LMFDB - Embedded newform 25.10.b.a.24.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,10,Mod(24,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1]))

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

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	25.b (of order $2$, degree $1$, not minimal)

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:	no
Analytic conductor:	$12.8758959041$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(i)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} + 1 $ x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.1
Root			$-1.00000i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.10.b.a.24.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000i q^{2} +114.000i q^{3} +448.000 q^{4} +912.000 q^{6} +4242.00i q^{7} -7680.00i q^{8} +6687.00 q^{9} +O(q^{10})$	\(q-8.00000i q^{2} +114.000i q^{3} +448.000 q^{4} +912.000 q^{6} +4242.00i q^{7} -7680.00i q^{8} +6687.00 q^{9} -46208.0 q^{11} +51072.0i q^{12} +115934. i q^{13} +33936.0 q^{14} +167936. q^{16} +494842. i q^{17} -53496.0i q^{18} +1.00874e6 q^{19} -483588. q^{21} +369664. i q^{22} +532554. i q^{23} +875520. q^{24} +927472. q^{26} +3.00618e6i q^{27} +1.90042e6i q^{28} -4.19639e6 q^{29} -3.36503e6 q^{31} -5.27565e6i q^{32} -5.26771e6i q^{33} +3.95874e6 q^{34} +2.99578e6 q^{36} -1.49314e7i q^{37} -8.06992e6i q^{38} -1.32165e7 q^{39} +1.10563e7 q^{41} +3.86870e6i q^{42} +6.39679e6i q^{43} -2.07012e7 q^{44} +4.26043e6 q^{46} -3.55592e7i q^{47} +1.91447e7i q^{48} +2.23590e7 q^{49} -5.64120e7 q^{51} +5.19384e7i q^{52} -3.97386e7i q^{53} +2.40494e7 q^{54} +3.25786e7 q^{56} +1.14996e8i q^{57} +3.35711e7i q^{58} +8.51856e7 q^{59} +4.57486e7 q^{61} +2.69202e7i q^{62} +2.83663e7i q^{63} +4.37780e7 q^{64} -4.21417e7 q^{66} -4.52862e7i q^{67} +2.21689e8i q^{68} -6.07112e7 q^{69} -1.89967e8 q^{71} -5.13562e7i q^{72} -4.12171e8i q^{73} -1.19451e8 q^{74} +4.51916e8 q^{76} -1.96014e8i q^{77} +1.05732e8i q^{78} -9.50408e7 q^{79} -2.11084e8 q^{81} -8.84501e7i q^{82} -2.61706e8i q^{83} -2.16647e8 q^{84} +5.11744e7 q^{86} -4.78388e8i q^{87} +3.54877e8i q^{88} +1.99386e7 q^{89} -4.91792e8 q^{91} +2.38584e8i q^{92} -3.83613e8i q^{93} -2.84473e8 q^{94} +6.01424e8 q^{96} -1.95034e7i q^{97} -1.78872e8i q^{98} -3.08993e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 896 q^{4} + 1824 q^{6} + 13374 q^{9}+O(q^{10}) $ 2 * q + 896 * q^4 + 1824 * q^6 + 13374 * q^9	$ 2 q + 896 q^{4} + 1824 q^{6} + 13374 q^{9} - 92416 q^{11} + 67872 q^{14} + 335872 q^{16} + 2017480 q^{19} - 967176 q^{21} + 1751040 q^{24} + 1854944 q^{26} - 8392780 q^{29} - 6730056 q^{31} + 7917472 q^{34} + 5991552 q^{36} - 26432952 q^{39} + 22112524 q^{41} - 41402368 q^{44} + 8520864 q^{46} + 44718086 q^{49} - 112823976 q^{51} + 48098880 q^{54} + 65157120 q^{56} + 170371240 q^{59} + 91497284 q^{61} + 87556096 q^{64} - 84283392 q^{66} - 121422312 q^{69} - 379934936 q^{71} - 238901728 q^{74} + 903831040 q^{76} - 190081680 q^{79} - 422168598 q^{81} - 433294848 q^{84} + 102348704 q^{86} + 39877260 q^{89} - 983584056 q^{91} - 568946528 q^{94} + 1202847744 q^{96} - 617985792 q^{99}+O(q^{100}) $ 2 * q + 896 * q^4 + 1824 * q^6 + 13374 * q^9 - 92416 * q^11 + 67872 * q^14 + 335872 * q^16 + 2017480 * q^19 - 967176 * q^21 + 1751040 * q^24 + 1854944 * q^26 - 8392780 * q^29 - 6730056 * q^31 + 7917472 * q^34 + 5991552 * q^36 - 26432952 * q^39 + 22112524 * q^41 - 41402368 * q^44 + 8520864 * q^46 + 44718086 * q^49 - 112823976 * q^51 + 48098880 * q^54 + 65157120 * q^56 + 170371240 * q^59 + 91497284 * q^61 + 87556096 * q^64 - 84283392 * q^66 - 121422312 * q^69 - 379934936 * q^71 - 238901728 * q^74 + 903831040 * q^76 - 190081680 * q^79 - 422168598 * q^81 - 433294848 * q^84 + 102348704 * q^86 + 39877260 * q^89 - 983584056 * q^91 - 568946528 * q^94 + 1202847744 * q^96 - 617985792 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$-1$

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 $

$2$	− 8.00000i	− 0.353553i	−0.984251	−	0.176777i	$-0.943433\pi$
$2$	− 8.00000i	− 0.353553i	0.984251	−	0.176777i	$-0.0565670\pi$
$3$	114.000i	0.812567i	0.913747	+	0.406284i	$0.133175\pi$
$3$	114.000i	0.812567i	−0.913747	+	0.406284i	$0.866825\pi$
$4$	448.000	0.875000
$5$	0	0
$5$	0	0
$6$	912.000	0.287286
$7$	4242.00i	0.667774i	0.942613	+	0.333887i	$0.108360\pi$
$7$	4242.00i	0.667774i	−0.942613	+	0.333887i	$0.891640\pi$
$8$	− 7680.00i	− 0.662913i
$9$	6687.00	0.339735
$10$	0	0
$11$	−46208.0	−0.951590	−0.475795	−	0.879556i	$-0.657840\pi$
$11$	−46208.0	−0.951590	−0.475795	+	0.879556i	$0.657840\pi$
$12$	51072.0i	0.710996i
$13$	115934.i	1.12581i	0.826521	+	0.562906i	$0.190317\pi$
$13$	115934.i	1.12581i	−0.826521	+	0.562906i	$0.809683\pi$
$14$	33936.0	0.236094
$15$	0	0
$16$	167936.	0.640625
$17$	494842.i	1.43697i	0.695545	+	0.718483i	$0.255163\pi$
$17$	494842.i	1.43697i	−0.695545	+	0.718483i	$0.744837\pi$
$18$	− 53496.0i	− 0.120114i
$19$	1.00874e6	1.77578	0.887888	−	0.460060i	$-0.152172\pi$
$19$	1.00874e6	1.77578	0.887888	+	0.460060i	$0.152172\pi$
$20$	0	0
$21$	−483588.	−0.542611
$22$	369664.i	0.336438i
$23$	532554.i	0.396815i	0.980120	+	0.198408i	$0.0635770\pi$
$23$	532554.i	0.396815i	−0.980120	+	0.198408i	$0.936423\pi$
$24$	875520.	0.538661
$25$	0	0
$26$	927472.	0.398035
$27$	3.00618e6i	1.08862i
$28$	1.90042e6i	0.584302i
$29$	−4.19639e6	−1.10175	−0.550877	−	0.834586i	$-0.685707\pi$
$29$	−4.19639e6	−1.10175	−0.550877	+	0.834586i	$0.685707\pi$
$30$	0	0
$31$	−3.36503e6	−0.654427	−0.327213	−	0.944950i	$-0.606110\pi$
$31$	−3.36503e6	−0.654427	−0.327213	+	0.944950i	$0.606110\pi$
$32$	− 5.27565e6i	− 0.889408i
$33$	− 5.26771e6i	− 0.773231i
$34$	3.95874e6	0.508044
$35$	0	0
$36$	2.99578e6	0.297268
$37$	− 1.49314e7i	− 1.30976i	−0.755733	−	0.654880i	$-0.772719\pi$
$37$	− 1.49314e7i	− 1.30976i	0.755733	−	0.654880i	$-0.227281\pi$
$38$	− 8.06992e6i	− 0.627831i
$39$	−1.32165e7	−0.914797
$40$	0	0
$41$	1.10563e7	0.611056	0.305528	−	0.952183i	$-0.401167\pi$
$41$	1.10563e7	0.611056	0.305528	+	0.952183i	$0.401167\pi$
$42$	3.86870e6i	0.191842i
$43$	6.39679e6i	0.285335i	0.989771	+	0.142667i	$0.0455679\pi$
$43$	6.39679e6i	0.285335i	−0.989771	+	0.142667i	$0.954432\pi$
$44$	−2.07012e7	−0.832642
$45$	0	0
$46$	4.26043e6	0.140295
$47$	− 3.55592e7i	− 1.06295i	−0.847075	−	0.531473i	$-0.821639\pi$
$47$	− 3.55592e7i	− 1.06295i	0.847075	−	0.531473i	$-0.178361\pi$
$48$	1.91447e7i	0.520551i
$49$	2.23590e7	0.554078
$50$	0	0
$51$	−5.64120e7	−1.16763
$52$	5.19384e7i	0.985085i
$53$	− 3.97386e7i	− 0.691785i	−0.938274	−	0.345892i	$-0.887576\pi$
$53$	− 3.97386e7i	− 0.691785i	0.938274	−	0.345892i	$-0.112424\pi$
$54$	2.40494e7	0.384887
$55$	0	0
$56$	3.25786e7	0.442676
$57$	1.14996e8i	1.44294i
$58$	3.35711e7i	0.389529i
$59$	8.51856e7	0.915234	0.457617	−	0.889149i	$-0.348703\pi$
$59$	8.51856e7	0.915234	0.457617	+	0.889149i	$0.348703\pi$
$60$	0	0
$61$	4.57486e7	0.423052	0.211526	−	0.977372i	$-0.432157\pi$
$61$	4.57486e7	0.423052	0.211526	+	0.977372i	$0.432157\pi$
$62$	2.69202e7i	0.231375i
$63$	2.83663e7i	0.226866i
$64$	4.37780e7	0.326172
$65$	0	0
$66$	−4.21417e7	−0.273378
$67$	− 4.52862e7i	− 0.274555i	−0.990533	−	0.137277i	$-0.956165\pi$
$67$	− 4.52862e7i	− 0.274555i	0.990533	−	0.137277i	$-0.0438352\pi$
$68$	2.21689e8i	1.25735i
$69$	−6.07112e7	−0.322439
$70$	0	0
$71$	−1.89967e8	−0.887190	−0.443595	−	0.896227i	$-0.646297\pi$
$71$	−1.89967e8	−0.887190	−0.443595	+	0.896227i	$0.646297\pi$
$72$	− 5.13562e7i	− 0.225214i
$73$	− 4.12171e8i	− 1.69873i	−0.527805	−	0.849365i	$-0.676985\pi$
$73$	− 4.12171e8i	− 1.69873i	0.527805	−	0.849365i	$-0.323015\pi$
$74$	−1.19451e8	−0.463070
$75$	0	0
$76$	4.51916e8	1.55380
$77$	− 1.96014e8i	− 0.635447i
$78$	1.05732e8i	0.323430i
$79$	−9.50408e7	−0.274529	−0.137265	−	0.990534i	$-0.543831\pi$
$79$	−9.50408e7	−0.274529	−0.137265	+	0.990534i	$0.543831\pi$
$80$	0	0
$81$	−2.11084e8	−0.544845
$82$	− 8.84501e7i	− 0.216041i
$83$	− 2.61706e8i	− 0.605289i	−0.953104	−	0.302645i	$-0.902131\pi$
$83$	− 2.61706e8i	− 0.605289i	0.953104	−	0.302645i	$-0.0978695\pi$
$84$	−2.16647e8	−0.474785
$85$	0	0
$86$	5.11744e7	0.100881
$87$	− 4.78388e8i	− 0.895249i
$88$	3.54877e8i	0.630821i
$89$	1.99386e7	0.0336853	0.0168426	−	0.999858i	$-0.494639\pi$
$89$	1.99386e7	0.0336853	0.0168426	+	0.999858i	$0.494639\pi$
$90$	0	0
$91$	−4.91792e8	−0.751788
$92$	2.38584e8i	0.347213i
$93$	− 3.83613e8i	− 0.531766i
$94$	−2.84473e8	−0.375808
$95$	0	0
$96$	6.01424e8	0.722703
$97$	− 1.95034e7i	− 0.0223685i	−0.999937	−	0.0111842i	$-0.996440\pi$
$97$	− 1.95034e7i	− 0.0223685i	0.999937	−	0.0111842i	$-0.00356013\pi$
$98$	− 1.78872e8i	− 0.195896i
$99$	−3.08993e8	−0.323288
$100$	0	0
$101$	−2.16672e8	−0.207184	−0.103592	−	0.994620i	$-0.533034\pi$
$101$	−2.16672e8	−0.207184	−0.103592	+	0.994620i	$0.533034\pi$
$102$	4.51296e8i	0.412820i
$103$	7.48234e8i	0.655043i	0.944844	+	0.327522i	$0.106213\pi$
$103$	7.48234e8i	0.655043i	−0.944844	+	0.327522i	$0.893787\pi$
$104$	8.90373e8	0.746315
$105$	0	0
$106$	−3.17909e8	−0.244583
$107$	1.05711e9i	0.779637i	0.920892	+	0.389819i	$0.127462\pi$
$107$	1.05711e9i	0.779637i	−0.920892	+	0.389819i	$0.872538\pi$
$108$	1.34677e9i	0.952546i
$109$	2.49659e9	1.69406	0.847029	−	0.531547i	$-0.178389\pi$
$109$	2.49659e9	1.69406	0.847029	+	0.531547i	$0.178389\pi$
$110$	0	0
$111$	1.70217e9	1.06427
$112$	7.12385e8i	0.427793i
$113$	− 1.11566e9i	− 0.643695i	−0.946791	−	0.321848i	$-0.895696\pi$
$113$	− 1.11566e9i	− 0.643695i	0.946791	−	0.321848i	$-0.104304\pi$
$114$	9.19971e8	0.510155
$115$	0	0
$116$	−1.87998e9	−0.964035
$117$	7.75251e8i	0.382477i
$118$	− 6.81485e8i	− 0.323584i
$119$	−2.09912e9	−0.959568
$120$	0	0
$121$	−2.22768e8	−0.0944756
$122$	− 3.65989e8i	− 0.149572i
$123$	1.26041e9i	0.496524i
$124$	−1.50753e9	−0.572623
$125$	0	0
$126$	2.26930e8	0.0802093
$127$	3.12054e8i	0.106442i	0.998583	+	0.0532210i	$0.0169488\pi$
$127$	3.12054e8i	0.106442i	−0.998583	+	0.0532210i	$0.983051\pi$
$128$	− 3.05136e9i	− 1.00473i
$129$	−7.29235e8	−0.231853
$130$	0	0
$131$	−2.81701e9	−0.835733	−0.417867	−	0.908508i	$-0.637222\pi$
$131$	−2.81701e9	−0.835733	−0.417867	+	0.908508i	$0.637222\pi$
$132$	− 2.35993e9i	− 0.676577i
$133$	4.27908e9i	1.18582i
$134$	−3.62289e8	−0.0970697
$135$	0	0
$136$	3.80039e9	0.952583
$137$	− 7.15311e9i	− 1.73481i	−0.497600	−	0.867406i	$-0.665785\pi$
$137$	− 7.15311e9i	− 1.73481i	0.497600	−	0.867406i	$-0.334215\pi$
$138$	4.85689e8i	0.113999i
$139$	−2.52323e9	−0.573310	−0.286655	−	0.958034i	$-0.592543\pi$
$139$	−2.52323e9	−0.573310	−0.286655	+	0.958034i	$0.592543\pi$
$140$	0	0
$141$	4.05374e9	0.863715
$142$	1.51974e9i	0.313669i
$143$	− 5.35708e9i	− 1.07131i
$144$	1.12299e9	0.217643
$145$	0	0
$146$	−3.29737e9	−0.600592
$147$	2.54893e9i	0.450225i
$148$	− 6.68925e9i	− 1.14604i
$149$	−1.46531e9	−0.243551	−0.121775	−	0.992558i	$-0.538859\pi$
$149$	−1.46531e9	−0.243551	−0.121775	+	0.992558i	$0.538859\pi$
$150$	0	0
$151$	3.65515e9	0.572149	0.286075	−	0.958207i	$-0.407650\pi$
$151$	3.65515e9	0.572149	0.286075	+	0.958207i	$0.407650\pi$
$152$	− 7.74712e9i	− 1.17718i
$153$	3.30901e9i	0.488187i
$154$	−1.56811e9	−0.224665
$155$	0	0
$156$	−5.92098e9	−0.800448
$157$	5.55191e9i	0.729279i	0.931149	+	0.364639i	$0.118808\pi$
$157$	5.55191e9i	0.729279i	−0.931149	+	0.364639i	$0.881192\pi$
$158$	7.60327e8i	0.0970607i
$159$	4.53020e9	0.562122
$160$	0	0
$161$	−2.25909e9	−0.264983
$162$	1.68867e9i	0.192632i
$163$	1.67637e10i	1.86006i	0.367485	+	0.930029i	$0.380219\pi$
$163$	1.67637e10i	1.86006i	−0.367485	+	0.930029i	$0.619781\pi$
$164$	4.95321e9	0.534674
$165$	0	0
$166$	−2.09365e9	−0.214002
$167$	1.39549e10i	1.38836i	0.719799	+	0.694182i	$0.244234\pi$
$167$	1.39549e10i	1.38836i	−0.719799	+	0.694182i	$0.755766\pi$
$168$	3.71396e9i	0.359704i
$169$	−2.83619e9	−0.267452
$170$	0	0
$171$	6.74544e9	0.603293
$172$	2.86576e9i	0.249668i
$173$	− 1.57000e10i	− 1.33258i	−0.745694	−	0.666289i	$-0.767882\pi$
$173$	− 1.57000e10i	− 1.33258i	0.745694	−	0.666289i	$-0.232118\pi$
$174$	−3.82711e9	−0.316518
$175$	0	0
$176$	−7.75999e9	−0.609613
$177$	9.71116e9i	0.743689i
$178$	− 1.59509e8i	− 0.0119095i
$179$	2.51902e10	1.83397	0.916985	−	0.398921i	$-0.130615\pi$
$179$	2.51902e10	1.83397	0.916985	+	0.398921i	$0.130615\pi$
$180$	0	0
$181$	1.04482e10	0.723579	0.361789	−	0.932260i	$-0.382166\pi$
$181$	1.04482e10	0.723579	0.361789	+	0.932260i	$0.382166\pi$
$182$	3.93434e9i	0.265797i
$183$	5.21535e9i	0.343758i
$184$	4.09001e9	0.263054
$185$	0	0
$186$	−3.06891e9	−0.188008
$187$	− 2.28657e10i	− 1.36740i
$188$	− 1.59305e10i	− 0.930078i
$189$	−1.27522e10	−0.726955
$190$	0	0
$191$	−9.68625e9	−0.526630	−0.263315	−	0.964710i	$-0.584816\pi$
$191$	−9.68625e9	−0.526630	−0.263315	+	0.964710i	$0.584816\pi$
$192$	4.99070e9i	0.265037i
$193$	2.04431e10i	1.06057i	0.847820	+	0.530285i	$0.177915\pi$
$193$	2.04431e10i	1.06057i	−0.847820	+	0.530285i	$0.822085\pi$
$194$	−1.56027e8	−0.00790845
$195$	0	0
$196$	1.00169e10	0.484818
$197$	− 2.52431e10i	− 1.19411i	−0.802200	−	0.597056i	$-0.796337\pi$
$197$	− 2.52431e10i	− 1.19411i	0.802200	−	0.597056i	$-0.203663\pi$
$198$	2.47194e9i	0.114300i
$199$	−8.06736e9	−0.364664	−0.182332	−	0.983237i	$-0.558365\pi$
$199$	−8.06736e9	−0.364664	−0.182332	+	0.983237i	$0.558365\pi$
$200$	0	0
$201$	5.16262e9	0.223094
$202$	1.73338e9i	0.0732506i
$203$	− 1.78011e10i	− 0.735723i
$204$	−2.52726e10	−1.02168
$205$	0	0
$206$	5.98587e9	0.231593
$207$	3.56119e9i	0.134812i
$208$	1.94695e10i	0.721223i
$209$	−4.66119e10	−1.68981
$210$	0	0
$211$	−8.04589e9	−0.279449	−0.139725	−	0.990190i	$-0.544622\pi$
$211$	−8.04589e9	−0.279449	−0.139725	+	0.990190i	$0.544622\pi$
$212$	− 1.78029e10i	− 0.605312i
$213$	− 2.16563e10i	− 0.720901i
$214$	8.45687e9	0.275643
$215$	0	0
$216$	2.30875e10	0.721663
$217$	− 1.42744e10i	− 0.437009i
$218$	− 1.99727e10i	− 0.598940i
$219$	4.69875e10	1.38033
$220$	0	0
$221$	−5.73690e10	−1.61775
$222$	− 1.36174e10i	− 0.376275i
$223$	− 3.18618e10i	− 0.862777i	−0.902166	−	0.431388i	$-0.858024\pi$
$223$	− 3.18618e10i	− 0.862777i	0.902166	−	0.431388i	$-0.141976\pi$
$224$	2.23793e10	0.593923
$225$	0	0
$226$	−8.92531e9	−0.227581
$227$	3.02621e10i	0.756454i	0.925713	+	0.378227i	$0.123466\pi$
$227$	3.02621e10i	0.756454i	−0.925713	+	0.378227i	$0.876534\pi$
$228$	5.15184e10i	1.26257i
$229$	−2.06101e10	−0.495245	−0.247623	−	0.968857i	$-0.579649\pi$
$229$	−2.06101e10	−0.495245	−0.247623	+	0.968857i	$0.579649\pi$
$230$	0	0
$231$	2.23456e10	0.516344
$232$	3.22283e10i	0.730367i
$233$	− 3.61735e9i	− 0.0804061i	−0.999192	−	0.0402031i	$-0.987200\pi$
$233$	− 3.61735e9i	− 0.0804061i	0.999192	−	0.0402031i	$-0.0128005\pi$
$234$	6.20201e9	0.135226
$235$	0	0
$236$	3.81632e10	0.800830
$237$	− 1.08347e10i	− 0.223073i
$238$	1.67930e10i	0.339259i
$239$	−2.21916e9	−0.0439945	−0.0219973	−	0.999758i	$-0.507003\pi$
$239$	−2.21916e9	−0.0439945	−0.0219973	+	0.999758i	$0.507003\pi$
$240$	0	0
$241$	2.57977e10	0.492611	0.246306	−	0.969192i	$-0.420783\pi$
$241$	2.57977e10	0.492611	0.246306	+	0.969192i	$0.420783\pi$
$242$	1.78215e9i	0.0334022i
$243$	3.51070e10i	0.645901i
$244$	2.04954e10	0.370171
$245$	0	0
$246$	1.00833e10	0.175548
$247$	1.16947e11i	1.99919i
$248$	2.58434e10i	0.433828i
$249$	2.98345e10	0.491838
$250$	0	0
$251$	−8.91848e10	−1.41827	−0.709135	−	0.705072i	$-0.750914\pi$
$251$	−8.91848e10	−1.41827	−0.709135	+	0.705072i	$0.750914\pi$
$252$	1.27081e10i	0.198508i
$253$	− 2.46083e10i	− 0.377606i
$254$	2.49643e9	0.0376329
$255$	0	0
$256$	−1.99649e9	−0.0290527
$257$	− 1.10058e11i	− 1.57371i	−0.617141	−	0.786853i	$-0.711709\pi$
$257$	− 1.10058e11i	− 1.57371i	0.617141	−	0.786853i	$-0.288291\pi$
$258$	5.83388e9i	0.0819726i
$259$	6.33388e10	0.874623
$260$	0	0
$261$	−2.80613e10	−0.374304
$262$	2.25361e10i	0.295476i
$263$	− 2.06374e10i	− 0.265983i	−0.991117	−	0.132992i	$-0.957542\pi$
$263$	− 2.06374e10i	− 0.265983i	0.991117	−	0.132992i	$-0.0424584\pi$
$264$	−4.04560e10	−0.512585
$265$	0	0
$266$	3.42326e10	0.419249
$267$	2.27300e9i	0.0273716i
$268$	− 2.02882e10i	− 0.240235i
$269$	2.64890e10	0.308446	0.154223	−	0.988036i	$-0.450713\pi$
$269$	2.64890e10	0.308446	0.154223	+	0.988036i	$0.450713\pi$
$270$	0	0
$271$	3.44004e10	0.387438	0.193719	−	0.981057i	$-0.437945\pi$
$271$	3.44004e10	0.387438	0.193719	+	0.981057i	$0.437945\pi$
$272$	8.31018e10i	0.920556i
$273$	− 5.60643e10i	− 0.610878i
$274$	−5.72249e10	−0.613349
$275$	0	0
$276$	−2.71986e10	−0.282134
$277$	− 1.06023e11i	− 1.08203i	−0.841012	−	0.541017i	$-0.818040\pi$
$277$	− 1.06023e11i	− 1.08203i	0.841012	−	0.541017i	$-0.181960\pi$
$278$	2.01858e10i	0.202696i
$279$	−2.25019e10	−0.222332
$280$	0	0
$281$	1.00299e11	0.959662	0.479831	−	0.877361i	$-0.340698\pi$
$281$	1.00299e11	0.959662	0.479831	+	0.877361i	$0.340698\pi$
$282$	− 3.24300e10i	− 0.305369i
$283$	2.49296e9i	0.0231035i	0.999933	+	0.0115517i	$0.00367711\pi$
$283$	2.49296e9i	0.0231035i	−0.999933	+	0.0115517i	$0.996323\pi$
$284$	−8.51054e10	−0.776291
$285$	0	0
$286$	−4.28566e10	−0.378766
$287$	4.69007e10i	0.408047i
$288$	− 3.52783e10i	− 0.302163i
$289$	−1.26281e11	−1.06487
$290$	0	0
$291$	2.22338e9	0.0181759
$292$	− 1.84653e11i	− 1.48639i
$293$	8.47068e10i	0.671451i	0.941960	+	0.335725i	$0.108981\pi$
$293$	8.47068e10i	0.671451i	−0.941960	+	0.335725i	$0.891019\pi$
$294$	2.03914e10	0.159179
$295$	0	0
$296$	−1.14673e11	−0.868256
$297$	− 1.38910e11i	− 1.03592i
$298$	1.17224e10i	0.0861083i
$299$	−6.17411e10	−0.446739
$300$	0	0
$301$	−2.71352e10	−0.190539
$302$	− 2.92412e10i	− 0.202285i
$303$	− 2.47006e10i	− 0.168351i
$304$	1.69404e11	1.13761
$305$	0	0
$306$	2.64721e10	0.172600
$307$	6.35507e9i	0.0408317i	0.999792	+	0.0204159i	$0.00649902\pi$
$307$	6.35507e9i	0.0408317i	−0.999792	+	0.0204159i	$0.993501\pi$
$308$	− 8.78144e10i	− 0.556016i
$309$	−8.52987e10	−0.532267
$310$	0	0
$311$	2.71253e11	1.64419	0.822096	−	0.569350i	$-0.192805\pi$
$311$	2.71253e11	1.64419	0.822096	+	0.569350i	$0.192805\pi$
$312$	1.01503e11i	0.606431i
$313$	− 1.63499e11i	− 0.962865i	−0.876483	−	0.481432i	$-0.840117\pi$
$313$	− 1.63499e11i	− 0.962865i	0.876483	−	0.481432i	$-0.159883\pi$
$314$	4.44153e10	0.257839
$315$	0	0
$316$	−4.25783e10	−0.240213
$317$	2.53606e11i	1.41056i	0.708927	+	0.705282i	$0.249180\pi$
$317$	2.53606e11i	1.41056i	−0.708927	+	0.705282i	$0.750820\pi$
$318$	− 3.62416e10i	− 0.198740i
$319$	1.93907e11	1.04842
$320$	0	0
$321$	−1.20510e11	−0.633508
$322$	1.80728e10i	0.0936856i
$323$	4.99167e11i	2.55173i
$324$	−9.45658e10	−0.476740
$325$	0	0
$326$	1.34110e11	0.657630
$327$	2.84611e11i	1.37654i
$328$	− 8.49121e10i	− 0.405077i
$329$	1.50842e11	0.709808
$330$	0	0
$331$	−2.40064e11	−1.09926	−0.549631	−	0.835408i	$-0.685232\pi$
$331$	−2.40064e11	−1.09926	−0.549631	+	0.835408i	$0.685232\pi$
$332$	− 1.17244e11i	− 0.529628i
$333$	− 9.98460e10i	− 0.444971i
$334$	1.11639e11	0.490861
$335$	0	0
$336$	−8.12118e10	−0.347610
$337$	− 5.13812e10i	− 0.217005i	−0.994096	−	0.108502i	$-0.965394\pi$
$337$	− 5.13812e10i	− 0.217005i	0.994096	−	0.108502i	$-0.0346055\pi$
$338$	2.26895e10i	0.0945585i
$339$	1.27186e11	0.523046
$340$	0	0
$341$	1.55491e11	0.622746
$342$	− 5.39636e10i	− 0.213296i
$343$	2.66027e11i	1.03777i
$344$	4.91274e10	0.189152
$345$	0	0
$346$	−1.25600e11	−0.471137
$347$	2.76560e11i	1.02401i	0.858981	+	0.512007i	$0.171098\pi$
$347$	2.76560e11i	1.02401i	−0.858981	+	0.512007i	$0.828902\pi$
$348$	− 2.14318e11i	− 0.783343i
$349$	−4.66592e11	−1.68354	−0.841770	−	0.539837i	$-0.818486\pi$
$349$	−4.66592e11	−1.68354	−0.841770	+	0.539837i	$0.818486\pi$
$350$	0	0
$351$	−3.48518e11	−1.22559
$352$	2.43777e11i	0.846352i
$353$	1.00998e11i	0.346198i	0.984904	+	0.173099i	$0.0553781\pi$
$353$	1.00998e11i	0.346198i	−0.984904	+	0.173099i	$0.944622\pi$
$354$	7.76893e10	0.262934
$355$	0	0
$356$	8.93251e9	0.0294746
$357$	− 2.39300e11i	− 0.779714i
$358$	− 2.01521e11i	− 0.648406i
$359$	1.66447e11	0.528874	0.264437	−	0.964403i	$-0.414814\pi$
$359$	1.66447e11	0.528874	0.264437	+	0.964403i	$0.414814\pi$
$360$	0	0
$361$	6.94869e11	2.15338
$362$	− 8.35852e10i	− 0.255824i
$363$	− 2.53956e10i	− 0.0767677i
$364$	−2.20323e11	−0.657814
$365$	0	0
$366$	4.17228e10	0.121537
$367$	− 2.97381e11i	− 0.855688i	−0.903853	−	0.427844i	$-0.859273\pi$
$367$	− 2.97381e11i	− 0.855688i	0.903853	−	0.427844i	$-0.140727\pi$
$368$	8.94350e10i	0.254210i
$369$	7.39332e10	0.207597
$370$	0	0
$371$	1.68571e11	0.461956
$372$	− 1.71859e11i	− 0.465295i
$373$	− 1.95714e11i	− 0.523517i	−0.965133	−	0.261759i	$-0.915698\pi$
$373$	− 1.95714e11i	− 0.523517i	0.965133	−	0.261759i	$-0.0843024\pi$
$374$	−1.82925e11	−0.483450
$375$	0	0
$376$	−2.73094e11	−0.704640
$377$	− 4.86504e11i	− 1.24037i
$378$	1.02018e11i	0.257017i
$379$	1.67009e11	0.415781	0.207890	−	0.978152i	$-0.433340\pi$
$379$	1.67009e11	0.415781	0.207890	+	0.978152i	$0.433340\pi$
$380$	0	0
$381$	−3.55741e10	−0.0864912
$382$	7.74900e10i	0.186192i
$383$	− 7.20782e10i	− 0.171163i	−0.996331	−	0.0855814i	$-0.972725\pi$
$383$	− 7.20782e10i	− 0.171163i	0.996331	−	0.0855814i	$-0.0272748\pi$
$384$	3.47855e11	0.816408
$385$	0	0
$386$	1.63545e11	0.374968
$387$	4.27754e10i	0.0969381i
$388$	− 8.73750e9i	− 0.0195724i
$389$	−7.92249e11	−1.75424	−0.877119	−	0.480272i	$-0.840538\pi$
$389$	−7.92249e11	−1.75424	−0.877119	+	0.480272i	$0.840538\pi$
$390$	0	0
$391$	−2.63530e11	−0.570210
$392$	− 1.71717e11i	− 0.367305i
$393$	− 3.21139e11i	− 0.679089i
$394$	−2.01945e11	−0.422182
$395$	0	0
$396$	−1.38429e11	−0.282877
$397$	− 1.47288e11i	− 0.297584i	−0.988869	−	0.148792i	$-0.952462\pi$
$397$	− 1.47288e11i	− 0.297584i	0.988869	−	0.148792i	$-0.0475384\pi$
$398$	6.45389e10i	0.128928i
$399$	−4.87815e11	−0.963555
$400$	0	0
$401$	−3.22101e11	−0.622075	−0.311037	−	0.950398i	$-0.600676\pi$
$401$	−3.22101e11	−0.622075	−0.311037	+	0.950398i	$0.600676\pi$
$402$	− 4.13010e10i	− 0.0788757i
$403$	− 3.90121e11i	− 0.736761i
$404$	−9.70690e10	−0.181286
$405$	0	0
$406$	−1.42409e11	−0.260117
$407$	6.89948e11i	1.24635i
$408$	4.33244e11i	0.774037i
$409$	3.96423e11	0.700493	0.350247	−	0.936658i	$-0.386098\pi$
$409$	3.96423e11	0.700493	0.350247	+	0.936658i	$0.386098\pi$
$410$	0	0
$411$	8.15455e11	1.40965
$412$	3.35209e11i	0.573163i
$413$	3.61357e11i	0.611170i
$414$	2.84895e10	0.0476632
$415$	0	0
$416$	6.11627e11	1.00131
$417$	− 2.87648e11i	− 0.465853i
$418$	3.72895e11i	0.597438i
$419$	1.23162e12	1.95215	0.976074	−	0.217441i	$-0.0697708\pi$
$419$	1.23162e12	1.95215	0.976074	+	0.217441i	$0.0697708\pi$
$420$	0	0
$421$	−1.17500e12	−1.82293	−0.911465	−	0.411379i	$-0.865047\pi$
$421$	−1.17500e12	−1.82293	−0.911465	+	0.411379i	$0.865047\pi$
$422$	6.43671e10i	0.0988002i
$423$	− 2.37784e11i	− 0.361120i
$424$	−3.05192e11	−0.458593
$425$	0	0
$426$	−1.73250e11	−0.254877
$427$	1.94066e11i	0.282503i
$428$	4.73585e11i	0.682183i
$429$	6.10707e11	0.870513
$430$	0	0
$431$	−2.32327e11	−0.324304	−0.162152	−	0.986766i	$-0.551843\pi$
$431$	−2.32327e11	−0.324304	−0.162152	+	0.986766i	$0.551843\pi$
$432$	5.04846e11i	0.697400i
$433$	1.51554e11i	0.207191i	0.994620	+	0.103596i	$0.0330347\pi$
$433$	1.51554e11i	0.207191i	−0.994620	+	0.103596i	$0.966965\pi$
$434$	−1.14196e11	−0.154506
$435$	0	0
$436$	1.11847e12	1.48230
$437$	5.37209e11i	0.704655i
$438$	− 3.75900e11i	− 0.488021i
$439$	5.21385e11	0.669990	0.334995	−	0.942220i	$-0.391265\pi$
$439$	5.21385e11	0.669990	0.334995	+	0.942220i	$0.391265\pi$
$440$	0	0
$441$	1.49515e11	0.188240
$442$	4.58952e11i	0.571962i
$443$	− 1.10169e12i	− 1.35908i	−0.733639	−	0.679539i	$-0.762180\pi$
$443$	− 1.10169e12i	− 1.35908i	0.733639	−	0.679539i	$-0.237820\pi$
$444$	7.62574e11	0.931234
$445$	0	0
$446$	−2.54894e11	−0.305038
$447$	− 1.67045e11i	− 0.197901i
$448$	1.85706e11i	0.217809i
$449$	−5.85672e11	−0.680058	−0.340029	−	0.940415i	$-0.610437\pi$
$449$	−5.85672e11	−0.680058	−0.340029	+	0.940415i	$0.610437\pi$
$450$	0	0
$451$	−5.10888e11	−0.581475
$452$	− 4.99817e11i	− 0.563233i
$453$	4.16687e11i	0.464909i
$454$	2.42097e11	0.267447
$455$	0	0
$456$	8.83172e11	0.956541
$457$	− 5.70804e11i	− 0.612159i	−0.952006	−	0.306079i	$-0.900983\pi$
$457$	− 5.70804e11i	− 0.612159i	0.952006	−	0.306079i	$-0.0990173\pi$
$458$	1.64881e11i	0.175096i
$459$	−1.48758e12	−1.56432
$460$	0	0
$461$	−7.60279e11	−0.784005	−0.392002	−	0.919964i	$-0.628218\pi$
$461$	−7.60279e11	−0.784005	−0.392002	+	0.919964i	$0.628218\pi$
$462$	− 1.78765e11i	− 0.182555i
$463$	7.14289e11i	0.722370i	0.932494	+	0.361185i	$0.117628\pi$
$463$	7.14289e11i	0.722370i	−0.932494	+	0.361185i	$0.882372\pi$
$464$	−7.04725e11	−0.705812
$465$	0	0
$466$	−2.89388e10	−0.0284279
$467$	7.82521e11i	0.761325i	0.924714	+	0.380662i	$0.124304\pi$
$467$	7.82521e11i	0.761325i	−0.924714	+	0.380662i	$0.875696\pi$
$468$	3.47312e11i	0.334668i
$469$	1.92104e11	0.183340
$470$	0	0
$471$	−6.32917e11	−0.592588
$472$	− 6.54226e11i	− 0.606720i
$473$	− 2.95583e11i	− 0.271522i
$474$	−8.66772e10	−0.0788683
$475$	0	0
$476$	−9.40406e11	−0.839622
$477$	− 2.65732e11i	− 0.235023i
$478$	1.77533e10i	0.0155544i
$479$	6.95738e11	0.603860	0.301930	−	0.953330i	$-0.402369\pi$
$479$	6.95738e11	0.603860	0.301930	+	0.953330i	$0.402369\pi$
$480$	0	0
$481$	1.73105e12	1.47454
$482$	− 2.06382e11i	− 0.174164i
$483$	− 2.57537e11i	− 0.215316i
$484$	−9.98003e10	−0.0826661
$485$	0	0
$486$	2.80856e11	0.228360
$487$	− 1.65196e12i	− 1.33082i	−0.746480	−	0.665408i	$-0.768258\pi$
$487$	− 1.65196e12i	− 1.33082i	0.746480	−	0.665408i	$-0.231742\pi$
$488$	− 3.51350e11i	− 0.280447i
$489$	−1.91107e12	−1.51142
$490$	0	0
$491$	1.19989e12	0.931694	0.465847	−	0.884865i	$-0.345750\pi$
$491$	1.19989e12	0.931694	0.465847	+	0.884865i	$0.345750\pi$
$492$	5.64665e11i	0.434458i
$493$	− 2.07655e12i	− 1.58318i
$494$	9.35578e11	0.706820
$495$	0	0
$496$	−5.65109e11	−0.419242
$497$	− 8.05842e11i	− 0.592442i
$498$	− 2.38676e11i	− 0.173891i
$499$	−1.43146e12	−1.03354	−0.516768	−	0.856125i	$-0.672865\pi$
$499$	−1.43146e12	−1.03354	−0.516768	+	0.856125i	$0.672865\pi$
$500$	0	0
$501$	−1.59086e12	−1.12814
$502$	7.13478e11i	0.501434i
$503$	− 1.41833e12i	− 0.987919i	−0.869485	−	0.493959i	$-0.835549\pi$
$503$	− 1.41833e12i	− 0.987919i	0.869485	−	0.493959i	$-0.164451\pi$
$504$	2.17853e11	0.150392
$505$	0	0
$506$	−1.96866e11	−0.133504
$507$	− 3.23326e11i	− 0.217323i
$508$	1.39800e11i	0.0931367i
$509$	1.16463e12	0.769059	0.384529	−	0.923113i	$-0.374364\pi$
$509$	1.16463e12	0.769059	0.384529	+	0.923113i	$0.374364\pi$
$510$	0	0
$511$	1.74843e12	1.13437
$512$	− 1.54632e12i	− 0.994455i
$513$	3.03245e12i	1.93315i
$514$	−8.80466e11	−0.556389
$515$	0	0
$516$	−3.26697e11	−0.202872
$517$	1.64312e12i	1.01149i
$518$	− 5.06711e11i	− 0.309226i
$519$	1.78980e12	1.08281
$520$	0	0
$521$	−8.36946e11	−0.497654	−0.248827	−	0.968548i	$-0.580045\pi$
$521$	−8.36946e11	−0.497654	−0.248827	+	0.968548i	$0.580045\pi$
$522$	2.24490e11i	0.132337i
$523$	2.60288e12i	1.52124i	0.649199	+	0.760618i	$0.275104\pi$
$523$	2.60288e12i	1.52124i	−0.649199	+	0.760618i	$0.724896\pi$
$524$	−1.26202e12	−0.731267
$525$	0	0
$526$	−1.65099e11	−0.0940394
$527$	− 1.66516e12i	− 0.940389i
$528$	− 8.84638e11i	− 0.495351i
$529$	1.51754e12	0.842538
$530$	0	0
$531$	5.69636e11	0.310937
$532$	1.91703e12i	1.03759i
$533$	1.28180e12i	0.687934i
$534$	1.81840e10	0.00967731
$535$	0	0
$536$	−3.47798e11	−0.182006
$537$	2.87168e12i	1.49022i
$538$	− 2.11912e11i	− 0.109052i
$539$	−1.03317e12	−0.527255
$540$	0	0
$541$	3.07406e12	1.54286	0.771428	−	0.636317i	$-0.219543\pi$
$541$	3.07406e12	1.54286	0.771428	+	0.636317i	$0.219543\pi$
$542$	− 2.75203e11i	− 0.136980i
$543$	1.19109e12i	0.587956i
$544$	2.61061e12	1.27805
$545$	0	0
$546$	−4.48514e11	−0.215978
$547$	1.32972e12i	0.635062i	0.948248	+	0.317531i	$0.102854\pi$
$547$	1.32972e12i	0.635062i	−0.948248	+	0.317531i	$0.897146\pi$
$548$	− 3.20460e12i	− 1.51796i
$549$	3.05921e11	0.143726
$550$	0	0
$551$	−4.23307e12	−1.95647
$552$	4.66262e11i	0.213749i
$553$	− 4.03163e11i	− 0.183323i
$554$	−8.48183e11	−0.382557
$555$	0	0
$556$	−1.13041e12	−0.501647
$557$	2.49418e12i	1.09794i	0.835841	+	0.548971i	$0.184980\pi$
$557$	2.49418e12i	1.09794i	−0.835841	+	0.548971i	$0.815020\pi$
$558$	1.80016e11i	0.0786061i
$559$	−7.41606e11	−0.321233
$560$	0	0
$561$	2.60669e12	1.11111
$562$	− 8.02392e11i	− 0.339292i
$563$	− 1.06689e12i	− 0.447541i	−0.974642	−	0.223770i	$-0.928163\pi$
$563$	− 1.06689e12i	− 0.447541i	0.974642	−	0.223770i	$-0.0718365\pi$
$564$	1.81608e12	0.755750
$565$	0	0
$566$	1.99437e10	0.00816831
$567$	− 8.95420e11i	− 0.363834i
$568$	1.45895e12i	0.588129i
$569$	4.57278e12	1.82884	0.914420	−	0.404768i	$-0.132648\pi$
$569$	4.57278e12	1.82884	0.914420	+	0.404768i	$0.132648\pi$
$570$	0	0
$571$	−2.32305e12	−0.914525	−0.457263	−	0.889332i	$-0.651170\pi$
$571$	−2.32305e12	−0.914525	−0.457263	+	0.889332i	$0.651170\pi$
$572$	− 2.39997e12i	− 0.937398i
$573$	− 1.10423e12i	− 0.427922i
$574$	3.75205e11	0.144266
$575$	0	0
$576$	2.92744e11	0.110812
$577$	1.01144e12i	0.379881i	0.981796	+	0.189940i	$0.0608295\pi$
$577$	1.01144e12i	0.379881i	−0.981796	+	0.189940i	$0.939171\pi$
$578$	1.01025e12i	0.376489i
$579$	−2.33051e12	−0.861784
$580$	0	0
$581$	1.11016e12	0.404196
$582$	− 1.77871e10i	− 0.00642615i
$583$	1.83624e12i	0.658296i
$584$	−3.16547e12	−1.12611
$585$	0	0
$586$	6.77654e11	0.237394
$587$	− 1.10143e12i	− 0.382899i	−0.981502	−	0.191449i	$-0.938681\pi$
$587$	− 1.10143e12i	− 0.382899i	0.981502	−	0.191449i	$-0.0613188\pi$
$588$	1.14192e12i	0.393947i
$589$	−3.39444e12	−1.16211
$590$	0	0
$591$	2.87772e12	0.970296
$592$	− 2.50751e12i	− 0.839065i
$593$	− 9.84366e11i	− 0.326897i	−0.986552	−	0.163448i	$-0.947738\pi$
$593$	− 9.84366e11i	− 0.326897i	0.986552	−	0.163448i	$-0.0522617\pi$
$594$	−1.11128e12	−0.366255
$595$	0	0
$596$	−6.56457e11	−0.213107
$597$	− 9.19679e11i	− 0.296314i
$598$	4.93929e11i	0.157946i
$599$	−4.51397e12	−1.43264	−0.716321	−	0.697771i	$-0.754175\pi$
$599$	−4.51397e12	−1.43264	−0.716321	+	0.697771i	$0.754175\pi$
$600$	0	0
$601$	−1.44212e12	−0.450885	−0.225443	−	0.974256i	$-0.572383\pi$
$601$	−1.44212e12	−0.450885	−0.225443	+	0.974256i	$0.572383\pi$
$602$	2.17082e11i	0.0673657i
$603$	− 3.02829e11i	− 0.0932758i
$604$	1.63751e12	0.500630
$605$	0	0
$606$	−1.97605e11	−0.0595211
$607$	− 4.12105e12i	− 1.23214i	−0.787692	−	0.616069i	$-0.788724\pi$
$607$	− 4.12105e12i	− 1.23214i	0.787692	−	0.616069i	$-0.211276\pi$
$608$	− 5.32176e12i	− 1.57939i
$609$	2.02932e12	0.597824
$610$	0	0
$611$	4.12252e12	1.19668
$612$	1.48244e12i	0.427164i
$613$	− 1.38470e12i	− 0.396080i	−0.980194	−	0.198040i	$-0.936542\pi$
$613$	− 1.38470e12i	− 0.396080i	0.980194	−	0.198040i	$-0.0634576\pi$
$614$	5.08406e10	0.0144362
$615$	0	0
$616$	−1.50539e12	−0.421246
$617$	6.22714e11i	0.172984i	0.996253	+	0.0864918i	$0.0275657\pi$
$617$	6.22714e11i	0.172984i	−0.996253	+	0.0864918i	$0.972434\pi$
$618$	6.82390e11i	0.188185i
$619$	−1.89438e12	−0.518631	−0.259315	−	0.965793i	$-0.583497\pi$
$619$	−1.89438e12	−0.518631	−0.259315	+	0.965793i	$0.583497\pi$
$620$	0	0
$621$	−1.60095e12	−0.431983
$622$	− 2.17002e12i	− 0.581309i
$623$	8.45797e10i	0.0224942i
$624$	−2.21952e12	−0.586042
$625$	0	0
$626$	−1.30799e12	−0.340424
$627$	− 5.31375e12i	− 1.37308i
$628$	2.48725e12i	0.638119i
$629$	7.38866e12	1.88208
$630$	0	0
$631$	−1.10160e12	−0.276624	−0.138312	−	0.990389i	$-0.544168\pi$
$631$	−1.10160e12	−0.276624	−0.138312	+	0.990389i	$0.544168\pi$
$632$	7.29914e11i	0.181989i
$633$	− 9.17231e11i	− 0.227071i
$634$	2.02885e12	0.498710
$635$	0	0
$636$	2.02953e12	0.491856
$637$	2.59217e12i	0.623787i
$638$	− 1.55125e12i	− 0.370672i
$639$	−1.27031e12	−0.301409
$640$	0	0
$641$	−4.85252e12	−1.13529	−0.567644	−	0.823274i	$-0.692145\pi$
$641$	−4.85252e12	−1.13529	−0.567644	+	0.823274i	$0.692145\pi$
$642$	9.64083e11i	0.223979i
$643$	− 1.57487e12i	− 0.363325i	−0.983361	−	0.181662i	$-0.941852\pi$
$643$	− 1.57487e12i	− 0.363325i	0.983361	−	0.181662i	$-0.0581478\pi$
$644$	−1.01207e12	−0.231860
$645$	0	0
$646$	3.99334e12	0.902172
$647$	6.93025e12i	1.55482i	0.628995	+	0.777410i	$0.283467\pi$
$647$	6.93025e12i	1.55482i	−0.628995	+	0.777410i	$0.716533\pi$
$648$	1.62113e12i	0.361185i
$649$	−3.93626e12	−0.870928
$650$	0	0
$651$	1.62729e12	0.355099
$652$	7.51015e12i	1.62755i
$653$	8.15499e12i	1.75515i	0.479440	+	0.877575i	$0.340840\pi$
$653$	8.15499e12i	1.75515i	−0.479440	+	0.877575i	$0.659160\pi$
$654$	2.27689e12	0.486679
$655$	0	0
$656$	1.85674e12	0.391458
$657$	− 2.75619e12i	− 0.577118i
$658$	− 1.20674e12i	− 0.250955i
$659$	2.92553e12	0.604255	0.302127	−	0.953268i	$-0.402303\pi$
$659$	2.92553e12	0.604255	0.302127	+	0.953268i	$0.402303\pi$
$660$	0	0
$661$	−1.62921e12	−0.331947	−0.165974	−	0.986130i	$-0.553077\pi$
$661$	−1.62921e12	−0.331947	−0.165974	+	0.986130i	$0.553077\pi$
$662$	1.92051e12i	0.388648i
$663$	− 6.54007e12i	− 1.31453i
$664$	−2.00990e12	−0.401254
$665$	0	0
$666$	−7.98768e11	−0.157321
$667$	− 2.23480e12i	− 0.437193i
$668$	6.25181e12i	1.21482i
$669$	3.63225e12	0.701064
$670$	0	0
$671$	−2.11395e12	−0.402572
$672$	2.55124e12i	0.482603i
$673$	2.87521e12i	0.540258i	0.962824	+	0.270129i	$0.0870664\pi$
$673$	2.87521e12i	0.540258i	−0.962824	+	0.270129i	$0.912934\pi$
$674$	−4.11049e11	−0.0767228
$675$	0	0
$676$	−1.27061e12	−0.234020
$677$	3.19620e12i	0.584769i	0.956301	+	0.292385i	$0.0944487\pi$
$677$	3.19620e12i	0.584769i	−0.956301	+	0.292385i	$0.905551\pi$
$678$	− 1.01749e12i	− 0.184925i
$679$	8.27332e10	0.0149371
$680$	0	0
$681$	−3.44988e12	−0.614670
$682$	− 1.24393e12i	− 0.220174i
$683$	5.47901e11i	0.0963406i	0.998839	+	0.0481703i	$0.0153390\pi$
$683$	5.47901e11i	0.0963406i	−0.998839	+	0.0481703i	$0.984661\pi$
$684$	3.02196e12	0.527881
$685$	0	0
$686$	2.12822e12	0.366908
$687$	− 2.34955e12i	− 0.402420i
$688$	1.07425e12i	0.182792i
$689$	4.60705e12	0.778819
$690$	0	0
$691$	5.90996e11	0.0986128	0.0493064	−	0.998784i	$-0.484299\pi$
$691$	5.90996e11	0.0986128	0.0493064	+	0.998784i	$0.484299\pi$
$692$	− 7.03361e12i	− 1.16601i
$693$	− 1.31075e12i	− 0.215884i
$694$	2.21248e12	0.362044
$695$	0	0
$696$	−3.67402e12	−0.593472
$697$	5.47110e12i	0.878066i
$698$	3.73274e12i	0.595221i
$699$	4.12378e11	0.0653354
$700$	0	0
$701$	7.12738e12	1.11481	0.557403	−	0.830242i	$-0.311798\pi$
$701$	7.12738e12	1.11481	0.557403	+	0.830242i	$0.311798\pi$
$702$	2.78815e12i	0.433310i
$703$	− 1.50619e13i	− 2.32584i
$704$	−2.02290e12	−0.310382
$705$	0	0
$706$	8.07981e11	0.122400
$707$	− 9.19122e11i	− 0.138352i
$708$	4.35060e12i	0.650728i
$709$	−9.09269e11	−0.135140	−0.0675701	−	0.997715i	$-0.521525\pi$
$709$	−9.09269e11	−0.135140	−0.0675701	+	0.997715i	$0.521525\pi$
$710$	0	0
$711$	−6.35538e11	−0.0932671
$712$	− 1.53129e11i	− 0.0223304i
$713$	− 1.79206e12i	− 0.259687i
$714$	−1.91440e12	−0.275670
$715$	0	0
$716$	1.12852e13	1.60472
$717$	− 2.52985e11i	− 0.0357485i
$718$	− 1.33158e12i	− 0.186985i
$719$	−1.08017e13	−1.50734	−0.753669	−	0.657254i	$-0.771718\pi$
$719$	−1.08017e13	−1.50734	−0.753669	+	0.657254i	$0.771718\pi$
$720$	0	0
$721$	−3.17401e12	−0.437421
$722$	− 5.55895e12i	− 0.761334i
$723$	2.94094e12i	0.400280i
$724$	4.68077e12	0.633132
$725$	0	0
$726$	−2.03165e11	−0.0271415
$727$	− 9.77691e12i	− 1.29807i	−0.760760	−	0.649033i	$-0.775174\pi$
$727$	− 9.77691e12i	− 1.29807i	0.760760	−	0.649033i	$-0.224826\pi$
$728$	3.77696e12i	0.498370i
$729$	−8.15697e12	−1.06968
$730$	0	0
$731$	−3.16540e12	−0.410016
$732$	2.33647e12i	0.300788i
$733$	− 3.52295e11i	− 0.0450753i	−0.999746	−	0.0225377i	$-0.992825\pi$
$733$	− 3.52295e11i	− 0.0450753i	0.999746	−	0.0225377i	$-0.00717457\pi$
$734$	−2.37905e12	−0.302531
$735$	0	0
$736$	2.80957e12	0.352931
$737$	2.09258e12i	0.261264i
$738$	− 5.91466e11i	− 0.0733966i
$739$	2.72124e12	0.335635	0.167818	−	0.985818i	$-0.446328\pi$
$739$	2.72124e12	0.335635	0.167818	+	0.985818i	$0.446328\pi$
$740$	0	0
$741$	−1.33320e13	−1.62447
$742$	− 1.34857e12i	− 0.163326i
$743$	5.85311e12i	0.704590i	0.935889	+	0.352295i	$0.114599\pi$
$743$	5.85311e12i	0.704590i	−0.935889	+	0.352295i	$0.885401\pi$
$744$	−2.94615e12	−0.352514
$745$	0	0
$746$	−1.56571e12	−0.185091
$747$	− 1.75003e12i	− 0.205638i
$748$	− 1.02438e13i	− 1.19648i
$749$	−4.48426e12	−0.520622
$750$	0	0
$751$	−5.13723e12	−0.589317	−0.294659	−	0.955603i	$-0.595206\pi$
$751$	−5.13723e12	−0.589317	−0.294659	+	0.955603i	$0.595206\pi$
$752$	− 5.97166e12i	− 0.680950i
$753$	− 1.01671e13i	− 1.15244i
$754$	−3.89203e12	−0.438536
$755$	0	0
$756$	−5.71299e12	−0.636086
$757$	− 1.45713e13i	− 1.61275i	−0.591407	−	0.806373i	$-0.701427\pi$
$757$	− 1.45713e13i	− 1.61275i	0.591407	−	0.806373i	$-0.298573\pi$
$758$	− 1.33607e12i	− 0.147001i
$759$	2.80534e12	0.306830
$760$	0	0
$761$	1.03936e13	1.12340	0.561700	−	0.827341i	$-0.310148\pi$
$761$	1.03936e13	1.12340	0.561700	+	0.827341i	$0.310148\pi$
$762$	2.84593e11i	0.0305793i
$763$	1.05905e13i	1.13125i
$764$	−4.33944e12	−0.460801
$765$	0	0
$766$	−5.76626e11	−0.0605152
$767$	9.87591e12i	1.03038i
$768$	− 2.27600e11i	− 0.0236073i
$769$	3.91664e12	0.403873	0.201936	−	0.979399i	$-0.435277\pi$
$769$	3.91664e12	0.403873	0.201936	+	0.979399i	$0.435277\pi$
$770$	0	0
$771$	1.25466e13	1.27874
$772$	9.15851e12i	0.927998i
$773$	6.36894e12i	0.641592i	0.947148	+	0.320796i	$0.103950\pi$
$773$	6.36894e12i	0.641592i	−0.947148	+	0.320796i	$0.896050\pi$
$774$	3.42203e11	0.0342728
$775$	0	0
$776$	−1.49786e11	−0.0148284
$777$	7.22063e12i	0.710690i
$778$	6.33800e12i	0.620217i
$779$	1.11529e13	1.08510
$780$	0	0
$781$	8.77802e12	0.844242
$782$	2.10824e12i	0.201600i
$783$	− 1.26151e13i	− 1.19940i
$784$	3.75489e12	0.354956
$785$	0	0
$786$	−2.56911e12	−0.240094
$787$	6.55343e11i	0.0608951i	0.999536	+	0.0304475i	$0.00969325\pi$
$787$	6.55343e11i	0.0608951i	−0.999536	+	0.0304475i	$0.990307\pi$
$788$	− 1.13089e13i	− 1.04485i
$789$	2.35267e12	0.216129
$790$	0	0
$791$	4.73265e12	0.429843
$792$	2.37307e12i	0.214312i
$793$	5.30382e12i	0.476277i
$794$	−1.17830e12	−0.105212
$795$	0	0
$796$	−3.61418e12	−0.319081
$797$	3.83799e12i	0.336931i	0.985708	+	0.168466i	$0.0538812\pi$
$797$	3.83799e12i	0.336931i	−0.985708	+	0.168466i	$0.946119\pi$
$798$	3.90252e12i	0.340668i
$799$	1.75962e13	1.52742
$800$	0	0
$801$	1.33330e11	0.0114441
$802$	2.57681e12i	0.219937i
$803$	1.90456e13i	1.61650i
$804$	2.31285e12	0.195207
$805$	0	0
$806$	−3.12097e12	−0.260484
$807$	3.01974e12i	0.250633i
$808$	1.66404e12i	0.137345i
$809$	−2.67581e12	−0.219627	−0.109814	−	0.993952i	$-0.535025\pi$
$809$	−2.67581e12	−0.219627	−0.109814	+	0.993952i	$0.535025\pi$
$810$	0	0
$811$	−2.32586e13	−1.88795	−0.943973	−	0.330023i	$-0.892943\pi$
$811$	−2.32586e13	−1.88795	−0.943973	+	0.330023i	$0.892943\pi$
$812$	− 7.97489e12i	− 0.643758i
$813$	3.92165e12i	0.314819i
$814$	5.51959e12	0.440653
$815$	0	0
$816$	−9.47360e12	−0.748014
$817$	6.45270e12i	0.506690i
$818$	− 3.17138e12i	− 0.247662i
$819$	−3.28861e12	−0.255408
$820$	0	0
$821$	1.65740e13	1.27316	0.636580	−	0.771211i	$-0.280349\pi$
$821$	1.65740e13	1.27316	0.636580	+	0.771211i	$0.280349\pi$
$822$	− 6.52364e12i	− 0.498387i
$823$	− 1.37332e13i	− 1.04345i	−0.853113	−	0.521726i	$-0.825288\pi$
$823$	− 1.37332e13i	− 1.04345i	0.853113	−	0.521726i	$-0.174712\pi$
$824$	5.74644e12	0.434236
$825$	0	0
$826$	2.89086e12	0.216081
$827$	1.80036e13i	1.33840i	0.743085	+	0.669198i	$0.233362\pi$
$827$	1.80036e13i	1.33840i	−0.743085	+	0.669198i	$0.766638\pi$
$828$	1.59541e12i	0.117960i
$829$	−2.11116e13	−1.55248	−0.776240	−	0.630438i	$-0.782875\pi$
$829$	−2.11116e13	−1.55248	−0.776240	+	0.630438i	$0.782875\pi$
$830$	0	0
$831$	1.20866e13	0.879225
$832$	5.07536e12i	0.367208i
$833$	1.10642e13i	0.796191i
$834$	−2.30118e12	−0.164704
$835$	0	0
$836$	−2.08821e13	−1.47858
$837$	− 1.01159e13i	− 0.712425i
$838$	− 9.85294e12i	− 0.690188i
$839$	3.47988e12	0.242458	0.121229	−	0.992625i	$-0.461317\pi$
$839$	3.47988e12	0.242458	0.121229	+	0.992625i	$0.461317\pi$
$840$	0	0
$841$	3.10254e12	0.213863
$842$	9.40003e12i	0.644503i
$843$	1.14341e13i	0.779789i
$844$	−3.60456e12	−0.244518
$845$	0	0
$846$	−1.90227e12	−0.127675
$847$	− 9.44984e11i	− 0.0630883i
$848$	− 6.67354e12i	− 0.443175i
$849$	−2.84198e11	−0.0187731
$850$	0	0
$851$	7.95175e12	0.519733
$852$	− 9.70202e12i	− 0.630789i
$853$	− 1.12686e13i	− 0.728784i	−0.931246	−	0.364392i	$-0.881277\pi$
$853$	− 1.12686e13i	− 0.728784i	0.931246	−	0.364392i	$-0.118723\pi$
$854$	1.55253e12	0.0998800
$855$	0	0
$856$	8.11860e12	0.516832
$857$	3.75227e12i	0.237618i	0.992917	+	0.118809i	$0.0379077\pi$
$857$	3.75227e12i	0.237618i	−0.992917	+	0.118809i	$0.962092\pi$
$858$	− 4.88566e12i	− 0.307773i
$859$	−1.57014e13	−0.983944	−0.491972	−	0.870611i	$-0.663724\pi$
$859$	−1.57014e13	−0.983944	−0.491972	+	0.870611i	$0.663724\pi$
$860$	0	0
$861$	−5.34668e12	−0.331566
$862$	1.85862e12i	0.114659i
$863$	1.39316e13i	0.854975i	0.904021	+	0.427487i	$0.140601\pi$
$863$	1.39316e13i	0.854975i	−0.904021	+	0.427487i	$0.859399\pi$
$864$	1.58595e13	0.968231
$865$	0	0
$866$	1.21243e12	0.0732531
$867$	− 1.43960e13i	− 0.865279i
$868$	− 6.39495e12i	− 0.382383i
$869$	4.39165e12	0.261239
$870$	0	0
$871$	5.25021e12	0.309097
$872$	− 1.91738e13i	− 1.12301i
$873$	− 1.30419e11i	− 0.00759935i
$874$	4.29767e12	0.249133
$875$	0	0
$876$	2.10504e13	1.20779
$877$	− 1.59832e13i	− 0.912357i	−0.889888	−	0.456179i	$-0.849218\pi$
$877$	− 1.59832e13i	− 0.912357i	0.889888	−	0.456179i	$-0.150782\pi$
$878$	− 4.17108e12i	− 0.236877i
$879$	−9.65658e12	−0.545599
$880$	0	0
$881$	−3.16227e13	−1.76851	−0.884255	−	0.467005i	$-0.845333\pi$
$881$	−3.16227e13	−1.76851	−0.884255	+	0.467005i	$0.845333\pi$
$882$	− 1.19612e12i	− 0.0665527i
$883$	1.48526e13i	0.822202i	0.911590	+	0.411101i	$0.134856\pi$
$883$	1.48526e13i	0.822202i	−0.911590	+	0.411101i	$0.865144\pi$
$884$	−2.57013e13	−1.41553
$885$	0	0
$886$	−8.81356e12	−0.480507
$887$	− 9.39325e12i	− 0.509518i	−0.967005	−	0.254759i	$-0.918004\pi$
$887$	− 9.39325e12i	− 0.509518i	0.967005	−	0.254759i	$-0.0819961\pi$
$888$	− 1.30727e13i	− 0.705516i
$889$	−1.32373e12	−0.0710792
$890$	0	0
$891$	9.75378e12	0.518470
$892$	− 1.42741e13i	− 0.754930i
$893$	− 3.58699e13i	− 1.88755i
$894$	−1.33636e12	−0.0699687
$895$	0	0
$896$	1.29439e13	0.670930
$897$	− 7.03849e12i	− 0.363006i
$898$	4.68538e12i	0.240437i
$899$	1.41210e13	0.721018
$900$	0	0
$901$	1.96643e13	0.994071
$902$	4.08710e12i	0.205582i
$903$	− 3.09341e12i	− 0.154826i
$904$	−8.56830e12	−0.426714
$905$	0	0
$906$	3.33350e12	0.164370
$907$	2.64429e13i	1.29741i	0.761041	+	0.648704i	$0.224689\pi$
$907$	2.64429e13i	1.29741i	−0.761041	+	0.648704i	$0.775311\pi$
$908$	1.35574e13i	0.661898i
$909$	−1.44888e12	−0.0703876
$910$	0	0
$911$	−3.41645e13	−1.64339	−0.821697	−	0.569924i	$-0.806972\pi$
$911$	−3.41645e13	−1.64339	−0.821697	+	0.569924i	$0.806972\pi$
$912$	1.93120e13i	0.924381i
$913$	1.20929e13i	0.575987i
$914$	−4.56643e12	−0.216431
$915$	0	0
$916$	−9.23333e12	−0.433340
$917$	− 1.19498e13i	− 0.558081i
$918$	1.19007e13i	0.553069i
$919$	−3.14366e13	−1.45384	−0.726920	−	0.686723i	$-0.759049\pi$
$919$	−3.14366e13	−1.45384	−0.726920	+	0.686723i	$0.759049\pi$
$920$	0	0
$921$	−7.24478e11	−0.0331785
$922$	6.08223e12i	0.277188i
$923$	− 2.20237e13i	− 0.998809i
$924$	1.00108e13	0.451801
$925$	0	0
$926$	5.71431e12	0.255396
$927$	5.00344e12i	0.222541i
$928$	2.21387e13i	0.979909i
$929$	8.77007e12	0.386307	0.193153	−	0.981169i	$-0.438128\pi$
$929$	8.77007e12	0.386307	0.193153	+	0.981169i	$0.438128\pi$
$930$	0	0
$931$	2.25545e13	0.983918
$932$	− 1.62057e12i	− 0.0703553i
$933$	3.09228e13i	1.33602i
$934$	6.26017e12	0.269169
$935$	0	0
$936$	5.95393e12	0.253549
$937$	− 1.66294e13i	− 0.704770i	−0.935855	−	0.352385i	$-0.885371\pi$
$937$	− 1.66294e13i	− 0.704770i	0.935855	−	0.352385i	$-0.114629\pi$
$938$	− 1.53683e12i	− 0.0648206i
$939$	1.86389e13	0.782392
$940$	0	0
$941$	−7.56052e12	−0.314339	−0.157169	−	0.987572i	$-0.550237\pi$
$941$	−7.56052e12	−0.314339	−0.157169	+	0.987572i	$0.550237\pi$
$942$	5.06334e12i	0.209512i
$943$	5.88806e12i	0.242476i
$944$	1.43057e13	0.586322
$945$	0	0
$946$	−2.36466e12	−0.0959974
$947$	3.40925e13i	1.37747i	0.725011	+	0.688737i	$0.241835\pi$
$947$	3.40925e13i	1.37747i	−0.725011	+	0.688737i	$0.758165\pi$
$948$	− 4.85393e12i	− 0.195189i
$949$	4.77846e13	1.91245
$950$	0	0
$951$	−2.89111e13	−1.14618
$952$	1.61212e13i	0.636110i
$953$	− 3.45885e13i	− 1.35836i	−0.733973	−	0.679178i	$-0.762336\pi$
$953$	− 3.45885e13i	− 1.35836i	0.733973	−	0.679178i	$-0.237664\pi$
$954$	−2.12586e12	−0.0830933
$955$	0	0
$956$	−9.94185e11	−0.0384952
$957$	2.21054e13i	0.851911i
$958$	− 5.56591e12i	− 0.213497i
$959$	3.03435e13	1.15846
$960$	0	0
$961$	−1.51162e13	−0.571726
$962$	− 1.38484e13i	− 0.521329i
$963$	7.06889e12i	0.264870i
$964$	1.15574e13	0.431035
$965$	0	0
$966$	−2.06029e12	−0.0761258
$967$	4.59891e13i	1.69136i	0.533691	+	0.845680i	$0.320805\pi$
$967$	4.59891e13i	1.69136i	−0.533691	+	0.845680i	$0.679195\pi$
$968$	1.71086e12i	0.0626290i
$969$	−5.69050e13	−2.07345
$970$	0	0
$971$	2.72663e13	0.984327	0.492164	−	0.870503i	$-0.336206\pi$
$971$	2.72663e13	0.984327	0.492164	+	0.870503i	$0.336206\pi$
$972$	1.57279e13i	0.565163i
$973$	− 1.07035e13i	− 0.382842i
$974$	−1.32156e13	−0.470515
$975$	0	0
$976$	7.68284e12	0.271018
$977$	− 4.92228e13i	− 1.72839i	−0.503160	−	0.864193i	$-0.667829\pi$
$977$	− 4.92228e13i	− 1.72839i	0.503160	−	0.864193i	$-0.332171\pi$
$978$	1.52885e13i	0.534368i
$979$	−9.21324e11	−0.0320546
$980$	0	0
$981$	1.66947e13	0.575530
$982$	− 9.59909e12i	− 0.329404i
$983$	− 3.98337e13i	− 1.36069i	−0.732891	−	0.680346i	$-0.761830\pi$
$983$	− 3.98337e13i	− 1.36069i	0.732891	−	0.680346i	$-0.238170\pi$
$984$	9.67998e12	0.329152
$985$	0	0
$986$	−1.66124e13	−0.559740
$987$	1.71960e13i	0.576766i
$988$	5.23924e13i	1.74929i
$989$	−3.40664e12	−0.113225
$990$	0	0
$991$	−2.56388e13	−0.844434	−0.422217	−	0.906495i	$-0.638748\pi$
$991$	−2.56388e13	−0.844434	−0.422217	+	0.906495i	$0.638748\pi$
$992$	1.77527e13i	0.582052i
$993$	− 2.73673e13i	− 0.893224i
$994$	−6.44674e12	−0.209460
$995$	0	0
$996$	1.33659e13	0.430358
$997$	− 4.97241e13i	− 1.59382i	−0.604099	−	0.796909i	$-0.706467\pi$
$997$	− 4.97241e13i	− 1.59382i	0.604099	−	0.796909i	$-0.293533\pi$
$998$	1.14517e13i	0.365410i
$999$	4.48863e13	1.42584

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.10.b.a.24.1		2
3.2	odd	2		225.10.b.d.199.2		2
4.3	odd	2		400.10.c.e.49.1		2
5.2	odd	4		25.10.a.a.1.1		1
5.3	odd	4		5.10.a.a.1.1	✓	1
5.4	even	2	inner	25.10.b.a.24.2		2
15.2	even	4		225.10.a.b.1.1		1
15.8	even	4		45.10.a.c.1.1		1
15.14	odd	2		225.10.b.d.199.1		2
20.3	even	4		80.10.a.d.1.1		1
20.7	even	4		400.10.a.c.1.1		1
20.19	odd	2		400.10.c.e.49.2		2
35.13	even	4		245.10.a.a.1.1		1
40.3	even	4		320.10.a.c.1.1		1
40.13	odd	4		320.10.a.h.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.10.a.a.1.1	✓	1	5.3	odd	4
25.10.a.a.1.1		1	5.2	odd	4
25.10.b.a.24.1		2	1.1	even	1	trivial
25.10.b.a.24.2		2	5.4	even	2	inner
45.10.a.c.1.1		1	15.8	even	4
80.10.a.d.1.1		1	20.3	even	4
225.10.a.b.1.1		1	15.2	even	4
225.10.b.d.199.1		2	15.14	odd	2
225.10.b.d.199.2		2	3.2	odd	2
245.10.a.a.1.1		1	35.13	even	4
320.10.a.c.1.1		1	40.3	even	4
320.10.a.h.1.1		1	40.13	odd	4
400.10.a.c.1.1		1	20.7	even	4
400.10.c.e.49.1		2	4.3	odd	2
400.10.c.e.49.2		2	20.19	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q-8.00000i q^{2} +114.000i q^{3} +448.000 q^{4} +912.000 q^{6} +4242.00i q^{7} -7680.00i q^{8} +6687.00 q^{9} +O(q^{10})\)	\(q-8.00000i q^{2} +114.000i q^{3} +448.000 q^{4} +912.000 q^{6} +4242.00i q^{7} -7680.00i q^{8} +6687.00 q^{9} -46208.0 q^{11} +51072.0i q^{12} +115934. i q^{13} +33936.0 q^{14} +167936. q^{16} +494842. i q^{17} -53496.0i q^{18} +1.00874e6 q^{19} -483588. q^{21} +369664. i q^{22} +532554. i q^{23} +875520. q^{24} +927472. q^{26} +3.00618e6i q^{27} +1.90042e6i q^{28} -4.19639e6 q^{29} -3.36503e6 q^{31} -5.27565e6i q^{32} -5.26771e6i q^{33} +3.95874e6 q^{34} +2.99578e6 q^{36} -1.49314e7i q^{37} -8.06992e6i q^{38} -1.32165e7 q^{39} +1.10563e7 q^{41} +3.86870e6i q^{42} +6.39679e6i q^{43} -2.07012e7 q^{44} +4.26043e6 q^{46} -3.55592e7i q^{47} +1.91447e7i q^{48} +2.23590e7 q^{49} -5.64120e7 q^{51} +5.19384e7i q^{52} -3.97386e7i q^{53} +2.40494e7 q^{54} +3.25786e7 q^{56} +1.14996e8i q^{57} +3.35711e7i q^{58} +8.51856e7 q^{59} +4.57486e7 q^{61} +2.69202e7i q^{62} +2.83663e7i q^{63} +4.37780e7 q^{64} -4.21417e7 q^{66} -4.52862e7i q^{67} +2.21689e8i q^{68} -6.07112e7 q^{69} -1.89967e8 q^{71} -5.13562e7i q^{72} -4.12171e8i q^{73} -1.19451e8 q^{74} +4.51916e8 q^{76} -1.96014e8i q^{77} +1.05732e8i q^{78} -9.50408e7 q^{79} -2.11084e8 q^{81} -8.84501e7i q^{82} -2.61706e8i q^{83} -2.16647e8 q^{84} +5.11744e7 q^{86} -4.78388e8i q^{87} +3.54877e8i q^{88} +1.99386e7 q^{89} -4.91792e8 q^{91} +2.38584e8i q^{92} -3.83613e8i q^{93} -2.84473e8 q^{94} +6.01424e8 q^{96} -1.95034e7i q^{97} -1.78872e8i q^{98} -3.08993e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 896 q^{4} + 1824 q^{6} + 13374 q^{9}+O(q^{10}) \) 2 * q + 896 * q^4 + 1824 * q^6 + 13374 * q^9	\( 2 q + 896 q^{4} + 1824 q^{6} + 13374 q^{9} - 92416 q^{11} + 67872 q^{14} + 335872 q^{16} + 2017480 q^{19} - 967176 q^{21} + 1751040 q^{24} + 1854944 q^{26} - 8392780 q^{29} - 6730056 q^{31} + 7917472 q^{34} + 5991552 q^{36} - 26432952 q^{39} + 22112524 q^{41} - 41402368 q^{44} + 8520864 q^{46} + 44718086 q^{49} - 112823976 q^{51} + 48098880 q^{54} + 65157120 q^{56} + 170371240 q^{59} + 91497284 q^{61} + 87556096 q^{64} - 84283392 q^{66} - 121422312 q^{69} - 379934936 q^{71} - 238901728 q^{74} + 903831040 q^{76} - 190081680 q^{79} - 422168598 q^{81} - 433294848 q^{84} + 102348704 q^{86} + 39877260 q^{89} - 983584056 q^{91} - 568946528 q^{94} + 1202847744 q^{96} - 617985792 q^{99}+O(q^{100}) \) 2 * q + 896 * q^4 + 1824 * q^6 + 13374 * q^9 - 92416 * q^11 + 67872 * q^14 + 335872 * q^16 + 2017480 * q^19 - 967176 * q^21 + 1751040 * q^24 + 1854944 * q^26 - 8392780 * q^29 - 6730056 * q^31 + 7917472 * q^34 + 5991552 * q^36 - 26432952 * q^39 + 22112524 * q^41 - 41402368 * q^44 + 8520864 * q^46 + 44718086 * q^49 - 112823976 * q^51 + 48098880 * q^54 + 65157120 * q^56 + 170371240 * q^59 + 91497284 * q^61 + 87556096 * q^64 - 84283392 * q^66 - 121422312 * q^69 - 379934936 * q^71 - 238901728 * q^74 + 903831040 * q^76 - 190081680 * q^79 - 422168598 * q^81 - 433294848 * q^84 + 102348704 * q^86 + 39877260 * q^89 - 983584056 * q^91 - 568946528 * q^94 + 1202847744 * q^96 - 617985792 * q^99

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