58699e13	1.63646	0.818230	+	0.574891i	$0.194956\pi$
$770$	−4.88931e12	−0.501233
$771$	−1.14939e10	−0.00117145
$772$	−2.19108e13	−2.22014
$773$	−1.21257e12	−0.122151	−0.0610755	−	0.998133i	$-0.519453\pi$
$773$	−1.21257e12	−0.122151	−0.0610755	+	0.998133i	$0.519453\pi$
$774$	−1.56957e13	−1.57197
$775$	−1.31739e13	−1.31177
$776$	−1.31044e13	−1.29730
$777$	−1.29422e10	−0.00127384
$778$	1.15757e13	1.13276
$779$	−5.16919e12	−0.502926
$780$	6.15923e10	0.00595800
$781$	2.15718e11	0.0207471
$782$	0	0
$783$	−1.91577e10	−0.00182144
$784$	2.33817e12	0.221031
$785$	−2.48213e12	−0.233298
$786$	5.38428e9	0.000503183 0
$787$	−1.14356e13	−1.06261	−0.531304	−	0.847181i	$-0.678298\pi$
$787$	−1.14356e13	−1.06261	−0.531304	+	0.847181i	$0.678298\pi$
$788$	1.87788e12	0.173500
$789$	6.08953e9	0.000559419 0
$790$	−8.44283e12	−0.771199
$791$	5.56764e12	0.505682
$792$	−3.78503e12	−0.341827
$793$	−1.28696e13	−1.15567
$794$	−3.87124e12	−0.345667
$795$	2.37237e10	0.00210635
$796$	1.79286e13	1.58285
$797$	1.15535e13	1.01427	0.507133	−	0.861868i	$-0.330705\pi$
$797$	1.15535e13	1.01427	0.507133	+	0.861868i	$0.330705\pi$
$798$	1.52742e10	0.00133335
$799$	0	0
$800$	−1.49000e13	−1.28612
$801$	1.25973e13	1.08126
$802$	5.98550e12	0.510876
$803$	9.61781e12	0.816313
$804$	1.02133e10	0.000862011 0
$805$	7.12762e12	0.598223
$806$	3.85872e13	3.22059
$807$	1.65804e10	0.00137615
$808$	9.64627e10	0.00796175
$809$	−1.64570e13	−1.35077	−0.675387	−	0.737464i	$-0.736023\pi$
$809$	−1.64570e13	−1.35077	−0.675387	+	0.737464i	$0.736023\pi$
$810$	2.76912e13	2.26026
$811$	−4.72555e12	−0.383582	−0.191791	−	0.981436i	$-0.561430\pi$
$811$	−4.72555e12	−0.383582	−0.191791	+	0.981436i	$0.561430\pi$
$812$	4.81751e12	0.388884
$813$	1.26130e10	0.00101254
$814$	−1.36924e13	−1.09313
$815$	−3.05813e13	−2.42799
$816$	0	0
$817$	1.29567e13	1.01741
$818$	1.09548e13	0.855490
$819$	−1.04267e13	−0.809786
$820$	−1.35681e13	−1.04799
$821$	1.56503e13	1.20221	0.601103	−	0.799172i	$-0.294728\pi$
$821$	1.56503e13	1.20221	0.601103	+	0.799172i	$0.294728\pi$
$822$	−1.42081e10	−0.00108546
$823$	−7.85441e12	−0.596780	−0.298390	−	0.954444i	$-0.596450\pi$
$823$	−7.85441e12	−0.596780	−0.298390	+	0.954444i	$0.596450\pi$
$824$	1.85957e13	1.40521
$825$	−1.08416e10	−0.000814798 0
$826$	1.38623e13	1.03616
$827$	2.59264e13	1.92738	0.963689	−	0.267026i	$-0.0860411\pi$
$827$	2.59264e13	1.92738	0.963689	+	0.267026i	$0.0860411\pi$
$828$	1.70275e13	1.25897
$829$	8.15862e12	0.599959	0.299979	−	0.953946i	$-0.403020\pi$
$829$	8.15862e12	0.599959	0.299979	+	0.953946i	$0.403020\pi$
$830$	5.31053e13	3.88407
$831$	−3.54784e10	−0.00258083
$832$	3.69975e13	2.67681
$833$	0	0
$834$	−2.66242e9	−0.000190559 0
$835$	−1.60140e13	−1.14002
$836$	9.64205e12	0.682717
$837$	−5.95978e10	−0.00419726
$838$	1.50820e13	1.05648
$839$	1.19352e13	0.831576	0.415788	−	0.909462i	$-0.363506\pi$
$839$	1.19352e13	0.831576	0.415788	+	0.909462i	$0.363506\pi$
$840$	1.29918e10	0.000900353 0
$841$	−1.03274e13	−0.711881
$842$	−5.34130e12	−0.366221
$843$	5.14725e9	0.000351036 0
$844$	3.83836e13	2.60378
$845$	3.68955e13	2.48954
$846$	−3.71041e13	−2.49032
$847$	5.83125e12	0.389302
$848$	3.78672e12	0.251468
$849$	3.60454e10	0.00238103
$850$	0	0
$851$	1.99608e13	1.30465
$852$	−1.76886e9	−0.000115004 0
$853$	−1.88383e13	−1.21835	−0.609174	−	0.793037i	$-0.708499\pi$
$853$	−1.88383e13	−1.21835	−0.609174	+	0.793037i	$0.708499\pi$
$854$	−8.37706e12	−0.538929
$855$	−2.28591e13	−1.46289
$856$	−1.09289e13	−0.695735
$857$	1.23172e13	0.780009	0.390005	−	0.920813i	$-0.372473\pi$
$857$	1.23172e13	0.780009	0.390005	+	0.920813i	$0.372473\pi$
$858$	3.17556e10	0.00200045
$859$	1.58752e13	0.994832	0.497416	−	0.867512i	$-0.334282\pi$
$859$	1.58752e13	0.994832	0.497416	+	0.867512i	$0.334282\pi$
$860$	3.40089e13	2.12006
$861$	−6.61213e9	−0.000410041 0
$862$	−4.05546e13	−2.50183
$863$	2.03855e13	1.25104	0.625521	−	0.780207i	$-0.284886\pi$
$863$	2.03855e13	1.25104	0.625521	+	0.780207i	$0.284886\pi$
$864$	−6.74064e10	−0.00411518
$865$	−1.34480e13	−0.816743
$866$	3.20889e13	1.93876
$867$	0	0
$868$	1.49868e13	0.896129
$869$	−2.59730e12	−0.154502
$870$	3.47844e10	0.00205849
$871$	9.64566e12	0.567872
$872$	2.08991e13	1.22406
$873$	2.94934e13	1.71854
$874$	−2.35574e13	−1.36561
$875$	−7.37736e11	−0.0425466
$876$	−7.88646e10	−0.00452495
$877$	−2.26963e13	−1.29556	−0.647778	−	0.761829i	$-0.724302\pi$
$877$	−2.26963e13	−1.29556	−0.647778	+	0.761829i	$0.724302\pi$
$878$	7.67696e12	0.435977
$879$	−1.05243e10	−0.000594625 0
$880$	−3.36225e12	−0.188999
$881$	−5.12762e12	−0.286764	−0.143382	−	0.989667i	$-0.545798\pi$
$881$	−5.12762e12	−0.286764	−0.143382	+	0.989667i	$0.545798\pi$
$882$	2.15127e13	1.19698
$883$	−2.76572e13	−1.53104	−0.765518	−	0.643415i	$-0.777517\pi$
$883$	−2.76572e13	−1.53104	−0.765518	+	0.643415i	$0.777517\pi$
$884$	0	0
$885$	5.97224e10	0.00327260
$886$	1.23882e13	0.675391
$887$	2.27687e13	1.23504	0.617521	−	0.786554i	$-0.288137\pi$
$887$	2.27687e13	1.23504	0.617521	+	0.786554i	$0.288137\pi$
$888$	3.63834e10	0.00196356
$889$	4.06064e12	0.218040
$890$	−4.57455e13	−2.44396
$891$	8.51875e12	0.452820
$892$	1.41145e13	0.746491
$893$	3.06294e13	1.61178
$894$	−1.59929e9	−8.37353e−5 0
$895$	−1.30482e13	−0.679748
$896$	1.26248e13	0.654394
$897$	−4.62933e10	−0.00238755
$898$	−3.86805e13	−1.98494
$899$	1.30029e13	0.663930
$900$	−3.08815e13	−1.56894
$901$	0	0
$902$	−6.99542e12	−0.351872
$903$	1.65735e10	0.000829505 0
$904$	−1.56519e13	−0.779485
$905$	3.24150e12	0.160630
$906$	−2.43573e10	−0.00120103
$907$	−1.29915e13	−0.637423	−0.318711	−	0.947852i	$-0.603250\pi$
$907$	−1.29915e13	−0.637423	−0.318711	+	0.947852i	$0.603250\pi$
$908$	5.11972e13	2.49954
$909$	−2.17104e11	−0.0105470
$910$	3.78635e13	1.83035
$911$	−2.54247e13	−1.22299	−0.611496	−	0.791248i	$-0.709432\pi$
$911$	−2.54247e13	−1.22299	−0.611496	+	0.791248i	$0.709432\pi$
$912$	1.05036e10	0.000502763 0
$913$	1.63370e13	0.778133
$914$	−3.17496e13	−1.50480
$915$	−3.60906e10	−0.00170216
$916$	−3.52639e12	−0.165501
$917$	1.97497e12	0.0922357
$918$	0	0
$919$	−2.91533e13	−1.34824	−0.674121	−	0.738621i	$-0.735477\pi$
$919$	−2.91533e13	−1.34824	−0.674121	+	0.738621i	$0.735477\pi$
$920$	−2.00373e13	−0.922134
$921$	−5.46494e10	−0.00250275
$922$	2.56949e13	1.17100
$923$	−1.67055e12	−0.0757621
$924$	1.23335e10	0.000556626 0
$925$	−3.62014e13	−1.62588
$926$	8.81261e12	0.393872
$927$	−4.18523e13	−1.86149
$928$	1.47066e13	0.650948
$929$	−3.16234e13	−1.39296	−0.696480	−	0.717576i	$-0.745251\pi$
$929$	−3.16234e13	−1.39296	−0.696480	+	0.717576i	$0.745251\pi$
$930$	1.08211e11	0.00474350
$931$	−1.77587e13	−0.774707
$932$	−2.33136e13	−1.01213
$933$	−1.12785e10	−0.000487286 0
$934$	1.33093e12	0.0572263
$935$	0	0
$936$	2.93118e13	1.24825
$937$	−3.18028e13	−1.34784	−0.673918	−	0.738806i	$-0.735390\pi$
$937$	−3.18028e13	−1.34784	−0.673918	+	0.738806i	$0.735390\pi$
$938$	6.27855e12	0.264817
$939$	6.24730e10	0.00262239
$940$	8.03961e13	3.35861
$941$	−2.16662e13	−0.900803	−0.450401	−	0.892826i	$-0.648719\pi$
$941$	−2.16662e13	−0.900803	−0.450401	+	0.892826i	$0.648719\pi$
$942$	1.04936e10	0.000434207 0
$943$	1.01979e13	0.419960
$944$	9.53275e12	0.390701
$945$	−5.84801e10	−0.00238542
$946$	1.75342e13	0.711830
$947$	1.15699e13	0.467470	0.233735	−	0.972300i	$-0.424905\pi$
$947$	1.15699e13	0.467470	0.233735	+	0.972300i	$0.424905\pi$
$948$	2.12975e10	0.000856428 0
$949$	−7.44817e13	−2.98093
$950$	4.27242e13	1.70184
$951$	2.16066e10	0.000856593 0
$952$	0	0
$953$	−1.14361e13	−0.449118	−0.224559	−	0.974461i	$-0.572094\pi$
$953$	−1.14361e13	−0.449118	−0.224559	+	0.974461i	$0.572094\pi$
$954$	3.48404e13	1.36180
$955$	−6.11681e13	−2.37963
$956$	5.72422e13	2.21644
$957$	1.07009e10	0.000412397 0
$958$	5.56479e12	0.213454
$959$	−5.21159e12	−0.198969
$960$	1.03753e11	0.00394259
$961$	1.40113e13	0.529936
$962$	1.06036e14	3.99177
$963$	2.45971e13	0.921648
$964$	−2.03230e13	−0.757951
$965$	−5.80303e13	−2.15418
$966$	−3.01332e10	−0.00111339
$967$	−1.44349e13	−0.530879	−0.265439	−	0.964128i	$-0.585517\pi$
$967$	−1.44349e13	−0.530879	−0.265439	+	0.964128i	$0.585517\pi$
$968$	−1.63929e13	−0.600091
$969$	0	0
$970$	−1.07102e14	−3.88440
$971$	−3.20825e13	−1.15819	−0.579097	−	0.815259i	$-0.696595\pi$
$971$	−3.20825e13	−1.15819	−0.579097	+	0.815259i	$0.696595\pi$
$972$	−2.09558e11	−0.00753020
$973$	−9.76586e11	−0.0349303
$974$	−2.51145e13	−0.894148
$975$	8.39587e10	0.00297540
$976$	−5.76069e12	−0.203213
$977$	1.42575e12	0.0500630	0.0250315	−	0.999687i	$-0.492031\pi$
$977$	1.42575e12	0.0500630	0.0250315	+	0.999687i	$0.492031\pi$
$978$	1.29287e11	0.00451888
$979$	−1.40729e13	−0.489622
$980$	−4.66130e13	−1.61432
$981$	−4.70365e13	−1.62153
$982$	9.62436e12	0.330271
$983$	−1.41784e13	−0.484323	−0.242161	−	0.970236i	$-0.577856\pi$
$983$	−1.41784e13	−0.484323	−0.242161	+	0.970236i	$0.577856\pi$
$984$	1.85881e10	0.000632059 0
$985$	4.97352e12	0.168345
$986$	0	0
$987$	3.91793e10	0.00131410
$988$	−7.46693e13	−2.49308
$989$	−2.55613e13	−0.849572
$990$	−3.09350e13	−1.02351
$991$	−2.24466e13	−0.739296	−0.369648	−	0.929172i	$-0.620522\pi$
$991$	−2.24466e13	−0.739296	−0.369648	+	0.929172i	$0.620522\pi$
$992$	4.57509e13	1.50002
$993$	−3.64292e10	−0.00118899
$994$	−1.08739e12	−0.0353304
$995$	4.74836e13	1.53582
$996$	−1.33961e11	−0.00431331
$997$	−1.92497e13	−0.617015	−0.308508	−	0.951222i	$-0.599830\pi$
$997$	−1.92497e13	−0.617015	−0.308508	+	0.951222i	$0.599830\pi$
$998$	−6.01737e13	−1.92008
$999$	−1.63773e11	−0.00520231

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.g.1.31	✓	36
17.16	even	2		289.10.a.h.1.31	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.31	✓	36	1.1	even	1	trivial
289.10.a.h.1.31	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)

\(f(q)\)	\(=\)	\(q+35.6294 q^{2} -0.238037 q^{3} +757.456 q^{4} +2006.11 q^{5} -8.48114 q^{6} -3110.91 q^{7} +8745.46 q^{8} -19682.9 q^{9} +O(q^{10})\)	\(q+35.6294 q^{2} -0.238037 q^{3} +757.456 q^{4} +2006.11 q^{5} -8.48114 q^{6} -3110.91 q^{7} +8745.46 q^{8} -19682.9 q^{9} +71476.4 q^{10} +21988.6 q^{11} -180.303 q^{12} -170282. q^{13} -110840. q^{14} -477.528 q^{15} -76221.9 q^{16} -701292. q^{18} +578915. q^{19} +1.51954e6 q^{20} +740.514 q^{21} +783440. q^{22} -1.14210e6 q^{23} -2081.75 q^{24} +2.07134e6 q^{25} -6.06707e6 q^{26} +9370.57 q^{27} -2.35638e6 q^{28} -2.04445e6 q^{29} -17014.1 q^{30} -6.36010e6 q^{31} -7.19342e6 q^{32} -5234.10 q^{33} -6.24082e6 q^{35} -1.49090e7 q^{36} -1.74773e7 q^{37} +2.06264e7 q^{38} +40533.6 q^{39} +1.75443e7 q^{40} -8.92910e6 q^{41} +26384.1 q^{42} +2.23811e7 q^{43} +1.66554e7 q^{44} -3.94861e7 q^{45} -4.06922e7 q^{46} +5.29083e7 q^{47} +18143.7 q^{48} -3.06758e7 q^{49} +7.38005e7 q^{50} -1.28981e8 q^{52} -4.96802e7 q^{53} +333868. q^{54} +4.41114e7 q^{55} -2.72064e7 q^{56} -137804. q^{57} -7.28426e7 q^{58} -1.25066e8 q^{59} -361707. q^{60} +7.55780e7 q^{61} -2.26607e8 q^{62} +6.12319e7 q^{63} -2.17272e8 q^{64} -3.41605e8 q^{65} -186488. q^{66} -5.66451e7 q^{67} +271862. q^{69} -2.22357e8 q^{70} +9.81048e6 q^{71} -1.72136e8 q^{72} +4.37401e8 q^{73} -6.22707e8 q^{74} -493056. q^{75} +4.38503e8 q^{76} -6.84045e7 q^{77} +1.44419e6 q^{78} -1.18121e8 q^{79} -1.52909e8 q^{80} +3.87417e8 q^{81} -3.18139e8 q^{82} +7.42977e8 q^{83} +560907. q^{84} +7.97425e8 q^{86} +486656. q^{87} +1.92300e8 q^{88} -6.40009e8 q^{89} -1.40687e9 q^{90} +5.29734e8 q^{91} -8.65088e8 q^{92} +1.51394e6 q^{93} +1.88509e9 q^{94} +1.16137e9 q^{95} +1.71230e6 q^{96} -1.49842e9 q^{97} -1.09296e9 q^{98} -4.32800e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 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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