LMFDB - Embedded newform 432.6.i.d.145.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [432,6,Mod(145,432)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(432, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("432.145");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 432 = 2^{4} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	432.i (of order $3$, degree $2$, not 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:	$69.2858101592$
Analytic rank:	$0$
Dimension:	$10$
Relative dimension:	$5$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 175x^{8} + 8800x^{6} + 124623x^{4} + 498609x^{2} + 442368 $ x^10 + 175x^8 + 8800x^6 + 124623x^4 + 498609x^2 + 442368
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{8}\cdot 3^{16} $
Twist minimal:	no (minimal twist has level 36)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			145.2
Root			$-9.84603i$ of defining polynomial
Character	$\chi$	$=$	432.145
Dual form			432.6.i.d.289.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-13.1603 + 22.7942i) q^{5} +(31.6287 + 54.7826i) q^{7} +O(q^{10})$	$q+(-13.1603 + 22.7942i) q^{5} +(31.6287 + 54.7826i) q^{7} +(-49.1194 - 85.0772i) q^{11} +(369.143 - 639.374i) q^{13} -250.060 q^{17} -1102.41 q^{19} +(-2204.70 + 3818.66i) q^{23} +(1216.12 + 2106.37i) q^{25} +(-3941.06 - 6826.11i) q^{29} +(-2305.65 + 3993.49i) q^{31} -1664.97 q^{35} +11896.3 q^{37} +(5040.58 - 8730.55i) q^{41} +(3518.99 + 6095.07i) q^{43} +(-7459.33 - 12919.9i) q^{47} +(6402.75 - 11089.9i) q^{49} -22451.7 q^{53} +2585.69 q^{55} +(-5405.25 + 9362.17i) q^{59} +(594.647 + 1029.96i) q^{61} +(9716.02 + 16828.6i) q^{65} +(29590.2 - 51251.8i) q^{67} +14326.6 q^{71} -53098.2 q^{73} +(3107.17 - 5381.77i) q^{77} +(-18695.6 - 32381.6i) q^{79} +(-60439.5 - 104684. i) q^{83} +(3290.85 - 5699.93i) q^{85} -97873.2 q^{89} +46702.1 q^{91} +(14507.9 - 25128.5i) q^{95} +(-53356.7 - 92416.4i) q^{97} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 21 q^{5} - 29 q^{7}+O(q^{10}) $ 10 * q + 21 * q^5 - 29 * q^7	$ 10 q + 21 q^{5} - 29 q^{7} + 177 q^{11} - 181 q^{13} - 2280 q^{17} + 832 q^{19} + 399 q^{23} - 4778 q^{25} + 6033 q^{29} - 2759 q^{31} + 37146 q^{35} - 15172 q^{37} + 18435 q^{41} - 1469 q^{43} - 25155 q^{47} - 4056 q^{49} - 116844 q^{53} - 14778 q^{55} - 90537 q^{59} + 1403 q^{61} + 148407 q^{65} - 13907 q^{67} + 229368 q^{71} + 15200 q^{73} + 211983 q^{77} - 29993 q^{79} - 228951 q^{83} - 49662 q^{85} - 598332 q^{89} - 124930 q^{91} - 394764 q^{95} + 40541 q^{97}+O(q^{100}) $ 10 * q + 21 * q^5 - 29 * q^7 + 177 * q^11 - 181 * q^13 - 2280 * q^17 + 832 * q^19 + 399 * q^23 - 4778 * q^25 + 6033 * q^29 - 2759 * q^31 + 37146 * q^35 - 15172 * q^37 + 18435 * q^41 - 1469 * q^43 - 25155 * q^47 - 4056 * q^49 - 116844 * q^53 - 14778 * q^55 - 90537 * q^59 + 1403 * q^61 + 148407 * q^65 - 13907 * q^67 + 229368 * q^71 + 15200 * q^73 + 211983 * q^77 - 29993 * q^79 - 228951 * q^83 - 49662 * q^85 - 598332 * q^89 - 124930 * q^91 - 394764 * q^95 + 40541 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/432\mathbb{Z}\right)^\times$.

$n$	$271$	$325$	$353$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$		0			0
$2$		0			0
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−13.1603	+	22.7942i	−0.235418	+	0.407755i	−0.959394	−	0.282069i	$-0.908979\pi$
$5$	−13.1603	+	22.7942i	−0.235418	+	0.407755i	0.723976	+	0.689825i	$0.242312\pi$
$6$		0			0
$7$	31.6287	+	54.7826i	0.243970	+	0.422569i	0.961842	−	0.273607i	$-0.0882168\pi$
$7$	31.6287	+	54.7826i	0.243970	+	0.422569i	−0.717871	+	0.696176i	$0.754883\pi$
$8$		0			0
$9$		0			0
$10$		0			0
$11$	−49.1194	−	85.0772i	−0.122397	−	0.211998i	0.798315	−	0.602240i	$-0.205725\pi$
$11$	−49.1194	−	85.0772i	−0.122397	−	0.211998i	−0.920712	+	0.390242i	$0.872391\pi$
$12$		0			0
$13$	369.143	−	639.374i	0.605809	−	1.04929i	−0.386114	−	0.922451i	$-0.626183\pi$
$13$	369.143	−	639.374i	0.605809	−	1.04929i	0.991923	−	0.126841i	$-0.0404839\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−250.060			−0.209856			−0.104928	−	0.994480i	$-0.533461\pi$
$17$	−250.060			−0.209856			−0.104928	+	0.994480i	$0.533461\pi$
$18$		0			0
$19$	−1102.41			−0.700579			−0.350290	−	0.936641i	$-0.613917\pi$
$19$	−1102.41			−0.700579			−0.350290	+	0.936641i	$0.613917\pi$
$20$		0			0
$21$		0			0
$22$		0			0
$23$	−2204.70	+	3818.66i	−0.869022	+	1.50519i	−0.00602414	+	0.999982i	$0.501918\pi$
$23$	−2204.70	+	3818.66i	−0.869022	+	1.50519i	−0.862998	+	0.505208i	$0.831416\pi$
$24$		0			0
$25$	1216.12	+	2106.37i	0.389157	+	0.674040i
$26$		0			0
$27$		0			0
$28$		0			0
$29$	−3941.06	−	6826.11i	−0.870197	−	1.50723i	−0.861792	−	0.507262i	$-0.830658\pi$
$29$	−3941.06	−	6826.11i	−0.870197	−	1.50723i	−0.00840534	−	0.999965i	$-0.502676\pi$
$30$		0			0
$31$	−2305.65	+	3993.49i	−0.430912	+	0.746361i	−0.996952	−	0.0780167i	$-0.975141\pi$
$31$	−2305.65	+	3993.49i	−0.430912	+	0.746361i	0.566040	+	0.824377i	$0.308475\pi$
$32$		0			0
$33$		0			0
$34$		0			0
$35$	−1664.97			−0.229740
$36$		0			0
$37$	11896.3			1.42859			0.714297	−	0.699843i	$-0.246747\pi$
$37$	11896.3			1.42859			0.714297	+	0.699843i	$0.246747\pi$
$38$		0			0
$39$		0			0
$40$		0			0
$41$	5040.58	−	8730.55i	0.468297	−	0.811114i	−0.531047	−	0.847343i	$-0.678201\pi$
$41$	5040.58	−	8730.55i	0.468297	−	0.811114i	0.999344	+	0.0362286i	$0.0115344\pi$
$42$		0			0
$43$	3518.99	+	6095.07i	0.290233	+	0.502698i	0.973865	−	0.227129i	$-0.0729338\pi$
$43$	3518.99	+	6095.07i	0.290233	+	0.502698i	−0.683632	+	0.729827i	$0.739600\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	−7459.33	−	12919.9i	−0.492555	−	0.853131i	0.507408	−	0.861706i	$-0.330604\pi$
$47$	−7459.33	−	12919.9i	−0.492555	−	0.853131i	−0.999963	+	0.00857499i	$0.997270\pi$
$48$		0			0
$49$	6402.75	−	11089.9i	0.380957	−	0.659837i
$50$		0			0
$51$		0			0
$52$		0			0
$53$	−22451.7			−1.09789			−0.548947	−	0.835857i	$-0.684971\pi$
$53$	−22451.7			−1.09789			−0.548947	+	0.835857i	$0.684971\pi$
$54$		0			0
$55$	2585.69			0.115258
$56$		0			0
$57$		0			0
$58$		0			0
$59$	−5405.25	+	9362.17i	−0.202156	+	0.350144i	−0.949223	−	0.314605i	$-0.898128\pi$
$59$	−5405.25	+	9362.17i	−0.202156	+	0.350144i	0.747067	+	0.664749i	$0.231461\pi$
$60$		0			0
$61$	594.647	+	1029.96i	0.0204614	+	0.0354401i	0.876075	−	0.482175i	$-0.160153\pi$
$61$	594.647	+	1029.96i	0.0204614	+	0.0354401i	−0.855613	+	0.517615i	$0.826820\pi$
$62$		0			0
$63$		0			0
$64$		0			0
$65$	9716.02	+	16828.6i	0.285236	+	0.494044i
$66$		0			0
$67$	29590.2	−	51251.8i	0.805307	−	1.39483i	−0.110776	−	0.993845i	$-0.535334\pi$
$67$	29590.2	−	51251.8i	0.805307	−	1.39483i	0.916084	−	0.400988i	$-0.131333\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	14326.6			0.337284			0.168642	−	0.985677i	$-0.446062\pi$
$71$	14326.6			0.337284			0.168642	+	0.985677i	$0.446062\pi$
$72$		0			0
$73$	−53098.2			−1.16620			−0.583099	−	0.812401i	$-0.698160\pi$
$73$	−53098.2			−1.16620			−0.583099	+	0.812401i	$0.698160\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	3107.17	−	5381.77i	0.0597225	−	0.103442i
$78$		0			0
$79$	−18695.6	−	32381.6i	−0.337032	−	0.583756i	0.646841	−	0.762625i	$-0.276090\pi$
$79$	−18695.6	−	32381.6i	−0.337032	−	0.583756i	−0.983873	+	0.178869i	$0.942756\pi$
$80$		0			0
$81$		0			0
$82$		0			0
$83$	−60439.5	−	104684.i	−0.962998	−	1.66796i	−0.714900	−	0.699226i	$-0.753528\pi$
$83$	−60439.5	−	104684.i	−0.962998	−	1.66796i	−0.248097	−	0.968735i	$-0.579805\pi$
$84$		0			0
$85$	3290.85	−	5699.93i	0.0494039	−	0.0855701i
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−97873.2			−1.30975			−0.654875	−	0.755737i	$-0.727279\pi$
$89$	−97873.2			−1.30975			−0.654875	+	0.755737i	$0.727279\pi$
$90$		0			0
$91$	46702.1			0.591198
$92$		0			0
$93$		0			0
$94$		0			0
$95$	14507.9	−	25128.5i	0.164929	−	0.285665i
$96$		0			0
$97$	−53356.7	−	92416.4i	−0.575784	−	0.997286i	−0.995956	−	0.0898422i	$-0.971364\pi$
$97$	−53356.7	−	92416.4i	−0.575784	−	0.997286i	0.420172	−	0.907444i	$-0.361970\pi$
$98$		0			0
$99$		0			0
$100$		0			0
$101$	48236.1	+	83547.3i	0.470510	+	0.814946i	0.999431	−	0.0337242i	$-0.0107368\pi$
$101$	48236.1	+	83547.3i	0.470510	+	0.814946i	−0.528922	+	0.848671i	$0.677403\pi$
$102$		0			0
$103$	14972.2	−	25932.6i	0.139057	−	0.240854i	−0.788083	−	0.615569i	$-0.788926\pi$
$103$	14972.2	−	25932.6i	0.139057	−	0.240854i	0.927140	+	0.374715i	$0.122260\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	22758.9			0.192173			0.0960865	−	0.995373i	$-0.469367\pi$
$107$	22758.9			0.192173			0.0960865	+	0.995373i	$0.469367\pi$
$108$		0			0
$109$	−2671.93			−0.0215407			−0.0107703	−	0.999942i	$-0.503428\pi$
$109$	−2671.93			−0.0215407			−0.0107703	+	0.999942i	$0.503428\pi$
$110$		0			0
$111$		0			0
$112$		0			0
$113$	65669.6	−	113743.i	0.483803	−	0.837971i	−0.516024	−	0.856574i	$-0.672588\pi$
$113$	65669.6	−	113743.i	0.483803	−	0.837971i	0.999827	+	0.0186028i	$0.00592179\pi$
$114$		0			0
$115$	−58028.9	−	100509.i	−0.409166	−	0.708697i
$116$		0			0
$117$		0			0
$118$		0			0
$119$	−7909.09	−	13698.9i	−0.0511987	−	0.0886787i
$120$		0			0
$121$	75700.1	−	131116.i	0.470038	−	0.814130i
$122$		0			0
$123$		0			0
$124$		0			0
$125$	−146269.			−0.837293
$126$		0			0
$127$	−236012.			−1.29845			−0.649223	−	0.760598i	$-0.724906\pi$
$127$	−236012.			−1.29845			−0.649223	+	0.760598i	$0.724906\pi$
$128$		0			0
$129$		0			0
$130$		0			0
$131$	−180183.	+	312086.i	−0.917352	+	1.58890i	−0.113930	+	0.993489i	$0.536344\pi$
$131$	−180183.	+	312086.i	−0.917352	+	1.58890i	−0.803421	+	0.595411i	$0.796989\pi$
$132$		0			0
$133$	−34867.7	−	60392.6i	−0.170920	−	0.296043i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−118833.	−	205825.i	−0.540923	−	0.936906i	−0.998851	−	0.0479167i	$-0.984742\pi$
$137$	−118833.	−	205825.i	−0.540923	−	0.936906i	0.457929	−	0.888989i	$-0.348592\pi$
$138$		0			0
$139$	81673.4	−	141462.i	0.358545	−	0.621018i	−0.629173	−	0.777265i	$-0.716606\pi$
$139$	81673.4	−	141462.i	0.358545	−	0.621018i	0.987718	+	0.156247i	$0.0499397\pi$
$140$		0			0
$141$		0			0
$142$		0			0
$143$	−72528.2			−0.296597
$144$		0			0
$145$	207461.			0.819440
$146$		0			0
$147$		0			0
$148$		0			0
$149$	167803.	−	290644.i	0.619205	−	1.07250i	−0.370426	−	0.928862i	$-0.620788\pi$
$149$	167803.	−	290644.i	0.619205	−	1.07250i	0.989631	−	0.143633i	$-0.0458785\pi$
$150$		0			0
$151$	−67788.5	−	117413.i	−0.241943	−	0.419058i	0.719325	−	0.694674i	$-0.244451\pi$
$151$	−67788.5	−	117413.i	−0.241943	−	0.419058i	−0.961268	+	0.275616i	$0.911118\pi$
$152$		0			0
$153$		0			0
$154$		0			0
$155$	−60685.7	−	105111.i	−0.202888	−	0.351413i
$156$		0			0
$157$	212716.	−	368435.i	0.688733	−	1.19292i	−0.283516	−	0.958968i	$-0.591501\pi$
$157$	212716.	−	368435.i	0.688733	−	1.19292i	0.972248	−	0.233952i	$-0.0751659\pi$
$158$		0			0
$159$		0			0
$160$		0			0
$161$	−278928.			−0.848062
$162$		0			0
$163$	158679.			0.467789			0.233895	−	0.972262i	$-0.424853\pi$
$163$	158679.			0.467789			0.233895	+	0.972262i	$0.424853\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	259223.	−	448988.i	0.719254	−	1.24579i	−0.242041	−	0.970266i	$-0.577817\pi$
$167$	259223.	−	448988.i	0.719254	−	1.24579i	0.961296	−	0.275519i	$-0.0888498\pi$
$168$		0			0
$169$	−86886.2	−	150491.i	−0.234010	−	0.405317i
$170$		0			0
$171$		0			0
$172$		0			0
$173$	−76589.0	−	132656.i	−0.194559	−	0.336986i	0.752197	−	0.658938i	$-0.228994\pi$
$173$	−76589.0	−	132656.i	−0.194559	−	0.336986i	−0.946756	+	0.321953i	$0.895661\pi$
$174$		0			0
$175$	−76928.4	+	133244.i	−0.189885	+	0.328891i
$176$		0			0
$177$		0			0
$178$		0			0
$179$	−736845.			−1.71887			−0.859437	−	0.511242i	$-0.829185\pi$
$179$	−736845.			−1.71887			−0.859437	+	0.511242i	$0.829185\pi$
$180$		0			0
$181$	28183.8			0.0639445			0.0319722	−	0.999489i	$-0.489821\pi$
$181$	28183.8			0.0639445			0.0319722	+	0.999489i	$0.489821\pi$
$182$		0			0
$183$		0			0
$184$		0			0
$185$	−156559.	+	271168.i	−0.336316	+	0.582517i
$186$		0			0
$187$	12282.8	+	21274.4i	0.0256858	+	0.0444891i
$188$		0			0
$189$		0			0
$190$		0			0
$191$	−49660.5	−	86014.5i	−0.0984981	−	0.170604i	0.812565	−	0.582870i	$-0.198071\pi$
$191$	−49660.5	−	86014.5i	−0.0984981	−	0.170604i	−0.911063	+	0.412267i	$0.864737\pi$
$192$		0			0
$193$	−208636.	+	361368.i	−0.403177	+	0.698324i	−0.994107	−	0.108399i	$-0.965428\pi$
$193$	−208636.	+	361368.i	−0.403177	+	0.698324i	0.590930	+	0.806723i	$0.298761\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−254565.			−0.467340			−0.233670	−	0.972316i	$-0.575073\pi$
$197$	−254565.			−0.467340			−0.233670	+	0.972316i	$0.575073\pi$
$198$		0			0
$199$	599702.			1.07350			0.536751	−	0.843741i	$-0.319652\pi$
$199$	599702.			1.07350			0.536751	+	0.843741i	$0.319652\pi$
$200$		0			0
$201$		0			0
$202$		0			0
$203$	249301.	−	431803.i	0.424604	−	0.735436i
$204$		0			0
$205$	132671.	+	229792.i	0.220491	+	0.381901i
$206$		0			0
$207$		0			0
$208$		0			0
$209$	54149.4	+	93789.6i	0.0857488	+	0.148521i
$210$		0			0
$211$	378292.	−	655221.i	0.584953	−	1.01317i	−0.409928	−	0.912118i	$-0.634446\pi$
$211$	378292.	−	655221.i	0.584953	−	1.01317i	0.994881	−	0.101051i	$-0.0322206\pi$
$212$		0			0
$213$		0			0
$214$		0			0
$215$	−185243.			−0.273304
$216$		0			0
$217$	−291699.			−0.420518
$218$		0			0
$219$		0			0
$220$		0			0
$221$	−92307.9	+	159882.i	−0.127133	+	0.220201i
$222$		0			0
$223$	−55602.4	−	96306.2i	−0.0748741	−	0.129686i	0.826157	−	0.563439i	$-0.190522\pi$
$223$	−55602.4	−	96306.2i	−0.0748741	−	0.129686i	−0.901032	+	0.433754i	$0.857189\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	245380.	+	425010.i	0.316063	+	0.547438i	0.979663	−	0.200650i	$-0.0643054\pi$
$227$	245380.	+	425010.i	0.316063	+	0.547438i	−0.663600	+	0.748088i	$0.730972\pi$
$228$		0			0
$229$	−380511.	+	659064.i	−0.479488	+	0.830498i	−0.999723	−	0.0235249i	$-0.992511\pi$
$229$	−380511.	+	659064.i	−0.479488	+	0.830498i	0.520235	+	0.854023i	$0.325844\pi$
$230$		0			0
$231$		0			0
$232$		0			0
$233$	356267.			0.429918			0.214959	−	0.976623i	$-0.431038\pi$
$233$	356267.			0.429918			0.214959	+	0.976623i	$0.431038\pi$
$234$		0			0
$235$	392667.			0.463825
$236$		0			0
$237$		0			0
$238$		0			0
$239$	453120.	−	784826.i	0.513119	−	0.888748i	−0.486765	−	0.873533i	$-0.661823\pi$
$239$	453120.	−	784826.i	0.513119	−	0.888748i	0.999884	−	0.0152152i	$-0.00484335\pi$
$240$		0			0
$241$	−261288.	−	452564.i	−0.289785	−	0.501923i	0.683973	−	0.729507i	$-0.260251\pi$
$241$	−261288.	−	452564.i	−0.289785	−	0.501923i	−0.973758	+	0.227584i	$0.926917\pi$
$242$		0			0
$243$		0			0
$244$		0			0
$245$	168523.	+	291891.i	0.179368	+	0.310675i
$246$		0			0
$247$	−406945.	+	704849.i	−0.424417	+	0.735113i
$248$		0			0
$249$		0			0
$250$		0			0
$251$	−625287.			−0.626462			−0.313231	−	0.949677i	$-0.601411\pi$
$251$	−625287.			−0.626462			−0.313231	+	0.949677i	$0.601411\pi$
$252$		0			0
$253$	433175.			0.425463
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−651106.	+	1.12775e6i	−0.614921	+	1.06507i	0.375478	+	0.926831i	$0.377479\pi$
$257$	−651106.	+	1.12775e6i	−0.614921	+	1.06507i	−0.990398	+	0.138243i	$0.955855\pi$
$258$		0			0
$259$	376266.	+	651712.i	0.348534	+	0.603679i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	716761.	+	1.24147e6i	0.638977	+	1.10674i	0.985658	+	0.168757i	$0.0539755\pi$
$263$	716761.	+	1.24147e6i	0.638977	+	1.10674i	−0.346681	+	0.937983i	$0.612691\pi$
$264$		0			0
$265$	295471.	−	511770.i	0.258464	−	0.447672i
$266$		0			0
$267$		0			0
$268$		0			0
$269$	1.52329e6			1.28352			0.641758	−	0.766907i	$-0.278205\pi$
$269$	1.52329e6			1.28352			0.641758	+	0.766907i	$0.278205\pi$
$270$		0			0
$271$	−1.60134e6			−1.32453			−0.662263	−	0.749271i	$-0.730404\pi$
$271$	−1.60134e6			−1.32453			−0.662263	+	0.749271i	$0.730404\pi$
$272$		0			0
$273$		0			0
$274$		0			0
$275$	119470.	−	206927.i	0.0952633	−	0.165001i
$276$		0			0
$277$	446972.	+	774178.i	0.350010	+	0.606235i	0.986251	−	0.165255i	$-0.0528448\pi$
$277$	446972.	+	774178.i	0.350010	+	0.606235i	−0.636241	+	0.771491i	$0.719511\pi$
$278$		0			0
$279$		0			0
$280$		0			0
$281$	−14200.0	−	24595.2i	−0.0107281	−	0.0185817i	0.860612	−	0.509262i	$-0.170082\pi$
$281$	−14200.0	−	24595.2i	−0.0107281	−	0.0185817i	−0.871340	+	0.490680i	$0.836748\pi$
$282$		0			0
$283$	−554783.	+	960912.i	−0.411772	+	0.713210i	−0.995084	−	0.0990384i	$-0.968423\pi$
$283$	−554783.	+	960912.i	−0.411772	+	0.713210i	0.583312	+	0.812248i	$0.301757\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	637709.			0.457002
$288$		0			0
$289$	−1.35733e6			−0.955960
$290$		0			0
$291$		0			0
$292$		0			0
$293$	1.22884e6	−	2.12841e6i	0.836230	−	1.44839i	−0.0567942	−	0.998386i	$-0.518088\pi$
$293$	1.22884e6	−	2.12841e6i	0.836230	−	1.44839i	0.893025	−	0.450008i	$-0.148579\pi$
$294$		0			0
$295$	−142269.	−	246417.i	−0.0951821	−	0.164860i
$296$		0			0
$297$		0			0
$298$		0			0
$299$	1.62770e6	+	2.81926e6i	1.05292	+	1.82372i
$300$		0			0
$301$	−222602.	+	385559.i	−0.141616	+	0.245287i
$302$		0			0
$303$		0			0
$304$		0			0
$305$	−31302.8			−0.0192679
$306$		0			0
$307$	−1.77336e6			−1.07387			−0.536934	−	0.843624i	$-0.680417\pi$
$307$	−1.77336e6			−1.07387			−0.536934	+	0.843624i	$0.680417\pi$
$308$		0			0
$309$		0			0
$310$		0			0
$311$	−752855.	+	1.30398e6i	−0.441378	+	0.764489i	−0.997792	−	0.0664162i	$-0.978844\pi$
$311$	−752855.	+	1.30398e6i	−0.441378	+	0.764489i	0.556414	+	0.830905i	$0.312177\pi$
$312$		0			0
$313$	406353.	+	703823.i	0.234446	+	0.406072i	0.959111	−	0.283029i	$-0.0913392\pi$
$313$	406353.	+	703823.i	0.234446	+	0.406072i	−0.724666	+	0.689100i	$0.758006\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	523798.	+	907244.i	0.292763	+	0.507080i	0.974462	−	0.224553i	$-0.0720921\pi$
$317$	523798.	+	907244.i	0.292763	+	0.507080i	−0.681699	+	0.731632i	$0.738759\pi$
$318$		0			0
$319$	−387164.	+	670588.i	−0.213019	+	0.368960i
$320$		0			0
$321$		0			0
$322$		0			0
$323$	275668.			0.147021
$324$		0			0
$325$	1.79568e6			0.943020
$326$		0			0
$327$		0			0
$328$		0			0
$329$	471858.	−	817283.i	0.240338	−	0.416277i
$330$		0			0
$331$	−34002.7	−	58894.4i	−0.0170586	−	0.0295463i	0.857370	−	0.514700i	$-0.172097\pi$
$331$	−34002.7	−	58894.4i	−0.0170586	−	0.0295463i	−0.874429	+	0.485154i	$0.838764\pi$
$332$		0			0
$333$		0			0
$334$		0			0
$335$	778830.	+	1.34897e6i	0.379167	+	0.656737i
$336$		0			0
$337$	208236.	−	360675.i	0.0998806	−	0.172998i	−0.811755	−	0.583999i	$-0.801487\pi$
$337$	208236.	−	360675.i	0.0998806	−	0.172998i	0.911635	+	0.411001i	$0.134821\pi$
$338$		0			0
$339$		0			0
$340$		0			0
$341$	453007.			0.210969
$342$		0			0
$343$	1.87321e6			0.859709
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.40370e6	−	2.43128e6i	0.625822	−	1.08396i	−0.362559	−	0.931961i	$-0.618097\pi$
$347$	1.40370e6	−	2.43128e6i	0.625822	−	1.08396i	0.988381	−	0.151995i	$-0.0485697\pi$
$348$		0			0
$349$	240986.	+	417401.i	0.105908	+	0.183438i	0.914109	−	0.405469i	$-0.132892\pi$
$349$	240986.	+	417401.i	0.105908	+	0.183438i	−0.808201	+	0.588907i	$0.799558\pi$
$350$		0			0
$351$		0			0
$352$		0			0
$353$	2.00019e6	+	3.46442e6i	0.854346	+	1.47977i	0.877251	+	0.480033i	$0.159375\pi$
$353$	2.00019e6	+	3.46442e6i	0.854346	+	1.47977i	−0.0229050	+	0.999738i	$0.507292\pi$
$354$		0			0
$355$	−188541.	+	326563.i	−0.0794027	+	0.137530i
$356$		0			0
$357$		0			0
$358$		0			0
$359$	−800858.			−0.327959			−0.163979	−	0.986464i	$-0.552433\pi$
$359$	−800858.			−0.327959			−0.163979	+	0.986464i	$0.552433\pi$
$360$		0			0
$361$	−1.26080e6			−0.509189
$362$		0			0
$363$		0			0
$364$		0			0
$365$	698785.	−	1.21033e6i	0.274544	−	0.475524i
$366$		0			0
$367$	1.50486e6	+	2.60649e6i	0.583218	+	1.01016i	0.995095	+	0.0989236i	$0.0315399\pi$
$367$	1.50486e6	+	2.60649e6i	0.583218	+	1.01016i	−0.411877	+	0.911239i	$0.635127\pi$
$368$		0			0
$369$		0			0
$370$		0			0
$371$	−710120.	−	1.22996e6i	−0.267853	−	0.463936i
$372$		0			0
$373$	−796653.	+	1.37984e6i	−0.296481	+	0.513520i	−0.975328	−	0.220759i	$-0.929147\pi$
$373$	−796653.	+	1.37984e6i	−0.296481	+	0.513520i	0.678847	+	0.734280i	$0.262480\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	−5.81925e6			−2.10869
$378$		0			0
$379$	297930.			0.106541			0.0532703	−	0.998580i	$-0.483035\pi$
$379$	297930.			0.106541			0.0532703	+	0.998580i	$0.483035\pi$
$380$		0			0
$381$		0			0
$382$		0			0
$383$	645151.	−	1.11743e6i	0.224732	−	0.389247i	−0.731507	−	0.681834i	$-0.761183\pi$
$383$	645151.	−	1.11743e6i	0.224732	−	0.389247i	0.956239	+	0.292587i	$0.0945160\pi$
$384$		0			0
$385$	81782.2	+	141651.i	0.0281194	+	0.0487043i
$386$		0			0
$387$		0			0
$388$		0			0
$389$	2.49937e6	+	4.32903e6i	0.837444	+	1.45050i	0.892025	+	0.451986i	$0.149284\pi$
$389$	2.49937e6	+	4.32903e6i	0.837444	+	1.45050i	−0.0545807	+	0.998509i	$0.517382\pi$
$390$		0			0
$391$	551309.	−	954894.i	0.182370	−	0.315874i
$392$		0			0
$393$		0			0
$394$		0			0
$395$	984153.			0.317373
$396$		0			0
$397$	−558980.			−0.178000			−0.0890000	−	0.996032i	$-0.528367\pi$
$397$	−558980.			−0.178000			−0.0890000	+	0.996032i	$0.528367\pi$
$398$		0			0
$399$		0			0
$400$		0			0
$401$	47103.6	−	81585.8i	0.0146283	−	0.0253369i	−0.858619	−	0.512615i	$-0.828677\pi$
$401$	47103.6	−	81585.8i	0.0146283	−	0.0253369i	0.873247	+	0.487278i	$0.162010\pi$
$402$		0			0
$403$	1.70222e6	+	2.94834e6i	0.522101	+	0.904305i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−584340.	−	1.01211e6i	−0.174856	−	0.302859i
$408$		0			0
$409$	−2.73115e6	+	4.73049e6i	−0.807304	+	1.39829i	0.107420	+	0.994214i	$0.465741\pi$
$409$	−2.73115e6	+	4.73049e6i	−0.807304	+	1.39829i	−0.914724	+	0.404078i	$0.867592\pi$
$410$		0			0
$411$		0			0
$412$		0			0
$413$	−683845.			−0.197280
$414$		0			0
$415$	3.18159e6			0.906827
$416$		0			0
$417$		0			0
$418$		0			0
$419$	418486.	−	724839.i	0.116452	−	0.201700i	−0.801907	−	0.597448i	$-0.796181\pi$
$419$	418486.	−	724839.i	0.116452	−	0.201700i	0.918359	+	0.395748i	$0.129515\pi$
$420$		0			0
$421$	3.21404e6	+	5.56689e6i	0.883785	+	1.53076i	0.847100	+	0.531433i	$0.178346\pi$
$421$	3.21404e6	+	5.56689e6i	0.883785	+	1.53076i	0.0366842	+	0.999327i	$0.488320\pi$
$422$		0			0
$423$		0			0
$424$		0			0
$425$	−304102.	−	526720.i	−0.0816671	−	0.141452i
$426$		0			0
$427$	−37615.8	+	65152.5i	−0.00998392	+	0.0172927i
$428$		0			0
$429$		0			0
$430$		0			0
$431$	−5.11509e6			−1.32636			−0.663178	−	0.748462i	$-0.730793\pi$
$431$	−5.11509e6			−1.32636			−0.663178	+	0.748462i	$0.730793\pi$
$432$		0			0
$433$	−1.39089e6			−0.356512			−0.178256	−	0.983984i	$-0.557045\pi$
$433$	−1.39089e6			−0.356512			−0.178256	+	0.983984i	$0.557045\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	2.43048e6	−	4.20971e6i	0.608819	−	1.05450i
$438$		0			0
$439$	−1.76266e6	−	3.05301e6i	−0.436523	−	0.756079i	0.560896	−	0.827886i	$-0.310457\pi$
$439$	−1.76266e6	−	3.05301e6i	−0.436523	−	0.756079i	−0.997419	+	0.0718069i	$0.977123\pi$
$440$		0			0
$441$		0			0
$442$		0			0
$443$	−1.02216e6	−	1.77043e6i	−0.247462	−	0.428617i	0.715359	−	0.698757i	$-0.246263\pi$
$443$	−1.02216e6	−	1.77043e6i	−0.247462	−	0.428617i	−0.962821	+	0.270140i	$0.912930\pi$
$444$		0			0
$445$	1.28804e6	−	2.23094e6i	0.308339	−	0.534058i
$446$		0			0
$447$		0			0
$448$		0			0
$449$	−7.70508e6			−1.80369			−0.901844	−	0.432062i	$-0.857786\pi$
$449$	−7.70508e6			−1.80369			−0.901844	+	0.432062i	$0.857786\pi$
$450$		0			0
$451$	−990361.			−0.229273
$452$		0			0
$453$		0			0
$454$		0			0
$455$	−614611.	+	1.06454e6i	−0.139178	+	0.241064i
$456$		0			0
$457$	−4.28846e6	−	7.42783e6i	−0.960529	−	1.66369i	−0.721175	−	0.692753i	$-0.756397\pi$
$457$	−4.28846e6	−	7.42783e6i	−0.960529	−	1.66369i	−0.239355	−	0.970932i	$-0.576936\pi$
$458$		0			0
$459$		0			0
$460$		0			0
$461$	716317.	+	1.24070e6i	0.156983	+	0.271903i	0.933779	−	0.357849i	$-0.116490\pi$
$461$	716317.	+	1.24070e6i	0.156983	+	0.271903i	−0.776796	+	0.629752i	$0.783157\pi$
$462$		0			0
$463$	1.47223e6	−	2.54998e6i	0.319172	−	0.552821i	−0.661144	−	0.750259i	$-0.729929\pi$
$463$	1.47223e6	−	2.54998e6i	0.319172	−	0.552821i	0.980315	+	0.197438i	$0.0632621\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	4.96160e6			1.05276			0.526380	−	0.850249i	$-0.323549\pi$
$467$	4.96160e6			1.05276			0.526380	+	0.850249i	$0.323549\pi$
$468$		0			0
$469$	3.74361e6			0.785884
$470$		0			0
$471$		0			0
$472$		0			0
$473$	345701.	−	598772.i	0.0710473	−	0.123058i
$474$		0			0
$475$	−1.34065e6	−	2.32208e6i	−0.272635	−	0.472218i
$476$		0			0
$477$		0			0
$478$		0			0
$479$	120757.	+	209157.i	0.0240476	+	0.0416517i	0.877799	−	0.479030i	$-0.159011\pi$
$479$	120757.	+	209157.i	0.0240476	+	0.0416517i	−0.853751	+	0.520681i	$0.825678\pi$
$480$		0			0
$481$	4.39145e6	−	7.60621e6i	0.865456	−	1.49901i
$482$		0			0
$483$		0			0
$484$		0			0
$485$	2.80875e6			0.542199
$486$		0			0
$487$	−325055.			−0.0621061			−0.0310530	−	0.999518i	$-0.509886\pi$
$487$	−325055.			−0.0621061			−0.0310530	+	0.999518i	$0.509886\pi$
$488$		0			0
$489$		0			0
$490$		0			0
$491$	−2.49023e6	+	4.31321e6i	−0.466162	+	0.807416i	−0.999253	−	0.0386419i	$-0.987697\pi$
$491$	−2.49023e6	+	4.31321e6i	−0.466162	+	0.807416i	0.533091	+	0.846058i	$0.321030\pi$
$492$		0			0
$493$	985502.	+	1.70694e6i	0.182617	+	0.316301i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	453131.	+	784846.i	0.0822873	+	0.142526i
$498$		0			0
$499$	−2.93247e6	+	5.07919e6i	−0.527209	+	0.913153i	0.472288	+	0.881444i	$0.343428\pi$
$499$	−2.93247e6	+	5.07919e6i	−0.527209	+	0.913153i	−0.999497	+	0.0317085i	$0.989905\pi$
$500$		0			0
$501$		0			0
$502$		0			0
$503$	−1.36396e6			−0.240370			−0.120185	−	0.992751i	$-0.538349\pi$
$503$	−1.36396e6			−0.240370			−0.120185	+	0.992751i	$0.538349\pi$
$504$		0			0
$505$	−2.53919e6			−0.443065
$506$		0			0
$507$		0			0
$508$		0			0
$509$	1.85023e6	−	3.20470e6i	0.316542	−	0.548268i	−0.663222	−	0.748423i	$-0.730811\pi$
$509$	1.85023e6	−	3.20470e6i	0.316542	−	0.548268i	0.979764	+	0.200155i	$0.0641447\pi$
$510$		0			0
$511$	−1.67943e6	−	2.90885e6i	−0.284517	−	0.492799i
$512$		0			0
$513$		0			0
$514$		0			0
$515$	394076.	+	682560.i	0.0654730	+	0.113403i
$516$		0			0
$517$	−732795.	+	1.26924e6i	−0.120575	+	0.208841i
$518$		0			0
$519$		0			0
$520$		0			0
$521$	285260.			0.0460412			0.0230206	−	0.999735i	$-0.492672\pi$
$521$	285260.			0.0460412			0.0230206	+	0.999735i	$0.492672\pi$
$522$		0			0
$523$	−8.28809e6			−1.32495			−0.662476	−	0.749083i	$-0.730494\pi$
$523$	−8.28809e6			−1.32495			−0.662476	+	0.749083i	$0.730494\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	576550.	−	998614.i	0.0904296	−	0.156629i
$528$		0			0
$529$	−6.50327e6	−	1.12640e7i	−1.01040	−	1.75006i
$530$		0			0
$531$		0			0
$532$		0			0
$533$	−3.72139e6	−	6.44564e6i	−0.567397	−	0.982761i
$534$		0			0
$535$	−299513.	+	518772.i	−0.0452409	+	0.0783596i
$536$		0			0
$537$		0			0
$538$		0			0
$539$	−1.25800e6			−0.186512
$540$		0			0
$541$	1.29750e7			1.90596			0.952982	−	0.303028i	$-0.0979975\pi$
$541$	1.29750e7			1.90596			0.952982	+	0.303028i	$0.0979975\pi$
$542$		0			0
$543$		0			0
$544$		0			0
$545$	35163.3	−	60904.6i	0.00507105	−	0.00878332i
$546$		0			0
$547$	−4.65800e6	−	8.06790e6i	−0.665628	−	1.15290i	−0.979115	−	0.203309i	$-0.934830\pi$
$547$	−4.65800e6	−	8.06790e6i	−0.665628	−	1.15290i	0.313487	−	0.949593i	$-0.398503\pi$
$548$		0			0
$549$		0			0
$550$		0			0
$551$	4.34464e6	+	7.52514e6i	0.609642	+	1.05593i
$552$		0			0
$553$	1.18263e6	−	2.04838e6i	0.164451	−	0.284838i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	4.18234e6			0.571192			0.285596	−	0.958350i	$-0.407809\pi$
$557$	4.18234e6			0.571192			0.285596	+	0.958350i	$0.407809\pi$
$558$		0			0
$559$	5.19604e6			0.703304
$560$		0			0
$561$		0			0
$562$		0			0
$563$	1.65660e6	−	2.86931e6i	0.220265	−	0.381511i	−0.734623	−	0.678475i	$-0.762641\pi$
$563$	1.65660e6	−	2.86931e6i	0.220265	−	0.381511i	0.954888	+	0.296965i	$0.0959744\pi$
$564$		0			0
$565$	1.72846e6	+	2.99378e6i	0.227792	+	0.394547i
$566$		0			0
$567$		0			0
$568$		0			0
$569$	−2.92695e6	−	5.06963e6i	−0.378996	−	0.656441i	0.611920	−	0.790920i	$-0.290397\pi$
$569$	−2.92695e6	−	5.06963e6i	−0.378996	−	0.656441i	−0.990917	+	0.134478i	$0.957064\pi$
$570$		0			0
$571$	6.75429e6	−	1.16988e7i	0.866941	−	1.50159i	0.00183339	−	0.999998i	$-0.499416\pi$
$571$	6.75429e6	−	1.16988e7i	0.866941	−	1.50159i	0.865107	−	0.501587i	$-0.167250\pi$
$572$		0			0
$573$		0			0
$574$		0			0
$575$	−1.07247e7			−1.35274
$576$		0			0
$577$	−1.12898e7			−1.41171			−0.705855	−	0.708356i	$-0.749437\pi$
$577$	−1.12898e7			−1.41171			−0.705855	+	0.708356i	$0.749437\pi$
$578$		0			0
$579$		0			0
$580$		0			0
$581$	3.82325e6	−	6.62206e6i	0.469886	−	0.813866i
$582$		0			0
$583$	1.10282e6	+	1.91013e6i	0.134379	+	0.232751i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	−991398.	−	1.71715e6i	−0.118755	−	0.205690i	0.800519	−	0.599307i	$-0.204557\pi$
$587$	−991398.	−	1.71715e6i	−0.118755	−	0.205690i	−0.919275	+	0.393617i	$0.871224\pi$
$588$		0			0
$589$	2.54176e6	−	4.40245e6i	0.301888	−	0.522885i
$590$		0			0
$591$		0			0
$592$		0			0
$593$	−1.22629e7			−1.43204			−0.716021	−	0.698078i	$-0.754039\pi$
$593$	−1.22629e7			−1.43204			−0.716021	+	0.698078i	$0.754039\pi$
$594$		0			0
$595$	416342.			0.0482123
$596$		0			0
$597$		0			0
$598$		0			0
$599$	7.84977e6	−	1.35962e7i	0.893902	−	1.54828i	0.0587438	−	0.998273i	$-0.481290\pi$
$599$	7.84977e6	−	1.35962e7i	0.893902	−	1.54828i	0.835158	−	0.550010i	$-0.185376\pi$
$600$		0			0
$601$	2.65972e6	+	4.60677e6i	0.300366	+	0.520248i	0.976219	−	0.216788i	$-0.0695580\pi$
$601$	2.65972e6	+	4.60677e6i	0.300366	+	0.520248i	−0.675853	+	0.737036i	$0.736225\pi$
$602$		0			0
$603$		0			0
$604$		0			0
$605$	1.99246e6	+	3.45105e6i	0.221311	+	0.383321i
$606$		0			0
$607$	2.18482e6	−	3.78422e6i	0.240682	−	0.416874i	−0.720226	−	0.693739i	$-0.755962\pi$
$607$	2.18482e6	−	3.78422e6i	0.240682	−	0.416874i	0.960909	+	0.276865i	$0.0892954\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	−1.10142e7			−1.19358
$612$		0			0
$613$	−7.62875e6			−0.819978			−0.409989	−	0.912091i	$-0.634467\pi$
$613$	−7.62875e6			−0.819978			−0.409989	+	0.912091i	$0.634467\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−7.16498e6	+	1.24101e7i	−0.757708	+	1.31239i	0.186309	+	0.982491i	$0.440348\pi$
$617$	−7.16498e6	+	1.24101e7i	−0.757708	+	1.31239i	−0.944017	+	0.329898i	$0.892986\pi$
$618$		0			0
$619$	5.40907e6	+	9.36878e6i	0.567408	+	0.982780i	0.996821	+	0.0796716i	$0.0253871\pi$
$619$	5.40907e6	+	9.36878e6i	0.567408	+	0.982780i	−0.429413	+	0.903108i	$0.641280\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−3.09560e6	−	5.36174e6i	−0.319540	−	0.553460i
$624$		0			0
$625$	−1.87542e6	+	3.24833e6i	−0.192043	+	0.332629i
$626$		0			0
$627$		0			0
$628$		0			0
$629$	−2.97480e6			−0.299800
$630$		0			0
$631$	−7.96579e6			−0.796444			−0.398222	−	0.917289i	$-0.630373\pi$
$631$	−7.96579e6			−0.796444			−0.398222	+	0.917289i	$0.630373\pi$
$632$		0			0
$633$		0			0
$634$		0			0
$635$	3.10597e6	−	5.37970e6i	0.305677	−	0.529448i
$636$		0			0
$637$	−4.72705e6	−	8.18750e6i	−0.461575	−	0.799471i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	3.40224e6	+	5.89285e6i	0.327054	+	0.566475i	0.981926	−	0.189266i	$-0.0606107\pi$
$641$	3.40224e6	+	5.89285e6i	0.327054	+	0.566475i	−0.654872	+	0.755740i	$0.727277\pi$
$642$		0			0
$643$	−2.66464e6	+	4.61530e6i	−0.254163	+	0.440223i	−0.964668	−	0.263469i	$-0.915133\pi$
$643$	−2.66464e6	+	4.61530e6i	−0.254163	+	0.440223i	0.710505	+	0.703692i	$0.248467\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−5.03021e6			−0.472417			−0.236208	−	0.971702i	$-0.575905\pi$
$647$	−5.03021e6			−0.472417			−0.236208	+	0.971702i	$0.575905\pi$
$648$		0			0
$649$	1.06201e6			0.0989731
$650$		0			0
$651$		0			0
$652$		0			0
$653$	−5.66704e6	+	9.81560e6i	−0.520084	+	0.900811i	0.479644	+	0.877463i	$0.340766\pi$
$653$	−5.66704e6	+	9.81560e6i	−0.520084	+	0.900811i	−0.999727	+	0.0233481i	$0.992567\pi$
$654$		0			0
$655$	−4.74251e6	−	8.21427e6i	−0.431922	−	0.748110i
$656$		0			0
$657$		0			0
$658$		0			0
$659$	−1.91003e6	−	3.30828e6i	−0.171328	−	0.296748i	0.767557	−	0.640981i	$-0.221472\pi$
$659$	−1.91003e6	−	3.30828e6i	−0.171328	−	0.296748i	−0.938884	+	0.344233i	$0.888139\pi$
$660$		0			0
$661$	−463286.	+	802435.i	−0.0412426	+	0.0714342i	−0.885910	−	0.463857i	$-0.846465\pi$
$661$	−463286.	+	802435.i	−0.0412426	+	0.0714342i	0.844667	+	0.535292i	$0.179798\pi$
$662$		0			0
$663$		0			0
$664$		0			0
$665$	1.83547e6			0.160951
$666$		0			0
$667$	3.47555e7			3.02488
$668$		0			0
$669$		0			0
$670$		0			0
$671$	58417.3	−	101182.i	0.00500882	−	0.00867553i
$672$		0			0
$673$	−2.45146e6	−	4.24605e6i	−0.208635	−	0.361366i	0.742650	−	0.669680i	$-0.233569\pi$
$673$	−2.45146e6	−	4.24605e6i	−0.208635	−	0.361366i	−0.951285	+	0.308314i	$0.900235\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−7.37201e6	−	1.27687e7i	−0.618179	−	1.07072i	−0.989818	−	0.142340i	$-0.954537\pi$
$677$	−7.37201e6	−	1.27687e7i	−0.618179	−	1.07072i	0.371639	−	0.928378i	$-0.378796\pi$
$678$		0			0
$679$	3.37521e6	−	5.84603e6i	0.280948	−	0.486616i
$680$		0			0
$681$		0			0
$682$		0			0
$683$	−6.53893e6			−0.536358			−0.268179	−	0.963369i	$-0.586422\pi$
$683$	−6.53893e6			−0.536358			−0.268179	+	0.963369i	$0.586422\pi$
$684$		0			0
$685$	6.25548e6			0.509371
$686$		0			0
$687$		0			0
$688$		0			0
$689$	−8.28790e6	+	1.43551e7i	−0.665114	+	1.15201i
$690$		0			0
$691$	−5.45248e6	−	9.44397e6i	−0.434409	−	0.752419i	0.562838	−	0.826567i	$-0.309709\pi$
$691$	−5.45248e6	−	9.44397e6i	−0.434409	−	0.752419i	−0.997247	+	0.0741485i	$0.976376\pi$
$692$		0			0
$693$		0			0
$694$		0			0
$695$	2.14968e6	+	3.72336e6i	0.168816	+	0.292397i
$696$		0			0
$697$	−1.26045e6	+	2.18316e6i	−0.0982751	+	0.170217i
$698$		0			0
$699$		0			0
$700$		0			0
$701$	1.89162e7			1.45391			0.726957	−	0.686683i	$-0.240934\pi$
$701$	1.89162e7			1.45391			0.726957	+	0.686683i	$0.240934\pi$
$702$		0			0
$703$	−1.31146e7			−1.00084
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−3.05129e6	+	5.28499e6i	−0.229581	+	0.397645i
$708$		0			0
$709$	9.63661e6	+	1.66911e7i	0.719960	+	1.24701i	0.961015	+	0.276496i	$0.0891733\pi$
$709$	9.63661e6	+	1.66911e7i	0.719960	+	1.24701i	−0.241055	+	0.970512i	$0.577493\pi$
$710$		0			0
$711$		0			0
$712$		0			0
$713$	−1.01665e7	−	1.76089e7i	−0.748943	−	1.29721i
$714$		0			0
$715$	954489.	−	1.65322e6i	0.0698242	−	0.120939i
$716$		0			0
$717$		0			0
$718$		0			0
$719$	1.42859e7			1.03059			0.515293	−	0.857014i	$-0.327683\pi$
$719$	1.42859e7			1.03059			0.515293	+	0.857014i	$0.327683\pi$
$720$		0			0
$721$	1.89421e6			0.135703
$722$		0			0
$723$		0			0
$724$		0			0
$725$	9.58556e6	−	1.66027e7i	0.677287	−	1.17310i
$726$		0			0
$727$	1.41386e7	+	2.44887e7i	0.992132	+	1.71842i	0.604491	+	0.796612i	$0.293377\pi$
$727$	1.41386e7	+	2.44887e7i	0.992132	+	1.71842i	0.387641	+	0.921810i	$0.373290\pi$
$728$		0			0
$729$		0			0
$730$		0			0
$731$	−879959.	−	1.52413e6i	−0.0609073	−	0.105494i
$732$		0			0
$733$	−4.93850e6	+	8.55373e6i	−0.339496	+	0.588025i	−0.984338	−	0.176291i	$-0.943590\pi$
$733$	−4.93850e6	+	8.55373e6i	−0.339496	+	0.588025i	0.644842	+	0.764316i	$0.276923\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−5.81381e6			−0.394269
$738$		0			0
$739$	−6.31081e6			−0.425083			−0.212542	−	0.977152i	$-0.568174\pi$
$739$	−6.31081e6			−0.425083			−0.212542	+	0.977152i	$0.568174\pi$
$740$		0			0
$741$		0			0
$742$		0			0
$743$	31529.9	−	54611.3i	0.00209532	−	0.00362920i	−0.864976	−	0.501814i	$-0.832666\pi$
$743$	31529.9	−	54611.3i	0.00209532	−	0.00362920i	0.867071	+	0.498184i	$0.166000\pi$
$744$		0			0
$745$	4.41667e6	+	7.64989e6i	0.291544	+	0.504969i
$746$		0			0
$747$		0			0
$748$		0			0
$749$	719836.	+	1.24679e6i	0.0468845	+	0.0812063i
$750$		0			0
$751$	−8.69183e6	+	1.50547e7i	−0.562356	+	0.974029i	0.434934	+	0.900462i	$0.356772\pi$
$751$	−8.69183e6	+	1.50547e7i	−0.562356	+	0.974029i	−0.997290	+	0.0735670i	$0.976562\pi$
$752$		0			0
$753$		0			0
$754$		0			0
$755$	3.56845e6			0.227831
$756$		0			0
$757$	9.43592e6			0.598473			0.299237	−	0.954179i	$-0.403268\pi$
$757$	9.43592e6			0.598473			0.299237	+	0.954179i	$0.403268\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	8.06409e6	−	1.39674e7i	0.504771	−	0.874288i	−0.495214	−	0.868771i	$-0.664910\pi$
$761$	8.06409e6	−	1.39674e7i	0.504771	−	0.874288i	0.999985	−	0.00551731i	$-0.00175622\pi$
$762$		0			0
$763$	−84509.8	−	146375.i	−0.00525528	−	0.00910241i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	3.99062e6	+	6.91196e6i	0.244936	+	0.424241i
$768$		0			0
$769$	1.28431e7	−	2.22450e7i	0.783169	−	1.35649i	−0.146918	−	0.989149i	$-0.546935\pi$
$769$	1.28431e7	−	2.22450e7i	0.783169	−	1.35649i	0.930087	−	0.367339i	$-0.119731\pi$
$770$		0			0
$771$		0			0
$772$		0			0
$773$	2.01235e7			1.21131			0.605654	−	0.795728i	$-0.292912\pi$
$773$	2.01235e7			1.21131			0.605654	+	0.795728i	$0.292912\pi$
$774$		0			0
$775$	−1.12157e7			−0.670769
$776$		0			0
$777$		0			0
$778$		0			0
$779$	−5.55677e6	+	9.62460e6i	−0.328079	+	0.568250i
$780$		0			0
$781$	−703712.	−	1.21886e6i	−0.0412826	−	0.0715036i
$782$		0			0
$783$		0			0
$784$		0			0
$785$	5.59879e6	+	9.69738e6i	0.324280	+	0.561669i
$786$		0			0
$787$	2.87640e6	−	4.98208e6i	0.165544	−	0.286730i	−0.771304	−	0.636466i	$-0.780395\pi$
$787$	2.87640e6	−	4.98208e6i	0.165544	−	0.286730i	0.936848	+	0.349736i	$0.113729\pi$
$788$		0			0
$789$		0			0
$790$		0			0
$791$	8.30819e6			0.472134
$792$		0			0
$793$	878038.			0.0495827
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−5.09822e6	+	8.83038e6i	−0.284298	+	0.492418i	−0.972439	−	0.233159i	$-0.925094\pi$
$797$	−5.09822e6	+	8.83038e6i	−0.284298	+	0.492418i	0.688141	+	0.725577i	$0.258427\pi$
$798$		0			0
$799$	1.86528e6	+	3.23076e6i	0.103366	+	0.179035i
$800$		0			0
$801$		0			0
$802$		0			0
$803$	2.60815e6	+	4.51744e6i	0.142739	+	0.247232i
$804$		0			0
$805$	3.67076e6	−	6.35795e6i	0.199649	−	0.345802i
$806$		0			0
$807$		0			0
$808$		0			0
$809$	−6.00420e6			−0.322540			−0.161270	−	0.986910i	$-0.551559\pi$
$809$	−6.00420e6			−0.322540			−0.161270	+	0.986910i	$0.551559\pi$
$810$		0			0
$811$	−3.23880e7			−1.72915			−0.864574	−	0.502506i	$-0.832411\pi$
$811$	−3.23880e7			−1.72915			−0.864574	+	0.502506i	$0.832411\pi$
$812$		0			0
$813$		0			0
$814$		0			0
$815$	−2.08826e6	+	3.61696e6i	−0.110126	+	0.190744i
$816$		0			0
$817$	−3.87935e6	−	6.71924e6i	−0.203331	−	0.352180i
$818$		0			0
$819$		0			0
$820$		0			0
$821$	7.83736e6	+	1.35747e7i	0.405800	+	0.702866i	0.994414	−	0.105548i	$-0.0336596\pi$
$821$	7.83736e6	+	1.35747e7i	0.405800	+	0.702866i	−0.588614	+	0.808414i	$0.700326\pi$
$822$		0			0
$823$	−1.35733e7	+	2.35097e7i	−0.698532	+	1.20989i	0.270443	+	0.962736i	$0.412830\pi$
$823$	−1.35733e7	+	2.35097e7i	−0.698532	+	1.20989i	−0.968975	+	0.247157i	$0.920504\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	2.28543e7			1.16199			0.580997	−	0.813906i	$-0.302663\pi$
$827$	2.28543e7			1.16199			0.580997	+	0.813906i	$0.302663\pi$
$828$		0			0
$829$	−2.05418e7			−1.03813			−0.519066	−	0.854734i	$-0.673720\pi$
$829$	−2.05418e7			−1.03813			−0.519066	+	0.854734i	$0.673720\pi$
$830$		0			0
$831$		0			0
$832$		0			0
$833$	−1.60107e6	+	2.77314e6i	−0.0799463	+	0.138471i
$834$		0			0
$835$	6.82288e6	+	1.18176e7i	0.338650	+	0.586560i
$836$		0			0
$837$		0			0
$838$		0			0
$839$	7.39436e6	+	1.28074e7i	0.362657	+	0.628140i	0.988397	−	0.151891i	$-0.0485364\pi$
$839$	7.39436e6	+	1.28074e7i	0.362657	+	0.628140i	−0.625740	+	0.780031i	$0.715203\pi$
$840$		0			0
$841$	−2.08083e7	+	3.60410e7i	−1.01449	+	1.75714i
$842$		0			0
$843$		0			0
$844$		0			0
$845$	4.57378e6			0.220360
$846$		0			0
$847$	9.57719e6			0.458701
$848$		0			0
$849$		0			0
$850$		0			0
$851$	−2.62279e7	+	4.54280e7i	−1.24148	+	2.15031i
$852$		0			0
$853$	5.26223e6	+	9.11445e6i	0.247627	+	0.428902i	0.962867	−	0.269977i	$-0.0870161\pi$
$853$	5.26223e6	+	9.11445e6i	0.247627	+	0.428902i	−0.715240	+	0.698879i	$0.753683\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	7.43357e6	+	1.28753e7i	0.345736	+	0.598833i	0.985487	−	0.169749i	$-0.0542958\pi$
$857$	7.43357e6	+	1.28753e7i	0.345736	+	0.598833i	−0.639751	+	0.768582i	$0.720962\pi$
$858$		0			0
$859$	−4.32340e6	+	7.48834e6i	−0.199913	+	0.346260i	−0.948500	−	0.316777i	$-0.897399\pi$
$859$	−4.32340e6	+	7.48834e6i	−0.199913	+	0.346260i	0.748587	+	0.663037i	$0.230733\pi$
$860$		0			0
$861$		0			0
$862$		0			0
$863$	2.38401e7			1.08964			0.544818	−	0.838555i	$-0.316599\pi$
$863$	2.38401e7			1.08964			0.544818	+	0.838555i	$0.316599\pi$
$864$		0			0
$865$	4.03172e6			0.183210
$866$		0			0
$867$		0			0
$868$		0			0
$869$	−1.83663e6	+	3.18113e6i	−0.0825033	+	0.142900i
$870$		0			0
$871$	−2.18460e7	−	3.78385e7i	−0.975725	−	1.69001i
$872$		0			0
$873$		0			0
$874$		0			0
$875$	−4.62631e6	−	8.01300e6i	−0.204275	−	0.353814i
$876$		0			0
$877$	19157.8	−	33182.4i	0.000841100	−	0.00145683i	−0.865605	−	0.500728i	$-0.833066\pi$
$877$	19157.8	−	33182.4i	0.000841100	−	0.00145683i	0.866446	+	0.499271i	$0.166399\pi$
$878$		0			0
$879$		0			0
$880$		0			0
$881$	2.55072e7			1.10719			0.553596	−	0.832785i	$-0.313255\pi$
$881$	2.55072e7			1.10719			0.553596	+	0.832785i	$0.313255\pi$
$882$		0			0
$883$	3.37096e7			1.45496			0.727482	−	0.686127i	$-0.240691\pi$
$883$	3.37096e7			1.45496			0.727482	+	0.686127i	$0.240691\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	1.32111e6	−	2.28823e6i	0.0563806	−	0.0976540i	−0.836458	−	0.548032i	$-0.815377\pi$
$887$	1.32111e6	−	2.28823e6i	0.0563806	−	0.0976540i	0.892838	+	0.450378i	$0.148711\pi$
$888$		0			0
$889$	−7.46475e6	−	1.29293e7i	−0.316782	−	0.548683i
$890$		0			0
$891$		0			0
$892$		0			0
$893$	8.22320e6	+	1.42430e7i	0.345074	+	0.597686i
$894$		0			0
$895$	9.69707e6	−	1.67958e7i	0.404653	−	0.700880i
$896$		0			0
$897$		0			0
$898$		0			0
$899$	3.63467e7			1.49991
$900$		0			0
$901$	5.61429e6			0.230400
$902$		0			0
$903$		0			0
$904$		0			0
$905$	−370906.	+	642428.i	−0.0150537	+	0.0260737i
$906$		0			0
$907$	3.56509e6	+	6.17492e6i	0.143897	+	0.249237i	0.928961	−	0.370178i	$-0.120703\pi$
$907$	3.56509e6	+	6.17492e6i	0.143897	+	0.249237i	−0.785064	+	0.619415i	$0.787370\pi$
$908$		0			0
$909$		0			0
$910$		0			0
$911$	−1.56577e7	−	2.71200e7i	−0.625075	−	1.08266i	−0.988526	−	0.151049i	$-0.951735\pi$
$911$	−1.56577e7	−	2.71200e7i	−0.625075	−	1.08266i	0.363451	−	0.931613i	$-0.381598\pi$
$912$		0			0
$913$	−5.93749e6	+	1.02840e7i	−0.235736	+	0.408307i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−2.27959e7			−0.895226
$918$		0			0
$919$	−2.28042e6			−0.0890687			−0.0445344	−	0.999008i	$-0.514180\pi$
$919$	−2.28042e6			−0.0890687			−0.0445344	+	0.999008i	$0.514180\pi$
$920$		0			0
$921$		0			0
$922$		0			0
$923$	5.28855e6	−	9.16003e6i	0.204330	−	0.353910i
$924$		0			0
$925$	1.44673e7	+	2.50581e7i	0.555947	+	0.962929i
$926$		0			0
$927$		0			0
$928$		0			0
$929$	5.28625e6	+	9.15605e6i	0.200959	+	0.348072i	0.948838	−	0.315764i	$-0.102261\pi$
$929$	5.28625e6	+	9.15605e6i	0.200959	+	0.348072i	−0.747879	+	0.663836i	$0.768927\pi$
$930$		0			0
$931$	−7.05842e6	+	1.22255e7i	−0.266891	+	0.462268i
$932$		0			0
$933$		0			0
$934$		0			0
$935$	−646579.			−0.0241876
$936$		0			0
$937$	−3.99327e7			−1.48587			−0.742934	−	0.669365i	$-0.766566\pi$
$937$	−3.99327e7			−1.48587			−0.742934	+	0.669365i	$0.766566\pi$
$938$		0			0
$939$		0			0
$940$		0			0
$941$	−4.16316e6	+	7.21080e6i	−0.153267	+	0.265466i	−0.932427	−	0.361359i	$-0.882313\pi$
$941$	−4.16316e6	+	7.21080e6i	−0.153267	+	0.265466i	0.779160	+	0.626826i	$0.215646\pi$
$942$		0			0
$943$	2.22260e7	+	3.84965e7i	0.813920	+	1.40975i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−1.37834e7	−	2.38735e7i	−0.499437	−	0.865050i	0.500563	−	0.865700i	$-0.333126\pi$
$947$	−1.37834e7	−	2.38735e7i	−0.499437	−	0.865050i	−1.00000		0.000650313i	$0.999793\pi$
$948$		0			0
$949$	−1.96008e7	+	3.39496e7i	−0.706493	+	1.22368i
$950$		0			0
$951$		0			0
$952$		0			0
$953$	3.81280e7			1.35992			0.679958	−	0.733251i	$-0.261998\pi$
$953$	3.81280e7			1.35992			0.679958	+	0.733251i	$0.261998\pi$
$954$		0			0
$955$	2.61418e6			0.0927528
$956$		0			0
$957$		0			0
$958$		0			0
$959$	7.51707e6	−	1.30199e7i	0.263938	−	0.457154i
$960$		0			0
$961$	3.68258e6	+	6.37841e6i	0.128630	+	0.222794i
$962$		0			0
$963$		0			0
$964$		0			0
$965$	−5.49141e6	−	9.51139e6i	−0.189830	−	0.328796i
$966$		0			0
$967$	−1.36356e6	+	2.36175e6i	−0.0468928	+	0.0812208i	−0.888519	−	0.458840i	$-0.848265\pi$
$967$	−1.36356e6	+	2.36175e6i	−0.0468928	+	0.0812208i	0.841626	+	0.540060i	$0.181599\pi$
$968$		0			0
$969$		0			0
$970$		0			0
$971$	1.26521e7			0.430641			0.215320	−	0.976543i	$-0.430920\pi$
$971$	1.26521e7			0.430641			0.215320	+	0.976543i	$0.430920\pi$
$972$		0			0
$973$	1.03329e7			0.349897
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−1.68626e7	+	2.92069e7i	−0.565182	+	0.978923i	0.431851	+	0.901945i	$0.357861\pi$
$977$	−1.68626e7	+	2.92069e7i	−0.565182	+	0.978923i	−0.997033	+	0.0769784i	$0.975473\pi$
$978$		0			0
$979$	4.80747e6	+	8.32678e6i	0.160310	+	0.277664i
$980$		0			0
$981$		0			0
$982$		0			0
$983$	−5.93714e6	−	1.02834e7i	−0.195972	−	0.339433i	0.751247	−	0.660021i	$-0.229453\pi$
$983$	−5.93714e6	−	1.02834e7i	−0.195972	−	0.339433i	−0.947219	+	0.320588i	$0.896119\pi$
$984$		0			0
$985$	3.35014e6	−	5.80260e6i	0.110020	−	0.190560i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−3.10333e7			−1.00888
$990$		0			0
$991$	2.31910e7			0.750128			0.375064	−	0.926999i	$-0.377621\pi$
$991$	2.31910e7			0.750128			0.375064	+	0.926999i	$0.377621\pi$
$992$		0			0
$993$		0			0
$994$		0			0
$995$	−7.89223e6	+	1.36697e7i	−0.252721	+	0.437726i
$996$		0			0
$997$	−1.93132e7	−	3.34515e7i	−0.615342	−	1.06580i	−0.990324	−	0.138772i	$-0.955685\pi$
$997$	−1.93132e7	−	3.34515e7i	−0.615342	−	1.06580i	0.374982	−	0.927032i	$-0.377649\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	432.6.i.d.145.2		10
3.2	odd	2		144.6.i.d.49.2		10
4.3	odd	2		108.6.e.a.37.2		10
9.2	odd	6		144.6.i.d.97.2		10
9.7	even	3	inner	432.6.i.d.289.2		10
12.11	even	2		36.6.e.a.13.4	✓	10
36.7	odd	6		108.6.e.a.73.2		10
36.11	even	6		36.6.e.a.25.4	yes	10
36.23	even	6		324.6.a.e.1.2		5
36.31	odd	6		324.6.a.d.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.6.e.a.13.4	✓	10	12.11	even	2
36.6.e.a.25.4	yes	10	36.11	even	6
108.6.e.a.37.2		10	4.3	odd	2
108.6.e.a.73.2		10	36.7	odd	6
144.6.i.d.49.2		10	3.2	odd	2
144.6.i.d.97.2		10	9.2	odd	6
324.6.a.d.1.4		5	36.31	odd	6
324.6.a.e.1.2		5	36.23	even	6
432.6.i.d.145.2		10	1.1	even	1	trivial
432.6.i.d.289.2		10	9.7	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 432 = 2^{4} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	432.i (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-13.1603 + 22.7942i) q^{5} +(31.6287 + 54.7826i) q^{7} +O(q^{10})\)	\(q+(-13.1603 + 22.7942i) q^{5} +(31.6287 + 54.7826i) q^{7} +(-49.1194 - 85.0772i) q^{11} +(369.143 - 639.374i) q^{13} -250.060 q^{17} -1102.41 q^{19} +(-2204.70 + 3818.66i) q^{23} +(1216.12 + 2106.37i) q^{25} +(-3941.06 - 6826.11i) q^{29} +(-2305.65 + 3993.49i) q^{31} -1664.97 q^{35} +11896.3 q^{37} +(5040.58 - 8730.55i) q^{41} +(3518.99 + 6095.07i) q^{43} +(-7459.33 - 12919.9i) q^{47} +(6402.75 - 11089.9i) q^{49} -22451.7 q^{53} +2585.69 q^{55} +(-5405.25 + 9362.17i) q^{59} +(594.647 + 1029.96i) q^{61} +(9716.02 + 16828.6i) q^{65} +(29590.2 - 51251.8i) q^{67} +14326.6 q^{71} -53098.2 q^{73} +(3107.17 - 5381.77i) q^{77} +(-18695.6 - 32381.6i) q^{79} +(-60439.5 - 104684. i) q^{83} +(3290.85 - 5699.93i) q^{85} -97873.2 q^{89} +46702.1 q^{91} +(14507.9 - 25128.5i) q^{95} +(-53356.7 - 92416.4i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 21 q^{5} - 29 q^{7}+O(q^{10}) \) 10 * q + 21 * q^5 - 29 * q^7	\( 10 q + 21 q^{5} - 29 q^{7} + 177 q^{11} - 181 q^{13} - 2280 q^{17} + 832 q^{19} + 399 q^{23} - 4778 q^{25} + 6033 q^{29} - 2759 q^{31} + 37146 q^{35} - 15172 q^{37} + 18435 q^{41} - 1469 q^{43} - 25155 q^{47} - 4056 q^{49} - 116844 q^{53} - 14778 q^{55} - 90537 q^{59} + 1403 q^{61} + 148407 q^{65} - 13907 q^{67} + 229368 q^{71} + 15200 q^{73} + 211983 q^{77} - 29993 q^{79} - 228951 q^{83} - 49662 q^{85} - 598332 q^{89} - 124930 q^{91} - 394764 q^{95} + 40541 q^{97}+O(q^{100}) \) 10 * q + 21 * q^5 - 29 * q^7 + 177 * q^11 - 181 * q^13 - 2280 * q^17 + 832 * q^19 + 399 * q^23 - 4778 * q^25 + 6033 * q^29 - 2759 * q^31 + 37146 * q^35 - 15172 * q^37 + 18435 * q^41 - 1469 * q^43 - 25155 * q^47 - 4056 * q^49 - 116844 * q^53 - 14778 * q^55 - 90537 * q^59 + 1403 * q^61 + 148407 * q^65 - 13907 * q^67 + 229368 * q^71 + 15200 * q^73 + 211983 * q^77 - 29993 * q^79 - 228951 * q^83 - 49662 * q^85 - 598332 * q^89 - 124930 * q^91 - 394764 * q^95 + 40541 * q^97

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