LMFDB - Embedded newform 25.9.c.b.7.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [25,9,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, 9, names="a")

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

chi := DirichletCharacter("25.7");

S:= CuspForms(chi, 9);

N := Newforms(S);

Level:	$ N $	$=$	$ 25 = 5^{2} $
Weight:	$ k $	$=$	$ 9 $
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:	$10.1844652515$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} - 30x^{3} + 1089x^{2} - 3168x + 4608 $ x^6 - 2x^5 + 2x^4 - 30x^3 + 1089x^2 - 3168*x + 4608
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6}\cdot 5^{2} $
Twist minimal:	no (minimal twist has level 5)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			7.2
Root			$-4.23471 + 4.23471i$ of defining polynomial
Character	$\chi$	$=$	25.7
Dual form			25.9.c.b.18.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(4.39608 + 4.39608i) q^{2} +(-75.2981 + 75.2981i) q^{3} -217.349i q^{4} -662.032 q^{6} +(-730.992 - 730.992i) q^{7} +(2080.88 - 2080.88i) q^{8} -4778.60i q^{9} +O(q^{10})$	\(q+(4.39608 + 4.39608i) q^{2} +(-75.2981 + 75.2981i) q^{3} -217.349i q^{4} -662.032 q^{6} +(-730.992 - 730.992i) q^{7} +(2080.88 - 2080.88i) q^{8} -4778.60i q^{9} +19599.8 q^{11} +(16366.0 + 16366.0i) q^{12} +(24915.1 - 24915.1i) q^{13} -6426.99i q^{14} -37346.0 q^{16} +(11288.6 + 11288.6i) q^{17} +(21007.1 - 21007.1i) q^{18} -171525. i q^{19} +110085. q^{21} +(86162.2 + 86162.2i) q^{22} +(132074. - 132074. i) q^{23} +313372. i q^{24} +219057. q^{26} +(-134211. - 134211. i) q^{27} +(-158880. + 158880. i) q^{28} -127019. i q^{29} -960715. q^{31} +(-696880. - 696880. i) q^{32} +(-1.47583e6 + 1.47583e6i) q^{33} +99251.5i q^{34} -1.03862e6 q^{36} +(243873. + 243873. i) q^{37} +(754036. - 754036. i) q^{38} +3.75212e6i q^{39} +2.50747e6 q^{41} +(483940. + 483940. i) q^{42} +(6763.95 - 6763.95i) q^{43} -4.26000e6i q^{44} +1.16122e6 q^{46} +(1.79394e6 + 1.79394e6i) q^{47} +(2.81208e6 - 2.81208e6i) q^{48} -4.69610e6i q^{49} -1.70003e6 q^{51} +(-5.41527e6 - 5.41527e6i) q^{52} +(2.97161e6 - 2.97161e6i) q^{53} -1.18001e6i q^{54} -3.04221e6 q^{56} +(1.29155e7 + 1.29155e7i) q^{57} +(558385. - 558385. i) q^{58} +313805. i q^{59} +1.76977e7 q^{61} +(-4.22338e6 - 4.22338e6i) q^{62} +(-3.49312e6 + 3.49312e6i) q^{63} +3.43349e6i q^{64} -1.29757e7 q^{66} +(-4.41349e6 - 4.41349e6i) q^{67} +(2.45358e6 - 2.45358e6i) q^{68} +1.98899e7i q^{69} -8.89315e6 q^{71} +(-9.94368e6 - 9.94368e6i) q^{72} +(-1.95076e7 + 1.95076e7i) q^{73} +2.14417e6i q^{74} -3.72808e7 q^{76} +(-1.43273e7 - 1.43273e7i) q^{77} +(-1.64946e7 + 1.64946e7i) q^{78} -1.11272e7i q^{79} +5.15641e7 q^{81} +(1.10230e7 + 1.10230e7i) q^{82} +(-1.58712e7 + 1.58712e7i) q^{83} -2.39268e7i q^{84} +59469.7 q^{86} +(9.56429e6 + 9.56429e6i) q^{87} +(4.07848e7 - 4.07848e7i) q^{88} +4.85032e7i q^{89} -3.64255e7 q^{91} +(-2.87062e7 - 2.87062e7i) q^{92} +(7.23400e7 - 7.23400e7i) q^{93} +1.57726e7i q^{94} +1.04948e8 q^{96} +(1.07411e8 + 1.07411e8i) q^{97} +(2.06444e7 - 2.06444e7i) q^{98} -9.36596e7i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 2 q^{2} + 72 q^{3} + 1752 q^{6} + 2352 q^{7} + 8220 q^{8}+O(q^{10}) $ 6 * q + 2 * q^2 + 72 * q^3 + 1752 * q^6 + 2352 * q^7 + 8220 * q^8	$ 6 q + 2 q^{2} + 72 q^{3} + 1752 q^{6} + 2352 q^{7} + 8220 q^{8} + 23192 q^{11} + 45912 q^{12} + 119142 q^{13} + 218616 q^{16} + 265502 q^{17} + 454062 q^{18} + 231672 q^{21} + 35664 q^{22} - 28888 q^{23} - 801388 q^{26} - 392040 q^{27} - 1305192 q^{28} - 747648 q^{31} - 3033928 q^{32} - 4269096 q^{33} - 3972804 q^{36} + 454002 q^{37} - 1443720 q^{38} + 2489432 q^{41} - 4223856 q^{42} - 792648 q^{43} - 3149928 q^{46} + 15313352 q^{47} + 21677712 q^{48} + 35567712 q^{51} + 735732 q^{52} + 13509122 q^{53} - 18454800 q^{56} + 34625520 q^{57} + 23903520 q^{58} + 24111192 q^{61} - 53913416 q^{62} - 44837688 q^{63} - 55047936 q^{66} + 32827752 q^{67} - 8118692 q^{68} - 13992928 q^{71} - 82596420 q^{72} - 111859638 q^{73} - 56470800 q^{76} - 26260136 q^{77} - 31125576 q^{78} + 65834226 q^{81} - 38023056 q^{82} + 14768432 q^{83} - 135560008 q^{86} + 133207680 q^{87} + 44555040 q^{88} + 167542032 q^{91} - 69931048 q^{92} + 96798024 q^{93} + 184867872 q^{96} + 186656202 q^{97} + 345959698 q^{98}+O(q^{100}) $ 6 * q + 2 * q^2 + 72 * q^3 + 1752 * q^6 + 2352 * q^7 + 8220 * q^8 + 23192 * q^11 + 45912 * q^12 + 119142 * q^13 + 218616 * q^16 + 265502 * q^17 + 454062 * q^18 + 231672 * q^21 + 35664 * q^22 - 28888 * q^23 - 801388 * q^26 - 392040 * q^27 - 1305192 * q^28 - 747648 * q^31 - 3033928 * q^32 - 4269096 * q^33 - 3972804 * q^36 + 454002 * q^37 - 1443720 * q^38 + 2489432 * q^41 - 4223856 * q^42 - 792648 * q^43 - 3149928 * q^46 + 15313352 * q^47 + 21677712 * q^48 + 35567712 * q^51 + 735732 * q^52 + 13509122 * q^53 - 18454800 * q^56 + 34625520 * q^57 + 23903520 * q^58 + 24111192 * q^61 - 53913416 * q^62 - 44837688 * q^63 - 55047936 * q^66 + 32827752 * q^67 - 8118692 * q^68 - 13992928 * q^71 - 82596420 * q^72 - 111859638 * q^73 - 56470800 * q^76 - 26260136 * q^77 - 31125576 * q^78 + 65834226 * q^81 - 38023056 * q^82 + 14768432 * q^83 - 135560008 * q^86 + 133207680 * q^87 + 44555040 * q^88 + 167542032 * q^91 - 69931048 * q^92 + 96798024 * q^93 + 184867872 * q^96 + 186656202 * q^97 + 345959698 * 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 $

$2$	4.39608	+	4.39608i	0.274755	+	0.274755i	0.831011	−	0.556256i	$-0.187763\pi$
$2$	4.39608	+	4.39608i	0.274755	+	0.274755i	−0.556256	+	0.831011i	$0.687763\pi$
$3$	−75.2981	+	75.2981i	−0.929606	+	0.929606i	−0.997680	−	0.0680745i	$-0.978314\pi$
$3$	−75.2981	+	75.2981i	−0.929606	+	0.929606i	0.0680745	+	0.997680i	$0.478314\pi$
$4$		−	217.349i		−	0.849020i
$5$		0			0
$5$		0			0
$6$	−662.032			−0.510827
$7$	−730.992	−	730.992i	−0.304453	−	0.304453i	0.538300	−	0.842753i	$-0.319067\pi$
$7$	−730.992	−	730.992i	−0.304453	−	0.304453i	−0.842753	+	0.538300i	$0.819067\pi$
$8$	2080.88	−	2080.88i	0.508027	−	0.508027i
$9$		−	4778.60i		−	0.728334i
$10$		0			0
$11$	19599.8			1.33869			0.669347	−	0.742950i	$-0.266574\pi$
$11$	19599.8			1.33869			0.669347	+	0.742950i	$0.266574\pi$
$12$	16366.0	+	16366.0i	0.789254	+	0.789254i
$13$	24915.1	−	24915.1i	0.872347	−	0.872347i	−0.120381	−	0.992728i	$-0.538412\pi$
$13$	24915.1	−	24915.1i	0.872347	−	0.872347i	0.992728	+	0.120381i	$0.0384115\pi$
$14$		−	6426.99i		−	0.167300i
$15$		0			0
$16$	−37346.0			−0.569854
$17$	11288.6	+	11288.6i	0.135159	+	0.135159i	0.771450	−	0.636290i	$-0.219532\pi$
$17$	11288.6	+	11288.6i	0.135159	+	0.135159i	−0.636290	+	0.771450i	$0.719532\pi$
$18$	21007.1	−	21007.1i	0.200113	−	0.200113i
$19$		−	171525.i		−	1.31617i	−0.752943	−	0.658086i	$-0.771366\pi$
$19$		−	171525.i		−	1.31617i	0.752943	−	0.658086i	$-0.228634\pi$
$20$		0			0
$21$	110085.			0.566043
$22$	86162.2	+	86162.2i	0.367812	+	0.367812i
$23$	132074.	−	132074.i	0.471961	−	0.471961i	−0.430587	−	0.902549i	$-0.641694\pi$
$23$	132074.	−	132074.i	0.471961	−	0.471961i	0.902549	+	0.430587i	$0.141694\pi$
$24$			313372.i			0.944529i
$25$		0			0
$26$	219057.			0.479363
$27$	−134211.	−	134211.i	−0.252542	−	0.252542i
$28$	−158880.	+	158880.i	−0.258487	+	0.258487i
$29$		−	127019.i		−	0.179588i	−0.995960	−	0.0897939i	$-0.971379\pi$
$29$		−	127019.i		−	0.179588i	0.995960	−	0.0897939i	$-0.0286208\pi$
$30$		0			0
$31$	−960715.			−1.04027			−0.520137	−	0.854083i	$-0.674119\pi$
$31$	−960715.			−1.04027			−0.520137	+	0.854083i	$0.674119\pi$
$32$	−696880.	−	696880.i	−0.664597	−	0.664597i
$33$	−1.47583e6	+	1.47583e6i	−1.24446	+	1.24446i
$34$			99251.5i			0.0742713i
$35$		0			0
$36$	−1.03862e6			−0.618370
$37$	243873.	+	243873.i	0.130124	+	0.130124i	0.769169	−	0.639045i	$-0.220670\pi$
$37$	243873.	+	243873.i	0.130124	+	0.130124i	−0.639045	+	0.769169i	$0.720670\pi$
$38$	754036.	−	754036.i	0.361625	−	0.361625i
$39$			3.75212e6i			1.62188i
$40$		0			0
$41$	2.50747e6			0.887360			0.443680	−	0.896185i	$-0.353673\pi$
$41$	2.50747e6			0.887360			0.443680	+	0.896185i	$0.353673\pi$
$42$	483940.	+	483940.i	0.155523	+	0.155523i
$43$	6763.95	−	6763.95i	0.00197846	−	0.00197846i	−0.706117	−	0.708095i	$-0.749555\pi$
$43$	6763.95	−	6763.95i	0.00197846	−	0.00197846i	0.708095	+	0.706117i	$0.249555\pi$
$44$		−	4.26000e6i		−	1.13658i
$45$		0			0
$46$	1.16122e6			0.259347
$47$	1.79394e6	+	1.79394e6i	0.367635	+	0.367635i	0.866614	−	0.498979i	$-0.166291\pi$
$47$	1.79394e6	+	1.79394e6i	0.367635	+	0.367635i	−0.498979	+	0.866614i	$0.666291\pi$
$48$	2.81208e6	−	2.81208e6i	0.529740	−	0.529740i
$49$		−	4.69610e6i		−	0.814617i
$50$		0			0
$51$	−1.70003e6			−0.251290
$52$	−5.41527e6	−	5.41527e6i	−0.740640	−	0.740640i
$53$	2.97161e6	−	2.97161e6i	0.376608	−	0.376608i	−0.493269	−	0.869877i	$-0.664198\pi$
$53$	2.97161e6	−	2.97161e6i	0.376608	−	0.376608i	0.869877	+	0.493269i	$0.164198\pi$
$54$		−	1.18001e6i		−	0.138774i
$55$		0			0
$56$	−3.04221e6			−0.309341
$57$	1.29155e7	+	1.29155e7i	1.22352	+	1.22352i
$58$	558385.	−	558385.i	0.0493426	−	0.0493426i
$59$			313805.i			0.0258972i	0.999916	+	0.0129486i	$0.00412178\pi$
$59$			313805.i			0.0258972i	−0.999916	+	0.0129486i	$0.995878\pi$
$60$		0			0
$61$	1.76977e7			1.27820			0.639098	−	0.769125i	$-0.279308\pi$
$61$	1.76977e7			1.27820			0.639098	+	0.769125i	$0.279308\pi$
$62$	−4.22338e6	−	4.22338e6i	−0.285820	−	0.285820i
$63$	−3.49312e6	+	3.49312e6i	−0.221744	+	0.221744i
$64$			3.43349e6i			0.204652i
$65$		0			0
$66$	−1.29757e7			−0.683841
$67$	−4.41349e6	−	4.41349e6i	−0.219020	−	0.219020i	0.589066	−	0.808085i	$-0.299496\pi$
$67$	−4.41349e6	−	4.41349e6i	−0.219020	−	0.219020i	−0.808085	+	0.589066i	$0.799496\pi$
$68$	2.45358e6	−	2.45358e6i	0.114753	−	0.114753i
$69$			1.98899e7i			0.877476i
$70$		0			0
$71$	−8.89315e6			−0.349963			−0.174982	−	0.984572i	$-0.555987\pi$
$71$	−8.89315e6			−0.349963			−0.174982	+	0.984572i	$0.555987\pi$
$72$	−9.94368e6	−	9.94368e6i	−0.370013	−	0.370013i
$73$	−1.95076e7	+	1.95076e7i	−0.686928	+	0.686928i	−0.961552	−	0.274624i	$-0.911447\pi$
$73$	−1.95076e7	+	1.95076e7i	−0.686928	+	0.686928i	0.274624	+	0.961552i	$0.411447\pi$
$74$			2.14417e6i			0.0715043i
$75$		0			0
$76$	−3.72808e7			−1.11746
$77$	−1.43273e7	−	1.43273e7i	−0.407569	−	0.407569i
$78$	−1.64946e7	+	1.64946e7i	−0.445619	+	0.445619i
$79$		−	1.11272e7i		−	0.285680i	−0.989746	−	0.142840i	$-0.954377\pi$
$79$		−	1.11272e7i		−	0.285680i	0.989746	−	0.142840i	$-0.0456234\pi$
$80$		0			0
$81$	5.15641e7			1.19786
$82$	1.10230e7	+	1.10230e7i	0.243806	+	0.243806i
$83$	−1.58712e7	+	1.58712e7i	−0.334423	+	0.334423i	−0.854264	−	0.519840i	$-0.825992\pi$
$83$	−1.58712e7	+	1.58712e7i	−0.334423	+	0.334423i	0.519840	+	0.854264i	$0.325992\pi$
$84$		−	2.39268e7i		−	0.480581i
$85$		0			0
$86$	59469.7			0.00108718
$87$	9.56429e6	+	9.56429e6i	0.166946	+	0.166946i
$88$	4.07848e7	−	4.07848e7i	0.680092	−	0.680092i
$89$			4.85032e7i			0.773056i	0.922278	+	0.386528i	$0.126326\pi$
$89$			4.85032e7i			0.773056i	−0.922278	+	0.386528i	$0.873674\pi$
$90$		0			0
$91$	−3.64255e7			−0.531178
$92$	−2.87062e7	−	2.87062e7i	−0.400704	−	0.400704i
$93$	7.23400e7	−	7.23400e7i	0.967045	−	0.967045i
$94$			1.57726e7i			0.202019i
$95$		0			0
$96$	1.04948e8			1.23563
$97$	1.07411e8	+	1.07411e8i	1.21329	+	1.21329i	0.969939	+	0.243348i	$0.0782457\pi$
$97$	1.07411e8	+	1.07411e8i	1.21329	+	1.21329i	0.243348	+	0.969939i	$0.421754\pi$
$98$	2.06444e7	−	2.06444e7i	0.223820	−	0.223820i
$99$		−	9.36596e7i		−	0.975016i
$100$		0			0
$101$	−7.16023e7			−0.688084			−0.344042	−	0.938954i	$-0.611796\pi$
$101$	−7.16023e7			−0.688084			−0.344042	+	0.938954i	$0.611796\pi$
$102$	−7.47344e6	−	7.47344e6i	−0.0690431	−	0.0690431i
$103$	−9.89158e7	+	9.89158e7i	−0.878854	+	0.878854i	−0.993416	−	0.114562i	$-0.963454\pi$
$103$	−9.89158e7	+	9.89158e7i	−0.878854	+	0.878854i	0.114562	+	0.993416i	$0.463454\pi$
$104$		−	1.03691e8i		−	0.886352i
$105$		0			0
$106$	2.61269e7			0.206949
$107$	−4.73497e7	−	4.73497e7i	−0.361228	−	0.361228i	0.503037	−	0.864265i	$-0.332216\pi$
$107$	−4.73497e7	−	4.73497e7i	−0.361228	−	0.361228i	−0.864265	+	0.503037i	$0.832216\pi$
$108$	−2.91707e7	+	2.91707e7i	−0.214414	+	0.214414i
$109$			2.29072e7i			0.162280i	0.996703	+	0.0811401i	$0.0258561\pi$
$109$			2.29072e7i			0.162280i	−0.996703	+	0.0811401i	$0.974144\pi$
$110$		0			0
$111$	−3.67264e7			−0.241928
$112$	2.72996e7	+	2.72996e7i	0.173494	+	0.173494i
$113$	1.95361e8	−	1.95361e8i	1.19819	−	1.19819i	0.223480	−	0.974709i	$-0.428258\pi$
$113$	1.95361e8	−	1.95361e8i	1.19819	−	1.19819i	0.974709	−	0.223480i	$-0.0717416\pi$
$114$			1.13555e8i			0.672337i
$115$		0			0
$116$	−2.76075e7			−0.152474
$117$	−1.19059e8	−	1.19059e8i	−0.635360	−	0.635360i
$118$	−1.37951e6	+	1.37951e6i	−0.00711537	+	0.00711537i
$119$		−	1.65038e7i		−	0.0822994i
$120$		0			0
$121$	1.69794e8			0.792100
$122$	7.78004e7	+	7.78004e7i	0.351190	+	0.351190i
$123$	−1.88808e8	+	1.88808e8i	−0.824895	+	0.824895i
$124$			2.08811e8i			0.883213i
$125$		0			0
$126$	−3.07120e7			−0.121850
$127$	−1.84792e8	−	1.84792e8i	−0.710343	−	0.710343i	0.256264	−	0.966607i	$-0.417508\pi$
$127$	−1.84792e8	−	1.84792e8i	−0.710343	−	0.710343i	−0.966607	+	0.256264i	$0.917508\pi$
$128$	−1.93495e8	+	1.93495e8i	−0.720826	+	0.720826i
$129$			1.01862e6i			0.00367837i
$130$		0			0
$131$	−3.05076e8			−1.03591			−0.517956	−	0.855407i	$-0.673307\pi$
$131$	−3.05076e8			−1.03591			−0.517956	+	0.855407i	$0.673307\pi$
$132$	3.20770e8	+	3.20770e8i	1.05657	+	1.05657i
$133$	−1.25383e8	+	1.25383e8i	−0.400713	+	0.400713i
$134$		−	3.88041e7i		−	0.120353i
$135$		0			0
$136$	4.69806e7			0.137329
$137$	−3.75735e8	−	3.75735e8i	−1.06659	−	1.06659i	−0.997618	−	0.0689766i	$-0.978027\pi$
$137$	−3.75735e8	−	3.75735e8i	−1.06659	−	1.06659i	−0.0689766	−	0.997618i	$-0.521973\pi$
$138$	−8.74373e7	+	8.74373e7i	−0.241091	+	0.241091i
$139$			1.10575e8i			0.296208i	0.988972	+	0.148104i	$0.0473171\pi$
$139$			1.10575e8i			0.296208i	−0.988972	+	0.148104i	$0.952683\pi$
$140$		0			0
$141$	−2.70161e8			−0.683512
$142$	−3.90950e7	−	3.90950e7i	−0.0961540	−	0.0961540i
$143$	4.88331e8	−	4.88331e8i	1.16781	−	1.16781i
$144$			1.78461e8i			0.415044i
$145$		0			0
$146$	−1.71513e8			−0.377474
$147$	3.53607e8	+	3.53607e8i	0.757272	+	0.757272i
$148$	5.30056e7	−	5.30056e7i	0.110478	−	0.110478i
$149$		−	7.23744e8i		−	1.46838i	−0.678942	−	0.734192i	$-0.737561\pi$
$149$		−	7.23744e8i		−	1.46838i	0.678942	−	0.734192i	$-0.262439\pi$
$150$		0			0
$151$	7.67246e8			1.47580			0.737899	−	0.674911i	$-0.235818\pi$
$151$	7.67246e8			1.47580			0.737899	+	0.674911i	$0.235818\pi$
$152$	−3.56922e8	−	3.56922e8i	−0.668651	−	0.668651i
$153$	5.39439e7	−	5.39439e7i	0.0984411	−	0.0984411i
$154$		−	1.25968e8i		−	0.223963i
$155$		0			0
$156$	8.15519e8			1.37701
$157$	8.03264e8	+	8.03264e8i	1.32209	+	1.32209i	0.912085	+	0.410001i	$0.134472\pi$
$157$	8.03264e8	+	8.03264e8i	1.32209	+	1.32209i	0.410001	+	0.912085i	$0.365528\pi$
$158$	4.89162e7	−	4.89162e7i	0.0784918	−	0.0784918i
$159$			4.47514e8i			0.700193i
$160$		0			0
$161$	−1.93090e8			−0.287380
$162$	2.26680e8	+	2.26680e8i	0.329119	+	0.329119i
$163$	4.34915e8	−	4.34915e8i	0.616103	−	0.616103i	−0.328426	−	0.944530i	$-0.606518\pi$
$163$	4.34915e8	−	4.34915e8i	0.616103	−	0.616103i	0.944530	+	0.328426i	$0.106518\pi$
$164$		−	5.44996e8i		−	0.753386i
$165$		0			0
$166$	−1.39542e8			−0.183769
$167$	−7.16803e8	−	7.16803e8i	−0.921582	−	0.921582i	0.0755590	−	0.997141i	$-0.475926\pi$
$167$	−7.16803e8	−	7.16803e8i	−0.921582	−	0.921582i	−0.997141	+	0.0755590i	$0.975926\pi$
$168$	2.29073e8	−	2.29073e8i	0.287565	−	0.287565i
$169$		−	4.25794e8i		−	0.521979i
$170$		0			0
$171$	−8.19649e8			−0.958613
$172$	−1.47014e6	−	1.47014e6i	−0.00167975	−	0.00167975i
$173$	−3.40359e8	+	3.40359e8i	−0.379973	+	0.379973i	−0.871092	−	0.491119i	$-0.836588\pi$
$173$	−3.40359e8	+	3.40359e8i	−0.379973	+	0.379973i	0.491119	+	0.871092i	$0.336588\pi$
$174$			8.40907e7i			0.0917383i
$175$		0			0
$176$	−7.31974e8			−0.762860
$177$	−2.36289e7	−	2.36289e7i	−0.0240741	−	0.0240741i
$178$	−2.13224e8	+	2.13224e8i	−0.212401	+	0.212401i
$179$			1.29181e9i			1.25830i	0.777283	+	0.629151i	$0.216597\pi$
$179$			1.29181e9i			1.25830i	−0.777283	+	0.629151i	$0.783403\pi$
$180$		0			0
$181$	1.92912e8			0.179740			0.0898700	−	0.995954i	$-0.471355\pi$
$181$	1.92912e8			0.179740			0.0898700	+	0.995954i	$0.471355\pi$
$182$	−1.60129e8	−	1.60129e8i	−0.145944	−	0.145944i
$183$	−1.33260e9	+	1.33260e9i	−1.18822	+	1.18822i
$184$		−	5.49660e8i		−	0.479538i
$185$		0			0
$186$	6.36024e8			0.531400
$187$	2.21255e8	+	2.21255e8i	0.180937	+	0.180937i
$188$	3.89912e8	−	3.89912e8i	0.312130	−	0.312130i
$189$			1.96215e8i			0.153775i
$190$		0			0
$191$	7.64646e8			0.574549			0.287274	−	0.957848i	$-0.407251\pi$
$191$	7.64646e8			0.574549			0.287274	+	0.957848i	$0.407251\pi$
$192$	−2.58535e8	−	2.58535e8i	−0.190246	−	0.190246i
$193$	−1.15389e8	+	1.15389e8i	−0.0831641	+	0.0831641i	−0.747465	−	0.664301i	$-0.768729\pi$
$193$	−1.15389e8	+	1.15389e8i	−0.0831641	+	0.0831641i	0.664301	+	0.747465i	$0.268729\pi$
$194$			9.44378e8i			0.666713i
$195$		0			0
$196$	−1.02069e9			−0.691626
$197$	9.95415e7	+	9.95415e7i	0.0660906	+	0.0660906i	0.739379	−	0.673289i	$-0.235119\pi$
$197$	9.95415e7	+	9.95415e7i	0.0660906	+	0.0660906i	−0.673289	+	0.739379i	$0.735119\pi$
$198$	4.11735e8	−	4.11735e8i	0.267890	−	0.267890i
$199$			1.71187e9i			1.09159i	0.837919	+	0.545795i	$0.183772\pi$
$199$			1.71187e9i			1.09159i	−0.837919	+	0.545795i	$0.816228\pi$
$200$		0			0
$201$	6.64655e8			0.407204
$202$	−3.14769e8	−	3.14769e8i	−0.189054	−	0.189054i
$203$	−9.28499e7	+	9.28499e7i	−0.0546761	+	0.0546761i
$204$			3.69499e8i			0.213350i
$205$		0			0
$206$	−8.69683e8			−0.482939
$207$	−6.31129e8	−	6.31129e8i	−0.343745	−	0.343745i
$208$	−9.30479e8	+	9.30479e8i	−0.497111	+	0.497111i
$209$		−	3.36185e9i		−	1.76195i
$210$		0			0
$211$	−6.81230e8			−0.343688			−0.171844	−	0.985124i	$-0.554972\pi$
$211$	−6.81230e8			−0.343688			−0.171844	+	0.985124i	$0.554972\pi$
$212$	−6.45878e8	−	6.45878e8i	−0.319747	−	0.319747i
$213$	6.69637e8	−	6.69637e8i	0.325328	−	0.325328i
$214$		−	4.16305e8i		−	0.198498i
$215$		0			0
$216$	−5.58555e8			−0.256597
$217$	7.02275e8	+	7.02275e8i	0.316715	+	0.316715i
$218$	−1.00702e8	+	1.00702e8i	−0.0445872	+	0.0445872i
$219$		−	2.93776e9i		−	1.27715i
$220$		0			0
$221$	5.62515e8			0.235812
$222$	−1.61452e8	−	1.61452e8i	−0.0664708	−	0.0664708i
$223$	−9.37608e8	+	9.37608e8i	−0.379142	+	0.379142i	−0.870793	−	0.491651i	$-0.836394\pi$
$223$	−9.37608e8	+	9.37608e8i	−0.379142	+	0.379142i	0.491651	+	0.870793i	$0.336394\pi$
$224$			1.01883e9i			0.404677i
$225$		0			0
$226$	1.71765e9			0.658416
$227$	3.47956e9	+	3.47956e9i	1.31045	+	1.31045i	0.921082	+	0.389368i	$0.127307\pi$
$227$	3.47956e9	+	3.47956e9i	1.31045	+	1.31045i	0.389368	+	0.921082i	$0.372693\pi$
$228$	2.80717e9	−	2.80717e9i	1.03879	−	1.03879i
$229$			3.67273e9i			1.33551i	0.744382	+	0.667754i	$0.232744\pi$
$229$			3.67273e9i			1.33551i	−0.744382	+	0.667754i	$0.767256\pi$
$230$		0			0
$231$	2.15764e9			0.757758
$232$	−2.64311e8	−	2.64311e8i	−0.0912354	−	0.0912354i
$233$	3.62893e9	−	3.62893e9i	1.23128	−	1.23128i	0.267801	−	0.963474i	$-0.413703\pi$
$233$	3.62893e9	−	3.62893e9i	1.23128	−	1.23128i	0.963474	−	0.267801i	$-0.0862970\pi$
$234$		−	1.04679e9i		−	0.349136i
$235$		0			0
$236$	6.82053e7			0.0219872
$237$	8.37860e8	+	8.37860e8i	0.265569	+	0.265569i
$238$	7.25520e7	−	7.25520e7i	0.0226121	−	0.0226121i
$239$			2.64336e9i			0.810148i	0.914284	+	0.405074i	$0.132754\pi$
$239$			2.64336e9i			0.810148i	−0.914284	+	0.405074i	$0.867246\pi$
$240$		0			0
$241$	−7.20231e7			−0.0213503			−0.0106751	−	0.999943i	$-0.503398\pi$
$241$	−7.20231e7			−0.0213503			−0.0106751	+	0.999943i	$0.503398\pi$
$242$	7.46425e8	+	7.46425e8i	0.217633	+	0.217633i
$243$	−3.00212e9	+	3.00212e9i	−0.860999	+	0.860999i
$244$		−	3.84658e9i		−	1.08521i
$245$		0			0
$246$	−1.66002e9			−0.453288
$247$	−4.27356e9	−	4.27356e9i	−1.14816	−	1.14816i
$248$	−1.99913e9	+	1.99913e9i	−0.528487	+	0.528487i
$249$		−	2.39014e9i		−	0.621764i
$250$		0			0
$251$	5.78911e7			0.0145854			0.00729268	−	0.999973i	$-0.497679\pi$
$251$	5.78911e7			0.0145854			0.00729268	+	0.999973i	$0.497679\pi$
$252$	7.59226e8	+	7.59226e8i	0.188265	+	0.188265i
$253$	2.58863e9	−	2.58863e9i	0.631811	−	0.631811i
$254$		−	1.62472e9i		−	0.390340i
$255$		0			0
$256$	−8.22267e8			−0.191449
$257$	4.73425e8	+	4.73425e8i	0.108522	+	0.108522i	0.759283	−	0.650761i	$-0.225550\pi$
$257$	4.73425e8	+	4.73425e8i	0.108522	+	0.108522i	−0.650761	+	0.759283i	$0.725550\pi$
$258$	−4.47795e6	+	4.47795e6i	−0.00101065	+	0.00101065i
$259$		−	3.56539e8i		−	0.0792333i
$260$		0			0
$261$	−6.06973e8			−0.130800
$262$	−1.34114e9	−	1.34114e9i	−0.284622	−	0.284622i
$263$	−6.55957e9	+	6.55957e9i	−1.37105	+	1.37105i	−0.512155	+	0.858893i	$0.671153\pi$
$263$	−6.55957e9	+	6.55957e9i	−1.37105	+	1.37105i	−0.858893	+	0.512155i	$0.828847\pi$
$264$			6.14204e9i			1.26444i
$265$		0			0
$266$	−1.10239e9			−0.220195
$267$	−3.65220e9	−	3.65220e9i	−0.718637	−	0.718637i
$268$	−9.59269e8	+	9.59269e8i	−0.185952	+	0.185952i
$269$			5.38818e9i			1.02904i	0.857478	+	0.514521i	$0.172030\pi$
$269$			5.38818e9i			1.02904i	−0.857478	+	0.514521i	$0.827970\pi$
$270$		0			0
$271$	−8.79497e9			−1.63064			−0.815318	−	0.579013i	$-0.803438\pi$
$271$	−8.79497e9			−1.63064			−0.815318	+	0.579013i	$0.803438\pi$
$272$	−4.21585e8	−	4.21585e8i	−0.0770211	−	0.0770211i
$273$	2.74277e9	−	2.74277e9i	0.493786	−	0.493786i
$274$		−	3.30352e9i		−	0.586104i
$275$		0			0
$276$	4.32304e9			0.744994
$277$	4.78151e9	+	4.78151e9i	0.812168	+	0.812168i	0.984959	−	0.172790i	$-0.0552783\pi$
$277$	4.78151e9	+	4.78151e9i	0.812168	+	0.812168i	−0.172790	+	0.984959i	$0.555278\pi$
$278$	−4.86096e8	+	4.86096e8i	−0.0813846	+	0.0813846i
$279$			4.59087e9i			0.757667i
$280$		0			0
$281$	1.22255e10			1.96083			0.980416	−	0.196936i	$-0.0630990\pi$
$281$	1.22255e10			1.96083			0.980416	+	0.196936i	$0.0630990\pi$
$282$	−1.18765e9	−	1.18765e9i	−0.187798	−	0.187798i
$283$	2.86857e8	−	2.86857e8i	0.0447219	−	0.0447219i	−0.684392	−	0.729114i	$-0.739932\pi$
$283$	2.86857e8	−	2.86857e8i	0.0447219	−	0.0447219i	0.729114	+	0.684392i	$0.239932\pi$
$284$			1.93292e9i			0.297126i
$285$		0			0
$286$	4.29348e9			0.641720
$287$	−1.83294e9	−	1.83294e9i	−0.270160	−	0.270160i
$288$	−3.33011e9	+	3.33011e9i	−0.484048	+	0.484048i
$289$		−	6.72089e9i		−	0.963464i
$290$		0			0
$291$	−1.61757e10			−2.25576
$292$	4.23995e9	+	4.23995e9i	0.583216	+	0.583216i
$293$	1.02814e9	−	1.02814e9i	0.139503	−	0.139503i	−0.633907	−	0.773410i	$-0.718550\pi$
$293$	1.02814e9	−	1.02814e9i	0.139503	−	0.139503i	0.773410	+	0.633907i	$0.218550\pi$
$294$			3.10897e9i			0.416128i
$295$		0			0
$296$	1.01494e9			0.132213
$297$	−2.63052e9	−	2.63052e9i	−0.338077	−	0.338077i
$298$	3.18163e9	−	3.18163e9i	0.403445	−	0.403445i
$299$		−	6.58128e9i		−	0.823428i
$300$		0			0
$301$	−9.88879e6			−0.00120469
$302$	3.37287e9	+	3.37287e9i	0.405482	+	0.405482i
$303$	5.39151e9	−	5.39151e9i	0.639647	−	0.639647i
$304$			6.40576e9i			0.750026i
$305$		0			0
$306$	4.74283e8			0.0540943
$307$	−7.92159e9	−	7.92159e9i	−0.891783	−	0.891783i	0.102908	−	0.994691i	$-0.467185\pi$
$307$	−7.92159e9	−	7.92159e9i	−0.891783	−	0.891783i	−0.994691	+	0.102908i	$0.967185\pi$
$308$	−3.11403e9	+	3.11403e9i	−0.346034	+	0.346034i
$309$		−	1.48963e10i		−	1.63398i
$310$		0			0
$311$	3.74059e9			0.399851			0.199926	−	0.979811i	$-0.435930\pi$
$311$	3.74059e9			0.399851			0.199926	+	0.979811i	$0.435930\pi$
$312$	7.80770e9	+	7.80770e9i	0.823958	+	0.823958i
$313$	4.79633e9	−	4.79633e9i	0.499725	−	0.499725i	−0.411627	−	0.911352i	$-0.635039\pi$
$313$	4.79633e9	−	4.79633e9i	0.499725	−	0.499725i	0.911352	+	0.411627i	$0.135039\pi$
$314$			7.06242e9i			0.726499i
$315$		0			0
$316$	−2.41850e9			−0.242548
$317$	5.54903e9	+	5.54903e9i	0.549516	+	0.549516i	0.926301	−	0.376785i	$-0.122970\pi$
$317$	5.54903e9	+	5.54903e9i	0.549516	+	0.549516i	−0.376785	+	0.926301i	$0.622970\pi$
$318$	−1.96730e9	+	1.96730e9i	−0.192381	+	0.192381i
$319$		−	2.48955e9i		−	0.240413i
$320$		0			0
$321$	7.13068e9			0.671600
$322$	−8.48839e8	−	8.48839e8i	−0.0789591	−	0.0789591i
$323$	1.93628e9	−	1.93628e9i	0.177893	−	0.177893i
$324$		−	1.12074e10i		−	1.01701i
$325$		0			0
$326$	3.82384e9			0.338555
$327$	−1.72487e9	−	1.72487e9i	−0.150857	−	0.150857i
$328$	5.21774e9	−	5.21774e9i	0.450803	−	0.450803i
$329$		−	2.62272e9i		−	0.223855i
$330$		0			0
$331$	1.49782e10			1.24780			0.623902	−	0.781503i	$-0.285546\pi$
$331$	1.49782e10			1.24780			0.623902	+	0.781503i	$0.285546\pi$
$332$	3.44958e9	+	3.44958e9i	0.283932	+	0.283932i
$333$	1.16537e9	−	1.16537e9i	0.0947737	−	0.0947737i
$334$		−	6.30224e9i		−	0.506418i
$335$		0			0
$336$	−4.11121e9			−0.322562
$337$	−6.29203e9	−	6.29203e9i	−0.487833	−	0.487833i	0.419789	−	0.907622i	$-0.362104\pi$
$337$	−6.29203e9	−	6.29203e9i	−0.487833	−	0.487833i	−0.907622	+	0.419789i	$0.862104\pi$
$338$	1.87182e9	−	1.87182e9i	0.143416	−	0.143416i
$339$			2.94207e10i			2.22769i
$340$		0			0
$341$	−1.88298e10			−1.39261
$342$	−3.60324e9	−	3.60324e9i	−0.263383	−	0.263383i
$343$	−7.64684e9	+	7.64684e9i	−0.552466	+	0.552466i
$344$		−	2.81499e7i		−	0.00201022i
$345$		0			0
$346$	−2.99249e9			−0.208799
$347$	8.28230e9	+	8.28230e9i	0.571259	+	0.571259i	0.932480	−	0.361221i	$-0.117640\pi$
$347$	8.28230e9	+	8.28230e9i	0.571259	+	0.571259i	−0.361221	+	0.932480i	$0.617640\pi$
$348$	2.07879e9	−	2.07879e9i	0.141740	−	0.141740i
$349$			1.11611e10i			0.752328i	0.926553	+	0.376164i	$0.122757\pi$
$349$			1.11611e10i			0.752328i	−0.926553	+	0.376164i	$0.877243\pi$
$350$		0			0
$351$	−6.68778e9			−0.440609
$352$	−1.36587e10	−	1.36587e10i	−0.889692	−	0.889692i
$353$	−1.05904e10	+	1.05904e10i	−0.682047	+	0.682047i	−0.960461	−	0.278414i	$-0.910191\pi$
$353$	−1.05904e10	+	1.05904e10i	−0.682047	+	0.682047i	0.278414	+	0.960461i	$0.410191\pi$
$354$		−	2.07749e8i		−	0.0132290i
$355$		0			0
$356$	1.05421e10			0.656339
$357$	1.24271e9	+	1.24271e9i	0.0765060	+	0.0765060i
$358$	−5.67888e9	+	5.67888e9i	−0.345725	+	0.345725i
$359$		−	9.48530e9i		−	0.571049i	−0.958371	−	0.285524i	$-0.907832\pi$
$359$		−	9.48530e9i		−	0.571049i	0.958371	−	0.285524i	$-0.0921677\pi$
$360$		0			0
$361$	−1.24372e10			−0.732309
$362$	8.48055e8	+	8.48055e8i	0.0493844	+	0.0493844i
$363$	−1.27851e10	+	1.27851e10i	−0.736340	+	0.736340i
$364$			7.91704e9i			0.450980i
$365$		0			0
$366$	−1.17164e10			−0.652937
$367$	9.59996e9	+	9.59996e9i	0.529182	+	0.529182i	0.920329	−	0.391146i	$-0.127921\pi$
$367$	9.59996e9	+	9.59996e9i	0.529182	+	0.529182i	−0.391146	+	0.920329i	$0.627921\pi$
$368$	−4.93244e9	+	4.93244e9i	−0.268949	+	0.268949i
$369$		−	1.19822e10i		−	0.646295i
$370$		0			0
$371$	−4.34445e9			−0.229319
$372$	−1.57230e10	−	1.57230e10i	−0.821040	−	0.821040i
$373$	−8.48382e9	+	8.48382e9i	−0.438285	+	0.438285i	−0.891434	−	0.453150i	$-0.850300\pi$
$373$	−8.48382e9	+	8.48382e9i	−0.438285	+	0.438285i	0.453150	+	0.891434i	$0.350300\pi$
$374$			1.94531e9i			0.0994265i
$375$		0			0
$376$	7.46595e9			0.373537
$377$	−3.16469e9	−	3.16469e9i	−0.156663	−	0.156663i
$378$	−8.62576e8	+	8.62576e8i	−0.0422503	+	0.0422503i
$379$			2.19075e10i			1.06178i	0.847440	+	0.530891i	$0.178143\pi$
$379$			2.19075e10i			1.06178i	−0.847440	+	0.530891i	$0.821857\pi$
$380$		0			0
$381$	2.78289e10			1.32068
$382$	3.36144e9	+	3.36144e9i	0.157860	+	0.157860i
$383$	2.31285e10	−	2.31285e10i	1.07486	−	1.07486i	0.0778987	−	0.996961i	$-0.475179\pi$
$383$	2.31285e10	−	2.31285e10i	1.07486	−	1.07486i	0.996961	−	0.0778987i	$-0.0248211\pi$
$384$		−	2.91396e10i		−	1.34017i
$385$		0			0
$386$	−1.01452e9			−0.0456995
$387$	−3.23222e7	−	3.23222e7i	−0.00144098	−	0.00144098i
$388$	2.33458e10	−	2.33458e10i	1.03010	−	1.03010i
$389$			2.23175e10i			0.974647i	0.873221	+	0.487324i	$0.162027\pi$
$389$			2.23175e10i			0.974647i	−0.873221	+	0.487324i	$0.837973\pi$
$390$		0			0
$391$	2.98188e9			0.127580
$392$	−9.77202e9	−	9.77202e9i	−0.413847	−	0.413847i
$393$	2.29716e10	−	2.29716e10i	0.962989	−	0.962989i
$394$			8.75184e8i			0.0363174i
$395$		0			0
$396$	−2.03568e10			−0.827807
$397$	2.26036e10	+	2.26036e10i	0.909947	+	0.909947i	0.996267	−	0.0863200i	$-0.0275108\pi$
$397$	2.26036e10	+	2.26036e10i	0.909947	+	0.909947i	−0.0863200	+	0.996267i	$0.527511\pi$
$398$	−7.52553e9	+	7.52553e9i	−0.299919	+	0.299919i
$399$		−	1.88822e10i		−	0.745010i
$400$		0			0
$401$	1.77913e10			0.688064			0.344032	−	0.938958i	$-0.388207\pi$
$401$	1.77913e10			0.688064			0.344032	+	0.938958i	$0.388207\pi$
$402$	2.92187e9	+	2.92187e9i	0.111881	+	0.111881i
$403$	−2.39363e10	+	2.39363e10i	−0.907480	+	0.907480i
$404$			1.55627e10i			0.584197i
$405$		0			0
$406$	−8.16350e8			−0.0300450
$407$	4.77987e9	+	4.77987e9i	0.174196	+	0.174196i
$408$	−3.53755e9	+	3.53755e9i	−0.127662	+	0.127662i
$409$		−	4.37112e10i		−	1.56206i	−0.624490	−	0.781032i	$-0.714693\pi$
$409$		−	4.37112e10i		−	1.56206i	0.624490	−	0.781032i	$-0.285307\pi$
$410$		0			0
$411$	5.65843e10			1.98303
$412$	2.14993e10	+	2.14993e10i	0.746165	+	0.746165i
$413$	2.29389e8	−	2.29389e8i	0.00788447	−	0.00788447i
$414$		−	5.54898e9i		−	0.188891i
$415$		0			0
$416$	−3.47257e10			−1.15952
$417$	−8.32607e9	−	8.32607e9i	−0.275357	−	0.275357i
$418$	1.47790e10	−	1.47790e10i	0.484104	−	0.484104i
$419$		−	2.98593e10i		−	0.968776i	−0.874853	−	0.484388i	$-0.839042\pi$
$419$		−	2.98593e10i		−	0.968776i	0.874853	−	0.484388i	$-0.160958\pi$
$420$		0			0
$421$	−5.33816e10			−1.69927			−0.849637	−	0.527368i	$-0.823179\pi$
$421$	−5.33816e10			−1.69927			−0.849637	+	0.527368i	$0.823179\pi$
$422$	−2.99474e9	−	2.99474e9i	−0.0944298	−	0.0944298i
$423$	8.57253e9	−	8.57253e9i	0.267761	−	0.267761i
$424$		−	1.23671e10i		−	0.382654i
$425$		0			0
$426$	5.88755e9			0.178771
$427$	−1.29369e10	−	1.29369e10i	−0.389151	−	0.389151i
$428$	−1.02914e10	+	1.02914e10i	−0.306690	+	0.306690i
$429$			7.35408e10i			2.17120i
$430$		0			0
$431$	1.68739e10			0.488997			0.244499	−	0.969650i	$-0.421377\pi$
$431$	1.68739e10			0.488997			0.244499	+	0.969650i	$0.421377\pi$
$432$	5.01225e9	+	5.01225e9i	0.143912	+	0.143912i
$433$	−7.15187e9	+	7.15187e9i	−0.203455	+	0.203455i	−0.801478	−	0.598024i	$-0.795953\pi$
$433$	−7.15187e9	+	7.15187e9i	−0.203455	+	0.203455i	0.598024	+	0.801478i	$0.295953\pi$
$434$			6.17451e9i			0.174038i
$435$		0			0
$436$	4.97885e9			0.137779
$437$	−2.26540e10	−	2.26540e10i	−0.621182	−	0.621182i
$438$	1.29146e10	−	1.29146e10i	0.350902	−	0.350902i
$439$			2.62124e9i			0.0705747i	0.999377	+	0.0352873i	$0.0112346\pi$
$439$			2.62124e9i			0.0705747i	−0.999377	+	0.0352873i	$0.988765\pi$
$440$		0			0
$441$	−2.24408e10			−0.593313
$442$	2.47286e9	+	2.47286e9i	0.0647904	+	0.0647904i
$443$	3.30317e10	−	3.30317e10i	0.857663	−	0.857663i	−0.133400	−	0.991062i	$-0.542589\pi$
$443$	3.30317e10	−	3.30317e10i	0.857663	−	0.857663i	0.991062	+	0.133400i	$0.0425894\pi$
$444$			7.98244e9i			0.205402i
$445$		0			0
$446$	−8.24359e9			−0.208342
$447$	5.44965e10	+	5.44965e10i	1.36502	+	1.36502i
$448$	2.50985e9	−	2.50985e9i	0.0623069	−	0.0623069i
$449$		−	2.56081e10i		−	0.630074i	−0.949079	−	0.315037i	$-0.897983\pi$
$449$		−	2.56081e10i		−	0.630074i	0.949079	−	0.315037i	$-0.102017\pi$
$450$		0			0
$451$	4.91459e10			1.18790
$452$	−4.24616e10	−	4.24616e10i	−1.01729	−	1.01729i
$453$	−5.77721e10	+	5.77721e10i	−1.37191	+	1.37191i
$454$			3.05928e10i			0.720105i
$455$		0			0
$456$	5.37511e10			1.24316
$457$	−1.31162e10	−	1.31162e10i	−0.300707	−	0.300707i	0.540583	−	0.841290i	$-0.318204\pi$
$457$	−1.31162e10	−	1.31162e10i	−0.300707	−	0.300707i	−0.841290	+	0.540583i	$0.818204\pi$
$458$	−1.61456e10	+	1.61456e10i	−0.366937	+	0.366937i
$459$		−	3.03013e9i		−	0.0682669i
$460$		0			0
$461$	−3.99207e10			−0.883883			−0.441942	−	0.897044i	$-0.645710\pi$
$461$	−3.99207e10			−0.883883			−0.441942	+	0.897044i	$0.645710\pi$
$462$	9.48513e9	+	9.48513e9i	0.208197	+	0.208197i
$463$	−1.43482e10	+	1.43482e10i	−0.312229	+	0.312229i	−0.845772	−	0.533544i	$-0.820860\pi$
$463$	−1.43482e10	+	1.43482e10i	−0.312229	+	0.312229i	0.533544	+	0.845772i	$0.320860\pi$
$464$			4.74365e9i			0.102339i
$465$		0			0
$466$	3.19061e10			0.676597
$467$	−2.44200e10	−	2.44200e10i	−0.513427	−	0.513427i	0.402148	−	0.915575i	$-0.368264\pi$
$467$	−2.44200e10	−	2.44200e10i	−0.513427	−	0.513427i	−0.915575	+	0.402148i	$0.868264\pi$
$468$	−2.58774e10	+	2.58774e10i	−0.539433	+	0.539433i
$469$			6.45246e9i			0.133363i
$470$		0			0
$471$	−1.20968e11			−2.45804
$472$	6.52990e8	+	6.52990e8i	0.0131565	+	0.0131565i
$473$	1.32572e8	−	1.32572e8i	0.00264855	−	0.00264855i
$474$			7.36659e9i			0.145933i
$475$		0			0
$476$	−3.58709e9			−0.0698738
$477$	−1.42002e10	−	1.42002e10i	−0.274296	−	0.274296i
$478$	−1.16204e10	+	1.16204e10i	−0.222592	+	0.222592i
$479$		−	9.03857e9i		−	0.171695i	−0.996308	−	0.0858475i	$-0.972640\pi$
$479$		−	9.03857e9i		−	0.171695i	0.996308	−	0.0858475i	$-0.0273598\pi$
$480$		0			0
$481$	1.21523e10			0.227026
$482$	−3.16619e8	−	3.16619e8i	−0.00586609	−	0.00586609i
$483$	1.45393e10	−	1.45393e10i	0.267150	−	0.267150i
$484$		−	3.69045e10i		−	0.672508i
$485$		0			0
$486$	−2.63951e10			−0.473127
$487$	−3.53950e10	−	3.53950e10i	−0.629255	−	0.629255i	0.318626	−	0.947881i	$-0.396779\pi$
$487$	−3.53950e10	−	3.53950e10i	−0.629255	−	0.629255i	−0.947881	+	0.318626i	$0.896779\pi$
$488$	3.68268e10	−	3.68268e10i	0.649358	−	0.649358i
$489$			6.54965e10i			1.14547i
$490$		0			0
$491$	−5.87159e10			−1.01025			−0.505126	−	0.863045i	$-0.668554\pi$
$491$	−5.87159e10			−1.01025			−0.505126	+	0.863045i	$0.668554\pi$
$492$	4.10371e10	+	4.10371e10i	0.700352	+	0.700352i
$493$	1.43387e9	−	1.43387e9i	0.0242730	−	0.0242730i
$494$		−	3.75738e10i		−	0.630924i
$495$		0			0
$496$	3.58788e10			0.592805
$497$	6.50082e9	+	6.50082e9i	0.106547	+	0.106547i
$498$	1.05072e10	−	1.05072e10i	0.170833	−	0.170833i
$499$			2.57394e10i			0.415141i	0.978220	+	0.207571i	$0.0665557\pi$
$499$			2.57394e10i			0.415141i	−0.978220	+	0.207571i	$0.933444\pi$
$500$		0			0
$501$	1.07948e11			1.71342
$502$	2.54494e8	+	2.54494e8i	0.00400740	+	0.00400740i
$503$	4.75499e10	−	4.75499e10i	0.742810	−	0.742810i	−0.230308	−	0.973118i	$-0.573973\pi$
$503$	4.75499e10	−	4.75499e10i	0.742810	−	0.742810i	0.973118	+	0.230308i	$0.0739733\pi$
$504$			1.45375e10i			0.225303i
$505$		0			0
$506$	2.27596e10			0.347186
$507$	3.20615e10	+	3.20615e10i	0.485235	+	0.485235i
$508$	−4.01643e10	+	4.01643e10i	−0.603095	+	0.603095i
$509$		−	8.69280e10i		−	1.29506i	−0.762042	−	0.647528i	$-0.775803\pi$
$509$		−	8.69280e10i		−	1.29506i	0.762042	−	0.647528i	$-0.224197\pi$
$510$		0			0
$511$	2.85197e10			0.418275
$512$	4.59200e10	+	4.59200e10i	0.668225	+	0.668225i
$513$	−2.30206e10	+	2.30206e10i	−0.332389	+	0.332389i
$514$			4.16243e9i			0.0596340i
$515$		0			0
$516$	2.21397e8			0.00312301
$517$	3.51609e10	+	3.51609e10i	0.492151	+	0.492151i
$518$	1.56737e9	−	1.56737e9i	0.0217697	−	0.0217697i
$519$		−	5.12568e10i		−	0.706451i
$520$		0			0
$521$	6.44123e10			0.874214			0.437107	−	0.899409i	$-0.356003\pi$
$521$	6.44123e10			0.874214			0.437107	+	0.899409i	$0.356003\pi$
$522$	−2.66830e9	−	2.66830e9i	−0.0359379	−	0.0359379i
$523$	5.99903e10	−	5.99903e10i	0.801815	−	0.801815i	−0.181564	−	0.983379i	$-0.558116\pi$
$523$	5.99903e10	−	5.99903e10i	0.801815	−	0.801815i	0.983379	+	0.181564i	$0.0581160\pi$
$524$			6.63079e10i			0.879509i
$525$		0			0
$526$	−5.76728e10			−0.753404
$527$	−1.08452e10	−	1.08452e10i	−0.140603	−	0.140603i
$528$	5.51162e10	−	5.51162e10i	0.709159	−	0.709159i
$529$			4.34238e10i			0.554505i
$530$		0			0
$531$	1.49955e9			0.0188618
$532$	2.72519e10	+	2.72519e10i	0.340213	+	0.340213i
$533$	6.24738e10	−	6.24738e10i	0.774086	−	0.774086i
$534$		−	3.21107e10i		−	0.394898i
$535$		0			0
$536$	−1.83679e10			−0.222536
$537$	−9.72705e10	−	9.72705e10i	−1.16973	−	1.16973i
$538$	−2.36869e10	+	2.36869e10i	−0.282734	+	0.282734i
$539$		−	9.20427e10i		−	1.09052i
$540$		0			0
$541$	−9.38341e10			−1.09540			−0.547698	−	0.836676i	$-0.684496\pi$
$541$	−9.38341e10			−1.09540			−0.547698	+	0.836676i	$0.684496\pi$
$542$	−3.86633e10	−	3.86633e10i	−0.448025	−	0.448025i
$543$	−1.45259e10	+	1.45259e10i	−0.167087	+	0.167087i
$544$		−	1.57337e10i		−	0.179653i
$545$		0			0
$546$	2.41148e10			0.271340
$547$	−1.86813e10	−	1.86813e10i	−0.208669	−	0.208669i	0.595032	−	0.803702i	$-0.297139\pi$
$547$	−1.86813e10	−	1.86813e10i	−0.208669	−	0.208669i	−0.803702	+	0.595032i	$0.797139\pi$
$548$	−8.16657e10	+	8.16657e10i	−0.905560	+	0.905560i
$549$		−	8.45702e10i		−	0.930954i
$550$		0			0
$551$	−2.17869e10			−0.236368
$552$	4.13884e10	+	4.13884e10i	0.445781	+	0.445781i
$553$	−8.13393e9	+	8.13393e9i	−0.0869761	+	0.0869761i
$554$			4.20398e10i			0.446294i
$555$		0			0
$556$	2.40333e10			0.251487
$557$	4.32331e9	+	4.32331e9i	0.0449154	+	0.0449154i	0.729208	−	0.684292i	$-0.239889\pi$
$557$	4.32331e9	+	4.32331e9i	0.0449154	+	0.0449154i	−0.684292	+	0.729208i	$0.739889\pi$
$558$	−2.01818e10	+	2.01818e10i	−0.208173	+	0.208173i
$559$		−	3.37049e8i		−	0.00345180i
$560$		0			0
$561$	−3.33202e10			−0.336400
$562$	5.37441e10	+	5.37441e10i	0.538748	+	0.538748i
$563$	−5.85471e10	+	5.85471e10i	−0.582736	+	0.582736i	−0.935654	−	0.352918i	$-0.885189\pi$
$563$	−5.85471e10	+	5.85471e10i	−0.582736	+	0.582736i	0.352918	+	0.935654i	$0.385189\pi$
$564$			5.87192e10i			0.580315i
$565$		0			0
$566$	2.52209e9			0.0245751
$567$	−3.76929e10	−	3.76929e10i	−0.364693	−	0.364693i
$568$	−1.85056e10	+	1.85056e10i	−0.177791	+	0.177791i
$569$			1.98793e11i			1.89650i	0.317524	+	0.948250i	$0.397149\pi$
$569$			1.98793e11i			1.89650i	−0.317524	+	0.948250i	$0.602851\pi$
$570$		0			0
$571$	6.21842e10			0.584973			0.292487	−	0.956270i	$-0.405517\pi$
$571$	6.21842e10			0.584973			0.292487	+	0.956270i	$0.405517\pi$
$572$	−1.06138e11	−	1.06138e11i	−0.991490	−	0.991490i
$573$	−5.75764e10	+	5.75764e10i	−0.534104	+	0.534104i
$574$		−	1.61155e10i		−	0.148455i
$575$		0			0
$576$	1.64073e10			0.149055
$577$	1.02056e11	+	1.02056e11i	0.920739	+	0.920739i	0.997082	−	0.0763427i	$-0.0243243\pi$
$577$	1.02056e11	+	1.02056e11i	0.920739	+	0.920739i	−0.0763427	+	0.997082i	$0.524324\pi$
$578$	2.95455e10	−	2.95455e10i	0.264716	−	0.264716i
$579$		−	1.73772e10i		−	0.154620i
$580$		0			0
$581$	2.32034e10			0.203633
$582$	−7.11098e10	−	7.11098e10i	−0.619780	−	0.619780i
$583$	5.82431e10	−	5.82431e10i	0.504162	−	0.504162i
$584$			8.11857e10i			0.697956i
$585$		0			0
$586$	9.03959e9			0.0766581
$587$	1.52761e11	+	1.52761e11i	1.28665	+	1.28665i	0.936811	+	0.349837i	$0.113763\pi$
$587$	1.52761e11	+	1.52761e11i	1.28665	+	1.28665i	0.349837	+	0.936811i	$0.386237\pi$
$588$	7.68562e10	−	7.68562e10i	0.642939	−	0.642939i
$589$			1.64787e11i			1.36918i
$590$		0			0
$591$	−1.49906e10			−0.122876
$592$	−9.10768e9	−	9.10768e9i	−0.0741517	−	0.0741517i
$593$	−9.35153e10	+	9.35153e10i	−0.756247	+	0.756247i	−0.975637	−	0.219390i	$-0.929593\pi$
$593$	−9.35153e10	+	9.35153e10i	−0.756247	+	0.756247i	0.219390	+	0.975637i	$0.429593\pi$
$594$		−	2.31279e10i		−	0.185776i
$595$		0			0
$596$	−1.57305e11			−1.24669
$597$	−1.28901e11	−	1.28901e11i	−1.01475	−	1.01475i
$598$	2.89318e10	−	2.89318e10i	0.226241	−	0.226241i
$599$		−	5.65120e10i		−	0.438968i	−0.975616	−	0.219484i	$-0.929563\pi$
$599$		−	5.65120e10i		−	0.438968i	0.975616	−	0.219484i	$-0.0704374\pi$
$600$		0			0
$601$	−9.99220e10			−0.765884			−0.382942	−	0.923772i	$-0.625089\pi$
$601$	−9.99220e10			−0.765884			−0.382942	+	0.923772i	$0.625089\pi$
$602$	−4.34719e7	−	4.34719e7i	−0.000330996	−	0.000330996i
$603$	−2.10903e10	+	2.10903e10i	−0.159520	+	0.159520i
$604$		−	1.66760e11i		−	1.25298i
$605$		0			0
$606$	4.74030e10			0.351492
$607$	−1.27776e11	−	1.27776e11i	−0.941229	−	0.941229i	0.0571370	−	0.998366i	$-0.481803\pi$
$607$	−1.27776e11	−	1.27776e11i	−0.941229	−	0.941229i	−0.998366	+	0.0571370i	$0.981803\pi$
$608$	−1.19532e11	+	1.19532e11i	−0.874724	+	0.874724i
$609$		−	1.39828e10i		−	0.101654i
$610$		0			0
$611$	8.93925e10			0.641411
$612$	−1.17247e10	−	1.17247e10i	−0.0835784	−	0.0835784i
$613$	−6.34636e10	+	6.34636e10i	−0.449452	+	0.449452i	−0.895172	−	0.445720i	$-0.852948\pi$
$613$	−6.34636e10	+	6.34636e10i	−0.449452	+	0.449452i	0.445720	+	0.895172i	$0.352948\pi$
$614$		−	6.96478e10i		−	0.490043i
$615$		0			0
$616$	−5.96267e10			−0.414112
$617$	6.39126e10	+	6.39126e10i	0.441007	+	0.441007i	0.892350	−	0.451343i	$-0.149055\pi$
$617$	6.39126e10	+	6.39126e10i	0.441007	+	0.441007i	−0.451343	+	0.892350i	$0.649055\pi$
$618$	6.54854e10	−	6.54854e10i	0.448943	−	0.448943i
$619$		−	5.76225e10i		−	0.392491i	−0.980555	−	0.196245i	$-0.937125\pi$
$619$		−	5.76225e10i		−	0.392491i	0.980555	−	0.196245i	$-0.0628749\pi$
$620$		0			0
$621$	−3.54517e10			−0.238381
$622$	1.64439e10	+	1.64439e10i	0.109861	+	0.109861i
$623$	3.54555e10	−	3.54555e10i	0.235359	−	0.235359i
$624$		−	1.40126e11i		−	0.924234i
$625$		0			0
$626$	4.21700e10			0.274604
$627$	2.53141e11	+	2.53141e11i	1.63792	+	1.63792i
$628$	1.74589e11	−	1.74589e11i	1.12248	−	1.12248i
$629$			5.50600e9i			0.0351749i
$630$		0			0
$631$	1.53061e11			0.965486			0.482743	−	0.875762i	$-0.339641\pi$
$631$	1.53061e11			0.965486			0.482743	+	0.875762i	$0.339641\pi$
$632$	−2.31544e10	−	2.31544e10i	−0.145133	−	0.145133i
$633$	5.12953e10	−	5.12953e10i	0.319494	−	0.319494i
$634$			4.87880e10i			0.301964i
$635$		0			0
$636$	9.72667e10			0.594478
$637$	−1.17004e11	−	1.17004e11i	−0.710628	−	0.710628i
$638$	1.09442e10	−	1.09442e10i	0.0660546	−	0.0660546i
$639$			4.24968e10i			0.254890i
$640$		0			0
$641$	1.10388e11			0.653867			0.326934	−	0.945047i	$-0.393985\pi$
$641$	1.10388e11			0.653867			0.326934	+	0.945047i	$0.393985\pi$
$642$	3.13470e10	+	3.13470e10i	0.184525	+	0.184525i
$643$	−4.62452e10	+	4.62452e10i	−0.270535	+	0.270535i	−0.829315	−	0.558781i	$-0.811269\pi$
$643$	−4.62452e10	+	4.62452e10i	−0.270535	+	0.270535i	0.558781	+	0.829315i	$0.311269\pi$
$644$			4.19680e10i			0.243991i
$645$		0			0
$646$	1.70241e10			0.0977539
$647$	9.64071e10	+	9.64071e10i	0.550164	+	0.550164i	0.926488	−	0.376324i	$-0.122812\pi$
$647$	9.64071e10	+	9.64071e10i	0.550164	+	0.550164i	−0.376324	+	0.926488i	$0.622812\pi$
$648$	1.07299e11	−	1.07299e11i	0.608547	−	0.608547i
$649$			6.15052e9i			0.0346683i
$650$		0			0
$651$	−1.05760e11			−0.588840
$652$	−9.45283e10	−	9.45283e10i	−0.523084	−	0.523084i
$653$	2.02786e11	−	2.02786e11i	1.11528	−	1.11528i	0.122857	−	0.992424i	$-0.460794\pi$
$653$	2.02786e11	−	2.02786e11i	1.11528	−	1.11528i	0.992424	−	0.122857i	$-0.0392057\pi$
$654$		−	1.51653e10i		−	0.0828971i
$655$		0			0
$656$	−9.36438e10			−0.505666
$657$	9.32188e10	+	9.32188e10i	0.500313	+	0.500313i
$658$	1.15297e10	−	1.15297e10i	0.0615053	−	0.0615053i
$659$			5.78139e10i			0.306542i	0.988184	+	0.153271i	$0.0489808\pi$
$659$			5.78139e10i			0.306542i	−0.988184	+	0.153271i	$0.951019\pi$
$660$		0			0
$661$	3.80376e10			0.199254			0.0996271	−	0.995025i	$-0.468235\pi$
$661$	3.80376e10			0.199254			0.0996271	+	0.995025i	$0.468235\pi$
$662$	6.58451e10	+	6.58451e10i	0.342840	+	0.342840i
$663$	−4.23563e10	+	4.23563e10i	−0.219212	+	0.219212i
$664$			6.60520e10i			0.339792i
$665$		0			0
$666$	1.02461e10			0.0520790
$667$	−1.67759e10	−	1.67759e10i	−0.0847585	−	0.0847585i
$668$	−1.55797e11	+	1.55797e11i	−0.782442	+	0.782442i
$669$		−	1.41200e11i		−	0.704905i
$670$		0			0
$671$	3.46872e11			1.71111
$672$	−7.67158e10	−	7.67158e10i	−0.376190	−	0.376190i
$673$	−1.23735e11	+	1.23735e11i	−0.603158	+	0.603158i	−0.941149	−	0.337991i	$-0.890253\pi$
$673$	−1.23735e11	+	1.23735e11i	−0.603158	+	0.603158i	0.337991	+	0.941149i	$0.390253\pi$
$674$		−	5.53205e10i		−	0.268069i
$675$		0			0
$676$	−9.25460e10			−0.443170
$677$	8.44279e10	+	8.44279e10i	0.401912	+	0.401912i	0.878906	−	0.476994i	$-0.158274\pi$
$677$	8.44279e10	+	8.44279e10i	0.401912	+	0.401912i	−0.476994	+	0.878906i	$0.658274\pi$
$678$	−1.29336e11	+	1.29336e11i	−0.612067	+	0.612067i
$679$		−	1.57034e11i		−	0.738778i
$680$		0			0
$681$	−5.24008e11			−2.43640
$682$	−8.27774e10	−	8.27774e10i	−0.382626	−	0.382626i
$683$	2.87370e10	−	2.87370e10i	0.132056	−	0.132056i	−0.637989	−	0.770045i	$-0.720234\pi$
$683$	2.87370e10	−	2.87370e10i	0.132056	−	0.132056i	0.770045	+	0.637989i	$0.220234\pi$
$684$			1.78150e11i			0.813881i
$685$		0			0
$686$	−6.72321e10			−0.303585
$687$	−2.76549e11	−	2.76549e11i	−1.24150	−	1.24150i
$688$	−2.52606e8	+	2.52606e8i	−0.00112743	+	0.00112743i
$689$		−	1.48076e11i		−	0.657065i
$690$		0			0
$691$	−8.87703e10			−0.389364			−0.194682	−	0.980866i	$-0.562367\pi$
$691$	−8.87703e10			−0.389364			−0.194682	+	0.980866i	$0.562367\pi$
$692$	7.39768e10	+	7.39768e10i	0.322605	+	0.322605i
$693$	−6.84644e10	+	6.84644e10i	−0.296847	+	0.296847i
$694$			7.28192e10i			0.313912i
$695$		0			0
$696$	3.98042e10			0.169626
$697$	2.83059e10	+	2.83059e10i	0.119935	+	0.119935i
$698$	−4.90652e10	+	4.90652e10i	−0.206706	+	0.206706i
$699$			5.46503e11i			2.28920i
$700$		0			0
$701$	1.22790e11			0.508499			0.254249	−	0.967139i	$-0.418172\pi$
$701$	1.22790e11			0.508499			0.254249	+	0.967139i	$0.418172\pi$
$702$	−2.94000e10	−	2.94000e10i	−0.121060	−	0.121060i
$703$	4.18303e10	−	4.18303e10i	0.171266	−	0.171266i
$704$			6.72957e10i			0.273966i
$705$		0			0
$706$	−9.31125e10			−0.374791
$707$	5.23407e10	+	5.23407e10i	0.209489	+	0.209489i
$708$	−5.13572e9	+	5.13572e9i	−0.0204394	+	0.0204394i
$709$		−	2.07670e11i		−	0.821842i	−0.911671	−	0.410921i	$-0.865207\pi$
$709$		−	2.07670e11i		−	0.821842i	0.911671	−	0.410921i	$-0.134793\pi$
$710$		0			0
$711$	−5.31726e10			−0.208070
$712$	1.00929e11	+	1.00929e11i	0.392733	+	0.392733i
$713$	−1.26886e11	+	1.26886e11i	−0.490969	+	0.490969i
$714$			1.09261e10i			0.0420408i
$715$		0			0
$716$	2.80773e11			1.06832
$717$	−1.99040e11	−	1.99040e11i	−0.753119	−	0.753119i
$718$	4.16981e10	−	4.16981e10i	0.156898	−	0.156898i
$719$			1.66571e11i			0.623281i	0.950200	+	0.311640i	$0.100878\pi$
$719$			1.66571e11i			0.623281i	−0.950200	+	0.311640i	$0.899122\pi$
$720$		0			0
$721$	1.44613e11			0.535140
$722$	−5.46750e10	−	5.46750e10i	−0.201205	−	0.201205i
$723$	5.42320e9	−	5.42320e9i	0.0198474	−	0.0198474i
$724$		−	4.19292e10i		−	0.152603i
$725$		0			0
$726$	−1.12409e11			−0.404626
$727$	−1.61369e11	−	1.61369e11i	−0.577673	−	0.577673i	0.356588	−	0.934262i	$-0.383940\pi$
$727$	−1.61369e11	−	1.61369e11i	−0.577673	−	0.577673i	−0.934262	+	0.356588i	$0.883940\pi$
$728$	−7.57970e10	+	7.57970e10i	−0.269853	+	0.269853i
$729$		−	1.13795e11i		−	0.402915i
$730$		0			0
$731$	1.52712e8			0.000534814
$732$	2.89640e11	+	2.89640e11i	1.00882	+	1.00882i
$733$	−4.72057e10	+	4.72057e10i	−0.163523	+	0.163523i	−0.784125	−	0.620603i	$-0.786888\pi$
$733$	−4.72057e10	+	4.72057e10i	−0.163523	+	0.163523i	0.620603	+	0.784125i	$0.286888\pi$
$734$			8.44043e10i			0.290791i
$735$		0			0
$736$	−1.84080e11			−0.627328
$737$	−8.65036e10	−	8.65036e10i	−0.293200	−	0.293200i
$738$	5.26746e10	−	5.26746e10i	0.177572	−	0.177572i
$739$		−	2.13693e11i		−	0.716494i	−0.933627	−	0.358247i	$-0.883375\pi$
$739$		−	2.13693e11i		−	0.716494i	0.933627	−	0.358247i	$-0.116625\pi$
$740$		0			0
$741$	6.43582e11			2.13467
$742$	−1.90985e10	−	1.90985e10i	−0.0630064	−	0.0630064i
$743$	3.10741e11	−	3.10741e11i	1.01963	−	1.01963i	0.0198284	−	0.999803i	$-0.493688\pi$
$743$	3.10741e11	−	3.10741e11i	1.01963	−	1.01963i	0.999803	−	0.0198284i	$-0.00631198\pi$
$744$		−	3.01061e11i		−	0.982570i
$745$		0			0
$746$	−7.45910e10			−0.240841
$747$	7.58420e10	+	7.58420e10i	0.243572	+	0.243572i
$748$	4.80896e10	−	4.80896e10i	0.153619	−	0.153619i
$749$			6.92245e10i			0.219954i
$750$		0			0
$751$	−5.29510e11			−1.66462			−0.832308	−	0.554313i	$-0.812981\pi$
$751$	−5.29510e11			−1.66462			−0.832308	+	0.554313i	$0.812981\pi$
$752$	−6.69965e10	−	6.69965e10i	−0.209498	−	0.209498i
$753$	−4.35909e9	+	4.35909e9i	−0.0135586	+	0.0135586i
$754$		−	2.78245e10i		−	0.0860877i
$755$		0			0
$756$	4.26471e10			0.130558
$757$	1.66172e11	+	1.66172e11i	0.506029	+	0.506029i	0.913305	−	0.407276i	$-0.133521\pi$
$757$	1.66172e11	+	1.66172e11i	0.506029	+	0.506029i	−0.407276	+	0.913305i	$0.633521\pi$
$758$	−9.63068e10	+	9.63068e10i	−0.291729	+	0.291729i
$759$			3.89837e11i			1.17467i
$760$		0			0
$761$	−3.61095e11			−1.07667			−0.538335	−	0.842731i	$-0.680946\pi$
$761$	−3.61095e11			−1.07667			−0.538335	+	0.842731i	$0.680946\pi$
$762$	1.22338e11	+	1.22338e11i	0.362862	+	0.362862i
$763$	1.67450e10	−	1.67450e10i	0.0494067	−	0.0494067i
$764$		−	1.66195e11i		−	0.487803i
$765$		0			0
$766$	2.03349e11			0.590646
$767$	7.81849e9	+	7.81849e9i	0.0225913	+	0.0225913i
$768$	6.19151e10	−	6.19151e10i	0.177972	−	0.177972i
$769$			2.04700e11i			0.585345i	0.956213	+	0.292672i	$0.0945446\pi$
$769$			2.04700e11i			0.585345i	−0.956213	+	0.292672i	$0.905455\pi$
$770$		0			0
$771$	−7.12960e10			−0.201766
$772$	2.50797e10	+	2.50797e10i	0.0706080	+	0.0706080i
$773$	8.07889e10	−	8.07889e10i	0.226274	−	0.226274i	−0.584860	−	0.811134i	$-0.698851\pi$
$773$	8.07889e10	−	8.07889e10i	0.226274	−	0.226274i	0.811134	+	0.584860i	$0.198851\pi$
$774$		−	2.84182e8i		−	0.000791831i
$775$		0			0
$776$	4.47020e11			1.23276
$777$	2.68467e10	+	2.68467e10i	0.0736557	+	0.0736557i
$778$	−9.81095e10	+	9.81095e10i	−0.267789	+	0.267789i
$779$		−	4.30093e11i		−	1.16792i
$780$		0			0
$781$	−1.74304e11			−0.468493
$782$	1.31086e10	+	1.31086e10i	0.0350532	+	0.0350532i
$783$	−1.70474e10	+	1.70474e10i	−0.0453535	+	0.0453535i
$784$			1.75380e11i			0.464213i
$785$		0			0
$786$	2.01970e11			0.529172
$787$	1.41727e11	+	1.41727e11i	0.369448	+	0.369448i	0.867276	−	0.497828i	$-0.165869\pi$
$787$	1.41727e11	+	1.41727e11i	0.369448	+	0.369448i	−0.497828	+	0.867276i	$0.665869\pi$
$788$	2.16353e10	−	2.16353e10i	0.0561122	−	0.0561122i
$789$		−	9.87846e11i		−	2.54907i
$790$		0			0
$791$	−2.85615e11			−0.729584
$792$	−1.94894e11	−	1.94894e11i	−0.495334	−	0.495334i
$793$	4.40940e11	−	4.40940e11i	1.11503	−	1.11503i
$794$			1.98735e11i			0.500025i
$795$		0			0
$796$	3.72074e11			0.926781
$797$	2.66505e11	+	2.66505e11i	0.660499	+	0.660499i	0.955498	−	0.294998i	$-0.0953191\pi$
$797$	2.66505e11	+	2.66505e11i	0.660499	+	0.660499i	−0.294998	+	0.955498i	$0.595319\pi$
$798$	8.30078e10	−	8.30078e10i	0.204695	−	0.204695i
$799$			4.05024e10i			0.0993787i
$800$		0			0
$801$	2.31778e11			0.563043
$802$	7.82117e10	+	7.82117e10i	0.189049	+	0.189049i
$803$	−3.82344e11	+	3.82344e11i	−0.919586	+	0.919586i
$804$		−	1.44462e11i		−	0.345724i
$805$		0			0
$806$	−2.10452e11			−0.498669
$807$	−4.05720e11	−	4.05720e11i	−0.956604	−	0.956604i
$808$	−1.48996e11	+	1.48996e11i	−0.349565	+	0.349565i
$809$			6.78011e11i			1.58286i	0.611259	+	0.791431i	$0.290663\pi$
$809$			6.78011e11i			1.58286i	−0.611259	+	0.791431i	$0.709337\pi$
$810$		0			0
$811$	4.62623e11			1.06941			0.534704	−	0.845039i	$-0.320423\pi$
$811$	4.62623e11			1.06941			0.534704	+	0.845039i	$0.320423\pi$
$812$	2.01808e10	+	2.01808e10i	0.0464211	+	0.0464211i
$813$	6.62244e11	−	6.62244e11i	1.51585	−	1.51585i
$814$			4.20253e10i			0.0957224i
$815$		0			0
$816$	6.34891e10			0.143199
$817$	−1.16019e9	−	1.16019e9i	−0.00260399	−	0.00260399i
$818$	1.92158e11	−	1.92158e11i	0.429185	−	0.429185i
$819$			1.74063e11i			0.386875i
$820$		0			0
$821$	−2.02486e11			−0.445678			−0.222839	−	0.974855i	$-0.571532\pi$
$821$	−2.02486e11			−0.445678			−0.222839	+	0.974855i	$0.571532\pi$
$822$	2.48749e11	+	2.48749e11i	0.544846	+	0.544846i
$823$	−5.67731e11	+	5.67731e11i	−1.23749	+	1.23749i	−0.276473	+	0.961022i	$0.589166\pi$
$823$	−5.67731e11	+	5.67731e11i	−1.23749	+	1.23749i	−0.961022	+	0.276473i	$0.910834\pi$
$824$			4.11664e11i			0.892963i
$825$		0			0
$826$	2.01682e9			0.00433259
$827$	−5.76065e11	−	5.76065e11i	−1.23154	−	1.23154i	−0.963371	−	0.268173i	$-0.913580\pi$
$827$	−5.76065e11	−	5.76065e11i	−1.23154	−	1.23154i	−0.268173	−	0.963371i	$-0.586420\pi$
$828$	−1.37175e11	+	1.37175e11i	−0.291847	+	0.291847i
$829$			2.12691e11i			0.450330i	0.974321	+	0.225165i	$0.0722922\pi$
$829$			2.12691e11i			0.450330i	−0.974321	+	0.225165i	$0.927708\pi$
$830$		0			0
$831$	−7.20077e11			−1.50999
$832$	8.55457e10	+	8.55457e10i	0.178527	+	0.178527i
$833$	5.30126e10	−	5.30126e10i	0.110103	−	0.110103i
$834$		−	7.32041e10i		−	0.151311i
$835$		0			0
$836$	−7.30696e11			−1.49593
$837$	1.28939e11	+	1.28939e11i	0.262713	+	0.262713i
$838$	1.31264e11	−	1.31264e11i	0.266176	−	0.266176i
$839$		−	8.36816e11i		−	1.68881i	−0.535701	−	0.844407i	$-0.679953\pi$
$839$		−	8.36816e11i		−	1.68881i	0.535701	−	0.844407i	$-0.320047\pi$
$840$		0			0
$841$	4.84113e11			0.967748
$842$	−2.34670e11	−	2.34670e11i	−0.466883	−	0.466883i
$843$	−9.20555e11	+	9.20555e11i	−1.82280	+	1.82280i
$844$			1.48065e11i			0.291797i
$845$		0			0
$846$	7.53710e10			0.147137
$847$	−1.24118e11	−	1.24118e11i	−0.241157	−	0.241157i
$848$	−1.10978e11	+	1.10978e11i	−0.214611	+	0.214611i
$849$			4.31996e10i			0.0831475i
$850$		0			0
$851$	6.44187e10			0.122827
$852$	−1.45545e11	−	1.45545e11i	−0.276210	−	0.276210i
$853$	−2.74662e11	+	2.74662e11i	−0.518803	+	0.518803i	−0.917209	−	0.398406i	$-0.869564\pi$
$853$	−2.74662e11	+	2.74662e11i	−0.518803	+	0.518803i	0.398406	+	0.917209i	$0.369564\pi$
$854$		−	1.13743e11i		−	0.213842i
$855$		0			0
$856$	−1.97058e11			−0.367027
$857$	9.65564e10	+	9.65564e10i	0.179002	+	0.179002i	0.790921	−	0.611919i	$-0.209602\pi$
$857$	9.65564e10	+	9.65564e10i	0.179002	+	0.179002i	−0.611919	+	0.790921i	$0.709602\pi$
$858$	−3.23291e11	+	3.23291e11i	−0.596547	+	0.596547i
$859$			7.22383e11i			1.32677i	0.748280	+	0.663383i	$0.230880\pi$
$859$			7.22383e11i			1.32677i	−0.748280	+	0.663383i	$0.769120\pi$
$860$		0			0
$861$	2.76034e11			0.502284
$862$	7.41790e10	+	7.41790e10i	0.134354	+	0.134354i
$863$	9.33124e10	−	9.33124e10i	0.168227	−	0.168227i	−0.617973	−	0.786200i	$-0.712046\pi$
$863$	9.33124e10	−	9.33124e10i	0.168227	−	0.168227i	0.786200	+	0.617973i	$0.212046\pi$
$864$			1.87059e11i			0.335678i
$865$		0			0
$866$	−6.28803e10			−0.111800
$867$	5.06070e11	+	5.06070e11i	0.895642	+	0.895642i
$868$	1.52639e11	−	1.52639e11i	0.268897	−	0.268897i
$869$		−	2.18092e11i		−	0.382437i
$870$		0			0
$871$	−2.19925e11			−0.382123
$872$	4.76670e10	+	4.76670e10i	0.0824427	+	0.0824427i
$873$	5.13276e11	−	5.13276e11i	0.883678	−	0.883678i
$874$		−	1.99177e11i		−	0.341346i
$875$		0			0
$876$	−6.38520e11			−1.08432
$877$	−5.23388e11	−	5.23388e11i	−0.884760	−	0.884760i	0.109254	−	0.994014i	$-0.465154\pi$
$877$	−5.23388e11	−	5.23388e11i	−0.884760	−	0.884760i	−0.994014	+	0.109254i	$0.965154\pi$
$878$	−1.15232e10	+	1.15232e10i	−0.0193907	+	0.0193907i
$879$			1.54834e11i			0.259365i
$880$		0			0
$881$	−8.15621e10			−0.135389			−0.0676947	−	0.997706i	$-0.521564\pi$
$881$	−8.15621e10			−0.135389			−0.0676947	+	0.997706i	$0.521564\pi$
$882$	−9.86514e10	−	9.86514e10i	−0.163015	−	0.163015i
$883$	3.22895e11	−	3.22895e11i	0.531151	−	0.531151i	−0.389764	−	0.920915i	$-0.627443\pi$
$883$	3.22895e11	−	3.22895e11i	0.531151	−	0.531151i	0.920915	+	0.389764i	$0.127443\pi$
$884$		−	1.22262e11i		−	0.200209i
$885$		0			0
$886$	2.90420e11			0.471294
$887$	−4.59932e11	−	4.59932e11i	−0.743018	−	0.743018i	0.230140	−	0.973158i	$-0.426082\pi$
$887$	−4.59932e11	−	4.59932e11i	−0.743018	−	0.743018i	−0.973158	+	0.230140i	$0.926082\pi$
$888$	−7.64231e10	+	7.64231e10i	−0.122906	+	0.122906i
$889$			2.70163e11i			0.432532i
$890$		0			0
$891$	1.01065e12			1.60357
$892$	2.03788e11	+	2.03788e11i	0.321899	+	0.321899i
$893$	3.07706e11	−	3.07706e11i	0.483871	−	0.483871i
$894$			4.79141e11i			0.750091i
$895$		0			0
$896$	2.82887e11			0.438915
$897$	4.95558e11	+	4.95558e11i	0.765464	+	0.765464i
$898$	1.12575e11	−	1.12575e11i	0.173116	−	0.173116i
$899$			1.22029e11i			0.186821i
$900$		0			0
$901$	6.70910e10			0.101804
$902$	2.16049e11	+	2.16049e11i	0.326382	+	0.326382i
$903$	7.44607e8	−	7.44607e8i	0.00111989	−	0.00111989i
$904$		−	8.13047e11i		−	1.21742i
$905$		0			0
$906$	−5.07941e11			−0.753877
$907$	7.98076e11	+	7.98076e11i	1.17928	+	1.17928i	0.979929	+	0.199347i	$0.0638820\pi$
$907$	7.98076e11	+	7.98076e11i	1.17928	+	1.17928i	0.199347	+	0.979929i	$0.436118\pi$
$908$	7.56278e11	−	7.56278e11i	1.11260	−	1.11260i
$909$			3.42159e11i			0.501155i
$910$		0			0
$911$	−1.50243e11			−0.218132			−0.109066	−	0.994034i	$-0.534786\pi$
$911$	−1.50243e11			−0.218132			−0.109066	+	0.994034i	$0.534786\pi$
$912$	−4.82341e11	−	4.82341e11i	−0.697229	−	0.697229i
$913$	−3.11072e11	+	3.11072e11i	−0.447690	+	0.447690i
$914$		−	1.15320e11i		−	0.165241i
$915$		0			0
$916$	7.98264e11			1.13387
$917$	2.23008e11	+	2.23008e11i	0.315387	+	0.315387i
$918$	1.33207e10	−	1.33207e10i	0.0187567	−	0.0187567i
$919$		−	1.02471e12i		−	1.43662i	−0.695725	−	0.718308i	$-0.744917\pi$
$919$		−	1.02471e12i		−	1.43662i	0.695725	−	0.718308i	$-0.255083\pi$
$920$		0			0
$921$	1.19296e12			1.65801
$922$	−1.75495e11	−	1.75495e11i	−0.242851	−	0.242851i
$923$	−2.21574e11	+	2.21574e11i	−0.305289	+	0.305289i
$924$		−	4.68960e11i		−	0.643351i
$925$		0			0
$926$	−1.26151e11			−0.171573
$927$	4.72679e11	+	4.72679e11i	0.640099	+	0.640099i
$928$	−8.85171e10	+	8.85171e10i	−0.119353	+	0.119353i
$929$		−	1.38553e12i		−	1.86017i	−0.367346	−	0.930084i	$-0.619734\pi$
$929$		−	1.38553e12i		−	1.86017i	0.367346	−	0.930084i	$-0.380266\pi$
$930$		0			0
$931$	−8.05498e11			−1.07218
$932$	−7.88745e11	−	7.88745e11i	−1.04538	−	1.04538i
$933$	−2.81659e11	+	2.81659e11i	−0.371704	+	0.371704i
$934$		−	2.14705e11i		−	0.282133i
$935$		0			0
$936$	−4.95496e11			−0.645560
$937$	7.72786e11	+	7.72786e11i	1.00254	+	1.00254i	0.999997	+	0.00254091i	$0.000808797\pi$
$937$	7.72786e11	+	7.72786e11i	1.00254	+	1.00254i	0.00254091	+	0.999997i	$0.499191\pi$
$938$	−2.83655e10	+	2.83655e10i	−0.0366420	+	0.0366420i
$939$			7.22308e11i			0.929095i
$940$		0			0
$941$	−6.91185e11			−0.881528			−0.440764	−	0.897623i	$-0.645292\pi$
$941$	−6.91185e11			−0.881528			−0.440764	+	0.897623i	$0.645292\pi$
$942$	−5.31786e11	−	5.31786e11i	−0.675357	−	0.675357i
$943$	3.31172e11	−	3.31172e11i	0.418800	−	0.418800i
$944$		−	1.17194e10i		−	0.0147576i
$945$		0			0
$946$	1.16559e9			0.00145540
$947$	−6.05426e11	−	6.05426e11i	−0.752768	−	0.752768i	0.222227	−	0.974995i	$-0.428667\pi$
$947$	−6.05426e11	−	6.05426e11i	−0.752768	−	0.752768i	−0.974995	+	0.222227i	$0.928667\pi$
$948$	1.82108e11	−	1.82108e11i	0.225474	−	0.225474i
$949$			9.72066e11i			1.19848i
$950$		0			0
$951$	−8.35663e11			−1.02167
$952$	−3.43424e10	−	3.43424e10i	−0.0418103	−	0.0418103i
$953$	3.45330e11	−	3.45330e11i	0.418661	−	0.418661i	−0.466081	−	0.884742i	$-0.654335\pi$
$953$	3.45330e11	−	3.45330e11i	0.418661	−	0.418661i	0.884742	+	0.466081i	$0.154335\pi$
$954$		−	1.24850e11i		−	0.150728i
$955$		0			0
$956$	5.74532e11			0.687832
$957$	1.87458e11	+	1.87458e11i	0.223489	+	0.223489i
$958$	3.97343e10	−	3.97343e10i	0.0471740	−	0.0471740i
$959$			5.49319e11i			0.649456i
$960$		0			0
$961$	7.00825e10			0.0821705
$962$	5.34222e10	+	5.34222e10i	0.0623766	+	0.0623766i
$963$	−2.26265e11	+	2.26265e11i	−0.263095	+	0.263095i
$964$			1.56542e10i			0.0181268i
$965$		0			0
$966$	1.27832e11			0.146802
$967$	1.77273e10	+	1.77273e10i	0.0202739	+	0.0202739i	0.717171	−	0.696897i	$-0.245437\pi$
$967$	1.77273e10	+	1.77273e10i	0.0202739	+	0.0202739i	−0.696897	+	0.717171i	$0.745437\pi$
$968$	3.53320e11	−	3.53320e11i	0.402408	−	0.402408i
$969$			2.91597e11i			0.330741i
$970$		0			0
$971$	1.52187e12			1.71199			0.855994	−	0.516986i	$-0.172946\pi$
$971$	1.52187e12			1.71199			0.855994	+	0.516986i	$0.172946\pi$
$972$	6.52507e11	+	6.52507e11i	0.731005	+	0.731005i
$973$	8.08294e10	−	8.08294e10i	0.0901816	−	0.0901816i
$974$		−	3.11199e11i		−	0.345782i
$975$		0			0
$976$	−6.60938e11			−0.728385
$977$	−2.88131e11	−	2.88131e11i	−0.316237	−	0.316237i	0.531083	−	0.847320i	$-0.321785\pi$
$977$	−2.88131e11	−	2.88131e11i	−0.316237	−	0.316237i	−0.847320	+	0.531083i	$0.821785\pi$
$978$	−2.87927e11	+	2.87927e11i	−0.314722	+	0.314722i
$979$			9.50654e11i			1.03488i
$980$		0			0
$981$	1.09464e11			0.118194
$982$	−2.58120e11	−	2.58120e11i	−0.277572	−	0.277572i
$983$	2.15222e9	−	2.15222e9i	0.00230501	−	0.00230501i	−0.705953	−	0.708258i	$-0.749481\pi$
$983$	2.15222e9	−	2.15222e9i	0.00230501	−	0.00230501i	0.708258	+	0.705953i	$0.249481\pi$
$984$			7.85771e11i			0.838138i
$985$		0			0
$986$	1.26068e10			0.0133382
$987$	1.97485e11	+	1.97485e11i	0.208097	+	0.208097i
$988$	−9.28854e11	+	9.28854e11i	−0.974810	+	0.974810i
$989$		−	1.78669e9i		−	0.00186751i
$990$		0			0
$991$	1.40286e10			0.0145452			0.00727261	−	0.999974i	$-0.497685\pi$
$991$	1.40286e10			0.0145452			0.00727261	+	0.999974i	$0.497685\pi$
$992$	6.69504e11	+	6.69504e11i	0.691363	+	0.691363i
$993$	−1.12783e12	+	1.12783e12i	−1.15997	+	1.15997i
$994$			5.71562e10i			0.0585488i
$995$		0			0
$996$	−5.19494e11			−0.527890
$997$	−7.09850e11	−	7.09850e11i	−0.718433	−	0.718433i	0.249851	−	0.968284i	$-0.419618\pi$
$997$	−7.09850e11	−	7.09850e11i	−0.718433	−	0.718433i	−0.968284	+	0.249851i	$0.919618\pi$
$998$	−1.13152e11	+	1.13152e11i	−0.114062	+	0.114062i
$999$		−	6.54611e10i		−	0.0657236i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	25.9.c.b.7.2		6
5.2	odd	4		5.9.c.a.3.2	yes	6
5.3	odd	4	inner	25.9.c.b.18.2		6
5.4	even	2		5.9.c.a.2.2	✓	6
15.2	even	4		45.9.g.a.28.2		6
15.14	odd	2		45.9.g.a.37.2		6
20.7	even	4		80.9.p.c.33.1		6
20.19	odd	2		80.9.p.c.17.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5.9.c.a.2.2	✓	6	5.4	even	2
5.9.c.a.3.2	yes	6	5.2	odd	4
25.9.c.b.7.2		6	1.1	even	1	trivial
25.9.c.b.18.2		6	5.3	odd	4	inner
45.9.g.a.28.2		6	15.2	even	4
45.9.g.a.37.2		6	15.14	odd	2
80.9.p.c.17.1		6	20.19	odd	2
80.9.p.c.33.1		6	20.7	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 25 = 5^{2} \)
Weight:	\( k \)	\(=\)	\( 9 \)
Character orbit:	\([\chi]\)	\(=\)	25.c (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(4.39608 + 4.39608i) q^{2} +(-75.2981 + 75.2981i) q^{3} -217.349i q^{4} -662.032 q^{6} +(-730.992 - 730.992i) q^{7} +(2080.88 - 2080.88i) q^{8} -4778.60i q^{9} +O(q^{10})\)	\(q+(4.39608 + 4.39608i) q^{2} +(-75.2981 + 75.2981i) q^{3} -217.349i q^{4} -662.032 q^{6} +(-730.992 - 730.992i) q^{7} +(2080.88 - 2080.88i) q^{8} -4778.60i q^{9} +19599.8 q^{11} +(16366.0 + 16366.0i) q^{12} +(24915.1 - 24915.1i) q^{13} -6426.99i q^{14} -37346.0 q^{16} +(11288.6 + 11288.6i) q^{17} +(21007.1 - 21007.1i) q^{18} -171525. i q^{19} +110085. q^{21} +(86162.2 + 86162.2i) q^{22} +(132074. - 132074. i) q^{23} +313372. i q^{24} +219057. q^{26} +(-134211. - 134211. i) q^{27} +(-158880. + 158880. i) q^{28} -127019. i q^{29} -960715. q^{31} +(-696880. - 696880. i) q^{32} +(-1.47583e6 + 1.47583e6i) q^{33} +99251.5i q^{34} -1.03862e6 q^{36} +(243873. + 243873. i) q^{37} +(754036. - 754036. i) q^{38} +3.75212e6i q^{39} +2.50747e6 q^{41} +(483940. + 483940. i) q^{42} +(6763.95 - 6763.95i) q^{43} -4.26000e6i q^{44} +1.16122e6 q^{46} +(1.79394e6 + 1.79394e6i) q^{47} +(2.81208e6 - 2.81208e6i) q^{48} -4.69610e6i q^{49} -1.70003e6 q^{51} +(-5.41527e6 - 5.41527e6i) q^{52} +(2.97161e6 - 2.97161e6i) q^{53} -1.18001e6i q^{54} -3.04221e6 q^{56} +(1.29155e7 + 1.29155e7i) q^{57} +(558385. - 558385. i) q^{58} +313805. i q^{59} +1.76977e7 q^{61} +(-4.22338e6 - 4.22338e6i) q^{62} +(-3.49312e6 + 3.49312e6i) q^{63} +3.43349e6i q^{64} -1.29757e7 q^{66} +(-4.41349e6 - 4.41349e6i) q^{67} +(2.45358e6 - 2.45358e6i) q^{68} +1.98899e7i q^{69} -8.89315e6 q^{71} +(-9.94368e6 - 9.94368e6i) q^{72} +(-1.95076e7 + 1.95076e7i) q^{73} +2.14417e6i q^{74} -3.72808e7 q^{76} +(-1.43273e7 - 1.43273e7i) q^{77} +(-1.64946e7 + 1.64946e7i) q^{78} -1.11272e7i q^{79} +5.15641e7 q^{81} +(1.10230e7 + 1.10230e7i) q^{82} +(-1.58712e7 + 1.58712e7i) q^{83} -2.39268e7i q^{84} +59469.7 q^{86} +(9.56429e6 + 9.56429e6i) q^{87} +(4.07848e7 - 4.07848e7i) q^{88} +4.85032e7i q^{89} -3.64255e7 q^{91} +(-2.87062e7 - 2.87062e7i) q^{92} +(7.23400e7 - 7.23400e7i) q^{93} +1.57726e7i q^{94} +1.04948e8 q^{96} +(1.07411e8 + 1.07411e8i) q^{97} +(2.06444e7 - 2.06444e7i) q^{98} -9.36596e7i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 2 q^{2} + 72 q^{3} + 1752 q^{6} + 2352 q^{7} + 8220 q^{8}+O(q^{10}) \) 6 * q + 2 * q^2 + 72 * q^3 + 1752 * q^6 + 2352 * q^7 + 8220 * q^8	\( 6 q + 2 q^{2} + 72 q^{3} + 1752 q^{6} + 2352 q^{7} + 8220 q^{8} + 23192 q^{11} + 45912 q^{12} + 119142 q^{13} + 218616 q^{16} + 265502 q^{17} + 454062 q^{18} + 231672 q^{21} + 35664 q^{22} - 28888 q^{23} - 801388 q^{26} - 392040 q^{27} - 1305192 q^{28} - 747648 q^{31} - 3033928 q^{32} - 4269096 q^{33} - 3972804 q^{36} + 454002 q^{37} - 1443720 q^{38} + 2489432 q^{41} - 4223856 q^{42} - 792648 q^{43} - 3149928 q^{46} + 15313352 q^{47} + 21677712 q^{48} + 35567712 q^{51} + 735732 q^{52} + 13509122 q^{53} - 18454800 q^{56} + 34625520 q^{57} + 23903520 q^{58} + 24111192 q^{61} - 53913416 q^{62} - 44837688 q^{63} - 55047936 q^{66} + 32827752 q^{67} - 8118692 q^{68} - 13992928 q^{71} - 82596420 q^{72} - 111859638 q^{73} - 56470800 q^{76} - 26260136 q^{77} - 31125576 q^{78} + 65834226 q^{81} - 38023056 q^{82} + 14768432 q^{83} - 135560008 q^{86} + 133207680 q^{87} + 44555040 q^{88} + 167542032 q^{91} - 69931048 q^{92} + 96798024 q^{93} + 184867872 q^{96} + 186656202 q^{97} + 345959698 q^{98}+O(q^{100}) \) 6 * q + 2 * q^2 + 72 * q^3 + 1752 * q^6 + 2352 * q^7 + 8220 * q^8 + 23192 * q^11 + 45912 * q^12 + 119142 * q^13 + 218616 * q^16 + 265502 * q^17 + 454062 * q^18 + 231672 * q^21 + 35664 * q^22 - 28888 * q^23 - 801388 * q^26 - 392040 * q^27 - 1305192 * q^28 - 747648 * q^31 - 3033928 * q^32 - 4269096 * q^33 - 3972804 * q^36 + 454002 * q^37 - 1443720 * q^38 + 2489432 * q^41 - 4223856 * q^42 - 792648 * q^43 - 3149928 * q^46 + 15313352 * q^47 + 21677712 * q^48 + 35567712 * q^51 + 735732 * q^52 + 13509122 * q^53 - 18454800 * q^56 + 34625520 * q^57 + 23903520 * q^58 + 24111192 * q^61 - 53913416 * q^62 - 44837688 * q^63 - 55047936 * q^66 + 32827752 * q^67 - 8118692 * q^68 - 13992928 * q^71 - 82596420 * q^72 - 111859638 * q^73 - 56470800 * q^76 - 26260136 * q^77 - 31125576 * q^78 + 65834226 * q^81 - 38023056 * q^82 + 14768432 * q^83 - 135560008 * q^86 + 133207680 * q^87 + 44555040 * q^88 + 167542032 * q^91 - 69931048 * q^92 + 96798024 * q^93 + 184867872 * q^96 + 186656202 * q^97 + 345959698 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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