LMFDB - Embedded newform 2970.2.t.b.2771.24

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [2970,2,Mod(791,2970)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(2970, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("2970.791"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 2970 = 2 \cdot 3^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2970.t (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [48,24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$23.7155694003$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 990)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			2771.24
Character	$\chi$	$=$	2970.2771
Dual form			2970.2.t.b.791.24

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-3.18423 + 1.83842i) q^{7} -1.00000 q^{8} +1.00000i q^{10} +(-0.851809 - 3.20537i) q^{11} +(1.88953 + 1.09092i) q^{13} +(-3.18423 - 1.83842i) q^{14} +(-0.500000 - 0.866025i) q^{16} -1.68359 q^{17} -7.86116i q^{19} +(-0.866025 + 0.500000i) q^{20} +(2.35003 - 2.34038i) q^{22} +(4.34269 + 2.50725i) q^{23} +(0.500000 + 0.866025i) q^{25} +2.18184i q^{26} -3.67683i q^{28} +(-3.65719 - 6.33444i) q^{29} +(2.78313 - 4.82052i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.841796 - 1.45803i) q^{34} -3.67683 q^{35} -9.84289 q^{37} +(6.80796 - 3.93058i) q^{38} +(-0.866025 - 0.500000i) q^{40} +(2.91945 - 5.05664i) q^{41} +(-2.89355 + 1.67059i) q^{43} +(3.20184 + 0.864999i) q^{44} +5.01450i q^{46} +(-4.46479 + 2.57775i) q^{47} +(3.25955 - 5.64570i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-1.88953 + 1.09092i) q^{52} +4.66886i q^{53} +(0.864999 - 3.20184i) q^{55} +(3.18423 - 1.83842i) q^{56} +(3.65719 - 6.33444i) q^{58} +(12.1117 + 6.99268i) q^{59} +(7.93110 - 4.57903i) q^{61} +5.56625 q^{62} +1.00000 q^{64} +(1.09092 + 1.88953i) q^{65} +(6.87891 - 11.9146i) q^{67} +(0.841796 - 1.45803i) q^{68} +(-1.83842 - 3.18423i) q^{70} -7.93786i q^{71} +4.80281i q^{73} +(-4.92145 - 8.52419i) q^{74} +(6.80796 + 3.93058i) q^{76} +(8.60517 + 8.64067i) q^{77} +(12.4035 - 7.16118i) q^{79} -1.00000i q^{80} +5.83891 q^{82} +(2.79143 + 4.83489i) q^{83} +(-1.45803 - 0.841796i) q^{85} +(-2.89355 - 1.67059i) q^{86} +(0.851809 + 3.20537i) q^{88} +12.9841i q^{89} -8.02226 q^{91} +(-4.34269 + 2.50725i) q^{92} +(-4.46479 - 2.57775i) q^{94} +(3.93058 - 6.80796i) q^{95} +(-7.38202 - 12.7860i) q^{97} +6.51910 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 24 q^{2} - 24 q^{4} - 48 q^{8} + 6 q^{11} + 24 q^{13} - 24 q^{16} + 12 q^{17} + 12 q^{22} - 36 q^{23} + 24 q^{25} + 24 q^{32} + 6 q^{34} + 6 q^{38} + 6 q^{41} + 30 q^{43} + 6 q^{44} + 24 q^{49} - 24 q^{50}+ \cdots + 48 q^{98}+O(q^{100}) $ 48 * q + 24 * q^2 - 24 * q^4 - 48 * q^8 + 6 * q^11 + 24 * q^13 - 24 * q^16 + 12 * q^17 + 12 * q^22 - 36 * q^23 + 24 * q^25 + 24 * q^32 + 6 * q^34 + 6 * q^38 + 6 * q^41 + 30 * q^43 + 6 * q^44 + 24 * q^49 - 24 * q^50 - 24 * q^52 + 54 * q^59 + 48 * q^64 - 6 * q^67 - 6 * q^68 + 6 * q^76 - 6 * q^77 + 12 * q^82 - 36 * q^83 + 30 * q^86 - 6 * q^88 + 24 * q^91 + 36 * q^92 + 6 * q^97 + 48 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/2970\mathbb{Z}\right)^\times$.

$n$	$541$	$1541$	$2377$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$5$	0.866025	+	0.500000i	0.387298	+	0.223607i
$6$		0			0
$7$	−3.18423	+	1.83842i	−1.20353	+	0.694856i	−0.961337	−	0.275373i	$-0.911199\pi$
$7$	−3.18423	+	1.83842i	−1.20353	+	0.694856i	−0.242188	+	0.970229i	$0.577865\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$			1.00000i			0.316228i
$11$	−0.851809	−	3.20537i	−0.256830	−	0.966457i
$11$	−0.851809	−	3.20537i	−0.256830	−	0.966457i
$12$		0			0
$13$	1.88953	+	1.09092i	0.524061	+	0.302567i	0.738595	−	0.674150i	$-0.235490\pi$
$13$	1.88953	+	1.09092i	0.524061	+	0.302567i	−0.214534	+	0.976717i	$0.568823\pi$
$14$	−3.18423	−	1.83842i	−0.851021	−	0.491337i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.68359			−0.408331			−0.204166	−	0.978936i	$-0.565448\pi$
$17$	−1.68359			−0.408331			−0.204166	+	0.978936i	$0.565448\pi$
$18$		0			0
$19$		−	7.86116i		−	1.80347i	−0.432285	−	0.901737i	$-0.642293\pi$
$19$		−	7.86116i		−	1.80347i	0.432285	−	0.901737i	$-0.357707\pi$
$20$	−0.866025	+	0.500000i	−0.193649	+	0.111803i
$21$		0			0
$22$	2.35003	−	2.34038i	0.501028	−	0.498970i
$23$	4.34269	+	2.50725i	0.905513	+	0.522798i	0.878985	−	0.476850i	$-0.158222\pi$
$23$	4.34269	+	2.50725i	0.905513	+	0.522798i	0.0265280	+	0.999648i	$0.491555\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$			2.18184i			0.427894i
$27$		0			0
$28$		−	3.67683i		−	0.694856i
$29$	−3.65719	−	6.33444i	−0.679124	−	1.17628i	−0.975245	−	0.221126i	$-0.929027\pi$
$29$	−3.65719	−	6.33444i	−0.679124	−	1.17628i	0.296122	−	0.955150i	$-0.404307\pi$
$30$		0			0
$31$	2.78313	−	4.82052i	0.499864	−	0.865790i	−0.500136	−	0.865947i	$-0.666717\pi$
$31$	2.78313	−	4.82052i	0.499864	−	0.865790i	1.00000		0.000156599i	$4.98469e-5\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$	−0.841796	−	1.45803i	−0.144367	−	0.250051i
$35$	−3.67683			−0.621498
$36$		0			0
$37$	−9.84289			−1.61816			−0.809081	−	0.587698i	$-0.800034\pi$
$37$	−9.84289			−1.61816			−0.809081	+	0.587698i	$0.800034\pi$
$38$	6.80796	−	3.93058i	1.10440	−	0.637624i
$39$		0			0
$40$	−0.866025	−	0.500000i	−0.136931	−	0.0790569i
$41$	2.91945	−	5.05664i	0.455942	−	0.789715i	−0.542800	−	0.839862i	$-0.682636\pi$
$41$	2.91945	−	5.05664i	0.455942	−	0.789715i	0.998742	+	0.0501472i	$0.0159691\pi$
$42$		0			0
$43$	−2.89355	+	1.67059i	−0.441262	+	0.254763i	−0.704133	−	0.710068i	$-0.748664\pi$
$43$	−2.89355	+	1.67059i	−0.441262	+	0.254763i	0.262871	+	0.964831i	$0.415331\pi$
$44$	3.20184	+	0.864999i	0.482695	+	0.130403i
$45$		0			0
$46$			5.01450i			0.739348i
$47$	−4.46479	+	2.57775i	−0.651256	+	0.376003i	−0.788937	−	0.614474i	$-0.789368\pi$
$47$	−4.46479	+	2.57775i	−0.651256	+	0.376003i	0.137681	+	0.990477i	$0.456035\pi$
$48$		0			0
$49$	3.25955	−	5.64570i	0.465650	−	0.806529i
$50$	−0.500000	+	0.866025i	−0.0707107	+	0.122474i
$51$		0			0
$52$	−1.88953	+	1.09092i	−0.262030	+	0.151283i
$53$			4.66886i			0.641317i	0.947195	+	0.320658i	$0.103904\pi$
$53$			4.66886i			0.641317i	−0.947195	+	0.320658i	$0.896096\pi$
$54$		0			0
$55$	0.864999	−	3.20184i	0.116636	−	0.431736i
$56$	3.18423	−	1.83842i	0.425511	−	0.245669i
$57$		0			0
$58$	3.65719	−	6.33444i	0.480213	−	0.831753i
$59$	12.1117	+	6.99268i	1.57681	+	0.910370i	0.995301	+	0.0968274i	$0.0308695\pi$
$59$	12.1117	+	6.99268i	1.57681	+	0.910370i	0.581506	+	0.813542i	$0.302464\pi$
$60$		0			0
$61$	7.93110	−	4.57903i	1.01547	−	0.586284i	0.102684	−	0.994714i	$-0.467257\pi$
$61$	7.93110	−	4.57903i	1.01547	−	0.586284i	0.912790	+	0.408430i	$0.133924\pi$
$62$	5.56625			0.706915
$63$		0			0
$64$	1.00000			0.125000
$65$	1.09092	+	1.88953i	0.135312	+	0.234367i
$66$		0			0
$67$	6.87891	−	11.9146i	0.840393	−	1.45560i	−0.0491705	−	0.998790i	$-0.515658\pi$
$67$	6.87891	−	11.9146i	0.840393	−	1.45560i	0.889563	−	0.456812i	$-0.151009\pi$
$68$	0.841796	−	1.45803i	0.102083	−	0.176813i
$69$		0			0
$70$	−1.83842	−	3.18423i	−0.219733	−	0.380588i
$71$		−	7.93786i		−	0.942050i	−0.882120	−	0.471025i	$-0.843884\pi$
$71$		−	7.93786i		−	0.942050i	0.882120	−	0.471025i	$-0.156116\pi$
$72$		0			0
$73$			4.80281i			0.562127i	0.959689	+	0.281063i	$0.0906871\pi$
$73$			4.80281i			0.562127i	−0.959689	+	0.281063i	$0.909313\pi$
$74$	−4.92145	−	8.52419i	−0.572106	−	0.990917i
$75$		0			0
$76$	6.80796	+	3.93058i	0.780927	+	0.450868i
$77$	8.60517	+	8.64067i	0.980650	+	0.984696i
$78$		0			0
$79$	12.4035	−	7.16118i	1.39551	−	0.805695i	0.401588	−	0.915821i	$-0.368459\pi$
$79$	12.4035	−	7.16118i	1.39551	−	0.805695i	0.993918	+	0.110125i	$0.0351252\pi$
$80$		−	1.00000i		−	0.111803i
$81$		0			0
$82$	5.83891			0.644800
$83$	2.79143	+	4.83489i	0.306399	+	0.530698i	0.977572	−	0.210602i	$-0.0675426\pi$
$83$	2.79143	+	4.83489i	0.306399	+	0.530698i	−0.671173	+	0.741301i	$0.734209\pi$
$84$		0			0
$85$	−1.45803	−	0.841796i	−0.158146	−	0.0913056i
$86$	−2.89355	−	1.67059i	−0.312019	−	0.180144i
$87$		0			0
$88$	0.851809	+	3.20537i	0.0908031	+	0.341694i
$89$			12.9841i			1.37631i	0.725565	+	0.688153i	$0.241578\pi$
$89$			12.9841i			1.37631i	−0.725565	+	0.688153i	$0.758422\pi$
$90$		0			0
$91$	−8.02226			−0.840961
$92$	−4.34269	+	2.50725i	−0.452756	+	0.261399i
$93$		0			0
$94$	−4.46479	−	2.57775i	−0.460508	−	0.265874i
$95$	3.93058	−	6.80796i	0.403269	−	0.698482i
$96$		0			0
$97$	−7.38202	−	12.7860i	−0.749531	−	1.29823i	−0.948048	−	0.318128i	$-0.896946\pi$
$97$	−7.38202	−	12.7860i	−0.749531	−	1.29823i	0.198517	−	0.980097i	$-0.436388\pi$
$98$	6.51910			0.658528
$99$		0			0
$100$	−1.00000			−0.100000
$101$	−0.670430	−	1.16122i	−0.0667103	−	0.115546i	0.830741	−	0.556659i	$-0.187917\pi$
$101$	−0.670430	−	1.16122i	−0.0667103	−	0.115546i	−0.897451	+	0.441113i	$0.854584\pi$
$102$		0			0
$103$	−0.170406	+	0.295152i	−0.0167906	+	0.0290822i	−0.874299	−	0.485388i	$-0.838678\pi$
$103$	−0.170406	+	0.295152i	−0.0167906	+	0.0290822i	0.857508	+	0.514471i	$0.172012\pi$
$104$	−1.88953	−	1.09092i	−0.185283	−	0.106973i
$105$		0			0
$106$	−4.04335	+	2.33443i	−0.392725	+	0.226740i
$107$	6.18150			0.597588			0.298794	−	0.954318i	$-0.403416\pi$
$107$	6.18150			0.597588			0.298794	+	0.954318i	$0.403416\pi$
$108$		0			0
$109$		−	6.26500i		−	0.600078i	−0.953927	−	0.300039i	$-0.903000\pi$
$109$		−	6.26500i		−	0.600078i	0.953927	−	0.300039i	$-0.0969997\pi$
$110$	3.20537	−	0.851809i	0.305620	−	0.0812168i
$111$		0			0
$112$	3.18423	+	1.83842i	0.300881	+	0.173714i
$113$	−1.73318	−	1.00065i	−0.163044	−	0.0941336i	0.416258	−	0.909247i	$-0.363341\pi$
$113$	−1.73318	−	1.00065i	−0.163044	−	0.0941336i	−0.579302	+	0.815113i	$0.696675\pi$
$114$		0			0
$115$	2.50725	+	4.34269i	0.233802	+	0.404958i
$116$	7.31439			0.679124
$117$		0			0
$118$			13.9854i			1.28746i
$119$	5.36094	−	3.09514i	0.491437	−	0.283731i
$120$		0			0
$121$	−9.54884	+	5.46073i	−0.868077	+	0.496430i
$122$	7.93110	+	4.57903i	0.718048	+	0.414565i
$123$		0			0
$124$	2.78313	+	4.82052i	0.249932	+	0.432895i
$125$			1.00000i			0.0894427i
$126$		0			0
$127$		−	16.4881i		−	1.46308i	−0.681797	−	0.731541i	$-0.738801\pi$
$127$		−	16.4881i		−	1.46308i	0.681797	−	0.731541i	$-0.261199\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−1.09092	+	1.88953i	−0.0956800	+	0.165723i
$131$	−2.63052	+	4.55620i	−0.229830	+	0.398077i	−0.957758	−	0.287577i	$-0.907150\pi$
$131$	−2.63052	+	4.55620i	−0.229830	+	0.398077i	0.727928	+	0.685654i	$0.240484\pi$
$132$		0			0
$133$	14.4521	+	25.0317i	1.25315	+	2.17053i
$134$	13.7578			1.18849
$135$		0			0
$136$	1.68359			0.144367
$137$	−1.72788	+	0.997591i	−0.147623	+	0.0852300i	−0.571992	−	0.820259i	$-0.693829\pi$
$137$	−1.72788	+	0.997591i	−0.147623	+	0.0852300i	0.424369	+	0.905489i	$0.360496\pi$
$138$		0			0
$139$	−13.3236	−	7.69241i	−1.13010	−	0.652462i	−0.186137	−	0.982524i	$-0.559597\pi$
$139$	−13.3236	−	7.69241i	−1.13010	−	0.652462i	−0.943959	+	0.330062i	$0.892930\pi$
$140$	1.83842	−	3.18423i	0.155375	−	0.269117i
$141$		0			0
$142$	6.87439	−	3.96893i	0.576886	−	0.333065i
$143$	1.88729	−	6.98590i	0.157823	−	0.584190i
$144$		0			0
$145$		−	7.31439i		−	0.607427i
$146$	−4.15936	+	2.40141i	−0.344231	+	0.198742i
$147$		0			0
$148$	4.92145	−	8.52419i	0.404540	−	0.700684i
$149$	−10.8574	+	18.8056i	−0.889476	+	1.54062i	−0.0489799	+	0.998800i	$0.515597\pi$
$149$	−10.8574	+	18.8056i	−0.889476	+	1.54062i	−0.840496	+	0.541818i	$0.817736\pi$
$150$		0			0
$151$	0.961201	−	0.554950i	0.0782214	−	0.0451612i	−0.460379	−	0.887722i	$-0.652287\pi$
$151$	0.961201	−	0.554950i	0.0782214	−	0.0451612i	0.538601	+	0.842561i	$0.318953\pi$
$152$			7.86116i			0.637624i
$153$		0			0
$154$	−3.18046	+	11.7726i	−0.256288	+	0.948665i
$155$	4.82052	−	2.78313i	0.387193	−	0.223546i
$156$		0			0
$157$	11.6455	−	20.1706i	0.929411	−	1.60979i	0.145102	−	0.989417i	$-0.453649\pi$
$157$	11.6455	−	20.1706i	0.929411	−	1.60979i	0.784309	−	0.620371i	$-0.213018\pi$
$158$	12.4035	+	7.16118i	0.986771	+	0.569713i
$159$		0			0
$160$	0.866025	−	0.500000i	0.0684653	−	0.0395285i
$161$	−18.4375			−1.45308
$162$		0			0
$163$	8.91357			0.698165			0.349082	−	0.937092i	$-0.386493\pi$
$163$	8.91357			0.698165			0.349082	+	0.937092i	$0.386493\pi$
$164$	2.91945	+	5.05664i	0.227971	+	0.394857i
$165$		0			0
$166$	−2.79143	+	4.83489i	−0.216657	+	0.375260i
$167$	5.12001	−	8.86811i	0.396198	−	0.686235i	−0.597055	−	0.802200i	$-0.703663\pi$
$167$	5.12001	−	8.86811i	0.396198	−	0.686235i	0.993253	+	0.115965i	$0.0369961\pi$
$168$		0			0
$169$	−4.11979	−	7.13568i	−0.316907	−	0.548899i
$170$		−	1.68359i		−	0.129126i
$171$		0			0
$172$		−	3.34118i		−	0.254763i
$173$	−6.65243	−	11.5223i	−0.505775	−	0.876027i	−0.999978	−	0.00668085i	$-0.997873\pi$
$173$	−6.65243	−	11.5223i	−0.505775	−	0.876027i	0.494203	−	0.869346i	$-0.335460\pi$
$174$		0			0
$175$	−3.18423	−	1.83842i	−0.240705	−	0.138971i
$176$	−2.35003	+	2.34038i	−0.177140	+	0.176412i
$177$		0			0
$178$	−11.2445	+	6.49203i	−0.842812	+	0.486598i
$179$		−	21.7749i		−	1.62753i	−0.581194	−	0.813765i	$-0.697414\pi$
$179$		−	21.7749i		−	1.62753i	0.581194	−	0.813765i	$-0.302586\pi$
$180$		0			0
$181$	17.9379			1.33331			0.666655	−	0.745366i	$-0.267725\pi$
$181$	17.9379			1.33331			0.666655	+	0.745366i	$0.267725\pi$
$182$	−4.01113	−	6.94748i	−0.297325	−	0.514981i
$183$		0			0
$184$	−4.34269	−	2.50725i	−0.320147	−	0.184837i
$185$	−8.52419	−	4.92145i	−0.626711	−	0.361832i
$186$		0			0
$187$	1.43410	+	5.39654i	0.104872	+	0.394634i
$188$		−	5.15549i		−	0.376003i
$189$		0			0
$190$	7.86116			0.570309
$191$	4.55854	−	2.63187i	0.329844	−	0.190436i	−0.325928	−	0.945395i	$-0.605677\pi$
$191$	4.55854	−	2.63187i	0.329844	−	0.190436i	0.655772	+	0.754959i	$0.272343\pi$
$192$		0			0
$193$	−2.26126	−	1.30554i	−0.162769	−	0.0939748i	0.416403	−	0.909180i	$-0.363291\pi$
$193$	−2.26126	−	1.30554i	−0.162769	−	0.0939748i	−0.579172	+	0.815205i	$0.696624\pi$
$194$	7.38202	−	12.7860i	0.529998	−	0.917984i
$195$		0			0
$196$	3.25955	+	5.64570i	0.232825	+	0.403264i
$197$	−12.7694			−0.909780			−0.454890	−	0.890548i	$-0.650321\pi$
$197$	−12.7694			−0.909780			−0.454890	+	0.890548i	$0.650321\pi$
$198$		0			0
$199$	−2.16043			−0.153149			−0.0765744	−	0.997064i	$-0.524398\pi$
$199$	−2.16043			−0.153149			−0.0765744	+	0.997064i	$0.524398\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$		0			0
$202$	0.670430	−	1.16122i	0.0471713	−	0.0817031i
$203$	23.2907	+	13.4469i	1.63469	+	0.943786i
$204$		0			0
$205$	5.05664	−	2.91945i	0.353171	−	0.203904i
$206$	−0.340812			−0.0237455
$207$		0			0
$208$		−	2.18184i		−	0.151283i
$209$	−25.1980	+	6.69621i	−1.74298	+	0.463186i
$210$		0			0
$211$	2.37810	+	1.37300i	0.163715	+	0.0945209i	0.579619	−	0.814888i	$-0.303201\pi$
$211$	2.37810	+	1.37300i	0.163715	+	0.0945209i	−0.415904	+	0.909409i	$0.636535\pi$
$212$	−4.04335	−	2.33443i	−0.277698	−	0.160329i
$213$		0			0
$214$	3.09075	+	5.35334i	0.211279	+	0.365947i
$215$	−3.34118			−0.227867
$216$		0			0
$217$			20.4662i			1.38933i
$218$	5.42565	−	3.13250i	0.367471	−	0.212160i
$219$		0			0
$220$	2.34038	+	2.35003i	0.157788	+	0.158439i
$221$	−3.18119	−	1.83666i	−0.213990	−	0.123547i
$222$		0			0
$223$	8.12070	+	14.0655i	0.543802	+	0.941893i	0.998681	+	0.0513397i	$0.0163491\pi$
$223$	8.12070	+	14.0655i	0.543802	+	0.941893i	−0.454879	+	0.890553i	$0.650318\pi$
$224$			3.67683i			0.245669i
$225$		0			0
$226$		−	2.00131i		−	0.133125i
$227$	0.0573427	+	0.0993205i	0.00380597	+	0.00659213i	0.867922	−	0.496700i	$-0.165455\pi$
$227$	0.0573427	+	0.0993205i	0.00380597	+	0.00659213i	−0.864116	+	0.503292i	$0.832122\pi$
$228$		0			0
$229$	6.68658	−	11.5815i	0.441862	−	0.765327i	−0.555966	−	0.831205i	$-0.687651\pi$
$229$	6.68658	−	11.5815i	0.441862	−	0.765327i	0.997828	+	0.0658780i	$0.0209848\pi$
$230$	−2.50725	+	4.34269i	−0.165323	+	0.286348i
$231$		0			0
$232$	3.65719	+	6.33444i	0.240106	+	0.415877i
$233$	5.42880			0.355652			0.177826	−	0.984062i	$-0.443094\pi$
$233$	5.42880			0.355652			0.177826	+	0.984062i	$0.443094\pi$
$234$		0			0
$235$	−5.15549			−0.336307
$236$	−12.1117	+	6.99268i	−0.788403	+	0.455185i
$237$		0			0
$238$	5.36094	+	3.09514i	0.347498	+	0.200628i
$239$	−2.95156	+	5.11225i	−0.190921	+	0.330684i	−0.945556	−	0.325461i	$-0.894481\pi$
$239$	−2.95156	+	5.11225i	−0.190921	+	0.330684i	0.754635	+	0.656145i	$0.227814\pi$
$240$		0			0
$241$	−25.7690	+	14.8778i	−1.65993	+	0.958361i	−0.687184	+	0.726483i	$0.741154\pi$
$241$	−25.7690	+	14.8778i	−1.65993	+	0.958361i	−0.972745	+	0.231878i	$0.925513\pi$
$242$	−9.50355	−	5.53917i	−0.610912	−	0.356072i
$243$		0			0
$244$			9.15805i			0.586284i
$245$	5.64570	−	3.25955i	0.360691	−	0.208245i
$246$		0			0
$247$	8.57589	−	14.8539i	0.545671	−	0.945130i
$248$	−2.78313	+	4.82052i	−0.176729	+	0.306103i
$249$		0			0
$250$	−0.866025	+	0.500000i	−0.0547723	+	0.0316228i
$251$		−	2.25143i		−	0.142109i	−0.997472	−	0.0710545i	$-0.977364\pi$
$251$		−	2.25143i		−	0.142109i	0.997472	−	0.0710545i	$-0.0226364\pi$
$252$		0			0
$253$	4.33754	−	16.0556i	0.272699	−	1.00941i
$254$	14.2791	−	8.24405i	0.895952	−	0.517278i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−18.5247	−	10.6952i	−1.15554	−	0.667151i	−0.205308	−	0.978697i	$-0.565820\pi$
$257$	−18.5247	−	10.6952i	−1.15554	−	0.667151i	−0.950231	+	0.311546i	$0.899153\pi$
$258$		0			0
$259$	31.3420	−	18.0953i	1.94750	−	1.12439i
$260$	−2.18184			−0.135312
$261$		0			0
$262$	−5.26104			−0.325028
$263$	−3.76673	−	6.52416i	−0.232266	−	0.402297i	0.726208	−	0.687475i	$-0.241281\pi$
$263$	−3.76673	−	6.52416i	−0.232266	−	0.402297i	−0.958475	+	0.285178i	$0.907947\pi$
$264$		0			0
$265$	−2.33443	+	4.04335i	−0.143403	+	0.248381i
$266$	−14.4521	+	25.0317i	−0.886114	+	1.53479i
$267$		0			0
$268$	6.87891	+	11.9146i	0.420196	+	0.727801i
$269$			16.3429i			0.996446i	0.867049	+	0.498223i	$0.166014\pi$
$269$			16.3429i			0.996446i	−0.867049	+	0.498223i	$0.833986\pi$
$270$		0			0
$271$			0.605209i			0.0367638i	0.999831	+	0.0183819i	$0.00585148\pi$
$271$			0.605209i			0.0367638i	−0.999831	+	0.0183819i	$0.994149\pi$
$272$	0.841796	+	1.45803i	0.0510414	+	0.0884063i
$273$		0			0
$274$	−1.72788	−	0.997591i	−0.104385	−	0.0602667i
$275$	2.35003	−	2.34038i	0.141712	−	0.141130i
$276$		0			0
$277$	−10.2745	+	5.93197i	−0.617333	+	0.356418i	−0.775830	−	0.630942i	$-0.782669\pi$
$277$	−10.2745	+	5.93197i	−0.617333	+	0.356418i	0.158497	+	0.987360i	$0.449335\pi$
$278$		−	15.3848i		−	0.922720i
$279$		0			0
$280$	3.67683			0.219733
$281$	−4.36042	−	7.55247i	−0.260121	−	0.450543i	0.706153	−	0.708059i	$-0.250429\pi$
$281$	−4.36042	−	7.55247i	−0.260121	−	0.450543i	−0.966274	+	0.257517i	$0.917096\pi$
$282$		0			0
$283$	−8.87392	−	5.12336i	−0.527500	−	0.304552i	0.212498	−	0.977162i	$-0.431840\pi$
$283$	−8.87392	−	5.12336i	−0.527500	−	0.304552i	−0.739998	+	0.672609i	$0.765174\pi$
$284$	6.87439	+	3.96893i	0.407920	+	0.235513i
$285$		0			0
$286$	6.99361	−	1.85851i	0.413541	−	0.109896i
$287$			21.4687i			1.26726i
$288$		0			0
$289$	−14.1655			−0.833266
$290$	6.33444	−	3.65719i	0.371971	−	0.214758i
$291$		0			0
$292$	−4.15936	−	2.40141i	−0.243408	−	0.140532i
$293$	−7.99621	+	13.8498i	−0.467143	+	0.809116i	−0.999295	−	0.0375328i	$-0.988050\pi$
$293$	−7.99621	+	13.8498i	−0.467143	+	0.809116i	0.532152	+	0.846649i	$0.321383\pi$
$294$		0			0
$295$	6.99268	+	12.1117i	0.407130	+	0.705169i
$296$	9.84289			0.572106
$297$		0			0
$298$	−21.7149			−1.25791
$299$	5.47042	+	9.47504i	0.316362	+	0.547956i
$300$		0			0
$301$	6.14248	−	10.6391i	0.354047	−	0.613227i
$302$	0.961201	+	0.554950i	0.0553109	+	0.0319338i
$303$		0			0
$304$	−6.80796	+	3.93058i	−0.390464	+	0.225434i
$305$	9.15805			0.524388
$306$		0			0
$307$			16.8203i			0.959986i	0.877272	+	0.479993i	$0.159361\pi$
$307$			16.8203i			0.959986i	−0.877272	+	0.479993i	$0.840639\pi$
$308$	−11.7856	+	3.13196i	−0.671548	+	0.178460i
$309$		0			0
$310$	4.82052	+	2.78313i	0.273787	+	0.158071i
$311$	−6.39007	−	3.68931i	−0.362348	−	0.209202i	0.307762	−	0.951463i	$-0.400420\pi$
$311$	−6.39007	−	3.68931i	−0.362348	−	0.209202i	−0.670110	+	0.742262i	$0.733753\pi$
$312$		0			0
$313$	−12.2973	−	21.2995i	−0.695082	−	1.20392i	−0.970153	−	0.242493i	$-0.922035\pi$
$313$	−12.2973	−	21.2995i	−0.695082	−	1.20392i	0.275071	−	0.961424i	$-0.411299\pi$
$314$	23.2910			1.31439
$315$		0			0
$316$			14.3224i			0.805695i
$317$	0.940567	−	0.543036i	0.0528275	−	0.0305000i	−0.473354	−	0.880872i	$-0.656957\pi$
$317$	0.940567	−	0.543036i	0.0528275	−	0.0305000i	0.526181	+	0.850373i	$0.323623\pi$
$318$		0			0
$319$	−17.1890	+	17.1184i	−0.962401	+	0.958447i
$320$	0.866025	+	0.500000i	0.0484123	+	0.0279508i
$321$		0			0
$322$	−9.21874	−	15.9673i	−0.513740	−	0.889824i
$323$			13.2350i			0.736414i
$324$		0			0
$325$			2.18184i			0.121027i
$326$	4.45679	+	7.71938i	0.246839	+	0.427537i
$327$		0			0
$328$	−2.91945	+	5.05664i	−0.161200	+	0.279206i
$329$	9.47794	−	16.4163i	0.522536	−	0.905058i
$330$		0			0
$331$	−2.48198	−	4.29891i	−0.136422	−	0.236290i	0.789718	−	0.613470i	$-0.210227\pi$
$331$	−2.48198	−	4.29891i	−0.136422	−	0.236290i	−0.926140	+	0.377181i	$0.876894\pi$
$332$	−5.58285			−0.306399
$333$		0			0
$334$	10.2400			0.560309
$335$	11.9146	−	6.87891i	0.650965	−	0.375835i
$336$		0			0
$337$	−15.0511	−	8.68976i	−0.819886	−	0.473361i	0.0304911	−	0.999535i	$-0.490293\pi$
$337$	−15.0511	−	8.68976i	−0.819886	−	0.473361i	−0.850377	+	0.526174i	$0.823626\pi$
$338$	4.11979	−	7.13568i	0.224087	−	0.388130i
$339$		0			0
$340$	1.45803	−	0.841796i	0.0790730	−	0.0456528i
$341$	−17.8223	−	4.81480i	−0.965129	−	0.260736i
$342$		0			0
$343$		−	1.76821i		−	0.0954742i
$344$	2.89355	−	1.67059i	0.156010	−	0.0900722i
$345$		0			0
$346$	6.65243	−	11.5223i	0.357637	−	0.619445i
$347$	−5.68546	+	9.84750i	−0.305211	+	0.528641i	−0.977308	−	0.211822i	$-0.932060\pi$
$347$	−5.68546	+	9.84750i	−0.305211	+	0.528641i	0.672097	+	0.740463i	$0.265394\pi$
$348$		0			0
$349$	5.30746	−	3.06426i	0.284102	−	0.164026i	−0.351177	−	0.936309i	$-0.614218\pi$
$349$	5.30746	−	3.06426i	0.284102	−	0.164026i	0.635279	+	0.772283i	$0.280885\pi$
$350$		−	3.67683i		−	0.196535i
$351$		0			0
$352$	−3.20184	−	0.864999i	−0.170659	−	0.0461046i
$353$	24.2020	−	13.9730i	1.28814	−	0.743708i	0.309818	−	0.950796i	$-0.399732\pi$
$353$	24.2020	−	13.9730i	1.28814	−	0.743708i	0.978322	+	0.207088i	$0.0663985\pi$
$354$		0			0
$355$	3.96893	−	6.87439i	0.210649	−	0.364855i
$356$	−11.2445	−	6.49203i	−0.595958	−	0.344077i
$357$		0			0
$358$	18.8576	−	10.8874i	0.996654	−	0.575419i
$359$	32.1274			1.69562			0.847809	−	0.530301i	$-0.177921\pi$
$359$	32.1274			1.69562			0.847809	+	0.530301i	$0.177921\pi$
$360$		0			0
$361$	−42.7978			−2.25252
$362$	8.96893	+	15.5346i	0.471396	+	0.816483i
$363$		0			0
$364$	4.01113	−	6.94748i	0.210240	−	0.364147i
$365$	−2.40141	+	4.15936i	−0.125695	+	0.217711i
$366$		0			0
$367$	7.97900	+	13.8200i	0.416500	+	0.721400i	0.995585	−	0.0938681i	$-0.0299232\pi$
$367$	7.97900	+	13.8200i	0.416500	+	0.721400i	−0.579084	+	0.815268i	$0.696590\pi$
$368$		−	5.01450i		−	0.261399i
$369$		0			0
$370$		−	9.84289i		−	0.511708i
$371$	−8.58330	−	14.8667i	−0.445623	−	0.771842i
$372$		0			0
$373$	18.1064	+	10.4537i	0.937513	+	0.541273i	0.889180	−	0.457558i	$-0.151276\pi$
$373$	18.1064	+	10.4537i	0.937513	+	0.541273i	0.0483331	+	0.998831i	$0.484609\pi$
$374$	−3.95649	+	3.94024i	−0.204585	+	0.203745i
$375$		0			0
$376$	4.46479	−	2.57775i	0.230254	−	0.132937i
$377$		−	15.9588i		−	0.821921i
$378$		0			0
$379$	−15.3751			−0.789767			−0.394884	−	0.918731i	$-0.629215\pi$
$379$	−15.3751			−0.789767			−0.394884	+	0.918731i	$0.629215\pi$
$380$	3.93058	+	6.80796i	0.201635	+	0.349241i
$381$		0			0
$382$	4.55854	+	2.63187i	0.233235	+	0.134658i
$383$	2.05066	+	1.18395i	0.104784	+	0.0604971i	0.551476	−	0.834191i	$-0.314065\pi$
$383$	2.05066	+	1.18395i	0.104784	+	0.0604971i	−0.446692	+	0.894688i	$0.647398\pi$
$384$		0			0
$385$	3.13196	+	11.7856i	0.159619	+	0.600651i
$386$		−	2.61108i		−	0.132900i
$387$		0			0
$388$	14.7640			0.749531
$389$	30.7171	−	17.7345i	1.55742	−	0.899176i	0.559916	−	0.828549i	$-0.310833\pi$
$389$	30.7171	−	17.7345i	1.55742	−	0.899176i	0.997503	−	0.0706272i	$-0.0225001\pi$
$390$		0			0
$391$	−7.31131	−	4.22119i	−0.369749	−	0.213475i
$392$	−3.25955	+	5.64570i	−0.164632	+	0.285151i
$393$		0			0
$394$	−6.38468	−	11.0586i	−0.321656	−	0.557124i
$395$	14.3224			0.720636
$396$		0			0
$397$	13.9573			0.700495			0.350248	−	0.936657i	$-0.386097\pi$
$397$	13.9573			0.700495			0.350248	+	0.936657i	$0.386097\pi$
$398$	−1.08022	−	1.87099i	−0.0541463	−	0.0937842i
$399$		0			0
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	−5.40421	−	3.12012i	−0.269873	−	0.155811i	0.358957	−	0.933354i	$-0.383133\pi$
$401$	−5.40421	−	3.12012i	−0.269873	−	0.155811i	−0.628830	+	0.777543i	$0.716466\pi$
$402$		0			0
$403$	10.5176	−	6.07234i	0.523919	−	0.302485i
$404$	1.34086			0.0667103
$405$		0			0
$406$			26.8938i			1.33472i
$407$	8.38426	+	31.5501i	0.415593	+	1.56388i
$408$		0			0
$409$	12.7021	+	7.33357i	0.628079	+	0.362622i	0.780008	−	0.625770i	$-0.215215\pi$
$409$	12.7021	+	7.33357i	0.628079	+	0.362622i	−0.151929	+	0.988391i	$0.548548\pi$
$410$	5.05664	+	2.91945i	0.249730	+	0.144182i
$411$		0			0
$412$	−0.170406	−	0.295152i	−0.00839530	−	0.0145411i
$413$	−51.4218			−2.53030
$414$		0			0
$415$			5.58285i			0.274051i
$416$	1.88953	−	1.09092i	0.0926417	−	0.0534867i
$417$		0			0
$418$	−18.3981	−	18.4740i	−0.899879	−	0.903591i
$419$	−26.1506	−	15.0981i	−1.27754	−	0.737588i	−0.301145	−	0.953578i	$-0.597369\pi$
$419$	−26.1506	−	15.0981i	−1.27754	−	0.737588i	−0.976396	+	0.215990i	$0.930702\pi$
$420$		0			0
$421$	4.66929	+	8.08745i	0.227567	+	0.394158i	0.957087	−	0.289802i	$-0.0935895\pi$
$421$	4.66929	+	8.08745i	0.227567	+	0.394158i	−0.729519	+	0.683960i	$0.760256\pi$
$422$			2.74599i			0.133673i
$423$		0			0
$424$		−	4.66886i		−	0.226740i
$425$	−0.841796	−	1.45803i	−0.0408331	−	0.0707250i
$426$		0			0
$427$	−16.8363	+	29.1613i	−0.814766	+	1.41122i
$428$	−3.09075	+	5.35334i	−0.149397	+	0.258763i
$429$		0			0
$430$	−1.67059	−	2.89355i	−0.0805631	−	0.139539i
$431$	24.4410			1.17728			0.588641	−	0.808394i	$-0.299663\pi$
$431$	24.4410			1.17728			0.588641	+	0.808394i	$0.299663\pi$
$432$		0			0
$433$	25.3732			1.21936			0.609680	−	0.792648i	$-0.291298\pi$
$433$	25.3732			1.21936			0.609680	+	0.792648i	$0.291298\pi$
$434$	−17.7242	+	10.2331i	−0.850790	+	0.491204i
$435$		0			0
$436$	5.42565	+	3.13250i	0.259841	+	0.150020i
$437$	19.7099	−	34.1386i	0.942853	−	1.63307i
$438$		0			0
$439$	−17.5588	+	10.1376i	−0.838034	+	0.483839i	−0.856596	−	0.515988i	$-0.827425\pi$
$439$	−17.5588	+	10.1376i	−0.838034	+	0.483839i	0.0185613	+	0.999828i	$0.494091\pi$
$440$	−0.864999	+	3.20184i	−0.0412372	+	0.152642i
$441$		0			0
$442$		−	3.67333i		−	0.174722i
$443$	−17.8653	+	10.3145i	−0.848804	+	0.490057i	−0.860247	−	0.509877i	$-0.829691\pi$
$443$	−17.8653	+	10.3145i	−0.848804	+	0.490057i	0.0114429	+	0.999935i	$0.496358\pi$
$444$		0			0
$445$	−6.49203	+	11.2445i	−0.307752	+	0.533041i
$446$	−8.12070	+	14.0655i	−0.384526	+	0.666019i
$447$		0			0
$448$	−3.18423	+	1.83842i	−0.150441	+	0.0868570i
$449$			29.2409i			1.37996i	0.723826	+	0.689982i	$0.242382\pi$
$449$			29.2409i			1.37996i	−0.723826	+	0.689982i	$0.757618\pi$
$450$		0			0
$451$	−18.6952	−	5.05065i	−0.880325	−	0.237826i
$452$	1.73318	−	1.00065i	0.0815221	−	0.0470668i
$453$		0			0
$454$	−0.0573427	+	0.0993205i	−0.00269123	+	0.00466134i
$455$	−6.94748	−	4.01113i	−0.325703	−	0.188045i
$456$		0			0
$457$	−26.9068	+	15.5347i	−1.25865	+	0.726681i	−0.972812	−	0.231597i	$-0.925605\pi$
$457$	−26.9068	+	15.5347i	−1.25865	+	0.726681i	−0.285837	+	0.958278i	$0.592272\pi$
$458$	13.3732			0.624887
$459$		0			0
$460$	−5.01450			−0.233802
$461$	14.4654	+	25.0548i	0.673722	+	1.16692i	0.976841	+	0.213968i	$0.0686387\pi$
$461$	14.4654	+	25.0548i	0.673722	+	1.16692i	−0.303119	+	0.952953i	$0.598028\pi$
$462$		0			0
$463$	1.25707	−	2.17732i	0.0584212	−	0.101188i	−0.835336	−	0.549740i	$-0.814727\pi$
$463$	1.25707	−	2.17732i	0.0584212	−	0.101188i	0.893757	+	0.448552i	$0.148060\pi$
$464$	−3.65719	+	6.33444i	−0.169781	+	0.294069i
$465$		0			0
$466$	2.71440	+	4.70148i	0.125742	+	0.217792i
$467$		−	2.01504i		−	0.0932448i	−0.998913	−	0.0466224i	$-0.985154\pi$
$467$		−	2.01504i		−	0.0932448i	0.998913	−	0.0466224i	$-0.0148457\pi$
$468$		0			0
$469$			50.5852i			2.33581i
$470$	−2.57775	−	4.46479i	−0.118903	−	0.205945i
$471$		0			0
$472$	−12.1117	−	6.99268i	−0.557485	−	0.321864i
$473$	7.81962	+	7.85188i	0.359547	+	0.361030i
$474$		0			0
$475$	6.80796	−	3.93058i	0.312371	−	0.180347i
$476$			6.19029i			0.283731i
$477$		0			0
$478$	−5.90312			−0.270002
$479$	−3.15987	−	5.47305i	−0.144378	−	0.250070i	0.784763	−	0.619796i	$-0.212785\pi$
$479$	−3.15987	−	5.47305i	−0.144378	−	0.250070i	−0.929141	+	0.369726i	$0.879451\pi$
$480$		0			0
$481$	−18.5984	−	10.7378i	−0.848015	−	0.489602i
$482$	−25.7690	−	14.8778i	−1.17375	−	0.677663i
$483$		0			0
$484$	0.0452884	−	10.9999i	0.00205856	−	0.499996i
$485$		−	14.7640i		−	0.670401i
$486$		0			0
$487$	−13.1443			−0.595626			−0.297813	−	0.954624i	$-0.596257\pi$
$487$	−13.1443			−0.595626			−0.297813	+	0.954624i	$0.596257\pi$
$488$	−7.93110	+	4.57903i	−0.359024	+	0.207283i
$489$		0			0
$490$	5.64570	+	3.25955i	0.255047	+	0.147251i
$491$	7.95737	−	13.7826i	0.359111	−	0.621999i	−0.628702	−	0.777647i	$-0.716413\pi$
$491$	7.95737	−	13.7826i	0.359111	−	0.621999i	0.987813	+	0.155648i	$0.0497466\pi$
$492$		0			0
$493$	6.15722	+	10.6646i	0.277307	+	0.480310i
$494$	17.1518			0.771695
$495$		0			0
$496$	−5.56625			−0.249932
$497$	14.5931	+	25.2760i	0.654589	+	1.13378i
$498$		0			0
$499$	17.8573	−	30.9298i	0.799403	−	1.38461i	−0.120602	−	0.992701i	$-0.538482\pi$
$499$	17.8573	−	30.9298i	0.799403	−	1.38461i	0.920005	−	0.391906i	$-0.128184\pi$
$500$	−0.866025	−	0.500000i	−0.0387298	−	0.0223607i
$501$		0			0
$502$	1.94980	−	1.12571i	0.0870236	−	0.0502431i
$503$	−21.6640			−0.965951			−0.482975	−	0.875634i	$-0.660444\pi$
$503$	−21.6640			−0.965951			−0.482975	+	0.875634i	$0.660444\pi$
$504$		0			0
$505$		−	1.34086i		−	0.0596675i
$506$	16.0734	−	4.27140i	0.714548	−	0.189887i
$507$		0			0
$508$	14.2791	+	8.24405i	0.633534	+	0.365771i
$509$	1.67154	+	0.965064i	0.0740897	+	0.0427757i	0.536587	−	0.843845i	$-0.319713\pi$
$509$	1.67154	+	0.965064i	0.0740897	+	0.0427757i	−0.462498	+	0.886621i	$0.653047\pi$
$510$		0			0
$511$	−8.82957	−	15.2933i	−0.390597	−	0.676534i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$		−	21.3905i		−	0.943494i
$515$	−0.295152	+	0.170406i	−0.0130059	+	0.00750898i
$516$		0			0
$517$	12.0658	+	12.1156i	0.530653	+	0.532842i
$518$	31.3420	+	18.0953i	1.37709	+	0.795063i
$519$		0			0
$520$	−1.09092	−	1.88953i	−0.0478400	−	0.0828613i
$521$			12.3020i			0.538960i	0.963006	+	0.269480i	$0.0868518\pi$
$521$			12.3020i			0.538960i	−0.963006	+	0.269480i	$0.913148\pi$
$522$		0			0
$523$			12.3025i			0.537949i	0.963147	+	0.268975i	$0.0866848\pi$
$523$			12.3025i			0.537949i	−0.963147	+	0.268975i	$0.913315\pi$
$524$	−2.63052	−	4.55620i	−0.114915	−	0.199038i
$525$		0			0
$526$	3.76673	−	6.52416i	0.164237	−	0.284467i
$527$	−4.68565	+	8.11578i	−0.204110	+	0.353529i
$528$		0			0
$529$	1.07262	+	1.85783i	0.0466355	+	0.0807750i
$530$	−4.66886			−0.202802
$531$		0			0
$532$	−28.9042			−1.25315
$533$	11.0328	−	6.36978i	0.477883	−	0.275906i
$534$		0			0
$535$	5.35334	+	3.09075i	0.231445	+	0.133625i
$536$	−6.87891	+	11.9146i	−0.297124	+	0.514633i
$537$		0			0
$538$	−14.1534	+	8.17146i	−0.610196	+	0.352297i
$539$	−20.8731	−	5.63901i	−0.899068	−	0.242889i
$540$		0			0
$541$		−	28.2186i		−	1.21321i	−0.795003	−	0.606606i	$-0.792531\pi$
$541$		−	28.2186i		−	1.21321i	0.795003	−	0.606606i	$-0.207469\pi$
$542$	−0.524126	+	0.302605i	−0.0225132	+	0.0129980i
$543$		0			0
$544$	−0.841796	+	1.45803i	−0.0360917	+	0.0625127i
$545$	3.13250	−	5.42565i	0.134182	−	0.232409i
$546$		0			0
$547$	−8.18909	+	4.72797i	−0.350140	+	0.202154i	−0.664747	−	0.747069i	$-0.731461\pi$
$547$	−8.18909	+	4.72797i	−0.350140	+	0.202154i	0.314607	+	0.949222i	$0.398127\pi$
$548$		−	1.99518i		−	0.0852300i
$549$		0			0
$550$	3.20184	+	0.864999i	0.136527	+	0.0368837i
$551$	−49.7961	+	28.7498i	−2.12138	+	1.22478i
$552$		0			0
$553$	−26.3304	+	45.6057i	−1.11968	+	1.93935i
$554$	−10.2745	−	5.93197i	−0.436521	−	0.252025i
$555$		0			0
$556$	13.3236	−	7.69241i	0.565048	−	0.326231i
$557$	−25.6402			−1.08641			−0.543205	−	0.839600i	$-0.682789\pi$
$557$	−25.6402			−1.08641			−0.543205	+	0.839600i	$0.682789\pi$
$558$		0			0
$559$	−7.28992			−0.308331
$560$	1.83842	+	3.18423i	0.0776873	+	0.134558i
$561$		0			0
$562$	4.36042	−	7.55247i	0.183933	−	0.318582i
$563$	9.85158	−	17.0634i	0.415194	−	0.719138i	−0.580254	−	0.814435i	$-0.697047\pi$
$563$	9.85158	−	17.0634i	0.415194	−	0.719138i	0.995449	+	0.0952975i	$0.0303802\pi$
$564$		0			0
$565$	−1.00065	−	1.73318i	−0.0420978	−	0.0729156i
$566$		−	10.2467i		−	0.430702i
$567$		0			0
$568$			7.93786i			0.333065i
$569$	0.958507	+	1.66018i	0.0401827	+	0.0695985i	0.885417	−	0.464797i	$-0.153873\pi$
$569$	0.958507	+	1.66018i	0.0401827	+	0.0695985i	−0.845235	+	0.534395i	$0.820539\pi$
$570$		0			0
$571$	0.599207	+	0.345953i	0.0250760	+	0.0144777i	0.512486	−	0.858696i	$-0.328725\pi$
$571$	0.599207	+	0.345953i	0.0250760	+	0.0144777i	−0.487410	+	0.873173i	$0.662058\pi$
$572$	5.10632	+	5.12739i	0.213506	+	0.214387i
$573$		0			0
$574$	−18.5924	+	10.7343i	−0.776033	+	0.448043i
$575$			5.01450i			0.209119i
$576$		0			0
$577$	−34.3382			−1.42952			−0.714760	−	0.699370i	$-0.753464\pi$
$577$	−34.3382			−1.42952			−0.714760	+	0.699370i	$0.753464\pi$
$578$	−7.08276	−	12.2677i	−0.294604	−	0.510269i
$579$		0			0
$580$	6.33444	+	3.65719i	0.263023	+	0.151857i
$581$	−17.7771	−	10.2636i	−0.737518	−	0.425806i
$582$		0			0
$583$	14.9654	−	3.97698i	0.619805	−	0.164709i
$584$		−	4.80281i		−	0.198742i
$585$		0			0
$586$	−15.9924			−0.660640
$587$	−21.0084	+	12.1292i	−0.867108	+	0.500625i	−0.866386	−	0.499375i	$-0.833563\pi$
$587$	−21.0084	+	12.1292i	−0.867108	+	0.500625i	−0.000721891		1.00000i	$0.500230\pi$
$588$		0			0
$589$	−37.8949	−	21.8786i	−1.56143	−	0.901492i
$590$	−6.99268	+	12.1117i	−0.287884	+	0.498630i
$591$		0			0
$592$	4.92145	+	8.52419i	0.202270	+	0.350342i
$593$	4.06153			0.166787			0.0833935	−	0.996517i	$-0.473424\pi$
$593$	4.06153			0.166787			0.0833935	+	0.996517i	$0.473424\pi$
$594$		0			0
$595$	6.19029			0.253777
$596$	−10.8574	−	18.8056i	−0.444738	−	0.770309i
$597$		0			0
$598$	−5.47042	+	9.47504i	−0.223702	+	0.387463i
$599$	5.16281	+	2.98075i	0.210947	+	0.121790i	0.601751	−	0.798683i	$-0.294470\pi$
$599$	5.16281	+	2.98075i	0.210947	+	0.121790i	−0.390805	+	0.920474i	$0.627803\pi$
$600$		0			0
$601$	9.95223	−	5.74592i	0.405960	−	0.234381i	−0.283093	−	0.959093i	$-0.591360\pi$
$601$	9.95223	−	5.74592i	0.405960	−	0.234381i	0.689052	+	0.724712i	$0.258027\pi$
$602$	12.2850			0.500698
$603$		0			0
$604$			1.10990i			0.0451612i
$605$	−10.9999	−	0.0452884i	−0.447210	−	0.00184123i
$606$		0			0
$607$	8.52188	+	4.92011i	0.345892	+	0.199701i	0.662875	−	0.748730i	$-0.269336\pi$
$607$	8.52188	+	4.92011i	0.345892	+	0.199701i	−0.316982	+	0.948431i	$0.602670\pi$
$608$	−6.80796	−	3.93058i	−0.276099	−	0.159406i
$609$		0			0
$610$	4.57903	+	7.93110i	0.185399	+	0.321121i
$611$	−11.2485			−0.455064
$612$		0			0
$613$		−	27.7570i		−	1.12109i	−0.828123	−	0.560547i	$-0.810591\pi$
$613$		−	27.7570i		−	1.12109i	0.828123	−	0.560547i	$-0.189409\pi$
$614$	−14.5668	+	8.41015i	−0.587869	+	0.339406i
$615$		0			0
$616$	−8.60517	−	8.64067i	−0.346712	−	0.348142i
$617$	−1.27815	−	0.737939i	−0.0514563	−	0.0297083i	0.474051	−	0.880497i	$-0.342791\pi$
$617$	−1.27815	−	0.737939i	−0.0514563	−	0.0297083i	−0.525507	+	0.850789i	$0.676125\pi$
$618$		0			0
$619$	−7.86282	−	13.6188i	−0.316034	−	0.547386i	0.663623	−	0.748067i	$-0.269018\pi$
$619$	−7.86282	−	13.6188i	−0.316034	−	0.547386i	−0.979657	+	0.200681i	$0.935685\pi$
$620$			5.56625i			0.223546i
$621$		0			0
$622$		−	7.37862i		−	0.295856i
$623$	−23.8701	−	41.3442i	−0.956335	−	1.65642i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	12.2973	−	21.2995i	0.491497	−	0.851298i
$627$		0			0
$628$	11.6455	+	20.1706i	0.464706	+	0.804894i
$629$	16.5714			0.660746
$630$		0			0
$631$	−40.8958			−1.62804			−0.814018	−	0.580840i	$-0.802724\pi$
$631$	−40.8958			−1.62804			−0.814018	+	0.580840i	$0.802724\pi$
$632$	−12.4035	+	7.16118i	−0.493386	+	0.284856i
$633$		0			0
$634$	0.940567	+	0.543036i	0.0373547	+	0.0215667i
$635$	8.24405	−	14.2791i	0.327155	−	0.566650i
$636$		0			0
$637$	12.3180	−	7.11181i	0.488057	−	0.281780i
$638$	−23.4195	−	6.32693i	−0.927186	−	0.250486i
$639$		0			0
$640$			1.00000i			0.0395285i
$641$	−38.6523	+	22.3159i	−1.52667	+	0.881426i	−0.527176	+	0.849756i	$0.676749\pi$
$641$	−38.6523	+	22.3159i	−1.52667	+	0.881426i	−0.999498	+	0.0316702i	$0.989917\pi$
$642$		0			0
$643$	0.176902	−	0.306403i	0.00697633	−	0.0120834i	−0.862516	−	0.506030i	$-0.831113\pi$
$643$	0.176902	−	0.306403i	0.00697633	−	0.0120834i	0.869492	+	0.493946i	$0.164446\pi$
$644$	9.21874	−	15.9673i	0.363269	−	0.629201i
$645$		0			0
$646$	−11.4618	+	6.61749i	−0.450960	+	0.260362i
$647$			9.75059i			0.383335i	0.981460	+	0.191668i	$0.0613896\pi$
$647$			9.75059i			0.383335i	−0.981460	+	0.191668i	$0.938610\pi$
$648$		0			0
$649$	12.0973	−	44.7789i	0.474861	−	1.75773i
$650$	−1.88953	+	1.09092i	−0.0741134	+	0.0427894i
$651$		0			0
$652$	−4.45679	+	7.71938i	−0.174541	+	0.302314i
$653$	13.4942	+	7.79085i	0.528067	+	0.304880i	0.740229	−	0.672355i	$-0.234717\pi$
$653$	13.4942	+	7.79085i	0.528067	+	0.304880i	−0.212162	+	0.977235i	$0.568050\pi$
$654$		0			0
$655$	−4.55620	+	2.63052i	−0.178025	+	0.102783i
$656$	−5.83891			−0.227971
$657$		0			0
$658$	18.9559			0.738977
$659$	20.3980	+	35.3304i	0.794594	+	1.37628i	0.923096	+	0.384569i	$0.125650\pi$
$659$	20.3980	+	35.3304i	0.794594	+	1.37628i	−0.128502	+	0.991709i	$0.541017\pi$
$660$		0			0
$661$	3.63429	−	6.29478i	0.141358	−	0.244839i	−0.786650	−	0.617399i	$-0.788187\pi$
$661$	3.63429	−	6.29478i	0.141358	−	0.244839i	0.928008	+	0.372560i	$0.121520\pi$
$662$	2.48198	−	4.29891i	0.0964648	−	0.167082i
$663$		0			0
$664$	−2.79143	−	4.83489i	−0.108328	−	0.187630i
$665$			28.9042i			1.12086i
$666$		0			0
$667$		−	36.6780i		−	1.42018i
$668$	5.12001	+	8.86811i	0.198099	+	0.343117i
$669$		0			0
$670$	11.9146	+	6.87891i	0.460302	+	0.265755i
$671$	−21.4333	−	21.5217i	−0.827422	−	0.830836i
$672$		0			0
$673$	−4.12089	+	2.37920i	−0.158849	+	0.0917114i	−0.577317	−	0.816520i	$-0.695900\pi$
$673$	−4.12089	+	2.37920i	−0.158849	+	0.0917114i	0.418468	+	0.908231i	$0.362567\pi$
$674$		−	17.3795i		−	0.669434i
$675$		0			0
$676$	8.23958			0.316907
$677$	−22.4648	−	38.9101i	−0.863391	−	1.49544i	−0.868636	−	0.495451i	$-0.835003\pi$
$677$	−22.4648	−	38.9101i	−0.863391	−	1.49544i	0.00524449	−	0.999986i	$-0.498331\pi$
$678$		0			0
$679$	47.0121	+	27.1425i	1.80416	+	1.04163i
$680$	1.45803	+	0.841796i	0.0559130	+	0.0322814i
$681$		0			0
$682$	−4.74139	−	17.8419i	−0.181557	−	0.683203i
$683$		−	5.30492i		−	0.202987i	−0.994836	−	0.101494i	$-0.967638\pi$
$683$		−	5.30492i		−	0.202987i	0.994836	−	0.101494i	$-0.0323621\pi$
$684$		0			0
$685$	−1.99518			−0.0762320
$686$	1.53131	−	0.884103i	0.0584658	−	0.0337552i
$687$		0			0
$688$	2.89355	+	1.67059i	0.110316	+	0.0636907i
$689$	−5.09335	+	8.82194i	−0.194041	+	0.336089i
$690$		0			0
$691$	−11.9138	−	20.6354i	−0.453224	−	0.785007i	0.545360	−	0.838202i	$-0.316393\pi$
$691$	−11.9138	−	20.6354i	−0.453224	−	0.785007i	−0.998584	+	0.0531948i	$0.983060\pi$
$692$	13.3049			0.505775
$693$		0			0
$694$	−11.3709			−0.431634
$695$	−7.69241	−	13.3236i	−0.291790	−	0.505395i
$696$		0			0
$697$	−4.91517	+	8.51332i	−0.186175	+	0.322465i
$698$	5.30746	+	3.06426i	0.200890	+	0.115984i
$699$		0			0
$700$	3.18423	−	1.83842i	0.120353	−	0.0694856i
$701$	33.8438			1.27826			0.639132	−	0.769097i	$-0.279294\pi$
$701$	33.8438			1.27826			0.639132	+	0.769097i	$0.279294\pi$
$702$		0			0
$703$			77.3765i			2.91831i
$704$	−0.851809	−	3.20537i	−0.0321038	−	0.120807i
$705$		0			0
$706$	24.2020	+	13.9730i	0.910853	+	0.525881i
$707$	4.26961	+	2.46506i	0.160575	+	0.0927081i
$708$		0			0
$709$	15.7982	+	27.3632i	0.593313	+	1.02765i	0.993783	+	0.111338i	$0.0355136\pi$
$709$	15.7982	+	27.3632i	0.593313	+	1.02765i	−0.400470	+	0.916310i	$0.631153\pi$
$710$	7.93786			0.297903
$711$		0			0
$712$		−	12.9841i		−	0.486598i
$713$	24.1725	−	13.9560i	0.905267	−	0.522656i
$714$		0			0
$715$	5.12739	−	5.10632i	0.191753	−	0.190966i
$716$	18.8576	+	10.8874i	0.704741	+	0.406882i
$717$		0			0
$718$	16.0637	+	27.8231i	0.599492	+	1.03835i
$719$		−	18.7053i		−	0.697590i	−0.937199	−	0.348795i	$-0.886591\pi$
$719$		−	18.7053i		−	0.697590i	0.937199	−	0.348795i	$-0.113409\pi$
$720$		0			0
$721$		−	1.25311i		−	0.0466682i
$722$	−21.3989	−	37.0640i	−0.796385	−	1.37938i
$723$		0			0
$724$	−8.96893	+	15.5346i	−0.333328	+	0.577340i
$725$	3.65719	−	6.33444i	0.135825	−	0.235255i
$726$		0			0
$727$	−10.6707	−	18.4822i	−0.395755	−	0.685468i	0.597442	−	0.801912i	$-0.296184\pi$
$727$	−10.6707	−	18.4822i	−0.395755	−	0.685468i	−0.993197	+	0.116444i	$0.962850\pi$
$728$	8.02226			0.297325
$729$		0			0
$730$	−4.80281			−0.177760
$731$	4.87156	−	2.81259i	0.180181	−	0.104028i
$732$		0			0
$733$	−16.3704	−	9.45144i	−0.604654	−	0.349097i	0.166216	−	0.986089i	$-0.446845\pi$
$733$	−16.3704	−	9.45144i	−0.604654	−	0.349097i	−0.770870	+	0.636992i	$0.780178\pi$
$734$	−7.97900	+	13.8200i	−0.294510	+	0.510106i
$735$		0			0
$736$	4.34269	−	2.50725i	0.160074	−	0.0924185i
$737$	−44.0503	−	11.9005i	−1.62261	−	0.438360i
$738$		0			0
$739$			24.3579i			0.896019i	0.894029	+	0.448009i	$0.147867\pi$
$739$			24.3579i			0.896019i	−0.894029	+	0.448009i	$0.852133\pi$
$740$	8.52419	−	4.92145i	0.313356	−	0.180916i
$741$		0			0
$742$	8.58330	−	14.8667i	0.315103	−	0.545774i
$743$	−4.94977	+	8.57325i	−0.181589	+	0.314522i	−0.942422	−	0.334426i	$-0.891457\pi$
$743$	−4.94977	+	8.57325i	−0.181589	+	0.314522i	0.760833	+	0.648948i	$0.224791\pi$
$744$		0			0
$745$	−18.8056	+	10.8574i	−0.688985	+	0.397786i
$746$			20.9074i			0.765476i
$747$		0			0
$748$	−5.39059	−	1.45630i	−0.197100	−	0.0532478i
$749$	−19.6833	+	11.3642i	−0.719213	+	0.415238i
$750$		0			0
$751$	4.08010	−	7.06694i	0.148885	−	0.257876i	−0.781931	−	0.623365i	$-0.785765\pi$
$751$	4.08010	−	7.06694i	0.148885	−	0.257876i	0.930816	+	0.365489i	$0.119098\pi$
$752$	4.46479	+	2.57775i	0.162814	+	0.0940007i
$753$		0			0
$754$	13.8207	−	7.97941i	0.503322	−	0.290593i
$755$	1.10990			0.0403934
$756$		0			0
$757$	−22.7954			−0.828515			−0.414257	−	0.910160i	$-0.635959\pi$
$757$	−22.7954			−0.828515			−0.414257	+	0.910160i	$0.635959\pi$
$758$	−7.68756	−	13.3152i	−0.279225	−	0.483632i
$759$		0			0
$760$	−3.93058	+	6.80796i	−0.142577	+	0.246951i
$761$	−25.0265	+	43.3472i	−0.907210	+	1.57133i	−0.0892860	+	0.996006i	$0.528459\pi$
$761$	−25.0265	+	43.3472i	−0.907210	+	1.57133i	−0.817924	+	0.575327i	$0.804875\pi$
$762$		0			0
$763$	11.5177	+	19.9492i	0.416968	+	0.722210i
$764$			5.26374i			0.190436i
$765$		0			0
$766$			2.36790i			0.0855558i
$767$	15.2569	+	26.4257i	0.550895	+	0.954178i
$768$		0			0
$769$	8.34447	+	4.81768i	0.300909	+	0.173730i	0.642851	−	0.765991i	$-0.277751\pi$
$769$	8.34447	+	4.81768i	0.300909	+	0.173730i	−0.341942	+	0.939721i	$0.611085\pi$
$770$	−8.64067	+	8.60517i	−0.311388	+	0.310109i
$771$		0			0
$772$	2.26126	−	1.30554i	0.0813846	−	0.0469874i
$773$			2.06723i			0.0743530i	0.999309	+	0.0371765i	$0.0118364\pi$
$773$			2.06723i			0.0743530i	−0.999309	+	0.0371765i	$0.988164\pi$
$774$		0			0
$775$	5.56625			0.199946
$776$	7.38202	+	12.7860i	0.264999	+	0.458992i
$777$		0			0
$778$	30.7171	+	17.7345i	1.10126	+	0.635814i
$779$	−39.7511	−	22.9503i	−1.42423	−	0.822280i
$780$		0			0
$781$	−25.4438	+	6.76154i	−0.910451	+	0.241947i
$782$		−	8.44238i		−	0.301899i
$783$		0			0
$784$	−6.51910			−0.232825
$785$	20.1706	−	11.6455i	0.719919	−	0.415645i
$786$		0			0
$787$	37.8141	+	21.8320i	1.34793	+	0.778225i	0.987955	−	0.154739i	$-0.0494536\pi$
$787$	37.8141	+	21.8320i	1.34793	+	0.778225i	0.359970	+	0.932964i	$0.382787\pi$
$788$	6.38468	−	11.0586i	0.227445	−	0.393946i
$789$		0			0
$790$	7.16118	+	12.4035i	0.254783	+	0.441298i
$791$	7.35847			0.261637
$792$		0			0
$793$	19.9814			0.709560
$794$	6.97864	+	12.0874i	0.247663	+	0.428964i
$795$		0			0
$796$	1.08022	−	1.87099i	0.0382872	−	0.0663154i
$797$	16.2279	+	9.36918i	0.574822	+	0.331873i	0.759073	−	0.651006i	$-0.225653\pi$
$797$	16.2279	+	9.36918i	0.574822	+	0.331873i	−0.184251	+	0.982879i	$0.558986\pi$
$798$		0			0
$799$	7.51688	−	4.33987i	0.265928	−	0.153534i
$800$	1.00000			0.0353553
$801$		0			0
$802$		−	6.24024i		−	0.220351i
$803$	15.3948	−	4.09108i	0.543271	−	0.144371i
$804$		0			0
$805$	−15.9673	−	9.21874i	−0.562774	−	0.324918i
$806$	10.5176	+	6.07234i	0.370466	+	0.213889i
$807$		0			0
$808$	0.670430	+	1.16122i	0.0235856	+	0.0408515i
$809$	−14.1963			−0.499117			−0.249558	−	0.968360i	$-0.580285\pi$
$809$	−14.1963			−0.499117			−0.249558	+	0.968360i	$0.580285\pi$
$810$		0			0
$811$			19.6216i			0.689008i	0.938785	+	0.344504i	$0.111953\pi$
$811$			19.6216i			0.689008i	−0.938785	+	0.344504i	$0.888047\pi$
$812$	−23.2907	+	13.4469i	−0.817343	+	0.471893i
$813$		0			0
$814$	−23.1311	+	23.0361i	−0.810745	+	0.807413i
$815$	7.71938	+	4.45679i	0.270398	+	0.156114i
$816$		0			0
$817$	13.1328	+	22.7467i	0.459458	+	0.795805i
$818$			14.6671i			0.512824i
$819$		0			0
$820$			5.83891i			0.203904i
$821$	−5.30945	−	9.19623i	−0.185301	−	0.320951i	0.758377	−	0.651816i	$-0.225993\pi$
$821$	−5.30945	−	9.19623i	−0.185301	−	0.320951i	−0.943678	+	0.330866i	$0.892659\pi$
$822$		0			0
$823$	−1.08143	+	1.87309i	−0.0376962	+	0.0652917i	−0.884258	−	0.466999i	$-0.845335\pi$
$823$	−1.08143	+	1.87309i	−0.0376962	+	0.0652917i	0.846562	+	0.532290i	$0.178669\pi$
$824$	0.170406	−	0.295152i	0.00593637	−	0.0102821i
$825$		0			0
$826$	−25.7109	−	44.5326i	−0.894597	−	1.54949i
$827$	14.4361			0.501992			0.250996	−	0.967988i	$-0.419242\pi$
$827$	14.4361			0.501992			0.250996	+	0.967988i	$0.419242\pi$
$828$		0			0
$829$	−26.4349			−0.918124			−0.459062	−	0.888404i	$-0.651814\pi$
$829$	−26.4349			−0.918124			−0.459062	+	0.888404i	$0.651814\pi$
$830$	−4.83489	+	2.79143i	−0.167822	+	0.0968918i
$831$		0			0
$832$	1.88953	+	1.09092i	0.0655076	+	0.0378208i
$833$	−5.48775	+	9.50506i	−0.190139	+	0.329331i
$834$		0			0
$835$	8.86811	−	5.12001i	0.306894	−	0.177185i
$836$	6.79989	−	25.1702i	0.235179	−	0.870529i
$837$		0			0
$838$		−	30.1961i		−	1.04311i
$839$	23.0961	−	13.3345i	0.797365	−	0.460359i	−0.0451843	−	0.998979i	$-0.514387\pi$
$839$	23.0961	−	13.3345i	0.797365	−	0.460359i	0.842549	+	0.538620i	$0.181054\pi$
$840$		0			0
$841$	−12.2501	+	21.2178i	−0.422418	+	0.731649i
$842$	−4.66929	+	8.08745i	−0.160914	+	0.278712i
$843$		0			0
$844$	−2.37810	+	1.37300i	−0.0818575	+	0.0472605i
$845$		−	8.23958i		−	0.283450i
$846$		0			0
$847$	20.3666	−	34.9430i	0.699805	−	1.20065i
$848$	4.04335	−	2.33443i	0.138849	−	0.0801646i
$849$		0			0
$850$	0.841796	−	1.45803i	0.0288734	−	0.0500101i
$851$	−42.7446	−	24.6786i	−1.46527	−	0.845972i
$852$		0			0
$853$	40.4073	−	23.3291i	1.38352	−	0.798775i	0.390944	−	0.920414i	$-0.372149\pi$
$853$	40.4073	−	23.3291i	1.38352	−	0.798775i	0.992574	+	0.121640i	$0.0388153\pi$
$854$	−33.6726			−1.15225
$855$		0			0
$856$	−6.18150			−0.211279
$857$	20.5060	+	35.5175i	0.700473	+	1.21325i	0.968301	+	0.249788i	$0.0803608\pi$
$857$	20.5060	+	35.5175i	0.700473	+	1.21325i	−0.267828	+	0.963467i	$0.586306\pi$
$858$		0			0
$859$	25.7734	−	44.6409i	0.879379	−	1.52313i	0.0273545	−	0.999626i	$-0.491292\pi$
$859$	25.7734	−	44.6409i	0.879379	−	1.52313i	0.852024	−	0.523503i	$-0.175375\pi$
$860$	1.67059	−	2.89355i	0.0569667	−	0.0986692i
$861$		0			0
$862$	12.2205	+	21.1665i	0.416232	+	0.720935i
$863$		−	52.0631i		−	1.77225i	−0.463446	−	0.886125i	$-0.653387\pi$
$863$		−	52.0631i		−	1.77225i	0.463446	−	0.886125i	$-0.346613\pi$
$864$		0			0
$865$		−	13.3049i		−	0.452379i
$866$	12.6866	+	21.9739i	0.431109	+	0.746703i
$867$		0			0
$868$	−17.7242	−	10.2331i	−0.601600	−	0.347334i
$869$	−33.5197	−	33.6580i	−1.13708	−	1.14177i
$870$		0			0
$871$	25.9958	−	15.0087i	0.880834	−	0.508550i
$872$			6.26500i			0.212160i
$873$		0			0
$874$	39.4198			1.33339
$875$	−1.83842	−	3.18423i	−0.0621498	−	0.107647i
$876$		0			0
$877$	25.4764	+	14.7088i	0.860278	+	0.496682i	0.864106	−	0.503311i	$-0.167885\pi$
$877$	25.4764	+	14.7088i	0.860278	+	0.496682i	−0.00382706	+	0.999993i	$0.501218\pi$
$878$	−17.5588	−	10.1376i	−0.592580	−	0.342126i
$879$		0			0
$880$	−3.20537	+	0.851809i	−0.108053	+	0.0287145i
$881$		−	10.8313i		−	0.364917i	−0.983214	−	0.182459i	$-0.941594\pi$
$881$		−	10.8313i		−	0.364917i	0.983214	−	0.182459i	$-0.0584056\pi$
$882$		0			0
$883$	−37.0003			−1.24516			−0.622580	−	0.782556i	$-0.713915\pi$
$883$	−37.0003			−1.24516			−0.622580	+	0.782556i	$0.713915\pi$
$884$	3.18119	−	1.83666i	0.106995	−	0.0617737i
$885$		0			0
$886$	−17.8653	−	10.3145i	−0.600195	−	0.346523i
$887$	19.9221	−	34.5061i	0.668918	−	1.15860i	−0.309289	−	0.950968i	$-0.600091\pi$
$887$	19.9221	−	34.5061i	0.668918	−	1.15860i	0.978207	−	0.207632i	$-0.0665757\pi$
$888$		0			0
$889$	30.3120	+	52.5019i	1.01663	+	1.76086i
$890$	−12.9841			−0.435226
$891$		0			0
$892$	−16.2414			−0.543802
$893$	20.2641	+	35.0984i	0.678111	+	1.17452i
$894$		0			0
$895$	10.8874	−	18.8576i	0.363927	−	0.630339i
$896$	−3.18423	−	1.83842i	−0.106378	−	0.0614172i
$897$		0			0
$898$	−25.3234	+	14.6205i	−0.845052	+	0.487891i
$899$	−40.7137			−1.35788
$900$		0			0
$901$		−	7.86045i		−	0.261870i
$902$	−4.97363	−	18.7159i	−0.165604	−	0.623171i
$903$		0			0
$904$	1.73318	+	1.00065i	0.0576448	+	0.0332812i
$905$	15.5346	+	8.96893i	0.516389	+	0.298137i
$906$		0			0
$907$	2.96024	+	5.12728i	0.0982931	+	0.170249i	0.910978	−	0.412454i	$-0.135328\pi$
$907$	2.96024	+	5.12728i	0.0982931	+	0.170249i	−0.812685	+	0.582703i	$0.801995\pi$
$908$	−0.114685			−0.00380597
$909$		0			0
$910$		−	8.02226i		−	0.265935i
$911$	−4.43890	+	2.56280i	−0.147067	+	0.0849093i	−0.571728	−	0.820443i	$-0.693727\pi$
$911$	−4.43890	+	2.56280i	−0.147067	+	0.0849093i	0.424661	+	0.905353i	$0.360393\pi$
$912$		0			0
$913$	13.1199	−	13.0660i	0.434204	−	0.432420i
$914$	−26.9068	−	15.5347i	−0.889999	−	0.513841i
$915$		0			0
$916$	6.68658	+	11.5815i	0.220931	+	0.382664i
$917$		−	19.3440i		−	0.638794i
$918$		0			0
$919$		−	44.4077i		−	1.46488i	−0.680834	−	0.732438i	$-0.738383\pi$
$919$		−	44.4077i		−	1.46488i	0.680834	−	0.732438i	$-0.261617\pi$
$920$	−2.50725	−	4.34269i	−0.0826616	−	0.143174i
$921$		0			0
$922$	−14.4654	+	25.0548i	−0.476393	+	0.825137i
$923$	8.65957	−	14.9988i	0.285033	−	0.493692i
$924$		0			0
$925$	−4.92145	−	8.52419i	−0.161816	−	0.280274i
$926$	2.51415			0.0826200
$927$		0			0
$928$	−7.31439			−0.240106
$929$	38.1637	−	22.0338i	1.25211	−	0.722906i	0.280581	−	0.959830i	$-0.409473\pi$
$929$	38.1637	−	22.0338i	1.25211	−	0.722906i	0.971528	+	0.236925i	$0.0761395\pi$
$930$		0			0
$931$	−44.3818	−	25.6238i	−1.45455	−	0.839787i
$932$	−2.71440	+	4.70148i	−0.0889131	+	0.154002i
$933$		0			0
$934$	1.74507	−	1.00752i	0.0571005	−	0.0329670i
$935$	−1.45630	+	5.39059i	−0.0476263	+	0.176291i
$936$		0			0
$937$			43.9178i			1.43473i	0.696697	+	0.717366i	$0.254652\pi$
$937$			43.9178i			1.43473i	−0.696697	+	0.717366i	$0.745348\pi$
$938$	−43.8081	+	25.2926i	−1.43038	+	0.825833i
$939$		0			0
$940$	2.57775	−	4.46479i	0.0840768	−	0.145625i
$941$	15.7681	−	27.3111i	0.514024	−	0.890316i	−0.485843	−	0.874046i	$-0.661487\pi$
$941$	15.7681	−	27.3111i	0.514024	−	0.890316i	0.999868	−	0.0162702i	$-0.00517921\pi$
$942$		0			0
$943$	25.3565	−	14.6396i	0.825723	−	0.476731i
$944$		−	13.9854i		−	0.455185i
$945$		0			0
$946$	−2.89012	+	10.6979i	−0.0939659	+	0.347820i
$947$	−14.2410	+	8.22205i	−0.462770	+	0.267181i	−0.713208	−	0.700952i	$-0.752759\pi$
$947$	−14.2410	+	8.22205i	−0.462770	+	0.267181i	0.250438	+	0.968133i	$0.419425\pi$
$948$		0			0
$949$	−5.23948	+	9.07505i	−0.170081	+	0.294589i
$950$	6.80796	+	3.93058i	0.220880	+	0.127525i
$951$		0			0
$952$	−5.36094	+	3.09514i	−0.173749	+	0.100314i
$953$	−15.2230			−0.493121			−0.246561	−	0.969127i	$-0.579300\pi$
$953$	−15.2230			−0.493121			−0.246561	+	0.969127i	$0.579300\pi$
$954$		0			0
$955$	5.26374			0.170331
$956$	−2.95156	−	5.11225i	−0.0954603	−	0.165342i
$957$		0			0
$958$	3.15987	−	5.47305i	0.102091	−	0.176826i
$959$	3.66797	−	6.35312i	0.118445	−	0.205153i
$960$		0			0
$961$	0.00840758	+	0.0145623i	0.000271212	+	0.000469753i
$962$		−	21.4756i		−	0.692401i
$963$		0			0
$964$		−	29.7555i		−	0.958361i
$965$	−1.30554	−	2.26126i	−0.0420268	−	0.0727926i
$966$		0			0
$967$	32.1737	+	18.5755i	1.03464	+	0.597347i	0.918309	−	0.395864i	$-0.129555\pi$
$967$	32.1737	+	18.5755i	1.03464	+	0.597347i	0.116326	+	0.993211i	$0.462888\pi$
$968$	9.54884	−	5.46073i	0.306911	−	0.175515i
$969$		0			0
$970$	12.7860	−	7.38202i	0.410535	−	0.237022i
$971$			41.9406i			1.34594i	0.739671	+	0.672969i	$0.234981\pi$
$971$			41.9406i			1.34594i	−0.739671	+	0.672969i	$0.765019\pi$
$972$		0			0
$973$	56.5674			1.81347
$974$	−6.57216	−	11.3833i	−0.210586	−	0.364745i
$975$		0			0
$976$	−7.93110	−	4.57903i	−0.253868	−	0.146571i
$977$	−16.4634	−	9.50512i	−0.526709	−	0.304096i	0.212966	−	0.977060i	$-0.431688\pi$
$977$	−16.4634	−	9.50512i	−0.526709	−	0.304096i	−0.739675	+	0.672964i	$0.765021\pi$
$978$		0			0
$979$	41.6187	−	11.0599i	1.33014	−	0.353477i
$980$			6.51910i			0.208245i
$981$		0			0
$982$	15.9147			0.507860
$983$	3.18190	−	1.83707i	0.101487	−	0.0585935i	−0.448397	−	0.893834i	$-0.648005\pi$
$983$	3.18190	−	1.83707i	0.101487	−	0.0585935i	0.549884	+	0.835241i	$0.314672\pi$
$984$		0			0
$985$	−11.0586	−	6.38468i	−0.352356	−	0.203433i
$986$	−6.15722	+	10.6646i	−0.196086	+	0.339631i
$987$		0			0
$988$	8.57589	+	14.8539i	0.272836	+	0.472565i
$989$	−16.7544			−0.532758
$990$		0			0
$991$	28.6189			0.909109			0.454555	−	0.890719i	$-0.349798\pi$
$991$	28.6189			0.909109			0.454555	+	0.890719i	$0.349798\pi$
$992$	−2.78313	−	4.82052i	−0.0883644	−	0.153052i
$993$		0			0
$994$	−14.5931	+	25.2760i	−0.462865	+	0.801705i
$995$	−1.87099	−	1.08022i	−0.0593143	−	0.0342451i
$996$		0			0
$997$	−6.92740	+	3.99954i	−0.219393	+	0.126667i	−0.605669	−	0.795717i	$-0.707095\pi$
$997$	−6.92740	+	3.99954i	−0.219393	+	0.126667i	0.386276	+	0.922383i	$0.373761\pi$
$998$	35.7146			1.13053
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2970.2.t.b.2771.24		48
3.2	odd	2		990.2.t.a.131.4	✓	48
9.2	odd	6		2970.2.t.a.791.24		48
9.7	even	3		990.2.t.b.461.4	yes	48
11.10	odd	2		2970.2.t.a.2771.24		48
33.32	even	2		990.2.t.b.131.4	yes	48
99.43	odd	6		990.2.t.a.461.4	yes	48
99.65	even	6	inner	2970.2.t.b.791.24		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
990.2.t.a.131.4	✓	48	3.2	odd	2
990.2.t.a.461.4	yes	48	99.43	odd	6
990.2.t.b.131.4	yes	48	33.32	even	2
990.2.t.b.461.4	yes	48	9.7	even	3
2970.2.t.a.791.24		48	9.2	odd	6
2970.2.t.a.2771.24		48	11.10	odd	2
2970.2.t.b.791.24		48	99.65	even	6	inner
2970.2.t.b.2771.24		48	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 2970 = 2 \cdot 3^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2970.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(0.866025 + 0.500000i) q^{5} +(-3.18423 + 1.83842i) q^{7} -1.00000 q^{8} +1.00000i q^{10} +(-0.851809 - 3.20537i) q^{11} +(1.88953 + 1.09092i) q^{13} +(-3.18423 - 1.83842i) q^{14} +(-0.500000 - 0.866025i) q^{16} -1.68359 q^{17} -7.86116i q^{19} +(-0.866025 + 0.500000i) q^{20} +(2.35003 - 2.34038i) q^{22} +(4.34269 + 2.50725i) q^{23} +(0.500000 + 0.866025i) q^{25} +2.18184i q^{26} -3.67683i q^{28} +(-3.65719 - 6.33444i) q^{29} +(2.78313 - 4.82052i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-0.841796 - 1.45803i) q^{34} -3.67683 q^{35} -9.84289 q^{37} +(6.80796 - 3.93058i) q^{38} +(-0.866025 - 0.500000i) q^{40} +(2.91945 - 5.05664i) q^{41} +(-2.89355 + 1.67059i) q^{43} +(3.20184 + 0.864999i) q^{44} +5.01450i q^{46} +(-4.46479 + 2.57775i) q^{47} +(3.25955 - 5.64570i) q^{49} +(-0.500000 + 0.866025i) q^{50} +(-1.88953 + 1.09092i) q^{52} +4.66886i q^{53} +(0.864999 - 3.20184i) q^{55} +(3.18423 - 1.83842i) q^{56} +(3.65719 - 6.33444i) q^{58} +(12.1117 + 6.99268i) q^{59} +(7.93110 - 4.57903i) q^{61} +5.56625 q^{62} +1.00000 q^{64} +(1.09092 + 1.88953i) q^{65} +(6.87891 - 11.9146i) q^{67} +(0.841796 - 1.45803i) q^{68} +(-1.83842 - 3.18423i) q^{70} -7.93786i q^{71} +4.80281i q^{73} +(-4.92145 - 8.52419i) q^{74} +(6.80796 + 3.93058i) q^{76} +(8.60517 + 8.64067i) q^{77} +(12.4035 - 7.16118i) q^{79} -1.00000i q^{80} +5.83891 q^{82} +(2.79143 + 4.83489i) q^{83} +(-1.45803 - 0.841796i) q^{85} +(-2.89355 - 1.67059i) q^{86} +(0.851809 + 3.20537i) q^{88} +12.9841i q^{89} -8.02226 q^{91} +(-4.34269 + 2.50725i) q^{92} +(-4.46479 - 2.57775i) q^{94} +(3.93058 - 6.80796i) q^{95} +(-7.38202 - 12.7860i) q^{97} +6.51910 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 24 q^{2} - 24 q^{4} - 48 q^{8} + 6 q^{11} + 24 q^{13} - 24 q^{16} + 12 q^{17} + 12 q^{22} - 36 q^{23} + 24 q^{25} + 24 q^{32} + 6 q^{34} + 6 q^{38} + 6 q^{41} + 30 q^{43} + 6 q^{44} + 24 q^{49} - 24 q^{50}+ \cdots + 48 q^{98}+O(q^{100}) \) 48 * q + 24 * q^2 - 24 * q^4 - 48 * q^8 + 6 * q^11 + 24 * q^13 - 24 * q^16 + 12 * q^17 + 12 * q^22 - 36 * q^23 + 24 * q^25 + 24 * q^32 + 6 * q^34 + 6 * q^38 + 6 * q^41 + 30 * q^43 + 6 * q^44 + 24 * q^49 - 24 * q^50 - 24 * q^52 + 54 * q^59 + 48 * q^64 - 6 * q^67 - 6 * q^68 + 6 * q^76 - 6 * q^77 + 12 * q^82 - 36 * q^83 + 30 * q^86 - 6 * q^88 + 24 * q^91 + 36 * q^92 + 6 * q^97 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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