LMFDB - Embedded newform 950.2.q.e.407.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [950,2,Mod(107,950)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(950, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([3, 10]))

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

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

chi := DirichletCharacter("950.107");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 950 = 2 \cdot 5^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	950.q (of order $12$, degree $4$, 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:	$7.58578819202$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			407.3
Character	$\chi$	$=$	950.407
Dual form			950.2.q.e.943.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(3.03794 - 0.814012i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.57255 - 2.72374i) q^{6} +(-2.05625 - 2.05625i) q^{7} +(0.707107 + 0.707107i) q^{8} +(5.96836 - 3.44584i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(3.03794 - 0.814012i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.57255 - 2.72374i) q^{6} +(-2.05625 - 2.05625i) q^{7} +(0.707107 + 0.707107i) q^{8} +(5.96836 - 3.44584i) q^{9} -5.34803 q^{11} +(-2.22392 + 2.22392i) q^{12} +(1.00724 - 3.75907i) q^{13} +(-1.45399 + 2.51839i) q^{14} +(0.500000 - 0.866025i) q^{16} +(2.56613 - 0.687594i) q^{17} +(-4.87315 - 4.87315i) q^{18} +(-3.18604 - 2.97475i) q^{19} +(-7.92059 - 4.57295i) q^{21} +(1.38417 + 5.16580i) q^{22} +(2.80890 + 0.752641i) q^{23} +(2.72374 + 1.57255i) q^{24} -3.89167 q^{26} +(8.65478 - 8.65478i) q^{27} +(2.80890 + 0.752641i) q^{28} +(3.53118 + 6.11619i) q^{29} -8.91158i q^{31} +(-0.965926 - 0.258819i) q^{32} +(-16.2470 + 4.35337i) q^{33} +(-1.32833 - 2.30073i) q^{34} +(-3.44584 + 5.96836i) q^{36} +(-3.67903 + 3.67903i) q^{37} +(-2.04878 + 3.84740i) q^{38} -12.2397i q^{39} +(4.61619 + 2.66516i) q^{41} +(-2.36713 + 8.83426i) q^{42} +(1.74459 + 6.51089i) q^{43} +(4.63153 - 2.67402i) q^{44} -2.90798i q^{46} +(0.622546 - 2.32337i) q^{47} +(0.814012 - 3.03794i) q^{48} +1.45636i q^{49} +(7.23604 - 4.17773i) q^{51} +(1.00724 + 3.75907i) q^{52} +(0.917161 - 3.42289i) q^{53} +(-10.5999 - 6.11985i) q^{54} -2.90798i q^{56} +(-12.1005 - 6.44362i) q^{57} +(4.99385 - 4.99385i) q^{58} +(4.58145 - 7.93531i) q^{59} +(0.199267 + 0.345141i) q^{61} +(-8.60792 + 2.30649i) q^{62} +(-19.3580 - 5.18696i) q^{63} +1.00000i q^{64} +(8.41006 + 14.5666i) q^{66} +(0.0355206 + 0.00951772i) q^{67} +(-1.87854 + 1.87854i) q^{68} +9.14590 q^{69} +(3.91692 + 2.26144i) q^{71} +(6.65684 + 1.78370i) q^{72} +(4.16029 + 15.5264i) q^{73} +(4.50587 + 2.60147i) q^{74} +(4.24657 + 0.983188i) q^{76} +(10.9969 + 10.9969i) q^{77} +(-11.8226 + 3.16787i) q^{78} +(1.15259 - 1.99634i) q^{79} +(8.91006 - 15.4327i) q^{81} +(1.37959 - 5.14869i) q^{82} +(3.45871 - 3.45871i) q^{83} +9.14590 q^{84} +(5.83751 - 3.37029i) q^{86} +(15.7062 + 15.7062i) q^{87} +(-3.78163 - 3.78163i) q^{88} +(6.68199 + 11.5735i) q^{89} +(-9.80073 + 5.65846i) q^{91} +(-2.80890 + 0.752641i) q^{92} +(-7.25414 - 27.0728i) q^{93} -2.40533 q^{94} -3.14510 q^{96} +(3.59188 + 13.4051i) q^{97} +(1.40674 - 0.376934i) q^{98} +(-31.9190 + 18.4284i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{6}+O(q^{10}) $ 24 * q - 12 * q^6	$ 24 q - 12 q^{6} - 48 q^{11} + 12 q^{16} - 84 q^{21} + 24 q^{26} - 24 q^{36} + 48 q^{41} + 12 q^{51} + 12 q^{61} + 24 q^{71} + 36 q^{76} + 12 q^{81} - 36 q^{86} - 228 q^{91} - 24 q^{96}+O(q^{100}) $ 24 * q - 12 * q^6 - 48 * q^11 + 12 * q^16 - 84 * q^21 + 24 * q^26 - 24 * q^36 + 48 * q^41 + 12 * q^51 + 12 * q^61 + 24 * q^71 + 36 * q^76 + 12 * q^81 - 36 * q^86 - 228 * q^91 - 24 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	3.03794	−	0.814012i	1.75395	−	0.469970i	0.768490	−	0.639861i	$-0.221008\pi$
$3$	3.03794	−	0.814012i	1.75395	−	0.469970i	0.985463	+	0.169891i	$0.0543416\pi$
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$		0			0
$5$		0			0
$6$	−1.57255	−	2.72374i	−0.641991	−	1.11196i
$7$	−2.05625	−	2.05625i	−0.777191	−	0.777191i	0.202161	−	0.979352i	$-0.435204\pi$
$7$	−2.05625	−	2.05625i	−0.777191	−	0.777191i	−0.979352	+	0.202161i	$0.935204\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	5.96836	−	3.44584i	1.98945	−	1.14861i
$10$		0			0
$11$	−5.34803			−1.61249			−0.806246	−	0.591580i	$-0.798504\pi$
$11$	−5.34803			−1.61249			−0.806246	+	0.591580i	$0.798504\pi$
$12$	−2.22392	+	2.22392i	−0.641991	+	0.641991i
$13$	1.00724	−	3.75907i	0.279358	−	1.04258i	−0.673507	−	0.739181i	$-0.735213\pi$
$13$	1.00724	−	3.75907i	0.279358	−	1.04258i	0.952865	−	0.303396i	$-0.0981205\pi$
$14$	−1.45399	+	2.51839i	−0.388596	+	0.673067i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.56613	−	0.687594i	0.622379	−	0.166766i	0.0661699	−	0.997808i	$-0.478922\pi$
$17$	2.56613	−	0.687594i	0.622379	−	0.166766i	0.556209	+	0.831042i	$0.312255\pi$
$18$	−4.87315	−	4.87315i	−1.14861	−	1.14861i
$19$	−3.18604	−	2.97475i	−0.730928	−	0.682454i
$19$	−3.18604	−	2.97475i	−0.730928	−	0.682454i
$20$		0			0
$21$	−7.92059	−	4.57295i	−1.72841	−	0.997900i
$22$	1.38417	+	5.16580i	0.295107	+	1.10135i
$23$	2.80890	+	0.752641i	0.585695	+	0.156937i	0.539485	−	0.841995i	$-0.318619\pi$
$23$	2.80890	+	0.752641i	0.585695	+	0.156937i	0.0462102	+	0.998932i	$0.485286\pi$
$24$	2.72374	+	1.57255i	0.555981	+	0.320996i
$25$		0			0
$26$	−3.89167			−0.763219
$27$	8.65478	−	8.65478i	1.66561	−	1.66561i
$28$	2.80890	+	0.752641i	0.530831	+	0.142236i
$29$	3.53118	+	6.11619i	0.655724	+	1.13575i	0.981712	+	0.190374i	$0.0609699\pi$
$29$	3.53118	+	6.11619i	0.655724	+	1.13575i	−0.325987	+	0.945374i	$0.605697\pi$
$30$		0			0
$31$		−	8.91158i		−	1.60057i	−0.599622	−	0.800283i	$-0.704682\pi$
$31$		−	8.91158i		−	1.60057i	0.599622	−	0.800283i	$-0.295318\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−16.2470	+	4.35337i	−2.82824	+	0.757824i
$34$	−1.32833	−	2.30073i	−0.227806	−	0.394572i
$35$		0			0
$36$	−3.44584	+	5.96836i	−0.574306	+	0.994727i
$37$	−3.67903	+	3.67903i	−0.604828	+	0.604828i	−0.941590	−	0.336762i	$-0.890668\pi$
$37$	−3.67903	+	3.67903i	−0.604828	+	0.604828i	0.336762	+	0.941590i	$0.390668\pi$
$38$	−2.04878	+	3.84740i	−0.332356	+	0.624131i
$39$		−	12.2397i		−	1.95992i
$40$		0			0
$41$	4.61619	+	2.66516i	0.720928	+	0.416228i	0.815094	−	0.579329i	$-0.196685\pi$
$41$	4.61619	+	2.66516i	0.720928	+	0.416228i	−0.0941664	+	0.995556i	$0.530019\pi$
$42$	−2.36713	+	8.83426i	−0.365257	+	1.36316i
$43$	1.74459	+	6.51089i	0.266047	+	0.992902i	0.961606	+	0.274433i	$0.0884901\pi$
$43$	1.74459	+	6.51089i	0.266047	+	0.992902i	−0.695559	+	0.718469i	$0.744843\pi$
$44$	4.63153	−	2.67402i	0.698230	−	0.403123i
$45$		0			0
$46$		−	2.90798i		−	0.428759i
$47$	0.622546	−	2.32337i	0.0908076	−	0.338899i	−0.905543	−	0.424255i	$-0.860536\pi$
$47$	0.622546	−	2.32337i	0.0908076	−	0.338899i	0.996351	+	0.0853560i	$0.0272028\pi$
$48$	0.814012	−	3.03794i	0.117493	−	0.438488i
$49$			1.45636i			0.208052i
$50$		0			0
$51$	7.23604	−	4.17773i	1.01325	−	0.584999i
$52$	1.00724	+	3.75907i	0.139679	+	0.521289i
$53$	0.917161	−	3.42289i	0.125982	−	0.470170i	−0.873891	−	0.486122i	$-0.838411\pi$
$53$	0.917161	−	3.42289i	0.125982	−	0.470170i	0.999873	+	0.0159517i	$0.00507779\pi$
$54$	−10.5999	−	6.11985i	−1.44246	−	0.832806i
$55$		0			0
$56$		−	2.90798i		−	0.388596i
$57$	−12.1005	−	6.44362i	−1.60275	−	0.853478i
$58$	4.99385	−	4.99385i	0.655724	−	0.655724i
$59$	4.58145	−	7.93531i	0.596454	−	1.03309i	−0.396886	−	0.917868i	$-0.629909\pi$
$59$	4.58145	−	7.93531i	0.596454	−	1.03309i	0.993340	−	0.115221i	$-0.0367576\pi$
$60$		0			0
$61$	0.199267	+	0.345141i	0.0255136	+	0.0441908i	0.878500	−	0.477742i	$-0.158545\pi$
$61$	0.199267	+	0.345141i	0.0255136	+	0.0441908i	−0.852987	+	0.521933i	$0.825211\pi$
$62$	−8.60792	+	2.30649i	−1.09321	+	0.292924i
$63$	−19.3580	−	5.18696i	−2.43888	−	0.653495i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	8.41006	+	14.5666i	1.03521	+	1.79303i
$67$	0.0355206	+	0.00951772i	0.00433953	+	0.00116277i	0.260988	−	0.965342i	$-0.415952\pi$
$67$	0.0355206	+	0.00951772i	0.00433953	+	0.00116277i	−0.256649	+	0.966505i	$0.582618\pi$
$68$	−1.87854	+	1.87854i	−0.227806	+	0.227806i
$69$	9.14590			1.10104
$70$		0			0
$71$	3.91692	+	2.26144i	0.464853	+	0.268383i	0.714083	−	0.700061i	$-0.246844\pi$
$71$	3.91692	+	2.26144i	0.464853	+	0.268383i	−0.249230	+	0.968444i	$0.580177\pi$
$72$	6.65684	+	1.78370i	0.784516	+	0.210211i
$73$	4.16029	+	15.5264i	0.486925	+	1.81723i	0.571234	+	0.820787i	$0.306465\pi$
$73$	4.16029	+	15.5264i	0.486925	+	1.81723i	−0.0843092	+	0.996440i	$0.526868\pi$
$74$	4.50587	+	2.60147i	0.523797	+	0.302414i
$75$		0			0
$76$	4.24657	+	0.983188i	0.487115	+	0.112779i
$77$	10.9969	+	10.9969i	1.25322	+	1.25322i
$78$	−11.8226	+	3.16787i	−1.33865	+	0.358690i
$79$	1.15259	−	1.99634i	0.129676	−	0.224605i	−0.793875	−	0.608081i	$-0.791940\pi$
$79$	1.15259	−	1.99634i	0.129676	−	0.224605i	0.923551	+	0.383476i	$0.125273\pi$
$80$		0			0
$81$	8.91006	−	15.4327i	0.990006	−	1.71474i
$82$	1.37959	−	5.14869i	0.152350	−	0.568578i
$83$	3.45871	−	3.45871i	0.379643	−	0.379643i	−0.491330	−	0.870973i	$-0.663489\pi$
$83$	3.45871	−	3.45871i	0.379643	−	0.379643i	0.870973	+	0.491330i	$0.163489\pi$
$84$	9.14590			0.997900
$85$		0			0
$86$	5.83751	−	3.37029i	0.629475	−	0.363427i
$87$	15.7062	+	15.7062i	1.68388	+	1.68388i
$88$	−3.78163	−	3.78163i	−0.403123	−	0.403123i
$89$	6.68199	+	11.5735i	0.708290	+	1.22679i	0.965491	+	0.260436i	$0.0838662\pi$
$89$	6.68199	+	11.5735i	0.708290	+	1.22679i	−0.257202	+	0.966358i	$0.582800\pi$
$90$		0			0
$91$	−9.80073	+	5.65846i	−1.02740	+	0.593167i
$92$	−2.80890	+	0.752641i	−0.292848	+	0.0784683i
$93$	−7.25414	−	27.0728i	−0.752219	−	2.80732i
$94$	−2.40533			−0.248091
$95$		0			0
$96$	−3.14510			−0.320996
$97$	3.59188	+	13.4051i	0.364700	+	1.36108i	0.867827	+	0.496866i	$0.165516\pi$
$97$	3.59188	+	13.4051i	0.364700	+	1.36108i	−0.503128	+	0.864212i	$0.667817\pi$
$98$	1.40674	−	0.376934i	0.142102	−	0.0380761i
$99$	−31.9190	+	18.4284i	−3.20798	+	1.85213i
$100$		0			0
$101$	−9.63824	−	16.6939i	−0.959041	−	1.66111i	−0.724838	−	0.688919i	$-0.758085\pi$
$101$	−9.63824	−	16.6939i	−0.959041	−	1.66111i	−0.234203	−	0.972188i	$-0.575248\pi$
$102$	−5.90820	−	5.90820i	−0.584999	−	0.584999i
$103$	10.5151	+	10.5151i	1.03608	+	1.03608i	0.999324	+	0.0367608i	$0.0117040\pi$
$103$	10.5151	+	10.5151i	1.03608	+	1.03608i	0.0367608	+	0.999324i	$0.488296\pi$
$104$	3.37029	−	1.94584i	0.330484	−	0.190805i
$105$		0			0
$106$	−3.54364			−0.344188
$107$	4.83744	−	4.83744i	0.467653	−	0.467653i	−0.433501	−	0.901153i	$-0.642722\pi$
$107$	4.83744	−	4.83744i	0.467653	−	0.467653i	0.901153	+	0.433501i	$0.142722\pi$
$108$	−3.16787	+	11.8226i	−0.304828	+	1.13763i
$109$	0.646547	−	1.11985i	0.0619280	−	0.107262i	−0.833399	−	0.552672i	$-0.813608\pi$
$109$	0.646547	−	1.11985i	0.0619280	−	0.107262i	0.895327	+	0.445409i	$0.146942\pi$
$110$		0			0
$111$	−8.18188	+	14.1714i	−0.776589	+	1.34509i
$112$	−2.80890	+	0.752641i	−0.265416	+	0.0711179i
$113$	4.45303	+	4.45303i	0.418906	+	0.418906i	0.884826	−	0.465921i	$-0.154277\pi$
$113$	4.45303	+	4.45303i	0.418906	+	0.418906i	−0.465921	+	0.884826i	$0.654277\pi$
$114$	−3.09223	+	13.3559i	−0.289614	+	1.25089i
$115$		0			0
$116$	−6.11619	−	3.53118i	−0.567874	−	0.327862i
$117$	−6.94156	−	25.9062i	−0.641747	−	2.39503i
$118$	−8.85069	−	2.37153i	−0.814772	−	0.218317i
$119$	−6.69049	−	3.86276i	−0.613316	−	0.354098i
$120$		0			0
$121$	17.6015			1.60013
$122$	0.281806	−	0.281806i	0.0255136	−	0.0255136i
$123$	16.1932	+	4.33894i	1.46009	+	0.391229i
$124$	4.45579	+	7.71765i	0.400142	+	0.693066i
$125$		0			0
$126$			20.0409i			1.78538i
$127$	−17.3531	−	4.64974i	−1.53984	−	0.412598i	−0.613623	−	0.789599i	$-0.710289\pi$
$127$	−17.3531	−	4.64974i	−1.53984	−	0.412598i	−0.926213	+	0.377001i	$0.876955\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	10.5999	+	18.3596i	0.933269	+	1.61647i
$130$		0			0
$131$	−8.08407	+	14.0020i	−0.706309	+	1.22336i	0.259908	+	0.965633i	$0.416308\pi$
$131$	−8.08407	+	14.0020i	−0.706309	+	1.22336i	−0.966217	+	0.257730i	$0.917026\pi$
$132$	11.8936	−	11.8936i	1.03521	−	1.03521i
$133$	0.434471	+	12.6682i	0.0376734	+	1.09847i
$134$		−	0.0367736i		−	0.00317676i
$135$		0			0
$136$	2.30073	+	1.32833i	0.197286	+	0.113903i
$137$	1.23125	−	4.59510i	0.105193	−	0.392586i	−0.893174	−	0.449711i	$-0.851527\pi$
$137$	1.23125	−	4.59510i	0.105193	−	0.392586i	0.998367	+	0.0571256i	$0.0181935\pi$
$138$	−2.36713	−	8.83426i	−0.201504	−	0.752023i
$139$	−12.3137	+	7.10932i	−1.04444	+	0.603005i	−0.921086	−	0.389358i	$-0.872697\pi$
$139$	−12.3137	+	7.10932i	−1.04444	+	0.603005i	−0.123349	+	0.992363i	$0.539363\pi$
$140$		0			0
$141$		−	7.56502i		−	0.637089i
$142$	1.17061	−	4.36876i	0.0982350	−	0.366618i
$143$	−5.38675	+	20.1036i	−0.450462	+	1.68115i
$144$		−	6.89167i		−	0.574306i
$145$		0			0
$146$	13.9206	−	8.03705i	1.15208	−	0.665151i
$147$	1.18550	+	4.42434i	0.0977782	+	0.364913i
$148$	1.34662	−	5.02565i	0.110691	−	0.413106i
$149$	−19.3039	−	11.1451i	−1.58144	−	0.913042i	−0.994650	−	0.103300i	$-0.967060\pi$
$149$	−19.3039	−	11.1451i	−1.58144	−	0.913042i	−0.586786	−	0.809742i	$-0.699607\pi$
$150$		0			0
$151$			0.824445i			0.0670924i	0.999437	+	0.0335462i	$0.0106801\pi$
$151$			0.824445i			0.0670924i	−0.999437	+	0.0335462i	$0.989320\pi$
$152$	−0.149406	−	4.35634i	−0.0121185	−	0.353346i
$153$	12.9463	−	12.9463i	1.04664	−	1.04664i
$154$	7.77599	−	13.4684i	0.626608	−	1.08532i
$155$		0			0
$156$	6.11985	+	10.5999i	0.489980	+	0.848671i
$157$	−1.91579	+	0.513335i	−0.152897	+	0.0409686i	−0.334456	−	0.942411i	$-0.608552\pi$
$157$	−1.91579	+	0.513335i	−0.152897	+	0.0409686i	0.181559	+	0.983380i	$0.441886\pi$
$158$	−2.22662	−	0.596622i	−0.177141	−	0.0474647i
$159$		−	11.1451i		−	0.883864i
$160$		0			0
$161$	−4.22818	−	7.32343i	−0.333227	−	0.577167i
$162$	−17.2129	−	4.61219i	−1.35237	−	0.362367i
$163$	0.272581	−	0.272581i	0.0213502	−	0.0213502i	−0.696351	−	0.717701i	$-0.745194\pi$
$163$	0.272581	−	0.272581i	0.0213502	−	0.0213502i	0.717701	+	0.696351i	$0.245194\pi$
$164$	−5.33032			−0.416228
$165$		0			0
$166$	−4.23604	−	2.44568i	−0.328781	−	0.189822i
$167$	−2.26803	−	0.607716i	−0.175505	−	0.0470265i	0.169996	−	0.985445i	$-0.445624\pi$
$167$	−2.26803	−	0.607716i	−0.175505	−	0.0470265i	−0.345501	+	0.938418i	$0.612291\pi$
$168$	−2.36713	−	8.83426i	−0.182628	−	0.681578i
$169$	−1.85771	−	1.07255i	−0.142901	−	0.0825039i
$170$		0			0
$171$	−29.2660	−	6.77581i	−2.23802	−	0.518159i
$172$	−4.76630	−	4.76630i	−0.363427	−	0.363427i
$173$	17.8985	−	4.79589i	1.36080	−	0.364625i	0.496689	−	0.867928i	$-0.334549\pi$
$173$	17.8985	−	4.79589i	1.36080	−	0.364625i	0.864110	+	0.503303i	$0.167882\pi$
$174$	11.1059	−	19.2360i	0.841939	−	1.45828i
$175$		0			0
$176$	−2.67402	+	4.63153i	−0.201562	+	0.349115i
$177$	7.45872	−	27.8363i	0.560632	−	2.09231i
$178$	9.44976	−	9.44976i	0.708290	−	0.708290i
$179$	6.96220			0.520380			0.260190	−	0.965557i	$-0.416215\pi$
$179$	6.96220			0.520380			0.260190	+	0.965557i	$0.416215\pi$
$180$		0			0
$181$	4.92059	−	2.84090i	0.365744	−	0.211163i	−0.305853	−	0.952079i	$-0.598942\pi$
$181$	4.92059	−	2.84090i	0.365744	−	0.211163i	0.671598	+	0.740916i	$0.265608\pi$
$182$	8.00226	+	8.00226i	0.593167	+	0.593167i
$183$	0.886310	+	0.886310i	0.0655179	+	0.0655179i
$184$	1.45399	+	2.51839i	0.107190	+	0.185658i
$185$		0			0
$186$	−24.2728	+	14.0139i	−1.77977	+	1.02755i
$187$	−13.7238	+	3.67727i	−1.00358	+	0.268909i
$188$	0.622546	+	2.32337i	0.0454038	+	0.169449i
$189$	−35.5928			−2.58900
$190$		0			0
$191$	−1.53631			−0.111163			−0.0555817	−	0.998454i	$-0.517701\pi$
$191$	−1.53631			−0.111163			−0.0555817	+	0.998454i	$0.517701\pi$
$192$	0.814012	+	3.03794i	0.0587463	+	0.219244i
$193$	−6.04035	+	1.61851i	−0.434794	+	0.116503i	−0.469576	−	0.882892i	$-0.655593\pi$
$193$	−6.04035	+	1.61851i	−0.434794	+	0.116503i	0.0347817	+	0.999395i	$0.488926\pi$
$194$	12.0187	−	6.93897i	0.862889	−	0.498189i
$195$		0			0
$196$	−0.728181	−	1.26125i	−0.0520130	−	0.0900891i
$197$	−2.31681	−	2.31681i	−0.165066	−	0.165066i	0.619741	−	0.784807i	$-0.287238\pi$
$197$	−2.31681	−	2.31681i	−0.165066	−	0.165066i	−0.784807	+	0.619741i	$0.787238\pi$
$198$	26.0618	+	26.0618i	1.85213	+	1.85213i
$199$	0.338795	−	0.195603i	0.0240165	−	0.0138660i	−0.487944	−	0.872875i	$-0.662253\pi$
$199$	0.338795	−	0.195603i	0.0240165	−	0.0138660i	0.511960	+	0.859009i	$0.328920\pi$
$200$		0			0
$201$	0.115657			0.00815780
$202$	−13.6305	+	13.6305i	−0.959041	+	0.959041i
$203$	5.31543	−	19.8374i	0.373070	−	1.39232i
$204$	−4.17773	+	7.23604i	−0.292500	+	0.506624i
$205$		0			0
$206$	7.43531	−	12.8783i	0.518042	−	0.897276i
$207$	19.3580	−	5.18696i	1.34547	−	0.360518i
$208$	−2.75183	−	2.75183i	−0.190805	−	0.190805i
$209$	17.0391	+	15.9091i	1.17862	+	1.10045i
$210$		0			0
$211$	17.4111	+	10.0523i	1.19863	+	0.692027i	0.960249	−	0.279145i	$-0.0900511\pi$
$211$	17.4111	+	10.0523i	1.19863	+	0.692027i	0.238377	+	0.971173i	$0.423384\pi$
$212$	0.917161	+	3.42289i	0.0629909	+	0.235085i
$213$	13.7402	+	3.68167i	0.941462	+	0.252264i
$214$	−5.92463	−	3.42059i	−0.404999	−	0.233826i
$215$		0			0
$216$	12.2397			0.832806
$217$	−18.3245	+	18.3245i	−1.24395	+	1.24395i
$218$	−1.24903	−	0.334677i	−0.0845952	−	0.0226672i
$219$	25.2774	+	43.7817i	1.70809	+	2.95849i
$220$		0			0
$221$		−	10.3388i		−	0.695465i
$222$	15.8062	+	4.23525i	1.06084	+	0.284251i
$223$	27.8452	−	7.46109i	1.86465	−	0.499632i	0.864654	−	0.502367i	$-0.167537\pi$
$223$	27.8452	−	7.46109i	1.86465	−	0.499632i	0.999996	+	0.00273558i	$0.000870762\pi$
$224$	1.45399	+	2.51839i	0.0971489	+	0.168267i
$225$		0			0
$226$	3.14877	−	5.45382i	0.209453	−	0.362783i
$227$	6.05756	−	6.05756i	0.402054	−	0.402054i	−0.476902	−	0.878956i	$-0.658240\pi$
$227$	6.05756	−	6.05756i	0.402054	−	0.402054i	0.878956	+	0.476902i	$0.158240\pi$
$228$	13.7011	−	0.469898i	0.907379	−	0.0311198i
$229$			2.35536i			0.155647i	0.996967	+	0.0778233i	$0.0247970\pi$
$229$			2.35536i			0.155647i	−0.996967	+	0.0778233i	$0.975203\pi$
$230$		0			0
$231$	42.3596	+	24.4563i	2.78705	+	1.60911i
$232$	−1.82787	+	6.82172i	−0.120006	+	0.447868i
$233$	4.02075	+	15.0056i	0.263408	+	0.983053i	0.963218	+	0.268723i	$0.0866016\pi$
$233$	4.02075	+	15.0056i	0.263408	+	0.983053i	−0.699809	+	0.714330i	$0.746732\pi$
$234$	−23.2269	+	13.4101i	−1.51839	+	0.876643i
$235$		0			0
$236$			9.16290i			0.596454i
$237$	1.87644	−	7.00296i	0.121888	−	0.454891i
$238$	−1.99951	+	7.46227i	−0.129609	+	0.483707i
$239$		−	21.1103i		−	1.36551i	−0.730646	−	0.682757i	$-0.760781\pi$
$239$		−	21.1103i		−	1.36551i	0.730646	−	0.682757i	$-0.239219\pi$
$240$		0			0
$241$	−24.8096	+	14.3238i	−1.59813	+	0.922679i	−0.606278	+	0.795253i	$0.707338\pi$
$241$	−24.8096	+	14.3238i	−1.59813	+	0.922679i	−0.991848	+	0.127426i	$0.959329\pi$
$242$	−4.55559	−	17.0017i	−0.292845	−	1.09291i
$243$	5.00219	−	18.6684i	0.320891	−	1.19758i
$244$	−0.345141	−	0.199267i	−0.0220954	−	0.0127568i
$245$		0			0
$246$		−	16.7644i		−	1.06886i
$247$	−14.3914	+	8.98026i	−0.915702	+	0.571400i
$248$	6.30144	−	6.30144i	0.400142	−	0.400142i
$249$	7.69191	−	13.3228i	0.487455	−	0.844297i
$250$		0			0
$251$	−0.590938	−	1.02353i	−0.0372997	−	0.0646050i	0.846773	−	0.531955i	$-0.178542\pi$
$251$	−0.590938	−	1.02353i	−0.0372997	−	0.0646050i	−0.884073	+	0.467350i	$0.845209\pi$
$252$	19.3580	−	5.18696i	1.21944	−	0.326748i
$253$	−15.0221	−	4.02515i	−0.944429	−	0.253059i
$254$			17.9652i			1.12724i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	15.8265	+	4.24070i	0.987230	+	0.264528i	0.716087	−	0.698011i	$-0.245931\pi$
$257$	15.8265	+	4.24070i	0.987230	+	0.264528i	0.271144	+	0.962539i	$0.412598\pi$
$258$	14.9905	−	14.9905i	0.933269	−	0.933269i
$259$	15.1300			0.940135
$260$		0			0
$261$	42.1508	+	24.3358i	2.60907	+	1.50635i
$262$	15.6172	+	4.18462i	0.964836	+	0.258527i
$263$	3.03320	+	11.3201i	0.187035	+	0.698025i	0.994186	+	0.107679i	$0.0343420\pi$
$263$	3.03320	+	11.3201i	0.187035	+	0.698025i	−0.807150	+	0.590346i	$0.798991\pi$
$264$	−14.5666	−	8.41006i	−0.896515	−	0.517603i
$265$		0			0
$266$	12.1240	−	3.69843i	0.743373	−	0.226765i
$267$	29.7205	+	29.7205i	1.81886	+	1.81886i
$268$	−0.0355206	+	0.00951772i	−0.00216977	+	0.000581387i
$269$	2.95806	−	5.12352i	0.180356	−	0.312386i	−0.761646	−	0.647994i	$-0.775608\pi$
$269$	2.95806	−	5.12352i	0.180356	−	0.312386i	0.942002	+	0.335608i	$0.108942\pi$
$270$		0			0
$271$	−5.28235	+	9.14929i	−0.320880	+	0.555780i	−0.980670	−	0.195670i	$-0.937312\pi$
$271$	−5.28235	+	9.14929i	−0.320880	+	0.555780i	0.659790	+	0.751450i	$0.270645\pi$
$272$	0.687594	−	2.56613i	0.0416915	−	0.155595i
$273$	−25.1679	+	25.1679i	−1.52323	+	1.52323i
$274$	−4.75720			−0.287393
$275$		0			0
$276$	−7.92059	+	4.57295i	−0.476763	+	0.275259i
$277$	5.51976	+	5.51976i	0.331650	+	0.331650i	0.853213	−	0.521563i	$-0.174651\pi$
$277$	5.51976	+	5.51976i	0.331650	+	0.331650i	−0.521563	+	0.853213i	$0.674651\pi$
$278$	10.0541	+	10.0541i	0.603005	+	0.603005i
$279$	−30.7078	−	53.1875i	−1.83843	−	3.18425i
$280$		0			0
$281$	2.77648	−	1.60300i	0.165631	−	0.0956270i	−0.414893	−	0.909870i	$-0.636181\pi$
$281$	2.77648	−	1.60300i	0.165631	−	0.0956270i	0.580524	+	0.814243i	$0.302848\pi$
$282$	−7.30724	+	1.95797i	−0.435140	+	0.116595i
$283$	−5.10982	−	19.0701i	−0.303747	−	1.13360i	−0.934018	−	0.357226i	$-0.883723\pi$
$283$	−5.10982	−	19.0701i	−0.303747	−	1.13360i	0.630271	−	0.776375i	$-0.282944\pi$
$284$	−4.52287			−0.268383
$285$		0			0
$286$	20.8128			1.23069
$287$	−4.01182	−	14.9723i	−0.236810	−	0.883787i
$288$	−6.65684	+	1.78370i	−0.392258	+	0.105105i
$289$	−8.61017	+	4.97109i	−0.506481	+	0.292417i
$290$		0			0
$291$	21.8238	+	37.7999i	1.27933	+	2.21587i
$292$	−11.3661	−	11.3661i	−0.665151	−	0.665151i
$293$	10.3865	+	10.3865i	0.606786	+	0.606786i	0.942105	−	0.335319i	$-0.108844\pi$
$293$	10.3865	+	10.3865i	0.606786	+	0.606786i	−0.335319	+	0.942105i	$0.608844\pi$
$294$	3.96675	−	2.29021i	0.231346	−	0.133567i
$295$		0			0
$296$	−5.20293			−0.302414
$297$	−46.2860	+	46.2860i	−2.68579	+	2.68579i
$298$	−5.76913	+	21.5307i	−0.334197	+	1.24724i
$299$	5.65846	−	9.80073i	0.327237	−	0.566791i
$300$		0			0
$301$	9.80073	−	16.9754i	0.564905	−	0.978444i
$302$	0.796353	−	0.213382i	0.0458249	−	0.0122788i
$303$	−42.8694	−	42.8694i	−2.46278	−	2.46278i
$304$	−4.16923	+	1.27182i	−0.239122	+	0.0729438i
$305$		0			0
$306$	−15.8559	−	9.15440i	−0.906421	−	0.523322i
$307$	1.48377	+	5.53750i	0.0846831	+	0.316042i	0.995254	−	0.0973112i	$-0.0310242\pi$
$307$	1.48377	+	5.53750i	0.0846831	+	0.316042i	−0.910571	+	0.413353i	$0.864358\pi$
$308$	−15.0221	−	4.02515i	−0.855962	−	0.229354i
$309$	40.5037	+	23.3848i	2.30417	+	1.33032i
$310$		0			0
$311$	−8.45636			−0.479516			−0.239758	−	0.970833i	$-0.577068\pi$
$311$	−8.45636			−0.479516			−0.239758	+	0.970833i	$0.577068\pi$
$312$	8.65478	−	8.65478i	0.489980	−	0.489980i
$313$	3.45924	+	0.926899i	0.195528	+	0.0523914i	0.355254	−	0.934770i	$-0.384394\pi$
$313$	3.45924	+	0.926899i	0.195528	+	0.0523914i	−0.159726	+	0.987161i	$0.551061\pi$
$314$	0.991688	+	1.71765i	0.0559642	+	0.0969328i
$315$		0			0
$316$			2.30517i			0.129676i
$317$	2.88452	+	0.772904i	0.162011	+	0.0434106i	0.338913	−	0.940818i	$-0.389941\pi$
$317$	2.88452	+	0.772904i	0.162011	+	0.0434106i	−0.176902	+	0.984228i	$0.556608\pi$
$318$	−10.7653	+	2.88456i	−0.603690	+	0.161758i
$319$	−18.8849	−	32.7096i	−1.05735	−	1.83139i
$320$		0			0
$321$	10.7581	−	18.6336i	0.600458	−	1.04002i
$322$	−5.97955	+	5.97955i	−0.333227	+	0.333227i
$323$	−10.2212	−	5.44290i	−0.568724	−	0.302851i
$324$			17.8201i			0.990006i
$325$		0			0
$326$	−0.333843	−	0.192744i	−0.0184898	−	0.0106751i
$327$	1.05259	−	3.92834i	0.0582086	−	0.217238i
$328$	1.37959	+	5.14869i	0.0761750	+	0.284289i
$329$	−6.05756	+	3.49733i	−0.333964	+	0.192814i
$330$		0			0
$331$		−	17.7892i		−	0.977781i	−0.872345	−	0.488890i	$-0.837402\pi$
$331$		−	17.7892i		−	0.977781i	0.872345	−	0.488890i	$-0.162598\pi$
$332$	−1.26598	+	4.72469i	−0.0694795	+	0.259301i
$333$	−9.28045	+	34.6351i	−0.508565	+	1.89799i
$334$			2.34803i			0.128479i
$335$		0			0
$336$	−7.92059	+	4.57295i	−0.432103	+	0.249475i
$337$	−6.74098	−	25.1577i	−0.367205	−	1.37043i	−0.864407	−	0.502792i	$-0.832306\pi$
$337$	−6.74098	−	25.1577i	−0.367205	−	1.37043i	0.497202	−	0.867635i	$-0.334361\pi$
$338$	−0.555193	+	2.07201i	−0.0301985	+	0.112702i
$339$	17.1528	+	9.90319i	0.931614	+	0.537868i
$340$		0			0
$341$			47.6594i			2.58090i
$342$	1.02966	+	30.0224i	0.0556776	+	1.62343i
$343$	−11.3991	+	11.3991i	−0.615495	+	0.615495i
$344$	−3.37029	+	5.83751i	−0.181714	+	0.314737i
$345$		0			0
$346$	−9.26496	−	16.0474i	−0.498087	−	0.862712i
$347$	19.2965	−	5.17047i	1.03589	−	0.277565i	0.299480	−	0.954103i	$-0.403187\pi$
$347$	19.2965	−	5.17047i	1.03589	−	0.277565i	0.736408	+	0.676537i	$0.236520\pi$
$348$	−21.4550	−	5.74885i	−1.15011	−	0.308171i
$349$		−	32.1976i		−	1.72350i	−0.507335	−	0.861749i	$-0.669369\pi$
$349$		−	32.1976i		−	1.72350i	0.507335	−	0.861749i	$-0.330631\pi$
$350$		0			0
$351$	−23.8165	−	41.2513i	−1.27123	−	2.20183i
$352$	5.16580	+	1.38417i	0.275338	+	0.0737767i
$353$	15.1593	−	15.1593i	0.806846	−	0.806846i	−0.177309	−	0.984155i	$-0.556739\pi$
$353$	15.1593	−	15.1593i	0.806846	−	0.806846i	0.984155	+	0.177309i	$0.0567393\pi$
$354$	−28.8183			−1.53167
$355$		0			0
$356$	−11.5735	−	6.68199i	−0.613397	−	0.354145i
$357$	−23.4696	−	6.28866i	−1.24214	−	0.332831i
$358$	−1.80195	−	6.72497i	−0.0952361	−	0.355426i
$359$	6.04394	+	3.48947i	0.318987	+	0.184167i	0.650941	−	0.759128i	$-0.274375\pi$
$359$	6.04394	+	3.48947i	0.318987	+	0.184167i	−0.331954	+	0.943296i	$0.607708\pi$
$360$		0			0
$361$	1.30173	+	18.9554i	0.0685120	+	0.997650i
$362$	−4.01764	−	4.01764i	−0.211163	−	0.211163i
$363$	53.4721	−	14.3278i	2.80656	−	0.752015i
$364$	5.65846	−	9.80073i	0.296584	−	0.513698i
$365$		0			0
$366$	0.626716	−	1.08550i	0.0327590	−	0.0567402i
$367$	4.52640	−	16.8928i	0.236276	−	0.881795i	−0.741293	−	0.671181i	$-0.765787\pi$
$367$	4.52640	−	16.8928i	0.236276	−	0.881795i	0.977569	−	0.210614i	$-0.0675462\pi$
$368$	2.05625	−	2.05625i	0.107190	−	0.107190i
$369$	36.7348			1.91234
$370$		0			0
$371$	−8.92425	+	5.15242i	−0.463324	+	0.267500i
$372$	19.8187	+	19.8187i	1.02755	+	1.02755i
$373$	−5.65167	−	5.65167i	−0.292633	−	0.292633i	0.545487	−	0.838119i	$-0.316345\pi$
$373$	−5.65167	−	5.65167i	−0.292633	−	0.292633i	−0.838119	+	0.545487i	$0.816345\pi$
$374$	7.10395	+	12.3044i	0.367336	+	0.636245i
$375$		0			0
$376$	2.08308	−	1.20267i	0.107427	−	0.0620228i
$377$	26.5479	−	7.11349i	1.36729	−	0.366363i
$378$	9.21211	+	34.3801i	0.473820	+	1.76832i
$379$	−33.9677			−1.74481			−0.872403	−	0.488788i	$-0.837439\pi$
$379$	−33.9677			−1.74481			−0.872403	+	0.488788i	$0.837439\pi$
$380$		0			0
$381$	−56.5025			−2.89471
$382$	0.397626	+	1.48396i	0.0203443	+	0.0759260i
$383$	−8.56025	+	2.29371i	−0.437408	+	0.117203i	−0.470802	−	0.882239i	$-0.656035\pi$
$383$	−8.56025	+	2.29371i	−0.437408	+	0.117203i	0.0333933	+	0.999442i	$0.489369\pi$
$384$	2.72374	−	1.57255i	0.138995	−	0.0802489i
$385$		0			0
$386$	3.12672	+	5.41563i	0.159146	+	0.275648i
$387$	32.8478	+	32.8478i	1.66975	+	1.66975i
$388$	−9.81319	−	9.81319i	−0.498189	−	0.498189i
$389$	26.2384	−	15.1488i	1.33034	−	0.768073i	0.344990	−	0.938607i	$-0.387882\pi$
$389$	26.2384	−	15.1488i	1.33034	−	0.768073i	0.985352	+	0.170534i	$0.0545491\pi$
$390$		0			0
$391$	7.72551			0.390696
$392$	−1.02980	+	1.02980i	−0.0520130	+	0.0520130i
$393$	−13.1611	+	49.1178i	−0.663888	+	2.47767i
$394$	−1.63824	+	2.83751i	−0.0825331	+	0.142952i
$395$		0			0
$396$	18.4284	−	31.9190i	0.926064	−	1.60399i
$397$	−5.27412	+	1.41320i	−0.264700	+	0.0709263i	−0.388728	−	0.921352i	$-0.627085\pi$
$397$	−5.27412	+	1.41320i	−0.264700	+	0.0709263i	0.124028	+	0.992279i	$0.460419\pi$
$398$	−0.276625	−	0.276625i	−0.0138660	−	0.0138660i
$399$	11.6319	+	38.1314i	0.582325	+	1.90896i
$400$		0			0
$401$	23.8228	+	13.7541i	1.18965	+	0.686847i	0.958228	−	0.286006i	$-0.0923278\pi$
$401$	23.8228	+	13.7541i	1.18965	+	0.686847i	0.231425	+	0.972853i	$0.425661\pi$
$402$	−0.0299342	−	0.111716i	−0.00149298	−	0.00557188i
$403$	−33.4992	−	8.97609i	−1.66871	−	0.447131i
$404$	16.6939	+	9.63824i	0.830554	+	0.479520i
$405$		0			0
$406$	−20.5372			−1.01925
$407$	19.6756	−	19.6756i	0.975282	−	0.975282i
$408$	8.07075	+	2.16255i	0.399562	+	0.107062i
$409$	−2.32002	−	4.01839i	−0.114717	−	0.198696i	0.802949	−	0.596047i	$-0.203263\pi$
$409$	−2.32002	−	4.01839i	−0.114717	−	0.198696i	−0.917667	+	0.397351i	$0.869930\pi$
$410$		0			0
$411$		−	14.9619i		−	0.738015i
$412$	−14.3639	−	3.84880i	−0.707659	−	0.189617i
$413$	−25.7376	+	6.89638i	−1.26647	+	0.339349i
$414$	−10.0204	−	17.3559i	−0.492477	−	0.852996i
$415$		0			0
$416$	−1.94584	+	3.37029i	−0.0954024	+	0.165242i
$417$	−31.6212	+	31.6212i	−1.54850	+	1.54850i
$418$	10.9569	−	20.5760i	0.535921	−	1.00641i
$419$			3.28181i			0.160327i	0.996782	+	0.0801636i	$0.0255443\pi$
$419$			3.28181i			0.160327i	−0.996782	+	0.0801636i	$0.974456\pi$
$420$		0			0
$421$	−11.6456	−	6.72357i	−0.567570	−	0.327687i	0.188608	−	0.982052i	$-0.439602\pi$
$421$	−11.6456	−	6.72357i	−0.567570	−	0.327687i	−0.756178	+	0.654366i	$0.772936\pi$
$422$	5.20344	−	19.4195i	0.253300	−	0.945327i
$423$	−4.29038	−	16.0119i	−0.208605	−	0.778526i
$424$	3.06888	−	1.77182i	0.149038	−	0.0860471i
$425$		0			0
$426$		−	14.2249i		−	0.689198i
$427$	0.299953	−	1.11944i	0.0145158	−	0.0541736i
$428$	−1.77063	+	6.60806i	−0.0855864	+	0.319413i
$429$			65.4584i			3.16036i
$430$		0			0
$431$	4.76396	−	2.75047i	0.229472	−	0.132486i	−0.380857	−	0.924634i	$-0.624371\pi$
$431$	4.76396	−	2.75047i	0.229472	−	0.132486i	0.610328	+	0.792149i	$0.291037\pi$
$432$	−3.16787	−	11.8226i	−0.152414	−	0.568817i
$433$	0.379106	−	1.41484i	0.0182187	−	0.0679930i	−0.956218	−	0.292655i	$-0.905461\pi$
$433$	0.379106	−	1.41484i	0.0182187	−	0.0679930i	0.974437	+	0.224662i	$0.0721279\pi$
$434$	22.4428	+	12.9574i	1.07729	+	0.621973i
$435$		0			0
$436$			1.29309i			0.0619280i
$437$	−6.71034	−	10.7537i	−0.320999	−	0.514420i
$438$	35.7476	−	35.7476i	1.70809	−	1.70809i
$439$	−9.80945	+	16.9905i	−0.468180	+	0.810911i	−0.999339	−	0.0363613i	$-0.988423\pi$
$439$	−9.80945	+	16.9905i	−0.468180	+	0.810911i	0.531159	+	0.847272i	$0.321757\pi$
$440$		0			0
$441$	5.01839	+	8.69210i	0.238971	+	0.413910i
$442$	−9.98655	+	2.67589i	−0.475012	+	0.127279i
$443$	9.16152	+	2.45482i	0.435277	+	0.116632i	0.469802	−	0.882772i	$-0.344325\pi$
$443$	9.16152	+	2.45482i	0.435277	+	0.116632i	−0.0345253	+	0.999404i	$0.510992\pi$
$444$		−	16.3638i		−	0.776589i
$445$		0			0
$446$	−14.4137	−	24.9653i	−0.682510	−	1.18214i
$447$	−67.7162	−	18.1445i	−3.20287	−	0.858206i
$448$	2.05625	−	2.05625i	0.0971489	−	0.0971489i
$449$	−30.7142			−1.44949			−0.724746	−	0.689016i	$-0.758043\pi$
$449$	−30.7142			−1.44949			−0.724746	+	0.689016i	$0.758043\pi$
$450$		0			0
$451$	−24.6875	−	14.2534i	−1.16249	−	0.671164i
$452$	−6.08295	−	1.62992i	−0.286118	−	0.0766651i
$453$	0.671108	+	2.50461i	0.0315314	+	0.117677i
$454$	−7.41897	−	4.28334i	−0.348189	−	0.201027i
$455$		0			0
$456$	−4.00000	−	13.1127i	−0.187317	−	0.614056i
$457$	−9.53261	−	9.53261i	−0.445917	−	0.445917i	0.448078	−	0.893995i	$-0.352109\pi$
$457$	−9.53261	−	9.53261i	−0.445917	−	0.445917i	−0.893995	+	0.448078i	$0.852109\pi$
$458$	2.27510	−	0.609612i	0.106309	−	0.0284853i
$459$	16.2584	−	28.1603i	0.758875	−	1.31441i
$460$		0			0
$461$	−16.1897	+	28.0414i	−0.754031	+	1.30602i	0.191823	+	0.981429i	$0.438560\pi$
$461$	−16.1897	+	28.0414i	−0.754031	+	1.30602i	−0.945855	+	0.324591i	$0.894773\pi$
$462$	12.6595	−	47.2459i	0.588974	−	2.19808i
$463$	17.9522	−	17.9522i	0.834307	−	0.834307i	−0.153795	−	0.988103i	$-0.549150\pi$
$463$	17.9522	−	17.9522i	0.834307	−	0.834307i	0.988103	+	0.153795i	$0.0491497\pi$
$464$	7.06237			0.327862
$465$		0			0
$466$	13.4537	−	7.76749i	0.623230	−	0.359822i
$467$	9.75292	+	9.75292i	0.451311	+	0.451311i	0.895790	−	0.444478i	$-0.146611\pi$
$467$	9.75292	+	9.75292i	0.451311	+	0.451311i	−0.444478	+	0.895790i	$0.646611\pi$
$468$	18.9647	+	18.9647i	0.876643	+	0.876643i
$469$	−0.0534685	−	0.0926102i	−0.00246895	−	0.00427634i
$470$		0			0
$471$	−5.40220	+	3.11896i	−0.248920	+	0.143714i
$472$	8.85069	−	2.37153i	0.407386	−	0.109159i
$473$	−9.33012	−	34.8205i	−0.428999	−	1.60105i
$474$	−7.25000			−0.333003
$475$		0			0
$476$	7.72551			0.354098
$477$	−6.32077	−	23.5894i	−0.289408	−	1.08009i
$478$	−20.3910	+	5.46375i	−0.932663	+	0.249906i
$479$	−22.9391	+	13.2439i	−1.04811	+	0.605129i	−0.922121	−	0.386902i	$-0.873545\pi$
$479$	−22.9391	+	13.2439i	−1.04811	+	0.605129i	−0.125994	+	0.992031i	$0.540212\pi$
$480$		0			0
$481$	10.1240	+	17.5354i	0.461617	+	0.799544i
$482$	20.2569	+	20.2569i	0.922679	+	0.922679i
$483$	−18.8063	−	18.8063i	−0.855716	−	0.855716i
$484$	−15.2433	+	8.80073i	−0.692878	+	0.400033i
$485$		0			0
$486$	−19.3270			−0.876690
$487$	−4.64712	+	4.64712i	−0.210581	+	0.210581i	−0.804514	−	0.593933i	$-0.797574\pi$
$487$	−4.64712	+	4.64712i	−0.210581	+	0.210581i	0.593933	+	0.804514i	$0.297574\pi$
$488$	−0.103148	+	0.384955i	−0.00466930	+	0.0174261i
$489$	0.606200	−	1.04997i	0.0274133	−	0.0474812i
$490$		0			0
$491$	6.17035	−	10.6874i	0.278464	−	0.482314i	−0.692539	−	0.721380i	$-0.743508\pi$
$491$	6.17035	−	10.6874i	0.278464	−	0.482314i	0.971003	+	0.239066i	$0.0768413\pi$
$492$	−16.1932	+	4.33894i	−0.730044	+	0.195615i
$493$	13.2669	+	13.2669i	0.597513	+	0.597513i
$494$	12.3990	+	11.5767i	0.557859	+	0.520862i
$495$		0			0
$496$	−7.71765	−	4.45579i	−0.346533	−	0.200071i
$497$	−3.40410	−	12.7043i	−0.152695	−	0.569864i
$498$	−14.8596	−	3.98163i	−0.665876	−	0.178421i
$499$	−8.74853	−	5.05096i	−0.391638	−	0.226112i	0.291232	−	0.956653i	$-0.405935\pi$
$499$	−8.74853	−	5.05096i	−0.391638	−	0.226112i	−0.682870	+	0.730540i	$0.739268\pi$
$500$		0			0
$501$	−7.38481			−0.329929
$502$	−0.835713	+	0.835713i	−0.0372997	+	0.0372997i
$503$	−38.8578	−	10.4119i	−1.73258	−	0.464245i	−0.751808	−	0.659382i	$-0.770818\pi$
$503$	−38.8578	−	10.4119i	−1.73258	−	0.464245i	−0.980776	+	0.195137i	$0.937485\pi$
$504$	−10.0204	−	17.3559i	−0.446345	−	0.773093i
$505$		0			0
$506$			15.5520i			0.691370i
$507$	−6.51668	−	1.74614i	−0.289416	−	0.0775488i
$508$	17.3531	−	4.64974i	0.769918	−	0.206299i
$509$	6.62341	+	11.4721i	0.293577	+	0.508491i	0.974653	−	0.223722i	$-0.0718208\pi$
$509$	6.62341	+	11.4721i	0.293577	+	0.508491i	−0.681076	+	0.732213i	$0.738487\pi$
$510$		0			0
$511$	23.3716	−	40.4808i	1.03390	−	1.79077i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	−53.3203	+	1.82869i	−2.35415	+	0.0807386i
$514$		−	16.3848i		−	0.722703i
$515$		0			0
$516$	−18.3596	−	10.5999i	−0.808234	−	0.466634i
$517$	−3.32940	+	12.4255i	−0.146427	+	0.546472i
$518$	−3.91594	−	14.6145i	−0.172057	−	0.642124i
$519$	50.4706	−	29.1392i	2.21542	−	1.27907i
$520$		0			0
$521$			11.1590i			0.488883i	0.969664	+	0.244442i	$0.0786047\pi$
$521$			11.1590i			0.488883i	−0.969664	+	0.244442i	$0.921395\pi$
$522$	12.5971	−	47.0131i	0.551361	−	2.05771i
$523$	−10.1130	+	37.7421i	−0.442210	+	1.65035i	0.280991	+	0.959711i	$0.409337\pi$
$523$	−10.1130	+	37.7421i	−0.442210	+	1.65035i	−0.723200	+	0.690638i	$0.757330\pi$
$524$		−	16.1681i		−	0.706309i
$525$		0			0
$526$	10.1493	−	5.85970i	0.442530	−	0.255495i
$527$	−6.12754	−	22.8683i	−0.266920	−	0.996159i
$528$	−4.35337	+	16.2470i	−0.189456	+	0.707059i
$529$	−12.5952	−	7.27182i	−0.547616	−	0.316166i
$530$		0			0
$531$		−	63.1477i		−	2.74038i
$532$	−6.71034	−	10.7537i	−0.290930	−	0.466232i
$533$	14.6681	−	14.6681i	0.635346	−	0.635346i
$534$	21.0155	−	36.4000i	0.909432	−	1.57518i
$535$		0			0
$536$	0.0183868	+	0.0318469i	0.000794189	+	0.00137558i
$537$	21.1507	−	5.66732i	0.912721	−	0.244563i
$538$	−5.71454	−	1.53121i	−0.246371	−	0.0660150i
$539$		−	7.78868i		−	0.335482i
$540$		0			0
$541$	−16.7544	−	29.0195i	−0.720329	−	1.24765i	−0.960868	−	0.277007i	$-0.910657\pi$
$541$	−16.7544	−	29.0195i	−0.720329	−	1.24765i	0.240539	−	0.970640i	$-0.422676\pi$
$542$	10.2047	+	2.73434i	0.438330	+	0.117450i
$543$	12.6359	−	12.6359i	0.542258	−	0.542258i
$544$	−2.65666			−0.113903
$545$		0			0
$546$	30.8243	+	17.7964i	1.31916	+	0.761617i
$547$	−17.0302	−	4.56322i	−0.728157	−	0.195109i	−0.124348	−	0.992239i	$-0.539684\pi$
$547$	−17.0302	−	4.56322i	−0.728157	−	0.195109i	−0.603808	+	0.797130i	$0.706351\pi$
$548$	1.23125	+	4.59510i	0.0525965	+	0.196293i
$549$	2.37860	+	1.37328i	0.101516	+	0.0586103i
$550$		0			0
$551$	6.94363	−	29.9908i	0.295809	−	1.27765i
$552$	6.46713	+	6.46713i	0.275259	+	0.275259i
$553$	−6.47498	+	1.73497i	−0.275344	+	0.0737783i
$554$	3.90306	−	6.76030i	0.165825	−	0.287217i
$555$		0			0
$556$	7.10932	−	12.3137i	0.301503	−	0.522218i
$557$	−6.11650	+	22.8271i	−0.259165	+	0.967215i	0.706562	+	0.707652i	$0.250245\pi$
$557$	−6.11650	+	22.8271i	−0.259165	+	0.967215i	−0.965726	+	0.259563i	$0.916421\pi$
$558$	−43.4274	+	43.4274i	−1.83843	+	1.83843i
$559$	26.2321			1.10950
$560$		0			0
$561$	−38.6986	+	22.3426i	−1.63386	+	0.943307i
$562$	−2.26699	−	2.26699i	−0.0956270	−	0.0956270i
$563$	−4.92515	−	4.92515i	−0.207570	−	0.207570i	0.595664	−	0.803234i	$-0.296889\pi$
$563$	−4.92515	−	4.92515i	−0.207570	−	0.207570i	−0.803234	+	0.595664i	$0.796889\pi$
$564$	3.78251	+	6.55150i	0.159272	+	0.275868i
$565$		0			0
$566$	−17.0978	+	9.87142i	−0.718674	+	0.414927i
$567$	−50.0548	+	13.4122i	−2.10211	+	0.563258i
$568$	1.17061	+	4.36876i	0.0491175	+	0.183309i
$569$	−30.5036			−1.27878			−0.639389	−	0.768883i	$-0.720813\pi$
$569$	−30.5036			−1.27878			−0.639389	+	0.768883i	$0.720813\pi$
$570$		0			0
$571$	−24.4741			−1.02421			−0.512104	−	0.858923i	$-0.671134\pi$
$571$	−24.4741			−1.02421			−0.512104	+	0.858923i	$0.671134\pi$
$572$	−5.38675	−	20.1036i	−0.225231	−	0.840574i
$573$	−4.66721	+	1.25057i	−0.194975	+	0.0522435i
$574$	−13.4238	+	7.75023i	−0.560298	+	0.323488i
$575$		0			0
$576$	3.44584	+	5.96836i	0.143576	+	0.248682i
$577$	21.0146	+	21.0146i	0.874848	+	0.874848i	0.992996	−	0.118148i	$-0.0376956\pi$
$577$	21.0146	+	21.0146i	0.874848	+	0.874848i	−0.118148	+	0.992996i	$0.537696\pi$
$578$	7.03018	+	7.03018i	0.292417	+	0.292417i
$579$	−17.0327	+	9.83384i	−0.707855	+	0.408681i
$580$		0			0
$581$	−14.2240			−0.590110
$582$	30.8635	−	30.8635i	1.27933	−	1.27933i
$583$	−4.90501	+	18.3057i	−0.203145	+	0.758146i
$584$	−8.03705	+	13.9206i	−0.332576	+	0.576038i
$585$		0			0
$586$	7.34437	−	12.7208i	0.303393	−	0.525492i
$587$	−16.9280	+	4.53584i	−0.698693	+	0.187214i	−0.590645	−	0.806932i	$-0.701127\pi$
$587$	−16.9280	+	4.53584i	−0.698693	+	0.187214i	−0.108048	+	0.994146i	$0.534460\pi$
$588$	−3.23884	−	3.23884i	−0.133567	−	0.133567i
$589$	−26.5097	+	28.3927i	−1.09231	+	1.16990i
$590$		0			0
$591$	−8.92425	−	5.15242i	−0.367095	−	0.211942i
$592$	1.34662	+	5.02565i	0.0553456	+	0.206553i
$593$	−15.0573	−	4.03459i	−0.618329	−	0.165681i	−0.0639609	−	0.997952i	$-0.520373\pi$
$593$	−15.0573	−	4.03459i	−0.618329	−	0.165681i	−0.554368	+	0.832272i	$0.687040\pi$
$594$	56.6886	+	32.7292i	2.32596	+	1.34289i
$595$		0			0
$596$	22.2902			0.913042
$597$	0.870014	−	0.870014i	0.0356073	−	0.0356073i
$598$	−10.9313	−	2.92903i	−0.447014	−	0.119777i
$599$	−17.8198	−	30.8647i	−0.728096	−	1.26110i	−0.957687	−	0.287812i	$-0.907072\pi$
$599$	−17.8198	−	30.8647i	−0.728096	−	1.26110i	0.229591	−	0.973287i	$-0.426261\pi$
$600$		0			0
$601$			2.58619i			0.105493i	0.998608	+	0.0527464i	$0.0167975\pi$
$601$			2.58619i			0.105493i	−0.998608	+	0.0527464i	$0.983203\pi$
$602$	−18.9336	−	5.07323i	−0.771674	−	0.206770i
$603$	0.244796	−	0.0655930i	0.00996887	−	0.00267115i
$604$	−0.412222	−	0.713990i	−0.0167731	−	0.0290518i
$605$		0			0
$606$	−30.3133	+	52.5041i	−1.23139	+	2.13283i
$607$	−8.03991	+	8.03991i	−0.326330	+	0.326330i	−0.851189	−	0.524859i	$-0.824118\pi$
$607$	−8.03991	+	8.03991i	−0.326330	+	0.326330i	0.524859	+	0.851189i	$0.324118\pi$
$608$	2.30756	+	3.69800i	0.0935839	+	0.149974i
$609$		−	64.5917i		−	2.61739i
$610$		0			0
$611$	−8.10666	−	4.68038i	−0.327960	−	0.189348i
$612$	−4.73867	+	17.6850i	−0.191549	+	0.714872i
$613$	6.70432	+	25.0209i	0.270785	+	1.01058i	0.958614	+	0.284710i	$0.0918974\pi$
$613$	6.70432	+	25.0209i	0.270785	+	1.01058i	−0.687828	+	0.725873i	$0.741436\pi$
$614$	4.96479	−	2.86642i	0.200362	−	0.115679i
$615$		0			0
$616$			15.5520i			0.626608i
$617$	−11.3008	+	42.1752i	−0.454954	+	1.69791i	0.233271	+	0.972412i	$0.425057\pi$
$617$	−11.3008	+	42.1752i	−0.454954	+	1.69791i	−0.688224	+	0.725498i	$0.741610\pi$
$618$	12.1049	−	45.1760i	0.486929	−	1.81724i
$619$			10.5647i			0.424631i	0.977201	+	0.212315i	$0.0681004\pi$
$619$			10.5647i			0.424631i	−0.977201	+	0.212315i	$0.931900\pi$
$620$		0			0
$621$	30.8243	−	17.7964i	1.23694	−	0.714146i
$622$	2.18867	+	8.16822i	0.0877576	+	0.327516i
$623$	10.0583	−	37.5380i	0.402977	−	1.50393i
$624$	−10.5999	−	6.11985i	−0.424335	−	0.244990i
$625$		0			0
$626$		−	3.58126i		−	0.143136i
$627$	64.7137	+	34.4607i	2.58442	+	1.37623i
$628$	1.40246	−	1.40246i	0.0559642	−	0.0559642i
$629$	−6.91120	+	11.9706i	−0.275568	+	0.477297i
$630$		0			0
$631$	20.5630	+	35.6162i	0.818601	+	1.41786i	0.906713	+	0.421748i	$0.138583\pi$
$631$	20.5630	+	35.6162i	0.818601	+	1.41786i	−0.0881123	+	0.996111i	$0.528083\pi$
$632$	2.22662	−	0.596622i	0.0885703	−	0.0237323i
$633$	61.0763	+	16.3654i	2.42757	+	0.650465i
$634$		−	2.98627i		−	0.118600i
$635$		0			0
$636$	5.57255	+	9.65194i	0.220966	+	0.382724i
$637$	5.47456	+	1.46690i	0.216910	+	0.0581209i
$638$	−26.7073	+	26.7073i	−1.05735	+	1.05735i
$639$	31.1701			1.23307
$640$		0			0
$641$	3.18821	+	1.84071i	0.125927	+	0.0727038i	0.561640	−	0.827382i	$-0.310171\pi$
$641$	3.18821	+	1.84071i	0.125927	+	0.0727038i	−0.435713	+	0.900085i	$0.643504\pi$
$642$	−20.7830	−	5.56880i	−0.820241	−	0.219783i
$643$	0.828243	+	3.09104i	0.0326627	+	0.121899i	0.980332	−	0.197354i	$-0.0632348\pi$
$643$	0.828243	+	3.09104i	0.0326627	+	0.121899i	−0.947670	+	0.319253i	$0.896568\pi$
$644$	7.32343	+	4.22818i	0.288583	+	0.166614i
$645$		0			0
$646$	−2.61199	+	11.2817i	−0.102767	+	0.443872i
$647$	18.2835	+	18.2835i	0.718800	+	0.718800i	0.968359	−	0.249559i	$-0.0802858\pi$
$647$	18.2835	+	18.2835i	0.718800	+	0.718800i	−0.249559	+	0.968359i	$0.580286\pi$
$648$	17.2129	−	4.61219i	0.676187	−	0.181184i
$649$	−24.5018	+	42.4383i	−0.961778	+	1.66585i
$650$		0			0
$651$	−40.7522	+	70.5849i	−1.59721	+	2.76644i
$652$	−0.0997717	+	0.372353i	−0.00390736	+	0.0145825i
$653$	−11.1338	+	11.1338i	−0.435698	+	0.435698i	−0.890561	−	0.454863i	$-0.849688\pi$
$653$	−11.1338	+	11.1338i	−0.435698	+	0.435698i	0.454863	+	0.890561i	$0.349688\pi$
$654$	−4.06691			−0.159029
$655$		0			0
$656$	4.61619	−	2.66516i	0.180232	−	0.104057i
$657$	78.3315	+	78.3315i	3.05600	+	3.05600i
$658$	4.94597	+	4.94597i	0.192814	+	0.192814i
$659$	9.01685	+	15.6176i	0.351247	+	0.608377i	0.986468	−	0.163953i	$-0.0524245\pi$
$659$	9.01685	+	15.6176i	0.351247	+	0.608377i	−0.635221	+	0.772330i	$0.719091\pi$
$660$		0			0
$661$	−0.974218	+	0.562465i	−0.0378927	+	0.0218774i	−0.518827	−	0.854879i	$-0.673631\pi$
$661$	−0.974218	+	0.562465i	−0.0378927	+	0.0218774i	0.480934	+	0.876757i	$0.340298\pi$
$662$	−17.1830	+	4.60417i	−0.667837	+	0.178946i
$663$	−8.41594	−	31.4087i	−0.326848	−	1.21981i
$664$	4.89136			0.189822
$665$		0			0
$666$	35.8569			1.38943
$667$	5.31543	+	19.8374i	0.205814	+	0.768109i
$668$	2.26803	−	0.607716i	0.0877526	−	0.0235132i
$669$	78.5184	−	45.3326i	3.03570	−	1.75266i
$670$		0			0
$671$	−1.06569	−	1.84583i	−0.0411404	−	0.0712573i
$672$	6.46713	+	6.46713i	0.249475	+	0.249475i
$673$	−25.9592	−	25.9592i	−1.00065	−	1.00065i	−1.00000		0.000652030i	$-0.999792\pi$
$673$	−25.9592	−	25.9592i	−1.00065	−	1.00065i	−0.000652030	−	1.00000i	$-0.500208\pi$
$674$	−22.5558	+	13.0226i	−0.868816	+	0.501611i
$675$		0			0
$676$	2.14510			0.0825039
$677$	10.8184	−	10.8184i	0.415785	−	0.415785i	−0.467963	−	0.883748i	$-0.655012\pi$
$677$	10.8184	−	10.8184i	0.415785	−	0.415785i	0.883748	+	0.467963i	$0.155012\pi$
$678$	5.12627	−	19.1315i	0.196873	−	0.734741i
$679$	20.1784	−	34.9500i	0.774376	−	1.34126i
$680$		0			0
$681$	13.4716	−	23.3334i	0.516231	−	0.894138i
$682$	46.0355	−	12.3352i	1.76279	−	0.472338i
$683$	7.72617	+	7.72617i	0.295634	+	0.295634i	0.839301	−	0.543667i	$-0.182965\pi$
$683$	7.72617	+	7.72617i	0.295634	+	0.295634i	−0.543667	+	0.839301i	$0.682965\pi$
$684$	28.7330	−	8.76496i	1.09863	−	0.335136i
$685$		0			0
$686$	13.9610	+	8.06040i	0.533034	+	0.307748i
$687$	1.91729	+	7.15544i	0.0731493	+	0.272997i
$688$	6.51089	+	1.74459i	0.248225	+	0.0665118i
$689$	−11.9431	−	6.89533i	−0.454995	−	0.262691i
$690$		0			0
$691$	42.3069			1.60943			0.804714	−	0.593662i	$-0.202319\pi$
$691$	42.3069			1.60943			0.804714	+	0.593662i	$0.202319\pi$
$692$	−13.1026	+	13.1026i	−0.498087	+	0.498087i
$693$	103.527	+	27.7400i	3.93267	+	1.05376i
$694$	−9.98858	−	17.3007i	−0.379161	−	0.656727i
$695$		0			0
$696$			22.2119i			0.841939i
$697$	13.6783	+	3.66509i	0.518103	+	0.138825i
$698$	−31.1005	+	8.33335i	−1.17717	+	0.315422i
$699$	24.4296	+	42.3133i	0.924011	+	1.60043i
$700$		0			0
$701$	2.32332	−	4.02410i	0.0877504	−	0.151988i	−0.818810	−	0.574065i	$-0.805366\pi$
$701$	2.32332	−	4.02410i	0.0877504	−	0.151988i	0.906560	+	0.422077i	$0.138699\pi$
$702$	−33.6815	+	33.6815i	−1.27123	+	1.27123i
$703$	22.6657	−	0.777351i	0.854854	−	0.0293183i
$704$		−	5.34803i		−	0.201562i
$705$		0			0
$706$	−18.5662	−	10.7192i	−0.698749	−	0.403423i
$707$	−14.5083	+	54.1456i	−0.545640	+	2.03636i
$708$	7.45872	+	27.8363i	0.280316	+	1.04615i
$709$	−27.5651	+	15.9147i	−1.03523	+	0.597690i	−0.918478	−	0.395471i	$-0.870581\pi$
$709$	−27.5651	+	15.9147i	−1.03523	+	0.597690i	−0.116751	+	0.993161i	$0.537248\pi$
$710$		0			0
$711$		−	15.8865i		−	0.595789i
$712$	−3.45885	+	12.9086i	−0.129626	+	0.483771i
$713$	6.70722	−	25.0317i	0.251187	−	0.937444i
$714$			24.2975i			0.909312i
$715$		0			0
$716$	−6.02945	+	3.48110i	−0.225331	+	0.130095i
$717$	−17.1841	−	64.1318i	−0.641751	−	2.39505i
$718$	1.80628	−	6.74114i	0.0674099	−	0.251577i
$719$	−25.6619	−	14.8159i	−0.957028	−	0.552541i	−0.0617712	−	0.998090i	$-0.519675\pi$
$719$	−25.6619	−	14.8159i	−0.957028	−	0.552541i	−0.895257	+	0.445550i	$0.853008\pi$
$720$		0			0
$721$		−	43.2435i		−	1.61047i
$722$	17.9726	−	6.16338i	0.668869	−	0.229377i
$723$	−63.7102	+	63.7102i	−2.36941	+	2.36941i
$724$	−2.84090	+	4.92059i	−0.105581	+	0.182872i
$725$		0			0
$726$	−27.6792	−	47.9418i	−1.02727	−	1.77929i
$727$	3.43055	−	0.919214i	0.127232	−	0.0340918i	−0.194641	−	0.980875i	$-0.562354\pi$
$727$	3.43055	−	0.919214i	0.127232	−	0.0340918i	0.321873	+	0.946783i	$0.395688\pi$
$728$	−10.9313	−	2.92903i	−0.405141	−	0.108557i
$729$		−	7.32499i		−	0.271296i
$730$		0			0
$731$	8.95369	+	15.5083i	0.331164	+	0.573594i
$732$	−1.21072	−	0.324412i	−0.0447496	−	0.0119906i
$733$	−7.56225	+	7.56225i	−0.279318	+	0.279318i	−0.832837	−	0.553519i	$-0.813285\pi$
$733$	−7.56225	+	7.56225i	−0.279318	+	0.279318i	0.553519	+	0.832837i	$0.313285\pi$
$734$	−17.4887			−0.645519
$735$		0			0
$736$	−2.51839	−	1.45399i	−0.0928290	−	0.0535948i
$737$	−0.189965	−	0.0509011i	−0.00699746	−	0.00187496i
$738$	−9.50766	−	35.4831i	−0.349982	−	1.30615i
$739$	2.44691	+	1.41273i	0.0900111	+	0.0519680i	0.544330	−	0.838871i	$-0.316784\pi$
$739$	2.44691	+	1.41273i	0.0900111	+	0.0519680i	−0.454319	+	0.890839i	$0.650117\pi$
$740$		0			0
$741$	−36.4101	+	38.9962i	−1.33756	+	1.43256i
$742$	7.28662	+	7.28662i	0.267500	+	0.267500i
$743$	−9.21845	+	2.47008i	−0.338192	+	0.0906183i	−0.423918	−	0.905700i	$-0.639346\pi$
$743$	−9.21845	+	2.47008i	−0.338192	+	0.0906183i	0.0857263	+	0.996319i	$0.472679\pi$
$744$	14.0139	−	24.2728i	0.513775	−	0.889885i
$745$		0			0
$746$	−3.99634	+	6.92186i	−0.146316	+	0.253427i
$747$	8.72470	−	32.5610i	0.319220	−	1.19134i
$748$	10.0465	−	10.0465i	0.367336	−	0.367336i
$749$	−19.8940			−0.726911
$750$		0			0
$751$	15.7486	−	9.09244i	0.574673	−	0.331788i	−0.184340	−	0.982862i	$-0.559015\pi$
$751$	15.7486	−	9.09244i	0.574673	−	0.331788i	0.759014	+	0.651075i	$0.225682\pi$
$752$	−1.70083	−	1.70083i	−0.0620228	−	0.0620228i
$753$	−2.62840	−	2.62840i	−0.0957843	−	0.0957843i
$754$	−13.7422	−	23.8022i	−0.500461	−	0.866825i
$755$		0			0
$756$	30.8243	−	17.7964i	1.12107	−	0.647250i
$757$	−6.25825	+	1.67689i	−0.227460	+	0.0609478i	−0.370749	−	0.928733i	$-0.620899\pi$
$757$	−6.25825	+	1.67689i	−0.227460	+	0.0609478i	0.143289	+	0.989681i	$0.454232\pi$
$758$	8.79150	+	32.8103i	0.319322	+	1.19172i
$759$	−48.9126			−1.77542
$760$		0			0
$761$	18.9220			0.685924			0.342962	−	0.939349i	$-0.388570\pi$
$761$	18.9220			0.685924			0.342962	+	0.939349i	$0.388570\pi$
$762$	14.6239	+	54.5772i	0.529768	+	1.97712i
$763$	−3.63217	+	0.973236i	−0.131493	+	0.0352335i
$764$	1.33048	−	0.768155i	0.0481352	−	0.0277909i
$765$		0			0
$766$	4.43111	+	7.67491i	0.160103	+	0.277306i
$767$	−25.2147	−	25.2147i	−0.910451	−	0.910451i
$768$	−2.22392	−	2.22392i	−0.0802489	−	0.0802489i
$769$	14.2907	−	8.25076i	0.515337	−	0.297530i	−0.219688	−	0.975570i	$-0.570504\pi$
$769$	14.2907	−	8.25076i	0.515337	−	0.297530i	0.735025	+	0.678040i	$0.237170\pi$
$770$		0			0
$771$	51.5319			1.85588
$772$	4.42184	−	4.42184i	0.159146	−	0.159146i
$773$	6.01133	−	22.4346i	0.216212	−	0.806915i	−0.769524	−	0.638618i	$-0.779506\pi$
$773$	6.01133	−	22.4346i	0.216212	−	0.806915i	0.985736	−	0.168297i	$-0.0538269\pi$
$774$	23.2269	−	40.2302i	0.834874	−	1.44604i
$775$		0			0
$776$	−6.93897	+	12.0187i	−0.249095	+	0.431444i
$777$	45.9641	−	12.3160i	1.64895	−	0.441835i
$778$	−21.4236	−	21.4236i	−0.768073	−	0.768073i
$779$	−6.77919	−	22.2233i	−0.242890	−	0.796233i
$780$		0			0
$781$	−20.9478	−	12.0942i	−0.749572	−	0.432766i
$782$	−1.99951	−	7.46227i	−0.0715023	−	0.266850i
$783$	83.4959	+	22.3726i	2.98390	+	0.799533i
$784$	1.26125	+	0.728181i	0.0450445	+	0.0260065i
$785$		0			0
$786$	50.8505			1.81378
$787$	18.2413	−	18.2413i	0.650231	−	0.650231i	−0.302817	−	0.953049i	$-0.597927\pi$
$787$	18.2413	−	18.2413i	0.650231	−	0.650231i	0.953049	+	0.302817i	$0.0979272\pi$
$788$	3.16483	+	0.848013i	0.112742	+	0.0302092i
$789$	18.4294	+	31.9206i	0.656103	+	1.13640i
$790$		0			0
$791$		−	18.3131i		−	0.651139i
$792$	−35.6010	−	9.53926i	−1.26503	−	0.338963i
$793$	1.49812	−	0.401419i	0.0531997	−	0.0142548i
$794$	2.73008	+	4.72865i	0.0968871	+	0.167813i
$795$		0			0
$796$	−0.195603	+	0.338795i	−0.00693298	+	0.0120083i
$797$	−9.48390	+	9.48390i	−0.335937	+	0.335937i	−0.854836	−	0.518899i	$-0.826342\pi$
$797$	−9.48390	+	9.48390i	−0.335937	+	0.335937i	0.518899	+	0.854836i	$0.326342\pi$
$798$	33.8215	−	21.1047i	1.19727	−	0.747099i
$799$		−	6.39014i		−	0.226067i
$800$		0			0
$801$	79.7611	+	46.0501i	2.81822	+	1.62710i
$802$	7.11964	−	26.5709i	0.251403	−	0.938250i
$803$	−22.2493	−	83.0357i	−0.785162	−	2.93027i
$804$	−0.100162	+	0.0578284i	−0.00353243	+	0.00203945i
$805$		0			0
$806$			34.6809i			1.22158i
$807$	4.81580	−	17.9728i	0.169524	−	0.632673i
$808$	4.98912	−	18.6196i	0.175517	−	0.655037i
$809$			8.42065i			0.296054i	0.988983	+	0.148027i	$0.0472923\pi$
$809$			8.42065i			0.296054i	−0.988983	+	0.148027i	$0.952708\pi$
$810$		0			0
$811$	26.5883	−	15.3507i	0.933640	−	0.539038i	0.0456794	−	0.998956i	$-0.485455\pi$
$811$	26.5883	−	15.3507i	0.933640	−	0.539038i	0.887961	+	0.459919i	$0.152121\pi$
$812$	5.31543	+	19.8374i	0.186535	+	0.696158i
$813$	−8.59979	+	32.0949i	−0.301608	+	1.12562i
$814$	−24.0975	−	13.9127i	−0.844619	−	0.487641i
$815$		0			0
$816$		−	8.35546i		−	0.292500i
$817$	13.8099	−	25.9337i	0.483149	−	0.907305i
$818$	−3.28100	+	3.28100i	−0.114717	+	0.114717i
$819$	−38.9962	+	67.5434i	−1.36264	+	2.36016i
$820$		0			0
$821$	15.0157	+	26.0080i	0.524052	+	0.907685i	0.999608	+	0.0279994i	$0.00891367\pi$
$821$	15.0157	+	26.0080i	0.524052	+	0.907685i	−0.475556	+	0.879686i	$0.657753\pi$
$822$	−14.4521	+	3.87242i	−0.504073	+	0.135066i
$823$	−21.3968	−	5.73326i	−0.745846	−	0.199849i	−0.134171	−	0.990958i	$-0.542837\pi$
$823$	−21.3968	−	5.73326i	−0.745846	−	0.199849i	−0.611675	+	0.791109i	$0.709504\pi$
$824$			14.8706i			0.518042i
$825$		0			0
$826$	13.3228	+	23.0757i	0.463559	+	0.802908i
$827$	−42.6296	−	11.4226i	−1.48238	−	0.397201i	−0.575220	−	0.817999i	$-0.695084\pi$
$827$	−42.6296	−	11.4226i	−1.48238	−	0.397201i	−0.907155	+	0.420797i	$0.861750\pi$
$828$	−14.1710	+	14.1710i	−0.492477	+	0.492477i
$829$	31.8391			1.10582			0.552909	−	0.833242i	$-0.313518\pi$
$829$	31.8391			1.10582			0.552909	+	0.833242i	$0.313518\pi$
$830$		0			0
$831$	21.2618	+	12.2755i	0.737564	+	0.425833i
$832$	3.75907	+	1.00724i	0.130322	+	0.0349197i
$833$	1.00139	+	3.73722i	0.0346960	+	0.129487i
$834$	38.7279	+	22.3596i	1.34104	+	0.774248i
$835$		0			0
$836$	−22.7108	−	5.25812i	−0.785469	−	0.181856i
$837$	−77.1277	−	77.1277i	−2.66592	−	2.66592i
$838$	3.16999	−	0.849396i	0.109505	−	0.0293419i
$839$	0.318407	−	0.551497i	0.0109926	−	0.0190398i	−0.860477	−	0.509490i	$-0.829834\pi$
$839$	0.318407	−	0.551497i	0.0109926	−	0.0190398i	0.871469	+	0.490450i	$0.163168\pi$
$840$		0			0
$841$	−10.4385	+	18.0800i	−0.359949	+	0.623449i
$842$	−3.48038	+	12.9889i	−0.119942	+	0.447629i
$843$	7.12990	−	7.12990i	0.245567	−	0.245567i
$844$	−20.1046			−0.692027
$845$		0			0
$846$	−14.3559	+	8.28838i	−0.493566	+	0.284960i
$847$	−36.1931	−	36.1931i	−1.24361	−	1.24361i
$848$	−2.50573	−	2.50573i	−0.0860471	−	0.0860471i
$849$	−31.0466	−	53.7743i	−1.06552	−	1.84553i
$850$		0			0
$851$	−13.1030	+	7.56502i	−0.449165	+	0.259325i
$852$	−13.7402	+	3.68167i	−0.470731	+	0.126132i
$853$	5.20959	+	19.4425i	0.178373	+	0.665698i	0.995952	+	0.0898816i	$0.0286489\pi$
$853$	5.20959	+	19.4425i	0.178373	+	0.665698i	−0.817579	+	0.575816i	$0.804684\pi$
$854$	−1.15893			−0.0396578
$855$		0			0
$856$	6.84117			0.233826
$857$	1.60544	+	5.99157i	0.0548407	+	0.204668i	0.987910	−	0.155028i	$-0.0495469\pi$
$857$	1.60544	+	5.99157i	0.0548407	+	0.204668i	−0.933069	+	0.359697i	$0.882880\pi$
$858$	63.2279	−	16.9419i	2.15857	−	0.578386i
$859$	−37.9676	+	21.9206i	−1.29544	+	0.747921i	−0.979612	−	0.200897i	$-0.935614\pi$
$859$	−37.9676	+	21.9206i	−1.29544	+	0.747921i	−0.315824	+	0.948818i	$0.602281\pi$
$860$		0			0
$861$	−24.3753	−	42.2192i	−0.830707	−	1.43883i
$862$	−3.88976	−	3.88976i	−0.132486	−	0.132486i
$863$	27.7012	+	27.7012i	0.942961	+	0.942961i	0.998459	−	0.0554975i	$-0.0176745\pi$
$863$	27.7012	+	27.7012i	0.942961	+	0.942961i	−0.0554975	+	0.998459i	$0.517674\pi$
$864$	−10.5999	+	6.11985i	−0.360616	+	0.208202i
$865$		0			0
$866$	−1.46475			−0.0497744
$867$	−22.1106	+	22.1106i	−0.750916	+	0.750916i
$868$	6.70722	−	25.0317i	0.227658	−	0.849631i
$869$	−6.16406	+	10.6765i	−0.209102	+	0.362175i
$870$		0			0
$871$	0.0715554	−	0.123938i	0.00242456	−	0.00419947i
$872$	1.24903	−	0.334677i	0.0422976	−	0.0113336i
$873$	67.6293	+	67.6293i	2.28890	+	2.28890i
$874$	−8.65052	+	9.26496i	−0.292608	+	0.313392i
$875$		0			0
$876$	−43.7817	−	25.2774i	−1.47925	−	0.854043i
$877$	−4.15797	−	15.5177i	−0.140405	−	0.523997i	−0.999917	−	0.0128823i	$-0.995899\pi$
$877$	−4.15797	−	15.5177i	−0.140405	−	0.523997i	0.859512	−	0.511115i	$-0.170767\pi$
$878$	18.9504	+	5.07775i	0.639545	+	0.171366i
$879$	40.0083	+	23.0988i	1.34945	+	0.779103i
$880$		0			0
$881$	−39.7348			−1.33870			−0.669350	−	0.742947i	$-0.733427\pi$
$881$	−39.7348			−1.33870			−0.669350	+	0.742947i	$0.733427\pi$
$882$	7.09707	−	7.09707i	0.238971	−	0.238971i
$883$	−16.7960	−	4.50048i	−0.565231	−	0.151453i	−0.0351224	−	0.999383i	$-0.511182\pi$
$883$	−16.7960	−	4.50048i	−0.565231	−	0.151453i	−0.530108	+	0.847930i	$0.677849\pi$
$884$	5.16942	+	8.95369i	0.173866	+	0.301145i
$885$		0			0
$886$		−	9.48470i		−	0.318645i
$887$	19.1732	+	5.13744i	0.643773	+	0.172499i	0.565912	−	0.824466i	$-0.308524\pi$
$887$	19.1732	+	5.13744i	0.643773	+	0.172499i	0.0778613	+	0.996964i	$0.475191\pi$
$888$	−15.8062	+	4.23525i	−0.530420	+	0.142126i
$889$	26.1213	+	45.2434i	0.876079	+	1.51741i
$890$		0			0
$891$	−47.6513	+	82.5345i	−1.59638	+	2.76501i
$892$	−20.3841	+	20.3841i	−0.682510	+	0.682510i
$893$	−8.89491	+	5.55044i	−0.297657	+	0.185739i
$894$			70.1050i			2.34466i
$895$		0			0
$896$	−2.51839	−	1.45399i	−0.0841334	−	0.0485744i
$897$	9.21211	−	34.3801i	0.307583	−	1.14792i
$898$	7.94942	+	29.6676i	0.265275	+	0.990021i
$899$	54.5049	−	31.4684i	1.81784	−	1.04953i
$900$		0			0
$901$		−	9.41423i		−	0.313633i
$902$	−7.37808	+	27.5354i	−0.245663	+	0.916827i
$903$	15.9558	−	59.5480i	0.530977	−	1.98163i
$904$			6.29753i			0.209453i
$905$		0			0
$906$	2.24557	−	1.29648i	0.0746041	−	0.0430727i
$907$	−1.38200	−	5.15770i	−0.0458886	−	0.171259i	0.939179	−	0.343429i	$-0.111589\pi$
$907$	−1.38200	−	5.15770i	−0.0458886	−	0.171259i	−0.985067	+	0.172171i	$0.944922\pi$
$908$	−2.21722	+	8.27478i	−0.0735811	+	0.274608i
$909$	−115.049	−	66.4236i	−3.81593	−	2.20313i
$910$		0			0
$911$			49.3278i			1.63430i	0.576423	+	0.817151i	$0.304448\pi$
$911$			49.3278i			1.63430i	−0.576423	+	0.817151i	$0.695552\pi$
$912$	−11.6306	+	7.25751i	−0.385127	+	0.240320i
$913$	−18.4973	+	18.4973i	−0.612172	+	0.612172i
$914$	−6.74057	+	11.6750i	−0.222958	+	0.386175i
$915$		0			0
$916$	−1.17768	−	2.03980i	−0.0389117	−	0.0673970i
$917$	45.4146	−	12.1688i	1.49972	−	0.401850i
$918$	−31.4087	−	8.41594i	−1.03664	−	0.277767i
$919$			34.4216i			1.13546i	0.823214	+	0.567732i	$0.192179\pi$
$919$			34.4216i			1.13546i	−0.823214	+	0.567732i	$0.807821\pi$
$920$		0			0
$921$	9.01519	+	15.6148i	0.297061	+	0.514524i
$922$	31.2762	+	8.38042i	1.03003	+	0.275995i
$923$	12.4462	−	12.4462i	0.409670	−	0.409670i
$924$	−48.9126			−1.60911
$925$		0			0
$926$	−21.9868	−	12.6941i	−0.722531	−	0.417154i
$927$	98.9914	+	26.5247i	3.25130	+	0.871184i
$928$	−1.82787	−	6.82172i	−0.0600029	−	0.223934i
$929$	0.672048	+	0.388007i	0.0220492	+	0.0127301i	0.510984	−	0.859590i	$-0.329281\pi$
$929$	0.672048	+	0.388007i	0.0220492	+	0.0127301i	−0.488935	+	0.872320i	$0.662614\pi$
$930$		0			0
$931$	4.33231	−	4.64003i	0.141986	−	0.152071i
$932$	−10.9849	−	10.9849i	−0.359822	−	0.359822i
$933$	−25.6899	+	6.88358i	−0.841049	+	0.225358i
$934$	6.89636	−	11.9448i	0.225656	−	0.390847i
$935$		0			0
$936$	13.4101	−	23.2269i	0.438321	−	0.759195i
$937$	5.70358	−	21.2860i	0.186328	−	0.695385i	−0.808015	−	0.589162i	$-0.799458\pi$
$937$	5.70358	−	21.2860i	0.186328	−	0.695385i	0.994342	−	0.106222i	$-0.0338755\pi$
$938$	−0.0756159	+	0.0756159i	−0.00246895	+	0.00246895i
$939$	11.2634			0.367569
$940$		0			0
$941$	19.2419	−	11.1093i	0.627268	−	0.362154i	−0.152425	−	0.988315i	$-0.548708\pi$
$941$	19.2419	−	11.1093i	0.627268	−	0.362154i	0.779693	+	0.626162i	$0.215375\pi$
$942$	4.41088	+	4.41088i	0.143714	+	0.143714i
$943$	10.9605	+	10.9605i	0.356922	+	0.356922i
$944$	−4.58145	−	7.93531i	−0.149114	−	0.258272i
$945$		0			0
$946$	−31.2192	+	18.0244i	−1.01502	+	0.586024i
$947$	36.5616	−	9.79664i	1.18809	−	0.318348i	0.389960	−	0.920832i	$-0.372489\pi$
$947$	36.5616	−	9.79664i	1.18809	−	0.318348i	0.798131	+	0.602484i	$0.205822\pi$
$948$	1.87644	+	7.00296i	0.0609439	+	0.227446i
$949$	62.5551			2.03063
$950$		0			0
$951$	9.39214			0.304561
$952$	−1.99951	−	7.46227i	−0.0648045	−	0.241854i
$953$	1.26143	−	0.337998i	0.0408616	−	0.0109488i	−0.238330	−	0.971184i	$-0.576600\pi$
$953$	1.26143	−	0.337998i	0.0408616	−	0.0109488i	0.279192	+	0.960235i	$0.409933\pi$
$954$	−21.1497	+	12.2108i	−0.684747	+	0.395339i
$955$		0			0
$956$	10.5552	+	18.2821i	0.341378	+	0.591285i
$957$	−83.9971	−	83.9971i	−2.71524	−	2.71524i
$958$	18.7297	+	18.7297i	0.605129	+	0.605129i
$959$	−11.9805	+	6.91692i	−0.386869	+	0.223359i
$960$		0			0
$961$	−48.4162			−1.56181
$962$	14.3176	−	14.3176i	0.461617	−	0.461617i
$963$	12.2026	−	45.5406i	0.393222	−	1.46753i
$964$	14.3238	−	24.8096i	0.461339	−	0.799063i
$965$		0			0
$966$	−13.2981	+	23.0329i	−0.427858	+	0.741072i
$967$	0.103293	−	0.0276774i	0.00332169	−	0.000890044i	−0.257158	−	0.966369i	$-0.582786\pi$
$967$	0.103293	−	0.0276774i	0.00332169	−	0.000890044i	0.260480	+	0.965479i	$0.416119\pi$
$968$	12.4461	+	12.4461i	0.400033	+	0.400033i
$969$	−35.4820	−	8.21499i	−1.13985	−	0.263903i
$970$		0			0
$971$	−28.3228	−	16.3522i	−0.908921	−	0.524766i	−0.0288374	−	0.999584i	$-0.509181\pi$
$971$	−28.3228	−	16.3522i	−0.908921	−	0.524766i	−0.880084	+	0.474818i	$0.842514\pi$
$972$	5.00219	+	18.6684i	0.160445	+	0.598790i
$973$	39.9387	+	10.7015i	1.28038	+	0.343076i
$974$	5.69154	+	3.28601i	0.182369	+	0.105291i
$975$		0			0
$976$	0.398534			0.0127568
$977$	2.79413	−	2.79413i	0.0893920	−	0.0893920i	−0.660997	−	0.750389i	$-0.729866\pi$
$977$	2.79413	−	2.79413i	0.0893920	−	0.0893920i	0.750389	+	0.660997i	$0.229866\pi$
$978$	−1.17109	−	0.313792i	−0.0374473	−	0.0100340i
$979$	−35.7355	−	61.8957i	−1.14211	−	1.97820i
$980$		0			0
$981$		−	8.91158i		−	0.284525i
$982$	−11.9202	−	3.19401i	−0.380389	−	0.101925i
$983$	9.12899	−	2.44611i	0.291170	−	0.0780187i	−0.110278	−	0.993901i	$-0.535174\pi$
$983$	9.12899	−	2.44611i	0.291170	−	0.0780187i	0.401447	+	0.915882i	$0.368507\pi$
$984$	8.38219	+	14.5184i	0.267215	+	0.462829i
$985$		0			0
$986$	9.38114	−	16.2486i	0.298756	−	0.517461i
$987$	−15.5556	+	15.5556i	−0.495140	+	0.495140i
$988$	7.97317	−	14.9728i	0.253660	−	0.476349i
$989$			19.6015i			0.623290i
$990$		0			0
$991$	14.4316	+	8.33211i	0.458436	+	0.264678i	0.711387	−	0.702801i	$-0.248068\pi$
$991$	14.4316	+	8.33211i	0.458436	+	0.264678i	−0.252950	+	0.967479i	$0.581401\pi$
$992$	−2.30649	+	8.60792i	−0.0732310	+	0.273302i
$993$	−14.4806	−	54.0423i	−0.459528	−	1.71498i
$994$	−11.3903	+	6.57622i	−0.361280	+	0.208585i
$995$		0			0
$996$			15.3838i			0.487455i
$997$	0.971062	−	3.62405i	0.0307538	−	0.114775i	−0.948843	−	0.315749i	$-0.897744\pi$
$997$	0.971062	−	3.62405i	0.0307538	−	0.114775i	0.979596	+	0.200974i	$0.0644108\pi$
$998$	−2.61457	+	9.75771i	−0.0827628	+	0.308875i
$999$			63.6823i			2.01482i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	950.2.q.e.407.3	yes	24
5.2	odd	4	inner	950.2.q.e.293.4	yes	24
5.3	odd	4	inner	950.2.q.e.293.3	yes	24
5.4	even	2	inner	950.2.q.e.407.4	yes	24
19.12	odd	6	inner	950.2.q.e.107.3	✓	24
95.12	even	12	inner	950.2.q.e.943.4	yes	24
95.69	odd	6	inner	950.2.q.e.107.4	yes	24
95.88	even	12	inner	950.2.q.e.943.3	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.q.e.107.3	✓	24	19.12	odd	6	inner
950.2.q.e.107.4	yes	24	95.69	odd	6	inner
950.2.q.e.293.3	yes	24	5.3	odd	4	inner
950.2.q.e.293.4	yes	24	5.2	odd	4	inner
950.2.q.e.407.3	yes	24	1.1	even	1	trivial
950.2.q.e.407.4	yes	24	5.4	even	2	inner
950.2.q.e.943.3	yes	24	95.88	even	12	inner
950.2.q.e.943.4	yes	24	95.12	even	12	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:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.q (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(3.03794 - 0.814012i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.57255 - 2.72374i) q^{6} +(-2.05625 - 2.05625i) q^{7} +(0.707107 + 0.707107i) q^{8} +(5.96836 - 3.44584i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(3.03794 - 0.814012i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(-1.57255 - 2.72374i) q^{6} +(-2.05625 - 2.05625i) q^{7} +(0.707107 + 0.707107i) q^{8} +(5.96836 - 3.44584i) q^{9} -5.34803 q^{11} +(-2.22392 + 2.22392i) q^{12} +(1.00724 - 3.75907i) q^{13} +(-1.45399 + 2.51839i) q^{14} +(0.500000 - 0.866025i) q^{16} +(2.56613 - 0.687594i) q^{17} +(-4.87315 - 4.87315i) q^{18} +(-3.18604 - 2.97475i) q^{19} +(-7.92059 - 4.57295i) q^{21} +(1.38417 + 5.16580i) q^{22} +(2.80890 + 0.752641i) q^{23} +(2.72374 + 1.57255i) q^{24} -3.89167 q^{26} +(8.65478 - 8.65478i) q^{27} +(2.80890 + 0.752641i) q^{28} +(3.53118 + 6.11619i) q^{29} -8.91158i q^{31} +(-0.965926 - 0.258819i) q^{32} +(-16.2470 + 4.35337i) q^{33} +(-1.32833 - 2.30073i) q^{34} +(-3.44584 + 5.96836i) q^{36} +(-3.67903 + 3.67903i) q^{37} +(-2.04878 + 3.84740i) q^{38} -12.2397i q^{39} +(4.61619 + 2.66516i) q^{41} +(-2.36713 + 8.83426i) q^{42} +(1.74459 + 6.51089i) q^{43} +(4.63153 - 2.67402i) q^{44} -2.90798i q^{46} +(0.622546 - 2.32337i) q^{47} +(0.814012 - 3.03794i) q^{48} +1.45636i q^{49} +(7.23604 - 4.17773i) q^{51} +(1.00724 + 3.75907i) q^{52} +(0.917161 - 3.42289i) q^{53} +(-10.5999 - 6.11985i) q^{54} -2.90798i q^{56} +(-12.1005 - 6.44362i) q^{57} +(4.99385 - 4.99385i) q^{58} +(4.58145 - 7.93531i) q^{59} +(0.199267 + 0.345141i) q^{61} +(-8.60792 + 2.30649i) q^{62} +(-19.3580 - 5.18696i) q^{63} +1.00000i q^{64} +(8.41006 + 14.5666i) q^{66} +(0.0355206 + 0.00951772i) q^{67} +(-1.87854 + 1.87854i) q^{68} +9.14590 q^{69} +(3.91692 + 2.26144i) q^{71} +(6.65684 + 1.78370i) q^{72} +(4.16029 + 15.5264i) q^{73} +(4.50587 + 2.60147i) q^{74} +(4.24657 + 0.983188i) q^{76} +(10.9969 + 10.9969i) q^{77} +(-11.8226 + 3.16787i) q^{78} +(1.15259 - 1.99634i) q^{79} +(8.91006 - 15.4327i) q^{81} +(1.37959 - 5.14869i) q^{82} +(3.45871 - 3.45871i) q^{83} +9.14590 q^{84} +(5.83751 - 3.37029i) q^{86} +(15.7062 + 15.7062i) q^{87} +(-3.78163 - 3.78163i) q^{88} +(6.68199 + 11.5735i) q^{89} +(-9.80073 + 5.65846i) q^{91} +(-2.80890 + 0.752641i) q^{92} +(-7.25414 - 27.0728i) q^{93} -2.40533 q^{94} -3.14510 q^{96} +(3.59188 + 13.4051i) q^{97} +(1.40674 - 0.376934i) q^{98} +(-31.9190 + 18.4284i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{6}+O(q^{10}) \) 24 * q - 12 * q^6	\( 24 q - 12 q^{6} - 48 q^{11} + 12 q^{16} - 84 q^{21} + 24 q^{26} - 24 q^{36} + 48 q^{41} + 12 q^{51} + 12 q^{61} + 24 q^{71} + 36 q^{76} + 12 q^{81} - 36 q^{86} - 228 q^{91} - 24 q^{96}+O(q^{100}) \) 24 * q - 12 * q^6 - 48 * q^11 + 12 * q^16 - 84 * q^21 + 24 * q^26 - 24 * q^36 + 48 * q^41 + 12 * q^51 + 12 * q^61 + 24 * q^71 + 36 * q^76 + 12 * q^81 - 36 * q^86 - 228 * q^91 - 24 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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