LMFDB - Embedded newform 1638.2.x.d.307.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1638,2,Mod(307,1638)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1638, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("1638.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1638.x (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$13.0794958511$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(i)$
Coefficient field:	8.0.7442857984.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 26x^{6} + 205x^{4} + 540x^{2} + 324 $ x^8 + 26x^6 + 205x^4 + 540*x^2 + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 546)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.3
Root			$2.73923i$ of defining polynomial
Character	$\chi$	$=$	1638.307
Dual form			1638.2.x.d.811.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.0951965 + 0.0951965i) q^{5} +(-2.64404 + 0.0951965i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.0951965 + 0.0951965i) q^{5} +(-2.64404 + 0.0951965i) q^{7} +(-0.707107 + 0.707107i) q^{8} -0.134628 q^{10} +(3.64404 - 3.64404i) q^{11} +(2.00000 + 3.00000i) q^{13} +(-1.93693 - 1.80230i) q^{14} -1.00000 q^{16} -5.98188 q^{17} +(-4.19288 + 4.19288i) q^{19} +(-0.0951965 - 0.0951965i) q^{20} +5.15345 q^{22} +4.69380i q^{23} +4.98188i q^{25} +(-0.707107 + 3.53553i) q^{26} +(-0.0951965 - 2.64404i) q^{28} +4.59428 q^{29} +(-0.739235 + 0.739235i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.22982 - 4.22982i) q^{34} +(0.242641 - 0.260765i) q^{35} +(-4.83443 + 4.83443i) q^{37} -5.92963 q^{38} -0.134628i q^{40} +(-3.04544 + 3.04544i) q^{41} +8.78467i q^{43} +(3.64404 + 3.64404i) q^{44} +(-3.31902 + 3.31902i) q^{46} +(-3.28808 - 3.28808i) q^{47} +(6.98188 - 0.503406i) q^{49} +(-3.52272 + 3.52272i) q^{50} +(-3.00000 + 2.00000i) q^{52} -1.09768 q^{53} +0.693799i q^{55} +(1.80230 - 1.93693i) q^{56} +(3.24864 + 3.24864i) q^{58} +(-1.30620 - 1.30620i) q^{59} -5.98188i q^{61} -1.04544 q^{62} -1.00000i q^{64} +(-0.475982 - 0.0951965i) q^{65} +(-0.0454356 - 0.0454356i) q^{67} -5.98188i q^{68} +(0.355962 - 0.0128161i) q^{70} +(-8.69380 - 8.69380i) q^{71} +(-4.83443 - 4.83443i) q^{73} -6.83692 q^{74} +(-4.19288 - 4.19288i) q^{76} +(-9.28808 + 9.98188i) q^{77} -11.5780 q^{79} +(0.0951965 - 0.0951965i) q^{80} -4.30690 q^{82} +(1.28808 - 1.28808i) q^{83} +(0.569453 - 0.569453i) q^{85} +(-6.21170 + 6.21170i) q^{86} +5.15345i q^{88} +(9.21770 + 9.21770i) q^{89} +(-5.57367 - 7.74172i) q^{91} -4.69380 q^{92} -4.65004i q^{94} -0.798295i q^{95} +(-9.97506 + 9.97506i) q^{97} +(5.29289 + 4.58097i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{5}+O(q^{10}) $ 8 * q + 4 * q^5	$ 8 q + 4 q^{5} + 4 q^{10} + 8 q^{11} + 16 q^{13} - 8 q^{16} + 12 q^{17} + 4 q^{19} + 4 q^{20} + 4 q^{22} + 4 q^{28} + 12 q^{29} + 20 q^{31} - 24 q^{34} - 32 q^{35} - 8 q^{37} - 12 q^{38} - 16 q^{41} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 4 q^{49} - 24 q^{50} - 24 q^{52} + 24 q^{53} + 4 q^{56} - 16 q^{58} - 28 q^{59} + 20 q^{65} + 8 q^{67} + 24 q^{70} - 52 q^{71} - 8 q^{73} + 4 q^{74} + 4 q^{76} - 32 q^{77} - 48 q^{79} - 4 q^{80} + 40 q^{82} - 32 q^{83} + 20 q^{85} + 20 q^{86} - 4 q^{89} + 12 q^{91} - 20 q^{92} - 36 q^{97} + 48 q^{98}+O(q^{100}) $ 8 * q + 4 * q^5 + 4 * q^10 + 8 * q^11 + 16 * q^13 - 8 * q^16 + 12 * q^17 + 4 * q^19 + 4 * q^20 + 4 * q^22 + 4 * q^28 + 12 * q^29 + 20 * q^31 - 24 * q^34 - 32 * q^35 - 8 * q^37 - 12 * q^38 - 16 * q^41 + 8 * q^44 - 20 * q^46 + 16 * q^47 - 4 * q^49 - 24 * q^50 - 24 * q^52 + 24 * q^53 + 4 * q^56 - 16 * q^58 - 28 * q^59 + 20 * q^65 + 8 * q^67 + 24 * q^70 - 52 * q^71 - 8 * q^73 + 4 * q^74 + 4 * q^76 - 32 * q^77 - 48 * q^79 - 4 * q^80 + 40 * q^82 - 32 * q^83 + 20 * q^85 + 20 * q^86 - 4 * q^89 + 12 * q^91 - 20 * q^92 - 36 * q^97 + 48 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times$.

$n$	$379$	$703$	$911$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0
$3$		0			0
$4$			1.00000i			0.500000i
$5$	−0.0951965	+	0.0951965i	−0.0425731	+	0.0425731i	−0.728073	−	0.685500i	$-0.759584\pi$
$5$	−0.0951965	+	0.0951965i	−0.0425731	+	0.0425731i	0.685500	+	0.728073i	$0.259584\pi$
$6$		0			0
$7$	−2.64404	+	0.0951965i	−0.999352	+	0.0359809i
$7$	−2.64404	+	0.0951965i	−0.999352	+	0.0359809i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$		0			0
$10$	−0.134628			−0.0425731
$11$	3.64404	−	3.64404i	1.09872	−	1.09872i	0.104158	−	0.994561i	$-0.466785\pi$
$11$	3.64404	−	3.64404i	1.09872	−	1.09872i	0.994561	−	0.104158i	$-0.0332148\pi$
$12$		0			0
$13$	2.00000	+	3.00000i	0.554700	+	0.832050i
$13$	2.00000	+	3.00000i	0.554700	+	0.832050i
$14$	−1.93693	−	1.80230i	−0.517667	−	0.481686i
$15$		0			0
$16$	−1.00000			−0.250000
$17$	−5.98188			−1.45082			−0.725409	−	0.688318i	$-0.758349\pi$
$17$	−5.98188			−1.45082			−0.725409	+	0.688318i	$0.758349\pi$
$18$		0			0
$19$	−4.19288	+	4.19288i	−0.961913	+	0.961913i	−0.999301	−	0.0373882i	$-0.988096\pi$
$19$	−4.19288	+	4.19288i	−0.961913	+	0.961913i	0.0373882	+	0.999301i	$0.488096\pi$
$20$	−0.0951965	−	0.0951965i	−0.0212866	−	0.0212866i
$21$		0			0
$22$	5.15345			1.09872
$23$			4.69380i			0.978725i	0.872081	+	0.489362i	$0.162770\pi$
$23$			4.69380i			0.978725i	−0.872081	+	0.489362i	$0.837230\pi$
$24$		0			0
$25$			4.98188i			0.996375i
$26$	−0.707107	+	3.53553i	−0.138675	+	0.693375i
$27$		0			0
$28$	−0.0951965	−	2.64404i	−0.0179904	−	0.499676i
$29$	4.59428			0.853136			0.426568	−	0.904456i	$-0.359723\pi$
$29$	4.59428			0.853136			0.426568	+	0.904456i	$0.359723\pi$
$30$		0			0
$31$	−0.739235	+	0.739235i	−0.132770	+	0.132770i	−0.770369	−	0.637598i	$-0.779928\pi$
$31$	−0.739235	+	0.739235i	−0.132770	+	0.132770i	0.637598	+	0.770369i	$0.279928\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$	−4.22982	−	4.22982i	−0.725409	−	0.725409i
$35$	0.242641	−	0.260765i	0.0410138	−	0.0440774i
$36$		0			0
$37$	−4.83443	+	4.83443i	−0.794776	+	0.794776i	−0.982266	−	0.187491i	$-0.939965\pi$
$37$	−4.83443	+	4.83443i	−0.794776	+	0.794776i	0.187491	+	0.982266i	$0.439965\pi$
$38$	−5.92963			−0.961913
$39$		0			0
$40$		−	0.134628i		−	0.0212866i
$41$	−3.04544	+	3.04544i	−0.475617	+	0.475617i	−0.903727	−	0.428110i	$-0.859180\pi$
$41$	−3.04544	+	3.04544i	−0.475617	+	0.475617i	0.428110	+	0.903727i	$0.359180\pi$
$42$		0			0
$43$			8.78467i			1.33965i	0.742519	+	0.669825i	$0.233631\pi$
$43$			8.78467i			1.33965i	−0.742519	+	0.669825i	$0.766369\pi$
$44$	3.64404	+	3.64404i	0.549359	+	0.549359i
$45$		0			0
$46$	−3.31902	+	3.31902i	−0.489362	+	0.489362i
$47$	−3.28808	−	3.28808i	−0.479615	−	0.479615i	0.425393	−	0.905009i	$-0.360136\pi$
$47$	−3.28808	−	3.28808i	−0.479615	−	0.479615i	−0.905009	+	0.425393i	$0.860136\pi$
$48$		0			0
$49$	6.98188	−	0.503406i	0.997411	−	0.0719152i
$50$	−3.52272	+	3.52272i	−0.498188	+	0.498188i
$51$		0			0
$52$	−3.00000	+	2.00000i	−0.416025	+	0.277350i
$53$	−1.09768			−0.150778			−0.0753892	−	0.997154i	$-0.524020\pi$
$53$	−1.09768			−0.150778			−0.0753892	+	0.997154i	$0.524020\pi$
$54$		0			0
$55$			0.693799i			0.0935518i
$56$	1.80230	−	1.93693i	0.240843	−	0.258833i
$57$		0			0
$58$	3.24864	+	3.24864i	0.426568	+	0.426568i
$59$	−1.30620	−	1.30620i	−0.170053	−	0.170053i	0.616950	−	0.787003i	$-0.288368\pi$
$59$	−1.30620	−	1.30620i	−0.170053	−	0.170053i	−0.787003	+	0.616950i	$0.788368\pi$
$60$		0			0
$61$		−	5.98188i		−	0.765901i	−0.923769	−	0.382950i	$-0.874908\pi$
$61$		−	5.98188i		−	0.765901i	0.923769	−	0.382950i	$-0.125092\pi$
$62$	−1.04544			−0.132770
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−0.475982	−	0.0951965i	−0.0590383	−	0.0118077i
$66$		0			0
$67$	−0.0454356	−	0.0454356i	−0.00555084	−	0.00555084i	0.704326	−	0.709877i	$-0.251249\pi$
$67$	−0.0454356	−	0.0454356i	−0.00555084	−	0.00555084i	−0.709877	+	0.704326i	$0.751249\pi$
$68$		−	5.98188i		−	0.725409i
$69$		0			0
$70$	0.355962	−	0.0128161i	0.0425456	−	0.00153182i
$71$	−8.69380	−	8.69380i	−1.03176	−	1.03176i	−0.999479	−	0.0322854i	$-0.989721\pi$
$71$	−8.69380	−	8.69380i	−1.03176	−	1.03176i	−0.0322854	−	0.999479i	$-0.510279\pi$
$72$		0			0
$73$	−4.83443	−	4.83443i	−0.565827	−	0.565827i	0.365129	−	0.930957i	$-0.381025\pi$
$73$	−4.83443	−	4.83443i	−0.565827	−	0.565827i	−0.930957	+	0.365129i	$0.881025\pi$
$74$	−6.83692			−0.794776
$75$		0			0
$76$	−4.19288	−	4.19288i	−0.480956	−	0.480956i
$77$	−9.28808	+	9.98188i	−1.05847	+	1.13754i
$78$		0			0
$79$	−11.5780			−1.30263			−0.651313	−	0.758809i	$-0.725781\pi$
$79$	−11.5780			−1.30263			−0.651313	+	0.758809i	$0.725781\pi$
$80$	0.0951965	−	0.0951965i	0.0106433	−	0.0106433i
$81$		0			0
$82$	−4.30690			−0.475617
$83$	1.28808	−	1.28808i	0.141385	−	0.141385i	−0.632872	−	0.774257i	$-0.718124\pi$
$83$	1.28808	−	1.28808i	0.141385	−	0.141385i	0.774257	+	0.632872i	$0.218124\pi$
$84$		0			0
$85$	0.569453	−	0.569453i	0.0617659	−	0.0617659i
$86$	−6.21170	+	6.21170i	−0.669825	+	0.669825i
$87$		0			0
$88$			5.15345i			0.549359i
$89$	9.21770	+	9.21770i	0.977075	+	0.977075i	0.999743	−	0.0226684i	$-0.00721619\pi$
$89$	9.21770	+	9.21770i	0.977075	+	0.977075i	−0.0226684	+	0.999743i	$0.507216\pi$
$90$		0			0
$91$	−5.57367	−	7.74172i	−0.584279	−	0.811553i
$92$	−4.69380			−0.489362
$93$		0			0
$94$		−	4.65004i		−	0.479615i
$95$		−	0.798295i		−	0.0819033i
$96$		0			0
$97$	−9.97506	+	9.97506i	−1.01281	+	1.01281i	−0.0128974	+	0.999917i	$0.504105\pi$
$97$	−9.97506	+	9.97506i	−1.01281	+	1.01281i	−0.999917	+	0.0128974i	$0.995895\pi$
$98$	5.29289	+	4.58097i	0.534663	+	0.462748i
$99$		0			0
$100$	−4.98188			−0.498188
$101$	3.09271			0.307736			0.153868	−	0.988091i	$-0.450827\pi$
$101$	3.09271			0.307736			0.153868	+	0.988091i	$0.450827\pi$
$102$		0			0
$103$	−8.31301			−0.819106			−0.409553	−	0.912286i	$-0.634315\pi$
$103$	−8.31301			−0.819106			−0.409553	+	0.912286i	$0.634315\pi$
$104$	−3.53553	−	0.707107i	−0.346688	−	0.0693375i
$105$		0			0
$106$	−0.776179	−	0.776179i	−0.0753892	−	0.0753892i
$107$	18.9569			1.83264			0.916318	−	0.400451i	$-0.131147\pi$
$107$	18.9569			1.83264			0.916318	+	0.400451i	$0.131147\pi$
$108$		0			0
$109$	11.3197	+	11.3197i	1.08423	+	1.08423i	0.996110	+	0.0881221i	$0.0280866\pi$
$109$	11.3197	+	11.3197i	1.08423	+	1.08423i	0.0881221	+	0.996110i	$0.471913\pi$
$110$	−0.490590	+	0.490590i	−0.0467759	+	0.0467759i
$111$		0			0
$112$	2.64404	−	0.0951965i	0.249838	−	0.00899522i
$113$	0.716898			0.0674400			0.0337200	−	0.999431i	$-0.489265\pi$
$113$	0.716898			0.0674400			0.0337200	+	0.999431i	$0.489265\pi$
$114$		0			0
$115$	−0.446833	−	0.446833i	−0.0416674	−	0.0416674i
$116$			4.59428i			0.426568i
$117$		0			0
$118$		−	1.84725i		−	0.170053i
$119$	15.8163	−	0.569453i	1.44988	−	0.0522017i
$120$		0			0
$121$		−	15.5580i		−	1.41437i
$122$	4.22982	−	4.22982i	0.382950	−	0.382950i
$123$		0			0
$124$	−0.739235	−	0.739235i	−0.0663852	−	0.0663852i
$125$	−0.950239	−	0.950239i	−0.0849920	−	0.0849920i
$126$		0			0
$127$		−	2.28126i		−	0.202429i	−0.994865	−	0.101215i	$-0.967727\pi$
$127$		−	2.28126i		−	0.202429i	0.994865	−	0.101215i	$-0.0322729\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	−0.269256	−	0.403884i	−0.0236153	−	0.0354230i
$131$			7.79148i			0.680745i	0.940291	+	0.340372i	$0.110553\pi$
$131$			7.79148i			0.680745i	−0.940291	+	0.340372i	$0.889447\pi$
$132$		0			0
$133$	10.6870	−	11.4853i	0.926679	−	0.995900i
$134$		−	0.0642556i		−	0.00555084i
$135$		0			0
$136$	4.22982	−	4.22982i	0.362704	−	0.362704i
$137$	−1.90480	+	1.90480i	−0.162738	+	0.162738i	−0.783779	−	0.621040i	$-0.786710\pi$
$137$	−1.90480	+	1.90480i	−0.162738	+	0.162738i	0.621040	+	0.783779i	$0.286710\pi$
$138$		0			0
$139$			0.716898i			0.0608065i	0.999538	+	0.0304032i	$0.00967914\pi$
$139$			0.716898i			0.0608065i	−0.999538	+	0.0304032i	$0.990321\pi$
$140$	0.260765	+	0.242641i	0.0220387	+	0.0205069i
$141$		0			0
$142$		−	12.2949i		−	1.03176i
$143$	18.2202	+	3.64404i	1.52365	+	0.304730i
$144$		0			0
$145$	−0.437359	+	0.437359i	−0.0363207	+	0.0363207i
$146$		−	6.83692i		−	0.565827i
$147$		0			0
$148$	−4.83443	−	4.83443i	−0.397388	−	0.397388i
$149$	8.22452	+	8.22452i	0.673779	+	0.673779i	0.958585	−	0.284806i	$-0.0919293\pi$
$149$	8.22452	+	8.22452i	0.673779	+	0.673779i	−0.284806	+	0.958585i	$0.591929\pi$
$150$		0			0
$151$	13.6713	−	13.6713i	1.11256	−	1.11256i	0.119755	−	0.992803i	$-0.461789\pi$
$151$	13.6713	−	13.6713i	1.11256	−	1.11256i	0.992803	−	0.119755i	$-0.0382110\pi$
$152$		−	5.92963i		−	0.480956i
$153$		0			0
$154$	−13.6259	+	0.490590i	−1.09801	+	0.0395329i
$155$		−	0.140745i		−	0.0113049i
$156$		0			0
$157$			12.3627i			0.986648i	0.869846	+	0.493324i	$0.164218\pi$
$157$			12.3627i			0.986648i	−0.869846	+	0.493324i	$0.835782\pi$
$158$	−8.18688	−	8.18688i	−0.651313	−	0.651313i
$159$		0			0
$160$	0.134628			0.0106433
$161$	−0.446833	−	12.4106i	−0.0352154	−	0.978091i
$162$		0			0
$163$	8.72111	−	8.72111i	0.683090	−	0.683090i	−0.277605	−	0.960695i	$-0.589541\pi$
$163$	8.72111	−	8.72111i	0.683090	−	0.683090i	0.960695	+	0.277605i	$0.0895407\pi$
$164$	−3.04544	−	3.04544i	−0.237809	−	0.237809i
$165$		0			0
$166$	1.82161			0.141385
$167$	13.3129	+	13.3129i	1.03018	+	1.03018i	0.999530	+	0.0306531i	$0.00975870\pi$
$167$	13.3129	+	13.3129i	1.03018	+	1.03018i	0.0306531	+	0.999530i	$0.490241\pi$
$168$		0			0
$169$	−5.00000	+	12.0000i	−0.384615	+	0.923077i
$170$	0.805329			0.0617659
$171$		0			0
$172$	−8.78467			−0.669825
$173$	−9.58296			−0.728579			−0.364290	−	0.931286i	$-0.618688\pi$
$173$	−9.58296			−0.728579			−0.364290	+	0.931286i	$0.618688\pi$
$174$		0			0
$175$	−0.474257	−	13.1723i	−0.0358504	−	0.995730i
$176$	−3.64404	+	3.64404i	−0.274680	+	0.274680i
$177$		0			0
$178$			13.0358i			0.977075i
$179$		−	6.90729i		−	0.516275i	−0.966108	−	0.258138i	$-0.916891\pi$
$179$		−	6.90729i		−	0.516275i	0.966108	−	0.258138i	$-0.0831088\pi$
$180$		0			0
$181$	22.3445			1.66086			0.830428	−	0.557126i	$-0.188096\pi$
$181$	22.3445			1.66086			0.830428	+	0.557126i	$0.188096\pi$
$182$	1.53305	−	9.41540i	0.113637	−	0.697916i
$183$		0			0
$184$	−3.31902	−	3.31902i	−0.244681	−	0.244681i
$185$		−	0.920441i		−	0.0676722i
$186$		0			0
$187$	−21.7982	+	21.7982i	−1.59404	+	1.59404i
$188$	3.28808	−	3.28808i	0.239808	−	0.239808i
$189$		0			0
$190$	0.564480	−	0.564480i	0.0409516	−	0.0409516i
$191$	−12.0315			−0.870570			−0.435285	−	0.900293i	$-0.643352\pi$
$191$	−12.0315			−0.870570			−0.435285	+	0.900293i	$0.643352\pi$
$192$		0			0
$193$	−14.2700	+	14.2700i	−1.02717	+	1.02717i	−0.0275533	+	0.999620i	$0.508772\pi$
$193$	−14.2700	+	14.2700i	−1.02717	+	1.02717i	−0.999620	+	0.0275533i	$0.991228\pi$
$194$	−14.1069			−1.01281
$195$		0			0
$196$	0.503406	+	6.98188i	0.0359576	+	0.498705i
$197$	5.54884	+	5.54884i	0.395339	+	0.395339i	0.876585	−	0.481247i	$-0.159816\pi$
$197$	5.54884	+	5.54884i	0.395339	+	0.395339i	−0.481247	+	0.876585i	$0.659816\pi$
$198$		0			0
$199$	9.16546			0.649722			0.324861	−	0.945762i	$-0.394682\pi$
$199$	9.16546			0.649722			0.324861	+	0.945762i	$0.394682\pi$
$200$	−3.52272	−	3.52272i	−0.249094	−	0.249094i
$201$		0			0
$202$	2.18688	+	2.18688i	0.153868	+	0.153868i
$203$	−12.1474	+	0.437359i	−0.852583	+	0.0306966i
$204$		0			0
$205$		−	0.579829i		−	0.0404970i
$206$	−5.87819	−	5.87819i	−0.409553	−	0.409553i
$207$		0			0
$208$	−2.00000	−	3.00000i	−0.138675	−	0.208013i
$209$			30.5580i			2.11374i
$210$		0			0
$211$	0.784670			0.0540189			0.0270095	−	0.999635i	$-0.491402\pi$
$211$	0.784670			0.0540189			0.0270095	+	0.999635i	$0.491402\pi$
$212$		−	1.09768i		−	0.0753892i
$213$		0			0
$214$	13.4046	+	13.4046i	0.916318	+	0.916318i
$215$	−0.836269	−	0.836269i	−0.0570331	−	0.0570331i
$216$		0			0
$217$	1.88419	−	2.02494i	0.127907	−	0.137462i
$218$			16.0085i			1.08423i
$219$		0			0
$220$	−0.693799			−0.0467759
$221$	−11.9638	−	17.9456i	−0.804769	−	1.20715i
$222$		0			0
$223$	19.2064	−	19.2064i	1.28616	−	1.28616i	0.349052	−	0.937104i	$-0.386504\pi$
$223$	19.2064	−	19.2064i	1.28616	−	1.28616i	0.937104	−	0.349052i	$-0.113496\pi$
$224$	1.93693	+	1.80230i	0.129417	+	0.120421i
$225$		0			0
$226$	0.506923	+	0.506923i	0.0337200	+	0.0337200i
$227$	11.9819	−	11.9819i	0.795265	−	0.795265i	−0.187080	−	0.982345i	$-0.559902\pi$
$227$	11.9819	−	11.9819i	0.795265	−	0.795265i	0.982345	+	0.187080i	$0.0599023\pi$
$228$		0			0
$229$	−8.98188	−	8.98188i	−0.593539	−	0.593539i	0.345047	−	0.938586i	$-0.387863\pi$
$229$	−8.98188	−	8.98188i	−0.593539	−	0.593539i	−0.938586	+	0.345047i	$0.887863\pi$
$230$		−	0.631917i		−	0.0416674i
$231$		0			0
$232$	−3.24864	+	3.24864i	−0.213284	+	0.213284i
$233$		−	13.1473i		−	0.861310i	−0.902517	−	0.430655i	$-0.858283\pi$
$233$		−	13.1473i		−	0.861310i	0.902517	−	0.430655i	$-0.141717\pi$
$234$		0			0
$235$	0.626026			0.0408375
$236$	1.30620	−	1.30620i	0.0850264	−	0.0850264i
$237$		0			0
$238$	11.5865	+	10.7812i	0.751040	+	0.698838i
$239$	−17.4834	−	17.4834i	−1.13091	−	1.13091i	−0.990026	−	0.140884i	$-0.955006\pi$
$239$	−17.4834	−	17.4834i	−1.13091	−	1.13091i	−0.140884	−	0.990026i	$-0.544994\pi$
$240$		0			0
$241$	−5.69380	−	5.69380i	−0.366770	−	0.366770i	0.499528	−	0.866298i	$-0.333507\pi$
$241$	−5.69380	−	5.69380i	−0.366770	−	0.366770i	−0.866298	+	0.499528i	$0.833507\pi$
$242$	11.0012	−	11.0012i	0.707183	−	0.707183i
$243$		0			0
$244$	5.98188			0.382950
$245$	−0.616727	+	0.712572i	−0.0394013	+	0.0455246i
$246$		0			0
$247$	−20.9644	−	4.19288i	−1.33393	−	0.266787i
$248$		−	1.04544i		−	0.0663852i
$249$		0			0
$250$		−	1.34384i		−	0.0849920i
$251$	12.4585			0.786374			0.393187	−	0.919459i	$-0.371373\pi$
$251$	12.4585			0.786374			0.393187	+	0.919459i	$0.371373\pi$
$252$		0			0
$253$	17.1044	+	17.1044i	1.07534	+	1.07534i
$254$	1.61310	−	1.61310i	0.101215	−	0.101215i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−31.6738			−1.97576			−0.987880	−	0.155221i	$-0.950391\pi$
$257$	−31.6738			−1.97576			−0.987880	+	0.155221i	$0.950391\pi$
$258$		0			0
$259$	12.3222	−	13.2426i	0.765664	−	0.822858i
$260$	0.0951965	−	0.475982i	0.00590383	−	0.0295192i
$261$		0			0
$262$	−5.50941	+	5.50941i	−0.340372	+	0.340372i
$263$	−23.4422			−1.44551			−0.722755	−	0.691105i	$-0.757124\pi$
$263$	−23.4422			−1.44551			−0.722755	+	0.691105i	$0.757124\pi$
$264$		0			0
$265$	0.104496	−	0.104496i	0.00641911	−	0.00641911i
$266$	15.6782	−	0.564480i	0.961290	−	0.0346105i
$267$		0			0
$268$	0.0454356	−	0.0454356i	0.00277542	−	0.00277542i
$269$			16.2813i			0.992686i	0.868126	+	0.496343i	$0.165324\pi$
$269$			16.2813i			0.992686i	−0.868126	+	0.496343i	$0.834676\pi$
$270$		0			0
$271$	−10.1499	−	10.1499i	−0.616564	−	0.616564i	0.328084	−	0.944649i	$-0.393597\pi$
$271$	−10.1499	−	10.1499i	−0.616564	−	0.616564i	−0.944649	+	0.328084i	$0.893597\pi$
$272$	5.98188			0.362704
$273$		0			0
$274$	−2.69380			−0.162738
$275$	18.1541	+	18.1541i	1.09474	+	1.09474i
$276$		0			0
$277$		−	1.09271i		−	0.0656546i	−0.999461	−	0.0328273i	$-0.989549\pi$
$277$		−	1.09271i		−	0.0656546i	0.999461	−	0.0328273i	$-0.0104511\pi$
$278$	−0.506923	+	0.506923i	−0.0304032	+	0.0304032i
$279$		0			0
$280$	0.0128161	+	0.355962i	0.000765910	+	0.0212728i
$281$	22.6284	−	22.6284i	1.34990	−	1.34990i	0.464130	−	0.885767i	$-0.346367\pi$
$281$	22.6284	−	22.6284i	1.34990	−	1.34990i	0.885767	−	0.464130i	$-0.153633\pi$
$282$		0			0
$283$	30.7167			1.82592			0.912958	−	0.408053i	$-0.133792\pi$
$283$	30.7167			1.82592			0.912958	+	0.408053i	$0.133792\pi$
$284$	8.69380	−	8.69380i	0.515882	−	0.515882i
$285$		0			0
$286$	10.3069	+	15.4603i	0.609460	+	0.914189i
$287$	7.76233	−	8.34216i	0.458196	−	0.492422i
$288$		0			0
$289$	18.7828			1.10487
$290$	−0.618519			−0.0363207
$291$		0			0
$292$	4.83443	−	4.83443i	0.282914	−	0.282914i
$293$	−15.5804	−	15.5804i	−0.910215	−	0.910215i	0.0860741	−	0.996289i	$-0.472568\pi$
$293$	−15.5804	−	15.5804i	−0.910215	−	0.910215i	−0.996289	+	0.0860741i	$0.972568\pi$
$294$		0			0
$295$	0.248691			0.0144794
$296$		−	6.83692i		−	0.397388i
$297$		0			0
$298$			11.6312i			0.673779i
$299$	−14.0814	+	9.38760i	−0.814348	+	0.542899i
$300$		0			0
$301$	−0.836269	−	23.2270i	−0.0482018	−	1.33878i
$302$	19.3342			1.11256
$303$		0			0
$304$	4.19288	−	4.19288i	0.240478	−	0.240478i
$305$	0.569453	+	0.569453i	0.0326068	+	0.0326068i
$306$		0			0
$307$	23.5058	+	23.5058i	1.34155	+	1.34155i	0.894522	+	0.447024i	$0.147516\pi$
$307$	23.5058	+	23.5058i	1.34155	+	1.34155i	0.447024	+	0.894522i	$0.352484\pi$
$308$	−9.98188	−	9.28808i	−0.568770	−	0.529237i
$309$		0			0
$310$	0.0995218	−	0.0995218i	0.00565246	−	0.00565246i
$311$	33.9687			1.92619			0.963095	−	0.269162i	$-0.0867468\pi$
$311$	33.9687			1.92619			0.963095	+	0.269162i	$0.0867468\pi$
$312$		0			0
$313$			29.8779i			1.68880i	0.535716	+	0.844398i	$0.320042\pi$
$313$			29.8779i			1.68880i	−0.535716	+	0.844398i	$0.679958\pi$
$314$	−8.74172	+	8.74172i	−0.493324	+	0.493324i
$315$		0			0
$316$		−	11.5780i		−	0.651313i
$317$	−15.1450	−	15.1450i	−0.850626	−	0.850626i	0.139585	−	0.990210i	$-0.455423\pi$
$317$	−15.1450	−	15.1450i	−0.850626	−	0.850626i	−0.990210	+	0.139585i	$0.955423\pi$
$318$		0			0
$319$	16.7417	−	16.7417i	0.937356	−	0.937356i
$320$	0.0951965	+	0.0951965i	0.00532164	+	0.00532164i
$321$		0			0
$322$	8.45965	−	9.09157i	0.471438	−	0.506653i
$323$	25.0813	−	25.0813i	1.39556	−	1.39556i
$324$		0			0
$325$	−14.9456	+	9.96375i	−0.829034	+	0.552689i
$326$	12.3335			0.683090
$327$		0			0
$328$		−	4.30690i		−	0.237809i
$329$	9.00681	+	8.38079i	0.496562	+	0.462048i
$330$		0			0
$331$	10.2408	+	10.2408i	0.562885	+	0.562885i	0.930126	−	0.367241i	$-0.119697\pi$
$331$	10.2408	+	10.2408i	0.562885	+	0.562885i	−0.367241	+	0.930126i	$0.619697\pi$
$332$	1.28808	+	1.28808i	0.0706924	+	0.0706924i
$333$		0			0
$334$			18.8273i			1.03018i
$335$	0.00865061			0.000472633
$336$		0			0
$337$			4.59428i			0.250266i	0.992140	+	0.125133i	$0.0399358\pi$
$337$			4.59428i			0.250266i	−0.992140	+	0.125133i	$0.960064\pi$
$338$	−12.0208	+	4.94975i	−0.653846	+	0.269231i
$339$		0			0
$340$	0.569453	+	0.569453i	0.0308829	+	0.0308829i
$341$			5.38760i			0.291755i
$342$		0			0
$343$	−18.4124	+	1.99567i	−0.994177	+	0.107756i
$344$	−6.21170	−	6.21170i	−0.334912	−	0.334912i
$345$		0			0
$346$	−6.77618	−	6.77618i	−0.364290	−	0.364290i
$347$	12.2500			0.657614			0.328807	−	0.944397i	$-0.393353\pi$
$347$	12.2500			0.657614			0.328807	+	0.944397i	$0.393353\pi$
$348$		0			0
$349$	−1.38576	−	1.38576i	−0.0741780	−	0.0741780i	0.669044	−	0.743222i	$-0.266704\pi$
$349$	−1.38576	−	1.38576i	−0.0741780	−	0.0741780i	−0.743222	+	0.669044i	$0.766704\pi$
$350$	8.97885	−	9.64955i	0.479940	−	0.515790i
$351$		0			0
$352$	−5.15345			−0.274680
$353$	−4.31041	+	4.31041i	−0.229420	+	0.229420i	−0.812450	−	0.583030i	$-0.801867\pi$
$353$	−4.31041	+	4.31041i	−0.229420	+	0.229420i	0.583030	+	0.812450i	$0.301867\pi$
$354$		0			0
$355$	1.65524			0.0878509
$356$	−9.21770	+	9.21770i	−0.488537	+	0.488537i
$357$		0			0
$358$	4.88419	−	4.88419i	0.258138	−	0.258138i
$359$	−0.213491	+	0.213491i	−0.0112676	+	0.0112676i	−0.712718	−	0.701451i	$-0.752536\pi$
$359$	−0.213491	+	0.213491i	−0.0112676	+	0.0112676i	0.701451	+	0.712718i	$0.252536\pi$
$360$		0			0
$361$		−	16.1605i		−	0.850552i
$362$	15.8000	+	15.8000i	0.830428	+	0.830428i
$363$		0			0
$364$	7.74172	−	5.57367i	0.405776	−	0.292139i
$365$	0.920441			0.0481781
$366$		0			0
$367$			1.09768i			0.0572986i	0.999590	+	0.0286493i	$0.00912060\pi$
$367$			1.09768i			0.0572986i	−0.999590	+	0.0286493i	$0.990879\pi$
$368$		−	4.69380i		−	0.244681i
$369$		0			0
$370$	0.650850	−	0.650850i	0.0338361	−	0.0338361i
$371$	2.90232	−	0.104496i	0.150681	−	0.00542514i
$372$		0			0
$373$	21.0565			1.09026			0.545131	−	0.838351i	$-0.316480\pi$
$373$	21.0565			1.09026			0.545131	+	0.838351i	$0.316480\pi$
$374$	−30.8273			−1.59404
$375$		0			0
$376$	4.65004			0.239808
$377$	9.18855	+	13.7828i	0.473235	+	0.709852i
$378$		0			0
$379$	−7.22452	−	7.22452i	−0.371098	−	0.371098i	0.496779	−	0.867877i	$-0.334516\pi$
$379$	−7.22452	−	7.22452i	−0.371098	−	0.371098i	−0.867877	+	0.496779i	$0.834516\pi$
$380$	0.798295			0.0409516
$381$		0			0
$382$	−8.50757	−	8.50757i	−0.435285	−	0.435285i
$383$	−5.97518	+	5.97518i	−0.305317	+	0.305317i	−0.843090	−	0.537773i	$-0.819266\pi$
$383$	−5.97518	+	5.97518i	−0.305317	+	0.305317i	0.537773	+	0.843090i	$0.319266\pi$
$384$		0			0
$385$	−0.0660472	−	1.83443i	−0.00336608	−	0.0934913i
$386$	−20.1808			−1.02717
$387$		0			0
$388$	−9.97506	−	9.97506i	−0.506407	−	0.506407i
$389$			25.0614i			1.27067i	0.772239	+	0.635333i	$0.219137\pi$
$389$			25.0614i			1.27067i	−0.772239	+	0.635333i	$0.780863\pi$
$390$		0			0
$391$		−	28.0777i		−	1.41995i
$392$	−4.58097	+	5.29289i	−0.231374	+	0.267331i
$393$		0			0
$394$			7.84725i			0.395339i
$395$	1.10218	−	1.10218i	0.0554569	−	0.0554569i
$396$		0			0
$397$	7.28624	+	7.28624i	0.365686	+	0.365686i	0.865901	−	0.500215i	$-0.166746\pi$
$397$	7.28624	+	7.28624i	0.365686	+	0.365686i	−0.500215	+	0.865901i	$0.666746\pi$
$398$	6.48096	+	6.48096i	0.324861	+	0.324861i
$399$		0			0
$400$		−	4.98188i		−	0.249094i
$401$	−11.1450	+	11.1450i	−0.556553	+	0.556553i	−0.928324	−	0.371772i	$-0.878750\pi$
$401$	−11.1450	+	11.1450i	−0.556553	+	0.556553i	0.371772	+	0.928324i	$0.378750\pi$
$402$		0			0
$403$	−3.69617	−	0.739235i	−0.184119	−	0.0368239i
$404$			3.09271i			0.153868i
$405$		0			0
$406$	−8.89880	−	8.28028i	−0.441640	−	0.410943i
$407$			35.2337i			1.74647i
$408$		0			0
$409$	14.6028	−	14.6028i	0.722063	−	0.722063i	−0.246962	−	0.969025i	$-0.579432\pi$
$409$	14.6028	−	14.6028i	0.722063	−	0.722063i	0.969025	+	0.246962i	$0.0794324\pi$
$410$	0.410001	−	0.410001i	0.0202485	−	0.0202485i
$411$		0			0
$412$		−	8.31301i		−	0.409553i
$413$	3.57799	+	3.32930i	0.176061	+	0.163824i
$414$		0			0
$415$			0.245241i			0.0120384i
$416$	0.707107	−	3.53553i	0.0346688	−	0.173344i
$417$		0			0
$418$	−21.6078	+	21.6078i	−1.05687	+	1.05687i
$419$		−	16.5630i		−	0.809156i	−0.914504	−	0.404578i	$-0.867418\pi$
$419$		−	16.5630i		−	0.809156i	0.914504	−	0.404578i	$-0.132582\pi$
$420$		0			0
$421$	−12.1655	−	12.1655i	−0.592908	−	0.592908i	0.345508	−	0.938416i	$-0.387707\pi$
$421$	−12.1655	−	12.1655i	−0.592908	−	0.592908i	−0.938416	+	0.345508i	$0.887707\pi$
$422$	0.554846	+	0.554846i	0.0270095	+	0.0270095i
$423$		0			0
$424$	0.776179	−	0.776179i	0.0376946	−	0.0376946i
$425$		−	29.8010i		−	1.44556i
$426$		0			0
$427$	0.569453	+	15.8163i	0.0275578	+	0.765405i
$428$			18.9569i			0.916318i
$429$		0			0
$430$		−	1.18266i		−	0.0570331i
$431$	−5.80961	−	5.80961i	−0.279839	−	0.279839i	0.553206	−	0.833045i	$-0.313404\pi$
$431$	−5.80961	−	5.80961i	−0.279839	−	0.279839i	−0.833045	+	0.553206i	$0.813404\pi$
$432$		0			0
$433$	30.1229			1.44761			0.723806	−	0.690003i	$-0.242391\pi$
$433$	30.1229			1.44761			0.723806	+	0.690003i	$0.242391\pi$
$434$	2.76417	−	0.0995218i	0.132684	−	0.00477720i
$435$		0			0
$436$	−11.3197	+	11.3197i	−0.542116	+	0.542116i
$437$	−19.6805	−	19.6805i	−0.941448	−	0.941448i
$438$		0			0
$439$	−8.65755			−0.413202			−0.206601	−	0.978425i	$-0.566240\pi$
$439$	−8.65755			−0.413202			−0.206601	+	0.978425i	$0.566240\pi$
$440$	−0.490590	−	0.490590i	−0.0233880	−	0.0233880i
$441$		0			0
$442$	4.22982	−	21.1491i	0.201192	−	1.00596i
$443$	−15.3839			−0.730912			−0.365456	−	0.930829i	$-0.619087\pi$
$443$	−15.3839			−0.730912			−0.365456	+	0.930829i	$0.619087\pi$
$444$		0			0
$445$	−1.75499			−0.0831943
$446$	27.1619			1.28616
$447$		0			0
$448$	0.0951965	+	2.64404i	0.00449761	+	0.124919i
$449$	−2.29056	+	2.29056i	−0.108098	+	0.108098i	−0.759087	−	0.650989i	$-0.774354\pi$
$449$	−2.29056	+	2.29056i	−0.108098	+	0.108098i	0.650989	+	0.759087i	$0.274354\pi$
$450$		0			0
$451$			22.1954i			1.04514i
$452$			0.716898i			0.0337200i
$453$		0			0
$454$	16.9449			0.795265
$455$	1.26758	+	0.206391i	0.0594250	+	0.00967577i
$456$		0			0
$457$	9.79829	+	9.79829i	0.458345	+	0.458345i	0.898112	−	0.439767i	$-0.144939\pi$
$457$	9.79829	+	9.79829i	0.458345	+	0.458345i	−0.439767	+	0.898112i	$0.644939\pi$
$458$		−	12.7023i		−	0.593539i
$459$		0			0
$460$	0.446833	−	0.446833i	0.0208337	−	0.0208337i
$461$	7.71441	−	7.71441i	0.359296	−	0.359296i	−0.504257	−	0.863553i	$-0.668234\pi$
$461$	7.71441	−	7.71441i	0.359296	−	0.359296i	0.863553	+	0.504257i	$0.168234\pi$
$462$		0			0
$463$	10.0521	−	10.0521i	0.467162	−	0.467162i	−0.433832	−	0.900994i	$-0.642839\pi$
$463$	10.0521	−	10.0521i	0.467162	−	0.467162i	0.900994	+	0.433832i	$0.142839\pi$
$464$	−4.59428			−0.213284
$465$		0			0
$466$	9.29657	−	9.29657i	0.430655	−	0.430655i
$467$	9.63711			0.445952			0.222976	−	0.974824i	$-0.428423\pi$
$467$	9.63711			0.445952			0.222976	+	0.974824i	$0.428423\pi$
$468$		0			0
$469$	0.124459	+	0.115808i	0.00574697	+	0.00534752i
$470$	0.442668	+	0.442668i	0.0204187	+	0.0204187i
$471$		0			0
$472$	1.84725			0.0850264
$473$	32.0117	+	32.0117i	1.47190	+	1.47190i
$474$		0			0
$475$	−20.8884	−	20.8884i	−0.958426	−	0.958426i
$476$	0.569453	+	15.8163i	0.0261008	+	0.724939i
$477$		0			0
$478$		−	24.7253i		−	1.13091i
$479$	−10.2288	−	10.2288i	−0.467368	−	0.467368i	0.433693	−	0.901061i	$-0.357210\pi$
$479$	−10.2288	−	10.2288i	−0.467368	−	0.467368i	−0.901061	+	0.433693i	$0.857210\pi$
$480$		0			0
$481$	−24.1722	−	4.83443i	−1.10216	−	0.220431i
$482$		−	8.05225i		−	0.366770i
$483$		0			0
$484$	15.5580			0.707183
$485$		−	1.89918i		−	0.0862374i
$486$		0			0
$487$	1.05675	+	1.05675i	0.0478858	+	0.0478858i	0.730644	−	0.682758i	$-0.239220\pi$
$487$	1.05675	+	1.05675i	0.0478858	+	0.0478858i	−0.682758	+	0.730644i	$0.739220\pi$
$488$	4.22982	+	4.22982i	0.191475	+	0.191475i
$489$		0			0
$490$	−0.939957	+	0.0677726i	−0.0424629	+	0.00306165i
$491$			1.19721i			0.0540291i	0.999635	+	0.0270146i	$0.00860005\pi$
$491$			1.19721i			0.0540291i	−0.999635	+	0.0270146i	$0.991400\pi$
$492$		0			0
$493$	−27.4824			−1.23774
$494$	−11.8593	−	17.7889i	−0.533573	−	0.800360i
$495$		0			0
$496$	0.739235	−	0.739235i	0.0331926	−	0.0331926i
$497$	23.8144	+	22.1591i	1.06822	+	0.993972i
$498$		0			0
$499$	−4.14128	−	4.14128i	−0.185389	−	0.185389i	0.608310	−	0.793699i	$-0.291848\pi$
$499$	−4.14128	−	4.14128i	−0.185389	−	0.185389i	−0.793699	+	0.608310i	$0.791848\pi$
$500$	0.950239	−	0.950239i	0.0424960	−	0.0424960i
$501$		0			0
$502$	8.80949	+	8.80949i	0.393187	+	0.393187i
$503$			12.0000i			0.535054i	0.963550	+	0.267527i	$0.0862064\pi$
$503$			12.0000i			0.535054i	−0.963550	+	0.267527i	$0.913794\pi$
$504$		0			0
$505$	−0.294415	+	0.294415i	−0.0131013	+	0.0131013i
$506$			24.1892i			1.07534i
$507$		0			0
$508$	2.28126			0.101215
$509$	−7.43292	+	7.43292i	−0.329458	+	0.329458i	−0.852380	−	0.522922i	$-0.824842\pi$
$509$	−7.43292	+	7.43292i	−0.329458	+	0.329458i	0.522922	+	0.852380i	$0.324842\pi$
$510$		0			0
$511$	13.2426	+	12.3222i	0.585820	+	0.545102i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$	−22.3968	−	22.3968i	−0.987880	−	0.987880i
$515$	0.791369	−	0.791369i	0.0348719	−	0.0348719i
$516$		0			0
$517$	−23.9638			−1.05392
$518$	18.0771	−	0.650850i	0.794261	−	0.0285967i
$519$		0			0
$520$	0.403884	−	0.269256i	0.0177115	−	0.0118077i
$521$			32.0002i			1.40196i	0.713183	+	0.700978i	$0.247253\pi$
$521$			32.0002i			1.40196i	−0.713183	+	0.700978i	$0.752747\pi$
$522$		0			0
$523$		−	1.89550i		−	0.0828846i	−0.999141	−	0.0414423i	$-0.986805\pi$
$523$		−	1.89550i		−	0.0828846i	0.999141	−	0.0414423i	$-0.0131953\pi$
$524$	−7.79148			−0.340372
$525$		0			0
$526$	−16.5762	−	16.5762i	−0.722755	−	0.722755i
$527$	4.42201	−	4.42201i	0.192626	−	0.192626i
$528$		0			0
$529$	0.968251			0.0420979
$530$	0.147779			0.00641911
$531$		0			0
$532$	11.4853	+	10.6870i	0.497950	+	0.463340i
$533$	−15.2272	−	3.04544i	−0.659562	−	0.131912i
$534$		0			0
$535$	−1.80463	+	1.80463i	−0.0780211	+	0.0780211i
$536$	0.0642556			0.00277542
$537$		0			0
$538$	−11.5126	+	11.5126i	−0.496343	+	0.496343i
$539$	23.6078	−	27.2767i	1.01686	−	1.17489i
$540$		0			0
$541$	−4.11753	+	4.11753i	−0.177027	+	0.177027i	−0.790058	−	0.613032i	$-0.789950\pi$
$541$	−4.11753	+	4.11753i	−0.177027	+	0.177027i	0.613032	+	0.790058i	$0.289950\pi$
$542$		−	14.3542i		−	0.616564i
$543$		0			0
$544$	4.22982	+	4.22982i	0.181352	+	0.181352i
$545$	−2.15519			−0.0923183
$546$		0			0
$547$	−44.5000			−1.90268			−0.951341	−	0.308141i	$-0.900293\pi$
$547$	−44.5000			−1.90268			−0.951341	+	0.308141i	$0.900293\pi$
$548$	−1.90480	−	1.90480i	−0.0813692	−	0.0813692i
$549$		0			0
$550$			25.6738i			1.09474i
$551$	−19.2633	+	19.2633i	−0.820642	+	0.820642i
$552$		0			0
$553$	30.6126	−	1.10218i	1.30178	−	0.0468696i
$554$	0.772662	−	0.772662i	0.0328273	−	0.0328273i
$555$		0			0
$556$	−0.716898			−0.0304032
$557$	9.50762	−	9.50762i	0.402851	−	0.402851i	−0.476386	−	0.879236i	$-0.658053\pi$
$557$	9.50762	−	9.50762i	0.402851	−	0.402851i	0.879236	+	0.476386i	$0.158053\pi$
$558$		0			0
$559$	−26.3540	+	17.5693i	−1.11466	+	0.743104i
$560$	−0.242641	+	0.260765i	−0.0102534	+	0.0110194i
$561$		0			0
$562$	32.0014			1.34990
$563$	−16.3640			−0.689659			−0.344829	−	0.938665i	$-0.612063\pi$
$563$	−16.3640			−0.689659			−0.344829	+	0.938665i	$0.612063\pi$
$564$		0			0
$565$	−0.0682461	+	0.0682461i	−0.00287114	+	0.00287114i
$566$	21.7200	+	21.7200i	0.912958	+	0.912958i
$567$		0			0
$568$	12.2949			0.515882
$569$		−	26.8760i		−	1.12670i	−0.826218	−	0.563351i	$-0.809512\pi$
$569$		−	26.8760i		−	1.12670i	0.826218	−	0.563351i	$-0.190488\pi$
$570$		0			0
$571$			26.1591i			1.09472i	0.836896	+	0.547362i	$0.184368\pi$
$571$			26.1591i			1.09472i	−0.836896	+	0.547362i	$0.815632\pi$
$572$	−3.64404	+	18.2202i	−0.152365	+	0.761824i
$573$		0			0
$574$	11.3876	−	0.410001i	0.475309	−	0.0171131i
$575$	−23.3839			−0.975177
$576$		0			0
$577$	3.83454	−	3.83454i	0.159634	−	0.159634i	−0.622770	−	0.782405i	$-0.713993\pi$
$577$	3.83454	−	3.83454i	0.159634	−	0.159634i	0.782405	+	0.622770i	$0.213993\pi$
$578$	13.2815	+	13.2815i	0.552436	+	0.552436i
$579$		0			0
$580$	−0.437359	−	0.437359i	−0.0181603	−	0.0181603i
$581$	−3.28310	+	3.52834i	−0.136206	+	0.146380i
$582$		0			0
$583$	−4.00000	+	4.00000i	−0.165663	+	0.165663i
$584$	6.83692			0.282914
$585$		0			0
$586$		−	22.0340i		−	0.910215i
$587$	15.5599	−	15.5599i	0.642224	−	0.642224i	−0.308877	−	0.951102i	$-0.599953\pi$
$587$	15.5599	−	15.5599i	0.642224	−	0.642224i	0.951102	+	0.308877i	$0.0999533\pi$
$588$		0			0
$589$		−	6.19904i		−	0.255427i
$590$	0.175851	+	0.175851i	0.00723969	+	0.00723969i
$591$		0			0
$592$	4.83443	−	4.83443i	0.198694	−	0.198694i
$593$	0.351637	+	0.351637i	0.0144400	+	0.0144400i	0.714290	−	0.699850i	$-0.246750\pi$
$593$	0.351637	+	0.351637i	0.0144400	+	0.0144400i	−0.699850	+	0.714290i	$0.746750\pi$
$594$		0			0
$595$	−1.45145	+	1.55987i	−0.0595035	+	0.0639483i
$596$	−8.22452	+	8.22452i	−0.336889	+	0.336889i
$597$		0			0
$598$	−16.5951	−	3.31902i	−0.678624	−	0.135725i
$599$	−34.9302			−1.42721			−0.713604	−	0.700549i	$-0.752938\pi$
$599$	−34.9302			−1.42721			−0.713604	+	0.700549i	$0.752938\pi$
$600$		0			0
$601$		−	0.993188i		−	0.0405130i	−0.999795	−	0.0202565i	$-0.993552\pi$
$601$		−	0.993188i		−	0.0405130i	0.999795	−	0.0202565i	$-0.00644828\pi$
$602$	15.8326	−	17.0153i	0.645290	−	0.693492i
$603$		0			0
$604$	13.6713	+	13.6713i	0.556279	+	0.556279i
$605$	1.48107	+	1.48107i	0.0602140	+	0.0602140i
$606$		0			0
$607$			20.6029i			0.836247i	0.908390	+	0.418124i	$0.137312\pi$
$607$			20.6029i			0.836247i	−0.908390	+	0.418124i	$0.862688\pi$
$608$	5.92963			0.240478
$609$		0			0
$610$			0.805329i			0.0326068i
$611$	3.28808	−	16.4404i	0.133021	−	0.665107i
$612$		0			0
$613$	−30.3315	−	30.3315i	−1.22508	−	1.22508i	−0.965804	−	0.259274i	$-0.916517\pi$
$613$	−30.3315	−	30.3315i	−1.22508	−	1.22508i	−0.259274	−	0.965804i	$-0.583483\pi$
$614$			33.2422i			1.34155i
$615$		0			0
$616$	−0.490590	−	13.6259i	−0.0197664	−	0.549004i
$617$	22.7622	+	22.7622i	0.916372	+	0.916372i	0.996763	−	0.0803909i	$-0.0256169\pi$
$617$	22.7622	+	22.7622i	0.916372	+	0.916372i	−0.0803909	+	0.996763i	$0.525617\pi$
$618$		0			0
$619$	−9.96126	−	9.96126i	−0.400377	−	0.400377i	0.477989	−	0.878366i	$-0.341366\pi$
$619$	−9.96126	−	9.96126i	−0.400377	−	0.400377i	−0.878366	+	0.477989i	$0.841366\pi$
$620$	0.140745			0.00565246
$621$		0			0
$622$	24.0195	+	24.0195i	0.963095	+	0.963095i
$623$	−25.2495	−	23.4945i	−1.01160	−	0.941286i
$624$		0			0
$625$	−24.7285			−0.989138
$626$	−21.1268	+	21.1268i	−0.844398	+	0.844398i
$627$		0			0
$628$	−12.3627			−0.493324
$629$	28.9190	−	28.9190i	1.15307	−	1.15307i
$630$		0			0
$631$	8.24750	−	8.24750i	0.328328	−	0.328328i	−0.523623	−	0.851950i	$-0.675420\pi$
$631$	8.24750	−	8.24750i	0.328328	−	0.328328i	0.851950	+	0.523623i	$0.175420\pi$
$632$	8.18688	−	8.18688i	0.325656	−	0.325656i
$633$		0			0
$634$		−	21.4182i		−	0.850626i
$635$	0.217168	+	0.217168i	0.00861806	+	0.00861806i
$636$		0			0
$637$	15.4740	+	19.9388i	0.613101	+	0.790005i
$638$	23.6764			0.937356
$639$		0			0
$640$			0.134628i			0.00532164i
$641$			27.4472i			1.08410i	0.840347	+	0.542049i	$0.182351\pi$
$641$			27.4472i			1.08410i	−0.840347	+	0.542049i	$0.817649\pi$
$642$		0			0
$643$	27.7346	−	27.7346i	1.09375	−	1.09375i	0.0986217	−	0.995125i	$-0.468557\pi$
$643$	27.7346	−	27.7346i	1.09375	−	1.09375i	0.995125	−	0.0986217i	$-0.0314434\pi$
$644$	12.4106	−	0.446833i	0.489046	−	0.0176077i
$645$		0			0
$646$	35.4703			1.39556
$647$	14.6620			0.576425			0.288212	−	0.957567i	$-0.406939\pi$
$647$	14.6620			0.576425			0.288212	+	0.957567i	$0.406939\pi$
$648$		0			0
$649$	−9.51969			−0.373681
$650$	−17.6136	−	3.52272i	−0.690862	−	0.138172i
$651$		0			0
$652$	8.72111	+	8.72111i	0.341545	+	0.341545i
$653$	−15.7965			−0.618163			−0.309082	−	0.951036i	$-0.600022\pi$
$653$	−15.7965			−0.618163			−0.309082	+	0.951036i	$0.600022\pi$
$654$		0			0
$655$	−0.741721	−	0.741721i	−0.0289815	−	0.0289815i
$656$	3.04544	−	3.04544i	0.118904	−	0.118904i
$657$		0			0
$658$	0.442668	+	12.2949i	0.0172570	+	0.479305i
$659$	−8.06825			−0.314294			−0.157147	−	0.987575i	$-0.550230\pi$
$659$	−8.06825			−0.314294			−0.157147	+	0.987575i	$0.550230\pi$
$660$		0			0
$661$	30.7552	+	30.7552i	1.19624	+	1.19624i	0.975284	+	0.220956i	$0.0709178\pi$
$661$	30.7552	+	30.7552i	1.19624	+	1.19624i	0.220956	+	0.975284i	$0.429082\pi$
$662$			14.4827i			0.562885i
$663$		0			0
$664$			1.82161i			0.0706924i
$665$	0.0759948	+	2.11072i	0.00294695	+	0.0818503i
$666$		0			0
$667$			21.5646i			0.834985i
$668$	−13.3129	+	13.3129i	−0.515092	+	0.515092i
$669$		0			0
$670$	0.00611691	+	0.00611691i	0.000236317	+	0.000236317i
$671$	−21.7982	−	21.7982i	−0.841509	−	0.841509i
$672$		0			0
$673$			43.5286i			1.67790i	0.544206	+	0.838952i	$0.316831\pi$
$673$			43.5286i			1.67790i	−0.544206	+	0.838952i	$0.683169\pi$
$674$	−3.24864	+	3.24864i	−0.125133	+	0.125133i
$675$		0			0
$676$	−12.0000	−	5.00000i	−0.461538	−	0.192308i
$677$		−	13.3826i		−	0.514336i	−0.966367	−	0.257168i	$-0.917211\pi$
$677$		−	13.3826i		−	0.514336i	0.966367	−	0.257168i	$-0.0827894\pi$
$678$		0			0
$679$	25.4249	−	27.3240i	0.975716	−	1.04860i
$680$			0.805329i			0.0308829i
$681$		0			0
$682$	−3.80961	+	3.80961i	−0.145877	+	0.145877i
$683$	−11.4536	+	11.4536i	−0.438262	+	0.438262i	−0.891427	−	0.453165i	$-0.850295\pi$
$683$	−11.4536	+	11.4536i	−0.438262	+	0.438262i	0.453165	+	0.891427i	$0.350295\pi$
$684$		0			0
$685$		−	0.362661i		−	0.0138566i
$686$	−14.4307	−	11.6084i	−0.550967	−	0.443211i
$687$		0			0
$688$		−	8.78467i		−	0.334912i
$689$	−2.19537	−	3.29305i	−0.0836368	−	0.125455i
$690$		0			0
$691$	−1.55068	+	1.55068i	−0.0589907	+	0.0589907i	−0.735987	−	0.676996i	$-0.763281\pi$
$691$	−1.55068	+	1.55068i	−0.0589907	+	0.0589907i	0.676996	+	0.735987i	$0.263281\pi$
$692$		−	9.58296i		−	0.364290i
$693$		0			0
$694$	8.66205	+	8.66205i	0.328807	+	0.328807i
$695$	−0.0682461	−	0.0682461i	−0.00258872	−	0.00258872i
$696$		0			0
$697$	18.2174	−	18.2174i	0.690034	−	0.690034i
$698$		−	1.95976i		−	0.0741780i
$699$		0			0
$700$	13.1723	−	0.474257i	0.497865	−	0.0179252i
$701$		−	8.43541i		−	0.318601i	−0.987230	−	0.159300i	$-0.949076\pi$
$701$		−	8.43541i		−	0.318601i	0.987230	−	0.159300i	$-0.0509239\pi$
$702$		0			0
$703$		−	40.5404i		−	1.52901i
$704$	−3.64404	−	3.64404i	−0.137340	−	0.137340i
$705$		0			0
$706$	−6.09584			−0.229420
$707$	−8.17724	+	0.294415i	−0.307537	+	0.0110726i
$708$		0			0
$709$	−19.8616	+	19.8616i	−0.745917	+	0.745917i	−0.973710	−	0.227793i	$-0.926849\pi$
$709$	−19.8616	+	19.8616i	−0.745917	+	0.745917i	0.227793	+	0.973710i	$0.426849\pi$
$710$	1.17043	+	1.17043i	0.0439254	+	0.0439254i
$711$		0			0
$712$	−13.0358			−0.488537
$713$	−3.46982	−	3.46982i	−0.129946	−	0.129946i
$714$		0			0
$715$	−2.08140	+	1.38760i	−0.0778398	+	0.0518932i
$716$	6.90729			0.258138
$717$		0			0
$718$	−0.301922			−0.0112676
$719$	−3.21983			−0.120079			−0.0600397	−	0.998196i	$-0.519123\pi$
$719$	−3.21983			−0.120079			−0.0600397	+	0.998196i	$0.519123\pi$
$720$		0			0
$721$	21.9799	−	0.791369i	0.818575	−	0.0294721i
$722$	11.4272	−	11.4272i	0.425276	−	0.425276i
$723$		0			0
$724$			22.3445i			0.830428i
$725$			22.8881i			0.850043i
$726$		0			0
$727$	13.4007			0.497006			0.248503	−	0.968631i	$-0.420061\pi$
$727$	13.4007			0.497006			0.248503	+	0.968631i	$0.420061\pi$
$728$	9.41540	+	1.53305i	0.348958	+	0.0568185i
$729$		0			0
$730$	0.650850	+	0.650850i	0.0240891	+	0.0240891i
$731$		−	52.5488i		−	1.94359i
$732$		0			0
$733$	−28.6644	+	28.6644i	−1.05874	+	1.05874i	−0.0605789	+	0.998163i	$0.519295\pi$
$733$	−28.6644	+	28.6644i	−1.05874	+	1.05874i	−0.998163	+	0.0605789i	$0.980705\pi$
$734$	−0.776179	+	0.776179i	−0.0286493	+	0.0286493i
$735$		0			0
$736$	3.31902	−	3.31902i	0.122341	−	0.122341i
$737$	−0.331138			−0.0121976
$738$		0			0
$739$	5.76417	−	5.76417i	0.212038	−	0.212038i	−0.593094	−	0.805133i	$-0.702094\pi$
$739$	5.76417	−	5.76417i	0.212038	−	0.212038i	0.805133	+	0.593094i	$0.202094\pi$
$740$	0.920441			0.0338361
$741$		0			0
$742$	2.12614	+	1.97836i	0.0780530	+	0.0726278i
$743$	−15.4107	−	15.4107i	−0.565364	−	0.565364i	0.365462	−	0.930826i	$-0.380911\pi$
$743$	−15.4107	−	15.4107i	−0.565364	−	0.565364i	−0.930826	+	0.365462i	$0.880911\pi$
$744$		0			0
$745$	−1.56589			−0.0573698
$746$	14.8892	+	14.8892i	0.545131	+	0.545131i
$747$		0			0
$748$	−21.7982	−	21.7982i	−0.797020	−	0.797020i
$749$	−50.1229	+	1.80463i	−1.83145	+	0.0659399i
$750$		0			0
$751$		−	4.11812i		−	0.150272i	−0.997173	−	0.0751362i	$-0.976061\pi$
$751$		−	4.11812i		−	0.150272i	0.997173	−	0.0751362i	$-0.0239391\pi$
$752$	3.28808	+	3.28808i	0.119904	+	0.119904i
$753$		0			0
$754$	−3.24864	+	16.2432i	−0.118309	+	0.591543i
$755$			2.60293i			0.0947302i
$756$		0			0
$757$	−18.1229			−0.658687			−0.329343	−	0.944210i	$-0.606827\pi$
$757$	−18.1229			−0.658687			−0.329343	+	0.944210i	$0.606827\pi$
$758$		−	10.2170i		−	0.371098i
$759$		0			0
$760$	0.564480	+	0.564480i	0.0204758	+	0.0204758i
$761$	−21.1268	−	21.1268i	−0.765847	−	0.765847i	0.211525	−	0.977372i	$-0.432157\pi$
$761$	−21.1268	−	21.1268i	−0.765847	−	0.765847i	−0.977372	+	0.211525i	$0.932157\pi$
$762$		0			0
$763$	−31.0073	−	28.8522i	−1.12254	−	1.04452i
$764$		−	12.0315i		−	0.435285i
$765$		0			0
$766$	−8.45018			−0.305317
$767$	1.30620	−	6.53100i	0.0471642	−	0.235821i
$768$		0			0
$769$	−2.12748	+	2.12748i	−0.0767189	+	0.0767189i	−0.744425	−	0.667706i	$-0.767276\pi$
$769$	−2.12748	+	2.12748i	−0.0767189	+	0.0767189i	0.667706	+	0.744425i	$0.267276\pi$
$770$	1.25044	−	1.34384i	0.0450626	−	0.0484287i
$771$		0			0
$772$	−14.2700	−	14.2700i	−0.513587	−	0.513587i
$773$	−3.62354	+	3.62354i	−0.130330	+	0.130330i	−0.769263	−	0.638933i	$-0.779376\pi$
$773$	−3.62354	+	3.62354i	−0.130330	+	0.130330i	0.638933	+	0.769263i	$0.279376\pi$
$774$		0			0
$775$	−3.68277	−	3.68277i	−0.132289	−	0.132289i
$776$		−	14.1069i		−	0.506407i
$777$		0			0
$778$	−17.7211	+	17.7211i	−0.635333	+	0.635333i
$779$		−	25.5383i		−	0.915004i
$780$		0			0
$781$	−63.3611			−2.26724
$782$	19.8539	−	19.8539i	0.709976	−	0.709976i
$783$		0			0
$784$	−6.98188	+	0.503406i	−0.249353	+	0.0179788i
$785$	−1.17688	−	1.17688i	−0.0420047	−	0.0420047i
$786$		0			0
$787$	1.94787	+	1.94787i	0.0694339	+	0.0694339i	0.740971	−	0.671537i	$-0.234366\pi$
$787$	1.94787	+	1.94787i	0.0694339	+	0.0694339i	−0.671537	+	0.740971i	$0.734366\pi$
$788$	−5.54884	+	5.54884i	−0.197669	+	0.197669i
$789$		0			0
$790$	1.55872			0.0554569
$791$	−1.89550	+	0.0682461i	−0.0673964	+	0.00242655i
$792$		0			0
$793$	17.9456	−	11.9638i	0.637268	−	0.424845i
$794$			10.3043i			0.365686i
$795$		0			0
$796$			9.16546i			0.324861i
$797$	−37.8727			−1.34152			−0.670759	−	0.741675i	$-0.734032\pi$
$797$	−37.8727			−1.34152			−0.670759	+	0.741675i	$0.734032\pi$
$798$		0			0
$799$	19.6689	+	19.6689i	0.695834	+	0.695834i
$800$	3.52272	−	3.52272i	0.124547	−	0.124547i
$801$		0			0
$802$	−15.7613			−0.556553
$803$	−35.2337			−1.24337
$804$		0			0
$805$	1.22398	+	1.13891i	0.0431396	+	0.0401412i
$806$	−2.09087	−	3.13631i	−0.0736478	−	0.110472i
$807$		0			0
$808$	−2.18688	+	2.18688i	−0.0769340	+	0.0769340i
$809$	30.9619			1.08856			0.544281	−	0.838903i	$-0.316802\pi$
$809$	30.9619			1.08856			0.544281	+	0.838903i	$0.316802\pi$
$810$		0			0
$811$	10.3882	−	10.3882i	0.364781	−	0.364781i	−0.500789	−	0.865569i	$-0.666957\pi$
$811$	10.3882	−	10.3882i	0.364781	−	0.364781i	0.865569	+	0.500789i	$0.166957\pi$
$812$	−0.437359	−	12.1474i	−0.0153483	−	0.426292i
$813$		0			0
$814$	−24.9140	+	24.9140i	−0.873235	+	0.873235i
$815$			1.66044i			0.0581626i
$816$		0			0
$817$	−36.8331	−	36.8331i	−1.28863	−	1.28863i
$818$	20.6515			0.722063
$819$		0			0
$820$	0.579829			0.0202485
$821$	28.9593	+	28.9593i	1.01069	+	1.01069i	0.999942	+	0.0107447i	$0.00342021\pi$
$821$	28.9593	+	28.9593i	1.01069	+	1.01069i	0.0107447	+	0.999942i	$0.496580\pi$
$822$		0			0
$823$			1.99480i			0.0695344i	0.999395	+	0.0347672i	$0.0110690\pi$
$823$			1.99480i			0.0695344i	−0.999395	+	0.0347672i	$0.988931\pi$
$824$	5.87819	−	5.87819i	0.204776	−	0.204776i
$825$		0			0
$826$	0.175851	+	4.88419i	0.00611865	+	0.169943i
$827$	25.3675	−	25.3675i	0.882115	−	0.882115i	−0.111634	−	0.993749i	$-0.535608\pi$
$827$	25.3675	−	25.3675i	0.882115	−	0.882115i	0.993749	+	0.111634i	$0.0356085\pi$
$828$		0			0
$829$	−25.3522			−0.880517			−0.440259	−	0.897871i	$-0.645113\pi$
$829$	−25.3522			−0.880517			−0.440259	+	0.897871i	$0.645113\pi$
$830$	−0.173411	+	0.173411i	−0.00601919	+	0.00601919i
$831$		0			0
$832$	3.00000	−	2.00000i	0.104006	−	0.0693375i
$833$	−41.7647	+	3.01131i	−1.44706	+	0.104336i
$834$		0			0
$835$	−2.53468			−0.0877163
$836$	−30.5580			−1.05687
$837$		0			0
$838$	11.7118	−	11.7118i	0.404578	−	0.404578i
$839$	34.3545	+	34.3545i	1.18605	+	1.18605i	0.978151	+	0.207898i	$0.0666622\pi$
$839$	34.3545	+	34.3545i	1.18605	+	1.18605i	0.207898	+	0.978151i	$0.433338\pi$
$840$		0			0
$841$	−7.89262			−0.272159
$842$		−	17.2046i		−	0.592908i
$843$		0			0
$844$			0.784670i			0.0270095i
$845$	−0.666375	−	1.61834i	−0.0229240	−	0.0556726i
$846$		0			0
$847$	1.48107	+	41.1360i	0.0508901	+	1.41345i
$848$	1.09768			0.0376946
$849$		0			0
$850$	21.0725	−	21.0725i	0.722779	−	0.722779i
$851$	−22.6918	−	22.6918i	−0.777867	−	0.777867i
$852$		0			0
$853$	−15.6489	−	15.6489i	−0.535808	−	0.535808i	0.386487	−	0.922295i	$-0.373688\pi$
$853$	−15.6489	−	15.6489i	−0.535808	−	0.535808i	−0.922295	+	0.386487i	$0.873688\pi$
$854$	−10.7812	+	11.5865i	−0.368923	+	0.396481i
$855$		0			0
$856$	−13.4046	+	13.4046i	−0.458159	+	0.458159i
$857$	44.8434			1.53182			0.765911	−	0.642946i	$-0.222288\pi$
$857$	44.8434			1.53182			0.765911	+	0.642946i	$0.222288\pi$
$858$		0			0
$859$			55.8416i			1.90529i	0.304083	+	0.952645i	$0.401650\pi$
$859$			55.8416i			1.90529i	−0.304083	+	0.952645i	$0.598350\pi$
$860$	0.836269	−	0.836269i	0.0285166	−	0.0285166i
$861$		0			0
$862$		−	8.21603i		−	0.279839i
$863$	−28.7122	−	28.7122i	−0.977374	−	0.977374i	0.0223760	−	0.999750i	$-0.492877\pi$
$863$	−28.7122	−	28.7122i	−0.977374	−	0.977374i	−0.999750	+	0.0223760i	$0.992877\pi$
$864$		0			0
$865$	0.912264	−	0.912264i	0.0310179	−	0.0310179i
$866$	21.3001	+	21.3001i	0.723806	+	0.723806i
$867$		0			0
$868$	2.02494	+	1.88419i	0.0687308	+	0.0639536i
$869$	−42.1906	+	42.1906i	−1.43122	+	1.43122i
$870$		0			0
$871$	0.0454356	−	0.227178i	0.00153953	−	0.00769763i
$872$	−16.0085			−0.542116
$873$		0			0
$874$		−	27.8325i		−	0.941448i
$875$	2.60293	+	2.42201i	0.0879950	+	0.0818789i
$876$		0			0
$877$	25.4259	+	25.4259i	0.858573	+	0.858573i	0.991170	−	0.132597i	$-0.0423317\pi$
$877$	25.4259	+	25.4259i	0.858573	+	0.858573i	−0.132597	+	0.991170i	$0.542332\pi$
$878$	−6.12181	−	6.12181i	−0.206601	−	0.206601i
$879$		0			0
$880$		−	0.693799i		−	0.0233880i
$881$	32.2182			1.08546			0.542730	−	0.839907i	$-0.317391\pi$
$881$	32.2182			1.08546			0.542730	+	0.839907i	$0.317391\pi$
$882$		0			0
$883$			16.0777i			0.541058i	0.962712	+	0.270529i	$0.0871987\pi$
$883$			16.0777i			0.541058i	−0.962712	+	0.270529i	$0.912801\pi$
$884$	17.9456	−	11.9638i	0.603577	−	0.402384i
$885$		0			0
$886$	−10.8781	−	10.8781i	−0.365456	−	0.365456i
$887$		−	48.6804i		−	1.63453i	−0.576263	−	0.817264i	$-0.695490\pi$
$887$		−	48.6804i		−	1.63453i	0.576263	−	0.817264i	$-0.304510\pi$
$888$		0			0
$889$	0.217168	+	6.03175i	0.00728359	+	0.202298i
$890$	−1.24096	−	1.24096i	−0.0415971	−	0.0415971i
$891$		0			0
$892$	19.2064	+	19.2064i	0.643078	+	0.643078i
$893$	27.5730			0.922696
$894$		0			0
$895$	0.657550	+	0.657550i	0.0219795	+	0.0219795i
$896$	−1.80230	+	1.93693i	−0.0602107	+	0.0647083i
$897$		0			0
$898$	−3.23935			−0.108098
$899$	−3.39625	+	3.39625i	−0.113271	+	0.113271i
$900$		0			0
$901$	6.56620			0.218752
$902$	−15.6945	+	15.6945i	−0.522569	+	0.522569i
$903$		0			0
$904$	−0.506923	+	0.506923i	−0.0168600	+	0.0168600i
$905$	−2.12712	+	2.12712i	−0.0707079	+	0.0707079i
$906$		0			0
$907$			9.60559i			0.318948i	0.987202	+	0.159474i	$0.0509799\pi$
$907$			9.60559i			0.318948i	−0.987202	+	0.159474i	$0.949020\pi$
$908$	11.9819	+	11.9819i	0.397632	+	0.397632i
$909$		0			0
$910$	0.750372	+	1.04225i	0.0248746	+	0.0345504i
$911$	20.1412			0.667308			0.333654	−	0.942696i	$-0.391718\pi$
$911$	20.1412			0.667308			0.333654	+	0.942696i	$0.391718\pi$
$912$		0			0
$913$		−	9.38760i		−	0.310684i
$914$			13.8569i			0.458345i
$915$		0			0
$916$	8.98188	−	8.98188i	0.296770	−	0.296770i
$917$	−0.741721	−	20.6010i	−0.0244938	−	0.680304i
$918$		0			0
$919$	−48.6806			−1.60583			−0.802913	−	0.596096i	$-0.796718\pi$
$919$	−48.6806			−1.60583			−0.802913	+	0.596096i	$0.796718\pi$
$920$	0.631917			0.0208337
$921$		0			0
$922$	10.9098			0.359296
$923$	8.69380	−	43.4690i	0.286160	−	1.43080i
$924$		0			0
$925$	−24.0845	−	24.0845i	−0.791895	−	0.791895i
$926$	14.2159			0.467162
$927$		0			0
$928$	−3.24864	−	3.24864i	−0.106642	−	0.106642i
$929$	−35.6667	+	35.6667i	−1.17019	+	1.17019i	−0.188023	+	0.982165i	$0.560208\pi$
$929$	−35.6667	+	35.6667i	−1.17019	+	1.17019i	−0.982165	+	0.188023i	$0.939792\pi$
$930$		0			0
$931$	−27.1634	+	31.3849i	−0.890246	+	1.02860i
$932$	13.1473			0.430655
$933$		0			0
$934$	6.81447	+	6.81447i	0.222976	+	0.222976i
$935$		−	4.15022i		−	0.135727i
$936$		0			0
$937$			38.9567i			1.27266i	0.771417	+	0.636330i	$0.219548\pi$
$937$			38.9567i			1.27266i	−0.771417	+	0.636330i	$0.780452\pi$
$938$	0.00611691	+	0.169894i	0.000199724	+	0.00554724i
$939$		0			0
$940$			0.626026i			0.0204187i
$941$	−23.3041	+	23.3041i	−0.759691	+	0.759691i	−0.976266	−	0.216575i	$-0.930511\pi$
$941$	−23.3041	+	23.3041i	−0.759691	+	0.759691i	0.216575	+	0.976266i	$0.430511\pi$
$942$		0			0
$943$	−14.2947	−	14.2947i	−0.465498	−	0.465498i
$944$	1.30620	+	1.30620i	0.0425132	+	0.0425132i
$945$		0			0
$946$			45.2713i			1.47190i
$947$	−5.45365	+	5.45365i	−0.177220	+	0.177220i	−0.790143	−	0.612923i	$-0.789994\pi$
$947$	−5.45365	+	5.45365i	−0.177220	+	0.177220i	0.612923	+	0.790143i	$0.289994\pi$
$948$		0			0
$949$	4.83443	−	24.1722i	0.156932	−	0.784661i
$950$		−	29.5407i		−	0.958426i
$951$		0			0
$952$	−10.7812	+	11.5865i	−0.349419	+	0.375520i
$953$			5.73711i			0.185843i	0.995673	+	0.0929216i	$0.0296206\pi$
$953$			5.73711i			0.185843i	−0.995673	+	0.0929216i	$0.970379\pi$
$954$		0			0
$955$	1.14536	−	1.14536i	0.0370629	−	0.0370629i
$956$	17.4834	−	17.4834i	0.565455	−	0.565455i
$957$		0			0
$958$		−	14.4658i		−	0.467368i
$959$	4.85504	−	5.21770i	0.156778	−	0.168488i
$960$		0			0
$961$			29.9071i			0.964744i
$962$	−13.6738	−	20.5108i	−0.440862	−	0.661293i
$963$		0			0
$964$	5.69380	−	5.69380i	0.183385	−	0.183385i
$965$		−	2.71690i		−	0.0874600i
$966$		0			0
$967$	13.7260	+	13.7260i	0.441397	+	0.441397i	0.892481	−	0.451084i	$-0.148963\pi$
$967$	13.7260	+	13.7260i	0.441397	+	0.441397i	−0.451084	+	0.892481i	$0.648963\pi$
$968$	11.0012	+	11.0012i	0.353592	+	0.353592i
$969$		0			0
$970$	1.34292	−	1.34292i	0.0431187	−	0.0431187i
$971$			43.6460i			1.40067i	0.713816	+	0.700334i	$0.246965\pi$
$971$			43.6460i			1.40067i	−0.713816	+	0.700334i	$0.753035\pi$
$972$		0			0
$973$	−0.0682461	−	1.89550i	−0.00218787	−	0.0607671i
$974$			1.49447i			0.0478858i
$975$		0			0
$976$			5.98188i			0.191475i
$977$	34.3951	+	34.3951i	1.10040	+	1.10040i	0.994363	+	0.106033i	$0.0338148\pi$
$977$	34.3951	+	34.3951i	1.10040	+	1.10040i	0.106033	+	0.994363i	$0.466185\pi$
$978$		0			0
$979$	67.1793			2.14706
$980$	−0.712572	−	0.616727i	−0.0227623	−	0.0197006i
$981$		0			0
$982$	−0.846552	+	0.846552i	−0.0270146	+	0.0270146i
$983$	34.2785	+	34.2785i	1.09331	+	1.09331i	0.995172	+	0.0981415i	$0.0312898\pi$
$983$	34.2785	+	34.2785i	1.09331	+	1.09331i	0.0981415	+	0.995172i	$0.468710\pi$
$984$		0			0
$985$	−1.05646			−0.0336616
$986$	−19.4330	−	19.4330i	−0.618872	−	0.618872i
$987$		0			0
$988$	4.19288	−	20.9644i	0.133393	−	0.666966i
$989$	−41.2335			−1.31115
$990$		0			0
$991$	56.0596			1.78079			0.890396	−	0.455187i	$-0.150428\pi$
$991$	56.0596			1.78079			0.890396	+	0.455187i	$0.150428\pi$
$992$	1.04544			0.0331926
$993$		0			0
$994$	1.17043	+	32.5082i	0.0371238	+	1.03110i
$995$	−0.872519	+	0.872519i	−0.0276607	+	0.0276607i
$996$		0			0
$997$		−	12.1817i		−	0.385800i	−0.981218	−	0.192900i	$-0.938211\pi$
$997$		−	12.1817i		−	0.385800i	0.981218	−	0.192900i	$-0.0617892\pi$
$998$		−	5.85666i		−	0.185389i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1638.2.x.d.307.3		8
3.2	odd	2		546.2.o.a.307.2	yes	8
7.6	odd	2		1638.2.x.b.307.4		8
13.5	odd	4		1638.2.x.b.811.4		8
21.20	even	2		546.2.o.d.307.1	yes	8
39.5	even	4		546.2.o.d.265.1	yes	8
91.83	even	4	inner	1638.2.x.d.811.3		8
273.83	odd	4		546.2.o.a.265.2	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.o.a.265.2	✓	8	273.83	odd	4
546.2.o.a.307.2	yes	8	3.2	odd	2
546.2.o.d.265.1	yes	8	39.5	even	4
546.2.o.d.307.1	yes	8	21.20	even	2
1638.2.x.b.307.4		8	7.6	odd	2
1638.2.x.b.811.4		8	13.5	odd	4
1638.2.x.d.307.3		8	1.1	even	1	trivial
1638.2.x.d.811.3		8	91.83	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1638.x (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.0951965 + 0.0951965i) q^{5} +(-2.64404 + 0.0951965i) q^{7} +(-0.707107 + 0.707107i) q^{8} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-0.0951965 + 0.0951965i) q^{5} +(-2.64404 + 0.0951965i) q^{7} +(-0.707107 + 0.707107i) q^{8} -0.134628 q^{10} +(3.64404 - 3.64404i) q^{11} +(2.00000 + 3.00000i) q^{13} +(-1.93693 - 1.80230i) q^{14} -1.00000 q^{16} -5.98188 q^{17} +(-4.19288 + 4.19288i) q^{19} +(-0.0951965 - 0.0951965i) q^{20} +5.15345 q^{22} +4.69380i q^{23} +4.98188i q^{25} +(-0.707107 + 3.53553i) q^{26} +(-0.0951965 - 2.64404i) q^{28} +4.59428 q^{29} +(-0.739235 + 0.739235i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(-4.22982 - 4.22982i) q^{34} +(0.242641 - 0.260765i) q^{35} +(-4.83443 + 4.83443i) q^{37} -5.92963 q^{38} -0.134628i q^{40} +(-3.04544 + 3.04544i) q^{41} +8.78467i q^{43} +(3.64404 + 3.64404i) q^{44} +(-3.31902 + 3.31902i) q^{46} +(-3.28808 - 3.28808i) q^{47} +(6.98188 - 0.503406i) q^{49} +(-3.52272 + 3.52272i) q^{50} +(-3.00000 + 2.00000i) q^{52} -1.09768 q^{53} +0.693799i q^{55} +(1.80230 - 1.93693i) q^{56} +(3.24864 + 3.24864i) q^{58} +(-1.30620 - 1.30620i) q^{59} -5.98188i q^{61} -1.04544 q^{62} -1.00000i q^{64} +(-0.475982 - 0.0951965i) q^{65} +(-0.0454356 - 0.0454356i) q^{67} -5.98188i q^{68} +(0.355962 - 0.0128161i) q^{70} +(-8.69380 - 8.69380i) q^{71} +(-4.83443 - 4.83443i) q^{73} -6.83692 q^{74} +(-4.19288 - 4.19288i) q^{76} +(-9.28808 + 9.98188i) q^{77} -11.5780 q^{79} +(0.0951965 - 0.0951965i) q^{80} -4.30690 q^{82} +(1.28808 - 1.28808i) q^{83} +(0.569453 - 0.569453i) q^{85} +(-6.21170 + 6.21170i) q^{86} +5.15345i q^{88} +(9.21770 + 9.21770i) q^{89} +(-5.57367 - 7.74172i) q^{91} -4.69380 q^{92} -4.65004i q^{94} -0.798295i q^{95} +(-9.97506 + 9.97506i) q^{97} +(5.29289 + 4.58097i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{5}+O(q^{10}) \) 8 * q + 4 * q^5	\( 8 q + 4 q^{5} + 4 q^{10} + 8 q^{11} + 16 q^{13} - 8 q^{16} + 12 q^{17} + 4 q^{19} + 4 q^{20} + 4 q^{22} + 4 q^{28} + 12 q^{29} + 20 q^{31} - 24 q^{34} - 32 q^{35} - 8 q^{37} - 12 q^{38} - 16 q^{41} + 8 q^{44} - 20 q^{46} + 16 q^{47} - 4 q^{49} - 24 q^{50} - 24 q^{52} + 24 q^{53} + 4 q^{56} - 16 q^{58} - 28 q^{59} + 20 q^{65} + 8 q^{67} + 24 q^{70} - 52 q^{71} - 8 q^{73} + 4 q^{74} + 4 q^{76} - 32 q^{77} - 48 q^{79} - 4 q^{80} + 40 q^{82} - 32 q^{83} + 20 q^{85} + 20 q^{86} - 4 q^{89} + 12 q^{91} - 20 q^{92} - 36 q^{97} + 48 q^{98}+O(q^{100}) \) 8 * q + 4 * q^5 + 4 * q^10 + 8 * q^11 + 16 * q^13 - 8 * q^16 + 12 * q^17 + 4 * q^19 + 4 * q^20 + 4 * q^22 + 4 * q^28 + 12 * q^29 + 20 * q^31 - 24 * q^34 - 32 * q^35 - 8 * q^37 - 12 * q^38 - 16 * q^41 + 8 * q^44 - 20 * q^46 + 16 * q^47 - 4 * q^49 - 24 * q^50 - 24 * q^52 + 24 * q^53 + 4 * q^56 - 16 * q^58 - 28 * q^59 + 20 * q^65 + 8 * q^67 + 24 * q^70 - 52 * q^71 - 8 * q^73 + 4 * q^74 + 4 * q^76 - 32 * q^77 - 48 * q^79 - 4 * q^80 + 40 * q^82 - 32 * q^83 + 20 * q^85 + 20 * q^86 - 4 * q^89 + 12 * q^91 - 20 * q^92 - 36 * q^97 + 48 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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