LMFDB - Embedded newform 100.11.b.e.51.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [100,11,Mod(51,100)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(100, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0]))

N = Newforms(chi, 11, names="a")

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

chi := DirichletCharacter("100.51");

S:= CuspForms(chi, 11);

N := Newforms(S);

Level:	$ N $	$=$	$ 100 = 2^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 11 $
Character orbit:	$[\chi]$	$=$	100.b (of order $2$, degree $1$, 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:	$63.5357252674$
Analytic rank:	$0$
Dimension:	$20$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 199481 x^{18} + 16413464051 x^{16} + 725560177607766 x^{14} + \cdots + 21\!\cdots\!25 $ x^20 + 199481x^18 + 16413464051x^16 + 725560177607766x^14 + 18834574233849489621x^12 + 294503164498899790078095x^10 + 2731275057520962661290869385x^8 + 14154171070179138865031966998950x^6 + 35770310815174676049504613026680775x^4 + 31929367165777304447910767061760715625*x^2 + 2155644618924695638814066662020965503125
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{97}\cdot 3^{4}\cdot 5^{29} $
Twist minimal:	no (minimal twist has level 20)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			51.6
Root			$-104.388i$ of defining polynomial
Character	$\chi$	$=$	100.51
Dual form			100.11.b.e.51.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-24.2624 + 20.8647i) q^{2} -208.777i q^{3} +(153.329 - 1012.46i) q^{4} +(4356.06 + 5065.43i) q^{6} +17557.3i q^{7} +(17404.4 + 27763.8i) q^{8} +15461.2 q^{9} +O(q^{10})$	\(q+(-24.2624 + 20.8647i) q^{2} -208.777i q^{3} +(153.329 - 1012.46i) q^{4} +(4356.06 + 5065.43i) q^{6} +17557.3i q^{7} +(17404.4 + 27763.8i) q^{8} +15461.2 q^{9} -265895. i q^{11} +(-211377. - 32011.6i) q^{12} -647096. q^{13} +(-366328. - 425983. i) q^{14} +(-1.00156e6 - 310478. i) q^{16} +2.51402e6 q^{17} +(-375126. + 322594. i) q^{18} +170501. i q^{19} +3.66556e6 q^{21} +(5.54781e6 + 6.45125e6i) q^{22} +5.21076e6i q^{23} +(5.79644e6 - 3.63364e6i) q^{24} +(1.57001e7 - 1.35015e7i) q^{26} -1.55560e7i q^{27} +(1.77760e7 + 2.69205e6i) q^{28} +6.80100e6 q^{29} +2.47062e7i q^{31} +(3.07782e7 - 1.33642e7i) q^{32} -5.55127e7 q^{33} +(-6.09962e7 + 5.24543e7i) q^{34} +(2.37066e6 - 1.56538e7i) q^{36} -9.23131e6 q^{37} +(-3.55745e6 - 4.13676e6i) q^{38} +1.35099e8i q^{39} +1.44940e8 q^{41} +(-8.89354e7 + 7.64809e7i) q^{42} -2.79512e7i q^{43} +(-2.69207e8 - 4.07695e7i) q^{44} +(-1.08721e8 - 1.26426e8i) q^{46} -1.10913e8i q^{47} +(-6.48207e7 + 2.09102e8i) q^{48} -2.57846e7 q^{49} -5.24869e8i q^{51} +(-9.92188e7 + 6.55156e8i) q^{52} -1.09572e8 q^{53} +(3.24571e8 + 3.77426e8i) q^{54} +(-4.87458e8 + 3.05575e8i) q^{56} +3.55966e7 q^{57} +(-1.65009e8 + 1.41901e8i) q^{58} -6.65268e8i q^{59} -7.40208e8 q^{61} +(-5.15487e8 - 5.99431e8i) q^{62} +2.71458e8i q^{63} +(-4.67913e8 + 9.66426e8i) q^{64} +(1.34687e9 - 1.15826e9i) q^{66} +4.17577e7i q^{67} +(3.85473e8 - 2.54533e9i) q^{68} +1.08789e9 q^{69} -6.30071e8i q^{71} +(2.69094e8 + 4.29262e8i) q^{72} -9.52604e8 q^{73} +(2.23974e8 - 1.92608e8i) q^{74} +(1.72624e8 + 2.61428e7i) q^{76} +4.66840e9 q^{77} +(-2.81879e9 - 3.27782e9i) q^{78} -2.24561e9i q^{79} -2.33477e9 q^{81} +(-3.51659e9 + 3.02413e9i) q^{82} -6.38664e9i q^{83} +(5.62038e8 - 3.71122e9i) q^{84} +(5.83192e8 + 6.78162e8i) q^{86} -1.41989e9i q^{87} +(7.38225e9 - 4.62775e9i) q^{88} -1.29920e9 q^{89} -1.13613e10i q^{91} +(5.27567e9 + 7.98963e8i) q^{92} +5.15808e9 q^{93} +(2.31416e9 + 2.69101e9i) q^{94} +(-2.79014e9 - 6.42578e9i) q^{96} -1.43562e10 q^{97} +(6.25596e8 - 5.37987e8i) q^{98} -4.11106e9i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9}+O(q^{10}) $ 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9	\( 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9} - 1329640 q^{12} + 278864 q^{13} - 2240504 q^{14} + 4261360 q^{16} + 1921656 q^{17} + 3556082 q^{18} + 4157512 q^{21} + 5811280 q^{22} - 19112144 q^{24} + 25066884 q^{26} + 87415400 q^{28} - 66014888 q^{29} + 33171328 q^{32} - 85980560 q^{33} - 27236084 q^{34} + 355456476 q^{36} + 153620656 q^{37} - 250352720 q^{38} + 477406160 q^{41} + 570662040 q^{42} + 339141040 q^{44} - 897549304 q^{46} + 479727360 q^{48} + 333772012 q^{49} + 110465096 q^{52} + 1669491824 q^{53} + 706139792 q^{54} - 1362290224 q^{56} - 3973032960 q^{57} - 2075027916 q^{58} - 4283166080 q^{61} - 1664032240 q^{62} + 340459456 q^{64} + 1884031760 q^{66} - 3042411896 q^{68} - 5321669928 q^{69} - 1632326712 q^{72} - 2474287656 q^{73} + 188682276 q^{74} + 2323171200 q^{76} - 410885040 q^{77} + 19914223760 q^{78} + 9939722652 q^{81} + 3197757116 q^{82} + 2383099552 q^{84} + 19648321456 q^{86} - 2774318240 q^{88} + 3011851592 q^{89} + 27349072440 q^{92} + 11861394640 q^{93} + 15684681576 q^{94} - 1990377984 q^{96} + 39984502056 q^{97} - 38416891998 q^{98}+O(q^{100}) \) 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9 - 1329640 * q^12 + 278864 * q^13 - 2240504 * q^14 + 4261360 * q^16 + 1921656 * q^17 + 3556082 * q^18 + 4157512 * q^21 + 5811280 * q^22 - 19112144 * q^24 + 25066884 * q^26 + 87415400 * q^28 - 66014888 * q^29 + 33171328 * q^32 - 85980560 * q^33 - 27236084 * q^34 + 355456476 * q^36 + 153620656 * q^37 - 250352720 * q^38 + 477406160 * q^41 + 570662040 * q^42 + 339141040 * q^44 - 897549304 * q^46 + 479727360 * q^48 + 333772012 * q^49 + 110465096 * q^52 + 1669491824 * q^53 + 706139792 * q^54 - 1362290224 * q^56 - 3973032960 * q^57 - 2075027916 * q^58 - 4283166080 * q^61 - 1664032240 * q^62 + 340459456 * q^64 + 1884031760 * q^66 - 3042411896 * q^68 - 5321669928 * q^69 - 1632326712 * q^72 - 2474287656 * q^73 + 188682276 * q^74 + 2323171200 * q^76 - 410885040 * q^77 + 19914223760 * q^78 + 9939722652 * q^81 + 3197757116 * q^82 + 2383099552 * q^84 + 19648321456 * q^86 - 2774318240 * q^88 + 3011851592 * q^89 + 27349072440 * q^92 + 11861394640 * q^93 + 15684681576 * q^94 - 1990377984 * q^96 + 39984502056 * q^97 - 38416891998 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/100\mathbb{Z}\right)^\times$.

$n$	$51$	$77$
$\chi(n)$	$-1$	$1$

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 $

$2$	−24.2624	+	20.8647i	−0.758200	+	0.652022i
$2$	−24.2624	+	20.8647i	−0.758200	+	0.652022i
$3$		−	208.777i		−	0.859164i	−0.903028	−	0.429582i	$-0.858661\pi$
$3$		−	208.777i		−	0.859164i	0.903028	−	0.429582i	$-0.141339\pi$
$4$	153.329	−	1012.46i	0.149736	−	0.988726i
$5$		0			0
$5$		0			0
$6$	4356.06	+	5065.43i	0.560194	+	0.651419i
$7$			17557.3i			1.04464i	0.852748	+	0.522322i	$0.174934\pi$
$7$			17557.3i			1.04464i	−0.852748	+	0.522322i	$0.825066\pi$
$8$	17404.4	+	27763.8i	0.531141	+	0.847283i
$9$	15461.2			0.261837
$10$		0			0
$11$		−	265895.i		−	1.65100i	−0.564404	−	0.825499i	$-0.690894\pi$
$11$		−	265895.i		−	1.65100i	0.564404	−	0.825499i	$-0.309106\pi$
$12$	−211377.	−	32011.6i	−0.849478	−	0.128647i
$13$	−647096.			−1.74282			−0.871409	−	0.490558i	$-0.836793\pi$
$13$	−647096.			−1.74282			−0.871409	+	0.490558i	$0.836793\pi$
$14$	−366328.	−	425983.i	−0.681130	−	0.792049i
$15$		0			0
$16$	−1.00156e6	−	310478.i	−0.955158	−	0.296095i
$17$	2.51402e6			1.77062			0.885308	−	0.465006i	$-0.153948\pi$
$17$	2.51402e6			1.77062			0.885308	+	0.465006i	$0.153948\pi$
$18$	−375126.	+	322594.i	−0.198525	+	0.170723i
$19$			170501.i			0.0688586i	0.999407	+	0.0344293i	$0.0109614\pi$
$19$			170501.i			0.0688586i	−0.999407	+	0.0344293i	$0.989039\pi$
$20$		0			0
$21$	3.66556e6			0.897520
$22$	5.54781e6	+	6.45125e6i	1.07649	+	1.25179i
$23$			5.21076e6i			0.809585i	0.914409	+	0.404792i	$0.132656\pi$
$23$			5.21076e6i			0.809585i	−0.914409	+	0.404792i	$0.867344\pi$
$24$	5.79644e6	−	3.63364e6i	0.727955	−	0.456337i
$25$		0			0
$26$	1.57001e7	−	1.35015e7i	1.32140	−	1.13635i
$27$		−	1.55560e7i		−	1.08413i
$28$	1.77760e7	+	2.69205e6i	1.03287	+	0.156420i
$29$	6.80100e6			0.331576			0.165788	−	0.986161i	$-0.446983\pi$
$29$	6.80100e6			0.331576			0.165788	+	0.986161i	$0.446983\pi$
$30$		0			0
$31$			2.47062e7i			0.862973i	0.902120	+	0.431486i	$0.142011\pi$
$31$			2.47062e7i			0.862973i	−0.902120	+	0.431486i	$0.857989\pi$
$32$	3.07782e7	−	1.33642e7i	0.917262	−	0.398285i
$33$	−5.55127e7			−1.41848
$34$	−6.09962e7	+	5.24543e7i	−1.34248	+	1.15448i
$35$		0			0
$36$	2.37066e6	−	1.56538e7i	0.0392063	−	0.258885i
$37$	−9.23131e6			−0.133124			−0.0665618	−	0.997782i	$-0.521203\pi$
$37$	−9.23131e6			−0.133124			−0.0665618	+	0.997782i	$0.521203\pi$
$38$	−3.55745e6	−	4.13676e6i	−0.0448973	−	0.0522086i
$39$			1.35099e8i			1.49737i
$40$		0			0
$41$	1.44940e8			1.25103			0.625516	−	0.780211i	$-0.284888\pi$
$41$	1.44940e8			1.25103			0.625516	+	0.780211i	$0.284888\pi$
$42$	−8.89354e7	+	7.64809e7i	−0.680500	+	0.585203i
$43$		−	2.79512e7i		−	0.190133i	−0.995471	−	0.0950665i	$-0.969694\pi$
$43$		−	2.79512e7i		−	0.190133i	0.995471	−	0.0950665i	$-0.0303064\pi$
$44$	−2.69207e8	−	4.07695e7i	−1.63238	−	0.247213i
$45$		0			0
$46$	−1.08721e8	−	1.26426e8i	−0.527867	−	0.613827i
$47$		−	1.10913e8i		−	0.483607i	−0.970325	−	0.241804i	$-0.922261\pi$
$47$		−	1.10913e8i		−	0.483607i	0.970325	−	0.241804i	$-0.0777389\pi$
$48$	−6.48207e7	+	2.09102e8i	−0.254394	+	0.820638i
$49$	−2.57846e7			−0.0912808
$50$		0			0
$51$		−	5.24869e8i		−	1.52125i
$52$	−9.92188e7	+	6.55156e8i	−0.260962	+	1.72317i
$53$	−1.09572e8			−0.262011			−0.131006	−	0.991382i	$-0.541821\pi$
$53$	−1.09572e8			−0.262011			−0.131006	+	0.991382i	$0.541821\pi$
$54$	3.24571e8	+	3.77426e8i	0.706873	+	0.821984i
$55$		0			0
$56$	−4.87458e8	+	3.05575e8i	−0.885109	+	0.554853i
$57$	3.55966e7			0.0591609
$58$	−1.65009e8	+	1.41901e8i	−0.251401	+	0.216194i
$59$		−	6.65268e8i		−	0.930543i	−0.885168	−	0.465271i	$-0.845957\pi$
$59$		−	6.65268e8i		−	0.930543i	0.885168	−	0.465271i	$-0.154043\pi$
$60$		0			0
$61$	−7.40208e8			−0.876405			−0.438202	−	0.898876i	$-0.644385\pi$
$61$	−7.40208e8			−0.876405			−0.438202	+	0.898876i	$0.644385\pi$
$62$	−5.15487e8	−	5.99431e8i	−0.562677	−	0.654306i
$63$			2.71458e8i			0.273527i
$64$	−4.67913e8	+	9.66426e8i	−0.435778	+	0.900054i
$65$		0			0
$66$	1.34687e9	−	1.15826e9i	1.07549	−	0.924878i
$67$			4.17577e7i			0.0309287i	0.999880	+	0.0154644i	$0.00492266\pi$
$67$			4.17577e7i			0.0309287i	−0.999880	+	0.0154644i	$0.995077\pi$
$68$	3.85473e8	−	2.54533e9i	0.265124	−	1.75065i
$69$	1.08789e9			0.695566
$70$		0			0
$71$		−	6.30071e8i		−	0.349219i	−0.984638	−	0.174609i	$-0.944134\pi$
$71$		−	6.30071e8i		−	0.349219i	0.984638	−	0.174609i	$-0.0558663\pi$
$72$	2.69094e8	+	4.29262e8i	0.139072	+	0.221850i
$73$	−9.52604e8			−0.459513			−0.229757	−	0.973248i	$-0.573793\pi$
$73$	−9.52604e8			−0.459513			−0.229757	+	0.973248i	$0.573793\pi$
$74$	2.23974e8	−	1.92608e8i	0.100934	−	0.0867994i
$75$		0			0
$76$	1.72624e8	+	2.61428e7i	0.0680823	+	0.0103106i
$77$	4.66840e9			1.72470
$78$	−2.81879e9	−	3.27782e9i	−0.976315	−	1.13530i
$79$		−	2.24561e9i		−	0.729793i	−0.931048	−	0.364896i	$-0.881104\pi$
$79$		−	2.24561e9i		−	0.729793i	0.931048	−	0.364896i	$-0.118896\pi$
$80$		0			0
$81$	−2.33477e9			−0.669604
$82$	−3.51659e9	+	3.02413e9i	−0.948533	+	0.815700i
$83$		−	6.38664e9i		−	1.62137i	−0.585483	−	0.810685i	$-0.699095\pi$
$83$		−	6.38664e9i		−	1.62137i	0.585483	−	0.810685i	$-0.300905\pi$
$84$	5.62038e8	−	3.71122e9i	0.134391	−	0.887402i
$85$		0			0
$86$	5.83192e8	+	6.78162e8i	0.123971	+	0.144159i
$87$		−	1.41989e9i		−	0.284878i
$88$	7.38225e9	−	4.62775e9i	1.39886	−	0.876913i
$89$	−1.29920e9			−0.232663			−0.116332	−	0.993210i	$-0.537114\pi$
$89$	−1.29920e9			−0.232663			−0.116332	+	0.993210i	$0.537114\pi$
$90$		0			0
$91$		−	1.13613e10i		−	1.82062i
$92$	5.27567e9	+	7.98963e8i	0.800457	+	0.121224i
$93$	5.15808e9			0.741435
$94$	2.31416e9	+	2.69101e9i	0.315322	+	0.366671i
$95$		0			0
$96$	−2.79014e9	−	6.42578e9i	−0.342192	−	0.788078i
$97$	−1.43562e10			−1.67178			−0.835892	−	0.548894i	$-0.815049\pi$
$97$	−1.43562e10			−1.67178			−0.835892	+	0.548894i	$0.815049\pi$
$98$	6.25596e8	−	5.37987e8i	0.0692091	−	0.0595170i
$99$		−	4.11106e9i		−	0.432292i
$100$		0			0
$101$	7.00408e9			0.666414			0.333207	−	0.942854i	$-0.391869\pi$
$101$	7.00408e9			0.666414			0.333207	+	0.942854i	$0.391869\pi$
$102$	1.09512e10	+	1.27346e10i	0.991887	+	1.15341i
$103$		−	1.99613e10i		−	1.72188i	−0.508711	−	0.860938i	$-0.669878\pi$
$103$		−	1.99613e10i		−	1.72188i	0.508711	−	0.860938i	$-0.330122\pi$
$104$	−1.12623e10	−	1.79658e10i	−0.925682	−	1.47666i
$105$		0			0
$106$	2.65848e9	−	2.28618e9i	0.198657	−	0.170837i
$107$			1.47384e10i			1.05083i	0.850846	+	0.525414i	$0.176090\pi$
$107$			1.47384e10i			1.05083i	−0.850846	+	0.525414i	$0.823910\pi$
$108$	−1.57498e10	−	2.38519e9i	−1.07190	−	0.162332i
$109$	1.01363e10			0.658787			0.329394	−	0.944193i	$-0.393156\pi$
$109$	1.01363e10			0.658787			0.329394	+	0.944193i	$0.393156\pi$
$110$		0			0
$111$			1.92728e9i			0.114375i
$112$	5.45117e9	−	1.75847e10i	0.309314	−	0.997800i
$113$	−1.71783e10			−0.932367			−0.466184	−	0.884688i	$-0.654371\pi$
$113$	−1.71783e10			−0.932367			−0.466184	+	0.884688i	$0.654371\pi$
$114$	−8.63660e8	+	7.42712e8i	−0.0448558	+	0.0385742i
$115$		0			0
$116$	1.04279e9	−	6.88571e9i	0.0496487	−	0.327837i
$117$	−1.00049e10			−0.456334
$118$	1.38806e10	+	1.61410e10i	0.606734	+	0.705538i
$119$			4.41395e10i			1.84966i
$120$		0			0
$121$	−4.47626e10			−1.72579
$122$	1.79592e10	−	1.54442e10i	0.664491	−	0.571435i
$123$		−	3.02601e10i		−	1.07484i
$124$	2.50139e10	+	3.78818e9i	0.853243	+	0.129218i
$125$		0			0
$126$	−5.66388e9	−	6.58622e9i	−0.178345	−	0.207388i
$127$		−	2.47585e10i		−	0.749385i	−0.927149	−	0.374693i	$-0.877748\pi$
$127$		−	2.47585e10i		−	0.749385i	0.927149	−	0.374693i	$-0.122252\pi$
$128$	−8.81147e9	−	3.32107e10i	−0.256448	−	0.966558i
$129$	−5.83555e9			−0.163355
$130$		0			0
$131$		−	6.21126e10i		−	1.60999i	−0.593282	−	0.804995i	$-0.702168\pi$
$131$		−	6.21126e10i		−	1.60999i	0.593282	−	0.804995i	$-0.297832\pi$
$132$	−8.51172e9	+	5.62041e10i	−0.212397	+	1.40249i
$133$	−2.99354e9			−0.0719327
$134$	−8.71261e8	−	1.01314e9i	−0.0201662	−	0.0234502i
$135$		0			0
$136$	4.37551e10	+	6.97987e10i	0.940447	+	1.50021i
$137$	−5.40807e10			−1.12057			−0.560285	−	0.828300i	$-0.689309\pi$
$137$	−5.40807e10			−1.12057			−0.560285	+	0.828300i	$0.689309\pi$
$138$	−2.63948e10	+	2.26984e10i	−0.527378	+	0.453524i
$139$		−	1.71319e9i		−	0.0330166i	−0.999864	−	0.0165083i	$-0.994745\pi$
$139$		−	1.71319e9i		−	0.0330166i	0.999864	−	0.0165083i	$-0.00525499\pi$
$140$		0			0
$141$	−2.31560e10			−0.415498
$142$	1.31462e10	+	1.52870e10i	0.227698	+	0.264778i
$143$			1.72059e11i			2.87739i
$144$	−1.54853e10	−	4.80037e9i	−0.250096	−	0.0775287i
$145$		0			0
$146$	2.31125e10	−	1.98758e10i	0.348403	−	0.299613i
$147$			5.38322e9i			0.0784252i
$148$	−1.41543e9	+	9.34629e9i	−0.0199333	+	0.131623i
$149$	−9.21894e10			−1.25531			−0.627653	−	0.778493i	$-0.715984\pi$
$149$	−9.21894e10			−1.25531			−0.627653	+	0.778493i	$0.715984\pi$
$150$		0			0
$151$		−	1.62044e10i		−	0.206418i	−0.994660	−	0.103209i	$-0.967089\pi$
$151$		−	1.62044e10i		−	0.206418i	0.994660	−	0.103209i	$-0.0329110\pi$
$152$	−4.73375e9	+	2.96747e9i	−0.0583428	+	0.0365737i
$153$	3.88698e10			0.463613
$154$	−1.13267e11	+	9.74048e10i	−1.30767	+	1.12454i
$155$		0			0
$156$	1.36781e11	+	2.07146e10i	1.48048	+	0.224209i
$157$	3.25976e10			0.341733			0.170867	−	0.985294i	$-0.445343\pi$
$157$	3.25976e10			0.341733			0.170867	+	0.985294i	$0.445343\pi$
$158$	4.68540e10	+	5.44840e10i	0.475841	+	0.553329i
$159$			2.28761e10i			0.225110i
$160$		0			0
$161$	−9.14871e10			−0.845728
$162$	5.66470e10	−	4.87142e10i	0.507694	−	0.436596i
$163$		−	1.38371e11i		−	1.20256i	−0.799037	−	0.601282i	$-0.794657\pi$
$163$		−	1.38371e11i		−	1.20256i	0.799037	−	0.601282i	$-0.205343\pi$
$164$	2.22235e10	−	1.46745e11i	0.187324	−	1.23693i
$165$		0			0
$166$	1.33255e11	+	1.54955e11i	1.05717	+	1.22932i
$167$		−	1.45798e11i		−	1.12246i	−0.827660	−	0.561229i	$-0.810329\pi$
$167$		−	1.45798e11i		−	1.12246i	0.827660	−	0.561229i	$-0.189671\pi$
$168$	6.37971e10	+	1.01770e11i	0.476710	+	0.760454i
$169$	2.80875e11			2.03741
$170$		0			0
$171$			2.63615e9i			0.0180297i
$172$	−2.82993e10	−	4.28573e9i	−0.187989	−	0.0284697i
$173$	−1.82593e10			−0.117830			−0.0589148	−	0.998263i	$-0.518764\pi$
$173$	−1.82593e10			−0.117830			−0.0589148	+	0.998263i	$0.518764\pi$
$174$	2.96256e10	+	3.44500e10i	0.185747	+	0.215994i
$175$		0			0
$176$	−8.25545e10	+	2.66309e11i	−0.488852	+	1.57696i
$177$	−1.38892e11			−0.799489
$178$	3.15218e10	−	2.71075e10i	0.176405	−	0.151701i
$179$		−	1.18186e11i		−	0.643134i	−0.946887	−	0.321567i	$-0.895791\pi$
$179$		−	1.18186e11i		−	0.643134i	0.946887	−	0.321567i	$-0.104209\pi$
$180$		0			0
$181$	−1.26493e11			−0.651138			−0.325569	−	0.945518i	$-0.605556\pi$
$181$	−1.26493e11			−0.651138			−0.325569	+	0.945518i	$0.605556\pi$
$182$	2.37050e11	+	2.75652e11i	1.18709	+	1.38040i
$183$			1.54538e11i			0.752976i
$184$	−1.44671e11	+	9.06904e10i	−0.685947	+	0.430004i
$185$		0			0
$186$	−1.25147e11	+	1.07622e11i	−0.562156	+	0.483432i
$187$		−	6.68465e11i		−	2.92328i
$188$	−1.12294e11	−	1.70062e10i	−0.478155	−	0.0724132i
$189$	2.73122e11			1.13252
$190$		0			0
$191$		−	5.22919e10i		−	0.205716i	−0.994696	−	0.102858i	$-0.967201\pi$
$191$		−	5.22919e10i		−	0.205716i	0.994696	−	0.102858i	$-0.0327987\pi$
$192$	2.01767e11	+	9.76895e10i	0.773294	+	0.374405i
$193$	−5.76304e10			−0.215211			−0.107606	−	0.994194i	$-0.534318\pi$
$193$	−5.76304e10			−0.215211			−0.107606	+	0.994194i	$0.534318\pi$
$194$	3.48315e11	−	2.99537e11i	1.26755	−	1.09004i
$195$		0			0
$196$	−3.95353e9	+	2.61057e10i	−0.0136680	+	0.0902517i
$197$	−2.43700e11			−0.821344			−0.410672	−	0.911783i	$-0.634706\pi$
$197$	−2.43700e11			−0.821344			−0.410672	+	0.911783i	$0.634706\pi$
$198$	8.57760e10	+	9.97442e10i	0.281864	+	0.327764i
$199$			1.54373e11i			0.494658i	0.968932	+	0.247329i	$0.0795528\pi$
$199$			1.54373e11i			0.494658i	−0.968932	+	0.247329i	$0.920447\pi$
$200$		0			0
$201$	8.71804e9			0.0265729
$202$	−1.69936e11	+	1.46138e11i	−0.505275	+	0.434516i
$203$			1.19407e11i			0.346378i
$204$	−5.31407e11	−	8.04778e10i	−1.50410	−	0.227785i
$205$		0			0
$206$	4.16485e11	+	4.84308e11i	1.12270	+	1.30553i
$207$			8.05648e10i			0.211979i
$208$	6.48103e11	+	2.00909e11i	1.66467	+	0.516040i
$209$	4.53353e10			0.113685
$210$		0			0
$211$			8.84929e10i			0.211591i	0.994388	+	0.105795i	$0.0337388\pi$
$211$			8.84929e10i			0.211591i	−0.994388	+	0.105795i	$0.966261\pi$
$212$	−1.68006e10	+	1.10937e11i	−0.0392324	+	0.259057i
$213$	−1.31544e11			−0.300036
$214$	−3.07513e11	−	3.57590e11i	−0.685163	−	0.796739i
$215$		0			0
$216$	4.31894e11	−	2.70744e11i	0.918561	−	0.575823i
$217$	−4.33774e11			−0.901499
$218$	−2.45930e11	+	2.11490e11i	−0.499493	+	0.429544i
$219$			1.98882e11i			0.394797i
$220$		0			0
$221$	−1.62681e12			−3.08586
$222$	−4.02122e10	−	4.67606e10i	−0.0745749	−	0.0867191i
$223$			1.09819e11i			0.199137i	0.995031	+	0.0995685i	$0.0317462\pi$
$223$			1.09819e11i			0.199137i	−0.995031	+	0.0995685i	$0.968254\pi$
$224$	2.34640e11	+	5.40383e11i	0.416066	+	0.958212i
$225$		0			0
$226$	4.16786e11	−	3.58419e11i	0.706921	−	0.607923i
$227$			4.71593e11i			0.782417i	0.920302	+	0.391208i	$0.127943\pi$
$227$			4.71593e11i			0.782417i	−0.920302	+	0.391208i	$0.872057\pi$
$228$	5.45800e9	−	3.60400e10i	0.00885849	−	0.0584939i
$229$	−2.85211e11			−0.452885			−0.226443	−	0.974025i	$-0.572710\pi$
$229$	−2.85211e11			−0.452885			−0.226443	+	0.974025i	$0.572710\pi$
$230$		0			0
$231$		−	9.74654e11i		−	1.48180i
$232$	1.18367e11	+	1.88821e11i	0.176113	+	0.280938i
$233$	−1.71346e11			−0.249514			−0.124757	−	0.992187i	$-0.539815\pi$
$233$	−1.71346e11			−0.249514			−0.124757	+	0.992187i	$0.539815\pi$
$234$	2.42743e11	−	2.08749e11i	0.345993	−	0.297540i
$235$		0			0
$236$	−6.73554e11	−	1.02005e11i	−0.920052	−	0.139335i
$237$	−4.68832e11			−0.627012
$238$	−9.20957e11	−	1.07093e12i	−1.20602	−	1.40241i
$239$			7.55431e11i			0.968735i	0.874865	+	0.484368i	$0.160950\pi$
$239$			7.55431e11i			0.968735i	−0.874865	+	0.484368i	$0.839050\pi$
$240$		0			0
$241$	1.27312e12			1.56598			0.782989	−	0.622036i	$-0.213694\pi$
$241$	1.27312e12			1.56598			0.782989	+	0.622036i	$0.213694\pi$
$242$	1.08605e12	−	9.33958e11i	1.30850	−	1.12525i
$243$		−	4.31122e11i		−	0.508825i
$244$	−1.13496e11	+	7.49428e11i	−0.131229	+	0.866524i
$245$		0			0
$246$	6.31367e11	+	7.34183e11i	0.700820	+	0.814946i
$247$		−	1.10330e11i		−	0.120008i
$248$	−6.85937e11	+	4.29997e11i	−0.731182	+	0.458360i
$249$	−1.33338e12			−1.39302
$250$		0			0
$251$		−	1.13923e12i		−	1.14351i	−0.820423	−	0.571757i	$-0.806262\pi$
$251$		−	1.13923e12i		−	1.14351i	0.820423	−	0.571757i	$-0.193738\pi$
$252$	2.74839e11	+	4.16224e10i	0.270443	+	0.0409567i
$253$	1.38552e12			1.33662
$254$	5.16578e11	+	6.00700e11i	0.488615	+	0.568184i
$255$		0			0
$256$	9.06718e11	+	6.21923e11i	0.824655	+	0.565635i
$257$	5.10456e11			0.455294			0.227647	−	0.973744i	$-0.426897\pi$
$257$	5.10456e11			0.455294			0.227647	+	0.973744i	$0.426897\pi$
$258$	1.41585e11	−	1.21757e11i	0.123856	−	0.106511i
$259$		−	1.62077e11i		−	0.139067i
$260$		0			0
$261$	1.05152e11			0.0868188
$262$	1.29596e12	+	1.50700e12i	1.04975	+	1.22069i
$263$		−	1.69927e12i		−	1.35047i	−0.737603	−	0.675235i	$-0.764042\pi$
$263$		−	1.69927e12i		−	1.35047i	0.737603	−	0.675235i	$-0.235958\pi$
$264$	−9.66167e11	−	1.54124e12i	−0.753412	−	1.20185i
$265$		0			0
$266$	7.26305e10	−	6.24593e10i	0.0545394	−	0.0469017i
$267$			2.71244e11i			0.199896i
$268$	4.22778e10	+	6.40267e9i	0.0305801	+	0.00463114i
$269$	3.81904e11			0.271140			0.135570	−	0.990768i	$-0.456713\pi$
$269$	3.81904e11			0.271140			0.135570	+	0.990768i	$0.456713\pi$
$270$		0			0
$271$		−	1.61226e12i		−	1.10304i	−0.834163	−	0.551518i	$-0.814049\pi$
$271$		−	1.61226e12i		−	1.10304i	0.834163	−	0.551518i	$-0.185951\pi$
$272$	−2.51793e12	−	7.80549e11i	−1.69122	−	0.524270i
$273$	−2.37197e12			−1.56421
$274$	1.31213e12	−	1.12838e12i	0.849617	−	0.730637i
$275$		0			0
$276$	1.66805e11	−	1.10144e12i	0.104151	−	0.687724i
$277$	1.26749e12			0.777225			0.388613	−	0.921401i	$-0.372954\pi$
$277$	1.26749e12			0.777225			0.388613	+	0.921401i	$0.372954\pi$
$278$	3.57452e10	+	4.15662e10i	0.0215275	+	0.0250332i
$279$			3.81988e11i			0.225958i
$280$		0			0
$281$	−1.44692e12			−0.825875			−0.412938	−	0.910759i	$-0.635497\pi$
$281$	−1.44692e12			−0.825875			−0.412938	+	0.910759i	$0.635497\pi$
$282$	5.61821e11	−	4.83144e11i	0.315031	−	0.270914i
$283$		−	1.60428e11i		−	0.0883788i	−0.999023	−	0.0441894i	$-0.985929\pi$
$283$		−	1.60428e11i		−	0.0883788i	0.999023	−	0.0441894i	$-0.0140705\pi$
$284$	−6.37919e11	−	9.66083e10i	−0.345282	−	0.0522905i
$285$		0			0
$286$	−3.58997e12	−	4.17458e12i	−1.87612	−	2.18164i
$287$			2.54476e12i			1.30688i
$288$	4.75869e11	−	2.06627e11i	0.240173	−	0.104286i
$289$	4.30431e12			2.13508
$290$		0			0
$291$			2.99724e12i			1.43634i
$292$	−1.46062e11	+	9.64469e11i	−0.0688055	+	0.454333i
$293$	1.75525e12			0.812831			0.406416	−	0.913688i	$-0.366778\pi$
$293$	1.75525e12			0.812831			0.406416	+	0.913688i	$0.366778\pi$
$294$	−1.12319e11	−	1.30610e11i	−0.0511349	−	0.0594620i
$295$		0			0
$296$	−1.60666e11	−	2.56296e11i	−0.0707074	−	0.112793i
$297$	−4.13626e12			−1.78989
$298$	2.23674e12	−	1.92350e12i	0.951774	−	0.818487i
$299$		−	3.37186e12i		−	1.41096i
$300$		0			0
$301$	4.90748e11			0.198621
$302$	3.38099e11	+	3.93157e11i	0.134589	+	0.156506i
$303$		−	1.46229e12i		−	0.572559i
$304$	5.29368e10	−	1.70766e11i	0.0203887	−	0.0657709i
$305$		0			0
$306$	−9.43076e11	+	8.11007e11i	−0.351511	+	0.302286i
$307$		−	3.35291e12i		−	1.22950i	−0.788720	−	0.614752i	$-0.789256\pi$
$307$		−	3.35291e12i		−	1.22950i	0.788720	−	0.614752i	$-0.210744\pi$
$308$	7.15803e11	−	4.72655e12i	0.258250	−	1.70526i
$309$	−4.16745e12			−1.47937
$310$		0			0
$311$			4.30452e12i			1.47953i	0.672867	+	0.739763i	$0.265062\pi$
$311$			4.30452e12i			1.47953i	−0.672867	+	0.739763i	$0.734938\pi$
$312$	−3.75085e12	+	2.35132e12i	−1.26869	+	0.795313i
$313$	−2.31790e12			−0.771566			−0.385783	−	0.922589i	$-0.626069\pi$
$313$	−2.31790e12			−0.771566			−0.385783	+	0.922589i	$0.626069\pi$
$314$	−7.90896e11	+	6.80138e11i	−0.259102	+	0.222817i
$315$		0			0
$316$	−2.27358e12	−	3.44318e11i	−0.721565	−	0.109276i
$317$	5.00628e12			1.56394			0.781968	−	0.623319i	$-0.214216\pi$
$317$	5.00628e12			1.56394			0.781968	+	0.623319i	$0.214216\pi$
$318$	−4.77302e11	−	5.55028e11i	−0.146777	−	0.170679i
$319$		−	1.80835e12i		−	0.547430i
$320$		0			0
$321$	3.07704e12			0.902835
$322$	2.21970e12	−	1.90885e12i	0.641231	−	0.551433i
$323$			4.28643e11i			0.121922i
$324$	−3.57988e11	+	2.36385e12i	−0.100264	+	0.662055i
$325$		0			0
$326$	2.88707e12	+	3.35722e12i	0.784097	+	0.911784i
$327$		−	2.11622e12i		−	0.566006i
$328$	2.52260e12	+	4.02408e12i	0.664475	+	1.05998i
$329$	1.94733e12			0.505197
$330$		0			0
$331$		−	4.10802e12i		−	1.03393i	−0.856005	−	0.516967i	$-0.827061\pi$
$331$		−	4.10802e12i		−	1.03393i	0.856005	−	0.516967i	$-0.172939\pi$
$332$	−6.46619e12	−	9.79259e11i	−1.60309	−	0.242777i
$333$	−1.42727e11			−0.0348567
$334$	3.04204e12	+	3.53742e12i	0.731867	+	0.851048i
$335$		0			0
$336$	−3.67127e12	−	1.13808e12i	−0.857274	−	0.265751i
$337$	5.62079e12			1.29315			0.646573	−	0.762852i	$-0.276201\pi$
$337$	5.62079e12			1.29315			0.646573	+	0.762852i	$0.276201\pi$
$338$	−6.81470e12	+	5.86036e12i	−1.54477	+	1.32844i
$339$			3.58642e12i			0.801056i
$340$		0			0
$341$	6.56924e12			1.42477
$342$	−5.50025e10	−	6.39594e10i	−0.0117558	−	0.0136702i
$343$			4.50680e12i			0.949288i
$344$	7.76030e11	−	4.86474e11i	0.161097	−	0.100987i
$345$		0			0
$346$	4.43015e11	−	3.80975e11i	0.0893384	−	0.0768274i
$347$			5.58470e12i			1.11008i	0.831825	+	0.555038i	$0.187296\pi$
$347$			5.58470e12i			1.11008i	−0.831825	+	0.555038i	$0.812704\pi$
$348$	−1.43758e12	−	2.17711e11i	−0.281666	−	0.0426564i
$349$	−4.24215e12			−0.819331			−0.409665	−	0.912236i	$-0.634355\pi$
$349$	−4.24215e12			−0.819331			−0.409665	+	0.912236i	$0.634355\pi$
$350$		0			0
$351$			1.00662e13i			1.88943i
$352$	−3.55348e12	−	8.18376e12i	−0.657567	−	1.51440i
$353$	9.65096e12			1.76075			0.880374	−	0.474280i	$-0.157292\pi$
$353$	9.65096e12			1.76075			0.880374	+	0.474280i	$0.157292\pi$
$354$	3.36987e12	−	2.89795e12i	0.606173	−	0.521284i
$355$		0			0
$356$	−1.99206e11	+	1.31539e12i	−0.0348380	+	0.230040i
$357$	9.21531e12			1.58916
$358$	2.46592e12	+	2.86748e12i	0.419337	+	0.487624i
$359$		−	7.95043e12i		−	1.33327i	−0.745384	−	0.666635i	$-0.767734\pi$
$359$		−	7.95043e12i		−	1.33327i	0.745384	−	0.666635i	$-0.232266\pi$
$360$		0			0
$361$	6.10200e12			0.995258
$362$	3.06902e12	−	2.63923e12i	0.493693	−	0.424556i
$363$			9.34540e12i			1.48274i
$364$	−1.15028e13	−	1.74202e12i	−1.80010	−	0.272612i
$365$		0			0
$366$	−3.22440e12	−	3.74947e12i	−0.490956	−	0.570906i
$367$			7.78220e12i			1.16889i	0.811435	+	0.584443i	$0.198687\pi$
$367$			7.78220e12i			1.16889i	−0.811435	+	0.584443i	$0.801313\pi$
$368$	1.61783e12	−	5.21887e12i	0.239714	−	0.773282i
$369$	2.24095e12			0.327567
$370$		0			0
$371$		−	1.92379e12i		−	0.273708i
$372$	7.90884e11	−	5.22232e12i	0.111019	−	0.733076i
$373$	−2.12996e12			−0.295003			−0.147502	−	0.989062i	$-0.547123\pi$
$373$	−2.12996e12			−0.295003			−0.147502	+	0.989062i	$0.547123\pi$
$374$	1.39473e13	+	1.62186e13i	1.90604	+	2.21643i
$375$		0			0
$376$	3.07936e12	−	1.93038e12i	0.409752	−	0.256864i
$377$	−4.40090e12			−0.577876
$378$	−6.62660e12	+	5.69861e12i	−0.858681	+	0.738431i
$379$			7.90603e12i			1.01103i	0.862819	+	0.505513i	$0.168697\pi$
$379$			7.90603e12i			1.01103i	−0.862819	+	0.505513i	$0.831303\pi$
$380$		0			0
$381$	−5.16900e12			−0.643845
$382$	1.09105e12	+	1.26873e12i	0.134131	+	0.155974i
$383$			1.22242e13i			1.48329i	0.670793	+	0.741645i	$0.265954\pi$
$383$			1.22242e13i			1.48329i	−0.670793	+	0.741645i	$0.734046\pi$
$384$	−6.93362e12	+	1.83963e12i	−0.830432	+	0.220331i
$385$		0			0
$386$	1.39825e12	−	1.20244e12i	0.163173	−	0.140322i
$387$		−	4.32159e11i		−	0.0497839i
$388$	−2.20122e12	+	1.45350e13i	−0.250326	+	1.65294i
$389$	−1.56498e13			−1.75695			−0.878476	−	0.477787i	$-0.841439\pi$
$389$	−1.56498e13			−1.75695			−0.878476	+	0.477787i	$0.841439\pi$
$390$		0			0
$391$			1.31000e13i			1.43346i
$392$	−4.48766e11	−	7.15877e11i	−0.0484830	−	0.0773407i
$393$	−1.29677e13			−1.38325
$394$	5.91276e12	−	5.08473e12i	0.622743	−	0.535534i
$395$		0			0
$396$	−4.16226e12	−	6.30346e11i	−0.427419	−	0.0647296i
$397$	−1.02802e13			−1.04244			−0.521219	−	0.853423i	$-0.674523\pi$
$397$	−1.02802e13			−1.04244			−0.521219	+	0.853423i	$0.674523\pi$
$398$	−3.22094e12	−	3.74545e12i	−0.322528	−	0.375050i
$399$			6.24982e11i			0.0618020i
$400$		0			0
$401$	5.11831e12			0.493633			0.246817	−	0.969062i	$-0.420615\pi$
$401$	5.11831e12			0.493633			0.246817	+	0.969062i	$0.420615\pi$
$402$	−2.11521e11	+	1.81899e11i	−0.0201476	+	0.0173261i
$403$		−	1.59873e13i		−	1.50400i
$404$	1.07393e12	−	7.09132e12i	0.0997859	−	0.658901i
$405$		0			0
$406$	−2.49140e12	−	2.89711e12i	−0.225846	−	0.262624i
$407$			2.45456e12i			0.219787i
$408$	1.45724e13	−	9.13505e12i	1.28893	−	0.807998i
$409$	−9.36298e12			−0.818083			−0.409042	−	0.912516i	$-0.634137\pi$
$409$	−9.36298e12			−0.818083			−0.409042	+	0.912516i	$0.634137\pi$
$410$		0			0
$411$			1.12908e13i			0.962754i
$412$	−2.02099e13	−	3.06064e12i	−1.70246	−	0.257826i
$413$	1.16803e13			0.972086
$414$	−1.68096e12	−	1.95470e12i	−0.138215	−	0.160723i
$415$		0			0
$416$	−1.99164e13	+	8.64793e12i	−1.59862	+	0.694137i
$417$	−3.57675e11			−0.0283667
$418$	−1.09994e12	+	9.45906e11i	−0.0861963	+	0.0741254i
$419$			1.70814e13i			1.32267i	0.750089	+	0.661337i	$0.230011\pi$
$419$			1.70814e13i			1.32267i	−0.750089	+	0.661337i	$0.769989\pi$
$420$		0			0
$421$	7.59949e12			0.574611			0.287306	−	0.957839i	$-0.407240\pi$
$421$	7.59949e12			0.574611			0.287306	+	0.957839i	$0.407240\pi$
$422$	−1.84638e12	−	2.14705e12i	−0.137962	−	0.160428i
$423$		−	1.71485e12i		−	0.126626i
$424$	−1.90704e12	−	3.04213e12i	−0.139165	−	0.221998i
$425$		0			0
$426$	3.19158e12	−	2.74463e12i	0.227488	−	0.195630i
$427$		−	1.29961e13i		−	0.915531i
$428$	1.49220e13	+	2.25983e12i	1.03898	+	0.157347i
$429$	3.59220e13			2.47215
$430$		0			0
$431$			6.00283e12i			0.403617i	0.979425	+	0.201809i	$0.0646819\pi$
$431$			6.00283e12i			0.403617i	−0.979425	+	0.201809i	$0.935318\pi$
$432$	−4.82980e12	+	1.55802e13i	−0.321004	+	1.03551i
$433$	2.69188e12			0.176855			0.0884273	−	0.996083i	$-0.471816\pi$
$433$	2.69188e12			0.176855			0.0884273	+	0.996083i	$0.471816\pi$
$434$	1.05244e13	−	9.05057e12i	0.683517	−	0.587797i
$435$		0			0
$436$	1.55419e12	−	1.02625e13i	0.0986439	−	0.651360i
$437$	−8.88439e11			−0.0557469
$438$	−4.14960e12	−	4.82535e12i	−0.257416	−	0.299335i
$439$		−	1.14520e13i		−	0.702360i	−0.936308	−	0.351180i	$-0.885781\pi$
$439$		−	1.14520e13i		−	0.702360i	0.936308	−	0.351180i	$-0.114219\pi$
$440$		0			0
$441$	−3.98661e11			−0.0239007
$442$	3.94704e13	−	3.39429e13i	2.33970	−	2.01205i
$443$		−	8.63257e12i		−	0.505966i	−0.967471	−	0.252983i	$-0.918588\pi$
$443$		−	8.63257e12i		−	0.505966i	0.967471	−	0.252983i	$-0.0814117\pi$
$444$	1.95129e12	+	2.95509e11i	0.113085	+	0.0171260i
$445$		0			0
$446$	−2.29133e12	−	2.66447e12i	−0.129842	−	0.150986i
$447$			1.92470e13i			1.07851i
$448$	−1.69679e13	−	8.21531e12i	−0.940236	−	0.455233i
$449$	−4.62556e11			−0.0253474			−0.0126737	−	0.999920i	$-0.504034\pi$
$449$	−4.62556e11			−0.0253474			−0.0126737	+	0.999920i	$0.504034\pi$
$450$		0			0
$451$		−	3.85388e13i		−	2.06545i
$452$	−2.63393e12	+	1.73922e13i	−0.139609	+	0.921856i
$453$	−3.38310e12			−0.177347
$454$	−9.83965e12	−	1.14420e13i	−0.510153	−	0.593229i
$455$		0			0
$456$	6.19539e11	+	9.88297e11i	0.0314228	+	0.0501260i
$457$	1.39645e13			0.700561			0.350280	−	0.936645i	$-0.386086\pi$
$457$	1.39645e13			0.700561			0.350280	+	0.936645i	$0.386086\pi$
$458$	6.91990e12	−	5.95083e12i	0.343378	−	0.295291i
$459$		−	3.91081e13i		−	1.91957i
$460$		0			0
$461$	−2.08164e13			−0.999772			−0.499886	−	0.866091i	$-0.666625\pi$
$461$	−2.08164e13			−0.999772			−0.499886	+	0.866091i	$0.666625\pi$
$462$	2.03359e13	+	2.36475e13i	0.966168	+	1.12350i
$463$		−	3.42763e13i		−	1.61098i	−0.592612	−	0.805488i	$-0.701903\pi$
$463$		−	3.42763e13i		−	1.61098i	0.592612	−	0.805488i	$-0.298097\pi$
$464$	−6.81158e12	−	2.11156e12i	−0.316707	−	0.0981779i
$465$		0			0
$466$	4.15727e12	−	3.57509e12i	0.189182	−	0.162688i
$467$			1.38159e13i			0.622007i	0.950409	+	0.311004i	$0.100665\pi$
$467$			1.38159e13i			0.622007i	−0.950409	+	0.311004i	$0.899335\pi$
$468$	−1.53404e12	+	1.01295e13i	−0.0683295	+	0.451190i
$469$	−7.33153e11			−0.0323095
$470$		0			0
$471$		−	6.80562e12i		−	0.293605i
$472$	1.84703e13	−	1.15786e13i	0.788433	−	0.494250i
$473$	−7.43207e12			−0.313909
$474$	1.13750e13	−	9.78204e12i	0.475400	−	0.408825i
$475$		0			0
$476$	4.46893e13	+	6.76788e12i	1.82881	+	0.276960i
$477$	−1.69411e12			−0.0686042
$478$	−1.57618e13	−	1.83286e13i	−0.631636	−	0.734495i
$479$		−	1.01623e13i		−	0.403007i	−0.979488	−	0.201504i	$-0.935417\pi$
$479$		−	1.01623e13i		−	0.403007i	0.979488	−	0.201504i	$-0.0645828\pi$
$480$		0			0
$481$	5.97354e12			0.232010
$482$	−3.08891e13	+	2.65633e13i	−1.18732	+	1.02105i
$483$			1.91004e13i			0.726619i
$484$	−6.86342e12	+	4.53202e13i	−0.258413	+	1.70634i
$485$		0			0
$486$	8.99522e12	+	1.04601e13i	0.331765	+	0.385791i
$487$		−	3.58386e13i		−	1.30830i	−0.756367	−	0.654148i	$-0.773027\pi$
$487$		−	3.58386e13i		−	1.30830i	0.756367	−	0.654148i	$-0.226973\pi$
$488$	−1.28829e13	−	2.05510e13i	−0.465495	−	0.742563i
$489$	−2.88887e13			−1.03320
$490$		0			0
$491$		−	4.60633e13i		−	1.61416i	−0.590440	−	0.807082i	$-0.701046\pi$
$491$		−	4.60633e13i		−	1.61416i	0.590440	−	0.807082i	$-0.298954\pi$
$492$	−3.06370e13	−	4.63976e12i	−1.06272	−	0.160942i
$493$	1.70978e13			0.587093
$494$	2.30201e12	+	2.67688e12i	0.0782478	+	0.0909901i
$495$		0			0
$496$	7.67073e12	−	2.47446e13i	0.255522	−	0.824276i
$497$	1.10624e13			0.364809
$498$	3.23511e13	−	2.78206e13i	1.05619	−	0.908280i
$499$			5.33675e13i			1.72494i	0.506106	+	0.862471i	$0.331084\pi$
$499$			5.33675e13i			1.72494i	−0.506106	+	0.862471i	$0.668916\pi$
$500$		0			0
$501$	−3.04393e13			−0.964376
$502$	2.37696e13	+	2.76404e13i	0.745595	+	0.867012i
$503$		−	2.57488e13i		−	0.799683i	−0.916584	−	0.399841i	$-0.869065\pi$
$503$		−	2.57488e13i		−	0.799683i	0.916584	−	0.399841i	$-0.130935\pi$
$504$	−7.53669e12	+	4.72457e12i	−0.231754	+	0.145281i
$505$		0			0
$506$	−3.36159e13	+	2.89083e13i	−1.01343	+	0.871506i
$507$		−	5.86401e13i		−	1.75047i
$508$	−2.50669e13	−	3.79620e12i	−0.740937	−	0.112210i
$509$	3.08784e13			0.903787			0.451893	−	0.892072i	$-0.350749\pi$
$509$	3.08784e13			0.903787			0.451893	+	0.892072i	$0.350749\pi$
$510$		0			0
$511$		−	1.67252e13i		−	0.480028i
$512$	−3.49754e13	+	3.82905e12i	−0.994061	+	0.108828i
$513$	2.65231e12			0.0746514
$514$	−1.23849e13	+	1.06505e13i	−0.345204	+	0.296862i
$515$		0			0
$516$	−8.94761e11	+	5.90824e12i	−0.0244601	+	0.161514i
$517$	−2.94912e13			−0.798434
$518$	3.38169e12	+	3.93238e12i	0.0906745	+	0.105440i
$519$			3.81213e12i			0.101235i
$520$		0			0
$521$	−4.01792e13			−1.04668			−0.523339	−	0.852125i	$-0.675314\pi$
$521$	−4.01792e13			−1.04668			−0.523339	+	0.852125i	$0.675314\pi$
$522$	−2.55123e12	+	2.19396e12i	−0.0658260	+	0.0566077i
$523$			3.84465e13i			0.982536i	0.871008	+	0.491268i	$0.163466\pi$
$523$			3.84465e13i			0.982536i	−0.871008	+	0.491268i	$0.836534\pi$
$524$	−6.28862e13	−	9.52368e12i	−1.59184	−	0.241073i
$525$		0			0
$526$	3.54548e13	+	4.12285e13i	0.880535	+	1.02393i
$527$			6.21118e13i			1.52799i
$528$	5.55991e13	+	1.72355e13i	1.35487	+	0.420004i
$529$	1.42745e13			0.344573
$530$		0			0
$531$		−	1.02858e13i		−	0.243651i
$532$	−4.58997e11	+	3.03082e12i	−0.0107709	+	0.0711218i
$533$	−9.37900e13			−2.18032
$534$	−5.65942e12	−	6.58103e12i	−0.130336	−	0.151561i
$535$		0			0
$536$	−1.15935e12	+	7.26769e11i	−0.0262054	+	0.0164275i
$537$	−2.46745e13			−0.552557
$538$	−9.26592e12	+	7.96831e12i	−0.205578	+	0.176789i
$539$			6.85598e12i			0.150704i
$540$		0			0
$541$	2.05539e13			0.443514			0.221757	−	0.975102i	$-0.428821\pi$
$541$	2.05539e13			0.443514			0.221757	+	0.975102i	$0.428821\pi$
$542$	3.36394e13	+	3.91174e13i	0.719203	+	0.836322i
$543$			2.64088e13i			0.559434i
$544$	7.73770e13	−	3.35979e13i	1.62412	−	0.705209i
$545$		0			0
$546$	5.75498e13	−	4.94905e13i	1.18599	−	1.01990i
$547$		−	3.41477e13i		−	0.697307i	−0.937252	−	0.348654i	$-0.886639\pi$
$547$		−	3.41477e13i		−	0.697307i	0.937252	−	0.348654i	$-0.113361\pi$
$548$	−8.29215e12	+	5.47543e13i	−0.167789	+	1.10794i
$549$	−1.14445e13			−0.229475
$550$		0			0
$551$			1.15958e12i			0.0228318i
$552$	1.89341e13	+	3.02039e13i	0.369444	+	0.589341i
$553$	3.94270e13			0.762373
$554$	−3.07524e13	+	2.64459e13i	−0.589292	+	0.506768i
$555$		0			0
$556$	−1.73453e12	−	2.62683e11i	−0.0326444	−	0.00494376i
$557$	−7.49932e13			−1.39877			−0.699384	−	0.714746i	$-0.746542\pi$
$557$	−7.49932e13			−1.39877			−0.699384	+	0.714746i	$0.746542\pi$
$558$	−7.97005e12	−	9.26794e12i	−0.147330	−	0.171322i
$559$			1.80871e13i			0.331367i
$560$		0			0
$561$	−1.39560e14			−2.51158
$562$	3.51059e13	−	3.01896e13i	0.626179	−	0.538488i
$563$		−	4.72984e13i		−	0.836190i	−0.908403	−	0.418095i	$-0.862698\pi$
$563$		−	4.72984e13i		−	0.836190i	0.908403	−	0.418095i	$-0.137302\pi$
$564$	−3.55050e12	+	2.34445e13i	−0.0622148	+	0.410813i
$565$		0			0
$566$	3.34728e12	+	3.89237e12i	0.0576249	+	0.0670089i
$567$		−	4.09922e13i		−	0.699498i
$568$	1.74931e13	−	1.09660e13i	0.295887	−	0.185484i
$569$	4.38722e13			0.735576			0.367788	−	0.929910i	$-0.380115\pi$
$569$	4.38722e13			0.735576			0.367788	+	0.929910i	$0.380115\pi$
$570$		0			0
$571$		−	1.82529e13i		−	0.300712i	−0.988632	−	0.150356i	$-0.951958\pi$
$571$		−	1.82529e13i		−	0.300712i	0.988632	−	0.150356i	$-0.0480420\pi$
$572$	1.74203e14	+	2.63818e13i	2.84495	+	0.430847i
$573$	−1.09173e13			−0.176744
$574$	−5.30956e13	−	6.17419e13i	−0.852116	−	0.990879i
$575$		0			0
$576$	−7.23451e12	+	1.49421e13i	−0.114103	+	0.235668i
$577$	−5.14350e13			−0.804229			−0.402114	−	0.915589i	$-0.631725\pi$
$577$	−5.14350e13			−0.804229			−0.402114	+	0.915589i	$0.631725\pi$
$578$	−1.04433e14	+	8.98080e13i	−1.61882	+	1.39212i
$579$			1.20319e13i			0.184902i
$580$		0			0
$581$	1.12132e14			1.69375
$582$	−6.25364e13	−	7.27202e13i	−0.936522	−	1.08903i
$583$			2.91346e13i			0.432580i
$584$	−1.65795e13	−	2.64479e13i	−0.244066	−	0.389338i
$585$		0			0
$586$	−4.25866e13	+	3.66227e13i	−0.616289	+	0.529984i
$587$		−	5.34075e13i		−	0.766323i	−0.923681	−	0.383161i	$-0.874835\pi$
$587$		−	5.34075e13i		−	0.766323i	0.923681	−	0.383161i	$-0.125165\pi$
$588$	5.45027e12	+	8.25405e11i	0.0775410	+	0.0117430i
$589$	−4.21242e12			−0.0594231
$590$		0			0
$591$			5.08790e13i			0.705669i
$592$	9.24568e12	+	2.86612e12i	0.127154	+	0.0394172i
$593$	6.93655e13			0.945954			0.472977	−	0.881075i	$-0.343179\pi$
$593$	6.93655e13			0.945954			0.472977	+	0.881075i	$0.343179\pi$
$594$	1.00356e14	−	8.63018e13i	1.35709	−	1.16705i
$595$		0			0
$596$	−1.41353e13	+	9.33377e13i	−0.187964	+	1.24115i
$597$	3.22294e13			0.424992
$598$	7.03529e13	+	8.18096e13i	0.919975	+	1.06979i
$599$			8.80310e13i			1.14157i	0.821100	+	0.570784i	$0.193361\pi$
$599$			8.80310e13i			1.14157i	−0.821100	+	0.570784i	$0.806639\pi$
$600$		0			0
$601$	1.72426e13			0.219902			0.109951	−	0.993937i	$-0.464931\pi$
$601$	1.72426e13			0.219902			0.109951	+	0.993937i	$0.464931\pi$
$602$	−1.19067e13	+	1.02393e13i	−0.150595	+	0.129505i
$603$			6.45625e11i			0.00809829i
$604$	−1.64062e13	−	2.48460e12i	−0.204091	−	0.0309081i
$605$		0			0
$606$	3.05102e13	+	3.54787e13i	0.373321	+	0.434114i
$607$			6.87730e13i			0.834593i	0.908770	+	0.417297i	$0.137022\pi$
$607$			6.87730e13i			0.834593i	−0.908770	+	0.417297i	$0.862978\pi$
$608$	2.27861e12	+	5.24771e12i	0.0274253	+	0.0631614i
$609$	2.49295e13			0.297596
$610$		0			0
$611$			7.17713e13i			0.842839i
$612$	5.95988e12	−	3.93540e13i	0.0694194	−	0.458386i
$613$	4.11211e13			0.475075			0.237537	−	0.971378i	$-0.423660\pi$
$613$	4.11211e13			0.475075			0.237537	+	0.971378i	$0.423660\pi$
$614$	6.99574e13	+	8.13497e13i	0.801663	+	0.932210i
$615$		0			0
$616$	8.12509e13	+	1.29613e14i	0.916062	+	1.46131i
$617$	4.43629e13			0.496128			0.248064	−	0.968744i	$-0.420206\pi$
$617$	4.43629e13			0.496128			0.248064	+	0.968744i	$0.420206\pi$
$618$	1.01112e14	−	8.69525e13i	1.12166	−	0.964583i
$619$		−	1.10379e14i		−	1.21460i	−0.794473	−	0.607300i	$-0.792253\pi$
$619$		−	1.10379e14i		−	1.21460i	0.794473	−	0.607300i	$-0.207747\pi$
$620$		0			0
$621$	8.10587e13			0.877691
$622$	−8.98125e13	−	1.04438e14i	−0.964683	−	1.12178i
$623$		−	2.28106e13i		−	0.243050i
$624$	4.19452e13	−	1.35309e14i	0.443363	−	1.43022i
$625$		0			0
$626$	5.62379e13	−	4.83623e13i	0.585002	−	0.503078i
$627$		−	9.46496e12i		−	0.0976744i
$628$	4.99816e12	−	3.30036e13i	0.0511696	−	0.337880i
$629$	−2.32077e13			−0.235711
$630$		0			0
$631$		−	7.39612e13i		−	0.739362i	−0.929159	−	0.369681i	$-0.879467\pi$
$631$		−	7.39612e13i		−	0.739362i	0.929159	−	0.369681i	$-0.120533\pi$
$632$	6.23467e13	−	3.90836e13i	0.618341	−	0.387623i
$633$	1.84753e13			0.181791
$634$	−1.21464e14	+	1.04454e14i	−1.18578	+	1.01972i
$635$		0			0
$636$	2.31610e13	+	3.50757e12i	0.222573	+	0.0337071i
$637$	1.66851e13			0.159086
$638$	3.77307e13	+	4.38749e13i	0.356937	+	0.415062i
$639$		−	9.74166e12i		−	0.0914384i
$640$		0			0
$641$	−1.00231e14			−0.926219			−0.463109	−	0.886301i	$-0.653266\pi$
$641$	−1.00231e14			−0.926219			−0.463109	+	0.886301i	$0.653266\pi$
$642$	−7.46564e13	+	6.42015e13i	−0.684529	+	0.588668i
$643$			1.21171e13i			0.110241i	0.998480	+	0.0551204i	$0.0175543\pi$
$643$			1.21171e13i			0.110241i	−0.998480	+	0.0551204i	$0.982446\pi$
$644$	−1.40277e13	+	9.26266e13i	−0.126636	+	0.836193i
$645$		0			0
$646$	−8.94349e12	−	1.03999e13i	−0.0794959	−	0.0924414i
$647$		−	4.51027e12i		−	0.0397815i	−0.999802	−	0.0198908i	$-0.993668\pi$
$647$		−	4.51027e12i		−	0.0397815i	0.999802	−	0.0198908i	$-0.00633185\pi$
$648$	−4.06353e13	−	6.48219e13i	−0.355654	−	0.567345i
$649$	−1.76891e14			−1.53632
$650$		0			0
$651$			9.05621e13i			0.774536i
$652$	−1.40095e14	−	2.12164e13i	−1.18901	−	0.180067i
$653$	2.71710e13			0.228844			0.114422	−	0.993432i	$-0.463498\pi$
$653$	2.71710e13			0.228844			0.114422	+	0.993432i	$0.463498\pi$
$654$	4.41542e13	+	5.13445e13i	0.369048	+	0.429146i
$655$		0			0
$656$	−1.45165e14	−	4.50007e13i	−1.19493	−	0.370424i
$657$	−1.47284e13			−0.120318
$658$	−4.72470e13	+	4.06305e13i	−0.383041	+	0.329399i
$659$			3.21903e13i			0.258999i	0.991579	+	0.129500i	$0.0413371\pi$
$659$			3.21903e13i			0.258999i	−0.991579	+	0.129500i	$0.958663\pi$
$660$		0			0
$661$	−2.23070e14			−1.76780			−0.883901	−	0.467673i	$-0.845092\pi$
$661$	−2.23070e14			−1.76780			−0.883901	+	0.467673i	$0.845092\pi$
$662$	8.57126e13	+	9.96705e13i	0.674147	+	0.783929i
$663$			3.39641e14i			2.65126i
$664$	1.77317e14	−	1.11156e14i	1.37376	−	0.861176i
$665$		0			0
$666$	3.46291e12	−	2.97796e12i	0.0264283	−	0.0227273i
$667$			3.54384e13i			0.268438i
$668$	−1.47614e14	−	2.23552e13i	−1.10980	−	0.168072i
$669$	2.29276e13			0.171091
$670$		0			0
$671$			1.96818e14i			1.44694i
$672$	1.12819e14	−	4.89874e13i	0.823261	−	0.357469i
$673$	−1.60450e14			−1.16216			−0.581079	−	0.813847i	$-0.697369\pi$
$673$	−1.60450e14			−1.16216			−0.581079	+	0.813847i	$0.697369\pi$
$674$	−1.36374e14	+	1.17276e14i	−0.980464	+	0.843160i
$675$		0			0
$676$	4.30663e13	−	2.84373e14i	0.305073	−	2.01444i
$677$	−7.42140e13			−0.521846			−0.260923	−	0.965360i	$-0.584027\pi$
$677$	−7.42140e13			−0.521846			−0.260923	+	0.965360i	$0.584027\pi$
$678$	−7.48296e13	−	8.70153e13i	−0.522306	−	0.607361i
$679$		−	2.52056e14i		−	1.74642i
$680$		0			0
$681$	9.84577e13			0.672224
$682$	−1.59386e14	+	1.37065e14i	−1.08026	+	0.928978i
$683$		−	1.52167e14i		−	1.02380i	−0.859044	−	0.511901i	$-0.828941\pi$
$683$		−	1.52167e14i		−	1.02380i	0.859044	−	0.511901i	$-0.171059\pi$
$684$	2.66898e12	+	4.04199e11i	0.0178265	+	0.00269969i
$685$		0			0
$686$	−9.40331e13	−	1.09346e14i	−0.618956	−	0.719750i
$687$			5.95454e13i			0.389103i
$688$	−8.67822e12	+	2.79947e13i	−0.0562974	+	0.181607i
$689$	7.09035e13			0.456637
$690$		0			0
$691$		−	2.33623e14i		−	1.48295i	−0.670981	−	0.741474i	$-0.734127\pi$
$691$		−	2.33623e14i		−	1.48295i	0.670981	−	0.741474i	$-0.265873\pi$
$692$	−2.79969e12	+	1.84868e13i	−0.0176433	+	0.116501i
$693$	7.21792e13			0.451592
$694$	−1.16523e14	−	1.35498e14i	−0.723793	−	0.841660i
$695$		0			0
$696$	3.94215e13	−	2.47124e13i	0.241372	−	0.151310i
$697$	3.64382e14			2.21510
$698$	1.02925e14	−	8.85112e13i	0.621217	−	0.534221i
$699$			3.57731e13i			0.214373i
$700$		0			0
$701$	3.29351e14			1.94567			0.972835	−	0.231498i	$-0.0743628\pi$
$701$	3.29351e14			1.94567			0.972835	+	0.231498i	$0.0743628\pi$
$702$	−2.10029e14	−	2.44231e14i	−1.23195	−	1.43257i
$703$		−	1.57395e12i		−	0.00916670i
$704$	2.56968e14	+	1.24416e14i	1.48599	+	0.719469i
$705$		0			0
$706$	−2.34156e14	+	2.01364e14i	−1.33500	+	1.14805i
$707$			1.22973e14i			0.696165i
$708$	−2.12963e13	+	1.40622e14i	−0.119712	+	0.790475i
$709$	3.11783e14			1.74029			0.870146	−	0.492795i	$-0.164025\pi$
$709$	3.11783e14			1.74029			0.870146	+	0.492795i	$0.164025\pi$
$710$		0			0
$711$		−	3.47199e13i		−	0.191087i
$712$	−2.26119e13	−	3.60708e13i	−0.123577	−	0.197132i
$713$	−1.28738e14			−0.698649
$714$	−2.23586e14	+	1.92274e14i	−1.20490	+	1.03617i
$715$		0			0
$716$	−1.19658e14	−	1.81214e13i	−0.635883	−	0.0963000i
$717$	1.57716e14			0.832303
$718$	1.65883e14	+	1.92897e14i	0.869321	+	1.01089i
$719$			3.50979e14i			1.82657i	0.407319	+	0.913286i	$0.366464\pi$
$719$			3.50979e14i			1.82657i	−0.407319	+	0.913286i	$0.633536\pi$
$720$		0			0
$721$	3.50466e14			1.79875
$722$	−1.48049e14	+	1.27316e14i	−0.754605	+	0.648930i
$723$		−	2.65799e14i		−	1.34543i
$724$	−1.93950e13	+	1.28068e14i	−0.0974985	+	0.643797i
$725$		0			0
$726$	−1.94989e14	−	2.26742e14i	−0.966778	−	1.12421i
$727$		−	1.35548e14i		−	0.667452i	−0.942670	−	0.333726i	$-0.891694\pi$
$727$		−	1.35548e14i		−	0.667452i	0.942670	−	0.333726i	$-0.108306\pi$
$728$	3.15432e14	−	1.97737e14i	1.54258	−	0.967008i
$729$	−2.27874e14			−1.10677
$730$		0			0
$731$		−	7.02698e13i		−	0.336652i
$732$	1.56463e14	+	2.36953e13i	0.744487	+	0.112747i
$733$	7.21264e13			0.340859			0.170429	−	0.985370i	$-0.445485\pi$
$733$	7.21264e13			0.340859			0.170429	+	0.985370i	$0.445485\pi$
$734$	−1.62373e14	−	1.88815e14i	−0.762138	−	0.886249i
$735$		0			0
$736$	6.96378e13	+	1.60378e14i	0.322445	+	0.742601i
$737$	1.11031e13			0.0510633
$738$	−5.43708e13	+	4.67567e13i	−0.248361	+	0.213581i
$739$		−	9.07050e13i		−	0.411537i	−0.978601	−	0.205769i	$-0.934031\pi$
$739$		−	9.07050e13i		−	0.411537i	0.978601	−	0.205769i	$-0.0659694\pi$
$740$		0			0
$741$	−2.30344e13			−0.103107
$742$	4.01393e13	+	4.66758e13i	0.178464	+	0.207526i
$743$		−	3.37748e14i		−	1.49159i	−0.666177	−	0.745794i	$-0.732070\pi$
$743$		−	3.37748e14i		−	1.49159i	0.666177	−	0.745794i	$-0.267930\pi$
$744$	8.97734e13	+	1.43208e14i	0.393807	+	0.628206i
$745$		0			0
$746$	5.16779e13	−	4.44409e13i	0.223672	−	0.192349i
$747$		−	9.87452e13i		−	0.424535i
$748$	−6.76791e14	−	1.02495e14i	−2.89033	−	0.437719i
$749$	−2.58767e14			−1.09774
$750$		0			0
$751$			4.16582e14i			1.74381i	0.489671	+	0.871907i	$0.337117\pi$
$751$			4.16582e14i			1.74381i	−0.489671	+	0.871907i	$0.662883\pi$
$752$	−3.44360e13	+	1.11085e14i	−0.143194	+	0.461921i
$753$	−2.37844e14			−0.982466
$754$	1.06776e14	−	9.18234e13i	0.438146	−	0.376787i
$755$		0			0
$756$	4.18776e13	−	2.76524e14i	0.169579	−	1.11976i
$757$	−1.87029e14			−0.752366			−0.376183	−	0.926545i	$-0.622764\pi$
$757$	−1.87029e14			−0.752366			−0.376183	+	0.926545i	$0.622764\pi$
$758$	−1.64957e14	−	1.91819e14i	−0.659211	−	0.766561i
$759$		−	2.89263e14i		−	1.14838i
$760$		0			0
$761$	1.62618e14			0.637155			0.318577	−	0.947897i	$-0.396795\pi$
$761$	1.62618e14			0.637155			0.318577	+	0.947897i	$0.396795\pi$
$762$	1.25412e14	−	1.07850e14i	0.488164	−	0.419801i
$763$			1.77966e14i			0.688198i
$764$	−5.29432e13	−	8.01788e12i	−0.203397	−	0.0308030i
$765$		0			0
$766$	−2.55054e14	−	2.96588e14i	−0.967137	−	1.12463i
$767$			4.30492e14i			1.62177i
$768$	1.29843e14	−	1.89302e14i	0.485974	−	0.708514i
$769$	−2.16562e13			−0.0805286			−0.0402643	−	0.999189i	$-0.512820\pi$
$769$	−2.16562e13			−0.0805286			−0.0402643	+	0.999189i	$0.512820\pi$
$770$		0			0
$771$		−	1.06571e14i		−	0.391173i
$772$	−8.83642e12	+	5.83482e13i	−0.0322248	+	0.212785i
$773$	1.67235e14			0.605942			0.302971	−	0.953000i	$-0.402021\pi$
$773$	1.67235e14			0.605942			0.302971	+	0.953000i	$0.402021\pi$
$774$	9.01686e12	+	1.04852e13i	0.0324602	+	0.0377462i
$775$		0			0
$776$	−2.49861e14	−	3.98582e14i	−0.887953	−	1.41647i
$777$	−3.38380e13			−0.119481
$778$	3.79701e14	−	3.26527e14i	1.33212	−	1.14557i
$779$			2.47124e13i			0.0861444i
$780$		0			0
$781$	−1.67533e14			−0.576559
$782$	−2.73327e14	−	3.17837e14i	−0.934649	−	1.08685i
$783$		−	1.05796e14i		−	0.359469i
$784$	2.58247e13	+	8.00554e12i	0.0871876	+	0.0270278i
$785$		0			0
$786$	3.14627e14	−	2.70566e14i	1.04878	−	0.901906i
$787$			3.25711e14i			1.07885i	0.842035	+	0.539423i	$0.181358\pi$
$787$			3.25711e14i			1.07885i	−0.842035	+	0.539423i	$0.818642\pi$
$788$	−3.73664e13	+	2.46736e14i	−0.122984	+	0.812084i
$789$	−3.54769e14			−1.16027
$790$		0			0
$791$		−	3.01604e14i		−	0.973992i
$792$	1.14139e14	−	7.15506e13i	0.366274	−	0.229608i
$793$	4.78986e14			1.52741
$794$	2.49423e14	−	2.14494e14i	0.790377	−	0.679692i
$795$		0			0
$796$	1.56295e14	+	2.36698e13i	0.489081	+	0.0740679i
$797$	3.41010e14			1.06041			0.530207	−	0.847868i	$-0.322114\pi$
$797$	3.41010e14			1.06041			0.530207	+	0.847868i	$0.322114\pi$
$798$	−1.30400e13	−	1.51636e13i	−0.0402963	−	0.0468583i
$799$		−	2.78837e14i		−	0.856282i
$800$		0			0
$801$	−2.00873e13			−0.0609198
$802$	−1.24182e14	+	1.06792e14i	−0.374273	+	0.321860i
$803$			2.53292e14i			0.758655i
$804$	1.33673e12	−	8.82662e12i	0.00397890	−	0.0262733i
$805$		0			0
$806$	3.33569e14	+	3.87890e14i	0.980643	+	1.14034i
$807$		−	7.97328e13i		−	0.232953i
$808$	1.21902e14	+	1.94460e14i	0.353960	+	0.564641i
$809$	4.70292e14			1.35714			0.678570	−	0.734536i	$-0.262600\pi$
$809$	4.70292e14			1.35714			0.678570	+	0.734536i	$0.262600\pi$
$810$		0			0
$811$			6.93252e14i			1.97600i	0.154455	+	0.988000i	$0.450638\pi$
$811$			6.93252e14i			1.97600i	−0.154455	+	0.988000i	$0.549362\pi$
$812$	1.20895e14	+	1.83086e13i	0.342473	+	0.0518652i
$813$	−3.36603e14			−0.947689
$814$	−5.12136e13	−	5.95535e13i	−0.143306	−	0.166642i
$815$		0			0
$816$	−1.62960e14	+	5.25686e14i	−0.450434	+	1.45303i
$817$	4.76569e12			0.0130923
$818$	2.27169e14	−	1.95356e14i	0.620271	−	0.533408i
$819$		−	1.75659e14i		−	0.476707i
$820$		0			0
$821$	−1.68591e14			−0.451980			−0.225990	−	0.974130i	$-0.572562\pi$
$821$	−1.68591e14			−0.451980			−0.225990	+	0.974130i	$0.572562\pi$
$822$	−2.35579e14	−	2.73942e14i	−0.627737	−	0.729961i
$823$		−	2.41032e14i		−	0.638373i	−0.947692	−	0.319187i	$-0.896590\pi$
$823$		−	2.41032e14i		−	0.638373i	0.947692	−	0.319187i	$-0.103410\pi$
$824$	5.54200e14	−	3.47414e14i	1.45892	−	0.914559i
$825$		0			0
$826$	−2.83393e14	+	2.43706e14i	−0.737036	+	0.633821i
$827$			7.67653e14i			1.98444i	0.124503	+	0.992219i	$0.460266\pi$
$827$			7.67653e14i			1.98444i	−0.124503	+	0.992219i	$0.539734\pi$
$828$	8.15682e13	+	1.23529e13i	0.209589	+	0.0317408i
$829$	1.04564e14			0.267062			0.133531	−	0.991045i	$-0.457368\pi$
$829$	1.04564e14			0.267062			0.133531	+	0.991045i	$0.457368\pi$
$830$		0			0
$831$		−	2.64623e14i		−	0.667764i
$832$	3.02785e14	−	6.25370e14i	0.759482	−	1.56863i
$833$	−6.48229e13			−0.161623
$834$	8.67806e12	−	7.46278e12i	0.0215076	−	0.0184957i
$835$		0			0
$836$	6.95122e12	−	4.58999e13i	0.0170228	−	0.112404i
$837$	3.84329e14			0.935570
$838$	−3.56398e14	−	4.14436e14i	−0.862412	−	1.00285i
$839$			4.91176e14i			1.18148i	0.806861	+	0.590741i	$0.201165\pi$
$839$			4.91176e14i			1.18148i	−0.806861	+	0.590741i	$0.798835\pi$
$840$		0			0
$841$	−3.74454e14			−0.890058
$842$	−1.84382e14	+	1.58561e14i	−0.435670	+	0.374659i
$843$			3.02084e14i			0.709562i
$844$	8.95951e13	+	1.35686e13i	0.209205	+	0.0316826i
$845$		0			0
$846$	3.57798e13	+	4.16064e13i	0.0825631	+	0.0960081i
$847$		−	7.85912e14i		−	1.80284i
$848$	1.09742e14	+	3.40197e13i	0.250262	+	0.0775802i
$849$	−3.34937e13			−0.0759319
$850$		0			0
$851$		−	4.81022e13i		−	0.107775i
$852$	−2.01696e13	+	1.33183e14i	−0.0449261	+	0.296654i
$853$	7.29444e14			1.61528			0.807638	−	0.589678i	$-0.200746\pi$
$853$	7.29444e14			1.61528			0.807638	+	0.589678i	$0.200746\pi$
$854$	2.71159e14	+	3.15316e14i	0.596946	+	0.694156i
$855$		0			0
$856$	−4.09194e14	+	2.56514e14i	−0.890350	+	0.558139i
$857$	−3.90478e14			−0.844680			−0.422340	−	0.906438i	$-0.638791\pi$
$857$	−3.90478e14			−0.844680			−0.422340	+	0.906438i	$0.638791\pi$
$858$	−8.71555e14	+	7.49502e14i	−1.87438	+	1.61189i
$859$			3.35693e14i			0.717756i	0.933384	+	0.358878i	$0.116841\pi$
$859$			3.35693e14i			0.717756i	−0.933384	+	0.358878i	$0.883159\pi$
$860$		0			0
$861$	5.31286e14			1.12283
$862$	−1.25247e14	−	1.45643e14i	−0.263167	−	0.306023i
$863$		−	1.64979e14i		−	0.344647i	−0.985040	−	0.172323i	$-0.944873\pi$
$863$		−	1.64979e14i		−	0.344647i	0.985040	−	0.172323i	$-0.0551274\pi$
$864$	−2.07894e14	−	4.78786e14i	−0.431790	−	0.994427i
$865$		0			0
$866$	−6.53115e13	+	5.61653e13i	−0.134091	+	0.115313i
$867$		−	8.98640e14i		−	1.83438i
$868$	−6.65103e13	+	4.39177e14i	−0.134987	+	0.891336i
$869$	−5.97097e14			−1.20489
$870$		0			0
$871$		−	2.70212e13i		−	0.0539032i
$872$	1.76416e14	+	2.81421e14i	0.349909	+	0.558180i
$873$	−2.21964e14			−0.437735
$874$	2.15557e13	−	1.85370e13i	0.0422673	−	0.0363482i
$875$		0			0
$876$	2.01359e14	+	3.04944e13i	0.390346	+	0.0591152i
$877$	−9.67288e14			−1.86448			−0.932240	−	0.361841i	$-0.882148\pi$
$877$	−9.67288e14			−1.86448			−0.932240	+	0.361841i	$0.882148\pi$
$878$	2.38943e14	+	2.77854e14i	0.457954	+	0.532530i
$879$		−	3.66455e14i		−	0.698356i
$880$		0			0
$881$	1.03943e13			0.0195846			0.00979230	−	0.999952i	$-0.496883\pi$
$881$	1.03943e13			0.0195846			0.00979230	+	0.999952i	$0.496883\pi$
$882$	9.67247e12	−	8.31793e12i	0.0181215	−	0.0155838i
$883$			6.42429e14i			1.19680i	0.801198	+	0.598400i	$0.204197\pi$
$883$			6.42429e14i			1.19680i	−0.801198	+	0.598400i	$0.795803\pi$
$884$	−2.49438e14	+	1.64708e15i	−0.462063	+	3.05107i
$885$		0			0
$886$	1.80116e14	+	2.09447e14i	0.329901	+	0.383624i
$887$			1.79852e14i			0.327565i	0.986496	+	0.163783i	$0.0523696\pi$
$887$			1.79852e14i			0.327565i	−0.986496	+	0.163783i	$0.947630\pi$
$888$	−5.35087e13	+	3.35433e13i	−0.0969080	+	0.0607492i
$889$	4.34693e14			0.782841
$890$		0			0
$891$			6.20802e14i			1.10551i
$892$	1.11186e14	+	1.68384e13i	0.196892	+	0.0298179i
$893$	1.89107e13			0.0333005
$894$	−4.01583e14	−	4.66979e14i	−0.703215	−	0.817730i
$895$		0			0
$896$	5.83091e14	−	1.54706e14i	1.00971	−	0.267896i
$897$	−7.03967e14			−1.21224
$898$	1.12227e13	−	9.65110e12i	0.0192184	−	0.0165270i
$899$			1.68027e14i			0.286141i
$900$		0			0
$901$	−2.75466e14			−0.463921
$902$	8.04099e14	+	9.35043e14i	1.34672	+	1.56603i
$903$		−	1.02457e14i		−	0.170648i
$904$	−2.98978e14	−	4.76933e14i	−0.495219	−	0.789979i
$905$		0			0
$906$	8.20821e13	−	7.05873e13i	0.134464	−	0.115634i
$907$			3.05101e14i			0.497059i	0.968624	+	0.248529i	$0.0799472\pi$
$907$			3.05101e14i			0.497059i	−0.968624	+	0.248529i	$0.920053\pi$
$908$	4.77467e14	+	7.23090e13i	0.773596	+	0.117156i
$909$	1.08292e14			0.174492
$910$		0			0
$911$		−	4.85024e14i		−	0.772985i	−0.922292	−	0.386493i	$-0.873686\pi$
$911$		−	4.85024e14i		−	0.772985i	0.922292	−	0.386493i	$-0.126314\pi$
$912$	−3.56520e13	−	1.10520e13i	−0.0565080	−	0.0175172i
$913$	−1.69817e15			−2.67688
$914$	−3.38814e14	+	2.91366e14i	−0.531165	+	0.456781i
$915$		0			0
$916$	−4.37311e13	+	2.88763e14i	−0.0678130	+	0.447779i
$917$	1.09053e15			1.68187
$918$	8.15979e14	+	9.48858e14i	1.25160	+	1.45542i
$919$			7.20957e14i			1.09985i	0.835215	+	0.549923i	$0.185343\pi$
$919$			7.20957e14i			1.09985i	−0.835215	+	0.549923i	$0.814657\pi$
$920$		0			0
$921$	−7.00010e14			−1.05635
$922$	5.05056e14	−	4.34328e14i	0.758027	−	0.651873i
$923$			4.07716e14i			0.608625i
$924$	−9.86794e14	−	1.49443e14i	−1.46510	−	0.221879i
$925$		0			0
$926$	7.15165e14	+	8.31626e14i	1.05039	+	1.22144i
$927$		−	3.08625e14i		−	0.450851i
$928$	2.09322e14	−	9.08900e13i	0.304142	−	0.132061i
$929$	2.60027e14			0.375785			0.187893	−	0.982190i	$-0.439834\pi$
$929$	2.60027e14			0.375785			0.187893	+	0.982190i	$0.439834\pi$
$930$		0			0
$931$		−	4.39629e12i		−	0.00628547i
$932$	−2.62724e13	+	1.73480e14i	−0.0373611	+	0.246701i
$933$	8.98684e14			1.27116
$934$	−2.88265e14	−	3.35208e14i	−0.405562	−	0.471606i
$935$		0			0
$936$	−1.74129e14	−	2.77774e14i	−0.242378	−	0.386644i
$937$	−2.28649e14			−0.316571			−0.158285	−	0.987393i	$-0.550597\pi$
$937$	−2.28649e14			−0.316571			−0.158285	+	0.987393i	$0.550597\pi$
$938$	1.77881e13	−	1.52970e13i	0.0244971	−	0.0210665i
$939$			4.83924e14i			0.662902i
$940$		0			0
$941$	4.79378e14			0.649726			0.324863	−	0.945761i	$-0.394682\pi$
$941$	4.79378e14			0.649726			0.324863	+	0.945761i	$0.394682\pi$
$942$	1.41997e14	+	1.65121e14i	0.191437	+	0.222611i
$943$			7.55247e14i			1.01282i
$944$	−2.06551e14	+	6.66303e14i	−0.275529	+	0.888816i
$945$		0			0
$946$	1.80320e14	−	1.55068e14i	0.238006	−	0.204676i
$947$		−	1.22091e15i		−	1.60300i	−0.597996	−	0.801499i	$-0.704036\pi$
$947$		−	1.22091e15i		−	1.60300i	0.597996	−	0.801499i	$-0.295964\pi$
$948$	−7.18857e13	+	4.74672e14i	−0.0938860	+	0.619943i
$949$	6.16426e14			0.800848
$950$		0			0
$951$		−	1.04520e15i		−	1.34368i
$952$	−1.22548e15	+	7.68223e14i	−1.56719	+	0.982432i
$953$	1.76783e14			0.224893			0.112447	−	0.993658i	$-0.464131\pi$
$953$	1.76783e14			0.224893			0.112447	+	0.993658i	$0.464131\pi$
$954$	4.11033e13	−	3.53472e13i	0.0520157	−	0.0447314i
$955$		0			0
$956$	7.64840e14	+	1.15830e14i	0.957814	+	0.145054i
$957$	−3.77542e14			−0.470333
$958$	2.12032e14	+	2.46561e14i	0.262769	+	0.305560i
$959$		−	9.49512e14i		−	1.17060i
$960$		0			0
$961$	2.09233e14			0.255278
$962$	−1.44933e14	+	1.24636e14i	−0.175910	+	0.151276i
$963$			2.27874e14i			0.275146i
$964$	1.95207e14	−	1.28898e15i	0.234483	−	1.54832i
$965$		0			0
$966$	−3.98524e14	−	4.63422e14i	−0.473771	−	0.550923i
$967$		−	8.92243e14i		−	1.05524i	−0.849481	−	0.527619i	$-0.823085\pi$
$967$		−	8.92243e14i		−	1.05524i	0.849481	−	0.527619i	$-0.176915\pi$
$968$	−7.79068e14	−	1.24278e15i	−0.916640	−	1.46224i
$969$	8.94906e13			0.104751
$970$		0			0
$971$			5.15365e14i			0.597062i	0.954400	+	0.298531i	$0.0964966\pi$
$971$			5.15365e14i			0.597062i	−0.954400	+	0.298531i	$0.903503\pi$
$972$	−4.36492e14	−	6.61036e13i	−0.503089	−	0.0761893i
$973$	3.00791e13			0.0344906
$974$	7.47761e14	+	8.69530e14i	0.853037	+	0.991950i
$975$		0			0
$976$	7.41360e14	+	2.29819e14i	0.837106	+	0.259499i
$977$	3.34826e14			0.376138			0.188069	−	0.982156i	$-0.439777\pi$
$977$	3.34826e14			0.376138			0.188069	+	0.982156i	$0.439777\pi$
$978$	7.00910e14	−	6.02754e14i	0.783372	−	0.673668i
$979$			3.45452e14i			0.384126i
$980$		0			0
$981$	1.56719e14			0.172495
$982$	9.61096e14	+	1.11761e15i	1.05247	+	1.22386i
$983$		−	4.72944e13i		−	0.0515278i	−0.999668	−	0.0257639i	$-0.991798\pi$
$983$		−	4.72944e13i		−	0.0515278i	0.999668	−	0.0257639i	$-0.00820182\pi$
$984$	8.40134e14	−	5.26660e14i	0.910696	−	0.570893i
$985$		0			0
$986$	−4.14835e14	+	3.56741e14i	−0.445134	+	0.382797i
$987$		−	4.06558e14i		−	0.434047i
$988$	−1.11705e14	−	1.69169e13i	−0.118655	−	0.0179695i
$989$	1.45647e14			0.153929
$990$		0			0
$991$		−	5.38725e14i		−	0.563637i	−0.959468	−	0.281818i	$-0.909062\pi$
$991$		−	5.38725e14i		−	0.563637i	0.959468	−	0.281818i	$-0.0909375\pi$
$992$	3.30179e14	+	7.60412e14i	0.343709	+	0.791572i
$993$	−8.57660e14			−0.888319
$994$	−2.68400e14	+	2.30813e14i	−0.276598	+	0.237864i
$995$		0			0
$996$	−2.04447e14	+	1.34999e15i	−0.208585	+	1.37732i
$997$	2.09210e14			0.212376			0.106188	−	0.994346i	$-0.466135\pi$
$997$	2.09210e14			0.212376			0.106188	+	0.994346i	$0.466135\pi$
$998$	−1.11350e15	−	1.29483e15i	−1.12470	−	1.30785i
$999$			1.43602e14i			0.144323i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	100.11.b.e.51.6		20
4.3	odd	2	inner	100.11.b.e.51.5		20
5.2	odd	4		100.11.d.c.99.11		40
5.3	odd	4		100.11.d.c.99.30		40
5.4	even	2		20.11.b.a.11.15	✓	20
15.14	odd	2		180.11.c.a.91.6		20
20.3	even	4		100.11.d.c.99.12		40
20.7	even	4		100.11.d.c.99.29		40
20.19	odd	2		20.11.b.a.11.16	yes	20
40.19	odd	2		320.11.b.d.191.15		20
40.29	even	2		320.11.b.d.191.6		20
60.59	even	2		180.11.c.a.91.5		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
20.11.b.a.11.15	✓	20	5.4	even	2
20.11.b.a.11.16	yes	20	20.19	odd	2
100.11.b.e.51.5		20	4.3	odd	2	inner
100.11.b.e.51.6		20	1.1	even	1	trivial
100.11.d.c.99.11		40	5.2	odd	4
100.11.d.c.99.12		40	20.3	even	4
100.11.d.c.99.29		40	20.7	even	4
100.11.d.c.99.30		40	5.3	odd	4
180.11.c.a.91.5		20	60.59	even	2
180.11.c.a.91.6		20	15.14	odd	2
320.11.b.d.191.6		20	40.29	even	2
320.11.b.d.191.15		20	40.19	odd	2

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:	\( N \)	\(=\)	\( 100 = 2^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 11 \)
Character orbit:	\([\chi]\)	\(=\)	100.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-24.2624 + 20.8647i) q^{2} -208.777i q^{3} +(153.329 - 1012.46i) q^{4} +(4356.06 + 5065.43i) q^{6} +17557.3i q^{7} +(17404.4 + 27763.8i) q^{8} +15461.2 q^{9} +O(q^{10})\)	\(q+(-24.2624 + 20.8647i) q^{2} -208.777i q^{3} +(153.329 - 1012.46i) q^{4} +(4356.06 + 5065.43i) q^{6} +17557.3i q^{7} +(17404.4 + 27763.8i) q^{8} +15461.2 q^{9} -265895. i q^{11} +(-211377. - 32011.6i) q^{12} -647096. q^{13} +(-366328. - 425983. i) q^{14} +(-1.00156e6 - 310478. i) q^{16} +2.51402e6 q^{17} +(-375126. + 322594. i) q^{18} +170501. i q^{19} +3.66556e6 q^{21} +(5.54781e6 + 6.45125e6i) q^{22} +5.21076e6i q^{23} +(5.79644e6 - 3.63364e6i) q^{24} +(1.57001e7 - 1.35015e7i) q^{26} -1.55560e7i q^{27} +(1.77760e7 + 2.69205e6i) q^{28} +6.80100e6 q^{29} +2.47062e7i q^{31} +(3.07782e7 - 1.33642e7i) q^{32} -5.55127e7 q^{33} +(-6.09962e7 + 5.24543e7i) q^{34} +(2.37066e6 - 1.56538e7i) q^{36} -9.23131e6 q^{37} +(-3.55745e6 - 4.13676e6i) q^{38} +1.35099e8i q^{39} +1.44940e8 q^{41} +(-8.89354e7 + 7.64809e7i) q^{42} -2.79512e7i q^{43} +(-2.69207e8 - 4.07695e7i) q^{44} +(-1.08721e8 - 1.26426e8i) q^{46} -1.10913e8i q^{47} +(-6.48207e7 + 2.09102e8i) q^{48} -2.57846e7 q^{49} -5.24869e8i q^{51} +(-9.92188e7 + 6.55156e8i) q^{52} -1.09572e8 q^{53} +(3.24571e8 + 3.77426e8i) q^{54} +(-4.87458e8 + 3.05575e8i) q^{56} +3.55966e7 q^{57} +(-1.65009e8 + 1.41901e8i) q^{58} -6.65268e8i q^{59} -7.40208e8 q^{61} +(-5.15487e8 - 5.99431e8i) q^{62} +2.71458e8i q^{63} +(-4.67913e8 + 9.66426e8i) q^{64} +(1.34687e9 - 1.15826e9i) q^{66} +4.17577e7i q^{67} +(3.85473e8 - 2.54533e9i) q^{68} +1.08789e9 q^{69} -6.30071e8i q^{71} +(2.69094e8 + 4.29262e8i) q^{72} -9.52604e8 q^{73} +(2.23974e8 - 1.92608e8i) q^{74} +(1.72624e8 + 2.61428e7i) q^{76} +4.66840e9 q^{77} +(-2.81879e9 - 3.27782e9i) q^{78} -2.24561e9i q^{79} -2.33477e9 q^{81} +(-3.51659e9 + 3.02413e9i) q^{82} -6.38664e9i q^{83} +(5.62038e8 - 3.71122e9i) q^{84} +(5.83192e8 + 6.78162e8i) q^{86} -1.41989e9i q^{87} +(7.38225e9 - 4.62775e9i) q^{88} -1.29920e9 q^{89} -1.13613e10i q^{91} +(5.27567e9 + 7.98963e8i) q^{92} +5.15808e9 q^{93} +(2.31416e9 + 2.69101e9i) q^{94} +(-2.79014e9 - 6.42578e9i) q^{96} -1.43562e10 q^{97} +(6.25596e8 - 5.37987e8i) q^{98} -4.11106e9i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9}+O(q^{10}) \) 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9	\( 20 q - 22 q^{2} - 644 q^{4} - 14784 q^{6} - 3448 q^{8} - 414868 q^{9} - 1329640 q^{12} + 278864 q^{13} - 2240504 q^{14} + 4261360 q^{16} + 1921656 q^{17} + 3556082 q^{18} + 4157512 q^{21} + 5811280 q^{22} - 19112144 q^{24} + 25066884 q^{26} + 87415400 q^{28} - 66014888 q^{29} + 33171328 q^{32} - 85980560 q^{33} - 27236084 q^{34} + 355456476 q^{36} + 153620656 q^{37} - 250352720 q^{38} + 477406160 q^{41} + 570662040 q^{42} + 339141040 q^{44} - 897549304 q^{46} + 479727360 q^{48} + 333772012 q^{49} + 110465096 q^{52} + 1669491824 q^{53} + 706139792 q^{54} - 1362290224 q^{56} - 3973032960 q^{57} - 2075027916 q^{58} - 4283166080 q^{61} - 1664032240 q^{62} + 340459456 q^{64} + 1884031760 q^{66} - 3042411896 q^{68} - 5321669928 q^{69} - 1632326712 q^{72} - 2474287656 q^{73} + 188682276 q^{74} + 2323171200 q^{76} - 410885040 q^{77} + 19914223760 q^{78} + 9939722652 q^{81} + 3197757116 q^{82} + 2383099552 q^{84} + 19648321456 q^{86} - 2774318240 q^{88} + 3011851592 q^{89} + 27349072440 q^{92} + 11861394640 q^{93} + 15684681576 q^{94} - 1990377984 q^{96} + 39984502056 q^{97} - 38416891998 q^{98}+O(q^{100}) \) 20 * q - 22 * q^2 - 644 * q^4 - 14784 * q^6 - 3448 * q^8 - 414868 * q^9 - 1329640 * q^12 + 278864 * q^13 - 2240504 * q^14 + 4261360 * q^16 + 1921656 * q^17 + 3556082 * q^18 + 4157512 * q^21 + 5811280 * q^22 - 19112144 * q^24 + 25066884 * q^26 + 87415400 * q^28 - 66014888 * q^29 + 33171328 * q^32 - 85980560 * q^33 - 27236084 * q^34 + 355456476 * q^36 + 153620656 * q^37 - 250352720 * q^38 + 477406160 * q^41 + 570662040 * q^42 + 339141040 * q^44 - 897549304 * q^46 + 479727360 * q^48 + 333772012 * q^49 + 110465096 * q^52 + 1669491824 * q^53 + 706139792 * q^54 - 1362290224 * q^56 - 3973032960 * q^57 - 2075027916 * q^58 - 4283166080 * q^61 - 1664032240 * q^62 + 340459456 * q^64 + 1884031760 * q^66 - 3042411896 * q^68 - 5321669928 * q^69 - 1632326712 * q^72 - 2474287656 * q^73 + 188682276 * q^74 + 2323171200 * q^76 - 410885040 * q^77 + 19914223760 * q^78 + 9939722652 * q^81 + 3197757116 * q^82 + 2383099552 * q^84 + 19648321456 * q^86 - 2774318240 * q^88 + 3011851592 * q^89 + 27349072440 * q^92 + 11861394640 * q^93 + 15684681576 * q^94 - 1990377984 * q^96 + 39984502056 * q^97 - 38416891998 * q^98

Introduction

L-functions

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