LMFDB - Embedded newform 25.33.c.b.7.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,33,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, 33, names="a")

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

chi := DirichletCharacter("25.7");

S:= CuspForms(chi, 33);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 33 $
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:	$162.166637856$
Analytic rank:	$0$
Dimension:	$30$
Relative dimension:	$15$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.10
Character	$\chi$	$=$	25.7
Dual form			25.33.c.b.18.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(37971.9 + 37971.9i) q^{2} +(-3.04306e7 + 3.04306e7i) q^{3} -1.41124e9i q^{4} -2.31101e12 q^{6} +(9.26812e12 + 9.26812e12i) q^{7} +(2.16675e14 - 2.16675e14i) q^{8} +9.78102e11i q^{9} +O(q^{10})$	\(q+(37971.9 + 37971.9i) q^{2} +(-3.04306e7 + 3.04306e7i) q^{3} -1.41124e9i q^{4} -2.31101e12 q^{6} +(9.26812e12 + 9.26812e12i) q^{7} +(2.16675e14 - 2.16675e14i) q^{8} +9.78102e11i q^{9} +1.98923e16 q^{11} +(4.29449e16 + 4.29449e16i) q^{12} +(8.93581e17 - 8.93581e17i) q^{13} +7.03856e17i q^{14} +1.03939e19 q^{16} +(3.66719e19 + 3.66719e19i) q^{17} +(-3.71404e16 + 3.71404e16i) q^{18} -2.80535e20i q^{19} -5.64069e20 q^{21} +(7.55348e20 + 7.55348e20i) q^{22} +(2.06972e21 - 2.06972e21i) q^{23} +1.31871e22i q^{24} +6.78619e22 q^{26} +(-5.64183e22 - 5.64183e22i) q^{27} +(1.30795e22 - 1.30795e22i) q^{28} +1.02359e23i q^{29} -9.64778e23 q^{31} +(-5.35937e23 - 5.35937e23i) q^{32} +(-6.05335e23 + 6.05335e23i) q^{33} +2.78500e24i q^{34} +1.38034e21 q^{36} +(-7.27232e24 - 7.27232e24i) q^{37} +(1.06524e25 - 1.06524e25i) q^{38} +5.43844e25i q^{39} +1.58648e25 q^{41} +(-2.14188e25 - 2.14188e25i) q^{42} +(9.21200e25 - 9.21200e25i) q^{43} -2.80728e25i q^{44} +1.57183e26 q^{46} +(3.74128e26 + 3.74128e26i) q^{47} +(-3.16293e26 + 3.16293e26i) q^{48} -9.32632e26i q^{49} -2.23189e27 q^{51} +(-1.26106e27 - 1.26106e27i) q^{52} +(-4.43458e27 + 4.43458e27i) q^{53} -4.28462e27i q^{54} +4.01635e27 q^{56} +(8.53685e27 + 8.53685e27i) q^{57} +(-3.88675e27 + 3.88675e27i) q^{58} +4.27569e27i q^{59} -5.42671e28 q^{61} +(-3.66344e28 - 3.66344e28i) q^{62} +(-9.06517e24 + 9.06517e24i) q^{63} -8.53426e28i q^{64} -4.59714e28 q^{66} +(-1.45709e29 - 1.45709e29i) q^{67} +(5.17528e28 - 5.17528e28i) q^{68} +1.25966e29i q^{69} -1.17360e29 q^{71} +(2.11931e26 + 2.11931e26i) q^{72} +(8.02415e28 - 8.02415e28i) q^{73} -5.52287e29i q^{74} -3.95902e29 q^{76} +(1.84364e29 + 1.84364e29i) q^{77} +(-2.06508e30 + 2.06508e30i) q^{78} -2.05013e30i q^{79} +3.43187e30 q^{81} +(6.02417e29 + 6.02417e29i) q^{82} +(4.06190e30 - 4.06190e30i) q^{83} +7.96036e29i q^{84} +6.99594e30 q^{86} +(-3.11484e30 - 3.11484e30i) q^{87} +(4.31017e30 - 4.31017e30i) q^{88} -1.23259e31i q^{89} +1.65636e31 q^{91} +(-2.92087e30 - 2.92087e30i) q^{92} +(2.93588e31 - 2.93588e31i) q^{93} +2.84127e31i q^{94} +3.26178e31 q^{96} +(-2.90974e31 - 2.90974e31i) q^{97} +(3.54138e31 - 3.54138e31i) q^{98} +1.94567e28i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 2 q^{2} + 2792232 q^{3} - 645476451240 q^{6} - 21807690136848 q^{7} - 340768936037220 q^{8}+O(q^{10}) $ 30 * q + 2 * q^2 + 2792232 * q^3 - 645476451240 * q^6 - 21807690136848 * q^7 - 340768936037220 * q^8	$ 30 q + 2 q^{2} + 2792232 q^{3} - 645476451240 q^{6} - 21807690136848 q^{7} - 340768936037220 q^{8} - 60\!\cdots\!40 q^{11}+ \cdots - 12\!\cdots\!02 q^{98}+O(q^{100}) $ 30 * q + 2 * q^2 + 2792232 * q^3 - 645476451240 * q^6 - 21807690136848 * q^7 - 340768936037220 * q^8 - 60908362837533640 * q^11 - 444566273630869608 * q^12 - 649759187023107138 * q^13 - 46108906958970522120 * q^16 + 218107661739005884502 * q^17 - 240407468159884203858 * q^18 + 4549905652154594876760 * q^21 + 11386561172247365212944 * q^22 - 13896091629970965206008 * q^23 - 23129486500762683557740 * q^26 - 176388356775702789525960 * q^27 - 59665474478272755491112 * q^28 - 1285786827516670637255040 * q^31 - 3122517776856150857591368 * q^32 + 1644615516923295701112504 * q^33 + 31947551193266858523505980 * q^36 + 126275105375668809211002 * q^37 - 57601564734016178366855880 * q^38 - 155417315271390260892986440 * q^41 - 797836438482097707185724336 * q^42 + 545147034084978191886568152 * q^43 - 3454637097270705106900721640 * q^46 - 2735203198488492729395621848 * q^47 + 3192952350241941373327314192 * q^48 - 6129415060408014316542923040 * q^51 - 6000870590399837156109494028 * q^52 + 11282171275183571262774628682 * q^53 - 47918174764291639802549158800 * q^56 - 44765351794015370451647799120 * q^57 + 29637988346430122895588672480 * q^58 + 50784540875895586667393303160 * q^61 + 218235799024898727529128868024 * q^62 - 213794735887989269330759842008 * q^63 + 1348836243659025586642346421120 * q^66 + 736483403252315334072161239752 * q^67 - 1085395947449178489054935855012 * q^68 + 817740403780342392034746361760 * q^71 + 951267702824572414087545605820 * q^72 + 379868722209495311437504600242 * q^73 - 6689750080738358201358794259600 * q^76 - 6381539826853244422672988941256 * q^77 + 9179143477318522110451614982584 * q^78 - 14239669107938661073624705472070 * q^81 - 2725313872720345364461277817936 * q^82 - 4996401755555614465785455997328 * q^83 + 16049932109847278395442966171960 * q^86 - 36834415428157346041110451524480 * q^87 + 47132513308908068698430156048160 * q^88 - 104150500668224029090357708737840 * q^91 + 18747876848872687606754750486552 * q^92 - 112210213536624471769268225064216 * q^93 + 380819283905835347723966665116960 * q^96 + 155781506757725945270376012026802 * q^97 - 125692870459469366775669291878702 * 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 $

$2$	37971.9	+	37971.9i	0.579405	+	0.579405i	0.934739	−	0.355334i	$-0.115633\pi$
$2$	37971.9	+	37971.9i	0.579405	+	0.579405i	−0.355334	+	0.934739i	$0.615633\pi$
$3$	−3.04306e7	+	3.04306e7i	−0.706920	+	0.706920i	−0.965886	−	0.258966i	$-0.916618\pi$
$3$	−3.04306e7	+	3.04306e7i	−0.706920	+	0.706920i	0.258966	+	0.965886i	$0.416618\pi$
$4$		−	1.41124e9i		−	0.328580i
$5$		0			0
$5$		0			0
$6$	−2.31101e12			−0.819186
$7$	9.26812e12	+	9.26812e12i	0.278884	+	0.278884i	0.832663	−	0.553780i	$-0.186815\pi$
$7$	9.26812e12	+	9.26812e12i	0.278884	+	0.278884i	−0.553780	+	0.832663i	$0.686815\pi$
$8$	2.16675e14	−	2.16675e14i	0.769786	−	0.769786i
$9$			9.78102e11i			0.000527842i
$10$		0			0
$11$	1.98923e16			0.432914			0.216457	−	0.976292i	$-0.430550\pi$
$11$	1.98923e16			0.432914			0.216457	+	0.976292i	$0.430550\pi$
$12$	4.29449e16	+	4.29449e16i	0.232280	+	0.232280i
$13$	8.93581e17	−	8.93581e17i	1.34289	−	1.34289i	0.449719	−	0.893170i	$-0.351524\pi$
$13$	8.93581e17	−	8.93581e17i	1.34289	−	1.34289i	0.893170	−	0.449719i	$-0.148476\pi$
$14$			7.03856e17i			0.323173i
$15$		0			0
$16$	1.03939e19			0.563455
$17$	3.66719e19	+	3.66719e19i	0.753617	+	0.753617i	0.975152	−	0.221536i	$-0.0711069\pi$
$17$	3.66719e19	+	3.66719e19i	0.753617	+	0.753617i	−0.221536	+	0.975152i	$0.571107\pi$
$18$	−3.71404e16	+	3.71404e16i	−0.000305834	+	0.000305834i
$19$		−	2.80535e20i		−	0.972589i	−0.873795	−	0.486295i	$-0.838348\pi$
$19$		−	2.80535e20i		−	0.972589i	0.873795	−	0.486295i	$-0.161652\pi$
$20$		0			0
$21$	−5.64069e20			−0.394297
$22$	7.55348e20	+	7.55348e20i	0.250833	+	0.250833i
$23$	2.06972e21	−	2.06972e21i	0.337495	−	0.337495i	−0.517929	−	0.855424i	$-0.673297\pi$
$23$	2.06972e21	−	2.06972e21i	0.337495	−	0.337495i	0.855424	+	0.517929i	$0.173297\pi$
$24$			1.31871e22i			1.08835i
$25$		0			0
$26$	6.78619e22			1.55615
$27$	−5.64183e22	−	5.64183e22i	−0.707293	−	0.707293i
$28$	1.30795e22	−	1.30795e22i	0.0916355	−	0.0916355i
$29$			1.02359e23i			0.409031i	0.978863	+	0.204516i	$0.0655620\pi$
$29$			1.02359e23i			0.409031i	−0.978863	+	0.204516i	$0.934438\pi$
$30$		0			0
$31$	−9.64778e23			−1.32630			−0.663148	−	0.748488i	$-0.730780\pi$
$31$	−9.64778e23			−1.32630			−0.663148	+	0.748488i	$0.730780\pi$
$32$	−5.35937e23	−	5.35937e23i	−0.443317	−	0.443317i
$33$	−6.05335e23	+	6.05335e23i	−0.306036	+	0.306036i
$34$			2.78500e24i			0.873298i
$35$		0			0
$36$	1.38034e21			0.000173438
$37$	−7.27232e24	−	7.27232e24i	−0.589448	−	0.589448i	0.348034	−	0.937482i	$-0.386849\pi$
$37$	−7.27232e24	−	7.27232e24i	−0.589448	−	0.589448i	−0.937482	+	0.348034i	$0.886849\pi$
$38$	1.06524e25	−	1.06524e25i	0.563523	−	0.563523i
$39$			5.43844e25i			1.89863i
$40$		0			0
$41$	1.58648e25			0.248825			0.124412	−	0.992231i	$-0.460295\pi$
$41$	1.58648e25			0.248825			0.124412	+	0.992231i	$0.460295\pi$
$42$	−2.14188e25	−	2.14188e25i	−0.228458	−	0.228458i
$43$	9.21200e25	−	9.21200e25i	0.674309	−	0.674309i	−0.284398	−	0.958706i	$-0.591794\pi$
$43$	9.21200e25	−	9.21200e25i	0.674309	−	0.674309i	0.958706	+	0.284398i	$0.0917936\pi$
$44$		−	2.80728e25i		−	0.142247i
$45$		0			0
$46$	1.57183e26			0.391092
$47$	3.74128e26	+	3.74128e26i	0.659863	+	0.659863i	0.955348	−	0.295484i	$-0.0954810\pi$
$47$	3.74128e26	+	3.74128e26i	0.659863	+	0.659863i	−0.295484	+	0.955348i	$0.595481\pi$
$48$	−3.16293e26	+	3.16293e26i	−0.398318	+	0.398318i
$49$		−	9.32632e26i		−	0.844448i
$50$		0			0
$51$	−2.23189e27			−1.06549
$52$	−1.26106e27	−	1.26106e27i	−0.441246	−	0.441246i
$53$	−4.43458e27	+	4.43458e27i	−1.14403	+	1.14403i	−0.156328	+	0.987705i	$0.549966\pi$
$53$	−4.43458e27	+	4.43458e27i	−1.14403	+	1.14403i	−0.987705	+	0.156328i	$0.950034\pi$
$54$		−	4.28462e27i		−	0.819618i
$55$		0			0
$56$	4.01635e27			0.429361
$57$	8.53685e27	+	8.53685e27i	0.687543	+	0.687543i
$58$	−3.88675e27	+	3.88675e27i	−0.236995	+	0.236995i
$59$			4.27569e27i			0.198323i	0.995071	+	0.0991617i	$0.0316161\pi$
$59$			4.27569e27i			0.198323i	−0.995071	+	0.0991617i	$0.968384\pi$
$60$		0			0
$61$	−5.42671e28			−1.47659			−0.738295	−	0.674478i	$-0.764369\pi$
$61$	−5.42671e28			−1.47659			−0.738295	+	0.674478i	$0.764369\pi$
$62$	−3.66344e28	−	3.66344e28i	−0.768462	−	0.768462i
$63$	−9.06517e24	+	9.06517e24i	−0.000147207	+	0.000147207i
$64$		−	8.53426e28i		−	1.07718i
$65$		0			0
$66$	−4.59714e28			−0.354637
$67$	−1.45709e29	−	1.45709e29i	−0.883669	−	0.883669i	0.110236	−	0.993905i	$-0.464839\pi$
$67$	−1.45709e29	−	1.45709e29i	−0.883669	−	0.883669i	−0.993905	+	0.110236i	$0.964839\pi$
$68$	5.17528e28	−	5.17528e28i	0.247623	−	0.247623i
$69$			1.25966e29i			0.477163i
$70$		0			0
$71$	−1.17360e29			−0.281441			−0.140720	−	0.990049i	$-0.544942\pi$
$71$	−1.17360e29			−0.281441			−0.140720	+	0.990049i	$0.544942\pi$
$72$	2.11931e26	+	2.11931e26i	0.000406325	+	0.000406325i
$73$	8.02415e28	−	8.02415e28i	0.123377	−	0.123377i	−0.642722	−	0.766099i	$-0.722195\pi$
$73$	8.02415e28	−	8.02415e28i	0.123377	−	0.123377i	0.766099	+	0.642722i	$0.222195\pi$
$74$		−	5.52287e29i		−	0.683058i
$75$		0			0
$76$	−3.95902e29			−0.319573
$77$	1.84364e29	+	1.84364e29i	0.120733	+	0.120733i
$78$	−2.06508e30	+	2.06508e30i	−1.10008	+	1.10008i
$79$		−	2.05013e30i		−	0.890734i	−0.895348	−	0.445367i	$-0.853073\pi$
$79$		−	2.05013e30i		−	0.890734i	0.895348	−	0.445367i	$-0.146927\pi$
$80$		0			0
$81$	3.43187e30			0.999472
$82$	6.02417e29	+	6.02417e29i	0.144170	+	0.144170i
$83$	4.06190e30	−	4.06190e30i	0.800718	−	0.800718i	−0.182490	−	0.983208i	$-0.558416\pi$
$83$	4.06190e30	−	4.06190e30i	0.800718	−	0.800718i	0.983208	+	0.182490i	$0.0584156\pi$
$84$			7.96036e29i			0.129558i
$85$		0			0
$86$	6.99594e30			0.781396
$87$	−3.11484e30	−	3.11484e30i	−0.289153	−	0.289153i
$88$	4.31017e30	−	4.31017e30i	0.333251	−	0.333251i
$89$		−	1.23259e31i		−	0.795386i	−0.917519	−	0.397693i	$-0.869811\pi$
$89$		−	1.23259e31i		−	0.795386i	0.917519	−	0.397693i	$-0.130189\pi$
$90$		0			0
$91$	1.65636e31			0.749019
$92$	−2.92087e30	−	2.92087e30i	−0.110894	−	0.110894i
$93$	2.93588e31	−	2.93588e31i	0.937585	−	0.937585i
$94$			2.84127e31i			0.764656i
$95$		0			0
$96$	3.26178e31			0.626779
$97$	−2.90974e31	−	2.90974e31i	−0.473704	−	0.473704i	0.429407	−	0.903111i	$-0.358723\pi$
$97$	−2.90974e31	−	2.90974e31i	−0.473704	−	0.473704i	−0.903111	+	0.429407i	$0.858723\pi$
$98$	3.54138e31	−	3.54138e31i	0.489277	−	0.489277i
$99$			1.94567e28i			0.000228510i
$100$		0			0
$101$	4.16959e31			0.355592			0.177796	−	0.984067i	$-0.443103\pi$
$101$	4.16959e31			0.355592			0.177796	+	0.984067i	$0.443103\pi$
$102$	−8.47492e31	−	8.47492e31i	−0.617352	−	0.617352i
$103$	−1.50389e32	+	1.50389e32i	−0.937176	+	0.937176i	−0.998140	−	0.0609644i	$-0.980582\pi$
$103$	−1.50389e32	+	1.50389e32i	−0.937176	+	0.937176i	0.0609644	+	0.998140i	$0.480582\pi$
$104$		−	3.87234e32i		−	2.06747i
$105$		0			0
$106$	−3.36779e32			−1.32572
$107$	4.62097e31	+	4.62097e31i	0.156528	+	0.156528i	0.781026	−	0.624498i	$-0.214696\pi$
$107$	4.62097e31	+	4.62097e31i	0.156528	+	0.156528i	−0.624498	+	0.781026i	$0.714696\pi$
$108$	−7.96197e31	+	7.96197e31i	−0.232402	+	0.232402i
$109$		−	5.38999e32i		−	1.35758i	−0.734334	−	0.678788i	$-0.762505\pi$
$109$		−	5.38999e32i		−	1.35758i	0.734334	−	0.678788i	$-0.237495\pi$
$110$		0			0
$111$	4.42602e32			0.833385
$112$	9.63321e31	+	9.63321e31i	0.157138	+	0.157138i
$113$	4.09133e32	−	4.09133e32i	0.578908	−	0.578908i	−0.355694	−	0.934602i	$-0.615756\pi$
$113$	4.09133e32	−	4.09133e32i	0.578908	−	0.578908i	0.934602	+	0.355694i	$0.115756\pi$
$114$			6.48320e32i			0.796732i
$115$		0			0
$116$	1.44453e32			0.134399
$117$	8.74013e29	+	8.74013e29i	0.000708833	+	0.000708833i
$118$	−1.62356e32	+	1.62356e32i	−0.114910	+	0.114910i
$119$			6.79759e32i			0.420343i
$120$		0			0
$121$	−1.71567e33			−0.812585
$122$	−2.06063e33	−	2.06063e33i	−0.855543	−	0.855543i
$123$	−4.82776e32	+	4.82776e32i	−0.175899	+	0.175899i
$124$			1.36153e33i			0.435794i
$125$		0			0
$126$	−6.88443e29			−0.000170584
$127$	5.06270e33	+	5.06270e33i	1.10541	+	1.10541i	0.993746	+	0.111661i	$0.0356171\pi$
$127$	5.06270e33	+	5.06270e33i	1.10541	+	1.10541i	0.111661	+	0.993746i	$0.464383\pi$
$128$	9.38787e32	−	9.38787e32i	0.180804	−	0.180804i
$129$			5.60654e33i			0.953365i
$130$		0			0
$131$	9.32687e32			0.123992			0.0619962	−	0.998076i	$-0.480253\pi$
$131$	9.32687e32			0.123992			0.0619962	+	0.998076i	$0.480253\pi$
$132$	8.54272e32	+	8.54272e32i	0.100557	+	0.100557i
$133$	2.60003e33	−	2.60003e33i	0.271239	−	0.271239i
$134$		−	1.10657e34i		−	1.02400i
$135$		0			0
$136$	1.58918e34			1.16025
$137$	1.30606e34	+	1.30606e34i	0.848072	+	0.848072i	0.989892	−	0.141820i	$-0.0452956\pi$
$137$	1.30606e34	+	1.30606e34i	0.848072	+	0.848072i	−0.141820	+	0.989892i	$0.545296\pi$
$138$	−4.78316e33	+	4.78316e33i	−0.276471	+	0.276471i
$139$			1.49340e34i			0.769025i	0.923120	+	0.384513i	$0.125631\pi$
$139$			1.49340e34i			0.769025i	−0.923120	+	0.384513i	$0.874369\pi$
$140$		0			0
$141$	−2.27698e34			−0.932941
$142$	−4.45639e33	−	4.45639e33i	−0.163068	−	0.163068i
$143$	1.77754e34	−	1.77754e34i	0.581356	−	0.581356i
$144$			1.01663e31i			0.000297416i
$145$		0			0
$146$	6.09384e33			0.142970
$147$	2.83805e34	+	2.83805e34i	0.596957	+	0.596957i
$148$	−1.02630e34	+	1.02630e34i	−0.193681	+	0.193681i
$149$		−	8.34768e33i		−	0.141444i	−0.997496	−	0.0707222i	$-0.977470\pi$
$149$		−	8.34768e33i		−	0.141444i	0.997496	−	0.0707222i	$-0.0225304\pi$
$150$		0			0
$151$	−5.21301e34			−0.713604			−0.356802	−	0.934180i	$-0.616133\pi$
$151$	−5.21301e34			−0.713604			−0.356802	+	0.934180i	$0.616133\pi$
$152$	−6.07851e34	−	6.07851e34i	−0.748685	−	0.748685i
$153$	−3.58688e31	+	3.58688e31i	−0.000397791	+	0.000397791i
$154$			1.40013e34i			0.139906i
$155$		0			0
$156$	7.67494e34			0.623852
$157$	−5.64726e34	−	5.64726e34i	−0.414422	−	0.414422i	0.468854	−	0.883276i	$-0.344667\pi$
$157$	−5.64726e34	−	5.64726e34i	−0.414422	−	0.414422i	−0.883276	+	0.468854i	$0.844667\pi$
$158$	7.78473e34	−	7.78473e34i	0.516096	−	0.516096i
$159$		−	2.69894e35i		−	1.61748i
$160$		0			0
$161$	3.83649e34			0.188243
$162$	1.30315e35	+	1.30315e35i	0.579099	+	0.579099i
$163$	1.65579e35	−	1.65579e35i	0.666814	−	0.666814i	−0.290163	−	0.956977i	$-0.593710\pi$
$163$	1.65579e35	−	1.65579e35i	0.666814	−	0.666814i	0.956977	+	0.290163i	$0.0937096\pi$
$164$		−	2.23891e34i		−	0.0817587i
$165$		0			0
$166$	3.08476e35			0.927880
$167$	2.81705e35	+	2.81705e35i	0.769718	+	0.769718i	0.978057	−	0.208339i	$-0.0668056\pi$
$167$	2.81705e35	+	2.81705e35i	0.769718	+	0.769718i	−0.208339	+	0.978057i	$0.566806\pi$
$168$	−1.22220e35	+	1.22220e35i	−0.303524	+	0.303524i
$169$		−	1.15419e36i		−	2.60670i
$170$		0			0
$171$	2.74392e32			0.000513374
$172$	−1.30003e35	−	1.30003e35i	−0.221564	−	0.221564i
$173$	8.17618e35	−	8.17618e35i	1.27003	−	1.27003i	0.323955	−	0.946073i	$-0.394988\pi$
$173$	8.17618e35	−	8.17618e35i	1.27003	−	1.27003i	0.946073	−	0.323955i	$-0.105012\pi$
$174$		−	2.36552e35i		−	0.335073i
$175$		0			0
$176$	2.06759e35			0.243928
$177$	−1.30112e35	−	1.30112e35i	−0.140199	−	0.140199i
$178$	4.68037e35	−	4.68037e35i	0.460851	−	0.460851i
$179$			1.95532e36i			1.76023i	0.474761	+	0.880115i	$0.342535\pi$
$179$			1.95532e36i			1.76023i	−0.474761	+	0.880115i	$0.657465\pi$
$180$		0			0
$181$	2.09841e36			1.58137			0.790683	−	0.612226i	$-0.209726\pi$
$181$	2.09841e36			1.58137			0.790683	+	0.612226i	$0.209726\pi$
$182$	6.28952e35	+	6.28952e35i	0.433986	+	0.433986i
$183$	1.65138e36	−	1.65138e36i	1.04383	−	1.04383i
$184$		−	8.96916e35i		−	0.519597i
$185$		0			0
$186$	2.22962e36			1.08648
$187$	7.29488e35	+	7.29488e35i	0.326251	+	0.326251i
$188$	5.27984e35	−	5.27984e35i	0.216818	−	0.216818i
$189$		−	1.04578e36i		−	0.394505i
$190$		0			0
$191$	−5.67177e36			−1.80794			−0.903972	−	0.427591i	$-0.859362\pi$
$191$	−5.67177e36			−1.80794			−0.903972	+	0.427591i	$0.859362\pi$
$192$	2.59703e36	+	2.59703e36i	0.761477	+	0.761477i
$193$	7.44448e35	−	7.44448e35i	0.200871	−	0.200871i	−0.599502	−	0.800373i	$-0.704635\pi$
$193$	7.44448e35	−	7.44448e35i	0.200871	−	0.200871i	0.800373	+	0.599502i	$0.204635\pi$
$194$		−	2.20977e36i		−	0.548933i
$195$		0			0
$196$	−1.31617e36			−0.277469
$197$	3.61428e36	+	3.61428e36i	0.702365	+	0.702365i	0.964918	−	0.262553i	$-0.0845645\pi$
$197$	3.61428e36	+	3.61428e36i	0.702365	+	0.702365i	−0.262553	+	0.964918i	$0.584564\pi$
$198$	−7.38808e32	+	7.38808e32i	−0.000132400	+	0.000132400i
$199$		−	9.57640e36i		−	1.58326i	−0.610998	−	0.791632i	$-0.709232\pi$
$199$		−	9.57640e36i		−	1.58326i	0.610998	−	0.791632i	$-0.290768\pi$
$200$		0			0
$201$	8.86803e36			1.24937
$202$	1.58327e36	+	1.58327e36i	0.206032	+	0.206032i
$203$	−9.48672e35	+	9.48672e35i	−0.114072	+	0.114072i
$204$			3.14974e36i			0.350100i
$205$		0			0
$206$	−1.14211e37			−1.08601
$207$	2.02440e33	+	2.02440e33i	0.000178144	+	0.000178144i
$208$	9.28780e36	−	9.28780e36i	0.756658	−	0.756658i
$209$		−	5.58049e36i		−	0.421048i
$210$		0			0
$211$	1.21317e37			0.785965			0.392982	−	0.919546i	$-0.371443\pi$
$211$	1.21317e37			0.785965			0.392982	+	0.919546i	$0.371443\pi$
$212$	6.25826e36	+	6.25826e36i	0.375906	+	0.375906i
$213$	3.57134e36	−	3.57134e36i	0.198956	−	0.198956i
$214$			3.50934e36i			0.181386i
$215$		0			0
$216$	−2.44489e37			−1.08893
$217$	−8.94168e36	−	8.94168e36i	−0.369882	−	0.369882i
$218$	2.04668e37	−	2.04668e37i	0.786586	−	0.786586i
$219$			4.88359e36i			0.174435i
$220$		0			0
$221$	6.55386e37			2.02405
$222$	1.68064e37	+	1.68064e37i	0.482867	+	0.482867i
$223$	1.59220e37	−	1.59220e37i	0.425716	−	0.425716i	−0.461450	−	0.887166i	$-0.652671\pi$
$223$	1.59220e37	−	1.59220e37i	0.425716	−	0.425716i	0.887166	+	0.461450i	$0.152671\pi$
$224$		−	9.93426e36i		−	0.247268i
$225$		0			0
$226$	3.10711e37			0.670844
$227$	−2.21352e37	−	2.21352e37i	−0.445318	−	0.445318i	0.448477	−	0.893795i	$-0.351967\pi$
$227$	−2.21352e37	−	2.21352e37i	−0.445318	−	0.445318i	−0.893795	+	0.448477i	$0.851967\pi$
$228$	1.20475e37	−	1.20475e37i	0.225913	−	0.225913i
$229$		−	3.22541e37i		−	0.563920i	−0.959426	−	0.281960i	$-0.909016\pi$
$229$		−	3.22541e37i		−	0.563920i	0.959426	−	0.281960i	$-0.0909845\pi$
$230$		0			0
$231$	−1.12206e37			−0.170697
$232$	2.21786e37	+	2.21786e37i	0.314867	+	0.314867i
$233$	−1.28133e37	+	1.28133e37i	−0.169812	+	0.169812i	−0.786897	−	0.617085i	$-0.788314\pi$
$233$	−1.28133e37	+	1.28133e37i	−0.169812	+	0.169812i	0.617085	+	0.786897i	$0.288314\pi$
$234$			6.63759e34i			0.000821403i
$235$		0			0
$236$	6.03403e36			0.0651651
$237$	6.23867e37	+	6.23867e37i	0.629678	+	0.629678i
$238$	−2.58117e37	+	2.58117e37i	−0.243549	+	0.243549i
$239$		−	1.92792e38i		−	1.70107i	−0.525915	−	0.850537i	$-0.676277\pi$
$239$		−	1.92792e38i		−	1.70107i	0.525915	−	0.850537i	$-0.323723\pi$
$240$		0			0
$241$	4.16303e37			0.321467			0.160734	−	0.986998i	$-0.448614\pi$
$241$	4.16303e37			0.321467			0.160734	+	0.986998i	$0.448614\pi$
$242$	−6.51474e37	−	6.51474e37i	−0.470816	−	0.470816i
$243$	1.10337e35	−	1.10337e35i	0.000746481	−	0.000746481i
$244$			7.65840e37i			0.485177i
$245$		0			0
$246$	−3.66638e37			−0.203834
$247$	−2.50681e38	−	2.50681e38i	−1.30608	−	1.30608i
$248$	−2.09044e38	+	2.09044e38i	−1.02096	+	1.02096i
$249$			2.47212e38i			1.13209i
$250$		0			0
$251$	−4.15942e38			−1.67592			−0.837961	−	0.545731i	$-0.816252\pi$
$251$	−4.15942e38			−1.67592			−0.837961	+	0.545731i	$0.816252\pi$
$252$	1.27931e34	+	1.27931e34i	4.83691e−5	+	4.83691e-5i
$253$	4.11715e37	−	4.11715e37i	0.146106	−	0.146106i
$254$			3.84480e38i			1.28096i
$255$		0			0
$256$	−2.95249e38			−0.867658
$257$	−1.31184e38	−	1.31184e38i	−0.362201	−	0.362201i	0.502422	−	0.864623i	$-0.332443\pi$
$257$	−1.31184e38	−	1.31184e38i	−0.362201	−	0.362201i	−0.864623	+	0.502422i	$0.832443\pi$
$258$	−2.12891e38	+	2.12891e38i	−0.552384	+	0.552384i
$259$		−	1.34801e38i		−	0.328775i
$260$		0			0
$261$	−1.00117e35			−0.000215904
$262$	3.54159e37	+	3.54159e37i	0.0718419	+	0.0718419i
$263$	−1.43361e38	+	1.43361e38i	−0.273614	+	0.273614i	−0.830553	−	0.556939i	$-0.811976\pi$
$263$	−1.43361e38	+	1.43361e38i	−0.273614	+	0.273614i	0.556939	+	0.830553i	$0.311976\pi$
$264$			2.62322e38i			0.471164i
$265$		0			0
$266$	1.97456e38			0.314315
$267$	3.75084e38	+	3.75084e38i	0.562274	+	0.562274i
$268$	−2.05630e38	+	2.05630e38i	−0.290356	+	0.290356i
$269$			5.49447e38i			0.730952i	0.930821	+	0.365476i	$0.119094\pi$
$269$			5.49447e38i			0.730952i	−0.930821	+	0.365476i	$0.880906\pi$
$270$		0			0
$271$	2.20854e38			0.260973			0.130487	−	0.991450i	$-0.458346\pi$
$271$	2.20854e38			0.260973			0.130487	+	0.991450i	$0.458346\pi$
$272$	3.81165e38	+	3.81165e38i	0.424629	+	0.424629i
$273$	−5.04041e38	+	5.04041e38i	−0.529497	+	0.529497i
$274$			9.91868e38i			0.982754i
$275$		0			0
$276$	1.77768e38			0.156786
$277$	−6.85301e38	−	6.85301e38i	−0.570433	−	0.570433i	0.361816	−	0.932249i	$-0.382157\pi$
$277$	−6.85301e38	−	6.85301e38i	−0.570433	−	0.570433i	−0.932249	+	0.361816i	$0.882157\pi$
$278$	−5.67074e38	+	5.67074e38i	−0.445577	+	0.445577i
$279$		−	9.43652e35i		−	0.000700075i
$280$		0			0
$281$	−2.22254e39			−1.47078			−0.735392	−	0.677642i	$-0.763002\pi$
$281$	−2.22254e39			−1.47078			−0.735392	+	0.677642i	$0.763002\pi$
$282$	−8.64614e38	−	8.64614e38i	−0.540551	−	0.540551i
$283$	−1.27238e39	+	1.27238e39i	−0.751683	+	0.751683i	−0.974793	−	0.223111i	$-0.928379\pi$
$283$	−1.27238e39	+	1.27238e39i	−0.751683	+	0.751683i	0.223111	+	0.974793i	$0.428379\pi$
$284$			1.65623e38i			0.0924758i
$285$		0			0
$286$	1.34993e39			0.673681
$287$	1.47037e38	+	1.47037e38i	0.0693931	+	0.0693931i
$288$	5.24201e35	−	5.24201e35i	0.000234001	−	0.000234001i
$289$			3.21742e38i			0.135876i
$290$		0			0
$291$	1.77090e39			0.669742
$292$	−1.13240e38	−	1.13240e38i	−0.0405391	−	0.0405391i
$293$	4.00474e39	−	4.00474e39i	1.35735	−	1.35735i	0.480181	−	0.877169i	$-0.340571\pi$
$293$	4.00474e39	−	4.00474e39i	1.35735	−	1.35735i	0.877169	−	0.480181i	$-0.159429\pi$
$294$			2.15532e39i			0.691760i
$295$		0			0
$296$	−3.15147e39			−0.907497
$297$	−1.12229e39	−	1.12229e39i	−0.306197	−	0.306197i
$298$	3.16977e38	−	3.16977e38i	0.0819536	−	0.0819536i
$299$		−	3.69893e39i		−	0.906435i
$300$		0			0
$301$	1.70756e39			0.376107
$302$	−1.97948e39	−	1.97948e39i	−0.413466	−	0.413466i
$303$	−1.26883e39	+	1.26883e39i	−0.251375	+	0.251375i
$304$		−	2.91586e39i		−	0.548011i
$305$		0			0
$306$	−2.72402e36			−0.000460964
$307$	−5.79148e39	−	5.79148e39i	−0.930199	−	0.930199i	0.0675191	−	0.997718i	$-0.478492\pi$
$307$	−5.79148e39	−	5.79148e39i	−0.930199	−	0.930199i	−0.997718	+	0.0675191i	$0.978492\pi$
$308$	2.60182e38	−	2.60182e38i	0.0396703	−	0.0396703i
$309$		−	9.15286e39i		−	1.32502i
$310$		0			0
$311$	2.40910e39			0.314549			0.157274	−	0.987555i	$-0.449729\pi$
$311$	2.40910e39			0.314549			0.157274	+	0.987555i	$0.449729\pi$
$312$	1.17838e40	+	1.17838e40i	1.46154	+	1.46154i
$313$	−9.69168e39	+	9.69168e39i	−1.14206	+	1.14206i	−0.153989	+	0.988073i	$0.549212\pi$
$313$	−9.69168e39	+	9.69168e39i	−1.14206	+	1.14206i	−0.988073	+	0.153989i	$0.950788\pi$
$314$		−	4.28874e39i		−	0.480237i
$315$		0			0
$316$	−2.89323e39			−0.292677
$317$	1.29890e39	+	1.29890e39i	0.124919	+	0.124919i	0.766802	−	0.641884i	$-0.221847\pi$
$317$	1.29890e39	+	1.29890e39i	0.124919	+	0.124919i	−0.641884	+	0.766802i	$0.721847\pi$
$318$	1.02484e40	−	1.02484e40i	0.937176	−	0.937176i
$319$			2.03615e39i			0.177076i
$320$		0			0
$321$	−2.81238e39			−0.221306
$322$	1.45679e39	+	1.45679e39i	0.109069	+	0.109069i
$323$	1.02877e40	−	1.02877e40i	0.732959	−	0.732959i
$324$		−	4.84319e39i		−	0.328406i
$325$		0			0
$326$	1.25747e40			0.772711
$327$	1.64021e40	+	1.64021e40i	0.959698	+	0.959698i
$328$	3.43752e39	−	3.43752e39i	0.191542	−	0.191542i
$329$			6.93492e39i			0.368050i
$330$		0			0
$331$	2.60902e40			1.25670			0.628348	−	0.777932i	$-0.283731\pi$
$331$	2.60902e40			1.25670			0.628348	+	0.777932i	$0.283731\pi$
$332$	−5.73231e39	−	5.73231e39i	−0.263100	−	0.263100i
$333$	7.11307e36	−	7.11307e36i	0.000311135	−	0.000311135i
$334$			2.13938e40i			0.891957i
$335$		0			0
$336$	−5.86288e39			−0.222169
$337$	4.28358e39	+	4.28358e39i	0.154785	+	0.154785i	0.780251	−	0.625466i	$-0.215091\pi$
$337$	4.28358e39	+	4.28358e39i	0.154785	+	0.154785i	−0.625466	+	0.780251i	$0.715091\pi$
$338$	4.38269e40	−	4.38269e40i	1.51034	−	1.51034i
$339$			2.49003e40i			0.818483i
$340$		0			0
$341$	−1.91917e40			−0.574173
$342$	1.04192e37	+	1.04192e37i	0.000297451	+	0.000297451i
$343$	1.88797e40	−	1.88797e40i	0.514386	−	0.514386i
$344$		−	3.99203e40i		−	1.03815i
$345$		0			0
$346$	6.20930e40			1.47172
$347$	3.86466e40	+	3.86466e40i	0.874660	+	0.874660i	0.992976	−	0.118316i	$-0.0377495\pi$
$347$	3.86466e40	+	3.86466e40i	0.874660	+	0.874660i	−0.118316	+	0.992976i	$0.537749\pi$
$348$	−4.39578e39	+	4.39578e39i	−0.0950097	+	0.0950097i
$349$		−	4.48483e40i		−	0.925847i	−0.886398	−	0.462923i	$-0.846800\pi$
$349$		−	4.48483e40i		−	0.925847i	0.886398	−	0.462923i	$-0.153200\pi$
$350$		0			0
$351$	−1.00829e41			−1.89963
$352$	−1.06610e40	−	1.06610e40i	−0.191918	−	0.191918i
$353$	−5.56911e40	+	5.56911e40i	−0.958055	+	0.958055i	−0.999155	−	0.0410999i	$-0.986914\pi$
$353$	−5.56911e40	+	5.56911e40i	−0.958055	+	0.958055i	0.0410999	+	0.999155i	$0.486914\pi$
$354$		−	9.88118e39i		−	0.162464i
$355$		0			0
$356$	−1.73948e40			−0.261348
$357$	−2.06855e40	−	2.06855e40i	−0.297149	−	0.297149i
$358$	−7.42472e40	+	7.42472e40i	−1.01989	+	1.01989i
$359$		−	1.15843e40i		−	0.152180i	−0.997101	−	0.0760901i	$-0.975756\pi$
$359$		−	1.15843e40i		−	0.152180i	0.997101	−	0.0760901i	$-0.0242437\pi$
$360$		0			0
$361$	4.49853e39			0.0540699
$362$	7.96805e40	+	7.96805e40i	0.916251	+	0.916251i
$363$	5.22090e40	−	5.22090e40i	0.574433	−	0.574433i
$364$		−	2.33752e40i		−	0.246113i
$365$		0			0
$366$	1.25412e41			1.20960
$367$	−1.27160e41	−	1.27160e41i	−1.17407	−	1.17407i	−0.981230	−	0.192841i	$-0.938230\pi$
$367$	−1.27160e41	−	1.27160e41i	−1.17407	−	1.17407i	−0.192841	−	0.981230i	$-0.561770\pi$
$368$	2.15125e40	−	2.15125e40i	0.190163	−	0.190163i
$369$			1.55174e37i			0.000131340i
$370$		0			0
$371$	−8.22005e40			−0.638104
$372$	−4.14323e40	−	4.14323e40i	−0.308072	−	0.308072i
$373$	5.10558e40	−	5.10558e40i	0.363667	−	0.363667i	−0.501494	−	0.865161i	$-0.667216\pi$
$373$	5.10558e40	−	5.10558e40i	0.363667	−	0.363667i	0.865161	+	0.501494i	$0.167216\pi$
$374$			5.54001e40i			0.378063i
$375$		0			0
$376$	1.62128e41			1.01591
$377$	9.14657e40	+	9.14657e40i	0.549284	+	0.549284i
$378$	3.97103e40	−	3.97103e40i	0.228578	−	0.228578i
$379$		−	1.53973e41i		−	0.849605i	−0.905286	−	0.424802i	$-0.860344\pi$
$379$		−	1.53973e41i		−	0.849605i	0.905286	−	0.424802i	$-0.139656\pi$
$380$		0			0
$381$	−3.08122e41			−1.56287
$382$	−2.15368e41	−	2.15368e41i	−1.04753	−	1.04753i
$383$	−1.85557e41	+	1.85557e41i	−0.865558	+	0.865558i	−0.991977	−	0.126419i	$-0.959652\pi$
$383$	−1.85557e41	+	1.85557e41i	−0.865558	+	0.865558i	0.126419	+	0.991977i	$0.459652\pi$
$384$			5.71357e40i			0.255628i
$385$		0			0
$386$	5.65362e40			0.232771
$387$	9.01028e37	+	9.01028e37i	0.000355929	+	0.000355929i
$388$	−4.10635e40	+	4.10635e40i	−0.155650	+	0.155650i
$389$			3.50497e41i			1.27494i	0.770474	+	0.637471i	$0.220020\pi$
$389$			3.50497e41i			1.27494i	−0.770474	+	0.637471i	$0.779980\pi$
$390$		0			0
$391$	1.51801e41			0.508683
$392$	−2.02078e41	−	2.02078e41i	−0.650044	−	0.650044i
$393$	−2.83822e40	+	2.83822e40i	−0.0876528	+	0.0876528i
$394$			2.74482e41i			0.813907i
$395$		0			0
$396$	2.74581e37			7.50839e−5
$397$	3.91560e40	+	3.91560e40i	0.102837	+	0.102837i	0.756653	−	0.653816i	$-0.226833\pi$
$397$	3.91560e40	+	3.91560e40i	0.102837	+	0.102837i	−0.653816	+	0.756653i	$0.726833\pi$
$398$	3.63634e41	−	3.63634e41i	0.917351	−	0.917351i
$399$			1.58241e41i			0.383489i
$400$		0			0
$401$	1.53765e41			0.343992			0.171996	−	0.985098i	$-0.444978\pi$
$401$	1.53765e41			0.343992			0.171996	+	0.985098i	$0.444978\pi$
$402$	3.36736e41	+	3.36736e41i	0.723890	+	0.723890i
$403$	−8.62107e41	+	8.62107e41i	−1.78107	+	1.78107i
$404$		−	5.88430e40i		−	0.116840i
$405$		0			0
$406$	−7.20458e40			−0.132188
$407$	−1.44663e41	−	1.44663e41i	−0.255180	−	0.255180i
$408$	−4.83597e41	+	4.83597e41i	−0.820202	+	0.820202i
$409$			7.74149e39i			0.0126256i	0.999980	+	0.00631279i	$0.00200944\pi$
$409$			7.74149e39i			0.0126256i	−0.999980	+	0.00631279i	$0.997991\pi$
$410$		0			0
$411$	−7.94881e41			−1.19904
$412$	2.12235e41	+	2.12235e41i	0.307937	+	0.307937i
$413$	−3.96276e40	+	3.96276e40i	−0.0553092	+	0.0553092i
$414$			1.53741e38i			0.000206435i
$415$		0			0
$416$	−9.57806e41			−1.19065
$417$	−4.54452e41	−	4.54452e41i	−0.543640	−	0.543640i
$418$	2.11902e41	−	2.11902e41i	0.243957	−	0.243957i
$419$		−	6.04668e41i		−	0.670027i	−0.942213	−	0.335014i	$-0.891259\pi$
$419$		−	6.04668e41i		−	0.670027i	0.942213	−	0.335014i	$-0.108741\pi$
$420$		0			0
$421$	1.44307e41			0.148175			0.0740875	−	0.997252i	$-0.476396\pi$
$421$	1.44307e41			0.148175			0.0740875	+	0.997252i	$0.476396\pi$
$422$	4.60664e41	+	4.60664e41i	0.455392	+	0.455392i
$423$	−3.65935e38	+	3.65935e38i	−0.000348304	+	0.000348304i
$424$			1.92173e42i			1.76132i
$425$		0			0
$426$	2.71221e41			0.230553
$427$	−5.02954e41	−	5.02954e41i	−0.411796	−	0.411796i
$428$	6.52129e40	−	6.52129e40i	0.0514320	−	0.0514320i
$429$			1.08183e42i			0.821945i
$430$		0			0
$431$	5.52569e41			0.389717			0.194859	−	0.980831i	$-0.437575\pi$
$431$	5.52569e41			0.389717			0.194859	+	0.980831i	$0.437575\pi$
$432$	−5.86407e41	−	5.86407e41i	−0.398528	−	0.398528i
$433$	8.29703e40	−	8.29703e40i	0.0543396	−	0.0543396i	−0.679415	−	0.733754i	$-0.737766\pi$
$433$	8.29703e40	−	8.29703e40i	0.0543396	−	0.0543396i	0.733754	+	0.679415i	$0.237766\pi$
$434$		−	6.79065e41i		−	0.428623i
$435$		0			0
$436$	−7.60657e41			−0.446072
$437$	−5.80630e41	−	5.80630e41i	−0.328244	−	0.328244i
$438$	−1.85439e41	+	1.85439e41i	−0.101068	+	0.101068i
$439$		−	1.61595e42i		−	0.849169i	−0.905388	−	0.424585i	$-0.860420\pi$
$439$		−	1.61595e42i		−	0.849169i	0.905388	−	0.424585i	$-0.139580\pi$
$440$		0			0
$441$	9.12209e38			0.000445735
$442$	2.48862e42	+	2.48862e42i	1.17274	+	1.17274i
$443$	6.83128e41	−	6.83128e41i	0.310486	−	0.310486i	−0.534611	−	0.845098i	$-0.679542\pi$
$443$	6.83128e41	−	6.83128e41i	0.310486	−	0.310486i	0.845098	+	0.534611i	$0.179542\pi$
$444$		−	6.24617e41i		−	0.273834i
$445$		0			0
$446$	1.20918e42			0.493324
$447$	2.54025e41	+	2.54025e41i	0.0999899	+	0.0999899i
$448$	7.90966e41	−	7.90966e41i	0.300407	−	0.300407i
$449$		−	2.87136e42i		−	1.05232i	−0.850386	−	0.526159i	$-0.823632\pi$
$449$		−	2.87136e42i		−	1.05232i	0.850386	−	0.526159i	$-0.176368\pi$
$450$		0			0
$451$	3.15588e41			0.107720
$452$	−5.77385e41	−	5.77385e41i	−0.190217	−	0.190217i
$453$	1.58635e42	−	1.58635e42i	0.504461	−	0.504461i
$454$		−	1.68103e42i		−	0.516039i
$455$		0			0
$456$	3.69945e42			1.05852
$457$	1.25651e42	+	1.25651e42i	0.347142	+	0.347142i	0.859044	−	0.511902i	$-0.171059\pi$
$457$	1.25651e42	+	1.25651e42i	0.347142	+	0.347142i	−0.511902	+	0.859044i	$0.671059\pi$
$458$	1.22475e42	−	1.22475e42i	0.326738	−	0.326738i
$459$		−	4.13793e42i		−	1.06606i
$460$		0			0
$461$	4.94269e42			1.18781			0.593907	−	0.804534i	$-0.297585\pi$
$461$	4.94269e42			1.18781			0.593907	+	0.804534i	$0.297585\pi$
$462$	−4.26068e41	−	4.26068e41i	−0.0989026	−	0.0989026i
$463$	3.60441e42	−	3.60441e42i	0.808236	−	0.808236i	−0.176131	−	0.984367i	$-0.556358\pi$
$463$	3.60441e42	−	3.60441e42i	0.808236	−	0.808236i	0.984367	+	0.176131i	$0.0563582\pi$
$464$			1.06391e42i			0.230471i
$465$		0			0
$466$	−9.73093e41			−0.196780
$467$	8.24322e41	+	8.24322e41i	0.161074	+	0.161074i	0.783043	−	0.621968i	$-0.213667\pi$
$467$	8.24322e41	+	8.24322e41i	0.161074	+	0.161074i	−0.621968	+	0.783043i	$0.713667\pi$
$468$	1.23344e39	−	1.23344e39i	0.000232908	−	0.000232908i
$469$		−	2.70090e42i		−	0.492882i
$470$		0			0
$471$	3.43699e42			0.585927
$472$	9.26437e41	+	9.26437e41i	0.152667	+	0.152667i
$473$	1.83248e42	−	1.83248e42i	0.291918	−	0.291918i
$474$			4.73788e42i			0.729677i
$475$		0			0
$476$	9.59302e41			0.138116
$477$	−4.33747e39	−	4.33747e39i	−0.000603869	−	0.000603869i
$478$	7.32069e42	−	7.32069e42i	0.985611	−	0.985611i
$479$		−	1.03862e41i		−	0.0135235i	−0.999977	−	0.00676176i	$-0.997848\pi$
$479$		−	1.03862e41i		−	0.0135235i	0.999977	−	0.00676176i	$-0.00215235\pi$
$480$		0			0
$481$	−1.29968e43			−1.58313
$482$	1.58078e42	+	1.58078e42i	0.186260	+	0.186260i
$483$	−1.16747e42	+	1.16747e42i	−0.133073	+	0.133073i
$484$			2.42123e42i			0.266999i
$485$		0			0
$486$	8.37937e39			0.000865030
$487$	7.70886e40	+	7.70886e40i	0.00770064	+	0.00770064i	0.710947	−	0.703246i	$-0.248267\pi$
$487$	7.70886e40	+	7.70886e40i	0.00770064	+	0.00770064i	−0.703246	+	0.710947i	$0.748267\pi$
$488$	−1.17584e43	+	1.17584e43i	−1.13666	+	1.13666i
$489$			1.00774e43i			0.942768i
$490$		0			0
$491$	6.83855e42			0.599322			0.299661	−	0.954046i	$-0.403126\pi$
$491$	6.83855e42			0.599322			0.299661	+	0.954046i	$0.403126\pi$
$492$	6.81312e41	+	6.81312e41i	0.0577969	+	0.0577969i
$493$	−3.75369e42	+	3.75369e42i	−0.308253	+	0.308253i
$494$		−	1.90376e43i		−	1.51350i
$495$		0			0
$496$	−1.00278e43			−0.747309
$497$	−1.08771e42	−	1.08771e42i	−0.0784893	−	0.0784893i
$498$	−9.38710e42	+	9.38710e42i	−0.655937	+	0.655937i
$499$		−	8.46275e42i		−	0.572668i	−0.958130	−	0.286334i	$-0.907563\pi$
$499$		−	8.46275e42i		−	0.572668i	0.958130	−	0.286334i	$-0.0924367\pi$
$500$		0			0
$501$	−1.71449e43			−1.08826
$502$	−1.57941e43	−	1.57941e43i	−0.971037	−	0.971037i
$503$	6.53699e42	−	6.53699e42i	0.389305	−	0.389305i	−0.485134	−	0.874440i	$-0.661229\pi$
$503$	6.53699e42	−	6.53699e42i	0.389305	−	0.389305i	0.874440	+	0.485134i	$0.161229\pi$
$504$			3.92840e39i			0.000226635i
$505$		0			0
$506$	3.12672e42			0.169309
$507$	3.51228e43	+	3.51228e43i	1.84273	+	1.84273i
$508$	7.14468e42	−	7.14468e42i	0.363215	−	0.363215i
$509$			2.49712e43i			1.23014i	0.788473	+	0.615069i	$0.210872\pi$
$509$			2.49712e43i			1.23014i	−0.788473	+	0.615069i	$0.789128\pi$
$510$		0			0
$511$	1.48738e42			0.0688155
$512$	−1.52432e43	−	1.52432e43i	−0.683529	−	0.683529i
$513$	−1.58273e43	+	1.58273e43i	−0.687906	+	0.687906i
$514$		−	9.96258e42i		−	0.419722i
$515$		0			0
$516$	7.91217e42			0.313257
$517$	7.44226e42	+	7.44226e42i	0.285664	+	0.285664i
$518$	5.11866e42	−	5.11866e42i	0.190494	−	0.190494i
$519$			4.97612e43i			1.79562i
$520$		0			0
$521$	2.71941e43			0.922721			0.461361	−	0.887213i	$-0.347361\pi$
$521$	2.71941e43			0.922721			0.461361	+	0.887213i	$0.347361\pi$
$522$	−3.80164e39	−	3.80164e39i	−0.000125096	−	0.000125096i
$523$	−4.64160e42	+	4.64160e42i	−0.148129	+	0.148129i	−0.777282	−	0.629153i	$-0.783402\pi$
$523$	−4.64160e42	+	4.64160e42i	−0.148129	+	0.148129i	0.629153	+	0.777282i	$0.283402\pi$
$524$		−	1.31625e42i		−	0.0407414i
$525$		0			0
$526$	−1.08874e43			−0.317067
$527$	−3.53802e43	−	3.53802e43i	−0.999518	−	0.999518i
$528$	−6.29180e42	+	6.29180e42i	−0.172438	+	0.172438i
$529$			2.90414e43i			0.772195i
$530$		0			0
$531$	−4.18206e39			−0.000104683
$532$	−3.66927e42	−	3.66927e42i	−0.0891237	−	0.0891237i
$533$	1.41765e43	−	1.41765e43i	0.334144	−	0.334144i
$534$			2.84853e43i			0.651569i
$535$		0			0
$536$	−6.31432e43			−1.36047
$537$	−5.95016e43	−	5.95016e43i	−1.24434	−	1.24434i
$538$	−2.08635e43	+	2.08635e43i	−0.423517	+	0.423517i
$539$		−	1.85522e43i		−	0.365574i
$540$		0			0
$541$	6.85680e43			1.27340			0.636701	−	0.771111i	$-0.280299\pi$
$541$	6.85680e43			1.27340			0.636701	+	0.771111i	$0.280299\pi$
$542$	8.38623e42	+	8.38623e42i	0.151209	+	0.151209i
$543$	−6.38558e43	+	6.38558e43i	−1.11790	+	1.11790i
$544$		−	3.93076e43i		−	0.668182i
$545$		0			0
$546$	−3.82788e43			−0.613586
$547$	1.12718e43	+	1.12718e43i	0.175467	+	0.175467i	0.789377	−	0.613909i	$-0.210404\pi$
$547$	1.12718e43	+	1.12718e43i	0.175467	+	0.175467i	−0.613909	+	0.789377i	$0.710404\pi$
$548$	1.84316e43	−	1.84316e43i	0.278659	−	0.278659i
$549$		−	5.30788e40i		−	0.000779406i
$550$		0			0
$551$	2.87152e43			0.397820
$552$	2.72937e43	+	2.72937e43i	0.367314	+	0.367314i
$553$	1.90009e43	−	1.90009e43i	0.248411	−	0.248411i
$554$		−	5.20443e43i		−	0.661024i
$555$		0			0
$556$	2.10755e43			0.252686
$557$	3.76653e43	+	3.76653e43i	0.438792	+	0.438792i	0.891605	−	0.452814i	$-0.149580\pi$
$557$	3.76653e43	+	3.76653e43i	0.438792	+	0.438792i	−0.452814	+	0.891605i	$0.649580\pi$
$558$	3.58322e40	−	3.58322e40i	0.000405627	−	0.000405627i
$559$		−	1.64633e44i		−	1.81104i
$560$		0			0
$561$	−4.43975e43			−0.461267
$562$	−8.43941e43	−	8.43941e43i	−0.852180	−	0.852180i
$563$	−8.27422e43	+	8.27422e43i	−0.812068	+	0.812068i	−0.984944	−	0.172876i	$-0.944694\pi$
$563$	−8.27422e43	+	8.27422e43i	−0.812068	+	0.812068i	0.172876	+	0.984944i	$0.444694\pi$
$564$			3.21337e43i			0.306546i
$565$		0			0
$566$	−9.66295e43			−0.871057
$567$	3.18070e43	+	3.18070e43i	0.278736	+	0.278736i
$568$	−2.54291e43	+	2.54291e43i	−0.216649	+	0.216649i
$569$			1.64760e44i			1.36476i	0.731000	+	0.682378i	$0.239054\pi$
$569$			1.64760e44i			1.36476i	−0.731000	+	0.682378i	$0.760946\pi$
$570$		0			0
$571$	−6.10122e43			−0.477792			−0.238896	−	0.971045i	$-0.576785\pi$
$571$	−6.10122e43			−0.477792			−0.238896	+	0.971045i	$0.576785\pi$
$572$	−2.50853e43	−	2.50853e43i	−0.191022	−	0.191022i
$573$	1.72595e44	−	1.72595e44i	1.27807	−	1.27807i
$574$			1.11665e43i			0.0804134i
$575$		0			0
$576$	8.34738e40			0.000568579
$577$	−4.83918e43	−	4.83918e43i	−0.320596	−	0.320596i	0.528399	−	0.848996i	$-0.322792\pi$
$577$	−4.83918e43	−	4.83918e43i	−0.320596	−	0.320596i	−0.848996	+	0.528399i	$0.822792\pi$
$578$	−1.22171e43	+	1.22171e43i	−0.0787271	+	0.0787271i
$579$			4.53080e43i			0.283999i
$580$		0			0
$581$	7.52923e43			0.446614
$582$	6.72446e43	+	6.72446e43i	0.388052	+	0.388052i
$583$	−8.82140e43	+	8.82140e43i	−0.495269	+	0.495269i
$584$		−	3.47727e43i		−	0.189947i
$585$		0			0
$586$	3.04135e44			1.57291
$587$	1.31935e44	+	1.31935e44i	0.663972	+	0.663972i	0.956314	−	0.292342i	$-0.0944344\pi$
$587$	1.31935e44	+	1.31935e44i	0.663972	+	0.663972i	−0.292342	+	0.956314i	$0.594434\pi$
$588$	4.00517e43	−	4.00517e43i	0.196148	−	0.196148i
$589$			2.70654e44i			1.28994i
$590$		0			0
$591$	−2.19970e44			−0.993031
$592$	−7.55879e43	−	7.55879e43i	−0.332128	−	0.332128i
$593$	2.91544e44	−	2.91544e44i	1.24689	−	1.24689i	0.289809	−	0.957084i	$-0.406408\pi$
$593$	2.91544e44	−	2.91544e44i	1.24689	−	1.24689i	0.957084	−	0.289809i	$-0.0935919\pi$
$594$		−	8.52309e43i		−	0.354825i
$595$		0			0
$596$	−1.17806e43			−0.0464758
$597$	2.91416e44	+	2.91416e44i	1.11924	+	1.11924i
$598$	1.40455e44	−	1.40455e44i	0.525193	−	0.525193i
$599$		−	2.34634e44i		−	0.854203i	−0.904204	−	0.427102i	$-0.859535\pi$
$599$		−	2.34634e44i		−	0.854203i	0.904204	−	0.427102i	$-0.140465\pi$
$600$		0			0
$601$	2.26082e44			0.780324			0.390162	−	0.920746i	$-0.372419\pi$
$601$	2.26082e44			0.780324			0.390162	+	0.920746i	$0.372419\pi$
$602$	6.48392e43	+	6.48392e43i	0.217918	+	0.217918i
$603$	1.42518e41	−	1.42518e41i	0.000466438	−	0.000466438i
$604$			7.35681e43i			0.234476i
$605$		0			0
$606$	−9.63599e43			−0.291296
$607$	2.69846e44	+	2.69846e44i	0.794505	+	0.794505i	0.982223	−	0.187718i	$-0.0601090\pi$
$607$	2.69846e44	+	2.69846e44i	0.794505	+	0.794505i	−0.187718	+	0.982223i	$0.560109\pi$
$608$	−1.50349e44	+	1.50349e44i	−0.431165	+	0.431165i
$609$		−	5.77373e43i		−	0.161280i
$610$		0			0
$611$	6.68626e44			1.77225
$612$	5.06195e40	+	5.06195e40i	0.000130706	+	0.000130706i
$613$	−3.04960e43	+	3.04960e43i	−0.0767142	+	0.0767142i	−0.744423	−	0.667709i	$-0.767275\pi$
$613$	−3.04960e43	+	3.04960e43i	−0.0767142	+	0.0767142i	0.667709	+	0.744423i	$0.267275\pi$
$614$		−	4.39827e44i		−	1.07792i
$615$		0			0
$616$	7.98944e43			0.185877
$617$	−2.96717e44	−	2.96717e44i	−0.672636	−	0.672636i	0.285687	−	0.958323i	$-0.407778\pi$
$617$	−2.96717e44	−	2.96717e44i	−0.672636	−	0.672636i	−0.958323	+	0.285687i	$0.907778\pi$
$618$	3.47551e44	−	3.47551e44i	0.767721	−	0.767721i
$619$		−	7.00694e44i		−	1.50827i	−0.656722	−	0.754133i	$-0.728058\pi$
$619$		−	7.00694e44i		−	1.50827i	0.656722	−	0.754133i	$-0.271942\pi$
$620$		0			0
$621$	−2.33540e44			−0.477415
$622$	9.14779e43	+	9.14779e43i	0.182251	+	0.182251i
$623$	1.14238e44	−	1.14238e44i	0.221820	−	0.221820i
$624$			5.65267e44i			1.06979i
$625$		0			0
$626$	−7.36022e44			−1.32343
$627$	1.69818e44	+	1.69818e44i	0.297647	+	0.297647i
$628$	−7.96963e43	+	7.96963e43i	−0.136171	+	0.136171i
$629$		−	5.33379e44i		−	0.888435i
$630$		0			0
$631$	−1.87514e44			−0.296868			−0.148434	−	0.988922i	$-0.547423\pi$
$631$	−1.87514e44			−0.296868			−0.148434	+	0.988922i	$0.547423\pi$
$632$	−4.44213e44	−	4.44213e44i	−0.685674	−	0.685674i
$633$	−3.69175e44	+	3.69175e44i	−0.555614	+	0.555614i
$634$			9.86432e43i			0.144757i
$635$		0			0
$636$	−3.80885e44			−0.531472
$637$	−8.33382e44	−	8.33382e44i	−1.13400	−	1.13400i
$638$	−7.73164e43	+	7.73164e43i	−0.102598	+	0.102598i
$639$		−	1.14790e41i		−	0.000148556i
$640$		0			0
$641$	4.10301e44			0.505096			0.252548	−	0.967584i	$-0.418731\pi$
$641$	4.10301e44			0.505096			0.252548	+	0.967584i	$0.418731\pi$
$642$	−1.06791e44	−	1.06791e44i	−0.128226	−	0.128226i
$643$	1.54009e44	−	1.54009e44i	0.180373	−	0.180373i	−0.611146	−	0.791518i	$-0.709291\pi$
$643$	1.54009e44	−	1.54009e44i	0.180373	−	0.180373i	0.791518	+	0.611146i	$0.209291\pi$
$644$		−	5.41420e43i		−	0.0618530i
$645$		0			0
$646$	7.81290e44			0.849361
$647$	2.43956e44	+	2.43956e44i	0.258727	+	0.258727i	0.824536	−	0.565809i	$-0.191436\pi$
$647$	2.43956e44	+	2.43956e44i	0.258727	+	0.258727i	−0.565809	+	0.824536i	$0.691436\pi$
$648$	7.43602e44	−	7.43602e44i	0.769379	−	0.769379i
$649$			8.50533e43i			0.0858571i
$650$		0			0
$651$	5.44201e44			0.522954
$652$	−2.33672e44	−	2.33672e44i	−0.219102	−	0.219102i
$653$	−9.56793e43	+	9.56793e43i	−0.0875401	+	0.0875401i	−0.749521	−	0.661981i	$-0.769716\pi$
$653$	−9.56793e43	+	9.56793e43i	−0.0875401	+	0.0875401i	0.661981	+	0.749521i	$0.269716\pi$
$654$			1.24563e45i			1.11211i
$655$		0			0
$656$	1.64898e44			0.140202
$657$	7.84844e40	+	7.84844e40i	6.51234e−5	+	6.51234e-5i
$658$	−2.63332e44	+	2.63332e44i	−0.213250	+	0.213250i
$659$			9.18988e44i			0.726346i	0.931722	+	0.363173i	$0.118307\pi$
$659$			9.18988e44i			0.726346i	−0.931722	+	0.363173i	$0.881693\pi$
$660$		0			0
$661$	−1.01864e45			−0.767005			−0.383503	−	0.923540i	$-0.625282\pi$
$661$	−1.01864e45			−0.767005			−0.383503	+	0.923540i	$0.625282\pi$
$662$	9.90696e44	+	9.90696e44i	0.728136	+	0.728136i
$663$	−1.99438e45	+	1.99438e45i	−1.43084	+	1.43084i
$664$		−	1.76023e45i		−	1.23276i
$665$		0			0
$666$	5.40193e41			0.000360547
$667$	2.11854e44	+	2.11854e44i	0.138046	+	0.138046i
$668$	3.97554e44	−	3.97554e44i	0.252914	−	0.252914i
$669$			9.69032e44i			0.601894i
$670$		0			0
$671$	−1.07950e45			−0.639237
$672$	3.02305e44	+	3.02305e44i	0.174798	+	0.174798i
$673$	−8.87557e44	+	8.87557e44i	−0.501136	+	0.501136i	−0.911791	−	0.410655i	$-0.865300\pi$
$673$	−8.87557e44	+	8.87557e44i	−0.501136	+	0.501136i	0.410655	+	0.911791i	$0.365300\pi$
$674$			3.25312e44i			0.179366i
$675$		0			0
$676$	−1.62884e45			−0.856510
$677$	−8.12647e44	−	8.12647e44i	−0.417334	−	0.417334i	0.466950	−	0.884284i	$-0.345353\pi$
$677$	−8.12647e44	−	8.12647e44i	−0.417334	−	0.417334i	−0.884284	+	0.466950i	$0.845353\pi$
$678$	−9.45512e44	+	9.45512e44i	−0.474233	+	0.474233i
$679$		−	5.39357e44i		−	0.264216i
$680$		0			0
$681$	1.34718e45			0.629608
$682$	−7.28743e44	−	7.28743e44i	−0.332678	−	0.332678i
$683$	−8.59093e44	+	8.59093e44i	−0.383097	+	0.383097i	−0.872217	−	0.489120i	$-0.837318\pi$
$683$	−8.59093e44	+	8.59093e44i	−0.383097	+	0.383097i	0.489120	+	0.872217i	$0.337318\pi$
$684$		−	3.87233e41i		−	0.000168684i
$685$		0			0
$686$	1.43380e45			0.596076
$687$	9.81511e44	+	9.81511e44i	0.398646	+	0.398646i
$688$	9.57488e44	−	9.57488e44i	0.379943	−	0.379943i
$689$			7.92531e45i			3.07262i
$690$		0			0
$691$	1.46043e44			0.0540547			0.0270273	−	0.999635i	$-0.491396\pi$
$691$	1.46043e44			0.0540547			0.0270273	+	0.999635i	$0.491396\pi$
$692$	−1.15386e45	−	1.15386e45i	−0.417305	−	0.417305i
$693$	−1.80327e41	+	1.80327e41i	−6.37278e−5	+	6.37278e-5i
$694$			2.93497e45i			1.01357i
$695$		0			0
$696$	−1.34982e45			−0.445171
$697$	5.81793e44	+	5.81793e44i	0.187518	+	0.187518i
$698$	1.70297e45	−	1.70297e45i	0.536440	−	0.536440i
$699$		−	7.79835e44i		−	0.240087i
$700$		0			0
$701$	−2.54008e45			−0.747066			−0.373533	−	0.927617i	$-0.621854\pi$
$701$	−2.54008e45			−0.747066			−0.373533	+	0.927617i	$0.621854\pi$
$702$	−3.82865e45	−	3.82865e45i	−1.10066	−	1.10066i
$703$	−2.04014e45	+	2.04014e45i	−0.573291	+	0.573291i
$704$		−	1.69766e45i		−	0.466325i
$705$		0			0
$706$	−4.22939e45			−1.11020
$707$	3.86443e44	+	3.86443e44i	0.0991687	+	0.0991687i
$708$	−1.83619e44	+	1.83619e44i	−0.0460665	+	0.0460665i
$709$		−	4.32665e45i		−	1.06124i	−0.847611	−	0.530618i	$-0.821960\pi$
$709$		−	4.32665e45i		−	1.06124i	0.847611	−	0.530618i	$-0.178040\pi$
$710$		0			0
$711$	2.00524e42			0.000470167
$712$	−2.67072e45	−	2.67072e45i	−0.612277	−	0.612277i
$713$	−1.99682e45	+	1.99682e45i	−0.447618	+	0.447618i
$714$		−	1.57093e45i		−	0.344339i
$715$		0			0
$716$	2.75943e45			0.578376
$717$	5.86679e45	+	5.86679e45i	1.20252	+	1.20252i
$718$	4.39877e44	−	4.39877e44i	0.0881740	−	0.0881740i
$719$		−	6.87903e45i		−	1.34854i	−0.738483	−	0.674272i	$-0.764458\pi$
$719$		−	6.87903e45i		−	1.34854i	0.738483	−	0.674272i	$-0.235542\pi$
$720$		0			0
$721$	−2.78765e45			−0.522726
$722$	1.70818e44	+	1.70818e44i	0.0313283	+	0.0313283i
$723$	−1.26684e45	+	1.26684e45i	−0.227252	+	0.227252i
$724$		−	2.96135e45i		−	0.519605i
$725$		0			0
$726$	3.96495e45			0.665658
$727$	5.53466e45	+	5.53466e45i	0.908951	+	0.908951i	0.996188	−	0.0872369i	$-0.0278037\pi$
$727$	5.53466e45	+	5.53466e45i	0.908951	+	0.908951i	−0.0872369	+	0.996188i	$0.527804\pi$
$728$	3.58893e45	−	3.58893e45i	0.576584	−	0.576584i
$729$			6.36604e45i			1.00053i
$730$		0			0
$731$	6.75643e45			1.01634
$732$	−2.33050e45	−	2.33050e45i	−0.342982	−	0.342982i
$733$	6.73077e45	−	6.73077e45i	0.969173	−	0.969173i	−0.0303658	−	0.999539i	$-0.509667\pi$
$733$	6.73077e45	−	6.73077e45i	0.969173	−	0.969173i	0.999539	+	0.0303658i	$0.00966721\pi$
$734$		−	9.65703e45i		−	1.36053i
$735$		0			0
$736$	−2.21848e45			−0.299234
$737$	−2.89849e45	−	2.89849e45i	−0.382553	−	0.382553i
$738$	−5.89225e41	+	5.89225e41i	−7.60991e−5	+	7.60991e-5i
$739$			4.32206e45i			0.546236i	0.961981	+	0.273118i	$0.0880549\pi$
$739$			4.32206e45i			0.546236i	−0.961981	+	0.273118i	$0.911945\pi$
$740$		0			0
$741$	1.52567e46			1.84659
$742$	−3.12131e45	−	3.12131e45i	−0.369721	−	0.369721i
$743$	−3.77652e45	+	3.77652e45i	−0.437796	+	0.437796i	−0.891270	−	0.453474i	$-0.850185\pi$
$743$	−3.77652e45	+	3.77652e45i	−0.437796	+	0.437796i	0.453474	+	0.891270i	$0.350185\pi$
$744$		−	1.27226e46i		−	1.44348i
$745$		0			0
$746$	3.87737e45			0.421421
$747$	3.97295e42	+	3.97295e42i	0.000422653	+	0.000422653i
$748$	1.02948e45	−	1.02948e45i	0.107200	−	0.107200i
$749$			8.56554e44i			0.0873063i
$750$		0			0
$751$	−1.22236e46			−1.19388			−0.596939	−	0.802286i	$-0.703617\pi$
$751$	−1.22236e46			−1.19388			−0.596939	+	0.802286i	$0.703617\pi$
$752$	3.88865e45	+	3.88865e45i	0.371804	+	0.371804i
$753$	1.26574e46	−	1.26574e46i	1.18474	−	1.18474i
$754$			6.94625e45i			0.636516i
$755$		0			0
$756$	−1.47585e45			−0.129626
$757$	1.49130e46	+	1.49130e46i	1.28242	+	1.28242i	0.939287	+	0.343132i	$0.111488\pi$
$757$	1.49130e46	+	1.49130e46i	1.28242	+	1.28242i	0.343132	+	0.939287i	$0.388512\pi$
$758$	5.84664e45	−	5.84664e45i	0.492265	−	0.492265i
$759$			2.50575e45i			0.206571i
$760$		0			0
$761$	1.95741e46			1.54713			0.773564	−	0.633718i	$-0.218472\pi$
$761$	1.95741e46			1.54713			0.773564	+	0.633718i	$0.218472\pi$
$762$	−1.17000e46	−	1.17000e46i	−0.905534	−	0.905534i
$763$	4.99551e45	−	4.99551e45i	0.378606	−	0.378606i
$764$			8.00423e45i			0.594054i
$765$		0			0
$766$	−1.40919e46			−1.00302
$767$	3.82067e45	+	3.82067e45i	0.266326	+	0.266326i
$768$	8.98459e45	−	8.98459e45i	0.613365	−	0.613365i
$769$		−	4.03487e45i		−	0.269779i	−0.990861	−	0.134889i	$-0.956932\pi$
$769$		−	4.03487e45i		−	0.269779i	0.990861	−	0.134889i	$-0.0430679\pi$
$770$		0			0
$771$	7.98399e45			0.512094
$772$	−1.05059e45	−	1.05059e45i	−0.0660022	−	0.0660022i
$773$	−3.16149e45	+	3.16149e45i	−0.194545	+	0.194545i	−0.797657	−	0.603112i	$-0.793927\pi$
$773$	−3.16149e45	+	3.16149e45i	−0.194545	+	0.194545i	0.603112	+	0.797657i	$0.293927\pi$
$774$			6.84275e42i			0.000412454i
$775$		0			0
$776$	−1.26094e46			−0.729301
$777$	4.10209e45	+	4.10209e45i	0.232417	+	0.232417i
$778$	−1.33090e46	+	1.33090e46i	−0.738708	+	0.738708i
$779$		−	4.45064e45i		−	0.242004i
$780$		0			0
$781$	−2.33456e45			−0.121840
$782$	5.76418e45	+	5.76418e45i	0.294733	+	0.294733i
$783$	5.77490e45	−	5.77490e45i	0.289305	−	0.289305i
$784$		−	9.69370e45i		−	0.475809i
$785$		0			0
$786$	−2.15545e45			−0.101573
$787$	−5.12679e45	−	5.12679e45i	−0.236728	−	0.236728i	0.578766	−	0.815494i	$-0.303535\pi$
$787$	−5.12679e45	−	5.12679e45i	−0.236728	−	0.236728i	−0.815494	+	0.578766i	$0.803535\pi$
$788$	5.10062e45	−	5.10062e45i	0.230783	−	0.230783i
$789$		−	8.72510e45i		−	0.386846i
$790$		0			0
$791$	7.58379e45			0.322896
$792$	4.21579e42	+	4.21579e42i	0.000175904	+	0.000175904i
$793$	−4.84921e46	+	4.84921e46i	−1.98290	+	1.98290i
$794$			2.97365e45i			0.119169i
$795$		0			0
$796$	−1.35146e46			−0.520229
$797$	1.66939e46	+	1.66939e46i	0.629830	+	0.629830i	0.948025	−	0.318195i	$-0.103077\pi$
$797$	1.66939e46	+	1.66939e46i	0.629830	+	0.629830i	−0.318195	+	0.948025i	$0.603077\pi$
$798$	−6.00871e45	+	6.00871e45i	−0.222195	+	0.222195i
$799$			2.74399e46i			0.994568i
$800$		0			0
$801$	1.20560e43			0.000419838
$802$	5.83876e45	+	5.83876e45i	0.199311	+	0.199311i
$803$	1.59619e45	−	1.59619e45i	0.0534116	−	0.0534116i
$804$		−	1.25149e46i		−	0.410517i
$805$		0			0
$806$	−6.54717e46			−2.06392
$807$	−1.67200e46	−	1.67200e46i	−0.516725	−	0.516725i
$808$	9.03449e45	−	9.03449e45i	0.273730	−	0.273730i
$809$			2.47482e46i			0.735135i	0.929997	+	0.367568i	$0.119809\pi$
$809$			2.47482e46i			0.735135i	−0.929997	+	0.367568i	$0.880191\pi$
$810$		0			0
$811$	4.20312e46			1.20016			0.600078	−	0.799941i	$-0.295136\pi$
$811$	4.20312e46			1.20016			0.600078	+	0.799941i	$0.295136\pi$
$812$	1.33880e45	+	1.33880e45i	0.0374818	+	0.0374818i
$813$	−6.72071e45	+	6.72071e45i	−0.184487	+	0.184487i
$814$		−	1.09863e46i		−	0.295706i
$815$		0			0
$816$	−2.31981e46			−0.600358
$817$	−2.58429e46	−	2.58429e46i	−0.655826	−	0.655826i
$818$	−2.93959e44	+	2.93959e44i	−0.00731533	+	0.00731533i
$819$			1.62009e43i			0.000395364i
$820$		0			0
$821$	1.83774e46			0.431313			0.215657	−	0.976469i	$-0.430811\pi$
$821$	1.83774e46			0.431313			0.215657	+	0.976469i	$0.430811\pi$
$822$	−3.01831e46	−	3.01831e46i	−0.694729	−	0.694729i
$823$	−2.81942e46	+	2.81942e46i	−0.636448	+	0.636448i	−0.949677	−	0.313229i	$-0.898589\pi$
$823$	−2.81942e46	+	2.81942e46i	−0.636448	+	0.636448i	0.313229	+	0.949677i	$0.398589\pi$
$824$			6.51713e46i			1.44285i
$825$		0			0
$826$	−3.00947e45			−0.0640928
$827$	1.05051e46	+	1.05051e46i	0.219438	+	0.219438i	0.808261	−	0.588824i	$-0.200409\pi$
$827$	1.05051e46	+	1.05051e46i	0.219438	+	0.219438i	−0.588824	+	0.808261i	$0.700409\pi$
$828$	2.85691e42	−	2.85691e42i	5.85345e−5	−	5.85345e-5i
$829$		−	6.99636e45i		−	0.140605i	−0.997526	−	0.0703023i	$-0.977604\pi$
$829$		−	6.99636e45i		−	0.140605i	0.997526	−	0.0703023i	$-0.0223964\pi$
$830$		0			0
$831$	4.17082e46			0.806502
$832$	−7.62605e46	−	7.62605e46i	−1.44653	−	1.44653i
$833$	3.42014e46	−	3.42014e46i	0.636390	−	0.636390i
$834$		−	3.45128e46i		−	0.629975i
$835$		0			0
$836$	−7.87541e45			−0.138348
$837$	5.44311e46	+	5.44311e46i	0.938080	+	0.938080i
$838$	2.29604e46	−	2.29604e46i	0.388217	−	0.388217i
$839$			1.09639e47i			1.81876i	0.415966	+	0.909380i	$0.363443\pi$
$839$			1.09639e47i			1.81876i	−0.415966	+	0.909380i	$0.636557\pi$
$840$		0			0
$841$	5.21460e46			0.832693
$842$	5.47962e45	+	5.47962e45i	0.0858534	+	0.0858534i
$843$	6.76333e46	−	6.76333e46i	1.03973	−	1.03973i
$844$		−	1.71208e46i		−	0.258252i
$845$		0			0
$846$	−2.77905e43			−0.000403618
$847$	−1.59011e46	−	1.59011e46i	−0.226617	−	0.226617i
$848$	−4.60927e46	+	4.60927e46i	−0.644612	+	0.644612i
$849$		−	7.74387e46i		−	1.06276i
$850$		0			0
$851$	−3.01034e46			−0.397871
$852$	−5.04002e45	−	5.04002e45i	−0.0653730	−	0.0653730i
$853$	−1.07796e47	+	1.07796e47i	−1.37220	+	1.37220i	−0.515016	+	0.857181i	$0.672214\pi$
$853$	−1.07796e47	+	1.07796e47i	−1.37220	+	1.37220i	−0.857181	+	0.515016i	$0.827786\pi$
$854$		−	3.81963e46i		−	0.477194i
$855$		0			0
$856$	2.00250e46			0.240986
$857$	2.27708e46	+	2.27708e46i	0.268958	+	0.268958i	0.828680	−	0.559722i	$-0.189092\pi$
$857$	2.27708e46	+	2.27708e46i	0.268958	+	0.268958i	−0.559722	+	0.828680i	$0.689092\pi$
$858$	−4.10791e46	+	4.10791e46i	−0.476239	+	0.476239i
$859$		−	6.87779e46i		−	0.782633i	−0.920256	−	0.391316i	$-0.872020\pi$
$859$		−	6.87779e46i		−	0.782633i	0.920256	−	0.391316i	$-0.127980\pi$
$860$		0			0
$861$	−8.94885e45			−0.0981108
$862$	2.09821e46	+	2.09821e46i	0.225804	+	0.225804i
$863$	−2.87435e46	+	2.87435e46i	−0.303646	+	0.303646i	−0.842438	−	0.538793i	$-0.818881\pi$
$863$	−2.87435e46	+	2.87435e46i	−0.303646	+	0.303646i	0.538793	+	0.842438i	$0.318881\pi$
$864$			6.04733e46i			0.627110i
$865$		0			0
$866$	6.30108e45			0.0629692
$867$	−9.79079e45	−	9.79079e45i	−0.0960533	−	0.0960533i
$868$	−1.26189e46	+	1.26189e46i	−0.121536	+	0.121536i
$869$		−	4.07818e46i		−	0.385612i
$870$		0			0
$871$	−2.60406e47			−2.37334
$872$	−1.16788e47	−	1.16788e47i	−1.04504	−	1.04504i
$873$	2.84603e43	−	2.84603e43i	0.000250041	−	0.000250041i
$874$		−	4.40952e46i		−	0.380372i
$875$		0			0
$876$	6.89192e45			0.0573158
$877$	4.81552e46	+	4.81552e46i	0.393233	+	0.393233i	0.875838	−	0.482605i	$-0.160309\pi$
$877$	4.81552e46	+	4.81552e46i	0.393233	+	0.393233i	−0.482605	+	0.875838i	$0.660309\pi$
$878$	6.13605e46	−	6.13605e46i	0.492013	−	0.492013i
$879$			2.43733e47i			1.91908i
$880$		0			0
$881$	1.32699e47			1.00752			0.503761	−	0.863843i	$-0.331949\pi$
$881$	1.32699e47			1.00752			0.503761	+	0.863843i	$0.331949\pi$
$882$	3.46383e43	+	3.46383e43i	0.000258261	+	0.000258261i
$883$	−3.88616e46	+	3.88616e46i	−0.284544	+	0.284544i	−0.834918	−	0.550374i	$-0.814485\pi$
$883$	−3.88616e46	+	3.88616e46i	−0.284544	+	0.284544i	0.550374	+	0.834918i	$0.314485\pi$
$884$		−	9.24906e46i		−	0.665061i
$885$		0			0
$886$	5.18793e46			0.359795
$887$	1.61402e47	+	1.61402e47i	1.09934	+	1.09934i	0.994488	+	0.104852i	$0.0334370\pi$
$887$	1.61402e47	+	1.61402e47i	1.09934	+	1.09934i	0.104852	+	0.994488i	$0.466563\pi$
$888$	9.59010e46	−	9.59010e46i	0.641528	−	0.641528i
$889$			9.38434e46i			0.616560i
$890$		0			0
$891$	6.82678e46			0.432686
$892$	−2.24698e46	−	2.24698e46i	−0.139882	−	0.139882i
$893$	1.04956e47	−	1.04956e47i	0.641776	−	0.641776i
$894$			1.92916e46i			0.115869i
$895$		0			0
$896$	1.74016e46			0.100846
$897$	1.12561e47	+	1.12561e47i	0.640777	+	0.640777i
$898$	1.09031e47	−	1.09031e47i	0.609718	−	0.609718i
$899$		−	9.87534e46i		−	0.542497i
$900$		0			0
$901$	−3.25249e47			−1.72433
$902$	1.19835e46	+	1.19835e46i	0.0624134	+	0.0624134i
$903$	−5.19620e46	+	5.19620e46i	−0.265878	+	0.265878i
$904$		−	1.77298e47i		−	0.891270i
$905$		0			0
$906$	1.20473e47			0.584575
$907$	−1.65407e47	−	1.65407e47i	−0.788567	−	0.788567i	0.192692	−	0.981259i	$-0.438278\pi$
$907$	−1.65407e47	−	1.65407e47i	−0.788567	−	0.788567i	−0.981259	+	0.192692i	$0.938278\pi$
$908$	−3.12381e46	+	3.12381e46i	−0.146322	+	0.146322i
$909$			4.07829e43i			0.000187696i
$910$		0			0
$911$	7.63769e46			0.339366			0.169683	−	0.985499i	$-0.445726\pi$
$911$	7.63769e46			0.339366			0.169683	+	0.985499i	$0.445726\pi$
$912$	8.87313e46	+	8.87313e46i	0.387400	+	0.387400i
$913$	8.08005e46	−	8.08005e46i	0.346642	−	0.346642i
$914$			9.54241e46i			0.402271i
$915$		0			0
$916$	−4.55183e46			−0.185293
$917$	8.64426e45	+	8.64426e45i	0.0345795	+	0.0345795i
$918$	1.57125e47	−	1.57125e47i	0.617678	−	0.617678i
$919$		−	1.49043e47i		−	0.575789i	−0.957662	−	0.287895i	$-0.907045\pi$
$919$		−	1.49043e47i		−	0.575789i	0.957662	−	0.287895i	$-0.0929553\pi$
$920$		0			0
$921$	3.52477e47			1.31515
$922$	1.87683e47	+	1.87683e47i	0.688225	+	0.688225i
$923$	−1.04871e47	+	1.04871e47i	−0.377944	+	0.377944i
$924$			1.58350e46i			0.0560875i
$925$		0			0
$926$	2.73732e47			0.936591
$927$	−1.47096e44	−	1.47096e44i	−0.000494681	−	0.000494681i
$928$	5.48578e46	−	5.48578e46i	0.181331	−	0.181331i
$929$		−	1.79815e46i		−	0.0584217i	−0.999573	−	0.0292108i	$-0.990701\pi$
$929$		−	1.79815e46i		−	0.0584217i	0.999573	−	0.0292108i	$-0.00929942\pi$
$930$		0			0
$931$	−2.61636e47			−0.821301
$932$	1.80827e46	+	1.80827e46i	0.0557967	+	0.0557967i
$933$	−7.33102e46	+	7.33102e46i	−0.222361	+	0.222361i
$934$			6.26021e46i			0.186655i
$935$		0			0
$936$	3.78754e44			0.00109130
$937$	1.10459e47	+	1.10459e47i	0.312873	+	0.312873i	0.846022	−	0.533149i	$-0.178991\pi$
$937$	1.10459e47	+	1.10459e47i	0.312873	+	0.312873i	−0.533149	+	0.846022i	$0.678991\pi$
$938$	1.02558e47	−	1.02558e47i	0.285578	−	0.285578i
$939$		−	5.89847e47i		−	1.61469i
$940$		0			0
$941$	2.98277e47			0.789197			0.394599	−	0.918854i	$-0.370884\pi$
$941$	2.98277e47			0.789197			0.394599	+	0.918854i	$0.370884\pi$
$942$	1.30509e47	+	1.30509e47i	0.339489	+	0.339489i
$943$	3.28358e46	−	3.28358e46i	0.0839769	−	0.0839769i
$944$			4.44412e46i			0.111746i
$945$		0			0
$946$	1.39165e47			0.338278
$947$	−2.75001e47	−	2.75001e47i	−0.657257	−	0.657257i	0.297473	−	0.954730i	$-0.403856\pi$
$947$	−2.75001e47	−	2.75001e47i	−0.657257	−	0.657257i	−0.954730	+	0.297473i	$0.903856\pi$
$948$	8.80426e46	−	8.80426e46i	0.206899	−	0.206899i
$949$		−	1.43405e47i		−	0.331363i
$950$		0			0
$951$	−7.90525e46			−0.176615
$952$	1.47287e47	+	1.47287e47i	0.323574	+	0.323574i
$953$	3.95004e47	−	3.95004e47i	0.853326	−	0.853326i	−0.137215	−	0.990541i	$-0.543815\pi$
$953$	3.95004e47	−	3.95004e47i	0.853326	−	0.853326i	0.990541	+	0.137215i	$0.0438151\pi$
$954$		−	3.29404e44i		−	0.000699770i
$955$		0			0
$956$	−2.72076e47			−0.558939
$957$	−6.19612e46	−	6.19612e46i	−0.125178	−	0.125178i
$958$	3.94384e45	−	3.94384e45i	0.00783559	−	0.00783559i
$959$			2.42094e47i			0.473027i
$960$		0			0
$961$	4.01653e47			0.759060
$962$	−4.93513e47	−	4.93513e47i	−0.917271	−	0.917271i
$963$	−4.51978e43	+	4.51978e43i	−8.26222e−5	+	8.26222e-5i
$964$		−	5.87504e46i		−	0.105628i
$965$		0			0
$966$	−8.86617e46			−0.154206
$967$	−4.04439e47	−	4.04439e47i	−0.691878	−	0.691878i	0.270767	−	0.962645i	$-0.412723\pi$
$967$	−4.04439e47	−	4.04439e47i	−0.691878	−	0.691878i	−0.962645	+	0.270767i	$0.912723\pi$
$968$	−3.71744e47	+	3.71744e47i	−0.625516	+	0.625516i
$969$			6.26125e47i			1.03629i
$970$		0			0
$971$	−2.93551e47			−0.470084			−0.235042	−	0.971985i	$-0.575523\pi$
$971$	−2.93551e47			−0.470084			−0.235042	+	0.971985i	$0.575523\pi$
$972$	−1.55711e44	−	1.55711e44i	−0.000245279	−	0.000245279i
$973$	−1.38411e47	+	1.38411e47i	−0.214469	+	0.214469i
$974$			5.85440e45i			0.00892358i
$975$		0			0
$976$	−5.64048e47			−0.831992
$977$	−3.14946e47	−	3.14946e47i	−0.457007	−	0.457007i	0.440664	−	0.897672i	$-0.354743\pi$
$977$	−3.14946e47	−	3.14946e47i	−0.457007	−	0.457007i	−0.897672	+	0.440664i	$0.854743\pi$
$978$	−3.82656e47	+	3.82656e47i	−0.546245	+	0.546245i
$979$		−	2.45190e47i		−	0.344334i
$980$		0			0
$981$	5.27196e44			0.000716586
$982$	2.59673e47	+	2.59673e47i	0.347250	+	0.347250i
$983$	−5.30346e47	+	5.30346e47i	−0.697756	+	0.697756i	−0.963926	−	0.266170i	$-0.914242\pi$
$983$	−5.30346e47	+	5.30346e47i	−0.697756	+	0.697756i	0.266170	+	0.963926i	$0.414242\pi$
$984$			2.09211e47i			0.270809i
$985$		0			0
$986$	−2.85069e47			−0.357206
$987$	−2.11034e47	−	2.11034e47i	−0.260182	−	0.260182i
$988$	−3.53771e47	+	3.53771e47i	−0.429151	+	0.429151i
$989$		−	3.81326e47i		−	0.455151i
$990$		0			0
$991$	−1.72114e48			−1.98902			−0.994509	−	0.104654i	$-0.966626\pi$
$991$	−1.72114e48			−1.98902			−0.994509	+	0.104654i	$0.966626\pi$
$992$	5.17060e47	+	5.17060e47i	0.587969	+	0.587969i
$993$	−7.93942e47	+	7.93942e47i	−0.888384	+	0.888384i
$994$		−	8.26047e46i		−	0.0909541i
$995$		0			0
$996$	3.48875e47			0.371981
$997$	1.10465e47	+	1.10465e47i	0.115905	+	0.115905i	0.762681	−	0.646775i	$-0.223883\pi$
$997$	1.10465e47	+	1.10465e47i	0.115905	+	0.115905i	−0.646775	+	0.762681i	$0.723883\pi$
$998$	3.21347e47	−	3.21347e47i	0.331807	−	0.331807i
$999$			8.20583e47i			0.833825i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.33.c.b.7.10		30
5.2	odd	4		5.33.c.a.3.6	yes	30
5.3	odd	4	inner	25.33.c.b.18.10		30
5.4	even	2		5.33.c.a.2.6	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.33.c.a.2.6	✓	30	5.4	even	2
5.33.c.a.3.6	yes	30	5.2	odd	4
25.33.c.b.7.10		30	1.1	even	1	trivial
25.33.c.b.18.10		30	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:	\( k \)	\(=\)	\( 33 \)
Character orbit:	\([\chi]\)	\(=\)	25.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(37971.9 + 37971.9i) q^{2} +(-3.04306e7 + 3.04306e7i) q^{3} -1.41124e9i q^{4} -2.31101e12 q^{6} +(9.26812e12 + 9.26812e12i) q^{7} +(2.16675e14 - 2.16675e14i) q^{8} +9.78102e11i q^{9} +O(q^{10})\)	\(q+(37971.9 + 37971.9i) q^{2} +(-3.04306e7 + 3.04306e7i) q^{3} -1.41124e9i q^{4} -2.31101e12 q^{6} +(9.26812e12 + 9.26812e12i) q^{7} +(2.16675e14 - 2.16675e14i) q^{8} +9.78102e11i q^{9} +1.98923e16 q^{11} +(4.29449e16 + 4.29449e16i) q^{12} +(8.93581e17 - 8.93581e17i) q^{13} +7.03856e17i q^{14} +1.03939e19 q^{16} +(3.66719e19 + 3.66719e19i) q^{17} +(-3.71404e16 + 3.71404e16i) q^{18} -2.80535e20i q^{19} -5.64069e20 q^{21} +(7.55348e20 + 7.55348e20i) q^{22} +(2.06972e21 - 2.06972e21i) q^{23} +1.31871e22i q^{24} +6.78619e22 q^{26} +(-5.64183e22 - 5.64183e22i) q^{27} +(1.30795e22 - 1.30795e22i) q^{28} +1.02359e23i q^{29} -9.64778e23 q^{31} +(-5.35937e23 - 5.35937e23i) q^{32} +(-6.05335e23 + 6.05335e23i) q^{33} +2.78500e24i q^{34} +1.38034e21 q^{36} +(-7.27232e24 - 7.27232e24i) q^{37} +(1.06524e25 - 1.06524e25i) q^{38} +5.43844e25i q^{39} +1.58648e25 q^{41} +(-2.14188e25 - 2.14188e25i) q^{42} +(9.21200e25 - 9.21200e25i) q^{43} -2.80728e25i q^{44} +1.57183e26 q^{46} +(3.74128e26 + 3.74128e26i) q^{47} +(-3.16293e26 + 3.16293e26i) q^{48} -9.32632e26i q^{49} -2.23189e27 q^{51} +(-1.26106e27 - 1.26106e27i) q^{52} +(-4.43458e27 + 4.43458e27i) q^{53} -4.28462e27i q^{54} +4.01635e27 q^{56} +(8.53685e27 + 8.53685e27i) q^{57} +(-3.88675e27 + 3.88675e27i) q^{58} +4.27569e27i q^{59} -5.42671e28 q^{61} +(-3.66344e28 - 3.66344e28i) q^{62} +(-9.06517e24 + 9.06517e24i) q^{63} -8.53426e28i q^{64} -4.59714e28 q^{66} +(-1.45709e29 - 1.45709e29i) q^{67} +(5.17528e28 - 5.17528e28i) q^{68} +1.25966e29i q^{69} -1.17360e29 q^{71} +(2.11931e26 + 2.11931e26i) q^{72} +(8.02415e28 - 8.02415e28i) q^{73} -5.52287e29i q^{74} -3.95902e29 q^{76} +(1.84364e29 + 1.84364e29i) q^{77} +(-2.06508e30 + 2.06508e30i) q^{78} -2.05013e30i q^{79} +3.43187e30 q^{81} +(6.02417e29 + 6.02417e29i) q^{82} +(4.06190e30 - 4.06190e30i) q^{83} +7.96036e29i q^{84} +6.99594e30 q^{86} +(-3.11484e30 - 3.11484e30i) q^{87} +(4.31017e30 - 4.31017e30i) q^{88} -1.23259e31i q^{89} +1.65636e31 q^{91} +(-2.92087e30 - 2.92087e30i) q^{92} +(2.93588e31 - 2.93588e31i) q^{93} +2.84127e31i q^{94} +3.26178e31 q^{96} +(-2.90974e31 - 2.90974e31i) q^{97} +(3.54138e31 - 3.54138e31i) q^{98} +1.94567e28i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 2 q^{2} + 2792232 q^{3} - 645476451240 q^{6} - 21807690136848 q^{7} - 340768936037220 q^{8}+O(q^{10}) \) 30 * q + 2 * q^2 + 2792232 * q^3 - 645476451240 * q^6 - 21807690136848 * q^7 - 340768936037220 * q^8	\( 30 q + 2 q^{2} + 2792232 q^{3} - 645476451240 q^{6} - 21807690136848 q^{7} - 340768936037220 q^{8} - 60\!\cdots\!40 q^{11}+ \cdots - 12\!\cdots\!02 q^{98}+O(q^{100}) \) 30 * q + 2 * q^2 + 2792232 * q^3 - 645476451240 * q^6 - 21807690136848 * q^7 - 340768936037220 * q^8 - 60908362837533640 * q^11 - 444566273630869608 * q^12 - 649759187023107138 * q^13 - 46108906958970522120 * q^16 + 218107661739005884502 * q^17 - 240407468159884203858 * q^18 + 4549905652154594876760 * q^21 + 11386561172247365212944 * q^22 - 13896091629970965206008 * q^23 - 23129486500762683557740 * q^26 - 176388356775702789525960 * q^27 - 59665474478272755491112 * q^28 - 1285786827516670637255040 * q^31 - 3122517776856150857591368 * q^32 + 1644615516923295701112504 * q^33 + 31947551193266858523505980 * q^36 + 126275105375668809211002 * q^37 - 57601564734016178366855880 * q^38 - 155417315271390260892986440 * q^41 - 797836438482097707185724336 * q^42 + 545147034084978191886568152 * q^43 - 3454637097270705106900721640 * q^46 - 2735203198488492729395621848 * q^47 + 3192952350241941373327314192 * q^48 - 6129415060408014316542923040 * q^51 - 6000870590399837156109494028 * q^52 + 11282171275183571262774628682 * q^53 - 47918174764291639802549158800 * q^56 - 44765351794015370451647799120 * q^57 + 29637988346430122895588672480 * q^58 + 50784540875895586667393303160 * q^61 + 218235799024898727529128868024 * q^62 - 213794735887989269330759842008 * q^63 + 1348836243659025586642346421120 * q^66 + 736483403252315334072161239752 * q^67 - 1085395947449178489054935855012 * q^68 + 817740403780342392034746361760 * q^71 + 951267702824572414087545605820 * q^72 + 379868722209495311437504600242 * q^73 - 6689750080738358201358794259600 * q^76 - 6381539826853244422672988941256 * q^77 + 9179143477318522110451614982584 * q^78 - 14239669107938661073624705472070 * q^81 - 2725313872720345364461277817936 * q^82 - 4996401755555614465785455997328 * q^83 + 16049932109847278395442966171960 * q^86 - 36834415428157346041110451524480 * q^87 + 47132513308908068698430156048160 * q^88 - 104150500668224029090357708737840 * q^91 + 18747876848872687606754750486552 * q^92 - 112210213536624471769268225064216 * q^93 + 380819283905835347723966665116960 * q^96 + 155781506757725945270376012026802 * q^97 - 125692870459469366775669291878702 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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