LMFDB - Embedded newform 675.2.u.b.499.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [675,2,Mod(49,675)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(675, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([14, 9]))

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

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

chi := DirichletCharacter("675.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 675 = 3^{3} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	675.u (of order $18$, degree $6$, 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:	$5.38990213644$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{18})$
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			499.2
Character	$\chi$	$=$	675.499
Dual form			675.2.u.b.349.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.03831 + 0.183082i) q^{2} +(-0.0916693 + 1.72962i) q^{3} +(-0.834822 + 0.303850i) q^{4} +(-0.221481 - 1.81266i) q^{6} +(0.841112 - 2.31094i) q^{7} +(2.63732 - 1.52266i) q^{8} +(-2.98319 - 0.317107i) q^{9} +O(q^{10})$	\(q+(-1.03831 + 0.183082i) q^{2} +(-0.0916693 + 1.72962i) q^{3} +(-0.834822 + 0.303850i) q^{4} +(-0.221481 - 1.81266i) q^{6} +(0.841112 - 2.31094i) q^{7} +(2.63732 - 1.52266i) q^{8} +(-2.98319 - 0.317107i) q^{9} +(-0.960783 + 0.806193i) q^{11} +(-0.449019 - 1.47178i) q^{12} +(4.47992 + 0.789931i) q^{13} +(-0.450243 + 2.55345i) q^{14} +(-1.09847 + 0.921724i) q^{16} +(5.75662 + 3.32358i) q^{17} +(3.15553 - 0.216914i) q^{18} +(0.124578 + 0.215776i) q^{19} +(3.91994 + 1.66665i) q^{21} +(0.849989 - 1.01298i) q^{22} +(0.287981 + 0.791222i) q^{23} +(2.39186 + 4.70115i) q^{24} -4.79615 q^{26} +(0.821942 - 5.13073i) q^{27} +2.18479i q^{28} +(0.0889744 + 0.504599i) q^{29} +(0.770551 - 0.280458i) q^{31} +(-2.94318 + 3.50754i) q^{32} +(-1.30634 - 1.73570i) q^{33} +(-6.58563 - 2.39697i) q^{34} +(2.58679 - 0.641717i) q^{36} +(-2.25865 - 1.30403i) q^{37} +(-0.168855 - 0.201233i) q^{38} +(-1.77695 + 7.67616i) q^{39} +(-1.41572 + 8.02895i) q^{41} +(-4.37524 - 1.01282i) q^{42} +(-2.78143 - 3.31478i) q^{43} +(0.557121 - 0.964962i) q^{44} +(-0.443871 - 0.768808i) q^{46} +(-1.81351 + 4.98256i) q^{47} +(-1.49354 - 1.98443i) q^{48} +(0.729356 + 0.612002i) q^{49} +(-6.27625 + 9.65211i) q^{51} +(-3.97996 + 0.701774i) q^{52} +10.4841i q^{53} +(0.0859140 + 5.47776i) q^{54} +(-1.30048 - 7.37539i) q^{56} +(-0.384630 + 0.195693i) q^{57} +(-0.184765 - 0.507639i) q^{58} +(2.30289 + 1.93235i) q^{59} +(-2.70930 - 0.986103i) q^{61} +(-0.748722 + 0.432275i) q^{62} +(-3.24201 + 6.62725i) q^{63} +(3.84771 - 6.66442i) q^{64} +(1.67415 + 1.56302i) q^{66} +(9.93303 + 1.75146i) q^{67} +(-5.81562 - 1.02545i) q^{68} +(-1.39492 + 0.425568i) q^{69} +(-0.0447378 + 0.0774882i) q^{71} +(-8.35047 + 3.70607i) q^{72} +(4.60824 - 2.66057i) q^{73} +(2.58391 + 0.940468i) q^{74} +(-0.169564 - 0.142281i) q^{76} +(1.05493 + 2.89841i) q^{77} +(0.439660 - 8.29554i) q^{78} +(-0.829503 - 4.70435i) q^{79} +(8.79889 + 1.89198i) q^{81} -8.59571i q^{82} +(7.91851 - 1.39625i) q^{83} +(-3.77887 - 0.200278i) q^{84} +(3.49486 + 2.93254i) q^{86} +(-0.880922 + 0.107636i) q^{87} +(-1.30634 + 3.58913i) q^{88} +(3.35189 + 5.80564i) q^{89} +(5.59359 - 9.68839i) q^{91} +(-0.480826 - 0.573026i) q^{92} +(0.414450 + 1.35847i) q^{93} +(0.970760 - 5.50545i) q^{94} +(-5.79693 - 5.41213i) q^{96} +(3.52928 + 4.20603i) q^{97} +(-0.869342 - 0.501915i) q^{98} +(3.12185 - 2.10036i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 12 q^{4}+O(q^{10}) $ 24 * q + 12 * q^4	$ 24 q + 12 q^{4} + 6 q^{11} - 30 q^{14} + 6 q^{19} - 24 q^{21} + 36 q^{24} - 60 q^{26} + 12 q^{29} + 6 q^{31} - 18 q^{34} + 36 q^{36} - 66 q^{39} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 24 q^{49} - 36 q^{51} + 108 q^{54} - 66 q^{56} + 24 q^{59} + 24 q^{61} - 24 q^{64} - 18 q^{66} - 18 q^{69} + 54 q^{71} - 66 q^{74} - 96 q^{76} + 84 q^{79} + 72 q^{81} - 12 q^{84} + 102 q^{86} - 18 q^{89} + 12 q^{91} + 30 q^{94} + 54 q^{99}+O(q^{100}) $ 24 * q + 12 * q^4 + 6 * q^11 - 30 * q^14 + 6 * q^19 - 24 * q^21 + 36 * q^24 - 60 * q^26 + 12 * q^29 + 6 * q^31 - 18 * q^34 + 36 * q^36 - 66 * q^39 + 30 * q^41 - 6 * q^44 - 6 * q^46 - 24 * q^49 - 36 * q^51 + 108 * q^54 - 66 * q^56 + 24 * q^59 + 24 * q^61 - 24 * q^64 - 18 * q^66 - 18 * q^69 + 54 * q^71 - 66 * q^74 - 96 * q^76 + 84 * q^79 + 72 * q^81 - 12 * q^84 + 102 * q^86 - 18 * q^89 + 12 * q^91 + 30 * q^94 + 54 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/675\mathbb{Z}\right)^\times$.

$n$	$326$	$352$
$\chi(n)$	$e\left(\frac{4}{9}\right)$	$-1$

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 $

$2$	−1.03831	+	0.183082i	−0.734194	+	0.129458i	−0.528230	−	0.849101i	$-0.677144\pi$
$2$	−1.03831	+	0.183082i	−0.734194	+	0.129458i	−0.205964	+	0.978560i	$0.566033\pi$
$3$	−0.0916693	+	1.72962i	−0.0529253	+	0.998598i
$3$	−0.0916693	+	1.72962i	−0.0529253	+	0.998598i
$4$	−0.834822	+	0.303850i	−0.417411	+	0.151925i
$5$		0			0
$5$		0			0
$6$	−0.221481	−	1.81266i	−0.0904194	−	0.740017i
$7$	0.841112	−	2.31094i	0.317910	−	0.873452i	−0.673086	−	0.739564i	$-0.735032\pi$
$7$	0.841112	−	2.31094i	0.317910	−	0.873452i	0.990997	−	0.133888i	$-0.0427461\pi$
$8$	2.63732	−	1.52266i	0.932432	−	0.538340i
$9$	−2.98319	−	0.317107i	−0.994398	−	0.105702i
$10$		0			0
$11$	−0.960783	+	0.806193i	−0.289687	+	0.243076i	−0.776036	−	0.630688i	$-0.782773\pi$
$11$	−0.960783	+	0.806193i	−0.289687	+	0.243076i	0.486349	+	0.873764i	$0.338328\pi$
$12$	−0.449019	−	1.47178i	−0.129621	−	0.424867i
$13$	4.47992	+	0.789931i	1.24251	+	0.219087i	0.755989	−	0.654584i	$-0.227156\pi$
$13$	4.47992	+	0.789931i	1.24251	+	0.219087i	0.486517	+	0.873671i	$0.338267\pi$
$14$	−0.450243	+	2.55345i	−0.120332	+	0.682439i
$15$		0			0
$16$	−1.09847	+	0.921724i	−0.274617	+	0.230431i
$17$	5.75662	+	3.32358i	1.39618	+	0.806088i	0.993990	−	0.109467i	$-0.0349143\pi$
$17$	5.75662	+	3.32358i	1.39618	+	0.806088i	0.402194	+	0.915554i	$0.368248\pi$
$18$	3.15553	−	0.216914i	0.743765	−	0.0511270i
$19$	0.124578	+	0.215776i	0.0285802	+	0.0495023i	0.879962	−	0.475045i	$-0.157568\pi$
$19$	0.124578	+	0.215776i	0.0285802	+	0.0495023i	−0.851382	+	0.524547i	$0.824235\pi$
$20$		0			0
$21$	3.91994	+	1.66665i	0.855402	+	0.363693i
$22$	0.849989	−	1.01298i	0.181218	−	0.215967i
$23$	0.287981	+	0.791222i	0.0600483	+	0.164981i	0.966089	−	0.258209i	$-0.0831324\pi$
$23$	0.287981	+	0.791222i	0.0600483	+	0.164981i	−0.906041	+	0.423190i	$0.860910\pi$
$24$	2.39186	+	4.70115i	0.488236	+	0.959617i
$25$		0			0
$26$	−4.79615			−0.940603
$27$	0.821942	−	5.13073i	0.158183	−	0.987410i
$28$			2.18479i			0.412887i
$29$	0.0889744	+	0.504599i	0.0165221	+	0.0937016i	0.991954	−	0.126601i	$-0.0404067\pi$
$29$	0.0889744	+	0.504599i	0.0165221	+	0.0937016i	−0.975432	+	0.220302i	$0.929296\pi$
$30$		0			0
$31$	0.770551	−	0.280458i	0.138395	−	0.0503717i	−0.271894	−	0.962327i	$-0.587650\pi$
$31$	0.770551	−	0.280458i	0.138395	−	0.0503717i	0.410289	+	0.911956i	$0.365428\pi$
$32$	−2.94318	+	3.50754i	−0.520286	+	0.620052i
$33$	−1.30634	−	1.73570i	−0.227404	−	0.302146i
$34$	−6.58563	−	2.39697i	−1.12943	−	0.411077i
$35$		0			0
$36$	2.58679	−	0.641717i	0.431131	−	0.106953i
$37$	−2.25865	−	1.30403i	−0.371319	−	0.214381i	0.302715	−	0.953081i	$-0.402107\pi$
$37$	−2.25865	−	1.30403i	−0.371319	−	0.214381i	−0.674035	+	0.738700i	$0.735440\pi$
$38$	−0.168855	−	0.201233i	−0.0273919	−	0.0326444i
$39$	−1.77695	+	7.67616i	−0.284540	+	1.22917i
$40$		0			0
$41$	−1.41572	+	8.02895i	−0.221099	+	1.25391i	0.648906	+	0.760869i	$0.275227\pi$
$41$	−1.41572	+	8.02895i	−0.221099	+	1.25391i	−0.870005	+	0.493044i	$0.835884\pi$
$42$	−4.37524	−	1.01282i	−0.675114	−	0.156282i
$43$	−2.78143	−	3.31478i	−0.424165	−	0.505500i	0.511065	−	0.859542i	$-0.329251\pi$
$43$	−2.78143	−	3.31478i	−0.424165	−	0.505500i	−0.935229	+	0.354042i	$0.884807\pi$
$44$	0.557121	−	0.964962i	0.0839891	−	0.145473i
$45$		0			0
$46$	−0.443871	−	0.768808i	−0.0654452	−	0.113354i
$47$	−1.81351	+	4.98256i	−0.264527	+	0.726782i	0.734321	+	0.678802i	$0.237501\pi$
$47$	−1.81351	+	4.98256i	−0.264527	+	0.726782i	−0.998848	+	0.0479798i	$0.984722\pi$
$48$	−1.49354	−	1.98443i	−0.215574	−	0.286428i
$49$	0.729356	+	0.612002i	0.104194	+	0.0874289i
$50$		0			0
$51$	−6.27625	+	9.65211i	−0.878851	+	1.35157i
$52$	−3.97996	+	0.701774i	−0.551921	+	0.0973185i
$53$			10.4841i			1.44010i	0.693920	+	0.720052i	$0.255882\pi$
$53$			10.4841i			1.44010i	−0.693920	+	0.720052i	$0.744118\pi$
$54$	0.0859140	+	5.47776i	0.0116914	+	0.745429i
$55$		0			0
$56$	−1.30048	−	7.37539i	−0.173784	−	0.985578i
$57$	−0.384630	+	0.195693i	−0.0509456	+	0.0259202i
$58$	−0.184765	−	0.507639i	−0.0242609	−	0.0666563i
$59$	2.30289	+	1.93235i	0.299810	+	0.251571i	0.780265	−	0.625449i	$-0.215084\pi$
$59$	2.30289	+	1.93235i	0.299810	+	0.251571i	−0.480455	+	0.877019i	$0.659529\pi$
$60$		0			0
$61$	−2.70930	−	0.986103i	−0.346890	−	0.126258i	0.162699	−	0.986676i	$-0.447980\pi$
$61$	−2.70930	−	0.986103i	−0.346890	−	0.126258i	−0.509589	+	0.860418i	$0.670202\pi$
$62$	−0.748722	+	0.432275i	−0.0950878	+	0.0548990i
$63$	−3.24201	+	6.62725i	−0.408455	+	0.834955i
$64$	3.84771	−	6.66442i	0.480963	−	0.833053i
$65$		0			0
$66$	1.67415	+	1.56302i	0.206074	+	0.192394i
$67$	9.93303	+	1.75146i	1.21351	+	0.213975i	0.743531	−	0.668701i	$-0.233149\pi$
$67$	9.93303	+	1.75146i	1.21351	+	0.213975i	0.469982	+	0.882676i	$0.344261\pi$
$68$	−5.81562	−	1.02545i	−0.705248	−	0.124354i
$69$	−1.39492	+	0.425568i	−0.167928	+	0.0512324i
$70$		0			0
$71$	−0.0447378	+	0.0774882i	−0.00530940	+	0.00919615i	−0.868668	−	0.495395i	$-0.835023\pi$
$71$	−0.0447378	+	0.0774882i	−0.00530940	+	0.00919615i	0.863358	+	0.504591i	$0.168357\pi$
$72$	−8.35047	+	3.70607i	−0.984112	+	0.436764i
$73$	4.60824	−	2.66057i	0.539354	−	0.311396i	−0.205463	−	0.978665i	$-0.565870\pi$
$73$	4.60824	−	2.66057i	0.539354	−	0.311396i	0.744817	+	0.667269i	$0.232537\pi$
$74$	2.58391	+	0.940468i	0.300374	+	0.109327i
$75$		0			0
$76$	−0.169564	−	0.142281i	−0.0194503	−	0.0163208i
$77$	1.05493	+	2.89841i	0.120221	+	0.330304i
$78$	0.439660	−	8.29554i	0.0497817	−	0.939285i
$79$	−0.829503	−	4.70435i	−0.0933264	−	0.529280i	−0.995247	−	0.0973792i	$-0.968954\pi$
$79$	−0.829503	−	4.70435i	−0.0933264	−	0.529280i	0.901921	−	0.431901i	$-0.142157\pi$
$80$		0			0
$81$	8.79889	+	1.89198i	0.977654	+	0.210220i
$82$		−	8.59571i		−	0.949238i
$83$	7.91851	−	1.39625i	0.869169	−	0.153258i	0.278759	−	0.960361i	$-0.410077\pi$
$83$	7.91851	−	1.39625i	0.869169	−	0.153258i	0.590410	+	0.807103i	$0.298966\pi$
$84$	−3.77887	−	0.200278i	−0.412308	−	0.0218522i
$85$		0			0
$86$	3.49486	+	2.93254i	0.376860	+	0.316223i
$87$	−0.880922	+	0.107636i	−0.0944448	+	0.0115398i
$88$	−1.30634	+	3.58913i	−0.139256	+	0.382602i
$89$	3.35189	+	5.80564i	0.355299	+	0.615396i	0.987169	−	0.159678i	$-0.0510457\pi$
$89$	3.35189	+	5.80564i	0.355299	+	0.615396i	−0.631870	+	0.775074i	$0.717712\pi$
$90$		0			0
$91$	5.59359	−	9.68839i	0.586368	−	1.01562i
$92$	−0.480826	−	0.573026i	−0.0501296	−	0.0597421i
$93$	0.414450	+	1.35847i	0.0429765	+	0.140867i
$94$	0.970760	−	5.50545i	0.100126	−	0.567844i
$95$		0			0
$96$	−5.79693	−	5.41213i	−0.591647	−	0.552373i
$97$	3.52928	+	4.20603i	0.358344	+	0.427057i	0.914855	−	0.403783i	$-0.132305\pi$
$97$	3.52928	+	4.20603i	0.358344	+	0.427057i	−0.556511	+	0.830840i	$0.687860\pi$
$98$	−0.869342	−	0.501915i	−0.0878168	−	0.0507010i
$99$	3.12185	−	2.10036i	0.313758	−	0.211094i
$100$		0			0
$101$	−4.70360	−	1.71197i	−0.468025	−	0.170347i	0.0972322	−	0.995262i	$-0.469001\pi$
$101$	−4.70360	−	1.71197i	−0.468025	−	0.170347i	−0.565258	+	0.824914i	$0.691223\pi$
$102$	4.74956	−	11.1709i	0.470276	−	1.10609i
$103$	7.46865	−	8.90079i	0.735908	−	0.877021i	−0.260164	−	0.965564i	$-0.583777\pi$
$103$	7.46865	−	8.90079i	0.735908	−	0.877021i	0.996072	+	0.0885431i	$0.0282211\pi$
$104$	13.0178	−	4.73808i	1.27650	−	0.464607i
$105$		0			0
$106$	−1.91945	−	10.8857i	−0.186433	−	1.05732i
$107$			19.4581i			1.88109i	0.339673	+	0.940544i	$0.389684\pi$
$107$			19.4581i			1.88109i	−0.339673	+	0.940544i	$0.610316\pi$
$108$	0.872799	+	4.53300i	0.0839852	+	0.436188i
$109$	−6.31515			−0.604881			−0.302441	−	0.953168i	$-0.597801\pi$
$109$	−6.31515			−0.604881			−0.302441	+	0.953168i	$0.597801\pi$
$110$		0			0
$111$	2.46253	−	3.78707i	0.233733	−	0.359453i
$112$	1.20611	+	3.31376i	0.113967	+	0.313121i
$113$	−4.44534	+	5.29775i	−0.418183	+	0.498371i	−0.933474	−	0.358644i	$-0.883239\pi$
$113$	−4.44534	+	5.29775i	−0.418183	+	0.498371i	0.515292	+	0.857015i	$0.327684\pi$
$114$	0.363537	−	0.273608i	0.0340483	−	0.0256258i
$115$		0			0
$116$	−0.227600	−	0.394215i	−0.0211322	−	0.0366020i
$117$	−13.1140	−	3.77713i	−1.21239	−	0.349196i
$118$	−2.74488	−	1.58476i	−0.252687	−	0.145889i
$119$	12.5226	−	10.5077i	1.14794	−	0.963236i
$120$		0			0
$121$	−1.63697	+	9.28373i	−0.148816	+	0.843976i
$122$	2.99362	+	0.527856i	0.271030	+	0.0477898i
$123$	−13.7573	−	3.18467i	−1.24045	−	0.287152i
$124$	−0.558056	+	0.468265i	−0.0501149	+	0.0420514i
$125$		0			0
$126$	2.15288	−	7.47467i	0.191794	−	0.665897i
$127$	10.4124	−	6.01162i	0.923954	−	0.533445i	0.0390598	−	0.999237i	$-0.487564\pi$
$127$	10.4124	−	6.01162i	0.923954	−	0.533445i	0.884894	+	0.465792i	$0.154230\pi$
$128$	0.357098	−	0.981117i	0.0315633	−	0.0867194i
$129$	5.98830	−	4.50697i	0.527240	−	0.396817i
$130$		0			0
$131$	13.2354	−	4.81728i	1.15638	−	0.420888i	0.308577	−	0.951199i	$-0.400147\pi$
$131$	13.2354	−	4.81728i	1.15638	−	0.420888i	0.847803	+	0.530311i	$0.177925\pi$
$132$	1.61795	+	1.05207i	0.140824	+	0.0915706i
$133$	0.603428	−	0.106401i	0.0523238	−	0.00922610i
$134$	−10.6342			−0.918655
$135$		0			0
$136$	20.2427			1.73580
$137$	−2.22383	+	0.392122i	−0.189995	+	0.0335012i	−0.267836	−	0.963465i	$-0.586308\pi$
$137$	−2.22383	+	0.392122i	−0.189995	+	0.0335012i	0.0778409	+	0.996966i	$0.475197\pi$
$138$	1.37044	−	0.697254i	0.116659	−	0.0593542i
$139$	−7.49414	+	2.72764i	−0.635644	+	0.231356i	−0.639686	−	0.768636i	$-0.720936\pi$
$139$	−7.49414	+	2.72764i	−0.635644	+	0.231356i	0.00404179	+	0.999992i	$0.498713\pi$
$140$		0			0
$141$	−8.45172	−	3.59343i	−0.711763	−	0.302621i
$142$	0.0322649	−	0.0886472i	0.00270761	−	0.00743911i
$143$	−4.94107	+	2.85273i	−0.413193	+	0.238557i
$144$	3.56923	−	2.40135i	0.297436	−	0.200113i
$145$		0			0
$146$	−4.29767	+	3.60617i	−0.355678	+	0.298449i
$147$	−1.12539	+	1.20541i	−0.0928208	+	0.0994204i
$148$	2.28180	+	0.402343i	0.187563	+	0.0330724i
$149$	0.0185697	−	0.105314i	0.00152129	−	0.00862764i	−0.984038	−	0.177960i	$-0.943050\pi$
$149$	0.0185697	−	0.105314i	0.00152129	−	0.00862764i	0.985559	+	0.169333i	$0.0541612\pi$
$150$		0			0
$151$	−15.5196	+	13.0225i	−1.26297	+	1.05976i	−0.267609	+	0.963528i	$0.586233\pi$
$151$	−15.5196	+	13.0225i	−1.26297	+	1.05976i	−0.995359	+	0.0962282i	$0.969322\pi$
$152$	0.657104	+	0.379379i	0.0532982	+	0.0307717i
$153$	−16.1192	−	11.7404i	−1.30316	−	0.949152i
$154$	−1.62599	−	2.81630i	−0.131026	−	0.226944i
$155$		0			0
$156$	−0.848964	−	6.94816i	−0.0679716	−	0.556298i
$157$	13.3377	−	15.8953i	1.06447	−	1.26858i	0.102701	−	0.994712i	$-0.467252\pi$
$157$	13.3377	−	15.8953i	1.06447	−	1.26858i	0.961767	−	0.273871i	$-0.0883040\pi$
$158$	1.72256	+	4.73269i	0.137039	+	0.376513i
$159$	−18.1336	−	0.961071i	−1.43809	−	0.0762179i
$160$		0			0
$161$	2.07069			0.163193
$162$	−9.48234	−	0.353543i	−0.745003	−	0.0277770i
$163$			20.1346i			1.57706i	0.614995	+	0.788531i	$0.289158\pi$
$163$			20.1346i			1.57706i	−0.614995	+	0.788531i	$0.710842\pi$
$164$	−1.25773	−	7.13292i	−0.0982119	−	0.556987i
$165$		0			0
$166$	−7.96622	+	2.89947i	−0.618298	+	0.225042i
$167$	12.7674	−	15.2156i	0.987974	−	1.17742i	0.00383999	−	0.999993i	$-0.498778\pi$
$167$	12.7674	−	15.2156i	0.987974	−	1.17742i	0.984134	−	0.177429i	$-0.0567779\pi$
$168$	12.8759	−	1.57325i	0.993395	−	0.121378i
$169$	7.22968	+	2.63139i	0.556130	+	0.202415i
$170$		0			0
$171$	−0.303217	−	0.683205i	−0.0231876	−	0.0522460i
$172$	3.32920	+	1.92212i	0.253849	+	0.146560i
$173$	−12.1648	−	14.4975i	−0.924875	−	1.10222i	−0.994509	−	0.104650i	$-0.966628\pi$
$173$	−12.1648	−	14.4975i	−0.924875	−	1.10222i	0.0696342	−	0.997573i	$-0.477817\pi$
$174$	0.894962	−	0.273040i	0.0678469	−	0.0206991i
$175$		0			0
$176$	0.312302	−	1.77115i	0.0235407	−	0.133506i
$177$	−3.55334	+	3.80599i	−0.267085	+	0.286075i
$178$	−4.54319	−	5.41436i	−0.340527	−	0.405824i
$179$	5.45683	−	9.45151i	0.407863	−	0.706439i	−0.586787	−	0.809741i	$-0.699608\pi$
$179$	5.45683	−	9.45151i	0.407863	−	0.706439i	0.994650	+	0.103302i	$0.0329409\pi$
$180$		0			0
$181$	8.97393	+	15.5433i	0.667027	+	1.15532i	0.978731	+	0.205146i	$0.0657668\pi$
$181$	8.97393	+	15.5433i	0.667027	+	1.15532i	−0.311704	+	0.950179i	$0.600900\pi$
$182$	−4.03410	+	11.0836i	−0.299028	+	0.821572i
$183$	1.95395	−	4.59567i	0.144440	−	0.339721i
$184$	1.96426	+	1.64821i	0.144807	+	0.121507i
$185$		0			0
$186$	−0.679038	−	1.33463i	−0.0497895	−	0.0978601i
$187$	−8.21031	+	1.44770i	−0.600397	+	0.105866i
$188$		−	4.71059i		−	0.343555i
$189$	−11.1654	−	6.21498i	−0.812167	−	0.452073i
$190$		0			0
$191$	−4.68261	−	26.5564i	−0.338822	−	1.92155i	−0.385641	−	0.922649i	$-0.626020\pi$
$191$	−4.68261	−	26.5564i	−0.338822	−	1.92155i	0.0468192	−	0.998903i	$-0.485092\pi$
$192$	11.1742	+	7.26601i	0.806430	+	0.524379i
$193$	−5.86729	−	16.1202i	−0.422337	−	1.16036i	−0.950366	−	0.311135i	$-0.899291\pi$
$193$	−5.86729	−	16.1202i	−0.422337	−	1.16036i	0.528029	−	0.849226i	$-0.322931\pi$
$194$	−4.43452	−	3.72100i	−0.318380	−	0.267152i
$195$		0			0
$196$	−0.794839	−	0.289298i	−0.0567742	−	0.0206641i
$197$	2.17567	−	1.25612i	0.155010	−	0.0894951i	−0.420489	−	0.907298i	$-0.638141\pi$
$197$	2.17567	−	1.25612i	0.155010	−	0.0894951i	0.575499	+	0.817803i	$0.304808\pi$
$198$	−2.85690	+	2.75237i	−0.203031	+	0.195602i
$199$	9.26942	−	16.0551i	0.657092	−	1.13812i	−0.324273	−	0.945964i	$-0.605120\pi$
$199$	9.26942	−	16.0551i	0.657092	−	1.13812i	0.981365	−	0.192153i	$-0.0615470\pi$
$200$		0			0
$201$	−3.93992	+	17.0198i	−0.277901	+	1.20049i
$202$	5.19721	+	0.916408i	0.365674	+	0.0644783i
$203$	1.24093	+	0.218810i	0.0870964	+	0.0153574i
$204$	2.30676	−	9.96484i	0.161505	−	0.697678i
$205$		0			0
$206$	−6.12519	+	10.6091i	−0.426762	+	0.739173i
$207$	−0.608202	−	2.45169i	−0.0422730	−	0.170404i
$208$	−5.64915	+	3.26154i	−0.391698	+	0.226147i
$209$	−0.293649	−	0.106880i	−0.0203121	−	0.00739301i
$210$		0			0
$211$	−2.82761	−	2.37264i	−0.194661	−	0.163340i	0.540248	−	0.841506i	$-0.318330\pi$
$211$	−2.82761	−	2.37264i	−0.194661	−	0.163340i	−0.734908	+	0.678166i	$0.762775\pi$
$212$	−3.18560	−	8.75237i	−0.218788	−	0.601115i
$213$	−0.129924	−	0.0844829i	−0.00890226	−	0.00578867i
$214$	−3.56242	−	20.2035i	−0.243522	−	1.38108i
$215$		0			0
$216$	−5.64462	−	14.7829i	−0.384067	−	1.00585i
$217$		−	2.01659i		−	0.136895i
$218$	6.55706	−	1.15619i	0.444100	−	0.0783069i
$219$	4.17935	+	8.21441i	0.282414	+	0.555079i
$220$		0			0
$221$	23.1638	+	19.4367i	1.55816	+	1.30746i
$222$	−1.86352	+	4.38299i	−0.125071	+	0.294167i
$223$	7.26487	−	19.9601i	0.486491	−	1.33662i	−0.417346	−	0.908748i	$-0.637040\pi$
$223$	7.26487	−	19.9601i	0.486491	−	1.33662i	0.903837	−	0.427876i	$-0.140738\pi$
$224$	5.63017	+	9.75174i	0.376181	+	0.651565i
$225$		0			0
$226$	3.64571	−	6.31456i	0.242509	−	0.420038i
$227$	−9.21761	−	10.9851i	−0.611794	−	0.729108i	0.367842	−	0.929888i	$-0.380097\pi$
$227$	−9.21761	−	10.9851i	−0.611794	−	0.729108i	−0.979636	+	0.200781i	$0.935652\pi$
$228$	0.261637	−	0.280239i	0.0173273	−	0.0185593i
$229$	−2.93219	+	16.6293i	−0.193765	+	1.09889i	0.720403	+	0.693556i	$0.243957\pi$
$229$	−2.93219	+	16.6293i	−0.193765	+	1.09889i	−0.914167	+	0.405337i	$0.867154\pi$
$230$		0			0
$231$	−5.10985	+	1.55894i	−0.336204	+	0.102571i
$232$	1.00298	+	1.19531i	0.0658491	+	0.0784759i
$233$	4.84926	+	2.79972i	0.317686	+	0.183416i	0.650361	−	0.759626i	$-0.274618\pi$
$233$	4.84926	+	2.79972i	0.317686	+	0.183416i	−0.332675	+	0.943042i	$0.607951\pi$
$234$	14.3079	+	1.52089i	0.935334	+	0.0994238i
$235$		0			0
$236$	−2.50964	−	0.913436i	−0.163364	−	0.0594596i
$237$	8.21279	−	1.00348i	0.533478	−	0.0651833i
$238$	−11.0785	+	13.2028i	−0.718112	+	0.855813i
$239$	−4.95620	+	1.80391i	−0.320590	+	0.116685i	−0.497302	−	0.867577i	$-0.665676\pi$
$239$	−4.95620	+	1.80391i	−0.320590	+	0.116685i	0.176712	+	0.984263i	$0.443454\pi$
$240$		0			0
$241$	−1.54590	−	8.76723i	−0.0995801	−	0.564747i	−0.993247	−	0.116017i	$-0.962987\pi$
$241$	−1.54590	−	8.76723i	−0.0995801	−	0.564747i	0.893667	−	0.448730i	$-0.148124\pi$
$242$		−	9.93907i		−	0.638907i
$243$	−4.07900	+	15.0453i	−0.261668	+	0.965158i
$244$	2.56141			0.163977
$245$		0			0
$246$	14.8673	+	0.787963i	0.947908	+	0.0502387i
$247$	0.387652	+	1.06507i	0.0246657	+	0.0677685i
$248$	1.60515	−	1.91294i	0.101927	−	0.121472i
$249$	1.68910	+	13.8240i	0.107042	+	0.876062i
$250$		0			0
$251$	3.89010	+	6.73786i	0.245541	+	0.425290i	0.962284	−	0.272048i	$-0.0877010\pi$
$251$	3.89010	+	6.73786i	0.245541	+	0.425290i	−0.716742	+	0.697338i	$0.754368\pi$
$252$	0.692812	−	6.51766i	0.0436431	−	0.410574i
$253$	−0.914565	−	0.528024i	−0.0574982	−	0.0331966i
$254$	−9.71069	+	8.14824i	−0.609303	+	0.511266i
$255$		0			0
$256$	−2.86374	+	16.2411i	−0.178984	+	1.01507i
$257$	−20.1261	−	3.54877i	−1.25543	−	0.221366i	−0.493913	−	0.869511i	$-0.664434\pi$
$257$	−20.1261	−	3.54877i	−1.25543	−	0.221366i	−0.761517	+	0.648145i	$0.775545\pi$
$258$	−5.39255	+	5.77597i	−0.335726	+	0.359596i
$259$	−4.91331	+	4.12275i	−0.305298	+	0.256175i
$260$		0			0
$261$	−0.105416	−	1.53353i	−0.00652510	−	0.0949231i
$262$	−12.8604	+	7.42498i	−0.794520	+	0.458717i
$263$	−3.85792	+	10.5996i	−0.237890	+	0.653596i	0.762092	+	0.647469i	$0.224173\pi$
$263$	−3.85792	+	10.5996i	−0.237890	+	0.653596i	−0.999981	+	0.00612723i	$0.998050\pi$
$264$	−6.08809	−	2.58848i	−0.374696	−	0.159310i
$265$		0			0
$266$	−0.607063	+	0.220953i	−0.0372214	+	0.0135475i
$267$	−10.3488	+	5.26530i	−0.633338	+	0.322231i
$268$	−8.82450	+	1.55600i	−0.539042	+	0.0950476i
$269$	0.307761			0.0187645			0.00938226	−	0.999956i	$-0.497013\pi$
$269$	0.307761			0.0187645			0.00938226	+	0.999956i	$0.497013\pi$
$270$		0			0
$271$	−2.22251			−0.135008			−0.0675040	−	0.997719i	$-0.521504\pi$
$271$	−2.22251			−0.135008			−0.0675040	+	0.997719i	$0.521504\pi$
$272$	−9.38689	+	1.65516i	−0.569164	+	0.100359i
$273$	16.2445	+	10.5629i	0.983162	+	0.639298i
$274$	2.23723	−	0.814286i	0.135156	−	0.0491928i
$275$		0			0
$276$	1.03520	−	0.779119i	0.0623115	−	0.0468975i
$277$	−7.97924	+	21.9228i	−0.479426	+	1.31721i	0.430556	+	0.902564i	$0.358317\pi$
$277$	−7.97924	+	21.9228i	−0.479426	+	1.31721i	−0.909982	+	0.414648i	$0.863905\pi$
$278$	7.28184	−	4.20417i	0.436735	−	0.252149i
$279$	−2.38764	+	0.592313i	−0.142944	+	0.0354608i
$280$		0			0
$281$	5.53502	−	4.64443i	0.330192	−	0.277064i	−0.462586	−	0.886574i	$-0.653078\pi$
$281$	5.53502	−	4.64443i	0.330192	−	0.277064i	0.792778	+	0.609511i	$0.208634\pi$
$282$	9.43337	+	2.18373i	0.561749	+	0.130039i
$283$	−7.01212	−	1.23643i	−0.416827	−	0.0734979i	−0.0386985	−	0.999251i	$-0.512321\pi$
$283$	−7.01212	−	1.23643i	−0.416827	−	0.0734979i	−0.378129	+	0.925753i	$0.623432\pi$
$284$	0.0138033	−	0.0782824i	0.000819076	−	0.00464521i
$285$		0			0
$286$	4.60806	−	3.86662i	0.272480	−	0.228638i
$287$	17.3636	+	10.0249i	1.02494	+	0.591751i
$288$	9.89234	−	9.53038i	0.582912	−	0.561583i
$289$	13.5924	+	23.5428i	0.799555	+	1.38487i
$290$		0			0
$291$	−7.59837	+	5.71875i	−0.445424	+	0.335239i
$292$	−3.03865	+	3.62132i	−0.177823	+	0.211922i
$293$	0.188961	+	0.519166i	0.0110392	+	0.0303300i	0.945090	−	0.326811i	$-0.105974\pi$
$293$	0.188961	+	0.519166i	0.0110392	+	0.0303300i	−0.934051	+	0.357141i	$0.883752\pi$
$294$	0.947815	−	1.45762i	0.0552777	−	0.0850103i
$295$		0			0
$296$	−7.94236			−0.461640
$297$	3.34665	+	5.59216i	0.194192	+	0.324490i
$298$			0.112748i			0.00653131i
$299$	0.665122	+	3.77210i	0.0384650	+	0.218146i
$300$		0			0
$301$	−9.99975	+	3.63961i	−0.576376	+	0.209784i
$302$	13.7299	−	16.3627i	0.790069	−	0.941568i
$303$	3.39224	−	7.97852i	0.194879	−	0.458354i
$304$	−0.335731	−	0.122196i	−0.0192555	−	0.00700842i
$305$		0			0
$306$	18.8861	+	9.23898i	1.07965	+	0.528157i
$307$	−5.82728	−	3.36438i	−0.332580	−	0.192015i	0.324406	−	0.945918i	$-0.394836\pi$
$307$	−5.82728	−	3.36438i	−0.332580	−	0.192015i	−0.656986	+	0.753903i	$0.728169\pi$
$308$	−1.76136	−	2.09911i	−0.100363	−	0.119608i
$309$	14.7104	+	13.7339i	0.836844	+	0.781293i
$310$		0			0
$311$	2.67825	−	15.1891i	0.151870	−	0.861297i	−0.809722	−	0.586814i	$-0.800382\pi$
$311$	2.67825	−	15.1891i	0.151870	−	0.861297i	0.961592	−	0.274483i	$-0.0885068\pi$
$312$	7.00176	+	22.9502i	0.396397	+	1.29930i
$313$	15.1446	+	18.0487i	0.856025	+	1.02017i	0.999534	+	0.0305223i	$0.00971706\pi$
$313$	15.1446	+	18.0487i	0.856025	+	1.02017i	−0.143509	+	0.989649i	$0.545838\pi$
$314$	−10.9385	+	18.9461i	−0.617297	+	1.06919i
$315$		0			0
$316$	2.12191	+	3.67525i	0.119367	+	0.206749i
$317$	2.48034	−	6.81469i	0.139310	−	0.382751i	−0.850344	−	0.526228i	$-0.823606\pi$
$317$	2.48034	−	6.81469i	0.139310	−	0.382751i	0.989654	+	0.143477i	$0.0458282\pi$
$318$	19.0042	−	2.32204i	1.06570	−	0.130213i
$319$	−0.492289	−	0.413079i	−0.0275629	−	0.0231280i
$320$		0			0
$321$	−33.6552	−	1.78371i	−1.87845	−	0.0995571i
$322$	−2.15001	+	0.379105i	−0.119815	+	0.0211267i
$323$			1.65618i			0.0921525i
$324$	−7.92038	+	1.09408i	−0.440021	+	0.0607821i
$325$		0			0
$326$	−3.68627	−	20.9059i	−0.204164	−	1.15787i
$327$	0.578905	−	10.9228i	0.0320135	−	0.604034i
$328$	8.49163	+	23.3306i	0.468872	+	1.28821i
$329$	9.98903	+	8.38179i	0.550713	+	0.462103i
$330$		0			0
$331$	−27.2835	−	9.93037i	−1.49964	−	0.545823i	−0.543669	−	0.839300i	$-0.682965\pi$
$331$	−27.2835	−	9.93037i	−1.49964	−	0.545823i	−0.955966	+	0.293477i	$0.905188\pi$
$332$	−6.18629	+	3.57166i	−0.339517	+	0.196020i
$333$	6.32447	+	4.60641i	0.346579	+	0.252430i
$334$	−10.4708	+	18.1360i	−0.572938	+	0.992357i
$335$		0			0
$336$	−5.84213	+	1.78235i	−0.318714	+	0.0972351i
$337$	−1.14149	−	0.201275i	−0.0621807	−	0.0109641i	0.142471	−	0.989799i	$-0.454495\pi$
$337$	−1.14149	−	0.201275i	−0.0621807	−	0.0109641i	−0.204652	+	0.978835i	$0.565606\pi$
$338$	−7.98839	−	1.40857i	−0.434511	−	0.0766161i
$339$	−8.75561	−	8.17441i	−0.475540	−	0.443973i
$340$		0			0
$341$	−0.514230	+	0.890672i	−0.0278471	+	0.0482326i
$342$	0.439914	+	0.653863i	0.0237878	+	0.0353569i
$343$	16.9362	−	9.77810i	0.914467	−	0.527968i
$344$	−12.3828	−	4.50697i	−0.667636	−	0.243000i
$345$		0			0
$346$	15.2851	+	12.8257i	0.821730	+	0.689513i
$347$	−2.01440	−	5.53452i	−0.108139	−	0.297108i	0.873807	−	0.486273i	$-0.161644\pi$
$347$	−2.01440	−	5.53452i	−0.108139	−	0.297108i	−0.981945	+	0.189165i	$0.939422\pi$
$348$	0.702708	−	0.357525i	0.0376691	−	0.0191654i
$349$	5.31237	+	30.1279i	0.284364	+	1.61271i	0.707547	+	0.706666i	$0.249802\pi$
$349$	5.31237	+	30.1279i	0.284364	+	1.61271i	−0.423183	+	0.906044i	$0.639087\pi$
$350$		0			0
$351$	7.73516	−	22.3360i	0.412872	−	1.19221i
$352$		−	5.74276i		−	0.306090i
$353$	36.3997	−	6.41826i	1.93736	−	0.341609i	0.937385	−	0.348294i	$-0.113239\pi$
$353$	36.3997	−	6.41826i	1.93736	−	0.341609i	0.999978	+	0.00668455i	$0.00212777\pi$
$354$	2.99265	−	4.60233i	0.159058	−	0.244611i
$355$		0			0
$356$	−4.56227	−	3.82820i	−0.241800	−	0.202894i
$357$	17.0264	+	22.6225i	0.901131	+	1.19731i
$358$	−3.93547	+	10.8126i	−0.207996	+	0.571464i
$359$	−13.1880	−	22.8423i	−0.696037	−	1.20557i	−0.969830	−	0.243783i	$-0.921611\pi$
$359$	−13.1880	−	22.8423i	−0.696037	−	1.20557i	0.273792	−	0.961789i	$-0.411722\pi$
$360$		0			0
$361$	9.46896	−	16.4007i	0.498366	−	0.863196i
$362$	−12.1634	−	14.4958i	−0.639294	−	0.761881i
$363$	−15.9073	−	3.68238i	−0.834917	−	0.193275i
$364$	−1.72583	+	9.78769i	−0.0904583	+	0.513015i
$365$		0			0
$366$	−1.18741	+	5.12944i	−0.0620671	+	0.268120i
$367$	−7.27194	−	8.66636i	−0.379592	−	0.452380i	0.542093	−	0.840318i	$-0.317632\pi$
$367$	−7.27194	−	8.66636i	−0.379592	−	0.452380i	−0.921685	+	0.387938i	$0.873187\pi$
$368$	−1.04563	−	0.603693i	−0.0545071	−	0.0314697i
$369$	6.76941	−	23.5030i	0.352401	−	1.22352i
$370$		0			0
$371$	24.2281	+	8.81831i	1.25786	+	0.457824i
$372$	−0.758765	−	1.00815i	−0.0393401	−	0.0522703i
$373$	3.75650	−	4.47682i	0.194504	−	0.231801i	−0.659974	−	0.751289i	$-0.729433\pi$
$373$	3.75650	−	4.47682i	0.194504	−	0.231801i	0.854478	+	0.519487i	$0.173877\pi$
$374$	8.25978	−	3.00631i	0.427103	−	0.155453i
$375$		0			0
$376$	2.80394	+	15.9019i	0.144602	+	0.820080i
$377$			2.33085i			0.120045i
$378$	12.7310	+	4.40887i	0.654813	+	0.226768i
$379$	−24.3265			−1.24957			−0.624783	−	0.780798i	$-0.714813\pi$
$379$	−24.3265			−1.24957			−0.624783	+	0.780798i	$0.714813\pi$
$380$		0			0
$381$	9.44334	+	18.5607i	0.483797	+	0.950892i
$382$	9.72397	+	26.7164i	0.497522	+	1.36693i
$383$	−2.45291	+	2.92326i	−0.125338	+	0.149372i	−0.825064	−	0.565039i	$-0.808861\pi$
$383$	−2.45291	+	2.92326i	−0.125338	+	0.149372i	0.699726	+	0.714411i	$0.253305\pi$
$384$	1.66423	+	0.707583i	0.0849273	+	0.0361087i
$385$		0			0
$386$	9.04337	+	15.6636i	0.460295	+	0.797255i
$387$	7.24642	+	10.7707i	0.368356	+	0.547503i
$388$	−4.22432	−	2.43891i	−0.214457	−	0.123817i
$389$	−8.30534	+	6.96901i	−0.421097	+	0.353343i	−0.828580	−	0.559870i	$-0.810851\pi$
$389$	−8.30534	+	6.96901i	−0.421097	+	0.353343i	0.407483	+	0.913213i	$0.366407\pi$
$390$		0			0
$391$	−0.971896	+	5.51189i	−0.0491509	+	0.278748i
$392$	2.85541	+	0.503486i	0.144220	+	0.0254299i
$393$	7.11881	+	23.3338i	0.359096	+	1.17704i
$394$	−2.02904	+	1.70257i	−0.102222	+	0.0857741i
$395$		0			0
$396$	−1.96799	+	2.70200i	−0.0988955	+	0.135781i
$397$	−9.10124	+	5.25461i	−0.456778	+	0.263721i	−0.710689	−	0.703507i	$-0.751617\pi$
$397$	−9.10124	+	5.25461i	−0.456778	+	0.263721i	0.253910	+	0.967228i	$0.418283\pi$
$398$	−6.68511	+	18.3672i	−0.335094	+	0.920665i
$399$	0.128717	+	1.05346i	0.00644392	+	0.0527388i
$400$		0			0
$401$	−13.4992	+	4.91332i	−0.674119	+	0.245359i	−0.656320	−	0.754482i	$-0.727888\pi$
$401$	−13.4992	+	4.91332i	−0.674119	+	0.245359i	−0.0177987	+	0.999842i	$0.505666\pi$
$402$	0.974829	−	18.3932i	0.0486201	−	0.917367i
$403$	3.67355	−	0.647746i	0.182993	−	0.0322665i
$404$	4.44685			0.221239
$405$		0			0
$406$	−1.32853			−0.0659338
$407$	3.22137	−	0.568014i	0.159677	−	0.0281554i
$408$	−1.85563	+	35.0122i	−0.0918675	+	1.73336i
$409$	16.6159	−	6.04769i	0.821603	−	0.299039i	0.103195	−	0.994661i	$-0.467093\pi$
$409$	16.6159	−	6.04769i	0.821603	−	0.299039i	0.718408	+	0.695622i	$0.244871\pi$
$410$		0			0
$411$	−0.474366	−	3.88234i	−0.0233988	−	0.191502i
$412$	−3.53049	+	9.69993i	−0.173935	+	0.477881i
$413$	6.40252	−	3.69650i	0.315047	−	0.181893i
$414$	1.08036	+	2.43426i	0.0530968	+	0.119637i
$415$		0			0
$416$	−15.9559	+	13.3886i	−0.782303	+	0.656431i
$417$	−4.03081	−	13.2121i	−0.197390	−	0.646998i
$418$	0.324466	+	0.0572121i	0.0158701	+	0.00279833i
$419$	−1.58606	+	8.99500i	−0.0774842	+	0.439435i	0.921243	+	0.388988i	$0.127175\pi$
$419$	−1.58606	+	8.99500i	−0.0774842	+	0.439435i	−0.998727	+	0.0504461i	$0.983936\pi$
$420$		0			0
$421$	18.5344	−	15.5522i	0.903310	−	0.757967i	−0.0675243	−	0.997718i	$-0.521510\pi$
$421$	18.5344	−	15.5522i	0.903310	−	0.757967i	0.970835	+	0.239750i	$0.0770656\pi$
$422$	3.37031	+	1.94585i	0.164064	+	0.0947226i
$423$	6.99004	−	14.2889i	0.339867	−	0.694749i
$424$	15.9637	+	27.6499i	0.775265	+	1.34280i
$425$		0			0
$426$	0.150369	+	0.0639324i	0.00728538	+	0.00309754i
$427$	−4.55764	+	5.43159i	−0.220560	+	0.262853i
$428$	−5.91236	−	16.2441i	−0.285785	−	0.785187i
$429$	−4.48120	−	8.80769i	−0.216354	−	0.425239i
$430$		0			0
$431$	−29.5332			−1.42256			−0.711282	−	0.702907i	$-0.751885\pi$
$431$	−29.5332			−1.42256			−0.711282	+	0.702907i	$0.751885\pi$
$432$	3.82624	+	6.39355i	0.184090	+	0.307610i
$433$		−	0.669754i		−	0.0321863i	−0.999870	−	0.0160932i	$-0.994877\pi$
$433$		−	0.669754i		−	0.0321863i	0.999870	−	0.0160932i	$-0.00512283\pi$
$434$	0.369201	+	2.09384i	0.0177222	+	0.100508i
$435$		0			0
$436$	5.27203	−	1.91886i	0.252484	−	0.0918967i
$437$	−0.134850	+	0.160708i	−0.00645076	+	0.00768772i
$438$	−5.84336	−	7.76392i	−0.279206	−	0.370975i
$439$	−5.96599	−	2.17144i	−0.284741	−	0.103637i	0.195701	−	0.980664i	$-0.437302\pi$
$439$	−5.96599	−	2.17144i	−0.284741	−	0.103637i	−0.480442	+	0.877026i	$0.659524\pi$
$440$		0			0
$441$	−1.98174	−	2.05700i	−0.0943685	−	0.0979526i
$442$	−27.6096	−	15.9404i	−1.31326	−	0.758209i
$443$	−9.86931	−	11.7618i	−0.468905	−	0.558819i	0.478818	−	0.877914i	$-0.341066\pi$
$443$	−9.86931	−	11.7618i	−0.468905	−	0.558819i	−0.947723	+	0.319095i	$0.896621\pi$
$444$	−0.905072	+	3.90977i	−0.0429528	+	0.185550i
$445$		0			0
$446$	−3.88884	+	22.0547i	−0.184142	+	1.04432i
$447$	0.180451	+	0.0417726i	0.00853503	+	0.00197577i
$448$	−12.1647	−	14.4973i	−0.574728	−	0.684934i
$449$	−16.0199	+	27.7473i	−0.756027	+	1.30948i	0.188836	+	0.982009i	$0.439529\pi$
$449$	−16.0199	+	27.7473i	−0.756027	+	1.30948i	−0.944862	+	0.327468i	$0.893805\pi$
$450$		0			0
$451$	−5.11268	−	8.85543i	−0.240747	−	0.416986i
$452$	2.10135	−	5.77340i	0.0988390	−	0.271558i
$453$	−21.1013	−	28.0368i	−0.991428	−	1.31729i
$454$	11.5819	+	9.71835i	0.543565	+	0.456105i
$455$		0			0
$456$	−0.716419	+	1.10176i	−0.0335494	+	0.0515949i
$457$	−18.8768	+	3.32849i	−0.883021	+	0.155700i	−0.596730	−	0.802442i	$-0.703534\pi$
$457$	−18.8768	+	3.32849i	−0.883021	+	0.155700i	−0.286291	+	0.958143i	$0.592422\pi$
$458$		−	17.8031i		−	0.831886i
$459$	21.7840	−	26.8039i	1.01679	−	1.25110i
$460$		0			0
$461$	−0.906494	−	5.14098i	−0.0422196	−	0.239440i	0.956394	−	0.292080i	$-0.0943474\pi$
$461$	−0.906494	−	5.14098i	−0.0422196	−	0.239440i	−0.998614	+	0.0526405i	$0.983236\pi$
$462$	5.02019	−	2.55418i	0.233560	−	0.118831i
$463$	0.580541	+	1.59502i	0.0269800	+	0.0741271i	0.952451	−	0.304690i	$-0.0985530\pi$
$463$	0.580541	+	1.59502i	0.0269800	+	0.0741271i	−0.925471	+	0.378818i	$0.876331\pi$
$464$	−0.562837	−	0.472276i	−0.0261290	−	0.0219249i
$465$		0			0
$466$	−5.54760	−	2.01916i	−0.256988	−	0.0935359i
$467$	17.0457	−	9.84136i	0.788783	−	0.455404i	−0.0507511	−	0.998711i	$-0.516162\pi$
$467$	17.0457	−	9.84136i	0.788783	−	0.455404i	0.839534	+	0.543307i	$0.182828\pi$
$468$	12.0955	−	0.831456i	0.559115	−	0.0384341i
$469$	12.4023	−	21.4814i	0.572685	−	0.991920i
$470$		0			0
$471$	26.2702	+	24.5264i	1.21047	+	1.13012i
$472$	9.01574	+	1.58972i	0.414983	+	0.0731727i
$473$	5.34471	+	0.942416i	0.245750	+	0.0433324i
$474$	−8.34368	+	2.54554i	−0.383238	+	0.116920i
$475$		0			0
$476$	−7.26134	+	12.5770i	−0.332823	+	0.576467i
$477$	3.32458	−	31.2761i	0.152222	−	1.43204i
$478$	4.81579	−	2.78040i	0.220269	−	0.127173i
$479$	−27.4892	−	10.0053i	−1.25601	−	0.457152i	−0.373585	−	0.927596i	$-0.621872\pi$
$479$	−27.4892	−	10.0053i	−1.25601	−	0.457152i	−0.882430	+	0.470444i	$0.844094\pi$
$480$		0			0
$481$	−9.08847	−	7.62613i	−0.414398	−	0.347722i
$482$	3.21024	+	8.82005i	0.146222	+	0.401742i
$483$	−0.189818	+	3.58151i	−0.00863704	+	0.162964i
$484$	−1.45429	−	8.24766i	−0.0661039	−	0.374894i
$485$		0			0
$486$	1.48074	−	16.3685i	0.0671675	−	0.742488i
$487$		−	20.5056i		−	0.929199i	−0.885521	−	0.464600i	$-0.846198\pi$
$487$		−	20.5056i		−	0.929199i	0.885521	−	0.464600i	$-0.153802\pi$
$488$	−8.64677	+	1.52466i	−0.391421	+	0.0690180i
$489$	−34.8252	−	1.84572i	−1.57485	−	0.0834664i
$490$		0			0
$491$	13.4265	+	11.2661i	0.605927	+	0.508433i	0.893345	−	0.449372i	$-0.148352\pi$
$491$	13.4265	+	11.2661i	0.605927	+	0.508433i	−0.287417	+	0.957805i	$0.592797\pi$
$492$	12.4526	−	1.52152i	0.561404	−	0.0685955i
$493$	−1.16489	+	3.20050i	−0.0524638	+	0.144143i
$494$	−0.597496	−	1.03489i	−0.0268826	−	0.0465620i
$495$		0			0
$496$	−0.587922	+	1.01831i	−0.0263985	+	0.0457235i
$497$	0.141441	+	0.168562i	0.00634448	+	0.00756106i
$498$	−4.28473	−	14.0443i	−0.192003	−	0.629342i
$499$	3.31772	−	18.8157i	0.148522	−	0.842307i	−0.815950	−	0.578122i	$-0.803786\pi$
$499$	3.31772	−	18.8157i	0.148522	−	0.842307i	0.964472	−	0.264185i	$-0.0851031\pi$
$500$		0			0
$501$	25.1469	+	23.4777i	1.12348	+	1.04890i
$502$	−5.27270	−	6.28376i	−0.235332	−	0.280458i
$503$	−9.49824	−	5.48381i	−0.423506	−	0.244511i	0.273070	−	0.961994i	$-0.411961\pi$
$503$	−9.49824	−	5.48381i	−0.423506	−	0.244511i	−0.696576	+	0.717483i	$0.745294\pi$
$504$	1.54080	+	22.4146i	0.0686327	+	0.998426i
$505$		0			0
$506$	1.04627	+	0.380811i	0.0465124	+	0.0169291i
$507$	−5.21405	+	12.2634i	−0.231564	+	0.544637i
$508$	−6.86590	+	8.18246i	−0.304625	+	0.363038i
$509$	−18.6993	+	6.80598i	−0.828831	+	0.301670i	−0.721379	−	0.692540i	$-0.756491\pi$
$509$	−18.6993	+	6.80598i	−0.828831	+	0.301670i	−0.107452	+	0.994210i	$0.534269\pi$
$510$		0			0
$511$	−2.27236	−	12.8872i	−0.100523	−	0.570096i
$512$		−	15.2994i		−	0.676143i
$513$	1.20948	−	0.461822i	0.0534000	−	0.0203899i
$514$	21.5468			0.950387
$515$		0			0
$516$	−3.62972	+	5.58207i	−0.159790	+	0.245737i
$517$	−2.27452	−	6.24920i	−0.100033	−	0.274839i
$518$	4.34672	−	5.18022i	0.190984	−	0.227606i
$519$	26.1903	−	19.7116i	1.14963	−	0.865243i
$520$		0			0
$521$	−17.5583	−	30.4119i	−0.769244	−	1.33237i	−0.937973	−	0.346708i	$-0.887300\pi$
$521$	−17.5583	−	30.4119i	−0.769244	−	1.33237i	0.168729	−	0.985662i	$-0.446034\pi$
$522$	0.390216	+	1.57298i	0.0170793	+	0.0688473i
$523$	−12.3369	−	7.12269i	−0.539453	−	0.311453i	0.205404	−	0.978677i	$-0.434149\pi$
$523$	−12.3369	−	7.12269i	−0.539453	−	0.311453i	−0.744857	+	0.667224i	$0.767482\pi$
$524$	−9.58545	+	8.04315i	−0.418742	+	0.351367i
$525$		0			0
$526$	2.06513	−	11.7119i	0.0900437	−	0.510663i
$527$	5.36789	+	0.946505i	0.233829	+	0.0412304i
$528$	3.03480	+	0.702526i	0.132073	+	0.0305735i
$529$	17.0759	−	14.3284i	0.742431	−	0.622974i
$530$		0			0
$531$	−6.25719	−	6.49483i	−0.271539	−	0.281852i
$532$	−0.471425	+	0.272177i	−0.0204389	+	0.0118004i
$533$	−12.6846	+	34.8507i	−0.549433	+	1.50955i
$534$	9.78128	−	7.36168i	0.423277	−	0.318571i
$535$		0			0
$536$	28.8634	−	10.5054i	1.24671	−	0.453765i
$537$	15.8473	+	10.3047i	0.683862	+	0.444679i
$538$	−0.319550	+	0.0563454i	−0.0137768	+	0.00242922i
$539$	−1.19414			−0.0514354
$540$		0			0
$541$	−13.2368			−0.569094			−0.284547	−	0.958662i	$-0.591843\pi$
$541$	−13.2368			−0.569094			−0.284547	+	0.958662i	$0.591843\pi$
$542$	2.30765	−	0.406901i	0.0991222	−	0.0174779i
$543$	−27.7067	+	14.0967i	−1.18901	+	0.604946i
$544$	−28.6004	+	10.4097i	−1.22623	+	0.446312i
$545$		0			0
$546$	−18.8007	−	7.99350i	−0.804594	−	0.342090i
$547$	−5.57661	+	15.3216i	−0.238439	+	0.655105i	0.761537	+	0.648121i	$0.224445\pi$
$547$	−5.57661	+	15.3216i	−0.238439	+	0.655105i	−0.999976	+	0.00698326i	$0.997777\pi$
$548$	1.73736	−	1.00306i	0.0742163	−	0.0428488i
$549$	7.76965	+	3.80087i	0.331601	+	0.162217i
$550$		0			0
$551$	−0.0977958	+	0.0820605i	−0.00416624	+	0.00349589i
$552$	−3.03084	+	3.24633i	−0.129001	+	0.138173i
$553$	−11.5692	−	2.03995i	−0.491970	−	0.0867476i
$554$	4.27124	−	24.2234i	0.181468	−	1.02915i
$555$		0			0
$556$	5.42748	−	4.55419i	0.230176	−	0.193141i
$557$	−26.7577	−	15.4486i	−1.13376	−	0.654577i	−0.188883	−	0.982000i	$-0.560487\pi$
$557$	−26.7577	−	15.4486i	−1.13376	−	0.654577i	−0.944878	+	0.327422i	$0.893820\pi$
$558$	2.37066	−	1.05214i	0.100358	−	0.0445404i
$559$	−9.84215	−	17.0471i	−0.416279	−	0.721016i
$560$		0			0
$561$	−1.75134	−	14.3335i	−0.0739417	−	0.605159i
$562$	−4.89674	+	5.83571i	−0.206557	+	0.246165i
$563$	9.15791	+	25.1612i	0.385960	+	1.06042i	0.968803	+	0.247832i	$0.0797180\pi$
$563$	9.15791	+	25.1612i	0.385960	+	1.06042i	−0.582843	+	0.812585i	$0.698060\pi$
$564$	8.14755	+	0.431816i	0.343074	+	0.0181827i
$565$		0			0
$566$	7.50710			0.315547
$567$	11.7731	−	18.7423i	0.494423	−	0.787102i
$568$			0.272481i			0.0114331i
$569$	−3.30985	−	18.7711i	−0.138756	−	0.786924i	−0.972170	−	0.234275i	$-0.924728\pi$
$569$	−3.30985	−	18.7711i	−0.138756	−	0.786924i	0.833414	−	0.552649i	$-0.186383\pi$
$570$		0			0
$571$	17.6420	−	6.42116i	0.738294	−	0.268717i	0.0546227	−	0.998507i	$-0.482604\pi$
$571$	17.6420	−	6.42116i	0.738294	−	0.268717i	0.683671	+	0.729790i	$0.260382\pi$
$572$	3.25811	−	3.88286i	0.136228	−	0.162351i
$573$	46.3618	−	5.66474i	1.93679	−	0.236648i
$574$	−19.8641	−	7.22996i	−0.829113	−	0.301773i
$575$		0			0
$576$	−13.5918	+	18.6611i	−0.566324	+	0.777547i
$577$	4.20856	+	2.42981i	0.175204	+	0.101154i	0.585038	−	0.811006i	$-0.301080\pi$
$577$	4.20856	+	2.42981i	0.175204	+	0.101154i	−0.409833	+	0.912161i	$0.634413\pi$
$578$	−18.4234	−	21.9561i	−0.766311	−	0.913254i
$579$	28.4198	−	8.67047i	1.18109	−	0.360332i
$580$		0			0
$581$	3.43371	−	19.4736i	0.142454	−	0.807899i
$582$	6.84244	−	7.32894i	0.283628	−	0.303795i
$583$	−8.45221	−	10.0730i	−0.350055	−	0.417179i
$584$	8.10226	−	14.0335i	0.335274	−	0.580712i
$585$		0			0
$586$	−0.291249	−	0.504459i	−0.0120314	−	0.0208390i
$587$	−11.2174	+	30.8194i	−0.462990	+	1.27205i	0.460236	+	0.887796i	$0.347765\pi$
$587$	−11.2174	+	30.8194i	−0.462990	+	1.27205i	−0.923226	+	0.384257i	$0.874458\pi$
$588$	0.573239	−	1.34825i	0.0236400	−	0.0556010i
$589$	0.156510	+	0.131327i	0.00644887	+	0.00541125i
$590$		0			0
$591$	1.97318	+	3.87824i	0.0811657	+	0.159529i
$592$	3.68301	−	0.649414i	0.151371	−	0.0266908i
$593$		−	17.3446i		−	0.712258i	−0.934437	−	0.356129i	$-0.884096\pi$
$593$		−	17.3446i		−	0.712258i	0.934437	−	0.356129i	$-0.115904\pi$
$594$	−4.49867	−	5.19367i	−0.184583	−	0.213099i
$595$		0			0
$596$	0.0164973	+	0.0935607i	0.000675754	+	0.00383239i
$597$	26.9196	+	17.5044i	1.10174	+	0.716406i
$598$	−1.38120	−	3.79482i	−0.0564816	−	0.155182i
$599$	−18.6975	−	15.6891i	−0.763961	−	0.641039i	0.175194	−	0.984534i	$-0.443945\pi$
$599$	−18.6975	−	15.6891i	−0.763961	−	0.641039i	−0.939155	+	0.343495i	$0.888389\pi$
$600$		0			0
$601$	−7.39563	−	2.69179i	−0.301674	−	0.109800i	0.186748	−	0.982408i	$-0.440205\pi$
$601$	−7.39563	−	2.69179i	−0.301674	−	0.109800i	−0.488422	+	0.872607i	$0.662427\pi$
$602$	9.71647	−	5.60981i	0.396014	−	0.228639i
$603$	−29.0768	−	8.37478i	−1.18410	−	0.341047i
$604$	8.99922	−	15.5871i	0.366173	−	0.634230i
$605$		0			0
$606$	−2.06147	+	8.90521i	−0.0837413	+	0.361749i
$607$	−10.0819	−	1.77772i	−0.409213	−	0.0721553i	−0.0347476	−	0.999396i	$-0.511063\pi$
$607$	−10.0819	−	1.77772i	−0.409213	−	0.0721553i	−0.374466	+	0.927241i	$0.622174\pi$
$608$	−1.12350	−	0.198103i	−0.0455639	−	0.00803414i
$609$	−0.492214	+	2.12629i	−0.0199455	+	0.0861615i
$610$		0			0
$611$	−12.0602	+	20.8889i	−0.487905	+	0.845076i
$612$	17.0240	+	4.90329i	0.688153	+	0.198204i
$613$	−1.93563	+	1.11753i	−0.0781792	+	0.0451368i	−0.538580	−	0.842574i	$-0.681039\pi$
$613$	−1.93563	+	1.11753i	−0.0781792	+	0.0451368i	0.460401	+	0.887711i	$0.347706\pi$
$614$	6.66646	+	2.42639i	0.269036	+	0.0979213i
$615$		0			0
$616$	7.19547	+	6.03771i	0.289914	+	0.243266i
$617$	−11.6204	−	31.9267i	−0.467818	−	1.28532i	−0.919482	−	0.393132i	$-0.871391\pi$
$617$	−11.6204	−	31.9267i	−0.467818	−	1.28532i	0.451664	−	0.892188i	$-0.350831\pi$
$618$	−17.7883	−	11.5668i	−0.715551	−	0.465285i
$619$	5.01079	+	28.4176i	0.201401	+	1.14220i	0.903004	+	0.429632i	$0.141357\pi$
$619$	5.01079	+	28.4176i	0.201401	+	1.14220i	−0.701604	+	0.712567i	$0.747532\pi$
$620$		0			0
$621$	4.29625	−	0.827216i	0.172403	−	0.0331950i
$622$			16.2613i			0.652020i
$623$	16.2358	−	2.86280i	0.650472	−	0.114696i
$624$	−5.12338	−	10.0699i	−0.205099	−	0.403118i
$625$		0			0
$626$	−19.0292	−	15.9674i	−0.760558	−	0.638184i
$627$	0.211780	−	0.498105i	0.00845768	−	0.0198924i
$628$	−6.30485	+	17.3224i	−0.251591	+	0.691240i
$629$	−8.66811	−	15.0136i	−0.345620	−	0.598632i
$630$		0			0
$631$	1.57039	−	2.71999i	0.0625162	−	0.108281i	−0.833073	−	0.553163i	$-0.813421\pi$
$631$	1.57039	−	2.71999i	0.0625162	−	0.108281i	0.895590	+	0.444881i	$0.146754\pi$
$632$	−9.35076	−	11.1438i	−0.371953	−	0.443277i
$633$	4.36299	−	4.67320i	0.173413	−	0.185743i
$634$	−1.32772	+	7.52985i	−0.0527303	+	0.299049i
$635$		0			0
$636$	15.4303	−	4.70757i	0.611852	−	0.186667i
$637$	2.78402	+	3.31786i	0.110307	+	0.131458i
$638$	0.586774	+	0.338774i	0.0232306	+	0.0134122i
$639$	0.158034	−	0.216976i	0.00625171	−	0.00858342i
$640$		0			0
$641$	29.9034	+	10.8839i	1.18111	+	0.429890i	0.856595	−	0.515989i	$-0.172576\pi$
$641$	29.9034	+	10.8839i	1.18111	+	0.429890i	0.324518	+	0.945879i	$0.394798\pi$
$642$	35.2710	−	4.30961i	1.39204	−	0.170087i
$643$	−8.25794	+	9.84142i	−0.325661	+	0.388108i	−0.903889	−	0.427768i	$-0.859300\pi$
$643$	−8.25794	+	9.84142i	−0.325661	+	0.388108i	0.578228	+	0.815876i	$0.303745\pi$
$644$	−1.72866	+	0.629179i	−0.0681186	+	0.0247931i
$645$		0			0
$646$	−0.303217	−	1.71963i	−0.0119299	−	0.0676578i
$647$			28.2444i			1.11040i	0.831717	+	0.555200i	$0.187358\pi$
$647$			28.2444i			1.11040i	−0.831717	+	0.555200i	$0.812642\pi$
$648$	26.0863	−	8.40792i	1.02477	−	0.330294i
$649$	−3.77042			−0.148002
$650$		0			0
$651$	3.48794	+	0.184859i	0.136703	+	0.00724521i
$652$	−6.11790	−	16.8088i	−0.239595	−	0.658283i
$653$	16.7064	−	19.9099i	0.653771	−	0.779134i	−0.332707	−	0.943030i	$-0.607962\pi$
$653$	16.7064	−	19.9099i	0.653771	−	0.779134i	0.986477	+	0.163897i	$0.0524064\pi$
$654$	1.39869	+	11.4472i	0.0546930	+	0.447622i
$655$		0			0
$656$	−5.84536	−	10.1245i	−0.228223	−	0.395294i
$657$	−14.5910	+	6.47569i	−0.569248	+	0.252641i
$658$	−11.9062	−	6.87407i	−0.464153	−	0.267979i
$659$	36.4774	−	30.6081i	1.42096	−	1.19232i	0.470131	−	0.882597i	$-0.344207\pi$
$659$	36.4774	−	30.6081i	1.42096	−	1.19232i	0.950826	−	0.309727i	$-0.100238\pi$
$660$		0			0
$661$	−0.152204	+	0.863192i	−0.00592005	+	0.0335743i	−0.987625	−	0.156836i	$-0.949871\pi$
$661$	−0.152204	+	0.863192i	−0.00592005	+	0.0335743i	0.981705	+	0.190410i	$0.0609818\pi$
$662$	30.1467	+	5.31568i	1.17168	+	0.206600i
$663$	−35.7416	+	38.2829i	−1.38809	+	1.48678i
$664$	18.7576	−	15.7395i	0.727936	−	0.610811i
$665$		0			0
$666$	−7.41009	−	3.62497i	−0.287135	−	0.140465i
$667$	−0.373627	+	0.215714i	−0.0144669	+	0.00835246i
$668$	−6.03526	+	16.5817i	−0.233511	+	0.641567i
$669$	33.8574	+	14.3952i	1.30900	+	0.556551i
$670$		0			0
$671$	3.39803	−	1.23678i	0.131180	−	0.0477455i
$672$	−17.3829	+	8.84413i	−0.670562	+	0.341170i
$673$	36.7722	−	6.48393i	1.41746	−	0.249937i	0.588164	−	0.808742i	$-0.299851\pi$
$673$	36.7722	−	6.48393i	1.41746	−	0.249937i	0.829299	+	0.558805i	$0.188740\pi$
$674$	1.22206			0.0470721
$675$		0			0
$676$	−6.83505			−0.262886
$677$	13.5107	−	2.38231i	0.519260	−	0.0915596i	0.0921251	−	0.995747i	$-0.470634\pi$
$677$	13.5107	−	2.38231i	0.519260	−	0.0915596i	0.427135	+	0.904188i	$0.359523\pi$
$678$	10.5876	+	6.88456i	0.406614	+	0.264400i
$679$	12.6884	−	4.61819i	0.486935	−	0.177230i
$680$		0			0
$681$	19.8451	−	14.9360i	0.760465	−	0.572348i
$682$	0.370863	−	1.01894i	0.0142011	−	0.0390171i
$683$	−43.2914	+	24.9943i	−1.65650	+	0.956381i	−0.682190	+	0.731175i	$0.738972\pi$
$683$	−43.2914	+	24.9943i	−1.65650	+	0.956381i	−0.974311	+	0.225206i	$0.927694\pi$
$684$	0.460724	+	0.478222i	0.0176162	+	0.0182853i
$685$		0			0
$686$	−15.7947	+	13.2534i	−0.603046	+	0.506016i
$687$	−28.4936	−	6.59598i	−1.08710	−	0.251652i
$688$	6.11064	+	1.07747i	0.232966	+	0.0410782i
$689$	−8.28172	+	46.9680i	−0.315509	+	1.78934i
$690$		0			0
$691$	18.2434	−	15.3080i	0.694011	−	0.582345i	−0.226052	−	0.974115i	$-0.572582\pi$
$691$	18.2434	−	15.3080i	0.694011	−	0.582345i	0.920063	+	0.391771i	$0.128137\pi$
$692$	14.5605	+	8.40653i	0.553508	+	0.319568i
$693$	−2.22797	−	8.98103i	−0.0846335	−	0.341161i
$694$	3.10483	+	5.37773i	0.117858	+	0.204136i
$695$		0			0
$696$	−2.15938	+	1.62521i	−0.0818510	+	0.0616035i
$697$	−34.8347	+	41.5144i	−1.31946	+	1.57247i
$698$	−11.0317	−	30.3094i	−0.417557	−	1.14723i
$699$	−5.28700	+	8.13075i	−0.199973	+	0.307533i
$700$		0			0
$701$	34.4493			1.30113			0.650565	−	0.759450i	$-0.274532\pi$
$701$	34.4493			1.30113			0.650565	+	0.759450i	$0.274532\pi$
$702$	−3.94216	+	24.6078i	−0.148787	+	0.928761i
$703$		−	0.649815i		−	0.0245082i
$704$	1.67600	+	9.50506i	0.0631665	+	0.358235i
$705$		0			0
$706$	−36.6191	+	13.3282i	−1.37818	+	0.501615i
$707$	−7.91250	+	9.42975i	−0.297580	+	0.354642i
$708$	1.80996	−	4.25701i	0.0680224	−	0.159988i
$709$	14.5871	+	5.30927i	0.547830	+	0.199394i	0.601082	−	0.799187i	$-0.294736\pi$
$709$	14.5871	+	5.30927i	0.547830	+	0.199394i	−0.0532520	+	0.998581i	$0.516959\pi$
$710$		0			0
$711$	0.982789	+	14.2970i	0.0368575	+	0.536180i
$712$	17.6800	+	10.2075i	0.662585	+	0.382543i
$713$	0.443809	+	0.528911i	0.0166208	+	0.0198079i
$714$	−21.8204	−	20.3719i	−0.816607	−	0.762400i
$715$		0			0
$716$	−1.68364	+	9.54839i	−0.0629205	+	0.356840i
$717$	−2.66575	−	8.73772i	−0.0995543	−	0.326316i
$718$	17.8752	+	21.3029i	0.667098	+	0.795016i
$719$	6.02686	−	10.4388i	0.224764	−	0.389303i	−0.731485	−	0.681858i	$-0.761172\pi$
$719$	6.02686	−	10.4388i	0.224764	−	0.389303i	0.956249	+	0.292555i	$0.0945056\pi$
$720$		0			0
$721$	−14.2872	−	24.7461i	−0.532083	−	0.921594i
$722$	−6.82902	+	18.7626i	−0.254150	+	0.698271i
$723$	15.3057	−	1.87014i	0.569226	−	0.0695512i
$724$	−12.2145	−	10.2492i	−0.453947	−	0.380907i
$725$		0			0
$726$	17.1908	+	0.911107i	0.638012	+	0.0338144i
$727$	31.1497	−	5.49253i	1.15528	−	0.203707i	0.437000	−	0.899462i	$-0.356041\pi$
$727$	31.1497	−	5.49253i	1.15528	−	0.203707i	0.718279	+	0.695755i	$0.244930\pi$
$728$		−	34.0685i		−	1.26266i
$729$	−25.6488	−	8.43433i	−0.949956	−	0.312383i
$730$		0			0
$731$	−4.99469	−	28.3263i	−0.184735	−	1.04769i
$732$	−0.234802	+	4.43027i	−0.00867855	+	0.163748i
$733$	−6.50891	−	17.8831i	−0.240412	−	0.660527i	−0.999949	−	0.0100630i	$-0.996797\pi$
$733$	−6.50891	−	17.8831i	−0.240412	−	0.660527i	0.759537	−	0.650464i	$-0.225425\pi$
$734$	9.13716	+	7.66699i	0.337259	+	0.282994i
$735$		0			0
$736$	−3.62283	−	1.31860i	−0.133539	−	0.0486043i
$737$	−10.9555	+	6.32516i	−0.403551	+	0.232990i
$738$	−2.72576	+	25.6427i	−0.100337	+	0.943920i
$739$	8.30036	−	14.3767i	0.305334	−	0.528854i	−0.672002	−	0.740550i	$-0.734565\pi$
$739$	8.30036	−	14.3767i	0.305334	−	0.528854i	0.977336	+	0.211696i	$0.0678986\pi$
$740$		0			0
$741$	−1.87770	+	0.572858i	−0.0689789	+	0.0210445i
$742$	−26.7707	−	4.72040i	−0.982783	−	0.173291i
$743$	32.7976	+	5.78310i	1.20323	+	0.212161i	0.739093	−	0.673604i	$-0.235255\pi$
$743$	32.7976	+	5.78310i	1.20323	+	0.212161i	0.464134	+	0.885765i	$0.346366\pi$
$744$	3.16152	+	2.95166i	0.115907	+	0.108213i
$745$		0			0
$746$	−3.08078	+	5.33606i	−0.112795	+	0.195367i
$747$	−24.0652	+	1.65426i	−0.880499	+	0.0605263i
$748$	6.41426	−	3.70328i	0.234529	−	0.135405i
$749$	44.9665	+	16.3665i	1.64304	+	0.598017i
$750$		0			0
$751$	21.2819	+	17.8577i	0.776589	+	0.651636i	0.942387	−	0.334524i	$-0.108576\pi$
$751$	21.2819	+	17.8577i	0.776589	+	0.651636i	−0.165798	+	0.986160i	$0.553020\pi$
$752$	−2.60047	−	7.14474i	−0.0948295	−	0.260542i
$753$	−12.0106	+	6.11076i	−0.437689	+	0.222688i
$754$	−0.426735	−	2.42013i	−0.0155408	−	0.0881361i
$755$		0			0
$756$	11.2096	+	1.79577i	0.407689	+	0.0653116i
$757$		−	3.12036i		−	0.113411i	−0.998391	−	0.0567057i	$-0.981940\pi$
$757$		−	3.12036i		−	0.113411i	0.998391	−	0.0567057i	$-0.0180597\pi$
$758$	25.2583	−	4.45373i	0.917424	−	0.161767i
$759$	0.997121	−	1.53345i	0.0361932	−	0.0556607i
$760$		0			0
$761$	−33.6747	−	28.2564i	−1.22071	−	1.02429i	−0.998787	−	0.0492297i	$-0.984323\pi$
$761$	−33.6747	−	28.2564i	−1.22071	−	1.02429i	−0.221919	−	0.975065i	$-0.571232\pi$
$762$	−13.2032	−	17.5428i	−0.478302	−	0.635508i
$763$	−5.31175	+	14.5939i	−0.192298	+	0.528335i
$764$	11.9783	+	20.7470i	0.433360	+	0.750602i
$765$		0			0
$766$	2.01168	−	3.48433i	0.0726849	−	0.125894i
$767$	8.79032	+	10.4759i	0.317400	+	0.378263i
$768$	−27.8284	−	6.44200i	−1.00417	−	0.232456i
$769$	−0.644731	+	3.65645i	−0.0232496	+	0.131855i	−0.994223	−	0.107331i	$-0.965769\pi$
$769$	−0.644731	+	3.65645i	−0.0232496	+	0.131855i	0.970974	+	0.239186i	$0.0768806\pi$
$770$		0			0
$771$	7.98298	−	34.4852i	0.287500	−	1.24195i
$772$	9.79629	+	11.6748i	0.352576	+	0.420184i
$773$	−7.76741	−	4.48452i	−0.279374	−	0.161297i	0.353766	−	0.935334i	$-0.384901\pi$
$773$	−7.76741	−	4.48452i	−0.279374	−	0.161297i	−0.633140	+	0.774037i	$0.718234\pi$
$774$	−9.49592	−	9.85656i	−0.341324	−	0.354287i
$775$		0			0
$776$	15.7121	+	5.71875i	0.564033	+	0.205291i
$777$	−6.68041	−	8.87610i	−0.239658	−	0.318428i
$778$	7.34760	−	8.75652i	0.263424	−	0.313937i
$779$	−1.90882	+	0.694754i	−0.0683906	+	0.0248921i
$780$		0			0
$781$	−0.0194871	−	0.110517i	−0.000697302	−	0.00395459i
$782$		−	5.90098i		−	0.211018i
$783$	2.66209	−	0.0417527i	0.0951354	−	0.00149212i
$784$	−1.36527			−0.0487597
$785$		0			0
$786$	−11.6635	−	22.9243i	−0.416023	−	0.817684i
$787$	−14.9981	−	41.2069i	−0.534624	−	1.46887i	−0.853512	−	0.521074i	$-0.825532\pi$
$787$	−14.9981	−	41.2069i	−0.534624	−	1.46887i	0.318888	−	0.947792i	$-0.396691\pi$
$788$	−1.43462	+	1.70972i	−0.0511063	+	0.0609062i
$789$	−17.9796	−	7.64441i	−0.640090	−	0.272148i
$790$		0			0
$791$	8.50374	+	14.7289i	0.302358	+	0.523699i
$792$	5.03519	−	10.2928i	0.178918	−	0.365739i
$793$	−11.3585	−	6.55782i	−0.403351	−	0.232875i
$794$	8.48787	−	7.12217i	0.301223	−	0.252756i
$795$		0			0
$796$	−2.85997	+	16.2197i	−0.101369	+	0.574891i
$797$	11.8335	+	2.08656i	0.419163	+	0.0739097i	0.379252	−	0.925294i	$-0.376181\pi$
$797$	11.8335	+	2.08656i	0.419163	+	0.0739097i	0.0399111	+	0.999203i	$0.487293\pi$
$798$	−0.326516	−	1.07025i	−0.0115586	−	0.0378863i
$799$	−26.9996	+	22.6554i	−0.955178	+	0.801490i
$800$		0			0
$801$	−8.15832	−	18.3822i	−0.288260	−	0.649504i
$802$	13.1168	−	7.57299i	0.463171	−	0.267412i
$803$	−2.28259	+	6.27136i	−0.0805508	+	0.221311i
$804$	−1.88235	−	15.4057i	−0.0663855	−	0.543317i
$805$		0			0
$806$	−3.69568	+	1.34512i	−0.130175	+	0.0473798i
$807$	−0.0282122	+	0.532311i	−0.000993117	+	0.0187382i
$808$	−15.0116	+	2.64695i	−0.528107	+	0.0931195i
$809$	8.02937			0.282298			0.141149	−	0.989988i	$-0.454920\pi$
$809$	8.02937			0.282298			0.141149	+	0.989988i	$0.454920\pi$
$810$		0			0
$811$	−12.8345			−0.450681			−0.225341	−	0.974280i	$-0.572349\pi$
$811$	−12.8345			−0.450681			−0.225341	+	0.974280i	$0.572349\pi$
$812$	−1.10244	+	0.194391i	−0.0386882	+	0.00682177i
$813$	0.203736	−	3.84411i	0.00714534	−	0.134819i
$814$	−3.24078	+	1.17955i	−0.113589	+	0.0413431i
$815$		0			0
$816$	−2.00232	−	16.3875i	−0.0700951	−	0.573678i
$817$	0.368744	−	1.01312i	0.0129007	−	0.0354444i
$818$	−16.1452	+	9.32142i	−0.564503	+	0.325916i
$819$	−19.7590	+	27.1286i	−0.690436	+	0.947949i
$820$		0			0
$821$	−22.7250	+	19.0685i	−0.793108	+	0.665497i	−0.946513	−	0.322667i	$-0.895421\pi$
$821$	−22.7250	+	19.0685i	−0.793108	+	0.665497i	0.153404	+	0.988163i	$0.450976\pi$
$822$	1.20332	+	3.94422i	0.0419707	+	0.137570i
$823$	−48.7881	−	8.60266i	−1.70065	−	0.299870i	−0.762726	−	0.646722i	$-0.776139\pi$
$823$	−48.7881	−	8.60266i	−1.70065	−	0.299870i	−0.937920	+	0.346852i	$0.887251\pi$
$824$	6.14436	−	34.8464i	0.214049	−	1.21393i
$825$		0			0
$826$	−5.97102	+	5.01028i	−0.207758	+	0.174330i
$827$	−35.3711	−	20.4215i	−1.22997	−	0.710126i	−0.262950	−	0.964809i	$-0.584695\pi$
$827$	−35.3711	−	20.4215i	−1.22997	−	0.710126i	−0.967025	+	0.254683i	$0.918029\pi$
$828$	1.25269	+	1.86192i	0.0435339	+	0.0647063i
$829$	−4.72638	−	8.18633i	−0.164154	−	0.284323i	0.772201	−	0.635379i	$-0.219156\pi$
$829$	−4.72638	−	8.18633i	−0.164154	−	0.284323i	−0.936355	+	0.351056i	$0.885823\pi$
$830$		0			0
$831$	−37.1867	−	15.8107i	−1.28999	−	0.548468i
$832$	22.5018	−	26.8167i	0.780111	−	0.929700i
$833$	2.16458	+	5.94714i	0.0749983	+	0.206056i
$834$	6.60411	+	12.9802i	0.228682	+	0.449468i
$835$		0			0
$836$	0.277620			0.00960170
$837$	−0.805605	−	4.18401i	−0.0278458	−	0.144621i
$838$		−	9.62995i		−	0.332661i
$839$	2.13360	+	12.1002i	0.0736599	+	0.417746i	0.999232	+	0.0391756i	$0.0124732\pi$
$839$	2.13360	+	12.1002i	0.0736599	+	0.417746i	−0.925572	+	0.378571i	$0.876416\pi$
$840$		0			0
$841$	27.0044	−	9.82879i	0.931186	−	0.338924i
$842$	−16.3971	+	19.5413i	−0.565080	+	0.673436i
$843$	7.52573	+	9.99925i	0.259200	+	0.344392i
$844$	3.08148	+	1.12157i	0.106069	+	0.0386059i
$845$		0			0
$846$	−4.64178	+	16.1160i	−0.159588	+	0.554079i
$847$	20.0772	+	11.5916i	0.689862	+	0.398292i
$848$	−9.66346	−	11.5165i	−0.331845	−	0.395477i
$849$	2.78135	−	12.0150i	0.0954556	−	0.412353i
$850$		0			0
$851$	0.381330	−	2.16263i	0.0130718	−	0.0741339i
$852$	0.134134	+	0.0310506i	0.00459535	+	0.00106378i
$853$	19.8402	+	23.6446i	0.679315	+	0.809576i	0.990020	−	0.140930i	$-0.0450094\pi$
$853$	19.8402	+	23.6446i	0.679315	+	0.809576i	−0.310704	+	0.950507i	$0.600565\pi$
$854$	3.73781	−	6.47408i	0.127905	−	0.221538i
$855$		0			0
$856$	29.6280	+	51.3172i	1.01266	+	1.75399i
$857$	3.81217	−	10.4738i	0.130221	−	0.357780i	−0.857397	−	0.514655i	$-0.827920\pi$
$857$	3.81217	−	10.4738i	0.130221	−	0.357780i	0.987618	+	0.156876i	$0.0501422\pi$
$858$	6.26539	+	8.32466i	0.213897	+	0.284199i
$859$	−3.17807	−	2.66672i	−0.108434	−	0.0909872i	0.586958	−	0.809617i	$-0.300325\pi$
$859$	−3.17807	−	2.66672i	−0.108434	−	0.0909872i	−0.695393	+	0.718630i	$0.744770\pi$
$860$		0			0
$861$	−18.9310	+	29.1135i	−0.645167	+	0.992187i
$862$	30.6645	−	5.40698i	1.04444	−	0.184163i
$863$			47.2534i			1.60852i	0.594275	+	0.804262i	$0.297439\pi$
$863$			47.2534i			1.60852i	−0.594275	+	0.804262i	$0.702561\pi$
$864$	15.5771	+	17.9837i	0.529945	+	0.611817i
$865$		0			0
$866$	0.122620	+	0.695411i	0.00416678	+	0.0236310i
$867$	−41.9662	+	21.3516i	−1.42525	+	0.725140i
$868$	0.612742	+	1.68349i	0.0207978	+	0.0571415i
$869$	4.58958	+	3.85112i	0.155691	+	0.130640i
$870$		0			0
$871$	43.1156	+	15.6928i	1.46092	+	0.531731i
$872$	−16.6550	+	9.61579i	−0.564011	+	0.325632i
$873$	−9.19475	−	13.6665i	−0.311195	−	0.462543i
$874$	0.110593	−	0.191553i	0.00374087	−	0.00647938i
$875$		0			0
$876$	−5.98497	−	5.58768i	−0.202213	−	0.188790i
$877$	34.6164	+	6.10381i	1.16891	+	0.206111i	0.724218	−	0.689571i	$-0.242201\pi$
$877$	34.6164	+	6.10381i	1.16891	+	0.206111i	0.444695	+	0.895682i	$0.353312\pi$
$878$	6.59208	+	1.16236i	0.222472	+	0.0392278i
$879$	−0.915284	+	0.279240i	−0.0308718	+	0.00941852i
$880$		0			0
$881$	9.67981	−	16.7659i	0.326121	−	0.564858i	−0.655618	−	0.755093i	$-0.727592\pi$
$881$	9.67981	−	16.7659i	0.326121	−	0.564858i	0.981739	+	0.190235i	$0.0609250\pi$
$882$	2.43425	+	1.77298i	0.0819656	+	0.0596994i
$883$	11.9391	−	6.89302i	0.401781	−	0.231969i	−0.285471	−	0.958387i	$-0.592150\pi$
$883$	11.9391	−	6.89302i	0.401781	−	0.231969i	0.687252	+	0.726419i	$0.258817\pi$
$884$	−25.2435	−	9.18788i	−0.849031	−	0.309022i
$885$		0			0
$886$	12.4007	+	10.4055i	0.416611	+	0.349578i
$887$	10.1982	+	28.0192i	0.342421	+	0.940794i	0.984690	+	0.174315i	$0.0557710\pi$
$887$	10.1982	+	28.0192i	0.342421	+	0.940794i	−0.642269	+	0.766479i	$0.722007\pi$
$888$	0.728070	−	13.7373i	0.0244324	−	0.460993i
$889$	−5.13445	−	29.1189i	−0.172204	−	0.976617i
$890$		0			0
$891$	−9.97912	+	5.27581i	−0.334313	+	0.176746i
$892$			18.8705i			0.631832i
$893$	−1.30104	+	0.229408i	−0.0435376	+	0.00767685i
$894$	−0.195011	−	0.0103355i	−0.00652215	−	0.000345671i
$895$		0			0
$896$	−1.96694	−	1.65046i	−0.0657109	−	0.0551380i
$897$	−6.58528	+	0.804626i	−0.219876	+	0.0268657i
$898$	11.5536	−	31.7432i	0.385548	−	1.05928i
$899$	0.210078	+	0.363866i	0.00700649	+	0.0121356i
$900$		0			0
$901$	−34.8448	+	60.3530i	−1.16085	+	2.01065i
$902$	6.92980	+	8.25862i	0.230737	+	0.274982i
$903$	−5.37849	−	17.6294i	−0.178985	−	0.586671i
$904$	−3.65712	+	20.7406i	−0.121634	+	0.689821i
$905$		0			0
$906$	27.0427	+	25.2476i	0.898434	+	0.838795i
$907$	−4.00558	−	4.77366i	−0.133003	−	0.158507i	0.695432	−	0.718592i	$-0.255213\pi$
$907$	−4.00558	−	4.77366i	−0.133003	−	0.158507i	−0.828435	+	0.560085i	$0.810769\pi$
$908$	11.0329	+	6.36984i	0.366139	+	0.211391i
$909$	13.4889	+	6.59868i	0.447397	+	0.218864i
$910$		0			0
$911$	29.7314	+	10.8213i	0.985044	+	0.358527i	0.783799	−	0.621014i	$-0.213279\pi$
$911$	29.7314	+	10.8213i	0.985044	+	0.358527i	0.201245	+	0.979541i	$0.435501\pi$
$912$	0.242129	−	0.569486i	0.00801770	−	0.0188576i
$913$	−6.48232	+	7.72533i	−0.214534	+	0.255671i
$914$	18.9906	−	6.91200i	0.628152	−	0.228629i
$915$		0			0
$916$	−2.60496	−	14.7734i	−0.0860701	−	0.488128i
$917$		−	34.6380i		−	1.14385i
$918$	−17.7112	+	31.8189i	−0.584557	+	1.05018i
$919$	−36.0031			−1.18763			−0.593816	−	0.804601i	$-0.702379\pi$
$919$	−36.0031			−1.18763			−0.593816	+	0.804601i	$0.702379\pi$
$920$		0			0
$921$	6.35329	−	9.77058i	0.209348	−	0.321952i
$922$	1.88244	+	5.17196i	0.0619948	+	0.170329i
$923$	−0.261632	+	0.311801i	−0.00861173	+	0.0102631i
$924$	3.79213	−	2.85407i	0.124752	−	0.0938921i
$925$		0			0
$926$	−0.894800	−	1.54984i	−0.0294049	−	0.0509309i
$927$	−25.1029	+	24.1844i	−0.824489	+	0.794321i
$928$	−2.03177	−	1.17304i	−0.0666961	−	0.0385070i
$929$	−19.4941	+	16.3575i	−0.639580	+	0.536672i	−0.903889	−	0.427767i	$-0.859301\pi$
$929$	−19.4941	+	16.3575i	−0.639580	+	0.536672i	0.264309	+	0.964438i	$0.414856\pi$
$930$		0			0
$931$	−0.0411934	+	0.233619i	−0.00135006	+	0.00765656i
$932$	−4.89897	−	0.863820i	−0.160471	−	0.0282954i
$933$	26.0260	+	6.02475i	0.852052	+	0.197241i
$934$	−15.8969	+	13.3391i	−0.520164	+	0.436469i
$935$		0			0
$936$	−40.3370	+	10.0066i	−1.31846	+	0.327075i
$937$	24.5127	−	14.1524i	0.800794	−	0.462338i	−0.0429549	−	0.999077i	$-0.513677\pi$
$937$	24.5127	−	14.1524i	0.800794	−	0.462338i	0.843749	+	0.536739i	$0.180344\pi$
$938$	−8.94455	+	24.5750i	−0.292050	+	0.802401i
$939$	−32.6057	+	24.5400i	−1.06405	+	0.800833i
$940$		0			0
$941$	−7.79422	+	2.83687i	−0.254084	+	0.0924792i	−0.465922	−	0.884826i	$-0.654277\pi$
$941$	−7.79422	+	2.83687i	−0.254084	+	0.0924792i	0.211838	+	0.977305i	$0.432055\pi$
$942$	−31.7669	−	20.6563i	−1.03502	−	0.673019i
$943$	−6.76039	+	1.19204i	−0.220149	+	0.0388181i
$944$	−4.31074			−0.140303
$945$		0			0
$946$	−5.72199			−0.186038
$947$	43.7753	−	7.71877i	1.42251	−	0.250826i	0.591148	−	0.806563i	$-0.298675\pi$
$947$	43.7753	−	7.71877i	1.42251	−	0.250826i	0.831358	+	0.555737i	$0.187564\pi$
$948$	−6.55131	+	3.33319i	−0.212777	+	0.108257i
$949$	22.7462	−	8.27895i	0.738373	−	0.268746i
$950$		0			0
$951$	11.5595	+	4.91476i	0.374842	+	0.159372i
$952$	17.0264	−	46.7796i	0.551828	−	1.51613i
$953$	8.37576	−	4.83574i	0.271317	−	0.156645i	−0.358169	−	0.933657i	$-0.616599\pi$
$953$	8.37576	−	4.83574i	0.271317	−	0.156645i	0.629486	+	0.777012i	$0.283265\pi$
$954$	2.27415	+	33.0829i	0.0736283	+	1.07110i
$955$		0			0
$956$	3.58942	−	3.01188i	0.116090	−	0.0974113i
$957$	0.759599	−	0.813608i	0.0245544	−	0.0263002i
$958$	30.3740	+	5.35576i	0.981341	+	0.173037i
$959$	−0.964325	+	5.46896i	−0.0311397	+	0.176602i
$960$		0			0
$961$	−23.2323	+	19.4942i	−0.749429	+	0.628845i
$962$	10.8328	+	6.25433i	0.349264	+	0.201648i
$963$	6.17030	−	58.0473i	0.198835	−	1.87055i
$964$	3.95448	+	6.84936i	0.127365	+	0.220603i
$965$		0			0
$966$	−0.458619	−	3.75346i	−0.0147558	−	0.120766i
$967$	21.2860	−	25.3676i	0.684510	−	0.815768i	−0.306170	−	0.951977i	$-0.599047\pi$
$967$	21.2860	−	25.3676i	0.684510	−	0.815768i	0.990680	+	0.136209i	$0.0434919\pi$
$968$	9.81871	+	26.9767i	0.315585	+	0.867064i
$969$	−2.86457	−	0.151821i	−0.0920234	−	0.00487720i
$970$		0			0
$971$	−27.4309			−0.880298			−0.440149	−	0.897925i	$-0.645074\pi$
$971$	−27.4309			−0.880298			−0.440149	+	0.897925i	$0.645074\pi$
$972$	−1.16629	−	13.7996i	−0.0374087	−	0.442622i
$973$			19.6127i			0.628755i
$974$	3.75420	+	21.2912i	0.120292	+	0.682213i
$975$		0			0
$976$	3.88499	−	1.41402i	0.124356	−	0.0452617i
$977$	−23.3831	+	27.8668i	−0.748090	+	0.891539i	−0.997033	−	0.0769792i	$-0.975473\pi$
$977$	−23.3831	+	27.8668i	−0.748090	+	0.891539i	0.248943	+	0.968518i	$0.419917\pi$
$978$	36.4972	−	4.45943i	1.16705	−	0.142597i
$979$	−7.90089	−	2.87569i	−0.252514	−	0.0919075i
$980$		0			0
$981$	18.8393	+	2.00258i	0.601493	+	0.0639373i
$982$	−16.0034	−	9.23957i	−0.510689	−	0.294847i
$983$	−27.0853	−	32.2790i	−0.863886	−	1.02954i	−0.999249	−	0.0387434i	$-0.987665\pi$
$983$	−27.0853	−	32.2790i	−0.863886	−	1.02954i	0.135363	−	0.990796i	$-0.456780\pi$
$984$	−41.1315	+	12.5486i	−1.31122	+	0.400035i
$985$		0			0
$986$	0.623557	−	3.53637i	0.0198581	−	0.112621i
$987$	−15.4130	+	16.5089i	−0.490602	+	0.525484i
$988$	−0.647241	−	0.771352i	−0.0205915	−	0.0245400i
$989$	1.82173	−	3.15533i	0.0579276	−	0.100334i
$990$		0			0
$991$	−12.7705	−	22.1191i	−0.405667	−	0.702635i	0.588732	−	0.808328i	$-0.299627\pi$
$991$	−12.7705	−	22.1191i	−0.405667	−	0.702635i	−0.994399	+	0.105693i	$0.966294\pi$
$992$	−1.28415	+	3.52818i	−0.0407719	+	0.112020i
$993$	19.6769	−	46.2798i	0.624426	−	1.46865i
$994$	−0.177720	−	0.149124i	−0.00563692	−	0.00472994i
$995$		0			0
$996$	−5.61053	−	11.0274i	−0.177776	−	0.349416i
$997$	−23.1754	+	4.08644i	−0.733971	+	0.129419i	−0.528126	−	0.849166i	$-0.677105\pi$
$997$	−23.1754	+	4.08644i	−0.733971	+	0.129419i	−0.205845	+	0.978585i	$0.565994\pi$
$998$			20.1439i			0.637644i
$999$	−8.54711	+	10.5167i	−0.270419	+	0.332733i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	675.2.u.b.499.2		24
5.2	odd	4		675.2.l.c.526.1		12
5.3	odd	4		27.2.e.a.13.2	✓	12
5.4	even	2	inner	675.2.u.b.499.3		24
15.8	even	4		81.2.e.a.10.1		12
20.3	even	4		432.2.u.c.337.2		12
27.25	even	9	inner	675.2.u.b.349.3		24
45.13	odd	12		243.2.e.d.190.1		12
45.23	even	12		243.2.e.a.190.2		12
45.38	even	12		243.2.e.b.109.1		12
45.43	odd	12		243.2.e.c.109.2		12
135.13	odd	36		729.2.c.e.244.2		12
135.23	even	36		729.2.c.b.487.5		12
135.38	even	36		243.2.e.a.55.2		12
135.43	odd	36		243.2.e.d.55.1		12
135.52	odd	36		675.2.l.c.376.1		12
135.58	odd	36		729.2.c.e.487.2		12
135.68	even	36		729.2.c.b.244.5		12
135.79	even	18	inner	675.2.u.b.349.2		24
135.83	even	36		81.2.e.a.73.1		12
135.88	odd	36		243.2.e.c.136.2		12
135.103	odd	36		729.2.a.a.1.5		6
135.113	even	36		729.2.a.d.1.2		6
135.128	even	36		243.2.e.b.136.1		12
135.133	odd	36		27.2.e.a.25.2	yes	12
540.403	even	36		432.2.u.c.241.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.2.e.a.13.2	✓	12	5.3	odd	4
27.2.e.a.25.2	yes	12	135.133	odd	36
81.2.e.a.10.1		12	15.8	even	4
81.2.e.a.73.1		12	135.83	even	36
243.2.e.a.55.2		12	135.38	even	36
243.2.e.a.190.2		12	45.23	even	12
243.2.e.b.109.1		12	45.38	even	12
243.2.e.b.136.1		12	135.128	even	36
243.2.e.c.109.2		12	45.43	odd	12
243.2.e.c.136.2		12	135.88	odd	36
243.2.e.d.55.1		12	135.43	odd	36
243.2.e.d.190.1		12	45.13	odd	12
432.2.u.c.241.2		12	540.403	even	36
432.2.u.c.337.2		12	20.3	even	4
675.2.l.c.376.1		12	135.52	odd	36
675.2.l.c.526.1		12	5.2	odd	4
675.2.u.b.349.2		24	135.79	even	18	inner
675.2.u.b.349.3		24	27.25	even	9	inner
675.2.u.b.499.2		24	1.1	even	1	trivial
675.2.u.b.499.3		24	5.4	even	2	inner
729.2.a.a.1.5		6	135.103	odd	36
729.2.a.d.1.2		6	135.113	even	36
729.2.c.b.244.5		12	135.68	even	36
729.2.c.b.487.5		12	135.23	even	36
729.2.c.e.244.2		12	135.13	odd	36
729.2.c.e.487.2		12	135.58	odd	36

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:	\( N \)	\(=\)	\( 675 = 3^{3} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	675.u (of order \(18\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.03831 + 0.183082i) q^{2} +(-0.0916693 + 1.72962i) q^{3} +(-0.834822 + 0.303850i) q^{4} +(-0.221481 - 1.81266i) q^{6} +(0.841112 - 2.31094i) q^{7} +(2.63732 - 1.52266i) q^{8} +(-2.98319 - 0.317107i) q^{9} +O(q^{10})\)	\(q+(-1.03831 + 0.183082i) q^{2} +(-0.0916693 + 1.72962i) q^{3} +(-0.834822 + 0.303850i) q^{4} +(-0.221481 - 1.81266i) q^{6} +(0.841112 - 2.31094i) q^{7} +(2.63732 - 1.52266i) q^{8} +(-2.98319 - 0.317107i) q^{9} +(-0.960783 + 0.806193i) q^{11} +(-0.449019 - 1.47178i) q^{12} +(4.47992 + 0.789931i) q^{13} +(-0.450243 + 2.55345i) q^{14} +(-1.09847 + 0.921724i) q^{16} +(5.75662 + 3.32358i) q^{17} +(3.15553 - 0.216914i) q^{18} +(0.124578 + 0.215776i) q^{19} +(3.91994 + 1.66665i) q^{21} +(0.849989 - 1.01298i) q^{22} +(0.287981 + 0.791222i) q^{23} +(2.39186 + 4.70115i) q^{24} -4.79615 q^{26} +(0.821942 - 5.13073i) q^{27} +2.18479i q^{28} +(0.0889744 + 0.504599i) q^{29} +(0.770551 - 0.280458i) q^{31} +(-2.94318 + 3.50754i) q^{32} +(-1.30634 - 1.73570i) q^{33} +(-6.58563 - 2.39697i) q^{34} +(2.58679 - 0.641717i) q^{36} +(-2.25865 - 1.30403i) q^{37} +(-0.168855 - 0.201233i) q^{38} +(-1.77695 + 7.67616i) q^{39} +(-1.41572 + 8.02895i) q^{41} +(-4.37524 - 1.01282i) q^{42} +(-2.78143 - 3.31478i) q^{43} +(0.557121 - 0.964962i) q^{44} +(-0.443871 - 0.768808i) q^{46} +(-1.81351 + 4.98256i) q^{47} +(-1.49354 - 1.98443i) q^{48} +(0.729356 + 0.612002i) q^{49} +(-6.27625 + 9.65211i) q^{51} +(-3.97996 + 0.701774i) q^{52} +10.4841i q^{53} +(0.0859140 + 5.47776i) q^{54} +(-1.30048 - 7.37539i) q^{56} +(-0.384630 + 0.195693i) q^{57} +(-0.184765 - 0.507639i) q^{58} +(2.30289 + 1.93235i) q^{59} +(-2.70930 - 0.986103i) q^{61} +(-0.748722 + 0.432275i) q^{62} +(-3.24201 + 6.62725i) q^{63} +(3.84771 - 6.66442i) q^{64} +(1.67415 + 1.56302i) q^{66} +(9.93303 + 1.75146i) q^{67} +(-5.81562 - 1.02545i) q^{68} +(-1.39492 + 0.425568i) q^{69} +(-0.0447378 + 0.0774882i) q^{71} +(-8.35047 + 3.70607i) q^{72} +(4.60824 - 2.66057i) q^{73} +(2.58391 + 0.940468i) q^{74} +(-0.169564 - 0.142281i) q^{76} +(1.05493 + 2.89841i) q^{77} +(0.439660 - 8.29554i) q^{78} +(-0.829503 - 4.70435i) q^{79} +(8.79889 + 1.89198i) q^{81} -8.59571i q^{82} +(7.91851 - 1.39625i) q^{83} +(-3.77887 - 0.200278i) q^{84} +(3.49486 + 2.93254i) q^{86} +(-0.880922 + 0.107636i) q^{87} +(-1.30634 + 3.58913i) q^{88} +(3.35189 + 5.80564i) q^{89} +(5.59359 - 9.68839i) q^{91} +(-0.480826 - 0.573026i) q^{92} +(0.414450 + 1.35847i) q^{93} +(0.970760 - 5.50545i) q^{94} +(-5.79693 - 5.41213i) q^{96} +(3.52928 + 4.20603i) q^{97} +(-0.869342 - 0.501915i) q^{98} +(3.12185 - 2.10036i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 12 q^{4}+O(q^{10}) \) 24 * q + 12 * q^4	\( 24 q + 12 q^{4} + 6 q^{11} - 30 q^{14} + 6 q^{19} - 24 q^{21} + 36 q^{24} - 60 q^{26} + 12 q^{29} + 6 q^{31} - 18 q^{34} + 36 q^{36} - 66 q^{39} + 30 q^{41} - 6 q^{44} - 6 q^{46} - 24 q^{49} - 36 q^{51} + 108 q^{54} - 66 q^{56} + 24 q^{59} + 24 q^{61} - 24 q^{64} - 18 q^{66} - 18 q^{69} + 54 q^{71} - 66 q^{74} - 96 q^{76} + 84 q^{79} + 72 q^{81} - 12 q^{84} + 102 q^{86} - 18 q^{89} + 12 q^{91} + 30 q^{94} + 54 q^{99}+O(q^{100}) \) 24 * q + 12 * q^4 + 6 * q^11 - 30 * q^14 + 6 * q^19 - 24 * q^21 + 36 * q^24 - 60 * q^26 + 12 * q^29 + 6 * q^31 - 18 * q^34 + 36 * q^36 - 66 * q^39 + 30 * q^41 - 6 * q^44 - 6 * q^46 - 24 * q^49 - 36 * q^51 + 108 * q^54 - 66 * q^56 + 24 * q^59 + 24 * q^61 - 24 * q^64 - 18 * q^66 - 18 * q^69 + 54 * q^71 - 66 * q^74 - 96 * q^76 + 84 * q^79 + 72 * q^81 - 12 * q^84 + 102 * q^86 - 18 * q^89 + 12 * q^91 + 30 * q^94 + 54 * q^99

Introduction

L-functions

Modular forms

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