LMFDB - Embedded newform 5.34.a.b.1.6

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			1.6
Root			$77152.3$ 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)

$f(q)$	$=$	$q+178863. q^{2} +8.55112e7 q^{3} +2.34019e10 q^{4} +1.52588e11 q^{5} +1.52948e13 q^{6} -8.09549e13 q^{7} +2.64931e15 q^{8} +1.75311e15 q^{9} +O(q^{10})$	\(q+178863. q^{2} +8.55112e7 q^{3} +2.34019e10 q^{4} +1.52588e11 q^{5} +1.52948e13 q^{6} -8.09549e13 q^{7} +2.64931e15 q^{8} +1.75311e15 q^{9} +2.72923e16 q^{10} +1.95800e17 q^{11} +2.00113e18 q^{12} -2.59207e18 q^{13} -1.44798e19 q^{14} +1.30480e19 q^{15} +2.72841e20 q^{16} -1.52177e20 q^{17} +3.13565e20 q^{18} +1.39526e21 q^{19} +3.57085e21 q^{20} -6.92255e21 q^{21} +3.50214e22 q^{22} -3.40316e22 q^{23} +2.26546e23 q^{24} +2.32831e22 q^{25} -4.63625e23 q^{26} -3.25452e23 q^{27} -1.89450e24 q^{28} -1.49246e24 q^{29} +2.33380e24 q^{30} -1.38398e24 q^{31} +2.60438e25 q^{32} +1.67431e25 q^{33} -2.72188e25 q^{34} -1.23527e25 q^{35} +4.10261e25 q^{36} +1.15380e26 q^{37} +2.49559e26 q^{38} -2.21651e26 q^{39} +4.04252e26 q^{40} -6.35087e25 q^{41} -1.23819e27 q^{42} -2.64294e26 q^{43} +4.58211e27 q^{44} +2.67503e26 q^{45} -6.08698e27 q^{46} +1.03700e27 q^{47} +2.33310e28 q^{48} -1.17730e27 q^{49} +4.16447e27 q^{50} -1.30128e28 q^{51} -6.06594e28 q^{52} +5.20280e28 q^{53} -5.82111e28 q^{54} +2.98768e28 q^{55} -2.14475e29 q^{56} +1.19310e29 q^{57} -2.66946e29 q^{58} -6.17754e28 q^{59} +3.05348e29 q^{60} -1.21654e29 q^{61} -2.47543e29 q^{62} -1.41923e29 q^{63} +2.31456e30 q^{64} -3.95519e29 q^{65} +2.99472e30 q^{66} -2.87484e29 q^{67} -3.56123e30 q^{68} -2.91008e30 q^{69} -2.20944e30 q^{70} -2.84409e30 q^{71} +4.64452e30 q^{72} -2.67045e30 q^{73} +2.06372e31 q^{74} +1.99096e30 q^{75} +3.26517e31 q^{76} -1.58510e31 q^{77} -3.96451e31 q^{78} -7.84640e30 q^{79} +4.16323e31 q^{80} -3.75754e31 q^{81} -1.13593e31 q^{82} +1.28723e31 q^{83} -1.62001e32 q^{84} -2.32203e31 q^{85} -4.72724e31 q^{86} -1.27622e32 q^{87} +5.18736e32 q^{88} -1.56902e32 q^{89} +4.78463e31 q^{90} +2.09841e32 q^{91} -7.96404e32 q^{92} -1.18346e32 q^{93} +1.85481e32 q^{94} +2.12899e32 q^{95} +2.22703e33 q^{96} +4.84738e32 q^{97} -2.10574e32 q^{98} +3.43259e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	178863.	1.92986	0.964928	−	0.262516i	$-0.0845524\pi$
$2$	178863.	1.92986	0.964928	+	0.262516i	$0.0845524\pi$
$3$	8.55112e7	1.14689	0.573446	−	0.819243i	$-0.305606\pi$
$3$	8.55112e7	1.14689	0.573446	+	0.819243i	$0.305606\pi$
$4$	2.34019e10	2.72434
$5$	1.52588e11	0.447214
$5$	1.52588e11	0.447214
$6$	1.52948e13	2.21333
$7$	−8.09549e13	−0.920716	−0.460358	−	0.887733i	$-0.652279\pi$
$7$	−8.09549e13	−0.920716	−0.460358	+	0.887733i	$0.652279\pi$
$8$	2.64931e15	3.32773
$9$	1.75311e15	0.315360
$10$	2.72923e16	0.863057
$11$	1.95800e17	1.28480	0.642398	−	0.766371i	$-0.277939\pi$
$11$	1.95800e17	1.28480	0.642398	+	0.766371i	$0.277939\pi$
$12$	2.00113e18	3.12452
$13$	−2.59207e18	−1.08039	−0.540197	−	0.841539i	$-0.681650\pi$
$13$	−2.59207e18	−1.08039	−0.540197	+	0.841539i	$0.681650\pi$
$14$	−1.44798e19	−1.77685
$15$	1.30480e19	0.512906
$16$	2.72841e20	3.69769
$17$	−1.52177e20	−0.758475	−0.379238	−	0.925299i	$-0.623814\pi$
$17$	−1.52177e20	−0.758475	−0.379238	+	0.925299i	$0.623814\pi$
$18$	3.13565e20	0.608600
$19$	1.39526e21	1.10974	0.554868	−	0.831938i	$-0.312769\pi$
$19$	1.39526e21	1.10974	0.554868	+	0.831938i	$0.312769\pi$
$20$	3.57085e21	1.21836
$21$	−6.92255e21	−1.05596
$22$	3.50214e22	2.47947
$23$	−3.40316e22	−1.15711	−0.578553	−	0.815645i	$-0.696382\pi$
$23$	−3.40316e22	−1.15711	−0.578553	+	0.815645i	$0.696382\pi$
$24$	2.26546e23	3.81654
$25$	2.32831e22	0.200000
$26$	−4.63625e23	−2.08500
$27$	−3.25452e23	−0.785207
$28$	−1.89450e24	−2.50834
$29$	−1.49246e24	−1.10748	−0.553741	−	0.832689i	$-0.686800\pi$
$29$	−1.49246e24	−1.10748	−0.553741	+	0.832689i	$0.686800\pi$
$30$	2.33380e24	0.989833
$31$	−1.38398e24	−0.341714	−0.170857	−	0.985296i	$-0.554654\pi$
$31$	−1.38398e24	−0.341714	−0.170857	+	0.985296i	$0.554654\pi$
$32$	2.60438e25	3.80828
$33$	1.67431e25	1.47352
$34$	−2.72188e25	−1.46375
$35$	−1.23527e25	−0.411757
$36$	4.10261e25	0.859149
$37$	1.15380e26	1.53745	0.768727	−	0.639577i	$-0.220891\pi$
$37$	1.15380e26	1.53745	0.768727	+	0.639577i	$0.220891\pi$
$38$	2.49559e26	2.14163
$39$	−2.21651e26	−1.23909
$40$	4.04252e26	1.48821
$41$	−6.35087e25	−0.155561	−0.0777804	−	0.996971i	$-0.524783\pi$
$41$	−6.35087e25	−0.155561	−0.0777804	+	0.996971i	$0.524783\pi$
$42$	−1.23819e27	−2.03785
$43$	−2.64294e26	−0.295025	−0.147512	−	0.989060i	$-0.547127\pi$
$43$	−2.64294e26	−0.295025	−0.147512	+	0.989060i	$0.547127\pi$
$44$	4.58211e27	3.50022
$45$	2.67503e26	0.141033
$46$	−6.08698e27	−2.23305
$47$	1.03700e27	0.266788	0.133394	−	0.991063i	$-0.457412\pi$
$47$	1.03700e27	0.266788	0.133394	+	0.991063i	$0.457412\pi$
$48$	2.33310e28	4.24085
$49$	−1.17730e27	−0.152283
$50$	4.16447e27	0.385971
$51$	−1.30128e28	−0.869889
$52$	−6.06594e28	−2.94336
$53$	5.20280e28	1.84368	0.921839	−	0.387574i	$-0.126687\pi$
$53$	5.20280e28	1.84368	0.921839	+	0.387574i	$0.126687\pi$
$54$	−5.82111e28	−1.51534
$55$	2.98768e28	0.574579
$56$	−2.14475e29	−3.06389
$57$	1.19310e29	1.27275
$58$	−2.66946e29	−2.13728
$59$	−6.17754e28	−0.373042	−0.186521	−	0.982451i	$-0.559721\pi$
$59$	−6.17754e28	−0.373042	−0.186521	+	0.982451i	$0.559721\pi$
$60$	3.05348e29	1.39733
$61$	−1.21654e29	−0.423822	−0.211911	−	0.977289i	$-0.567969\pi$
$61$	−1.21654e29	−0.423822	−0.211911	+	0.977289i	$0.567969\pi$
$62$	−2.47543e29	−0.659458
$63$	−1.41923e29	−0.290357
$64$	2.31456e30	3.65174
$65$	−3.95519e29	−0.483167
$66$	2.99472e30	2.84369
$67$	−2.87484e29	−0.213000	−0.106500	−	0.994313i	$-0.533964\pi$
$67$	−2.87484e29	−0.213000	−0.106500	+	0.994313i	$0.533964\pi$
$68$	−3.56123e30	−2.06634
$69$	−2.91008e30	−1.32707
$70$	−2.20944e30	−0.794631
$71$	−2.84409e30	−0.809432	−0.404716	−	0.914442i	$-0.632630\pi$
$71$	−2.84409e30	−0.809432	−0.404716	+	0.914442i	$0.632630\pi$
$72$	4.64452e30	1.04943
$73$	−2.67045e30	−0.480570	−0.240285	−	0.970702i	$-0.577241\pi$
$73$	−2.67045e30	−0.480570	−0.240285	+	0.970702i	$0.577241\pi$
$74$	2.06372e31	2.96706
$75$	1.99096e30	0.229378
$76$	3.26517e31	3.02330
$77$	−1.58510e31	−1.18293
$78$	−3.96451e31	−2.39127
$79$	−7.84640e30	−0.383551	−0.191776	−	0.981439i	$-0.561425\pi$
$79$	−7.84640e30	−0.383551	−0.191776	+	0.981439i	$0.561425\pi$
$80$	4.16323e31	1.65366
$81$	−3.75754e31	−1.21591
$82$	−1.13593e31	−0.300210
$83$	1.28723e31	0.278527	0.139263	−	0.990255i	$-0.455527\pi$
$83$	1.28723e31	0.278527	0.139263	+	0.990255i	$0.455527\pi$
$84$	−1.62001e32	−2.87680
$85$	−2.32203e31	−0.339200
$86$	−4.72724e31	−0.569355
$87$	−1.27622e32	−1.27016
$88$	5.18736e32	4.27545
$89$	−1.56902e32	−1.07323	−0.536616	−	0.843826i	$-0.680298\pi$
$89$	−1.56902e32	−1.07323	−0.536616	+	0.843826i	$0.680298\pi$
$90$	4.78463e31	0.272174
$91$	2.09841e32	0.994735
$92$	−7.96404e32	−3.15235
$93$	−1.18346e32	−0.391909
$94$	1.85481e32	0.514862
$95$	2.12899e32	0.496289
$96$	2.22703e33	4.36769
$97$	4.84738e32	0.801259	0.400630	−	0.916240i	$-0.368791\pi$
$97$	4.84738e32	0.801259	0.400630	+	0.916240i	$0.368791\pi$
$98$	−2.10574e32	−0.293883
$99$	3.43259e32	0.405174
$100$	5.44868e32	0.544868
$101$	2.51128e32	0.213105	0.106552	−	0.994307i	$-0.466019\pi$
$101$	2.51128e32	0.213105	0.106552	+	0.994307i	$0.466019\pi$
$102$	−2.32751e33	−1.67876
$103$	−2.60164e33	−1.59747	−0.798737	−	0.601681i	$-0.794498\pi$
$103$	−2.60164e33	−1.59747	−0.798737	+	0.601681i	$0.794498\pi$
$104$	−6.86720e33	−3.59525
$105$	−1.05630e33	−0.472240
$106$	9.30586e33	3.55803
$107$	3.74478e33	1.22629	0.613146	−	0.789970i	$-0.289904\pi$
$107$	3.74478e33	1.22629	0.613146	+	0.789970i	$0.289904\pi$
$108$	−7.61619e33	−2.13917
$109$	−2.76732e33	−0.667609	−0.333805	−	0.942642i	$-0.608333\pi$
$109$	−2.76732e33	−0.667609	−0.333805	+	0.942642i	$0.608333\pi$
$110$	5.34384e33	1.10885
$111$	9.86628e33	1.76329
$112$	−2.20879e34	−3.40452
$113$	1.26307e34	1.68125	0.840626	−	0.541617i	$-0.182188\pi$
$113$	1.26307e34	1.68125	0.840626	+	0.541617i	$0.182188\pi$
$114$	2.13401e34	2.45622
$115$	−5.19281e33	−0.517473
$116$	−3.49265e34	−3.01716
$117$	−4.54418e33	−0.340713
$118$	−1.10493e34	−0.719917
$119$	1.23195e34	0.698340
$120$	3.45681e34	1.70681
$121$	1.51127e34	0.650703
$122$	−2.17593e34	−0.817915
$123$	−5.43071e33	−0.178411
$124$	−3.23878e34	−0.930945
$125$	3.55271e33	0.0894427
$126$	−2.53847e34	−0.560348
$127$	−2.24824e33	−0.0435594	−0.0217797	−	0.999763i	$-0.506933\pi$
$127$	−2.24824e33	−0.0435594	−0.0217797	+	0.999763i	$0.506933\pi$
$128$	1.90275e35	3.23905
$129$	−2.26001e34	−0.338361
$130$	−7.07435e34	−0.932441
$131$	7.19207e34	0.835368	0.417684	−	0.908592i	$-0.362842\pi$
$131$	7.19207e34	0.835368	0.417684	+	0.908592i	$0.362842\pi$
$132$	3.91821e35	4.01438
$133$	−1.12953e35	−1.02175
$134$	−5.14202e34	−0.411059
$135$	−4.96600e34	−0.351155
$136$	−4.03163e35	−2.52400
$137$	2.56636e35	1.42373	0.711867	−	0.702314i	$-0.247850\pi$
$137$	2.56636e35	1.42373	0.711867	+	0.702314i	$0.247850\pi$
$138$	−5.20505e35	−2.56106
$139$	7.81097e34	0.341162	0.170581	−	0.985344i	$-0.445436\pi$
$139$	7.81097e34	0.341162	0.170581	+	0.985344i	$0.445436\pi$
$140$	−2.89078e35	−1.12177
$141$	8.86755e34	0.305977
$142$	−5.08701e35	−1.56209
$143$	−5.07529e35	−1.38809
$144$	4.78320e35	1.16611
$145$	−2.27732e35	−0.495281
$146$	−4.77643e35	−0.927431
$147$	−1.00672e35	−0.174652
$148$	2.70011e36	4.18855
$149$	−1.40823e35	−0.195479	−0.0977397	−	0.995212i	$-0.531161\pi$
$149$	−1.40823e35	−0.195479	−0.0977397	+	0.995212i	$0.531161\pi$
$150$	3.56109e35	0.442667
$151$	4.46232e35	0.497097	0.248548	−	0.968619i	$-0.420046\pi$
$151$	4.46232e35	0.497097	0.248548	+	0.968619i	$0.420046\pi$
$152$	3.69647e36	3.69290
$153$	−2.66782e35	−0.239193
$154$	−2.83515e36	−2.28289
$155$	−2.11179e35	−0.152819
$156$	−5.18706e36	−3.37571
$157$	7.61070e35	0.445739	0.222869	−	0.974848i	$-0.428458\pi$
$157$	7.61070e35	0.445739	0.222869	+	0.974848i	$0.428458\pi$
$158$	−1.40343e36	−0.740199
$159$	4.44897e36	2.11450
$160$	3.97396e36	1.70311
$161$	2.75502e36	1.06537
$162$	−6.72084e36	−2.34653
$163$	1.95336e36	0.616152	0.308076	−	0.951362i	$-0.400315\pi$
$163$	1.95336e36	0.616152	0.308076	+	0.951362i	$0.400315\pi$
$164$	−1.48623e36	−0.423800
$165$	2.55480e36	0.658979
$166$	2.30237e36	0.537516
$167$	2.87170e36	0.607180	0.303590	−	0.952803i	$-0.401815\pi$
$167$	2.87170e36	0.607180	0.303590	+	0.952803i	$0.401815\pi$
$168$	−1.83400e37	−3.51395
$169$	9.62710e35	0.167249
$170$	−4.15325e36	−0.654608
$171$	2.44604e36	0.349967
$172$	−6.18499e36	−0.803748
$173$	1.61105e37	1.90261	0.951303	−	0.308258i	$-0.0997461\pi$
$173$	1.61105e37	1.90261	0.951303	+	0.308258i	$0.0997461\pi$
$174$	−2.28269e37	−2.45123
$175$	−1.88488e36	−0.184143
$176$	5.34225e37	4.75078
$177$	−5.28249e36	−0.427839
$178$	−2.80639e37	−2.07118
$179$	9.06671e33	0.000610063 0	0.000305031	−	1.00000i	$-0.499903\pi$
$179$	9.06671e33	0.000610063 0	0.000305031		1.00000i	$0.499903\pi$
$180$	6.26008e36	0.384223
$181$	1.89723e36	0.106273	0.0531364	−	0.998587i	$-0.483078\pi$
$181$	1.89723e36	0.106273	0.0531364	+	0.998587i	$0.483078\pi$
$182$	3.75327e37	1.91969
$183$	−1.04028e37	−0.486078
$184$	−9.01602e37	−3.85053
$185$	1.76056e37	0.687570
$186$	−2.11677e37	−0.756327
$187$	−2.97963e37	−0.974487
$188$	2.42679e37	0.726821
$189$	2.63469e37	0.722953
$190$	3.80798e37	0.957767
$191$	−6.88314e37	−1.58758	−0.793790	−	0.608192i	$-0.791895\pi$
$191$	−6.88314e37	−1.58758	−0.793790	+	0.608192i	$0.791895\pi$
$192$	1.97921e38	4.18815
$193$	5.10528e37	0.991571	0.495786	−	0.868445i	$-0.334880\pi$
$193$	5.10528e37	0.991571	0.495786	+	0.868445i	$0.334880\pi$
$194$	8.67015e37	1.54631
$195$	−3.38213e37	−0.554140
$196$	−2.75510e37	−0.414869
$197$	−6.02889e37	−0.834727	−0.417364	−	0.908740i	$-0.637046\pi$
$197$	−6.02889e37	−0.834727	−0.417364	+	0.908740i	$0.637046\pi$
$198$	6.13963e37	0.781927
$199$	−1.42678e38	−1.67218	−0.836089	−	0.548594i	$-0.815163\pi$
$199$	−1.42678e38	−1.67218	−0.836089	+	0.548594i	$0.815163\pi$
$200$	6.16840e37	0.665546
$201$	−2.45831e37	−0.244288
$202$	4.49175e37	0.411261
$203$	1.20822e38	1.01968
$204$	−3.04525e38	−2.36987
$205$	−9.69067e36	−0.0695689
$206$	−4.65337e38	−3.08289
$207$	−5.96610e37	−0.364905
$208$	−7.07225e38	−3.99496
$209$	2.73192e38	1.42579
$210$	−1.88932e38	−0.911355
$211$	3.27612e38	1.46116	0.730582	−	0.682825i	$-0.239249\pi$
$211$	3.27612e38	1.46116	0.730582	+	0.682825i	$0.239249\pi$
$212$	1.21755e39	5.02280
$213$	−2.43201e38	−0.928331
$214$	6.69801e38	2.36656
$215$	−4.03281e37	−0.131939
$216$	−8.62222e38	−2.61296
$217$	1.12040e38	0.314621
$218$	−4.94971e38	−1.28839
$219$	−2.28353e38	−0.551162
$220$	6.99174e38	1.56535
$221$	3.94453e38	0.819451
$222$	1.76471e39	3.40290
$223$	−3.22330e38	−0.577126	−0.288563	−	0.957461i	$-0.593177\pi$
$223$	−3.22330e38	−0.577126	−0.288563	+	0.957461i	$0.593177\pi$
$224$	−2.10837e39	−3.50634
$225$	4.08177e37	0.0630721
$226$	2.25916e39	3.24457
$227$	−6.02003e38	−0.803845	−0.401922	−	0.915674i	$-0.631658\pi$
$227$	−6.02003e38	−0.803845	−0.401922	+	0.915674i	$0.631658\pi$
$228$	2.79209e39	3.46740
$229$	−3.71091e38	−0.428741	−0.214370	−	0.976752i	$-0.568770\pi$
$229$	−3.71091e38	−0.428741	−0.214370	+	0.976752i	$0.568770\pi$
$230$	−9.28799e38	−0.998649
$231$	−1.35544e39	−1.35670
$232$	−3.95400e39	−3.68540
$233$	−3.81211e38	−0.330973	−0.165486	−	0.986212i	$-0.552919\pi$
$233$	−3.81211e38	−0.330973	−0.165486	+	0.986212i	$0.552919\pi$
$234$	−8.12784e38	−0.657527
$235$	1.58234e38	0.119311
$236$	−1.44566e39	−1.01629
$237$	−6.70955e38	−0.439892
$238$	2.20349e39	1.34770
$239$	8.52350e38	0.486466	0.243233	−	0.969968i	$-0.421792\pi$
$239$	8.52350e38	0.486466	0.243233	+	0.969968i	$0.421792\pi$
$240$	3.56003e39	1.89657
$241$	3.41820e39	1.70027	0.850133	−	0.526568i	$-0.176522\pi$
$241$	3.41820e39	1.70027	0.850133	+	0.526568i	$0.176522\pi$
$242$	2.70309e39	1.25576
$243$	−1.40391e39	−0.609308
$244$	−2.84693e39	−1.15464
$245$	−1.79641e38	−0.0681028
$246$	−9.71351e38	−0.344308
$247$	−3.61661e39	−1.19895
$248$	−3.66660e39	−1.13713
$249$	1.10072e39	0.319440
$250$	6.35448e38	0.172611
$251$	2.52321e39	0.641706	0.320853	−	0.947129i	$-0.396030\pi$
$251$	2.52321e39	0.641706	0.320853	+	0.947129i	$0.396030\pi$
$252$	−3.32126e39	−0.791032
$253$	−6.66340e39	−1.48665
$254$	−4.02127e38	−0.0840633
$255$	−1.98560e39	−0.389026
$256$	1.41511e40	2.59915
$257$	4.18511e39	0.720793	0.360396	−	0.932799i	$-0.382641\pi$
$257$	4.18511e39	0.720793	0.360396	+	0.932799i	$0.382641\pi$
$258$	−4.04232e39	−0.652988
$259$	−9.34058e39	−1.41556
$260$	−9.25590e39	−1.31631
$261$	−2.61645e39	−0.349256
$262$	1.28639e40	1.61214
$263$	1.15657e40	1.36114	0.680570	−	0.732683i	$-0.261732\pi$
$263$	1.15657e40	1.36114	0.680570	+	0.732683i	$0.261732\pi$
$264$	4.43577e40	4.90348
$265$	7.93884e39	0.824518
$266$	−2.02031e40	−1.97183
$267$	−1.34169e40	−1.23088
$268$	−6.72768e39	−0.580284
$269$	−7.21991e39	−0.585624	−0.292812	−	0.956170i	$-0.594591\pi$
$269$	−7.21991e39	−0.585624	−0.292812	+	0.956170i	$0.594591\pi$
$270$	−8.88232e39	−0.677679
$271$	2.28804e40	1.64237	0.821183	−	0.570665i	$-0.193315\pi$
$271$	2.28804e40	1.64237	0.821183	+	0.570665i	$0.193315\pi$
$272$	−4.15202e40	−2.80461
$273$	1.79438e40	1.14085
$274$	4.59026e40	2.74760
$275$	4.55884e39	0.256959
$276$	−6.81015e40	−3.61540
$277$	2.67522e40	1.33796	0.668981	−	0.743279i	$-0.266731\pi$
$277$	2.67522e40	1.33796	0.668981	+	0.743279i	$0.266731\pi$
$278$	1.39709e40	0.658394
$279$	−2.42627e39	−0.107763
$280$	−3.27262e40	−1.37021
$281$	−2.51780e40	−0.993955	−0.496977	−	0.867763i	$-0.665557\pi$
$281$	−2.51780e40	−0.993955	−0.496977	+	0.867763i	$0.665557\pi$
$282$	1.58607e40	0.590490
$283$	4.17854e40	1.46740	0.733699	−	0.679475i	$-0.237792\pi$
$283$	4.17854e40	1.46740	0.733699	+	0.679475i	$0.237792\pi$
$284$	−6.65571e40	−2.20517
$285$	1.82053e40	0.569190
$286$	−9.07780e40	−2.67880
$287$	5.14135e39	0.143227
$288$	4.56575e40	1.20098
$289$	−1.70967e40	−0.424715
$290$	−4.07327e40	−0.955821
$291$	4.14505e40	0.918958
$292$	−6.24936e40	−1.30924
$293$	−1.81801e40	−0.359981	−0.179991	−	0.983668i	$-0.557607\pi$
$293$	−1.81801e40	−0.359981	−0.179991	+	0.983668i	$0.557607\pi$
$294$	−1.80064e40	−0.337052
$295$	−9.42619e39	−0.166829
$296$	3.05677e41	5.11623
$297$	−6.37236e40	−1.00883
$298$	−2.51880e40	−0.377247
$299$	8.82124e40	1.25013
$300$	4.65923e40	0.624905
$301$	2.13959e40	0.271634
$302$	7.98142e40	0.959325
$303$	2.14743e40	0.244408
$304$	3.80684e41	4.10346
$305$	−1.85629e40	−0.189539
$306$	−4.77174e40	−0.461608
$307$	−1.04678e40	−0.0959564	−0.0479782	−	0.998848i	$-0.515278\pi$
$307$	−1.04678e40	−0.0959564	−0.0479782	+	0.998848i	$0.515278\pi$
$308$	−3.70944e41	−3.22271
$309$	−2.22470e41	−1.83213
$310$	−3.77720e40	−0.294919
$311$	1.01794e41	0.753660	0.376830	−	0.926282i	$-0.377014\pi$
$311$	1.01794e41	0.753660	0.376830	+	0.926282i	$0.377014\pi$
$312$	−5.87223e41	−4.12337
$313$	−2.12567e41	−1.41584	−0.707921	−	0.706292i	$-0.750367\pi$
$313$	−2.12567e41	−1.41584	−0.707921	+	0.706292i	$0.750367\pi$
$314$	1.36127e41	0.860212
$315$	−2.16557e40	−0.129852
$316$	−1.83621e41	−1.04492
$317$	5.12986e40	0.277094	0.138547	−	0.990356i	$-0.455757\pi$
$317$	5.12986e40	0.277094	0.138547	+	0.990356i	$0.455757\pi$
$318$	7.95755e41	4.08067
$319$	−2.92225e41	−1.42289
$320$	3.53174e41	1.63311
$321$	3.20220e41	1.40642
$322$	4.92771e41	2.05600
$323$	−2.12326e41	−0.841708
$324$	−8.79336e41	−3.31255
$325$	−6.03514e40	−0.216079
$326$	3.49384e41	1.18908
$327$	−2.36637e41	−0.765676
$328$	−1.68254e41	−0.517664
$329$	−8.39506e40	−0.245636
$330$	4.56958e41	1.27173
$331$	−4.71143e41	−1.24736	−0.623679	−	0.781681i	$-0.714363\pi$
$331$	−4.71143e41	−1.24736	−0.623679	+	0.781681i	$0.714363\pi$
$332$	3.01236e41	0.758802
$333$	2.02274e41	0.484852
$334$	5.13640e41	1.17177
$335$	−4.38666e40	−0.0952565
$336$	−1.88876e42	−3.90462
$337$	8.62495e40	0.169771	0.0848854	−	0.996391i	$-0.472948\pi$
$337$	8.62495e40	0.169771	0.0848854	+	0.996391i	$0.472948\pi$
$338$	1.72193e41	0.322767
$339$	1.08007e42	1.92821
$340$	−5.43400e41	−0.924097
$341$	−2.70984e41	−0.439033
$342$	4.37505e41	0.675386
$343$	7.21170e41	1.06092
$344$	−7.00197e41	−0.981762
$345$	−4.44043e41	−0.593486
$346$	2.88157e42	3.67175
$347$	2.78000e41	0.337760	0.168880	−	0.985637i	$-0.445985\pi$
$347$	2.78000e41	0.337760	0.168880	+	0.985637i	$0.445985\pi$
$348$	−2.98661e42	−3.46036
$349$	−1.12911e42	−1.24772	−0.623860	−	0.781536i	$-0.714437\pi$
$349$	−1.12911e42	−1.24772	−0.623860	+	0.781536i	$0.714437\pi$
$350$	−3.37134e41	−0.355370
$351$	8.43594e41	0.848333
$352$	5.09938e42	4.89287
$353$	1.75490e42	1.60683	0.803413	−	0.595422i	$-0.203015\pi$
$353$	1.75490e42	1.60683	0.803413	+	0.595422i	$0.203015\pi$
$354$	−9.44841e41	−0.825667
$355$	−4.33973e41	−0.361989
$356$	−3.67181e42	−2.92385
$357$	1.05345e42	0.800920
$358$	1.62170e39	0.00117733
$359$	−2.42990e42	−1.68473	−0.842365	−	0.538907i	$-0.818837\pi$
$359$	−2.42990e42	−1.68473	−0.842365	+	0.538907i	$0.818837\pi$
$360$	7.08698e41	0.469321
$361$	3.65974e41	0.231516
$362$	3.39343e41	0.205091
$363$	1.29230e42	0.746286
$364$	4.91068e42	2.71000
$365$	−4.07478e41	−0.214918
$366$	−1.86067e42	−0.938060
$367$	−2.37509e42	−1.14470	−0.572349	−	0.820010i	$-0.693968\pi$
$367$	−2.37509e42	−1.14470	−0.572349	+	0.820010i	$0.693968\pi$
$368$	−9.28523e42	−4.27862
$369$	−1.11338e41	−0.0490577
$370$	3.14898e42	1.32691
$371$	−4.21192e42	−1.69750
$372$	−2.76952e42	−1.06769
$373$	1.58778e42	0.585592	0.292796	−	0.956175i	$-0.405414\pi$
$373$	1.58778e42	0.585592	0.292796	+	0.956175i	$0.405414\pi$
$374$	−5.32944e42	−1.88062
$375$	3.03797e41	0.102581
$376$	2.74734e42	0.887797
$377$	3.86858e42	1.19652
$378$	4.71248e42	1.39519
$379$	−2.74032e42	−0.776703	−0.388351	−	0.921511i	$-0.626955\pi$
$379$	−2.74032e42	−0.776703	−0.388351	+	0.921511i	$0.626955\pi$
$380$	4.98225e42	1.35206
$381$	−1.92250e41	−0.0499579
$382$	−1.23114e43	−3.06380
$383$	3.57273e42	0.851570	0.425785	−	0.904824i	$-0.359998\pi$
$383$	3.57273e42	0.851570	0.425785	+	0.904824i	$0.359998\pi$
$384$	1.62706e43	3.71483
$385$	−2.41867e42	−0.529024
$386$	9.13144e42	1.91359
$387$	−4.63336e41	−0.0930391
$388$	1.13438e43	2.18290
$389$	−2.24258e42	−0.413599	−0.206799	−	0.978383i	$-0.566305\pi$
$389$	−2.24258e42	−0.413599	−0.206799	+	0.978383i	$0.566305\pi$
$390$	−6.04937e42	−1.06941
$391$	5.17882e42	0.877636
$392$	−3.11902e42	−0.506755
$393$	6.15003e42	0.958077
$394$	−1.07834e43	−1.61090
$395$	−1.19727e42	−0.171529
$396$	8.03292e42	1.10383
$397$	−8.69665e41	−0.114633	−0.0573164	−	0.998356i	$-0.518254\pi$
$397$	−8.69665e41	−0.114633	−0.0573164	+	0.998356i	$0.518254\pi$
$398$	−2.55198e43	−3.22706
$399$	−9.65875e42	−1.17184
$400$	6.35259e42	0.739538
$401$	1.79590e41	0.0200632	0.0100316	−	0.999950i	$-0.496807\pi$
$401$	1.79590e41	0.0200632	0.0100316	+	0.999950i	$0.496807\pi$
$402$	−4.39700e42	−0.471440
$403$	3.58738e42	0.369185
$404$	5.87688e42	0.580569
$405$	−5.73355e42	−0.543771
$406$	2.16106e43	1.96783
$407$	2.25915e43	1.97532
$408$	−3.44750e43	−2.89475
$409$	1.72895e43	1.39427	0.697136	−	0.716939i	$-0.254457\pi$
$409$	1.72895e43	1.39427	0.697136	+	0.716939i	$0.254457\pi$
$410$	−1.73330e42	−0.134258
$411$	2.19453e43	1.63287
$412$	−6.08834e43	−4.35206
$413$	5.00103e42	0.343466
$414$	−1.06711e43	−0.704214
$415$	1.96415e42	0.124561
$416$	−6.75073e43	−4.11444
$417$	6.67926e42	0.391276
$418$	4.88639e43	2.75156
$419$	−3.07423e43	−1.66420	−0.832099	−	0.554628i	$-0.812861\pi$
$419$	−3.07423e43	−1.66420	−0.832099	+	0.554628i	$0.812861\pi$
$420$	−2.47194e43	−1.28654
$421$	−1.46291e43	−0.732090	−0.366045	−	0.930597i	$-0.619288\pi$
$421$	−1.46291e43	−0.732090	−0.366045	+	0.930597i	$0.619288\pi$
$422$	5.85975e43	2.81983
$423$	1.81798e42	0.0841343
$424$	1.37838e44	6.13526
$425$	−3.54314e42	−0.151695
$426$	−4.34997e43	−1.79154
$427$	9.84848e42	0.390220
$428$	8.76349e43	3.34083
$429$	−4.33994e43	−1.59198
$430$	−7.21319e42	−0.254623
$431$	3.24328e43	1.10182	0.550909	−	0.834565i	$-0.314281\pi$
$431$	3.24328e43	1.10182	0.550909	+	0.834565i	$0.314281\pi$
$432$	−8.87967e43	−2.90345
$433$	−2.61817e42	−0.0824040	−0.0412020	−	0.999151i	$-0.513119\pi$
$433$	−2.61817e42	−0.0824040	−0.0412020	+	0.999151i	$0.513119\pi$
$434$	2.00398e43	0.607174
$435$	−1.94736e43	−0.568034
$436$	−6.47606e43	−1.81880
$437$	−4.74828e43	−1.28408
$438$	−4.08439e43	−1.06366
$439$	−6.39695e43	−1.60438	−0.802192	−	0.597066i	$-0.796333\pi$
$439$	−6.39695e43	−1.60438	−0.802192	+	0.597066i	$0.796333\pi$
$440$	7.91528e43	1.91204
$441$	−2.06393e42	−0.0480239
$442$	7.05530e43	1.58142
$443$	1.30321e43	0.281418	0.140709	−	0.990051i	$-0.455062\pi$
$443$	1.30321e43	0.281418	0.140709	+	0.990051i	$0.455062\pi$
$444$	2.30890e44	4.80381
$445$	−2.39414e43	−0.479964
$446$	−5.76528e43	−1.11377
$447$	−1.20420e43	−0.224194
$448$	−1.87375e44	−3.36221
$449$	−9.56472e43	−1.65428	−0.827138	−	0.561999i	$-0.810032\pi$
$449$	−9.56472e43	−1.65428	−0.827138	+	0.561999i	$0.810032\pi$
$450$	7.30076e42	0.121720
$451$	−1.24350e43	−0.199864
$452$	2.95582e44	4.58030
$453$	3.81578e43	0.570116
$454$	−1.07676e44	−1.55130
$455$	3.20192e43	0.444859
$456$	3.16090e44	4.23536
$457$	−3.78578e42	−0.0489258	−0.0244629	−	0.999701i	$-0.507788\pi$
$457$	−3.78578e42	−0.0489258	−0.0244629	+	0.999701i	$0.507788\pi$
$458$	−6.63743e43	−0.827408
$459$	4.95262e43	0.595560
$460$	−1.21522e44	−1.40977
$461$	7.04190e43	0.788179	0.394089	−	0.919072i	$-0.371060\pi$
$461$	7.04190e43	0.788179	0.394089	+	0.919072i	$0.371060\pi$
$462$	−2.42437e44	−2.61823
$463$	1.41714e44	1.47682	0.738409	−	0.674353i	$-0.235577\pi$
$463$	1.41714e44	1.47682	0.738409	+	0.674353i	$0.235577\pi$
$464$	−4.07206e44	−4.09513
$465$	−1.80582e43	−0.175267
$466$	−6.81843e43	−0.638729
$467$	−1.83277e44	−1.65721	−0.828606	−	0.559831i	$-0.810866\pi$
$467$	−1.83277e44	−1.65721	−0.828606	+	0.559831i	$0.810866\pi$
$468$	−1.06343e44	−0.928219
$469$	2.32732e43	0.196112
$470$	2.83022e43	0.230253
$471$	6.50801e43	0.511214
$472$	−1.63662e44	−1.24138
$473$	−5.17490e43	−0.379047
$474$	−1.20009e44	−0.848928
$475$	3.24859e43	0.221947
$476$	2.88299e44	1.90252
$477$	9.12106e43	0.581423
$478$	1.52454e44	0.938809
$479$	−6.67837e43	−0.397314	−0.198657	−	0.980069i	$-0.563658\pi$
$479$	−6.67837e43	−0.397314	−0.198657	+	0.980069i	$0.563658\pi$
$480$	3.39818e44	1.95329
$481$	−2.99073e44	−1.66105
$482$	6.11389e44	3.28127
$483$	2.35586e44	1.22186
$484$	3.53666e44	1.77274
$485$	7.39651e43	0.358334
$486$	−2.51108e44	−1.17588
$487$	−1.75263e44	−0.793345	−0.396673	−	0.917960i	$-0.629835\pi$
$487$	−1.75263e44	−0.793345	−0.396673	+	0.917960i	$0.629835\pi$
$488$	−3.22299e44	−1.41036
$489$	1.67035e44	0.706659
$490$	−3.21311e43	−0.131429
$491$	3.92240e44	1.55134	0.775670	−	0.631139i	$-0.217412\pi$
$491$	3.92240e44	1.55134	0.775670	+	0.631139i	$0.217412\pi$
$492$	−1.27089e44	−0.486053
$493$	2.27118e44	0.839998
$494$	−6.46876e44	−2.31380
$495$	5.23772e43	0.181199
$496$	−3.77608e44	−1.26355
$497$	2.30243e44	0.745257
$498$	1.96878e44	0.616473
$499$	7.64433e43	0.231569	0.115785	−	0.993274i	$-0.463062\pi$
$499$	7.64433e43	0.231569	0.115785	+	0.993274i	$0.463062\pi$
$500$	8.31403e43	0.243672
$501$	2.45563e44	0.696370
$502$	4.51307e44	1.23840
$503$	−4.88916e44	−1.29826	−0.649132	−	0.760676i	$-0.724868\pi$
$503$	−4.88916e44	−1.29826	−0.649132	+	0.760676i	$0.724868\pi$
$504$	−3.75997e44	−0.966230
$505$	3.83191e43	0.0953033
$506$	−1.19183e45	−2.86901
$507$	8.23225e43	0.191817
$508$	−5.26132e43	−0.118671
$509$	−3.35020e44	−0.731522	−0.365761	−	0.930709i	$-0.619191\pi$
$509$	−3.35020e44	−0.731522	−0.365761	+	0.930709i	$0.619191\pi$
$510$	−3.55150e44	−0.750764
$511$	2.16186e44	0.442469
$512$	8.96657e44	1.77694
$513$	−4.54089e44	−0.871374
$514$	7.48560e44	1.39103
$515$	−3.96979e44	−0.714412
$516$	−5.28886e44	−0.921812
$517$	2.03046e44	0.342768
$518$	−1.67068e45	−2.73182
$519$	1.37763e45	2.18208
$520$	−1.04785e45	−1.60785
$521$	−5.22367e44	−0.776521	−0.388261	−	0.921550i	$-0.626924\pi$
$521$	−5.22367e44	−0.776521	−0.388261	+	0.921550i	$0.626924\pi$
$522$	−4.67985e44	−0.674014
$523$	−1.10438e45	−1.54113	−0.770566	−	0.637360i	$-0.780026\pi$
$523$	−1.10438e45	−1.54113	−0.770566	+	0.637360i	$0.780026\pi$
$524$	1.68308e45	2.27583
$525$	−1.61178e44	−0.211192
$526$	2.06868e45	2.62680
$527$	2.10610e44	0.259182
$528$	4.56822e45	5.44863
$529$	2.93144e44	0.338893
$530$	1.41996e45	1.59120
$531$	−1.08299e44	−0.117643
$532$	−2.64332e45	−2.78360
$533$	1.64619e44	0.168067
$534$	−2.39978e45	−2.37542
$535$	5.71408e44	0.548414
$536$	−7.61634e44	−0.708806
$537$	7.75305e41	0.000699676 0
$538$	−1.29137e45	−1.13017
$539$	−2.30515e44	−0.195652
$540$	−1.16214e45	−0.956667
$541$	−1.40716e45	−1.12354	−0.561772	−	0.827292i	$-0.689880\pi$
$541$	−1.40716e45	−1.12354	−0.561772	+	0.827292i	$0.689880\pi$
$542$	4.09244e45	3.16953
$543$	1.62234e44	0.121883
$544$	−3.96326e45	−2.88849
$545$	−4.22260e44	−0.298564
$546$	3.20947e45	2.20168
$547$	−1.00599e45	−0.669579	−0.334789	−	0.942293i	$-0.608665\pi$
$547$	−1.00599e45	−0.669579	−0.334789	+	0.942293i	$0.608665\pi$
$548$	6.00578e45	3.87874
$549$	−2.13272e44	−0.133657
$550$	8.15405e44	0.495894
$551$	−2.08237e45	−1.22901
$552$	−7.70971e45	−4.41614
$553$	6.35205e44	0.353142
$554$	4.78498e45	2.58207
$555$	1.50548e45	0.788568
$556$	1.82792e45	0.929442
$557$	6.35386e44	0.313637	0.156818	−	0.987627i	$-0.449876\pi$
$557$	6.35386e44	0.313637	0.156818	+	0.987627i	$0.449876\pi$
$558$	−4.33969e44	−0.207967
$559$	6.85070e44	0.318743
$560$	−3.37034e45	−1.52255
$561$	−2.54792e45	−1.11763
$562$	−4.50340e45	−1.91819
$563$	−1.73714e45	−0.718534	−0.359267	−	0.933235i	$-0.616973\pi$
$563$	−1.73714e45	−0.718534	−0.359267	+	0.933235i	$0.616973\pi$
$564$	2.07518e45	0.833584
$565$	1.92729e45	0.751878
$566$	7.47384e45	2.83187
$567$	3.04191e45	1.11951
$568$	−7.53487e45	−2.69357
$569$	3.27076e45	1.13579	0.567894	−	0.823102i	$-0.307759\pi$
$569$	3.27076e45	1.13579	0.567894	+	0.823102i	$0.307759\pi$
$570$	3.25625e45	1.09845
$571$	2.07979e45	0.681591	0.340795	−	0.940137i	$-0.389304\pi$
$571$	2.07979e45	0.681591	0.340795	+	0.940137i	$0.389304\pi$
$572$	−1.18771e46	−3.78162
$573$	−5.88585e45	−1.82078
$574$	9.19595e44	0.276408
$575$	−7.92360e44	−0.231421
$576$	4.05768e45	1.15161
$577$	−2.30164e45	−0.634800	−0.317400	−	0.948292i	$-0.602810\pi$
$577$	−2.30164e45	−0.634800	−0.317400	+	0.948292i	$0.602810\pi$
$578$	−3.05796e45	−0.819639
$579$	4.36559e45	1.13722
$580$	−5.32936e45	−1.34931
$581$	−1.04207e45	−0.256444
$582$	7.41395e45	1.77346
$583$	1.01871e46	2.36875
$584$	−7.07484e45	−1.59921
$585$	−6.93387e44	−0.152372
$586$	−3.25174e45	−0.694712
$587$	1.99372e45	0.414128	0.207064	−	0.978327i	$-0.433609\pi$
$587$	1.99372e45	0.414128	0.207064	+	0.978327i	$0.433609\pi$
$588$	−2.35592e45	−0.475810
$589$	−1.93101e45	−0.379213
$590$	−1.68599e45	−0.321957
$591$	−5.15538e45	−0.957341
$592$	3.14804e46	5.68503
$593$	−6.54556e45	−1.14959	−0.574797	−	0.818296i	$-0.694919\pi$
$593$	−6.54556e45	−1.14959	−0.574797	+	0.818296i	$0.694919\pi$
$594$	−1.13978e46	−1.94690
$595$	1.87980e45	0.312307
$596$	−3.29553e45	−0.532553
$597$	−1.22006e46	−1.91781
$598$	1.57779e46	2.41257
$599$	1.89735e45	0.282231	0.141115	−	0.989993i	$-0.454931\pi$
$599$	1.89735e45	0.282231	0.141115	+	0.989993i	$0.454931\pi$
$600$	5.27468e45	0.763309
$601$	−8.66013e45	−1.21926	−0.609629	−	0.792687i	$-0.708681\pi$
$601$	−8.66013e45	−1.21926	−0.609629	+	0.792687i	$0.708681\pi$
$602$	3.82693e45	0.524214
$603$	−5.03991e44	−0.0671718
$604$	1.04427e46	1.35426
$605$	2.30601e45	0.291003
$606$	3.84095e45	0.471672
$607$	8.81789e45	1.05378	0.526892	−	0.849932i	$-0.323357\pi$
$607$	8.81789e45	1.05378	0.526892	+	0.849932i	$0.323357\pi$
$608$	3.63378e46	4.22619
$609$	1.03317e46	1.16946
$610$	−3.32021e45	−0.365783
$611$	−2.68799e45	−0.288236
$612$	−6.24322e45	−0.651643
$613$	−1.91712e46	−1.94783	−0.973915	−	0.226912i	$-0.927137\pi$
$613$	−1.91712e46	−1.94783	−0.973915	+	0.226912i	$0.927137\pi$
$614$	−1.87231e45	−0.185182
$615$	−8.28661e44	−0.0797879
$616$	−4.19942e46	−3.93648
$617$	−1.53369e46	−1.39969	−0.699844	−	0.714295i	$-0.746747\pi$
$617$	−1.53369e46	−1.39969	−0.699844	+	0.714295i	$0.746747\pi$
$618$	−3.97915e46	−3.53574
$619$	8.04204e45	0.695778	0.347889	−	0.937536i	$-0.386899\pi$
$619$	8.04204e45	0.695778	0.347889	+	0.937536i	$0.386899\pi$
$620$	−4.94199e45	−0.416331
$621$	1.10756e46	0.908568
$622$	1.82071e46	1.45446
$623$	1.27020e46	0.988142
$624$	−6.04757e46	−4.58179
$625$	5.42101e44	0.0400000
$626$	−3.80203e46	−2.73237
$627$	2.33610e46	1.63522
$628$	1.78105e46	1.21434
$629$	−1.75582e46	−1.16612
$630$	−3.87339e45	−0.250595
$631$	2.52921e46	1.59405	0.797023	−	0.603949i	$-0.206407\pi$
$631$	2.52921e46	1.59405	0.797023	+	0.603949i	$0.206407\pi$
$632$	−2.07875e46	−1.27635
$633$	2.80145e46	1.67580
$634$	9.17540e45	0.534752
$635$	−3.43055e44	−0.0194804
$636$	1.04114e47	5.76061
$637$	3.05163e45	0.164525
$638$	−5.22682e46	−2.74597
$639$	−4.98599e45	−0.255263
$640$	2.90337e46	1.44855
$641$	2.51177e46	1.22130	0.610651	−	0.791900i	$-0.290908\pi$
$641$	2.51177e46	1.22130	0.610651	+	0.791900i	$0.290908\pi$
$642$	5.72755e46	2.71419
$643$	−1.47547e46	−0.681473	−0.340736	−	0.940159i	$-0.610676\pi$
$643$	−1.47547e46	−0.681473	−0.340736	+	0.940159i	$0.610676\pi$
$644$	6.44728e46	2.90242
$645$	−3.44851e45	−0.151320
$646$	−3.79772e46	−1.62437
$647$	−4.64548e46	−1.93691	−0.968457	−	0.249182i	$-0.919838\pi$
$647$	−4.64548e46	−1.93691	−0.968457	+	0.249182i	$0.919838\pi$
$648$	−9.95488e46	−4.04621
$649$	−1.20957e46	−0.479283
$650$	−1.07946e46	−0.417000
$651$	9.58069e45	0.360837
$652$	4.57124e46	1.67861
$653$	3.12135e46	1.11757	0.558786	−	0.829312i	$-0.311267\pi$
$653$	3.12135e46	1.11757	0.558786	+	0.829312i	$0.311267\pi$
$654$	−4.23255e46	−1.47764
$655$	1.09742e46	0.373588
$656$	−1.73278e46	−0.575215
$657$	−4.68158e45	−0.151553
$658$	−1.50156e46	−0.474041
$659$	1.16512e46	0.358724	0.179362	−	0.983783i	$-0.442597\pi$
$659$	1.16512e46	0.358724	0.179362	+	0.983783i	$0.442597\pi$
$660$	5.97872e46	1.79528
$661$	−1.14126e46	−0.334241	−0.167121	−	0.985936i	$-0.553447\pi$
$661$	−1.14126e46	−0.334241	−0.167121	+	0.985936i	$0.553447\pi$
$662$	−8.42699e46	−2.40722
$663$	3.37302e46	0.939822
$664$	3.41026e46	0.926861
$665$	−1.72353e46	−0.456942
$666$	3.61792e46	0.935694
$667$	5.07909e46	1.28147
$668$	6.72033e46	1.65417
$669$	−2.75628e46	−0.661901
$670$	−7.84609e45	−0.183831
$671$	−2.38199e46	−0.544525
$672$	−1.80289e47	−4.02140
$673$	4.26138e45	0.0927475	0.0463737	−	0.998924i	$-0.485233\pi$
$673$	4.26138e45	0.0927475	0.0463737	+	0.998924i	$0.485233\pi$
$674$	1.54268e46	0.327633
$675$	−7.57751e45	−0.157041
$676$	2.25292e46	0.455644
$677$	−6.45770e46	−1.27457	−0.637287	−	0.770627i	$-0.719943\pi$
$677$	−6.45770e46	−1.27457	−0.637287	+	0.770627i	$0.719943\pi$
$678$	1.93183e47	3.72117
$679$	−3.92419e46	−0.737732
$680$	−6.15179e46	−1.12877
$681$	−5.14780e46	−0.921923
$682$	−4.84690e46	−0.847270
$683$	3.35691e46	0.572794	0.286397	−	0.958111i	$-0.407542\pi$
$683$	3.35691e46	0.572794	0.286397	+	0.958111i	$0.407542\pi$
$684$	5.72419e46	0.953430
$685$	3.91596e46	0.636713
$686$	1.28990e47	2.04743
$687$	−3.17324e46	−0.491719
$688$	−7.21105e46	−1.09091
$689$	−1.34860e47	−1.99190
$690$	−7.94228e46	−1.14534
$691$	−4.55000e46	−0.640654	−0.320327	−	0.947307i	$-0.603793\pi$
$691$	−4.55000e46	−0.640654	−0.320327	+	0.947307i	$0.603793\pi$
$692$	3.77017e47	5.18334
$693$	−2.77885e46	−0.373050
$694$	4.97238e46	0.651828
$695$	1.19186e46	0.152572
$696$	−3.38111e47	−4.22676
$697$	9.66456e45	0.117989
$698$	−2.01956e47	−2.40792
$699$	−3.25978e46	−0.379590
$700$	−4.41098e46	−0.501669
$701$	−1.37611e47	−1.52864	−0.764320	−	0.644837i	$-0.776925\pi$
$701$	−1.37611e47	−1.52864	−0.764320	+	0.644837i	$0.776925\pi$
$702$	1.50888e47	1.63716
$703$	1.60985e47	1.70617
$704$	4.53193e47	4.69174
$705$	1.35308e46	0.136837
$706$	3.13885e47	3.10094
$707$	−2.03301e46	−0.196209
$708$	−1.23620e47	−1.16558
$709$	−1.72099e47	−1.58531	−0.792656	−	0.609670i	$-0.791302\pi$
$709$	−1.72099e47	−1.58531	−0.792656	+	0.609670i	$0.791302\pi$
$710$	−7.76216e46	−0.698586
$711$	−1.37556e46	−0.120957
$712$	−4.15682e47	−3.57143
$713$	4.70991e46	0.395399
$714$	1.88423e47	1.54566
$715$	−7.74428e46	−0.620771
$716$	2.12178e44	0.00166202
$717$	7.28855e46	0.557924
$718$	−4.34619e47	−3.25128
$719$	1.00489e47	0.734667	0.367334	−	0.930089i	$-0.380271\pi$
$719$	1.00489e47	0.734667	0.367334	+	0.930089i	$0.380271\pi$
$720$	7.29859e46	0.521498
$721$	2.10616e47	1.47082
$722$	6.54591e46	0.446793
$723$	2.92295e47	1.95002
$724$	4.43987e46	0.289524
$725$	−3.47491e46	−0.221497
$726$	2.31145e47	1.44022
$727$	1.79204e47	1.09151	0.545757	−	0.837944i	$-0.316242\pi$
$727$	1.79204e47	1.09151	0.545757	+	0.837944i	$0.316242\pi$
$728$	5.55934e47	3.31021
$729$	8.88336e46	0.517098
$730$	−7.28826e46	−0.414760
$731$	4.02195e46	0.223769
$732$	−2.43445e47	−1.32424
$733$	1.91032e46	0.101599	0.0507996	−	0.998709i	$-0.483823\pi$
$733$	1.91032e46	0.101599	0.0507996	+	0.998709i	$0.483823\pi$
$734$	−4.24816e47	−2.20910
$735$	−1.53613e46	−0.0781065
$736$	−8.86310e47	−4.40658
$737$	−5.62895e46	−0.273662
$738$	−1.99141e46	−0.0946742
$739$	2.81727e47	1.30977	0.654886	−	0.755728i	$-0.272717\pi$
$739$	2.81727e47	1.30977	0.654886	+	0.755728i	$0.272717\pi$
$740$	4.12004e47	1.87318
$741$	−3.09261e47	−1.37507
$742$	−7.53355e47	−3.27593
$743$	−5.77441e46	−0.245580	−0.122790	−	0.992433i	$-0.539184\pi$
$743$	−5.77441e46	−0.245580	−0.122790	+	0.992433i	$0.539184\pi$
$744$	−3.13535e47	−1.30417
$745$	−2.14879e46	−0.0874211
$746$	2.83995e47	1.13011
$747$	2.25665e46	0.0878363
$748$	−6.97290e47	−2.65483
$749$	−3.03158e47	−1.12907
$750$	5.43379e46	0.197967
$751$	2.71539e47	0.967772	0.483886	−	0.875131i	$-0.339225\pi$
$751$	2.71539e47	0.967772	0.483886	+	0.875131i	$0.339225\pi$
$752$	2.82938e47	0.986498
$753$	2.15762e47	0.735968
$754$	6.91944e47	2.30910
$755$	6.80896e46	0.222308
$756$	6.16568e47	1.96957
$757$	2.34370e47	0.732521	0.366260	−	0.930512i	$-0.380638\pi$
$757$	2.34370e47	0.732521	0.366260	+	0.930512i	$0.380638\pi$
$758$	−4.90141e47	−1.49892
$759$	−5.69796e47	−1.70502
$760$	5.64036e47	1.65152
$761$	−3.85769e47	−1.10530	−0.552651	−	0.833413i	$-0.686384\pi$
$761$	−3.85769e47	−1.10530	−0.552651	+	0.833413i	$0.686384\pi$
$762$	−3.43863e46	−0.0964115
$763$	2.24028e47	0.614679
$764$	−1.61079e48	−4.32511
$765$	−4.07078e46	−0.106970
$766$	6.39028e47	1.64341
$767$	1.60126e47	0.403032
$768$	1.21008e48	2.98094
$769$	5.88677e47	1.41936	0.709679	−	0.704525i	$-0.248840\pi$
$769$	5.88677e47	1.41936	0.709679	+	0.704525i	$0.248840\pi$
$770$	−4.32610e47	−1.02094
$771$	3.57874e47	0.826671
$772$	1.19473e48	2.70138
$773$	−4.68346e47	−1.03659	−0.518293	−	0.855203i	$-0.673432\pi$
$773$	−4.68346e47	−1.03659	−0.518293	+	0.855203i	$0.673432\pi$
$774$	−8.28736e46	−0.179552
$775$	−3.22234e46	−0.0683428
$776$	1.28422e48	2.66637
$777$	−7.98724e47	−1.62349
$778$	−4.01113e47	−0.798185
$779$	−8.86111e46	−0.172631
$780$	−7.91483e47	−1.50967
$781$	−5.56874e47	−1.03996
$782$	9.26297e47	1.69371
$783$	4.85725e47	0.869604
$784$	−3.21215e47	−0.563094
$785$	1.16130e47	0.199341
$786$	1.10001e48	1.84895
$787$	−3.57150e47	−0.587851	−0.293926	−	0.955828i	$-0.594962\pi$
$787$	−3.57150e47	−0.587851	−0.293926	+	0.955828i	$0.594962\pi$
$788$	−1.41087e48	−2.27408
$789$	9.88999e47	1.56108
$790$	−2.14146e47	−0.331027
$791$	−1.02252e48	−1.54795
$792$	9.09400e47	1.34831
$793$	3.15336e47	0.457895
$794$	−1.55551e47	−0.221225
$795$	6.78859e47	0.945632
$796$	−3.33895e48	−4.55558
$797$	−3.36343e47	−0.449490	−0.224745	−	0.974418i	$-0.572155\pi$
$797$	−3.36343e47	−0.449490	−0.224745	+	0.974418i	$0.572155\pi$
$798$	−1.72759e48	−2.26148
$799$	−1.57808e47	−0.202352
$800$	6.06378e47	0.761656
$801$	−2.75066e47	−0.338455
$802$	3.21219e46	0.0387190
$803$	−5.22875e47	−0.617435
$804$	−5.75292e47	−0.665523
$805$	4.20383e47	0.476446
$806$	6.41649e47	0.712474
$807$	−6.17383e47	−0.671647
$808$	6.65316e47	0.709154
$809$	8.08353e47	0.844210	0.422105	−	0.906547i	$-0.361291\pi$
$809$	8.08353e47	0.844210	0.422105	+	0.906547i	$0.361291\pi$
$810$	−1.02552e48	−1.04940
$811$	−1.18729e48	−1.19045	−0.595225	−	0.803559i	$-0.702937\pi$
$811$	−1.18729e48	−1.19045	−0.595225	+	0.803559i	$0.702937\pi$
$812$	2.82747e48	2.77795
$813$	1.95653e48	1.88362
$814$	4.04077e48	3.81207
$815$	2.98060e47	0.275551
$816$	−3.55044e48	−3.21658
$817$	−3.68759e47	−0.327400
$818$	3.09244e48	2.69074
$819$	3.67874e47	0.313700
$820$	−2.26780e47	−0.189529
$821$	−1.55006e48	−1.26966	−0.634829	−	0.772653i	$-0.718929\pi$
$821$	−1.55006e48	−1.26966	−0.634829	+	0.772653i	$0.718929\pi$
$822$	3.92519e48	3.15120
$823$	2.91534e47	0.229399	0.114700	−	0.993400i	$-0.463409\pi$
$823$	2.91534e47	0.229399	0.114700	+	0.993400i	$0.463409\pi$
$824$	−6.89256e48	−5.31596
$825$	3.89832e47	0.294705
$826$	8.94497e47	0.662839
$827$	−1.33839e48	−0.972166	−0.486083	−	0.873913i	$-0.661575\pi$
$827$	−1.33839e48	−0.972166	−0.486083	+	0.873913i	$0.661575\pi$
$828$	−1.39618e48	−0.994126
$829$	−2.06685e47	−0.144264	−0.0721321	−	0.997395i	$-0.522980\pi$
$829$	−2.06685e47	−0.144264	−0.0721321	+	0.997395i	$0.522980\pi$
$830$	3.51314e47	0.240385
$831$	2.28762e48	1.53450
$832$	−5.99952e48	−3.94531
$833$	1.79157e47	0.115502
$834$	1.19467e48	0.755106
$835$	4.38187e47	0.271539
$836$	6.39322e48	3.88433
$837$	4.50419e47	0.268316
$838$	−5.49865e48	−3.21166
$839$	−1.80225e48	−1.03215	−0.516075	−	0.856544i	$-0.672607\pi$
$839$	−1.80225e48	−1.03215	−0.516075	+	0.856544i	$0.672607\pi$
$840$	−2.79846e48	−1.57149
$841$	4.11374e47	0.226518
$842$	−2.61661e48	−1.41283
$843$	−2.15300e48	−1.13996
$844$	7.66674e48	3.98071
$845$	1.46898e47	0.0747962
$846$	3.25169e47	0.162367
$847$	−1.22345e48	−0.599113
$848$	1.41954e49	6.81735
$849$	3.57312e48	1.68295
$850$	−6.33736e47	−0.292749
$851$	−3.92656e48	−1.77900
$852$	−5.69138e48	−2.52909
$853$	−3.50343e48	−1.52699	−0.763493	−	0.645816i	$-0.776517\pi$
$853$	−3.50343e48	−1.52699	−0.763493	+	0.645816i	$0.776517\pi$
$854$	1.76153e48	0.753068
$855$	3.73236e47	0.156510
$856$	9.92107e48	4.08076
$857$	4.03540e48	1.62818	0.814091	−	0.580737i	$-0.197236\pi$
$857$	4.03540e48	1.62818	0.814091	+	0.580737i	$0.197236\pi$
$858$	−7.76254e48	−3.07230
$859$	−4.93399e46	−0.0191563	−0.00957813	−	0.999954i	$-0.503049\pi$
$859$	−4.93399e46	−0.0191563	−0.00957813	+	0.999954i	$0.503049\pi$
$860$	−9.43755e47	−0.359447
$861$	4.39643e47	0.164266
$862$	5.80102e48	2.12635
$863$	−5.86818e47	−0.211021	−0.105510	−	0.994418i	$-0.533648\pi$
$863$	−5.86818e47	−0.211021	−0.105510	+	0.994418i	$0.533648\pi$
$864$	−8.47598e48	−2.99029
$865$	2.45827e48	0.850871
$866$	−4.68294e47	−0.159028
$867$	−1.46196e48	−0.487103
$868$	2.62195e48	0.857136
$869$	−1.53633e48	−0.492786
$870$	−3.48311e48	−1.09622
$871$	7.45180e47	0.230124
$872$	−7.33149e48	−2.22162
$873$	8.49797e47	0.252686
$874$	−8.49291e48	−2.47809
$875$	−2.87610e47	−0.0823513
$876$	−5.34390e48	−1.50155
$877$	−5.15342e48	−1.42103	−0.710514	−	0.703683i	$-0.751537\pi$
$877$	−5.15342e48	−1.42103	−0.710514	+	0.703683i	$0.751537\pi$
$878$	−1.14418e49	−3.09623
$879$	−1.55460e48	−0.412860
$880$	8.15163e48	2.12461
$881$	7.21570e48	1.84576	0.922882	−	0.385084i	$-0.125827\pi$
$881$	7.21570e48	1.84576	0.922882	+	0.385084i	$0.125827\pi$
$882$	−3.69159e47	−0.0926791
$883$	7.21502e48	1.77781	0.888906	−	0.458089i	$-0.151466\pi$
$883$	7.21502e48	1.77781	0.888906	+	0.458089i	$0.151466\pi$
$884$	9.23096e48	2.23246
$885$	−8.06045e47	−0.191335
$886$	2.33095e48	0.543097
$887$	−2.04483e48	−0.467647	−0.233824	−	0.972279i	$-0.575124\pi$
$887$	−2.04483e48	−0.467647	−0.233824	+	0.972279i	$0.575124\pi$
$888$	2.61388e49	5.86776
$889$	1.82006e47	0.0401058
$890$	−4.28222e48	−0.926261
$891$	−7.35728e48	−1.56220
$892$	−7.54314e48	−1.57229
$893$	1.44689e48	0.296064
$894$	−2.15386e48	−0.432661
$895$	1.38347e45	0.000272828 0
$896$	−1.54037e49	−2.98224
$897$	7.54315e48	1.43376
$898$	−1.71077e49	−3.19251
$899$	2.06554e48	0.378442
$900$	9.55213e47	0.171830
$901$	−7.91745e48	−1.39838
$902$	−2.22416e48	−0.385708
$903$	1.82959e48	0.311535
$904$	3.34626e49	5.59475
$905$	2.89494e47	0.0475267
$906$	6.82501e48	1.10024
$907$	4.33823e48	0.686739	0.343370	−	0.939200i	$-0.388432\pi$
$907$	4.33823e48	0.686739	0.343370	+	0.939200i	$0.388432\pi$
$908$	−1.40880e49	−2.18995
$909$	4.40255e47	0.0672048
$910$	5.72704e48	0.858513
$911$	−1.54797e48	−0.227882	−0.113941	−	0.993488i	$-0.536348\pi$
$911$	−1.54797e48	−0.227882	−0.113941	+	0.993488i	$0.536348\pi$
$912$	3.25528e49	4.70623
$913$	2.52040e48	0.357850
$914$	−6.77134e47	−0.0944196
$915$	−1.58734e48	−0.217381
$916$	−8.68424e48	−1.16804
$917$	−5.82234e48	−0.769136
$918$	8.85839e48	1.14935
$919$	4.44681e48	0.566686	0.283343	−	0.959019i	$-0.408557\pi$
$919$	4.44681e48	0.566686	0.283343	+	0.959019i	$0.408557\pi$
$920$	−1.37574e49	−1.72201
$921$	−8.95118e47	−0.110052
$922$	1.25953e49	1.52107
$923$	7.37208e48	0.874505
$924$	−3.17199e49	−3.69610
$925$	2.68640e48	0.307491
$926$	2.53474e49	2.85005
$927$	−4.56096e48	−0.503780
$928$	−3.88694e49	−4.21760
$929$	7.81292e48	0.832826	0.416413	−	0.909176i	$-0.363287\pi$
$929$	7.81292e48	0.832826	0.416413	+	0.909176i	$0.363287\pi$
$930$	−3.22993e48	−0.338240
$931$	−1.64263e48	−0.168994
$932$	−8.92105e48	−0.901682
$933$	8.70453e48	0.864367
$934$	−3.27813e49	−3.19818
$935$	−4.54655e48	−0.435804
$936$	−1.20389e49	−1.13380
$937$	1.29441e49	1.19776	0.598880	−	0.800839i	$-0.295613\pi$
$937$	1.29441e49	1.19776	0.598880	+	0.800839i	$0.295613\pi$
$938$	4.16271e48	0.378469
$939$	−1.81769e49	−1.62382
$940$	3.70298e48	0.325044
$941$	−5.82381e47	−0.0502318	−0.0251159	−	0.999685i	$-0.507995\pi$
$941$	−5.82381e47	−0.0502318	−0.0251159	+	0.999685i	$0.507995\pi$
$942$	1.16404e49	0.986569
$943$	2.16130e48	0.180000
$944$	−1.68549e49	−1.37939
$945$	4.02022e48	0.323314
$946$	−9.25596e48	−0.731505
$947$	1.87865e49	1.45905	0.729526	−	0.683953i	$-0.239741\pi$
$947$	1.87865e49	1.45905	0.729526	+	0.683953i	$0.239741\pi$
$948$	−1.57016e49	−1.19842
$949$	6.92200e48	0.519205
$950$	5.81051e48	0.428326
$951$	4.38661e48	0.317797
$952$	3.26381e49	2.32389
$953$	1.71040e49	1.19692	0.598459	−	0.801154i	$-0.295780\pi$
$953$	1.71040e49	1.19692	0.598459	+	0.801154i	$0.295780\pi$
$954$	1.63142e49	1.12206
$955$	−1.05028e49	−0.709988
$956$	1.99466e49	1.32530
$957$	−2.49885e49	−1.63190
$958$	−1.19451e49	−0.766759
$959$	−2.07760e49	−1.31085
$960$	3.02004e49	1.87300
$961$	−1.44881e49	−0.883232
$962$	−5.34930e49	−3.20559
$963$	6.56500e48	0.386724
$964$	7.99925e49	4.63210
$965$	7.79004e48	0.443444
$966$	4.21374e49	2.35801
$967$	−3.31445e49	−1.82337	−0.911683	−	0.410893i	$-0.865217\pi$
$967$	−3.31445e49	−1.82337	−0.911683	+	0.410893i	$0.865217\pi$
$968$	4.00382e49	2.16536
$969$	−1.81562e49	−0.965348
$970$	1.32296e49	0.691533
$971$	−1.48405e49	−0.762662	−0.381331	−	0.924439i	$-0.624534\pi$
$971$	−1.48405e49	−0.762662	−0.381331	+	0.924439i	$0.624534\pi$
$972$	−3.28542e49	−1.65996
$973$	−6.32337e48	−0.314113
$974$	−3.13480e49	−1.53104
$975$	−5.16072e48	−0.247819
$976$	−3.31922e49	−1.56716
$977$	−7.11883e47	−0.0330482	−0.0165241	−	0.999863i	$-0.505260\pi$
$977$	−7.11883e47	−0.0330482	−0.0165241	+	0.999863i	$0.505260\pi$
$978$	2.98762e49	1.36375
$979$	−3.07215e49	−1.37889
$980$	−4.20394e48	−0.185535
$981$	−4.85141e48	−0.210538
$982$	7.01570e49	2.99386
$983$	3.13902e49	1.31723	0.658614	−	0.752481i	$-0.271143\pi$
$983$	3.13902e49	1.31723	0.658614	+	0.752481i	$0.271143\pi$
$984$	−1.43876e49	−0.593704
$985$	−9.19935e48	−0.373301
$986$	4.06230e49	1.62107
$987$	−7.17872e48	−0.281717
$988$	−8.46356e49	−3.26635
$989$	8.99436e48	0.341375
$990$	9.36833e48	0.349689
$991$	2.53674e49	0.931239	0.465619	−	0.884985i	$-0.345832\pi$
$991$	2.53674e49	0.931239	0.465619	+	0.884985i	$0.345832\pi$
$992$	−3.60441e49	−1.30134
$993$	−4.02880e49	−1.43058
$994$	4.11819e49	1.43824
$995$	−2.17710e49	−0.747821
$996$	2.57590e49	0.870263
$997$	4.24313e48	0.140999	0.0704995	−	0.997512i	$-0.477541\pi$
$997$	4.24313e48	0.140999	0.0704995	+	0.997512i	$0.477541\pi$
$998$	1.36729e49	0.446895
$999$	−3.75506e49	−1.20722

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.34.a.b.1.6	✓	6
5.2	odd	4		25.34.b.c.24.12		12
5.3	odd	4		25.34.b.c.24.1		12
5.4	even	2		25.34.a.c.1.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.b.1.6	✓	6	1.1	even	1	trivial
25.34.a.c.1.1		6	5.4	even	2
25.34.b.c.24.1		12	5.3	odd	4
25.34.b.c.24.12		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)

\(f(q)\)	\(=\)	\(q+178863. q^{2} +8.55112e7 q^{3} +2.34019e10 q^{4} +1.52588e11 q^{5} +1.52948e13 q^{6} -8.09549e13 q^{7} +2.64931e15 q^{8} +1.75311e15 q^{9} +O(q^{10})\)	\(q+178863. q^{2} +8.55112e7 q^{3} +2.34019e10 q^{4} +1.52588e11 q^{5} +1.52948e13 q^{6} -8.09549e13 q^{7} +2.64931e15 q^{8} +1.75311e15 q^{9} +2.72923e16 q^{10} +1.95800e17 q^{11} +2.00113e18 q^{12} -2.59207e18 q^{13} -1.44798e19 q^{14} +1.30480e19 q^{15} +2.72841e20 q^{16} -1.52177e20 q^{17} +3.13565e20 q^{18} +1.39526e21 q^{19} +3.57085e21 q^{20} -6.92255e21 q^{21} +3.50214e22 q^{22} -3.40316e22 q^{23} +2.26546e23 q^{24} +2.32831e22 q^{25} -4.63625e23 q^{26} -3.25452e23 q^{27} -1.89450e24 q^{28} -1.49246e24 q^{29} +2.33380e24 q^{30} -1.38398e24 q^{31} +2.60438e25 q^{32} +1.67431e25 q^{33} -2.72188e25 q^{34} -1.23527e25 q^{35} +4.10261e25 q^{36} +1.15380e26 q^{37} +2.49559e26 q^{38} -2.21651e26 q^{39} +4.04252e26 q^{40} -6.35087e25 q^{41} -1.23819e27 q^{42} -2.64294e26 q^{43} +4.58211e27 q^{44} +2.67503e26 q^{45} -6.08698e27 q^{46} +1.03700e27 q^{47} +2.33310e28 q^{48} -1.17730e27 q^{49} +4.16447e27 q^{50} -1.30128e28 q^{51} -6.06594e28 q^{52} +5.20280e28 q^{53} -5.82111e28 q^{54} +2.98768e28 q^{55} -2.14475e29 q^{56} +1.19310e29 q^{57} -2.66946e29 q^{58} -6.17754e28 q^{59} +3.05348e29 q^{60} -1.21654e29 q^{61} -2.47543e29 q^{62} -1.41923e29 q^{63} +2.31456e30 q^{64} -3.95519e29 q^{65} +2.99472e30 q^{66} -2.87484e29 q^{67} -3.56123e30 q^{68} -2.91008e30 q^{69} -2.20944e30 q^{70} -2.84409e30 q^{71} +4.64452e30 q^{72} -2.67045e30 q^{73} +2.06372e31 q^{74} +1.99096e30 q^{75} +3.26517e31 q^{76} -1.58510e31 q^{77} -3.96451e31 q^{78} -7.84640e30 q^{79} +4.16323e31 q^{80} -3.75754e31 q^{81} -1.13593e31 q^{82} +1.28723e31 q^{83} -1.62001e32 q^{84} -2.32203e31 q^{85} -4.72724e31 q^{86} -1.27622e32 q^{87} +5.18736e32 q^{88} -1.56902e32 q^{89} +4.78463e31 q^{90} +2.09841e32 q^{91} -7.96404e32 q^{92} -1.18346e32 q^{93} +1.85481e32 q^{94} +2.12899e32 q^{95} +2.22703e33 q^{96} +4.84738e32 q^{97} -2.10574e32 q^{98} +3.43259e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 147350 q^{2} + 26513900 q^{3} + 29520645652 q^{4} + 915527343750 q^{5} + 6615759249352 q^{6} + 19113832847500 q^{7} + 30\!\cdots\!00 q^{8}+ \cdots + 13\!\cdots\!38 q^{9}+O(q^{10}) \) 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

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more