LMFDB - Embedded newform 845.2.k.d.577.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(268,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("845.268");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.k (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 26 x^{18} + 279 x^{16} + 1604 x^{14} + 5353 x^{12} + 10466 x^{10} + 11441 x^{8} + 6176 x^{6} + \cdots + 1 $ x^20 + 26x^18 + 279x^16 + 1604x^14 + 5353x^12 + 10466x^10 + 11441x^8 + 6176x^6 + 1263x^4 + 78*x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			577.5
Root			$0.493902i$ of defining polynomial
Character	$\chi$	$=$	845.577
Dual form			845.2.k.d.268.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.493902 q^{2} +(-0.664960 + 0.664960i) q^{3} -1.75606 q^{4} +(2.21791 - 0.284413i) q^{5} +(0.328425 - 0.328425i) q^{6} +3.67549i q^{7} +1.85513 q^{8} +2.11566i q^{9} +O(q^{10})$	\(q-0.493902 q^{2} +(-0.664960 + 0.664960i) q^{3} -1.75606 q^{4} +(2.21791 - 0.284413i) q^{5} +(0.328425 - 0.328425i) q^{6} +3.67549i q^{7} +1.85513 q^{8} +2.11566i q^{9} +(-1.09543 + 0.140472i) q^{10} +(0.486270 + 0.486270i) q^{11} +(1.16771 - 1.16771i) q^{12} -1.81533i q^{14} +(-1.28570 + 1.66394i) q^{15} +2.59587 q^{16} +(1.67902 - 1.67902i) q^{17} -1.04493i q^{18} +(-3.87304 - 3.87304i) q^{19} +(-3.89478 + 0.499446i) q^{20} +(-2.44406 - 2.44406i) q^{21} +(-0.240170 - 0.240170i) q^{22} +(0.957603 + 0.957603i) q^{23} +(-1.23358 + 1.23358i) q^{24} +(4.83822 - 1.26160i) q^{25} +(-3.40171 - 3.40171i) q^{27} -6.45439i q^{28} +9.51628i q^{29} +(0.635008 - 0.821824i) q^{30} +(-4.81595 + 4.81595i) q^{31} -4.99236 q^{32} -0.646700 q^{33} +(-0.829273 + 0.829273i) q^{34} +(1.04536 + 8.15190i) q^{35} -3.71522i q^{36} -1.83523i q^{37} +(1.91290 + 1.91290i) q^{38} +(4.11449 - 0.527621i) q^{40} +(-0.391638 + 0.391638i) q^{41} +(1.20712 + 1.20712i) q^{42} +(1.53207 + 1.53207i) q^{43} +(-0.853919 - 0.853919i) q^{44} +(0.601719 + 4.69233i) q^{45} +(-0.472962 - 0.472962i) q^{46} +3.80918i q^{47} +(-1.72615 + 1.72615i) q^{48} -6.50924 q^{49} +(-2.38961 + 0.623107i) q^{50} +2.23297i q^{51} +(-2.47293 + 2.47293i) q^{53} +(1.68011 + 1.68011i) q^{54} +(1.21680 + 0.940200i) q^{55} +6.81850i q^{56} +5.15084 q^{57} -4.70011i q^{58} +(-7.35770 + 7.35770i) q^{59} +(2.25776 - 2.92199i) q^{60} +6.19808 q^{61} +(2.37861 - 2.37861i) q^{62} -7.77608 q^{63} -2.72601 q^{64} +0.319406 q^{66} -12.2474 q^{67} +(-2.94847 + 2.94847i) q^{68} -1.27354 q^{69} +(-0.516303 - 4.02624i) q^{70} +(4.74012 - 4.74012i) q^{71} +3.92481i q^{72} -3.37642 q^{73} +0.906424i q^{74} +(-2.37831 + 4.05614i) q^{75} +(6.80130 + 6.80130i) q^{76} +(-1.78728 + 1.78728i) q^{77} +3.12149i q^{79} +(5.75740 - 0.738299i) q^{80} -1.82297 q^{81} +(0.193431 - 0.193431i) q^{82} +2.13918i q^{83} +(4.29191 + 4.29191i) q^{84} +(3.24638 - 4.20145i) q^{85} +(-0.756694 - 0.756694i) q^{86} +(-6.32795 - 6.32795i) q^{87} +(0.902091 + 0.902091i) q^{88} +(-2.38835 + 2.38835i) q^{89} +(-0.297190 - 2.31755i) q^{90} +(-1.68161 - 1.68161i) q^{92} -6.40483i q^{93} -1.88136i q^{94} +(-9.69159 - 7.48850i) q^{95} +(3.31972 - 3.31972i) q^{96} -7.07377 q^{97} +3.21493 q^{98} +(-1.02878 + 1.02878i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 8 q^{2} + 4 q^{3} + 12 q^{4} + 6 q^{5} - 4 q^{6} - 12 q^{8}+O(q^{10}) $ 20 * q - 8 * q^2 + 4 * q^3 + 12 * q^4 + 6 * q^5 - 4 * q^6 - 12 * q^8	$ 20 q - 8 q^{2} + 4 q^{3} + 12 q^{4} + 6 q^{5} - 4 q^{6} - 12 q^{8} + 8 q^{10} - 8 q^{11} + 24 q^{12} + 24 q^{15} + 4 q^{16} + 14 q^{17} + 4 q^{19} + 22 q^{20} - 4 q^{21} - 32 q^{22} - 8 q^{23} - 4 q^{24} - 18 q^{25} + 4 q^{27} - 40 q^{30} - 12 q^{32} - 36 q^{33} + 2 q^{34} - 20 q^{35} + 8 q^{38} - 16 q^{40} + 38 q^{41} + 16 q^{42} + 32 q^{43} - 36 q^{44} + 20 q^{45} - 4 q^{46} + 28 q^{48} + 36 q^{49} + 52 q^{50} - 10 q^{53} + 36 q^{54} - 16 q^{55} + 12 q^{57} + 8 q^{59} + 92 q^{60} + 32 q^{61} - 4 q^{62} - 64 q^{63} - 20 q^{64} - 32 q^{66} - 116 q^{67} - 50 q^{68} - 32 q^{69} - 32 q^{70} + 40 q^{71} - 72 q^{73} - 4 q^{75} + 16 q^{76} + 28 q^{77} + 34 q^{80} + 28 q^{81} + 34 q^{82} + 8 q^{84} - 60 q^{86} - 28 q^{87} + 32 q^{88} + 12 q^{89} - 46 q^{90} - 8 q^{92} - 40 q^{95} - 56 q^{96} - 44 q^{97} + 8 q^{98} + 60 q^{99}+O(q^{100}) $ 20 * q - 8 * q^2 + 4 * q^3 + 12 * q^4 + 6 * q^5 - 4 * q^6 - 12 * q^8 + 8 * q^10 - 8 * q^11 + 24 * q^12 + 24 * q^15 + 4 * q^16 + 14 * q^17 + 4 * q^19 + 22 * q^20 - 4 * q^21 - 32 * q^22 - 8 * q^23 - 4 * q^24 - 18 * q^25 + 4 * q^27 - 40 * q^30 - 12 * q^32 - 36 * q^33 + 2 * q^34 - 20 * q^35 + 8 * q^38 - 16 * q^40 + 38 * q^41 + 16 * q^42 + 32 * q^43 - 36 * q^44 + 20 * q^45 - 4 * q^46 + 28 * q^48 + 36 * q^49 + 52 * q^50 - 10 * q^53 + 36 * q^54 - 16 * q^55 + 12 * q^57 + 8 * q^59 + 92 * q^60 + 32 * q^61 - 4 * q^62 - 64 * q^63 - 20 * q^64 - 32 * q^66 - 116 * q^67 - 50 * q^68 - 32 * q^69 - 32 * q^70 + 40 * q^71 - 72 * q^73 - 4 * q^75 + 16 * q^76 + 28 * q^77 + 34 * q^80 + 28 * q^81 + 34 * q^82 + 8 * q^84 - 60 * q^86 - 28 * q^87 + 32 * q^88 + 12 * q^89 - 46 * q^90 - 8 * q^92 - 40 * q^95 - 56 * q^96 - 44 * q^97 + 8 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/845\mathbb{Z}\right)^\times$.

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.493902			−0.349241			−0.174621	−	0.984636i	$-0.555870\pi$
$2$	−0.493902			−0.349241			−0.174621	+	0.984636i	$0.555870\pi$
$3$	−0.664960	+	0.664960i	−0.383915	+	0.383915i	−0.872510	−	0.488595i	$-0.837509\pi$
$3$	−0.664960	+	0.664960i	−0.383915	+	0.383915i	0.488595	+	0.872510i	$0.337509\pi$
$4$	−1.75606			−0.878030
$5$	2.21791	−	0.284413i	0.991878	−	0.127193i
$5$	2.21791	−	0.284413i	0.991878	−	0.127193i
$6$	0.328425	−	0.328425i	0.134079	−	0.134079i
$7$			3.67549i			1.38921i	0.719394	+	0.694603i	$0.244420\pi$
$7$			3.67549i			1.38921i	−0.719394	+	0.694603i	$0.755580\pi$
$8$	1.85513			0.655886
$9$			2.11566i			0.705219i
$10$	−1.09543	+	0.140472i	−0.346405	+	0.0444211i
$11$	0.486270	+	0.486270i	0.146616	+	0.146616i	0.776604	−	0.629989i	$-0.216940\pi$
$11$	0.486270	+	0.486270i	0.146616	+	0.146616i	−0.629989	+	0.776604i	$0.716940\pi$
$12$	1.16771	−	1.16771i	0.337089	−	0.337089i
$13$		0			0
$13$		0			0
$14$		−	1.81533i		−	0.485168i
$15$	−1.28570	+	1.66394i	−0.331965	+	0.429628i
$16$	2.59587			0.648968
$17$	1.67902	−	1.67902i	0.407223	−	0.407223i	−0.473546	−	0.880769i	$-0.657026\pi$
$17$	1.67902	−	1.67902i	0.407223	−	0.407223i	0.880769	+	0.473546i	$0.157026\pi$
$18$		−	1.04493i		−	0.246291i
$19$	−3.87304	−	3.87304i	−0.888537	−	0.888537i	0.105846	−	0.994383i	$-0.466245\pi$
$19$	−3.87304	−	3.87304i	−0.888537	−	0.888537i	−0.994383	+	0.105846i	$0.966245\pi$
$20$	−3.89478	+	0.499446i	−0.870899	+	0.111679i
$21$	−2.44406	−	2.44406i	−0.533337	−	0.533337i
$22$	−0.240170	−	0.240170i	−0.0512043	−	0.0512043i
$23$	0.957603	+	0.957603i	0.199674	+	0.199674i	0.799860	−	0.600186i	$-0.204907\pi$
$23$	0.957603	+	0.957603i	0.199674	+	0.199674i	−0.600186	+	0.799860i	$0.704907\pi$
$24$	−1.23358	+	1.23358i	−0.251804	+	0.251804i
$25$	4.83822	−	1.26160i	0.967644	−	0.252320i
$26$		0			0
$27$	−3.40171	−	3.40171i	−0.654659	−	0.654659i
$28$		−	6.45439i		−	1.21976i
$29$			9.51628i			1.76713i	0.468310	+	0.883564i	$0.344863\pi$
$29$			9.51628i			1.76713i	−0.468310	+	0.883564i	$0.655137\pi$
$30$	0.635008	−	0.821824i	0.115936	−	0.150044i
$31$	−4.81595	+	4.81595i	−0.864970	+	0.864970i	−0.991910	−	0.126940i	$-0.959484\pi$
$31$	−4.81595	+	4.81595i	−0.864970	+	0.864970i	0.126940	+	0.991910i	$0.459484\pi$
$32$	−4.99236			−0.882532
$33$	−0.646700			−0.112576
$34$	−0.829273	+	0.829273i	−0.142219	+	0.142219i
$35$	1.04536	+	8.15190i	0.176697	+	1.37792i
$36$		−	3.71522i		−	0.619203i
$37$		−	1.83523i		−	0.301710i	−0.988556	−	0.150855i	$-0.951797\pi$
$37$		−	1.83523i		−	0.301710i	0.988556	−	0.150855i	$-0.0482027\pi$
$38$	1.91290	+	1.91290i	0.310314	+	0.310314i
$39$		0			0
$40$	4.11449	−	0.527621i	0.650559	−	0.0834242i
$41$	−0.391638	+	0.391638i	−0.0611636	+	0.0611636i	−0.737027	−	0.675863i	$-0.763771\pi$
$41$	−0.391638	+	0.391638i	−0.0611636	+	0.0611636i	0.675863	+	0.737027i	$0.263771\pi$
$42$	1.20712	+	1.20712i	0.186263	+	0.186263i
$43$	1.53207	+	1.53207i	0.233639	+	0.233639i	0.814210	−	0.580571i	$-0.197171\pi$
$43$	1.53207	+	1.53207i	0.233639	+	0.233639i	−0.580571	+	0.814210i	$0.697171\pi$
$44$	−0.853919	−	0.853919i	−0.128733	−	0.128733i
$45$	0.601719	+	4.69233i	0.0896990	+	0.699491i
$46$	−0.472962	−	0.472962i	−0.0697344	−	0.0697344i
$47$			3.80918i			0.555626i	0.960635	+	0.277813i	$0.0896096\pi$
$47$			3.80918i			0.555626i	−0.960635	+	0.277813i	$0.910390\pi$
$48$	−1.72615	+	1.72615i	−0.249149	+	0.249149i
$49$	−6.50924			−0.929892
$50$	−2.38961	+	0.623107i	−0.337941	+	0.0881207i
$51$			2.23297i			0.312678i
$52$		0			0
$53$	−2.47293	+	2.47293i	−0.339683	+	0.339683i	−0.856248	−	0.516565i	$-0.827211\pi$
$53$	−2.47293	+	2.47293i	−0.339683	+	0.339683i	0.516565	+	0.856248i	$0.327211\pi$
$54$	1.68011	+	1.68011i	0.228634	+	0.228634i
$55$	1.21680	+	0.940200i	0.164074	+	0.126776i
$56$			6.81850i			0.911160i
$57$	5.15084			0.682245
$58$		−	4.70011i		−	0.617154i
$59$	−7.35770	+	7.35770i	−0.957891	+	0.957891i	−0.999149	−	0.0412579i	$-0.986863\pi$
$59$	−7.35770	+	7.35770i	−0.957891	+	0.957891i	0.0412579	+	0.999149i	$0.486863\pi$
$60$	2.25776	−	2.92199i	0.291476	−	0.377227i
$61$	6.19808			0.793583			0.396792	−	0.917909i	$-0.370124\pi$
$61$	6.19808			0.793583			0.396792	+	0.917909i	$0.370124\pi$
$62$	2.37861	−	2.37861i	0.302083	−	0.302083i
$63$	−7.77608			−0.979693
$64$	−2.72601			−0.340751
$65$		0			0
$66$	0.319406			0.0393162
$67$	−12.2474			−1.49626			−0.748130	−	0.663552i	$-0.769048\pi$
$67$	−12.2474			−1.49626			−0.748130	+	0.663552i	$0.769048\pi$
$68$	−2.94847	+	2.94847i	−0.357554	+	0.357554i
$69$	−1.27354			−0.153316
$70$	−0.516303	−	4.02624i	−0.0617101	−	0.481227i
$71$	4.74012	−	4.74012i	0.562549	−	0.562549i	−0.367482	−	0.930031i	$-0.619780\pi$
$71$	4.74012	−	4.74012i	0.562549	−	0.562549i	0.930031	+	0.367482i	$0.119780\pi$
$72$			3.92481i			0.462543i
$73$	−3.37642			−0.395180			−0.197590	−	0.980285i	$-0.563312\pi$
$73$	−3.37642			−0.395180			−0.197590	+	0.980285i	$0.563312\pi$
$74$			0.906424i			0.105370i
$75$	−2.37831	+	4.05614i	−0.274623	+	0.468362i
$76$	6.80130	+	6.80130i	0.780162	+	0.780162i
$77$	−1.78728	+	1.78728i	−0.203680	+	0.203680i
$78$		0			0
$79$			3.12149i			0.351195i	0.984462	+	0.175598i	$0.0561857\pi$
$79$			3.12149i			0.351195i	−0.984462	+	0.175598i	$0.943814\pi$
$80$	5.75740	−	0.738299i	0.643697	−	0.0825443i
$81$	−1.82297			−0.202552
$82$	0.193431	−	0.193431i	0.0213609	−	0.0213609i
$83$			2.13918i			0.234805i	0.993084	+	0.117403i	$0.0374568\pi$
$83$			2.13918i			0.234805i	−0.993084	+	0.117403i	$0.962543\pi$
$84$	4.29191	+	4.29191i	0.468286	+	0.468286i
$85$	3.24638	−	4.20145i	0.352119	−	0.455711i
$86$	−0.756694	−	0.756694i	−0.0815964	−	0.0815964i
$87$	−6.32795	−	6.32795i	−0.678427	−	0.678427i
$88$	0.902091	+	0.902091i	0.0961633	+	0.0961633i
$89$	−2.38835	+	2.38835i	−0.253165	+	0.253165i	−0.822267	−	0.569102i	$-0.807291\pi$
$89$	−2.38835	+	2.38835i	−0.253165	+	0.253165i	0.569102	+	0.822267i	$0.307291\pi$
$90$	−0.297190	−	2.31755i	−0.0313266	−	0.244291i
$91$		0			0
$92$	−1.68161	−	1.68161i	−0.175320	−	0.175320i
$93$		−	6.40483i		−	0.664150i
$94$		−	1.88136i		−	0.194048i
$95$	−9.69159	−	7.48850i	−0.994336	−	0.768304i
$96$	3.31972	−	3.31972i	0.338817	−	0.338817i
$97$	−7.07377			−0.718232			−0.359116	−	0.933293i	$-0.616922\pi$
$97$	−7.07377			−0.718232			−0.359116	+	0.933293i	$0.616922\pi$
$98$	3.21493			0.324757
$99$	−1.02878	+	1.02878i	−0.103396	+	0.103396i
$100$	−8.49621	+	2.21545i	−0.849621	+	0.221545i
$101$			14.9697i			1.48954i	0.667323	+	0.744769i	$0.267440\pi$
$101$			14.9697i			1.48954i	−0.667323	+	0.744769i	$0.732560\pi$
$102$		−	1.10287i		−	0.109200i
$103$	3.17851	+	3.17851i	0.313188	+	0.313188i	0.846143	−	0.532956i	$-0.178919\pi$
$103$	3.17851	+	3.17851i	0.313188	+	0.313188i	−0.532956	+	0.846143i	$0.678919\pi$
$104$		0			0
$105$	−6.11581	−	4.72557i	−0.596842	−	0.461168i
$106$	1.22139	−	1.22139i	0.118632	−	0.118632i
$107$	−10.7852	−	10.7852i	−1.04265	−	1.04265i	−0.999049	−	0.0435984i	$-0.986118\pi$
$107$	−10.7852	−	10.7852i	−1.04265	−	1.04265i	−0.0435984	−	0.999049i	$-0.513882\pi$
$108$	5.97361	+	5.97361i	0.574811	+	0.574811i
$109$	2.25902	+	2.25902i	0.216375	+	0.216375i	0.806969	−	0.590594i	$-0.201107\pi$
$109$	2.25902	+	2.25902i	0.216375	+	0.216375i	−0.590594	+	0.806969i	$0.701107\pi$
$110$	−0.600981	−	0.464366i	−0.0573013	−	0.0442756i
$111$	1.22036	+	1.22036i	0.115831	+	0.115831i
$112$			9.54111i			0.901550i
$113$	11.7173	−	11.7173i	1.10227	−	1.10227i	0.108132	−	0.994137i	$-0.465513\pi$
$113$	11.7173	−	11.7173i	1.10227	−	1.10227i	0.994137	−	0.108132i	$-0.0344870\pi$
$114$	−2.54401			−0.238268
$115$	2.39623	+	1.85152i	0.223450	+	0.172655i
$116$		−	16.7112i		−	1.55159i
$117$		0			0
$118$	3.63398	−	3.63398i	0.334535	−	0.334535i
$119$	6.17124	+	6.17124i	0.565716	+	0.565716i
$120$	−2.38513	+	3.08682i	−0.217731	+	0.281787i
$121$		−	10.5271i		−	0.957008i
$122$	−3.06124			−0.277152
$123$		−	0.520848i		−	0.0469633i
$124$	8.45710	−	8.45710i	0.759470	−	0.759470i
$125$	10.3719	−	4.17416i	0.927691	−	0.373349i
$126$	3.84062			0.342149
$127$	5.86876	−	5.86876i	0.520768	−	0.520768i	−0.397035	−	0.917803i	$-0.629961\pi$
$127$	5.86876	−	5.86876i	0.520768	−	0.520768i	0.917803	+	0.397035i	$0.129961\pi$
$128$	11.3311			1.00154
$129$	−2.03754			−0.179395
$130$		0			0
$131$	1.37409			0.120054			0.0600272	−	0.998197i	$-0.480881\pi$
$131$	1.37409			0.120054			0.0600272	+	0.998197i	$0.480881\pi$
$132$	1.13564			0.0988452
$133$	14.2353	−	14.2353i	1.23436	−	1.23436i
$134$	6.04902			0.522556
$135$	−8.51216	−	6.57718i	−0.732610	−	0.566074i
$136$	3.11480	−	3.11480i	0.267092	−	0.267092i
$137$		−	12.3276i		−	1.05322i	−0.850108	−	0.526609i	$-0.823463\pi$
$137$		−	12.3276i		−	1.05322i	0.850108	−	0.526609i	$-0.176537\pi$
$138$	0.629002			0.0535442
$139$			6.40157i			0.542974i	0.962442	+	0.271487i	$0.0875153\pi$
$139$			6.40157i			0.542974i	−0.962442	+	0.271487i	$0.912485\pi$
$140$	−1.83571	−	14.3152i	−0.155146	−	1.20986i
$141$	−2.53295	−	2.53295i	−0.213313	−	0.213313i
$142$	−2.34115	+	2.34115i	−0.196465	+	0.196465i
$143$		0			0
$144$			5.49197i			0.457664i
$145$	2.70655	+	21.1062i	0.224767	+	1.75278i
$146$	1.66762			0.138013
$147$	4.32839	−	4.32839i	0.356999	−	0.356999i
$148$			3.22278i			0.264911i
$149$	11.8812	+	11.8812i	0.973345	+	0.973345i	0.999654	−	0.0263084i	$-0.00837520\pi$
$149$	11.8812	+	11.8812i	0.973345	+	0.973345i	−0.0263084	+	0.999654i	$0.508375\pi$
$150$	1.17465	−	2.00333i	0.0959099	−	0.163572i
$151$	3.31542	+	3.31542i	0.269805	+	0.269805i	0.829022	−	0.559217i	$-0.188898\pi$
$151$	3.31542	+	3.31542i	0.269805	+	0.269805i	−0.559217	+	0.829022i	$0.688898\pi$
$152$	−7.18498	−	7.18498i	−0.582779	−	0.582779i
$153$	3.55223	+	3.55223i	0.287181	+	0.287181i
$154$	0.882741	−	0.882741i	0.0711333	−	0.0711333i
$155$	−9.31161	+	12.0510i	−0.747926	+	0.967963i
$156$		0			0
$157$	9.87941	+	9.87941i	0.788463	+	0.788463i	0.981242	−	0.192779i	$-0.0617501\pi$
$157$	9.87941	+	9.87941i	0.788463	+	0.788463i	−0.192779	+	0.981242i	$0.561750\pi$
$158$		−	1.54171i		−	0.122652i
$159$		−	3.28880i		−	0.260819i
$160$	−11.0726	+	1.41989i	−0.875364	+	0.112252i
$161$	−3.51966	+	3.51966i	−0.277388	+	0.277388i
$162$	0.900366			0.0707395
$163$	−0.131970			−0.0103367			−0.00516833	−	0.999987i	$-0.501645\pi$
$163$	−0.131970			−0.0103367			−0.00516833	+	0.999987i	$0.501645\pi$
$164$	0.687741	−	0.687741i	0.0537035	−	0.0537035i
$165$	−1.43432	+	0.183930i	−0.111662	+	0.0143189i
$166$		−	1.05654i		−	0.0820038i
$167$		−	21.6368i		−	1.67430i	−0.546971	−	0.837152i	$-0.684219\pi$
$167$		−	21.6368i		−	1.67430i	0.546971	−	0.837152i	$-0.315781\pi$
$168$	−4.53403	−	4.53403i	−0.349808	−	0.349808i
$169$		0			0
$170$	−1.60339	+	2.07510i	−0.122975	+	0.159153i
$171$	8.19402	−	8.19402i	0.626613	−	0.626613i
$172$	−2.69042	−	2.69042i	−0.205142	−	0.205142i
$173$	5.46851	+	5.46851i	0.415763	+	0.415763i	0.883741	−	0.467977i	$-0.155017\pi$
$173$	5.46851	+	5.46851i	0.415763	+	0.415763i	−0.467977	+	0.883741i	$0.655017\pi$
$174$	3.12539	+	3.12539i	0.236935	+	0.236935i
$175$	4.63701	+	17.7828i	0.350525	+	1.34426i
$176$	1.26229	+	1.26229i	0.0951490	+	0.0951490i
$177$		−	9.78515i		−	0.735497i
$178$	1.17961	−	1.17961i	0.0884157	−	0.0884157i
$179$	16.3536			1.22233			0.611164	−	0.791504i	$-0.290702\pi$
$179$	16.3536			1.22233			0.611164	+	0.791504i	$0.290702\pi$
$180$	−1.05666	−	8.24001i	−0.0787585	−	0.614174i
$181$			18.0387i			1.34081i	0.741997	+	0.670403i	$0.233879\pi$
$181$			18.0387i			1.34081i	−0.741997	+	0.670403i	$0.766121\pi$
$182$		0			0
$183$	−4.12148	+	4.12148i	−0.304668	+	0.304668i
$184$	1.77647	+	1.77647i	0.130963	+	0.130963i
$185$	−0.521963	−	4.07037i	−0.0383755	−	0.299260i
$186$			3.16336i			0.231949i
$187$	1.63292			0.119411
$188$		−	6.68916i		−	0.487857i
$189$	12.5030	−	12.5030i	0.909456	−	0.909456i
$190$	4.78669	+	3.69858i	0.347263	+	0.268324i
$191$	5.19103			0.375610			0.187805	−	0.982206i	$-0.439863\pi$
$191$	5.19103			0.375610			0.187805	+	0.982206i	$0.439863\pi$
$192$	1.81269	−	1.81269i	0.130820	−	0.130820i
$193$	10.1015			0.727119			0.363560	−	0.931571i	$-0.381561\pi$
$193$	10.1015			0.727119			0.363560	+	0.931571i	$0.381561\pi$
$194$	3.49375			0.250836
$195$		0			0
$196$	11.4306			0.816473
$197$	−13.0639			−0.930767			−0.465384	−	0.885109i	$-0.654084\pi$
$197$	−13.0639			−0.930767			−0.465384	+	0.885109i	$0.654084\pi$
$198$	0.508116	−	0.508116i	0.0361102	−	0.0361102i
$199$	−7.85012			−0.556480			−0.278240	−	0.960512i	$-0.589751\pi$
$199$	−7.85012			−0.556480			−0.278240	+	0.960512i	$0.589751\pi$
$200$	8.97550	−	2.34043i	0.634664	−	0.165493i
$201$	8.14405	−	8.14405i	0.574437	−	0.574437i
$202$		−	7.39354i		−	0.520208i
$203$	−34.9770			−2.45491
$204$		−	3.92123i		−	0.274541i
$205$	−0.757230	+	0.980004i	−0.0528872	+	0.0684464i
$206$	−1.56987	−	1.56987i	−0.109378	−	0.109378i
$207$	−2.02596	+	2.02596i	−0.140814	+	0.140814i
$208$		0			0
$209$		−	3.76669i		−	0.260547i
$210$	3.02061	+	2.33397i	0.208442	+	0.161059i
$211$	12.4241			0.855310			0.427655	−	0.903942i	$-0.359340\pi$
$211$	12.4241			0.855310			0.427655	+	0.903942i	$0.359340\pi$
$212$	4.34262	−	4.34262i	0.298252	−	0.298252i
$213$			6.30398i			0.431942i
$214$	5.32684	+	5.32684i	0.364136	+	0.364136i
$215$	3.83374	+	2.96226i	0.261459	+	0.202024i
$216$	−6.31059	−	6.31059i	−0.429382	−	0.429382i
$217$	−17.7010	−	17.7010i	−1.20162	−	1.20162i
$218$	−1.11573	−	1.11573i	−0.0755670	−	0.0755670i
$219$	2.24519	−	2.24519i	0.151716	−	0.151716i
$220$	−2.13678	−	1.65105i	−0.144062	−	0.111314i
$221$		0			0
$222$	−0.602736	−	0.602736i	−0.0404530	−	0.0404530i
$223$			9.94495i			0.665963i	0.942933	+	0.332981i	$0.108055\pi$
$223$			9.94495i			0.665963i	−0.942933	+	0.332981i	$0.891945\pi$
$224$		−	18.3494i		−	1.22602i
$225$	2.66911	+	10.2360i	0.177941	+	0.682400i
$226$	−5.78718	+	5.78718i	−0.384958	+	0.384958i
$227$	−14.6058			−0.969421			−0.484710	−	0.874675i	$-0.661075\pi$
$227$	−14.6058			−0.969421			−0.484710	+	0.874675i	$0.661075\pi$
$228$	−9.04518			−0.599032
$229$	15.6183	−	15.6183i	1.03209	−	1.03209i	0.0326207	−	0.999468i	$-0.489615\pi$
$229$	15.6183	−	15.6183i	1.03209	−	1.03209i	0.999468	−	0.0326207i	$-0.0103853\pi$
$230$	−1.18350	−	0.914469i	−0.0780378	−	0.0602983i
$231$		−	2.37694i		−	0.156391i
$232$			17.6539i			1.15903i
$233$	−16.5625	−	16.5625i	−1.08505	−	1.08505i	−0.996030	−	0.0890148i	$-0.971628\pi$
$233$	−16.5625	−	16.5625i	−1.08505	−	1.08505i	−0.0890148	−	0.996030i	$-0.528372\pi$
$234$		0			0
$235$	1.08338	+	8.44841i	0.0706719	+	0.551113i
$236$	12.9206	−	12.9206i	0.841057	−	0.841057i
$237$	−2.07567	−	2.07567i	−0.134829	−	0.134829i
$238$	−3.04798	−	3.04798i	−0.197572	−	0.197572i
$239$	−14.6022	−	14.6022i	−0.944535	−	0.944535i	0.0540053	−	0.998541i	$-0.482801\pi$
$239$	−14.6022	−	14.6022i	−0.944535	−	0.944535i	−0.998541	+	0.0540053i	$0.982801\pi$
$240$	−3.33750	+	4.31938i	−0.215435	+	0.278815i
$241$	2.19128	+	2.19128i	0.141153	+	0.141153i	0.774152	−	0.632999i	$-0.218176\pi$
$241$	2.19128	+	2.19128i	0.141153	+	0.141153i	−0.632999	+	0.774152i	$0.718176\pi$
$242$			5.19935i			0.334227i
$243$	11.4173	−	11.4173i	0.732422	−	0.732422i
$244$	−10.8842			−0.696790
$245$	−14.4369	+	1.85131i	−0.922339	+	0.118276i
$246$			0.257248i			0.0164015i
$247$		0			0
$248$	−8.93419	+	8.93419i	−0.567322	+	0.567322i
$249$	−1.42247	−	1.42247i	−0.0901453	−	0.0901453i
$250$	−5.12270	+	2.06163i	−0.323988	+	0.130389i
$251$			29.5289i			1.86385i	0.362652	+	0.931925i	$0.381872\pi$
$251$			29.5289i			1.86385i	−0.362652	+	0.931925i	$0.618128\pi$
$252$	13.6553			0.860201
$253$			0.931307i			0.0585508i
$254$	−2.89859	+	2.89859i	−0.181874	+	0.181874i
$255$	0.635084	+	4.95251i	0.0397705	+	0.310138i
$256$	−0.144429			−0.00902681
$257$	5.06650	−	5.06650i	0.316040	−	0.316040i	−0.531204	−	0.847244i	$-0.678260\pi$
$257$	5.06650	−	5.06650i	0.316040	−	0.316040i	0.847244	+	0.531204i	$0.178260\pi$
$258$	1.00634			0.0626522
$259$	6.74538			0.419137
$260$		0			0
$261$	−20.1332			−1.24621
$262$	−0.678663			−0.0419280
$263$	−9.52151	+	9.52151i	−0.587121	+	0.587121i	−0.936851	−	0.349729i	$-0.886274\pi$
$263$	−9.52151	+	9.52151i	−0.587121	+	0.587121i	0.349729	+	0.936851i	$0.386274\pi$
$264$	−1.19971			−0.0738370
$265$	−4.78140	+	6.18807i	−0.293719	+	0.380130i
$266$	−7.03086	+	7.03086i	−0.431090	+	0.431090i
$267$		−	3.17632i		−	0.194388i
$268$	21.5072			1.31376
$269$		−	8.10376i		−	0.494095i	−0.969003	−	0.247047i	$-0.920540\pi$
$269$		−	8.10376i		−	0.494095i	0.969003	−	0.247047i	$-0.0794603\pi$
$270$	4.20417	+	3.24848i	0.255858	+	0.197696i
$271$	6.50299	+	6.50299i	0.395028	+	0.395028i	0.876475	−	0.481447i	$-0.159889\pi$
$271$	6.50299	+	6.50299i	0.395028	+	0.395028i	−0.481447	+	0.876475i	$0.659889\pi$
$272$	4.35853	−	4.35853i	0.264275	−	0.264275i
$273$		0			0
$274$			6.08862i			0.367827i
$275$	2.96616	+	1.73920i	0.178866	+	0.104878i
$276$	2.23641			0.134616
$277$	18.2750	−	18.2750i	1.09804	−	1.09804i	0.103397	−	0.994640i	$-0.467029\pi$
$277$	18.2750	−	18.2750i	1.09804	−	1.09804i	0.994640	−	0.103397i	$-0.0329713\pi$
$278$		−	3.16174i		−	0.189629i
$279$	−10.1889	−	10.1889i	−0.609993	−	0.609993i
$280$	1.93927	+	15.1228i	0.115893	+	0.903760i
$281$	−5.41928	−	5.41928i	−0.323287	−	0.323287i	0.526740	−	0.850027i	$-0.323414\pi$
$281$	−5.41928	−	5.41928i	−0.323287	−	0.323287i	−0.850027	+	0.526740i	$0.823414\pi$
$282$	1.25103	+	1.25103i	0.0744978	+	0.0744978i
$283$	6.21235	+	6.21235i	0.369286	+	0.369286i	0.867217	−	0.497931i	$-0.165907\pi$
$283$	6.21235	+	6.21235i	0.369286	+	0.369286i	−0.497931	+	0.867217i	$0.665907\pi$
$284$	−8.32394	+	8.32394i	−0.493935	+	0.493935i
$285$	11.4241	−	1.46496i	0.676704	−	0.0867769i
$286$		0			0
$287$	−1.43946	−	1.43946i	−0.0849688	−	0.0849688i
$288$		−	10.5621i		−	0.622378i
$289$			11.3618i			0.668339i
$290$	−1.33677	−	10.4244i	−0.0784978	−	0.612142i
$291$	4.70377	−	4.70377i	0.275740	−	0.275740i
$292$	5.92921			0.346981
$293$	13.2360			0.773253			0.386626	−	0.922236i	$-0.373640\pi$
$293$	13.2360			0.773253			0.386626	+	0.922236i	$0.373640\pi$
$294$	−2.13780	+	2.13780i	−0.124679	+	0.124679i
$295$	−14.2261	+	18.4113i	−0.828273	+	1.07195i
$296$		−	3.40458i		−	0.197887i
$297$		−	3.30830i		−	0.191967i
$298$	−5.86814	−	5.86814i	−0.339932	−	0.339932i
$299$		0			0
$300$	4.17646	−	7.12283i	0.241128	−	0.411237i
$301$	−5.63113	+	5.63113i	−0.324573	+	0.324573i
$302$	−1.63749	−	1.63749i	−0.0942270	−	0.0942270i
$303$	−9.95423	−	9.95423i	−0.571856	−	0.571856i
$304$	−10.0539	−	10.0539i	−0.576632	−	0.576632i
$305$	13.7468	−	1.76281i	0.787138	−	0.100938i
$306$	−1.75446	−	1.75446i	−0.100296	−	0.100296i
$307$			15.4782i			0.883389i	0.897165	+	0.441695i	$0.145623\pi$
$307$			15.4782i			0.883389i	−0.897165	+	0.441695i	$0.854377\pi$
$308$	3.13857	−	3.13857i	0.178837	−	0.178837i
$309$	−4.22716			−0.240475
$310$	4.59902	−	5.95203i	0.261207	−	0.338053i
$311$			5.34922i			0.303326i	0.988432	+	0.151663i	$0.0484629\pi$
$311$			5.34922i			0.303326i	−0.988432	+	0.151663i	$0.951537\pi$
$312$		0			0
$313$	24.3923	−	24.3923i	1.37873	−	1.37873i	0.531967	−	0.846765i	$-0.321453\pi$
$313$	24.3923	−	24.3923i	1.37873	−	1.37873i	0.846765	−	0.531967i	$-0.178547\pi$
$314$	−4.87946	−	4.87946i	−0.275364	−	0.275364i
$315$	−17.2466	+	2.21161i	−0.971736	+	0.124610i
$316$		−	5.48153i		−	0.308360i
$317$	18.9851			1.06631			0.533156	−	0.846017i	$-0.321006\pi$
$317$	18.9851			1.06631			0.533156	+	0.846017i	$0.321006\pi$
$318$			1.62435i			0.0910888i
$319$	−4.62748	+	4.62748i	−0.259089	+	0.259089i
$320$	−6.04604	+	0.775312i	−0.337984	+	0.0433412i
$321$	14.3435			0.800576
$322$	1.73837	−	1.73837i	0.0968755	−	0.0968755i
$323$	−13.0059			−0.723665
$324$	3.20124			0.177847
$325$		0			0
$326$	0.0651800			0.00360999
$327$	−3.00431			−0.166139
$328$	−0.726538	+	0.726538i	−0.0401163	+	0.0401163i
$329$	−14.0006			−0.771879
$330$	0.708414	−	0.0908432i	0.0389969	−	0.00500075i
$331$	4.96159	−	4.96159i	0.272714	−	0.272714i	−0.557478	−	0.830192i	$-0.688231\pi$
$331$	4.96159	−	4.96159i	0.272714	−	0.272714i	0.830192	+	0.557478i	$0.188231\pi$
$332$		−	3.75653i		−	0.206166i
$333$	3.88272			0.212772
$334$			10.6864i			0.584736i
$335$	−27.1636	+	3.48332i	−1.48411	+	0.190314i
$336$	−6.34446	−	6.34446i	−0.346119	−	0.346119i
$337$	1.10195	−	1.10195i	0.0600271	−	0.0600271i	−0.676456	−	0.736483i	$-0.736485\pi$
$337$	1.10195	−	1.10195i	0.0600271	−	0.0600271i	0.736483	+	0.676456i	$0.236485\pi$
$338$		0			0
$339$			15.5830i			0.846355i
$340$	−5.70084	+	7.37801i	−0.309172	+	0.400129i
$341$	−4.68370			−0.253637
$342$	−4.04704	+	4.04704i	−0.218839	+	0.218839i
$343$			1.80378i			0.0973947i
$344$	2.84219	+	2.84219i	0.153241	+	0.153241i
$345$	−2.82458	+	0.362210i	−0.152071	+	0.0195007i
$346$	−2.70091	−	2.70091i	−0.145202	−	0.145202i
$347$	18.2654	+	18.2654i	0.980539	+	0.980539i	0.999814	−	0.0192754i	$-0.00613592\pi$
$347$	18.2654	+	18.2654i	0.980539	+	0.980539i	−0.0192754	+	0.999814i	$0.506136\pi$
$348$	11.1123	+	11.1123i	0.595680	+	0.595680i
$349$	6.64671	−	6.64671i	0.355790	−	0.355790i	−0.506468	−	0.862259i	$-0.669049\pi$
$349$	6.64671	−	6.64671i	0.355790	−	0.355790i	0.862259	+	0.506468i	$0.169049\pi$
$350$	−2.29023	−	8.78298i	−0.122418	−	0.469470i
$351$		0			0
$352$	−2.42763	−	2.42763i	−0.129393	−	0.129393i
$353$		−	3.26547i		−	0.173803i	−0.996217	−	0.0869017i	$-0.972303\pi$
$353$		−	3.26547i		−	0.173803i	0.996217	−	0.0869017i	$-0.0276966\pi$
$354$			4.83291i			0.256866i
$355$	9.16499	−	11.8613i	0.486427	−	0.629532i
$356$	4.19410	−	4.19410i	0.222287	−	0.222287i
$357$	−8.20725			−0.434374
$358$	−8.07709			−0.426887
$359$	3.12090	−	3.12090i	0.164715	−	0.164715i	−0.619937	−	0.784652i	$-0.712842\pi$
$359$	3.12090	−	3.12090i	0.164715	−	0.164715i	0.784652	+	0.619937i	$0.212842\pi$
$360$	1.11626	+	8.70485i	0.0588323	+	0.458786i
$361$			11.0009i			0.578995i
$362$		−	8.90935i		−	0.468265i
$363$	7.00009	+	7.00009i	0.367410	+	0.367410i
$364$		0			0
$365$	−7.48859	+	0.960297i	−0.391971	+	0.0502643i
$366$	2.03561	−	2.03561i	0.106403	−	0.106403i
$367$	17.7411	+	17.7411i	0.926080	+	0.926080i	0.997450	−	0.0713698i	$-0.0227371\pi$
$367$	17.7411	+	17.7411i	0.926080	+	0.926080i	−0.0713698	+	0.997450i	$0.522737\pi$
$368$	2.48582	+	2.48582i	0.129582	+	0.129582i
$369$	−0.828572	−	0.828572i	−0.0431337	−	0.0431337i
$370$	0.257798	+	2.01036i	0.0134023	+	0.104514i
$371$	−9.08925	−	9.08925i	−0.471890	−	0.471890i
$372$			11.2473i			0.583144i
$373$	−8.07976	+	8.07976i	−0.418354	+	0.418354i	−0.884636	−	0.466282i	$-0.845593\pi$
$373$	−8.07976	+	8.07976i	−0.418354	+	0.418354i	0.466282	+	0.884636i	$0.345593\pi$
$374$	−0.806500			−0.0417031
$375$	−4.12125	+	9.67256i	−0.212820	+	0.499489i
$376$			7.06651i			0.364427i
$377$		0			0
$378$	−6.17523	+	6.17523i	−0.317620	+	0.317620i
$379$	1.42096	+	1.42096i	0.0729900	+	0.0729900i	0.742659	−	0.669669i	$-0.233564\pi$
$379$	1.42096	+	1.42096i	0.0729900	+	0.0729900i	−0.669669	+	0.742659i	$0.733564\pi$
$380$	17.0190	+	13.1503i	0.873057	+	0.674594i
$381$			7.80499i			0.399862i
$382$	−2.56386			−0.131179
$383$		−	26.4516i		−	1.35161i	−0.737080	−	0.675806i	$-0.763796\pi$
$383$		−	26.4516i		−	1.35161i	0.737080	−	0.675806i	$-0.236204\pi$
$384$	−7.53473	+	7.53473i	−0.384505	+	0.384505i
$385$	−3.45570	+	4.47235i	−0.176119	+	0.227932i
$386$	−4.98913			−0.253940
$387$	−3.24134	+	3.24134i	−0.164767	+	0.164767i
$388$	12.4220			0.630630
$389$	0.650094			0.0329611			0.0164805	−	0.999864i	$-0.494754\pi$
$389$	0.650094			0.0329611			0.0164805	+	0.999864i	$0.494754\pi$
$390$		0			0
$391$	3.21568			0.162624
$392$	−12.0755			−0.609903
$393$	−0.913712	+	0.913712i	−0.0460907	+	0.0460907i
$394$	6.45230			0.325062
$395$	0.887791	+	6.92317i	0.0446696	+	0.348343i
$396$	1.80660	−	1.80660i	0.0907850	−	0.0907850i
$397$			27.0082i			1.35550i	0.735292	+	0.677750i	$0.237045\pi$
$397$			27.0082i			1.35550i	−0.735292	+	0.677750i	$0.762955\pi$
$398$	3.87719			0.194346
$399$			18.9319i			0.947779i
$400$	12.5594	−	3.27496i	0.627970	−	0.163748i
$401$	3.50630	+	3.50630i	0.175096	+	0.175096i	0.789214	−	0.614118i	$-0.210488\pi$
$401$	3.50630	+	3.50630i	0.175096	+	0.175096i	−0.614118	+	0.789214i	$0.710488\pi$
$402$	−4.02236	+	4.02236i	−0.200617	+	0.200617i
$403$		0			0
$404$		−	26.2876i		−	1.30786i
$405$	−4.04317	+	0.518474i	−0.200907	+	0.0257632i
$406$	17.2752			0.857354
$407$	0.892417	−	0.892417i	0.0442355	−	0.0442355i
$408$			4.14243i			0.205081i
$409$	−4.27492	−	4.27492i	−0.211381	−	0.211381i	0.593473	−	0.804854i	$-0.297756\pi$
$409$	−4.27492	−	4.27492i	−0.211381	−	0.211381i	−0.804854	+	0.593473i	$0.797756\pi$
$410$	0.373997	−	0.484026i	0.0184704	−	0.0239043i
$411$	8.19736	+	8.19736i	0.404346	+	0.404346i
$412$	−5.58165	−	5.58165i	−0.274988	−	0.274988i
$413$	−27.0432	−	27.0432i	−1.33071	−	1.33071i
$414$	1.00062	−	1.00062i	0.0491780	−	0.0491780i
$415$	0.608410	+	4.74450i	0.0298657	+	0.232898i
$416$		0			0
$417$	−4.25679	−	4.25679i	−0.208456	−	0.208456i
$418$			1.86037i			0.0909938i
$419$		−	5.37068i		−	0.262375i	−0.991358	−	0.131187i	$-0.958121\pi$
$419$		−	5.37068i		−	0.262375i	0.991358	−	0.131187i	$-0.0418790\pi$
$420$	10.7397	+	8.29839i	0.524045	+	0.404920i
$421$	−14.1377	+	14.1377i	−0.689029	+	0.689029i	−0.962017	−	0.272988i	$-0.911988\pi$
$421$	−14.1377	+	14.1377i	−0.689029	+	0.689029i	0.272988	+	0.962017i	$0.411988\pi$
$422$	−6.13629			−0.298710
$423$	−8.05892			−0.391838
$424$	−4.58760	+	4.58760i	−0.222794	+	0.222794i
$425$	6.00522	−	10.2417i	0.291296	−	0.496797i
$426$		−	3.11355i		−	0.150852i
$427$			22.7810i			1.10245i
$428$	18.9395	+	18.9395i	0.915476	+	0.915476i
$429$		0			0
$430$	−1.89349	−	1.46306i	−0.0913122	−	0.0705552i
$431$	11.8020	−	11.8020i	0.568485	−	0.568485i	−0.363219	−	0.931704i	$-0.618322\pi$
$431$	11.8020	−	11.8020i	0.568485	−	0.568485i	0.931704	+	0.363219i	$0.118322\pi$
$432$	−8.83040	−	8.83040i	−0.424853	−	0.424853i
$433$	5.36952	+	5.36952i	0.258043	+	0.258043i	0.824258	−	0.566215i	$-0.191593\pi$
$433$	5.36952	+	5.36952i	0.258043	+	0.258043i	−0.566215	+	0.824258i	$0.691593\pi$
$434$	8.74255	+	8.74255i	0.419656	+	0.419656i
$435$	−15.8345	−	12.2350i	−0.759208	−	0.586626i
$436$	−3.96697	−	3.96697i	−0.189984	−	0.189984i
$437$		−	7.41767i		−	0.354835i
$438$	−1.10890	+	1.10890i	−0.0529854	+	0.0529854i
$439$	13.6907			0.653422			0.326711	−	0.945124i	$-0.394060\pi$
$439$	13.6907			0.653422			0.326711	+	0.945124i	$0.394060\pi$
$440$	2.25732	+	1.74419i	0.107614	+	0.0831509i
$441$		−	13.7713i		−	0.655777i
$442$		0			0
$443$	6.46290	−	6.46290i	0.307062	−	0.307062i	−0.536707	−	0.843769i	$-0.680332\pi$
$443$	6.46290	−	6.46290i	0.307062	−	0.307062i	0.843769	+	0.536707i	$0.180332\pi$
$444$	−2.14302	−	2.14302i	−0.101703	−	0.101703i
$445$	−4.61787	+	5.97642i	−0.218908	+	0.283310i
$446$		−	4.91183i		−	0.232582i
$447$	−15.8010			−0.747364
$448$		−	10.0194i		−	0.473373i
$449$	−18.1807	+	18.1807i	−0.857998	+	0.857998i	−0.991102	−	0.133104i	$-0.957506\pi$
$449$	−18.1807	+	18.1807i	−0.857998	+	0.857998i	0.133104	+	0.991102i	$0.457506\pi$
$450$	−1.31828	−	5.05558i	−0.0621443	−	0.238322i
$451$	−0.380884			−0.0179351
$452$	−20.5763	+	20.5763i	−0.967825	+	0.967825i
$453$	−4.40924			−0.207164
$454$	7.21383			0.338562
$455$		0			0
$456$	9.55545			0.447475
$457$	−0.827533			−0.0387104			−0.0193552	−	0.999813i	$-0.506161\pi$
$457$	−0.827533			−0.0387104			−0.0193552	+	0.999813i	$0.506161\pi$
$458$	−7.71392	+	7.71392i	−0.360448	+	0.360448i
$459$	−11.4231			−0.533184
$460$	−4.20792	−	3.25138i	−0.196195	−	0.151596i
$461$	−17.0267	+	17.0267i	−0.793011	+	0.793011i	−0.981983	−	0.188972i	$-0.939485\pi$
$461$	−17.0267	+	17.0267i	−0.793011	+	0.793011i	0.188972	+	0.981983i	$0.439485\pi$
$462$			1.17398i			0.0546183i
$463$	−6.35566			−0.295373			−0.147686	−	0.989034i	$-0.547183\pi$
$463$	−6.35566			−0.295373			−0.147686	+	0.989034i	$0.547183\pi$
$464$			24.7030i			1.14681i
$465$	−1.82161	−	14.2053i	−0.0844753	−	0.658756i
$466$	8.18025	+	8.18025i	0.378943	+	0.378943i
$467$	15.6194	−	15.6194i	0.722781	−	0.722781i	−0.246390	−	0.969171i	$-0.579244\pi$
$467$	15.6194	−	15.6194i	0.722781	−	0.722781i	0.969171	+	0.246390i	$0.0792443\pi$
$468$		0			0
$469$		−	45.0153i		−	2.07861i
$470$	−0.535083	−	4.17269i	−0.0246815	−	0.192472i
$471$	−13.1388			−0.605406
$472$	−13.6495	+	13.6495i	−0.628267	+	0.628267i
$473$			1.49000i			0.0685104i
$474$	1.02518	+	1.02518i	0.0470879	+	0.0470879i
$475$	−23.6249	−	13.8524i	−1.08398	−	0.635591i
$476$	−10.8371	−	10.8371i	−0.496716	−	0.496716i
$477$	−5.23187	−	5.23187i	−0.239551	−	0.239551i
$478$	7.21204	+	7.21204i	0.329871	+	0.329871i
$479$	−6.69175	+	6.69175i	−0.305754	+	0.305754i	−0.843260	−	0.537506i	$-0.819367\pi$
$479$	−6.69175	+	6.69175i	−0.305754	+	0.305754i	0.537506	+	0.843260i	$0.319367\pi$
$480$	6.41866	−	8.30700i	0.292970	−	0.379161i
$481$		0			0
$482$	−1.08228	−	1.08228i	−0.0492964	−	0.0492964i
$483$		−	4.68087i		−	0.212987i
$484$			18.4862i			0.840282i
$485$	−15.6890	+	2.01187i	−0.712399	+	0.0913543i
$486$	−5.63904	+	5.63904i	−0.255792	+	0.255792i
$487$	−6.15896			−0.279089			−0.139545	−	0.990216i	$-0.544564\pi$
$487$	−6.15896			−0.279089			−0.139545	+	0.990216i	$0.544564\pi$
$488$	11.4982			0.520500
$489$	0.0877545	−	0.0877545i	0.00396840	−	0.00396840i
$490$	7.13041	−	0.914366i	0.322119	−	0.0413068i
$491$			14.8136i			0.668530i	0.942479	+	0.334265i	$0.108488\pi$
$491$			14.8136i			0.668530i	−0.942479	+	0.334265i	$0.891512\pi$
$492$			0.914640i			0.0412352i
$493$	15.9781	+	15.9781i	0.719615	+	0.719615i
$494$		0			0
$495$	−1.98914	+	2.57433i	−0.0894051	+	0.115708i
$496$	−12.5016	+	12.5016i	−0.561338	+	0.561338i
$497$	17.4223	+	17.4223i	0.781496	+	0.781496i
$498$	0.702560	+	0.702560i	0.0314825	+	0.0314825i
$499$	21.0529	+	21.0529i	0.942459	+	0.942459i	0.998432	−	0.0559733i	$-0.0178262\pi$
$499$	21.0529	+	21.0529i	0.942459	+	0.942459i	−0.0559733	+	0.998432i	$0.517826\pi$
$500$	−18.2137	+	7.33009i	−0.814541	+	0.327811i
$501$	14.3876	+	14.3876i	0.642790	+	0.642790i
$502$		−	14.5844i		−	0.650933i
$503$	−27.4075	+	27.4075i	−1.22204	+	1.22204i	−0.255133	+	0.966906i	$0.582119\pi$
$503$	−27.4075	+	27.4075i	−1.22204	+	1.22204i	−0.966906	+	0.255133i	$0.917881\pi$
$504$	−14.4256			−0.642567
$505$	4.25756	+	33.2013i	0.189459	+	1.47744i
$506$		−	0.459974i		−	0.0204484i
$507$		0			0
$508$	−10.3059	+	10.3059i	−0.457250	+	0.457250i
$509$	−3.92592	−	3.92592i	−0.174013	−	0.174013i	0.614727	−	0.788740i	$-0.289266\pi$
$509$	−3.92592	−	3.92592i	−0.174013	−	0.174013i	−0.788740	+	0.614727i	$0.789266\pi$
$510$	−0.313669	−	2.44606i	−0.0138895	−	0.108313i
$511$		−	12.4100i		−	0.548987i
$512$	−22.5909			−0.998384
$513$			26.3499i			1.16338i
$514$	−2.50236	+	2.50236i	−0.110374	+	0.110374i
$515$	7.95364	+	6.14563i	0.350479	+	0.270809i
$516$	3.57804			0.157514
$517$	−1.85229	+	1.85229i	−0.0814636	+	0.0814636i
$518$	−3.33155			−0.146380
$519$	−7.27269			−0.319236
$520$		0			0
$521$	−13.8692			−0.607619			−0.303809	−	0.952733i	$-0.598259\pi$
$521$	−13.8692			−0.607619			−0.303809	+	0.952733i	$0.598259\pi$
$522$	9.94381			0.435229
$523$	22.1520	−	22.1520i	0.968638	−	0.968638i	−0.0308854	−	0.999523i	$-0.509833\pi$
$523$	22.1520	−	22.1520i	0.968638	−	0.968638i	0.999523	+	0.0308854i	$0.00983268\pi$
$524$	−2.41298			−0.105411
$525$	−14.9083	−	8.74146i	−0.650652	−	0.381508i
$526$	4.70269	−	4.70269i	0.205047	−	0.205047i
$527$			16.1722i			0.704471i
$528$	−1.67875			−0.0730583
$529$		−	21.1660i		−	0.920261i
$530$	2.36154	−	3.05630i	0.102579	−	0.132757i
$531$	−15.5664	−	15.5664i	−0.675522	−	0.675522i
$532$	−24.9981	+	24.9981i	−1.08381	+	1.08381i
$533$		0			0
$534$			1.56879i			0.0678882i
$535$	−26.9881	−	20.8532i	−1.16680	−	0.901561i
$536$	−22.7205			−0.981376
$537$	−10.8745	+	10.8745i	−0.469270	+	0.469270i
$538$			4.00246i			0.172558i
$539$	−3.16525	−	3.16525i	−0.136337	−	0.136337i
$540$	14.9479	+	11.5499i	0.643254	+	0.497030i
$541$	10.7732	+	10.7732i	0.463175	+	0.463175i	0.899695	−	0.436520i	$-0.143789\pi$
$541$	10.7732	+	10.7732i	0.463175	+	0.463175i	−0.436520	+	0.899695i	$0.643789\pi$
$542$	−3.21184	−	3.21184i	−0.137960	−	0.137960i
$543$	−11.9950	−	11.9950i	−0.514756	−	0.514756i
$544$	−8.38228	+	8.38228i	−0.359387	+	0.359387i
$545$	5.65278	+	4.36780i	0.242139	+	0.187096i
$546$		0			0
$547$	14.2704	+	14.2704i	0.610159	+	0.610159i	0.942987	−	0.332828i	$-0.108003\pi$
$547$	14.2704	+	14.2704i	0.610159	+	0.610159i	−0.332828	+	0.942987i	$0.608003\pi$
$548$			21.6480i			0.924757i
$549$			13.1130i			0.559650i
$550$	−1.46499	−	0.858995i	−0.0624674	−	0.0366277i
$551$	36.8569	−	36.8569i	1.57016	−	1.57016i
$552$	−2.36257			−0.100558
$553$	−11.4730			−0.487882
$554$	−9.02605	+	9.02605i	−0.383480	+	0.383480i
$555$	3.05372	+	2.35955i	0.129623	+	0.100157i
$556$		−	11.2415i		−	0.476747i
$557$		−	16.7117i		−	0.708096i	−0.935227	−	0.354048i	$-0.884805\pi$
$557$		−	16.7117i		−	0.708096i	0.935227	−	0.354048i	$-0.115195\pi$
$558$	5.03231	+	5.03231i	0.213035	+	0.213035i
$559$		0			0
$560$	2.71361	+	21.1613i	0.114671	+	0.894227i
$561$	−1.08582	+	1.08582i	−0.0458435	+	0.0458435i
$562$	2.67659	+	2.67659i	0.112905	+	0.112905i
$563$	15.9601	+	15.9601i	0.672637	+	0.672637i	0.958323	−	0.285686i	$-0.0922215\pi$
$563$	15.9601	+	15.9601i	0.672637	+	0.672637i	−0.285686	+	0.958323i	$0.592221\pi$
$564$	4.44802	+	4.44802i	0.187296	+	0.187296i
$565$	22.6553	−	29.3204i	0.953115	−	1.23352i
$566$	−3.06829	−	3.06829i	−0.128970	−	0.128970i
$567$		−	6.70030i		−	0.281386i
$568$	8.79352	−	8.79352i	0.368968	−	0.368968i
$569$	5.73685			0.240501			0.120251	−	0.992744i	$-0.461630\pi$
$569$	5.73685			0.240501			0.120251	+	0.992744i	$0.461630\pi$
$570$	−5.64237	+	0.723548i	−0.236333	+	0.0303061i
$571$		−	46.5634i		−	1.94862i	−0.225214	−	0.974309i	$-0.572308\pi$
$571$		−	46.5634i		−	1.94862i	0.225214	−	0.974309i	$-0.427692\pi$
$572$		0			0
$573$	−3.45183	+	3.45183i	−0.144202	+	0.144202i
$574$	0.710953	+	0.710953i	0.0296746	+	0.0296746i
$575$	5.84121	+	3.42498i	0.243595	+	0.142832i
$576$		−	5.76730i		−	0.240304i
$577$	28.9429			1.20491			0.602455	−	0.798153i	$-0.294189\pi$
$577$	28.9429			1.20491			0.602455	+	0.798153i	$0.294189\pi$
$578$		−	5.61160i		−	0.233412i
$579$	−6.71707	+	6.71707i	−0.279152	+	0.279152i
$580$	−4.75287	−	37.0638i	−0.197352	−	1.53899i
$581$	−7.86254			−0.326193
$582$	−2.32320	+	2.32320i	−0.0962999	+	0.0962999i
$583$	−2.40503			−0.0996060
$584$	−6.26369			−0.259193
$585$		0			0
$586$	−6.53726			−0.270052
$587$	19.6915			0.812757			0.406379	−	0.913705i	$-0.366791\pi$
$587$	19.6915			0.812757			0.406379	+	0.913705i	$0.366791\pi$
$588$	−7.60091	+	7.60091i	−0.313456	+	0.313456i
$589$	37.3047			1.53712
$590$	7.02628	−	9.09338i	0.289267	−	0.374368i
$591$	8.68700	−	8.68700i	0.357335	−	0.357335i
$592$		−	4.76402i		−	0.195800i
$593$	21.8216			0.896106			0.448053	−	0.894007i	$-0.352118\pi$
$593$	21.8216			0.896106			0.448053	+	0.894007i	$0.352118\pi$
$594$			1.63397i			0.0670427i
$595$	15.4424	+	11.9320i	0.633077	+	0.489166i
$596$	−20.8641	−	20.8641i	−0.854627	−	0.854627i
$597$	5.22002	−	5.22002i	0.213641	−	0.213641i
$598$		0			0
$599$			37.6041i			1.53646i	0.640172	+	0.768232i	$0.278863\pi$
$599$			37.6041i			1.53646i	−0.640172	+	0.768232i	$0.721137\pi$
$600$	−4.41206	+	7.52464i	−0.180122	+	0.307192i
$601$	−20.2975			−0.827952			−0.413976	−	0.910288i	$-0.635860\pi$
$601$	−20.2975			−0.827952			−0.413976	+	0.910288i	$0.635860\pi$
$602$	2.78122	−	2.78122i	0.113354	−	0.113354i
$603$		−	25.9113i		−	1.05519i
$604$	−5.82207	−	5.82207i	−0.236897	−	0.236897i
$605$	−2.99404	−	23.3481i	−0.121725	−	0.949235i
$606$	4.91641	+	4.91641i	0.199716	+	0.199716i
$607$	24.3632	+	24.3632i	0.988874	+	0.988874i	0.999939	−	0.0110652i	$-0.00352225\pi$
$607$	24.3632	+	24.3632i	0.988874	+	0.988874i	−0.0110652	+	0.999939i	$0.503522\pi$
$608$	19.3356	+	19.3356i	0.784162	+	0.784162i
$609$	23.2583	−	23.2583i	0.942475	−	0.942475i
$610$	−6.78955	+	0.870657i	−0.274901	+	0.0352519i
$611$		0			0
$612$	−6.23794	−	6.23794i	−0.252154	−	0.252154i
$613$		−	24.8665i		−	1.00435i	−0.864767	−	0.502173i	$-0.832534\pi$
$613$		−	24.8665i		−	1.00435i	0.864767	−	0.502173i	$-0.167466\pi$
$614$		−	7.64473i		−	0.308516i
$615$	−0.148136	−	1.15519i	−0.00597341	−	0.0465818i
$616$	−3.31563	+	3.31563i	−0.133591	+	0.133591i
$617$	27.8161			1.11983			0.559917	−	0.828548i	$-0.310833\pi$
$617$	27.8161			1.11983			0.559917	+	0.828548i	$0.310833\pi$
$618$	2.08780			0.0839838
$619$	−19.5593	+	19.5593i	−0.786156	+	0.786156i	−0.980862	−	0.194705i	$-0.937625\pi$
$619$	−19.5593	+	19.5593i	−0.786156	+	0.786156i	0.194705	+	0.980862i	$0.437625\pi$
$620$	16.3518	−	21.1624i	0.656702	−	0.849901i
$621$		−	6.51497i		−	0.261437i
$622$		−	2.64199i		−	0.105934i
$623$	−8.77838	−	8.77838i	−0.351698	−	0.351698i
$624$		0			0
$625$	21.8167	−	12.2078i	0.872669	−	0.488312i
$626$	−12.0474	+	12.0474i	−0.481510	+	0.481510i
$627$	2.50470	+	2.50470i	0.100028	+	0.100028i
$628$	−17.3489	−	17.3489i	−0.692295	−	0.692295i
$629$	−3.08139	−	3.08139i	−0.122863	−	0.122863i
$630$	8.51813	−	1.09232i	0.339371	−	0.0435191i
$631$	9.23751	+	9.23751i	0.367739	+	0.367739i	0.866652	−	0.498913i	$-0.166267\pi$
$631$	9.23751	+	9.23751i	0.367739	+	0.367739i	−0.498913	+	0.866652i	$0.666267\pi$
$632$			5.79076i			0.230344i
$633$	−8.26153	+	8.26153i	−0.328366	+	0.328366i
$634$	−9.37679			−0.372400
$635$	11.3472	−	14.6855i	0.450300	−	0.582777i
$636$			5.77534i			0.229007i
$637$		0			0
$638$	2.28552	−	2.28552i	0.0904846	−	0.0904846i
$639$	10.0285	+	10.0285i	0.396720	+	0.396720i
$640$	25.1313	−	3.22271i	0.993402	−	0.127389i
$641$		−	27.3770i		−	1.08133i	−0.841239	−	0.540663i	$-0.818173\pi$
$641$		−	27.3770i		−	1.08133i	0.841239	−	0.540663i	$-0.181827\pi$
$642$	−7.08428			−0.279594
$643$			31.5021i			1.24232i	0.783683	+	0.621161i	$0.213339\pi$
$643$			31.5021i			1.24232i	−0.783683	+	0.621161i	$0.786661\pi$
$644$	6.18074	−	6.18074i	0.243555	−	0.243555i
$645$	−4.51907	+	0.579501i	−0.177938	+	0.0228178i
$646$	6.42361			0.252734
$647$	29.5351	−	29.5351i	1.16114	−	1.16114i	0.176919	−	0.984225i	$-0.443387\pi$
$647$	29.5351	−	29.5351i	1.16114	−	1.16114i	0.984225	−	0.176919i	$-0.0566131\pi$
$648$	−3.38183			−0.132851
$649$	−7.15565			−0.280884
$650$		0			0
$651$	23.5409			0.922641
$652$	0.231747			0.00907589
$653$	−10.7389	+	10.7389i	−0.420244	+	0.420244i	−0.885288	−	0.465044i	$-0.846039\pi$
$653$	−10.7389	+	10.7389i	−0.420244	+	0.420244i	0.465044	+	0.885288i	$0.346039\pi$
$654$	1.48384			0.0580226
$655$	3.04759	−	0.390807i	0.119079	−	0.0152701i
$656$	−1.01664	+	1.01664i	−0.0396932	+	0.0396932i
$657$		−	7.14335i		−	0.278689i
$658$	6.91493			0.269572
$659$		−	28.5112i		−	1.11064i	−0.831638	−	0.555319i	$-0.812596\pi$
$659$		−	28.5112i		−	1.11064i	0.831638	−	0.555319i	$-0.187404\pi$
$660$	2.51875	−	0.322992i	0.0980424	−	0.0125724i
$661$	4.45573	+	4.45573i	0.173308	+	0.173308i	0.788431	−	0.615123i	$-0.210894\pi$
$661$	4.45573	+	4.45573i	0.173308	+	0.173308i	−0.615123	+	0.788431i	$0.710894\pi$
$662$	−2.45054	+	2.45054i	−0.0952430	+	0.0952430i
$663$		0			0
$664$			3.96845i			0.154006i
$665$	27.5239	−	35.6213i	1.06733	−	1.38134i
$666$	−1.91768			−0.0743086
$667$	−9.11282	+	9.11282i	−0.352850	+	0.352850i
$668$			37.9955i			1.47009i
$669$	−6.61299	−	6.61299i	−0.255673	−	0.255673i
$670$	13.4162	−	1.72042i	0.518312	−	0.0664656i
$671$	3.01394	+	3.01394i	0.116352	+	0.116352i
$672$	12.2016	+	12.2016i	0.470687	+	0.470687i
$673$	−16.1992	−	16.1992i	−0.624433	−	0.624433i	0.322229	−	0.946662i	$-0.395568\pi$
$673$	−16.1992	−	16.1992i	−0.624433	−	0.624433i	−0.946662	+	0.322229i	$0.895568\pi$
$674$	−0.544256	+	0.544256i	−0.0209640	+	0.0209640i
$675$	−20.7498	−	12.1666i	−0.798660	−	0.468293i
$676$		0			0
$677$	−16.1247	−	16.1247i	−0.619724	−	0.619724i	0.325736	−	0.945461i	$-0.394388\pi$
$677$	−16.1247	−	16.1247i	−0.619724	−	0.619724i	−0.945461	+	0.325736i	$0.894388\pi$
$678$		−	7.69650i		−	0.295582i
$679$		−	25.9996i		−	0.997772i
$680$	6.02244	−	7.79422i	0.230950	−	0.298895i
$681$	9.71227	−	9.71227i	0.372175	−	0.372175i
$682$	2.31329			0.0885804
$683$	32.0480			1.22628			0.613142	−	0.789973i	$-0.289905\pi$
$683$	32.0480			1.22628			0.613142	+	0.789973i	$0.289905\pi$
$684$	−14.3892	+	14.3892i	−0.550185	+	0.550185i
$685$	−3.50612	−	27.3415i	−0.133962	−	1.04466i
$686$		−	0.890888i		−	0.0340143i
$687$			20.7711i			0.792468i
$688$	3.97707	+	3.97707i	0.151624	+	0.151624i
$689$		0			0
$690$	1.39507	−	0.178896i	0.0531093	−	0.00681046i
$691$	−0.389645	+	0.389645i	−0.0148228	+	0.0148228i	−0.714479	−	0.699657i	$-0.753336\pi$
$691$	−0.389645	+	0.389645i	−0.0148228	+	0.0148228i	0.699657	+	0.714479i	$0.253336\pi$
$692$	−9.60305	−	9.60305i	−0.365053	−	0.365053i
$693$	−3.78127	−	3.78127i	−0.143639	−	0.143639i
$694$	−9.02132	−	9.02132i	−0.342445	−	0.342445i
$695$	1.82069	+	14.1981i	0.0690626	+	0.538564i
$696$	−11.7391	−	11.7391i	−0.444971	−	0.444971i
$697$			1.31514i			0.0498144i
$698$	−3.28282	+	3.28282i	−0.124257	+	0.124257i
$699$	22.0268			0.833130
$700$	−8.14286	−	31.2277i	−0.307771	−	1.18030i
$701$			9.52279i			0.359671i	0.983697	+	0.179835i	$0.0575565\pi$
$701$			9.52279i			0.359671i	−0.983697	+	0.179835i	$0.942443\pi$
$702$		0			0
$703$	−7.10792	+	7.10792i	−0.268080	+	0.268080i
$704$	−1.32558	−	1.32558i	−0.0499595	−	0.0499595i
$705$	−6.33826	−	4.89745i	−0.238713	−	0.184449i
$706$			1.61282i			0.0606993i
$707$	−55.0209			−2.06927
$708$			17.1833i			0.645789i
$709$	22.9477	−	22.9477i	0.861819	−	0.861819i	−0.129730	−	0.991549i	$-0.541411\pi$
$709$	22.9477	−	22.9477i	0.861819	−	0.861819i	0.991549	+	0.129730i	$0.0414112\pi$
$710$	−4.52661	+	5.85831i	−0.169881	+	0.219859i
$711$	−6.60400			−0.247669
$712$	−4.43070	+	4.43070i	−0.166047	+	0.166047i
$713$	−9.22354			−0.345424
$714$	4.05358			0.151701
$715$		0			0
$716$	−28.7180			−1.07324
$717$	19.4197			0.725243
$718$	−1.54142	+	1.54142i	−0.0575251	+	0.0575251i
$719$	8.42479			0.314192			0.157096	−	0.987583i	$-0.449787\pi$
$719$	8.42479			0.314192			0.157096	+	0.987583i	$0.449787\pi$
$720$	1.56199	+	12.1807i	0.0582118	+	0.453947i
$721$	−11.6826	+	11.6826i	−0.435082	+	0.435082i
$722$		−	5.43336i		−	0.202209i
$723$	−2.91423			−0.108381
$724$		−	31.6771i		−	1.17727i
$725$	12.0058	+	46.0418i	0.445882	+	1.70995i
$726$	−3.45736	−	3.45736i	−0.128315	−	0.128315i
$727$	8.33682	−	8.33682i	0.309195	−	0.309195i	−0.535402	−	0.844597i	$-0.679840\pi$
$727$	8.33682	−	8.33682i	0.309195	−	0.309195i	0.844597	+	0.535402i	$0.179840\pi$
$728$		0			0
$729$			9.71523i			0.359824i
$730$	3.69863	−	0.474293i	0.136892	−	0.0175544i
$731$	5.14477			0.190286
$732$	7.23757	−	7.23757i	0.267508	−	0.267508i
$733$		−	18.6238i		−	0.687887i	−0.938990	−	0.343944i	$-0.888237\pi$
$733$		−	18.6238i		−	0.687887i	0.938990	−	0.343944i	$-0.111763\pi$
$734$	−8.76238	−	8.76238i	−0.323425	−	0.323425i
$735$	8.36891	−	10.8310i	0.308692	−	0.399508i
$736$	−4.78070	−	4.78070i	−0.176219	−	0.176219i
$737$	−5.95555	−	5.95555i	−0.219375	−	0.219375i
$738$	0.409233	+	0.409233i	0.0150641	+	0.0150641i
$739$	23.3334	−	23.3334i	0.858332	−	0.858332i	−0.132809	−	0.991142i	$-0.542400\pi$
$739$	23.3334	−	23.3334i	0.858332	−	0.858332i	0.991142	+	0.132809i	$0.0423998\pi$
$740$	0.916598	+	7.14782i	0.0336948	+	0.262759i
$741$		0			0
$742$	4.48920	+	4.48920i	0.164804	+	0.164804i
$743$			37.5700i			1.37831i	0.724614	+	0.689155i	$0.242018\pi$
$743$			37.5700i			1.37831i	−0.724614	+	0.689155i	$0.757982\pi$
$744$		−	11.8818i		−	0.435607i
$745$	29.7305	+	22.9722i	1.08924	+	0.841637i
$746$	3.99061	−	3.99061i	0.146107	−	0.146107i
$747$	−4.52577			−0.165589
$748$	−2.86750			−0.104846
$749$	39.6410	−	39.6410i	1.44845	−	1.44845i
$750$	2.03549	−	4.77729i	0.0743257	−	0.174442i
$751$		−	33.6077i		−	1.22636i	−0.789943	−	0.613181i	$-0.789890\pi$
$751$		−	33.6077i		−	1.22636i	0.789943	−	0.613181i	$-0.210110\pi$
$752$			9.88815i			0.360584i
$753$	−19.6356	−	19.6356i	−0.715560	−	0.715560i
$754$		0			0
$755$	8.29623	+	6.41034i	0.301931	+	0.233296i
$756$	−21.9559	+	21.9559i	−0.798530	+	0.798530i
$757$	−11.4105	−	11.4105i	−0.414722	−	0.414722i	0.468658	−	0.883380i	$-0.344738\pi$
$757$	−11.4105	−	11.4105i	−0.414722	−	0.414722i	−0.883380	+	0.468658i	$0.844738\pi$
$758$	−0.701816	−	0.701816i	−0.0254911	−	0.0254911i
$759$	−0.619282	−	0.619282i	−0.0224785	−	0.0224785i
$760$	−17.9791	−	13.8921i	−0.652171	−	0.503920i
$761$	−11.0788	−	11.0788i	−0.401608	−	0.401608i	0.477192	−	0.878799i	$-0.341655\pi$
$761$	−11.0788	−	11.0788i	−0.401608	−	0.401608i	−0.878799	+	0.477192i	$0.841655\pi$
$762$		−	3.85490i		−	0.139648i
$763$	−8.30300	+	8.30300i	−0.300589	+	0.300589i
$764$	−9.11577			−0.329797
$765$	8.88882	+	6.86822i	0.321376	+	0.248321i
$766$			13.0645i			0.472039i
$767$		0			0
$768$	0.0960396	−	0.0960396i	0.00346553	−	0.00346553i
$769$	23.0566	+	23.0566i	0.831442	+	0.831442i	0.987714	−	0.156272i	$-0.0499477\pi$
$769$	23.0566	+	23.0566i	0.831442	+	0.831442i	−0.156272	+	0.987714i	$0.549948\pi$
$770$	1.70677	−	2.20890i	0.0615079	−	0.0796032i
$771$			6.73805i			0.242665i
$772$	−17.7388			−0.638433
$773$			23.9061i			0.859843i	0.902866	+	0.429921i	$0.141459\pi$
$773$			23.9061i			0.859843i	−0.902866	+	0.429921i	$0.858541\pi$
$774$	1.60090	−	1.60090i	0.0575433	−	0.0575433i
$775$	−17.2248	+	29.3764i	−0.618733	+	1.05523i
$776$	−13.1227			−0.471078
$777$	−4.48541	+	4.48541i	−0.160913	+	0.160913i
$778$	−0.321083			−0.0115114
$779$	3.03366			0.108692
$780$		0			0
$781$	4.60995			0.164957
$782$	−1.58823			−0.0567949
$783$	32.3716	−	32.3716i	1.15687	−	1.15687i
$784$	−16.8972			−0.603470
$785$	24.7214	+	19.1018i	0.882346	+	0.681772i
$786$	0.451284	−	0.451284i	0.0160968	−	0.0160968i
$787$		−	15.7114i		−	0.560052i	−0.959992	−	0.280026i	$-0.909657\pi$
$787$		−	15.7114i		−	0.560052i	0.959992	−	0.280026i	$-0.0903431\pi$
$788$	22.9411			0.817242
$789$		−	12.6629i		−	0.450809i
$790$	−0.438482	−	3.41937i	−0.0156005	−	0.121656i
$791$	43.0668	+	43.0668i	1.53128	+	1.53128i
$792$	−1.90851	+	1.90851i	−0.0678161	+	0.0678161i
$793$		0			0
$794$		−	13.3394i		−	0.473397i
$795$	−0.935377	−	7.29426i	−0.0331744	−	0.258701i
$796$	13.7853			0.488606
$797$	−22.0835	+	22.0835i	−0.782237	+	0.782237i	−0.980208	−	0.197971i	$-0.936565\pi$
$797$	−22.0835	+	22.0835i	−0.782237	+	0.782237i	0.197971	+	0.980208i	$0.436565\pi$
$798$		−	9.35048i		−	0.331003i
$799$	6.39570	+	6.39570i	0.226264	+	0.226264i
$800$	−24.1541	+	6.29836i	−0.853977	+	0.222681i
$801$	−5.05293	−	5.05293i	−0.178537	−	0.178537i
$802$	−1.73177	−	1.73177i	−0.0611508	−	0.0611508i
$803$	−1.64185	−	1.64185i	−0.0579397	−	0.0579397i
$804$	−14.3014	+	14.3014i	−0.504373	+	0.504373i
$805$	−6.80525	+	8.80732i	−0.239853	+	0.310417i
$806$		0			0
$807$	5.38868	+	5.38868i	0.189690	+	0.189690i
$808$			27.7706i			0.976966i
$809$		−	13.2266i		−	0.465023i	−0.972594	−	0.232512i	$-0.925306\pi$
$809$		−	13.2266i		−	0.465023i	0.972594	−	0.232512i	$-0.0746944\pi$
$810$	1.99693	−	0.256076i	0.0701649	−	0.00899758i
$811$	−22.0736	+	22.0736i	−0.775109	+	0.775109i	−0.978995	−	0.203886i	$-0.934643\pi$
$811$	−22.0736	+	22.0736i	−0.775109	+	0.775109i	0.203886	+	0.978995i	$0.434643\pi$
$812$	61.4218			2.15548
$813$	−8.64846			−0.303315
$814$	−0.440767	+	0.440767i	−0.0154489	+	0.0154489i
$815$	−0.292696	+	0.0375338i	−0.0102527	+	0.00131475i
$816$			5.79650i			0.202918i
$817$		−	11.8676i		−	0.415194i
$818$	2.11139	+	2.11139i	0.0738230	+	0.0738230i
$819$		0			0
$820$	1.32974	−	1.72095i	0.0464366	−	0.0600981i
$821$	−6.40442	+	6.40442i	−0.223516	+	0.223516i	−0.809977	−	0.586461i	$-0.800521\pi$
$821$	−6.40442	+	6.40442i	−0.223516	+	0.223516i	0.586461	+	0.809977i	$0.300521\pi$
$822$	−4.04869	−	4.04869i	−0.141214	−	0.141214i
$823$	−29.6566	−	29.6566i	−1.03376	−	1.03376i	−0.999410	−	0.0343543i	$-0.989063\pi$
$823$	−29.6566	−	29.6566i	−1.03376	−	1.03376i	−0.0343543	−	0.999410i	$-0.510937\pi$
$824$	5.89653	+	5.89653i	0.205415	+	0.205415i
$825$	−3.12888	+	0.815878i	−0.108934	+	0.0284052i
$826$	13.3567	+	13.3567i	0.464738	+	0.464738i
$827$		−	38.2009i		−	1.32838i	−0.747566	−	0.664188i	$-0.768778\pi$
$827$		−	38.2009i		−	1.32838i	0.747566	−	0.664188i	$-0.231222\pi$
$828$	3.55771	−	3.55771i	0.123639	−	0.123639i
$829$	−29.3499			−1.01936			−0.509682	−	0.860363i	$-0.670237\pi$
$829$	−29.3499			−1.01936			−0.509682	+	0.860363i	$0.670237\pi$
$830$	−0.300495	−	2.34332i	−0.0104303	−	0.0813377i
$831$			24.3043i			0.843106i
$832$		0			0
$833$	−10.9292	+	10.9292i	−0.378673	+	0.378673i
$834$	2.10243	+	2.10243i	0.0728014	+	0.0728014i
$835$	−6.15377	−	47.9883i	−0.212960	−	1.66070i
$836$			6.61453i			0.228768i
$837$	32.7649			1.13252
$838$			2.65259i			0.0916321i
$839$	24.9140	−	24.9140i	0.860125	−	0.860125i	−0.131227	−	0.991352i	$-0.541892\pi$
$839$	24.9140	−	24.9140i	0.860125	−	0.860125i	0.991352	+	0.131227i	$0.0418917\pi$
$840$	−11.3456	−	8.76652i	−0.391460	−	0.302474i
$841$	−61.5596			−2.12274
$842$	6.98264	−	6.98264i	0.240638	−	0.240638i
$843$	7.20721			0.248230
$844$	−21.8175			−0.750988
$845$		0			0
$846$	3.98031			0.136846
$847$	38.6922			1.32948
$848$	−6.41942	+	6.41942i	−0.220444	+	0.220444i
$849$	−8.26193			−0.283549
$850$	−2.96599	+	5.05841i	−0.101733	+	0.173502i
$851$	1.75742	−	1.75742i	0.0602437	−	0.0602437i
$852$		−	11.0702i		−	0.379258i
$853$	−17.6392			−0.603954			−0.301977	−	0.953315i	$-0.597647\pi$
$853$	−17.6392			−0.603954			−0.301977	+	0.953315i	$0.597647\pi$
$854$		−	11.2516i		−	0.385021i
$855$	15.8431	−	20.5041i	0.541822	−	0.701224i
$856$	−20.0080	−	20.0080i	−0.683858	−	0.683858i
$857$	−6.30427	+	6.30427i	−0.215350	+	0.215350i	−0.806535	−	0.591186i	$-0.798660\pi$
$857$	−6.30427	+	6.30427i	−0.215350	+	0.215350i	0.591186	+	0.806535i	$0.298660\pi$
$858$		0			0
$859$			29.2307i			0.997338i	0.866793	+	0.498669i	$0.166178\pi$
$859$			29.2307i			0.997338i	−0.866793	+	0.498669i	$0.833822\pi$
$860$	−6.73228	−	5.20190i	−0.229569	−	0.177383i
$861$	1.91437			0.0652416
$862$	−5.82905	+	5.82905i	−0.198538	+	0.198538i
$863$		−	15.7688i		−	0.536775i	−0.963311	−	0.268387i	$-0.913509\pi$
$863$		−	15.7688i		−	0.536775i	0.963311	−	0.268387i	$-0.0864907\pi$
$864$	16.9825	+	16.9825i	0.577758	+	0.577758i
$865$	13.6840	+	10.5733i	0.465269	+	0.359504i
$866$	−2.65202	−	2.65202i	−0.0901192	−	0.0901192i
$867$	−7.55512	−	7.55512i	−0.256585	−	0.256585i
$868$	31.0840	+	31.0840i	1.05506	+	1.05506i
$869$	−1.51789	+	1.51789i	−0.0514908	+	0.0514908i
$870$	7.82071	+	6.04291i	0.265147	+	0.204874i
$871$		0			0
$872$	4.19076	+	4.19076i	0.141917	+	0.141917i
$873$		−	14.9657i		−	0.506511i
$874$			3.66360i			0.123923i
$875$	15.3421	+	38.1218i	0.518658	+	1.28875i
$876$	−3.94269	+	3.94269i	−0.133211	+	0.133211i
$877$	44.7226			1.51018			0.755088	−	0.655623i	$-0.227594\pi$
$877$	44.7226			1.51018			0.755088	+	0.655623i	$0.227594\pi$
$878$	−6.76187			−0.228202
$879$	−8.80139	+	8.80139i	−0.296863	+	0.296863i
$880$	3.15866	+	2.44064i	0.106479	+	0.0822739i
$881$		−	20.8220i		−	0.701510i	−0.936467	−	0.350755i	$-0.885925\pi$
$881$		−	20.8220i		−	0.701510i	0.936467	−	0.350755i	$-0.114075\pi$
$882$			6.80168i			0.229024i
$883$	−5.33747	−	5.33747i	−0.179620	−	0.179620i	0.611570	−	0.791190i	$-0.290538\pi$
$883$	−5.33747	−	5.33747i	−0.179620	−	0.179620i	−0.791190	+	0.611570i	$0.790538\pi$
$884$		0			0
$885$	−2.78302	−	21.7026i	−0.0935502	−	0.729523i
$886$	−3.19204	+	3.19204i	−0.107239	+	0.107239i
$887$	−18.9536	−	18.9536i	−0.636399	−	0.636399i	0.313266	−	0.949665i	$-0.398577\pi$
$887$	−18.9536	−	18.9536i	−0.636399	−	0.636399i	−0.949665	+	0.313266i	$0.898577\pi$
$888$	2.26391	+	2.26391i	0.0759719	+	0.0759719i
$889$	21.5706	+	21.5706i	0.723454	+	0.723454i
$890$	2.28077	−	2.95177i	0.0764517	−	0.0989435i
$891$	−0.886453	−	0.886453i	−0.0296973	−	0.0296973i
$892$		−	17.4639i		−	0.584736i
$893$	14.7531	−	14.7531i	0.493694	−	0.493694i
$894$	7.80417			0.261010
$895$	36.2708	−	4.65118i	1.21240	−	0.155472i
$896$			41.6474i			1.39134i
$897$		0			0
$898$	8.97946	−	8.97946i	0.299648	−	0.299648i
$899$	−45.8299	−	45.8299i	−1.52851	−	1.52851i
$900$	−4.68713	−	17.9750i	−0.156238	−	0.599168i
$901$			8.30422i			0.276654i
$902$	0.188119			0.00626368
$903$		−	7.48895i		−	0.249217i
$904$	21.7370	−	21.7370i	0.722962	−	0.722962i
$905$	5.13044	+	40.0082i	0.170542	+	1.32992i
$906$	2.17773			0.0723503
$907$	−28.6677	+	28.6677i	−0.951895	+	0.951895i	−0.998895	−	0.0470002i	$-0.985034\pi$
$907$	−28.6677	+	28.6677i	−0.951895	+	0.951895i	0.0470002	+	0.998895i	$0.485034\pi$
$908$	25.6487			0.851181
$909$	−31.6707			−1.05045
$910$		0			0
$911$	8.00072			0.265076			0.132538	−	0.991178i	$-0.457687\pi$
$911$	8.00072			0.265076			0.132538	+	0.991178i	$0.457687\pi$
$912$	13.3709			0.442755
$913$	−1.04022	+	1.04022i	−0.0344262	+	0.0344262i
$914$	0.408720			0.0135193
$915$	−7.96885	+	10.3133i	−0.263442	+	0.340946i
$916$	−27.4267	+	27.4267i	−0.906205	+	0.906205i
$917$			5.05044i			0.166780i
$918$	5.64189			0.186210
$919$		−	2.12738i		−	0.0701759i	−0.999384	−	0.0350879i	$-0.988829\pi$
$919$		−	2.12738i		−	0.0701759i	0.999384	−	0.0350879i	$-0.0111711\pi$
$920$	4.44531	+	3.43480i	0.146557	+	0.113242i
$921$	−10.2924	−	10.2924i	−0.339146	−	0.339146i
$922$	8.40950	−	8.40950i	0.276952	−	0.276952i
$923$		0			0
$924$			4.17405i			0.137316i
$925$	−2.31533	−	8.87925i	−0.0761276	−	0.291948i
$926$	3.13907			0.103156
$927$	−6.72463	+	6.72463i	−0.220866	+	0.220866i
$928$		−	47.5087i		−	1.55955i
$929$	−14.0930	−	14.0930i	−0.462378	−	0.462378i	0.437056	−	0.899434i	$-0.356021\pi$
$929$	−14.0930	−	14.0930i	−0.462378	−	0.462378i	−0.899434	+	0.437056i	$0.856021\pi$
$930$	0.899699	+	7.01603i	0.0295023	+	0.230065i
$931$	25.2106	+	25.2106i	0.826243	+	0.826243i
$932$	29.0848	+	29.0848i	0.952703	+	0.952703i
$933$	−3.55702	−	3.55702i	−0.116452	−	0.116452i
$934$	−7.71447	+	7.71447i	−0.252425	+	0.252425i
$935$	3.62166	−	0.464422i	0.118441	−	0.0151882i
$936$		0			0
$937$	17.2774	+	17.2774i	0.564427	+	0.564427i	0.930562	−	0.366135i	$-0.119319\pi$
$937$	17.2774	+	17.2774i	0.564427	+	0.564427i	−0.366135	+	0.930562i	$0.619319\pi$
$938$			22.2331i			0.725938i
$939$			32.4398i			1.05863i
$940$	−1.90248	−	14.8359i	−0.0620521	−	0.483894i
$941$	−24.2129	+	24.2129i	−0.789319	+	0.789319i	−0.981383	−	0.192063i	$-0.938482\pi$
$941$	−24.2129	+	24.2129i	−0.789319	+	0.789319i	0.192063	+	0.981383i	$0.438482\pi$
$942$	6.48929			0.211433
$943$	−0.750068			−0.0244256
$944$	−19.0996	+	19.0996i	−0.621640	+	0.621640i
$945$	24.1744	−	31.2864i	0.786393	−	1.01775i
$946$		−	0.735915i		−	0.0239267i
$947$			8.30091i			0.269743i	0.990863	+	0.134872i	$0.0430622\pi$
$947$			8.30091i			0.269743i	−0.990863	+	0.134872i	$0.956938\pi$
$948$	3.64500	+	3.64500i	0.118384	+	0.118384i
$949$		0			0
$950$	11.6684	+	6.84172i	0.378572	+	0.221975i
$951$	−12.6244	+	12.6244i	−0.409373	+	0.409373i
$952$	11.4484	+	11.4484i	0.371045	+	0.371045i
$953$	−3.38386	−	3.38386i	−0.109614	−	0.109614i	0.650173	−	0.759787i	$-0.274697\pi$
$953$	−3.38386	−	3.38386i	−0.109614	−	0.109614i	−0.759787	+	0.650173i	$0.774697\pi$
$954$	2.58403	+	2.58403i	0.0836611	+	0.0836611i
$955$	11.5132	−	1.47640i	0.372559	−	0.0477750i
$956$	25.6423	+	25.6423i	0.829331	+	0.829331i
$957$		−	6.15418i		−	0.198936i
$958$	3.30507	−	3.30507i	0.106782	−	0.106782i
$959$	45.3100			1.46314
$960$	3.50482	−	4.53592i	0.113118	−	0.146396i
$961$		−	15.3867i		−	0.496346i
$962$		0			0
$963$	22.8178	−	22.8178i	0.735294	−	0.735294i
$964$	−3.84803	−	3.84803i	−0.123937	−	0.123937i
$965$	22.4041	−	2.87298i	0.721214	−	0.0924846i
$966$			2.31189i			0.0743839i
$967$	−8.78782			−0.282597			−0.141299	−	0.989967i	$-0.545128\pi$
$967$	−8.78782			−0.282597			−0.141299	+	0.989967i	$0.545128\pi$
$968$		−	19.5291i		−	0.627688i
$969$	8.64837	−	8.64837i	0.277826	−	0.277826i
$970$	7.74880	−	0.993666i	0.248799	−	0.0319047i
$971$	−5.43386			−0.174381			−0.0871905	−	0.996192i	$-0.527789\pi$
$971$	−5.43386			−0.174381			−0.0871905	+	0.996192i	$0.527789\pi$
$972$	−20.0495	+	20.0495i	−0.643089	+	0.643089i
$973$	−23.5289			−0.754302
$974$	3.04192			0.0974695
$975$		0			0
$976$	16.0894			0.515010
$977$	18.6725			0.597387			0.298693	−	0.954349i	$-0.403449\pi$
$977$	18.6725			0.597387			0.298693	+	0.954349i	$0.403449\pi$
$978$	−0.0433421	+	0.0433421i	−0.00138593	+	0.00138593i
$979$	−2.32277			−0.0742360
$980$	25.3521	−	3.25101i	0.809842	−	0.103850i
$981$	−4.77930	+	4.77930i	−0.152591	+	0.152591i
$982$		−	7.31648i		−	0.233478i
$983$	−6.62470			−0.211295			−0.105648	−	0.994404i	$-0.533692\pi$
$983$	−6.62470			−0.211295			−0.105648	+	0.994404i	$0.533692\pi$
$984$		−	0.966238i		−	0.0308025i
$985$	−28.9746	+	3.71555i	−0.923207	+	0.118387i
$986$	−7.89159	−	7.89159i	−0.251319	−	0.251319i
$987$	9.30986	−	9.30986i	0.296336	−	0.296336i
$988$		0			0
$989$			2.93424i			0.0933033i
$990$	0.982439	−	1.27147i	0.0312240	−	0.0404099i
$991$	−43.2271			−1.37315			−0.686576	−	0.727058i	$-0.740887\pi$
$991$	−43.2271			−1.37315			−0.686576	+	0.727058i	$0.740887\pi$
$992$	24.0429	−	24.0429i	0.763364	−	0.763364i
$993$			6.59853i			0.209398i
$994$	−8.60489	−	8.60489i	−0.272931	−	0.272931i
$995$	−17.4108	+	2.23267i	−0.551960	+	0.0707805i
$996$	2.49794	+	2.49794i	0.0791504	+	0.0791504i
$997$	31.9653	+	31.9653i	1.01235	+	1.01235i	0.999923	+	0.0124293i	$0.00395647\pi$
$997$	31.9653	+	31.9653i	1.01235	+	1.01235i	0.0124293	+	0.999923i	$0.496044\pi$
$998$	−10.3981	−	10.3981i	−0.329146	−	0.329146i
$999$	−6.24292	+	6.24292i	−0.197517	+	0.197517i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.k.d.577.5		20
5.3	odd	4		845.2.f.d.408.6		20
13.2	odd	12		65.2.t.a.7.3	yes	20
13.3	even	3		845.2.o.f.357.3		20
13.4	even	6		65.2.o.a.2.3	✓	20
13.5	odd	4		845.2.f.e.437.6		20
13.6	odd	12		845.2.t.f.427.3		20
13.7	odd	12		845.2.t.e.427.3		20
13.8	odd	4		845.2.f.d.437.5		20
13.9	even	3		845.2.o.g.587.3		20
13.10	even	6		845.2.o.e.357.3		20
13.11	odd	12		845.2.t.g.657.3		20
13.12	even	2		845.2.k.e.577.6		20
39.2	even	12		585.2.dp.a.397.3		20
39.17	odd	6		585.2.cf.a.262.3		20
65.2	even	12		325.2.s.b.293.3		20
65.3	odd	12		845.2.t.e.188.3		20
65.4	even	6		325.2.s.b.132.3		20
65.8	even	4	inner	845.2.k.d.268.5		20
65.17	odd	12		325.2.x.b.93.3		20
65.18	even	4		845.2.k.e.268.6		20
65.23	odd	12		845.2.t.f.188.3		20
65.28	even	12		65.2.o.a.33.3	yes	20
65.33	even	12		845.2.o.f.258.3		20
65.38	odd	4		845.2.f.e.408.5		20
65.43	odd	12		65.2.t.a.28.3	yes	20
65.48	odd	12		845.2.t.g.418.3		20
65.54	odd	12		325.2.x.b.7.3		20
65.58	even	12		845.2.o.e.258.3		20
65.63	even	12		845.2.o.g.488.3		20
195.158	odd	12		585.2.cf.a.163.3		20
195.173	even	12		585.2.dp.a.28.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.3	✓	20	13.4	even	6
65.2.o.a.33.3	yes	20	65.28	even	12
65.2.t.a.7.3	yes	20	13.2	odd	12
65.2.t.a.28.3	yes	20	65.43	odd	12
325.2.s.b.132.3		20	65.4	even	6
325.2.s.b.293.3		20	65.2	even	12
325.2.x.b.7.3		20	65.54	odd	12
325.2.x.b.93.3		20	65.17	odd	12
585.2.cf.a.163.3		20	195.158	odd	12
585.2.cf.a.262.3		20	39.17	odd	6
585.2.dp.a.28.3		20	195.173	even	12
585.2.dp.a.397.3		20	39.2	even	12
845.2.f.d.408.6		20	5.3	odd	4
845.2.f.d.437.5		20	13.8	odd	4
845.2.f.e.408.5		20	65.38	odd	4
845.2.f.e.437.6		20	13.5	odd	4
845.2.k.d.268.5		20	65.8	even	4	inner
845.2.k.d.577.5		20	1.1	even	1	trivial
845.2.k.e.268.6		20	65.18	even	4
845.2.k.e.577.6		20	13.12	even	2
845.2.o.e.258.3		20	65.58	even	12
845.2.o.e.357.3		20	13.10	even	6
845.2.o.f.258.3		20	65.33	even	12
845.2.o.f.357.3		20	13.3	even	3
845.2.o.g.488.3		20	65.63	even	12
845.2.o.g.587.3		20	13.9	even	3
845.2.t.e.188.3		20	65.3	odd	12
845.2.t.e.427.3		20	13.7	odd	12
845.2.t.f.188.3		20	65.23	odd	12
845.2.t.f.427.3		20	13.6	odd	12
845.2.t.g.418.3		20	65.48	odd	12
845.2.t.g.657.3		20	13.11	odd	12

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:	\( N \)	\(=\)	\( 845 = 5 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	845.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.493902 q^{2} +(-0.664960 + 0.664960i) q^{3} -1.75606 q^{4} +(2.21791 - 0.284413i) q^{5} +(0.328425 - 0.328425i) q^{6} +3.67549i q^{7} +1.85513 q^{8} +2.11566i q^{9} +O(q^{10})\)	\(q-0.493902 q^{2} +(-0.664960 + 0.664960i) q^{3} -1.75606 q^{4} +(2.21791 - 0.284413i) q^{5} +(0.328425 - 0.328425i) q^{6} +3.67549i q^{7} +1.85513 q^{8} +2.11566i q^{9} +(-1.09543 + 0.140472i) q^{10} +(0.486270 + 0.486270i) q^{11} +(1.16771 - 1.16771i) q^{12} -1.81533i q^{14} +(-1.28570 + 1.66394i) q^{15} +2.59587 q^{16} +(1.67902 - 1.67902i) q^{17} -1.04493i q^{18} +(-3.87304 - 3.87304i) q^{19} +(-3.89478 + 0.499446i) q^{20} +(-2.44406 - 2.44406i) q^{21} +(-0.240170 - 0.240170i) q^{22} +(0.957603 + 0.957603i) q^{23} +(-1.23358 + 1.23358i) q^{24} +(4.83822 - 1.26160i) q^{25} +(-3.40171 - 3.40171i) q^{27} -6.45439i q^{28} +9.51628i q^{29} +(0.635008 - 0.821824i) q^{30} +(-4.81595 + 4.81595i) q^{31} -4.99236 q^{32} -0.646700 q^{33} +(-0.829273 + 0.829273i) q^{34} +(1.04536 + 8.15190i) q^{35} -3.71522i q^{36} -1.83523i q^{37} +(1.91290 + 1.91290i) q^{38} +(4.11449 - 0.527621i) q^{40} +(-0.391638 + 0.391638i) q^{41} +(1.20712 + 1.20712i) q^{42} +(1.53207 + 1.53207i) q^{43} +(-0.853919 - 0.853919i) q^{44} +(0.601719 + 4.69233i) q^{45} +(-0.472962 - 0.472962i) q^{46} +3.80918i q^{47} +(-1.72615 + 1.72615i) q^{48} -6.50924 q^{49} +(-2.38961 + 0.623107i) q^{50} +2.23297i q^{51} +(-2.47293 + 2.47293i) q^{53} +(1.68011 + 1.68011i) q^{54} +(1.21680 + 0.940200i) q^{55} +6.81850i q^{56} +5.15084 q^{57} -4.70011i q^{58} +(-7.35770 + 7.35770i) q^{59} +(2.25776 - 2.92199i) q^{60} +6.19808 q^{61} +(2.37861 - 2.37861i) q^{62} -7.77608 q^{63} -2.72601 q^{64} +0.319406 q^{66} -12.2474 q^{67} +(-2.94847 + 2.94847i) q^{68} -1.27354 q^{69} +(-0.516303 - 4.02624i) q^{70} +(4.74012 - 4.74012i) q^{71} +3.92481i q^{72} -3.37642 q^{73} +0.906424i q^{74} +(-2.37831 + 4.05614i) q^{75} +(6.80130 + 6.80130i) q^{76} +(-1.78728 + 1.78728i) q^{77} +3.12149i q^{79} +(5.75740 - 0.738299i) q^{80} -1.82297 q^{81} +(0.193431 - 0.193431i) q^{82} +2.13918i q^{83} +(4.29191 + 4.29191i) q^{84} +(3.24638 - 4.20145i) q^{85} +(-0.756694 - 0.756694i) q^{86} +(-6.32795 - 6.32795i) q^{87} +(0.902091 + 0.902091i) q^{88} +(-2.38835 + 2.38835i) q^{89} +(-0.297190 - 2.31755i) q^{90} +(-1.68161 - 1.68161i) q^{92} -6.40483i q^{93} -1.88136i q^{94} +(-9.69159 - 7.48850i) q^{95} +(3.31972 - 3.31972i) q^{96} -7.07377 q^{97} +3.21493 q^{98} +(-1.02878 + 1.02878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 8 q^{2} + 4 q^{3} + 12 q^{4} + 6 q^{5} - 4 q^{6} - 12 q^{8}+O(q^{10}) \) 20 * q - 8 * q^2 + 4 * q^3 + 12 * q^4 + 6 * q^5 - 4 * q^6 - 12 * q^8	\( 20 q - 8 q^{2} + 4 q^{3} + 12 q^{4} + 6 q^{5} - 4 q^{6} - 12 q^{8} + 8 q^{10} - 8 q^{11} + 24 q^{12} + 24 q^{15} + 4 q^{16} + 14 q^{17} + 4 q^{19} + 22 q^{20} - 4 q^{21} - 32 q^{22} - 8 q^{23} - 4 q^{24} - 18 q^{25} + 4 q^{27} - 40 q^{30} - 12 q^{32} - 36 q^{33} + 2 q^{34} - 20 q^{35} + 8 q^{38} - 16 q^{40} + 38 q^{41} + 16 q^{42} + 32 q^{43} - 36 q^{44} + 20 q^{45} - 4 q^{46} + 28 q^{48} + 36 q^{49} + 52 q^{50} - 10 q^{53} + 36 q^{54} - 16 q^{55} + 12 q^{57} + 8 q^{59} + 92 q^{60} + 32 q^{61} - 4 q^{62} - 64 q^{63} - 20 q^{64} - 32 q^{66} - 116 q^{67} - 50 q^{68} - 32 q^{69} - 32 q^{70} + 40 q^{71} - 72 q^{73} - 4 q^{75} + 16 q^{76} + 28 q^{77} + 34 q^{80} + 28 q^{81} + 34 q^{82} + 8 q^{84} - 60 q^{86} - 28 q^{87} + 32 q^{88} + 12 q^{89} - 46 q^{90} - 8 q^{92} - 40 q^{95} - 56 q^{96} - 44 q^{97} + 8 q^{98} + 60 q^{99}+O(q^{100}) \) 20 * q - 8 * q^2 + 4 * q^3 + 12 * q^4 + 6 * q^5 - 4 * q^6 - 12 * q^8 + 8 * q^10 - 8 * q^11 + 24 * q^12 + 24 * q^15 + 4 * q^16 + 14 * q^17 + 4 * q^19 + 22 * q^20 - 4 * q^21 - 32 * q^22 - 8 * q^23 - 4 * q^24 - 18 * q^25 + 4 * q^27 - 40 * q^30 - 12 * q^32 - 36 * q^33 + 2 * q^34 - 20 * q^35 + 8 * q^38 - 16 * q^40 + 38 * q^41 + 16 * q^42 + 32 * q^43 - 36 * q^44 + 20 * q^45 - 4 * q^46 + 28 * q^48 + 36 * q^49 + 52 * q^50 - 10 * q^53 + 36 * q^54 - 16 * q^55 + 12 * q^57 + 8 * q^59 + 92 * q^60 + 32 * q^61 - 4 * q^62 - 64 * q^63 - 20 * q^64 - 32 * q^66 - 116 * q^67 - 50 * q^68 - 32 * q^69 - 32 * q^70 + 40 * q^71 - 72 * q^73 - 4 * q^75 + 16 * q^76 + 28 * q^77 + 34 * q^80 + 28 * q^81 + 34 * q^82 + 8 * q^84 - 60 * q^86 - 28 * q^87 + 32 * q^88 + 12 * q^89 - 46 * q^90 - 8 * q^92 - 40 * q^95 - 56 * q^96 - 44 * q^97 + 8 * q^98 + 60 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more