LMFDB - Embedded newform 5.34.a.b.1.3

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			1.3
Root			$-21408.2$ 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)

$f(q)$	$=$	$q-18258.4 q^{2} -3.67420e7 q^{3} -8.25656e9 q^{4} +1.52588e11 q^{5} +6.70852e11 q^{6} -1.51681e13 q^{7} +3.07591e14 q^{8} -4.20908e15 q^{9} +O(q^{10})$	\(q-18258.4 q^{2} -3.67420e7 q^{3} -8.25656e9 q^{4} +1.52588e11 q^{5} +6.70852e11 q^{6} -1.51681e13 q^{7} +3.07591e14 q^{8} -4.20908e15 q^{9} -2.78602e15 q^{10} -2.61480e17 q^{11} +3.03363e17 q^{12} -3.70714e17 q^{13} +2.76946e17 q^{14} -5.60639e18 q^{15} +6.53072e19 q^{16} -3.71730e20 q^{17} +7.68513e19 q^{18} +1.42255e21 q^{19} -1.25985e21 q^{20} +5.57308e20 q^{21} +4.77422e21 q^{22} -3.26990e22 q^{23} -1.13015e22 q^{24} +2.32831e22 q^{25} +6.76865e21 q^{26} +3.58901e23 q^{27} +1.25237e23 q^{28} +6.41343e23 q^{29} +1.02364e23 q^{30} -1.44554e23 q^{31} -3.83459e24 q^{32} +9.60732e24 q^{33} +6.78720e24 q^{34} -2.31447e24 q^{35} +3.47526e25 q^{36} +1.34909e26 q^{37} -2.59736e25 q^{38} +1.36208e25 q^{39} +4.69346e25 q^{40} +6.37865e26 q^{41} -1.01756e25 q^{42} +3.37044e26 q^{43} +2.15893e27 q^{44} -6.42255e26 q^{45} +5.97033e26 q^{46} +3.12828e27 q^{47} -2.39952e27 q^{48} -7.50092e27 q^{49} -4.25112e26 q^{50} +1.36581e28 q^{51} +3.06082e27 q^{52} -4.06250e28 q^{53} -6.55298e27 q^{54} -3.98988e28 q^{55} -4.66557e27 q^{56} -5.22675e28 q^{57} -1.17099e28 q^{58} -8.77955e28 q^{59} +4.62895e28 q^{60} -1.84902e28 q^{61} +2.63933e27 q^{62} +6.38439e28 q^{63} -4.90971e29 q^{64} -5.65664e28 q^{65} -1.75415e29 q^{66} +7.69531e29 q^{67} +3.06921e30 q^{68} +1.20143e30 q^{69} +4.22586e28 q^{70} +2.72988e30 q^{71} -1.29468e30 q^{72} +4.44452e30 q^{73} -2.46323e30 q^{74} -8.55467e29 q^{75} -1.17454e31 q^{76} +3.96617e30 q^{77} -2.48694e29 q^{78} -1.16758e31 q^{79} +9.96509e30 q^{80} +1.02118e31 q^{81} -1.16464e31 q^{82} -4.84088e31 q^{83} -4.60145e30 q^{84} -5.67215e31 q^{85} -6.15390e30 q^{86} -2.35643e31 q^{87} -8.04290e31 q^{88} +1.18101e32 q^{89} +1.17266e31 q^{90} +5.62303e30 q^{91} +2.69981e32 q^{92} +5.31122e30 q^{93} -5.71176e31 q^{94} +2.17064e32 q^{95} +1.40891e32 q^{96} -2.71846e31 q^{97} +1.36955e32 q^{98} +1.10059e33 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−18258.4	−0.197001	−0.0985006	−	0.995137i	$-0.531405\pi$
$2$	−18258.4	−0.197001	−0.0985006	+	0.995137i	$0.531405\pi$
$3$	−3.67420e7	−0.492791	−0.246395	−	0.969169i	$-0.579246\pi$
$3$	−3.67420e7	−0.492791	−0.246395	+	0.969169i	$0.579246\pi$
$4$	−8.25656e9	−0.961191
$5$	1.52588e11	0.447214
$5$	1.52588e11	0.447214
$6$	6.70852e11	0.0970803
$7$	−1.51681e13	−0.172510	−0.0862550	−	0.996273i	$-0.527490\pi$
$7$	−1.51681e13	−0.172510	−0.0862550	+	0.996273i	$0.527490\pi$
$8$	3.07591e14	0.386357
$9$	−4.20908e15	−0.757157
$10$	−2.78602e15	−0.0881016
$11$	−2.61480e17	−1.71577	−0.857887	−	0.513839i	$-0.828223\pi$
$11$	−2.61480e17	−1.71577	−0.857887	+	0.513839i	$0.828223\pi$
$12$	3.03363e17	0.473666
$13$	−3.70714e17	−0.154516	−0.0772580	−	0.997011i	$-0.524617\pi$
$13$	−3.70714e17	−0.154516	−0.0772580	+	0.997011i	$0.524617\pi$
$14$	2.76946e17	0.0339847
$15$	−5.60639e18	−0.220383
$16$	6.53072e19	0.885078
$17$	−3.71730e20	−1.85276	−0.926382	−	0.376585i	$-0.877098\pi$
$17$	−3.71730e20	−1.85276	−0.926382	+	0.376585i	$0.877098\pi$
$18$	7.68513e19	0.149161
$19$	1.42255e21	1.13145	0.565723	−	0.824595i	$-0.308597\pi$
$19$	1.42255e21	1.13145	0.565723	+	0.824595i	$0.308597\pi$
$20$	−1.25985e21	−0.429857
$21$	5.57308e20	0.0850113
$22$	4.77422e21	0.338009
$23$	−3.26990e22	−1.11180	−0.555898	−	0.831250i	$-0.687626\pi$
$23$	−3.26990e22	−1.11180	−0.555898	+	0.831250i	$0.687626\pi$
$24$	−1.13015e22	−0.190393
$25$	2.32831e22	0.200000
$26$	6.76865e21	0.0304398
$27$	3.58901e23	0.865911
$28$	1.25237e23	0.165815
$29$	6.41343e23	0.475909	0.237954	−	0.971276i	$-0.423523\pi$
$29$	6.41343e23	0.475909	0.237954	+	0.971276i	$0.423523\pi$
$30$	1.02364e23	0.0434156
$31$	−1.44554e23	−0.0356914	−0.0178457	−	0.999841i	$-0.505681\pi$
$31$	−1.44554e23	−0.0356914	−0.0178457	+	0.999841i	$0.505681\pi$
$32$	−3.83459e24	−0.560718
$33$	9.60732e24	0.845517
$34$	6.78720e24	0.364997
$35$	−2.31447e24	−0.0771488
$36$	3.47526e25	0.727772
$37$	1.34909e26	1.79768	0.898842	−	0.438273i	$-0.144410\pi$
$37$	1.34909e26	1.79768	0.898842	+	0.438273i	$0.144410\pi$
$38$	−2.59736e25	−0.222896
$39$	1.36208e25	0.0761440
$40$	4.69346e25	0.172784
$41$	6.37865e26	1.56241	0.781205	−	0.624275i	$-0.214605\pi$
$41$	6.37865e26	1.56241	0.781205	+	0.624275i	$0.214605\pi$
$42$	−1.01756e25	−0.0167473
$43$	3.37044e26	0.376233	0.188117	−	0.982147i	$-0.439762\pi$
$43$	3.37044e26	0.376233	0.188117	+	0.982147i	$0.439762\pi$
$44$	2.15893e27	1.64919
$45$	−6.42255e26	−0.338611
$46$	5.97033e26	0.219025
$47$	3.12828e27	0.804807	0.402403	−	0.915462i	$-0.368175\pi$
$47$	3.12828e27	0.804807	0.402403	+	0.915462i	$0.368175\pi$
$48$	−2.39952e27	−0.436158
$49$	−7.50092e27	−0.970240
$50$	−4.25112e26	−0.0394002
$51$	1.36581e28	0.913025
$52$	3.06082e27	0.148519
$53$	−4.06250e28	−1.43960	−0.719799	−	0.694182i	$-0.755766\pi$
$53$	−4.06250e28	−1.43960	−0.719799	+	0.694182i	$0.755766\pi$
$54$	−6.55298e27	−0.170585
$55$	−3.98988e28	−0.767317
$56$	−4.66557e27	−0.0666504
$57$	−5.22675e28	−0.557566
$58$	−1.17099e28	−0.0937545
$59$	−8.77955e28	−0.530169	−0.265084	−	0.964225i	$-0.585400\pi$
$59$	−8.77955e28	−0.530169	−0.265084	+	0.964225i	$0.585400\pi$
$60$	4.62895e28	0.211830
$61$	−1.84902e28	−0.0644168	−0.0322084	−	0.999481i	$-0.510254\pi$
$61$	−1.84902e28	−0.0644168	−0.0322084	+	0.999481i	$0.510254\pi$
$62$	2.63933e27	0.00703124
$63$	6.38439e28	0.130617
$64$	−4.90971e29	−0.774616
$65$	−5.65664e28	−0.0691016
$66$	−1.75415e29	−0.166568
$67$	7.69531e29	0.570154	0.285077	−	0.958505i	$-0.407981\pi$
$67$	7.69531e29	0.570154	0.285077	+	0.958505i	$0.407981\pi$
$68$	3.06921e30	1.78086
$69$	1.20143e30	0.547883
$70$	4.22586e28	0.0151984
$71$	2.72988e30	0.776929	0.388464	−	0.921464i	$-0.373006\pi$
$71$	2.72988e30	0.776929	0.388464	+	0.921464i	$0.373006\pi$
$72$	−1.29468e30	−0.292533
$73$	4.44452e30	0.799831	0.399915	−	0.916552i	$-0.369040\pi$
$73$	4.44452e30	0.799831	0.399915	+	0.916552i	$0.369040\pi$
$74$	−2.46323e30	−0.354146
$75$	−8.55467e29	−0.0985581
$76$	−1.17454e31	−1.08754
$77$	3.96617e30	0.295988
$78$	−2.48694e29	−0.0150005
$79$	−1.16758e31	−0.570743	−0.285371	−	0.958417i	$-0.592117\pi$
$79$	−1.16758e31	−0.570743	−0.285371	+	0.958417i	$0.592117\pi$
$80$	9.96509e30	0.395819
$81$	1.02118e31	0.330445
$82$	−1.16464e31	−0.307796
$83$	−4.84088e31	−1.04746	−0.523728	−	0.851886i	$-0.675459\pi$
$83$	−4.84088e31	−1.04746	−0.523728	+	0.851886i	$0.675459\pi$
$84$	−4.60145e30	−0.0817121
$85$	−5.67215e31	−0.828581
$86$	−6.15390e30	−0.0741184
$87$	−2.35643e31	−0.234523
$88$	−8.04290e31	−0.662901
$89$	1.18101e32	0.807831	0.403915	−	0.914796i	$-0.367649\pi$
$89$	1.18101e32	0.807831	0.403915	+	0.914796i	$0.367649\pi$
$90$	1.17266e31	0.0667067
$91$	5.62303e30	0.0266555
$92$	2.69981e32	1.06865
$93$	5.31122e30	0.0175884
$94$	−5.71176e31	−0.158548
$95$	2.17064e32	0.505998
$96$	1.40891e32	0.276317
$97$	−2.71846e31	−0.0449355	−0.0224678	−	0.999748i	$-0.507152\pi$
$97$	−2.71846e31	−0.0449355	−0.0224678	+	0.999748i	$0.507152\pi$
$98$	1.36955e32	0.191138
$99$	1.10059e33	1.29911
$100$	−1.92238e32	−0.192238
$101$	−1.30031e33	−1.10343	−0.551714	−	0.834033i	$-0.686026\pi$
$101$	−1.30031e33	−1.10343	−0.551714	+	0.834033i	$0.686026\pi$
$102$	−2.49376e32	−0.179867
$103$	1.73233e33	1.06369	0.531846	−	0.846841i	$-0.321498\pi$
$103$	1.73233e33	1.06369	0.531846	+	0.846841i	$0.321498\pi$
$104$	−1.14028e32	−0.0596983
$105$	8.50384e31	0.0380182
$106$	7.41749e32	0.283603
$107$	3.72062e32	0.121838	0.0609191	−	0.998143i	$-0.480597\pi$
$107$	3.72062e32	0.121838	0.0609191	+	0.998143i	$0.480597\pi$
$108$	−2.96329e33	−0.832305
$109$	−5.92448e33	−1.42927	−0.714633	−	0.699500i	$-0.753406\pi$
$109$	−5.92448e33	−1.42927	−0.714633	+	0.699500i	$0.753406\pi$
$110$	7.28489e32	0.151162
$111$	−4.95684e33	−0.885882
$112$	−9.90588e32	−0.152685
$113$	2.74196e33	0.364978	0.182489	−	0.983208i	$-0.441585\pi$
$113$	2.74196e33	0.364978	0.182489	+	0.983208i	$0.441585\pi$
$114$	9.54322e32	0.109841
$115$	−4.98947e33	−0.497210
$116$	−5.29529e33	−0.457439
$117$	1.56036e33	0.116993
$118$	1.60301e33	0.104444
$119$	5.63844e33	0.319620
$120$	−1.72447e33	−0.0851463
$121$	4.51469e34	1.94388
$122$	3.37602e32	0.0126902
$123$	−2.34364e34	−0.769941
$124$	1.19352e33	0.0343062
$125$	3.55271e33	0.0894427
$126$	−1.16569e33	−0.0257317
$127$	7.72774e34	1.49724	0.748619	−	0.663000i	$-0.230717\pi$
$127$	7.72774e34	1.49724	0.748619	+	0.663000i	$0.230717\pi$
$128$	4.19033e34	0.713318
$129$	−1.23837e34	−0.185404
$130$	1.03281e33	0.0136131
$131$	−1.77088e34	−0.205690	−0.102845	−	0.994697i	$-0.532795\pi$
$131$	−1.77088e34	−0.205690	−0.102845	+	0.994697i	$0.532795\pi$
$132$	−7.93235e34	−0.812703
$133$	−2.15774e34	−0.195186
$134$	−1.40504e34	−0.112321
$135$	5.47640e34	0.387247
$136$	−1.14341e35	−0.715828
$137$	−1.26744e35	−0.703133	−0.351567	−	0.936163i	$-0.614351\pi$
$137$	−1.26744e35	−0.703133	−0.351567	+	0.936163i	$0.614351\pi$
$138$	−2.19362e34	−0.107934
$139$	1.04160e35	0.454941	0.227471	−	0.973785i	$-0.426954\pi$
$139$	1.04160e35	0.454941	0.227471	+	0.973785i	$0.426954\pi$
$140$	1.91096e34	0.0741547
$141$	−1.14940e35	−0.396601
$142$	−4.98434e34	−0.153056
$143$	9.69344e34	0.265114
$144$	−2.74884e35	−0.670143
$145$	9.78612e34	0.212833
$146$	−8.11501e34	−0.157568
$147$	2.75599e35	0.478125
$148$	−1.11389e36	−1.72792
$149$	−3.09463e35	−0.429572	−0.214786	−	0.976661i	$-0.568905\pi$
$149$	−3.09463e35	−0.429572	−0.214786	+	0.976661i	$0.568905\pi$
$150$	1.56195e34	0.0194161
$151$	1.12720e36	1.25569	0.627844	−	0.778340i	$-0.283938\pi$
$151$	1.12720e36	1.25569	0.627844	+	0.778340i	$0.283938\pi$
$152$	4.37564e35	0.437142
$153$	1.56464e36	1.40283
$154$	−7.24160e34	−0.0583100
$155$	−2.20572e34	−0.0159617
$156$	−1.12461e35	−0.0731889
$157$	1.58631e36	0.929061	0.464530	−	0.885557i	$-0.346223\pi$
$157$	1.58631e36	0.929061	0.464530	+	0.885557i	$0.346223\pi$
$158$	2.13182e35	0.112437
$159$	1.49264e36	0.709421
$160$	−5.85112e35	−0.250761
$161$	4.95982e35	0.191796
$162$	−1.86451e35	−0.0650979
$163$	−3.56599e36	−1.12483	−0.562413	−	0.826857i	$-0.690127\pi$
$163$	−3.56599e36	−1.12483	−0.562413	+	0.826857i	$0.690127\pi$
$164$	−5.26657e36	−1.50177
$165$	1.46596e36	0.378127
$166$	8.83869e35	0.206350
$167$	6.77798e36	1.43311	0.716553	−	0.697532i	$-0.245719\pi$
$167$	6.77798e36	1.43311	0.716553	+	0.697532i	$0.245719\pi$
$168$	1.71423e35	0.0328447
$169$	−5.61870e36	−0.976125
$170$	1.03565e36	0.163231
$171$	−5.98764e36	−0.856683
$172$	−2.78283e36	−0.361632
$173$	1.72200e36	0.203364	0.101682	−	0.994817i	$-0.467578\pi$
$173$	1.72200e36	0.203364	0.101682	+	0.994817i	$0.467578\pi$
$174$	4.30247e35	0.0462014
$175$	−3.53160e35	−0.0345020
$176$	−1.70766e37	−1.51859
$177$	3.22578e36	0.261262
$178$	−2.15635e36	−0.159144
$179$	−6.69163e36	−0.450253	−0.225127	−	0.974330i	$-0.572280\pi$
$179$	−6.69163e36	−0.450253	−0.225127	+	0.974330i	$0.572280\pi$
$180$	5.30282e36	0.325470
$181$	1.34636e37	0.754163	0.377082	−	0.926180i	$-0.376928\pi$
$181$	1.34636e37	0.754163	0.377082	+	0.926180i	$0.376928\pi$
$182$	−1.02668e35	−0.00525117
$183$	6.79367e35	0.0317440
$184$	−1.00579e37	−0.429550
$185$	2.05855e37	0.803949
$186$	−9.69745e34	−0.00346493
$187$	9.72001e37	3.17892
$188$	−2.58289e37	−0.773573
$189$	−5.44386e36	−0.149378
$190$	−3.96325e36	−0.0996822
$191$	−6.65942e36	−0.153598	−0.0767990	−	0.997047i	$-0.524470\pi$
$191$	−6.65942e36	−0.153598	−0.0767990	+	0.997047i	$0.524470\pi$
$192$	1.80393e37	0.381723
$193$	−5.05982e37	−0.982742	−0.491371	−	0.870950i	$-0.663504\pi$
$193$	−5.05982e37	−0.982742	−0.491371	+	0.870950i	$0.663504\pi$
$194$	4.96349e35	0.00885235
$195$	2.07837e36	0.0340526
$196$	6.19318e37	0.932586
$197$	2.33016e37	0.322621	0.161311	−	0.986904i	$-0.448428\pi$
$197$	2.33016e37	0.322621	0.161311	+	0.986904i	$0.448428\pi$
$198$	−2.00951e37	−0.255926
$199$	−1.24079e38	−1.45420	−0.727100	−	0.686531i	$-0.759132\pi$
$199$	−1.24079e38	−1.45420	−0.727100	+	0.686531i	$0.759132\pi$
$200$	7.16165e36	0.0772713
$201$	−2.82742e37	−0.280967
$202$	2.37416e37	0.217377
$203$	−9.72798e36	−0.0820990
$204$	−1.12769e38	−0.877591
$205$	9.73304e37	0.698731
$206$	−3.16296e37	−0.209549
$207$	1.37633e38	0.841805
$208$	−2.42103e37	−0.136759
$209$	−3.71970e38	−1.94130
$210$	−1.55267e36	−0.00748963
$211$	−2.15498e38	−0.961133	−0.480567	−	0.876958i	$-0.659569\pi$
$211$	−2.15498e38	−0.961133	−0.480567	+	0.876958i	$0.659569\pi$
$212$	3.35423e38	1.38373
$213$	−1.00301e38	−0.382863
$214$	−6.79328e36	−0.0240023
$215$	5.14289e37	0.168257
$216$	1.10395e38	0.334550
$217$	2.19262e36	0.00615711
$218$	1.08172e38	0.281567
$219$	−1.63301e38	−0.394149
$220$	3.29427e38	0.737538
$221$	1.37805e38	0.286282
$222$	9.05042e37	0.174520
$223$	−1.94520e37	−0.0348285	−0.0174142	−	0.999848i	$-0.505543\pi$
$223$	−1.94520e37	−0.0348285	−0.0174142	+	0.999848i	$0.505543\pi$
$224$	5.81636e37	0.0967294
$225$	−9.80004e37	−0.151431
$226$	−5.00639e37	−0.0719011
$227$	1.37345e39	1.83395	0.916974	−	0.398947i	$-0.130624\pi$
$227$	1.37345e39	1.83395	0.916974	+	0.398947i	$0.130624\pi$
$228$	4.31550e38	0.535927
$229$	−3.69693e38	−0.427126	−0.213563	−	0.976929i	$-0.568507\pi$
$229$	−3.69693e38	−0.427126	−0.213563	+	0.976929i	$0.568507\pi$
$230$	9.10999e37	0.0979510
$231$	−1.45725e38	−0.145860
$232$	1.97271e38	0.183871
$233$	−2.02428e39	−1.75751	−0.878754	−	0.477275i	$-0.841625\pi$
$233$	−2.02428e39	−1.75751	−0.878754	+	0.477275i	$0.841625\pi$
$234$	−2.84898e37	−0.0230477
$235$	4.77338e38	0.359920
$236$	7.24889e38	0.509593
$237$	4.28994e38	0.281257
$238$	−1.02949e38	−0.0629655
$239$	−6.31944e38	−0.360673	−0.180336	−	0.983605i	$-0.557719\pi$
$239$	−6.31944e38	−0.360673	−0.180336	+	0.983605i	$0.557719\pi$
$240$	−3.66138e38	−0.195056
$241$	−1.82829e39	−0.909420	−0.454710	−	0.890640i	$-0.650257\pi$
$241$	−1.82829e39	−0.909420	−0.454710	+	0.890640i	$0.650257\pi$
$242$	−8.24311e38	−0.382946
$243$	−2.37036e39	−1.02875
$244$	1.52665e38	0.0619168
$245$	−1.14455e39	−0.433905
$246$	4.27913e38	0.151679
$247$	−5.27360e38	−0.174826
$248$	−4.44636e37	−0.0137896
$249$	1.77864e39	0.516177
$250$	−6.48670e37	−0.0176203
$251$	−2.17903e39	−0.554174	−0.277087	−	0.960845i	$-0.589369\pi$
$251$	−2.17903e39	−0.554174	−0.277087	+	0.960845i	$0.589369\pi$
$252$	−5.27131e38	−0.125548
$253$	8.55015e39	1.90759
$254$	−1.41096e39	−0.294958
$255$	2.08406e39	0.408317
$256$	3.45232e39	0.634091
$257$	−1.48926e39	−0.256492	−0.128246	−	0.991742i	$-0.540935\pi$
$257$	−1.48926e39	−0.256492	−0.128246	+	0.991742i	$0.540935\pi$
$258$	2.26107e38	0.0365249
$259$	−2.04632e39	−0.310118
$260$	4.67044e38	0.0664198
$261$	−2.69947e39	−0.360338
$262$	3.23335e38	0.0405211
$263$	1.17319e40	1.38069	0.690346	−	0.723479i	$-0.257458\pi$
$263$	1.17319e40	1.38069	0.690346	+	0.723479i	$0.257458\pi$
$264$	2.95512e39	0.326671
$265$	−6.19888e39	−0.643808
$266$	3.93970e38	0.0384518
$267$	−4.33929e39	−0.398091
$268$	−6.35369e39	−0.548027
$269$	2.30936e40	1.87318	0.936590	−	0.350428i	$-0.113964\pi$
$269$	2.30936e40	1.87318	0.936590	+	0.350428i	$0.113964\pi$
$270$	−9.99905e38	−0.0762881
$271$	2.16176e40	1.55172	0.775861	−	0.630903i	$-0.217316\pi$
$271$	2.16176e40	1.55172	0.775861	+	0.630903i	$0.217316\pi$
$272$	−2.42766e40	−1.63984
$273$	−2.06602e38	−0.0131356
$274$	2.31414e39	0.138518
$275$	−6.08807e39	−0.343155
$276$	−9.91967e39	−0.526620
$277$	−1.86721e40	−0.933847	−0.466924	−	0.884298i	$-0.654638\pi$
$277$	−1.86721e40	−0.933847	−0.466924	+	0.884298i	$0.654638\pi$
$278$	−1.90179e39	−0.0896239
$279$	6.08441e38	0.0270240
$280$	−7.11910e38	−0.0298070
$281$	−6.80173e39	−0.268513	−0.134256	−	0.990947i	$-0.542865\pi$
$281$	−6.80173e39	−0.268513	−0.134256	+	0.990947i	$0.542865\pi$
$282$	2.09862e39	0.0781309
$283$	−3.60211e40	−1.26497	−0.632485	−	0.774573i	$-0.717965\pi$
$283$	−3.60211e40	−1.26497	−0.632485	+	0.774573i	$0.717965\pi$
$284$	−2.25395e40	−0.746777
$285$	−7.97538e39	−0.249351
$286$	−1.76987e39	−0.0522278
$287$	−9.67521e39	−0.269531
$288$	1.61401e40	0.424552
$289$	9.79285e40	2.43274
$290$	−1.78679e39	−0.0419283
$291$	9.98819e38	0.0221438
$292$	−3.66965e40	−0.768790
$293$	6.02024e40	1.19206	0.596030	−	0.802962i	$-0.296744\pi$
$293$	6.02024e40	1.19206	0.596030	+	0.802962i	$0.296744\pi$
$294$	−5.03201e39	−0.0941912
$295$	−1.33965e40	−0.237099
$296$	4.14968e40	0.694547
$297$	−9.38457e40	−1.48571
$298$	5.65032e39	0.0846261
$299$	1.21220e40	0.171790
$300$	7.06322e39	0.0947332
$301$	−5.11233e39	−0.0649040
$302$	−2.05809e40	−0.247372
$303$	4.77760e40	0.543759
$304$	9.29029e40	1.00142
$305$	−2.82138e39	−0.0288081
$306$	−2.85679e40	−0.276360
$307$	2.05983e41	1.88820	0.944098	−	0.329664i	$-0.106936\pi$
$307$	2.05983e41	1.88820	0.944098	+	0.329664i	$0.106936\pi$
$308$	−3.27469e40	−0.284501
$309$	−6.36493e40	−0.524178
$310$	4.02731e38	0.00314446
$311$	−1.19843e41	−0.887294	−0.443647	−	0.896202i	$-0.646316\pi$
$311$	−1.19843e41	−0.887294	−0.443647	+	0.896202i	$0.646316\pi$
$312$	4.18962e39	0.0294188
$313$	2.13282e41	1.42060	0.710302	−	0.703897i	$-0.248558\pi$
$313$	2.13282e41	1.42060	0.710302	+	0.703897i	$0.248558\pi$
$314$	−2.89636e40	−0.183026
$315$	9.74180e39	0.0584138
$316$	9.64022e40	0.548593
$317$	−2.31538e41	−1.25068	−0.625338	−	0.780354i	$-0.715039\pi$
$317$	−2.31538e41	−1.25068	−0.625338	+	0.780354i	$0.715039\pi$
$318$	−2.72534e40	−0.139757
$319$	−1.67699e41	−0.816552
$320$	−7.49162e40	−0.346419
$321$	−1.36703e40	−0.0600407
$322$	−9.05586e39	−0.0377840
$323$	−5.28805e41	−2.09630
$324$	−8.43142e40	−0.317620
$325$	−8.63135e39	−0.0309032
$326$	6.51094e40	0.221592
$327$	2.17677e41	0.704329
$328$	1.96201e41	0.603647
$329$	−4.74502e40	−0.138837
$330$	−2.67662e40	−0.0744914
$331$	−3.27790e40	−0.0867830	−0.0433915	−	0.999058i	$-0.513816\pi$
$331$	−3.27790e40	−0.0867830	−0.0433915	+	0.999058i	$0.513816\pi$
$332$	3.99690e41	1.00680
$333$	−5.67844e41	−1.36113
$334$	−1.23755e41	−0.282324
$335$	1.17421e41	0.254981
$336$	3.63962e40	0.0752416
$337$	5.05149e41	0.994321	0.497160	−	0.867659i	$-0.334376\pi$
$337$	5.05149e41	0.994321	0.497160	+	0.867659i	$0.334376\pi$
$338$	1.02589e41	0.192298
$339$	−1.00745e41	−0.179858
$340$	4.68324e41	0.796425
$341$	3.77981e40	0.0612383
$342$	1.09325e41	0.168767
$343$	2.31040e41	0.339886
$344$	1.03672e41	0.145360
$345$	1.83323e41	0.245021
$346$	−3.14411e40	−0.0400629
$347$	5.54748e40	0.0673999	0.0337000	−	0.999432i	$-0.489271\pi$
$347$	5.54748e40	0.0673999	0.0337000	+	0.999432i	$0.489271\pi$
$348$	1.94560e41	0.225422
$349$	−4.36140e41	−0.481955	−0.240978	−	0.970531i	$-0.577468\pi$
$349$	−4.36140e41	−0.481955	−0.240978	+	0.970531i	$0.577468\pi$
$350$	6.44816e39	0.00679693
$351$	−1.33050e41	−0.133797
$352$	1.00267e42	0.962065
$353$	2.19124e41	0.200635	0.100318	−	0.994955i	$-0.468014\pi$
$353$	2.19124e41	0.200635	0.100318	+	0.994955i	$0.468014\pi$
$354$	−5.88978e40	−0.0514689
$355$	4.16547e41	0.347453
$356$	−9.75113e41	−0.776479
$357$	−2.07168e41	−0.157506
$358$	1.22179e41	0.0887004
$359$	−1.83249e42	−1.27053	−0.635264	−	0.772295i	$-0.719109\pi$
$359$	−1.83249e42	−1.27053	−0.635264	+	0.772295i	$0.719109\pi$
$360$	−1.97552e41	−0.130825
$361$	4.42885e41	0.280170
$362$	−2.45825e41	−0.148571
$363$	−1.65879e42	−0.957925
$364$	−4.64269e40	−0.0256211
$365$	6.78181e41	0.357695
$366$	−1.24042e40	−0.00625360
$367$	2.46022e42	1.18572	0.592862	−	0.805304i	$-0.297998\pi$
$367$	2.46022e42	1.18572	0.592862	+	0.805304i	$0.297998\pi$
$368$	−2.13548e42	−0.984026
$369$	−2.68483e42	−1.18299
$370$	−3.75859e41	−0.158379
$371$	6.16205e41	0.248345
$372$	−4.38524e40	−0.0169058
$373$	9.17264e41	0.338297	0.169149	−	0.985591i	$-0.445898\pi$
$373$	9.17264e41	0.338297	0.169149	+	0.985591i	$0.445898\pi$
$374$	−1.77472e42	−0.626251
$375$	−1.30534e41	−0.0440765
$376$	9.62231e41	0.310942
$377$	−2.37755e41	−0.0735355
$378$	9.93964e40	0.0294277
$379$	5.49346e42	1.55704	0.778518	−	0.627622i	$-0.215972\pi$
$379$	5.49346e42	1.55704	0.778518	+	0.627622i	$0.215972\pi$
$380$	−1.79220e42	−0.486361
$381$	−2.83933e42	−0.737825
$382$	1.21591e41	0.0302590
$383$	2.70725e42	0.645281	0.322640	−	0.946522i	$-0.395430\pi$
$383$	2.70725e42	0.645281	0.322640	+	0.946522i	$0.395430\pi$
$384$	−1.53961e42	−0.351517
$385$	6.05189e41	0.132370
$386$	9.23844e41	0.193601
$387$	−1.41865e42	−0.284868
$388$	2.24452e41	0.0431916
$389$	5.33079e42	0.983157	0.491579	−	0.870833i	$-0.336420\pi$
$389$	5.33079e42	0.983157	0.491579	+	0.870833i	$0.336420\pi$
$390$	−3.79477e40	−0.00670841
$391$	1.21552e43	2.05990
$392$	−2.30721e42	−0.374859
$393$	6.50657e41	0.101362
$394$	−4.25451e41	−0.0635568
$395$	−1.78159e42	−0.255244
$396$	−9.08712e42	−1.24869
$397$	8.08784e42	1.06608	0.533039	−	0.846091i	$-0.321050\pi$
$397$	8.08784e42	1.06608	0.533039	+	0.846091i	$0.321050\pi$
$398$	2.26550e42	0.286479
$399$	7.92799e41	0.0961857
$400$	1.52055e42	0.177016
$401$	−1.16113e43	−1.29717	−0.648587	−	0.761140i	$-0.724640\pi$
$401$	−1.16113e43	−1.29717	−0.648587	+	0.761140i	$0.724640\pi$
$402$	5.16242e41	0.0553507
$403$	5.35882e40	0.00551488
$404$	1.07361e43	1.06061
$405$	1.55819e42	0.147779
$406$	1.77618e41	0.0161736
$407$	−3.52761e43	−3.08442
$408$	4.20111e42	0.352753
$409$	4.40488e42	0.355222	0.177611	−	0.984101i	$-0.443163\pi$
$409$	4.40488e42	0.355222	0.177611	+	0.984101i	$0.443163\pi$
$410$	−1.77710e42	−0.137651
$411$	4.65683e42	0.346498
$412$	−1.43031e43	−1.02241
$413$	1.33169e42	0.0914594
$414$	−2.51296e42	−0.165836
$415$	−7.38660e42	−0.468437
$416$	1.42154e42	0.0866399
$417$	−3.82704e42	−0.224191
$418$	6.79158e42	0.382439
$419$	2.34926e43	1.27174	0.635871	−	0.771796i	$-0.280641\pi$
$419$	2.34926e43	1.27174	0.635871	+	0.771796i	$0.280641\pi$
$420$	−7.02125e41	−0.0365427
$421$	−4.10149e42	−0.205252	−0.102626	−	0.994720i	$-0.532724\pi$
$421$	−4.10149e42	−0.205252	−0.102626	+	0.994720i	$0.532724\pi$
$422$	3.93466e42	0.189344
$423$	−1.31672e43	−0.609365
$424$	−1.24959e43	−0.556199
$425$	−8.65501e42	−0.370553
$426$	1.83135e42	0.0754245
$427$	2.80461e41	0.0111125
$428$	−3.07196e42	−0.117110
$429$	−3.56157e42	−0.130646
$430$	−9.39011e41	−0.0331468
$431$	1.92923e43	0.655404	0.327702	−	0.944781i	$-0.393726\pi$
$431$	1.92923e43	0.655404	0.327702	+	0.944781i	$0.393726\pi$
$432$	2.34389e43	0.766398
$433$	1.20050e43	0.377843	0.188922	−	0.981992i	$-0.439501\pi$
$433$	1.20050e43	0.377843	0.188922	+	0.981992i	$0.439501\pi$
$434$	−4.00338e40	−0.00121296
$435$	−3.59562e42	−0.104882
$436$	4.89159e43	1.37380
$437$	−4.65160e43	−1.25794
$438$	2.98162e42	0.0776478
$439$	3.55254e43	0.890993	0.445496	−	0.895284i	$-0.353027\pi$
$439$	3.55254e43	0.890993	0.445496	+	0.895284i	$0.353027\pi$
$440$	−1.22725e43	−0.296458
$441$	3.15720e43	0.734625
$442$	−2.51611e42	−0.0563978
$443$	4.50074e43	0.971901	0.485951	−	0.873986i	$-0.338474\pi$
$443$	4.50074e43	0.971901	0.485951	+	0.873986i	$0.338474\pi$
$444$	4.09265e43	0.851501
$445$	1.80209e43	0.361273
$446$	3.55163e41	0.00686124
$447$	1.13703e43	0.211689
$448$	7.44711e42	0.133629
$449$	−4.48522e43	−0.775745	−0.387872	−	0.921713i	$-0.626790\pi$
$449$	−4.48522e43	−0.775745	−0.387872	+	0.921713i	$0.626790\pi$
$450$	1.78933e42	0.0298322
$451$	−1.66789e44	−2.68074
$452$	−2.26392e43	−0.350814
$453$	−4.14156e43	−0.618791
$454$	−2.50771e43	−0.361290
$455$	8.58006e41	0.0119207
$456$	−1.60770e43	−0.215419
$457$	5.99465e43	0.774723	0.387362	−	0.921928i	$-0.373386\pi$
$457$	5.99465e43	0.774723	0.387362	+	0.921928i	$0.373386\pi$
$458$	6.75002e42	0.0841442
$459$	−1.33414e44	−1.60433
$460$	4.11959e43	0.477914
$461$	3.64117e43	0.407546	0.203773	−	0.979018i	$-0.434680\pi$
$461$	3.64117e43	0.407546	0.203773	+	0.979018i	$0.434680\pi$
$462$	2.66071e42	0.0287346
$463$	−4.93497e43	−0.514278	−0.257139	−	0.966374i	$-0.582780\pi$
$463$	−4.93497e43	−0.514278	−0.257139	+	0.966374i	$0.582780\pi$
$464$	4.18844e43	0.421216
$465$	8.10428e41	0.00786576
$466$	3.69601e43	0.346231
$467$	6.19636e43	0.560284	0.280142	−	0.959959i	$-0.409619\pi$
$467$	6.19636e43	0.560284	0.280142	+	0.959959i	$0.409619\pi$
$468$	−1.28833e43	−0.112452
$469$	−1.16723e43	−0.0983572
$470$	−8.71545e42	−0.0709047
$471$	−5.82843e43	−0.457832
$472$	−2.70051e43	−0.204834
$473$	−8.81305e43	−0.645531
$474$	−7.83275e42	−0.0554079
$475$	3.31214e43	0.226289
$476$	−4.65542e43	−0.307216
$477$	1.70994e44	1.09000
$478$	1.15383e43	0.0710530
$479$	1.65648e44	0.985483	0.492741	−	0.870176i	$-0.335995\pi$
$479$	1.65648e44	0.985483	0.492741	+	0.870176i	$0.335995\pi$
$480$	2.14982e43	0.123573
$481$	−5.00127e43	−0.277771
$482$	3.33818e43	0.179157
$483$	−1.82234e43	−0.0945152
$484$	−3.72758e44	−1.86844
$485$	−4.14805e42	−0.0200958
$486$	4.32790e43	0.202665
$487$	3.41088e44	1.54397	0.771984	−	0.635642i	$-0.219264\pi$
$487$	3.41088e44	1.54397	0.771984	+	0.635642i	$0.219264\pi$
$488$	−5.68741e42	−0.0248879
$489$	1.31022e44	0.554303
$490$	2.08977e43	0.0854797
$491$	4.35160e44	1.72109	0.860547	−	0.509371i	$-0.170122\pi$
$491$	4.35160e44	1.72109	0.860547	+	0.509371i	$0.170122\pi$
$492$	1.93505e44	0.740060
$493$	−2.38406e44	−0.881747
$494$	9.62876e42	0.0344410
$495$	1.67937e44	0.580980
$496$	−9.44044e42	−0.0315896
$497$	−4.14072e43	−0.134028
$498$	−3.24751e43	−0.101687
$499$	−6.19626e44	−1.87703	−0.938514	−	0.345242i	$-0.887797\pi$
$499$	−6.19626e44	−1.87703	−0.938514	+	0.345242i	$0.887797\pi$
$500$	−2.93332e43	−0.0859715
$501$	−2.49037e44	−0.706222
$502$	3.97856e43	0.109173
$503$	5.28443e44	1.40322	0.701611	−	0.712560i	$-0.252464\pi$
$503$	5.28443e44	1.40322	0.701611	+	0.712560i	$0.252464\pi$
$504$	1.96378e43	0.0504648
$505$	−1.98412e44	−0.493468
$506$	−1.56112e44	−0.375797
$507$	2.06443e44	0.481025
$508$	−6.38046e44	−1.43913
$509$	−4.72823e43	−0.103242	−0.0516209	−	0.998667i	$-0.516439\pi$
$509$	−4.72823e43	−0.103242	−0.0516209	+	0.998667i	$0.516439\pi$
$510$	−3.80517e43	−0.0804389
$511$	−6.74151e43	−0.137979
$512$	−4.22980e44	−0.838235
$513$	5.10556e44	0.979731
$514$	2.71916e43	0.0505293
$515$	2.64332e44	0.475698
$516$	1.02247e44	0.178209
$517$	−8.17985e44	−1.38087
$518$	3.73626e43	0.0610937
$519$	−6.32699e43	−0.100216
$520$	−1.73993e43	−0.0266979
$521$	−4.38738e44	−0.652203	−0.326102	−	0.945335i	$-0.605735\pi$
$521$	−4.38738e44	−0.652203	−0.326102	+	0.945335i	$0.605735\pi$
$522$	4.92881e43	0.0709869
$523$	−1.40016e44	−0.195389	−0.0976944	−	0.995216i	$-0.531147\pi$
$523$	−1.40016e44	−0.195389	−0.0976944	+	0.995216i	$0.531147\pi$
$524$	1.46214e44	0.197707
$525$	1.29758e43	0.0170023
$526$	−2.14205e44	−0.271998
$527$	5.37351e43	0.0661277
$528$	6.27428e44	0.748349
$529$	2.04220e44	0.236091
$530$	1.13182e44	0.126831
$531$	3.69539e44	0.401421
$532$	1.78156e44	0.187611
$533$	−2.36465e44	−0.241417
$534$	7.92286e43	0.0784244
$535$	5.67722e43	0.0544877
$536$	2.36701e44	0.220283
$537$	2.45864e44	0.221881
$538$	−4.21653e44	−0.369018
$539$	1.96134e45	1.66471
$540$	−4.52163e44	−0.372218
$541$	1.56960e45	1.25324	0.626622	−	0.779324i	$-0.284437\pi$
$541$	1.56960e45	1.25324	0.626622	+	0.779324i	$0.284437\pi$
$542$	−3.94704e44	−0.305691
$543$	−4.94681e44	−0.371645
$544$	1.42543e45	1.03888
$545$	−9.04004e44	−0.639187
$546$	3.77222e42	0.00258773
$547$	−2.11683e45	−1.40895	−0.704474	−	0.709730i	$-0.748817\pi$
$547$	−2.11683e45	−1.40895	−0.704474	+	0.709730i	$0.748817\pi$
$548$	1.04647e45	0.675845
$549$	7.78267e43	0.0487736
$550$	1.11159e44	0.0676018
$551$	9.12345e44	0.538465
$552$	3.69548e44	0.211678
$553$	1.77100e44	0.0984588
$554$	3.40922e44	0.183969
$555$	−7.56354e44	−0.396178
$556$	−8.60001e44	−0.437285
$557$	−1.56733e45	−0.773661	−0.386830	−	0.922151i	$-0.626430\pi$
$557$	−1.56733e45	−0.773661	−0.386830	+	0.922151i	$0.626430\pi$
$558$	−1.11092e43	−0.00532375
$559$	−1.24947e44	−0.0581341
$560$	−1.51152e44	−0.0682827
$561$	−3.57133e45	−1.56654
$562$	1.24189e44	0.0528974
$563$	1.29413e44	0.0535291	0.0267646	−	0.999642i	$-0.491480\pi$
$563$	1.29413e44	0.0535291	0.0267646	+	0.999642i	$0.491480\pi$
$564$	9.49006e44	0.381209
$565$	4.18390e44	0.163223
$566$	6.57688e44	0.249200
$567$	−1.54894e44	−0.0570050
$568$	8.39687e44	0.300172
$569$	−2.93499e45	−1.01919	−0.509593	−	0.860415i	$-0.670204\pi$
$569$	−2.93499e45	−1.01919	−0.509593	+	0.860415i	$0.670204\pi$
$570$	1.45618e44	0.0491224
$571$	−9.20277e44	−0.301594	−0.150797	−	0.988565i	$-0.548184\pi$
$571$	−9.20277e44	−0.301594	−0.150797	+	0.988565i	$0.548184\pi$
$572$	−8.00345e44	−0.254825
$573$	2.44681e44	0.0756917
$574$	1.76654e44	0.0530979
$575$	−7.61333e44	−0.222359
$576$	2.06654e45	0.586506
$577$	−6.78370e45	−1.87097	−0.935483	−	0.353371i	$-0.885035\pi$
$577$	−6.78370e45	−1.87097	−0.935483	+	0.353371i	$0.885035\pi$
$578$	−1.78802e45	−0.479251
$579$	1.85908e45	0.484286
$580$	−8.07998e44	−0.204573
$581$	7.34270e44	0.180697
$582$	−1.82369e43	−0.00436236
$583$	1.06226e46	2.47003
$584$	1.36709e45	0.309020
$585$	2.38093e44	0.0523208
$586$	−1.09920e45	−0.234837
$587$	1.92291e45	0.399421	0.199710	−	0.979855i	$-0.436000\pi$
$587$	1.92291e45	0.399421	0.199710	+	0.979855i	$0.436000\pi$
$588$	−2.27550e45	−0.459570
$589$	−2.05636e44	−0.0403828
$590$	2.44600e44	0.0467087
$591$	−8.56148e44	−0.158985
$592$	8.81055e45	1.59109
$593$	−3.84061e45	−0.674524	−0.337262	−	0.941411i	$-0.609501\pi$
$593$	−3.84061e45	−0.674524	−0.337262	+	0.941411i	$0.609501\pi$
$594$	1.71348e45	0.292686
$595$	8.60358e44	0.142939
$596$	2.55510e45	0.412900
$597$	4.55893e45	0.716616
$598$	−2.21328e44	−0.0338429
$599$	−1.48464e45	−0.220840	−0.110420	−	0.993885i	$-0.535220\pi$
$599$	−1.48464e45	−0.220840	−0.110420	+	0.993885i	$0.535220\pi$
$600$	−2.63134e44	−0.0380786
$601$	5.01345e45	0.705843	0.352921	−	0.935653i	$-0.385188\pi$
$601$	5.01345e45	0.705843	0.352921	+	0.935653i	$0.385188\pi$
$602$	9.33431e43	0.0127862
$603$	−3.23902e45	−0.431696
$604$	−9.30680e45	−1.20695
$605$	6.88887e45	0.869329
$606$	−8.72316e44	−0.107121
$607$	3.29284e45	0.393511	0.196756	−	0.980453i	$-0.436959\pi$
$607$	3.29284e45	0.393511	0.196756	+	0.980453i	$0.436959\pi$
$608$	−5.45491e45	−0.634422
$609$	3.57426e44	0.0404576
$610$	5.15140e43	0.00567522
$611$	−1.15970e45	−0.124355
$612$	−1.29186e46	−1.34839
$613$	−1.00399e46	−1.02008	−0.510038	−	0.860152i	$-0.670369\pi$
$613$	−1.00399e46	−1.02008	−0.510038	+	0.860152i	$0.670369\pi$
$614$	−3.76092e45	−0.371977
$615$	−3.57612e45	−0.344328
$616$	1.21996e45	0.114357
$617$	1.43698e46	1.31144	0.655718	−	0.755006i	$-0.272366\pi$
$617$	1.43698e46	1.31144	0.655718	+	0.755006i	$0.272366\pi$
$618$	1.16214e45	0.103264
$619$	1.61224e46	1.39487	0.697435	−	0.716648i	$-0.254325\pi$
$619$	1.61224e46	1.39487	0.697435	+	0.716648i	$0.254325\pi$
$620$	1.82117e44	0.0153422
$621$	−1.17357e46	−0.962716
$622$	2.18815e45	0.174798
$623$	−1.79138e45	−0.139359
$624$	8.89535e44	0.0673934
$625$	5.42101e44	0.0400000
$626$	−3.89420e45	−0.279861
$627$	1.36669e46	0.956657
$628$	−1.30975e46	−0.893004
$629$	−5.01498e46	−3.33068
$630$	−1.77870e44	−0.0115076
$631$	2.47683e46	1.56103	0.780516	−	0.625136i	$-0.214957\pi$
$631$	2.47683e46	1.56103	0.780516	+	0.625136i	$0.214957\pi$
$632$	−3.59138e45	−0.220510
$633$	7.91785e45	0.473638
$634$	4.22752e45	0.246384
$635$	1.17916e46	0.669586
$636$	−1.23241e46	−0.681889
$637$	2.78069e45	0.149918
$638$	3.06192e45	0.160862
$639$	−1.14903e46	−0.588257
$640$	6.39393e45	0.319006
$641$	−3.57575e46	−1.73864	−0.869321	−	0.494249i	$-0.835443\pi$
$641$	−3.57575e46	−1.73864	−0.869321	+	0.494249i	$0.835443\pi$
$642$	2.49599e44	0.0118281
$643$	1.88292e46	0.869663	0.434831	−	0.900512i	$-0.356808\pi$
$643$	1.88292e46	0.869663	0.434831	+	0.900512i	$0.356808\pi$
$644$	−4.09511e45	−0.184352
$645$	−1.88960e45	−0.0829153
$646$	9.65515e45	0.412974
$647$	2.33501e46	0.973573	0.486787	−	0.873521i	$-0.338169\pi$
$647$	2.33501e46	0.973573	0.486787	+	0.873521i	$0.338169\pi$
$648$	3.14105e45	0.127669
$649$	2.29568e46	0.909649
$650$	1.57595e44	0.00608796
$651$	−8.05612e43	−0.00303417
$652$	2.94428e46	1.08117
$653$	2.35876e46	0.844531	0.422266	−	0.906472i	$-0.361235\pi$
$653$	2.35876e46	0.844531	0.422266	+	0.906472i	$0.361235\pi$
$654$	−3.97445e45	−0.138754
$655$	−2.70215e45	−0.0919873
$656$	4.16572e46	1.38285
$657$	−1.87074e46	−0.605598
$658$	8.66366e44	0.0273511
$659$	2.73242e46	0.841276	0.420638	−	0.907228i	$-0.361806\pi$
$659$	2.73242e46	0.841276	0.420638	+	0.907228i	$0.361806\pi$
$660$	−1.21038e46	−0.363452
$661$	−2.72690e46	−0.798629	−0.399315	−	0.916814i	$-0.630752\pi$
$661$	−2.72690e46	−0.798629	−0.399315	+	0.916814i	$0.630752\pi$
$662$	5.98494e44	0.0170963
$663$	−5.06325e45	−0.141077
$664$	−1.48901e46	−0.404692
$665$	−3.29246e45	−0.0872897
$666$	1.03679e46	0.268144
$667$	−2.09713e46	−0.529114
$668$	−5.59628e46	−1.37749
$669$	7.14706e44	0.0171631
$670$	−2.14393e45	−0.0502315
$671$	4.83482e45	0.110525
$672$	−2.13705e45	−0.0476674
$673$	−1.12643e46	−0.245163	−0.122581	−	0.992458i	$-0.539117\pi$
$673$	−1.12643e46	−0.245163	−0.122581	+	0.992458i	$0.539117\pi$
$674$	−9.22324e45	−0.195882
$675$	8.35633e45	0.173182
$676$	4.63912e46	0.938242
$677$	−4.69606e46	−0.926874	−0.463437	−	0.886130i	$-0.653384\pi$
$677$	−4.69606e46	−0.926874	−0.463437	+	0.886130i	$0.653384\pi$
$678$	1.83945e45	0.0354322
$679$	4.12340e44	0.00775183
$680$	−1.74470e46	−0.320128
$681$	−5.04634e46	−0.903753
$682$	−6.90134e44	−0.0120640
$683$	−1.23577e46	−0.210860	−0.105430	−	0.994427i	$-0.533622\pi$
$683$	−1.23577e46	−0.210860	−0.105430	+	0.994427i	$0.533622\pi$
$684$	4.94373e46	0.823435
$685$	−1.93396e46	−0.314451
$686$	−4.21842e45	−0.0669579
$687$	1.35833e46	0.210484
$688$	2.20114e46	0.332996
$689$	1.50602e46	0.222441
$690$	−3.34720e45	−0.0482693
$691$	−3.45406e46	−0.486342	−0.243171	−	0.969983i	$-0.578188\pi$
$691$	−3.45406e46	−0.486342	−0.243171	+	0.969983i	$0.578188\pi$
$692$	−1.42178e46	−0.195471
$693$	−1.66939e46	−0.224109
$694$	−1.01288e45	−0.0132779
$695$	1.58935e46	0.203456
$696$	−7.24815e45	−0.0906097
$697$	−2.37113e47	−2.89478
$698$	7.96324e45	0.0949457
$699$	7.43761e46	0.866084
$700$	2.91589e45	0.0331630
$701$	4.58600e46	0.509433	0.254716	−	0.967016i	$-0.418018\pi$
$701$	4.58600e46	0.509433	0.254716	+	0.967016i	$0.418018\pi$
$702$	2.42928e45	0.0263582
$703$	1.91915e47	2.03398
$704$	1.28379e47	1.32907
$705$	−1.75384e46	−0.177365
$706$	−4.00086e45	−0.0395254
$707$	1.97233e46	0.190352
$708$	−2.66339e46	−0.251123
$709$	1.01825e46	0.0937978	0.0468989	−	0.998900i	$-0.485066\pi$
$709$	1.01825e46	0.0937978	0.0468989	+	0.998900i	$0.485066\pi$
$710$	−7.60550e45	−0.0684486
$711$	4.91445e46	0.432142
$712$	3.63269e46	0.312111
$713$	4.72678e45	0.0396815
$714$	3.78256e45	0.0310288
$715$	1.47910e46	0.118563
$716$	5.52498e46	0.432779
$717$	2.32189e46	0.177736
$718$	3.34585e46	0.250295
$719$	−2.37751e46	−0.173818	−0.0869092	−	0.996216i	$-0.527699\pi$
$719$	−2.37751e46	−0.173818	−0.0869092	+	0.996216i	$0.527699\pi$
$720$	−4.19439e46	−0.299697
$721$	−2.62762e46	−0.183498
$722$	−8.08638e45	−0.0551938
$723$	6.71752e46	0.448154
$724$	−1.11163e47	−0.724895
$725$	1.49324e46	0.0951818
$726$	3.02869e46	0.188712
$727$	−7.60235e46	−0.463053	−0.231526	−	0.972829i	$-0.574372\pi$
$727$	−7.60235e46	−0.463053	−0.231526	+	0.972829i	$0.574372\pi$
$728$	1.72959e45	0.0102985
$729$	3.03238e46	0.176514
$730$	−1.23825e46	−0.0704663
$731$	−1.25289e47	−0.697072
$732$	−5.60924e45	−0.0305120
$733$	−9.46431e46	−0.503354	−0.251677	−	0.967811i	$-0.580982\pi$
$733$	−9.46431e46	−0.503354	−0.251677	+	0.967811i	$0.580982\pi$
$734$	−4.49197e46	−0.233589
$735$	4.20531e46	0.213824
$736$	1.25387e47	0.623404
$737$	−2.01217e47	−0.978255
$738$	4.90207e46	0.233050
$739$	1.36554e46	0.0634851	0.0317425	−	0.999496i	$-0.489894\pi$
$739$	1.36554e46	0.0634851	0.0317425	+	0.999496i	$0.489894\pi$
$740$	−1.69966e47	−0.772748
$741$	1.93763e46	0.0861529
$742$	−1.12509e46	−0.0489243
$743$	2.14591e47	0.912632	0.456316	−	0.889818i	$-0.349169\pi$
$743$	2.14591e47	0.912632	0.456316	+	0.889818i	$0.349169\pi$
$744$	1.63368e45	0.00679538
$745$	−4.72203e46	−0.192110
$746$	−1.67478e46	−0.0666449
$747$	2.03757e47	0.793089
$748$	−8.02539e47	−3.05555
$749$	−5.64349e45	−0.0210183
$750$	2.38335e45	0.00868313
$751$	−3.00124e47	−1.06965	−0.534825	−	0.844963i	$-0.679622\pi$
$751$	−3.00124e47	−1.06965	−0.534825	+	0.844963i	$0.679622\pi$
$752$	2.04300e47	0.712317
$753$	8.00619e46	0.273092
$754$	4.34103e45	0.0144866
$755$	1.71997e47	0.561560
$756$	4.49476e46	0.143581
$757$	3.75997e47	1.17517	0.587587	−	0.809161i	$-0.300078\pi$
$757$	3.75997e47	1.17517	0.587587	+	0.809161i	$0.300078\pi$
$758$	−1.00302e47	−0.306738
$759$	−3.14150e47	−0.940043
$760$	6.67670e46	0.195496
$761$	2.05125e47	0.587723	0.293861	−	0.955848i	$-0.405060\pi$
$761$	2.05125e47	0.587723	0.293861	+	0.955848i	$0.405060\pi$
$762$	5.18417e46	0.145352
$763$	8.98632e46	0.246563
$764$	5.49839e46	0.147637
$765$	2.38745e47	0.627366
$766$	−4.94302e46	−0.127121
$767$	3.25470e46	0.0819195
$768$	−1.26845e47	−0.312474
$769$	−3.91739e47	−0.944522	−0.472261	−	0.881459i	$-0.656562\pi$
$769$	−3.91739e47	−0.944522	−0.472261	+	0.881459i	$0.656562\pi$
$770$	−1.10498e46	−0.0260770
$771$	5.47185e46	0.126397
$772$	4.17767e47	0.944602
$773$	6.18683e47	1.36933	0.684663	−	0.728860i	$-0.259949\pi$
$773$	6.18683e47	1.36933	0.684663	+	0.728860i	$0.259949\pi$
$774$	2.59023e46	0.0561193
$775$	−3.36567e45	−0.00713827
$776$	−8.36174e45	−0.0173611
$777$	7.51860e46	0.152823
$778$	−9.73319e46	−0.193683
$779$	9.07396e47	1.76778
$780$	−1.71602e46	−0.0327311
$781$	−7.13811e47	−1.33303
$782$	−2.21935e47	−0.405802
$783$	2.30179e47	0.412095
$784$	−4.89864e47	−0.858738
$785$	2.42052e47	0.415488
$786$	−1.18800e46	−0.0199684
$787$	2.50651e45	0.00412559	0.00206280	−	0.999998i	$-0.499343\pi$
$787$	2.50651e45	0.00412559	0.00206280	+	0.999998i	$0.499343\pi$
$788$	−1.92391e47	−0.310101
$789$	−4.31052e47	−0.680392
$790$	3.25290e46	0.0502833
$791$	−4.15904e46	−0.0629624
$792$	3.38532e47	0.501920
$793$	6.85457e45	0.00995342
$794$	−1.47671e47	−0.210019
$795$	2.27760e47	0.317263
$796$	1.02447e48	1.39776
$797$	7.37335e47	0.985378	0.492689	−	0.870206i	$-0.336014\pi$
$797$	7.37335e47	0.985378	0.492689	+	0.870206i	$0.336014\pi$
$798$	−1.44753e46	−0.0189487
$799$	−1.16288e48	−1.49112
$800$	−8.92811e46	−0.112144
$801$	−4.97099e47	−0.611655
$802$	2.12004e47	0.255545
$803$	−1.16216e48	−1.37233
$804$	2.33447e47	0.270062
$805$	7.56809e46	0.0857737
$806$	−9.78438e44	−0.00108644
$807$	−8.48506e47	−0.923085
$808$	−3.99963e47	−0.426317
$809$	−9.92771e47	−1.03681	−0.518404	−	0.855136i	$-0.673474\pi$
$809$	−9.92771e47	−1.03681	−0.518404	+	0.855136i	$0.673474\pi$
$810$	−2.84502e46	−0.0291127
$811$	1.07185e47	0.107470	0.0537351	−	0.998555i	$-0.482887\pi$
$811$	1.07185e47	0.107470	0.0537351	+	0.998555i	$0.482887\pi$
$812$	8.03197e46	0.0789128
$813$	−7.94274e47	−0.764674
$814$	6.44087e47	0.607634
$815$	−5.44127e47	−0.503037
$816$	8.91973e47	0.808098
$817$	4.79463e47	0.425688
$818$	−8.04262e46	−0.0699791
$819$	−2.36678e46	−0.0201824
$820$	−8.03615e47	−0.671614
$821$	−1.20939e48	−0.990610	−0.495305	−	0.868719i	$-0.664944\pi$
$821$	−1.20939e48	−0.990610	−0.495305	+	0.868719i	$0.664944\pi$
$822$	−8.50264e46	−0.0682604
$823$	2.45743e48	1.93367	0.966837	−	0.255396i	$-0.0822059\pi$
$823$	2.45743e48	1.93367	0.966837	+	0.255396i	$0.0822059\pi$
$824$	5.32848e47	0.410965
$825$	2.23688e47	0.169103
$826$	−2.43146e46	−0.0180176
$827$	−1.80057e48	−1.30789	−0.653943	−	0.756544i	$-0.726886\pi$
$827$	−1.80057e48	−1.30789	−0.653943	+	0.756544i	$0.726886\pi$
$828$	−1.13637e48	−0.809135
$829$	6.57735e47	0.459094	0.229547	−	0.973298i	$-0.426276\pi$
$829$	6.57735e47	0.459094	0.229547	+	0.973298i	$0.426276\pi$
$830$	1.34868e47	0.0922825
$831$	6.86049e47	0.460191
$832$	1.82010e47	0.119691
$833$	2.78832e48	1.79763
$834$	6.98757e46	0.0441658
$835$	1.03424e48	0.640905
$836$	3.07119e48	1.86596
$837$	−5.18807e46	−0.0309055
$838$	−4.28937e47	−0.250534
$839$	6.26140e47	0.358591	0.179295	−	0.983795i	$-0.442618\pi$
$839$	6.26140e47	0.358591	0.179295	+	0.983795i	$0.442618\pi$
$840$	2.61570e46	0.0146886
$841$	−1.40475e48	−0.773511
$842$	7.48868e46	0.0404348
$843$	2.49910e47	0.132321
$844$	1.77928e48	0.923832
$845$	−8.57346e47	−0.436536
$846$	2.40413e47	0.120046
$847$	−6.84793e47	−0.335338
$848$	−2.65311e48	−1.27416
$849$	1.32349e48	0.623365
$850$	1.58027e47	0.0729993
$851$	−4.41140e48	−1.99866
$852$	8.28145e47	0.368005
$853$	3.16331e48	1.37874	0.689370	−	0.724410i	$-0.257888\pi$
$853$	3.16331e48	1.37874	0.689370	+	0.724410i	$0.257888\pi$
$854$	−5.12079e45	−0.00218918
$855$	−9.13642e47	−0.383120
$856$	1.14443e47	0.0470730
$857$	−3.13666e48	−1.26556	−0.632782	−	0.774330i	$-0.718087\pi$
$857$	−3.13666e48	−1.26556	−0.632782	+	0.774330i	$0.718087\pi$
$858$	6.50286e46	0.0257374
$859$	2.20270e48	0.855202	0.427601	−	0.903968i	$-0.359359\pi$
$859$	2.20270e48	0.855202	0.427601	+	0.903968i	$0.359359\pi$
$860$	−4.24626e47	−0.161727
$861$	3.55487e47	0.132822
$862$	−3.52247e47	−0.129115
$863$	5.00806e47	0.180091	0.0900453	−	0.995938i	$-0.471299\pi$
$863$	5.00806e47	0.180091	0.0900453	+	0.995938i	$0.471299\pi$
$864$	−1.37624e48	−0.485532
$865$	2.62757e47	0.0909470
$866$	−2.19192e47	−0.0744356
$867$	−3.59809e48	−1.19883
$868$	−1.81035e46	−0.00591816
$869$	3.05300e48	0.979266
$870$	6.56504e46	0.0206619
$871$	−2.85276e47	−0.0880979
$872$	−1.82232e48	−0.552207
$873$	1.14422e47	0.0340233
$874$	8.49310e47	0.247815
$875$	−5.38880e46	−0.0154298
$876$	1.34830e48	0.378852
$877$	−1.77120e48	−0.488400	−0.244200	−	0.969725i	$-0.578525\pi$
$877$	−1.77120e48	−0.488400	−0.244200	+	0.969725i	$0.578525\pi$
$878$	−6.48638e47	−0.175527
$879$	−2.21196e48	−0.587436
$880$	−2.60568e48	−0.679135
$881$	1.59935e48	0.409111	0.204555	−	0.978855i	$-0.434425\pi$
$881$	1.59935e48	0.409111	0.204555	+	0.978855i	$0.434425\pi$
$882$	−5.76455e47	−0.144722
$883$	−2.38704e48	−0.588177	−0.294089	−	0.955778i	$-0.595016\pi$
$883$	−2.38704e48	−0.588177	−0.294089	+	0.955778i	$0.595016\pi$
$884$	−1.13780e48	−0.275171
$885$	4.92216e47	0.116840
$886$	−8.21764e47	−0.191466
$887$	5.13361e48	1.17404	0.587020	−	0.809572i	$-0.300301\pi$
$887$	5.13361e48	1.17404	0.587020	+	0.809572i	$0.300301\pi$
$888$	−1.52468e48	−0.342266
$889$	−1.17215e48	−0.258289
$890$	−3.29033e47	−0.0711711
$891$	−2.67018e48	−0.566968
$892$	1.60607e47	0.0334768
$893$	4.45015e48	0.910595
$894$	−2.07604e47	−0.0417030
$895$	−1.02106e48	−0.201359
$896$	−6.35594e47	−0.123054
$897$	−4.45386e47	−0.0846566
$898$	8.18931e47	0.152823
$899$	−9.27089e46	−0.0169858
$900$	8.09146e47	0.145554
$901$	1.51015e49	2.66724
$902$	3.04531e48	0.528109
$903$	1.87837e47	0.0319841
$904$	8.43402e47	0.141012
$905$	2.05439e48	0.337272
$906$	7.56185e47	0.121903
$907$	5.18589e48	0.820924	0.410462	−	0.911878i	$-0.365368\pi$
$907$	5.18589e48	0.820924	0.410462	+	0.911878i	$0.365368\pi$
$908$	−1.13400e49	−1.76277
$909$	5.47311e48	0.835469
$910$	−1.56659e46	−0.00234839
$911$	−6.63747e48	−0.977123	−0.488562	−	0.872529i	$-0.662478\pi$
$911$	−6.63747e48	−0.977123	−0.488562	+	0.872529i	$0.662478\pi$
$912$	−3.41344e48	−0.493489
$913$	1.26580e49	1.79720
$914$	−1.09453e48	−0.152621
$915$	1.03663e47	0.0141963
$916$	3.05239e48	0.410549
$917$	2.68609e47	0.0354835
$918$	2.43594e48	0.316054
$919$	−7.10984e48	−0.906054	−0.453027	−	0.891497i	$-0.649656\pi$
$919$	−7.10984e48	−0.906054	−0.453027	+	0.891497i	$0.649656\pi$
$920$	−1.53472e48	−0.192101
$921$	−7.56822e48	−0.930486
$922$	−6.64821e47	−0.0802869
$923$	−1.01200e48	−0.120048
$924$	1.20319e48	0.140199
$925$	3.14110e48	0.359537
$926$	9.01048e47	0.101313
$927$	−7.29151e48	−0.805382
$928$	−2.45929e48	−0.266851
$929$	−1.17316e49	−1.25054	−0.625272	−	0.780407i	$-0.715012\pi$
$929$	−1.17316e49	−1.25054	−0.625272	+	0.780407i	$0.715012\pi$
$930$	−1.47971e46	−0.00154956
$931$	−1.06705e49	−1.09777
$932$	1.67136e49	1.68930
$933$	4.40329e48	0.437250
$934$	−1.13136e48	−0.110376
$935$	1.48316e49	1.42166
$936$	4.79954e47	0.0452010
$937$	7.60807e48	0.703998	0.351999	−	0.936000i	$-0.385502\pi$
$937$	7.60807e48	0.703998	0.351999	+	0.936000i	$0.385502\pi$
$938$	2.13119e47	0.0193765
$939$	−7.83643e48	−0.700061
$940$	−3.94117e48	−0.345952
$941$	−5.90432e48	−0.509262	−0.254631	−	0.967038i	$-0.581954\pi$
$941$	−5.90432e48	−0.509262	−0.254631	+	0.967038i	$0.581954\pi$
$942$	1.06418e48	0.0901935
$943$	−2.08575e49	−1.73708
$944$	−5.73368e48	−0.469241
$945$	−8.30667e47	−0.0668040
$946$	1.60912e48	0.127170
$947$	−7.50195e47	−0.0582639	−0.0291319	−	0.999576i	$-0.509274\pi$
$947$	−7.50195e47	−0.0582639	−0.0291319	+	0.999576i	$0.509274\pi$
$948$	−3.54201e48	−0.270341
$949$	−1.64765e48	−0.123587
$950$	−6.04745e47	−0.0445792
$951$	8.50718e48	0.616321
$952$	1.73433e48	0.123487
$953$	−1.06031e49	−0.741993	−0.370997	−	0.928634i	$-0.620984\pi$
$953$	−1.06031e49	−0.741993	−0.370997	+	0.928634i	$0.620984\pi$
$954$	−3.12208e48	−0.214732
$955$	−1.01615e48	−0.0686911
$956$	5.21769e48	0.346675
$957$	6.16159e48	0.402389
$958$	−3.02447e48	−0.194141
$959$	1.92247e48	0.121297
$960$	2.75258e48	0.170712
$961$	−1.63826e49	−0.998726
$962$	9.13154e47	0.0547212
$963$	−1.56604e48	−0.0922507
$964$	1.50954e49	0.874126
$965$	−7.72067e48	−0.439496
$966$	3.32731e47	0.0186196
$967$	−3.31961e48	−0.182621	−0.0913104	−	0.995822i	$-0.529106\pi$
$967$	−3.31961e48	−0.182621	−0.0913104	+	0.995822i	$0.529106\pi$
$968$	1.38868e49	0.751030
$969$	1.94294e49	1.03304
$970$	7.57368e46	0.00395889
$971$	1.67736e49	0.862003	0.431001	−	0.902351i	$-0.358160\pi$
$971$	1.67736e49	0.862003	0.431001	+	0.902351i	$0.358160\pi$
$972$	1.95710e49	0.988826
$973$	−1.57991e48	−0.0784819
$974$	−6.22773e48	−0.304164
$975$	3.17133e47	0.0152288
$976$	−1.20754e48	−0.0570139
$977$	2.50785e49	1.16424	0.582118	−	0.813104i	$-0.302224\pi$
$977$	2.50785e49	1.16424	0.582118	+	0.813104i	$0.302224\pi$
$978$	−2.39225e48	−0.109198
$979$	−3.08812e49	−1.38605
$980$	9.45005e48	0.417065
$981$	2.49366e49	1.08218
$982$	−7.94535e48	−0.339058
$983$	1.24304e49	0.521616	0.260808	−	0.965391i	$-0.416011\pi$
$983$	1.24304e49	0.521616	0.260808	+	0.965391i	$0.416011\pi$
$984$	−7.20883e48	−0.297472
$985$	3.55554e48	0.144281
$986$	4.35293e48	0.173705
$987$	1.74342e48	0.0684177
$988$	4.35418e48	0.168042
$989$	−1.10210e49	−0.418295
$990$	−3.06627e48	−0.114454
$991$	−2.48644e49	−0.912774	−0.456387	−	0.889781i	$-0.650857\pi$
$991$	−2.48644e49	−0.912774	−0.456387	+	0.889781i	$0.650857\pi$
$992$	5.54307e47	0.0200128
$993$	1.20437e48	0.0427658
$994$	7.56031e47	0.0264037
$995$	−1.89330e49	−0.650338
$996$	−1.46854e49	−0.496144
$997$	−2.01041e49	−0.668058	−0.334029	−	0.942563i	$-0.608408\pi$
$997$	−2.01041e49	−0.668058	−0.334029	+	0.942563i	$0.608408\pi$
$998$	1.13134e49	0.369777
$999$	4.84191e49	1.55663

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.34.a.b.1.3	✓	6
5.2	odd	4		25.34.b.c.24.6		12
5.3	odd	4		25.34.b.c.24.7		12
5.4	even	2		25.34.a.c.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.b.1.3	✓	6	1.1	even	1	trivial
25.34.a.c.1.4		6	5.4	even	2
25.34.b.c.24.6		12	5.2	odd	4
25.34.b.c.24.7		12	5.3	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-18258.4 q^{2} -3.67420e7 q^{3} -8.25656e9 q^{4} +1.52588e11 q^{5} +6.70852e11 q^{6} -1.51681e13 q^{7} +3.07591e14 q^{8} -4.20908e15 q^{9} +O(q^{10})\)	\(q-18258.4 q^{2} -3.67420e7 q^{3} -8.25656e9 q^{4} +1.52588e11 q^{5} +6.70852e11 q^{6} -1.51681e13 q^{7} +3.07591e14 q^{8} -4.20908e15 q^{9} -2.78602e15 q^{10} -2.61480e17 q^{11} +3.03363e17 q^{12} -3.70714e17 q^{13} +2.76946e17 q^{14} -5.60639e18 q^{15} +6.53072e19 q^{16} -3.71730e20 q^{17} +7.68513e19 q^{18} +1.42255e21 q^{19} -1.25985e21 q^{20} +5.57308e20 q^{21} +4.77422e21 q^{22} -3.26990e22 q^{23} -1.13015e22 q^{24} +2.32831e22 q^{25} +6.76865e21 q^{26} +3.58901e23 q^{27} +1.25237e23 q^{28} +6.41343e23 q^{29} +1.02364e23 q^{30} -1.44554e23 q^{31} -3.83459e24 q^{32} +9.60732e24 q^{33} +6.78720e24 q^{34} -2.31447e24 q^{35} +3.47526e25 q^{36} +1.34909e26 q^{37} -2.59736e25 q^{38} +1.36208e25 q^{39} +4.69346e25 q^{40} +6.37865e26 q^{41} -1.01756e25 q^{42} +3.37044e26 q^{43} +2.15893e27 q^{44} -6.42255e26 q^{45} +5.97033e26 q^{46} +3.12828e27 q^{47} -2.39952e27 q^{48} -7.50092e27 q^{49} -4.25112e26 q^{50} +1.36581e28 q^{51} +3.06082e27 q^{52} -4.06250e28 q^{53} -6.55298e27 q^{54} -3.98988e28 q^{55} -4.66557e27 q^{56} -5.22675e28 q^{57} -1.17099e28 q^{58} -8.77955e28 q^{59} +4.62895e28 q^{60} -1.84902e28 q^{61} +2.63933e27 q^{62} +6.38439e28 q^{63} -4.90971e29 q^{64} -5.65664e28 q^{65} -1.75415e29 q^{66} +7.69531e29 q^{67} +3.06921e30 q^{68} +1.20143e30 q^{69} +4.22586e28 q^{70} +2.72988e30 q^{71} -1.29468e30 q^{72} +4.44452e30 q^{73} -2.46323e30 q^{74} -8.55467e29 q^{75} -1.17454e31 q^{76} +3.96617e30 q^{77} -2.48694e29 q^{78} -1.16758e31 q^{79} +9.96509e30 q^{80} +1.02118e31 q^{81} -1.16464e31 q^{82} -4.84088e31 q^{83} -4.60145e30 q^{84} -5.67215e31 q^{85} -6.15390e30 q^{86} -2.35643e31 q^{87} -8.04290e31 q^{88} +1.18101e32 q^{89} +1.17266e31 q^{90} +5.62303e30 q^{91} +2.69981e32 q^{92} +5.31122e30 q^{93} -5.71176e31 q^{94} +2.17064e32 q^{95} +1.40891e32 q^{96} -2.71846e31 q^{97} +1.36955e32 q^{98} +1.10059e33 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 147350 q^{2} + 26513900 q^{3} + 29520645652 q^{4} + 915527343750 q^{5} + 6615759249352 q^{6} + 19113832847500 q^{7} + 30\!\cdots\!00 q^{8}+ \cdots + 13\!\cdots\!38 q^{9}+O(q^{10}) \) 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

Varieties

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