LMFDB - Embedded newform 10.26.a.b.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [10,26,Mod(1,10)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(10, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 26, names="a")

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

chi := DirichletCharacter("10.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 10 = 2 \cdot 5 $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	10.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:	$39.5996779952$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\mathbb{Q}[x]/(x^{2} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 6900880 $ x^2 - x - 6900880
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{2}\cdot 3^{3}\cdot 5 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2627.45$ of defining polynomial
Character	$\chi$	$=$	10.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-4096.00 q^{2} -1.63785e6 q^{3} +1.67772e7 q^{4} +2.44141e8 q^{5} +6.70863e9 q^{6} -2.07876e10 q^{7} -6.87195e10 q^{8} +1.83526e12 q^{9} -1.00000e12 q^{10} +4.14605e12 q^{11} -2.74785e13 q^{12} -1.30955e14 q^{13} +8.51459e13 q^{14} -3.99865e14 q^{15} +2.81475e14 q^{16} -4.62477e15 q^{17} -7.51722e15 q^{18} -5.62727e15 q^{19} +4.09600e15 q^{20} +3.40469e16 q^{21} -1.69822e16 q^{22} -2.45654e16 q^{23} +1.12552e17 q^{24} +5.96046e16 q^{25} +5.36390e17 q^{26} -1.61815e18 q^{27} -3.48758e17 q^{28} -1.86225e18 q^{29} +1.63785e18 q^{30} +7.10276e17 q^{31} -1.15292e18 q^{32} -6.79060e18 q^{33} +1.89431e19 q^{34} -5.07509e18 q^{35} +3.07905e19 q^{36} +5.29105e19 q^{37} +2.30493e19 q^{38} +2.14484e20 q^{39} -1.67772e19 q^{40} -2.57715e20 q^{41} -1.39456e20 q^{42} -1.94678e19 q^{43} +6.95591e19 q^{44} +4.48061e20 q^{45} +1.00620e20 q^{46} +1.05479e21 q^{47} -4.61013e20 q^{48} -9.08945e20 q^{49} -2.44141e20 q^{50} +7.57467e21 q^{51} -2.19705e21 q^{52} +1.71922e21 q^{53} +6.62792e21 q^{54} +1.01222e21 q^{55} +1.42851e21 q^{56} +9.21661e21 q^{57} +7.62780e21 q^{58} -2.29629e22 q^{59} -6.70863e21 q^{60} -9.00207e20 q^{61} -2.90929e21 q^{62} -3.81506e22 q^{63} +4.72237e21 q^{64} -3.19713e22 q^{65} +2.78143e22 q^{66} -1.50272e22 q^{67} -7.75908e22 q^{68} +4.02345e22 q^{69} +2.07876e22 q^{70} +2.23447e23 q^{71} -1.26118e23 q^{72} -3.25252e23 q^{73} -2.16721e23 q^{74} -9.76234e22 q^{75} -9.44099e22 q^{76} -8.61863e22 q^{77} -8.78525e23 q^{78} +6.06979e23 q^{79} +6.87195e22 q^{80} +1.09528e24 q^{81} +1.05560e24 q^{82} -7.26128e23 q^{83} +5.71212e23 q^{84} -1.12909e24 q^{85} +7.97403e22 q^{86} +3.05009e24 q^{87} -2.84914e23 q^{88} +1.91182e24 q^{89} -1.83526e24 q^{90} +2.72223e24 q^{91} -4.12140e23 q^{92} -1.16332e24 q^{93} -4.32043e24 q^{94} -1.37384e24 q^{95} +1.88831e24 q^{96} -1.71656e24 q^{97} +3.72304e24 q^{98} +7.60907e24 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 8192 q^{2} - 438588 q^{3} + 33554432 q^{4} + 488281250 q^{5} + 1796456448 q^{6} - 34008596636 q^{7} - 137438953472 q^{8} + 2426195859786 q^{9} - 2000000000000 q^{10} + 19344682791984 q^{11} - 7358285611008 q^{12}+ \cdots + 16\!\cdots\!12 q^{99}+O(q^{100}) $ 2 * q - 8192 * q^2 - 438588 * q^3 + 33554432 * q^4 + 488281250 * q^5 + 1796456448 * q^6 - 34008596636 * q^7 - 137438953472 * q^8 + 2426195859786 * q^9 - 2000000000000 * q^10 + 19344682791984 * q^11 - 7358285611008 * q^12 - 127796048033588 * q^13 + 139299211821056 * q^14 - 107077148437500 * q^15 + 562949953421312 * q^16 - 2998857935578476 * q^17 - 9937698241683456 * q^18 + 13534782395320 * q^19 + 8192000000000000 * q^20 + 18191471686615584 * q^21 - 79235820715966464 * q^22 - 176800520782624068 * q^23 + 30139537862688768 * q^24 + 119209289550781250 * q^25 + 523452612745576448 * q^26 - 1925577931602663000 * q^27 - 570569571619045376 * q^28 - 1676097487309033380 * q^29 + 438588000000000000 * q^30 + 7125865156346376664 * q^31 - 2305843009213693952 * q^32 + 11436524032432880304 * q^33 + 12283322104129437696 * q^34 - 8302880038085937500 * q^35 + 40704811997935435776 * q^36 + 84009823521808944364 * q^37 - 55438468691230720 * q^38 + 218271507658245788472 * q^39 - 33554432000000000000 * q^40 - 278976945138543009756 * q^41 - 74512268028377432064 * q^42 + 426481602906822493732 * q^43 + 324549921652598636544 * q^44 + 592332973580566406250 * q^45 + 724174933125628182528 * q^46 + 1107620660641184540244 * q^47 - 123451547085573193728 * q^48 - 2075218430900234303166 * q^49 - 488281250000000000000 * q^50 + 9524566337524637542344 * q^51 - 2144061901805881131008 * q^52 + 4105636904637626409852 * q^53 + 7887167207844507648000 * q^54 + 4722822947261718750000 * q^55 + 2337052965351609860096 * q^56 + 15981397362106388525520 * q^57 + 6865295308017800724480 * q^58 - 3765561121989768768360 * q^59 - 1796456448000000000000 * q^60 + 1088840609004402816124 * q^61 - 29187543680394758815744 * q^62 - 45963382166122467752748 * q^63 + 9444732965739290427392 * q^64 - 31200207039450195312500 * q^65 - 46844002436845077725184 * q^66 - 118164954526157928047156 * q^67 - 50312487338514176802816 * q^68 - 142335029641186502306208 * q^69 + 34008596636000000000000 * q^70 + 121487502051587284868424 * q^71 - 166726909943543544938496 * q^72 + 1543159074817774555972 * q^73 - 344104237145329436114944 * q^74 - 26141881942749023437500 * q^75 + 227075967759281029120 * q^76 - 287127672428028283409712 * q^77 - 894040095368174749581312 * q^78 + 821388705533644841730640 * q^79 + 137438953472000000000000 * q^80 + 225897583488924285462402 * q^81 + 1142689567287472167960576 * q^82 + 1078689963931157206149252 * q^83 + 305202249844233961734144 * q^84 - 732143050678338867187500 * q^85 - 1746868645506344934326272 * q^86 + 3273342747249083127820920 * q^87 - 1329356479089044015284224 * q^88 + 5059219929404495720992980 * q^89 - 2426195859786000000000000 * q^90 + 2680469809760336269552184 * q^91 - 2966220526082573035634688 * q^92 + 6530638201511067276729984 * q^93 - 4536814225986291876839424 * q^94 + 3304390233232421875000 * q^95 + 505657536862507801509888 * q^96 + 2393368330790785393982164 * q^97 + 8500094692967359705767936 * q^98 + 16590506333144186236452912 * q^99

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 $

$2$	−4096.00	−0.707107
$2$	−4096.00	−0.707107
$3$	−1.63785e6	−1.77934	−0.889668	−	0.456608i	$-0.849064\pi$
$3$	−1.63785e6	−1.77934	−0.889668	+	0.456608i	$0.849064\pi$
$4$	1.67772e7	0.500000
$5$	2.44141e8	0.447214
$5$	2.44141e8	0.447214
$6$	6.70863e9	1.25818
$7$	−2.07876e10	−0.567647	−0.283824	−	0.958877i	$-0.591603\pi$
$7$	−2.07876e10	−0.567647	−0.283824	+	0.958877i	$0.591603\pi$
$8$	−6.87195e10	−0.353553
$9$	1.83526e12	2.16604
$10$	−1.00000e12	−0.316228
$11$	4.14605e12	0.398314	0.199157	−	0.979968i	$-0.436180\pi$
$11$	4.14605e12	0.398314	0.199157	+	0.979968i	$0.436180\pi$
$12$	−2.74785e13	−0.889668
$13$	−1.30955e14	−1.55894	−0.779469	−	0.626441i	$-0.784511\pi$
$13$	−1.30955e14	−1.55894	−0.779469	+	0.626441i	$0.784511\pi$
$14$	8.51459e13	0.401387
$15$	−3.99865e14	−0.795743
$16$	2.81475e14	0.250000
$17$	−4.62477e15	−1.92521	−0.962606	−	0.270904i	$-0.912677\pi$
$17$	−4.62477e15	−1.92521	−0.962606	+	0.270904i	$0.912677\pi$
$18$	−7.51722e15	−1.53162
$19$	−5.62727e15	−0.583280	−0.291640	−	0.956528i	$-0.594201\pi$
$19$	−5.62727e15	−0.583280	−0.291640	+	0.956528i	$0.594201\pi$
$20$	4.09600e15	0.223607
$21$	3.40469e16	1.01004
$22$	−1.69822e16	−0.281651
$23$	−2.45654e16	−0.233737	−0.116868	−	0.993147i	$-0.537286\pi$
$23$	−2.45654e16	−0.233737	−0.116868	+	0.993147i	$0.537286\pi$
$24$	1.12552e17	0.629090
$25$	5.96046e16	0.200000
$26$	5.36390e17	1.10234
$27$	−1.61815e18	−2.07477
$28$	−3.48758e17	−0.283824
$29$	−1.86225e18	−0.977382	−0.488691	−	0.872457i	$-0.662525\pi$
$29$	−1.86225e18	−0.977382	−0.488691	+	0.872457i	$0.662525\pi$
$30$	1.63785e18	0.562676
$31$	7.10276e17	0.161959	0.0809796	−	0.996716i	$-0.474195\pi$
$31$	7.10276e17	0.161959	0.0809796	+	0.996716i	$0.474195\pi$
$32$	−1.15292e18	−0.176777
$33$	−6.79060e18	−0.708735
$34$	1.89431e19	1.36133
$35$	−5.07509e18	−0.253860
$36$	3.07905e19	1.08302
$37$	5.29105e19	1.32136	0.660679	−	0.750669i	$-0.270269\pi$
$37$	5.29105e19	1.32136	0.660679	+	0.750669i	$0.270269\pi$
$38$	2.30493e19	0.412442
$39$	2.14484e20	2.77387
$40$	−1.67772e19	−0.158114
$41$	−2.57715e20	−1.78378	−0.891892	−	0.452249i	$-0.850622\pi$
$41$	−2.57715e20	−1.78378	−0.891892	+	0.452249i	$0.850622\pi$
$42$	−1.39456e20	−0.714203
$43$	−1.94678e19	−0.0742954	−0.0371477	−	0.999310i	$-0.511827\pi$
$43$	−1.94678e19	−0.0742954	−0.0371477	+	0.999310i	$0.511827\pi$
$44$	6.95591e19	0.199157
$45$	4.48061e20	0.968681
$46$	1.00620e20	0.165277
$47$	1.05479e21	1.32417	0.662085	−	0.749428i	$-0.269672\pi$
$47$	1.05479e21	1.32417	0.662085	+	0.749428i	$0.269672\pi$
$48$	−4.61013e20	−0.444834
$49$	−9.08945e20	−0.677777
$50$	−2.44141e20	−0.141421
$51$	7.57467e21	3.42560
$52$	−2.19705e21	−0.779469
$53$	1.71922e21	0.480709	0.240354	−	0.970685i	$-0.422736\pi$
$53$	1.71922e21	0.480709	0.240354	+	0.970685i	$0.422736\pi$
$54$	6.62792e21	1.46709
$55$	1.01222e21	0.178132
$56$	1.42851e21	0.200694
$57$	9.21661e21	1.03785
$58$	7.62780e21	0.691113
$59$	−2.29629e22	−1.68026	−0.840130	−	0.542386i	$-0.817521\pi$
$59$	−2.29629e22	−1.68026	−0.840130	+	0.542386i	$0.817521\pi$
$60$	−6.70863e21	−0.397872
$61$	−9.00207e20	−0.0434230	−0.0217115	−	0.999764i	$-0.506912\pi$
$61$	−9.00207e20	−0.0434230	−0.0217115	+	0.999764i	$0.506912\pi$
$62$	−2.90929e21	−0.114523
$63$	−3.81506e22	−1.22955
$64$	4.72237e21	0.125000
$65$	−3.19713e22	−0.697178
$66$	2.78143e22	0.501151
$67$	−1.50272e22	−0.224358	−0.112179	−	0.993688i	$-0.535783\pi$
$67$	−1.50272e22	−0.224358	−0.112179	+	0.993688i	$0.535783\pi$
$68$	−7.75908e22	−0.962606
$69$	4.02345e22	0.415896
$70$	2.07876e22	0.179506
$71$	2.23447e23	1.61602	0.808008	−	0.589172i	$-0.200546\pi$
$71$	2.23447e23	1.61602	0.808008	+	0.589172i	$0.200546\pi$
$72$	−1.26118e23	−0.765810
$73$	−3.25252e23	−1.66220	−0.831101	−	0.556122i	$-0.812289\pi$
$73$	−3.25252e23	−1.66220	−0.831101	+	0.556122i	$0.812289\pi$
$74$	−2.16721e23	−0.934341
$75$	−9.76234e22	−0.355867
$76$	−9.44099e22	−0.291640
$77$	−8.61863e22	−0.226102
$78$	−8.78525e23	−1.96142
$79$	6.06979e23	1.15567	0.577837	−	0.816152i	$-0.303897\pi$
$79$	6.06979e23	1.15567	0.577837	+	0.816152i	$0.303897\pi$
$80$	6.87195e22	0.111803
$81$	1.09528e24	1.52568
$82$	1.05560e24	1.26133
$83$	−7.26128e23	−0.745653	−0.372827	−	0.927901i	$-0.621611\pi$
$83$	−7.26128e23	−0.745653	−0.372827	+	0.927901i	$0.621611\pi$
$84$	5.71212e23	0.505018
$85$	−1.12909e24	−0.860981
$86$	7.97403e22	0.0525348
$87$	3.05009e24	1.73909
$88$	−2.84914e23	−0.140825
$89$	1.91182e24	0.820488	0.410244	−	0.911976i	$-0.365444\pi$
$89$	1.91182e24	0.820488	0.410244	+	0.911976i	$0.365444\pi$
$90$	−1.83526e24	−0.684961
$91$	2.72223e24	0.884926
$92$	−4.12140e23	−0.116868
$93$	−1.16332e24	−0.288180
$94$	−4.32043e24	−0.936330
$95$	−1.37384e24	−0.260851
$96$	1.88831e24	0.314545
$97$	−1.71656e24	−0.251195	−0.125598	−	0.992081i	$-0.540085\pi$
$97$	−1.71656e24	−0.251195	−0.125598	+	0.992081i	$0.540085\pi$
$98$	3.72304e24	0.479260
$99$	7.60907e24	0.862763
$100$	1.00000e24	0.100000
$101$	1.34215e25	1.18518	0.592590	−	0.805504i	$-0.298105\pi$
$101$	1.34215e25	1.18518	0.592590	+	0.805504i	$0.298105\pi$
$102$	−3.10259e25	−2.42227
$103$	2.08010e25	1.43754	0.718769	−	0.695249i	$-0.244706\pi$
$103$	2.08010e25	1.43754	0.718769	+	0.695249i	$0.244706\pi$
$104$	8.99913e24	0.551168
$105$	8.31223e24	0.451701
$106$	−7.04191e24	−0.339912
$107$	2.98949e25	1.28322	0.641609	−	0.767032i	$-0.278267\pi$
$107$	2.98949e25	1.28322	0.641609	+	0.767032i	$0.278267\pi$
$108$	−2.71480e25	−1.03739
$109$	5.99753e24	0.204240	0.102120	−	0.994772i	$-0.467437\pi$
$109$	5.99753e24	0.204240	0.102120	+	0.994772i	$0.467437\pi$
$110$	−4.14605e24	−0.125958
$111$	−8.66594e25	−2.35114
$112$	−5.85118e24	−0.141912
$113$	−3.21651e25	−0.698080	−0.349040	−	0.937108i	$-0.613492\pi$
$113$	−3.21651e25	−0.698080	−0.349040	+	0.937108i	$0.613492\pi$
$114$	−3.77512e25	−0.733872
$115$	−5.99742e24	−0.104530
$116$	−3.12435e25	−0.488691
$117$	−2.40335e26	−3.37672
$118$	9.40560e25	1.18812
$119$	9.61378e25	1.09284
$120$	2.74785e25	0.281338
$121$	−9.11573e25	−0.841346
$122$	3.68725e24	0.0307047
$123$	4.22099e26	3.17395
$124$	1.19165e25	0.0809796
$125$	1.45519e25	0.0894427
$126$	1.56265e26	0.869420
$127$	−1.12460e26	−0.566829	−0.283414	−	0.958998i	$-0.591467\pi$
$127$	−1.12460e26	−0.566829	−0.283414	+	0.958998i	$0.591467\pi$
$128$	−1.93428e25	−0.0883883
$129$	3.18854e25	0.132197
$130$	1.30955e26	0.492979
$131$	2.26749e26	0.775630	0.387815	−	0.921737i	$-0.373230\pi$
$131$	2.26749e26	0.775630	0.387815	+	0.921737i	$0.373230\pi$
$132$	−1.13927e26	−0.354367
$133$	1.16977e26	0.331098
$134$	6.15513e25	0.158645
$135$	−3.95055e26	−0.927867
$136$	3.17812e26	0.680665
$137$	6.81423e26	1.33171	0.665855	−	0.746081i	$-0.268067\pi$
$137$	6.81423e26	1.33171	0.665855	+	0.746081i	$0.268067\pi$
$138$	−1.64800e26	−0.294083
$139$	5.03091e26	0.820279	0.410140	−	0.912023i	$-0.365480\pi$
$139$	5.03091e26	0.820279	0.410140	+	0.912023i	$0.365480\pi$
$140$	−8.51459e25	−0.126930
$141$	−1.72759e27	−2.35614
$142$	−9.15240e26	−1.14270
$143$	−5.42944e26	−0.620947
$144$	5.16579e26	0.541509
$145$	−4.54652e26	−0.437098
$146$	1.33223e27	1.17535
$147$	1.48871e27	1.20599
$148$	8.87691e26	0.660679
$149$	7.27393e26	0.497669	0.248835	−	0.968546i	$-0.419952\pi$
$149$	7.27393e26	0.497669	0.248835	+	0.968546i	$0.419952\pi$
$150$	3.99865e26	0.251636
$151$	9.92827e25	0.0574992	0.0287496	−	0.999587i	$-0.490847\pi$
$151$	9.92827e25	0.0574992	0.0287496	+	0.999587i	$0.490847\pi$
$152$	3.86703e26	0.206221
$153$	−8.48765e27	−4.17008
$154$	3.53019e26	0.159878
$155$	1.73407e26	0.0724304
$156$	3.59844e27	1.38694
$157$	−2.27168e26	−0.0808355	−0.0404177	−	0.999183i	$-0.512869\pi$
$157$	−2.27168e26	−0.0808355	−0.0404177	+	0.999183i	$0.512869\pi$
$158$	−2.48619e27	−0.817184
$159$	−2.81581e27	−0.855342
$160$	−2.81475e26	−0.0790569
$161$	5.10656e26	0.132680
$162$	−4.48628e27	−1.07882
$163$	5.17654e27	1.15264	0.576322	−	0.817223i	$-0.304488\pi$
$163$	5.17654e27	1.15264	0.576322	+	0.817223i	$0.304488\pi$
$164$	−4.32375e27	−0.891892
$165$	−1.65786e27	−0.316956
$166$	2.97422e27	0.527256
$167$	1.02965e27	0.169330	0.0846652	−	0.996409i	$-0.473018\pi$
$167$	1.02965e27	0.169330	0.0846652	+	0.996409i	$0.473018\pi$
$168$	−2.33969e27	−0.357101
$169$	1.00927e28	1.43029
$170$	4.62477e27	0.608806
$171$	−1.03275e28	−1.26341
$172$	−3.26616e26	−0.0371477
$173$	1.24548e28	1.31753	0.658766	−	0.752348i	$-0.271079\pi$
$173$	1.24548e28	1.31753	0.658766	+	0.752348i	$0.271079\pi$
$174$	−1.24932e28	−1.22972
$175$	−1.23904e27	−0.113529
$176$	1.16701e27	0.0995785
$177$	3.76097e28	2.98975
$178$	−7.83082e27	−0.580173
$179$	4.58615e27	0.316800	0.158400	−	0.987375i	$-0.449366\pi$
$179$	4.58615e27	0.316800	0.158400	+	0.987375i	$0.449366\pi$
$180$	7.51722e27	0.484341
$181$	−1.24754e28	−0.750019	−0.375010	−	0.927021i	$-0.622361\pi$
$181$	−1.24754e28	−0.750019	−0.375010	+	0.927021i	$0.622361\pi$
$182$	−1.11502e28	−0.625737
$183$	1.47440e27	0.0772641
$184$	1.68812e27	0.0826384
$185$	1.29176e28	0.590929
$186$	4.76498e27	0.203774
$187$	−1.91745e28	−0.766839
$188$	1.76965e28	0.662085
$189$	3.36373e28	1.17774
$190$	5.62727e27	0.184449
$191$	−5.82809e28	−1.78900	−0.894498	−	0.447072i	$-0.852467\pi$
$191$	−5.82809e28	−1.78900	−0.894498	+	0.447072i	$0.852467\pi$
$192$	−7.73452e27	−0.222417
$193$	−2.07224e28	−0.558437	−0.279218	−	0.960228i	$-0.590075\pi$
$193$	−2.07224e28	−0.558437	−0.279218	+	0.960228i	$0.590075\pi$
$194$	7.03102e27	0.177622
$195$	5.23642e28	1.24051
$196$	−1.52496e28	−0.338888
$197$	2.21753e28	0.462425	0.231213	−	0.972903i	$-0.425731\pi$
$197$	2.21753e28	0.462425	0.231213	+	0.972903i	$0.425731\pi$
$198$	−3.11668e28	−0.610066
$199$	−2.56881e28	−0.472138	−0.236069	−	0.971736i	$-0.575859\pi$
$199$	−2.56881e28	−0.472138	−0.236069	+	0.971736i	$0.575859\pi$
$200$	−4.09600e27	−0.0707107
$201$	2.46122e28	0.399209
$202$	−5.49745e28	−0.838049
$203$	3.87118e28	0.554808
$204$	1.27082e29	1.71280
$205$	−6.29188e28	−0.797732
$206$	−8.52010e28	−1.01649
$207$	−4.50839e28	−0.506282
$208$	−3.68604e28	−0.389734
$209$	−2.33309e28	−0.232329
$210$	−3.40469e28	−0.319401
$211$	−1.69750e29	−1.50065	−0.750323	−	0.661072i	$-0.770102\pi$
$211$	−1.69750e29	−1.50065	−0.750323	+	0.661072i	$0.770102\pi$
$212$	2.88437e28	0.240354
$213$	−3.65973e29	−2.87543
$214$	−1.22450e29	−0.907372
$215$	−4.75289e27	−0.0332259
$216$	1.11198e29	0.733543
$217$	−1.47649e28	−0.0919357
$218$	−2.45659e28	−0.144420
$219$	5.32713e29	2.95762
$220$	1.69822e28	0.0890658
$221$	6.05635e29	3.00129
$222$	3.54957e29	1.66251
$223$	−1.64686e29	−0.729197	−0.364598	−	0.931165i	$-0.618794\pi$
$223$	−1.64686e29	−0.729197	−0.364598	+	0.931165i	$0.618794\pi$
$224$	2.39665e28	0.100347
$225$	1.09390e29	0.433207
$226$	1.31748e29	0.493617
$227$	−5.10933e29	−1.81151	−0.905754	−	0.423803i	$-0.860695\pi$
$227$	−5.10933e29	−1.81151	−0.905754	+	0.423803i	$0.860695\pi$
$228$	1.54629e29	0.518926
$229$	1.25023e29	0.397235	0.198617	−	0.980077i	$-0.436355\pi$
$229$	1.25023e29	0.397235	0.198617	+	0.980077i	$0.436355\pi$
$230$	2.45654e28	0.0739140
$231$	1.41160e29	0.402311
$232$	1.27973e29	0.345557
$233$	−5.70548e29	−1.45997	−0.729984	−	0.683464i	$-0.760472\pi$
$233$	−5.70548e29	−1.45997	−0.729984	+	0.683464i	$0.760472\pi$
$234$	9.84414e29	2.38770
$235$	2.57518e29	0.592187
$236$	−3.85253e29	−0.840130
$237$	−9.94140e29	−2.05633
$238$	−3.93780e29	−0.772756
$239$	6.05498e29	1.12756	0.563780	−	0.825925i	$-0.309347\pi$
$239$	6.05498e29	1.12756	0.563780	+	0.825925i	$0.309347\pi$
$240$	−1.12552e29	−0.198936
$241$	−5.11295e29	−0.857943	−0.428972	−	0.903318i	$-0.641124\pi$
$241$	−5.11295e29	−0.857943	−0.428972	+	0.903318i	$0.641124\pi$
$242$	3.73380e29	0.594921
$243$	−4.22872e29	−0.639927
$244$	−1.51030e28	−0.0217115
$245$	−2.21910e29	−0.303111
$246$	−1.72892e30	−2.24432
$247$	7.36916e29	0.909298
$248$	−4.88098e28	−0.0572613
$249$	1.18929e30	1.32677
$250$	−5.96046e28	−0.0632456
$251$	2.51767e29	0.254142	0.127071	−	0.991894i	$-0.459442\pi$
$251$	2.51767e29	0.254142	0.127071	+	0.991894i	$0.459442\pi$
$252$	−6.40061e29	−0.614773
$253$	−1.01850e29	−0.0931006
$254$	4.60636e29	0.400808
$255$	1.84929e30	1.53198
$256$	7.92282e28	0.0625000
$257$	4.32516e29	0.324967	0.162483	−	0.986711i	$-0.448050\pi$
$257$	4.32516e29	0.324967	0.162483	+	0.986711i	$0.448050\pi$
$258$	−1.30603e29	−0.0934771
$259$	−1.09988e30	−0.750065
$260$	−5.36390e29	−0.348589
$261$	−3.41772e30	−2.11705
$262$	−9.28765e29	−0.548454
$263$	3.00951e30	1.69453	0.847265	−	0.531171i	$-0.178248\pi$
$263$	3.00951e30	1.69453	0.847265	+	0.531171i	$0.178248\pi$
$264$	4.66646e29	0.250576
$265$	4.19730e29	0.214979
$266$	−4.79139e29	−0.234121
$267$	−3.13127e30	−1.45992
$268$	−2.52114e29	−0.112179
$269$	5.09495e29	0.216390	0.108195	−	0.994130i	$-0.465493\pi$
$269$	5.09495e29	0.216390	0.108195	+	0.994130i	$0.465493\pi$
$270$	1.61815e30	0.656101
$271$	1.05937e30	0.410140	0.205070	−	0.978747i	$-0.434258\pi$
$271$	1.05937e30	0.410140	0.205070	+	0.978747i	$0.434258\pi$
$272$	−1.30176e30	−0.481303
$273$	−4.45860e30	−1.57458
$274$	−2.79111e30	−0.941661
$275$	2.47124e29	0.0796628
$276$	6.75022e29	0.207948
$277$	5.67674e30	1.67148	0.835741	−	0.549124i	$-0.185039\pi$
$277$	5.67674e30	1.67148	0.835741	+	0.549124i	$0.185039\pi$
$278$	−2.06066e30	−0.580025
$279$	1.30354e30	0.350810
$280$	3.48758e29	0.0897529
$281$	−1.50424e30	−0.370245	−0.185122	−	0.982715i	$-0.559268\pi$
$281$	−1.50424e30	−0.370245	−0.185122	+	0.982715i	$0.559268\pi$
$282$	7.07621e30	1.66605
$283$	−4.46973e30	−1.00682	−0.503409	−	0.864048i	$-0.667921\pi$
$283$	−4.46973e30	−1.00682	−0.503409	+	0.864048i	$0.667921\pi$
$284$	3.74882e30	0.808008
$285$	2.25015e30	0.464142
$286$	2.22390e30	0.439076
$287$	5.35728e30	1.01256
$288$	−2.11591e30	−0.382905
$289$	1.56179e31	2.70644
$290$	1.86225e30	0.309075
$291$	2.81146e30	0.446961
$292$	−5.45682e30	−0.831101
$293$	4.32602e30	0.631311	0.315655	−	0.948874i	$-0.397776\pi$
$293$	4.32602e30	0.631311	0.315655	+	0.948874i	$0.397776\pi$
$294$	−6.09777e30	−0.852766
$295$	−5.60617e30	−0.751435
$296$	−3.63598e30	−0.467170
$297$	−6.70891e30	−0.826411
$298$	−2.97940e30	−0.351905
$299$	3.21696e30	0.364381
$300$	−1.63785e30	−0.177934
$301$	4.04689e29	0.0421736
$302$	−4.06662e29	−0.0406581
$303$	−2.19824e31	−2.10883
$304$	−1.58393e30	−0.145820
$305$	−2.19777e29	−0.0194193
$306$	3.47654e31	2.94869
$307$	1.40982e31	1.14798	0.573991	−	0.818862i	$-0.305395\pi$
$307$	1.40982e31	1.14798	0.573991	+	0.818862i	$0.305395\pi$
$308$	−1.44597e30	−0.113051
$309$	−3.40689e31	−2.55786
$310$	−7.10276e29	−0.0512160
$311$	−4.30946e30	−0.298482	−0.149241	−	0.988801i	$-0.547683\pi$
$311$	−4.30946e30	−0.298482	−0.149241	+	0.988801i	$0.547683\pi$
$312$	−1.47392e31	−0.980712
$313$	−2.24958e30	−0.143813	−0.0719065	−	0.997411i	$-0.522908\pi$
$313$	−2.24958e30	−0.143813	−0.0719065	+	0.997411i	$0.522908\pi$
$314$	9.30481e29	0.0571593
$315$	−9.31411e30	−0.549869
$316$	1.01834e31	0.577837
$317$	7.47129e30	0.407525	0.203763	−	0.979020i	$-0.434683\pi$
$317$	7.47129e30	0.407525	0.203763	+	0.979020i	$0.434683\pi$
$318$	1.15336e31	0.604818
$319$	−7.72100e30	−0.389305
$320$	1.15292e30	0.0559017
$321$	−4.89634e31	−2.28328
$322$	−2.09165e30	−0.0938189
$323$	2.60248e31	1.12294
$324$	1.83758e31	0.762840
$325$	−7.80550e30	−0.311787
$326$	−2.12031e31	−0.815042
$327$	−9.82304e30	−0.363412
$328$	1.77101e31	0.630663
$329$	−2.19266e31	−0.751662
$330$	6.79060e30	0.224122
$331$	−1.01412e31	−0.322286	−0.161143	−	0.986931i	$-0.551518\pi$
$331$	−1.01412e31	−0.322286	−0.161143	+	0.986931i	$0.551518\pi$
$332$	−1.21824e31	−0.372827
$333$	9.71045e31	2.86211
$334$	−4.21746e30	−0.119735
$335$	−3.66874e30	−0.100336
$336$	9.58335e30	0.252509
$337$	−4.27054e31	−1.08420	−0.542099	−	0.840315i	$-0.682370\pi$
$337$	−4.27054e31	−1.08420	−0.542099	+	0.840315i	$0.682370\pi$
$338$	−4.13396e31	−1.01136
$339$	5.26816e31	1.24212
$340$	−1.89431e31	−0.430491
$341$	2.94484e30	0.0645107
$342$	4.23014e31	0.893364
$343$	4.67723e31	0.952385
$344$	1.33782e30	0.0262674
$345$	9.82287e30	0.185994
$346$	−5.10149e31	−0.931636
$347$	1.42992e30	0.0251880	0.0125940	−	0.999921i	$-0.495991\pi$
$347$	1.42992e30	0.0251880	0.0125940	+	0.999921i	$0.495991\pi$
$348$	5.11720e31	0.869545
$349$	3.55571e30	0.0582920	0.0291460	−	0.999575i	$-0.490721\pi$
$349$	3.55571e30	0.0582920	0.0291460	+	0.999575i	$0.490721\pi$
$350$	5.07509e30	0.0802774
$351$	2.11903e32	3.23444
$352$	−4.78007e30	−0.0704127
$353$	6.63973e31	0.943988	0.471994	−	0.881602i	$-0.343534\pi$
$353$	6.63973e31	0.943988	0.471994	+	0.881602i	$0.343534\pi$
$354$	−1.54049e32	−2.11407
$355$	5.45525e31	0.722704
$356$	3.20750e31	0.410244
$357$	−1.57459e32	−1.94453
$358$	−1.87849e31	−0.224012
$359$	−1.86335e31	−0.214593	−0.107296	−	0.994227i	$-0.534219\pi$
$359$	−1.86335e31	−0.214593	−0.107296	+	0.994227i	$0.534219\pi$
$360$	−3.07905e31	−0.342481
$361$	−6.14104e31	−0.659784
$362$	5.10992e31	0.530344
$363$	1.49302e32	1.49704
$364$	4.56714e31	0.442463
$365$	−7.94071e31	−0.743359
$366$	−6.03915e30	−0.0546339
$367$	8.66272e31	0.757406	0.378703	−	0.925518i	$-0.376370\pi$
$367$	8.66272e31	0.757406	0.378703	+	0.925518i	$0.376370\pi$
$368$	−6.91456e30	−0.0584341
$369$	−4.72975e32	−3.86374
$370$	−5.29105e31	−0.417850
$371$	−3.57383e31	−0.272873
$372$	−1.95173e31	−0.144090
$373$	−2.52885e32	−1.80536	−0.902678	−	0.430316i	$-0.858402\pi$
$373$	−2.52885e32	−1.80536	−0.902678	+	0.430316i	$0.858402\pi$
$374$	7.85388e31	0.542237
$375$	−2.38338e31	−0.159149
$376$	−7.24848e31	−0.468165
$377$	2.43871e32	1.52368
$378$	−1.37779e32	−0.832787
$379$	−7.89983e31	−0.461985	−0.230992	−	0.972956i	$-0.574197\pi$
$379$	−7.89983e31	−0.461985	−0.230992	+	0.972956i	$0.574197\pi$
$380$	−2.30493e31	−0.130425
$381$	1.84192e32	1.00858
$382$	2.38719e32	1.26501
$383$	2.10109e32	1.07761	0.538803	−	0.842432i	$-0.318877\pi$
$383$	2.10109e32	1.07761	0.538803	+	0.842432i	$0.318877\pi$
$384$	3.16806e31	0.157273
$385$	−2.10416e31	−0.101116
$386$	8.48790e31	0.394874
$387$	−3.57285e31	−0.160927
$388$	−2.87991e31	−0.125598
$389$	1.39534e32	0.589264	0.294632	−	0.955611i	$-0.404803\pi$
$389$	1.39534e32	0.589264	0.294632	+	0.955611i	$0.404803\pi$
$390$	−2.14484e32	−0.877176
$391$	1.13610e32	0.449993
$392$	6.24622e31	0.239630
$393$	−3.71381e32	−1.38011
$394$	−9.08300e31	−0.326984
$395$	1.48188e32	0.516833
$396$	1.27659e32	0.431382
$397$	−1.58963e32	−0.520494	−0.260247	−	0.965542i	$-0.583804\pi$
$397$	−1.58963e32	−0.520494	−0.260247	+	0.965542i	$0.583804\pi$
$398$	1.05219e32	0.333852
$399$	−1.91591e32	−0.589134
$400$	1.67772e31	0.0500000
$401$	4.43370e32	1.28074	0.640371	−	0.768066i	$-0.278781\pi$
$401$	4.43370e32	1.28074	0.640371	+	0.768066i	$0.278781\pi$
$402$	−1.00812e32	−0.282283
$403$	−9.30138e31	−0.252484
$404$	2.25176e32	0.592590
$405$	2.67403e32	0.682305
$406$	−1.58563e32	−0.392308
$407$	2.19369e32	0.526315
$408$	−5.20528e32	−1.21113
$409$	−1.41371e32	−0.319021	−0.159510	−	0.987196i	$-0.550992\pi$
$409$	−1.41371e32	−0.319021	−0.159510	+	0.987196i	$0.550992\pi$
$410$	2.57715e32	0.564082
$411$	−1.11607e33	−2.36956
$412$	3.48983e32	0.718769
$413$	4.77343e32	0.953795
$414$	1.84664e32	0.357996
$415$	−1.77277e32	−0.333466
$416$	1.50980e32	0.275584
$417$	−8.23987e32	−1.45955
$418$	9.55634e31	0.164281
$419$	5.65693e32	0.943856	0.471928	−	0.881637i	$-0.343558\pi$
$419$	5.65693e32	0.943856	0.471928	+	0.881637i	$0.343558\pi$
$420$	1.39456e32	0.225851
$421$	−9.28896e32	−1.46030	−0.730148	−	0.683289i	$-0.760549\pi$
$421$	−9.28896e32	−1.46030	−0.730148	+	0.683289i	$0.760549\pi$
$422$	6.95294e32	1.06112
$423$	1.93582e33	2.86820
$424$	−1.18144e32	−0.169956
$425$	−2.75658e32	−0.385043
$426$	1.49902e33	2.03324
$427$	1.87131e31	0.0246489
$428$	5.01554e32	0.641609
$429$	8.89260e32	1.10487
$430$	1.94678e31	0.0234943
$431$	−1.00278e33	−1.17555	−0.587773	−	0.809026i	$-0.699995\pi$
$431$	−1.00278e33	−1.17555	−0.587773	+	0.809026i	$0.699995\pi$
$432$	−4.55467e32	−0.518693
$433$	−5.32205e31	−0.0588817	−0.0294408	−	0.999567i	$-0.509373\pi$
$433$	−5.32205e31	−0.0588817	−0.0294408	+	0.999567i	$0.509373\pi$
$434$	6.04771e31	0.0650084
$435$	7.44651e32	0.777745
$436$	1.00622e32	0.102120
$437$	1.38236e32	0.136334
$438$	−2.18199e33	−2.09135
$439$	−4.95347e32	−0.461427	−0.230714	−	0.973022i	$-0.574106\pi$
$439$	−4.95347e32	−0.461427	−0.230714	+	0.973022i	$0.574106\pi$
$440$	−6.95591e31	−0.0629790
$441$	−1.66815e33	−1.46809
$442$	−2.48068e33	−2.12223
$443$	−6.00200e32	−0.499171	−0.249585	−	0.968353i	$-0.580294\pi$
$443$	−6.00200e32	−0.499171	−0.249585	+	0.968353i	$0.580294\pi$
$444$	−1.45390e33	−1.17557
$445$	4.66753e32	0.366933
$446$	6.74552e32	0.515620
$447$	−1.19136e33	−0.885521
$448$	−9.81666e31	−0.0709559
$449$	2.44542e31	0.0171899	0.00859497	−	0.999963i	$-0.497264\pi$
$449$	2.44542e31	0.0171899	0.00859497	+	0.999963i	$0.497264\pi$
$450$	−4.48061e32	−0.306324
$451$	−1.06850e33	−0.710506
$452$	−5.39642e32	−0.349040
$453$	−1.62610e32	−0.102310
$454$	2.09278e33	1.28093
$455$	6.64606e32	0.395751
$456$	−6.33361e32	−0.366936
$457$	−1.65246e33	−0.931492	−0.465746	−	0.884918i	$-0.654214\pi$
$457$	−1.65246e33	−0.931492	−0.465746	+	0.884918i	$0.654214\pi$
$458$	−5.12095e32	−0.280887
$459$	7.48355e33	3.99438
$460$	−1.00620e32	−0.0522651
$461$	1.16768e33	0.590284	0.295142	−	0.955453i	$-0.404633\pi$
$461$	1.16768e33	0.590284	0.295142	+	0.955453i	$0.404633\pi$
$462$	−5.78192e32	−0.284477
$463$	−2.39229e33	−1.14565	−0.572823	−	0.819679i	$-0.694152\pi$
$463$	−2.39229e33	−1.14565	−0.572823	+	0.819679i	$0.694152\pi$
$464$	−5.24178e32	−0.244345
$465$	−2.84015e32	−0.128878
$466$	2.33697e33	1.03235
$467$	4.47360e33	1.92396	0.961981	−	0.273116i	$-0.0880544\pi$
$467$	4.47360e33	1.92396	0.961981	+	0.273116i	$0.0880544\pi$
$468$	−4.03216e33	−1.68836
$469$	3.12379e32	0.127356
$470$	−1.05479e33	−0.418740
$471$	3.72067e32	0.143834
$472$	1.57800e33	0.594061
$473$	−8.07146e31	−0.0295929
$474$	4.07200e33	1.45405
$475$	−3.35411e32	−0.116656
$476$	1.61292e33	0.546421
$477$	3.15521e33	1.04123
$478$	−2.48012e33	−0.797305
$479$	2.33765e33	0.732127	0.366064	−	0.930590i	$-0.380705\pi$
$479$	2.33765e33	0.732127	0.366064	+	0.930590i	$0.380705\pi$
$480$	4.61013e32	0.140669
$481$	−6.92887e33	−2.05991
$482$	2.09426e33	0.606657
$483$	−8.36377e32	−0.236082
$484$	−1.52937e33	−0.420673
$485$	−4.19082e32	−0.112338
$486$	1.73208e33	0.452496
$487$	−1.27777e33	−0.325343	−0.162672	−	0.986680i	$-0.552011\pi$
$487$	−1.27777e33	−0.325343	−0.162672	+	0.986680i	$0.552011\pi$
$488$	6.18618e31	0.0153523
$489$	−8.47839e33	−2.05094
$490$	9.08945e32	0.214332
$491$	5.48118e33	1.25996	0.629978	−	0.776613i	$-0.283064\pi$
$491$	5.48118e33	1.25996	0.629978	+	0.776613i	$0.283064\pi$
$492$	7.08164e33	1.58698
$493$	8.61250e33	1.88167
$494$	−3.01841e33	−0.642970
$495$	1.85768e33	0.385840
$496$	1.99925e32	0.0404898
$497$	−4.64493e33	−0.917327
$498$	−4.87132e33	−0.938167
$499$	3.23941e33	0.608429	0.304214	−	0.952604i	$-0.401606\pi$
$499$	3.23941e33	0.608429	0.304214	+	0.952604i	$0.401606\pi$
$500$	2.44141e32	0.0447214
$501$	−1.68642e33	−0.301296
$502$	−1.03124e33	−0.179706
$503$	−4.70148e33	−0.799162	−0.399581	−	0.916698i	$-0.630844\pi$
$503$	−4.70148e33	−0.799162	−0.399581	+	0.916698i	$0.630844\pi$
$504$	2.62169e33	0.434710
$505$	3.27674e33	0.530029
$506$	4.17176e32	0.0658321
$507$	−1.65303e34	−2.54496
$508$	−1.88677e33	−0.283414
$509$	−7.74677e32	−0.113540	−0.0567699	−	0.998387i	$-0.518080\pi$
$509$	−7.74677e32	−0.113540	−0.0567699	+	0.998387i	$0.518080\pi$
$510$	−7.57467e33	−1.08327
$511$	6.76120e33	0.943544
$512$	−3.24519e32	−0.0441942
$513$	9.10574e33	1.21017
$514$	−1.77159e33	−0.229786
$515$	5.07837e33	0.642887
$516$	5.34948e32	0.0660983
$517$	4.37322e33	0.527436
$518$	4.50512e33	0.530376
$519$	−2.03991e34	−2.34433
$520$	2.19705e33	0.246490
$521$	−7.09925e33	−0.777573	−0.388786	−	0.921328i	$-0.627106\pi$
$521$	−7.09925e33	−0.777573	−0.388786	+	0.921328i	$0.627106\pi$
$522$	1.39990e34	1.49698
$523$	−8.65615e33	−0.903761	−0.451880	−	0.892079i	$-0.649247\pi$
$523$	−8.65615e33	−0.903761	−0.451880	+	0.892079i	$0.649247\pi$
$524$	3.80422e33	0.387815
$525$	2.02935e33	0.202007
$526$	−1.23270e34	−1.19821
$527$	−3.28486e33	−0.311806
$528$	−1.91138e33	−0.177184
$529$	−1.04423e34	−0.945367
$530$	−1.71922e33	−0.152013
$531$	−4.21428e34	−3.63950
$532$	1.96255e33	0.165549
$533$	3.37490e34	2.78081
$534$	1.28257e34	1.03232
$535$	7.29857e33	0.573873
$536$	1.03266e33	0.0793226
$537$	−7.51142e33	−0.563694
$538$	−2.08689e33	−0.153011
$539$	−3.76853e33	−0.269968
$540$	−6.62792e33	−0.463933
$541$	2.82575e34	1.93272	0.966358	−	0.257202i	$-0.0828007\pi$
$541$	2.82575e34	1.93272	0.966358	+	0.257202i	$0.0828007\pi$
$542$	−4.33918e33	−0.290013
$543$	2.04328e34	1.33454
$544$	5.33200e33	0.340333
$545$	1.46424e33	0.0913389
$546$	1.82624e34	1.11340
$547$	1.70002e34	1.01300	0.506502	−	0.862239i	$-0.330938\pi$
$547$	1.70002e34	1.01300	0.506502	+	0.862239i	$0.330938\pi$
$548$	1.14324e34	0.665855
$549$	−1.65211e33	−0.0940558
$550$	−1.01222e33	−0.0563301
$551$	1.04794e34	0.570088
$552$	−2.76489e33	−0.147041
$553$	−1.26176e34	−0.656015
$554$	−2.32519e34	−1.18192
$555$	−2.11571e34	−1.05146
$556$	8.44047e33	0.410140
$557$	1.04504e34	0.496529	0.248264	−	0.968692i	$-0.420140\pi$
$557$	1.04504e34	0.496529	0.248264	+	0.968692i	$0.420140\pi$
$558$	−5.33930e33	−0.248060
$559$	2.54940e33	0.115822
$560$	−1.42851e33	−0.0634649
$561$	3.14050e34	1.36447
$562$	6.16138e33	0.261803
$563$	−1.28118e34	−0.532421	−0.266211	−	0.963915i	$-0.585772\pi$
$563$	−1.28118e34	−0.532421	−0.266211	+	0.963915i	$0.585772\pi$
$564$	−2.89842e34	−1.17807
$565$	−7.85282e33	−0.312191
$566$	1.83080e34	0.711927
$567$	−2.27683e34	−0.866048
$568$	−1.53552e34	−0.571348
$569$	−6.19441e33	−0.225474	−0.112737	−	0.993625i	$-0.535962\pi$
$569$	−6.19441e33	−0.225474	−0.112737	+	0.993625i	$0.535962\pi$
$570$	−9.21661e33	−0.328198
$571$	5.43372e32	0.0189298	0.00946490	−	0.999955i	$-0.496987\pi$
$571$	5.43372e32	0.0189298	0.00946490	+	0.999955i	$0.496987\pi$
$572$	−9.10908e33	−0.310473
$573$	9.54553e34	3.18322
$574$	−2.19434e34	−0.715988
$575$	−1.46421e33	−0.0467473
$576$	8.66677e33	0.270755
$577$	1.51288e34	0.462495	0.231248	−	0.972895i	$-0.425719\pi$
$577$	1.51288e34	0.462495	0.231248	+	0.972895i	$0.425719\pi$
$578$	−6.39708e34	−1.91374
$579$	3.39402e34	0.993646
$580$	−7.62780e33	−0.218549
$581$	1.50944e34	0.423268
$582$	−1.15157e34	−0.316049
$583$	7.12795e33	0.191473
$584$	2.23511e34	0.587677
$585$	−5.86756e34	−1.51011
$586$	−1.77194e34	−0.446404
$587$	−3.71765e33	−0.0916837	−0.0458418	−	0.998949i	$-0.514597\pi$
$587$	−3.71765e33	−0.0916837	−0.0458418	+	0.998949i	$0.514597\pi$
$588$	2.49765e34	0.602996
$589$	−3.99691e33	−0.0944677
$590$	2.29629e34	0.531345
$591$	−3.63198e34	−0.822810
$592$	1.48930e34	0.330339
$593$	−4.27000e34	−0.927351	−0.463676	−	0.886005i	$-0.653470\pi$
$593$	−4.27000e34	−0.927351	−0.463676	+	0.886005i	$0.653470\pi$
$594$	2.74797e34	0.584361
$595$	2.34711e34	0.488734
$596$	1.22036e34	0.248835
$597$	4.20733e34	0.840093
$598$	−1.31767e34	−0.257656
$599$	−3.95633e34	−0.757631	−0.378816	−	0.925472i	$-0.623669\pi$
$599$	−3.95633e34	−0.757631	−0.378816	+	0.925472i	$0.623669\pi$
$600$	6.70863e33	0.125818
$601$	−5.03622e33	−0.0925069	−0.0462535	−	0.998930i	$-0.514728\pi$
$601$	−5.03622e33	−0.0925069	−0.0462535	+	0.998930i	$0.514728\pi$
$602$	−1.65761e33	−0.0298212
$603$	−2.75787e34	−0.485969
$604$	1.66569e33	0.0287496
$605$	−2.22552e34	−0.376261
$606$	9.00400e34	1.49117
$607$	−1.09922e35	−1.78331	−0.891655	−	0.452716i	$-0.850455\pi$
$607$	−1.09922e35	−1.78331	−0.891655	+	0.452716i	$0.850455\pi$
$608$	6.48780e33	0.103110
$609$	−6.34040e34	−0.987190
$610$	9.00207e32	0.0137315
$611$	−1.38130e35	−2.06430
$612$	−1.42399e35	−2.08504
$613$	−7.49713e34	−1.07557	−0.537786	−	0.843082i	$-0.680739\pi$
$613$	−7.49713e34	−1.07557	−0.537786	+	0.843082i	$0.680739\pi$
$614$	−5.77463e34	−0.811745
$615$	1.03051e35	1.41943
$616$	5.92268e33	0.0799391
$617$	9.19873e34	1.21664	0.608321	−	0.793691i	$-0.291843\pi$
$617$	9.19873e34	1.21664	0.608321	+	0.793691i	$0.291843\pi$
$618$	1.39546e35	1.80868
$619$	1.17365e35	1.49075	0.745375	−	0.666646i	$-0.232271\pi$
$619$	1.17365e35	1.49075	0.745375	+	0.666646i	$0.232271\pi$
$620$	2.90929e33	0.0362152
$621$	3.97505e34	0.484950
$622$	1.76515e34	0.211058
$623$	−3.97422e34	−0.465748
$624$	6.03718e34	0.693468
$625$	3.55271e33	0.0400000
$626$	9.21430e33	0.101691
$627$	3.82125e34	0.413391
$628$	−3.81125e33	−0.0404177
$629$	−2.44699e35	−2.54389
$630$	3.81506e34	0.388816
$631$	−5.93583e34	−0.593082	−0.296541	−	0.955020i	$-0.595833\pi$
$631$	−5.93583e34	−0.593082	−0.296541	+	0.955020i	$0.595833\pi$
$632$	−4.17113e34	−0.408592
$633$	2.78024e35	2.67015
$634$	−3.06024e34	−0.288164
$635$	−2.74561e34	−0.253493
$636$	−4.72415e34	−0.427671
$637$	1.19030e35	1.05661
$638$	3.16252e34	0.275280
$639$	4.10083e35	3.50035
$640$	−4.72237e33	−0.0395285
$641$	−6.98225e34	−0.573152	−0.286576	−	0.958058i	$-0.592517\pi$
$641$	−6.98225e34	−0.573152	−0.286576	+	0.958058i	$0.592517\pi$
$642$	2.00554e35	1.61452
$643$	4.37990e34	0.345802	0.172901	−	0.984939i	$-0.444686\pi$
$643$	4.37990e34	0.345802	0.172901	+	0.984939i	$0.444686\pi$
$644$	8.56739e33	0.0663400
$645$	7.78452e33	0.0591201
$646$	−1.06598e35	−0.794038
$647$	2.19963e35	1.60711	0.803555	−	0.595231i	$-0.202939\pi$
$647$	2.19963e35	1.60711	0.803555	+	0.595231i	$0.202939\pi$
$648$	−7.52673e34	−0.539410
$649$	−9.52052e34	−0.669271
$650$	3.19713e34	0.220467
$651$	2.41827e34	0.163585
$652$	8.68480e34	0.576322
$653$	−5.77474e34	−0.375939	−0.187970	−	0.982175i	$-0.560191\pi$
$653$	−5.77474e34	−0.375939	−0.187970	+	0.982175i	$0.560191\pi$
$654$	4.02352e34	0.256971
$655$	5.53587e34	0.346872
$656$	−7.25404e34	−0.445946
$657$	−5.96921e35	−3.60039
$658$	8.98113e34	0.531505
$659$	−2.55494e34	−0.148359	−0.0741793	−	0.997245i	$-0.523634\pi$
$659$	−2.55494e34	−0.148359	−0.0741793	+	0.997245i	$0.523634\pi$
$660$	−2.78143e34	−0.158478
$661$	1.14583e35	0.640623	0.320312	−	0.947312i	$-0.396212\pi$
$661$	1.14583e35	0.640623	0.320312	+	0.947312i	$0.396212\pi$
$662$	4.15385e34	0.227890
$663$	−9.91938e35	−5.34030
$664$	4.98991e34	0.263628
$665$	2.85589e34	0.148071
$666$	−3.97740e35	−2.02382
$667$	4.57471e34	0.228450
$668$	1.72747e34	0.0846652
$669$	2.69730e35	1.29749
$670$	1.50272e34	0.0709483
$671$	−3.73230e33	−0.0172960
$672$	−3.92534e34	−0.178551
$673$	1.32743e34	0.0592683	0.0296342	−	0.999561i	$-0.490566\pi$
$673$	1.32743e34	0.0592683	0.0296342	+	0.999561i	$0.490566\pi$
$674$	1.74921e35	0.766644
$675$	−9.64490e34	−0.414955
$676$	1.69327e35	0.715143
$677$	−1.09080e35	−0.452257	−0.226128	−	0.974098i	$-0.572607\pi$
$677$	−1.09080e35	−0.452257	−0.226128	+	0.974098i	$0.572607\pi$
$678$	−2.15784e35	−0.878310
$679$	3.56831e34	0.142590
$680$	7.75908e34	0.304403
$681$	8.36830e35	3.22328
$682$	−1.20621e34	−0.0456159
$683$	−2.56303e35	−0.951690	−0.475845	−	0.879529i	$-0.657858\pi$
$683$	−2.56303e35	−0.951690	−0.475845	+	0.879529i	$0.657858\pi$
$684$	−1.73267e35	−0.631704
$685$	1.66363e35	0.595559
$686$	−1.91580e35	−0.673438
$687$	−2.04769e35	−0.706814
$688$	−5.47971e33	−0.0185739
$689$	−2.25139e35	−0.749395
$690$	−4.02345e34	−0.131518
$691$	1.27544e35	0.409436	0.204718	−	0.978821i	$-0.434372\pi$
$691$	1.27544e35	0.409436	0.204718	+	0.978821i	$0.434372\pi$
$692$	2.08957e35	0.658766
$693$	−1.58174e35	−0.489745
$694$	−5.85696e33	−0.0178106
$695$	1.22825e35	0.366840
$696$	−2.09601e35	−0.614861
$697$	1.19187e36	3.43416
$698$	−1.45642e34	−0.0412187
$699$	9.34471e35	2.59777
$700$	−2.07876e34	−0.0567647
$701$	−3.29520e35	−0.883907	−0.441953	−	0.897038i	$-0.645714\pi$
$701$	−3.29520e35	−0.883907	−0.441953	+	0.897038i	$0.645714\pi$
$702$	−8.67957e35	−2.28709
$703$	−2.97742e35	−0.770722
$704$	1.95792e34	0.0497893
$705$	−4.21775e35	−1.05370
$706$	−2.71963e35	−0.667500
$707$	−2.79001e35	−0.672764
$708$	6.30987e35	1.49487
$709$	−3.54372e35	−0.824863	−0.412432	−	0.910989i	$-0.635320\pi$
$709$	−3.54372e35	−0.824863	−0.412432	+	0.910989i	$0.635320\pi$
$710$	−2.23447e35	−0.511029
$711$	1.11396e36	2.50323
$712$	−1.31379e35	−0.290086
$713$	−1.74482e34	−0.0378558
$714$	6.44953e35	1.37499
$715$	−1.32555e35	−0.277696
$716$	7.69429e34	0.158400
$717$	−9.91715e35	−2.00631
$718$	7.63230e34	0.151740
$719$	8.25549e34	0.161299	0.0806495	−	0.996743i	$-0.474301\pi$
$719$	8.25549e34	0.161299	0.0806495	+	0.996743i	$0.474301\pi$
$720$	1.26118e35	0.242170
$721$	−4.32403e35	−0.816014
$722$	2.51537e35	0.466538
$723$	8.37424e35	1.52657
$724$	−2.09302e35	−0.375010
$725$	−1.10999e35	−0.195476
$726$	−6.11541e35	−1.05857
$727$	8.59682e35	1.46271	0.731354	−	0.681998i	$-0.238889\pi$
$727$	8.59682e35	1.46271	0.731354	+	0.681998i	$0.238889\pi$
$728$	−1.87070e35	−0.312869
$729$	−2.35421e35	−0.387036
$730$	3.25252e35	0.525634
$731$	9.00343e34	0.143035
$732$	2.47364e34	0.0386320
$733$	1.11362e36	1.70977	0.854883	−	0.518821i	$-0.173629\pi$
$733$	1.11362e36	1.70977	0.854883	+	0.518821i	$0.173629\pi$
$734$	−3.54825e35	−0.535567
$735$	3.63456e35	0.539336
$736$	2.83220e34	0.0413192
$737$	−6.23034e34	−0.0893651
$738$	1.93730e36	2.73208
$739$	8.39662e34	0.116426	0.0582129	−	0.998304i	$-0.481460\pi$
$739$	8.39662e34	0.116426	0.0582129	+	0.998304i	$0.481460\pi$
$740$	2.16721e35	0.295465
$741$	−1.20696e36	−1.61795
$742$	1.46384e35	0.192950
$743$	−8.61824e35	−1.11701	−0.558506	−	0.829500i	$-0.688625\pi$
$743$	−8.61824e35	−1.11701	−0.558506	+	0.829500i	$0.688625\pi$
$744$	7.99430e34	0.101887
$745$	1.77586e35	0.222564
$746$	1.03582e36	1.27658
$747$	−1.33263e36	−1.61511
$748$	−3.21695e35	−0.383420
$749$	−6.21444e35	−0.728415
$750$	9.76234e34	0.112535
$751$	−8.00202e35	−0.907195	−0.453597	−	0.891207i	$-0.649860\pi$
$751$	−8.00202e35	−0.907195	−0.453597	+	0.891207i	$0.649860\pi$
$752$	2.96898e35	0.331043
$753$	−4.12356e35	−0.452204
$754$	−9.98894e35	−1.07740
$755$	2.42389e34	0.0257144
$756$	5.64341e35	0.588869
$757$	−7.91448e35	−0.812314	−0.406157	−	0.913803i	$-0.633131\pi$
$757$	−7.91448e35	−0.812314	−0.406157	+	0.913803i	$0.633131\pi$
$758$	3.23577e35	0.326673
$759$	1.66814e35	0.165657
$760$	9.44099e34	0.0922247
$761$	2.09934e34	0.0201732	0.0100866	−	0.999949i	$-0.496789\pi$
$761$	2.09934e34	0.0201732	0.0100866	+	0.999949i	$0.496789\pi$
$762$	−7.54452e35	−0.713173
$763$	−1.24674e35	−0.115936
$764$	−9.77792e35	−0.894498
$765$	−2.07218e36	−1.86492
$766$	−8.60607e35	−0.761983
$767$	3.00709e36	2.61942
$768$	−1.29764e35	−0.111209
$769$	−7.23123e35	−0.609723	−0.304862	−	0.952397i	$-0.598610\pi$
$769$	−7.23123e35	−0.609723	−0.304862	+	0.952397i	$0.598610\pi$
$770$	8.61863e34	0.0714997
$771$	−7.08396e35	−0.578225
$772$	−3.47664e35	−0.279218
$773$	−1.19333e36	−0.943014	−0.471507	−	0.881862i	$-0.656290\pi$
$773$	−1.19333e36	−0.943014	−0.471507	+	0.881862i	$0.656290\pi$
$774$	1.46344e35	0.113792
$775$	4.23357e34	0.0323919
$776$	1.17961e35	0.0888110
$777$	1.80144e36	1.33462
$778$	−5.71531e35	−0.416672
$779$	1.45023e36	1.04045
$780$	8.78525e35	0.620257
$781$	9.26423e35	0.643682
$782$	−4.65345e35	−0.318193
$783$	3.01340e36	2.02784
$784$	−2.55845e35	−0.169444
$785$	−5.54610e34	−0.0361507
$786$	1.52118e36	0.975883
$787$	4.78974e35	0.302432	0.151216	−	0.988501i	$-0.451681\pi$
$787$	4.78974e35	0.302432	0.151216	+	0.988501i	$0.451681\pi$
$788$	3.72040e35	0.231213
$789$	−4.92912e36	−3.01514
$790$	−6.06979e35	−0.365456
$791$	6.68636e35	0.396263
$792$	−5.22891e35	−0.305033
$793$	1.17886e35	0.0676937
$794$	6.51114e35	0.368045
$795$	−6.87455e35	−0.382521
$796$	−4.30975e35	−0.236069
$797$	2.29881e36	1.23958	0.619788	−	0.784769i	$-0.287218\pi$
$797$	2.29881e36	1.23958	0.619788	+	0.784769i	$0.287218\pi$
$798$	7.84757e35	0.416581
$799$	−4.87818e36	−2.54931
$800$	−6.87195e34	−0.0353553
$801$	3.50869e36	1.77721
$802$	−1.81604e36	−0.905621
$803$	−1.34851e36	−0.662078
$804$	4.12925e35	0.199604
$805$	1.24672e35	0.0593363
$806$	3.80985e35	0.178533
$807$	−8.34476e35	−0.385030
$808$	−9.22320e35	−0.419025
$809$	1.08839e36	0.486885	0.243442	−	0.969915i	$-0.421723\pi$
$809$	1.08839e36	0.486885	0.243442	+	0.969915i	$0.421723\pi$
$810$	−1.09528e36	−0.482463
$811$	4.47699e36	1.94189	0.970946	−	0.239299i	$-0.0769178\pi$
$811$	4.47699e36	1.94189	0.970946	+	0.239299i	$0.0769178\pi$
$812$	6.49476e35	0.277404
$813$	−1.73509e36	−0.729776
$814$	−8.98537e35	−0.372161
$815$	1.26380e36	0.515478
$816$	2.13208e36	0.856400
$817$	1.09551e35	0.0433351
$818$	5.79056e35	0.225582
$819$	4.99599e36	1.91678
$820$	−1.05560e36	−0.398866
$821$	3.35501e36	1.24855	0.624274	−	0.781206i	$-0.285395\pi$
$821$	3.35501e36	1.24855	0.624274	+	0.781206i	$0.285395\pi$
$822$	4.57141e36	1.67553
$823$	−1.04609e36	−0.377636	−0.188818	−	0.982012i	$-0.560466\pi$
$823$	−1.04609e36	−0.377636	−0.188818	+	0.982012i	$0.560466\pi$
$824$	−1.42944e36	−0.508246
$825$	−4.04751e35	−0.141747
$826$	−1.95520e36	−0.674435
$827$	−1.70274e36	−0.578535	−0.289267	−	0.957248i	$-0.593412\pi$
$827$	−1.70274e36	−0.578535	−0.289267	+	0.957248i	$0.593412\pi$
$828$	−7.56383e35	−0.253141
$829$	3.63214e36	1.19738	0.598688	−	0.800983i	$-0.295689\pi$
$829$	3.63214e36	1.19738	0.598688	+	0.800983i	$0.295689\pi$
$830$	7.26128e35	0.235796
$831$	−9.29763e36	−2.97413
$832$	−6.18415e35	−0.194867
$833$	4.20366e36	1.30486
$834$	3.37505e36	1.03206
$835$	2.51380e35	0.0757269
$836$	−3.91428e35	−0.116164
$837$	−1.14933e36	−0.336029
$838$	−2.31708e36	−0.667407
$839$	−4.10710e36	−1.16550	−0.582748	−	0.812653i	$-0.698023\pi$
$839$	−4.10710e36	−1.16550	−0.582748	+	0.812653i	$0.698023\pi$
$840$	−5.71212e35	−0.159701
$841$	−1.62368e35	−0.0447251
$842$	3.80476e36	1.03258
$843$	2.46372e36	0.658790
$844$	−2.84793e36	−0.750323
$845$	2.46403e36	0.639643
$846$	−7.92911e36	−2.02813
$847$	1.89494e36	0.477588
$848$	4.83916e35	0.120177
$849$	7.32074e36	1.79147
$850$	1.12909e36	0.272266
$851$	−1.29977e36	−0.308850
$852$	−6.14000e36	−1.43772
$853$	2.01380e36	0.464680	0.232340	−	0.972635i	$-0.425362\pi$
$853$	2.01380e36	0.464680	0.232340	+	0.972635i	$0.425362\pi$
$854$	−7.66490e34	−0.0174294
$855$	−2.52136e36	−0.565013
$856$	−2.05437e36	−0.453686
$857$	−3.20819e36	−0.698232	−0.349116	−	0.937080i	$-0.613518\pi$
$857$	−3.20819e36	−0.698232	−0.349116	+	0.937080i	$0.613518\pi$
$858$	−3.64241e36	−0.781263
$859$	−1.62270e36	−0.343024	−0.171512	−	0.985182i	$-0.554865\pi$
$859$	−1.62270e36	−0.343024	−0.171512	+	0.985182i	$0.554865\pi$
$860$	−7.97403e34	−0.0166130
$861$	−8.77441e36	−1.80168
$862$	4.10739e36	0.831237
$863$	2.34665e36	0.468074	0.234037	−	0.972228i	$-0.424806\pi$
$863$	2.34665e36	0.468074	0.234037	+	0.972228i	$0.424806\pi$
$864$	1.86559e36	0.366771
$865$	3.04073e36	0.589218
$866$	2.17991e35	0.0416356
$867$	−2.55797e37	−4.81567
$868$	−2.47714e35	−0.0459679
$869$	2.51656e36	0.460321
$870$	−3.05009e36	−0.549949
$871$	1.96788e36	0.349761
$872$	−4.12147e35	−0.0722098
$873$	−3.15033e36	−0.544099
$874$	−5.66216e35	−0.0964027
$875$	−3.02499e35	−0.0507719
$876$	8.93744e36	1.47881
$877$	−1.82745e36	−0.298092	−0.149046	−	0.988830i	$-0.547620\pi$
$877$	−1.82745e36	−0.298092	−0.149046	+	0.988830i	$0.547620\pi$
$878$	2.02894e36	0.326278
$879$	−7.08537e36	−1.12331
$880$	2.84914e35	0.0445329
$881$	1.92548e36	0.296715	0.148358	−	0.988934i	$-0.452601\pi$
$881$	1.92548e36	0.296715	0.148358	+	0.988934i	$0.452601\pi$
$882$	6.83274e36	1.03810
$883$	5.88853e36	0.882060	0.441030	−	0.897492i	$-0.354613\pi$
$883$	5.88853e36	0.882060	0.441030	+	0.897492i	$0.354613\pi$
$884$	1.01609e37	1.50064
$885$	9.18206e36	1.33706
$886$	2.45842e36	0.352967
$887$	1.17351e37	1.66128	0.830640	−	0.556809i	$-0.187975\pi$
$887$	1.17351e37	1.66128	0.830640	+	0.556809i	$0.187975\pi$
$888$	5.95519e36	0.831253
$889$	2.33777e36	0.321759
$890$	−1.91182e36	−0.259461
$891$	4.54110e36	0.607700
$892$	−2.76296e36	−0.364598
$893$	−5.93560e36	−0.772363
$894$	4.87981e36	0.626158
$895$	1.11967e36	0.141677
$896$	4.02090e35	0.0501734
$897$	−5.26889e36	−0.648356
$898$	−1.00164e35	−0.0121551
$899$	−1.32271e36	−0.158296
$900$	1.83526e36	0.216604
$901$	−7.95098e36	−0.925467
$902$	4.37658e36	0.502404
$903$	−6.62820e35	−0.0750410
$904$	2.21037e36	0.246808
$905$	−3.04575e36	−0.335419
$906$	6.66051e35	0.0723444
$907$	9.60913e36	1.02942	0.514711	−	0.857364i	$-0.327899\pi$
$907$	9.60913e36	1.02942	0.514711	+	0.857364i	$0.327899\pi$
$908$	−8.57203e36	−0.905754
$909$	2.46320e37	2.56715
$910$	−2.72223e36	−0.279838
$911$	3.31132e36	0.335754	0.167877	−	0.985808i	$-0.446309\pi$
$911$	3.31132e36	0.335754	0.167877	+	0.985808i	$0.446309\pi$
$912$	2.59424e36	0.259463
$913$	−3.01056e36	−0.297004
$914$	6.76849e36	0.658665
$915$	3.59962e35	0.0345535
$916$	2.09754e36	0.198617
$917$	−4.71357e36	−0.440284
$918$	−3.06526e37	−2.82445
$919$	−6.37787e36	−0.579738	−0.289869	−	0.957066i	$-0.593612\pi$
$919$	−6.37787e36	−0.579738	−0.289869	+	0.957066i	$0.593612\pi$
$920$	4.12140e35	0.0369570
$921$	−2.30908e37	−2.04264
$922$	−4.78281e36	−0.417394
$923$	−2.92614e37	−2.51927
$924$	2.36827e36	0.201156
$925$	3.15371e36	0.264272
$926$	9.79880e36	0.810094
$927$	3.81753e37	3.11376
$928$	2.14703e36	0.172778
$929$	−1.01760e37	−0.807940	−0.403970	−	0.914772i	$-0.632370\pi$
$929$	−1.01760e37	−0.807940	−0.403970	+	0.914772i	$0.632370\pi$
$930$	1.16332e36	0.0911305
$931$	5.11488e36	0.395334
$932$	−9.57221e36	−0.729984
$933$	7.05824e36	0.531099
$934$	−1.83239e37	−1.36045
$935$	−4.68128e36	−0.342941
$936$	1.65157e37	1.19385
$937$	5.01714e36	0.357859	0.178929	−	0.983862i	$-0.442737\pi$
$937$	5.01714e36	0.357859	0.178929	+	0.983862i	$0.442737\pi$
$938$	−1.27950e36	−0.0900546
$939$	3.68448e36	0.255892
$940$	4.32043e36	0.296094
$941$	1.04889e37	0.709348	0.354674	−	0.934990i	$-0.384592\pi$
$941$	1.04889e37	0.709348	0.354674	+	0.934990i	$0.384592\pi$
$942$	−1.52399e36	−0.101706
$943$	6.33089e36	0.416936
$944$	−6.46348e36	−0.420065
$945$	8.21224e36	0.526701
$946$	3.30607e35	0.0209254
$947$	−3.09440e37	−1.93286	−0.966432	−	0.256923i	$-0.917291\pi$
$947$	−3.09440e37	−1.93286	−0.966432	+	0.256923i	$0.917291\pi$
$948$	−1.66789e37	−1.02817
$949$	4.25932e37	2.59127
$950$	1.37384e36	0.0824883
$951$	−1.22368e37	−0.725125
$952$	−6.60654e36	−0.386378
$953$	−2.63074e34	−0.00151851	−0.000759254	−	1.00000i	$-0.500242\pi$
$953$	−2.63074e34	−0.00151851	−0.000759254		1.00000i	$0.500242\pi$
$954$	−1.29237e37	−0.736263
$955$	−1.42287e37	−0.800063
$956$	1.01586e37	0.563780
$957$	1.26458e37	0.692704
$958$	−9.57503e36	−0.517692
$959$	−1.41651e37	−0.755941
$960$	−1.88831e36	−0.0994679
$961$	−1.87283e37	−0.973769
$962$	2.83807e37	1.45658
$963$	5.48650e37	2.77950
$964$	−8.57811e36	−0.428972
$965$	−5.05918e36	−0.249740
$966$	3.42580e36	0.166935
$967$	−1.63641e37	−0.787158	−0.393579	−	0.919291i	$-0.628763\pi$
$967$	−1.63641e37	−0.787158	−0.393579	+	0.919291i	$0.628763\pi$
$968$	6.26429e36	0.297461
$969$	−4.26247e37	−1.99809
$970$	1.71656e36	0.0794350
$971$	−3.01907e37	−1.37922	−0.689610	−	0.724181i	$-0.742218\pi$
$971$	−3.01907e37	−1.37922	−0.689610	+	0.724181i	$0.742218\pi$
$972$	−7.09461e36	−0.319963
$973$	−1.04581e37	−0.465629
$974$	5.23376e36	0.230053
$975$	1.27842e37	0.554775
$976$	−2.53386e35	−0.0108557
$977$	−3.79611e36	−0.160567	−0.0802837	−	0.996772i	$-0.525583\pi$
$977$	−3.79611e36	−0.160567	−0.0802837	+	0.996772i	$0.525583\pi$
$978$	3.47275e37	1.45023
$979$	7.92650e36	0.326812
$980$	−3.72304e36	−0.151555
$981$	1.10070e37	0.442392
$982$	−2.24509e37	−0.890923
$983$	−6.46957e36	−0.253487	−0.126744	−	0.991936i	$-0.540453\pi$
$983$	−6.46957e36	−0.253487	−0.126744	+	0.991936i	$0.540453\pi$
$984$	−2.90064e37	−1.12216
$985$	5.41389e36	0.206803
$986$	−3.52768e37	−1.33054
$987$	3.59124e37	1.33746
$988$	1.23634e37	0.454649
$989$	4.78236e35	0.0173656
$990$	−7.60907e36	−0.272830
$991$	−3.19318e37	−1.13058	−0.565291	−	0.824891i	$-0.691236\pi$
$991$	−3.19318e37	−1.13058	−0.565291	+	0.824891i	$0.691236\pi$
$992$	−8.18892e35	−0.0286306
$993$	1.66098e37	0.573455
$994$	1.90256e37	0.648648
$995$	−6.27152e36	−0.211147
$996$	1.99529e37	0.663384
$997$	3.10721e37	1.02019	0.510095	−	0.860118i	$-0.329610\pi$
$997$	3.10721e37	1.02019	0.510095	+	0.860118i	$0.329610\pi$
$998$	−1.32686e37	−0.430224
$999$	−8.56169e37	−2.74152

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	10.26.a.b.1.1	✓	2
5.2	odd	4		50.26.b.f.49.2		4
5.3	odd	4		50.26.b.f.49.3		4
5.4	even	2		50.26.a.f.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
10.26.a.b.1.1	✓	2	1.1	even	1	trivial
50.26.a.f.1.2		2	5.4	even	2
50.26.b.f.49.2		4	5.2	odd	4
50.26.b.f.49.3		4	5.3	odd	4

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:	\( N \)	\(=\)	\( 10 = 2 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	10.a (trivial)

\(f(q)\)	\(=\)	\(q-4096.00 q^{2} -1.63785e6 q^{3} +1.67772e7 q^{4} +2.44141e8 q^{5} +6.70863e9 q^{6} -2.07876e10 q^{7} -6.87195e10 q^{8} +1.83526e12 q^{9} -1.00000e12 q^{10} +4.14605e12 q^{11} -2.74785e13 q^{12} -1.30955e14 q^{13} +8.51459e13 q^{14} -3.99865e14 q^{15} +2.81475e14 q^{16} -4.62477e15 q^{17} -7.51722e15 q^{18} -5.62727e15 q^{19} +4.09600e15 q^{20} +3.40469e16 q^{21} -1.69822e16 q^{22} -2.45654e16 q^{23} +1.12552e17 q^{24} +5.96046e16 q^{25} +5.36390e17 q^{26} -1.61815e18 q^{27} -3.48758e17 q^{28} -1.86225e18 q^{29} +1.63785e18 q^{30} +7.10276e17 q^{31} -1.15292e18 q^{32} -6.79060e18 q^{33} +1.89431e19 q^{34} -5.07509e18 q^{35} +3.07905e19 q^{36} +5.29105e19 q^{37} +2.30493e19 q^{38} +2.14484e20 q^{39} -1.67772e19 q^{40} -2.57715e20 q^{41} -1.39456e20 q^{42} -1.94678e19 q^{43} +6.95591e19 q^{44} +4.48061e20 q^{45} +1.00620e20 q^{46} +1.05479e21 q^{47} -4.61013e20 q^{48} -9.08945e20 q^{49} -2.44141e20 q^{50} +7.57467e21 q^{51} -2.19705e21 q^{52} +1.71922e21 q^{53} +6.62792e21 q^{54} +1.01222e21 q^{55} +1.42851e21 q^{56} +9.21661e21 q^{57} +7.62780e21 q^{58} -2.29629e22 q^{59} -6.70863e21 q^{60} -9.00207e20 q^{61} -2.90929e21 q^{62} -3.81506e22 q^{63} +4.72237e21 q^{64} -3.19713e22 q^{65} +2.78143e22 q^{66} -1.50272e22 q^{67} -7.75908e22 q^{68} +4.02345e22 q^{69} +2.07876e22 q^{70} +2.23447e23 q^{71} -1.26118e23 q^{72} -3.25252e23 q^{73} -2.16721e23 q^{74} -9.76234e22 q^{75} -9.44099e22 q^{76} -8.61863e22 q^{77} -8.78525e23 q^{78} +6.06979e23 q^{79} +6.87195e22 q^{80} +1.09528e24 q^{81} +1.05560e24 q^{82} -7.26128e23 q^{83} +5.71212e23 q^{84} -1.12909e24 q^{85} +7.97403e22 q^{86} +3.05009e24 q^{87} -2.84914e23 q^{88} +1.91182e24 q^{89} -1.83526e24 q^{90} +2.72223e24 q^{91} -4.12140e23 q^{92} -1.16332e24 q^{93} -4.32043e24 q^{94} -1.37384e24 q^{95} +1.88831e24 q^{96} -1.71656e24 q^{97} +3.72304e24 q^{98} +7.60907e24 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 8192 q^{2} - 438588 q^{3} + 33554432 q^{4} + 488281250 q^{5} + 1796456448 q^{6} - 34008596636 q^{7} - 137438953472 q^{8} + 2426195859786 q^{9} - 2000000000000 q^{10} + 19344682791984 q^{11} - 7358285611008 q^{12}+ \cdots + 16\!\cdots\!12 q^{99}+O(q^{100}) \) 2 * q - 8192 * q^2 - 438588 * q^3 + 33554432 * q^4 + 488281250 * q^5 + 1796456448 * q^6 - 34008596636 * q^7 - 137438953472 * q^8 + 2426195859786 * q^9 - 2000000000000 * q^10 + 19344682791984 * q^11 - 7358285611008 * q^12 - 127796048033588 * q^13 + 139299211821056 * q^14 - 107077148437500 * q^15 + 562949953421312 * q^16 - 2998857935578476 * q^17 - 9937698241683456 * q^18 + 13534782395320 * q^19 + 8192000000000000 * q^20 + 18191471686615584 * q^21 - 79235820715966464 * q^22 - 176800520782624068 * q^23 + 30139537862688768 * q^24 + 119209289550781250 * q^25 + 523452612745576448 * q^26 - 1925577931602663000 * q^27 - 570569571619045376 * q^28 - 1676097487309033380 * q^29 + 438588000000000000 * q^30 + 7125865156346376664 * q^31 - 2305843009213693952 * q^32 + 11436524032432880304 * q^33 + 12283322104129437696 * q^34 - 8302880038085937500 * q^35 + 40704811997935435776 * q^36 + 84009823521808944364 * q^37 - 55438468691230720 * q^38 + 218271507658245788472 * q^39 - 33554432000000000000 * q^40 - 278976945138543009756 * q^41 - 74512268028377432064 * q^42 + 426481602906822493732 * q^43 + 324549921652598636544 * q^44 + 592332973580566406250 * q^45 + 724174933125628182528 * q^46 + 1107620660641184540244 * q^47 - 123451547085573193728 * q^48 - 2075218430900234303166 * q^49 - 488281250000000000000 * q^50 + 9524566337524637542344 * q^51 - 2144061901805881131008 * q^52 + 4105636904637626409852 * q^53 + 7887167207844507648000 * q^54 + 4722822947261718750000 * q^55 + 2337052965351609860096 * q^56 + 15981397362106388525520 * q^57 + 6865295308017800724480 * q^58 - 3765561121989768768360 * q^59 - 1796456448000000000000 * q^60 + 1088840609004402816124 * q^61 - 29187543680394758815744 * q^62 - 45963382166122467752748 * q^63 + 9444732965739290427392 * q^64 - 31200207039450195312500 * q^65 - 46844002436845077725184 * q^66 - 118164954526157928047156 * q^67 - 50312487338514176802816 * q^68 - 142335029641186502306208 * q^69 + 34008596636000000000000 * q^70 + 121487502051587284868424 * q^71 - 166726909943543544938496 * q^72 + 1543159074817774555972 * q^73 - 344104237145329436114944 * q^74 - 26141881942749023437500 * q^75 + 227075967759281029120 * q^76 - 287127672428028283409712 * q^77 - 894040095368174749581312 * q^78 + 821388705533644841730640 * q^79 + 137438953472000000000000 * q^80 + 225897583488924285462402 * q^81 + 1142689567287472167960576 * q^82 + 1078689963931157206149252 * q^83 + 305202249844233961734144 * q^84 - 732143050678338867187500 * q^85 - 1746868645506344934326272 * q^86 + 3273342747249083127820920 * q^87 - 1329356479089044015284224 * q^88 + 5059219929404495720992980 * q^89 - 2426195859786000000000000 * q^90 + 2680469809760336269552184 * q^91 - 2966220526082573035634688 * q^92 + 6530638201511067276729984 * q^93 - 4536814225986291876839424 * q^94 + 3304390233232421875000 * q^95 + 505657536862507801509888 * q^96 + 2393368330790785393982164 * q^97 + 8500094692967359705767936 * q^98 + 16590506333144186236452912 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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