LMFDB - Embedded newform 5.34.a.b.1.1

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			1.1
Root			$-75479.4$ 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)

$f(q)$	$=$	$q-126401. q^{2} -8.63211e7 q^{3} +7.38725e9 q^{4} +1.52588e11 q^{5} +1.09111e13 q^{6} +7.78650e13 q^{7} +1.52021e14 q^{8} +1.89228e15 q^{9} +O(q^{10})$	\(q-126401. q^{2} -8.63211e7 q^{3} +7.38725e9 q^{4} +1.52588e11 q^{5} +1.09111e13 q^{6} +7.78650e13 q^{7} +1.52021e14 q^{8} +1.89228e15 q^{9} -1.92872e16 q^{10} +1.61939e17 q^{11} -6.37676e17 q^{12} -2.28706e18 q^{13} -9.84220e18 q^{14} -1.31716e19 q^{15} -8.26715e19 q^{16} +2.46494e20 q^{17} -2.39186e20 q^{18} -1.53881e21 q^{19} +1.12720e21 q^{20} -6.72140e21 q^{21} -2.04692e22 q^{22} -2.16284e22 q^{23} -1.31226e22 q^{24} +2.32831e22 q^{25} +2.89086e23 q^{26} +3.16521e23 q^{27} +5.75208e23 q^{28} -2.07535e23 q^{29} +1.66490e24 q^{30} +1.75532e24 q^{31} +9.14391e24 q^{32} -1.39788e25 q^{33} -3.11571e25 q^{34} +1.18813e25 q^{35} +1.39787e25 q^{36} +8.12289e25 q^{37} +1.94506e26 q^{38} +1.97422e26 q^{39} +2.31965e25 q^{40} -1.92486e26 q^{41} +8.49590e26 q^{42} +8.01003e26 q^{43} +1.19628e27 q^{44} +2.88739e26 q^{45} +2.73385e27 q^{46} -7.53703e27 q^{47} +7.13630e27 q^{48} -1.66804e27 q^{49} -2.94300e27 q^{50} -2.12777e28 q^{51} -1.68951e28 q^{52} +1.75257e28 q^{53} -4.00085e28 q^{54} +2.47099e28 q^{55} +1.18371e28 q^{56} +1.32832e29 q^{57} +2.62326e28 q^{58} -2.97225e29 q^{59} -9.73016e28 q^{60} -3.70944e29 q^{61} -2.21873e29 q^{62} +1.47342e29 q^{63} -4.45655e29 q^{64} -3.48978e29 q^{65} +1.76693e30 q^{66} +8.43824e29 q^{67} +1.82091e30 q^{68} +1.86699e30 q^{69} -1.50180e30 q^{70} +5.92473e30 q^{71} +2.87666e29 q^{72} +7.49289e30 q^{73} -1.02674e31 q^{74} -2.00982e30 q^{75} -1.13675e31 q^{76} +1.26094e31 q^{77} -2.49543e31 q^{78} +6.07295e30 q^{79} -1.26147e31 q^{80} -3.78417e31 q^{81} +2.43304e31 q^{82} +3.47153e31 q^{83} -4.96526e31 q^{84} +3.76120e31 q^{85} -1.01248e32 q^{86} +1.79147e31 q^{87} +2.46181e31 q^{88} +1.80671e32 q^{89} -3.64969e31 q^{90} -1.78082e32 q^{91} -1.59775e32 q^{92} -1.51521e32 q^{93} +9.52688e32 q^{94} -2.34803e32 q^{95} -7.89312e32 q^{96} +1.09143e33 q^{97} +2.10841e32 q^{98} +3.06434e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−126401.	−1.36381	−0.681907	−	0.731439i	$-0.738849\pi$
$2$	−126401.	−1.36381	−0.681907	+	0.731439i	$0.738849\pi$
$3$	−8.63211e7	−1.15775	−0.578877	−	0.815415i	$-0.696509\pi$
$3$	−8.63211e7	−1.15775	−0.578877	+	0.815415i	$0.696509\pi$
$4$	7.38725e9	0.859989
$5$	1.52588e11	0.447214
$5$	1.52588e11	0.447214
$6$	1.09111e13	1.57896
$7$	7.78650e13	0.885573	0.442787	−	0.896627i	$-0.353990\pi$
$7$	7.78650e13	0.885573	0.442787	+	0.896627i	$0.353990\pi$
$8$	1.52021e14	0.190949
$9$	1.89228e15	0.340396
$10$	−1.92872e16	−0.609916
$11$	1.61939e17	1.06260	0.531302	−	0.847182i	$-0.321703\pi$
$11$	1.61939e17	1.06260	0.531302	+	0.847182i	$0.321703\pi$
$12$	−6.37676e17	−0.995656
$13$	−2.28706e18	−0.953262	−0.476631	−	0.879104i	$-0.658142\pi$
$13$	−2.28706e18	−0.953262	−0.476631	+	0.879104i	$0.658142\pi$
$14$	−9.84220e18	−1.20776
$15$	−1.31716e19	−0.517764
$16$	−8.26715e19	−1.12041
$17$	2.46494e20	1.22857	0.614284	−	0.789085i	$-0.289445\pi$
$17$	2.46494e20	1.22857	0.614284	+	0.789085i	$0.289445\pi$
$18$	−2.39186e20	−0.464236
$19$	−1.53881e21	−1.22391	−0.611955	−	0.790893i	$-0.709617\pi$
$19$	−1.53881e21	−1.22391	−0.611955	+	0.790893i	$0.709617\pi$
$20$	1.12720e21	0.384599
$21$	−6.72140e21	−1.02528
$22$	−2.04692e22	−1.44920
$23$	−2.16284e22	−0.735387	−0.367693	−	0.929947i	$-0.619852\pi$
$23$	−2.16284e22	−0.735387	−0.367693	+	0.929947i	$0.619852\pi$
$24$	−1.31226e22	−0.221072
$25$	2.32831e22	0.200000
$26$	2.89086e23	1.30007
$27$	3.16521e23	0.763660
$28$	5.75208e23	0.761583
$29$	−2.07535e23	−0.154001	−0.0770007	−	0.997031i	$-0.524534\pi$
$29$	−2.07535e23	−0.154001	−0.0770007	+	0.997031i	$0.524534\pi$
$30$	1.66490e24	0.706133
$31$	1.75532e24	0.433398	0.216699	−	0.976238i	$-0.430471\pi$
$31$	1.75532e24	0.433398	0.216699	+	0.976238i	$0.430471\pi$
$32$	9.14391e24	1.33708
$33$	−1.39788e25	−1.23024
$34$	−3.11571e25	−1.67554
$35$	1.18813e25	0.396040
$36$	1.39787e25	0.292736
$37$	8.12289e25	1.08239	0.541193	−	0.840898i	$-0.317973\pi$
$37$	8.12289e25	1.08239	0.541193	+	0.840898i	$0.317973\pi$
$38$	1.94506e26	1.66919
$39$	1.97422e26	1.10364
$40$	2.31965e25	0.0853951
$41$	−1.92486e26	−0.471483	−0.235741	−	0.971816i	$-0.575752\pi$
$41$	−1.92486e26	−0.471483	−0.235741	+	0.971816i	$0.575752\pi$
$42$	8.49590e26	1.39829
$43$	8.01003e26	0.894139	0.447069	−	0.894499i	$-0.352468\pi$
$43$	8.01003e26	0.894139	0.447069	+	0.894499i	$0.352468\pi$
$44$	1.19628e27	0.913828
$45$	2.88739e26	0.152230
$46$	2.73385e27	1.00293
$47$	−7.53703e27	−1.93904	−0.969518	−	0.245021i	$-0.921205\pi$
$47$	−7.53703e27	−1.93904	−0.969518	+	0.245021i	$0.921205\pi$
$48$	7.13630e27	1.29716
$49$	−1.66804e27	−0.215760
$50$	−2.94300e27	−0.272763
$51$	−2.12777e28	−1.42238
$52$	−1.68951e28	−0.819795
$53$	1.75257e28	0.621047	0.310523	−	0.950566i	$-0.399496\pi$
$53$	1.75257e28	0.621047	0.310523	+	0.950566i	$0.399496\pi$
$54$	−4.00085e28	−1.04149
$55$	2.47099e28	0.475211
$56$	1.18371e28	0.169100
$57$	1.32832e29	1.41699
$58$	2.62326e28	0.210029
$59$	−2.97225e29	−1.79484	−0.897422	−	0.441172i	$-0.854563\pi$
$59$	−2.97225e29	−1.79484	−0.897422	+	0.441172i	$0.854563\pi$
$60$	−9.73016e28	−0.445271
$61$	−3.70944e29	−1.29231	−0.646154	−	0.763207i	$-0.723624\pi$
$61$	−3.70944e29	−1.29231	−0.646154	+	0.763207i	$0.723624\pi$
$62$	−2.21873e29	−0.591075
$63$	1.47342e29	0.301445
$64$	−4.45655e29	−0.703119
$65$	−3.48978e29	−0.426312
$66$	1.76693e30	1.67781
$67$	8.43824e29	0.625198	0.312599	−	0.949885i	$-0.398800\pi$
$67$	8.43824e29	0.625198	0.312599	+	0.949885i	$0.398800\pi$
$68$	1.82091e30	1.05656
$69$	1.86699e30	0.851397
$70$	−1.50180e30	−0.540126
$71$	5.92473e30	1.68619	0.843094	−	0.537767i	$-0.180732\pi$
$71$	5.92473e30	1.68619	0.843094	+	0.537767i	$0.180732\pi$
$72$	2.87666e29	0.0649982
$73$	7.49289e30	1.34841	0.674205	−	0.738544i	$-0.264486\pi$
$73$	7.49289e30	1.34841	0.674205	+	0.738544i	$0.264486\pi$
$74$	−1.02674e31	−1.47617
$75$	−2.00982e30	−0.231551
$76$	−1.13675e31	−1.05255
$77$	1.26094e31	0.941015
$78$	−2.49543e31	−1.50516
$79$	6.07295e30	0.296861	0.148430	−	0.988923i	$-0.452578\pi$
$79$	6.07295e30	0.296861	0.148430	+	0.988923i	$0.452578\pi$
$80$	−1.26147e31	−0.501062
$81$	−3.78417e31	−1.22453
$82$	2.43304e31	0.643015
$83$	3.47153e31	0.751160	0.375580	−	0.926790i	$-0.377444\pi$
$83$	3.47153e31	0.751160	0.375580	+	0.926790i	$0.377444\pi$
$84$	−4.96526e31	−0.881727
$85$	3.76120e31	0.549433
$86$	−1.01248e32	−1.21944
$87$	1.79147e31	0.178296
$88$	2.46181e31	0.202904
$89$	1.80671e32	1.23582	0.617909	−	0.786250i	$-0.287980\pi$
$89$	1.80671e32	1.23582	0.617909	+	0.786250i	$0.287980\pi$
$90$	−3.64969e31	−0.207613
$91$	−1.78082e32	−0.844183
$92$	−1.59775e32	−0.632424
$93$	−1.51521e32	−0.501769
$94$	9.52688e32	2.64448
$95$	−2.34803e32	−0.547349
$96$	−7.89312e32	−1.54801
$97$	1.09143e33	1.80411	0.902055	−	0.431622i	$-0.142058\pi$
$97$	1.09143e33	1.80411	0.902055	+	0.431622i	$0.142058\pi$
$98$	2.10841e32	0.294256
$99$	3.06434e32	0.361706
$100$	1.71998e32	0.171998
$101$	−7.13542e32	−0.605504	−0.302752	−	0.953069i	$-0.597905\pi$
$101$	−7.13542e32	−0.605504	−0.302752	+	0.953069i	$0.597905\pi$
$102$	2.68952e33	1.93986
$103$	−1.80265e33	−1.10687	−0.553437	−	0.832891i	$-0.686684\pi$
$103$	−1.80265e33	−1.10687	−0.553437	+	0.832891i	$0.686684\pi$
$104$	−3.47680e32	−0.182025
$105$	−1.02560e33	−0.458518
$106$	−2.21527e33	−0.846992
$107$	4.02336e33	1.31752	0.658759	−	0.752354i	$-0.271082\pi$
$107$	4.02336e33	1.31752	0.658759	+	0.752354i	$0.271082\pi$
$108$	2.33822e33	0.656739
$109$	2.00598e33	0.483937	0.241968	−	0.970284i	$-0.422207\pi$
$109$	2.00598e33	0.483937	0.241968	+	0.970284i	$0.422207\pi$
$110$	−3.12335e33	−0.648100
$111$	−7.01177e33	−1.25314
$112$	−6.43722e33	−0.992204
$113$	−6.69356e33	−0.890970	−0.445485	−	0.895289i	$-0.646969\pi$
$113$	−6.69356e33	−0.890970	−0.445485	+	0.895289i	$0.646969\pi$
$114$	−1.67900e34	−1.93251
$115$	−3.30024e33	−0.328875
$116$	−1.53311e33	−0.132440
$117$	−4.32776e33	−0.324486
$118$	3.75695e34	2.44783
$119$	1.91933e34	1.08799
$120$	−2.00235e33	−0.0988665
$121$	2.99905e33	0.129129
$122$	4.68877e34	1.76247
$123$	1.66156e34	0.545861
$124$	1.29670e34	0.372718
$125$	3.55271e33	0.0894427
$126$	−1.86242e34	−0.411115
$127$	−1.27300e34	−0.246643	−0.123321	−	0.992367i	$-0.539355\pi$
$127$	−1.27300e34	−0.246643	−0.123321	+	0.992367i	$0.539355\pi$
$128$	−2.22144e34	−0.378155
$129$	−6.91435e34	−1.03519
$130$	4.41111e34	0.581410
$131$	1.12002e35	1.30092	0.650461	−	0.759540i	$-0.274576\pi$
$131$	1.12002e35	1.30092	0.650461	+	0.759540i	$0.274576\pi$
$132$	−1.03264e35	−1.05799
$133$	−1.19819e35	−1.08386
$134$	−1.06660e35	−0.852653
$135$	4.82972e34	0.341519
$136$	3.74722e34	0.234594
$137$	7.78279e34	0.431763	0.215882	−	0.976420i	$-0.430737\pi$
$137$	7.78279e34	0.431763	0.215882	+	0.976420i	$0.430737\pi$
$138$	−2.35989e35	−1.16115
$139$	3.58047e35	1.56385	0.781925	−	0.623372i	$-0.214238\pi$
$139$	3.58047e35	1.56385	0.781925	+	0.623372i	$0.214238\pi$
$140$	8.77698e34	0.340590
$141$	6.50605e35	2.24493
$142$	−7.48891e35	−2.29965
$143$	−3.70364e35	−1.01294
$144$	−1.56438e35	−0.381382
$145$	−3.16674e34	−0.0688716
$146$	−9.47108e35	−1.83898
$147$	1.43987e35	0.249797
$148$	6.00058e35	0.930840
$149$	−1.72179e35	−0.239005	−0.119502	−	0.992834i	$-0.538130\pi$
$149$	−1.72179e35	−0.239005	−0.119502	+	0.992834i	$0.538130\pi$
$150$	2.54043e35	0.315792
$151$	1.08017e36	1.20330	0.601651	−	0.798759i	$-0.294510\pi$
$151$	1.08017e36	1.20330	0.601651	+	0.798759i	$0.294510\pi$
$152$	−2.33930e35	−0.233705
$153$	4.66436e35	0.418199
$154$	−1.59384e36	−1.28337
$155$	2.67840e35	0.193822
$156$	1.45840e36	0.949121
$157$	2.63407e36	1.54271	0.771353	−	0.636407i	$-0.219580\pi$
$157$	2.63407e36	1.54271	0.771353	+	0.636407i	$0.219580\pi$
$158$	−7.67626e35	−0.404863
$159$	−1.51284e36	−0.719019
$160$	1.39525e36	0.597960
$161$	−1.68410e36	−0.651239
$162$	4.78323e36	1.67003
$163$	5.17457e36	1.63222	0.816111	−	0.577896i	$-0.196126\pi$
$163$	5.17457e36	1.63222	0.816111	+	0.577896i	$0.196126\pi$
$164$	−1.42194e36	−0.405470
$165$	−2.13299e36	−0.550178
$166$	−4.38804e36	−1.02444
$167$	−4.37605e36	−0.925252	−0.462626	−	0.886553i	$-0.653093\pi$
$167$	−4.37605e36	−0.925252	−0.462626	+	0.886553i	$0.653093\pi$
$168$	−1.02179e36	−0.195776
$169$	−5.25488e35	−0.0912919
$170$	−4.75419e36	−0.749324
$171$	−2.91185e36	−0.416614
$172$	5.91721e36	0.768949
$173$	−1.16497e37	−1.37580	−0.687900	−	0.725805i	$-0.741467\pi$
$173$	−1.16497e37	−1.37580	−0.687900	+	0.725805i	$0.741467\pi$
$174$	−2.26443e36	−0.243162
$175$	1.81294e36	0.177115
$176$	−1.33877e37	−1.19055
$177$	2.56568e37	2.07799
$178$	−2.28370e37	−1.68543
$179$	3.52955e36	0.237490	0.118745	−	0.992925i	$-0.462113\pi$
$179$	3.52955e36	0.237490	0.118745	+	0.992925i	$0.462113\pi$
$180$	2.13299e36	0.130916
$181$	−1.74051e37	−0.974947	−0.487473	−	0.873138i	$-0.662081\pi$
$181$	−1.74051e37	−0.974947	−0.487473	+	0.873138i	$0.662081\pi$
$182$	2.25097e37	1.15131
$183$	3.20203e37	1.49618
$184$	−3.28797e36	−0.140421
$185$	1.23945e37	0.484058
$186$	1.91524e37	0.684320
$187$	3.99170e37	1.30548
$188$	−5.56779e37	−1.66755
$189$	2.46459e37	0.676277
$190$	2.96793e37	0.746483
$191$	−2.24606e36	−0.0518048	−0.0259024	−	0.999664i	$-0.508246\pi$
$191$	−2.24606e36	−0.0518048	−0.0259024	+	0.999664i	$0.508246\pi$
$192$	3.84694e37	0.814040
$193$	2.96630e37	0.576129	0.288064	−	0.957611i	$-0.406988\pi$
$193$	2.96630e37	0.576129	0.288064	+	0.957611i	$0.406988\pi$
$194$	−1.37958e38	−2.46047
$195$	3.01241e37	0.493564
$196$	−1.23222e37	−0.185551
$197$	−5.56817e37	−0.770939	−0.385470	−	0.922721i	$-0.625961\pi$
$197$	−5.56817e37	−0.770939	−0.385470	+	0.922721i	$0.625961\pi$
$198$	−3.87335e37	−0.493300
$199$	−6.53016e36	−0.0765328	−0.0382664	−	0.999268i	$-0.512184\pi$
$199$	−6.53016e36	−0.0765328	−0.0382664	+	0.999268i	$0.512184\pi$
$200$	3.53951e36	0.0381898
$201$	−7.28398e37	−0.723826
$202$	9.01924e37	0.825795
$203$	−1.61597e37	−0.136380
$204$	−1.57183e38	−1.22323
$205$	−2.93711e37	−0.210853
$206$	2.27857e38	1.50957
$207$	−4.09270e37	−0.250322
$208$	1.89075e38	1.06804
$209$	−2.49193e38	−1.30053
$210$	1.29637e38	0.625333
$211$	4.18954e38	1.86856	0.934278	−	0.356545i	$-0.116045\pi$
$211$	4.18954e38	1.86856	0.934278	+	0.356545i	$0.116045\pi$
$212$	1.29467e38	0.534093
$213$	−5.11429e38	−1.95219
$214$	−5.08556e38	−1.79685
$215$	1.22223e38	0.399871
$216$	4.81177e37	0.145820
$217$	1.36678e38	0.383806
$218$	−2.53557e38	−0.660000
$219$	−6.46795e38	−1.56113
$220$	1.82538e38	0.408677
$221$	−5.63747e38	−1.17115
$222$	8.86294e38	1.70905
$223$	−1.62044e38	−0.290136	−0.145068	−	0.989422i	$-0.546340\pi$
$223$	−1.62044e38	−0.290136	−0.145068	+	0.989422i	$0.546340\pi$
$224$	7.11990e38	1.18408
$225$	4.40581e37	0.0680791
$226$	8.46072e38	1.21512
$227$	9.68892e38	1.29375	0.646873	−	0.762598i	$-0.276076\pi$
$227$	9.68892e38	1.29375	0.646873	+	0.762598i	$0.276076\pi$
$228$	9.81259e38	1.21859
$229$	4.72860e38	0.546320	0.273160	−	0.961969i	$-0.411931\pi$
$229$	4.72860e38	0.546320	0.273160	+	0.961969i	$0.411931\pi$
$230$	4.17153e38	0.448524
$231$	−1.08846e39	−1.08946
$232$	−3.15496e37	−0.0294065
$233$	−2.32086e38	−0.201501	−0.100750	−	0.994912i	$-0.532124\pi$
$233$	−2.32086e38	−0.201501	−0.100750	+	0.994912i	$0.532124\pi$
$234$	5.47032e38	0.442539
$235$	−1.15006e39	−0.867163
$236$	−2.19567e39	−1.54355
$237$	−5.24224e38	−0.343692
$238$	−2.42605e39	−1.48381
$239$	1.78755e39	1.02022	0.510109	−	0.860110i	$-0.329605\pi$
$239$	1.78755e39	1.02022	0.510109	+	0.860110i	$0.329605\pi$
$240$	1.08891e39	0.580106
$241$	−2.68792e39	−1.33701	−0.668506	−	0.743707i	$-0.733066\pi$
$241$	−2.68792e39	−1.33701	−0.668506	+	0.743707i	$0.733066\pi$
$242$	−3.79082e38	−0.176108
$243$	1.50698e39	0.654041
$244$	−2.74026e39	−1.11137
$245$	−2.54522e38	−0.0964906
$246$	−2.10023e39	−0.744453
$247$	3.51934e39	1.16671
$248$	2.66844e38	0.0827571
$249$	−2.99666e39	−0.869659
$250$	−4.49066e38	−0.121983
$251$	2.18494e39	0.555677	0.277838	−	0.960628i	$-0.410382\pi$
$251$	2.18494e39	0.555677	0.277838	+	0.960628i	$0.410382\pi$
$252$	1.08845e39	0.259240
$253$	−3.50248e39	−0.781426
$254$	1.60909e39	0.336375
$255$	−3.24671e39	−0.636108
$256$	6.63606e39	1.21885
$257$	8.25568e39	1.42186	0.710929	−	0.703264i	$-0.248275\pi$
$257$	8.25568e39	1.42186	0.710929	+	0.703264i	$0.248275\pi$
$258$	8.73980e39	1.41181
$259$	6.32489e39	0.958532
$260$	−2.57798e39	−0.366623
$261$	−3.92715e38	−0.0524214
$262$	−1.41572e40	−1.77422
$263$	2.69949e39	0.317697	0.158848	−	0.987303i	$-0.449222\pi$
$263$	2.69949e39	0.317697	0.158848	+	0.987303i	$0.449222\pi$
$264$	−2.12506e39	−0.234912
$265$	2.67421e39	0.277740
$266$	1.51452e40	1.47819
$267$	−1.55958e40	−1.43077
$268$	6.23353e39	0.537663
$269$	1.21756e40	0.987592	0.493796	−	0.869578i	$-0.335609\pi$
$269$	1.21756e40	0.987592	0.493796	+	0.869578i	$0.335609\pi$
$270$	−6.10481e39	−0.465769
$271$	−9.05453e39	−0.649939	−0.324969	−	0.945725i	$-0.605354\pi$
$271$	−9.05453e39	−0.649939	−0.324969	+	0.945725i	$0.605354\pi$
$272$	−2.03781e40	−1.37650
$273$	1.53722e40	0.977357
$274$	−9.83751e39	−0.588845
$275$	3.77043e39	0.212521
$276$	1.37919e40	0.732192
$277$	−6.18766e39	−0.309464	−0.154732	−	0.987956i	$-0.549451\pi$
$277$	−6.18766e39	−0.309464	−0.154732	+	0.987956i	$0.549451\pi$
$278$	−4.52574e40	−2.13280
$279$	3.32155e39	0.147527
$280$	1.80620e39	0.0756236
$281$	4.51611e39	0.178283	0.0891415	−	0.996019i	$-0.471588\pi$
$281$	4.51611e39	0.178283	0.0891415	+	0.996019i	$0.471588\pi$
$282$	−8.22371e40	−3.06166
$283$	3.25719e40	1.14384	0.571921	−	0.820308i	$-0.306198\pi$
$283$	3.25719e40	1.14384	0.571921	+	0.820308i	$0.306198\pi$
$284$	4.37674e40	1.45010
$285$	2.02685e40	0.633696
$286$	4.68143e40	1.38146
$287$	−1.49879e40	−0.417533
$288$	1.73028e40	0.455136
$289$	2.05049e40	0.509382
$290$	4.00278e39	0.0939280
$291$	−9.42136e40	−2.08872
$292$	5.53518e40	1.15962
$293$	−6.99032e40	−1.38414	−0.692072	−	0.721829i	$-0.743302\pi$
$293$	−6.99032e40	−1.38414	−0.692072	+	0.721829i	$0.743302\pi$
$294$	−1.82001e40	−0.340676
$295$	−4.53529e40	−0.802679
$296$	1.23485e40	0.206681
$297$	5.12570e40	0.811469
$298$	2.17636e40	0.325958
$299$	4.94655e40	0.701016
$300$	−1.48470e40	−0.199131
$301$	6.23701e40	0.791825
$302$	−1.36535e41	−1.64108
$303$	6.15938e40	0.701025
$304$	1.27215e41	1.37128
$305$	−5.66016e40	−0.577938
$306$	−5.89579e40	−0.570346
$307$	1.35007e40	0.123758	0.0618788	−	0.998084i	$-0.480291\pi$
$307$	1.35007e40	0.123758	0.0618788	+	0.998084i	$0.480291\pi$
$308$	9.31485e40	0.809262
$309$	1.55607e41	1.28149
$310$	−3.38552e40	−0.264337
$311$	5.12682e40	0.379579	0.189789	−	0.981825i	$-0.439220\pi$
$311$	5.12682e40	0.379579	0.189789	+	0.981825i	$0.439220\pi$
$312$	3.00122e40	0.210740
$313$	1.36507e39	0.00909232	0.00454616	−	0.999990i	$-0.498553\pi$
$313$	1.36507e39	0.00909232	0.00454616	+	0.999990i	$0.498553\pi$
$314$	−3.32949e41	−2.10397
$315$	2.24827e40	0.134810
$316$	4.48624e40	0.255297
$317$	2.88324e41	1.55741	0.778705	−	0.627390i	$-0.215877\pi$
$317$	2.88324e41	1.55741	0.778705	+	0.627390i	$0.215877\pi$
$318$	1.91224e41	0.980609
$319$	−3.36080e40	−0.163643
$320$	−6.80015e40	−0.314444
$321$	−3.47301e41	−1.52536
$322$	2.12871e41	0.888169
$323$	−3.79307e41	−1.50366
$324$	−2.79546e41	−1.05308
$325$	−5.32498e40	−0.190652
$326$	−6.54070e41	−2.22605
$327$	−1.73158e41	−0.560280
$328$	−2.92619e40	−0.0900292
$329$	−5.86871e41	−1.71716
$330$	2.69612e41	0.750341
$331$	1.22306e41	0.323808	0.161904	−	0.986807i	$-0.448237\pi$
$331$	1.22306e41	0.323808	0.161904	+	0.986807i	$0.448237\pi$
$332$	2.56450e41	0.645989
$333$	1.53708e41	0.368439
$334$	5.53136e41	1.26187
$335$	1.28757e41	0.279597
$336$	5.55668e41	1.14873
$337$	1.95036e40	0.0383902	0.0191951	−	0.999816i	$-0.493890\pi$
$337$	1.95036e40	0.0383902	0.0191951	+	0.999816i	$0.493890\pi$
$338$	6.64222e40	0.124505
$339$	5.77796e41	1.03152
$340$	2.77849e41	0.472506
$341$	2.84254e41	0.460531
$342$	3.68061e41	0.568183
$343$	−7.31855e41	−1.07664
$344$	1.21769e41	0.170735
$345$	2.84880e41	0.380756
$346$	1.47254e42	1.87634
$347$	−8.38690e41	−1.01898	−0.509490	−	0.860477i	$-0.670166\pi$
$347$	−8.38690e41	−1.01898	−0.509490	+	0.860477i	$0.670166\pi$
$348$	1.32340e41	0.153333
$349$	−2.92359e40	−0.0323070	−0.0161535	−	0.999870i	$-0.505142\pi$
$349$	−2.92359e40	−0.0323070	−0.0161535	+	0.999870i	$0.505142\pi$
$350$	−2.29157e41	−0.241552
$351$	−7.23902e41	−0.727968
$352$	1.48075e42	1.42079
$353$	−1.88083e42	−1.72213	−0.861067	−	0.508492i	$-0.830203\pi$
$353$	−1.88083e42	−1.72213	−0.861067	+	0.508492i	$0.830203\pi$
$354$	−3.24304e42	−2.83399
$355$	9.04042e41	0.754086
$356$	1.33466e42	1.06279
$357$	−1.65679e42	−1.25962
$358$	−4.46139e41	−0.323892
$359$	1.60953e41	0.111594	0.0557968	−	0.998442i	$-0.482230\pi$
$359$	1.60953e41	0.111594	0.0557968	+	0.998442i	$0.482230\pi$
$360$	4.38943e40	0.0290681
$361$	7.87154e41	0.497956
$362$	2.20002e42	1.32965
$363$	−2.58881e41	−0.149500
$364$	−1.31554e42	−0.725988
$365$	1.14332e42	0.603028
$366$	−4.04740e42	−2.04051
$367$	2.15460e42	1.03843	0.519213	−	0.854645i	$-0.326225\pi$
$367$	2.15460e42	1.03843	0.519213	+	0.854645i	$0.326225\pi$
$368$	1.78806e42	0.823933
$369$	−3.64238e41	−0.160491
$370$	−1.56668e42	−0.660165
$371$	1.36464e42	0.549982
$372$	−1.11932e42	−0.431516
$373$	2.59028e42	0.955325	0.477663	−	0.878543i	$-0.341484\pi$
$373$	2.59028e42	0.955325	0.477663	+	0.878543i	$0.341484\pi$
$374$	−5.04554e42	−1.78044
$375$	−3.06674e41	−0.103553
$376$	−1.14578e42	−0.370257
$377$	4.74646e41	0.146804
$378$	−3.11526e42	−0.922316
$379$	4.01905e42	1.13914	0.569568	−	0.821944i	$-0.307110\pi$
$379$	4.01905e42	1.13914	0.569568	+	0.821944i	$0.307110\pi$
$380$	−1.73455e42	−0.470714
$381$	1.09887e42	0.285551
$382$	2.83904e41	0.0706522
$383$	5.03299e42	1.19963	0.599813	−	0.800140i	$-0.295242\pi$
$383$	5.03299e42	1.19963	0.599813	+	0.800140i	$0.295242\pi$
$384$	1.91757e42	0.437811
$385$	1.92404e42	0.420835
$386$	−3.74943e42	−0.785732
$387$	1.51572e42	0.304361
$388$	8.06268e42	1.55151
$389$	4.14807e42	0.765029	0.382515	−	0.923949i	$-0.375058\pi$
$389$	4.14807e42	0.765029	0.382515	+	0.923949i	$0.375058\pi$
$390$	−3.80772e42	−0.673130
$391$	−5.33128e42	−0.903473
$392$	−2.53576e41	−0.0411991
$393$	−9.66818e42	−1.50615
$394$	7.03822e42	1.05142
$395$	9.26658e41	0.132760
$396$	2.26370e42	0.311063
$397$	−8.89168e42	−1.17203	−0.586017	−	0.810299i	$-0.699305\pi$
$397$	−8.89168e42	−1.17203	−0.586017	+	0.810299i	$0.699305\pi$
$398$	8.25418e41	0.104377
$399$	1.03429e43	1.25485
$400$	−1.92485e42	−0.224082
$401$	1.71192e41	0.0191250	0.00956251	−	0.999954i	$-0.496956\pi$
$401$	1.71192e41	0.0191250	0.00956251	+	0.999954i	$0.496956\pi$
$402$	9.20702e42	0.987163
$403$	−4.01451e42	−0.413142
$404$	−5.27111e42	−0.520727
$405$	−5.77419e42	−0.547625
$406$	2.04260e42	0.185996
$407$	1.31541e43	1.15015
$408$	−3.23464e42	−0.271603
$409$	1.40883e43	1.13612	0.568061	−	0.822986i	$-0.307694\pi$
$409$	1.40883e43	1.13612	0.568061	+	0.822986i	$0.307694\pi$
$410$	3.71253e42	0.287565
$411$	−6.71819e42	−0.499876
$412$	−1.33166e43	−0.951899
$413$	−2.31434e43	−1.58947
$414$	5.17321e42	0.341393
$415$	5.29713e42	0.335929
$416$	−2.09127e43	−1.27459
$417$	−3.09070e43	−1.81056
$418$	3.14982e43	1.77369
$419$	−2.03304e43	−1.10056	−0.550280	−	0.834980i	$-0.685479\pi$
$419$	−2.03304e43	−1.10056	−0.550280	+	0.834980i	$0.685479\pi$
$420$	−7.57639e42	−0.394320
$421$	2.81610e43	1.40927	0.704633	−	0.709572i	$-0.251111\pi$
$421$	2.81610e43	1.40927	0.704633	+	0.709572i	$0.251111\pi$
$422$	−5.29562e43	−2.54836
$423$	−1.42622e43	−0.660039
$424$	2.66427e42	0.118588
$425$	5.73914e42	0.245714
$426$	6.46451e43	2.66243
$427$	−2.88836e43	−1.14443
$428$	2.97216e43	1.13305
$429$	3.19702e43	1.17274
$430$	−1.54491e43	−0.545350
$431$	−1.08445e43	−0.368412	−0.184206	−	0.982888i	$-0.558971\pi$
$431$	−1.08445e43	−0.368412	−0.184206	+	0.982888i	$0.558971\pi$
$432$	−2.61673e43	−0.855611
$433$	3.95138e43	1.24365	0.621825	−	0.783156i	$-0.286392\pi$
$433$	3.95138e43	1.24365	0.621825	+	0.783156i	$0.286392\pi$
$434$	−1.72762e43	−0.523440
$435$	2.73356e42	0.0797364
$436$	1.48186e43	0.416180
$437$	3.32820e43	0.900047
$438$	8.17554e43	2.12909
$439$	1.22543e43	0.307342	0.153671	−	0.988122i	$-0.450890\pi$
$439$	1.22543e43	0.307342	0.153671	+	0.988122i	$0.450890\pi$
$440$	3.75642e42	0.0907412
$441$	−3.15639e42	−0.0734436
$442$	7.12581e43	1.59723
$443$	−5.64830e43	−1.21971	−0.609855	−	0.792513i	$-0.708772\pi$
$443$	−5.64830e43	−1.21971	−0.609855	+	0.792513i	$0.708772\pi$
$444$	−5.17977e43	−1.07768
$445$	2.75683e43	0.552674
$446$	2.04825e43	0.395692
$447$	1.48627e43	0.276709
$448$	−3.47009e43	−0.622664
$449$	2.63282e43	0.455362	0.227681	−	0.973736i	$-0.426886\pi$
$449$	2.63282e43	0.455362	0.227681	+	0.973736i	$0.426886\pi$
$450$	−5.56898e42	−0.0928473
$451$	−3.11710e43	−0.501000
$452$	−4.94470e43	−0.766224
$453$	−9.32419e43	−1.39313
$454$	−1.22469e44	−1.76443
$455$	−2.71731e43	−0.377530
$456$	2.01931e43	0.270573
$457$	−4.92089e43	−0.635955	−0.317977	−	0.948098i	$-0.603004\pi$
$457$	−4.92089e43	−0.635955	−0.317977	+	0.948098i	$0.603004\pi$
$458$	−5.97700e43	−0.745079
$459$	7.80205e43	0.938209
$460$	−2.43797e43	−0.282829
$461$	−1.35047e44	−1.51154	−0.755771	−	0.654836i	$-0.772737\pi$
$461$	−1.35047e44	−1.51154	−0.755771	+	0.654836i	$0.772737\pi$
$462$	1.37582e44	1.48583
$463$	9.98444e42	0.104049	0.0520244	−	0.998646i	$-0.483433\pi$
$463$	9.98444e42	0.104049	0.0520244	+	0.998646i	$0.483433\pi$
$464$	1.71573e43	0.172544
$465$	−2.31203e43	−0.224398
$466$	2.93359e43	0.274810
$467$	1.53367e44	1.38677	0.693384	−	0.720568i	$-0.256119\pi$
$467$	1.53367e44	1.38677	0.693384	+	0.720568i	$0.256119\pi$
$468$	−3.19702e43	−0.279054
$469$	6.57043e43	0.553659
$470$	1.45369e44	1.18265
$471$	−2.27376e44	−1.78608
$472$	−4.51843e43	−0.342724
$473$	1.29714e44	0.950116
$474$	6.62624e43	0.468732
$475$	−3.58281e43	−0.244782
$476$	1.41785e44	0.935658
$477$	3.31636e43	0.211401
$478$	−2.25948e44	−1.39139
$479$	5.80916e43	0.345603	0.172802	−	0.984957i	$-0.444718\pi$
$479$	5.80916e43	0.345603	0.172802	+	0.984957i	$0.444718\pi$
$480$	−1.20440e44	−0.692291
$481$	−1.85775e44	−1.03180
$482$	3.39755e44	1.82344
$483$	1.45373e44	0.753975
$484$	2.21547e43	0.111050
$485$	1.66539e44	0.806822
$486$	−1.90484e44	−0.891990
$487$	6.21415e43	0.281290	0.140645	−	0.990060i	$-0.455082\pi$
$487$	6.21415e43	0.281290	0.140645	+	0.990060i	$0.455082\pi$
$488$	−5.63912e43	−0.246765
$489$	−4.46675e44	−1.88971
$490$	3.21718e43	0.131595
$491$	1.52856e44	0.604557	0.302278	−	0.953220i	$-0.402253\pi$
$491$	1.52856e44	0.604557	0.302278	+	0.953220i	$0.402253\pi$
$492$	1.22744e44	0.469435
$493$	−5.11562e43	−0.189201
$494$	−4.44848e44	−1.59117
$495$	4.67581e43	0.161760
$496$	−1.45115e44	−0.485583
$497$	4.61329e44	1.49324
$498$	3.78781e44	1.18605
$499$	9.99203e43	0.302688	0.151344	−	0.988481i	$-0.451640\pi$
$499$	9.99203e43	0.302688	0.151344	+	0.988481i	$0.451640\pi$
$500$	2.62448e43	0.0769197
$501$	3.77745e44	1.07122
$502$	−2.76178e44	−0.757840
$503$	9.03153e43	0.239822	0.119911	−	0.992785i	$-0.461739\pi$
$503$	9.03153e43	0.239822	0.119911	+	0.992785i	$0.461739\pi$
$504$	2.23991e43	0.0575607
$505$	−1.08878e44	−0.270790
$506$	4.42717e44	1.06572
$507$	4.53607e43	0.105694
$508$	−9.40399e43	−0.212110
$509$	−5.47217e44	−1.19486	−0.597429	−	0.801922i	$-0.703811\pi$
$509$	−5.47217e44	−1.19486	−0.597429	+	0.801922i	$0.703811\pi$
$510$	4.10387e44	0.867533
$511$	5.83434e44	1.19412
$512$	−6.47984e44	−1.28413
$513$	−4.87064e44	−0.934651
$514$	−1.04353e45	−1.93915
$515$	−2.75063e44	−0.495009
$516$	−5.10780e44	−0.890254
$517$	−1.22054e45	−2.06043
$518$	−7.99471e44	−1.30726
$519$	1.00562e45	1.59284
$520$	−5.30518e43	−0.0814038
$521$	1.19671e45	1.77897	0.889484	−	0.456966i	$-0.151064\pi$
$521$	1.19671e45	1.77897	0.889484	+	0.456966i	$0.151064\pi$
$522$	4.96395e43	0.0714931
$523$	−6.44705e43	−0.0899670	−0.0449835	−	0.998988i	$-0.514324\pi$
$523$	−6.44705e43	−0.0899670	−0.0449835	+	0.998988i	$0.514324\pi$
$524$	8.27390e44	1.11878
$525$	−1.56495e44	−0.205055
$526$	−3.41218e44	−0.433279
$527$	4.32675e44	0.532460
$528$	1.15564e45	1.37837
$529$	−3.97216e44	−0.459206
$530$	−3.38023e44	−0.378786
$531$	−5.62432e44	−0.610957
$532$	−8.85134e44	−0.932110
$533$	4.40227e44	0.449446
$534$	1.97132e45	1.95131
$535$	6.13916e44	0.589212
$536$	1.28279e44	0.119381
$537$	−3.04675e44	−0.274955
$538$	−1.53901e45	−1.34689
$539$	−2.70120e44	−0.229267
$540$	3.56784e44	0.293703
$541$	−3.00892e44	−0.240246	−0.120123	−	0.992759i	$-0.538329\pi$
$541$	−3.00892e44	−0.240246	−0.120123	+	0.992759i	$0.538329\pi$
$542$	1.14450e45	0.886396
$543$	1.50243e45	1.12875
$544$	2.25392e45	1.64269
$545$	3.06088e44	0.216423
$546$	−1.94306e45	−1.33293
$547$	9.15780e44	0.609537	0.304769	−	0.952426i	$-0.401421\pi$
$547$	9.15780e44	0.609537	0.304769	+	0.952426i	$0.401421\pi$
$548$	5.74934e44	0.371312
$549$	−7.01930e44	−0.439896
$550$	−4.76586e44	−0.289839
$551$	3.19357e44	0.188484
$552$	2.83821e44	0.162574
$553$	4.72870e44	0.262892
$554$	7.82126e44	0.422052
$555$	−1.06991e45	−0.560420
$556$	2.64498e45	1.34489
$557$	−3.51921e45	−1.73714	−0.868569	−	0.495568i	$-0.834960\pi$
$557$	−3.51921e45	−1.73714	−0.868569	+	0.495568i	$0.834960\pi$
$558$	−4.19847e44	−0.201199
$559$	−1.83194e45	−0.852348
$560$	−9.82241e44	−0.443727
$561$	−3.44568e45	−1.51143
$562$	−5.70840e44	−0.243145
$563$	1.25910e45	0.520802	0.260401	−	0.965501i	$-0.416145\pi$
$563$	1.25910e45	0.520802	0.260401	+	0.965501i	$0.416145\pi$
$564$	4.80618e45	1.93061
$565$	−1.02136e45	−0.398454
$566$	−4.11711e45	−1.55999
$567$	−2.94655e45	−1.08441
$568$	9.00681e44	0.321976
$569$	−1.60105e45	−0.555972	−0.277986	−	0.960585i	$-0.589667\pi$
$569$	−1.60105e45	−0.555972	−0.277986	+	0.960585i	$0.589667\pi$
$570$	−2.56195e45	−0.864244
$571$	5.75140e44	0.188485	0.0942427	−	0.995549i	$-0.469957\pi$
$571$	5.75140e44	0.188485	0.0942427	+	0.995549i	$0.469957\pi$
$572$	−2.73597e45	−0.871118
$573$	1.93882e44	0.0599773
$574$	1.89449e45	0.569437
$575$	−5.03576e44	−0.147077
$576$	−8.43303e44	−0.239339
$577$	3.64572e45	1.00550	0.502750	−	0.864432i	$-0.332321\pi$
$577$	3.64572e45	1.00550	0.502750	+	0.864432i	$0.332321\pi$
$578$	−2.59184e45	−0.694702
$579$	−2.56054e45	−0.667016
$580$	−2.33935e44	−0.0592288
$581$	2.70311e45	0.665207
$582$	1.19087e46	2.84862
$583$	2.83810e45	0.659927
$584$	1.13907e45	0.257478
$585$	−6.60363e44	−0.145115
$586$	8.83582e45	1.88771
$587$	−2.48055e45	−0.515251	−0.257626	−	0.966245i	$-0.582940\pi$
$587$	−2.48055e45	−0.515251	−0.257626	+	0.966245i	$0.582940\pi$
$588$	1.06367e45	0.214822
$589$	−2.70109e45	−0.530441
$590$	5.73265e45	1.09470
$591$	4.80651e45	0.892558
$592$	−6.71532e45	−1.21271
$593$	2.97630e45	0.522726	0.261363	−	0.965241i	$-0.415828\pi$
$593$	2.97630e45	0.522726	0.261363	+	0.965241i	$0.415828\pi$
$594$	−6.47893e45	−1.10669
$595$	2.92866e45	0.486563
$596$	−1.27193e45	−0.205541
$597$	5.63691e44	0.0886062
$598$	−6.25249e45	−0.956056
$599$	−3.09884e45	−0.460953	−0.230476	−	0.973078i	$-0.574028\pi$
$599$	−3.09884e45	−0.460953	−0.230476	+	0.973078i	$0.574028\pi$
$600$	−3.05534e44	−0.0442145
$601$	−5.90335e45	−0.831132	−0.415566	−	0.909563i	$-0.636417\pi$
$601$	−5.90335e45	−0.831132	−0.415566	+	0.909563i	$0.636417\pi$
$602$	−7.88364e45	−1.07990
$603$	1.59675e45	0.212815
$604$	7.97952e45	1.03483
$605$	4.57619e44	0.0577484
$606$	−7.78551e45	−0.956068
$607$	6.02204e45	0.719664	0.359832	−	0.933017i	$-0.382834\pi$
$607$	6.02204e45	0.719664	0.359832	+	0.933017i	$0.382834\pi$
$608$	−1.40707e46	−1.63646
$609$	1.39493e45	0.157894
$610$	7.15449e45	0.788200
$611$	1.72376e46	1.84841
$612$	3.44568e45	0.359647
$613$	7.92968e45	0.805671	0.402836	−	0.915272i	$-0.368025\pi$
$613$	7.92968e45	0.805671	0.402836	+	0.915272i	$0.368025\pi$
$614$	−1.70650e45	−0.168782
$615$	2.53534e45	0.244117
$616$	1.91688e45	0.179686
$617$	−7.56919e45	−0.690787	−0.345394	−	0.938458i	$-0.612255\pi$
$617$	−7.56919e45	−0.690787	−0.345394	+	0.938458i	$0.612255\pi$
$618$	−1.96689e46	−1.74771
$619$	−4.72940e45	−0.409176	−0.204588	−	0.978848i	$-0.565585\pi$
$619$	−4.72940e45	−0.409176	−0.204588	+	0.978848i	$0.565585\pi$
$620$	1.97860e45	0.166684
$621$	−6.84585e45	−0.561585
$622$	−6.48035e45	−0.517675
$623$	1.40680e46	1.09441
$624$	−1.63211e46	−1.23653
$625$	5.42101e44	0.0400000
$626$	−1.72547e44	−0.0124002
$627$	2.15106e46	1.50570
$628$	1.94585e46	1.32671
$629$	2.00225e46	1.32979
$630$	−2.84183e45	−0.183856
$631$	−9.12534e45	−0.575128	−0.287564	−	0.957761i	$-0.592845\pi$
$631$	−9.12534e45	−0.575128	−0.287564	+	0.957761i	$0.592845\pi$
$632$	9.23213e44	0.0566853
$633$	−3.61646e46	−2.16333
$634$	−3.64444e46	−2.12402
$635$	−1.94245e45	−0.110302
$636$	−1.11757e46	−0.618349
$637$	3.81490e45	0.205675
$638$	4.24808e45	0.223178
$639$	1.12112e46	0.573971
$640$	−3.38965e45	−0.169116
$641$	−1.89987e46	−0.923774	−0.461887	−	0.886939i	$-0.652827\pi$
$641$	−1.89987e46	−0.923774	−0.461887	+	0.886939i	$0.652827\pi$
$642$	4.38992e46	2.08031
$643$	−1.26235e46	−0.583040	−0.291520	−	0.956565i	$-0.594161\pi$
$643$	−1.26235e46	−0.583040	−0.291520	+	0.956565i	$0.594161\pi$
$644$	−1.24408e46	−0.560058
$645$	−1.05505e46	−0.462952
$646$	4.79447e46	2.05071
$647$	1.12690e46	0.469855	0.234927	−	0.972013i	$-0.424515\pi$
$647$	1.12690e46	0.469855	0.234927	+	0.972013i	$0.424515\pi$
$648$	−5.75272e45	−0.233822
$649$	−4.81323e46	−1.90721
$650$	6.73082e45	0.260014
$651$	−1.17982e46	−0.444353
$652$	3.82258e46	1.40369
$653$	−3.57189e45	−0.127888	−0.0639440	−	0.997953i	$-0.520368\pi$
$653$	−3.57189e45	−0.127888	−0.0639440	+	0.997953i	$0.520368\pi$
$654$	2.18873e46	0.764118
$655$	1.70902e46	0.581790
$656$	1.59131e46	0.528253
$657$	1.41786e46	0.458993
$658$	7.41810e46	2.34189
$659$	4.26159e46	1.31209	0.656043	−	0.754723i	$-0.272229\pi$
$659$	4.26159e46	1.31209	0.656043	+	0.754723i	$0.272229\pi$
$660$	−1.57569e46	−0.473147
$661$	−2.93053e46	−0.858268	−0.429134	−	0.903241i	$-0.641181\pi$
$661$	−2.93053e46	−0.858268	−0.429134	+	0.903241i	$0.641181\pi$
$662$	−1.54596e46	−0.441613
$663$	4.86633e46	1.35590
$664$	5.27744e45	0.143433
$665$	−1.82830e46	−0.484718
$666$	−1.94288e46	−0.502483
$667$	4.48866e45	0.113251
$668$	−3.23269e46	−0.795707
$669$	1.39878e46	0.335907
$670$	−1.62750e46	−0.381318
$671$	−6.00703e46	−1.37321
$672$	−6.14598e46	−1.37088
$673$	−7.94628e44	−0.0172948	−0.00864740	−	0.999963i	$-0.502753\pi$
$673$	−7.94628e44	−0.0172948	−0.00864740	+	0.999963i	$0.502753\pi$
$674$	−2.46527e45	−0.0523571
$675$	7.36957e45	0.152732
$676$	−3.88191e45	−0.0785100
$677$	−5.41689e46	−1.06915	−0.534573	−	0.845122i	$-0.679527\pi$
$677$	−5.41689e46	−1.06915	−0.534573	+	0.845122i	$0.679527\pi$
$678$	−7.30339e46	−1.40681
$679$	8.49843e46	1.59767
$680$	5.71780e45	0.104914
$681$	−8.36359e46	−1.49784
$682$	−3.59299e46	−0.628079
$683$	4.80553e46	0.819973	0.409986	−	0.912092i	$-0.365533\pi$
$683$	4.80553e46	0.819973	0.409986	+	0.912092i	$0.365533\pi$
$684$	−2.15106e46	−0.358283
$685$	1.18756e46	0.193090
$686$	9.25072e46	1.46834
$687$	−4.08178e46	−0.632505
$688$	−6.62202e46	−1.00180
$689$	−4.00824e46	−0.592020
$690$	−3.60091e46	−0.519281
$691$	9.58471e46	1.34956	0.674779	−	0.738020i	$-0.264239\pi$
$691$	9.58471e46	1.34956	0.674779	+	0.738020i	$0.264239\pi$
$692$	−8.60595e46	−1.18317
$693$	2.38605e46	0.320317
$694$	1.06011e47	1.38970
$695$	5.46336e46	0.699375
$696$	2.72340e45	0.0340455
$697$	−4.74467e46	−0.579249
$698$	3.69544e45	0.0440607
$699$	2.00340e46	0.233288
$700$	1.33926e46	0.152317
$701$	3.14053e46	0.348863	0.174432	−	0.984669i	$-0.444191\pi$
$701$	3.14053e46	0.348863	0.174432	+	0.984669i	$0.444191\pi$
$702$	9.15018e46	0.992813
$703$	−1.24996e47	−1.32474
$704$	−7.21688e46	−0.747138
$705$	9.92745e46	1.00396
$706$	2.37738e47	2.34867
$707$	−5.55600e46	−0.536218
$708$	1.89533e47	1.78705
$709$	−1.07691e47	−0.992009	−0.496005	−	0.868320i	$-0.665200\pi$
$709$	−1.07691e47	−0.992009	−0.496005	+	0.868320i	$0.665200\pi$
$710$	−1.14272e47	−1.02843
$711$	1.14917e46	0.101050
$712$	2.74658e46	0.235978
$713$	−3.79647e46	−0.318715
$714$	2.09419e47	1.71789
$715$	−5.65130e46	−0.453001
$716$	2.60737e46	0.204239
$717$	−1.54303e47	−1.18116
$718$	−2.03445e46	−0.152193
$719$	2.02046e47	1.47715	0.738573	−	0.674174i	$-0.235500\pi$
$719$	2.02046e47	1.47715	0.738573	+	0.674174i	$0.235500\pi$
$720$	−2.38705e46	−0.170559
$721$	−1.40364e47	−0.980218
$722$	−9.94970e46	−0.679120
$723$	2.32024e47	1.54793
$724$	−1.28576e47	−0.838444
$725$	−4.83206e45	−0.0308003
$726$	3.27228e46	0.203890
$727$	−2.34830e47	−1.43033	−0.715164	−	0.698957i	$-0.753648\pi$
$727$	−2.34830e47	−1.43033	−0.715164	+	0.698957i	$0.753648\pi$
$728$	−2.70721e46	−0.161196
$729$	8.02799e46	0.467308
$730$	−1.44517e47	−0.822417
$731$	1.97443e47	1.09851
$732$	2.36542e47	1.28669
$733$	7.07756e46	0.376416	0.188208	−	0.982129i	$-0.439732\pi$
$733$	7.07756e46	0.376416	0.188208	+	0.982129i	$0.439732\pi$
$734$	−2.72343e47	−1.41622
$735$	2.19706e46	0.111712
$736$	−1.97768e47	−0.983270
$737$	1.36648e47	0.664338
$738$	4.60399e46	0.218879
$739$	−3.25905e47	−1.51516	−0.757578	−	0.652744i	$-0.773618\pi$
$739$	−3.25905e47	−1.51516	−0.757578	+	0.652744i	$0.773618\pi$
$740$	9.15616e46	0.416284
$741$	−3.03794e47	−1.35076
$742$	−1.72492e47	−0.750074
$743$	−1.42154e47	−0.604568	−0.302284	−	0.953218i	$-0.597749\pi$
$743$	−1.42154e47	−0.604568	−0.302284	+	0.953218i	$0.597749\pi$
$744$	−2.30343e46	−0.0958124
$745$	−2.62724e46	−0.106886
$746$	−3.27414e47	−1.30289
$747$	6.56910e46	0.255691
$748$	2.94877e47	1.12270
$749$	3.13279e47	1.16676
$750$	3.87639e46	0.141227
$751$	−8.07948e45	−0.0287955	−0.0143978	−	0.999896i	$-0.504583\pi$
$751$	−8.07948e45	−0.0287955	−0.0143978	+	0.999896i	$0.504583\pi$
$752$	6.23098e47	2.17251
$753$	−1.88606e47	−0.643338
$754$	−5.99956e46	−0.200213
$755$	1.64822e47	0.538133
$756$	1.82065e47	0.581591
$757$	2.98356e47	0.932509	0.466255	−	0.884651i	$-0.345603\pi$
$757$	2.98356e47	0.932509	0.466255	+	0.884651i	$0.345603\pi$
$758$	−5.08011e47	−1.55357
$759$	3.02338e47	0.904699
$760$	−3.56949e46	−0.104516
$761$	8.91821e46	0.255524	0.127762	−	0.991805i	$-0.459221\pi$
$761$	8.91821e46	0.255524	0.127762	+	0.991805i	$0.459221\pi$
$762$	−1.38898e47	−0.389439
$763$	1.56195e47	0.428562
$764$	−1.65922e46	−0.0445516
$765$	7.11725e46	0.187024
$766$	−6.36174e47	−1.63607
$767$	6.79771e47	1.71096
$768$	−5.72833e47	−1.41113
$769$	−3.11972e47	−0.752195	−0.376098	−	0.926580i	$-0.622734\pi$
$769$	−3.11972e47	−0.752195	−0.376098	+	0.926580i	$0.622734\pi$
$770$	−2.43200e47	−0.573940
$771$	−7.12640e47	−1.64616
$772$	2.19128e47	0.495464
$773$	5.84176e47	1.29295	0.646475	−	0.762935i	$-0.276242\pi$
$773$	5.84176e47	1.29295	0.646475	+	0.762935i	$0.276242\pi$
$774$	−1.91589e47	−0.415092
$775$	4.08691e46	0.0866797
$776$	1.65920e47	0.344493
$777$	−5.45972e47	−1.10974
$778$	−5.24320e47	−1.04336
$779$	2.96199e47	0.577053
$780$	2.22535e47	0.424460
$781$	9.59444e47	1.79175
$782$	6.73879e47	1.23217
$783$	−6.56892e46	−0.117605
$784$	1.37899e47	0.241739
$785$	4.01927e47	0.689919
$786$	1.22207e48	2.05411
$787$	3.46036e47	0.569559	0.284779	−	0.958593i	$-0.408080\pi$
$787$	3.46036e47	0.569559	0.284779	+	0.958593i	$0.408080\pi$
$788$	−4.11335e47	−0.662999
$789$	−2.33023e47	−0.367815
$790$	−1.17130e47	−0.181060
$791$	−5.21194e47	−0.789019
$792$	4.65842e46	0.0690675
$793$	8.48371e47	1.23191
$794$	1.12392e48	1.59844
$795$	−2.30841e47	−0.321555
$796$	−4.82399e46	−0.0658174
$797$	−8.43355e47	−1.12706	−0.563532	−	0.826095i	$-0.690558\pi$
$797$	−8.43355e47	−1.12706	−0.563532	+	0.826095i	$0.690558\pi$
$798$	−1.30735e48	−1.71138
$799$	−1.85784e48	−2.38224
$800$	2.12898e47	0.267416
$801$	3.41881e47	0.420667
$802$	−2.16388e46	−0.0260830
$803$	1.21339e48	1.43283
$804$	−5.38086e47	−0.622482
$805$	−2.56973e47	−0.291243
$806$	5.07438e47	0.563449
$807$	−1.05101e48	−1.14339
$808$	−1.08473e47	−0.115620
$809$	−1.87301e48	−1.95609	−0.978045	−	0.208392i	$-0.933177\pi$
$809$	−1.87301e48	−1.95609	−0.978045	+	0.208392i	$0.933177\pi$
$810$	7.29863e47	0.746859
$811$	−1.53865e48	−1.54275	−0.771376	−	0.636380i	$-0.780431\pi$
$811$	−1.53865e48	−1.54275	−0.771376	+	0.636380i	$0.780431\pi$
$812$	−1.19376e47	−0.117285
$813$	7.81597e47	0.752470
$814$	−1.66269e48	−1.56859
$815$	7.89577e47	0.729951
$816$	1.75906e48	1.59365
$817$	−1.23259e48	−1.09435
$818$	−1.78078e48	−1.54946
$819$	−3.36981e47	−0.287356
$820$	−2.16971e47	−0.181332
$821$	−1.66705e48	−1.36548	−0.682742	−	0.730660i	$-0.739213\pi$
$821$	−1.66705e48	−1.36548	−0.682742	+	0.730660i	$0.739213\pi$
$822$	8.49185e47	0.681738
$823$	2.01297e48	1.58394	0.791972	−	0.610557i	$-0.209055\pi$
$823$	2.01297e48	1.58394	0.791972	+	0.610557i	$0.209055\pi$
$824$	−2.74041e47	−0.211357
$825$	−3.25468e47	−0.246047
$826$	2.92535e48	2.16774
$827$	1.15395e48	0.838195	0.419098	−	0.907941i	$-0.362347\pi$
$827$	1.15395e48	0.838195	0.419098	+	0.907941i	$0.362347\pi$
$828$	−3.02338e47	−0.215274
$829$	1.78893e48	1.24866	0.624331	−	0.781160i	$-0.285372\pi$
$829$	1.78893e48	1.24866	0.624331	+	0.781160i	$0.285372\pi$
$830$	−6.69562e47	−0.458144
$831$	5.34126e47	0.358284
$832$	1.01924e48	0.670257
$833$	−4.11161e47	−0.265076
$834$	3.90667e48	2.46926
$835$	−6.67732e47	−0.413785
$836$	−1.84085e48	−1.11844
$837$	5.55594e47	0.330969
$838$	2.56978e48	1.50096
$839$	2.30591e48	1.32059	0.660297	−	0.751004i	$-0.270430\pi$
$839$	2.30591e48	1.32059	0.660297	+	0.751004i	$0.270430\pi$
$840$	−1.55913e47	−0.0875536
$841$	−1.77300e48	−0.976284
$842$	−3.55957e48	−1.92198
$843$	−3.89835e47	−0.206408
$844$	3.09492e48	1.60694
$845$	−8.01831e46	−0.0408270
$846$	1.80275e48	0.900171
$847$	2.33521e47	0.114354
$848$	−1.44888e48	−0.695826
$849$	−2.81164e48	−1.32429
$850$	−7.25432e47	−0.335108
$851$	−1.75685e48	−0.795972
$852$	−3.77806e48	−1.67886
$853$	3.23565e48	1.41027	0.705135	−	0.709073i	$-0.250886\pi$
$853$	3.23565e48	1.41027	0.705135	+	0.709073i	$0.250886\pi$
$854$	3.65091e48	1.56080
$855$	−4.44313e47	−0.186315
$856$	6.11634e47	0.251579
$857$	1.13232e48	0.456864	0.228432	−	0.973560i	$-0.426640\pi$
$857$	1.13232e48	0.456864	0.228432	+	0.973560i	$0.426640\pi$
$858$	−4.04107e48	−1.59939
$859$	−1.69678e48	−0.658777	−0.329388	−	0.944195i	$-0.606843\pi$
$859$	−1.69678e48	−0.658777	−0.329388	+	0.944195i	$0.606843\pi$
$860$	9.02895e47	0.343885
$861$	1.29378e48	0.483400
$862$	1.37075e48	0.502445
$863$	−4.68742e48	−1.68561	−0.842803	−	0.538223i	$-0.819096\pi$
$863$	−4.68742e48	−1.68561	−0.842803	+	0.538223i	$0.819096\pi$
$864$	2.89424e48	1.02107
$865$	−1.77761e48	−0.615277
$866$	−4.99457e48	−1.69611
$867$	−1.77001e48	−0.589739
$868$	1.00967e48	0.330069
$869$	9.83446e47	0.315446
$870$	−3.45525e47	−0.108746
$871$	−1.92987e48	−0.595977
$872$	3.04950e47	0.0924073
$873$	2.06529e48	0.614111
$874$	−4.20687e48	−1.22750
$875$	2.76632e47	0.0792081
$876$	−4.77803e48	−1.34255
$877$	6.18989e48	1.70683	0.853414	−	0.521234i	$-0.174528\pi$
$877$	6.18989e48	1.70683	0.853414	+	0.521234i	$0.174528\pi$
$878$	−1.54895e48	−0.419158
$879$	6.03412e48	1.60250
$880$	−2.04281e48	−0.532431
$881$	2.27101e48	0.580919	0.290460	−	0.956887i	$-0.406192\pi$
$881$	2.27101e48	0.580919	0.290460	+	0.956887i	$0.406192\pi$
$882$	3.98971e47	0.100163
$883$	6.78750e48	1.67247	0.836234	−	0.548372i	$-0.184752\pi$
$883$	6.78750e48	1.67247	0.836234	+	0.548372i	$0.184752\pi$
$884$	−4.16454e48	−1.00717
$885$	3.91492e48	0.929305
$886$	7.13950e48	1.66346
$887$	−6.24043e48	−1.42717	−0.713583	−	0.700570i	$-0.752929\pi$
$887$	−6.24043e48	−1.42717	−0.713583	+	0.700570i	$0.752929\pi$
$888$	−1.06593e48	−0.239285
$889$	−9.91224e47	−0.218420
$890$	−3.48465e48	−0.753745
$891$	−6.12805e48	−1.30119
$892$	−1.19706e48	−0.249514
$893$	1.15980e49	2.37321
$894$	−1.87866e48	−0.377379
$895$	5.38567e47	0.106209
$896$	−1.72972e48	−0.334884
$897$	−4.26992e48	−0.811605
$898$	−3.32791e48	−0.621030
$899$	−3.64290e47	−0.0667440
$900$	3.25468e47	0.0585473
$901$	4.31999e48	0.762998
$902$	3.94004e48	0.683271
$903$	−5.38386e48	−0.916739
$904$	−1.01756e48	−0.170130
$905$	−2.65581e48	−0.436010
$906$	1.17859e49	1.89997
$907$	−6.86902e48	−1.08736	−0.543681	−	0.839292i	$-0.682970\pi$
$907$	−6.86902e48	−1.08736	−0.543681	+	0.839292i	$0.682970\pi$
$908$	7.15745e48	1.11261
$909$	−1.35022e48	−0.206111
$910$	3.43471e48	0.514881
$911$	7.47750e48	1.10079	0.550393	−	0.834906i	$-0.314478\pi$
$911$	7.47750e48	1.10079	0.550393	+	0.834906i	$0.314478\pi$
$912$	−1.09814e49	−1.58760
$913$	5.62176e48	0.798186
$914$	6.22004e48	0.867324
$915$	4.88591e48	0.669110
$916$	3.49314e48	0.469829
$917$	8.72107e48	1.15206
$918$	−9.86186e48	−1.27954
$919$	−1.28656e49	−1.63955	−0.819777	−	0.572683i	$-0.805903\pi$
$919$	−1.28656e49	−1.63955	−0.819777	+	0.572683i	$0.805903\pi$
$920$	−5.01704e47	−0.0627984
$921$	−1.16539e48	−0.143281
$922$	1.70701e49	2.06146
$923$	−1.35502e49	−1.60738
$924$	−8.04069e48	−0.936927
$925$	1.89126e48	0.216477
$926$	−1.26204e48	−0.141903
$927$	−3.41112e48	−0.376775
$928$	−1.89768e48	−0.205912
$929$	8.12716e48	0.866322	0.433161	−	0.901316i	$-0.357398\pi$
$929$	8.12716e48	0.866322	0.433161	+	0.901316i	$0.357398\pi$
$930$	2.92242e48	0.306037
$931$	2.56678e48	0.264070
$932$	−1.71448e48	−0.173288
$933$	−4.42553e48	−0.439459
$934$	−1.93857e49	−1.89129
$935$	6.09085e48	0.583830
$936$	−6.57908e47	−0.0619603
$937$	2.32824e48	0.215439	0.107720	−	0.994181i	$-0.465645\pi$
$937$	2.32824e48	0.215439	0.107720	+	0.994181i	$0.465645\pi$
$938$	−8.30508e48	−0.755087
$939$	−1.17835e47	−0.0105267
$940$	−8.49578e48	−0.745751
$941$	3.65122e48	0.314926	0.157463	−	0.987525i	$-0.449668\pi$
$941$	3.65122e48	0.314926	0.157463	+	0.987525i	$0.449668\pi$
$942$	2.87405e49	2.43588
$943$	4.16317e48	0.346722
$944$	2.45720e49	2.01096
$945$	3.76066e48	0.302440
$946$	−1.63959e49	−1.29578
$947$	−1.76048e49	−1.36728	−0.683639	−	0.729821i	$-0.739604\pi$
$947$	−1.76048e49	−1.36728	−0.683639	+	0.729821i	$0.739604\pi$
$948$	−3.87257e48	−0.295571
$949$	−1.71367e49	−1.28539
$950$	4.52871e48	0.333837
$951$	−2.48885e49	−1.80310
$952$	2.91777e48	0.207750
$953$	−1.48539e49	−1.03946	−0.519731	−	0.854330i	$-0.673968\pi$
$953$	−1.48539e49	−1.03946	−0.519731	+	0.854330i	$0.673968\pi$
$954$	−4.19190e48	−0.288312
$955$	−3.42721e47	−0.0231678
$956$	1.32051e49	0.877377
$957$	2.90108e48	0.189458
$958$	−7.34283e48	−0.471338
$959$	6.06007e48	0.382358
$960$	5.86997e48	0.364050
$961$	−1.33223e49	−0.812166
$962$	2.34822e49	1.40718
$963$	7.61332e48	0.448477
$964$	−1.98563e49	−1.14981
$965$	4.52621e48	0.257653
$966$	−1.83753e49	−1.02828
$967$	−7.36558e47	−0.0405200	−0.0202600	−	0.999795i	$-0.506449\pi$
$967$	−7.36558e47	−0.0405200	−0.0202600	+	0.999795i	$0.506449\pi$
$968$	4.55917e47	0.0246571
$969$	3.27422e49	1.74087
$970$	−2.10507e49	−1.10036
$971$	−1.98790e49	−1.02159	−0.510797	−	0.859702i	$-0.670649\pi$
$971$	−1.98790e49	−1.02159	−0.510797	+	0.859702i	$0.670649\pi$
$972$	1.11325e49	0.562468
$973$	2.78793e49	1.38490
$974$	−7.85474e48	−0.383627
$975$	4.59658e48	0.220729
$976$	3.06665e49	1.44791
$977$	−1.42950e49	−0.663626	−0.331813	−	0.943345i	$-0.607660\pi$
$977$	−1.42950e49	−0.663626	−0.331813	+	0.943345i	$0.607660\pi$
$978$	5.64601e49	2.57721
$979$	2.92577e49	1.31319
$980$	−1.88022e48	−0.0829809
$981$	3.79587e48	0.164730
$982$	−1.93211e49	−0.824503
$983$	−1.85942e49	−0.780271	−0.390136	−	0.920757i	$-0.627572\pi$
$983$	−1.85942e49	−0.780271	−0.390136	+	0.920757i	$0.627572\pi$
$984$	2.52592e48	0.104232
$985$	−8.49636e48	−0.344774
$986$	6.46619e48	0.258036
$987$	5.06594e49	1.98805
$988$	2.59983e49	1.00335
$989$	−1.73245e49	−0.657538
$990$	−5.91026e48	−0.220610
$991$	3.51455e49	1.29019	0.645095	−	0.764102i	$-0.276818\pi$
$991$	3.51455e49	1.29019	0.645095	+	0.764102i	$0.276818\pi$
$992$	1.60504e49	0.579488
$993$	−1.05576e49	−0.374890
$994$	−5.83124e49	−2.03651
$995$	−9.96423e47	−0.0342265
$996$	−2.21371e49	−0.747897
$997$	2.49733e49	0.829862	0.414931	−	0.909853i	$-0.363806\pi$
$997$	2.49733e49	0.829862	0.414931	+	0.909853i	$0.363806\pi$
$998$	−1.26300e49	−0.412810
$999$	2.57106e49	0.826575

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5.34.a.b.1.1	✓	6
5.2	odd	4		25.34.b.c.24.3		12
5.3	odd	4		25.34.b.c.24.10		12
5.4	even	2		25.34.a.c.1.6		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.34.a.b.1.1	✓	6	1.1	even	1	trivial
25.34.a.c.1.6		6	5.4	even	2
25.34.b.c.24.3		12	5.2	odd	4
25.34.b.c.24.10		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)

\(f(q)\)	\(=\)	\(q-126401. q^{2} -8.63211e7 q^{3} +7.38725e9 q^{4} +1.52588e11 q^{5} +1.09111e13 q^{6} +7.78650e13 q^{7} +1.52021e14 q^{8} +1.89228e15 q^{9} +O(q^{10})\)	\(q-126401. q^{2} -8.63211e7 q^{3} +7.38725e9 q^{4} +1.52588e11 q^{5} +1.09111e13 q^{6} +7.78650e13 q^{7} +1.52021e14 q^{8} +1.89228e15 q^{9} -1.92872e16 q^{10} +1.61939e17 q^{11} -6.37676e17 q^{12} -2.28706e18 q^{13} -9.84220e18 q^{14} -1.31716e19 q^{15} -8.26715e19 q^{16} +2.46494e20 q^{17} -2.39186e20 q^{18} -1.53881e21 q^{19} +1.12720e21 q^{20} -6.72140e21 q^{21} -2.04692e22 q^{22} -2.16284e22 q^{23} -1.31226e22 q^{24} +2.32831e22 q^{25} +2.89086e23 q^{26} +3.16521e23 q^{27} +5.75208e23 q^{28} -2.07535e23 q^{29} +1.66490e24 q^{30} +1.75532e24 q^{31} +9.14391e24 q^{32} -1.39788e25 q^{33} -3.11571e25 q^{34} +1.18813e25 q^{35} +1.39787e25 q^{36} +8.12289e25 q^{37} +1.94506e26 q^{38} +1.97422e26 q^{39} +2.31965e25 q^{40} -1.92486e26 q^{41} +8.49590e26 q^{42} +8.01003e26 q^{43} +1.19628e27 q^{44} +2.88739e26 q^{45} +2.73385e27 q^{46} -7.53703e27 q^{47} +7.13630e27 q^{48} -1.66804e27 q^{49} -2.94300e27 q^{50} -2.12777e28 q^{51} -1.68951e28 q^{52} +1.75257e28 q^{53} -4.00085e28 q^{54} +2.47099e28 q^{55} +1.18371e28 q^{56} +1.32832e29 q^{57} +2.62326e28 q^{58} -2.97225e29 q^{59} -9.73016e28 q^{60} -3.70944e29 q^{61} -2.21873e29 q^{62} +1.47342e29 q^{63} -4.45655e29 q^{64} -3.48978e29 q^{65} +1.76693e30 q^{66} +8.43824e29 q^{67} +1.82091e30 q^{68} +1.86699e30 q^{69} -1.50180e30 q^{70} +5.92473e30 q^{71} +2.87666e29 q^{72} +7.49289e30 q^{73} -1.02674e31 q^{74} -2.00982e30 q^{75} -1.13675e31 q^{76} +1.26094e31 q^{77} -2.49543e31 q^{78} +6.07295e30 q^{79} -1.26147e31 q^{80} -3.78417e31 q^{81} +2.43304e31 q^{82} +3.47153e31 q^{83} -4.96526e31 q^{84} +3.76120e31 q^{85} -1.01248e32 q^{86} +1.79147e31 q^{87} +2.46181e31 q^{88} +1.80671e32 q^{89} -3.64969e31 q^{90} -1.78082e32 q^{91} -1.59775e32 q^{92} -1.51521e32 q^{93} +9.52688e32 q^{94} -2.34803e32 q^{95} -7.89312e32 q^{96} +1.09143e33 q^{97} +2.10841e32 q^{98} +3.06434e32 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 147350 q^{2} + 26513900 q^{3} + 29520645652 q^{4} + 915527343750 q^{5} + 6615759249352 q^{6} + 19113832847500 q^{7} + 30\!\cdots\!00 q^{8}+ \cdots + 13\!\cdots\!38 q^{9}+O(q^{10}) \) 6 * q + 147350 * q^2 + 26513900 * q^3 + 29520645652 * q^4 + 915527343750 * q^5 + 6615759249352 * q^6 + 19113832847500 * q^7 + 3069820115785800 * q^8 + 13602102583345438 * q^9	\( 6 q + 147350 q^{2} + 26513900 q^{3} + 29520645652 q^{4} + 915527343750 q^{5} + 6615759249352 q^{6} + 19113832847500 q^{7} + 30\!\cdots\!00 q^{8}+ \cdots + 16\!\cdots\!16 q^{99}+O(q^{100}) \) 6 * q + 147350 * q^2 + 26513900 * q^3 + 29520645652 * q^4 + 915527343750 * q^5 + 6615759249352 * q^6 + 19113832847500 * q^7 + 3069820115785800 * q^8 + 13602102583345438 * q^9 + 22483825683593750 * q^10 + 150760896555890192 * q^11 + 466351581756413200 * q^12 - 1403095636752804700 * q^13 - 7086110008989891456 * q^14 + 4045700073242187500 * q^15 + 64511520005858668816 * q^16 + 134380842798611834300 * q^17 + 673397185005127949150 * q^18 + 1711584362599986612200 * q^19 + 4504493049926757812500 * q^20 - 10560397660826154148128 * q^21 + 2470897477250007236200 * q^22 + 6879744551224024319700 * q^23 + 211895016154723698861600 * q^24 + 139698386192321777343750 * q^25 - 361829246667436498168588 * q^26 - 340705501428703899968200 * q^27 - 1750376606004032278695200 * q^28 + 1305223406410727358015700 * q^29 + 1009484748741455078125000 * q^30 + 10825321396800575904753352 * q^31 + 26818258713124955338861600 * q^32 + 34856079507682787436662800 * q^33 + 8872409666654531735490124 * q^34 + 2916539435958862304687500 * q^35 + 168714411751774892911163396 * q^36 + 276757164463535626747584900 * q^37 + 835386866362613528909982200 * q^38 + 579964086232605925635188456 * q^39 + 468417376065948486328125000 * q^40 + 448008579649522993395821932 * q^41 + 1478478813030145693383604800 * q^42 + 2250588086104897739543439500 * q^43 + 7171805342222267509050250864 * q^44 + 2075516141257543640136718750 * q^45 + 3493759290976330924493595072 * q^46 + 3830785379519133075460228700 * q^47 + 24576343390562635665291611200 * q^48 - 7173427073564666873529235258 * q^49 + 3430759534239768981933593750 * q^50 - 54920362805063671320868694888 * q^51 - 90553915669177954388890305000 * q^52 + 47034713551772209628037134900 * q^53 - 182647187168263097239229399600 * q^54 + 23004287194197111816406250000 * q^55 - 392573339390998146620750750400 * q^56 - 242119765146738617914766400400 * q^57 - 443272639260736798552560798700 * q^58 - 178315156221037727069533799800 * q^59 + 71159604149843322753906250000 * q^60 - 282317689060586014253208287308 * q^61 + 3477509804797272360008839200 * q^62 - 559259159226762324796386276900 * q^63 + 1937968534792541396434479607872 * q^64 - 214095403557251693725585937500 * q^65 + 5061208746155430260544773159264 * q^66 + 3357382217232044190774976063300 * q^67 + 3866973693935427075529380663400 * q^68 + 316127240816983184255653823136 * q^69 - 1081254579008467324218750000000 * q^70 + 8451218031993742702656617170072 * q^71 + 8740278584811466598158058687400 * q^72 - 1719044326022105657749673125300 * q^73 + 20494727417173075429289542476484 * q^74 + 617324840277433395385742187500 * q^75 + 29410039922734837753629694458000 * q^76 - 1179300749517366199915257594000 * q^77 - 57229303014236704407408363530000 * q^78 - 22052505351402355443894747635600 * q^79 + 9843676758706461916503906250000 * q^80 - 133163964889176760661905573719674 * q^81 - 156059027108947085834404172875300 * q^82 - 47087087002138304263127820978900 * q^83 - 235991611992224148517578838651776 * q^84 + 20504889343049901473999023437500 * q^85 - 128823880621545855657554048105608 * q^86 - 175316396211912369693639217216600 * q^87 + 497433069891524019720739466805600 * q^88 - 336491358341169481948206213360900 * q^89 + 102752256012745353569030761718750 * q^90 + 194633769402343866156602864483432 * q^91 - 419043430758613276035983032687200 * q^92 + 212928090391747529239858474972800 * q^93 + 1486141097168392212687292135345264 * q^94 + 261167047515867097808837890625000 * q^95 + 3151728990173122672564203081529472 * q^96 + 2569321197832638009639208504856700 * q^97 + 6985460513399098756137635798950 * q^98 + 1660882302442227079414567162624016 * q^99

Introduction

L-functions

Modular forms

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