LMFDB - Embedded newform 912.2.bn.l.449.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [912,2,Mod(65,912)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(912, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("912.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 912 = 2^{4} \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	912.bn (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.28235666434$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			449.2
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	912.449
Dual form			912.2.bn.l.65.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 1.65831i) q^{3} +(3.68614 - 2.12819i) q^{5} +2.37228 q^{7} +(-2.50000 + 1.65831i) q^{9} +O(q^{10})$	\(q+(0.500000 + 1.65831i) q^{3} +(3.68614 - 2.12819i) q^{5} +2.37228 q^{7} +(-2.50000 + 1.65831i) q^{9} +1.58457i q^{11} +(1.50000 + 0.866025i) q^{13} +(5.37228 + 5.04868i) q^{15} +(-2.31386 + 1.33591i) q^{17} +(-4.00000 + 1.73205i) q^{19} +(1.18614 + 3.93398i) q^{21} +(3.68614 + 2.12819i) q^{23} +(6.55842 - 11.3595i) q^{25} +(-4.00000 - 3.31662i) q^{27} +(2.31386 - 4.00772i) q^{29} -7.57301i q^{31} +(-2.62772 + 0.792287i) q^{33} +(8.74456 - 5.04868i) q^{35} +4.10891i q^{37} +(-0.686141 + 2.92048i) q^{39} +(5.05842 + 8.76144i) q^{41} +(-4.87228 - 8.43904i) q^{43} +(-5.68614 + 11.4333i) q^{45} +(-2.31386 - 1.33591i) q^{47} -1.37228 q^{49} +(-3.37228 - 3.16915i) q^{51} +(-3.68614 + 6.38458i) q^{53} +(3.37228 + 5.84096i) q^{55} +(-4.87228 - 5.76722i) q^{57} +(3.68614 + 6.38458i) q^{59} +(4.87228 - 8.43904i) q^{61} +(-5.93070 + 3.93398i) q^{63} +7.37228 q^{65} +(1.50000 + 0.866025i) q^{67} +(-1.68614 + 7.17687i) q^{69} +(-5.05842 - 8.76144i) q^{71} +(-1.12772 - 1.95327i) q^{73} +(22.1168 + 5.19615i) q^{75} +3.75906i q^{77} +(-8.61684 + 4.97494i) q^{79} +(3.50000 - 8.29156i) q^{81} +8.51278i q^{83} +(-5.68614 + 9.84868i) q^{85} +(7.80298 + 1.83324i) q^{87} +(-3.68614 + 6.38458i) q^{89} +(3.55842 + 2.05446i) q^{91} +(12.5584 - 3.78651i) q^{93} +(-11.0584 + 14.8974i) q^{95} +(-15.1753 + 8.76144i) q^{97} +(-2.62772 - 3.96143i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{3} + 9 q^{5} - 2 q^{7} - 10 q^{9}+O(q^{10}) $ 4 * q + 2 * q^3 + 9 * q^5 - 2 * q^7 - 10 * q^9	$ 4 q + 2 q^{3} + 9 q^{5} - 2 q^{7} - 10 q^{9} + 6 q^{13} + 10 q^{15} - 15 q^{17} - 16 q^{19} - q^{21} + 9 q^{23} + 9 q^{25} - 16 q^{27} + 15 q^{29} - 22 q^{33} + 12 q^{35} + 3 q^{39} + 3 q^{41} - 8 q^{43} - 17 q^{45} - 15 q^{47} + 6 q^{49} - 2 q^{51} - 9 q^{53} + 2 q^{55} - 8 q^{57} + 9 q^{59} + 8 q^{61} + 5 q^{63} + 18 q^{65} + 6 q^{67} - q^{69} - 3 q^{71} - 16 q^{73} + 54 q^{75} + 14 q^{81} - 17 q^{85} - 9 q^{87} - 9 q^{89} - 3 q^{91} + 33 q^{93} - 27 q^{95} - 9 q^{97} - 22 q^{99}+O(q^{100}) $ 4 * q + 2 * q^3 + 9 * q^5 - 2 * q^7 - 10 * q^9 + 6 * q^13 + 10 * q^15 - 15 * q^17 - 16 * q^19 - q^21 + 9 * q^23 + 9 * q^25 - 16 * q^27 + 15 * q^29 - 22 * q^33 + 12 * q^35 + 3 * q^39 + 3 * q^41 - 8 * q^43 - 17 * q^45 - 15 * q^47 + 6 * q^49 - 2 * q^51 - 9 * q^53 + 2 * q^55 - 8 * q^57 + 9 * q^59 + 8 * q^61 + 5 * q^63 + 18 * q^65 + 6 * q^67 - q^69 - 3 * q^71 - 16 * q^73 + 54 * q^75 + 14 * q^81 - 17 * q^85 - 9 * q^87 - 9 * q^89 - 3 * q^91 + 33 * q^93 - 27 * q^95 - 9 * q^97 - 22 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/912\mathbb{Z}\right)^\times$.

$n$	$97$	$229$	$305$	$799$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.500000	+	1.65831i	0.288675	+	0.957427i
$3$	0.500000	+	1.65831i	0.288675	+	0.957427i
$4$		0			0
$5$	3.68614	−	2.12819i	1.64849	−	0.951757i	0.670820	−	0.741620i	$-0.265942\pi$
$5$	3.68614	−	2.12819i	1.64849	−	0.951757i	0.977672	−	0.210138i	$-0.0673912\pi$
$6$		0			0
$7$	2.37228			0.896638			0.448319	−	0.893874i	$-0.352023\pi$
$7$	2.37228			0.896638			0.448319	+	0.893874i	$0.352023\pi$
$8$		0			0
$9$	−2.50000	+	1.65831i	−0.833333	+	0.552771i
$10$		0			0
$11$			1.58457i			0.477767i	0.971048	+	0.238884i	$0.0767814\pi$
$11$			1.58457i			0.477767i	−0.971048	+	0.238884i	$0.923219\pi$
$12$		0			0
$13$	1.50000	+	0.866025i	0.416025	+	0.240192i	0.693375	−	0.720577i	$-0.256123\pi$
$13$	1.50000	+	0.866025i	0.416025	+	0.240192i	−0.277350	+	0.960769i	$0.589456\pi$
$14$		0			0
$15$	5.37228	+	5.04868i	1.38712	+	1.30356i
$16$		0			0
$17$	−2.31386	+	1.33591i	−0.561193	+	0.324005i	−0.753624	−	0.657305i	$-0.771696\pi$
$17$	−2.31386	+	1.33591i	−0.561193	+	0.324005i	0.192431	+	0.981311i	$0.438363\pi$
$18$		0			0
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$20$		0			0
$21$	1.18614	+	3.93398i	0.258837	+	0.858466i
$22$		0			0
$23$	3.68614	+	2.12819i	0.768613	+	0.443759i	0.832380	−	0.554206i	$-0.186978\pi$
$23$	3.68614	+	2.12819i	0.768613	+	0.443759i	−0.0637663	+	0.997965i	$0.520311\pi$
$24$		0			0
$25$	6.55842	−	11.3595i	1.31168	−	2.27190i
$26$		0			0
$27$	−4.00000	−	3.31662i	−0.769800	−	0.638285i
$28$		0			0
$29$	2.31386	−	4.00772i	0.429673	−	0.744215i	−0.567171	−	0.823600i	$-0.691962\pi$
$29$	2.31386	−	4.00772i	0.429673	−	0.744215i	0.996844	+	0.0793847i	$0.0252955\pi$
$30$		0			0
$31$		−	7.57301i		−	1.36015i	−0.733141	−	0.680077i	$-0.761946\pi$
$31$		−	7.57301i		−	1.36015i	0.733141	−	0.680077i	$-0.238054\pi$
$32$		0			0
$33$	−2.62772	+	0.792287i	−0.457427	+	0.137919i
$34$		0			0
$35$	8.74456	−	5.04868i	1.47810	−	0.853382i
$36$		0			0
$37$			4.10891i			0.675501i	0.941236	+	0.337750i	$0.109666\pi$
$37$			4.10891i			0.675501i	−0.941236	+	0.337750i	$0.890334\pi$
$38$		0			0
$39$	−0.686141	+	2.92048i	−0.109870	+	0.467651i
$40$		0			0
$41$	5.05842	+	8.76144i	0.789993	+	1.36831i	0.925971	+	0.377596i	$0.123249\pi$
$41$	5.05842	+	8.76144i	0.789993	+	1.36831i	−0.135978	+	0.990712i	$0.543418\pi$
$42$		0			0
$43$	−4.87228	−	8.43904i	−0.743016	−	1.28694i	−0.951116	−	0.308834i	$-0.900061\pi$
$43$	−4.87228	−	8.43904i	−0.743016	−	1.28694i	0.208100	−	0.978108i	$-0.433272\pi$
$44$		0			0
$45$	−5.68614	+	11.4333i	−0.847640	+	1.70437i
$46$		0			0
$47$	−2.31386	−	1.33591i	−0.337511	−	0.194862i	0.321660	−	0.946855i	$-0.395759\pi$
$47$	−2.31386	−	1.33591i	−0.337511	−	0.194862i	−0.659171	+	0.751993i	$0.729093\pi$
$48$		0			0
$49$	−1.37228			−0.196040
$50$		0			0
$51$	−3.37228	−	3.16915i	−0.472214	−	0.443769i
$52$		0			0
$53$	−3.68614	+	6.38458i	−0.506330	+	0.876990i	0.493643	+	0.869665i	$0.335665\pi$
$53$	−3.68614	+	6.38458i	−0.506330	+	0.876990i	−0.999973	+	0.00732516i	$0.997668\pi$
$54$		0			0
$55$	3.37228	+	5.84096i	0.454718	+	0.787595i
$56$		0			0
$57$	−4.87228	−	5.76722i	−0.645349	−	0.763888i
$58$		0			0
$59$	3.68614	+	6.38458i	0.479895	+	0.831202i	0.999734	−	0.0230621i	$-0.00734155\pi$
$59$	3.68614	+	6.38458i	0.479895	+	0.831202i	−0.519839	+	0.854264i	$0.674008\pi$
$60$		0			0
$61$	4.87228	−	8.43904i	0.623832	−	1.08051i	−0.364934	−	0.931033i	$-0.618908\pi$
$61$	4.87228	−	8.43904i	0.623832	−	1.08051i	0.988766	−	0.149475i	$-0.0477583\pi$
$62$		0			0
$63$	−5.93070	+	3.93398i	−0.747198	+	0.495635i
$64$		0			0
$65$	7.37228			0.914419
$66$		0			0
$67$	1.50000	+	0.866025i	0.183254	+	0.105802i	0.588821	−	0.808264i	$-0.299592\pi$
$67$	1.50000	+	0.866025i	0.183254	+	0.105802i	−0.405567	+	0.914066i	$0.632926\pi$
$68$		0			0
$69$	−1.68614	+	7.17687i	−0.202987	+	0.863994i
$70$		0			0
$71$	−5.05842	−	8.76144i	−0.600324	−	1.03979i	−0.992772	−	0.120018i	$-0.961705\pi$
$71$	−5.05842	−	8.76144i	−0.600324	−	1.03979i	0.392448	−	0.919774i	$-0.371628\pi$
$72$		0			0
$73$	−1.12772	−	1.95327i	−0.131989	−	0.228612i	0.792454	−	0.609932i	$-0.208803\pi$
$73$	−1.12772	−	1.95327i	−0.131989	−	0.228612i	−0.924443	+	0.381319i	$0.875470\pi$
$74$		0			0
$75$	22.1168	+	5.19615i	2.55383	+	0.600000i
$76$		0			0
$77$			3.75906i			0.428384i
$78$		0			0
$79$	−8.61684	+	4.97494i	−0.969471	+	0.559724i	−0.899075	−	0.437795i	$-0.855760\pi$
$79$	−8.61684	+	4.97494i	−0.969471	+	0.559724i	−0.0703959	+	0.997519i	$0.522426\pi$
$80$		0			0
$81$	3.50000	−	8.29156i	0.388889	−	0.921285i
$82$		0			0
$83$			8.51278i			0.934399i	0.884152	+	0.467199i	$0.154737\pi$
$83$			8.51278i			0.934399i	−0.884152	+	0.467199i	$0.845263\pi$
$84$		0			0
$85$	−5.68614	+	9.84868i	−0.616749	+	1.06824i
$86$		0			0
$87$	7.80298	+	1.83324i	0.836568	+	0.196544i
$88$		0			0
$89$	−3.68614	+	6.38458i	−0.390730	+	0.676764i	−0.992546	−	0.121870i	$-0.961111\pi$
$89$	−3.68614	+	6.38458i	−0.390730	+	0.676764i	0.601816	+	0.798635i	$0.294444\pi$
$90$		0			0
$91$	3.55842	+	2.05446i	0.373024	+	0.215365i
$92$		0			0
$93$	12.5584	−	3.78651i	1.30225	−	0.392642i
$94$		0			0
$95$	−11.0584	+	14.8974i	−1.13457	+	1.52844i
$96$		0			0
$97$	−15.1753	+	8.76144i	−1.54081	+	0.889590i	−0.542027	+	0.840361i	$0.682343\pi$
$97$	−15.1753	+	8.76144i	−1.54081	+	0.889590i	−0.998788	+	0.0492290i	$0.984324\pi$
$98$		0			0
$99$	−2.62772	−	3.96143i	−0.264096	−	0.398139i
$100$		0			0
$101$	0.430703	+	0.248667i	0.0428566	+	0.0247433i	0.521275	−	0.853389i	$-0.325457\pi$
$101$	0.430703	+	0.248667i	0.0428566	+	0.0247433i	−0.478419	+	0.878132i	$0.658790\pi$
$102$		0			0
$103$		−	6.28339i		−	0.619121i	−0.950880	−	0.309561i	$-0.899818\pi$
$103$		−	6.28339i		−	0.619121i	0.950880	−	0.309561i	$-0.100182\pi$
$104$		0			0
$105$	12.7446	+	11.9769i	1.24374	+	1.16882i
$106$		0			0
$107$	5.48913			0.530654			0.265327	−	0.964159i	$-0.414520\pi$
$107$	5.48913			0.530654			0.265327	+	0.964159i	$0.414520\pi$
$108$		0			0
$109$	11.0584	−	6.38458i	1.05920	−	0.611532i	0.133993	−	0.990982i	$-0.457220\pi$
$109$	11.0584	−	6.38458i	1.05920	−	0.611532i	0.925212	+	0.379450i	$0.123887\pi$
$110$		0			0
$111$	−6.81386	+	2.05446i	−0.646743	+	0.195000i
$112$		0			0
$113$	−2.74456			−0.258187			−0.129093	−	0.991632i	$-0.541207\pi$
$113$	−2.74456			−0.258187			−0.129093	+	0.991632i	$0.541207\pi$
$114$		0			0
$115$	18.1168			1.68940
$116$		0			0
$117$	−5.18614	+	0.322405i	−0.479459	+	0.0298064i
$118$		0			0
$119$	−5.48913	+	3.16915i	−0.503187	+	0.290515i
$120$		0			0
$121$	8.48913			0.771739
$122$		0			0
$123$	−12.0000	+	12.7692i	−1.08200	+	1.15136i
$124$		0			0
$125$		−	34.5484i		−	3.09011i
$126$		0			0
$127$	−2.05842	−	1.18843i	−0.182655	−	0.105456i	0.405884	−	0.913924i	$-0.366964\pi$
$127$	−2.05842	−	1.18843i	−0.182655	−	0.105456i	−0.588540	+	0.808468i	$0.700297\pi$
$128$		0			0
$129$	11.5584	−	12.2993i	1.01766	−	1.08289i
$130$		0			0
$131$	2.31386	−	1.33591i	0.202163	−	0.116719i	−0.395501	−	0.918466i	$-0.629429\pi$
$131$	2.31386	−	1.33591i	0.202163	−	0.116719i	0.597664	+	0.801747i	$0.296096\pi$
$132$		0			0
$133$	−9.48913	+	4.10891i	−0.822812	+	0.356288i
$134$		0			0
$135$	−21.8030	−	3.71277i	−1.87650	−	0.319544i
$136$		0			0
$137$	−19.8030	−	11.4333i	−1.69188	−	0.976809i	−0.952997	−	0.302978i	$-0.902019\pi$
$137$	−19.8030	−	11.4333i	−1.69188	−	0.976809i	−0.738886	−	0.673831i	$-0.764648\pi$
$138$		0			0
$139$	8.50000	−	14.7224i	0.720961	−	1.24874i	−0.239655	−	0.970858i	$-0.577034\pi$
$139$	8.50000	−	14.7224i	0.720961	−	1.24874i	0.960615	−	0.277882i	$-0.0896325\pi$
$140$		0			0
$141$	1.05842	−	4.50506i	0.0891352	−	0.379394i
$142$		0			0
$143$	−1.37228	+	2.37686i	−0.114756	+	0.198763i
$144$		0			0
$145$		−	19.6974i		−	1.63578i
$146$		0			0
$147$	−0.686141	−	2.27567i	−0.0565919	−	0.187694i
$148$		0			0
$149$	−16.5475	+	9.55373i	−1.35563	+	0.782672i	−0.989031	−	0.147708i	$-0.952810\pi$
$149$	−16.5475	+	9.55373i	−1.35563	+	0.782672i	−0.366597	+	0.930380i	$0.619477\pi$
$150$		0			0
$151$			3.46410i			0.281905i	0.990016	+	0.140952i	$0.0450164\pi$
$151$			3.46410i			0.281905i	−0.990016	+	0.140952i	$0.954984\pi$
$152$		0			0
$153$	3.56930	−	7.17687i	0.288561	−	0.580216i
$154$		0			0
$155$	−16.1168	−	27.9152i	−1.29454	−	2.24220i
$156$		0			0
$157$	−6.61684	−	11.4607i	−0.528082	−	0.914664i	−0.999464	−	0.0327353i	$-0.989578\pi$
$157$	−6.61684	−	11.4607i	−0.528082	−	0.914664i	0.471382	−	0.881929i	$-0.343755\pi$
$158$		0			0
$159$	−12.4307	−	2.92048i	−0.985819	−	0.231609i
$160$		0			0
$161$	8.74456	+	5.04868i	0.689168	+	0.397891i
$162$		0			0
$163$	11.1168			0.870738			0.435369	−	0.900252i	$-0.356618\pi$
$163$	11.1168			0.870738			0.435369	+	0.900252i	$0.356618\pi$
$164$		0			0
$165$	−8.00000	+	8.51278i	−0.622799	+	0.662719i
$166$		0			0
$167$	−6.43070	+	11.1383i	−0.497623	+	0.861908i	−0.999996	−	0.00274283i	$-0.999127\pi$
$167$	−6.43070	+	11.1383i	−0.497623	+	0.861908i	0.502373	+	0.864651i	$0.332460\pi$
$168$		0			0
$169$	−5.00000	−	8.66025i	−0.384615	−	0.666173i
$170$		0			0
$171$	7.12772	−	10.9634i	0.545070	−	0.838390i
$172$		0			0
$173$	2.31386	+	4.00772i	0.175919	+	0.304701i	0.940479	−	0.339852i	$-0.110377\pi$
$173$	2.31386	+	4.00772i	0.175919	+	0.304701i	−0.764560	+	0.644553i	$0.777044\pi$
$174$		0			0
$175$	15.5584	−	26.9480i	1.17611	−	2.03708i
$176$		0			0
$177$	−8.74456	+	9.30506i	−0.657282	+	0.699411i
$178$		0			0
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	−0.941578	−	0.543620i	−0.0699869	−	0.0404070i	0.464598	−	0.885522i	$-0.346199\pi$
$181$	−0.941578	−	0.543620i	−0.0699869	−	0.0404070i	−0.534585	+	0.845115i	$0.679532\pi$
$182$		0			0
$183$	16.4307	+	3.86025i	1.21459	+	0.285358i
$184$		0			0
$185$	8.74456	+	15.1460i	0.642913	+	1.11356i
$186$		0			0
$187$	−2.11684	−	3.66648i	−0.154799	−	0.268120i
$188$		0			0
$189$	−9.48913	−	7.86797i	−0.690232	−	0.572310i
$190$		0			0
$191$		−	7.92287i		−	0.573279i	−0.958039	−	0.286639i	$-0.907462\pi$
$191$		−	7.92287i		−	0.573279i	0.958039	−	0.286639i	$-0.0925381\pi$
$192$		0			0
$193$	−10.5000	+	6.06218i	−0.755807	+	0.436365i	−0.827788	−	0.561041i	$-0.810401\pi$
$193$	−10.5000	+	6.06218i	−0.755807	+	0.436365i	0.0719816	+	0.997406i	$0.477068\pi$
$194$		0			0
$195$	3.68614	+	12.2255i	0.263970	+	0.875489i
$196$		0			0
$197$		−	3.75906i		−	0.267822i	−0.990993	−	0.133911i	$-0.957246\pi$
$197$		−	3.75906i		−	0.267822i	0.990993	−	0.133911i	$-0.0427536\pi$
$198$		0			0
$199$	−1.87228	+	3.24289i	−0.132723	+	0.229882i	−0.924725	−	0.380636i	$-0.875705\pi$
$199$	−1.87228	+	3.24289i	−0.132723	+	0.229882i	0.792003	+	0.610518i	$0.209039\pi$
$200$		0			0
$201$	−0.686141	+	2.92048i	−0.0483966	+	0.205995i
$202$		0			0
$203$	5.48913	−	9.50744i	0.385261	−	0.667292i
$204$		0			0
$205$	37.2921	+	21.5306i	2.60459	+	1.50376i
$206$		0			0
$207$	−12.7446	+	0.792287i	−0.885808	+	0.0550678i
$208$		0			0
$209$	−2.74456	−	6.33830i	−0.189845	−	0.438429i
$210$		0			0
$211$	−9.73369	+	5.61975i	−0.670095	+	0.386879i	−0.796113	−	0.605149i	$-0.793114\pi$
$211$	−9.73369	+	5.61975i	−0.670095	+	0.386879i	0.126018	+	0.992028i	$0.459780\pi$
$212$		0			0
$213$	12.0000	−	12.7692i	0.822226	−	0.874929i
$214$		0			0
$215$	−35.9198	−	20.7383i	−2.44971	−	1.41434i
$216$		0			0
$217$		−	17.9653i		−	1.21957i
$218$		0			0
$219$	2.67527	−	2.84674i	0.180778	−	0.192365i
$220$		0			0
$221$	−4.62772			−0.311294
$222$		0			0
$223$	−14.6168	+	8.43904i	−0.978816	+	0.565120i	−0.901913	−	0.431919i	$-0.857837\pi$
$223$	−14.6168	+	8.43904i	−0.978816	+	0.565120i	−0.0769037	+	0.997039i	$0.524503\pi$
$224$		0			0
$225$	2.44158	+	39.2747i	0.162772	+	2.61831i
$226$		0			0
$227$	22.9783			1.52512			0.762560	−	0.646917i	$-0.223942\pi$
$227$	22.9783			1.52512			0.762560	+	0.646917i	$0.223942\pi$
$228$		0			0
$229$	−8.37228			−0.553256			−0.276628	−	0.960977i	$-0.589217\pi$
$229$	−8.37228			−0.553256			−0.276628	+	0.960977i	$0.589217\pi$
$230$		0			0
$231$	−6.23369	+	1.87953i	−0.410147	+	0.123664i
$232$		0			0
$233$	9.68614	−	5.59230i	0.634560	−	0.366363i	−0.147956	−	0.988994i	$-0.547269\pi$
$233$	9.68614	−	5.59230i	0.634560	−	0.366363i	0.782516	+	0.622630i	$0.213936\pi$
$234$		0			0
$235$	−11.3723			−0.741846
$236$		0			0
$237$	−12.5584	−	11.8020i	−0.815757	−	0.766619i
$238$		0			0
$239$			1.58457i			0.102498i	0.998686	+	0.0512488i	$0.0163201\pi$
$239$			1.58457i			0.102498i	−0.998686	+	0.0512488i	$0.983680\pi$
$240$		0			0
$241$	−11.6168	−	6.70699i	−0.748307	−	0.432035i	0.0767751	−	0.997048i	$-0.475538\pi$
$241$	−11.6168	−	6.70699i	−0.748307	−	0.432035i	−0.825082	+	0.565013i	$0.808871\pi$
$242$		0			0
$243$	15.5000	+	1.65831i	0.994325	+	0.106381i
$244$		0			0
$245$	−5.05842	+	2.92048i	−0.323171	+	0.186583i
$246$		0			0
$247$	−7.50000	−	0.866025i	−0.477214	−	0.0551039i
$248$		0			0
$249$	−14.1168	+	4.25639i	−0.894619	+	0.269738i
$250$		0			0
$251$	−14.3139	−	8.26411i	−0.903483	−	0.521626i	−0.0251543	−	0.999684i	$-0.508008\pi$
$251$	−14.3139	−	8.26411i	−0.903483	−	0.521626i	−0.878329	+	0.478058i	$0.841341\pi$
$252$		0			0
$253$	−3.37228	+	5.84096i	−0.212014	+	0.367218i
$254$		0			0
$255$	−19.1753	−	4.50506i	−1.20080	−	0.282118i
$256$		0			0
$257$	−0.941578	+	1.63086i	−0.0587340	+	0.101730i	−0.893897	−	0.448272i	$-0.852040\pi$
$257$	−0.941578	+	1.63086i	−0.0587340	+	0.101730i	0.835163	+	0.550002i	$0.185373\pi$
$258$		0			0
$259$			9.74749i			0.605680i
$260$		0			0
$261$	0.861407	+	13.8564i	0.0533197	+	0.857690i
$262$		0			0
$263$	14.3139	−	8.26411i	0.882630	−	0.509587i	0.0111056	−	0.999938i	$-0.496465\pi$
$263$	14.3139	−	8.26411i	0.882630	−	0.509587i	0.871525	+	0.490351i	$0.163132\pi$
$264$		0			0
$265$			31.3793i			1.92761i
$266$		0			0
$267$	−12.4307	−	2.92048i	−0.760747	−	0.178731i
$268$		0			0
$269$	−3.68614	−	6.38458i	−0.224748	−	0.389275i	0.731496	−	0.681846i	$-0.238823\pi$
$269$	−3.68614	−	6.38458i	−0.224748	−	0.389275i	−0.956244	+	0.292571i	$0.905489\pi$
$270$		0			0
$271$	3.05842	+	5.29734i	0.185786	+	0.321791i	0.943841	−	0.330400i	$-0.107184\pi$
$271$	3.05842	+	5.29734i	0.185786	+	0.321791i	−0.758055	+	0.652190i	$0.773850\pi$
$272$		0			0
$273$	−1.62772	+	6.92820i	−0.0985140	+	0.419314i
$274$		0			0
$275$	18.0000	+	10.3923i	1.08544	+	0.626680i
$276$		0			0
$277$	8.51087			0.511369			0.255684	−	0.966760i	$-0.417699\pi$
$277$	8.51087			0.511369			0.255684	+	0.966760i	$0.417699\pi$
$278$		0			0
$279$	12.5584	+	18.9325i	0.751853	+	1.13346i
$280$		0			0
$281$	−6.43070	+	11.1383i	−0.383624	+	0.664456i	−0.991577	−	0.129517i	$-0.958657\pi$
$281$	−6.43070	+	11.1383i	−0.383624	+	0.664456i	0.607954	+	0.793973i	$0.291991\pi$
$282$		0			0
$283$	−5.68614	−	9.84868i	−0.338006	−	0.585444i	0.646052	−	0.763294i	$-0.276419\pi$
$283$	−5.68614	−	9.84868i	−0.338006	−	0.585444i	−0.984058	+	0.177850i	$0.943086\pi$
$284$		0			0
$285$	−30.2337	−	10.8896i	−1.79089	−	0.645046i
$286$		0			0
$287$	12.0000	+	20.7846i	0.708338	+	1.22688i
$288$		0			0
$289$	−4.93070	+	8.54023i	−0.290041	+	0.502366i
$290$		0			0
$291$	−22.1168	−	20.7846i	−1.29651	−	1.21842i
$292$		0			0
$293$	20.2337			1.18206			0.591032	−	0.806648i	$-0.298721\pi$
$293$	20.2337			1.18206			0.591032	+	0.806648i	$0.298721\pi$
$294$		0			0
$295$	27.1753	+	15.6896i	1.58221	+	0.913487i
$296$		0			0
$297$	5.25544	−	6.33830i	0.304951	−	0.367785i
$298$		0			0
$299$	3.68614	+	6.38458i	0.213175	+	0.369230i
$300$		0			0
$301$	−11.5584	−	20.0198i	−0.666216	−	1.15392i
$302$		0			0
$303$	−0.197015	+	0.838574i	−0.0113182	+	0.0481748i
$304$		0			0
$305$		−	41.4766i		−	2.37495i
$306$		0			0
$307$	−9.94158	+	5.73977i	−0.567396	+	0.327586i	−0.756109	−	0.654446i	$-0.772902\pi$
$307$	−9.94158	+	5.73977i	−0.567396	+	0.327586i	0.188713	+	0.982032i	$0.439568\pi$
$308$		0			0
$309$	10.4198	−	3.14170i	0.592763	−	0.178725i
$310$		0			0
$311$		−	12.2718i		−	0.695872i	−0.937518	−	0.347936i	$-0.886883\pi$
$311$		−	12.2718i		−	0.695872i	0.937518	−	0.347936i	$-0.113117\pi$
$312$		0			0
$313$	−1.94158	+	3.36291i	−0.109744	+	0.190083i	−0.915667	−	0.401938i	$-0.868337\pi$
$313$	−1.94158	+	3.36291i	−0.109744	+	0.190083i	0.805922	+	0.592021i	$0.201670\pi$
$314$		0			0
$315$	−13.4891	+	27.1229i	−0.760026	+	1.52820i
$316$		0			0
$317$	−0.941578	+	1.63086i	−0.0528843	+	0.0915983i	−0.891256	−	0.453501i	$-0.850175\pi$
$317$	−0.941578	+	1.63086i	−0.0528843	+	0.0915983i	0.838371	+	0.545099i	$0.183508\pi$
$318$		0			0
$319$	6.35053	+	3.66648i	0.355562	+	0.205284i
$320$		0			0
$321$	2.74456	+	9.10268i	0.153187	+	0.508062i
$322$		0			0
$323$	6.94158	−	9.35135i	0.386240	−	0.520323i
$324$		0			0
$325$	19.6753	−	11.3595i	1.09139	−	0.630113i
$326$		0			0
$327$	16.1168	+	15.1460i	0.891264	+	0.837577i
$328$		0			0
$329$	−5.48913	−	3.16915i	−0.302625	−	0.174721i
$330$		0			0
$331$			14.5012i			0.797059i	0.917156	+	0.398529i	$0.130479\pi$
$331$			14.5012i			0.797059i	−0.917156	+	0.398529i	$0.869521\pi$
$332$		0			0
$333$	−6.81386	−	10.2723i	−0.373397	−	0.562917i
$334$		0			0
$335$	7.37228			0.402791
$336$		0			0
$337$	7.50000	−	4.33013i	0.408551	−	0.235877i	−0.281616	−	0.959527i	$-0.590870\pi$
$337$	7.50000	−	4.33013i	0.408551	−	0.235877i	0.690167	+	0.723650i	$0.257537\pi$
$338$		0			0
$339$	−1.37228	−	4.55134i	−0.0745321	−	0.247195i
$340$		0			0
$341$	12.0000			0.649836
$342$		0			0
$343$	−19.8614			−1.07242
$344$		0			0
$345$	9.05842	+	30.0434i	0.487689	+	1.61748i
$346$		0			0
$347$	−3.68614	+	2.12819i	−0.197882	+	0.114247i	−0.595667	−	0.803231i	$-0.703112\pi$
$347$	−3.68614	+	2.12819i	−0.197882	+	0.114247i	0.397785	+	0.917479i	$0.369779\pi$
$348$		0			0
$349$	−1.86141			−0.0996388			−0.0498194	−	0.998758i	$-0.515865\pi$
$349$	−1.86141			−0.0996388			−0.0498194	+	0.998758i	$0.515865\pi$
$350$		0			0
$351$	−3.12772	−	8.43904i	−0.166945	−	0.450443i
$352$		0			0
$353$		−	13.2665i		−	0.706105i	−0.935604	−	0.353052i	$-0.885144\pi$
$353$		−	13.2665i		−	0.706105i	0.935604	−	0.353052i	$-0.114856\pi$
$354$		0			0
$355$	−37.2921	−	21.5306i	−1.97926	−	1.14273i
$356$		0			0
$357$	−8.00000	−	7.51811i	−0.423405	−	0.397901i
$358$		0			0
$359$	−21.6861	+	12.5205i	−1.14455	+	0.660807i	−0.947553	−	0.319597i	$-0.896452\pi$
$359$	−21.6861	+	12.5205i	−1.14455	+	0.660807i	−0.196997	+	0.980404i	$0.563119\pi$
$360$		0			0
$361$	13.0000	−	13.8564i	0.684211	−	0.729285i
$362$		0			0
$363$	4.24456	+	14.0776i	0.222782	+	0.738884i
$364$		0			0
$365$	−8.31386	−	4.80001i	−0.435167	−	0.251244i
$366$		0			0
$367$	−3.50000	+	6.06218i	−0.182699	+	0.316443i	−0.942799	−	0.333363i	$-0.891817\pi$
$367$	−3.50000	+	6.06218i	−0.182699	+	0.316443i	0.760100	+	0.649806i	$0.225150\pi$
$368$		0			0
$369$	−27.1753	−	13.5152i	−1.41469	−	0.703571i
$370$		0			0
$371$	−8.74456	+	15.1460i	−0.453995	+	0.786343i
$372$		0			0
$373$			20.7846i			1.07619i	0.842885	+	0.538093i	$0.180855\pi$
$373$			20.7846i			1.07619i	−0.842885	+	0.538093i	$0.819145\pi$
$374$		0			0
$375$	57.2921	−	17.2742i	2.95855	−	0.892037i
$376$		0			0
$377$	6.94158	−	4.00772i	0.357509	−	0.206408i
$378$		0			0
$379$		−	15.7908i		−	0.811121i	−0.914068	−	0.405560i	$-0.867076\pi$
$379$		−	15.7908i		−	0.811121i	0.914068	−	0.405560i	$-0.132924\pi$
$380$		0			0
$381$	0.941578	−	4.00772i	0.0482385	−	0.205322i
$382$		0			0
$383$	3.68614	+	6.38458i	0.188353	+	0.326237i	0.944701	−	0.327932i	$-0.106352\pi$
$383$	3.68614	+	6.38458i	0.188353	+	0.326237i	−0.756348	+	0.654169i	$0.773018\pi$
$384$		0			0
$385$	8.00000	+	13.8564i	0.407718	+	0.706188i
$386$		0			0
$387$	26.1753	+	13.0178i	1.33056	+	0.661734i
$388$		0			0
$389$	18.4307	+	10.6410i	0.934474	+	0.539519i	0.888224	−	0.459411i	$-0.151940\pi$
$389$	18.4307	+	10.6410i	0.934474	+	0.539519i	0.0462501	+	0.998930i	$0.485273\pi$
$390$		0			0
$391$	−11.3723			−0.575121
$392$		0			0
$393$	3.37228	+	3.16915i	0.170109	+	0.159862i
$394$		0			0
$395$	−21.1753	+	36.6766i	−1.06544	+	1.84540i
$396$		0			0
$397$	0.500000	+	0.866025i	0.0250943	+	0.0434646i	0.878300	−	0.478110i	$-0.158678\pi$
$397$	0.500000	+	0.866025i	0.0250943	+	0.0434646i	−0.853206	+	0.521575i	$0.825345\pi$
$398$		0			0
$399$	−11.5584	−	13.6815i	−0.578645	−	0.684931i
$400$		0			0
$401$	13.8030	+	23.9075i	0.689288	+	1.19388i	0.972068	+	0.234697i	$0.0754099\pi$
$401$	13.8030	+	23.9075i	0.689288	+	1.19388i	−0.282780	+	0.959185i	$0.591257\pi$
$402$		0			0
$403$	6.55842	−	11.3595i	0.326698	−	0.565858i
$404$		0			0
$405$	−4.74456	−	38.0125i	−0.235759	−	1.88886i
$406$		0			0
$407$	−6.51087			−0.322732
$408$		0			0
$409$	−18.9416	−	10.9359i	−0.936601	−	0.540747i	−0.0477076	−	0.998861i	$-0.515192\pi$
$409$	−18.9416	−	10.9359i	−0.936601	−	0.540747i	−0.888893	+	0.458115i	$0.848525\pi$
$410$		0			0
$411$	9.05842	−	38.5562i	0.446819	−	1.90184i
$412$		0			0
$413$	8.74456	+	15.1460i	0.430292	+	0.745287i
$414$		0			0
$415$	18.1168	+	31.3793i	0.889321	+	1.54035i
$416$		0			0
$417$	28.6644	+	6.73444i	1.40370	+	0.329787i
$418$		0			0
$419$		−	12.2718i		−	0.599518i	−0.954015	−	0.299759i	$-0.903094\pi$
$419$		−	12.2718i		−	0.599518i	0.954015	−	0.299759i	$-0.0969063\pi$
$420$		0			0
$421$	31.2921	−	18.0665i	1.52508	−	0.880508i	0.525526	−	0.850777i	$-0.323868\pi$
$421$	31.2921	−	18.0665i	1.52508	−	0.880508i	0.999558	−	0.0297303i	$-0.00946484\pi$
$422$		0			0
$423$	8.00000	−	0.497333i	0.388973	−	0.0241812i
$424$		0			0
$425$			35.0458i			1.69997i
$426$		0			0
$427$	11.5584	−	20.0198i	0.559351	−	0.968825i
$428$		0			0
$429$	−4.62772	−	1.08724i	−0.223428	−	0.0524925i
$430$		0			0
$431$	17.0584	−	29.5461i	0.821675	−	1.42318i	−0.0827587	−	0.996570i	$-0.526373\pi$
$431$	17.0584	−	29.5461i	0.821675	−	1.42318i	0.904434	−	0.426614i	$-0.140294\pi$
$432$		0			0
$433$	−24.7337	−	14.2800i	−1.18863	−	0.686253i	−0.230631	−	0.973041i	$-0.574079\pi$
$433$	−24.7337	−	14.2800i	−1.18863	−	0.686253i	−0.957994	+	0.286788i	$0.907412\pi$
$434$		0			0
$435$	32.6644	−	9.84868i	1.56614	−	0.472208i
$436$		0			0
$437$	−18.4307	−	2.12819i	−0.881660	−	0.101805i
$438$		0			0
$439$	5.61684	−	3.24289i	0.268077	−	0.154775i	−0.359936	−	0.932977i	$-0.617202\pi$
$439$	5.61684	−	3.24289i	0.268077	−	0.154775i	0.628014	+	0.778202i	$0.283868\pi$
$440$		0			0
$441$	3.43070	−	2.27567i	0.163367	−	0.108365i
$442$		0			0
$443$	21.6861	+	12.5205i	1.03034	+	0.594867i	0.917082	−	0.398699i	$-0.130538\pi$
$443$	21.6861	+	12.5205i	1.03034	+	0.594867i	0.113258	+	0.993566i	$0.463871\pi$
$444$		0			0
$445$			31.3793i			1.48752i
$446$		0			0
$447$	−24.1168	−	22.6641i	−1.14069	−	1.07198i
$448$		0			0
$449$	−9.25544			−0.436791			−0.218396	−	0.975860i	$-0.570082\pi$
$449$	−9.25544			−0.436791			−0.218396	+	0.975860i	$0.570082\pi$
$450$		0			0
$451$	−13.8832	+	8.01544i	−0.653732	+	0.377433i
$452$		0			0
$453$	−5.74456	+	1.73205i	−0.269903	+	0.0813788i
$454$		0			0
$455$	17.4891			0.819903
$456$		0			0
$457$	23.3505			1.09229			0.546146	−	0.837690i	$-0.316094\pi$
$457$	23.3505			1.09229			0.546146	+	0.837690i	$0.316094\pi$
$458$		0			0
$459$	13.6861	+	2.33057i	0.638814	+	0.108782i
$460$		0			0
$461$	23.9198	−	13.8101i	1.11406	−	0.643201i	0.174180	−	0.984714i	$-0.444272\pi$
$461$	23.9198	−	13.8101i	1.11406	−	0.643201i	0.939877	+	0.341512i	$0.110939\pi$
$462$		0			0
$463$	14.3723			0.667937			0.333968	−	0.942584i	$-0.391612\pi$
$463$	14.3723			0.667937			0.333968	+	0.942584i	$0.391612\pi$
$464$		0			0
$465$	38.2337	−	40.6844i	1.77304	−	1.88669i
$466$		0			0
$467$		−	14.8511i		−	0.687226i	−0.939111	−	0.343613i	$-0.888349\pi$
$467$		−	14.8511i		−	0.687226i	0.939111	−	0.343613i	$-0.111651\pi$
$468$		0			0
$469$	3.55842	+	2.05446i	0.164313	+	0.0948660i
$470$		0			0
$471$	15.6970	−	16.7031i	0.723280	−	0.769640i
$472$		0			0
$473$	13.3723	−	7.72049i	0.614858	−	0.354989i
$474$		0			0
$475$	−6.55842	+	56.7976i	−0.300921	+	2.60605i
$476$		0			0
$477$	−1.37228	−	22.0742i	−0.0628324	−	1.01071i
$478$		0			0
$479$	−14.3139	−	8.26411i	−0.654017	−	0.377597i	0.135977	−	0.990712i	$-0.456583\pi$
$479$	−14.3139	−	8.26411i	−0.654017	−	0.377597i	−0.789994	+	0.613115i	$0.789916\pi$
$480$		0			0
$481$	−3.55842	+	6.16337i	−0.162250	+	0.281025i
$482$		0			0
$483$	−4.00000	+	17.0256i	−0.182006	+	0.774690i
$484$		0			0
$485$	−37.2921	+	64.5918i	−1.69335	+	2.93296i
$486$		0			0
$487$			0.884861i			0.0400969i	0.999799	+	0.0200484i	$0.00638204\pi$
$487$			0.884861i			0.0400969i	−0.999799	+	0.0200484i	$0.993618\pi$
$488$		0			0
$489$	5.55842	+	18.4352i	0.251361	+	0.833669i
$490$		0			0
$491$	−21.6861	+	12.5205i	−0.978682	+	0.565042i	−0.901872	−	0.432004i	$-0.857807\pi$
$491$	−21.6861	+	12.5205i	−0.978682	+	0.565042i	−0.0768099	+	0.997046i	$0.524473\pi$
$492$		0			0
$493$			12.3644i			0.556865i
$494$		0			0
$495$	−18.1168	−	9.01011i	−0.814292	−	0.404974i
$496$		0			0
$497$	−12.0000	−	20.7846i	−0.538274	−	0.932317i
$498$		0			0
$499$	−4.87228	−	8.43904i	−0.218113	−	0.377783i	0.736118	−	0.676853i	$-0.236657\pi$
$499$	−4.87228	−	8.43904i	−0.218113	−	0.377783i	−0.954231	+	0.299070i	$0.903324\pi$
$500$		0			0
$501$	−21.6861	−	5.09496i	−0.968865	−	0.227626i
$502$		0			0
$503$	29.9198	+	17.2742i	1.33406	+	0.770219i	0.985919	−	0.167223i	$-0.0534800\pi$
$503$	29.9198	+	17.2742i	1.33406	+	0.770219i	0.348140	+	0.937443i	$0.386813\pi$
$504$		0			0
$505$	2.11684			0.0941983
$506$		0			0
$507$	11.8614	−	12.6217i	0.526784	−	0.560549i
$508$		0			0
$509$	−15.1753	+	26.2843i	−0.672632	+	1.16503i	0.304523	+	0.952505i	$0.401503\pi$
$509$	−15.1753	+	26.2843i	−0.672632	+	1.16503i	−0.977155	+	0.212528i	$0.931830\pi$
$510$		0			0
$511$	−2.67527	−	4.63370i	−0.118347	−	0.204983i
$512$		0			0
$513$	21.7446	+	6.33830i	0.960046	+	0.279843i
$514$		0			0
$515$	−13.3723	−	23.1615i	−0.589253	−	1.02062i
$516$		0			0
$517$	2.11684	−	3.66648i	0.0930987	−	0.161252i
$518$		0			0
$519$	−5.48913	+	5.84096i	−0.240946	+	0.256390i
$520$		0			0
$521$	−21.2554			−0.931218			−0.465609	−	0.884991i	$-0.654165\pi$
$521$	−21.2554			−0.931218			−0.465609	+	0.884991i	$0.654165\pi$
$522$		0			0
$523$	13.5000	+	7.79423i	0.590314	+	0.340818i	0.765222	−	0.643767i	$-0.222629\pi$
$523$	13.5000	+	7.79423i	0.590314	+	0.340818i	−0.174908	+	0.984585i	$0.555963\pi$
$524$		0			0
$525$	52.4674	+	12.3267i	2.28986	+	0.537983i
$526$		0			0
$527$	10.1168	+	17.5229i	0.440697	+	0.763309i
$528$		0			0
$529$	−2.44158	−	4.22894i	−0.106156	−	0.183867i
$530$		0			0
$531$	−19.8030	−	9.84868i	−0.859376	−	0.427397i
$532$		0			0
$533$			17.5229i			0.759001i
$534$		0			0
$535$	20.2337	−	11.6819i	0.874779	−	0.505054i
$536$		0			0
$537$	6.00000	+	19.8997i	0.258919	+	0.858738i
$538$		0			0
$539$		−	2.17448i		−	0.0936615i
$540$		0			0
$541$	−18.6168	+	32.2453i	−0.800401	+	1.38633i	0.118952	+	0.992900i	$0.462047\pi$
$541$	−18.6168	+	32.2453i	−0.800401	+	1.38633i	−0.919353	+	0.393435i	$0.871287\pi$
$542$		0			0
$543$	0.430703	−	1.83324i	0.0184832	−	0.0786719i
$544$		0			0
$545$	27.1753	−	47.0689i	1.16406	−	2.01621i
$546$		0			0
$547$	2.61684	+	1.51084i	0.111888	+	0.0645987i	0.554900	−	0.831917i	$-0.312757\pi$
$547$	2.61684	+	1.51084i	0.111888	+	0.0645987i	−0.443012	+	0.896516i	$0.646090\pi$
$548$		0			0
$549$	1.81386	+	29.1774i	0.0774136	+	1.24526i
$550$		0			0
$551$	−2.31386	+	20.0386i	−0.0985737	+	0.853673i
$552$		0			0
$553$	−20.4416	+	11.8020i	−0.869264	+	0.501870i
$554$		0			0
$555$	−20.7446	+	22.0742i	−0.880558	+	0.936999i
$556$		0			0
$557$	4.19702	+	2.42315i	0.177833	+	0.102672i	0.586274	−	0.810113i	$-0.300594\pi$
$557$	4.19702	+	2.42315i	0.177833	+	0.102672i	−0.408441	+	0.912785i	$0.633927\pi$
$558$		0			0
$559$		−	16.8781i		−	0.713867i
$560$		0			0
$561$	5.02175	−	5.34363i	0.212018	−	0.225608i
$562$		0			0
$563$	5.48913			0.231339			0.115670	−	0.993288i	$-0.463099\pi$
$563$	5.48913			0.231339			0.115670	+	0.993288i	$0.463099\pi$
$564$		0			0
$565$	−10.1168	+	5.84096i	−0.425619	+	0.245731i
$566$		0			0
$567$	8.30298	−	19.6699i	0.348693	−	0.826059i
$568$		0			0
$569$	−33.2554			−1.39414			−0.697070	−	0.717003i	$-0.745513\pi$
$569$	−33.2554			−1.39414			−0.697070	+	0.717003i	$0.745513\pi$
$570$		0			0
$571$	11.1168			0.465225			0.232613	−	0.972569i	$-0.425273\pi$
$571$	11.1168			0.465225			0.232613	+	0.972569i	$0.425273\pi$
$572$		0			0
$573$	13.1386	−	3.96143i	0.548873	−	0.165491i
$574$		0			0
$575$	48.3505	−	27.9152i	2.01636	−	1.16414i
$576$		0			0
$577$	24.9783			1.03986			0.519929	−	0.854209i	$-0.325958\pi$
$577$	24.9783			1.03986			0.519929	+	0.854209i	$0.325958\pi$
$578$		0			0
$579$	−15.3030	−	14.3812i	−0.635970	−	0.597662i
$580$		0			0
$581$			20.1947i			0.837817i
$582$		0			0
$583$	−10.1168	−	5.84096i	−0.418997	−	0.241908i
$584$		0			0
$585$	−18.4307	+	12.2255i	−0.762016	+	0.505464i
$586$		0			0
$587$	−11.9198	+	6.88192i	−0.491984	+	0.284047i	−0.725397	−	0.688331i	$-0.758344\pi$
$587$	−11.9198	+	6.88192i	−0.491984	+	0.284047i	0.233413	+	0.972378i	$0.425011\pi$
$588$		0			0
$589$	13.1168	+	30.2921i	0.540470	+	1.24816i
$590$		0			0
$591$	6.23369	−	1.87953i	0.256420	−	0.0773134i
$592$		0			0
$593$	18.4307	+	10.6410i	0.756858	+	0.436972i	0.828167	−	0.560482i	$-0.189384\pi$
$593$	18.4307	+	10.6410i	0.756858	+	0.436972i	−0.0713083	+	0.997454i	$0.522717\pi$
$594$		0			0
$595$	−13.4891	+	23.3639i	−0.553000	+	0.957824i
$596$		0			0
$597$	−6.31386	−	1.48338i	−0.258409	−	0.0607109i
$598$		0			0
$599$	−15.6861	+	27.1692i	−0.640918	+	1.11010i	0.344310	+	0.938856i	$0.388113\pi$
$599$	−15.6861	+	27.1692i	−0.640918	+	1.11010i	−0.985228	+	0.171247i	$0.945220\pi$
$600$		0			0
$601$		−	19.2549i		−	0.785425i	−0.919661	−	0.392713i	$-0.871537\pi$
$601$		−	19.2549i		−	0.785425i	0.919661	−	0.392713i	$-0.128463\pi$
$602$		0			0
$603$	−5.18614	+	0.322405i	−0.211196	+	0.0131293i
$604$		0			0
$605$	31.2921	−	18.0665i	1.27221	−	0.734508i
$606$		0			0
$607$		−	0.644810i		−	0.0261720i	−0.999914	−	0.0130860i	$-0.995834\pi$
$607$		−	0.644810i		−	0.0261720i	0.999914	−	0.0130860i	$-0.00416553\pi$
$608$		0			0
$609$	18.5109	+	4.34896i	0.750098	+	0.176229i
$610$		0			0
$611$	−2.31386	−	4.00772i	−0.0936087	−	0.162135i
$612$		0			0
$613$	13.3139	+	23.0603i	0.537742	+	0.931396i	0.999025	+	0.0441432i	$0.0140558\pi$
$613$	13.3139	+	23.0603i	0.537742	+	0.931396i	−0.461284	+	0.887253i	$0.652611\pi$
$614$		0			0
$615$	−17.0584	+	72.6073i	−0.687862	+	2.92781i
$616$		0			0
$617$	30.4307	+	17.5692i	1.22509	+	0.707308i	0.966000	−	0.258544i	$-0.0832426\pi$
$617$	30.4307	+	17.5692i	1.22509	+	0.707308i	0.259094	+	0.965852i	$0.416576\pi$
$618$		0			0
$619$	20.8832			0.839365			0.419682	−	0.907671i	$-0.362141\pi$
$619$	20.8832			0.839365			0.419682	+	0.907671i	$0.362141\pi$
$620$		0			0
$621$	−7.68614	−	20.7383i	−0.308434	−	0.832200i
$622$		0			0
$623$	−8.74456	+	15.1460i	−0.350344	+	0.606813i
$624$		0			0
$625$	−40.7337	−	70.5528i	−1.62935	−	2.82211i
$626$		0			0
$627$	9.13859	−	7.72049i	0.364960	−	0.308327i
$628$		0			0
$629$	−5.48913	−	9.50744i	−0.218866	−	0.379087i
$630$		0			0
$631$	−8.98913	+	15.5696i	−0.357851	+	0.619817i	−0.987602	−	0.156981i	$-0.949824\pi$
$631$	−8.98913	+	15.5696i	−0.357851	+	0.619817i	0.629750	+	0.776798i	$0.283157\pi$
$632$		0			0
$633$	−14.1861	−	13.3316i	−0.563848	−	0.529884i
$634$		0			0
$635$	−10.1168			−0.401475
$636$		0			0
$637$	−2.05842	−	1.18843i	−0.0815576	−	0.0470873i
$638$		0			0
$639$	27.1753	+	13.5152i	1.07504	+	0.534652i
$640$		0			0
$641$	−15.1753	−	26.2843i	−0.599387	−	1.03817i	−0.992912	−	0.118855i	$-0.962078\pi$
$641$	−15.1753	−	26.2843i	−0.599387	−	1.03817i	0.393525	−	0.919314i	$-0.371256\pi$
$642$		0			0
$643$	2.24456	+	3.88770i	0.0885169	+	0.153316i	0.906884	−	0.421379i	$-0.138454\pi$
$643$	2.24456	+	3.88770i	0.0885169	+	0.153316i	−0.818368	+	0.574695i	$0.805121\pi$
$644$		0			0
$645$	16.4307	−	69.9355i	0.646958	−	2.75371i
$646$		0			0
$647$			22.3692i			0.879423i	0.898139	+	0.439712i	$0.144919\pi$
$647$			22.3692i			0.879423i	−0.898139	+	0.439712i	$0.855081\pi$
$648$		0			0
$649$	−10.1168	+	5.84096i	−0.397121	+	0.229278i
$650$		0			0
$651$	29.7921	−	8.98266i	1.16764	−	0.352058i
$652$		0			0
$653$		−	6.33830i		−	0.248037i	−0.992280	−	0.124018i	$-0.960422\pi$
$653$		−	6.33830i		−	0.248037i	0.992280	−	0.124018i	$-0.0395782\pi$
$654$		0			0
$655$	5.68614	−	9.84868i	0.222176	−	0.384820i
$656$		0			0
$657$	6.05842	+	3.01306i	0.236362	+	0.117550i
$658$		0			0
$659$	−21.1753	+	36.6766i	−0.824871	+	1.42872i	0.0771464	+	0.997020i	$0.475419\pi$
$659$	−21.1753	+	36.6766i	−0.824871	+	1.42872i	−0.902018	+	0.431699i	$0.857914\pi$
$660$		0			0
$661$	19.2921	+	11.1383i	0.750376	+	0.433230i	0.825830	−	0.563919i	$-0.190707\pi$
$661$	19.2921	+	11.1383i	0.750376	+	0.433230i	−0.0754537	+	0.997149i	$0.524041\pi$
$662$		0			0
$663$	−2.31386	−	7.67420i	−0.0898629	−	0.298041i
$664$		0			0
$665$	−26.2337	+	35.3407i	−1.01730	+	1.37045i
$666$		0			0
$667$	17.0584	−	9.84868i	0.660505	−	0.381343i
$668$		0			0
$669$	−21.3030	−	20.0198i	−0.823621	−	0.774009i
$670$		0			0
$671$	13.3723	+	7.72049i	0.516231	+	0.298046i
$672$		0			0
$673$			11.0371i			0.425450i	0.977112	+	0.212725i	$0.0682338\pi$
$673$			11.0371i			0.425450i	−0.977112	+	0.212725i	$0.931766\pi$
$674$		0			0
$675$	−63.9090	+	23.6863i	−2.45986	+	0.911684i
$676$		0			0
$677$	44.2337			1.70004			0.850019	−	0.526751i	$-0.176590\pi$
$677$	44.2337			1.70004			0.850019	+	0.526751i	$0.176590\pi$
$678$		0			0
$679$	−36.0000	+	20.7846i	−1.38155	+	0.797640i
$680$		0			0
$681$	11.4891	+	38.1051i	0.440264	+	1.46019i
$682$		0			0
$683$	−28.4674			−1.08927			−0.544637	−	0.838672i	$-0.683333\pi$
$683$	−28.4674			−1.08927			−0.544637	+	0.838672i	$0.683333\pi$
$684$		0			0
$685$	−97.3288			−3.71874
$686$		0			0
$687$	−4.18614	−	13.8839i	−0.159711	−	0.529702i
$688$		0			0
$689$	−11.0584	+	6.38458i	−0.421292	+	0.243233i
$690$		0			0
$691$	32.4674			1.23512			0.617559	−	0.786525i	$-0.288122\pi$
$691$	32.4674			1.23512			0.617559	+	0.786525i	$0.288122\pi$
$692$		0			0
$693$	−6.23369	−	9.39764i	−0.236798	−	0.356987i
$694$		0			0
$695$		−	72.3586i		−	2.74472i
$696$		0			0
$697$	−23.4090	−	13.5152i	−0.886677	−	0.511923i
$698$		0			0
$699$	14.1168	+	13.2665i	0.533948	+	0.501785i
$700$		0			0
$701$	11.9198	−	6.88192i	0.450206	−	0.259926i	−0.257711	−	0.966222i	$-0.582968\pi$
$701$	11.9198	−	6.88192i	0.450206	−	0.259926i	0.707917	+	0.706296i	$0.249635\pi$
$702$		0			0
$703$	−7.11684	−	16.4356i	−0.268417	−	0.619882i
$704$		0			0
$705$	−5.68614	−	18.8588i	−0.214152	−	0.710263i
$706$		0			0
$707$	1.02175	+	0.589907i	0.0384268	+	0.0221857i
$708$		0			0
$709$	−12.6168	+	21.8530i	−0.473836	+	0.820707i	−0.999551	−	0.0299531i	$-0.990464\pi$
$709$	−12.6168	+	21.8530i	−0.473836	+	0.820707i	0.525716	+	0.850660i	$0.323798\pi$
$710$		0			0
$711$	13.2921	−	26.7268i	0.498493	−	1.00233i
$712$		0			0
$713$	16.1168	−	27.9152i	0.603581	−	1.04543i
$714$		0			0
$715$			11.6819i			0.436879i
$716$		0			0
$717$	−2.62772	+	0.792287i	−0.0981340	+	0.0295885i
$718$		0			0
$719$	−11.9198	+	6.88192i	−0.444535	+	0.256652i	−0.705519	−	0.708691i	$-0.749286\pi$
$719$	−11.9198	+	6.88192i	−0.444535	+	0.256652i	0.260985	+	0.965343i	$0.415953\pi$
$720$		0			0
$721$		−	14.9060i		−	0.555128i
$722$		0			0
$723$	5.31386	−	22.6179i	0.197625	−	0.841167i
$724$		0			0
$725$	−30.3505	−	52.5687i	−1.12719	−	1.95235i
$726$		0			0
$727$	11.5000	+	19.9186i	0.426511	+	0.738739i	0.996560	−	0.0828714i	$-0.0264091\pi$
$727$	11.5000	+	19.9186i	0.426511	+	0.738739i	−0.570049	+	0.821611i	$0.693076\pi$
$728$		0			0
$729$	5.00000	+	26.5330i	0.185185	+	0.982704i
$730$		0			0
$731$	22.5475	+	13.0178i	0.833951	+	0.481482i
$732$		0			0
$733$	2.00000			0.0738717			0.0369358	−	0.999318i	$-0.488240\pi$
$733$	2.00000			0.0738717			0.0369358	+	0.999318i	$0.488240\pi$
$734$		0			0
$735$	−7.37228	−	6.92820i	−0.271931	−	0.255551i
$736$		0			0
$737$	−1.37228	+	2.37686i	−0.0505486	+	0.0875528i
$738$		0			0
$739$	−6.50000	−	11.2583i	−0.239106	−	0.414144i	0.721352	−	0.692569i	$-0.243521\pi$
$739$	−6.50000	−	11.2583i	−0.239106	−	0.414144i	−0.960458	+	0.278425i	$0.910188\pi$
$740$		0			0
$741$	−2.31386	−	12.8704i	−0.0850017	−	0.472804i
$742$		0			0
$743$	−23.0584	−	39.9384i	−0.845931	−	1.46520i	−0.884810	−	0.465952i	$-0.845712\pi$
$743$	−23.0584	−	39.9384i	−0.845931	−	1.46520i	0.0388784	−	0.999244i	$-0.487622\pi$
$744$		0			0
$745$	−40.6644	+	70.4328i	−1.48983	+	2.58046i
$746$		0			0
$747$	−14.1168	−	21.2819i	−0.516508	−	0.778666i
$748$		0			0
$749$	13.0217			0.475804
$750$		0			0
$751$	−19.8505	−	11.4607i	−0.724356	−	0.418207i	0.0919977	−	0.995759i	$-0.470675\pi$
$751$	−19.8505	−	11.4607i	−0.724356	−	0.418207i	−0.816354	+	0.577552i	$0.804008\pi$
$752$		0			0
$753$	6.54755	−	27.8689i	0.238606	−	1.01560i
$754$		0			0
$755$	7.37228	+	12.7692i	0.268305	+	0.464718i
$756$		0			0
$757$	−11.5000	−	19.9186i	−0.417975	−	0.723953i	0.577761	−	0.816206i	$-0.303927\pi$
$757$	−11.5000	−	19.9186i	−0.417975	−	0.723953i	−0.995736	+	0.0922527i	$0.970593\pi$
$758$		0			0
$759$	−11.3723	−	2.67181i	−0.412788	−	0.0969807i
$760$		0			0
$761$		−	13.2665i		−	0.480910i	−0.970660	−	0.240455i	$-0.922703\pi$
$761$		−	13.2665i		−	0.480910i	0.970660	−	0.240455i	$-0.0772967\pi$
$762$		0			0
$763$	26.2337	−	15.1460i	0.949723	−	0.548323i
$764$		0			0
$765$	−2.11684	−	34.0511i	−0.0765347	−	1.23112i
$766$		0			0
$767$			12.7692i			0.461068i
$768$		0			0
$769$	16.3614	−	28.3388i	0.590007	−	1.02192i	−0.404223	−	0.914660i	$-0.632458\pi$
$769$	16.3614	−	28.3388i	0.590007	−	1.02192i	0.994231	−	0.107262i	$-0.0342085\pi$
$770$		0			0
$771$	−3.17527	−	0.746000i	−0.114354	−	0.0268665i
$772$		0			0
$773$	−0.430703	+	0.746000i	−0.0154913	+	0.0268318i	−0.873667	−	0.486524i	$-0.838265\pi$
$773$	−0.430703	+	0.746000i	−0.0154913	+	0.0268318i	0.858176	+	0.513356i	$0.171598\pi$
$774$		0			0
$775$	−86.0258	−	49.6670i	−3.09014	−	1.78409i
$776$		0			0
$777$	−16.1644	+	4.87375i	−0.579894	+	0.174845i
$778$		0			0
$779$	−35.4090	−	26.2843i	−1.26866	−	0.941734i
$780$		0			0
$781$	13.8832	−	8.01544i	0.496778	−	0.286815i
$782$		0			0
$783$	−22.5475	+	8.35668i	−0.805784	+	0.298644i
$784$		0			0
$785$	−48.7812	−	28.1639i	−1.74108	−	1.00521i
$786$		0			0
$787$			22.7190i			0.809846i	0.914351	+	0.404923i	$0.132702\pi$
$787$			22.7190i			0.809846i	−0.914351	+	0.404923i	$0.867298\pi$
$788$		0			0
$789$	20.8614	+	19.6048i	0.742686	+	0.697949i
$790$		0			0
$791$	−6.51087			−0.231500
$792$		0			0
$793$	14.6168	−	8.43904i	0.519059	−	0.299679i
$794$		0			0
$795$	−52.0367	+	15.6896i	−1.84555	+	0.556454i
$796$		0			0
$797$	−3.76631			−0.133410			−0.0667048	−	0.997773i	$-0.521249\pi$
$797$	−3.76631			−0.133410			−0.0667048	+	0.997773i	$0.521249\pi$
$798$		0			0
$799$	7.13859			0.252545
$800$		0			0
$801$	−1.37228	−	22.0742i	−0.0484872	−	0.779955i
$802$		0			0
$803$	3.09509	−	1.78695i	0.109224	−	0.0630602i
$804$		0			0
$805$	42.9783			1.51478
$806$		0			0
$807$	8.74456	−	9.30506i	0.307823	−	0.327554i
$808$		0			0
$809$			5.74839i			0.202103i	0.994881	+	0.101051i	$0.0322206\pi$
$809$			5.74839i			0.202103i	−0.994881	+	0.101051i	$0.967779\pi$
$810$		0			0
$811$	38.4090	+	22.1754i	1.34872	+	0.778684i	0.988068	−	0.154016i	$-0.0492207\pi$
$811$	38.4090	+	22.1754i	1.34872	+	0.778684i	0.360652	+	0.932700i	$0.382554\pi$
$812$		0			0
$813$	−7.25544	+	7.72049i	−0.254459	+	0.270769i
$814$		0			0
$815$	40.9783	−	23.6588i	1.43541	−	0.828732i
$816$		0			0
$817$	34.1060	+	25.3171i	1.19322	+	0.885734i
$818$		0			0
$819$	−12.3030	+	0.764836i	−0.429901	+	0.0267255i
$820$		0			0
$821$	12.4307	+	7.17687i	0.433835	+	0.250474i	0.700979	−	0.713182i	$-0.252747\pi$
$821$	12.4307	+	7.17687i	0.433835	+	0.250474i	−0.267144	+	0.963657i	$0.586080\pi$
$822$		0			0
$823$	−7.05842	+	12.2255i	−0.246041	+	0.426156i	−0.962424	−	0.271552i	$-0.912463\pi$
$823$	−7.05842	+	12.2255i	−0.246041	+	0.426156i	0.716383	+	0.697708i	$0.245796\pi$
$824$		0			0
$825$	−8.23369	+	35.0458i	−0.286660	+	1.22014i
$826$		0			0
$827$	19.8030	−	34.2998i	0.688617	−	1.19272i	−0.283668	−	0.958923i	$-0.591551\pi$
$827$	19.8030	−	34.2998i	0.688617	−	1.19272i	0.972285	−	0.233798i	$-0.0751153\pi$
$828$		0			0
$829$		−	5.39853i		−	0.187499i	−0.995596	−	0.0937494i	$-0.970115\pi$
$829$		−	5.39853i		−	0.187499i	0.995596	−	0.0937494i	$-0.0298852\pi$
$830$		0			0
$831$	4.25544	+	14.1137i	0.147619	+	0.489598i
$832$		0			0
$833$	3.17527	−	1.83324i	0.110016	−	0.0635180i
$834$		0			0
$835$			54.7431i			1.89446i
$836$		0			0
$837$	−25.1168	+	30.2921i	−0.868165	+	1.04705i
$838$		0			0
$839$	12.9416	+	22.4155i	0.446793	+	0.773868i	0.998175	−	0.0603847i	$-0.0192328\pi$
$839$	12.9416	+	22.4155i	0.446793	+	0.773868i	−0.551382	+	0.834253i	$0.685899\pi$
$840$		0			0
$841$	3.79211	+	6.56813i	0.130762	+	0.226487i
$842$		0			0
$843$	−21.6861	−	5.09496i	−0.746910	−	0.175480i
$844$		0			0
$845$	−36.8614	−	21.2819i	−1.26807	−	0.732121i
$846$		0			0
$847$	20.1386			0.691970
$848$		0			0
$849$	13.4891	−	14.3537i	0.462946	−	0.492619i
$850$		0			0
$851$	−8.74456	+	15.1460i	−0.299760	+	0.519199i
$852$		0			0
$853$	26.7337	+	46.3041i	0.915344	+	1.58542i	0.806397	+	0.591375i	$0.201415\pi$
$853$	26.7337	+	46.3041i	0.915344	+	1.58542i	0.108947	+	0.994048i	$0.465252\pi$
$854$		0			0
$855$	2.94158	−	55.5817i	0.100600	−	1.90085i
$856$		0			0
$857$	7.80298	+	13.5152i	0.266545	+	0.461669i	0.967967	−	0.251077i	$-0.0807846\pi$
$857$	7.80298	+	13.5152i	0.266545	+	0.461669i	−0.701422	+	0.712746i	$0.747451\pi$
$858$		0			0
$859$	−22.1060	+	38.2887i	−0.754246	+	1.30639i	0.191502	+	0.981492i	$0.438664\pi$
$859$	−22.1060	+	38.2887i	−0.754246	+	1.30639i	−0.945748	+	0.324900i	$0.894669\pi$
$860$		0			0
$861$	−28.4674	+	30.2921i	−0.970166	+	1.03235i
$862$		0			0
$863$	40.4674			1.37753			0.688763	−	0.724987i	$-0.258154\pi$
$863$	40.4674			1.37753			0.688763	+	0.724987i	$0.258154\pi$
$864$		0			0
$865$	17.0584	+	9.84868i	0.580004	+	0.334865i
$866$		0			0
$867$	−16.6277	−	3.90653i	−0.564707	−	0.132673i
$868$		0			0
$869$	−7.88316	−	13.6540i	−0.267418	−	0.463181i
$870$		0			0
$871$	1.50000	+	2.59808i	0.0508256	+	0.0880325i
$872$		0			0
$873$	23.4090	−	47.0689i	0.792273	−	1.59304i
$874$		0			0
$875$		−	81.9586i		−	2.77071i
$876$		0			0
$877$	5.26631	−	3.04051i	0.177831	−	0.102671i	−0.408442	−	0.912784i	$-0.633928\pi$
$877$	5.26631	−	3.04051i	0.177831	−	0.102671i	0.586273	+	0.810114i	$0.300595\pi$
$878$		0			0
$879$	10.1168	+	33.5538i	0.341233	+	1.13174i
$880$		0			0
$881$			0.589907i			0.0198745i	0.999951	+	0.00993724i	$0.00316317\pi$
$881$			0.589907i			0.0198745i	−0.999951	+	0.00993724i	$0.996837\pi$
$882$		0			0
$883$	18.8723	−	32.6878i	0.635103	−	1.10003i	−0.351391	−	0.936229i	$-0.614291\pi$
$883$	18.8723	−	32.6878i	0.635103	−	1.10003i	0.986493	−	0.163801i	$-0.0523756\pi$
$884$		0			0
$885$	−12.4307	+	52.9099i	−0.417854	+	1.77855i
$886$		0			0
$887$	23.0584	−	39.9384i	0.774226	−	1.34100i	−0.161002	−	0.986954i	$-0.551473\pi$
$887$	23.0584	−	39.9384i	0.774226	−	1.34100i	0.935228	−	0.354045i	$-0.115194\pi$
$888$		0			0
$889$	−4.88316	−	2.81929i	−0.163776	−	0.0945560i
$890$		0			0
$891$	13.1386	+	5.54601i	0.440159	+	0.185798i
$892$		0			0
$893$	11.5693	+	1.33591i	0.387152	+	0.0447044i
$894$		0			0
$895$	44.2337	−	25.5383i	1.47857	−	0.853652i
$896$		0			0
$897$	−8.74456	+	9.30506i	−0.291972	+	0.310687i
$898$		0			0
$899$	−30.3505	−	17.5229i	−1.01225	−	0.584421i
$900$		0			0
$901$		−	19.6974i		−	0.656215i
$902$		0			0
$903$	27.4198	−	29.1774i	0.912475	−	0.970962i
$904$		0			0
$905$	−4.62772			−0.153831
$906$		0			0
$907$	−36.1753	+	20.8858i	−1.20118	+	0.693502i	−0.960818	−	0.277182i	$-0.910600\pi$
$907$	−36.1753	+	20.8858i	−1.20118	+	0.693502i	−0.240362	+	0.970683i	$0.577266\pi$
$908$		0			0
$909$	−1.48913	+	0.0925740i	−0.0493912	+	0.00307048i
$910$		0			0
$911$		0			0			−	1.00000i	$-0.5\pi$
$911$		0			0				1.00000i	$0.5\pi$
$912$		0			0
$913$	−13.4891			−0.446425
$914$		0			0
$915$	68.7812	−	20.7383i	2.27384	−	0.685588i
$916$		0			0
$917$	5.48913	−	3.16915i	0.181267	−	0.104654i
$918$		0			0
$919$	−0.883156			−0.0291326			−0.0145663	−	0.999894i	$-0.504637\pi$
$919$	−0.883156			−0.0291326			−0.0145663	+	0.999894i	$0.504637\pi$
$920$		0			0
$921$	−14.4891	−	13.6164i	−0.477433	−	0.448674i
$922$		0			0
$923$		−	17.5229i		−	0.576773i
$924$		0			0
$925$	46.6753	+	26.9480i	1.53467	+	0.886044i
$926$		0			0
$927$	10.4198	+	15.7085i	0.342232	+	0.515934i
$928$		0			0
$929$	−48.7812	+	28.1639i	−1.60046	+	0.924026i	−0.609066	+	0.793120i	$0.708455\pi$
$929$	−48.7812	+	28.1639i	−1.60046	+	0.924026i	−0.991395	+	0.130906i	$0.958211\pi$
$930$		0			0
$931$	5.48913	−	2.37686i	0.179899	−	0.0778985i
$932$		0			0
$933$	20.3505	−	6.13592i	0.666247	−	0.200881i
$934$		0			0
$935$	−15.6060	−	9.01011i	−0.510370	−	0.294662i
$936$		0			0
$937$	−13.7337	+	23.7874i	−0.448660	+	0.777102i	−0.998299	−	0.0583003i	$-0.981432\pi$
$937$	−13.7337	+	23.7874i	−0.448660	+	0.777102i	0.549639	+	0.835402i	$0.314765\pi$
$938$		0			0
$939$	−6.54755	−	1.53829i	−0.213671	−	0.0502001i
$940$		0			0
$941$	11.5693	−	20.0386i	0.377148	−	0.653240i	−0.613498	−	0.789696i	$-0.710238\pi$
$941$	11.5693	−	20.0386i	0.377148	−	0.653240i	0.990646	+	0.136456i	$0.0435714\pi$
$942$		0			0
$943$			43.0612i			1.40227i
$944$		0			0
$945$	−51.7228	−	8.80773i	−1.68254	−	0.286516i
$946$		0			0
$947$	−29.9198	+	17.2742i	−0.972264	+	0.561337i	−0.899926	−	0.436043i	$-0.856379\pi$
$947$	−29.9198	+	17.2742i	−0.972264	+	0.561337i	−0.0723382	+	0.997380i	$0.523046\pi$
$948$		0			0
$949$		−	3.90653i		−	0.126811i
$950$		0			0
$951$	−3.17527	−	0.746000i	−0.102965	−	0.0241907i
$952$		0			0
$953$	5.56930	+	9.64630i	0.180407	+	0.312474i	0.942019	−	0.335559i	$-0.108925\pi$
$953$	5.56930	+	9.64630i	0.180407	+	0.312474i	−0.761612	+	0.648033i	$0.775592\pi$
$954$		0			0
$955$	−16.8614	−	29.2048i	−0.545622	−	0.945046i
$956$		0			0
$957$	−2.90491	+	12.3644i	−0.0939023	+	0.399684i
$958$		0			0
$959$	−46.9783	−	27.1229i	−1.51701	−	0.875844i
$960$		0			0
$961$	−26.3505			−0.850017
$962$		0			0
$963$	−13.7228	+	9.10268i	−0.442211	+	0.293330i
$964$		0			0
$965$	−25.8030	+	44.6921i	−0.830627	+	1.43869i
$966$		0			0
$967$	19.7337	+	34.1798i	0.634593	+	1.09915i	0.986601	+	0.163150i	$0.0521654\pi$
$967$	19.7337	+	34.1798i	0.634593	+	1.09915i	−0.352009	+	0.935997i	$0.614501\pi$
$968$		0			0
$969$	18.9783	+	6.83563i	0.609669	+	0.219592i
$970$		0			0
$971$	24.4307	+	42.3152i	0.784019	+	1.35796i	0.929584	+	0.368611i	$0.120167\pi$
$971$	24.4307	+	42.3152i	0.784019	+	1.35796i	−0.145565	+	0.989349i	$0.546500\pi$
$972$		0			0
$973$	20.1644	−	34.9258i	0.646441	−	1.11967i
$974$		0			0
$975$	28.6753	+	26.9480i	0.918343	+	0.863026i
$976$		0			0
$977$	38.7446			1.23955			0.619774	−	0.784780i	$-0.287224\pi$
$977$	38.7446			1.23955			0.619774	+	0.784780i	$0.287224\pi$
$978$		0			0
$979$	−10.1168	−	5.84096i	−0.323336	−	0.186678i
$980$		0			0
$981$	−17.0584	+	34.2998i	−0.544633	+	1.09511i
$982$		0			0
$983$	26.6644	+	46.1841i	0.850462	+	1.47304i	0.880792	+	0.473503i	$0.157011\pi$
$983$	26.6644	+	46.1841i	0.850462	+	1.47304i	−0.0303300	+	0.999540i	$0.509656\pi$
$984$		0			0
$985$	−8.00000	−	13.8564i	−0.254901	−	0.441502i
$986$		0			0
$987$	2.51087	−	10.6873i	0.0799220	−	0.340179i
$988$		0			0
$989$		−	41.4766i		−	1.31888i
$990$		0			0
$991$	−51.7337	+	29.8685i	−1.64337	+	0.948803i	−0.663753	+	0.747952i	$0.731037\pi$
$991$	−51.7337	+	29.8685i	−1.64337	+	0.948803i	−0.979622	+	0.200851i	$0.935629\pi$
$992$		0			0
$993$	−24.0475	+	7.25061i	−0.763126	+	0.230091i
$994$		0			0
$995$			15.9383i			0.505279i
$996$		0			0
$997$	1.61684	−	2.80046i	0.0512060	−	0.0886913i	−0.839286	−	0.543690i	$-0.817027\pi$
$997$	1.61684	−	2.80046i	0.0512060	−	0.0886913i	0.890492	+	0.454998i	$0.150360\pi$
$998$		0			0
$999$	13.6277	−	16.4356i	0.431162	−	0.520001i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	912.2.bn.l.449.2		4
3.2	odd	2		912.2.bn.k.449.1		4
4.3	odd	2		228.2.p.c.221.1	yes	4
12.11	even	2		228.2.p.d.221.2	yes	4
19.8	odd	6		912.2.bn.k.65.1		4
57.8	even	6	inner	912.2.bn.l.65.1		4
76.27	even	6		228.2.p.d.65.2	yes	4
228.179	odd	6		228.2.p.c.65.2	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.2.p.c.65.2	✓	4	228.179	odd	6
228.2.p.c.221.1	yes	4	4.3	odd	2
228.2.p.d.65.2	yes	4	76.27	even	6
228.2.p.d.221.2	yes	4	12.11	even	2
912.2.bn.k.65.1		4	19.8	odd	6
912.2.bn.k.449.1		4	3.2	odd	2
912.2.bn.l.65.1		4	57.8	even	6	inner
912.2.bn.l.449.2		4	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 912 = 2^{4} \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	912.bn (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 1.65831i) q^{3} +(3.68614 - 2.12819i) q^{5} +2.37228 q^{7} +(-2.50000 + 1.65831i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 1.65831i) q^{3} +(3.68614 - 2.12819i) q^{5} +2.37228 q^{7} +(-2.50000 + 1.65831i) q^{9} +1.58457i q^{11} +(1.50000 + 0.866025i) q^{13} +(5.37228 + 5.04868i) q^{15} +(-2.31386 + 1.33591i) q^{17} +(-4.00000 + 1.73205i) q^{19} +(1.18614 + 3.93398i) q^{21} +(3.68614 + 2.12819i) q^{23} +(6.55842 - 11.3595i) q^{25} +(-4.00000 - 3.31662i) q^{27} +(2.31386 - 4.00772i) q^{29} -7.57301i q^{31} +(-2.62772 + 0.792287i) q^{33} +(8.74456 - 5.04868i) q^{35} +4.10891i q^{37} +(-0.686141 + 2.92048i) q^{39} +(5.05842 + 8.76144i) q^{41} +(-4.87228 - 8.43904i) q^{43} +(-5.68614 + 11.4333i) q^{45} +(-2.31386 - 1.33591i) q^{47} -1.37228 q^{49} +(-3.37228 - 3.16915i) q^{51} +(-3.68614 + 6.38458i) q^{53} +(3.37228 + 5.84096i) q^{55} +(-4.87228 - 5.76722i) q^{57} +(3.68614 + 6.38458i) q^{59} +(4.87228 - 8.43904i) q^{61} +(-5.93070 + 3.93398i) q^{63} +7.37228 q^{65} +(1.50000 + 0.866025i) q^{67} +(-1.68614 + 7.17687i) q^{69} +(-5.05842 - 8.76144i) q^{71} +(-1.12772 - 1.95327i) q^{73} +(22.1168 + 5.19615i) q^{75} +3.75906i q^{77} +(-8.61684 + 4.97494i) q^{79} +(3.50000 - 8.29156i) q^{81} +8.51278i q^{83} +(-5.68614 + 9.84868i) q^{85} +(7.80298 + 1.83324i) q^{87} +(-3.68614 + 6.38458i) q^{89} +(3.55842 + 2.05446i) q^{91} +(12.5584 - 3.78651i) q^{93} +(-11.0584 + 14.8974i) q^{95} +(-15.1753 + 8.76144i) q^{97} +(-2.62772 - 3.96143i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{3} + 9 q^{5} - 2 q^{7} - 10 q^{9}+O(q^{10}) \) 4 * q + 2 * q^3 + 9 * q^5 - 2 * q^7 - 10 * q^9	\( 4 q + 2 q^{3} + 9 q^{5} - 2 q^{7} - 10 q^{9} + 6 q^{13} + 10 q^{15} - 15 q^{17} - 16 q^{19} - q^{21} + 9 q^{23} + 9 q^{25} - 16 q^{27} + 15 q^{29} - 22 q^{33} + 12 q^{35} + 3 q^{39} + 3 q^{41} - 8 q^{43} - 17 q^{45} - 15 q^{47} + 6 q^{49} - 2 q^{51} - 9 q^{53} + 2 q^{55} - 8 q^{57} + 9 q^{59} + 8 q^{61} + 5 q^{63} + 18 q^{65} + 6 q^{67} - q^{69} - 3 q^{71} - 16 q^{73} + 54 q^{75} + 14 q^{81} - 17 q^{85} - 9 q^{87} - 9 q^{89} - 3 q^{91} + 33 q^{93} - 27 q^{95} - 9 q^{97} - 22 q^{99}+O(q^{100}) \) 4 * q + 2 * q^3 + 9 * q^5 - 2 * q^7 - 10 * q^9 + 6 * q^13 + 10 * q^15 - 15 * q^17 - 16 * q^19 - q^21 + 9 * q^23 + 9 * q^25 - 16 * q^27 + 15 * q^29 - 22 * q^33 + 12 * q^35 + 3 * q^39 + 3 * q^41 - 8 * q^43 - 17 * q^45 - 15 * q^47 + 6 * q^49 - 2 * q^51 - 9 * q^53 + 2 * q^55 - 8 * q^57 + 9 * q^59 + 8 * q^61 + 5 * q^63 + 18 * q^65 + 6 * q^67 - q^69 - 3 * q^71 - 16 * q^73 + 54 * q^75 + 14 * q^81 - 17 * q^85 - 9 * q^87 - 9 * q^89 - 3 * q^91 + 33 * q^93 - 27 * q^95 - 9 * q^97 - 22 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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