LMFDB - Embedded newform 700.5.o.c.649.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [700,5,Mod(549,700)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(700, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("700.549");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 700 = 2^{2} \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	700.o (of order $6$, 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:	$72.3589741587$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			649.16
Character	$\chi$	$=$	700.649
Dual form			700.5.o.c.549.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.90019 + 6.75532i) q^{3} +(-42.4445 - 24.4840i) q^{7} +(10.0771 - 17.4540i) q^{9} +(43.4634 + 75.2808i) q^{11} -96.0363 q^{13} +(-137.604 - 238.338i) q^{17} +(591.243 + 341.355i) q^{19} +(-0.144398 - 382.218i) q^{21} +(564.591 + 325.967i) q^{23} +789.040 q^{27} -1567.32 q^{29} +(-431.771 + 249.283i) q^{31} +(-339.031 + 587.219i) q^{33} +(-2316.59 - 1337.48i) q^{37} +(-374.560 - 648.756i) q^{39} +2424.75i q^{41} +1217.90i q^{43} +(634.569 - 1099.11i) q^{47} +(1202.07 + 2078.42i) q^{49} +(1073.37 - 1859.12i) q^{51} +(2200.20 - 1270.29i) q^{53} +5325.39i q^{57} +(-5499.15 + 3174.93i) q^{59} +(-4319.72 - 2493.99i) q^{61} +(-855.059 + 494.099i) q^{63} +(-2481.53 + 1432.71i) q^{67} +5085.33i q^{69} -3838.27 q^{71} +(1029.26 + 1782.73i) q^{73} +(-1.60917 - 4259.41i) q^{77} +(-1886.38 + 3267.30i) q^{79} +(2261.16 + 3916.45i) q^{81} -9810.30 q^{83} +(-6112.84 - 10587.8i) q^{87} +(-2862.93 - 1652.91i) q^{89} +(4076.21 + 2351.35i) q^{91} +(-3367.98 - 1944.50i) q^{93} -9079.39 q^{97} +1751.93 q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 684 q^{9} - 300 q^{11} + 540 q^{19} - 190 q^{21} - 528 q^{29} - 2334 q^{31} - 852 q^{39} + 4092 q^{49} - 3902 q^{51} + 9414 q^{59} - 23598 q^{61} + 32820 q^{71} - 4890 q^{79} - 23710 q^{81} - 37764 q^{89}+ \cdots + 168180 q^{99}+O(q^{100}) $ 44 * q - 684 * q^9 - 300 * q^11 + 540 * q^19 - 190 * q^21 - 528 * q^29 - 2334 * q^31 - 852 * q^39 + 4092 * q^49 - 3902 * q^51 + 9414 * q^59 - 23598 * q^61 + 32820 * q^71 - 4890 * q^79 - 23710 * q^81 - 37764 * q^89 + 6418 * q^91 + 168180 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/700\mathbb{Z}\right)^\times$.

$n$	$101$	$351$	$477$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	3.90019	+	6.75532i	0.433354	+	0.750592i	0.997160	−	0.0753161i	$-0.0239966\pi$
$3$	3.90019	+	6.75532i	0.433354	+	0.750592i	−0.563805	+	0.825908i	$0.690663\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	−42.4445	−	24.4840i	−0.866214	−	0.499673i
$7$	−42.4445	−	24.4840i	−0.866214	−	0.499673i
$8$		0			0
$9$	10.0771	−	17.4540i	0.124408	−	0.215481i
$10$		0			0
$11$	43.4634	+	75.2808i	0.359202	+	0.622156i	0.987828	−	0.155552i	$-0.0497157\pi$
$11$	43.4634	+	75.2808i	0.359202	+	0.622156i	−0.628626	+	0.777708i	$0.716382\pi$
$12$		0			0
$13$	−96.0363			−0.568262			−0.284131	−	0.958785i	$-0.591705\pi$
$13$	−96.0363			−0.568262			−0.284131	+	0.958785i	$0.591705\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−137.604	−	238.338i	−0.476140	−	0.824698i	0.523487	−	0.852034i	$-0.324631\pi$
$17$	−137.604	−	238.338i	−0.476140	−	0.824698i	−0.999626	+	0.0273359i	$0.991298\pi$
$18$		0			0
$19$	591.243	+	341.355i	1.63779	+	0.945581i	0.981591	+	0.190996i	$0.0611718\pi$
$19$	591.243	+	341.355i	1.63779	+	0.945581i	0.656203	+	0.754585i	$0.272162\pi$
$20$		0			0
$21$	−0.144398	−	382.218i	−0.000327434	−	0.866708i
$22$		0			0
$23$	564.591	+	325.967i	1.06728	+	0.616194i	0.927437	−	0.373979i	$-0.122007\pi$
$23$	564.591	+	325.967i	1.06728	+	0.616194i	0.139843	+	0.990174i	$0.455340\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	789.040			1.08236
$28$		0			0
$29$	−1567.32			−1.86364			−0.931819	−	0.362923i	$-0.881779\pi$
$29$	−1567.32			−1.86364			−0.931819	+	0.362923i	$0.881779\pi$
$30$		0			0
$31$	−431.771	+	249.283i	−0.449293	+	0.259400i	−0.707532	−	0.706682i	$-0.750191\pi$
$31$	−431.771	+	249.283i	−0.449293	+	0.259400i	0.258238	+	0.966081i	$0.416858\pi$
$32$		0			0
$33$	−339.031	+	587.219i	−0.311323	+	0.539228i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−2316.59	−	1337.48i	−1.69217	−	0.976977i	−0.952760	−	0.303725i	$-0.901769\pi$
$37$	−2316.59	−	1337.48i	−1.69217	−	0.976977i	−0.739414	−	0.673251i	$-0.764897\pi$
$38$		0			0
$39$	−374.560	−	648.756i	−0.246259	−	0.426533i
$40$		0			0
$41$			2424.75i			1.44244i	0.692704	+	0.721222i	$0.256419\pi$
$41$			2424.75i			1.44244i	−0.692704	+	0.721222i	$0.743581\pi$
$42$		0			0
$43$			1217.90i			0.658679i	0.944212	+	0.329339i	$0.106826\pi$
$43$			1217.90i			0.658679i	−0.944212	+	0.329339i	$0.893174\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	634.569	−	1099.11i	0.287265	−	0.497558i	−0.685891	−	0.727705i	$-0.740587\pi$
$47$	634.569	−	1099.11i	0.287265	−	0.497558i	0.973156	+	0.230147i	$0.0739205\pi$
$48$		0			0
$49$	1202.07	+	2078.42i	0.500654	+	0.865647i
$50$		0			0
$51$	1073.37	−	1859.12i	0.412674	−	0.714773i
$52$		0			0
$53$	2200.20	−	1270.29i	0.783269	−	0.452221i	−0.0543185	−	0.998524i	$-0.517299\pi$
$53$	2200.20	−	1270.29i	0.783269	−	0.452221i	0.837588	+	0.546303i	$0.183965\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$			5325.39i			1.63909i
$58$		0			0
$59$	−5499.15	+	3174.93i	−1.57976	+	0.912075i	−0.584869	+	0.811127i	$0.698854\pi$
$59$	−5499.15	+	3174.93i	−1.57976	+	0.912075i	−0.994892	+	0.100948i	$0.967812\pi$
$60$		0			0
$61$	−4319.72	−	2493.99i	−1.16090	−	0.670248i	−0.209384	−	0.977834i	$-0.567146\pi$
$61$	−4319.72	−	2493.99i	−1.16090	−	0.670248i	−0.951521	+	0.307585i	$0.900479\pi$
$62$		0			0
$63$	−855.059	+	494.099i	−0.215434	+	0.124490i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−2481.53	+	1432.71i	−0.552803	+	0.319161i	−0.750252	−	0.661152i	$-0.770068\pi$
$67$	−2481.53	+	1432.71i	−0.552803	+	0.319161i	0.197449	+	0.980313i	$0.436734\pi$
$68$		0			0
$69$			5085.33i			1.06812i
$70$		0			0
$71$	−3838.27			−0.761410			−0.380705	−	0.924696i	$-0.624319\pi$
$71$	−3838.27			−0.761410			−0.380705	+	0.924696i	$0.624319\pi$
$72$		0			0
$73$	1029.26	+	1782.73i	0.193144	+	0.334534i	0.946290	−	0.323318i	$-0.104798\pi$
$73$	1029.26	+	1782.73i	0.193144	+	0.334534i	−0.753147	+	0.657852i	$0.771465\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$	−1.60917	−	4259.41i	−0.000271406	−	0.718404i
$78$		0			0
$79$	−1886.38	+	3267.30i	−0.302256	+	0.523522i	−0.976647	−	0.214852i	$-0.931073\pi$
$79$	−1886.38	+	3267.30i	−0.302256	+	0.523522i	0.674391	+	0.738375i	$0.264406\pi$
$80$		0			0
$81$	2261.16	+	3916.45i	0.344637	+	0.596929i
$82$		0			0
$83$	−9810.30			−1.42405			−0.712027	−	0.702152i	$-0.752223\pi$
$83$	−9810.30			−1.42405			−0.712027	+	0.702152i	$0.752223\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−6112.84	−	10587.8i	−0.807615	−	1.39883i
$88$		0			0
$89$	−2862.93	−	1652.91i	−0.361435	−	0.208675i	0.308275	−	0.951297i	$-0.400248\pi$
$89$	−2862.93	−	1652.91i	−0.361435	−	0.208675i	−0.669710	+	0.742623i	$0.733582\pi$
$90$		0			0
$91$	4076.21	+	2351.35i	0.492237	+	0.283945i
$92$		0			0
$93$	−3367.98	−	1944.50i	−0.389406	−	0.224824i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−9079.39			−0.964968			−0.482484	−	0.875905i	$-0.660265\pi$
$97$	−9079.39			−0.964968			−0.482484	+	0.875905i	$0.660265\pi$
$98$		0			0
$99$	1751.93			0.178751
$100$		0			0
$101$	9553.75	−	5515.86i	0.936550	−	0.540718i	0.0476730	−	0.998863i	$-0.484819\pi$
$101$	9553.75	−	5515.86i	0.936550	−	0.540718i	0.888877	+	0.458145i	$0.151486\pi$
$102$		0			0
$103$	1662.25	−	2879.10i	0.156683	−	0.271383i	−0.776988	−	0.629516i	$-0.783253\pi$
$103$	1662.25	−	2879.10i	0.156683	−	0.271383i	0.933671	+	0.358133i	$0.116587\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$	5122.23	+	2957.32i	0.447395	+	0.258304i	0.706730	−	0.707484i	$-0.250170\pi$
$107$	5122.23	+	2957.32i	0.447395	+	0.258304i	−0.259334	+	0.965788i	$0.583503\pi$
$108$		0			0
$109$	5832.79	+	10102.7i	0.490934	+	0.850323i	0.999946	−	0.0104368i	$-0.00332220\pi$
$109$	5832.79	+	10102.7i	0.490934	+	0.850323i	−0.509011	+	0.860760i	$0.669989\pi$
$110$		0			0
$111$		−	20865.7i		−	1.69351i
$112$		0			0
$113$		−	9410.74i		−	0.736999i	−0.929628	−	0.368499i	$-0.879872\pi$
$113$		−	9410.74i		−	0.736999i	0.929628	−	0.368499i	$-0.120128\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	−967.764	+	1676.22i	−0.0706965	+	0.122450i
$118$		0			0
$119$	5.09459	+	13485.2i	0.000359762	+	0.952279i
$120$		0			0
$121$	3542.36	−	6135.55i	0.241948	−	0.419067i
$122$		0			0
$123$	−16380.0	+	9456.97i	−1.08269	+	0.625089i
$124$		0			0
$125$		0			0
$126$		0			0
$127$		−	29678.9i		−	1.84009i	−0.391809	−	0.920046i	$-0.628151\pi$
$127$		−	29678.9i		−	1.84009i	0.391809	−	0.920046i	$-0.371849\pi$
$128$		0			0
$129$	−8227.29	+	4750.03i	−0.494399	+	0.285441i
$130$		0			0
$131$	9188.13	+	5304.77i	0.535408	+	0.309118i	0.743216	−	0.669052i	$-0.233300\pi$
$131$	9188.13	+	5304.77i	0.535408	+	0.309118i	−0.207808	+	0.978170i	$0.566633\pi$
$132$		0			0
$133$	−16737.3	−	28964.6i	−0.946199	−	1.63744i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−18772.6	+	10838.4i	−1.00019	+	0.577461i	−0.908305	−	0.418309i	$-0.862623\pi$
$137$	−18772.6	+	10838.4i	−1.00019	+	0.577461i	−0.0918864	+	0.995769i	$0.529290\pi$
$138$		0			0
$139$		−	412.731i		−	0.0213618i	−0.999943	−	0.0106809i	$-0.996600\pi$
$139$		−	412.731i		−	0.0213618i	0.999943	−	0.0106809i	$-0.00339990\pi$
$140$		0			0
$141$	9899.75			0.497950
$142$		0			0
$143$	−4174.07	−	7229.69i	−0.204121	−	0.353548i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−9352.09	+	16226.6i	−0.432787	+	0.750919i
$148$		0			0
$149$	−19021.5	+	32946.2i	−0.856786	+	1.48400i	0.0181929	+	0.999834i	$0.494209\pi$
$149$	−19021.5	+	32946.2i	−0.856786	+	1.48400i	−0.874979	+	0.484162i	$0.839125\pi$
$150$		0			0
$151$	1709.25	+	2960.51i	0.0749639	+	0.129841i	0.901071	−	0.433673i	$-0.142783\pi$
$151$	1709.25	+	2960.51i	0.0749639	+	0.129841i	−0.826107	+	0.563514i	$0.809449\pi$
$152$		0			0
$153$	−5546.59			−0.236943
$154$		0			0
$155$		0			0
$156$		0			0
$157$	17789.0	+	30811.5i	0.721694	+	1.25001i	0.960321	+	0.278899i	$0.0899693\pi$
$157$	17789.0	+	30811.5i	0.721694	+	1.25001i	−0.238627	+	0.971111i	$0.576697\pi$
$158$		0			0
$159$	17162.4	+	9908.72i	0.678866	+	0.391943i
$160$		0			0
$161$	−15982.8	−	27658.9i	−0.616598	−	1.06705i
$162$		0			0
$163$	−44412.5	−	25641.6i	−1.67159	−	0.965093i	−0.966749	−	0.255729i	$-0.917685\pi$
$163$	−44412.5	−	25641.6i	−1.67159	−	0.965093i	−0.704842	−	0.709365i	$-0.748982\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	−28151.1			−1.00940			−0.504700	−	0.863295i	$-0.668397\pi$
$167$	−28151.1			−1.00940			−0.504700	+	0.863295i	$0.668397\pi$
$168$		0			0
$169$	−19338.0			−0.677078
$170$		0			0
$171$	11916.0	−	6879.71i	0.407510	−	0.235276i
$172$		0			0
$173$	−13435.4	+	23270.8i	−0.448909	+	0.777533i	−0.998315	−	0.0580223i	$-0.981521\pi$
$173$	−13435.4	+	23270.8i	−0.448909	+	0.777533i	0.549406	+	0.835555i	$0.314854\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−42895.4	−	24765.7i	−1.36919	−	0.790504i
$178$		0			0
$179$	19587.1	+	33925.9i	0.611315	+	1.05883i	0.991019	+	0.133720i	$0.0426924\pi$
$179$	19587.1	+	33925.9i	0.611315	+	1.05883i	−0.379704	+	0.925108i	$0.623974\pi$
$180$		0			0
$181$		−	17960.6i		−	0.548231i	−0.961697	−	0.274115i	$-0.911615\pi$
$181$		−	17960.6i		−	0.548231i	0.961697	−	0.274115i	$-0.0883850\pi$
$182$		0			0
$183$		−	38908.2i		−	1.16182i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	11961.5	−	20717.9i	0.342060	−	0.592466i
$188$		0			0
$189$	−33490.4	−	19318.8i	−0.937555	−	0.540826i
$190$		0			0
$191$	−6606.98	+	11443.6i	−0.181107	+	0.313687i	−0.942258	−	0.334888i	$-0.891301\pi$
$191$	−6606.98	+	11443.6i	−0.181107	+	0.313687i	0.761151	+	0.648575i	$0.224635\pi$
$192$		0			0
$193$	−15888.3	+	9173.09i	−0.426542	+	0.246264i	−0.697872	−	0.716222i	$-0.745870\pi$
$193$	−15888.3	+	9173.09i	−0.426542	+	0.246264i	0.271331	+	0.962486i	$0.412536\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$			2088.11i			0.0538048i	0.999638	+	0.0269024i	$0.00856434\pi$
$197$			2088.11i			0.0538048i	−0.999638	+	0.0269024i	$0.991436\pi$
$198$		0			0
$199$	−32781.3	+	18926.3i	−0.827790	+	0.477925i	−0.853095	−	0.521755i	$-0.825278\pi$
$199$	−32781.3	+	18926.3i	−0.827790	+	0.477925i	0.0253053	+	0.999680i	$0.491944\pi$
$200$		0			0
$201$	−19356.9	−	11175.7i	−0.479119	−	0.276620i
$202$		0			0
$203$	66524.1	+	38374.2i	1.61431	+	0.931209i
$204$		0			0
$205$		0			0
$206$		0			0
$207$	11378.8	−	6569.58i	0.265557	−	0.153319i
$208$		0			0
$209$			59345.7i			1.35862i
$210$		0			0
$211$	−17846.4			−0.400854			−0.200427	−	0.979709i	$-0.564233\pi$
$211$	−17846.4			−0.400854			−0.200427	+	0.979709i	$0.564233\pi$
$212$		0			0
$213$	−14970.0	−	25928.8i	−0.329960	−	0.571508i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	24429.7	−	9.22932i	0.518799	−	0.000195997i
$218$		0			0
$219$	−8028.63	+	13906.0i	−0.167399	+	0.289944i
$220$		0			0
$221$	13215.0	+	22889.1i	0.270572	+	0.468645i
$222$		0			0
$223$	−40705.2			−0.818541			−0.409270	−	0.912413i	$-0.634217\pi$
$223$	−40705.2			−0.818541			−0.409270	+	0.912413i	$0.634217\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−22255.9	−	38548.3i	−0.431910	−	0.748090i	0.565128	−	0.825003i	$-0.308827\pi$
$227$	−22255.9	−	38548.3i	−0.431910	−	0.748090i	−0.997038	+	0.0769134i	$0.975493\pi$
$228$		0			0
$229$	−12311.4	−	7107.98i	−0.234766	−	0.135542i	0.378003	−	0.925805i	$-0.376611\pi$
$229$	−12311.4	−	7107.98i	−0.234766	−	0.135542i	−0.612769	+	0.790262i	$0.709944\pi$
$230$		0			0
$231$	28767.4	−	16623.4i	0.539110	−	0.311527i
$232$		0			0
$233$	32267.0	+	18629.3i	0.594355	+	0.343151i	0.766818	−	0.641865i	$-0.221839\pi$
$233$	32267.0	+	18629.3i	0.594355	+	0.343151i	−0.172462	+	0.985016i	$0.555172\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$	−29428.9			−0.523935
$238$		0			0
$239$	15939.9			0.279055			0.139527	−	0.990218i	$-0.455442\pi$
$239$	15939.9			0.279055			0.139527	+	0.990218i	$0.455442\pi$
$240$		0			0
$241$	55441.8	−	32009.3i	0.954560	−	0.551115i	0.0600654	−	0.998194i	$-0.480869\pi$
$241$	55441.8	−	32009.3i	0.954560	−	0.551115i	0.894494	+	0.447079i	$0.147536\pi$
$242$		0			0
$243$	14318.2	−	24799.9i	0.242480	−	0.419988i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−56780.8	−	32782.4i	−0.930696	−	0.537338i
$248$		0			0
$249$	−38262.0	−	66271.8i	−0.617120	−	1.06888i
$250$		0			0
$251$			93024.3i			1.47655i	0.674499	+	0.738276i	$0.264360\pi$
$251$			93024.3i			1.47655i	−0.674499	+	0.738276i	$0.735640\pi$
$252$		0			0
$253$			56670.5i			0.885353i
$254$		0			0
$255$		0			0
$256$		0			0
$257$	−7125.99	+	12342.6i	−0.107890	+	0.186870i	−0.914915	−	0.403646i	$-0.867743\pi$
$257$	−7125.99	+	12342.6i	−0.107890	+	0.186870i	0.807026	+	0.590517i	$0.201076\pi$
$258$		0			0
$259$	65579.5	+	113488.i	0.977616	+	1.69180i
$260$		0			0
$261$	−15794.0	+	27356.0i	−0.231852	+	0.401579i
$262$		0			0
$263$	−42188.6	+	24357.6i	−0.609935	+	0.352146i	−0.772940	−	0.634479i	$-0.781215\pi$
$263$	−42188.6	+	24357.6i	−0.609935	+	0.352146i	0.163005	+	0.986625i	$0.447881\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$		−	25786.7i		−	0.361720i
$268$		0			0
$269$	7995.48	−	4616.19i	0.110494	−	0.0637939i	−0.443734	−	0.896158i	$-0.646347\pi$
$269$	7995.48	−	4616.19i	0.110494	−	0.0637939i	0.554229	+	0.832364i	$0.313013\pi$
$270$		0			0
$271$	−25894.9	−	14950.4i	−0.352595	−	0.203571i	0.313233	−	0.949676i	$-0.398588\pi$
$271$	−25894.9	−	14950.4i	−0.352595	−	0.203571i	−0.665828	+	0.746106i	$0.731921\pi$
$272$		0			0
$273$	13.8675	+	36706.8i	0.000186068	+	0.492518i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−71484.0	+	41271.3i	−0.931643	+	0.537884i	−0.887331	−	0.461133i	$-0.847443\pi$
$277$	−71484.0	+	41271.3i	−0.931643	+	0.537884i	−0.0443122	+	0.999018i	$0.514110\pi$
$278$		0			0
$279$			10048.2i			0.129086i
$280$		0			0
$281$	−99980.5			−1.26620			−0.633101	−	0.774069i	$-0.718218\pi$
$281$	−99980.5			−1.26620			−0.633101	+	0.774069i	$0.718218\pi$
$282$		0			0
$283$	52882.1	+	91594.4i	0.660291	+	1.14366i	0.980539	+	0.196324i	$0.0629004\pi$
$283$	52882.1	+	91594.4i	0.660291	+	1.14366i	−0.320248	+	0.947334i	$0.603766\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	59367.5	−	102917.i	0.720750	−	1.24947i
$288$		0			0
$289$	3890.59	−	6738.70i	0.0465822	−	0.0806828i
$290$		0			0
$291$	−35411.3	−	61334.2i	−0.418173	−	0.724297i
$292$		0			0
$293$	44148.4			0.514256			0.257128	−	0.966377i	$-0.417224\pi$
$293$	44148.4			0.514256			0.257128	+	0.966377i	$0.417224\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	34294.4	+	59399.6i	0.388786	+	0.673396i
$298$		0			0
$299$	−54221.3	−	31304.7i	−0.606495	−	0.350160i
$300$		0			0
$301$	29819.0	−	51693.0i	0.329124	−	0.570557i
$302$		0			0
$303$	74522.8	+	43025.8i	0.811716	+	0.468644i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	127957.			1.35765			0.678824	−	0.734301i	$-0.262490\pi$
$307$	127957.			1.35765			0.678824	+	0.734301i	$0.262490\pi$
$308$		0			0
$309$	25932.3			0.271597
$310$		0			0
$311$	77050.7	−	44485.2i	0.796628	−	0.459934i	−0.0456624	−	0.998957i	$-0.514540\pi$
$311$	77050.7	−	44485.2i	0.796628	−	0.459934i	0.842291	+	0.539023i	$0.181207\pi$
$312$		0			0
$313$	8978.22	−	15550.7i	0.0916435	−	0.158731i	−0.816559	−	0.577262i	$-0.804121\pi$
$313$	8978.22	−	15550.7i	0.0916435	−	0.158731i	0.908203	+	0.418530i	$0.137455\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$	81549.8	+	47082.8i	0.811530	+	0.468537i	0.847487	−	0.530816i	$-0.178115\pi$
$317$	81549.8	+	47082.8i	0.811530	+	0.468537i	−0.0359570	+	0.999353i	$0.511448\pi$
$318$		0			0
$319$	−68121.1	−	117989.i	−0.669422	−	1.15947i
$320$		0			0
$321$			46136.4i			0.447748i
$322$		0			0
$323$		−	187887.i		−	1.80091i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−45498.0	+	78804.8i	−0.425497	+	0.736982i
$328$		0			0
$329$	−53844.4	+	31114.2i	−0.497449	+	0.287453i
$330$		0			0
$331$	−104990.	+	181848.i	−0.958276	+	1.65978i	−0.231590	+	0.972813i	$0.574393\pi$
$331$	−104990.	+	181848.i	−0.958276	+	1.65978i	−0.726686	+	0.686970i	$0.758940\pi$
$332$		0			0
$333$	−46688.8	+	26955.8i	−0.421041	+	0.243088i
$334$		0			0
$335$		0			0
$336$		0			0
$337$			85225.8i			0.750432i	0.926937	+	0.375216i	$0.122431\pi$
$337$			85225.8i			0.750432i	−0.926937	+	0.375216i	$0.877569\pi$
$338$		0			0
$339$	63572.6	−	36703.6i	0.553185	−	0.319382i
$340$		0			0
$341$	−37532.5	−	21669.4i	−0.322774	−	0.186354i
$342$		0			0
$343$	−133.340	−	117649.i	−0.00113337	−	0.999999i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	12700.9	−	7332.85i	0.105481	−	0.0608995i	−0.446331	−	0.894868i	$-0.647270\pi$
$347$	12700.9	−	7332.85i	0.105481	−	0.0608995i	0.551812	+	0.833968i	$0.313936\pi$
$348$		0			0
$349$		−	184573.i		−	1.51537i	−0.652622	−	0.757684i	$-0.726331\pi$
$349$		−	184573.i		−	1.51537i	0.652622	−	0.757684i	$-0.273669\pi$
$350$		0			0
$351$	−75776.5			−0.615064
$352$		0			0
$353$	−34274.1	−	59364.5i	−0.275053	−	0.476406i	0.695095	−	0.718917i	$-0.255362\pi$
$353$	−34274.1	−	59364.5i	−0.275053	−	0.476406i	−0.970149	+	0.242512i	$0.922029\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−91077.2	+	52629.3i	−0.714617	+	0.412944i
$358$		0			0
$359$	102011.	−	176688.i	0.791511	−	1.37094i	−0.133521	−	0.991046i	$-0.542628\pi$
$359$	102011.	−	176688.i	0.791511	−	1.37094i	0.925031	−	0.379891i	$-0.124038\pi$
$360$		0			0
$361$	167885.	+	290786.i	1.28825	+	2.23131i
$362$		0			0
$363$	55263.5			0.419397
$364$		0			0
$365$		0			0
$366$		0			0
$367$	78767.7	+	136430.i	0.584812	+	1.01292i	0.994899	+	0.100877i	$0.0321650\pi$
$367$	78767.7	+	136430.i	0.584812	+	1.01292i	−0.410087	+	0.912046i	$0.634502\pi$
$368$		0			0
$369$	42321.5	+	24434.3i	0.310820	+	0.179452i
$370$		0			0
$371$	−124488.	+	47.0305i	−0.904441	+	0.000341689i
$372$		0			0
$373$	79861.1	+	46107.8i	0.574007	+	0.331403i	0.758748	−	0.651384i	$-0.225811\pi$
$373$	79861.1	+	46107.8i	0.574007	+	0.331403i	−0.184741	+	0.982787i	$0.559145\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	150520.			1.05904
$378$		0			0
$379$	202448.			1.40940			0.704702	−	0.709503i	$-0.251081\pi$
$379$	202448.			1.40940			0.704702	+	0.709503i	$0.251081\pi$
$380$		0			0
$381$	200490.	−	115753.i	1.38116	−	0.797412i
$382$		0			0
$383$	−69653.8	+	120644.i	−0.474840	+	0.822446i	−0.999585	−	0.0288130i	$-0.990827\pi$
$383$	−69653.8	+	120644.i	−0.474840	+	0.822446i	0.524745	+	0.851259i	$0.324161\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	21257.2	+	12272.8i	0.141933	+	0.0819451i
$388$		0			0
$389$	2378.96	+	4120.48i	0.0157213	+	0.0272301i	0.873779	−	0.486323i	$-0.161662\pi$
$389$	2378.96	+	4120.48i	0.0157213	+	0.0272301i	−0.858058	+	0.513553i	$0.828329\pi$
$390$		0			0
$391$		−	179418.i		−	1.17358i
$392$		0			0
$393$			82758.4i			0.535830i
$394$		0			0
$395$		0			0
$396$		0			0
$397$	138638.	−	240128.i	0.879633	−	1.52357i	0.0278883	−	0.999611i	$-0.491122\pi$
$397$	138638.	−	240128.i	0.879633	−	1.52357i	0.851744	−	0.523957i	$-0.175545\pi$
$398$		0			0
$399$	130387.	−	226033.i	0.819006	−	1.41980i
$400$		0			0
$401$	93734.3	−	162353.i	0.582921	−	1.00965i	−0.412210	−	0.911089i	$-0.635243\pi$
$401$	93734.3	−	162353.i	0.582921	−	1.00965i	0.995131	−	0.0985602i	$-0.0314237\pi$
$402$		0			0
$403$	41465.7	−	23940.2i	0.255316	−	0.147407i
$404$		0			0
$405$		0			0
$406$		0			0
$407$		−	232526.i		−	1.40373i
$408$		0			0
$409$	1786.30	−	1031.32i	0.0106784	−	0.00616521i	−0.494651	−	0.869092i	$-0.664704\pi$
$409$	1786.30	−	1031.32i	0.0106784	−	0.00616521i	0.505330	+	0.862926i	$0.331371\pi$
$410$		0			0
$411$	−146433.	−	84543.3i	−0.866874	−	0.500490i
$412$		0			0
$413$	311144.	−	117.547i	1.82415	−	0.000689147i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	2788.13	−	1609.73i	0.0160340	−	0.00925721i
$418$		0			0
$419$		−	109818.i		−	0.625524i	−0.949832	−	0.312762i	$-0.898746\pi$
$419$		−	109818.i		−	0.625524i	0.949832	−	0.312762i	$-0.101254\pi$
$420$		0			0
$421$	85459.4			0.482165			0.241083	−	0.970505i	$-0.422498\pi$
$421$	85459.4			0.482165			0.241083	+	0.970505i	$0.422498\pi$
$422$		0			0
$423$	−12789.2	−	22151.5i	−0.0714763	−	0.123801i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	122286.	+	211620.i	0.670687	+	1.16065i
$428$		0			0
$429$	32559.3	−	56394.3i	0.176913	−	0.306423i
$430$		0			0
$431$	116210.	+	201281.i	0.625588	+	1.08355i	0.988427	+	0.151698i	$0.0484740\pi$
$431$	116210.	+	201281.i	0.625588	+	1.08355i	−0.362839	+	0.931852i	$0.618193\pi$
$432$		0			0
$433$	−106205.			−0.566462			−0.283231	−	0.959052i	$-0.591406\pi$
$433$	−106205.			−0.566462			−0.283231	+	0.959052i	$0.591406\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	222541.	+	385452.i	1.16532	+	2.01840i
$438$		0			0
$439$	−38310.0	−	22118.3i	−0.198785	−	0.114768i	0.397304	−	0.917687i	$-0.369946\pi$
$439$	−38310.0	−	22118.3i	−0.198785	−	0.114768i	−0.596088	+	0.802919i	$0.703279\pi$
$440$		0			0
$441$	48390.1	−	36.5626i	0.248816	−	0.000188001i
$442$		0			0
$443$	−97622.4	−	56362.3i	−0.497442	−	0.287198i	0.230215	−	0.973140i	$-0.426057\pi$
$443$	−97622.4	−	56362.3i	−0.497442	−	0.287198i	−0.727656	+	0.685942i	$0.759390\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−296750.			−1.48517
$448$		0			0
$449$	196030.			0.972368			0.486184	−	0.873857i	$-0.338389\pi$
$449$	196030.			0.972368			0.486184	+	0.873857i	$0.338389\pi$
$450$		0			0
$451$	−182537.	+	105388.i	−0.897425	+	0.518128i
$452$		0			0
$453$	−13332.8	+	23093.1i	−0.0649718	+	0.112534i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−14191.0	−	8193.15i	−0.0679484	−	0.0392300i	0.465641	−	0.884974i	$-0.345824\pi$
$457$	−14191.0	−	8193.15i	−0.0679484	−	0.0392300i	−0.533589	+	0.845744i	$0.679157\pi$
$458$		0			0
$459$	−108575.	−	188058.i	−0.515354	−	0.892620i
$460$		0			0
$461$			103435.i			0.486704i	0.969938	+	0.243352i	$0.0782469\pi$
$461$			103435.i			0.486704i	−0.969938	+	0.243352i	$0.921753\pi$
$462$		0			0
$463$		−	3367.13i		−	0.0157072i	−0.999969	−	0.00785359i	$-0.997500\pi$
$463$		−	3367.13i		−	0.0157072i	0.999969	−	0.00785359i	$-0.00249990\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	122371.	−	211953.i	0.561108	−	0.971867i	−0.436293	−	0.899805i	$-0.643709\pi$
$467$	122371.	−	211953.i	0.561108	−	0.971867i	0.997400	−	0.0720619i	$-0.0229579\pi$
$468$		0			0
$469$	140406.	−	53.0441i	0.638322	−	0.000241152i
$470$		0			0
$471$	−138761.	+	240341.i	−0.625498	+	1.08339i
$472$		0			0
$473$	−91684.3	+	52934.0i	−0.409801	+	0.236599i
$474$		0			0
$475$		0			0
$476$		0			0
$477$		−	51203.1i		−	0.225040i
$478$		0			0
$479$	257514.	−	148676.i	1.12235	−	0.647992i	0.180354	−	0.983602i	$-0.442276\pi$
$479$	257514.	−	148676.i	1.12235	−	0.647992i	0.942001	+	0.335610i	$0.108942\pi$
$480$		0			0
$481$	222476.	+	128447.i	0.961598	+	0.555179i
$482$		0			0
$483$	124509.	−	215844.i	0.533711	−	0.925222i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	41016.9	−	23681.1i	0.172944	−	0.0998492i	−0.411029	−	0.911622i	$-0.634831\pi$
$487$	41016.9	−	23681.1i	0.172944	−	0.0998492i	0.583973	+	0.811773i	$0.301497\pi$
$488$		0			0
$489$		−	400028.i		−	1.67291i
$490$		0			0
$491$	−98500.3			−0.408578			−0.204289	−	0.978911i	$-0.565488\pi$
$491$	−98500.3			−0.408578			−0.204289	+	0.978911i	$0.565488\pi$
$492$		0			0
$493$	215670.	+	373551.i	0.887352	+	1.53694i
$494$		0			0
$495$		0			0
$496$		0			0
$497$	162913.	+	93976.1i	0.659545	+	0.380456i
$498$		0			0
$499$	−200380.	+	347069.i	−0.804737	+	1.39385i	0.111732	+	0.993738i	$0.464360\pi$
$499$	−200380.	+	347069.i	−0.804737	+	1.39385i	−0.916468	+	0.400107i	$0.868973\pi$
$500$		0			0
$501$	−109795.	−	190170.i	−0.437427	−	0.757647i
$502$		0			0
$503$	−88425.6			−0.349496			−0.174748	−	0.984613i	$-0.555911\pi$
$503$	−88425.6			−0.349496			−0.174748	+	0.984613i	$0.555911\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−75421.9	−	130635.i	−0.293415	−	0.508209i
$508$		0			0
$509$	−153664.	−	88717.7i	−0.593110	−	0.342432i	0.173216	−	0.984884i	$-0.444584\pi$
$509$	−153664.	−	88717.7i	−0.593110	−	0.342432i	−0.766326	+	0.642451i	$0.777917\pi$
$510$		0			0
$511$	−38.1068	−	100868.i	−0.000145936	−	0.386287i
$512$		0			0
$513$	466515.	+	269343.i	1.77268	+	1.02346i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	110322.			0.412745
$518$		0			0
$519$	−209602.			−0.778146
$520$		0			0
$521$	198162.	−	114409.i	0.730038	−	0.421488i	−0.0883980	−	0.996085i	$-0.528175\pi$
$521$	198162.	−	114409.i	0.730038	−	0.421488i	0.818436	+	0.574597i	$0.194841\pi$
$522$		0			0
$523$	−2206.18	+	3821.22i	−0.00806563	+	0.0139701i	−0.870030	−	0.492999i	$-0.835901\pi$
$523$	−2206.18	+	3821.22i	−0.00806563	+	0.0139701i	0.861964	+	0.506969i	$0.169234\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	118827.	+	68604.9i	0.427853	+	0.247021i
$528$		0			0
$529$	72588.3	+	125727.i	0.259391	+	0.449279i
$530$		0			0
$531$			127976.i			0.453879i
$532$		0			0
$533$		−	232864.i		−	0.819686i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	−152787.	+	264635.i	−0.529832	+	0.917695i
$538$		0			0
$539$	−104219.	+	180828.i	−0.358732	+	0.622427i
$540$		0			0
$541$	−242415.	+	419876.i	−0.828258	+	1.43459i	0.0711453	+	0.997466i	$0.477335\pi$
$541$	−242415.	+	419876.i	−0.828258	+	1.43459i	−0.899404	+	0.437119i	$0.855999\pi$
$542$		0			0
$543$	121330.	−	70049.7i	0.411497	−	0.237578i
$544$		0			0
$545$		0			0
$546$		0			0
$547$			208361.i			0.696374i	0.937425	+	0.348187i	$0.113203\pi$
$547$			208361.i			0.696374i	−0.937425	+	0.348187i	$0.886797\pi$
$548$		0			0
$549$	−87060.3	+	50264.3i	−0.288852	+	0.166769i
$550$		0			0
$551$	−926668.	−	535012.i	−3.05225	−	1.76222i
$552$		0			0
$553$	160063.	−	92493.0i	0.523408	−	0.302454i
$554$		0			0
$555$		0			0
$556$		0			0
$557$	−113052.	+	65270.3i	−0.364390	+	0.210381i	−0.671005	−	0.741453i	$-0.734137\pi$
$557$	−113052.	+	65270.3i	−0.364390	+	0.210381i	0.306615	+	0.951834i	$0.400804\pi$
$558$		0			0
$559$		−	116962.i		−	0.374302i
$560$		0			0
$561$	186609.			0.592933
$562$		0			0
$563$	−82840.9	−	143485.i	−0.261353	−	0.452677i	0.705249	−	0.708960i	$-0.250835\pi$
$563$	−82840.9	−	143485.i	−0.261353	−	0.452677i	−0.966602	+	0.256283i	$0.917502\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	−83.7161	−	221594.i	−0.000260401	−	0.689274i
$568$		0			0
$569$	53514.5	−	92689.8i	0.165290	−	0.286291i	−0.771468	−	0.636268i	$-0.780477\pi$
$569$	53514.5	−	92689.8i	0.165290	−	0.286291i	0.936758	+	0.349977i	$0.113811\pi$
$570$		0			0
$571$	81007.0	+	140308.i	0.248456	+	0.430339i	0.963098	−	0.269152i	$-0.0867434\pi$
$571$	81007.0	+	140308.i	0.248456	+	0.430339i	−0.714641	+	0.699491i	$0.753410\pi$
$572$		0			0
$573$	−103074.			−0.313935
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−161769.	−	280192.i	−0.485896	−	0.841597i	0.513973	−	0.857807i	$-0.328173\pi$
$577$	−161769.	−	280192.i	−0.485896	−	0.841597i	−0.999869	+	0.0162099i	$0.994840\pi$
$578$		0			0
$579$	−123934.	−	71553.5i	−0.369687	−	0.213439i
$580$		0			0
$581$	416393.	+	240195.i	1.23354	+	0.711561i
$582$		0			0
$583$	191257.	+	110422.i	0.562703	+	0.324877i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	268042.			0.777905			0.388952	−	0.921258i	$-0.372837\pi$
$587$	268042.			0.777905			0.388952	+	0.921258i	$0.372837\pi$
$588$		0			0
$589$	−340376.			−0.981133
$590$		0			0
$591$	−14105.9	+	8144.03i	−0.0403854	+	0.0233165i
$592$		0			0
$593$	−308934.	+	535089.i	−0.878529	+	1.52166i	−0.0255734	+	0.999673i	$0.508141\pi$
$593$	−308934.	+	535089.i	−0.878529	+	1.52166i	−0.852955	+	0.521984i	$0.825192\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	−255707.	−	147632.i	−0.717453	−	0.414222i
$598$		0			0
$599$	132826.	+	230062.i	0.370194	+	0.641196i	0.989595	−	0.143879i	$-0.0459577\pi$
$599$	132826.	+	230062.i	0.370194	+	0.641196i	−0.619401	+	0.785075i	$0.712624\pi$
$600$		0			0
$601$		−	86658.3i		−	0.239917i	−0.992779	−	0.119959i	$-0.961724\pi$
$601$		−	86658.3i		−	0.239917i	0.992779	−	0.119959i	$-0.0382762\pi$
$602$		0			0
$603$			57750.2i			0.158825i
$604$		0			0
$605$		0			0
$606$		0			0
$607$	13808.7	−	23917.4i	0.0374780	−	0.0649137i	−0.846678	−	0.532106i	$-0.821401\pi$
$607$	13808.7	−	23917.4i	0.0374780	−	0.0649137i	0.884156	+	0.467192i	$0.154734\pi$
$608$		0			0
$609$	226.319	+	599058.i	0.000610219	+	1.61523i
$610$		0			0
$611$	−60941.7	+	105554.i	−0.163242	+	0.282743i
$612$		0			0
$613$	−498966.	+	288078.i	−1.32785	+	0.766636i	−0.984967	−	0.172741i	$-0.944737\pi$
$613$	−498966.	+	288078.i	−1.32785	+	0.766636i	−0.342885	+	0.939377i	$0.611404\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$			177703.i			0.466794i	0.972382	+	0.233397i	$0.0749841\pi$
$617$			177703.i			0.466794i	−0.972382	+	0.233397i	$0.925016\pi$
$618$		0			0
$619$	245526.	−	141755.i	0.640792	−	0.369961i	−0.144128	−	0.989559i	$-0.546038\pi$
$619$	245526.	−	141755.i	0.640792	−	0.369961i	0.784919	+	0.619598i	$0.212704\pi$
$620$		0			0
$621$	445485.	+	257201.i	1.15518	+	0.666944i
$622$		0			0
$623$	81045.7	+	140253.i	0.208811	+	0.361356i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	−400900.	+	231460.i	−1.01977	+	0.588762i
$628$		0			0
$629$			736173.i			1.86071i
$630$		0			0
$631$	−635329.			−1.59566			−0.797829	−	0.602884i	$-0.794018\pi$
$631$	−635329.			−1.59566			−0.797829	+	0.602884i	$0.794018\pi$
$632$		0			0
$633$	−69604.3	−	120558.i	−0.173712	−	0.300877i
$634$		0			0
$635$		0			0
$636$		0			0
$637$	−115442.	−	199604.i	−0.284503	−	0.491915i
$638$		0			0
$639$	−38678.5	+	66993.1i	−0.0947257	+	0.164070i
$640$		0			0
$641$	−246063.	−	426194.i	−0.598867	−	1.03727i	−0.992989	−	0.118210i	$-0.962284\pi$
$641$	−246063.	−	426194.i	−0.598867	−	1.03727i	0.394122	−	0.919058i	$-0.371049\pi$
$642$		0			0
$643$	−2134.72			−0.00516321			−0.00258161	−	0.999997i	$-0.500822\pi$
$643$	−2134.72			−0.00516321			−0.00258161	+	0.999997i	$0.500822\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	90738.2	+	157163.i	0.216761	+	0.375441i	0.953816	−	0.300392i	$-0.0971174\pi$
$647$	90738.2	+	157163.i	0.216761	+	0.375441i	−0.737055	+	0.675833i	$0.763784\pi$
$648$		0			0
$649$	−478024.	−	275987.i	−1.13491	−	0.655238i
$650$		0			0
$651$	95342.9	+	164995.i	0.224971	+	0.389321i
$652$		0			0
$653$	−30672.6	−	17708.8i	−0.0719323	−	0.0415302i	0.463602	−	0.886043i	$-0.346557\pi$
$653$	−30672.6	−	17708.8i	−0.0719323	−	0.0415302i	−0.535535	+	0.844513i	$0.679890\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	41487.8			0.0961146
$658$		0			0
$659$	220647.			0.508075			0.254037	−	0.967194i	$-0.418241\pi$
$659$	220647.			0.508075			0.254037	+	0.967194i	$0.418241\pi$
$660$		0			0
$661$	532676.	−	307541.i	1.21916	−	0.703881i	0.254420	−	0.967094i	$-0.418115\pi$
$661$	532676.	−	307541.i	1.21916	−	0.703881i	0.964738	+	0.263212i	$0.0847820\pi$
$662$		0			0
$663$	−103082.	+	178543.i	−0.234507	+	0.406178i
$664$		0			0
$665$		0			0
$666$		0			0
$667$	−884895.	−	510894.i	−1.98902	−	1.14836i
$668$		0			0
$669$	−158758.	−	274977.i	−0.354718	−	0.614390i
$670$		0			0
$671$		−	433590.i		−	0.963018i
$672$		0			0
$673$		−	94530.9i		−	0.208710i	−0.994540	−	0.104355i	$-0.966722\pi$
$673$		−	94530.9i		−	0.208710i	0.994540	−	0.104355i	$-0.0332778\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	343590.	−	595116.i	0.749659	−	1.29845i	−0.198328	−	0.980136i	$-0.563551\pi$
$677$	343590.	−	595116.i	0.749659	−	1.29845i	0.947986	−	0.318311i	$-0.103116\pi$
$678$		0			0
$679$	385370.	+	222299.i	0.835869	+	0.482168i
$680$		0			0
$681$	173604.	−	300691.i	0.374340	−	0.648376i
$682$		0			0
$683$	721857.	−	416764.i	1.54743	−	0.893406i	0.549088	−	0.835765i	$-0.314975\pi$
$683$	721857.	−	416764.i	1.54743	−	0.893406i	0.998337	−	0.0576419i	$-0.0183582\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$		−	110890.i		−	0.234951i
$688$		0			0
$689$	−211299.	+	121994.i	−0.445102	+	0.256980i
$690$		0			0
$691$	307473.	+	177520.i	0.643949	+	0.371784i	0.786134	−	0.618056i	$-0.212079\pi$
$691$	307473.	+	177520.i	0.643949	+	0.371784i	−0.142185	+	0.989840i	$0.545413\pi$
$692$		0			0
$693$	−74360.0	−	42894.3i	−0.154836	−	0.0893168i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	577909.	−	333656.i	1.18958	−	0.686805i
$698$		0			0
$699$			290632.i			0.594824i
$700$		0			0
$701$	498723.			1.01490			0.507451	−	0.861681i	$-0.330588\pi$
$701$	498723.			1.01490			0.507451	+	0.861681i	$0.330588\pi$
$702$		0			0
$703$	−913111.	−	1.58155e6i	−1.84762	−	3.20017i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	−540554.	+	204.216i	−1.08144	+	0.000408556i
$708$		0			0
$709$	−215894.	+	373939.i	−0.429485	+	0.743890i	−0.996828	−	0.0795922i	$-0.974638\pi$
$709$	−215894.	+	373939.i	−0.429485	+	0.743890i	0.567343	+	0.823482i	$0.307972\pi$
$710$		0			0
$711$	38018.3	+	65849.7i	0.0752062	+	0.130261i
$712$		0			0
$713$	−325032.			−0.639363
$714$		0			0
$715$		0			0
$716$		0			0
$717$	62168.5	+	107679.i	0.120929	+	0.209456i
$718$		0			0
$719$	237052.	+	136862.i	0.458549	+	0.264743i	0.711434	−	0.702753i	$-0.248046\pi$
$719$	237052.	+	136862.i	0.458549	+	0.264743i	−0.252885	+	0.967496i	$0.581379\pi$
$720$		0			0
$721$	−141045.	+	81503.5i	−0.271324	+	0.156785i
$722$		0			0
$723$	432467.	+	249685.i	0.827325	+	0.477656i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−119072.			−0.225289			−0.112644	−	0.993635i	$-0.535932\pi$
$727$	−119072.			−0.225289			−0.112644	+	0.993635i	$0.535932\pi$
$728$		0			0
$729$	589683.			1.10959
$730$		0			0
$731$	290271.	−	167588.i	0.543211	−	0.313623i
$732$		0			0
$733$	−460056.	+	796840.i	−0.856253	+	1.48307i	0.0192238	+	0.999815i	$0.493881\pi$
$733$	−460056.	+	796840.i	−0.856253	+	1.48307i	−0.875477	+	0.483259i	$0.839453\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	−215712.	−	124541.i	−0.397136	−	0.229287i
$738$		0			0
$739$	−134271.	−	232564.i	−0.245863	−	0.425846i	0.716511	−	0.697576i	$-0.245738\pi$
$739$	−134271.	−	232564.i	−0.245863	−	0.425846i	−0.962374	+	0.271729i	$0.912405\pi$
$740$		0			0
$741$		−	511431.i		−	0.931430i
$742$		0			0
$743$		−	731118.i		−	1.32437i	−0.749340	−	0.662185i	$-0.769629\pi$
$743$		−	731118.i		−	1.32437i	0.749340	−	0.662185i	$-0.230371\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−98859.1	+	171229.i	−0.177164	+	0.306857i
$748$		0			0
$749$	−145004.	−	250935.i	−0.258473	−	0.447298i
$750$		0			0
$751$	48233.3	−	83542.6i	0.0855200	−	0.148125i	−0.820093	−	0.572231i	$-0.806078\pi$
$751$	48233.3	−	83542.6i	0.0855200	−	0.148125i	0.905613	+	0.424106i	$0.139412\pi$
$752$		0			0
$753$	−628409.	+	362812.i	−1.10829	+	0.639870i
$754$		0			0
$755$		0			0
$756$		0			0
$757$			932641.i			1.62751i	0.581211	+	0.813753i	$0.302579\pi$
$757$			932641.i			1.62751i	−0.581211	+	0.813753i	$0.697421\pi$
$758$		0			0
$759$	−382828.	+	221026.i	−0.664538	+	0.383671i
$760$		0			0
$761$	−344258.	−	198757.i	−0.594448	−	0.343205i	0.172406	−	0.985026i	$-0.444846\pi$
$761$	−344258.	−	198757.i	−0.594448	−	0.343205i	−0.766855	+	0.641821i	$0.778179\pi$
$762$		0			0
$763$	−215.950	−	571613.i	−0.000370941	−	0.981868i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	528118.	−	304909.i	0.897719	−	0.518298i
$768$		0			0
$769$			334165.i			0.565078i	0.959256	+	0.282539i	$0.0911766\pi$
$769$			334165.i			0.565078i	−0.959256	+	0.282539i	$0.908823\pi$
$770$		0			0
$771$	−111171.			−0.187018
$772$		0			0
$773$	−360380.	−	624197.i	−0.603118	−	1.04463i	−0.992346	−	0.123490i	$-0.960591\pi$
$773$	−360380.	−	624197.i	−0.603118	−	1.04463i	0.389228	−	0.921141i	$-0.372742\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−510875.	+	885635.i	−0.846200	+	1.46694i
$778$		0			0
$779$	−827699.	+	1.43362e6i	−1.36395	+	2.36243i
$780$		0			0
$781$	−166824.	−	288948.i	−0.273500	−	0.473716i
$782$		0			0
$783$	−1.23668e6			−2.01713
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−162620.	−	281667.i	−0.262558	−	0.454764i	0.704363	−	0.709840i	$-0.251233\pi$
$787$	−162620.	−	281667.i	−0.262558	−	0.454764i	−0.966921	+	0.255076i	$0.917899\pi$
$788$		0			0
$789$	−329087.	−	189998.i	−0.528636	−	0.305208i
$790$		0			0
$791$	−230412.	+	399434.i	−0.368258	+	0.638399i
$792$		0			0
$793$	414850.	+	239514.i	0.659698	+	0.380877i
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−425576.			−0.669978			−0.334989	−	0.942222i	$-0.608733\pi$
$797$	−425576.			−0.669978			−0.334989	+	0.942222i	$0.608733\pi$
$798$		0			0
$799$	−349278.			−0.547113
$800$		0			0
$801$	−57699.8	+	33313.0i	−0.0899310	+	0.0519217i
$802$		0			0
$803$	−89470.5	+	154967.i	−0.138755	+	0.240331i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	62367.7	+	36008.0i	0.0957664	+	0.0552907i
$808$		0			0
$809$	340716.	+	590138.i	0.520590	+	0.901688i	0.999713	+	0.0239405i	$0.00762123\pi$
$809$	340716.	+	590138.i	0.520590	+	0.901688i	−0.479124	+	0.877747i	$0.659045\pi$
$810$		0			0
$811$			316445.i			0.481123i	0.970634	+	0.240562i	$0.0773316\pi$
$811$			316445.i			0.481123i	−0.970634	+	0.240562i	$0.922668\pi$
$812$		0			0
$813$		−	233238.i		−	0.352873i
$814$		0			0
$815$		0			0
$816$		0			0
$817$	−415735.	+	720074.i	−0.622834	+	1.07878i
$818$		0			0
$819$	82116.7	−	47451.5i	0.122423	−	0.0707427i
$820$		0			0
$821$	−238713.	+	413463.i	−0.354152	+	0.613409i	−0.986972	−	0.160889i	$-0.948564\pi$
$821$	−238713.	+	413463.i	−0.354152	+	0.613409i	0.632821	+	0.774298i	$0.281897\pi$
$822$		0			0
$823$	−983486.	+	567816.i	−1.45201	+	0.838317i	−0.998595	−	0.0529848i	$-0.983127\pi$
$823$	−983486.	+	567816.i	−1.45201	+	0.838317i	−0.453412	+	0.891301i	$0.649793\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	1.14924e6i		−	1.68034i	−0.542321	−	0.840171i	$-0.682454\pi$
$827$		−	1.14924e6i		−	1.68034i	0.542321	−	0.840171i	$-0.317546\pi$
$828$		0			0
$829$	605000.	−	349297.i	0.880332	−	0.508260i	0.00956421	−	0.999954i	$-0.496956\pi$
$829$	605000.	−	349297.i	0.880332	−	0.508260i	0.870768	+	0.491694i	$0.163622\pi$
$830$		0			0
$831$	−557602.	−	321932.i	−0.807463	−	0.466189i
$832$		0			0
$833$	329956.	−	572498.i	0.475516	−	0.825057i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−340685.	+	196694.i	−0.486297	+	0.280764i
$838$		0			0
$839$		−	918115.i		−	1.30429i	−0.758095	−	0.652144i	$-0.773870\pi$
$839$		−	918115.i		−	1.30429i	0.758095	−	0.652144i	$-0.226130\pi$
$840$		0			0
$841$	1.74921e6			2.47315
$842$		0			0
$843$	−389943.	−	675401.i	−0.548714	−	0.950400i
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−300576.	+	173689.i	−0.418975	+	0.242106i
$848$		0			0
$849$	−412500.	+	714471.i	−0.572280	+	0.991218i
$850$		0			0
$851$	−871949.	−	1.51026e6i	−1.20402	−	2.08542i
$852$		0			0
$853$	622696.			0.855811			0.427906	−	0.903823i	$-0.359252\pi$
$853$	622696.			0.855811			0.427906	+	0.903823i	$0.359252\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	28588.2	+	49516.2i	0.0389247	+	0.0674195i	0.884831	−	0.465911i	$-0.154273\pi$
$857$	28588.2	+	49516.2i	0.0389247	+	0.0674195i	−0.845907	+	0.533331i	$0.820940\pi$
$858$		0			0
$859$	690265.	+	398525.i	0.935469	+	0.540093i	0.888537	−	0.458805i	$-0.151722\pi$
$859$	690265.	+	398525.i	0.935469	+	0.540093i	0.0469321	+	0.998898i	$0.485056\pi$
$860$		0			0
$861$	926783.	−	350.130i	1.25018	−	0.000472305i
$862$		0			0
$863$	−1105.47	−	638.243i	−0.00148431	−	0.000856967i	0.499258	−	0.866454i	$-0.333606\pi$
$863$	−1105.47	−	638.243i	−0.00148431	−	0.000856967i	−0.500742	+	0.865597i	$0.666939\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	60696.2			0.0807464
$868$		0			0
$869$	−327954.			−0.434283
$870$		0			0
$871$	238317.	−	137593.i	0.314137	−	0.181367i
$872$		0			0
$873$	−91493.6	+	158472.i	−0.120050	+	0.207933i
$874$		0			0
$875$		0			0
$876$		0			0
$877$	880872.	+	508572.i	1.14529	+	0.661231i	0.947734	−	0.319062i	$-0.103368\pi$
$877$	880872.	+	508572.i	1.14529	+	0.661231i	0.197551	+	0.980293i	$0.436701\pi$
$878$		0			0
$879$	172187.	+	298237.i	0.222855	+	0.385996i
$880$		0			0
$881$		−	1.22607e6i		−	1.57966i	−0.613323	−	0.789832i	$-0.710168\pi$
$881$		−	1.22607e6i		−	1.57966i	0.613323	−	0.789832i	$-0.289832\pi$
$882$		0			0
$883$			454065.i			0.582367i	0.956667	+	0.291184i	$0.0940490\pi$
$883$			454065.i			0.582367i	−0.956667	+	0.291184i	$0.905951\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	462093.	−	800369.i	0.587330	−	1.01729i	−0.407250	−	0.913317i	$-0.633512\pi$
$887$	462093.	−	800369.i	0.587330	−	1.01729i	0.994581	−	0.103969i	$-0.0331544\pi$
$888$		0			0
$889$	−726656.	+	1.25970e6i	−0.919444	+	1.59391i
$890$		0			0
$891$	−196556.	+	340445.i	−0.247588	+	0.428836i
$892$		0			0
$893$	750370.	−	433226.i	0.940962	−	0.543265i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		−	488376.i		−	0.606973i
$898$		0			0
$899$	676723.	−	390706.i	0.837320	−	0.483427i
$900$		0			0
$901$	−605515.	−	349594.i	−0.745891	−	0.430640i
$902$		0			0
$903$	465503.	−	175.862i	0.570882	−	0.000215674i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	67656.5	−	39061.5i	0.0822422	−	0.0474826i	−0.458315	−	0.888790i	$-0.651547\pi$
$907$	67656.5	−	39061.5i	0.0822422	−	0.0474826i	0.540557	+	0.841307i	$0.318213\pi$
$908$		0			0
$909$		−	222335.i		−	0.269079i
$910$		0			0
$911$	1.27606e6			1.53756			0.768781	−	0.639512i	$-0.220863\pi$
$911$	1.27606e6			1.53756			0.768781	+	0.639512i	$0.220863\pi$
$912$		0			0
$913$	−426389.	−	738528.i	−0.511523	−	0.885983i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−260104.	−	450120.i	−0.309320	−	0.535291i
$918$		0			0
$919$	−203067.	+	351722.i	−0.240441	+	0.416455i	−0.960840	−	0.277104i	$-0.910625\pi$
$919$	−203067.	+	351722.i	−0.240441	+	0.416455i	0.720399	+	0.693560i	$0.243959\pi$
$920$		0			0
$921$	499056.	+	864391.i	0.588342	+	1.01904i
$922$		0			0
$923$	368613.			0.432681
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−33501.2	−	58025.8i	−0.0389853	−	0.0675245i
$928$		0			0
$929$	−1.42047e6	−	820109.i	−1.64589	−	0.950255i	−0.978681	−	0.205385i	$-0.934155\pi$
$929$	−1.42047e6	−	820109.i	−1.64589	−	0.950255i	−0.667209	−	0.744870i	$-0.732511\pi$
$930$		0			0
$931$	1238.54	+	1.63918e6i	0.00142893	+	1.89116i
$932$		0			0
$933$	601024.	+	347002.i	0.690445	+	0.398628i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	−1.32405e6			−1.50809			−0.754044	−	0.656824i	$-0.771900\pi$
$937$	−1.32405e6			−1.50809			−0.754044	+	0.656824i	$0.771900\pi$
$938$		0			0
$939$	140067.			0.158856
$940$		0			0
$941$	−893873.	+	516078.i	−1.00948	+	0.582822i	−0.911039	−	0.412321i	$-0.864718\pi$
$941$	−893873.	+	516078.i	−1.00948	+	0.582822i	−0.0984387	+	0.995143i	$0.531385\pi$
$942$		0			0
$943$	−790388.	+	1.36899e6i	−0.888826	+	1.53949i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	−549121.	−	317035.i	−0.612306	−	0.353515i	0.161561	−	0.986863i	$-0.448347\pi$
$947$	−549121.	−	317035.i	−0.612306	−	0.353515i	−0.773867	+	0.633348i	$0.781680\pi$
$948$		0			0
$949$	−98846.5	−	171207.i	−0.109756	−	0.190103i
$950$		0			0
$951$			734527.i			0.812170i
$952$		0			0
$953$			1.12638e6i			1.24022i	0.784516	+	0.620108i	$0.212911\pi$
$953$			1.12638e6i			1.24022i	−0.784516	+	0.620108i	$0.787089\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$	531370.	−	920360.i	0.580194	−	1.00493i
$958$		0			0
$959$	1.06216e6	−	401.274i	1.15492	−	0.000436318i
$960$		0			0
$961$	−337476.	+	584526.i	−0.365424	+	0.632932i
$962$		0			0
$963$	103234.	−	59602.2i	0.111319	−	0.0642703i
$964$		0			0
$965$		0			0
$966$		0			0
$967$			629660.i			0.673369i	0.941618	+	0.336684i	$0.109306\pi$
$967$			629660.i			0.673369i	−0.941618	+	0.336684i	$0.890694\pi$
$968$		0			0
$969$	1.26924e6	−	732797.i	1.35175	−	0.780433i
$970$		0			0
$971$	−1.18846e6	−	686157.i	−1.26051	−	0.727755i	−0.287336	−	0.957830i	$-0.592770\pi$
$971$	−1.18846e6	−	686157.i	−1.26051	−	0.727755i	−0.973173	+	0.230075i	$0.926103\pi$
$972$		0			0
$973$	−10105.3	+	17518.2i	−0.0106739	+	0.0185039i
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−259439.	+	149787.i	−0.271797	+	0.156922i	−0.629704	−	0.776835i	$-0.716824\pi$
$977$	−259439.	+	149787.i	−0.271797	+	0.156922i	0.357907	+	0.933757i	$0.383491\pi$
$978$		0			0
$979$		−	287365.i		−	0.299825i
$980$		0			0
$981$	235110.			0.244305
$982$		0			0
$983$	392753.	+	680268.i	0.406455	+	0.704001i	0.994490	−	0.104835i	$-0.0334315\pi$
$983$	392753.	+	680268.i	0.406455	+	0.704001i	−0.588035	+	0.808836i	$0.700098\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	−420190.	−	242385.i	−0.431332	−	0.248812i
$988$		0			0
$989$	−396994.	+	687614.i	−0.405874	+	0.702995i
$990$		0			0
$991$	−350582.	−	607225.i	−0.356978	−	0.618304i	0.630476	−	0.776209i	$-0.282860\pi$
$991$	−350582.	−	607225.i	−0.356978	−	0.618304i	−0.987454	+	0.157904i	$0.949526\pi$
$992$		0			0
$993$	−1.63792e6			−1.66109
$994$		0			0
$995$		0			0
$996$		0			0
$997$	118236.	+	204790.i	0.118948	+	0.206025i	0.919351	−	0.393438i	$-0.128714\pi$
$997$	118236.	+	204790.i	0.118948	+	0.206025i	−0.800403	+	0.599463i	$0.795381\pi$
$998$		0			0
$999$	−1.82788e6	−	1.05533e6i	−1.83154	−	1.05744i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	700.5.o.c.649.16		44
5.2	odd	4		700.5.s.d.201.8	yes	22
5.3	odd	4		700.5.s.c.201.4	yes	22
5.4	even	2	inner	700.5.o.c.649.7		44
7.3	odd	6	inner	700.5.o.c.549.7		44
35.3	even	12		700.5.s.c.101.4	✓	22
35.17	even	12		700.5.s.d.101.8	yes	22
35.24	odd	6	inner	700.5.o.c.549.16		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
700.5.o.c.549.7		44	7.3	odd	6	inner
700.5.o.c.549.16		44	35.24	odd	6	inner
700.5.o.c.649.7		44	5.4	even	2	inner
700.5.o.c.649.16		44	1.1	even	1	trivial
700.5.s.c.101.4	✓	22	35.3	even	12
700.5.s.c.201.4	yes	22	5.3	odd	4
700.5.s.d.101.8	yes	22	35.17	even	12
700.5.s.d.201.8	yes	22	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 700 = 2^{2} \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	700.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(3.90019 + 6.75532i) q^{3} +(-42.4445 - 24.4840i) q^{7} +(10.0771 - 17.4540i) q^{9} +(43.4634 + 75.2808i) q^{11} -96.0363 q^{13} +(-137.604 - 238.338i) q^{17} +(591.243 + 341.355i) q^{19} +(-0.144398 - 382.218i) q^{21} +(564.591 + 325.967i) q^{23} +789.040 q^{27} -1567.32 q^{29} +(-431.771 + 249.283i) q^{31} +(-339.031 + 587.219i) q^{33} +(-2316.59 - 1337.48i) q^{37} +(-374.560 - 648.756i) q^{39} +2424.75i q^{41} +1217.90i q^{43} +(634.569 - 1099.11i) q^{47} +(1202.07 + 2078.42i) q^{49} +(1073.37 - 1859.12i) q^{51} +(2200.20 - 1270.29i) q^{53} +5325.39i q^{57} +(-5499.15 + 3174.93i) q^{59} +(-4319.72 - 2493.99i) q^{61} +(-855.059 + 494.099i) q^{63} +(-2481.53 + 1432.71i) q^{67} +5085.33i q^{69} -3838.27 q^{71} +(1029.26 + 1782.73i) q^{73} +(-1.60917 - 4259.41i) q^{77} +(-1886.38 + 3267.30i) q^{79} +(2261.16 + 3916.45i) q^{81} -9810.30 q^{83} +(-6112.84 - 10587.8i) q^{87} +(-2862.93 - 1652.91i) q^{89} +(4076.21 + 2351.35i) q^{91} +(-3367.98 - 1944.50i) q^{93} -9079.39 q^{97} +1751.93 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 684 q^{9} - 300 q^{11} + 540 q^{19} - 190 q^{21} - 528 q^{29} - 2334 q^{31} - 852 q^{39} + 4092 q^{49} - 3902 q^{51} + 9414 q^{59} - 23598 q^{61} + 32820 q^{71} - 4890 q^{79} - 23710 q^{81} - 37764 q^{89}+ \cdots + 168180 q^{99}+O(q^{100}) \) 44 * q - 684 * q^9 - 300 * q^11 + 540 * q^19 - 190 * q^21 - 528 * q^29 - 2334 * q^31 - 852 * q^39 + 4092 * q^49 - 3902 * q^51 + 9414 * q^59 - 23598 * q^61 + 32820 * q^71 - 4890 * q^79 - 23710 * q^81 - 37764 * q^89 + 6418 * q^91 + 168180 * q^99

Introduction

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