LMFDB - Embedded newform 289.10.a.g.1.30

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			1.30
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)

$f(q)$	$=$	$q+31.0070 q^{2} +53.8250 q^{3} +449.436 q^{4} +1141.73 q^{5} +1668.95 q^{6} +10049.6 q^{7} -1939.93 q^{8} -16785.9 q^{9} +O(q^{10})$	\(q+31.0070 q^{2} +53.8250 q^{3} +449.436 q^{4} +1141.73 q^{5} +1668.95 q^{6} +10049.6 q^{7} -1939.93 q^{8} -16785.9 q^{9} +35401.7 q^{10} -19297.2 q^{11} +24190.9 q^{12} -149324. q^{13} +311609. q^{14} +61453.7 q^{15} -290263. q^{16} -520480. q^{18} -789308. q^{19} +513135. q^{20} +540920. q^{21} -598350. q^{22} +649564. q^{23} -104417. q^{24} -649573. q^{25} -4.63009e6 q^{26} -1.96294e6 q^{27} +4.51666e6 q^{28} -5.71826e6 q^{29} +1.90550e6 q^{30} +139880. q^{31} -8.00694e6 q^{32} -1.03867e6 q^{33} +1.14740e7 q^{35} -7.54417e6 q^{36} -107316. q^{37} -2.44741e7 q^{38} -8.03736e6 q^{39} -2.21488e6 q^{40} +2.16829e6 q^{41} +1.67723e7 q^{42} -3.93320e7 q^{43} -8.67287e6 q^{44} -1.91650e7 q^{45} +2.01410e7 q^{46} -2.88624e7 q^{47} -1.56234e7 q^{48} +6.06411e7 q^{49} -2.01413e7 q^{50} -6.71116e7 q^{52} -1.39754e7 q^{53} -6.08648e7 q^{54} -2.20323e7 q^{55} -1.94955e7 q^{56} -4.24845e7 q^{57} -1.77306e8 q^{58} +7.21306e7 q^{59} +2.76195e7 q^{60} +1.66987e8 q^{61} +4.33725e6 q^{62} -1.68692e8 q^{63} -9.96569e7 q^{64} -1.70488e8 q^{65} -3.22062e7 q^{66} +2.47694e8 q^{67} +3.49628e7 q^{69} +3.55774e8 q^{70} +2.68803e8 q^{71} +3.25634e7 q^{72} +3.16534e7 q^{73} -3.32755e6 q^{74} -3.49633e7 q^{75} -3.54743e8 q^{76} -1.93930e8 q^{77} -2.49215e8 q^{78} -4.91473e7 q^{79} -3.31402e8 q^{80} +2.24741e8 q^{81} +6.72323e7 q^{82} +8.25474e8 q^{83} +2.43109e8 q^{84} -1.21957e9 q^{86} -3.07785e8 q^{87} +3.74352e7 q^{88} -1.30963e8 q^{89} -5.94249e8 q^{90} -1.50065e9 q^{91} +2.91937e8 q^{92} +7.52902e6 q^{93} -8.94939e8 q^{94} -9.01178e8 q^{95} -4.30973e8 q^{96} +8.84811e8 q^{97} +1.88030e9 q^{98} +3.23921e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	31.0070	1.37033	0.685165	−	0.728388i	$-0.259730\pi$
$2$	31.0070	1.37033	0.685165	+	0.728388i	$0.259730\pi$
$3$	53.8250	0.383653	0.191826	−	0.981429i	$-0.438559\pi$
$3$	53.8250	0.383653	0.191826	+	0.981429i	$0.438559\pi$
$4$	449.436	0.877805
$5$	1141.73	0.816957	0.408478	−	0.912768i	$-0.366060\pi$
$5$	1141.73	0.816957	0.408478	+	0.912768i	$0.366060\pi$
$6$	1668.95	0.525731
$7$	10049.6	1.58201	0.791003	−	0.611812i	$-0.209559\pi$
$7$	10049.6	1.58201	0.791003	+	0.611812i	$0.209559\pi$
$8$	−1939.93	−0.167448
$9$	−16785.9	−0.852811
$10$	35401.7	1.11950
$11$	−19297.2	−0.397400	−0.198700	−	0.980060i	$-0.563672\pi$
$11$	−19297.2	−0.397400	−0.198700	+	0.980060i	$0.563672\pi$
$12$	24190.9	0.336772
$13$	−149324.	−1.45006	−0.725028	−	0.688720i	$-0.758173\pi$
$13$	−149324.	−1.45006	−0.725028	+	0.688720i	$0.758173\pi$
$14$	311609.	2.16787
$15$	61453.7	0.313428
$16$	−290263.	−1.10726
$17$	0	0
$17$	0	0
$18$	−520480.	−1.16863
$19$	−789308.	−1.38949	−0.694745	−	0.719257i	$-0.744483\pi$
$19$	−789308.	−1.38949	−0.694745	+	0.719257i	$0.744483\pi$
$20$	513135.	0.717128
$21$	540920.	0.606941
$22$	−598350.	−0.544569
$23$	649564.	0.484001	0.242001	−	0.970276i	$-0.422196\pi$
$23$	649564.	0.484001	0.242001	+	0.970276i	$0.422196\pi$
$24$	−104417.	−0.0642419
$25$	−649573.	−0.332581
$26$	−4.63009e6	−1.98705
$27$	−1.96294e6	−0.710836
$28$	4.51666e6	1.38869
$29$	−5.71826e6	−1.50132	−0.750659	−	0.660690i	$-0.770264\pi$
$29$	−5.71826e6	−1.50132	−0.750659	+	0.660690i	$0.770264\pi$
$30$	1.90550e6	0.429500
$31$	139880.	0.0272036	0.0136018	−	0.999907i	$-0.495670\pi$
$31$	139880.	0.0272036	0.0136018	+	0.999907i	$0.495670\pi$
$32$	−8.00694e6	−1.34987
$33$	−1.03867e6	−0.152464
$34$	0	0
$35$	1.14740e7	1.29243
$36$	−7.54417e6	−0.748601
$37$	−107316.	−0.00941362	−0.00470681	−	0.999989i	$-0.501498\pi$
$37$	−107316.	−0.00941362	−0.00470681	+	0.999989i	$0.501498\pi$
$38$	−2.44741e7	−1.90406
$39$	−8.03736e6	−0.556318
$40$	−2.21488e6	−0.136798
$41$	2.16829e6	0.119837	0.0599185	−	0.998203i	$-0.480916\pi$
$41$	2.16829e6	0.119837	0.0599185	+	0.998203i	$0.480916\pi$
$42$	1.67723e7	0.831710
$43$	−3.93320e7	−1.75444	−0.877220	−	0.480089i	$-0.840604\pi$
$43$	−3.93320e7	−1.75444	−0.877220	+	0.480089i	$0.840604\pi$
$44$	−8.67287e6	−0.348839
$45$	−1.91650e7	−0.696709
$46$	2.01410e7	0.663242
$47$	−2.88624e7	−0.862765	−0.431383	−	0.902169i	$-0.641974\pi$
$47$	−2.88624e7	−0.862765	−0.431383	+	0.902169i	$0.641974\pi$
$48$	−1.56234e7	−0.424805
$49$	6.06411e7	1.50274
$50$	−2.01413e7	−0.455746
$51$	0	0
$52$	−6.71116e7	−1.27287
$53$	−1.39754e7	−0.243290	−0.121645	−	0.992574i	$-0.538817\pi$
$53$	−1.39754e7	−0.243290	−0.121645	+	0.992574i	$0.538817\pi$
$54$	−6.08648e7	−0.974080
$55$	−2.20323e7	−0.324659
$56$	−1.94955e7	−0.264904
$57$	−4.24845e7	−0.533081
$58$	−1.77306e8	−2.05730
$59$	7.21306e7	0.774972	0.387486	−	0.921876i	$-0.373344\pi$
$59$	7.21306e7	0.774972	0.387486	+	0.921876i	$0.373344\pi$
$60$	2.76195e7	0.275128
$61$	1.66987e8	1.54418	0.772092	−	0.635511i	$-0.219211\pi$
$61$	1.66987e8	1.54418	0.772092	+	0.635511i	$0.219211\pi$
$62$	4.33725e6	0.0372780
$63$	−1.68692e8	−1.34915
$64$	−9.96569e7	−0.742502
$65$	−1.70488e8	−1.18463
$66$	−3.22062e7	−0.208925
$67$	2.47694e8	1.50169	0.750843	−	0.660480i	$-0.229647\pi$
$67$	2.47694e8	1.50169	0.750843	+	0.660480i	$0.229647\pi$
$68$	0	0
$69$	3.49628e7	0.185688
$70$	3.55774e8	1.77106
$71$	2.68803e8	1.25537	0.627684	−	0.778468i	$-0.284003\pi$
$71$	2.68803e8	1.25537	0.627684	+	0.778468i	$0.284003\pi$
$72$	3.25634e7	0.142802
$73$	3.16534e7	0.130457	0.0652284	−	0.997870i	$-0.479222\pi$
$73$	3.16534e7	0.130457	0.0652284	+	0.997870i	$0.479222\pi$
$74$	−3.32755e6	−0.0128998
$75$	−3.49633e7	−0.127596
$76$	−3.54743e8	−1.21970
$77$	−1.93930e8	−0.628689
$78$	−2.49215e8	−0.762339
$79$	−4.91473e7	−0.141964	−0.0709819	−	0.997478i	$-0.522613\pi$
$79$	−4.91473e7	−0.141964	−0.0709819	+	0.997478i	$0.522613\pi$
$80$	−3.31402e8	−0.904587
$81$	2.24741e8	0.580096
$82$	6.72323e7	0.164216
$83$	8.25474e8	1.90920	0.954601	−	0.297888i	$-0.0962821\pi$
$83$	8.25474e8	1.90920	0.954601	+	0.297888i	$0.0962821\pi$
$84$	2.43109e8	0.532776
$85$	0	0
$86$	−1.21957e9	−2.40416
$87$	−3.07785e8	−0.575985
$88$	3.74352e7	0.0665439
$89$	−1.30963e8	−0.221256	−0.110628	−	0.993862i	$-0.535286\pi$
$89$	−1.30963e8	−0.221256	−0.110628	+	0.993862i	$0.535286\pi$
$90$	−5.94249e8	−0.954722
$91$	−1.50065e9	−2.29400
$92$	2.91937e8	0.424859
$93$	7.52902e6	0.0104368
$94$	−8.94939e8	−1.18227
$95$	−9.01178e8	−1.13515
$96$	−4.30973e8	−0.517881
$97$	8.84811e8	1.01479	0.507397	−	0.861713i	$-0.330608\pi$
$97$	8.84811e8	1.01479	0.507397	+	0.861713i	$0.330608\pi$
$98$	1.88030e9	2.05925
$99$	3.23921e8	0.338907
$100$	−2.91941e8	−0.291941
$101$	−6.77943e8	−0.648257	−0.324128	−	0.946013i	$-0.605071\pi$
$101$	−6.77943e8	−0.648257	−0.324128	+	0.946013i	$0.605071\pi$
$102$	0	0
$103$	−1.16420e9	−1.01920	−0.509601	−	0.860411i	$-0.670207\pi$
$103$	−1.16420e9	−1.01920	−0.509601	+	0.860411i	$0.670207\pi$
$104$	2.89678e8	0.242809
$105$	6.17586e8	0.495845
$106$	−4.33336e8	−0.333387
$107$	1.13491e9	0.837017	0.418508	−	0.908213i	$-0.362553\pi$
$107$	1.13491e9	0.837017	0.418508	+	0.908213i	$0.362553\pi$
$108$	−8.82214e8	−0.623975
$109$	−1.50045e9	−1.01812	−0.509062	−	0.860730i	$-0.670008\pi$
$109$	−1.50045e9	−1.01812	−0.509062	+	0.860730i	$0.670008\pi$
$110$	−6.83155e8	−0.444889
$111$	−5.77628e6	−0.00361156
$112$	−2.91703e9	−1.75170
$113$	3.11200e9	1.79550	0.897752	−	0.440501i	$-0.145199\pi$
$113$	3.11200e9	1.79550	0.897752	+	0.440501i	$0.145199\pi$
$114$	−1.31732e9	−0.730497
$115$	7.41628e8	0.395408
$116$	−2.56999e9	−1.31786
$117$	2.50653e9	1.23662
$118$	2.23656e9	1.06197
$119$	0	0
$120$	−1.19216e8	−0.0524829
$121$	−1.98556e9	−0.842073
$122$	5.17778e9	2.11604
$123$	1.16708e8	0.0459758
$124$	6.28670e7	0.0238795
$125$	−2.97158e9	−1.08866
$126$	−5.23062e9	−1.84878
$127$	−5.00555e9	−1.70740	−0.853699	−	0.520767i	$-0.825646\pi$
$127$	−5.00555e9	−1.70740	−0.853699	+	0.520767i	$0.825646\pi$
$128$	1.00949e9	0.332396
$129$	−2.11705e9	−0.673096
$130$	−5.28633e9	−1.62334
$131$	−2.33318e8	−0.0692194	−0.0346097	−	0.999401i	$-0.511019\pi$
$131$	−2.33318e8	−0.0692194	−0.0346097	+	0.999401i	$0.511019\pi$
$132$	−4.66817e8	−0.133833
$133$	−7.93224e9	−2.19818
$134$	7.68026e9	2.05781
$135$	−2.24115e9	−0.580722
$136$	0	0
$137$	−7.37764e9	−1.78927	−0.894633	−	0.446802i	$-0.852563\pi$
$137$	−7.37764e9	−1.78927	−0.894633	+	0.446802i	$0.852563\pi$
$138$	1.08409e9	0.254454
$139$	−3.70573e9	−0.841991	−0.420995	−	0.907063i	$-0.638319\pi$
$139$	−3.70573e9	−0.841991	−0.420995	+	0.907063i	$0.638319\pi$
$140$	5.15681e9	1.13450
$141$	−1.55352e9	−0.331002
$142$	8.33478e9	1.72027
$143$	2.88154e9	0.576252
$144$	4.87231e9	0.944286
$145$	−6.52872e9	−1.22651
$146$	9.81477e8	0.178769
$147$	3.26401e9	0.576532
$148$	−4.82317e7	−0.00826332
$149$	−5.60954e9	−0.932372	−0.466186	−	0.884687i	$-0.654372\pi$
$149$	−5.60954e9	−0.932372	−0.466186	+	0.884687i	$0.654372\pi$
$150$	−1.08411e9	−0.174848
$151$	4.72353e9	0.739385	0.369692	−	0.929154i	$-0.379463\pi$
$151$	4.72353e9	0.739385	0.369692	+	0.929154i	$0.379463\pi$
$152$	1.53120e9	0.232667
$153$	0	0
$154$	−6.01318e9	−0.861512
$155$	1.59705e8	0.0222242
$156$	−3.61228e9	−0.488338
$157$	−2.12404e9	−0.279007	−0.139503	−	0.990222i	$-0.544551\pi$
$157$	−2.12404e9	−0.279007	−0.139503	+	0.990222i	$0.544551\pi$
$158$	−1.52391e9	−0.194537
$159$	−7.52227e8	−0.0933387
$160$	−9.14178e9	−1.10278
$161$	6.52787e9	0.765693
$162$	6.96856e9	0.794924
$163$	−6.96419e9	−0.772728	−0.386364	−	0.922346i	$-0.626269\pi$
$163$	−6.96419e9	−0.772728	−0.386364	+	0.922346i	$0.626269\pi$
$164$	9.74509e8	0.105193
$165$	−1.18589e9	−0.124556
$166$	2.55955e10	2.61624
$167$	1.47347e9	0.146594	0.0732971	−	0.997310i	$-0.476648\pi$
$167$	1.47347e9	0.146594	0.0732971	+	0.997310i	$0.476648\pi$
$168$	−1.04935e9	−0.101631
$169$	1.16932e10	1.10266
$170$	0	0
$171$	1.32492e10	1.18497
$172$	−1.76772e10	−1.54005
$173$	−1.29320e10	−1.09764	−0.548819	−	0.835941i	$-0.684922\pi$
$173$	−1.29320e10	−1.09764	−0.548819	+	0.835941i	$0.684922\pi$
$174$	−9.54351e9	−0.789289
$175$	−6.52796e9	−0.526146
$176$	5.60126e9	0.440027
$177$	3.88243e9	0.297320
$178$	−4.06078e9	−0.303194
$179$	−1.15426e10	−0.840358	−0.420179	−	0.907441i	$-0.638033\pi$
$179$	−1.15426e10	−0.840358	−0.420179	+	0.907441i	$0.638033\pi$
$180$	−8.61342e9	−0.611575
$181$	−2.51937e10	−1.74477	−0.872384	−	0.488822i	$-0.837427\pi$
$181$	−2.51937e10	−1.74477	−0.872384	+	0.488822i	$0.837427\pi$
$182$	−4.65307e10	−3.14353
$183$	8.98808e9	0.592430
$184$	−1.26011e9	−0.0810451
$185$	−1.22526e8	−0.00769052
$186$	2.33453e8	0.0143018
$187$	0	0
$188$	−1.29718e10	−0.757339
$189$	−1.97268e10	−1.12455
$190$	−2.79429e10	−1.55553
$191$	7.47180e9	0.406233	0.203116	−	0.979155i	$-0.434893\pi$
$191$	7.47180e9	0.406233	0.203116	+	0.979155i	$0.434893\pi$
$192$	−5.36403e9	−0.284863
$193$	1.79297e10	0.930177	0.465089	−	0.885264i	$-0.346022\pi$
$193$	1.79297e10	0.930177	0.465089	+	0.885264i	$0.346022\pi$
$194$	2.74354e10	1.39060
$195$	−9.17652e9	−0.454488
$196$	2.72543e10	1.31912
$197$	2.91218e10	1.37759	0.688795	−	0.724956i	$-0.258140\pi$
$197$	2.91218e10	1.37759	0.688795	+	0.724956i	$0.258140\pi$
$198$	1.00438e10	0.464414
$199$	−1.83017e9	−0.0827280	−0.0413640	−	0.999144i	$-0.513170\pi$
$199$	−1.83017e9	−0.0827280	−0.0413640	+	0.999144i	$0.513170\pi$
$200$	1.26012e9	0.0556901
$201$	1.33321e10	0.576126
$202$	−2.10210e10	−0.888326
$203$	−5.74663e10	−2.37509
$204$	0	0
$205$	2.47561e9	0.0979016
$206$	−3.60984e10	−1.39664
$207$	−1.09035e10	−0.412762
$208$	4.33432e10	1.60559
$209$	1.52315e10	0.552183
$210$	1.91495e10	0.679471
$211$	2.37220e10	0.823911	0.411956	−	0.911204i	$-0.364846\pi$
$211$	2.37220e10	0.823911	0.411956	+	0.911204i	$0.364846\pi$
$212$	−6.28106e9	−0.213561
$213$	1.44683e10	0.481626
$214$	3.51902e10	1.14699
$215$	−4.49066e10	−1.43330
$216$	3.80795e9	0.119028
$217$	1.40574e9	0.0430363
$218$	−4.65243e10	−1.39517
$219$	1.70374e9	0.0500501
$220$	−9.90209e9	−0.284987
$221$	0	0
$222$	−1.79105e8	−0.00494903
$223$	1.54932e10	0.419537	0.209769	−	0.977751i	$-0.432729\pi$
$223$	1.54932e10	0.419537	0.209769	+	0.977751i	$0.432729\pi$
$224$	−8.04666e10	−2.13550
$225$	1.09036e10	0.283629
$226$	9.64939e10	2.46043
$227$	7.62225e10	1.90531	0.952657	−	0.304047i	$-0.0983379\pi$
$227$	7.62225e10	1.90531	0.952657	+	0.304047i	$0.0983379\pi$
$228$	−1.90941e10	−0.467941
$229$	2.17147e10	0.521789	0.260894	−	0.965367i	$-0.415983\pi$
$229$	2.17147e10	0.521789	0.260894	+	0.965367i	$0.415983\pi$
$230$	2.29957e10	0.541840
$231$	−1.04383e10	−0.241198
$232$	1.10930e10	0.251393
$233$	−3.10512e10	−0.690202	−0.345101	−	0.938566i	$-0.612155\pi$
$233$	−3.10512e10	−0.690202	−0.345101	+	0.938566i	$0.612155\pi$
$234$	7.77202e10	1.69458
$235$	−3.29532e10	−0.704842
$236$	3.24181e10	0.680274
$237$	−2.64535e9	−0.0544648
$238$	0	0
$239$	−2.93690e10	−0.582236	−0.291118	−	0.956687i	$-0.594027\pi$
$239$	−2.93690e10	−0.582236	−0.291118	+	0.956687i	$0.594027\pi$
$240$	−1.78377e10	−0.347047
$241$	1.95317e10	0.372960	0.186480	−	0.982459i	$-0.440292\pi$
$241$	1.95317e10	0.372960	0.186480	+	0.982459i	$0.440292\pi$
$242$	−6.15665e10	−1.15392
$243$	5.07332e10	0.933391
$244$	7.50500e10	1.35549
$245$	6.92359e10	1.22768
$246$	3.61878e9	0.0630020
$247$	1.17863e11	2.01484
$248$	−2.71356e8	−0.00455520
$249$	4.44311e10	0.732471
$250$	−9.21400e10	−1.49183
$251$	−1.44535e10	−0.229848	−0.114924	−	0.993374i	$-0.536662\pi$
$251$	−1.44535e10	−0.229848	−0.114924	+	0.993374i	$0.536662\pi$
$252$	−7.58160e10	−1.18429
$253$	−1.25348e10	−0.192342
$254$	−1.55207e11	−2.33970
$255$	0	0
$256$	8.23255e10	1.19799
$257$	−2.07523e10	−0.296734	−0.148367	−	0.988932i	$-0.547402\pi$
$257$	−2.07523e10	−0.296734	−0.148367	+	0.988932i	$0.547402\pi$
$258$	−6.56433e10	−0.922363
$259$	−1.07848e9	−0.0148924
$260$	−7.66234e10	−1.03988
$261$	9.59859e10	1.28034
$262$	−7.23450e9	−0.0948534
$263$	1.65098e10	0.212785	0.106392	−	0.994324i	$-0.466070\pi$
$263$	1.65098e10	0.212785	0.106392	+	0.994324i	$0.466070\pi$
$264$	2.01495e9	0.0255297
$265$	−1.59562e10	−0.198757
$266$	−2.45955e11	−3.01223
$267$	−7.04910e9	−0.0848854
$268$	1.11323e11	1.31819
$269$	1.13193e10	0.131806	0.0659028	−	0.997826i	$-0.479007\pi$
$269$	1.13193e10	0.131806	0.0659028	+	0.997826i	$0.479007\pi$
$270$	−6.94913e10	−0.795781
$271$	−6.48755e10	−0.730666	−0.365333	−	0.930877i	$-0.619045\pi$
$271$	−6.48755e10	−0.730666	−0.365333	+	0.930877i	$0.619045\pi$
$272$	0	0
$273$	−8.07724e10	−0.880098
$274$	−2.28759e11	−2.45188
$275$	1.25350e10	0.132168
$276$	1.57135e10	0.162998
$277$	−1.78844e11	−1.82522	−0.912608	−	0.408835i	$-0.865935\pi$
$277$	−1.78844e11	−1.82522	−0.912608	+	0.408835i	$0.865935\pi$
$278$	−1.14904e11	−1.15381
$279$	−2.34800e9	−0.0231996
$280$	−2.22587e10	−0.216415
$281$	−5.70196e10	−0.545564	−0.272782	−	0.962076i	$-0.587944\pi$
$281$	−5.70196e10	−0.545564	−0.272782	+	0.962076i	$0.587944\pi$
$282$	−4.81701e10	−0.453582
$283$	1.70549e11	1.58055	0.790276	−	0.612751i	$-0.209937\pi$
$283$	1.70549e11	1.58055	0.790276	+	0.612751i	$0.209937\pi$
$284$	1.20810e11	1.10197
$285$	−4.85059e10	−0.435505
$286$	8.93480e10	0.789655
$287$	2.17905e10	0.189583
$288$	1.34403e11	1.15118
$289$	0	0
$290$	−2.02436e11	−1.68073
$291$	4.76249e10	0.389328
$292$	1.42262e10	0.114516
$293$	1.07691e11	0.853639	0.426820	−	0.904337i	$-0.359634\pi$
$293$	1.07691e11	0.853639	0.426820	+	0.904337i	$0.359634\pi$
$294$	1.01207e11	0.790039
$295$	8.23539e10	0.633118
$296$	2.08185e8	0.00157629
$297$	3.78792e10	0.282486
$298$	−1.73935e11	−1.27766
$299$	−9.69955e10	−0.701829
$300$	−1.57137e10	−0.112004
$301$	−3.95272e11	−2.77553
$302$	1.46463e11	1.01320
$303$	−3.64903e10	−0.248705
$304$	2.29106e11	1.53853
$305$	1.90655e11	1.26153
$306$	0	0
$307$	−6.36292e9	−0.0408822	−0.0204411	−	0.999791i	$-0.506507\pi$
$307$	−6.36292e9	−0.0408822	−0.0204411	+	0.999791i	$0.506507\pi$
$308$	−8.71590e10	−0.551866
$309$	−6.26631e10	−0.391020
$310$	4.95198e9	0.0304545
$311$	6.10770e10	0.370217	0.185108	−	0.982718i	$-0.440736\pi$
$311$	6.10770e10	0.370217	0.185108	+	0.982718i	$0.440736\pi$
$312$	1.55919e10	0.0931544
$313$	−2.69912e11	−1.58954	−0.794772	−	0.606908i	$-0.792410\pi$
$313$	−2.69912e11	−1.58954	−0.794772	+	0.606908i	$0.792410\pi$
$314$	−6.58602e10	−0.382331
$315$	−1.92600e11	−1.10220
$316$	−2.20886e10	−0.124616
$317$	−7.17777e10	−0.399230	−0.199615	−	0.979874i	$-0.563969\pi$
$317$	−7.17777e10	−0.399230	−0.199615	+	0.979874i	$0.563969\pi$
$318$	−2.33243e10	−0.127905
$319$	1.10347e11	0.596624
$320$	−1.13781e11	−0.606592
$321$	6.10865e10	0.321124
$322$	2.02410e11	1.04925
$323$	0	0
$324$	1.01007e11	0.509211
$325$	9.69969e10	0.482261
$326$	−2.15939e11	−1.05889
$327$	−8.07614e10	−0.390606
$328$	−4.20633e9	−0.0200665
$329$	−2.90056e11	−1.36490
$330$	−3.67708e10	−0.170683
$331$	−1.24902e11	−0.571929	−0.285965	−	0.958240i	$-0.592314\pi$
$331$	−1.24902e11	−0.571929	−0.285965	+	0.958240i	$0.592314\pi$
$332$	3.70998e11	1.67591
$333$	1.80139e9	0.00802804
$334$	4.56879e10	0.200882
$335$	2.82800e11	1.22681
$336$	−1.57009e11	−0.672044
$337$	−3.00210e11	−1.26792	−0.633959	−	0.773367i	$-0.718571\pi$
$337$	−3.00210e11	−1.26792	−0.633959	+	0.773367i	$0.718571\pi$
$338$	3.62570e11	1.51101
$339$	1.67503e11	0.688850
$340$	0	0
$341$	−2.69929e9	−0.0108107
$342$	4.10819e11	1.62380
$343$	2.03882e11	0.795343
$344$	7.63013e10	0.293778
$345$	3.99181e10	0.151699
$346$	−4.00984e11	−1.50413
$347$	2.67538e11	0.990610	0.495305	−	0.868719i	$-0.335056\pi$
$347$	2.67538e11	0.990610	0.495305	+	0.868719i	$0.335056\pi$
$348$	−1.38330e11	−0.505602
$349$	−4.04067e11	−1.45794	−0.728969	−	0.684546i	$-0.760000\pi$
$349$	−4.04067e11	−1.45794	−0.728969	+	0.684546i	$0.760000\pi$
$350$	−2.02413e11	−0.720993
$351$	2.93114e11	1.03075
$352$	1.54512e11	0.536438
$353$	−3.87001e11	−1.32656	−0.663278	−	0.748373i	$-0.730835\pi$
$353$	−3.87001e11	−1.32656	−0.663278	+	0.748373i	$0.730835\pi$
$354$	1.20383e11	0.407427
$355$	3.06901e11	1.02558
$356$	−5.88596e10	−0.194219
$357$	0	0
$358$	−3.57901e11	−1.15157
$359$	−1.50661e11	−0.478714	−0.239357	−	0.970932i	$-0.576937\pi$
$359$	−1.50661e11	−0.478714	−0.239357	+	0.970932i	$0.576937\pi$
$360$	3.71786e10	0.116663
$361$	3.00319e11	0.930680
$362$	−7.81180e11	−2.39091
$363$	−1.06873e11	−0.323064
$364$	−6.74445e11	−2.01368
$365$	3.61397e10	0.106578
$366$	2.78694e11	0.811825
$367$	1.26285e11	0.363375	0.181688	−	0.983356i	$-0.441844\pi$
$367$	1.26285e11	0.363375	0.181688	+	0.983356i	$0.441844\pi$
$368$	−1.88544e11	−0.535917
$369$	−3.63967e10	−0.102198
$370$	−3.79917e9	−0.0105386
$371$	−1.40448e11	−0.384886
$372$	3.38381e9	0.00916143
$373$	4.73905e9	0.0126766	0.00633828	−	0.999980i	$-0.497982\pi$
$373$	4.73905e9	0.0126766	0.00633828	+	0.999980i	$0.497982\pi$
$374$	0	0
$375$	−1.59945e11	−0.417668
$376$	5.59910e10	0.144468
$377$	8.53873e11	2.17699
$378$	−6.11668e11	−1.54100
$379$	5.25598e11	1.30851	0.654255	−	0.756274i	$-0.272982\pi$
$379$	5.25598e11	1.30851	0.654255	+	0.756274i	$0.272982\pi$
$380$	−4.05022e11	−0.996442
$381$	−2.69424e11	−0.655048
$382$	2.31678e11	0.556673
$383$	−5.38071e11	−1.27775	−0.638874	−	0.769311i	$-0.720600\pi$
$383$	−5.38071e11	−1.27775	−0.638874	+	0.769311i	$0.720600\pi$
$384$	5.43356e10	0.127525
$385$	−2.21416e11	−0.513612
$386$	5.55947e11	1.27465
$387$	6.60223e11	1.49620
$388$	3.97666e11	0.890790
$389$	−3.57957e11	−0.792607	−0.396303	−	0.918120i	$-0.629707\pi$
$389$	−3.57957e11	−0.792607	−0.396303	+	0.918120i	$0.629707\pi$
$390$	−2.84537e11	−0.622798
$391$	0	0
$392$	−1.17639e11	−0.251632
$393$	−1.25583e10	−0.0265562
$394$	9.02981e11	1.88775
$395$	−5.61130e10	−0.115978
$396$	1.45582e11	0.297494
$397$	8.11886e11	1.64036	0.820178	−	0.572109i	$-0.193875\pi$
$397$	8.11886e11	1.64036	0.820178	+	0.572109i	$0.193875\pi$
$398$	−5.67481e10	−0.113365
$399$	−4.26953e11	−0.843338
$400$	1.88547e11	0.368255
$401$	−8.87187e11	−1.71343	−0.856713	−	0.515793i	$-0.827497\pi$
$401$	−8.87187e11	−1.71343	−0.856713	+	0.515793i	$0.827497\pi$
$402$	4.13390e11	0.789483
$403$	−2.08874e10	−0.0394468
$404$	−3.04692e11	−0.569043
$405$	2.56594e11	0.473914
$406$	−1.78186e12	−3.25466
$407$	2.07090e9	0.00374097
$408$	0	0
$409$	6.58796e11	1.16412	0.582058	−	0.813147i	$-0.302248\pi$
$409$	6.58796e11	1.16412	0.582058	+	0.813147i	$0.302248\pi$
$410$	7.67613e10	0.134158
$411$	−3.97101e11	−0.686457
$412$	−5.23234e11	−0.894660
$413$	7.24885e11	1.22601
$414$	−3.38085e11	−0.565619
$415$	9.42470e11	1.55974
$416$	1.19563e12	1.95738
$417$	−1.99461e11	−0.323032
$418$	4.72282e11	0.756673
$419$	1.19033e12	1.88670	0.943352	−	0.331794i	$-0.107654\pi$
$419$	1.19033e12	1.88670	0.943352	+	0.331794i	$0.107654\pi$
$420$	2.77565e11	0.435255
$421$	−1.00113e12	−1.55317	−0.776587	−	0.630010i	$-0.783051\pi$
$421$	−1.00113e12	−1.55317	−0.776587	+	0.630010i	$0.783051\pi$
$422$	7.35549e11	1.12903
$423$	4.84481e11	0.735775
$424$	2.71113e10	0.0407384
$425$	0	0
$426$	4.48619e11	0.659986
$427$	1.67816e12	2.44291
$428$	5.10069e11	0.734737
$429$	1.55099e11	0.221081
$430$	−1.39242e12	−1.96410
$431$	−1.16192e11	−0.162192	−0.0810962	−	0.996706i	$-0.525842\pi$
$431$	−1.16192e11	−0.162192	−0.0810962	+	0.996706i	$0.525842\pi$
$432$	5.69767e11	0.787083
$433$	−1.16924e12	−1.59849	−0.799243	−	0.601007i	$-0.794766\pi$
$433$	−1.16924e12	−1.59849	−0.799243	+	0.601007i	$0.794766\pi$
$434$	4.35877e10	0.0589740
$435$	−3.51408e11	−0.470555
$436$	−6.74354e11	−0.893714
$437$	−5.12706e11	−0.672515
$438$	5.28280e10	0.0685852
$439$	1.03242e11	0.132667	0.0663337	−	0.997797i	$-0.478870\pi$
$439$	1.03242e11	0.132667	0.0663337	+	0.997797i	$0.478870\pi$
$440$	4.27410e10	0.0543635
$441$	−1.01791e12	−1.28156
$442$	0	0
$443$	7.45116e11	0.919194	0.459597	−	0.888128i	$-0.347994\pi$
$443$	7.45116e11	0.919194	0.459597	+	0.888128i	$0.347994\pi$
$444$	−2.59607e9	−0.00317025
$445$	−1.49525e11	−0.180756
$446$	4.80400e11	0.574905
$447$	−3.01934e11	−0.357707
$448$	−1.00151e12	−1.17464
$449$	1.20015e12	1.39357	0.696784	−	0.717281i	$-0.254613\pi$
$449$	1.20015e12	1.39357	0.696784	+	0.717281i	$0.254613\pi$
$450$	3.38090e11	0.388665
$451$	−4.18420e10	−0.0476232
$452$	1.39864e12	1.57610
$453$	2.54244e11	0.283667
$454$	2.36343e12	2.61091
$455$	−1.71334e12	−1.87410
$456$	8.24168e10	0.0892635
$457$	−8.33431e11	−0.893814	−0.446907	−	0.894581i	$-0.647474\pi$
$457$	−8.33431e11	−0.893814	−0.446907	+	0.894581i	$0.647474\pi$
$458$	6.73309e11	0.715023
$459$	0	0
$460$	3.33314e11	0.347091
$461$	4.67123e11	0.481700	0.240850	−	0.970562i	$-0.422574\pi$
$461$	4.67123e11	0.481700	0.240850	+	0.970562i	$0.422574\pi$
$462$	−3.23660e11	−0.330521
$463$	−5.85748e11	−0.592374	−0.296187	−	0.955130i	$-0.595715\pi$
$463$	−5.85748e11	−0.592374	−0.296187	+	0.955130i	$0.595715\pi$
$464$	1.65980e12	1.66236
$465$	8.59613e9	0.00852638
$466$	−9.62804e11	−0.945804
$467$	1.36513e12	1.32815	0.664075	−	0.747666i	$-0.268825\pi$
$467$	1.36513e12	1.32815	0.664075	+	0.747666i	$0.268825\pi$
$468$	1.12653e12	1.08551
$469$	2.48923e12	2.37568
$470$	−1.02178e12	−0.965866
$471$	−1.14327e11	−0.107042
$472$	−1.39928e11	−0.129768
$473$	7.58999e11	0.697214
$474$	−8.20245e10	−0.0746348
$475$	5.12713e11	0.462118
$476$	0	0
$477$	2.34590e11	0.207480
$478$	−9.10646e11	−0.797855
$479$	−2.06482e12	−1.79214	−0.896071	−	0.443910i	$-0.853591\pi$
$479$	−2.06482e12	−1.79214	−0.896071	+	0.443910i	$0.853591\pi$
$480$	−4.92056e11	−0.423086
$481$	1.60249e10	0.0136503
$482$	6.05619e11	0.511079
$483$	3.51362e11	0.293760
$484$	−8.92384e11	−0.739176
$485$	1.01022e12	0.829043
$486$	1.57309e12	1.27905
$487$	7.61982e11	0.613853	0.306926	−	0.951733i	$-0.400699\pi$
$487$	7.61982e11	0.613853	0.306926	+	0.951733i	$0.400699\pi$
$488$	−3.23943e11	−0.258571
$489$	−3.74848e11	−0.296459
$490$	2.14680e12	1.68232
$491$	−9.26040e11	−0.719057	−0.359528	−	0.933134i	$-0.617062\pi$
$491$	−9.26040e11	−0.719057	−0.359528	+	0.933134i	$0.617062\pi$
$492$	5.24529e10	0.0403577
$493$	0	0
$494$	3.65457e12	2.76099
$495$	3.69831e11	0.276872
$496$	−4.06018e10	−0.0301216
$497$	2.70136e12	1.98600
$498$	1.37768e12	1.00373
$499$	1.46595e12	1.05844	0.529219	−	0.848485i	$-0.322485\pi$
$499$	1.46595e12	1.05844	0.529219	+	0.848485i	$0.322485\pi$
$500$	−1.33554e12	−0.955632
$501$	7.93094e10	0.0562412
$502$	−4.48160e11	−0.314968
$503$	−3.47465e11	−0.242022	−0.121011	−	0.992651i	$-0.538614\pi$
$503$	−3.47465e11	−0.242022	−0.121011	+	0.992651i	$0.538614\pi$
$504$	3.27249e11	0.225913
$505$	−7.74029e11	−0.529598
$506$	−3.88666e11	−0.263572
$507$	6.29385e11	0.423039
$508$	−2.24967e12	−1.49876
$509$	1.70164e12	1.12367	0.561834	−	0.827250i	$-0.310096\pi$
$509$	1.70164e12	1.12367	0.561834	+	0.827250i	$0.310096\pi$
$510$	0	0
$511$	3.18104e11	0.206384
$512$	2.03581e12	1.30925
$513$	1.54936e12	0.987699
$514$	−6.43468e11	−0.406624
$515$	−1.32921e12	−0.832644
$516$	−9.51477e11	−0.590846
$517$	5.56965e11	0.342863
$518$	−3.34406e10	−0.0204075
$519$	−6.96066e11	−0.421112
$520$	3.30734e11	0.198365
$521$	−1.96790e11	−0.117013	−0.0585065	−	0.998287i	$-0.518634\pi$
$521$	−1.96790e11	−0.117013	−0.0585065	+	0.998287i	$0.518634\pi$
$522$	2.97624e12	1.75449
$523$	−1.11906e12	−0.654027	−0.327013	−	0.945020i	$-0.606042\pi$
$523$	−1.11906e12	−0.654027	−0.327013	+	0.945020i	$0.606042\pi$
$524$	−1.04862e11	−0.0607611
$525$	−3.51367e11	−0.201857
$526$	5.11919e11	0.291585
$527$	0	0
$528$	3.01488e11	0.168817
$529$	−1.37922e12	−0.765743
$530$	−4.94754e11	−0.272363
$531$	−1.21078e12	−0.660904
$532$	−3.56503e12	−1.92957
$533$	−3.23778e11	−0.173770
$534$	−2.18572e11	−0.116321
$535$	1.29576e12	0.683807
$536$	−4.80509e11	−0.251455
$537$	−6.21279e11	−0.322406
$538$	3.50977e11	0.180617
$539$	−1.17021e12	−0.597190
$540$	−1.00725e12	−0.509761
$541$	−7.15211e11	−0.358960	−0.179480	−	0.983762i	$-0.557442\pi$
$541$	−7.15211e11	−0.358960	−0.179480	+	0.983762i	$0.557442\pi$
$542$	−2.01160e12	−1.00125
$543$	−1.35605e12	−0.669385
$544$	0	0
$545$	−1.71311e12	−0.831764
$546$	−2.50451e12	−1.20602
$547$	−6.84615e11	−0.326967	−0.163483	−	0.986546i	$-0.552273\pi$
$547$	−6.84615e11	−0.326967	−0.163483	+	0.986546i	$0.552273\pi$
$548$	−3.31577e12	−1.57063
$549$	−2.80303e12	−1.31690
$550$	3.88672e11	0.181114
$551$	4.51347e12	2.08607
$552$	−6.78252e10	−0.0310932
$553$	−4.93911e11	−0.224588
$554$	−5.54541e12	−2.50115
$555$	−6.59497e9	−0.00295049
$556$	−1.66549e12	−0.739103
$557$	1.49708e12	0.659015	0.329508	−	0.944153i	$-0.393117\pi$
$557$	1.49708e12	0.659015	0.329508	+	0.944153i	$0.393117\pi$
$558$	−7.28046e10	−0.0317910
$559$	5.87322e12	2.54403
$560$	−3.33046e12	−1.43106
$561$	0	0
$562$	−1.76801e12	−0.747602
$563$	3.38224e12	1.41879	0.709393	−	0.704813i	$-0.248969\pi$
$563$	3.38224e12	1.41879	0.709393	+	0.704813i	$0.248969\pi$
$564$	−6.98208e11	−0.290555
$565$	3.55307e12	1.46685
$566$	5.28820e12	2.16588
$567$	2.25856e12	0.917716
$568$	−5.21458e11	−0.210209
$569$	−1.27892e11	−0.0511490	−0.0255745	−	0.999673i	$-0.508142\pi$
$569$	−1.27892e11	−0.0511490	−0.0255745	+	0.999673i	$0.508142\pi$
$570$	−1.50402e12	−0.596785
$571$	−1.00196e12	−0.394444	−0.197222	−	0.980359i	$-0.563192\pi$
$571$	−1.00196e12	−0.394444	−0.197222	+	0.980359i	$0.563192\pi$
$572$	1.29507e12	0.505837
$573$	4.02169e11	0.155852
$574$	6.75659e11	0.259791
$575$	−4.21939e11	−0.160970
$576$	1.67283e12	0.633213
$577$	−3.75406e11	−0.140997	−0.0704986	−	0.997512i	$-0.522459\pi$
$577$	−3.75406e11	−0.140997	−0.0704986	+	0.997512i	$0.522459\pi$
$578$	0	0
$579$	9.65067e11	0.356865
$580$	−2.93424e12	−1.07664
$581$	8.29569e12	3.02037
$582$	1.47671e12	0.533508
$583$	2.69687e11	0.0966833
$584$	−6.14052e10	−0.0218448
$585$	2.86179e12	1.01027
$586$	3.33917e12	1.16977
$587$	3.94381e11	0.137102	0.0685511	−	0.997648i	$-0.478162\pi$
$587$	3.94381e11	0.137102	0.0685511	+	0.997648i	$0.478162\pi$
$588$	1.46696e12	0.506082
$589$	−1.10408e11	−0.0377992
$590$	2.55355e12	0.867581
$591$	1.56748e12	0.528517
$592$	3.11498e10	0.0104234
$593$	−3.77125e12	−1.25239	−0.626195	−	0.779666i	$-0.715389\pi$
$593$	−3.77125e12	−1.25239	−0.626195	+	0.779666i	$0.715389\pi$
$594$	1.17452e12	0.387099
$595$	0	0
$596$	−2.52113e12	−0.818441
$597$	−9.85088e10	−0.0317388
$598$	−3.00754e12	−0.961737
$599$	−2.55448e12	−0.810740	−0.405370	−	0.914153i	$-0.632857\pi$
$599$	−2.55448e12	−0.810740	−0.405370	+	0.914153i	$0.632857\pi$
$600$	6.78262e10	0.0213657
$601$	−6.12364e11	−0.191458	−0.0957292	−	0.995407i	$-0.530518\pi$
$601$	−6.12364e11	−0.191458	−0.0957292	+	0.995407i	$0.530518\pi$
$602$	−1.22562e13	−3.80340
$603$	−4.15776e12	−1.28065
$604$	2.12292e12	0.649035
$605$	−2.26698e12	−0.687938
$606$	−1.13146e12	−0.340809
$607$	−1.75946e12	−0.526053	−0.263027	−	0.964789i	$-0.584721\pi$
$607$	−1.75946e12	−0.526053	−0.263027	+	0.964789i	$0.584721\pi$
$608$	6.31994e12	1.87563
$609$	−3.09312e12	−0.911212
$610$	5.91163e12	1.72871
$611$	4.30986e12	1.25106
$612$	0	0
$613$	−1.24362e12	−0.355725	−0.177863	−	0.984055i	$-0.556918\pi$
$613$	−1.24362e12	−0.355725	−0.177863	+	0.984055i	$0.556918\pi$
$614$	−1.97295e11	−0.0560221
$615$	1.33250e11	0.0375602
$616$	3.76209e11	0.105273
$617$	3.95577e12	1.09887	0.549437	−	0.835535i	$-0.314842\pi$
$617$	3.95577e12	1.09887	0.549437	+	0.835535i	$0.314842\pi$
$618$	−1.94300e12	−0.535826
$619$	−4.31640e12	−1.18172	−0.590859	−	0.806774i	$-0.701211\pi$
$619$	−4.31640e12	−1.18172	−0.590859	+	0.806774i	$0.701211\pi$
$620$	7.17772e10	0.0195085
$621$	−1.27505e12	−0.344046
$622$	1.89382e12	0.507319
$623$	−1.31613e12	−0.350028
$624$	2.33295e12	0.615991
$625$	−2.12405e12	−0.556808
$626$	−8.36917e12	−2.17820
$627$	8.19833e11	0.211847
$628$	−9.54621e11	−0.244913
$629$	0	0
$630$	−5.97197e12	−1.51038
$631$	2.88522e12	0.724513	0.362257	−	0.932078i	$-0.382006\pi$
$631$	2.88522e12	0.724513	0.362257	+	0.932078i	$0.382006\pi$
$632$	9.53421e10	0.0237716
$633$	1.27684e12	0.316096
$634$	−2.22561e12	−0.547077
$635$	−5.71499e12	−1.39487
$636$	−3.38078e11	−0.0819332
$637$	−9.05518e12	−2.17906
$638$	3.42152e12	0.817572
$639$	−4.51209e12	−1.07059
$640$	1.15256e12	0.271553
$641$	−5.39283e12	−1.26170	−0.630850	−	0.775905i	$-0.717294\pi$
$641$	−5.39283e12	−1.26170	−0.630850	+	0.775905i	$0.717294\pi$
$642$	1.89411e12	0.440046
$643$	−2.99884e12	−0.691836	−0.345918	−	0.938265i	$-0.612433\pi$
$643$	−2.99884e12	−0.691836	−0.345918	+	0.938265i	$0.612433\pi$
$644$	2.93386e12	0.672129
$645$	−2.41710e12	−0.549890
$646$	0	0
$647$	−6.57141e12	−1.47431	−0.737156	−	0.675722i	$-0.763832\pi$
$647$	−6.57141e12	−1.47431	−0.737156	+	0.675722i	$0.763832\pi$
$648$	−4.35982e11	−0.0971361
$649$	−1.39192e12	−0.307974
$650$	3.00758e12	0.660857
$651$	7.56638e10	0.0165110
$652$	−3.12996e12	−0.678304
$653$	1.00670e12	0.216666	0.108333	−	0.994115i	$-0.465449\pi$
$653$	1.00670e12	0.216666	0.108333	+	0.994115i	$0.465449\pi$
$654$	−2.50417e12	−0.535260
$655$	−2.66387e11	−0.0565493
$656$	−6.29374e11	−0.132691
$657$	−5.31329e11	−0.111255
$658$	−8.99379e12	−1.87036
$659$	−3.16289e11	−0.0653282	−0.0326641	−	0.999466i	$-0.510399\pi$
$659$	−3.16289e11	−0.0653282	−0.0326641	+	0.999466i	$0.510399\pi$
$660$	−5.32980e11	−0.109336
$661$	7.77865e12	1.58488	0.792442	−	0.609947i	$-0.208809\pi$
$661$	7.77865e12	1.58488	0.792442	+	0.609947i	$0.208809\pi$
$662$	−3.87283e12	−0.783732
$663$	0	0
$664$	−1.60136e12	−0.319692
$665$	−9.05649e12	−1.79582
$666$	5.58558e10	0.0110011
$667$	−3.71437e12	−0.726640
$668$	6.62229e11	0.128681
$669$	8.33924e11	0.160957
$670$	8.76880e12	1.68114
$671$	−3.22239e12	−0.613658
$672$	−4.33112e12	−0.819291
$673$	3.79653e12	0.713377	0.356688	−	0.934223i	$-0.383906\pi$
$673$	3.79653e12	0.713377	0.356688	+	0.934223i	$0.383906\pi$
$674$	−9.30863e12	−1.73747
$675$	1.27507e12	0.236411
$676$	5.25533e12	0.967921
$677$	−4.11221e12	−0.752362	−0.376181	−	0.926546i	$-0.622763\pi$
$677$	−4.11221e12	−0.752362	−0.376181	+	0.926546i	$0.622763\pi$
$678$	5.19378e12	0.943952
$679$	8.89201e12	1.60541
$680$	0	0
$681$	4.10267e12	0.730979
$682$	−8.36970e10	−0.0148143
$683$	−9.35979e12	−1.64578	−0.822892	−	0.568197i	$-0.807641\pi$
$683$	−9.35979e12	−1.64578	−0.822892	+	0.568197i	$0.807641\pi$
$684$	5.95467e12	1.04017
$685$	−8.42328e12	−1.46175
$686$	6.32177e12	1.08988
$687$	1.16880e12	0.200186
$688$	1.14166e13	1.94263
$689$	2.08687e12	0.352783
$690$	1.23774e12	0.207878
$691$	1.29891e12	0.216734	0.108367	−	0.994111i	$-0.465438\pi$
$691$	1.29891e12	0.216734	0.108367	+	0.994111i	$0.465438\pi$
$692$	−5.81212e12	−0.963511
$693$	3.25528e12	0.536153
$694$	8.29555e12	1.35746
$695$	−4.23095e12	−0.687870
$696$	5.97081e11	0.0964476
$697$	0	0
$698$	−1.25289e13	−1.99786
$699$	−1.67133e12	−0.264798
$700$	−2.93390e12	−0.461853
$701$	−5.92387e12	−0.926562	−0.463281	−	0.886211i	$-0.653328\pi$
$701$	−5.92387e12	−0.926562	−0.463281	+	0.886211i	$0.653328\pi$
$702$	9.08858e12	1.41247
$703$	8.47054e10	0.0130801
$704$	1.92310e12	0.295070
$705$	−1.77370e12	−0.270415
$706$	−1.19997e13	−1.81782
$707$	−6.81307e12	−1.02555
$708$	1.74490e12	0.260989
$709$	−3.45867e12	−0.514045	−0.257022	−	0.966405i	$-0.582741\pi$
$709$	−3.45867e12	−0.514045	−0.257022	+	0.966405i	$0.582741\pi$
$710$	9.51608e12	1.40539
$711$	8.24980e11	0.121068
$712$	2.54059e11	0.0370489
$713$	9.08608e10	0.0131666
$714$	0	0
$715$	3.28995e12	0.470773
$716$	−5.18765e12	−0.737670
$717$	−1.58079e12	−0.223376
$718$	−4.67155e12	−0.655996
$719$	−4.97594e10	−0.00694377	−0.00347188	−	0.999994i	$-0.501105\pi$
$719$	−4.97594e10	−0.00694377	−0.00347188	+	0.999994i	$0.501105\pi$
$720$	5.56287e12	0.771441
$721$	−1.16998e13	−1.61238
$722$	9.31200e12	1.27534
$723$	1.05129e12	0.143087
$724$	−1.13229e13	−1.53156
$725$	3.71443e12	0.499311
$726$	−3.31381e12	−0.442704
$727$	−9.82294e11	−0.130418	−0.0652089	−	0.997872i	$-0.520771\pi$
$727$	−9.82294e11	−0.130418	−0.0652089	+	0.997872i	$0.520771\pi$
$728$	2.91115e12	0.384126
$729$	−1.69287e12	−0.221998
$730$	1.12058e12	0.146047
$731$	0	0
$732$	4.03957e12	0.520038
$733$	7.22406e12	0.924301	0.462151	−	0.886802i	$-0.347078\pi$
$733$	7.22406e12	0.924301	0.462151	+	0.886802i	$0.347078\pi$
$734$	3.91573e12	0.497944
$735$	3.72662e12	0.471002
$736$	−5.20102e12	−0.653338
$737$	−4.77981e12	−0.596770
$738$	−1.12855e12	−0.140045
$739$	9.71249e12	1.19793	0.598964	−	0.800776i	$-0.295579\pi$
$739$	9.71249e12	1.19793	0.598964	+	0.800776i	$0.295579\pi$
$740$	−5.50676e10	−0.00675078
$741$	6.34395e12	0.772998
$742$	−4.35486e12	−0.527420
$743$	−1.04007e13	−1.25202	−0.626012	−	0.779813i	$-0.715314\pi$
$743$	−1.04007e13	−1.25202	−0.626012	+	0.779813i	$0.715314\pi$
$744$	−1.46058e10	−0.00174762
$745$	−6.40460e12	−0.761708
$746$	1.46944e11	0.0173711
$747$	−1.38563e13	−1.62819
$748$	0	0
$749$	1.14054e13	1.32417
$750$	−4.95943e12	−0.572343
$751$	−1.32487e13	−1.51982	−0.759911	−	0.650027i	$-0.774757\pi$
$751$	−1.32487e13	−1.51982	−0.759911	+	0.650027i	$0.774757\pi$
$752$	8.37769e12	0.955309
$753$	−7.77959e11	−0.0881819
$754$	2.64761e13	2.98320
$755$	5.39301e12	0.604045
$756$	−8.86591e12	−0.987132
$757$	−4.44291e12	−0.491740	−0.245870	−	0.969303i	$-0.579074\pi$
$757$	−4.44291e12	−0.491740	−0.245870	+	0.969303i	$0.579074\pi$
$758$	1.62972e13	1.79309
$759$	−6.74684e11	−0.0737926
$760$	1.74822e12	0.190079
$761$	2.09223e12	0.226141	0.113070	−	0.993587i	$-0.463931\pi$
$761$	2.09223e12	0.226141	0.113070	+	0.993587i	$0.463931\pi$
$762$	−8.35402e12	−0.897632
$763$	−1.50789e13	−1.61068
$764$	3.35809e12	0.356593
$765$	0	0
$766$	−1.66840e13	−1.75094
$767$	−1.07708e13	−1.12375
$768$	4.43117e12	0.459614
$769$	−4.94365e12	−0.509776	−0.254888	−	0.966971i	$-0.582039\pi$
$769$	−4.94365e12	−0.509776	−0.254888	+	0.966971i	$0.582039\pi$
$770$	−6.86544e12	−0.703818
$771$	−1.11699e12	−0.113843
$772$	8.05826e12	0.816514
$773$	−9.50527e12	−0.957540	−0.478770	−	0.877940i	$-0.658917\pi$
$773$	−9.50527e12	−0.957540	−0.478770	+	0.877940i	$0.658917\pi$
$774$	2.04715e13	2.05029
$775$	−9.08621e10	−0.00904743
$776$	−1.71647e12	−0.169925
$777$	−5.80494e10	−0.00571351
$778$	−1.10992e13	−1.08613
$779$	−1.71145e12	−0.166512
$780$	−4.12426e12	−0.398951
$781$	−5.18715e12	−0.498883
$782$	0	0
$783$	1.12246e13	1.06719
$784$	−1.76018e13	−1.66393
$785$	−2.42509e12	−0.227936
$786$	−3.89397e11	−0.0363908
$787$	5.91450e12	0.549581	0.274790	−	0.961504i	$-0.411392\pi$
$787$	5.91450e12	0.549581	0.274790	+	0.961504i	$0.411392\pi$
$788$	1.30884e13	1.20926
$789$	8.88638e11	0.0816354
$790$	−1.73990e12	−0.158929
$791$	3.12744e13	2.84050
$792$	−6.28382e11	−0.0567493
$793$	−2.49352e13	−2.23915
$794$	2.51742e13	2.24783
$795$	−8.58842e11	−0.0762537
$796$	−8.22544e11	−0.0726190
$797$	1.23941e13	1.08806	0.544029	−	0.839067i	$-0.316898\pi$
$797$	1.23941e13	1.08806	0.544029	+	0.839067i	$0.316898\pi$
$798$	−1.32385e13	−1.15565
$799$	0	0
$800$	5.20109e12	0.448941
$801$	2.19833e12	0.188689
$802$	−2.75090e13	−2.34796
$803$	−6.10822e11	−0.0518436
$804$	5.99194e12	0.505726
$805$	7.45307e12	0.625538
$806$	−6.47656e11	−0.0540551
$807$	6.09260e11	0.0505675
$808$	1.31516e12	0.108549
$809$	3.25319e11	0.0267019	0.0133509	−	0.999911i	$-0.495750\pi$
$809$	3.25319e11	0.0267019	0.0133509	+	0.999911i	$0.495750\pi$
$810$	7.95623e12	0.649418
$811$	1.73188e12	0.140580	0.0702899	−	0.997527i	$-0.477608\pi$
$811$	1.73188e12	0.140580	0.0702899	+	0.997527i	$0.477608\pi$
$812$	−2.58274e13	−2.08487
$813$	−3.49192e12	−0.280322
$814$	6.42125e10	0.00512637
$815$	−7.95124e12	−0.631285
$816$	0	0
$817$	3.10451e13	2.43777
$818$	2.04273e13	1.59522
$819$	2.51897e13	1.95634
$820$	1.11263e12	0.0859385
$821$	−6.79797e12	−0.522198	−0.261099	−	0.965312i	$-0.584085\pi$
$821$	−6.79797e12	−0.522198	−0.261099	+	0.965312i	$0.584085\pi$
$822$	−1.23129e13	−0.940672
$823$	7.36235e12	0.559393	0.279697	−	0.960088i	$-0.409766\pi$
$823$	7.36235e12	0.559393	0.279697	+	0.960088i	$0.409766\pi$
$824$	2.25846e12	0.170664
$825$	6.74694e11	0.0507065
$826$	2.24765e13	1.68004
$827$	2.22177e13	1.65167	0.825836	−	0.563911i	$-0.190704\pi$
$827$	2.22177e13	1.65167	0.825836	+	0.563911i	$0.190704\pi$
$828$	−4.90042e12	−0.362324
$829$	8.11644e12	0.596857	0.298428	−	0.954432i	$-0.403538\pi$
$829$	8.11644e12	0.596857	0.298428	+	0.954432i	$0.403538\pi$
$830$	2.92232e13	2.13735
$831$	−9.62626e12	−0.700249
$832$	1.48812e13	1.07667
$833$	0	0
$834$	−6.18469e12	−0.442661
$835$	1.68231e12	0.119761
$836$	6.84556e12	0.484709
$837$	−2.74575e11	−0.0193373
$838$	3.69085e13	2.58541
$839$	7.13705e12	0.497267	0.248634	−	0.968598i	$-0.420019\pi$
$839$	7.13705e12	0.497267	0.248634	+	0.968598i	$0.420019\pi$
$840$	−1.19807e12	−0.0830283
$841$	1.81913e13	1.25396
$842$	−3.10420e13	−2.12836
$843$	−3.06908e12	−0.209307
$844$	1.06615e13	0.723233
$845$	1.33505e13	0.900826
$846$	1.50223e13	1.00826
$847$	−1.99542e13	−1.33217
$848$	4.05654e12	0.269386
$849$	9.17977e12	0.606383
$850$	0	0
$851$	−6.97086e10	−0.00455621
$852$	6.50258e12	0.422773
$853$	−7.08729e12	−0.458363	−0.229182	−	0.973384i	$-0.573605\pi$
$853$	−7.08729e12	−0.458363	−0.229182	+	0.973384i	$0.573605\pi$
$854$	5.20347e13	3.34759
$855$	1.51271e13	0.968070
$856$	−2.20164e12	−0.140157
$857$	2.66839e13	1.68980	0.844900	−	0.534925i	$-0.179660\pi$
$857$	2.66839e13	1.68980	0.844900	+	0.534925i	$0.179660\pi$
$858$	4.80915e12	0.302953
$859$	1.11623e13	0.699496	0.349748	−	0.936844i	$-0.386267\pi$
$859$	1.11623e13	0.699496	0.349748	+	0.936844i	$0.386267\pi$
$860$	−2.01827e13	−1.25816
$861$	1.17287e12	0.0727339
$862$	−3.60278e12	−0.222257
$863$	1.18982e13	0.730183	0.365091	−	0.930972i	$-0.381038\pi$
$863$	1.18982e13	0.730183	0.365091	+	0.930972i	$0.381038\pi$
$864$	1.57171e13	0.959535
$865$	−1.47649e13	−0.896723
$866$	−3.62547e13	−2.19045
$867$	0	0
$868$	6.31789e11	0.0377775
$869$	9.48406e11	0.0564164
$870$	−1.08961e13	−0.644815
$871$	−3.69867e13	−2.17753
$872$	2.91075e12	0.170483
$873$	−1.48523e13	−0.865427
$874$	−1.58975e13	−0.921567
$875$	−2.98633e13	−1.72227
$876$	7.65723e11	0.0439342
$877$	7.48241e12	0.427113	0.213557	−	0.976931i	$-0.431495\pi$
$877$	7.48241e12	0.427113	0.213557	+	0.976931i	$0.431495\pi$
$878$	3.20121e12	0.181798
$879$	5.79646e12	0.327501
$880$	6.39514e12	0.359483
$881$	8.69387e12	0.486208	0.243104	−	0.970000i	$-0.421834\pi$
$881$	8.69387e12	0.486208	0.243104	+	0.970000i	$0.421834\pi$
$882$	−3.15625e13	−1.75615
$883$	2.71253e13	1.50159	0.750794	−	0.660536i	$-0.229671\pi$
$883$	2.71253e13	1.50159	0.750794	+	0.660536i	$0.229671\pi$
$884$	0	0
$885$	4.43270e12	0.242898
$886$	2.31038e13	1.25960
$887$	1.80206e13	0.977494	0.488747	−	0.872426i	$-0.337454\pi$
$887$	1.80206e13	0.977494	0.488747	+	0.872426i	$0.337454\pi$
$888$	1.12056e10	0.000604749 0
$889$	−5.03038e13	−2.70111
$890$	−4.63633e12	−0.247696
$891$	−4.33688e12	−0.230530
$892$	6.96322e12	0.368272
$893$	2.27813e13	1.19880
$894$	−9.36207e12	−0.490177
$895$	−1.31785e13	−0.686536
$896$	1.01450e13	0.525853
$897$	−5.22078e12	−0.269259
$898$	3.72132e13	1.90965
$899$	−7.99868e11	−0.0408413
$900$	4.90049e12	0.248971
$901$	0	0
$902$	−1.29740e12	−0.0652595
$903$	−2.12755e13	−1.06484
$904$	−6.03705e12	−0.300654
$905$	−2.87644e13	−1.42540
$906$	7.88335e12	0.388717
$907$	−2.15751e13	−1.05857	−0.529286	−	0.848443i	$-0.677540\pi$
$907$	−2.15751e13	−1.05857	−0.529286	+	0.848443i	$0.677540\pi$
$908$	3.42571e13	1.67249
$909$	1.13799e13	0.552840
$910$	−5.31255e13	−2.56813
$911$	−1.37712e13	−0.662430	−0.331215	−	0.943555i	$-0.607458\pi$
$911$	−1.37712e13	−0.662430	−0.331215	+	0.943555i	$0.607458\pi$
$912$	1.23317e13	0.590262
$913$	−1.59294e13	−0.758717
$914$	−2.58422e13	−1.22482
$915$	1.02620e13	0.483990
$916$	9.75938e12	0.458029
$917$	−2.34476e12	−0.109505
$918$	0	0
$919$	7.38530e12	0.341546	0.170773	−	0.985310i	$-0.445374\pi$
$919$	7.38530e12	0.341546	0.170773	+	0.985310i	$0.445374\pi$
$920$	−1.43870e12	−0.0662104
$921$	−3.42484e11	−0.0156846
$922$	1.44841e13	0.660088
$923$	−4.01387e13	−1.82035
$924$	−4.69133e12	−0.211725
$925$	6.97096e10	0.00313080
$926$	−1.81623e13	−0.811748
$927$	1.95421e13	0.869187
$928$	4.57857e13	2.02658
$929$	−2.18632e13	−0.963038	−0.481519	−	0.876436i	$-0.659915\pi$
$929$	−2.18632e13	−0.963038	−0.481519	+	0.876436i	$0.659915\pi$
$930$	2.66540e11	0.0116840
$931$	−4.78645e13	−2.08805
$932$	−1.39555e13	−0.605862
$933$	3.28747e12	0.142035
$934$	4.23286e13	1.82000
$935$	0	0
$936$	−4.86249e12	−0.207070
$937$	1.65419e13	0.701062	0.350531	−	0.936551i	$-0.386001\pi$
$937$	1.65419e13	0.701062	0.350531	+	0.936551i	$0.386001\pi$
$938$	7.71837e13	3.25546
$939$	−1.45280e13	−0.609833
$940$	−1.48103e13	−0.618714
$941$	−1.02461e13	−0.425995	−0.212998	−	0.977053i	$-0.568323\pi$
$941$	−1.02461e13	−0.425995	−0.212998	+	0.977053i	$0.568323\pi$
$942$	−3.54493e12	−0.146682
$943$	1.40844e12	0.0580012
$944$	−2.09368e13	−0.858098
$945$	−2.25227e13	−0.918706
$946$	2.35343e13	0.955414
$947$	1.33810e13	0.540648	0.270324	−	0.962769i	$-0.412869\pi$
$947$	1.33810e13	0.540648	0.270324	+	0.962769i	$0.412869\pi$
$948$	−1.18892e12	−0.0478095
$949$	−4.72661e12	−0.189170
$950$	1.58977e13	0.633255
$951$	−3.86344e12	−0.153166
$952$	0	0
$953$	−4.84663e13	−1.90336	−0.951682	−	0.307084i	$-0.900647\pi$
$953$	−4.84663e13	−1.90336	−0.951682	+	0.307084i	$0.900647\pi$
$954$	7.27393e12	0.284316
$955$	8.53079e12	0.331875
$956$	−1.31995e13	−0.511089
$957$	5.93940e12	0.228896
$958$	−6.40240e13	−2.45583
$959$	−7.41424e13	−2.83063
$960$	−6.12429e12	−0.232721
$961$	−2.64201e13	−0.999260
$962$	4.96883e11	0.0187054
$963$	−1.90504e13	−0.713817
$964$	8.77823e12	0.327386
$965$	2.04709e13	0.759915
$966$	1.08947e13	0.402549
$967$	−9.25582e12	−0.340405	−0.170202	−	0.985409i	$-0.554442\pi$
$967$	−9.25582e12	−0.340405	−0.170202	+	0.985409i	$0.554442\pi$
$968$	3.85185e12	0.141004
$969$	0	0
$970$	3.13238e13	1.13606
$971$	4.19377e13	1.51397	0.756986	−	0.653431i	$-0.226671\pi$
$971$	4.19377e13	1.51397	0.756986	+	0.653431i	$0.226671\pi$
$972$	2.28013e13	0.819335
$973$	−3.72412e13	−1.33203
$974$	2.36268e13	0.841181
$975$	5.22086e12	0.185021
$976$	−4.84701e13	−1.70982
$977$	−1.16863e13	−0.410346	−0.205173	−	0.978726i	$-0.565776\pi$
$977$	−1.16863e13	−0.410346	−0.205173	+	0.978726i	$0.565776\pi$
$978$	−1.16229e13	−0.406247
$979$	2.52723e12	0.0879271
$980$	3.11171e13	1.07766
$981$	2.51863e13	0.868267
$982$	−2.87137e13	−0.985345
$983$	−2.32178e13	−0.793103	−0.396551	−	0.918013i	$-0.629793\pi$
$983$	−2.32178e13	−0.793103	−0.396551	+	0.918013i	$0.629793\pi$
$984$	−2.26406e11	−0.00769856
$985$	3.32493e13	1.12543
$986$	0	0
$987$	−1.56123e13	−0.523648
$988$	5.29717e13	1.76863
$989$	−2.55487e13	−0.849151
$990$	1.14674e13	0.379406
$991$	−2.74583e13	−0.904361	−0.452181	−	0.891926i	$-0.649354\pi$
$991$	−2.74583e13	−0.904361	−0.452181	+	0.891926i	$0.649354\pi$
$992$	−1.12001e12	−0.0367213
$993$	−6.72283e12	−0.219422
$994$	8.37613e13	2.72148
$995$	−2.08956e12	−0.0675852
$996$	1.99689e13	0.642966
$997$	6.82596e12	0.218794	0.109397	−	0.993998i	$-0.465108\pi$
$997$	6.82596e12	0.218794	0.109397	+	0.993998i	$0.465108\pi$
$998$	4.54546e13	1.45041
$999$	2.10655e11	0.00669154

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.g.1.30	✓	36
17.16	even	2		289.10.a.h.1.30	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.30	✓	36	1.1	even	1	trivial
289.10.a.h.1.30	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)

\(f(q)\)	\(=\)	\(q+31.0070 q^{2} +53.8250 q^{3} +449.436 q^{4} +1141.73 q^{5} +1668.95 q^{6} +10049.6 q^{7} -1939.93 q^{8} -16785.9 q^{9} +O(q^{10})\)	\(q+31.0070 q^{2} +53.8250 q^{3} +449.436 q^{4} +1141.73 q^{5} +1668.95 q^{6} +10049.6 q^{7} -1939.93 q^{8} -16785.9 q^{9} +35401.7 q^{10} -19297.2 q^{11} +24190.9 q^{12} -149324. q^{13} +311609. q^{14} +61453.7 q^{15} -290263. q^{16} -520480. q^{18} -789308. q^{19} +513135. q^{20} +540920. q^{21} -598350. q^{22} +649564. q^{23} -104417. q^{24} -649573. q^{25} -4.63009e6 q^{26} -1.96294e6 q^{27} +4.51666e6 q^{28} -5.71826e6 q^{29} +1.90550e6 q^{30} +139880. q^{31} -8.00694e6 q^{32} -1.03867e6 q^{33} +1.14740e7 q^{35} -7.54417e6 q^{36} -107316. q^{37} -2.44741e7 q^{38} -8.03736e6 q^{39} -2.21488e6 q^{40} +2.16829e6 q^{41} +1.67723e7 q^{42} -3.93320e7 q^{43} -8.67287e6 q^{44} -1.91650e7 q^{45} +2.01410e7 q^{46} -2.88624e7 q^{47} -1.56234e7 q^{48} +6.06411e7 q^{49} -2.01413e7 q^{50} -6.71116e7 q^{52} -1.39754e7 q^{53} -6.08648e7 q^{54} -2.20323e7 q^{55} -1.94955e7 q^{56} -4.24845e7 q^{57} -1.77306e8 q^{58} +7.21306e7 q^{59} +2.76195e7 q^{60} +1.66987e8 q^{61} +4.33725e6 q^{62} -1.68692e8 q^{63} -9.96569e7 q^{64} -1.70488e8 q^{65} -3.22062e7 q^{66} +2.47694e8 q^{67} +3.49628e7 q^{69} +3.55774e8 q^{70} +2.68803e8 q^{71} +3.25634e7 q^{72} +3.16534e7 q^{73} -3.32755e6 q^{74} -3.49633e7 q^{75} -3.54743e8 q^{76} -1.93930e8 q^{77} -2.49215e8 q^{78} -4.91473e7 q^{79} -3.31402e8 q^{80} +2.24741e8 q^{81} +6.72323e7 q^{82} +8.25474e8 q^{83} +2.43109e8 q^{84} -1.21957e9 q^{86} -3.07785e8 q^{87} +3.74352e7 q^{88} -1.30963e8 q^{89} -5.94249e8 q^{90} -1.50065e9 q^{91} +2.91937e8 q^{92} +7.52902e6 q^{93} -8.94939e8 q^{94} -9.01178e8 q^{95} -4.30973e8 q^{96} +8.84811e8 q^{97} +1.88030e9 q^{98} +3.23921e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 486 q^{3} + 9216 q^{4} - 3750 q^{5} - 11061 q^{6} - 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 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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