LMFDB - Embedded newform 845.2.t.f.188.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [845,2,Mod(188,845)]

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, 5]))

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

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

chi := DirichletCharacter("845.188");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 845 = 5 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	845.t (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			188.1
Root			$-1.51805i$ of defining polynomial
Character	$\chi$	$=$	845.188
Dual form			845.2.t.f.427.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.31467 - 0.759023i) q^{2} +(-0.653367 + 0.175069i) q^{3} +(0.152233 + 0.263675i) q^{4} +(-2.15400 - 0.600231i) q^{5} +(0.991842 + 0.265763i) q^{6} +(-1.29744 - 2.24723i) q^{7} +2.57390i q^{8} +(-2.20184 + 1.27123i) q^{9} +(2.37621 + 2.42404i) q^{10} +(-4.82908 + 1.29395i) q^{11} +(-0.145625 - 0.145625i) q^{12} +3.93915i q^{14} +(1.51244 + 0.0150717i) q^{15} +(2.25812 - 3.91117i) q^{16} +(-0.0211881 + 0.0790751i) q^{17} +3.85958 q^{18} +(0.726525 - 2.71143i) q^{19} +(-0.169644 - 0.659330i) q^{20} +(1.24113 + 1.24113i) q^{21} +(7.33077 + 1.96427i) q^{22} +(1.05016 + 3.91925i) q^{23} +(-0.450611 - 1.68170i) q^{24} +(4.27945 + 2.58580i) q^{25} +(2.65095 - 2.65095i) q^{27} +(0.395026 - 0.684205i) q^{28} +(-4.31701 - 2.49243i) q^{29} +(-1.97691 - 1.16779i) q^{30} +(-2.32124 + 2.32124i) q^{31} +(-1.47921 + 0.854024i) q^{32} +(2.92863 - 1.69085i) q^{33} +(0.0878751 - 0.0878751i) q^{34} +(1.44583 + 5.61931i) q^{35} +(-0.670383 - 0.387046i) q^{36} +(-0.285750 + 0.494934i) q^{37} +(-3.01318 + 3.01318i) q^{38} +(1.54493 - 5.54419i) q^{40} +(-2.69458 - 10.0563i) q^{41} +(-0.689624 - 2.57371i) q^{42} +(-0.132121 - 0.0354017i) q^{43} +(-1.07633 - 1.07633i) q^{44} +(5.50579 - 1.41662i) q^{45} +(1.59419 - 5.94960i) q^{46} -2.30053 q^{47} +(-0.790653 + 2.95076i) q^{48} +(0.133293 - 0.230870i) q^{49} +(-3.66337 - 6.64766i) q^{50} -0.0553744i q^{51} +(6.70735 + 6.70735i) q^{53} +(-5.49724 + 1.47298i) q^{54} +(11.1785 + 0.111396i) q^{55} +(5.78416 - 3.33948i) q^{56} +1.89875i q^{57} +(3.78362 + 6.55343i) q^{58} +(2.59045 + 0.694109i) q^{59} +(0.226268 + 0.401085i) q^{60} +(-2.74237 - 4.74992i) q^{61} +(4.81352 - 1.28978i) q^{62} +(5.71351 + 3.29870i) q^{63} -6.43957 q^{64} -5.13357 q^{66} +(13.6718 + 7.89339i) q^{67} +(-0.0240756 + 0.00645104i) q^{68} +(-1.37228 - 2.37686i) q^{69} +(2.36440 - 8.48494i) q^{70} +(7.42495 + 1.98951i) q^{71} +(-3.27202 - 5.66731i) q^{72} -6.61894i q^{73} +(0.751333 - 0.433783i) q^{74} +(-3.24874 - 0.940275i) q^{75} +(0.825536 - 0.221202i) q^{76} +(9.17326 + 9.17326i) q^{77} -5.71054i q^{79} +(-7.21159 + 7.06928i) q^{80} +(2.54575 - 4.40937i) q^{81} +(-4.09050 + 15.2660i) q^{82} +3.70736 q^{83} +(-0.138314 + 0.516194i) q^{84} +(0.0931025 - 0.157610i) q^{85} +(0.146824 + 0.146824i) q^{86} +(3.25694 + 0.872695i) q^{87} +(-3.33050 - 12.4296i) q^{88} +(4.63094 + 17.2829i) q^{89} +(-8.31353 - 2.31664i) q^{90} +(-0.873538 + 0.873538i) q^{92} +(1.11024 - 1.92300i) q^{93} +(3.02443 + 1.74616i) q^{94} +(-3.19242 + 5.40434i) q^{95} +(0.816956 - 0.816956i) q^{96} +(-4.65043 + 2.68493i) q^{97} +(-0.350471 + 0.202345i) q^{98} +(8.98794 - 8.98794i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 4 q^{6} - 2 q^{7} - 12 q^{9} + 10 q^{10} + 8 q^{11} - 24 q^{12} - 8 q^{15} - 2 q^{16} + 10 q^{17} + 16 q^{19} + 12 q^{20} + 4 q^{21} + 16 q^{22} + 2 q^{23} - 28 q^{24}+ \cdots + 60 q^{99}+O(q^{100}) $ 20 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 4 * q^6 - 2 * q^7 - 12 * q^9 + 10 * q^10 + 8 * q^11 - 24 * q^12 - 8 * q^15 - 2 * q^16 + 10 * q^17 + 16 * q^19 + 12 * q^20 + 4 * q^21 + 16 * q^22 + 2 * q^23 - 28 * q^24 + 18 * q^25 + 4 * q^27 + 18 * q^28 - 14 * q^30 - 48 * q^32 - 18 * q^33 + 2 * q^34 - 20 * q^35 - 36 * q^36 - 4 * q^37 - 8 * q^38 - 16 * q^40 + 28 * q^41 - 56 * q^42 + 22 * q^43 - 36 * q^44 + 6 * q^45 - 8 * q^46 - 40 * q^47 + 28 * q^48 + 18 * q^49 - 78 * q^50 - 10 * q^53 + 12 * q^54 + 26 * q^55 + 8 * q^59 + 28 * q^60 - 16 * q^61 + 40 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 + 28 * q^68 - 16 * q^69 - 12 * q^70 + 56 * q^71 + 4 * q^72 - 18 * q^74 + 34 * q^75 + 80 * q^76 - 28 * q^77 - 110 * q^80 - 14 * q^81 - 22 * q^82 + 48 * q^83 + 32 * q^84 + 28 * q^85 + 60 * q^86 + 62 * q^87 - 50 * q^88 - 6 * q^89 + 46 * q^90 - 8 * q^92 + 32 * q^93 + 48 * q^94 - 14 * q^95 + 56 * q^96 - 66 * q^97 + 30 * q^98 + 60 * q^99

Character values

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

$n$	$171$	$677$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	−1.31467	−	0.759023i	−0.929610	−	0.536710i	−0.0429217	−	0.999078i	$-0.513667\pi$
$2$	−1.31467	−	0.759023i	−0.929610	−	0.536710i	−0.886688	+	0.462368i	$0.847000\pi$
$3$	−0.653367	+	0.175069i	−0.377222	+	0.101076i	−0.442448	−	0.896794i	$-0.645890\pi$
$3$	−0.653367	+	0.175069i	−0.377222	+	0.101076i	0.0652261	+	0.997871i	$0.479223\pi$
$4$	0.152233	+	0.263675i	0.0761163	+	0.131837i
$5$	−2.15400	−	0.600231i	−0.963299	−	0.268431i
$5$	−2.15400	−	0.600231i	−0.963299	−	0.268431i
$6$	0.991842	+	0.265763i	0.404918	+	0.108497i
$7$	−1.29744	−	2.24723i	−0.490387	−	0.849375i	0.509552	−	0.860440i	$-0.329811\pi$
$7$	−1.29744	−	2.24723i	−0.490387	−	0.849375i	−0.999939	+	0.0110652i	$0.996478\pi$
$8$			2.57390i			0.910011i
$9$	−2.20184	+	1.27123i	−0.733946	+	0.423744i
$10$	2.37621	+	2.42404i	0.751422	+	0.766549i
$11$	−4.82908	+	1.29395i	−1.45602	+	0.390140i	−0.898114	−	0.439762i	$-0.855063\pi$
$11$	−4.82908	+	1.29395i	−1.45602	+	0.390140i	−0.557909	+	0.829902i	$0.688396\pi$
$12$	−0.145625	−	0.145625i	−0.0420383	−	0.0420383i
$13$		0			0
$13$		0			0
$14$			3.93915i			1.05278i
$15$	1.51244	+	0.0150717i	0.390509	+	0.00389149i
$16$	2.25812	−	3.91117i	0.564529	−	0.977793i
$17$	−0.0211881	+	0.0790751i	−0.00513887	+	0.0191785i	−0.968448	−	0.249217i	$-0.919827\pi$
$17$	−0.0211881	+	0.0790751i	−0.00513887	+	0.0191785i	0.963309	+	0.268396i	$0.0864934\pi$
$18$	3.85958			0.909711
$19$	0.726525	−	2.71143i	0.166676	−	0.622045i	−0.831144	−	0.556057i	$-0.812314\pi$
$19$	0.726525	−	2.71143i	0.166676	−	0.622045i	0.997820	−	0.0659876i	$-0.0210198\pi$
$20$	−0.169644	−	0.659330i	−0.0379335	−	0.147431i
$21$	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	0.984730	+	0.174089i	$0.0556982\pi$
$23$	1.05016	+	3.91925i	0.218973	+	0.817220i	−0.765756	+	0.643131i	$0.777635\pi$
$24$	−0.450611	−	1.68170i	−0.0919805	−	0.343276i
$25$	4.27945	+	2.58580i	0.855889	+	0.517159i
$26$		0			0
$27$	2.65095	−	2.65095i	0.510175	−	0.510175i
$28$	0.395026	−	0.684205i	0.0746528	−	0.129303i
$29$	−4.31701	−	2.49243i	−0.801649	−	0.462833i	0.0423981	−	0.999101i	$-0.486500\pi$
$29$	−4.31701	−	2.49243i	−0.801649	−	0.462833i	−0.844048	+	0.536268i	$0.819834\pi$
$30$	−1.97691	−	1.16779i	−0.360933	−	0.213208i
$31$	−2.32124	+	2.32124i	−0.416906	+	0.416906i	−0.884136	−	0.467230i	$-0.845252\pi$
$31$	−2.32124	+	2.32124i	−0.416906	+	0.416906i	0.467230	+	0.884136i	$0.345252\pi$
$32$	−1.47921	+	0.854024i	−0.261490	+	0.150972i
$33$	2.92863	−	1.69085i	0.509809	−	0.294339i
$34$	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
$37$	−0.285750	+	0.494934i	−0.0469771	+	0.0813667i	−0.888558	−	0.458765i	$-0.848292\pi$
$37$	−0.285750	+	0.494934i	−0.0469771	+	0.0813667i	0.841581	+	0.540131i	$0.181625\pi$
$38$	−3.01318	+	3.01318i	−0.488802	+	0.488802i
$39$		0			0
$40$	1.54493	−	5.54419i	0.244276	−	0.876613i
$41$	−2.69458	−	10.0563i	−0.420823	−	1.57053i	−0.772879	−	0.634554i	$-0.781184\pi$
$41$	−2.69458	−	10.0563i	−0.420823	−	1.57053i	0.352056	−	0.935979i	$-0.385483\pi$
$42$	−0.689624	−	2.57371i	−0.106411	−	0.397132i
$43$	−0.132121	−	0.0354017i	−0.0201483	−	0.00539871i	0.248731	−	0.968573i	$-0.419987\pi$
$43$	−0.132121	−	0.0354017i	−0.0201483	−	0.00539871i	−0.268879	+	0.963174i	$0.586653\pi$
$44$	−1.07633	−	1.07633i	−0.162262	−	0.162262i
$45$	5.50579	−	1.41662i	0.820755	−	0.211178i
$46$	1.59419	−	5.94960i	0.235051	−	0.877221i
$47$	−2.30053			−0.335567			−0.167784	−	0.985824i	$-0.553661\pi$
$47$	−2.30053			−0.335567			−0.167784	+	0.985824i	$0.553661\pi$
$48$	−0.790653	+	2.95076i	−0.114121	+	0.425905i
$49$	0.133293	−	0.230870i	0.0190418	−	0.0329814i
$50$	−3.66337	−	6.64766i	−0.518078	−	0.940121i
$51$		−	0.0553744i		−	0.00775397i
$52$		0			0
$53$	6.70735	+	6.70735i	0.921326	+	0.921326i	0.997123	−	0.0757974i	$-0.0241502\pi$
$53$	6.70735	+	6.70735i	0.921326	+	0.921326i	−0.0757974	+	0.997123i	$0.524150\pi$
$54$	−5.49724	+	1.47298i	−0.748080	+	0.200447i
$55$	11.1785	+	0.111396i	1.50731	+	0.0150206i
$56$	5.78416	−	3.33948i	0.772941	−	0.446257i
$57$			1.89875i			0.251496i
$58$	3.78362	+	6.55343i	0.496814	+	0.860507i
$59$	2.59045	+	0.694109i	0.337248	+	0.0903653i	0.423469	−	0.905911i	$-0.360812\pi$
$59$	2.59045	+	0.694109i	0.337248	+	0.0903653i	−0.0862207	+	0.996276i	$0.527479\pi$
$60$	0.226268	+	0.401085i	0.0292111	+	0.0517799i
$61$	−2.74237	−	4.74992i	−0.351124	−	0.608165i	0.635322	−	0.772247i	$-0.280867\pi$
$61$	−2.74237	−	4.74992i	−0.351124	−	0.608165i	−0.986447	+	0.164082i	$0.947534\pi$
$62$	4.81352	−	1.28978i	0.611318	−	0.163802i
$63$	5.71351	+	3.29870i	0.719834	+	0.415597i
$64$	−6.43957			−0.804946
$65$		0			0
$66$	−5.13357			−0.631899
$67$	13.6718	+	7.89339i	1.67027	+	0.964331i	0.967485	+	0.252930i	$0.0813942\pi$
$67$	13.6718	+	7.89339i	1.67027	+	0.964331i	0.702786	+	0.711401i	$0.251939\pi$
$68$	−0.0240756	+	0.00645104i	−0.00291960	+	0.000782303i
$69$	−1.37228	−	2.37686i	−0.165203	−	0.286140i
$70$	2.36440	−	8.48494i	0.282600	−	1.01414i
$71$	7.42495	+	1.98951i	0.881180	+	0.236111i	0.670916	−	0.741533i	$-0.265901\pi$
$71$	7.42495	+	1.98951i	0.881180	+	0.236111i	0.210264	+	0.977645i	$0.432568\pi$
$72$	−3.27202	−	5.66731i	−0.385612	−	0.667899i
$73$		−	6.61894i		−	0.774688i	−0.921935	−	0.387344i	$-0.873393\pi$
$73$		−	6.61894i		−	0.774688i	0.921935	−	0.387344i	$-0.126607\pi$
$74$	0.751333	−	0.433783i	0.0873407	−	0.0504262i
$75$	−3.24874	−	0.940275i	−0.375132	−	0.108574i
$76$	0.825536	−	0.221202i	0.0946955	−	0.0253736i
$77$	9.17326	+	9.17326i	1.04539	+	1.04539i
$78$		0			0
$79$		−	5.71054i		−	0.642486i	−0.946997	−	0.321243i	$-0.895899\pi$
$79$		−	5.71054i		−	0.642486i	0.946997	−	0.321243i	$-0.104101\pi$
$80$	−7.21159	+	7.06928i	−0.806280	+	0.790369i
$81$	2.54575	−	4.40937i	0.282861	−	0.489930i
$82$	−4.09050	+	15.2660i	−0.451720	+	1.68584i
$83$	3.70736			0.406936			0.203468	−	0.979082i	$-0.434779\pi$
$83$	3.70736			0.406936			0.203468	+	0.979082i	$0.434779\pi$
$84$	−0.138314	+	0.516194i	−0.0150913	+	0.0563213i
$85$	0.0931025	−	0.157610i	0.0100984	−	0.0170952i
$86$	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
$89$	4.63094	+	17.2829i	0.490878	+	1.83198i	0.551989	+	0.833851i	$0.313869\pi$
$89$	4.63094	+	17.2829i	0.490878	+	1.83198i	−0.0611111	+	0.998131i	$0.519464\pi$
$90$	−8.31353	−	2.31664i	−0.876323	−	0.244195i
$91$		0			0
$92$	−0.873538	+	0.873538i	−0.0910726	+	0.0910726i
$93$	1.11024	−	1.92300i	0.115127	−	0.199405i
$94$	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
$97$	−4.65043	+	2.68493i	−0.472180	+	0.272613i	−0.717152	−	0.696917i	$-0.754555\pi$
$97$	−4.65043	+	2.68493i	−0.472180	+	0.272613i	0.244972	+	0.969530i	$0.421221\pi$
$98$	−0.350471	+	0.202345i	−0.0354029	+	0.0204399i
$99$	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	$-0.373200\pi$
$101$	−2.17443	−	1.25541i	−0.216363	−	0.124918i	−0.604265	+	0.796783i	$0.706533\pi$
$102$	−0.0420305	+	0.0727989i	−0.00416164	+	0.00720817i
$103$	4.71738	−	4.71738i	0.464817	−	0.464817i	−0.435414	−	0.900230i	$-0.643398\pi$
$103$	4.71738	−	4.71738i	0.464817	−	0.464817i	0.900230	+	0.435414i	$0.143398\pi$
$104$		0			0
$105$	−1.92843	−	3.41835i	−0.188195	−	0.333597i
$106$	−3.72690	−	13.9090i	−0.361988	−	1.35096i
$107$	0.939155	+	3.50497i	0.0907915	+	0.338838i	0.996348	−	0.0853876i	$-0.0272129\pi$
$107$	0.939155	+	3.50497i	0.0907915	+	0.338838i	−0.905556	+	0.424226i	$0.860546\pi$
$108$	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	$0.715757\pi$
$110$	−14.6115	−	8.63120i	−1.39315	−	0.822953i
$111$	0.100052	−	0.373400i	0.00949653	−	0.0354416i
$112$	−11.7191			−1.10735
$113$	1.48231	−	5.53206i	0.139444	−	0.520412i	−0.860496	−	0.509457i	$-0.829846\pi$
$113$	1.48231	−	5.53206i	0.139444	−	0.520412i	0.999940	−	0.0109551i	$-0.00348719\pi$
$114$	1.44120	−	2.49623i	0.134980	−	0.233793i
$115$	0.0904081	−	9.07241i	0.00843060	−	0.846006i
$116$		−	1.51772i		−	0.140916i
$117$		0			0
$118$	−2.87873	−	2.87873i	−0.265009	−	0.265009i
$119$	0.205190	−	0.0549806i	0.0188098	−	0.00504007i
$120$	−0.0387930	+	3.89286i	−0.00354130	+	0.355368i
$121$	12.1195	−	6.99717i	1.10177	−	0.636106i
$122$			8.32609i			0.753809i
$123$	3.52110	+	6.09873i	0.317487	+	0.549904i
$124$	−0.965419	−	0.258683i	−0.0866972	−	0.0232304i
$125$	−7.66586	−	8.13846i	−0.685655	−	0.727926i
$126$	−5.00757	−	8.67337i	−0.446110	−	0.772685i
$127$	−0.786718	+	0.210801i	−0.0698100	+	0.0187055i	−0.293555	−	0.955942i	$-0.594838\pi$
$127$	−0.786718	+	0.210801i	−0.0698100	+	0.0187055i	0.223745	+	0.974648i	$0.428172\pi$
$128$	11.4243	+	6.59583i	1.00978	+	0.582994i
$129$	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	$0.748427\pi$
$132$	0.891667	+	0.514804i	0.0776096	+	0.0448079i
$133$	−7.03584	+	1.88525i	−0.610085	+	0.163472i
$134$	−11.9825	−	20.7544i	−1.03513	−	1.79290i
$135$	−7.30133	+	4.11897i	−0.628398	+	0.354504i
$136$	−0.203531	−	0.0545361i	−0.0174527	−	0.00467643i
$137$	9.61871	+	16.6601i	0.821782	+	1.42337i	0.904354	+	0.426783i	$0.140353\pi$
$137$	9.61871	+	16.6601i	0.821782	+	1.42337i	−0.0825721	+	0.996585i	$0.526313\pi$
$138$			4.16637i			0.354665i
$139$	−13.7257	+	7.92451i	−1.16419	+	0.672148i	−0.952306	−	0.305146i	$-0.901295\pi$
$139$	−13.7257	+	7.92451i	−1.16419	+	0.672148i	−0.211889	+	0.977294i	$0.567962\pi$
$140$	−1.26157	+	1.23667i	−0.106622	+	0.104518i
$141$	1.50309	−	0.402752i	0.126583	−	0.0339178i
$142$	−8.25125	−	8.25125i	−0.692430	−	0.692430i
$143$		0			0
$144$			11.4823i			0.956862i
$145$	7.80282	+	7.95990i	0.647989	+	0.661034i
$146$	−5.02393	+	8.70170i	−0.415783	+	0.720158i
$147$	−0.0466709	+	0.174178i	−0.00384935	+	0.0143660i
$148$	−0.174002			−0.0143029
$149$	0.372772	−	1.39120i	0.0305387	−	0.113972i	−0.948974	−	0.315354i	$-0.897877\pi$
$149$	0.372772	−	1.39120i	0.0305387	−	0.113972i	0.979513	+	0.201382i	$0.0645433\pi$
$150$	3.55732	+	3.70202i	0.290454	+	0.302269i
$151$	13.9253	+	13.9253i	1.13322	+	1.13322i	0.989638	+	0.143585i	$0.0458631\pi$
$151$	13.9253	+	13.9253i	1.13322	+	1.13322i	0.143585	+	0.989638i	$0.454137\pi$
$152$	6.97895	+	1.87000i	0.566068	+	0.151677i
$153$	−0.0538699	−	0.201045i	−0.00435513	−	0.0162536i
$154$	−5.09706	−	19.0225i	−0.410733	−	1.53288i
$155$	6.39322	−	3.60667i	0.513516	−	0.289695i
$156$		0			0
$157$	4.54644	−	4.54644i	0.362845	−	0.362845i	−0.502014	−	0.864859i	$-0.667408\pi$
$157$	4.54644	−	4.54644i	0.362845	−	0.362845i	0.864859	+	0.502014i	$0.167408\pi$
$158$	−4.33444	+	7.50746i	−0.344829	+	0.597262i
$159$	−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
$162$	−6.69363	+	3.86457i	−0.525901	+	0.303629i
$163$	−11.3759	+	6.56789i	−0.891031	+	0.514437i	−0.874280	−	0.485423i	$-0.838666\pi$
$163$	−11.3759	+	6.56789i	−0.891031	+	0.514437i	−0.0167516	+	0.999860i	$0.505332\pi$
$164$	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
$167$	−1.64258	+	2.84503i	−0.127107	+	0.220155i	−0.922554	−	0.385867i	$-0.873902\pi$
$167$	−1.64258	+	2.84503i	−0.127107	+	0.220155i	0.795448	+	0.606022i	$0.207236\pi$
$168$	−3.19454	+	3.19454i	−0.246464	+	0.246464i
$169$		0			0
$170$	−0.242028	+	0.136538i	−0.0185627	+	0.0104720i
$171$	1.84716	+	6.89371i	0.141256	+	0.527175i
$172$	−0.0107786	−	0.0402263i	−0.000821860	−	0.00306722i
$173$	4.09367	+	1.09689i	0.311236	+	0.0833953i	0.411056	−	0.911610i	$-0.365160\pi$
$173$	4.09367	+	1.09689i	0.311236	+	0.0833953i	−0.0998202	+	0.995005i	$0.531827\pi$
$174$	−3.61940	−	3.61940i	−0.274386	−	0.274386i
$175$	0.258559	−	12.9718i	0.0195452	−	0.980579i
$176$	−5.84377	+	21.8093i	−0.440491	+	1.64393i
$177$	−1.81403			−0.136351
$178$	7.02997	−	26.2362i	0.526919	−	1.96649i
$179$	−6.98083	+	12.0912i	−0.521772	+	0.903735i	0.477907	+	0.878410i	$0.341395\pi$
$179$	−6.98083	+	12.0912i	−0.521772	+	0.903735i	−0.999679	+	0.0253252i	$0.991938\pi$
$180$	1.21169	+	1.23608i	0.0903139	+	0.0921321i
$181$		−	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
$184$	−10.0878	+	2.70301i	−0.743680	+	0.199268i
$185$	0.912582	−	0.894573i	0.0670944	−	0.0657703i
$186$	−2.91920	+	1.68540i	−0.214046	+	0.123579i
$187$		−	0.409276i		−	0.0299292i
$188$	−0.350216	−	0.606592i	−0.0255421	−	0.0442402i
$189$	−9.39675	−	2.51785i	−0.683513	−	0.183147i
$190$	8.29899	−	4.68179i	0.602072	−	0.339653i
$191$	−8.45647	−	14.6470i	−0.611889	−	1.05982i	−0.990922	−	0.134439i	$-0.957077\pi$
$191$	−8.45647	−	14.6470i	−0.611889	−	1.05982i	0.379033	−	0.925383i	$-0.376257\pi$
$192$	4.20740	−	1.12737i	0.303643	−	0.0813609i
$193$	−7.40936	−	4.27780i	−0.533338	−	0.307923i	0.209037	−	0.977908i	$-0.432967\pi$
$193$	−7.40936	−	4.27780i	−0.533338	−	0.307923i	−0.742375	+	0.669985i	$0.766300\pi$
$194$	8.15169			0.585257
$195$		0			0
$196$	0.0811660			0.00579757
$197$	6.63101	+	3.82842i	0.472440	+	0.272764i	0.717261	−	0.696805i	$-0.245396\pi$
$197$	6.63101	+	3.82842i	0.472440	+	0.272764i	−0.244820	+	0.969568i	$0.578729\pi$
$198$	−18.6382	+	4.99409i	−1.32456	+	0.354915i
$199$	7.66380	+	13.2741i	0.543272	+	0.940975i	0.998713	+	0.0507092i	$0.0161482\pi$
$199$	7.66380	+	13.2741i	0.543272	+	0.940975i	−0.455441	+	0.890266i	$0.650519\pi$
$200$	−6.65558	+	11.0149i	−0.470621	+	0.778869i
$201$	−10.3146	−	2.76378i	−0.727533	−	0.194942i
$202$	1.90576	+	3.30088i	0.134089	+	0.232249i
$203$			12.9351i			0.907868i
$204$	0.0146008	−	0.00842979i	0.00102226	−	0.000590203i
$205$	−0.231976	+	23.2787i	−0.0162019	+	1.62585i
$206$	−9.78238	+	2.62118i	−0.681570	+	0.182626i
$207$	−7.29455	−	7.29455i	−0.507006	−	0.507006i
$208$		0			0
$209$			14.0338i			0.970739i
$210$	−0.0593697	+	5.95771i	−0.00409690	+	0.411121i
$211$	−9.91788	+	17.1783i	−0.682775	+	1.18260i	0.291355	+	0.956615i	$0.405894\pi$
$211$	−9.91788	+	17.1783i	−0.682775	+	1.18260i	−0.974130	+	0.225986i	$0.927440\pi$
$212$	−0.747481	+	2.78964i	−0.0513372	+	0.191593i
$213$	−5.19952			−0.356265
$214$	1.42568	−	5.32071i	0.0974575	−	0.363716i
$215$	0.263340	+	0.155559i	0.0179596	+	0.0106090i
$216$	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
$219$	1.15877	+	4.32460i	0.0783025	+	0.292229i
$220$	1.67236	+	2.96445i	0.112751	+	0.199863i
$221$		0			0
$222$	−0.414955	+	0.414955i	−0.0278499	+	0.0278499i
$223$	9.48653	−	16.4311i	0.635265	−	1.10031i	−0.351194	−	0.936303i	$-0.614224\pi$
$223$	9.48653	−	16.4311i	0.635265	−	1.10031i	0.986459	−	0.164008i	$-0.0524424\pi$
$224$	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
$227$	−23.3469	+	13.4794i	−1.54959	+	0.894656i	−0.551417	+	0.834230i	$0.685913\pi$
$227$	−23.3469	+	13.4794i	−1.54959	+	0.894656i	−0.998173	+	0.0604265i	$0.980754\pi$
$228$	−0.500652	+	0.289052i	−0.0331565	+	0.0191429i
$229$	−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
$232$	6.41527	−	11.1116i	0.421183	−	0.729510i
$233$	6.75797	−	6.75797i	0.442729	−	0.442729i	−0.450199	−	0.892928i	$-0.648647\pi$
$233$	6.75797	−	6.75797i	0.442729	−	0.442729i	0.892928	+	0.450199i	$0.148647\pi$
$234$		0			0
$235$	4.95535	+	1.38085i	0.323251	+	0.0900767i
$236$	0.211332	+	0.788702i	0.0137565	+	0.0513401i
$237$	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	$0.721021\pi$
$240$	3.47420	−	5.88136i	0.224259	−	0.379640i
$241$	0.710443	−	2.65141i	0.0457637	−	0.170792i	−0.939262	−	0.343202i	$-0.888489\pi$
$241$	0.710443	−	2.65141i	0.0457637	−	0.170792i	0.985025	+	0.172409i	$0.0551552\pi$
$242$	−21.2441			−1.36562
$243$	−3.80231	+	14.1904i	−0.243918	+	0.910315i
$244$	0.834956	−	1.44619i	0.0534526	−	0.0925826i
$245$	−0.425688	+	0.417287i	−0.0271962	+	0.0266595i
$246$		−	10.6904i		−	0.681595i
$247$		0			0
$248$	−5.97463	−	5.97463i	−0.379389	−	0.379389i
$249$	−2.42227	+	0.649045i	−0.153505	+	0.0411316i
$250$	3.90077	+	16.5179i	0.246706	+	1.04469i
$251$	2.45414	−	1.41690i	0.154904	−	0.0894337i	−0.420545	−	0.907272i	$-0.638161\pi$
$251$	2.45414	−	1.41690i	0.154904	−	0.0894337i	0.575448	+	0.817838i	$0.304828\pi$
$252$			2.00868i			0.126535i
$253$	−10.1426	−	17.5675i	−0.637661	−	1.10446i
$254$	1.19428	+	0.320005i	0.0749355	+	0.0200789i
$255$	−0.0332374	+	0.119277i	−0.00208141	+	0.00746939i
$256$	−3.57321	−	6.18898i	−0.223325	−	0.386811i
$257$	19.3784	−	5.19242i	1.20879	−	0.323894i	0.402502	−	0.915419i	$-0.368141\pi$
$257$	19.3784	−	5.19242i	1.20879	−	0.323894i	0.806287	+	0.591525i	$0.201474\pi$
$258$	−0.121635	−	0.0702258i	−0.00757265	−	0.00437207i
$259$	1.48298			0.0921478
$260$		0			0
$261$	12.6738			0.784490
$262$	21.1743	+	12.2250i	1.30815	+	0.755264i
$263$	−9.10077	+	2.43854i	−0.561177	+	0.150367i	−0.528247	−	0.849091i	$-0.677151\pi$
$263$	−9.10077	+	2.43854i	−0.561177	+	0.150367i	−0.0329302	+	0.999458i	$0.510484\pi$
$264$	4.35207	+	7.53801i	0.267851	+	0.463932i
$265$	−10.4217	−	18.4736i	−0.640199	−	1.13482i
$266$	10.6807	+	2.86189i	0.654878	+	0.175474i
$267$	−6.05140	−	10.4813i	−0.370340	−	0.641447i
$268$			4.80653i			0.293605i
$269$	2.78417	−	1.60744i	0.169754	−	0.0980075i	−0.412716	−	0.910860i	$-0.635420\pi$
$269$	2.78417	−	1.60744i	0.169754	−	0.0980075i	0.582470	+	0.812852i	$0.302086\pi$
$270$	12.7252	+	0.126809i	0.774431	+	0.00771734i
$271$	14.6694	−	3.93065i	0.891102	−	0.238770i	0.215911	−	0.976413i	$-0.430728\pi$
$271$	14.6694	−	3.93065i	0.891102	−	0.238770i	0.675191	+	0.737643i	$0.264061\pi$
$272$	0.261431	+	0.261431i	0.0158516	+	0.0158516i
$273$		0			0
$274$		−	29.2033i		−	1.76424i
$275$	−24.0117	−	6.94964i	−1.44796	−	0.419079i
$276$	0.417811	−	0.723671i	0.0251493	−	0.0435598i
$277$	−2.76028	+	10.3015i	−0.165849	+	0.618956i	0.832082	+	0.554653i	$0.187149\pi$
$277$	−2.76028	+	10.3015i	−0.165849	+	0.618956i	−0.997930	+	0.0643031i	$0.979518\pi$
$278$	24.0595			1.44300
$279$	2.16016	−	8.06181i	0.129325	−	0.482648i
$280$	−14.4635	+	3.72143i	−0.864362	+	0.222398i
$281$	−12.7630	−	12.7630i	−0.761379	−	0.761379i	0.215193	−	0.976572i	$-0.430962\pi$
$281$	−12.7630	−	12.7630i	−0.761379	−	0.761379i	−0.976572	+	0.215193i	$0.930962\pi$
$282$	−2.28176	−	0.611396i	−0.135877	−	0.0364081i
$283$	1.49018	+	5.56143i	0.0885820	+	0.330592i	0.995968	−	0.0897050i	$-0.0285924\pi$
$283$	1.49018	+	5.56143i	0.0885820	+	0.330592i	−0.907386	+	0.420297i	$0.861926\pi$
$284$	0.605736	+	2.26064i	0.0359438	+	0.134144i
$285$	1.13969	−	4.08991i	0.0675093	−	0.242266i
$286$		0			0
$287$	−19.1028	+	19.1028i	−1.12760	+	1.12760i
$288$	2.17132	−	3.76084i	0.127946	−	0.221610i
$289$	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
$292$	1.74525	−	1.00762i	0.102133	−	0.0589664i
$293$	−2.76788	+	1.59804i	−0.161701	+	0.0933583i	−0.578667	−	0.815564i	$-0.696427\pi$
$293$	−2.76788	+	1.59804i	−0.161701	+	0.0933583i	0.416966	+	0.908922i	$0.363094\pi$
$294$	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
$297$	−9.37145	+	16.2318i	−0.543787	+	0.941867i
$298$	−1.54603	+	1.54603i	−0.0895590	+	0.0895590i
$299$		0			0
$300$	−0.246638	−	0.999751i	−0.0142396	−	0.0577207i
$301$	0.0918633	+	0.342839i	0.00529491	+	0.0197609i
$302$	−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
$305$	3.05602	+	11.8774i	0.174987	+	0.680098i
$306$	−0.0817771	+	0.305196i	−0.00467488	+	0.0174469i
$307$	24.2740			1.38539			0.692695	−	0.721231i	$-0.256423\pi$
$307$	24.2740			1.38539			0.692695	+	0.721231i	$0.256423\pi$
$308$	−1.02229	+	3.81522i	−0.0582501	+	0.217393i
$309$	−2.25631	+	3.90804i	−0.128357	+	0.222321i
$310$	−11.1425	−	0.111037i	−0.632852	−	0.00630648i
$311$			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	0.428285	−	0.903644i	$-0.359118\pi$
$313$	−8.40997	−	8.40997i	−0.475359	−	0.475359i	−0.903644	+	0.428285i	$0.859118\pi$
$314$	−9.42790	+	2.52620i	−0.532047	+	0.142562i
$315$	−10.3269	−	10.5348i	−0.581856	−	0.593570i
$316$	1.50573	−	0.869331i	0.0847037	−	0.0489037i
$317$		−	11.9484i		−	0.671087i	−0.942025	−	0.335543i	$-0.891080\pi$
$317$		−	11.9484i		−	0.671087i	0.942025	−	0.335543i	$-0.108920\pi$
$318$	4.87006	+	8.43520i	0.273100	+	0.473022i
$319$	24.0723	+	6.45015i	1.34779	+	0.361139i
$320$	13.8708	+	3.86523i	0.775403	+	0.216073i
$321$	−1.22723	−	2.12562i	−0.0684970	−	0.118640i
$322$	−15.4385	+	4.13674i	−0.860355	+	0.230531i
$323$	0.199013	+	0.114900i	0.0110734	+	0.00639321i
$324$	1.55018			0.0861214
$325$		0			0
$326$	19.9407			1.10442
$327$	−1.31331	−	0.758238i	−0.0726260	−	0.0419307i
$328$	25.8840	−	6.93559i	1.42920	−	0.382954i
$329$	2.98480	+	5.16983i	0.164558	+	0.285022i
$330$	11.0577	+	3.08133i	0.608707	+	0.169621i
$331$	20.7179	+	5.55136i	1.13876	+	0.305130i	0.778453	−	0.627703i	$-0.216005\pi$
$331$	20.7179	+	5.55136i	1.13876	+	0.305130i	0.360308	+	0.932833i	$0.382671\pi$
$332$	0.564382	+	0.977538i	0.0309745	+	0.0536494i
$333$		−	1.45302i		−	0.0796250i
$334$	4.31889	−	2.49351i	0.236319	−	0.136439i
$335$	−24.7111	−	25.2086i	−1.35011	−	1.37729i
$336$	7.65687	−	2.05165i	0.417716	−	0.111927i
$337$	14.1264	+	14.1264i	0.769514	+	0.769514i	0.978021	−	0.208507i	$-0.0668604\pi$
$337$	14.1264	+	14.1264i	0.769514	+	0.769514i	−0.208507	+	0.978021i	$0.566860\pi$
$338$		0			0
$339$			3.87397i			0.210405i
$340$	0.0557310		0.000555369i	0.00302244		3.01191e-5i
$341$	8.20588	−	14.2130i	0.444373	−	0.769677i
$342$	2.80408	−	10.4650i	0.151627	−	0.565881i
$343$	−18.8559			−1.01812
$344$	0.0911205	−	0.340067i	0.00491289	−	0.0183352i
$345$	1.52923	+	5.94344i	0.0823309	+	0.319984i
$346$	−4.54924	−	4.54924i	−0.244569	−	0.244569i
$347$	23.7906	+	6.37467i	1.27715	+	0.342210i	0.832765	−	0.553627i	$-0.186757\pi$
$347$	23.7906	+	6.37467i	1.27715	+	0.342210i	0.444382	+	0.895837i	$0.353423\pi$
$348$	0.265705	+	0.991626i	0.0142433	+	0.0531567i
$349$	−7.05214	−	26.3190i	−0.377493	−	1.40882i	−0.849669	−	0.527317i	$-0.823198\pi$
$349$	−7.05214	−	26.3190i	−0.377493	−	1.40882i	0.472176	−	0.881504i	$-0.343469\pi$
$350$	−10.1858	+	16.8574i	−0.544456	+	0.901065i
$351$		0			0
$352$	6.03818	−	6.03818i	0.321836	−	0.321836i
$353$	4.39963	−	7.62038i	0.234169	−	0.405592i	−0.724862	−	0.688894i	$-0.758097\pi$
$353$	4.39963	−	7.62038i	0.234169	−	0.405592i	0.959031	+	0.283302i	$0.0914299\pi$
$354$	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
$357$	−0.124439	+	0.0718451i	−0.00658603	+	0.00380244i
$358$	18.3549	−	10.5972i	0.970089	−	0.560081i
$359$	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
$362$	−6.56385	+	11.3689i	−0.344988	+	0.597537i
$363$	−6.69346	+	6.69346i	−0.351316	+	0.351316i
$364$		0			0
$365$	−3.97289	+	14.2572i	−0.207951	+	0.746256i
$366$	−1.45764	−	5.43999i	−0.0761921	−	0.284353i
$367$	2.84144	+	10.6044i	0.148322	+	0.553545i	0.999585	+	0.0288057i	$0.00917042\pi$
$367$	2.84144	+	10.6044i	0.148322	+	0.553545i	−0.851263	+	0.524739i	$0.824163\pi$
$368$	17.7002	+	4.74276i	0.922689	+	0.247234i
$369$	18.7169	+	18.7169i	0.974365	+	0.974365i
$370$	−1.87874	+	0.483395i	−0.0976712	+	0.0251305i
$371$	6.37060	−	23.7754i	0.330745	−	1.23436i
$372$	0.676060			0.0350521
$373$	2.73825	−	10.2193i	0.141781	−	0.529135i	−0.858096	−	0.513489i	$-0.828353\pi$
$373$	2.73825	−	10.2193i	0.141781	−	0.529135i	0.999878	−	0.0156462i	$-0.00498054\pi$
$374$	−0.310650	+	0.538062i	−0.0160633	+	0.0278225i
$375$	6.43341	+	3.97535i	0.332220	+	0.205286i
$376$		−	5.92134i		−	0.305370i
$377$		0			0
$378$	10.4425	+	10.4425i	0.537104	+	0.537104i
$379$	9.46800	−	2.53694i	0.486338	−	0.130314i	−0.00731411	−	0.999973i	$-0.502328\pi$
$379$	9.46800	−	2.53694i	0.486338	−	0.130314i	0.493652	+	0.869659i	$0.335662\pi$
$380$	−1.91098	−	0.0190432i	−0.0980311	−	0.000976897i
$381$	0.477111	−	0.275460i	0.0244431	−	0.0141123i
$382$			25.6746i			1.31363i
$383$	13.0283	+	22.5658i	0.665718	+	1.15306i	0.979090	+	0.203426i	$0.0652078\pi$
$383$	13.0283	+	22.5658i	0.665718	+	1.15306i	−0.313373	+	0.949630i	$0.601459\pi$
$384$	−8.61899	−	2.30945i	−0.439836	−	0.117854i
$385$	−14.2531	−	25.2653i	−0.726407	−	1.28764i
$386$	6.49390	+	11.2478i	0.330531	+	0.572496i
$387$	0.335913	−	0.0900076i	0.0170754	−	0.00457534i
$388$	−1.41589	−	0.817467i	−0.0718812	−	0.0415006i
$389$	−32.4888			−1.64725			−0.823623	−	0.567138i	$-0.808050\pi$
$389$	−32.4888			−1.64725			−0.823623	+	0.567138i	$0.808050\pi$
$390$		0			0
$391$	−0.332166			−0.0167983
$392$	0.594236	+	0.343082i	0.0300134	+	0.0173283i
$393$	10.5233	−	2.81971i	0.530830	−	0.142235i
$394$	−5.81172	−	10.0662i	−0.292790	−	0.507127i
$395$	−3.42764	+	12.3005i	−0.172463	+	0.618906i
$396$	3.73815	+	1.00163i	0.187849	+	0.0503340i
$397$	−12.0927	−	20.9451i	−0.606914	−	1.05121i	−0.991746	−	0.128219i	$-0.959074\pi$
$397$	−12.0927	−	20.9451i	−0.606914	−	1.05121i	0.384832	−	0.922987i	$-0.374259\pi$
$398$		−	23.2680i		−	1.16632i
$399$	4.26694	−	2.46352i	0.213614	−	0.123330i
$400$	19.7770	−	10.8986i	0.988849	−	0.544931i
$401$	31.7194	−	8.49918i	1.58399	−	0.424429i	0.643832	−	0.765167i	$-0.277343\pi$
$401$	31.7194	−	8.49918i	1.58399	−	0.424429i	0.940158	+	0.340738i	$0.110677\pi$
$402$	11.4624	+	11.4624i	0.571695	+	0.571695i
$403$		0			0
$404$		−	0.764454i		−	0.0380330i
$405$	−8.13019	+	7.96975i	−0.403992	+	0.396020i
$406$	9.81806	−	17.0054i	0.487262	−	0.843963i
$407$	0.739493	−	2.75983i	0.0366553	−	0.136799i
$408$	0.142528			0.00705620
$409$	−3.61312	+	13.4843i	−0.178657	+	0.666758i	0.817243	+	0.576294i	$0.195502\pi$
$409$	−3.61312	+	13.4843i	−0.178657	+	0.666758i	−0.995900	+	0.0904639i	$0.971165\pi$
$410$	17.9740	−	30.4277i	0.887675	−	1.50271i
$411$	−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
$414$	4.05317	+	15.1266i	0.199203	+	0.743434i
$415$	−7.98567	−	2.22527i	−0.392001	−	0.109234i
$416$		0			0
$417$	7.58055	−	7.58055i	0.371221	−	0.371221i
$418$	10.6520	−	18.4498i	0.521006	−	0.902408i
$419$	1.92240	+	1.10990i	0.0939155	+	0.0542221i	0.546222	−	0.837640i	$-0.316065\pi$
$419$	1.92240	+	1.10990i	0.0939155	+	0.0542221i	−0.452307	+	0.891862i	$0.649399\pi$
$420$	0.607763	−	1.02886i	0.0296558	−	0.0502033i
$421$	24.4795	−	24.4795i	1.19306	−	1.19306i	0.216853	−	0.976204i	$-0.430421\pi$
$421$	24.4795	−	24.4795i	1.19306	−	1.19306i	0.976204	−	0.216853i	$-0.0695792\pi$
$422$	26.0774	−	15.0558i	1.26943	−	0.732905i
$423$	5.06540	−	2.92451i	0.246288	−	0.142194i
$424$	−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
$427$	−7.11613	+	12.3255i	−0.344374	+	0.596472i
$428$	−0.781202	+	0.781202i	−0.0377608	+	0.0377608i
$429$		0			0
$430$	−0.228132	−	0.404389i	−0.0110015	−	0.0195014i
$431$	−0.427704	−	1.59621i	−0.0206018	−	0.0768868i	0.954860	−	0.297057i	$-0.0960053\pi$
$431$	−0.427704	−	1.59621i	−0.0206018	−	0.0768868i	−0.975461	+	0.220171i	$0.929339\pi$
$432$	−4.38216	−	16.3545i	−0.210837	−	0.786854i
$433$	14.3111	+	3.83465i	0.687748	+	0.184281i	0.585736	−	0.810502i	$-0.300805\pi$
$433$	14.3111	+	3.83465i	0.687748	+	0.184281i	0.102012	+	0.994783i	$0.467472\pi$
$434$	−9.14370	−	9.14370i	−0.438912	−	0.438912i
$435$	−6.49164	−	3.83470i	−0.311250	−	0.183860i
$436$	−0.176667	+	0.659331i	−0.00846083	+	0.0315762i
$437$	11.3897			0.544845
$438$	1.75907	−	6.56494i	0.0840516	−	0.313685i
$439$	10.9363	−	18.9422i	0.521959	−	0.904060i	−0.477714	−	0.878515i	$-0.658535\pi$
$439$	10.9363	−	18.9422i	0.521959	−	0.904060i	0.999674	−	0.0255448i	$-0.00813206\pi$
$440$	−0.286722	+	28.7724i	−0.0136689	+	1.37167i
$441$			0.677783i			0.0322754i
$442$		0			0
$443$	−6.14972	−	6.14972i	−0.292182	−	0.292182i	0.545760	−	0.837942i	$-0.316241\pi$
$443$	−6.14972	−	6.14972i	−0.292182	−	0.292182i	−0.837942	+	0.545760i	$0.816241\pi$
$444$	0.113687	−	0.0304624i	0.00539536	−	0.00144568i
$445$	0.398677	−	40.0070i	0.0188991	−	1.89651i
$446$	−24.9432	+	14.4010i	−1.18110	+	0.681907i
$447$			0.974228i			0.0460794i
$448$	8.35496	+	14.4712i	0.394735	+	0.683701i
$449$	−4.51557	−	1.20994i	−0.213103	−	0.0571008i	0.150688	−	0.988581i	$-0.451851\pi$
$449$	−4.51557	−	1.20994i	−0.213103	−	0.0571008i	−0.363791	+	0.931481i	$0.618518\pi$
$450$	16.5168	+	9.98008i	0.778612	+	0.470465i
$451$	26.0247	+	45.0761i	1.22546	+	2.12255i
$452$	1.68432	−	0.451312i	0.0792237	−	0.0212279i
$453$	−11.5362	−	6.66043i	−0.542018	−	0.312934i
$454$	40.9246			1.92069
$455$		0			0
$456$	−4.88720			−0.228864
$457$	−26.0120	−	15.0180i	−1.21679	−	0.702514i	−0.252560	−	0.967581i	$-0.581273\pi$
$457$	−26.0120	−	15.0180i	−1.21679	−	0.702514i	−0.964230	+	0.265067i	$0.914606\pi$
$458$	23.1840	−	6.21213i	1.08332	−	0.290274i
$459$	0.153455	+	0.265792i	0.00716268	+	0.0124061i
$460$	2.40593	−	1.35728i	0.112177	−	0.0632834i
$461$	−2.53796	−	0.680045i	−0.118205	−	0.0316729i	0.199232	−	0.979952i	$-0.436155\pi$
$461$	−2.53796	−	0.680045i	−0.118205	−	0.0316729i	−0.317436	+	0.948280i	$0.602822\pi$
$462$	6.66050	+	11.5363i	0.309875	+	0.536719i
$463$			25.1475i			1.16870i	0.811500	+	0.584352i	$0.198651\pi$
$463$			25.1475i			1.16870i	−0.811500	+	0.584352i	$0.801349\pi$
$464$	−19.4966	+	11.2564i	−0.905109	+	0.522565i
$465$	−3.54570	+	3.47573i	−0.164428	+	0.161183i
$466$	−14.0139	+	3.75502i	−0.649183	+	0.173948i
$467$	−14.9907	−	14.9907i	−0.693688	−	0.693688i	0.269354	−	0.963041i	$-0.413190\pi$
$467$	−14.9907	−	14.9907i	−0.693688	−	0.693688i	−0.963041	+	0.269354i	$0.913190\pi$
$468$		0			0
$469$		−	40.9648i		−	1.89158i
$470$	−5.46654	−	5.57658i	−0.252152	−	0.257229i
$471$	−2.17455	+	3.76643i	−0.100198	+	0.173548i
$472$	−1.78657	+	6.66756i	−0.0822335	+	0.306899i
$473$	0.683832			0.0314426
$474$	1.51765	−	5.66395i	0.0697081	−	0.260154i
$475$	10.1203	−	9.72477i	0.464353	−	0.446203i
$476$	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
$479$	−0.592587	−	2.21157i	−0.0270760	−	0.101049i	0.951066	−	0.308989i	$-0.0999907\pi$
$479$	−0.592587	−	2.21157i	−0.0270760	−	0.101049i	−0.978142	+	0.207940i	$0.933324\pi$
$480$	−2.25009	+	1.26936i	−0.102702	+	0.0579382i
$481$		0			0
$482$	−2.94648	+	2.94648i	−0.134208	+	0.134208i
$483$	−3.56090	+	6.16767i	−0.162027	+	0.280639i
$484$	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
$487$	4.82067	−	2.78321i	0.218445	−	0.126119i	−0.386785	−	0.922170i	$-0.626414\pi$
$487$	4.82067	−	2.78321i	0.218445	−	0.126119i	0.605230	+	0.796050i	$0.293081\pi$
$488$	12.2258	−	7.05859i	0.553437	−	0.319527i
$489$	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	$-0.377359\pi$
$491$	−5.29139	−	3.05498i	−0.238797	−	0.137869i	−0.614624	+	0.788820i	$0.710692\pi$
$492$	−1.07205	+	1.85685i	−0.0483319	+	0.0837133i
$493$	0.288558	−	0.288558i	0.0129960	−	0.0129960i
$494$		0			0
$495$	−24.7549	+	13.9652i	−1.11265	+	0.627689i
$496$	3.83713	+	14.3204i	0.172292	+	0.643004i
$497$	−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	$0.813160\pi$
$500$	0.978912	−	3.26023i	0.0437783	−	0.145802i
$501$	0.575130	−	2.14642i	0.0256949	−	0.0958948i
$502$	−4.30183			−0.192000
$503$	0.951461	−	3.55090i	0.0424236	−	0.158327i	−0.941465	−	0.337112i	$-0.890550\pi$
$503$	0.951461	−	3.55090i	0.0424236	−	0.158327i	0.983888	+	0.178785i	$0.0572166\pi$
$504$	−8.49051	+	14.7060i	−0.378198	+	0.655057i
$505$	3.93018	+	4.00930i	0.174891	+	0.178412i
$506$			30.7939i			1.36896i
$507$		0			0
$508$	−0.175347	−	0.175347i	−0.00777976	−	0.00777976i
$509$	10.8248	−	2.90050i	0.479802	−	0.128563i	−0.0108085	−	0.999942i	$-0.503441\pi$
$509$	10.8248	−	2.90050i	0.479802	−	0.128563i	0.490610	+	0.871379i	$0.336774\pi$
$510$	0.134230	−	0.131581i	0.00594380	−	0.00582650i
$511$	−14.8743	+	8.58768i	−0.658000	+	0.379897i
$512$		−	15.5347i		−	0.686544i
$513$	−5.26188	−	9.11384i	−0.232318	−	0.402386i
$514$	−29.4173	−	7.88233i	−1.29754	−	0.347675i
$515$	−12.9927	+	7.32972i	−0.572529	+	0.322986i
$516$	0.0140848	+	0.0243955i	0.000620047	+	0.00107395i
$517$	11.1095	−	2.97677i	0.488593	−	0.130918i
$518$	−1.94962	−	1.12561i	−0.0856615	−	0.0494567i
$519$	−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	$0.211258\pi$
$522$	−16.6618	−	9.61972i	−0.729269	−	0.421044i
$523$	8.10636	−	2.17209i	0.354467	−	0.0949790i	−0.0771917	−	0.997016i	$-0.524595\pi$
$523$	8.10636	−	2.17209i	0.354467	−	0.0949790i	0.431658	+	0.902037i	$0.357929\pi$
$524$	−2.45189	−	4.24681i	−0.107112	−	0.185523i
$525$	2.10203	+	8.52064i	0.0917403	+	0.371871i
$526$	13.8154	+	3.70182i	0.602380	+	0.161407i
$527$	−0.134369	−	0.232734i	−0.00585322	−	0.0101381i
$528$		−	15.2725i		−	0.664651i
$529$	5.66090	−	3.26832i	0.246126	−	0.142101i
$530$	−0.320848	+	32.1969i	−0.0139368	+	1.39855i
$531$	−6.58612	+	1.76475i	−0.285813	+	0.0765835i
$532$	−1.56818	−	1.56818i	−0.0679891	−	0.0679891i
$533$		0			0
$534$			18.3726i			0.795061i
$535$	0.0808517	−	8.11343i	0.00349552	−	0.350774i
$536$	−20.3168	+	35.1897i	−0.877552	+	1.51997i
$537$	2.44426	−	9.12209i	0.105477	−	0.393647i
$538$	−4.88034			−0.210407
$539$	−0.344948	+	1.28736i	−0.0148580	+	0.0554506i
$540$	−2.19757	−	1.29813i	−0.0945682	−	0.0558628i
$541$	4.13066	+	4.13066i	0.177591	+	0.177591i	0.790305	−	0.612714i	$-0.209922\pi$
$541$	4.13066	+	4.13066i	0.177591	+	0.177591i	−0.612714	+	0.790305i	$0.709922\pi$
$542$	−22.2688	−	5.96691i	−0.956528	−	0.256301i
$543$	1.51396	+	5.65016i	0.0649700	+	0.242471i
$544$	−0.0361903	−	0.135064i	−0.00155165	−	0.00579082i
$545$	−2.46317	−	4.36624i	−0.105511	−	0.187029i
$546$		0			0
$547$	−7.90229	+	7.90229i	−0.337877	+	0.337877i	−0.855568	−	0.517691i	$-0.826792\pi$
$547$	−7.90229	+	7.90229i	−0.337877	+	0.337877i	0.517691	+	0.855568i	$0.326792\pi$
$548$	−2.92856	+	5.07242i	−0.125102	+	0.216683i
$549$	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
$552$	6.11780	−	3.53211i	0.260391	−	0.150337i
$553$	−12.8329	+	7.40909i	−0.545712	+	0.315067i
$554$	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
$557$	5.89341	−	10.2077i	0.249712	−	0.432513i	−0.713734	−	0.700417i	$-0.752997\pi$
$557$	5.89341	−	10.2077i	0.249712	−	0.432513i	0.963446	+	0.267903i	$0.0863308\pi$
$558$	−8.95899	+	8.95899i	−0.379264	+	0.379264i
$559$		0			0
$560$	25.2429	+	7.03416i	1.06671	+	0.297247i
$561$	0.0716517	+	0.267408i	0.00302514	+	0.0112900i
$562$	7.09170	+	26.4666i	0.299145	+	1.11643i
$563$	−31.0602	−	8.32255i	−1.30903	−	0.350754i	−0.464172	−	0.885745i	$-0.653648\pi$
$563$	−31.0602	−	8.32255i	−1.30903	−	0.350754i	−0.844858	+	0.534991i	$0.820315\pi$
$564$	0.335015	+	0.335015i	0.0141067	+	0.0141067i
$565$	−6.51341	+	11.0263i	−0.274021	+	0.463882i
$566$	2.26216	−	8.44250i	0.0950858	−	0.354865i
$567$	−13.2118			−0.554845
$568$	−5.12080	+	19.1111i	−0.214864	+	0.801883i
$569$	4.64237	−	8.04082i	0.194618	−	0.337089i	−0.752157	−	0.658984i	$-0.770987\pi$
$569$	4.64237	−	8.04082i	0.194618	−	0.337089i	0.946775	+	0.321895i	$0.104320\pi$
$570$	−4.60265	+	4.51182i	−0.192784	+	0.188979i
$571$			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
$574$	39.6134	−	10.6144i	1.65343	−	0.443035i
$575$	−5.64028	+	19.4877i	−0.235216	+	0.812694i
$576$	14.1789	−	8.18618i	0.590786	−	0.341091i
$577$		−	4.57285i		−	0.190370i	−0.995460	−	0.0951852i	$-0.969656\pi$
$577$		−	4.57285i		−	0.190370i	0.995460	−	0.0951852i	$-0.0303443\pi$
$578$	−12.8983	−	22.3405i	−0.536499	−	0.929243i
$579$	5.58994	+	1.49782i	0.232310	+	0.0622473i
$580$	−0.910980	+	3.26916i	−0.0378264	+	0.135745i
$581$	−4.81009	−	8.33132i	−0.199556	−	0.345641i
$582$	−5.32605	+	1.42711i	−0.220772	+	0.0591556i
$583$	−41.0693	−	23.7114i	−1.70092	−	0.982025i
$584$	17.0365			0.704975
$585$		0			0
$586$	4.85179			0.200425
$587$	−6.22829	−	3.59590i	−0.257069	−	0.148419i	0.365928	−	0.930643i	$-0.380752\pi$
$587$	−6.22829	−	3.59590i	−0.257069	−	0.148419i	−0.622997	+	0.782224i	$0.714085\pi$
$588$	−0.0530312	+	0.0142097i	−0.00218697	+	0.000585997i
$589$	4.60743	+	7.98031i	0.189846	+	0.328823i
$590$	4.47289	+	7.92870i	0.184146	+	0.326420i
$591$	−5.00272	−	1.34048i	−0.205785	−	0.0551398i
$592$	1.29052	+	2.23524i	0.0530399	+	0.0918677i
$593$			28.0561i			1.15212i	0.817406	+	0.576062i	$0.195411\pi$
$593$			28.0561i			1.15212i	−0.817406	+	0.576062i	$0.804589\pi$
$594$	24.6407	−	14.2263i	1.01102	−	0.583712i
$595$	−0.474982	−	0.00473328i	−0.0194724	−	0.000194045i
$596$	0.423573	−	0.113496i	0.0173502	−	0.00464898i
$597$	−7.33116	−	7.33116i	−0.300044	−	0.300044i
$598$		0			0
$599$		−	0.912959i		−	0.0373025i	−0.999826	−	0.0186513i	$-0.994063\pi$
$599$		−	0.912959i		−	0.0373025i	0.999826	−	0.0186513i	$-0.00593722\pi$
$600$	2.42017	−	8.36194i	0.0988032	−	0.341375i
$601$	−6.22691	+	10.7853i	−0.254001	+	0.439943i	−0.964624	−	0.263631i	$-0.915080\pi$
$601$	−6.22691	+	10.7853i	−0.254001	+	0.439943i	0.710623	+	0.703573i	$0.248413\pi$
$602$	0.139453	−	0.520445i	0.00568367	−	0.0212118i
$603$	−40.1373			−1.63452
$604$	−1.55186	+	5.79162i	−0.0631443	+	0.235658i
$605$	−30.3052	+	7.79745i	−1.23208	+	0.317011i
$606$	−1.82305	−	1.82305i	−0.0740562	−	0.0740562i
$607$	37.4512	+	10.0350i	1.52010	+	0.407309i	0.919774	−	0.392448i	$-0.128372\pi$
$607$	37.4512	+	10.0350i	1.52010	+	0.407309i	0.600324	+	0.799757i	$0.295038\pi$
$608$	1.24094	+	4.63125i	0.0503268	+	0.187822i
$609$	−2.26454	−	8.45138i	−0.0917638	−	0.342467i
$610$	4.99757	−	17.9344i	0.202346	−	0.726143i
$611$		0			0
$612$	0.0448098	−	0.0448098i	0.00181133	−	0.00181133i
$613$	−12.3057	+	21.3140i	−0.497021	+	0.860865i	−0.999994	−	0.00343656i	$-0.998906\pi$
$613$	−12.3057	+	21.3140i	−0.497021	+	0.860865i	0.502973	+	0.864302i	$0.332239\pi$
$614$	−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
$617$	13.3501	−	7.70769i	0.537455	−	0.310300i	−0.206592	−	0.978427i	$-0.566237\pi$
$617$	13.3501	−	7.70769i	0.537455	−	0.310300i	0.744047	+	0.668127i	$0.232904\pi$
$618$	5.93259	−	3.42518i	0.238644	−	0.137781i
$619$	−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
$622$	12.8316	−	22.2249i	0.514498	−	0.891137i
$623$	32.8303	−	32.8303i	1.31532	−	1.31532i
$624$		0			0
$625$	11.6273	+	22.1315i	0.465093	+	0.885262i
$626$	4.67294	+	17.4397i	0.186768	+	0.697029i
$627$	−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
$630$	5.58030	+	21.6882i	0.222324	+	0.864077i
$631$	−3.26195	+	12.1738i	−0.129856	+	0.484631i	−0.999966	−	0.00822739i	$-0.997381\pi$
$631$	−3.26195	+	12.1738i	−0.129856	+	0.484631i	0.870110	+	0.492858i	$0.164048\pi$
$632$	14.6984			0.584670
$633$	3.47263	−	12.9600i	0.138025	−	0.515115i
$634$	−9.06908	+	15.7081i	−0.360179	+	0.623849i
$635$	1.82112	+	0.0181478i	0.0722690	+	0.000720173i
$636$		−	1.95352i		−	0.0774620i
$637$		0			0
$638$	−26.7512	−	26.7512i	−1.05909	−	1.05909i
$639$	−18.8777	+	5.05825i	−0.746789	+	0.200101i
$640$	−20.6490	−	21.0646i	−0.816222	−	0.832653i
$641$	8.45341	−	4.88058i	0.333890	−	0.192771i	−0.323677	−	0.946168i	$-0.604919\pi$
$641$	8.45341	−	4.88058i	0.333890	−	0.192771i	0.657567	+	0.753396i	$0.271586\pi$
$642$			3.72597i			0.147052i
$643$	−13.9057	−	24.0854i	−0.548387	−	0.949834i	−0.998385	−	0.0568044i	$-0.981909\pi$
$643$	−13.9057	−	24.0854i	−0.548387	−	0.949834i	0.449999	−	0.893029i	$-0.351424\pi$
$644$	3.09641	+	0.829680i	0.122016	+	0.0326940i
$645$	−0.199291	−	0.0555341i	−0.00784708	−	0.00218665i
$646$	−0.174424	−	0.302111i	−0.00686261	−	0.0118864i
$647$	17.7967	−	4.76862i	0.699662	−	0.187474i	0.108583	−	0.994087i	$-0.465369\pi$
$647$	17.7967	−	4.76862i	0.699662	−	0.187474i	0.591079	+	0.806613i	$0.298702\pi$
$648$	11.3493	+	6.55251i	0.445842	+	0.257407i
$649$	−13.4076			−0.526296
$650$		0			0
$651$	−5.76190			−0.225826
$652$	−3.46357	−	1.99970i	−0.135644	−	0.0783141i
$653$	−7.12491	+	1.90911i	−0.278819	+	0.0747094i	−0.395519	−	0.918458i	$-0.629435\pi$
$653$	−7.12491	+	1.90911i	−0.278819	+	0.0747094i	0.116700	+	0.993167i	$0.462769\pi$
$654$	1.15104	+	1.99366i	0.0450093	+	0.0779583i
$655$	34.6929	+	9.66746i	1.35556	+	0.377739i
$656$	−45.4167	−	12.1694i	−1.77322	−	0.475134i
$657$	8.41420	+	14.5738i	0.328269	+	0.568579i
$658$		−	9.06214i		−	0.353279i
$659$	12.0786	−	6.97358i	0.470515	−	0.271652i	−0.245940	−	0.969285i	$-0.579097\pi$
$659$	12.0786	−	6.97358i	0.470515	−	0.271652i	0.716455	+	0.697633i	$0.245763\pi$
$660$	−1.61165	−	1.64409i	−0.0627334	−	0.0639963i
$661$	−0.218940	+	0.0586648i	−0.00851578	+	0.00228180i	−0.263074	−	0.964776i	$-0.584736\pi$
$661$	−0.218940	+	0.0586648i	−0.00851578	+	0.00228180i	0.254559	+	0.967057i	$0.418070\pi$
$662$	−23.0236	−	23.0236i	−0.894837	−	0.894837i
$663$		0			0
$664$			9.54239i			0.370317i
$665$	16.2868	+	0.162301i	0.631575	+	0.00629375i
$666$	−1.10288	+	1.91024i	−0.0427356	+	0.0740202i
$667$	5.23490	−	19.5369i	0.202696	−	0.756472i
$668$	−1.00022			−0.0386996
$669$	−3.32160	+	12.3964i	−0.128420	+	0.479271i
$670$	13.3530	+	51.8972i	0.515871	+	2.00496i
$671$	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	0.903431	+	0.428734i	$0.141040\pi$
$673$	8.70112	+	32.4730i	0.335404	+	1.25174i	−0.568027	+	0.823010i	$0.692293\pi$
$674$	−7.84924	−	29.2938i	−0.302341	−	1.12835i
$675$	18.1994	−	4.48978i	0.700495	−	0.172812i
$676$		0			0
$677$	25.1691	−	25.1691i	0.967326	−	0.967326i	−0.0321566	−	0.999483i	$-0.510238\pi$
$677$	25.1691	−	25.1691i	0.967326	−	0.967326i	0.999483	+	0.0321566i	$0.0102375\pi$
$678$	2.94044	−	5.09298i	0.112927	−	0.195595i
$679$	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
$682$	−21.5760	+	12.4569i	−0.826187	+	0.477000i
$683$	−26.6361	+	15.3784i	−1.01920	+	0.588437i	−0.913873	−	0.406001i	$-0.866923\pi$
$683$	−26.6361	+	15.3784i	−1.01920	+	0.588437i	−0.105329	+	0.994437i	$0.533590\pi$
$684$	−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
$687$	5.34740	−	9.26197i	0.204016	−	0.353366i
$688$	−0.436807	+	0.436807i	−0.0166531	+	0.0166531i
$689$		0			0
$690$	2.50078	−	8.97436i	0.0952032	−	0.341648i
$691$	10.0271	+	37.4215i	0.381447	+	1.42358i	0.843692	+	0.536828i	$0.180378\pi$
$691$	10.0271	+	37.4215i	0.381447	+	1.42358i	−0.462244	+	0.886753i	$0.652956\pi$
$692$	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
$695$	34.3216	−	8.83085i	1.30189	−	0.334973i
$696$	−2.24623	+	8.38305i	−0.0851432	+	0.317759i
$697$	0.852297			0.0322831
$698$	−10.7055	+	39.9534i	−0.405208	+	1.51226i
$699$	−3.23232	+	5.59854i	−0.122258	+	0.211756i
$700$	3.45970	−	1.90656i	0.130765	−	0.0720612i
$701$		−	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
$704$	31.0972	−	8.33247i	1.17202	−	0.314042i
$705$	−3.47941	−	0.0346729i	−0.131042	−	0.00130586i
$706$	−11.5681	+	6.67884i	−0.435371	+	0.251361i
$707$			6.51526i			0.245032i
$708$	−0.276155	−	0.478314i	−0.0103785	−	0.0179761i
$709$	30.7830	+	8.24828i	1.15608	+	0.309771i	0.785399	−	0.618990i	$-0.212458\pi$
$709$	30.7830	+	8.24828i	1.15608	+	0.309771i	0.370680	+	0.928760i	$0.379125\pi$
$710$	12.8206	+	22.7259i	0.481147	+	0.852887i
$711$	7.25942	+	12.5737i	0.272250	+	0.471550i
$712$	−44.4844	+	11.9196i	−1.66712	+	0.446705i
$713$	−11.5352	−	6.65983i	−0.431996	−	0.249413i
$714$	0.218128			0.00816325
$715$		0			0
$716$	−4.25084			−0.158861
$717$	−1.64665	−	0.950692i	−0.0614951	−	0.0355042i
$718$	−23.0710	+	6.18186i	−0.861002	+	0.230705i
$719$	15.4818	+	26.8152i	0.577372	+	1.00004i	0.995779	+	0.0917785i	$0.0292552\pi$
$719$	15.4818	+	26.8152i	0.577372	+	1.00004i	−0.418407	+	0.908260i	$0.637411\pi$
$720$	6.89206	−	24.7330i	0.256852	−	0.921744i
$721$	−16.7216	−	4.48053i	−0.622744	−	0.166864i
$722$	−8.44057	−	14.6195i	−0.314126	−	0.544081i
$723$			1.85672i			0.0690522i
$724$	2.28019	−	1.31647i	0.0847427	−	0.0489262i
$725$	−12.0295	−	21.8291i	−0.446765	−	0.810714i
$726$	13.8802	−	3.71918i	0.515141	−	0.138032i
$727$	16.2588	+	16.2588i	0.603007	+	0.603007i	0.941109	−	0.338103i	$-0.109785\pi$
$727$	16.2588	+	16.2588i	0.603007	+	0.603007i	−0.338103	+	0.941109i	$0.609785\pi$
$728$		0			0
$729$			5.33729i			0.197678i
$730$	16.0446	−	15.7280i	0.593836	−	0.582118i
$731$	0.00559879	−	0.00969739i	0.000207079	−	0.000358671i
$732$	−0.292350	+	1.09107i	−0.0108056	+	0.0403269i
$733$	31.2515			1.15430			0.577150	−	0.816638i	$-0.304165\pi$
$733$	31.2515			1.15430			0.577150	+	0.816638i	$0.304165\pi$
$734$	4.31344	−	16.0980i	0.159212	−	0.594187i
$735$	0.205076	−	0.347167i	0.00756435	−	0.0128054i
$736$	−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
$739$	7.06496	+	26.3668i	0.259889	+	0.969918i	0.965305	+	0.261125i	$0.0840933\pi$
$739$	7.06496	+	26.3668i	0.259889	+	0.969918i	−0.705416	+	0.708793i	$0.749240\pi$
$740$	0.374801	+	0.104441i	0.0137780	+	0.00383934i
$741$		0			0
$742$	−26.4213	+	26.4213i	−0.969956	+	0.969956i
$743$	−16.4830	+	28.5494i	−0.604703	+	1.04738i	0.387395	+	0.921914i	$0.373375\pi$
$743$	−16.4830	+	28.5494i	−0.604703	+	1.04738i	−0.992098	+	0.125463i	$0.959958\pi$
$744$	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
$747$	−8.16301	+	4.71292i	−0.298669	+	0.172437i
$748$	0.107916	−	0.0623052i	0.00394579	−	0.00227810i
$749$	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	$-0.524506\pi$
$751$	−26.8241	−	15.4869i	−0.978826	−	0.565125i	−0.901915	+	0.431913i	$0.857839\pi$
$752$	−5.19487	+	8.99777i	−0.189437	+	0.328115i
$753$	−1.35540	+	1.35540i	−0.0493934	+	0.0493934i
$754$		0			0
$755$	−21.6367	−	38.3535i	−0.787440	−	1.39583i
$756$	−0.766598	−	2.86098i	−0.0278809	−	0.104053i
$757$	13.2249	+	49.3561i	0.480668	+	1.79388i	0.598822	+	0.800882i	$0.295636\pi$
$757$	13.2249	+	49.3561i	0.480668	+	1.79388i	−0.118154	+	0.992995i	$0.537698\pi$
$758$	−14.3729	−	3.85120i	−0.522046	−	0.139882i
$759$	9.70238	+	9.70238i	0.352174	+	0.352174i
$760$	−13.9102	−	8.21697i	−0.504577	−	0.298061i
$761$	−0.299592	+	1.11809i	−0.0108602	+	0.0405308i	−0.971143	−	0.238497i	$-0.923345\pi$
$761$	−0.299592	+	1.11809i	−0.0108602	+	0.0405308i	0.960283	+	0.279027i	$0.0900121\pi$
$762$	−0.836323			−0.0302968
$763$	1.50569	−	5.61932i	0.0545097	−	0.203433i
$764$	2.57470	−	4.45951i	0.0931494	−	0.161339i
$765$	−0.00463766	+	0.465386i	−0.000167675	+	0.0168261i
$766$		−	39.5553i		−	1.42919i
$767$		0			0
$768$	3.41812	+	3.41812i	0.123341	+	0.123341i
$769$	−29.2004	+	7.82422i	−1.05299	+	0.282148i	−0.743488	−	0.668750i	$-0.766830\pi$
$769$	−29.2004	+	7.82422i	−1.05299	+	0.282148i	−0.309505	+	0.950898i	$0.600163\pi$
$770$	−0.438805	+	44.0339i	−0.0158134	+	1.58687i
$771$	−11.7522	+	6.78511i	−0.423243	+	0.244360i
$772$		−	2.60488i		−	0.0937517i
$773$	−3.59641	−	6.22916i	−0.129354	−	0.224047i	0.794073	−	0.607823i	$-0.207957\pi$
$773$	−3.59641	−	6.22916i	−0.129354	−	0.224047i	−0.923426	+	0.383776i	$0.874624\pi$
$774$	−0.509931	−	0.136636i	−0.0183291	−	0.00491127i
$775$	−15.9358	+	3.93136i	−0.572432	+	0.141219i
$776$	−6.91074	−	11.9698i	−0.248081	−	0.429689i
$777$	−0.968929	+	0.259624i	−0.0347601	+	0.00931395i
$778$	42.7119	+	24.6597i	1.53130	+	0.884094i
$779$	−29.2247			−1.04708
$780$		0			0
$781$	−38.4300			−1.37513
$782$	0.436687	+	0.252122i	0.0156159	+	0.00901585i
$783$	−18.0515	+	4.83688i	−0.645107	+	0.172856i
$784$	−0.601981	−	1.04266i	−0.0214993	−	0.0372379i
$785$	−12.5219	+	7.06412i	−0.446927	+	0.252129i
$786$	−15.9748	−	4.28044i	−0.569804	−	0.152678i
$787$	−3.58943	−	6.21708i	−0.127949	−	0.221615i	0.794933	−	0.606698i	$-0.207506\pi$
$787$	−3.58943	−	6.21708i	−0.127949	−	0.221615i	−0.922882	+	0.385083i	$0.874173\pi$
$788$			2.33124i			0.0830470i
$789$	5.51923	−	3.18653i	0.196490	−	0.113443i
$790$	13.8426	−	13.5694i	0.492497	−	0.482778i
$791$	−14.3550	+	3.84642i	−0.510407	+	0.136763i
$792$	23.1341	+	23.1341i	0.822034	+	0.822034i
$793$		0			0
$794$			36.7145i			1.30295i
$795$	10.0433	+	10.2455i	0.356201	+	0.363372i
$796$	−2.33336	+	4.04150i	−0.0827037	+	0.143247i
$797$	10.1969	−	38.0553i	0.361192	−	1.34799i	−0.511318	−	0.859391i	$-0.670843\pi$
$797$	10.1969	−	38.0553i	0.361192	−	1.34799i	0.872510	−	0.488596i	$-0.162491\pi$
$798$	−7.47947			−0.264770
$799$	0.0487439	−	0.181915i	0.00172443	−	0.00643568i
$800$	−8.53854	−	0.170193i	−0.301883	−	0.00601723i
$801$	−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
$804$	−0.841474	−	3.14043i	−0.0296765	−	0.110754i
$805$	−20.5051	+	11.5677i	−0.722711	+	0.407710i
$806$		0			0
$807$	−1.53767	+	1.53767i	−0.0541286	+	0.0541286i
$808$	3.23129	−	5.59676i	0.113676	−	0.196893i
$809$	−24.2062	−	13.9754i	−0.851043	−	0.491350i	0.00995956	−	0.999950i	$-0.496830\pi$
$809$	−24.2062	−	13.9754i	−0.851043	−	0.491350i	−0.861003	+	0.508600i	$0.830163\pi$
$810$	16.7377	−	4.30656i	0.588103	−	0.151317i
$811$	−23.2784	+	23.2784i	−0.817415	+	0.817415i	−0.985733	−	0.168317i	$-0.946167\pi$
$811$	−23.2784	+	23.2784i	−0.817415	+	0.817415i	0.168317	+	0.985733i	$0.446167\pi$
$812$	−3.41066	+	1.96915i	−0.119691	+	0.0691035i
$813$	−8.89636	+	5.13632i	−0.312009	+	0.180138i
$814$	−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
$817$	−0.191979	+	0.332517i	−0.00671648	+	0.0116333i
$818$	14.9850	−	14.9850i	0.523937	−	0.523937i
$819$		0			0
$820$	−6.17331	+	3.48261i	−0.215582	+	0.121618i
$821$	−5.06082	−	18.8872i	−0.176624	−	0.659169i	−0.996269	−	0.0862981i	$-0.972496\pi$
$821$	−5.06082	−	18.8872i	−0.176624	−	0.659169i	0.819646	−	0.572871i	$-0.194170\pi$
$822$	5.11260	+	19.0805i	0.178322	+	0.665508i
$823$	39.4302	+	10.5653i	1.37445	+	0.368283i	0.869102	−	0.494633i	$-0.164697\pi$
$823$	39.4302	+	10.5653i	1.37445	+	0.368283i	0.505348	+	0.862915i	$0.331364\pi$
$824$	12.1421	+	12.1421i	0.422989	+	0.422989i
$825$	16.9051	+	0.336958i	0.588560	+	0.0117314i
$826$	−2.73420	+	10.2042i	−0.0951350	+	0.355049i
$827$	31.8649			1.10805			0.554026	−	0.832499i	$-0.313091\pi$
$827$	31.8649			1.10805			0.554026	+	0.832499i	$0.313091\pi$
$828$	0.812920	−	3.03386i	0.0282509	−	0.105434i
$829$	27.6391	−	47.8724i	0.959946	−	1.66268i	0.237326	−	0.971430i	$-0.423729\pi$
$829$	27.6391	−	47.8724i	0.959946	−	1.66268i	0.722620	−	0.691246i	$-0.242938\pi$
$830$	8.80946	+	8.98680i	0.305781	+	0.311937i
$831$		−	7.21389i		−	0.250247i
$832$		0			0
$833$	0.0154318	+	0.0154318i	0.000534681	+	0.000534681i
$834$	−15.7197	+	4.21208i	−0.544329	+	0.145853i
$835$	5.24580	−	5.14228i	0.181538	−	0.177956i
$836$	−3.70036	+	2.13640i	−0.127980	+	0.0738890i
$837$			12.3070i			0.425390i
$838$	−1.68488	−	2.91830i	−0.0582032	−	0.100811i
$839$	−3.76762	−	1.00953i	−0.130073	−	0.0348528i	0.193195	−	0.981160i	$-0.438115\pi$
$839$	−3.76762	−	1.00953i	−0.130073	−	0.0348528i	−0.323268	+	0.946307i	$0.604782\pi$
$840$	8.79850	−	4.96358i	0.303577	−	0.171260i
$841$	−2.07559	−	3.59503i	−0.0715721	−	0.123966i
$842$	−50.7629	+	13.6019i	−1.74940	+	0.468751i
$843$	10.5734	+	6.10453i	0.364166	+	0.210251i
$844$	−6.03930			−0.207881
$845$		0			0
$846$	−8.87908			−0.305269
$847$	−31.4485	−	18.1568i	−1.08058	−	0.623876i
$848$	41.3796	−	11.0876i	1.42098	−	0.380751i
$849$	−1.94727	−	3.37277i	−0.0668301	−	0.115753i
$850$	0.603284	−	0.148830i	0.0206925	−	0.00510482i
$851$	−2.23986	−	0.600167i	−0.0767812	−	0.0205735i
$852$	−0.791536	−	1.37098i	−0.0271176	−	0.0469690i
$853$		−	53.5726i		−	1.83429i	−0.398554	−	0.917145i	$-0.630488\pi$
$853$		−	53.5726i		−	1.83429i	0.398554	−	0.917145i	$-0.369512\pi$
$854$	18.7107	−	10.8026i	0.640266	−	0.369658i
$855$	0.159022	−	15.9578i	0.00543844	−	0.545745i
$856$	−9.02145	+	2.41729i	−0.308347	+	0.0826213i
$857$	−18.9164	−	18.9164i	−0.646171	−	0.646171i	0.305894	−	0.952066i	$-0.401045\pi$
$857$	−18.9164	−	18.9164i	−0.646171	−	0.646171i	−0.952066	+	0.305894i	$0.901045\pi$
$858$		0			0
$859$		−	18.1203i		−	0.618258i	−0.951020	−	0.309129i	$-0.899963\pi$
$859$		−	18.1203i		−	0.618258i	0.951020	−	0.309129i	$-0.100037\pi$
$860$	−0.000927928		0.0931171i	−3.16421e−5		0.00317527i
$861$	9.13685	−	15.8255i	0.311383	−	0.539331i
$862$	−0.649274	+	2.42312i	−0.0221144	+	0.0825320i
$863$	21.4967			0.731757			0.365879	−	0.930663i	$-0.380768\pi$
$863$	21.4967			0.731757			0.365879	+	0.930663i	$0.380768\pi$
$864$	−1.65734	+	6.18529i	−0.0563840	+	0.210428i
$865$	−8.15937	−	4.81986i	−0.277427	−	0.163880i
$866$	−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
$869$	7.38915	+	27.5767i	0.250660	+	0.935475i
$870$	5.62372	+	9.96866i	0.190662	+	0.337969i
$871$		0			0
$872$	−4.08036	+	4.08036i	−0.138179	+	0.138179i
$873$	6.82633	−	11.8235i	0.231036	−	0.400167i
$874$	−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
$877$	18.4889	−	10.6745i	0.624324	−	0.360454i	−0.154226	−	0.988036i	$-0.549289\pi$
$877$	18.4889	−	10.6745i	0.624324	−	0.360454i	0.778551	+	0.627582i	$0.215955\pi$
$878$	−28.7551	+	16.6018i	−0.970437	+	0.560282i
$879$	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	$-0.404955\pi$
$881$	−11.4703	−	6.62238i	−0.386444	−	0.223114i	−0.680618	+	0.732638i	$0.738289\pi$
$882$	0.514453	−	0.891059i	0.0173225	−	0.0300035i
$883$	−32.5668	+	32.5668i	−1.09596	+	1.09596i	−0.101082	+	0.994878i	$0.532230\pi$
$883$	−32.5668	+	32.5668i	−1.09596	+	1.09596i	−0.994878	+	0.101082i	$0.967770\pi$
$884$		0			0
$885$	3.90743	+	1.08884i	0.131347	+	0.0366009i
$886$	3.41705	+	12.7526i	0.114798	+	0.428432i
$887$	4.13600	+	15.4358i	0.138873	+	0.518282i	0.999952	+	0.00981024i	$0.00312275\pi$
$887$	4.13600	+	15.4358i	0.138873	+	0.518282i	−0.861079	+	0.508472i	$0.830211\pi$
$888$	0.961094	+	0.257524i	0.0322522	+	0.00864195i
$889$	1.49444	+	1.49444i	0.0501219	+	0.0501219i
$890$	−30.8904	+	52.2933i	−1.03545	+	1.75287i
$891$	−6.58814	+	24.5873i	−0.220711	+	0.823705i
$892$	5.77663			0.193416
$893$	−1.67139	+	6.23773i	−0.0559311	+	0.208738i
$894$	0.739462	−	1.28079i	0.0247313	−	0.0428359i
$895$	22.2942	−	21.8543i	0.745213	−	0.730507i
$896$		−	34.2308i		−	1.14357i
$897$		0			0
$898$	5.01810	+	5.01810i	0.167456	+	0.167456i
$899$	15.8063	−	4.23529i	0.527170	−	0.141255i
$900$	−1.86805	−	3.38981i	−0.0622682	−	0.112994i
$901$	−0.672500	+	0.388268i	−0.0224042	+	0.0129351i
$902$		−	79.0135i		−	2.63086i
$903$	−0.120041	−	0.207917i	−0.00399471	−	0.00691905i
$904$	14.2390	+	3.81532i	0.473581	+	0.126896i
$905$	−5.19065	+	18.6273i	−0.172543	+	0.619192i
$906$	10.1108	+	17.5125i	0.335910	+	0.581814i
$907$	−5.07458	+	1.35973i	−0.168499	+	0.0451491i	−0.342082	−	0.939670i	$-0.611132\pi$
$907$	−5.07458	+	1.35973i	−0.168499	+	0.0451491i	0.173583	+	0.984819i	$0.444465\pi$
$908$	−7.10833	−	4.10399i	−0.235898	−	0.136196i
$909$	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	$0.449712\pi$
$912$	7.42634	+	4.28760i	0.245911	+	0.141977i
$913$	−17.9032	+	4.79714i	−0.592508	+	0.158762i
$914$	22.7981	+	39.4874i	0.754093	+	1.30613i
$915$	−4.07607	−	7.22529i	−0.134751	−	0.238861i
$916$	−4.64987	−	1.24593i	−0.153636	−	0.0411666i
$917$	20.8969	+	36.1945i	0.690076	+	1.19525i
$918$		−	0.465905i		−	0.0153771i
$919$	−45.6207	+	26.3391i	−1.50489	+	0.868847i	−0.504903	+	0.863176i	$0.668472\pi$
$919$	−45.6207	+	26.3391i	−1.50489	+	0.868847i	−0.999984	+	0.00567026i	$0.998195\pi$
$920$	23.3515	+	0.232702i	0.769875	+	0.00767194i
$921$	−15.8598	+	4.24963i	−0.522599	+	0.140030i
$922$	2.82041	+	2.82041i	0.0928851	+	0.0928851i
$923$		0			0
$924$		−	2.67171i		−	0.0878929i
$925$	−2.50265	+	1.37915i	−0.0822867	+	0.0453463i
$926$	19.0876	−	33.0606i	0.627256	−	1.08644i
$927$	−4.39002	+	16.3838i	−0.144187	+	0.538114i
$928$	8.51438			0.279498
$929$	2.15657	−	8.04841i	0.0707546	−	0.264060i	−0.921483	−	0.388420i	$-0.873021\pi$
$929$	2.15657	−	8.04841i	0.0707546	−	0.264060i	0.992237	+	0.124360i	$0.0396877\pi$
$930$	7.29958	−	1.87816i	0.239363	−	0.0615873i
$931$	−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
$934$	8.32950	+	31.0861i	0.272549	+	1.01717i
$935$	−0.245660	+	0.881582i	−0.00803395	+	0.0288308i
$936$		0			0
$937$	16.3814	−	16.3814i	0.535156	−	0.535156i	−0.386947	−	0.922102i	$-0.626470\pi$
$937$	16.3814	−	16.3814i	0.535156	−	0.535156i	0.922102	+	0.386947i	$0.126470\pi$
$938$	−31.0933	+	53.8551i	−1.01523	+	1.75843i
$939$	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	−0.981487	−	0.191530i	$-0.938655\pi$
$941$	−24.2325	+	24.2325i	−0.789956	+	0.789956i	0.191530	+	0.981487i	$0.438655\pi$
$942$	5.71762	−	3.30107i	0.186290	−	0.107555i
$943$	36.5835	−	21.1215i	1.19132	−	0.687810i
$944$	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
$947$	16.7208	−	28.9613i	0.543353	−	0.941114i	−0.455356	−	0.890309i	$-0.650488\pi$
$947$	16.7208	−	28.9613i	0.543353	−	0.941114i	0.998709	−	0.0508048i	$-0.0161786\pi$
$948$	−0.831598	+	0.831598i	−0.0270091	+	0.0270091i
$949$		0			0
$950$	−20.6862	+	5.10327i	−0.671149	+	0.165572i
$951$	2.09179	+	7.80666i	0.0678309	+	0.253148i
$952$	0.141515	+	0.528140i	0.00458652	+	0.0171171i
$953$	−14.5138	−	3.88895i	−0.470147	−	0.125975i	0.0159642	−	0.999873i	$-0.494918\pi$
$953$	−14.5138	−	3.88895i	−0.470147	−	0.125975i	−0.486111	+	0.873897i	$0.661585\pi$
$954$	25.8875	+	25.8875i	0.838140	+	0.838140i
$955$	9.42365	+	36.6256i	0.304942	+	1.18518i
$956$	−0.221508	+	0.826681i	−0.00716409	+	0.0267368i
$957$	−16.8573			−0.544918
$958$	−0.899575	+	3.35726i	−0.0290640	+	0.108468i
$959$	24.9594	−	43.2310i	0.805982	−	1.39600i
$960$	−9.73943	−	0.0970551i	−0.314339	−	0.00313244i
$961$			20.2237i			0.652378i
$962$		0			0
$963$	−6.52350	−	6.52350i	−0.210217	−	0.210217i
$964$	0.807262	−	0.216305i	0.0260002	−	0.00696672i
$965$	13.3921	+	13.6617i	0.431107	+	0.439786i
$966$	9.36281	−	5.40562i	0.301243	−	0.173923i
$967$		−	7.49252i		−	0.240943i	−0.992717	−	0.120472i	$-0.961559\pi$
$967$		−	7.49252i		−	0.240943i	0.992717	−	0.120472i	$-0.0384407\pi$
$968$	18.0100	+	31.1943i	0.578864	+	1.00262i
$969$	−0.150144	−	0.0402309i	−0.00482332	−	0.00129240i
$970$	−17.5588	−	4.89290i	−0.563778	−	0.157101i
$971$	−13.9303	−	24.1280i	−0.447045	−	0.774304i	0.551147	−	0.834408i	$-0.314190\pi$
$971$	−13.9303	−	24.1280i	−0.447045	−	0.774304i	−0.998192	+	0.0601036i	$0.980857\pi$
$972$	−4.32048	+	1.15767i	−0.138580	+	0.0371323i
$973$	35.6165	+	20.5632i	1.14181	+	0.659225i
$974$	−8.45010			−0.270759
$975$		0			0
$976$	−24.7704			−0.792880
$977$	33.6679	+	19.4382i	1.07713	+	0.621883i	0.930122	−	0.367252i	$-0.119701\pi$
$977$	33.6679	+	19.4382i	1.07713	+	0.621883i	0.147011	+	0.989135i	$0.453035\pi$
$978$	−13.0286	+	3.49101i	−0.416609	+	0.111630i
$979$	−44.7263	−	77.4683i	−1.42946	−	2.47590i
$980$	−0.174832	−	0.0487183i	−0.00558479	−	0.00155625i
$981$	−5.50580	−	1.47527i	−0.175787	−	0.0471019i
$982$	4.63761	+	8.03257i	0.147992	+	0.256330i
$983$			0.207440i			0.00661630i	0.999995	+	0.00330815i	$0.00105302\pi$
$983$			0.207440i			0.00661630i	−0.999995	+	0.00330815i	$0.998947\pi$
$984$	−15.6975	+	9.06297i	−0.500419	+	0.288917i
$985$	−11.9853	−	12.2266i	−0.381883	−	0.389571i
$986$	−0.598381	+	0.160336i	−0.0190563	+	0.00510613i
$987$	−2.85525	−	2.85525i	−0.0908836	−	0.0908836i
$988$		0			0
$989$		−	0.554993i		−	0.0176477i
$990$	43.1443	+	0.429941i	1.37122	+	0.0136644i
$991$	12.7480	−	22.0803i	0.404955	−	0.701402i	−0.589361	−	0.807869i	$-0.700621\pi$
$991$	12.7480	−	22.0803i	0.404955	−	0.701402i	0.994316	+	0.106467i	$0.0339539\pi$
$992$	1.45121	−	5.41599i	0.0460760	−	0.171958i
$993$	−14.5083			−0.460407
$994$	−7.83698	+	29.2480i	−0.248574	+	0.927691i
$995$	−8.54032	−	33.1924i	−0.270746	−	1.05227i
$996$	−0.539885	−	0.539885i	−0.0171069	−	0.0171069i
$997$	33.4743	+	8.96942i	1.06014	+	0.284064i	0.746437	−	0.665456i	$-0.231763\pi$
$997$	33.4743	+	8.96942i	1.06014	+	0.284064i	0.313706	+	0.949520i	$0.398429\pi$
$998$	3.46020	+	12.9137i	0.109531	+	0.408774i
$999$	0.554536	+	2.06955i	0.0175447	+	0.0654778i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	845.2.t.f.188.1		20
5.2	odd	4		845.2.o.e.357.5		20
13.2	odd	12		845.2.o.f.258.1		20
13.3	even	3		65.2.t.a.28.5	yes	20
13.4	even	6		845.2.f.d.408.2		20
13.5	odd	4		845.2.o.g.488.1		20
13.6	odd	12		845.2.k.d.268.9		20
13.7	odd	12		845.2.k.e.268.2		20
13.8	odd	4		65.2.o.a.33.5	yes	20
13.9	even	3		845.2.f.e.408.9		20
13.10	even	6		845.2.t.g.418.1		20
13.11	odd	12		845.2.o.e.258.5		20
13.12	even	2		845.2.t.e.188.5		20
39.8	even	4		585.2.cf.a.163.1		20
39.29	odd	6		585.2.dp.a.28.1		20
65.2	even	12		845.2.t.e.427.5		20
65.3	odd	12		325.2.s.b.132.1		20
65.7	even	12		845.2.f.e.437.2		20
65.8	even	4		325.2.x.b.7.1		20
65.12	odd	4		845.2.o.f.357.1		20
65.17	odd	12		845.2.k.d.577.9		20
65.22	odd	12		845.2.k.e.577.2		20
65.29	even	6		325.2.x.b.93.1		20
65.32	even	12		845.2.f.d.437.9		20
65.34	odd	4		325.2.s.b.293.1		20
65.37	even	12	inner	845.2.t.f.427.1		20
65.42	odd	12		65.2.o.a.2.5	✓	20
65.47	even	4		65.2.t.a.7.5	yes	20
65.57	even	4		845.2.t.g.657.1		20
65.62	odd	12		845.2.o.g.587.1		20
195.47	odd	4		585.2.dp.a.397.1		20
195.107	even	12		585.2.cf.a.262.1		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.o.a.2.5	✓	20	65.42	odd	12
65.2.o.a.33.5	yes	20	13.8	odd	4
65.2.t.a.7.5	yes	20	65.47	even	4
65.2.t.a.28.5	yes	20	13.3	even	3
325.2.s.b.132.1		20	65.3	odd	12
325.2.s.b.293.1		20	65.34	odd	4
325.2.x.b.7.1		20	65.8	even	4
325.2.x.b.93.1		20	65.29	even	6
585.2.cf.a.163.1		20	39.8	even	4
585.2.cf.a.262.1		20	195.107	even	12
585.2.dp.a.28.1		20	39.29	odd	6
585.2.dp.a.397.1		20	195.47	odd	4
845.2.f.d.408.2		20	13.4	even	6
845.2.f.d.437.9		20	65.32	even	12
845.2.f.e.408.9		20	13.9	even	3
845.2.f.e.437.2		20	65.7	even	12
845.2.k.d.268.9		20	13.6	odd	12
845.2.k.d.577.9		20	65.17	odd	12
845.2.k.e.268.2		20	13.7	odd	12
845.2.k.e.577.2		20	65.22	odd	12
845.2.o.e.258.5		20	13.11	odd	12
845.2.o.e.357.5		20	5.2	odd	4
845.2.o.f.258.1		20	13.2	odd	12
845.2.o.f.357.1		20	65.12	odd	4
845.2.o.g.488.1		20	13.5	odd	4
845.2.o.g.587.1		20	65.62	odd	12
845.2.t.e.188.5		20	13.12	even	2
845.2.t.e.427.5		20	65.2	even	12
845.2.t.f.188.1		20	1.1	even	1	trivial
845.2.t.f.427.1		20	65.37	even	12	inner
845.2.t.g.418.1		20	13.10	even	6
845.2.t.g.657.1		20	65.57	even	4

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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.t (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.31467 - 0.759023i) q^{2} +(-0.653367 + 0.175069i) q^{3} +(0.152233 + 0.263675i) q^{4} +(-2.15400 - 0.600231i) q^{5} +(0.991842 + 0.265763i) q^{6} +(-1.29744 - 2.24723i) q^{7} +2.57390i q^{8} +(-2.20184 + 1.27123i) q^{9} +(2.37621 + 2.42404i) q^{10} +(-4.82908 + 1.29395i) q^{11} +(-0.145625 - 0.145625i) q^{12} +3.93915i q^{14} +(1.51244 + 0.0150717i) q^{15} +(2.25812 - 3.91117i) q^{16} +(-0.0211881 + 0.0790751i) q^{17} +3.85958 q^{18} +(0.726525 - 2.71143i) q^{19} +(-0.169644 - 0.659330i) q^{20} +(1.24113 + 1.24113i) q^{21} +(7.33077 + 1.96427i) q^{22} +(1.05016 + 3.91925i) q^{23} +(-0.450611 - 1.68170i) q^{24} +(4.27945 + 2.58580i) q^{25} +(2.65095 - 2.65095i) q^{27} +(0.395026 - 0.684205i) q^{28} +(-4.31701 - 2.49243i) q^{29} +(-1.97691 - 1.16779i) q^{30} +(-2.32124 + 2.32124i) q^{31} +(-1.47921 + 0.854024i) q^{32} +(2.92863 - 1.69085i) q^{33} +(0.0878751 - 0.0878751i) q^{34} +(1.44583 + 5.61931i) q^{35} +(-0.670383 - 0.387046i) q^{36} +(-0.285750 + 0.494934i) q^{37} +(-3.01318 + 3.01318i) q^{38} +(1.54493 - 5.54419i) q^{40} +(-2.69458 - 10.0563i) q^{41} +(-0.689624 - 2.57371i) q^{42} +(-0.132121 - 0.0354017i) q^{43} +(-1.07633 - 1.07633i) q^{44} +(5.50579 - 1.41662i) q^{45} +(1.59419 - 5.94960i) q^{46} -2.30053 q^{47} +(-0.790653 + 2.95076i) q^{48} +(0.133293 - 0.230870i) q^{49} +(-3.66337 - 6.64766i) q^{50} -0.0553744i q^{51} +(6.70735 + 6.70735i) q^{53} +(-5.49724 + 1.47298i) q^{54} +(11.1785 + 0.111396i) q^{55} +(5.78416 - 3.33948i) q^{56} +1.89875i q^{57} +(3.78362 + 6.55343i) q^{58} +(2.59045 + 0.694109i) q^{59} +(0.226268 + 0.401085i) q^{60} +(-2.74237 - 4.74992i) q^{61} +(4.81352 - 1.28978i) q^{62} +(5.71351 + 3.29870i) q^{63} -6.43957 q^{64} -5.13357 q^{66} +(13.6718 + 7.89339i) q^{67} +(-0.0240756 + 0.00645104i) q^{68} +(-1.37228 - 2.37686i) q^{69} +(2.36440 - 8.48494i) q^{70} +(7.42495 + 1.98951i) q^{71} +(-3.27202 - 5.66731i) q^{72} -6.61894i q^{73} +(0.751333 - 0.433783i) q^{74} +(-3.24874 - 0.940275i) q^{75} +(0.825536 - 0.221202i) q^{76} +(9.17326 + 9.17326i) q^{77} -5.71054i q^{79} +(-7.21159 + 7.06928i) q^{80} +(2.54575 - 4.40937i) q^{81} +(-4.09050 + 15.2660i) q^{82} +3.70736 q^{83} +(-0.138314 + 0.516194i) q^{84} +(0.0931025 - 0.157610i) q^{85} +(0.146824 + 0.146824i) q^{86} +(3.25694 + 0.872695i) q^{87} +(-3.33050 - 12.4296i) q^{88} +(4.63094 + 17.2829i) q^{89} +(-8.31353 - 2.31664i) q^{90} +(-0.873538 + 0.873538i) q^{92} +(1.11024 - 1.92300i) q^{93} +(3.02443 + 1.74616i) q^{94} +(-3.19242 + 5.40434i) q^{95} +(0.816956 - 0.816956i) q^{96} +(-4.65043 + 2.68493i) q^{97} +(-0.350471 + 0.202345i) q^{98} +(8.98794 - 8.98794i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} - 2 q^{3} + 6 q^{4} + 4 q^{6} - 2 q^{7} - 12 q^{9} + 10 q^{10} + 8 q^{11} - 24 q^{12} - 8 q^{15} - 2 q^{16} + 10 q^{17} + 16 q^{19} + 12 q^{20} + 4 q^{21} + 16 q^{22} + 2 q^{23} - 28 q^{24}+ \cdots + 60 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 - 2 * q^3 + 6 * q^4 + 4 * q^6 - 2 * q^7 - 12 * q^9 + 10 * q^10 + 8 * q^11 - 24 * q^12 - 8 * q^15 - 2 * q^16 + 10 * q^17 + 16 * q^19 + 12 * q^20 + 4 * q^21 + 16 * q^22 + 2 * q^23 - 28 * q^24 + 18 * q^25 + 4 * q^27 + 18 * q^28 - 14 * q^30 - 48 * q^32 - 18 * q^33 + 2 * q^34 - 20 * q^35 - 36 * q^36 - 4 * q^37 - 8 * q^38 - 16 * q^40 + 28 * q^41 - 56 * q^42 + 22 * q^43 - 36 * q^44 + 6 * q^45 - 8 * q^46 - 40 * q^47 + 28 * q^48 + 18 * q^49 - 78 * q^50 - 10 * q^53 + 12 * q^54 + 26 * q^55 + 8 * q^59 + 28 * q^60 - 16 * q^61 + 40 * q^62 + 36 * q^63 + 20 * q^64 - 32 * q^66 - 18 * q^67 + 28 * q^68 - 16 * q^69 - 12 * q^70 + 56 * q^71 + 4 * q^72 - 18 * q^74 + 34 * q^75 + 80 * q^76 - 28 * q^77 - 110 * q^80 - 14 * q^81 - 22 * q^82 + 48 * q^83 + 32 * q^84 + 28 * q^85 + 60 * q^86 + 62 * q^87 - 50 * q^88 - 6 * q^89 + 46 * q^90 - 8 * q^92 + 32 * q^93 + 48 * q^94 - 14 * q^95 + 56 * q^96 - 66 * q^97 + 30 * q^98 + 60 * q^99

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