LMFDB - Embedded newform 25.35.c.b.7.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,35,Mod(7,25)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(25, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1]))

N = Newforms(chi, 35, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("25.7");

S:= CuspForms(chi, 35);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 35 $
Character orbit:	$[\chi]$	$=$	25.c (of order $4$, degree $2$, minimal)

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:	no
Analytic conductor:	$183.064135107$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.12
Character	$\chi$	$=$	25.7
Dual form			25.35.c.b.18.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(85294.4 + 85294.4i) q^{2} +(1.68126e8 - 1.68126e8i) q^{3} -2.62960e9i q^{4} +2.86804e13 q^{6} +(-2.04951e14 - 2.04951e14i) q^{7} +(1.68964e15 - 1.68964e15i) q^{8} -3.98554e16i q^{9} +O(q^{10})$	\(q+(85294.4 + 85294.4i) q^{2} +(1.68126e8 - 1.68126e8i) q^{3} -2.62960e9i q^{4} +2.86804e13 q^{6} +(-2.04951e14 - 2.04951e14i) q^{7} +(1.68964e15 - 1.68964e15i) q^{8} -3.98554e16i q^{9} -4.22981e17 q^{11} +(-4.42103e17 - 4.42103e17i) q^{12} +(-8.97147e18 + 8.97147e18i) q^{13} -3.49623e19i q^{14} +2.43057e20 q^{16} +(2.34375e20 + 2.34375e20i) q^{17} +(3.39944e21 - 3.39944e21i) q^{18} -3.96974e21i q^{19} -6.89150e22 q^{21} +(-3.60779e22 - 3.60779e22i) q^{22} +(1.87042e22 - 1.87042e22i) q^{23} -5.68143e23i q^{24} -1.53043e24 q^{26} +(-3.89685e24 - 3.89685e24i) q^{27} +(-5.38937e23 + 5.38937e23i) q^{28} +3.22017e24i q^{29} +3.15358e25 q^{31} +(-8.29633e24 - 8.29633e24i) q^{32} +(-7.11140e25 + 7.11140e25i) q^{33} +3.99818e25i q^{34} -1.04804e26 q^{36} +(-3.27113e26 - 3.27113e26i) q^{37} +(3.38597e26 - 3.38597e26i) q^{38} +3.01667e27i q^{39} -9.81913e26 q^{41} +(-5.87806e27 - 5.87806e27i) q^{42} +(-2.79636e27 + 2.79636e27i) q^{43} +1.11227e27i q^{44} +3.19073e27 q^{46} +(9.12764e27 + 9.12764e27i) q^{47} +(4.08642e28 - 4.08642e28i) q^{48} +2.98926e28i q^{49} +7.88090e28 q^{51} +(2.35913e28 + 2.35913e28i) q^{52} +(-2.57016e28 + 2.57016e28i) q^{53} -6.64760e29i q^{54} -6.92584e29 q^{56} +(-6.67416e29 - 6.67416e29i) q^{57} +(-2.74663e29 + 2.74663e29i) q^{58} +7.57873e29i q^{59} -3.27487e30 q^{61} +(2.68983e30 + 2.68983e30i) q^{62} +(-8.16839e30 + 8.16839e30i) q^{63} -5.59095e30i q^{64} -1.21312e31 q^{66} +(-3.29839e30 - 3.29839e30i) q^{67} +(6.16312e29 - 6.16312e29i) q^{68} -6.28932e30i q^{69} -1.48986e31 q^{71} +(-6.73411e31 - 6.73411e31i) q^{72} +(4.68046e31 - 4.68046e31i) q^{73} -5.58018e31i q^{74} -1.04388e31 q^{76} +(8.66902e31 + 8.66902e31i) q^{77} +(-2.57305e32 + 2.57305e32i) q^{78} +5.17250e31i q^{79} -6.45648e32 q^{81} +(-8.37517e31 - 8.37517e31i) q^{82} +(-1.93953e32 + 1.93953e32i) q^{83} +1.81219e32i q^{84} -4.77027e32 q^{86} +(5.41394e32 + 5.41394e32i) q^{87} +(-7.14684e32 + 7.14684e32i) q^{88} -4.72898e32i q^{89} +3.67742e33 q^{91} +(-4.91845e31 - 4.91845e31i) q^{92} +(5.30198e33 - 5.30198e33i) q^{93} +1.55707e33i q^{94} -2.78965e33 q^{96} +(5.55075e33 + 5.55075e33i) q^{97} +(-2.54967e33 + 2.54967e33i) q^{98} +1.68581e34i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 131070 q^{2} + 78988260 q^{3} - 44043049959816 q^{6} - 5337954235100 q^{7} + 45\!\cdots\!20 q^{8}+O(q^{10}) $ 32 * q - 131070 * q^2 + 78988260 * q^3 - 44043049959816 * q^6 - 5337954235100 * q^7 + 4536119823236220 * q^8	$ 32 q - 131070 q^{2} + 78988260 q^{3} - 44043049959816 q^{6} - 5337954235100 q^{7} + 45\!\cdots\!20 q^{8}+ \cdots - 25\!\cdots\!70 q^{98}+O(q^{100}) $ 32 * q - 131070 * q^2 + 78988260 * q^3 - 44043049959816 * q^6 - 5337954235100 * q^7 + 4536119823236220 * q^8 + 365981602487621544 * q^11 + 5313878568511975560 * q^12 + 11000397968713344520 * q^13 - 1456002327393916605448 * q^16 - 496656489553605410760 * q^17 - 1956191845428178111890 * q^18 - 142103646776097180182616 * q^21 - 204776256011020418595040 * q^22 + 436662638834307282633780 * q^23 - 5758044909260756123220396 * q^26 - 7995615376341697400032560 * q^27 - 884081328441809235881080 * q^28 + 84491420536973998188491704 * q^31 + 184975661677973569185317880 * q^32 - 73478673331281977814021480 * q^33 + 1137988291793068131741823932 * q^36 + 333379985446943362532279920 * q^37 + 1419101265678050265971769480 * q^38 + 3652223875741628991126246984 * q^41 + 4739529391137459161391231840 * q^42 - 16353372323322642143796902300 * q^43 + 131432785549604658942769746424 * q^46 + 164755893091890118218758986260 * q^47 - 267416366563859197412890248720 * q^48 + 879726622206121123479191444184 * q^51 + 1364297502096066356787005826100 * q^52 - 827578466548898383340593310640 * q^53 + 2582027089558247357967654389520 * q^56 + 3021243382907908474517658024480 * q^57 - 2354096772250584899097633644880 * q^58 + 10984341568764658290951563973544 * q^61 + 17271108259627677777618202511160 * q^62 - 8610875544094751042813983810860 * q^63 - 27230920485870501670249585219872 * q^66 - 23820125360634701614572823748060 * q^67 + 16651918880901511226895130538460 * q^68 - 162839011061674956057132387035976 * q^71 - 414631921651932227241773986664580 * q^72 + 290761010682860591477846798111680 * q^73 - 588265232627198985506540939882160 * q^76 - 319978294665614883220802415073800 * q^77 - 251541126280658548479082634723400 * q^78 + 46998375893846038447057289461032 * q^81 + 480327268957748332277390888075360 * q^82 + 987023986692010851073141552006740 * q^83 + 2563129008649864341703296140749464 * q^86 + 3601816973758507596709087426821120 * q^87 - 4467012425011508421563596255937760 * q^88 + 9733965316721903607010024138955704 * q^91 + 5821741665997247478385288152437640 * q^92 - 1188287280403911040224754269765480 * q^93 + 24207915861230982937605202170100704 * q^96 + 29449480417814037063188176022138560 * q^97 - 25177080070348305002521179770557470 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/25\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	85294.4	+	85294.4i	0.650745	+	0.650745i	0.953172	−	0.302428i	$-0.0977971\pi$
$2$	85294.4	+	85294.4i	0.650745	+	0.650745i	−0.302428	+	0.953172i	$0.597797\pi$
$3$	1.68126e8	−	1.68126e8i	1.30189	−	1.30189i	0.374767	−	0.927119i	$-0.377723\pi$
$3$	1.68126e8	−	1.68126e8i	1.30189	−	1.30189i	0.927119	−	0.374767i	$-0.122277\pi$
$4$		−	2.62960e9i		−	0.153063i
$5$		0			0
$5$		0			0
$6$	2.86804e13			1.69439
$7$	−2.04951e14	−	2.04951e14i	−0.881014	−	0.881014i	0.112624	−	0.993638i	$-0.464074\pi$
$7$	−2.04951e14	−	2.04951e14i	−0.881014	−	0.881014i	−0.993638	+	0.112624i	$0.964074\pi$
$8$	1.68964e15	−	1.68964e15i	0.750349	−	0.750349i
$9$		−	3.98554e16i		−	2.38982i
$10$		0			0
$11$	−4.22981e17			−0.836845			−0.418422	−	0.908253i	$-0.637417\pi$
$11$	−4.22981e17			−0.836845			−0.418422	+	0.908253i	$0.637417\pi$
$12$	−4.42103e17	−	4.42103e17i	−0.199270	−	0.199270i
$13$	−8.97147e18	+	8.97147e18i	−1.03711	+	1.03711i	−0.0378303	+	0.999284i	$0.512045\pi$
$13$	−8.97147e18	+	8.97147e18i	−1.03711	+	1.03711i	−0.999284	+	0.0378303i	$0.987955\pi$
$14$		−	3.49623e19i		−	1.14663i
$15$		0			0
$16$	2.43057e20			0.823509
$17$	2.34375e20	+	2.34375e20i	0.283322	+	0.283322i	0.834432	−	0.551111i	$-0.185796\pi$
$17$	2.34375e20	+	2.34375e20i	0.283322	+	0.283322i	−0.551111	+	0.834432i	$0.685796\pi$
$18$	3.39944e21	−	3.39944e21i	1.55516	−	1.55516i
$19$		−	3.96974e21i		−	0.724355i	−0.932109	−	0.362177i	$-0.882033\pi$
$19$		−	3.96974e21i		−	0.724355i	0.932109	−	0.362177i	$-0.117967\pi$
$20$		0			0
$21$	−6.89150e22			−2.29396
$22$	−3.60779e22	−	3.60779e22i	−0.544572	−	0.544572i
$23$	1.87042e22	−	1.87042e22i	0.132607	−	0.132607i	−0.637688	−	0.770295i	$-0.720109\pi$
$23$	1.87042e22	−	1.87042e22i	0.132607	−	0.132607i	0.770295	+	0.637688i	$0.220109\pi$
$24$		−	5.68143e23i		−	1.95374i
$25$		0			0
$26$	−1.53043e24			−1.34979
$27$	−3.89685e24	−	3.89685e24i	−1.80938	−	1.80938i
$28$	−5.38937e23	+	5.38937e23i	−0.134850	+	0.134850i
$29$			3.22017e24i			0.443724i	0.975078	+	0.221862i	$0.0712135\pi$
$29$			3.22017e24i			0.443724i	−0.975078	+	0.221862i	$0.928787\pi$
$30$		0			0
$31$	3.15358e25			1.39848			0.699238	−	0.714889i	$-0.253523\pi$
$31$	3.15358e25			1.39848			0.699238	+	0.714889i	$0.253523\pi$
$32$	−8.29633e24	−	8.29633e24i	−0.214455	−	0.214455i
$33$	−7.11140e25	+	7.11140e25i	−1.08948	+	1.08948i
$34$			3.99818e25i			0.368740i
$35$		0			0
$36$	−1.04804e26			−0.365791
$37$	−3.27113e26	−	3.27113e26i	−0.716586	−	0.716586i	0.251318	−	0.967904i	$-0.419136\pi$
$37$	−3.27113e26	−	3.27113e26i	−0.716586	−	0.716586i	−0.967904	+	0.251318i	$0.919136\pi$
$38$	3.38597e26	−	3.38597e26i	0.471370	−	0.471370i
$39$			3.01667e27i			2.70041i
$40$		0			0
$41$	−9.81913e26			−0.375619			−0.187810	−	0.982205i	$-0.560139\pi$
$41$	−9.81913e26			−0.375619			−0.187810	+	0.982205i	$0.560139\pi$
$42$	−5.87806e27	−	5.87806e27i	−1.49278	−	1.49278i
$43$	−2.79636e27	+	2.79636e27i	−0.476024	+	0.476024i	−0.903858	−	0.427833i	$-0.859277\pi$
$43$	−2.79636e27	+	2.79636e27i	−0.476024	+	0.476024i	0.427833	+	0.903858i	$0.359277\pi$
$44$			1.11227e27i			0.128090i
$45$		0			0
$46$	3.19073e27			0.172587
$47$	9.12764e27	+	9.12764e27i	0.342527	+	0.342527i	0.857317	−	0.514789i	$-0.172130\pi$
$47$	9.12764e27	+	9.12764e27i	0.342527	+	0.342527i	−0.514789	+	0.857317i	$0.672130\pi$
$48$	4.08642e28	−	4.08642e28i	1.07212	−	1.07212i
$49$			2.98926e28i			0.552370i
$50$		0			0
$51$	7.88090e28			0.737705
$52$	2.35913e28	+	2.35913e28i	0.158743	+	0.158743i
$53$	−2.57016e28	+	2.57016e28i	−0.125104	+	0.125104i	−0.766886	−	0.641783i	$-0.778195\pi$
$53$	−2.57016e28	+	2.57016e28i	−0.125104	+	0.125104i	0.641783	+	0.766886i	$0.278195\pi$
$54$		−	6.64760e29i		−	2.35489i
$55$		0			0
$56$	−6.92584e29			−1.32214
$57$	−6.67416e29	−	6.67416e29i	−0.943027	−	0.943027i
$58$	−2.74663e29	+	2.74663e29i	−0.288751	+	0.288751i
$59$			7.57873e29i			0.595816i	0.954595	+	0.297908i	$0.0962888\pi$
$59$			7.57873e29i			0.595816i	−0.954595	+	0.297908i	$0.903711\pi$
$60$		0			0
$61$	−3.27487e30			−1.46079			−0.730393	−	0.683027i	$-0.760663\pi$
$61$	−3.27487e30			−1.46079			−0.730393	+	0.683027i	$0.760663\pi$
$62$	2.68983e30	+	2.68983e30i	0.910051	+	0.910051i
$63$	−8.16839e30	+	8.16839e30i	−2.10546	+	2.10546i
$64$		−	5.59095e30i		−	1.10262i
$65$		0			0
$66$	−1.21312e31			−1.41794
$67$	−3.29839e30	−	3.29839e30i	−0.298559	−	0.298559i	0.541890	−	0.840449i	$-0.317709\pi$
$67$	−3.29839e30	−	3.29839e30i	−0.298559	−	0.298559i	−0.840449	+	0.541890i	$0.817709\pi$
$68$	6.16312e29	−	6.16312e29i	0.0433659	−	0.0433659i
$69$		−	6.28932e30i		−	0.345278i
$70$		0			0
$71$	−1.48986e31			−0.503216			−0.251608	−	0.967829i	$-0.580959\pi$
$71$	−1.48986e31			−0.503216			−0.251608	+	0.967829i	$0.580959\pi$
$72$	−6.73411e31	−	6.73411e31i	−1.79320	−	1.79320i
$73$	4.68046e31	−	4.68046e31i	0.985824	−	0.985824i	−0.0140764	−	0.999901i	$-0.504481\pi$
$73$	4.68046e31	−	4.68046e31i	0.985824	−	0.985824i	0.999901	+	0.0140764i	$0.00448082\pi$
$74$		−	5.58018e31i		−	0.932629i
$75$		0			0
$76$	−1.04388e31			−0.110872
$77$	8.66902e31	+	8.66902e31i	0.737272	+	0.737272i
$78$	−2.57305e32	+	2.57305e32i	−1.75728	+	1.75728i
$79$			5.17250e31i			0.284472i	0.989833	+	0.142236i	$0.0454292\pi$
$79$			5.17250e31i			0.284472i	−0.989833	+	0.142236i	$0.954571\pi$
$80$		0			0
$81$	−6.45648e32			−2.32140
$82$	−8.37517e31	−	8.37517e31i	−0.244432	−	0.244432i
$83$	−1.93953e32	+	1.93953e32i	−0.460648	+	0.460648i	−0.898868	−	0.438220i	$-0.855609\pi$
$83$	−1.93953e32	+	1.93953e32i	−0.460648	+	0.460648i	0.438220	+	0.898868i	$0.355609\pi$
$84$			1.81219e32i			0.351119i
$85$		0			0
$86$	−4.77027e32			−0.619540
$87$	5.41394e32	+	5.41394e32i	0.577678	+	0.577678i
$88$	−7.14684e32	+	7.14684e32i	−0.627926	+	0.627926i
$89$		−	4.72898e32i		−	0.342876i	−0.985195	−	0.171438i	$-0.945159\pi$
$89$		−	4.72898e32i		−	0.342876i	0.985195	−	0.171438i	$-0.0548414\pi$
$90$		0			0
$91$	3.67742e33			1.82742
$92$	−4.91845e31	−	4.91845e31i	−0.0202972	−	0.0202972i
$93$	5.30198e33	−	5.30198e33i	1.82066	−	1.82066i
$94$			1.55707e33i			0.445795i
$95$		0			0
$96$	−2.78965e33			−0.558392
$97$	5.55075e33	+	5.55075e33i	0.931605	+	0.931605i	0.997806	−	0.0662012i	$-0.0210879\pi$
$97$	5.55075e33	+	5.55075e33i	0.931605	+	0.931605i	−0.0662012	+	0.997806i	$0.521088\pi$
$98$	−2.54967e33	+	2.54967e33i	−0.359452	+	0.359452i
$99$			1.68581e34i			1.99990i
$100$		0			0
$101$	1.80233e34			1.52185			0.760923	−	0.648842i	$-0.224746\pi$
$101$	1.80233e34			1.52185			0.760923	+	0.648842i	$0.224746\pi$
$102$	6.72196e33	+	6.72196e33i	0.480057	+	0.480057i
$103$	4.68995e33	−	4.68995e33i	0.283750	−	0.283750i	−0.550853	−	0.834603i	$-0.685697\pi$
$103$	4.68995e33	−	4.68995e33i	0.283750	−	0.283750i	0.834603	+	0.550853i	$0.185697\pi$
$104$			3.03171e34i			1.55640i
$105$		0			0
$106$	−4.38440e33			−0.162821
$107$	1.13148e33	+	1.13148e33i	0.0358198	+	0.0358198i	0.724790	−	0.688970i	$-0.241937\pi$
$107$	1.13148e33	+	1.13148e33i	0.0358198	+	0.0358198i	−0.688970	+	0.724790i	$0.741937\pi$
$108$	−1.02472e34	+	1.02472e34i	−0.276949	+	0.276949i
$109$			5.39670e34i			1.24703i	0.781811	+	0.623516i	$0.214296\pi$
$109$			5.39670e34i			1.24703i	−0.781811	+	0.623516i	$0.785704\pi$
$110$		0			0
$111$	−1.09992e35			−1.86583
$112$	−4.98147e34	−	4.98147e34i	−0.725523	−	0.725523i
$113$	−5.55309e34	+	5.55309e34i	−0.695346	+	0.695346i	−0.963403	−	0.268057i	$-0.913618\pi$
$113$	−5.55309e34	+	5.55309e34i	−0.695346	+	0.695346i	0.268057	+	0.963403i	$0.413618\pi$
$114$		−	1.13854e35i		−	1.22734i
$115$		0			0
$116$	8.46775e33			0.0679176
$117$	3.57561e35	+	3.57561e35i	2.47851	+	2.47851i
$118$	−6.46423e34	+	6.46423e34i	−0.387724	+	0.387724i
$119$		−	9.60706e34i		−	0.499220i
$120$		0			0
$121$	−7.65640e34			−0.299691
$122$	−2.79328e35	−	2.79328e35i	−0.950599	−	0.950599i
$123$	−1.65085e35	+	1.65085e35i	−0.489013	+	0.489013i
$124$		−	8.29264e34i		−	0.214054i
$125$		0			0
$126$	−1.39344e36			−2.74023
$127$	−6.96208e35	−	6.96208e35i	−1.19695	−	1.19695i	−0.975076	−	0.221873i	$-0.928783\pi$
$127$	−6.96208e35	−	6.96208e35i	−1.19695	−	1.19695i	−0.221873	−	0.975076i	$-0.571217\pi$
$128$	3.34347e35	−	3.34347e35i	0.503069	−	0.503069i
$129$			9.40280e35i			1.23946i
$130$		0			0
$131$	1.35390e36			1.37396			0.686980	−	0.726677i	$-0.258936\pi$
$131$	1.35390e36			1.37396			0.686980	+	0.726677i	$0.258936\pi$
$132$	1.87001e35	+	1.87001e35i	0.166758	+	0.166758i
$133$	−8.13601e35	+	8.13601e35i	−0.638166	+	0.638166i
$134$		−	5.62668e35i		−	0.388571i
$135$		0			0
$136$	7.92017e35			0.425180
$137$	5.58799e35	+	5.58799e35i	0.264854	+	0.264854i	0.827023	−	0.562169i	$-0.190033\pi$
$137$	5.58799e35	+	5.58799e35i	0.264854	+	0.264854i	−0.562169	+	0.827023i	$0.690033\pi$
$138$	5.36444e35	−	5.36444e35i	0.224688	−	0.224688i
$139$			2.74512e36i			1.01697i	0.861070	+	0.508486i	$0.169795\pi$
$139$			2.74512e36i			1.01697i	−0.861070	+	0.508486i	$0.830205\pi$
$140$		0			0
$141$	3.06918e36			0.891863
$142$	−1.27077e36	−	1.27077e36i	−0.327465	−	0.327465i
$143$	3.79476e36	−	3.79476e36i	0.867904	−	0.867904i
$144$		−	9.68713e36i		−	1.96803i
$145$		0			0
$146$	7.98434e36			1.28304
$147$	5.02571e36	+	5.02571e36i	0.719122	+	0.719122i
$148$	−8.60175e35	+	8.60175e35i	−0.109683	+	0.109683i
$149$		−	4.53639e36i		−	0.515875i	−0.966162	−	0.257937i	$-0.916957\pi$
$149$		−	4.53639e36i		−	0.515875i	0.966162	−	0.257937i	$-0.0830428\pi$
$150$		0			0
$151$	−3.59636e36			−0.326028			−0.163014	−	0.986624i	$-0.552122\pi$
$151$	−3.59636e36			−0.326028			−0.163014	+	0.986624i	$0.552122\pi$
$152$	−6.70742e36	−	6.70742e36i	−0.543519	−	0.543519i
$153$	9.34111e36	−	9.34111e36i	0.677086	−	0.677086i
$154$			1.47884e37i			0.959551i
$155$		0			0
$156$	7.93263e36			0.413332
$157$	8.56486e36	+	8.56486e36i	0.400338	+	0.400338i	0.878352	−	0.478014i	$-0.158643\pi$
$157$	8.56486e36	+	8.56486e36i	0.400338	+	0.400338i	−0.478014	+	0.878352i	$0.658643\pi$
$158$	−4.41185e36	+	4.41185e36i	−0.185119	+	0.185119i
$159$			8.64220e36i			0.325742i
$160$		0			0
$161$	−7.66688e36			−0.233657
$162$	−5.50701e37	−	5.50701e37i	−1.51064	−	1.51064i
$163$	−2.62684e37	+	2.62684e37i	−0.648999	+	0.648999i	−0.952751	−	0.303752i	$-0.901761\pi$
$163$	−2.62684e37	+	2.62684e37i	−0.648999	+	0.648999i	0.303752	+	0.952751i	$0.401761\pi$
$164$			2.58204e36i			0.0574932i
$165$		0			0
$166$	−3.30862e37			−0.599528
$167$	−4.43155e37	−	4.43155e37i	−0.725063	−	0.725063i	0.244569	−	0.969632i	$-0.421353\pi$
$167$	−4.43155e37	−	4.43155e37i	−0.725063	−	0.725063i	−0.969632	+	0.244569i	$0.921353\pi$
$168$	−1.16441e38	+	1.16441e38i	−1.72127	+	1.72127i
$169$		−	8.61449e37i		−	1.15121i
$170$		0			0
$171$	−1.58216e38			−1.73107
$172$	7.35329e36	+	7.35329e36i	0.0728615	+	0.0728615i
$173$	8.60303e37	−	8.60303e37i	0.772445	−	0.772445i	−0.206088	−	0.978533i	$-0.566073\pi$
$173$	8.60303e37	−	8.60303e37i	0.772445	−	0.772445i	0.978533	+	0.206088i	$0.0660735\pi$
$174$			9.23557e37i			0.751842i
$175$		0			0
$176$	−1.02808e38			−0.689149
$177$	1.27418e38	+	1.27418e38i	0.775684	+	0.775684i
$178$	4.03356e37	−	4.03356e37i	0.223125	−	0.223125i
$179$			9.70082e37i			0.487873i	0.969791	+	0.243937i	$0.0784389\pi$
$179$			9.70082e37i			0.487873i	−0.969791	+	0.243937i	$0.921561\pi$
$180$		0			0
$181$	−1.40900e38			−0.586644			−0.293322	−	0.956014i	$-0.594761\pi$
$181$	−1.40900e38			−0.586644			−0.293322	+	0.956014i	$0.594761\pi$
$182$	3.13663e38	+	3.13663e38i	1.18919	+	1.18919i
$183$	−5.50590e38	+	5.50590e38i	−1.90178	+	1.90178i
$184$		−	6.32067e37i		−	0.199003i
$185$		0			0
$186$	9.04459e38			2.36957
$187$	−9.91361e37	−	9.91361e37i	−0.237096	−	0.237096i
$188$	2.40020e37	−	2.40020e37i	0.0524281	−	0.0524281i
$189$			1.59733e39i			3.18818i
$190$		0			0
$191$	−7.16817e38			−1.19630			−0.598151	−	0.801383i	$-0.704098\pi$
$191$	−7.16817e38			−1.19630			−0.598151	+	0.801383i	$0.704098\pi$
$192$	−9.39983e38	−	9.39983e38i	−1.43549	−	1.43549i
$193$	6.33285e38	−	6.33285e38i	0.885370	−	0.885370i	−0.108704	−	0.994074i	$-0.534670\pi$
$193$	6.33285e38	−	6.33285e38i	0.885370	−	0.885370i	0.994074	+	0.108704i	$0.0346701\pi$
$194$			9.46895e38i			1.21247i
$195$		0			0
$196$	7.86054e37			0.0845472
$197$	−8.98078e38	−	8.98078e38i	−0.885907	−	0.885907i	0.108220	−	0.994127i	$-0.465485\pi$
$197$	−8.98078e38	−	8.98078e38i	−0.885907	−	0.885907i	−0.994127	+	0.108220i	$0.965485\pi$
$198$	−1.43790e39	+	1.43790e39i	−1.30143	+	1.30143i
$199$		−	5.54406e38i		−	0.460602i	−0.973119	−	0.230301i	$-0.926029\pi$
$199$		−	5.54406e38i		−	0.460602i	0.973119	−	0.230301i	$-0.0739710\pi$
$200$		0			0
$201$	−1.10909e39			−0.777379
$202$	1.53729e39	+	1.53729e39i	0.990333	+	0.990333i
$203$	6.59976e38	−	6.59976e38i	0.390927	−	0.390927i
$204$		−	2.07236e38i		−	0.112915i
$205$		0			0
$206$	8.00054e38			0.369297
$207$	−7.45464e38	−	7.45464e38i	−0.316906	−	0.316906i
$208$	−2.18058e39	+	2.18058e39i	−0.854073	+	0.854073i
$209$			1.67912e39i			0.606172i
$210$		0			0
$211$	2.98296e39			0.915896			0.457948	−	0.888979i	$-0.348585\pi$
$211$	2.98296e39			0.915896			0.457948	+	0.888979i	$0.348585\pi$
$212$	6.75848e37	+	6.75848e37i	0.0191487	+	0.0191487i
$213$	−2.50485e39	+	2.50485e39i	−0.655131	+	0.655131i
$214$			1.93018e38i			0.0466191i
$215$		0			0
$216$	−1.31685e40			−2.71534
$217$	−6.46328e39	−	6.46328e39i	−1.23208	−	1.23208i
$218$	−4.60308e39	+	4.60308e39i	−0.811499	+	0.811499i
$219$		−	1.57381e40i		−	2.56686i
$220$		0			0
$221$	−4.20538e39			−0.587674
$222$	−9.38172e39	−	9.38172e39i	−1.21418	−	1.21418i
$223$	−8.16356e39	+	8.16356e39i	−0.978807	+	0.978807i	−0.999780	−	0.0209734i	$-0.993323\pi$
$223$	−8.16356e39	+	8.16356e39i	−0.978807	+	0.978807i	0.0209734	+	0.999780i	$0.493323\pi$
$224$			3.40068e39i			0.377876i
$225$		0			0
$226$	−9.47294e39			−0.904985
$227$	−7.50469e39	−	7.50469e39i	−0.665109	−	0.665109i	0.291471	−	0.956580i	$-0.405855\pi$
$227$	−7.50469e39	−	7.50469e39i	−0.665109	−	0.665109i	−0.956580	+	0.291471i	$0.905855\pi$
$228$	−1.75504e39	+	1.75504e39i	−0.144342	+	0.144342i
$229$			2.26746e40i			1.73116i	0.500771	+	0.865580i	$0.333050\pi$
$229$			2.26746e40i			1.73116i	−0.500771	+	0.865580i	$0.666950\pi$
$230$		0			0
$231$	2.91497e40			1.91969
$232$	5.44092e39	+	5.44092e39i	0.332948	+	0.332948i
$233$	3.16358e39	−	3.16358e39i	0.179940	−	0.179940i	−0.611390	−	0.791330i	$-0.709389\pi$
$233$	3.16358e39	−	3.16358e39i	0.179940	−	0.179940i	0.791330	+	0.611390i	$0.209389\pi$
$234$			6.09960e40i			3.22576i
$235$		0			0
$236$	1.99290e39			0.0911971
$237$	8.69631e39	+	8.69631e39i	0.370350	+	0.370350i
$238$	8.19429e39	−	8.19429e39i	0.324865	−	0.324865i
$239$		−	4.01203e40i		−	1.48115i	−0.671972	−	0.740576i	$-0.734553\pi$
$239$		−	4.01203e40i		−	1.48115i	0.671972	−	0.740576i	$-0.265447\pi$
$240$		0			0
$241$	1.37564e40			0.440772			0.220386	−	0.975413i	$-0.429268\pi$
$241$	1.37564e40			0.440772			0.220386	+	0.975413i	$0.429268\pi$
$242$	−6.53048e39	−	6.53048e39i	−0.195022	−	0.195022i
$243$	−4.35615e40	+	4.35615e40i	−1.21282	+	1.21282i
$244$			8.61158e39i			0.223592i
$245$		0			0
$246$	−2.81617e40			−0.636446
$247$	3.56144e40	+	3.56144e40i	0.751239	+	0.751239i
$248$	5.32841e40	−	5.32841e40i	1.04935	−	1.04935i
$249$			6.52170e40i			1.19942i
$250$		0			0
$251$	−5.54426e40			−0.890000			−0.445000	−	0.895530i	$-0.646796\pi$
$251$	−5.54426e40			−0.890000			−0.445000	+	0.895530i	$0.646796\pi$
$252$	2.14796e40	+	2.14796e40i	0.322267	+	0.322267i
$253$	−7.91152e39	+	7.91152e39i	−0.110971	+	0.110971i
$254$		−	1.18765e41i		−	1.55782i
$255$		0			0
$256$	−3.90159e40			−0.447881
$257$	−1.05489e41	−	1.05489e41i	−1.13330	−	1.13330i	−0.989626	−	0.143670i	$-0.954110\pi$
$257$	−1.05489e41	−	1.05489e41i	−1.13330	−	1.13330i	−0.143670	−	0.989626i	$-0.545890\pi$
$258$	−8.02006e40	+	8.02006e40i	−0.806571	+	0.806571i
$259$			1.34084e41i			1.26264i
$260$		0			0
$261$	1.28341e41			1.06042
$262$	1.15480e41	+	1.15480e41i	0.894097	+	0.894097i
$263$	−1.85299e41	+	1.85299e41i	−1.34470	+	1.34470i	−0.453389	+	0.891313i	$0.649785\pi$
$263$	−1.85299e41	+	1.85299e41i	−1.34470	+	1.34470i	−0.891313	+	0.453389i	$0.850215\pi$
$264$			2.40314e41i			1.63498i
$265$		0			0
$266$	−1.38791e41			−0.830567
$267$	−7.95064e40	−	7.95064e40i	−0.446386	−	0.446386i
$268$	−8.67342e39	+	8.67342e39i	−0.0456982	+	0.0456982i
$269$		−	3.04872e41i		−	1.50775i	−0.657019	−	0.753874i	$-0.728183\pi$
$269$		−	3.04872e41i		−	1.50775i	0.657019	−	0.753874i	$-0.271817\pi$
$270$		0			0
$271$	−1.91988e41			−0.837134			−0.418567	−	0.908186i	$-0.637468\pi$
$271$	−1.91988e41			−0.837134			−0.418567	+	0.908186i	$0.637468\pi$
$272$	5.69665e40	+	5.69665e40i	0.233318	+	0.233318i
$273$	6.18269e41	−	6.18269e41i	2.37910	−	2.37910i
$274$			9.53249e40i			0.344704i
$275$		0			0
$276$	−1.65384e40			−0.0528492
$277$	−2.65593e41	−	2.65593e41i	−0.798105	−	0.798105i	0.184691	−	0.982797i	$-0.440871\pi$
$277$	−2.65593e41	−	2.65593e41i	−0.798105	−	0.798105i	−0.982797	+	0.184691i	$0.940871\pi$
$278$	−2.34143e41	+	2.34143e41i	−0.661789	+	0.661789i
$279$		−	1.25687e42i		−	3.34210i
$280$		0			0
$281$	9.81792e40			0.231213			0.115606	−	0.993295i	$-0.463119\pi$
$281$	9.81792e40			0.231213			0.115606	+	0.993295i	$0.463119\pi$
$282$	2.61784e41	+	2.61784e41i	0.580375	+	0.580375i
$283$	5.47664e41	−	5.47664e41i	1.14326	−	1.14326i	0.155408	−	0.987850i	$-0.450331\pi$
$283$	5.47664e41	−	5.47664e41i	1.14326	−	1.14326i	0.987850	−	0.155408i	$-0.0496693\pi$
$284$			3.91774e40i			0.0770236i
$285$		0			0
$286$	6.47344e41			1.12957
$287$	2.01244e41	+	2.01244e41i	0.330925	+	0.330925i
$288$	−3.30654e41	+	3.30654e41i	−0.512508	+	0.512508i
$289$		−	5.74463e41i		−	0.839458i
$290$		0			0
$291$	1.86645e42			2.42569
$292$	−1.23077e41	−	1.23077e41i	−0.150893	−	0.150893i
$293$	4.10085e41	−	4.10085e41i	0.474378	−	0.474378i	−0.428950	−	0.903328i	$-0.641116\pi$
$293$	4.10085e41	−	4.10085e41i	0.474378	−	0.474378i	0.903328	+	0.428950i	$0.141116\pi$
$294$			8.57330e41i			0.935930i
$295$		0			0
$296$	−1.10540e42			−1.07538
$297$	1.64829e42	+	1.64829e42i	1.51417	+	1.51417i
$298$	3.86929e41	−	3.86929e41i	0.335703	−	0.335703i
$299$			3.35609e41i			0.275057i
$300$		0			0
$301$	1.14623e42			0.838767
$302$	−3.06749e41	−	3.06749e41i	−0.212161	−	0.212161i
$303$	3.03018e42	−	3.03018e42i	1.98127	−	1.98127i
$304$		−	9.64874e41i		−	0.596513i
$305$		0			0
$306$	1.59349e42			0.881220
$307$	−2.36572e42	−	2.36572e42i	−1.23769	−	1.23769i	−0.960944	−	0.276743i	$-0.910745\pi$
$307$	−2.36572e42	−	2.36572e42i	−1.23769	−	1.23769i	−0.276743	−	0.960944i	$-0.589255\pi$
$308$	2.27960e41	−	2.27960e41i	0.112849	−	0.112849i
$309$		−	1.57700e42i		−	0.738820i
$310$		0			0
$311$	−2.28886e42			−0.960931			−0.480466	−	0.877014i	$-0.659532\pi$
$311$	−2.28886e42			−0.960931			−0.480466	+	0.877014i	$0.659532\pi$
$312$	5.09708e42	+	5.09708e42i	2.02625	+	2.02625i
$313$	−1.36674e42	+	1.36674e42i	−0.514556	+	0.514556i	−0.915919	−	0.401363i	$-0.868537\pi$
$313$	−1.36674e42	+	1.36674e42i	−0.514556	+	0.514556i	0.401363	+	0.915919i	$0.368537\pi$
$314$			1.46107e42i			0.521035i
$315$		0			0
$316$	1.36016e41			0.0435421
$317$	−4.32364e42	−	4.32364e42i	−1.31172	−	1.31172i	−0.920145	−	0.391578i	$-0.871929\pi$
$317$	−4.32364e42	−	4.32364e42i	−1.31172	−	1.31172i	−0.391578	−	0.920145i	$-0.628071\pi$
$318$	−7.37132e41	+	7.37132e41i	−0.211975	+	0.211975i
$319$		−	1.36207e42i		−	0.371328i
$320$		0			0
$321$	3.80463e41			0.0932667
$322$	−6.53942e41	−	6.53942e41i	−0.152051	−	0.152051i
$323$	9.30409e41	−	9.30409e41i	0.205225	−	0.205225i
$324$			1.69779e42i			0.355320i
$325$		0			0
$326$	−4.48109e42			−0.844666
$327$	9.07324e42	+	9.07324e42i	1.62349	+	1.62349i
$328$	−1.65908e42	+	1.65908e42i	−0.281846	+	0.281846i
$329$		−	3.74143e42i		−	0.603542i
$330$		0			0
$331$	−1.24196e42			−0.180730			−0.0903650	−	0.995909i	$-0.528803\pi$
$331$	−1.24196e42			−0.180730			−0.0903650	+	0.995909i	$0.528803\pi$
$332$	5.10018e41	+	5.10018e41i	0.0705079	+	0.0705079i
$333$	−1.30372e43	+	1.30372e43i	−1.71251	+	1.71251i
$334$		−	7.55973e42i		−	0.943661i
$335$		0			0
$336$	−1.67503e43			−1.88910
$337$	−6.40623e42	−	6.40623e42i	−0.686901	−	0.686901i	0.274645	−	0.961546i	$-0.411440\pi$
$337$	−6.40623e42	−	6.40623e42i	−0.686901	−	0.686901i	−0.961546	+	0.274645i	$0.911440\pi$
$338$	7.34768e42	−	7.34768e42i	0.749146	−	0.749146i
$339$			1.86723e43i			1.81052i
$340$		0			0
$341$	−1.33390e43			−1.17031
$342$	−1.34949e43	−	1.34949e43i	−1.12649	−	1.12649i
$343$	−4.96480e42	+	4.96480e42i	−0.394368	+	0.394368i
$344$			9.44966e42i			0.714369i
$345$		0			0
$346$	1.46758e43			1.00533
$347$	1.23849e43	+	1.23849e43i	0.807780	+	0.807780i	0.984297	−	0.176518i	$-0.0564833\pi$
$347$	1.23849e43	+	1.23849e43i	0.807780	+	0.807780i	−0.176518	+	0.984297i	$0.556483\pi$
$348$	1.42365e42	−	1.42365e42i	0.0884209	−	0.0884209i
$349$		−	8.06417e42i		−	0.477010i	−0.971141	−	0.238505i	$-0.923343\pi$
$349$		−	8.06417e42i		−	0.477010i	0.971141	−	0.238505i	$-0.0766573\pi$
$350$		0			0
$351$	6.99210e43			3.75307
$352$	3.50919e42	+	3.50919e42i	0.179466	+	0.179466i
$353$	2.40687e43	−	2.40687e43i	1.17296	−	1.17296i	0.191459	−	0.981501i	$-0.438678\pi$
$353$	2.40687e43	−	2.40687e43i	1.17296	−	1.17296i	0.981501	−	0.191459i	$-0.0613218\pi$
$354$			2.17361e43i			1.00955i
$355$		0			0
$356$	−1.24353e42			−0.0524815
$357$	−1.61519e43	−	1.61519e43i	−0.649928	−	0.649928i
$358$	−8.27426e42	+	8.27426e42i	−0.317481	+	0.317481i
$359$		−	2.81349e42i		−	0.102953i	−0.998674	−	0.0514766i	$-0.983607\pi$
$359$		−	2.81349e42i		−	0.102953i	0.998674	−	0.0514766i	$-0.0163928\pi$
$360$		0			0
$361$	1.42758e43			0.475310
$362$	−1.20180e43	−	1.20180e43i	−0.381755	−	0.381755i
$363$	−1.28724e43	+	1.28724e43i	−0.390163	+	0.390163i
$364$		−	9.67012e42i		−	0.279710i
$365$		0			0
$366$	−9.39245e43			−2.47514
$367$	−6.84643e42	−	6.84643e42i	−0.172243	−	0.172243i	0.615721	−	0.787964i	$-0.288865\pi$
$367$	−6.84643e42	−	6.84643e42i	−0.172243	−	0.172243i	−0.787964	+	0.615721i	$0.788865\pi$
$368$	4.54619e42	−	4.54619e42i	0.109203	−	0.109203i
$369$			3.91345e43i			0.897660i
$370$		0			0
$371$	1.05351e43			0.220436
$372$	−1.39421e43	−	1.39421e43i	−0.278675	−	0.278675i
$373$	−2.53693e43	+	2.53693e43i	−0.484460	+	0.484460i	−0.906553	−	0.422093i	$-0.861296\pi$
$373$	−2.53693e43	+	2.53693e43i	−0.484460	+	0.484460i	0.422093	+	0.906553i	$0.361296\pi$
$374$		−	1.69115e43i		−	0.308578i
$375$		0			0
$376$	3.08448e43			0.514030
$377$	−2.88897e43	−	2.88897e43i	−0.460193	−	0.460193i
$378$	−1.36243e44	+	1.36243e44i	−2.07469	+	2.07469i
$379$		−	1.00784e43i		−	0.146732i	−0.997305	−	0.0733658i	$-0.976626\pi$
$379$		−	1.00784e43i		−	0.146732i	0.997305	−	0.0733658i	$-0.0233740\pi$
$380$		0			0
$381$	−2.34101e44			−3.11658
$382$	−6.11405e43	−	6.11405e43i	−0.778488	−	0.778488i
$383$	−5.72676e43	+	5.72676e43i	−0.697477	+	0.697477i	−0.963866	−	0.266389i	$-0.914170\pi$
$383$	−5.72676e43	+	5.72676e43i	−0.697477	+	0.697477i	0.266389	+	0.963866i	$0.414170\pi$
$384$		−	1.12425e44i		−	1.30988i
$385$		0			0
$386$	1.08031e44			1.15230
$387$	1.11450e44	+	1.11450e44i	1.13761	+	1.13761i
$388$	1.45962e43	−	1.45962e43i	0.142594	−	0.142594i
$389$			1.41542e44i			1.32355i	0.749702	+	0.661776i	$0.230197\pi$
$389$			1.41542e44i			1.32355i	−0.749702	+	0.661776i	$0.769803\pi$
$390$		0			0
$391$	8.76760e42			0.0751408
$392$	5.05076e43	+	5.05076e43i	0.414470	+	0.414470i
$393$	2.27625e44	−	2.27625e44i	1.78874	−	1.78874i
$394$		−	1.53202e44i		−	1.15300i
$395$		0			0
$396$	4.43299e43			0.306111
$397$	−1.26432e44	−	1.26432e44i	−0.836410	−	0.836410i	0.151974	−	0.988384i	$-0.451437\pi$
$397$	−1.26432e44	−	1.26432e44i	−0.836410	−	0.836410i	−0.988384	+	0.151974i	$0.951437\pi$
$398$	4.72877e43	−	4.72877e43i	0.299734	−	0.299734i
$399$			2.73575e44i			1.66164i
$400$		0			0
$401$	−2.21014e44			−1.23301			−0.616504	−	0.787352i	$-0.711451\pi$
$401$	−2.21014e44			−1.23301			−0.616504	+	0.787352i	$0.711451\pi$
$402$	−9.45990e43	−	9.45990e43i	−0.505875	−	0.505875i
$403$	−2.82923e44	+	2.82923e44i	−1.45038	+	1.45038i
$404$		−	4.73940e43i		−	0.232938i
$405$		0			0
$406$	1.12585e44			0.508787
$407$	1.38362e44	+	1.38362e44i	0.599671	+	0.599671i
$408$	1.33159e44	−	1.33159e44i	0.553536	−	0.553536i
$409$			3.75907e44i			1.49894i	0.662038	+	0.749471i	$0.269692\pi$
$409$			3.75907e44i			1.49894i	−0.662038	+	0.749471i	$0.730308\pi$
$410$		0			0
$411$	1.87897e44			0.689619
$412$	−1.23327e43	−	1.23327e43i	−0.0434315	−	0.0434315i
$413$	1.55326e44	−	1.55326e44i	0.524922	−	0.524922i
$414$		−	1.27168e44i		−	0.412450i
$415$		0			0
$416$	1.48861e44			0.444829
$417$	4.61525e44	+	4.61525e44i	1.32398	+	1.32398i
$418$	−1.43220e44	+	1.43220e44i	−0.394463	+	0.394463i
$419$			1.85614e44i			0.490877i	0.969412	+	0.245439i	$0.0789320\pi$
$419$			1.85614e44i			0.490877i	−0.969412	+	0.245439i	$0.921068\pi$
$420$		0			0
$421$	4.17457e44			1.01816			0.509080	−	0.860719i	$-0.329986\pi$
$421$	4.17457e44			1.01816			0.509080	+	0.860719i	$0.329986\pi$
$422$	2.54430e44	+	2.54430e44i	0.596014	+	0.596014i
$423$	3.63786e44	−	3.63786e44i	0.818577	−	0.818577i
$424$			8.68527e43i			0.187743i
$425$		0			0
$426$	−4.27299e44			−0.852646
$427$	6.71186e44	+	6.71186e44i	1.28697	+	1.28697i
$428$	2.97534e42	−	2.97534e42i	0.00548268	−	0.00548268i
$429$		−	1.27599e45i		−	2.25982i
$430$		0			0
$431$	4.23613e44			0.693195			0.346597	−	0.938014i	$-0.387337\pi$
$431$	4.23613e44			0.693195			0.346597	+	0.938014i	$0.387337\pi$
$432$	−9.47158e44	−	9.47158e44i	−1.49004	−	1.49004i
$433$	1.41662e44	−	1.41662e44i	0.214269	−	0.214269i	−0.591809	−	0.806078i	$-0.701586\pi$
$433$	1.41662e44	−	1.41662e44i	0.214269	−	0.214269i	0.806078	+	0.591809i	$0.201586\pi$
$434$		−	1.10256e45i		−	1.60353i
$435$		0			0
$436$	1.41911e44			0.190874
$437$	−7.42510e43	−	7.42510e43i	−0.0960545	−	0.0960545i
$438$	1.34237e45	−	1.34237e45i	1.67037	−	1.67037i
$439$		−	6.28256e44i		−	0.752038i	−0.926612	−	0.376019i	$-0.877293\pi$
$439$		−	6.28256e44i		−	0.752038i	0.926612	−	0.376019i	$-0.122707\pi$
$440$		0			0
$441$	1.19138e45			1.32006
$442$	−3.58695e44	−	3.58695e44i	−0.382426	−	0.382426i
$443$	8.62803e44	−	8.62803e44i	0.885215	−	0.885215i	−0.108844	−	0.994059i	$-0.534715\pi$
$443$	8.62803e44	−	8.62803e44i	0.885215	−	0.885215i	0.994059	+	0.108844i	$0.0347150\pi$
$444$			2.89235e44i			0.285588i
$445$		0			0
$446$	−1.39261e45			−1.27391
$447$	−7.62685e44	−	7.62685e44i	−0.671610	−	0.671610i
$448$	−1.14587e45	+	1.14587e45i	−0.971423	+	0.971423i
$449$			1.12611e45i			0.919162i	0.888136	+	0.459581i	$0.152000\pi$
$449$			1.12611e45i			0.919162i	−0.888136	+	0.459581i	$0.848000\pi$
$450$		0			0
$451$	4.15330e44			0.314335
$452$	1.46024e44	+	1.46024e44i	0.106431	+	0.106431i
$453$	−6.04641e44	+	6.04641e44i	−0.424452	+	0.424452i
$454$		−	1.28022e45i		−	0.865632i
$455$		0			0
$456$	−2.25538e45			−1.41520
$457$	2.31901e44	+	2.31901e44i	0.140193	+	0.140193i	0.773720	−	0.633527i	$-0.218394\pi$
$457$	2.31901e44	+	2.31901e44i	0.140193	+	0.140193i	−0.633527	+	0.773720i	$0.718394\pi$
$458$	−1.93402e45	+	1.93402e45i	−1.12654	+	1.12654i
$459$		−	1.82665e45i		−	1.02527i
$460$		0			0
$461$	−1.90680e44			−0.0994007			−0.0497004	−	0.998764i	$-0.515827\pi$
$461$	−1.90680e44			−0.0994007			−0.0497004	+	0.998764i	$0.515827\pi$
$462$	2.48631e45	+	2.48631e45i	1.24923	+	1.24923i
$463$	5.36450e44	−	5.36450e44i	0.259808	−	0.259808i	−0.565168	−	0.824976i	$-0.691189\pi$
$463$	5.36450e44	−	5.36450e44i	0.259808	−	0.259808i	0.824976	+	0.565168i	$0.191189\pi$
$464$			7.82685e44i			0.365411i
$465$		0			0
$466$	5.39671e44			0.234190
$467$	−2.83937e45	−	2.83937e45i	−1.18805	−	1.18805i	−0.977606	−	0.210443i	$-0.932509\pi$
$467$	−2.83937e45	−	2.83937e45i	−1.18805	−	1.18805i	−0.210443	−	0.977606i	$-0.567491\pi$
$468$	9.40242e44	−	9.40242e44i	0.379368	−	0.379368i
$469$			1.35201e45i			0.526069i
$470$		0			0
$471$	2.87995e45			1.04239
$472$	1.28053e45	+	1.28053e45i	0.447070	+	0.447070i
$473$	1.18281e45	−	1.18281e45i	0.398358	−	0.398358i
$474$			1.48349e45i			0.482007i
$475$		0			0
$476$	−2.52627e44			−0.0764120
$477$	1.02435e45	+	1.02435e45i	0.298975	+	0.298975i
$478$	3.42204e45	−	3.42204e45i	0.963852	−	0.963852i
$479$		−	1.44109e45i		−	0.391730i	−0.980631	−	0.195865i	$-0.937249\pi$
$479$		−	1.44109e45i		−	0.391730i	0.980631	−	0.195865i	$-0.0627514\pi$
$480$		0			0
$481$	5.86937e45			1.48636
$482$	1.17334e45	+	1.17334e45i	0.286830	+	0.286830i
$483$	−1.28900e45	+	1.28900e45i	−0.304195	+	0.304195i
$484$			2.01332e44i			0.0458715i
$485$		0			0
$486$	−7.43111e45			−1.57847
$487$	2.28460e44	+	2.28460e44i	0.0468616	+	0.0468616i	0.730149	−	0.683288i	$-0.239451\pi$
$487$	2.28460e44	+	2.28460e44i	0.0468616	+	0.0468616i	−0.683288	+	0.730149i	$0.739451\pi$
$488$	−5.53334e45	+	5.53334e45i	−1.09610	+	1.09610i
$489$			8.83279e45i			1.68985i
$490$		0			0
$491$	−5.92591e44			−0.105772			−0.0528859	−	0.998601i	$-0.516842\pi$
$491$	−5.92591e44			−0.105772			−0.0528859	+	0.998601i	$0.516842\pi$
$492$	4.34107e44	+	4.34107e44i	0.0748497	+	0.0748497i
$493$	−7.54727e44	+	7.54727e44i	−0.125717	+	0.125717i
$494$			6.07543e45i			0.977729i
$495$		0			0
$496$	7.66500e45			1.15166
$497$	3.05349e45	+	3.05349e45i	0.443341	+	0.443341i
$498$	−5.56265e45	+	5.56265e45i	−0.780517	+	0.780517i
$499$			2.28620e45i			0.310031i	0.987912	+	0.155015i	$0.0495427\pi$
$499$			2.28620e45i			0.310031i	−0.987912	+	0.155015i	$0.950457\pi$
$500$		0			0
$501$	−1.49012e46			−1.88790
$502$	−4.72894e45	−	4.72894e45i	−0.579163	−	0.579163i
$503$	2.39993e45	−	2.39993e45i	0.284147	−	0.284147i	−0.550613	−	0.834761i	$-0.685606\pi$
$503$	2.39993e45	−	2.39993e45i	0.284147	−	0.284147i	0.834761	+	0.550613i	$0.185606\pi$
$504$			2.76032e46i			3.15966i
$505$		0			0
$506$	−1.34962e45			−0.144428
$507$	−1.44832e46	−	1.44832e46i	−1.49875	−	1.49875i
$508$	−1.83074e45	+	1.83074e45i	−0.183208	+	0.183208i
$509$		−	1.59596e46i		−	1.54461i	−0.635250	−	0.772306i	$-0.719103\pi$
$509$		−	1.59596e46i		−	1.54461i	0.635250	−	0.772306i	$-0.280897\pi$
$510$		0			0
$511$	−1.91853e46			−1.73705
$512$	−9.07188e45	−	9.07188e45i	−0.794525	−	0.794525i
$513$	−1.54695e46	+	1.54695e46i	−1.31063	+	1.31063i
$514$		−	1.79952e46i		−	1.47497i
$515$		0			0
$516$	2.47256e45			0.189715
$517$	−3.86082e45	−	3.86082e45i	−0.286642	−	0.286642i
$518$	−1.14366e46	+	1.14366e46i	−0.821659	+	0.821659i
$519$		−	2.89278e46i		−	2.01127i
$520$		0			0
$521$	2.30990e46			1.50436			0.752180	−	0.658957i	$-0.229002\pi$
$521$	2.30990e46			1.50436			0.752180	+	0.658957i	$0.229002\pi$
$522$	1.09468e46	+	1.09468e46i	0.690062	+	0.690062i
$523$	2.19496e46	−	2.19496e46i	1.33936	−	1.33936i	0.442683	−	0.896678i	$-0.354027\pi$
$523$	2.19496e46	−	2.19496e46i	1.33936	−	1.33936i	0.896678	−	0.442683i	$-0.145973\pi$
$524$		−	3.56020e45i		−	0.210302i
$525$		0			0
$526$	−3.16100e46			−1.75011
$527$	7.39120e45	+	7.39120e45i	0.396219	+	0.396219i
$528$	−1.72847e46	+	1.72847e46i	−0.897194	+	0.897194i
$529$			1.91954e46i			0.964831i
$530$		0			0
$531$	3.02053e46			1.42389
$532$	2.13944e45	+	2.13944e45i	0.0976794	+	0.0976794i
$533$	8.80921e45	−	8.80921e45i	0.389560	−	0.389560i
$534$		−	1.35629e46i		−	0.580966i
$535$		0			0
$536$	−1.11461e46			−0.448047
$537$	1.63096e46	+	1.63096e46i	0.635156	+	0.635156i
$538$	2.60039e46	−	2.60039e46i	0.981159	−	0.981159i
$539$		−	1.26440e46i		−	0.462248i
$540$		0			0
$541$	−3.79707e46			−1.30345			−0.651726	−	0.758454i	$-0.725955\pi$
$541$	−3.79707e46			−1.30345			−0.651726	+	0.758454i	$0.725955\pi$
$542$	−1.63755e46	−	1.63755e46i	−0.544761	−	0.544761i
$543$	−2.36889e46	+	2.36889e46i	−0.763743	+	0.763743i
$544$		−	3.88891e45i		−	0.121520i
$545$		0			0
$546$	1.05470e47			3.09637
$547$	−1.84073e46	−	1.84073e46i	−0.523849	−	0.523849i	0.394883	−	0.918732i	$-0.370785\pi$
$547$	−1.84073e46	−	1.84073e46i	−0.523849	−	0.523849i	−0.918732	+	0.394883i	$0.870785\pi$
$548$	1.46942e45	−	1.46942e45i	0.0405392	−	0.0405392i
$549$			1.30521e47i			3.49101i
$550$		0			0
$551$	1.27833e46			0.321414
$552$	−1.06267e46	−	1.06267e46i	−0.259079	−	0.259079i
$553$	1.06011e46	−	1.06011e46i	0.250624	−	0.250624i
$554$		−	4.53072e46i		−	1.03873i
$555$		0			0
$556$	7.21855e45			0.155660
$557$	−2.22516e46	−	2.22516e46i	−0.465396	−	0.465396i	0.435023	−	0.900419i	$-0.356740\pi$
$557$	−2.22516e46	−	2.22516e46i	−0.465396	−	0.465396i	−0.900419	+	0.435023i	$0.856740\pi$
$558$	1.07204e47	−	1.07204e47i	2.17485	−	2.17485i
$559$		−	5.01749e46i		−	0.987383i
$560$		0			0
$561$	−3.33347e46			−0.617344
$562$	8.37414e45	+	8.37414e45i	0.150461	+	0.150461i
$563$	2.08546e46	−	2.08546e46i	0.363546	−	0.363546i	−0.501571	−	0.865117i	$-0.667244\pi$
$563$	2.08546e46	−	2.08546e46i	0.363546	−	0.363546i	0.865117	+	0.501571i	$0.167244\pi$
$564$		−	8.07071e45i		−	0.136511i
$565$		0			0
$566$	9.34253e46			1.48794
$567$	1.32326e47	+	1.32326e47i	2.04519	+	2.04519i
$568$	−2.51733e46	+	2.51733e46i	−0.377588	+	0.377588i
$569$			5.30670e46i			0.772531i	0.922388	+	0.386266i	$0.126235\pi$
$569$			5.30670e46i			0.772531i	−0.922388	+	0.386266i	$0.873765\pi$
$570$		0			0
$571$	−4.33016e44			−0.00593868			−0.00296934	−	0.999996i	$-0.500945\pi$
$571$	−4.33016e44			−0.00593868			−0.00296934	+	0.999996i	$0.500945\pi$
$572$	−9.97868e45	−	9.97868e45i	−0.132844	−	0.132844i
$573$	−1.20515e47	+	1.20515e47i	−1.55745	+	1.55745i
$574$			3.43299e46i			0.430696i
$575$		0			0
$576$	−2.22829e47			−2.63506
$577$	6.15680e46	+	6.15680e46i	0.706914	+	0.706914i	0.965885	−	0.258971i	$-0.0833835\pi$
$577$	6.15680e46	+	6.15680e46i	0.706914	+	0.706914i	−0.258971	+	0.965885i	$0.583384\pi$
$578$	4.89985e46	−	4.89985e46i	0.546273	−	0.546273i
$579$		−	2.12943e47i		−	2.30530i
$580$		0			0
$581$	7.95016e46			0.811674
$582$	1.59198e47	+	1.59198e47i	1.57850	+	1.57850i
$583$	1.08713e46	−	1.08713e46i	0.104692	−	0.104692i
$584$		−	1.58165e47i		−	1.47943i
$585$		0			0
$586$	6.99560e46			0.617398
$587$	−1.55255e47	−	1.55255e47i	−1.33106	−	1.33106i	−0.904422	−	0.426640i	$-0.859697\pi$
$587$	−1.55255e47	−	1.55255e47i	−1.33106	−	1.33106i	−0.426640	−	0.904422i	$-0.640303\pi$
$588$	1.32156e46	−	1.32156e46i	0.110071	−	0.110071i
$589$		−	1.25189e47i		−	1.01299i
$590$		0			0
$591$	−3.01980e47			−2.30670
$592$	−7.95071e46	−	7.95071e46i	−0.590115	−	0.590115i
$593$	1.17644e47	−	1.17644e47i	0.848479	−	0.848479i	−0.141464	−	0.989943i	$-0.545181\pi$
$593$	1.17644e47	−	1.17644e47i	0.848479	−	0.848479i	0.989943	+	0.141464i	$0.0451811\pi$
$594$			2.81181e47i			1.97068i
$595$		0			0
$596$	−1.19289e46			−0.0789611
$597$	−9.32099e46	−	9.32099e46i	−0.599651	−	0.599651i
$598$	−2.86256e46	+	2.86256e46i	−0.178992	+	0.178992i
$599$			2.87592e47i			1.74792i	0.486001	+	0.873958i	$0.338455\pi$
$599$			2.87592e47i			1.74792i	−0.486001	+	0.873958i	$0.661545\pi$
$600$		0			0
$601$	−9.48352e45			−0.0544632			−0.0272316	−	0.999629i	$-0.508669\pi$
$601$	−9.48352e45			−0.0544632			−0.0272316	+	0.999629i	$0.508669\pi$
$602$	9.77671e46	+	9.77671e46i	0.545823	+	0.545823i
$603$	−1.31458e47	+	1.31458e47i	−0.713500	+	0.713500i
$604$			9.45697e45i			0.0499027i
$605$		0			0
$606$	5.16915e47			2.57860
$607$	−9.65121e45	−	9.65121e45i	−0.0468138	−	0.0468138i	0.683312	−	0.730126i	$-0.260539\pi$
$607$	−9.65121e45	−	9.65121e45i	−0.0468138	−	0.0468138i	−0.730126	+	0.683312i	$0.760539\pi$
$608$	−3.29343e46	+	3.29343e46i	−0.155342	+	0.155342i
$609$		−	2.21918e47i		−	1.01788i
$610$		0			0
$611$	−1.63777e47			−0.710480
$612$	−2.45633e46	−	2.45633e46i	−0.103637	−	0.103637i
$613$	9.88922e46	−	9.88922e46i	0.405820	−	0.405820i	−0.474458	−	0.880278i	$-0.657356\pi$
$613$	9.88922e46	−	9.88922e46i	0.405820	−	0.405820i	0.880278	+	0.474458i	$0.157356\pi$
$614$		−	4.03565e47i		−	1.61084i
$615$		0			0
$616$	2.92950e47			1.10642
$617$	−8.59582e46	−	8.59582e46i	−0.315820	−	0.315820i	0.531339	−	0.847159i	$-0.321689\pi$
$617$	−8.59582e46	−	8.59582e46i	−0.315820	−	0.315820i	−0.847159	+	0.531339i	$0.821689\pi$
$618$	1.34510e47	−	1.34510e47i	0.480783	−	0.480783i
$619$			4.62891e46i			0.160967i	0.996756	+	0.0804836i	$0.0256465\pi$
$619$			4.62891e46i			0.160967i	−0.996756	+	0.0804836i	$0.974354\pi$
$620$		0			0
$621$	−1.45775e47			−0.479873
$622$	−1.95227e47	−	1.95227e47i	−0.625321	−	0.625321i
$623$	−9.69207e46	+	9.69207e46i	−0.302079	+	0.302079i
$624$			7.33223e47i			2.22381i
$625$		0			0
$626$	−2.33151e47			−0.669690
$627$	2.82304e47	+	2.82304e47i	0.789167	+	0.789167i
$628$	2.25221e46	−	2.25221e46i	0.0612767	−	0.0612767i
$629$		−	1.53334e47i		−	0.406048i
$630$		0			0
$631$	6.32322e47			1.58650			0.793248	−	0.608899i	$-0.208388\pi$
$631$	6.32322e47			1.58650			0.793248	+	0.608899i	$0.208388\pi$
$632$	8.73965e46	+	8.73965e46i	0.213454	+	0.213454i
$633$	5.01513e47	−	5.01513e47i	1.19239	−	1.19239i
$634$		−	7.37565e47i		−	1.70719i
$635$		0			0
$636$	2.27255e46			0.0498589
$637$	−2.68180e47	−	2.68180e47i	−0.572871	−	0.572871i
$638$	1.16177e47	−	1.16177e47i	0.241640	−	0.241640i
$639$			5.93791e47i			1.20259i
$640$		0			0
$641$	1.86014e47			0.357240			0.178620	−	0.983918i	$-0.442837\pi$
$641$	1.86014e47			0.357240			0.178620	+	0.983918i	$0.442837\pi$
$642$	3.24514e46	+	3.24514e46i	0.0606928	+	0.0606928i
$643$	−5.29874e47	+	5.29874e47i	−0.965130	+	0.965130i	−0.999412	−	0.0342822i	$-0.989086\pi$
$643$	−5.29874e47	+	5.29874e47i	−0.965130	+	0.965130i	0.0342822	+	0.999412i	$0.489086\pi$
$644$			2.01608e46i			0.0357642i
$645$		0			0
$646$	1.58717e47			0.267099
$647$	4.85584e47	+	4.85584e47i	0.795961	+	0.795961i	0.982456	−	0.186495i	$-0.0597129\pi$
$647$	4.85584e47	+	4.85584e47i	0.795961	+	0.795961i	−0.186495	+	0.982456i	$0.559713\pi$
$648$	−1.09091e48	+	1.09091e48i	−1.74186	+	1.74186i
$649$		−	3.20566e47i		−	0.498605i
$650$		0			0
$651$	−2.17329e48			−3.20805
$652$	6.90753e46	+	6.90753e46i	0.0993375	+	0.0993375i
$653$	−5.22981e47	+	5.22981e47i	−0.732760	+	0.732760i	−0.971166	−	0.238406i	$-0.923375\pi$
$653$	−5.22981e47	+	5.22981e47i	−0.732760	+	0.732760i	0.238406	+	0.971166i	$0.423375\pi$
$654$			1.54779e48i			2.11296i
$655$		0			0
$656$	−2.38661e47			−0.309326
$657$	−1.86541e48	−	1.86541e48i	−2.35594	−	2.35594i
$658$	3.19123e47	−	3.19123e47i	0.392752	−	0.392752i
$659$		−	9.74805e47i		−	1.16914i	−0.811344	−	0.584569i	$-0.801264\pi$
$659$		−	9.74805e47i		−	1.16914i	0.811344	−	0.584569i	$-0.198736\pi$
$660$		0			0
$661$	1.14821e48			1.30796			0.653980	−	0.756511i	$-0.273098\pi$
$661$	1.14821e48			1.30796			0.653980	+	0.756511i	$0.273098\pi$
$662$	−1.05932e47	−	1.05932e47i	−0.117609	−	0.117609i
$663$	−7.07032e47	+	7.07032e47i	−0.765084	+	0.765084i
$664$			6.55420e47i			0.691293i
$665$		0			0
$666$	−2.22400e48			−2.22881
$667$	6.02308e46	+	6.02308e46i	0.0588409	+	0.0588409i
$668$	−1.16532e47	+	1.16532e47i	−0.110980	+	0.110980i
$669$			2.74501e48i			2.54859i
$670$		0			0
$671$	1.38521e48			1.22245
$672$	5.71742e47	+	5.71742e47i	0.491951	+	0.491951i
$673$	6.66267e47	−	6.66267e47i	0.558974	−	0.558974i	−0.370041	−	0.929015i	$-0.620656\pi$
$673$	6.66267e47	−	6.66267e47i	0.558974	−	0.558974i	0.929015	+	0.370041i	$0.120656\pi$
$674$		−	1.09283e48i		−	0.893994i
$675$		0			0
$676$	−2.26526e47			−0.176208
$677$	−5.90123e47	−	5.90123e47i	−0.447647	−	0.447647i	0.446925	−	0.894572i	$-0.352519\pi$
$677$	−5.90123e47	−	5.90123e47i	−0.447647	−	0.447647i	−0.894572	+	0.446925i	$0.852519\pi$
$678$	−1.59265e48	+	1.59265e48i	−1.17819	+	1.17819i
$679$		−	2.27526e48i		−	1.64151i
$680$		0			0
$681$	−2.52346e48			−1.73179
$682$	−1.13775e48	−	1.13775e48i	−0.761572	−	0.761572i
$683$	7.59213e47	−	7.59213e47i	0.495692	−	0.495692i	−0.414402	−	0.910094i	$-0.636009\pi$
$683$	7.59213e47	−	7.59213e47i	0.495692	−	0.495692i	0.910094	+	0.414402i	$0.136009\pi$
$684$			4.16043e47i			0.264963i
$685$		0			0
$686$	−8.46940e47			−0.513266
$687$	3.81219e48	+	3.81219e48i	2.25377	+	2.25377i
$688$	−6.79674e47	+	6.79674e47i	−0.392010	+	0.392010i
$689$		−	4.61162e47i		−	0.259494i
$690$		0			0
$691$	1.92933e48			1.03343			0.516713	−	0.856159i	$-0.327155\pi$
$691$	1.92933e48			1.03343			0.516713	+	0.856159i	$0.327155\pi$
$692$	−2.26225e47	−	2.26225e47i	−0.118232	−	0.118232i
$693$	3.45507e48	−	3.45507e48i	1.76194	−	1.76194i
$694$			2.11273e48i			1.05132i
$695$		0			0
$696$	1.82952e48			0.866921
$697$	−2.30136e47	−	2.30136e47i	−0.106421	−	0.106421i
$698$	6.87828e47	−	6.87828e47i	0.310412	−	0.310412i
$699$		−	1.06376e48i		−	0.468523i
$700$		0			0
$701$	1.70540e48			0.715518			0.357759	−	0.933814i	$-0.383541\pi$
$701$	1.70540e48			0.715518			0.357759	+	0.933814i	$0.383541\pi$
$702$	5.96387e48	+	5.96387e48i	2.44229	+	2.44229i
$703$	−1.29855e48	+	1.29855e48i	−0.519062	+	0.519062i
$704$			2.36486e48i			0.922722i
$705$		0			0
$706$	4.10585e48			1.52659
$707$	−3.69388e48	−	3.69388e48i	−1.34077	−	1.34077i
$708$	3.35058e47	−	3.35058e47i	0.118728	−	0.118728i
$709$		−	2.98436e48i		−	1.03244i	−0.856456	−	0.516220i	$-0.827339\pi$
$709$		−	2.98436e48i		−	1.03244i	0.856456	−	0.516220i	$-0.172661\pi$
$710$		0			0
$711$	2.06152e48			0.679836
$712$	−7.99026e47	−	7.99026e47i	−0.257277	−	0.257277i
$713$	5.89853e47	−	5.89853e47i	0.185448	−	0.185448i
$714$		−	2.75534e48i		−	0.845874i
$715$		0			0
$716$	2.55092e47			0.0746752
$717$	−6.74526e48	−	6.74526e48i	−1.92829	−	1.92829i
$718$	2.39975e47	−	2.39975e47i	0.0669963	−	0.0669963i
$719$		−	3.29072e48i		−	0.897221i	−0.893727	−	0.448610i	$-0.851919\pi$
$719$		−	3.29072e48i		−	0.897221i	0.893727	−	0.448610i	$-0.148081\pi$
$720$		0			0
$721$	−1.92242e48			−0.499975
$722$	1.21764e48	+	1.21764e48i	0.309306	+	0.309306i
$723$	2.31280e48	−	2.31280e48i	0.573835	−	0.573835i
$724$			3.70509e47i			0.0897932i
$725$		0			0
$726$	−2.19589e48			−0.507793
$727$	1.41242e48	+	1.41242e48i	0.319065	+	0.319065i	0.848408	−	0.529343i	$-0.177561\pi$
$727$	1.41242e48	+	1.41242e48i	0.319065	+	0.319065i	−0.529343	+	0.848408i	$0.677561\pi$
$728$	6.21350e48	−	6.21350e48i	1.37121	−	1.37121i
$729$			3.88004e48i			0.836504i
$730$		0			0
$731$	−1.31079e48			−0.269736
$732$	1.44783e48	+	1.44783e48i	0.291091	+	0.291091i
$733$	3.04904e48	−	3.04904e48i	0.598958	−	0.598958i	−0.341078	−	0.940035i	$-0.610792\pi$
$733$	3.04904e48	−	3.04904e48i	0.598958	−	0.598958i	0.940035	+	0.341078i	$0.110792\pi$
$734$		−	1.16792e48i		−	0.224172i
$735$		0			0
$736$	−3.10353e47			−0.0568765
$737$	1.39515e48	+	1.39515e48i	0.249847	+	0.249847i
$738$	−3.33796e48	+	3.33796e48i	−0.584148	+	0.584148i
$739$			2.98474e47i			0.0510448i	0.999674	+	0.0255224i	$0.00812491\pi$
$739$			2.98474e47i			0.0510448i	−0.999674	+	0.0255224i	$0.991875\pi$
$740$		0			0
$741$	1.19754e49			1.95605
$742$	8.98587e47	+	8.98587e47i	0.143448	+	0.143448i
$743$	−2.06291e48	+	2.06291e48i	−0.321863	+	0.321863i	−0.849482	−	0.527618i	$-0.823085\pi$
$743$	−2.06291e48	+	2.06291e48i	−0.321863	+	0.321863i	0.527618	+	0.849482i	$0.323085\pi$
$744$		−	1.79168e49i		−	2.73226i
$745$		0			0
$746$	−4.32772e48			−0.630520
$747$	7.73007e48	+	7.73007e48i	1.10086	+	1.10086i
$748$	−2.60688e47	+	2.60688e47i	−0.0362906	+	0.0362906i
$749$		−	4.63796e47i		−	0.0631155i
$750$		0			0
$751$	−1.26606e49			−1.64656			−0.823279	−	0.567637i	$-0.807858\pi$
$751$	−1.26606e49			−1.64656			−0.823279	+	0.567637i	$0.807858\pi$
$752$	2.21854e48	+	2.21854e48i	0.282074	+	0.282074i
$753$	−9.32133e48	+	9.32133e48i	−1.15868	+	1.15868i
$754$		−	4.92825e48i		−	0.598936i
$755$		0			0
$756$	4.20032e48			0.487991
$757$	2.96983e48	+	2.96983e48i	0.337367	+	0.337367i	0.855375	−	0.518009i	$-0.173327\pi$
$757$	2.96983e48	+	2.96983e48i	0.337367	+	0.337367i	−0.518009	+	0.855375i	$0.673327\pi$
$758$	8.59628e47	−	8.59628e47i	0.0954848	−	0.0954848i
$759$			2.66026e48i			0.288944i
$760$		0			0
$761$	3.79918e48			0.394594			0.197297	−	0.980344i	$-0.436784\pi$
$761$	3.79918e48			0.394594			0.197297	+	0.980344i	$0.436784\pi$
$762$	−1.99675e49	−	1.99675e49i	−2.02810	−	2.02810i
$763$	1.10606e49	−	1.10606e49i	1.09865	−	1.09865i
$764$			1.88494e48i			0.183109i
$765$		0			0
$766$	−9.76922e48			−0.907759
$767$	−6.79923e48	−	6.79923e48i	−0.617929	−	0.617929i
$768$	−6.55959e48	+	6.55959e48i	−0.583090	+	0.583090i
$769$			5.40314e48i			0.469785i	0.972021	+	0.234892i	$0.0754737\pi$
$769$			5.40314e48i			0.469785i	−0.972021	+	0.234892i	$0.924526\pi$
$770$		0			0
$771$	−3.54708e49			−2.95084
$772$	−1.66528e48	−	1.66528e48i	−0.135517	−	0.135517i
$773$	−5.25200e48	+	5.25200e48i	−0.418093	+	0.418093i	−0.884546	−	0.466453i	$-0.845532\pi$
$773$	−5.25200e48	+	5.25200e48i	−0.418093	+	0.418093i	0.466453	+	0.884546i	$0.345532\pi$
$774$			1.90121e49i			1.48059i
$775$		0			0
$776$	1.87575e49			1.39806
$777$	2.25430e49	+	2.25430e49i	1.64382	+	1.64382i
$778$	−1.20727e49	+	1.20727e49i	−0.861294	+	0.861294i
$779$			3.89794e48i			0.272081i
$780$		0			0
$781$	6.30184e48			0.421114
$782$	7.47828e47	+	7.47828e47i	0.0488975	+	0.0488975i
$783$	1.25485e49	−	1.25485e49i	0.802866	−	0.802866i
$784$			7.26560e48i			0.454881i
$785$		0			0
$786$	3.88303e49			2.32802
$787$	8.12455e46	+	8.12455e46i	0.00476682	+	0.00476682i	0.709486	−	0.704719i	$-0.248927\pi$
$787$	8.12455e46	+	8.12455e46i	0.00476682	+	0.00476682i	−0.704719	+	0.709486i	$0.748927\pi$
$788$	−2.36158e48	+	2.36158e48i	−0.135599	+	0.135599i
$789$			6.23072e49i			3.50130i
$790$		0			0
$791$	2.27622e49			1.22522
$792$	2.84840e49	+	2.84840e49i	1.50063	+	1.50063i
$793$	2.93804e49	−	2.93804e49i	1.51500	−	1.51500i
$794$		−	2.15679e49i		−	1.08858i
$795$		0			0
$796$	−1.45786e48			−0.0705009
$797$	−1.01208e49	−	1.01208e49i	−0.479098	−	0.479098i	0.425745	−	0.904843i	$-0.360012\pi$
$797$	−1.01208e49	−	1.01208e49i	−0.479098	−	0.479098i	−0.904843	+	0.425745i	$0.860012\pi$
$798$	−2.33344e49	+	2.33344e49i	−1.08130	+	1.08130i
$799$			4.27858e48i			0.194091i
$800$		0			0
$801$	−1.88475e49			−0.819411
$802$	−1.88513e49	−	1.88513e49i	−0.802373	−	0.802373i
$803$	−1.97974e49	+	1.97974e49i	−0.824982	+	0.824982i
$804$			2.91645e48i			0.118988i
$805$		0			0
$806$	−4.82634e49			−1.88765
$807$	−5.12568e49	−	5.12568e49i	−1.96292	−	1.96292i
$808$	3.04528e49	−	3.04528e49i	1.14192	−	1.14192i
$809$		−	1.75446e49i		−	0.644198i	−0.946706	−	0.322099i	$-0.895612\pi$
$809$		−	1.75446e49i		−	0.644198i	0.946706	−	0.322099i	$-0.104388\pi$
$810$		0			0
$811$	3.94617e48			0.138938			0.0694691	−	0.997584i	$-0.477869\pi$
$811$	3.94617e48			0.138938			0.0694691	+	0.997584i	$0.477869\pi$
$812$	−1.73547e48	−	1.73547e48i	−0.0598363	−	0.0598363i
$813$	−3.22781e49	+	3.22781e49i	−1.08985	+	1.08985i
$814$			2.36031e49i			0.780466i
$815$		0			0
$816$	1.91551e49			0.607507
$817$	1.11008e49	+	1.11008e49i	0.344810	+	0.344810i
$818$	−3.20628e49	+	3.20628e49i	−0.975428	+	0.975428i
$819$		−	1.46565e50i		−	4.36721i
$820$		0			0
$821$	−5.27119e49			−1.50687			−0.753434	−	0.657524i	$-0.771604\pi$
$821$	−5.27119e49			−1.50687			−0.753434	+	0.657524i	$0.771604\pi$
$822$	1.60266e49	+	1.60266e49i	0.448766	+	0.448766i
$823$	−1.19020e49	+	1.19020e49i	−0.326454	+	0.326454i	−0.851236	−	0.524783i	$-0.824147\pi$
$823$	−1.19020e49	+	1.19020e49i	−0.326454	+	0.326454i	0.524783	+	0.851236i	$0.324147\pi$
$824$		−	1.58486e49i		−	0.425823i
$825$		0			0
$826$	2.64970e49			0.683180
$827$	−2.47455e49	−	2.47455e49i	−0.625032	−	0.625032i	0.321782	−	0.946814i	$-0.395718\pi$
$827$	−2.47455e49	−	2.47455e49i	−0.625032	−	0.625032i	−0.946814	+	0.321782i	$0.895718\pi$
$828$	−1.96027e48	+	1.96027e48i	−0.0485065	+	0.0485065i
$829$			3.49190e49i			0.846515i	0.906009	+	0.423257i	$0.139113\pi$
$829$			3.49190e49i			0.846515i	−0.906009	+	0.423257i	$0.860887\pi$
$830$		0			0
$831$	−8.93060e49			−2.07808
$832$	5.01590e49	+	5.01590e49i	1.14354	+	1.14354i
$833$	−7.00607e48	+	7.00607e48i	−0.156498	+	0.156498i
$834$			7.87310e49i			1.72315i
$835$		0			0
$836$	4.41542e48			0.0927823
$837$	−1.22890e50	−	1.22890e50i	−2.53038	−	2.53038i
$838$	−1.58319e49	+	1.58319e49i	−0.319436	+	0.319436i
$839$			5.57906e49i			1.10308i	0.834148	+	0.551541i	$0.185960\pi$
$839$			5.57906e49i			1.10308i	−0.834148	+	0.551541i	$0.814040\pi$
$840$		0			0
$841$	4.22967e49			0.803109
$842$	3.56068e49	+	3.56068e49i	0.662563	+	0.662563i
$843$	1.65065e49	−	1.65065e49i	0.301013	−	0.301013i
$844$		−	7.84398e48i		−	0.140189i
$845$		0			0
$846$	6.20578e49			1.06537
$847$	1.56918e49	+	1.56918e49i	0.264032	+	0.264032i
$848$	−6.24695e48	+	6.24695e48i	−0.103024	+	0.103024i
$849$		−	1.84153e50i		−	2.97678i
$850$		0			0
$851$	−1.22368e49			−0.190049
$852$	6.58673e48	+	6.58673e48i	0.100276	+	0.100276i
$853$	1.56661e49	−	1.56661e49i	0.233791	−	0.233791i	−0.580482	−	0.814273i	$-0.697136\pi$
$853$	1.56661e49	−	1.56661e49i	0.233791	−	0.233791i	0.814273	+	0.580482i	$0.197136\pi$
$854$			1.14497e50i			1.67498i
$855$		0			0
$856$	3.82359e48			0.0537548
$857$	2.76522e49	+	2.76522e49i	0.381115	+	0.381115i	0.871504	−	0.490389i	$-0.163145\pi$
$857$	2.76522e49	+	2.76522e49i	0.381115	+	0.381115i	−0.490389	+	0.871504i	$0.663145\pi$
$858$	1.08835e50	−	1.08835e50i	1.47057	−	1.47057i
$859$		−	1.47603e48i		−	0.0195529i	−0.999952	−	0.00977645i	$-0.996888\pi$
$859$		−	1.47603e48i		−	0.0195529i	0.999952	−	0.00977645i	$-0.00311199\pi$
$860$		0			0
$861$	6.76685e49			0.861655
$862$	3.61318e49	+	3.61318e49i	0.451093	+	0.451093i
$863$	−2.79334e49	+	2.79334e49i	−0.341932	+	0.341932i	−0.857093	−	0.515161i	$-0.827732\pi$
$863$	−2.79334e49	+	2.79334e49i	−0.341932	+	0.341932i	0.515161	+	0.857093i	$0.327732\pi$
$864$			6.46592e49i			0.776062i
$865$		0			0
$866$	2.41660e49			0.278869
$867$	−9.65821e49	−	9.65821e49i	−1.09288	−	1.09288i
$868$	−1.69958e49	+	1.69958e49i	−0.188585	+	0.188585i
$869$		−	2.18787e49i		−	0.238059i
$870$		0			0
$871$	5.91828e49			0.619279
$872$	9.11845e49	+	9.11845e49i	0.935709	+	0.935709i
$873$	2.21227e50	−	2.21227e50i	2.22636	−	2.22636i
$874$		−	1.26664e49i		−	0.125014i
$875$		0			0
$876$	−4.13849e49			−0.392891
$877$	5.00262e49	+	5.00262e49i	0.465806	+	0.465806i	0.900553	−	0.434747i	$-0.143162\pi$
$877$	5.00262e49	+	5.00262e49i	0.465806	+	0.465806i	−0.434747	+	0.900553i	$0.643162\pi$
$878$	5.35867e49	−	5.35867e49i	0.489384	−	0.489384i
$879$		−	1.37892e50i		−	1.23517i
$880$		0			0
$881$	−1.73655e50			−1.49657			−0.748283	−	0.663380i	$-0.769121\pi$
$881$	−1.73655e50			−1.49657			−0.748283	+	0.663380i	$0.769121\pi$
$882$	1.01618e50	+	1.01618e50i	0.859023	+	0.859023i
$883$	−1.11469e50	+	1.11469e50i	−0.924321	+	0.924321i	−0.997331	−	0.0730104i	$-0.976739\pi$
$883$	−1.11469e50	+	1.11469e50i	−0.924321	+	0.924321i	0.0730104	+	0.997331i	$0.476739\pi$
$884$			1.10584e49i			0.0899509i
$885$		0			0
$886$	1.47185e50			1.15210
$887$	6.57423e49	+	6.57423e49i	0.504828	+	0.504828i	0.912934	−	0.408106i	$-0.133811\pi$
$887$	6.57423e49	+	6.57423e49i	0.504828	+	0.504828i	−0.408106	+	0.912934i	$0.633811\pi$
$888$	−1.85847e50	+	1.85847e50i	−1.40002	+	1.40002i
$889$			2.85376e50i			2.10906i
$890$		0			0
$891$	2.73097e50			1.94265
$892$	2.14669e49	+	2.14669e49i	0.149819	+	0.149819i
$893$	3.62344e49	−	3.62344e49i	0.248111	−	0.248111i
$894$		−	1.30105e50i		−	0.874093i
$895$		0			0
$896$	−1.37049e50			−0.886422
$897$	5.64245e49	+	5.64245e49i	0.358093	+	0.358093i
$898$	−9.60507e49	+	9.60507e49i	−0.598140	+	0.598140i
$899$			1.01551e50i			0.620538i
$900$		0			0
$901$	−1.20476e49			−0.0708892
$902$	3.54254e49	+	3.54254e49i	0.204552	+	0.204552i
$903$	1.92711e50	−	1.92711e50i	1.09198	−	1.09198i
$904$			1.87654e50i			1.04350i
$905$		0			0
$906$	−1.03145e50			−0.552419
$907$	3.18252e49	+	3.18252e49i	0.167281	+	0.167281i	0.785783	−	0.618502i	$-0.212260\pi$
$907$	3.18252e49	+	3.18252e49i	0.167281	+	0.167281i	−0.618502	+	0.785783i	$0.712260\pi$
$908$	−1.97343e49	+	1.97343e49i	−0.101803	+	0.101803i
$909$		−	7.18325e50i		−	3.63693i
$910$		0			0
$911$	−1.16089e50			−0.566212			−0.283106	−	0.959089i	$-0.591365\pi$
$911$	−1.16089e50			−0.566212			−0.283106	+	0.959089i	$0.591365\pi$
$912$	−1.62220e50	−	1.62220e50i	−0.776592	−	0.776592i
$913$	8.20384e49	−	8.20384e49i	0.385491	−	0.385491i
$914$			3.95596e49i			0.182460i
$915$		0			0
$916$	5.96251e49			0.264976
$917$	−2.77482e50	−	2.77482e50i	−1.21048	−	1.21048i
$918$	1.55803e50	−	1.55803e50i	0.667191	−	0.667191i
$919$			3.83346e48i			0.0161149i	0.999968	+	0.00805745i	$0.00256479\pi$
$919$			3.83346e48i			0.0161149i	−0.999968	+	0.00805745i	$0.997435\pi$
$920$		0			0
$921$	−7.95477e50			−3.22265
$922$	−1.62639e49	−	1.62639e49i	−0.0646845	−	0.0646845i
$923$	1.33663e50	−	1.33663e50i	0.521893	−	0.521893i
$924$		−	7.66519e49i		−	0.293832i
$925$		0			0
$926$	9.15124e49			0.338137
$927$	−1.86920e50	−	1.86920e50i	−0.678110	−	0.678110i
$928$	2.67156e49	−	2.67156e49i	0.0951589	−	0.0951589i
$929$		−	2.38164e50i		−	0.832931i	−0.909151	−	0.416466i	$-0.863269\pi$
$929$		−	2.38164e50i		−	0.832931i	0.909151	−	0.416466i	$-0.136731\pi$
$930$		0			0
$931$	1.18666e50			0.400112
$932$	−8.31893e48	−	8.31893e48i	−0.0275421	−	0.0275421i
$933$	−3.84816e50	+	3.84816e50i	−1.25102	+	1.25102i
$934$		−	4.84364e50i		−	1.54623i
$935$		0			0
$936$	1.20830e51			3.71950
$937$	2.21104e50	+	2.21104e50i	0.668379	+	0.668379i	0.957341	−	0.288962i	$-0.0933100\pi$
$937$	2.21104e50	+	2.21104e50i	0.668379	+	0.668379i	−0.288962	+	0.957341i	$0.593310\pi$
$938$	−1.15319e50	+	1.15319e50i	−0.342336	+	0.342336i
$939$			4.59569e50i			1.33979i
$940$		0			0
$941$	3.91033e50			1.09949			0.549743	−	0.835334i	$-0.314725\pi$
$941$	3.91033e50			1.09949			0.549743	+	0.835334i	$0.314725\pi$
$942$	2.45644e50	+	2.45644e50i	0.678328	+	0.678328i
$943$	−1.83659e49	+	1.83659e49i	−0.0498097	+	0.0498097i
$944$			1.84206e50i			0.490660i
$945$		0			0
$946$	2.01773e50			0.518459
$947$	−1.89974e50	−	1.89974e50i	−0.479452	−	0.479452i	0.425504	−	0.904956i	$-0.360097\pi$
$947$	−1.89974e50	−	1.89974e50i	−0.479452	−	0.479452i	−0.904956	+	0.425504i	$0.860097\pi$
$948$	2.28678e49	−	2.28678e49i	0.0566868	−	0.0566868i
$949$			8.39812e50i			2.04483i
$950$		0			0
$951$	−1.45383e51			−3.41543
$952$	−1.62324e50	−	1.62324e50i	−0.374590	−	0.374590i
$953$	−3.09042e50	+	3.09042e50i	−0.700548	+	0.700548i	−0.964528	−	0.263980i	$-0.914965\pi$
$953$	−3.09042e50	+	3.09042e50i	−0.700548	+	0.700548i	0.263980	+	0.964528i	$0.414965\pi$
$954$			1.74742e50i			0.389113i
$955$		0			0
$956$	−1.05500e50			−0.226709
$957$	−2.28999e50	−	2.28999e50i	−0.483427	−	0.483427i
$958$	1.22917e50	−	1.22917e50i	0.254916	−	0.254916i
$959$		−	2.29052e50i		−	0.466679i
$960$		0			0
$961$	4.85999e50			0.955736
$962$	5.00624e50	+	5.00624e50i	0.967243	+	0.967243i
$963$	4.50957e49	−	4.50957e49i	0.0856028	−	0.0856028i
$964$		−	3.61737e49i		−	0.0674658i
$965$		0			0
$966$	−2.19889e50			−0.395907
$967$	−3.71546e50	−	3.71546e50i	−0.657298	−	0.657298i	0.297442	−	0.954740i	$-0.403867\pi$
$967$	−3.71546e50	−	3.71546e50i	−0.657298	−	0.657298i	−0.954740	+	0.297442i	$0.903867\pi$
$968$	−1.29365e50	+	1.29365e50i	−0.224873	+	0.224873i
$969$		−	3.12851e50i		−	0.534360i
$970$		0			0
$971$	−2.46011e50			−0.405721			−0.202860	−	0.979208i	$-0.565024\pi$
$971$	−2.46011e50			−0.405721			−0.202860	+	0.979208i	$0.565024\pi$
$972$	1.14549e50	+	1.14549e50i	0.185637	+	0.185637i
$973$	5.62613e50	−	5.62613e50i	0.895966	−	0.895966i
$974$			3.89727e49i			0.0609899i
$975$		0			0
$976$	−7.95980e50			−1.20297
$977$	3.70268e50	+	3.70268e50i	0.549932	+	0.549932i	0.926421	−	0.376489i	$-0.122869\pi$
$977$	3.70268e50	+	3.70268e50i	0.549932	+	0.549932i	−0.376489	+	0.926421i	$0.622869\pi$
$978$	−7.53387e50	+	7.53387e50i	−1.09966	+	1.09966i
$979$			2.00027e50i			0.286934i
$980$		0			0
$981$	2.15087e51			2.98017
$982$	−5.05447e49	−	5.05447e49i	−0.0688304	−	0.0688304i
$983$	1.41845e50	−	1.41845e50i	0.189848	−	0.189848i	−0.605783	−	0.795630i	$-0.707140\pi$
$983$	1.41845e50	−	1.41845e50i	0.189848	−	0.189848i	0.795630	+	0.605783i	$0.207140\pi$
$984$			5.57867e50i			0.733862i
$985$		0			0
$986$	−1.28748e50			−0.163619
$987$	−6.29031e50	−	6.29031e50i	−0.785743	−	0.785743i
$988$	9.36516e49	−	9.36516e49i	0.114987	−	0.114987i
$989$			1.04607e50i			0.126248i
$990$		0			0
$991$	−3.82190e50			−0.445684			−0.222842	−	0.974855i	$-0.571533\pi$
$991$	−3.82190e50			−0.445684			−0.222842	+	0.974855i	$0.571533\pi$
$992$	−2.61632e50	−	2.61632e50i	−0.299910	−	0.299910i
$993$	−2.08805e50	+	2.08805e50i	−0.235290	+	0.235290i
$994$			5.20891e50i			0.577003i
$995$		0			0
$996$	1.71494e50			0.183587
$997$	5.76473e50	+	5.76473e50i	0.606682	+	0.606682i	0.942077	−	0.335396i	$-0.108870\pi$
$997$	5.76473e50	+	5.76473e50i	0.606682	+	0.606682i	−0.335396	+	0.942077i	$0.608870\pi$
$998$	−1.95000e50	+	1.95000e50i	−0.201751	+	0.201751i
$999$			2.54942e51i			2.59315i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.35.c.b.7.12		32
5.2	odd	4		5.35.c.a.3.5	yes	32
5.3	odd	4	inner	25.35.c.b.18.12		32
5.4	even	2		5.35.c.a.2.5	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.35.c.a.2.5	✓	32	5.4	even	2
5.35.c.a.3.5	yes	32	5.2	odd	4
25.35.c.b.7.12		32	1.1	even	1	trivial
25.35.c.b.18.12		32	5.3	odd	4	inner

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:	\( k \)	\(=\)	\( 35 \)
Character orbit:	\([\chi]\)	\(=\)	25.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(85294.4 + 85294.4i) q^{2} +(1.68126e8 - 1.68126e8i) q^{3} -2.62960e9i q^{4} +2.86804e13 q^{6} +(-2.04951e14 - 2.04951e14i) q^{7} +(1.68964e15 - 1.68964e15i) q^{8} -3.98554e16i q^{9} +O(q^{10})\)	\(q+(85294.4 + 85294.4i) q^{2} +(1.68126e8 - 1.68126e8i) q^{3} -2.62960e9i q^{4} +2.86804e13 q^{6} +(-2.04951e14 - 2.04951e14i) q^{7} +(1.68964e15 - 1.68964e15i) q^{8} -3.98554e16i q^{9} -4.22981e17 q^{11} +(-4.42103e17 - 4.42103e17i) q^{12} +(-8.97147e18 + 8.97147e18i) q^{13} -3.49623e19i q^{14} +2.43057e20 q^{16} +(2.34375e20 + 2.34375e20i) q^{17} +(3.39944e21 - 3.39944e21i) q^{18} -3.96974e21i q^{19} -6.89150e22 q^{21} +(-3.60779e22 - 3.60779e22i) q^{22} +(1.87042e22 - 1.87042e22i) q^{23} -5.68143e23i q^{24} -1.53043e24 q^{26} +(-3.89685e24 - 3.89685e24i) q^{27} +(-5.38937e23 + 5.38937e23i) q^{28} +3.22017e24i q^{29} +3.15358e25 q^{31} +(-8.29633e24 - 8.29633e24i) q^{32} +(-7.11140e25 + 7.11140e25i) q^{33} +3.99818e25i q^{34} -1.04804e26 q^{36} +(-3.27113e26 - 3.27113e26i) q^{37} +(3.38597e26 - 3.38597e26i) q^{38} +3.01667e27i q^{39} -9.81913e26 q^{41} +(-5.87806e27 - 5.87806e27i) q^{42} +(-2.79636e27 + 2.79636e27i) q^{43} +1.11227e27i q^{44} +3.19073e27 q^{46} +(9.12764e27 + 9.12764e27i) q^{47} +(4.08642e28 - 4.08642e28i) q^{48} +2.98926e28i q^{49} +7.88090e28 q^{51} +(2.35913e28 + 2.35913e28i) q^{52} +(-2.57016e28 + 2.57016e28i) q^{53} -6.64760e29i q^{54} -6.92584e29 q^{56} +(-6.67416e29 - 6.67416e29i) q^{57} +(-2.74663e29 + 2.74663e29i) q^{58} +7.57873e29i q^{59} -3.27487e30 q^{61} +(2.68983e30 + 2.68983e30i) q^{62} +(-8.16839e30 + 8.16839e30i) q^{63} -5.59095e30i q^{64} -1.21312e31 q^{66} +(-3.29839e30 - 3.29839e30i) q^{67} +(6.16312e29 - 6.16312e29i) q^{68} -6.28932e30i q^{69} -1.48986e31 q^{71} +(-6.73411e31 - 6.73411e31i) q^{72} +(4.68046e31 - 4.68046e31i) q^{73} -5.58018e31i q^{74} -1.04388e31 q^{76} +(8.66902e31 + 8.66902e31i) q^{77} +(-2.57305e32 + 2.57305e32i) q^{78} +5.17250e31i q^{79} -6.45648e32 q^{81} +(-8.37517e31 - 8.37517e31i) q^{82} +(-1.93953e32 + 1.93953e32i) q^{83} +1.81219e32i q^{84} -4.77027e32 q^{86} +(5.41394e32 + 5.41394e32i) q^{87} +(-7.14684e32 + 7.14684e32i) q^{88} -4.72898e32i q^{89} +3.67742e33 q^{91} +(-4.91845e31 - 4.91845e31i) q^{92} +(5.30198e33 - 5.30198e33i) q^{93} +1.55707e33i q^{94} -2.78965e33 q^{96} +(5.55075e33 + 5.55075e33i) q^{97} +(-2.54967e33 + 2.54967e33i) q^{98} +1.68581e34i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 131070 q^{2} + 78988260 q^{3} - 44043049959816 q^{6} - 5337954235100 q^{7} + 45\!\cdots\!20 q^{8}+O(q^{10}) \) 32 * q - 131070 * q^2 + 78988260 * q^3 - 44043049959816 * q^6 - 5337954235100 * q^7 + 4536119823236220 * q^8	\( 32 q - 131070 q^{2} + 78988260 q^{3} - 44043049959816 q^{6} - 5337954235100 q^{7} + 45\!\cdots\!20 q^{8}+ \cdots - 25\!\cdots\!70 q^{98}+O(q^{100}) \) 32 * q - 131070 * q^2 + 78988260 * q^3 - 44043049959816 * q^6 - 5337954235100 * q^7 + 4536119823236220 * q^8 + 365981602487621544 * q^11 + 5313878568511975560 * q^12 + 11000397968713344520 * q^13 - 1456002327393916605448 * q^16 - 496656489553605410760 * q^17 - 1956191845428178111890 * q^18 - 142103646776097180182616 * q^21 - 204776256011020418595040 * q^22 + 436662638834307282633780 * q^23 - 5758044909260756123220396 * q^26 - 7995615376341697400032560 * q^27 - 884081328441809235881080 * q^28 + 84491420536973998188491704 * q^31 + 184975661677973569185317880 * q^32 - 73478673331281977814021480 * q^33 + 1137988291793068131741823932 * q^36 + 333379985446943362532279920 * q^37 + 1419101265678050265971769480 * q^38 + 3652223875741628991126246984 * q^41 + 4739529391137459161391231840 * q^42 - 16353372323322642143796902300 * q^43 + 131432785549604658942769746424 * q^46 + 164755893091890118218758986260 * q^47 - 267416366563859197412890248720 * q^48 + 879726622206121123479191444184 * q^51 + 1364297502096066356787005826100 * q^52 - 827578466548898383340593310640 * q^53 + 2582027089558247357967654389520 * q^56 + 3021243382907908474517658024480 * q^57 - 2354096772250584899097633644880 * q^58 + 10984341568764658290951563973544 * q^61 + 17271108259627677777618202511160 * q^62 - 8610875544094751042813983810860 * q^63 - 27230920485870501670249585219872 * q^66 - 23820125360634701614572823748060 * q^67 + 16651918880901511226895130538460 * q^68 - 162839011061674956057132387035976 * q^71 - 414631921651932227241773986664580 * q^72 + 290761010682860591477846798111680 * q^73 - 588265232627198985506540939882160 * q^76 - 319978294665614883220802415073800 * q^77 - 251541126280658548479082634723400 * q^78 + 46998375893846038447057289461032 * q^81 + 480327268957748332277390888075360 * q^82 + 987023986692010851073141552006740 * q^83 + 2563129008649864341703296140749464 * q^86 + 3601816973758507596709087426821120 * q^87 - 4467012425011508421563596255937760 * q^88 + 9733965316721903607010024138955704 * q^91 + 5821741665997247478385288152437640 * q^92 - 1188287280403911040224754269765480 * q^93 + 24207915861230982937605202170100704 * q^96 + 29449480417814037063188176022138560 * q^97 - 25177080070348305002521179770557470 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more