LMFDB - Embedded newform 775.2.o.d.749.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [775,2,Mod(149,775)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("775.149"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(775, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 775 = 5^{2} \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	775.o (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,-8,0,-12] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$6.18840615665$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 31)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			749.1
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	775.749
Dual form			775.2.o.d.149.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.41421i q^{2} +(-2.09077 - 1.20711i) q^{3} -3.82843 q^{4} +(-2.91421 + 5.04757i) q^{6} +(-2.09077 - 1.20711i) q^{7} +4.41421i q^{8} +(1.41421 + 2.44949i) q^{9} +(2.62132 + 4.54026i) q^{11} +(8.00436 + 4.62132i) q^{12} +(-1.58346 + 0.914214i) q^{13} +(-2.91421 + 5.04757i) q^{14} +3.00000 q^{16} +(0.148586 + 0.0857864i) q^{17} +(5.91359 - 3.41421i) q^{18} +(0.792893 - 1.37333i) q^{19} +(2.91421 + 5.04757i) q^{21} +(10.9612 - 6.32843i) q^{22} +4.00000i q^{23} +(5.32843 - 9.22911i) q^{24} +(2.20711 + 3.82282i) q^{26} +0.414214i q^{27} +(8.00436 + 4.62132i) q^{28} +1.17157 q^{29} +(-5.00000 - 2.44949i) q^{31} +1.58579i q^{32} -12.6569i q^{33} +(0.207107 - 0.358719i) q^{34} +(-5.41421 - 9.37769i) q^{36} +(-0.866025 - 0.500000i) q^{37} +(-3.31552 - 1.91421i) q^{38} +4.41421 q^{39} +(-4.74264 - 8.21449i) q^{41} +(12.1859 - 7.03553i) q^{42} +(7.70719 + 4.44975i) q^{43} +(-10.0355 - 17.3821i) q^{44} +9.65685 q^{46} -1.65685i q^{47} +(-6.27231 - 3.62132i) q^{48} +(-0.585786 - 1.01461i) q^{49} +(-0.207107 - 0.358719i) q^{51} +(6.06218 - 3.50000i) q^{52} +(-0.148586 + 0.0857864i) q^{53} +1.00000 q^{54} +(5.32843 - 9.22911i) q^{56} +(-3.31552 + 1.91421i) q^{57} -2.82843i q^{58} +(-5.03553 + 8.72180i) q^{59} +2.82843 q^{61} +(-5.91359 + 12.0711i) q^{62} -6.82843i q^{63} +9.82843 q^{64} -30.5563 q^{66} +(-4.54026 + 2.62132i) q^{67} +(-0.568852 - 0.328427i) q^{68} +(4.82843 - 8.36308i) q^{69} +(7.03553 + 12.1859i) q^{71} +(-10.8126 + 6.24264i) q^{72} +(-3.31552 + 1.91421i) q^{73} +(-1.20711 + 2.09077i) q^{74} +(-3.03553 + 5.25770i) q^{76} -12.6569i q^{77} -10.6569i q^{78} +(-7.62132 + 13.2005i) q^{79} +(4.74264 - 8.21449i) q^{81} +(-19.8315 + 11.4497i) q^{82} +(-3.52565 + 2.03553i) q^{83} +(-11.1569 - 19.3242i) q^{84} +(10.7426 - 18.6068i) q^{86} +(-2.44949 - 1.41421i) q^{87} +(-20.0417 + 11.5711i) q^{88} +12.4853 q^{89} +4.41421 q^{91} -15.3137i q^{92} +(7.49706 + 11.1569i) q^{93} -4.00000 q^{94} +(1.91421 - 3.31552i) q^{96} +10.8284i q^{97} +(-2.44949 + 1.41421i) q^{98} +(-7.41421 + 12.8418i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} - 12 q^{6} + 4 q^{11} - 12 q^{14} + 24 q^{16} + 12 q^{19} + 12 q^{21} + 20 q^{24} + 12 q^{26} + 32 q^{29} - 40 q^{31} - 4 q^{34} - 32 q^{36} + 24 q^{39} - 4 q^{41} - 52 q^{44} + 32 q^{46}+ \cdots - 48 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 - 12 * q^6 + 4 * q^11 - 12 * q^14 + 24 * q^16 + 12 * q^19 + 12 * q^21 + 20 * q^24 + 12 * q^26 + 32 * q^29 - 40 * q^31 - 4 * q^34 - 32 * q^36 + 24 * q^39 - 4 * q^41 - 52 * q^44 + 32 * q^46 - 16 * q^49 + 4 * q^51 + 8 * q^54 + 20 * q^56 - 12 * q^59 + 56 * q^64 - 120 * q^66 + 16 * q^69 + 28 * q^71 - 4 * q^74 + 4 * q^76 - 44 * q^79 + 4 * q^81 - 44 * q^84 + 52 * q^86 + 32 * q^89 + 24 * q^91 - 32 * q^94 + 4 * q^96 - 48 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/775\mathbb{Z}\right)^\times$.

$n$	$251$	$652$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$		−	2.41421i		−	1.70711i	−0.521005	−	0.853553i	$-0.674443\pi$
$2$		−	2.41421i		−	1.70711i	0.521005	−	0.853553i	$-0.325557\pi$
$3$	−2.09077	−	1.20711i	−1.20711	−	0.696923i	−0.244981	−	0.969528i	$-0.578782\pi$
$3$	−2.09077	−	1.20711i	−1.20711	−	0.696923i	−0.962126	+	0.272605i	$0.912115\pi$
$4$	−3.82843			−1.91421
$5$		0			0
$5$		0			0
$6$	−2.91421	+	5.04757i	−1.18972	+	2.06066i
$7$	−2.09077	−	1.20711i	−0.790237	−	0.456243i	0.0498090	−	0.998759i	$-0.484139\pi$
$7$	−2.09077	−	1.20711i	−0.790237	−	0.456243i	−0.840046	+	0.542515i	$0.817472\pi$
$8$			4.41421i			1.56066i
$9$	1.41421	+	2.44949i	0.471405	+	0.816497i
$10$		0			0
$11$	2.62132	+	4.54026i	0.790358	+	1.36894i	0.925745	+	0.378147i	$0.123439\pi$
$11$	2.62132	+	4.54026i	0.790358	+	1.36894i	−0.135388	+	0.990793i	$0.543228\pi$
$12$	8.00436	+	4.62132i	2.31066	+	1.33406i
$13$	−1.58346	+	0.914214i	−0.439174	+	0.253557i	−0.703247	−	0.710945i	$-0.748267\pi$
$13$	−1.58346	+	0.914214i	−0.439174	+	0.253557i	0.264073	+	0.964503i	$0.414934\pi$
$14$	−2.91421	+	5.04757i	−0.778856	+	1.34902i
$15$		0			0
$16$	3.00000			0.750000
$17$	0.148586	+	0.0857864i	0.0360375	+	0.0208063i	0.517911	−	0.855435i	$-0.326710\pi$
$17$	0.148586	+	0.0857864i	0.0360375	+	0.0208063i	−0.481873	+	0.876241i	$0.660043\pi$
$18$	5.91359	−	3.41421i	1.39385	−	0.804738i
$19$	0.792893	−	1.37333i	0.181902	−	0.315064i	−0.760626	−	0.649190i	$-0.775108\pi$
$19$	0.792893	−	1.37333i	0.181902	−	0.315064i	0.942528	+	0.334126i	$0.108441\pi$
$20$		0			0
$21$	2.91421	+	5.04757i	0.635934	+	1.10147i
$22$	10.9612	−	6.32843i	2.33693	−	1.34923i
$23$			4.00000i			0.834058i	0.908893	+	0.417029i	$0.136929\pi$
$23$			4.00000i			0.834058i	−0.908893	+	0.417029i	$0.863071\pi$
$24$	5.32843	−	9.22911i	1.08766	−	1.88388i
$25$		0			0
$26$	2.20711	+	3.82282i	0.432849	+	0.749717i
$27$			0.414214i			0.0797154i
$28$	8.00436	+	4.62132i	1.51268	+	0.873347i
$29$	1.17157			0.217556			0.108778	−	0.994066i	$-0.465306\pi$
$29$	1.17157			0.217556			0.108778	+	0.994066i	$0.465306\pi$
$30$		0			0
$31$	−5.00000	−	2.44949i	−0.898027	−	0.439941i
$31$	−5.00000	−	2.44949i	−0.898027	−	0.439941i
$32$			1.58579i			0.280330i
$33$		−	12.6569i		−	2.20328i
$34$	0.207107	−	0.358719i	0.0355185	−	0.0615199i
$35$		0			0
$36$	−5.41421	−	9.37769i	−0.902369	−	1.56295i
$37$	−0.866025	−	0.500000i	−0.142374	−	0.0821995i	0.427121	−	0.904194i	$-0.359528\pi$
$37$	−0.866025	−	0.500000i	−0.142374	−	0.0821995i	−0.569495	+	0.821995i	$0.692861\pi$
$38$	−3.31552	−	1.91421i	−0.537848	−	0.310526i
$39$	4.41421			0.706840
$40$		0			0
$41$	−4.74264	−	8.21449i	−0.740676	−	1.28289i	−0.952188	−	0.305513i	$-0.901172\pi$
$41$	−4.74264	−	8.21449i	−0.740676	−	1.28289i	0.211512	−	0.977375i	$-0.432161\pi$
$42$	12.1859	−	7.03553i	1.88033	−	1.08561i
$43$	7.70719	+	4.44975i	1.17534	+	0.678580i	0.954931	−	0.296828i	$-0.0959290\pi$
$43$	7.70719	+	4.44975i	1.17534	+	0.678580i	0.220404	+	0.975409i	$0.429262\pi$
$44$	−10.0355	−	17.3821i	−1.51291	−	2.62044i
$45$		0			0
$46$	9.65685			1.42383
$47$		−	1.65685i		−	0.241677i	−0.992672	−	0.120839i	$-0.961442\pi$
$47$		−	1.65685i		−	0.241677i	0.992672	−	0.120839i	$-0.0385583\pi$
$48$	−6.27231	−	3.62132i	−0.905330	−	0.522693i
$49$	−0.585786	−	1.01461i	−0.0836838	−	0.144945i
$50$		0			0
$51$	−0.207107	−	0.358719i	−0.0290008	−	0.0502308i
$52$	6.06218	−	3.50000i	0.840673	−	0.485363i
$53$	−0.148586	+	0.0857864i	−0.0204099	+	0.0117837i	−0.510170	−	0.860073i	$-0.670418\pi$
$53$	−0.148586	+	0.0857864i	−0.0204099	+	0.0117837i	0.489760	+	0.871857i	$0.337084\pi$
$54$	1.00000			0.136083
$55$		0			0
$56$	5.32843	−	9.22911i	0.712041	−	1.23329i
$57$	−3.31552	+	1.91421i	−0.439151	+	0.253544i
$58$		−	2.82843i		−	0.371391i
$59$	−5.03553	+	8.72180i	−0.655571	+	1.13548i	0.326180	+	0.945308i	$0.394239\pi$
$59$	−5.03553	+	8.72180i	−0.655571	+	1.13548i	−0.981750	+	0.190174i	$0.939095\pi$
$60$		0			0
$61$	2.82843			0.362143			0.181071	−	0.983470i	$-0.442043\pi$
$61$	2.82843			0.362143			0.181071	+	0.983470i	$0.442043\pi$
$62$	−5.91359	+	12.0711i	−0.751027	+	1.53303i
$63$		−	6.82843i		−	0.860301i
$64$	9.82843			1.22855
$65$		0			0
$66$	−30.5563			−3.76123
$67$	−4.54026	+	2.62132i	−0.554681	+	0.320245i	−0.751008	−	0.660293i	$-0.770432\pi$
$67$	−4.54026	+	2.62132i	−0.554681	+	0.320245i	0.196327	+	0.980539i	$0.437099\pi$
$68$	−0.568852	−	0.328427i	−0.0689835	−	0.0398276i
$69$	4.82843	−	8.36308i	0.581274	−	1.00680i
$70$		0			0
$71$	7.03553	+	12.1859i	0.834964	+	1.44620i	0.894060	+	0.447948i	$0.147845\pi$
$71$	7.03553	+	12.1859i	0.834964	+	1.44620i	−0.0590953	+	0.998252i	$0.518822\pi$
$72$	−10.8126	+	6.24264i	−1.27427	+	0.735702i
$73$	−3.31552	+	1.91421i	−0.388052	+	0.224042i	−0.681316	−	0.731990i	$-0.738592\pi$
$73$	−3.31552	+	1.91421i	−0.388052	+	0.224042i	0.293264	+	0.956032i	$0.405259\pi$
$74$	−1.20711	+	2.09077i	−0.140323	+	0.243047i
$75$		0			0
$76$	−3.03553	+	5.25770i	−0.348200	+	0.603099i
$77$		−	12.6569i		−	1.44238i
$78$		−	10.6569i		−	1.20665i
$79$	−7.62132	+	13.2005i	−0.857466	+	1.48517i	0.0168732	+	0.999858i	$0.494629\pi$
$79$	−7.62132	+	13.2005i	−0.857466	+	1.48517i	−0.874339	+	0.485316i	$0.838704\pi$
$80$		0			0
$81$	4.74264	−	8.21449i	0.526960	−	0.912722i
$82$	−19.8315	+	11.4497i	−2.19003	+	1.26441i
$83$	−3.52565	+	2.03553i	−0.386990	+	0.223429i	−0.680855	−	0.732418i	$-0.738392\pi$
$83$	−3.52565	+	2.03553i	−0.386990	+	0.223429i	0.293865	+	0.955847i	$0.405058\pi$
$84$	−11.1569	−	19.3242i	−1.21731	−	2.10845i
$85$		0			0
$86$	10.7426	−	18.6068i	1.15841	−	2.00642i
$87$	−2.44949	−	1.41421i	−0.262613	−	0.151620i
$88$	−20.0417	+	11.5711i	−2.13645	+	1.23348i
$89$	12.4853			1.32344			0.661719	−	0.749752i	$-0.269827\pi$
$89$	12.4853			1.32344			0.661719	+	0.749752i	$0.269827\pi$
$90$		0			0
$91$	4.41421			0.462735
$92$		−	15.3137i		−	1.59656i
$93$	7.49706	+	11.1569i	0.777408	+	1.15691i
$94$	−4.00000			−0.412568
$95$		0			0
$96$	1.91421	−	3.31552i	0.195369	−	0.338388i
$97$			10.8284i			1.09946i	0.835342	+	0.549730i	$0.185269\pi$
$97$			10.8284i			1.09946i	−0.835342	+	0.549730i	$0.814731\pi$
$98$	−2.44949	+	1.41421i	−0.247436	+	0.142857i
$99$	−7.41421	+	12.8418i	−0.745157	+	1.29065i
$100$		0			0
$101$	8.48528			0.844317			0.422159	−	0.906522i	$-0.361273\pi$
$101$	8.48528			0.844317			0.422159	+	0.906522i	$0.361273\pi$
$102$	−0.866025	+	0.500000i	−0.0857493	+	0.0495074i
$103$	10.4539	−	6.03553i	1.03005	−	0.594699i	0.113050	−	0.993589i	$-0.463938\pi$
$103$	10.4539	−	6.03553i	1.03005	−	0.594699i	0.916999	+	0.398890i	$0.130605\pi$
$104$	−4.03553	−	6.98975i	−0.395717	−	0.685401i
$105$		0			0
$106$	0.207107	+	0.358719i	0.0201160	+	0.0348419i
$107$	−8.30153	−	4.79289i	−0.802540	−	0.463346i	0.0418188	−	0.999125i	$-0.486685\pi$
$107$	−8.30153	−	4.79289i	−0.802540	−	0.463346i	−0.844358	+	0.535779i	$0.820018\pi$
$108$		−	1.58579i		−	0.152592i
$109$	5.17157			0.495347			0.247673	−	0.968844i	$-0.420334\pi$
$109$	5.17157			0.495347			0.247673	+	0.968844i	$0.420334\pi$
$110$		0			0
$111$	1.20711	+	2.09077i	0.114574	+	0.198447i
$112$	−6.27231	−	3.62132i	−0.592678	−	0.342183i
$113$	−4.62730	+	2.67157i	−0.435300	+	0.251320i	−0.701602	−	0.712569i	$-0.747531\pi$
$113$	−4.62730	+	2.67157i	−0.435300	+	0.251320i	0.266302	+	0.963890i	$0.414198\pi$
$114$	4.62132	+	8.00436i	0.432826	+	0.749677i
$115$		0			0
$116$	−4.48528			−0.416448
$117$	−4.47871	−	2.58579i	−0.414057	−	0.239056i
$118$	21.0563	+	12.1569i	1.93839	+	1.11913i
$119$	−0.207107	−	0.358719i	−0.0189854	−	0.0328838i
$120$		0			0
$121$	−8.24264	+	14.2767i	−0.749331	+	1.29788i
$122$		−	6.82843i		−	0.618217i
$123$			22.8995i			2.06478i
$124$	19.1421	+	9.37769i	1.71901	+	0.842142i
$125$		0			0
$126$	−16.4853			−1.46863
$127$	9.43924	+	5.44975i	0.837597	+	0.483587i	0.856447	−	0.516235i	$-0.172667\pi$
$127$	9.43924	+	5.44975i	0.837597	+	0.483587i	−0.0188496	+	0.999822i	$0.506000\pi$
$128$		−	20.5563i		−	1.81694i
$129$	−10.7426	−	18.6068i	−0.945837	−	1.63824i
$130$		0			0
$131$	2.37868	−	4.11999i	0.207826	−	0.359966i	−0.743203	−	0.669066i	$-0.766694\pi$
$131$	2.37868	−	4.11999i	0.207826	−	0.359966i	0.951030	+	0.309100i	$0.100028\pi$
$132$			48.4558i			4.21754i
$133$	−3.31552	+	1.91421i	−0.287492	+	0.165983i
$134$	6.32843	+	10.9612i	0.546693	+	0.946900i
$135$		0			0
$136$	−0.378680	+	0.655892i	−0.0324715	+	0.0562423i
$137$	−6.48244	+	3.74264i	−0.553833	+	0.319755i	−0.750666	−	0.660681i	$-0.770267\pi$
$137$	−6.48244	+	3.74264i	−0.553833	+	0.319755i	0.196834	+	0.980437i	$0.436934\pi$
$138$	−20.1903	−	11.6569i	−1.71871	−	0.992297i
$139$		0			0			−	1.00000i	$-0.5\pi$
$139$		0			0				1.00000i	$0.5\pi$
$140$		0			0
$141$	−2.00000	+	3.46410i	−0.168430	+	0.291730i
$142$	29.4194	−	16.9853i	2.46882	−	1.42537i
$143$	−8.30153	−	4.79289i	−0.694209	−	0.400802i
$144$	4.24264	+	7.34847i	0.353553	+	0.612372i
$145$		0			0
$146$	4.62132	+	8.00436i	0.382463	+	0.662446i
$147$			2.82843i			0.233285i
$148$	3.31552	+	1.91421i	0.272534	+	0.157347i
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	−0.844818	−	0.535054i	$-0.820291\pi$
$149$	0.500000	−	0.866025i	0.0409616	−	0.0709476i	0.885779	+	0.464107i	$0.153625\pi$
$150$		0			0
$151$	−17.3137			−1.40897			−0.704485	−	0.709719i	$-0.748822\pi$
$151$	−17.3137			−1.40897			−0.704485	+	0.709719i	$0.748822\pi$
$152$	6.06218	+	3.50000i	0.491708	+	0.283887i
$153$			0.485281i			0.0392327i
$154$	−30.5563			−2.46230
$155$		0			0
$156$	−16.8995			−1.35304
$157$			14.8284i			1.18344i	0.806145	+	0.591719i	$0.201550\pi$
$157$			14.8284i			1.18344i	−0.806145	+	0.591719i	$0.798450\pi$
$158$	31.8689	+	18.3995i	2.53535	+	1.46379i
$159$	0.414214			0.0328493
$160$		0			0
$161$	4.82843	−	8.36308i	0.380533	−	0.659103i
$162$	−19.8315	−	11.4497i	−1.55811	−	0.899577i
$163$			12.9706i			1.01593i	0.861377	+	0.507966i	$0.169603\pi$
$163$			12.9706i			1.01593i	−0.861377	+	0.507966i	$0.830397\pi$
$164$	18.1569	+	31.4486i	1.41781	+	2.45572i
$165$		0			0
$166$	4.91421	+	8.51167i	0.381417	+	0.660634i
$167$	7.41002	+	4.27817i	0.573404	+	0.331055i	0.758508	−	0.651664i	$-0.225929\pi$
$167$	7.41002	+	4.27817i	0.573404	+	0.331055i	−0.185104	+	0.982719i	$0.559262\pi$
$168$	−22.2810	+	12.8640i	−1.71902	+	0.992476i
$169$	−4.82843	+	8.36308i	−0.371417	+	0.643314i
$170$		0			0
$171$	4.48528			0.342998
$172$	−29.5064	−	17.0355i	−2.24984	−	1.29895i
$173$	12.3960	−	7.15685i	0.942453	−	0.544126i	0.0517246	−	0.998661i	$-0.483528\pi$
$173$	12.3960	−	7.15685i	0.942453	−	0.544126i	0.890728	+	0.454536i	$0.150195\pi$
$174$	−3.41421	+	5.91359i	−0.258831	+	0.448308i
$175$		0			0
$176$	7.86396	+	13.6208i	0.592768	+	1.02670i
$177$	21.0563	−	12.1569i	1.58269	−	0.913765i
$178$		−	30.1421i		−	2.25925i
$179$	−3.37868	+	5.85204i	−0.252534	+	0.437402i	−0.964223	−	0.265093i	$-0.914597\pi$
$179$	−3.37868	+	5.85204i	−0.252534	+	0.437402i	0.711689	+	0.702495i	$0.247931\pi$
$180$		0			0
$181$	5.15685	+	8.93193i	0.383306	+	0.663905i	0.991533	−	0.129858i	$-0.0414522\pi$
$181$	5.15685	+	8.93193i	0.383306	+	0.663905i	−0.608227	+	0.793763i	$0.708119\pi$
$182$		−	10.6569i		−	0.789939i
$183$	−5.91359	−	3.41421i	−0.437145	−	0.252386i
$184$	−17.6569			−1.30168
$185$		0			0
$186$	26.9350	−	18.0995i	1.97497	−	1.32712i
$187$			0.899495i			0.0657776i
$188$			6.34315i			0.462621i
$189$	0.500000	−	0.866025i	0.0363696	−	0.0629941i
$190$		0			0
$191$	0.550253	+	0.953065i	0.0398149	+	0.0689614i	0.885246	−	0.465123i	$-0.153990\pi$
$191$	0.550253	+	0.953065i	0.0398149	+	0.0689614i	−0.845431	+	0.534084i	$0.820657\pi$
$192$	−20.5490	−	11.8640i	−1.48300	−	0.856208i
$193$	−18.3096	−	10.5711i	−1.31796	−	0.760922i	−0.334556	−	0.942376i	$-0.608586\pi$
$193$	−18.3096	−	10.5711i	−1.31796	−	0.760922i	−0.983399	+	0.181454i	$0.941920\pi$
$194$	26.1421			1.87690
$195$		0			0
$196$	2.24264	+	3.88437i	0.160189	+	0.277455i
$197$	3.01834	−	1.74264i	0.215048	−	0.124158i	−0.388607	−	0.921404i	$-0.627044\pi$
$197$	3.01834	−	1.74264i	0.215048	−	0.124158i	0.603655	+	0.797245i	$0.293710\pi$
$198$	31.0028	+	17.8995i	2.20328	+	1.27206i
$199$	7.79289	+	13.4977i	0.552424	+	0.956826i	0.998099	+	0.0616310i	$0.0196302\pi$
$199$	7.79289	+	13.4977i	0.552424	+	0.956826i	−0.445675	+	0.895195i	$0.647036\pi$
$200$		0			0
$201$	12.6569			0.892746
$202$		−	20.4853i		−	1.44134i
$203$	−2.44949	−	1.41421i	−0.171920	−	0.0992583i
$204$	0.792893	+	1.37333i	0.0555136	+	0.0961524i
$205$		0			0
$206$	−14.5711	−	25.2378i	−1.01521	−	1.75840i
$207$	−9.79796	+	5.65685i	−0.681005	+	0.393179i
$208$	−4.75039	+	2.74264i	−0.329380	+	0.190168i
$209$	8.31371			0.575071
$210$		0			0
$211$	−3.79289	+	6.56948i	−0.261114	+	0.452262i	−0.966538	−	0.256523i	$-0.917423\pi$
$211$	−3.79289	+	6.56948i	−0.261114	+	0.452262i	0.705425	+	0.708785i	$0.250756\pi$
$212$	0.568852	−	0.328427i	0.0390689	−	0.0225565i
$213$		−	33.9706i		−	2.32762i
$214$	−11.5711	+	20.0417i	−0.790982	+	1.37002i
$215$		0			0
$216$	−1.82843			−0.124409
$217$	7.49706	+	11.1569i	0.508933	+	0.757377i
$218$		−	12.4853i		−	0.845610i
$219$	9.24264			0.624560
$220$		0			0
$221$	−0.313708			−0.0211023
$222$	5.04757	−	2.91421i	0.338770	−	0.195589i
$223$	1.49642	+	0.863961i	0.100208	+	0.0578551i	0.549266	−	0.835647i	$-0.314907\pi$
$223$	1.49642	+	0.863961i	0.100208	+	0.0578551i	−0.449059	+	0.893502i	$0.648241\pi$
$224$	1.91421	−	3.31552i	0.127899	−	0.221527i
$225$		0			0
$226$	6.44975	+	11.1713i	0.429031	+	0.743103i
$227$	−13.4977	+	7.79289i	−0.895873	+	0.517232i	−0.875859	−	0.482567i	$-0.839704\pi$
$227$	−13.4977	+	7.79289i	−0.895873	+	0.517232i	−0.0200140	+	0.999800i	$0.506371\pi$
$228$	12.6932	−	7.32843i	0.840628	−	0.485337i
$229$	5.74264	−	9.94655i	0.379484	−	0.657286i	−0.611503	−	0.791242i	$-0.709435\pi$
$229$	5.74264	−	9.94655i	0.379484	−	0.657286i	0.990987	+	0.133956i	$0.0427681\pi$
$230$		0			0
$231$	−15.2782	+	26.4626i	−1.00523	+	1.74111i
$232$			5.17157i			0.339530i
$233$			14.8284i			0.971443i	0.874114	+	0.485721i	$0.161443\pi$
$233$			14.8284i			0.971443i	−0.874114	+	0.485721i	$0.838557\pi$
$234$	−6.24264	+	10.8126i	−0.408094	+	0.706840i
$235$		0			0
$236$	19.2782	−	33.3908i	1.25490	−	2.17355i
$237$	31.8689	−	18.3995i	2.07010	−	1.19518i
$238$	−0.866025	+	0.500000i	−0.0561361	+	0.0324102i
$239$	−6.37868	−	11.0482i	−0.412602	−	0.714648i	0.582571	−	0.812780i	$-0.302047\pi$
$239$	−6.37868	−	11.0482i	−0.412602	−	0.714648i	−0.995173	+	0.0981314i	$0.968713\pi$
$240$		0			0
$241$	−12.3284	+	21.3535i	−0.794144	+	1.37550i	0.129238	+	0.991614i	$0.458747\pi$
$241$	−12.3284	+	21.3535i	−0.794144	+	1.37550i	−0.923381	+	0.383884i	$0.874586\pi$
$242$	34.4669	+	19.8995i	2.21562	+	1.27919i
$243$	−18.7554	+	10.8284i	−1.20316	+	0.694644i
$244$	−10.8284			−0.693219
$245$		0			0
$246$	55.2843			3.52480
$247$			2.89949i			0.184490i
$248$	10.8126	−	22.0711i	0.686599	−	1.40151i
$249$	9.82843			0.622851
$250$		0			0
$251$	−1.79289	+	3.10538i	−0.113166	+	0.196010i	−0.917045	−	0.398783i	$-0.869433\pi$
$251$	−1.79289	+	3.10538i	−0.113166	+	0.196010i	0.803879	+	0.594793i	$0.202766\pi$
$252$			26.1421i			1.64680i
$253$	−18.1610	+	10.4853i	−1.14177	+	0.659204i
$254$	13.1569	−	22.7883i	0.825534	−	1.42987i
$255$		0			0
$256$	−29.9706			−1.87316
$257$	−0.271680	+	0.156854i	−0.0169469	+	0.00978430i	−0.508450	−	0.861092i	$-0.669781\pi$
$257$	−0.271680	+	0.156854i	−0.0169469	+	0.00978430i	0.491503	+	0.870876i	$0.336448\pi$
$258$	−44.9208	+	25.9350i	−2.79665	+	1.61464i
$259$	1.20711	+	2.09077i	0.0750060	+	0.129914i
$260$		0			0
$261$	1.65685	+	2.86976i	0.102557	+	0.177633i
$262$	−9.94655	−	5.74264i	−0.614500	−	0.354782i
$263$			0.686292i			0.0423185i	0.999776	+	0.0211593i	$0.00673571\pi$
$263$			0.686292i			0.0423185i	−0.999776	+	0.0211593i	$0.993264\pi$
$264$	55.8701			3.43856
$265$		0			0
$266$	4.62132	+	8.00436i	0.283351	+	0.490779i
$267$	−26.1039	−	15.0711i	−1.59753	−	0.922334i
$268$	17.3821	−	10.0355i	1.06178	−	0.613018i
$269$	−15.9142	−	27.5642i	−0.970307	−	1.68062i	−0.694626	−	0.719371i	$-0.744430\pi$
$269$	−15.9142	−	27.5642i	−0.970307	−	1.68062i	−0.275681	−	0.961249i	$-0.588903\pi$
$270$		0			0
$271$	−23.3137			−1.41621			−0.708103	−	0.706109i	$-0.750449\pi$
$271$	−23.3137			−1.41621			−0.708103	+	0.706109i	$0.750449\pi$
$272$	0.445759	+	0.257359i	0.0270281	+	0.0156047i
$273$	−9.22911	−	5.32843i	−0.558571	−	0.322491i
$274$	9.03553	+	15.6500i	0.545857	+	0.945451i
$275$		0			0
$276$	−18.4853	+	32.0174i	−1.11268	+	1.92722i
$277$		−	14.1421i		−	0.849719i	−0.905259	−	0.424859i	$-0.860324\pi$
$277$		−	14.1421i		−	0.849719i	0.905259	−	0.424859i	$-0.139676\pi$
$278$		0			0
$279$	−1.07107	−	15.7116i	−0.0641232	−	0.940626i
$280$		0			0
$281$	2.00000			0.119310			0.0596550	−	0.998219i	$-0.481000\pi$
$281$	2.00000			0.119310			0.0596550	+	0.998219i	$0.481000\pi$
$282$	8.36308	+	4.82843i	0.498014	+	0.287529i
$283$			2.34315i			0.139286i	0.997572	+	0.0696428i	$0.0221859\pi$
$283$			2.34315i			0.139286i	−0.997572	+	0.0696428i	$0.977814\pi$
$284$	−26.9350	−	46.6528i	−1.59830	−	2.76834i
$285$		0			0
$286$	−11.5711	+	20.0417i	−0.684212	+	1.18509i
$287$			22.8995i			1.35171i
$288$	−3.88437	+	2.24264i	−0.228889	+	0.132149i
$289$	−8.48528	−	14.6969i	−0.499134	−	0.864526i
$290$		0			0
$291$	13.0711	−	22.6398i	0.766240	−	1.32717i
$292$	12.6932	−	7.32843i	0.742814	−	0.428864i
$293$	−21.4766	−	12.3995i	−1.25467	−	0.724386i	−0.282640	−	0.959226i	$-0.591210\pi$
$293$	−21.4766	−	12.3995i	−1.25467	−	0.724386i	−0.972034	+	0.234840i	$0.924543\pi$
$294$	6.82843			0.398242
$295$		0			0
$296$	2.20711	−	3.82282i	0.128285	−	0.222197i
$297$	−1.88064	+	1.08579i	−0.109126	+	0.0630037i
$298$	−2.09077	−	1.20711i	−0.121115	−	0.0699258i
$299$	−3.65685	−	6.33386i	−0.211481	−	0.366296i
$300$		0			0
$301$	−10.7426	−	18.6068i	−0.619196	−	1.07248i
$302$			41.7990i			2.40526i
$303$	−17.7408	−	10.2426i	−1.01918	−	0.588424i
$304$	2.37868	−	4.11999i	0.136427	−	0.236298i
$305$		0			0
$306$	1.17157			0.0669744
$307$	2.38794	+	1.37868i	0.136287	+	0.0786854i	0.566593	−	0.823998i	$-0.308261\pi$
$307$	2.38794	+	1.37868i	0.136287	+	0.0786854i	−0.430306	+	0.902683i	$0.641594\pi$
$308$			48.4558i			2.76103i
$309$	−29.1421			−1.65784
$310$		0			0
$311$	−11.3137			−0.641542			−0.320771	−	0.947157i	$-0.603942\pi$
$311$	−11.3137			−0.641542			−0.320771	+	0.947157i	$0.603942\pi$
$312$			19.4853i			1.10314i
$313$	3.31552	+	1.91421i	0.187404	+	0.108198i	0.590767	−	0.806842i	$-0.298825\pi$
$313$	3.31552	+	1.91421i	0.187404	+	0.108198i	−0.403363	+	0.915040i	$0.632159\pi$
$314$	35.7990			2.02025
$315$		0			0
$316$	29.1777	−	50.5372i	1.64137	−	2.84294i
$317$	1.88064	+	1.08579i	0.105627	+	0.0609838i	0.551883	−	0.833922i	$-0.313910\pi$
$317$	1.88064	+	1.08579i	0.105627	+	0.0609838i	−0.446256	+	0.894905i	$0.647243\pi$
$318$		−	1.00000i		−	0.0560772i
$319$	3.07107	+	5.31925i	0.171947	+	0.297821i
$320$		0			0
$321$	11.5711	+	20.0417i	0.645834	+	1.11862i
$322$	−20.1903	−	11.6569i	−1.12516	−	0.649611i
$323$	0.235626	−	0.136039i	0.0131106	−	0.00756941i
$324$	−18.1569	+	31.4486i	−1.00871	+	1.74714i
$325$		0			0
$326$	31.3137			1.73431
$327$	−10.8126	−	6.24264i	−0.597937	−	0.345219i
$328$	36.2605	−	20.9350i	2.00215	−	1.15594i
$329$	−2.00000	+	3.46410i	−0.110264	+	0.190982i
$330$		0			0
$331$	−0.378680	−	0.655892i	−0.0208141	−	0.0360511i	0.855431	−	0.517917i	$-0.173292\pi$
$331$	−0.378680	−	0.655892i	−0.0208141	−	0.0360511i	−0.876245	+	0.481866i	$0.839959\pi$
$332$	13.4977	−	7.79289i	0.740782	−	0.427691i
$333$		−	2.82843i		−	0.154997i
$334$	10.3284	−	17.8894i	0.565146	−	0.978862i
$335$		0			0
$336$	8.74264	+	15.1427i	0.476950	+	0.826102i
$337$		−	13.3137i		−	0.725244i	−0.931936	−	0.362622i	$-0.881882\pi$
$337$		−	13.3137i		−	0.725244i	0.931936	−	0.362622i	$-0.118118\pi$
$338$	20.1903	+	11.6569i	1.09821	+	0.634049i
$339$	12.8995			0.700604
$340$		0			0
$341$	−1.98528	−	29.1222i	−0.107509	−	1.57706i
$342$		−	10.8284i		−	0.585534i
$343$			19.7279i			1.06521i
$344$	−19.6421	+	34.0212i	−1.05903	+	1.83430i
$345$		0			0
$346$	−17.2782	−	29.9267i	−0.928880	−	1.60887i
$347$	−19.5344	−	11.2782i	−1.04866	−	0.605444i	−0.126386	−	0.991981i	$-0.540338\pi$
$347$	−19.5344	−	11.2782i	−1.04866	−	0.605444i	−0.922274	+	0.386537i	$0.873671\pi$
$348$	9.37769	+	5.41421i	0.502697	+	0.290232i
$349$	−35.1127			−1.87954			−0.939770	−	0.341808i	$-0.888961\pi$
$349$	−35.1127			−1.87954			−0.939770	+	0.341808i	$0.888961\pi$
$350$		0			0
$351$	−0.378680	−	0.655892i	−0.0202124	−	0.0350089i
$352$	−7.19988	+	4.15685i	−0.383755	+	0.221561i
$353$	2.59808	+	1.50000i	0.138282	+	0.0798369i	0.567545	−	0.823343i	$-0.307893\pi$
$353$	2.59808	+	1.50000i	0.138282	+	0.0798369i	−0.429263	+	0.903179i	$0.641227\pi$
$354$	−29.3492	−	50.8344i	−1.55989	−	2.70182i
$355$		0			0
$356$	−47.7990			−2.53334
$357$			1.00000i			0.0529256i
$358$	14.1281	+	8.15685i	0.746693	+	0.431103i
$359$	13.4497	+	23.2956i	0.709851	+	1.22950i	0.964912	+	0.262572i	$0.0845709\pi$
$359$	13.4497	+	23.2956i	0.709851	+	1.22950i	−0.255062	+	0.966925i	$0.582096\pi$
$360$		0			0
$361$	8.24264	+	14.2767i	0.433823	+	0.751404i
$362$	21.5636	−	12.4497i	1.13336	−	0.654344i
$363$	34.4669	−	19.8995i	1.80904	−	1.04445i
$364$	−16.8995			−0.885774
$365$		0			0
$366$	−8.24264	+	14.2767i	−0.430850	+	0.746254i
$367$	15.7731	−	9.10660i	0.823349	−	0.475361i	−0.0282210	−	0.999602i	$-0.508984\pi$
$367$	15.7731	−	9.10660i	0.823349	−	0.475361i	0.851570	+	0.524241i	$0.175651\pi$
$368$			12.0000i			0.625543i
$369$	13.4142	−	23.2341i	0.698316	−	1.20952i
$370$		0			0
$371$	0.414214			0.0215049
$372$	−28.7019	−	42.7132i	−1.48813	−	2.21458i
$373$		−	10.0000i		−	0.517780i	−0.965907	−	0.258890i	$-0.916643\pi$
$373$		−	10.0000i		−	0.517780i	0.965907	−	0.258890i	$-0.0833568\pi$
$374$	2.17157			0.112289
$375$		0			0
$376$	7.31371			0.377176
$377$	−1.85514	+	1.07107i	−0.0955448	+	0.0551628i
$378$	−2.09077	−	1.20711i	−0.107538	−	0.0620869i
$379$	−14.6924	+	25.4480i	−0.754697	+	1.30717i	0.190827	+	0.981624i	$0.438883\pi$
$379$	−14.6924	+	25.4480i	−0.754697	+	1.30717i	−0.945525	+	0.325550i	$0.894450\pi$
$380$		0			0
$381$	−13.1569	−	22.7883i	−0.674046	−	1.16748i
$382$	2.30090	−	1.32843i	0.117724	−	0.0679682i
$383$	−21.5636	+	12.4497i	−1.10185	+	0.636152i	−0.936706	−	0.350117i	$-0.886142\pi$
$383$	−21.5636	+	12.4497i	−1.10185	+	0.636152i	−0.165142	+	0.986270i	$0.552808\pi$
$384$	−24.8137	+	42.9786i	−1.26627	+	2.19324i
$385$		0			0
$386$	−25.5208	+	44.2033i	−1.29898	+	2.24989i
$387$			25.1716i			1.27954i
$388$		−	41.4558i		−	2.10460i
$389$	8.57107	−	14.8455i	0.434570	−	0.752698i	−0.562690	−	0.826668i	$-0.690234\pi$
$389$	8.57107	−	14.8455i	0.434570	−	0.752698i	0.997260	+	0.0739699i	$0.0235669\pi$
$390$		0			0
$391$	−0.343146	+	0.594346i	−0.0173536	+	0.0300574i
$392$	4.47871	−	2.58579i	0.226209	−	0.130602i
$393$	−9.94655	+	5.74264i	−0.501737	+	0.289678i
$394$	−4.20711	−	7.28692i	−0.211951	−	0.367110i
$395$		0			0
$396$	28.3848	−	49.1639i	1.42639	−	2.47058i
$397$	14.3022	+	8.25736i	0.717805	+	0.414425i	0.813944	−	0.580943i	$-0.197316\pi$
$397$	14.3022	+	8.25736i	0.717805	+	0.414425i	−0.0961392	+	0.995368i	$0.530649\pi$
$398$	32.5863	−	18.8137i	1.63340	−	0.943046i
$399$	9.24264			0.462711
$400$		0			0
$401$	−21.1716			−1.05726			−0.528629	−	0.848853i	$-0.677294\pi$
$401$	−21.1716			−1.05726			−0.528629	+	0.848853i	$0.677294\pi$
$402$		−	30.5563i		−	1.52401i
$403$	10.1567	−	0.692388i	0.505940	−	0.0344903i
$404$	−32.4853			−1.61620
$405$		0			0
$406$	−3.41421	+	5.91359i	−0.169445	+	0.293487i
$407$		−	5.24264i		−	0.259868i
$408$	1.58346	−	0.914214i	0.0783932	−	0.0452603i
$409$	4.67157	−	8.09140i	0.230994	−	0.400094i	−0.727107	−	0.686525i	$-0.759135\pi$
$409$	4.67157	−	8.09140i	0.230994	−	0.400094i	0.958101	+	0.286431i	$0.0924688\pi$
$410$		0			0
$411$	18.0711			0.891380
$412$	−40.0218	+	23.1066i	−1.97173	+	1.13838i
$413$	21.0563	−	12.1569i	1.03611	−	0.598200i
$414$	13.6569	+	23.6544i	0.671198	+	1.16255i
$415$		0			0
$416$	−1.44975	−	2.51104i	−0.0710797	−	0.123114i
$417$		0			0
$418$		−	20.0711i		−	0.981708i
$419$	−28.0000			−1.36789			−0.683945	−	0.729534i	$-0.739737\pi$
$419$	−28.0000			−1.36789			−0.683945	+	0.729534i	$0.739737\pi$
$420$		0			0
$421$	1.42893	+	2.47498i	0.0696419	+	0.120623i	0.898744	−	0.438474i	$-0.144481\pi$
$421$	1.42893	+	2.47498i	0.0696419	+	0.120623i	−0.829102	+	0.559098i	$0.811148\pi$
$422$	15.8601	+	9.15685i	0.772059	+	0.445749i
$423$	4.05845	−	2.34315i	0.197328	−	0.113928i
$424$	−0.378680	−	0.655892i	−0.0183903	−	0.0318530i
$425$		0			0
$426$	−82.0122			−3.97350
$427$	−5.91359	−	3.41421i	−0.286179	−	0.165225i
$428$	31.7818	+	18.3492i	1.53623	+	0.886944i
$429$	11.5711	+	20.0417i	0.558656	+	0.967621i
$430$		0			0
$431$	12.6213	−	21.8608i	0.607948	−	1.05300i	−0.383631	−	0.923487i	$-0.625326\pi$
$431$	12.6213	−	21.8608i	0.607948	−	1.05300i	0.991578	−	0.129510i	$-0.0413403\pi$
$432$			1.24264i			0.0597866i
$433$			35.1127i			1.68741i	0.536808	+	0.843704i	$0.319630\pi$
$433$			35.1127i			1.68741i	−0.536808	+	0.843704i	$0.680370\pi$
$434$	26.9350	−	18.0995i	1.29292	−	0.868803i
$435$		0			0
$436$	−19.7990			−0.948200
$437$	5.49333	+	3.17157i	0.262781	+	0.151717i
$438$		−	22.3137i		−	1.06619i
$439$	−6.03553	−	10.4539i	−0.288060	−	0.498935i	0.685286	−	0.728274i	$-0.259677\pi$
$439$	−6.03553	−	10.4539i	−0.288060	−	0.498935i	−0.973347	+	0.229339i	$0.926344\pi$
$440$		0			0
$441$	1.65685	−	2.86976i	0.0788978	−	0.136655i
$442$			0.757359i			0.0360239i
$443$	11.4685	−	6.62132i	0.544883	−	0.314588i	−0.202173	−	0.979350i	$-0.564800\pi$
$443$	11.4685	−	6.62132i	0.544883	−	0.314588i	0.747056	+	0.664761i	$0.231467\pi$
$444$	−4.62132	−	8.00436i	−0.219318	−	0.379870i
$445$		0			0
$446$	2.08579	−	3.61269i	0.0987649	−	0.171066i
$447$	−2.09077	+	1.20711i	−0.0988900	+	0.0570942i
$448$	−20.5490	−	11.8640i	−0.970848	−	0.560519i
$449$	−4.62742			−0.218381			−0.109191	−	0.994021i	$-0.534826\pi$
$449$	−4.62742			−0.218381			−0.109191	+	0.994021i	$0.534826\pi$
$450$		0			0
$451$	24.8640	−	43.0656i	1.17080	−	2.02788i
$452$	17.7153	−	10.2279i	0.833257	−	0.481081i
$453$	36.1990	+	20.8995i	1.70078	+	0.981944i
$454$	18.8137	+	32.5863i	0.882971	+	1.52935i
$455$		0			0
$456$	−8.44975	−	14.6354i	−0.395696	−	0.685365i
$457$			31.1127i			1.45539i	0.685901	+	0.727695i	$0.259409\pi$
$457$			31.1127i			1.45539i	−0.685901	+	0.727695i	$0.740591\pi$
$458$	−24.0131	−	13.8640i	−1.12206	−	0.647820i
$459$	−0.0355339	+	0.0615465i	−0.00165858	+	0.00287275i
$460$		0			0
$461$	26.1421			1.21756			0.608780	−	0.793339i	$-0.291659\pi$
$461$	26.1421			1.21756			0.608780	+	0.793339i	$0.291659\pi$
$462$	63.8863	+	36.8848i	2.97226	+	1.71604i
$463$		−	24.9706i		−	1.16048i	−0.814445	−	0.580240i	$-0.802959\pi$
$463$		−	24.9706i		−	1.16048i	0.814445	−	0.580240i	$-0.197041\pi$
$464$	3.51472			0.163167
$465$		0			0
$466$	35.7990			1.65836
$467$		−	8.00000i		−	0.370196i	−0.982720	−	0.185098i	$-0.940740\pi$
$467$		−	8.00000i		−	0.370196i	0.982720	−	0.185098i	$-0.0592602\pi$
$468$	17.1464	+	9.89949i	0.792594	+	0.457604i
$469$	12.6569			0.584439
$470$		0			0
$471$	17.8995	−	31.0028i	0.824765	−	1.42854i
$472$	−38.4999	−	22.2279i	−1.77210	−	1.02312i
$473$			46.6569i			2.14528i
$474$	−44.4203	−	76.9382i	−2.04029	−	3.53389i
$475$		0			0
$476$	0.792893	+	1.37333i	0.0363422	+	0.0629465i
$477$	−0.420266	−	0.242641i	−0.0192427	−	0.0111098i
$478$	−26.6727	+	15.3995i	−1.21998	+	0.704357i
$479$	4.86396	−	8.42463i	0.222240	−	0.384931i	−0.733248	−	0.679962i	$-0.761996\pi$
$479$	4.86396	−	8.42463i	0.222240	−	0.384931i	0.955488	+	0.295030i	$0.0953298\pi$
$480$		0			0
$481$	1.82843			0.0833691
$482$	51.5518	+	29.7635i	2.34812	+	1.35569i
$483$	−20.1903	+	11.6569i	−0.918689	+	0.530405i
$484$	31.5563	−	54.6572i	1.43438	−	2.48442i
$485$		0			0
$486$	26.1421	+	45.2795i	1.18583	+	2.05392i
$487$	−15.0557	+	8.69239i	−0.682237	+	0.393890i	−0.800697	−	0.599069i	$-0.795537\pi$
$487$	−15.0557	+	8.69239i	−0.682237	+	0.393890i	0.118460	+	0.992959i	$0.462204\pi$
$488$			12.4853i			0.565182i
$489$	15.6569	−	27.1185i	0.708027	−	1.22634i
$490$		0			0
$491$	−2.20711	−	3.82282i	−0.0996053	−	0.172522i	0.811916	−	0.583774i	$-0.198425\pi$
$491$	−2.20711	−	3.82282i	−0.0996053	−	0.172522i	−0.911521	+	0.411253i	$0.865091\pi$
$492$		−	87.6690i		−	3.95243i
$493$	0.174080	+	0.100505i	0.00784016	+	0.00452652i
$494$	7.00000			0.314945
$495$		0			0
$496$	−15.0000	−	7.34847i	−0.673520	−	0.329956i
$497$		−	33.9706i		−	1.52379i
$498$		−	23.7279i		−	1.06327i
$499$	20.1066	−	34.8257i	0.900095	−	1.55901i	0.0727259	−	0.997352i	$-0.476830\pi$
$499$	20.1066	−	34.8257i	0.900095	−	1.55901i	0.827369	−	0.561659i	$-0.189837\pi$
$500$		0			0
$501$	−10.3284	−	17.8894i	−0.461440	−	0.799238i
$502$	7.49706	+	4.32843i	0.334610	+	0.193187i
$503$	20.2518	+	11.6924i	0.902984	+	0.521338i	0.878167	−	0.478354i	$-0.158766\pi$
$503$	20.2518	+	11.6924i	0.902984	+	0.521338i	0.0248166	+	0.999692i	$0.492100\pi$
$504$	30.1421			1.34264
$505$		0			0
$506$	25.3137	+	43.8446i	1.12533	+	1.94913i
$507$	20.1903	−	11.6569i	0.896681	−	0.517699i
$508$	−36.1374	−	20.8640i	−1.60334	−	0.925689i
$509$	3.39949	+	5.88810i	0.150680	+	0.260985i	0.931478	−	0.363799i	$-0.118520\pi$
$509$	3.39949	+	5.88810i	0.150680	+	0.260985i	−0.780798	+	0.624784i	$0.785187\pi$
$510$		0			0
$511$	9.24264			0.408870
$512$			31.2426i			1.38074i
$513$	0.568852	+	0.328427i	0.0251154	+	0.0145004i
$514$	0.378680	+	0.655892i	0.0167028	+	0.0289302i
$515$		0			0
$516$	41.1274	+	71.2348i	1.81053	+	3.13594i
$517$	7.52255	−	4.34315i	0.330841	−	0.191011i
$518$	5.04757	−	2.91421i	0.221777	−	0.128043i
$519$	−34.5563			−1.51686
$520$		0			0
$521$	−15.2279	+	26.3755i	−0.667147	+	1.15553i	0.311551	+	0.950229i	$0.399152\pi$
$521$	−15.2279	+	26.3755i	−0.667147	+	1.15553i	−0.978698	+	0.205304i	$0.934182\pi$
$522$	6.92820	−	4.00000i	0.303239	−	0.175075i
$523$			8.00000i			0.349816i	0.984585	+	0.174908i	$0.0559627\pi$
$523$			8.00000i			0.349816i	−0.984585	+	0.174908i	$0.944037\pi$
$524$	−9.10660	+	15.7731i	−0.397824	+	0.689051i
$525$		0			0
$526$	1.65685			0.0722423
$527$	−0.532799	−	0.792893i	−0.0232091	−	0.0345390i
$528$		−	37.9706i		−	1.65246i
$529$	7.00000			0.304348
$530$		0			0
$531$	−28.4853			−1.23616
$532$	12.6932	−	7.32843i	0.550320	−	0.317728i
$533$	15.0196	+	8.67157i	0.650571	+	0.375608i
$534$	−36.3848	+	63.0203i	−1.57452	+	2.72715i
$535$		0			0
$536$	−11.5711	−	20.0417i	−0.499794	−	0.865669i
$537$	14.1281	−	8.15685i	0.609672	−	0.351994i
$538$	−66.5459	+	38.4203i	−2.86900	+	1.65642i
$539$	3.07107	−	5.31925i	0.132280	−	0.229116i
$540$		0			0
$541$	−12.6421	+	21.8968i	−0.543528	+	0.941418i	0.455170	+	0.890405i	$0.349578\pi$
$541$	−12.6421	+	21.8968i	−0.543528	+	0.941418i	−0.998698	+	0.0510134i	$0.983755\pi$
$542$			56.2843i			2.41762i
$543$		−	24.8995i		−	1.06854i
$544$	−0.136039	+	0.235626i	−0.00583262	+	0.0101024i
$545$		0			0
$546$	−12.8640	+	22.2810i	−0.550527	+	0.953540i
$547$	4.96053	−	2.86396i	0.212097	−	0.122454i	−0.390189	−	0.920735i	$-0.627590\pi$
$547$	4.96053	−	2.86396i	0.212097	−	0.122454i	0.602285	+	0.798281i	$0.294257\pi$
$548$	24.8176	−	14.3284i	1.06015	−	0.612080i
$549$	4.00000	+	6.92820i	0.170716	+	0.295689i
$550$		0			0
$551$	0.928932	−	1.60896i	0.0395738	−	0.0685439i
$552$	36.9164	+	21.3137i	1.57127	+	0.907172i
$553$	31.8689	−	18.3995i	1.35520	−	0.782426i
$554$	−34.1421			−1.45056
$555$		0			0
$556$		0			0
$557$			44.4853i			1.88490i	0.334344	+	0.942451i	$0.391485\pi$
$557$			44.4853i			1.88490i	−0.334344	+	0.942451i	$0.608515\pi$
$558$	−37.9310	+	2.58579i	−1.60575	+	0.109465i
$559$	−16.2721			−0.688236
$560$		0			0
$561$	1.08579	−	1.88064i	0.0458419	−	0.0794006i
$562$		−	4.82843i		−	0.203675i
$563$	−4.11999	+	2.37868i	−0.173637	+	0.100249i	−0.584300	−	0.811538i	$-0.698631\pi$
$563$	−4.11999	+	2.37868i	−0.173637	+	0.100249i	0.410663	+	0.911787i	$0.365297\pi$
$564$	7.65685	−	13.2621i	0.322412	−	0.558433i
$565$		0			0
$566$	5.65685			0.237775
$567$	−19.8315	+	11.4497i	−0.832847	+	0.480844i
$568$	−53.7912	+	31.0563i	−2.25703	+	1.30310i
$569$	7.57107	+	13.1135i	0.317396	+	0.549745i	0.979944	−	0.199274i	$-0.0638583\pi$
$569$	7.57107	+	13.1135i	0.317396	+	0.549745i	−0.662548	+	0.749019i	$0.730525\pi$
$570$		0			0
$571$	20.4497	+	35.4200i	0.855795	+	1.48228i	0.875905	+	0.482483i	$0.160265\pi$
$571$	20.4497	+	35.4200i	0.855795	+	1.48228i	−0.0201099	+	0.999798i	$0.506402\pi$
$572$	31.7818	+	18.3492i	1.32886	+	0.767220i
$573$		−	2.65685i		−	0.110992i
$574$	55.2843			2.30752
$575$		0			0
$576$	13.8995	+	24.0746i	0.579146	+	1.00311i
$577$	29.4194	+	16.9853i	1.22474	+	0.707107i	0.965926	−	0.258819i	$-0.0833335\pi$
$577$	29.4194	+	16.9853i	1.22474	+	0.707107i	0.258819	+	0.965926i	$0.416667\pi$
$578$	−35.4815	+	20.4853i	−1.47584	+	0.852075i
$579$	25.5208	+	44.2033i	1.06061	+	1.83703i
$580$		0			0
$581$	9.82843			0.407752
$582$	−54.6572	−	31.5563i	−2.26561	−	1.30805i
$583$	−0.778985	−	0.449747i	−0.0322623	−	0.0186266i
$584$	−8.44975	−	14.6354i	−0.349653	−	0.605617i
$585$		0			0
$586$	−29.9350	+	51.8490i	−1.23660	+	2.14186i
$587$		−	20.3431i		−	0.839651i	−0.907605	−	0.419826i	$-0.862091\pi$
$587$		−	20.3431i		−	0.839651i	0.907605	−	0.419826i	$-0.137909\pi$
$588$		−	10.8284i		−	0.446557i
$589$	−7.32843	+	4.92447i	−0.301963	+	0.202909i
$590$		0			0
$591$	−8.41421			−0.346114
$592$	−2.59808	−	1.50000i	−0.106780	−	0.0616496i
$593$		−	21.3137i		−	0.875249i	−0.899158	−	0.437625i	$-0.855820\pi$
$593$		−	21.3137i		−	0.875249i	0.899158	−	0.437625i	$-0.144180\pi$
$594$	2.62132	+	4.54026i	0.107554	+	0.186289i
$595$		0			0
$596$	−1.91421	+	3.31552i	−0.0784092	+	0.135809i
$597$		−	37.6274i		−	1.53999i
$598$	−15.2913	+	8.82843i	−0.625307	+	0.361021i
$599$	17.4497	+	30.2238i	0.712977	+	1.23491i	0.963734	+	0.266863i	$0.0859871\pi$
$599$	17.4497	+	30.2238i	0.712977	+	1.23491i	−0.250757	+	0.968050i	$0.580680\pi$
$600$		0			0
$601$	11.7426	−	20.3389i	0.478992	−	0.829639i	−0.520717	−	0.853729i	$-0.674336\pi$
$601$	11.7426	−	20.3389i	0.478992	−	0.829639i	0.999710	+	0.0240900i	$0.00766884\pi$
$602$	−44.9208	+	25.9350i	−1.83083	+	1.05703i
$603$	−12.8418	−	7.41421i	−0.522958	−	0.301930i
$604$	66.2843			2.69707
$605$		0			0
$606$	−24.7279	+	42.8300i	−1.00450	+	1.73985i
$607$	−3.82282	+	2.20711i	−0.155164	+	0.0895837i	−0.575571	−	0.817752i	$-0.695220\pi$
$607$	−3.82282	+	2.20711i	−0.155164	+	0.0895837i	0.420408	+	0.907335i	$0.361887\pi$
$608$	2.17781	+	1.25736i	0.0883219	+	0.0509927i
$609$	3.41421	+	5.91359i	0.138351	+	0.239631i
$610$		0			0
$611$	1.51472	+	2.62357i	0.0612790	+	0.106138i
$612$		−	1.85786i		−	0.0750997i
$613$	−8.93193	−	5.15685i	−0.360757	−	0.208283i	0.308656	−	0.951174i	$-0.400121\pi$
$613$	−8.93193	−	5.15685i	−0.360757	−	0.208283i	−0.669413	+	0.742890i	$0.733454\pi$
$614$	3.32843	−	5.76500i	0.134324	−	0.232657i
$615$		0			0
$616$	55.8701			2.25107
$617$	−20.1648	−	11.6421i	−0.811803	−	0.468695i	0.0357786	−	0.999360i	$-0.488609\pi$
$617$	−20.1648	−	11.6421i	−0.811803	−	0.468695i	−0.847582	+	0.530665i	$0.821942\pi$
$618$			70.3553i			2.83011i
$619$	31.6569			1.27240			0.636198	−	0.771526i	$-0.280506\pi$
$619$	31.6569			1.27240			0.636198	+	0.771526i	$0.280506\pi$
$620$		0			0
$621$	−1.65685			−0.0664873
$622$			27.3137i			1.09518i
$623$	−26.1039	−	15.0711i	−1.04583	−	0.603810i
$624$	13.2426			0.530130
$625$		0			0
$626$	4.62132	−	8.00436i	0.184705	−	0.319919i
$627$	−17.3821	−	10.0355i	−0.694172	−	0.400781i
$628$		−	56.7696i		−	2.26535i
$629$	−0.0857864	−	0.148586i	−0.00342053	−	0.00592453i
$630$		0			0
$631$	16.0061	+	27.7234i	0.637193	+	1.10365i	0.986046	+	0.166473i	$0.0532378\pi$
$631$	16.0061	+	27.7234i	0.637193	+	1.10365i	−0.348853	+	0.937177i	$0.613429\pi$
$632$	−58.2699	−	33.6421i	−2.31785	−	1.33821i
$633$	15.8601	−	9.15685i	0.630384	−	0.363952i
$634$	2.62132	−	4.54026i	0.104106	−	0.180317i
$635$		0			0
$636$	−1.58579			−0.0628805
$637$	1.85514	+	1.07107i	0.0735035	+	0.0424373i
$638$	12.8418	−	7.41421i	0.508412	−	0.293532i
$639$	−19.8995	+	34.4669i	−0.787212	+	1.36349i
$640$		0			0
$641$	−9.98528	−	17.2950i	−0.394395	−	0.683112i	0.598629	−	0.801027i	$-0.295712\pi$
$641$	−9.98528	−	17.2950i	−0.394395	−	0.683112i	−0.993024	+	0.117915i	$0.962379\pi$
$642$	48.3849	−	27.9350i	1.90960	−	1.10251i
$643$		−	12.6863i		−	0.500298i	−0.968207	−	0.250149i	$-0.919520\pi$
$643$		−	12.6863i		−	0.500298i	0.968207	−	0.250149i	$-0.0804797\pi$
$644$	−18.4853	+	32.0174i	−0.728422	+	1.26166i
$645$		0			0
$646$	−0.328427	−	0.568852i	−0.0129218	−	0.0223812i
$647$		−	22.6863i		−	0.891890i	−0.895060	−	0.445945i	$-0.852868\pi$
$647$		−	22.6863i		−	0.891890i	0.895060	−	0.445945i	$-0.147132\pi$
$648$	36.2605	+	20.9350i	1.42445	+	0.822406i
$649$	−52.7990			−2.07254
$650$		0			0
$651$	−2.20711	−	32.3762i	−0.0865033	−	1.26892i
$652$		−	49.6569i		−	1.94471i
$653$		−	22.1421i		−	0.866489i	−0.901276	−	0.433244i	$-0.857369\pi$
$653$		−	22.1421i		−	0.866489i	0.901276	−	0.433244i	$-0.142631\pi$
$654$	−15.0711	+	26.1039i	−0.589325	+	1.02074i
$655$		0			0
$656$	−14.2279	−	24.6435i	−0.555507	−	0.962166i
$657$	−9.37769	−	5.41421i	−0.365859	−	0.211229i
$658$	8.36308	+	4.82843i	0.326027	+	0.188232i
$659$	−9.65685			−0.376178			−0.188089	−	0.982152i	$-0.560229\pi$
$659$	−9.65685			−0.376178			−0.188089	+	0.982152i	$0.560229\pi$
$660$		0			0
$661$	−16.5711	−	28.7019i	−0.644540	−	1.11638i	−0.984408	−	0.175903i	$-0.943716\pi$
$661$	−16.5711	−	28.7019i	−0.644540	−	1.11638i	0.339868	−	0.940473i	$-0.389618\pi$
$662$	−1.58346	+	0.914214i	−0.0615431	+	0.0355319i
$663$	0.655892	+	0.378680i	0.0254728	+	0.0147067i
$664$	−8.98528	−	15.5630i	−0.348697	−	0.603960i
$665$		0			0
$666$	−6.82843			−0.264596
$667$			4.68629i			0.181454i
$668$	−28.3687	−	16.3787i	−1.09762	−	0.633710i
$669$	−2.08579	−	3.61269i	−0.0806412	−	0.139675i
$670$		0			0
$671$	7.41421	+	12.8418i	0.286223	+	0.495752i
$672$	−8.00436	+	4.62132i	−0.308775	+	0.178271i
$673$	−17.8894	+	10.3284i	−0.689584	+	0.398132i	−0.803456	−	0.595364i	$-0.797008\pi$
$673$	−17.8894	+	10.3284i	−0.689584	+	0.398132i	0.113872	+	0.993495i	$0.463675\pi$
$674$	−32.1421			−1.23807
$675$		0			0
$676$	18.4853	−	32.0174i	0.710972	−	1.23144i
$677$	35.1589	−	20.2990i	1.35127	−	0.780154i	0.362839	−	0.931852i	$-0.381808\pi$
$677$	35.1589	−	20.2990i	1.35127	−	0.780154i	0.988427	+	0.151698i	$0.0484742\pi$
$678$		−	31.1421i		−	1.19601i
$679$	13.0711	−	22.6398i	0.501622	−	0.868834i
$680$		0			0
$681$	37.6274			1.44189
$682$	−70.3072	+	4.79289i	−2.69220	+	0.183529i
$683$			46.6274i			1.78415i	0.451889	+	0.892074i	$0.350750\pi$
$683$			46.6274i			1.78415i	−0.451889	+	0.892074i	$0.649250\pi$
$684$	−17.1716			−0.656571
$685$		0			0
$686$	47.6274			1.81842
$687$	−24.0131	+	13.8640i	−0.916156	+	0.528943i
$688$	23.1216	+	13.3492i	0.881501	+	0.508935i
$689$	0.156854	−	0.271680i	0.00597567	−	0.0103502i
$690$		0			0
$691$	−7.03553	−	12.1859i	−0.267644	−	0.463574i	0.700609	−	0.713546i	$-0.252912\pi$
$691$	−7.03553	−	12.1859i	−0.267644	−	0.463574i	−0.968253	+	0.249972i	$0.919579\pi$
$692$	−47.4573	+	27.3995i	−1.80406	+	1.04157i
$693$	31.0028	−	17.8995i	1.17770	−	0.679946i
$694$	−27.2279	+	47.1601i	−1.03356	+	1.79017i
$695$		0			0
$696$	6.24264	−	10.8126i	0.236627	−	0.409849i
$697$		−	1.62742i		−	0.0616428i
$698$			84.7696i			3.20857i
$699$	17.8995	−	31.0028i	0.677021	−	1.17263i
$700$		0			0
$701$	−1.74264	+	3.01834i	−0.0658186	+	0.114001i	−0.897057	−	0.441915i	$-0.854299\pi$
$701$	−1.74264	+	3.01834i	−0.0658186	+	0.114001i	0.831238	+	0.555916i	$0.187633\pi$
$702$	−1.58346	+	0.914214i	−0.0597640	+	0.0345048i
$703$	−1.37333	+	0.792893i	−0.0517962	+	0.0299045i
$704$	25.7635	+	44.6236i	0.970997	+	1.68182i
$705$		0			0
$706$	3.62132	−	6.27231i	0.136290	−	0.236062i
$707$	−17.7408	−	10.2426i	−0.667210	−	0.385214i
$708$	−80.6125	+	46.5416i	−3.02960	+	1.74914i
$709$	5.31371			0.199561			0.0997803	−	0.995009i	$-0.468186\pi$
$709$	5.31371			0.199561			0.0997803	+	0.995009i	$0.468186\pi$
$710$		0			0
$711$	−43.1127			−1.61685
$712$			55.1127i			2.06544i
$713$	9.79796	−	20.0000i	0.366936	−	0.749006i
$714$	2.41421			0.0903497
$715$		0			0
$716$	12.9350	−	22.4041i	0.483405	−	0.837282i
$717$			30.7990i			1.15021i
$718$	56.2407	−	32.4706i	2.09888	−	1.21179i
$719$	3.03553	−	5.25770i	0.113206	−	0.196079i	−0.803855	−	0.594825i	$-0.797221\pi$
$719$	3.03553	−	5.25770i	0.113206	−	0.196079i	0.917061	+	0.398746i	$0.130555\pi$
$720$		0			0
$721$	−29.1421			−1.08531
$722$	34.4669	−	19.8995i	1.28273	−	0.740583i
$723$	51.5518	−	29.7635i	1.91723	−	1.10691i
$724$	−19.7426	−	34.1953i	−0.733729	−	1.27086i
$725$		0			0
$726$	−48.0416	−	83.2105i	−1.78299	−	3.08823i
$727$	40.5652	+	23.4203i	1.50448	+	0.868611i	0.999987	+	0.00519502i	$0.00165363\pi$
$727$	40.5652	+	23.4203i	1.50448	+	0.868611i	0.504492	+	0.863416i	$0.331680\pi$
$728$			19.4853i			0.722173i
$729$	23.8284			0.882534
$730$		0			0
$731$	0.763456	+	1.32234i	0.0282374	+	0.0489087i
$732$	22.6398	+	13.0711i	0.836789	+	0.483121i
$733$	25.6581	−	14.8137i	0.947703	−	0.547157i	0.0553366	−	0.998468i	$-0.482377\pi$
$733$	25.6581	−	14.8137i	0.947703	−	0.547157i	0.892367	+	0.451311i	$0.149043\pi$
$734$	−21.9853	−	38.0796i	−0.811492	−	1.40554i
$735$		0			0
$736$	−6.34315			−0.233811
$737$	−23.8030	−	13.7426i	−0.876793	−	0.506217i
$738$	−56.0921	−	32.3848i	−2.06478	−	1.19210i
$739$	−3.93503	−	6.81567i	−0.144752	−	0.250718i	0.784528	−	0.620093i	$-0.212905\pi$
$739$	−3.93503	−	6.81567i	−0.144752	−	0.250718i	−0.929281	+	0.369375i	$0.879572\pi$
$740$		0			0
$741$	3.50000	−	6.06218i	0.128576	−	0.222700i
$742$		−	1.00000i		−	0.0367112i
$743$			5.65685i			0.207530i	0.994602	+	0.103765i	$0.0330890\pi$
$743$			5.65685i			0.207530i	−0.994602	+	0.103765i	$0.966911\pi$
$744$	−49.2487	+	33.0936i	−1.80555	+	1.21327i
$745$		0			0
$746$	−24.1421			−0.883906
$747$	−9.97204	−	5.75736i	−0.364858	−	0.210651i
$748$		−	3.44365i		−	0.125912i
$749$	11.5711	+	20.0417i	0.422798	+	0.732307i
$750$		0			0
$751$	0.621320	−	1.07616i	0.0226723	−	0.0392696i	−0.854467	−	0.519506i	$-0.826116\pi$
$751$	0.621320	−	1.07616i	0.0226723	−	0.0392696i	0.877139	+	0.480237i	$0.159449\pi$
$752$		−	4.97056i		−	0.181258i
$753$	7.49706	−	4.32843i	0.273208	−	0.157737i
$754$	2.58579	+	4.47871i	0.0941688	+	0.163105i
$755$		0			0
$756$	−1.91421	+	3.31552i	−0.0696193	+	0.120584i
$757$	30.0137	−	17.3284i	1.09087	−	0.629812i	0.157060	−	0.987589i	$-0.449798\pi$
$757$	30.0137	−	17.3284i	1.09087	−	0.629812i	0.933807	+	0.357777i	$0.116465\pi$
$758$	61.4368	+	35.4706i	2.23149	+	1.28835i
$759$	50.6274			1.83766
$760$		0			0
$761$	10.2279	−	17.7153i	0.370762	−	0.642178i	−0.618921	−	0.785453i	$-0.712430\pi$
$761$	10.2279	−	17.7153i	0.370762	−	0.642178i	0.989683	+	0.143275i	$0.0457633\pi$
$762$	−55.0159	+	31.7635i	−1.99302	+	1.15067i
$763$	−10.8126	−	6.24264i	−0.391441	−	0.225999i
$764$	−2.10660	−	3.64874i	−0.0762142	−	0.132007i
$765$		0			0
$766$	30.0563	+	52.0591i	1.08598	+	1.88097i
$767$		−	18.4142i		−	0.664899i
$768$	62.6616	+	36.1777i	2.26110	+	1.30545i
$769$	−13.0563	+	22.6143i	−0.470824	+	0.815491i	−0.999443	−	0.0333680i	$-0.989377\pi$
$769$	−13.0563	+	22.6143i	−0.470824	+	0.815491i	0.528619	+	0.848859i	$0.322710\pi$
$770$		0			0
$771$	0.757359			0.0272756
$772$	70.0971	+	40.4706i	2.52285	+	1.45657i
$773$		−	18.0000i		−	0.647415i	−0.946157	−	0.323708i	$-0.895071\pi$
$773$		−	18.0000i		−	0.647415i	0.946157	−	0.323708i	$-0.104929\pi$
$774$	60.7696			2.18432
$775$		0			0
$776$	−47.7990			−1.71588
$777$		−	5.82843i		−	0.209094i
$778$	−35.8403	−	20.6924i	−1.28494	−	0.741858i
$779$	−15.0416			−0.538922
$780$		0			0
$781$	−36.8848	+	63.8863i	−1.31984	+	2.28603i
$782$	1.43488	+	0.828427i	0.0513111	+	0.0296245i
$783$			0.485281i			0.0173425i
$784$	−1.75736	−	3.04384i	−0.0627628	−	0.108708i
$785$		0			0
$786$	13.8640	+	24.0131i	0.494511	+	0.856518i
$787$	−34.2823	−	19.7929i	−1.22203	−	0.705540i	−0.256681	−	0.966496i	$-0.582629\pi$
$787$	−34.2823	−	19.7929i	−1.22203	−	0.705540i	−0.965351	+	0.260956i	$0.915962\pi$
$788$	−11.5555	+	6.67157i	−0.411648	+	0.237665i
$789$	0.828427	−	1.43488i	0.0294928	−	0.0510830i
$790$		0			0
$791$	12.8995			0.458653
$792$	−56.6864	−	32.7279i	−2.01426	−	1.16294i
$793$	−4.47871	+	2.58579i	−0.159044	+	0.0918240i
$794$	19.9350	−	34.5285i	0.707468	−	1.22537i
$795$		0			0
$796$	−29.8345	−	51.6749i	−1.05746	−	1.83157i
$797$	−19.4473	+	11.2279i	−0.688860	+	0.397713i	−0.803185	−	0.595730i	$-0.796863\pi$
$797$	−19.4473	+	11.2279i	−0.688860	+	0.397713i	0.114325	+	0.993443i	$0.463529\pi$
$798$		−	22.3137i		−	0.789897i
$799$	0.142136	−	0.246186i	0.00502840	−	0.00870944i
$800$		0			0
$801$	17.6569	+	30.5826i	0.623874	+	1.08058i
$802$			51.1127i			1.80485i
$803$	−17.3821	−	10.0355i	−0.613399	−	0.354146i
$804$	−48.4558			−1.70891
$805$		0			0
$806$	−1.67157	−	24.5204i	−0.0588786	−	0.863694i
$807$			76.8406i			2.70492i
$808$			37.4558i			1.31769i
$809$	−22.9853	+	39.8117i	−0.808119	+	1.39970i	0.106045	+	0.994361i	$0.466181\pi$
$809$	−22.9853	+	39.8117i	−0.808119	+	1.39970i	−0.914165	+	0.405343i	$0.867152\pi$
$810$		0			0
$811$	−5.86396	−	10.1567i	−0.205912	−	0.356649i	0.744511	−	0.667610i	$-0.232683\pi$
$811$	−5.86396	−	10.1567i	−0.205912	−	0.356649i	−0.950423	+	0.310961i	$0.899349\pi$
$812$	9.37769	+	5.41421i	0.329093	+	0.190002i
$813$	48.7436	+	28.1421i	1.70951	+	0.986988i
$814$	−12.6569			−0.443623
$815$		0			0
$816$	−0.621320	−	1.07616i	−0.0217506	−	0.0376731i
$817$	12.2220	−	7.05635i	0.427592	−	0.246870i
$818$	−19.5344	−	11.2782i	−0.683003	−	0.394332i
$819$	6.24264	+	10.8126i	0.218136	+	0.377822i
$820$		0			0
$821$	−8.48528			−0.296138			−0.148069	−	0.988977i	$-0.547306\pi$
$821$	−8.48528			−0.296138			−0.148069	+	0.988977i	$0.547306\pi$
$822$		−	43.6274i		−	1.52168i
$823$	−5.38079	−	3.10660i	−0.187563	−	0.108289i	0.403278	−	0.915077i	$-0.367871\pi$
$823$	−5.38079	−	3.10660i	−0.187563	−	0.108289i	−0.590841	+	0.806788i	$0.701204\pi$
$824$	26.6421	+	46.1455i	0.928123	+	1.60756i
$825$		0			0
$826$	−29.3492	−	50.8344i	−1.02119	−	1.76875i
$827$	14.8095	−	8.55025i	0.514976	−	0.297321i	−0.219901	−	0.975522i	$-0.570573\pi$
$827$	14.8095	−	8.55025i	0.514976	−	0.297321i	0.734877	+	0.678201i	$0.237240\pi$
$828$	37.5108	−	21.6569i	1.30359	−	0.752628i
$829$	46.4264			1.61246			0.806228	−	0.591605i	$-0.201506\pi$
$829$	46.4264			1.61246			0.806228	+	0.591605i	$0.201506\pi$
$830$		0			0
$831$	−17.0711	+	29.5680i	−0.592189	+	1.02570i
$832$	−15.5630	+	8.98528i	−0.539549	+	0.311509i
$833$		−	0.201010i		−	0.00696459i
$834$		0			0
$835$		0			0
$836$	−31.8284			−1.10081
$837$	1.01461	−	2.07107i	0.0350701	−	0.0715866i
$838$			67.5980i			2.33513i
$839$	−30.6274			−1.05738			−0.528688	−	0.848816i	$-0.677316\pi$
$839$	−30.6274			−1.05738			−0.528688	+	0.848816i	$0.677316\pi$
$840$		0			0
$841$	−27.6274			−0.952670
$842$	5.97514	−	3.44975i	0.205917	−	0.118886i
$843$	−4.18154	−	2.41421i	−0.144020	−	0.0831499i
$844$	14.5208	−	25.1508i	0.499827	−	0.865726i
$845$		0			0
$846$	−5.65685	−	9.79796i	−0.194487	−	0.336861i
$847$	34.4669	−	19.8995i	1.18430	−	0.683755i
$848$	−0.445759	+	0.257359i	−0.0153074	+	0.00883776i
$849$	2.82843	−	4.89898i	0.0970714	−	0.168133i
$850$		0			0
$851$	2.00000	−	3.46410i	0.0685591	−	0.118748i
$852$			130.054i			4.45557i
$853$			32.4853i			1.11227i	0.831090	+	0.556137i	$0.187717\pi$
$853$			32.4853i			1.11227i	−0.831090	+	0.556137i	$0.812283\pi$
$854$	−8.24264	+	14.2767i	−0.282057	+	0.488538i
$855$		0			0
$856$	21.1569	−	36.6447i	0.723126	−	1.25249i
$857$	−2.17781	+	1.25736i	−0.0743926	+	0.0429506i	−0.536735	−	0.843751i	$-0.680342\pi$
$857$	−2.17781	+	1.25736i	−0.0743926	+	0.0429506i	0.462342	+	0.886702i	$0.347009\pi$
$858$	48.3849	−	27.9350i	1.65183	−	0.953686i
$859$	−6.30761	−	10.9251i	−0.215213	−	0.372760i	0.738125	−	0.674663i	$-0.235711\pi$
$859$	−6.30761	−	10.9251i	−0.215213	−	0.372760i	−0.953338	+	0.301904i	$0.902378\pi$
$860$		0			0
$861$	27.6421	−	47.8776i	0.942041	−	1.63166i
$862$	−52.7766	−	30.4706i	−1.79758	−	1.03783i
$863$	34.1082	−	19.6924i	1.16106	−	0.670337i	0.209500	−	0.977809i	$-0.432816\pi$
$863$	34.1082	−	19.6924i	1.16106	−	0.670337i	0.951557	+	0.307472i	$0.0994830\pi$
$864$	−0.656854			−0.0223466
$865$		0			0
$866$	84.7696			2.88059
$867$			40.9706i			1.39143i
$868$	−28.7019	−	42.7132i	−0.974207	−	1.44978i
$869$	−79.9117			−2.71082
$870$		0			0
$871$	4.79289	−	8.30153i	0.162401	−	0.281287i
$872$			22.8284i			0.773068i
$873$	−26.5241	+	15.3137i	−0.897705	+	0.518291i
$874$	7.65685	−	13.2621i	0.258997	−	0.448596i
$875$		0			0
$876$	−35.3848			−1.19554
$877$	41.7178	−	24.0858i	1.40871	−	0.813319i	0.413446	−	0.910529i	$-0.364325\pi$
$877$	41.7178	−	24.0858i	1.40871	−	0.813319i	0.995264	+	0.0972093i	$0.0309916\pi$
$878$	−25.2378	+	14.5711i	−0.851735	+	0.491750i
$879$	29.9350	+	51.8490i	1.00968	+	1.74882i
$880$		0			0
$881$	−17.1569	−	29.7165i	−0.578029	−	1.00118i	−0.995705	−	0.0925798i	$-0.970489\pi$
$881$	−17.1569	−	29.7165i	−0.578029	−	1.00118i	0.417676	−	0.908596i	$-0.362845\pi$
$882$	−6.92820	−	4.00000i	−0.233285	−	0.134687i
$883$		−	26.2843i		−	0.884536i	−0.896883	−	0.442268i	$-0.854174\pi$
$883$		−	26.2843i		−	0.884536i	0.896883	−	0.442268i	$-0.145826\pi$
$884$	1.20101			0.0403943
$885$		0			0
$886$	−15.9853	−	27.6873i	−0.537036	−	0.930174i
$887$	−46.1816	−	26.6630i	−1.55063	−	0.895254i	−0.998091	−	0.0617647i	$-0.980327\pi$
$887$	−46.1816	−	26.6630i	−1.55063	−	0.895254i	−0.552535	−	0.833490i	$-0.686339\pi$
$888$	−9.22911	+	5.32843i	−0.309709	+	0.178810i
$889$	−13.1569	−	22.7883i	−0.441267	−	0.764296i
$890$		0			0
$891$	49.7279			1.66595
$892$	−5.72895	−	3.30761i	−0.191819	−	0.110747i
$893$	−2.27541	−	1.31371i	−0.0761437	−	0.0439616i
$894$	2.91421	+	5.04757i	0.0974659	+	0.168816i
$895$		0			0
$896$	−24.8137	+	42.9786i	−0.828968	+	1.43581i
$897$			17.6569i			0.589545i
$898$			11.1716i			0.372800i
$899$	−5.85786	−	2.86976i	−0.195371	−	0.0957117i
$900$		0			0
$901$	−0.0294373			−0.000980697
$902$	−103.970	−	60.0269i	−3.46181	−	1.99868i
$903$			51.8701i			1.72613i
$904$	−11.7929	−	20.4259i	−0.392226	−	0.679355i
$905$		0			0
$906$	50.4558	−	87.3921i	1.67628	−	2.90341i
$907$			55.3137i			1.83666i	0.395814	+	0.918331i	$0.370463\pi$
$907$			55.3137i			1.83666i	−0.395814	+	0.918331i	$0.629537\pi$
$908$	51.6749	−	29.8345i	1.71489	−	0.990093i
$909$	12.0000	+	20.7846i	0.398015	+	0.689382i
$910$		0			0
$911$	−24.5208	+	42.4713i	−0.812411	+	1.40714i	0.0987614	+	0.995111i	$0.468512\pi$
$911$	−24.5208	+	42.4713i	−0.812411	+	1.40714i	−0.911172	+	0.412026i	$0.864821\pi$
$912$	−9.94655	+	5.74264i	−0.329363	+	0.190158i
$913$	−18.4837	−	10.6716i	−0.611721	−	0.353178i
$914$	75.1127			2.48451
$915$		0			0
$916$	−21.9853	+	38.0796i	−0.726414	+	1.25819i
$917$	−9.94655	+	5.74264i	−0.328464	+	0.189639i
$918$	0.148586	+	0.0857864i	0.00490408	+	0.00283137i
$919$	−7.55025	−	13.0774i	−0.249060	−	0.431384i	0.714205	−	0.699936i	$-0.246788\pi$
$919$	−7.55025	−	13.0774i	−0.249060	−	0.431384i	−0.963265	+	0.268552i	$0.913455\pi$
$920$		0			0
$921$	−3.32843	−	5.76500i	−0.109675	−	0.189963i
$922$		−	63.1127i		−	2.07851i
$923$	−22.2810	−	12.8640i	−0.733389	−	0.423422i
$924$	58.4914	−	101.310i	1.92423	−	3.33286i
$925$		0			0
$926$	−60.2843			−1.98106
$927$	29.5680	+	17.0711i	0.971139	+	0.560687i
$928$			1.85786i			0.0609874i
$929$	−24.4853			−0.803336			−0.401668	−	0.915785i	$-0.631569\pi$
$929$	−24.4853			−0.803336			−0.401668	+	0.915785i	$0.631569\pi$
$930$		0			0
$931$	−1.85786			−0.0608890
$932$		−	56.7696i		−	1.85955i
$933$	23.6544	+	13.6569i	0.774409	+	0.447105i
$934$	−19.3137			−0.631964
$935$		0			0
$936$	11.4142	−	19.7700i	0.373085	−	0.646203i
$937$	−33.1806	−	19.1569i	−1.08396	−	0.625827i	−0.152001	−	0.988380i	$-0.548572\pi$
$937$	−33.1806	−	19.1569i	−1.08396	−	0.625827i	−0.931963	+	0.362553i	$0.881905\pi$
$938$		−	30.5563i		−	0.997700i
$939$	−4.62132	−	8.00436i	−0.150811	−	0.261212i
$940$		0			0
$941$	17.5000	+	30.3109i	0.570484	+	0.988107i	0.996516	+	0.0833989i	$0.0265776\pi$
$941$	17.5000	+	30.3109i	0.570484	+	0.988107i	−0.426033	+	0.904708i	$0.640089\pi$
$942$	−74.8475	−	43.2132i	−2.43866	−	1.40796i
$943$	32.8580	−	18.9706i	1.07000	−	0.617767i
$944$	−15.1066	+	26.1654i	−0.491678	+	0.851611i
$945$		0			0
$946$	112.640			3.66223
$947$	−33.6880	−	19.4497i	−1.09471	−	0.632032i	−0.159884	−	0.987136i	$-0.551112\pi$
$947$	−33.6880	−	19.4497i	−1.09471	−	0.632032i	−0.934827	+	0.355104i	$0.884445\pi$
$948$	−122.008	+	70.4411i	−3.96262	+	2.28782i
$949$	3.50000	−	6.06218i	0.113615	−	0.196787i
$950$		0			0
$951$	−2.62132	−	4.54026i	−0.0850021	−	0.147228i
$952$	1.58346	−	0.914214i	0.0513204	−	0.0296298i
$953$		−	20.4853i		−	0.663583i	−0.943353	−	0.331792i	$-0.892347\pi$
$953$		−	20.4853i		−	0.663583i	0.943353	−	0.331792i	$-0.107653\pi$
$954$	−0.585786	+	1.01461i	−0.0189655	+	0.0328493i
$955$		0			0
$956$	24.4203	+	42.2972i	0.789809	+	1.36799i
$957$		−	14.8284i		−	0.479335i
$958$	−20.3389	−	11.7426i	−0.657118	−	0.379387i
$959$	18.0711			0.583545
$960$		0			0
$961$	19.0000	+	24.4949i	0.612903	+	0.790158i
$962$		−	4.41421i		−	0.142320i
$963$		−	27.1127i		−	0.873694i
$964$	47.1985	−	81.7502i	1.52016	−	2.63300i
$965$		0			0
$966$	28.1421	+	48.7436i	0.905458	+	1.56830i
$967$	40.3190	+	23.2782i	1.29657	+	0.748576i	0.979810	−	0.199930i	$-0.0640714\pi$
$967$	40.3190	+	23.2782i	1.29657	+	0.748576i	0.316761	+	0.948505i	$0.397405\pi$
$968$	−63.0203	−	36.3848i	−2.02555	−	1.16945i
$969$	−0.656854			−0.0211012
$970$		0			0
$971$	−29.3492	−	50.8344i	−0.941862	−	1.63135i	−0.761915	−	0.647676i	$-0.775741\pi$
$971$	−29.3492	−	50.8344i	−0.941862	−	1.63135i	−0.179947	−	0.983676i	$-0.557592\pi$
$972$	71.8036	−	41.4558i	2.30310	−	1.32970i
$973$		0			0
$974$	20.9853	+	36.3476i	0.672412	+	1.16465i
$975$		0			0
$976$	8.48528			0.271607
$977$			16.4853i			0.527411i	0.964603	+	0.263705i	$0.0849447\pi$
$977$			16.4853i			0.527411i	−0.964603	+	0.263705i	$0.915055\pi$
$978$	−65.4698	−	37.7990i	−2.09349	−	1.20868i
$979$	32.7279	+	56.6864i	1.04599	+	1.81171i
$980$		0			0
$981$	7.31371	+	12.6677i	0.233509	+	0.404449i
$982$	−9.22911	+	5.32843i	−0.294513	+	0.170037i
$983$	−42.2972	+	24.4203i	−1.34907	+	0.778887i	−0.988118	−	0.153697i	$-0.950882\pi$
$983$	−42.2972	+	24.4203i	−1.34907	+	0.778887i	−0.360954	+	0.932584i	$0.617549\pi$
$984$	−101.083			−3.22242
$985$		0			0
$986$	0.242641	−	0.420266i	0.00772725	−	0.0133840i
$987$	8.36308	−	4.82843i	0.266200	−	0.153691i
$988$		−	11.1005i		−	0.353154i
$989$	−17.7990	+	30.8288i	−0.565975	+	0.980297i
$990$		0			0
$991$	−19.9411			−0.633451			−0.316725	−	0.948517i	$-0.602583\pi$
$991$	−19.9411			−0.633451			−0.316725	+	0.948517i	$0.602583\pi$
$992$	3.88437	−	7.92893i	0.123329	−	0.251744i
$993$			1.82843i			0.0580234i
$994$	−82.0122			−2.60127
$995$		0			0
$996$	−37.6274			−1.19227
$997$	−40.3550	+	23.2990i	−1.27806	+	0.737886i	−0.976491	−	0.215559i	$-0.930843\pi$
$997$	−40.3550	+	23.2990i	−1.27806	+	0.737886i	−0.301566	+	0.953445i	$0.597509\pi$
$998$	−84.0766	−	48.5416i	−2.66140	−	1.53656i
$999$	0.207107	−	0.358719i	0.00655257	−	0.0113494i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	775.2.o.d.749.1		8
5.2	odd	4		775.2.e.e.501.2		4
5.3	odd	4		31.2.c.a.5.1	✓	4
5.4	even	2	inner	775.2.o.d.749.4		8
15.8	even	4		279.2.h.c.253.2		4
20.3	even	4		496.2.i.h.129.1		4
31.25	even	3	inner	775.2.o.d.149.1		8
155.3	even	60		961.2.g.r.448.1		16
155.8	odd	20		961.2.g.o.816.2		16
155.13	even	60		961.2.d.i.628.1		8
155.18	odd	60		961.2.d.l.628.1		8
155.23	even	20		961.2.g.r.816.2		16
155.28	odd	60		961.2.g.o.448.1		16
155.33	odd	20		961.2.g.o.547.1		16
155.38	odd	60		961.2.g.o.338.2		16
155.43	even	60		961.2.g.r.844.1		16
155.48	even	60		961.2.g.r.732.2		16
155.53	even	60		961.2.d.i.374.2		8
155.58	even	20		961.2.g.r.235.2		16
155.68	even	12		961.2.c.a.521.1		4
155.73	even	60		961.2.d.i.388.2		8
155.78	odd	20		961.2.g.o.846.1		16
155.83	even	60		961.2.d.i.531.1		8
155.87	odd	12		775.2.e.e.676.2		4
155.88	even	12		961.2.a.c.1.1		2
155.98	odd	12		961.2.a.a.1.1		2
155.103	odd	60		961.2.d.l.531.1		8
155.108	even	20		961.2.g.r.846.1		16
155.113	odd	60		961.2.d.l.388.2		8
155.118	odd	12		31.2.c.a.25.1	yes	4
155.123	even	4		961.2.c.a.439.1		4
155.128	odd	20		961.2.g.o.235.2		16
155.133	odd	60		961.2.d.l.374.2		8
155.138	odd	60		961.2.g.o.732.2		16
155.143	odd	60		961.2.g.o.844.1		16
155.148	even	60		961.2.g.r.338.2		16
155.149	even	6	inner	775.2.o.d.149.4		8
155.153	even	20		961.2.g.r.547.1		16
465.98	even	12		8649.2.a.l.1.2		2
465.398	odd	12		8649.2.a.k.1.2		2
465.428	even	12		279.2.h.c.118.2		4
620.583	even	12		496.2.i.h.273.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.2.c.a.5.1	✓	4	5.3	odd	4
31.2.c.a.25.1	yes	4	155.118	odd	12
279.2.h.c.118.2		4	465.428	even	12
279.2.h.c.253.2		4	15.8	even	4
496.2.i.h.129.1		4	20.3	even	4
496.2.i.h.273.1		4	620.583	even	12
775.2.e.e.501.2		4	5.2	odd	4
775.2.e.e.676.2		4	155.87	odd	12
775.2.o.d.149.1		8	31.25	even	3	inner
775.2.o.d.149.4		8	155.149	even	6	inner
775.2.o.d.749.1		8	1.1	even	1	trivial
775.2.o.d.749.4		8	5.4	even	2	inner
961.2.a.a.1.1		2	155.98	odd	12
961.2.a.c.1.1		2	155.88	even	12
961.2.c.a.439.1		4	155.123	even	4
961.2.c.a.521.1		4	155.68	even	12
961.2.d.i.374.2		8	155.53	even	60
961.2.d.i.388.2		8	155.73	even	60
961.2.d.i.531.1		8	155.83	even	60
961.2.d.i.628.1		8	155.13	even	60
961.2.d.l.374.2		8	155.133	odd	60
961.2.d.l.388.2		8	155.113	odd	60
961.2.d.l.531.1		8	155.103	odd	60
961.2.d.l.628.1		8	155.18	odd	60
961.2.g.o.235.2		16	155.128	odd	20
961.2.g.o.338.2		16	155.38	odd	60
961.2.g.o.448.1		16	155.28	odd	60
961.2.g.o.547.1		16	155.33	odd	20
961.2.g.o.732.2		16	155.138	odd	60
961.2.g.o.816.2		16	155.8	odd	20
961.2.g.o.844.1		16	155.143	odd	60
961.2.g.o.846.1		16	155.78	odd	20
961.2.g.r.235.2		16	155.58	even	20
961.2.g.r.338.2		16	155.148	even	60
961.2.g.r.448.1		16	155.3	even	60
961.2.g.r.547.1		16	155.153	even	20
961.2.g.r.732.2		16	155.48	even	60
961.2.g.r.816.2		16	155.23	even	20
961.2.g.r.844.1		16	155.43	even	60
961.2.g.r.846.1		16	155.108	even	20
8649.2.a.k.1.2		2	465.398	odd	12
8649.2.a.l.1.2		2	465.98	even	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 775 = 5^{2} \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	775.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.41421i q^{2} +(-2.09077 - 1.20711i) q^{3} -3.82843 q^{4} +(-2.91421 + 5.04757i) q^{6} +(-2.09077 - 1.20711i) q^{7} +4.41421i q^{8} +(1.41421 + 2.44949i) q^{9} +(2.62132 + 4.54026i) q^{11} +(8.00436 + 4.62132i) q^{12} +(-1.58346 + 0.914214i) q^{13} +(-2.91421 + 5.04757i) q^{14} +3.00000 q^{16} +(0.148586 + 0.0857864i) q^{17} +(5.91359 - 3.41421i) q^{18} +(0.792893 - 1.37333i) q^{19} +(2.91421 + 5.04757i) q^{21} +(10.9612 - 6.32843i) q^{22} +4.00000i q^{23} +(5.32843 - 9.22911i) q^{24} +(2.20711 + 3.82282i) q^{26} +0.414214i q^{27} +(8.00436 + 4.62132i) q^{28} +1.17157 q^{29} +(-5.00000 - 2.44949i) q^{31} +1.58579i q^{32} -12.6569i q^{33} +(0.207107 - 0.358719i) q^{34} +(-5.41421 - 9.37769i) q^{36} +(-0.866025 - 0.500000i) q^{37} +(-3.31552 - 1.91421i) q^{38} +4.41421 q^{39} +(-4.74264 - 8.21449i) q^{41} +(12.1859 - 7.03553i) q^{42} +(7.70719 + 4.44975i) q^{43} +(-10.0355 - 17.3821i) q^{44} +9.65685 q^{46} -1.65685i q^{47} +(-6.27231 - 3.62132i) q^{48} +(-0.585786 - 1.01461i) q^{49} +(-0.207107 - 0.358719i) q^{51} +(6.06218 - 3.50000i) q^{52} +(-0.148586 + 0.0857864i) q^{53} +1.00000 q^{54} +(5.32843 - 9.22911i) q^{56} +(-3.31552 + 1.91421i) q^{57} -2.82843i q^{58} +(-5.03553 + 8.72180i) q^{59} +2.82843 q^{61} +(-5.91359 + 12.0711i) q^{62} -6.82843i q^{63} +9.82843 q^{64} -30.5563 q^{66} +(-4.54026 + 2.62132i) q^{67} +(-0.568852 - 0.328427i) q^{68} +(4.82843 - 8.36308i) q^{69} +(7.03553 + 12.1859i) q^{71} +(-10.8126 + 6.24264i) q^{72} +(-3.31552 + 1.91421i) q^{73} +(-1.20711 + 2.09077i) q^{74} +(-3.03553 + 5.25770i) q^{76} -12.6569i q^{77} -10.6569i q^{78} +(-7.62132 + 13.2005i) q^{79} +(4.74264 - 8.21449i) q^{81} +(-19.8315 + 11.4497i) q^{82} +(-3.52565 + 2.03553i) q^{83} +(-11.1569 - 19.3242i) q^{84} +(10.7426 - 18.6068i) q^{86} +(-2.44949 - 1.41421i) q^{87} +(-20.0417 + 11.5711i) q^{88} +12.4853 q^{89} +4.41421 q^{91} -15.3137i q^{92} +(7.49706 + 11.1569i) q^{93} -4.00000 q^{94} +(1.91421 - 3.31552i) q^{96} +10.8284i q^{97} +(-2.44949 + 1.41421i) q^{98} +(-7.41421 + 12.8418i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} - 12 q^{6} + 4 q^{11} - 12 q^{14} + 24 q^{16} + 12 q^{19} + 12 q^{21} + 20 q^{24} + 12 q^{26} + 32 q^{29} - 40 q^{31} - 4 q^{34} - 32 q^{36} + 24 q^{39} - 4 q^{41} - 52 q^{44} + 32 q^{46}+ \cdots - 48 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 - 12 * q^6 + 4 * q^11 - 12 * q^14 + 24 * q^16 + 12 * q^19 + 12 * q^21 + 20 * q^24 + 12 * q^26 + 32 * q^29 - 40 * q^31 - 4 * q^34 - 32 * q^36 + 24 * q^39 - 4 * q^41 - 52 * q^44 + 32 * q^46 - 16 * q^49 + 4 * q^51 + 8 * q^54 + 20 * q^56 - 12 * q^59 + 56 * q^64 - 120 * q^66 + 16 * q^69 + 28 * q^71 - 4 * q^74 + 4 * q^76 - 44 * q^79 + 4 * q^81 - 44 * q^84 + 52 * q^86 + 32 * q^89 + 24 * q^91 - 32 * q^94 + 4 * q^96 - 48 * q^99

Introduction

L-functions

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