LMFDB - Embedded newform 5.34.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5,34,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, 34, names="a")

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

chi := DirichletCharacter("5.1");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 5 $
Weight:	$ k $	$=$	$ 34 $
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:	$34.4914144405$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} - 9680197848 x^{4} + 8052423720422 x^{3} + \cdots - 10\!\cdots\!50 $ x^6 - x^5 - 9680197848x^4 + 8052423720422x^3 + 24239866893261762265x^2 - 69081627028404093368325x - 10572274201725134136583265250
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{21}\cdot 3^{5}\cdot 5^{6}\cdot 7\cdot 11^{2} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$25925.6$ 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)

$f(q)$	$=$	$q+76409.2 q^{2} +7.43191e7 q^{3} -2.75157e9 q^{4} +1.52588e11 q^{5} +5.67866e12 q^{6} +1.36987e14 q^{7} -8.66595e14 q^{8} -3.57381e13 q^{9} +O(q^{10})$	\(q+76409.2 q^{2} +7.43191e7 q^{3} -2.75157e9 q^{4} +1.52588e11 q^{5} +5.67866e12 q^{6} +1.36987e14 q^{7} -8.66595e14 q^{8} -3.57381e13 q^{9} +1.16591e16 q^{10} +3.84389e16 q^{11} -2.04494e17 q^{12} +2.57012e18 q^{13} +1.04671e19 q^{14} +1.13402e19 q^{15} -4.25800e19 q^{16} +1.44621e20 q^{17} -2.73072e18 q^{18} -2.79512e20 q^{19} -4.19856e20 q^{20} +1.01808e22 q^{21} +2.93708e21 q^{22} +3.71118e22 q^{23} -6.44045e22 q^{24} +2.32831e22 q^{25} +1.96381e23 q^{26} -4.15800e23 q^{27} -3.76930e23 q^{28} -1.90470e24 q^{29} +8.66495e23 q^{30} +5.88152e24 q^{31} +4.19049e24 q^{32} +2.85674e24 q^{33} +1.10503e25 q^{34} +2.09026e25 q^{35} +9.83358e22 q^{36} +1.05655e26 q^{37} -2.13573e25 q^{38} +1.91009e26 q^{39} -1.32232e26 q^{40} -2.64164e25 q^{41} +7.77905e26 q^{42} +1.20441e27 q^{43} -1.05767e26 q^{44} -5.45320e24 q^{45} +2.83569e27 q^{46} -3.53827e27 q^{47} -3.16451e27 q^{48} +1.10345e28 q^{49} +1.77904e27 q^{50} +1.07481e28 q^{51} -7.07187e27 q^{52} -3.25098e28 q^{53} -3.17710e28 q^{54} +5.86531e27 q^{55} -1.18713e29 q^{56} -2.07731e28 q^{57} -1.45537e29 q^{58} +3.41770e28 q^{59} -3.12033e28 q^{60} -6.01152e28 q^{61} +4.49402e29 q^{62} -4.89566e27 q^{63} +6.85952e29 q^{64} +3.92169e29 q^{65} +2.18281e29 q^{66} -2.17962e30 q^{67} -3.97934e29 q^{68} +2.75812e30 q^{69} +1.59715e30 q^{70} +9.20055e29 q^{71} +3.09704e28 q^{72} -4.72873e30 q^{73} +8.07302e30 q^{74} +1.73038e30 q^{75} +7.69097e29 q^{76} +5.26564e30 q^{77} +1.45948e31 q^{78} -2.14123e31 q^{79} -6.49720e30 q^{80} -3.07032e31 q^{81} -2.01845e30 q^{82} -6.60838e31 q^{83} -2.80131e31 q^{84} +2.20674e31 q^{85} +9.20283e31 q^{86} -1.41556e32 q^{87} -3.33109e31 q^{88} -6.08523e31 q^{89} -4.16674e29 q^{90} +3.52074e32 q^{91} -1.02116e32 q^{92} +4.37109e32 q^{93} -2.70356e32 q^{94} -4.26502e31 q^{95} +3.11433e32 q^{96} +6.12049e30 q^{97} +8.43141e32 q^{98} -1.37373e30 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 147350 q^{2} + 26513900 q^{3} + 29520645652 q^{4} + 915527343750 q^{5} + 6615759249352 q^{6} + 19113832847500 q^{7} + 30\!\cdots\!00 q^{8}+ \cdots + 13\!\cdots\!38 q^{9}+O(q^{10}) $ 6 * q + 147350 * q^2 + 26513900 * q^3 + 29520645652 * q^4 + 915527343750 * q^5 + 6615759249352 * q^6 + 19113832847500 * q^7 + 3069820115785800 * q^8 + 13602102583345438 * q^9	$ 6 q + 147350 q^{2} + 26513900 q^{3} + 29520645652 q^{4} + 915527343750 q^{5} + 6615759249352 q^{6} + 19113832847500 q^{7} + 30\!\cdots\!00 q^{8}+ \cdots + 16\!\cdots\!16 q^{99}+O(q^{100}) $ 6 * q + 147350 * q^2 + 26513900 * q^3 + 29520645652 * q^4 + 915527343750 * q^5 + 6615759249352 * q^6 + 19113832847500 * q^7 + 3069820115785800 * q^8 + 13602102583345438 * q^9 + 22483825683593750 * q^10 + 150760896555890192 * q^11 + 466351581756413200 * q^12 - 1403095636752804700 * q^13 - 7086110008989891456 * q^14 + 4045700073242187500 * q^15 + 64511520005858668816 * q^16 + 134380842798611834300 * q^17 + 673397185005127949150 * q^18 + 1711584362599986612200 * q^19 + 4504493049926757812500 * q^20 - 10560397660826154148128 * q^21 + 2470897477250007236200 * q^22 + 6879744551224024319700 * q^23 + 211895016154723698861600 * q^24 + 139698386192321777343750 * q^25 - 361829246667436498168588 * q^26 - 340705501428703899968200 * q^27 - 1750376606004032278695200 * q^28 + 1305223406410727358015700 * q^29 + 1009484748741455078125000 * q^30 + 10825321396800575904753352 * q^31 + 26818258713124955338861600 * q^32 + 34856079507682787436662800 * q^33 + 8872409666654531735490124 * q^34 + 2916539435958862304687500 * q^35 + 168714411751774892911163396 * q^36 + 276757164463535626747584900 * q^37 + 835386866362613528909982200 * q^38 + 579964086232605925635188456 * q^39 + 468417376065948486328125000 * q^40 + 448008579649522993395821932 * q^41 + 1478478813030145693383604800 * q^42 + 2250588086104897739543439500 * q^43 + 7171805342222267509050250864 * q^44 + 2075516141257543640136718750 * q^45 + 3493759290976330924493595072 * q^46 + 3830785379519133075460228700 * q^47 + 24576343390562635665291611200 * q^48 - 7173427073564666873529235258 * q^49 + 3430759534239768981933593750 * q^50 - 54920362805063671320868694888 * q^51 - 90553915669177954388890305000 * q^52 + 47034713551772209628037134900 * q^53 - 182647187168263097239229399600 * q^54 + 23004287194197111816406250000 * q^55 - 392573339390998146620750750400 * q^56 - 242119765146738617914766400400 * q^57 - 443272639260736798552560798700 * q^58 - 178315156221037727069533799800 * q^59 + 71159604149843322753906250000 * q^60 - 282317689060586014253208287308 * q^61 + 3477509804797272360008839200 * q^62 - 559259159226762324796386276900 * q^63 + 1937968534792541396434479607872 * q^64 - 214095403557251693725585937500 * q^65 + 5061208746155430260544773159264 * q^66 + 3357382217232044190774976063300 * q^67 + 3866973693935427075529380663400 * q^68 + 316127240816983184255653823136 * q^69 - 1081254579008467324218750000000 * q^70 + 8451218031993742702656617170072 * q^71 + 8740278584811466598158058687400 * q^72 - 1719044326022105657749673125300 * q^73 + 20494727417173075429289542476484 * q^74 + 617324840277433395385742187500 * q^75 + 29410039922734837753629694458000 * q^76 - 1179300749517366199915257594000 * q^77 - 57229303014236704407408363530000 * q^78 - 22052505351402355443894747635600 * q^79 + 9843676758706461916503906250000 * q^80 - 133163964889176760661905573719674 * q^81 - 156059027108947085834404172875300 * q^82 - 47087087002138304263127820978900 * q^83 - 235991611992224148517578838651776 * q^84 + 20504889343049901473999023437500 * q^85 - 128823880621545855657554048105608 * q^86 - 175316396211912369693639217216600 * q^87 + 497433069891524019720739466805600 * q^88 - 336491358341169481948206213360900 * q^89 + 102752256012745353569030761718750 * q^90 + 194633769402343866156602864483432 * q^91 - 419043430758613276035983032687200 * q^92 + 212928090391747529239858474972800 * q^93 + 1486141097168392212687292135345264 * q^94 + 261167047515867097808837890625000 * q^95 + 3151728990173122672564203081529472 * q^96 + 2569321197832638009639208504856700 * q^97 + 6985460513399098756137635798950 * q^98 + 1660882302442227079414567162624016 * 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 $

$2$	76409.2	0.824424	0.412212	−	0.911088i	$-0.364756\pi$
$2$	76409.2	0.824424	0.412212	+	0.911088i	$0.364756\pi$
$3$	7.43191e7	0.996780	0.498390	−	0.866953i	$-0.333925\pi$
$3$	7.43191e7	0.996780	0.498390	+	0.866953i	$0.333925\pi$
$4$	−2.75157e9	−0.320325
$5$	1.52588e11	0.447214
$5$	1.52588e11	0.447214
$6$	5.67866e12	0.821770
$7$	1.36987e14	1.55798	0.778992	−	0.627034i	$-0.215731\pi$
$7$	1.36987e14	1.55798	0.778992	+	0.627034i	$0.215731\pi$
$8$	−8.66595e14	−1.08851
$9$	−3.57381e13	−0.00642880
$10$	1.16591e16	0.368694
$11$	3.84389e16	0.252227	0.126113	−	0.992016i	$-0.459750\pi$
$11$	3.84389e16	0.252227	0.126113	+	0.992016i	$0.459750\pi$
$12$	−2.04494e17	−0.319294
$13$	2.57012e18	1.07124	0.535622	−	0.844458i	$-0.320077\pi$
$13$	2.57012e18	1.07124	0.535622	+	0.844458i	$0.320077\pi$
$14$	1.04671e19	1.28444
$15$	1.13402e19	0.445774
$16$	−4.25800e19	−0.577067
$17$	1.44621e20	0.720814	0.360407	−	0.932795i	$-0.382638\pi$
$17$	1.44621e20	0.720814	0.360407	+	0.932795i	$0.382638\pi$
$18$	−2.73072e18	−0.00530005
$19$	−2.79512e20	−0.222314	−0.111157	−	0.993803i	$-0.535456\pi$
$19$	−2.79512e20	−0.222314	−0.111157	+	0.993803i	$0.535456\pi$
$20$	−4.19856e20	−0.143254
$21$	1.01808e22	1.55297
$22$	2.93708e21	0.207942
$23$	3.71118e22	1.26184	0.630918	−	0.775849i	$-0.282678\pi$
$23$	3.71118e22	1.26184	0.630918	+	0.775849i	$0.282678\pi$
$24$	−6.44045e22	−1.08500
$25$	2.32831e22	0.200000
$26$	1.96381e23	0.883159
$27$	−4.15800e23	−1.00319
$28$	−3.76930e23	−0.499061
$29$	−1.90470e24	−1.41339	−0.706693	−	0.707520i	$-0.749814\pi$
$29$	−1.90470e24	−1.41339	−0.706693	+	0.707520i	$0.749814\pi$
$30$	8.66495e23	0.367507
$31$	5.88152e24	1.45218	0.726092	−	0.687597i	$-0.241334\pi$
$31$	5.88152e24	1.45218	0.726092	+	0.687597i	$0.241334\pi$
$32$	4.19049e24	0.612760
$33$	2.85674e24	0.251415
$34$	1.10503e25	0.594256
$35$	2.09026e25	0.696751
$36$	9.83358e22	0.00205930
$37$	1.05655e26	1.40787	0.703934	−	0.710265i	$-0.251425\pi$
$37$	1.05655e26	1.40787	0.703934	+	0.710265i	$0.251425\pi$
$38$	−2.13573e25	−0.183281
$39$	1.91009e26	1.06779
$40$	−1.32232e26	−0.486795
$41$	−2.64164e25	−0.0647052	−0.0323526	−	0.999477i	$-0.510300\pi$
$41$	−2.64164e25	−0.0647052	−0.0323526	+	0.999477i	$0.510300\pi$
$42$	7.77905e26	1.28030
$43$	1.20441e27	1.34446	0.672228	−	0.740344i	$-0.265338\pi$
$43$	1.20441e27	1.34446	0.672228	+	0.740344i	$0.265338\pi$
$44$	−1.05767e26	−0.0807946
$45$	−5.45320e24	−0.00287505
$46$	2.83569e27	1.04029
$47$	−3.53827e27	−0.910282	−0.455141	−	0.890419i	$-0.650411\pi$
$47$	−3.53827e27	−0.910282	−0.455141	+	0.890419i	$0.650411\pi$
$48$	−3.16451e27	−0.575209
$49$	1.10345e28	1.42731
$50$	1.77904e27	0.164885
$51$	1.07481e28	0.718493
$52$	−7.07187e27	−0.343146
$53$	−3.25098e28	−1.15203	−0.576014	−	0.817440i	$-0.695392\pi$
$53$	−3.25098e28	−1.15203	−0.576014	+	0.817440i	$0.695392\pi$
$54$	−3.17710e28	−0.827053
$55$	5.86531e27	0.112799
$56$	−1.18713e29	−1.69588
$57$	−2.07731e28	−0.221598
$58$	−1.45537e29	−1.16523
$59$	3.41770e28	0.206384	0.103192	−	0.994661i	$-0.467094\pi$
$59$	3.41770e28	0.206384	0.103192	+	0.994661i	$0.467094\pi$
$60$	−3.12033e28	−0.142792
$61$	−6.01152e28	−0.209431	−0.104716	−	0.994502i	$-0.533393\pi$
$61$	−6.01152e28	−0.209431	−0.104716	+	0.994502i	$0.533393\pi$
$62$	4.49402e29	1.19722
$63$	−4.89566e27	−0.0100160
$64$	6.85952e29	1.08224
$65$	3.92169e29	0.479075
$66$	2.18281e29	0.207272
$67$	−2.17962e30	−1.61490	−0.807451	−	0.589934i	$-0.799154\pi$
$67$	−2.17962e30	−1.61490	−0.807451	+	0.589934i	$0.799154\pi$
$68$	−3.97934e29	−0.230895
$69$	2.75812e30	1.25777
$70$	1.59715e30	0.574419
$71$	9.20055e29	0.261849	0.130924	−	0.991392i	$-0.458205\pi$
$71$	9.20055e29	0.261849	0.130924	+	0.991392i	$0.458205\pi$
$72$	3.09704e28	0.00699779
$73$	−4.72873e30	−0.850977	−0.425488	−	0.904964i	$-0.639898\pi$
$73$	−4.72873e30	−0.850977	−0.425488	+	0.904964i	$0.639898\pi$
$74$	8.07302e30	1.16068
$75$	1.73038e30	0.199356
$76$	7.69097e29	0.0712126
$77$	5.26564e30	0.392965
$78$	1.45948e31	0.880316
$79$	−2.14123e31	−1.04668	−0.523342	−	0.852122i	$-0.675315\pi$
$79$	−2.14123e31	−1.04668	−0.523342	+	0.852122i	$0.675315\pi$
$80$	−6.49720e30	−0.258072
$81$	−3.07032e31	−0.993530
$82$	−2.01845e30	−0.0533445
$83$	−6.60838e31	−1.42990	−0.714951	−	0.699174i	$-0.753551\pi$
$83$	−6.60838e31	−1.42990	−0.714951	+	0.699174i	$0.753551\pi$
$84$	−2.80131e31	−0.497454
$85$	2.20674e31	0.322358
$86$	9.20283e31	1.10840
$87$	−1.41556e32	−1.40884
$88$	−3.33109e31	−0.274551
$89$	−6.08523e31	−0.416238	−0.208119	−	0.978104i	$-0.566734\pi$
$89$	−6.08523e31	−0.416238	−0.208119	+	0.978104i	$0.566734\pi$
$90$	−4.16674e29	−0.00237026
$91$	3.52074e32	1.66898
$92$	−1.02116e32	−0.404198
$93$	4.37109e32	1.44751
$94$	−2.70356e32	−0.750458
$95$	−4.26502e31	−0.0994217
$96$	3.11433e32	0.610787
$97$	6.12049e30	0.0101170	0.00505851	−	0.999987i	$-0.498390\pi$
$97$	6.12049e30	0.0101170	0.00505851	+	0.999987i	$0.498390\pi$
$98$	8.43141e32	1.17671
$99$	−1.37373e30	−0.00162152
$100$	−6.40650e31	−0.0640650
$101$	1.27681e33	1.08349	0.541743	−	0.840544i	$-0.317765\pi$
$101$	1.27681e33	1.08349	0.541743	+	0.840544i	$0.317765\pi$
$102$	8.21251e32	0.592343
$103$	−1.91249e33	−1.17432	−0.587158	−	0.809473i	$-0.699753\pi$
$103$	−1.91249e33	−1.17432	−0.587158	+	0.809473i	$0.699753\pi$
$104$	−2.22725e33	−1.16606
$105$	1.55346e33	0.694508
$106$	−2.48405e33	−0.949759
$107$	−5.25843e33	−1.72196	−0.860981	−	0.508638i	$-0.830149\pi$
$107$	−5.25843e33	−1.72196	−0.860981	+	0.508638i	$0.830149\pi$
$108$	1.14410e33	0.321346
$109$	1.63289e33	0.393930	0.196965	−	0.980411i	$-0.436891\pi$
$109$	1.63289e33	0.393930	0.196965	+	0.980411i	$0.436891\pi$
$110$	4.48163e32	0.0929945
$111$	7.85219e33	1.40334
$112$	−5.83293e33	−0.899061
$113$	−1.10961e34	−1.47699	−0.738495	−	0.674259i	$-0.764463\pi$
$113$	−1.10961e34	−1.47699	−0.738495	+	0.674259i	$0.764463\pi$
$114$	−1.58725e33	−0.182691
$115$	5.66282e33	0.564311
$116$	5.24093e33	0.452743
$117$	−9.18512e31	−0.00688681
$118$	2.61144e33	0.170148
$119$	1.98112e34	1.12302
$120$	−9.82735e33	−0.485228
$121$	−2.17476e34	−0.936382
$122$	−4.59335e33	−0.172660
$123$	−1.96324e33	−0.0644969
$124$	−1.61834e34	−0.465171
$125$	3.55271e33	0.0894427
$126$	−3.74074e32	−0.00825740
$127$	9.92625e34	1.92320	0.961599	−	0.274458i	$-0.0884985\pi$
$127$	9.92625e34	1.92320	0.961599	+	0.274458i	$0.0884985\pi$
$128$	1.64170e34	0.279466
$129$	8.95110e34	1.34013
$130$	2.99653e34	0.394961
$131$	5.93400e34	0.689241	0.344621	−	0.938742i	$-0.388008\pi$
$131$	5.93400e34	0.689241	0.344621	+	0.938742i	$0.388008\pi$
$132$	−7.86052e33	−0.0805344
$133$	−3.82896e34	−0.346361
$134$	−1.66543e35	−1.33136
$135$	−6.34461e34	−0.448640
$136$	−1.25328e35	−0.784611
$137$	−7.72864e34	−0.428759	−0.214380	−	0.976750i	$-0.568773\pi$
$137$	−7.72864e34	−0.428759	−0.214380	+	0.976750i	$0.568773\pi$
$138$	2.10746e35	1.03694
$139$	−3.33723e35	−1.45761	−0.728806	−	0.684720i	$-0.759925\pi$
$139$	−3.33723e35	−1.45761	−0.728806	+	0.684720i	$0.759925\pi$
$140$	−5.75150e34	−0.223187
$141$	−2.62961e35	−0.907351
$142$	7.03006e34	0.215875
$143$	9.87926e34	0.270196
$144$	1.52173e33	0.00370985
$145$	−2.90635e35	−0.632085
$146$	−3.61319e35	−0.701566
$147$	8.20077e35	1.42272
$148$	−2.90717e35	−0.450975
$149$	9.18769e35	1.27536	0.637680	−	0.770301i	$-0.279894\pi$
$149$	9.18769e35	1.27536	0.637680	+	0.770301i	$0.279894\pi$
$150$	1.32217e35	0.164354
$151$	−1.06733e33	−0.00118899	−0.000594497	−	1.00000i	$-0.500189\pi$
$151$	−1.06733e33	−0.00118899	−0.000594497		1.00000i	$0.500189\pi$
$152$	2.42224e35	0.241990
$153$	−5.16846e33	−0.00463397
$154$	4.02343e35	0.323970
$155$	8.97449e35	0.649437
$156$	−5.25575e35	−0.342041
$157$	2.04504e36	1.19773	0.598863	−	0.800851i	$-0.295619\pi$
$157$	2.04504e36	1.19773	0.598863	+	0.800851i	$0.295619\pi$
$158$	−1.63610e36	−0.862912
$159$	−2.41610e36	−1.14832
$160$	6.39418e35	0.274034
$161$	5.08385e36	1.96592
$162$	−2.34601e36	−0.819090
$163$	8.53783e35	0.269310	0.134655	−	0.990893i	$-0.457007\pi$
$163$	8.53783e35	0.269310	0.134655	+	0.990893i	$0.457007\pi$
$164$	7.26865e34	0.0207267
$165$	4.35904e35	0.112436
$166$	−5.04941e36	−1.17885
$167$	2.30718e36	0.487819	0.243910	−	0.969798i	$-0.421570\pi$
$167$	2.30718e36	0.487819	0.243910	+	0.969798i	$0.421570\pi$
$168$	−8.82261e36	−1.69042
$169$	8.49393e35	0.147563
$170$	1.68615e36	0.265759
$171$	9.98922e33	0.00142921
$172$	−3.31403e36	−0.430663
$173$	7.44289e36	0.878984	0.439492	−	0.898247i	$-0.355158\pi$
$173$	7.44289e36	0.878984	0.439492	+	0.898247i	$0.355158\pi$
$174$	−1.08162e37	−1.16148
$175$	3.18949e36	0.311597
$176$	−1.63673e36	−0.145552
$177$	2.54000e36	0.205719
$178$	−4.64967e36	−0.343157
$179$	−1.14363e37	−0.769506	−0.384753	−	0.923020i	$-0.625713\pi$
$179$	−1.14363e37	−0.769506	−0.384753	+	0.923020i	$0.625713\pi$
$180$	1.50049e34	0.000920949 0
$181$	9.37075e36	0.524902	0.262451	−	0.964945i	$-0.415469\pi$
$181$	9.37075e36	0.524902	0.262451	+	0.964945i	$0.415469\pi$
$182$	2.69017e37	1.37595
$183$	−4.46770e36	−0.208757
$184$	−3.21609e37	−1.37352
$185$	1.61217e37	0.629618
$186$	3.33992e37	1.19336
$187$	5.55906e36	0.181809
$188$	9.73579e36	0.291586
$189$	−5.69594e37	−1.56295
$190$	−3.25886e36	−0.0819656
$191$	1.69883e37	0.391831	0.195915	−	0.980621i	$-0.437232\pi$
$191$	1.69883e37	0.391831	0.195915	+	0.980621i	$0.437232\pi$
$192$	5.09793e37	1.07876
$193$	7.50799e36	0.145824	0.0729119	−	0.997338i	$-0.476771\pi$
$193$	7.50799e36	0.145824	0.0729119	+	0.997338i	$0.476771\pi$
$194$	4.67662e35	0.00834072
$195$	2.91457e37	0.477532
$196$	−3.03623e37	−0.457204
$197$	1.41045e38	1.95284	0.976418	−	0.215886i	$-0.0692641\pi$
$197$	1.41045e38	1.95284	0.976418	+	0.215886i	$0.0692641\pi$
$198$	−1.04966e35	−0.00133682
$199$	1.95572e37	0.229208	0.114604	−	0.993411i	$-0.463440\pi$
$199$	1.95572e37	0.229208	0.114604	+	0.993411i	$0.463440\pi$
$200$	−2.01770e37	−0.217702
$201$	−1.61987e38	−1.60970
$202$	9.75600e37	0.893252
$203$	−2.60921e38	−2.20203
$204$	−2.95741e37	−0.230151
$205$	−4.03082e36	−0.0289371
$206$	−1.46132e38	−0.968134
$207$	−1.32631e36	−0.00811209
$208$	−1.09436e38	−0.618179
$209$	−1.07441e37	−0.0560735
$210$	1.18699e38	0.572569
$211$	−2.65891e38	−1.18589	−0.592944	−	0.805244i	$-0.702034\pi$
$211$	−2.65891e38	−1.18589	−0.592944	+	0.805244i	$0.702034\pi$
$212$	8.94530e37	0.369023
$213$	6.83776e37	0.261006
$214$	−4.01792e38	−1.41963
$215$	1.83779e38	0.601259
$216$	3.60330e38	1.09198
$217$	8.05694e38	2.26248
$218$	1.24768e38	0.324765
$219$	−3.51435e38	−0.848237
$220$	−1.61388e37	−0.0361324
$221$	3.71693e38	0.772167
$222$	5.99979e38	1.15694
$223$	−2.18179e38	−0.390645	−0.195323	−	0.980739i	$-0.562575\pi$
$223$	−2.18179e38	−0.390645	−0.195323	+	0.980739i	$0.562575\pi$
$224$	5.74044e38	0.954670
$225$	−8.32092e35	−0.00128576
$226$	−8.47847e38	−1.21767
$227$	−5.43077e38	−0.725161	−0.362581	−	0.931952i	$-0.618104\pi$
$227$	−5.43077e38	−0.725161	−0.362581	+	0.931952i	$0.618104\pi$
$228$	5.71586e37	0.0709833
$229$	−1.10600e39	−1.27782	−0.638908	−	0.769284i	$-0.720613\pi$
$229$	−1.10600e39	−1.27782	−0.638908	+	0.769284i	$0.720613\pi$
$230$	4.32691e38	0.465231
$231$	3.91337e38	0.391700
$232$	1.65061e39	1.53848
$233$	−5.67177e38	−0.492431	−0.246216	−	0.969215i	$-0.579187\pi$
$233$	−5.67177e38	−0.492431	−0.246216	+	0.969215i	$0.579187\pi$
$234$	−7.01827e36	−0.00567765
$235$	−5.39897e38	−0.407091
$236$	−9.40404e37	−0.0661099
$237$	−1.59134e39	−1.04332
$238$	1.51376e39	0.925842
$239$	−2.69103e39	−1.53587	−0.767933	−	0.640530i	$-0.778715\pi$
$239$	−2.69103e39	−1.53587	−0.767933	+	0.640530i	$0.778715\pi$
$240$	−4.82866e38	−0.257241
$241$	3.85216e39	1.91612	0.958061	−	0.286565i	$-0.0925134\pi$
$241$	3.85216e39	1.91612	0.958061	+	0.286565i	$0.0925134\pi$
$242$	−1.66172e39	−0.771976
$243$	2.96249e37	0.0128574
$244$	1.65411e38	0.0670861
$245$	1.68374e39	0.638314
$246$	−1.50009e38	−0.0531728
$247$	−7.18380e38	−0.238152
$248$	−5.09690e39	−1.58071
$249$	−4.91128e39	−1.42530
$250$	2.71460e38	0.0737387
$251$	1.40214e37	0.00356594	0.00178297	−	0.999998i	$-0.499432\pi$
$251$	1.40214e37	0.00356594	0.00178297	+	0.999998i	$0.499432\pi$
$252$	1.34708e37	0.00320836
$253$	1.42654e39	0.318269
$254$	7.58457e39	1.58553
$255$	1.64003e39	0.321320
$256$	−4.63787e39	−0.851843
$257$	−3.74219e39	−0.644510	−0.322255	−	0.946653i	$-0.604441\pi$
$257$	−3.74219e39	−0.644510	−0.322255	+	0.946653i	$0.604441\pi$
$258$	6.83946e39	1.10483
$259$	1.44734e40	2.19344
$260$	−1.07908e39	−0.153460
$261$	6.80705e37	0.00908637
$262$	4.53412e39	0.568227
$263$	−8.59682e39	−1.01174	−0.505869	−	0.862610i	$-0.668828\pi$
$263$	−8.59682e39	−1.01174	−0.505869	+	0.862610i	$0.668828\pi$
$264$	−2.47564e39	−0.273667
$265$	−4.96060e39	−0.515202
$266$	−2.92568e39	−0.285548
$267$	−4.52248e39	−0.414898
$268$	5.99737e39	0.517293
$269$	2.20144e40	1.78564	0.892820	−	0.450414i	$-0.148724\pi$
$269$	2.20144e40	1.78564	0.892820	+	0.450414i	$0.148724\pi$
$270$	−4.84786e39	−0.369869
$271$	4.26536e39	0.306170	0.153085	−	0.988213i	$-0.451079\pi$
$271$	4.26536e39	0.306170	0.153085	+	0.988213i	$0.451079\pi$
$272$	−6.15795e39	−0.415958
$273$	2.61658e40	1.66361
$274$	−5.90539e39	−0.353480
$275$	8.94975e38	0.0504454
$276$	−7.58915e39	−0.402896
$277$	−2.32580e40	−1.16321	−0.581603	−	0.813473i	$-0.697574\pi$
$277$	−2.32580e40	−1.16321	−0.581603	+	0.813473i	$0.697574\pi$
$278$	−2.54995e40	−1.20169
$279$	−2.10194e38	−0.00933580
$280$	−1.81141e40	−0.758419
$281$	−3.04347e39	−0.120147	−0.0600737	−	0.998194i	$-0.519134\pi$
$281$	−3.04347e39	−0.120147	−0.0600737	+	0.998194i	$0.519134\pi$
$282$	−2.00926e40	−0.748042
$283$	1.78513e40	0.626893	0.313447	−	0.949606i	$-0.398516\pi$
$283$	1.78513e40	0.626893	0.313447	+	0.949606i	$0.398516\pi$
$284$	−2.53160e39	−0.0838768
$285$	−3.16972e39	−0.0991016
$286$	7.54866e39	0.222756
$287$	−3.61871e39	−0.100810
$288$	−1.49760e38	−0.00393931
$289$	−1.93394e40	−0.480427
$290$	−2.22072e40	−0.521106
$291$	4.54869e38	0.0100844
$292$	1.30114e40	0.272589
$293$	5.63289e39	0.111536	0.0557681	−	0.998444i	$-0.482239\pi$
$293$	5.63289e39	0.111536	0.0557681	+	0.998444i	$0.482239\pi$
$294$	6.26614e40	1.17292
$295$	5.21499e39	0.0922976
$296$	−9.15602e40	−1.53248
$297$	−1.59829e40	−0.253031
$298$	7.02024e40	1.05144
$299$	9.53819e40	1.35174
$300$	−4.76125e39	−0.0638587
$301$	1.64990e41	2.09464
$302$	−8.15540e37	−0.000980236 0
$303$	9.48913e40	1.08000
$304$	1.19016e40	0.128290
$305$	−9.17284e39	−0.0936605
$306$	−3.94918e38	−0.00382035
$307$	−1.51598e41	−1.38966	−0.694832	−	0.719173i	$-0.744521\pi$
$307$	−1.51598e41	−1.38966	−0.694832	+	0.719173i	$0.744521\pi$
$308$	−1.44888e40	−0.125877
$309$	−1.42134e41	−1.17053
$310$	6.85734e40	0.535411
$311$	1.38324e41	1.02412	0.512062	−	0.858949i	$-0.328882\pi$
$311$	1.38324e41	1.02412	0.512062	+	0.858949i	$0.328882\pi$
$312$	−1.65527e41	−1.16230
$313$	−2.31070e41	−1.53908	−0.769540	−	0.638598i	$-0.779515\pi$
$313$	−2.31070e41	−1.53908	−0.769540	+	0.638598i	$0.779515\pi$
$314$	1.56260e41	0.987434
$315$	−7.47019e38	−0.00447927
$316$	5.89174e40	0.335279
$317$	−1.18117e41	−0.638022	−0.319011	−	0.947751i	$-0.603351\pi$
$317$	−1.18117e41	−0.638022	−0.319011	+	0.947751i	$0.603351\pi$
$318$	−1.84612e41	−0.946701
$319$	−7.32147e40	−0.356494
$320$	1.04668e41	0.483993
$321$	−3.90801e41	−1.71642
$322$	3.88453e41	1.62075
$323$	−4.04232e40	−0.160247
$324$	8.44820e40	0.318252
$325$	5.98403e40	0.214249
$326$	6.52369e40	0.222026
$327$	1.21355e41	0.392662
$328$	2.28923e40	0.0704321
$329$	−4.84698e41	−1.41820
$330$	3.33071e40	0.0926951
$331$	2.42794e41	0.642801	0.321400	−	0.946943i	$-0.395847\pi$
$331$	2.42794e41	0.642801	0.321400	+	0.946943i	$0.395847\pi$
$332$	1.81834e41	0.458033
$333$	−3.77591e39	−0.00905090
$334$	1.76290e41	0.402170
$335$	−3.32583e41	−0.722206
$336$	−4.33498e41	−0.896166
$337$	5.79957e41	1.14157	0.570785	−	0.821100i	$-0.306639\pi$
$337$	5.79957e41	1.14157	0.570785	+	0.821100i	$0.306639\pi$
$338$	6.49015e40	0.121655
$339$	−8.24654e41	−1.47223
$340$	−6.07199e40	−0.103259
$341$	2.26079e41	0.366280
$342$	7.63268e38	0.00117827
$343$	4.52545e41	0.665747
$344$	−1.04374e42	−1.46345
$345$	4.20855e41	0.562494
$346$	5.68705e41	0.724656
$347$	1.00536e42	1.22148	0.610739	−	0.791832i	$-0.290872\pi$
$347$	1.00536e42	1.22148	0.610739	+	0.791832i	$0.290872\pi$
$348$	3.89501e41	0.451285
$349$	1.46484e42	1.61872	0.809360	−	0.587313i	$-0.199814\pi$
$349$	1.46484e42	1.61872	0.809360	+	0.587313i	$0.199814\pi$
$350$	2.43706e41	0.256888
$351$	−1.06866e42	−1.07466
$352$	1.61078e41	0.154554
$353$	−7.67079e40	−0.0702356	−0.0351178	−	0.999383i	$-0.511181\pi$
$353$	−7.67079e40	−0.0702356	−0.0351178	+	0.999383i	$0.511181\pi$
$354$	1.94079e41	0.169600
$355$	1.40389e41	0.117102
$356$	1.67439e41	0.133331
$357$	1.47235e42	1.11940
$358$	−8.73842e41	−0.634399
$359$	−2.27621e42	−1.57817	−0.789084	−	0.614285i	$-0.789445\pi$
$359$	−2.27621e42	−1.57817	−0.789084	+	0.614285i	$0.789445\pi$
$360$	4.72571e39	0.00312951
$361$	−1.50264e42	−0.950577
$362$	7.16012e41	0.432742
$363$	−1.61626e42	−0.933367
$364$	−9.68757e41	−0.534616
$365$	−7.21548e41	−0.380568
$366$	−3.41373e41	−0.172104
$367$	2.44390e42	1.17786	0.588929	−	0.808185i	$-0.299550\pi$
$367$	2.44390e42	1.17786	0.588929	+	0.808185i	$0.299550\pi$
$368$	−1.58022e42	−0.728165
$369$	9.44070e38	0.000415977 0
$370$	1.23184e42	0.519072
$371$	−4.45343e42	−1.79484
$372$	−1.20274e42	−0.463673
$373$	2.18298e42	0.805108	0.402554	−	0.915396i	$-0.368123\pi$
$373$	2.18298e42	0.805108	0.402554	+	0.915396i	$0.368123\pi$
$374$	4.24763e41	0.149887
$375$	2.64034e41	0.0891548
$376$	3.06625e42	0.990849
$377$	−4.89532e42	−1.51408
$378$	−4.35222e42	−1.28853
$379$	3.29619e42	0.934254	0.467127	−	0.884190i	$-0.345289\pi$
$379$	3.29619e42	0.934254	0.467127	+	0.884190i	$0.345289\pi$
$380$	1.17355e41	0.0318472
$381$	7.37710e42	1.91701
$382$	1.29806e42	0.323035
$383$	2.10779e42	0.502399	0.251199	−	0.967935i	$-0.419175\pi$
$383$	2.10779e42	0.502399	0.251199	+	0.967935i	$0.419175\pi$
$384$	1.22009e42	0.278566
$385$	8.03473e41	0.175739
$386$	5.73680e41	0.120221
$387$	−4.30434e40	−0.00864323
$388$	−1.68410e40	−0.00324073
$389$	−4.71038e42	−0.868735	−0.434368	−	0.900736i	$-0.643028\pi$
$389$	−4.71038e42	−0.868735	−0.434368	+	0.900736i	$0.643028\pi$
$390$	2.22700e42	0.393689
$391$	5.36714e42	0.909550
$392$	−9.56249e42	−1.55364
$393$	4.41009e42	0.687022
$394$	1.07772e43	1.60997
$395$	−3.26726e42	−0.468092
$396$	3.77992e39	0.000519412 0
$397$	4.19658e42	0.553162	0.276581	−	0.960991i	$-0.410799\pi$
$397$	4.19658e42	0.553162	0.276581	+	0.960991i	$0.410799\pi$
$398$	1.49435e42	0.188965
$399$	−2.84565e42	−0.345246
$400$	−9.91394e41	−0.115413
$401$	5.75416e42	0.642835	0.321418	−	0.946938i	$-0.395841\pi$
$401$	5.75416e42	0.642835	0.321418	+	0.946938i	$0.395841\pi$
$402$	−1.23773e43	−1.32708
$403$	1.51162e43	1.55564
$404$	−3.51323e42	−0.347068
$405$	−4.68494e42	−0.444320
$406$	−1.99367e43	−1.81541
$407$	4.06126e42	0.355102
$408$	−9.31423e42	−0.782085
$409$	−1.41308e43	−1.13954	−0.569772	−	0.821803i	$-0.692968\pi$
$409$	−1.41308e43	−1.13954	−0.569772	+	0.821803i	$0.692968\pi$
$410$	−3.07991e41	−0.0238564
$411$	−5.74385e42	−0.427379
$412$	5.26235e42	0.376162
$413$	4.68182e42	0.321543
$414$	−1.01342e41	−0.00668780
$415$	−1.00836e43	−0.639472
$416$	1.07701e43	0.656415
$417$	−2.48020e43	−1.45292
$418$	−8.20950e41	−0.0462283
$419$	2.86224e43	1.54944	0.774720	−	0.632305i	$-0.217891\pi$
$419$	2.86224e43	1.54944	0.774720	+	0.632305i	$0.217891\pi$
$420$	−4.27446e42	−0.222468
$421$	1.34194e43	0.671549	0.335774	−	0.941942i	$-0.391002\pi$
$421$	1.34194e43	0.671549	0.335774	+	0.941942i	$0.391002\pi$
$422$	−2.03165e43	−0.977674
$423$	1.26451e41	0.00585202
$424$	2.81729e43	1.25399
$425$	3.36721e42	0.144163
$426$	5.22468e42	0.215180
$427$	−8.23502e42	−0.326291
$428$	1.44689e43	0.551587
$429$	7.34217e42	0.269327
$430$	1.40424e43	0.495692
$431$	−4.00130e43	−1.35933	−0.679667	−	0.733521i	$-0.737876\pi$
$431$	−4.00130e43	−1.35933	−0.679667	+	0.733521i	$0.737876\pi$
$432$	1.77048e43	0.578907
$433$	−1.03509e43	−0.325783	−0.162891	−	0.986644i	$-0.552082\pi$
$433$	−1.03509e43	−0.325783	−0.162891	+	0.986644i	$0.552082\pi$
$434$	6.15625e43	1.86524
$435$	−2.15997e43	−0.630050
$436$	−4.49300e42	−0.126186
$437$	−1.03732e43	−0.280524
$438$	−2.68529e43	−0.699307
$439$	3.15434e42	0.0791122	0.0395561	−	0.999217i	$-0.487406\pi$
$439$	3.15434e42	0.0791122	0.0395561	+	0.999217i	$0.487406\pi$
$440$	−5.08285e42	−0.122783
$441$	−3.94353e41	−0.00917591
$442$	2.84007e43	0.636593
$443$	−1.66215e43	−0.358929	−0.179464	−	0.983764i	$-0.557436\pi$
$443$	−1.66215e43	−0.358929	−0.179464	+	0.983764i	$0.557436\pi$
$444$	−2.16058e43	−0.449523
$445$	−9.28532e42	−0.186147
$446$	−1.66709e43	−0.322057
$447$	6.82821e43	1.27125
$448$	9.39667e43	1.68611
$449$	−2.11347e43	−0.365537	−0.182768	−	0.983156i	$-0.558506\pi$
$449$	−2.11347e43	−0.365537	−0.182768	+	0.983156i	$0.558506\pi$
$450$	−6.35795e40	−0.00106001
$451$	−1.01542e42	−0.0163204
$452$	3.05318e43	0.473117
$453$	−7.93231e40	−0.00118517
$454$	−4.14961e43	−0.597840
$455$	5.37223e43	0.746391
$456$	1.80018e43	0.241211
$457$	−1.42828e44	−1.84585	−0.922924	−	0.384981i	$-0.874208\pi$
$457$	−1.42828e44	−1.84585	−0.922924	+	0.384981i	$0.874208\pi$
$458$	−8.45082e43	−1.05346
$459$	−6.01333e43	−0.723112
$460$	−1.55816e43	−0.180763
$461$	3.53458e43	0.395615	0.197807	−	0.980241i	$-0.436618\pi$
$461$	3.53458e43	0.395615	0.197807	+	0.980241i	$0.436618\pi$
$462$	2.99018e43	0.322927
$463$	−3.07914e43	−0.320880	−0.160440	−	0.987046i	$-0.551291\pi$
$463$	−3.07914e43	−0.320880	−0.160440	+	0.987046i	$0.551291\pi$
$464$	8.11024e43	0.815618
$465$	6.66976e43	0.647346
$466$	−4.33375e43	−0.405972
$467$	−3.68923e43	−0.333586	−0.166793	−	0.985992i	$-0.553341\pi$
$467$	−3.68923e43	−0.333586	−0.166793	+	0.985992i	$0.553341\pi$
$468$	2.52735e41	0.00220602
$469$	−2.98580e44	−2.51599
$470$	−4.12531e43	−0.335615
$471$	1.51985e44	1.19387
$472$	−2.96176e43	−0.224650
$473$	4.62963e43	0.339108
$474$	−1.21593e44	−0.860134
$475$	−6.50790e42	−0.0444627
$476$	−5.45119e43	−0.359730
$477$	1.16184e42	0.00740615
$478$	−2.05619e44	−1.26620
$479$	−3.09046e43	−0.183860	−0.0919300	−	0.995765i	$-0.529304\pi$
$479$	−3.09046e43	−0.183860	−0.0919300	+	0.995765i	$0.529304\pi$
$480$	4.75209e43	0.273152
$481$	2.71546e44	1.50817
$482$	2.94340e44	1.57970
$483$	3.77827e44	1.95959
$484$	5.98401e43	0.299946
$485$	9.33913e41	0.00452447
$486$	2.26361e42	0.0105999
$487$	4.31638e44	1.95385	0.976926	−	0.213578i	$-0.0685118\pi$
$487$	4.31638e44	1.95385	0.976926	+	0.213578i	$0.0685118\pi$
$488$	5.20955e43	0.227968
$489$	6.34524e43	0.268443
$490$	1.28653e44	0.526241
$491$	−2.93145e44	−1.15941	−0.579706	−	0.814826i	$-0.696832\pi$
$491$	−2.93145e44	−1.15941	−0.579706	+	0.814826i	$0.696832\pi$
$492$	5.40199e42	0.0206600
$493$	−2.75460e44	−1.01879
$494$	−5.48908e43	−0.196338
$495$	−2.09615e41	−0.000725164 0
$496$	−2.50435e44	−0.838008
$497$	1.26036e44	0.407956
$498$	−3.75267e44	−1.17505
$499$	−9.00632e42	−0.0272828	−0.0136414	−	0.999907i	$-0.504342\pi$
$499$	−9.00632e42	−0.0272828	−0.0136414	+	0.999907i	$0.504342\pi$
$500$	−9.77554e42	−0.0286507
$501$	1.71467e44	0.486249
$502$	1.07136e42	0.00293985
$503$	−3.10986e44	−0.825789	−0.412895	−	0.910779i	$-0.635482\pi$
$503$	−3.10986e44	−0.825789	−0.412895	+	0.910779i	$0.635482\pi$
$504$	4.24256e42	0.0109024
$505$	1.94826e44	0.484550
$506$	1.09001e44	0.262389
$507$	6.31261e43	0.147088
$508$	−2.73128e44	−0.616048
$509$	7.95788e43	0.173762	0.0868808	−	0.996219i	$-0.472310\pi$
$509$	7.95788e43	0.173762	0.0868808	+	0.996219i	$0.472310\pi$
$510$	1.25313e44	0.264904
$511$	−6.47777e44	−1.32581
$512$	−4.95397e44	−0.981745
$513$	1.16221e44	0.223023
$514$	−2.85938e44	−0.531350
$515$	−2.91823e44	−0.525170
$516$	−2.46296e44	−0.429276
$517$	−1.36007e44	−0.229598
$518$	1.10590e45	1.80832
$519$	5.53149e44	0.876154
$520$	−3.39852e44	−0.521477
$521$	1.27119e44	0.188968	0.0944841	−	0.995526i	$-0.469880\pi$
$521$	1.27119e44	0.188968	0.0944841	+	0.995526i	$0.469880\pi$
$522$	5.20121e42	0.00749102
$523$	−1.19591e44	−0.166887	−0.0834434	−	0.996513i	$-0.526592\pi$
$523$	−1.19591e44	−0.166887	−0.0834434	+	0.996513i	$0.526592\pi$
$524$	−1.63278e44	−0.220781
$525$	2.37040e44	0.310594
$526$	−6.56876e44	−0.834101
$527$	8.50590e44	1.04675
$528$	−1.21640e44	−0.145083
$529$	5.12284e44	0.592233
$530$	−3.79036e44	−0.424745
$531$	−1.22142e42	−0.00132680
$532$	1.05357e44	0.110948
$533$	−6.78932e43	−0.0693151
$534$	−3.45559e44	−0.342052
$535$	−8.02372e44	−0.770085
$536$	1.88885e45	1.75783
$537$	−8.49938e44	−0.767029
$538$	1.68210e45	1.47212
$539$	4.24156e44	0.360007
$540$	1.74576e44	0.143710
$541$	−1.24548e45	−0.994451	−0.497225	−	0.867621i	$-0.665648\pi$
$541$	−1.24548e45	−0.994451	−0.497225	+	0.867621i	$0.665648\pi$
$542$	3.25913e44	0.252414
$543$	6.96426e44	0.523212
$544$	6.06031e44	0.441686
$545$	2.49159e44	0.176171
$546$	1.99931e45	1.37152
$547$	−9.41755e44	−0.626826	−0.313413	−	0.949617i	$-0.601472\pi$
$547$	−9.41755e44	−0.626826	−0.313413	+	0.949617i	$0.601472\pi$
$548$	2.12659e44	0.137342
$549$	2.14840e42	0.00134639
$550$	6.83843e43	0.0415884
$551$	5.32388e44	0.314215
$552$	−2.39017e45	−1.36910
$553$	−2.93321e45	−1.63072
$554$	−1.77713e45	−0.958975
$555$	1.19815e45	0.627591
$556$	9.18263e44	0.466910
$557$	−2.81038e45	−1.38725	−0.693624	−	0.720338i	$-0.743987\pi$
$557$	−2.81038e45	−1.38725	−0.693624	+	0.720338i	$0.743987\pi$
$558$	−1.60608e43	−0.00769666
$559$	3.09549e45	1.44024
$560$	−8.90034e44	−0.402072
$561$	4.13144e44	0.181223
$562$	−2.32549e44	−0.0990524
$563$	2.48634e45	1.02842	0.514212	−	0.857663i	$-0.328084\pi$
$563$	2.48634e45	1.02842	0.514212	+	0.857663i	$0.328084\pi$
$564$	7.23555e44	0.290647
$565$	−1.69314e45	−0.660530
$566$	1.36400e45	0.516826
$567$	−4.20595e45	−1.54790
$568$	−7.97315e44	−0.285025
$569$	1.50472e45	0.522521	0.261261	−	0.965268i	$-0.415862\pi$
$569$	1.50472e45	0.522521	0.261261	+	0.965268i	$0.415862\pi$
$570$	−2.42196e44	−0.0817017
$571$	−2.28889e45	−0.750117	−0.375059	−	0.927001i	$-0.622377\pi$
$571$	−2.28889e45	−0.750117	−0.375059	+	0.927001i	$0.622377\pi$
$572$	−2.71835e44	−0.0865507
$573$	1.26255e45	0.390569
$574$	−2.76503e44	−0.0831099
$575$	8.64077e44	0.252367
$576$	−2.45146e43	−0.00695751
$577$	1.59455e45	0.439781	0.219891	−	0.975525i	$-0.429430\pi$
$577$	1.59455e45	0.439781	0.219891	+	0.975525i	$0.429430\pi$
$578$	−1.47771e45	−0.396076
$579$	5.57987e44	0.145354
$580$	7.99702e44	0.202473
$581$	−9.05264e45	−2.22776
$582$	3.47562e43	0.00831386
$583$	−1.24964e45	−0.290572
$584$	4.09790e45	0.926295
$585$	−1.40154e43	−0.00307987
$586$	4.30405e44	0.0919531
$587$	5.55956e45	1.15481	0.577407	−	0.816457i	$-0.304065\pi$
$587$	5.55956e45	1.15481	0.577407	+	0.816457i	$0.304065\pi$
$588$	−2.25650e45	−0.455732
$589$	−1.64396e45	−0.322841
$590$	3.98473e44	0.0760924
$591$	1.04824e46	1.94655
$592$	−4.49880e45	−0.812434
$593$	−1.33454e45	−0.234384	−0.117192	−	0.993109i	$-0.537389\pi$
$593$	−1.33454e45	−0.234384	−0.117192	+	0.993109i	$0.537389\pi$
$594$	−1.22124e45	−0.208605
$595$	3.02295e45	0.502228
$596$	−2.52806e45	−0.408530
$597$	1.45347e45	0.228470
$598$	7.28806e45	1.11440
$599$	2.61382e45	0.388806	0.194403	−	0.980922i	$-0.437723\pi$
$599$	2.61382e45	0.388806	0.194403	+	0.980922i	$0.437723\pi$
$600$	−1.49954e45	−0.217001
$601$	1.12433e45	0.158295	0.0791474	−	0.996863i	$-0.474780\pi$
$601$	1.12433e45	0.158295	0.0791474	+	0.996863i	$0.474780\pi$
$602$	1.26067e46	1.72687
$603$	7.78954e43	0.0103819
$604$	2.93684e42	0.000380865 0
$605$	−3.31842e45	−0.418763
$606$	7.25056e45	0.890376
$607$	1.38809e46	1.65884	0.829418	−	0.558628i	$-0.188672\pi$
$607$	1.38809e46	1.65884	0.829418	+	0.558628i	$0.188672\pi$
$608$	−1.17129e45	−0.136225
$609$	−1.93914e46	−2.19494
$610$	−7.00890e44	−0.0772160
$611$	−9.09378e45	−0.975134
$612$	1.42214e43	0.00148437
$613$	1.28344e46	1.30400	0.652001	−	0.758218i	$-0.273930\pi$
$613$	1.28344e46	1.30400	0.652001	+	0.758218i	$0.273930\pi$
$614$	−1.15835e46	−1.14567
$615$	−2.99566e44	−0.0288439
$616$	−4.56318e45	−0.427746
$617$	−1.41494e46	−1.29131	−0.645657	−	0.763628i	$-0.723416\pi$
$617$	−1.41494e46	−1.29131	−0.645657	+	0.763628i	$0.723416\pi$
$618$	−1.08604e46	−0.965017
$619$	3.49373e45	0.302269	0.151134	−	0.988513i	$-0.451707\pi$
$619$	3.49373e45	0.302269	0.151134	+	0.988513i	$0.451707\pi$
$620$	−2.46939e45	−0.208031
$621$	−1.54311e46	−1.26586
$622$	1.05693e46	0.844312
$623$	−8.33600e45	−0.648492
$624$	−8.13317e45	−0.616189
$625$	5.42101e44	0.0400000
$626$	−1.76558e46	−1.26885
$627$	−7.98494e44	−0.0558929
$628$	−5.62707e45	−0.383662
$629$	1.52799e46	1.01481
$630$	−5.70791e43	−0.00369282
$631$	2.21383e46	1.39528	0.697638	−	0.716451i	$-0.254234\pi$
$631$	2.21383e46	1.39528	0.697638	+	0.716451i	$0.254234\pi$
$632$	1.85558e46	1.13932
$633$	−1.97608e46	−1.18207
$634$	−9.02525e45	−0.526001
$635$	1.51463e46	0.860080
$636$	6.64807e45	0.367835
$637$	2.83601e46	1.52900
$638$	−5.59428e45	−0.293902
$639$	−3.28810e43	−0.00168337
$640$	2.50503e45	0.124981
$641$	−4.90058e45	−0.238281	−0.119141	−	0.992877i	$-0.538014\pi$
$641$	−4.90058e45	−0.238281	−0.119141	+	0.992877i	$0.538014\pi$
$642$	−2.98608e46	−1.41506
$643$	2.98051e46	1.37661	0.688303	−	0.725423i	$-0.258356\pi$
$643$	2.98051e46	1.37661	0.688303	+	0.725423i	$0.258356\pi$
$644$	−1.39886e46	−0.629734
$645$	1.36583e46	0.599323
$646$	−3.08871e45	−0.132111
$647$	−3.18321e45	−0.132723	−0.0663613	−	0.997796i	$-0.521139\pi$
$647$	−3.18321e45	−0.132723	−0.0663613	+	0.997796i	$0.521139\pi$
$648$	2.66073e46	1.08146
$649$	1.31372e45	0.0520555
$650$	4.57235e45	0.176632
$651$	5.98785e46	2.25520
$652$	−2.34924e45	−0.0862666
$653$	−4.44872e46	−1.59282	−0.796411	−	0.604756i	$-0.793271\pi$
$653$	−4.44872e46	−1.59282	−0.796411	+	0.604756i	$0.793271\pi$
$654$	9.27261e45	0.323720
$655$	9.05457e45	0.308238
$656$	1.12481e45	0.0373392
$657$	1.68996e44	0.00547076
$658$	−3.70354e46	−1.16920
$659$	−3.64438e46	−1.12206	−0.561028	−	0.827797i	$-0.689594\pi$
$659$	−3.64438e46	−1.12206	−0.561028	+	0.827797i	$0.689594\pi$
$660$	−1.19942e45	−0.0360161
$661$	−2.16411e46	−0.633804	−0.316902	−	0.948458i	$-0.602643\pi$
$661$	−2.16411e46	−0.633804	−0.316902	+	0.948458i	$0.602643\pi$
$662$	1.85517e46	0.529940
$663$	2.76238e46	0.769681
$664$	5.72679e46	1.55646
$665$	−5.84253e45	−0.154897
$666$	−2.88514e44	−0.00746178
$667$	−7.06871e46	−1.78346
$668$	−6.34836e45	−0.156261
$669$	−1.62148e46	−0.389387
$670$	−2.54124e46	−0.595404
$671$	−2.31076e45	−0.0528242
$672$	4.26624e46	0.951596
$673$	5.34875e46	1.16414	0.582068	−	0.813140i	$-0.302244\pi$
$673$	5.34875e46	1.16414	0.582068	+	0.813140i	$0.302244\pi$
$674$	4.43140e46	0.941137
$675$	−9.68110e45	−0.200638
$676$	−2.33717e45	−0.0472682
$677$	−3.90814e46	−0.771359	−0.385679	−	0.922633i	$-0.626033\pi$
$677$	−3.90814e46	−0.771359	−0.385679	+	0.922633i	$0.626033\pi$
$678$	−6.30112e46	−1.21375
$679$	8.38430e44	0.0157622
$680$	−1.91235e46	−0.350889
$681$	−4.03610e46	−0.722826
$682$	1.72745e46	0.301970
$683$	9.82421e46	1.67632	0.838158	−	0.545427i	$-0.183632\pi$
$683$	9.82421e46	1.67632	0.838158	+	0.545427i	$0.183632\pi$
$684$	−2.74860e43	−0.000457811 0
$685$	−1.17930e46	−0.191747
$686$	3.45786e46	0.548858
$687$	−8.21966e46	−1.27370
$688$	−5.12840e46	−0.775841
$689$	−8.35542e46	−1.23410
$690$	3.21572e46	0.463733
$691$	−7.20065e46	−1.01387	−0.506937	−	0.861983i	$-0.669222\pi$
$691$	−7.20065e46	−1.01387	−0.506937	+	0.861983i	$0.669222\pi$
$692$	−2.04796e46	−0.281560
$693$	−1.88184e44	−0.00252629
$694$	7.68188e46	1.00702
$695$	−5.09221e46	−0.651864
$696$	1.22672e47	1.53353
$697$	−3.82035e45	−0.0466404
$698$	1.11927e47	1.33451
$699$	−4.21520e46	−0.490846
$700$	−8.77609e45	−0.0998122
$701$	−3.78749e46	−0.420731	−0.210366	−	0.977623i	$-0.567465\pi$
$701$	−3.78749e46	−0.420731	−0.210366	+	0.977623i	$0.567465\pi$
$702$	−8.16552e46	−0.885975
$703$	−2.95319e46	−0.312988
$704$	2.63672e46	0.272970
$705$	−4.01246e46	−0.405780
$706$	−5.86119e45	−0.0579039
$707$	1.74907e47	1.68805
$708$	−6.98899e45	−0.0658970
$709$	8.09313e46	0.745510	0.372755	−	0.927930i	$-0.378413\pi$
$709$	8.09313e46	0.745510	0.372755	+	0.927930i	$0.378413\pi$
$710$	1.07270e46	0.0965421
$711$	7.65234e44	0.00672892
$712$	5.27343e46	0.453078
$713$	2.18274e47	1.83242
$714$	1.12501e47	0.922861
$715$	1.50746e46	0.120836
$716$	3.14679e46	0.246492
$717$	−1.99995e47	−1.53092
$718$	−1.73923e47	−1.30108
$719$	1.77184e47	1.29538	0.647692	−	0.761902i	$-0.275734\pi$
$719$	1.77184e47	1.29538	0.647692	+	0.761902i	$0.275734\pi$
$720$	2.32197e44	0.00165909
$721$	−2.61987e47	−1.82956
$722$	−1.14816e47	−0.783678
$723$	2.86289e47	1.90995
$724$	−2.57843e46	−0.168139
$725$	−4.43474e46	−0.282677
$726$	−1.23497e47	−0.769490
$727$	1.73206e47	1.05498	0.527490	−	0.849561i	$-0.323133\pi$
$727$	1.73206e47	1.05498	0.527490	+	0.849561i	$0.323133\pi$
$728$	−3.05106e47	−1.81670
$729$	1.72883e47	1.00635
$730$	−5.51329e46	−0.313750
$731$	1.74183e47	0.969102
$732$	1.22932e46	0.0668701
$733$	−2.26618e47	−1.20525	−0.602626	−	0.798024i	$-0.705879\pi$
$733$	−2.26618e47	−1.20525	−0.602626	+	0.798024i	$0.705879\pi$
$734$	1.86736e47	0.971054
$735$	1.25134e47	0.636259
$736$	1.55517e47	0.773203
$737$	−8.37821e46	−0.407322
$738$	7.21356e43	0.000342941 0
$739$	3.80934e46	0.177099	0.0885496	−	0.996072i	$-0.471777\pi$
$739$	3.80934e46	0.177099	0.0885496	+	0.996072i	$0.471777\pi$
$740$	−4.43599e46	−0.201682
$741$	−5.33893e46	−0.237385
$742$	−3.40283e47	−1.47971
$743$	−1.22091e47	−0.519238	−0.259619	−	0.965711i	$-0.583597\pi$
$743$	−1.22091e47	−0.519238	−0.259619	+	0.965711i	$0.583597\pi$
$744$	−3.78797e47	−1.57563
$745$	1.40193e47	0.570359
$746$	1.66800e47	0.663750
$747$	2.36171e45	0.00919255
$748$	−1.52961e46	−0.0582378
$749$	−7.20338e47	−2.68279
$750$	2.01747e46	0.0735013
$751$	−2.36534e46	−0.0843014	−0.0421507	−	0.999111i	$-0.513421\pi$
$751$	−2.36534e46	−0.0843014	−0.0421507	+	0.999111i	$0.513421\pi$
$752$	1.50660e47	0.525294
$753$	1.04206e45	0.00355446
$754$	−3.74048e47	−1.24824
$755$	−1.62862e44	−0.000531735 0
$756$	1.56728e47	0.500652
$757$	−1.36056e47	−0.425243	−0.212621	−	0.977135i	$-0.568200\pi$
$757$	−1.36056e47	−0.425243	−0.212621	+	0.977135i	$0.568200\pi$
$758$	2.51859e47	0.770222
$759$	1.06019e47	0.317245
$760$	3.69604e46	0.108221
$761$	2.10711e47	0.603727	0.301863	−	0.953351i	$-0.402391\pi$
$761$	2.10711e47	0.603727	0.301863	+	0.953351i	$0.402391\pi$
$762$	5.63678e47	1.58043
$763$	2.23685e47	0.613737
$764$	−4.67444e46	−0.125513
$765$	−7.88645e44	−0.00207237
$766$	1.61055e47	0.414189
$767$	8.78390e46	0.221087
$768$	−3.44682e47	−0.849100
$769$	3.42055e47	0.824728	0.412364	−	0.911019i	$-0.364703\pi$
$769$	3.42055e47	0.824728	0.412364	+	0.911019i	$0.364703\pi$
$770$	6.13927e46	0.144884
$771$	−2.78116e47	−0.642435
$772$	−2.06588e46	−0.0467110
$773$	2.59138e47	0.573549	0.286774	−	0.957998i	$-0.407417\pi$
$773$	2.59138e47	0.573549	0.286774	+	0.957998i	$0.407417\pi$
$774$	−3.28892e45	−0.00712569
$775$	1.36940e47	0.290437
$776$	−5.30399e45	−0.0110125
$777$	1.07565e48	2.18637
$778$	−3.59916e47	−0.716206
$779$	7.38369e45	0.0143849
$780$	−8.01963e46	−0.152966
$781$	3.53659e46	0.0660454
$782$	4.10099e47	0.749855
$783$	7.91977e47	1.41789
$784$	−4.69851e47	−0.823655
$785$	3.12048e47	0.535639
$786$	3.36972e47	0.566398
$787$	−3.31448e47	−0.545546	−0.272773	−	0.962078i	$-0.587941\pi$
$787$	−3.31448e47	−0.545546	−0.272773	+	0.962078i	$0.587941\pi$
$788$	−3.88096e47	−0.625542
$789$	−6.38908e47	−1.00848
$790$	−2.49648e47	−0.385906
$791$	−1.52003e48	−2.30113
$792$	1.19047e45	0.00176503
$793$	−1.54503e47	−0.224352
$794$	3.20658e47	0.456040
$795$	−3.68667e47	−0.513543
$796$	−5.38129e46	−0.0734211
$797$	−1.21980e48	−1.63015	−0.815076	−	0.579354i	$-0.803305\pi$
$797$	−1.21980e48	−1.63015	−0.815076	+	0.579354i	$0.803305\pi$
$798$	−2.17434e47	−0.284629
$799$	−5.11707e47	−0.656144
$800$	9.75675e46	0.122552
$801$	2.17474e45	0.00267591
$802$	4.39671e47	0.529969
$803$	−1.81767e47	−0.214639
$804$	4.45719e47	0.515628
$805$	7.75735e47	0.879187
$806$	1.15502e48	1.28251
$807$	1.63609e48	1.77989
$808$	−1.10648e48	−1.17938
$809$	−2.89096e47	−0.301920	−0.150960	−	0.988540i	$-0.548236\pi$
$809$	−2.89096e47	−0.301920	−0.150960	+	0.988540i	$0.548236\pi$
$810$	−3.57972e47	−0.366308
$811$	−8.79228e47	−0.881571	−0.440786	−	0.897612i	$-0.645300\pi$
$811$	−8.79228e47	−0.881571	−0.440786	+	0.897612i	$0.645300\pi$
$812$	7.17941e47	0.705366
$813$	3.16998e47	0.305184
$814$	3.10318e47	0.292755
$815$	1.30277e47	0.120439
$816$	−4.57653e47	−0.414619
$817$	−3.36648e47	−0.298891
$818$	−1.07972e48	−0.939467
$819$	−1.25825e46	−0.0107295
$820$	1.10911e46	0.00926926
$821$	−6.16314e47	−0.504824	−0.252412	−	0.967620i	$-0.581224\pi$
$821$	−6.16314e47	−0.504824	−0.252412	+	0.967620i	$0.581224\pi$
$822$	−4.38883e47	−0.352342
$823$	−1.89117e47	−0.148810	−0.0744052	−	0.997228i	$-0.523706\pi$
$823$	−1.89117e47	−0.148810	−0.0744052	+	0.997228i	$0.523706\pi$
$824$	1.65735e48	1.27825
$825$	6.65137e46	0.0502830
$826$	3.57734e47	0.265087
$827$	−9.51973e47	−0.691486	−0.345743	−	0.938329i	$-0.612373\pi$
$827$	−9.51973e47	−0.691486	−0.345743	+	0.938329i	$0.612373\pi$
$828$	3.64942e45	0.00259851
$829$	2.56276e48	1.78878	0.894392	−	0.447284i	$-0.147609\pi$
$829$	2.56276e48	1.78878	0.894392	+	0.447284i	$0.147609\pi$
$830$	−7.70479e47	−0.527196
$831$	−1.72851e48	−1.15946
$832$	1.76298e48	1.15934
$833$	1.59582e48	1.02883
$834$	−1.89510e48	−1.19782
$835$	3.52047e47	0.218159
$836$	2.95632e46	0.0179617
$837$	−2.44554e48	−1.45682
$838$	2.18701e48	1.27740
$839$	−5.48536e47	−0.314147	−0.157073	−	0.987587i	$-0.550206\pi$
$839$	−5.48536e47	−0.314147	−0.157073	+	0.987587i	$0.550206\pi$
$840$	−1.34622e48	−0.755978
$841$	1.81182e48	0.997659
$842$	1.02536e48	0.553641
$843$	−2.26188e47	−0.119761
$844$	7.31618e47	0.379869
$845$	1.29607e47	0.0659923
$846$	9.66201e45	0.00482454
$847$	−2.97915e48	−1.45887
$848$	1.38427e48	0.664797
$849$	1.32669e48	0.624875
$850$	2.57286e47	0.118851
$851$	3.92105e48	1.77650
$852$	−1.88146e47	−0.0836067
$853$	6.63073e47	0.289003	0.144501	−	0.989505i	$-0.453842\pi$
$853$	6.63073e47	0.289003	0.144501	+	0.989505i	$0.453842\pi$
$854$	−6.29231e47	−0.269002
$855$	1.52423e45	0.000639162 0
$856$	4.55693e48	1.87437
$857$	−3.61344e48	−1.45793	−0.728966	−	0.684550i	$-0.759999\pi$
$857$	−3.61344e48	−1.45793	−0.728966	+	0.684550i	$0.759999\pi$
$858$	5.61009e47	0.222039
$859$	−2.95644e47	−0.114784	−0.0573921	−	0.998352i	$-0.518279\pi$
$859$	−2.95644e47	−0.114784	−0.0573921	+	0.998352i	$0.518279\pi$
$860$	−5.05681e47	−0.192598
$861$	−2.68939e47	−0.100485
$862$	−3.05736e48	−1.12067
$863$	1.94226e48	0.698440	0.349220	−	0.937041i	$-0.386447\pi$
$863$	1.94226e48	0.698440	0.349220	+	0.937041i	$0.386447\pi$
$864$	−1.74241e48	−0.614713
$865$	1.13570e48	0.393094
$866$	−7.90904e47	−0.268583
$867$	−1.43728e48	−0.478881
$868$	−2.21692e48	−0.724729
$869$	−8.23064e47	−0.264002
$870$	−1.65042e48	−0.519429
$871$	−5.60188e48	−1.72995
$872$	−1.41505e48	−0.428796
$873$	−2.18735e44	−6.50403e−5 0
$874$	−7.92608e47	−0.231270
$875$	4.86677e47	0.139350
$876$	9.66998e47	0.271711
$877$	3.36176e48	0.926985	0.463493	−	0.886101i	$-0.346596\pi$
$877$	3.36176e48	0.926985	0.463493	+	0.886101i	$0.346596\pi$
$878$	2.41020e47	0.0652220
$879$	4.18631e47	0.111177
$880$	−2.49745e47	−0.0650928
$881$	2.89868e47	0.0741477	0.0370738	−	0.999313i	$-0.488196\pi$
$881$	2.89868e47	0.0741477	0.0370738	+	0.999313i	$0.488196\pi$
$882$	−3.01322e46	−0.00756484
$883$	−2.27915e48	−0.561592	−0.280796	−	0.959767i	$-0.590598\pi$
$883$	−2.27915e48	−0.561592	−0.280796	+	0.959767i	$0.590598\pi$
$884$	−1.02274e48	−0.247344
$885$	3.87573e47	0.0920005
$886$	−1.27003e48	−0.295910
$887$	−3.67815e48	−0.841180	−0.420590	−	0.907251i	$-0.638177\pi$
$887$	−3.67815e48	−0.841180	−0.420590	+	0.907251i	$0.638177\pi$
$888$	−6.80467e48	−1.52754
$889$	1.35977e49	2.99631
$890$	−7.09484e47	−0.153464
$891$	−1.18020e48	−0.250595
$892$	6.00334e47	0.125133
$893$	9.88988e47	0.202368
$894$	5.21738e48	1.04805
$895$	−1.74505e48	−0.344134
$896$	2.24892e48	0.435403
$897$	7.08870e48	1.34738
$898$	−1.61488e48	−0.301357
$899$	−1.12026e49	−2.05250
$900$	2.28956e45	0.000411861 0
$901$	−4.70159e48	−0.830397
$902$	−7.75870e46	−0.0134549
$903$	1.22619e49	2.08790
$904$	9.61586e48	1.60771
$905$	1.42986e48	0.234743
$906$	−6.06102e45	−0.000977080 0
$907$	−1.60568e48	−0.254178	−0.127089	−	0.991891i	$-0.540563\pi$
$907$	−1.60568e48	−0.254178	−0.127089	+	0.991891i	$0.540563\pi$
$908$	1.49431e48	0.232287
$909$	−4.56307e46	−0.00696551
$910$	4.10487e48	0.615342
$911$	7.70098e48	1.13369	0.566843	−	0.823826i	$-0.308165\pi$
$911$	7.70098e48	1.13369	0.566843	+	0.823826i	$0.308165\pi$
$912$	8.84518e47	0.127877
$913$	−2.54019e48	−0.360660
$914$	−1.09134e49	−1.52176
$915$	−6.81717e47	−0.0933590
$916$	3.04322e48	0.409316
$917$	8.12883e48	1.07383
$918$	−4.59474e48	−0.596151
$919$	5.42603e48	0.691474	0.345737	−	0.938331i	$-0.387629\pi$
$919$	5.42603e48	0.691474	0.345737	+	0.938331i	$0.387629\pi$
$920$	−4.90737e48	−0.614256
$921$	−1.12666e49	−1.38519
$922$	2.70074e48	0.326154
$923$	2.36465e48	0.280504
$924$	−1.07679e48	−0.125471
$925$	2.45997e48	0.281574
$926$	−2.35275e48	−0.264542
$927$	6.83487e46	0.00754944
$928$	−7.98165e48	−0.866066
$929$	−7.82524e48	−0.834139	−0.417070	−	0.908875i	$-0.636943\pi$
$929$	−7.82524e48	−0.834139	−0.417070	+	0.908875i	$0.636943\pi$
$930$	5.09631e48	0.533688
$931$	−3.08429e48	−0.317311
$932$	1.56063e48	0.157738
$933$	1.02801e49	1.02083
$934$	−2.81891e48	−0.275016
$935$	8.48245e47	0.0813073
$936$	7.95978e46	0.00749634
$937$	1.34653e49	1.24599	0.622994	−	0.782227i	$-0.285916\pi$
$937$	1.34653e49	1.24599	0.622994	+	0.782227i	$0.285916\pi$
$938$	−2.28143e49	−2.07424
$939$	−1.71729e49	−1.53413
$940$	1.48556e48	0.130401
$941$	−1.57761e49	−1.36073	−0.680365	−	0.732874i	$-0.738179\pi$
$941$	−1.57761e49	−1.36073	−0.680365	+	0.732874i	$0.738179\pi$
$942$	1.16131e49	0.984255
$943$	−9.80360e47	−0.0816474
$944$	−1.45526e48	−0.119097
$945$	−8.69131e48	−0.698973
$946$	3.53747e48	0.279569
$947$	7.45162e48	0.578730	0.289365	−	0.957219i	$-0.406556\pi$
$947$	7.45162e48	0.578730	0.289365	+	0.957219i	$0.406556\pi$
$948$	4.37869e48	0.334200
$949$	−1.21534e49	−0.911604
$950$	−4.97263e47	−0.0366561
$951$	−8.77837e48	−0.635968
$952$	−1.71683e49	−1.22241
$953$	2.12970e49	1.49034	0.745171	−	0.666874i	$-0.232368\pi$
$953$	2.12970e49	1.49034	0.745171	+	0.666874i	$0.232368\pi$
$954$	8.87751e46	0.00610581
$955$	2.59220e48	0.175232
$956$	7.40456e48	0.491976
$957$	−5.44125e48	−0.355346
$958$	−2.36140e48	−0.151579
$959$	−1.05873e49	−0.668000
$960$	7.77882e48	0.482435
$961$	1.81888e49	1.10884
$962$	2.07486e49	1.24337
$963$	1.87926e47	0.0110701
$964$	−1.05995e49	−0.613781
$965$	1.14563e48	0.0652144
$966$	2.88695e49	1.61553
$967$	7.81881e47	0.0430134	0.0215067	−	0.999769i	$-0.493154\pi$
$967$	7.81881e47	0.0430134	0.0215067	+	0.999769i	$0.493154\pi$
$968$	1.88464e49	1.01926
$969$	−3.00422e48	−0.159731
$970$	7.13595e46	0.00373008
$971$	2.07870e49	1.06825	0.534127	−	0.845404i	$-0.320640\pi$
$971$	2.07870e49	1.06825	0.534127	+	0.845404i	$0.320640\pi$
$972$	−8.15149e46	−0.00411854
$973$	−4.57159e49	−2.27094
$974$	3.29811e49	1.61080
$975$	4.44727e48	0.213559
$976$	2.55971e48	0.120856
$977$	−1.16244e49	−0.539647	−0.269824	−	0.962910i	$-0.586965\pi$
$977$	−1.16244e49	−0.539647	−0.269824	+	0.962910i	$0.586965\pi$
$978$	4.84834e48	0.221311
$979$	−2.33909e48	−0.104986
$980$	−4.63292e48	−0.204468
$981$	−5.83563e46	−0.00253250
$982$	−2.23990e49	−0.955846
$983$	−2.37943e49	−0.998482	−0.499241	−	0.866463i	$-0.666388\pi$
$983$	−2.37943e49	−0.998482	−0.499241	+	0.866463i	$0.666388\pi$
$984$	1.70133e48	0.0702054
$985$	2.15218e49	0.873335
$986$	−2.10476e49	−0.839913
$987$	−3.60223e49	−1.41364
$988$	1.97667e48	0.0762861
$989$	4.46980e49	1.69648
$990$	−1.60165e46	−0.000597842 0
$991$	−3.80696e49	−1.39754	−0.698768	−	0.715348i	$-0.746268\pi$
$991$	−3.80696e49	−1.39754	−0.698768	+	0.715348i	$0.746268\pi$
$992$	2.46465e49	0.889840
$993$	1.80442e49	0.640731
$994$	9.63030e48	0.336329
$995$	2.98419e48	0.102505
$996$	1.35137e49	0.456559
$997$	6.76901e48	0.224934	0.112467	−	0.993655i	$-0.464125\pi$
$997$	6.76901e48	0.224934	0.112467	+	0.993655i	$0.464125\pi$
$998$	−6.88166e47	−0.0224926
$999$	−4.39314e49	−1.41236

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.34.a.b.1.4	✓	6
5.2	odd	4		25.34.b.c.24.8		12
5.3	odd	4		25.34.b.c.24.5		12
5.4	even	2		25.34.a.c.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.b.1.4	✓	6	1.1	even	1	trivial
25.34.a.c.1.3		6	5.4	even	2
25.34.b.c.24.5		12	5.3	odd	4
25.34.b.c.24.8		12	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 5 \)
Weight:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	5.a (trivial)

\(f(q)\)	\(=\)	\(q+76409.2 q^{2} +7.43191e7 q^{3} -2.75157e9 q^{4} +1.52588e11 q^{5} +5.67866e12 q^{6} +1.36987e14 q^{7} -8.66595e14 q^{8} -3.57381e13 q^{9} +O(q^{10})\)	\(q+76409.2 q^{2} +7.43191e7 q^{3} -2.75157e9 q^{4} +1.52588e11 q^{5} +5.67866e12 q^{6} +1.36987e14 q^{7} -8.66595e14 q^{8} -3.57381e13 q^{9} +1.16591e16 q^{10} +3.84389e16 q^{11} -2.04494e17 q^{12} +2.57012e18 q^{13} +1.04671e19 q^{14} +1.13402e19 q^{15} -4.25800e19 q^{16} +1.44621e20 q^{17} -2.73072e18 q^{18} -2.79512e20 q^{19} -4.19856e20 q^{20} +1.01808e22 q^{21} +2.93708e21 q^{22} +3.71118e22 q^{23} -6.44045e22 q^{24} +2.32831e22 q^{25} +1.96381e23 q^{26} -4.15800e23 q^{27} -3.76930e23 q^{28} -1.90470e24 q^{29} +8.66495e23 q^{30} +5.88152e24 q^{31} +4.19049e24 q^{32} +2.85674e24 q^{33} +1.10503e25 q^{34} +2.09026e25 q^{35} +9.83358e22 q^{36} +1.05655e26 q^{37} -2.13573e25 q^{38} +1.91009e26 q^{39} -1.32232e26 q^{40} -2.64164e25 q^{41} +7.77905e26 q^{42} +1.20441e27 q^{43} -1.05767e26 q^{44} -5.45320e24 q^{45} +2.83569e27 q^{46} -3.53827e27 q^{47} -3.16451e27 q^{48} +1.10345e28 q^{49} +1.77904e27 q^{50} +1.07481e28 q^{51} -7.07187e27 q^{52} -3.25098e28 q^{53} -3.17710e28 q^{54} +5.86531e27 q^{55} -1.18713e29 q^{56} -2.07731e28 q^{57} -1.45537e29 q^{58} +3.41770e28 q^{59} -3.12033e28 q^{60} -6.01152e28 q^{61} +4.49402e29 q^{62} -4.89566e27 q^{63} +6.85952e29 q^{64} +3.92169e29 q^{65} +2.18281e29 q^{66} -2.17962e30 q^{67} -3.97934e29 q^{68} +2.75812e30 q^{69} +1.59715e30 q^{70} +9.20055e29 q^{71} +3.09704e28 q^{72} -4.72873e30 q^{73} +8.07302e30 q^{74} +1.73038e30 q^{75} +7.69097e29 q^{76} +5.26564e30 q^{77} +1.45948e31 q^{78} -2.14123e31 q^{79} -6.49720e30 q^{80} -3.07032e31 q^{81} -2.01845e30 q^{82} -6.60838e31 q^{83} -2.80131e31 q^{84} +2.20674e31 q^{85} +9.20283e31 q^{86} -1.41556e32 q^{87} -3.33109e31 q^{88} -6.08523e31 q^{89} -4.16674e29 q^{90} +3.52074e32 q^{91} -1.02116e32 q^{92} +4.37109e32 q^{93} -2.70356e32 q^{94} -4.26502e31 q^{95} +3.11433e32 q^{96} +6.12049e30 q^{97} +8.43141e32 q^{98} -1.37373e30 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 147350 q^{2} + 26513900 q^{3} + 29520645652 q^{4} + 915527343750 q^{5} + 6615759249352 q^{6} + 19113832847500 q^{7} + 30\!\cdots\!00 q^{8}+ \cdots + 13\!\cdots\!38 q^{9}+O(q^{10}) \) 6 * q + 147350 * q^2 + 26513900 * q^3 + 29520645652 * q^4 + 915527343750 * q^5 + 6615759249352 * q^6 + 19113832847500 * q^7 + 3069820115785800 * q^8 + 13602102583345438 * q^9	\( 6 q + 147350 q^{2} + 26513900 q^{3} + 29520645652 q^{4} + 915527343750 q^{5} + 6615759249352 q^{6} + 19113832847500 q^{7} + 30\!\cdots\!00 q^{8}+ \cdots + 16\!\cdots\!16 q^{99}+O(q^{100}) \) 6 * q + 147350 * q^2 + 26513900 * q^3 + 29520645652 * q^4 + 915527343750 * q^5 + 6615759249352 * q^6 + 19113832847500 * q^7 + 3069820115785800 * q^8 + 13602102583345438 * q^9 + 22483825683593750 * q^10 + 150760896555890192 * q^11 + 466351581756413200 * q^12 - 1403095636752804700 * q^13 - 7086110008989891456 * q^14 + 4045700073242187500 * q^15 + 64511520005858668816 * q^16 + 134380842798611834300 * q^17 + 673397185005127949150 * q^18 + 1711584362599986612200 * q^19 + 4504493049926757812500 * q^20 - 10560397660826154148128 * q^21 + 2470897477250007236200 * q^22 + 6879744551224024319700 * q^23 + 211895016154723698861600 * q^24 + 139698386192321777343750 * q^25 - 361829246667436498168588 * q^26 - 340705501428703899968200 * q^27 - 1750376606004032278695200 * q^28 + 1305223406410727358015700 * q^29 + 1009484748741455078125000 * q^30 + 10825321396800575904753352 * q^31 + 26818258713124955338861600 * q^32 + 34856079507682787436662800 * q^33 + 8872409666654531735490124 * q^34 + 2916539435958862304687500 * q^35 + 168714411751774892911163396 * q^36 + 276757164463535626747584900 * q^37 + 835386866362613528909982200 * q^38 + 579964086232605925635188456 * q^39 + 468417376065948486328125000 * q^40 + 448008579649522993395821932 * q^41 + 1478478813030145693383604800 * q^42 + 2250588086104897739543439500 * q^43 + 7171805342222267509050250864 * q^44 + 2075516141257543640136718750 * q^45 + 3493759290976330924493595072 * q^46 + 3830785379519133075460228700 * q^47 + 24576343390562635665291611200 * q^48 - 7173427073564666873529235258 * q^49 + 3430759534239768981933593750 * q^50 - 54920362805063671320868694888 * q^51 - 90553915669177954388890305000 * q^52 + 47034713551772209628037134900 * q^53 - 182647187168263097239229399600 * q^54 + 23004287194197111816406250000 * q^55 - 392573339390998146620750750400 * q^56 - 242119765146738617914766400400 * q^57 - 443272639260736798552560798700 * q^58 - 178315156221037727069533799800 * q^59 + 71159604149843322753906250000 * q^60 - 282317689060586014253208287308 * q^61 + 3477509804797272360008839200 * q^62 - 559259159226762324796386276900 * q^63 + 1937968534792541396434479607872 * q^64 - 214095403557251693725585937500 * q^65 + 5061208746155430260544773159264 * q^66 + 3357382217232044190774976063300 * q^67 + 3866973693935427075529380663400 * q^68 + 316127240816983184255653823136 * q^69 - 1081254579008467324218750000000 * q^70 + 8451218031993742702656617170072 * q^71 + 8740278584811466598158058687400 * q^72 - 1719044326022105657749673125300 * q^73 + 20494727417173075429289542476484 * q^74 + 617324840277433395385742187500 * q^75 + 29410039922734837753629694458000 * q^76 - 1179300749517366199915257594000 * q^77 - 57229303014236704407408363530000 * q^78 - 22052505351402355443894747635600 * q^79 + 9843676758706461916503906250000 * q^80 - 133163964889176760661905573719674 * q^81 - 156059027108947085834404172875300 * q^82 - 47087087002138304263127820978900 * q^83 - 235991611992224148517578838651776 * q^84 + 20504889343049901473999023437500 * q^85 - 128823880621545855657554048105608 * q^86 - 175316396211912369693639217216600 * q^87 + 497433069891524019720739466805600 * q^88 - 336491358341169481948206213360900 * q^89 + 102752256012745353569030761718750 * q^90 + 194633769402343866156602864483432 * q^91 - 419043430758613276035983032687200 * q^92 + 212928090391747529239858474972800 * q^93 + 1486141097168392212687292135345264 * q^94 + 261167047515867097808837890625000 * q^95 + 3151728990173122672564203081529472 * q^96 + 2569321197832638009639208504856700 * q^97 + 6985460513399098756137635798950 * q^98 + 1660882302442227079414567162624016 * q^99

Introduction

L-functions

Modular forms

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