LMFDB - Embedded newform 5.34.a.b.1.2

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			1.2
Root			$-60371.0$ 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)

$f(q)$	$=$	$q-96184.0 q^{2} +1.07272e8 q^{3} +6.61431e8 q^{4} +1.52588e11 q^{5} -1.03179e13 q^{6} -8.61302e13 q^{7} +7.62595e14 q^{8} +5.94832e15 q^{9} +O(q^{10})$	\(q-96184.0 q^{2} +1.07272e8 q^{3} +6.61431e8 q^{4} +1.52588e11 q^{5} -1.03179e13 q^{6} -8.61302e13 q^{7} +7.62595e14 q^{8} +5.94832e15 q^{9} -1.46765e16 q^{10} +9.57101e16 q^{11} +7.09533e16 q^{12} +2.44486e18 q^{13} +8.28435e18 q^{14} +1.63685e19 q^{15} -7.90311e19 q^{16} -6.06607e19 q^{17} -5.72133e20 q^{18} -1.50149e21 q^{19} +1.00926e20 q^{20} -9.23940e21 q^{21} -9.20578e21 q^{22} +1.88217e22 q^{23} +8.18055e22 q^{24} +2.32831e22 q^{25} -2.35157e23 q^{26} +4.17567e22 q^{27} -5.69692e22 q^{28} +2.67431e24 q^{29} -1.57439e24 q^{30} +2.64569e24 q^{31} +1.05089e24 q^{32} +1.02671e25 q^{33} +5.83459e24 q^{34} -1.31424e25 q^{35} +3.93440e24 q^{36} -1.12777e26 q^{37} +1.44419e26 q^{38} +2.62266e26 q^{39} +1.16363e26 q^{40} +7.31837e26 q^{41} +8.88682e26 q^{42} +3.88890e26 q^{43} +6.33056e25 q^{44} +9.07641e26 q^{45} -1.81034e27 q^{46} +3.28337e27 q^{47} -8.47786e27 q^{48} -3.12582e26 q^{49} -2.23946e27 q^{50} -6.50723e27 q^{51} +1.61711e27 q^{52} +3.35567e28 q^{53} -4.01633e27 q^{54} +1.46042e28 q^{55} -6.56825e28 q^{56} -1.61068e29 q^{57} -2.57226e29 q^{58} +2.93443e29 q^{59} +1.08266e28 q^{60} +7.07686e28 q^{61} -2.54473e29 q^{62} -5.12330e29 q^{63} +5.77794e29 q^{64} +3.73057e29 q^{65} -9.87527e29 q^{66} +1.99482e30 q^{67} -4.01229e28 q^{68} +2.01905e30 q^{69} +1.26409e30 q^{70} -1.15434e30 q^{71} +4.53616e30 q^{72} -2.83903e30 q^{73} +1.08474e31 q^{74} +2.49763e30 q^{75} -9.93131e29 q^{76} -8.24353e30 q^{77} -2.52258e31 q^{78} +6.93520e30 q^{79} -1.20592e31 q^{80} -2.85877e31 q^{81} -7.03910e31 q^{82} +4.09391e31 q^{83} -6.11122e30 q^{84} -9.25610e30 q^{85} -3.74050e31 q^{86} +2.86880e32 q^{87} +7.29881e31 q^{88} -1.49837e32 q^{89} -8.73006e31 q^{90} -2.10577e32 q^{91} +1.24492e31 q^{92} +2.83809e32 q^{93} -3.15807e32 q^{94} -2.29109e32 q^{95} +1.12731e32 q^{96} +1.00351e33 q^{97} +3.00654e31 q^{98} +5.69314e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−96184.0	−1.03779	−0.518893	−	0.854839i	$-0.673656\pi$
$2$	−96184.0	−1.03779	−0.518893	+	0.854839i	$0.673656\pi$
$3$	1.07272e8	1.43876	0.719379	−	0.694618i	$-0.244427\pi$
$3$	1.07272e8	1.43876	0.719379	+	0.694618i	$0.244427\pi$
$4$	6.61431e8	0.0770007
$5$	1.52588e11	0.447214
$5$	1.52588e11	0.447214
$6$	−1.03179e13	−1.49312
$7$	−8.61302e13	−0.979575	−0.489788	−	0.871842i	$-0.662926\pi$
$7$	−8.61302e13	−0.979575	−0.489788	+	0.871842i	$0.662926\pi$
$8$	7.62595e14	0.957876
$9$	5.94832e15	1.07002
$10$	−1.46765e16	−0.464112
$11$	9.57101e16	0.628027	0.314014	−	0.949418i	$-0.398326\pi$
$11$	9.57101e16	0.628027	0.314014	+	0.949418i	$0.398326\pi$
$12$	7.09533e16	0.110785
$13$	2.44486e18	1.01904	0.509518	−	0.860460i	$-0.329824\pi$
$13$	2.44486e18	1.01904	0.509518	+	0.860460i	$0.329824\pi$
$14$	8.28435e18	1.01659
$15$	1.63685e19	0.643432
$16$	−7.90311e19	−1.07107
$17$	−6.06607e19	−0.302343	−0.151172	−	0.988508i	$-0.548305\pi$
$17$	−6.06607e19	−0.302343	−0.151172	+	0.988508i	$0.548305\pi$
$18$	−5.72133e20	−1.11045
$19$	−1.50149e21	−1.19423	−0.597115	−	0.802156i	$-0.703686\pi$
$19$	−1.50149e21	−1.19423	−0.597115	+	0.802156i	$0.703686\pi$
$20$	1.00926e20	0.0344358
$21$	−9.23940e21	−1.40937
$22$	−9.20578e21	−0.651758
$23$	1.88217e22	0.639955	0.319977	−	0.947425i	$-0.396325\pi$
$23$	1.88217e22	0.639955	0.319977	+	0.947425i	$0.396325\pi$
$24$	8.18055e22	1.37815
$25$	2.32831e22	0.200000
$26$	−2.35157e23	−1.05754
$27$	4.17567e22	0.100745
$28$	−5.69692e22	−0.0754280
$29$	2.67431e24	1.98447	0.992235	−	0.124376i	$-0.0396929\pi$
$29$	2.67431e24	1.98447	0.992235	+	0.124376i	$0.0396929\pi$
$30$	−1.57439e24	−0.667745
$31$	2.64569e24	0.653236	0.326618	−	0.945156i	$-0.394091\pi$
$31$	2.64569e24	0.653236	0.326618	+	0.945156i	$0.394091\pi$
$32$	1.05089e24	0.153667
$33$	1.02671e25	0.903579
$34$	5.83459e24	0.313768
$35$	−1.31424e25	−0.438079
$36$	3.93440e24	0.0823925
$37$	−1.12777e26	−1.50277	−0.751387	−	0.659862i	$-0.770615\pi$
$37$	−1.12777e26	−1.50277	−0.751387	+	0.659862i	$0.770615\pi$
$38$	1.44419e26	1.23935
$39$	2.62266e26	1.46614
$40$	1.16363e26	0.428375
$41$	7.31837e26	1.79259	0.896294	−	0.443460i	$-0.146249\pi$
$41$	7.31837e26	1.79259	0.896294	+	0.443460i	$0.146249\pi$
$42$	8.88682e26	1.46263
$43$	3.88890e26	0.434107	0.217054	−	0.976160i	$-0.430355\pi$
$43$	3.88890e26	0.434107	0.217054	+	0.976160i	$0.430355\pi$
$44$	6.33056e25	0.0483585
$45$	9.07641e26	0.478529
$46$	−1.81034e27	−0.664136
$47$	3.28337e27	0.844704	0.422352	−	0.906432i	$-0.361205\pi$
$47$	3.28337e27	0.844704	0.422352	+	0.906432i	$0.361205\pi$
$48$	−8.47786e27	−1.54101
$49$	−3.12582e26	−0.0404323
$50$	−2.23946e27	−0.207557
$51$	−6.50723e27	−0.434999
$52$	1.61711e27	0.0784664
$53$	3.35567e28	1.18912	0.594562	−	0.804050i	$-0.297325\pi$
$53$	3.35567e28	1.18912	0.594562	+	0.804050i	$0.297325\pi$
$54$	−4.01633e27	−0.104552
$55$	1.46042e28	0.280862
$56$	−6.56825e28	−0.938312
$57$	−1.61068e29	−1.71821
$58$	−2.57226e29	−2.05946
$59$	2.93443e29	1.77201	0.886005	−	0.463676i	$-0.153470\pi$
$59$	2.93443e29	1.77201	0.886005	+	0.463676i	$0.153470\pi$
$60$	1.08266e28	0.0495447
$61$	7.07686e28	0.246546	0.123273	−	0.992373i	$-0.460661\pi$
$61$	7.07686e28	0.246546	0.123273	+	0.992373i	$0.460661\pi$
$62$	−2.54473e29	−0.677920
$63$	−5.12330e29	−1.04817
$64$	5.77794e29	0.911598
$65$	3.73057e29	0.455726
$66$	−9.87527e29	−0.937722
$67$	1.99482e30	1.47798	0.738991	−	0.673715i	$-0.235302\pi$
$67$	1.99482e30	1.47798	0.738991	+	0.673715i	$0.235302\pi$
$68$	−4.01229e28	−0.0232807
$69$	2.01905e30	0.920739
$70$	1.26409e30	0.454633
$71$	−1.15434e30	−0.328527	−0.164263	−	0.986417i	$-0.552525\pi$
$71$	−1.15434e30	−0.328527	−0.164263	+	0.986417i	$0.552525\pi$
$72$	4.53616e30	1.02495
$73$	−2.83903e30	−0.510908	−0.255454	−	0.966821i	$-0.582225\pi$
$73$	−2.83903e30	−0.510908	−0.255454	+	0.966821i	$0.582225\pi$
$74$	1.08474e31	1.55956
$75$	2.49763e30	0.287751
$76$	−9.93131e29	−0.0919565
$77$	−8.24353e30	−0.615200
$78$	−2.52258e31	−1.52154
$79$	6.93520e30	0.339010	0.169505	−	0.985529i	$-0.445783\pi$
$79$	6.93520e30	0.339010	0.169505	+	0.985529i	$0.445783\pi$
$80$	−1.20592e31	−0.478998
$81$	−2.85877e31	−0.925075
$82$	−7.03910e31	−1.86032
$83$	4.09391e31	0.885828	0.442914	−	0.896564i	$-0.353945\pi$
$83$	4.09391e31	0.885828	0.442914	+	0.896564i	$0.353945\pi$
$84$	−6.11122e30	−0.108523
$85$	−9.25610e30	−0.135212
$86$	−3.74050e31	−0.450510
$87$	2.86880e32	2.85517
$88$	7.29881e31	0.601572
$89$	−1.49837e32	−1.02491	−0.512454	−	0.858715i	$-0.671264\pi$
$89$	−1.49837e32	−1.02491	−0.512454	+	0.858715i	$0.671264\pi$
$90$	−8.73006e31	−0.496610
$91$	−2.10577e32	−0.998222
$92$	1.24492e31	0.0492769
$93$	2.83809e32	0.939849
$94$	−3.15807e32	−0.876623
$95$	−2.29109e32	−0.534075
$96$	1.12731e32	0.221090
$97$	1.00351e33	1.65878	0.829388	−	0.558673i	$-0.188689\pi$
$97$	1.00351e33	1.65878	0.829388	+	0.558673i	$0.188689\pi$
$98$	3.00654e31	0.0419601
$99$	5.69314e32	0.672003
$100$	1.54001e31	0.0154001
$101$	−8.22627e31	−0.0698072	−0.0349036	−	0.999391i	$-0.511112\pi$
$101$	−8.22627e31	−0.0698072	−0.0349036	+	0.999391i	$0.511112\pi$
$102$	6.25891e32	0.451436
$103$	1.80950e33	1.11108	0.555539	−	0.831491i	$-0.312512\pi$
$103$	1.80950e33	1.11108	0.555539	+	0.831491i	$0.312512\pi$
$104$	1.86444e33	0.976110
$105$	−1.40982e33	−0.630290
$106$	−3.22762e33	−1.23406
$107$	−2.36850e33	−0.775605	−0.387802	−	0.921743i	$-0.626766\pi$
$107$	−2.36850e33	−0.775605	−0.387802	+	0.921743i	$0.626766\pi$
$108$	2.76192e31	0.00775744
$109$	−3.69273e33	−0.890862	−0.445431	−	0.895316i	$-0.646949\pi$
$109$	−3.69273e33	−0.890862	−0.445431	+	0.895316i	$0.646949\pi$
$110$	−1.40469e33	−0.291475
$111$	−1.20979e34	−2.16213
$112$	6.80697e33	1.04920
$113$	−1.24016e34	−1.65076	−0.825382	−	0.564575i	$-0.809040\pi$
$113$	−1.24016e34	−1.65076	−0.825382	+	0.564575i	$0.809040\pi$
$114$	1.54922e34	1.78313
$115$	2.87196e33	0.286196
$116$	1.76887e33	0.152806
$117$	1.45428e34	1.09039
$118$	−2.82246e34	−1.83897
$119$	5.22472e33	0.296168
$120$	1.24825e34	0.616328
$121$	−1.40647e34	−0.605582
$122$	−6.80681e33	−0.255862
$123$	7.85059e34	2.57910
$124$	1.74994e33	0.0502997
$125$	3.55271e33	0.0894427
$126$	4.92780e34	1.08777
$127$	−3.85830e34	−0.747541	−0.373771	−	0.927521i	$-0.621935\pi$
$127$	−3.85830e34	−0.747541	−0.373771	+	0.927521i	$0.621935\pi$
$128$	−6.46016e34	−1.09971
$129$	4.17171e34	0.624575
$130$	−3.58821e34	−0.472947
$131$	7.28441e34	0.846093	0.423046	−	0.906108i	$-0.360961\pi$
$131$	7.28441e34	0.846093	0.423046	+	0.906108i	$0.360961\pi$
$132$	6.79095e33	0.0695762
$133$	1.29324e35	1.16984
$134$	−1.91870e35	−1.53383
$135$	6.37157e33	0.0450546
$136$	−4.62596e34	−0.289608
$137$	−1.31044e35	−0.726990	−0.363495	−	0.931596i	$-0.618417\pi$
$137$	−1.31044e35	−0.726990	−0.363495	+	0.931596i	$0.618417\pi$
$138$	−1.94200e35	−0.955531
$139$	−2.86050e35	−1.24939	−0.624694	−	0.780870i	$-0.714776\pi$
$139$	−2.86050e35	−1.24939	−0.624694	+	0.780870i	$0.714776\pi$
$140$	−8.69281e33	−0.0337324
$141$	3.52215e35	1.21532
$142$	1.11029e35	0.340941
$143$	2.33998e35	0.639982
$144$	−4.70102e35	−1.14607
$145$	4.08067e35	0.887482
$146$	2.73069e35	0.530214
$147$	−3.35314e34	−0.0581723
$148$	−7.45944e34	−0.115715
$149$	−4.76533e35	−0.661485	−0.330742	−	0.943721i	$-0.607299\pi$
$149$	−4.76533e35	−0.661485	−0.330742	+	0.943721i	$0.607299\pi$
$150$	−2.40232e35	−0.298625
$151$	2.97234e35	0.331115	0.165557	−	0.986200i	$-0.447058\pi$
$151$	2.97234e35	0.331115	0.165557	+	0.986200i	$0.447058\pi$
$152$	−1.14503e36	−1.14392
$153$	−3.60829e35	−0.323514
$154$	7.92896e35	0.638446
$155$	4.03700e35	0.292136
$156$	1.73471e35	0.112894
$157$	2.26342e36	1.32562	0.662812	−	0.748786i	$-0.269363\pi$
$157$	2.26342e36	1.32562	0.662812	+	0.748786i	$0.269363\pi$
$158$	−6.67056e35	−0.351820
$159$	3.59971e36	1.71086
$160$	1.60353e35	0.0687221
$161$	−1.62112e36	−0.626884
$162$	2.74968e36	0.960030
$163$	1.48676e35	0.0468970	0.0234485	−	0.999725i	$-0.492535\pi$
$163$	1.48676e35	0.0468970	0.0234485	+	0.999725i	$0.492535\pi$
$164$	4.84059e35	0.138031
$165$	1.56663e36	0.404093
$166$	−3.93768e36	−0.919300
$167$	1.71469e36	0.362546	0.181273	−	0.983433i	$-0.441978\pi$
$167$	1.71469e36	0.362546	0.181273	+	0.983433i	$0.441978\pi$
$168$	−7.04592e36	−1.35000
$169$	2.21226e35	0.0384331
$170$	8.90288e35	0.140321
$171$	−8.93133e36	−1.27785
$172$	2.57224e35	0.0334265
$173$	−6.70788e36	−0.792181	−0.396090	−	0.918211i	$-0.629633\pi$
$173$	−6.70788e36	−0.792181	−0.396090	+	0.918211i	$0.629633\pi$
$174$	−2.75932e37	−2.96306
$175$	−2.00538e36	−0.195915
$176$	−7.56408e36	−0.672662
$177$	3.14784e37	2.54949
$178$	1.44120e37	1.06364
$179$	−7.92192e36	−0.533035	−0.266517	−	0.963830i	$-0.585873\pi$
$179$	−7.92192e36	−0.533035	−0.266517	+	0.963830i	$0.585873\pi$
$180$	6.00342e35	0.0368470
$181$	2.84989e37	1.59637	0.798183	−	0.602416i	$-0.205795\pi$
$181$	2.84989e37	1.59637	0.798183	+	0.602416i	$0.205795\pi$
$182$	2.02541e37	1.03594
$183$	7.59152e36	0.354720
$184$	1.43533e37	0.612997
$185$	−1.72085e37	−0.672061
$186$	−2.72979e37	−0.975362
$187$	−5.80585e36	−0.189880
$188$	2.17172e36	0.0650428
$189$	−3.59651e36	−0.0986874
$190$	2.20366e37	0.554256
$191$	−1.67422e37	−0.386155	−0.193077	−	0.981184i	$-0.561847\pi$
$191$	−1.67422e37	−0.386155	−0.193077	+	0.981184i	$0.561847\pi$
$192$	6.19813e37	1.31157
$193$	2.80272e37	0.544357	0.272179	−	0.962247i	$-0.412256\pi$
$193$	2.80272e37	0.544357	0.272179	+	0.962247i	$0.412256\pi$
$194$	−9.65216e37	−1.72146
$195$	4.00187e37	0.655680
$196$	−2.06751e35	−0.00311332
$197$	5.75950e37	0.797428	0.398714	−	0.917075i	$-0.369457\pi$
$197$	5.75950e37	0.797428	0.398714	+	0.917075i	$0.369457\pi$
$198$	−5.47589e37	−0.697396
$199$	−1.44611e38	−1.69483	−0.847415	−	0.530931i	$-0.821842\pi$
$199$	−1.44611e38	−1.69483	−0.847415	+	0.530931i	$0.821842\pi$
$200$	1.77556e37	0.191575
$201$	2.13989e38	2.12646
$202$	7.91236e36	0.0724450
$203$	−2.30339e38	−1.94394
$204$	−4.30408e36	−0.0334952
$205$	1.11669e38	0.801670
$206$	−1.74045e38	−1.15306
$207$	1.11957e38	0.684766
$208$	−1.93220e38	−1.09146
$209$	−1.43708e38	−0.750008
$210$	1.35602e38	0.654106
$211$	−4.42459e37	−0.197339	−0.0986695	−	0.995120i	$-0.531459\pi$
$211$	−4.42459e37	−0.197339	−0.0986695	+	0.995120i	$0.531459\pi$
$212$	2.21954e37	0.0915634
$213$	−1.23829e38	−0.472670
$214$	2.27812e38	0.804912
$215$	5.93398e37	0.194139
$216$	3.18435e37	0.0965014
$217$	−2.27873e38	−0.639894
$218$	3.55182e38	0.924524
$219$	−3.04550e38	−0.735073
$220$	9.65967e36	0.0216266
$221$	−1.48307e38	−0.308099
$222$	1.16363e39	2.24383
$223$	−4.20819e38	−0.753469	−0.376734	−	0.926321i	$-0.622953\pi$
$223$	−4.20819e38	−0.753469	−0.376734	+	0.926321i	$0.622953\pi$
$224$	−9.05132e37	−0.150529
$225$	1.38495e38	0.214004
$226$	1.19284e39	1.71314
$227$	−2.29758e38	−0.306793	−0.153396	−	0.988165i	$-0.549021\pi$
$227$	−2.29758e38	−0.306793	−0.153396	+	0.988165i	$0.549021\pi$
$228$	−1.06536e38	−0.132303
$229$	−1.22734e39	−1.41801	−0.709007	−	0.705202i	$-0.750856\pi$
$229$	−1.22734e39	−1.41801	−0.709007	+	0.705202i	$0.750856\pi$
$230$	−2.76237e38	−0.297011
$231$	−8.84304e38	−0.885123
$232$	2.03942e39	1.90088
$233$	2.11378e39	1.83522	0.917608	−	0.397486i	$-0.130117\pi$
$233$	2.11378e39	1.83522	0.917608	+	0.397486i	$0.130117\pi$
$234$	−1.39879e39	−1.13159
$235$	5.01002e38	0.377763
$236$	1.94093e38	0.136446
$237$	7.43956e38	0.487753
$238$	−5.02535e38	−0.307359
$239$	−9.09248e38	−0.518940	−0.259470	−	0.965751i	$-0.583548\pi$
$239$	−9.09248e38	−0.518940	−0.259470	+	0.965751i	$0.583548\pi$
$240$	−1.29362e39	−0.689162
$241$	−1.71576e39	−0.853443	−0.426722	−	0.904383i	$-0.640332\pi$
$241$	−1.71576e39	−0.853443	−0.426722	+	0.904383i	$0.640332\pi$
$242$	1.35280e39	0.628465
$243$	−3.29880e39	−1.43170
$244$	4.68085e37	0.0189842
$245$	−4.76962e37	−0.0180819
$246$	−7.55101e39	−2.67655
$247$	−3.67093e39	−1.21696
$248$	2.01759e39	0.625720
$249$	4.39163e39	1.27449
$250$	−3.41714e38	−0.0928224
$251$	3.71395e39	0.944537	0.472269	−	0.881455i	$-0.343435\pi$
$251$	3.71395e39	0.944537	0.472269	+	0.881455i	$0.343435\pi$
$252$	−3.38871e38	−0.0807096
$253$	1.80143e39	0.401909
$254$	3.71107e39	0.775788
$255$	−9.92924e38	−0.194537
$256$	1.25043e39	0.229668
$257$	3.64681e39	0.628082	0.314041	−	0.949409i	$-0.398317\pi$
$257$	3.64681e39	0.628082	0.314041	+	0.949409i	$0.398317\pi$
$258$	−4.01252e39	−0.648175
$259$	9.71354e39	1.47208
$260$	2.46751e38	0.0350913
$261$	1.59076e40	2.12343
$262$	−7.00644e39	−0.878064
$263$	3.70275e39	0.435767	0.217884	−	0.975975i	$-0.430085\pi$
$263$	3.70275e39	0.435767	0.217884	+	0.975975i	$0.430085\pi$
$264$	7.82961e39	0.865517
$265$	5.12035e39	0.531793
$266$	−1.24389e40	−1.21404
$267$	−1.60734e40	−1.47459
$268$	1.31944e39	0.113806
$269$	−1.93097e40	−1.56626	−0.783129	−	0.621859i	$-0.786378\pi$
$269$	−1.93097e40	−1.56626	−0.783129	+	0.621859i	$0.786378\pi$
$270$	−6.12843e38	−0.0467570
$271$	−5.56561e37	−0.00399502	−0.00199751	−	0.999998i	$-0.500636\pi$
$271$	−5.56561e37	−0.00399502	−0.00199751	+	0.999998i	$0.500636\pi$
$272$	4.79409e39	0.323831
$273$	−2.25891e40	−1.43620
$274$	1.26044e40	0.754460
$275$	2.22842e39	0.125605
$276$	1.33546e39	0.0708976
$277$	−2.59199e40	−1.29634	−0.648168	−	0.761497i	$-0.724465\pi$
$277$	−2.59199e40	−1.29634	−0.648168	+	0.761497i	$0.724465\pi$
$278$	2.75134e40	1.29660
$279$	1.57374e40	0.698977
$280$	−1.00224e40	−0.419626
$281$	4.04959e40	1.59866	0.799331	−	0.600891i	$-0.205187\pi$
$281$	4.04959e40	1.59866	0.799331	+	0.600891i	$0.205187\pi$
$282$	−3.38774e40	−1.26125
$283$	4.05121e40	1.42269	0.711343	−	0.702846i	$-0.248087\pi$
$283$	4.05121e40	1.42269	0.711343	+	0.702846i	$0.248087\pi$
$284$	−7.63516e38	−0.0252968
$285$	−2.45771e40	−0.768405
$286$	−2.25069e40	−0.664165
$287$	−6.30332e40	−1.75597
$288$	6.25102e39	0.164428
$289$	−3.65748e40	−0.908588
$290$	−3.92495e40	−0.921017
$291$	1.07649e41	2.38658
$292$	−1.87782e39	−0.0393403
$293$	7.90241e38	0.0156475	0.00782373	−	0.999969i	$-0.497510\pi$
$293$	7.90241e38	0.0156475	0.00782373	+	0.999969i	$0.497510\pi$
$294$	3.22519e39	0.0603704
$295$	4.47759e40	0.792467
$296$	−8.60035e40	−1.43947
$297$	3.99654e39	0.0632707
$298$	4.58349e40	0.686480
$299$	4.60164e40	0.652136
$300$	1.65201e39	0.0221571
$301$	−3.34951e40	−0.425241
$302$	−2.85891e40	−0.343627
$303$	−8.82452e39	−0.100436
$304$	1.18664e41	1.27910
$305$	1.07984e40	0.110259
$306$	3.47060e40	0.335739
$307$	1.53513e41	1.40722	0.703612	−	0.710585i	$-0.251569\pi$
$307$	1.53513e41	1.40722	0.703612	+	0.710585i	$0.251569\pi$
$308$	−5.45253e39	−0.0473708
$309$	1.94110e41	1.59857
$310$	−3.88295e40	−0.303175
$311$	−2.01085e41	−1.48879	−0.744395	−	0.667739i	$-0.767262\pi$
$311$	−2.01085e41	−1.48879	−0.744395	+	0.667739i	$0.767262\pi$
$312$	2.00003e41	1.40438
$313$	−6.89540e40	−0.459280	−0.229640	−	0.973276i	$-0.573755\pi$
$313$	−6.89540e40	−0.459280	−0.229640	+	0.973276i	$0.573755\pi$
$314$	−2.17705e41	−1.37571
$315$	−7.81753e40	−0.468755
$316$	4.58716e39	0.0261040
$317$	−2.25823e41	−1.21981	−0.609903	−	0.792476i	$-0.708792\pi$
$317$	−2.25823e41	−1.21981	−0.609903	+	0.792476i	$0.708792\pi$
$318$	−3.46234e41	−1.77551
$319$	2.55958e41	1.24630
$320$	8.81643e40	0.407679
$321$	−2.54075e41	−1.11591
$322$	1.55925e41	0.650571
$323$	9.10814e40	0.361067
$324$	−1.89088e40	−0.0712314
$325$	5.69239e40	0.203807
$326$	−1.43002e40	−0.0486691
$327$	−3.96128e41	−1.28173
$328$	5.58095e41	1.71708
$329$	−2.82797e41	−0.827451
$330$	−1.50685e41	−0.419362
$331$	−1.74008e41	−0.460688	−0.230344	−	0.973109i	$-0.573985\pi$
$331$	−1.74008e41	−0.460688	−0.230344	+	0.973109i	$0.573985\pi$
$332$	2.70784e40	0.0682094
$333$	−6.70836e41	−1.60800
$334$	−1.64925e41	−0.376245
$335$	3.04385e41	0.660974
$336$	7.30200e41	1.50954
$337$	8.05374e41	1.58527	0.792636	−	0.609695i	$-0.208708\pi$
$337$	8.05374e41	1.58527	0.792636	+	0.609695i	$0.208708\pi$
$338$	−2.12784e40	−0.0398853
$339$	−1.33035e42	−2.37505
$340$	−6.12227e39	−0.0104114
$341$	2.53219e41	0.410250
$342$	8.59052e41	1.32614
$343$	6.92795e41	1.01918
$344$	2.96565e41	0.415821
$345$	3.08082e41	0.411767
$346$	6.45191e41	0.822115
$347$	6.26061e41	0.760642	0.380321	−	0.924854i	$-0.375813\pi$
$347$	6.26061e41	0.760642	0.380321	+	0.924854i	$0.375813\pi$
$348$	1.89751e41	0.219850
$349$	−9.05089e40	−0.100017	−0.0500083	−	0.998749i	$-0.515925\pi$
$349$	−9.05089e40	−0.100017	−0.0500083	+	0.998749i	$0.515925\pi$
$350$	1.92885e41	0.203318
$351$	1.02089e41	0.102663
$352$	1.00581e41	0.0965073
$353$	−1.08093e42	−0.989725	−0.494862	−	0.868971i	$-0.664782\pi$
$353$	−1.08093e42	−0.989725	−0.494862	+	0.868971i	$0.664782\pi$
$354$	−3.02772e42	−2.64583
$355$	−1.76138e41	−0.146922
$356$	−9.91071e40	−0.0789186
$357$	5.60469e41	0.426114
$358$	7.61962e41	0.553176
$359$	−2.08351e41	−0.144456	−0.0722282	−	0.997388i	$-0.523011\pi$
$359$	−2.08351e41	−0.144456	−0.0722282	+	0.997388i	$0.523011\pi$
$360$	6.92163e41	0.458371
$361$	6.73698e41	0.426183
$362$	−2.74114e42	−1.65669
$363$	−1.50876e42	−0.871285
$364$	−1.39282e41	−0.0768638
$365$	−4.33202e41	−0.228485
$366$	−7.30183e41	−0.368124
$367$	−1.16121e42	−0.559654	−0.279827	−	0.960050i	$-0.590277\pi$
$367$	−1.16121e42	−0.559654	−0.279827	+	0.960050i	$0.590277\pi$
$368$	−1.48750e42	−0.685437
$369$	4.35320e42	1.91811
$370$	1.65518e42	0.697456
$371$	−2.89024e42	−1.16484
$372$	1.87720e41	0.0723690
$373$	−1.34955e42	−0.497728	−0.248864	−	0.968538i	$-0.580057\pi$
$373$	−1.34955e42	−0.497728	−0.248864	+	0.968538i	$0.580057\pi$
$374$	5.58430e41	0.197055
$375$	3.81108e41	0.128686
$376$	2.50388e42	0.809122
$377$	6.53832e42	2.02225
$378$	3.45927e41	0.102416
$379$	3.19198e42	0.904717	0.452358	−	0.891836i	$-0.350583\pi$
$379$	3.19198e42	0.904717	0.452358	+	0.891836i	$0.350583\pi$
$380$	−1.51540e41	−0.0411242
$381$	−4.13890e42	−1.07553
$382$	1.61033e42	0.400746
$383$	−3.06206e42	−0.729849	−0.364925	−	0.931037i	$-0.618905\pi$
$383$	−3.06206e42	−0.729849	−0.364925	+	0.931037i	$0.618905\pi$
$384$	−6.92997e42	−1.58222
$385$	−1.25786e42	−0.275126
$386$	−2.69577e42	−0.564926
$387$	2.31324e42	0.464504
$388$	6.63752e41	0.127727
$389$	5.44019e42	1.00333	0.501667	−	0.865061i	$-0.332720\pi$
$389$	5.44019e42	1.00333	0.501667	+	0.865061i	$0.332720\pi$
$390$	−3.84916e42	−0.680456
$391$	−1.14174e42	−0.193486
$392$	−2.38374e41	−0.0387292
$393$	7.81416e42	1.21732
$394$	−5.53971e42	−0.827560
$395$	1.05823e42	0.151610
$396$	3.76562e41	0.0517447
$397$	4.34919e42	0.573277	0.286639	−	0.958039i	$-0.407462\pi$
$397$	4.34919e42	0.573277	0.286639	+	0.958039i	$0.407462\pi$
$398$	1.39093e43	1.75887
$399$	1.38729e43	1.68311
$400$	−1.84009e42	−0.214214
$401$	−1.13262e42	−0.126532	−0.0632660	−	0.997997i	$-0.520152\pi$
$401$	−1.13262e42	−0.126532	−0.0632660	+	0.997997i	$0.520152\pi$
$402$	−2.05823e43	−2.20681
$403$	6.46834e42	0.665671
$404$	−5.44111e40	−0.00537520
$405$	−4.36214e42	−0.413706
$406$	2.21549e43	2.01739
$407$	−1.07939e43	−0.943783
$408$	−4.96238e42	−0.416675
$409$	6.57876e42	0.530530	0.265265	−	0.964176i	$-0.414541\pi$
$409$	6.57876e42	0.530530	0.265265	+	0.964176i	$0.414541\pi$
$410$	−1.07408e43	−0.831962
$411$	−1.40574e43	−1.04596
$412$	1.19686e42	0.0855538
$413$	−2.52743e43	−1.73582
$414$	−1.07685e43	−0.710640
$415$	6.24681e42	0.396154
$416$	2.56928e42	0.156593
$417$	−3.06853e43	−1.79757
$418$	1.38224e43	0.778349
$419$	−2.13895e43	−1.15789	−0.578947	−	0.815365i	$-0.696536\pi$
$419$	−2.13895e43	−1.15789	−0.578947	+	0.815365i	$0.696536\pi$
$420$	−9.32499e41	−0.0485328
$421$	−5.34625e42	−0.267544	−0.133772	−	0.991012i	$-0.542709\pi$
$421$	−5.34625e42	−0.267544	−0.133772	+	0.991012i	$0.542709\pi$
$422$	4.25575e42	0.204796
$423$	1.95305e43	0.903852
$424$	2.55902e43	1.13903
$425$	−1.41237e42	−0.0604687
$426$	1.19104e43	0.490531
$427$	−6.09531e42	−0.241511
$428$	−1.56660e42	−0.0597221
$429$	2.51016e43	0.920779
$430$	−5.70754e42	−0.201474
$431$	2.33735e43	0.794053	0.397026	−	0.917807i	$-0.370042\pi$
$431$	2.33735e43	0.794053	0.397026	+	0.917807i	$0.370042\pi$
$432$	−3.30008e42	−0.107905
$433$	−1.61313e43	−0.507714	−0.253857	−	0.967242i	$-0.581699\pi$
$433$	−1.61313e43	−0.507714	−0.253857	+	0.967242i	$0.581699\pi$
$434$	2.19178e43	0.664074
$435$	4.37744e43	1.27687
$436$	−2.44249e42	−0.0685970
$437$	−2.82605e43	−0.764252
$438$	2.92928e43	0.762849
$439$	4.60088e43	1.15392	0.576961	−	0.816772i	$-0.304238\pi$
$439$	4.60088e43	1.15392	0.576961	+	0.816772i	$0.304238\pi$
$440$	1.11371e43	0.269031
$441$	−1.85934e42	−0.0432635
$442$	1.42648e43	0.319741
$443$	−5.92450e43	−1.27935	−0.639676	−	0.768644i	$-0.720932\pi$
$443$	−5.92450e43	−1.27935	−0.639676	+	0.768644i	$0.720932\pi$
$444$	−8.00193e42	−0.166485
$445$	−2.28634e43	−0.458353
$446$	4.04761e43	0.781940
$447$	−5.11189e43	−0.951716
$448$	−4.97655e43	−0.892978
$449$	−1.64413e43	−0.284361	−0.142181	−	0.989841i	$-0.545411\pi$
$449$	−1.64413e43	−0.284361	−0.142181	+	0.989841i	$0.545411\pi$
$450$	−1.33210e43	−0.222091
$451$	7.00442e43	1.12579
$452$	−8.20283e42	−0.127110
$453$	3.18850e43	0.476394
$454$	2.20991e43	0.318385
$455$	−3.21314e43	−0.446418
$456$	−1.22830e44	−1.64583
$457$	2.69494e42	0.0348283	0.0174141	−	0.999848i	$-0.494457\pi$
$457$	2.69494e42	0.0348283	0.0174141	+	0.999848i	$0.494457\pi$
$458$	1.18051e44	1.47160
$459$	−2.53299e42	−0.0304596
$460$	1.89960e42	0.0220373
$461$	−8.91542e43	−0.997876	−0.498938	−	0.866638i	$-0.666276\pi$
$461$	−8.91542e43	−0.997876	−0.498938	+	0.866638i	$0.666276\pi$
$462$	8.50559e43	0.918569
$463$	−7.81223e43	−0.814121	−0.407060	−	0.913401i	$-0.633446\pi$
$463$	−7.81223e43	−0.814121	−0.407060	+	0.913401i	$0.633446\pi$
$464$	−2.11354e44	−2.12551
$465$	4.33059e43	0.420313
$466$	−2.03312e44	−1.90456
$467$	1.34336e44	1.21469	0.607344	−	0.794439i	$-0.292235\pi$
$467$	1.34336e44	1.21469	0.607344	+	0.794439i	$0.292235\pi$
$468$	9.61907e42	0.0839608
$469$	−1.71814e44	−1.44780
$470$	−4.81884e43	−0.392038
$471$	2.42802e44	1.90725
$472$	2.23779e44	1.69737
$473$	3.72207e43	0.272631
$474$	−7.15567e43	−0.506183
$475$	−3.49593e43	−0.238846
$476$	3.45579e42	0.0228052
$477$	1.99606e44	1.27239
$478$	8.74551e43	0.538549
$479$	6.08543e43	0.362039	0.181020	−	0.983479i	$-0.442060\pi$
$479$	6.08543e43	0.362039	0.181020	+	0.983479i	$0.442060\pi$
$480$	1.72014e43	0.0988745
$481$	−2.75725e44	−1.53138
$482$	1.65028e44	0.885692
$483$	−1.73901e44	−0.901933
$484$	−9.30285e42	−0.0466302
$485$	1.53123e44	0.741827
$486$	3.17292e44	1.48580
$487$	−2.29550e44	−1.03908	−0.519541	−	0.854446i	$-0.673897\pi$
$487$	−2.29550e44	−1.03908	−0.519541	+	0.854446i	$0.673897\pi$
$488$	5.39678e43	0.236161
$489$	1.59488e43	0.0674734
$490$	4.58761e42	0.0187651
$491$	−5.01787e43	−0.198461	−0.0992305	−	0.995064i	$-0.531638\pi$
$491$	−5.01787e43	−0.198461	−0.0992305	+	0.995064i	$0.531638\pi$
$492$	5.19262e43	0.198592
$493$	−1.62226e44	−0.599992
$494$	3.53085e44	1.26295
$495$	8.68705e43	0.300529
$496$	−2.09092e44	−0.699663
$497$	9.94235e43	0.321817
$498$	−4.22405e44	−1.32265
$499$	−1.28404e44	−0.388974	−0.194487	−	0.980905i	$-0.562304\pi$
$499$	−1.28404e44	−0.388974	−0.194487	+	0.980905i	$0.562304\pi$
$500$	2.34987e42	0.00688715
$501$	1.83939e44	0.521615
$502$	−3.57222e44	−0.980228
$503$	3.85407e44	1.02341	0.511703	−	0.859163i	$-0.329015\pi$
$503$	3.85407e44	1.02341	0.511703	+	0.859163i	$0.329015\pi$
$504$	−3.90700e44	−1.00401
$505$	−1.25523e43	−0.0312187
$506$	−1.73268e44	−0.417096
$507$	2.37314e43	0.0552959
$508$	−2.55200e43	−0.0575612
$509$	5.40769e44	1.18078	0.590389	−	0.807119i	$-0.298974\pi$
$509$	5.40769e44	1.18078	0.590389	+	0.807119i	$0.298974\pi$
$510$	9.55034e43	0.201888
$511$	2.44526e44	0.500473
$512$	4.34652e44	0.861365
$513$	−6.26972e43	−0.120313
$514$	−3.50765e44	−0.651815
$515$	2.76108e44	0.496889
$516$	2.75930e43	0.0480927
$517$	3.14251e44	0.530497
$518$	−9.34287e44	−1.52770
$519$	−7.19570e44	−1.13976
$520$	2.84491e44	0.436530
$521$	−9.57656e42	−0.0142360	−0.00711799	−	0.999975i	$-0.502266\pi$
$521$	−9.57656e42	−0.0142360	−0.00711799	+	0.999975i	$0.502266\pi$
$522$	−1.53006e45	−2.20366
$523$	−7.88861e43	−0.110084	−0.0550418	−	0.998484i	$-0.517529\pi$
$523$	−7.88861e43	−0.110084	−0.0550418	+	0.998484i	$0.517529\pi$
$524$	4.81813e43	0.0651497
$525$	−2.15122e44	−0.281874
$526$	−3.56145e44	−0.452233
$527$	−1.60489e44	−0.197502
$528$	−8.11417e44	−0.967798
$529$	−5.10749e44	−0.590458
$530$	−4.92495e44	−0.551887
$531$	1.74549e45	1.89609
$532$	8.55386e43	0.0900783
$533$	1.78924e45	1.82671
$534$	1.54601e45	1.53031
$535$	−3.61404e44	−0.346861
$536$	1.52124e45	1.41572
$537$	−8.49804e44	−0.766907
$538$	1.85729e45	1.62544
$539$	−2.99173e43	−0.0253926
$540$	4.21435e42	0.00346923
$541$	−1.96609e45	−1.56981	−0.784907	−	0.619613i	$-0.787289\pi$
$541$	−1.96609e45	−1.56981	−0.784907	+	0.619613i	$0.787289\pi$
$542$	5.35323e42	0.00414598
$543$	3.05715e45	2.29678
$544$	−6.37476e43	−0.0464603
$545$	−5.63466e44	−0.398405
$546$	2.17271e45	1.49047
$547$	−4.44935e44	−0.296146	−0.148073	−	0.988976i	$-0.547307\pi$
$547$	−4.44935e44	−0.296146	−0.148073	+	0.988976i	$0.547307\pi$
$548$	−8.66767e43	−0.0559787
$549$	4.20954e44	0.263810
$550$	−2.14339e44	−0.130352
$551$	−4.01544e45	−2.36991
$552$	1.53972e45	0.881954
$553$	−5.97331e44	−0.332086
$554$	2.49308e45	1.34532
$555$	−1.84599e45	−0.966932
$556$	−1.89202e44	−0.0962037
$557$	−1.02978e45	−0.508318	−0.254159	−	0.967162i	$-0.581799\pi$
$557$	−1.02978e45	−0.508318	−0.254159	+	0.967162i	$0.581799\pi$
$558$	−1.51368e45	−0.725389
$559$	9.50782e44	0.442370
$560$	1.03866e45	0.469214
$561$	−6.22807e44	−0.273191
$562$	−3.89506e45	−1.65907
$563$	−3.82628e45	−1.58266	−0.791331	−	0.611388i	$-0.790612\pi$
$563$	−3.82628e45	−1.58266	−0.791331	+	0.611388i	$0.790612\pi$
$564$	2.32966e44	0.0935808
$565$	−1.89234e45	−0.738244
$566$	−3.89662e45	−1.47644
$567$	2.46227e45	0.906180
$568$	−8.80294e44	−0.314688
$569$	−1.77526e45	−0.616468	−0.308234	−	0.951311i	$-0.599738\pi$
$569$	−1.77526e45	−0.616468	−0.308234	+	0.951311i	$0.599738\pi$
$570$	2.36392e45	0.797440
$571$	1.00861e45	0.330544	0.165272	−	0.986248i	$-0.447150\pi$
$571$	1.00861e45	0.330544	0.165272	+	0.986248i	$0.447150\pi$
$572$	1.54774e44	0.0492791
$573$	−1.79597e45	−0.555583
$574$	6.06279e45	1.82233
$575$	4.38226e44	0.127991
$576$	3.43690e45	0.975430
$577$	3.07790e45	0.848895	0.424448	−	0.905452i	$-0.360468\pi$
$577$	3.07790e45	0.848895	0.424448	+	0.905452i	$0.360468\pi$
$578$	3.51791e45	0.942921
$579$	3.00654e45	0.783198
$580$	2.69908e44	0.0683367
$581$	−3.52609e45	−0.867735
$582$	−1.03541e46	−2.47676
$583$	3.21171e45	0.746803
$584$	−2.16503e45	−0.489387
$585$	2.21906e45	0.487638
$586$	−7.60085e43	−0.0162387
$587$	3.80587e45	0.790544	0.395272	−	0.918564i	$-0.370650\pi$
$587$	3.80587e45	0.790544	0.395272	+	0.918564i	$0.370650\pi$
$588$	−2.21787e43	−0.00447931
$589$	−3.97247e45	−0.780114
$590$	−4.30673e45	−0.822411
$591$	6.17835e45	1.14731
$592$	8.91292e45	1.60958
$593$	−1.41796e45	−0.249036	−0.124518	−	0.992217i	$-0.539738\pi$
$593$	−1.41796e45	−0.249036	−0.124518	+	0.992217i	$0.539738\pi$
$594$	−3.84403e44	−0.0656615
$595$	7.97229e44	0.132450
$596$	−3.15194e44	−0.0509348
$597$	−1.55128e46	−2.43845
$598$	−4.42605e45	−0.676778
$599$	7.86874e45	1.17048	0.585239	−	0.810861i	$-0.301001\pi$
$599$	7.86874e45	1.17048	0.585239	+	0.810861i	$0.301001\pi$
$600$	1.90468e45	0.275630
$601$	6.55936e45	0.923491	0.461746	−	0.887012i	$-0.347223\pi$
$601$	6.55936e45	0.923491	0.461746	+	0.887012i	$0.347223\pi$
$602$	3.22170e45	0.441309
$603$	1.18658e46	1.58147
$604$	1.96600e44	0.0254961
$605$	−2.14611e45	−0.270824
$606$	8.48778e44	0.104231
$607$	1.16821e46	1.39607	0.698037	−	0.716062i	$-0.254057\pi$
$607$	1.16821e46	1.39607	0.698037	+	0.716062i	$0.254057\pi$
$608$	−1.57790e45	−0.183514
$609$	−2.47090e46	−2.79685
$610$	−1.03864e45	−0.114425
$611$	8.02738e45	0.860783
$612$	−2.38664e44	−0.0249108
$613$	−2.09504e45	−0.212860	−0.106430	−	0.994320i	$-0.533942\pi$
$613$	−2.09504e45	−0.212860	−0.106430	+	0.994320i	$0.533942\pi$
$614$	−1.47655e46	−1.46040
$615$	1.19791e46	1.15341
$616$	−6.28648e45	−0.589285
$617$	1.98589e45	0.181238	0.0906192	−	0.995886i	$-0.471115\pi$
$617$	1.98589e45	0.181238	0.0906192	+	0.995886i	$0.471115\pi$
$618$	−1.86702e46	−1.65898
$619$	−8.02615e45	−0.694403	−0.347201	−	0.937791i	$-0.612868\pi$
$619$	−8.02615e45	−0.694403	−0.347201	+	0.937791i	$0.612868\pi$
$620$	2.67019e44	0.0224947
$621$	7.85931e44	0.0644723
$622$	1.93412e46	1.54505
$623$	1.29055e46	1.00397
$624$	−2.07272e46	−1.57035
$625$	5.42101e44	0.0400000
$626$	6.63227e45	0.476635
$627$	−1.54159e46	−1.07908
$628$	1.49709e45	0.102074
$629$	6.84116e45	0.454354
$630$	7.51922e45	0.486467
$631$	−2.32504e46	−1.46536	−0.732682	−	0.680571i	$-0.761732\pi$
$631$	−2.32504e46	−1.46536	−0.732682	+	0.680571i	$0.761732\pi$
$632$	5.28875e45	0.324729
$633$	−4.74637e45	−0.283923
$634$	2.17206e46	1.26590
$635$	−5.88731e45	−0.334311
$636$	2.38096e45	0.131738
$637$	−7.64220e44	−0.0412020
$638$	−2.46191e46	−1.29339
$639$	−6.86638e45	−0.351531
$640$	−9.85742e45	−0.491806
$641$	1.10320e46	0.536412	0.268206	−	0.963362i	$-0.413569\pi$
$641$	1.10320e46	0.536412	0.268206	+	0.963362i	$0.413569\pi$
$642$	2.44379e46	1.15807
$643$	1.90982e46	0.882085	0.441042	−	0.897486i	$-0.354609\pi$
$643$	1.90982e46	0.882085	0.441042	+	0.897486i	$0.354609\pi$
$644$	−1.07226e45	−0.0482705
$645$	6.36553e45	0.279318
$646$	−8.76058e45	−0.374711
$647$	2.77860e46	1.15853	0.579263	−	0.815141i	$-0.303341\pi$
$647$	2.77860e46	1.15853	0.579263	+	0.815141i	$0.303341\pi$
$648$	−2.18009e46	−0.886107
$649$	2.80855e46	1.11287
$650$	−5.47517e45	−0.211508
$651$	−2.44445e46	−0.920652
$652$	9.83389e43	0.00361110
$653$	−1.10232e46	−0.394676	−0.197338	−	0.980335i	$-0.563230\pi$
$653$	−1.10232e46	−0.394676	−0.197338	+	0.980335i	$0.563230\pi$
$654$	3.81012e46	1.33017
$655$	1.11151e46	0.378384
$656$	−5.78379e46	−1.91999
$657$	−1.68875e46	−0.546683
$658$	2.72006e46	0.858718
$659$	2.82127e46	0.868632	0.434316	−	0.900761i	$-0.356990\pi$
$659$	2.82127e46	0.868632	0.434316	+	0.900761i	$0.356990\pi$
$660$	1.03622e45	0.0311154
$661$	3.86133e44	0.0113087	0.00565435	−	0.999984i	$-0.498200\pi$
$661$	3.86133e44	0.0113087	0.00565435	+	0.999984i	$0.498200\pi$
$662$	1.67368e46	0.478096
$663$	−1.59093e46	−0.443279
$664$	3.12199e46	0.848514
$665$	1.97332e46	0.523167
$666$	6.45237e46	1.66876
$667$	5.03350e46	1.26997
$668$	1.13415e45	0.0279163
$669$	−4.51423e46	−1.08406
$670$	−2.92770e46	−0.685950
$671$	6.77327e45	0.154838
$672$	−9.70957e45	−0.216574
$673$	−3.62752e46	−0.789517	−0.394759	−	0.918785i	$-0.629172\pi$
$673$	−3.62752e46	−0.789517	−0.394759	+	0.918785i	$0.629172\pi$
$674$	−7.74641e46	−1.64517
$675$	9.72224e44	0.0201490
$676$	1.46326e44	0.00295937
$677$	−6.71996e46	−1.32634	−0.663168	−	0.748471i	$-0.730788\pi$
$677$	−6.71996e46	−1.32634	−0.663168	+	0.748471i	$0.730788\pi$
$678$	1.27959e47	2.46479
$679$	−8.64325e46	−1.62490
$680$	−7.05866e45	−0.129516
$681$	−2.46468e46	−0.441400
$682$	−2.43556e46	−0.425752
$683$	5.58915e45	0.0953684	0.0476842	−	0.998862i	$-0.484816\pi$
$683$	5.58915e45	0.0953684	0.0476842	+	0.998862i	$0.484816\pi$
$684$	−5.90746e45	−0.0983955
$685$	−1.99958e46	−0.325120
$686$	−6.66358e46	−1.05769
$687$	−1.31660e47	−2.04018
$688$	−3.07344e46	−0.464960
$689$	8.20415e46	1.21176
$690$	−2.96326e46	−0.427326
$691$	5.89510e46	0.830048	0.415024	−	0.909810i	$-0.363773\pi$
$691$	5.89510e46	0.830048	0.415024	+	0.909810i	$0.363773\pi$
$692$	−4.43680e45	−0.0609985
$693$	−4.90352e46	−0.658278
$694$	−6.02171e46	−0.789384
$695$	−4.36477e46	−0.558743
$696$	2.18773e47	2.73490
$697$	−4.43938e46	−0.541977
$698$	8.70551e45	0.103796
$699$	2.26750e47	2.64043
$700$	−1.32642e45	−0.0150856
$701$	−9.67830e46	−1.07511	−0.537554	−	0.843229i	$-0.680651\pi$
$701$	−9.67830e46	−1.07511	−0.537554	+	0.843229i	$0.680651\pi$
$702$	−9.81937e45	−0.106542
$703$	1.69334e47	1.79466
$704$	5.53007e46	0.572508
$705$	5.37437e46	0.543510
$706$	1.03968e47	1.02712
$707$	7.08530e45	0.0683814
$708$	2.08208e46	0.196313
$709$	−1.89011e46	−0.174110	−0.0870552	−	0.996203i	$-0.527746\pi$
$709$	−1.89011e46	−0.174110	−0.0870552	+	0.996203i	$0.527746\pi$
$710$	1.69417e46	0.152473
$711$	4.12528e46	0.362748
$712$	−1.14265e47	−0.981735
$713$	4.97963e46	0.418042
$714$	−5.39081e46	−0.442215
$715$	3.57053e46	0.286209
$716$	−5.23980e45	−0.0410440
$717$	−9.75372e46	−0.746628
$718$	2.00400e46	0.149915
$719$	1.61675e47	1.18199	0.590997	−	0.806674i	$-0.298735\pi$
$719$	1.61675e47	1.18199	0.590997	+	0.806674i	$0.298735\pi$
$720$	−7.17319e46	−0.512538
$721$	−1.55853e47	−1.08838
$722$	−6.47989e46	−0.442287
$723$	−1.84053e47	−1.22790
$724$	1.88501e46	0.122921
$725$	6.22661e46	0.396894
$726$	1.45118e47	0.904208
$727$	6.77908e44	0.00412908	0.00206454	−	0.999998i	$-0.499343\pi$
$727$	6.77908e44	0.00412908	0.00206454	+	0.999998i	$0.499343\pi$
$728$	−1.60585e47	−0.956173
$729$	−1.94950e47	−1.13480
$730$	4.16671e46	0.237119
$731$	−2.35903e46	−0.131249
$732$	5.02127e45	0.0273137
$733$	1.03172e46	0.0548714	0.0274357	−	0.999624i	$-0.491266\pi$
$733$	1.03172e46	0.0548714	0.0274357	+	0.999624i	$0.491266\pi$
$734$	1.11690e47	0.580802
$735$	−5.11649e45	−0.0260154
$736$	1.97795e46	0.0983401
$737$	1.90924e47	0.928213
$738$	−4.18708e47	−1.99059
$739$	3.22918e46	0.150127	0.0750636	−	0.997179i	$-0.476084\pi$
$739$	3.22918e46	0.150127	0.0750636	+	0.997179i	$0.476084\pi$
$740$	−1.13822e46	−0.0517491
$741$	−3.93790e47	−1.75091
$742$	2.77995e47	1.20885
$743$	3.20296e47	1.36218	0.681092	−	0.732198i	$-0.261506\pi$
$743$	3.20296e47	1.36218	0.681092	+	0.732198i	$0.261506\pi$
$744$	2.16432e47	0.900259
$745$	−7.27132e46	−0.295825
$746$	1.29805e47	0.516535
$747$	2.43519e47	0.947856
$748$	−3.84017e45	−0.0146209
$749$	2.03999e47	0.759763
$750$	−3.66565e46	−0.133549
$751$	−5.04227e47	−1.79708	−0.898540	−	0.438891i	$-0.855371\pi$
$751$	−5.04227e47	−1.79708	−0.898540	+	0.438891i	$0.855371\pi$
$752$	−2.59488e47	−0.904739
$753$	3.98404e47	1.35896
$754$	−6.28882e47	−2.09866
$755$	4.53543e46	0.148079
$756$	−2.37884e45	−0.00759900
$757$	−5.03192e47	−1.57272	−0.786361	−	0.617767i	$-0.788038\pi$
$757$	−5.03192e47	−1.57272	−0.786361	+	0.617767i	$0.788038\pi$
$758$	−3.07017e47	−0.938903
$759$	1.93243e47	0.578249
$760$	−1.74717e47	−0.511578
$761$	−3.34360e47	−0.958004	−0.479002	−	0.877814i	$-0.659001\pi$
$761$	−3.34360e47	−0.958004	−0.479002	+	0.877814i	$0.659001\pi$
$762$	3.98096e47	1.11617
$763$	3.18055e47	0.872666
$764$	−1.10738e46	−0.0297342
$765$	−5.50582e46	−0.144680
$766$	2.94521e47	0.757428
$767$	7.17429e47	1.80574
$768$	1.34137e47	0.330436
$769$	−5.27752e47	−1.27246	−0.636231	−	0.771498i	$-0.719508\pi$
$769$	−5.27752e47	−1.27246	−0.636231	+	0.771498i	$0.719508\pi$
$770$	1.20986e47	0.285522
$771$	3.91202e47	0.903658
$772$	1.85380e46	0.0419159
$773$	1.62889e47	0.360520	0.180260	−	0.983619i	$-0.442306\pi$
$773$	1.62889e47	0.360520	0.180260	+	0.983619i	$0.442306\pi$
$774$	−2.22497e47	−0.482056
$775$	6.15997e46	0.130647
$776$	7.65272e47	1.58890
$777$	1.04200e48	2.11797
$778$	−5.23259e47	−1.04125
$779$	−1.09884e48	−2.14076
$780$	2.64696e46	0.0504878
$781$	−1.10482e47	−0.206324
$782$	1.09817e47	0.200797
$783$	1.11670e47	0.199926
$784$	2.47037e46	0.0433059
$785$	3.45370e47	0.592837
$786$	−7.51598e47	−1.26332
$787$	1.50460e46	0.0247649	0.0123825	−	0.999923i	$-0.496058\pi$
$787$	1.50460e46	0.0247649	0.0123825	+	0.999923i	$0.496058\pi$
$788$	3.80951e46	0.0614025
$789$	3.97203e47	0.626963
$790$	−1.01785e47	−0.157339
$791$	1.06816e48	1.61705
$792$	4.34156e47	0.643696
$793$	1.73020e47	0.251239
$794$	−4.18322e47	−0.594939
$795$	5.49272e47	0.765121
$796$	−9.56503e46	−0.130503
$797$	−5.86479e47	−0.783773	−0.391887	−	0.920014i	$-0.628177\pi$
$797$	−5.86479e47	−0.783773	−0.391887	+	0.920014i	$0.628177\pi$
$798$	−1.33435e48	−1.74671
$799$	−1.99171e47	−0.255391
$800$	2.44679e46	0.0307335
$801$	−8.91280e47	−1.09667
$802$	1.08940e47	0.131313
$803$	−2.71724e47	−0.320864
$804$	1.41539e47	0.163739
$805$	−2.47363e47	−0.280351
$806$	−6.22151e47	−0.690824
$807$	−2.07140e48	−2.25347
$808$	−6.27331e46	−0.0668667
$809$	1.28166e48	1.33852	0.669258	−	0.743030i	$-0.266612\pi$
$809$	1.28166e48	1.33852	0.669258	+	0.743030i	$0.266612\pi$
$810$	4.19568e47	0.429338
$811$	−2.05018e47	−0.205564	−0.102782	−	0.994704i	$-0.532774\pi$
$811$	−2.05018e47	−0.205564	−0.102782	+	0.994704i	$0.532774\pi$
$812$	−1.52353e47	−0.149685
$813$	−5.97037e45	−0.00574787
$814$	1.03820e48	0.979445
$815$	2.26861e46	0.0209730
$816$	5.14274e47	0.465915
$817$	−5.83913e47	−0.518423
$818$	−6.32772e47	−0.550576
$819$	−1.25258e48	−1.06812
$820$	7.38616e46	0.0617291
$821$	8.74853e47	0.716594	0.358297	−	0.933608i	$-0.383358\pi$
$821$	8.74853e47	0.716594	0.358297	+	0.933608i	$0.383358\pi$
$822$	1.35210e48	1.08549
$823$	−2.06347e47	−0.162368	−0.0811841	−	0.996699i	$-0.525870\pi$
$823$	−2.06347e47	−0.162368	−0.0811841	+	0.996699i	$0.525870\pi$
$824$	1.37992e48	1.06427
$825$	2.39049e47	0.180716
$826$	2.43099e48	1.80141
$827$	−2.59525e48	−1.88512	−0.942559	−	0.334038i	$-0.891588\pi$
$827$	−2.59525e48	−1.88512	−0.942559	+	0.334038i	$0.891588\pi$
$828$	7.40521e46	0.0527274
$829$	−2.60174e48	−1.81599	−0.907996	−	0.418978i	$-0.862388\pi$
$829$	−2.60174e48	−1.81599	−0.907996	+	0.418978i	$0.862388\pi$
$830$	−6.00843e47	−0.411124
$831$	−2.78050e48	−1.86511
$832$	1.41263e48	0.928950
$833$	1.89615e46	0.0122244
$834$	2.95143e48	1.86549
$835$	2.61640e47	0.162135
$836$	−9.50527e46	−0.0577512
$837$	1.10475e47	0.0658104
$838$	2.05733e48	1.20165
$839$	−2.01476e48	−1.15386	−0.576928	−	0.816795i	$-0.695749\pi$
$839$	−2.01476e48	−1.15386	−0.576928	+	0.816795i	$0.695749\pi$
$840$	−1.07512e48	−0.603740
$841$	5.33585e48	2.93812
$842$	5.14224e47	0.277653
$843$	4.34409e48	2.30009
$844$	−2.92656e46	−0.0151952
$845$	3.37564e46	0.0171878
$846$	−1.87852e48	−0.938006
$847$	1.21140e48	0.593213
$848$	−2.65202e48	−1.27364
$849$	4.34583e48	2.04690
$850$	1.35847e47	0.0627536
$851$	−2.12266e48	−0.961707
$852$	−8.19042e46	−0.0363959
$853$	1.85939e48	0.810422	0.405211	−	0.914223i	$-0.367198\pi$
$853$	1.85939e48	0.810422	0.405211	+	0.914223i	$0.367198\pi$
$854$	5.86272e47	0.250636
$855$	−1.36281e48	−0.571473
$856$	−1.80621e48	−0.742933
$857$	1.28606e48	0.518891	0.259446	−	0.965758i	$-0.416460\pi$
$857$	1.28606e48	0.518891	0.259446	+	0.965758i	$0.416460\pi$
$858$	−2.41437e48	−0.955572
$859$	−3.42147e48	−1.32839	−0.664195	−	0.747559i	$-0.731226\pi$
$859$	−3.42147e48	−1.32839	−0.664195	+	0.747559i	$0.731226\pi$
$860$	3.92492e46	0.0149488
$861$	−6.76173e48	−2.52642
$862$	−2.24816e48	−0.824057
$863$	1.37063e48	0.492882	0.246441	−	0.969158i	$-0.420739\pi$
$863$	1.37063e48	0.492882	0.246441	+	0.969158i	$0.420739\pi$
$864$	4.38816e46	0.0154812
$865$	−1.02354e48	−0.354274
$866$	1.55157e48	0.526899
$867$	−3.92347e48	−1.30724
$868$	−1.50723e47	−0.0492723
$869$	6.63769e47	0.212907
$870$	−4.21039e48	−1.32512
$871$	4.87706e48	1.50612
$872$	−2.81606e48	−0.853335
$873$	5.96919e48	1.77493
$874$	2.71821e48	0.793131
$875$	−3.05996e47	−0.0876159
$876$	−2.01439e47	−0.0566011
$877$	−1.64670e48	−0.454069	−0.227035	−	0.973887i	$-0.572903\pi$
$877$	−1.64670e48	−0.454069	−0.227035	+	0.973887i	$0.572903\pi$
$878$	−4.42531e48	−1.19753
$879$	8.47711e46	0.0225129
$880$	−1.15419e48	−0.300824
$881$	−3.42124e48	−0.875148	−0.437574	−	0.899182i	$-0.644162\pi$
$881$	−3.42124e48	−0.875148	−0.437574	+	0.899182i	$0.644162\pi$
$882$	1.78839e47	0.0448983
$883$	7.49779e48	1.84749	0.923743	−	0.383012i	$-0.125113\pi$
$883$	7.49779e48	1.84749	0.923743	+	0.383012i	$0.125113\pi$
$884$	−9.80950e46	−0.0237238
$885$	4.80322e48	1.14017
$886$	5.69842e48	1.32769
$887$	1.29073e48	0.295186	0.147593	−	0.989048i	$-0.452847\pi$
$887$	1.29073e48	0.295186	0.147593	+	0.989048i	$0.452847\pi$
$888$	−9.22581e48	−2.07105
$889$	3.32317e48	0.732273
$890$	2.19909e48	0.475672
$891$	−2.73613e48	−0.580972
$892$	−2.78343e47	−0.0580176
$893$	−4.92994e48	−1.00877
$894$	4.91682e48	0.987678
$895$	−1.20879e48	−0.238380
$896$	5.56415e48	1.07725
$897$	4.93630e48	0.938266
$898$	1.58139e48	0.295106
$899$	7.07538e48	1.29633
$900$	9.16049e46	0.0164785
$901$	−2.03557e48	−0.359524
$902$	−6.73713e48	−1.16833
$903$	−3.59311e48	−0.611818
$904$	−9.45743e48	−1.58123
$905$	4.34859e48	0.713916
$906$	−3.06683e48	−0.494395
$907$	−4.05607e48	−0.642074	−0.321037	−	0.947067i	$-0.604031\pi$
$907$	−4.05607e48	−0.642074	−0.321037	+	0.947067i	$0.604031\pi$
$908$	−1.51969e47	−0.0236232
$909$	−4.89325e47	−0.0746953
$910$	3.09053e48	0.463287
$911$	−7.15538e48	−1.05337	−0.526683	−	0.850062i	$-0.676564\pi$
$911$	−7.15538e48	−1.05337	−0.526683	+	0.850062i	$0.676564\pi$
$912$	1.27294e49	1.84032
$913$	3.91828e48	0.556324
$914$	−2.59210e47	−0.0361443
$915$	1.15837e48	0.158636
$916$	−8.11802e47	−0.109188
$917$	−6.27408e48	−0.828812
$918$	2.43633e47	0.0316106
$919$	−1.51037e49	−1.92476	−0.962382	−	0.271700i	$-0.912414\pi$
$919$	−1.51037e49	−1.92476	−0.962382	+	0.271700i	$0.912414\pi$
$920$	2.19014e48	0.274141
$921$	1.64678e49	2.02465
$922$	8.57521e48	1.03558
$923$	−2.82220e48	−0.334780
$924$	−5.84906e47	−0.0681551
$925$	−2.62580e48	−0.300555
$926$	7.51412e48	0.844884
$927$	1.07635e49	1.18888
$928$	2.81040e48	0.304948
$929$	1.54374e49	1.64557	0.822783	−	0.568356i	$-0.192420\pi$
$929$	1.54374e49	1.64557	0.822783	+	0.568356i	$0.192420\pi$
$930$	−4.16533e48	−0.436195
$931$	4.69338e47	0.0482854
$932$	1.39812e48	0.141313
$933$	−2.15709e49	−2.14201
$934$	−1.29210e49	−1.26059
$935$	−8.85902e47	−0.0849169
$936$	1.10903e49	1.04446
$937$	−8.72693e48	−0.807530	−0.403765	−	0.914863i	$-0.632299\pi$
$937$	−8.72693e48	−0.807530	−0.403765	+	0.914863i	$0.632299\pi$
$938$	1.65258e49	1.50250
$939$	−7.39687e48	−0.660793
$940$	3.31378e47	0.0290880
$941$	−6.99024e48	−0.602925	−0.301463	−	0.953478i	$-0.597475\pi$
$941$	−6.99024e48	−0.602925	−0.301463	+	0.953478i	$0.597475\pi$
$942$	−2.33537e49	−1.97932
$943$	1.37744e49	1.14717
$944$	−2.31912e49	−1.89795
$945$	−5.48784e47	−0.0441344
$946$	−3.58003e48	−0.282933
$947$	2.43383e48	0.189024	0.0945118	−	0.995524i	$-0.469871\pi$
$947$	2.43383e48	0.189024	0.0945118	+	0.995524i	$0.469871\pi$
$948$	4.92076e47	0.0375573
$949$	−6.94104e48	−0.520634
$950$	3.36252e48	0.247871
$951$	−2.42246e49	−1.75501
$952$	3.98435e48	0.283692
$953$	−2.16685e48	−0.151633	−0.0758167	−	0.997122i	$-0.524156\pi$
$953$	−2.16685e48	−0.151633	−0.0758167	+	0.997122i	$0.524156\pi$
$954$	−1.91989e49	−1.32047
$955$	−2.55465e48	−0.172694
$956$	−6.01405e47	−0.0399587
$957$	2.74573e49	1.79313
$958$	−5.85321e48	−0.375719
$959$	1.12869e49	0.712141
$960$	9.45760e48	0.586551
$961$	−9.40382e48	−0.573282
$962$	2.65204e49	1.58924
$963$	−1.40886e49	−0.829915
$964$	−1.13485e48	−0.0657157
$965$	4.27661e48	0.243444
$966$	1.67265e49	0.936014
$967$	3.10853e49	1.71009	0.855044	−	0.518556i	$-0.173530\pi$
$967$	3.10853e49	1.71009	0.855044	+	0.518556i	$0.173530\pi$
$968$	−1.07257e49	−0.580072
$969$	9.77053e48	0.519488
$970$	−1.47280e49	−0.769858
$971$	−1.05532e49	−0.542334	−0.271167	−	0.962532i	$-0.587410\pi$
$971$	−1.05532e49	−0.542334	−0.271167	+	0.962532i	$0.587410\pi$
$972$	−2.18193e48	−0.110242
$973$	2.46375e49	1.22387
$974$	2.20790e49	1.07834
$975$	6.10637e48	0.293229
$976$	−5.59292e48	−0.264069
$977$	1.91994e49	0.891306	0.445653	−	0.895206i	$-0.352971\pi$
$977$	1.91994e49	0.891306	0.445653	+	0.895206i	$0.352971\pi$
$978$	−1.53402e48	−0.0700230
$979$	−1.43409e49	−0.643670
$980$	−3.15478e46	−0.00139232
$981$	−2.19655e49	−0.953242
$982$	4.82639e48	0.205960
$983$	−5.26490e48	−0.220931	−0.110466	−	0.993880i	$-0.535234\pi$
$983$	−5.26490e48	−0.220931	−0.110466	+	0.993880i	$0.535234\pi$
$984$	5.98682e49	2.47046
$985$	8.78829e48	0.356621
$986$	1.56035e49	0.622663
$987$	−3.03363e49	−1.19050
$988$	−2.42807e48	−0.0937069
$989$	7.31956e48	0.277809
$990$	−8.35555e48	−0.311885
$991$	−1.70362e48	−0.0625398	−0.0312699	−	0.999511i	$-0.509955\pi$
$991$	−1.70362e48	−0.0625398	−0.0312699	+	0.999511i	$0.509955\pi$
$992$	2.78032e48	0.100381
$993$	−1.86663e49	−0.662819
$994$	−9.56295e48	−0.333977
$995$	−2.20659e49	−0.757951
$996$	2.90476e48	0.0981367
$997$	−3.60379e49	−1.19754	−0.598770	−	0.800921i	$-0.704344\pi$
$997$	−3.60379e49	−1.19754	−0.598770	+	0.800921i	$0.704344\pi$
$998$	1.23504e49	0.403672
$999$	−4.70921e48	−0.151397

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.34.a.b.1.2	✓	6
5.2	odd	4		25.34.b.c.24.4		12
5.3	odd	4		25.34.b.c.24.9		12
5.4	even	2		25.34.a.c.1.5		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.b.1.2	✓	6	1.1	even	1	trivial
25.34.a.c.1.5		6	5.4	even	2
25.34.b.c.24.4		12	5.2	odd	4
25.34.b.c.24.9		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)

\(f(q)\)	\(=\)	\(q-96184.0 q^{2} +1.07272e8 q^{3} +6.61431e8 q^{4} +1.52588e11 q^{5} -1.03179e13 q^{6} -8.61302e13 q^{7} +7.62595e14 q^{8} +5.94832e15 q^{9} +O(q^{10})\)	\(q-96184.0 q^{2} +1.07272e8 q^{3} +6.61431e8 q^{4} +1.52588e11 q^{5} -1.03179e13 q^{6} -8.61302e13 q^{7} +7.62595e14 q^{8} +5.94832e15 q^{9} -1.46765e16 q^{10} +9.57101e16 q^{11} +7.09533e16 q^{12} +2.44486e18 q^{13} +8.28435e18 q^{14} +1.63685e19 q^{15} -7.90311e19 q^{16} -6.06607e19 q^{17} -5.72133e20 q^{18} -1.50149e21 q^{19} +1.00926e20 q^{20} -9.23940e21 q^{21} -9.20578e21 q^{22} +1.88217e22 q^{23} +8.18055e22 q^{24} +2.32831e22 q^{25} -2.35157e23 q^{26} +4.17567e22 q^{27} -5.69692e22 q^{28} +2.67431e24 q^{29} -1.57439e24 q^{30} +2.64569e24 q^{31} +1.05089e24 q^{32} +1.02671e25 q^{33} +5.83459e24 q^{34} -1.31424e25 q^{35} +3.93440e24 q^{36} -1.12777e26 q^{37} +1.44419e26 q^{38} +2.62266e26 q^{39} +1.16363e26 q^{40} +7.31837e26 q^{41} +8.88682e26 q^{42} +3.88890e26 q^{43} +6.33056e25 q^{44} +9.07641e26 q^{45} -1.81034e27 q^{46} +3.28337e27 q^{47} -8.47786e27 q^{48} -3.12582e26 q^{49} -2.23946e27 q^{50} -6.50723e27 q^{51} +1.61711e27 q^{52} +3.35567e28 q^{53} -4.01633e27 q^{54} +1.46042e28 q^{55} -6.56825e28 q^{56} -1.61068e29 q^{57} -2.57226e29 q^{58} +2.93443e29 q^{59} +1.08266e28 q^{60} +7.07686e28 q^{61} -2.54473e29 q^{62} -5.12330e29 q^{63} +5.77794e29 q^{64} +3.73057e29 q^{65} -9.87527e29 q^{66} +1.99482e30 q^{67} -4.01229e28 q^{68} +2.01905e30 q^{69} +1.26409e30 q^{70} -1.15434e30 q^{71} +4.53616e30 q^{72} -2.83903e30 q^{73} +1.08474e31 q^{74} +2.49763e30 q^{75} -9.93131e29 q^{76} -8.24353e30 q^{77} -2.52258e31 q^{78} +6.93520e30 q^{79} -1.20592e31 q^{80} -2.85877e31 q^{81} -7.03910e31 q^{82} +4.09391e31 q^{83} -6.11122e30 q^{84} -9.25610e30 q^{85} -3.74050e31 q^{86} +2.86880e32 q^{87} +7.29881e31 q^{88} -1.49837e32 q^{89} -8.73006e31 q^{90} -2.10577e32 q^{91} +1.24492e31 q^{92} +2.83809e32 q^{93} -3.15807e32 q^{94} -2.29109e32 q^{95} +1.12731e32 q^{96} +1.00351e33 q^{97} +3.00654e31 q^{98} +5.69314e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 147350 q^{2} + 26513900 q^{3} + 29520645652 q^{4} + 915527343750 q^{5} + 6615759249352 q^{6} + 19113832847500 q^{7} + 30\!\cdots\!00 q^{8}+ \cdots + 13\!\cdots\!38 q^{9}+O(q^{10}) \) 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

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