LMFDB - Embedded newform 825.2.bx.f.499.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [825,2,Mod(49,825)]

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, 5, 4]))

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

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

chi := DirichletCharacter("825.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 825 = 3 \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	825.bx (of order $10$, 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:	$6.58765816676$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - x^{14} + 15x^{12} - 59x^{10} + 104x^{8} - 59x^{6} + 15x^{4} - x^{2} + 1 $ x^16 - x^14 + 15x^12 - 59x^10 + 104x^8 - 59x^6 + 15*x^4 - x^2 + 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:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			499.3
Root			$0.701538 + 0.227943i$ of defining polynomial
Character	$\chi$	$=$	825.499
Dual form			825.2.bx.f.124.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.154211 - 0.212253i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.596764 + 1.83665i) q^{4} +(0.212253 - 0.154211i) q^{6} +(-3.03722 + 0.986854i) q^{7} +(0.980901 + 0.318714i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(0.154211 - 0.212253i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.596764 + 1.83665i) q^{4} +(0.212253 - 0.154211i) q^{6} +(-3.03722 + 0.986854i) q^{7} +(0.980901 + 0.318714i) q^{8} +(0.809017 + 0.587785i) q^{9} +(3.27115 + 0.547326i) q^{11} +1.93117i q^{12} +(-0.658088 + 0.905781i) q^{13} +(-0.258911 + 0.796845i) q^{14} +(-2.90578 + 2.11117i) q^{16} +(-0.0518582 - 0.0713767i) q^{17} +(0.249519 - 0.0810736i) q^{18} +(0.0212704 - 0.0654637i) q^{19} -3.19353 q^{21} +(0.620620 - 0.609909i) q^{22} +6.65450i q^{23} +(0.834404 + 0.606230i) q^{24} +(0.0907705 + 0.279363i) q^{26} +(0.587785 + 0.809017i) q^{27} +(-3.62501 - 4.98940i) q^{28} +(-1.15444 - 3.55299i) q^{29} +(7.75430 + 5.63383i) q^{31} +3.00509i q^{32} +(2.94192 + 1.53138i) q^{33} -0.0231471 q^{34} +(-0.596764 + 1.83665i) q^{36} +(-7.92250 + 2.57418i) q^{37} +(-0.0106148 - 0.0146100i) q^{38} +(-0.905781 + 0.658088i) q^{39} +(-3.60489 + 11.0947i) q^{41} +(-0.492478 + 0.677837i) q^{42} -11.8217i q^{43} +(0.946857 + 6.33458i) q^{44} +(1.41244 + 1.02620i) q^{46} +(-0.863579 - 0.280594i) q^{47} +(-3.41595 + 1.10991i) q^{48} +(2.58773 - 1.88010i) q^{49} +(-0.0272635 - 0.0839083i) q^{51} +(-2.05632 - 0.668140i) q^{52} +(0.512771 - 0.705768i) q^{53} +0.262360 q^{54} -3.29374 q^{56} +(0.0404588 - 0.0556868i) q^{57} +(-0.932160 - 0.302877i) q^{58} +(-0.567369 - 1.74618i) q^{59} +(8.13881 - 5.91319i) q^{61} +(2.39160 - 0.777078i) q^{62} +(-3.03722 - 0.986854i) q^{63} +(-5.17372 - 3.75893i) q^{64} +(0.778717 - 0.388276i) q^{66} -9.53916i q^{67} +(0.100147 - 0.137840i) q^{68} +(-2.05635 + 6.32881i) q^{69} +(3.77370 - 2.74175i) q^{71} +(0.606230 + 0.834404i) q^{72} +(6.80989 - 2.21267i) q^{73} +(-0.675360 + 2.07854i) q^{74} +0.132927 q^{76} +(-10.4754 + 1.56580i) q^{77} +0.293740i q^{78} +(0.640209 + 0.465139i) q^{79} +(0.309017 + 0.951057i) q^{81} +(1.79898 + 2.47608i) q^{82} +(-0.145318 - 0.200012i) q^{83} +(-1.90578 - 5.86539i) q^{84} +(-2.50920 - 1.82304i) q^{86} -3.73583i q^{87} +(3.03423 + 1.57943i) q^{88} +14.5788 q^{89} +(1.10489 - 3.40050i) q^{91} +(-12.2220 + 3.97116i) q^{92} +(5.63383 + 7.75430i) q^{93} +(-0.192730 + 0.140027i) q^{94} +(-0.928623 + 2.85801i) q^{96} +(2.40521 - 3.31048i) q^{97} -0.839188i q^{98} +(2.32471 + 2.36553i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4} + 8 q^{6} + 4 q^{9}+O(q^{10}) $ 16 * q - 4 * q^4 + 8 * q^6 + 4 * q^9	$ 16 q - 4 q^{4} + 8 q^{6} + 4 q^{9} + 6 q^{11} + 8 q^{14} - 24 q^{16} - 4 q^{19} - 24 q^{21} - 8 q^{24} + 4 q^{26} - 20 q^{29} + 38 q^{31} + 12 q^{34} + 4 q^{36} + 8 q^{39} - 18 q^{41} - 34 q^{44} - 44 q^{46} - 2 q^{49} + 20 q^{51} + 12 q^{54} - 32 q^{56} - 26 q^{59} + 26 q^{61} - 78 q^{64} - 22 q^{66} - 18 q^{69} - 22 q^{71} + 86 q^{74} - 76 q^{76} + 44 q^{79} - 4 q^{81} - 8 q^{84} + 40 q^{86} + 40 q^{89} - 22 q^{91} + 70 q^{94} - 16 q^{96} + 14 q^{99}+O(q^{100}) $ 16 * q - 4 * q^4 + 8 * q^6 + 4 * q^9 + 6 * q^11 + 8 * q^14 - 24 * q^16 - 4 * q^19 - 24 * q^21 - 8 * q^24 + 4 * q^26 - 20 * q^29 + 38 * q^31 + 12 * q^34 + 4 * q^36 + 8 * q^39 - 18 * q^41 - 34 * q^44 - 44 * q^46 - 2 * q^49 + 20 * q^51 + 12 * q^54 - 32 * q^56 - 26 * q^59 + 26 * q^61 - 78 * q^64 - 22 * q^66 - 18 * q^69 - 22 * q^71 + 86 * q^74 - 76 * q^76 + 44 * q^79 - 4 * q^81 - 8 * q^84 + 40 * q^86 + 40 * q^89 - 22 * q^91 + 70 * q^94 - 16 * q^96 + 14 * 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 $

$2$	0.154211	−	0.212253i	0.109044	−	0.150086i	−0.751007	−	0.660294i	$-0.770432\pi$
$2$	0.154211	−	0.212253i	0.109044	−	0.150086i	0.860051	+	0.510208i	$0.170432\pi$
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	0.596764	+	1.83665i	0.298382	+	0.918325i
$5$		0			0
$5$		0			0
$6$	0.212253	−	0.154211i	0.0866521	−	0.0629564i
$7$	−3.03722	+	0.986854i	−1.14796	+	0.372996i	−0.820376	−	0.571825i	$-0.806236\pi$
$7$	−3.03722	+	0.986854i	−1.14796	+	0.372996i	−0.327587	+	0.944821i	$0.606236\pi$
$8$	0.980901	+	0.318714i	0.346801	+	0.112682i
$9$	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
$12$			1.93117i			0.557480i
$13$	−0.658088	+	0.905781i	−0.182521	+	0.251218i	−0.890467	−	0.455048i	$-0.849622\pi$
$13$	−0.658088	+	0.905781i	−0.182521	+	0.251218i	0.707946	+	0.706267i	$0.249622\pi$
$14$	−0.258911	+	0.796845i	−0.0691968	+	0.212966i
$15$		0			0
$16$	−2.90578	+	2.11117i	−0.726445	+	0.527793i
$17$	−0.0518582	−	0.0713767i	−0.0125775	−	0.0173114i	0.802682	−	0.596407i	$-0.203406\pi$
$17$	−0.0518582	−	0.0713767i	−0.0125775	−	0.0173114i	−0.815259	+	0.579096i	$0.803406\pi$
$18$	0.249519	−	0.0810736i	0.0588122	−	0.0191092i
$19$	0.0212704	−	0.0654637i	0.00487977	−	0.0150184i	−0.948587	−	0.316517i	$-0.897487\pi$
$19$	0.0212704	−	0.0654637i	0.00487977	−	0.0150184i	0.953467	+	0.301498i	$0.0974867\pi$
$20$		0			0
$21$	−3.19353			−0.696885
$22$	0.620620	−	0.609909i	0.132317	−	0.130033i
$23$			6.65450i			1.38756i	0.720187	+	0.693780i	$0.244056\pi$
$23$			6.65450i			1.38756i	−0.720187	+	0.693780i	$0.755944\pi$
$24$	0.834404	+	0.606230i	0.170322	+	0.123746i
$25$		0			0
$26$	0.0907705	+	0.279363i	0.0178016	+	0.0547876i
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	−3.62501	−	4.98940i	−0.685062	−	0.942908i
$29$	−1.15444	−	3.55299i	−0.214373	−	0.659773i	−0.999197	−	0.0400546i	$-0.987247\pi$
$29$	−1.15444	−	3.55299i	−0.214373	−	0.659773i	0.784824	−	0.619718i	$-0.212753\pi$
$30$		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	$0.369998\pi$
$32$			3.00509i			0.531230i
$33$	2.94192	+	1.53138i	0.512122	+	0.266579i
$34$	−0.0231471			−0.00396969
$35$		0			0
$36$	−0.596764	+	1.83665i	−0.0994606	+	0.306108i
$37$	−7.92250	+	2.57418i	−1.30245	+	0.423192i	−0.876433	−	0.481523i	$-0.840084\pi$
$37$	−7.92250	+	2.57418i	−1.30245	+	0.423192i	−0.426017	+	0.904715i	$0.640084\pi$
$38$	−0.0106148	−	0.0146100i	−0.00172194	−	0.00237005i
$39$	−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	$0.735362\pi$
$42$	−0.492478	+	0.677837i	−0.0759909	+	0.104593i
$43$		−	11.8217i		−	1.80280i	−0.432989	−	0.901399i	$-0.642541\pi$
$43$		−	11.8217i		−	1.80280i	0.432989	−	0.901399i	$-0.357459\pi$
$44$	0.946857	+	6.33458i	0.142744	+	0.954974i
$45$		0			0
$46$	1.41244	+	1.02620i	0.208253	+	0.151305i
$47$	−0.863579	−	0.280594i	−0.125966	−	0.0409288i	0.245356	−	0.969433i	$-0.421095\pi$
$47$	−0.863579	−	0.280594i	−0.125966	−	0.0409288i	−0.371322	+	0.928504i	$0.621095\pi$
$48$	−3.41595	+	1.10991i	−0.493050	+	0.160202i
$49$	2.58773	−	1.88010i	0.369676	−	0.268586i
$50$		0			0
$51$	−0.0272635	−	0.0839083i	−0.00381765	−	0.0117495i
$52$	−2.05632	−	0.668140i	−0.285161	−	0.0926544i
$53$	0.512771	−	0.705768i	0.0704344	−	0.0969447i	−0.772346	−	0.635202i	$-0.780917\pi$
$53$	0.512771	−	0.705768i	0.0704344	−	0.0969447i	0.842781	+	0.538257i	$0.180917\pi$
$54$	0.262360			0.0357026
$55$		0			0
$56$	−3.29374			−0.440144
$57$	0.0404588	−	0.0556868i	0.00535890	−	0.00737589i
$58$	−0.932160	−	0.302877i	−0.122399	−	0.0397697i
$59$	−0.567369	−	1.74618i	−0.0738651	−	0.227333i	0.907307	−	0.420469i	$-0.138134\pi$
$59$	−0.567369	−	1.74618i	−0.0738651	−	0.227333i	−0.981172	+	0.193135i	$0.938134\pi$
$60$		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	$0.0772597\pi$
$62$	2.39160	−	0.777078i	0.303733	−	0.0986890i
$63$	−3.03722	−	0.986854i	−0.382654	−	0.124332i
$64$	−5.17372	−	3.75893i	−0.646715	−	0.469866i
$65$		0			0
$66$	0.778717	−	0.388276i	0.0958534	−	0.0477935i
$67$		−	9.53916i		−	1.16539i	−0.812690	−	0.582697i	$-0.801997\pi$
$67$		−	9.53916i		−	1.16539i	0.812690	−	0.582697i	$-0.198003\pi$
$68$	0.100147	−	0.137840i	0.0121446	−	0.0167156i
$69$	−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	$0.210729\pi$
$72$	0.606230	+	0.834404i	0.0714449	+	0.0983354i
$73$	6.80989	−	2.21267i	0.797037	−	0.258973i	0.117939	−	0.993021i	$-0.462371\pi$
$73$	6.80989	−	2.21267i	0.797037	−	0.258973i	0.679098	+	0.734048i	$0.262371\pi$
$74$	−0.675360	+	2.07854i	−0.0785090	+	0.241626i
$75$		0			0
$76$	0.132927			0.0152478
$77$	−10.4754	+	1.56580i	−1.19378	+	0.178439i
$78$			0.293740i			0.0332595i
$79$	0.640209	+	0.465139i	0.0720292	+	0.0523323i	0.623217	−	0.782049i	$-0.285825\pi$
$79$	0.640209	+	0.465139i	0.0720292	+	0.0523323i	−0.551188	+	0.834381i	$0.685825\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	1.79898	+	2.47608i	0.198664	+	0.273437i
$83$	−0.145318	−	0.200012i	−0.0159507	−	0.0219542i	0.800967	−	0.598708i	$-0.204319\pi$
$83$	−0.145318	−	0.200012i	−0.0159507	−	0.0219542i	−0.816918	+	0.576754i	$0.804319\pi$
$84$	−1.90578	−	5.86539i	−0.207938	−	0.639966i
$85$		0			0
$86$	−2.50920	−	1.82304i	−0.270574	−	0.196584i
$87$		−	3.73583i		−	0.400523i
$88$	3.03423	+	1.57943i	0.323450	+	0.168368i
$89$	14.5788			1.54535			0.772673	−	0.634804i	$-0.218919\pi$
$89$	14.5788			1.54535			0.772673	+	0.634804i	$0.218919\pi$
$90$		0			0
$91$	1.10489	−	3.40050i	0.115824	−	0.356469i
$92$	−12.2220	+	3.97116i	−1.27423	+	0.414022i
$93$	5.63383	+	7.75430i	0.584201	+	0.804084i
$94$	−0.192730	+	0.140027i	−0.0198786	+	0.0144427i
$95$		0			0
$96$	−0.928623	+	2.85801i	−0.0947772	+	0.291694i
$97$	2.40521	−	3.31048i	0.244212	−	0.336128i	−0.669262	−	0.743027i	$-0.733390\pi$
$97$	2.40521	−	3.31048i	0.244212	−	0.336128i	0.913474	+	0.406898i	$0.133390\pi$
$98$		−	0.839188i		−	0.0847708i
$99$	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	$0.768493\pi$
$102$	−0.0220142	−	0.00715284i	−0.00217973	−	0.000708236i
$103$	−1.99038	+	0.646712i	−0.196118	+	0.0637224i	−0.405429	−	0.914127i	$-0.632878\pi$
$103$	−1.99038	+	0.646712i	−0.196118	+	0.0637224i	0.209311	+	0.977849i	$0.432878\pi$
$104$	−0.934204	+	0.678739i	−0.0916062	+	0.0665558i
$105$		0			0
$106$	−0.0707268	−	0.217675i	−0.00686959	−	0.0211424i
$107$	14.9705	+	4.86421i	1.44725	+	0.470241i	0.924151	−	0.382029i	$-0.124774\pi$
$107$	14.9705	+	4.86421i	1.44725	+	0.470241i	0.523103	+	0.852270i	$0.324774\pi$
$108$	−1.13511	+	1.56235i	−0.109226	+	0.150337i
$109$	4.13271			0.395842			0.197921	−	0.980218i	$-0.436581\pi$
$109$	4.13271			0.395842			0.197921	+	0.980218i	$0.436581\pi$
$110$		0			0
$111$	−8.33021			−0.790668
$112$	6.74209	−	9.27969i	0.637067	−	0.876848i
$113$	13.0818	+	4.25053i	1.23063	+	0.399856i	0.850943	−	0.525258i	$-0.176031\pi$
$113$	13.0818	+	4.25053i	1.23063	+	0.399856i	0.379688	+	0.925114i	$0.376031\pi$
$114$	−0.00558051	−	0.0171750i	−0.000522662	−	0.00160859i
$115$		0			0
$116$	5.83666	−	4.24059i	0.541921	−	0.393728i
$117$	−1.06481	+	0.345977i	−0.0984416	+	0.0319856i
$118$	−0.458127	−	0.148855i	−0.0421740	−	0.0137032i
$119$	0.227943	+	0.165611i	0.0208955	+	0.0151815i
$120$		0			0
$121$	10.4009	+	3.58078i	0.945533	+	0.325525i
$122$		−	2.63937i		−	0.238957i
$123$	−6.85690	+	9.43772i	−0.618266	+	0.850971i
$124$	−5.71989	+	17.6040i	−0.513661	+	1.58089i
$125$		0			0
$126$	−0.677837	+	0.492478i	−0.0603865	+	0.0438734i
$127$	4.64338	+	6.39106i	0.412033	+	0.567115i	0.963713	−	0.266941i	$-0.0860129\pi$
$127$	4.64338	+	6.39106i	0.412033	+	0.567115i	−0.551680	+	0.834056i	$0.686013\pi$
$128$	−7.31171	+	2.37572i	−0.646270	+	0.209986i
$129$	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	$0.753310\pi$
$132$	−1.05698	+	6.31714i	−0.0919982	+	0.549837i
$133$			0.219819i			0.0190607i
$134$	−2.02472	−	1.47104i	−0.174909	−	0.127079i
$135$		0			0
$136$	−0.0281190	−	0.0865414i	−0.00241118	−	0.00742086i
$137$	4.54480	+	6.25538i	0.388289	+	0.534433i	0.957757	−	0.287580i	$-0.0928508\pi$
$137$	4.54480	+	6.25538i	0.388289	+	0.534433i	−0.569468	+	0.822013i	$0.692851\pi$
$138$	1.02620	+	1.41244i	0.0873558	+	0.120235i
$139$	−6.23796	−	19.1985i	−0.529097	−	1.62839i	−0.756069	−	0.654492i	$-0.772883\pi$
$139$	−6.23796	−	19.1985i	−0.529097	−	1.62839i	0.226972	−	0.973901i	$-0.427117\pi$
$140$		0			0
$141$	−0.734604	−	0.533721i	−0.0618648	−	0.0449474i
$142$		−	1.22379i		−	0.102698i
$143$	−2.64846	+	2.60276i	−0.221476	+	0.217653i
$144$	−3.59174			−0.299312
$145$		0			0
$146$	0.580514	−	1.78664i	0.0480437	−	0.147863i
$147$	3.04206	−	0.988426i	0.250905	−	0.0815240i
$148$	−9.45572	−	13.0147i	−0.777255	−	1.06980i
$149$	7.84361	−	5.69872i	0.642573	−	0.466857i	−0.218160	−	0.975913i	$-0.570005\pi$
$149$	7.84361	−	5.69872i	0.642573	−	0.466857i	0.860733	+	0.509056i	$0.170005\pi$
$150$		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	$-0.111616\pi$
$152$	0.0417284	−	0.0574342i	0.00338462	−	0.00465853i
$153$		−	0.0882264i		−	0.00713268i
$154$	−1.28307	+	2.46489i	−0.103393	+	0.198627i
$155$		0			0
$156$	−1.74921	−	1.27088i	−0.140049	−	0.101752i
$157$	14.1522	+	4.59834i	1.12947	+	0.366987i	0.813375	−	0.581740i	$-0.197628\pi$
$157$	14.1522	+	4.59834i	1.12947	+	0.366987i	0.316096	+	0.948727i	$0.397628\pi$
$158$	0.197455	−	0.0641570i	0.0157087	−	0.00510405i
$159$	0.705768	−	0.512771i	0.0559710	−	0.0406653i
$160$		0			0
$161$	−6.56702	−	20.2112i	−0.517554	−	1.59287i
$162$	0.249519	+	0.0810736i	0.0196041	+	0.00636974i
$163$	1.99914	−	2.75158i	0.156585	−	0.215521i	−0.723516	−	0.690308i	$-0.757475\pi$
$163$	1.99914	−	2.75158i	0.156585	−	0.215521i	0.880101	+	0.474787i	$0.157475\pi$
$164$	−22.5283			−1.75917
$165$		0			0
$166$	−0.0648629			−0.00503434
$167$	13.2936	−	18.2970i	1.02869	−	1.41587i	0.122757	−	0.992437i	$-0.460826\pi$
$167$	13.2936	−	18.2970i	1.02869	−	1.41587i	0.905929	−	0.423429i	$-0.139174\pi$
$168$	−3.13253	−	1.01782i	−0.241680	−	0.0785266i
$169$	3.62986	+	11.1716i	0.279220	+	0.859351i
$170$		0			0
$171$	0.0556868	−	0.0404588i	0.00425847	−	0.00309396i
$172$	21.7124	−	7.05478i	1.65555	−	0.537922i
$173$	−12.4506	−	4.04543i	−0.946598	−	0.307568i	−0.205266	−	0.978706i	$-0.565806\pi$
$173$	−12.4506	−	4.04543i	−0.946598	−	0.307568i	−0.741333	+	0.671138i	$0.765806\pi$
$174$	−0.792943	−	0.576107i	−0.0601128	−	0.0436745i
$175$		0			0
$176$	−10.6607	+	5.31556i	−0.803584	+	0.400675i
$177$		−	1.83604i		−	0.138005i
$178$	2.24821	−	3.09439i	0.168510	−	0.231935i
$179$	4.69008	−	14.4346i	0.350553	−	1.07889i	−0.607990	−	0.793944i	$-0.708024\pi$
$179$	4.69008	−	14.4346i	0.350553	−	1.07889i	0.958543	−	0.284947i	$-0.0919759\pi$
$180$		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	$0.316729\pi$
$182$	−0.551381	−	0.758911i	−0.0408711	−	0.0562542i
$183$	9.56775	−	3.10875i	0.707268	−	0.229805i
$184$	−2.12088	+	6.52740i	−0.156354	+	0.481207i
$185$		0			0
$186$	2.51468			0.184385
$187$	−0.130570	−	0.261867i	−0.00954820	−	0.0191496i
$188$		−	1.75354i		−	0.127890i
$189$	−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	$0.843165\pi$
$192$	−3.75893	−	5.17372i	−0.271277	−	0.373381i
$193$	−5.71320	−	7.86354i	−0.411245	−	0.566030i	0.552276	−	0.833661i	$-0.313759\pi$
$193$	−5.71320	−	7.86354i	−0.411245	−	0.566030i	−0.963522	+	0.267631i	$0.913759\pi$
$194$	−0.331752	−	1.02103i	−0.0238184	−	0.0733054i
$195$		0			0
$196$	4.99735	+	3.63079i	0.356953	+	0.259342i
$197$			8.88764i			0.633218i	0.948556	+	0.316609i	$0.102544\pi$
$197$			8.88764i			0.633218i	−0.948556	+	0.316609i	$0.897456\pi$
$198$	0.860588	−	0.128636i	0.0611593	−	0.00914175i
$199$	−18.0381			−1.27869			−0.639343	−	0.768921i	$-0.720794\pi$
$199$	−18.0381			−1.27869			−0.639343	+	0.768921i	$0.720794\pi$
$200$		0			0
$201$	2.94776	−	9.07228i	0.207919	−	0.639909i
$202$	−1.07086	+	0.347945i	−0.0753457	+	0.0244813i
$203$	7.01256	+	9.65196i	0.492185	+	0.677435i
$204$	0.137840	−	0.100147i	0.00965075	−	0.00701168i
$205$		0			0
$206$	−0.169671	+	0.522194i	−0.0118216	+	0.0363830i
$207$	−3.91142	+	5.38361i	−0.271862	+	0.374186i
$208$		−	4.02134i		−	0.278830i
$209$	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	$0.912390\pi$
$212$	1.60225	+	0.520603i	0.110043	+	0.0357552i
$213$	4.43625	−	1.44142i	0.303967	−	0.0987647i
$214$	3.34106	−	2.42743i	0.228390	−	0.165935i
$215$		0			0
$216$	0.318714	+	0.980901i	0.0216857	+	0.0667418i
$217$	−29.1113	−	9.45884i	−1.97621	−	0.642108i
$218$	0.637310	−	0.877182i	0.0431641	−	0.0594103i
$219$	7.16034			0.483851
$220$		0			0
$221$	0.0987789			0.00664459
$222$	−1.28461	+	1.76812i	−0.0862174	+	0.118668i
$223$	−13.0760	−	4.24865i	−0.875635	−	0.284511i	−0.163491	−	0.986545i	$-0.552276\pi$
$223$	−13.0760	−	4.24865i	−0.875635	−	0.284511i	−0.712144	+	0.702034i	$0.752276\pi$
$224$	−2.96558	−	9.12713i	−0.198146	−	0.609832i
$225$		0			0
$226$	2.91955	−	2.12118i	0.194205	−	0.141099i
$227$	0.630298	−	0.204796i	0.0418344	−	0.0135928i	−0.288025	−	0.957623i	$-0.592999\pi$
$227$	0.630298	−	0.204796i	0.0418344	−	0.0135928i	0.329859	+	0.944030i	$0.392999\pi$
$228$	0.126421	+	0.0410768i	0.00837246	+	0.00272038i
$229$	−6.05987	−	4.40275i	−0.400447	−	0.290942i	0.369276	−	0.929320i	$-0.379606\pi$
$229$	−6.05987	−	4.40275i	−0.400447	−	0.290942i	−0.769723	+	0.638378i	$0.779606\pi$
$230$		0			0
$231$	−10.4465	−	1.74790i	−0.687330	−	0.115004i
$232$		−	3.85306i		−	0.252966i
$233$	6.18665	−	8.51520i	0.405301	−	0.557849i	−0.556763	−	0.830671i	$-0.687957\pi$
$233$	6.18665	−	8.51520i	0.405301	−	0.557849i	0.962065	+	0.272822i	$0.0879570\pi$
$234$	−0.0907705	+	0.279363i	−0.00593385	+	0.0182625i
$235$		0			0
$236$	2.86854	−	2.08411i	0.186726	−	0.135664i
$237$	0.465139	+	0.640209i	0.0302140	+	0.0415861i
$238$	0.0703028	−	0.0228428i	0.00455706	−	0.00148068i
$239$	−5.27684	+	16.2404i	−0.341330	+	1.05051i	0.622189	+	0.782867i	$0.286244\pi$
$239$	−5.27684	+	16.2404i	−0.341330	+	1.05051i	−0.963519	+	0.267640i	$0.913756\pi$
$240$		0			0
$241$	−16.7082			−1.07627			−0.538135	−	0.842859i	$-0.680871\pi$
$241$	−16.7082			−1.07627			−0.538135	+	0.842859i	$0.680871\pi$
$242$	2.36396	−	1.65542i	0.151961	−	0.106415i
$243$			1.00000i			0.0641500i
$244$	15.7174	+	11.4194i	1.00620	+	0.731050i
$245$		0			0
$246$	0.945777	+	2.91080i	0.0603006	+	0.185586i
$247$	0.0452979	+	0.0623472i	0.00288224	+	0.00396706i
$248$	5.81062	+	7.99763i	0.368975	+	0.507850i
$249$	−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	$0.648159\pi$
$252$		−	6.16724i		−	0.388499i
$253$	−3.64219	+	21.7679i	−0.228982	+	1.36854i
$254$	2.07259			0.130046
$255$		0			0
$256$	3.32908	−	10.2458i	0.208067	−	0.640366i
$257$	−3.51724	+	1.14282i	−0.219399	+	0.0712872i	−0.416654	−	0.909065i	$-0.636797\pi$
$257$	−3.51724	+	1.14282i	−0.219399	+	0.0712872i	0.197255	+	0.980352i	$0.436797\pi$
$258$	−1.82304	−	2.50920i	−0.113498	−	0.156216i
$259$	21.5221	−	15.6367i	1.33732	−	0.971617i
$260$		0			0
$261$	1.15444	−	3.55299i	0.0714577	−	0.219924i
$262$	−2.52195	+	3.47116i	−0.155806	+	0.214449i
$263$			31.6315i			1.95048i	0.221147	+	0.975241i	$0.429020\pi$
$263$			31.6315i			1.95048i	−0.221147	+	0.975241i	$0.570980\pi$
$264$	2.39766	+	2.43976i	0.147566	+	0.150157i
$265$		0			0
$266$	0.0466573	+	0.0338985i	0.00286074	+	0.00207845i
$267$	13.8652	+	4.50509i	0.848539	+	0.275707i
$268$	17.5201	−	5.69262i	1.07021	−	0.347732i
$269$	−11.9536	+	8.68479i	−0.728823	+	0.529521i	−0.889191	−	0.457536i	$-0.848732\pi$
$269$	−11.9536	+	8.68479i	−0.728823	+	0.529521i	0.160368	+	0.987057i	$0.448732\pi$
$270$		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	$-0.302812\pi$
$272$	0.301377	+	0.0979234i	0.0182737	+	0.00593748i
$273$	2.10162	−	2.89263i	0.127196	−	0.175070i
$274$	2.02859			0.122551
$275$		0			0
$276$	−12.8510			−0.773537
$277$	−15.1122	+	20.8001i	−0.908002	+	1.24976i	0.0598418	+	0.998208i	$0.480940\pi$
$277$	−15.1122	+	20.8001i	−0.908002	+	1.24976i	−0.967844	+	0.251550i	$0.919060\pi$
$278$	−5.03691	−	1.63659i	−0.302094	−	0.0981561i
$279$	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	$0.00656732\pi$
$282$	−0.226568	+	0.0736165i	−0.0134919	+	0.00438380i
$283$	6.87970	+	2.23535i	0.408956	+	0.132878i	0.506268	−	0.862376i	$-0.331025\pi$
$283$	6.87970	+	2.23535i	0.408956	+	0.132878i	−0.0973123	+	0.995254i	$0.531025\pi$
$284$	7.28764	+	5.29478i	0.432442	+	0.314187i
$285$		0			0
$286$	0.144021	+	0.963520i	0.00851616	+	0.0569741i
$287$		−	37.2546i		−	2.19907i
$288$	−1.76635	+	2.43117i	−0.104083	+	0.143258i
$289$	5.25088	−	16.1606i	0.308876	−	0.950621i
$290$		0			0
$291$	3.31048	−	2.40521i	0.194064	−	0.140996i
$292$	8.12778	+	11.1869i	0.475643	+	0.654666i
$293$	−13.8804	+	4.51002i	−0.810902	+	0.263478i	−0.684980	−	0.728562i	$-0.740189\pi$
$293$	−13.8804	+	4.51002i	−0.810902	+	0.263478i	−0.125922	+	0.992040i	$0.540189\pi$
$294$	0.259323	−	0.798115i	0.0151240	−	0.0465470i
$295$		0			0
$296$	−8.59161			−0.499377
$297$	1.47994	+	2.96813i	0.0858747	+	0.172228i
$298$		−	2.54364i		−	0.147349i
$299$	−6.02752	−	4.37925i	−0.348580	−	0.253258i
$300$		0			0
$301$	11.6663	+	35.9053i	0.672436	+	2.06955i
$302$	−2.33807	−	3.21807i	−0.134541	−	0.185179i
$303$	−2.52261	−	3.47207i	−0.144920	−	0.199465i
$304$	0.0763980	+	0.235129i	0.00438172	+	0.0134856i
$305$		0			0
$306$	−0.0187264	−	0.0136055i	−0.00107052	−	0.000777775i
$307$		−	28.5445i		−	1.62912i	−0.580080	−	0.814559i	$-0.696979\pi$
$307$		−	28.5445i		−	1.62912i	0.580080	−	0.814559i	$-0.303021\pi$
$308$	−9.12713	−	18.3051i	−0.520066	−	1.04303i
$309$	−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	$0.191015\pi$
$312$	−1.09822	+	0.356834i	−0.0621746	+	0.0202018i
$313$	9.65786	+	13.2929i	0.545894	+	0.751359i	0.989448	−	0.144889i	$-0.0462824\pi$
$313$	9.65786	+	13.2929i	0.545894	+	0.751359i	−0.443554	+	0.896248i	$0.646282\pi$
$314$	3.15844	−	2.29474i	0.178241	−	0.129500i
$315$		0			0
$316$	−0.472244	+	1.45342i	−0.0265658	+	0.0817612i
$317$	−8.35278	+	11.4966i	−0.469139	+	0.645714i	−0.976373	−	0.216094i	$-0.930668\pi$
$317$	−8.35278	+	11.4966i	−0.469139	+	0.645714i	0.507234	+	0.861809i	$0.330668\pi$
$318$		−	0.228877i		−	0.0128348i
$319$	−1.83169	−	12.2542i	−0.102555	−	0.686104i
$320$		0			0
$321$	12.7347	+	9.25228i	0.710780	+	0.516412i
$322$	−5.30261	−	1.72292i	−0.295503	−	0.0960147i
$323$	−0.00577563	+	0.00187662i	−0.000321365	+	0.000104418i
$324$	−1.56235	+	1.13511i	−0.0867971	+	0.0630618i
$325$		0			0
$326$	−0.275743	−	0.848650i	−0.0152720	−	0.0470024i
$327$	3.93044	+	1.27708i	0.217354	+	0.0706226i
$328$	−7.07207	+	9.73387i	−0.390490	+	0.537463i
$329$	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	$0.596949\pi$
$332$	0.280633	−	0.386258i	0.0154017	−	0.0211986i
$333$	−7.92250	−	2.57418i	−0.434150	−	0.141064i
$334$	−1.83359	−	5.64321i	−0.100330	−	0.308783i
$335$		0			0
$336$	9.27969	−	6.74209i	0.506249	−	0.367811i
$337$	−5.59800	+	1.81890i	−0.304943	+	0.0990819i	−0.457491	−	0.889214i	$-0.651252\pi$
$337$	−5.59800	+	1.81890i	−0.304943	+	0.0990819i	0.152549	+	0.988296i	$0.451252\pi$
$338$	2.93097	+	0.952330i	0.159424	+	0.0517999i
$339$	11.1280	+	8.08499i	0.604392	+	0.439116i
$340$		0			0
$341$	22.2820	+	22.6732i	1.20664	+	1.22783i
$342$		−	0.0180589i		−	0.000976514i
$343$	7.13561	−	9.82132i	0.385287	−	0.530302i
$344$	3.76775	−	11.5959i	0.203144	−	0.625212i
$345$		0			0
$346$	−2.77867	+	2.01882i	−0.149382	+	0.108533i
$347$	20.2811	+	27.9145i	1.08875	+	1.49853i	0.849512	+	0.527569i	$0.176896\pi$
$347$	20.2811	+	27.9145i	1.08875	+	1.49853i	0.239234	+	0.970962i	$0.423104\pi$
$348$	6.86141	−	2.22941i	0.367810	−	0.119509i
$349$	1.70378	−	5.24371i	0.0912014	−	0.280689i	−0.895044	−	0.445978i	$-0.852856\pi$
$349$	1.70378	−	5.24371i	0.0912014	−	0.280689i	0.986245	+	0.165289i	$0.0528558\pi$
$350$		0			0
$351$	−1.11961			−0.0597602
$352$	−1.64476	+	9.83010i	−0.0876662	+	0.523946i
$353$		−	29.8740i		−	1.59003i	−0.606589	−	0.795016i	$-0.707463\pi$
$353$		−	29.8740i		−	1.59003i	0.606589	−	0.795016i	$-0.292537\pi$
$354$	−0.389706	−	0.283138i	−0.0207127	−	0.0150486i
$355$		0			0
$356$	8.70008	+	26.7761i	0.461103	+	1.41913i
$357$	0.165611	+	0.227943i	0.00876504	+	0.0120640i
$358$	−2.34053	−	3.22146i	−0.123701	−	0.170259i
$359$	11.0978	+	34.1554i	0.585717	+	1.80265i	0.596372	+	0.802708i	$0.296608\pi$
$359$	11.0978	+	34.1554i	0.585717	+	1.80265i	−0.0106548	+	0.999943i	$0.503392\pi$
$360$		0			0
$361$	15.3675	+	11.1651i	0.808815	+	0.587639i
$362$			0.370840i			0.0194909i
$363$	8.78529	+	6.61956i	0.461108	+	0.347437i
$364$	6.90488			0.361914
$365$		0			0
$366$	0.815611	−	2.51019i	0.0426326	−	0.131210i
$367$	−8.58887	+	2.79069i	−0.448335	+	0.145673i	−0.524478	−	0.851424i	$-0.675740\pi$
$367$	−8.58887	+	2.79069i	−0.448335	+	0.145673i	0.0761428	+	0.997097i	$0.475740\pi$
$368$	−14.0488	−	19.3365i	−0.732345	−	1.00799i
$369$	−9.43772	+	6.85690i	−0.491308	+	0.356956i
$370$		0			0
$371$	−0.860909	+	2.64961i	−0.0446962	+	0.137561i
$372$	−10.8799	+	14.9749i	−0.564095	+	0.776410i
$373$			17.1994i			0.890553i	0.895393	+	0.445277i	$0.146895\pi$
$373$			17.1994i			0.890553i	−0.895393	+	0.445277i	$0.853105\pi$
$374$	−0.0757176	−	0.0126690i	−0.00391526	−	0.000655098i
$375$		0			0
$376$	−0.757656	−	0.550469i	−0.0390731	−	0.0283883i
$377$	3.97795	+	1.29251i	0.204875	+	0.0665678i
$378$	−0.796845	+	0.258911i	−0.0409853	+	0.0133169i
$379$	−6.47382	+	4.70350i	−0.332538	+	0.241603i	−0.741507	−	0.670946i	$-0.765888\pi$
$379$	−6.47382	+	4.70350i	−0.332538	+	0.241603i	0.408969	+	0.912548i	$0.365888\pi$
$380$		0			0
$381$	2.44117	+	7.51314i	0.125065	+	0.384910i
$382$	1.22492	+	0.398002i	0.0626725	+	0.0203635i
$383$	17.4649	−	24.0384i	0.892417	−	1.22831i	−0.0804076	−	0.996762i	$-0.525622\pi$
$383$	17.4649	−	24.0384i	0.892417	−	1.22831i	0.972824	−	0.231544i	$-0.0743778\pi$
$384$	−7.68799			−0.392326
$385$		0			0
$386$	−2.55010			−0.129797
$387$	6.94864	−	9.56399i	0.353219	−	0.486165i
$388$	7.51553	+	2.44194i	0.381543	+	0.123971i
$389$	0.183988	+	0.566256i	0.00932855	+	0.0287103i	0.955612	−	0.294627i	$-0.0951953\pi$
$389$	0.183988	+	0.566256i	0.00932855	+	0.0287103i	−0.946284	+	0.323337i	$0.895195\pi$
$390$		0			0
$391$	0.474976	−	0.345090i	0.0240206	−	0.0174520i
$392$	3.13752	−	1.01944i	0.158469	−	0.0514897i
$393$	−15.5534	−	5.05362i	−0.784568	−	0.254922i
$394$	1.88643	+	1.37057i	0.0950371	+	0.0690485i
$395$		0			0
$396$	−2.95735	+	5.68133i	−0.148612	+	0.285498i
$397$		−	1.66950i		−	0.0837898i	−0.999122	−	0.0418949i	$-0.986661\pi$
$397$		−	1.66950i		−	0.0837898i	0.999122	−	0.0418949i	$-0.0133395\pi$
$398$	−2.78168	+	3.82865i	−0.139433	+	0.191913i
$399$	−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	$0.208381\pi$
$402$	−1.47104	−	2.02472i	−0.0733690	−	0.100984i
$403$	−10.2060	+	3.31614i	−0.508398	+	0.165189i
$404$	2.56114	−	7.88237i	0.127421	−	0.392163i
$405$		0			0
$406$	3.13008			0.155343
$407$	−27.3246	+	4.08433i	−1.35443	+	0.202453i
$408$		−	0.0909950i		−	0.00450492i
$409$	−6.95565	−	5.05358i	−0.343935	−	0.249883i	0.402385	−	0.915470i	$-0.368181\pi$
$409$	−6.95565	−	5.05358i	−0.343935	−	0.249883i	−0.746320	+	0.665587i	$0.768181\pi$
$410$		0			0
$411$	2.38934	+	7.35364i	0.117858	+	0.362728i
$412$	−2.37557	−	3.26969i	−0.117036	−	0.161086i
$413$	3.44645	+	4.74363i	0.169589	+	0.233419i
$414$	0.539504	+	1.66042i	0.0265152	+	0.0816054i
$415$		0			0
$416$	−2.72195	−	1.97761i	−0.133455	−	0.0969604i
$417$		−	20.1865i		−	0.988536i
$418$	−0.0267261	−	0.0536011i	−0.00130721	−	0.00262172i
$419$	−31.3915			−1.53358			−0.766789	−	0.641899i	$-0.778147\pi$
$419$	−31.3915			−1.53358			−0.766789	+	0.641899i	$0.778147\pi$
$420$		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	$0.135592\pi$
$422$	−4.48580	+	1.45753i	−0.218366	+	0.0709513i
$423$	−0.533721	−	0.734604i	−0.0259504	−	0.0357177i
$424$	0.727915	−	0.528861i	0.0353507	−	0.0256838i
$425$		0			0
$426$	0.378171	−	1.16389i	0.0183225	−	0.0563908i
$427$	−18.8839	+	25.9915i	−0.913858	+	1.25782i
$428$			30.3983i			1.46936i
$429$	−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	$0.825149\pi$
$432$	−3.41595	−	1.10991i	−0.164350	−	0.0534005i
$433$	−15.0295	+	4.88338i	−0.722272	+	0.234680i	−0.647008	−	0.762483i	$-0.723980\pi$
$433$	−15.0295	+	4.88338i	−0.722272	+	0.234680i	−0.0752639	+	0.997164i	$0.523980\pi$
$434$	−6.49696	+	4.72032i	−0.311864	+	0.226583i
$435$		0			0
$436$	2.46625	+	7.59034i	0.118112	+	0.363511i
$437$	0.435628	+	0.141544i	0.0208389	+	0.00677098i
$438$	1.10420	−	1.51981i	0.0527609	−	0.0726192i
$439$	−21.5227			−1.02722			−0.513611	−	0.858023i	$-0.671693\pi$
$439$	−21.5227			−1.02722			−0.513611	+	0.858023i	$0.671693\pi$
$440$		0			0
$441$	3.19862			0.152315
$442$	0.0152328	−	0.0209662i	0.000724551	−	0.000997258i
$443$	9.67881	+	3.14484i	0.459854	+	0.149416i	0.529777	−	0.848137i	$-0.322275\pi$
$443$	9.67881	+	3.14484i	0.459854	+	0.149416i	−0.0699233	+	0.997552i	$0.522275\pi$
$444$	−4.97116	−	15.2997i	−0.235921	−	0.726090i
$445$		0			0
$446$	−2.91826	+	2.12024i	−0.138184	+	0.100396i
$447$	9.22071	−	2.99599i	0.436125	−	0.141706i
$448$	19.4233	+	6.31100i	0.917663	+	0.298167i
$449$	31.2352	+	22.6937i	1.47408	+	1.07098i	0.979406	+	0.201902i	$0.0647121\pi$
$449$	31.2352	+	22.6937i	1.47408	+	1.07098i	0.494673	+	0.869079i	$0.335288\pi$
$450$		0			0
$451$	−17.8646	+	34.3194i	−0.841209	+	1.61604i
$452$			26.5632i			1.24943i
$453$	8.91168	−	12.2659i	0.418707	−	0.576301i
$454$	0.0537303	−	0.165365i	0.00252169	−	0.00776096i
$455$		0			0
$456$	0.0574342	−	0.0417284i	0.00268960	−	0.00195411i
$457$	13.7329	+	18.9017i	0.642396	+	0.884183i	0.998741	−	0.0501720i	$-0.0159769\pi$
$457$	13.7329	+	18.9017i	0.642396	+	0.884183i	−0.356344	+	0.934355i	$0.615977\pi$
$458$	−1.86900	+	0.607275i	−0.0873326	+	0.0283761i
$459$	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	$0.463366\pi$
$462$	−1.98197	+	1.94776i	−0.0922094	+	0.0906181i
$463$			26.9648i			1.25316i	0.779357	+	0.626580i	$0.215546\pi$
$463$			26.9648i			1.25316i	−0.779357	+	0.626580i	$0.784454\pi$
$464$	10.8555	+	7.88699i	0.503954	+	0.366144i
$465$		0			0
$466$	−0.853329	−	2.62628i	−0.0395297	−	0.121660i
$467$	−13.9175	−	19.1558i	−0.644024	−	0.886423i	0.354798	−	0.934943i	$-0.384550\pi$
$467$	−13.9175	−	19.1558i	−0.644024	−	0.886423i	−0.998822	+	0.0485201i	$0.984550\pi$
$468$	−1.27088	−	1.74921i	−0.0587464	−	0.0808574i
$469$	9.41376	+	28.9726i	0.434687	+	1.33783i
$470$		0			0
$471$	12.0386	+	8.74655i	0.554709	+	0.403020i
$472$		−	1.89366i		−	0.0871627i
$473$	6.47035	−	38.6707i	0.297507	−	1.77808i
$474$	0.207616			0.00953613
$475$		0			0
$476$	−0.168140	+	0.517482i	−0.00770669	+	0.0237188i
$477$	0.829680	−	0.269579i	0.0379884	−	0.0123432i
$478$	2.63334	+	3.62449i	0.120446	+	0.165780i
$479$	−10.9412	+	7.94922i	−0.499915	+	0.363209i	−0.808984	−	0.587830i	$-0.799982\pi$
$479$	−10.9412	+	7.94922i	−0.499915	+	0.363209i	0.309070	+	0.951039i	$0.399982\pi$
$480$		0			0
$481$	2.88206	−	8.87008i	0.131411	−	0.404441i
$482$	−2.57659	+	3.54637i	−0.117361	+	0.161533i
$483$		−	21.2513i		−	0.966969i
$484$	−0.369771	+	21.2396i	−0.0168078	+	0.965437i
$485$		0			0
$486$	0.212253	+	0.154211i	0.00962801	+	0.00699516i
$487$	8.20480	+	2.66590i	0.371795	+	0.120803i	0.488954	−	0.872310i	$-0.337379\pi$
$487$	8.20480	+	2.66590i	0.371795	+	0.120803i	−0.117159	+	0.993113i	$0.537379\pi$
$488$	9.86798	−	3.20630i	0.446703	−	0.145142i
$489$	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	$-0.298740\pi$
$492$	−21.4257	−	6.96164i	−0.965947	−	0.313855i
$493$	−0.193733	+	0.266651i	−0.00872532	+	0.0120094i
$494$	0.0202189			0.000909690
$495$		0			0
$496$	−34.4263			−1.54579
$497$	−8.75585	+	12.0514i	−0.392754	+	0.540579i
$498$	−0.0616883	−	0.0200437i	−0.00276432	−	0.000898182i
$499$	8.66717	+	26.6748i	0.387996	+	1.19413i	0.934284	+	0.356531i	$0.116040\pi$
$499$	8.66717	+	26.6748i	0.387996	+	1.19413i	−0.546288	+	0.837597i	$0.683960\pi$
$500$		0			0
$501$	18.2970	−	13.2936i	0.817450	−	0.593913i
$502$	1.28194	−	0.416529i	0.0572160	−	0.0185906i
$503$	27.9610	+	9.08507i	1.24672	+	0.405083i	0.856744	−	0.515743i	$-0.172484\pi$
$503$	27.9610	+	9.08507i	1.24672	+	0.405083i	0.389974	+	0.920826i	$0.372484\pi$
$504$	−2.66469	−	1.93601i	−0.118695	−	0.0862368i
$505$		0			0
$506$	4.05864	+	4.12992i	0.180429	+	0.183597i
$507$			11.7465i			0.521680i
$508$	−8.96714	+	12.3422i	−0.397853	+	0.547597i
$509$	5.99195	−	18.4413i	0.265589	−	0.817398i	−0.725969	−	0.687728i	$-0.758608\pi$
$509$	5.99195	−	18.4413i	0.265589	−	0.817398i	0.991557	−	0.129670i	$-0.0413918\pi$
$510$		0			0
$511$	−18.4996	+	13.4407i	−0.818373	+	0.594583i
$512$	−10.6991	−	14.7261i	−0.472838	−	0.650806i
$513$	0.0654637	−	0.0212704i	0.00289029	−	0.000939113i
$514$	−0.299830	+	0.922782i	−0.0132249	+	0.0407022i
$515$		0			0
$516$	22.8298			1.00502
$517$	−2.67132	−	1.39052i	−0.117485	−	0.0611552i
$518$		−	6.97949i		−	0.306661i
$519$	−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	$0.715477\pi$
$522$	−0.576107	−	0.792943i	−0.0252155	−	0.0347062i
$523$	1.28585	+	1.76982i	0.0562262	+	0.0773887i	0.836204	−	0.548418i	$-0.184770\pi$
$523$	1.28585	+	1.76982i	0.0562262	+	0.0773887i	−0.779978	+	0.625807i	$0.784770\pi$
$524$	−9.75939	−	30.0363i	−0.426341	−	1.31214i
$525$		0			0
$526$	6.71389	+	4.87793i	0.292740	+	0.212688i
$527$		−	0.845637i		−	0.0368365i
$528$	−11.7816	+	1.76104i	−0.512727	+	0.0766395i
$529$	−21.2824			−0.925322
$530$		0			0
$531$	0.567369	−	1.74618i	0.0246217	−	0.0757778i
$532$	−0.403730	+	0.131180i	−0.0175039	+	0.00568737i
$533$	−7.67703	−	10.5665i	−0.332529	−	0.457687i
$534$	3.09439	−	2.24821i	0.133908	−	0.0972895i
$535$		0			0
$536$	3.04026	−	9.35697i	0.131319	−	0.404159i
$537$	8.92106	−	12.2788i	0.384972	−	0.529869i
$538$			3.87648i			0.167127i
$539$	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	$0.794141\pi$
$542$	−4.88731	−	1.58798i	−0.209928	−	0.0682097i
$543$	−1.34430	+	0.436789i	−0.0576894	+	0.0187444i
$544$	0.214493	−	0.155838i	0.00919632	−	0.00668152i
$545$		0			0
$546$	−0.289878	−	0.892153i	−0.0124056	−	0.0381806i
$547$	3.53110	+	1.14732i	0.150979	+	0.0490560i	0.383531	−	0.923528i	$-0.374708\pi$
$547$	3.53110	+	1.14732i	0.150979	+	0.0490560i	−0.232553	+	0.972584i	$0.574708\pi$
$548$	−8.77677	+	12.0802i	−0.374925	+	0.516040i
$549$	10.0601			0.429356
$550$		0			0
$551$	−0.257147			−0.0109548
$552$	−4.03416	+	5.55254i	−0.171705	+	0.236332i
$553$	−2.40348	−	0.780939i	−0.102207	−	0.0332089i
$554$	2.08443	+	6.41522i	0.0885590	+	0.272557i
$555$		0			0
$556$	31.5383	−	22.9139i	1.33752	−	0.971766i
$557$	6.25339	−	2.03185i	0.264964	−	0.0860922i	−0.173522	−	0.984830i	$-0.555515\pi$
$557$	6.25339	−	2.03185i	0.264964	−	0.0860922i	0.438486	+	0.898738i	$0.355515\pi$
$558$	2.39160	+	0.777078i	0.101244	+	0.0328963i
$559$	10.7079	+	7.77974i	0.452896	+	0.329048i
$560$		0			0
$561$	−0.0432577	−	0.289399i	−0.00182634	−	0.0122184i
$562$		−	7.00786i		−	0.295609i
$563$	−4.06087	+	5.58931i	−0.171145	+	0.235561i	−0.885970	−	0.463742i	$-0.846506\pi$
$563$	−4.06087	+	5.58931i	−0.171145	+	0.235561i	0.714825	+	0.699303i	$0.246506\pi$
$564$	0.541873	−	1.66771i	0.0228170	−	0.0702235i
$565$		0			0
$566$	1.53539	−	1.11552i	0.0645372	−	0.0468890i
$567$	−1.87711	−	2.58362i	−0.0788311	−	0.108502i
$568$	4.57545	−	1.48666i	0.191982	−	0.0623787i
$569$	2.08515	−	6.41743i	0.0874140	−	0.269033i	−0.897789	−	0.440427i	$-0.854827\pi$
$569$	2.08515	−	6.41743i	0.0874140	−	0.269033i	0.985203	+	0.171394i	$0.0548272\pi$
$570$		0			0
$571$	9.68928			0.405484			0.202742	−	0.979232i	$-0.435015\pi$
$571$	9.68928			0.405484			0.202742	+	0.979232i	$0.435015\pi$
$572$	−6.36086	−	3.31107i	−0.265961	−	0.138443i
$573$			4.90914i			0.205082i
$574$	−7.90742	−	5.74508i	−0.330049	−	0.239795i
$575$		0			0
$576$	−1.97619	−	6.08207i	−0.0823411	−	0.253420i
$577$	8.90484	+	12.2565i	0.370713	+	0.510243i	0.953095	−	0.302673i	$-0.0978789\pi$
$577$	8.90484	+	12.2565i	0.370713	+	0.510243i	−0.582381	+	0.812916i	$0.697879\pi$
$578$	−2.62039	−	3.60666i	−0.108994	−	0.150017i
$579$	−3.00361	−	9.24415i	−0.124826	−	0.384174i
$580$		0			0
$581$	0.638745	+	0.464076i	0.0264996	+	0.0192531i
$582$		−	1.07357i		−	0.0445009i
$583$	2.06364	−	2.02802i	0.0854671	−	0.0839921i
$584$	7.38503			0.305595
$585$		0			0
$586$	−1.18325	+	3.64166i	−0.0488795	+	0.150436i
$587$	−25.6892	+	8.34693i	−1.06031	+	0.344514i	−0.786705	−	0.617329i	$-0.788215\pi$
$587$	−25.6892	+	8.34693i	−1.06031	+	0.344514i	−0.273601	+	0.961843i	$0.588215\pi$
$588$	3.63079	+	4.99735i	0.149731	+	0.206087i
$589$	0.533749	−	0.387791i	0.0219927	−	0.0159787i
$590$		0			0
$591$	−2.74643	+	8.45265i	−0.112973	+	0.347696i
$592$	17.5865	−	24.2058i	0.722801	−	0.994850i
$593$		−	22.1863i		−	0.911084i	−0.890214	−	0.455542i	$-0.849446\pi$
$593$		−	22.1863i		−	0.911084i	0.890214	−	0.455542i	$-0.150554\pi$
$594$	0.858218	+	0.143596i	0.0352131	+	0.00589183i
$595$		0			0
$596$	15.1473	+	11.0052i	0.620458	+	0.450789i
$597$	−17.1552	−	5.57408i	−0.702118	−	0.228132i
$598$	−1.85902	+	0.604033i	−0.0760210	+	0.0247007i
$599$	9.50487	−	6.90569i	0.388359	−	0.282159i	−0.376424	−	0.926448i	$-0.622846\pi$
$599$	9.50487	−	6.90569i	0.388359	−	0.282159i	0.764783	+	0.644289i	$0.222846\pi$
$600$		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	$0.652645\pi$
$602$	9.42010	+	3.06077i	0.383934	+	0.124748i
$603$	5.60698	−	7.71734i	0.228334	−	0.314274i
$604$	29.2793			1.19136
$605$		0			0
$606$	−1.12597			−0.0457395
$607$	−8.01137	+	11.0267i	−0.325172	+	0.447560i	−0.940037	−	0.341071i	$-0.889210\pi$
$607$	−8.01137	+	11.0267i	−0.325172	+	0.447560i	0.614866	+	0.788632i	$0.289210\pi$
$608$	0.196724	+	0.0639196i	0.00797822	+	0.00259228i
$609$	3.68672	+	11.3466i	0.149393	+	0.459786i
$610$		0			0
$611$	0.822467	−	0.597557i	0.0332735	−	0.0241746i
$612$	0.162041	−	0.0526503i	0.00655012	−	0.00212826i
$613$	−6.49565	−	2.11057i	−0.262357	−	0.0852450i	0.174885	−	0.984589i	$-0.444045\pi$
$613$	−6.49565	−	2.11057i	−0.262357	−	0.0852450i	−0.437242	+	0.899344i	$0.644045\pi$
$614$	−6.05866	−	4.40187i	−0.244508	−	0.177645i
$615$		0			0
$616$	−10.7743	−	1.80275i	−0.434110	−	0.0726349i
$617$		−	30.3730i		−	1.22277i	−0.791333	−	0.611386i	$-0.790612\pi$
$617$		−	30.3730i		−	1.22277i	0.791333	−	0.611386i	$-0.209388\pi$
$618$	−0.322734	+	0.444205i	−0.0129823	+	0.0178685i
$619$	7.96890	−	24.5258i	0.320297	−	0.985773i	−0.653222	−	0.757167i	$-0.726583\pi$
$619$	7.96890	−	24.5258i	0.320297	−	0.985773i	0.973519	−	0.228607i	$-0.0734170\pi$
$620$		0			0
$621$	−5.38361	+	3.91142i	−0.216037	+	0.156960i
$622$	1.53410	+	2.11150i	0.0615117	+	0.0846635i
$623$	−44.2790	+	14.3871i	−1.77400	+	0.576408i
$624$	1.24266	−	3.82452i	0.0497463	−	0.153103i
$625$		0			0
$626$	4.31081			0.172295
$627$	0.162826	−	0.160016i	0.00650263	−	0.00639041i
$628$			28.7368i			1.14672i
$629$	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	$-0.269939\pi$
$632$	0.479735	+	0.660299i	0.0190828	+	0.0262653i
$633$	−10.5671	−	14.5444i	−0.420004	−	0.578086i
$634$	1.15210	+	3.54581i	0.0457559	+	0.140822i
$635$		0			0
$636$	1.36296	+	0.990246i	0.0540447	+	0.0392658i
$637$			3.58119i			0.141892i
$638$	−2.88347	−	1.50095i	−0.114157	−	0.0594233i
$639$	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	$0.125629\pi$
$642$	3.92766	−	1.27617i	0.155012	−	0.0503665i
$643$	−6.65950	−	9.16601i	−0.262625	−	0.361472i	0.657258	−	0.753666i	$-0.271716\pi$
$643$	−6.65950	−	9.16601i	−0.262625	−	0.361472i	−0.919883	+	0.392194i	$0.871716\pi$
$644$	33.2020	−	24.1226i	1.30834	−	0.950565i
$645$		0			0
$646$	−0.000492348		0.00151529i	−1.93712e−5		5.96184e-5i
$647$	21.6587	−	29.8107i	0.851492	−	1.17198i	−0.132040	−	0.991244i	$-0.542153\pi$
$647$	21.6587	−	29.8107i	0.851492	−	1.17198i	0.983532	−	0.180734i	$-0.0578472\pi$
$648$			1.03138i			0.0405164i
$649$	−0.900218	−	6.02256i	−0.0353366	−	0.236406i
$650$		0			0
$651$	−24.7636	−	17.9918i	−0.970561	−	0.705154i
$652$	6.24671	+	2.02968i	0.244640	+	0.0794883i
$653$	−14.5291	+	4.72079i	−0.568568	+	0.184739i	−0.579173	−	0.815205i	$-0.696624\pi$
$653$	−14.5291	+	4.72079i	−0.568568	+	0.184739i	0.0106050	+	0.999944i	$0.496624\pi$
$654$	0.877182	−	0.637310i	0.0343005	−	0.0249208i
$655$		0			0
$656$	−12.9478	−	39.8493i	−0.505528	−	1.55585i
$657$	6.80989	+	2.21267i	0.265679	+	0.0863243i
$658$	0.447180	−	0.615490i	0.0174329	−	0.0239943i
$659$	−11.8996			−0.463544			−0.231772	−	0.972770i	$-0.574452\pi$
$659$	−11.8996			−0.463544			−0.231772	+	0.972770i	$0.574452\pi$
$660$		0			0
$661$	−44.8648			−1.74504			−0.872520	−	0.488578i	$-0.837516\pi$
$661$	−44.8648			−1.74504			−0.872520	+	0.488578i	$0.837516\pi$
$662$	−1.68274	+	2.31609i	−0.0654015	+	0.0900174i
$663$	0.0939443	+	0.0305244i	0.00364849	+	0.00118547i
$664$	−0.0787953	−	0.242507i	−0.00305785	−	0.00941110i
$665$		0			0
$666$	−1.76812	+	1.28461i	−0.0685131	+	0.0497777i
$667$	23.6434	−	7.68219i	0.915474	−	0.297456i
$668$	41.5383	+	13.4966i	1.60717	+	0.522200i
$669$	−11.1231	−	8.08142i	−0.430045	−	0.312446i
$670$		0			0
$671$	29.8597	−	14.8884i	1.15272	−	0.574759i
$672$		−	9.59683i		−	0.370206i
$673$	−11.2306	+	15.4576i	−0.432909	+	0.595848i	−0.968618	−	0.248555i	$-0.920044\pi$
$673$	−11.2306	+	15.4576i	−0.432909	+	0.595848i	0.535709	+	0.844403i	$0.320044\pi$
$674$	−0.477207	+	1.46869i	−0.0183813	+	0.0565719i
$675$		0			0
$676$	−18.3521	+	13.3336i	−0.705849	+	0.512830i
$677$	27.3093	+	37.5881i	1.04958	+	1.44463i	0.889170	+	0.457578i	$0.151283\pi$
$677$	27.3093	+	37.5881i	1.04958	+	1.44463i	0.160414	+	0.987050i	$0.448717\pi$
$678$	3.43213	−	1.11517i	0.131810	−	0.0428278i
$679$	−4.03819	+	12.4283i	−0.154971	+	0.476953i
$680$		0			0
$681$	0.662735			0.0253961
$682$	8.24860	−	1.23295i	0.315855	−	0.0472122i
$683$		−	42.5651i		−	1.62871i	−0.580367	−	0.814355i	$-0.697091\pi$
$683$		−	42.5651i		−	1.62871i	0.580367	−	0.814355i	$-0.302909\pi$
$684$	0.107540	+	0.0781327i	0.00411191	+	0.00298748i
$685$		0			0
$686$	−0.984219	−	3.02912i	−0.0375777	−	0.115652i
$687$	−4.40275	−	6.05987i	−0.167976	−	0.231198i
$688$	24.9577	+	34.3514i	0.951505	+	1.30963i
$689$	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	$0.932979\pi$
$692$		−	25.2815i		−	0.961057i
$693$	−9.39509	−	4.89050i	−0.356890	−	0.185775i
$694$	9.05253			0.343629
$695$		0			0
$696$	1.19066	−	3.66448i	0.0451319	−	0.138902i
$697$	0.978846	−	0.318046i	0.0370764	−	0.0120469i
$698$	−0.850252	−	1.17027i	−0.0321825	−	0.0442954i
$699$	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	$0.903358\pi$
$702$	−0.172656	+	0.237640i	−0.00651647	+	0.00896916i
$703$			0.573390i			0.0216258i
$704$	−14.8667	−	15.1277i	−0.560309	−	0.570148i
$705$		0			0
$706$	−6.34086	−	4.60690i	−0.238641	−	0.173383i
$707$	13.0349	+	4.23530i	0.490228	+	0.159285i
$708$	3.37217	−	1.09568i	0.126734	−	0.0411783i
$709$	12.2100	−	8.87107i	0.458555	−	0.333160i	−0.334409	−	0.942428i	$-0.608537\pi$
$709$	12.2100	−	8.87107i	0.458555	−	0.333160i	0.792964	+	0.609268i	$0.208537\pi$
$710$		0			0
$711$	0.244538	+	0.752611i	0.00917090	+	0.0282251i
$712$	14.3003	+	4.64646i	0.535927	+	0.174133i
$713$	−37.4903	+	51.6010i	−1.40402	+	1.93247i
$714$	0.0739208			0.00276642
$715$		0			0
$716$	29.3101			1.09537
$717$	−10.0371	+	13.8149i	−0.374844	+	0.515929i
$718$	8.96099	+	2.91160i	0.334421	+	0.108660i
$719$	1.91288	+	5.88723i	0.0713383	+	0.219557i	0.980369	−	0.197173i	$-0.0631761\pi$
$719$	1.91288	+	5.88723i	0.0713383	+	0.219557i	−0.909030	+	0.416730i	$0.863176\pi$
$720$		0			0
$721$	5.40701	−	3.92842i	0.201367	−	0.146302i
$722$	4.73968	−	1.54001i	0.176393	−	0.0573134i
$723$	−15.8904	−	5.16312i	−0.590972	−	0.192018i
$724$	−2.20835	−	1.60446i	−0.0820725	−	0.0596292i
$725$		0			0
$726$	2.75982	−	0.843898i	0.102426	−	0.0313200i
$727$			18.1515i			0.673200i	0.941648	+	0.336600i	$0.109277\pi$
$727$			18.1515i			0.673200i	−0.941648	+	0.336600i	$0.890723\pi$
$728$	2.16757	−	2.98341i	0.0803355	−	0.110572i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$		0			0
$731$	−0.843796	+	0.613054i	−0.0312089	+	0.0226746i
$732$	11.4194	+	15.7174i	0.422072	+	0.580932i
$733$	27.3342	−	8.88142i	1.00961	−	0.328043i	0.242912	−	0.970048i	$-0.421897\pi$
$733$	27.3342	−	8.88142i	1.00961	−	0.328043i	0.766700	+	0.642005i	$0.221897\pi$
$734$	−0.732165	+	2.25337i	−0.0270247	+	0.0831735i
$735$		0			0
$736$	−19.9974			−0.737113
$737$	5.22103	−	31.2040i	0.192319	−	1.14942i
$738$			3.06060i			0.112662i
$739$	−37.8896	−	27.5284i	−1.39379	−	1.01265i	−0.995437	−	0.0954172i	$-0.969581\pi$
$739$	−37.8896	−	27.5284i	−1.39379	−	1.01265i	−0.398354	−	0.917232i	$-0.630419\pi$
$740$		0			0
$741$	0.0238145	+	0.0732936i	0.000874848	+	0.00269251i
$742$	0.429626	+	0.591330i	0.0157721	+	0.0217084i
$743$	−15.6414	−	21.5286i	−0.573828	−	0.789806i	0.419174	−	0.907906i	$-0.362320\pi$
$743$	−15.6414	−	21.5286i	−0.573828	−	0.789806i	−0.993002	+	0.118100i	$0.962320\pi$
$744$	3.05482	+	9.40178i	0.111995	+	0.344686i
$745$		0			0
$746$	3.65064	+	2.65235i	0.133659	+	0.0971093i
$747$		−	0.247229i		−	0.00904564i
$748$	0.403039	−	0.396084i	0.0147366	−	0.0144823i
$749$	−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	$-0.165379\pi$
$752$	3.10175	−	1.00782i	0.113109	−	0.0367514i
$753$	3.01984	+	4.15646i	0.110049	+	0.151470i
$754$	0.887784	−	0.645013i	0.0323312	−	0.0234900i
$755$		0			0
$756$	1.90578	−	5.86539i	0.0693126	−	0.213322i
$757$	−19.2311	+	26.4693i	−0.698966	+	0.962045i	0.300998	+	0.953625i	$0.402680\pi$
$757$	−19.2311	+	26.4693i	−0.698966	+	0.962045i	−0.999965	+	0.00841989i	$0.997320\pi$
$758$			2.09942i			0.0762545i
$759$	−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	$0.684824\pi$
$762$	1.97115	+	0.640464i	0.0714071	+	0.0232016i
$763$	−12.5520	+	4.07838i	−0.454412	+	0.147647i
$764$	−7.66978	+	5.57242i	−0.277483	+	0.201603i
$765$		0			0
$766$	−2.40895	−	7.41399i	−0.0870389	−	0.267878i
$767$	1.95503	+	0.635229i	0.0705922	+	0.0229368i
$768$	6.33228	−	8.71564i	0.228497	−	0.314499i
$769$	−3.23559			−0.116678			−0.0583392	−	0.998297i	$-0.518581\pi$
$769$	−3.23559			−0.116678			−0.0583392	+	0.998297i	$0.518581\pi$
$770$		0			0
$771$	−3.69824			−0.133189
$772$	11.0331	−	15.1858i	0.397092	−	0.546550i
$773$	41.5008	+	13.4844i	1.49268	+	0.485001i	0.937873	−	0.346979i	$-0.112792\pi$
$773$	41.5008	+	13.4844i	1.49268	+	0.485001i	0.554806	+	0.831980i	$0.312792\pi$
$774$	−0.958431	−	2.94975i	−0.0344501	−	0.106026i
$775$		0			0
$776$	3.41436	−	2.48068i	0.122569	−	0.0890512i
$777$	25.3007	−	8.22070i	0.907658	−	0.294916i
$778$	0.148563	+	0.0482710i	0.00532623	+	0.00173060i
$779$	0.649623	+	0.471979i	0.0232752	+	0.0169104i
$780$		0			0
$781$	13.8450	−	6.90324i	0.495412	−	0.247017i
$782$		−	0.154032i		−	0.00550818i
$783$	2.19587	−	3.02235i	0.0784739	−	0.108010i
$784$	−3.55017	+	10.9263i	−0.126792	+	0.390225i
$785$		0			0
$786$	−3.47116	+	2.52195i	−0.123812	+	0.0899549i
$787$	−2.68277	−	3.69251i	−0.0956304	−	0.131624i	0.758521	−	0.651649i	$-0.225923\pi$
$787$	−2.68277	−	3.69251i	−0.0956304	−	0.131624i	−0.854151	+	0.520025i	$0.825923\pi$
$788$	−16.3235	+	5.30382i	−0.581500	+	0.188941i
$789$	−9.77467	+	30.0833i	−0.347987	+	1.07100i
$790$		0			0
$791$	−43.9270			−1.56186
$792$	1.52638	+	3.06127i	0.0542375	+	0.108777i
$793$			11.2634i			0.399974i
$794$	−0.354357	−	0.257455i	−0.0125757	−	0.00913675i
$795$		0			0
$796$	−10.7645	−	33.1297i	−0.381537	−	1.17425i
$797$	−6.57177	−	9.04526i	−0.232784	−	0.320400i	0.676605	−	0.736346i	$-0.263450\pi$
$797$	−6.57177	−	9.04526i	−0.232784	−	0.320400i	−0.909389	+	0.415946i	$0.863450\pi$
$798$	0.0338985	+	0.0466573i	0.00119999	+	0.00165165i
$799$	0.0247558	+	0.0761905i	0.000875797	+	0.00269543i
$800$		0			0
$801$	11.7945	+	8.56919i	0.416737	+	0.302777i
$802$		−	2.98277i		−	0.105325i
$803$	23.4872	−	3.51074i	0.828846	−	0.123891i
$804$	18.4217			0.649684
$805$		0			0
$806$	−0.870021	+	2.67765i	−0.0306452	+	0.0943162i
$807$	−14.0523	+	4.56586i	−0.494664	+	0.160726i
$808$	−2.60176	−	3.58102i	−0.0915298	−	0.125980i
$809$	−36.8440	+	26.7687i	−1.29537	+	0.941139i	−0.999899	−	0.0142137i	$-0.995475\pi$
$809$	−36.8440	+	26.7687i	−1.29537	+	0.941139i	−0.295468	+	0.955353i	$0.595475\pi$
$810$		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	$0.0842131\pi$
$812$	−13.5424	+	18.6395i	−0.475246	+	0.654120i
$813$		−	19.5869i		−	0.686943i
$814$	−3.34685	+	6.42959i	−0.117307	+	0.225357i
$815$		0			0
$816$	0.256367	+	0.186261i	0.00897463	+	0.00652045i
$817$	−0.773895	−	0.251454i	−0.0270751	−	0.00879725i
$818$	−2.14528	+	0.697043i	−0.0750079	+	0.0243715i
$819$	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	$-0.233961\pi$
$822$	1.92930	+	0.626867i	0.0672920	+	0.0218645i
$823$	27.0996	−	37.2994i	0.944633	−	1.30018i	−0.00923747	−	0.999957i	$-0.502940\pi$
$823$	27.0996	−	37.2994i	0.944633	−	1.30018i	0.953870	−	0.300218i	$-0.0970596\pi$
$824$	−2.15848			−0.0751941
$825$		0			0
$826$	1.53833			0.0535255
$827$	25.5390	−	35.1515i	0.888079	−	1.22234i	−0.0860379	−	0.996292i	$-0.527421\pi$
$827$	25.5390	−	35.1515i	0.888079	−	1.22234i	0.974117	−	0.226044i	$-0.0725794\pi$
$828$	−12.2220	−	3.97116i	−0.424743	−	0.138007i
$829$	−4.78085	−	14.7139i	−0.166046	−	0.511036i	0.833066	−	0.553173i	$-0.186583\pi$
$829$	−4.78085	−	14.7139i	−0.166046	−	0.511036i	−0.999112	+	0.0421372i	$0.986583\pi$
$830$		0			0
$831$	−20.8001	+	15.1122i	−0.721548	+	0.524235i
$832$	6.80953	−	2.21255i	0.236078	−	0.0767064i
$833$	−0.268390	−	0.0872053i	−0.00929918	−	0.00302149i
$834$	−4.28465	−	3.11298i	−0.148365	−	0.107794i
$835$		0			0
$836$	0.434825	+	0.0727546i	0.0150387	+	0.00251627i
$837$			9.58484i			0.331301i
$838$	−4.84093	+	6.66296i	−0.167227	+	0.230168i
$839$	−9.33790	+	28.7391i	−0.322380	+	0.992184i	0.650229	+	0.759738i	$0.274673\pi$
$839$	−9.33790	+	28.7391i	−0.322380	+	0.992184i	−0.972609	+	0.232446i	$0.925327\pi$
$840$		0			0
$841$	12.1705	−	8.84239i	0.419673	−	0.304910i
$842$	0.706122	+	0.971894i	0.0243346	+	0.0334937i
$843$	25.4036	−	8.25411i	0.874945	−	0.284287i
$844$	10.7285	−	33.0189i	0.369290	−	1.13656i
$845$		0			0
$846$	−0.238228			−0.00819045
$847$	−35.1235	−	0.611482i	−1.20686	−	0.0210108i
$848$			3.13335i			0.107600i
$849$	5.85223	+	4.25189i	0.200848	+	0.145925i
$850$		0			0
$851$	−17.1299	−	52.7203i	−0.587204	−	1.80723i
$852$	5.29478	+	7.28764i	0.181396	+	0.249670i
$853$	1.18091	+	1.62538i	0.0404336	+	0.0556521i	0.828755	−	0.559611i	$-0.189050\pi$
$853$	1.18091	+	1.62538i	0.0404336	+	0.0556521i	−0.788322	+	0.615263i	$0.789050\pi$
$854$	2.60467	+	8.01636i	0.0891301	+	0.274314i
$855$		0			0
$856$	13.1343	+	9.54262i	0.448921	+	0.326160i
$857$			33.6095i			1.14808i	0.818828	+	0.574039i	$0.194624\pi$
$857$			33.6095i			1.14808i	−0.818828	+	0.574039i	$0.805376\pi$
$858$	−0.160771	+	0.960867i	−0.00548865	+	0.0328034i
$859$	13.7301			0.468466			0.234233	−	0.972180i	$-0.424742\pi$
$859$	13.7301			0.468466			0.234233	+	0.972180i	$0.424742\pi$
$860$		0			0
$861$	11.5123	−	35.4312i	0.392338	−	1.20749i
$862$	−3.96920	+	1.28967i	−0.135192	+	0.0439264i
$863$	−5.14799	−	7.08560i	−0.175240	−	0.241197i	0.712358	−	0.701816i	$-0.247627\pi$
$863$	−5.14799	−	7.08560i	−0.175240	−	0.241197i	−0.887598	+	0.460620i	$0.847627\pi$
$864$	−2.43117	+	1.76635i	−0.0827100	+	0.0600923i
$865$		0			0
$866$	−1.28120	+	3.94314i	−0.0435370	+	0.133993i
$867$	9.98777	−	13.7470i	0.339203	−	0.466872i
$868$		−	59.1120i		−	2.00639i
$869$	1.83964	+	1.87194i	0.0624055	+	0.0635014i
$870$		0			0
$871$	8.64038	+	6.27761i	0.292768	+	0.212709i
$872$	4.05378	+	1.31715i	0.137278	+	0.0446044i
$873$	3.89170	−	1.26449i	0.131714	−	0.0427965i
$874$	0.0972220	−	0.0706359i	0.00328858	−	0.00238930i
$875$		0			0
$876$	4.27303	+	13.1510i	0.144372	+	0.444332i
$877$	14.5001	+	4.71136i	0.489633	+	0.159091i	0.543420	−	0.839461i	$-0.317129\pi$
$877$	14.5001	+	4.71136i	0.489633	+	0.159091i	−0.0537871	+	0.998552i	$0.517129\pi$
$878$	−3.31904	+	4.56827i	−0.112012	+	0.154172i
$879$	−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	$0.586025\pi$
$882$	0.493262	−	0.678917i	0.0166090	−	0.0228603i
$883$	−31.3474	−	10.1854i	−1.05492	−	0.342765i	−0.270324	−	0.962769i	$-0.587131\pi$
$883$	−31.3474	−	10.1854i	−1.05492	−	0.342765i	−0.784598	+	0.620004i	$0.787131\pi$
$884$	0.0589476	+	0.181422i	0.00198262	+	0.00610189i
$885$		0			0
$886$	2.16008	−	1.56939i	0.0725694	−	0.0527247i
$887$	10.7017	−	3.47720i	0.359328	−	0.116753i	−0.123789	−	0.992309i	$-0.539505\pi$
$887$	10.7017	−	3.47720i	0.359328	−	0.116753i	0.483117	+	0.875556i	$0.339505\pi$
$888$	−8.17111	−	2.65495i	−0.274204	−	0.0890944i
$889$	−20.4100	−	14.8288i	−0.684530	−	0.497340i
$890$		0			0
$891$	0.490303	+	3.28018i	0.0164258	+	0.109890i
$892$		−	26.5515i		−	0.889010i
$893$	−0.0367374	+	0.0505647i	−0.00122937	+	0.00169208i
$894$	0.786027	−	2.41914i	0.0262887	−	0.0809083i
$895$		0			0
$896$	19.8628	−	14.4312i	0.663570	−	0.482112i
$897$	−4.37925	−	6.02752i	−0.146219	−	0.201253i
$898$	9.63362	−	3.13015i	0.321478	−	0.104455i
$899$	11.0651	−	34.0548i	0.369041	−	1.13579i
$900$		0			0
$901$	−0.0769667			−0.00256413
$902$	4.52950	+	9.08425i	0.150816	+	0.302472i
$903$			37.7530i			1.25634i
$904$	11.4772	+	8.33870i	0.381727	+	0.277341i
$905$		0			0
$906$	−1.22919	−	3.78307i	−0.0408372	−	0.125684i
$907$	−14.9147	−	20.5284i	−0.495236	−	0.681634i	0.486107	−	0.873899i	$-0.338417\pi$
$907$	−14.9147	−	20.5284i	−0.495236	−	0.681634i	−0.981343	+	0.192266i	$0.938417\pi$
$908$	0.752278	+	1.03542i	0.0249652	+	0.0343617i
$909$	−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	$0.606890\pi$
$912$			0.247229i			0.00818657i
$913$	−0.365884	−	0.733807i	−0.0121090	−	0.0242855i
$914$	6.12971			0.202753
$915$		0			0
$916$	4.47000	−	13.7573i	0.147693	−	0.454553i
$917$	49.6704	−	16.1389i	1.64026	−	0.532953i
$918$	−0.0136055	−	0.0187264i	−0.000449048	−	0.000618062i
$919$	−26.6133	+	19.3357i	−0.877890	+	0.637825i	−0.932692	−	0.360673i	$-0.882547\pi$
$919$	−26.6133	+	19.3357i	−0.877890	+	0.637825i	0.0548022	+	0.998497i	$0.482547\pi$
$920$		0			0
$921$	8.82072	−	27.1474i	0.290653	−	0.894537i
$922$	0.760446	−	1.04666i	0.0250440	−	0.0344701i
$923$			5.22245i			0.171899i
$924$	−3.02381	−	20.2297i	−0.0994762	−	0.665507i
$925$		0			0
$926$	5.72337	+	4.15827i	0.188082	+	0.136649i
$927$	−1.99038	−	0.646712i	−0.0653725	−	0.0212408i
$928$	10.6770	−	3.46918i	0.350491	−	0.113881i
$929$	26.9509	−	19.5810i	0.884230	−	0.642431i	−0.0501368	−	0.998742i	$-0.515966\pi$
$929$	26.9509	−	19.5810i	0.884230	−	0.642431i	0.934367	+	0.356311i	$0.115966\pi$
$930$		0			0
$931$	−0.0680360	−	0.209393i	−0.00222979	−	0.00686258i
$932$	19.3314	+	6.28115i	0.633221	+	0.205746i
$933$	−5.84730	+	8.04812i	−0.191432	+	0.263484i
$934$	−6.21211			−0.203266
$935$		0			0
$936$	−1.15474			−0.0377438
$937$	14.0267	−	19.3061i	0.458233	−	0.630704i	−0.515908	−	0.856644i	$-0.672545\pi$
$937$	14.0267	−	19.3061i	0.458233	−	0.630704i	0.974141	+	0.225940i	$0.0725453\pi$
$938$	7.60123	+	2.46979i	0.248189	+	0.0806415i
$939$	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	$0.258765\pi$
$942$	3.71297	−	1.20642i	0.120975	−	0.0393072i
$943$	−73.8297	−	23.9887i	−2.40423	−	0.781181i
$944$	5.33514	+	3.87620i	0.173644	+	0.126160i
$945$		0			0
$946$	−7.21019	−	7.33681i	−0.234423	−	0.238540i
$947$			2.15429i			0.0700050i	0.999387	+	0.0350025i	$0.0111439\pi$
$947$			2.15429i			0.0700050i	−0.999387	+	0.0350025i	$0.988856\pi$
$948$	−0.898262	+	1.23635i	−0.0291742	+	0.0401548i
$949$	−2.47731	+	7.62439i	−0.0804170	+	0.247498i
$950$		0			0
$951$	−11.4966	+	8.35278i	−0.372803	+	0.270858i
$952$	0.170807	+	0.235096i	0.00553590	+	0.00761951i
$953$	5.69971	−	1.85195i	0.184632	−	0.0599904i	−0.215242	−	0.976561i	$-0.569054\pi$
$953$	5.69971	−	1.85195i	0.184632	−	0.0599904i	0.399874	+	0.916570i	$0.369054\pi$
$954$	0.0707268	−	0.217675i	0.00228986	−	0.00704748i
$955$		0			0
$956$	−32.9770			−1.06655
$957$	2.04472	−	12.2205i	0.0660964	−	0.395032i
$958$			3.54816i			0.114636i
$959$	−19.9767	−	14.5139i	−0.645082	−	0.468680i
$960$		0			0
$961$	18.8096	+	57.8901i	0.606762	+	1.86742i
$962$	−1.43826	−	1.97959i	−0.0463713	−	0.0638246i
$963$	9.25228	+	12.7347i	0.298151	+	0.410369i
$964$	−9.97085	−	30.6871i	−0.321139	−	0.988365i
$965$		0			0
$966$	−4.51067	−	3.27719i	−0.145128	−	0.105442i
$967$		−	22.2784i		−	0.716424i	−0.933640	−	0.358212i	$-0.883387\pi$
$967$		−	22.2784i		−	0.716424i	0.933640	−	0.358212i	$-0.116613\pi$
$968$	9.06097	+	6.82729i	0.291231	+	0.219437i
$969$	−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	$0.899626\pi$
$972$	−1.83665	+	0.596764i	−0.0589106	+	0.0191412i
$973$	37.8922	+	52.1541i	1.21477	+	1.67198i
$974$	1.83112	−	1.33039i	0.0586728	−	0.0426283i
$975$		0			0
$976$	−11.1658	+	34.3649i	−0.357409	+	1.09999i
$977$	−16.4018	+	22.5751i	−0.524739	+	0.722242i	−0.986317	−	0.164858i	$-0.947283\pi$
$977$	−16.4018	+	22.5751i	−0.524739	+	0.722242i	0.461578	+	0.887100i	$0.347283\pi$
$978$		−	0.892323i		−	0.0285333i
$979$	47.6894	+	7.97935i	1.52416	+	0.255021i
$980$		0			0
$981$	3.34343	+	2.42915i	0.106748	+	0.0775567i
$982$	−6.46424	−	2.10036i	−0.206282	−	0.0670252i
$983$	−9.31294	+	3.02596i	−0.297037	+	0.0965130i	−0.453744	−	0.891132i	$-0.649912\pi$
$983$	−9.31294	+	3.02596i	−0.297037	+	0.0965130i	0.156708	+	0.987645i	$0.449912\pi$
$984$	−9.73387	+	7.07207i	−0.310305	+	0.225449i
$985$		0			0
$986$	0.0267218	+	0.0822412i	0.000850995	+	0.00261909i
$987$	2.75786	+	0.896084i	0.0877837	+	0.0285227i
$988$	−0.0874779	+	0.120403i	−0.00278304	+	0.00383053i
$989$	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	$0.312497\pi$
$992$	−16.9302	+	23.3024i	−0.537533	+	0.739851i
$993$	−10.3778	−	3.37196i	−0.329331	−	0.107006i
$994$	1.20770	+	3.71692i	0.0383059	+	0.117894i
$995$		0			0
$996$	0.386258	−	0.280633i	0.0122390	−	0.00889218i
$997$	−12.1501	+	3.94779i	−0.384796	+	0.125028i	−0.495026	−	0.868878i	$-0.664841\pi$
$997$	−12.1501	+	3.94779i	−0.384796	+	0.125028i	0.110230	+	0.993906i	$0.464841\pi$
$998$	6.99839	+	2.27392i	0.221530	+	0.0719795i
$999$	−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.bx.f.499.3		16
5.2	odd	4		165.2.m.d.136.1	yes	8
5.3	odd	4		825.2.n.g.301.2		8
5.4	even	2	inner	825.2.bx.f.499.2		16
11.3	even	5	inner	825.2.bx.f.124.2		16
15.2	even	4		495.2.n.a.136.2		8
55.3	odd	20		825.2.n.g.751.2		8
55.14	even	10	inner	825.2.bx.f.124.3		16
55.17	even	20		1815.2.a.w.1.2		4
55.27	odd	20		1815.2.a.p.1.3		4
55.28	even	20		9075.2.a.cm.1.3		4
55.38	odd	20		9075.2.a.di.1.2		4
55.47	odd	20		165.2.m.d.91.1	✓	8
165.17	odd	20		5445.2.a.bf.1.3		4
165.47	even	20		495.2.n.a.91.2		8
165.137	even	20		5445.2.a.bt.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.d.91.1	✓	8	55.47	odd	20
165.2.m.d.136.1	yes	8	5.2	odd	4
495.2.n.a.91.2		8	165.47	even	20
495.2.n.a.136.2		8	15.2	even	4
825.2.n.g.301.2		8	5.3	odd	4
825.2.n.g.751.2		8	55.3	odd	20
825.2.bx.f.124.2		16	11.3	even	5	inner
825.2.bx.f.124.3		16	55.14	even	10	inner
825.2.bx.f.499.2		16	5.4	even	2	inner
825.2.bx.f.499.3		16	1.1	even	1	trivial
1815.2.a.p.1.3		4	55.27	odd	20
1815.2.a.w.1.2		4	55.17	even	20
5445.2.a.bf.1.3		4	165.17	odd	20
5445.2.a.bt.1.2		4	165.137	even	20
9075.2.a.cm.1.3		4	55.28	even	20
9075.2.a.di.1.2		4	55.38	odd	20

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.bx (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.154211 - 0.212253i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.596764 + 1.83665i) q^{4} +(0.212253 - 0.154211i) q^{6} +(-3.03722 + 0.986854i) q^{7} +(0.980901 + 0.318714i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.154211 - 0.212253i) q^{2} +(0.951057 + 0.309017i) q^{3} +(0.596764 + 1.83665i) q^{4} +(0.212253 - 0.154211i) q^{6} +(-3.03722 + 0.986854i) q^{7} +(0.980901 + 0.318714i) q^{8} +(0.809017 + 0.587785i) q^{9} +(3.27115 + 0.547326i) q^{11} +1.93117i q^{12} +(-0.658088 + 0.905781i) q^{13} +(-0.258911 + 0.796845i) q^{14} +(-2.90578 + 2.11117i) q^{16} +(-0.0518582 - 0.0713767i) q^{17} +(0.249519 - 0.0810736i) q^{18} +(0.0212704 - 0.0654637i) q^{19} -3.19353 q^{21} +(0.620620 - 0.609909i) q^{22} +6.65450i q^{23} +(0.834404 + 0.606230i) q^{24} +(0.0907705 + 0.279363i) q^{26} +(0.587785 + 0.809017i) q^{27} +(-3.62501 - 4.98940i) q^{28} +(-1.15444 - 3.55299i) q^{29} +(7.75430 + 5.63383i) q^{31} +3.00509i q^{32} +(2.94192 + 1.53138i) q^{33} -0.0231471 q^{34} +(-0.596764 + 1.83665i) q^{36} +(-7.92250 + 2.57418i) q^{37} +(-0.0106148 - 0.0146100i) q^{38} +(-0.905781 + 0.658088i) q^{39} +(-3.60489 + 11.0947i) q^{41} +(-0.492478 + 0.677837i) q^{42} -11.8217i q^{43} +(0.946857 + 6.33458i) q^{44} +(1.41244 + 1.02620i) q^{46} +(-0.863579 - 0.280594i) q^{47} +(-3.41595 + 1.10991i) q^{48} +(2.58773 - 1.88010i) q^{49} +(-0.0272635 - 0.0839083i) q^{51} +(-2.05632 - 0.668140i) q^{52} +(0.512771 - 0.705768i) q^{53} +0.262360 q^{54} -3.29374 q^{56} +(0.0404588 - 0.0556868i) q^{57} +(-0.932160 - 0.302877i) q^{58} +(-0.567369 - 1.74618i) q^{59} +(8.13881 - 5.91319i) q^{61} +(2.39160 - 0.777078i) q^{62} +(-3.03722 - 0.986854i) q^{63} +(-5.17372 - 3.75893i) q^{64} +(0.778717 - 0.388276i) q^{66} -9.53916i q^{67} +(0.100147 - 0.137840i) q^{68} +(-2.05635 + 6.32881i) q^{69} +(3.77370 - 2.74175i) q^{71} +(0.606230 + 0.834404i) q^{72} +(6.80989 - 2.21267i) q^{73} +(-0.675360 + 2.07854i) q^{74} +0.132927 q^{76} +(-10.4754 + 1.56580i) q^{77} +0.293740i q^{78} +(0.640209 + 0.465139i) q^{79} +(0.309017 + 0.951057i) q^{81} +(1.79898 + 2.47608i) q^{82} +(-0.145318 - 0.200012i) q^{83} +(-1.90578 - 5.86539i) q^{84} +(-2.50920 - 1.82304i) q^{86} -3.73583i q^{87} +(3.03423 + 1.57943i) q^{88} +14.5788 q^{89} +(1.10489 - 3.40050i) q^{91} +(-12.2220 + 3.97116i) q^{92} +(5.63383 + 7.75430i) q^{93} +(-0.192730 + 0.140027i) q^{94} +(-0.928623 + 2.85801i) q^{96} +(2.40521 - 3.31048i) q^{97} -0.839188i q^{98} +(2.32471 + 2.36553i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4} + 8 q^{6} + 4 q^{9}+O(q^{10}) \) 16 * q - 4 * q^4 + 8 * q^6 + 4 * q^9	\( 16 q - 4 q^{4} + 8 q^{6} + 4 q^{9} + 6 q^{11} + 8 q^{14} - 24 q^{16} - 4 q^{19} - 24 q^{21} - 8 q^{24} + 4 q^{26} - 20 q^{29} + 38 q^{31} + 12 q^{34} + 4 q^{36} + 8 q^{39} - 18 q^{41} - 34 q^{44} - 44 q^{46} - 2 q^{49} + 20 q^{51} + 12 q^{54} - 32 q^{56} - 26 q^{59} + 26 q^{61} - 78 q^{64} - 22 q^{66} - 18 q^{69} - 22 q^{71} + 86 q^{74} - 76 q^{76} + 44 q^{79} - 4 q^{81} - 8 q^{84} + 40 q^{86} + 40 q^{89} - 22 q^{91} + 70 q^{94} - 16 q^{96} + 14 q^{99}+O(q^{100}) \) 16 * q - 4 * q^4 + 8 * q^6 + 4 * q^9 + 6 * q^11 + 8 * q^14 - 24 * q^16 - 4 * q^19 - 24 * q^21 - 8 * q^24 + 4 * q^26 - 20 * q^29 + 38 * q^31 + 12 * q^34 + 4 * q^36 + 8 * q^39 - 18 * q^41 - 34 * q^44 - 44 * q^46 - 2 * q^49 + 20 * q^51 + 12 * q^54 - 32 * q^56 - 26 * q^59 + 26 * q^61 - 78 * q^64 - 22 * q^66 - 18 * q^69 - 22 * q^71 + 86 * q^74 - 76 * q^76 + 44 * q^79 - 4 * q^81 - 8 * q^84 + 40 * q^86 + 40 * q^89 - 22 * q^91 + 70 * q^94 - 16 * q^96 + 14 * q^99

Introduction

L-functions

Modular forms

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Database

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