LMFDB - Embedded newform 950.2.q.e.107.3

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			107.3
Character	$\chi$	$=$	950.107
Dual form			950.2.q.e.293.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 - 0.258819i) q^{2} +(0.814012 - 3.03794i) q^{3} +(0.866025 + 0.500000i) q^{4} +(-1.57255 + 2.72374i) q^{6} +(-2.05625 - 2.05625i) q^{7} +(-0.707107 - 0.707107i) q^{8} +(-5.96836 - 3.44584i) q^{9} +O(q^{10})$	\(q+(-0.965926 - 0.258819i) q^{2} +(0.814012 - 3.03794i) 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} +(3.75907 - 1.00724i) q^{13} +(1.45399 + 2.51839i) q^{14} +(0.500000 + 0.866025i) q^{16} +(-0.687594 + 2.56613i) q^{17} +(4.87315 + 4.87315i) q^{18} +(3.18604 - 2.97475i) q^{19} +(-7.92059 + 4.57295i) q^{21} +(5.16580 + 1.38417i) q^{22} +(-0.752641 - 2.80890i) q^{23} +(-2.72374 + 1.57255i) q^{24} -3.89167 q^{26} +(-8.65478 + 8.65478i) q^{27} +(-0.752641 - 2.80890i) q^{28} +(-3.53118 + 6.11619i) q^{29} +8.91158i q^{31} +(-0.258819 - 0.965926i) q^{32} +(-4.35337 + 16.2470i) q^{33} +(1.32833 - 2.30073i) q^{34} +(-3.44584 - 5.96836i) q^{36} +(3.67903 - 3.67903i) q^{37} +(-3.84740 + 2.04878i) q^{38} -12.2397i q^{39} +(4.61619 - 2.66516i) q^{41} +(8.83426 - 2.36713i) q^{42} +(-6.51089 - 1.74459i) q^{43} +(-4.63153 - 2.67402i) q^{44} +2.90798i q^{46} +(-2.32337 + 0.622546i) q^{47} +(3.03794 - 0.814012i) q^{48} +1.45636i q^{49} +(7.23604 + 4.17773i) q^{51} +(3.75907 + 1.00724i) q^{52} +(3.42289 - 0.917161i) q^{53} +(10.5999 - 6.11985i) q^{54} +2.90798i q^{56} +(-6.44362 - 12.1005i) q^{57} +(4.99385 - 4.99385i) q^{58} +(-4.58145 - 7.93531i) q^{59} +(0.199267 - 0.345141i) q^{61} +(2.30649 - 8.60792i) q^{62} +(5.18696 + 19.3580i) q^{63} +1.00000i q^{64} +(8.41006 - 14.5666i) q^{66} +(0.00951772 + 0.0355206i) q^{67} +(-1.87854 + 1.87854i) q^{68} -9.14590 q^{69} +(3.91692 - 2.26144i) q^{71} +(1.78370 + 6.65684i) q^{72} +(-15.5264 - 4.16029i) q^{73} +(-4.50587 + 2.60147i) q^{74} +(4.24657 - 0.983188i) q^{76} +(10.9969 + 10.9969i) q^{77} +(-3.16787 + 11.8226i) q^{78} +(-1.15259 - 1.99634i) q^{79} +(8.91006 + 15.4327i) q^{81} +(-5.14869 + 1.37959i) 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} +(0.752641 - 2.80890i) q^{92} +(27.0728 + 7.25414i) q^{93} +2.40533 q^{94} -3.14510 q^{96} +(13.4051 + 3.59188i) q^{97} +(0.376934 - 1.40674i) 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 $\left(\mathbb{Z}/950\mathbb{Z}\right)^\times$.

$n$	$77$	$401$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$2$	−0.965926	−	0.258819i	−0.683013	−	0.183013i
$3$	0.814012	−	3.03794i	0.469970	−	1.75395i	−0.169891	−	0.985463i	$-0.554342\pi$
$3$	0.814012	−	3.03794i	0.469970	−	1.75395i	0.639861	−	0.768490i	$-0.278992\pi$
$4$	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
$13$	3.75907	−	1.00724i	1.04258	−	0.279358i	0.303396	−	0.952865i	$-0.401879\pi$
$13$	3.75907	−	1.00724i	1.04258	−	0.279358i	0.739181	+	0.673507i	$0.235213\pi$
$14$	1.45399	+	2.51839i	0.388596	+	0.673067i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	−0.687594	+	2.56613i	−0.166766	+	0.622379i	0.831042	+	0.556209i	$0.187745\pi$
$17$	−0.687594	+	2.56613i	−0.166766	+	0.622379i	−0.997808	+	0.0661699i	$0.978922\pi$
$18$	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
$22$	5.16580	+	1.38417i	1.10135	+	0.295107i
$23$	−0.752641	−	2.80890i	−0.156937	−	0.585695i	−0.998932	−	0.0462102i	$-0.985286\pi$
$23$	−0.752641	−	2.80890i	−0.156937	−	0.585695i	0.841995	−	0.539485i	$-0.181381\pi$
$24$	−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
$28$	−0.752641	−	2.80890i	−0.142236	−	0.530831i
$29$	−3.53118	+	6.11619i	−0.655724	+	1.13575i	0.325987	+	0.945374i	$0.394303\pi$
$29$	−3.53118	+	6.11619i	−0.655724	+	1.13575i	−0.981712	+	0.190374i	$0.939030\pi$
$30$		0			0
$31$			8.91158i			1.60057i	0.599622	+	0.800283i	$0.295318\pi$
$31$			8.91158i			1.60057i	−0.599622	+	0.800283i	$0.704682\pi$
$32$	−0.258819	−	0.965926i	−0.0457532	−	0.170753i
$33$	−4.35337	+	16.2470i	−0.757824	+	2.82824i
$34$	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	−0.336762	−	0.941590i	$-0.609332\pi$
$37$	3.67903	−	3.67903i	0.604828	−	0.604828i	0.941590	+	0.336762i	$0.109332\pi$
$38$	−3.84740	+	2.04878i	−0.624131	+	0.332356i
$39$		−	12.2397i		−	1.95992i
$40$		0			0
$41$	4.61619	−	2.66516i	0.720928	−	0.416228i	−0.0941664	−	0.995556i	$-0.530019\pi$
$41$	4.61619	−	2.66516i	0.720928	−	0.416228i	0.815094	+	0.579329i	$0.196685\pi$
$42$	8.83426	−	2.36713i	1.36316	−	0.365257i
$43$	−6.51089	−	1.74459i	−0.992902	−	0.266047i	−0.274433	−	0.961606i	$-0.588490\pi$
$43$	−6.51089	−	1.74459i	−0.992902	−	0.266047i	−0.718469	+	0.695559i	$0.755157\pi$
$44$	−4.63153	−	2.67402i	−0.698230	−	0.403123i
$45$		0			0
$46$			2.90798i			0.428759i
$47$	−2.32337	+	0.622546i	−0.338899	+	0.0908076i	−0.424255	−	0.905543i	$-0.639464\pi$
$47$	−2.32337	+	0.622546i	−0.338899	+	0.0908076i	0.0853560	+	0.996351i	$0.472797\pi$
$48$	3.03794	−	0.814012i	0.438488	−	0.117493i
$49$			1.45636i			0.208052i
$50$		0			0
$51$	7.23604	+	4.17773i	1.01325	+	0.584999i
$52$	3.75907	+	1.00724i	0.521289	+	0.139679i
$53$	3.42289	−	0.917161i	0.470170	−	0.125982i	−0.0159517	−	0.999873i	$-0.505078\pi$
$53$	3.42289	−	0.917161i	0.470170	−	0.125982i	0.486122	+	0.873891i	$0.338411\pi$
$54$	10.5999	−	6.11985i	1.44246	−	0.832806i
$55$		0			0
$56$			2.90798i			0.388596i
$57$	−6.44362	−	12.1005i	−0.853478	−	1.60275i
$58$	4.99385	−	4.99385i	0.655724	−	0.655724i
$59$	−4.58145	−	7.93531i	−0.596454	−	1.03309i	−0.993340	−	0.115221i	$-0.963242\pi$
$59$	−4.58145	−	7.93531i	−0.596454	−	1.03309i	0.396886	−	0.917868i	$-0.370091\pi$
$60$		0			0
$61$	0.199267	−	0.345141i	0.0255136	−	0.0441908i	−0.852987	−	0.521933i	$-0.825211\pi$
$61$	0.199267	−	0.345141i	0.0255136	−	0.0441908i	0.878500	+	0.477742i	$0.158545\pi$
$62$	2.30649	−	8.60792i	0.292924	−	1.09321i
$63$	5.18696	+	19.3580i	0.653495	+	2.43888i
$64$			1.00000i			0.125000i
$65$		0			0
$66$	8.41006	−	14.5666i	1.03521	−	1.79303i
$67$	0.00951772	+	0.0355206i	0.00116277	+	0.00433953i	0.966505	−	0.256649i	$-0.0826183\pi$
$67$	0.00951772	+	0.0355206i	0.00116277	+	0.00433953i	−0.965342	+	0.260988i	$0.915952\pi$
$68$	−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	−0.249230	−	0.968444i	$-0.580177\pi$
$71$	3.91692	−	2.26144i	0.464853	−	0.268383i	0.714083	+	0.700061i	$0.246844\pi$
$72$	1.78370	+	6.65684i	0.210211	+	0.784516i
$73$	−15.5264	−	4.16029i	−1.81723	−	0.486925i	−0.820787	−	0.571234i	$-0.806465\pi$
$73$	−15.5264	−	4.16029i	−1.81723	−	0.486925i	−0.996440	+	0.0843092i	$0.973132\pi$
$74$	−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
$78$	−3.16787	+	11.8226i	−0.358690	+	1.33865i
$79$	−1.15259	−	1.99634i	−0.129676	−	0.224605i	0.793875	−	0.608081i	$-0.208060\pi$
$79$	−1.15259	−	1.99634i	−0.129676	−	0.224605i	−0.923551	+	0.383476i	$0.874727\pi$
$80$		0			0
$81$	8.91006	+	15.4327i	0.990006	+	1.71474i
$82$	−5.14869	+	1.37959i	−0.568578	+	0.152350i
$83$	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	0.257202	+	0.966358i	$0.417200\pi$
$89$	−6.68199	+	11.5735i	−0.708290	+	1.22679i	−0.965491	+	0.260436i	$0.916134\pi$
$90$		0			0
$91$	−9.80073	−	5.65846i	−1.02740	−	0.593167i
$92$	0.752641	−	2.80890i	0.0784683	−	0.292848i
$93$	27.0728	+	7.25414i	2.80732	+	0.752219i
$94$	2.40533			0.248091
$95$		0			0
$96$	−3.14510			−0.320996
$97$	13.4051	+	3.59188i	1.36108	+	0.364700i	0.864212	−	0.503128i	$-0.167817\pi$
$97$	13.4051	+	3.59188i	1.36108	+	0.364700i	0.496866	+	0.867827i	$0.334484\pi$
$98$	0.376934	−	1.40674i	0.0380761	−	0.142102i
$99$	31.9190	+	18.4284i	3.20798	+	1.85213i
$100$		0			0
$101$	−9.63824	+	16.6939i	−0.959041	+	1.66111i	−0.234203	+	0.972188i	$0.575248\pi$
$101$	−9.63824	+	16.6939i	−0.959041	+	1.66111i	−0.724838	+	0.688919i	$0.758085\pi$
$102$	−5.90820	−	5.90820i	−0.584999	−	0.584999i
$103$	−10.5151	−	10.5151i	−1.03608	−	1.03608i	−0.999324	−	0.0367608i	$-0.988296\pi$
$103$	−10.5151	−	10.5151i	−1.03608	−	1.03608i	−0.0367608	−	0.999324i	$-0.511704\pi$
$104$	−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	−0.901153	−	0.433501i	$-0.857278\pi$
$107$	−4.83744	+	4.83744i	−0.467653	+	0.467653i	0.433501	+	0.901153i	$0.357278\pi$
$108$	−11.8226	+	3.16787i	−1.13763	+	0.304828i
$109$	−0.646547	−	1.11985i	−0.0619280	−	0.107262i	0.833399	−	0.552672i	$-0.186392\pi$
$109$	−0.646547	−	1.11985i	−0.0619280	−	0.107262i	−0.895327	+	0.445409i	$0.853058\pi$
$110$		0			0
$111$	−8.18188	−	14.1714i	−0.776589	−	1.34509i
$112$	0.752641	−	2.80890i	0.0711179	−	0.265416i
$113$	−4.45303	−	4.45303i	−0.418906	−	0.418906i	0.465921	−	0.884826i	$-0.345723\pi$
$113$	−4.45303	−	4.45303i	−0.418906	−	0.418906i	−0.884826	+	0.465921i	$0.845723\pi$
$114$	3.09223	+	13.3559i	0.289614	+	1.25089i
$115$		0			0
$116$	−6.11619	+	3.53118i	−0.567874	+	0.327862i
$117$	−25.9062	−	6.94156i	−2.39503	−	0.641747i
$118$	2.37153	+	8.85069i	0.218317	+	0.814772i
$119$	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
$123$	−4.33894	−	16.1932i	−0.391229	−	1.46009i
$124$	−4.45579	+	7.71765i	−0.400142	+	0.693066i
$125$		0			0
$126$		−	20.0409i		−	1.78538i
$127$	−4.64974	−	17.3531i	−0.412598	−	1.53984i	−0.789599	−	0.613623i	$-0.789711\pi$
$127$	−4.64974	−	17.3531i	−0.412598	−	1.53984i	0.377001	−	0.926213i	$-0.376955\pi$
$128$	0.258819	−	0.965926i	0.0228766	−	0.0853766i
$129$	−10.5999	+	18.3596i	−0.933269	+	1.61647i
$130$		0			0
$131$	−8.08407	−	14.0020i	−0.706309	−	1.22336i	−0.966217	−	0.257730i	$-0.917026\pi$
$131$	−8.08407	−	14.0020i	−0.706309	−	1.22336i	0.259908	−	0.965633i	$-0.416308\pi$
$132$	−11.8936	+	11.8936i	−1.03521	+	1.03521i
$133$	−12.6682	−	0.434471i	−1.09847	−	0.0376734i
$134$		−	0.0367736i		−	0.00317676i
$135$		0			0
$136$	2.30073	−	1.32833i	0.197286	−	0.113903i
$137$	−4.59510	+	1.23125i	−0.392586	+	0.105193i	−0.449711	−	0.893174i	$-0.648473\pi$
$137$	−4.59510	+	1.23125i	−0.392586	+	0.105193i	0.0571256	+	0.998367i	$0.481806\pi$
$138$	8.83426	+	2.36713i	0.752023	+	0.201504i
$139$	12.3137	+	7.10932i	1.04444	+	0.603005i	0.921086	−	0.389358i	$-0.127303\pi$
$139$	12.3137	+	7.10932i	1.04444	+	0.603005i	0.123349	+	0.992363i	$0.460637\pi$
$140$		0			0
$141$			7.56502i			0.637089i
$142$	−4.36876	+	1.17061i	−0.366618	+	0.0982350i
$143$	−20.1036	+	5.38675i	−1.68115	+	0.450462i
$144$		−	6.89167i		−	0.574306i
$145$		0			0
$146$	13.9206	+	8.03705i	1.15208	+	0.665151i
$147$	4.42434	+	1.18550i	0.364913	+	0.0977782i
$148$	5.02565	−	1.34662i	0.413106	−	0.110691i
$149$	19.3039	−	11.1451i	1.58144	−	0.913042i	0.586786	−	0.809742i	$-0.300393\pi$
$149$	19.3039	−	11.1451i	1.58144	−	0.913042i	0.994650	−	0.103300i	$-0.0329402\pi$
$150$		0			0
$151$		−	0.824445i		−	0.0670924i	−0.999437	−	0.0335462i	$-0.989320\pi$
$151$		−	0.824445i		−	0.0670924i	0.999437	−	0.0335462i	$-0.0106801\pi$
$152$	−4.35634	−	0.149406i	−0.353346	−	0.0121185i
$153$	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
$157$	0.513335	−	1.91579i	0.0409686	−	0.152897i	−0.942411	−	0.334456i	$-0.891448\pi$
$157$	0.513335	−	1.91579i	0.0409686	−	0.152897i	0.983380	+	0.181559i	$0.0581142\pi$
$158$	0.596622	+	2.22662i	0.0474647	+	0.177141i
$159$		−	11.1451i		−	0.883864i
$160$		0			0
$161$	−4.22818	+	7.32343i	−0.333227	+	0.577167i
$162$	−4.61219	−	17.2129i	−0.362367	−	1.35237i
$163$	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
$167$	−0.607716	−	2.26803i	−0.0470265	−	0.175505i	0.938418	−	0.345501i	$-0.112291\pi$
$167$	−0.607716	−	2.26803i	−0.0470265	−	0.175505i	−0.985445	+	0.169996i	$0.945624\pi$
$168$	8.83426	+	2.36713i	0.681578	+	0.182628i
$169$	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
$173$	4.79589	−	17.8985i	0.364625	−	1.36080i	−0.503303	−	0.864110i	$-0.667882\pi$
$173$	4.79589	−	17.8985i	0.364625	−	1.36080i	0.867928	−	0.496689i	$-0.165451\pi$
$174$	−11.1059	−	19.2360i	−0.841939	−	1.45828i
$175$		0			0
$176$	−2.67402	−	4.63153i	−0.201562	−	0.349115i
$177$	−27.8363	+	7.45872i	−2.09231	+	0.560632i
$178$	9.44976	−	9.44976i	0.708290	−	0.708290i
$179$	−6.96220			−0.520380			−0.260190	−	0.965557i	$-0.583785\pi$
$179$	−6.96220			−0.520380			−0.260190	+	0.965557i	$0.583785\pi$
$180$		0			0
$181$	4.92059	+	2.84090i	0.365744	+	0.211163i	0.671598	−	0.740916i	$-0.265608\pi$
$181$	4.92059	+	2.84090i	0.365744	+	0.211163i	−0.305853	+	0.952079i	$0.598942\pi$
$182$	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
$187$	3.67727	−	13.7238i	0.268909	−	1.00358i
$188$	−2.32337	−	0.622546i	−0.169449	−	0.0454038i
$189$	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	$0.517701\pi$
$192$	3.03794	+	0.814012i	0.219244	+	0.0587463i
$193$	−1.61851	+	6.04035i	−0.116503	+	0.434794i	−0.999395	−	0.0347817i	$-0.988926\pi$
$193$	−1.61851	+	6.04035i	−0.116503	+	0.434794i	0.882892	+	0.469576i	$0.155593\pi$
$194$	−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	$-0.337747\pi$
$199$	−0.338795	−	0.195603i	−0.0240165	−	0.0138660i	−0.511960	+	0.859009i	$0.671080\pi$
$200$		0			0
$201$	0.115657			0.00815780
$202$	13.6305	−	13.6305i	0.959041	−	0.959041i
$203$	19.8374	−	5.31543i	1.39232	−	0.373070i
$204$	4.17773	+	7.23604i	0.292500	+	0.506624i
$205$		0			0
$206$	7.43531	+	12.8783i	0.518042	+	0.897276i
$207$	−5.18696	+	19.3580i	−0.360518	+	1.34547i
$208$	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	0.238377	−	0.971173i	$-0.423384\pi$
$211$	17.4111	−	10.0523i	1.19863	−	0.692027i	0.960249	+	0.279145i	$0.0900511\pi$
$212$	3.42289	+	0.917161i	0.235085	+	0.0629909i
$213$	−3.68167	−	13.7402i	−0.252264	−	0.941462i
$214$	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
$218$	0.334677	+	1.24903i	0.0226672	+	0.0845952i
$219$	−25.2774	+	43.7817i	−1.70809	+	2.95849i
$220$		0			0
$221$			10.3388i			0.695465i
$222$	4.23525	+	15.8062i	0.284251	+	1.06084i
$223$	7.46109	−	27.8452i	0.499632	−	1.86465i	−0.00273558	−	0.999996i	$-0.500871\pi$
$223$	7.46109	−	27.8452i	0.499632	−	1.86465i	0.502367	−	0.864654i	$-0.332463\pi$
$224$	−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	−0.878956	−	0.476902i	$-0.841760\pi$
$227$	−6.05756	+	6.05756i	−0.402054	+	0.402054i	0.476902	+	0.878956i	$0.341760\pi$
$228$	0.469898	−	13.7011i	0.0311198	−	0.907379i
$229$			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
$232$	6.82172	−	1.82787i	0.447868	−	0.120006i
$233$	−15.0056	−	4.02075i	−0.983053	−	0.263408i	−0.268723	−	0.963218i	$-0.586602\pi$
$233$	−15.0056	−	4.02075i	−0.983053	−	0.263408i	−0.714330	+	0.699809i	$0.753268\pi$
$234$	23.2269	+	13.4101i	1.51839	+	0.876643i
$235$		0			0
$236$		−	9.16290i		−	0.596454i
$237$	−7.00296	+	1.87644i	−0.454891	+	0.121888i
$238$	−7.46227	+	1.99951i	−0.483707	+	0.129609i
$239$		−	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	−0.991848	−	0.127426i	$-0.959329\pi$
$241$	−24.8096	−	14.3238i	−1.59813	−	0.922679i	−0.606278	−	0.795253i	$-0.707338\pi$
$242$	−17.0017	−	4.55559i	−1.09291	−	0.292845i
$243$	18.6684	−	5.00219i	1.19758	−	0.320891i
$244$	0.345141	−	0.199267i	0.0220954	−	0.0127568i
$245$		0			0
$246$			16.7644i			1.06886i
$247$	8.98026	−	14.3914i	0.571400	−	0.915702i
$248$	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	−0.884073	−	0.467350i	$-0.845209\pi$
$251$	−0.590938	+	1.02353i	−0.0372997	+	0.0646050i	0.846773	+	0.531955i	$0.178542\pi$
$252$	−5.18696	+	19.3580i	−0.326748	+	1.21944i
$253$	4.02515	+	15.0221i	0.253059	+	0.944429i
$254$			17.9652i			1.12724i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.24070	+	15.8265i	0.264528	+	0.987230i	0.962539	+	0.271144i	$0.0874019\pi$
$257$	4.24070	+	15.8265i	0.264528	+	0.987230i	−0.698011	+	0.716087i	$0.745931\pi$
$258$	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
$262$	4.18462	+	15.6172i	0.258527	+	0.964836i
$263$	−11.3201	−	3.03320i	−0.698025	−	0.187035i	−0.107679	−	0.994186i	$-0.534342\pi$
$263$	−11.3201	−	3.03320i	−0.698025	−	0.187035i	−0.590346	+	0.807150i	$0.701009\pi$
$264$	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
$268$	−0.00951772	+	0.0355206i	−0.000581387	+	0.00216977i
$269$	−2.95806	−	5.12352i	−0.180356	−	0.312386i	0.761646	−	0.647994i	$-0.224392\pi$
$269$	−2.95806	−	5.12352i	−0.180356	−	0.312386i	−0.942002	+	0.335608i	$0.891058\pi$
$270$		0			0
$271$	−5.28235	−	9.14929i	−0.320880	−	0.555780i	0.659790	−	0.751450i	$-0.270645\pi$
$271$	−5.28235	−	9.14929i	−0.320880	−	0.555780i	−0.980670	+	0.195670i	$0.937312\pi$
$272$	−2.56613	+	0.687594i	−0.155595	+	0.0416915i
$273$	−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	0.580524	−	0.814243i	$-0.302848\pi$
$281$	2.77648	+	1.60300i	0.165631	+	0.0956270i	−0.414893	+	0.909870i	$0.636181\pi$
$282$	1.95797	−	7.30724i	0.116595	−	0.435140i
$283$	19.0701	+	5.10982i	1.13360	+	0.303747i	0.776375	−	0.630271i	$-0.217056\pi$
$283$	19.0701	+	5.10982i	1.13360	+	0.303747i	0.357226	+	0.934018i	$0.383723\pi$
$284$	4.52287			0.268383
$285$		0			0
$286$	20.8128			1.23069
$287$	−14.9723	−	4.01182i	−0.883787	−	0.236810i
$288$	−1.78370	+	6.65684i	−0.105105	+	0.392258i
$289$	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	0.335319	−	0.942105i	$-0.391156\pi$
$293$	−10.3865	−	10.3865i	−0.606786	−	0.606786i	−0.942105	+	0.335319i	$0.891156\pi$
$294$	−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
$298$	−21.5307	+	5.76913i	−1.24724	+	0.334197i
$299$	−5.65846	−	9.80073i	−0.327237	−	0.566791i
$300$		0			0
$301$	9.80073	+	16.9754i	0.564905	+	0.978444i
$302$	−0.213382	+	0.796353i	−0.0122788	+	0.0458249i
$303$	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
$307$	5.53750	+	1.48377i	0.316042	+	0.0846831i	0.413353	−	0.910571i	$-0.364358\pi$
$307$	5.53750	+	1.48377i	0.316042	+	0.0846831i	−0.0973112	+	0.995254i	$0.531024\pi$
$308$	4.02515	+	15.0221i	0.229354	+	0.855962i
$309$	−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
$313$	−0.926899	−	3.45924i	−0.0523914	−	0.195528i	0.934770	−	0.355254i	$-0.115606\pi$
$313$	−0.926899	−	3.45924i	−0.0523914	−	0.195528i	−0.987161	+	0.159726i	$0.948939\pi$
$314$	−0.991688	+	1.71765i	−0.0559642	+	0.0969328i
$315$		0			0
$316$		−	2.30517i		−	0.129676i
$317$	0.772904	+	2.88452i	0.0434106	+	0.162011i	0.984228	−	0.176902i	$-0.0566076\pi$
$317$	0.772904	+	2.88452i	0.0434106	+	0.162011i	−0.940818	+	0.338913i	$0.889941\pi$
$318$	−2.88456	+	10.7653i	−0.161758	+	0.603690i
$319$	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
$323$	5.44290	+	10.2212i	0.302851	+	0.568724i
$324$			17.8201i			0.990006i
$325$		0			0
$326$	−0.333843	+	0.192744i	−0.0184898	+	0.0106751i
$327$	−3.92834	+	1.05259i	−0.217238	+	0.0582086i
$328$	−5.14869	−	1.37959i	−0.284289	−	0.0761750i
$329$	6.05756	+	3.49733i	0.333964	+	0.192814i
$330$		0			0
$331$			17.7892i			0.977781i	0.872345	+	0.488890i	$0.162598\pi$
$331$			17.7892i			0.977781i	−0.872345	+	0.488890i	$0.837402\pi$
$332$	4.72469	−	1.26598i	0.259301	−	0.0694795i
$333$	−34.6351	+	9.28045i	−1.89799	+	0.508565i
$334$			2.34803i			0.128479i
$335$		0			0
$336$	−7.92059	−	4.57295i	−0.432103	−	0.249475i
$337$	−25.1577	−	6.74098i	−1.37043	−	0.367205i	−0.502792	−	0.864407i	$-0.667694\pi$
$337$	−25.1577	−	6.74098i	−1.37043	−	0.367205i	−0.867635	+	0.497202i	$0.834361\pi$
$338$	−2.07201	+	0.555193i	−0.112702	+	0.0301985i
$339$	−17.1528	+	9.90319i	−0.931614	+	0.537868i
$340$		0			0
$341$		−	47.6594i		−	2.58090i
$342$	30.0224	+	1.02966i	1.62343	+	0.0556776i
$343$	−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
$347$	−5.17047	+	19.2965i	−0.277565	+	1.03589i	0.676537	+	0.736408i	$0.263480\pi$
$347$	−5.17047	+	19.2965i	−0.277565	+	1.03589i	−0.954103	+	0.299480i	$0.903187\pi$
$348$	5.74885	+	21.4550i	0.308171	+	1.15011i
$349$		−	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
$352$	1.38417	+	5.16580i	0.0737767	+	0.275338i
$353$	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
$357$	−6.28866	−	23.4696i	−0.332831	−	1.24214i
$358$	6.72497	+	1.80195i	0.355426	+	0.0952361i
$359$	−6.04394	+	3.48947i	−0.318987	+	0.184167i	−0.650941	−	0.759128i	$-0.725625\pi$
$359$	−6.04394	+	3.48947i	−0.318987	+	0.184167i	0.331954	+	0.943296i	$0.392292\pi$
$360$		0			0
$361$	1.30173	−	18.9554i	0.0685120	−	0.997650i
$362$	−4.01764	−	4.01764i	−0.211163	−	0.211163i
$363$	14.3278	−	53.4721i	0.752015	−	2.80656i
$364$	−5.65846	−	9.80073i	−0.296584	−	0.513698i
$365$		0			0
$366$	0.626716	+	1.08550i	0.0327590	+	0.0567402i
$367$	−16.8928	+	4.52640i	−0.881795	+	0.236276i	−0.671181	−	0.741293i	$-0.734213\pi$
$367$	−16.8928	+	4.52640i	−0.881795	+	0.236276i	−0.210614	+	0.977569i	$0.567546\pi$
$368$	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	0.838119	−	0.545487i	$-0.183655\pi$
$373$	5.65167	+	5.65167i	0.292633	+	0.292633i	−0.545487	+	0.838119i	$0.683655\pi$
$374$	−7.10395	+	12.3044i	−0.367336	+	0.636245i
$375$		0			0
$376$	2.08308	+	1.20267i	0.107427	+	0.0620228i
$377$	−7.11349	+	26.5479i	−0.366363	+	1.36729i
$378$	−34.3801	−	9.21211i	−1.76832	−	0.473820i
$379$	33.9677			1.74481			0.872403	−	0.488788i	$-0.162561\pi$
$379$	33.9677			1.74481			0.872403	+	0.488788i	$0.162561\pi$
$380$		0			0
$381$	−56.5025			−2.89471
$382$	1.48396	+	0.397626i	0.0759260	+	0.0203443i
$383$	−2.29371	+	8.56025i	−0.117203	+	0.437408i	−0.999442	−	0.0333933i	$-0.989369\pi$
$383$	−2.29371	+	8.56025i	−0.117203	+	0.437408i	0.882239	+	0.470802i	$0.156035\pi$
$384$	−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	$-0.612118\pi$
$389$	−26.2384	−	15.1488i	−1.33034	−	0.768073i	−0.985352	+	0.170534i	$0.945451\pi$
$390$		0			0
$391$	7.72551			0.390696
$392$	1.02980	−	1.02980i	0.0520130	−	0.0520130i
$393$	−49.1178	+	13.1611i	−2.47767	+	0.663888i
$394$	1.63824	+	2.83751i	0.0825331	+	0.142952i
$395$		0			0
$396$	18.4284	+	31.9190i	0.926064	+	1.60399i
$397$	1.41320	−	5.27412i	0.0709263	−	0.264700i	−0.921352	−	0.388728i	$-0.872915\pi$
$397$	1.41320	−	5.27412i	0.0709263	−	0.264700i	0.992279	+	0.124028i	$0.0395812\pi$
$398$	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	0.231425	−	0.972853i	$-0.425661\pi$
$401$	23.8228	−	13.7541i	1.18965	−	0.686847i	0.958228	+	0.286006i	$0.0923278\pi$
$402$	−0.111716	−	0.0299342i	−0.00557188	−	0.00149298i
$403$	8.97609	+	33.4992i	0.447131	+	1.66871i
$404$	−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
$408$	−2.16255	−	8.07075i	−0.107062	−	0.399562i
$409$	2.32002	−	4.01839i	0.114717	−	0.198696i	−0.802949	−	0.596047i	$-0.796737\pi$
$409$	2.32002	−	4.01839i	0.114717	−	0.198696i	0.917667	+	0.397351i	$0.130070\pi$
$410$		0			0
$411$			14.9619i			0.738015i
$412$	−3.84880	−	14.3639i	−0.189617	−	0.707659i
$413$	−6.89638	+	25.7376i	−0.339349	+	1.26647i
$414$	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
$418$	20.5760	−	10.9569i	1.00641	−	0.535921i
$419$			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	−0.756178	−	0.654366i	$-0.772936\pi$
$421$	−11.6456	+	6.72357i	−0.567570	+	0.327687i	0.188608	+	0.982052i	$0.439602\pi$
$422$	−19.4195	+	5.20344i	−0.945327	+	0.253300i
$423$	16.0119	+	4.29038i	0.778526	+	0.208605i
$424$	−3.06888	−	1.77182i	−0.149038	−	0.0860471i
$425$		0			0
$426$			14.2249i			0.689198i
$427$	−1.11944	+	0.299953i	−0.0541736	+	0.0145158i
$428$	−6.60806	+	1.77063i	−0.319413	+	0.0855864i
$429$			65.4584i			3.16036i
$430$		0			0
$431$	4.76396	+	2.75047i	0.229472	+	0.132486i	0.610328	−	0.792149i	$-0.291037\pi$
$431$	4.76396	+	2.75047i	0.229472	+	0.132486i	−0.380857	+	0.924634i	$0.624371\pi$
$432$	−11.8226	−	3.16787i	−0.568817	−	0.152414i
$433$	1.41484	−	0.379106i	0.0679930	−	0.0182187i	−0.224662	−	0.974437i	$-0.572128\pi$
$433$	1.41484	−	0.379106i	0.0679930	−	0.0182187i	0.292655	+	0.956218i	$0.405461\pi$
$434$	−22.4428	+	12.9574i	−1.07729	+	0.621973i
$435$		0			0
$436$		−	1.29309i		−	0.0619280i
$437$	−10.7537	−	6.71034i	−0.514420	−	0.320999i
$438$	35.7476	−	35.7476i	1.70809	−	1.70809i
$439$	9.80945	+	16.9905i	0.468180	+	0.810911i	0.999339	−	0.0363613i	$-0.0115767\pi$
$439$	9.80945	+	16.9905i	0.468180	+	0.810911i	−0.531159	+	0.847272i	$0.678243\pi$
$440$		0			0
$441$	5.01839	−	8.69210i	0.238971	−	0.413910i
$442$	2.67589	−	9.98655i	0.127279	−	0.475012i
$443$	−2.45482	−	9.16152i	−0.116632	−	0.435277i	0.882772	−	0.469802i	$-0.155675\pi$
$443$	−2.45482	−	9.16152i	−0.116632	−	0.435277i	−0.999404	+	0.0345253i	$0.989008\pi$
$444$		−	16.3638i		−	0.776589i
$445$		0			0
$446$	−14.4137	+	24.9653i	−0.682510	+	1.18214i
$447$	−18.1445	−	67.7162i	−0.858206	−	3.20287i
$448$	2.05625	−	2.05625i	0.0971489	−	0.0971489i
$449$	30.7142			1.44949			0.724746	−	0.689016i	$-0.241957\pi$
$449$	30.7142			1.44949			0.724746	+	0.689016i	$0.241957\pi$
$450$		0			0
$451$	−24.6875	+	14.2534i	−1.16249	+	0.671164i
$452$	−1.62992	−	6.08295i	−0.0766651	−	0.286118i
$453$	−2.50461	−	0.671108i	−0.117677	−	0.0315314i
$454$	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	$0.852109\pi$
$458$	0.609612	−	2.27510i	0.0284853	−	0.106309i
$459$	−16.2584	−	28.1603i	−0.758875	−	1.31441i
$460$		0			0
$461$	−16.1897	−	28.0414i	−0.754031	−	1.30602i	−0.945855	−	0.324591i	$-0.894773\pi$
$461$	−16.1897	−	28.0414i	−0.754031	−	1.30602i	0.191823	−	0.981429i	$-0.438560\pi$
$462$	−47.2459	+	12.6595i	−2.19808	+	0.588974i
$463$	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
$472$	−2.37153	+	8.85069i	−0.109159	+	0.407386i
$473$	34.8205	+	9.33012i	1.60105	+	0.428999i
$474$	7.25000			0.333003
$475$		0			0
$476$	7.72551			0.354098
$477$	−23.5894	−	6.32077i	−1.08009	−	0.289408i
$478$	−5.46375	+	20.3910i	−0.249906	+	0.932663i
$479$	22.9391	+	13.2439i	1.04811	+	0.605129i	0.922121	−	0.386902i	$-0.126455\pi$
$479$	22.9391	+	13.2439i	1.04811	+	0.605129i	0.125994	+	0.992031i	$0.459788\pi$
$480$		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	−0.593933	−	0.804514i	$-0.702426\pi$
$487$	4.64712	−	4.64712i	0.210581	−	0.210581i	0.804514	+	0.593933i	$0.202426\pi$
$488$	−0.384955	+	0.103148i	−0.0174261	+	0.00466930i
$489$	−0.606200	−	1.04997i	−0.0274133	−	0.0474812i
$490$		0			0
$491$	6.17035	+	10.6874i	0.278464	+	0.482314i	0.971003	−	0.239066i	$-0.0768413\pi$
$491$	6.17035	+	10.6874i	0.278464	+	0.482314i	−0.692539	+	0.721380i	$0.743508\pi$
$492$	4.33894	−	16.1932i	0.195615	−	0.730044i
$493$	−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
$497$	−12.7043	−	3.40410i	−0.569864	−	0.152695i
$498$	3.98163	+	14.8596i	0.178421	+	0.665876i
$499$	8.74853	−	5.05096i	0.391638	−	0.226112i	−0.291232	−	0.956653i	$-0.594065\pi$
$499$	8.74853	−	5.05096i	0.391638	−	0.226112i	0.682870	+	0.730540i	$0.260732\pi$
$500$		0			0
$501$	−7.38481			−0.329929
$502$	0.835713	−	0.835713i	0.0372997	−	0.0372997i
$503$	10.4119	+	38.8578i	0.464245	+	1.73258i	0.659382	+	0.751808i	$0.270818\pi$
$503$	10.4119	+	38.8578i	0.464245	+	1.73258i	−0.195137	+	0.980776i	$0.562515\pi$
$504$	10.0204	−	17.3559i	0.446345	−	0.773093i
$505$		0			0
$506$		−	15.5520i		−	0.691370i
$507$	−1.74614	−	6.51668i	−0.0775488	−	0.289416i
$508$	4.64974	−	17.3531i	0.206299	−	0.769918i
$509$	−6.62341	+	11.4721i	−0.293577	+	0.508491i	−0.974653	−	0.223722i	$-0.928179\pi$
$509$	−6.62341	+	11.4721i	−0.293577	+	0.508491i	0.681076	+	0.732213i	$0.261513\pi$
$510$		0			0
$511$	23.3716	+	40.4808i	1.03390	+	1.79077i
$512$	0.707107	−	0.707107i	0.0312500	−	0.0312500i
$513$	−1.82869	+	53.3203i	−0.0807386	+	2.35415i
$514$		−	16.3848i		−	0.722703i
$515$		0			0
$516$	−18.3596	+	10.5999i	−0.808234	+	0.466634i
$517$	12.4255	−	3.32940i	0.546472	−	0.146427i
$518$	14.6145	+	3.91594i	0.642124	+	0.172057i
$519$	−50.4706	−	29.1392i	−2.21542	−	1.27907i
$520$		0			0
$521$		−	11.1590i		−	0.488883i	−0.969664	−	0.244442i	$-0.921395\pi$
$521$		−	11.1590i		−	0.488883i	0.969664	−	0.244442i	$-0.0786047\pi$
$522$	−47.0131	+	12.5971i	−2.05771	+	0.551361i
$523$	−37.7421	+	10.1130i	−1.65035	+	0.442210i	−0.959711	−	0.280991i	$-0.909337\pi$
$523$	−37.7421	+	10.1130i	−1.65035	+	0.442210i	−0.690638	+	0.723200i	$0.742670\pi$
$524$		−	16.1681i		−	0.706309i
$525$		0			0
$526$	10.1493	+	5.85970i	0.442530	+	0.255495i
$527$	−22.8683	−	6.12754i	−0.996159	−	0.266920i
$528$	−16.2470	+	4.35337i	−0.707059	+	0.189456i
$529$	12.5952	−	7.27182i	0.547616	−	0.316166i
$530$		0			0
$531$			63.1477i			2.74038i
$532$	−10.7537	−	6.71034i	−0.466232	−	0.290930i
$533$	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
$537$	−5.66732	+	21.1507i	−0.244563	+	0.912721i
$538$	1.53121	+	5.71454i	0.0660150	+	0.246371i
$539$		−	7.78868i		−	0.335482i
$540$		0			0
$541$	−16.7544	+	29.0195i	−0.720329	+	1.24765i	0.240539	+	0.970640i	$0.422676\pi$
$541$	−16.7544	+	29.0195i	−0.720329	+	1.24765i	−0.960868	+	0.277007i	$0.910657\pi$
$542$	2.73434	+	10.2047i	0.117450	+	0.438330i
$543$	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
$547$	−4.56322	−	17.0302i	−0.195109	−	0.728157i	−0.992239	−	0.124348i	$-0.960316\pi$
$547$	−4.56322	−	17.0302i	−0.195109	−	0.728157i	0.797130	−	0.603808i	$-0.206351\pi$
$548$	−4.59510	−	1.23125i	−0.196293	−	0.0525965i
$549$	−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
$553$	−1.73497	+	6.47498i	−0.0737783	+	0.275344i
$554$	−3.90306	−	6.76030i	−0.165825	−	0.287217i
$555$		0			0
$556$	7.10932	+	12.3137i	0.301503	+	0.522218i
$557$	22.8271	−	6.11650i	0.967215	−	0.259165i	0.259563	−	0.965726i	$-0.416421\pi$
$557$	22.8271	−	6.11650i	0.967215	−	0.259165i	0.707652	+	0.706562i	$0.249755\pi$
$558$	−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	0.803234	−	0.595664i	$-0.203111\pi$
$563$	4.92515	+	4.92515i	0.207570	+	0.207570i	−0.595664	+	0.803234i	$0.703111\pi$
$564$	−3.78251	+	6.55150i	−0.159272	+	0.275868i
$565$		0			0
$566$	−17.0978	−	9.87142i	−0.718674	−	0.414927i
$567$	13.4122	−	50.0548i	0.563258	−	2.10211i
$568$	−4.36876	−	1.17061i	−0.183309	−	0.0491175i
$569$	30.5036			1.27878			0.639389	−	0.768883i	$-0.279187\pi$
$569$	30.5036			1.27878			0.639389	+	0.768883i	$0.279187\pi$
$570$		0			0
$571$	−24.4741			−1.02421			−0.512104	−	0.858923i	$-0.671134\pi$
$571$	−24.4741			−1.02421			−0.512104	+	0.858923i	$0.671134\pi$
$572$	−20.1036	−	5.38675i	−0.840574	−	0.225231i
$573$	−1.25057	+	4.66721i	−0.0522435	+	0.194975i
$574$	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
$583$	−18.3057	+	4.90501i	−0.758146	+	0.203145i
$584$	8.03705	+	13.9206i	0.332576	+	0.576038i
$585$		0			0
$586$	7.34437	+	12.7208i	0.303393	+	0.525492i
$587$	4.53584	−	16.9280i	0.187214	−	0.698693i	−0.806932	−	0.590645i	$-0.798873\pi$
$587$	4.53584	−	16.9280i	0.187214	−	0.698693i	0.994146	−	0.108048i	$-0.0344599\pi$
$588$	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
$592$	5.02565	+	1.34662i	0.206553	+	0.0553456i
$593$	4.03459	+	15.0573i	0.165681	+	0.618329i	0.997952	+	0.0639609i	$0.0203733\pi$
$593$	4.03459	+	15.0573i	0.165681	+	0.618329i	−0.832272	+	0.554368i	$0.812960\pi$
$594$	−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
$598$	2.92903	+	10.9313i	0.119777	+	0.447014i
$599$	17.8198	−	30.8647i	0.728096	−	1.26110i	−0.229591	−	0.973287i	$-0.573739\pi$
$599$	17.8198	−	30.8647i	0.728096	−	1.26110i	0.957687	−	0.287812i	$-0.0929279\pi$
$600$		0			0
$601$		−	2.58619i		−	0.105493i	−0.998608	−	0.0527464i	$-0.983203\pi$
$601$		−	2.58619i		−	0.105493i	0.998608	−	0.0527464i	$-0.0167975\pi$
$602$	−5.07323	−	18.9336i	−0.206770	−	0.771674i
$603$	0.0655930	−	0.244796i	0.00267115	−	0.00996887i
$604$	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	−0.524859	−	0.851189i	$-0.675882\pi$
$607$	8.03991	−	8.03991i	0.326330	−	0.326330i	0.851189	+	0.524859i	$0.175882\pi$
$608$	−3.69800	−	2.30756i	−0.149974	−	0.0935839i
$609$		−	64.5917i		−	2.61739i
$610$		0			0
$611$	−8.10666	+	4.68038i	−0.327960	+	0.189348i
$612$	17.6850	−	4.73867i	0.714872	−	0.191549i
$613$	−25.0209	−	6.70432i	−1.01058	−	0.270785i	−0.284710	−	0.958614i	$-0.591897\pi$
$613$	−25.0209	−	6.70432i	−1.01058	−	0.270785i	−0.725873	+	0.687828i	$0.758564\pi$
$614$	−4.96479	−	2.86642i	−0.200362	−	0.115679i
$615$		0			0
$616$		−	15.5520i		−	0.626608i
$617$	42.1752	−	11.3008i	1.69791	−	0.454954i	0.725498	−	0.688224i	$-0.241610\pi$
$617$	42.1752	−	11.3008i	1.69791	−	0.454954i	0.972412	+	0.233271i	$0.0749429\pi$
$618$	45.1760	−	12.1049i	1.81724	−	0.486929i
$619$			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
$622$	8.16822	+	2.18867i	0.327516	+	0.0877576i
$623$	37.5380	−	10.0583i	1.50393	−	0.402977i
$624$	10.5999	−	6.11985i	0.424335	−	0.244990i
$625$		0			0
$626$			3.58126i			0.143136i
$627$	34.4607	+	64.7137i	1.37623	+	2.58442i
$628$	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	−0.0881123	−	0.996111i	$-0.528083\pi$
$631$	20.5630	−	35.6162i	0.818601	−	1.41786i	0.906713	−	0.421748i	$-0.138583\pi$
$632$	−0.596622	+	2.22662i	−0.0237323	+	0.0885703i
$633$	−16.3654	−	61.0763i	−0.650465	−	2.42757i
$634$		−	2.98627i		−	0.118600i
$635$		0			0
$636$	5.57255	−	9.65194i	0.220966	−	0.382724i
$637$	1.46690	+	5.47456i	0.0581209	+	0.216910i
$638$	−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	−0.435713	−	0.900085i	$-0.643504\pi$
$641$	3.18821	−	1.84071i	0.125927	−	0.0727038i	0.561640	+	0.827382i	$0.310171\pi$
$642$	−5.56880	−	20.7830i	−0.219783	−	0.820241i
$643$	−3.09104	−	0.828243i	−0.121899	−	0.0326627i	0.197354	−	0.980332i	$-0.436765\pi$
$643$	−3.09104	−	0.828243i	−0.121899	−	0.0326627i	−0.319253	+	0.947670i	$0.603432\pi$
$644$	−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	$0.580286\pi$
$648$	4.61219	−	17.2129i	0.181184	−	0.676187i
$649$	24.5018	+	42.4383i	0.961778	+	1.66585i
$650$		0			0
$651$	−40.7522	−	70.5849i	−1.59721	−	2.76644i
$652$	0.372353	−	0.0997717i	0.0145825	−	0.00390736i
$653$	−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	$-0.947576\pi$
$659$	−9.01685	+	15.6176i	−0.351247	+	0.608377i	0.635221	+	0.772330i	$0.280909\pi$
$660$		0			0
$661$	−0.974218	−	0.562465i	−0.0378927	−	0.0218774i	0.480934	−	0.876757i	$-0.340298\pi$
$661$	−0.974218	−	0.562465i	−0.0378927	−	0.0218774i	−0.518827	+	0.854879i	$0.673631\pi$
$662$	4.60417	−	17.1830i	0.178946	−	0.667837i
$663$	31.4087	+	8.41594i	1.21981	+	0.326848i
$664$	−4.89136			−0.189822
$665$		0			0
$666$	35.8569			1.38943
$667$	19.8374	+	5.31543i	0.768109	+	0.205814i
$668$	0.607716	−	2.26803i	0.0235132	−	0.0877526i
$669$	−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	$0.000207548\pi$
$673$	25.9592	+	25.9592i	1.00065	+	1.00065i	0.000652030		1.00000i	$0.499792\pi$
$674$	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	−0.883748	−	0.467963i	$-0.844988\pi$
$677$	−10.8184	+	10.8184i	−0.415785	+	0.415785i	0.467963	+	0.883748i	$0.344988\pi$
$678$	19.1315	−	5.12627i	0.734741	−	0.196873i
$679$	−20.1784	−	34.9500i	−0.774376	−	1.34126i
$680$		0			0
$681$	13.4716	+	23.3334i	0.516231	+	0.894138i
$682$	−12.3352	+	46.0355i	−0.472338	+	1.76279i
$683$	−7.72617	−	7.72617i	−0.295634	−	0.295634i	0.543667	−	0.839301i	$-0.317035\pi$
$683$	−7.72617	−	7.72617i	−0.295634	−	0.295634i	−0.839301	+	0.543667i	$0.817035\pi$
$684$	−28.7330	−	8.76496i	−1.09863	−	0.335136i
$685$		0			0
$686$	13.9610	−	8.06040i	0.533034	−	0.307748i
$687$	7.15544	+	1.91729i	0.272997	+	0.0731493i
$688$	−1.74459	−	6.51089i	−0.0665118	−	0.248225i
$689$	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
$693$	−27.7400	−	103.527i	−1.05376	−	3.93267i
$694$	9.98858	−	17.3007i	0.379161	−	0.656727i
$695$		0			0
$696$		−	22.2119i		−	0.841939i
$697$	3.66509	+	13.6783i	0.138825	+	0.518103i
$698$	−8.33335	+	31.1005i	−0.315422	+	1.17717i
$699$	−24.4296	+	42.3133i	−0.924011	+	1.60043i
$700$		0			0
$701$	2.32332	+	4.02410i	0.0877504	+	0.151988i	0.906560	−	0.422077i	$-0.138699\pi$
$701$	2.32332	+	4.02410i	0.0877504	+	0.151988i	−0.818810	+	0.574065i	$0.805366\pi$
$702$	33.6815	−	33.6815i	1.27123	−	1.27123i
$703$	0.777351	−	22.6657i	0.0293183	−	0.854854i
$704$		−	5.34803i		−	0.201562i
$705$		0			0
$706$	−18.5662	+	10.7192i	−0.698749	+	0.403423i
$707$	54.1456	−	14.5083i	2.03636	−	0.545640i
$708$	−27.8363	−	7.45872i	−1.04615	−	0.280316i
$709$	27.5651	+	15.9147i	1.03523	+	0.597690i	0.918478	−	0.395471i	$-0.129419\pi$
$709$	27.5651	+	15.9147i	1.03523	+	0.597690i	0.116751	+	0.993161i	$0.462752\pi$
$710$		0			0
$711$			15.8865i			0.595789i
$712$	12.9086	−	3.45885i	0.483771	−	0.129626i
$713$	25.0317	−	6.70722i	0.937444	−	0.251187i
$714$			24.2975i			0.909312i
$715$		0			0
$716$	−6.02945	−	3.48110i	−0.225331	−	0.130095i
$717$	−64.1318	−	17.1841i	−2.39505	−	0.641751i
$718$	6.74114	−	1.80628i	0.251577	−	0.0674099i
$719$	25.6619	−	14.8159i	0.957028	−	0.552541i	0.0617712	−	0.998090i	$-0.480325\pi$
$719$	25.6619	−	14.8159i	0.957028	−	0.552541i	0.895257	+	0.445550i	$0.146992\pi$
$720$		0			0
$721$			43.2435i			1.61047i
$722$	−6.16338	+	17.9726i	−0.229377	+	0.668869i
$723$	−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
$727$	−0.919214	+	3.43055i	−0.0340918	+	0.127232i	−0.980875	−	0.194641i	$-0.937646\pi$
$727$	−0.919214	+	3.43055i	−0.0340918	+	0.127232i	0.946783	+	0.321873i	$0.104312\pi$
$728$	2.92903	+	10.9313i	0.108557	+	0.405141i
$729$		−	7.32499i		−	0.271296i
$730$		0			0
$731$	8.95369	−	15.5083i	0.331164	−	0.573594i
$732$	−0.324412	−	1.21072i	−0.0119906	−	0.0447496i
$733$	−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
$737$	−0.0509011	−	0.189965i	−0.00187496	−	0.00699746i
$738$	35.4831	+	9.50766i	1.30615	+	0.349982i
$739$	−2.44691	+	1.41273i	−0.0900111	+	0.0519680i	−0.544330	−	0.838871i	$-0.683216\pi$
$739$	−2.44691	+	1.41273i	−0.0900111	+	0.0519680i	0.454319	+	0.890839i	$0.349883\pi$
$740$		0			0
$741$	−36.4101	−	38.9962i	−1.33756	−	1.43256i
$742$	7.28662	+	7.28662i	0.267500	+	0.267500i
$743$	−2.47008	+	9.21845i	−0.0906183	+	0.338192i	−0.996319	−	0.0857263i	$-0.972679\pi$
$743$	−2.47008	+	9.21845i	−0.0906183	+	0.338192i	0.905700	+	0.423918i	$0.139346\pi$
$744$	−14.0139	−	24.2728i	−0.513775	−	0.889885i
$745$		0			0
$746$	−3.99634	−	6.92186i	−0.146316	−	0.253427i
$747$	−32.5610	+	8.72470i	−1.19134	+	0.319220i
$748$	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	0.759014	−	0.651075i	$-0.225682\pi$
$751$	15.7486	+	9.09244i	0.574673	+	0.331788i	−0.184340	+	0.982862i	$0.559015\pi$
$752$	−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
$757$	1.67689	−	6.25825i	0.0609478	−	0.227460i	−0.928733	−	0.370749i	$-0.879101\pi$
$757$	1.67689	−	6.25825i	0.0609478	−	0.227460i	0.989681	+	0.143289i	$0.0457677\pi$
$758$	−32.8103	−	8.79150i	−1.19172	−	0.319322i
$759$	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	$0.388570\pi$
$762$	54.5772	+	14.6239i	1.97712	+	0.529768i
$763$	−0.973236	+	3.63217i	−0.0352335	+	0.131493i
$764$	−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	$-0.429496\pi$
$769$	−14.2907	−	8.25076i	−0.515337	−	0.297530i	−0.735025	+	0.678040i	$0.762830\pi$
$770$		0			0
$771$	51.5319			1.85588
$772$	−4.42184	+	4.42184i	−0.159146	+	0.159146i
$773$	22.4346	−	6.01133i	0.806915	−	0.216212i	0.168297	−	0.985736i	$-0.446173\pi$
$773$	22.4346	−	6.01133i	0.806915	−	0.216212i	0.638618	+	0.769524i	$0.279506\pi$
$774$	−23.2269	−	40.2302i	−0.834874	−	1.44604i
$775$		0			0
$776$	−6.93897	−	12.0187i	−0.249095	−	0.431444i
$777$	−12.3160	+	45.9641i	−0.441835	+	1.64895i
$778$	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
$782$	−7.46227	−	1.99951i	−0.266850	−	0.0715023i
$783$	−22.3726	−	83.4959i	−0.799533	−	2.98390i
$784$	−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	−0.953049	−	0.302817i	$-0.902073\pi$
$787$	−18.2413	+	18.2413i	−0.650231	+	0.650231i	0.302817	+	0.953049i	$0.402073\pi$
$788$	−0.848013	−	3.16483i	−0.0302092	−	0.112742i
$789$	−18.4294	+	31.9206i	−0.656103	+	1.13640i
$790$		0			0
$791$			18.3131i			0.651139i
$792$	−9.53926	−	35.6010i	−0.338963	−	1.26503i
$793$	0.401419	−	1.49812i	0.0142548	−	0.0531997i
$794$	−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	−0.518899	−	0.854836i	$-0.673658\pi$
$797$	9.48390	−	9.48390i	0.335937	−	0.335937i	0.854836	+	0.518899i	$0.173658\pi$
$798$	21.1047	−	33.8215i	0.747099	−	1.19727i
$799$		−	6.39014i		−	0.226067i
$800$		0			0
$801$	79.7611	−	46.0501i	2.81822	−	1.62710i
$802$	−26.5709	+	7.11964i	−0.938250	+	0.251403i
$803$	83.0357	+	22.2493i	2.93027	+	0.785162i
$804$	0.100162	+	0.0578284i	0.00353243	+	0.00203945i
$805$		0			0
$806$		−	34.6809i		−	1.22158i
$807$	−17.9728	+	4.81580i	−0.632673	+	0.169524i
$808$	18.6196	−	4.98912i	0.655037	−	0.175517i
$809$			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	0.887961	−	0.459919i	$-0.152121\pi$
$811$	26.5883	+	15.3507i	0.933640	+	0.539038i	0.0456794	+	0.998956i	$0.485455\pi$
$812$	19.8374	+	5.31543i	0.696158	+	0.186535i
$813$	−32.0949	+	8.59979i	−1.12562	+	0.301608i
$814$	24.0975	−	13.9127i	0.844619	−	0.487641i
$815$		0			0
$816$			8.35546i			0.292500i
$817$	−25.9337	+	13.8099i	−0.907305	+	0.483149i
$818$	−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	−0.475556	−	0.879686i	$-0.657753\pi$
$821$	15.0157	−	26.0080i	0.524052	−	0.907685i	0.999608	−	0.0279994i	$-0.00891367\pi$
$822$	3.87242	−	14.4521i	0.135066	−	0.504073i
$823$	5.73326	+	21.3968i	0.199849	+	0.745846i	0.990958	+	0.134171i	$0.0428373\pi$
$823$	5.73326	+	21.3968i	0.199849	+	0.745846i	−0.791109	+	0.611675i	$0.790496\pi$
$824$			14.8706i			0.518042i
$825$		0			0
$826$	13.3228	−	23.0757i	0.463559	−	0.802908i
$827$	−11.4226	−	42.6296i	−0.397201	−	1.48238i	−0.817999	−	0.575220i	$-0.804916\pi$
$827$	−11.4226	−	42.6296i	−0.397201	−	1.48238i	0.420797	−	0.907155i	$-0.361750\pi$
$828$	−14.1710	+	14.1710i	−0.492477	+	0.492477i
$829$	−31.8391			−1.10582			−0.552909	−	0.833242i	$-0.686482\pi$
$829$	−31.8391			−1.10582			−0.552909	+	0.833242i	$0.686482\pi$
$830$		0			0
$831$	21.2618	−	12.2755i	0.737564	−	0.425833i
$832$	1.00724	+	3.75907i	0.0349197	+	0.130322i
$833$	−3.73722	−	1.00139i	−0.129487	−	0.0346960i
$834$	−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
$838$	0.849396	−	3.16999i	0.0293419	−	0.109505i
$839$	−0.318407	−	0.551497i	−0.0109926	−	0.0190398i	0.860477	−	0.509490i	$-0.170166\pi$
$839$	−0.318407	−	0.551497i	−0.0109926	−	0.0190398i	−0.871469	+	0.490450i	$0.836832\pi$
$840$		0			0
$841$	−10.4385	−	18.0800i	−0.359949	−	0.623449i
$842$	12.9889	−	3.48038i	0.447629	−	0.119942i
$843$	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
$852$	3.68167	−	13.7402i	0.126132	−	0.470731i
$853$	−19.4425	−	5.20959i	−0.665698	−	0.178373i	−0.0898816	−	0.995952i	$-0.528649\pi$
$853$	−19.4425	−	5.20959i	−0.665698	−	0.178373i	−0.575816	+	0.817579i	$0.695316\pi$
$854$	1.15893			0.0396578
$855$		0			0
$856$	6.84117			0.233826
$857$	5.99157	+	1.60544i	0.204668	+	0.0548407i	0.359697	−	0.933069i	$-0.382880\pi$
$857$	5.99157	+	1.60544i	0.204668	+	0.0548407i	−0.155028	+	0.987910i	$0.549547\pi$
$858$	16.9419	−	63.2279i	0.578386	−	2.15857i
$859$	37.9676	+	21.9206i	1.29544	+	0.747921i	0.979612	−	0.200897i	$-0.0643856\pi$
$859$	37.9676	+	21.9206i	1.29544	+	0.747921i	0.315824	+	0.948818i	$0.397719\pi$
$860$		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	0.0554975	−	0.998459i	$-0.482326\pi$
$863$	−27.7012	−	27.7012i	−0.942961	−	0.942961i	−0.998459	+	0.0554975i	$0.982326\pi$
$864$	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
$868$	25.0317	−	6.70722i	0.849631	−	0.227658i
$869$	6.16406	+	10.6765i	0.209102	+	0.362175i
$870$		0			0
$871$	0.0715554	+	0.123938i	0.00242456	+	0.00419947i
$872$	−0.334677	+	1.24903i	−0.0113336	+	0.0422976i
$873$	−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
$877$	−15.5177	−	4.15797i	−0.523997	−	0.140405i	−0.0128823	−	0.999917i	$-0.504101\pi$
$877$	−15.5177	−	4.15797i	−0.523997	−	0.140405i	−0.511115	+	0.859512i	$0.670767\pi$
$878$	−5.07775	−	18.9504i	−0.171366	−	0.639545i
$879$	−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
$883$	4.50048	+	16.7960i	0.151453	+	0.565231i	0.999383	+	0.0351224i	$0.0111821\pi$
$883$	4.50048	+	16.7960i	0.151453	+	0.565231i	−0.847930	+	0.530108i	$0.822151\pi$
$884$	−5.16942	+	8.95369i	−0.173866	+	0.301145i
$885$		0			0
$886$			9.48470i			0.318645i
$887$	5.13744	+	19.1732i	0.172499	+	0.643773i	0.996964	+	0.0778613i	$0.0248091\pi$
$887$	5.13744	+	19.1732i	0.172499	+	0.643773i	−0.824466	+	0.565912i	$0.808524\pi$
$888$	−4.23525	+	15.8062i	−0.142126	+	0.530420i
$889$	−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
$893$	−5.55044	+	8.89491i	−0.185739	+	0.297657i
$894$			70.1050i			2.34466i
$895$		0			0
$896$	−2.51839	+	1.45399i	−0.0841334	+	0.0485744i
$897$	−34.3801	+	9.21211i	−1.14792	+	0.307583i
$898$	−29.6676	−	7.94942i	−0.990021	−	0.265275i
$899$	−54.5049	−	31.4684i	−1.81784	−	1.04953i
$900$		0			0
$901$			9.41423i			0.313633i
$902$	27.5354	−	7.37808i	0.916827	−	0.245663i
$903$	59.5480	−	15.9558i	1.98163	−	0.530977i
$904$			6.29753i			0.209453i
$905$		0			0
$906$	2.24557	+	1.29648i	0.0746041	+	0.0430727i
$907$	−5.15770	−	1.38200i	−0.171259	−	0.0458886i	0.172171	−	0.985067i	$-0.444922\pi$
$907$	−5.15770	−	1.38200i	−0.171259	−	0.0458886i	−0.343429	+	0.939179i	$0.611589\pi$
$908$	−8.27478	+	2.21722i	−0.274608	+	0.0735811i
$909$	115.049	−	66.4236i	3.81593	−	2.20313i
$910$		0			0
$911$		−	49.3278i		−	1.63430i	−0.576423	−	0.817151i	$-0.695552\pi$
$911$		−	49.3278i		−	1.63430i	0.576423	−	0.817151i	$-0.304448\pi$
$912$	7.25751	−	11.6306i	0.240320	−	0.385127i
$913$	−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
$917$	−12.1688	+	45.4146i	−0.401850	+	1.49972i
$918$	8.41594	+	31.4087i	0.277767	+	1.03664i
$919$			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
$922$	8.38042	+	31.2762i	0.275995	+	1.03003i
$923$	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
$927$	26.5247	+	98.9914i	0.871184	+	3.25130i
$928$	6.82172	+	1.82787i	0.223934	+	0.0600029i
$929$	−0.672048	+	0.388007i	−0.0220492	+	0.0127301i	−0.510984	−	0.859590i	$-0.670719\pi$
$929$	−0.672048	+	0.388007i	−0.0220492	+	0.0127301i	0.488935	+	0.872320i	$0.337386\pi$
$930$		0			0
$931$	4.33231	+	4.64003i	0.141986	+	0.152071i
$932$	−10.9849	−	10.9849i	−0.359822	−	0.359822i
$933$	−6.88358	+	25.6899i	−0.225358	+	0.841049i
$934$	−6.89636	−	11.9448i	−0.225656	−	0.390847i
$935$		0			0
$936$	13.4101	+	23.2269i	0.438321	+	0.759195i
$937$	−21.2860	+	5.70358i	−0.695385	+	0.186328i	−0.589162	−	0.808015i	$-0.700542\pi$
$937$	−21.2860	+	5.70358i	−0.695385	+	0.186328i	−0.106222	+	0.994342i	$0.533875\pi$
$938$	−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	0.779693	−	0.626162i	$-0.215375\pi$
$941$	19.2419	+	11.1093i	0.627268	+	0.362154i	−0.152425	+	0.988315i	$0.548708\pi$
$942$	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
$947$	−9.79664	+	36.5616i	−0.318348	+	1.18809i	0.602484	+	0.798131i	$0.294178\pi$
$947$	−9.79664	+	36.5616i	−0.318348	+	1.18809i	−0.920832	+	0.389960i	$0.872489\pi$
$948$	−7.00296	−	1.87644i	−0.227446	−	0.0609439i
$949$	−62.5551			−2.03063
$950$		0			0
$951$	9.39214			0.304561
$952$	−7.46227	−	1.99951i	−0.241854	−	0.0648045i
$953$	0.337998	−	1.26143i	0.0109488	−	0.0408616i	−0.960235	−	0.279192i	$-0.909933\pi$
$953$	0.337998	−	1.26143i	0.0109488	−	0.0408616i	0.971184	+	0.238330i	$0.0766001\pi$
$954$	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
$963$	45.5406	−	12.2026i	1.46753	−	0.393222i
$964$	−14.3238	−	24.8096i	−0.461339	−	0.799063i
$965$		0			0
$966$	−13.2981	−	23.0329i	−0.427858	−	0.741072i
$967$	−0.0276774	+	0.103293i	−0.000890044	+	0.00332169i	−0.966369	−	0.257158i	$-0.917214\pi$
$967$	−0.0276774	+	0.103293i	−0.000890044	+	0.00332169i	0.965479	+	0.260480i	$0.0838806\pi$
$968$	−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	−0.880084	−	0.474818i	$-0.842514\pi$
$971$	−28.3228	+	16.3522i	−0.908921	+	0.524766i	−0.0288374	+	0.999584i	$0.509181\pi$
$972$	18.6684	+	5.00219i	0.598790	+	0.160445i
$973$	−10.7015	−	39.9387i	−0.343076	−	1.28038i
$974$	−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	−0.750389	−	0.660997i	$-0.770134\pi$
$977$	−2.79413	+	2.79413i	−0.0893920	+	0.0893920i	0.660997	+	0.750389i	$0.270134\pi$
$978$	0.313792	+	1.17109i	0.0100340	+	0.0374473i
$979$	35.7355	−	61.8957i	1.14211	−	1.97820i
$980$		0			0
$981$			8.91158i			0.284525i
$982$	−3.19401	−	11.9202i	−0.101925	−	0.380389i
$983$	2.44611	−	9.12899i	0.0780187	−	0.291170i	−0.915882	−	0.401447i	$-0.868507\pi$
$983$	2.44611	−	9.12899i	0.0780187	−	0.291170i	0.993901	+	0.110278i	$0.0351740\pi$
$984$	−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
$988$	14.9728	−	7.97317i	0.476349	−	0.253660i
$989$			19.6015i			0.623290i
$990$		0			0
$991$	14.4316	−	8.33211i	0.458436	−	0.264678i	−0.252950	−	0.967479i	$-0.581401\pi$
$991$	14.4316	−	8.33211i	0.458436	−	0.264678i	0.711387	+	0.702801i	$0.248068\pi$
$992$	8.60792	−	2.30649i	0.273302	−	0.0732310i
$993$	54.0423	+	14.4806i	1.71498	+	0.459528i
$994$	11.3903	+	6.57622i	0.361280	+	0.208585i
$995$		0			0
$996$		−	15.3838i		−	0.487455i
$997$	−3.62405	+	0.971062i	−0.114775	+	0.0307538i	−0.315749	−	0.948843i	$-0.602256\pi$
$997$	−3.62405	+	0.971062i	−0.114775	+	0.0307538i	0.200974	+	0.979596i	$0.435589\pi$
$998$	−9.75771	+	2.61457i	−0.308875	+	0.0827628i
$999$			63.6823i			2.01482i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
950.2.q.e.107.3	✓	24	1.1	even	1	trivial
950.2.q.e.107.4	yes	24	5.4	even	2	inner
950.2.q.e.293.3	yes	24	95.8	even	12	inner
950.2.q.e.293.4	yes	24	95.27	even	12	inner
950.2.q.e.407.3	yes	24	19.8	odd	6	inner
950.2.q.e.407.4	yes	24	95.84	odd	6	inner
950.2.q.e.943.3	yes	24	5.3	odd	4	inner
950.2.q.e.943.4	yes	24	5.2	odd	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 950 = 2 \cdot 5^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	950.q (of order \(12\), degree \(4\), minimal)

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