LMFDB - Embedded newform 5.26.a.a.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,26,Mod(1,5)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("5.1");

S:= CuspForms(chi, 26);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 26 $
Character orbit:	$[\chi]$	$=$	5.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$19.7998389976$
Analytic rank:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 1769856x^{2} + 106836475x + 628040620025 $ x^4 - x^3 - 1769856x^2 + 106836475x + 628040620025
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{14}\cdot 3^{2}\cdot 5^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-642.094$ of defining polynomial
Character	$\chi$	$=$	5.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+5288.75 q^{2} +887362. q^{3} -5.58351e6 q^{4} -2.44141e8 q^{5} +4.69304e9 q^{6} -4.61897e10 q^{7} -2.06991e11 q^{8} -5.98771e10 q^{9} +O(q^{10})$	\(q+5288.75 q^{2} +887362. q^{3} -5.58351e6 q^{4} -2.44141e8 q^{5} +4.69304e9 q^{6} -4.61897e10 q^{7} -2.06991e11 q^{8} -5.98771e10 q^{9} -1.29120e12 q^{10} -6.88197e12 q^{11} -4.95459e12 q^{12} +3.13663e13 q^{13} -2.44286e14 q^{14} -2.16641e14 q^{15} -9.07373e14 q^{16} +4.15331e15 q^{17} -3.16675e14 q^{18} -3.97884e15 q^{19} +1.36316e15 q^{20} -4.09870e16 q^{21} -3.63970e16 q^{22} -1.93808e17 q^{23} -1.83676e17 q^{24} +5.96046e16 q^{25} +1.65889e17 q^{26} -8.04984e17 q^{27} +2.57901e17 q^{28} +7.10227e17 q^{29} -1.14576e18 q^{30} -1.60031e18 q^{31} +2.14659e18 q^{32} -6.10680e18 q^{33} +2.19658e19 q^{34} +1.12768e19 q^{35} +3.34325e17 q^{36} +3.00137e19 q^{37} -2.10431e19 q^{38} +2.78333e19 q^{39} +5.05349e19 q^{40} +1.19350e20 q^{41} -2.16770e20 q^{42} -1.88176e20 q^{43} +3.84255e19 q^{44} +1.46184e19 q^{45} -1.02500e21 q^{46} -5.95693e20 q^{47} -8.05168e20 q^{48} +7.92424e20 q^{49} +3.15234e20 q^{50} +3.68549e21 q^{51} -1.75134e20 q^{52} +2.79965e21 q^{53} -4.25737e21 q^{54} +1.68017e21 q^{55} +9.56086e21 q^{56} -3.53067e21 q^{57} +3.75622e21 q^{58} -2.32784e22 q^{59} +1.20962e21 q^{60} +2.60942e22 q^{61} -8.46364e21 q^{62} +2.76571e21 q^{63} +4.17992e22 q^{64} -7.65779e21 q^{65} -3.22973e22 q^{66} -9.26710e22 q^{67} -2.31900e22 q^{68} -1.71978e23 q^{69} +5.96402e22 q^{70} +1.22456e23 q^{71} +1.23940e22 q^{72} -1.25561e23 q^{73} +1.58735e23 q^{74} +5.28909e22 q^{75} +2.22159e22 q^{76} +3.17876e23 q^{77} +1.47203e23 q^{78} +6.26797e23 q^{79} +2.21527e23 q^{80} -6.63579e23 q^{81} +6.31215e23 q^{82} -8.02193e23 q^{83} +2.28851e23 q^{84} -1.01399e24 q^{85} -9.95217e23 q^{86} +6.30229e23 q^{87} +1.42451e24 q^{88} -3.94911e24 q^{89} +7.73134e22 q^{90} -1.44880e24 q^{91} +1.08213e24 q^{92} -1.42005e24 q^{93} -3.15048e24 q^{94} +9.71397e23 q^{95} +1.90480e24 q^{96} +1.06033e25 q^{97} +4.19094e24 q^{98} +4.12073e23 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 600 q^{2} - 798600 q^{3} + 92413888 q^{4} - 976562500 q^{5} - 3965174832 q^{6} - 48938107000 q^{7} + 224433484800 q^{8} + 2087565807492 q^{9}+O(q^{10}) $ 4 * q + 600 * q^2 - 798600 * q^3 + 92413888 * q^4 - 976562500 * q^5 - 3965174832 * q^6 - 48938107000 * q^7 + 224433484800 * q^8 + 2087565807492 * q^9	$ 4 q + 600 q^{2} - 798600 q^{3} + 92413888 q^{4} - 976562500 q^{5} - 3965174832 q^{6} - 48938107000 q^{7} + 224433484800 q^{8} + 2087565807492 q^{9} - 146484375000 q^{10} - 23641453790592 q^{11} - 42051883516800 q^{12} + 109063914225800 q^{13} + 109980501036336 q^{14} + 194970703125000 q^{15} - 28\!\cdots\!76 q^{16}+ \cdots - 19\!\cdots\!16 q^{99}+O(q^{100}) $ 4 * q + 600 * q^2 - 798600 * q^3 + 92413888 * q^4 - 976562500 * q^5 - 3965174832 * q^6 - 48938107000 * q^7 + 224433484800 * q^8 + 2087565807492 * q^9 - 146484375000 * q^10 - 23641453790592 * q^11 - 42051883516800 * q^12 + 109063914225800 * q^13 + 109980501036336 * q^14 + 194970703125000 * q^15 - 2811357146648576 * q^16 - 337440158866200 * q^17 - 8986517054418600 * q^18 - 5765957235759760 * q^19 - 22561984375000000 * q^20 - 76777748650758672 * q^21 - 247170171892300800 * q^22 - 84289919171581800 * q^23 - 750163283268986880 * q^24 + 238418579101562500 * q^25 - 2172668626545951312 * q^26 - 2324539610168425200 * q^27 + 715367314323708800 * q^28 - 1530771705074446440 * q^29 + 968060261718750000 * q^30 - 3405335632352491792 * q^31 + 8794451084429721600 * q^32 + 38579776790129836800 * q^33 + 12360736169963080176 * q^34 + 11947780029296875000 * q^35 + 29754645353627097024 * q^36 + 54849661150838347400 * q^37 + 167830012254298039200 * q^38 + 26980019582506147824 * q^39 - 54793331250000000000 * q^40 + 294765092997163901208 * q^41 - 275649307903658959200 * q^42 - 1266847513533640537000 * q^43 - 739285598894744039424 * q^44 - 509659620969726562500 * q^45 - 669486761007570298992 * q^46 + 826481836956124900200 * q^47 - 389112939053996236800 * q^48 - 2497667097456123567372 * q^49 + 35762786865234375000 * q^50 - 732051781800631123152 * q^51 - 3824820275638519888000 * q^52 + 7304325845439007895400 * q^53 + 15784899184389947603040 * q^54 + 5771839304343750000000 * q^55 + 14029366421126577776640 * q^56 + 15974193201590955213600 * q^57 + 11714010248956820950800 * q^58 - 2217164203172823251280 * q^59 + 10266573124218750000000 * q^60 - 50917697960481835727992 * q^61 - 24701477049499711624800 * q^62 + 2223612189174803070600 * q^63 - 20457521683182533476352 * q^64 - 26626932184033203125000 * q^65 - 16106812566256687908864 * q^66 - 76670956029519070862200 * q^67 - 318284068848532686249600 * q^68 - 211835176227690988743216 * q^69 - 26850708260824218750000 * q^70 + 150298050225701362285008 * q^71 + 399372518437664399078400 * q^72 - 106773821938777386935800 * q^73 + 286932321536483813083056 * q^74 - 47600269317626953125000 * q^75 + 793491830268069721114880 * q^76 - 215630079777610746336000 * q^77 + 1847661803543761572804000 * q^78 - 151978174282543555164640 * q^79 + 686366490881000000000000 * q^80 - 1579018732178689012033836 * q^81 + 3094333027045954774045200 * q^82 + 117573693202171400616600 * q^83 - 1614703102161158475120384 * q^84 + 82382851285693359375000 * q^85 - 1608810179612708665216752 * q^86 - 2896477998479054993943600 * q^87 - 4936697892190706144870400 * q^88 - 6860971673379749077360920 * q^89 + 2193973890238916015625000 * q^90 - 5097829330173411603898352 * q^91 + 6577026773676031203676800 * q^92 - 13171898336704209119455200 * q^93 + 1406225817996660389994096 * q^94 + 1407704403261660156250000 * q^95 + 13005904207859351375904768 * q^96 + 8538350425643241402216200 * q^97 + 10780561809722171059198200 * q^98 - 19223568526197742048146816 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	5288.75	0.913016	0.456508	−	0.889719i	$-0.349100\pi$
$2$	5288.75	0.913016	0.456508	+	0.889719i	$0.349100\pi$
$3$	887362.	0.964018	0.482009	−	0.876166i	$-0.339907\pi$
$3$	887362.	0.964018	0.482009	+	0.876166i	$0.339907\pi$
$4$	−5.58351e6	−0.166402
$5$	−2.44141e8	−0.447214
$5$	−2.44141e8	−0.447214
$6$	4.69304e9	0.880164
$7$	−4.61897e10	−1.26130	−0.630652	−	0.776065i	$-0.717213\pi$
$7$	−4.61897e10	−1.26130	−0.630652	+	0.776065i	$0.717213\pi$
$8$	−2.06991e11	−1.06494
$9$	−5.98771e10	−0.0706691
$10$	−1.29120e12	−0.408313
$11$	−6.88197e12	−0.661156	−0.330578	−	0.943779i	$-0.607244\pi$
$11$	−6.88197e12	−0.661156	−0.330578	+	0.943779i	$0.607244\pi$
$12$	−4.95459e12	−0.160414
$13$	3.13663e13	0.373397	0.186699	−	0.982417i	$-0.440221\pi$
$13$	3.13663e13	0.373397	0.186699	+	0.982417i	$0.440221\pi$
$14$	−2.44286e14	−1.15159
$15$	−2.16641e14	−0.431122
$16$	−9.07373e14	−0.805909
$17$	4.15331e15	1.72895	0.864475	−	0.502675i	$-0.167651\pi$
$17$	4.15331e15	1.72895	0.864475	+	0.502675i	$0.167651\pi$
$18$	−3.16675e14	−0.0645220
$19$	−3.97884e15	−0.412417	−0.206208	−	0.978508i	$-0.566113\pi$
$19$	−3.97884e15	−0.412417	−0.206208	+	0.978508i	$0.566113\pi$
$20$	1.36316e15	0.0744170
$21$	−4.09870e16	−1.21592
$22$	−3.63970e16	−0.603646
$23$	−1.93808e17	−1.84405	−0.922026	−	0.387128i	$-0.873467\pi$
$23$	−1.93808e17	−1.84405	−0.922026	+	0.387128i	$0.873467\pi$
$24$	−1.83676e17	−1.02662
$25$	5.96046e16	0.200000
$26$	1.65889e17	0.340918
$27$	−8.04984e17	−1.03214
$28$	2.57901e17	0.209883
$29$	7.10227e17	0.372754	0.186377	−	0.982478i	$-0.440325\pi$
$29$	7.10227e17	0.372754	0.186377	+	0.982478i	$0.440325\pi$
$30$	−1.14576e18	−0.393621
$31$	−1.60031e18	−0.364907	−0.182454	−	0.983214i	$-0.558404\pi$
$31$	−1.60031e18	−0.364907	−0.182454	+	0.983214i	$0.558404\pi$
$32$	2.14659e18	0.329135
$33$	−6.10680e18	−0.637366
$34$	2.19658e19	1.57856
$35$	1.12768e19	0.564073
$36$	3.34325e17	0.0117594
$37$	3.00137e19	0.749544	0.374772	−	0.927117i	$-0.377721\pi$
$37$	3.00137e19	0.749544	0.374772	+	0.927117i	$0.377721\pi$
$38$	−2.10431e19	−0.376543
$39$	2.78333e19	0.359962
$40$	5.05349e19	0.476257
$41$	1.19350e20	0.826087	0.413043	−	0.910711i	$-0.364466\pi$
$41$	1.19350e20	0.826087	0.413043	+	0.910711i	$0.364466\pi$
$42$	−2.16770e20	−1.11016
$43$	−1.88176e20	−0.718139	−0.359069	−	0.933311i	$-0.616906\pi$
$43$	−1.88176e20	−0.718139	−0.359069	+	0.933311i	$0.616906\pi$
$44$	3.84255e19	0.110017
$45$	1.46184e19	0.0316042
$46$	−1.02500e21	−1.68365
$47$	−5.95693e20	−0.747824	−0.373912	−	0.927464i	$-0.621984\pi$
$47$	−5.95693e20	−0.747824	−0.373912	+	0.927464i	$0.621984\pi$
$48$	−8.05168e20	−0.776911
$49$	7.92424e20	0.590890
$50$	3.15234e20	0.182603
$51$	3.68549e21	1.66674
$52$	−1.75134e20	−0.0621339
$53$	2.79965e21	0.782807	0.391404	−	0.920219i	$-0.371990\pi$
$53$	2.79965e21	0.782807	0.391404	+	0.920219i	$0.371990\pi$
$54$	−4.25737e21	−0.942365
$55$	1.68017e21	0.295678
$56$	9.56086e21	1.34322
$57$	−3.53067e21	−0.397577
$58$	3.75622e21	0.340331
$59$	−2.32784e22	−1.70334	−0.851672	−	0.524075i	$-0.824411\pi$
$59$	−2.32784e22	−1.70334	−0.851672	+	0.524075i	$0.824411\pi$
$60$	1.20962e21	0.0717394
$61$	2.60942e22	1.25870	0.629349	−	0.777123i	$-0.283322\pi$
$61$	2.60942e22	1.25870	0.629349	+	0.777123i	$0.283322\pi$
$62$	−8.46364e21	−0.333166
$63$	2.76571e21	0.0891353
$64$	4.17992e22	1.10642
$65$	−7.65779e21	−0.166988
$66$	−3.22973e22	−0.581926
$67$	−9.26710e22	−1.38359	−0.691797	−	0.722092i	$-0.743181\pi$
$67$	−9.26710e22	−1.38359	−0.691797	+	0.722092i	$0.743181\pi$
$68$	−2.31900e22	−0.287700
$69$	−1.71978e23	−1.77770
$70$	5.96402e22	0.515007
$71$	1.22456e23	0.885628	0.442814	−	0.896614i	$-0.353980\pi$
$71$	1.22456e23	0.885628	0.442814	+	0.896614i	$0.353980\pi$
$72$	1.23940e22	0.0752586
$73$	−1.25561e23	−0.641678	−0.320839	−	0.947134i	$-0.603965\pi$
$73$	−1.25561e23	−0.641678	−0.320839	+	0.947134i	$0.603965\pi$
$74$	1.58735e23	0.684346
$75$	5.28909e22	0.192804
$76$	2.22159e22	0.0686268
$77$	3.17876e23	0.833919
$78$	1.47203e23	0.328651
$79$	6.26797e23	1.19341	0.596703	−	0.802462i	$-0.296477\pi$
$79$	6.26797e23	1.19341	0.596703	+	0.802462i	$0.296477\pi$
$80$	2.21527e23	0.360413
$81$	−6.63579e23	−0.924337
$82$	6.31215e23	0.754231
$83$	−8.02193e23	−0.823764	−0.411882	−	0.911237i	$-0.635128\pi$
$83$	−8.02193e23	−0.823764	−0.411882	+	0.911237i	$0.635128\pi$
$84$	2.28851e23	0.202331
$85$	−1.01399e24	−0.773210
$86$	−9.95217e23	−0.655672
$87$	6.30229e23	0.359342
$88$	1.42451e24	0.704094
$89$	−3.94911e24	−1.69482	−0.847411	−	0.530938i	$-0.821840\pi$
$89$	−3.94911e24	−1.69482	−0.847411	+	0.530938i	$0.821840\pi$
$90$	7.73134e22	0.0288551
$91$	−1.44880e24	−0.470968
$92$	1.08213e24	0.306853
$93$	−1.42005e24	−0.351777
$94$	−3.15048e24	−0.682776
$95$	9.71397e23	0.184438
$96$	1.90480e24	0.317293
$97$	1.06033e25	1.55166	0.775828	−	0.630944i	$-0.217332\pi$
$97$	1.06033e25	1.55166	0.775828	+	0.630944i	$0.217332\pi$
$98$	4.19094e24	0.539492
$99$	4.12073e23	0.0467233
$100$	−3.32803e23	−0.0332803
$101$	−1.05560e25	−0.932147	−0.466073	−	0.884746i	$-0.654332\pi$
$101$	−1.05560e25	−0.932147	−0.466073	+	0.884746i	$0.654332\pi$
$102$	1.94916e25	1.52176
$103$	−1.05714e25	−0.730579	−0.365289	−	0.930894i	$-0.619030\pi$
$103$	−1.05714e25	−0.730579	−0.365289	+	0.930894i	$0.619030\pi$
$104$	−6.49254e24	−0.397647
$105$	1.00066e25	0.543776
$106$	1.48066e25	0.714716
$107$	−2.61435e25	−1.12219	−0.561094	−	0.827752i	$-0.689620\pi$
$107$	−2.61435e25	−1.12219	−0.561094	+	0.827752i	$0.689620\pi$
$108$	4.49464e24	0.171750
$109$	−1.59852e25	−0.544361	−0.272180	−	0.962246i	$-0.587745\pi$
$109$	−1.59852e25	−0.544361	−0.272180	+	0.962246i	$0.587745\pi$
$110$	8.88600e24	0.269959
$111$	2.66330e25	0.722574
$112$	4.19113e25	1.01650
$113$	−6.65820e25	−1.44503	−0.722514	−	0.691356i	$-0.757014\pi$
$113$	−6.65820e25	−1.44503	−0.722514	+	0.691356i	$0.757014\pi$
$114$	−1.86729e25	−0.362995
$115$	4.73163e25	0.824685
$116$	−3.96556e24	−0.0620269
$117$	−1.87812e24	−0.0263877
$118$	−1.23114e26	−1.55518
$119$	−1.91840e26	−2.18073
$120$	4.48428e25	0.459121
$121$	−6.09856e25	−0.562873
$122$	1.38006e26	1.14921
$123$	1.05907e26	0.796363
$124$	8.93534e24	0.0607211
$125$	−1.45519e25	−0.0894427
$126$	1.46272e25	0.0813820
$127$	3.71494e26	1.87243	0.936215	−	0.351427i	$-0.114303\pi$
$127$	3.71494e26	1.87243	0.936215	+	0.351427i	$0.114303\pi$
$128$	1.49038e26	0.681039
$129$	−1.66980e26	−0.692299
$130$	−4.05001e25	−0.152463
$131$	4.48668e26	1.53474	0.767368	−	0.641207i	$-0.221566\pi$
$131$	4.48668e26	1.53474	0.767368	+	0.641207i	$0.221566\pi$
$132$	3.40974e25	0.106059
$133$	1.83782e26	0.520184
$134$	−4.90114e26	−1.26324
$135$	1.96529e26	0.461589
$136$	−8.59697e26	−1.84123
$137$	4.27131e26	0.834745	0.417373	−	0.908735i	$-0.362951\pi$
$137$	4.27131e26	0.834745	0.417373	+	0.908735i	$0.362951\pi$
$138$	−9.09547e26	−1.62307
$139$	7.86093e25	0.128171	0.0640854	−	0.997944i	$-0.479587\pi$
$139$	7.86093e25	0.128171	0.0640854	+	0.997944i	$0.479587\pi$
$140$	−6.29641e25	−0.0938625
$141$	−5.28596e26	−0.720916
$142$	6.47640e26	0.808592
$143$	−2.15862e26	−0.246874
$144$	5.43309e25	0.0569529
$145$	−1.73395e26	−0.166701
$146$	−6.64059e26	−0.585863
$147$	7.03167e26	0.569629
$148$	−1.67581e26	−0.124725
$149$	−4.19433e24	−0.00286969	−0.00143484	−	0.999999i	$-0.500457\pi$
$149$	−4.19433e24	−0.00286969	−0.00143484	+	0.999999i	$0.500457\pi$
$150$	2.79727e26	0.176033
$151$	1.40076e26	0.0811242	0.0405621	−	0.999177i	$-0.487085\pi$
$151$	1.40076e26	0.0811242	0.0405621	+	0.999177i	$0.487085\pi$
$152$	8.23584e26	0.439201
$153$	−2.48688e26	−0.122183
$154$	1.68117e27	0.761382
$155$	3.90700e26	0.163192
$156$	−1.55407e26	−0.0598982
$157$	−4.54552e27	−1.61748	−0.808738	−	0.588169i	$-0.799849\pi$
$157$	−4.54552e27	−1.61748	−0.808738	+	0.588169i	$0.799849\pi$
$158$	3.31498e27	1.08960
$159$	2.48430e27	0.754640
$160$	−5.24070e26	−0.147194
$161$	8.95193e27	2.32591
$162$	−3.50951e27	−0.843934
$163$	−4.69254e27	−1.04487	−0.522436	−	0.852678i	$-0.674977\pi$
$163$	−4.69254e27	−1.04487	−0.522436	+	0.852678i	$0.674977\pi$
$164$	−6.66394e26	−0.137462
$165$	1.49092e27	0.285039
$166$	−4.24260e27	−0.752110
$167$	−4.55685e27	−0.749392	−0.374696	−	0.927148i	$-0.622253\pi$
$167$	−4.55685e27	−0.749392	−0.374696	+	0.927148i	$0.622253\pi$
$168$	8.48394e27	1.29489
$169$	−6.07257e27	−0.860574
$170$	−5.36275e27	−0.705953
$171$	2.38242e26	0.0291451
$172$	1.05068e27	0.119499
$173$	8.94086e27	0.945808	0.472904	−	0.881114i	$-0.343206\pi$
$173$	8.94086e27	0.945808	0.472904	+	0.881114i	$0.343206\pi$
$174$	3.33313e27	0.328085
$175$	−2.75312e27	−0.252261
$176$	6.24451e27	0.532832
$177$	−2.06563e28	−1.64205
$178$	−2.08859e28	−1.54740
$179$	−2.84964e27	−0.196846	−0.0984231	−	0.995145i	$-0.531380\pi$
$179$	−2.84964e27	−0.196846	−0.0984231	+	0.995145i	$0.531380\pi$
$180$	−8.16222e25	−0.00525899
$181$	5.53249e27	0.332612	0.166306	−	0.986074i	$-0.446816\pi$
$181$	5.53249e27	0.332612	0.166306	+	0.986074i	$0.446816\pi$
$182$	−7.66235e27	−0.430001
$183$	2.31550e28	1.21341
$184$	4.01164e28	1.96381
$185$	−7.32755e27	−0.335206
$186$	−7.51031e27	−0.321178
$187$	−2.85829e28	−1.14311
$188$	3.32606e27	0.124439
$189$	3.71820e28	1.30185
$190$	5.13748e27	0.168395
$191$	−1.48961e28	−0.457253	−0.228627	−	0.973514i	$-0.573423\pi$
$191$	−1.48961e28	−0.457253	−0.228627	+	0.973514i	$0.573423\pi$
$192$	3.70910e28	1.06660
$193$	−1.46143e26	−0.00393833	−0.00196916	−	0.999998i	$-0.500627\pi$
$193$	−1.46143e26	−0.00393833	−0.00196916	+	0.999998i	$0.500627\pi$
$194$	5.60784e28	1.41669
$195$	−6.79523e27	−0.160980
$196$	−4.42451e27	−0.0983250
$197$	5.50772e28	1.14853	0.574267	−	0.818668i	$-0.305287\pi$
$197$	5.50772e28	1.14853	0.574267	+	0.818668i	$0.305287\pi$
$198$	2.17935e27	0.0426591
$199$	−9.88995e28	−1.81773	−0.908867	−	0.417085i	$-0.863052\pi$
$199$	−9.88995e28	−1.81773	−0.908867	+	0.417085i	$0.863052\pi$
$200$	−1.23376e28	−0.212989
$201$	−8.22327e28	−1.33381
$202$	−5.58284e28	−0.851065
$203$	−3.28052e28	−0.470157
$204$	−2.05780e28	−0.277348
$205$	−2.91383e28	−0.369437
$206$	−5.59095e28	−0.667030
$207$	1.16047e28	0.130318
$208$	−2.84609e28	−0.300924
$209$	2.73823e28	0.272672
$210$	5.29224e28	0.496477
$211$	1.54452e29	1.36541	0.682704	−	0.730695i	$-0.260804\pi$
$211$	1.54452e29	1.36541	0.682704	+	0.730695i	$0.260804\pi$
$212$	−1.56319e28	−0.130260
$213$	1.08663e29	0.853761
$214$	−1.38266e29	−1.02458
$215$	4.59414e28	0.321161
$216$	1.66625e29	1.09918
$217$	7.39178e28	0.460259
$218$	−8.45418e28	−0.497010
$219$	−1.11418e29	−0.618590
$220$	−9.38123e27	−0.0492013
$221$	1.30274e29	0.645586
$222$	1.40855e29	0.659722
$223$	3.22003e28	0.142577	0.0712884	−	0.997456i	$-0.477289\pi$
$223$	3.22003e28	0.142577	0.0712884	+	0.997456i	$0.477289\pi$
$224$	−9.91505e28	−0.415140
$225$	−3.56896e27	−0.0141338
$226$	−3.52136e29	−1.31933
$227$	2.79885e29	0.992331	0.496165	−	0.868228i	$-0.334741\pi$
$227$	2.79885e29	0.992331	0.496165	+	0.868228i	$0.334741\pi$
$228$	1.97135e28	0.0661575
$229$	−2.86114e29	−0.909068	−0.454534	−	0.890729i	$-0.650194\pi$
$229$	−2.86114e29	−0.909068	−0.454534	+	0.890729i	$0.650194\pi$
$230$	2.50244e29	0.752951
$231$	2.82071e29	0.803913
$232$	−1.47011e29	−0.396962
$233$	−1.80352e29	−0.461501	−0.230750	−	0.973013i	$-0.574118\pi$
$233$	−1.80352e29	−0.461501	−0.230750	+	0.973013i	$0.574118\pi$
$234$	−9.93293e27	−0.0240924
$235$	1.45433e29	0.334437
$236$	1.29975e29	0.283439
$237$	5.56196e29	1.15047
$238$	−1.01460e30	−1.99105
$239$	1.98855e29	0.370308	0.185154	−	0.982710i	$-0.440722\pi$
$239$	1.98855e29	0.370308	0.185154	+	0.982710i	$0.440722\pi$
$240$	1.96574e29	0.347445
$241$	−1.04030e30	−1.74561	−0.872804	−	0.488071i	$-0.837701\pi$
$241$	−1.04030e30	−1.74561	−0.872804	+	0.488071i	$0.837701\pi$
$242$	−3.22538e29	−0.513912
$243$	9.32189e28	0.141067
$244$	−1.45697e29	−0.209449
$245$	−1.93463e29	−0.264254
$246$	5.60116e29	0.727092
$247$	−1.24801e29	−0.153995
$248$	3.31249e29	0.388606
$249$	−7.11836e29	−0.794123
$250$	−7.69615e28	−0.0816626
$251$	−4.00841e29	−0.404623	−0.202311	−	0.979321i	$-0.564845\pi$
$251$	−4.00841e29	−0.404623	−0.202311	+	0.979321i	$0.564845\pi$
$252$	−1.54424e28	−0.0148322
$253$	1.33378e30	1.21921
$254$	1.96474e30	1.70956
$255$	−8.99777e29	−0.745389
$256$	−6.14323e29	−0.484615
$257$	1.83914e30	1.38182	0.690908	−	0.722942i	$-0.257211\pi$
$257$	1.83914e30	1.38182	0.690908	+	0.722942i	$0.257211\pi$
$258$	−8.83117e29	−0.632080
$259$	−1.38632e30	−0.945404
$260$	4.27573e28	0.0277871
$261$	−4.25264e28	−0.0263422
$262$	2.37289e30	1.40124
$263$	2.00661e30	1.12984	0.564920	−	0.825146i	$-0.308907\pi$
$263$	2.00661e30	1.12984	0.564920	+	0.825146i	$0.308907\pi$
$264$	1.26405e30	0.678759
$265$	−6.83507e29	−0.350082
$266$	9.71976e29	0.474936
$267$	−3.50429e30	−1.63384
$268$	5.17429e29	0.230232
$269$	−6.95648e29	−0.295451	−0.147726	−	0.989028i	$-0.547195\pi$
$269$	−6.95648e29	−0.295451	−0.147726	+	0.989028i	$0.547195\pi$
$270$	1.03940e30	0.421438
$271$	2.54266e29	0.0984401	0.0492201	−	0.998788i	$-0.484326\pi$
$271$	2.54266e29	0.0984401	0.0492201	+	0.998788i	$0.484326\pi$
$272$	−3.76860e30	−1.39338
$273$	−1.28561e30	−0.454022
$274$	2.25899e30	0.762136
$275$	−4.10197e29	−0.132231
$276$	9.60238e29	0.295812
$277$	−4.42740e30	−1.30362	−0.651811	−	0.758381i	$-0.725990\pi$
$277$	−4.42740e30	−1.30362	−0.651811	+	0.758381i	$0.725990\pi$
$278$	4.15745e29	0.117022
$279$	9.58219e28	0.0257877
$280$	−2.33419e30	−0.600705
$281$	−6.66343e29	−0.164009	−0.0820047	−	0.996632i	$-0.526132\pi$
$281$	−6.66343e29	−0.164009	−0.0820047	+	0.996632i	$0.526132\pi$
$282$	−2.79561e30	−0.658208
$283$	−1.08095e30	−0.243487	−0.121743	−	0.992562i	$-0.538848\pi$
$283$	−1.08095e30	−0.243487	−0.121743	+	0.992562i	$0.538848\pi$
$284$	−6.83735e29	−0.147370
$285$	8.61981e29	0.177802
$286$	−1.14164e30	−0.225400
$287$	−5.51276e30	−1.04195
$288$	−1.28532e29	−0.0232597
$289$	1.14793e31	1.98927
$290$	−9.17046e29	−0.152200
$291$	9.40899e30	1.49583
$292$	7.01068e29	0.106776
$293$	5.05131e30	0.737155	0.368577	−	0.929597i	$-0.379845\pi$
$293$	5.05131e30	0.737155	0.368577	+	0.929597i	$0.379845\pi$
$294$	3.71888e30	0.520080
$295$	5.68320e30	0.761759
$296$	−6.21256e30	−0.798222
$297$	5.53988e30	0.682409
$298$	−2.21828e28	−0.00262007
$299$	−6.07903e30	−0.688564
$300$	−2.95317e29	−0.0320828
$301$	8.69180e30	0.905792
$302$	7.40825e29	0.0740677
$303$	−9.36704e30	−0.898606
$304$	3.61029e30	0.332371
$305$	−6.37066e30	−0.562907
$306$	−1.31525e30	−0.111555
$307$	−6.50023e30	−0.529297	−0.264648	−	0.964345i	$-0.585256\pi$
$307$	−6.50023e30	−0.529297	−0.264648	+	0.964345i	$0.585256\pi$
$308$	−1.77487e30	−0.138765
$309$	−9.38066e30	−0.704291
$310$	2.06632e30	0.148996
$311$	−3.02760e30	−0.209698	−0.104849	−	0.994488i	$-0.533436\pi$
$311$	−3.02760e30	−0.209698	−0.104849	+	0.994488i	$0.533436\pi$
$312$	−5.76123e30	−0.383339
$313$	1.79321e31	1.14638	0.573188	−	0.819424i	$-0.305706\pi$
$313$	1.79321e31	1.14638	0.573188	+	0.819424i	$0.305706\pi$
$314$	−2.40401e31	−1.47678
$315$	−6.75222e29	−0.0398625
$316$	−3.49973e30	−0.198585
$317$	2.23806e31	1.22076	0.610380	−	0.792108i	$-0.291017\pi$
$317$	2.23806e31	1.22076	0.610380	+	0.792108i	$0.291017\pi$
$318$	1.31389e31	0.688999
$319$	−4.88776e30	−0.246449
$320$	−1.02049e31	−0.494804
$321$	−2.31987e31	−1.08181
$322$	4.73446e31	2.12359
$323$	−1.65253e31	−0.713049
$324$	3.70510e30	0.153811
$325$	1.86958e30	0.0746795
$326$	−2.48177e31	−0.953986
$327$	−1.41847e31	−0.524774
$328$	−2.47045e31	−0.879736
$329$	2.75149e31	0.943234
$330$	7.88510e30	0.260245
$331$	−1.11758e31	−0.355163	−0.177581	−	0.984106i	$-0.556827\pi$
$331$	−1.11758e31	−0.355163	−0.177581	+	0.984106i	$0.556827\pi$
$332$	4.47905e30	0.137076
$333$	−1.79713e30	−0.0529696
$334$	−2.41001e31	−0.684207
$335$	2.26247e31	0.618762
$336$	3.71905e31	0.979921
$337$	5.93131e31	1.50583	0.752916	−	0.658116i	$-0.228647\pi$
$337$	5.93131e31	1.50583	0.752916	+	0.658116i	$0.228647\pi$
$338$	−3.21163e31	−0.785718
$339$	−5.90824e31	−1.39303
$340$	5.66163e30	0.128663
$341$	1.10133e31	0.241261
$342$	1.26000e30	0.0266100
$343$	2.53418e31	0.516012
$344$	3.89507e31	0.764777
$345$	4.19867e31	0.795011
$346$	4.72860e31	0.863538
$347$	3.38483e31	0.596236	0.298118	−	0.954529i	$-0.403641\pi$
$347$	3.38483e31	0.596236	0.298118	+	0.954529i	$0.403641\pi$
$348$	−3.51889e30	−0.0597950
$349$	3.48809e31	0.571834	0.285917	−	0.958254i	$-0.407702\pi$
$349$	3.48809e31	0.571834	0.285917	+	0.958254i	$0.407702\pi$
$350$	−1.45606e31	−0.230318
$351$	−2.52494e31	−0.385400
$352$	−1.47728e31	−0.217610
$353$	−4.05894e31	−0.577070	−0.288535	−	0.957469i	$-0.593168\pi$
$353$	−4.05894e31	−0.577070	−0.288535	+	0.957469i	$0.593168\pi$
$354$	−1.09246e32	−1.49922
$355$	−2.98965e31	−0.396065
$356$	2.20499e31	0.282021
$357$	−1.70232e32	−2.10227
$358$	−1.50710e31	−0.179724
$359$	3.69036e31	0.425000	0.212500	−	0.977161i	$-0.431840\pi$
$359$	3.69036e31	0.425000	0.212500	+	0.977161i	$0.431840\pi$
$360$	−3.02589e30	−0.0336567
$361$	−7.72453e31	−0.829912
$362$	2.92600e31	0.303680
$363$	−5.41163e31	−0.542619
$364$	8.08939e30	0.0783698
$365$	3.06544e31	0.286967
$366$	1.22461e32	1.10786
$367$	−4.82660e31	−0.422003	−0.211002	−	0.977486i	$-0.567673\pi$
$367$	−4.82660e31	−0.422003	−0.211002	+	0.977486i	$0.567673\pi$
$368$	1.75856e32	1.48614
$369$	−7.14636e30	−0.0583788
$370$	−3.87536e31	−0.306049
$371$	−1.29315e32	−0.987359
$372$	7.92888e30	0.0585363
$373$	−3.59445e31	−0.256609	−0.128305	−	0.991735i	$-0.540954\pi$
$373$	−3.59445e31	−0.256609	−0.128305	+	0.991735i	$0.540954\pi$
$374$	−1.51168e32	−1.04367
$375$	−1.29128e31	−0.0862244
$376$	1.23303e32	0.796391
$377$	2.22772e31	0.139185
$378$	1.96647e32	1.18861
$379$	1.15257e32	0.674026	0.337013	−	0.941500i	$-0.390583\pi$
$379$	1.15257e32	0.674026	0.337013	+	0.941500i	$0.390583\pi$
$380$	−5.42380e30	−0.0306908
$381$	3.29650e32	1.80506
$382$	−7.87820e31	−0.417480
$383$	5.26887e30	0.0270230	0.0135115	−	0.999909i	$-0.495699\pi$
$383$	5.26887e30	0.0270230	0.0135115	+	0.999909i	$0.495699\pi$
$384$	1.32251e32	0.656534
$385$	−7.76065e31	−0.372940
$386$	−7.72914e29	−0.00359575
$387$	1.12674e31	0.0507502
$388$	−5.92038e31	−0.258198
$389$	3.45715e32	1.45999	0.729993	−	0.683455i	$-0.239523\pi$
$389$	3.45715e32	1.45999	0.729993	+	0.683455i	$0.239523\pi$
$390$	−3.59383e31	−0.146977
$391$	−8.04943e32	−3.18827
$392$	−1.64025e32	−0.629264
$393$	3.98131e32	1.47951
$394$	2.91290e32	1.04863
$395$	−1.53027e32	−0.533708
$396$	−2.30081e30	−0.00777483
$397$	1.54786e32	0.506817	0.253408	−	0.967359i	$-0.418448\pi$
$397$	1.54786e32	0.506817	0.253408	+	0.967359i	$0.418448\pi$
$398$	−5.23055e32	−1.65962
$399$	1.63081e32	0.501466
$400$	−5.40836e31	−0.161182
$401$	−4.57177e30	−0.0132063	−0.00660313	−	0.999978i	$-0.502102\pi$
$401$	−4.57177e30	−0.0132063	−0.00660313	+	0.999978i	$0.502102\pi$
$402$	−4.34909e32	−1.21779
$403$	−5.01957e31	−0.136255
$404$	5.89398e31	0.155111
$405$	1.62007e32	0.413376
$406$	−1.73499e32	−0.429261
$407$	−2.06553e32	−0.495566
$408$	−7.62863e32	−1.77498
$409$	3.06260e31	0.0691113	0.0345556	−	0.999403i	$-0.488998\pi$
$409$	3.06260e31	0.0691113	0.0345556	+	0.999403i	$0.488998\pi$
$410$	−1.54105e32	−0.337302
$411$	3.79020e32	0.804709
$412$	5.90255e31	0.121569
$413$	1.07522e33	2.14844
$414$	6.13742e31	0.118982
$415$	1.95848e32	0.368398
$416$	6.73306e31	0.122898
$417$	6.97549e31	0.123559
$418$	1.44818e32	0.248954
$419$	−8.57243e32	−1.43030	−0.715152	−	0.698969i	$-0.753643\pi$
$419$	−8.57243e32	−1.43030	−0.715152	+	0.698969i	$0.753643\pi$
$420$	−5.58719e31	−0.0904852
$421$	3.39875e32	0.534310	0.267155	−	0.963654i	$-0.413916\pi$
$421$	3.39875e32	0.534310	0.267155	+	0.963654i	$0.413916\pi$
$422$	8.16858e32	1.24664
$423$	3.56684e31	0.0528481
$424$	−5.79502e32	−0.833645
$425$	2.47556e32	0.345790
$426$	5.74692e32	0.779498
$427$	−1.20529e33	−1.58760
$428$	1.45972e32	0.186734
$429$	−1.91548e32	−0.237991
$430$	2.42973e32	0.293226
$431$	1.48748e31	0.0174375	0.00871877	−	0.999962i	$-0.497225\pi$
$431$	1.48748e31	0.0174375	0.00871877	+	0.999962i	$0.497225\pi$
$432$	7.30421e32	0.831814
$433$	−4.93215e32	−0.545680	−0.272840	−	0.962059i	$-0.587963\pi$
$433$	−4.93215e32	−0.545680	−0.272840	+	0.962059i	$0.587963\pi$
$434$	3.90933e32	0.420224
$435$	−1.53864e32	−0.160703
$436$	8.92535e31	0.0905825
$437$	7.71130e32	0.760518
$438$	−5.89261e32	−0.564782
$439$	−5.04170e32	−0.469646	−0.234823	−	0.972038i	$-0.575451\pi$
$439$	−5.04170e32	−0.469646	−0.234823	+	0.972038i	$0.575451\pi$
$440$	−3.47780e32	−0.314880
$441$	−4.74481e31	−0.0417577
$442$	6.88986e32	0.589430
$443$	1.73797e33	1.44543	0.722713	−	0.691148i	$-0.242895\pi$
$443$	1.73797e33	1.44543	0.722713	+	0.691148i	$0.242895\pi$
$444$	−1.48705e32	−0.120237
$445$	9.64138e32	0.757947
$446$	1.70299e32	0.130175
$447$	−3.72189e30	−0.00276643
$448$	−1.93069e33	−1.39553
$449$	−2.06132e33	−1.44899	−0.724497	−	0.689278i	$-0.757928\pi$
$449$	−2.06132e33	−1.44899	−0.724497	+	0.689278i	$0.757928\pi$
$450$	−1.88753e31	−0.0129044
$451$	−8.21366e32	−0.546172
$452$	3.71761e32	0.240455
$453$	1.24298e32	0.0782052
$454$	1.48024e33	0.906014
$455$	3.53711e32	0.210623
$456$	7.30817e32	0.423397
$457$	−1.72194e33	−0.970656	−0.485328	−	0.874332i	$-0.661300\pi$
$457$	−1.72194e33	−0.970656	−0.485328	+	0.874332i	$0.661300\pi$
$458$	−1.51319e33	−0.829993
$459$	−3.34335e33	−1.78453
$460$	−2.64191e32	−0.137229
$461$	−1.25235e33	−0.633090	−0.316545	−	0.948577i	$-0.602523\pi$
$461$	−1.25235e33	−0.633090	−0.316545	+	0.948577i	$0.602523\pi$
$462$	1.49181e33	0.733986
$463$	−2.26037e33	−1.08247	−0.541237	−	0.840870i	$-0.682044\pi$
$463$	−2.26037e33	−1.08247	−0.541237	+	0.840870i	$0.682044\pi$
$464$	−6.44441e32	−0.300406
$465$	3.46693e32	0.157320
$466$	−9.53838e32	−0.421357
$467$	3.54181e33	1.52322	0.761612	−	0.648033i	$-0.224408\pi$
$467$	3.54181e33	1.52322	0.761612	+	0.648033i	$0.224408\pi$
$468$	1.04865e31	0.00439095
$469$	4.28045e33	1.74513
$470$	7.69159e32	0.305347
$471$	−4.03352e33	−1.55928
$472$	4.81841e33	1.81397
$473$	1.29502e33	0.474802
$474$	2.94158e33	1.05039
$475$	−2.37157e32	−0.0824834
$476$	1.07114e33	0.362877
$477$	−1.67635e32	−0.0553203
$478$	1.05170e33	0.338097
$479$	2.05391e33	0.643261	0.321631	−	0.946865i	$-0.395769\pi$
$479$	2.05391e33	0.643261	0.321631	+	0.946865i	$0.395769\pi$
$480$	−4.65040e32	−0.141898
$481$	9.41417e32	0.279878
$482$	−5.50191e33	−1.59377
$483$	7.94360e33	2.24222
$484$	3.40514e32	0.0936628
$485$	−2.58870e33	−0.693922
$486$	4.93012e32	0.128796
$487$	−1.24188e33	−0.316204	−0.158102	−	0.987423i	$-0.550538\pi$
$487$	−1.24188e33	−0.316204	−0.158102	+	0.987423i	$0.550538\pi$
$488$	−5.40127e33	−1.34044
$489$	−4.16399e33	−1.00728
$490$	−1.02318e33	−0.241268
$491$	2.86576e33	0.658750	0.329375	−	0.944199i	$-0.393162\pi$
$491$	2.86576e33	0.658750	0.329375	+	0.944199i	$0.393162\pi$
$492$	−5.91333e32	−0.132516
$493$	2.94979e33	0.644473
$494$	−6.60044e32	−0.140600
$495$	−1.00604e32	−0.0208953
$496$	1.45208e33	0.294082
$497$	−5.65622e33	−1.11705
$498$	−3.76472e33	−0.725047
$499$	−4.46957e33	−0.839478	−0.419739	−	0.907645i	$-0.637878\pi$
$499$	−4.46957e33	−0.839478	−0.419739	+	0.907645i	$0.637878\pi$
$500$	8.12507e31	0.0148834
$501$	−4.04358e33	−0.722428
$502$	−2.11995e33	−0.369427
$503$	4.97050e33	0.844890	0.422445	−	0.906388i	$-0.361172\pi$
$503$	4.97050e33	0.844890	0.422445	+	0.906388i	$0.361172\pi$
$504$	−5.72477e32	−0.0949241
$505$	2.57716e33	0.416869
$506$	7.05403e33	1.11315
$507$	−5.38856e33	−0.829609
$508$	−2.07424e33	−0.311575
$509$	1.69698e33	0.248716	0.124358	−	0.992237i	$-0.460313\pi$
$509$	1.69698e33	0.248716	0.124358	+	0.992237i	$0.460313\pi$
$510$	−4.75870e33	−0.680552
$511$	5.79961e33	0.809352
$512$	−8.24988e33	−1.12350
$513$	3.20291e33	0.425674
$514$	9.72675e33	1.26162
$515$	2.58091e33	0.326725
$516$	9.32335e32	0.115200
$517$	4.09954e33	0.494429
$518$	−7.33192e33	−0.863169
$519$	7.93378e33	0.911776
$520$	1.58509e33	0.177833
$521$	−1.49376e34	−1.63610	−0.818051	−	0.575146i	$-0.804945\pi$
$521$	−1.49376e34	−1.63610	−0.818051	+	0.575146i	$0.804945\pi$
$522$	−2.24912e32	−0.0240509
$523$	2.03879e33	0.212863	0.106432	−	0.994320i	$-0.466057\pi$
$523$	2.03879e33	0.212863	0.106432	+	0.994320i	$0.466057\pi$
$524$	−2.50514e33	−0.255382
$525$	−2.44302e33	−0.243184
$526$	1.06125e34	1.03156
$527$	−6.64657e33	−0.630907
$528$	5.54114e33	0.513659
$529$	2.65157e34	2.40053
$530$	−3.61490e33	−0.319631
$531$	1.39384e33	0.120374
$532$	−1.02615e33	−0.0865593
$533$	3.74358e33	0.308459
$534$	−1.85333e34	−1.49172
$535$	6.38268e33	0.501858
$536$	1.91821e34	1.47345
$537$	−2.52866e33	−0.189763
$538$	−3.67911e33	−0.269752
$539$	−5.45344e33	−0.390671
$540$	−1.09732e33	−0.0768091
$541$	−2.54751e34	−1.74241	−0.871203	−	0.490923i	$-0.836660\pi$
$541$	−2.54751e34	−1.74241	−0.871203	+	0.490923i	$0.836660\pi$
$542$	1.34475e33	0.0898774
$543$	4.90932e33	0.320644
$544$	8.91545e33	0.569059
$545$	3.90264e33	0.243446
$546$	−6.79928e33	−0.414529
$547$	−1.10600e34	−0.659045	−0.329523	−	0.944148i	$-0.606888\pi$
$547$	−1.10600e34	−0.659045	−0.329523	+	0.944148i	$0.606888\pi$
$548$	−2.38489e33	−0.138903
$549$	−1.56245e33	−0.0889511
$550$	−2.16943e33	−0.120729
$551$	−2.82588e33	−0.153730
$552$	3.55978e34	1.89315
$553$	−2.89516e34	−1.50525
$554$	−2.34154e34	−1.19023
$555$	−6.50219e33	−0.323145
$556$	−4.38916e32	−0.0213278
$557$	3.16063e34	1.50170	0.750852	−	0.660471i	$-0.229643\pi$
$557$	3.16063e34	1.50170	0.750852	+	0.660471i	$0.229643\pi$
$558$	5.06779e32	0.0235446
$559$	−5.90238e33	−0.268151
$560$	−1.02323e34	−0.454591
$561$	−2.53634e34	−1.10198
$562$	−3.52413e33	−0.149743
$563$	3.39106e34	1.40923	0.704613	−	0.709592i	$-0.251121\pi$
$563$	3.39106e34	1.40923	0.704613	+	0.709592i	$0.251121\pi$
$564$	2.95142e33	0.119962
$565$	1.62554e34	0.646237
$566$	−5.71688e33	−0.222307
$567$	3.06506e34	1.16587
$568$	−2.53473e34	−0.943143
$569$	−3.52206e34	−1.28202	−0.641008	−	0.767534i	$-0.721484\pi$
$569$	−3.52206e34	−1.28202	−0.641008	+	0.767534i	$0.721484\pi$
$570$	4.55880e33	0.162336
$571$	1.74585e32	0.00608213	0.00304106	−	0.999995i	$-0.499032\pi$
$571$	1.74585e32	0.00608213	0.00304106	+	0.999995i	$0.499032\pi$
$572$	1.20527e33	0.0410802
$573$	−1.32183e34	−0.440800
$574$	−2.91557e34	−0.951315
$575$	−1.15518e34	−0.368810
$576$	−2.50282e33	−0.0781894
$577$	−2.09951e34	−0.641830	−0.320915	−	0.947108i	$-0.603990\pi$
$577$	−2.09951e34	−0.641830	−0.320915	+	0.947108i	$0.603990\pi$
$578$	6.07114e34	1.81624
$579$	−1.29682e32	−0.00379662
$580$	9.68155e32	0.0277393
$581$	3.70531e34	1.03902
$582$	4.97619e34	1.36571
$583$	−1.92671e34	−0.517558
$584$	2.59899e34	0.683351
$585$	4.58526e32	0.0118009
$586$	2.67151e34	0.673034
$587$	1.56145e34	0.385082	0.192541	−	0.981289i	$-0.438327\pi$
$587$	1.56145e34	0.385082	0.192541	+	0.981289i	$0.438327\pi$
$588$	−3.92614e33	−0.0947871
$589$	6.36737e33	0.150494
$590$	3.00570e34	0.695498
$591$	4.88734e34	1.10721
$592$	−2.72336e34	−0.604065
$593$	−4.75715e34	−1.03315	−0.516575	−	0.856242i	$-0.672793\pi$
$593$	−4.75715e34	−1.03315	−0.516575	+	0.856242i	$0.672793\pi$
$594$	2.92990e34	0.623050
$595$	4.68360e34	0.975254
$596$	2.34191e31	0.000477520 0
$597$	−8.77596e34	−1.75233
$598$	−3.21505e34	−0.628670
$599$	−3.07153e34	−0.588193	−0.294097	−	0.955776i	$-0.595019\pi$
$599$	−3.07153e34	−0.588193	−0.294097	+	0.955776i	$0.595019\pi$
$600$	−1.09479e34	−0.205325
$601$	−5.54764e34	−1.01901	−0.509504	−	0.860469i	$-0.670171\pi$
$601$	−5.54764e34	−1.01901	−0.509504	+	0.860469i	$0.670171\pi$
$602$	4.59688e34	0.827003
$603$	5.54887e33	0.0977774
$604$	−7.82113e32	−0.0134992
$605$	1.48891e34	0.251724
$606$	−4.95400e34	−0.820442
$607$	1.70386e34	0.276424	0.138212	−	0.990403i	$-0.455864\pi$
$607$	1.70386e34	0.276424	0.138212	+	0.990403i	$0.455864\pi$
$608$	−8.54095e33	−0.135741
$609$	−2.91101e34	−0.453239
$610$	−3.36929e34	−0.513943
$611$	−1.86847e34	−0.279236
$612$	1.38855e33	0.0203315
$613$	−5.26192e34	−0.754899	−0.377449	−	0.926030i	$-0.623199\pi$
$613$	−5.26192e34	−0.754899	−0.377449	+	0.926030i	$0.623199\pi$
$614$	−3.43781e34	−0.483256
$615$	−2.58562e34	−0.356144
$616$	−6.57975e34	−0.888077
$617$	−8.20494e34	−1.08520	−0.542601	−	0.839990i	$-0.682560\pi$
$617$	−8.20494e34	−1.08520	−0.542601	+	0.839990i	$0.682560\pi$
$618$	−4.96120e34	−0.643029
$619$	4.09848e34	0.520583	0.260292	−	0.965530i	$-0.416181\pi$
$619$	4.09848e34	0.520583	0.260292	+	0.965530i	$0.416181\pi$
$620$	−2.18148e33	−0.0271553
$621$	1.56012e35	1.90333
$622$	−1.60122e34	−0.191458
$623$	1.82408e35	2.13769
$624$	−2.52551e34	−0.290096
$625$	3.55271e33	0.0400000
$626$	9.48386e34	1.04666
$627$	2.42980e34	0.262861
$628$	2.53799e34	0.269150
$629$	1.24656e35	1.29593
$630$	−3.57108e33	−0.0363951
$631$	1.04707e34	0.104619	0.0523094	−	0.998631i	$-0.483342\pi$
$631$	1.04707e34	0.104619	0.0523094	+	0.998631i	$0.483342\pi$
$632$	−1.29741e35	−1.27091
$633$	1.37055e35	1.31628
$634$	1.18365e35	1.11457
$635$	−9.06969e34	−0.837376
$636$	−1.38711e34	−0.125573
$637$	2.48554e34	0.220637
$638$	−2.58502e34	−0.225012
$639$	−7.33232e33	−0.0625865
$640$	−3.63862e34	−0.304570
$641$	−1.05784e35	−0.868353	−0.434176	−	0.900828i	$-0.642960\pi$
$641$	−1.05784e35	−0.868353	−0.434176	+	0.900828i	$0.642960\pi$
$642$	−1.22692e35	−0.987710
$643$	−1.70961e34	−0.134977	−0.0674884	−	0.997720i	$-0.521499\pi$
$643$	−1.70961e34	−0.134977	−0.0674884	+	0.997720i	$0.521499\pi$
$644$	−4.99832e34	−0.387035
$645$	4.07667e34	0.309605
$646$	−8.73985e34	−0.651025
$647$	1.84776e35	1.35003	0.675013	−	0.737806i	$-0.264138\pi$
$647$	1.84776e35	1.35003	0.675013	+	0.737806i	$0.264138\pi$
$648$	1.37355e35	0.984366
$649$	1.60201e35	1.12618
$650$	9.88773e33	0.0681836
$651$	6.55919e34	0.443698
$652$	2.62009e34	0.173868
$653$	−2.83628e35	−1.84644	−0.923219	−	0.384275i	$-0.874452\pi$
$653$	−2.83628e35	−1.84644	−0.923219	+	0.384275i	$0.874452\pi$
$654$	−7.50192e34	−0.479127
$655$	−1.09538e35	−0.686355
$656$	−1.08295e35	−0.665751
$657$	7.51821e33	0.0453469
$658$	1.45520e35	0.861188
$659$	−8.65874e34	−0.502791	−0.251395	−	0.967885i	$-0.580889\pi$
$659$	−8.65874e34	−0.502791	−0.251395	+	0.967885i	$0.580889\pi$
$660$	−8.32455e33	−0.0474309
$661$	−5.16150e34	−0.288574	−0.144287	−	0.989536i	$-0.546089\pi$
$661$	−5.16150e34	−0.288574	−0.144287	+	0.989536i	$0.546089\pi$
$662$	−5.91059e34	−0.324269
$663$	1.15600e35	0.622356
$664$	1.66047e35	0.877262
$665$	−4.48686e34	−0.232633
$666$	−9.50459e33	−0.0483621
$667$	−1.37648e35	−0.687378
$668$	2.54432e34	0.124700
$669$	2.85733e34	0.137447
$670$	1.19657e35	0.564940
$671$	−1.79580e35	−0.832196
$672$	−8.79824e34	−0.400203
$673$	−9.88745e34	−0.441465	−0.220732	−	0.975334i	$-0.570845\pi$
$673$	−9.88745e34	−0.441465	−0.220732	+	0.975334i	$0.570845\pi$
$674$	3.13692e35	1.37485
$675$	−4.79808e34	−0.206429
$676$	3.39062e34	0.143201
$677$	−5.20506e33	−0.0215808	−0.0107904	−	0.999942i	$-0.503435\pi$
$677$	−5.20506e33	−0.0215808	−0.0107904	+	0.999942i	$0.503435\pi$
$678$	−3.12472e35	−1.27186
$679$	−4.89765e35	−1.95711
$680$	2.09887e35	0.823425
$681$	2.48359e35	0.956625
$682$	5.82465e34	0.220275
$683$	−2.25265e35	−0.836442	−0.418221	−	0.908345i	$-0.637346\pi$
$683$	−2.25265e35	−0.836442	−0.418221	+	0.908345i	$0.637346\pi$
$684$	−1.33022e33	−0.00484980
$685$	−1.04280e35	−0.373309
$686$	1.34026e35	0.471128
$687$	−2.53887e35	−0.876358
$688$	1.70746e35	0.578755
$689$	8.78145e34	0.292298
$690$	2.22057e35	0.725858
$691$	4.87271e35	1.56421	0.782104	−	0.623147i	$-0.214146\pi$
$691$	4.87271e35	1.56421	0.782104	+	0.623147i	$0.214146\pi$
$692$	−4.99214e34	−0.157384
$693$	−1.90335e34	−0.0589324
$694$	1.79015e35	0.544373
$695$	−1.91917e34	−0.0573197
$696$	−1.30452e35	−0.382679
$697$	4.95699e35	1.42826
$698$	1.84477e35	0.522094
$699$	−1.60038e35	−0.444895
$700$	1.53721e34	0.0419766
$701$	1.53661e34	0.0412182	0.0206091	−	0.999788i	$-0.493439\pi$
$701$	1.53661e34	0.0412182	0.0206091	+	0.999788i	$0.493439\pi$
$702$	−1.33538e35	−0.351876
$703$	−1.19420e35	−0.309125
$704$	−2.87661e35	−0.731513
$705$	1.29052e35	0.322403
$706$	−2.14667e35	−0.526874
$707$	4.87581e35	1.17572
$708$	1.15335e35	0.273240
$709$	−2.35646e35	−0.548508	−0.274254	−	0.961657i	$-0.588431\pi$
$709$	−2.35646e35	−0.548508	−0.274254	+	0.961657i	$0.588431\pi$
$710$	−1.58115e35	−0.361614
$711$	−3.75308e34	−0.0843370
$712$	8.17430e35	1.80489
$713$	3.10152e35	0.672908
$714$	−9.00314e35	−1.91940
$715$	5.27006e34	0.110405
$716$	1.59110e34	0.0327555
$717$	1.76456e35	0.356983
$718$	1.95174e35	0.388031
$719$	−5.92455e35	−1.15756	−0.578781	−	0.815483i	$-0.696472\pi$
$719$	−5.92455e35	−1.15756	−0.578781	+	0.815483i	$0.696472\pi$
$720$	−1.32644e34	−0.0254701
$721$	4.88290e35	0.921483
$722$	−4.08532e35	−0.757723
$723$	−9.23125e35	−1.68280
$724$	−3.08907e34	−0.0553472
$725$	4.23329e34	0.0745508
$726$	−2.86208e35	−0.495420
$727$	−1.03950e35	−0.176866	−0.0884330	−	0.996082i	$-0.528186\pi$
$727$	−1.03950e35	−0.176866	−0.0884330	+	0.996082i	$0.528186\pi$
$728$	2.99889e35	0.501554
$729$	6.44962e35	1.06033
$730$	1.62124e35	0.262006
$731$	−7.81553e35	−1.24163
$732$	−1.29286e35	−0.201913
$733$	−7.19639e35	−1.10488	−0.552440	−	0.833553i	$-0.686303\pi$
$733$	−7.19639e35	−1.10488	−0.552440	+	0.833553i	$0.686303\pi$
$734$	−2.55267e35	−0.385296
$735$	−1.71672e35	−0.254746
$736$	−4.16026e35	−0.606943
$737$	6.37759e35	0.914772
$738$	−3.77953e34	−0.0533008
$739$	1.95103e35	0.270526	0.135263	−	0.990810i	$-0.456812\pi$
$739$	1.95103e35	0.270526	0.135263	+	0.990810i	$0.456812\pi$
$740$	4.09135e34	0.0557789
$741$	−1.10744e35	−0.148454
$742$	−6.83915e35	−0.901474
$743$	4.64482e35	0.602017	0.301008	−	0.953621i	$-0.402677\pi$
$743$	4.64482e35	0.602017	0.301008	+	0.953621i	$0.402677\pi$
$744$	2.93938e35	0.374623
$745$	1.02401e33	0.00128336
$746$	−1.90102e35	−0.234288
$747$	4.80330e34	0.0582147
$748$	1.59593e35	0.190215
$749$	1.20756e36	1.41542
$750$	−6.82927e34	−0.0787243
$751$	4.14134e35	0.469507	0.234753	−	0.972055i	$-0.424572\pi$
$751$	4.14134e35	0.469507	0.234753	+	0.972055i	$0.424572\pi$
$752$	5.40516e35	0.602678
$753$	−3.55691e35	−0.390064
$754$	1.17819e35	0.127079
$755$	−3.41981e34	−0.0362799
$756$	−2.07606e35	−0.216630
$757$	4.04064e34	0.0414717	0.0207358	−	0.999785i	$-0.493399\pi$
$757$	4.04064e34	0.0414717	0.0207358	+	0.999785i	$0.493399\pi$
$758$	6.09565e35	0.615397
$759$	1.18354e36	1.17534
$760$	−2.01070e35	−0.196417
$761$	3.03175e33	0.00291330	0.00145665	−	0.999999i	$-0.499536\pi$
$761$	3.03175e33	0.00291330	0.00145665	+	0.999999i	$0.499536\pi$
$762$	1.74344e36	1.64805
$763$	7.38353e35	0.686605
$764$	8.31727e34	0.0760876
$765$	6.07149e34	0.0546421
$766$	2.78658e34	0.0246724
$767$	−7.30156e35	−0.636024
$768$	−5.45127e35	−0.467178
$769$	−5.91774e35	−0.498973	−0.249486	−	0.968378i	$-0.580262\pi$
$769$	−5.91774e35	−0.498973	−0.249486	+	0.968378i	$0.580262\pi$
$770$	−4.10442e35	−0.340500
$771$	1.63198e36	1.33210
$772$	8.15990e32	0.000655343 0
$773$	−1.47826e36	−1.16818	−0.584088	−	0.811690i	$-0.698548\pi$
$773$	−1.47826e36	−1.16818	−0.584088	+	0.811690i	$0.698548\pi$
$774$	5.95907e34	0.0463358
$775$	−9.53858e34	−0.0729815
$776$	−2.19479e36	−1.65243
$777$	−1.23017e36	−0.911387
$778$	1.82840e36	1.33299
$779$	−4.74876e35	−0.340692
$780$	3.79412e34	0.0267873
$781$	−8.42739e35	−0.585538
$782$	−4.25715e36	−2.91095
$783$	−5.71722e35	−0.384736
$784$	−7.19024e35	−0.476204
$785$	1.10975e36	0.723357
$786$	2.10562e36	1.35082
$787$	−2.45801e36	−1.55203	−0.776014	−	0.630716i	$-0.782761\pi$
$787$	−2.45801e36	−1.55203	−0.776014	+	0.630716i	$0.782761\pi$
$788$	−3.07524e35	−0.191118
$789$	1.78059e36	1.08919
$790$	−8.09320e35	−0.487284
$791$	3.07541e36	1.82262
$792$	−8.52953e34	−0.0497577
$793$	8.18479e35	0.469994
$794$	8.18626e35	0.462732
$795$	−6.06519e35	−0.337485
$796$	5.52206e35	0.302474
$797$	4.34299e35	0.234185	0.117093	−	0.993121i	$-0.462643\pi$
$797$	4.34299e35	0.234185	0.117093	+	0.993121i	$0.462643\pi$
$798$	8.62495e35	0.457847
$799$	−2.47410e36	−1.29295
$800$	1.27947e35	0.0658271
$801$	2.36461e35	0.119772
$802$	−2.41790e34	−0.0120575
$803$	8.64104e35	0.424250
$804$	4.59147e35	0.221948
$805$	−2.18553e36	−1.04018
$806$	−2.65473e35	−0.124403
$807$	−6.17291e35	−0.284820
$808$	2.18501e36	0.992683
$809$	1.22565e36	0.548291	0.274146	−	0.961688i	$-0.411605\pi$
$809$	1.22565e36	0.548291	0.274146	+	0.961688i	$0.411605\pi$
$810$	8.56814e35	0.377419
$811$	−1.02405e36	−0.444182	−0.222091	−	0.975026i	$-0.571288\pi$
$811$	−1.02405e36	−0.444182	−0.222091	+	0.975026i	$0.571288\pi$
$812$	1.83168e35	0.0782348
$813$	2.25626e35	0.0948981
$814$	−1.09241e36	−0.452460
$815$	1.14564e36	0.467281
$816$	−3.34411e36	−1.34324
$817$	7.48722e35	0.296173
$818$	1.61973e35	0.0630997
$819$	8.67501e34	0.0332829
$820$	1.62694e35	0.0614749
$821$	6.48379e35	0.241290	0.120645	−	0.992696i	$-0.461504\pi$
$821$	6.48379e35	0.241290	0.120645	+	0.992696i	$0.461504\pi$
$822$	2.00454e36	0.734713
$823$	−5.11224e36	−1.84550	−0.922749	−	0.385402i	$-0.874063\pi$
$823$	−5.11224e36	−1.84550	−0.922749	+	0.385402i	$0.874063\pi$
$824$	2.18818e36	0.778025
$825$	−3.63993e35	−0.127473
$826$	5.68658e36	1.96156
$827$	7.96901e35	0.270761	0.135380	−	0.990794i	$-0.456774\pi$
$827$	7.96901e35	0.270761	0.135380	+	0.990794i	$0.456774\pi$
$828$	−6.47947e34	−0.0216850
$829$	−1.51687e36	−0.500054	−0.250027	−	0.968239i	$-0.580439\pi$
$829$	−1.51687e36	−0.500054	−0.250027	+	0.968239i	$0.580439\pi$
$830$	1.03579e36	0.336354
$831$	−3.92871e36	−1.25672
$832$	1.31109e36	0.413132
$833$	3.29118e36	1.02162
$834$	3.68917e35	0.112811
$835$	1.11251e36	0.335138
$836$	−1.52889e35	−0.0453730
$837$	1.28822e36	0.376637
$838$	−4.53375e36	−1.30589
$839$	6.07612e36	1.72426	0.862128	−	0.506690i	$-0.169131\pi$
$839$	6.07612e36	1.72426	0.862128	+	0.506690i	$0.169131\pi$
$840$	−2.07128e36	−0.579091
$841$	−3.12594e36	−0.861054
$842$	1.79752e36	0.487834
$843$	−5.91288e35	−0.158108
$844$	−8.62383e35	−0.227206
$845$	1.48256e36	0.384861
$846$	1.88641e35	0.0482512
$847$	2.81691e36	0.709954
$848$	−2.54032e36	−0.630871
$849$	−9.59194e35	−0.234726
$850$	1.30927e36	0.315712
$851$	−5.81688e36	−1.38220
$852$	−6.06720e35	−0.142067
$853$	3.09454e35	0.0714058	0.0357029	−	0.999362i	$-0.488633\pi$
$853$	3.09454e35	0.0714058	0.0357029	+	0.999362i	$0.488633\pi$
$854$	−6.37446e36	−1.44951
$855$	−5.81645e34	−0.0130341
$856$	5.41146e36	1.19507
$857$	−2.80070e36	−0.609546	−0.304773	−	0.952425i	$-0.598581\pi$
$857$	−2.80070e36	−0.609546	−0.304773	+	0.952425i	$0.598581\pi$
$858$	−1.01305e36	−0.217290
$859$	−5.42278e36	−1.14632	−0.573162	−	0.819442i	$-0.694283\pi$
$859$	−5.42278e36	−1.14632	−0.573162	+	0.819442i	$0.694283\pi$
$860$	−2.56514e35	−0.0534418
$861$	−4.89182e36	−1.00446
$862$	7.86691e34	0.0159207
$863$	3.30591e36	0.659411	0.329706	−	0.944084i	$-0.393050\pi$
$863$	3.30591e36	0.659411	0.329706	+	0.944084i	$0.393050\pi$
$864$	−1.72797e36	−0.339715
$865$	−2.18283e36	−0.422978
$866$	−2.60850e36	−0.498215
$867$	1.01863e37	1.91769
$868$	−4.12721e35	−0.0765879
$869$	−4.31360e36	−0.789028
$870$	−8.13751e35	−0.146724
$871$	−2.90674e36	−0.516630
$872$	3.30879e36	0.579714
$873$	−6.34897e35	−0.109654
$874$	4.07832e36	0.694365
$875$	6.72149e35	0.112815
$876$	6.22102e35	0.102934
$877$	−7.96071e35	−0.129854	−0.0649272	−	0.997890i	$-0.520682\pi$
$877$	−7.96071e35	−0.129854	−0.0649272	+	0.997890i	$0.520682\pi$
$878$	−2.66643e36	−0.428795
$879$	4.48234e36	0.710630
$880$	−1.52454e36	−0.238290
$881$	7.87266e36	1.21317	0.606586	−	0.795018i	$-0.292539\pi$
$881$	7.87266e36	1.21317	0.606586	+	0.795018i	$0.292539\pi$
$882$	−2.50941e35	−0.0381254
$883$	1.24923e37	1.87126	0.935628	−	0.352987i	$-0.114834\pi$
$883$	1.24923e37	1.87126	0.935628	+	0.352987i	$0.114834\pi$
$884$	−7.27385e35	−0.107426
$885$	5.04305e36	0.734349
$886$	9.19170e36	1.31970
$887$	5.74446e36	0.813212	0.406606	−	0.913604i	$-0.366712\pi$
$887$	5.74446e36	0.813212	0.406606	+	0.913604i	$0.366712\pi$
$888$	−5.51279e36	−0.769501
$889$	−1.71592e37	−2.36171
$890$	5.09909e36	0.692018
$891$	4.56673e36	0.611131
$892$	−1.79790e35	−0.0237250
$893$	2.37017e36	0.308415
$894$	−1.96842e34	−0.00252579
$895$	6.95713e35	0.0880323
$896$	−6.88402e36	−0.858998
$897$	−5.39430e36	−0.663788
$898$	−1.09018e37	−1.32295
$899$	−1.13658e36	−0.136021
$900$	1.99273e34	0.00235189
$901$	1.16278e37	1.35344
$902$	−4.34400e36	−0.498664
$903$	7.71277e36	0.873200
$904$	1.37819e37	1.53887
$905$	−1.35071e36	−0.148749
$906$	6.57380e35	0.0714026
$907$	−7.99817e36	−0.856840	−0.428420	−	0.903580i	$-0.640930\pi$
$907$	−7.99817e36	−0.856840	−0.428420	+	0.903580i	$0.640930\pi$
$908$	−1.56274e36	−0.165125
$909$	6.32066e35	0.0658740
$910$	1.87069e36	0.192302
$911$	−2.21384e36	−0.224474	−0.112237	−	0.993681i	$-0.535802\pi$
$911$	−2.21384e36	−0.224474	−0.112237	+	0.993681i	$0.535802\pi$
$912$	3.20364e36	0.320411
$913$	5.52067e36	0.544636
$914$	−9.10691e36	−0.886224
$915$	−5.65308e36	−0.542652
$916$	1.59752e36	0.151270
$917$	−2.07238e37	−1.93577
$918$	−1.76821e37	−1.62930
$919$	2.02245e37	1.83837	0.919187	−	0.393820i	$-0.128847\pi$
$919$	2.02245e37	1.83837	0.919187	+	0.393820i	$0.128847\pi$
$920$	−9.79405e36	−0.878243
$921$	−5.76806e36	−0.510252
$922$	−6.62339e36	−0.578021
$923$	3.84099e36	0.330691
$924$	−1.57495e36	−0.133772
$925$	1.78895e36	0.149909
$926$	−1.19546e37	−0.988316
$927$	6.32985e35	0.0516294
$928$	1.52457e36	0.122687
$929$	−9.92849e36	−0.788291	−0.394146	−	0.919048i	$-0.628959\pi$
$929$	−9.92849e36	−0.788291	−0.394146	+	0.919048i	$0.628959\pi$
$930$	1.83357e36	0.143635
$931$	−3.15293e36	−0.243693
$932$	1.00700e36	0.0767944
$933$	−2.68658e36	−0.202153
$934$	1.87317e37	1.39073
$935$	6.97825e36	0.511213
$936$	3.88755e35	0.0281014
$937$	1.66049e37	1.18438	0.592191	−	0.805798i	$-0.298263\pi$
$937$	1.66049e37	1.18438	0.592191	+	0.805798i	$0.298263\pi$
$938$	2.26382e37	1.59334
$939$	1.59123e37	1.10513
$940$	−8.12026e35	−0.0556509
$941$	−1.55363e37	−1.05070	−0.525348	−	0.850888i	$-0.676065\pi$
$941$	−1.55363e37	−1.05070	−0.525348	+	0.850888i	$0.676065\pi$
$942$	−2.13323e37	−1.42364
$943$	−2.31310e37	−1.52335
$944$	2.11222e37	1.37274
$945$	−9.07764e36	−0.582204
$946$	6.84905e36	0.433502
$947$	−1.44848e37	−0.904772	−0.452386	−	0.891822i	$-0.649427\pi$
$947$	−1.44848e37	−0.904772	−0.452386	+	0.891822i	$0.649427\pi$
$948$	−3.10553e36	−0.191439
$949$	−3.93837e36	−0.239601
$950$	−1.25427e36	−0.0753087
$951$	1.98597e37	1.17684
$952$	3.97092e37	2.32236
$953$	2.85413e37	1.64745	0.823726	−	0.566988i	$-0.191892\pi$
$953$	2.85413e37	1.64745	0.823726	+	0.566988i	$0.191892\pi$
$954$	−8.86579e35	−0.0505083
$955$	3.63675e36	0.204490
$956$	−1.11031e36	−0.0616197
$957$	−4.33721e36	−0.237581
$958$	1.08626e37	0.587308
$959$	−1.97291e37	−1.05287
$960$	−9.05542e36	−0.477000
$961$	−1.66718e37	−0.866843
$962$	4.97892e36	0.255533
$963$	1.56540e36	0.0793041
$964$	5.80854e36	0.290472
$965$	3.56794e34	0.00176127
$966$	4.20118e37	2.04718
$967$	−3.20243e37	−1.54046	−0.770228	−	0.637769i	$-0.779858\pi$
$967$	−3.20243e37	−1.54046	−0.770228	+	0.637769i	$0.779858\pi$
$968$	1.26235e37	0.599427
$969$	−1.46640e37	−0.687392
$970$	−1.36910e37	−0.633562
$971$	−2.57617e37	−1.17689	−0.588443	−	0.808539i	$-0.700259\pi$
$971$	−2.57617e37	−1.17689	−0.588443	+	0.808539i	$0.700259\pi$
$972$	−5.20489e35	−0.0234738
$973$	−3.63095e36	−0.161662
$974$	−6.56800e36	−0.288700
$975$	1.65899e36	0.0719924
$976$	−2.36772e37	−1.01440
$977$	−1.00193e37	−0.423795	−0.211898	−	0.977292i	$-0.567964\pi$
$977$	−1.00193e37	−0.423795	−0.211898	+	0.977292i	$0.567964\pi$
$978$	−2.20223e37	−0.919659
$979$	2.71776e37	1.12054
$980$	1.08020e36	0.0439723
$981$	9.57148e35	0.0384695
$982$	1.51563e37	0.601449
$983$	3.97162e37	1.55614	0.778070	−	0.628178i	$-0.216199\pi$
$983$	3.97162e37	1.55614	0.778070	+	0.628178i	$0.216199\pi$
$984$	−2.19218e37	−0.848081
$985$	−1.34466e37	−0.513640
$986$	1.56007e37	0.588415
$987$	2.44157e37	0.909295
$988$	6.96830e35	0.0256251
$989$	3.64700e37	1.32429
$990$	−5.32068e35	−0.0190778
$991$	−2.53577e37	−0.897820	−0.448910	−	0.893577i	$-0.648188\pi$
$991$	−2.53577e37	−0.897820	−0.448910	+	0.893577i	$0.648188\pi$
$992$	−3.43521e36	−0.120104
$993$	−9.91695e36	−0.342383
$994$	−2.99143e37	−1.01988
$995$	2.41454e37	0.812916
$996$	3.97454e36	0.132143
$997$	1.18814e37	0.390102	0.195051	−	0.980793i	$-0.437513\pi$
$997$	1.18814e37	0.390102	0.195051	+	0.980793i	$0.437513\pi$
$998$	−2.36385e37	−0.766457
$999$	−2.41605e37	−0.773638

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.26.a.a.1.3	✓	4
3.2	odd	2		45.26.a.c.1.2		4
5.2	odd	4		25.26.b.b.24.5		8
5.3	odd	4		25.26.b.b.24.4		8
5.4	even	2		25.26.a.b.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.26.a.a.1.3	✓	4	1.1	even	1	trivial
25.26.a.b.1.2		4	5.4	even	2
25.26.b.b.24.4		8	5.3	odd	4
25.26.b.b.24.5		8	5.2	odd	4
45.26.a.c.1.2		4	3.2	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:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 26 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q+5288.75 q^{2} +887362. q^{3} -5.58351e6 q^{4} -2.44141e8 q^{5} +4.69304e9 q^{6} -4.61897e10 q^{7} -2.06991e11 q^{8} -5.98771e10 q^{9} +O(q^{10})\)	\(q+5288.75 q^{2} +887362. q^{3} -5.58351e6 q^{4} -2.44141e8 q^{5} +4.69304e9 q^{6} -4.61897e10 q^{7} -2.06991e11 q^{8} -5.98771e10 q^{9} -1.29120e12 q^{10} -6.88197e12 q^{11} -4.95459e12 q^{12} +3.13663e13 q^{13} -2.44286e14 q^{14} -2.16641e14 q^{15} -9.07373e14 q^{16} +4.15331e15 q^{17} -3.16675e14 q^{18} -3.97884e15 q^{19} +1.36316e15 q^{20} -4.09870e16 q^{21} -3.63970e16 q^{22} -1.93808e17 q^{23} -1.83676e17 q^{24} +5.96046e16 q^{25} +1.65889e17 q^{26} -8.04984e17 q^{27} +2.57901e17 q^{28} +7.10227e17 q^{29} -1.14576e18 q^{30} -1.60031e18 q^{31} +2.14659e18 q^{32} -6.10680e18 q^{33} +2.19658e19 q^{34} +1.12768e19 q^{35} +3.34325e17 q^{36} +3.00137e19 q^{37} -2.10431e19 q^{38} +2.78333e19 q^{39} +5.05349e19 q^{40} +1.19350e20 q^{41} -2.16770e20 q^{42} -1.88176e20 q^{43} +3.84255e19 q^{44} +1.46184e19 q^{45} -1.02500e21 q^{46} -5.95693e20 q^{47} -8.05168e20 q^{48} +7.92424e20 q^{49} +3.15234e20 q^{50} +3.68549e21 q^{51} -1.75134e20 q^{52} +2.79965e21 q^{53} -4.25737e21 q^{54} +1.68017e21 q^{55} +9.56086e21 q^{56} -3.53067e21 q^{57} +3.75622e21 q^{58} -2.32784e22 q^{59} +1.20962e21 q^{60} +2.60942e22 q^{61} -8.46364e21 q^{62} +2.76571e21 q^{63} +4.17992e22 q^{64} -7.65779e21 q^{65} -3.22973e22 q^{66} -9.26710e22 q^{67} -2.31900e22 q^{68} -1.71978e23 q^{69} +5.96402e22 q^{70} +1.22456e23 q^{71} +1.23940e22 q^{72} -1.25561e23 q^{73} +1.58735e23 q^{74} +5.28909e22 q^{75} +2.22159e22 q^{76} +3.17876e23 q^{77} +1.47203e23 q^{78} +6.26797e23 q^{79} +2.21527e23 q^{80} -6.63579e23 q^{81} +6.31215e23 q^{82} -8.02193e23 q^{83} +2.28851e23 q^{84} -1.01399e24 q^{85} -9.95217e23 q^{86} +6.30229e23 q^{87} +1.42451e24 q^{88} -3.94911e24 q^{89} +7.73134e22 q^{90} -1.44880e24 q^{91} +1.08213e24 q^{92} -1.42005e24 q^{93} -3.15048e24 q^{94} +9.71397e23 q^{95} +1.90480e24 q^{96} +1.06033e25 q^{97} +4.19094e24 q^{98} +4.12073e23 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 600 q^{2} - 798600 q^{3} + 92413888 q^{4} - 976562500 q^{5} - 3965174832 q^{6} - 48938107000 q^{7} + 224433484800 q^{8} + 2087565807492 q^{9}+O(q^{10}) \) 4 * q + 600 * q^2 - 798600 * q^3 + 92413888 * q^4 - 976562500 * q^5 - 3965174832 * q^6 - 48938107000 * q^7 + 224433484800 * q^8 + 2087565807492 * q^9	\( 4 q + 600 q^{2} - 798600 q^{3} + 92413888 q^{4} - 976562500 q^{5} - 3965174832 q^{6} - 48938107000 q^{7} + 224433484800 q^{8} + 2087565807492 q^{9} - 146484375000 q^{10} - 23641453790592 q^{11} - 42051883516800 q^{12} + 109063914225800 q^{13} + 109980501036336 q^{14} + 194970703125000 q^{15} - 28\!\cdots\!76 q^{16}+ \cdots - 19\!\cdots\!16 q^{99}+O(q^{100}) \) 4 * q + 600 * q^2 - 798600 * q^3 + 92413888 * q^4 - 976562500 * q^5 - 3965174832 * q^6 - 48938107000 * q^7 + 224433484800 * q^8 + 2087565807492 * q^9 - 146484375000 * q^10 - 23641453790592 * q^11 - 42051883516800 * q^12 + 109063914225800 * q^13 + 109980501036336 * q^14 + 194970703125000 * q^15 - 2811357146648576 * q^16 - 337440158866200 * q^17 - 8986517054418600 * q^18 - 5765957235759760 * q^19 - 22561984375000000 * q^20 - 76777748650758672 * q^21 - 247170171892300800 * q^22 - 84289919171581800 * q^23 - 750163283268986880 * q^24 + 238418579101562500 * q^25 - 2172668626545951312 * q^26 - 2324539610168425200 * q^27 + 715367314323708800 * q^28 - 1530771705074446440 * q^29 + 968060261718750000 * q^30 - 3405335632352491792 * q^31 + 8794451084429721600 * q^32 + 38579776790129836800 * q^33 + 12360736169963080176 * q^34 + 11947780029296875000 * q^35 + 29754645353627097024 * q^36 + 54849661150838347400 * q^37 + 167830012254298039200 * q^38 + 26980019582506147824 * q^39 - 54793331250000000000 * q^40 + 294765092997163901208 * q^41 - 275649307903658959200 * q^42 - 1266847513533640537000 * q^43 - 739285598894744039424 * q^44 - 509659620969726562500 * q^45 - 669486761007570298992 * q^46 + 826481836956124900200 * q^47 - 389112939053996236800 * q^48 - 2497667097456123567372 * q^49 + 35762786865234375000 * q^50 - 732051781800631123152 * q^51 - 3824820275638519888000 * q^52 + 7304325845439007895400 * q^53 + 15784899184389947603040 * q^54 + 5771839304343750000000 * q^55 + 14029366421126577776640 * q^56 + 15974193201590955213600 * q^57 + 11714010248956820950800 * q^58 - 2217164203172823251280 * q^59 + 10266573124218750000000 * q^60 - 50917697960481835727992 * q^61 - 24701477049499711624800 * q^62 + 2223612189174803070600 * q^63 - 20457521683182533476352 * q^64 - 26626932184033203125000 * q^65 - 16106812566256687908864 * q^66 - 76670956029519070862200 * q^67 - 318284068848532686249600 * q^68 - 211835176227690988743216 * q^69 - 26850708260824218750000 * q^70 + 150298050225701362285008 * q^71 + 399372518437664399078400 * q^72 - 106773821938777386935800 * q^73 + 286932321536483813083056 * q^74 - 47600269317626953125000 * q^75 + 793491830268069721114880 * q^76 - 215630079777610746336000 * q^77 + 1847661803543761572804000 * q^78 - 151978174282543555164640 * q^79 + 686366490881000000000000 * q^80 - 1579018732178689012033836 * q^81 + 3094333027045954774045200 * q^82 + 117573693202171400616600 * q^83 - 1614703102161158475120384 * q^84 + 82382851285693359375000 * q^85 - 1608810179612708665216752 * q^86 - 2896477998479054993943600 * q^87 - 4936697892190706144870400 * q^88 - 6860971673379749077360920 * q^89 + 2193973890238916015625000 * q^90 - 5097829330173411603898352 * q^91 + 6577026773676031203676800 * q^92 - 13171898336704209119455200 * q^93 + 1406225817996660389994096 * q^94 + 1407704403261660156250000 * q^95 + 13005904207859351375904768 * q^96 + 8538350425643241402216200 * q^97 + 10780561809722171059198200 * q^98 - 19223568526197742048146816 * q^99

Introduction

L-functions

Modular forms

Varieties

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