LMFDB - Embedded newform 825.2.bx.f.499.4

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			499.4
Root			$-1.28932 - 0.418926i$ of defining polynomial
Character	$\chi$	$=$	825.499
Dual form			825.2.bx.f.124.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.38463 - 1.90578i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-1.09676 - 3.37549i) q^{4} +(1.90578 - 1.38463i) q^{6} +(0.184055 - 0.0598032i) q^{7} +(-3.47080 - 1.12773i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(1.38463 - 1.90578i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-1.09676 - 3.37549i) q^{4} +(1.90578 - 1.38463i) q^{6} +(0.184055 - 0.0598032i) q^{7} +(-3.47080 - 1.12773i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-1.96213 - 2.67395i) q^{11} -3.54920i q^{12} +(0.572331 - 0.787747i) q^{13} +(0.140877 - 0.433574i) q^{14} +(-1.21225 + 0.880754i) q^{16} +(-1.57274 - 2.16469i) q^{17} +(2.24038 - 0.727943i) q^{18} +(1.71480 - 5.27760i) q^{19} +0.193527 q^{21} +(-7.81280 + 0.0369604i) q^{22} -4.80040i q^{23} +(-2.95244 - 2.14507i) q^{24} +(-0.708805 - 2.18148i) q^{26} +(0.587785 + 0.809017i) q^{27} +(-0.403730 - 0.555687i) q^{28} +(3.12657 + 9.62260i) q^{29} +(2.02685 + 1.47259i) q^{31} -3.76902i q^{32} +(-1.03980 - 3.14941i) q^{33} -6.30309 q^{34} +(1.09676 - 3.37549i) q^{36} +(5.43260 - 1.76516i) q^{37} +(-7.68359 - 10.5756i) q^{38} +(0.787747 - 0.572331i) q^{39} +(-2.55823 + 7.87342i) q^{41} +(0.267964 - 0.368820i) q^{42} +5.11353i q^{43} +(-6.87391 + 9.55586i) q^{44} +(-9.14851 - 6.64678i) q^{46} +(10.3211 + 3.35354i) q^{47} +(-1.42509 + 0.463040i) q^{48} +(-5.63282 + 4.09248i) q^{49} +(-0.826838 - 2.54475i) q^{51} +(-3.28674 - 1.06793i) q^{52} +(-5.45981 + 7.51479i) q^{53} +2.35567 q^{54} -0.706260 q^{56} +(3.26174 - 4.48940i) q^{57} +(22.6677 + 7.36518i) q^{58} +(3.46656 + 10.6690i) q^{59} +(-0.975693 + 0.708883i) q^{61} +(5.61288 - 1.82374i) q^{62} +(0.184055 + 0.0598032i) q^{63} +(-9.60743 - 6.98021i) q^{64} +(-7.44184 - 2.37914i) q^{66} -3.25922i q^{67} +(-5.58197 + 7.68293i) q^{68} +(1.48341 - 4.56545i) q^{69} +(-4.84664 + 3.52129i) q^{71} +(-2.14507 - 2.95244i) q^{72} +(-3.14442 + 1.02168i) q^{73} +(4.15814 - 12.7974i) q^{74} -19.6952 q^{76} +(-0.521052 - 0.374813i) q^{77} -2.29374i q^{78} +(8.21389 + 5.96774i) q^{79} +(0.309017 + 0.951057i) q^{81} +(11.4628 + 15.7772i) q^{82} +(-4.88748 - 6.72704i) q^{83} +(-0.212253 - 0.653249i) q^{84} +(9.74527 + 7.08035i) q^{86} +10.1178i q^{87} +(3.79468 + 11.4935i) q^{88} -7.34270 q^{89} +(0.0582308 - 0.179216i) q^{91} +(-16.2037 + 5.26490i) q^{92} +(1.47259 + 2.02685i) q^{93} +(20.6821 - 15.0264i) q^{94} +(1.16469 - 3.58455i) q^{96} +(9.31774 - 12.8248i) q^{97} +16.4015i q^{98} +(-0.0156899 - 3.31659i) 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 $

$2$	1.38463	−	1.90578i	0.979082	−	1.34759i	0.0417590	−	0.999128i	$-0.486704\pi$
$2$	1.38463	−	1.90578i	0.979082	−	1.34759i	0.937323	−	0.348463i	$-0.113296\pi$
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$3$	0.951057	+	0.309017i	0.549093	+	0.178411i
$4$	−1.09676	−	3.37549i	−0.548382	−	1.68775i
$5$		0			0
$5$		0			0
$6$	1.90578	−	1.38463i	0.778032	−	0.565273i
$7$	0.184055	−	0.0598032i	0.0695663	−	0.0226035i	−0.274027	−	0.961722i	$-0.588356\pi$
$7$	0.184055	−	0.0598032i	0.0695663	−	0.0226035i	0.343593	+	0.939119i	$0.388356\pi$
$8$	−3.47080	−	1.12773i	−1.22711	−	0.398713i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$		0			0
$11$	−1.96213	−	2.67395i	−0.591606	−	0.806227i
$11$	−1.96213	−	2.67395i	−0.591606	−	0.806227i
$12$		−	3.54920i		−	1.02457i
$13$	0.572331	−	0.787747i	0.158736	−	0.218482i	−0.722240	−	0.691643i	$-0.756887\pi$
$13$	0.572331	−	0.787747i	0.158736	−	0.218482i	0.880976	+	0.473161i	$0.156887\pi$
$14$	0.140877	−	0.433574i	0.0376509	−	0.115878i
$15$		0			0
$16$	−1.21225	+	0.880754i	−0.303063	+	0.220188i
$17$	−1.57274	−	2.16469i	−0.381446	−	0.525015i	0.574521	−	0.818490i	$-0.305188\pi$
$17$	−1.57274	−	2.16469i	−0.381446	−	0.525015i	−0.955967	+	0.293475i	$0.905188\pi$
$18$	2.24038	−	0.727943i	0.528062	−	0.171578i
$19$	1.71480	−	5.27760i	0.393402	−	1.21077i	−0.536798	−	0.843711i	$-0.680366\pi$
$19$	1.71480	−	5.27760i	0.393402	−	1.21077i	0.930199	−	0.367055i	$-0.119634\pi$
$20$		0			0
$21$	0.193527			0.0422311
$22$	−7.81280	+	0.0369604i	−1.66569	+	0.00787998i
$23$		−	4.80040i		−	1.00095i	−0.865750	−	0.500476i	$-0.833158\pi$
$23$		−	4.80040i		−	1.00095i	0.865750	−	0.500476i	$-0.166842\pi$
$24$	−2.95244	−	2.14507i	−0.602664	−	0.437861i
$25$		0			0
$26$	−0.708805	−	2.18148i	−0.139008	−	0.427823i
$27$	0.587785	+	0.809017i	0.113119	+	0.155695i
$28$	−0.403730	−	0.555687i	−0.0762978	−	0.105015i
$29$	3.12657	+	9.62260i	0.580590	+	1.78687i	0.616303	+	0.787509i	$0.288630\pi$
$29$	3.12657	+	9.62260i	0.580590	+	1.78687i	−0.0357132	+	0.999362i	$0.511370\pi$
$30$		0			0
$31$	2.02685	+	1.47259i	0.364033	+	0.264486i	0.754732	−	0.656033i	$-0.227767\pi$
$31$	2.02685	+	1.47259i	0.364033	+	0.264486i	−0.390699	+	0.920518i	$0.627767\pi$
$32$		−	3.76902i		−	0.666275i
$33$	−1.03980	−	3.14941i	−0.181007	−	0.548243i
$34$	−6.30309			−1.08097
$35$		0			0
$36$	1.09676	−	3.37549i	0.182794	−	0.562582i
$37$	5.43260	−	1.76516i	0.893114	−	0.290190i	0.173722	−	0.984795i	$-0.444421\pi$
$37$	5.43260	−	1.76516i	0.893114	−	0.290190i	0.719392	+	0.694604i	$0.244421\pi$
$38$	−7.68359	−	10.5756i	−1.24644	−	1.71558i
$39$	0.787747	−	0.572331i	0.126140	−	0.0916464i
$40$		0			0
$41$	−2.55823	+	7.87342i	−0.399529	+	1.22962i	0.525850	+	0.850577i	$0.323747\pi$
$41$	−2.55823	+	7.87342i	−0.399529	+	1.22962i	−0.925378	+	0.379045i	$0.876253\pi$
$42$	0.267964	−	0.368820i	0.0413477	−	0.0569102i
$43$			5.11353i			0.779807i	0.920856	+	0.389903i	$0.127492\pi$
$43$			5.11353i			0.779807i	−0.920856	+	0.389903i	$0.872508\pi$
$44$	−6.87391	+	9.55586i	−1.03628	+	1.44060i
$45$		0			0
$46$	−9.14851	−	6.64678i	−1.34887	−	0.980014i
$47$	10.3211	+	3.35354i	1.50549	+	0.489164i	0.941614	−	0.336693i	$-0.109308\pi$
$47$	10.3211	+	3.35354i	1.50549	+	0.489164i	0.563879	+	0.825857i	$0.309308\pi$
$48$	−1.42509	+	0.463040i	−0.205694	+	0.0668340i
$49$	−5.63282	+	4.09248i	−0.804688	+	0.584640i
$50$		0			0
$51$	−0.826838	−	2.54475i	−0.115781	−	0.356336i
$52$	−3.28674	−	1.06793i	−0.455789	−	0.148095i
$53$	−5.45981	+	7.51479i	−0.749963	+	1.03224i	0.248020	+	0.968755i	$0.420220\pi$
$53$	−5.45981	+	7.51479i	−0.749963	+	1.03224i	−0.997983	+	0.0634803i	$0.979780\pi$
$54$	2.35567			0.320567
$55$		0			0
$56$	−0.706260			−0.0943780
$57$	3.26174	−	4.48940i	0.432028	−	0.594635i
$58$	22.6677	+	7.36518i	2.97642	+	0.967096i
$59$	3.46656	+	10.6690i	0.451307	+	1.38898i	0.875416	+	0.483369i	$0.160587\pi$
$59$	3.46656	+	10.6690i	0.451307	+	1.38898i	−0.424109	+	0.905611i	$0.639413\pi$
$60$		0			0
$61$	−0.975693	+	0.708883i	−0.124925	+	0.0907631i	−0.648493	−	0.761221i	$-0.724600\pi$
$61$	−0.975693	+	0.708883i	−0.124925	+	0.0907631i	0.523568	+	0.851984i	$0.324600\pi$
$62$	5.61288	−	1.82374i	0.712836	−	0.231615i
$63$	0.184055	+	0.0598032i	0.0231888	+	0.00753449i
$64$	−9.60743	−	6.98021i	−1.20093	−	0.872526i
$65$		0			0
$66$	−7.44184	−	2.37914i	−0.916027	−	0.292851i
$67$		−	3.25922i		−	0.398176i	−0.979982	−	0.199088i	$-0.936202\pi$
$67$		−	3.25922i		−	0.398176i	0.979982	−	0.199088i	$-0.0637980\pi$
$68$	−5.58197	+	7.68293i	−0.676914	+	0.931692i
$69$	1.48341	−	4.56545i	0.178581	−	0.549616i
$70$		0			0
$71$	−4.84664	+	3.52129i	−0.575191	+	0.417901i	−0.836987	−	0.547222i	$-0.815685\pi$
$71$	−4.84664	+	3.52129i	−0.575191	+	0.417901i	0.261796	+	0.965123i	$0.415685\pi$
$72$	−2.14507	−	2.95244i	−0.252799	−	0.347948i
$73$	−3.14442	+	1.02168i	−0.368026	+	0.119579i	−0.487191	−	0.873296i	$-0.661978\pi$
$73$	−3.14442	+	1.02168i	−0.368026	+	0.119579i	0.119165	+	0.992875i	$0.461978\pi$
$74$	4.15814	−	12.7974i	0.483374	−	1.48767i
$75$		0			0
$76$	−19.6952			−2.25920
$77$	−0.521052	−	0.374813i	−0.0593794	−	0.0427139i
$78$		−	2.29374i		−	0.259715i
$79$	8.21389	+	5.96774i	0.924135	+	0.671423i	0.944550	−	0.328368i	$-0.106499\pi$
$79$	8.21389	+	5.96774i	0.924135	+	0.671423i	−0.0204147	+	0.999792i	$0.506499\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$	11.4628	+	15.7772i	1.26586	+	1.74230i
$83$	−4.88748	−	6.72704i	−0.536471	−	0.738388i	0.451629	−	0.892206i	$-0.350843\pi$
$83$	−4.88748	−	6.72704i	−0.536471	−	0.738388i	−0.988099	+	0.153818i	$0.950843\pi$
$84$	−0.212253	−	0.653249i	−0.0231588	−	0.0712753i
$85$		0			0
$86$	9.74527	+	7.08035i	1.05086	+	0.763494i
$87$			10.1178i			1.08474i
$88$	3.79468	+	11.4935i	0.404514	+	1.22521i
$89$	−7.34270			−0.778325			−0.389163	−	0.921169i	$-0.627236\pi$
$89$	−7.34270			−0.778325			−0.389163	+	0.921169i	$0.627236\pi$
$90$		0			0
$91$	0.0582308	−	0.179216i	0.00610425	−	0.0187869i
$92$	−16.2037	+	5.26490i	−1.68935	+	0.548904i
$93$	1.47259	+	2.02685i	0.152701	+	0.210175i
$94$	20.6821	−	15.0264i	2.13319	−	1.54986i
$95$		0			0
$96$	1.16469	−	3.58455i	0.118871	−	0.365847i
$97$	9.31774	−	12.8248i	0.946074	−	1.30216i	−0.00717602	−	0.999974i	$-0.502284\pi$
$97$	9.31774	−	12.8248i	0.946074	−	1.30216i	0.953250	−	0.302184i	$-0.0977158\pi$
$98$			16.4015i			1.65680i
$99$	−0.0156899	−	3.31659i	−0.00157690	−	0.333330i
$100$		0			0
$101$	−10.6460	−	7.73475i	−1.05931	−	0.769636i	−0.0853519	−	0.996351i	$-0.527201\pi$
$101$	−10.6460	−	7.73475i	−1.05931	−	0.769636i	−0.973961	+	0.226715i	$0.927201\pi$
$102$	−5.99460	−	1.94776i	−0.593553	−	0.192857i
$103$	−3.80172	+	1.23525i	−0.374595	+	0.121713i	−0.490263	−	0.871575i	$-0.663099\pi$
$103$	−3.80172	+	1.23525i	−0.374595	+	0.121713i	0.115668	+	0.993288i	$0.463099\pi$
$104$	−2.87481	+	2.08867i	−0.281899	+	0.204811i
$105$		0			0
$106$	6.76171	+	20.8104i	0.656755	+	2.02129i
$107$	−4.64764	−	1.51011i	−0.449304	−	0.145988i	0.0756201	−	0.997137i	$-0.475906\pi$
$107$	−4.64764	−	1.51011i	−0.449304	−	0.145988i	−0.524924	+	0.851149i	$0.675906\pi$
$108$	2.08617	−	2.87136i	0.200742	−	0.276297i
$109$	7.51977			0.720263			0.360131	−	0.932902i	$-0.382732\pi$
$109$	7.51977			0.720263			0.360131	+	0.932902i	$0.382732\pi$
$110$		0			0
$111$	5.71217			0.542176
$112$	−0.170450	+	0.234604i	−0.0161060	+	0.0221680i
$113$	19.2339	+	6.24947i	1.80937	+	0.587901i	1.00000		0.000604375i	$0.000192378\pi$
$113$	19.2339	+	6.24947i	1.80937	+	0.587901i	0.809372	+	0.587296i	$0.199808\pi$
$114$	−4.03950	−	12.4323i	−0.378334	−	1.16439i
$115$		0			0
$116$	29.0519	−	21.1074i	2.69740	−	1.95978i
$117$	0.926052	−	0.300892i	0.0856135	−	0.0278175i
$118$	25.1326	+	8.16608i	2.31364	+	0.751748i
$119$	−0.418926	−	0.304368i	−0.0384029	−	0.0279014i
$120$		0			0
$121$	−3.30005	+	10.4933i	−0.300005	+	0.953938i
$122$			2.84100i			0.257212i
$123$	−4.86604	+	6.69754i	−0.438756	+	0.603896i
$124$	2.74775	−	8.45670i	0.246755	−	0.759434i
$125$		0			0
$126$	0.368820	−	0.267964i	0.0328571	−	0.0238721i
$127$	4.17340	+	5.74419i	0.370329	+	0.509715i	0.952990	−	0.303001i	$-0.0979884\pi$
$127$	4.17340	+	5.74419i	0.370329	+	0.509715i	−0.582661	+	0.812715i	$0.697988\pi$
$128$	−19.4364	+	6.31526i	−1.71795	+	0.558196i
$129$	−1.58017	+	4.86326i	−0.139126	+	0.428186i
$130$		0			0
$131$	−2.50024			−0.218447			−0.109223	−	0.994017i	$-0.534836\pi$
$131$	−2.50024			−0.218447			−0.109223	+	0.994017i	$0.534836\pi$
$132$	−9.49040	+	6.96401i	−0.826033	+	0.606139i
$133$		−	1.07392i		−	0.0931207i
$134$	−6.21135	−	4.51281i	−0.536579	−	0.389847i
$135$		0			0
$136$	3.01748	+	9.28684i	0.258746	+	0.796340i
$137$	−8.98981	−	12.3734i	−0.768052	−	1.05713i	−0.996501	−	0.0835766i	$-0.973366\pi$
$137$	−8.98981	−	12.3734i	−0.768052	−	1.05713i	0.228450	−	0.973556i	$-0.426634\pi$
$138$	−6.64678	−	9.14851i	−0.565812	−	0.778773i
$139$	6.07484	+	18.6964i	0.515261	+	1.58581i	0.782806	+	0.622266i	$0.213788\pi$
$139$	6.07484	+	18.6964i	0.515261	+	1.58581i	−0.267544	+	0.963546i	$0.586212\pi$
$140$		0			0
$141$	8.77969	+	6.37882i	0.739383	+	0.537193i
$142$			14.1123i			1.18428i
$143$	−3.22939	+	0.0152774i	−0.270055	+	0.00127756i
$144$	−1.49843			−0.124869
$145$		0			0
$146$	−2.40675	+	7.40722i	−0.199184	+	0.613026i
$147$	−6.62178	+	2.15155i	−0.546155	+	0.177456i
$148$	−11.9166	−	16.4017i	−0.979535	−	1.34821i
$149$	−8.19771	+	5.95599i	−0.671583	+	0.487933i	−0.870555	−	0.492072i	$-0.836240\pi$
$149$	−8.19771	+	5.95599i	−0.671583	+	0.487933i	0.198972	+	0.980005i	$0.436240\pi$
$150$		0			0
$151$	3.69682	−	11.3776i	0.300843	−	0.925899i	−0.680353	−	0.732884i	$-0.738174\pi$
$151$	3.69682	−	11.3776i	0.300843	−	0.925899i	0.981196	−	0.193015i	$-0.0618264\pi$
$152$	−11.9034	+	16.3837i	−0.965496	+	1.32889i
$153$		−	2.67571i		−	0.216318i
$154$	−1.43578	+	0.474033i	−0.115698	+	0.0381987i
$155$		0			0
$156$	−2.79587	−	2.03132i	−0.223849	−	0.162636i
$157$	2.49752	+	0.811494i	0.199324	+	0.0647643i	0.406978	−	0.913438i	$-0.366583\pi$
$157$	2.49752	+	0.811494i	0.199324	+	0.0647643i	−0.207654	+	0.978202i	$0.566583\pi$
$158$	22.7464	−	7.39076i	1.80961	−	0.587977i
$159$	−7.51479	+	5.45981i	−0.595961	+	0.432991i
$160$		0			0
$161$	−0.287079	−	0.883539i	−0.0226250	−	0.0696326i
$162$	2.24038	+	0.727943i	0.176021	+	0.0571926i
$163$	13.9443	−	19.1927i	1.09220	−	1.50329i	0.246868	−	0.969049i	$-0.420598\pi$
$163$	13.9443	−	19.1927i	1.09220	−	1.50329i	0.845334	−	0.534238i	$-0.179402\pi$
$164$	29.3825			2.29438
$165$		0			0
$166$	−19.5876			−1.52029
$167$	−2.05240	+	2.82488i	−0.158819	+	0.218596i	−0.881010	−	0.473098i	$-0.843135\pi$
$167$	−2.05240	+	2.82488i	−0.158819	+	0.218596i	0.722190	+	0.691694i	$0.243135\pi$
$168$	−0.671694	−	0.218246i	−0.0518223	−	0.0168381i
$169$	3.72424	+	11.4620i	0.286480	+	0.881695i
$170$		0			0
$171$	4.48940	−	3.26174i	0.343313	−	0.249431i
$172$	17.2607	−	5.60834i	1.31612	−	0.427632i
$173$	−19.3631	−	6.29145i	−1.47215	−	0.478330i	−0.540392	−	0.841413i	$-0.681724\pi$
$173$	−19.3631	−	6.29145i	−1.47215	−	0.478330i	−0.931757	+	0.363083i	$0.881724\pi$
$174$	19.2823	+	14.0094i	1.46179	+	1.06205i
$175$		0			0
$176$	4.73370	+	1.51335i	0.356816	+	0.114073i
$177$			11.2180i			0.843197i
$178$	−10.1669	+	13.9936i	−0.762044	+	1.04886i
$179$	−1.19008	+	3.66268i	−0.0889506	+	0.273762i	−0.985630	−	0.168919i	$-0.945972\pi$
$179$	−1.19008	+	3.66268i	−0.0889506	+	0.273762i	0.896679	+	0.442681i	$0.145972\pi$
$180$		0			0
$181$	14.2509	−	10.3539i	1.05926	−	0.769599i	0.0853107	−	0.996354i	$-0.472812\pi$
$181$	14.2509	−	10.3539i	1.05926	−	0.769599i	0.973952	+	0.226755i	$0.0728117\pi$
$182$	−0.260918	−	0.359123i	−0.0193406	−	0.0266200i
$183$	−1.14700	+	0.372682i	−0.0847884	+	0.0275494i
$184$	−5.41356	+	16.6612i	−0.399093	+	1.22828i
$185$		0			0
$186$	5.90173			0.432736
$187$	−2.70236	+	8.45285i	−0.197616	+	0.618134i
$188$		−	38.5170i		−	2.80914i
$189$	0.156567	+	0.113752i	0.0113886	+	0.00827427i
$190$		0			0
$191$	0.128891	+	0.396685i	0.00932620	+	0.0287031i	0.955611	−	0.294630i	$-0.0951965\pi$
$191$	0.128891	+	0.396685i	0.00932620	+	0.0287031i	−0.946285	+	0.323333i	$0.895196\pi$
$192$	−6.98021	−	9.60743i	−0.503753	−	0.693357i
$193$	−6.87505	−	9.46269i	−0.494877	−	0.681140i	0.486401	−	0.873736i	$-0.338309\pi$
$193$	−6.87505	−	9.46269i	−0.494877	−	0.681140i	−0.981278	+	0.192596i	$0.938309\pi$
$194$	−11.5396	−	35.5151i	−0.828493	−	2.54984i
$195$		0			0
$196$	19.9920	+	14.5250i	1.42800	+	1.03750i
$197$		−	21.5958i		−	1.53864i	−0.638863	−	0.769320i	$-0.720595\pi$
$197$		−	21.5958i		−	1.53864i	0.638863	−	0.769320i	$-0.279405\pi$
$198$	−6.34241	−	4.56235i	−0.450736	−	0.324232i
$199$	−7.76028			−0.550111			−0.275056	−	0.961428i	$-0.588696\pi$
$199$	−7.76028			−0.550111			−0.275056	+	0.961428i	$0.588696\pi$
$200$		0			0
$201$	1.00715	−	3.09970i	0.0710391	−	0.218636i
$202$	−29.4815	+	9.57911i	−2.07431	+	0.673984i
$203$	1.15092	+	1.58411i	0.0807790	+	0.111183i
$204$	−7.68293	+	5.58197i	−0.537912	+	0.390816i
$205$		0			0
$206$	−2.90986	+	8.95561i	−0.202739	+	0.623967i
$207$	2.82160	−	3.88361i	0.196115	−	0.269929i
$208$			1.45903i			0.101166i
$209$	−17.4767	+	5.77008i	−1.20889	+	0.399125i
$210$		0			0
$211$	10.1173	+	7.35065i	0.696504	+	0.506040i	0.878792	−	0.477205i	$-0.158350\pi$
$211$	10.1173	+	7.35065i	0.696504	+	0.506040i	−0.182288	+	0.983245i	$0.558350\pi$
$212$	31.3542	+	10.1876i	2.15342	+	0.699687i
$213$	−5.69757	+	1.85125i	−0.390391	+	0.126846i
$214$	−9.31320	+	6.76644i	−0.636637	+	0.462544i
$215$		0			0
$216$	−1.12773	−	3.47080i	−0.0767324	−	0.236158i
$217$	0.461118	+	0.149826i	0.0313027	+	0.0101709i
$218$	10.4121	−	14.3310i	0.705196	−	0.970619i
$219$	−3.30624			−0.223415
$220$		0			0
$221$	−2.60536			−0.175255
$222$	7.90925	−	10.8861i	0.530834	−	0.730631i
$223$	−5.11257	−	1.66118i	−0.342363	−	0.111241i	0.132789	−	0.991144i	$-0.457607\pi$
$223$	−5.11257	−	1.66118i	−0.342363	−	0.111241i	−0.475152	+	0.879904i	$0.657607\pi$
$224$	−0.225399	−	0.693708i	−0.0150601	−	0.0463503i
$225$		0			0
$226$	38.5419	−	28.0024i	2.56377	−	1.86269i
$227$	−20.6882	+	6.72202i	−1.37313	+	0.446156i	−0.900404	−	0.435055i	$-0.856729\pi$
$227$	−20.6882	+	6.72202i	−1.37313	+	0.446156i	−0.472723	+	0.881211i	$0.656729\pi$
$228$	−18.7313	−	6.08616i	−1.24051	−	0.403066i
$229$	2.16068	+	1.56983i	0.142782	+	0.103737i	0.656883	−	0.753992i	$-0.271874\pi$
$229$	2.16068	+	1.56983i	0.142782	+	0.103737i	−0.514101	+	0.857730i	$0.671874\pi$
$230$		0			0
$231$	−0.379726	−	0.517482i	−0.0249842	−	0.0340478i
$232$		−	36.9240i		−	2.42418i
$233$	−3.36624	+	4.63323i	−0.220530	+	0.303533i	−0.904919	−	0.425584i	$-0.860069\pi$
$233$	−3.36624	+	4.63323i	−0.220530	+	0.303533i	0.684389	+	0.729117i	$0.260069\pi$
$234$	0.708805	−	2.18148i	0.0463360	−	0.142608i
$235$		0			0
$236$	32.2110	−	23.4027i	2.09676	−	1.52338i
$237$	5.96774	+	8.21389i	0.387647	+	0.533550i
$238$	−1.16012	+	0.376945i	−0.0751992	+	0.0244337i
$239$	7.53013	−	23.1754i	0.487084	−	1.49909i	−0.341857	−	0.939752i	$-0.611056\pi$
$239$	7.53013	−	23.1754i	0.487084	−	1.49909i	0.828940	−	0.559337i	$-0.188944\pi$
$240$		0			0
$241$	−16.7082			−1.07627			−0.538135	−	0.842859i	$-0.680871\pi$
$241$	−16.7082			−1.07627			−0.538135	+	0.842859i	$0.680871\pi$
$242$	15.4286	+	20.8185i	0.991788	+	1.33827i
$243$			1.00000i			0.0641500i
$244$	3.46293	+	2.51597i	0.221691	+	0.161068i
$245$		0			0
$246$	6.02636	+	18.5472i	0.384227	+	1.18253i
$247$	−3.17598	−	4.37136i	−0.202083	−	0.278143i
$248$	−5.37410	−	7.39682i	−0.341256	−	0.469698i
$249$	−2.56950	−	7.90811i	−0.162835	−	0.501156i
$250$		0			0
$251$	13.0239	+	9.46240i	0.822060	+	0.597262i	0.917302	−	0.398193i	$-0.130362\pi$
$251$	13.0239	+	9.46240i	0.822060	+	0.597262i	−0.0952418	+	0.995454i	$0.530362\pi$
$252$		−	0.686867i		−	0.0432685i
$253$	−12.8360	+	9.41903i	−0.806995	+	0.592169i
$254$	16.7258			1.04947
$255$		0			0
$256$	−7.53728	+	23.1974i	−0.471080	+	1.44984i
$257$	5.67662	−	1.84445i	0.354098	−	0.115053i	−0.126566	−	0.991958i	$-0.540396\pi$
$257$	5.67662	−	1.84445i	0.354098	−	0.115053i	0.480664	+	0.876905i	$0.340396\pi$
$258$	7.08035	+	9.74527i	0.440804	+	0.606714i
$259$	0.894336	−	0.649773i	0.0555713	−	0.0403749i
$260$		0			0
$261$	−3.12657	+	9.62260i	−0.193530	+	0.595624i
$262$	−3.46191	+	4.76490i	−0.213877	+	0.294377i
$263$		−	0.451149i		−	0.0278190i	−0.999903	−	0.0139095i	$-0.995572\pi$
$263$		−	0.451149i		−	0.0278190i	0.999903	−	0.0139095i	$-0.00442768\pi$
$264$	0.0572591	+	12.1036i	0.00352405	+	0.744925i
$265$		0			0
$266$	−2.04666	−	1.48698i	−0.125489	−	0.0911728i
$267$	−6.98333	−	2.26902i	−0.427373	−	0.138862i
$268$	−11.0015	+	3.57459i	−0.672021	+	0.218353i
$269$	11.9085	−	8.65203i	0.726074	−	0.527524i	−0.162245	−	0.986751i	$-0.551873\pi$
$269$	11.9085	−	8.65203i	0.726074	−	0.527524i	0.888319	+	0.459227i	$0.151873\pi$
$270$		0			0
$271$	1.36829	+	4.21115i	0.0831175	+	0.255809i	0.983975	−	0.178305i	$-0.0570614\pi$
$271$	1.36829	+	4.21115i	0.0831175	+	0.255809i	−0.900858	+	0.434114i	$0.857061\pi$
$272$	3.81312	+	1.23896i	0.231204	+	0.0751228i
$273$	0.110762	−	0.152450i	0.00670360	−	0.00922671i
$274$	−36.0286			−2.17657
$275$		0			0
$276$	−17.0376			−1.02554
$277$	0.0542702	−	0.0746965i	0.00326078	−	0.00448808i	−0.807383	−	0.590027i	$-0.799117\pi$
$277$	0.0542702	−	0.0746965i	0.00326078	−	0.00448808i	0.810644	+	0.585539i	$0.199117\pi$
$278$	44.0427	+	14.3104i	2.64151	+	0.858278i
$279$	0.774188	+	2.38271i	0.0463494	+	0.142649i
$280$		0			0
$281$	−4.19314	+	3.04650i	−0.250142	+	0.181739i	−0.705790	−	0.708421i	$-0.749408\pi$
$281$	−4.19314	+	3.04650i	−0.250142	+	0.181739i	0.455648	+	0.890160i	$0.349408\pi$
$282$	24.3133	−	7.89985i	1.44783	−	0.470429i
$283$	1.48805	+	0.483496i	0.0884552	+	0.0287408i	0.352910	−	0.935657i	$-0.385192\pi$
$283$	1.48805	+	0.483496i	0.0884552	+	0.0287408i	−0.264455	+	0.964398i	$0.585192\pi$
$284$	17.2017	+	12.4978i	1.02073	+	0.741607i
$285$		0			0
$286$	−4.44240	+	6.17566i	−0.262684	+	0.365174i
$287$			1.60214i			0.0945710i
$288$	2.21537	−	3.04920i	0.130542	−	0.179676i
$289$	3.04091	−	9.35897i	0.178877	−	0.550527i
$290$		0			0
$291$	12.8248	−	9.31774i	0.751802	−	0.546216i
$292$	6.89736	+	9.49341i	0.403638	+	0.555560i
$293$	22.0236	−	7.15592i	1.28664	−	0.418053i	0.415723	−	0.909491i	$-0.363529\pi$
$293$	22.0236	−	7.15592i	1.28664	−	0.418053i	0.870912	+	0.491438i	$0.163529\pi$
$294$	−5.06834	+	15.5987i	−0.295592	+	0.909737i
$295$		0			0
$296$	−20.8461			−1.21165
$297$	1.00996	−	3.15911i	0.0586038	−	0.183310i
$298$			23.8699i			1.38274i
$299$	−3.78150	−	2.74742i	−0.218690	−	0.158887i
$300$		0			0
$301$	0.305805	+	0.941172i	0.0176263	+	0.0542483i
$302$	−16.5646	−	22.7991i	−0.953183	−	1.31194i
$303$	−7.73475	−	10.6460i	−0.444350	−	0.611595i
$304$	2.56950	+	7.90811i	0.147371	+	0.453561i
$305$		0			0
$306$	−5.09931	−	3.70486i	−0.291508	−	0.211793i
$307$			7.72480i			0.440878i	0.975401	+	0.220439i	$0.0707490\pi$
$307$			7.72480i			0.440878i	−0.975401	+	0.220439i	$0.929251\pi$
$308$	−0.693708	+	2.16989i	−0.0395277	+	0.123641i
$309$	−3.99737			−0.227402
$310$		0			0
$311$	−5.90867	+	18.1850i	−0.335050	+	1.03118i	0.631647	+	0.775256i	$0.282379\pi$
$311$	−5.90867	+	18.1850i	−0.335050	+	1.03118i	−0.966697	+	0.255922i	$0.917621\pi$
$312$	−3.37955	+	1.09808i	−0.191329	+	0.0621666i
$313$	−1.70638	−	2.34863i	−0.0964503	−	0.132752i	0.758064	−	0.652180i	$-0.226145\pi$
$313$	−1.70638	−	2.34863i	−0.0964503	−	0.132752i	−0.854515	+	0.519427i	$0.826145\pi$
$314$	5.00468	−	3.63611i	0.282430	−	0.205198i
$315$		0			0
$316$	11.1354	−	34.2711i	0.626413	−	1.92790i
$317$	−1.32930	+	1.82962i	−0.0746607	+	0.102762i	−0.844714	−	0.535218i	$-0.820230\pi$
$317$	−1.32930	+	1.82962i	−0.0746607	+	0.102762i	0.770053	+	0.637979i	$0.220230\pi$
$318$			21.8814i			1.22705i
$319$	19.5956	−	27.2411i	1.09714	−	1.52521i
$320$		0			0
$321$	−3.95352	−	2.87240i	−0.220664	−	0.160322i
$322$	−2.08133	−	0.676265i	−0.115988	−	0.0376868i
$323$	−14.1213	+	4.58829i	−0.785731	+	0.255299i
$324$	2.87136	−	2.08617i	0.159520	−	0.115898i
$325$		0			0
$326$	−17.2693	−	53.1496i	−0.956460	−	2.94368i
$327$	7.15172	+	2.32374i	0.395491	+	0.128503i
$328$	17.7582	−	24.4421i	0.980533	−	1.34959i
$329$	2.10021			0.115788
$330$		0			0
$331$	6.02336			0.331074			0.165537	−	0.986204i	$-0.447064\pi$
$331$	6.02336			0.331074			0.165537	+	0.986204i	$0.447064\pi$
$332$	−17.3466	+	23.8756i	−0.952021	+	1.31034i
$333$	5.43260	+	1.76516i	0.297705	+	0.0967301i
$334$	2.54179	+	7.82284i	0.139081	+	0.428047i
$335$		0			0
$336$	−0.234604	+	0.170450i	−0.0127987	+	0.00929879i
$337$	−13.8519	+	4.50076i	−0.754562	+	0.245172i	−0.660943	−	0.750436i	$-0.729843\pi$
$337$	−13.8519	+	4.50076i	−0.754562	+	0.245172i	−0.0936187	+	0.995608i	$0.529843\pi$
$338$	27.0008	+	8.77310i	1.46865	+	0.477193i
$339$	16.3613	+	11.8872i	0.888625	+	0.645624i
$340$		0			0
$341$	−0.0393084	−	8.30913i	−0.00212867	−	0.449965i
$342$		−	13.0721i		−	0.706859i
$343$	−1.58827	+	2.18607i	−0.0857587	+	0.118037i
$344$	5.76669	−	17.7480i	0.310919	−	0.956911i
$345$		0			0
$346$	−38.8009	+	28.1905i	−2.08595	+	1.51553i
$347$	16.9489	+	23.3281i	0.909863	+	1.25232i	0.967213	+	0.253965i	$0.0817347\pi$
$347$	16.9489	+	23.3281i	0.909863	+	1.25232i	−0.0573506	+	0.998354i	$0.518265\pi$
$348$	34.1525	−	11.0968i	1.83077	−	0.594853i
$349$	0.504421	−	1.55245i	0.0270010	−	0.0831006i	−0.936648	−	0.350272i	$-0.886089\pi$
$349$	0.504421	−	1.55245i	0.0270010	−	0.0831006i	0.963649	+	0.267172i	$0.0860891\pi$
$350$		0			0
$351$	0.973708			0.0519727
$352$	−10.0782	+	7.39533i	−0.537169	+	0.394172i
$353$			24.9297i			1.32687i	0.748232	+	0.663437i	$0.230903\pi$
$353$			24.9297i			1.32687i	−0.748232	+	0.663437i	$0.769097\pi$
$354$	21.3791	+	15.5328i	1.13628	+	0.825559i
$355$		0			0
$356$	8.05321	+	24.7852i	0.426819	+	1.31361i
$357$	−0.304368	−	0.418926i	−0.0161089	−	0.0221719i
$358$	5.33245	+	7.33949i	0.281829	+	0.387904i
$359$	−8.78874	−	27.0489i	−0.463852	−	1.42759i	−0.860421	−	0.509584i	$-0.829799\pi$
$359$	−8.78874	−	27.0489i	−0.463852	−	1.42759i	0.396569	−	0.918005i	$-0.370201\pi$
$360$		0			0
$361$	−9.54125	−	6.93213i	−0.502171	−	0.364849i
$362$		−	41.4955i		−	2.18095i
$363$	−6.38115	+	8.95996i	−0.334924	+	0.470276i
$364$	−0.668808			−0.0350550
$365$		0			0
$366$	−0.877916	+	2.70195i	−0.0458894	+	0.141233i
$367$	−9.93023	+	3.22653i	−0.518354	+	0.168423i	−0.556498	−	0.830849i	$-0.687855\pi$
$367$	−9.93023	+	3.22653i	−0.518354	+	0.168423i	0.0381442	+	0.999272i	$0.487855\pi$
$368$	4.22797	+	5.81930i	0.220398	+	0.303352i
$369$	−6.69754	+	4.86604i	−0.348660	+	0.253316i
$370$		0			0
$371$	−0.555499	+	1.70965i	−0.0288401	+	0.0887606i
$372$	5.22653	−	7.19370i	0.270983	−	0.372976i
$373$		−	2.81747i		−	0.145883i	−0.997336	−	0.0729416i	$-0.976761\pi$
$373$		−	2.81747i		−	0.145883i	0.997336	−	0.0729416i	$-0.0232387\pi$
$374$	12.3675	+	16.8542i	0.639509	+	0.871508i
$375$		0			0
$376$	−32.0407	−	23.2789i	−1.65237	−	1.20052i
$377$	9.36960	+	3.04437i	0.482559	+	0.156793i
$378$	0.433574	−	0.140877i	0.0223006	−	0.00724592i
$379$	7.22711	−	5.25080i	0.371231	−	0.269715i	−0.386490	−	0.922294i	$-0.626313\pi$
$379$	7.22711	−	5.25080i	0.371231	−	0.269715i	0.757721	+	0.652578i	$0.226313\pi$
$380$		0			0
$381$	2.19409	+	6.75270i	0.112406	+	0.345951i
$382$	0.934460	+	0.303625i	0.0478111	+	0.0155348i
$383$	−5.01545	+	6.90317i	−0.256278	+	0.352736i	−0.917697	−	0.397280i	$-0.869954\pi$
$383$	−5.01545	+	6.90317i	−0.256278	+	0.352736i	0.661420	+	0.750016i	$0.269954\pi$
$384$	−20.4366			−1.04290
$385$		0			0
$386$	−27.5532			−1.40242
$387$	−3.00566	+	4.13694i	−0.152786	+	0.210292i
$388$	−53.5093	−	17.3862i	−2.71652	−	0.882651i
$389$	−3.63890	−	11.1994i	−0.184500	−	0.567832i	0.815440	−	0.578842i	$-0.196495\pi$
$389$	−3.63890	−	11.1994i	−0.184500	−	0.567832i	−0.999939	+	0.0110104i	$0.996495\pi$
$390$		0			0
$391$	−10.3914	+	7.54978i	−0.525515	+	0.381809i
$392$	24.1656	−	7.85188i	1.22055	−	0.396580i
$393$	−2.37787	−	0.772616i	−0.119948	−	0.0389733i
$394$	−41.1569	−	29.9023i	−2.07346	−	1.50645i
$395$		0			0
$396$	−11.1779	+	3.69047i	−0.561711	+	0.185453i
$397$			1.41214i			0.0708735i	0.999372	+	0.0354368i	$0.0112822\pi$
$397$			1.41214i			0.0708735i	−0.999372	+	0.0354368i	$0.988718\pi$
$398$	−10.7451	+	14.7894i	−0.538604	+	0.741325i
$399$	0.331860	−	1.02136i	0.0166138	−	0.0511319i
$400$		0			0
$401$	−6.84361	+	4.97217i	−0.341753	+	0.248298i	−0.745401	−	0.666616i	$-0.767742\pi$
$401$	−6.84361	+	4.97217i	−0.341753	+	0.248298i	0.403648	+	0.914914i	$0.367742\pi$
$402$	−4.51281	−	6.21135i	−0.225078	−	0.309794i
$403$	2.32006	−	0.753833i	0.115570	−	0.0375511i
$404$	−14.4325	+	44.4185i	−0.718042	+	2.20991i
$405$		0			0
$406$	4.61257			0.228918
$407$	−15.3794	−	11.0630i	−0.762331	−	0.548375i
$408$			9.76476i			0.483428i
$409$	8.19172	+	5.95163i	0.405054	+	0.294289i	0.771597	−	0.636112i	$-0.219458\pi$
$409$	8.19172	+	5.95163i	0.405054	+	0.294289i	−0.366542	+	0.930401i	$0.619458\pi$
$410$		0			0
$411$	−4.72622	−	14.5458i	−0.233127	−	0.717493i
$412$	8.33918	+	11.4779i	0.410842	+	0.565475i
$413$	1.27608	+	1.75637i	0.0627915	+	0.0864252i
$414$	−3.49442	−	10.7547i	−0.171741	−	0.528566i
$415$		0			0
$416$	−2.96903	−	2.15713i	−0.145569	−	0.105762i
$417$			19.6586i			0.962686i
$418$	−13.2023	+	41.2962i	−0.645746	+	2.01987i
$419$	−32.8019			−1.60248			−0.801240	−	0.598343i	$-0.795826\pi$
$419$	−32.8019			−1.60248			−0.801240	+	0.598343i	$0.795826\pi$
$420$		0			0
$421$	−4.36619	+	13.4377i	−0.212795	+	0.654915i	0.786508	+	0.617580i	$0.211887\pi$
$421$	−4.36619	+	13.4377i	−0.212795	+	0.654915i	−0.999303	+	0.0373351i	$0.988113\pi$
$422$	28.0175	−	9.10342i	1.36387	−	0.443148i
$423$	6.37882	+	8.77969i	0.310149	+	0.426883i
$424$	27.4246	−	19.9251i	1.33185	−	0.967649i
$425$		0			0
$426$	−4.36095	+	13.4216i	−0.211289	+	0.650280i
$427$	−0.137188	+	0.188823i	−0.00663899	+	0.00913779i
$428$			17.3443i			0.838368i
$429$	−3.07605	−	0.983406i	−0.148513	−	0.0474793i
$430$		0			0
$431$	−15.4569	−	11.2301i	−0.744531	−	0.540933i	0.149596	−	0.988747i	$-0.452203\pi$
$431$	−15.4569	−	11.2301i	−0.744531	−	0.540933i	−0.894127	+	0.447814i	$0.852203\pi$
$432$	−1.42509	−	0.463040i	−0.0685646	−	0.0222780i
$433$	−14.3800	+	4.67235i	−0.691059	+	0.224539i	−0.633431	−	0.773799i	$-0.718354\pi$
$433$	−14.3800	+	4.67235i	−0.691059	+	0.224539i	−0.0576283	+	0.998338i	$0.518354\pi$
$434$	0.924015	−	0.671336i	0.0443541	−	0.0322252i
$435$		0			0
$436$	−8.24740	−	25.3829i	−0.394979	−	1.21562i
$437$	−25.3346	−	8.23171i	−1.21192	−	0.393776i
$438$	−4.57791	+	6.30096i	−0.218741	+	0.301071i
$439$	−37.1642			−1.77375			−0.886876	−	0.462008i	$-0.847129\pi$
$439$	−37.1642			−1.77375			−0.886876	+	0.462008i	$0.847129\pi$
$440$		0			0
$441$	−6.96255			−0.331550
$442$	−3.60746	+	4.96524i	−0.171589	+	0.236172i
$443$	−2.62539	−	0.853040i	−0.124736	−	0.0405291i	0.245984	−	0.969274i	$-0.420889\pi$
$443$	−2.62539	−	0.853040i	−0.124736	−	0.0405291i	−0.370720	+	0.928745i	$0.620889\pi$
$444$	−6.26490	−	19.2814i	−0.297319	−	0.915054i
$445$		0			0
$446$	−10.2449	+	7.44333i	−0.485108	+	0.352452i
$447$	−9.63699	+	3.13125i	−0.455814	+	0.148103i
$448$	−2.18574	−	0.710189i	−0.103266	−	0.0335533i
$449$	−14.4540	−	10.5015i	−0.682127	−	0.495594i	0.191936	−	0.981408i	$-0.438524\pi$
$449$	−14.4540	−	10.5015i	−0.682127	−	0.495594i	−0.874063	+	0.485813i	$0.838524\pi$
$450$		0			0
$451$	26.0728	−	8.60813i	1.22772	−	0.405341i
$452$		−	71.7780i		−	3.37615i
$453$	7.03177	−	9.67840i	0.330381	−	0.454731i
$454$	−15.8349	+	48.7348i	−0.743168	+	2.28724i
$455$		0			0
$456$	−16.3837	+	11.9034i	−0.767236	+	0.557429i
$457$	−12.4388	−	17.1205i	−0.581862	−	0.800864i	0.412036	−	0.911167i	$-0.364818\pi$
$457$	−12.4388	−	17.1205i	−0.581862	−	0.800864i	−0.993898	+	0.110304i	$0.964818\pi$
$458$	5.98350	−	1.94416i	0.279590	−	0.0908444i
$459$	0.826838	−	2.54475i	0.0385935	−	0.118779i
$460$		0			0
$461$	−34.3476			−1.59973			−0.799864	−	0.600181i	$-0.795095\pi$
$461$	−34.3476			−1.59973			−0.799864	+	0.600181i	$0.795095\pi$
$462$	−1.51199	+	0.00715284i	−0.0703441	+	0.000332780i
$463$			10.4516i			0.485727i	0.970060	+	0.242864i	$0.0780867\pi$
$463$			10.4516i			0.485727i	−0.970060	+	0.242864i	$0.921913\pi$
$464$	−12.2653	−	8.91129i	−0.569404	−	0.413696i
$465$		0			0
$466$	4.16892	+	12.8306i	0.193122	+	0.594367i
$467$	17.4239	+	23.9820i	0.806284	+	1.10975i	0.991886	+	0.127129i	$0.0405764\pi$
$467$	17.4239	+	23.9820i	0.806284	+	1.10975i	−0.185602	+	0.982625i	$0.559424\pi$
$468$	−2.03132	−	2.79587i	−0.0938978	−	0.129239i
$469$	−0.194911	−	0.599875i	−0.00900017	−	0.0276997i
$470$		0			0
$471$	2.12452	+	1.54355i	0.0978927	+	0.0711232i
$472$		−	40.9392i		−	1.88438i
$473$	13.6734	−	10.0334i	0.628701	−	0.461338i
$474$	23.9170			1.09854
$475$		0			0
$476$	−0.567928	+	1.74790i	−0.0260309	+	0.0801150i
$477$	−8.83416	+	2.87039i	−0.404488	+	0.131426i
$478$	−33.7407	−	46.4401i	−1.54326	−	2.12412i
$479$	−10.6941	+	7.76971i	−0.488625	+	0.355007i	−0.804655	−	0.593742i	$-0.797650\pi$
$479$	−10.6941	+	7.76971i	−0.488625	+	0.355007i	0.316030	+	0.948749i	$0.397650\pi$
$480$		0			0
$481$	1.71875	−	5.28977i	0.0783682	−	0.241193i
$482$	−23.1347	+	31.8422i	−1.05376	+	1.45037i
$483$		−	0.929007i		−	0.0422713i
$484$	39.0395	−	0.369380i	1.77452	−	0.0167900i
$485$		0			0
$486$	1.90578	+	1.38463i	0.0864480	+	0.0628081i
$487$	40.4176	+	13.1325i	1.83150	+	0.595089i	0.999167	+	0.0408075i	$0.0129930\pi$
$487$	40.4176	+	13.1325i	1.83150	+	0.595089i	0.832329	+	0.554282i	$0.187007\pi$
$488$	4.18586	−	1.36007i	0.189485	−	0.0615675i
$489$	19.1927	−	13.9443i	0.867923	−	0.630583i
$490$		0			0
$491$	−4.86568	−	14.9750i	−0.219585	−	0.675813i	−0.998796	−	0.0490515i	$-0.984380\pi$
$491$	−4.86568	−	14.9750i	−0.219585	−	0.675813i	0.779211	−	0.626761i	$-0.215620\pi$
$492$	27.9444	+	9.07968i	1.25983	+	0.409343i
$493$	15.9127	−	21.9019i	0.716670	−	0.986412i
$494$	−12.7284			−0.572679
$495$		0			0
$496$	−3.75405			−0.168562
$497$	−0.681466	+	0.937957i	−0.0305679	+	0.0420731i
$498$	−18.6289	−	6.05291i	−0.834782	−	0.271237i
$499$	10.3607	+	31.8869i	0.463808	+	1.42746i	0.860475	+	0.509493i	$0.170167\pi$
$499$	10.3607	+	31.8869i	0.463808	+	1.42746i	−0.396666	+	0.917963i	$0.629833\pi$
$500$		0			0
$501$	−2.82488	+	2.05240i	−0.126206	+	0.0916943i
$502$	36.0665	−	11.7187i	1.60973	−	0.523032i
$503$	−21.6996	−	7.05063i	−0.967537	−	0.314372i	−0.217716	−	0.976012i	$-0.569861\pi$
$503$	−21.6996	−	7.05063i	−0.967537	−	0.314372i	−0.749821	+	0.661640i	$0.769861\pi$
$504$	−0.571377	−	0.415129i	−0.0254511	−	0.0184913i
$505$		0			0
$506$	0.177425	+	37.5046i	0.00788749	+	1.66728i
$507$			12.0519i			0.535243i
$508$	14.8122	−	20.3873i	0.657187	−	0.904540i
$509$	−12.2731	+	37.7727i	−0.543996	+	1.67425i	0.179370	+	0.983782i	$0.442594\pi$
$509$	−12.2731	+	37.7727i	−0.543996	+	1.67425i	−0.723365	+	0.690465i	$0.757406\pi$
$510$		0			0
$511$	−0.517646	+	0.376092i	−0.0228993	+	0.0166373i
$512$	9.74805	+	13.4170i	0.430807	+	0.592955i
$513$	5.27760	−	1.71480i	0.233012	−	0.0757102i
$514$	4.34491	−	13.3723i	0.191646	−	0.589826i
$515$		0			0
$516$	18.1490			0.798963
$517$	−11.2843	−	34.1784i	−0.496281	−	1.50316i
$518$		−	2.60410i		−	0.114418i
$519$	−16.4712	−	11.9670i	−0.723007	−	0.525295i
$520$		0			0
$521$	7.88005	+	24.2523i	0.345231	+	1.06251i	0.961460	+	0.274945i	$0.0886597\pi$
$521$	7.88005	+	24.2523i	0.345231	+	1.06251i	−0.616229	+	0.787567i	$0.711340\pi$
$522$	14.0094	+	19.2823i	0.613175	+	0.843963i
$523$	9.06977	+	12.4835i	0.396593	+	0.545864i	0.959885	−	0.280394i	$-0.0904652\pi$
$523$	9.06977	+	12.4835i	0.396593	+	0.545864i	−0.563291	+	0.826258i	$0.690465\pi$
$524$	2.74217	+	8.43953i	0.119792	+	0.368683i
$525$		0			0
$526$	−0.859791	−	0.624675i	−0.0374887	−	0.0272371i
$527$		−	6.70351i		−	0.292010i
$528$	4.03436	+	2.90208i	0.175573	+	0.126297i
$529$	−0.0438407			−0.00190612
$530$		0			0
$531$	−3.46656	+	10.6690i	−0.150436	+	0.462993i
$532$	−3.62501	+	1.17784i	−0.157164	+	0.0510657i
$533$	4.73811	+	6.52145i	0.205230	+	0.282475i
$534$	−13.9936	+	10.1669i	−0.605561	+	0.439966i
$535$		0			0
$536$	−3.67552	+	11.3121i	−0.158758	+	0.488607i
$537$	−2.26366	+	3.11567i	−0.0976843	+	0.134451i
$538$		−	34.6749i		−	1.49494i
$539$	21.9955	+	7.03189i	0.947411	+	0.302885i
$540$		0			0
$541$	−22.3294	−	16.2233i	−0.960018	−	0.697494i	−0.00686309	−	0.999976i	$-0.502185\pi$
$541$	−22.3294	−	16.2233i	−0.960018	−	0.697494i	−0.953155	+	0.302483i	$0.902185\pi$
$542$	9.92010	+	3.22324i	0.426105	+	0.138450i
$543$	16.7530	−	5.44337i	0.718938	−	0.233597i
$544$	−8.15877	+	5.92769i	−0.349804	+	0.254148i
$545$		0			0
$546$	−0.137173	−	0.422175i	−0.00587046	−	0.0180674i
$547$	−29.2626	−	9.50800i	−1.25118	−	0.406533i	−0.392836	−	0.919608i	$-0.628506\pi$
$547$	−29.2626	−	9.50800i	−1.25118	−	0.406533i	−0.858343	+	0.513076i	$0.828506\pi$
$548$	−31.9067	+	43.9157i	−1.36298	+	1.87599i
$549$	−1.20602			−0.0514718
$550$		0			0
$551$	56.1457			2.39189
$552$	−10.2972	+	14.1729i	−0.438278	+	0.603238i
$553$	1.86870	+	0.607177i	0.0794652	+	0.0258198i
$554$	−0.0672109	−	0.206854i	−0.00285552	−	0.00878838i
$555$		0			0
$556$	56.4470	−	41.0112i	2.39389	−	1.73926i
$557$	−13.2538	+	4.30642i	−0.561582	+	0.182469i	−0.576033	−	0.817427i	$-0.695400\pi$
$557$	−13.2538	+	4.30642i	−0.561582	+	0.182469i	0.0144509	+	0.999896i	$0.495400\pi$
$558$	5.61288	+	1.82374i	0.237612	+	0.0772049i
$559$	4.02817	+	2.92664i	0.170373	+	0.123783i
$560$		0			0
$561$	−5.18217	+	7.20406i	−0.218791	+	0.304156i
$562$			12.2095i			0.515026i
$563$	3.43259	−	4.72456i	0.144667	−	0.199117i	−0.730534	−	0.682876i	$-0.760729\pi$
$563$	3.43259	−	4.72456i	0.144667	−	0.199117i	0.875201	+	0.483759i	$0.160729\pi$
$564$	11.9024	−	36.6318i	0.501181	−	1.54248i
$565$		0			0
$566$	2.98183	−	2.16643i	0.125336	−	0.0910618i
$567$	0.113752	+	0.156567i	0.00477715	+	0.00657518i
$568$	20.7928	−	6.75599i	0.872447	−	0.283475i
$569$	1.68536	−	5.18701i	0.0706540	−	0.217451i	−0.909494	−	0.415716i	$-0.863531\pi$
$569$	1.68536	−	5.18701i	0.0706540	−	0.217451i	0.980148	+	0.198266i	$0.0635309\pi$
$570$		0			0
$571$	40.2894			1.68606			0.843030	−	0.537866i	$-0.180770\pi$
$571$	40.2894			1.68606			0.843030	+	0.537866i	$0.180770\pi$
$572$	3.59344	+	10.8840i	0.150249	+	0.455084i
$573$			0.417099i			0.0174246i
$574$	3.05332	+	2.21837i	0.127443	+	0.0925928i
$575$		0			0
$576$	−3.66971	−	11.2942i	−0.152905	−	0.470592i
$577$	−14.0032	−	19.2737i	−0.582959	−	0.802374i	0.411057	−	0.911610i	$-0.365160\pi$
$577$	−14.0032	−	19.2737i	−0.582959	−	0.802374i	−0.994016	+	0.109236i	$0.965160\pi$
$578$	−13.6256	−	18.7540i	−0.566750	−	0.780065i
$579$	−3.61443	−	11.1241i	−0.150210	−	0.462300i
$580$		0			0
$581$	−1.30186	−	0.945860i	−0.0540104	−	0.0392409i
$582$		−	37.3428i		−	1.54791i
$583$	30.8071	−	0.145740i	1.27590	−	0.00603595i
$584$	12.0658			0.499287
$585$		0			0
$586$	16.8570	−	51.8805i	0.696357	−	2.14317i
$587$	18.6483	−	6.05919i	0.769697	−	0.250090i	0.102262	−	0.994758i	$-0.467392\pi$
$587$	18.6483	−	6.05919i	0.769697	−	0.250090i	0.667435	+	0.744668i	$0.267392\pi$
$588$	14.5250	+	19.9920i	0.599003	+	0.824457i
$589$	11.2474	−	8.17172i	0.463441	−	0.336710i
$590$		0			0
$591$	6.67348	−	20.5389i	0.274510	−	0.844856i
$592$	−5.03102	+	6.92460i	−0.206774	+	0.284599i
$593$			3.31095i			0.135964i	0.997687	+	0.0679822i	$0.0216561\pi$
$593$			3.31095i			0.135964i	−0.997687	+	0.0679822i	$0.978344\pi$
$594$	−4.62215	−	6.29896i	−0.189649	−	0.258450i
$595$		0			0
$596$	29.0953	+	21.1390i	1.19179	+	0.865887i
$597$	−7.38046	−	2.39806i	−0.302062	−	0.0981460i
$598$	−10.4720	+	3.40255i	−0.428230	+	0.139140i
$599$	25.9460	−	18.8509i	1.06012	−	0.770225i	0.0860126	−	0.996294i	$-0.472587\pi$
$599$	25.9460	−	18.8509i	1.06012	−	0.770225i	0.974111	+	0.226069i	$0.0725875\pi$
$600$		0			0
$601$	−9.05125	−	27.8569i	−0.369208	−	1.13631i	−0.947304	−	0.320337i	$-0.896204\pi$
$601$	−9.05125	−	27.8569i	−0.369208	−	1.13631i	0.578095	−	0.815969i	$-0.303796\pi$
$602$	2.21710	+	0.720378i	0.0903621	+	0.0293604i
$603$	1.91572	−	2.63676i	0.0780141	−	0.107377i
$604$	−42.4596			−1.72766
$605$		0			0
$606$	−30.9986			−1.25923
$607$	22.9710	−	31.6169i	0.932364	−	1.28329i	−0.0265657	−	0.999647i	$-0.508457\pi$
$607$	22.9710	−	31.6169i	0.932364	−	1.28329i	0.958930	−	0.283642i	$-0.0915429\pi$
$608$	−19.8914	−	6.46311i	−0.806703	−	0.262114i
$609$	0.605076	+	1.86223i	0.0245189	+	0.0754615i
$610$		0			0
$611$	8.54886	−	6.21111i	0.345850	−	0.251275i
$612$	−9.03182	+	2.93462i	−0.365090	+	0.118625i
$613$	−12.1092	−	3.93452i	−0.489086	−	0.158914i	0.0540840	−	0.998536i	$-0.482776\pi$
$613$	−12.1092	−	3.93452i	−0.489086	−	0.158914i	−0.543170	+	0.839623i	$0.682776\pi$
$614$	14.7218	+	10.6960i	0.594123	+	0.431655i
$615$		0			0
$616$	1.38578	+	1.88851i	0.0558346	+	0.0760901i
$617$			8.97789i			0.361436i	0.983535	+	0.180718i	$0.0578422\pi$
$617$			8.97789i			0.361436i	−0.983535	+	0.180718i	$0.942158\pi$
$618$	−5.53487	+	7.61810i	−0.222645	+	0.306445i
$619$	6.86392	−	21.1250i	0.275884	−	0.849084i	−0.713100	−	0.701062i	$-0.752710\pi$
$619$	6.86392	−	21.1250i	0.275884	−	0.849084i	0.988984	−	0.148022i	$-0.0472905\pi$
$620$		0			0
$621$	3.88361	−	2.82160i	0.155844	−	0.113227i
$622$	26.4753	+	36.4402i	1.06156	+	1.46112i
$623$	−1.35146	+	0.439117i	−0.0541452	+	0.0175928i
$624$	−0.450866	+	1.38762i	−0.0180491	+	0.0555493i
$625$		0			0
$626$	−6.83868			−0.273329
$627$	−18.4044	+	0.0870666i	−0.735001	+	0.00347711i
$628$		−	9.32038i		−	0.371924i
$629$	−12.3651	−	8.98377i	−0.493029	−	0.358206i
$630$		0			0
$631$	8.27153	+	25.4572i	0.329285	+	1.01343i	0.969469	+	0.245213i	$0.0788578\pi$
$631$	8.27153	+	25.4572i	0.329285	+	1.01343i	−0.640185	+	0.768221i	$0.721142\pi$
$632$	−21.7788	−	29.9759i	−0.866313	−	1.19238i
$633$	7.35065	+	10.1173i	0.292162	+	0.402127i
$634$	1.64627	+	5.06670i	0.0653817	+	0.201224i
$635$		0			0
$636$	26.6715	+	19.3780i	1.05759	+	0.768386i
$637$			6.77949i			0.268613i
$638$	−24.7829	−	75.0639i	−0.981166	−	2.97181i
$639$	−5.99078			−0.236992
$640$		0			0
$641$	4.65770	−	14.3349i	0.183968	−	0.566195i	−0.815961	−	0.578107i	$-0.803792\pi$
$641$	4.65770	−	14.3349i	0.183968	−	0.566195i	0.999929	+	0.0119117i	$0.00379170\pi$
$642$	−10.9483	+	3.55733i	−0.432096	+	0.140396i
$643$	23.0925	+	31.7840i	0.910678	+	1.25344i	0.966935	+	0.255024i	$0.0820834\pi$
$643$	23.0925	+	31.7840i	0.910678	+	1.25344i	−0.0562569	+	0.998416i	$0.517917\pi$
$644$	−2.66752	+	1.93807i	−0.105115	+	0.0763705i
$645$		0			0
$646$	−10.8085	+	33.2652i	−0.425256	+	1.30880i
$647$	−13.9973	+	19.2656i	−0.550289	+	0.757408i	−0.990051	−	0.140706i	$-0.955063\pi$
$647$	−13.9973	+	19.2656i	−0.550289	+	0.757408i	0.439762	+	0.898114i	$0.355063\pi$
$648$		−	3.64941i		−	0.143363i
$649$	21.7265	−	30.2033i	0.852838	−	1.18559i
$650$		0			0
$651$	0.392251	+	0.284987i	0.0153735	+	0.0111695i
$652$	−80.0784	−	26.0190i	−3.13611	−	1.01898i
$653$	−6.56566	+	2.13331i	−0.256934	+	0.0834829i	−0.434652	−	0.900599i	$-0.643129\pi$
$653$	−6.56566	+	2.13331i	−0.256934	+	0.0834829i	0.177718	+	0.984081i	$0.443129\pi$
$654$	14.3310	−	10.4121i	0.560387	−	0.407145i
$655$		0			0
$656$	−3.83332	−	11.7978i	−0.149666	−	0.460625i
$657$	−3.14442	−	1.02168i	−0.122675	−	0.0398596i
$658$	2.90802	−	4.00254i	0.113366	−	0.156035i
$659$	20.3718			0.793571			0.396786	−	0.917911i	$-0.370126\pi$
$659$	20.3718			0.793571			0.396786	+	0.917911i	$0.370126\pi$
$660$		0			0
$661$	−19.7451			−0.767994			−0.383997	−	0.923334i	$-0.625453\pi$
$661$	−19.7451			−0.767994			−0.383997	+	0.923334i	$0.625453\pi$
$662$	8.34013	−	11.4792i	0.324148	−	0.446152i
$663$	−2.47784	−	0.805099i	−0.0962314	−	0.0312675i
$664$	9.37717	+	28.8600i	0.363905	+	1.11998i
$665$		0			0
$666$	10.8861	−	7.90925i	0.421830	−	0.306477i
$667$	46.1923	−	15.0088i	1.78857	−	0.581143i
$668$	11.7864	+	3.82962i	0.456028	+	0.148172i
$669$	−4.34901	−	3.15974i	−0.168143	−	0.122163i
$670$		0			0
$671$	3.80996	+	1.21803i	0.147082	+	0.0470217i
$672$		−	0.729407i		−	0.0281375i
$673$	21.5207	−	29.6207i	0.829563	−	1.14180i	−0.158441	−	0.987368i	$-0.550647\pi$
$673$	21.5207	−	29.6207i	0.829563	−	1.14180i	0.988004	−	0.154427i	$-0.0493532\pi$
$674$	−10.6023	+	32.6306i	−0.408386	+	1.25688i
$675$		0			0
$676$	34.6054	−	25.1423i	1.33098	−	0.967011i
$677$	4.33279	+	5.96357i	0.166523	+	0.229199i	0.884120	−	0.467259i	$-0.154758\pi$
$677$	4.33279	+	5.96357i	0.166523	+	0.229199i	−0.717598	+	0.696458i	$0.754758\pi$
$678$	45.3088	−	14.7217i	1.74007	−	0.565384i
$679$	0.948017	−	2.91770i	0.0363816	−	0.111971i
$680$		0			0
$681$	−21.7529			−0.833573
$682$	−15.8898	−	11.4302i	−0.608452	−	0.437684i
$683$			24.5651i			0.939959i	0.882677	+	0.469979i	$0.155739\pi$
$683$			24.5651i			0.939959i	−0.882677	+	0.469979i	$0.844261\pi$
$684$	−15.9338	−	11.5766i	−0.609243	−	0.442641i
$685$		0			0
$686$	1.96700	+	6.05380i	0.0751004	+	0.231135i
$687$	1.56983	+	2.16068i	0.0598927	+	0.0824352i
$688$	−4.50376	−	6.19890i	−0.171704	−	0.236331i
$689$	2.79492	+	8.60189i	0.106478	+	0.327706i
$690$		0			0
$691$	−24.1439	−	17.5416i	−0.918479	−	0.667314i	0.0246662	−	0.999696i	$-0.492148\pi$
$691$	−24.1439	−	17.5416i	−0.918479	−	0.667314i	−0.943145	+	0.332382i	$0.892148\pi$
$692$			72.2602i			2.74692i
$693$	−0.201230	−	0.609497i	−0.00764410	−	0.0231529i
$694$	67.9262			2.57844
$695$		0			0
$696$	11.4102	−	35.1168i	0.432501	−	1.33110i
$697$	21.0670	−	6.84507i	0.797968	−	0.259276i
$698$	−2.26019	−	3.11088i	−0.0855494	−	0.117749i
$699$	−4.63323	+	3.36624i	−0.175245	+	0.127323i
$700$		0			0
$701$	−4.45569	+	13.7132i	−0.168289	+	0.517940i	−0.999264	−	0.0383701i	$-0.987783\pi$
$701$	−4.45569	+	13.7132i	−0.168289	+	0.517940i	0.830975	+	0.556310i	$0.187783\pi$
$702$	1.34823	−	1.85567i	0.0508855	−	0.0700379i
$703$		−	31.6980i		−	1.19551i
$704$	0.186325	+	39.3859i	0.00702238	+	1.48441i
$705$		0			0
$706$	47.5106	+	34.5184i	1.78808	+	1.29912i
$707$	−2.42201	−	0.786958i	−0.0910890	−	0.0295966i
$708$	37.8663	−	12.3035i	1.42310	−	0.462394i
$709$	−36.0084	+	26.1616i	−1.35232	+	0.982520i	−0.353430	+	0.935461i	$0.614985\pi$
$709$	−36.0084	+	26.1616i	−1.35232	+	0.982520i	−0.998892	+	0.0470585i	$0.985015\pi$
$710$		0			0
$711$	3.13743	+	9.65601i	0.117663	+	0.362129i
$712$	25.4850	+	8.28059i	0.955093	+	0.310328i
$713$	7.06904	−	9.72970i	0.264738	−	0.364380i
$714$	−1.21982			−0.0456506
$715$		0			0
$716$	13.6686			0.510819
$717$	14.3232	−	19.7141i	0.534908	−	0.736238i
$718$	−63.7185	−	20.7034i	−2.37795	−	0.772644i
$719$	−1.11044	−	3.41758i	−0.0414124	−	0.127454i	0.928213	−	0.372050i	$-0.121345\pi$
$719$	−1.11044	−	3.41758i	−0.0414124	−	0.127454i	−0.969625	+	0.244595i	$0.921345\pi$
$720$		0			0
$721$	−0.625854	+	0.454710i	−0.0233080	+	0.0169343i
$722$	−26.4222	+	8.58510i	−0.983333	+	0.319504i
$723$	−15.8904	−	5.16312i	−0.590972	−	0.192018i
$724$	−50.5794	−	36.7481i	−1.87977	−	1.36573i
$725$		0			0
$726$	8.24018	+	24.5673i	0.305822	+	0.911778i
$727$			39.0846i			1.44957i	0.688976	+	0.724784i	$0.258060\pi$
$727$			39.0846i			1.44957i	−0.688976	+	0.724784i	$0.741940\pi$
$728$	−0.404215	+	0.556354i	−0.0149812	+	0.0206199i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$		0			0
$731$	11.0692	−	8.04226i	0.409410	−	0.297454i
$732$	2.51597	+	3.46293i	0.0929928	+	0.127994i
$733$	−35.8610	+	11.6519i	−1.32455	+	0.430374i	−0.884057	−	0.467379i	$-0.845198\pi$
$733$	−35.8610	+	11.6519i	−1.32455	+	0.430374i	−0.440498	+	0.897753i	$0.645198\pi$
$734$	−7.60065	+	23.3924i	−0.280545	+	0.863429i
$735$		0			0
$736$	−18.0928			−0.666910
$737$	−8.71499	+	6.39502i	−0.321021	+	0.235564i
$738$			19.5017i			0.717868i
$739$	12.0806	+	8.77706i	0.444392	+	0.322869i	0.787377	−	0.616471i	$-0.211438\pi$
$739$	12.0806	+	8.77706i	0.444392	+	0.322869i	−0.342986	+	0.939341i	$0.611438\pi$
$740$		0			0
$741$	−1.66971	−	5.13885i	−0.0613384	−	0.188780i
$742$	2.48906	+	3.42589i	0.0913761	+	0.125768i
$743$	−7.85749	−	10.8149i	−0.288263	−	0.396760i	0.640186	−	0.768220i	$-0.278857\pi$
$743$	−7.85749	−	10.8149i	−0.288263	−	0.396760i	−0.928449	+	0.371460i	$0.878857\pi$
$744$	−2.82533	−	8.69548i	−0.103582	−	0.318792i
$745$		0			0
$746$	−5.36949	−	3.90116i	−0.196591	−	0.142832i
$747$		−	8.31508i		−	0.304233i
$748$	31.4964	−	0.149001i	1.15162	−	0.00544803i
$749$	−0.945731			−0.0345563
$750$		0			0
$751$	12.5045	−	38.4849i	0.456296	−	1.40434i	−0.413310	−	0.910590i	$-0.635627\pi$
$751$	12.5045	−	38.4849i	0.456296	−	1.40434i	0.869606	−	0.493745i	$-0.164373\pi$
$752$	−15.4655	+	5.02504i	−0.563968	+	0.183244i
$753$	9.46240	+	13.0239i	0.344829	+	0.474617i
$754$	18.7753	−	13.6411i	0.683757	−	0.496779i
$755$		0			0
$756$	0.212253	−	0.653249i	0.00771958	−	0.0237584i
$757$	5.01826	−	6.90704i	0.182392	−	0.251040i	−0.708025	−	0.706188i	$-0.750413\pi$
$757$	5.01826	−	6.90704i	0.182392	−	0.251040i	0.890416	+	0.455147i	$0.150413\pi$
$758$		−	21.0437i		−	0.764341i
$759$	−15.1184	+	4.99148i	−0.548765	+	0.181179i
$760$		0			0
$761$	17.2162	+	12.5083i	0.624089	+	0.453427i	0.854347	−	0.519703i	$-0.173957\pi$
$761$	17.2162	+	12.5083i	0.624089	+	0.453427i	−0.230259	+	0.973129i	$0.573957\pi$
$762$	15.9072	+	5.16855i	0.576256	+	0.187237i
$763$	1.38405	−	0.449706i	0.0501060	−	0.0162804i
$764$	1.19764	−	0.870139i	0.0433292	−	0.0314805i
$765$		0			0
$766$	6.21139	+	19.1167i	0.224427	+	0.690714i
$767$	10.3885	+	3.37541i	0.375105	+	0.121879i
$768$	−14.3368	+	19.7329i	−0.517333	+	0.712048i
$769$	24.4717			0.882471			0.441235	−	0.897391i	$-0.354540\pi$
$769$	24.4717			0.882471			0.441235	+	0.897391i	$0.354540\pi$
$770$		0			0
$771$	5.96875			0.214959
$772$	−24.4009	+	33.5850i	−0.878209	+	1.20875i
$773$	12.9792	+	4.21721i	0.466830	+	0.151682i	0.532981	−	0.846127i	$-0.321072\pi$
$773$	12.9792	+	4.21721i	0.466830	+	0.151682i	−0.0661505	+	0.997810i	$0.521072\pi$
$774$	3.72236	+	11.4563i	0.133798	+	0.411787i
$775$		0			0
$776$	−46.8029	+	34.0043i	−1.68013	+	1.22068i
$777$	1.05136	−	0.341606i	0.0377172	−	0.0122550i
$778$	−26.3821	−	8.57207i	−0.945845	−	0.307324i
$779$	37.1660	+	27.0027i	1.33161	+	0.967471i
$780$		0			0
$781$	18.9255	+	6.05045i	0.677209	+	0.216502i
$782$			30.2574i			1.08200i
$783$	−5.94709	+	8.18547i	−0.212532	+	0.292525i
$784$	3.22394	−	9.92225i	0.115141	−	0.354366i
$785$		0			0
$786$	−4.76490	+	3.46191i	−0.169958	+	0.123482i
$787$	−4.38317	−	6.03291i	−0.156243	−	0.215050i	0.723718	−	0.690096i	$-0.242432\pi$
$787$	−4.38317	−	6.03291i	−0.156243	−	0.215050i	−0.879961	+	0.475046i	$0.842432\pi$
$788$	−72.8966	+	23.6855i	−2.59683	+	0.843762i
$789$	0.139413	−	0.429068i	0.00496322	−	0.0152752i
$790$		0			0
$791$	3.91383			0.139160
$792$	−3.68576	+	11.5289i	−0.130968	+	0.409662i
$793$			1.17431i			0.0417011i
$794$	2.69124	+	1.95530i	0.0955085	+	0.0693910i
$795$		0			0
$796$	8.51119	+	26.1947i	0.301671	+	0.928448i
$797$	7.07379	+	9.73624i	0.250567	+	0.344875i	0.915710	−	0.401841i	$-0.131629\pi$
$797$	7.07379	+	9.73624i	0.250567	+	0.344875i	−0.665143	+	0.746716i	$0.731629\pi$
$798$	−1.48698	−	2.04666i	−0.0526386	−	0.0724509i
$799$	−8.97309	−	27.6163i	−0.317445	−	0.976996i
$800$		0			0
$801$	−5.94037	−	4.31593i	−0.209893	−	0.152496i
$802$			19.9270i			0.703648i
$803$	8.90170	+	6.40334i	0.314134	+	0.225969i
$804$	−11.5676			−0.407958
$805$		0			0
$806$	1.77579	−	5.46531i	0.0625494	−	0.192507i
$807$	13.9993	−	4.54864i	0.492798	−	0.160120i
$808$	28.2273	+	38.8515i	0.993033	+	1.36679i
$809$	−40.4782	+	29.4091i	−1.42314	+	1.03397i	−0.431892	+	0.901925i	$0.642154\pi$
$809$	−40.4782	+	29.4091i	−1.42314	+	1.03397i	−0.991244	+	0.132044i	$0.957846\pi$
$810$		0			0
$811$	−3.46678	+	10.6697i	−0.121735	+	0.374663i	−0.993292	−	0.115632i	$-0.963111\pi$
$811$	−3.46678	+	10.6697i	−0.121735	+	0.374663i	0.871557	+	0.490294i	$0.163111\pi$
$812$	4.08486	−	5.62233i	0.143350	−	0.197305i
$813$			4.42787i			0.155292i
$814$	−42.3786	+	13.9916i	−1.48537	+	0.490406i
$815$		0			0
$816$	3.24363	+	2.35664i	0.113550	+	0.0824988i
$817$	26.9872	+	8.76867i	0.944163	+	0.306777i
$818$	22.6850	−	7.37080i	0.793163	−	0.257714i
$819$	0.152450	−	0.110762i	0.00532704	−	0.00387032i
$820$		0			0
$821$	2.27969	+	7.01616i	0.0795617	+	0.244866i	0.982924	−	0.184013i	$-0.0589088\pi$
$821$	2.27969	+	7.01616i	0.0795617	+	0.244866i	−0.903362	+	0.428879i	$0.858909\pi$
$822$	−34.2652	−	11.1334i	−1.19514	−	0.388323i
$823$	20.9475	−	28.8318i	0.730184	−	1.00501i	−0.268939	−	0.963157i	$-0.586673\pi$
$823$	20.9475	−	28.8318i	0.730184	−	1.00501i	0.999124	−	0.0418554i	$-0.0133269\pi$
$824$	14.5880			0.508198
$825$		0			0
$826$	5.11414			0.177944
$827$	29.7003	−	40.8789i	1.03278	−	1.42150i	0.129940	−	0.991522i	$-0.458522\pi$
$827$	29.7003	−	40.8789i	1.03278	−	1.42150i	0.902840	−	0.429977i	$-0.141478\pi$
$828$	−16.2037	−	5.26490i	−0.563118	−	0.182968i
$829$	1.89888	+	5.84416i	0.0659509	+	0.202976i	0.978602	−	0.205765i	$-0.0659681\pi$
$829$	1.89888	+	5.84416i	0.0659509	+	0.202976i	−0.912651	+	0.408741i	$0.865968\pi$
$830$		0			0
$831$	0.0746965	−	0.0542702i	0.00259119	−	0.00188261i
$832$	−10.9973	+	3.57323i	−0.381262	+	0.123879i
$833$	17.7179	+	5.75690i	0.613890	+	0.199465i
$834$	37.4650	+	27.2199i	1.29731	+	0.942548i
$835$		0			0
$836$	38.6447	+	52.6641i	1.33655	+	1.82143i
$837$			2.50533i			0.0865967i
$838$	−45.4186	+	62.5133i	−1.56896	+	2.15949i
$839$	11.5953	−	35.6865i	0.400312	−	1.23204i	−0.524434	−	0.851451i	$-0.675723\pi$
$839$	11.5953	−	35.6865i	0.400312	−	1.23204i	0.924746	−	0.380584i	$-0.124277\pi$
$840$		0			0
$841$	−59.3574	+	43.1257i	−2.04681	+	1.48709i
$842$	19.5638	+	26.9273i	0.674214	+	0.927976i
$843$	−4.92934	+	1.60164i	−0.169775	+	0.0551633i
$844$	13.7158	−	42.2128i	0.472116	−	1.45302i
$845$		0			0
$846$	25.5645			0.878924
$847$	0.0201412	+	2.12870i	0.000692058	+	0.0731431i
$848$		−	13.9186i		−	0.477966i
$849$	1.26581	+	0.919664i	0.0434424	+	0.0315628i
$850$		0			0
$851$	−8.47347	−	26.0787i	−0.290467	−	0.893965i
$852$	12.4978	+	17.2017i	0.428167	+	0.589321i
$853$	15.8774	+	21.8533i	0.543631	+	0.748244i	0.989131	−	0.147038i	$-0.0469740\pi$
$853$	15.8774	+	21.8533i	0.543631	+	0.748244i	−0.445500	+	0.895282i	$0.646974\pi$
$854$	0.169901	+	0.522900i	0.00581388	+	0.0178933i
$855$		0			0
$856$	14.4280	+	10.4826i	0.493140	+	0.358287i
$857$			2.51515i			0.0859159i	0.999077	+	0.0429580i	$0.0136782\pi$
$857$			2.51515i			0.0859159i	−0.999077	+	0.0429580i	$0.986322\pi$
$858$	−6.13335	+	4.50063i	−0.209389	+	0.153649i
$859$	−6.70885			−0.228903			−0.114451	−	0.993429i	$-0.536511\pi$
$859$	−6.70885			−0.228903			−0.114451	+	0.993429i	$0.536511\pi$
$860$		0			0
$861$	−0.495087	+	1.52372i	−0.0168725	+	0.0519283i
$862$	−42.8041	+	13.9079i	−1.45791	+	0.473705i
$863$	1.94406	+	2.67577i	0.0661767	+	0.0910844i	0.840822	−	0.541311i	$-0.182072\pi$
$863$	1.94406	+	2.67577i	0.0661767	+	0.0910844i	−0.774646	+	0.632395i	$0.782072\pi$
$864$	3.04920	−	2.21537i	0.103736	−	0.0753686i
$865$		0			0
$866$	−11.0065	+	33.8746i	−0.374017	+	1.15111i
$867$	5.78416	−	7.96121i	0.196440	−	0.270377i
$868$		−	1.72082i		−	0.0584086i
$869$	−0.159299	−	33.6731i	−0.00540384	−	1.14228i
$870$		0			0
$871$	−2.56744	−	1.86535i	−0.0869942	−	0.0632050i
$872$	−26.0996	−	8.48027i	−0.883844	−	0.287178i
$873$	15.0764	−	4.89863i	0.510260	−	0.165793i
$874$	−50.7669	+	36.8843i	−1.71722	+	1.24763i
$875$		0			0
$876$	3.62616	+	11.1602i	0.122517	+	0.377067i
$877$	−30.5293	−	9.91956i	−1.03090	−	0.334960i	−0.255754	−	0.966742i	$-0.582324\pi$
$877$	−30.5293	−	9.91956i	−1.03090	−	0.334960i	−0.775146	+	0.631782i	$0.782324\pi$
$878$	−51.4587	+	70.8269i	−1.73665	+	2.39029i
$879$	23.1570			0.781067
$880$		0			0
$881$	−35.2547			−1.18776			−0.593881	−	0.804553i	$-0.702405\pi$
$881$	−35.2547			−1.18776			−0.593881	+	0.804553i	$0.702405\pi$
$882$	−9.64056	+	13.2691i	−0.324614	+	0.446793i
$883$	−0.433541	−	0.140866i	−0.0145898	−	0.00474052i	0.301713	−	0.953399i	$-0.402442\pi$
$883$	−0.433541	−	0.140866i	−0.0145898	−	0.00474052i	−0.316303	+	0.948658i	$0.602442\pi$
$884$	2.85746	+	8.79436i	0.0961068	+	0.295786i
$885$		0			0
$886$	−5.26090	+	3.82226i	−0.176743	+	0.128411i
$887$	−1.71342	+	0.556725i	−0.0575312	+	0.0186930i	−0.337641	−	0.941275i	$-0.609629\pi$
$887$	−1.71342	+	0.556725i	−0.0575312	+	0.0186930i	0.280110	+	0.959968i	$0.409629\pi$
$888$	−19.8258	−	6.44179i	−0.665310	−	0.216172i
$889$	1.11166	+	0.807666i	0.0372838	+	0.0270882i
$890$		0			0
$891$	1.93675	−	2.69240i	0.0648835	−	0.0901987i
$892$			19.0794i			0.638824i
$893$	35.3973	−	48.7203i	1.18453	−	1.63036i
$894$	−7.37620	+	22.7016i	−0.246697	+	0.759255i
$895$		0			0
$896$	−3.19970	+	2.32471i	−0.106894	+	0.0776633i
$897$	−2.74742	−	3.78150i	−0.0917337	−	0.126261i
$898$	−40.0269	+	13.0055i	−1.33572	+	0.434001i
$899$	−7.83308	+	24.1077i	−0.261248	+	0.804038i
$900$		0			0
$901$	24.8541			0.828009
$902$	19.6959	−	61.6080i	0.655803	−	2.05132i
$903$			0.989607i			0.0329321i
$904$	−59.7092	−	43.3813i	−1.98590	−	1.44284i
$905$		0			0
$906$	−8.70850	−	26.8020i	−0.289321	−	0.890437i
$907$	−20.7764	−	28.5962i	−0.689868	−	0.949522i	0.310131	−	0.950694i	$-0.399627\pi$
$907$	−20.7764	−	28.5962i	−0.689868	−	0.949522i	−0.999999	+	0.00117159i	$0.999627\pi$
$908$	45.3802	+	62.4605i	1.50600	+	2.07282i
$909$	−4.06640	−	12.5151i	−0.134874	−	0.415099i
$910$		0			0
$911$	1.33388	+	0.969123i	0.0441935	+	0.0321085i	0.609663	−	0.792661i	$-0.291305\pi$
$911$	1.33388	+	0.969123i	0.0441935	+	0.0321085i	−0.565469	+	0.824769i	$0.691305\pi$
$912$			8.31508i			0.275340i
$913$	−8.39789	+	26.2682i	−0.277930	+	0.869352i
$914$	−49.8511			−1.64893
$915$		0			0
$916$	2.92918	−	9.01510i	0.0967829	−	0.297867i
$917$	−0.460182	+	0.149522i	−0.0151965	+	0.00493765i
$918$	−3.70486	−	5.09931i	−0.122279	−	0.168302i
$919$	−0.258068	+	0.187498i	−0.00851288	+	0.00618497i	−0.592034	−	0.805913i	$-0.701675\pi$
$919$	−0.258068	+	0.187498i	−0.00851288	+	0.00618497i	0.583521	+	0.812098i	$0.301675\pi$
$920$		0			0
$921$	−2.38710	+	7.34672i	−0.0786575	+	0.242083i
$922$	−47.5588	+	65.4590i	−1.56626	+	2.15578i
$923$			5.83327i			0.192005i
$924$	−1.33029	+	1.84932i	−0.0437632	+	0.0608381i
$925$		0			0
$926$	19.9185	+	14.4716i	0.654561	+	0.475567i
$927$	−3.80172	−	1.23525i	−0.124865	−	0.0405711i
$928$	36.2678	−	11.7841i	1.19055	−	0.386832i
$929$	45.4270	−	33.0046i	1.49041	−	1.08285i	0.516400	−	0.856347i	$-0.327272\pi$
$929$	45.4270	−	33.0046i	1.49041	−	1.08285i	0.974011	−	0.226500i	$-0.0727283\pi$
$930$		0			0
$931$	11.9394	+	36.7456i	0.391297	+	1.20429i
$932$	19.3314	+	6.28115i	0.633221	+	0.205746i
$933$	−11.2390	+	15.4691i	−0.367947	+	0.506436i
$934$	69.8301			2.28491
$935$		0			0
$936$	−3.55346			−0.116149
$937$	−21.6554	+	29.8061i	−0.707452	+	0.973724i	0.292396	+	0.956297i	$0.405547\pi$
$937$	−21.6554	+	29.8061i	−0.707452	+	0.973724i	−0.999848	+	0.0174269i	$0.994453\pi$
$938$	−1.41311	−	0.459148i	−0.0461397	−	0.0149917i
$939$	−0.897097	−	2.76098i	−0.0292756	−	0.0901012i
$940$		0			0
$941$	12.3865	−	8.99929i	0.403787	−	0.293368i	−0.367295	−	0.930105i	$-0.619716\pi$
$941$	12.3865	−	8.99929i	0.403787	−	0.293368i	0.771082	+	0.636736i	$0.219716\pi$
$942$	5.88335	−	1.91162i	0.191690	−	0.0622838i
$943$	37.7956	+	12.2805i	1.23079	+	0.399909i
$944$	−13.5991	−	9.88030i	−0.442612	−	0.321576i
$945$		0			0
$946$	−0.188998	−	39.9510i	−0.00614486	−	1.29892i
$947$			22.6654i			0.736526i	0.929722	+	0.368263i	$0.120047\pi$
$947$			22.6654i			0.736526i	−0.929722	+	0.368263i	$0.879953\pi$
$948$	21.1807	−	29.1528i	0.687918	−	0.946838i
$949$	−0.994821	+	3.06174i	−0.0322933	+	0.0993884i
$950$		0			0
$951$	−1.82962	+	1.32930i	−0.0593295	+	0.0431054i
$952$	1.11076	+	1.52884i	0.0360001	+	0.0495499i
$953$	−37.4074	+	12.1544i	−1.21174	+	0.393719i	−0.844069	−	0.536235i	$-0.819846\pi$
$953$	−37.4074	+	12.1544i	−1.21174	+	0.393719i	−0.367675	+	0.929955i	$0.619846\pi$
$954$	−6.76171	+	20.8104i	−0.218918	+	0.673762i
$955$		0			0
$956$	−86.4870			−2.79719
$957$	27.0545	−	19.8525i	0.874548	−	0.641740i
$958$			31.1388i			1.00605i
$959$	−2.39459	−	1.73977i	−0.0773254	−	0.0561802i
$960$		0			0
$961$	−7.63993	−	23.5133i	−0.246449	−	0.758493i
$962$	−7.70130	−	10.5999i	−0.248300	−	0.341756i
$963$	−2.87240	−	3.95352i	−0.0925618	−	0.127400i
$964$	18.3249	+	56.3984i	0.590207	+	1.81647i
$965$		0			0
$966$	−1.77048	−	1.28633i	−0.0569644	−	0.0413871i
$967$		−	3.06103i		−	0.0984360i	−0.998788	−	0.0492180i	$-0.984327\pi$
$967$		−	3.06103i		−	0.0984360i	0.998788	−	0.0492180i	$-0.0156729\pi$
$968$	23.2875	−	32.6986i	0.748487	−	1.05097i
$969$	−14.8480			−0.476987
$970$		0			0
$971$	9.90043	−	30.4704i	0.317720	−	0.977841i	−0.656900	−	0.753977i	$-0.728133\pi$
$971$	9.90043	−	30.4704i	0.317720	−	0.977841i	0.974620	−	0.223864i	$-0.0718672\pi$
$972$	3.37549	−	1.09676i	0.108269	−	0.0351787i
$973$	2.23621	+	3.07788i	0.0716897	+	0.0986724i
$974$	80.9911	−	58.8434i	2.59512	−	1.88547i
$975$		0			0
$976$	0.558436	−	1.71869i	0.0178751	−	0.0550139i
$977$	31.2679	−	43.0366i	1.00035	−	1.37686i	0.0752388	−	0.997166i	$-0.476028\pi$
$977$	31.2679	−	43.0366i	1.00035	−	1.37686i	0.925111	−	0.379697i	$-0.123972\pi$
$978$		−	55.8848i		−	1.78700i
$979$	14.4074	+	19.6340i	0.460462	+	0.627507i
$980$		0			0
$981$	6.08362	+	4.42001i	0.194235	+	0.141120i
$982$	−35.2762	−	11.4619i	−1.12571	−	0.365765i
$983$	23.3013	−	7.57104i	0.743195	−	0.241479i	0.0871446	−	0.996196i	$-0.472226\pi$
$983$	23.3013	−	7.57104i	0.743195	−	0.241479i	0.656051	+	0.754717i	$0.272226\pi$
$984$	24.4421	−	17.7582i	0.779185	−	0.566111i
$985$		0			0
$986$	−19.7071	−	60.6521i	−0.627601	−	1.93156i
$987$	1.99742	+	0.649001i	0.0635786	+	0.0206579i
$988$	−11.2722	+	15.5149i	−0.358616	+	0.493593i
$989$	24.5470			0.780549
$990$		0			0
$991$	−6.34819			−0.201657			−0.100828	−	0.994904i	$-0.532149\pi$
$991$	−6.34819			−0.201657			−0.100828	+	0.994904i	$0.532149\pi$
$992$	5.55023	−	7.63924i	0.176220	−	0.242546i
$993$	5.72856	+	1.86132i	0.181790	+	0.0590673i
$994$	0.843962	+	2.59745i	0.0267689	+	0.0823861i
$995$		0			0
$996$	−23.8756	+	17.3466i	−0.756528	+	0.549650i
$997$	−24.6761	+	8.01777i	−0.781501	+	0.253925i	−0.672481	−	0.740114i	$-0.734771\pi$
$997$	−24.6761	+	8.01777i	−0.781501	+	0.253925i	−0.109020	+	0.994040i	$0.534771\pi$
$998$	75.1152	+	24.4064i	2.37773	+	0.772572i
$999$	4.62125	+	3.35753i	0.146210	+	0.106228i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	825.2.bx.f.499.4		16
5.2	odd	4		165.2.m.d.136.2	yes	8
5.3	odd	4		825.2.n.g.301.1		8
5.4	even	2	inner	825.2.bx.f.499.1		16
11.3	even	5	inner	825.2.bx.f.124.1		16
15.2	even	4		495.2.n.a.136.1		8
55.3	odd	20		825.2.n.g.751.1		8
55.14	even	10	inner	825.2.bx.f.124.4		16
55.17	even	20		1815.2.a.w.1.4		4
55.27	odd	20		1815.2.a.p.1.1		4
55.28	even	20		9075.2.a.cm.1.1		4
55.38	odd	20		9075.2.a.di.1.4		4
55.47	odd	20		165.2.m.d.91.2	✓	8
165.17	odd	20		5445.2.a.bf.1.1		4
165.47	even	20		495.2.n.a.91.1		8
165.137	even	20		5445.2.a.bt.1.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
165.2.m.d.91.2	✓	8	55.47	odd	20
165.2.m.d.136.2	yes	8	5.2	odd	4
495.2.n.a.91.1		8	165.47	even	20
495.2.n.a.136.1		8	15.2	even	4
825.2.n.g.301.1		8	5.3	odd	4
825.2.n.g.751.1		8	55.3	odd	20
825.2.bx.f.124.1		16	11.3	even	5	inner
825.2.bx.f.124.4		16	55.14	even	10	inner
825.2.bx.f.499.1		16	5.4	even	2	inner
825.2.bx.f.499.4		16	1.1	even	1	trivial
1815.2.a.p.1.1		4	55.27	odd	20
1815.2.a.w.1.4		4	55.17	even	20
5445.2.a.bf.1.1		4	165.17	odd	20
5445.2.a.bt.1.4		4	165.137	even	20
9075.2.a.cm.1.1		4	55.28	even	20
9075.2.a.di.1.4		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)

\(f(q)\)	\(=\)	\(q+(1.38463 - 1.90578i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-1.09676 - 3.37549i) q^{4} +(1.90578 - 1.38463i) q^{6} +(0.184055 - 0.0598032i) q^{7} +(-3.47080 - 1.12773i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(1.38463 - 1.90578i) q^{2} +(0.951057 + 0.309017i) q^{3} +(-1.09676 - 3.37549i) q^{4} +(1.90578 - 1.38463i) q^{6} +(0.184055 - 0.0598032i) q^{7} +(-3.47080 - 1.12773i) q^{8} +(0.809017 + 0.587785i) q^{9} +(-1.96213 - 2.67395i) q^{11} -3.54920i q^{12} +(0.572331 - 0.787747i) q^{13} +(0.140877 - 0.433574i) q^{14} +(-1.21225 + 0.880754i) q^{16} +(-1.57274 - 2.16469i) q^{17} +(2.24038 - 0.727943i) q^{18} +(1.71480 - 5.27760i) q^{19} +0.193527 q^{21} +(-7.81280 + 0.0369604i) q^{22} -4.80040i q^{23} +(-2.95244 - 2.14507i) q^{24} +(-0.708805 - 2.18148i) q^{26} +(0.587785 + 0.809017i) q^{27} +(-0.403730 - 0.555687i) q^{28} +(3.12657 + 9.62260i) q^{29} +(2.02685 + 1.47259i) q^{31} -3.76902i q^{32} +(-1.03980 - 3.14941i) q^{33} -6.30309 q^{34} +(1.09676 - 3.37549i) q^{36} +(5.43260 - 1.76516i) q^{37} +(-7.68359 - 10.5756i) q^{38} +(0.787747 - 0.572331i) q^{39} +(-2.55823 + 7.87342i) q^{41} +(0.267964 - 0.368820i) q^{42} +5.11353i q^{43} +(-6.87391 + 9.55586i) q^{44} +(-9.14851 - 6.64678i) q^{46} +(10.3211 + 3.35354i) q^{47} +(-1.42509 + 0.463040i) q^{48} +(-5.63282 + 4.09248i) q^{49} +(-0.826838 - 2.54475i) q^{51} +(-3.28674 - 1.06793i) q^{52} +(-5.45981 + 7.51479i) q^{53} +2.35567 q^{54} -0.706260 q^{56} +(3.26174 - 4.48940i) q^{57} +(22.6677 + 7.36518i) q^{58} +(3.46656 + 10.6690i) q^{59} +(-0.975693 + 0.708883i) q^{61} +(5.61288 - 1.82374i) q^{62} +(0.184055 + 0.0598032i) q^{63} +(-9.60743 - 6.98021i) q^{64} +(-7.44184 - 2.37914i) q^{66} -3.25922i q^{67} +(-5.58197 + 7.68293i) q^{68} +(1.48341 - 4.56545i) q^{69} +(-4.84664 + 3.52129i) q^{71} +(-2.14507 - 2.95244i) q^{72} +(-3.14442 + 1.02168i) q^{73} +(4.15814 - 12.7974i) q^{74} -19.6952 q^{76} +(-0.521052 - 0.374813i) q^{77} -2.29374i q^{78} +(8.21389 + 5.96774i) q^{79} +(0.309017 + 0.951057i) q^{81} +(11.4628 + 15.7772i) q^{82} +(-4.88748 - 6.72704i) q^{83} +(-0.212253 - 0.653249i) q^{84} +(9.74527 + 7.08035i) q^{86} +10.1178i q^{87} +(3.79468 + 11.4935i) q^{88} -7.34270 q^{89} +(0.0582308 - 0.179216i) q^{91} +(-16.2037 + 5.26490i) q^{92} +(1.47259 + 2.02685i) q^{93} +(20.6821 - 15.0264i) q^{94} +(1.16469 - 3.58455i) q^{96} +(9.31774 - 12.8248i) q^{97} +16.4015i q^{98} +(-0.0156899 - 3.31659i) 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

Varieties

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Representations

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Database

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