LMFDB - Embedded newform 825.2.n.g.301.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(301,825)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(825, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("825.301");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.n (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.13140625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 3x^{7} + 5x^{6} - 3x^{5} + 4x^{4} + 3x^{3} + 5x^{2} + 3x + 1 $ x^8 - 3x^7 + 5x^6 - 3x^5 + 4x^4 + 3x^3 + 5x^2 + 3*x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 165)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			301.2
Root			$-0.227943 - 0.701538i$ of defining polynomial
Character	$\chi$	$=$	825.301
Dual form			825.2.n.g.751.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.212253 - 0.154211i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.596764 - 1.83665i) q^{4} +(0.212253 - 0.154211i) q^{6} +(0.986854 + 3.03722i) q^{7} +(-0.318714 + 0.980901i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.212253 - 0.154211i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.596764 - 1.83665i) q^{4} +(0.212253 - 0.154211i) q^{6} +(0.986854 + 3.03722i) q^{7} +(-0.318714 + 0.980901i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(3.27115 + 0.547326i) q^{11} +1.93117 q^{12} +(-0.905781 - 0.658088i) q^{13} +(0.258911 - 0.796845i) q^{14} +(-2.90578 + 2.11117i) q^{16} +(-0.0713767 + 0.0518582i) q^{17} +(0.0810736 + 0.249519i) q^{18} +(-0.0212704 + 0.0654637i) q^{19} -3.19353 q^{21} +(-0.609909 - 0.620620i) q^{22} -6.65450 q^{23} +(-0.834404 - 0.606230i) q^{24} +(0.0907705 + 0.279363i) q^{26} +(0.809017 - 0.587785i) q^{27} +(4.98940 - 3.62501i) q^{28} +(1.15444 + 3.55299i) q^{29} +(7.75430 + 5.63383i) q^{31} +3.00509 q^{32} +(-1.53138 + 2.94192i) q^{33} +0.0231471 q^{34} +(-0.596764 + 1.83665i) q^{36} +(2.57418 + 7.92250i) q^{37} +(0.0146100 - 0.0106148i) q^{38} +(0.905781 - 0.658088i) q^{39} +(-3.60489 + 11.0947i) q^{41} +(0.677837 + 0.492478i) q^{42} +11.8217 q^{43} +(-0.946857 - 6.33458i) q^{44} +(1.41244 + 1.02620i) q^{46} +(-0.280594 + 0.863579i) q^{47} +(-1.10991 - 3.41595i) q^{48} +(-2.58773 + 1.88010i) q^{49} +(-0.0272635 - 0.0839083i) q^{51} +(-0.668140 + 2.05632i) q^{52} +(0.705768 + 0.512771i) q^{53} -0.262360 q^{54} -3.29374 q^{56} +(-0.0556868 - 0.0404588i) q^{57} +(0.302877 - 0.932160i) q^{58} +(0.567369 + 1.74618i) q^{59} +(8.13881 - 5.91319i) q^{61} +(-0.777078 - 2.39160i) q^{62} +(0.986854 - 3.03722i) q^{63} +(5.17372 + 3.75893i) q^{64} +(0.778717 - 0.388276i) q^{66} -9.53916 q^{67} +(0.137840 + 0.100147i) q^{68} +(2.05635 - 6.32881i) q^{69} +(3.77370 - 2.74175i) q^{71} +(0.834404 - 0.606230i) q^{72} +(2.21267 + 6.80989i) q^{73} +(0.675360 - 2.07854i) q^{74} +0.132927 q^{76} +(1.56580 + 10.4754i) q^{77} -0.293740 q^{78} +(-0.640209 - 0.465139i) q^{79} +(0.309017 + 0.951057i) q^{81} +(2.47608 - 1.79898i) q^{82} +(0.200012 - 0.145318i) q^{83} +(1.90578 + 5.86539i) q^{84} +(-2.50920 - 1.82304i) q^{86} -3.73583 q^{87} +(-1.57943 + 3.03423i) q^{88} -14.5788 q^{89} +(1.10489 - 3.40050i) q^{91} +(3.97116 + 12.2220i) q^{92} +(-7.75430 + 5.63383i) q^{93} +(0.192730 - 0.140027i) q^{94} +(-0.928623 + 2.85801i) q^{96} +(-3.31048 - 2.40521i) q^{97} +0.839188 q^{98} +(-2.32471 - 2.36553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{6} - 3 q^{7} + q^{8} - 2 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^6 - 3 * q^7 + q^8 - 2 * q^9	$ 8 q - 4 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{6} - 3 q^{7} + q^{8} - 2 q^{9} + 3 q^{11} - 2 q^{12} + 4 q^{13} - 4 q^{14} - 12 q^{16} + q^{18} + 2 q^{19} - 12 q^{21} - 9 q^{22} + 6 q^{23} + 4 q^{24} + 2 q^{26} + 2 q^{27} + 11 q^{28} + 10 q^{29} + 19 q^{31} - 12 q^{32} + 2 q^{33} - 6 q^{34} + 2 q^{36} + q^{37} + 20 q^{38} - 4 q^{39} - 9 q^{41} - q^{42} + 17 q^{44} - 22 q^{46} + 19 q^{47} - 13 q^{48} + q^{49} + 10 q^{51} + 2 q^{52} - 25 q^{53} - 6 q^{54} - 16 q^{56} - 7 q^{57} + 12 q^{58} + 13 q^{59} + 13 q^{61} - 35 q^{62} - 3 q^{63} + 39 q^{64} - 11 q^{66} - 2 q^{67} - 19 q^{68} + 9 q^{69} - 11 q^{71} - 4 q^{72} + 7 q^{73} - 43 q^{74} - 38 q^{76} + 7 q^{77} + 8 q^{78} - 22 q^{79} - 2 q^{81} + 35 q^{82} + 21 q^{83} + 4 q^{84} + 20 q^{86} + 30 q^{87} - 59 q^{88} - 20 q^{89} - 11 q^{91} + 28 q^{92} - 19 q^{93} - 35 q^{94} - 8 q^{96} - 31 q^{97} - 22 q^{98} - 7 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^6 - 3 * q^7 + q^8 - 2 * q^9 + 3 * q^11 - 2 * q^12 + 4 * q^13 - 4 * q^14 - 12 * q^16 + q^18 + 2 * q^19 - 12 * q^21 - 9 * q^22 + 6 * q^23 + 4 * q^24 + 2 * q^26 + 2 * q^27 + 11 * q^28 + 10 * q^29 + 19 * q^31 - 12 * q^32 + 2 * q^33 - 6 * q^34 + 2 * q^36 + q^37 + 20 * q^38 - 4 * q^39 - 9 * q^41 - q^42 + 17 * q^44 - 22 * q^46 + 19 * q^47 - 13 * q^48 + q^49 + 10 * q^51 + 2 * q^52 - 25 * q^53 - 6 * q^54 - 16 * q^56 - 7 * q^57 + 12 * q^58 + 13 * q^59 + 13 * q^61 - 35 * q^62 - 3 * q^63 + 39 * q^64 - 11 * q^66 - 2 * q^67 - 19 * q^68 + 9 * q^69 - 11 * q^71 - 4 * q^72 + 7 * q^73 - 43 * q^74 - 38 * q^76 + 7 * q^77 + 8 * q^78 - 22 * q^79 - 2 * q^81 + 35 * q^82 + 21 * q^83 + 4 * q^84 + 20 * q^86 + 30 * q^87 - 59 * q^88 - 20 * q^89 - 11 * q^91 + 28 * q^92 - 19 * q^93 - 35 * q^94 - 8 * q^96 - 31 * q^97 - 22 * q^98 - 7 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/825\mathbb{Z}\right)^\times$.

$n$	$376$	$551$	$727$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$	$1$

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 $

$2$	−0.212253	−	0.154211i	−0.150086	−	0.109044i	0.510208	−	0.860051i	$-0.329568\pi$
$2$	−0.212253	−	0.154211i	−0.150086	−	0.109044i	−0.660294	+	0.751007i	$0.729568\pi$
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$3$	−0.309017	+	0.951057i	−0.178411	+	0.549093i
$4$	−0.596764	−	1.83665i	−0.298382	−	0.918325i
$5$		0			0
$5$		0			0
$6$	0.212253	−	0.154211i	0.0866521	−	0.0629564i
$7$	0.986854	+	3.03722i	0.372996	+	1.14796i	0.944821	+	0.327587i	$0.106236\pi$
$7$	0.986854	+	3.03722i	0.372996	+	1.14796i	−0.571825	+	0.820376i	$0.693764\pi$
$8$	−0.318714	+	0.980901i	−0.112682	+	0.346801i
$9$	−0.809017	−	0.587785i	−0.269672	−	0.195928i
$10$		0			0
$11$	3.27115	+	0.547326i	0.986289	+	0.165025i
$11$	3.27115	+	0.547326i	0.986289	+	0.165025i
$12$	1.93117			0.557480
$13$	−0.905781	−	0.658088i	−0.251218	−	0.182521i	0.455048	−	0.890467i	$-0.349622\pi$
$13$	−0.905781	−	0.658088i	−0.251218	−	0.182521i	−0.706267	+	0.707946i	$0.749622\pi$
$14$	0.258911	−	0.796845i	0.0691968	−	0.212966i
$15$		0			0
$16$	−2.90578	+	2.11117i	−0.726445	+	0.527793i
$17$	−0.0713767	+	0.0518582i	−0.0173114	+	0.0125775i	−0.596407	−	0.802682i	$-0.703406\pi$
$17$	−0.0713767	+	0.0518582i	−0.0173114	+	0.0125775i	0.579096	+	0.815259i	$0.303406\pi$
$18$	0.0810736	+	0.249519i	0.0191092	+	0.0588122i
$19$	−0.0212704	+	0.0654637i	−0.00487977	+	0.0150184i	−0.953467	−	0.301498i	$-0.902513\pi$
$19$	−0.0212704	+	0.0654637i	−0.00487977	+	0.0150184i	0.948587	+	0.316517i	$0.102513\pi$
$20$		0			0
$21$	−3.19353			−0.696885
$22$	−0.609909	−	0.620620i	−0.130033	−	0.132317i
$23$	−6.65450			−1.38756			−0.693780	−	0.720187i	$-0.744056\pi$
$23$	−6.65450			−1.38756			−0.693780	+	0.720187i	$0.744056\pi$
$24$	−0.834404	−	0.606230i	−0.170322	−	0.123746i
$25$		0			0
$26$	0.0907705	+	0.279363i	0.0178016	+	0.0547876i
$27$	0.809017	−	0.587785i	0.155695	−	0.113119i
$28$	4.98940	−	3.62501i	0.942908	−	0.685062i
$29$	1.15444	+	3.55299i	0.214373	+	0.659773i	0.999197	+	0.0400546i	$0.0127532\pi$
$29$	1.15444	+	3.55299i	0.214373	+	0.659773i	−0.784824	+	0.619718i	$0.787247\pi$
$30$		0			0
$31$	7.75430	+	5.63383i	1.39271	+	1.01187i	0.995562	+	0.0941130i	$0.0300015\pi$
$31$	7.75430	+	5.63383i	1.39271	+	1.01187i	0.397152	+	0.917753i	$0.369998\pi$
$32$	3.00509			0.531230
$33$	−1.53138	+	2.94192i	−0.266579	+	0.512122i
$34$	0.0231471			0.00396969
$35$		0			0
$36$	−0.596764	+	1.83665i	−0.0994606	+	0.306108i
$37$	2.57418	+	7.92250i	0.423192	+	1.30245i	0.904715	+	0.426017i	$0.140084\pi$
$37$	2.57418	+	7.92250i	0.423192	+	1.30245i	−0.481523	+	0.876433i	$0.659916\pi$
$38$	0.0146100	−	0.0106148i	0.00237005	−	0.00172194i
$39$	0.905781	−	0.658088i	0.145041	−	0.105378i
$40$		0			0
$41$	−3.60489	+	11.0947i	−0.562989	+	1.73270i	0.110863	+	0.993836i	$0.464638\pi$
$41$	−3.60489	+	11.0947i	−0.562989	+	1.73270i	−0.673852	+	0.738866i	$0.735362\pi$
$42$	0.677837	+	0.492478i	0.104593	+	0.0759909i
$43$	11.8217			1.80280			0.901399	−	0.432989i	$-0.142541\pi$
$43$	11.8217			1.80280			0.901399	+	0.432989i	$0.142541\pi$
$44$	−0.946857	−	6.33458i	−0.142744	−	0.954974i
$45$		0			0
$46$	1.41244	+	1.02620i	0.208253	+	0.151305i
$47$	−0.280594	+	0.863579i	−0.0409288	+	0.125966i	−0.969433	−	0.245356i	$-0.921095\pi$
$47$	−0.280594	+	0.863579i	−0.0409288	+	0.125966i	0.928504	+	0.371322i	$0.121095\pi$
$48$	−1.10991	−	3.41595i	−0.160202	−	0.493050i
$49$	−2.58773	+	1.88010i	−0.369676	+	0.268586i
$50$		0			0
$51$	−0.0272635	−	0.0839083i	−0.00381765	−	0.0117495i
$52$	−0.668140	+	2.05632i	−0.0926544	+	0.285161i
$53$	0.705768	+	0.512771i	0.0969447	+	0.0704344i	0.635202	−	0.772346i	$-0.280917\pi$
$53$	0.705768	+	0.512771i	0.0969447	+	0.0704344i	−0.538257	+	0.842781i	$0.680917\pi$
$54$	−0.262360			−0.0357026
$55$		0			0
$56$	−3.29374			−0.440144
$57$	−0.0556868	−	0.0404588i	−0.00737589	−	0.00535890i
$58$	0.302877	−	0.932160i	0.0397697	−	0.122399i
$59$	0.567369	+	1.74618i	0.0738651	+	0.227333i	0.981172	−	0.193135i	$-0.0618656\pi$
$59$	0.567369	+	1.74618i	0.0738651	+	0.227333i	−0.907307	+	0.420469i	$0.861866\pi$
$60$		0			0
$61$	8.13881	−	5.91319i	1.04207	−	0.757107i	0.0713799	−	0.997449i	$-0.477260\pi$
$61$	8.13881	−	5.91319i	1.04207	−	0.757107i	0.970688	+	0.240342i	$0.0772597\pi$
$62$	−0.777078	−	2.39160i	−0.0986890	−	0.303733i
$63$	0.986854	−	3.03722i	0.124332	−	0.382654i
$64$	5.17372	+	3.75893i	0.646715	+	0.469866i
$65$		0			0
$66$	0.778717	−	0.388276i	0.0958534	−	0.0477935i
$67$	−9.53916			−1.16539			−0.582697	−	0.812690i	$-0.698003\pi$
$67$	−9.53916			−1.16539			−0.582697	+	0.812690i	$0.698003\pi$
$68$	0.137840	+	0.100147i	0.0167156	+	0.0121446i
$69$	2.05635	−	6.32881i	0.247556	−	0.761899i
$70$		0			0
$71$	3.77370	−	2.74175i	0.447855	−	0.325386i	−0.340893	−	0.940102i	$-0.610729\pi$
$71$	3.77370	−	2.74175i	0.447855	−	0.325386i	0.788748	+	0.614716i	$0.210729\pi$
$72$	0.834404	−	0.606230i	0.0983354	−	0.0714449i
$73$	2.21267	+	6.80989i	0.258973	+	0.797037i	0.993021	+	0.117939i	$0.0376288\pi$
$73$	2.21267	+	6.80989i	0.258973	+	0.797037i	−0.734048	+	0.679098i	$0.762371\pi$
$74$	0.675360	−	2.07854i	0.0785090	−	0.241626i
$75$		0			0
$76$	0.132927			0.0152478
$77$	1.56580	+	10.4754i	0.178439	+	1.19378i
$78$	−0.293740			−0.0332595
$79$	−0.640209	−	0.465139i	−0.0720292	−	0.0523323i	0.551188	−	0.834381i	$-0.314175\pi$
$79$	−0.640209	−	0.465139i	−0.0720292	−	0.0523323i	−0.623217	+	0.782049i	$0.714175\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	2.47608	−	1.79898i	0.273437	−	0.198664i
$83$	0.200012	−	0.145318i	0.0219542	−	0.0159507i	−0.576754	−	0.816918i	$-0.695681\pi$
$83$	0.200012	−	0.145318i	0.0219542	−	0.0159507i	0.598708	+	0.800967i	$0.295681\pi$
$84$	1.90578	+	5.86539i	0.207938	+	0.639966i
$85$		0			0
$86$	−2.50920	−	1.82304i	−0.270574	−	0.196584i
$87$	−3.73583			−0.400523
$88$	−1.57943	+	3.03423i	−0.168368	+	0.323450i
$89$	−14.5788			−1.54535			−0.772673	−	0.634804i	$-0.781081\pi$
$89$	−14.5788			−1.54535			−0.772673	+	0.634804i	$0.781081\pi$
$90$		0			0
$91$	1.10489	−	3.40050i	0.115824	−	0.356469i
$92$	3.97116	+	12.2220i	0.414022	+	1.27423i
$93$	−7.75430	+	5.63383i	−0.804084	+	0.584201i
$94$	0.192730	−	0.140027i	0.0198786	−	0.0144427i
$95$		0			0
$96$	−0.928623	+	2.85801i	−0.0947772	+	0.291694i
$97$	−3.31048	−	2.40521i	−0.336128	−	0.244212i	0.406898	−	0.913474i	$-0.366610\pi$
$97$	−3.31048	−	2.40521i	−0.336128	−	0.244212i	−0.743027	+	0.669262i	$0.766610\pi$
$98$	0.839188			0.0847708
$99$	−2.32471	−	2.36553i	−0.233642	−	0.237745i
$100$		0			0
$101$	−3.47207	−	2.52261i	−0.345484	−	0.251009i	0.401488	−	0.915864i	$-0.368493\pi$
$101$	−3.47207	−	2.52261i	−0.345484	−	0.251009i	−0.746972	+	0.664856i	$0.768493\pi$
$102$	−0.00715284	+	0.0220142i	−0.000708236	+	0.00217973i
$103$	−0.646712	−	1.99038i	−0.0637224	−	0.196118i	0.914127	−	0.405429i	$-0.132878\pi$
$103$	−0.646712	−	1.99038i	−0.0637224	−	0.196118i	−0.977849	+	0.209311i	$0.932878\pi$
$104$	0.934204	−	0.678739i	0.0916062	−	0.0665558i
$105$		0			0
$106$	−0.0707268	−	0.217675i	−0.00686959	−	0.0211424i
$107$	4.86421	−	14.9705i	0.470241	−	1.44725i	−0.382029	−	0.924151i	$-0.624774\pi$
$107$	4.86421	−	14.9705i	0.470241	−	1.44725i	0.852270	−	0.523103i	$-0.175226\pi$
$108$	−1.56235	−	1.13511i	−0.150337	−	0.109226i
$109$	−4.13271			−0.395842			−0.197921	−	0.980218i	$-0.563419\pi$
$109$	−4.13271			−0.395842			−0.197921	+	0.980218i	$0.563419\pi$
$110$		0			0
$111$	−8.33021			−0.790668
$112$	−9.27969	−	6.74209i	−0.876848	−	0.637067i
$113$	−4.25053	+	13.0818i	−0.399856	+	1.23063i	0.525258	+	0.850943i	$0.323969\pi$
$113$	−4.25053	+	13.0818i	−0.399856	+	1.23063i	−0.925114	+	0.379688i	$0.876031\pi$
$114$	0.00558051	+	0.0171750i	0.000522662	+	0.00160859i
$115$		0			0
$116$	5.83666	−	4.24059i	0.541921	−	0.393728i
$117$	0.345977	+	1.06481i	0.0319856	+	0.0984416i
$118$	0.148855	−	0.458127i	0.0137032	−	0.0421740i
$119$	−0.227943	−	0.165611i	−0.0208955	−	0.0151815i
$120$		0			0
$121$	10.4009	+	3.58078i	0.945533	+	0.325525i
$122$	−2.63937			−0.238957
$123$	−9.43772	−	6.85690i	−0.850971	−	0.618266i
$124$	5.71989	−	17.6040i	0.513661	−	1.58089i
$125$		0			0
$126$	−0.677837	+	0.492478i	−0.0603865	+	0.0438734i
$127$	6.39106	−	4.64338i	0.567115	−	0.412033i	−0.266941	−	0.963713i	$-0.586013\pi$
$127$	6.39106	−	4.64338i	0.567115	−	0.412033i	0.834056	+	0.551680i	$0.186013\pi$
$128$	−2.37572	−	7.31171i	−0.209986	−	0.646270i
$129$	−3.65312	+	11.2431i	−0.321639	+	0.989903i
$130$		0			0
$131$	−16.3539			−1.42884			−0.714422	−	0.699715i	$-0.753310\pi$
$131$	−16.3539			−1.42884			−0.714422	+	0.699715i	$0.753310\pi$
$132$	6.31714	+	1.05698i	0.549837	+	0.0919982i
$133$	−0.219819			−0.0190607
$134$	2.02472	+	1.47104i	0.174909	+	0.127079i
$135$		0			0
$136$	−0.0281190	−	0.0865414i	−0.00241118	−	0.00742086i
$137$	6.25538	−	4.54480i	0.534433	−	0.388289i	−0.287580	−	0.957757i	$-0.592851\pi$
$137$	6.25538	−	4.54480i	0.534433	−	0.388289i	0.822013	+	0.569468i	$0.192851\pi$
$138$	−1.41244	+	1.02620i	−0.120235	+	0.0873558i
$139$	6.23796	+	19.1985i	0.529097	+	1.62839i	0.756069	+	0.654492i	$0.227117\pi$
$139$	6.23796	+	19.1985i	0.529097	+	1.62839i	−0.226972	+	0.973901i	$0.572883\pi$
$140$		0			0
$141$	−0.734604	−	0.533721i	−0.0618648	−	0.0449474i
$142$	−1.22379			−0.102698
$143$	−2.60276	−	2.64846i	−0.217653	−	0.221476i
$144$	3.59174			0.299312
$145$		0			0
$146$	0.580514	−	1.78664i	0.0480437	−	0.147863i
$147$	−0.988426	−	3.04206i	−0.0815240	−	0.250905i
$148$	13.0147	−	9.45572i	1.06980	−	0.777255i
$149$	−7.84361	+	5.69872i	−0.642573	+	0.466857i	−0.860733	−	0.509056i	$-0.829995\pi$
$149$	−7.84361	+	5.69872i	−0.642573	+	0.466857i	0.218160	+	0.975913i	$0.429995\pi$
$150$		0			0
$151$	4.68515	−	14.4194i	0.381272	−	1.17343i	−0.557877	−	0.829924i	$-0.688384\pi$
$151$	4.68515	−	14.4194i	0.381272	−	1.17343i	0.939149	−	0.343511i	$-0.111616\pi$
$152$	−0.0574342	−	0.0417284i	−0.00465853	−	0.00338462i
$153$	0.0882264			0.00713268
$154$	1.28307	−	2.46489i	0.103393	−	0.198627i
$155$		0			0
$156$	−1.74921	−	1.27088i	−0.140049	−	0.101752i
$157$	4.59834	−	14.1522i	0.366987	−	1.12947i	−0.581740	−	0.813375i	$-0.697628\pi$
$157$	4.59834	−	14.1522i	0.366987	−	1.12947i	0.948727	−	0.316096i	$-0.102372\pi$
$158$	0.0641570	+	0.197455i	0.00510405	+	0.0157087i
$159$	−0.705768	+	0.512771i	−0.0559710	+	0.0406653i
$160$		0			0
$161$	−6.56702	−	20.2112i	−0.517554	−	1.59287i
$162$	0.0810736	−	0.249519i	0.00636974	−	0.0196041i
$163$	2.75158	+	1.99914i	0.215521	+	0.156585i	0.690308	−	0.723516i	$-0.257475\pi$
$163$	2.75158	+	1.99914i	0.215521	+	0.156585i	−0.474787	+	0.880101i	$0.657475\pi$
$164$	22.5283			1.75917
$165$		0			0
$166$	−0.0648629			−0.00503434
$167$	−18.2970	−	13.2936i	−1.41587	−	1.02869i	−0.992437	−	0.122757i	$-0.960826\pi$
$167$	−18.2970	−	13.2936i	−1.41587	−	1.02869i	−0.423429	−	0.905929i	$-0.639174\pi$
$168$	1.01782	−	3.13253i	0.0785266	−	0.241680i
$169$	−3.62986	−	11.1716i	−0.279220	−	0.859351i
$170$		0			0
$171$	0.0556868	−	0.0404588i	0.00425847	−	0.00309396i
$172$	−7.05478	−	21.7124i	−0.537922	−	1.65555i
$173$	4.04543	−	12.4506i	0.307568	−	0.946598i	−0.671138	−	0.741333i	$-0.734194\pi$
$173$	4.04543	−	12.4506i	0.307568	−	0.946598i	0.978706	−	0.205266i	$-0.0658058\pi$
$174$	0.792943	+	0.576107i	0.0601128	+	0.0436745i
$175$		0			0
$176$	−10.6607	+	5.31556i	−0.803584	+	0.400675i
$177$	−1.83604			−0.138005
$178$	3.09439	+	2.24821i	0.231935	+	0.168510i
$179$	−4.69008	+	14.4346i	−0.350553	+	1.07889i	0.607990	+	0.793944i	$0.291976\pi$
$179$	−4.69008	+	14.4346i	−0.350553	+	1.07889i	−0.958543	+	0.284947i	$0.908024\pi$
$180$		0			0
$181$	−1.14353	+	0.830823i	−0.0849978	+	0.0617546i	−0.629473	−	0.777023i	$-0.716729\pi$
$181$	−1.14353	+	0.830823i	−0.0849978	+	0.0617546i	0.544475	+	0.838777i	$0.316729\pi$
$182$	−0.758911	+	0.551381i	−0.0562542	+	0.0408711i
$183$	3.10875	+	9.56775i	0.229805	+	0.707268i
$184$	2.12088	−	6.52740i	0.156354	−	0.481207i
$185$		0			0
$186$	2.51468			0.184385
$187$	−0.261867	+	0.130570i	−0.0191496	+	0.00954820i
$188$	1.75354			0.127890
$189$	2.58362	+	1.87711i	0.187931	+	0.136540i
$190$		0			0
$191$	1.51701	+	4.66887i	0.109767	+	0.337827i	0.990820	−	0.135190i	$-0.0431646\pi$
$191$	1.51701	+	4.66887i	0.109767	+	0.337827i	−0.881053	+	0.473018i	$0.843165\pi$
$192$	−5.17372	+	3.75893i	−0.373381	+	0.271277i
$193$	7.86354	−	5.71320i	0.566030	−	0.411245i	−0.267631	−	0.963522i	$-0.586241\pi$
$193$	7.86354	−	5.71320i	0.566030	−	0.411245i	0.833661	+	0.552276i	$0.186241\pi$
$194$	0.331752	+	1.02103i	0.0238184	+	0.0733054i
$195$		0			0
$196$	4.99735	+	3.63079i	0.356953	+	0.259342i
$197$	8.88764			0.633218			0.316609	−	0.948556i	$-0.397456\pi$
$197$	8.88764			0.633218			0.316609	+	0.948556i	$0.397456\pi$
$198$	0.128636	+	0.860588i	0.00914175	+	0.0611593i
$199$	18.0381			1.27869			0.639343	−	0.768921i	$-0.279206\pi$
$199$	18.0381			1.27869			0.639343	+	0.768921i	$0.279206\pi$
$200$		0			0
$201$	2.94776	−	9.07228i	0.207919	−	0.639909i
$202$	0.347945	+	1.07086i	0.0244813	+	0.0753457i
$203$	−9.65196	+	7.01256i	−0.677435	+	0.492185i
$204$	−0.137840	+	0.100147i	−0.00965075	+	0.00701168i
$205$		0			0
$206$	−0.169671	+	0.522194i	−0.0118216	+	0.0363830i
$207$	5.38361	+	3.91142i	0.374186	+	0.271862i
$208$	4.02134			0.278830
$209$	−0.105409	+	0.202500i	−0.00729128	+	0.0140072i
$210$		0			0
$211$	−14.5444	−	10.5671i	−1.00127	−	0.727469i	−0.0389136	−	0.999243i	$-0.512390\pi$
$211$	−14.5444	−	10.5671i	−1.00127	−	0.727469i	−0.962361	+	0.271774i	$0.912390\pi$
$212$	0.520603	−	1.60225i	0.0357552	−	0.110043i
$213$	1.44142	+	4.43625i	0.0987647	+	0.303967i
$214$	−3.34106	+	2.42743i	−0.228390	+	0.165935i
$215$		0			0
$216$	0.318714	+	0.980901i	0.0216857	+	0.0667418i
$217$	−9.45884	+	29.1113i	−0.642108	+	1.97621i
$218$	0.877182	+	0.637310i	0.0594103	+	0.0431641i
$219$	−7.16034			−0.483851
$220$		0			0
$221$	0.0987789			0.00664459
$222$	1.76812	+	1.28461i	0.118668	+	0.0862174i
$223$	4.24865	−	13.0760i	0.284511	−	0.875635i	−0.702034	−	0.712144i	$-0.747724\pi$
$223$	4.24865	−	13.0760i	0.284511	−	0.875635i	0.986545	−	0.163491i	$-0.0522755\pi$
$224$	2.96558	+	9.12713i	0.198146	+	0.609832i
$225$		0			0
$226$	2.91955	−	2.12118i	0.194205	−	0.141099i
$227$	−0.204796	−	0.630298i	−0.0135928	−	0.0418344i	0.944030	−	0.329859i	$-0.107001\pi$
$227$	−0.204796	−	0.630298i	−0.0135928	−	0.0418344i	−0.957623	+	0.288025i	$0.907001\pi$
$228$	−0.0410768	+	0.126421i	−0.00272038	+	0.00837246i
$229$	6.05987	+	4.40275i	0.400447	+	0.290942i	0.769723	−	0.638378i	$-0.220394\pi$
$229$	6.05987	+	4.40275i	0.400447	+	0.290942i	−0.369276	+	0.929320i	$0.620394\pi$
$230$		0			0
$231$	−10.4465	−	1.74790i	−0.687330	−	0.115004i
$232$	−3.85306			−0.252966
$233$	8.51520	+	6.18665i	0.557849	+	0.405301i	0.830671	−	0.556763i	$-0.187957\pi$
$233$	8.51520	+	6.18665i	0.557849	+	0.405301i	−0.272822	+	0.962065i	$0.587957\pi$
$234$	0.0907705	−	0.279363i	0.00593385	−	0.0182625i
$235$		0			0
$236$	2.86854	−	2.08411i	0.186726	−	0.135664i
$237$	0.640209	−	0.465139i	0.0415861	−	0.0302140i
$238$	0.0228428	+	0.0703028i	0.00148068	+	0.00455706i
$239$	5.27684	−	16.2404i	0.341330	−	1.05051i	−0.622189	−	0.782867i	$-0.713756\pi$
$239$	5.27684	−	16.2404i	0.341330	−	1.05051i	0.963519	−	0.267640i	$-0.0862437\pi$
$240$		0			0
$241$	−16.7082			−1.07627			−0.538135	−	0.842859i	$-0.680871\pi$
$241$	−16.7082			−1.07627			−0.538135	+	0.842859i	$0.680871\pi$
$242$	−1.65542	−	2.36396i	−0.106415	−	0.151961i
$243$	−1.00000			−0.0641500
$244$	−15.7174	−	11.4194i	−1.00620	−	0.731050i
$245$		0			0
$246$	0.945777	+	2.91080i	0.0603006	+	0.185586i
$247$	0.0623472	−	0.0452979i	0.00396706	−	0.00288224i
$248$	−7.99763	+	5.81062i	−0.507850	+	0.368975i
$249$	0.0763980	+	0.235129i	0.00484152	+	0.0149007i
$250$		0			0
$251$	4.15646	+	3.01984i	0.262353	+	0.190611i	0.711184	−	0.703006i	$-0.248159\pi$
$251$	4.15646	+	3.01984i	0.262353	+	0.190611i	−0.448831	+	0.893617i	$0.648159\pi$
$252$	−6.16724			−0.388499
$253$	−21.7679	−	3.64219i	−1.36854	−	0.228982i
$254$	−2.07259			−0.130046
$255$		0			0
$256$	3.32908	−	10.2458i	0.208067	−	0.640366i
$257$	1.14282	+	3.51724i	0.0712872	+	0.219399i	0.980352	−	0.197255i	$-0.0632026\pi$
$257$	1.14282	+	3.51724i	0.0712872	+	0.219399i	−0.909065	+	0.416654i	$0.863203\pi$
$258$	2.50920	−	1.82304i	0.156216	−	0.113498i
$259$	−21.5221	+	15.6367i	−1.33732	+	0.971617i
$260$		0			0
$261$	1.15444	−	3.55299i	0.0714577	−	0.219924i
$262$	3.47116	+	2.52195i	0.214449	+	0.155806i
$263$	−31.6315			−1.95048			−0.975241	−	0.221147i	$-0.929020\pi$
$263$	−31.6315			−1.95048			−0.975241	+	0.221147i	$0.929020\pi$
$264$	−2.39766	−	2.43976i	−0.147566	−	0.150157i
$265$		0			0
$266$	0.0466573	+	0.0338985i	0.00286074	+	0.00207845i
$267$	4.50509	−	13.8652i	0.275707	−	0.848539i
$268$	5.69262	+	17.5201i	0.347732	+	1.07021i
$269$	11.9536	−	8.68479i	0.728823	−	0.529521i	−0.160368	−	0.987057i	$-0.551268\pi$
$269$	11.9536	−	8.68479i	0.728823	−	0.529521i	0.889191	+	0.457536i	$0.151268\pi$
$270$		0			0
$271$	−6.05269	−	18.6283i	−0.367675	−	1.13159i	−0.948289	−	0.317408i	$-0.897188\pi$
$271$	−6.05269	−	18.6283i	−0.367675	−	1.13159i	0.580614	−	0.814179i	$-0.302812\pi$
$272$	0.0979234	−	0.301377i	0.00593748	−	0.0182737i
$273$	2.89263	+	2.10162i	0.175070	+	0.127196i
$274$	−2.02859			−0.122551
$275$		0			0
$276$	−12.8510			−0.773537
$277$	20.8001	+	15.1122i	1.24976	+	0.908002i	0.998208	−	0.0598418i	$-0.0190596\pi$
$277$	20.8001	+	15.1122i	1.24976	+	0.908002i	0.251550	+	0.967844i	$0.419060\pi$
$278$	1.63659	−	5.03691i	0.0981561	−	0.302094i
$279$	−2.96188	−	9.11573i	−0.177323	−	0.545744i
$280$		0			0
$281$	21.6096	−	15.7003i	1.28912	−	0.936599i	0.289331	−	0.957229i	$-0.406567\pi$
$281$	21.6096	−	15.7003i	1.28912	−	0.936599i	0.999787	+	0.0206304i	$0.00656732\pi$
$282$	0.0736165	+	0.226568i	0.00438380	+	0.0134919i
$283$	−2.23535	+	6.87970i	−0.132878	+	0.408956i	−0.995254	−	0.0973123i	$-0.968975\pi$
$283$	−2.23535	+	6.87970i	−0.132878	+	0.408956i	0.862376	+	0.506268i	$0.168975\pi$
$284$	−7.28764	−	5.29478i	−0.432442	−	0.314187i
$285$		0			0
$286$	0.144021	+	0.963520i	0.00851616	+	0.0569741i
$287$	−37.2546			−2.19907
$288$	−2.43117	−	1.76635i	−0.143258	−	0.104083i
$289$	−5.25088	+	16.1606i	−0.308876	+	0.950621i
$290$		0			0
$291$	3.31048	−	2.40521i	0.194064	−	0.140996i
$292$	11.1869	−	8.12778i	0.654666	−	0.475643i
$293$	−4.51002	−	13.8804i	−0.263478	−	0.810902i	−0.992040	−	0.125922i	$-0.959811\pi$
$293$	−4.51002	−	13.8804i	−0.263478	−	0.810902i	0.728562	−	0.684980i	$-0.240189\pi$
$294$	−0.259323	+	0.798115i	−0.0151240	+	0.0465470i
$295$		0			0
$296$	−8.59161			−0.499377
$297$	2.96813	−	1.47994i	0.172228	−	0.0858747i
$298$	2.54364			0.147349
$299$	6.02752	+	4.37925i	0.348580	+	0.253258i
$300$		0			0
$301$	11.6663	+	35.9053i	0.672436	+	2.06955i
$302$	−3.21807	+	2.33807i	−0.185179	+	0.134541i
$303$	3.47207	−	2.52261i	0.199465	−	0.144920i
$304$	−0.0763980	−	0.235129i	−0.00438172	−	0.0134856i
$305$		0			0
$306$	−0.0187264	−	0.0136055i	−0.00107052	−	0.000777775i
$307$	−28.5445			−1.62912			−0.814559	−	0.580080i	$-0.803021\pi$
$307$	−28.5445			−1.62912			−0.814559	+	0.580080i	$0.803021\pi$
$308$	18.3051	−	9.12713i	1.04303	−	0.520066i
$309$	2.09280			0.119055
$310$		0			0
$311$	−3.07411	+	9.46113i	−0.174317	+	0.536492i	−0.999602	−	0.0282249i	$-0.991015\pi$
$311$	−3.07411	+	9.46113i	−0.174317	+	0.536492i	0.825285	+	0.564717i	$0.191015\pi$
$312$	0.356834	+	1.09822i	0.0202018	+	0.0621746i
$313$	−13.2929	+	9.65786i	−0.751359	+	0.545894i	−0.896248	−	0.443554i	$-0.853718\pi$
$313$	−13.2929	+	9.65786i	−0.751359	+	0.545894i	0.144889	+	0.989448i	$0.453718\pi$
$314$	−3.15844	+	2.29474i	−0.178241	+	0.129500i
$315$		0			0
$316$	−0.472244	+	1.45342i	−0.0265658	+	0.0817612i
$317$	11.4966	+	8.35278i	0.645714	+	0.469139i	0.861809	−	0.507234i	$-0.169332\pi$
$317$	11.4966	+	8.35278i	0.645714	+	0.469139i	−0.216094	+	0.976373i	$0.569332\pi$
$318$	0.228877			0.0128348
$319$	1.83169	+	12.2542i	0.102555	+	0.686104i
$320$		0			0
$321$	12.7347	+	9.25228i	0.710780	+	0.516412i
$322$	−1.72292	+	5.30261i	−0.0960147	+	0.295503i
$323$	−0.00187662	−	0.00577563i	−0.000104418	−	0.000321365i
$324$	1.56235	−	1.13511i	0.0867971	−	0.0630618i
$325$		0			0
$326$	−0.275743	−	0.848650i	−0.0152720	−	0.0470024i
$327$	1.27708	−	3.93044i	0.0706226	−	0.217354i
$328$	−9.73387	−	7.07207i	−0.537463	−	0.390490i
$329$	−2.89979			−0.159870
$330$		0			0
$331$	−10.9119			−0.599773			−0.299886	−	0.953975i	$-0.596949\pi$
$331$	−10.9119			−0.599773			−0.299886	+	0.953975i	$0.596949\pi$
$332$	−0.386258	−	0.280633i	−0.0211986	−	0.0154017i
$333$	2.57418	−	7.92250i	0.141064	−	0.434150i
$334$	1.83359	+	5.64321i	0.100330	+	0.308783i
$335$		0			0
$336$	9.27969	−	6.74209i	0.506249	−	0.367811i
$337$	1.81890	+	5.59800i	0.0990819	+	0.304943i	0.988296	−	0.152549i	$-0.0487481\pi$
$337$	1.81890	+	5.59800i	0.0990819	+	0.304943i	−0.889214	+	0.457491i	$0.848748\pi$
$338$	−0.952330	+	2.93097i	−0.0517999	+	0.159424i
$339$	−11.1280	−	8.08499i	−0.604392	−	0.439116i
$340$		0			0
$341$	22.2820	+	22.6732i	1.20664	+	1.22783i
$342$	−0.0180589			−0.000976514
$343$	9.82132	+	7.13561i	0.530302	+	0.385287i
$344$	−3.76775	+	11.5959i	−0.203144	+	0.625212i
$345$		0			0
$346$	−2.77867	+	2.01882i	−0.149382	+	0.108533i
$347$	27.9145	−	20.2811i	1.49853	−	1.08875i	0.527569	−	0.849512i	$-0.323104\pi$
$347$	27.9145	−	20.2811i	1.49853	−	1.08875i	0.970962	−	0.239234i	$-0.0768962\pi$
$348$	2.22941	+	6.86141i	0.119509	+	0.367810i
$349$	−1.70378	+	5.24371i	−0.0912014	+	0.280689i	−0.986245	−	0.165289i	$-0.947144\pi$
$349$	−1.70378	+	5.24371i	−0.0912014	+	0.280689i	0.895044	+	0.445978i	$0.147144\pi$
$350$		0			0
$351$	−1.11961			−0.0597602
$352$	9.83010	+	1.64476i	0.523946	+	0.0876662i
$353$	29.8740			1.59003			0.795016	−	0.606589i	$-0.207463\pi$
$353$	29.8740			1.59003			0.795016	+	0.606589i	$0.207463\pi$
$354$	0.389706	+	0.283138i	0.0207127	+	0.0150486i
$355$		0			0
$356$	8.70008	+	26.7761i	0.461103	+	1.41913i
$357$	0.227943	−	0.165611i	0.0120640	−	0.00876504i
$358$	3.22146	−	2.34053i	0.170259	−	0.123701i
$359$	−11.0978	−	34.1554i	−0.585717	−	1.80265i	−0.596372	−	0.802708i	$-0.703392\pi$
$359$	−11.0978	−	34.1554i	−0.585717	−	1.80265i	0.0106548	−	0.999943i	$-0.496608\pi$
$360$		0			0
$361$	15.3675	+	11.1651i	0.808815	+	0.587639i
$362$	0.370840			0.0194909
$363$	−6.61956	+	8.78529i	−0.347437	+	0.461108i
$364$	−6.90488			−0.361914
$365$		0			0
$366$	0.815611	−	2.51019i	0.0426326	−	0.131210i
$367$	2.79069	+	8.58887i	0.145673	+	0.448335i	0.997097	−	0.0761428i	$-0.0242605\pi$
$367$	2.79069	+	8.58887i	0.145673	+	0.448335i	−0.851424	+	0.524478i	$0.824260\pi$
$368$	19.3365	−	14.0488i	1.00799	−	0.732345i
$369$	9.43772	−	6.85690i	0.491308	−	0.356956i
$370$		0			0
$371$	−0.860909	+	2.64961i	−0.0446962	+	0.137561i
$372$	14.9749	+	10.8799i	0.776410	+	0.564095i
$373$	−17.1994			−0.890553			−0.445277	−	0.895393i	$-0.646895\pi$
$373$	−17.1994			−0.890553			−0.445277	+	0.895393i	$0.646895\pi$
$374$	0.0757176	+	0.0126690i	0.00391526	+	0.000655098i
$375$		0			0
$376$	−0.757656	−	0.550469i	−0.0390731	−	0.0283883i
$377$	1.29251	−	3.97795i	0.0665678	−	0.204875i
$378$	−0.258911	−	0.796845i	−0.0133169	−	0.0409853i
$379$	6.47382	−	4.70350i	0.332538	−	0.241603i	−0.408969	−	0.912548i	$-0.634112\pi$
$379$	6.47382	−	4.70350i	0.332538	−	0.241603i	0.741507	+	0.670946i	$0.234112\pi$
$380$		0			0
$381$	2.44117	+	7.51314i	0.125065	+	0.384910i
$382$	0.398002	−	1.22492i	0.0203635	−	0.0626725i
$383$	24.0384	+	17.4649i	1.22831	+	0.892417i	0.996762	−	0.0804076i	$-0.0256222\pi$
$383$	24.0384	+	17.4649i	1.22831	+	0.892417i	0.231544	+	0.972824i	$0.425622\pi$
$384$	7.68799			0.392326
$385$		0			0
$386$	−2.55010			−0.129797
$387$	−9.56399	−	6.94864i	−0.486165	−	0.353219i
$388$	−2.44194	+	7.51553i	−0.123971	+	0.381543i
$389$	−0.183988	−	0.566256i	−0.00932855	−	0.0287103i	0.946284	−	0.323337i	$-0.104805\pi$
$389$	−0.183988	−	0.566256i	−0.00932855	−	0.0287103i	−0.955612	+	0.294627i	$0.904805\pi$
$390$		0			0
$391$	0.474976	−	0.345090i	0.0240206	−	0.0174520i
$392$	−1.01944	−	3.13752i	−0.0514897	−	0.158469i
$393$	5.05362	−	15.5534i	0.254922	−	0.784568i
$394$	−1.88643	−	1.37057i	−0.0950371	−	0.0690485i
$395$		0			0
$396$	−2.95735	+	5.68133i	−0.148612	+	0.285498i
$397$	−1.66950			−0.0837898			−0.0418949	−	0.999122i	$-0.513339\pi$
$397$	−1.66950			−0.0837898			−0.0418949	+	0.999122i	$0.513339\pi$
$398$	−3.82865	−	2.78168i	−0.191913	−	0.139433i
$399$	0.0679277	−	0.209060i	0.00340064	−	0.0104661i
$400$		0			0
$401$	9.19771	−	6.68253i	0.459312	−	0.333710i	−0.333949	−	0.942591i	$-0.608381\pi$
$401$	9.19771	−	6.68253i	0.459312	−	0.333710i	0.793261	+	0.608881i	$0.208381\pi$
$402$	−2.02472	+	1.47104i	−0.100984	+	0.0733690i
$403$	−3.31614	−	10.2060i	−0.165189	−	0.508398i
$404$	−2.56114	+	7.88237i	−0.127421	+	0.392163i
$405$		0			0
$406$	3.13008			0.155343
$407$	4.08433	+	27.3246i	0.202453	+	1.35443i
$408$	0.0909950			0.00450492
$409$	6.95565	+	5.05358i	0.343935	+	0.249883i	0.746320	−	0.665587i	$-0.231819\pi$
$409$	6.95565	+	5.05358i	0.343935	+	0.249883i	−0.402385	+	0.915470i	$0.631819\pi$
$410$		0			0
$411$	2.38934	+	7.35364i	0.117858	+	0.362728i
$412$	−3.26969	+	2.37557i	−0.161086	+	0.117036i
$413$	−4.74363	+	3.44645i	−0.233419	+	0.169589i
$414$	−0.539504	−	1.66042i	−0.0265152	−	0.0816054i
$415$		0			0
$416$	−2.72195	−	1.97761i	−0.133455	−	0.0969604i
$417$	−20.1865			−0.988536
$418$	0.0536011	−	0.0267261i	0.00262172	−	0.00130721i
$419$	31.3915			1.53358			0.766789	−	0.641899i	$-0.221853\pi$
$419$	31.3915			1.53358			0.766789	+	0.641899i	$0.221853\pi$
$420$		0			0
$421$	−1.41497	+	4.35482i	−0.0689613	+	0.212241i	−0.979598	−	0.200967i	$-0.935592\pi$
$421$	−1.41497	+	4.35482i	−0.0689613	+	0.212241i	0.910637	+	0.413208i	$0.135592\pi$
$422$	1.45753	+	4.48580i	0.0709513	+	0.218366i
$423$	0.734604	−	0.533721i	0.0357177	−	0.0259504i
$424$	−0.727915	+	0.528861i	−0.0353507	+	0.0256838i
$425$		0			0
$426$	0.378171	−	1.16389i	0.0183225	−	0.0563908i
$427$	25.9915	+	18.8839i	1.25782	+	0.913858i
$428$	−30.3983			−1.46936
$429$	3.32313	−	1.65695i	0.160442	−	0.0799982i
$430$		0			0
$431$	−12.8694	−	9.35015i	−0.619896	−	0.450381i	0.232989	−	0.972479i	$-0.425149\pi$
$431$	−12.8694	−	9.35015i	−0.619896	−	0.450381i	−0.852885	+	0.522098i	$0.825149\pi$
$432$	−1.10991	+	3.41595i	−0.0534005	+	0.164350i
$433$	−4.88338	−	15.0295i	−0.234680	−	0.722272i	−0.997164	−	0.0752639i	$-0.976020\pi$
$433$	−4.88338	−	15.0295i	−0.234680	−	0.722272i	0.762483	−	0.647008i	$-0.223980\pi$
$434$	6.49696	−	4.72032i	0.311864	−	0.226583i
$435$		0			0
$436$	2.46625	+	7.59034i	0.118112	+	0.363511i
$437$	0.141544	−	0.435628i	0.00677098	−	0.0208389i
$438$	1.51981	+	1.10420i	0.0726192	+	0.0527609i
$439$	21.5227			1.02722			0.513611	−	0.858023i	$-0.328307\pi$
$439$	21.5227			1.02722			0.513611	+	0.858023i	$0.328307\pi$
$440$		0			0
$441$	3.19862			0.152315
$442$	−0.0209662	−	0.0152328i	−0.000997258	−	0.000724551i
$443$	−3.14484	+	9.67881i	−0.149416	+	0.459854i	−0.997552	−	0.0699233i	$-0.977725\pi$
$443$	−3.14484	+	9.67881i	−0.149416	+	0.459854i	0.848137	+	0.529777i	$0.177725\pi$
$444$	4.97116	+	15.2997i	0.235921	+	0.726090i
$445$		0			0
$446$	−2.91826	+	2.12024i	−0.138184	+	0.100396i
$447$	−2.99599	−	9.22071i	−0.141706	−	0.436125i
$448$	−6.31100	+	19.4233i	−0.298167	+	0.917663i
$449$	−31.2352	−	22.6937i	−1.47408	−	1.07098i	−0.979406	−	0.201902i	$-0.935288\pi$
$449$	−31.2352	−	22.6937i	−1.47408	−	1.07098i	−0.494673	−	0.869079i	$-0.664712\pi$
$450$		0			0
$451$	−17.8646	+	34.3194i	−0.841209	+	1.61604i
$452$	26.5632			1.24943
$453$	12.2659	+	8.91168i	0.576301	+	0.418707i
$454$	−0.0537303	+	0.165365i	−0.00252169	+	0.00776096i
$455$		0			0
$456$	0.0574342	−	0.0417284i	0.00268960	−	0.00195411i
$457$	18.9017	−	13.7329i	0.884183	−	0.642396i	−0.0501720	−	0.998741i	$-0.515977\pi$
$457$	18.9017	−	13.7329i	0.884183	−	0.642396i	0.934355	+	0.356344i	$0.115977\pi$
$458$	−0.607275	−	1.86900i	−0.0283761	−	0.0873326i
$459$	−0.0272635	+	0.0839083i	−0.00127255	+	0.00391651i
$460$		0			0
$461$	4.93120			0.229669			0.114834	−	0.993385i	$-0.463366\pi$
$461$	4.93120			0.229669			0.114834	+	0.993385i	$0.463366\pi$
$462$	1.94776	+	1.98197i	0.0906181	+	0.0922094i
$463$	−26.9648			−1.25316			−0.626580	−	0.779357i	$-0.715546\pi$
$463$	−26.9648			−1.25316			−0.626580	+	0.779357i	$0.715546\pi$
$464$	−10.8555	−	7.88699i	−0.503954	−	0.366144i
$465$		0			0
$466$	−0.853329	−	2.62628i	−0.0395297	−	0.121660i
$467$	−19.1558	+	13.9175i	−0.886423	+	0.644024i	−0.934943	−	0.354798i	$-0.884550\pi$
$467$	−19.1558	+	13.9175i	−0.886423	+	0.644024i	0.0485201	+	0.998822i	$0.484550\pi$
$468$	1.74921	−	1.27088i	0.0808574	−	0.0587464i
$469$	−9.41376	−	28.9726i	−0.434687	−	1.33783i
$470$		0			0
$471$	12.0386	+	8.74655i	0.554709	+	0.403020i
$472$	−1.89366			−0.0871627
$473$	38.6707	+	6.47035i	1.77808	+	0.297507i
$474$	−0.207616			−0.00953613
$475$		0			0
$476$	−0.168140	+	0.517482i	−0.00770669	+	0.0237188i
$477$	−0.269579	−	0.829680i	−0.0123432	−	0.0379884i
$478$	−3.62449	+	2.63334i	−0.165780	+	0.120446i
$479$	10.9412	−	7.94922i	0.499915	−	0.363209i	−0.309070	−	0.951039i	$-0.600018\pi$
$479$	10.9412	−	7.94922i	0.499915	−	0.363209i	0.808984	+	0.587830i	$0.200018\pi$
$480$		0			0
$481$	2.88206	−	8.87008i	0.131411	−	0.404441i
$482$	3.54637	+	2.57659i	0.161533	+	0.117361i
$483$	21.2513			0.966969
$484$	0.369771	−	21.2396i	0.0168078	−	0.965437i
$485$		0			0
$486$	0.212253	+	0.154211i	0.00962801	+	0.00699516i
$487$	2.66590	−	8.20480i	0.120803	−	0.371795i	−0.872310	−	0.488954i	$-0.837379\pi$
$487$	2.66590	−	8.20480i	0.120803	−	0.371795i	0.993113	+	0.117159i	$0.0373787\pi$
$488$	3.20630	+	9.86798i	0.145142	+	0.446703i
$489$	−2.75158	+	1.99914i	−0.124431	+	0.0904043i
$490$		0			0
$491$	−8.00565	−	24.6388i	−0.361290	−	1.11194i	−0.952272	−	0.305251i	$-0.901260\pi$
$491$	−8.00565	−	24.6388i	−0.361290	−	1.11194i	0.590982	−	0.806685i	$-0.298740\pi$
$492$	−6.96164	+	21.4257i	−0.313855	+	0.965947i
$493$	−0.266651	−	0.193733i	−0.0120094	−	0.00872532i
$494$	−0.0202189			−0.000909690
$495$		0			0
$496$	−34.4263			−1.54579
$497$	12.0514	+	8.75585i	0.540579	+	0.392754i
$498$	0.0200437	−	0.0616883i	0.000898182	−	0.00276432i
$499$	−8.66717	−	26.6748i	−0.387996	−	1.19413i	−0.934284	−	0.356531i	$-0.883960\pi$
$499$	−8.66717	−	26.6748i	−0.387996	−	1.19413i	0.546288	−	0.837597i	$-0.316040\pi$
$500$		0			0
$501$	18.2970	−	13.2936i	0.817450	−	0.593913i
$502$	−0.416529	−	1.28194i	−0.0185906	−	0.0572160i
$503$	−9.08507	+	27.9610i	−0.405083	+	1.24672i	0.515743	+	0.856744i	$0.327516\pi$
$503$	−9.08507	+	27.9610i	−0.405083	+	1.24672i	−0.920826	+	0.389974i	$0.872484\pi$
$504$	2.66469	+	1.93601i	0.118695	+	0.0862368i
$505$		0			0
$506$	4.05864	+	4.12992i	0.180429	+	0.183597i
$507$	11.7465			0.521680
$508$	−12.3422	−	8.96714i	−0.547597	−	0.397853i
$509$	−5.99195	+	18.4413i	−0.265589	+	0.817398i	0.725969	+	0.687728i	$0.241392\pi$
$509$	−5.99195	+	18.4413i	−0.265589	+	0.817398i	−0.991557	+	0.129670i	$0.958608\pi$
$510$		0			0
$511$	−18.4996	+	13.4407i	−0.818373	+	0.594583i
$512$	−14.7261	+	10.6991i	−0.650806	+	0.472838i
$513$	0.0212704	+	0.0654637i	0.000939113	+	0.00289029i
$514$	0.299830	−	0.922782i	0.0132249	−	0.0407022i
$515$		0			0
$516$	22.8298			1.00502
$517$	−1.39052	+	2.67132i	−0.0611552	+	0.117485i
$518$	6.97949			0.306661
$519$	10.5911	+	7.69487i	0.464897	+	0.337767i
$520$		0			0
$521$	7.72734	+	23.7823i	0.338541	+	1.04192i	0.964951	+	0.262429i	$0.0845235\pi$
$521$	7.72734	+	23.7823i	0.338541	+	1.04192i	−0.626410	+	0.779493i	$0.715477\pi$
$522$	−0.792943	+	0.576107i	−0.0347062	+	0.0252155i
$523$	−1.76982	+	1.28585i	−0.0773887	+	0.0562262i	−0.625807	−	0.779978i	$-0.715230\pi$
$523$	−1.76982	+	1.28585i	−0.0773887	+	0.0562262i	0.548418	+	0.836204i	$0.315230\pi$
$524$	9.75939	+	30.0363i	0.426341	+	1.31214i
$525$		0			0
$526$	6.71389	+	4.87793i	0.292740	+	0.212688i
$527$	−0.845637			−0.0368365
$528$	−1.76104	−	11.7816i	−0.0766395	−	0.512727i
$529$	21.2824			0.925322
$530$		0			0
$531$	0.567369	−	1.74618i	0.0246217	−	0.0757778i
$532$	0.131180	+	0.403730i	0.00568737	+	0.0175039i
$533$	10.5665	−	7.67703i	0.457687	−	0.332529i
$534$	−3.09439	+	2.24821i	−0.133908	+	0.0972895i
$535$		0			0
$536$	3.04026	−	9.35697i	0.131319	−	0.404159i
$537$	−12.2788	−	8.92106i	−0.529869	−	0.384972i
$538$	−3.87648			−0.167127
$539$	−9.49390	+	4.73375i	−0.408931	+	0.203897i
$540$		0			0
$541$	−10.9689	−	7.96939i	−0.471591	−	0.342631i	0.326470	−	0.945208i	$-0.394141\pi$
$541$	−10.9689	−	7.96939i	−0.471591	−	0.342631i	−0.798061	+	0.602577i	$0.794141\pi$
$542$	−1.58798	+	4.88731i	−0.0682097	+	0.209928i
$543$	−0.436789	−	1.34430i	−0.0187444	−	0.0576894i
$544$	−0.214493	+	0.155838i	−0.00919632	+	0.00668152i
$545$		0			0
$546$	−0.289878	−	0.892153i	−0.0124056	−	0.0381806i
$547$	1.14732	−	3.53110i	0.0490560	−	0.150979i	−0.923528	−	0.383531i	$-0.874708\pi$
$547$	1.14732	−	3.53110i	0.0490560	−	0.150979i	0.972584	+	0.232553i	$0.0747078\pi$
$548$	−12.0802	−	8.77677i	−0.516040	−	0.374925i
$549$	−10.0601			−0.429356
$550$		0			0
$551$	−0.257147			−0.0109548
$552$	5.55254	+	4.03416i	0.236332	+	0.171705i
$553$	0.780939	−	2.40348i	0.0332089	−	0.102207i
$554$	−2.08443	−	6.41522i	−0.0885590	−	0.272557i
$555$		0			0
$556$	31.5383	−	22.9139i	1.33752	−	0.971766i
$557$	−2.03185	−	6.25339i	−0.0860922	−	0.264964i	0.898738	−	0.438486i	$-0.144485\pi$
$557$	−2.03185	−	6.25339i	−0.0860922	−	0.264964i	−0.984830	+	0.173522i	$0.944485\pi$
$558$	−0.777078	+	2.39160i	−0.0328963	+	0.101244i
$559$	−10.7079	−	7.77974i	−0.452896	−	0.329048i
$560$		0			0
$561$	−0.0432577	−	0.289399i	−0.00182634	−	0.0122184i
$562$	−7.00786			−0.295609
$563$	−5.58931	−	4.06087i	−0.235561	−	0.171145i	0.463742	−	0.885970i	$-0.346506\pi$
$563$	−5.58931	−	4.06087i	−0.235561	−	0.171145i	−0.699303	+	0.714825i	$0.746506\pi$
$564$	−0.541873	+	1.66771i	−0.0228170	+	0.0702235i
$565$		0			0
$566$	1.53539	−	1.11552i	0.0645372	−	0.0468890i
$567$	−2.58362	+	1.87711i	−0.108502	+	0.0788311i
$568$	1.48666	+	4.57545i	0.0623787	+	0.191982i
$569$	−2.08515	+	6.41743i	−0.0874140	+	0.269033i	−0.985203	−	0.171394i	$-0.945173\pi$
$569$	−2.08515	+	6.41743i	−0.0874140	+	0.269033i	0.897789	+	0.440427i	$0.145173\pi$
$570$		0			0
$571$	9.68928			0.405484			0.202742	−	0.979232i	$-0.435015\pi$
$571$	9.68928			0.405484			0.202742	+	0.979232i	$0.435015\pi$
$572$	−3.31107	+	6.36086i	−0.138443	+	0.265961i
$573$	−4.90914			−0.205082
$574$	7.90742	+	5.74508i	0.330049	+	0.239795i
$575$		0			0
$576$	−1.97619	−	6.08207i	−0.0823411	−	0.253420i
$577$	12.2565	−	8.90484i	0.510243	−	0.370713i	−0.302673	−	0.953095i	$-0.597879\pi$
$577$	12.2565	−	8.90484i	0.510243	−	0.370713i	0.812916	+	0.582381i	$0.197879\pi$
$578$	3.60666	−	2.62039i	0.150017	−	0.108994i
$579$	3.00361	+	9.24415i	0.124826	+	0.384174i
$580$		0			0
$581$	0.638745	+	0.464076i	0.0264996	+	0.0192531i
$582$	−1.07357			−0.0445009
$583$	2.02802	+	2.06364i	0.0839921	+	0.0854671i
$584$	−7.38503			−0.305595
$585$		0			0
$586$	−1.18325	+	3.64166i	−0.0488795	+	0.150436i
$587$	8.34693	+	25.6892i	0.344514	+	1.06031i	0.961843	+	0.273601i	$0.0882149\pi$
$587$	8.34693	+	25.6892i	0.344514	+	1.06031i	−0.617329	+	0.786705i	$0.711785\pi$
$588$	−4.99735	+	3.63079i	−0.206087	+	0.149731i
$589$	−0.533749	+	0.387791i	−0.0219927	+	0.0159787i
$590$		0			0
$591$	−2.74643	+	8.45265i	−0.112973	+	0.347696i
$592$	−24.2058	−	17.5865i	−0.994850	−	0.722801i
$593$	22.1863			0.911084			0.455542	−	0.890214i	$-0.349446\pi$
$593$	22.1863			0.911084			0.455542	+	0.890214i	$0.349446\pi$
$594$	−0.858218	−	0.143596i	−0.0352131	−	0.00589183i
$595$		0			0
$596$	15.1473	+	11.0052i	0.620458	+	0.450789i
$597$	−5.57408	+	17.1552i	−0.228132	+	0.702118i
$598$	−0.604033	−	1.85902i	−0.0247007	−	0.0760210i
$599$	−9.50487	+	6.90569i	−0.388359	+	0.282159i	−0.764783	−	0.644289i	$-0.777154\pi$
$599$	−9.50487	+	6.90569i	−0.388359	+	0.282159i	0.376424	+	0.926448i	$0.377154\pi$
$600$		0			0
$601$	10.6242	+	32.6979i	0.433370	+	1.33378i	0.894747	+	0.446572i	$0.147355\pi$
$601$	10.6242	+	32.6979i	0.433370	+	1.33378i	−0.461377	+	0.887204i	$0.652645\pi$
$602$	3.06077	−	9.42010i	0.124748	−	0.383934i
$603$	7.71734	+	5.60698i	0.314274	+	0.228334i
$604$	−29.2793			−1.19136
$605$		0			0
$606$	−1.12597			−0.0457395
$607$	11.0267	+	8.01137i	0.447560	+	0.325172i	0.788632	−	0.614866i	$-0.210790\pi$
$607$	11.0267	+	8.01137i	0.447560	+	0.325172i	−0.341071	+	0.940037i	$0.610790\pi$
$608$	−0.0639196	+	0.196724i	−0.00259228	+	0.00797822i
$609$	−3.68672	−	11.3466i	−0.149393	−	0.459786i
$610$		0			0
$611$	0.822467	−	0.597557i	0.0332735	−	0.0241746i
$612$	−0.0526503	−	0.162041i	−0.00212826	−	0.00655012i
$613$	2.11057	−	6.49565i	0.0852450	−	0.262357i	−0.899344	−	0.437242i	$-0.855955\pi$
$613$	2.11057	−	6.49565i	0.0852450	−	0.262357i	0.984589	+	0.174885i	$0.0559553\pi$
$614$	6.05866	+	4.40187i	0.244508	+	0.177645i
$615$		0			0
$616$	−10.7743	−	1.80275i	−0.434110	−	0.0726349i
$617$	−30.3730			−1.22277			−0.611386	−	0.791333i	$-0.709388\pi$
$617$	−30.3730			−1.22277			−0.611386	+	0.791333i	$0.709388\pi$
$618$	−0.444205	−	0.322734i	−0.0178685	−	0.0129823i
$619$	−7.96890	+	24.5258i	−0.320297	+	0.985773i	0.653222	+	0.757167i	$0.273417\pi$
$619$	−7.96890	+	24.5258i	−0.320297	+	0.985773i	−0.973519	+	0.228607i	$0.926583\pi$
$620$		0			0
$621$	−5.38361	+	3.91142i	−0.216037	+	0.156960i
$622$	2.11150	−	1.53410i	0.0846635	−	0.0615117i
$623$	−14.3871	−	44.2790i	−0.576408	−	1.77400i
$624$	−1.24266	+	3.82452i	−0.0497463	+	0.153103i
$625$		0			0
$626$	4.31081			0.172295
$627$	−0.160016	−	0.162826i	−0.00639041	−	0.00650263i
$628$	−28.7368			−1.14672
$629$	−0.594583	−	0.431990i	−0.0237076	−	0.0172246i
$630$		0			0
$631$	−7.90021	−	24.3143i	−0.314502	−	0.967939i	−0.975959	−	0.217955i	$-0.930061\pi$
$631$	−7.90021	−	24.3143i	−0.314502	−	0.967939i	0.661456	−	0.749984i	$-0.269939\pi$
$632$	0.660299	−	0.479735i	0.0262653	−	0.0190828i
$633$	14.5444	−	10.5671i	0.578086	−	0.420004i
$634$	−1.15210	−	3.54581i	−0.0457559	−	0.140822i
$635$		0			0
$636$	1.36296	+	0.990246i	0.0540447	+	0.0392658i
$637$	3.58119			0.141892
$638$	1.50095	−	2.88347i	0.0594233	−	0.114157i
$639$	−4.66454			−0.184527
$640$		0			0
$641$	−1.25851	+	3.87329i	−0.0497081	+	0.152986i	−0.972829	−	0.231523i	$-0.925629\pi$
$641$	−1.25851	+	3.87329i	−0.0497081	+	0.152986i	0.923121	+	0.384509i	$0.125629\pi$
$642$	−1.27617	−	3.92766i	−0.0503665	−	0.155012i
$643$	9.16601	−	6.65950i	0.361472	−	0.262625i	−0.392194	−	0.919883i	$-0.628284\pi$
$643$	9.16601	−	6.65950i	0.361472	−	0.262625i	0.753666	+	0.657258i	$0.228284\pi$
$644$	−33.2020	+	24.1226i	−1.30834	+	0.950565i
$645$		0			0
$646$	−0.000492348		0.00151529i	−1.93712e−5		5.96184e-5i
$647$	−29.8107	−	21.6587i	−1.17198	−	0.851492i	−0.180734	−	0.983532i	$-0.557847\pi$
$647$	−29.8107	−	21.6587i	−1.17198	−	0.851492i	−0.991244	+	0.132040i	$0.957847\pi$
$648$	−1.03138			−0.0405164
$649$	0.900218	+	6.02256i	0.0353366	+	0.236406i
$650$		0			0
$651$	−24.7636	−	17.9918i	−0.970561	−	0.705154i
$652$	2.02968	−	6.24671i	0.0794883	−	0.244640i
$653$	−4.72079	−	14.5291i	−0.184739	−	0.568568i	0.815205	−	0.579173i	$-0.196624\pi$
$653$	−4.72079	−	14.5291i	−0.184739	−	0.568568i	−0.999944	+	0.0106050i	$0.996624\pi$
$654$	−0.877182	+	0.637310i	−0.0343005	+	0.0249208i
$655$		0			0
$656$	−12.9478	−	39.8493i	−0.505528	−	1.55585i
$657$	2.21267	−	6.80989i	0.0863243	−	0.265679i
$658$	0.615490	+	0.447180i	0.0239943	+	0.0174329i
$659$	11.8996			0.463544			0.231772	−	0.972770i	$-0.425548\pi$
$659$	11.8996			0.463544			0.231772	+	0.972770i	$0.425548\pi$
$660$		0			0
$661$	−44.8648			−1.74504			−0.872520	−	0.488578i	$-0.837516\pi$
$661$	−44.8648			−1.74504			−0.872520	+	0.488578i	$0.837516\pi$
$662$	2.31609	+	1.68274i	0.0900174	+	0.0654015i
$663$	−0.0305244	+	0.0939443i	−0.00118547	+	0.00364849i
$664$	0.0787953	+	0.242507i	0.00305785	+	0.00941110i
$665$		0			0
$666$	−1.76812	+	1.28461i	−0.0685131	+	0.0497777i
$667$	−7.68219	−	23.6434i	−0.297456	−	0.915474i
$668$	−13.4966	+	41.5383i	−0.522200	+	1.60717i
$669$	11.1231	+	8.08142i	0.430045	+	0.312446i
$670$		0			0
$671$	29.8597	−	14.8884i	1.15272	−	0.574759i
$672$	−9.59683			−0.370206
$673$	−15.4576	−	11.2306i	−0.595848	−	0.432909i	0.248555	−	0.968618i	$-0.420044\pi$
$673$	−15.4576	−	11.2306i	−0.595848	−	0.432909i	−0.844403	+	0.535709i	$0.820044\pi$
$674$	0.477207	−	1.46869i	0.0183813	−	0.0565719i
$675$		0			0
$676$	−18.3521	+	13.3336i	−0.705849	+	0.512830i
$677$	37.5881	−	27.3093i	1.44463	−	1.04958i	0.457578	−	0.889170i	$-0.348717\pi$
$677$	37.5881	−	27.3093i	1.44463	−	1.04958i	0.987050	−	0.160414i	$-0.0512829\pi$
$678$	1.11517	+	3.43213i	0.0428278	+	0.131810i
$679$	4.03819	−	12.4283i	0.154971	−	0.476953i
$680$		0			0
$681$	0.662735			0.0253961
$682$	−1.23295	−	8.24860i	−0.0472122	−	0.315855i
$683$	42.5651			1.62871			0.814355	−	0.580367i	$-0.197091\pi$
$683$	42.5651			1.62871			0.814355	+	0.580367i	$0.197091\pi$
$684$	−0.107540	−	0.0781327i	−0.00411191	−	0.00298748i
$685$		0			0
$686$	−0.984219	−	3.02912i	−0.0375777	−	0.115652i
$687$	−6.05987	+	4.40275i	−0.231198	+	0.167976i
$688$	−34.3514	+	24.9577i	−1.30963	+	0.951505i
$689$	−0.301823	−	0.928915i	−0.0114985	−	0.0353888i
$690$		0			0
$691$	−28.4249	−	20.6519i	−1.08134	−	0.785636i	−0.103420	−	0.994638i	$-0.532979\pi$
$691$	−28.4249	−	20.6519i	−1.08134	−	0.785636i	−0.977915	+	0.209001i	$0.932979\pi$
$692$	−25.2815			−0.961057
$693$	4.89050	−	9.39509i	0.185775	−	0.356890i
$694$	−9.05253			−0.343629
$695$		0			0
$696$	1.19066	−	3.66448i	0.0451319	−	0.138902i
$697$	−0.318046	−	0.978846i	−0.0120469	−	0.0370764i
$698$	1.17027	−	0.850252i	0.0442954	−	0.0321825i
$699$	−8.51520	+	6.18665i	−0.322074	+	0.234001i
$700$		0			0
$701$	−9.47794	+	29.1701i	−0.357977	+	1.10174i	0.596286	+	0.802772i	$0.296642\pi$
$701$	−9.47794	+	29.1701i	−0.357977	+	1.10174i	−0.954263	+	0.298968i	$0.903358\pi$
$702$	0.237640	+	0.172656i	0.00896916	+	0.00651647i
$703$	−0.573390			−0.0216258
$704$	14.8667	+	15.1277i	0.560309	+	0.570148i
$705$		0			0
$706$	−6.34086	−	4.60690i	−0.238641	−	0.173383i
$707$	4.23530	−	13.0349i	0.159285	−	0.490228i
$708$	1.09568	+	3.37217i	0.0411783	+	0.126734i
$709$	−12.2100	+	8.87107i	−0.458555	+	0.333160i	−0.792964	−	0.609268i	$-0.791463\pi$
$709$	−12.2100	+	8.87107i	−0.458555	+	0.333160i	0.334409	+	0.942428i	$0.391463\pi$
$710$		0			0
$711$	0.244538	+	0.752611i	0.00917090	+	0.0282251i
$712$	4.64646	−	14.3003i	0.174133	−	0.535927i
$713$	−51.6010	−	37.4903i	−1.93247	−	1.40402i
$714$	−0.0739208			−0.00276642
$715$		0			0
$716$	29.3101			1.09537
$717$	13.8149	+	10.0371i	0.515929	+	0.374844i
$718$	−2.91160	+	8.96099i	−0.108660	+	0.334421i
$719$	−1.91288	−	5.88723i	−0.0713383	−	0.219557i	0.909030	−	0.416730i	$-0.136824\pi$
$719$	−1.91288	−	5.88723i	−0.0713383	−	0.219557i	−0.980369	+	0.197173i	$0.936824\pi$
$720$		0			0
$721$	5.40701	−	3.92842i	0.201367	−	0.146302i
$722$	−1.54001	−	4.73968i	−0.0573134	−	0.176393i
$723$	5.16312	−	15.8904i	0.192018	−	0.590972i
$724$	2.20835	+	1.60446i	0.0820725	+	0.0596292i
$725$		0			0
$726$	2.75982	−	0.843898i	0.102426	−	0.0313200i
$727$	18.1515			0.673200			0.336600	−	0.941648i	$-0.390723\pi$
$727$	18.1515			0.673200			0.336600	+	0.941648i	$0.390723\pi$
$728$	2.98341	+	2.16757i	0.110572	+	0.0803355i
$729$	0.309017	−	0.951057i	0.0114451	−	0.0352243i
$730$		0			0
$731$	−0.843796	+	0.613054i	−0.0312089	+	0.0226746i
$732$	15.7174	−	11.4194i	0.580932	−	0.422072i
$733$	8.88142	+	27.3342i	0.328043	+	1.00961i	0.970048	+	0.242912i	$0.0781027\pi$
$733$	8.88142	+	27.3342i	0.328043	+	1.00961i	−0.642005	+	0.766700i	$0.721897\pi$
$734$	0.732165	−	2.25337i	0.0270247	−	0.0831735i
$735$		0			0
$736$	−19.9974			−0.737113
$737$	−31.2040	−	5.22103i	−1.14942	−	0.192319i
$738$	−3.06060			−0.112662
$739$	37.8896	+	27.5284i	1.39379	+	1.01265i	0.995437	+	0.0954172i	$0.0304185\pi$
$739$	37.8896	+	27.5284i	1.39379	+	1.01265i	0.398354	+	0.917232i	$0.369581\pi$
$740$		0			0
$741$	0.0238145	+	0.0732936i	0.000874848	+	0.00269251i
$742$	0.591330	−	0.429626i	0.0217084	−	0.0157721i
$743$	21.5286	−	15.6414i	0.789806	−	0.573828i	−0.118100	−	0.993002i	$-0.537680\pi$
$743$	21.5286	−	15.6414i	0.789806	−	0.573828i	0.907906	+	0.419174i	$0.137680\pi$
$744$	−3.05482	−	9.40178i	−0.111995	−	0.344686i
$745$		0			0
$746$	3.65064	+	2.65235i	0.133659	+	0.0971093i
$747$	−0.247229			−0.00904564
$748$	0.396084	+	0.403039i	0.0144823	+	0.0147366i
$749$	50.2691			1.83679
$750$		0			0
$751$	12.5406	−	38.5959i	0.457612	−	1.40838i	−0.410430	−	0.911892i	$-0.634621\pi$
$751$	12.5406	−	38.5959i	0.457612	−	1.40838i	0.868041	−	0.496492i	$-0.165379\pi$
$752$	−1.00782	−	3.10175i	−0.0367514	−	0.113109i
$753$	−4.15646	+	3.01984i	−0.151470	+	0.110049i
$754$	−0.887784	+	0.645013i	−0.0323312	+	0.0234900i
$755$		0			0
$756$	1.90578	−	5.86539i	0.0693126	−	0.213322i
$757$	26.4693	+	19.2311i	0.962045	+	0.698966i	0.953625	−	0.300998i	$-0.0973198\pi$
$757$	26.4693	+	19.2311i	0.962045	+	0.698966i	0.00841989	+	0.999965i	$0.497320\pi$
$758$	−2.09942			−0.0762545
$759$	10.1906	−	19.5770i	0.369894	−	0.710600i
$760$		0			0
$761$	2.12721	+	1.54551i	0.0771113	+	0.0560246i	0.625673	−	0.780085i	$-0.284824\pi$
$761$	2.12721	+	1.54551i	0.0771113	+	0.0560246i	−0.548562	+	0.836110i	$0.684824\pi$
$762$	0.640464	−	1.97115i	0.0232016	−	0.0714071i
$763$	−4.07838	−	12.5520i	−0.147647	−	0.454412i
$764$	7.66978	−	5.57242i	0.277483	−	0.201603i
$765$		0			0
$766$	−2.40895	−	7.41399i	−0.0870389	−	0.267878i
$767$	0.635229	−	1.95503i	0.0229368	−	0.0705922i
$768$	8.71564	+	6.33228i	0.314499	+	0.228497i
$769$	3.23559			0.116678			0.0583392	−	0.998297i	$-0.481419\pi$
$769$	3.23559			0.116678			0.0583392	+	0.998297i	$0.481419\pi$
$770$		0			0
$771$	−3.69824			−0.133189
$772$	−15.1858	−	11.0331i	−0.546550	−	0.397092i
$773$	−13.4844	+	41.5008i	−0.485001	+	1.49268i	0.346979	+	0.937873i	$0.387208\pi$
$773$	−13.4844	+	41.5008i	−0.485001	+	1.49268i	−0.831980	+	0.554806i	$0.812792\pi$
$774$	0.958431	+	2.94975i	0.0344501	+	0.106026i
$775$		0			0
$776$	3.41436	−	2.48068i	0.122569	−	0.0890512i
$777$	−8.22070	−	25.3007i	−0.294916	−	0.907658i
$778$	−0.0482710	+	0.148563i	−0.00173060	+	0.00532623i
$779$	−0.649623	−	0.471979i	−0.0232752	−	0.0169104i
$780$		0			0
$781$	13.8450	−	6.90324i	0.495412	−	0.247017i
$782$	−0.154032			−0.00550818
$783$	3.02235	+	2.19587i	0.108010	+	0.0784739i
$784$	3.55017	−	10.9263i	0.126792	−	0.390225i
$785$		0			0
$786$	−3.47116	+	2.52195i	−0.123812	+	0.0899549i
$787$	−3.69251	+	2.68277i	−0.131624	+	0.0956304i	−0.651649	−	0.758521i	$-0.725923\pi$
$787$	−3.69251	+	2.68277i	−0.131624	+	0.0956304i	0.520025	+	0.854151i	$0.325923\pi$
$788$	−5.30382	−	16.3235i	−0.188941	−	0.581500i
$789$	9.77467	−	30.0833i	0.347987	−	1.07100i
$790$		0			0
$791$	−43.9270			−1.56186
$792$	3.06127	−	1.52638i	0.108777	−	0.0542375i
$793$	−11.2634			−0.399974
$794$	0.354357	+	0.257455i	0.0125757	+	0.00913675i
$795$		0			0
$796$	−10.7645	−	33.1297i	−0.381537	−	1.17425i
$797$	−9.04526	+	6.57177i	−0.320400	+	0.232784i	−0.736346	−	0.676605i	$-0.763450\pi$
$797$	−9.04526	+	6.57177i	−0.320400	+	0.232784i	0.415946	+	0.909389i	$0.363450\pi$
$798$	−0.0466573	+	0.0338985i	−0.00165165	+	0.00119999i
$799$	−0.0247558	−	0.0761905i	−0.000875797	−	0.00269543i
$800$		0			0
$801$	11.7945	+	8.56919i	0.416737	+	0.302777i
$802$	−2.98277			−0.105325
$803$	3.51074	+	23.4872i	0.123891	+	0.828846i
$804$	−18.4217			−0.649684
$805$		0			0
$806$	−0.870021	+	2.67765i	−0.0306452	+	0.0943162i
$807$	4.56586	+	14.0523i	0.160726	+	0.494664i
$808$	3.58102	−	2.60176i	0.125980	−	0.0915298i
$809$	36.8440	−	26.7687i	1.29537	−	0.941139i	0.295468	−	0.955353i	$-0.404525\pi$
$809$	36.8440	−	26.7687i	1.29537	−	0.941139i	0.999899	+	0.0142137i	$0.00452452\pi$
$810$		0			0
$811$	0.872550	−	2.68543i	0.0306394	−	0.0942983i	−0.934567	−	0.355786i	$-0.884213\pi$
$811$	0.872550	−	2.68543i	0.0306394	−	0.0942983i	0.965207	+	0.261488i	$0.0842131\pi$
$812$	18.6395	+	13.5424i	0.654120	+	0.475246i
$813$	19.5869			0.686943
$814$	3.34685	−	6.42959i	0.117307	−	0.225357i
$815$		0			0
$816$	0.256367	+	0.186261i	0.00897463	+	0.00652045i
$817$	−0.251454	+	0.773895i	−0.00879725	+	0.0270751i
$818$	−0.697043	−	2.14528i	−0.0243715	−	0.0750079i
$819$	−2.89263	+	2.10162i	−0.101077	+	0.0734366i
$820$		0			0
$821$	−7.23460	−	22.2658i	−0.252489	−	0.777083i	−0.994314	−	0.106488i	$-0.966039\pi$
$821$	−7.23460	−	22.2658i	−0.252489	−	0.777083i	0.741825	−	0.670594i	$-0.233961\pi$
$822$	0.626867	−	1.92930i	0.0218645	−	0.0672920i
$823$	37.2994	+	27.0996i	1.30018	+	0.944633i	0.999957	−	0.00923747i	$-0.00294042\pi$
$823$	37.2994	+	27.0996i	1.30018	+	0.944633i	0.300218	+	0.953870i	$0.402940\pi$
$824$	2.15848			0.0751941
$825$		0			0
$826$	1.53833			0.0535255
$827$	−35.1515	−	25.5390i	−1.22234	−	0.888079i	−0.226044	−	0.974117i	$-0.572579\pi$
$827$	−35.1515	−	25.5390i	−1.22234	−	0.888079i	−0.996292	+	0.0860379i	$0.972579\pi$
$828$	3.97116	−	12.2220i	0.138007	−	0.424743i
$829$	4.78085	+	14.7139i	0.166046	+	0.511036i	0.999112	−	0.0421372i	$-0.0134167\pi$
$829$	4.78085	+	14.7139i	0.166046	+	0.511036i	−0.833066	+	0.553173i	$0.813417\pi$
$830$		0			0
$831$	−20.8001	+	15.1122i	−0.721548	+	0.524235i
$832$	−2.21255	−	6.80953i	−0.0767064	−	0.236078i
$833$	0.0872053	−	0.268390i	0.00302149	−	0.00929918i
$834$	4.28465	+	3.11298i	0.148365	+	0.107794i
$835$		0			0
$836$	0.434825	+	0.0727546i	0.0150387	+	0.00251627i
$837$	9.58484			0.331301
$838$	−6.66296	−	4.84093i	−0.230168	−	0.167227i
$839$	9.33790	−	28.7391i	0.322380	−	0.992184i	−0.650229	−	0.759738i	$-0.725327\pi$
$839$	9.33790	−	28.7391i	0.322380	−	0.992184i	0.972609	−	0.232446i	$-0.0746728\pi$
$840$		0			0
$841$	12.1705	−	8.84239i	0.419673	−	0.304910i
$842$	0.971894	−	0.706122i	0.0334937	−	0.0243346i
$843$	8.25411	+	25.4036i	0.284287	+	0.874945i
$844$	−10.7285	+	33.0189i	−0.369290	+	1.13656i
$845$		0			0
$846$	−0.238228			−0.00819045
$847$	−0.611482	+	35.1235i	−0.0210108	+	1.20686i
$848$	−3.13335			−0.107600
$849$	−5.85223	−	4.25189i	−0.200848	−	0.145925i
$850$		0			0
$851$	−17.1299	−	52.7203i	−0.587204	−	1.80723i
$852$	7.28764	−	5.29478i	0.249670	−	0.181396i
$853$	−1.62538	+	1.18091i	−0.0556521	+	0.0404336i	−0.615263	−	0.788322i	$-0.710950\pi$
$853$	−1.62538	+	1.18091i	−0.0556521	+	0.0404336i	0.559611	+	0.828755i	$0.310950\pi$
$854$	−2.60467	−	8.01636i	−0.0891301	−	0.274314i
$855$		0			0
$856$	13.1343	+	9.54262i	0.448921	+	0.326160i
$857$	33.6095			1.14808			0.574039	−	0.818828i	$-0.305376\pi$
$857$	33.6095			1.14808			0.574039	+	0.818828i	$0.305376\pi$
$858$	−0.960867	−	0.160771i	−0.0328034	−	0.00548865i
$859$	−13.7301			−0.468466			−0.234233	−	0.972180i	$-0.575258\pi$
$859$	−13.7301			−0.468466			−0.234233	+	0.972180i	$0.575258\pi$
$860$		0			0
$861$	11.5123	−	35.4312i	0.392338	−	1.20749i
$862$	1.28967	+	3.96920i	0.0439264	+	0.135192i
$863$	7.08560	−	5.14799i	0.241197	−	0.175240i	−0.460620	−	0.887598i	$-0.652373\pi$
$863$	7.08560	−	5.14799i	0.241197	−	0.175240i	0.701816	+	0.712358i	$0.252373\pi$
$864$	2.43117	−	1.76635i	0.0827100	−	0.0600923i
$865$		0			0
$866$	−1.28120	+	3.94314i	−0.0435370	+	0.133993i
$867$	−13.7470	−	9.98777i	−0.466872	−	0.339203i
$868$	59.1120			2.00639
$869$	−1.83964	−	1.87194i	−0.0624055	−	0.0635014i
$870$		0			0
$871$	8.64038	+	6.27761i	0.292768	+	0.212709i
$872$	1.31715	−	4.05378i	0.0446044	−	0.137278i
$873$	1.26449	+	3.89170i	0.0427965	+	0.131714i
$874$	−0.0972220	+	0.0706359i	−0.00328858	+	0.00238930i
$875$		0			0
$876$	4.27303	+	13.1510i	0.144372	+	0.444332i
$877$	4.71136	−	14.5001i	0.159091	−	0.489633i	−0.839461	−	0.543420i	$-0.817129\pi$
$877$	4.71136	−	14.5001i	0.159091	−	0.489633i	0.998552	+	0.0537871i	$0.0171292\pi$
$878$	−4.56827	−	3.31904i	−0.154172	−	0.112012i
$879$	14.5947			0.492268
$880$		0			0
$881$	−15.8486			−0.533953			−0.266977	−	0.963703i	$-0.586025\pi$
$881$	−15.8486			−0.533953			−0.266977	+	0.963703i	$0.586025\pi$
$882$	−0.678917	−	0.493262i	−0.0228603	−	0.0166090i
$883$	10.1854	−	31.3474i	0.342765	−	1.05492i	−0.620004	−	0.784598i	$-0.712869\pi$
$883$	10.1854	−	31.3474i	0.342765	−	1.05492i	0.962769	−	0.270324i	$-0.0871308\pi$
$884$	−0.0589476	−	0.181422i	−0.00198262	−	0.00610189i
$885$		0			0
$886$	2.16008	−	1.56939i	0.0725694	−	0.0527247i
$887$	−3.47720	−	10.7017i	−0.116753	−	0.359328i	0.875556	−	0.483117i	$-0.160495\pi$
$887$	−3.47720	−	10.7017i	−0.116753	−	0.359328i	−0.992309	+	0.123789i	$0.960495\pi$
$888$	2.65495	−	8.17111i	0.0890944	−	0.274204i
$889$	20.4100	+	14.8288i	0.684530	+	0.497340i
$890$		0			0
$891$	0.490303	+	3.28018i	0.0164258	+	0.109890i
$892$	−26.5515			−0.889010
$893$	−0.0505647	−	0.0367374i	−0.00169208	−	0.00122937i
$894$	−0.786027	+	2.41914i	−0.0262887	+	0.0809083i
$895$		0			0
$896$	19.8628	−	14.4312i	0.663570	−	0.482112i
$897$	−6.02752	+	4.37925i	−0.201253	+	0.146219i
$898$	3.13015	+	9.63362i	0.104455	+	0.321478i
$899$	−11.0651	+	34.0548i	−0.369041	+	1.13579i
$900$		0			0
$901$	−0.0769667			−0.00256413
$902$	9.08425	−	4.52950i	0.302472	−	0.150816i
$903$	−37.7530			−1.25634
$904$	−11.4772	−	8.33870i	−0.381727	−	0.277341i
$905$		0			0
$906$	−1.22919	−	3.78307i	−0.0408372	−	0.125684i
$907$	−20.5284	+	14.9147i	−0.681634	+	0.495236i	−0.873899	−	0.486107i	$-0.838417\pi$
$907$	−20.5284	+	14.9147i	−0.681634	+	0.495236i	0.192266	+	0.981343i	$0.438417\pi$
$908$	−1.03542	+	0.752278i	−0.0343617	+	0.0249652i
$909$	1.32621	+	4.08166i	0.0439877	+	0.135380i
$910$		0			0
$911$	14.0825	+	10.2316i	0.466575	+	0.338986i	0.796105	−	0.605159i	$-0.206890\pi$
$911$	14.0825	+	10.2316i	0.466575	+	0.338986i	−0.329530	+	0.944145i	$0.606890\pi$
$912$	0.247229			0.00818657
$913$	0.733807	−	0.365884i	0.0242855	−	0.0121090i
$914$	−6.12971			−0.202753
$915$		0			0
$916$	4.47000	−	13.7573i	0.147693	−	0.454553i
$917$	−16.1389	−	49.6704i	−0.532953	−	1.64026i
$918$	0.0187264	−	0.0136055i	0.000618062	−	0.000449048i
$919$	26.6133	−	19.3357i	0.877890	−	0.637825i	−0.0548022	−	0.998497i	$-0.517453\pi$
$919$	26.6133	−	19.3357i	0.877890	−	0.637825i	0.932692	+	0.360673i	$0.117453\pi$
$920$		0			0
$921$	8.82072	−	27.1474i	0.290653	−	0.894537i
$922$	−1.04666	−	0.760446i	−0.0344701	−	0.0250440i
$923$	−5.22245			−0.171899
$924$	3.02381	+	20.2297i	0.0994762	+	0.665507i
$925$		0			0
$926$	5.72337	+	4.15827i	0.188082	+	0.136649i
$927$	−0.646712	+	1.99038i	−0.0212408	+	0.0653725i
$928$	3.46918	+	10.6770i	0.113881	+	0.350491i
$929$	−26.9509	+	19.5810i	−0.884230	+	0.642431i	−0.934367	−	0.356311i	$-0.884034\pi$
$929$	−26.9509	+	19.5810i	−0.884230	+	0.642431i	0.0501368	+	0.998742i	$0.484034\pi$
$930$		0			0
$931$	−0.0680360	−	0.209393i	−0.00222979	−	0.00686258i
$932$	6.28115	−	19.3314i	0.205746	−	0.633221i
$933$	−8.04812	−	5.84730i	−0.263484	−	0.191432i
$934$	6.21211			0.203266
$935$		0			0
$936$	−1.15474			−0.0377438
$937$	−19.3061	−	14.0267i	−0.630704	−	0.458233i	0.225940	−	0.974141i	$-0.427455\pi$
$937$	−19.3061	−	14.0267i	−0.630704	−	0.458233i	−0.856644	+	0.515908i	$0.827455\pi$
$938$	−2.46979	+	7.60123i	−0.0806415	+	0.248189i
$939$	−5.07744	−	15.6267i	−0.165696	−	0.509959i
$940$		0			0
$941$	6.41192	−	4.65853i	0.209023	−	0.151864i	−0.478349	−	0.878170i	$-0.658765\pi$
$941$	6.41192	−	4.65853i	0.209023	−	0.151864i	0.687371	+	0.726306i	$0.258765\pi$
$942$	−1.20642	−	3.71297i	−0.0393072	−	0.120975i
$943$	23.9887	−	73.8297i	0.781181	−	2.40423i
$944$	−5.33514	−	3.87620i	−0.173644	−	0.126160i
$945$		0			0
$946$	−7.21019	−	7.33681i	−0.234423	−	0.238540i
$947$	2.15429			0.0700050			0.0350025	−	0.999387i	$-0.488856\pi$
$947$	2.15429			0.0700050			0.0350025	+	0.999387i	$0.488856\pi$
$948$	−1.23635	−	0.898262i	−0.0401548	−	0.0291742i
$949$	2.47731	−	7.62439i	0.0804170	−	0.247498i
$950$		0			0
$951$	−11.4966	+	8.35278i	−0.372803	+	0.270858i
$952$	0.235096	−	0.170807i	0.00761951	−	0.00553590i
$953$	1.85195	+	5.69971i	0.0599904	+	0.184632i	0.976561	−	0.215242i	$-0.0690540\pi$
$953$	1.85195	+	5.69971i	0.0599904	+	0.184632i	−0.916570	+	0.399874i	$0.869054\pi$
$954$	−0.0707268	+	0.217675i	−0.00228986	+	0.00704748i
$955$		0			0
$956$	−32.9770			−1.06655
$957$	−12.2205	−	2.04472i	−0.395032	−	0.0660964i
$958$	−3.54816			−0.114636
$959$	19.9767	+	14.5139i	0.645082	+	0.468680i
$960$		0			0
$961$	18.8096	+	57.8901i	0.606762	+	1.86742i
$962$	−1.97959	+	1.43826i	−0.0638246	+	0.0463713i
$963$	−12.7347	+	9.25228i	−0.410369	+	0.298151i
$964$	9.97085	+	30.6871i	0.321139	+	0.988365i
$965$		0			0
$966$	−4.51067	−	3.27719i	−0.145128	−	0.105442i
$967$	−22.2784			−0.716424			−0.358212	−	0.933640i	$-0.616613\pi$
$967$	−22.2784			−0.716424			−0.358212	+	0.933640i	$0.616613\pi$
$968$	−6.82729	+	9.06097i	−0.219437	+	0.291231i
$969$	0.00607286			0.000195088
$970$		0			0
$971$	−11.3381	+	34.8952i	−0.363858	+	1.11984i	0.586835	+	0.809706i	$0.300374\pi$
$971$	−11.3381	+	34.8952i	−0.363858	+	1.11984i	−0.950693	+	0.310133i	$0.899626\pi$
$972$	0.596764	+	1.83665i	0.0191412	+	0.0589106i
$973$	−52.1541	+	37.8922i	−1.67198	+	1.21477i
$974$	−1.83112	+	1.33039i	−0.0586728	+	0.0426283i
$975$		0			0
$976$	−11.1658	+	34.3649i	−0.357409	+	1.09999i
$977$	22.5751	+	16.4018i	0.722242	+	0.524739i	0.887100	−	0.461578i	$-0.152717\pi$
$977$	22.5751	+	16.4018i	0.722242	+	0.524739i	−0.164858	+	0.986317i	$0.552717\pi$
$978$	0.892323			0.0285333
$979$	−47.6894	−	7.97935i	−1.52416	−	0.255021i
$980$		0			0
$981$	3.34343	+	2.42915i	0.106748	+	0.0775567i
$982$	−2.10036	+	6.46424i	−0.0670252	+	0.206282i
$983$	−3.02596	−	9.31294i	−0.0965130	−	0.297037i	0.891132	−	0.453744i	$-0.149912\pi$
$983$	−3.02596	−	9.31294i	−0.0965130	−	0.297037i	−0.987645	+	0.156708i	$0.949912\pi$
$984$	9.73387	−	7.07207i	0.310305	−	0.225449i
$985$		0			0
$986$	0.0267218	+	0.0822412i	0.000850995	+	0.00261909i
$987$	0.896084	−	2.75786i	0.0285227	−	0.0877837i
$988$	−0.120403	−	0.0874779i	−0.00383053	−	0.00278304i
$989$	−78.6678			−2.50149
$990$		0			0
$991$	34.9794			1.11116			0.555578	−	0.831464i	$-0.312497\pi$
$991$	34.9794			1.11116			0.555578	+	0.831464i	$0.312497\pi$
$992$	23.3024	+	16.9302i	0.739851	+	0.537533i
$993$	3.37196	−	10.3778i	0.107006	−	0.329331i
$994$	−1.20770	−	3.71692i	−0.0383059	−	0.117894i
$995$		0			0
$996$	0.386258	−	0.280633i	0.0122390	−	0.00889218i
$997$	3.94779	+	12.1501i	0.125028	+	0.384796i	0.993906	−	0.110230i	$-0.0351586\pi$
$997$	3.94779	+	12.1501i	0.125028	+	0.384796i	−0.868878	+	0.495026i	$0.835159\pi$
$998$	−2.27392	+	6.99839i	−0.0719795	+	0.221530i
$999$	6.73928	+	4.89637i	0.213221	+	0.154914i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.n.g.301.2		8
5.2	odd	4		825.2.bx.f.499.3		16
5.3	odd	4		825.2.bx.f.499.2		16
5.4	even	2		165.2.m.d.136.1	yes	8
11.3	even	5	inner	825.2.n.g.751.2		8
11.5	even	5		9075.2.a.di.1.2		4
11.6	odd	10		9075.2.a.cm.1.3		4
15.14	odd	2		495.2.n.a.136.2		8
55.3	odd	20		825.2.bx.f.124.3		16
55.14	even	10		165.2.m.d.91.1	✓	8
55.39	odd	10		1815.2.a.w.1.2		4
55.47	odd	20		825.2.bx.f.124.2		16
55.49	even	10		1815.2.a.p.1.3		4
165.14	odd	10		495.2.n.a.91.2		8
165.104	odd	10		5445.2.a.bt.1.2		4
165.149	even	10		5445.2.a.bf.1.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.d.91.1	✓	8	55.14	even	10
165.2.m.d.136.1	yes	8	5.4	even	2
495.2.n.a.91.2		8	165.14	odd	10
495.2.n.a.136.2		8	15.14	odd	2
825.2.n.g.301.2		8	1.1	even	1	trivial
825.2.n.g.751.2		8	11.3	even	5	inner
825.2.bx.f.124.2		16	55.47	odd	20
825.2.bx.f.124.3		16	55.3	odd	20
825.2.bx.f.499.2		16	5.3	odd	4
825.2.bx.f.499.3		16	5.2	odd	4
1815.2.a.p.1.3		4	55.49	even	10
1815.2.a.w.1.2		4	55.39	odd	10
5445.2.a.bf.1.3		4	165.149	even	10
5445.2.a.bt.1.2		4	165.104	odd	10
9075.2.a.cm.1.3		4	11.6	odd	10
9075.2.a.di.1.2		4	11.5	even	5

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:	\( N \)	\(=\)	\( 825 = 3 \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	825.n (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.212253 - 0.154211i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.596764 - 1.83665i) q^{4} +(0.212253 - 0.154211i) q^{6} +(0.986854 + 3.03722i) q^{7} +(-0.318714 + 0.980901i) q^{8} +(-0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.212253 - 0.154211i) q^{2} +(-0.309017 + 0.951057i) q^{3} +(-0.596764 - 1.83665i) q^{4} +(0.212253 - 0.154211i) q^{6} +(0.986854 + 3.03722i) q^{7} +(-0.318714 + 0.980901i) q^{8} +(-0.809017 - 0.587785i) q^{9} +(3.27115 + 0.547326i) q^{11} +1.93117 q^{12} +(-0.905781 - 0.658088i) q^{13} +(0.258911 - 0.796845i) q^{14} +(-2.90578 + 2.11117i) q^{16} +(-0.0713767 + 0.0518582i) q^{17} +(0.0810736 + 0.249519i) q^{18} +(-0.0212704 + 0.0654637i) q^{19} -3.19353 q^{21} +(-0.609909 - 0.620620i) q^{22} -6.65450 q^{23} +(-0.834404 - 0.606230i) q^{24} +(0.0907705 + 0.279363i) q^{26} +(0.809017 - 0.587785i) q^{27} +(4.98940 - 3.62501i) q^{28} +(1.15444 + 3.55299i) q^{29} +(7.75430 + 5.63383i) q^{31} +3.00509 q^{32} +(-1.53138 + 2.94192i) q^{33} +0.0231471 q^{34} +(-0.596764 + 1.83665i) q^{36} +(2.57418 + 7.92250i) q^{37} +(0.0146100 - 0.0106148i) q^{38} +(0.905781 - 0.658088i) q^{39} +(-3.60489 + 11.0947i) q^{41} +(0.677837 + 0.492478i) q^{42} +11.8217 q^{43} +(-0.946857 - 6.33458i) q^{44} +(1.41244 + 1.02620i) q^{46} +(-0.280594 + 0.863579i) q^{47} +(-1.10991 - 3.41595i) q^{48} +(-2.58773 + 1.88010i) q^{49} +(-0.0272635 - 0.0839083i) q^{51} +(-0.668140 + 2.05632i) q^{52} +(0.705768 + 0.512771i) q^{53} -0.262360 q^{54} -3.29374 q^{56} +(-0.0556868 - 0.0404588i) q^{57} +(0.302877 - 0.932160i) q^{58} +(0.567369 + 1.74618i) q^{59} +(8.13881 - 5.91319i) q^{61} +(-0.777078 - 2.39160i) q^{62} +(0.986854 - 3.03722i) q^{63} +(5.17372 + 3.75893i) q^{64} +(0.778717 - 0.388276i) q^{66} -9.53916 q^{67} +(0.137840 + 0.100147i) q^{68} +(2.05635 - 6.32881i) q^{69} +(3.77370 - 2.74175i) q^{71} +(0.834404 - 0.606230i) q^{72} +(2.21267 + 6.80989i) q^{73} +(0.675360 - 2.07854i) q^{74} +0.132927 q^{76} +(1.56580 + 10.4754i) q^{77} -0.293740 q^{78} +(-0.640209 - 0.465139i) q^{79} +(0.309017 + 0.951057i) q^{81} +(2.47608 - 1.79898i) q^{82} +(0.200012 - 0.145318i) q^{83} +(1.90578 + 5.86539i) q^{84} +(-2.50920 - 1.82304i) q^{86} -3.73583 q^{87} +(-1.57943 + 3.03423i) q^{88} -14.5788 q^{89} +(1.10489 - 3.40050i) q^{91} +(3.97116 + 12.2220i) q^{92} +(-7.75430 + 5.63383i) q^{93} +(0.192730 - 0.140027i) q^{94} +(-0.928623 + 2.85801i) q^{96} +(-3.31048 - 2.40521i) q^{97} +0.839188 q^{98} +(-2.32471 - 2.36553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{6} - 3 q^{7} + q^{8} - 2 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^6 - 3 * q^7 + q^8 - 2 * q^9	\( 8 q - 4 q^{2} + 2 q^{3} + 2 q^{4} + 4 q^{6} - 3 q^{7} + q^{8} - 2 q^{9} + 3 q^{11} - 2 q^{12} + 4 q^{13} - 4 q^{14} - 12 q^{16} + q^{18} + 2 q^{19} - 12 q^{21} - 9 q^{22} + 6 q^{23} + 4 q^{24} + 2 q^{26} + 2 q^{27} + 11 q^{28} + 10 q^{29} + 19 q^{31} - 12 q^{32} + 2 q^{33} - 6 q^{34} + 2 q^{36} + q^{37} + 20 q^{38} - 4 q^{39} - 9 q^{41} - q^{42} + 17 q^{44} - 22 q^{46} + 19 q^{47} - 13 q^{48} + q^{49} + 10 q^{51} + 2 q^{52} - 25 q^{53} - 6 q^{54} - 16 q^{56} - 7 q^{57} + 12 q^{58} + 13 q^{59} + 13 q^{61} - 35 q^{62} - 3 q^{63} + 39 q^{64} - 11 q^{66} - 2 q^{67} - 19 q^{68} + 9 q^{69} - 11 q^{71} - 4 q^{72} + 7 q^{73} - 43 q^{74} - 38 q^{76} + 7 q^{77} + 8 q^{78} - 22 q^{79} - 2 q^{81} + 35 q^{82} + 21 q^{83} + 4 q^{84} + 20 q^{86} + 30 q^{87} - 59 q^{88} - 20 q^{89} - 11 q^{91} + 28 q^{92} - 19 q^{93} - 35 q^{94} - 8 q^{96} - 31 q^{97} - 22 q^{98} - 7 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 + 2 * q^3 + 2 * q^4 + 4 * q^6 - 3 * q^7 + q^8 - 2 * q^9 + 3 * q^11 - 2 * q^12 + 4 * q^13 - 4 * q^14 - 12 * q^16 + q^18 + 2 * q^19 - 12 * q^21 - 9 * q^22 + 6 * q^23 + 4 * q^24 + 2 * q^26 + 2 * q^27 + 11 * q^28 + 10 * q^29 + 19 * q^31 - 12 * q^32 + 2 * q^33 - 6 * q^34 + 2 * q^36 + q^37 + 20 * q^38 - 4 * q^39 - 9 * q^41 - q^42 + 17 * q^44 - 22 * q^46 + 19 * q^47 - 13 * q^48 + q^49 + 10 * q^51 + 2 * q^52 - 25 * q^53 - 6 * q^54 - 16 * q^56 - 7 * q^57 + 12 * q^58 + 13 * q^59 + 13 * q^61 - 35 * q^62 - 3 * q^63 + 39 * q^64 - 11 * q^66 - 2 * q^67 - 19 * q^68 + 9 * q^69 - 11 * q^71 - 4 * q^72 + 7 * q^73 - 43 * q^74 - 38 * q^76 + 7 * q^77 + 8 * q^78 - 22 * q^79 - 2 * q^81 + 35 * q^82 + 21 * q^83 + 4 * q^84 + 20 * q^86 + 30 * q^87 - 59 * q^88 - 20 * q^89 - 11 * q^91 + 28 * q^92 - 19 * q^93 - 35 * q^94 - 8 * q^96 - 31 * q^97 - 22 * q^98 - 7 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more