LMFDB - Embedded newform 1600.2.j.e.1007.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1600,2,Mod(143,1600)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1600, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 3]))

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

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

chi := DirichletCharacter("1600.143");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1600 = 2^{6} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1600.j (of order $4$, 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:	$12.7760643234$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 400)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			1007.5
Character	$\chi$	$=$	1600.1007
Dual form			1600.2.j.e.143.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.790153i q^{3} +(0.139907 + 0.139907i) q^{7} +2.37566 q^{9} +O(q^{10})$	$q-0.790153i q^{3} +(0.139907 + 0.139907i) q^{7} +2.37566 q^{9} +(-2.94816 - 2.94816i) q^{11} +0.235568 q^{13} +(-2.06145 - 2.06145i) q^{17} +(-2.55293 - 2.55293i) q^{19} +(0.110548 - 0.110548i) q^{21} +(-4.62421 + 4.62421i) q^{23} -4.24759i q^{27} +(6.66417 - 6.66417i) q^{29} -3.43202i q^{31} +(-2.32950 + 2.32950i) q^{33} -1.38457 q^{37} -0.186135i q^{39} +8.26242i q^{41} -5.40057 q^{43} +(6.84602 - 6.84602i) q^{47} -6.96085i q^{49} +(-1.62886 + 1.62886i) q^{51} +8.19252i q^{53} +(-2.01720 + 2.01720i) q^{57} +(4.32313 - 4.32313i) q^{59} +(-9.15188 - 9.15188i) q^{61} +(0.332372 + 0.332372i) q^{63} -5.00083 q^{67} +(3.65383 + 3.65383i) q^{69} +6.06473 q^{71} +(-11.3646 - 11.3646i) q^{73} -0.824938i q^{77} +4.44776 q^{79} +3.77073 q^{81} -11.4778i q^{83} +(-5.26571 - 5.26571i) q^{87} -5.84762 q^{89} +(0.0329576 + 0.0329576i) q^{91} -2.71182 q^{93} +(0.515382 + 0.515382i) q^{97} +(-7.00383 - 7.00383i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 40 q^{9}+O(q^{10}) $ 24 * q - 40 * q^9	$ 24 q - 40 q^{9} + 20 q^{11} + 12 q^{19} + 8 q^{29} - 20 q^{51} - 8 q^{59} - 48 q^{61} - 64 q^{69} + 16 q^{71} + 104 q^{79} + 48 q^{81} + 96 q^{89} - 64 q^{91} - 128 q^{99}+O(q^{100}) $ 24 * q - 40 * q^9 + 20 * q^11 + 12 * q^19 + 8 * q^29 - 20 * q^51 - 8 * q^59 - 48 * q^61 - 64 * q^69 + 16 * q^71 + 104 * q^79 + 48 * q^81 + 96 * q^89 - 64 * q^91 - 128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1600\mathbb{Z}\right)^\times$.

$n$	$577$	$901$	$1151$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$	$-1$

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
$3$		−	0.790153i		−	0.456195i	−0.973638	−	0.228097i	$-0.926750\pi$
$3$		−	0.790153i		−	0.456195i	0.973638	−	0.228097i	$-0.0732505\pi$
$4$		0			0
$5$		0			0
$5$		0			0
$6$		0			0
$7$	0.139907	+	0.139907i	0.0528800	+	0.0528800i	0.733052	−	0.680172i	$-0.238095\pi$
$7$	0.139907	+	0.139907i	0.0528800	+	0.0528800i	−0.680172	+	0.733052i	$0.738095\pi$
$8$		0			0
$9$	2.37566			0.791886
$10$		0			0
$11$	−2.94816	−	2.94816i	−0.888904	−	0.888904i	0.105514	−	0.994418i	$-0.466351\pi$
$11$	−2.94816	−	2.94816i	−0.888904	−	0.888904i	−0.994418	+	0.105514i	$0.966351\pi$
$12$		0			0
$13$	0.235568			0.0653348			0.0326674	−	0.999466i	$-0.489600\pi$
$13$	0.235568			0.0653348			0.0326674	+	0.999466i	$0.489600\pi$
$14$		0			0
$15$		0			0
$16$		0			0
$17$	−2.06145	−	2.06145i	−0.499975	−	0.499975i	0.411455	−	0.911430i	$-0.365021\pi$
$17$	−2.06145	−	2.06145i	−0.499975	−	0.499975i	−0.911430	+	0.411455i	$0.865021\pi$
$18$		0			0
$19$	−2.55293	−	2.55293i	−0.585682	−	0.585682i	0.350777	−	0.936459i	$-0.385917\pi$
$19$	−2.55293	−	2.55293i	−0.585682	−	0.585682i	−0.936459	+	0.350777i	$0.885917\pi$
$20$		0			0
$21$	0.110548	−	0.110548i	0.0241236	−	0.0241236i
$22$		0			0
$23$	−4.62421	+	4.62421i	−0.964214	+	0.964214i	−0.999381	−	0.0351672i	$-0.988804\pi$
$23$	−4.62421	+	4.62421i	−0.964214	+	0.964214i	0.0351672	+	0.999381i	$0.488804\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$		−	4.24759i		−	0.817449i
$28$		0			0
$29$	6.66417	−	6.66417i	1.23751	−	1.23751i	0.276488	−	0.961017i	$-0.410829\pi$
$29$	6.66417	−	6.66417i	1.23751	−	1.23751i	0.961017	−	0.276488i	$-0.0891705\pi$
$30$		0			0
$31$		−	3.43202i		−	0.616408i	−0.951320	−	0.308204i	$-0.900272\pi$
$31$		−	3.43202i		−	0.616408i	0.951320	−	0.308204i	$-0.0997280\pi$
$32$		0			0
$33$	−2.32950	+	2.32950i	−0.405513	+	0.405513i
$34$		0			0
$35$		0			0
$36$		0			0
$37$	−1.38457			−0.227621			−0.113811	−	0.993502i	$-0.536306\pi$
$37$	−1.38457			−0.227621			−0.113811	+	0.993502i	$0.536306\pi$
$38$		0			0
$39$		−	0.186135i		−	0.0298054i
$40$		0			0
$41$			8.26242i			1.29037i	0.764025	+	0.645187i	$0.223220\pi$
$41$			8.26242i			1.29037i	−0.764025	+	0.645187i	$0.776780\pi$
$42$		0			0
$43$	−5.40057			−0.823580			−0.411790	−	0.911279i	$-0.635096\pi$
$43$	−5.40057			−0.823580			−0.411790	+	0.911279i	$0.635096\pi$
$44$		0			0
$45$		0			0
$46$		0			0
$47$	6.84602	−	6.84602i	0.998594	−	0.998594i	−0.00140497	−	0.999999i	$-0.500447\pi$
$47$	6.84602	−	6.84602i	0.998594	−	0.998594i	0.999999	+	0.00140497i	$0.000447216\pi$
$48$		0			0
$49$		−	6.96085i		−	0.994407i
$50$		0			0
$51$	−1.62886	+	1.62886i	−0.228086	+	0.228086i
$52$		0			0
$53$			8.19252i			1.12533i	0.826685	+	0.562665i	$0.190224\pi$
$53$			8.19252i			1.12533i	−0.826685	+	0.562665i	$0.809776\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−2.01720	+	2.01720i	−0.267185	+	0.267185i
$58$		0			0
$59$	4.32313	−	4.32313i	0.562823	−	0.562823i	−0.367285	−	0.930108i	$-0.619713\pi$
$59$	4.32313	−	4.32313i	0.562823	−	0.562823i	0.930108	+	0.367285i	$0.119713\pi$
$60$		0			0
$61$	−9.15188	−	9.15188i	−1.17178	−	1.17178i	−0.981786	−	0.189992i	$-0.939154\pi$
$61$	−9.15188	−	9.15188i	−1.17178	−	1.17178i	−0.189992	−	0.981786i	$-0.560846\pi$
$62$		0			0
$63$	0.332372	+	0.332372i	0.0418749	+	0.0418749i
$64$		0			0
$65$		0			0
$66$		0			0
$67$	−5.00083			−0.610948			−0.305474	−	0.952200i	$-0.598815\pi$
$67$	−5.00083			−0.610948			−0.305474	+	0.952200i	$0.598815\pi$
$68$		0			0
$69$	3.65383	+	3.65383i	0.439870	+	0.439870i
$70$		0			0
$71$	6.06473			0.719751			0.359875	−	0.933000i	$-0.382819\pi$
$71$	6.06473			0.719751			0.359875	+	0.933000i	$0.382819\pi$
$72$		0			0
$73$	−11.3646	−	11.3646i	−1.33012	−	1.33012i	−0.905258	−	0.424863i	$-0.860322\pi$
$73$	−11.3646	−	11.3646i	−1.33012	−	1.33012i	−0.424863	−	0.905258i	$-0.639678\pi$
$74$		0			0
$75$		0			0
$76$		0			0
$77$		−	0.824938i		−	0.0940104i
$78$		0			0
$79$	4.44776			0.500413			0.250206	−	0.968193i	$-0.419502\pi$
$79$	4.44776			0.500413			0.250206	+	0.968193i	$0.419502\pi$
$80$		0			0
$81$	3.77073			0.418970
$82$		0			0
$83$		−	11.4778i		−	1.25986i	−0.776654	−	0.629928i	$-0.783085\pi$
$83$		−	11.4778i		−	1.25986i	0.776654	−	0.629928i	$-0.216915\pi$
$84$		0			0
$85$		0			0
$86$		0			0
$87$	−5.26571	−	5.26571i	−0.564543	−	0.564543i
$88$		0			0
$89$	−5.84762			−0.619846			−0.309923	−	0.950762i	$-0.600303\pi$
$89$	−5.84762			−0.619846			−0.309923	+	0.950762i	$0.600303\pi$
$90$		0			0
$91$	0.0329576	+	0.0329576i	0.00345490	+	0.00345490i
$92$		0			0
$93$	−2.71182			−0.281202
$94$		0			0
$95$		0			0
$96$		0			0
$97$	0.515382	+	0.515382i	0.0523291	+	0.0523291i	0.732787	−	0.680458i	$-0.238219\pi$
$97$	0.515382	+	0.515382i	0.0523291	+	0.0523291i	−0.680458	+	0.732787i	$0.738219\pi$
$98$		0			0
$99$	−7.00383	−	7.00383i	−0.703911	−	0.703911i
$100$		0			0
$101$	3.56668	−	3.56668i	0.354898	−	0.354898i	−0.507030	−	0.861928i	$-0.669257\pi$
$101$	3.56668	−	3.56668i	0.354898	−	0.354898i	0.861928	+	0.507030i	$0.169257\pi$
$102$		0			0
$103$	−11.6666	+	11.6666i	−1.14954	+	1.14954i	−0.162901	+	0.986642i	$0.552085\pi$
$103$	−11.6666	+	11.6666i	−1.14954	+	1.14954i	−0.986642	+	0.162901i	$0.947915\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		−	5.00083i		−	0.483448i	−0.970345	−	0.241724i	$-0.922287\pi$
$107$		−	5.00083i		−	0.483448i	0.970345	−	0.241724i	$-0.0777129\pi$
$108$		0			0
$109$	3.69574	−	3.69574i	0.353988	−	0.353988i	−0.507603	−	0.861591i	$-0.669468\pi$
$109$	3.69574	−	3.69574i	0.353988	−	0.353988i	0.861591	+	0.507603i	$0.169468\pi$
$110$		0			0
$111$			1.09402i			0.103840i
$112$		0			0
$113$	−11.6416	+	11.6416i	−1.09515	+	1.09515i	−0.100184	+	0.994969i	$0.531943\pi$
$113$	−11.6416	+	11.6416i	−1.09515	+	1.09515i	−0.994969	+	0.100184i	$0.968057\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	0.559629			0.0517377
$118$		0			0
$119$		−	0.576823i		−	0.0528773i
$120$		0			0
$121$			6.38331i			0.580301i
$122$		0			0
$123$	6.52858			0.588662
$124$		0			0
$125$		0			0
$126$		0			0
$127$	−5.40562	+	5.40562i	−0.479671	+	0.479671i	−0.905026	−	0.425355i	$-0.860149\pi$
$127$	−5.40562	+	5.40562i	−0.479671	+	0.479671i	0.425355	+	0.905026i	$0.360149\pi$
$128$		0			0
$129$			4.26728i			0.375713i
$130$		0			0
$131$	−15.2758	+	15.2758i	−1.33465	+	1.33465i	−0.433500	+	0.901154i	$0.642722\pi$
$131$	−15.2758	+	15.2758i	−1.33465	+	1.33465i	−0.901154	+	0.433500i	$0.857278\pi$
$132$		0			0
$133$		−	0.714346i		−	0.0619417i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	4.41140	−	4.41140i	0.376891	−	0.376891i	−0.493088	−	0.869979i	$-0.664132\pi$
$137$	4.41140	−	4.41140i	0.376891	−	0.376891i	0.869979	+	0.493088i	$0.164132\pi$
$138$		0			0
$139$	10.3472	−	10.3472i	0.877640	−	0.877640i	−0.115650	−	0.993290i	$-0.536895\pi$
$139$	10.3472	−	10.3472i	0.877640	−	0.877640i	0.993290	+	0.115650i	$0.0368952\pi$
$140$		0			0
$141$	−5.40940	−	5.40940i	−0.455553	−	0.455553i
$142$		0			0
$143$	−0.694492	−	0.694492i	−0.0580763	−	0.0580763i
$144$		0			0
$145$		0			0
$146$		0			0
$147$	−5.50014			−0.453644
$148$		0			0
$149$	−7.12848	−	7.12848i	−0.583987	−	0.583987i	0.352009	−	0.935997i	$-0.385499\pi$
$149$	−7.12848	−	7.12848i	−0.583987	−	0.583987i	−0.935997	+	0.352009i	$0.885499\pi$
$150$		0			0
$151$	19.7239			1.60511			0.802555	−	0.596578i	$-0.203473\pi$
$151$	19.7239			1.60511			0.802555	+	0.596578i	$0.203473\pi$
$152$		0			0
$153$	−4.89730	−	4.89730i	−0.395923	−	0.395923i
$154$		0			0
$155$		0			0
$156$		0			0
$157$		−	16.0585i		−	1.28161i	−0.767704	−	0.640804i	$-0.778601\pi$
$157$		−	16.0585i		−	1.28161i	0.767704	−	0.640804i	$-0.221399\pi$
$158$		0			0
$159$	6.47334			0.513370
$160$		0			0
$161$	−1.29392			−0.101975
$162$		0			0
$163$			1.10043i			0.0861920i	0.999071	+	0.0430960i	$0.0137221\pi$
$163$			1.10043i			0.0861920i	−0.999071	+	0.0430960i	$0.986278\pi$
$164$		0			0
$165$		0			0
$166$		0			0
$167$	11.6039	+	11.6039i	0.897940	+	0.897940i	0.995254	−	0.0973136i	$-0.0310250\pi$
$167$	11.6039	+	11.6039i	0.897940	+	0.897940i	−0.0973136	+	0.995254i	$0.531025\pi$
$168$		0			0
$169$	−12.9445			−0.995731
$170$		0			0
$171$	−6.06489	−	6.06489i	−0.463794	−	0.463794i
$172$		0			0
$173$	14.7116			1.11851			0.559253	−	0.828997i	$-0.311088\pi$
$173$	14.7116			1.11851			0.559253	+	0.828997i	$0.311088\pi$
$174$		0			0
$175$		0			0
$176$		0			0
$177$	−3.41593	−	3.41593i	−0.256757	−	0.256757i
$178$		0			0
$179$	1.97591	+	1.97591i	0.147686	+	0.147686i	0.777084	−	0.629397i	$-0.216698\pi$
$179$	1.97591	+	1.97591i	0.147686	+	0.147686i	−0.629397	+	0.777084i	$0.716698\pi$
$180$		0			0
$181$	1.45673	−	1.45673i	0.108278	−	0.108278i	−0.650892	−	0.759170i	$-0.725605\pi$
$181$	1.45673	−	1.45673i	0.108278	−	0.108278i	0.759170	+	0.650892i	$0.225605\pi$
$182$		0			0
$183$	−7.23138	+	7.23138i	−0.534559	+	0.534559i
$184$		0			0
$185$		0			0
$186$		0			0
$187$			12.1550i			0.888860i
$188$		0			0
$189$	0.594269	−	0.594269i	0.0432267	−	0.0432267i
$190$		0			0
$191$			0.285625i			0.0206671i	0.999947	+	0.0103336i	$0.00328933\pi$
$191$			0.285625i			0.0206671i	−0.999947	+	0.0103336i	$0.996711\pi$
$192$		0			0
$193$	8.95931	−	8.95931i	0.644905	−	0.644905i	−0.306852	−	0.951757i	$-0.599276\pi$
$193$	8.95931	−	8.95931i	0.644905	−	0.644905i	0.951757	+	0.306852i	$0.0992756\pi$
$194$		0			0
$195$		0			0
$196$		0			0
$197$	12.8094			0.912632			0.456316	−	0.889818i	$-0.349169\pi$
$197$	12.8094			0.912632			0.456316	+	0.889818i	$0.349169\pi$
$198$		0			0
$199$			18.2117i			1.29099i	0.763763	+	0.645497i	$0.223350\pi$
$199$			18.2117i			1.29099i	−0.763763	+	0.645497i	$0.776650\pi$
$200$		0			0
$201$			3.95142i			0.278711i
$202$		0			0
$203$	1.86473			0.130878
$204$		0			0
$205$		0			0
$206$		0			0
$207$	−10.9855	+	10.9855i	−0.763548	+	0.763548i
$208$		0			0
$209$			15.0529i			1.04123i
$210$		0			0
$211$	−2.40291	+	2.40291i	−0.165423	+	0.165423i	−0.784964	−	0.619541i	$-0.787319\pi$
$211$	−2.40291	+	2.40291i	−0.165423	+	0.165423i	0.619541	+	0.784964i	$0.287319\pi$
$212$		0			0
$213$		−	4.79206i		−	0.328347i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	0.480164	−	0.480164i	0.0325956	−	0.0325956i
$218$		0			0
$219$	−8.97973	+	8.97973i	−0.606794	+	0.606794i
$220$		0			0
$221$	−0.485611	−	0.485611i	−0.0326657	−	0.0326657i
$222$		0			0
$223$	8.26331	+	8.26331i	0.553352	+	0.553352i	0.927407	−	0.374054i	$-0.122033\pi$
$223$	8.26331	+	8.26331i	0.553352	+	0.553352i	−0.374054	+	0.927407i	$0.622033\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	10.5895			0.702847			0.351423	−	0.936217i	$-0.385698\pi$
$227$	10.5895			0.702847			0.351423	+	0.936217i	$0.385698\pi$
$228$		0			0
$229$	4.51111	+	4.51111i	0.298102	+	0.298102i	0.840270	−	0.542168i	$-0.182396\pi$
$229$	4.51111	+	4.51111i	0.298102	+	0.298102i	−0.542168	+	0.840270i	$0.682396\pi$
$230$		0			0
$231$	−0.651827			−0.0428871
$232$		0			0
$233$	−1.60312	−	1.60312i	−0.105024	−	0.105024i	0.652642	−	0.757666i	$-0.273660\pi$
$233$	−1.60312	−	1.60312i	−0.105024	−	0.105024i	−0.757666	+	0.652642i	$0.773660\pi$
$234$		0			0
$235$		0			0
$236$		0			0
$237$		−	3.51441i		−	0.228286i
$238$		0			0
$239$	14.1546			0.915587			0.457794	−	0.889058i	$-0.348640\pi$
$239$	14.1546			0.915587			0.457794	+	0.889058i	$0.348640\pi$
$240$		0			0
$241$	4.25207			0.273900			0.136950	−	0.990578i	$-0.456270\pi$
$241$	4.25207			0.273900			0.136950	+	0.990578i	$0.456270\pi$
$242$		0			0
$243$		−	15.7222i		−	1.00858i
$244$		0			0
$245$		0			0
$246$		0			0
$247$	−0.601388	−	0.601388i	−0.0382654	−	0.0382654i
$248$		0			0
$249$	−9.06923			−0.574739
$250$		0			0
$251$	1.29050	+	1.29050i	0.0814559	+	0.0814559i	0.746661	−	0.665205i	$-0.231656\pi$
$251$	1.29050	+	1.29050i	0.0814559	+	0.0814559i	−0.665205	+	0.746661i	$0.731656\pi$
$252$		0			0
$253$	27.2658			1.71419
$254$		0			0
$255$		0			0
$256$		0			0
$257$	5.72463	+	5.72463i	0.357093	+	0.357093i	0.862740	−	0.505647i	$-0.168746\pi$
$257$	5.72463	+	5.72463i	0.357093	+	0.357093i	−0.505647	+	0.862740i	$0.668746\pi$
$258$		0			0
$259$	−0.193711	−	0.193711i	−0.0120366	−	0.0120366i
$260$		0			0
$261$	15.8318	−	15.8318i	0.979963	−	0.979963i
$262$		0			0
$263$	17.0683	−	17.0683i	1.05248	−	1.05248i	0.0539323	−	0.998545i	$-0.482824\pi$
$263$	17.0683	−	17.0683i	1.05248	−	1.05248i	0.998545	−	0.0539323i	$-0.0171755\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$			4.62051i			0.282771i
$268$		0			0
$269$	−6.15456	+	6.15456i	−0.375250	+	0.375250i	−0.869385	−	0.494135i	$-0.835485\pi$
$269$	−6.15456	+	6.15456i	−0.375250	+	0.375250i	0.494135	+	0.869385i	$0.335485\pi$
$270$		0			0
$271$		−	18.4342i		−	1.11980i	−0.828561	−	0.559899i	$-0.810840\pi$
$271$		−	18.4342i		−	1.11980i	0.828561	−	0.559899i	$-0.189160\pi$
$272$		0			0
$273$	0.0260416	−	0.0260416i	0.00157611	−	0.00157611i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	−15.2281			−0.914967			−0.457484	−	0.889218i	$-0.651249\pi$
$277$	−15.2281			−0.914967			−0.457484	+	0.889218i	$0.651249\pi$
$278$		0			0
$279$		−	8.15330i		−	0.488125i
$280$		0			0
$281$			7.07835i			0.422259i	0.977458	+	0.211129i	$0.0677142\pi$
$281$			7.07835i			0.422259i	−0.977458	+	0.211129i	$0.932286\pi$
$282$		0			0
$283$	19.9173			1.18396			0.591979	−	0.805953i	$-0.298347\pi$
$283$	19.9173			1.18396			0.591979	+	0.805953i	$0.298347\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−1.15597	+	1.15597i	−0.0682349	+	0.0682349i
$288$		0			0
$289$		−	8.50085i		−	0.500050i
$290$		0			0
$291$	0.407231	−	0.407231i	0.0238723	−	0.0238723i
$292$		0			0
$293$			23.1293i			1.35123i	0.737256	+	0.675614i	$0.236121\pi$
$293$			23.1293i			1.35123i	−0.737256	+	0.675614i	$0.763879\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	−12.5226	+	12.5226i	−0.726634	+	0.726634i
$298$		0			0
$299$	−1.08931	+	1.08931i	−0.0629967	+	0.0629967i
$300$		0			0
$301$	−0.755579	−	0.755579i	−0.0435509	−	0.0435509i
$302$		0			0
$303$	−2.81822	−	2.81822i	−0.161903	−	0.161903i
$304$		0			0
$305$		0			0
$306$		0			0
$307$	3.82901			0.218533			0.109267	−	0.994012i	$-0.465150\pi$
$307$	3.82901			0.218533			0.109267	+	0.994012i	$0.465150\pi$
$308$		0			0
$309$	9.21839	+	9.21839i	0.524416	+	0.524416i
$310$		0			0
$311$	−9.07002			−0.514314			−0.257157	−	0.966370i	$-0.582786\pi$
$311$	−9.07002			−0.514314			−0.257157	+	0.966370i	$0.582786\pi$
$312$		0			0
$313$	2.78399	+	2.78399i	0.157361	+	0.157361i	0.781396	−	0.624035i	$-0.214508\pi$
$313$	2.78399	+	2.78399i	0.157361	+	0.157361i	−0.624035	+	0.781396i	$0.714508\pi$
$314$		0			0
$315$		0			0
$316$		0			0
$317$			14.8639i			0.834838i	0.908714	+	0.417419i	$0.137065\pi$
$317$			14.8639i			0.834838i	−0.908714	+	0.417419i	$0.862935\pi$
$318$		0			0
$319$	−39.2941			−2.20005
$320$		0			0
$321$	−3.95142			−0.220547
$322$		0			0
$323$			10.5255i			0.585653i
$324$		0			0
$325$		0			0
$326$		0			0
$327$	−2.92020	−	2.92020i	−0.161487	−	0.161487i
$328$		0			0
$329$	1.91561			0.105611
$330$		0			0
$331$	8.73942	+	8.73942i	0.480362	+	0.480362i	0.905247	−	0.424885i	$-0.139686\pi$
$331$	8.73942	+	8.73942i	0.480362	+	0.480362i	−0.424885	+	0.905247i	$0.639686\pi$
$332$		0			0
$333$	−3.28926			−0.180250
$334$		0			0
$335$		0			0
$336$		0			0
$337$	20.3405	+	20.3405i	1.10802	+	1.10802i	0.993411	+	0.114607i	$0.0365610\pi$
$337$	20.3405	+	20.3405i	1.10802	+	1.10802i	0.114607	+	0.993411i	$0.463439\pi$
$338$		0			0
$339$	9.19867	+	9.19867i	0.499603	+	0.499603i
$340$		0			0
$341$	−10.1181	+	10.1181i	−0.547928	+	0.547928i
$342$		0			0
$343$	1.95322	−	1.95322i	0.105464	−	0.105464i
$344$		0			0
$345$		0			0
$346$		0			0
$347$		−	7.33669i		−	0.393854i	−0.980418	−	0.196927i	$-0.936904\pi$
$347$		−	7.33669i		−	0.393854i	0.980418	−	0.196927i	$-0.0630963\pi$
$348$		0			0
$349$	−4.99392	+	4.99392i	−0.267319	+	0.267319i	−0.828019	−	0.560700i	$-0.810532\pi$
$349$	−4.99392	+	4.99392i	−0.267319	+	0.267319i	0.560700	+	0.828019i	$0.310532\pi$
$350$		0			0
$351$		−	1.00060i		−	0.0534078i
$352$		0			0
$353$	5.74673	−	5.74673i	0.305868	−	0.305868i	−0.537436	−	0.843304i	$-0.680607\pi$
$353$	5.74673	−	5.74673i	0.305868	−	0.305868i	0.843304	+	0.537436i	$0.180607\pi$
$354$		0			0
$355$		0			0
$356$		0			0
$357$	−0.455778			−0.0241224
$358$		0			0
$359$			22.2959i			1.17673i	0.808594	+	0.588366i	$0.200229\pi$
$359$			22.2959i			1.17673i	−0.808594	+	0.588366i	$0.799771\pi$
$360$		0			0
$361$		−	5.96511i		−	0.313953i
$362$		0			0
$363$	5.04379			0.264730
$364$		0			0
$365$		0			0
$366$		0			0
$367$	22.1923	−	22.1923i	1.15843	−	1.15843i	0.173615	−	0.984814i	$-0.444455\pi$
$367$	22.1923	−	22.1923i	1.15843	−	1.15843i	0.984814	−	0.173615i	$-0.0555448\pi$
$368$		0			0
$369$			19.6287i			1.02183i
$370$		0			0
$371$	−1.14619	+	1.14619i	−0.0595074	+	0.0595074i
$372$		0			0
$373$		−	27.1593i		−	1.40625i	−0.711064	−	0.703127i	$-0.751786\pi$
$373$		−	27.1593i		−	1.40625i	0.711064	−	0.703127i	$-0.248214\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$	1.56986	−	1.56986i	0.0808521	−	0.0808521i
$378$		0			0
$379$	−14.7602	+	14.7602i	−0.758180	+	0.758180i	−0.975991	−	0.217811i	$-0.930108\pi$
$379$	−14.7602	+	14.7602i	−0.758180	+	0.758180i	0.217811	+	0.975991i	$0.430108\pi$
$380$		0			0
$381$	4.27126	+	4.27126i	0.218823	+	0.218823i
$382$		0			0
$383$	14.5976	+	14.5976i	0.745901	+	0.745901i	0.973707	−	0.227805i	$-0.0731550\pi$
$383$	14.5976	+	14.5976i	0.745901	+	0.745901i	−0.227805	+	0.973707i	$0.573155\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−12.8299			−0.652182
$388$		0			0
$389$	3.93745	+	3.93745i	0.199637	+	0.199637i	0.799844	−	0.600208i	$-0.204915\pi$
$389$	3.93745	+	3.93745i	0.199637	+	0.199637i	−0.600208	+	0.799844i	$0.704915\pi$
$390$		0			0
$391$	19.0651			0.964166
$392$		0			0
$393$	12.0702	+	12.0702i	0.608862	+	0.608862i
$394$		0			0
$395$		0			0
$396$		0			0
$397$			27.0000i			1.35509i	0.735481	+	0.677545i	$0.236956\pi$
$397$			27.0000i			1.35509i	−0.735481	+	0.677545i	$0.763044\pi$
$398$		0			0
$399$	−0.564442			−0.0282575
$400$		0			0
$401$	3.02550			0.151086			0.0755432	−	0.997143i	$-0.475931\pi$
$401$	3.02550			0.151086			0.0755432	+	0.997143i	$0.475931\pi$
$402$		0			0
$403$		−	0.808473i		−	0.0402729i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	4.08193	+	4.08193i	0.202334	+	0.202334i
$408$		0			0
$409$	19.6553			0.971894			0.485947	−	0.873988i	$-0.338475\pi$
$409$	19.6553			0.971894			0.485947	+	0.873988i	$0.338475\pi$
$410$		0			0
$411$	−3.48568	−	3.48568i	−0.171936	−	0.171936i
$412$		0			0
$413$	1.20967			0.0595241
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−8.17588	−	8.17588i	−0.400375	−	0.400375i
$418$		0			0
$419$	−16.1834	−	16.1834i	−0.790609	−	0.790609i	0.190984	−	0.981593i	$-0.438832\pi$
$419$	−16.1834	−	16.1834i	−0.790609	−	0.790609i	−0.981593	+	0.190984i	$0.938832\pi$
$420$		0			0
$421$	−23.1841	+	23.1841i	−1.12993	+	1.12993i	−0.139737	+	0.990189i	$0.544626\pi$
$421$	−23.1841	+	23.1841i	−1.12993	+	1.12993i	−0.990189	+	0.139737i	$0.955374\pi$
$422$		0			0
$423$	16.2638	−	16.2638i	0.790773	−	0.790773i
$424$		0			0
$425$		0			0
$426$		0			0
$427$		−	2.56083i		−	0.123927i
$428$		0			0
$429$	−0.548755	+	0.548755i	−0.0264941	+	0.0264941i
$430$		0			0
$431$			29.7907i			1.43497i	0.696575	+	0.717484i	$0.254706\pi$
$431$			29.7907i			1.43497i	−0.696575	+	0.717484i	$0.745294\pi$
$432$		0			0
$433$	19.0587	−	19.0587i	0.915903	−	0.915903i	−0.0808251	−	0.996728i	$-0.525756\pi$
$433$	19.0587	−	19.0587i	0.915903	−	0.915903i	0.996728	+	0.0808251i	$0.0257555\pi$
$434$		0			0
$435$		0			0
$436$		0			0
$437$	23.6105			1.12945
$438$		0			0
$439$			6.10665i			0.291454i	0.989325	+	0.145727i	$0.0465522\pi$
$439$			6.10665i			0.291454i	−0.989325	+	0.145727i	$0.953448\pi$
$440$		0			0
$441$		−	16.5366i		−	0.787458i
$442$		0			0
$443$	16.1163			0.765708			0.382854	−	0.923809i	$-0.374941\pi$
$443$	16.1163			0.765708			0.382854	+	0.923809i	$0.374941\pi$
$444$		0			0
$445$		0			0
$446$		0			0
$447$	−5.63258	+	5.63258i	−0.266412	+	0.266412i
$448$		0			0
$449$			1.87161i			0.0883268i	0.999024	+	0.0441634i	$0.0140622\pi$
$449$			1.87161i			0.0883268i	−0.999024	+	0.0441634i	$0.985938\pi$
$450$		0			0
$451$	24.3590	−	24.3590i	1.14702	−	1.14702i
$452$		0			0
$453$		−	15.5849i		−	0.732243i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−10.7459	+	10.7459i	−0.502673	+	0.502673i	−0.912268	−	0.409594i	$-0.865670\pi$
$457$	−10.7459	+	10.7459i	−0.502673	+	0.502673i	0.409594	+	0.912268i	$0.365670\pi$
$458$		0			0
$459$	−8.75619	+	8.75619i	−0.408704	+	0.408704i
$460$		0			0
$461$	16.5710	+	16.5710i	0.771790	+	0.771790i	0.978419	−	0.206630i	$-0.0662495\pi$
$461$	16.5710	+	16.5710i	0.771790	+	0.771790i	−0.206630	+	0.978419i	$0.566249\pi$
$462$		0			0
$463$	−19.1271	−	19.1271i	−0.888912	−	0.888912i	0.105507	−	0.994419i	$-0.466354\pi$
$463$	−19.1271	−	19.1271i	−0.888912	−	0.888912i	−0.994419	+	0.105507i	$0.966354\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	35.9184			1.66210			0.831052	−	0.556195i	$-0.187739\pi$
$467$	35.9184			1.66210			0.831052	+	0.556195i	$0.187739\pi$
$468$		0			0
$469$	−0.699652	−	0.699652i	−0.0323069	−	0.0323069i
$470$		0			0
$471$	−12.6887			−0.584663
$472$		0			0
$473$	15.9218	+	15.9218i	0.732083	+	0.732083i
$474$		0			0
$475$		0			0
$476$		0			0
$477$			19.4626i			0.891133i
$478$		0			0
$479$	−7.66614			−0.350275			−0.175137	−	0.984544i	$-0.556037\pi$
$479$	−7.66614			−0.350275			−0.175137	+	0.984544i	$0.556037\pi$
$480$		0			0
$481$	−0.326159			−0.0148716
$482$		0			0
$483$			1.02239i			0.0465206i
$484$		0			0
$485$		0			0
$486$		0			0
$487$	−0.0452267	−	0.0452267i	−0.00204942	−	0.00204942i	0.706081	−	0.708131i	$-0.250461\pi$
$487$	−0.0452267	−	0.0452267i	−0.00204942	−	0.00204942i	−0.708131	+	0.706081i	$0.750461\pi$
$488$		0			0
$489$	0.869504			0.0393203
$490$		0			0
$491$	−3.49963	−	3.49963i	−0.157936	−	0.157936i	0.623715	−	0.781651i	$-0.285622\pi$
$491$	−3.49963	−	3.49963i	−0.157936	−	0.157936i	−0.781651	+	0.623715i	$0.785622\pi$
$492$		0			0
$493$	−27.4757			−1.23744
$494$		0			0
$495$		0			0
$496$		0			0
$497$	0.848499	+	0.848499i	0.0380604	+	0.0380604i
$498$		0			0
$499$	18.7985	+	18.7985i	0.841535	+	0.841535i	0.989059	−	0.147523i	$-0.0471301\pi$
$499$	18.7985	+	18.7985i	0.841535	+	0.841535i	−0.147523	+	0.989059i	$0.547130\pi$
$500$		0			0
$501$	9.16889	−	9.16889i	0.409636	−	0.409636i
$502$		0			0
$503$	−11.4064	+	11.4064i	−0.508588	+	0.508588i	−0.914093	−	0.405505i	$-0.867096\pi$
$503$	−11.4064	+	11.4064i	−0.508588	+	0.508588i	0.405505	+	0.914093i	$0.367096\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$			10.2281i			0.454247i
$508$		0			0
$509$	−9.87431	+	9.87431i	−0.437671	+	0.437671i	−0.891228	−	0.453556i	$-0.850155\pi$
$509$	−9.87431	+	9.87431i	−0.437671	+	0.437671i	0.453556	+	0.891228i	$0.350155\pi$
$510$		0			0
$511$		−	3.17997i		−	0.140673i
$512$		0			0
$513$	−10.8438	+	10.8438i	−0.478765	+	0.478765i
$514$		0			0
$515$		0			0
$516$		0			0
$517$	−40.3663			−1.77531
$518$		0			0
$519$		−	11.6244i		−	0.510256i
$520$		0			0
$521$			21.6730i			0.949512i	0.880117	+	0.474756i	$0.157464\pi$
$521$			21.6730i			0.949512i	−0.880117	+	0.474756i	$0.842536\pi$
$522$		0			0
$523$	−40.3785			−1.76563			−0.882813	−	0.469724i	$-0.844353\pi$
$523$	−40.3785			−1.76563			−0.882813	+	0.469724i	$0.844353\pi$
$524$		0			0
$525$		0			0
$526$		0			0
$527$	−7.07493	+	7.07493i	−0.308189	+	0.308189i
$528$		0			0
$529$		−	19.7666i		−	0.859418i
$530$		0			0
$531$	10.2703	−	10.2703i	0.445692	−	0.445692i
$532$		0			0
$533$			1.94636i			0.0843063i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	1.56127	−	1.56127i	0.0673737	−	0.0673737i
$538$		0			0
$539$	−20.5217	+	20.5217i	−0.883933	+	0.883933i
$540$		0			0
$541$	6.26728	+	6.26728i	0.269451	+	0.269451i	0.828879	−	0.559428i	$-0.188979\pi$
$541$	6.26728	+	6.26728i	0.269451	+	0.269451i	−0.559428	+	0.828879i	$0.688979\pi$
$542$		0			0
$543$	−1.15104	−	1.15104i	−0.0493958	−	0.0493958i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	−34.5372			−1.47671			−0.738353	−	0.674415i	$-0.764396\pi$
$547$	−34.5372			−1.47671			−0.738353	+	0.674415i	$0.764396\pi$
$548$		0			0
$549$	−21.7417	−	21.7417i	−0.927915	−	0.927915i
$550$		0			0
$551$	−34.0263			−1.44957
$552$		0			0
$553$	0.622274	+	0.622274i	0.0264618	+	0.0264618i
$554$		0			0
$555$		0			0
$556$		0			0
$557$		−	21.4740i		−	0.909881i	−0.890522	−	0.454940i	$-0.849661\pi$
$557$		−	21.4740i		−	0.909881i	0.890522	−	0.454940i	$-0.150339\pi$
$558$		0			0
$559$	−1.27220			−0.0538084
$560$		0			0
$561$	9.60428			0.405493
$562$		0			0
$563$			6.10126i			0.257138i	0.991701	+	0.128569i	$0.0410383\pi$
$563$			6.10126i			0.257138i	−0.991701	+	0.128569i	$0.958962\pi$
$564$		0			0
$565$		0			0
$566$		0			0
$567$	0.527553	+	0.527553i	0.0221551	+	0.0221551i
$568$		0			0
$569$	31.1884			1.30749			0.653744	−	0.756716i	$-0.273198\pi$
$569$	31.1884			1.30749			0.653744	+	0.756716i	$0.273198\pi$
$570$		0			0
$571$	9.39471	+	9.39471i	0.393156	+	0.393156i	0.875811	−	0.482654i	$-0.160327\pi$
$571$	9.39471	+	9.39471i	0.393156	+	0.393156i	−0.482654	+	0.875811i	$0.660327\pi$
$572$		0			0
$573$	0.225688			0.00942824
$574$		0			0
$575$		0			0
$576$		0			0
$577$	−16.2136	−	16.2136i	−0.674980	−	0.674980i	0.283880	−	0.958860i	$-0.408378\pi$
$577$	−16.2136	−	16.2136i	−0.674980	−	0.674980i	−0.958860	+	0.283880i	$0.908378\pi$
$578$		0			0
$579$	−7.07922	−	7.07922i	−0.294203	−	0.294203i
$580$		0			0
$581$	1.60583	−	1.60583i	0.0666211	−	0.0666211i
$582$		0			0
$583$	24.1529	−	24.1529i	1.00031	−	1.00031i
$584$		0			0
$585$		0			0
$586$		0			0
$587$		−	22.3084i		−	0.920765i	−0.887721	−	0.460382i	$-0.847712\pi$
$587$		−	22.3084i		−	0.920765i	0.887721	−	0.460382i	$-0.152288\pi$
$588$		0			0
$589$	−8.76169	+	8.76169i	−0.361019	+	0.361019i
$590$		0			0
$591$		−	10.1214i		−	0.416338i
$592$		0			0
$593$	5.08162	−	5.08162i	0.208677	−	0.208677i	−0.595028	−	0.803705i	$-0.702859\pi$
$593$	5.08162	−	5.08162i	0.208677	−	0.208677i	0.803705	+	0.595028i	$0.202859\pi$
$594$		0			0
$595$		0			0
$596$		0			0
$597$	14.3900			0.588945
$598$		0			0
$599$		−	45.7467i		−	1.86916i	−0.355752	−	0.934580i	$-0.615775\pi$
$599$		−	45.7467i		−	1.86916i	0.355752	−	0.934580i	$-0.384225\pi$
$600$		0			0
$601$		−	34.5280i		−	1.40843i	−0.709989	−	0.704213i	$-0.751300\pi$
$601$		−	34.5280i		−	1.40843i	0.709989	−	0.704213i	$-0.248700\pi$
$602$		0			0
$603$	−11.8803			−0.483802
$604$		0			0
$605$		0			0
$606$		0			0
$607$	−0.881912	+	0.881912i	−0.0357957	+	0.0357957i	−0.724778	−	0.688982i	$-0.758058\pi$
$607$	−0.881912	+	0.881912i	−0.0357957	+	0.0357957i	0.688982	+	0.724778i	$0.258058\pi$
$608$		0			0
$609$		−	1.47342i		−	0.0597061i
$610$		0			0
$611$	1.61270	−	1.61270i	0.0652429	−	0.0652429i
$612$		0			0
$613$			19.7457i			0.797521i	0.917055	+	0.398760i	$0.130560\pi$
$613$			19.7457i			0.797521i	−0.917055	+	0.398760i	$0.869440\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	24.0643	−	24.0643i	0.968793	−	0.968793i	−0.0307346	−	0.999528i	$-0.509785\pi$
$617$	24.0643	−	24.0643i	0.968793	−	0.968793i	0.999528	+	0.0307346i	$0.00978467\pi$
$618$		0			0
$619$	29.9131	−	29.9131i	1.20231	−	1.20231i	0.228846	−	0.973463i	$-0.426505\pi$
$619$	29.9131	−	29.9131i	1.20231	−	1.20231i	0.973463	−	0.228846i	$-0.0734953\pi$
$620$		0			0
$621$	19.6417	+	19.6417i	0.788196	+	0.788196i
$622$		0			0
$623$	−0.818124	−	0.818124i	−0.0327774	−	0.0327774i
$624$		0			0
$625$		0			0
$626$		0			0
$627$	11.8941			0.475004
$628$		0			0
$629$	2.85421	+	2.85421i	0.113805	+	0.113805i
$630$		0			0
$631$	−49.7586			−1.98086			−0.990429	−	0.138022i	$-0.955926\pi$
$631$	−49.7586			−1.98086			−0.990429	+	0.138022i	$0.955926\pi$
$632$		0			0
$633$	1.89867	+	1.89867i	0.0754652	+	0.0754652i
$634$		0			0
$635$		0			0
$636$		0			0
$637$		−	1.63975i		−	0.0649694i
$638$		0			0
$639$	14.4077			0.569961
$640$		0			0
$641$	−17.3779			−0.686386			−0.343193	−	0.939265i	$-0.611509\pi$
$641$	−17.3779			−0.686386			−0.343193	+	0.939265i	$0.611509\pi$
$642$		0			0
$643$			36.4216i			1.43633i	0.695873	+	0.718165i	$0.255018\pi$
$643$			36.4216i			1.43633i	−0.695873	+	0.718165i	$0.744982\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	3.55333	+	3.55333i	0.139696	+	0.139696i	0.773496	−	0.633801i	$-0.218506\pi$
$647$	3.55333	+	3.55333i	0.139696	+	0.139696i	−0.633801	+	0.773496i	$0.718506\pi$
$648$		0			0
$649$	−25.4906			−1.00059
$650$		0			0
$651$	−0.379403	−	0.379403i	−0.0148700	−	0.0148700i
$652$		0			0
$653$	−38.4729			−1.50556			−0.752781	−	0.658271i	$-0.771288\pi$
$653$	−38.4729			−1.50556			−0.752781	+	0.658271i	$0.771288\pi$
$654$		0			0
$655$		0			0
$656$		0			0
$657$	−26.9983	−	26.9983i	−1.05330	−	1.05330i
$658$		0			0
$659$	17.1857	+	17.1857i	0.669459	+	0.669459i	0.957591	−	0.288132i	$-0.0930342\pi$
$659$	17.1857	+	17.1857i	0.669459	+	0.669459i	−0.288132	+	0.957591i	$0.593034\pi$
$660$		0			0
$661$	−4.63141	+	4.63141i	−0.180141	+	0.180141i	−0.791417	−	0.611276i	$-0.790656\pi$
$661$	−4.63141	+	4.63141i	−0.180141	+	0.180141i	0.611276	+	0.791417i	$0.290656\pi$
$662$		0			0
$663$	−0.383707	+	0.383707i	−0.0149019	+	0.0149019i
$664$		0			0
$665$		0			0
$666$		0			0
$667$			61.6330i			2.38644i
$668$		0			0
$669$	6.52928	−	6.52928i	0.252436	−	0.252436i
$670$		0			0
$671$			53.9624i			2.08320i
$672$		0			0
$673$	3.70786	−	3.70786i	0.142928	−	0.142928i	−0.632022	−	0.774950i	$-0.717775\pi$
$673$	3.70786	−	3.70786i	0.142928	−	0.142928i	0.774950	+	0.632022i	$0.217775\pi$
$674$		0			0
$675$		0			0
$676$		0			0
$677$	35.7948			1.37570			0.687852	−	0.725851i	$-0.258554\pi$
$677$	35.7948			1.37570			0.687852	+	0.725851i	$0.258554\pi$
$678$		0			0
$679$			0.144211i			0.00553432i
$680$		0			0
$681$		−	8.36729i		−	0.320635i
$682$		0			0
$683$	−30.5276			−1.16810			−0.584052	−	0.811716i	$-0.698534\pi$
$683$	−30.5276			−1.16810			−0.584052	+	0.811716i	$0.698534\pi$
$684$		0			0
$685$		0			0
$686$		0			0
$687$	3.56446	−	3.56446i	0.135993	−	0.135993i
$688$		0			0
$689$			1.92989i			0.0735231i
$690$		0			0
$691$	16.3626	−	16.3626i	0.622463	−	0.622463i	−0.323698	−	0.946161i	$-0.604926\pi$
$691$	16.3626	−	16.3626i	0.622463	−	0.622463i	0.946161	+	0.323698i	$0.104926\pi$
$692$		0			0
$693$		−	1.95977i		−	0.0744456i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	17.0326	−	17.0326i	0.645155	−	0.645155i
$698$		0			0
$699$	−1.26671	+	1.26671i	−0.0479114	+	0.0479114i
$700$		0			0
$701$	−5.97112	−	5.97112i	−0.225526	−	0.225526i	0.585295	−	0.810821i	$-0.300979\pi$
$701$	−5.97112	−	5.97112i	−0.225526	−	0.225526i	−0.810821	+	0.585295i	$0.800979\pi$
$702$		0			0
$703$	3.53470	+	3.53470i	0.133314	+	0.133314i
$704$		0			0
$705$		0			0
$706$		0			0
$707$	0.998009			0.0375340
$708$		0			0
$709$	4.50479	+	4.50479i	0.169181	+	0.169181i	0.786619	−	0.617438i	$-0.211830\pi$
$709$	4.50479	+	4.50479i	0.169181	+	0.169181i	−0.617438	+	0.786619i	$0.711830\pi$
$710$		0			0
$711$	10.5664			0.396270
$712$		0			0
$713$	15.8704	+	15.8704i	0.594350	+	0.594350i
$714$		0			0
$715$		0			0
$716$		0			0
$717$		−	11.1843i		−	0.417686i
$718$		0			0
$719$	34.8855			1.30101			0.650504	−	0.759503i	$-0.274558\pi$
$719$	34.8855			1.30101			0.650504	+	0.759503i	$0.274558\pi$
$720$		0			0
$721$	−3.26448			−0.121576
$722$		0			0
$723$		−	3.35979i		−	0.124952i
$724$		0			0
$725$		0			0
$726$		0			0
$727$	−20.1354	−	20.1354i	−0.746781	−	0.746781i	0.227092	−	0.973873i	$-0.427078\pi$
$727$	−20.1354	−	20.1354i	−0.746781	−	0.746781i	−0.973873	+	0.227092i	$0.927078\pi$
$728$		0			0
$729$	−1.11076			−0.0411393
$730$		0			0
$731$	11.1330	+	11.1330i	0.411769	+	0.411769i
$732$		0			0
$733$	−29.8111			−1.10110			−0.550549	−	0.834803i	$-0.685581\pi$
$733$	−29.8111			−1.10110			−0.550549	+	0.834803i	$0.685581\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	14.7432	+	14.7432i	0.543074	+	0.543074i
$738$		0			0
$739$	18.8014	+	18.8014i	0.691620	+	0.691620i	0.962588	−	0.270969i	$-0.0873439\pi$
$739$	18.8014	+	18.8014i	0.691620	+	0.691620i	−0.270969	+	0.962588i	$0.587344\pi$
$740$		0			0
$741$	−0.475188	+	0.475188i	−0.0174565	+	0.0174565i
$742$		0			0
$743$	8.34445	−	8.34445i	0.306128	−	0.306128i	−0.537277	−	0.843406i	$-0.680547\pi$
$743$	8.34445	−	8.34445i	0.306128	−	0.306128i	0.843406	+	0.537277i	$0.180547\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$		−	27.2674i		−	0.997662i
$748$		0			0
$749$	0.699652	−	0.699652i	0.0255647	−	0.0255647i
$750$		0			0
$751$		−	40.1477i		−	1.46501i	−0.680761	−	0.732505i	$-0.738351\pi$
$751$		−	40.1477i		−	1.46501i	0.680761	−	0.732505i	$-0.261649\pi$
$752$		0			0
$753$	1.01970	−	1.01970i	0.0371598	−	0.0371598i
$754$		0			0
$755$		0			0
$756$		0			0
$757$	−31.5795			−1.14778			−0.573888	−	0.818934i	$-0.694565\pi$
$757$	−31.5795			−1.14778			−0.573888	+	0.818934i	$0.694565\pi$
$758$		0			0
$759$		−	21.5442i		−	0.782004i
$760$		0			0
$761$		−	29.0804i		−	1.05416i	−0.849815	−	0.527081i	$-0.823286\pi$
$761$		−	29.0804i		−	1.05416i	0.849815	−	0.527081i	$-0.176714\pi$
$762$		0			0
$763$	1.03412			0.0374377
$764$		0			0
$765$		0			0
$766$		0			0
$767$	1.01839	−	1.01839i	0.0367719	−	0.0367719i
$768$		0			0
$769$		−	44.9984i		−	1.62268i	−0.584573	−	0.811341i	$-0.698738\pi$
$769$		−	44.9984i		−	1.62268i	0.584573	−	0.811341i	$-0.301262\pi$
$770$		0			0
$771$	4.52333	−	4.52333i	0.162904	−	0.162904i
$772$		0			0
$773$		−	35.9788i		−	1.29407i	−0.762461	−	0.647035i	$-0.776009\pi$
$773$		−	35.9788i		−	1.29407i	0.762461	−	0.647035i	$-0.223991\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−0.153061	+	0.153061i	−0.00549104	+	0.00549104i
$778$		0			0
$779$	21.0934	−	21.0934i	0.755749	−	0.755749i
$780$		0			0
$781$	−17.8798	−	17.8798i	−0.639789	−	0.639789i
$782$		0			0
$783$	−28.3067	−	28.3067i	−1.01160	−	1.01160i
$784$		0			0
$785$		0			0
$786$		0			0
$787$	−18.5853			−0.662496			−0.331248	−	0.943544i	$-0.607470\pi$
$787$	−18.5853			−0.662496			−0.331248	+	0.943544i	$0.607470\pi$
$788$		0			0
$789$	−13.4866	−	13.4866i	−0.480135	−	0.480135i
$790$		0			0
$791$	−3.25750			−0.115823
$792$		0			0
$793$	−2.15589	−	2.15589i	−0.0765578	−	0.0765578i
$794$		0			0
$795$		0			0
$796$		0			0
$797$		−	27.5437i		−	0.975649i	−0.872942	−	0.487824i	$-0.837791\pi$
$797$		−	27.5437i		−	0.975649i	0.872942	−	0.487824i	$-0.162209\pi$
$798$		0			0
$799$	−28.2254			−0.998544
$800$		0			0
$801$	−13.8919			−0.490848
$802$		0			0
$803$			67.0091i			2.36470i
$804$		0			0
$805$		0			0
$806$		0			0
$807$	4.86304	+	4.86304i	0.171187	+	0.171187i
$808$		0			0
$809$	45.0587			1.58418			0.792090	−	0.610404i	$-0.208993\pi$
$809$	45.0587			1.58418			0.792090	+	0.610404i	$0.208993\pi$
$810$		0			0
$811$	19.2189	+	19.2189i	0.674865	+	0.674865i	0.958834	−	0.283968i	$-0.0916511\pi$
$811$	19.2189	+	19.2189i	0.674865	+	0.674865i	−0.283968	+	0.958834i	$0.591651\pi$
$812$		0			0
$813$	−14.5658			−0.510846
$814$		0			0
$815$		0			0
$816$		0			0
$817$	13.7873	+	13.7873i	0.482356	+	0.482356i
$818$		0			0
$819$	0.0782961	+	0.0782961i	0.00273589	+	0.00273589i
$820$		0			0
$821$	−30.5315	+	30.5315i	−1.06556	+	1.06556i	−0.0678632	+	0.997695i	$0.521618\pi$
$821$	−30.5315	+	30.5315i	−1.06556	+	1.06556i	−0.997695	+	0.0678632i	$0.978382\pi$
$822$		0			0
$823$	−18.1848	+	18.1848i	−0.633884	+	0.633884i	−0.949040	−	0.315156i	$-0.897943\pi$
$823$	−18.1848	+	18.1848i	−0.633884	+	0.633884i	0.315156	+	0.949040i	$0.397943\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$		−	20.7073i		−	0.720063i	−0.932940	−	0.360032i	$-0.882766\pi$
$827$		−	20.7073i		−	0.720063i	0.932940	−	0.360032i	$-0.117234\pi$
$828$		0			0
$829$	−19.5152	+	19.5152i	−0.677790	+	0.677790i	−0.959500	−	0.281710i	$-0.909099\pi$
$829$	−19.5152	+	19.5152i	−0.677790	+	0.677790i	0.281710	+	0.959500i	$0.409099\pi$
$830$		0			0
$831$			12.0325i			0.417403i
$832$		0			0
$833$	−14.3494	+	14.3494i	−0.497179	+	0.497179i
$834$		0			0
$835$		0			0
$836$		0			0
$837$	−14.5778			−0.503882
$838$		0			0
$839$		−	10.8185i		−	0.373496i	−0.982408	−	0.186748i	$-0.940205\pi$
$839$		−	10.8185i		−	0.373496i	0.982408	−	0.186748i	$-0.0597948\pi$
$840$		0			0
$841$		−	59.8223i		−	2.06284i
$842$		0			0
$843$	5.59298			0.192632
$844$		0			0
$845$		0			0
$846$		0			0
$847$	−0.893071	+	0.893071i	−0.0306863	+	0.0306863i
$848$		0			0
$849$		−	15.7377i		−	0.540116i
$850$		0			0
$851$	6.40253	−	6.40253i	0.219476	−	0.219476i
$852$		0			0
$853$			5.42003i			0.185578i	0.995686	+	0.0927892i	$0.0295783\pi$
$853$			5.42003i			0.185578i	−0.995686	+	0.0927892i	$0.970422\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	4.89352	−	4.89352i	0.167160	−	0.167160i	−0.618570	−	0.785730i	$-0.712288\pi$
$857$	4.89352	−	4.89352i	0.167160	−	0.167160i	0.785730	+	0.618570i	$0.212288\pi$
$858$		0			0
$859$	33.4966	−	33.4966i	1.14289	−	1.14289i	0.154969	−	0.987919i	$-0.450472\pi$
$859$	33.4966	−	33.4966i	1.14289	−	1.14289i	0.987919	−	0.154969i	$-0.0495279\pi$
$860$		0			0
$861$	0.913395	+	0.913395i	0.0311284	+	0.0311284i
$862$		0			0
$863$	28.0996	+	28.0996i	0.956521	+	0.956521i	0.999093	−	0.0425724i	$-0.0135553\pi$
$863$	28.0996	+	28.0996i	0.956521	+	0.956521i	−0.0425724	+	0.999093i	$0.513555\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−6.71697			−0.228120
$868$		0			0
$869$	−13.1127	−	13.1127i	−0.444819	−	0.444819i
$870$		0			0
$871$	−1.17803			−0.0399162
$872$		0			0
$873$	1.22437	+	1.22437i	0.0414387	+	0.0414387i
$874$		0			0
$875$		0			0
$876$		0			0
$877$		−	21.3398i		−	0.720593i	−0.932838	−	0.360296i	$-0.882676\pi$
$877$		−	21.3398i		−	0.720593i	0.932838	−	0.360296i	$-0.117324\pi$
$878$		0			0
$879$	18.2757			0.616423
$880$		0			0
$881$	−34.8632			−1.17457			−0.587285	−	0.809380i	$-0.699803\pi$
$881$	−34.8632			−1.17457			−0.587285	+	0.809380i	$0.699803\pi$
$882$		0			0
$883$		−	16.9490i		−	0.570381i	−0.958471	−	0.285190i	$-0.907943\pi$
$883$		−	16.9490i		−	0.570381i	0.958471	−	0.285190i	$-0.0920568\pi$
$884$		0			0
$885$		0			0
$886$		0			0
$887$	−33.7217	−	33.7217i	−1.13226	−	1.13226i	−0.989800	−	0.142464i	$-0.954498\pi$
$887$	−33.7217	−	33.7217i	−1.13226	−	1.13226i	−0.142464	−	0.989800i	$-0.545502\pi$
$888$		0			0
$889$	−1.51257			−0.0507300
$890$		0			0
$891$	−11.1167	−	11.1167i	−0.372424	−	0.372424i
$892$		0			0
$893$	−34.9548			−1.16972
$894$		0			0
$895$		0			0
$896$		0			0
$897$	0.860725	+	0.860725i	0.0287388	+	0.0287388i
$898$		0			0
$899$	−22.8715	−	22.8715i	−0.762808	−	0.762808i
$900$		0			0
$901$	16.8885	−	16.8885i	0.562637	−	0.562637i
$902$		0			0
$903$	−0.597023	+	0.597023i	−0.0198677	+	0.0198677i
$904$		0			0
$905$		0			0
$906$		0			0
$907$		−	18.9797i		−	0.630210i	−0.949057	−	0.315105i	$-0.897960\pi$
$907$		−	18.9797i		−	0.630210i	0.949057	−	0.315105i	$-0.102040\pi$
$908$		0			0
$909$	8.47322	−	8.47322i	0.281039	−	0.281039i
$910$		0			0
$911$			15.0326i			0.498053i	0.968497	+	0.249027i	$0.0801107\pi$
$911$			15.0326i			0.498053i	−0.968497	+	0.249027i	$0.919889\pi$
$912$		0			0
$913$	−33.8385	+	33.8385i	−1.11989	+	1.11989i
$914$		0			0
$915$		0			0
$916$		0			0
$917$	−4.27439			−0.141153
$918$		0			0
$919$		−	37.9183i		−	1.25081i	−0.780301	−	0.625404i	$-0.784934\pi$
$919$		−	37.9183i		−	1.25081i	0.780301	−	0.625404i	$-0.215066\pi$
$920$		0			0
$921$		−	3.02550i		−	0.0996938i
$922$		0			0
$923$	1.42865			0.0470247
$924$		0			0
$925$		0			0
$926$		0			0
$927$	−27.7158	+	27.7158i	−0.910308	+	0.910308i
$928$		0			0
$929$			22.5607i			0.740193i	0.928993	+	0.370096i	$0.120675\pi$
$929$			22.5607i			0.740193i	−0.928993	+	0.370096i	$0.879325\pi$
$930$		0			0
$931$	−17.7706	+	17.7706i	−0.582406	+	0.582406i
$932$		0			0
$933$			7.16670i			0.234627i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	7.98622	−	7.98622i	0.260898	−	0.260898i	−0.564521	−	0.825419i	$-0.690939\pi$
$937$	7.98622	−	7.98622i	0.260898	−	0.260898i	0.825419	+	0.564521i	$0.190939\pi$
$938$		0			0
$939$	2.19978	−	2.19978i	0.0717871	−	0.0717871i
$940$		0			0
$941$	26.4926	+	26.4926i	0.863633	+	0.863633i	0.991758	−	0.128125i	$-0.0408958\pi$
$941$	26.4926	+	26.4926i	0.863633	+	0.863633i	−0.128125	+	0.991758i	$0.540896\pi$
$942$		0			0
$943$	−38.2072	−	38.2072i	−1.24420	−	1.24420i
$944$		0			0
$945$		0			0
$946$		0			0
$947$	25.8742			0.840797			0.420399	−	0.907339i	$-0.361890\pi$
$947$	25.8742			0.840797			0.420399	+	0.907339i	$0.361890\pi$
$948$		0			0
$949$	−2.67712	−	2.67712i	−0.0869031	−	0.0869031i
$950$		0			0
$951$	11.7447			0.380849
$952$		0			0
$953$	−0.934991	−	0.934991i	−0.0302873	−	0.0302873i	0.691801	−	0.722088i	$-0.256818\pi$
$953$	−0.934991	−	0.934991i	−0.0302873	−	0.0302873i	−0.722088	+	0.691801i	$0.756818\pi$
$954$		0			0
$955$		0			0
$956$		0			0
$957$			31.0483i			1.00365i
$958$		0			0
$959$	1.23437			0.0398600
$960$		0			0
$961$	19.2213			0.620041
$962$		0			0
$963$		−	11.8803i		−	0.382836i
$964$		0			0
$965$		0			0
$966$		0			0
$967$	−1.89923	−	1.89923i	−0.0610752	−	0.0610752i	0.675909	−	0.736985i	$-0.263751\pi$
$967$	−1.89923	−	1.89923i	−0.0610752	−	0.0610752i	−0.736985	+	0.675909i	$0.763751\pi$
$968$		0			0
$969$	8.31672			0.267172
$970$		0			0
$971$	−11.8787	−	11.8787i	−0.381204	−	0.381204i	0.490332	−	0.871536i	$-0.336876\pi$
$971$	−11.8787	−	11.8787i	−0.381204	−	0.381204i	−0.871536	+	0.490332i	$0.836876\pi$
$972$		0			0
$973$	2.89530			0.0928191
$974$		0			0
$975$		0			0
$976$		0			0
$977$	−23.4462	−	23.4462i	−0.750109	−	0.750109i	0.224390	−	0.974499i	$-0.427961\pi$
$977$	−23.4462	−	23.4462i	−0.750109	−	0.750109i	−0.974499	+	0.224390i	$0.927961\pi$
$978$		0			0
$979$	17.2397	+	17.2397i	0.550984	+	0.550984i
$980$		0			0
$981$	8.77982	−	8.77982i	0.280318	−	0.280318i
$982$		0			0
$983$	−5.90331	+	5.90331i	−0.188286	+	0.188286i	−0.794955	−	0.606669i	$-0.792506\pi$
$983$	−5.90331	+	5.90331i	−0.188286	+	0.188286i	0.606669	+	0.794955i	$0.292506\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$		−	1.51363i		−	0.0481793i
$988$		0			0
$989$	24.9734	−	24.9734i	0.794107	−	0.794107i
$990$		0			0
$991$		−	8.28808i		−	0.263280i	−0.991298	−	0.131640i	$-0.957976\pi$
$991$		−	8.28808i		−	0.263280i	0.991298	−	0.131640i	$-0.0420242\pi$
$992$		0			0
$993$	6.90548	−	6.90548i	0.219139	−	0.219139i
$994$		0			0
$995$		0			0
$996$		0			0
$997$	12.9184			0.409130			0.204565	−	0.978853i	$-0.434422\pi$
$997$	12.9184			0.409130			0.204565	+	0.978853i	$0.434422\pi$
$998$		0			0
$999$			5.88107i			0.186069i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1600.2.j.e.1007.5		24
4.3	odd	2		400.2.j.e.307.6	yes	24
5.2	odd	4		1600.2.s.e.943.5		24
5.3	odd	4		1600.2.s.e.943.8		24
5.4	even	2	inner	1600.2.j.e.1007.8		24
16.5	even	4		400.2.s.e.107.1	yes	24
16.11	odd	4		1600.2.s.e.207.8		24
20.3	even	4		400.2.s.e.243.1	yes	24
20.7	even	4		400.2.s.e.243.12	yes	24
20.19	odd	2		400.2.j.e.307.7	yes	24
80.27	even	4	inner	1600.2.j.e.143.5		24
80.37	odd	4		400.2.j.e.43.7	yes	24
80.43	even	4	inner	1600.2.j.e.143.8		24
80.53	odd	4		400.2.j.e.43.6	✓	24
80.59	odd	4		1600.2.s.e.207.5		24
80.69	even	4		400.2.s.e.107.12	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
400.2.j.e.43.6	✓	24	80.53	odd	4
400.2.j.e.43.7	yes	24	80.37	odd	4
400.2.j.e.307.6	yes	24	4.3	odd	2
400.2.j.e.307.7	yes	24	20.19	odd	2
400.2.s.e.107.1	yes	24	16.5	even	4
400.2.s.e.107.12	yes	24	80.69	even	4
400.2.s.e.243.1	yes	24	20.3	even	4
400.2.s.e.243.12	yes	24	20.7	even	4
1600.2.j.e.143.5		24	80.27	even	4	inner
1600.2.j.e.143.8		24	80.43	even	4	inner
1600.2.j.e.1007.5		24	1.1	even	1	trivial
1600.2.j.e.1007.8		24	5.4	even	2	inner
1600.2.s.e.207.5		24	80.59	odd	4
1600.2.s.e.207.8		24	16.11	odd	4
1600.2.s.e.943.5		24	5.2	odd	4
1600.2.s.e.943.8		24	5.3	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:	\( N \)	\(=\)	\( 1600 = 2^{6} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1600.j (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-0.790153i q^{3} +(0.139907 + 0.139907i) q^{7} +2.37566 q^{9} +O(q^{10})\)	\(q-0.790153i q^{3} +(0.139907 + 0.139907i) q^{7} +2.37566 q^{9} +(-2.94816 - 2.94816i) q^{11} +0.235568 q^{13} +(-2.06145 - 2.06145i) q^{17} +(-2.55293 - 2.55293i) q^{19} +(0.110548 - 0.110548i) q^{21} +(-4.62421 + 4.62421i) q^{23} -4.24759i q^{27} +(6.66417 - 6.66417i) q^{29} -3.43202i q^{31} +(-2.32950 + 2.32950i) q^{33} -1.38457 q^{37} -0.186135i q^{39} +8.26242i q^{41} -5.40057 q^{43} +(6.84602 - 6.84602i) q^{47} -6.96085i q^{49} +(-1.62886 + 1.62886i) q^{51} +8.19252i q^{53} +(-2.01720 + 2.01720i) q^{57} +(4.32313 - 4.32313i) q^{59} +(-9.15188 - 9.15188i) q^{61} +(0.332372 + 0.332372i) q^{63} -5.00083 q^{67} +(3.65383 + 3.65383i) q^{69} +6.06473 q^{71} +(-11.3646 - 11.3646i) q^{73} -0.824938i q^{77} +4.44776 q^{79} +3.77073 q^{81} -11.4778i q^{83} +(-5.26571 - 5.26571i) q^{87} -5.84762 q^{89} +(0.0329576 + 0.0329576i) q^{91} -2.71182 q^{93} +(0.515382 + 0.515382i) q^{97} +(-7.00383 - 7.00383i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 40 q^{9}+O(q^{10}) \) 24 * q - 40 * q^9	\( 24 q - 40 q^{9} + 20 q^{11} + 12 q^{19} + 8 q^{29} - 20 q^{51} - 8 q^{59} - 48 q^{61} - 64 q^{69} + 16 q^{71} + 104 q^{79} + 48 q^{81} + 96 q^{89} - 64 q^{91} - 128 q^{99}+O(q^{100}) \) 24 * q - 40 * q^9 + 20 * q^11 + 12 * q^19 + 8 * q^29 - 20 * q^51 - 8 * q^59 - 48 * q^61 - 64 * q^69 + 16 * q^71 + 104 * q^79 + 48 * q^81 + 96 * q^89 - 64 * q^91 - 128 * q^99

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