LMFDB - Embedded newform 289.10.a.h.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [289,10,Mod(1,289)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(289, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 10, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("289.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	289.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$148.845356651$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
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)

$f(q)$	$=$	$q-22.4936 q^{2} +161.121 q^{3} -6.03889 q^{4} +1284.66 q^{5} -3624.20 q^{6} +9354.17 q^{7} +11652.5 q^{8} +6277.10 q^{9} +O(q^{10})$	\(q-22.4936 q^{2} +161.121 q^{3} -6.03889 q^{4} +1284.66 q^{5} -3624.20 q^{6} +9354.17 q^{7} +11652.5 q^{8} +6277.10 q^{9} -28896.7 q^{10} +57101.0 q^{11} -972.994 q^{12} -147205. q^{13} -210409. q^{14} +206987. q^{15} -259016. q^{16} -141194. q^{18} -495550. q^{19} -7757.93 q^{20} +1.50716e6 q^{21} -1.28441e6 q^{22} +2.06028e6 q^{23} +1.87747e6 q^{24} -302768. q^{25} +3.31117e6 q^{26} -2.15998e6 q^{27} -56488.8 q^{28} +1.09429e6 q^{29} -4.65587e6 q^{30} +8.20471e6 q^{31} -139917. q^{32} +9.20020e6 q^{33} +1.20169e7 q^{35} -37906.7 q^{36} +1.78074e7 q^{37} +1.11467e7 q^{38} -2.37179e7 q^{39} +1.49696e7 q^{40} -1.40060e7 q^{41} -3.39013e7 q^{42} -2.12860e6 q^{43} -344827. q^{44} +8.06395e6 q^{45} -4.63431e7 q^{46} +1.57971e7 q^{47} -4.17330e7 q^{48} +4.71468e7 q^{49} +6.81033e6 q^{50} +888955. q^{52} -3.85001e7 q^{53} +4.85856e7 q^{54} +7.33555e7 q^{55} +1.09000e8 q^{56} -7.98436e7 q^{57} -2.46146e7 q^{58} +6.56446e7 q^{59} -1.24997e6 q^{60} +4.06936e7 q^{61} -1.84553e8 q^{62} +5.87170e7 q^{63} +1.35763e8 q^{64} -1.89109e8 q^{65} -2.06945e8 q^{66} +1.29000e8 q^{67} +3.31955e8 q^{69} -2.70304e8 q^{70} -1.56798e8 q^{71} +7.31442e7 q^{72} +2.48477e8 q^{73} -4.00551e8 q^{74} -4.87823e7 q^{75} +2.99257e6 q^{76} +5.34133e8 q^{77} +5.33500e8 q^{78} +5.41804e8 q^{79} -3.32748e8 q^{80} -4.71571e8 q^{81} +3.15045e8 q^{82} +7.51897e7 q^{83} -9.10155e6 q^{84} +4.78798e7 q^{86} +1.76314e8 q^{87} +6.65373e8 q^{88} +4.56857e8 q^{89} -1.81387e8 q^{90} -1.37698e9 q^{91} -1.24418e7 q^{92} +1.32195e9 q^{93} -3.55333e8 q^{94} -6.36614e8 q^{95} -2.25436e7 q^{96} -1.00520e9 q^{97} -1.06050e9 q^{98} +3.58429e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−22.4936	−0.994085	−0.497043	−	0.867726i	$-0.665581\pi$
$2$	−22.4936	−0.994085	−0.497043	+	0.867726i	$0.665581\pi$
$3$	161.121	1.14844	0.574219	−	0.818702i	$-0.305306\pi$
$3$	161.121	1.14844	0.574219	+	0.818702i	$0.305306\pi$
$4$	−6.03889	−0.0117947
$5$	1284.66	0.919230	0.459615	−	0.888118i	$-0.347987\pi$
$5$	1284.66	0.919230	0.459615	+	0.888118i	$0.347987\pi$
$6$	−3624.20	−1.14165
$7$	9354.17	1.47253	0.736265	−	0.676694i	$-0.236588\pi$
$7$	9354.17	1.47253	0.736265	+	0.676694i	$0.236588\pi$
$8$	11652.5	1.00581
$9$	6277.10	0.318910
$10$	−28896.7	−0.913792
$11$	57101.0	1.17592	0.587959	−	0.808891i	$-0.299932\pi$
$11$	57101.0	1.17592	0.587959	+	0.808891i	$0.299932\pi$
$12$	−972.994	−0.0135455
$13$	−147205.	−1.42948	−0.714739	−	0.699391i	$-0.753455\pi$
$13$	−147205.	−1.42948	−0.714739	+	0.699391i	$0.753455\pi$
$14$	−210409.	−1.46382
$15$	206987.	1.05568
$16$	−259016.	−0.988066
$17$	0	0
$17$	0	0
$18$	−141194.	−0.317023
$19$	−495550.	−0.872360	−0.436180	−	0.899859i	$-0.643669\pi$
$19$	−495550.	−0.872360	−0.436180	+	0.899859i	$0.643669\pi$
$20$	−7757.93	−0.0108420
$21$	1.50716e6	1.69111
$22$	−1.28441e6	−1.16896
$23$	2.06028e6	1.53515	0.767576	−	0.640958i	$-0.221463\pi$
$23$	2.06028e6	1.53515	0.767576	+	0.640958i	$0.221463\pi$
$24$	1.87747e6	1.15511
$25$	−302768.	−0.155017
$26$	3.31117e6	1.42102
$27$	−2.15998e6	−0.782190
$28$	−56488.8	−0.0173680
$29$	1.09429e6	0.287305	0.143652	−	0.989628i	$-0.454115\pi$
$29$	1.09429e6	0.287305	0.143652	+	0.989628i	$0.454115\pi$
$30$	−4.65587e6	−1.04943
$31$	8.20471e6	1.59564	0.797822	−	0.602894i	$-0.205986\pi$
$31$	8.20471e6	1.59564	0.797822	+	0.602894i	$0.205986\pi$
$32$	−139917.	−0.0235882
$33$	9.20020e6	1.35047
$34$	0	0
$35$	1.20169e7	1.35359
$36$	−37906.7	−0.00376144
$37$	1.78074e7	1.56204	0.781019	−	0.624507i	$-0.214700\pi$
$37$	1.78074e7	1.56204	0.781019	+	0.624507i	$0.214700\pi$
$38$	1.11467e7	0.867201
$39$	−2.37179e7	−1.64167
$40$	1.49696e7	0.924570
$41$	−1.40060e7	−0.774082	−0.387041	−	0.922062i	$-0.626503\pi$
$41$	−1.40060e7	−0.774082	−0.387041	+	0.922062i	$0.626503\pi$
$42$	−3.39013e7	−1.68111
$43$	−2.12860e6	−0.0949479	−0.0474740	−	0.998872i	$-0.515117\pi$
$43$	−2.12860e6	−0.0949479	−0.0474740	+	0.998872i	$0.515117\pi$
$44$	−344827.	−0.0138696
$45$	8.06395e6	0.293151
$46$	−4.63431e7	−1.52607
$47$	1.57971e7	0.472212	0.236106	−	0.971727i	$-0.424129\pi$
$47$	1.57971e7	0.472212	0.236106	+	0.971727i	$0.424129\pi$
$48$	−4.17330e7	−1.13473
$49$	4.71468e7	1.16834
$50$	6.81033e6	0.154100
$51$	0	0
$52$	888955.	0.0168603
$53$	−3.85001e7	−0.670225	−0.335113	−	0.942178i	$-0.608774\pi$
$53$	−3.85001e7	−0.670225	−0.335113	+	0.942178i	$0.608774\pi$
$54$	4.85856e7	0.777564
$55$	7.33555e7	1.08094
$56$	1.09000e8	1.48108
$57$	−7.98436e7	−1.00185
$58$	−2.46146e7	−0.285605
$59$	6.56446e7	0.705285	0.352643	−	0.935758i	$-0.385283\pi$
$59$	6.56446e7	0.705285	0.352643	+	0.935758i	$0.385283\pi$
$60$	−1.24997e6	−0.0124514
$61$	4.06936e7	0.376307	0.188153	−	0.982140i	$-0.439750\pi$
$61$	4.06936e7	0.376307	0.188153	+	0.982140i	$0.439750\pi$
$62$	−1.84553e8	−1.58621
$63$	5.87170e7	0.469604
$64$	1.35763e8	1.01151
$65$	−1.89109e8	−1.31402
$66$	−2.06945e8	−1.34248
$67$	1.29000e8	0.782083	0.391041	−	0.920373i	$-0.372115\pi$
$67$	1.29000e8	0.782083	0.391041	+	0.920373i	$0.372115\pi$
$68$	0	0
$69$	3.31955e8	1.76303
$70$	−2.70304e8	−1.34559
$71$	−1.56798e8	−0.732280	−0.366140	−	0.930560i	$-0.619321\pi$
$71$	−1.56798e8	−0.732280	−0.366140	+	0.930560i	$0.619321\pi$
$72$	7.31442e7	0.320762
$73$	2.48477e8	1.02408	0.512039	−	0.858962i	$-0.328890\pi$
$73$	2.48477e8	1.02408	0.512039	+	0.858962i	$0.328890\pi$
$74$	−4.00551e8	−1.55280
$75$	−4.87823e7	−0.178027
$76$	2.99257e6	0.0102892
$77$	5.34133e8	1.73157
$78$	5.33500e8	1.63196
$79$	5.41804e8	1.56502	0.782511	−	0.622637i	$-0.213939\pi$
$79$	5.41804e8	1.56502	0.782511	+	0.622637i	$0.213939\pi$
$80$	−3.32748e8	−0.908260
$81$	−4.71571e8	−1.21721
$82$	3.15045e8	0.769504
$83$	7.51897e7	0.173903	0.0869515	−	0.996213i	$-0.472287\pi$
$83$	7.51897e7	0.173903	0.0869515	+	0.996213i	$0.472287\pi$
$84$	−9.10155e6	−0.0199461
$85$	0	0
$86$	4.78798e7	0.0943863
$87$	1.76314e8	0.329952
$88$	6.65373e8	1.18275
$89$	4.56857e8	0.771836	0.385918	−	0.922533i	$-0.373885\pi$
$89$	4.56857e8	0.771836	0.385918	+	0.922533i	$0.373885\pi$
$90$	−1.81387e8	−0.291417
$91$	−1.37698e9	−2.10495
$92$	−1.24418e7	−0.0181067
$93$	1.32195e9	1.83250
$94$	−3.55333e8	−0.469419
$95$	−6.36614e8	−0.801899
$96$	−2.25436e7	−0.0270896
$97$	−1.00520e9	−1.15287	−0.576437	−	0.817142i	$-0.695557\pi$
$97$	−1.00520e9	−1.15287	−0.576437	+	0.817142i	$0.695557\pi$
$98$	−1.06050e9	−1.16143
$99$	3.58429e8	0.375011
$100$	1.82838e6	0.00182838
$101$	−7.94017e8	−0.759248	−0.379624	−	0.925141i	$-0.623947\pi$
$101$	−7.94017e8	−0.759248	−0.379624	+	0.925141i	$0.623947\pi$
$102$	0	0
$103$	1.53373e9	1.34271	0.671353	−	0.741138i	$-0.265714\pi$
$103$	1.53373e9	1.34271	0.671353	+	0.741138i	$0.265714\pi$
$104$	−1.71531e9	−1.43778
$105$	1.93619e9	1.55452
$106$	8.66006e8	0.666261
$107$	−1.65042e9	−1.21722	−0.608609	−	0.793471i	$-0.708272\pi$
$107$	−1.65042e9	−1.21722	−0.608609	+	0.793471i	$0.708272\pi$
$108$	1.30439e7	0.00922570
$109$	−8.41832e8	−0.571223	−0.285612	−	0.958345i	$-0.592197\pi$
$109$	−8.41832e8	−0.571223	−0.285612	+	0.958345i	$0.592197\pi$
$110$	−1.65003e9	−1.07454
$111$	2.86915e9	1.79390
$112$	−2.42288e9	−1.45496
$113$	−2.33505e9	−1.34723	−0.673617	−	0.739081i	$-0.735260\pi$
$113$	−2.33505e9	−1.34723	−0.673617	+	0.739081i	$0.735260\pi$
$114$	1.79597e9	0.995926
$115$	2.64677e9	1.41116
$116$	−6.60832e6	−0.00338867
$117$	−9.24020e8	−0.455874
$118$	−1.47658e9	−0.701114
$119$	0	0
$120$	2.41192e9	1.06181
$121$	9.02580e8	0.382782
$122$	−9.15344e8	−0.374081
$123$	−2.25667e9	−0.888985
$124$	−4.95474e7	−0.0188201
$125$	−2.89806e9	−1.06173
$126$	−1.32076e9	−0.466826
$127$	−1.32135e9	−0.450715	−0.225357	−	0.974276i	$-0.572355\pi$
$127$	−1.32135e9	−0.450715	−0.225357	+	0.974276i	$0.572355\pi$
$128$	−2.98216e9	−0.981944
$129$	−3.42963e8	−0.109042
$130$	4.25373e9	1.30625
$131$	5.89659e9	1.74936	0.874681	−	0.484698i	$-0.161071\pi$
$131$	5.89659e9	1.74936	0.874681	+	0.484698i	$0.161071\pi$
$132$	−5.55590e7	−0.0159284
$133$	−4.63545e9	−1.28458
$134$	−2.90167e9	−0.777457
$135$	−2.77484e9	−0.719012
$136$	0	0
$137$	−4.07749e9	−0.988896	−0.494448	−	0.869207i	$-0.664630\pi$
$137$	−4.07749e9	−0.988896	−0.494448	+	0.869207i	$0.664630\pi$
$138$	−7.46687e9	−1.75260
$139$	8.32735e9	1.89208	0.946041	−	0.324046i	$-0.105043\pi$
$139$	8.32735e9	1.89208	0.946041	+	0.324046i	$0.105043\pi$
$140$	−7.25690e7	−0.0159652
$141$	2.54525e9	0.542306
$142$	3.52694e9	0.727949
$143$	−8.40556e9	−1.68095
$144$	−1.62587e9	−0.315104
$145$	1.40580e9	0.264099
$146$	−5.58913e9	−1.01802
$147$	7.59636e9	1.34177
$148$	−1.07537e8	−0.0184238
$149$	1.09294e10	1.81660	0.908301	−	0.418317i	$-0.137380\pi$
$149$	1.09294e10	1.81660	0.908301	+	0.418317i	$0.137380\pi$
$150$	1.09729e9	0.176974
$151$	−1.08934e10	−1.70517	−0.852586	−	0.522586i	$-0.824967\pi$
$151$	−1.08934e10	−1.70517	−0.852586	+	0.522586i	$0.824967\pi$
$152$	−5.77442e9	−0.877429
$153$	0	0
$154$	−1.20146e10	−1.72133
$155$	1.05403e10	1.46676
$156$	1.43230e8	0.0193630
$157$	3.77707e7	0.00496143	0.00248072	−	0.999997i	$-0.499210\pi$
$157$	3.77707e7	0.00496143	0.00248072	+	0.999997i	$0.499210\pi$
$158$	−1.21871e10	−1.55576
$159$	−6.20320e9	−0.769712
$160$	−1.79746e8	−0.0216829
$161$	1.92722e10	2.26056
$162$	1.06073e10	1.21001
$163$	4.13858e9	0.459205	0.229603	−	0.973284i	$-0.426257\pi$
$163$	4.13858e9	0.459205	0.229603	+	0.973284i	$0.426257\pi$
$164$	8.45807e7	0.00913007
$165$	1.18191e10	1.24139
$166$	−1.69129e9	−0.172874
$167$	1.30060e10	1.29396	0.646978	−	0.762508i	$-0.276032\pi$
$167$	1.30060e10	1.29396	0.646978	+	0.762508i	$0.276032\pi$
$168$	1.75622e10	1.70093
$169$	1.10648e10	1.04341
$170$	0	0
$171$	−3.11061e9	−0.278204
$172$	1.28544e7	0.00111988
$173$	−4.63053e9	−0.393028	−0.196514	−	0.980501i	$-0.562962\pi$
$173$	−4.63053e9	−0.393028	−0.196514	+	0.980501i	$0.562962\pi$
$174$	−3.96593e9	−0.328000
$175$	−2.83214e9	−0.228267
$176$	−1.47901e10	−1.16188
$177$	1.05767e10	0.809976
$178$	−1.02763e10	−0.767271
$179$	−1.45886e9	−0.106212	−0.0531062	−	0.998589i	$-0.516912\pi$
$179$	−1.45886e9	−0.106212	−0.0531062	+	0.998589i	$0.516912\pi$
$180$	−4.86973e7	−0.00345763
$181$	7.76243e9	0.537582	0.268791	−	0.963199i	$-0.413376\pi$
$181$	7.76243e9	0.537582	0.268791	+	0.963199i	$0.413376\pi$
$182$	3.09732e10	2.09250
$183$	6.55661e9	0.432165
$184$	2.40075e10	1.54407
$185$	2.28764e10	1.43587
$186$	−2.97355e10	−1.82166
$187$	0	0
$188$	−9.53969e7	−0.00556960
$189$	−2.02048e10	−1.15180
$190$	1.43197e10	0.797156
$191$	−3.61087e9	−0.196319	−0.0981595	−	0.995171i	$-0.531296\pi$
$191$	−3.61087e9	−0.196319	−0.0981595	+	0.995171i	$0.531296\pi$
$192$	2.18744e10	1.16166
$193$	1.09453e10	0.567833	0.283917	−	0.958849i	$-0.408366\pi$
$193$	1.09453e10	0.567833	0.283917	+	0.958849i	$0.408366\pi$
$194$	2.26106e10	1.14605
$195$	−3.04695e10	−1.50907
$196$	−2.84714e8	−0.0137803
$197$	3.82220e9	0.180807	0.0904034	−	0.995905i	$-0.471184\pi$
$197$	3.82220e9	0.180807	0.0904034	+	0.995905i	$0.471184\pi$
$198$	−8.06234e9	−0.372793
$199$	−1.97634e10	−0.893352	−0.446676	−	0.894696i	$-0.647392\pi$
$199$	−1.97634e10	−0.893352	−0.446676	+	0.894696i	$0.647392\pi$
$200$	−3.52802e9	−0.155918
$201$	2.07846e10	0.898174
$202$	1.78603e10	0.754757
$203$	1.02362e10	0.423065
$204$	0	0
$205$	−1.79930e10	−0.711559
$206$	−3.44990e10	−1.33476
$207$	1.29326e10	0.489575
$208$	3.81284e10	1.41242
$209$	−2.82964e10	−1.02582
$210$	−4.35518e10	−1.54532
$211$	4.98585e9	0.173168	0.0865840	−	0.996245i	$-0.472405\pi$
$211$	4.98585e9	0.173168	0.0865840	+	0.996245i	$0.472405\pi$
$212$	2.32498e8	0.00790511
$213$	−2.52635e10	−0.840978
$214$	3.71239e10	1.21002
$215$	−2.73453e9	−0.0872790
$216$	−2.51692e10	−0.786735
$217$	7.67483e10	2.34963
$218$	1.89358e10	0.567845
$219$	4.00349e10	1.17609
$220$	−4.42986e8	−0.0127493
$221$	0	0
$222$	−6.45374e10	−1.78329
$223$	−6.96358e10	−1.88565	−0.942824	−	0.333291i	$-0.891841\pi$
$223$	−6.96358e10	−1.88565	−0.942824	+	0.333291i	$0.891841\pi$
$224$	−1.30880e9	−0.0347343
$225$	−1.90050e9	−0.0494364
$226$	5.25236e10	1.33927
$227$	2.88086e10	0.720122	0.360061	−	0.932929i	$-0.382756\pi$
$227$	2.88086e10	0.720122	0.360061	+	0.932929i	$0.382756\pi$
$228$	4.82167e8	0.0118165
$229$	−7.61079e9	−0.182882	−0.0914408	−	0.995811i	$-0.529147\pi$
$229$	−7.61079e9	−0.182882	−0.0914408	+	0.995811i	$0.529147\pi$
$230$	−5.95353e10	−1.40281
$231$	8.60602e10	1.98860
$232$	1.27513e10	0.288974
$233$	6.47083e10	1.43833	0.719165	−	0.694839i	$-0.244525\pi$
$233$	6.47083e10	1.43833	0.719165	+	0.694839i	$0.244525\pi$
$234$	2.07845e10	0.453178
$235$	2.02939e10	0.434071
$236$	−3.96420e8	−0.00831863
$237$	8.72962e10	1.79733
$238$	0	0
$239$	3.98151e10	0.789328	0.394664	−	0.918825i	$-0.370861\pi$
$239$	3.98151e10	0.789328	0.394664	+	0.918825i	$0.370861\pi$
$240$	−5.36128e10	−1.04308
$241$	6.98581e10	1.33395	0.666975	−	0.745080i	$-0.267589\pi$
$241$	6.98581e10	1.33395	0.666975	+	0.745080i	$0.267589\pi$
$242$	−2.03023e10	−0.380518
$243$	−3.34653e10	−0.615696
$244$	−2.45744e8	−0.00443842
$245$	6.05678e10	1.07397
$246$	5.07605e10	0.883727
$247$	7.29474e10	1.24702
$248$	9.56058e10	1.60491
$249$	1.21147e10	0.199717
$250$	6.51878e10	1.05545
$251$	9.47934e10	1.50746	0.753731	−	0.657183i	$-0.228252\pi$
$251$	9.47934e10	1.50746	0.753731	+	0.657183i	$0.228252\pi$
$252$	−3.54586e8	−0.00553884
$253$	1.17644e11	1.80521
$254$	2.97219e10	0.448049
$255$	0	0
$256$	−2.43124e9	−0.0353792
$257$	3.19715e10	0.457156	0.228578	−	0.973526i	$-0.426592\pi$
$257$	3.19715e10	0.457156	0.228578	+	0.973526i	$0.426592\pi$
$258$	7.71446e9	0.108397
$259$	1.66573e11	2.30015
$260$	1.14201e9	0.0154985
$261$	6.86898e9	0.0916242
$262$	−1.32635e11	−1.73902
$263$	−1.28301e11	−1.65360	−0.826798	−	0.562498i	$-0.809840\pi$
$263$	−1.28301e11	−1.65360	−0.826798	+	0.562498i	$0.809840\pi$
$264$	1.07206e11	1.35831
$265$	−4.94597e10	−0.616091
$266$	1.04268e11	1.27698
$267$	7.36094e10	0.886406
$268$	−7.79016e8	−0.00922444
$269$	3.10336e10	0.361366	0.180683	−	0.983541i	$-0.442169\pi$
$269$	3.10336e10	0.361366	0.180683	+	0.983541i	$0.442169\pi$
$270$	6.24161e10	0.714759
$271$	−1.15285e11	−1.29841	−0.649203	−	0.760615i	$-0.724897\pi$
$271$	−1.15285e11	−1.29841	−0.649203	+	0.760615i	$0.724897\pi$
$272$	0	0
$273$	−2.21861e11	−2.41740
$274$	9.17174e10	0.983047
$275$	−1.72883e10	−0.182287
$276$	−2.00464e9	−0.0207944
$277$	1.43535e11	1.46487	0.732436	−	0.680835i	$-0.238383\pi$
$277$	1.43535e11	1.46487	0.732436	+	0.680835i	$0.238383\pi$
$278$	−1.87312e11	−1.88089
$279$	5.15018e10	0.508866
$280$	1.40028e11	1.36146
$281$	9.65223e10	0.923526	0.461763	−	0.887003i	$-0.347217\pi$
$281$	9.65223e10	0.923526	0.461763	+	0.887003i	$0.347217\pi$
$282$	−5.72517e10	−0.539098
$283$	−1.85654e10	−0.172055	−0.0860273	−	0.996293i	$-0.527417\pi$
$283$	−1.85654e10	−0.172055	−0.0860273	+	0.996293i	$0.527417\pi$
$284$	9.46885e8	0.00863703
$285$	−1.02572e11	−0.920932
$286$	1.89071e11	1.67101
$287$	−1.31015e11	−1.13986
$288$	−8.78270e8	−0.00752249
$289$	0	0
$290$	−3.16214e10	−0.262537
$291$	−1.61960e11	−1.32400
$292$	−1.50052e9	−0.0120787
$293$	−6.88004e10	−0.545364	−0.272682	−	0.962104i	$-0.587911\pi$
$293$	−6.88004e10	−0.545364	−0.272682	+	0.962104i	$0.587911\pi$
$294$	−1.70869e11	−1.33383
$295$	8.43311e10	0.648319
$296$	2.07501e11	1.57111
$297$	−1.23337e11	−0.919791
$298$	−2.45842e11	−1.80586
$299$	−3.03284e11	−2.19447
$300$	2.94591e8	0.00209978
$301$	−1.99113e10	−0.139814
$302$	2.45032e11	1.69509
$303$	−1.27933e11	−0.871949
$304$	1.28355e11	0.861950
$305$	5.22775e10	0.345912
$306$	0	0
$307$	9.12146e10	0.586059	0.293030	−	0.956103i	$-0.405337\pi$
$307$	9.12146e10	0.586059	0.293030	+	0.956103i	$0.405337\pi$
$308$	−3.22557e9	−0.0204234
$309$	2.47116e11	1.54201
$310$	−2.37089e11	−1.45809
$311$	−2.25280e11	−1.36553	−0.682763	−	0.730640i	$-0.739222\pi$
$311$	−2.25280e11	−1.36553	−0.682763	+	0.730640i	$0.739222\pi$
$312$	−2.76374e11	−1.65121
$313$	−1.70381e11	−1.00340	−0.501699	−	0.865043i	$-0.667291\pi$
$313$	−1.70381e11	−1.00340	−0.501699	+	0.865043i	$0.667291\pi$
$314$	−8.49599e8	−0.00493209
$315$	7.54315e10	0.431674
$316$	−3.27190e9	−0.0184590
$317$	1.59870e11	0.889203	0.444602	−	0.895728i	$-0.353345\pi$
$317$	1.59870e11	0.889203	0.444602	+	0.895728i	$0.353345\pi$
$318$	1.39532e11	0.765160
$319$	6.24853e10	0.337847
$320$	1.74410e11	0.929814
$321$	−2.65918e11	−1.39790
$322$	−4.33501e11	−2.24719
$323$	0	0
$324$	2.84776e9	0.0143566
$325$	4.45689e10	0.221594
$326$	−9.30914e10	−0.456489
$327$	−1.35637e11	−0.656015
$328$	−1.63206e11	−0.778580
$329$	1.47769e11	0.695345
$330$	−2.65855e11	−1.23405
$331$	1.59564e11	0.730648	0.365324	−	0.930880i	$-0.380958\pi$
$331$	1.59564e11	0.730648	0.365324	+	0.930880i	$0.380958\pi$
$332$	−4.54062e8	−0.00205113
$333$	1.11778e11	0.498149
$334$	−2.92552e11	−1.28630
$335$	1.65721e11	0.718914
$336$	−3.90377e11	−1.67093
$337$	−1.20392e11	−0.508466	−0.254233	−	0.967143i	$-0.581823\pi$
$337$	−1.20392e11	−0.508466	−0.254233	+	0.967143i	$0.581823\pi$
$338$	−2.48888e11	−1.03724
$339$	−3.76226e11	−1.54721
$340$	0	0
$341$	4.68498e11	1.87634
$342$	6.99688e10	0.276559
$343$	6.35449e10	0.247889
$344$	−2.48036e10	−0.0954996
$345$	4.26451e11	1.62063
$346$	1.04157e11	0.390703
$347$	−1.84318e11	−0.682472	−0.341236	−	0.939978i	$-0.610845\pi$
$347$	−1.84318e11	−0.682472	−0.341236	+	0.939978i	$0.610845\pi$
$348$	−1.06474e9	−0.00389168
$349$	−3.67126e10	−0.132465	−0.0662325	−	0.997804i	$-0.521098\pi$
$349$	−3.67126e10	−0.132465	−0.0662325	+	0.997804i	$0.521098\pi$
$350$	6.37050e10	0.226917
$351$	3.17960e11	1.11812
$352$	−7.98938e9	−0.0277378
$353$	2.10064e11	0.720055	0.360027	−	0.932942i	$-0.382767\pi$
$353$	2.10064e11	0.720055	0.360027	+	0.932942i	$0.382767\pi$
$354$	−2.37909e11	−0.805185
$355$	−2.01432e11	−0.673134
$356$	−2.75891e9	−0.00910358
$357$	0	0
$358$	3.28150e10	0.105584
$359$	−4.88942e11	−1.55358	−0.776788	−	0.629762i	$-0.783152\pi$
$359$	−4.88942e11	−1.55358	−0.776788	+	0.629762i	$0.783152\pi$
$360$	9.39656e10	0.294854
$361$	−7.71182e10	−0.238987
$362$	−1.74605e11	−0.534402
$363$	1.45425e11	0.439601
$364$	8.31544e9	0.0248273
$365$	3.19209e11	0.941362
$366$	−1.47482e11	−0.429608
$367$	−2.50484e11	−0.720748	−0.360374	−	0.932808i	$-0.617351\pi$
$367$	−2.50484e11	−0.720748	−0.360374	+	0.932808i	$0.617351\pi$
$368$	−5.33645e11	−1.51683
$369$	−8.79171e10	−0.246862
$370$	−5.14573e11	−1.42738
$371$	−3.60137e11	−0.986926
$372$	−7.98314e9	−0.0216138
$373$	3.12819e11	0.836766	0.418383	−	0.908271i	$-0.362597\pi$
$373$	3.12819e11	0.836766	0.418383	+	0.908271i	$0.362597\pi$
$374$	0	0
$375$	−4.66939e11	−1.21933
$376$	1.84076e11	0.474955
$377$	−1.61086e11	−0.410696
$378$	4.54478e11	1.14499
$379$	−1.31869e11	−0.328298	−0.164149	−	0.986436i	$-0.552488\pi$
$379$	−1.31869e11	−0.328298	−0.164149	+	0.986436i	$0.552488\pi$
$380$	3.84444e9	0.00945817
$381$	−2.12898e11	−0.517618
$382$	8.12215e10	0.195158
$383$	4.82378e11	1.14549	0.572747	−	0.819732i	$-0.305878\pi$
$383$	4.82378e11	1.14549	0.572747	+	0.819732i	$0.305878\pi$
$384$	−4.80490e11	−1.12770
$385$	6.86180e11	1.59171
$386$	−2.46200e11	−0.564475
$387$	−1.33614e10	−0.0302798
$388$	6.07032e9	0.0135978
$389$	−5.41960e10	−0.120004	−0.0600018	−	0.998198i	$-0.519111\pi$
$389$	−5.41960e10	−0.120004	−0.0600018	+	0.998198i	$0.519111\pi$
$390$	6.85367e11	1.50014
$391$	0	0
$392$	5.49381e11	1.17513
$393$	9.50066e11	2.00903
$394$	−8.59749e10	−0.179737
$395$	6.96035e11	1.43861
$396$	−2.16451e9	−0.00442315
$397$	−6.99376e11	−1.41304	−0.706519	−	0.707694i	$-0.749735\pi$
$397$	−6.99376e11	−1.41304	−0.706519	+	0.707694i	$0.749735\pi$
$398$	4.44550e11	0.888068
$399$	−7.46871e11	−1.47526
$400$	7.84216e10	0.153167
$401$	−2.39362e10	−0.0462280	−0.0231140	−	0.999733i	$-0.507358\pi$
$401$	−2.39362e10	−0.0462280	−0.0231140	+	0.999733i	$0.507358\pi$
$402$	−4.67521e11	−0.892861
$403$	−1.20778e12	−2.28094
$404$	4.79498e9	0.00895510
$405$	−6.05809e11	−1.11889
$406$	−2.30249e11	−0.420562
$407$	1.01682e12	1.83683
$408$	0	0
$409$	3.57952e11	0.632514	0.316257	−	0.948674i	$-0.397574\pi$
$409$	3.57952e11	0.632514	0.316257	+	0.948674i	$0.397574\pi$
$410$	4.04727e11	0.707350
$411$	−6.56971e11	−1.13569
$412$	−9.26201e9	−0.0158368
$413$	6.14050e11	1.03855
$414$	−2.90900e11	−0.486679
$415$	9.65934e10	0.159857
$416$	2.05964e10	0.0337188
$417$	1.34171e12	2.17294
$418$	6.36487e11	1.01976
$419$	−1.71160e11	−0.271293	−0.135646	−	0.990757i	$-0.543311\pi$
$419$	−1.71160e11	−0.271293	−0.135646	+	0.990757i	$0.543311\pi$
$420$	−1.16924e10	−0.0183351
$421$	1.13078e11	0.175432	0.0877159	−	0.996146i	$-0.472043\pi$
$421$	1.13078e11	0.175432	0.0877159	+	0.996146i	$0.472043\pi$
$422$	−1.12150e11	−0.172144
$423$	9.91598e10	0.150593
$424$	−4.48625e11	−0.674119
$425$	0	0
$426$	5.68266e11	0.836004
$427$	3.80655e11	0.554122
$428$	9.96672e9	0.0143567
$429$	−1.35432e12	−1.93047
$430$	6.15094e10	0.0867627
$431$	1.20420e12	1.68093	0.840466	−	0.541864i	$-0.182281\pi$
$431$	1.20420e12	1.68093	0.840466	+	0.541864i	$0.182281\pi$
$432$	5.59468e11	0.772856
$433$	2.53234e11	0.346200	0.173100	−	0.984904i	$-0.444622\pi$
$433$	2.53234e11	0.346200	0.173100	+	0.984904i	$0.444622\pi$
$434$	−1.72634e12	−2.33573
$435$	2.26504e11	0.303301
$436$	5.08373e9	0.00673741
$437$	−1.02097e12	−1.33921
$438$	−9.00528e11	−1.16913
$439$	6.92143e11	0.889417	0.444709	−	0.895675i	$-0.353307\pi$
$439$	6.92143e11	0.889417	0.444709	+	0.895675i	$0.353307\pi$
$440$	8.54779e11	1.08722
$441$	2.95945e11	0.372595
$442$	0	0
$443$	4.01866e11	0.495752	0.247876	−	0.968792i	$-0.420267\pi$
$443$	4.01866e11	0.495752	0.247876	+	0.968792i	$0.420267\pi$
$444$	−1.73265e10	−0.0211586
$445$	5.86907e11	0.709495
$446$	1.56636e12	1.87449
$447$	1.76097e12	2.08625
$448$	1.26995e12	1.48949
$449$	−1.26065e11	−0.146381	−0.0731907	−	0.997318i	$-0.523318\pi$
$449$	−1.26065e11	−0.146381	−0.0731907	+	0.997318i	$0.523318\pi$
$450$	4.27491e10	0.0491440
$451$	−7.99758e11	−0.910257
$452$	1.41011e10	0.0158902
$453$	−1.75516e12	−1.95828
$454$	−6.48009e11	−0.715863
$455$	−1.76896e12	−1.93493
$456$	−9.30382e11	−1.00767
$457$	1.28002e12	1.37276	0.686380	−	0.727243i	$-0.259199\pi$
$457$	1.28002e12	1.37276	0.686380	+	0.727243i	$0.259199\pi$
$458$	1.71194e11	0.181800
$459$	0	0
$460$	−1.59835e10	−0.0166442
$461$	−2.46980e11	−0.254687	−0.127344	−	0.991859i	$-0.540645\pi$
$461$	−2.46980e11	−0.254687	−0.127344	+	0.991859i	$0.540645\pi$
$462$	−1.93580e12	−1.97684
$463$	−1.06166e12	−1.07367	−0.536833	−	0.843688i	$-0.680380\pi$
$463$	−1.06166e12	−1.07367	−0.536833	+	0.843688i	$0.680380\pi$
$464$	−2.83439e11	−0.283876
$465$	1.69827e12	1.68449
$466$	−1.45552e12	−1.42982
$467$	2.02752e11	0.197260	0.0986302	−	0.995124i	$-0.468554\pi$
$467$	2.02752e11	0.197260	0.0986302	+	0.995124i	$0.468554\pi$
$468$	5.58006e9	0.00537690
$469$	1.20669e12	1.15164
$470$	−4.56483e11	−0.431503
$471$	6.08567e9	0.00569790
$472$	7.64927e11	0.709383
$473$	−1.21545e11	−0.111651
$474$	−1.96360e12	−1.78670
$475$	1.50036e11	0.135231
$476$	0	0
$477$	−2.41669e11	−0.213741
$478$	−8.95585e11	−0.784659
$479$	−1.25765e12	−1.09157	−0.545783	−	0.837927i	$-0.683768\pi$
$479$	−1.25765e12	−1.09157	−0.545783	+	0.837927i	$0.683768\pi$
$480$	−2.89609e10	−0.0249015
$481$	−2.62133e12	−2.23290
$482$	−1.57136e12	−1.32606
$483$	3.10517e12	2.59611
$484$	−5.45058e9	−0.00451480
$485$	−1.29135e12	−1.05976
$486$	7.52754e11	0.612054
$487$	3.15297e11	0.254003	0.127002	−	0.991903i	$-0.459465\pi$
$487$	3.15297e11	0.254003	0.127002	+	0.991903i	$0.459465\pi$
$488$	4.74184e11	0.378493
$489$	6.66813e11	0.527369
$490$	−1.36239e12	−1.06762
$491$	−1.29498e12	−1.00553	−0.502765	−	0.864423i	$-0.667684\pi$
$491$	−1.29498e12	−1.00553	−0.502765	+	0.864423i	$0.667684\pi$
$492$	1.36278e10	0.0104853
$493$	0	0
$494$	−1.64085e12	−1.23964
$495$	4.60460e11	0.344721
$496$	−2.12515e12	−1.57660
$497$	−1.46671e12	−1.07830
$498$	−2.72502e11	−0.198535
$499$	2.19676e12	1.58610	0.793050	−	0.609157i	$-0.208492\pi$
$499$	2.19676e12	1.58610	0.793050	+	0.609157i	$0.208492\pi$
$500$	1.75011e10	0.0125227
$501$	2.09554e12	1.48603
$502$	−2.13224e12	−1.49855
$503$	−8.02912e10	−0.0559258	−0.0279629	−	0.999609i	$-0.508902\pi$
$503$	−8.02912e10	−0.0559258	−0.0279629	+	0.999609i	$0.508902\pi$
$504$	6.84203e11	0.472332
$505$	−1.02004e12	−0.697923
$506$	−2.64624e12	−1.79453
$507$	1.78278e12	1.19829
$508$	7.97949e9	0.00531605
$509$	−2.24252e12	−1.48083	−0.740417	−	0.672148i	$-0.765372\pi$
$509$	−2.24252e12	−1.48083	−0.740417	+	0.672148i	$0.765372\pi$
$510$	0	0
$511$	2.32429e12	1.50798
$512$	1.58155e12	1.01711
$513$	1.07038e12	0.682352
$514$	−7.19154e11	−0.454452
$515$	1.97032e12	1.23425
$516$	2.07111e9	0.00128612
$517$	9.02030e11	0.555282
$518$	−3.74682e12	−2.28654
$519$	−7.46078e11	−0.451368
$520$	−2.20360e12	−1.32165
$521$	−4.21783e11	−0.250795	−0.125398	−	0.992107i	$-0.540021\pi$
$521$	−4.21783e11	−0.250795	−0.125398	+	0.992107i	$0.540021\pi$
$522$	−1.54508e11	−0.0910823
$523$	6.85779e11	0.400799	0.200399	−	0.979714i	$-0.435776\pi$
$523$	6.85779e11	0.400799	0.200399	+	0.979714i	$0.435776\pi$
$524$	−3.56088e10	−0.0206332
$525$	−4.56318e11	−0.262151
$526$	2.88595e12	1.64382
$527$	0	0
$528$	−2.38299e12	−1.33435
$529$	2.44361e12	1.35669
$530$	1.11253e12	0.612447
$531$	4.12057e11	0.224922
$532$	2.79930e10	0.0151512
$533$	2.06176e12	1.10653
$534$	−1.65574e12	−0.881163
$535$	−2.12024e12	−1.11890
$536$	1.50318e12	0.786627
$537$	−2.35054e11	−0.121978
$538$	−6.98057e11	−0.359228
$539$	2.69213e12	1.37387
$540$	1.67570e10	0.00848054
$541$	1.41665e12	0.711011	0.355505	−	0.934674i	$-0.384309\pi$
$541$	1.41665e12	0.711011	0.355505	+	0.934674i	$0.384309\pi$
$542$	2.59317e12	1.29073
$543$	1.25069e12	0.617379
$544$	0	0
$545$	−1.08147e12	−0.525085
$546$	4.99045e12	2.40310
$547$	−1.74223e12	−0.832076	−0.416038	−	0.909347i	$-0.636582\pi$
$547$	−1.74223e12	−0.832076	−0.416038	+	0.909347i	$0.636582\pi$
$548$	2.46235e10	0.0116637
$549$	2.55438e11	0.120008
$550$	3.88877e11	0.181209
$551$	−5.42277e11	−0.250633
$552$	3.86813e12	1.77327
$553$	5.06813e12	2.30454
$554$	−3.22862e12	−1.45621
$555$	3.68588e12	1.64901
$556$	−5.02879e10	−0.0223166
$557$	9.15412e11	0.402966	0.201483	−	0.979492i	$-0.435424\pi$
$557$	9.15412e11	0.402966	0.201483	+	0.979492i	$0.435424\pi$
$558$	−1.15846e12	−0.505856
$559$	3.13340e11	0.135726
$560$	−3.11258e12	−1.33744
$561$	0	0
$562$	−2.17113e12	−0.918064
$563$	−3.05435e12	−1.28124	−0.640620	−	0.767858i	$-0.721323\pi$
$563$	−3.05435e12	−1.28124	−0.640620	+	0.767858i	$0.721323\pi$
$564$	−1.53705e10	−0.00639634
$565$	−2.99975e12	−1.23842
$566$	4.17603e11	0.171037
$567$	−4.41115e12	−1.79237
$568$	−1.82709e12	−0.736535
$569$	−2.05865e11	−0.0823335	−0.0411668	−	0.999152i	$-0.513107\pi$
$569$	−2.05865e11	−0.0823335	−0.0411668	+	0.999152i	$0.513107\pi$
$570$	2.30721e12	0.915485
$571$	−1.37439e12	−0.541062	−0.270531	−	0.962711i	$-0.587199\pi$
$571$	−1.37439e12	−0.541062	−0.270531	+	0.962711i	$0.587199\pi$
$572$	5.07603e10	0.0198263
$573$	−5.81789e11	−0.225460
$574$	2.94699e12	1.13312
$575$	−6.23787e11	−0.237975
$576$	8.52199e11	0.322582
$577$	−1.39056e12	−0.522275	−0.261138	−	0.965302i	$-0.584098\pi$
$577$	−1.39056e12	−0.522275	−0.261138	+	0.965302i	$0.584098\pi$
$578$	0	0
$579$	1.76353e12	0.652121
$580$	−8.48946e9	−0.00311497
$581$	7.03337e11	0.256077
$582$	3.64306e12	1.31617
$583$	−2.19840e12	−0.788130
$584$	2.89539e12	1.03003
$585$	−1.18705e12	−0.419053
$586$	1.54757e12	0.542138
$587$	−2.02089e12	−0.702539	−0.351269	−	0.936274i	$-0.614250\pi$
$587$	−2.02089e12	−0.702539	−0.351269	+	0.936274i	$0.614250\pi$
$588$	−4.58736e10	−0.0158258
$589$	−4.06584e12	−1.39198
$590$	−1.89691e12	−0.644484
$591$	6.15837e11	0.207645
$592$	−4.61238e12	−1.54340
$593$	−2.56146e12	−0.850630	−0.425315	−	0.905045i	$-0.639837\pi$
$593$	−2.56146e12	−0.850630	−0.425315	+	0.905045i	$0.639837\pi$
$594$	2.77429e12	0.914351
$595$	0	0
$596$	−6.60017e10	−0.0214263
$597$	−3.18431e12	−1.02596
$598$	6.82194e12	2.18149
$599$	−1.66546e12	−0.528583	−0.264291	−	0.964443i	$-0.585138\pi$
$599$	−1.66546e12	−0.528583	−0.264291	+	0.964443i	$0.585138\pi$
$600$	−5.68439e11	−0.179062
$601$	−2.30323e12	−0.720114	−0.360057	−	0.932930i	$-0.617243\pi$
$601$	−2.30323e12	−0.720114	−0.360057	+	0.932930i	$0.617243\pi$
$602$	4.47875e11	0.138987
$603$	8.09745e11	0.249414
$604$	6.57842e10	0.0201120
$605$	1.15951e12	0.351865
$606$	2.87767e12	0.866791
$607$	5.08694e12	1.52092	0.760461	−	0.649383i	$-0.224973\pi$
$607$	5.08694e12	1.52092	0.760461	+	0.649383i	$0.224973\pi$
$608$	6.93356e10	0.0205774
$609$	1.64927e12	0.485863
$610$	−1.17591e12	−0.343866
$611$	−2.32541e12	−0.675016
$612$	0	0
$613$	5.87867e12	1.68154	0.840770	−	0.541393i	$-0.182103\pi$
$613$	5.87867e12	1.68154	0.840770	+	0.541393i	$0.182103\pi$
$614$	−2.05174e12	−0.582593
$615$	−2.89906e12	−0.817182
$616$	6.22401e12	1.74163
$617$	−2.77401e12	−0.770592	−0.385296	−	0.922793i	$-0.625901\pi$
$617$	−2.77401e12	−0.770592	−0.385296	+	0.922793i	$0.625901\pi$
$618$	−5.55853e12	−1.53289
$619$	1.51857e12	0.415744	0.207872	−	0.978156i	$-0.433346\pi$
$619$	1.51857e12	0.415744	0.207872	+	0.978156i	$0.433346\pi$
$620$	−6.36516e10	−0.0173000
$621$	−4.45016e12	−1.20078
$622$	5.06734e12	1.35745
$623$	4.27351e12	1.13655
$624$	6.14330e12	1.62208
$625$	−3.13169e12	−0.820953
$626$	3.83249e12	0.997462
$627$	−4.55915e12	−1.17810
$628$	−2.28093e8	−5.85186e−5 0
$629$	0	0
$630$	−1.69672e12	−0.429120
$631$	−6.49509e12	−1.63100	−0.815499	−	0.578759i	$-0.803537\pi$
$631$	−6.49509e12	−1.63100	−0.815499	+	0.578759i	$0.803537\pi$
$632$	6.31340e12	1.57411
$633$	8.03326e11	0.198873
$634$	−3.59605e12	−0.883944
$635$	−1.69749e12	−0.414310
$636$	3.74604e10	0.00907853
$637$	−6.94025e12	−1.67012
$638$	−1.40552e12	−0.335848
$639$	−9.84235e11	−0.233531
$640$	−3.83107e12	−0.902632
$641$	−4.72982e12	−1.10658	−0.553291	−	0.832988i	$-0.686628\pi$
$641$	−4.72982e12	−1.10658	−0.553291	+	0.832988i	$0.686628\pi$
$642$	5.98145e12	1.38963
$643$	9.58308e11	0.221083	0.110542	−	0.993872i	$-0.464741\pi$
$643$	9.58308e11	0.221083	0.110542	+	0.993872i	$0.464741\pi$
$644$	−1.16383e11	−0.0266626
$645$	−4.40591e11	−0.100234
$646$	0	0
$647$	1.17064e12	0.262635	0.131317	−	0.991340i	$-0.458079\pi$
$647$	1.17064e12	0.262635	0.131317	+	0.991340i	$0.458079\pi$
$648$	−5.49500e12	−1.22428
$649$	3.74837e12	0.829357
$650$	−1.00251e12	−0.220283
$651$	1.23658e13	2.69841
$652$	−2.49924e10	−0.00541619
$653$	−5.02539e12	−1.08158	−0.540792	−	0.841156i	$-0.681875\pi$
$653$	−5.02539e12	−1.08158	−0.540792	+	0.841156i	$0.681875\pi$
$654$	3.05096e12	0.652134
$655$	7.57512e12	1.60807
$656$	3.62778e12	0.764844
$657$	1.55971e12	0.326588
$658$	−3.32384e12	−0.691232
$659$	−3.15795e12	−0.652261	−0.326130	−	0.945325i	$-0.605745\pi$
$659$	−3.15795e12	−0.652261	−0.326130	+	0.945325i	$0.605745\pi$
$660$	−7.13745e10	−0.0146418
$661$	−1.46675e12	−0.298846	−0.149423	−	0.988773i	$-0.547742\pi$
$661$	−1.46675e12	−0.298846	−0.149423	+	0.988773i	$0.547742\pi$
$662$	−3.58916e12	−0.726326
$663$	0	0
$664$	8.76152e11	0.174913
$665$	−5.95499e12	−1.18082
$666$	−2.51430e12	−0.495202
$667$	2.25455e12	0.441057
$668$	−7.85418e10	−0.0152618
$669$	−1.12198e13	−2.16555
$670$	−3.72767e12	−0.714661
$671$	2.32365e12	0.442505
$672$	−2.10876e11	−0.0398902
$673$	7.74648e12	1.45558	0.727791	−	0.685799i	$-0.240547\pi$
$673$	7.74648e12	1.45558	0.727791	+	0.685799i	$0.240547\pi$
$674$	2.70804e12	0.505459
$675$	6.53971e11	0.121253
$676$	−6.68193e10	−0.0123067
$677$	7.62527e12	1.39510	0.697551	−	0.716535i	$-0.254273\pi$
$677$	7.62527e12	1.39510	0.697551	+	0.716535i	$0.254273\pi$
$678$	8.46268e12	1.53806
$679$	−9.40285e12	−1.69764
$680$	0	0
$681$	4.64169e12	0.827016
$682$	−1.05382e13	−1.86525
$683$	6.54245e12	1.15040	0.575198	−	0.818014i	$-0.304925\pi$
$683$	6.54245e12	1.15040	0.575198	+	0.818014i	$0.304925\pi$
$684$	1.87846e10	0.00328134
$685$	−5.23820e12	−0.909023
$686$	−1.42935e12	−0.246423
$687$	−1.22626e12	−0.210028
$688$	5.51340e11	0.0938148
$689$	5.66742e12	0.958073
$690$	−9.59240e12	−1.61104
$691$	−4.12042e12	−0.687528	−0.343764	−	0.939056i	$-0.611702\pi$
$691$	−4.12042e12	−0.687528	−0.343764	+	0.939056i	$0.611702\pi$
$692$	2.79633e10	0.00463565
$693$	3.35280e12	0.552215
$694$	4.14597e12	0.678435
$695$	1.06978e13	1.73926
$696$	2.05451e12	0.331869
$697$	0	0
$698$	8.25798e11	0.131681
$699$	1.04259e13	1.65183
$700$	1.71030e10	0.00269234
$701$	−8.29792e12	−1.29789	−0.648945	−	0.760835i	$-0.724789\pi$
$701$	−8.29792e12	−1.29789	−0.648945	+	0.760835i	$0.724789\pi$
$702$	−7.15205e12	−1.11151
$703$	−8.82443e12	−1.36266
$704$	7.75222e12	1.18946
$705$	3.26978e12	0.498503
$706$	−4.72509e12	−0.715796
$707$	−7.42736e12	−1.11801
$708$	−6.38718e10	−0.00955343
$709$	9.99767e12	1.48590	0.742952	−	0.669345i	$-0.233425\pi$
$709$	9.99767e12	1.48590	0.742952	+	0.669345i	$0.233425\pi$
$710$	4.53093e12	0.669152
$711$	3.40096e12	0.499100
$712$	5.32355e12	0.776321
$713$	1.69040e13	2.44956
$714$	0	0
$715$	−1.07983e13	−1.54518
$716$	8.80989e9	0.00125274
$717$	6.41507e12	0.906494
$718$	1.09981e13	1.54439
$719$	4.37408e12	0.610389	0.305194	−	0.952290i	$-0.401279\pi$
$719$	4.37408e12	0.610389	0.305194	+	0.952290i	$0.401279\pi$
$720$	−2.08869e12	−0.289653
$721$	1.43467e13	1.97717
$722$	1.73467e12	0.237574
$723$	1.12556e13	1.53196
$724$	−4.68765e10	−0.00634062
$725$	−3.31317e11	−0.0445371
$726$	−3.27113e12	−0.437001
$727$	3.97360e12	0.527568	0.263784	−	0.964582i	$-0.415029\pi$
$727$	3.97360e12	0.527568	0.263784	+	0.964582i	$0.415029\pi$
$728$	−1.60453e13	−2.11718
$729$	3.88995e12	0.510118
$730$	−7.18014e12	−0.935794
$731$	0	0
$732$	−3.95946e10	−0.00509726
$733$	7.96904e12	1.01962	0.509810	−	0.860287i	$-0.329716\pi$
$733$	7.96904e12	1.01962	0.509810	+	0.860287i	$0.329716\pi$
$734$	5.63429e12	0.716485
$735$	9.75876e12	1.23339
$736$	−2.88268e11	−0.0362114
$737$	7.36603e12	0.919665
$738$	1.97757e12	0.245402
$739$	−3.39911e12	−0.419243	−0.209621	−	0.977783i	$-0.567223\pi$
$739$	−3.39911e12	−0.419243	−0.209621	+	0.977783i	$0.567223\pi$
$740$	−1.38148e11	−0.0169357
$741$	1.17534e13	1.43213
$742$	8.10076e12	0.981089
$743$	7.05502e12	0.849276	0.424638	−	0.905363i	$-0.360401\pi$
$743$	7.05502e12	0.849276	0.424638	+	0.905363i	$0.360401\pi$
$744$	1.54041e13	1.84314
$745$	1.40406e13	1.66987
$746$	−7.03643e12	−0.831816
$747$	4.71973e11	0.0554593
$748$	0	0
$749$	−1.54383e13	−1.79239
$750$	1.05031e13	1.21211
$751$	−1.65358e13	−1.89690	−0.948452	−	0.316920i	$-0.897351\pi$
$751$	−1.65358e13	−1.89690	−0.948452	+	0.316920i	$0.897351\pi$
$752$	−4.09169e12	−0.466576
$753$	1.52732e13	1.73123
$754$	3.62339e12	0.408267
$755$	−1.39944e13	−1.56745
$756$	1.22015e11	0.0135851
$757$	−5.91466e11	−0.0654634	−0.0327317	−	0.999464i	$-0.510421\pi$
$757$	−5.91466e11	−0.0654634	−0.0327317	+	0.999464i	$0.510421\pi$
$758$	2.96622e12	0.326356
$759$	1.89550e13	2.07317
$760$	−7.41818e12	−0.806559
$761$	−4.42291e12	−0.478054	−0.239027	−	0.971013i	$-0.576829\pi$
$761$	−4.42291e12	−0.478054	−0.239027	+	0.971013i	$0.576829\pi$
$762$	4.78884e12	0.514556
$763$	−7.87463e12	−0.841143
$764$	2.18057e10	0.00231552
$765$	0	0
$766$	−1.08504e13	−1.13872
$767$	−9.66321e12	−1.00819
$768$	−3.91724e11	−0.0406308
$769$	−3.54128e12	−0.365167	−0.182583	−	0.983190i	$-0.558446\pi$
$769$	−3.54128e12	−0.365167	−0.182583	+	0.983190i	$0.558446\pi$
$770$	−1.54346e13	−1.58230
$771$	5.15130e12	0.525015
$772$	−6.60976e10	−0.00669743
$773$	−1.02567e13	−1.03323	−0.516617	−	0.856217i	$-0.672809\pi$
$773$	−1.02567e13	−1.03323	−0.516617	+	0.856217i	$0.672809\pi$
$774$	3.00546e11	0.0301007
$775$	−2.48412e12	−0.247352
$776$	−1.17132e13	−1.15957
$777$	2.68385e13	2.64158
$778$	1.21906e12	0.119294
$779$	6.94067e12	0.675279
$780$	1.84002e11	0.0177990
$781$	−8.95332e12	−0.861101
$782$	0	0
$783$	−2.36365e12	−0.224727
$784$	−1.22118e13	−1.15440
$785$	4.85227e10	0.00456070
$786$	−2.13704e13	−1.99715
$787$	−9.34742e11	−0.0868571	−0.0434285	−	0.999057i	$-0.513828\pi$
$787$	−9.34742e11	−0.0868571	−0.0434285	+	0.999057i	$0.513828\pi$
$788$	−2.30818e10	−0.00213256
$789$	−2.06721e13	−1.89905
$790$	−1.56563e13	−1.43011
$791$	−2.18424e13	−1.98384
$792$	4.17661e12	0.377190
$793$	−5.99030e12	−0.537922
$794$	1.57315e13	1.40468
$795$	−7.96901e12	−0.707542
$796$	1.19349e11	0.0105368
$797$	1.26917e13	1.11418	0.557091	−	0.830452i	$-0.311918\pi$
$797$	1.26917e13	1.11418	0.557091	+	0.830452i	$0.311918\pi$
$798$	1.67998e13	1.46653
$799$	0	0
$800$	4.23622e10	0.00365657
$801$	2.86773e12	0.246146
$802$	5.38411e11	0.0459546
$803$	1.41883e13	1.20423
$804$	−1.25516e11	−0.0105937
$805$	2.47583e13	2.07797
$806$	2.71672e13	2.26745
$807$	5.00018e12	0.415006
$808$	−9.25232e12	−0.763659
$809$	6.05218e11	0.0496757	0.0248378	−	0.999691i	$-0.492093\pi$
$809$	6.05218e11	0.0496757	0.0248378	+	0.999691i	$0.492093\pi$
$810$	1.36268e13	1.11227
$811$	−2.19232e13	−1.77955	−0.889774	−	0.456402i	$-0.849138\pi$
$811$	−2.19232e13	−1.77955	−0.889774	+	0.456402i	$0.849138\pi$
$812$	−6.18153e10	−0.00498992
$813$	−1.85749e13	−1.49114
$814$	−2.28719e13	−1.82596
$815$	5.31668e12	0.422115
$816$	0	0
$817$	1.05483e12	0.0828288
$818$	−8.05163e12	−0.628773
$819$	−8.64344e12	−0.671288
$820$	1.08658e11	0.00839263
$821$	−3.11270e12	−0.239107	−0.119554	−	0.992828i	$-0.538146\pi$
$821$	−3.11270e12	−0.239107	−0.119554	+	0.992828i	$0.538146\pi$
$822$	1.47776e13	1.12897
$823$	−2.30422e13	−1.75075	−0.875375	−	0.483444i	$-0.839386\pi$
$823$	−2.30422e13	−1.75075	−0.875375	+	0.483444i	$0.839386\pi$
$824$	1.78718e13	1.35051
$825$	−2.78552e12	−0.209346
$826$	−1.38122e13	−1.03241
$827$	−1.32673e13	−0.986297	−0.493148	−	0.869945i	$-0.664154\pi$
$827$	−1.32673e13	−0.986297	−0.493148	+	0.869945i	$0.664154\pi$
$828$	−7.80985e10	−0.00577439
$829$	7.58786e12	0.557987	0.278994	−	0.960293i	$-0.409999\pi$
$829$	7.58786e12	0.557987	0.278994	+	0.960293i	$0.409999\pi$
$830$	−2.17273e12	−0.158911
$831$	2.31266e13	1.68232
$832$	−1.99850e13	−1.44594
$833$	0	0
$834$	−3.01799e13	−2.16009
$835$	1.67083e13	1.18944
$836$	1.70879e11	0.0120993
$837$	−1.77220e13	−1.24810
$838$	3.84999e12	0.269688
$839$	2.06984e13	1.44214	0.721070	−	0.692862i	$-0.243651\pi$
$839$	2.06984e13	1.44214	0.721070	+	0.692862i	$0.243651\pi$
$840$	2.25615e13	1.56355
$841$	−1.33097e13	−0.917456
$842$	−2.54353e12	−0.174394
$843$	1.55518e13	1.06061
$844$	−3.01090e10	−0.00204247
$845$	1.42146e13	0.959133
$846$	−2.23046e12	−0.149702
$847$	8.44289e12	0.563658
$848$	9.97214e12	0.662227
$849$	−2.99129e12	−0.197594
$850$	0	0
$851$	3.66882e13	2.39797
$852$	1.52563e11	0.00991909
$853$	−7.03835e12	−0.455198	−0.227599	−	0.973755i	$-0.573087\pi$
$853$	−7.03835e12	−0.455198	−0.227599	+	0.973755i	$0.573087\pi$
$854$	−8.56228e12	−0.550845
$855$	−3.99609e12	−0.255733
$856$	−1.92316e13	−1.22429
$857$	1.87674e13	1.18848	0.594239	−	0.804289i	$-0.297453\pi$
$857$	1.87674e13	1.18848	0.594239	+	0.804289i	$0.297453\pi$
$858$	3.04634e13	1.91905
$859$	−4.63544e12	−0.290484	−0.145242	−	0.989396i	$-0.546396\pi$
$859$	−4.63544e12	−0.290484	−0.145242	+	0.989396i	$0.546396\pi$
$860$	1.65135e10	0.00102943
$861$	−2.11092e13	−1.30906
$862$	−2.70867e13	−1.67099
$863$	2.59525e13	1.59269	0.796343	−	0.604845i	$-0.206765\pi$
$863$	2.59525e13	1.59269	0.796343	+	0.604845i	$0.206765\pi$
$864$	3.02217e11	0.0184504
$865$	−5.94867e12	−0.361283
$866$	−5.69614e12	−0.344152
$867$	0	0
$868$	−4.63474e11	−0.0277132
$869$	3.09376e13	1.84034
$870$	−5.09489e12	−0.301507
$871$	−1.89894e13	−1.11797
$872$	−9.80948e12	−0.574542
$873$	−6.30977e12	−0.367662
$874$	2.29653e13	1.33128
$875$	−2.71089e13	−1.56342
$876$	−2.41766e11	−0.0138716
$877$	1.01903e13	0.581688	0.290844	−	0.956771i	$-0.406064\pi$
$877$	1.01903e13	0.581688	0.290844	+	0.956771i	$0.406064\pi$
$878$	−1.55688e13	−0.884157
$879$	−1.10852e13	−0.626317
$880$	−1.90002e13	−1.06804
$881$	2.42334e12	0.135526	0.0677630	−	0.997701i	$-0.478414\pi$
$881$	2.42334e12	0.135526	0.0677630	+	0.997701i	$0.478414\pi$
$882$	−6.65687e12	−0.370392
$883$	−7.32457e12	−0.405470	−0.202735	−	0.979234i	$-0.564983\pi$
$883$	−7.32457e12	−0.405470	−0.202735	+	0.979234i	$0.564983\pi$
$884$	0	0
$885$	1.35875e13	0.744554
$886$	−9.03941e12	−0.492820
$887$	8.53993e12	0.463232	0.231616	−	0.972807i	$-0.425599\pi$
$887$	8.53993e12	0.463232	0.231616	+	0.972807i	$0.425599\pi$
$888$	3.34329e13	1.80433
$889$	−1.23601e13	−0.663690
$890$	−1.32016e13	−0.705298
$891$	−2.69272e13	−1.43133
$892$	4.20523e11	0.0222407
$893$	−7.82824e12	−0.411939
$894$	−3.96104e13	−2.07391
$895$	−1.87414e12	−0.0976335
$896$	−2.78957e13	−1.44594
$897$	−4.88655e13	−2.52021
$898$	2.83565e12	0.145516
$899$	8.97836e12	0.458436
$900$	1.14769e10	0.000583088 0
$901$	0	0
$902$	1.79894e13	0.904873
$903$	−3.20813e12	−0.160567
$904$	−2.72093e13	−1.35506
$905$	9.97211e12	0.494161
$906$	3.94799e13	1.94670
$907$	−7.40422e11	−0.0363284	−0.0181642	−	0.999835i	$-0.505782\pi$
$907$	−7.40422e11	−0.0363284	−0.0181642	+	0.999835i	$0.505782\pi$
$908$	−1.73972e11	−0.00849363
$909$	−4.98412e12	−0.242131
$910$	3.97901e13	1.92349
$911$	3.49415e12	0.168077	0.0840385	−	0.996463i	$-0.473218\pi$
$911$	3.49415e12	0.168077	0.0840385	+	0.996463i	$0.473218\pi$
$912$	2.06807e13	0.989896
$913$	4.29341e12	0.204495
$914$	−2.87923e13	−1.36464
$915$	8.42303e12	0.397259
$916$	4.59607e10	0.00215704
$917$	5.51577e13	2.57599
$918$	0	0
$919$	−7.01277e11	−0.0324317	−0.0162158	−	0.999869i	$-0.505162\pi$
$919$	−7.01277e11	−0.0324317	−0.0162158	+	0.999869i	$0.505162\pi$
$920$	3.08416e13	1.41936
$921$	1.46966e13	0.673053
$922$	5.55546e12	0.253181
$923$	2.30814e13	1.04678
$924$	−5.19708e11	−0.0234550
$925$	−5.39149e12	−0.242143
$926$	2.38804e13	1.06732
$927$	9.62736e12	0.428202
$928$	−1.53110e11	−0.00677700
$929$	1.21293e13	0.534276	0.267138	−	0.963658i	$-0.413922\pi$
$929$	1.21293e13	0.534276	0.267138	+	0.963658i	$0.413922\pi$
$930$	−3.82001e13	−1.67452
$931$	−2.33636e13	−1.01922
$932$	−3.90766e11	−0.0169647
$933$	−3.62974e13	−1.56822
$934$	−4.56063e12	−0.196094
$935$	0	0
$936$	−1.07672e13	−0.458523
$937$	−2.23656e13	−0.947879	−0.473939	−	0.880558i	$-0.657168\pi$
$937$	−2.23656e13	−0.947879	−0.473939	+	0.880558i	$0.657168\pi$
$938$	−2.71427e13	−1.14483
$939$	−2.74521e13	−1.15234
$940$	−1.22553e11	−0.00511974
$941$	−3.98663e13	−1.65750	−0.828748	−	0.559621i	$-0.810947\pi$
$941$	−3.98663e13	−1.65750	−0.828748	+	0.559621i	$0.810947\pi$
$942$	−1.36889e11	−0.00566420
$943$	−2.88563e13	−1.18833
$944$	−1.70030e13	−0.696868
$945$	−2.59563e13	−1.05877
$946$	2.73399e12	0.110991
$947$	5.17204e12	0.208972	0.104486	−	0.994526i	$-0.466680\pi$
$947$	5.17204e12	0.208972	0.104486	+	0.994526i	$0.466680\pi$
$948$	−5.27172e11	−0.0211990
$949$	−3.65770e13	−1.46390
$950$	−3.37486e12	−0.134431
$951$	2.57585e13	1.02119
$952$	0	0
$953$	3.55006e13	1.39417	0.697087	−	0.716986i	$-0.254479\pi$
$953$	3.55006e13	1.39417	0.697087	+	0.716986i	$0.254479\pi$
$954$	5.43600e12	0.212477
$955$	−4.63875e12	−0.180462
$956$	−2.40439e11	−0.00930990
$957$	1.00677e13	0.387996
$958$	2.82890e13	1.08511
$959$	−3.81416e13	−1.45618
$960$	2.81012e13	1.06783
$961$	4.08777e13	1.54608
$962$	5.89632e13	2.21969
$963$	−1.03599e13	−0.388182
$964$	−4.21865e11	−0.0157336
$965$	1.40611e13	0.521969
$966$	−6.98463e13	−2.58075
$967$	−1.41239e13	−0.519440	−0.259720	−	0.965684i	$-0.583630\pi$
$967$	−1.41239e13	−0.519440	−0.259720	+	0.965684i	$0.583630\pi$
$968$	1.05174e13	0.385006
$969$	0	0
$970$	2.90470e13	1.05349
$971$	1.57589e13	0.568905	0.284452	−	0.958690i	$-0.408188\pi$
$971$	1.57589e13	0.568905	0.284452	+	0.958690i	$0.408188\pi$
$972$	2.02093e11	0.00726195
$973$	7.78954e13	2.78615
$974$	−7.09215e12	−0.252501
$975$	7.18101e12	0.254486
$976$	−1.05403e13	−0.371816
$977$	2.30148e13	0.808132	0.404066	−	0.914730i	$-0.367597\pi$
$977$	2.30148e13	0.808132	0.404066	+	0.914730i	$0.367597\pi$
$978$	−1.49990e13	−0.524250
$979$	2.60870e13	0.907616
$980$	−3.65762e11	−0.0126672
$981$	−5.28426e12	−0.182169
$982$	2.91287e13	0.999583
$983$	−3.30550e11	−0.0112914	−0.00564568	−	0.999984i	$-0.501797\pi$
$983$	−3.30550e11	−0.0112914	−0.00564568	+	0.999984i	$0.501797\pi$
$984$	−2.62959e13	−0.894150
$985$	4.91023e12	0.166203
$986$	0	0
$987$	2.38087e13	0.798561
$988$	−4.40521e11	−0.0147082
$989$	−4.38551e12	−0.145760
$990$	−1.03574e13	−0.342683
$991$	−2.41937e13	−0.796839	−0.398420	−	0.917203i	$-0.630441\pi$
$991$	−2.41937e13	−0.796839	−0.398420	+	0.917203i	$0.630441\pi$
$992$	−1.14798e12	−0.0376383
$993$	2.57091e13	0.839104
$994$	3.29916e13	1.07193
$995$	−2.53893e13	−0.821196
$996$	−7.31591e10	−0.00235560
$997$	−5.11973e13	−1.64104	−0.820519	−	0.571619i	$-0.806315\pi$
$997$	−5.11973e13	−1.64104	−0.820519	+	0.571619i	$0.806315\pi$
$998$	−4.94130e13	−1.57672
$999$	−3.84635e13	−1.22181

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.10.a.h.1.10	yes	36
17.16	even	2		289.10.a.g.1.10	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
289.10.a.g.1.10	✓	36	17.16	even	2
289.10.a.h.1.10	yes	36	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	289.a (trivial)

\(f(q)\)	\(=\)	\(q-22.4936 q^{2} +161.121 q^{3} -6.03889 q^{4} +1284.66 q^{5} -3624.20 q^{6} +9354.17 q^{7} +11652.5 q^{8} +6277.10 q^{9} +O(q^{10})\)	\(q-22.4936 q^{2} +161.121 q^{3} -6.03889 q^{4} +1284.66 q^{5} -3624.20 q^{6} +9354.17 q^{7} +11652.5 q^{8} +6277.10 q^{9} -28896.7 q^{10} +57101.0 q^{11} -972.994 q^{12} -147205. q^{13} -210409. q^{14} +206987. q^{15} -259016. q^{16} -141194. q^{18} -495550. q^{19} -7757.93 q^{20} +1.50716e6 q^{21} -1.28441e6 q^{22} +2.06028e6 q^{23} +1.87747e6 q^{24} -302768. q^{25} +3.31117e6 q^{26} -2.15998e6 q^{27} -56488.8 q^{28} +1.09429e6 q^{29} -4.65587e6 q^{30} +8.20471e6 q^{31} -139917. q^{32} +9.20020e6 q^{33} +1.20169e7 q^{35} -37906.7 q^{36} +1.78074e7 q^{37} +1.11467e7 q^{38} -2.37179e7 q^{39} +1.49696e7 q^{40} -1.40060e7 q^{41} -3.39013e7 q^{42} -2.12860e6 q^{43} -344827. q^{44} +8.06395e6 q^{45} -4.63431e7 q^{46} +1.57971e7 q^{47} -4.17330e7 q^{48} +4.71468e7 q^{49} +6.81033e6 q^{50} +888955. q^{52} -3.85001e7 q^{53} +4.85856e7 q^{54} +7.33555e7 q^{55} +1.09000e8 q^{56} -7.98436e7 q^{57} -2.46146e7 q^{58} +6.56446e7 q^{59} -1.24997e6 q^{60} +4.06936e7 q^{61} -1.84553e8 q^{62} +5.87170e7 q^{63} +1.35763e8 q^{64} -1.89109e8 q^{65} -2.06945e8 q^{66} +1.29000e8 q^{67} +3.31955e8 q^{69} -2.70304e8 q^{70} -1.56798e8 q^{71} +7.31442e7 q^{72} +2.48477e8 q^{73} -4.00551e8 q^{74} -4.87823e7 q^{75} +2.99257e6 q^{76} +5.34133e8 q^{77} +5.33500e8 q^{78} +5.41804e8 q^{79} -3.32748e8 q^{80} -4.71571e8 q^{81} +3.15045e8 q^{82} +7.51897e7 q^{83} -9.10155e6 q^{84} +4.78798e7 q^{86} +1.76314e8 q^{87} +6.65373e8 q^{88} +4.56857e8 q^{89} -1.81387e8 q^{90} -1.37698e9 q^{91} -1.24418e7 q^{92} +1.32195e9 q^{93} -3.55333e8 q^{94} -6.36614e8 q^{95} -2.25436e7 q^{96} -1.00520e9 q^{97} -1.06050e9 q^{98} +3.58429e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q + 486 q^{3} + 9216 q^{4} + 3750 q^{5} + 11061 q^{6} + 29040 q^{7} + 24837 q^{8} + 236196 q^{9}+O(q^{10}) \) 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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