LMFDB - Embedded newform 845.2.f.e.408.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(408,845)]

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, 3]))

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

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

chi := DirichletCharacter("845.408");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.f (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			408.5
Root			$-0.493902i$ of defining polynomial
Character	$\chi$	$=$	845.408
Dual form			845.2.f.e.437.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.493902i q^{2} +(-0.664960 - 0.664960i) q^{3} +1.75606 q^{4} +(-0.284413 + 2.21791i) q^{5} +(-0.328425 + 0.328425i) q^{6} -3.67549 q^{7} -1.85513i q^{8} -2.11566i q^{9} +O(q^{10})$	\(q-0.493902i q^{2} +(-0.664960 - 0.664960i) q^{3} +1.75606 q^{4} +(-0.284413 + 2.21791i) q^{5} +(-0.328425 + 0.328425i) q^{6} -3.67549 q^{7} -1.85513i 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} +(1.66394 - 1.28570i) q^{15} +2.59587 q^{16} +(-1.67902 - 1.67902i) q^{17} -1.04493 q^{18} +(-3.87304 - 3.87304i) q^{19} +(-0.499446 + 3.89478i) 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} -6.45439 q^{28} -9.51628i q^{29} +(-0.635008 - 0.821824i) q^{30} +(4.81595 - 4.81595i) q^{31} -4.99236i q^{32} +0.646700i q^{33} +(-0.829273 + 0.829273i) q^{34} +(1.04536 - 8.15190i) q^{35} -3.71522i q^{36} +1.83523 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} +(4.69233 + 0.601719i) q^{45} +(0.472962 + 0.472962i) q^{46} -3.80918 q^{47} +(-1.72615 - 1.72615i) q^{48} +6.50924 q^{49} +(-0.623107 + 2.38961i) 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} +5.15084i q^{57} -4.70011 q^{58} +(-7.35770 + 7.35770i) q^{59} +(2.92199 - 2.25776i) q^{60} +6.19808 q^{61} +(-2.37861 - 2.37861i) q^{62} +7.77608i q^{63} +2.72601 q^{64} +0.319406 q^{66} -12.2474i q^{67} +(-2.94847 - 2.94847i) q^{68} +1.27354 q^{69} +(-4.02624 - 0.516303i) q^{70} +(-4.74012 + 4.74012i) q^{71} -3.92481 q^{72} +3.37642i 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} +(-0.738299 + 5.75740i) q^{80} -1.82297 q^{81} +(-0.193431 - 0.193431i) q^{82} +2.13918 q^{83} +(4.29191 + 4.29191i) q^{84} +(4.20145 - 3.24638i) 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} -6.40483 q^{93} +1.88136i q^{94} +(9.69159 - 7.48850i) q^{95} +(-3.31972 + 3.31972i) q^{96} -7.07377i q^{97} -3.21493i q^{98} +(-1.02878 + 1.02878i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{3} - 12 q^{4} + 4 q^{6} + 4 q^{7}+O(q^{10}) $ 20 * q + 4 * q^3 - 12 * q^4 + 4 * q^6 + 4 * q^7	$ 20 q + 4 q^{3} - 12 q^{4} + 4 q^{6} + 4 q^{7} - 8 q^{10} + 8 q^{11} - 24 q^{12} + 28 q^{15} + 4 q^{16} - 14 q^{17} + 4 q^{19} - 12 q^{20} + 4 q^{21} - 32 q^{22} + 8 q^{23} - 4 q^{24} + 18 q^{25} + 4 q^{27} - 36 q^{28} + 40 q^{30} + 2 q^{34} - 20 q^{35} + 8 q^{37} - 8 q^{38} - 16 q^{40} - 38 q^{41} + 16 q^{42} - 32 q^{43} - 36 q^{44} - 6 q^{45} + 4 q^{46} - 40 q^{47} + 28 q^{48} - 36 q^{49} + 42 q^{50} - 10 q^{53} + 36 q^{54} - 16 q^{55} + 8 q^{59} + 28 q^{60} + 32 q^{61} + 4 q^{62} + 20 q^{64} - 32 q^{66} - 50 q^{68} + 32 q^{69} - 12 q^{70} - 40 q^{71} - 8 q^{72} + 4 q^{75} - 16 q^{76} - 28 q^{77} + 112 q^{80} + 28 q^{81} - 34 q^{82} + 48 q^{83} + 8 q^{84} - 2 q^{85} + 60 q^{86} - 28 q^{87} - 32 q^{88} + 12 q^{89} + 46 q^{90} - 8 q^{92} - 64 q^{93} + 40 q^{95} + 56 q^{96} + 60 q^{99}+O(q^{100}) $ 20 * q + 4 * q^3 - 12 * q^4 + 4 * q^6 + 4 * q^7 - 8 * q^10 + 8 * q^11 - 24 * q^12 + 28 * q^15 + 4 * q^16 - 14 * q^17 + 4 * q^19 - 12 * q^20 + 4 * q^21 - 32 * q^22 + 8 * q^23 - 4 * q^24 + 18 * q^25 + 4 * q^27 - 36 * q^28 + 40 * q^30 + 2 * q^34 - 20 * q^35 + 8 * q^37 - 8 * q^38 - 16 * q^40 - 38 * q^41 + 16 * q^42 - 32 * q^43 - 36 * q^44 - 6 * q^45 + 4 * q^46 - 40 * q^47 + 28 * q^48 - 36 * q^49 + 42 * q^50 - 10 * q^53 + 36 * q^54 - 16 * q^55 + 8 * q^59 + 28 * q^60 + 32 * q^61 + 4 * q^62 + 20 * q^64 - 32 * q^66 - 50 * q^68 + 32 * q^69 - 12 * q^70 - 40 * q^71 - 8 * q^72 + 4 * q^75 - 16 * q^76 - 28 * q^77 + 112 * q^80 + 28 * q^81 - 34 * q^82 + 48 * q^83 + 8 * q^84 - 2 * q^85 + 60 * q^86 - 28 * q^87 - 32 * q^88 + 12 * q^89 + 46 * q^90 - 8 * q^92 - 64 * q^93 + 40 * q^95 + 56 * q^96 + 60 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$		−	0.493902i		−	0.349241i	−0.984636	−	0.174621i	$-0.944130\pi$
$2$		−	0.493902i		−	0.349241i	0.984636	−	0.174621i	$-0.0558699\pi$
$3$	−0.664960	−	0.664960i	−0.383915	−	0.383915i	0.488595	−	0.872510i	$-0.337509\pi$
$3$	−0.664960	−	0.664960i	−0.383915	−	0.383915i	−0.872510	+	0.488595i	$0.837509\pi$
$4$	1.75606			0.878030
$5$	−0.284413	+	2.21791i	−0.127193	+	0.991878i
$5$	−0.284413	+	2.21791i	−0.127193	+	0.991878i
$6$	−0.328425	+	0.328425i	−0.134079	+	0.134079i
$7$	−3.67549			−1.38921			−0.694603	−	0.719394i	$-0.744420\pi$
$7$	−3.67549			−1.38921			−0.694603	+	0.719394i	$0.744420\pi$
$8$		−	1.85513i		−	0.655886i
$9$		−	2.11566i		−	0.705219i
$10$	1.09543	+	0.140472i	0.346405	+	0.0444211i
$11$	−0.486270	−	0.486270i	−0.146616	−	0.146616i	0.629989	−	0.776604i	$-0.283060\pi$
$11$	−0.486270	−	0.486270i	−0.146616	−	0.146616i	−0.776604	+	0.629989i	$0.783060\pi$
$12$	−1.16771	−	1.16771i	−0.337089	−	0.337089i
$13$		0			0
$13$		0			0
$14$			1.81533i			0.485168i
$15$	1.66394	−	1.28570i	0.429628	−	0.331965i
$16$	2.59587			0.648968
$17$	−1.67902	−	1.67902i	−0.407223	−	0.407223i	0.473546	−	0.880769i	$-0.342974\pi$
$17$	−1.67902	−	1.67902i	−0.407223	−	0.407223i	−0.880769	+	0.473546i	$0.842974\pi$
$18$	−1.04493			−0.246291
$19$	−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	$0.966245\pi$
$20$	−0.499446	+	3.89478i	−0.111679	+	0.870899i
$21$	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	$-0.795093\pi$
$23$	−0.957603	+	0.957603i	−0.199674	+	0.199674i	0.600186	+	0.799860i	$0.295093\pi$
$24$	−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
$28$	−6.45439			−1.21976
$29$		−	9.51628i		−	1.76713i	−0.468310	−	0.883564i	$-0.655137\pi$
$29$		−	9.51628i		−	1.76713i	0.468310	−	0.883564i	$-0.344863\pi$
$30$	−0.635008	−	0.821824i	−0.115936	−	0.150044i
$31$	4.81595	−	4.81595i	0.864970	−	0.864970i	−0.126940	−	0.991910i	$-0.540516\pi$
$31$	4.81595	−	4.81595i	0.864970	−	0.864970i	0.991910	+	0.126940i	$0.0405157\pi$
$32$		−	4.99236i		−	0.882532i
$33$			0.646700i			0.112576i
$34$	−0.829273	+	0.829273i	−0.142219	+	0.142219i
$35$	1.04536	−	8.15190i	0.176697	−	1.37792i
$36$		−	3.71522i		−	0.619203i
$37$	1.83523			0.301710			0.150855	−	0.988556i	$-0.451797\pi$
$37$	1.83523			0.301710			0.150855	+	0.988556i	$0.451797\pi$
$38$	−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	−0.675863	−	0.737027i	$-0.736229\pi$
$41$	0.391638	−	0.391638i	0.0611636	−	0.0611636i	0.737027	+	0.675863i	$0.236229\pi$
$42$	1.20712	−	1.20712i	0.186263	−	0.186263i
$43$	−1.53207	+	1.53207i	−0.233639	+	0.233639i	−0.814210	−	0.580571i	$-0.802829\pi$
$43$	−1.53207	+	1.53207i	−0.233639	+	0.233639i	0.580571	+	0.814210i	$0.302829\pi$
$44$	−0.853919	−	0.853919i	−0.128733	−	0.128733i
$45$	4.69233	+	0.601719i	0.699491	+	0.0896990i
$46$	0.472962	+	0.472962i	0.0697344	+	0.0697344i
$47$	−3.80918			−0.555626			−0.277813	−	0.960635i	$-0.589610\pi$
$47$	−3.80918			−0.555626			−0.277813	+	0.960635i	$0.589610\pi$
$48$	−1.72615	−	1.72615i	−0.249149	−	0.249149i
$49$	6.50924			0.929892
$50$	−0.623107	+	2.38961i	−0.0881207	+	0.337941i
$51$			2.23297i			0.312678i
$52$		0			0
$53$	−2.47293	−	2.47293i	−0.339683	−	0.339683i	0.516565	−	0.856248i	$-0.327211\pi$
$53$	−2.47293	−	2.47293i	−0.339683	−	0.339683i	−0.856248	+	0.516565i	$0.827211\pi$
$54$	1.68011	+	1.68011i	0.228634	+	0.228634i
$55$	1.21680	−	0.940200i	0.164074	−	0.126776i
$56$			6.81850i			0.911160i
$57$			5.15084i			0.682245i
$58$	−4.70011			−0.617154
$59$	−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	$0.486863\pi$
$60$	2.92199	−	2.25776i	0.377227	−	0.291476i
$61$	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
$63$			7.77608i			0.979693i
$64$	2.72601			0.340751
$65$		0			0
$66$	0.319406			0.0393162
$67$		−	12.2474i		−	1.49626i	−0.663552	−	0.748130i	$-0.730952\pi$
$67$		−	12.2474i		−	1.49626i	0.663552	−	0.748130i	$-0.269048\pi$
$68$	−2.94847	−	2.94847i	−0.357554	−	0.357554i
$69$	1.27354			0.153316
$70$	−4.02624	−	0.516303i	−0.481227	−	0.0617101i
$71$	−4.74012	+	4.74012i	−0.562549	+	0.562549i	−0.930031	−	0.367482i	$-0.880220\pi$
$71$	−4.74012	+	4.74012i	−0.562549	+	0.562549i	0.367482	+	0.930031i	$0.380220\pi$
$72$	−3.92481			−0.462543
$73$			3.37642i			0.395180i	0.980285	+	0.197590i	$0.0633115\pi$
$73$			3.37642i			0.395180i	−0.980285	+	0.197590i	$0.936688\pi$
$74$		−	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	$-0.943814\pi$
$79$		−	3.12149i		−	0.351195i	0.984462	−	0.175598i	$-0.0561857\pi$
$80$	−0.738299	+	5.75740i	−0.0825443	+	0.643697i
$81$	−1.82297			−0.202552
$82$	−0.193431	−	0.193431i	−0.0213609	−	0.0213609i
$83$	2.13918			0.234805			0.117403	−	0.993084i	$-0.462543\pi$
$83$	2.13918			0.234805			0.117403	+	0.993084i	$0.462543\pi$
$84$	4.29191	+	4.29191i	0.468286	+	0.468286i
$85$	4.20145	−	3.24638i	0.455711	−	0.352119i
$86$	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
$93$	−6.40483			−0.664150
$94$			1.88136i			0.194048i
$95$	9.69159	−	7.48850i	0.994336	−	0.768304i
$96$	−3.31972	+	3.31972i	−0.338817	+	0.338817i
$97$		−	7.07377i		−	0.718232i	−0.933293	−	0.359116i	$-0.883078\pi$
$97$		−	7.07377i		−	0.718232i	0.933293	−	0.359116i	$-0.116922\pi$
$98$		−	3.21493i		−	0.324757i
$99$	−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	$0.732560\pi$
$102$	1.10287			0.109200
$103$	−3.17851	+	3.17851i	−0.313188	+	0.313188i	−0.846143	−	0.532956i	$-0.821081\pi$
$103$	−3.17851	+	3.17851i	−0.313188	+	0.313188i	0.532956	+	0.846143i	$0.321081\pi$
$104$		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	−0.0435984	+	0.999049i	$0.513882\pi$
$107$	−10.7852	+	10.7852i	−1.04265	+	1.04265i	−0.999049	+	0.0435984i	$0.986118\pi$
$108$	−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	$0.701107\pi$
$110$	−0.464366	−	0.600981i	−0.0442756	−	0.0573013i
$111$	−1.22036	−	1.22036i	−0.115831	−	0.115831i
$112$	−9.54111			−0.901550
$113$	11.7173	+	11.7173i	1.10227	+	1.10227i	0.994137	+	0.108132i	$0.0344870\pi$
$113$	11.7173	+	11.7173i	1.10227	+	1.10227i	0.108132	+	0.994137i	$0.465513\pi$
$114$	2.54401			0.238268
$115$	−1.85152	−	2.39623i	−0.172655	−	0.223450i
$116$		−	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
$122$		−	3.06124i		−	0.277152i
$123$	−0.520848			−0.0469633
$124$	8.45710	−	8.45710i	0.759470	−	0.759470i
$125$	4.17416	−	10.3719i	0.373349	−	0.927691i
$126$	3.84062			0.342149
$127$	−5.86876	−	5.86876i	−0.520768	−	0.520768i	0.397035	−	0.917803i	$-0.370039\pi$
$127$	−5.86876	−	5.86876i	−0.520768	−	0.520768i	−0.917803	+	0.397035i	$0.870039\pi$
$128$		−	11.3311i		−	1.00154i
$129$	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	$0.480881\pi$
$132$			1.13564i			0.0988452i
$133$	14.2353	+	14.2353i	1.23436	+	1.23436i
$134$	−6.04902			−0.522556
$135$	−6.57718	−	8.51216i	−0.566074	−	0.732610i
$136$	−3.11480	+	3.11480i	−0.267092	+	0.267092i
$137$	12.3276			1.05322			0.526609	−	0.850108i	$-0.323463\pi$
$137$	12.3276			1.05322			0.526609	+	0.850108i	$0.323463\pi$
$138$		−	0.629002i		−	0.0535442i
$139$		−	6.40157i		−	0.542974i	−0.962442	−	0.271487i	$-0.912485\pi$
$139$		−	6.40157i		−	0.542974i	0.962442	−	0.271487i	$-0.0875153\pi$
$140$	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
$145$	21.1062	+	2.70655i	1.75278	+	0.224767i
$146$	1.66762			0.138013
$147$	−4.32839	−	4.32839i	−0.356999	−	0.356999i
$148$	3.22278			0.264911
$149$	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	$0.508375\pi$
$150$	2.00333	−	1.17465i	0.163572	−	0.0959099i
$151$	−3.31542	−	3.31542i	−0.269805	−	0.269805i	0.559217	−	0.829022i	$-0.311102\pi$
$151$	−3.31542	−	3.31542i	−0.269805	−	0.269805i	−0.829022	+	0.559217i	$0.811102\pi$
$152$	−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	−0.192779	−	0.981242i	$-0.561750\pi$
$157$	9.87941	−	9.87941i	0.788463	−	0.788463i	0.981242	+	0.192779i	$0.0617501\pi$
$158$	−1.54171			−0.122652
$159$			3.28880i			0.260819i
$160$	11.0726	+	1.41989i	0.875364	+	0.112252i
$161$	3.51966	−	3.51966i	0.277388	−	0.277388i
$162$			0.900366i			0.0707395i
$163$			0.131970i			0.0103367i	0.999987	+	0.00516833i	$0.00164514\pi$
$163$			0.131970i			0.0103367i	−0.999987	+	0.00516833i	$0.998355\pi$
$164$	0.687741	−	0.687741i	0.0537035	−	0.0537035i
$165$	−1.43432	−	0.183930i	−0.111662	−	0.0143189i
$166$		−	1.05654i		−	0.0820038i
$167$	21.6368			1.67430			0.837152	−	0.546971i	$-0.184219\pi$
$167$	21.6368			1.67430			0.837152	+	0.546971i	$0.184219\pi$
$168$	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	$-0.844983\pi$
$173$	−5.46851	+	5.46851i	−0.415763	+	0.415763i	0.467977	+	0.883741i	$0.344983\pi$
$174$	3.12539	+	3.12539i	0.236935	+	0.236935i
$175$	17.7828	+	4.63701i	1.34426	+	0.350525i
$176$	−1.26229	−	1.26229i	−0.0951490	−	0.0951490i
$177$	9.78515			0.735497
$178$	1.17961	+	1.17961i	0.0884157	+	0.0884157i
$179$	−16.3536			−1.22233			−0.611164	−	0.791504i	$-0.709298\pi$
$179$	−16.3536			−1.22233			−0.611164	+	0.791504i	$0.709298\pi$
$180$	8.24001	+	1.05666i	0.614174	+	0.0787585i
$181$			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
$187$			1.63292i			0.119411i
$188$	−6.68916			−0.487857
$189$	12.5030	−	12.5030i	0.909456	−	0.909456i
$190$	−3.69858	−	4.78669i	−0.268324	−	0.347263i
$191$	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
$193$		−	10.1015i		−	0.727119i	−0.931571	−	0.363560i	$-0.881561\pi$
$193$		−	10.1015i		−	0.727119i	0.931571	−	0.363560i	$-0.118439\pi$
$194$	−3.49375			−0.250836
$195$		0			0
$196$	11.4306			0.816473
$197$		−	13.0639i		−	0.930767i	−0.885109	−	0.465384i	$-0.845916\pi$
$197$		−	13.0639i		−	0.930767i	0.885109	−	0.465384i	$-0.154084\pi$
$198$	0.508116	+	0.508116i	0.0361102	+	0.0361102i
$199$	7.85012			0.556480			0.278240	−	0.960512i	$-0.410249\pi$
$199$	7.85012			0.556480			0.278240	+	0.960512i	$0.410249\pi$
$200$	−2.34043	+	8.97550i	−0.165493	+	0.634664i
$201$	−8.14405	+	8.14405i	−0.574437	+	0.574437i
$202$	7.39354			0.520208
$203$			34.9770i			2.45491i
$204$			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
$210$	2.33397	+	3.02061i	0.161059	+	0.208442i
$211$	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
$213$	6.30398			0.431942
$214$	5.32684	+	5.32684i	0.364136	+	0.364136i
$215$	−2.96226	−	3.83374i	−0.202024	−	0.261459i
$216$	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
$223$	9.94495			0.665963			0.332981	−	0.942933i	$-0.391945\pi$
$223$	9.94495			0.665963			0.332981	+	0.942933i	$0.391945\pi$
$224$			18.3494i			1.22602i
$225$	−2.66911	+	10.2360i	−0.177941	+	0.682400i
$226$	5.78718	−	5.78718i	0.384958	−	0.384958i
$227$		−	14.6058i		−	0.969421i	−0.874675	−	0.484710i	$-0.838925\pi$
$227$		−	14.6058i		−	0.969421i	0.874675	−	0.484710i	$-0.161075\pi$
$228$			9.04518i			0.599032i
$229$	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
$232$	−17.6539			−1.15903
$233$	16.5625	−	16.5625i	1.08505	−	1.08505i	0.0890148	−	0.996030i	$-0.471628\pi$
$233$	16.5625	−	16.5625i	1.08505	−	1.08505i	0.996030	−	0.0890148i	$-0.0283719\pi$
$234$		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	$0.982801\pi$
$240$	4.31938	−	3.33750i	0.278815	−	0.215435i
$241$	−2.19128	−	2.19128i	−0.141153	−	0.141153i	0.632999	−	0.774152i	$-0.281824\pi$
$241$	−2.19128	−	2.19128i	−0.141153	−	0.141153i	−0.774152	+	0.632999i	$0.781824\pi$
$242$	−5.19935			−0.334227
$243$	11.4173	+	11.4173i	0.732422	+	0.732422i
$244$	10.8842			0.696790
$245$	−1.85131	+	14.4369i	−0.118276	+	0.922339i
$246$			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	$0.618128\pi$
$252$			13.6553i			0.860201i
$253$	0.931307			0.0585508
$254$	−2.89859	+	2.89859i	−0.181874	+	0.181874i
$255$	−4.95251	−	0.635084i	−0.310138	−	0.0397705i
$256$	−0.144429			−0.00902681
$257$	−5.06650	−	5.06650i	−0.316040	−	0.316040i	0.531204	−	0.847244i	$-0.321740\pi$
$257$	−5.06650	−	5.06650i	−0.316040	−	0.316040i	−0.847244	+	0.531204i	$0.821740\pi$
$258$		−	1.00634i		−	0.0626522i
$259$	−6.74538			−0.419137
$260$		0			0
$261$	−20.1332			−1.24621
$262$		−	0.678663i		−	0.0419280i
$263$	−9.52151	−	9.52151i	−0.587121	−	0.587121i	0.349729	−	0.936851i	$-0.386274\pi$
$263$	−9.52151	−	9.52151i	−0.587121	−	0.587121i	−0.936851	+	0.349729i	$0.886274\pi$
$264$	1.19971			0.0738370
$265$	6.18807	−	4.78140i	0.380130	−	0.293719i
$266$	7.03086	−	7.03086i	0.431090	−	0.431090i
$267$	3.17632			0.194388
$268$		−	21.5072i		−	1.31376i
$269$			8.10376i			0.494095i	0.969003	+	0.247047i	$0.0794603\pi$
$269$			8.10376i			0.494095i	−0.969003	+	0.247047i	$0.920540\pi$
$270$	−4.20417	+	3.24848i	−0.255858	+	0.197696i
$271$	−6.50299	−	6.50299i	−0.395028	−	0.395028i	0.481447	−	0.876475i	$-0.340111\pi$
$271$	−6.50299	−	6.50299i	−0.395028	−	0.395028i	−0.876475	+	0.481447i	$0.840111\pi$
$272$	−4.35853	−	4.35853i	−0.264275	−	0.264275i
$273$		0			0
$274$		−	6.08862i		−	0.367827i
$275$	1.73920	+	2.96616i	0.104878	+	0.178866i
$276$	2.23641			0.134616
$277$	−18.2750	−	18.2750i	−1.09804	−	1.09804i	−0.994640	−	0.103397i	$-0.967029\pi$
$277$	−18.2750	−	18.2750i	−1.09804	−	1.09804i	−0.103397	−	0.994640i	$-0.532971\pi$
$278$	−3.16174			−0.189629
$279$	−10.1889	−	10.1889i	−0.609993	−	0.609993i
$280$	−15.1228	−	1.93927i	−0.903760	−	0.115893i
$281$	5.41928	+	5.41928i	0.323287	+	0.323287i	0.850027	−	0.526740i	$-0.176586\pi$
$281$	5.41928	+	5.41928i	0.323287	+	0.323287i	−0.526740	+	0.850027i	$0.676586\pi$
$282$	1.25103	−	1.25103i	0.0744978	−	0.0744978i
$283$	−6.21235	+	6.21235i	−0.369286	+	0.369286i	−0.867217	−	0.497931i	$-0.834093\pi$
$283$	−6.21235	+	6.21235i	−0.369286	+	0.369286i	0.497931	+	0.867217i	$0.334093\pi$
$284$	−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
$288$	−10.5621			−0.622378
$289$		−	11.3618i		−	0.668339i
$290$	1.33677	−	10.4244i	0.0784978	−	0.612142i
$291$	−4.70377	+	4.70377i	−0.275740	+	0.275740i
$292$			5.92921i			0.346981i
$293$		−	13.2360i		−	0.773253i	−0.922236	−	0.386626i	$-0.873640\pi$
$293$		−	13.2360i		−	0.773253i	0.922236	−	0.386626i	$-0.126360\pi$
$294$	−2.13780	+	2.13780i	−0.124679	+	0.124679i
$295$	−14.2261	−	18.4113i	−0.828273	−	1.07195i
$296$		−	3.40458i		−	0.197887i
$297$	3.30830			0.191967
$298$	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
$305$	−1.76281	+	13.7468i	−0.100938	+	0.787138i
$306$	1.75446	+	1.75446i	0.100296	+	0.100296i
$307$	−15.4782			−0.883389			−0.441695	−	0.897165i	$-0.645623\pi$
$307$	−15.4782			−0.883389			−0.441695	+	0.897165i	$0.645623\pi$
$308$	3.13857	+	3.13857i	0.178837	+	0.178837i
$309$	4.22716			0.240475
$310$	5.95203	−	4.59902i	0.338053	−	0.261207i
$311$			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	0.846765	+	0.531967i	$0.178547\pi$
$313$	24.3923	+	24.3923i	1.37873	+	1.37873i	0.531967	+	0.846765i	$0.321453\pi$
$314$	−4.87946	−	4.87946i	−0.275364	−	0.275364i
$315$	−17.2466	−	2.21161i	−0.971736	−	0.124610i
$316$		−	5.48153i		−	0.308360i
$317$			18.9851i			1.06631i	0.846017	+	0.533156i	$0.178994\pi$
$317$			18.9851i			1.06631i	−0.846017	+	0.533156i	$0.821006\pi$
$318$	1.62435			0.0910888
$319$	−4.62748	+	4.62748i	−0.259089	+	0.259089i
$320$	−0.775312	+	6.04604i	−0.0433412	+	0.337984i
$321$	14.3435			0.800576
$322$	−1.73837	−	1.73837i	−0.0968755	−	0.0968755i
$323$			13.0059i			0.723665i
$324$	−3.20124			−0.177847
$325$		0			0
$326$	0.0651800			0.00360999
$327$		−	3.00431i		−	0.166139i
$328$	−0.726538	−	0.726538i	−0.0401163	−	0.0401163i
$329$	14.0006			0.771879
$330$	−0.0908432	+	0.708414i	−0.00500075	+	0.0389969i
$331$	−4.96159	+	4.96159i	−0.272714	+	0.272714i	−0.830192	−	0.557478i	$-0.811769\pi$
$331$	−4.96159	+	4.96159i	−0.272714	+	0.272714i	0.557478	+	0.830192i	$0.311769\pi$
$332$	3.75653			0.206166
$333$		−	3.88272i		−	0.212772i
$334$		−	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	$-0.263515\pi$
$337$	−1.10195	−	1.10195i	−0.0600271	−	0.0600271i	−0.736483	+	0.676456i	$0.763515\pi$
$338$		0			0
$339$		−	15.5830i		−	0.846355i
$340$	7.37801	−	5.70084i	0.400129	−	0.309172i
$341$	−4.68370			−0.253637
$342$	4.04704	+	4.04704i	0.218839	+	0.218839i
$343$	1.80378			0.0973947
$344$	2.84219	+	2.84219i	0.153241	+	0.153241i
$345$	−0.362210	+	2.82458i	−0.0195007	+	0.152071i
$346$	2.70091	+	2.70091i	0.145202	+	0.145202i
$347$	18.2654	−	18.2654i	0.980539	−	0.980539i	−0.0192754	−	0.999814i	$-0.506136\pi$
$347$	18.2654	−	18.2654i	0.980539	−	0.980539i	0.999814	+	0.0192754i	$0.00613592\pi$
$348$	−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
$353$	−3.26547			−0.173803			−0.0869017	−	0.996217i	$-0.527697\pi$
$353$	−3.26547			−0.173803			−0.0869017	+	0.996217i	$0.527697\pi$
$354$		−	4.83291i		−	0.256866i
$355$	−9.16499	−	11.8613i	−0.486427	−	0.629532i
$356$	−4.19410	+	4.19410i	−0.222287	+	0.222287i
$357$		−	8.20725i		−	0.434374i
$358$			8.07709i			0.426887i
$359$	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
$362$	8.90935			0.468265
$363$	−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	−0.0713698	−	0.997450i	$-0.522737\pi$
$367$	17.7411	−	17.7411i	0.926080	−	0.926080i	0.997450	+	0.0713698i	$0.0227371\pi$
$368$	−2.48582	+	2.48582i	−0.129582	+	0.129582i
$369$	−0.828572	−	0.828572i	−0.0431337	−	0.0431337i
$370$	2.01036	+	0.257798i	0.104514	+	0.0134023i
$371$	9.08925	+	9.08925i	0.471890	+	0.471890i
$372$	−11.2473			−0.583144
$373$	−8.07976	−	8.07976i	−0.418354	−	0.418354i	0.466282	−	0.884636i	$-0.345593\pi$
$373$	−8.07976	−	8.07976i	−0.418354	−	0.418354i	−0.884636	+	0.466282i	$0.845593\pi$
$374$	0.806500			0.0417031
$375$	−9.67256	+	4.12125i	−0.499489	+	0.212820i
$376$			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
$382$		−	2.56386i		−	0.131179i
$383$	−26.4516			−1.35161			−0.675806	−	0.737080i	$-0.736204\pi$
$383$	−26.4516			−1.35161			−0.675806	+	0.737080i	$0.736204\pi$
$384$	−7.53473	+	7.53473i	−0.384505	+	0.384505i
$385$	−4.47235	+	3.45570i	−0.227932	+	0.176119i
$386$	−4.98913			−0.253940
$387$	3.24134	+	3.24134i	0.164767	+	0.164767i
$388$		−	12.4220i		−	0.630630i
$389$	−0.650094			−0.0329611			−0.0164805	−	0.999864i	$-0.505246\pi$
$389$	−0.650094			−0.0329611			−0.0164805	+	0.999864i	$0.505246\pi$
$390$		0			0
$391$	3.21568			0.162624
$392$		−	12.0755i		−	0.609903i
$393$	−0.913712	−	0.913712i	−0.0460907	−	0.0460907i
$394$	−6.45230			−0.325062
$395$	6.92317	+	0.887791i	0.348343	+	0.0446696i
$396$	−1.80660	+	1.80660i	−0.0907850	+	0.0907850i
$397$	−27.0082			−1.35550			−0.677750	−	0.735292i	$-0.737045\pi$
$397$	−27.0082			−1.35550			−0.677750	+	0.735292i	$0.737045\pi$
$398$		−	3.87719i		−	0.194346i
$399$		−	18.9319i		−	0.947779i
$400$	−12.5594	−	3.27496i	−0.627970	−	0.163748i
$401$	−3.50630	−	3.50630i	−0.175096	−	0.175096i	0.614118	−	0.789214i	$-0.289512\pi$
$401$	−3.50630	−	3.50630i	−0.175096	−	0.175096i	−0.789214	+	0.614118i	$0.789512\pi$
$402$	4.02236	+	4.02236i	0.200617	+	0.200617i
$403$		0			0
$404$			26.2876i			1.30786i
$405$	0.518474	−	4.04317i	0.0257632	−	0.200907i
$406$	17.2752			0.857354
$407$	−0.892417	−	0.892417i	−0.0442355	−	0.0442355i
$408$	4.14243			0.205081
$409$	−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	$0.797756\pi$
$410$	0.484026	−	0.373997i	0.0239043	−	0.0184704i
$411$	−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
$418$	1.86037			0.0909938
$419$			5.37068i			0.262375i	0.991358	+	0.131187i	$0.0418790\pi$
$419$			5.37068i			0.262375i	−0.991358	+	0.131187i	$0.958121\pi$
$420$	−10.7397	+	8.29839i	−0.524045	+	0.404920i
$421$	14.1377	−	14.1377i	0.689029	−	0.689029i	−0.272988	−	0.962017i	$-0.588012\pi$
$421$	14.1377	−	14.1377i	0.689029	−	0.689029i	0.962017	+	0.272988i	$0.0880119\pi$
$422$		−	6.13629i		−	0.298710i
$423$			8.05892i			0.391838i
$424$	−4.58760	+	4.58760i	−0.222794	+	0.222794i
$425$	6.00522	+	10.2417i	0.291296	+	0.496797i
$426$		−	3.11355i		−	0.150852i
$427$	−22.7810			−1.10245
$428$	−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	−0.931704	−	0.363219i	$-0.881678\pi$
$431$	−11.8020	+	11.8020i	−0.568485	+	0.568485i	0.363219	+	0.931704i	$0.381678\pi$
$432$	−8.83040	+	8.83040i	−0.424853	+	0.424853i
$433$	−5.36952	+	5.36952i	−0.258043	+	0.258043i	−0.824258	−	0.566215i	$-0.808407\pi$
$433$	−5.36952	+	5.36952i	−0.258043	+	0.258043i	0.566215	+	0.824258i	$0.308407\pi$
$434$	8.74255	+	8.74255i	0.419656	+	0.419656i
$435$	−12.2350	−	15.8345i	−0.586626	−	0.759208i
$436$	3.96697	+	3.96697i	0.189984	+	0.189984i
$437$	7.41767			0.354835
$438$	−1.10890	−	1.10890i	−0.0529854	−	0.0529854i
$439$	−13.6907			−0.653422			−0.326711	−	0.945124i	$-0.605940\pi$
$439$	−13.6907			−0.653422			−0.326711	+	0.945124i	$0.605940\pi$
$440$	−1.74419	−	2.25732i	−0.0831509	−	0.107614i
$441$		−	13.7713i		−	0.655777i
$442$		0			0
$443$	6.46290	+	6.46290i	0.307062	+	0.307062i	0.843769	−	0.536707i	$-0.180332\pi$
$443$	6.46290	+	6.46290i	0.307062	+	0.307062i	−0.536707	+	0.843769i	$0.680332\pi$
$444$	−2.14302	−	2.14302i	−0.101703	−	0.101703i
$445$	−4.61787	−	5.97642i	−0.218908	−	0.283310i
$446$		−	4.91183i		−	0.232582i
$447$		−	15.8010i		−	0.747364i
$448$	−10.0194			−0.473373
$449$	−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	$0.457506\pi$
$450$	5.05558	+	1.31828i	0.238322	+	0.0621443i
$451$	−0.380884			−0.0179351
$452$	20.5763	+	20.5763i	0.967825	+	0.967825i
$453$			4.40924i			0.207164i
$454$	−7.21383			−0.338562
$455$		0			0
$456$	9.55545			0.447475
$457$		−	0.827533i		−	0.0387104i	−0.999813	−	0.0193552i	$-0.993839\pi$
$457$		−	0.827533i		−	0.0387104i	0.999813	−	0.0193552i	$-0.00616133\pi$
$458$	−7.71392	−	7.71392i	−0.360448	−	0.360448i
$459$	11.4231			0.533184
$460$	−3.25138	−	4.20792i	−0.151596	−	0.196195i
$461$	17.0267	−	17.0267i	0.793011	−	0.793011i	−0.188972	−	0.981983i	$-0.560515\pi$
$461$	17.0267	−	17.0267i	0.793011	−	0.793011i	0.981983	+	0.188972i	$0.0605154\pi$
$462$	−1.17398			−0.0546183
$463$			6.35566i			0.295373i	0.989034	+	0.147686i	$0.0471826\pi$
$463$			6.35566i			0.295373i	−0.989034	+	0.147686i	$0.952817\pi$
$464$		−	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	$-0.420756\pi$
$467$	−15.6194	−	15.6194i	−0.722781	−	0.722781i	−0.969171	+	0.246390i	$0.920756\pi$
$468$		0			0
$469$			45.0153i			2.07861i
$470$	−4.17269	−	0.535083i	−0.192472	−	0.0246815i
$471$	−13.1388			−0.605406
$472$	13.6495	+	13.6495i	0.628267	+	0.628267i
$473$	1.49000			0.0685104
$474$	1.02518	+	1.02518i	0.0470879	+	0.0470879i
$475$	13.8524	+	23.6249i	0.635591	+	1.08398i
$476$	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
$483$	−4.68087			−0.212987
$484$		−	18.4862i		−	0.840282i
$485$	15.6890	+	2.01187i	0.712399	+	0.0913543i
$486$	5.63904	−	5.63904i	0.255792	−	0.255792i
$487$		−	6.15896i		−	0.279089i	−0.990216	−	0.139545i	$-0.955436\pi$
$487$		−	6.15896i		−	0.279089i	0.990216	−	0.139545i	$-0.0445638\pi$
$488$		−	11.4982i		−	0.520500i
$489$	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	$0.891512\pi$
$492$	−0.914640			−0.0412352
$493$	−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	$0.517826\pi$
$500$	7.33009	−	18.2137i	0.327811	−	0.814541i
$501$	−14.3876	−	14.3876i	−0.642790	−	0.642790i
$502$	14.5844			0.650933
$503$	−27.4075	−	27.4075i	−1.22204	−	1.22204i	−0.966906	−	0.255133i	$-0.917881\pi$
$503$	−27.4075	−	27.4075i	−1.22204	−	1.22204i	−0.255133	−	0.966906i	$-0.582119\pi$
$504$	14.4256			0.642567
$505$	−33.2013	−	4.25756i	−1.47744	−	0.189459i
$506$		−	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
$512$		−	22.5909i		−	0.998384i
$513$	26.3499			1.16338
$514$	−2.50236	+	2.50236i	−0.110374	+	0.110374i
$515$	−6.14563	−	7.95364i	−0.270809	−	0.350479i
$516$	3.57804			0.157514
$517$	1.85229	+	1.85229i	0.0814636	+	0.0814636i
$518$			3.33155i			0.146380i
$519$	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	$0.598259\pi$
$522$			9.94381i			0.435229i
$523$	22.1520	+	22.1520i	0.968638	+	0.968638i	0.999523	−	0.0308854i	$-0.00983268\pi$
$523$	22.1520	+	22.1520i	0.968638	+	0.968638i	−0.0308854	+	0.999523i	$0.509833\pi$
$524$	2.41298			0.105411
$525$	−8.74146	−	14.9083i	−0.381508	−	0.650652i
$526$	−4.70269	+	4.70269i	−0.205047	+	0.205047i
$527$	−16.1722			−0.704471
$528$			1.67875i			0.0730583i
$529$			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
$535$	−20.8532	−	26.9881i	−0.901561	−	1.16680i
$536$	−22.7205			−0.981376
$537$	10.8745	+	10.8745i	0.469270	+	0.469270i
$538$	4.00246			0.172558
$539$	−3.16525	−	3.16525i	−0.136337	−	0.136337i
$540$	−11.5499	−	14.9479i	−0.497030	−	0.643254i
$541$	−10.7732	−	10.7732i	−0.463175	−	0.463175i	0.436520	−	0.899695i	$-0.356211\pi$
$541$	−10.7732	−	10.7732i	−0.463175	−	0.463175i	−0.899695	+	0.436520i	$0.856211\pi$
$542$	−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	−0.332828	−	0.942987i	$-0.608003\pi$
$547$	14.2704	−	14.2704i	0.610159	−	0.610159i	0.942987	+	0.332828i	$0.108003\pi$
$548$	21.6480			0.924757
$549$		−	13.1130i		−	0.559650i
$550$	1.46499	−	0.858995i	0.0624674	−	0.0366277i
$551$	−36.8569	+	36.8569i	−1.57016	+	1.57016i
$552$		−	2.36257i		−	0.100558i
$553$			11.4730i			0.487882i
$554$	−9.02605	+	9.02605i	−0.383480	+	0.383480i
$555$	3.05372	−	2.35955i	0.129623	−	0.100157i
$556$		−	11.2415i		−	0.476747i
$557$	16.7117			0.708096			0.354048	−	0.935227i	$-0.384805\pi$
$557$	16.7117			0.708096			0.354048	+	0.935227i	$0.384805\pi$
$558$	−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	$-0.907779\pi$
$563$	−15.9601	+	15.9601i	−0.672637	+	0.672637i	0.285686	+	0.958323i	$0.407779\pi$
$564$	4.44802	+	4.44802i	0.187296	+	0.187296i
$565$	−29.3204	+	22.6553i	−1.23352	+	0.953115i
$566$	3.06829	+	3.06829i	0.128970	+	0.128970i
$567$	6.70030			0.281386
$568$	8.79352	+	8.79352i	0.368968	+	0.368968i
$569$	−5.73685			−0.240501			−0.120251	−	0.992744i	$-0.538370\pi$
$569$	−5.73685			−0.240501			−0.120251	+	0.992744i	$0.538370\pi$
$570$	−0.723548	+	5.64237i	−0.0303061	+	0.236333i
$571$		−	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
$577$			28.9429i			1.20491i	0.798153	+	0.602455i	$0.205811\pi$
$577$			28.9429i			1.20491i	−0.798153	+	0.602455i	$0.794189\pi$
$578$	−5.61160			−0.233412
$579$	−6.71707	+	6.71707i	−0.279152	+	0.279152i
$580$	37.0638	+	4.75287i	1.53899	+	0.197352i
$581$	−7.86254			−0.326193
$582$	2.32320	+	2.32320i	0.0962999	+	0.0962999i
$583$			2.40503i			0.0996060i
$584$	6.26369			0.259193
$585$		0			0
$586$	−6.53726			−0.270052
$587$			19.6915i			0.812757i	0.913705	+	0.406379i	$0.133209\pi$
$587$			19.6915i			0.812757i	−0.913705	+	0.406379i	$0.866791\pi$
$588$	−7.60091	−	7.60091i	−0.313456	−	0.313456i
$589$	−37.3047			−1.53712
$590$	−9.09338	+	7.02628i	−0.374368	+	0.289267i
$591$	−8.68700	+	8.68700i	−0.357335	+	0.357335i
$592$	4.76402			0.195800
$593$		−	21.8216i		−	0.896106i	−0.894007	−	0.448053i	$-0.852118\pi$
$593$		−	21.8216i		−	0.896106i	0.894007	−	0.448053i	$-0.147882\pi$
$594$		−	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	$-0.721137\pi$
$599$		−	37.6041i		−	1.53646i	0.640172	−	0.768232i	$-0.278863\pi$
$600$	7.52464	−	4.41206i	0.307192	−	0.180122i
$601$	−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
$603$	−25.9113			−1.05519
$604$	−5.82207	−	5.82207i	−0.236897	−	0.236897i
$605$	23.3481	+	2.99404i	0.949235	+	0.121725i
$606$	−4.91641	−	4.91641i	−0.199716	−	0.199716i
$607$	24.3632	−	24.3632i	0.988874	−	0.988874i	−0.0110652	−	0.999939i	$-0.503522\pi$
$607$	24.3632	−	24.3632i	0.988874	−	0.988874i	0.999939	+	0.0110652i	$0.00352225\pi$
$608$	−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
$613$	−24.8665			−1.00435			−0.502173	−	0.864767i	$-0.667466\pi$
$613$	−24.8665			−1.00435			−0.502173	+	0.864767i	$0.667466\pi$
$614$			7.64473i			0.308516i
$615$	0.148136	−	1.15519i	0.00597341	−	0.0465818i
$616$	3.31563	−	3.31563i	0.133591	−	0.133591i
$617$			27.8161i			1.11983i	0.828548	+	0.559917i	$0.189167\pi$
$617$			27.8161i			1.11983i	−0.828548	+	0.559917i	$0.810833\pi$
$618$		−	2.08780i		−	0.0839838i
$619$	−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
$622$	2.64199			0.105934
$623$	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
$630$	−1.09232	+	8.51813i	−0.0435191	+	0.339371i
$631$	−9.23751	−	9.23751i	−0.367739	−	0.367739i	0.498913	−	0.866652i	$-0.333733\pi$
$631$	−9.23751	−	9.23751i	−0.367739	−	0.367739i	−0.866652	+	0.498913i	$0.833733\pi$
$632$	−5.79076			−0.230344
$633$	−8.26153	−	8.26153i	−0.328366	−	0.328366i
$634$	9.37679			0.372400
$635$	14.6855	−	11.3472i	0.582777	−	0.450300i
$636$			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	$-0.181827\pi$
$642$		−	7.08428i		−	0.279594i
$643$	31.5021			1.24232			0.621161	−	0.783683i	$-0.286661\pi$
$643$	31.5021			1.24232			0.621161	+	0.783683i	$0.286661\pi$
$644$	6.18074	−	6.18074i	0.243555	−	0.243555i
$645$	−0.579501	+	4.51907i	−0.0228178	+	0.177938i
$646$	6.42361			0.252734
$647$	−29.5351	−	29.5351i	−1.16114	−	1.16114i	−0.984225	−	0.176919i	$-0.943387\pi$
$647$	−29.5351	−	29.5351i	−1.16114	−	1.16114i	−0.176919	−	0.984225i	$-0.556613\pi$
$648$			3.38183i			0.132851i
$649$	7.15565			0.280884
$650$		0			0
$651$	23.5409			0.922641
$652$			0.231747i			0.00907589i
$653$	−10.7389	−	10.7389i	−0.420244	−	0.420244i	0.465044	−	0.885288i	$-0.346039\pi$
$653$	−10.7389	−	10.7389i	−0.420244	−	0.420244i	−0.885288	+	0.465044i	$0.846039\pi$
$654$	−1.48384			−0.0580226
$655$	−0.390807	+	3.04759i	−0.0152701	+	0.119079i
$656$	1.01664	−	1.01664i	0.0396932	−	0.0396932i
$657$	7.14335			0.278689
$658$		−	6.91493i		−	0.269572i
$659$			28.5112i			1.11064i	0.831638	+	0.555319i	$0.187404\pi$
$659$			28.5112i			1.11064i	−0.831638	+	0.555319i	$0.812596\pi$
$660$	−2.51875	−	0.322992i	−0.0980424	−	0.0125724i
$661$	−4.45573	−	4.45573i	−0.173308	−	0.173308i	0.615123	−	0.788431i	$-0.289106\pi$
$661$	−4.45573	−	4.45573i	−0.173308	−	0.173308i	−0.788431	+	0.615123i	$0.789106\pi$
$662$	2.45054	+	2.45054i	0.0952430	+	0.0952430i
$663$		0			0
$664$		−	3.96845i		−	0.154006i
$665$	−35.6213	+	27.5239i	−1.38134	+	1.06733i
$666$	−1.91768			−0.0743086
$667$	9.11282	+	9.11282i	0.352850	+	0.352850i
$668$	37.9955			1.47009
$669$	−6.61299	−	6.61299i	−0.255673	−	0.255673i
$670$	1.72042	−	13.4162i	0.0664656	−	0.518312i
$671$	−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	$-0.604432\pi$
$673$	16.1992	−	16.1992i	0.624433	−	0.624433i	0.946662	+	0.322229i	$0.104432\pi$
$674$	−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	−0.945461	−	0.325736i	$-0.894388\pi$
$677$	−16.1247	+	16.1247i	−0.619724	+	0.619724i	0.325736	+	0.945461i	$0.394388\pi$
$678$	−7.69650			−0.295582
$679$			25.9996i			0.997772i
$680$	−6.02244	−	7.79422i	−0.230950	−	0.298895i
$681$	−9.71227	+	9.71227i	−0.372175	+	0.372175i
$682$			2.31329i			0.0885804i
$683$		−	32.0480i		−	1.22628i	−0.789973	−	0.613142i	$-0.789905\pi$
$683$		−	32.0480i		−	1.22628i	0.789973	−	0.613142i	$-0.210095\pi$
$684$	−14.3892	+	14.3892i	−0.550185	+	0.550185i
$685$	−3.50612	+	27.3415i	−0.133962	+	1.04466i
$686$		−	0.890888i		−	0.0340143i
$687$	−20.7711			−0.792468
$688$	−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	−0.699657	−	0.714479i	$-0.746664\pi$
$691$	0.389645	−	0.389645i	0.0148228	−	0.0148228i	0.714479	+	0.699657i	$0.246664\pi$
$692$	−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
$695$	14.1981	+	1.82069i	0.538564	+	0.0690626i
$696$	11.7391	+	11.7391i	0.444971	+	0.444971i
$697$	−1.31514			−0.0498144
$698$	−3.28282	−	3.28282i	−0.124257	−	0.124257i
$699$	−22.0268			−0.833130
$700$	31.2277	+	8.14286i	1.18030	+	0.307771i
$701$			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
$707$		−	55.0209i		−	2.06927i
$708$	17.1833			0.645789
$709$	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	$0.0414112\pi$
$710$	−5.85831	+	4.52661i	−0.219859	+	0.169881i
$711$	−6.60400			−0.247669
$712$	4.43070	+	4.43070i	0.166047	+	0.166047i
$713$			9.22354i			0.345424i
$714$	−4.05358			−0.151701
$715$		0			0
$716$	−28.7180			−1.07324
$717$			19.4197i			0.725243i
$718$	−1.54142	−	1.54142i	−0.0575251	−	0.0575251i
$719$	−8.42479			−0.314192			−0.157096	−	0.987583i	$-0.550213\pi$
$719$	−8.42479			−0.314192			−0.157096	+	0.987583i	$0.550213\pi$
$720$	12.1807	+	1.56199i	0.453947	+	0.0582118i
$721$	11.6826	−	11.6826i	0.435082	−	0.435082i
$722$	5.43336			0.202209
$723$			2.91423i			0.108381i
$724$			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	$-0.320160\pi$
$727$	−8.33682	−	8.33682i	−0.309195	−	0.309195i	−0.844597	+	0.535402i	$0.820160\pi$
$728$		0			0
$729$		−	9.71523i		−	0.359824i
$730$	−0.474293	+	3.69863i	−0.0175544	+	0.136892i
$731$	5.14477			0.190286
$732$	−7.23757	−	7.23757i	−0.267508	−	0.267508i
$733$	−18.6238			−0.687887			−0.343944	−	0.938990i	$-0.611763\pi$
$733$	−18.6238			−0.687887			−0.343944	+	0.938990i	$0.611763\pi$
$734$	−8.76238	−	8.76238i	−0.323425	−	0.323425i
$735$	10.8310	−	8.36891i	0.399508	−	0.308692i
$736$	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
$743$	37.5700			1.37831			0.689155	−	0.724614i	$-0.257982\pi$
$743$	37.5700			1.37831			0.689155	+	0.724614i	$0.257982\pi$
$744$			11.8818i			0.435607i
$745$	−29.7305	+	22.9722i	−1.08924	+	0.841637i
$746$	−3.99061	+	3.99061i	−0.146107	+	0.146107i
$747$		−	4.52577i		−	0.165589i
$748$			2.86750i			0.104846i
$749$	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	$-0.210110\pi$
$752$	−9.88815			−0.360584
$753$	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	−0.883380	−	0.468658i	$-0.844738\pi$
$757$	−11.4105	+	11.4105i	−0.414722	+	0.414722i	0.468658	+	0.883380i	$0.344738\pi$
$758$	0.701816	−	0.701816i	0.0254911	−	0.0254911i
$759$	−0.619282	−	0.619282i	−0.0224785	−	0.0224785i
$760$	−13.8921	−	17.9791i	−0.503920	−	0.652171i
$761$	11.0788	+	11.0788i	0.401608	+	0.401608i	0.878799	−	0.477192i	$-0.158345\pi$
$761$	11.0788	+	11.0788i	0.401608	+	0.401608i	−0.477192	+	0.878799i	$0.658345\pi$
$762$	3.85490			0.139648
$763$	−8.30300	−	8.30300i	−0.300589	−	0.300589i
$764$	9.11577			0.329797
$765$	−6.86822	−	8.88882i	−0.248321	−	0.321376i
$766$			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
$772$		−	17.7388i		−	0.638433i
$773$	23.9061			0.859843			0.429921	−	0.902866i	$-0.358541\pi$
$773$	23.9061			0.859843			0.429921	+	0.902866i	$0.358541\pi$
$774$	1.60090	−	1.60090i	0.0575433	−	0.0575433i
$775$	−29.3764	+	17.2248i	−1.05523	+	0.618733i
$776$	−13.1227			−0.471078
$777$	4.48541	+	4.48541i	0.160913	+	0.160913i
$778$			0.321083i			0.0115114i
$779$	−3.03366			−0.108692
$780$		0			0
$781$	4.60995			0.164957
$782$		−	1.58823i		−	0.0567949i
$783$	32.3716	+	32.3716i	1.15687	+	1.15687i
$784$	16.8972			0.603470
$785$	19.1018	+	24.7214i	0.681772	+	0.882346i
$786$	−0.451284	+	0.451284i	−0.0160968	+	0.0160968i
$787$	15.7114			0.560052			0.280026	−	0.959992i	$-0.409657\pi$
$787$	15.7114			0.560052			0.280026	+	0.959992i	$0.409657\pi$
$788$		−	22.9411i		−	0.817242i
$789$			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
$795$	−7.29426	−	0.935377i	−0.258701	−	0.0331744i
$796$	13.7853			0.488606
$797$	22.0835	+	22.0835i	0.782237	+	0.782237i	0.980208	−	0.197971i	$-0.0634351\pi$
$797$	22.0835	+	22.0835i	0.782237	+	0.782237i	−0.197971	+	0.980208i	$0.563435\pi$
$798$	−9.35048			−0.331003
$799$	6.39570	+	6.39570i	0.226264	+	0.226264i
$800$	−6.29836	+	24.1541i	−0.222681	+	0.853977i
$801$	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
$808$	27.7706			0.976966
$809$			13.2266i			0.465023i	0.972594	+	0.232512i	$0.0746944\pi$
$809$			13.2266i			0.465023i	−0.972594	+	0.232512i	$0.925306\pi$
$810$	−1.99693	−	0.256076i	−0.0701649	−	0.00899758i
$811$	22.0736	−	22.0736i	0.775109	−	0.775109i	−0.203886	−	0.978995i	$-0.565357\pi$
$811$	22.0736	−	22.0736i	0.775109	−	0.775109i	0.978995	+	0.203886i	$0.0653572\pi$
$812$			61.4218i			2.15548i
$813$			8.64846i			0.303315i
$814$	−0.440767	+	0.440767i	−0.0154489	+	0.0154489i
$815$	−0.292696	−	0.0375338i	−0.0102527	−	0.00131475i
$816$			5.79650i			0.202918i
$817$	11.8676			0.415194
$818$	−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	−0.586461	−	0.809977i	$-0.699479\pi$
$821$	6.40442	−	6.40442i	0.223516	−	0.223516i	0.809977	+	0.586461i	$0.199479\pi$
$822$	−4.04869	+	4.04869i	−0.141214	+	0.141214i
$823$	29.6566	−	29.6566i	1.03376	−	1.03376i	0.0343543	−	0.999410i	$-0.489063\pi$
$823$	29.6566	−	29.6566i	1.03376	−	1.03376i	0.999410	−	0.0343543i	$-0.0109375\pi$
$824$	5.89653	+	5.89653i	0.205415	+	0.205415i
$825$	0.815878	−	3.12888i	0.0284052	−	0.108934i
$826$	−13.3567	−	13.3567i	−0.464738	−	0.464738i
$827$	38.2009			1.32838			0.664188	−	0.747566i	$-0.268778\pi$
$827$	38.2009			1.32838			0.664188	+	0.747566i	$0.268778\pi$
$828$	3.55771	+	3.55771i	0.123639	+	0.123639i
$829$	29.3499			1.01936			0.509682	−	0.860363i	$-0.329763\pi$
$829$	29.3499			1.01936			0.509682	+	0.860363i	$0.329763\pi$
$830$	2.34332	+	0.300495i	0.0813377	+	0.0104303i
$831$			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
$837$			32.7649i			1.13252i
$838$	2.65259			0.0916321
$839$	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	$0.0418917\pi$
$840$	8.76652	+	11.3456i	0.302474	+	0.391460i
$841$	−61.5596			−2.12274
$842$	−6.98264	−	6.98264i	−0.240638	−	0.240638i
$843$		−	7.20721i		−	0.248230i
$844$	21.8175			0.750988
$845$		0			0
$846$	3.98031			0.136846
$847$			38.6922i			1.32948i
$848$	−6.41942	−	6.41942i	−0.220444	−	0.220444i
$849$	8.26193			0.283549
$850$	5.05841	−	2.96599i	0.173502	−	0.101733i
$851$	−1.75742	+	1.75742i	−0.0602437	+	0.0602437i
$852$	11.0702			0.379258
$853$			17.6392i			0.603954i	0.953315	+	0.301977i	$0.0976465\pi$
$853$			17.6392i			0.603954i	−0.953315	+	0.301977i	$0.902353\pi$
$854$			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	$-0.201340\pi$
$857$	6.30427	+	6.30427i	0.215350	+	0.215350i	−0.591186	+	0.806535i	$0.701340\pi$
$858$		0			0
$859$		−	29.2307i		−	0.997338i	−0.866793	−	0.498669i	$-0.833822\pi$
$859$		−	29.2307i		−	0.997338i	0.866793	−	0.498669i	$-0.166178\pi$
$860$	−5.20190	−	6.73228i	−0.177383	−	0.229569i
$861$	1.91437			0.0652416
$862$	5.82905	+	5.82905i	0.198538	+	0.198538i
$863$	−15.7688			−0.536775			−0.268387	−	0.963311i	$-0.586491\pi$
$863$	−15.7688			−0.536775			−0.268387	+	0.963311i	$0.586491\pi$
$864$	16.9825	+	16.9825i	0.577758	+	0.577758i
$865$	−10.5733	−	13.6840i	−0.359504	−	0.465269i
$866$	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
$873$	−14.9657			−0.506511
$874$		−	3.66360i		−	0.123923i
$875$	−15.3421	+	38.1218i	−0.518658	+	1.28875i
$876$	3.94269	−	3.94269i	0.133211	−	0.133211i
$877$			44.7226i			1.51018i	0.655623	+	0.755088i	$0.272406\pi$
$877$			44.7226i			1.51018i	−0.655623	+	0.755088i	$0.727594\pi$
$878$			6.76187i			0.228202i
$879$	−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	$-0.114075\pi$
$882$	−6.80168			−0.229024
$883$	5.33747	−	5.33747i	0.179620	−	0.179620i	−0.611570	−	0.791190i	$-0.709462\pi$
$883$	5.33747	−	5.33747i	0.179620	−	0.179620i	0.791190	+	0.611570i	$0.209462\pi$
$884$		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	−0.949665	−	0.313266i	$-0.898577\pi$
$887$	−18.9536	+	18.9536i	−0.636399	+	0.636399i	0.313266	+	0.949665i	$0.398577\pi$
$888$	−2.26391	+	2.26391i	−0.0759719	+	0.0759719i
$889$	21.5706	+	21.5706i	0.723454	+	0.723454i
$890$	−2.95177	+	2.28077i	−0.0989435	+	0.0764517i
$891$	0.886453	+	0.886453i	0.0296973	+	0.0296973i
$892$	17.4639			0.584736
$893$	14.7531	+	14.7531i	0.493694	+	0.493694i
$894$	−7.80417			−0.261010
$895$	4.65118	−	36.2708i	0.155472	−	1.21240i
$896$			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
$902$			0.188119i			0.00626368i
$903$	−7.48895			−0.249217
$904$	21.7370	−	21.7370i	0.722962	−	0.722962i
$905$	−40.0082	−	5.13044i	−1.32992	−	0.170542i
$906$	2.17773			0.0723503
$907$	28.6677	+	28.6677i	0.951895	+	0.951895i	0.998895	−	0.0470002i	$-0.0149661\pi$
$907$	28.6677	+	28.6677i	0.951895	+	0.951895i	−0.0470002	+	0.998895i	$0.514966\pi$
$908$		−	25.6487i		−	0.851181i
$909$	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	$0.457687\pi$
$912$			13.3709i			0.442755i
$913$	−1.04022	−	1.04022i	−0.0344262	−	0.0344262i
$914$	−0.408720			−0.0135193
$915$	10.3133	−	7.96885i	0.340946	−	0.263442i
$916$	27.4267	−	27.4267i	0.906205	−	0.906205i
$917$	−5.05044			−0.166780
$918$		−	5.64189i		−	0.186210i
$919$			2.12738i			0.0701759i	0.999384	+	0.0350879i	$0.0111711\pi$
$919$			2.12738i			0.0701759i	−0.999384	+	0.0350879i	$0.988829\pi$
$920$	−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
$925$	−8.87925	−	2.31533i	−0.291948	−	0.0761276i
$926$	3.13907			0.103156
$927$	6.72463	+	6.72463i	0.220866	+	0.220866i
$928$	−47.5087			−1.55955
$929$	−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	$0.856021\pi$
$930$	−7.01603	−	0.899699i	−0.230065	−	0.0295023i
$931$	−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	−0.366135	−	0.930562i	$-0.619319\pi$
$937$	17.2774	−	17.2774i	0.564427	−	0.564427i	0.930562	+	0.366135i	$0.119319\pi$
$938$	22.2331			0.725938
$939$		−	32.4398i		−	1.05863i
$940$	1.90248	−	14.8359i	0.0620521	−	0.483894i
$941$	24.2129	−	24.2129i	0.789319	−	0.789319i	−0.192063	−	0.981383i	$-0.561518\pi$
$941$	24.2129	−	24.2129i	0.789319	−	0.789319i	0.981383	+	0.192063i	$0.0615179\pi$
$942$			6.48929i			0.211433i
$943$			0.750068i			0.0244256i
$944$	−19.0996	+	19.0996i	−0.621640	+	0.621640i
$945$	24.1744	+	31.2864i	0.786393	+	1.01775i
$946$		−	0.735915i		−	0.0239267i
$947$	−8.30091			−0.269743			−0.134872	−	0.990863i	$-0.543062\pi$
$947$	−8.30091			−0.269743			−0.134872	+	0.990863i	$0.543062\pi$
$948$	−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	$-0.725303\pi$
$953$	3.38386	−	3.38386i	0.109614	−	0.109614i	0.759787	+	0.650173i	$0.225303\pi$
$954$	2.58403	+	2.58403i	0.0836611	+	0.0836611i
$955$	−1.47640	+	11.5132i	−0.0477750	+	0.372559i
$956$	−25.6423	−	25.6423i	−0.829331	−	0.829331i
$957$	6.15418			0.198936
$958$	3.30507	+	3.30507i	0.106782	+	0.106782i
$959$	−45.3100			−1.46314
$960$	4.53592	−	3.50482i	0.146396	−	0.113118i
$961$		−	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
$967$		−	8.78782i		−	0.282597i	−0.989967	−	0.141299i	$-0.954872\pi$
$967$		−	8.78782i		−	0.282597i	0.989967	−	0.141299i	$-0.0451278\pi$
$968$	−19.5291			−0.627688
$969$	8.64837	−	8.64837i	0.277826	−	0.277826i
$970$	0.993666	−	7.74880i	0.0319047	−	0.248799i
$971$	−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
$973$			23.5289i			0.754302i
$974$	−3.04192			−0.0974695
$975$		0			0
$976$	16.0894			0.515010
$977$			18.6725i			0.597387i	0.954349	+	0.298693i	$0.0965508\pi$
$977$			18.6725i			0.597387i	−0.954349	+	0.298693i	$0.903449\pi$
$978$	−0.0433421	−	0.0433421i	−0.00138593	−	0.00138593i
$979$	2.32277			0.0742360
$980$	−3.25101	+	25.3521i	−0.103850	+	0.809842i
$981$	4.77930	−	4.77930i	0.152591	−	0.152591i
$982$	7.31648			0.233478
$983$			6.62470i			0.211295i	0.994404	+	0.105648i	$0.0336915\pi$
$983$			6.62470i			0.211295i	−0.994404	+	0.105648i	$0.966308\pi$
$984$			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
$990$	−1.27147	+	0.982439i	−0.0404099	+	0.0312240i
$991$	−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
$993$	6.59853			0.209398
$994$	−8.60489	−	8.60489i	−0.272931	−	0.272931i
$995$	−2.23267	+	17.4108i	−0.0707805	+	0.551960i
$996$	−2.49794	−	2.49794i	−0.0791504	−	0.0791504i
$997$	31.9653	−	31.9653i	1.01235	−	1.01235i	0.0124293	−	0.999923i	$-0.496044\pi$
$997$	31.9653	−	31.9653i	1.01235	−	1.01235i	0.999923	−	0.0124293i	$-0.00395647\pi$
$998$	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.f.e.408.5		20
5.2	odd	4		845.2.k.e.577.6		20
13.2	odd	12		845.2.o.g.488.3		20
13.3	even	3		845.2.t.f.188.3		20
13.4	even	6		845.2.t.g.418.3		20
13.5	odd	4		845.2.k.d.268.5		20
13.6	odd	12		845.2.o.f.258.3		20
13.7	odd	12		845.2.o.e.258.3		20
13.8	odd	4		845.2.k.e.268.6		20
13.9	even	3		65.2.t.a.28.3	yes	20
13.10	even	6		845.2.t.e.188.3		20
13.11	odd	12		65.2.o.a.33.3	yes	20
13.12	even	2		845.2.f.d.408.6		20
39.11	even	12		585.2.cf.a.163.3		20
39.35	odd	6		585.2.dp.a.28.3		20
65.2	even	12		845.2.t.g.657.3		20
65.7	even	12		845.2.t.f.427.3		20
65.9	even	6		325.2.x.b.93.3		20
65.12	odd	4		845.2.k.d.577.5		20
65.17	odd	12		845.2.o.g.587.3		20
65.22	odd	12		65.2.o.a.2.3	✓	20
65.24	odd	12		325.2.s.b.293.3		20
65.32	even	12		845.2.t.e.427.3		20
65.37	even	12		65.2.t.a.7.3	yes	20
65.42	odd	12		845.2.o.e.357.3		20
65.47	even	4	inner	845.2.f.e.437.6		20
65.48	odd	12		325.2.s.b.132.3		20
65.57	even	4		845.2.f.d.437.5		20
65.62	odd	12		845.2.o.f.357.3		20
65.63	even	12		325.2.x.b.7.3		20
195.152	even	12		585.2.cf.a.262.3		20
195.167	odd	12		585.2.dp.a.397.3		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.3	✓	20	65.22	odd	12
65.2.o.a.33.3	yes	20	13.11	odd	12
65.2.t.a.7.3	yes	20	65.37	even	12
65.2.t.a.28.3	yes	20	13.9	even	3
325.2.s.b.132.3		20	65.48	odd	12
325.2.s.b.293.3		20	65.24	odd	12
325.2.x.b.7.3		20	65.63	even	12
325.2.x.b.93.3		20	65.9	even	6
585.2.cf.a.163.3		20	39.11	even	12
585.2.cf.a.262.3		20	195.152	even	12
585.2.dp.a.28.3		20	39.35	odd	6
585.2.dp.a.397.3		20	195.167	odd	12
845.2.f.d.408.6		20	13.12	even	2
845.2.f.d.437.5		20	65.57	even	4
845.2.f.e.408.5		20	1.1	even	1	trivial
845.2.f.e.437.6		20	65.47	even	4	inner
845.2.k.d.268.5		20	13.5	odd	4
845.2.k.d.577.5		20	65.12	odd	4
845.2.k.e.268.6		20	13.8	odd	4
845.2.k.e.577.6		20	5.2	odd	4
845.2.o.e.258.3		20	13.7	odd	12
845.2.o.e.357.3		20	65.42	odd	12
845.2.o.f.258.3		20	13.6	odd	12
845.2.o.f.357.3		20	65.62	odd	12
845.2.o.g.488.3		20	13.2	odd	12
845.2.o.g.587.3		20	65.17	odd	12
845.2.t.e.188.3		20	13.10	even	6
845.2.t.e.427.3		20	65.32	even	12
845.2.t.f.188.3		20	13.3	even	3
845.2.t.f.427.3		20	65.7	even	12
845.2.t.g.418.3		20	13.4	even	6
845.2.t.g.657.3		20	65.2	even	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.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-0.493902i q^{2} +(-0.664960 - 0.664960i) q^{3} +1.75606 q^{4} +(-0.284413 + 2.21791i) q^{5} +(-0.328425 + 0.328425i) q^{6} -3.67549 q^{7} -1.85513i q^{8} -2.11566i q^{9} +O(q^{10})\)	\(q-0.493902i q^{2} +(-0.664960 - 0.664960i) q^{3} +1.75606 q^{4} +(-0.284413 + 2.21791i) q^{5} +(-0.328425 + 0.328425i) q^{6} -3.67549 q^{7} -1.85513i 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} +(1.66394 - 1.28570i) q^{15} +2.59587 q^{16} +(-1.67902 - 1.67902i) q^{17} -1.04493 q^{18} +(-3.87304 - 3.87304i) q^{19} +(-0.499446 + 3.89478i) 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} -6.45439 q^{28} -9.51628i q^{29} +(-0.635008 - 0.821824i) q^{30} +(4.81595 - 4.81595i) q^{31} -4.99236i q^{32} +0.646700i q^{33} +(-0.829273 + 0.829273i) q^{34} +(1.04536 - 8.15190i) q^{35} -3.71522i q^{36} +1.83523 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} +(4.69233 + 0.601719i) q^{45} +(0.472962 + 0.472962i) q^{46} -3.80918 q^{47} +(-1.72615 - 1.72615i) q^{48} +6.50924 q^{49} +(-0.623107 + 2.38961i) 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} +5.15084i q^{57} -4.70011 q^{58} +(-7.35770 + 7.35770i) q^{59} +(2.92199 - 2.25776i) q^{60} +6.19808 q^{61} +(-2.37861 - 2.37861i) q^{62} +7.77608i q^{63} +2.72601 q^{64} +0.319406 q^{66} -12.2474i q^{67} +(-2.94847 - 2.94847i) q^{68} +1.27354 q^{69} +(-4.02624 - 0.516303i) q^{70} +(-4.74012 + 4.74012i) q^{71} -3.92481 q^{72} +3.37642i 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} +(-0.738299 + 5.75740i) q^{80} -1.82297 q^{81} +(-0.193431 - 0.193431i) q^{82} +2.13918 q^{83} +(4.29191 + 4.29191i) q^{84} +(4.20145 - 3.24638i) 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} -6.40483 q^{93} +1.88136i q^{94} +(9.69159 - 7.48850i) q^{95} +(-3.31972 + 3.31972i) q^{96} -7.07377i q^{97} -3.21493i q^{98} +(-1.02878 + 1.02878i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{3} - 12 q^{4} + 4 q^{6} + 4 q^{7}+O(q^{10}) \) 20 * q + 4 * q^3 - 12 * q^4 + 4 * q^6 + 4 * q^7	\( 20 q + 4 q^{3} - 12 q^{4} + 4 q^{6} + 4 q^{7} - 8 q^{10} + 8 q^{11} - 24 q^{12} + 28 q^{15} + 4 q^{16} - 14 q^{17} + 4 q^{19} - 12 q^{20} + 4 q^{21} - 32 q^{22} + 8 q^{23} - 4 q^{24} + 18 q^{25} + 4 q^{27} - 36 q^{28} + 40 q^{30} + 2 q^{34} - 20 q^{35} + 8 q^{37} - 8 q^{38} - 16 q^{40} - 38 q^{41} + 16 q^{42} - 32 q^{43} - 36 q^{44} - 6 q^{45} + 4 q^{46} - 40 q^{47} + 28 q^{48} - 36 q^{49} + 42 q^{50} - 10 q^{53} + 36 q^{54} - 16 q^{55} + 8 q^{59} + 28 q^{60} + 32 q^{61} + 4 q^{62} + 20 q^{64} - 32 q^{66} - 50 q^{68} + 32 q^{69} - 12 q^{70} - 40 q^{71} - 8 q^{72} + 4 q^{75} - 16 q^{76} - 28 q^{77} + 112 q^{80} + 28 q^{81} - 34 q^{82} + 48 q^{83} + 8 q^{84} - 2 q^{85} + 60 q^{86} - 28 q^{87} - 32 q^{88} + 12 q^{89} + 46 q^{90} - 8 q^{92} - 64 q^{93} + 40 q^{95} + 56 q^{96} + 60 q^{99}+O(q^{100}) \) 20 * q + 4 * q^3 - 12 * q^4 + 4 * q^6 + 4 * q^7 - 8 * q^10 + 8 * q^11 - 24 * q^12 + 28 * q^15 + 4 * q^16 - 14 * q^17 + 4 * q^19 - 12 * q^20 + 4 * q^21 - 32 * q^22 + 8 * q^23 - 4 * q^24 + 18 * q^25 + 4 * q^27 - 36 * q^28 + 40 * q^30 + 2 * q^34 - 20 * q^35 + 8 * q^37 - 8 * q^38 - 16 * q^40 - 38 * q^41 + 16 * q^42 - 32 * q^43 - 36 * q^44 - 6 * q^45 + 4 * q^46 - 40 * q^47 + 28 * q^48 - 36 * q^49 + 42 * q^50 - 10 * q^53 + 36 * q^54 - 16 * q^55 + 8 * q^59 + 28 * q^60 + 32 * q^61 + 4 * q^62 + 20 * q^64 - 32 * q^66 - 50 * q^68 + 32 * q^69 - 12 * q^70 - 40 * q^71 - 8 * q^72 + 4 * q^75 - 16 * q^76 - 28 * q^77 + 112 * q^80 + 28 * q^81 - 34 * q^82 + 48 * q^83 + 8 * q^84 - 2 * q^85 + 60 * q^86 - 28 * q^87 - 32 * q^88 + 12 * q^89 + 46 * q^90 - 8 * q^92 - 64 * q^93 + 40 * q^95 + 56 * q^96 + 60 * q^99

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