LMFDB - Embedded newform 25.34.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,34,Mod(1,25)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, 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("25.1");

S:= CuspForms(chi, 34);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 34 $
Character orbit:	$[\chi]$	$=$	25.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:	$172.457072203$
Analytic rank:	$1$
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:	no (minimal twist has level 5)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Root			$-75479.4$ of defining polynomial
Character	$\chi$	$=$	25.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+126401. q^{2} +8.63211e7 q^{3} +7.38725e9 q^{4} +1.09111e13 q^{6} -7.78650e13 q^{7} -1.52021e14 q^{8} +1.89228e15 q^{9} +O(q^{10})$	\(q+126401. q^{2} +8.63211e7 q^{3} +7.38725e9 q^{4} +1.09111e13 q^{6} -7.78650e13 q^{7} -1.52021e14 q^{8} +1.89228e15 q^{9} +1.61939e17 q^{11} +6.37676e17 q^{12} +2.28706e18 q^{13} -9.84220e18 q^{14} -8.26715e19 q^{16} -2.46494e20 q^{17} +2.39186e20 q^{18} -1.53881e21 q^{19} -6.72140e21 q^{21} +2.04692e22 q^{22} +2.16284e22 q^{23} -1.31226e22 q^{24} +2.89086e23 q^{26} -3.16521e23 q^{27} -5.75208e23 q^{28} -2.07535e23 q^{29} +1.75532e24 q^{31} -9.14391e24 q^{32} +1.39788e25 q^{33} -3.11571e25 q^{34} +1.39787e25 q^{36} -8.12289e25 q^{37} -1.94506e26 q^{38} +1.97422e26 q^{39} -1.92486e26 q^{41} -8.49590e26 q^{42} -8.01003e26 q^{43} +1.19628e27 q^{44} +2.73385e27 q^{46} +7.53703e27 q^{47} -7.13630e27 q^{48} -1.66804e27 q^{49} -2.12777e28 q^{51} +1.68951e28 q^{52} -1.75257e28 q^{53} -4.00085e28 q^{54} +1.18371e28 q^{56} -1.32832e29 q^{57} -2.62326e28 q^{58} -2.97225e29 q^{59} -3.70944e29 q^{61} +2.21873e29 q^{62} -1.47342e29 q^{63} -4.45655e29 q^{64} +1.76693e30 q^{66} -8.43824e29 q^{67} -1.82091e30 q^{68} +1.86699e30 q^{69} +5.92473e30 q^{71} -2.87666e29 q^{72} -7.49289e30 q^{73} -1.02674e31 q^{74} -1.13675e31 q^{76} -1.26094e31 q^{77} +2.49543e31 q^{78} +6.07295e30 q^{79} -3.78417e31 q^{81} -2.43304e31 q^{82} -3.47153e31 q^{83} -4.96526e31 q^{84} -1.01248e32 q^{86} -1.79147e31 q^{87} -2.46181e31 q^{88} +1.80671e32 q^{89} -1.78082e32 q^{91} +1.59775e32 q^{92} +1.51521e32 q^{93} +9.52688e32 q^{94} -7.89312e32 q^{96} -1.09143e33 q^{97} -2.10841e32 q^{98} +3.06434e32 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 147350 q^{2} - 26513900 q^{3} + 29520645652 q^{4} + 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 + 6615759249352 * q^6 - 19113832847500 * q^7 - 3069820115785800 * q^8 + 13602102583345438 * q^9	$ 6 q - 147350 q^{2} - 26513900 q^{3} + 29520645652 q^{4} + 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 + 6615759249352 * q^6 - 19113832847500 * q^7 - 3069820115785800 * q^8 + 13602102583345438 * q^9 + 150760896555890192 * q^11 - 466351581756413200 * q^12 + 1403095636752804700 * q^13 - 7086110008989891456 * q^14 + 64511520005858668816 * q^16 - 134380842798611834300 * q^17 - 673397185005127949150 * q^18 + 1711584362599986612200 * q^19 - 10560397660826154148128 * q^21 - 2470897477250007236200 * q^22 - 6879744551224024319700 * q^23 + 211895016154723698861600 * q^24 - 361829246667436498168588 * q^26 + 340705501428703899968200 * q^27 + 1750376606004032278695200 * q^28 + 1305223406410727358015700 * q^29 + 10825321396800575904753352 * q^31 - 26818258713124955338861600 * q^32 - 34856079507682787436662800 * q^33 + 8872409666654531735490124 * q^34 + 168714411751774892911163396 * q^36 - 276757164463535626747584900 * q^37 - 835386866362613528909982200 * q^38 + 579964086232605925635188456 * q^39 + 448008579649522993395821932 * q^41 - 1478478813030145693383604800 * q^42 - 2250588086104897739543439500 * q^43 + 7171805342222267509050250864 * q^44 + 3493759290976330924493595072 * q^46 - 3830785379519133075460228700 * q^47 - 24576343390562635665291611200 * q^48 - 7173427073564666873529235258 * q^49 - 54920362805063671320868694888 * q^51 + 90553915669177954388890305000 * q^52 - 47034713551772209628037134900 * q^53 - 182647187168263097239229399600 * q^54 - 392573339390998146620750750400 * q^56 + 242119765146738617914766400400 * q^57 + 443272639260736798552560798700 * q^58 - 178315156221037727069533799800 * q^59 - 282317689060586014253208287308 * q^61 - 3477509804797272360008839200 * q^62 + 559259159226762324796386276900 * q^63 + 1937968534792541396434479607872 * q^64 + 5061208746155430260544773159264 * q^66 - 3357382217232044190774976063300 * q^67 - 3866973693935427075529380663400 * q^68 + 316127240816983184255653823136 * q^69 + 8451218031993742702656617170072 * q^71 - 8740278584811466598158058687400 * q^72 + 1719044326022105657749673125300 * q^73 + 20494727417173075429289542476484 * q^74 + 29410039922734837753629694458000 * q^76 + 1179300749517366199915257594000 * q^77 + 57229303014236704407408363530000 * q^78 - 22052505351402355443894747635600 * q^79 - 133163964889176760661905573719674 * q^81 + 156059027108947085834404172875300 * q^82 + 47087087002138304263127820978900 * q^83 - 235991611992224148517578838651776 * q^84 - 128823880621545855657554048105608 * q^86 + 175316396211912369693639217216600 * q^87 - 497433069891524019720739466805600 * q^88 - 336491358341169481948206213360900 * q^89 + 194633769402343866156602864483432 * q^91 + 419043430758613276035983032687200 * q^92 - 212928090391747529239858474972800 * q^93 + 1486141097168392212687292135345264 * q^94 + 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	$-0.261151\pi$
$2$	126401.	1.36381	0.681907	+	0.731439i	$0.261151\pi$
$3$	8.63211e7	1.15775	0.578877	−	0.815415i	$-0.303491\pi$
$3$	8.63211e7	1.15775	0.578877	+	0.815415i	$0.303491\pi$
$4$	7.38725e9	0.859989
$5$	0	0
$5$	0	0
$6$	1.09111e13	1.57896
$7$	−7.78650e13	−0.885573	−0.442787	−	0.896627i	$-0.646010\pi$
$7$	−7.78650e13	−0.885573	−0.442787	+	0.896627i	$0.646010\pi$
$8$	−1.52021e14	−0.190949
$9$	1.89228e15	0.340396
$10$	0	0
$11$	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	$-0.341858\pi$
$13$	2.28706e18	0.953262	0.476631	+	0.879104i	$0.341858\pi$
$14$	−9.84220e18	−1.20776
$15$	0	0
$16$	−8.26715e19	−1.12041
$17$	−2.46494e20	−1.22857	−0.614284	−	0.789085i	$-0.710555\pi$
$17$	−2.46494e20	−1.22857	−0.614284	+	0.789085i	$0.710555\pi$
$18$	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	$0.709617\pi$
$20$	0	0
$21$	−6.72140e21	−1.02528
$22$	2.04692e22	1.44920
$23$	2.16284e22	0.735387	0.367693	−	0.929947i	$-0.380148\pi$
$23$	2.16284e22	0.735387	0.367693	+	0.929947i	$0.380148\pi$
$24$	−1.31226e22	−0.221072
$25$	0	0
$26$	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	$0.524534\pi$
$30$	0	0
$31$	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
$35$	0	0
$36$	1.39787e25	0.292736
$37$	−8.12289e25	−1.08239	−0.541193	−	0.840898i	$-0.682027\pi$
$37$	−8.12289e25	−1.08239	−0.541193	+	0.840898i	$0.682027\pi$
$38$	−1.94506e26	−1.66919
$39$	1.97422e26	1.10364
$40$	0	0
$41$	−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	$-0.647532\pi$
$43$	−8.01003e26	−0.894139	−0.447069	+	0.894499i	$0.647532\pi$
$44$	1.19628e27	0.913828
$45$	0	0
$46$	2.73385e27	1.00293
$47$	7.53703e27	1.93904	0.969518	−	0.245021i	$-0.0787947\pi$
$47$	7.53703e27	1.93904	0.969518	+	0.245021i	$0.0787947\pi$
$48$	−7.13630e27	−1.29716
$49$	−1.66804e27	−0.215760
$50$	0	0
$51$	−2.12777e28	−1.42238
$52$	1.68951e28	0.819795
$53$	−1.75257e28	−0.621047	−0.310523	−	0.950566i	$-0.600504\pi$
$53$	−1.75257e28	−0.621047	−0.310523	+	0.950566i	$0.600504\pi$
$54$	−4.00085e28	−1.04149
$55$	0	0
$56$	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	$0.854563\pi$
$60$	0	0
$61$	−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
$65$	0	0
$66$	1.76693e30	1.67781
$67$	−8.43824e29	−0.625198	−0.312599	−	0.949885i	$-0.601200\pi$
$67$	−8.43824e29	−0.625198	−0.312599	+	0.949885i	$0.601200\pi$
$68$	−1.82091e30	−1.05656
$69$	1.86699e30	0.851397
$70$	0	0
$71$	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	$-0.735514\pi$
$73$	−7.49289e30	−1.34841	−0.674205	+	0.738544i	$0.735514\pi$
$74$	−1.02674e31	−1.47617
$75$	0	0
$76$	−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	$0.452578\pi$
$80$	0	0
$81$	−3.78417e31	−1.22453
$82$	−2.43304e31	−0.643015
$83$	−3.47153e31	−0.751160	−0.375580	−	0.926790i	$-0.622556\pi$
$83$	−3.47153e31	−0.751160	−0.375580	+	0.926790i	$0.622556\pi$
$84$	−4.96526e31	−0.881727
$85$	0	0
$86$	−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	$0.287980\pi$
$90$	0	0
$91$	−1.78082e32	−0.844183
$92$	1.59775e32	0.632424
$93$	1.51521e32	0.501769
$94$	9.52688e32	2.64448
$95$	0	0
$96$	−7.89312e32	−1.54801
$97$	−1.09143e33	−1.80411	−0.902055	−	0.431622i	$-0.857942\pi$
$97$	−1.09143e33	−1.80411	−0.902055	+	0.431622i	$0.857942\pi$
$98$	−2.10841e32	−0.294256
$99$	3.06434e32	0.361706
$100$	0	0
$101$	−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	$-0.313316\pi$
$103$	1.80265e33	1.10687	0.553437	+	0.832891i	$0.313316\pi$
$104$	−3.47680e32	−0.182025
$105$	0	0
$106$	−2.21527e33	−0.846992
$107$	−4.02336e33	−1.31752	−0.658759	−	0.752354i	$-0.728918\pi$
$107$	−4.02336e33	−1.31752	−0.658759	+	0.752354i	$0.728918\pi$
$108$	−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	$0.422207\pi$
$110$	0	0
$111$	−7.01177e33	−1.25314
$112$	6.43722e33	0.992204
$113$	6.69356e33	0.890970	0.445485	−	0.895289i	$-0.353031\pi$
$113$	6.69356e33	0.890970	0.445485	+	0.895289i	$0.353031\pi$
$114$	−1.67900e34	−1.93251
$115$	0	0
$116$	−1.53311e33	−0.132440
$117$	4.32776e33	0.324486
$118$	−3.75695e34	−2.44783
$119$	1.91933e34	1.08799
$120$	0	0
$121$	2.99905e33	0.129129
$122$	−4.68877e34	−1.76247
$123$	−1.66156e34	−0.545861
$124$	1.29670e34	0.372718
$125$	0	0
$126$	−1.86242e34	−0.411115
$127$	1.27300e34	0.246643	0.123321	−	0.992367i	$-0.460645\pi$
$127$	1.27300e34	0.246643	0.123321	+	0.992367i	$0.460645\pi$
$128$	2.22144e34	0.378155
$129$	−6.91435e34	−1.03519
$130$	0	0
$131$	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
$135$	0	0
$136$	3.74722e34	0.234594
$137$	−7.78279e34	−0.431763	−0.215882	−	0.976420i	$-0.569263\pi$
$137$	−7.78279e34	−0.431763	−0.215882	+	0.976420i	$0.569263\pi$
$138$	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	$0.214238\pi$
$140$	0	0
$141$	6.50605e35	2.24493
$142$	7.48891e35	2.29965
$143$	3.70364e35	1.01294
$144$	−1.56438e35	−0.381382
$145$	0	0
$146$	−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	$0.538130\pi$
$150$	0	0
$151$	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
$155$	0	0
$156$	1.45840e36	0.949121
$157$	−2.63407e36	−1.54271	−0.771353	−	0.636407i	$-0.780420\pi$
$157$	−2.63407e36	−1.54271	−0.771353	+	0.636407i	$0.780420\pi$
$158$	7.67626e35	0.404863
$159$	−1.51284e36	−0.719019
$160$	0	0
$161$	−1.68410e36	−0.651239
$162$	−4.78323e36	−1.67003
$163$	−5.17457e36	−1.63222	−0.816111	−	0.577896i	$-0.803874\pi$
$163$	−5.17457e36	−1.63222	−0.816111	+	0.577896i	$0.803874\pi$
$164$	−1.42194e36	−0.405470
$165$	0	0
$166$	−4.38804e36	−1.02444
$167$	4.37605e36	0.925252	0.462626	−	0.886553i	$-0.346907\pi$
$167$	4.37605e36	0.925252	0.462626	+	0.886553i	$0.346907\pi$
$168$	1.02179e36	0.195776
$169$	−5.25488e35	−0.0912919
$170$	0	0
$171$	−2.91185e36	−0.416614
$172$	−5.91721e36	−0.768949
$173$	1.16497e37	1.37580	0.687900	−	0.725805i	$-0.258533\pi$
$173$	1.16497e37	1.37580	0.687900	+	0.725805i	$0.258533\pi$
$174$	−2.26443e36	−0.243162
$175$	0	0
$176$	−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	$0.462113\pi$
$180$	0	0
$181$	−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
$185$	0	0
$186$	1.91524e37	0.684320
$187$	−3.99170e37	−1.30548
$188$	5.56779e37	1.66755
$189$	2.46459e37	0.676277
$190$	0	0
$191$	−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	$-0.593012\pi$
$193$	−2.96630e37	−0.576129	−0.288064	+	0.957611i	$0.593012\pi$
$194$	−1.37958e38	−2.46047
$195$	0	0
$196$	−1.23222e37	−0.185551
$197$	5.56817e37	0.770939	0.385470	−	0.922721i	$-0.374039\pi$
$197$	5.56817e37	0.770939	0.385470	+	0.922721i	$0.374039\pi$
$198$	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	$0.512184\pi$
$200$	0	0
$201$	−7.28398e37	−0.723826
$202$	−9.01924e37	−0.825795
$203$	1.61597e37	0.136380
$204$	−1.57183e38	−1.22323
$205$	0	0
$206$	2.27857e38	1.50957
$207$	4.09270e37	0.250322
$208$	−1.89075e38	−1.06804
$209$	−2.49193e38	−1.30053
$210$	0	0
$211$	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
$215$	0	0
$216$	4.81177e37	0.145820
$217$	−1.36678e38	−0.383806
$218$	2.53557e38	0.660000
$219$	−6.46795e38	−1.56113
$220$	0	0
$221$	−5.63747e38	−1.17115
$222$	−8.86294e38	−1.70905
$223$	1.62044e38	0.290136	0.145068	−	0.989422i	$-0.453660\pi$
$223$	1.62044e38	0.290136	0.145068	+	0.989422i	$0.453660\pi$
$224$	7.11990e38	1.18408
$225$	0	0
$226$	8.46072e38	1.21512
$227$	−9.68892e38	−1.29375	−0.646873	−	0.762598i	$-0.723924\pi$
$227$	−9.68892e38	−1.29375	−0.646873	+	0.762598i	$0.723924\pi$
$228$	−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	$0.411931\pi$
$230$	0	0
$231$	−1.08846e39	−1.08946
$232$	3.15496e37	0.0294065
$233$	2.32086e38	0.201501	0.100750	−	0.994912i	$-0.467876\pi$
$233$	2.32086e38	0.201501	0.100750	+	0.994912i	$0.467876\pi$
$234$	5.47032e38	0.442539
$235$	0	0
$236$	−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	$0.329605\pi$
$240$	0	0
$241$	−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
$245$	0	0
$246$	−2.10023e39	−0.744453
$247$	−3.51934e39	−1.16671
$248$	−2.66844e38	−0.0827571
$249$	−2.99666e39	−0.869659
$250$	0	0
$251$	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
$255$	0	0
$256$	6.63606e39	1.21885
$257$	−8.25568e39	−1.42186	−0.710929	−	0.703264i	$-0.751725\pi$
$257$	−8.25568e39	−1.42186	−0.710929	+	0.703264i	$0.751725\pi$
$258$	−8.73980e39	−1.41181
$259$	6.32489e39	0.958532
$260$	0	0
$261$	−3.92715e38	−0.0524214
$262$	1.41572e40	1.77422
$263$	−2.69949e39	−0.317697	−0.158848	−	0.987303i	$-0.550778\pi$
$263$	−2.69949e39	−0.317697	−0.158848	+	0.987303i	$0.550778\pi$
$264$	−2.12506e39	−0.234912
$265$	0	0
$266$	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	$0.335609\pi$
$270$	0	0
$271$	−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
$275$	0	0
$276$	1.37919e40	0.732192
$277$	6.18766e39	0.309464	0.154732	−	0.987956i	$-0.450549\pi$
$277$	6.18766e39	0.309464	0.154732	+	0.987956i	$0.450549\pi$
$278$	4.52574e40	2.13280
$279$	3.32155e39	0.147527
$280$	0	0
$281$	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	$-0.693802\pi$
$283$	−3.25719e40	−1.14384	−0.571921	+	0.820308i	$0.693802\pi$
$284$	4.37674e40	1.45010
$285$	0	0
$286$	4.68143e40	1.38146
$287$	1.49879e40	0.417533
$288$	−1.73028e40	−0.455136
$289$	2.05049e40	0.509382
$290$	0	0
$291$	−9.42136e40	−2.08872
$292$	−5.53518e40	−1.15962
$293$	6.99032e40	1.38414	0.692072	−	0.721829i	$-0.256698\pi$
$293$	6.99032e40	1.38414	0.692072	+	0.721829i	$0.256698\pi$
$294$	−1.82001e40	−0.340676
$295$	0	0
$296$	1.23485e40	0.206681
$297$	−5.12570e40	−0.811469
$298$	−2.17636e40	−0.325958
$299$	4.94655e40	0.701016
$300$	0	0
$301$	6.23701e40	0.791825
$302$	1.36535e41	1.64108
$303$	−6.15938e40	−0.701025
$304$	1.27215e41	1.37128
$305$	0	0
$306$	−5.89579e40	−0.570346
$307$	−1.35007e40	−0.123758	−0.0618788	−	0.998084i	$-0.519709\pi$
$307$	−1.35007e40	−0.123758	−0.0618788	+	0.998084i	$0.519709\pi$
$308$	−9.31485e40	−0.809262
$309$	1.55607e41	1.28149
$310$	0	0
$311$	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	$-0.501447\pi$
$313$	−1.36507e39	−0.00909232	−0.00454616	+	0.999990i	$0.501447\pi$
$314$	−3.32949e41	−2.10397
$315$	0	0
$316$	4.48624e40	0.255297
$317$	−2.88324e41	−1.55741	−0.778705	−	0.627390i	$-0.784123\pi$
$317$	−2.88324e41	−1.55741	−0.778705	+	0.627390i	$0.784123\pi$
$318$	−1.91224e41	−0.980609
$319$	−3.36080e40	−0.163643
$320$	0	0
$321$	−3.47301e41	−1.52536
$322$	−2.12871e41	−0.888169
$323$	3.79307e41	1.50366
$324$	−2.79546e41	−1.05308
$325$	0	0
$326$	−6.54070e41	−2.22605
$327$	1.73158e41	0.560280
$328$	2.92619e40	0.0900292
$329$	−5.86871e41	−1.71716
$330$	0	0
$331$	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
$335$	0	0
$336$	5.55668e41	1.14873
$337$	−1.95036e40	−0.0383902	−0.0191951	−	0.999816i	$-0.506110\pi$
$337$	−1.95036e40	−0.0383902	−0.0191951	+	0.999816i	$0.506110\pi$
$338$	−6.64222e40	−0.124505
$339$	5.77796e41	1.03152
$340$	0	0
$341$	2.84254e41	0.460531
$342$	−3.68061e41	−0.568183
$343$	7.31855e41	1.07664
$344$	1.21769e41	0.170735
$345$	0	0
$346$	1.47254e42	1.87634
$347$	8.38690e41	1.01898	0.509490	−	0.860477i	$-0.329834\pi$
$347$	8.38690e41	1.01898	0.509490	+	0.860477i	$0.329834\pi$
$348$	−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	$0.505142\pi$
$350$	0	0
$351$	−7.23902e41	−0.727968
$352$	−1.48075e42	−1.42079
$353$	1.88083e42	1.72213	0.861067	−	0.508492i	$-0.169797\pi$
$353$	1.88083e42	1.72213	0.861067	+	0.508492i	$0.169797\pi$
$354$	−3.24304e42	−2.83399
$355$	0	0
$356$	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	$0.482230\pi$
$360$	0	0
$361$	7.87154e41	0.497956
$362$	−2.20002e42	−1.32965
$363$	2.58881e41	0.149500
$364$	−1.31554e42	−0.725988
$365$	0	0
$366$	−4.04740e42	−2.04051
$367$	−2.15460e42	−1.03843	−0.519213	−	0.854645i	$-0.673775\pi$
$367$	−2.15460e42	−1.03843	−0.519213	+	0.854645i	$0.673775\pi$
$368$	−1.78806e42	−0.823933
$369$	−3.64238e41	−0.160491
$370$	0	0
$371$	1.36464e42	0.549982
$372$	1.11932e42	0.431516
$373$	−2.59028e42	−0.955325	−0.477663	−	0.878543i	$-0.658516\pi$
$373$	−2.59028e42	−0.955325	−0.477663	+	0.878543i	$0.658516\pi$
$374$	−5.04554e42	−1.78044
$375$	0	0
$376$	−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	$0.307110\pi$
$380$	0	0
$381$	1.09887e42	0.285551
$382$	−2.83904e41	−0.0706522
$383$	−5.03299e42	−1.19963	−0.599813	−	0.800140i	$-0.704758\pi$
$383$	−5.03299e42	−1.19963	−0.599813	+	0.800140i	$0.704758\pi$
$384$	1.91757e42	0.437811
$385$	0	0
$386$	−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	$0.375058\pi$
$390$	0	0
$391$	−5.33128e42	−0.903473
$392$	2.53576e41	0.0411991
$393$	9.66818e42	1.50615
$394$	7.03822e42	1.05142
$395$	0	0
$396$	2.26370e42	0.311063
$397$	8.89168e42	1.17203	0.586017	−	0.810299i	$-0.300695\pi$
$397$	8.89168e42	1.17203	0.586017	+	0.810299i	$0.300695\pi$
$398$	−8.25418e41	−0.104377
$399$	1.03429e43	1.25485
$400$	0	0
$401$	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
$405$	0	0
$406$	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	$0.307694\pi$
$410$	0	0
$411$	−6.71819e42	−0.499876
$412$	1.33166e43	0.951899
$413$	2.31434e43	1.58947
$414$	5.17321e42	0.341393
$415$	0	0
$416$	−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	$0.685479\pi$
$420$	0	0
$421$	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
$425$	0	0
$426$	6.46451e43	2.66243
$427$	2.88836e43	1.14443
$428$	−2.97216e43	−1.13305
$429$	3.19702e43	1.17274
$430$	0	0
$431$	−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	$-0.713608\pi$
$433$	−3.95138e43	−1.24365	−0.621825	+	0.783156i	$0.713608\pi$
$434$	−1.72762e43	−0.523440
$435$	0	0
$436$	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	$0.450890\pi$
$440$	0	0
$441$	−3.15639e42	−0.0734436
$442$	−7.12581e43	−1.59723
$443$	5.64830e43	1.21971	0.609855	−	0.792513i	$-0.291228\pi$
$443$	5.64830e43	1.21971	0.609855	+	0.792513i	$0.291228\pi$
$444$	−5.17977e43	−1.07768
$445$	0	0
$446$	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	$0.426886\pi$
$450$	0	0
$451$	−3.11710e43	−0.501000
$452$	4.94470e43	0.766224
$453$	9.32419e43	1.39313
$454$	−1.22469e44	−1.76443
$455$	0	0
$456$	2.01931e43	0.270573
$457$	4.92089e43	0.635955	0.317977	−	0.948098i	$-0.396996\pi$
$457$	4.92089e43	0.635955	0.317977	+	0.948098i	$0.396996\pi$
$458$	5.97700e43	0.745079
$459$	7.80205e43	0.938209
$460$	0	0
$461$	−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	$-0.516567\pi$
$463$	−9.98444e42	−0.104049	−0.0520244	+	0.998646i	$0.516567\pi$
$464$	1.71573e43	0.172544
$465$	0	0
$466$	2.93359e43	0.274810
$467$	−1.53367e44	−1.38677	−0.693384	−	0.720568i	$-0.743881\pi$
$467$	−1.53367e44	−1.38677	−0.693384	+	0.720568i	$0.743881\pi$
$468$	3.19702e43	0.279054
$469$	6.57043e43	0.553659
$470$	0	0
$471$	−2.27376e44	−1.78608
$472$	4.51843e43	0.342724
$473$	−1.29714e44	−0.950116
$474$	6.62624e43	0.468732
$475$	0	0
$476$	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	$0.444718\pi$
$480$	0	0
$481$	−1.85775e44	−1.03180
$482$	−3.39755e44	−1.82344
$483$	−1.45373e44	−0.753975
$484$	2.21547e43	0.111050
$485$	0	0
$486$	−1.90484e44	−0.891990
$487$	−6.21415e43	−0.281290	−0.140645	−	0.990060i	$-0.544918\pi$
$487$	−6.21415e43	−0.281290	−0.140645	+	0.990060i	$0.544918\pi$
$488$	5.63912e43	0.246765
$489$	−4.46675e44	−1.88971
$490$	0	0
$491$	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
$495$	0	0
$496$	−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	$0.451640\pi$
$500$	0	0
$501$	3.77745e44	1.07122
$502$	2.76178e44	0.757840
$503$	−9.03153e43	−0.239822	−0.119911	−	0.992785i	$-0.538261\pi$
$503$	−9.03153e43	−0.239822	−0.119911	+	0.992785i	$0.538261\pi$
$504$	2.23991e43	0.0575607
$505$	0	0
$506$	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	$0.703811\pi$
$510$	0	0
$511$	5.83434e44	1.19412
$512$	6.47984e44	1.28413
$513$	4.87064e44	0.934651
$514$	−1.04353e45	−1.93915
$515$	0	0
$516$	−5.10780e44	−0.890254
$517$	1.22054e45	2.06043
$518$	7.99471e44	1.30726
$519$	1.00562e45	1.59284
$520$	0	0
$521$	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	$-0.485676\pi$
$523$	6.44705e43	0.0899670	0.0449835	+	0.998988i	$0.485676\pi$
$524$	8.27390e44	1.11878
$525$	0	0
$526$	−3.41218e44	−0.433279
$527$	−4.32675e44	−0.532460
$528$	−1.15564e45	−1.37837
$529$	−3.97216e44	−0.459206
$530$	0	0
$531$	−5.62432e44	−0.610957
$532$	8.85134e44	0.932110
$533$	−4.40227e44	−0.449446
$534$	1.97132e45	1.95131
$535$	0	0
$536$	1.28279e44	0.119381
$537$	3.04675e44	0.274955
$538$	1.53901e45	1.34689
$539$	−2.70120e44	−0.229267
$540$	0	0
$541$	−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
$545$	0	0
$546$	−1.94306e45	−1.33293
$547$	−9.15780e44	−0.609537	−0.304769	−	0.952426i	$-0.598579\pi$
$547$	−9.15780e44	−0.609537	−0.304769	+	0.952426i	$0.598579\pi$
$548$	−5.74934e44	−0.371312
$549$	−7.01930e44	−0.439896
$550$	0	0
$551$	3.19357e44	0.188484
$552$	−2.83821e44	−0.162574
$553$	−4.72870e44	−0.262892
$554$	7.82126e44	0.422052
$555$	0	0
$556$	2.64498e45	1.34489
$557$	3.51921e45	1.73714	0.868569	−	0.495568i	$-0.165040\pi$
$557$	3.51921e45	1.73714	0.868569	+	0.495568i	$0.165040\pi$
$558$	4.19847e44	0.201199
$559$	−1.83194e45	−0.852348
$560$	0	0
$561$	−3.44568e45	−1.51143
$562$	5.70840e44	0.243145
$563$	−1.25910e45	−0.520802	−0.260401	−	0.965501i	$-0.583855\pi$
$563$	−1.25910e45	−0.520802	−0.260401	+	0.965501i	$0.583855\pi$
$564$	4.80618e45	1.93061
$565$	0	0
$566$	−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	$0.589667\pi$
$570$	0	0
$571$	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
$575$	0	0
$576$	−8.43303e44	−0.239339
$577$	−3.64572e45	−1.00550	−0.502750	−	0.864432i	$-0.667679\pi$
$577$	−3.64572e45	−1.00550	−0.502750	+	0.864432i	$0.667679\pi$
$578$	2.59184e45	0.694702
$579$	−2.56054e45	−0.667016
$580$	0	0
$581$	2.70311e45	0.665207
$582$	−1.19087e46	−2.84862
$583$	−2.83810e45	−0.659927
$584$	1.13907e45	0.257478
$585$	0	0
$586$	8.83582e45	1.88771
$587$	2.48055e45	0.515251	0.257626	−	0.966245i	$-0.417060\pi$
$587$	2.48055e45	0.515251	0.257626	+	0.966245i	$0.417060\pi$
$588$	−1.06367e45	−0.214822
$589$	−2.70109e45	−0.530441
$590$	0	0
$591$	4.80651e45	0.892558
$592$	6.71532e45	1.21271
$593$	−2.97630e45	−0.522726	−0.261363	−	0.965241i	$-0.584172\pi$
$593$	−2.97630e45	−0.522726	−0.261363	+	0.965241i	$0.584172\pi$
$594$	−6.47893e45	−1.10669
$595$	0	0
$596$	−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	$0.574028\pi$
$600$	0	0
$601$	−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
$605$	0	0
$606$	−7.78551e45	−0.956068
$607$	−6.02204e45	−0.719664	−0.359832	−	0.933017i	$-0.617166\pi$
$607$	−6.02204e45	−0.719664	−0.359832	+	0.933017i	$0.617166\pi$
$608$	1.40707e46	1.63646
$609$	1.39493e45	0.157894
$610$	0	0
$611$	1.72376e46	1.84841
$612$	−3.44568e45	−0.359647
$613$	−7.92968e45	−0.805671	−0.402836	−	0.915272i	$-0.631975\pi$
$613$	−7.92968e45	−0.805671	−0.402836	+	0.915272i	$0.631975\pi$
$614$	−1.70650e45	−0.168782
$615$	0	0
$616$	1.91688e45	0.179686
$617$	7.56919e45	0.690787	0.345394	−	0.938458i	$-0.387745\pi$
$617$	7.56919e45	0.690787	0.345394	+	0.938458i	$0.387745\pi$
$618$	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	$0.565585\pi$
$620$	0	0
$621$	−6.84585e45	−0.561585
$622$	6.48035e45	0.517675
$623$	−1.40680e46	−1.09441
$624$	−1.63211e46	−1.23653
$625$	0	0
$626$	−1.72547e44	−0.0124002
$627$	−2.15106e46	−1.50570
$628$	−1.94585e46	−1.32671
$629$	2.00225e46	1.32979
$630$	0	0
$631$	−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
$635$	0	0
$636$	−1.11757e46	−0.618349
$637$	−3.81490e45	−0.205675
$638$	−4.24808e45	−0.223178
$639$	1.12112e46	0.573971
$640$	0	0
$641$	−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	$-0.405839\pi$
$643$	1.26235e46	0.583040	0.291520	+	0.956565i	$0.405839\pi$
$644$	−1.24408e46	−0.560058
$645$	0	0
$646$	4.79447e46	2.05071
$647$	−1.12690e46	−0.469855	−0.234927	−	0.972013i	$-0.575485\pi$
$647$	−1.12690e46	−0.469855	−0.234927	+	0.972013i	$0.575485\pi$
$648$	5.75272e45	0.233822
$649$	−4.81323e46	−1.90721
$650$	0	0
$651$	−1.17982e46	−0.444353
$652$	−3.82258e46	−1.40369
$653$	3.57189e45	0.127888	0.0639440	−	0.997953i	$-0.479632\pi$
$653$	3.57189e45	0.127888	0.0639440	+	0.997953i	$0.479632\pi$
$654$	2.18873e46	0.764118
$655$	0	0
$656$	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	$0.272229\pi$
$660$	0	0
$661$	−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
$665$	0	0
$666$	−1.94288e46	−0.502483
$667$	−4.48866e45	−0.113251
$668$	3.23269e46	0.795707
$669$	1.39878e46	0.335907
$670$	0	0
$671$	−6.00703e46	−1.37321
$672$	6.14598e46	1.37088
$673$	7.94628e44	0.0172948	0.00864740	−	0.999963i	$-0.497247\pi$
$673$	7.94628e44	0.0172948	0.00864740	+	0.999963i	$0.497247\pi$
$674$	−2.46527e45	−0.0523571
$675$	0	0
$676$	−3.88191e45	−0.0785100
$677$	5.41689e46	1.06915	0.534573	−	0.845122i	$-0.320473\pi$
$677$	5.41689e46	1.06915	0.534573	+	0.845122i	$0.320473\pi$
$678$	7.30339e46	1.40681
$679$	8.49843e46	1.59767
$680$	0	0
$681$	−8.36359e46	−1.49784
$682$	3.59299e46	0.628079
$683$	−4.80553e46	−0.819973	−0.409986	−	0.912092i	$-0.634467\pi$
$683$	−4.80553e46	−0.819973	−0.409986	+	0.912092i	$0.634467\pi$
$684$	−2.15106e46	−0.358283
$685$	0	0
$686$	9.25072e46	1.46834
$687$	4.08178e46	0.632505
$688$	6.62202e46	1.00180
$689$	−4.00824e46	−0.592020
$690$	0	0
$691$	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
$695$	0	0
$696$	2.72340e45	0.0340455
$697$	4.74467e46	0.579249
$698$	−3.69544e45	−0.0440607
$699$	2.00340e46	0.233288
$700$	0	0
$701$	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
$705$	0	0
$706$	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	$0.665200\pi$
$710$	0	0
$711$	1.14917e46	0.101050
$712$	−2.74658e46	−0.235978
$713$	3.79647e46	0.318715
$714$	2.09419e47	1.71789
$715$	0	0
$716$	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	$0.235500\pi$
$720$	0	0
$721$	−1.40364e47	−0.980218
$722$	9.94970e46	0.679120
$723$	−2.32024e47	−1.54793
$724$	−1.28576e47	−0.838444
$725$	0	0
$726$	3.27228e46	0.203890
$727$	2.34830e47	1.43033	0.715164	−	0.698957i	$-0.246352\pi$
$727$	2.34830e47	1.43033	0.715164	+	0.698957i	$0.246352\pi$
$728$	2.70721e46	0.161196
$729$	8.02799e46	0.467308
$730$	0	0
$731$	1.97443e47	1.09851
$732$	−2.36542e47	−1.28669
$733$	−7.07756e46	−0.376416	−0.188208	−	0.982129i	$-0.560268\pi$
$733$	−7.07756e46	−0.376416	−0.188208	+	0.982129i	$0.560268\pi$
$734$	−2.72343e47	−1.41622
$735$	0	0
$736$	−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	$0.773618\pi$
$740$	0	0
$741$	−3.03794e47	−1.35076
$742$	1.72492e47	0.750074
$743$	1.42154e47	0.604568	0.302284	−	0.953218i	$-0.402251\pi$
$743$	1.42154e47	0.604568	0.302284	+	0.953218i	$0.402251\pi$
$744$	−2.30343e46	−0.0958124
$745$	0	0
$746$	−3.27414e47	−1.30289
$747$	−6.56910e46	−0.255691
$748$	−2.94877e47	−1.12270
$749$	3.13279e47	1.16676
$750$	0	0
$751$	−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
$755$	0	0
$756$	1.82065e47	0.581591
$757$	−2.98356e47	−0.932509	−0.466255	−	0.884651i	$-0.654397\pi$
$757$	−2.98356e47	−0.932509	−0.466255	+	0.884651i	$0.654397\pi$
$758$	5.08011e47	1.55357
$759$	3.02338e47	0.904699
$760$	0	0
$761$	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
$765$	0	0
$766$	−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	$0.622734\pi$
$770$	0	0
$771$	−7.12640e47	−1.64616
$772$	−2.19128e47	−0.495464
$773$	−5.84176e47	−1.29295	−0.646475	−	0.762935i	$-0.723758\pi$
$773$	−5.84176e47	−1.29295	−0.646475	+	0.762935i	$0.723758\pi$
$774$	−1.91589e47	−0.415092
$775$	0	0
$776$	1.65920e47	0.344493
$777$	5.45972e47	1.10974
$778$	5.24320e47	1.04336
$779$	2.96199e47	0.577053
$780$	0	0
$781$	9.59444e47	1.79175
$782$	−6.73879e47	−1.23217
$783$	6.56892e46	0.117605
$784$	1.37899e47	0.241739
$785$	0	0
$786$	1.22207e48	2.05411
$787$	−3.46036e47	−0.569559	−0.284779	−	0.958593i	$-0.591920\pi$
$787$	−3.46036e47	−0.569559	−0.284779	+	0.958593i	$0.591920\pi$
$788$	4.11335e47	0.662999
$789$	−2.33023e47	−0.367815
$790$	0	0
$791$	−5.21194e47	−0.789019
$792$	−4.65842e46	−0.0690675
$793$	−8.48371e47	−1.23191
$794$	1.12392e48	1.59844
$795$	0	0
$796$	−4.82399e46	−0.0658174
$797$	8.43355e47	1.12706	0.563532	−	0.826095i	$-0.309442\pi$
$797$	8.43355e47	1.12706	0.563532	+	0.826095i	$0.309442\pi$
$798$	1.30735e48	1.71138
$799$	−1.85784e48	−2.38224
$800$	0	0
$801$	3.41881e47	0.420667
$802$	2.16388e46	0.0260830
$803$	−1.21339e48	−1.43283
$804$	−5.38086e47	−0.622482
$805$	0	0
$806$	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	$0.933177\pi$
$810$	0	0
$811$	−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
$815$	0	0
$816$	1.75906e48	1.59365
$817$	1.23259e48	1.09435
$818$	1.78078e48	1.54946
$819$	−3.36981e47	−0.287356
$820$	0	0
$821$	−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	$-0.790945\pi$
$823$	−2.01297e48	−1.58394	−0.791972	+	0.610557i	$0.790945\pi$
$824$	−2.74041e47	−0.211357
$825$	0	0
$826$	2.92535e48	2.16774
$827$	−1.15395e48	−0.838195	−0.419098	−	0.907941i	$-0.637653\pi$
$827$	−1.15395e48	−0.838195	−0.419098	+	0.907941i	$0.637653\pi$
$828$	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	$0.285372\pi$
$830$	0	0
$831$	5.34126e47	0.358284
$832$	−1.01924e48	−0.670257
$833$	4.11161e47	0.265076
$834$	3.90667e48	2.46926
$835$	0	0
$836$	−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	$0.270430\pi$
$840$	0	0
$841$	−1.77300e48	−0.976284
$842$	3.55957e48	1.92198
$843$	3.89835e47	0.206408
$844$	3.09492e48	1.60694
$845$	0	0
$846$	1.80275e48	0.900171
$847$	−2.33521e47	−0.114354
$848$	1.44888e48	0.695826
$849$	−2.81164e48	−1.32429
$850$	0	0
$851$	−1.75685e48	−0.795972
$852$	3.77806e48	1.67886
$853$	−3.23565e48	−1.41027	−0.705135	−	0.709073i	$-0.749114\pi$
$853$	−3.23565e48	−1.41027	−0.705135	+	0.709073i	$0.749114\pi$
$854$	3.65091e48	1.56080
$855$	0	0
$856$	6.11634e47	0.251579
$857$	−1.13232e48	−0.456864	−0.228432	−	0.973560i	$-0.573360\pi$
$857$	−1.13232e48	−0.456864	−0.228432	+	0.973560i	$0.573360\pi$
$858$	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	$0.606843\pi$
$860$	0	0
$861$	1.29378e48	0.483400
$862$	−1.37075e48	−0.502445
$863$	4.68742e48	1.68561	0.842803	−	0.538223i	$-0.180904\pi$
$863$	4.68742e48	1.68561	0.842803	+	0.538223i	$0.180904\pi$
$864$	2.89424e48	1.02107
$865$	0	0
$866$	−4.99457e48	−1.69611
$867$	1.77001e48	0.589739
$868$	−1.00967e48	−0.330069
$869$	9.83446e47	0.315446
$870$	0	0
$871$	−1.92987e48	−0.595977
$872$	−3.04950e47	−0.0924073
$873$	−2.06529e48	−0.614111
$874$	−4.20687e48	−1.22750
$875$	0	0
$876$	−4.77803e48	−1.34255
$877$	−6.18989e48	−1.70683	−0.853414	−	0.521234i	$-0.825472\pi$
$877$	−6.18989e48	−1.70683	−0.853414	+	0.521234i	$0.825472\pi$
$878$	1.54895e48	0.419158
$879$	6.03412e48	1.60250
$880$	0	0
$881$	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	$-0.815248\pi$
$883$	−6.78750e48	−1.67247	−0.836234	+	0.548372i	$0.815248\pi$
$884$	−4.16454e48	−1.00717
$885$	0	0
$886$	7.13950e48	1.66346
$887$	6.24043e48	1.42717	0.713583	−	0.700570i	$-0.247071\pi$
$887$	6.24043e48	1.42717	0.713583	+	0.700570i	$0.247071\pi$
$888$	1.06593e48	0.239285
$889$	−9.91224e47	−0.218420
$890$	0	0
$891$	−6.12805e48	−1.30119
$892$	1.19706e48	0.249514
$893$	−1.15980e49	−2.37321
$894$	−1.87866e48	−0.377379
$895$	0	0
$896$	−1.72972e48	−0.334884
$897$	4.26992e48	0.811605
$898$	3.32791e48	0.621030
$899$	−3.64290e47	−0.0667440
$900$	0	0
$901$	4.31999e48	0.762998
$902$	−3.94004e48	−0.683271
$903$	5.38386e48	0.916739
$904$	−1.01756e48	−0.170130
$905$	0	0
$906$	1.17859e49	1.89997
$907$	6.86902e48	1.08736	0.543681	−	0.839292i	$-0.317030\pi$
$907$	6.86902e48	1.08736	0.543681	+	0.839292i	$0.317030\pi$
$908$	−7.15745e48	−1.11261
$909$	−1.35022e48	−0.206111
$910$	0	0
$911$	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
$915$	0	0
$916$	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	$0.805903\pi$
$920$	0	0
$921$	−1.16539e48	−0.143281
$922$	−1.70701e49	−2.06146
$923$	1.35502e49	1.60738
$924$	−8.04069e48	−0.936927
$925$	0	0
$926$	−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	$0.357398\pi$
$930$	0	0
$931$	2.56678e48	0.264070
$932$	1.71448e48	0.173288
$933$	4.42553e48	0.439459
$934$	−1.93857e49	−1.89129
$935$	0	0
$936$	−6.57908e47	−0.0619603
$937$	−2.32824e48	−0.215439	−0.107720	−	0.994181i	$-0.534355\pi$
$937$	−2.32824e48	−0.215439	−0.107720	+	0.994181i	$0.534355\pi$
$938$	8.30508e48	0.755087
$939$	−1.17835e47	−0.0105267
$940$	0	0
$941$	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
$945$	0	0
$946$	−1.63959e49	−1.29578
$947$	1.76048e49	1.36728	0.683639	−	0.729821i	$-0.260396\pi$
$947$	1.76048e49	1.36728	0.683639	+	0.729821i	$0.260396\pi$
$948$	3.87257e48	0.295571
$949$	−1.71367e49	−1.28539
$950$	0	0
$951$	−2.48885e49	−1.80310
$952$	−2.91777e48	−0.207750
$953$	1.48539e49	1.03946	0.519731	−	0.854330i	$-0.326032\pi$
$953$	1.48539e49	1.03946	0.519731	+	0.854330i	$0.326032\pi$
$954$	−4.19190e48	−0.288312
$955$	0	0
$956$	1.32051e49	0.877377
$957$	−2.90108e48	−0.189458
$958$	7.34283e48	0.471338
$959$	6.06007e48	0.382358
$960$	0	0
$961$	−1.33223e49	−0.812166
$962$	−2.34822e49	−1.40718
$963$	−7.61332e48	−0.448477
$964$	−1.98563e49	−1.14981
$965$	0	0
$966$	−1.83753e49	−1.02828
$967$	7.36558e47	0.0405200	0.0202600	−	0.999795i	$-0.493551\pi$
$967$	7.36558e47	0.0405200	0.0202600	+	0.999795i	$0.493551\pi$
$968$	−4.55917e47	−0.0246571
$969$	3.27422e49	1.74087
$970$	0	0
$971$	−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
$975$	0	0
$976$	3.06665e49	1.44791
$977$	1.42950e49	0.663626	0.331813	−	0.943345i	$-0.392340\pi$
$977$	1.42950e49	0.663626	0.331813	+	0.943345i	$0.392340\pi$
$978$	−5.64601e49	−2.57721
$979$	2.92577e49	1.31319
$980$	0	0
$981$	3.79587e48	0.164730
$982$	1.93211e49	0.824503
$983$	1.85942e49	0.780271	0.390136	−	0.920757i	$-0.372428\pi$
$983$	1.85942e49	0.780271	0.390136	+	0.920757i	$0.372428\pi$
$984$	2.52592e48	0.104232
$985$	0	0
$986$	6.46619e48	0.258036
$987$	−5.06594e49	−1.98805
$988$	−2.59983e49	−1.00335
$989$	−1.73245e49	−0.657538
$990$	0	0
$991$	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
$995$	0	0
$996$	−2.21371e49	−0.747897
$997$	−2.49733e49	−0.829862	−0.414931	−	0.909853i	$-0.636194\pi$
$997$	−2.49733e49	−0.829862	−0.414931	+	0.909853i	$0.636194\pi$
$998$	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	25.34.a.c.1.6		6
5.2	odd	4		25.34.b.c.24.10		12
5.3	odd	4		25.34.b.c.24.3		12
5.4	even	2		5.34.a.b.1.1	✓	6

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 34 \)
Character orbit:	\([\chi]\)	\(=\)	25.a (trivial)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more