LMFDB - Embedded newform 845.2.o.g.587.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(258,845)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(845, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([9, 7]))

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

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

chi := DirichletCharacter("845.258");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.o (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.74735897080$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$5$ over $\Q(\zeta_{12})$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			587.1
Root			$-1.51805i$ of defining polynomial
Character	$\chi$	$=$	845.587
Dual form			845.2.o.g.488.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.759023 - 1.31467i) q^{2} +(-0.653367 - 0.175069i) q^{3} +(-0.152233 + 0.263675i) q^{4} +(-0.600231 - 2.15400i) q^{5} +(0.265763 + 0.991842i) q^{6} +(2.24723 + 1.29744i) q^{7} -2.57390 q^{8} +(-2.20184 - 1.27123i) q^{9} +(-2.37621 + 2.42404i) q^{10} +(-1.29395 + 4.82908i) q^{11} +(0.145625 - 0.145625i) q^{12} -3.93915i q^{14} +(0.0150717 + 1.51244i) q^{15} +(2.25812 + 3.91117i) q^{16} +(0.0211881 + 0.0790751i) q^{17} +3.85958i q^{18} +(-2.71143 + 0.726525i) q^{19} +(0.659330 + 0.169644i) q^{20} +(-1.24113 - 1.24113i) q^{21} +(7.33077 - 1.96427i) q^{22} +(-1.05016 + 3.91925i) q^{23} +(1.68170 + 0.450611i) q^{24} +(-4.27945 + 2.58580i) q^{25} +(2.65095 + 2.65095i) q^{27} +(-0.684205 + 0.395026i) q^{28} +(-4.31701 + 2.49243i) q^{29} +(1.97691 - 1.16779i) q^{30} +(2.32124 - 2.32124i) q^{31} +(0.854024 - 1.47921i) q^{32} +(1.69085 - 2.92863i) q^{33} +(0.0878751 - 0.0878751i) q^{34} +(1.44583 - 5.61931i) q^{35} +(0.670383 - 0.387046i) q^{36} +(-0.494934 + 0.285750i) q^{37} +(3.01318 + 3.01318i) q^{38} +(1.54493 + 5.54419i) q^{40} +(-10.0563 - 2.69458i) q^{41} +(-0.689624 + 2.57371i) q^{42} +(0.132121 - 0.0354017i) q^{43} +(-1.07633 - 1.07633i) q^{44} +(-1.41662 + 5.50579i) q^{45} +(5.94960 - 1.59419i) q^{46} +2.30053i q^{47} +(-0.790653 - 2.95076i) q^{48} +(-0.133293 - 0.230870i) q^{49} +(6.64766 + 3.66337i) q^{50} -0.0553744i q^{51} +(6.70735 - 6.70735i) q^{53} +(1.47298 - 5.49724i) q^{54} +(11.1785 - 0.111396i) q^{55} +(-5.78416 - 3.33948i) q^{56} +1.89875 q^{57} +(6.55343 + 3.78362i) q^{58} +(-0.694109 - 2.59045i) q^{59} +(-0.401085 - 0.226268i) q^{60} +(-2.74237 + 4.74992i) q^{61} +(-4.81352 - 1.28978i) q^{62} +(-3.29870 - 5.71351i) q^{63} +6.43957 q^{64} -5.13357 q^{66} +(7.89339 + 13.6718i) q^{67} +(-0.0240756 - 0.00645104i) q^{68} +(1.37228 - 2.37686i) q^{69} +(-8.48494 + 2.36440i) q^{70} +(1.98951 + 7.42495i) q^{71} +(5.66731 + 3.27202i) q^{72} +6.61894 q^{73} +(0.751333 + 0.433783i) q^{74} +(3.24874 - 0.940275i) q^{75} +(0.221202 - 0.825536i) q^{76} +(-9.17326 + 9.17326i) q^{77} +5.71054i q^{79} +(7.06928 - 7.21159i) q^{80} +(2.54575 + 4.40937i) q^{81} +(4.09050 + 15.2660i) q^{82} +3.70736i q^{83} +(0.516194 - 0.138314i) q^{84} +(0.157610 - 0.0931025i) q^{85} +(-0.146824 - 0.146824i) q^{86} +(3.25694 - 0.872695i) q^{87} +(3.33050 - 12.4296i) q^{88} +(-17.2829 - 4.63094i) q^{89} +(8.31353 - 2.31664i) q^{90} +(-0.873538 - 0.873538i) q^{92} +(-1.92300 + 1.11024i) q^{93} +(3.02443 - 1.74616i) q^{94} +(3.19242 + 5.40434i) q^{95} +(-0.816956 + 0.816956i) q^{96} +(2.68493 - 4.65043i) q^{97} +(-0.202345 + 0.350471i) q^{98} +(8.98794 - 8.98794i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 4 q^{2} - 2 q^{3} - 6 q^{4} + 6 q^{5} + 8 q^{6} + 6 q^{7} - 12 q^{8} - 12 q^{9} - 10 q^{10} + 16 q^{11} + 24 q^{12} - 12 q^{15} - 2 q^{16} - 10 q^{17} - 20 q^{19} - 14 q^{20} - 4 q^{21} + 16 q^{22}+ \cdots + 60 q^{99}+O(q^{100}) $ 20 * q + 4 * q^2 - 2 * q^3 - 6 * q^4 + 6 * q^5 + 8 * q^6 + 6 * q^7 - 12 * q^8 - 12 * q^9 - 10 * q^10 + 16 * q^11 + 24 * q^12 - 12 * q^15 - 2 * q^16 - 10 * q^17 - 20 * q^19 - 14 * q^20 - 4 * q^21 + 16 * q^22 - 2 * q^23 + 32 * q^24 - 18 * q^25 + 4 * q^27 - 6 * q^28 + 14 * q^30 + 6 * q^32 + 18 * q^33 + 2 * q^34 - 20 * q^35 + 36 * q^36 - 42 * q^37 + 8 * q^38 - 16 * q^40 - 10 * q^41 - 56 * q^42 - 22 * q^43 - 36 * q^44 - 52 * q^45 - 4 * q^46 + 28 * q^48 - 18 * q^49 - 44 * q^50 - 10 * q^53 - 48 * q^54 + 26 * q^55 + 12 * q^57 + 90 * q^58 - 16 * q^59 + 92 * q^60 - 16 * q^61 - 40 * q^62 + 32 * q^63 - 20 * q^64 - 32 * q^66 + 58 * q^67 + 28 * q^68 + 16 * q^69 - 32 * q^70 + 16 * q^71 + 66 * q^72 - 72 * q^73 - 18 * q^74 - 34 * q^75 + 64 * q^76 + 28 * q^77 + 34 * q^80 - 14 * q^81 + 22 * q^82 - 40 * q^84 + 6 * q^85 - 60 * q^86 + 62 * q^87 + 50 * q^88 - 6 * q^89 - 46 * q^90 - 8 * q^92 - 48 * q^93 + 48 * q^94 + 14 * q^95 - 56 * q^96 + 22 * q^97 - 4 * q^98 + 60 * q^99

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$	−0.759023	−	1.31467i	−0.536710	−	0.929610i	−0.999078	−	0.0429217i	$-0.986333\pi$
$2$	−0.759023	−	1.31467i	−0.536710	−	0.929610i	0.462368	−	0.886688i	$-0.347000\pi$
$3$	−0.653367	−	0.175069i	−0.377222	−	0.101076i	0.0652261	−	0.997871i	$-0.479223\pi$
$3$	−0.653367	−	0.175069i	−0.377222	−	0.101076i	−0.442448	+	0.896794i	$0.645890\pi$
$4$	−0.152233	+	0.263675i	−0.0761163	+	0.131837i
$5$	−0.600231	−	2.15400i	−0.268431	−	0.963299i
$5$	−0.600231	−	2.15400i	−0.268431	−	0.963299i
$6$	0.265763	+	0.991842i	0.108497	+	0.404918i
$7$	2.24723	+	1.29744i	0.849375	+	0.490387i	0.860440	−	0.509552i	$-0.170189\pi$
$7$	2.24723	+	1.29744i	0.849375	+	0.490387i	−0.0110652	+	0.999939i	$0.503522\pi$
$8$	−2.57390			−0.910011
$9$	−2.20184	−	1.27123i	−0.733946	−	0.423744i
$10$	−2.37621	+	2.42404i	−0.751422	+	0.766549i
$11$	−1.29395	+	4.82908i	−0.390140	+	1.45602i	0.439762	+	0.898114i	$0.355063\pi$
$11$	−1.29395	+	4.82908i	−0.390140	+	1.45602i	−0.829902	+	0.557909i	$0.811604\pi$
$12$	0.145625	−	0.145625i	0.0420383	−	0.0420383i
$13$		0			0
$13$		0			0
$14$		−	3.93915i		−	1.05278i
$15$	0.0150717	+	1.51244i	0.00389149	+	0.390509i
$16$	2.25812	+	3.91117i	0.564529	+	0.977793i
$17$	0.0211881	+	0.0790751i	0.00513887	+	0.0191785i	0.968448	−	0.249217i	$-0.0801732\pi$
$17$	0.0211881	+	0.0790751i	0.00513887	+	0.0191785i	−0.963309	+	0.268396i	$0.913507\pi$
$18$			3.85958i			0.909711i
$19$	−2.71143	+	0.726525i	−0.622045	+	0.166676i	−0.556057	−	0.831144i	$-0.687686\pi$
$19$	−2.71143	+	0.726525i	−0.622045	+	0.166676i	−0.0659876	+	0.997820i	$0.521020\pi$
$20$	0.659330	+	0.169644i	0.147431	+	0.0379335i
$21$	−1.24113	−	1.24113i	−0.270836	−	0.270836i
$22$	7.33077	−	1.96427i	1.56293	−	0.418785i
$23$	−1.05016	+	3.91925i	−0.218973	+	0.817220i	0.765756	+	0.643131i	$0.222365\pi$
$23$	−1.05016	+	3.91925i	−0.218973	+	0.817220i	−0.984730	+	0.174089i	$0.944302\pi$
$24$	1.68170	+	0.450611i	0.343276	+	0.0919805i
$25$	−4.27945	+	2.58580i	−0.855889	+	0.517159i
$26$		0			0
$27$	2.65095	+	2.65095i	0.510175	+	0.510175i
$28$	−0.684205	+	0.395026i	−0.129303	+	0.0746528i
$29$	−4.31701	+	2.49243i	−0.801649	+	0.462833i	−0.844048	−	0.536268i	$-0.819834\pi$
$29$	−4.31701	+	2.49243i	−0.801649	+	0.462833i	0.0423981	+	0.999101i	$0.486500\pi$
$30$	1.97691	−	1.16779i	0.360933	−	0.213208i
$31$	2.32124	−	2.32124i	0.416906	−	0.416906i	−0.467230	−	0.884136i	$-0.654748\pi$
$31$	2.32124	−	2.32124i	0.416906	−	0.416906i	0.884136	+	0.467230i	$0.154748\pi$
$32$	0.854024	−	1.47921i	0.150972	−	0.261490i
$33$	1.69085	−	2.92863i	0.294339	−	0.509809i
$34$	0.0878751	−	0.0878751i	0.0150705	−	0.0150705i
$35$	1.44583	−	5.61931i	0.244390	−	0.949837i
$36$	0.670383	−	0.387046i	0.111730	−	0.0645076i
$37$	−0.494934	+	0.285750i	−0.0813667	+	0.0469771i	−0.540131	−	0.841581i	$-0.681625\pi$
$37$	−0.494934	+	0.285750i	−0.0813667	+	0.0469771i	0.458765	+	0.888558i	$0.348292\pi$
$38$	3.01318	+	3.01318i	0.488802	+	0.488802i
$39$		0			0
$40$	1.54493	+	5.54419i	0.244276	+	0.876613i
$41$	−10.0563	−	2.69458i	−1.57053	−	0.420823i	−0.634554	−	0.772879i	$-0.718816\pi$
$41$	−10.0563	−	2.69458i	−1.57053	−	0.420823i	−0.935979	+	0.352056i	$0.885483\pi$
$42$	−0.689624	+	2.57371i	−0.106411	+	0.397132i
$43$	0.132121	−	0.0354017i	0.0201483	−	0.00539871i	−0.248731	−	0.968573i	$-0.580013\pi$
$43$	0.132121	−	0.0354017i	0.0201483	−	0.00539871i	0.268879	+	0.963174i	$0.413347\pi$
$44$	−1.07633	−	1.07633i	−0.162262	−	0.162262i
$45$	−1.41662	+	5.50579i	−0.211178	+	0.820755i
$46$	5.94960	−	1.59419i	0.877221	−	0.235051i
$47$			2.30053i			0.335567i	0.985824	+	0.167784i	$0.0536610\pi$
$47$			2.30053i			0.335567i	−0.985824	+	0.167784i	$0.946339\pi$
$48$	−0.790653	−	2.95076i	−0.114121	−	0.425905i
$49$	−0.133293	−	0.230870i	−0.0190418	−	0.0329814i
$50$	6.64766	+	3.66337i	0.940121	+	0.518078i
$51$		−	0.0553744i		−	0.00775397i
$52$		0			0
$53$	6.70735	−	6.70735i	0.921326	−	0.921326i	−0.0757974	−	0.997123i	$-0.524150\pi$
$53$	6.70735	−	6.70735i	0.921326	−	0.921326i	0.997123	+	0.0757974i	$0.0241502\pi$
$54$	1.47298	−	5.49724i	0.200447	−	0.748080i
$55$	11.1785	−	0.111396i	1.50731	−	0.0150206i
$56$	−5.78416	−	3.33948i	−0.772941	−	0.446257i
$57$	1.89875			0.251496
$58$	6.55343	+	3.78362i	0.860507	+	0.496814i
$59$	−0.694109	−	2.59045i	−0.0903653	−	0.337248i	0.905911	−	0.423469i	$-0.139188\pi$
$59$	−0.694109	−	2.59045i	−0.0903653	−	0.337248i	−0.996276	+	0.0862207i	$0.972521\pi$
$60$	−0.401085	−	0.226268i	−0.0517799	−	0.0292111i
$61$	−2.74237	+	4.74992i	−0.351124	+	0.608165i	−0.986447	−	0.164082i	$-0.947534\pi$
$61$	−2.74237	+	4.74992i	−0.351124	+	0.608165i	0.635322	+	0.772247i	$0.280867\pi$
$62$	−4.81352	−	1.28978i	−0.611318	−	0.163802i
$63$	−3.29870	−	5.71351i	−0.415597	−	0.719834i
$64$	6.43957			0.804946
$65$		0			0
$66$	−5.13357			−0.631899
$67$	7.89339	+	13.6718i	0.964331	+	1.67027i	0.711401	+	0.702786i	$0.248061\pi$
$67$	7.89339	+	13.6718i	0.964331	+	1.67027i	0.252930	+	0.967485i	$0.418606\pi$
$68$	−0.0240756	−	0.00645104i	−0.00291960	−	0.000782303i
$69$	1.37228	−	2.37686i	0.165203	−	0.286140i
$70$	−8.48494	+	2.36440i	−1.01414	+	0.282600i
$71$	1.98951	+	7.42495i	0.236111	+	0.881180i	0.977645	+	0.210264i	$0.0674322\pi$
$71$	1.98951	+	7.42495i	0.236111	+	0.881180i	−0.741533	+	0.670916i	$0.765901\pi$
$72$	5.66731	+	3.27202i	0.667899	+	0.385612i
$73$	6.61894			0.774688			0.387344	−	0.921935i	$-0.373393\pi$
$73$	6.61894			0.774688			0.387344	+	0.921935i	$0.373393\pi$
$74$	0.751333	+	0.433783i	0.0873407	+	0.0504262i
$75$	3.24874	−	0.940275i	0.375132	−	0.108574i
$76$	0.221202	−	0.825536i	0.0253736	−	0.0946955i
$77$	−9.17326	+	9.17326i	−1.04539	+	1.04539i
$78$		0			0
$79$			5.71054i			0.642486i	0.946997	+	0.321243i	$0.104101\pi$
$79$			5.71054i			0.642486i	−0.946997	+	0.321243i	$0.895899\pi$
$80$	7.06928	−	7.21159i	0.790369	−	0.806280i
$81$	2.54575	+	4.40937i	0.282861	+	0.489930i
$82$	4.09050	+	15.2660i	0.451720	+	1.68584i
$83$			3.70736i			0.406936i	0.979082	+	0.203468i	$0.0652213\pi$
$83$			3.70736i			0.406936i	−0.979082	+	0.203468i	$0.934779\pi$
$84$	0.516194	−	0.138314i	0.0563213	−	0.0150913i
$85$	0.157610	−	0.0931025i	0.0170952	−	0.0100984i
$86$	−0.146824	−	0.146824i	−0.0158325	−	0.0158325i
$87$	3.25694	−	0.872695i	0.349181	−	0.0935627i
$88$	3.33050	−	12.4296i	0.355032	−	1.32500i
$89$	−17.2829	−	4.63094i	−1.83198	−	0.490878i	−0.833851	−	0.551989i	$-0.813869\pi$
$89$	−17.2829	−	4.63094i	−1.83198	−	0.490878i	−0.998131	+	0.0611111i	$0.980536\pi$
$90$	8.31353	−	2.31664i	0.876323	−	0.244195i
$91$		0			0
$92$	−0.873538	−	0.873538i	−0.0910726	−	0.0910726i
$93$	−1.92300	+	1.11024i	−0.199405	+	0.115127i
$94$	3.02443	−	1.74616i	0.311946	−	0.180102i
$95$	3.19242	+	5.40434i	0.327535	+	0.554474i
$96$	−0.816956	+	0.816956i	−0.0833802	+	0.0833802i
$97$	2.68493	−	4.65043i	0.272613	−	0.472180i	−0.696917	−	0.717152i	$-0.745445\pi$
$97$	2.68493	−	4.65043i	0.272613	−	0.472180i	0.969530	+	0.244972i	$0.0787787\pi$
$98$	−0.202345	+	0.350471i	−0.0204399	+	0.0354029i
$99$	8.98794	−	8.98794i	0.903322	−	0.903322i
$100$	−0.0303375	−	1.52202i	−0.00303375	−	0.152202i
$101$	2.17443	−	1.25541i	0.216363	−	0.124918i	−0.387902	−	0.921701i	$-0.626800\pi$
$101$	2.17443	−	1.25541i	0.216363	−	0.124918i	0.604265	+	0.796783i	$0.293467\pi$
$102$	−0.0727989	+	0.0420305i	−0.00720817	+	0.00416164i
$103$	−4.71738	−	4.71738i	−0.464817	−	0.464817i	0.435414	−	0.900230i	$-0.356602\pi$
$103$	−4.71738	−	4.71738i	−0.464817	−	0.464817i	−0.900230	+	0.435414i	$0.856602\pi$
$104$		0			0
$105$	−1.92843	+	3.41835i	−0.188195	+	0.333597i
$106$	−13.9090	−	3.72690i	−1.35096	−	0.361988i
$107$	0.939155	−	3.50497i	0.0907915	−	0.338838i	−0.905556	−	0.424226i	$-0.860546\pi$
$107$	0.939155	−	3.50497i	0.0907915	−	0.338838i	0.996348	+	0.0853876i	$0.0272129\pi$
$108$	−1.10255	+	0.295427i	−0.106093	+	0.0284275i
$109$	1.58528	+	1.58528i	0.151843	+	0.151843i	0.778941	−	0.627098i	$-0.215757\pi$
$109$	1.58528	+	1.58528i	0.151843	+	0.151843i	−0.627098	+	0.778941i	$0.715757\pi$
$110$	−8.63120	−	14.6115i	−0.822953	−	1.39315i
$111$	0.373400	−	0.100052i	0.0354416	−	0.00949653i
$112$			11.7191i			1.10735i
$113$	1.48231	+	5.53206i	0.139444	+	0.520412i	0.999940	+	0.0109551i	$0.00348719\pi$
$113$	1.48231	+	5.53206i	0.139444	+	0.520412i	−0.860496	+	0.509457i	$0.829846\pi$
$114$	−1.44120	−	2.49623i	−0.134980	−	0.233793i
$115$	9.07241	−	0.0904081i	0.846006	−	0.00843060i
$116$		−	1.51772i		−	0.140916i
$117$		0			0
$118$	−2.87873	+	2.87873i	−0.265009	+	0.265009i
$119$	−0.0549806	+	0.205190i	−0.00504007	+	0.0188098i
$120$	−0.0387930	−	3.89286i	−0.00354130	−	0.355368i
$121$	−12.1195	−	6.99717i	−1.10177	−	0.636106i
$122$	8.32609			0.753809
$123$	6.09873	+	3.52110i	0.549904	+	0.317487i
$124$	0.258683	+	0.965419i	0.0232304	+	0.0866972i
$125$	8.13846	+	7.66586i	0.727926	+	0.685655i
$126$	−5.00757	+	8.67337i	−0.446110	+	0.772685i
$127$	0.786718	+	0.210801i	0.0698100	+	0.0187055i	0.293555	−	0.955942i	$-0.405162\pi$
$127$	0.786718	+	0.210801i	0.0698100	+	0.0187055i	−0.223745	+	0.974648i	$0.571828\pi$
$128$	−6.59583	−	11.4243i	−0.582994	−	1.00978i
$129$	−0.0925213			−0.00814605
$130$		0			0
$131$	−16.1062			−1.40721			−0.703604	−	0.710592i	$-0.748427\pi$
$131$	−16.1062			−1.40721			−0.703604	+	0.710592i	$0.748427\pi$
$132$	0.514804	+	0.891667i	0.0448079	+	0.0776096i
$133$	−7.03584	−	1.88525i	−0.610085	−	0.163472i
$134$	11.9825	−	20.7544i	1.03513	−	1.79290i
$135$	4.11897	−	7.30133i	0.354504	−	0.628398i
$136$	−0.0545361	−	0.203531i	−0.00467643	−	0.0174527i
$137$	−16.6601	−	9.61871i	−1.42337	−	0.821782i	−0.426783	−	0.904354i	$-0.640353\pi$
$137$	−16.6601	−	9.61871i	−1.42337	−	0.821782i	−0.996585	+	0.0825721i	$0.973687\pi$
$138$	−4.16637			−0.354665
$139$	−13.7257	−	7.92451i	−1.16419	−	0.672148i	−0.211889	−	0.977294i	$-0.567962\pi$
$139$	−13.7257	−	7.92451i	−1.16419	−	0.672148i	−0.952306	+	0.305146i	$0.901295\pi$
$140$	1.26157	+	1.23667i	0.106622	+	0.104518i
$141$	0.402752	−	1.50309i	0.0339178	−	0.126583i
$142$	8.25125	−	8.25125i	0.692430	−	0.692430i
$143$		0			0
$144$		−	11.4823i		−	0.956862i
$145$	7.95990	+	7.80282i	0.661034	+	0.647989i
$146$	−5.02393	−	8.70170i	−0.415783	−	0.720158i
$147$	0.0466709	+	0.174178i	0.00384935	+	0.0143660i
$148$		−	0.174002i		−	0.0143029i
$149$	−1.39120	+	0.372772i	−0.113972	+	0.0305387i	−0.315354	−	0.948974i	$-0.602123\pi$
$149$	−1.39120	+	0.372772i	−0.113972	+	0.0305387i	0.201382	+	0.979513i	$0.435457\pi$
$150$	−3.70202	−	3.55732i	−0.302269	−	0.290454i
$151$	−13.9253	−	13.9253i	−1.13322	−	1.13322i	−0.989638	−	0.143585i	$-0.954137\pi$
$151$	−13.9253	−	13.9253i	−1.13322	−	1.13322i	−0.143585	−	0.989638i	$-0.545863\pi$
$152$	6.97895	−	1.87000i	0.566068	−	0.151677i
$153$	0.0538699	−	0.201045i	0.00435513	−	0.0162536i
$154$	19.0225	+	5.09706i	1.53288	+	0.410733i
$155$	−6.39322	−	3.60667i	−0.513516	−	0.289695i
$156$		0			0
$157$	4.54644	+	4.54644i	0.362845	+	0.362845i	0.864859	−	0.502014i	$-0.167408\pi$
$157$	4.54644	+	4.54644i	0.362845	+	0.362845i	−0.502014	+	0.864859i	$0.667408\pi$
$158$	7.50746	−	4.33444i	0.597262	−	0.344829i
$159$	−5.55661	+	3.20811i	−0.440668	+	0.254420i
$160$	−3.69884	−	0.951700i	−0.292419	−	0.0752385i
$161$	−7.44495	+	7.44495i	−0.586744	+	0.586744i
$162$	3.86457	−	6.69363i	0.303629	−	0.525901i
$163$	−6.56789	+	11.3759i	−0.514437	+	0.891031i	0.485423	+	0.874280i	$0.338666\pi$
$163$	−6.56789	+	11.3759i	−0.514437	+	0.891031i	−0.999860	+	0.0167516i	$0.994668\pi$
$164$	2.24139	−	2.24139i	0.175023	−	0.175023i
$165$	−7.32318	−	1.88423i	−0.570109	−	0.146687i
$166$	4.87395	−	2.81398i	0.378292	−	0.218407i
$167$	−2.84503	+	1.64258i	−0.220155	+	0.127107i	−0.606022	−	0.795448i	$-0.707236\pi$
$167$	−2.84503	+	1.64258i	−0.220155	+	0.127107i	0.385867	+	0.922554i	$0.373902\pi$
$168$	3.19454	+	3.19454i	0.246464	+	0.246464i
$169$		0			0
$170$	−0.242028	−	0.136538i	−0.0185627	−	0.0104720i
$171$	6.89371	+	1.84716i	0.527175	+	0.141256i
$172$	−0.0107786	+	0.0402263i	−0.000821860	+	0.00306722i
$173$	−4.09367	+	1.09689i	−0.311236	+	0.0833953i	−0.411056	−	0.911610i	$-0.634840\pi$
$173$	−4.09367	+	1.09689i	−0.311236	+	0.0833953i	0.0998202	+	0.995005i	$0.468173\pi$
$174$	−3.61940	−	3.61940i	−0.274386	−	0.274386i
$175$	−12.9718	+	0.258559i	−0.980579	+	0.0195452i
$176$	−21.8093	+	5.84377i	−1.64393	+	0.440491i
$177$			1.81403i			0.136351i
$178$	7.02997	+	26.2362i	0.526919	+	1.96649i
$179$	6.98083	+	12.0912i	0.521772	+	0.903735i	0.999679	+	0.0253252i	$0.00806213\pi$
$179$	6.98083	+	12.0912i	0.521772	+	0.903735i	−0.477907	+	0.878410i	$0.658605\pi$
$180$	−1.23608	−	1.21169i	−0.0921321	−	0.0903139i
$181$		−	8.64775i		−	0.642782i	−0.946947	−	0.321391i	$-0.895850\pi$
$181$		−	8.64775i		−	0.642782i	0.946947	−	0.321391i	$-0.104150\pi$
$182$		0			0
$183$	2.62334	−	2.62334i	0.193923	−	0.193923i
$184$	2.70301	−	10.0878i	0.199268	−	0.743680i
$185$	0.912582	+	0.894573i	0.0670944	+	0.0657703i
$186$	2.91920	+	1.68540i	0.214046	+	0.123579i
$187$	−0.409276			−0.0299292
$188$	−0.606592	−	0.350216i	−0.0442402	−	0.0255421i
$189$	2.51785	+	9.39675i	0.183147	+	0.683513i
$190$	4.68179	−	8.29899i	0.339653	−	0.602072i
$191$	−8.45647	+	14.6470i	−0.611889	+	1.05982i	0.379033	+	0.925383i	$0.376257\pi$
$191$	−8.45647	+	14.6470i	−0.611889	+	1.05982i	−0.990922	+	0.134439i	$0.957077\pi$
$192$	−4.20740	−	1.12737i	−0.303643	−	0.0813609i
$193$	4.27780	+	7.40936i	0.307923	+	0.533338i	0.977908	−	0.209037i	$-0.0670329\pi$
$193$	4.27780	+	7.40936i	0.307923	+	0.533338i	−0.669985	+	0.742375i	$0.733700\pi$
$194$	−8.15169			−0.585257
$195$		0			0
$196$	0.0811660			0.00579757
$197$	3.82842	+	6.63101i	0.272764	+	0.472440i	0.969568	−	0.244820i	$-0.0787290\pi$
$197$	3.82842	+	6.63101i	0.272764	+	0.472440i	−0.696805	+	0.717261i	$0.745396\pi$
$198$	−18.6382	−	4.99409i	−1.32456	−	0.354915i
$199$	−7.66380	+	13.2741i	−0.543272	+	0.940975i	0.455441	+	0.890266i	$0.349481\pi$
$199$	−7.66380	+	13.2741i	−0.543272	+	0.940975i	−0.998713	+	0.0507092i	$0.983852\pi$
$200$	11.0149	−	6.65558i	0.778869	−	0.470621i
$201$	−2.76378	−	10.3146i	−0.194942	−	0.727533i
$202$	−3.30088	−	1.90576i	−0.232249	−	0.134089i
$203$	−12.9351			−0.907868
$204$	0.0146008	+	0.00842979i	0.00102226	+	0.000590203i
$205$	0.231976	+	23.2787i	0.0162019	+	1.62585i
$206$	−2.62118	+	9.78238i	−0.182626	+	0.681570i
$207$	7.29455	−	7.29455i	0.507006	−	0.507006i
$208$		0			0
$209$		−	14.0338i		−	0.970739i
$210$	5.95771	−	0.0593697i	0.411121	−	0.00409690i
$211$	−9.91788	−	17.1783i	−0.682775	−	1.18260i	−0.974130	−	0.225986i	$-0.927440\pi$
$211$	−9.91788	−	17.1783i	−0.682775	−	1.18260i	0.291355	−	0.956615i	$-0.405894\pi$
$212$	0.747481	+	2.78964i	0.0513372	+	0.191593i
$213$		−	5.19952i		−	0.356265i
$214$	−5.32071	+	1.42568i	−0.363716	+	0.0974575i
$215$	−0.155559	−	0.263340i	−0.0106090	−	0.0179596i
$216$	−6.82328	−	6.82328i	−0.464265	−	0.464265i
$217$	8.22803	−	2.20469i	0.558555	−	0.149664i
$218$	0.880853	−	3.28739i	0.0596589	−	0.222650i
$219$	−4.32460	−	1.15877i	−0.292229	−	0.0783025i
$220$	−1.67236	+	2.96445i	−0.112751	+	0.199863i
$221$		0			0
$222$	−0.414955	−	0.414955i	−0.0278499	−	0.0278499i
$223$	−16.4311	+	9.48653i	−1.10031	+	0.635265i	−0.936303	−	0.351194i	$-0.885776\pi$
$223$	−16.4311	+	9.48653i	−1.10031	+	0.635265i	−0.164008	+	0.986459i	$0.552442\pi$
$224$	3.83838	−	2.21609i	0.256463	−	0.148069i
$225$	12.7098	−	0.253336i	0.847319	−	0.0168890i
$226$	6.14771	−	6.14771i	0.408939	−	0.408939i
$227$	13.4794	−	23.3469i	0.894656	−	1.54959i	0.0604265	−	0.998173i	$-0.480754\pi$
$227$	13.4794	−	23.3469i	0.894656	−	1.54959i	0.834230	−	0.551417i	$-0.185913\pi$
$228$	−0.289052	+	0.500652i	−0.0191429	+	0.0331565i
$229$	−11.1801	+	11.1801i	−0.738799	+	0.738799i	−0.972346	−	0.233547i	$-0.924967\pi$
$229$	−11.1801	+	11.1801i	−0.738799	+	0.738799i	0.233547	+	0.972346i	$0.424967\pi$
$230$	−7.00503	−	11.8586i	−0.461898	−	0.781931i
$231$	7.59946	−	4.38755i	0.500008	−	0.288680i
$232$	11.1116	−	6.41527i	0.729510	−	0.421183i
$233$	−6.75797	−	6.75797i	−0.442729	−	0.442729i	0.450199	−	0.892928i	$-0.351353\pi$
$233$	−6.75797	−	6.75797i	−0.442729	−	0.442729i	−0.892928	+	0.450199i	$0.851353\pi$
$234$		0			0
$235$	4.95535	−	1.38085i	0.323251	−	0.0900767i
$236$	0.788702	+	0.211332i	0.0513401	+	0.0137565i
$237$	0.999740	−	3.73108i	0.0649401	−	0.242360i
$238$	0.311489	−	0.0834631i	0.0201908	−	0.00541011i
$239$	1.98766	+	1.98766i	0.128571	+	0.128571i	0.768464	−	0.639893i	$-0.221021\pi$
$239$	1.98766	+	1.98766i	0.128571	+	0.128571i	−0.639893	+	0.768464i	$0.721021\pi$
$240$	−5.88136	+	3.47420i	−0.379640	+	0.224259i
$241$	2.65141	−	0.710443i	0.170792	−	0.0457637i	−0.172409	−	0.985025i	$-0.555155\pi$
$241$	2.65141	−	0.710443i	0.170792	−	0.0457637i	0.343202	+	0.939262i	$0.388489\pi$
$242$			21.2441i			1.36562i
$243$	−3.80231	−	14.1904i	−0.243918	−	0.910315i
$244$	−0.834956	−	1.44619i	−0.0534526	−	0.0925826i
$245$	−0.417287	+	0.425688i	−0.0266595	+	0.0271962i
$246$		−	10.6904i		−	0.681595i
$247$		0			0
$248$	−5.97463	+	5.97463i	−0.379389	+	0.379389i
$249$	0.649045	−	2.42227i	0.0411316	−	0.153505i
$250$	3.90077	−	16.5179i	0.246706	−	1.04469i
$251$	−2.45414	−	1.41690i	−0.154904	−	0.0894337i	0.420545	−	0.907272i	$-0.361839\pi$
$251$	−2.45414	−	1.41690i	−0.154904	−	0.0894337i	−0.575448	+	0.817838i	$0.695172\pi$
$252$	2.00868			0.126535
$253$	−17.5675	−	10.1426i	−1.10446	−	0.637661i
$254$	−0.320005	−	1.19428i	−0.0200789	−	0.0749355i
$255$	−0.119277	+	0.0332374i	−0.00746939	+	0.00208141i
$256$	−3.57321	+	6.18898i	−0.223325	+	0.386811i
$257$	−19.3784	−	5.19242i	−1.20879	−	0.323894i	−0.402502	−	0.915419i	$-0.631859\pi$
$257$	−19.3784	−	5.19242i	−1.20879	−	0.323894i	−0.806287	+	0.591525i	$0.798526\pi$
$258$	0.0702258	+	0.121635i	0.00437207	+	0.00757265i
$259$	−1.48298			−0.0921478
$260$		0			0
$261$	12.6738			0.784490
$262$	12.2250	+	21.1743i	0.755264	+	1.30815i
$263$	−9.10077	−	2.43854i	−0.561177	−	0.150367i	−0.0329302	−	0.999458i	$-0.510484\pi$
$263$	−9.10077	−	2.43854i	−0.561177	−	0.150367i	−0.528247	+	0.849091i	$0.677151\pi$
$264$	−4.35207	+	7.53801i	−0.267851	+	0.463932i
$265$	−18.4736	−	10.4217i	−1.13482	−	0.640199i
$266$	2.86189	+	10.6807i	0.175474	+	0.654878i
$267$	10.4813	+	6.05140i	0.641447	+	0.370340i
$268$	−4.80653			−0.293605
$269$	2.78417	+	1.60744i	0.169754	+	0.0980075i	0.582470	−	0.812852i	$-0.302086\pi$
$269$	2.78417	+	1.60744i	0.169754	+	0.0980075i	−0.412716	+	0.910860i	$0.635420\pi$
$270$	−12.7252	+	0.126809i	−0.774431	+	0.00771734i
$271$	3.93065	−	14.6694i	0.238770	−	0.891102i	−0.737643	−	0.675191i	$-0.764061\pi$
$271$	3.93065	−	14.6694i	0.238770	−	0.891102i	0.976413	−	0.215911i	$-0.0692721\pi$
$272$	−0.261431	+	0.261431i	−0.0158516	+	0.0158516i
$273$		0			0
$274$			29.2033i			1.76424i
$275$	−6.94964	−	24.0117i	−0.419079	−	1.44796i
$276$	0.417811	+	0.723671i	0.0251493	+	0.0435598i
$277$	2.76028	+	10.3015i	0.165849	+	0.618956i	0.997930	+	0.0643031i	$0.0204824\pi$
$277$	2.76028	+	10.3015i	0.165849	+	0.618956i	−0.832082	+	0.554653i	$0.812851\pi$
$278$			24.0595i			1.44300i
$279$	−8.06181	+	2.16016i	−0.482648	+	0.129325i
$280$	−3.72143	+	14.4635i	−0.222398	+	0.864362i
$281$	12.7630	+	12.7630i	0.761379	+	0.761379i	0.976572	−	0.215193i	$-0.0690380\pi$
$281$	12.7630	+	12.7630i	0.761379	+	0.761379i	−0.215193	+	0.976572i	$0.569038\pi$
$282$	−2.28176	+	0.611396i	−0.135877	+	0.0364081i
$283$	−1.49018	+	5.56143i	−0.0885820	+	0.330592i	−0.995968	−	0.0897050i	$-0.971408\pi$
$283$	−1.49018	+	5.56143i	−0.0885820	+	0.330592i	0.907386	+	0.420297i	$0.138074\pi$
$284$	−2.26064	−	0.605736i	−0.134144	−	0.0359438i
$285$	−1.13969	−	4.08991i	−0.0675093	−	0.242266i
$286$		0			0
$287$	−19.1028	−	19.1028i	−1.12760	−	1.12760i
$288$	−3.76084	+	2.17132i	−0.221610	+	0.127946i
$289$	14.7166	−	8.49665i	0.865684	−	0.499803i
$290$	4.21636	−	16.3871i	0.247593	−	0.962286i
$291$	−2.56839	+	2.56839i	−0.150562	+	0.150562i
$292$	−1.00762	+	1.74525i	−0.0589664	+	0.102133i
$293$	−1.59804	+	2.76788i	−0.0933583	+	0.161701i	−0.908922	−	0.416966i	$-0.863094\pi$
$293$	−1.59804	+	2.76788i	−0.0933583	+	0.161701i	0.815564	+	0.578667i	$0.196427\pi$
$294$	0.193562	−	0.193562i	0.0112888	−	0.0112888i
$295$	−5.16321	+	3.04998i	−0.300614	+	0.177577i
$296$	1.27391	−	0.735493i	0.0740446	−	0.0427497i
$297$	−16.2318	+	9.37145i	−0.941867	+	0.543787i
$298$	1.54603	+	1.54603i	0.0895590	+	0.0895590i
$299$		0			0
$300$	−0.246638	+	0.999751i	−0.0142396	+	0.0577207i
$301$	0.342839	+	0.0918633i	0.0197609	+	0.00529491i
$302$	−7.73749	+	28.8767i	−0.445243	+	1.66167i
$303$	−1.64048	+	0.439566i	−0.0942432	+	0.0252524i
$304$	−8.96429	−	8.96429i	−0.514137	−	0.514137i
$305$	11.8774	+	3.05602i	0.680098	+	0.174987i
$306$	−0.305196	+	0.0817771i	−0.0174469	+	0.00467488i
$307$		−	24.2740i		−	1.38539i	−0.721231	−	0.692695i	$-0.756423\pi$
$307$		−	24.2740i		−	1.38539i	0.721231	−	0.692695i	$-0.243577\pi$
$308$	−1.02229	−	3.81522i	−0.0582501	−	0.217393i
$309$	2.25631	+	3.90804i	0.128357	+	0.222321i
$310$	0.111037	+	11.1425i	0.00630648	+	0.632852i
$311$			16.9053i			0.958614i	0.877647	+	0.479307i	$0.159112\pi$
$311$			16.9053i			0.958614i	−0.877647	+	0.479307i	$0.840888\pi$
$312$		0			0
$313$	−8.40997	+	8.40997i	−0.475359	+	0.475359i	−0.903644	−	0.428285i	$-0.859118\pi$
$313$	−8.40997	+	8.40997i	−0.475359	+	0.475359i	0.428285	+	0.903644i	$0.359118\pi$
$314$	2.52620	−	9.42790i	0.142562	−	0.532047i
$315$	−10.3269	+	10.5348i	−0.581856	+	0.593570i
$316$	−1.50573	−	0.869331i	−0.0847037	−	0.0489037i
$317$	−11.9484			−0.671087			−0.335543	−	0.942025i	$-0.608920\pi$
$317$	−11.9484			−0.671087			−0.335543	+	0.942025i	$0.608920\pi$
$318$	8.43520	+	4.87006i	0.473022	+	0.273100i
$319$	−6.45015	−	24.0723i	−0.361139	−	1.34779i
$320$	−3.86523	−	13.8708i	−0.216073	−	0.775403i
$321$	−1.22723	+	2.12562i	−0.0684970	+	0.118640i
$322$	15.4385	+	4.13674i	0.860355	+	0.230531i
$323$	−0.114900	−	0.199013i	−0.00639321	−	0.0110734i
$324$	−1.55018			−0.0861214
$325$		0			0
$326$	19.9407			1.10442
$327$	−0.758238	−	1.31331i	−0.0419307	−	0.0726260i
$328$	25.8840	+	6.93559i	1.42920	+	0.382954i
$329$	−2.98480	+	5.16983i	−0.164558	+	0.285022i
$330$	3.08133	+	11.0577i	0.169621	+	0.608707i
$331$	5.55136	+	20.7179i	0.305130	+	1.13876i	0.932833	+	0.360308i	$0.117329\pi$
$331$	5.55136	+	20.7179i	0.305130	+	1.13876i	−0.627703	+	0.778453i	$0.716005\pi$
$332$	−0.977538	−	0.564382i	−0.0536494	−	0.0309745i
$333$	1.45302			0.0796250
$334$	4.31889	+	2.49351i	0.236319	+	0.136439i
$335$	24.7111	−	25.2086i	1.35011	−	1.37729i
$336$	2.05165	−	7.65687i	0.111927	−	0.417716i
$337$	−14.1264	+	14.1264i	−0.769514	+	0.769514i	−0.978021	−	0.208507i	$-0.933140\pi$
$337$	−14.1264	+	14.1264i	−0.769514	+	0.769514i	0.208507	+	0.978021i	$0.433140\pi$
$338$		0			0
$339$		−	3.87397i		−	0.210405i
$340$	0.000555369		0.0557310i	3.01191e−5		0.00302244i
$341$	8.20588	+	14.2130i	0.444373	+	0.769677i
$342$	−2.80408	−	10.4650i	−0.151627	−	0.565881i
$343$		−	18.8559i		−	1.01812i
$344$	−0.340067	+	0.0911205i	−0.0183352	+	0.00491289i
$345$	−5.94344	−	1.52923i	−0.319984	−	0.0823309i
$346$	4.54924	+	4.54924i	0.244569	+	0.244569i
$347$	23.7906	−	6.37467i	1.27715	−	0.342210i	0.444382	−	0.895837i	$-0.353423\pi$
$347$	23.7906	−	6.37467i	1.27715	−	0.342210i	0.832765	+	0.553627i	$0.186757\pi$
$348$	−0.265705	+	0.991626i	−0.0142433	+	0.0531567i
$349$	26.3190	+	7.05214i	1.40882	+	0.377493i	0.881504	−	0.472176i	$-0.156531\pi$
$349$	26.3190	+	7.05214i	1.40882	+	0.377493i	0.527317	+	0.849669i	$0.323198\pi$
$350$	10.1858	+	16.8574i	0.544456	+	0.901065i
$351$		0			0
$352$	6.03818	+	6.03818i	0.321836	+	0.321836i
$353$	−7.62038	+	4.39963i	−0.405592	+	0.234169i	−0.688894	−	0.724862i	$-0.741903\pi$
$353$	−7.62038	+	4.39963i	−0.405592	+	0.234169i	0.283302	+	0.959031i	$0.408570\pi$
$354$	2.38485	−	1.37689i	0.126753	−	0.0731810i
$355$	14.7992	−	8.74209i	0.785460	−	0.463982i
$356$	3.85208	−	3.85208i	0.204160	−	0.204160i
$357$	0.0718451	−	0.124439i	0.00380244	−	0.00658603i
$358$	10.5972	−	18.3549i	0.560081	−	0.970089i
$359$	11.1256	−	11.1256i	0.587186	−	0.587186i	−0.349683	−	0.936868i	$-0.613711\pi$
$359$	11.1256	−	11.1256i	0.587186	−	0.587186i	0.936868	+	0.349683i	$0.113711\pi$
$360$	3.64625	−	14.1714i	0.192174	−	0.746896i
$361$	−9.63047	+	5.56015i	−0.506867	+	0.292640i
$362$	−11.3689	+	6.56385i	−0.597537	+	0.344988i
$363$	6.69346	+	6.69346i	0.351316	+	0.351316i
$364$		0			0
$365$	−3.97289	−	14.2572i	−0.207951	−	0.746256i
$366$	−5.43999	−	1.45764i	−0.284353	−	0.0761921i
$367$	2.84144	−	10.6044i	0.148322	−	0.553545i	−0.851263	−	0.524739i	$-0.824163\pi$
$367$	2.84144	−	10.6044i	0.148322	−	0.553545i	0.999585	−	0.0288057i	$-0.00917042\pi$
$368$	−17.7002	+	4.74276i	−0.922689	+	0.247234i
$369$	18.7169	+	18.7169i	0.974365	+	0.974365i
$370$	0.483395	−	1.87874i	0.0251305	−	0.0976712i
$371$	23.7754	−	6.37060i	1.23436	−	0.330745i
$372$		−	0.676060i		−	0.0350521i
$373$	2.73825	+	10.2193i	0.141781	+	0.529135i	0.999878	+	0.0156462i	$0.00498054\pi$
$373$	2.73825	+	10.2193i	0.141781	+	0.529135i	−0.858096	+	0.513489i	$0.828353\pi$
$374$	0.310650	+	0.538062i	0.0160633	+	0.0278225i
$375$	−3.97535	−	6.43341i	−0.205286	−	0.332220i
$376$		−	5.92134i		−	0.305370i
$377$		0			0
$378$	10.4425	−	10.4425i	0.537104	−	0.537104i
$379$	−2.53694	+	9.46800i	−0.130314	+	0.486338i	−0.999973	−	0.00731411i	$-0.997672\pi$
$379$	−2.53694	+	9.46800i	−0.130314	+	0.486338i	0.869659	+	0.493652i	$0.164338\pi$
$380$	−1.91098	+	0.0190432i	−0.0980311	+	0.000976897i
$381$	−0.477111	−	0.275460i	−0.0244431	−	0.0141123i
$382$	25.6746			1.31363
$383$	22.5658	+	13.0283i	1.15306	+	0.665718i	0.949630	−	0.313373i	$-0.101459\pi$
$383$	22.5658	+	13.0283i	1.15306	+	0.665718i	0.203426	+	0.979090i	$0.434792\pi$
$384$	2.30945	+	8.61899i	0.117854	+	0.439836i
$385$	25.2653	+	14.2531i	1.28764	+	0.726407i
$386$	6.49390	−	11.2478i	0.330531	−	0.572496i
$387$	−0.335913	−	0.0900076i	−0.0170754	−	0.00457534i
$388$	0.817467	+	1.41589i	0.0415006	+	0.0718812i
$389$	32.4888			1.64725			0.823623	−	0.567138i	$-0.191950\pi$
$389$	32.4888			1.64725			0.823623	+	0.567138i	$0.191950\pi$
$390$		0			0
$391$	−0.332166			−0.0167983
$392$	0.343082	+	0.594236i	0.0173283	+	0.0300134i
$393$	10.5233	+	2.81971i	0.530830	+	0.142235i
$394$	5.81172	−	10.0662i	0.292790	−	0.507127i
$395$	12.3005	−	3.42764i	0.618906	−	0.172463i
$396$	1.00163	+	3.73815i	0.0503340	+	0.187849i
$397$	20.9451	+	12.0927i	1.05121	+	0.606914i	0.922987	−	0.384832i	$-0.125741\pi$
$397$	20.9451	+	12.0927i	1.05121	+	0.606914i	0.128219	+	0.991746i	$0.459074\pi$
$398$	23.2680			1.16632
$399$	4.26694	+	2.46352i	0.213614	+	0.123330i
$400$	−19.7770	−	10.8986i	−0.988849	−	0.544931i
$401$	8.49918	−	31.7194i	0.424429	−	1.58399i	−0.340738	−	0.940158i	$-0.610677\pi$
$401$	8.49918	−	31.7194i	0.424429	−	1.58399i	0.765167	−	0.643832i	$-0.222657\pi$
$402$	−11.4624	+	11.4624i	−0.571695	+	0.571695i
$403$		0			0
$404$			0.764454i			0.0380330i
$405$	7.96975	−	8.13019i	0.396020	−	0.403992i
$406$	9.81806	+	17.0054i	0.487262	+	0.843963i
$407$	−0.739493	−	2.75983i	−0.0366553	−	0.136799i
$408$			0.142528i			0.00705620i
$409$	13.4843	−	3.61312i	0.666758	−	0.178657i	0.0904639	−	0.995900i	$-0.471165\pi$
$409$	13.4843	−	3.61312i	0.666758	−	0.178657i	0.576294	+	0.817243i	$0.304498\pi$
$410$	30.4277	−	17.9740i	1.50271	−	0.887675i
$411$	9.20122	+	9.20122i	0.453863	+	0.453863i
$412$	1.96199	−	0.525714i	0.0966603	−	0.0259001i
$413$	1.80113	−	6.72192i	0.0886279	−	0.330764i
$414$	−15.1266	−	4.05317i	−0.743434	−	0.199203i
$415$	7.98567	−	2.22527i	0.392001	−	0.109234i
$416$		0			0
$417$	7.58055	+	7.58055i	0.371221	+	0.371221i
$418$	−18.4498	+	10.6520i	−0.902408	+	0.521006i
$419$	1.92240	−	1.10990i	0.0939155	−	0.0542221i	−0.452307	−	0.891862i	$-0.649399\pi$
$419$	1.92240	−	1.10990i	0.0939155	−	0.0542221i	0.546222	+	0.837640i	$0.316065\pi$
$420$	−0.607763	−	1.02886i	−0.0296558	−	0.0502033i
$421$	−24.4795	+	24.4795i	−1.19306	+	1.19306i	−0.216853	+	0.976204i	$0.569579\pi$
$421$	−24.4795	+	24.4795i	−1.19306	+	1.19306i	−0.976204	+	0.216853i	$0.930421\pi$
$422$	−15.0558	+	26.0774i	−0.732905	+	1.26943i
$423$	2.92451	−	5.06540i	0.142194	−	0.246288i
$424$	−17.2641	+	17.2641i	−0.838417	+	0.838417i
$425$	−0.295145	−	0.283609i	−0.0143166	−	0.0137571i
$426$	−6.83564	+	3.94656i	−0.331188	+	0.191211i
$427$	−12.3255	+	7.11613i	−0.596472	+	0.344374i
$428$	0.781202	+	0.781202i	0.0377608	+	0.0377608i
$429$		0			0
$430$	−0.228132	+	0.404389i	−0.0110015	+	0.0195014i
$431$	−1.59621	−	0.427704i	−0.0768868	−	0.0206018i	0.220171	−	0.975461i	$-0.429339\pi$
$431$	−1.59621	−	0.427704i	−0.0768868	−	0.0206018i	−0.297057	+	0.954860i	$0.596005\pi$
$432$	−4.38216	+	16.3545i	−0.210837	+	0.786854i
$433$	−14.3111	+	3.83465i	−0.687748	+	0.184281i	−0.585736	−	0.810502i	$-0.699195\pi$
$433$	−14.3111	+	3.83465i	−0.687748	+	0.184281i	−0.102012	+	0.994783i	$0.532528\pi$
$434$	−9.14370	−	9.14370i	−0.438912	−	0.438912i
$435$	−3.83470	−	6.49164i	−0.183860	−	0.311250i
$436$	−0.659331	+	0.176667i	−0.0315762	+	0.00846083i
$437$		−	11.3897i		−	0.544845i
$438$	1.75907	+	6.56494i	0.0840516	+	0.313685i
$439$	−10.9363	−	18.9422i	−0.521959	−	0.904060i	−0.999674	−	0.0255448i	$-0.991868\pi$
$439$	−10.9363	−	18.9422i	−0.521959	−	0.904060i	0.477714	−	0.878515i	$-0.341465\pi$
$440$	−28.7724	+	0.286722i	−1.37167	+	0.0136689i
$441$			0.677783i			0.0322754i
$442$		0			0
$443$	−6.14972	+	6.14972i	−0.292182	+	0.292182i	−0.837942	−	0.545760i	$-0.816241\pi$
$443$	−6.14972	+	6.14972i	−0.292182	+	0.292182i	0.545760	+	0.837942i	$0.316241\pi$
$444$	−0.0304624	+	0.113687i	−0.00144568	+	0.00539536i
$445$	0.398677	+	40.0070i	0.0188991	+	1.89651i
$446$	24.9432	+	14.4010i	1.18110	+	0.681907i
$447$	0.974228			0.0460794
$448$	14.4712	+	8.35496i	0.683701	+	0.394735i
$449$	1.20994	+	4.51557i	0.0571008	+	0.213103i	0.988581	−	0.150688i	$-0.0481489\pi$
$449$	1.20994	+	4.51557i	0.0571008	+	0.213103i	−0.931481	+	0.363791i	$0.881482\pi$
$450$	−9.98008	−	16.5168i	−0.470465	−	0.778612i
$451$	26.0247	−	45.0761i	1.22546	−	2.12255i
$452$	−1.68432	−	0.451312i	−0.0792237	−	0.0212279i
$453$	6.66043	+	11.5362i	0.312934	+	0.542018i
$454$	−40.9246			−1.92069
$455$		0			0
$456$	−4.88720			−0.228864
$457$	−15.0180	−	26.0120i	−0.702514	−	1.21679i	−0.967581	−	0.252560i	$-0.918727\pi$
$457$	−15.0180	−	26.0120i	−0.702514	−	1.21679i	0.265067	−	0.964230i	$-0.414606\pi$
$458$	23.1840	+	6.21213i	1.08332	+	0.290274i
$459$	−0.153455	+	0.265792i	−0.00716268	+	0.0124061i
$460$	−1.35728	+	2.40593i	−0.0632834	+	0.112177i
$461$	−0.680045	−	2.53796i	−0.0316729	−	0.118205i	0.948280	−	0.317436i	$-0.102822\pi$
$461$	−0.680045	−	2.53796i	−0.0316729	−	0.118205i	−0.979952	+	0.199232i	$0.936155\pi$
$462$	−11.5363	−	6.66050i	−0.536719	−	0.309875i
$463$	−25.1475			−1.16870			−0.584352	−	0.811500i	$-0.698651\pi$
$463$	−25.1475			−1.16870			−0.584352	+	0.811500i	$0.698651\pi$
$464$	−19.4966	−	11.2564i	−0.905109	−	0.522565i
$465$	3.54570	+	3.47573i	0.164428	+	0.161183i
$466$	−3.75502	+	14.0139i	−0.173948	+	0.649183i
$467$	14.9907	−	14.9907i	0.693688	−	0.693688i	−0.269354	−	0.963041i	$-0.586810\pi$
$467$	14.9907	−	14.9907i	0.693688	−	0.693688i	0.963041	+	0.269354i	$0.0868100\pi$
$468$		0			0
$469$			40.9648i			1.89158i
$470$	−5.57658	−	5.46654i	−0.257229	−	0.252152i
$471$	−2.17455	−	3.76643i	−0.100198	−	0.173548i
$472$	1.78657	+	6.66756i	0.0822335	+	0.306899i
$473$			0.683832i			0.0314426i
$474$	−5.66395	+	1.51765i	−0.260154	+	0.0697081i
$475$	9.72477	−	10.1203i	0.446203	−	0.464353i
$476$	−0.0457337	−	0.0457337i	−0.00209620	−	0.00209620i
$477$	−23.2951	+	6.24190i	−1.06661	+	0.285797i
$478$	1.10443	−	4.12178i	0.0505154	−	0.188526i
$479$	2.21157	+	0.592587i	0.101049	+	0.0270760i	0.308989	−	0.951066i	$-0.400009\pi$
$479$	2.21157	+	0.592587i	0.101049	+	0.0270760i	−0.207940	+	0.978142i	$0.566676\pi$
$480$	2.25009	+	1.26936i	0.102702	+	0.0579382i
$481$		0			0
$482$	−2.94648	−	2.94648i	−0.134208	−	0.134208i
$483$	6.16767	−	3.56090i	0.280639	−	0.162027i
$484$	3.68995	−	2.13039i	0.167725	−	0.0968361i
$485$	−11.6286	−	2.99201i	−0.528028	−	0.135860i
$486$	−15.7696	+	15.7696i	−0.715324	+	0.715324i
$487$	−2.78321	+	4.82067i	−0.126119	+	0.218445i	−0.922170	−	0.386785i	$-0.873586\pi$
$487$	−2.78321	+	4.82067i	−0.126119	+	0.218445i	0.796050	+	0.605230i	$0.206919\pi$
$488$	7.05859	−	12.2258i	0.319527	−	0.553437i
$489$	6.28282	−	6.28282i	0.284119	−	0.284119i
$490$	0.876368	+	0.225487i	0.0395903	+	0.0101865i
$491$	5.29139	−	3.05498i	0.238797	−	0.137869i	−0.375827	−	0.926690i	$-0.622641\pi$
$491$	5.29139	−	3.05498i	0.238797	−	0.137869i	0.614624	+	0.788820i	$0.289308\pi$
$492$	−1.85685	+	1.07205i	−0.0837133	+	0.0483319i
$493$	−0.288558	−	0.288558i	−0.0129960	−	0.0129960i
$494$		0			0
$495$	−24.7549	−	13.9652i	−1.11265	−	0.627689i
$496$	14.3204	+	3.83713i	0.643004	+	0.172292i
$497$	−5.16254	+	19.2669i	−0.231572	+	0.864237i
$498$	−3.67712	+	0.985281i	−0.164776	+	0.0441515i
$499$	−6.22738	−	6.22738i	−0.278776	−	0.278776i	0.553844	−	0.832620i	$-0.313160\pi$
$499$	−6.22738	−	6.22738i	−0.278776	−	0.278776i	−0.832620	+	0.553844i	$0.813160\pi$
$500$	−3.26023	+	0.978912i	−0.145802	+	0.0437783i
$501$	2.14642	−	0.575130i	0.0958948	−	0.0256949i
$502$			4.30183i			0.192000i
$503$	0.951461	+	3.55090i	0.0424236	+	0.158327i	0.983888	−	0.178785i	$-0.0572166\pi$
$503$	0.951461	+	3.55090i	0.0424236	+	0.158327i	−0.941465	+	0.337112i	$0.890550\pi$
$504$	8.49051	+	14.7060i	0.378198	+	0.655057i
$505$	−4.00930	−	3.93018i	−0.178412	−	0.174891i
$506$			30.7939i			1.36896i
$507$		0			0
$508$	−0.175347	+	0.175347i	−0.00777976	+	0.00777976i
$509$	−2.90050	+	10.8248i	−0.128563	+	0.479802i	−0.999942	−	0.0108085i	$-0.996559\pi$
$509$	−2.90050	+	10.8248i	−0.128563	+	0.479802i	0.871379	+	0.490610i	$0.163226\pi$
$510$	0.134230	+	0.131581i	0.00594380	+	0.00582650i
$511$	14.8743	+	8.58768i	0.658000	+	0.379897i
$512$	−15.5347			−0.686544
$513$	−9.11384	−	5.26188i	−0.402386	−	0.232318i
$514$	7.88233	+	29.4173i	0.347675	+	1.29754i
$515$	−7.32972	+	12.9927i	−0.322986	+	0.572529i
$516$	0.0140848	−	0.0243955i	0.000620047	−	0.00107395i
$517$	−11.1095	−	2.97677i	−0.488593	−	0.130918i
$518$	1.12561	+	1.94962i	0.0494567	+	0.0856615i
$519$	2.86670			0.125834
$520$		0			0
$521$	35.9604			1.57545			0.787726	−	0.616026i	$-0.211258\pi$
$521$	35.9604			1.57545			0.787726	+	0.616026i	$0.211258\pi$
$522$	−9.61972	−	16.6618i	−0.421044	−	0.729269i
$523$	8.10636	+	2.17209i	0.354467	+	0.0949790i	0.431658	−	0.902037i	$-0.357929\pi$
$523$	8.10636	+	2.17209i	0.354467	+	0.0949790i	−0.0771917	+	0.997016i	$0.524595\pi$
$524$	2.45189	−	4.24681i	0.107112	−	0.185523i
$525$	8.52064	+	2.10203i	0.371871	+	0.0917403i
$526$	3.70182	+	13.8154i	0.161407	+	0.602380i
$527$	0.232734	+	0.134369i	0.0101381	+	0.00585322i
$528$	15.2725			0.664651
$529$	5.66090	+	3.26832i	0.246126	+	0.142101i
$530$	0.320848	+	32.1969i	0.0139368	+	1.39855i
$531$	−1.76475	+	6.58612i	−0.0765835	+	0.285813i
$532$	1.56818	−	1.56818i	0.0679891	−	0.0679891i
$533$		0			0
$534$		−	18.3726i		−	0.795061i
$535$	−8.11343	+	0.0808517i	−0.350774	+	0.00349552i
$536$	−20.3168	−	35.1897i	−0.877552	−	1.51997i
$537$	−2.44426	−	9.12209i	−0.105477	−	0.393647i
$538$		−	4.88034i		−	0.210407i
$539$	1.28736	−	0.344948i	0.0554506	−	0.0148580i
$540$	1.29813	+	2.19757i	0.0558628	+	0.0945682i
$541$	−4.13066	−	4.13066i	−0.177591	−	0.177591i	0.612714	−	0.790305i	$-0.290078\pi$
$541$	−4.13066	−	4.13066i	−0.177591	−	0.177591i	−0.790305	+	0.612714i	$0.790078\pi$
$542$	−22.2688	+	5.96691i	−0.956528	+	0.256301i
$543$	−1.51396	+	5.65016i	−0.0649700	+	0.242471i
$544$	0.135064	+	0.0361903i	0.00579082	+	0.00155165i
$545$	2.46317	−	4.36624i	0.105511	−	0.187029i
$546$		0			0
$547$	−7.90229	−	7.90229i	−0.337877	−	0.337877i	0.517691	−	0.855568i	$-0.326792\pi$
$547$	−7.90229	−	7.90229i	−0.337877	−	0.337877i	−0.855568	+	0.517691i	$0.826792\pi$
$548$	5.07242	−	2.92856i	0.216683	−	0.125102i
$549$	12.0765	−	6.97237i	0.515413	−	0.297574i
$550$	−26.2924	+	27.3619i	−1.12111	+	1.16671i
$551$	9.89447	−	9.89447i	0.421519	−	0.421519i
$552$	−3.53211	+	6.11780i	−0.150337	+	0.260391i
$553$	−7.40909	+	12.8329i	−0.315067	+	0.545712i
$554$	11.4479	−	11.4479i	0.486375	−	0.486375i
$555$	−0.439639	−	0.744250i	−0.0186616	−	0.0315916i
$556$	4.17898	−	2.41274i	0.177228	−	0.102323i
$557$	10.2077	−	5.89341i	0.432513	−	0.249712i	−0.267903	−	0.963446i	$-0.586331\pi$
$557$	10.2077	−	5.89341i	0.432513	−	0.249712i	0.700417	+	0.713734i	$0.252997\pi$
$558$	8.95899	+	8.95899i	0.379264	+	0.379264i
$559$		0			0
$560$	25.2429	−	7.03416i	1.06671	−	0.297247i
$561$	0.267408	+	0.0716517i	0.0112900	+	0.00302514i
$562$	7.09170	−	26.4666i	0.299145	−	1.11643i
$563$	31.0602	−	8.32255i	1.30903	−	0.350754i	0.464172	−	0.885745i	$-0.346352\pi$
$563$	31.0602	−	8.32255i	1.30903	−	0.350754i	0.844858	+	0.534991i	$0.179685\pi$
$564$	0.335015	+	0.335015i	0.0141067	+	0.0141067i
$565$	11.0263	−	6.51341i	0.463882	−	0.274021i
$566$	8.44250	−	2.26216i	0.354865	−	0.0950858i
$567$			13.2118i			0.554845i
$568$	−5.12080	−	19.1111i	−0.214864	−	0.801883i
$569$	−4.64237	−	8.04082i	−0.194618	−	0.337089i	0.752157	−	0.658984i	$-0.229013\pi$
$569$	−4.64237	−	8.04082i	−0.194618	−	0.337089i	−0.946775	+	0.321895i	$0.895680\pi$
$570$	−4.51182	+	4.60265i	−0.188979	+	0.192784i
$571$			31.1596i			1.30399i	0.758223	+	0.651995i	$0.226068\pi$
$571$			31.1596i			1.30399i	−0.758223	+	0.651995i	$0.773932\pi$
$572$		0			0
$573$	8.08942	−	8.08942i	0.337940	−	0.337940i
$574$	−10.6144	+	39.6134i	−0.443035	+	1.65343i
$575$	−5.64028	−	19.4877i	−0.235216	−	0.812694i
$576$	−14.1789	−	8.18618i	−0.590786	−	0.341091i
$577$	−4.57285			−0.190370			−0.0951852	−	0.995460i	$-0.530344\pi$
$577$	−4.57285			−0.190370			−0.0951852	+	0.995460i	$0.530344\pi$
$578$	−22.3405	−	12.8983i	−0.929243	−	0.536499i
$579$	−1.49782	−	5.58994i	−0.0622473	−	0.232310i
$580$	−3.26916	+	0.910980i	−0.135745	+	0.0378264i
$581$	−4.81009	+	8.33132i	−0.199556	+	0.345641i
$582$	5.32605	+	1.42711i	0.220772	+	0.0591556i
$583$	23.7114	+	41.0693i	0.982025	+	1.70092i
$584$	−17.0365			−0.704975
$585$		0			0
$586$	4.85179			0.200425
$587$	−3.59590	−	6.22829i	−0.148419	−	0.257069i	0.782224	−	0.622997i	$-0.214085\pi$
$587$	−3.59590	−	6.22829i	−0.148419	−	0.257069i	−0.930643	+	0.365928i	$0.880752\pi$
$588$	−0.0530312	−	0.0142097i	−0.00218697	−	0.000585997i
$589$	−4.60743	+	7.98031i	−0.189846	+	0.328823i
$590$	7.92870	+	4.47289i	0.326420	+	0.184146i
$591$	−1.34048	−	5.00272i	−0.0551398	−	0.205785i
$592$	−2.23524	−	1.29052i	−0.0918677	−	0.0530399i
$593$	−28.0561			−1.15212			−0.576062	−	0.817406i	$-0.695411\pi$
$593$	−28.0561			−1.15212			−0.576062	+	0.817406i	$0.695411\pi$
$594$	24.6407	+	14.2263i	1.01102	+	0.583712i
$595$	0.474982	−	0.00473328i	0.0194724	−	0.000194045i
$596$	0.113496	−	0.423573i	0.00464898	−	0.0173502i
$597$	7.33116	−	7.33116i	0.300044	−	0.300044i
$598$		0			0
$599$			0.912959i			0.0373025i	0.999826	+	0.0186513i	$0.00593722\pi$
$599$			0.912959i			0.0373025i	−0.999826	+	0.0186513i	$0.994063\pi$
$600$	−8.36194	+	2.42017i	−0.341375	+	0.0988032i
$601$	−6.22691	−	10.7853i	−0.254001	−	0.439943i	0.710623	−	0.703573i	$-0.248413\pi$
$601$	−6.22691	−	10.7853i	−0.254001	−	0.439943i	−0.964624	+	0.263631i	$0.915080\pi$
$602$	−0.139453	−	0.520445i	−0.00568367	−	0.0212118i
$603$		−	40.1373i		−	1.63452i
$604$	5.79162	−	1.55186i	0.235658	−	0.0631443i
$605$	−7.79745	+	30.3052i	−0.317011	+	1.23208i
$606$	1.82305	+	1.82305i	0.0740562	+	0.0740562i
$607$	37.4512	−	10.0350i	1.52010	−	0.407309i	0.600324	−	0.799757i	$-0.295038\pi$
$607$	37.4512	−	10.0350i	1.52010	−	0.407309i	0.919774	+	0.392448i	$0.128372\pi$
$608$	−1.24094	+	4.63125i	−0.0503268	+	0.187822i
$609$	8.45138	+	2.26454i	0.342467	+	0.0917638i
$610$	−4.99757	−	17.9344i	−0.202346	−	0.726143i
$611$		0			0
$612$	0.0448098	+	0.0448098i	0.00181133	+	0.00181133i
$613$	21.3140	−	12.3057i	0.860865	−	0.497021i	−0.00343656	−	0.999994i	$-0.501094\pi$
$613$	21.3140	−	12.3057i	0.860865	−	0.497021i	0.864302	+	0.502973i	$0.167761\pi$
$614$	−31.9122	+	18.4245i	−1.28787	+	0.743553i
$615$	3.92382	−	15.2501i	0.158224	−	0.614945i
$616$	23.6110	−	23.6110i	0.951316	−	0.951316i
$617$	−7.70769	+	13.3501i	−0.310300	+	0.537455i	−0.978427	−	0.206592i	$-0.933763\pi$
$617$	−7.70769	+	13.3501i	−0.310300	+	0.537455i	0.668127	+	0.744047i	$0.267096\pi$
$618$	3.42518	−	5.93259i	0.137781	−	0.238644i
$619$	−20.7915	+	20.7915i	−0.835683	+	0.835683i	−0.988287	−	0.152604i	$-0.951234\pi$
$619$	−20.7915	+	20.7915i	−0.835683	+	0.835683i	0.152604	+	0.988287i	$0.451234\pi$
$620$	1.92424	−	1.13668i	0.0772795	−	0.0456501i
$621$	−13.1736	+	7.60581i	−0.528640	+	0.305211i
$622$	22.2249	−	12.8316i	0.891137	−	0.514498i
$623$	−32.8303	−	32.8303i	−1.31532	−	1.31532i
$624$		0			0
$625$	11.6273	−	22.1315i	0.465093	−	0.885262i
$626$	17.4397	+	4.67294i	0.697029	+	0.186768i
$627$	−2.45689	+	9.16923i	−0.0981186	+	0.366184i
$628$	−1.89090	+	0.506664i	−0.0754549	+	0.0202181i
$629$	−0.0330825	−	0.0330825i	−0.00131908	−	0.00131908i
$630$	21.6882	+	5.58030i	0.864077	+	0.222324i
$631$	−12.1738	+	3.26195i	−0.484631	+	0.129856i	−0.492858	−	0.870110i	$-0.664048\pi$
$631$	−12.1738	+	3.26195i	−0.484631	+	0.129856i	0.00822739	+	0.999966i	$0.497381\pi$
$632$		−	14.6984i		−	0.584670i
$633$	3.47263	+	12.9600i	0.138025	+	0.515115i
$634$	9.06908	+	15.7081i	0.360179	+	0.623849i
$635$	−0.0181478	−	1.82112i	−0.000720173	−	0.0722690i
$636$		−	1.95352i		−	0.0774620i
$637$		0			0
$638$	−26.7512	+	26.7512i	−1.05909	+	1.05909i
$639$	5.05825	−	18.8777i	0.200101	−	0.746789i
$640$	−20.6490	+	21.0646i	−0.816222	+	0.832653i
$641$	−8.45341	−	4.88058i	−0.333890	−	0.192771i	0.323677	−	0.946168i	$-0.395081\pi$
$641$	−8.45341	−	4.88058i	−0.333890	−	0.192771i	−0.657567	+	0.753396i	$0.728414\pi$
$642$	3.72597			0.147052
$643$	−24.0854	−	13.9057i	−0.949834	−	0.548387i	−0.0568044	−	0.998385i	$-0.518091\pi$
$643$	−24.0854	−	13.9057i	−0.949834	−	0.548387i	−0.893029	+	0.449999i	$0.851424\pi$
$644$	−0.829680	−	3.09641i	−0.0326940	−	0.122016i
$645$	0.0555341	+	0.199291i	0.00218665	+	0.00784708i
$646$	−0.174424	+	0.302111i	−0.00686261	+	0.0118864i
$647$	−17.7967	−	4.76862i	−0.699662	−	0.187474i	−0.108583	−	0.994087i	$-0.534631\pi$
$647$	−17.7967	−	4.76862i	−0.699662	−	0.187474i	−0.591079	+	0.806613i	$0.701298\pi$
$648$	−6.55251	−	11.3493i	−0.257407	−	0.445842i
$649$	13.4076			0.526296
$650$		0			0
$651$	−5.76190			−0.225826
$652$	−1.99970	−	3.46357i	−0.0783141	−	0.135644i
$653$	−7.12491	−	1.90911i	−0.278819	−	0.0747094i	0.116700	−	0.993167i	$-0.462769\pi$
$653$	−7.12491	−	1.90911i	−0.278819	−	0.0747094i	−0.395519	+	0.918458i	$0.629435\pi$
$654$	−1.15104	+	1.99366i	−0.0450093	+	0.0779583i
$655$	9.66746	+	34.6929i	0.377739	+	1.35556i
$656$	−12.1694	−	45.4167i	−0.475134	−	1.77322i
$657$	−14.5738	−	8.41420i	−0.568579	−	0.328269i
$658$	9.06214			0.353279
$659$	12.0786	+	6.97358i	0.470515	+	0.271652i	0.716455	−	0.697633i	$-0.245763\pi$
$659$	12.0786	+	6.97358i	0.470515	+	0.271652i	−0.245940	+	0.969285i	$0.579097\pi$
$660$	1.61165	−	1.64409i	0.0627334	−	0.0639963i
$661$	−0.0586648	+	0.218940i	−0.00228180	+	0.00851578i	−0.967057	−	0.254559i	$-0.918070\pi$
$661$	−0.0586648	+	0.218940i	−0.00228180	+	0.00851578i	0.964776	+	0.263074i	$0.0847365\pi$
$662$	23.0236	−	23.0236i	0.894837	−	0.894837i
$663$		0			0
$664$		−	9.54239i		−	0.370317i
$665$	0.162301	+	16.2868i	0.00629375	+	0.631575i
$666$	−1.10288	−	1.91024i	−0.0427356	−	0.0740202i
$667$	−5.23490	−	19.5369i	−0.202696	−	0.756472i
$668$		−	1.00022i		−	0.0386996i
$669$	12.3964	−	3.32160i	0.479271	−	0.128420i
$670$	−51.8972	−	13.3530i	−2.00496	−	0.515871i
$671$	−19.3893	−	19.3893i	−0.748515	−	0.748515i
$672$	−2.89584	+	0.775939i	−0.111710	+	0.0299325i
$673$	−8.70112	+	32.4730i	−0.335404	+	1.25174i	0.568027	+	0.823010i	$0.307707\pi$
$673$	−8.70112	+	32.4730i	−0.335404	+	1.25174i	−0.903431	+	0.428734i	$0.858960\pi$
$674$	29.2938	+	7.84924i	1.12835	+	0.302341i
$675$	−18.1994	−	4.48978i	−0.700495	−	0.172812i
$676$		0			0
$677$	25.1691	+	25.1691i	0.967326	+	0.967326i	0.999483	−	0.0321566i	$-0.0102375\pi$
$677$	25.1691	+	25.1691i	0.967326	+	0.967326i	−0.0321566	+	0.999483i	$0.510238\pi$
$678$	−5.09298	+	2.94044i	−0.195595	+	0.112927i
$679$	12.0673	−	6.96707i	0.463101	−	0.267372i
$680$	−0.405673	+	0.239637i	−0.0155568	+	0.00918964i
$681$	−12.8943	+	12.8943i	−0.494110	+	0.494110i
$682$	12.4569	−	21.5760i	0.477000	−	0.826187i
$683$	−15.3784	+	26.6361i	−0.588437	+	1.01920i	0.406001	+	0.913873i	$0.366923\pi$
$683$	−15.3784	+	26.6361i	−0.588437	+	1.01920i	−0.994437	+	0.105329i	$0.966410\pi$
$684$	−1.53650	+	1.53650i	−0.0587494	+	0.0587494i
$685$	−10.7188	+	41.6593i	−0.409545	+	1.59172i
$686$	−24.7893	+	14.3121i	−0.946459	+	0.546438i
$687$	9.26197	−	5.34740i	0.353366	−	0.204016i
$688$	0.436807	+	0.436807i	0.0166531	+	0.0166531i
$689$		0			0
$690$	2.50078	+	8.97436i	0.0952032	+	0.341648i
$691$	37.4215	+	10.0271i	1.42358	+	0.381447i	0.886753	−	0.462244i	$-0.152956\pi$
$691$	37.4215	+	10.0271i	1.42358	+	0.381447i	0.536828	+	0.843692i	$0.319622\pi$
$692$	0.333966	−	1.24638i	0.0126955	−	0.0473802i
$693$	31.8593	−	8.53668i	1.21024	−	0.324282i
$694$	−26.4382	−	26.4382i	−1.00358	−	1.00358i
$695$	−8.83085	+	34.3216i	−0.334973	+	1.30189i
$696$	−8.38305	+	2.24623i	−0.317759	+	0.0851432i
$697$		−	0.852297i		−	0.0322831i
$698$	−10.7055	−	39.9534i	−0.405208	−	1.51226i
$699$	3.23232	+	5.59854i	0.122258	+	0.211756i
$700$	1.90656	−	3.45970i	0.0720612	−	0.130765i
$701$		−	19.8876i		−	0.751143i	−0.926793	−	0.375571i	$-0.877447\pi$
$701$		−	19.8876i		−	0.751143i	0.926793	−	0.375571i	$-0.122553\pi$
$702$		0			0
$703$	1.13437	−	1.13437i	0.0427838	−	0.0427838i
$704$	−8.33247	+	31.0972i	−0.314042	+	1.17202i
$705$	−3.47941	+	0.0346729i	−0.131042	+	0.00130586i
$706$	11.5681	+	6.67884i	0.435371	+	0.251361i
$707$	6.51526			0.245032
$708$	−0.478314	−	0.276155i	−0.0179761	−	0.0103785i
$709$	−8.24828	−	30.7830i	−0.309771	−	1.15608i	−0.928760	−	0.370680i	$-0.879125\pi$
$709$	−8.24828	−	30.7830i	−0.309771	−	1.15608i	0.618990	−	0.785399i	$-0.287542\pi$
$710$	−22.7259	−	12.8206i	−0.852887	−	0.481147i
$711$	7.25942	−	12.5737i	0.272250	−	0.471550i
$712$	44.4844	+	11.9196i	1.66712	+	0.446705i
$713$	6.65983	+	11.5352i	0.249413	+	0.431996i
$714$	−0.218128			−0.00816325
$715$		0			0
$716$	−4.25084			−0.158861
$717$	−0.950692	−	1.64665i	−0.0355042	−	0.0614951i
$718$	−23.0710	−	6.18186i	−0.861002	−	0.230705i
$719$	−15.4818	+	26.8152i	−0.577372	+	1.00004i	0.418407	+	0.908260i	$0.362589\pi$
$719$	−15.4818	+	26.8152i	−0.577372	+	1.00004i	−0.995779	+	0.0917785i	$0.970745\pi$
$720$	−24.7330	+	6.89206i	−0.921744	+	0.256852i
$721$	−4.48053	−	16.7216i	−0.166864	−	0.622744i
$722$	14.6195	+	8.44057i	0.544081	+	0.314126i
$723$	−1.85672			−0.0690522
$724$	2.28019	+	1.31647i	0.0847427	+	0.0489262i
$725$	12.0295	−	21.8291i	0.446765	−	0.810714i
$726$	3.71918	−	13.8802i	0.138032	−	0.515141i
$727$	−16.2588	+	16.2588i	−0.603007	+	0.603007i	−0.941109	−	0.338103i	$-0.890215\pi$
$727$	−16.2588	+	16.2588i	−0.603007	+	0.603007i	0.338103	+	0.941109i	$0.390215\pi$
$728$		0			0
$729$		−	5.33729i		−	0.197678i
$730$	−15.7280	+	16.0446i	−0.582118	+	0.593836i
$731$	0.00559879	+	0.00969739i	0.000207079	+	0.000358671i
$732$	0.292350	+	1.09107i	0.0108056	+	0.0403269i
$733$			31.2515i			1.15430i	0.816638	+	0.577150i	$0.195835\pi$
$733$			31.2515i			1.15430i	−0.816638	+	0.577150i	$0.804165\pi$
$734$	−16.0980	+	4.31344i	−0.594187	+	0.159212i
$735$	0.347167	−	0.205076i	0.0128054	−	0.00756435i
$736$	4.90054	+	4.90054i	0.180636	+	0.180636i
$737$	−76.2357	+	20.4273i	−2.80818	+	0.752449i
$738$	10.3999	−	38.8131i	0.382827	−	1.42873i
$739$	−26.3668	−	7.06496i	−0.969918	−	0.259889i	−0.261125	−	0.965305i	$-0.584093\pi$
$739$	−26.3668	−	7.06496i	−0.969918	−	0.259889i	−0.708793	+	0.705416i	$0.750760\pi$
$740$	−0.374801	+	0.104441i	−0.0137780	+	0.00383934i
$741$		0			0
$742$	−26.4213	−	26.4213i	−0.969956	−	0.969956i
$743$	28.5494	−	16.4830i	1.04738	−	0.604703i	0.125463	−	0.992098i	$-0.459958\pi$
$743$	28.5494	−	16.4830i	1.04738	−	0.604703i	0.921914	+	0.387395i	$0.126625\pi$
$744$	4.94960	−	2.85765i	0.181461	−	0.104767i
$745$	1.63800	+	2.77291i	0.0600115	+	0.101591i
$746$	11.3566	−	11.3566i	0.415794	−	0.415794i
$747$	4.71292	−	8.16301i	0.172437	−	0.298669i
$748$	0.0623052	−	0.107916i	0.00227810	−	0.00394579i
$749$	6.65800	−	6.65800i	0.243278	−	0.243278i
$750$	−5.44041	+	10.1094i	−0.198656	+	0.369142i
$751$	26.8241	−	15.4869i	0.978826	−	0.565125i	0.0769103	−	0.997038i	$-0.475494\pi$
$751$	26.8241	−	15.4869i	0.978826	−	0.565125i	0.901915	+	0.431913i	$0.142161\pi$
$752$	−8.99777	+	5.19487i	−0.328115	+	0.189437i
$753$	1.35540	+	1.35540i	0.0493934	+	0.0493934i
$754$		0			0
$755$	−21.6367	+	38.3535i	−0.787440	+	1.39583i
$756$	−2.86098	−	0.766598i	−0.104053	−	0.0278809i
$757$	13.2249	−	49.3561i	0.480668	−	1.79388i	−0.118154	−	0.992995i	$-0.537698\pi$
$757$	13.2249	−	49.3561i	0.480668	−	1.79388i	0.598822	−	0.800882i	$-0.295636\pi$
$758$	14.3729	−	3.85120i	0.522046	−	0.139882i
$759$	9.70238	+	9.70238i	0.352174	+	0.352174i
$760$	−8.21697	−	13.9102i	−0.298061	−	0.504577i
$761$	−1.11809	+	0.299592i	−0.0405308	+	0.0108602i	−0.279027	−	0.960283i	$-0.590012\pi$
$761$	−1.11809	+	0.299592i	−0.0405308	+	0.0108602i	0.238497	+	0.971143i	$0.423345\pi$
$762$			0.836323i			0.0302968i
$763$	1.50569	+	5.61932i	0.0545097	+	0.203433i
$764$	−2.57470	−	4.45951i	−0.0931494	−	0.161339i
$765$	−0.465386	+	0.00463766i	−0.0168261	+	0.000167675i
$766$		−	39.5553i		−	1.42919i
$767$		0			0
$768$	3.41812	−	3.41812i	0.123341	−	0.123341i
$769$	7.82422	−	29.2004i	0.282148	−	1.05299i	−0.668750	−	0.743488i	$-0.733170\pi$
$769$	7.82422	−	29.2004i	0.282148	−	1.05299i	0.950898	−	0.309505i	$-0.100163\pi$
$770$	−0.438805	−	44.0339i	−0.0158134	−	1.58687i
$771$	11.7522	+	6.78511i	0.423243	+	0.244360i
$772$	−2.60488			−0.0937517
$773$	−6.22916	−	3.59641i	−0.224047	−	0.129354i	0.383776	−	0.923426i	$-0.374624\pi$
$773$	−6.22916	−	3.59641i	−0.224047	−	0.129354i	−0.607823	+	0.794073i	$0.707957\pi$
$774$	0.136636	+	0.509931i	0.00491127	+	0.0183291i
$775$	−3.93136	+	15.9358i	−0.141219	+	0.572432i
$776$	−6.91074	+	11.9698i	−0.248081	+	0.429689i
$777$	0.968929	+	0.259624i	0.0347601	+	0.00931395i
$778$	−24.6597	−	42.7119i	−0.884094	−	1.53130i
$779$	29.2247			1.04708
$780$		0			0
$781$	−38.4300			−1.37513
$782$	0.252122	+	0.436687i	0.00901585	+	0.0156159i
$783$	−18.0515	−	4.83688i	−0.645107	−	0.172856i
$784$	0.601981	−	1.04266i	0.0214993	−	0.0372379i
$785$	7.06412	−	12.5219i	0.252129	−	0.446927i
$786$	−4.28044	−	15.9748i	−0.152678	−	0.569804i
$787$	6.21708	+	3.58943i	0.221615	+	0.127949i	0.606698	−	0.794933i	$-0.292494\pi$
$787$	6.21708	+	3.58943i	0.221615	+	0.127949i	−0.385083	+	0.922882i	$0.625827\pi$
$788$	−2.33124			−0.0830470
$789$	5.51923	+	3.18653i	0.196490	+	0.113443i
$790$	−13.8426	−	13.5694i	−0.492497	−	0.482778i
$791$	−3.84642	+	14.3550i	−0.136763	+	0.510407i
$792$	−23.1341	+	23.1341i	−0.822034	+	0.822034i
$793$		0			0
$794$		−	36.7145i		−	1.30295i
$795$	10.2455	+	10.0433i	0.363372	+	0.356201i
$796$	−2.33336	−	4.04150i	−0.0827037	−	0.143247i
$797$	−10.1969	−	38.0553i	−0.361192	−	1.34799i	−0.872510	−	0.488596i	$-0.837509\pi$
$797$	−10.1969	−	38.0553i	−0.361192	−	1.34799i	0.511318	−	0.859391i	$-0.329157\pi$
$798$		−	7.47947i		−	0.264770i
$799$	−0.181915	+	0.0487439i	−0.00643568	+	0.00172443i
$800$	0.170193	+	8.53854i	0.00601723	+	0.301883i
$801$	32.1671	+	32.1671i	1.13657	+	1.13657i
$802$	−48.1515	+	12.9022i	−1.70029	+	0.455591i
$803$	−8.56456	+	31.9634i	−0.302237	+	1.12796i
$804$	3.14043	+	0.841474i	0.110754	+	0.0296765i
$805$	20.5051	+	11.5677i	0.722711	+	0.407710i
$806$		0			0
$807$	−1.53767	−	1.53767i	−0.0541286	−	0.0541286i
$808$	−5.59676	+	3.23129i	−0.196893	+	0.113676i
$809$	−24.2062	+	13.9754i	−0.851043	+	0.491350i	−0.861003	−	0.508600i	$-0.830163\pi$
$809$	−24.2062	+	13.9754i	−0.851043	+	0.491350i	0.00995956	+	0.999950i	$0.496830\pi$
$810$	−16.7377	−	4.30656i	−0.588103	−	0.151317i
$811$	23.2784	−	23.2784i	0.817415	−	0.817415i	−0.168317	−	0.985733i	$-0.553833\pi$
$811$	23.2784	−	23.2784i	0.817415	−	0.817415i	0.985733	+	0.168317i	$0.0538334\pi$
$812$	1.96915	−	3.41066i	0.0691035	−	0.119691i
$813$	−5.13632	+	8.89636i	−0.180138	+	0.312009i
$814$	−3.06696	+	3.06696i	−0.107497	+	0.107497i
$815$	28.4460	+	7.31907i	0.996420	+	0.256376i
$816$	0.216579	−	0.125042i	0.00758178	−	0.00437734i
$817$	−0.332517	+	0.191979i	−0.0116333	+	0.00671648i
$818$	−14.9850	−	14.9850i	−0.523937	−	0.523937i
$819$		0			0
$820$	−6.17331	−	3.48261i	−0.215582	−	0.121618i
$821$	−18.8872	−	5.06082i	−0.659169	−	0.176624i	−0.0862981	−	0.996269i	$-0.527504\pi$
$821$	−18.8872	−	5.06082i	−0.659169	−	0.176624i	−0.572871	+	0.819646i	$0.694170\pi$
$822$	5.11260	−	19.0805i	0.178322	−	0.665508i
$823$	−39.4302	+	10.5653i	−1.37445	+	0.368283i	−0.869102	−	0.494633i	$-0.835303\pi$
$823$	−39.4302	+	10.5653i	−1.37445	+	0.368283i	−0.505348	+	0.862915i	$0.668636\pi$
$824$	12.1421	+	12.1421i	0.422989	+	0.422989i
$825$	0.336958	+	16.9051i	0.0117314	+	0.588560i
$826$	−10.2042	+	2.73420i	−0.355049	+	0.0951350i
$827$		−	31.8649i		−	1.10805i	−0.832499	−	0.554026i	$-0.813091\pi$
$827$		−	31.8649i		−	1.10805i	0.832499	−	0.554026i	$-0.186909\pi$
$828$	0.812920	+	3.03386i	0.0282509	+	0.105434i
$829$	−27.6391	−	47.8724i	−0.959946	−	1.66268i	−0.722620	−	0.691246i	$-0.757062\pi$
$829$	−27.6391	−	47.8724i	−0.959946	−	1.66268i	−0.237326	−	0.971430i	$-0.576271\pi$
$830$	−8.98680	−	8.80946i	−0.311937	−	0.305781i
$831$		−	7.21389i		−	0.250247i
$832$		0			0
$833$	0.0154318	−	0.0154318i	0.000534681	−	0.000534681i
$834$	4.21208	−	15.7197i	0.145853	−	0.544329i
$835$	5.24580	+	5.14228i	0.181538	+	0.177956i
$836$	3.70036	+	2.13640i	0.127980	+	0.0738890i
$837$	12.3070			0.425390
$838$	−2.91830	−	1.68488i	−0.100811	−	0.0582032i
$839$	1.00953	+	3.76762i	0.0348528	+	0.130073i	0.981160	−	0.193195i	$-0.0618851\pi$
$839$	1.00953	+	3.76762i	0.0348528	+	0.130073i	−0.946307	+	0.323268i	$0.895218\pi$
$840$	4.96358	−	8.79850i	0.171260	−	0.303577i
$841$	−2.07559	+	3.59503i	−0.0715721	+	0.123966i
$842$	50.7629	+	13.6019i	1.74940	+	0.468751i
$843$	−6.10453	−	10.5734i	−0.210251	−	0.364166i
$844$	6.03930			0.207881
$845$		0			0
$846$	−8.87908			−0.305269
$847$	−18.1568	−	31.4485i	−0.623876	−	1.08058i
$848$	41.3796	+	11.0876i	1.42098	+	0.380751i
$849$	1.94727	−	3.37277i	0.0668301	−	0.115753i
$850$	−0.148830	+	0.603284i	−0.00510482	+	0.0206925i
$851$	−0.600167	−	2.23986i	−0.0205735	−	0.0767812i
$852$	1.37098	+	0.791536i	0.0469690	+	0.0271176i
$853$	53.5726			1.83429			0.917145	−	0.398554i	$-0.130488\pi$
$853$	53.5726			1.83429			0.917145	+	0.398554i	$0.130488\pi$
$854$	18.7107	+	10.8026i	0.640266	+	0.369658i
$855$	−0.159022	−	15.9578i	−0.00543844	−	0.545745i
$856$	−2.41729	+	9.02145i	−0.0826213	+	0.308347i
$857$	18.9164	−	18.9164i	0.646171	−	0.646171i	−0.305894	−	0.952066i	$-0.598955\pi$
$857$	18.9164	−	18.9164i	0.646171	−	0.646171i	0.952066	+	0.305894i	$0.0989554\pi$
$858$		0			0
$859$			18.1203i			0.618258i	0.951020	+	0.309129i	$0.100037\pi$
$859$			18.1203i			0.618258i	−0.951020	+	0.309129i	$0.899963\pi$
$860$	0.0931171		0.000927928i	0.00317527		3.16421e-5i
$861$	9.13685	+	15.8255i	0.311383	+	0.539331i
$862$	0.649274	+	2.42312i	0.0221144	+	0.0825320i
$863$			21.4967i			0.731757i	0.930663	+	0.365879i	$0.119232\pi$
$863$			21.4967i			0.731757i	−0.930663	+	0.365879i	$0.880768\pi$
$864$	6.18529	−	1.65734i	0.210428	−	0.0563840i
$865$	4.81986	+	8.15937i	0.163880	+	0.277427i
$866$	15.9037	+	15.9037i	0.540431	+	0.540431i
$867$	−11.1029	+	2.97500i	−0.377073	+	0.101036i
$868$	−0.671252	+	2.50515i	−0.0227838	+	0.0850303i
$869$	−27.5767	−	7.38915i	−0.935475	−	0.250660i
$870$	−5.62372	+	9.96866i	−0.190662	+	0.337969i
$871$		0			0
$872$	−4.08036	−	4.08036i	−0.138179	−	0.138179i
$873$	−11.8235	+	6.82633i	−0.400167	+	0.231036i
$874$	−14.9737	+	8.64508i	−0.506493	+	0.292424i
$875$	8.34303	+	27.7862i	0.282046	+	0.939344i
$876$	0.963883	−	0.963883i	0.0325666	−	0.0325666i
$877$	−10.6745	+	18.4889i	−0.360454	+	0.624324i	−0.988036	−	0.154226i	$-0.950711\pi$
$877$	−10.6745	+	18.4889i	−0.360454	+	0.624324i	0.627582	+	0.778551i	$0.284045\pi$
$878$	−16.6018	+	28.7551i	−0.560282	+	0.970437i
$879$	1.52867	−	1.52867i	0.0515609	−	0.0515609i
$880$	25.6781	+	43.4696i	0.865608	+	1.46536i
$881$	11.4703	−	6.62238i	0.386444	−	0.223114i	−0.294174	−	0.955752i	$-0.595045\pi$
$881$	11.4703	−	6.62238i	0.386444	−	0.223114i	0.680618	+	0.732638i	$0.261711\pi$
$882$	0.891059	−	0.514453i	0.0300035	−	0.0173225i
$883$	32.5668	+	32.5668i	1.09596	+	1.09596i	0.994878	+	0.101082i	$0.0322304\pi$
$883$	32.5668	+	32.5668i	1.09596	+	1.09596i	0.101082	+	0.994878i	$0.467770\pi$
$884$		0			0
$885$	3.90743	−	1.08884i	0.131347	−	0.0366009i
$886$	12.7526	+	3.41705i	0.428432	+	0.114798i
$887$	4.13600	−	15.4358i	0.138873	−	0.518282i	−0.861079	−	0.508472i	$-0.830211\pi$
$887$	4.13600	−	15.4358i	0.138873	−	0.518282i	0.999952	−	0.00981024i	$-0.00312275\pi$
$888$	−0.961094	+	0.257524i	−0.0322522	+	0.00864195i
$889$	1.49444	+	1.49444i	0.0501219	+	0.0501219i
$890$	52.2933	−	30.8904i	1.75287	−	1.03545i
$891$	−24.5873	+	6.58814i	−0.823705	+	0.220711i
$892$		−	5.77663i		−	0.193416i
$893$	−1.67139	−	6.23773i	−0.0559311	−	0.208738i
$894$	−0.739462	−	1.28079i	−0.0247313	−	0.0428359i
$895$	21.8543	−	22.2942i	0.730507	−	0.745213i
$896$		−	34.2308i		−	1.14357i
$897$		0			0
$898$	5.01810	−	5.01810i	0.167456	−	0.167456i
$899$	−4.23529	+	15.8063i	−0.141255	+	0.527170i
$900$	−1.86805	+	3.38981i	−0.0622682	+	0.112994i
$901$	0.672500	+	0.388268i	0.0224042	+	0.0129351i
$902$	−79.0135			−2.63086
$903$	−0.207917	−	0.120041i	−0.00691905	−	0.00399471i
$904$	−3.81532	−	14.2390i	−0.126896	−	0.473581i
$905$	−18.6273	+	5.19065i	−0.619192	+	0.172543i
$906$	10.1108	−	17.5125i	0.335910	−	0.581814i
$907$	5.07458	+	1.35973i	0.168499	+	0.0451491i	0.342082	−	0.939670i	$-0.388868\pi$
$907$	5.07458	+	1.35973i	0.168499	+	0.0451491i	−0.173583	+	0.984819i	$0.555535\pi$
$908$	4.10399	+	7.10833i	0.136196	+	0.235898i
$909$	−6.38364			−0.211732
$910$		0			0
$911$	9.49722			0.314657			0.157328	−	0.987546i	$-0.449712\pi$
$911$	9.49722			0.314657			0.157328	+	0.987546i	$0.449712\pi$
$912$	4.28760	+	7.42634i	0.141977	+	0.245911i
$913$	−17.9032	−	4.79714i	−0.592508	−	0.158762i
$914$	−22.7981	+	39.4874i	−0.754093	+	1.30613i
$915$	−7.22529	−	4.07607i	−0.238861	−	0.134751i
$916$	−1.24593	−	4.64987i	−0.0411666	−	0.153636i
$917$	−36.1945	−	20.8969i	−1.19525	−	0.690076i
$918$	0.465905			0.0153771
$919$	−45.6207	−	26.3391i	−1.50489	−	0.868847i	−0.999984	−	0.00567026i	$-0.998195\pi$
$919$	−45.6207	−	26.3391i	−1.50489	−	0.868847i	−0.504903	−	0.863176i	$-0.668472\pi$
$920$	−23.3515	+	0.232702i	−0.769875	+	0.00767194i
$921$	−4.24963	+	15.8598i	−0.140030	+	0.522599i
$922$	−2.82041	+	2.82041i	−0.0928851	+	0.0928851i
$923$		0			0
$924$			2.67171i			0.0878929i
$925$	1.37915	−	2.50265i	0.0453463	−	0.0822867i
$926$	19.0876	+	33.0606i	0.627256	+	1.08644i
$927$	4.39002	+	16.3838i	0.144187	+	0.538114i
$928$			8.51438i			0.279498i
$929$	−8.04841	+	2.15657i	−0.264060	+	0.0707546i	−0.388420	−	0.921483i	$-0.626979\pi$
$929$	−8.04841	+	2.15657i	−0.264060	+	0.0707546i	0.124360	+	0.992237i	$0.460312\pi$
$930$	1.87816	−	7.29958i	0.0615873	−	0.239363i
$931$	0.529147	+	0.529147i	0.0173421	+	0.0173421i
$932$	2.81069	−	0.753121i	0.0920671	−	0.0246693i
$933$	2.95960	−	11.0454i	0.0968931	−	0.361610i
$934$	−31.0861	−	8.32950i	−1.01717	−	0.272549i
$935$	0.245660	+	0.881582i	0.00803395	+	0.0288308i
$936$		0			0
$937$	16.3814	+	16.3814i	0.535156	+	0.535156i	0.922102	−	0.386947i	$-0.126470\pi$
$937$	16.3814	+	16.3814i	0.535156	+	0.535156i	−0.386947	+	0.922102i	$0.626470\pi$
$938$	53.8551	−	31.0933i	1.75843	−	1.01523i
$939$	6.96712	−	4.02247i	0.227363	−	0.131268i
$940$	−0.390271	+	1.51681i	−0.0127292	+	0.0494729i
$941$	24.2325	−	24.2325i	0.789956	−	0.789956i	−0.191530	−	0.981487i	$-0.561345\pi$
$941$	24.2325	−	24.2325i	0.789956	−	0.789956i	0.981487	+	0.191530i	$0.0613451\pi$
$942$	−3.30107	+	5.71762i	−0.107555	+	0.186290i
$943$	21.1215	−	36.5835i	0.687810	−	1.19132i
$944$	8.56432	−	8.56432i	0.278745	−	0.278745i
$945$	18.7293	−	11.0637i	0.609265	−	0.359901i
$946$	0.899011	−	0.519044i	0.0292294	−	0.0168756i
$947$	28.9613	−	16.7208i	0.941114	−	0.543353i	0.0508048	−	0.998709i	$-0.483821\pi$
$947$	28.9613	−	16.7208i	0.941114	−	0.543353i	0.890309	+	0.455356i	$0.150488\pi$
$948$	0.831598	+	0.831598i	0.0270091	+	0.0270091i
$949$		0			0
$950$	−20.6862	−	5.10327i	−0.671149	−	0.165572i
$951$	7.80666	+	2.09179i	0.253148	+	0.0678309i
$952$	0.141515	−	0.528140i	0.00458652	−	0.0171171i
$953$	14.5138	−	3.88895i	0.470147	−	0.125975i	−0.0159642	−	0.999873i	$-0.505082\pi$
$953$	14.5138	−	3.88895i	0.470147	−	0.125975i	0.486111	+	0.873897i	$0.338415\pi$
$954$	25.8875	+	25.8875i	0.838140	+	0.838140i
$955$	36.6256	+	9.42365i	1.18518	+	0.304942i
$956$	−0.826681	+	0.221508i	−0.0267368	+	0.00716409i
$957$			16.8573i			0.544918i
$958$	−0.899575	−	3.35726i	−0.0290640	−	0.108468i
$959$	−24.9594	−	43.2310i	−0.805982	−	1.39600i
$960$	0.0970551	+	9.73943i	0.00313244	+	0.314339i
$961$			20.2237i			0.652378i
$962$		0			0
$963$	−6.52350	+	6.52350i	−0.210217	+	0.210217i
$964$	−0.216305	+	0.807262i	−0.00696672	+	0.0260002i
$965$	13.3921	−	13.6617i	0.431107	−	0.439786i
$966$	−9.36281	−	5.40562i	−0.301243	−	0.173923i
$967$	−7.49252			−0.240943			−0.120472	−	0.992717i	$-0.538441\pi$
$967$	−7.49252			−0.240943			−0.120472	+	0.992717i	$0.538441\pi$
$968$	31.1943	+	18.0100i	1.00262	+	0.578864i
$969$	0.0402309	+	0.150144i	0.00129240	+	0.00482332i
$970$	4.89290	+	17.5588i	0.157101	+	0.563778i
$971$	−13.9303	+	24.1280i	−0.447045	+	0.774304i	−0.998192	−	0.0601036i	$-0.980857\pi$
$971$	−13.9303	+	24.1280i	−0.447045	+	0.774304i	0.551147	+	0.834408i	$0.314190\pi$
$972$	4.32048	+	1.15767i	0.138580	+	0.0371323i
$973$	−20.5632	−	35.6165i	−0.659225	−	1.14181i
$974$	8.45010			0.270759
$975$		0			0
$976$	−24.7704			−0.792880
$977$	19.4382	+	33.6679i	0.621883	+	1.07713i	0.989135	+	0.147011i	$0.0469654\pi$
$977$	19.4382	+	33.6679i	0.621883	+	1.07713i	−0.367252	+	0.930122i	$0.619701\pi$
$978$	−13.0286	−	3.49101i	−0.416609	−	0.111630i
$979$	44.7263	−	77.4683i	1.42946	−	2.47590i
$980$	−0.0487183	−	0.174832i	−0.00155625	−	0.00558479i
$981$	−1.47527	−	5.50580i	−0.0471019	−	0.175787i
$982$	−8.03257	−	4.63761i	−0.256330	−	0.147992i
$983$	−0.207440			−0.00661630			−0.00330815	−	0.999995i	$-0.501053\pi$
$983$	−0.207440			−0.00661630			−0.00330815	+	0.999995i	$0.501053\pi$
$984$	−15.6975	−	9.06297i	−0.500419	−	0.288917i
$985$	11.9853	−	12.2266i	0.381883	−	0.389571i
$986$	−0.160336	+	0.598381i	−0.00510613	+	0.0190563i
$987$	2.85525	−	2.85525i	0.0908836	−	0.0908836i
$988$		0			0
$989$			0.554993i			0.0176477i
$990$	0.429941	+	43.1443i	0.0136644	+	1.37122i
$991$	12.7480	+	22.0803i	0.404955	+	0.701402i	0.994316	−	0.106467i	$-0.0339539\pi$
$991$	12.7480	+	22.0803i	0.404955	+	0.701402i	−0.589361	+	0.807869i	$0.700621\pi$
$992$	−1.45121	−	5.41599i	−0.0460760	−	0.171958i
$993$		−	14.5083i		−	0.460407i
$994$	29.2480	−	7.83698i	0.927691	−	0.248574i
$995$	33.1924	+	8.54032i	1.05227	+	0.270746i
$996$	0.539885	+	0.539885i	0.0171069	+	0.0171069i
$997$	33.4743	−	8.96942i	1.06014	−	0.284064i	0.313706	−	0.949520i	$-0.398429\pi$
$997$	33.4743	−	8.96942i	1.06014	−	0.284064i	0.746437	+	0.665456i	$0.231763\pi$
$998$	−3.46020	+	12.9137i	−0.109531	+	0.408774i
$999$	−2.06955	−	0.554536i	−0.0654778	−	0.0175447i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.o.g.587.1		20
5.3	odd	4		845.2.t.g.418.1		20
13.2	odd	12		845.2.f.e.437.2		20
13.3	even	3		845.2.k.d.577.9		20
13.4	even	6		845.2.o.e.357.5		20
13.5	odd	4		845.2.t.f.427.1		20
13.6	odd	12		65.2.t.a.7.5	yes	20
13.7	odd	12		845.2.t.g.657.1		20
13.8	odd	4		845.2.t.e.427.5		20
13.9	even	3		845.2.o.f.357.1		20
13.10	even	6		845.2.k.e.577.2		20
13.11	odd	12		845.2.f.d.437.9		20
13.12	even	2		65.2.o.a.2.5	✓	20
39.32	even	12		585.2.dp.a.397.1		20
39.38	odd	2		585.2.cf.a.262.1		20
65.3	odd	12		845.2.f.d.408.2		20
65.8	even	4		845.2.o.f.258.1		20
65.12	odd	4		325.2.x.b.93.1		20
65.18	even	4		845.2.o.e.258.5		20
65.19	odd	12		325.2.x.b.7.1		20
65.23	odd	12		845.2.f.e.408.9		20
65.28	even	12		845.2.k.e.268.2		20
65.32	even	12		325.2.s.b.293.1		20
65.33	even	12	inner	845.2.o.g.488.1		20
65.38	odd	4		65.2.t.a.28.5	yes	20
65.43	odd	12		845.2.t.f.188.1		20
65.48	odd	12		845.2.t.e.188.5		20
65.58	even	12		65.2.o.a.33.5	yes	20
65.63	even	12		845.2.k.d.268.9		20
65.64	even	2		325.2.s.b.132.1		20
195.38	even	4		585.2.dp.a.28.1		20
195.188	odd	12		585.2.cf.a.163.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.5	✓	20	13.12	even	2
65.2.o.a.33.5	yes	20	65.58	even	12
65.2.t.a.7.5	yes	20	13.6	odd	12
65.2.t.a.28.5	yes	20	65.38	odd	4
325.2.s.b.132.1		20	65.64	even	2
325.2.s.b.293.1		20	65.32	even	12
325.2.x.b.7.1		20	65.19	odd	12
325.2.x.b.93.1		20	65.12	odd	4
585.2.cf.a.163.1		20	195.188	odd	12
585.2.cf.a.262.1		20	39.38	odd	2
585.2.dp.a.28.1		20	195.38	even	4
585.2.dp.a.397.1		20	39.32	even	12
845.2.f.d.408.2		20	65.3	odd	12
845.2.f.d.437.9		20	13.11	odd	12
845.2.f.e.408.9		20	65.23	odd	12
845.2.f.e.437.2		20	13.2	odd	12
845.2.k.d.268.9		20	65.63	even	12
845.2.k.d.577.9		20	13.3	even	3
845.2.k.e.268.2		20	65.28	even	12
845.2.k.e.577.2		20	13.10	even	6
845.2.o.e.258.5		20	65.18	even	4
845.2.o.e.357.5		20	13.4	even	6
845.2.o.f.258.1		20	65.8	even	4
845.2.o.f.357.1		20	13.9	even	3
845.2.o.g.488.1		20	65.33	even	12	inner
845.2.o.g.587.1		20	1.1	even	1	trivial
845.2.t.e.188.5		20	65.48	odd	12
845.2.t.e.427.5		20	13.8	odd	4
845.2.t.f.188.1		20	65.43	odd	12
845.2.t.f.427.1		20	13.5	odd	4
845.2.t.g.418.1		20	5.3	odd	4
845.2.t.g.657.1		20	13.7	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.o (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.759023 - 1.31467i) q^{2} +(-0.653367 - 0.175069i) q^{3} +(-0.152233 + 0.263675i) q^{4} +(-0.600231 - 2.15400i) q^{5} +(0.265763 + 0.991842i) q^{6} +(2.24723 + 1.29744i) q^{7} -2.57390 q^{8} +(-2.20184 - 1.27123i) q^{9} +(-2.37621 + 2.42404i) q^{10} +(-1.29395 + 4.82908i) q^{11} +(0.145625 - 0.145625i) q^{12} -3.93915i q^{14} +(0.0150717 + 1.51244i) q^{15} +(2.25812 + 3.91117i) q^{16} +(0.0211881 + 0.0790751i) q^{17} +3.85958i q^{18} +(-2.71143 + 0.726525i) q^{19} +(0.659330 + 0.169644i) q^{20} +(-1.24113 - 1.24113i) q^{21} +(7.33077 - 1.96427i) q^{22} +(-1.05016 + 3.91925i) q^{23} +(1.68170 + 0.450611i) q^{24} +(-4.27945 + 2.58580i) q^{25} +(2.65095 + 2.65095i) q^{27} +(-0.684205 + 0.395026i) q^{28} +(-4.31701 + 2.49243i) q^{29} +(1.97691 - 1.16779i) q^{30} +(2.32124 - 2.32124i) q^{31} +(0.854024 - 1.47921i) q^{32} +(1.69085 - 2.92863i) q^{33} +(0.0878751 - 0.0878751i) q^{34} +(1.44583 - 5.61931i) q^{35} +(0.670383 - 0.387046i) q^{36} +(-0.494934 + 0.285750i) q^{37} +(3.01318 + 3.01318i) q^{38} +(1.54493 + 5.54419i) q^{40} +(-10.0563 - 2.69458i) q^{41} +(-0.689624 + 2.57371i) q^{42} +(0.132121 - 0.0354017i) q^{43} +(-1.07633 - 1.07633i) q^{44} +(-1.41662 + 5.50579i) q^{45} +(5.94960 - 1.59419i) q^{46} +2.30053i q^{47} +(-0.790653 - 2.95076i) q^{48} +(-0.133293 - 0.230870i) q^{49} +(6.64766 + 3.66337i) q^{50} -0.0553744i q^{51} +(6.70735 - 6.70735i) q^{53} +(1.47298 - 5.49724i) q^{54} +(11.1785 - 0.111396i) q^{55} +(-5.78416 - 3.33948i) q^{56} +1.89875 q^{57} +(6.55343 + 3.78362i) q^{58} +(-0.694109 - 2.59045i) q^{59} +(-0.401085 - 0.226268i) q^{60} +(-2.74237 + 4.74992i) q^{61} +(-4.81352 - 1.28978i) q^{62} +(-3.29870 - 5.71351i) q^{63} +6.43957 q^{64} -5.13357 q^{66} +(7.89339 + 13.6718i) q^{67} +(-0.0240756 - 0.00645104i) q^{68} +(1.37228 - 2.37686i) q^{69} +(-8.48494 + 2.36440i) q^{70} +(1.98951 + 7.42495i) q^{71} +(5.66731 + 3.27202i) q^{72} +6.61894 q^{73} +(0.751333 + 0.433783i) q^{74} +(3.24874 - 0.940275i) q^{75} +(0.221202 - 0.825536i) q^{76} +(-9.17326 + 9.17326i) q^{77} +5.71054i q^{79} +(7.06928 - 7.21159i) q^{80} +(2.54575 + 4.40937i) q^{81} +(4.09050 + 15.2660i) q^{82} +3.70736i q^{83} +(0.516194 - 0.138314i) q^{84} +(0.157610 - 0.0931025i) q^{85} +(-0.146824 - 0.146824i) q^{86} +(3.25694 - 0.872695i) q^{87} +(3.33050 - 12.4296i) q^{88} +(-17.2829 - 4.63094i) q^{89} +(8.31353 - 2.31664i) q^{90} +(-0.873538 - 0.873538i) q^{92} +(-1.92300 + 1.11024i) q^{93} +(3.02443 - 1.74616i) q^{94} +(3.19242 + 5.40434i) q^{95} +(-0.816956 + 0.816956i) q^{96} +(2.68493 - 4.65043i) q^{97} +(-0.202345 + 0.350471i) q^{98} +(8.98794 - 8.98794i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 4 q^{2} - 2 q^{3} - 6 q^{4} + 6 q^{5} + 8 q^{6} + 6 q^{7} - 12 q^{8} - 12 q^{9} - 10 q^{10} + 16 q^{11} + 24 q^{12} - 12 q^{15} - 2 q^{16} - 10 q^{17} - 20 q^{19} - 14 q^{20} - 4 q^{21} + 16 q^{22}+ \cdots + 60 q^{99}+O(q^{100}) \) 20 * q + 4 * q^2 - 2 * q^3 - 6 * q^4 + 6 * q^5 + 8 * q^6 + 6 * q^7 - 12 * q^8 - 12 * q^9 - 10 * q^10 + 16 * q^11 + 24 * q^12 - 12 * q^15 - 2 * q^16 - 10 * q^17 - 20 * q^19 - 14 * q^20 - 4 * q^21 + 16 * q^22 - 2 * q^23 + 32 * q^24 - 18 * q^25 + 4 * q^27 - 6 * q^28 + 14 * q^30 + 6 * q^32 + 18 * q^33 + 2 * q^34 - 20 * q^35 + 36 * q^36 - 42 * q^37 + 8 * q^38 - 16 * q^40 - 10 * q^41 - 56 * q^42 - 22 * q^43 - 36 * q^44 - 52 * q^45 - 4 * q^46 + 28 * q^48 - 18 * q^49 - 44 * q^50 - 10 * q^53 - 48 * q^54 + 26 * q^55 + 12 * q^57 + 90 * q^58 - 16 * q^59 + 92 * q^60 - 16 * q^61 - 40 * q^62 + 32 * q^63 - 20 * q^64 - 32 * q^66 + 58 * q^67 + 28 * q^68 + 16 * q^69 - 32 * q^70 + 16 * q^71 + 66 * q^72 - 72 * q^73 - 18 * q^74 - 34 * q^75 + 64 * q^76 + 28 * q^77 + 34 * q^80 - 14 * q^81 + 22 * q^82 - 40 * q^84 + 6 * q^85 - 60 * q^86 + 62 * q^87 + 50 * q^88 - 6 * q^89 - 46 * q^90 - 8 * q^92 - 48 * q^93 + 48 * q^94 + 14 * q^95 - 56 * q^96 + 22 * q^97 - 4 * q^98 + 60 * q^99

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