LMFDB - Embedded newform 1400.2.x.b.993.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1400,2,Mod(657,1400)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1400, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 0, 1, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("1400.657");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1400 = 2^{3} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1400.x (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$11.1790562830$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 280)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			993.3
Character	$\chi$	$=$	1400.993
Dual form			1400.2.x.b.657.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.41195 + 1.41195i) q^{3} +(-2.64529 + 0.0496428i) q^{7} -0.987218i q^{9} +O(q^{10})$	$q+(-1.41195 + 1.41195i) q^{3} +(-2.64529 + 0.0496428i) q^{7} -0.987218i q^{9} -5.75599 q^{11} +(2.89353 - 2.89353i) q^{13} +(-2.13286 - 2.13286i) q^{17} +2.18921 q^{19} +(3.66492 - 3.80511i) q^{21} +(4.79842 + 4.79842i) q^{23} +(-2.84195 - 2.84195i) q^{27} +5.19456i q^{29} -6.68465i q^{31} +(8.12718 - 8.12718i) q^{33} +(6.50613 - 6.50613i) q^{37} +8.17106i q^{39} -0.846034i q^{41} +(-2.68215 - 2.68215i) q^{43} +(4.55094 + 4.55094i) q^{47} +(6.99507 - 0.262639i) q^{49} +6.02299 q^{51} +(0.750143 + 0.750143i) q^{53} +(-3.09107 + 3.09107i) q^{57} +4.25478 q^{59} +7.62115i q^{61} +(0.0490083 + 2.61147i) q^{63} +(2.14628 - 2.14628i) q^{67} -13.5503 q^{69} -2.44951 q^{71} +(-3.51423 + 3.51423i) q^{73} +(15.2262 - 0.285743i) q^{77} +1.15879i q^{79} +10.9871 q^{81} +(11.1544 - 11.1544i) q^{83} +(-7.33447 - 7.33447i) q^{87} +5.57119 q^{89} +(-7.51057 + 7.79786i) q^{91} +(9.43841 + 9.43841i) q^{93} +(-5.66525 - 5.66525i) q^{97} +5.68242i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{7}+O(q^{10}) $ 24 * q - 4 * q^7	$ 24 q - 4 q^{7} + 8 q^{11} + 16 q^{21} + 32 q^{23} + 8 q^{37} - 16 q^{43} - 24 q^{51} + 16 q^{53} - 20 q^{63} + 32 q^{67} - 32 q^{71} + 40 q^{77} - 72 q^{81} - 64 q^{91} - 72 q^{93}+O(q^{100}) $ 24 * q - 4 * q^7 + 8 * q^11 + 16 * q^21 + 32 * q^23 + 8 * q^37 - 16 * q^43 - 24 * q^51 + 16 * q^53 - 20 * q^63 + 32 * q^67 - 32 * q^71 + 40 * q^77 - 72 * q^81 - 64 * q^91 - 72 * q^93

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1400\mathbb{Z}\right)^\times$.

$n$	$351$	$701$	$801$	$1177$
$\chi(n)$	$1$	$1$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	−1.41195	+	1.41195i	−0.815191	+	0.815191i	−0.985407	−	0.170216i	$-0.945554\pi$
$3$	−1.41195	+	1.41195i	−0.815191	+	0.815191i	0.170216	+	0.985407i	$0.445554\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−2.64529	+	0.0496428i	−0.999824	+	0.0187632i
$7$	−2.64529	+	0.0496428i	−0.999824	+	0.0187632i
$8$		0			0
$9$		−	0.987218i		−	0.329073i
$10$		0			0
$11$	−5.75599			−1.73550			−0.867748	−	0.497004i	$-0.834433\pi$
$11$	−5.75599			−1.73550			−0.867748	+	0.497004i	$0.834433\pi$
$12$		0			0
$13$	2.89353	−	2.89353i	0.802521	−	0.802521i	−0.180968	−	0.983489i	$-0.557923\pi$
$13$	2.89353	−	2.89353i	0.802521	−	0.802521i	0.983489	+	0.180968i	$0.0579230\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.13286	−	2.13286i	−0.517294	−	0.517294i	0.399458	−	0.916752i	$-0.369198\pi$
$17$	−2.13286	−	2.13286i	−0.517294	−	0.517294i	−0.916752	+	0.399458i	$0.869198\pi$
$18$		0			0
$19$	2.18921			0.502240			0.251120	−	0.967956i	$-0.419201\pi$
$19$	2.18921			0.502240			0.251120	+	0.967956i	$0.419201\pi$
$20$		0			0
$21$	3.66492	−	3.80511i	0.799752	−	0.830343i
$22$		0			0
$23$	4.79842	+	4.79842i	1.00054	+	1.00054i	1.00000		0.000540386i	$0.000172010\pi$
$23$	4.79842	+	4.79842i	1.00054	+	1.00054i	0.000540386		1.00000i	$0.499828\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	−2.84195	−	2.84195i	−0.546934	−	0.546934i
$28$		0			0
$29$			5.19456i			0.964606i	0.876005	+	0.482303i	$0.160199\pi$
$29$			5.19456i			0.964606i	−0.876005	+	0.482303i	$0.839801\pi$
$30$		0			0
$31$		−	6.68465i		−	1.20060i	−0.799775	−	0.600299i	$-0.795048\pi$
$31$		−	6.68465i		−	1.20060i	0.799775	−	0.600299i	$-0.204952\pi$
$32$		0			0
$33$	8.12718	−	8.12718i	1.41476	−	1.41476i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	6.50613	−	6.50613i	1.06960	−	1.06960i	0.0722123	−	0.997389i	$-0.476994\pi$
$37$	6.50613	−	6.50613i	1.06960	−	1.06960i	0.997389	−	0.0722123i	$-0.0230059\pi$
$38$		0			0
$39$			8.17106i			1.30842i
$40$		0			0
$41$		−	0.846034i		−	0.132128i	−0.997815	−	0.0660642i	$-0.978956\pi$
$41$		−	0.846034i		−	0.132128i	0.997815	−	0.0660642i	$-0.0210442\pi$
$42$		0			0
$43$	−2.68215	−	2.68215i	−0.409024	−	0.409024i	0.472374	−	0.881398i	$-0.343397\pi$
$43$	−2.68215	−	2.68215i	−0.409024	−	0.409024i	−0.881398	+	0.472374i	$0.843397\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	4.55094	+	4.55094i	0.663823	+	0.663823i	0.956279	−	0.292456i	$-0.0944726\pi$
$47$	4.55094	+	4.55094i	0.663823	+	0.663823i	−0.292456	+	0.956279i	$0.594473\pi$
$48$		0			0
$49$	6.99507	−	0.262639i	0.999296	−	0.0375198i
$50$		0			0
$51$	6.02299			0.843387
$52$		0			0
$53$	0.750143	+	0.750143i	0.103040	+	0.103040i	0.756747	−	0.653707i	$-0.226787\pi$
$53$	0.750143	+	0.750143i	0.103040	+	0.103040i	−0.653707	+	0.756747i	$0.726787\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−3.09107	+	3.09107i	−0.409422	+	0.409422i
$58$		0			0
$59$	4.25478			0.553926			0.276963	−	0.960881i	$-0.410672\pi$
$59$	4.25478			0.553926			0.276963	+	0.960881i	$0.410672\pi$
$60$		0			0
$61$			7.62115i			0.975788i	0.872903	+	0.487894i	$0.162235\pi$
$61$			7.62115i			0.975788i	−0.872903	+	0.487894i	$0.837765\pi$
$62$		0			0
$63$	0.0490083	+	2.61147i	0.00617446	+	0.329015i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	2.14628	−	2.14628i	0.262210	−	0.262210i	−0.563741	−	0.825951i	$-0.690639\pi$
$67$	2.14628	−	2.14628i	0.262210	−	0.262210i	0.825951	+	0.563741i	$0.190639\pi$
$68$		0			0
$69$	−13.5503			−1.63126
$70$		0			0
$71$	−2.44951			−0.290704			−0.145352	−	0.989380i	$-0.546431\pi$
$71$	−2.44951			−0.290704			−0.145352	+	0.989380i	$0.546431\pi$
$72$		0			0
$73$	−3.51423	+	3.51423i	−0.411310	+	0.411310i	−0.882195	−	0.470885i	$-0.843935\pi$
$73$	−3.51423	+	3.51423i	−0.411310	+	0.411310i	0.470885	+	0.882195i	$0.343935\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	15.2262	−	0.285743i	1.73519	−	0.0325635i
$78$		0			0
$79$			1.15879i			0.130374i	0.997873	+	0.0651871i	$0.0207644\pi$
$79$			1.15879i			0.130374i	−0.997873	+	0.0651871i	$0.979236\pi$
$80$		0			0
$81$	10.9871			1.22078
$82$		0			0
$83$	11.1544	−	11.1544i	1.22436	−	1.22436i	0.258290	−	0.966067i	$-0.416841\pi$
$83$	11.1544	−	11.1544i	1.22436	−	1.22436i	0.966067	−	0.258290i	$-0.0831590\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−7.33447	−	7.33447i	−0.786338	−	0.786338i
$88$		0			0
$89$	5.57119			0.590545			0.295273	−	0.955413i	$-0.404590\pi$
$89$	5.57119			0.590545			0.295273	+	0.955413i	$0.404590\pi$
$90$		0			0
$91$	−7.51057	+	7.79786i	−0.787322	+	0.817438i
$92$		0			0
$93$	9.43841	+	9.43841i	0.978717	+	0.978717i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−5.66525	−	5.66525i	−0.575219	−	0.575219i	0.358363	−	0.933582i	$-0.383335\pi$
$97$	−5.66525	−	5.66525i	−0.575219	−	0.575219i	−0.933582	+	0.358363i	$0.883335\pi$
$98$		0			0
$99$			5.68242i			0.571104i
$100$		0			0
$101$		−	17.3456i		−	1.72595i	−0.505247	−	0.862975i	$-0.668599\pi$
$101$		−	17.3456i		−	1.72595i	0.505247	−	0.862975i	$-0.331401\pi$
$102$		0			0
$103$	−0.942158	+	0.942158i	−0.0928336	+	0.0928336i	−0.751998	−	0.659165i	$-0.770910\pi$
$103$	−0.942158	+	0.942158i	−0.0928336	+	0.0928336i	0.659165	+	0.751998i	$0.270910\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	−1.87928	+	1.87928i	−0.181677	+	0.181677i	−0.792086	−	0.610409i	$-0.791005\pi$
$107$	−1.87928	+	1.87928i	−0.181677	+	0.181677i	0.610409	+	0.792086i	$0.291005\pi$
$108$		0			0
$109$		−	11.9743i		−	1.14693i	−0.819231	−	0.573464i	$-0.805599\pi$
$109$		−	11.9743i		−	1.14693i	0.819231	−	0.573464i	$-0.194401\pi$
$110$		0			0
$111$			18.3727i			1.74386i
$112$		0			0
$113$	11.4209	+	11.4209i	1.07439	+	1.07439i	0.997001	+	0.0773881i	$0.0246580\pi$
$113$	11.4209	+	11.4209i	1.07439	+	1.07439i	0.0773881	+	0.997001i	$0.475342\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−2.85655	−	2.85655i	−0.264088	−	0.264088i
$118$		0			0
$119$	5.74790	+	5.53614i	0.526909	+	0.507497i
$120$		0			0
$121$	22.1314			2.01195
$122$		0			0
$123$	1.19456	+	1.19456i	0.107710	+	0.107710i
$124$		0			0
$125$		0			0
$126$		0			0
$127$	5.75155	−	5.75155i	0.510367	−	0.510367i	−0.404272	−	0.914639i	$-0.632475\pi$
$127$	5.75155	−	5.75155i	0.510367	−	0.510367i	0.914639	+	0.404272i	$0.132475\pi$
$128$		0			0
$129$	7.57413			0.666865
$130$		0			0
$131$			2.88815i			0.252339i	0.992009	+	0.126169i	$0.0402683\pi$
$131$			2.88815i			0.252339i	−0.992009	+	0.126169i	$0.959732\pi$
$132$		0			0
$133$	−5.79110	+	0.108679i	−0.502152	+	0.00942364i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	0.755989	−	0.755989i	0.0645885	−	0.0645885i	−0.674075	−	0.738663i	$-0.735457\pi$
$137$	0.755989	−	0.755989i	0.0645885	−	0.0645885i	0.738663	+	0.674075i	$0.235457\pi$
$138$		0			0
$139$	13.0811			1.10952			0.554761	−	0.832010i	$-0.312810\pi$
$139$	13.0811			1.10952			0.554761	+	0.832010i	$0.312810\pi$
$140$		0			0
$141$	−12.8514			−1.08228
$142$		0			0
$143$	−16.6551	+	16.6551i	−1.39277	+	1.39277i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−9.50587	+	10.2475i	−0.784031	+	0.845203i
$148$		0			0
$149$		−	11.1067i		−	0.909898i	−0.890517	−	0.454949i	$-0.849657\pi$
$149$		−	11.1067i		−	0.909898i	0.890517	−	0.454949i	$-0.150343\pi$
$150$		0			0
$151$	13.9630			1.13629			0.568146	−	0.822928i	$-0.307661\pi$
$151$	13.9630			1.13629			0.568146	+	0.822928i	$0.307661\pi$
$152$		0			0
$153$	−2.10560	+	2.10560i	−0.170227	+	0.170227i
$154$		0			0
$155$		0			0
$156$		0			0
$157$	−13.3990	−	13.3990i	−1.06936	−	1.06936i	−0.997408	−	0.0719505i	$-0.977078\pi$
$157$	−13.3990	−	13.3990i	−1.06936	−	1.06936i	−0.0719505	−	0.997408i	$-0.522922\pi$
$158$		0			0
$159$	−2.11833			−0.167995
$160$		0			0
$161$	−12.9314	−	12.4550i	−1.01914	−	0.981591i
$162$		0			0
$163$	−7.57526	−	7.57526i	−0.593340	−	0.593340i	0.345192	−	0.938532i	$-0.387814\pi$
$163$	−7.57526	−	7.57526i	−0.593340	−	0.593340i	−0.938532	+	0.345192i	$0.887814\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	10.6666	+	10.6666i	0.825405	+	0.825405i	0.986877	−	0.161472i	$-0.0516242\pi$
$167$	10.6666	+	10.6666i	0.825405	+	0.825405i	−0.161472	+	0.986877i	$0.551624\pi$
$168$		0			0
$169$		−	3.74505i		−	0.288081i
$170$		0			0
$171$		−	2.16123i		−	0.165274i
$172$		0			0
$173$	3.56140	−	3.56140i	0.270768	−	0.270768i	−0.558641	−	0.829409i	$-0.688677\pi$
$173$	3.56140	−	3.56140i	0.270768	−	0.270768i	0.829409	+	0.558641i	$0.188677\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−6.00755	+	6.00755i	−0.451555	+	0.451555i
$178$		0			0
$179$		−	14.9523i		−	1.11758i	−0.829308	−	0.558792i	$-0.811265\pi$
$179$		−	14.9523i		−	1.11758i	0.829308	−	0.558792i	$-0.188735\pi$
$180$		0			0
$181$		−	4.34072i		−	0.322643i	−0.986902	−	0.161322i	$-0.948424\pi$
$181$		−	4.34072i		−	0.322643i	0.986902	−	0.161322i	$-0.0515757\pi$
$182$		0			0
$183$	−10.7607	−	10.7607i	−0.795454	−	0.795454i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	12.2767	+	12.2767i	0.897762	+	0.897762i
$188$		0			0
$189$	7.65886	+	7.37669i	0.557100	+	0.536575i
$190$		0			0
$191$	−1.64962			−0.119362			−0.0596812	−	0.998217i	$-0.519008\pi$
$191$	−1.64962			−0.119362			−0.0596812	+	0.998217i	$0.519008\pi$
$192$		0			0
$193$	14.3957	+	14.3957i	1.03623	+	1.03623i	0.999319	+	0.0369067i	$0.0117504\pi$
$193$	14.3957	+	14.3957i	1.03623	+	1.03623i	0.0369067	+	0.999319i	$0.488250\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	−3.51856	+	3.51856i	−0.250687	+	0.250687i	−0.821252	−	0.570565i	$-0.806724\pi$
$197$	−3.51856	+	3.51856i	−0.250687	+	0.250687i	0.570565	+	0.821252i	$0.306724\pi$
$198$		0			0
$199$	−13.3332			−0.945166			−0.472583	−	0.881286i	$-0.656678\pi$
$199$	−13.3332			−0.945166			−0.472583	+	0.881286i	$0.656678\pi$
$200$		0			0
$201$			6.06089i			0.427502i
$202$		0			0
$203$	−0.257872	−	13.7411i	−0.0180991	−	0.964436i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	4.73709	−	4.73709i	0.329251	−	0.329251i
$208$		0			0
$209$	−12.6011			−0.871636
$210$		0			0
$211$	−13.0953			−0.901515			−0.450757	−	0.892646i	$-0.648846\pi$
$211$	−13.0953			−0.901515			−0.450757	+	0.892646i	$0.648846\pi$
$212$		0			0
$213$	3.45859	−	3.45859i	0.236979	−	0.236979i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.331845	+	17.6828i	0.0225271	+	1.20039i
$218$		0			0
$219$		−	9.92385i		−	0.670592i
$220$		0			0
$221$	−12.3430			−0.830279
$222$		0			0
$223$	3.29822	−	3.29822i	0.220865	−	0.220865i	−0.587997	−	0.808863i	$-0.700083\pi$
$223$	3.29822	−	3.29822i	0.220865	−	0.220865i	0.808863	+	0.587997i	$0.200083\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	0.320738	+	0.320738i	0.0212882	+	0.0212882i	0.717671	−	0.696383i	$-0.245208\pi$
$227$	0.320738	+	0.320738i	0.0212882	+	0.0212882i	−0.696383	+	0.717671i	$0.745208\pi$
$228$		0			0
$229$	−20.6219			−1.36273			−0.681365	−	0.731943i	$-0.738614\pi$
$229$	−20.6219			−1.36273			−0.681365	+	0.731943i	$0.738614\pi$
$230$		0			0
$231$	−21.0953	+	21.9022i	−1.38797	+	1.44106i
$232$		0			0
$233$	−12.0752	−	12.0752i	−0.791076	−	0.791076i	0.190593	−	0.981669i	$-0.438959\pi$
$233$	−12.0752	−	12.0752i	−0.791076	−	0.791076i	−0.981669	+	0.190593i	$0.938959\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−1.63616	−	1.63616i	−0.106280	−	0.106280i
$238$		0			0
$239$			6.59501i			0.426595i	0.976987	+	0.213298i	$0.0684204\pi$
$239$			6.59501i			0.426595i	−0.976987	+	0.213298i	$0.931580\pi$
$240$		0			0
$241$		−	8.34354i		−	0.537455i	−0.963216	−	0.268727i	$-0.913397\pi$
$241$		−	8.34354i		−	0.537455i	0.963216	−	0.268727i	$-0.0866031\pi$
$242$		0			0
$243$	−6.98734	+	6.98734i	−0.448238	+	0.448238i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	6.33456	−	6.33456i	0.403058	−	0.403058i
$248$		0			0
$249$			31.4990i			1.99617i
$250$		0			0
$251$		−	17.0870i		−	1.07852i	−0.842139	−	0.539260i	$-0.818704\pi$
$251$		−	17.0870i		−	1.07852i	0.842139	−	0.539260i	$-0.181296\pi$
$252$		0			0
$253$	−27.6197	−	27.6197i	−1.73643	−	1.73643i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−8.97415	−	8.97415i	−0.559792	−	0.559792i	0.369456	−	0.929248i	$-0.379544\pi$
$257$	−8.97415	−	8.97415i	−0.559792	−	0.559792i	−0.929248	+	0.369456i	$0.879544\pi$
$258$		0			0
$259$	−16.8876	+	17.5336i	−1.04934	+	1.08948i
$260$		0			0
$261$	5.12816			0.317425
$262$		0			0
$263$	−7.06106	−	7.06106i	−0.435404	−	0.435404i	0.455058	−	0.890462i	$-0.349618\pi$
$263$	−7.06106	−	7.06106i	−0.435404	−	0.435404i	−0.890462	+	0.455058i	$0.849618\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−7.86626	+	7.86626i	−0.481407	+	0.481407i
$268$		0			0
$269$	−21.2159			−1.29356			−0.646779	−	0.762677i	$-0.723884\pi$
$269$	−21.2159			−1.29356			−0.646779	+	0.762677i	$0.723884\pi$
$270$		0			0
$271$		−	24.7526i		−	1.50361i	−0.659383	−	0.751807i	$-0.729182\pi$
$271$		−	24.7526i		−	1.50361i	0.659383	−	0.751807i	$-0.270818\pi$
$272$		0			0
$273$	−0.405634	−	21.6148i	−0.0245501	−	1.30819i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−6.78756	+	6.78756i	−0.407825	+	0.407825i	−0.880980	−	0.473154i	$-0.843115\pi$
$277$	−6.78756	+	6.78756i	−0.407825	+	0.407825i	0.473154	+	0.880980i	$0.343115\pi$
$278$		0			0
$279$	−6.59921			−0.395084
$280$		0			0
$281$	−3.02185			−0.180269			−0.0901343	−	0.995930i	$-0.528730\pi$
$281$	−3.02185			−0.180269			−0.0901343	+	0.995930i	$0.528730\pi$
$282$		0			0
$283$	1.64288	−	1.64288i	0.0976592	−	0.0976592i	−0.656589	−	0.754248i	$-0.728001\pi$
$283$	1.64288	−	1.64288i	0.0976592	−	0.0976592i	0.754248	+	0.656589i	$0.228001\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	0.0419995	+	2.23800i	0.00247915	+	0.132105i
$288$		0			0
$289$		−	7.90183i		−	0.464814i
$290$		0			0
$291$	15.9981			0.937827
$292$		0			0
$293$	−18.8850	+	18.8850i	−1.10327	+	1.10327i	−0.109260	+	0.994013i	$0.534848\pi$
$293$	−18.8850	+	18.8850i	−1.10327	+	1.10327i	−0.994013	+	0.109260i	$0.965152\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	16.3582	+	16.3582i	0.949202	+	0.949202i
$298$		0			0
$299$	27.7688			1.60591
$300$		0			0
$301$	7.22819	+	6.96189i	0.416626	+	0.401277i
$302$		0			0
$303$	24.4911	+	24.4911i	1.40698	+	1.40698i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	−13.4992	−	13.4992i	−0.770442	−	0.770442i	0.207742	−	0.978184i	$-0.433389\pi$
$307$	−13.4992	−	13.4992i	−0.770442	−	0.770442i	−0.978184	+	0.207742i	$0.933389\pi$
$308$		0			0
$309$		−	2.66056i		−	0.151354i
$310$		0			0
$311$			24.8641i			1.40992i	0.709250	+	0.704958i	$0.249034\pi$
$311$			24.8641i			1.40992i	−0.709250	+	0.704958i	$0.750966\pi$
$312$		0			0
$313$	−0.561667	+	0.561667i	−0.0317473	+	0.0317473i	−0.722802	−	0.691055i	$-0.757146\pi$
$313$	−0.561667	+	0.561667i	−0.0317473	+	0.0317473i	0.691055	+	0.722802i	$0.257146\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	15.5043	−	15.5043i	0.870808	−	0.870808i	−0.121753	−	0.992560i	$-0.538851\pi$
$317$	15.5043	−	15.5043i	0.870808	−	0.870808i	0.992560	+	0.121753i	$0.0388515\pi$
$318$		0			0
$319$		−	29.8998i		−	1.67407i
$320$		0			0
$321$		−	5.30692i		−	0.296203i
$322$		0			0
$323$	−4.66928	−	4.66928i	−0.259806	−	0.259806i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	16.9071	+	16.9071i	0.934965	+	0.934965i
$328$		0			0
$329$	−12.2645	−	11.8126i	−0.676161	−	0.651250i
$330$		0			0
$331$	−6.54142			−0.359549			−0.179774	−	0.983708i	$-0.557537\pi$
$331$	−6.54142			−0.359549			−0.179774	+	0.983708i	$0.557537\pi$
$332$		0			0
$333$	−6.42297	−	6.42297i	−0.351977	−	0.351977i
$334$		0			0
$335$		0			0
$336$		0			0
$337$	0.409971	−	0.409971i	0.0223325	−	0.0223325i	−0.695852	−	0.718185i	$-0.744973\pi$
$337$	0.409971	−	0.409971i	0.0223325	−	0.0223325i	0.718185	+	0.695852i	$0.244973\pi$
$338$		0			0
$339$	−32.2516			−1.75166
$340$		0			0
$341$			38.4768i			2.08363i
$342$		0			0
$343$	−18.4909	+	1.04201i	−0.998416	+	0.0562632i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	1.47700	−	1.47700i	0.0792894	−	0.0792894i	−0.666350	−	0.745639i	$-0.732144\pi$
$347$	1.47700	−	1.47700i	0.0792894	−	0.0792894i	0.745639	+	0.666350i	$0.232144\pi$
$348$		0			0
$349$	4.11409			0.220222			0.110111	−	0.993919i	$-0.464879\pi$
$349$	4.11409			0.220222			0.110111	+	0.993919i	$0.464879\pi$
$350$		0			0
$351$	−16.4466			−0.877852
$352$		0			0
$353$	3.54149	−	3.54149i	0.188495	−	0.188495i	−0.606550	−	0.795045i	$-0.707447\pi$
$353$	3.54149	−	3.54149i	0.188495	−	0.188495i	0.795045	+	0.606550i	$0.207447\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−15.9325	+	0.298998i	−0.843238	+	0.0158246i
$358$		0			0
$359$			2.10171i			0.110924i	0.998461	+	0.0554620i	$0.0176632\pi$
$359$			2.10171i			0.110924i	−0.998461	+	0.0554620i	$0.982337\pi$
$360$		0			0
$361$	−14.2073			−0.747755
$362$		0			0
$363$	−31.2485	+	31.2485i	−1.64012	+	1.64012i
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−9.14816	−	9.14816i	−0.477530	−	0.477530i	0.426811	−	0.904341i	$-0.359637\pi$
$367$	−9.14816	−	9.14816i	−0.477530	−	0.477530i	−0.904341	+	0.426811i	$0.859637\pi$
$368$		0			0
$369$	−0.835220			−0.0434798
$370$		0			0
$371$	−2.02158	−	1.94710i	−0.104955	−	0.101089i
$372$		0			0
$373$	19.6238	+	19.6238i	1.01608	+	1.01608i	0.999869	+	0.0162153i	$0.00516172\pi$
$373$	19.6238	+	19.6238i	1.01608	+	1.01608i	0.0162153	+	0.999869i	$0.494838\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	15.0306	+	15.0306i	0.774116	+	0.774116i
$378$		0			0
$379$		−	10.9778i		−	0.563893i	−0.959430	−	0.281946i	$-0.909020\pi$
$379$		−	10.9778i		−	0.563893i	0.959430	−	0.281946i	$-0.0909800\pi$
$380$		0			0
$381$			16.2418i			0.832094i
$382$		0			0
$383$	7.07844	−	7.07844i	0.361691	−	0.361691i	−0.502744	−	0.864435i	$-0.667676\pi$
$383$	7.07844	−	7.07844i	0.361691	−	0.361691i	0.864435	+	0.502744i	$0.167676\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−2.64786	+	2.64786i	−0.134598	+	0.134598i
$388$		0			0
$389$		−	23.4863i		−	1.19080i	−0.803429	−	0.595400i	$-0.796994\pi$
$389$		−	23.4863i		−	1.19080i	0.803429	−	0.595400i	$-0.203006\pi$
$390$		0			0
$391$		−	20.4687i		−	1.03515i
$392$		0			0
$393$	−4.07793	−	4.07793i	−0.205704	−	0.205704i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	4.35063	+	4.35063i	0.218352	+	0.218352i	0.807804	−	0.589452i	$-0.200656\pi$
$397$	4.35063	+	4.35063i	0.218352	+	0.218352i	−0.589452	+	0.807804i	$0.700656\pi$
$398$		0			0
$399$	8.02330	−	8.33020i	0.401668	−	0.417032i
$400$		0			0
$401$	26.3132			1.31402			0.657009	−	0.753883i	$-0.271821\pi$
$401$	26.3132			1.31402			0.657009	+	0.753883i	$0.271821\pi$
$402$		0			0
$403$	−19.3422	−	19.3422i	−0.963506	−	0.963506i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−37.4492	+	37.4492i	−1.85629	+	1.85629i
$408$		0			0
$409$	37.3895			1.84879			0.924397	−	0.381432i	$-0.124569\pi$
$409$	37.3895			1.84879			0.924397	+	0.381432i	$0.124569\pi$
$410$		0			0
$411$			2.13484i			0.105304i
$412$		0			0
$413$	−11.2551	+	0.211219i	−0.553828	+	0.0103934i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−18.4698	+	18.4698i	−0.904472	+	0.904472i
$418$		0			0
$419$	36.6112			1.78858			0.894288	−	0.447492i	$-0.147683\pi$
$419$	36.6112			1.78858			0.894288	+	0.447492i	$0.147683\pi$
$420$		0			0
$421$	−7.86103			−0.383123			−0.191562	−	0.981481i	$-0.561355\pi$
$421$	−7.86103			−0.383123			−0.191562	+	0.981481i	$0.561355\pi$
$422$		0			0
$423$	4.49277	−	4.49277i	0.218446	−	0.218446i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	−0.378335	−	20.1601i	−0.0183089	−	0.975617i
$428$		0			0
$429$		−	47.0325i		−	2.27075i
$430$		0			0
$431$	13.1182			0.631880			0.315940	−	0.948779i	$-0.397680\pi$
$431$	13.1182			0.631880			0.315940	+	0.948779i	$0.397680\pi$
$432$		0			0
$433$	−18.9505	+	18.9505i	−0.910705	+	0.910705i	−0.996328	−	0.0856227i	$-0.972712\pi$
$433$	−18.9505	+	18.9505i	−0.910705	+	0.910705i	0.0856227	+	0.996328i	$0.472712\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	10.5048	+	10.5048i	0.502511	+	0.502511i
$438$		0			0
$439$	−11.7996			−0.563162			−0.281581	−	0.959537i	$-0.590859\pi$
$439$	−11.7996			−0.563162			−0.281581	+	0.959537i	$0.590859\pi$
$440$		0			0
$441$	−0.259282	−	6.90566i	−0.0123467	−	0.328841i
$442$		0			0
$443$	21.4990	+	21.4990i	1.02145	+	1.02145i	0.999765	+	0.0216811i	$0.00690184\pi$
$443$	21.4990	+	21.4990i	1.02145	+	1.02145i	0.0216811	+	0.999765i	$0.493098\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	15.6822	+	15.6822i	0.741741	+	0.741741i
$448$		0			0
$449$			41.3757i			1.95264i	0.216336	+	0.976319i	$0.430589\pi$
$449$			41.3757i			1.95264i	−0.216336	+	0.976319i	$0.569411\pi$
$450$		0			0
$451$			4.86976i			0.229308i
$452$		0			0
$453$	−19.7151	+	19.7151i	−0.926294	+	0.926294i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	24.8225	−	24.8225i	1.16115	−	1.16115i	0.176921	−	0.984225i	$-0.443386\pi$
$457$	24.8225	−	24.8225i	1.16115	−	1.16115i	0.984225	−	0.176921i	$-0.0566136\pi$
$458$		0			0
$459$			12.1230i			0.565851i
$460$		0			0
$461$			17.6084i			0.820103i	0.912062	+	0.410051i	$0.134489\pi$
$461$			17.6084i			0.820103i	−0.912062	+	0.410051i	$0.865511\pi$
$462$		0			0
$463$	6.93785	+	6.93785i	0.322429	+	0.322429i	0.849698	−	0.527269i	$-0.176784\pi$
$463$	6.93785	+	6.93785i	0.322429	+	0.322429i	−0.527269	+	0.849698i	$0.676784\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−19.7206	−	19.7206i	−0.912559	−	0.912559i	0.0839138	−	0.996473i	$-0.473258\pi$
$467$	−19.7206	−	19.7206i	−0.912559	−	0.912559i	−0.996473	+	0.0839138i	$0.973258\pi$
$468$		0			0
$469$	−5.57098	+	5.78407i	−0.257244	+	0.267084i
$470$		0			0
$471$	37.8376			1.74346
$472$		0			0
$473$	15.4384	+	15.4384i	0.709859	+	0.709859i
$474$		0			0
$475$		0			0
$476$		0			0
$477$	0.740555	−	0.740555i	0.0339077	−	0.0339077i
$478$		0			0
$479$	13.7850			0.629854			0.314927	−	0.949116i	$-0.398020\pi$
$479$	13.7850			0.629854			0.314927	+	0.949116i	$0.398020\pi$
$480$		0			0
$481$		−	37.6514i		−	1.71676i
$482$		0			0
$483$	35.8444	−	0.672674i	1.63098	−	0.0306077i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	29.4914	−	29.4914i	1.33638	−	1.33638i	0.436847	−	0.899536i	$-0.356095\pi$
$487$	29.4914	−	29.4914i	1.33638	−	1.33638i	0.899536	−	0.436847i	$-0.143905\pi$
$488$		0			0
$489$	21.3918			0.967371
$490$		0			0
$491$	3.24344			0.146374			0.0731872	−	0.997318i	$-0.476683\pi$
$491$	3.24344			0.146374			0.0731872	+	0.997318i	$0.476683\pi$
$492$		0			0
$493$	11.0793	−	11.0793i	0.498985	−	0.498985i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	6.47966	−	0.121601i	0.290652	−	0.00545453i
$498$		0			0
$499$		−	21.9000i		−	0.980378i	−0.871616	−	0.490189i	$-0.836928\pi$
$499$		−	21.9000i		−	0.980378i	0.871616	−	0.490189i	$-0.163072\pi$
$500$		0			0
$501$	−30.1214			−1.34573
$502$		0			0
$503$	20.8581	−	20.8581i	0.930015	−	0.930015i	−0.0676912	−	0.997706i	$-0.521563\pi$
$503$	20.8581	−	20.8581i	0.930015	−	0.930015i	0.997706	+	0.0676912i	$0.0215633\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	5.28783	+	5.28783i	0.234841	+	0.234841i
$508$		0			0
$509$	32.7888			1.45334			0.726669	−	0.686988i	$-0.241067\pi$
$509$	32.7888			1.45334			0.726669	+	0.686988i	$0.241067\pi$
$510$		0			0
$511$	9.12169	−	9.47060i	0.403520	−	0.418955i
$512$		0			0
$513$	−6.22164	−	6.22164i	−0.274692	−	0.274692i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−26.1952	−	26.1952i	−1.15206	−	1.15206i
$518$		0			0
$519$			10.0570i			0.441455i
$520$		0			0
$521$			40.2275i			1.76240i	0.472746	+	0.881199i	$0.343263\pi$
$521$			40.2275i			1.76240i	−0.472746	+	0.881199i	$0.656737\pi$
$522$		0			0
$523$	−16.0560	+	16.0560i	−0.702082	+	0.702082i	−0.964857	−	0.262775i	$-0.915362\pi$
$523$	−16.0560	+	16.0560i	−0.702082	+	0.702082i	0.262775	+	0.964857i	$0.415362\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−14.2574	+	14.2574i	−0.621063	+	0.621063i
$528$		0			0
$529$			23.0497i			1.00216i
$530$		0			0
$531$		−	4.20040i		−	0.182282i
$532$		0			0
$533$	−2.44803	−	2.44803i	−0.106036	−	0.106036i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	21.1119	+	21.1119i	0.911044	+	0.911044i
$538$		0			0
$539$	−40.2636	+	1.51175i	−1.73427	+	0.0651155i
$540$		0			0
$541$	43.0574			1.85118			0.925590	−	0.378527i	$-0.123569\pi$
$541$	43.0574			1.85118			0.925590	+	0.378527i	$0.123569\pi$
$542$		0			0
$543$	6.12889	+	6.12889i	0.263016	+	0.263016i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	30.9251	−	30.9251i	1.32226	−	1.32226i	0.410322	−	0.911941i	$-0.365416\pi$
$547$	30.9251	−	30.9251i	1.32226	−	1.32226i	0.911941	−	0.410322i	$-0.134584\pi$
$548$		0			0
$549$	7.52374			0.321105
$550$		0			0
$551$			11.3720i			0.484464i
$552$		0			0
$553$	−0.0575256	−	3.06533i	−0.00244624	−	0.130351i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−18.1524	+	18.1524i	−0.769142	+	0.769142i	−0.977955	−	0.208814i	$-0.933040\pi$
$557$	−18.1524	+	18.1524i	−0.769142	+	0.769142i	0.208814	+	0.977955i	$0.433040\pi$
$558$		0			0
$559$	−15.5218			−0.656500
$560$		0			0
$561$	−34.6682			−1.46369
$562$		0			0
$563$	28.1810	−	28.1810i	1.18769	−	1.18769i	0.209984	−	0.977705i	$-0.432659\pi$
$563$	28.1810	−	28.1810i	1.18769	−	1.18769i	0.977705	−	0.209984i	$-0.0673411\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−29.0639	+	0.545428i	−1.22057	+	0.0229058i
$568$		0			0
$569$			6.85477i			0.287367i	0.989624	+	0.143683i	$0.0458947\pi$
$569$			6.85477i			0.287367i	−0.989624	+	0.143683i	$0.954105\pi$
$570$		0			0
$571$	10.9061			0.456407			0.228203	−	0.973613i	$-0.426715\pi$
$571$	10.9061			0.456407			0.228203	+	0.973613i	$0.426715\pi$
$572$		0			0
$573$	2.32919	−	2.32919i	0.0973032	−	0.0973032i
$574$		0			0
$575$		0			0
$576$		0			0
$577$	20.8631	+	20.8631i	0.868543	+	0.868543i	0.992311	−	0.123768i	$-0.0394980\pi$
$577$	20.8631	+	20.8631i	0.868543	+	0.868543i	−0.123768	+	0.992311i	$0.539498\pi$
$578$		0			0
$579$	−40.6521			−1.68944
$580$		0			0
$581$	−28.9529	+	30.0604i	−1.20117	+	1.24711i
$582$		0			0
$583$	−4.31782	−	4.31782i	−0.178826	−	0.178826i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	5.18377	+	5.18377i	0.213957	+	0.213957i	0.805946	−	0.591989i	$-0.201657\pi$
$587$	5.18377	+	5.18377i	0.213957	+	0.213957i	−0.591989	+	0.805946i	$0.701657\pi$
$588$		0			0
$589$		−	14.6341i		−	0.602989i
$590$		0			0
$591$		−	9.93608i		−	0.408716i
$592$		0			0
$593$	0.930542	−	0.930542i	0.0382128	−	0.0382128i	−0.687742	−	0.725955i	$-0.741398\pi$
$593$	0.930542	−	0.930542i	0.0382128	−	0.0382128i	0.725955	+	0.687742i	$0.241398\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	18.8259	−	18.8259i	0.770491	−	0.770491i
$598$		0			0
$599$			19.0106i			0.776753i	0.921501	+	0.388376i	$0.126964\pi$
$599$			19.0106i			0.776753i	−0.921501	+	0.388376i	$0.873036\pi$
$600$		0			0
$601$		−	2.50399i		−	0.102140i	−0.998695	−	0.0510699i	$-0.983737\pi$
$601$		−	2.50399i		−	0.102140i	0.998695	−	0.0510699i	$-0.0162631\pi$
$602$		0			0
$603$	−2.11885	−	2.11885i	−0.0862861	−	0.0862861i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−32.0088	−	32.0088i	−1.29920	−	1.29920i	−0.928921	−	0.370278i	$-0.879263\pi$
$607$	−32.0088	−	32.0088i	−1.29920	−	1.29920i	−0.370278	−	0.928921i	$-0.620737\pi$
$608$		0			0
$609$	19.7659	+	19.0377i	0.800954	+	0.771445i
$610$		0			0
$611$	26.3366			1.06546
$612$		0			0
$613$	−7.06328	−	7.06328i	−0.285283	−	0.285283i	0.549929	−	0.835212i	$-0.314655\pi$
$613$	−7.06328	−	7.06328i	−0.285283	−	0.285283i	−0.835212	+	0.549929i	$0.814655\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	−10.5163	+	10.5163i	−0.423372	+	0.423372i	−0.886363	−	0.462991i	$-0.846776\pi$
$617$	−10.5163	+	10.5163i	−0.423372	+	0.423372i	0.462991	+	0.886363i	$0.346776\pi$
$618$		0			0
$619$	−36.7114			−1.47556			−0.737778	−	0.675043i	$-0.764125\pi$
$619$	−36.7114			−1.47556			−0.737778	+	0.675043i	$0.764125\pi$
$620$		0			0
$621$		−	27.2738i		−	1.09446i
$622$		0			0
$623$	−14.7374	+	0.276569i	−0.590441	+	0.0110805i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	17.7921	−	17.7921i	0.710550	−	0.710550i
$628$		0			0
$629$	−27.7533			−1.10660
$630$		0			0
$631$	−12.9845			−0.516905			−0.258453	−	0.966024i	$-0.583213\pi$
$631$	−12.9845			−0.516905			−0.258453	+	0.966024i	$0.583213\pi$
$632$		0			0
$633$	18.4899	−	18.4899i	0.734907	−	0.734907i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	19.4805	−	21.0004i	0.771846	−	0.832067i
$638$		0			0
$639$			2.41820i			0.0956627i
$640$		0			0
$641$	2.81307			0.111110			0.0555548	−	0.998456i	$-0.482307\pi$
$641$	2.81307			0.111110			0.0555548	+	0.998456i	$0.482307\pi$
$642$		0			0
$643$	−1.00819	+	1.00819i	−0.0397592	+	0.0397592i	−0.726707	−	0.686948i	$-0.758950\pi$
$643$	−1.00819	+	1.00819i	−0.0397592	+	0.0397592i	0.686948	+	0.726707i	$0.258950\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−0.810020	−	0.810020i	−0.0318452	−	0.0318452i	0.691005	−	0.722850i	$-0.257168\pi$
$647$	−0.810020	−	0.810020i	−0.0318452	−	0.0318452i	−0.722850	+	0.691005i	$0.757168\pi$
$648$		0			0
$649$	−24.4905			−0.961336
$650$		0			0
$651$	−25.4358	−	24.4987i	−0.996909	−	0.960181i
$652$		0			0
$653$	−8.40887	−	8.40887i	−0.329064	−	0.329064i	0.523166	−	0.852231i	$-0.324751\pi$
$653$	−8.40887	−	8.40887i	−0.329064	−	0.329064i	−0.852231	+	0.523166i	$0.824751\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	3.46931	+	3.46931i	0.135351	+	0.135351i
$658$		0			0
$659$			37.6355i			1.46607i	0.680191	+	0.733035i	$0.261897\pi$
$659$			37.6355i			1.46607i	−0.680191	+	0.733035i	$0.738103\pi$
$660$		0			0
$661$		−	19.5181i		−	0.759167i	−0.925158	−	0.379583i	$-0.876067\pi$
$661$		−	19.5181i		−	0.759167i	0.925158	−	0.379583i	$-0.123933\pi$
$662$		0			0
$663$	17.4277	−	17.4277i	0.676836	−	0.676836i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−24.9257	+	24.9257i	−0.965127	+	0.965127i
$668$		0			0
$669$			9.31387i			0.360095i
$670$		0			0
$671$		−	43.8673i		−	1.69348i
$672$		0			0
$673$	−8.41284	−	8.41284i	−0.324291	−	0.324291i	0.526119	−	0.850411i	$-0.323646\pi$
$673$	−8.41284	−	8.41284i	−0.324291	−	0.324291i	−0.850411	+	0.526119i	$0.823646\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	−32.7720	−	32.7720i	−1.25953	−	1.25953i	−0.951318	−	0.308212i	$-0.900269\pi$
$677$	−32.7720	−	32.7720i	−1.25953	−	1.25953i	−0.308212	−	0.951318i	$-0.599731\pi$
$678$		0			0
$679$	15.2674	+	14.7050i	0.585911	+	0.564325i
$680$		0			0
$681$	−0.905735			−0.0347078
$682$		0			0
$683$	14.8873	+	14.8873i	0.569645	+	0.569645i	0.932029	−	0.362384i	$-0.118037\pi$
$683$	14.8873	+	14.8873i	0.569645	+	0.569645i	−0.362384	+	0.932029i	$0.618037\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	29.1171	−	29.1171i	1.11089	−	1.11089i
$688$		0			0
$689$	4.34113			0.165384
$690$		0			0
$691$		−	7.73539i		−	0.294268i	−0.989117	−	0.147134i	$-0.952995\pi$
$691$		−	7.73539i		−	0.294268i	0.989117	−	0.147134i	$-0.0470049\pi$
$692$		0			0
$693$	−0.282091	−	15.0316i	−0.0107158	−	0.571004i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	−1.80447	+	1.80447i	−0.0683492	+	0.0683492i
$698$		0			0
$699$	34.0993			1.28976
$700$		0			0
$701$	−9.03502			−0.341248			−0.170624	−	0.985336i	$-0.554578\pi$
$701$	−9.03502			−0.341248			−0.170624	+	0.985336i	$0.554578\pi$
$702$		0			0
$703$	14.2433	−	14.2433i	0.537197	−	0.537197i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.861083	+	45.8840i	0.0323843	+	1.72565i
$708$		0			0
$709$			45.0946i			1.69356i	0.531940	+	0.846782i	$0.321463\pi$
$709$			45.0946i			1.69356i	−0.531940	+	0.846782i	$0.678537\pi$
$710$		0			0
$711$	1.14398			0.0429026
$712$		0			0
$713$	32.0758	−	32.0758i	1.20125	−	1.20125i
$714$		0			0
$715$		0			0
$716$		0			0
$717$	−9.31183	−	9.31183i	−0.347757	−	0.347757i
$718$		0			0
$719$	6.81054			0.253990			0.126995	−	0.991903i	$-0.459467\pi$
$719$	6.81054			0.253990			0.126995	+	0.991903i	$0.459467\pi$
$720$		0			0
$721$	2.44551	−	2.53905i	0.0910754	−	0.0945591i
$722$		0			0
$723$	11.7807	+	11.7807i	0.438128	+	0.438128i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	2.49077	+	2.49077i	0.0923777	+	0.0923777i	0.751785	−	0.659408i	$-0.229193\pi$
$727$	2.49077	+	2.49077i	0.0923777	+	0.0923777i	−0.659408	+	0.751785i	$0.729193\pi$
$728$		0			0
$729$			13.2296i			0.489984i
$730$		0			0
$731$			11.4413i			0.423171i
$732$		0			0
$733$	−10.6856	+	10.6856i	−0.394683	+	0.394683i	−0.876353	−	0.481670i	$-0.840030\pi$
$733$	−10.6856	+	10.6856i	−0.394683	+	0.394683i	0.481670	+	0.876353i	$0.340030\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−12.3540	+	12.3540i	−0.455064	+	0.455064i
$738$		0			0
$739$		−	32.6044i		−	1.19937i	−0.800235	−	0.599687i	$-0.795292\pi$
$739$		−	32.6044i		−	1.19937i	0.800235	−	0.599687i	$-0.204708\pi$
$740$		0			0
$741$			17.8882i			0.657139i
$742$		0			0
$743$	−6.50673	−	6.50673i	−0.238709	−	0.238709i	0.577607	−	0.816315i	$-0.303987\pi$
$743$	−6.50673	−	6.50673i	−0.238709	−	0.238709i	−0.816315	+	0.577607i	$0.803987\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−11.0119	−	11.0119i	−0.402903	−	0.402903i
$748$		0			0
$749$	4.87795	−	5.06453i	0.178236	−	0.185054i
$750$		0			0
$751$	14.7404			0.537886			0.268943	−	0.963156i	$-0.413326\pi$
$751$	14.7404			0.537886			0.268943	+	0.963156i	$0.413326\pi$
$752$		0			0
$753$	24.1260	+	24.1260i	0.879200	+	0.879200i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−11.4224	+	11.4224i	−0.415154	+	0.415154i	−0.883530	−	0.468375i	$-0.844839\pi$
$757$	−11.4224	+	11.4224i	−0.415154	+	0.415154i	0.468375	+	0.883530i	$0.344839\pi$
$758$		0			0
$759$	77.9953			2.83105
$760$		0			0
$761$		−	28.2230i		−	1.02308i	−0.859258	−	0.511542i	$-0.829074\pi$
$761$		−	28.2230i		−	1.02308i	0.859258	−	0.511542i	$-0.170926\pi$
$762$		0			0
$763$	0.594436	+	31.6754i	0.0215200	+	1.14673i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	12.3114	−	12.3114i	0.444537	−	0.444537i
$768$		0			0
$769$	36.1420			1.30331			0.651657	−	0.758514i	$-0.274074\pi$
$769$	36.1420			1.30331			0.651657	+	0.758514i	$0.274074\pi$
$770$		0			0
$771$	25.3421			0.912675
$772$		0			0
$773$	−5.37362	+	5.37362i	−0.193276	+	0.193276i	−0.797110	−	0.603834i	$-0.793639\pi$
$773$	−5.37362	+	5.37362i	−0.193276	+	0.193276i	0.603834	+	0.797110i	$0.293639\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−0.912072	−	48.6010i	−0.0327204	−	1.74355i
$778$		0			0
$779$		−	1.85215i		−	0.0663602i
$780$		0			0
$781$	14.0994			0.504515
$782$		0			0
$783$	14.7627	−	14.7627i	0.527575	−	0.527575i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	22.1977	+	22.1977i	0.791262	+	0.791262i	0.981699	−	0.190437i	$-0.0609905\pi$
$787$	22.1977	+	22.1977i	0.791262	+	0.791262i	−0.190437	+	0.981699i	$0.560990\pi$
$788$		0			0
$789$	19.9398			0.709874
$790$		0			0
$791$	−30.7785	−	29.6446i	−1.09436	−	1.05404i
$792$		0			0
$793$	22.0520	+	22.0520i	0.783091	+	0.783091i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	6.63224	+	6.63224i	0.234926	+	0.234926i	0.814745	−	0.579819i	$-0.196877\pi$
$797$	6.63224	+	6.63224i	0.234926	+	0.234926i	−0.579819	+	0.814745i	$0.696877\pi$
$798$		0			0
$799$		−	19.4130i		−	0.686783i
$800$		0			0
$801$		−	5.49998i		−	0.194332i
$802$		0			0
$803$	20.2279	−	20.2279i	0.713826	−	0.713826i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	29.9559	−	29.9559i	1.05450	−	1.05450i
$808$		0			0
$809$		−	8.88851i		−	0.312503i	−0.987717	−	0.156252i	$-0.950059\pi$
$809$		−	8.88851i		−	0.312503i	0.987717	−	0.156252i	$-0.0499411\pi$
$810$		0			0
$811$			31.9472i			1.12182i	0.827878	+	0.560908i	$0.189548\pi$
$811$			31.9472i			1.12182i	−0.827878	+	0.560908i	$0.810452\pi$
$812$		0			0
$813$	34.9495	+	34.9495i	1.22573	+	1.22573i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−5.87179	−	5.87179i	−0.205428	−	0.205428i
$818$		0			0
$819$	7.69819	+	7.41458i	0.268997	+	0.259086i
$820$		0			0
$821$	−23.0833			−0.805611			−0.402806	−	0.915286i	$-0.631965\pi$
$821$	−23.0833			−0.805611			−0.402806	+	0.915286i	$0.631965\pi$
$822$		0			0
$823$	−3.18317	−	3.18317i	−0.110958	−	0.110958i	0.649448	−	0.760406i	$-0.275000\pi$
$823$	−3.18317	−	3.18317i	−0.110958	−	0.110958i	−0.760406	+	0.649448i	$0.775000\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	6.62511	−	6.62511i	0.230378	−	0.230378i	−0.582473	−	0.812850i	$-0.697915\pi$
$827$	6.62511	−	6.62511i	0.230378	−	0.230378i	0.812850	+	0.582473i	$0.197915\pi$
$828$		0			0
$829$	−24.4276			−0.848405			−0.424203	−	0.905567i	$-0.639446\pi$
$829$	−24.4276			−0.848405			−0.424203	+	0.905567i	$0.639446\pi$
$830$		0			0
$831$		−	19.1674i		−	0.664911i
$832$		0			0
$833$	−15.4797	−	14.3593i	−0.536339	−	0.497521i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−18.9975	+	18.9975i	−0.656648	+	0.656648i
$838$		0			0
$839$	−34.7373			−1.19926			−0.599632	−	0.800276i	$-0.704686\pi$
$839$	−34.7373			−1.19926			−0.599632	+	0.800276i	$0.704686\pi$
$840$		0			0
$841$	2.01655			0.0695361
$842$		0			0
$843$	4.26671	−	4.26671i	0.146953	−	0.146953i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−58.5439	+	1.09866i	−2.01159	+	0.0377506i
$848$		0			0
$849$			4.63934i			0.159222i
$850$		0			0
$851$	62.4383			2.14036
$852$		0			0
$853$	28.8464	−	28.8464i	0.987683	−	0.987683i	−0.0122418	−	0.999925i	$-0.503897\pi$
$853$	28.8464	−	28.8464i	0.987683	−	0.987683i	0.999925	+	0.0122418i	$0.00389679\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−5.93614	−	5.93614i	−0.202775	−	0.202775i	0.598413	−	0.801188i	$-0.295798\pi$
$857$	−5.93614	−	5.93614i	−0.202775	−	0.202775i	−0.801188	+	0.598413i	$0.795798\pi$
$858$		0			0
$859$	39.2524			1.33928			0.669638	−	0.742688i	$-0.266449\pi$
$859$	39.2524			1.33928			0.669638	+	0.742688i	$0.266449\pi$
$860$		0			0
$861$	−3.21925	−	3.10065i	−0.109712	−	0.105670i
$862$		0			0
$863$	29.3394	+	29.3394i	0.998723	+	0.998723i	0.999999	−	0.00127595i	$-0.000406149\pi$
$863$	29.3394	+	29.3394i	0.998723	+	0.998723i	−0.00127595	+	0.999999i	$0.500406\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	11.1570	+	11.1570i	0.378912	+	0.378912i
$868$		0			0
$869$		−	6.66999i		−	0.226264i
$870$		0			0
$871$		−	12.4207i		−	0.420858i
$872$		0			0
$873$	−5.59284	+	5.59284i	−0.189289	+	0.189289i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	0.558130	−	0.558130i	0.0188467	−	0.0188467i	−0.697621	−	0.716467i	$-0.745758\pi$
$877$	0.558130	−	0.558130i	0.0188467	−	0.0188467i	0.716467	+	0.697621i	$0.245758\pi$
$878$		0			0
$879$		−	53.3294i		−	1.79876i
$880$		0			0
$881$			43.9605i			1.48107i	0.672019	+	0.740534i	$0.265427\pi$
$881$			43.9605i			1.48107i	−0.672019	+	0.740534i	$0.734573\pi$
$882$		0			0
$883$	22.3788	+	22.3788i	0.753108	+	0.753108i	0.975058	−	0.221950i	$-0.0712423\pi$
$883$	22.3788	+	22.3788i	0.753108	+	0.753108i	−0.221950	+	0.975058i	$0.571242\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−28.0123	−	28.0123i	−0.940560	−	0.940560i	0.0577703	−	0.998330i	$-0.481601\pi$
$887$	−28.0123	−	28.0123i	−0.940560	−	0.940560i	−0.998330	+	0.0577703i	$0.981601\pi$
$888$		0			0
$889$	−14.9290	+	15.5000i	−0.500701	+	0.519854i
$890$		0			0
$891$	−63.2414			−2.11867
$892$		0			0
$893$	9.96298	+	9.96298i	0.333398	+	0.333398i
$894$		0			0
$895$		0			0
$896$		0			0
$897$	−39.2082	+	39.2082i	−1.30912	+	1.30912i
$898$		0			0
$899$	34.7238			1.15810
$900$		0			0
$901$		−	3.19990i		−	0.106604i
$902$		0			0
$903$	−20.0357	+	0.376001i	−0.666747	+	0.0125125i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	20.7686	−	20.7686i	0.689609	−	0.689609i	−0.272537	−	0.962145i	$-0.587863\pi$
$907$	20.7686	−	20.7686i	0.689609	−	0.689609i	0.962145	+	0.272537i	$0.0878626\pi$
$908$		0			0
$909$	−17.1239			−0.567963
$910$		0			0
$911$	9.20686			0.305037			0.152518	−	0.988301i	$-0.451262\pi$
$911$	9.20686			0.305037			0.152518	+	0.988301i	$0.451262\pi$
$912$		0			0
$913$	−64.2048	+	64.2048i	−2.12487	+	2.12487i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−0.143376	−	7.63998i	−0.00473469	−	0.252294i
$918$		0			0
$919$		−	12.0883i		−	0.398756i	−0.979923	−	0.199378i	$-0.936108\pi$
$919$		−	12.0883i		−	0.398756i	0.979923	−	0.199378i	$-0.0638922\pi$
$920$		0			0
$921$	38.1205			1.25611
$922$		0			0
$923$	−7.08774	+	7.08774i	−0.233296	+	0.233296i
$924$		0			0
$925$		0			0
$926$		0			0
$927$	0.930116	+	0.930116i	0.0305490	+	0.0305490i
$928$		0			0
$929$	−11.3052			−0.370912			−0.185456	−	0.982653i	$-0.559376\pi$
$929$	−11.3052			−0.370912			−0.185456	+	0.982653i	$0.559376\pi$
$930$		0			0
$931$	15.3137	−	0.574972i	0.501887	−	0.0188440i
$932$		0			0
$933$	−35.1070	−	35.1070i	−1.14935	−	1.14935i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−1.10705	−	1.10705i	−0.0361656	−	0.0361656i	0.688793	−	0.724958i	$-0.258141\pi$
$937$	−1.10705	−	1.10705i	−0.0361656	−	0.0361656i	−0.724958	+	0.688793i	$0.758141\pi$
$938$		0			0
$939$		−	1.58609i		−	0.0517602i
$940$		0			0
$941$			12.0730i			0.393570i	0.980447	+	0.196785i	$0.0630500\pi$
$941$			12.0730i			0.393570i	−0.980447	+	0.196785i	$0.936950\pi$
$942$		0			0
$943$	4.05963	−	4.05963i	0.132200	−	0.132200i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	24.6928	−	24.6928i	0.802408	−	0.802408i	−0.181063	−	0.983471i	$-0.557954\pi$
$947$	24.6928	−	24.6928i	0.802408	−	0.802408i	0.983471	+	0.181063i	$0.0579538\pi$
$948$		0			0
$949$			20.3371i			0.660169i
$950$		0			0
$951$			43.7826i			1.41975i
$952$		0			0
$953$	−13.1077	−	13.1077i	−0.424600	−	0.424600i	0.462184	−	0.886784i	$-0.347066\pi$
$953$	−13.1077	−	13.1077i	−0.424600	−	0.424600i	−0.886784	+	0.462184i	$0.847066\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	42.2171	+	42.2171i	1.36469	+	1.36469i
$958$		0			0
$959$	−1.96228	+	2.03734i	−0.0633653	+	0.0657890i
$960$		0			0
$961$	−13.6846			−0.441437
$962$		0			0
$963$	1.85526	+	1.85526i	0.0597850	+	0.0597850i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−10.3836	+	10.3836i	−0.333913	+	0.333913i	−0.854071	−	0.520157i	$-0.825873\pi$
$967$	−10.3836	+	10.3836i	−0.333913	+	0.333913i	0.520157	+	0.854071i	$0.325873\pi$
$968$		0			0
$969$	13.1856			0.423583
$970$		0			0
$971$			27.6210i			0.886400i	0.896423	+	0.443200i	$0.146157\pi$
$971$			27.6210i			0.886400i	−0.896423	+	0.443200i	$0.853843\pi$
$972$		0			0
$973$	−34.6032	+	0.649381i	−1.10933	+	0.0208182i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	1.79030	−	1.79030i	0.0572768	−	0.0572768i	−0.677888	−	0.735165i	$-0.737105\pi$
$977$	1.79030	−	1.79030i	0.0572768	−	0.0572768i	0.735165	+	0.677888i	$0.237105\pi$
$978$		0			0
$979$	−32.0677			−1.02489
$980$		0			0
$981$	−11.8212			−0.377423
$982$		0			0
$983$	−23.1547	+	23.1547i	−0.738521	+	0.738521i	−0.972292	−	0.233771i	$-0.924894\pi$
$983$	−23.1547	+	23.1547i	−0.738521	+	0.738521i	0.233771	+	0.972292i	$0.424894\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	33.9957	−	0.637980i	1.08209	−	0.0203071i
$988$		0			0
$989$		−	25.7401i		−	0.818489i
$990$		0			0
$991$	7.57676			0.240684			0.120342	−	0.992733i	$-0.461601\pi$
$991$	7.57676			0.240684			0.120342	+	0.992733i	$0.461601\pi$
$992$		0			0
$993$	9.23617	−	9.23617i	0.293101	−	0.293101i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	0.450741	+	0.450741i	0.0142751	+	0.0142751i	0.714208	−	0.699933i	$-0.246787\pi$
$997$	0.450741	+	0.450741i	0.0142751	+	0.0142751i	−0.699933	+	0.714208i	$0.746787\pi$
$998$		0			0
$999$	−36.9802			−1.17000

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1400.2.x.b.993.3		24
5.2	odd	4	inner	1400.2.x.b.657.10		24
5.3	odd	4		280.2.x.a.97.3	✓	24
5.4	even	2		280.2.x.a.153.10	yes	24
7.6	odd	2	inner	1400.2.x.b.993.10		24
20.3	even	4		560.2.bj.d.97.10		24
20.19	odd	2		560.2.bj.d.433.3		24
35.13	even	4		280.2.x.a.97.10	yes	24
35.27	even	4	inner	1400.2.x.b.657.3		24
35.34	odd	2		280.2.x.a.153.3	yes	24
140.83	odd	4		560.2.bj.d.97.3		24
140.139	even	2		560.2.bj.d.433.10		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
280.2.x.a.97.3	✓	24	5.3	odd	4
280.2.x.a.97.10	yes	24	35.13	even	4
280.2.x.a.153.3	yes	24	35.34	odd	2
280.2.x.a.153.10	yes	24	5.4	even	2
560.2.bj.d.97.3		24	140.83	odd	4
560.2.bj.d.97.10		24	20.3	even	4
560.2.bj.d.433.3		24	20.19	odd	2
560.2.bj.d.433.10		24	140.139	even	2
1400.2.x.b.657.3		24	35.27	even	4	inner
1400.2.x.b.657.10		24	5.2	odd	4	inner
1400.2.x.b.993.3		24	1.1	even	1	trivial
1400.2.x.b.993.10		24	7.6	odd	2	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:	\( N \)	\(=\)	\( 1400 = 2^{3} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1400.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.41195 + 1.41195i) q^{3} +(-2.64529 + 0.0496428i) q^{7} -0.987218i q^{9} +O(q^{10})\)	\(q+(-1.41195 + 1.41195i) q^{3} +(-2.64529 + 0.0496428i) q^{7} -0.987218i q^{9} -5.75599 q^{11} +(2.89353 - 2.89353i) q^{13} +(-2.13286 - 2.13286i) q^{17} +2.18921 q^{19} +(3.66492 - 3.80511i) q^{21} +(4.79842 + 4.79842i) q^{23} +(-2.84195 - 2.84195i) q^{27} +5.19456i q^{29} -6.68465i q^{31} +(8.12718 - 8.12718i) q^{33} +(6.50613 - 6.50613i) q^{37} +8.17106i q^{39} -0.846034i q^{41} +(-2.68215 - 2.68215i) q^{43} +(4.55094 + 4.55094i) q^{47} +(6.99507 - 0.262639i) q^{49} +6.02299 q^{51} +(0.750143 + 0.750143i) q^{53} +(-3.09107 + 3.09107i) q^{57} +4.25478 q^{59} +7.62115i q^{61} +(0.0490083 + 2.61147i) q^{63} +(2.14628 - 2.14628i) q^{67} -13.5503 q^{69} -2.44951 q^{71} +(-3.51423 + 3.51423i) q^{73} +(15.2262 - 0.285743i) q^{77} +1.15879i q^{79} +10.9871 q^{81} +(11.1544 - 11.1544i) q^{83} +(-7.33447 - 7.33447i) q^{87} +5.57119 q^{89} +(-7.51057 + 7.79786i) q^{91} +(9.43841 + 9.43841i) q^{93} +(-5.66525 - 5.66525i) q^{97} +5.68242i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{7}+O(q^{10}) \) 24 * q - 4 * q^7	\( 24 q - 4 q^{7} + 8 q^{11} + 16 q^{21} + 32 q^{23} + 8 q^{37} - 16 q^{43} - 24 q^{51} + 16 q^{53} - 20 q^{63} + 32 q^{67} - 32 q^{71} + 40 q^{77} - 72 q^{81} - 64 q^{91} - 72 q^{93}+O(q^{100}) \) 24 * q - 4 * q^7 + 8 * q^11 + 16 * q^21 + 32 * q^23 + 8 * q^37 - 16 * q^43 - 24 * q^51 + 16 * q^53 - 20 * q^63 + 32 * q^67 - 32 * q^71 + 40 * q^77 - 72 * q^81 - 64 * q^91 - 72 * q^93

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