LMFDB - Embedded newform 25.20.b.a.24.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,20,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, 20, names="a")

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

chi := DirichletCharacter("25.24");

S:= CuspForms(chi, 20);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 20 $
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:	$57.2041741391$
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:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2 $
Twist minimal:	no (minimal twist has level 1)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			24.2
Root			$1.00000i$ of defining polynomial
Character	$\chi$	$=$	25.24
Dual form			25.20.b.a.24.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+456.000i q^{2} -50652.0i q^{3} +316352. q^{4} +2.30973e7 q^{6} -1.69175e7i q^{7} +3.83332e8i q^{8} -1.40336e9 q^{9} +O(q^{10})$	\(q+456.000i q^{2} -50652.0i q^{3} +316352. q^{4} +2.30973e7 q^{6} -1.69175e7i q^{7} +3.83332e8i q^{8} -1.40336e9 q^{9} -1.62121e7 q^{11} -1.60239e10i q^{12} -5.04216e10i q^{13} +7.71440e9 q^{14} -8.93976e9 q^{16} +2.25070e11i q^{17} -6.39934e11i q^{18} +1.71028e12 q^{19} -8.56907e11 q^{21} -7.39272e9i q^{22} -1.40365e13i q^{23} +1.94165e13 q^{24} +2.29923e13 q^{26} +1.22123e13i q^{27} -5.35190e12i q^{28} -1.13784e12 q^{29} -1.04627e14 q^{31} +1.96900e14i q^{32} +8.21176e11i q^{33} -1.02632e14 q^{34} -4.43957e14 q^{36} -1.69392e14i q^{37} +7.79887e14i q^{38} -2.55396e15 q^{39} -3.30998e15 q^{41} -3.90750e14i q^{42} -1.12791e15i q^{43} -5.12873e12 q^{44} +6.40066e15 q^{46} +3.49869e15i q^{47} +4.52817e14i q^{48} +1.11127e16 q^{49} +1.14003e16 q^{51} -1.59510e16i q^{52} -2.99563e16i q^{53} -5.56881e15 q^{54} +6.48503e15 q^{56} -8.66290e16i q^{57} -5.18853e14i q^{58} -5.83914e16 q^{59} +2.33737e16 q^{61} -4.77099e16i q^{62} +2.37415e16i q^{63} -9.44733e16 q^{64} -3.74456e14 q^{66} -2.05103e17i q^{67} +7.12014e16i q^{68} -7.10979e17 q^{69} -1.77902e17 q^{71} -5.37954e17i q^{72} -2.99854e17i q^{73} +7.72429e16 q^{74} +5.41050e17 q^{76} +2.74269e14i q^{77} -1.16460e18i q^{78} +9.22271e16 q^{79} -1.01250e18 q^{81} -1.50935e18i q^{82} -1.20854e18i q^{83} -2.71084e17 q^{84} +5.14329e17 q^{86} +5.76336e16i q^{87} -6.21462e15i q^{88} -4.37120e18 q^{89} -8.53010e17 q^{91} -4.44049e18i q^{92} +5.29956e18i q^{93} -1.59540e18 q^{94} +9.97337e18 q^{96} -6.35013e17i q^{97} +5.06739e18i q^{98} +2.27515e16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 632704 q^{4} + 46194624 q^{6} - 2806727274 q^{9}+O(q^{10}) $ 2 * q + 632704 * q^4 + 46194624 * q^6 - 2806727274 * q^9	$ 2 q + 632704 q^{4} + 46194624 q^{6} - 2806727274 q^{9} - 32424216 q^{11} + 15428800128 q^{14} - 17879523328 q^{16} + 3420557145320 q^{19} - 1713814877376 q^{21} + 38833048719360 q^{24} + 45984512936544 q^{26} - 2275670539020 q^{29} - 209253760283456 q^{31} - 205263930749472 q^{34} - 887913786584448 q^{36} - 51\!\cdots\!48 q^{39}+ \cdots + 45\!\cdots\!92 q^{99}+O(q^{100}) $ 2 * q + 632704 * q^4 + 46194624 * q^6 - 2806727274 * q^9 - 32424216 * q^11 + 15428800128 * q^14 - 17879523328 * q^16 + 3420557145320 * q^19 - 1713814877376 * q^21 + 38833048719360 * q^24 + 45984512936544 * q^26 - 2275670539020 * q^29 - 209253760283456 * q^31 - 205263930749472 * q^34 - 887913786584448 * q^36 - 5107911292240848 * q^39 - 6619969501121676 * q^41 - 10257465580032 * q^44 + 12801319727451264 * q^46 + 22225383780762414 * q^49 + 22800501360355824 * q^51 - 11137624088734080 * q^54 + 12970066539601920 * q^56 - 116782795285464840 * q^59 + 46747370265345484 * q^61 - 188946593725546496 * q^64 - 748912233307392 * q^66 - 1421957120251889088 * q^69 - 355804683900835536 * q^71 + 154485802561981728 * q^74 + 1082100094036272640 * q^76 + 184454180288014880 * q^79 - 2024995398986399598 * q^81 - 542168764087652352 * q^84 + 1028657141360464704 * q^86 - 8742402384580608660 * q^89 - 1706019782724895456 * q^91 - 3190808916758921472 * q^94 + 19946732518257721344 * q^96 + 45502965692633592 * 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 $

$2$	456.000i	0.629767i	0.949130	+	0.314883i	$0.101965\pi$
$2$	456.000i	0.629767i	−0.949130	+	0.314883i	$0.898035\pi$
$3$	− 50652.0i	− 1.48575i	−0.669432	−	0.742873i	$-0.733463\pi$
$3$	− 50652.0i	− 1.48575i	0.669432	−	0.742873i	$-0.266537\pi$
$4$	316352.	0.603394
$5$	0	0
$5$	0	0
$6$	2.30973e7	0.935674
$7$	− 1.69175e7i	− 0.158455i	−0.996857	−	0.0792275i	$-0.974755\pi$
$7$	− 1.69175e7i	− 0.158455i	0.996857	−	0.0792275i	$-0.0252454\pi$
$8$	3.83332e8i	1.00976i
$9$	−1.40336e9	−1.20744
$10$	0	0
$11$	−1.62121e7	−0.00207305	−0.00103652	−	0.999999i	$-0.500330\pi$
$11$	−1.62121e7	−0.00207305	−0.00103652	+	0.999999i	$0.500330\pi$
$12$	− 1.60239e10i	− 0.896490i
$13$	− 5.04216e10i	− 1.31873i	−0.751824	−	0.659364i	$-0.770826\pi$
$13$	− 5.04216e10i	− 1.31873i	0.751824	−	0.659364i	$-0.229174\pi$
$14$	7.71440e9	0.0997897
$15$	0	0
$16$	−8.93976e9	−0.0325227
$17$	2.25070e11i	0.460313i	0.973154	+	0.230156i	$0.0739238\pi$
$17$	2.25070e11i	0.460313i	−0.973154	+	0.230156i	$0.926076\pi$
$18$	− 6.39934e11i	− 0.760407i
$19$	1.71028e12	1.21593	0.607964	−	0.793965i	$-0.291987\pi$
$19$	1.71028e12	1.21593	0.607964	+	0.793965i	$0.291987\pi$
$20$	0	0
$21$	−8.56907e11	−0.235424
$22$	− 7.39272e9i	− 0.00130554i
$23$	− 1.40365e13i	− 1.62497i	−0.582982	−	0.812485i	$-0.698114\pi$
$23$	− 1.40365e13i	− 1.62497i	0.582982	−	0.812485i	$-0.301886\pi$
$24$	1.94165e13	1.50025
$25$	0	0
$26$	2.29923e13	0.830491
$27$	1.22123e13i	0.308207i
$28$	− 5.35190e12i	− 0.0956107i
$29$	−1.13784e12	−0.0145646	−0.00728230	−	0.999973i	$-0.502318\pi$
$29$	−1.13784e12	−0.0145646	−0.00728230	+	0.999973i	$0.502318\pi$
$30$	0	0
$31$	−1.04627e14	−0.710734	−0.355367	−	0.934727i	$-0.615644\pi$
$31$	−1.04627e14	−0.710734	−0.355367	+	0.934727i	$0.615644\pi$
$32$	1.96900e14i	0.989283i
$33$	8.21176e11i	0.00308002i
$34$	−1.02632e14	−0.289890
$35$	0	0
$36$	−4.43957e14	−0.728563
$37$	− 1.69392e14i	− 0.214278i	−0.994244	−	0.107139i	$-0.965831\pi$
$37$	− 1.69392e14i	− 0.214278i	0.994244	−	0.107139i	$-0.0341690\pi$
$38$	7.79887e14i	0.765751i
$39$	−2.55396e15	−1.95929
$40$	0	0
$41$	−3.30998e15	−1.57899	−0.789495	−	0.613757i	$-0.789657\pi$
$41$	−3.30998e15	−1.57899	−0.789495	+	0.613757i	$0.789657\pi$
$42$	− 3.90750e14i	− 0.148262i
$43$	− 1.12791e15i	− 0.342236i	−0.985251	−	0.171118i	$-0.945262\pi$
$43$	− 1.12791e15i	− 0.342236i	0.985251	−	0.171118i	$-0.0547379\pi$
$44$	−5.12873e12	−0.00125086
$45$	0	0
$46$	6.40066e15	1.02335
$47$	3.49869e15i	0.456012i	0.973660	+	0.228006i	$0.0732206\pi$
$47$	3.49869e15i	0.456012i	−0.973660	+	0.228006i	$0.926779\pi$
$48$	4.52817e14i	0.0483204i
$49$	1.11127e16	0.974892
$50$	0	0
$51$	1.14003e16	0.683908
$52$	− 1.59510e16i	− 0.795711i
$53$	− 2.99563e16i	− 1.24700i	−0.781822	−	0.623501i	$-0.785710\pi$
$53$	− 2.99563e16i	− 1.24700i	0.781822	−	0.623501i	$-0.214290\pi$
$54$	−5.56881e15	−0.194098
$55$	0	0
$56$	6.48503e15	0.160002
$57$	− 8.66290e16i	− 1.80656i
$58$	− 5.18853e14i	− 0.00917230i
$59$	−5.83914e16	−0.877515	−0.438758	−	0.898605i	$-0.644581\pi$
$59$	−5.83914e16	−0.877515	−0.438758	+	0.898605i	$0.644581\pi$
$60$	0	0
$61$	2.33737e16	0.255914	0.127957	−	0.991780i	$-0.459158\pi$
$61$	2.33737e16	0.255914	0.127957	+	0.991780i	$0.459158\pi$
$62$	− 4.77099e16i	− 0.447597i
$63$	2.37415e16i	0.191325i
$64$	−9.44733e16	−0.655540
$65$	0	0
$66$	−3.74456e14	−0.00193970
$67$	− 2.05103e17i	− 0.921002i	−0.887659	−	0.460501i	$-0.847670\pi$
$67$	− 2.05103e17i	− 0.921002i	0.887659	−	0.460501i	$-0.152330\pi$
$68$	7.12014e16i	0.277750i
$69$	−7.10979e17	−2.41429
$70$	0	0
$71$	−1.77902e17	−0.460498	−0.230249	−	0.973132i	$-0.573954\pi$
$71$	−1.77902e17	−0.460498	−0.230249	+	0.973132i	$0.573954\pi$
$72$	− 5.37954e17i	− 1.21923i
$73$	− 2.99854e17i	− 0.596132i	−0.954545	−	0.298066i	$-0.903658\pi$
$73$	− 2.99854e17i	− 0.596132i	0.954545	−	0.298066i	$-0.0963415\pi$
$74$	7.72429e16	0.134945
$75$	0	0
$76$	5.41050e17	0.733683
$77$	2.74269e14i	0 0.000328485i
$78$	− 1.16460e18i	− 1.23390i
$79$	9.22271e16	0.0865767	0.0432884	−	0.999063i	$-0.486217\pi$
$79$	9.22271e16	0.0865767	0.0432884	+	0.999063i	$0.486217\pi$
$80$	0	0
$81$	−1.01250e18	−0.749525
$82$	− 1.50935e18i	− 0.994396i
$83$	− 1.20854e18i	− 0.709611i	−0.934940	−	0.354805i	$-0.884547\pi$
$83$	− 1.20854e18i	− 0.709611i	0.934940	−	0.354805i	$-0.115453\pi$
$84$	−2.71084e17	−0.142053
$85$	0	0
$86$	5.14329e17	0.215529
$87$	5.76336e16i	0.0216393i
$88$	− 6.21462e15i	− 0.00209329i
$89$	−4.37120e18	−1.32250	−0.661250	−	0.750166i	$-0.729974\pi$
$89$	−4.37120e18	−1.32250	−0.661250	+	0.750166i	$0.729974\pi$
$90$	0	0
$91$	−8.53010e17	−0.208959
$92$	− 4.44049e18i	− 0.980497i
$93$	5.29956e18i	1.05597i
$94$	−1.59540e18	−0.287181
$95$	0	0
$96$	9.97337e18	1.46982
$97$	− 6.35013e17i	− 0.0848108i	−0.999100	−	0.0424054i	$-0.986498\pi$
$97$	− 6.35013e17i	− 0.0848108i	0.999100	−	0.0424054i	$-0.0135021\pi$
$98$	5.06739e18i	0.613955i
$99$	2.27515e16	0.00250308
$100$	0	0
$101$	−1.42252e19	−1.29421	−0.647105	−	0.762401i	$-0.724021\pi$
$101$	−1.42252e19	−1.29421	−0.647105	+	0.762401i	$0.724021\pi$
$102$	5.19851e18i	0.430703i
$103$	− 4.90729e18i	− 0.370586i	−0.982683	−	0.185293i	$-0.940677\pi$
$103$	− 4.90729e18i	− 0.370586i	0.982683	−	0.185293i	$-0.0593233\pi$
$104$	1.93282e19	1.33160
$105$	0	0
$106$	1.36601e19	0.785321
$107$	2.64625e19i	1.39151i	0.718281	+	0.695753i	$0.244929\pi$
$107$	2.64625e19i	1.39151i	−0.718281	+	0.695753i	$0.755071\pi$
$108$	3.86339e18i	0.185970i
$109$	1.84178e19	0.812242	0.406121	−	0.913819i	$-0.366881\pi$
$109$	1.84178e19	0.812242	0.406121	+	0.913819i	$0.366881\pi$
$110$	0	0
$111$	−8.58006e18	−0.318363
$112$	1.51239e17i	0.00515338i
$113$	− 2.57421e19i	− 0.806118i	−0.915174	−	0.403059i	$-0.867947\pi$
$113$	− 2.57421e19i	− 0.806118i	0.915174	−	0.403059i	$-0.132053\pi$
$114$	3.95028e19	1.13771
$115$	0	0
$116$	−3.59956e17	−0.00878818
$117$	7.07599e19i	1.59229i
$118$	− 2.66265e19i	− 0.552630i
$119$	3.80763e18	0.0729389
$120$	0	0
$121$	−6.11588e19	−0.999996
$122$	1.06584e19i	0.161166i
$123$	1.67657e20i	2.34598i
$124$	−3.30989e19	−0.428852
$125$	0	0
$126$	−1.08261e19	−0.120490
$127$	8.80720e19i	0.909290i	0.890673	+	0.454645i	$0.150234\pi$
$127$	8.80720e19i	0.909290i	−0.890673	+	0.454645i	$0.849766\pi$
$128$	6.01524e19i	0.576445i
$129$	−5.71311e19	−0.508476
$130$	0	0
$131$	7.19289e19	0.553129	0.276564	−	0.960995i	$-0.410804\pi$
$131$	7.19289e19	0.553129	0.276564	+	0.960995i	$0.410804\pi$
$132$	2.59781e17i	0.00185846i
$133$	− 2.89337e19i	− 0.192670i
$134$	9.35268e19	0.580016
$135$	0	0
$136$	−8.62765e19	−0.464807
$137$	− 2.95426e20i	− 1.48458i	−0.670079	−	0.742290i	$-0.733740\pi$
$137$	− 2.95426e20i	− 1.48458i	0.670079	−	0.742290i	$-0.266260\pi$
$138$	− 3.24206e20i	− 1.52044i
$139$	−1.38478e20	−0.606375	−0.303187	−	0.952931i	$-0.598051\pi$
$139$	−1.38478e20	−0.606375	−0.303187	+	0.952931i	$0.598051\pi$
$140$	0	0
$141$	1.77216e20	0.677518
$142$	− 8.11235e19i	− 0.290006i
$143$	8.17441e17i	0.00273378i
$144$	1.25457e19	0.0392692
$145$	0	0
$146$	1.36733e20	0.375424
$147$	− 5.62880e20i	− 1.44844i
$148$	− 5.35876e19i	− 0.129294i
$149$	2.66021e20	0.602070	0.301035	−	0.953613i	$-0.402668\pi$
$149$	2.66021e20	0.602070	0.301035	+	0.953613i	$0.402668\pi$
$150$	0	0
$151$	5.75578e20	1.14769	0.573844	−	0.818965i	$-0.305452\pi$
$151$	5.75578e20	1.14769	0.573844	+	0.818965i	$0.305452\pi$
$152$	6.55604e20i	1.22780i
$153$	− 3.15855e20i	− 0.555801i
$154$	−1.25067e17	−0.000206869 0
$155$	0	0
$156$	−8.07949e20	−1.18223
$157$	− 1.07238e21i	− 1.47673i	−0.674403	−	0.738363i	$-0.735599\pi$
$157$	− 1.07238e21i	− 1.47673i	0.674403	−	0.738363i	$-0.264401\pi$
$158$	4.20556e19i	0.0545232i
$159$	−1.51735e21	−1.85273
$160$	0	0
$161$	−2.37464e20	−0.257485
$162$	− 4.61699e20i	− 0.472026i
$163$	5.80765e20i	0.560039i	0.959994	+	0.280019i	$0.0903409\pi$
$163$	5.80765e20i	0.560039i	−0.959994	+	0.280019i	$0.909659\pi$
$164$	−1.04712e21	−0.952752
$165$	0	0
$166$	5.51096e20	0.446889
$167$	2.43392e20i	0.186423i	0.995646	+	0.0932117i	$0.0297133\pi$
$167$	2.43392e20i	0.186423i	−0.995646	+	0.0932117i	$0.970287\pi$
$168$	− 3.28480e20i	− 0.237723i
$169$	−1.08042e21	−0.739041
$170$	0	0
$171$	−2.40014e21	−1.46816
$172$	− 3.56818e20i	− 0.206503i
$173$	1.19350e21i	0.653711i	0.945074	+	0.326855i	$0.105989\pi$
$173$	1.19350e21i	0.653711i	−0.945074	+	0.326855i	$0.894011\pi$
$174$	−2.62809e19	−0.0136277
$175$	0	0
$176$	1.44932e17	6.74210e−5 0
$177$	2.95764e21i	1.30377i
$178$	− 1.99327e21i	− 0.832867i
$179$	4.14664e21	1.64283	0.821415	−	0.570331i	$-0.193185\pi$
$179$	4.14664e21	1.64283	0.821415	+	0.570331i	$0.193185\pi$
$180$	0	0
$181$	3.32364e21	1.18486	0.592430	−	0.805622i	$-0.298169\pi$
$181$	3.32364e21	1.18486	0.592430	+	0.805622i	$0.298169\pi$
$182$	− 3.88973e20i	− 0.131595i
$183$	− 1.18392e21i	− 0.380223i
$184$	5.38065e21	1.64084
$185$	0	0
$186$	−2.41660e21	−0.665015
$187$	− 3.64886e18i	0 0.000954250i
$188$	1.10682e21i	0.275155i
$189$	2.06602e20	0.0488369
$190$	0	0
$191$	6.19380e21	1.32477	0.662384	−	0.749164i	$-0.269545\pi$
$191$	6.19380e21	1.32477	0.662384	+	0.749164i	$0.269545\pi$
$192$	4.78526e21i	0.973966i
$193$	5.20697e21i	1.00877i	0.863480	+	0.504383i	$0.168280\pi$
$193$	5.20697e21i	1.00877i	−0.863480	+	0.504383i	$0.831720\pi$
$194$	2.89566e20	0.0534111
$195$	0	0
$196$	3.51552e21	0.588244
$197$	2.42384e21i	0.386433i	0.981156	+	0.193216i	$0.0618920\pi$
$197$	2.42384e21i	0.386433i	−0.981156	+	0.193216i	$0.938108\pi$
$198$	1.03747e19i	0.00157636i
$199$	1.05907e21	0.153399	0.0766993	−	0.997054i	$-0.475562\pi$
$199$	1.05907e21	0.153399	0.0766993	+	0.997054i	$0.475562\pi$
$200$	0	0
$201$	−1.03889e22	−1.36837
$202$	− 6.48668e21i	− 0.815051i
$203$	1.92494e19i	0.00230783i
$204$	3.60649e21	0.412666
$205$	0	0
$206$	2.23773e21	0.233383
$207$	1.96984e22i	1.96206i
$208$	4.50757e20i	0.0428885i
$209$	−2.77272e19	−0.00252067
$210$	0	0
$211$	−1.32424e22	−1.09972	−0.549861	−	0.835256i	$-0.685319\pi$
$211$	−1.32424e22	−1.09972	−0.549861	+	0.835256i	$0.685319\pi$
$212$	− 9.47673e21i	− 0.752433i
$213$	9.01111e21i	0.684183i
$214$	−1.20669e22	−0.876325
$215$	0	0
$216$	−4.68137e21	−0.311216
$217$	1.77003e21i	0.112619i
$218$	8.39851e21i	0.511523i
$219$	−1.51882e22	−0.885701
$220$	0	0
$221$	1.13484e22	0.607027
$222$	− 3.91251e21i	− 0.200494i
$223$	− 2.00921e22i	− 0.986575i	−0.869866	−	0.493287i	$-0.835795\pi$
$223$	− 2.00921e22i	− 0.986575i	0.869866	−	0.493287i	$-0.164205\pi$
$224$	3.33106e21	0.156757
$225$	0	0
$226$	1.17384e22	0.507667
$227$	− 2.03494e22i	− 0.843929i	−0.906612	−	0.421965i	$-0.861341\pi$
$227$	− 2.03494e22i	− 0.843929i	0.906612	−	0.421965i	$-0.138659\pi$
$228$	− 2.74053e22i	− 1.09007i
$229$	3.99900e22	1.52586	0.762930	−	0.646481i	$-0.223760\pi$
$229$	3.99900e22	1.52586	0.762930	+	0.646481i	$0.223760\pi$
$230$	0	0
$231$	1.38923e19	0.000488045 0
$232$	− 4.36168e20i	− 0.0147068i
$233$	− 2.42170e22i	− 0.783862i	−0.919995	−	0.391931i	$-0.871807\pi$
$233$	− 2.42170e22i	− 0.783862i	0.919995	−	0.391931i	$-0.128193\pi$
$234$	−3.22665e22	−1.00277
$235$	0	0
$236$	−1.84722e22	−0.529487
$237$	− 4.67149e21i	− 0.128631i
$238$	1.73628e21i	0.0459345i
$239$	−2.62411e22	−0.667116	−0.333558	−	0.942730i	$-0.608249\pi$
$239$	−2.62411e22	−0.667116	−0.333558	+	0.942730i	$0.608249\pi$
$240$	0	0
$241$	7.36445e22	1.72973	0.864865	−	0.502004i	$-0.167404\pi$
$241$	7.36445e22	1.72973	0.864865	+	0.502004i	$0.167404\pi$
$242$	− 2.78884e22i	− 0.629764i
$243$	6.54789e22i	1.42181i
$244$	7.39431e21	0.154417
$245$	0	0
$246$	−7.64518e22	−1.47742
$247$	− 8.62350e22i	− 1.60348i
$248$	− 4.01068e22i	− 0.717674i
$249$	−6.12151e22	−1.05430
$250$	0	0
$251$	7.29309e22	1.16416	0.582078	−	0.813133i	$-0.302240\pi$
$251$	7.29309e22	1.16416	0.582078	+	0.813133i	$0.302240\pi$
$252$	7.51066e21i	0.115444i
$253$	2.27562e20i	0.00336864i
$254$	−4.01608e22	−0.572641
$255$	0	0
$256$	−7.69607e22	−1.01857
$257$	− 6.38120e22i	− 0.813838i	−0.913464	−	0.406919i	$-0.866603\pi$
$257$	− 6.38120e22i	− 0.813838i	0.913464	−	0.406919i	$-0.133397\pi$
$258$	− 2.60518e22i	− 0.320221i
$259$	−2.86570e21	−0.0339534
$260$	0	0
$261$	1.59680e21	0.0175859
$262$	3.27996e22i	0.348342i
$263$	1.35820e23i	1.39118i	0.718439	+	0.695590i	$0.244857\pi$
$263$	1.35820e23i	1.39118i	−0.718439	+	0.695590i	$0.755143\pi$
$264$	−3.14783e20	−0.00311010
$265$	0	0
$266$	1.31938e22	0.121337
$267$	2.21410e23i	1.96490i
$268$	− 6.48846e22i	− 0.555726i
$269$	1.33672e23	1.10508	0.552540	−	0.833486i	$-0.313659\pi$
$269$	1.33672e23	1.10508	0.552540	+	0.833486i	$0.313659\pi$
$270$	0	0
$271$	2.00548e23	1.54529	0.772643	−	0.634840i	$-0.218934\pi$
$271$	2.00548e23	1.54529	0.772643	+	0.634840i	$0.218934\pi$
$272$	− 2.01207e21i	− 0.0149706i
$273$	4.32067e22i	0.310460i
$274$	1.34714e23	0.934939
$275$	0	0
$276$	−2.24919e23	−1.45677
$277$	2.00223e23i	1.25301i	0.779416	+	0.626507i	$0.215516\pi$
$277$	2.00223e23i	1.25301i	−0.779416	+	0.626507i	$0.784484\pi$
$278$	− 6.31461e22i	− 0.381875i
$279$	1.46830e23	0.858170
$280$	0	0
$281$	−1.19239e23	−0.651194	−0.325597	−	0.945509i	$-0.605565\pi$
$281$	−1.19239e23	−0.651194	−0.325597	+	0.945509i	$0.605565\pi$
$282$	8.08104e22i	0.426679i
$283$	3.46108e21i	0.0176702i	0.999961	+	0.00883509i	$0.00281233\pi$
$283$	3.46108e21i	0.0176702i	−0.999961	+	0.00883509i	$0.997188\pi$
$284$	−5.62798e22	−0.277861
$285$	0	0
$286$	−3.72753e20	−0.00172165
$287$	5.59968e22i	0.250199i
$288$	− 2.76322e23i	− 1.19450i
$289$	1.88416e23	0.788112
$290$	0	0
$291$	−3.21647e22	−0.126007
$292$	− 9.48593e22i	− 0.359702i
$293$	2.13236e23i	0.782739i	0.920234	+	0.391370i	$0.127999\pi$
$293$	2.13236e23i	0.782739i	−0.920234	+	0.391370i	$0.872001\pi$
$294$	2.56673e23	0.912181
$295$	0	0
$296$	6.49335e22	0.216370
$297$	− 1.97987e20i	0 0.000638927i
$298$	1.21306e23i	0.379164i
$299$	−7.07745e23	−2.14289
$300$	0	0
$301$	−1.90815e22	−0.0542290
$302$	2.62464e23i	0.722776i
$303$	7.20534e23i	1.92287i
$304$	−1.52895e22	−0.0395452
$305$	0	0
$306$	1.44030e23	0.350025
$307$	1.91887e23i	0.452097i	0.974116	+	0.226048i	$0.0725807\pi$
$307$	1.91887e23i	0.452097i	−0.974116	+	0.226048i	$0.927419\pi$
$308$	8.67656e19i	0 0.000198205i
$309$	−2.48564e23	−0.550596
$310$	0	0
$311$	−1.54522e23	−0.321933	−0.160967	−	0.986960i	$-0.551461\pi$
$311$	−1.54522e23	−0.321933	−0.160967	+	0.986960i	$0.551461\pi$
$312$	− 9.79013e23i	− 1.97843i
$313$	− 2.87408e23i	− 0.563413i	−0.959501	−	0.281707i	$-0.909100\pi$
$313$	− 2.87408e23i	− 0.563413i	0.959501	−	0.281707i	$-0.0909005\pi$
$314$	4.89003e23	0.929994
$315$	0	0
$316$	2.91762e22	0.0522398
$317$	2.63533e22i	0.0457901i	0.999738	+	0.0228950i	$0.00728836\pi$
$317$	2.63533e22i	0.0457901i	−0.999738	+	0.0228950i	$0.992712\pi$
$318$	− 6.91910e23i	− 1.16679i
$319$	1.84467e19	3.01931e−5 0
$320$	0	0
$321$	1.34038e24	2.06743
$322$	− 1.08283e23i	− 0.162155i
$323$	3.84933e23i	0.559707i
$324$	−3.20306e23	−0.452259
$325$	0	0
$326$	−2.64829e23	−0.352694
$327$	− 9.32897e23i	− 1.20679i
$328$	− 1.26882e24i	− 1.59441i
$329$	5.91893e22	0.0722574
$330$	0	0
$331$	−1.05338e24	−1.21400	−0.606998	−	0.794703i	$-0.707626\pi$
$331$	−1.05338e24	−1.21400	−0.606998	+	0.794703i	$0.707626\pi$
$332$	− 3.82325e23i	− 0.428175i
$333$	2.37719e23i	0.258728i
$334$	−1.10987e23	−0.117403
$335$	0	0
$336$	7.66055e21	0.00765661
$337$	6.76160e23i	0.657000i	0.944504	+	0.328500i	$0.106543\pi$
$337$	6.76160e23i	0.657000i	−0.944504	+	0.328500i	$0.893457\pi$
$338$	− 4.92671e23i	− 0.465424i
$339$	−1.30389e24	−1.19769
$340$	0	0
$341$	1.69622e21	0.00147338
$342$	− 1.09447e24i	− 0.924600i
$343$	− 3.80841e23i	− 0.312932i
$344$	4.32365e23	0.345578
$345$	0	0
$346$	−5.44237e23	−0.411685
$347$	1.06325e24i	0.782535i	0.920277	+	0.391268i	$0.127963\pi$
$347$	1.06325e24i	0.782535i	−0.920277	+	0.391268i	$0.872037\pi$
$348$	1.82325e22i	0.0130570i
$349$	7.14667e23	0.498037	0.249019	−	0.968499i	$-0.419892\pi$
$349$	7.14667e23	0.498037	0.249019	+	0.968499i	$0.419892\pi$
$350$	0	0
$351$	6.15764e23	0.406440
$352$	− 3.19216e21i	− 0.00205083i
$353$	5.07321e23i	0.317266i	0.987338	+	0.158633i	$0.0507086\pi$
$353$	5.07321e23i	0.317266i	−0.987338	+	0.158633i	$0.949291\pi$
$354$	−1.34868e24	−0.821068
$355$	0	0
$356$	−1.38284e24	−0.797988
$357$	− 1.92864e23i	− 0.108369i
$358$	1.89087e24i	1.03460i
$359$	−3.32006e24	−1.76909	−0.884544	−	0.466458i	$-0.845530\pi$
$359$	−3.32006e24	−1.76909	−0.884544	+	0.466458i	$0.845530\pi$
$360$	0	0
$361$	9.46633e23	0.478479
$362$	1.51558e24i	0.746186i
$363$	3.09782e24i	1.48574i
$364$	−2.69851e23	−0.126084
$365$	0	0
$366$	5.39869e23	0.239452
$367$	− 2.24430e24i	− 0.969958i	−0.874526	−	0.484979i	$-0.838827\pi$
$367$	− 2.24430e24i	− 0.969958i	0.874526	−	0.484979i	$-0.161173\pi$
$368$	1.25483e23i	0.0528484i
$369$	4.64511e24	1.90654
$370$	0	0
$371$	−5.06787e23	−0.197594
$372$	1.67653e24i	0.637166i
$373$	− 5.10606e24i	− 1.89170i	−0.324603	−	0.945850i	$-0.605231\pi$
$373$	− 5.10606e24i	− 1.89170i	0.324603	−	0.945850i	$-0.394769\pi$
$374$	1.66388e21	0.000600955 0
$375$	0	0
$376$	−1.34116e24	−0.460465
$377$	5.73715e22i	0.0192067i
$378$	9.42106e22i	0.0307559i
$379$	4.28975e24	1.36571	0.682857	−	0.730552i	$-0.260737\pi$
$379$	4.28975e24	1.36571	0.682857	+	0.730552i	$0.260737\pi$
$380$	0	0
$381$	4.46102e24	1.35098
$382$	2.82437e24i	0.834295i
$383$	1.86803e24i	0.538264i	0.963103	+	0.269132i	$0.0867369\pi$
$383$	1.86803e24i	0.538264i	−0.963103	+	0.269132i	$0.913263\pi$
$384$	3.04684e24	0.856451
$385$	0	0
$386$	−2.37438e24	−0.635288
$387$	1.58287e24i	0.413230i
$388$	− 2.00888e23i	− 0.0511743i
$389$	6.47448e24	1.60947	0.804737	−	0.593632i	$-0.202306\pi$
$389$	6.47448e24	1.60947	0.804737	+	0.593632i	$0.202306\pi$
$390$	0	0
$391$	3.15920e24	0.747995
$392$	4.25985e24i	0.984411i
$393$	− 3.64334e24i	− 0.821809i
$394$	−1.10527e24	−0.243363
$395$	0	0
$396$	7.19748e21	0.00151034
$397$	1.22760e24i	0.251505i	0.992062	+	0.125752i	$0.0401345\pi$
$397$	1.22760e24i	0.251505i	−0.992062	+	0.125752i	$0.959866\pi$
$398$	4.82937e23i	0.0966054i
$399$	−1.46555e24	−0.286258
$400$	0	0
$401$	−5.17895e23	−0.0964651	−0.0482326	−	0.998836i	$-0.515359\pi$
$401$	−5.17895e23	−0.0964651	−0.0482326	+	0.998836i	$0.515359\pi$
$402$	− 4.73732e24i	− 0.861757i
$403$	5.27546e24i	0.937264i
$404$	−4.50017e24	−0.780918
$405$	0	0
$406$	−8.77772e21	−0.00145340
$407$	2.74621e21i	0 0.000444208i
$408$	4.37008e24i	0.690586i
$409$	−2.81877e24	−0.435199	−0.217599	−	0.976038i	$-0.569823\pi$
$409$	−2.81877e24	−0.435199	−0.217599	+	0.976038i	$0.569823\pi$
$410$	0	0
$411$	−1.49639e25	−2.20571
$412$	− 1.55243e24i	− 0.223609i
$413$	9.87839e23i	0.139047i
$414$	−8.98245e24	−1.23564
$415$	0	0
$416$	9.92800e24	1.30459
$417$	7.01420e24i	0.900919i
$418$	− 1.26436e22i	− 0.00158744i
$419$	−8.65571e24	−1.06235	−0.531177	−	0.847261i	$-0.678250\pi$
$419$	−8.65571e24	−1.06235	−0.531177	+	0.847261i	$0.678250\pi$
$420$	0	0
$421$	−5.21652e24	−0.611929	−0.305964	−	0.952043i	$-0.598979\pi$
$421$	−5.21652e24	−0.611929	−0.305964	+	0.952043i	$0.598979\pi$
$422$	− 6.03853e24i	− 0.692569i
$423$	− 4.90994e24i	− 0.550608i
$424$	1.14832e25	1.25918
$425$	0	0
$426$	−4.10907e24	−0.430876
$427$	− 3.95425e23i	− 0.0405508i
$428$	8.37147e24i	0.839626i
$429$	4.14050e22	0.00406171
$430$	0	0
$431$	1.04364e25	0.979526	0.489763	−	0.871856i	$-0.337083\pi$
$431$	1.04364e25	0.979526	0.489763	+	0.871856i	$0.337083\pi$
$432$	− 1.09175e23i	− 0.0100237i
$433$	− 1.45110e25i	− 1.30335i	−0.758499	−	0.651675i	$-0.774067\pi$
$433$	− 1.45110e25i	− 1.30335i	0.758499	−	0.651675i	$-0.225933\pi$
$434$	−8.07134e23	−0.0709240
$435$	0	0
$436$	5.82650e24	0.490102
$437$	− 2.40064e25i	− 1.97585i
$438$	− 6.92582e24i	− 0.557785i
$439$	−1.79857e25	−1.41747	−0.708735	−	0.705474i	$-0.750734\pi$
$439$	−1.79857e25	−1.41747	−0.708735	+	0.705474i	$0.750734\pi$
$440$	0	0
$441$	−1.55951e25	−1.17713
$442$	5.17487e24i	0.382286i
$443$	− 8.73685e24i	− 0.631712i	−0.948807	−	0.315856i	$-0.897708\pi$
$443$	− 8.73685e24i	− 0.631712i	0.948807	−	0.315856i	$-0.102292\pi$
$444$	−2.71432e24	−0.192098
$445$	0	0
$446$	9.16201e24	0.621312
$447$	− 1.34745e25i	− 0.894523i
$448$	1.59826e24i	0.103874i
$449$	1.60576e25	1.02174	0.510870	−	0.859658i	$-0.329323\pi$
$449$	1.60576e25	1.02174	0.510870	+	0.859658i	$0.329323\pi$
$450$	0	0
$451$	5.36618e22	0.00327332
$452$	− 8.14357e24i	− 0.486407i
$453$	− 2.91542e25i	− 1.70517i
$454$	9.27933e24	0.531479
$455$	0	0
$456$	3.32077e25	1.82420
$457$	− 2.67587e24i	− 0.143966i	−0.997406	−	0.0719831i	$-0.977067\pi$
$457$	− 2.67587e24i	− 0.143966i	0.997406	−	0.0719831i	$-0.0229328\pi$
$458$	1.82355e25i	0.960936i
$459$	−2.74863e24	−0.141871
$460$	0	0
$461$	6.96807e24	0.345107	0.172553	−	0.985000i	$-0.444798\pi$
$461$	6.96807e24	0.345107	0.172553	+	0.985000i	$0.444798\pi$
$462$	6.33488e21i	0 0.000307354i
$463$	2.49843e25i	1.18754i	0.804635	+	0.593770i	$0.202361\pi$
$463$	2.49843e25i	1.18754i	−0.804635	+	0.593770i	$0.797639\pi$
$464$	1.01720e22	0.000473679 0
$465$	0	0
$466$	1.10430e25	0.493650
$467$	1.94531e25i	0.852075i	0.904706	+	0.426037i	$0.140091\pi$
$467$	1.94531e25i	0.852075i	−0.904706	+	0.426037i	$0.859909\pi$
$468$	2.23850e25i	0.960776i
$469$	−3.46983e24	−0.145937
$470$	0	0
$471$	−5.43180e25	−2.19404
$472$	− 2.23833e25i	− 0.886084i
$473$	1.82859e22i	0 0.000709471i
$474$	2.13020e24	0.0810076
$475$	0	0
$476$	1.20455e24	0.0440108
$477$	4.20396e25i	1.50568i
$478$	− 1.19659e25i	− 0.420128i
$479$	−3.34153e25	−1.15016	−0.575080	−	0.818097i	$-0.695029\pi$
$479$	−3.34153e25	−1.15016	−0.575080	+	0.818097i	$0.695029\pi$
$480$	0	0
$481$	−8.54103e24	−0.282574
$482$	3.35819e25i	1.08933i
$483$	1.20280e25i	0.382557i
$484$	−1.93477e25	−0.603391
$485$	0	0
$486$	−2.98584e25	−0.895410
$487$	− 4.86181e25i	− 1.42979i	−0.699231	−	0.714896i	$-0.746474\pi$
$487$	− 4.86181e25i	− 1.42979i	0.699231	−	0.714896i	$-0.253526\pi$
$488$	8.95988e24i	0.258413i
$489$	2.94169e25	0.832075
$490$	0	0
$491$	9.86730e24	0.268488	0.134244	−	0.990948i	$-0.457139\pi$
$491$	9.86730e24	0.268488	0.134244	+	0.990948i	$0.457139\pi$
$492$	5.30387e25i	1.41555i
$493$	− 2.56093e23i	− 0.00670427i
$494$	3.93232e25	1.00982
$495$	0	0
$496$	9.35339e23	0.0231150
$497$	3.00967e24i	0.0729681i
$498$	− 2.79141e25i	− 0.663964i
$499$	3.54150e25	0.826481	0.413240	−	0.910622i	$-0.364397\pi$
$499$	3.54150e25	0.826481	0.413240	+	0.910622i	$0.364397\pi$
$500$	0	0
$501$	1.23283e25	0.276978
$502$	3.32565e25i	0.733147i
$503$	− 1.47204e25i	− 0.318436i	−0.987243	−	0.159218i	$-0.949103\pi$
$503$	− 1.47204e25i	− 0.318436i	0.987243	−	0.159218i	$-0.0508973\pi$
$504$	−9.10086e24	−0.193193
$505$	0	0
$506$	−1.03768e23	−0.00212146
$507$	5.47254e25i	1.09803i
$508$	2.78618e25i	0.548660i
$509$	4.88290e25	0.943754	0.471877	−	0.881664i	$-0.343577\pi$
$509$	4.88290e25	0.943754	0.471877	+	0.881664i	$0.343577\pi$
$510$	0	0
$511$	−5.07279e24	−0.0944601
$512$	− 3.55692e24i	− 0.0650143i
$513$	2.08864e25i	0.374757i
$514$	2.90983e25	0.512528
$515$	0	0
$516$	−1.80735e25	−0.306811
$517$	− 5.67212e22i	0 0.000945334i
$518$	− 1.30676e24i	− 0.0213827i
$519$	6.04533e25	0.971248
$520$	0	0
$521$	7.14445e25	1.10665	0.553325	−	0.832965i	$-0.313359\pi$
$521$	7.14445e25	1.10665	0.553325	+	0.832965i	$0.313359\pi$
$522$	7.28139e23i	0.0110750i
$523$	− 8.99895e25i	− 1.34408i	−0.740514	−	0.672041i	$-0.765418\pi$
$523$	− 8.99895e25i	− 1.34408i	0.740514	−	0.672041i	$-0.234582\pi$
$524$	2.27548e25	0.333754
$525$	0	0
$526$	−6.19338e25	−0.876120
$527$	− 2.35484e25i	− 0.327160i
$528$	− 7.34111e21i	0 0.000100170i
$529$	−1.22409e26	−1.64053
$530$	0	0
$531$	8.19444e25	1.05955
$532$	− 9.15324e24i	− 0.116256i
$533$	1.66895e26i	2.08226i
$534$	−1.00963e26	−1.23743
$535$	0	0
$536$	7.86223e25	0.929995
$537$	− 2.10036e26i	− 2.44083i
$538$	6.09544e25i	0.695943i
$539$	−1.80160e23	−0.00202100
$540$	0	0
$541$	−9.33602e25	−1.01109	−0.505543	−	0.862802i	$-0.668708\pi$
$541$	−9.33602e25	−1.01109	−0.505543	+	0.862802i	$0.668708\pi$
$542$	9.14497e25i	0.973171i
$543$	− 1.68349e26i	− 1.76040i
$544$	−4.43162e25	−0.455379
$545$	0	0
$546$	−1.97022e25	−0.195517
$547$	− 2.74670e25i	− 0.267875i	−0.990990	−	0.133938i	$-0.957238\pi$
$547$	− 2.74670e25i	− 0.267875i	0.990990	−	0.133938i	$-0.0427621\pi$
$548$	− 9.34587e25i	− 0.895786i
$549$	−3.28018e25	−0.309001
$550$	0	0
$551$	−1.94602e24	−0.0177095
$552$	− 2.72541e26i	− 2.43787i
$553$	− 1.56026e24i	− 0.0137185i
$554$	−9.13016e25	−0.789106
$555$	0	0
$556$	−4.38079e25	−0.365882
$557$	1.42589e26i	1.17074i	0.810766	+	0.585370i	$0.199051\pi$
$557$	1.42589e26i	1.17074i	−0.810766	+	0.585370i	$0.800949\pi$
$558$	6.69543e25i	0.540447i
$559$	−5.68712e25	−0.451316
$560$	0	0
$561$	−1.84822e23	−0.00141777
$562$	− 5.43732e25i	− 0.410100i
$563$	1.72252e26i	1.27742i	0.769446	+	0.638712i	$0.220533\pi$
$563$	1.72252e26i	1.27742i	−0.769446	+	0.638712i	$0.779467\pi$
$564$	5.60626e25	0.408810
$565$	0	0
$566$	−1.57825e24	−0.0111281
$567$	1.71290e25i	0.118766i
$568$	− 6.81956e25i	− 0.464994i
$569$	−5.24893e25	−0.351969	−0.175984	−	0.984393i	$-0.556311\pi$
$569$	−5.24893e25	−0.351969	−0.175984	+	0.984393i	$0.556311\pi$
$570$	0	0
$571$	−3.21674e24	−0.0208628	−0.0104314	−	0.999946i	$-0.503320\pi$
$571$	−3.21674e24	−0.0208628	−0.0104314	+	0.999946i	$0.503320\pi$
$572$	2.58599e23i	0.00164955i
$573$	− 3.13728e26i	− 1.96827i
$574$	−2.55345e25	−0.157567
$575$	0	0
$576$	1.32580e26	0.791527
$577$	1.17453e26i	0.689752i	0.938648	+	0.344876i	$0.112079\pi$
$577$	1.17453e26i	0.689752i	−0.938648	+	0.344876i	$0.887921\pi$
$578$	8.59176e25i	0.496327i
$579$	2.63744e26	1.49877
$580$	0	0
$581$	−2.04456e25	−0.112441
$582$	− 1.46671e25i	− 0.0793553i
$583$	4.85655e23i	0.00258509i
$584$	1.14943e26	0.601953
$585$	0	0
$586$	−9.72354e25	−0.492943
$587$	1.86886e24i	0.00932213i	0.999989	+	0.00466107i	$0.00148367\pi$
$587$	1.86886e24i	0.00932213i	−0.999989	+	0.00466107i	$0.998516\pi$
$588$	− 1.78068e26i	− 0.873981i
$589$	−1.78941e26	−0.864201
$590$	0	0
$591$	1.22772e26	0.574141
$592$	1.51433e24i	0.00696889i
$593$	1.50165e26i	0.680063i	0.940414	+	0.340032i	$0.110438\pi$
$593$	1.50165e26i	0.680063i	−0.940414	+	0.340032i	$0.889562\pi$
$594$	9.02822e22	0.000402375 0
$595$	0	0
$596$	8.41563e25	0.363285
$597$	− 5.36441e25i	− 0.227911i
$598$	− 3.22732e26i	− 1.34952i
$599$	−1.65804e26	−0.682403	−0.341201	−	0.939990i	$-0.610834\pi$
$599$	−1.65804e26	−0.682403	−0.341201	+	0.939990i	$0.610834\pi$
$600$	0	0
$601$	−2.54795e26	−1.01598	−0.507989	−	0.861364i	$-0.669611\pi$
$601$	−2.54795e26	−1.01598	−0.507989	+	0.861364i	$0.669611\pi$
$602$	− 8.70118e24i	− 0.0341516i
$603$	2.87833e26i	1.11206i
$604$	1.82085e26	0.692507
$605$	0	0
$606$	−3.28564e26	−1.21096
$607$	3.14191e26i	1.13999i	0.821648	+	0.569996i	$0.193055\pi$
$607$	3.14191e26i	1.13999i	−0.821648	+	0.569996i	$0.806945\pi$
$608$	3.36753e26i	1.20290i
$609$	9.75020e23	0.00342885
$610$	0	0
$611$	1.76410e26	0.601355
$612$	− 9.99214e25i	− 0.335367i
$613$	3.91478e26i	1.29370i	0.762619	+	0.646848i	$0.223913\pi$
$613$	3.91478e26i	1.29370i	−0.762619	+	0.646848i	$0.776087\pi$
$614$	−8.75005e25	−0.284715
$615$	0	0
$616$	−1.05136e23	−0.000331692 0
$617$	4.86066e26i	1.51003i	0.655706	+	0.755016i	$0.272371\pi$
$617$	4.86066e26i	1.51003i	−0.655706	+	0.755016i	$0.727629\pi$
$618$	− 1.13345e26i	− 0.346747i
$619$	4.51098e26	1.35897	0.679485	−	0.733689i	$-0.262203\pi$
$619$	4.51098e26	1.35897	0.679485	+	0.733689i	$0.262203\pi$
$620$	0	0
$621$	1.71418e26	0.500827
$622$	− 7.04619e25i	− 0.202743i
$623$	7.39500e25i	0.209557i
$624$	2.28318e25	0.0637215
$625$	0	0
$626$	1.31058e26	0.354819
$627$	1.40444e24i	0.00374508i
$628$	− 3.39248e26i	− 0.891047i
$629$	3.81251e25	0.0986349
$630$	0	0
$631$	2.03805e26	0.511607	0.255803	−	0.966729i	$-0.417660\pi$
$631$	2.03805e26	0.511607	0.255803	+	0.966729i	$0.417660\pi$
$632$	3.53536e25i	0.0874221i
$633$	6.70753e26i	1.63391i
$634$	−1.20171e25	−0.0288371
$635$	0	0
$636$	−4.80016e26	−1.11793
$637$	− 5.60320e26i	− 1.28562i
$638$	8.41170e21i	0 1.90146e-5i
$639$	2.49662e26	0.556024
$640$	0	0
$641$	5.77927e26	1.24946	0.624729	−	0.780842i	$-0.285209\pi$
$641$	5.77927e26	1.24946	0.624729	+	0.780842i	$0.285209\pi$
$642$	6.11213e26i	1.30200i
$643$	− 7.72049e26i	− 1.62047i	−0.586106	−	0.810235i	$-0.699340\pi$
$643$	− 7.72049e26i	− 1.62047i	0.586106	−	0.810235i	$-0.300660\pi$
$644$	−7.51221e25	−0.155365
$645$	0	0
$646$	−1.75529e26	−0.352485
$647$	− 1.39226e24i	− 0.00275504i	−0.999999	−	0.00137752i	$-0.999562\pi$
$647$	− 1.39226e24i	− 0.00275504i	0.999999	−	0.00137752i	$-0.000438479\pi$
$648$	− 3.88123e26i	− 0.756844i
$649$	9.46648e23	0.00181913
$650$	0	0
$651$	8.96556e25	0.167324
$652$	1.83726e26i	0.337924i
$653$	6.19470e26i	1.12291i	0.827507	+	0.561455i	$0.189758\pi$
$653$	6.19470e26i	1.12291i	−0.827507	+	0.561455i	$0.810242\pi$
$654$	4.25401e26	0.759994
$655$	0	0
$656$	2.95905e25	0.0513530
$657$	4.20804e26i	0.719795i
$658$	2.69903e25i	0.0455053i
$659$	7.96627e25	0.132386	0.0661932	−	0.997807i	$-0.478915\pi$
$659$	7.96627e25	0.132386	0.0661932	+	0.997807i	$0.478915\pi$
$660$	0	0
$661$	−1.85436e26	−0.299420	−0.149710	−	0.988730i	$-0.547834\pi$
$661$	−1.85436e26	−0.299420	−0.149710	+	0.988730i	$0.547834\pi$
$662$	− 4.80339e26i	− 0.764535i
$663$	− 5.74819e26i	− 0.901888i
$664$	4.63273e26	0.716540
$665$	0	0
$666$	−1.08400e26	−0.162938
$667$	1.59713e25i	0.0236670i
$668$	7.69977e25i	0.112487i
$669$	−1.01771e27	−1.46580
$670$	0	0
$671$	−3.78937e23	−0.000530521 0
$672$	− 1.68725e26i	− 0.232901i
$673$	− 5.91532e26i	− 0.805073i	−0.915404	−	0.402536i	$-0.868129\pi$
$673$	− 5.91532e26i	− 0.805073i	0.915404	−	0.402536i	$-0.131871\pi$
$674$	−3.08329e26	−0.413757
$675$	0	0
$676$	−3.41793e26	−0.445933
$677$	− 2.97418e26i	− 0.382626i	−0.981529	−	0.191313i	$-0.938725\pi$
$677$	− 2.97418e26i	− 0.382626i	0.981529	−	0.191313i	$-0.0612746\pi$
$678$	− 5.94573e26i	− 0.754264i
$679$	−1.07429e25	−0.0134387
$680$	0	0
$681$	−1.03074e27	−1.25387
$682$	7.73477e23i	0 0.000927889i
$683$	1.25943e27i	1.48997i	0.667084	+	0.744983i	$0.267542\pi$
$683$	1.25943e27i	1.48997i	−0.667084	+	0.744983i	$0.732458\pi$
$684$	−7.59290e26	−0.885880
$685$	0	0
$686$	1.73663e26	0.197074
$687$	− 2.02558e27i	− 2.26704i
$688$	1.00833e25i	0.0111304i
$689$	−1.51044e27	−1.64446
$690$	0	0
$691$	3.19965e25	0.0338891	0.0169446	−	0.999856i	$-0.494606\pi$
$691$	3.19965e25	0.0338891	0.0169446	+	0.999856i	$0.494606\pi$
$692$	3.77567e26i	0.394445i
$693$	− 3.84899e23i	0 0.000396626i
$694$	−4.84840e26	−0.492815
$695$	0	0
$696$	−2.20928e25	−0.0218506
$697$	− 7.44979e26i	− 0.726829i
$698$	3.25888e26i	0.313648i
$699$	−1.22664e27	−1.16462
$700$	0	0
$701$	2.06463e27	1.90775	0.953874	−	0.300208i	$-0.0970562\pi$
$701$	2.06463e27	1.90775	0.953874	+	0.300208i	$0.0970562\pi$
$702$	2.80788e26i	0.255963i
$703$	− 2.89708e26i	− 0.260546i
$704$	1.53161e24	0.00135897
$705$	0	0
$706$	−2.31338e26	−0.199803
$707$	2.40655e26i	0.205074i
$708$	9.35656e26i	0.786684i
$709$	1.44096e27	1.19539	0.597697	−	0.801722i	$-0.296082\pi$
$709$	1.44096e27	1.19539	0.597697	+	0.801722i	$0.296082\pi$
$710$	0	0
$711$	−1.29428e26	−0.104536
$712$	− 1.67562e27i	− 1.33541i
$713$	1.46860e27i	1.15492i
$714$	8.79461e25	0.0682470
$715$	0	0
$716$	1.31180e27	0.991273
$717$	1.32916e27i	0.991165i
$718$	− 1.51395e27i	− 1.11411i
$719$	1.26393e27	0.917907	0.458953	−	0.888460i	$-0.348224\pi$
$719$	1.26393e27	0.917907	0.458953	+	0.888460i	$0.348224\pi$
$720$	0	0
$721$	−8.30194e25	−0.0587211
$722$	4.31665e26i	0.301331i
$723$	− 3.73024e27i	− 2.56994i
$724$	1.05144e27	0.714937
$725$	0	0
$726$	−1.41260e27	−0.935670
$727$	5.54468e26i	0.362493i	0.983438	+	0.181246i	$0.0580132\pi$
$727$	5.54468e26i	0.362493i	−0.983438	+	0.181246i	$0.941987\pi$
$728$	− 3.26986e26i	− 0.210999i
$729$	2.13985e27	1.36293
$730$	0	0
$731$	2.53860e26	0.157536
$732$	− 3.74537e26i	− 0.229424i
$733$	− 8.06563e26i	− 0.487698i	−0.969813	−	0.243849i	$-0.921590\pi$
$733$	− 8.06563e26i	− 0.487698i	0.969813	−	0.243849i	$-0.0784101\pi$
$734$	1.02340e27	0.610848
$735$	0	0
$736$	2.76379e27	1.60755
$737$	3.32514e24i	0.00190928i
$738$	2.11817e27i	1.20068i
$739$	−6.63850e26	−0.371490	−0.185745	−	0.982598i	$-0.559470\pi$
$739$	−6.63850e26	−0.371490	−0.185745	+	0.982598i	$0.559470\pi$
$740$	0	0
$741$	−4.36798e27	−2.38236
$742$	− 2.31095e26i	− 0.124438i
$743$	3.64095e27i	1.93562i	0.251677	+	0.967811i	$0.419018\pi$
$743$	3.64095e27i	1.93562i	−0.251677	+	0.967811i	$0.580982\pi$
$744$	−2.03149e27	−1.06628
$745$	0	0
$746$	2.32837e27	1.19133
$747$	1.69603e27i	0.856814i
$748$	− 1.15432e24i	0 0.000575788i
$749$	4.47681e26	0.220491
$750$	0	0
$751$	−1.55458e27	−0.746505	−0.373253	−	0.927730i	$-0.621758\pi$
$751$	−1.55458e27	−0.746505	−0.373253	+	0.927730i	$0.621758\pi$
$752$	− 3.12775e25i	− 0.0148307i
$753$	− 3.69410e27i	− 1.72964i
$754$	−2.61614e25	−0.0120958
$755$	0	0
$756$	6.53590e25	0.0294679
$757$	1.33406e27i	0.593970i	0.954882	+	0.296985i	$0.0959812\pi$
$757$	1.33406e27i	0.593970i	−0.954882	+	0.296985i	$0.904019\pi$
$758$	1.95613e27i	0.860081i
$759$	1.15265e25	0.00500494
$760$	0	0
$761$	−6.89829e25	−0.0292137	−0.0146069	−	0.999893i	$-0.504650\pi$
$761$	−6.89829e25	−0.0292137	−0.0146069	+	0.999893i	$0.504650\pi$
$762$	2.03423e27i	0.850799i
$763$	− 3.11584e26i	− 0.128704i
$764$	1.95942e27	0.799357
$765$	0	0
$766$	−8.51822e26	−0.338981
$767$	2.94419e27i	1.15720i
$768$	3.89821e27i	1.51333i
$769$	8.09673e26	0.310463	0.155231	−	0.987878i	$-0.450388\pi$
$769$	8.09673e26	0.310463	0.155231	+	0.987878i	$0.450388\pi$
$770$	0	0
$771$	−3.23221e27	−1.20916
$772$	1.64724e27i	0.608683i
$773$	− 1.00924e27i	− 0.368374i	−0.982891	−	0.184187i	$-0.941035\pi$
$773$	− 1.00924e27i	− 0.368374i	0.982891	−	0.184187i	$-0.0589652\pi$
$774$	−7.21790e26	−0.260239
$775$	0	0
$776$	2.43421e26	0.0856389
$777$	1.45154e26i	0.0504461i
$778$	2.95236e27i	1.01359i
$779$	−5.66100e27	−1.91994
$780$	0	0
$781$	2.88417e24	0.000954633 0
$782$	1.44060e27i	0.471062i
$783$	− 1.38956e25i	− 0.00448890i
$784$	−9.93448e25	−0.0317061
$785$	0	0
$786$	1.66136e27	0.517548
$787$	− 4.88307e27i	− 1.50291i	−0.659784	−	0.751456i	$-0.729352\pi$
$787$	− 4.88307e27i	− 1.50291i	0.659784	−	0.751456i	$-0.270648\pi$
$788$	7.66785e26i	0.233171i
$789$	6.87955e27	2.06694
$790$	0	0
$791$	−4.35493e26	−0.127733
$792$	8.72137e24i	0.00252752i
$793$	− 1.17854e27i	− 0.337480i
$794$	−5.59784e26	−0.158389
$795$	0	0
$796$	3.35040e26	0.0925598
$797$	1.18346e27i	0.323072i	0.986867	+	0.161536i	$0.0516447\pi$
$797$	1.18346e27i	0.323072i	−0.986867	+	0.161536i	$0.948355\pi$
$798$	− 6.68291e26i	− 0.180276i
$799$	−7.87451e26	−0.209908
$800$	0	0
$801$	6.13438e27	1.59684
$802$	− 2.36160e26i	− 0.0607506i
$803$	4.86126e24i	0.00123581i
$804$	−3.28653e27	−0.825669
$805$	0	0
$806$	−2.40561e27	−0.590258
$807$	− 6.77075e27i	− 1.64187i
$808$	− 5.45297e27i	− 1.30685i
$809$	5.08495e27	1.20441	0.602207	−	0.798340i	$-0.294288\pi$
$809$	5.08495e27	1.20441	0.602207	+	0.798340i	$0.294288\pi$
$810$	0	0
$811$	−2.72133e25	−0.00629627	−0.00314813	−	0.999995i	$-0.501002\pi$
$811$	−2.72133e25	−0.00629627	−0.00314813	+	0.999995i	$0.501002\pi$
$812$	6.08958e24i	0.00139253i
$813$	− 1.01581e28i	− 2.29590i
$814$	−1.25227e24	−0.000279748 0
$815$	0	0
$816$	−1.01916e26	−0.0222425
$817$	− 1.92905e27i	− 0.416134i
$818$	− 1.28536e27i	− 0.274074i
$819$	1.19708e27	0.252306
$820$	0	0
$821$	−5.16381e26	−0.106343	−0.0531716	−	0.998585i	$-0.516933\pi$
$821$	−5.16381e26	−0.106343	−0.0531716	+	0.998585i	$0.516933\pi$
$822$	− 6.82355e27i	− 1.38908i
$823$	1.97624e27i	0.397687i	0.980031	+	0.198843i	$0.0637185\pi$
$823$	1.97624e27i	0.397687i	−0.980031	+	0.198843i	$0.936282\pi$
$824$	1.88112e27	0.374204
$825$	0	0
$826$	−4.50455e26	−0.0875670
$827$	− 1.16795e27i	− 0.224450i	−0.993683	−	0.112225i	$-0.964202\pi$
$827$	− 1.16795e27i	− 0.224450i	0.993683	−	0.112225i	$-0.0357978\pi$
$828$	6.23162e27i	1.18389i
$829$	−4.20809e27	−0.790345	−0.395173	−	0.918607i	$-0.629315\pi$
$829$	−4.20809e27	−0.790345	−0.395173	+	0.918607i	$0.629315\pi$
$830$	0	0
$831$	1.01417e28	1.86166
$832$	4.76350e27i	0.864479i
$833$	2.50113e27i	0.448755i
$834$	−3.19848e27	−0.567369
$835$	0	0
$836$	−8.77156e24	−0.00152096
$837$	− 1.27774e27i	− 0.219053i
$838$	− 3.94700e27i	− 0.669036i
$839$	−8.49254e27	−1.42331	−0.711654	−	0.702530i	$-0.752053\pi$
$839$	−8.49254e27	−1.42331	−0.711654	+	0.702530i	$0.752053\pi$
$840$	0	0
$841$	−6.10197e27	−0.999788
$842$	− 2.37873e27i	− 0.385372i
$843$	6.03972e27i	0.967508i
$844$	−4.18926e27	−0.663565
$845$	0	0
$846$	2.23893e27	0.346755
$847$	1.03466e27i	0.158454i
$848$	2.67802e26i	0.0405558i
$849$	1.75311e26	0.0262534
$850$	0	0
$851$	−2.37768e27	−0.348195
$852$	2.85068e27i	0.412831i
$853$	9.33345e27i	1.33668i	0.743857	+	0.668338i	$0.232994\pi$
$853$	9.33345e27i	1.33668i	−0.743857	+	0.668338i	$0.767006\pi$
$854$	1.80314e26	0.0255376
$855$	0	0
$856$	−1.01439e28	−1.40509
$857$	− 1.11037e28i	− 1.52108i	−0.649292	−	0.760539i	$-0.724935\pi$
$857$	− 1.11037e28i	− 1.52108i	0.649292	−	0.760539i	$-0.275065\pi$
$858$	1.88807e25i	0.00255793i
$859$	−1.11478e28	−1.49367	−0.746834	−	0.665011i	$-0.768427\pi$
$859$	−1.11478e28	−1.49367	−0.746834	+	0.665011i	$0.768427\pi$
$860$	0	0
$861$	2.83635e27	0.371732
$862$	4.75899e27i	0.616873i
$863$	− 1.15445e28i	− 1.48004i	−0.672583	−	0.740021i	$-0.734815\pi$
$863$	− 1.15445e28i	− 1.48004i	0.672583	−	0.740021i	$-0.265185\pi$
$864$	−2.40460e27	−0.304903
$865$	0	0
$866$	6.61699e27	0.820806
$867$	− 9.54364e27i	− 1.17093i
$868$	5.59952e26i	0.0679538i
$869$	−1.49520e24	−0.000179478 0
$870$	0	0
$871$	−1.03416e28	−1.21455
$872$	7.06012e27i	0.820173i
$873$	8.91154e26i	0.102404i
$874$	1.09469e28	1.24432
$875$	0	0
$876$	−4.80482e27	−0.534426
$877$	1.55912e28i	1.71547i	0.514094	+	0.857734i	$0.328128\pi$
$877$	1.55912e28i	1.71547i	−0.514094	+	0.857734i	$0.671872\pi$
$878$	− 8.20147e27i	− 0.892676i
$879$	1.08008e28	1.16295
$880$	0	0
$881$	3.35920e26	0.0353969	0.0176985	−	0.999843i	$-0.494366\pi$
$881$	3.35920e26	0.0353969	0.0176985	+	0.999843i	$0.494366\pi$
$882$	− 7.11139e27i	− 0.741315i
$883$	1.34374e26i	0.0138576i	0.999976	+	0.00692882i	$0.00220553\pi$
$883$	1.34374e26i	0.0138576i	−0.999976	+	0.00692882i	$0.997794\pi$
$884$	3.59009e27	0.366276
$885$	0	0
$886$	3.98400e27	0.397832
$887$	9.23887e27i	0.912735i	0.889791	+	0.456367i	$0.150850\pi$
$887$	9.23887e27i	0.912735i	−0.889791	+	0.456367i	$0.849150\pi$
$888$	− 3.28901e27i	− 0.321471i
$889$	1.48996e27	0.144082
$890$	0	0
$891$	1.64147e25	0.00155380
$892$	− 6.35619e27i	− 0.595293i
$893$	5.98374e27i	0.554478i
$894$	6.14437e27	0.563341
$895$	0	0
$896$	1.01763e27	0.0913406
$897$	3.58487e28i	3.18379i
$898$	7.32226e27i	0.643458i
$899$	1.19048e26	0.0103516
$900$	0	0
$901$	6.74227e27	0.574011
$902$	2.44698e25i	0.00206143i
$903$	9.66517e26i	0.0805705i
$904$	9.86777e27	0.813990
$905$	0	0
$906$	1.32943e28	1.07386
$907$	− 1.80585e28i	− 1.44349i	−0.692161	−	0.721743i	$-0.743341\pi$
$907$	− 1.80585e28i	− 1.44349i	0.692161	−	0.721743i	$-0.256659\pi$
$908$	− 6.43758e27i	− 0.509222i
$909$	1.99631e28	1.56268
$910$	0	0
$911$	−1.99304e28	−1.52789	−0.763943	−	0.645283i	$-0.776739\pi$
$911$	−1.99304e28	−1.52789	−0.763943	+	0.645283i	$0.776739\pi$
$912$	7.74443e26i	0.0587541i
$913$	1.95930e25i	0.00147106i
$914$	1.22020e27	0.0906651
$915$	0	0
$916$	1.26509e28	0.920694
$917$	− 1.21686e27i	− 0.0876460i
$918$	− 1.25337e27i	− 0.0893460i
$919$	−1.04320e28	−0.735984	−0.367992	−	0.929829i	$-0.619955\pi$
$919$	−1.04320e28	−0.735984	−0.367992	+	0.929829i	$0.619955\pi$
$920$	0	0
$921$	9.71946e27	0.671701
$922$	3.17744e27i	0.217337i
$923$	8.97012e27i	0.607271i
$924$	4.39485e24	0.000294483 0
$925$	0	0
$926$	−1.13929e28	−0.747874
$927$	6.88672e27i	0.447461i
$928$	− 2.24039e26i	− 0.0144085i
$929$	5.17736e27	0.329578	0.164789	−	0.986329i	$-0.447306\pi$
$929$	5.17736e27	0.329578	0.164789	+	0.986329i	$0.447306\pi$
$930$	0	0
$931$	1.90058e28	1.18540
$932$	− 7.66111e27i	− 0.472977i
$933$	7.82683e27i	0.478311i
$934$	−8.87060e27	−0.536609
$935$	0	0
$936$	−2.71245e28	−1.60783
$937$	9.33202e27i	0.547582i	0.961789	+	0.273791i	$0.0882777\pi$
$937$	9.33202e27i	0.547582i	−0.961789	+	0.273791i	$0.911722\pi$
$938$	− 1.58224e27i	− 0.0919065i
$939$	−1.45578e28	−0.837089
$940$	0	0
$941$	4.50115e27	0.253642	0.126821	−	0.991926i	$-0.459523\pi$
$941$	4.50115e27	0.253642	0.126821	+	0.991926i	$0.459523\pi$
$942$	− 2.47690e28i	− 1.38173i
$943$	4.64607e28i	2.56581i
$944$	5.22005e26	0.0285391
$945$	0	0
$946$	−8.33835e24	−0.000446801 0
$947$	1.76126e28i	0.934324i	0.884172	+	0.467162i	$0.154724\pi$
$947$	1.76126e28i	0.934324i	−0.884172	+	0.467162i	$0.845276\pi$
$948$	− 1.47783e27i	− 0.0776151i
$949$	−1.51191e28	−0.786135
$950$	0	0
$951$	1.33485e27	0.0680325
$952$	1.45959e27i	0.0736511i
$953$	− 5.93730e27i	− 0.296624i	−0.988941	−	0.148312i	$-0.952616\pi$
$953$	− 5.93730e27i	− 0.296624i	0.988941	−	0.148312i	$-0.0473840\pi$
$954$	−1.91700e28	−0.948230
$955$	0	0
$956$	−8.30141e27	−0.402534
$957$	− 9.34363e23i	0 4.48593e-5i
$958$	− 1.52374e28i	− 0.724333i
$959$	−4.99789e27	−0.235239
$960$	0	0
$961$	−1.07239e28	−0.494857
$962$	− 3.89471e27i	− 0.177956i
$963$	− 3.71365e28i	− 1.68016i
$964$	2.32976e28	1.04371
$965$	0	0
$966$	−5.48477e27	−0.240922
$967$	− 2.58489e28i	− 1.12432i	−0.827028	−	0.562160i	$-0.809970\pi$
$967$	− 2.58489e28i	− 1.12432i	0.827028	−	0.562160i	$-0.190030\pi$
$968$	− 2.34441e28i	− 1.00976i
$969$	1.94976e28	0.831583
$970$	0	0
$971$	2.05732e28	0.860438	0.430219	−	0.902725i	$-0.358436\pi$
$971$	2.05732e28	0.860438	0.430219	+	0.902725i	$0.358436\pi$
$972$	2.07144e28i	0.857912i
$973$	2.34271e27i	0.0960831i
$974$	2.21698e28	0.900435
$975$	0	0
$976$	−2.08955e26	−0.00832300
$977$	− 2.34524e28i	− 0.925099i	−0.886593	−	0.462550i	$-0.846935\pi$
$977$	− 2.34524e28i	− 0.925099i	0.886593	−	0.462550i	$-0.153065\pi$
$978$	1.34141e28i	0.524014i
$979$	7.08664e25	0.00274160
$980$	0	0
$981$	−2.58468e28	−0.980736
$982$	4.49949e27i	0.169085i
$983$	− 4.25526e28i	− 1.58368i	−0.610729	−	0.791840i	$-0.709123\pi$
$983$	− 4.25526e28i	− 1.58368i	0.610729	−	0.791840i	$-0.290877\pi$
$984$	−6.42684e28	−2.36889
$985$	0	0
$986$	1.16778e26	0.00422213
$987$	− 2.99806e27i	− 0.107356i
$988$	− 2.72806e28i	− 0.967527i
$989$	−1.58320e28	−0.556123
$990$	0	0
$991$	5.21472e28	1.79693	0.898466	−	0.439044i	$-0.144683\pi$
$991$	5.21472e28	1.79693	0.898466	+	0.439044i	$0.144683\pi$
$992$	− 2.06010e28i	− 0.703117i
$993$	5.33556e28i	1.80369i
$994$	−1.37241e27	−0.0459529
$995$	0	0
$996$	−1.93655e28	−0.636159
$997$	− 1.61541e27i	− 0.0525629i	−0.999655	−	0.0262815i	$-0.991633\pi$
$997$	− 1.61541e27i	− 0.0525629i	0.999655	−	0.0262815i	$-0.00836661\pi$
$998$	1.61493e28i	0.520490i
$999$	2.06867e27	0.0660419

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.20.b.a.24.2		2
5.2	odd	4		25.20.a.a.1.1		1
5.3	odd	4		1.20.a.a.1.1	✓	1
5.4	even	2	inner	25.20.b.a.24.1		2
15.8	even	4		9.20.a.a.1.1		1
20.3	even	4		16.20.a.a.1.1		1
35.13	even	4		49.20.a.b.1.1		1
40.3	even	4		64.20.a.h.1.1		1
40.13	odd	4		64.20.a.b.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1.20.a.a.1.1	✓	1	5.3	odd	4
9.20.a.a.1.1		1	15.8	even	4
16.20.a.a.1.1		1	20.3	even	4
25.20.a.a.1.1		1	5.2	odd	4
25.20.b.a.24.1		2	5.4	even	2	inner
25.20.b.a.24.2		2	1.1	even	1	trivial
49.20.a.b.1.1		1	35.13	even	4
64.20.a.b.1.1		1	40.13	odd	4
64.20.a.h.1.1		1	40.3	even	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:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 20 \)
Character orbit:	\([\chi]\)	\(=\)	25.b (of order \(2\), degree \(1\), not minimal)

\(f(q)\)	\(=\)	\(q+456.000i q^{2} -50652.0i q^{3} +316352. q^{4} +2.30973e7 q^{6} -1.69175e7i q^{7} +3.83332e8i q^{8} -1.40336e9 q^{9} +O(q^{10})\)	\(q+456.000i q^{2} -50652.0i q^{3} +316352. q^{4} +2.30973e7 q^{6} -1.69175e7i q^{7} +3.83332e8i q^{8} -1.40336e9 q^{9} -1.62121e7 q^{11} -1.60239e10i q^{12} -5.04216e10i q^{13} +7.71440e9 q^{14} -8.93976e9 q^{16} +2.25070e11i q^{17} -6.39934e11i q^{18} +1.71028e12 q^{19} -8.56907e11 q^{21} -7.39272e9i q^{22} -1.40365e13i q^{23} +1.94165e13 q^{24} +2.29923e13 q^{26} +1.22123e13i q^{27} -5.35190e12i q^{28} -1.13784e12 q^{29} -1.04627e14 q^{31} +1.96900e14i q^{32} +8.21176e11i q^{33} -1.02632e14 q^{34} -4.43957e14 q^{36} -1.69392e14i q^{37} +7.79887e14i q^{38} -2.55396e15 q^{39} -3.30998e15 q^{41} -3.90750e14i q^{42} -1.12791e15i q^{43} -5.12873e12 q^{44} +6.40066e15 q^{46} +3.49869e15i q^{47} +4.52817e14i q^{48} +1.11127e16 q^{49} +1.14003e16 q^{51} -1.59510e16i q^{52} -2.99563e16i q^{53} -5.56881e15 q^{54} +6.48503e15 q^{56} -8.66290e16i q^{57} -5.18853e14i q^{58} -5.83914e16 q^{59} +2.33737e16 q^{61} -4.77099e16i q^{62} +2.37415e16i q^{63} -9.44733e16 q^{64} -3.74456e14 q^{66} -2.05103e17i q^{67} +7.12014e16i q^{68} -7.10979e17 q^{69} -1.77902e17 q^{71} -5.37954e17i q^{72} -2.99854e17i q^{73} +7.72429e16 q^{74} +5.41050e17 q^{76} +2.74269e14i q^{77} -1.16460e18i q^{78} +9.22271e16 q^{79} -1.01250e18 q^{81} -1.50935e18i q^{82} -1.20854e18i q^{83} -2.71084e17 q^{84} +5.14329e17 q^{86} +5.76336e16i q^{87} -6.21462e15i q^{88} -4.37120e18 q^{89} -8.53010e17 q^{91} -4.44049e18i q^{92} +5.29956e18i q^{93} -1.59540e18 q^{94} +9.97337e18 q^{96} -6.35013e17i q^{97} +5.06739e18i q^{98} +2.27515e16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 632704 q^{4} + 46194624 q^{6} - 2806727274 q^{9}+O(q^{10}) \) 2 * q + 632704 * q^4 + 46194624 * q^6 - 2806727274 * q^9	\( 2 q + 632704 q^{4} + 46194624 q^{6} - 2806727274 q^{9} - 32424216 q^{11} + 15428800128 q^{14} - 17879523328 q^{16} + 3420557145320 q^{19} - 1713814877376 q^{21} + 38833048719360 q^{24} + 45984512936544 q^{26} - 2275670539020 q^{29} - 209253760283456 q^{31} - 205263930749472 q^{34} - 887913786584448 q^{36} - 51\!\cdots\!48 q^{39}+ \cdots + 45\!\cdots\!92 q^{99}+O(q^{100}) \) 2 * q + 632704 * q^4 + 46194624 * q^6 - 2806727274 * q^9 - 32424216 * q^11 + 15428800128 * q^14 - 17879523328 * q^16 + 3420557145320 * q^19 - 1713814877376 * q^21 + 38833048719360 * q^24 + 45984512936544 * q^26 - 2275670539020 * q^29 - 209253760283456 * q^31 - 205263930749472 * q^34 - 887913786584448 * q^36 - 5107911292240848 * q^39 - 6619969501121676 * q^41 - 10257465580032 * q^44 + 12801319727451264 * q^46 + 22225383780762414 * q^49 + 22800501360355824 * q^51 - 11137624088734080 * q^54 + 12970066539601920 * q^56 - 116782795285464840 * q^59 + 46747370265345484 * q^61 - 188946593725546496 * q^64 - 748912233307392 * q^66 - 1421957120251889088 * q^69 - 355804683900835536 * q^71 + 154485802561981728 * q^74 + 1082100094036272640 * q^76 + 184454180288014880 * q^79 - 2024995398986399598 * q^81 - 542168764087652352 * q^84 + 1028657141360464704 * q^86 - 8742402384580608660 * q^89 - 1706019782724895456 * q^91 - 3190808916758921472 * q^94 + 19946732518257721344 * q^96 + 45502965692633592 * q^99

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