LMFDB - Embedded newform 225.2.k.b.124.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(49,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("225.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.k (of order $6$, degree $2$, 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:	$1.79663404548$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 16x^{8} - 24x^{7} + 96x^{5} + 304x^{4} + 384x^{3} + 288x^{2} + 144x + 36 $ x^12 - 16x^8 - 24x^7 + 96x^5 + 304x^4 + 384x^3 + 288x^2 + 144*x + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	no (minimal twist has level 45)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			124.5
Root			$0.583700 + 2.17840i$ of defining polynomial
Character	$\chi$	$=$	225.124
Dual form			225.2.k.b.49.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.80664 + 1.04307i) q^{2} +(1.38276 + 1.04307i) q^{3} +(1.17597 + 2.03684i) q^{4} +(1.41016 + 3.32675i) q^{6} +(-3.53869 - 2.04307i) q^{7} +0.734191i q^{8} +(0.824030 + 2.88461i) q^{9} +O(q^{10})$	\(q+(1.80664 + 1.04307i) q^{2} +(1.38276 + 1.04307i) q^{3} +(1.17597 + 2.03684i) q^{4} +(1.41016 + 3.32675i) q^{6} +(-3.53869 - 2.04307i) q^{7} +0.734191i q^{8} +(0.824030 + 2.88461i) q^{9} +(0.675970 - 1.17081i) q^{11} +(-0.498476 + 4.04307i) q^{12} +(-0.561237 + 0.324030i) q^{13} +(-4.26210 - 7.38217i) q^{14} +(1.58613 - 2.74726i) q^{16} -1.35194i q^{17} +(-1.52011 + 6.07097i) q^{18} -0.648061 q^{19} +(-2.76210 - 6.51615i) q^{21} +(2.44247 - 1.41016i) q^{22} +(-4.14827 + 2.39500i) q^{23} +(-0.765809 + 1.01521i) q^{24} -1.35194 q^{26} +(-1.86940 + 4.84823i) q^{27} -9.61033i q^{28} +(1.93807 - 3.35683i) q^{29} +(3.84823 + 6.66533i) q^{31} +(7.00279 - 4.04307i) q^{32} +(2.15594 - 0.913870i) q^{33} +(1.41016 - 2.44247i) q^{34} +(-4.90645 + 5.07063i) q^{36} +7.52420i q^{37} +(-1.17081 - 0.675970i) q^{38} +(-1.11404 - 0.137352i) q^{39} +(0.0898394 + 0.155606i) q^{41} +(1.80664 - 14.6534i) q^{42} +(-0.710419 - 0.410161i) q^{43} +3.17968 q^{44} -9.99258 q^{46} +(-9.44526 - 5.45323i) q^{47} +(5.05880 - 2.14435i) q^{48} +(4.84823 + 8.39738i) q^{49} +(1.41016 - 1.86940i) q^{51} +(-1.32000 - 0.762100i) q^{52} -4.17226i q^{53} +(-8.43436 + 6.80911i) q^{54} +(1.50000 - 2.59808i) q^{56} +(-0.896110 - 0.675970i) q^{57} +(7.00279 - 4.04307i) q^{58} +(2.08613 + 3.61328i) q^{59} +(1.91016 - 3.30850i) q^{61} +16.0558i q^{62} +(2.97746 - 11.8913i) q^{63} +10.5242 q^{64} +(4.84823 + 0.597746i) q^{66} +(7.05113 - 4.07097i) q^{67} +(2.75368 - 1.58984i) q^{68} +(-8.23419 - 1.01521i) q^{69} -6.11644 q^{71} +(-2.11785 + 0.604996i) q^{72} +12.3445i q^{73} +(-7.84823 + 13.5935i) q^{74} +(-0.762100 - 1.32000i) q^{76} +(-4.78410 + 2.76210i) q^{77} +(-1.86940 - 1.41016i) q^{78} +(5.17226 - 8.95862i) q^{79} +(-7.64195 + 4.75401i) q^{81} +0.374833i q^{82} +(-10.6161 - 6.12920i) q^{83} +(10.0242 - 13.2887i) q^{84} +(-0.855648 - 1.48203i) q^{86} +(6.18127 - 2.62015i) q^{87} +(0.859601 + 0.496291i) q^{88} +3.00000 q^{89} +2.64806 q^{91} +(-9.75648 - 5.63290i) q^{92} +(-1.63121 + 13.2305i) q^{93} +(-11.3761 - 19.7041i) q^{94} +(13.9003 + 1.71380i) q^{96} +(11.7606 + 6.79001i) q^{97} +20.2281i q^{98} +(3.93436 + 0.985122i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 10 q^{4} - 8 q^{6} + 14 q^{9}+O(q^{10}) $ 12 * q + 10 * q^4 - 8 * q^6 + 14 * q^9	$ 12 q + 10 q^{4} - 8 q^{6} + 14 q^{9} + 4 q^{11} - 18 q^{14} - 10 q^{16} - 16 q^{19} - 30 q^{24} - 8 q^{26} - 14 q^{29} - 16 q^{31} - 8 q^{34} + 20 q^{36} + 28 q^{39} + 26 q^{41} + 88 q^{44} - 12 q^{46} - 4 q^{49} - 8 q^{51} - 10 q^{54} + 18 q^{56} - 4 q^{59} - 2 q^{61} + 60 q^{64} - 4 q^{66} - 78 q^{69} - 40 q^{71} - 32 q^{74} + 24 q^{76} + 4 q^{79} - 38 q^{81} + 54 q^{84} - 56 q^{86} + 36 q^{89} + 40 q^{91} - 62 q^{94} + 26 q^{96} - 44 q^{99}+O(q^{100}) $ 12 * q + 10 * q^4 - 8 * q^6 + 14 * q^9 + 4 * q^11 - 18 * q^14 - 10 * q^16 - 16 * q^19 - 30 * q^24 - 8 * q^26 - 14 * q^29 - 16 * q^31 - 8 * q^34 + 20 * q^36 + 28 * q^39 + 26 * q^41 + 88 * q^44 - 12 * q^46 - 4 * q^49 - 8 * q^51 - 10 * q^54 + 18 * q^56 - 4 * q^59 - 2 * q^61 + 60 * q^64 - 4 * q^66 - 78 * q^69 - 40 * q^71 - 32 * q^74 + 24 * q^76 + 4 * q^79 - 38 * q^81 + 54 * q^84 - 56 * q^86 + 36 * q^89 + 40 * q^91 - 62 * q^94 + 26 * q^96 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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 $

$2$	1.80664	+	1.04307i	1.27749	+	0.737558i	0.976386	−	0.216033i	$-0.0693120\pi$
$2$	1.80664	+	1.04307i	1.27749	+	0.737558i	0.301103	+	0.953592i	$0.402645\pi$
$3$	1.38276	+	1.04307i	0.798335	+	0.602214i
$3$	1.38276	+	1.04307i	0.798335	+	0.602214i
$4$	1.17597	+	2.03684i	0.587985	+	1.01842i
$5$		0			0
$5$		0			0
$6$	1.41016	+	3.32675i	0.575696	+	1.35814i
$7$	−3.53869	−	2.04307i	−1.33750	−	0.772206i	−0.351064	−	0.936351i	$-0.614180\pi$
$7$	−3.53869	−	2.04307i	−1.33750	−	0.772206i	−0.986436	+	0.164145i	$0.947513\pi$
$8$			0.734191i			0.259576i
$9$	0.824030	+	2.88461i	0.274677	+	0.961537i
$10$		0			0
$11$	0.675970	−	1.17081i	0.203813	−	0.353014i	−0.745941	−	0.666012i	$-0.768000\pi$
$11$	0.675970	−	1.17081i	0.203813	−	0.353014i	0.949754	+	0.312998i	$0.101333\pi$
$12$	−0.498476	+	4.04307i	−0.143898	+	1.16713i
$13$	−0.561237	+	0.324030i	−0.155659	+	0.0898699i	−0.575806	−	0.817586i	$-0.695312\pi$
$13$	−0.561237	+	0.324030i	−0.155659	+	0.0898699i	0.420147	+	0.907456i	$0.361978\pi$
$14$	−4.26210	−	7.38217i	−1.13909	−	1.97297i
$15$		0			0
$16$	1.58613	−	2.74726i	0.396533	−	0.686815i
$17$		−	1.35194i		−	0.327893i	−0.986469	−	0.163947i	$-0.947577\pi$
$17$		−	1.35194i		−	0.327893i	0.986469	−	0.163947i	$-0.0524225\pi$
$18$	−1.52011	+	6.07097i	−0.358293	+	1.43094i
$19$	−0.648061			−0.148675			−0.0743377	−	0.997233i	$-0.523684\pi$
$19$	−0.648061			−0.148675			−0.0743377	+	0.997233i	$0.523684\pi$
$20$		0			0
$21$	−2.76210	−	6.51615i	−0.602740	−	1.42194i
$22$	2.44247	−	1.41016i	0.520736	−	0.300647i
$23$	−4.14827	+	2.39500i	−0.864974	+	0.499393i	−0.865675	−	0.500607i	$-0.833110\pi$
$23$	−4.14827	+	2.39500i	−0.864974	+	0.499393i	0.000700856		1.00000i	$0.499777\pi$
$24$	−0.765809	+	1.01521i	−0.156320	+	0.207228i
$25$		0			0
$26$	−1.35194			−0.265137
$27$	−1.86940	+	4.84823i	−0.359767	+	0.933042i
$28$		−	9.61033i		−	1.81618i
$29$	1.93807	−	3.35683i	0.359890	−	0.623349i	−0.628052	−	0.778172i	$-0.716147\pi$
$29$	1.93807	−	3.35683i	0.359890	−	0.623349i	0.987942	+	0.154823i	$0.0494807\pi$
$30$		0			0
$31$	3.84823	+	6.66533i	0.691163	+	1.19713i	0.971457	+	0.237215i	$0.0762345\pi$
$31$	3.84823	+	6.66533i	0.691163	+	1.19713i	−0.280295	+	0.959914i	$0.590432\pi$
$32$	7.00279	−	4.04307i	1.23793	−	0.714720i
$33$	2.15594	−	0.913870i	0.375300	−	0.159084i
$34$	1.41016	−	2.44247i	0.241841	−	0.418880i
$35$		0			0
$36$	−4.90645	+	5.07063i	−0.817742	+	0.845105i
$37$			7.52420i			1.23697i	0.785796	+	0.618485i	$0.212253\pi$
$37$			7.52420i			1.23697i	−0.785796	+	0.618485i	$0.787747\pi$
$38$	−1.17081	−	0.675970i	−0.189931	−	0.109657i
$39$	−1.11404	−	0.137352i	−0.178389	−	0.0219939i
$40$		0			0
$41$	0.0898394	+	0.155606i	0.0140306	+	0.0243016i	0.872955	−	0.487800i	$-0.162200\pi$
$41$	0.0898394	+	0.155606i	0.0140306	+	0.0243016i	−0.858925	+	0.512102i	$0.828867\pi$
$42$	1.80664	−	14.6534i	0.278771	−	2.26107i
$43$	−0.710419	−	0.410161i	−0.108338	−	0.0625489i	0.444852	−	0.895604i	$-0.353256\pi$
$43$	−0.710419	−	0.410161i	−0.108338	−	0.0625489i	−0.553190	+	0.833055i	$0.686590\pi$
$44$	3.17968			0.479355
$45$		0			0
$46$	−9.99258			−1.47333
$47$	−9.44526	−	5.45323i	−1.37773	−	0.795435i	−0.385847	−	0.922563i	$-0.626091\pi$
$47$	−9.44526	−	5.45323i	−1.37773	−	0.795435i	−0.991886	+	0.127128i	$0.959424\pi$
$48$	5.05880	−	2.14435i	0.730175	−	0.309510i
$49$	4.84823	+	8.39738i	0.692604	+	1.19963i
$50$		0			0
$51$	1.41016	−	1.86940i	0.197462	−	0.261769i
$52$	−1.32000	−	0.762100i	−0.183050	−	0.105684i
$53$		−	4.17226i		−	0.573104i	−0.958065	−	0.286552i	$-0.907491\pi$
$53$		−	4.17226i		−	0.573104i	0.958065	−	0.286552i	$-0.0925091\pi$
$54$	−8.43436	+	6.80911i	−1.14777	+	0.926602i
$55$		0			0
$56$	1.50000	−	2.59808i	0.200446	−	0.347183i
$57$	−0.896110	−	0.675970i	−0.118693	−	0.0895344i
$58$	7.00279	−	4.04307i	0.919512	−	0.530880i
$59$	2.08613	+	3.61328i	0.271591	+	0.470409i	0.969269	−	0.246002i	$-0.0791169\pi$
$59$	2.08613	+	3.61328i	0.271591	+	0.470409i	−0.697678	+	0.716411i	$0.745784\pi$
$60$		0			0
$61$	1.91016	−	3.30850i	0.244571	−	0.423609i	−0.717440	−	0.696620i	$-0.754686\pi$
$61$	1.91016	−	3.30850i	0.244571	−	0.423609i	0.962011	+	0.273011i	$0.0880195\pi$
$62$			16.0558i			2.03909i
$63$	2.97746	−	11.8913i	0.375124	−	1.49816i
$64$	10.5242			1.31552
$65$		0			0
$66$	4.84823	+	0.597746i	0.596776	+	0.0735775i
$67$	7.05113	−	4.07097i	0.861433	−	0.497349i	−0.00305885	−	0.999995i	$-0.500974\pi$
$67$	7.05113	−	4.07097i	0.861433	−	0.497349i	0.864492	+	0.502647i	$0.167640\pi$
$68$	2.75368	−	1.58984i	0.333933	−	0.192796i
$69$	−8.23419	−	1.01521i	−0.991280	−	0.122217i
$70$		0			0
$71$	−6.11644			−0.725888			−0.362944	−	0.931811i	$-0.618228\pi$
$71$	−6.11644			−0.725888			−0.362944	+	0.931811i	$0.618228\pi$
$72$	−2.11785	+	0.604996i	−0.249592	+	0.0712994i
$73$			12.3445i			1.44482i	0.691467	+	0.722408i	$0.256965\pi$
$73$			12.3445i			1.44482i	−0.691467	+	0.722408i	$0.743035\pi$
$74$	−7.84823	+	13.5935i	−0.912338	+	1.58022i
$75$		0			0
$76$	−0.762100	−	1.32000i	−0.0874188	−	0.151414i
$77$	−4.78410	+	2.76210i	−0.545198	+	0.314770i
$78$	−1.86940	−	1.41016i	−0.211668	−	0.159669i
$79$	5.17226	−	8.95862i	0.581925	−	1.00792i	−0.413326	−	0.910583i	$-0.635633\pi$
$79$	5.17226	−	8.95862i	0.581925	−	1.00792i	0.995251	−	0.0973403i	$-0.0310335\pi$
$80$		0			0
$81$	−7.64195	+	4.75401i	−0.849105	+	0.528224i
$82$			0.374833i			0.0413934i
$83$	−10.6161	−	6.12920i	−1.16527	−	0.672767i	−0.212706	−	0.977116i	$-0.568228\pi$
$83$	−10.6161	−	6.12920i	−1.16527	−	0.672767i	−0.952560	+	0.304350i	$0.901561\pi$
$84$	10.0242	−	13.2887i	1.09373	−	1.44992i
$85$		0			0
$86$	−0.855648	−	1.48203i	−0.0922669	−	0.159811i
$87$	6.18127	−	2.62015i	0.662702	−	0.280910i
$88$	0.859601	+	0.496291i	0.0916338	+	0.0529048i
$89$	3.00000			0.317999			0.159000	−	0.987279i	$-0.449173\pi$
$89$	3.00000			0.317999			0.159000	+	0.987279i	$0.449173\pi$
$90$		0			0
$91$	2.64806			0.277592
$92$	−9.75648	−	5.63290i	−1.01718	−	0.587271i
$93$	−1.63121	+	13.2305i	−0.169148	+	1.37194i
$94$	−11.3761	−	19.7041i	−1.17336	−	2.03232i
$95$		0			0
$96$	13.9003	+	1.71380i	1.41870	+	0.174914i
$97$	11.7606	+	6.79001i	1.19411	+	0.689421i	0.959237	−	0.282605i	$-0.0911984\pi$
$97$	11.7606	+	6.79001i	1.19411	+	0.689421i	0.234876	+	0.972025i	$0.424532\pi$
$98$			20.2281i			2.04334i
$99$	3.93436	+	0.985122i	0.395418	+	0.0990085i
$100$		0			0
$101$	0.734191	−	1.27166i	0.0730547	−	0.126535i	−0.827184	−	0.561931i	$-0.810059\pi$
$101$	0.734191	−	1.27166i	0.0730547	−	0.126535i	0.900239	+	0.435397i	$0.143392\pi$
$102$	4.49756	−	1.90645i	0.445325	−	0.188767i
$103$	−6.51615	+	3.76210i	−0.642055	+	0.370691i	−0.785406	−	0.618981i	$-0.787546\pi$
$103$	−6.51615	+	3.76210i	−0.642055	+	0.370691i	0.143351	+	0.989672i	$0.454212\pi$
$104$	−0.237900	−	0.412055i	−0.0233280	−	0.0404053i
$105$		0			0
$106$	4.35194	−	7.53778i	0.422698	−	0.732134i
$107$			1.20999i			0.116974i	0.998288	+	0.0584871i	$0.0186277\pi$
$107$			1.20999i			0.116974i	−0.998288	+	0.0584871i	$0.981372\pi$
$108$	−12.0734	+	1.89370i	−1.16177	+	0.182221i
$109$	−14.1042			−1.35094			−0.675469	−	0.737388i	$-0.736059\pi$
$109$	−14.1042			−1.35094			−0.675469	+	0.737388i	$0.736059\pi$
$110$		0			0
$111$	−7.84823	+	10.4041i	−0.744921	+	0.987517i
$112$	−11.2257	+	6.48113i	−1.06072	+	0.612410i
$113$	10.3270	−	5.96227i	0.971478	−	0.560883i	0.0717915	−	0.997420i	$-0.477128\pi$
$113$	10.3270	−	5.96227i	0.971478	−	0.560883i	0.899687	+	0.436537i	$0.143795\pi$
$114$	−0.913870	−	2.15594i	−0.0855917	−	0.201922i
$115$		0			0
$116$	9.11644			0.846440
$117$	−1.39718	−	1.35194i	−0.129169	−	0.124987i
$118$			8.70388i			0.801257i
$119$	−2.76210	+	4.78410i	−0.253201	+	0.438557i
$120$		0			0
$121$	4.58613	+	7.94341i	0.416921	+	0.722128i
$122$	6.90195	−	3.98484i	0.624873	−	0.360771i
$123$	−0.0380816	+	0.308874i	−0.00343370	+	0.0278502i
$124$	−9.05080	+	15.6765i	−0.812786	+	1.40779i
$125$		0			0
$126$	17.7826	−	18.3776i	1.58420	−	1.63721i
$127$		−	7.07871i		−	0.628134i	−0.949401	−	0.314067i	$-0.898308\pi$
$127$		−	7.07871i		−	0.628134i	0.949401	−	0.314067i	$-0.101692\pi$
$128$	5.00787	+	2.89130i	0.442637	+	0.255557i
$129$	−0.554512	−	1.30817i	−0.0488221	−	0.115178i
$130$		0			0
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	0.966803	−	0.255524i	$-0.0822479\pi$
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	−0.704692	+	0.709514i	$0.748915\pi$
$132$	4.39672	+	3.31661i	0.382685	+	0.288674i
$133$	2.29329	+	1.32403i	0.198853	+	0.114808i
$134$	16.9852			1.46729
$135$		0			0
$136$	0.992582			0.0851132
$137$	6.46781	+	3.73419i	0.552582	+	0.319033i	0.750163	−	0.661253i	$-0.229975\pi$
$137$	6.46781	+	3.73419i	0.552582	+	0.319033i	−0.197581	+	0.980287i	$0.563308\pi$
$138$	−13.8173	−	10.4229i	−1.17621	−	0.887257i
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	0.984297	−	0.176522i	$-0.0564848\pi$
$139$	4.00000	+	6.92820i	0.339276	+	0.587643i	−0.645021	+	0.764165i	$0.723151\pi$
$140$		0			0
$141$	−7.37243	−	17.3925i	−0.620871	−	1.46471i
$142$	−11.0502	−	6.37985i	−0.927314	−	0.535385i
$143$			0.876139i			0.0732664i
$144$	9.23179	+	2.31154i	0.769316	+	0.192629i
$145$		0			0
$146$	−12.8761	+	22.3021i	−1.06564	+	1.84574i
$147$	−2.05509	+	16.6686i	−0.169501	+	1.37480i
$148$	−15.3256	+	8.84823i	−1.25976	+	0.727320i
$149$	−5.29241	−	9.16673i	−0.433571	−	0.750968i	0.563607	−	0.826043i	$-0.309413\pi$
$149$	−5.29241	−	9.16673i	−0.433571	−	0.750968i	−0.997178	+	0.0750759i	$0.976080\pi$
$150$		0			0
$151$	−8.84823	+	15.3256i	−0.720059	+	1.24718i	0.240917	+	0.970546i	$0.422552\pi$
$151$	−8.84823	+	15.3256i	−0.720059	+	1.24718i	−0.960976	+	0.276633i	$0.910781\pi$
$152$		−	0.475800i		−	0.0385925i
$153$	3.89982	−	1.11404i	0.315282	−	0.0900647i
$154$	−11.5242			−0.928646
$155$		0			0
$156$	−1.03031	−	2.43064i	−0.0824910	−	0.194607i
$157$	−2.19245	+	1.26581i	−0.174976	+	0.101023i	−0.584930	−	0.811084i	$-0.698878\pi$
$157$	−2.19245	+	1.26581i	−0.174976	+	0.101023i	0.409954	+	0.912106i	$0.365545\pi$
$158$	18.6888	−	10.7900i	1.48680	−	0.858407i
$159$	4.35194	−	5.76922i	0.345131	−	0.457529i
$160$		0			0
$161$	19.5726			1.54254
$162$	−18.7650	+	0.617748i	−1.47432	+	0.0485349i
$163$		−	8.47580i		−	0.663876i	−0.943301	−	0.331938i	$-0.892298\pi$
$163$		−	8.47580i		−	0.663876i	0.943301	−	0.331938i	$-0.107702\pi$
$164$	−0.211297	+	0.365977i	−0.0164995	+	0.0285780i
$165$		0			0
$166$	−12.7863	−	22.1465i	−0.992409	−	1.71890i
$167$	11.0281	−	6.36710i	0.853383	−	0.492701i	−0.00840816	−	0.999965i	$-0.502676\pi$
$167$	11.0281	−	6.36710i	0.853383	−	0.492701i	0.861791	+	0.507264i	$0.169343\pi$
$168$	4.78410	−	2.02791i	0.369101	−	0.156457i
$169$	−6.29001	+	10.8946i	−0.483847	+	0.838047i
$170$		0			0
$171$	−0.534022	−	1.86940i	−0.0408377	−	0.142957i
$172$		−	1.92935i		−	0.147111i
$173$	19.9605	+	11.5242i	1.51757	+	0.876169i	0.999787	+	0.0206561i	$0.00657550\pi$
$173$	19.9605	+	11.5242i	1.51757	+	0.876169i	0.517782	+	0.855513i	$0.326758\pi$
$174$	13.9003	+	1.71380i	1.05378	+	0.129923i
$175$		0			0
$176$	−2.14435	−	3.71413i	−0.161637	−	0.279963i
$177$	−0.884280	+	7.17226i	−0.0664666	+	0.539100i
$178$	5.41993	+	3.12920i	0.406241	+	0.234543i
$179$	−2.22808			−0.166534			−0.0832672	−	0.996527i	$-0.526535\pi$
$179$	−2.22808			−0.166534			−0.0832672	+	0.996527i	$0.526535\pi$
$180$		0			0
$181$	0.468382			0.0348146			0.0174073	−	0.999848i	$-0.494459\pi$
$181$	0.468382			0.0348146			0.0174073	+	0.999848i	$0.494459\pi$
$182$	4.78410	+	2.76210i	0.354621	+	0.204740i
$183$	6.09226	−	2.58242i	0.450353	−	0.190898i
$184$	−1.75839	−	3.04562i	−0.129630	−	0.224526i
$185$		0			0
$186$	−16.7473	+	22.2013i	−1.22797	+	1.62788i
$187$	−1.58287	−	0.913870i	−0.115751	−	0.0668288i
$188$		−	25.6513i		−	1.87081i
$189$	16.5205	−	13.3371i	1.20169	−	0.970130i
$190$		0			0
$191$	10.1140	−	17.5180i	0.731826	−	1.26756i	−0.224276	−	0.974526i	$-0.572002\pi$
$191$	10.1140	−	17.5180i	0.731826	−	1.26756i	0.956102	−	0.293034i	$-0.0946650\pi$
$192$	14.5524	+	10.9774i	1.05023	+	0.792227i
$193$	17.2593	−	9.96467i	1.24235	−	0.717273i	0.272780	−	0.962076i	$-0.412057\pi$
$193$	17.2593	−	9.96467i	1.24235	−	0.717273i	0.969573	+	0.244804i	$0.0787235\pi$
$194$	14.1648	+	24.5342i	1.01698	+	1.76145i
$195$		0			0
$196$	−11.4027	+	19.7501i	−0.814482	+	1.41072i
$197$		−	15.5800i		−	1.11003i	−0.831840	−	0.555015i	$-0.812712\pi$
$197$		−	15.5800i		−	1.11003i	0.831840	−	0.555015i	$-0.187288\pi$
$198$	6.08043	+	5.88356i	0.432118	+	0.418126i
$199$	−3.58482			−0.254121			−0.127061	−	0.991895i	$-0.540554\pi$
$199$	−3.58482			−0.254121			−0.127061	+	0.991895i	$0.540554\pi$
$200$		0			0
$201$	13.9963	+	1.72563i	0.987222	+	0.121716i
$202$	2.65284	−	1.53162i	0.186653	−	0.107764i
$203$	−13.7165	+	7.91920i	−0.962707	+	0.555819i
$204$	5.46598	+	0.673910i	0.382695	+	0.0471831i
$205$		0			0
$206$	−15.6965			−1.09362
$207$	−10.3270	−	9.99258i	−0.717773	−	0.694532i
$208$			2.05582i			0.142545i
$209$	−0.438069	+	0.758758i	−0.0303019	+	0.0524844i
$210$		0			0
$211$	−7.49629	−	12.9840i	−0.516066	−	0.893852i	−0.999826	−	0.0186518i	$-0.994063\pi$
$211$	−7.49629	−	12.9840i	−0.516066	−	0.893852i	0.483760	−	0.875201i	$-0.339271\pi$
$212$	8.49822	−	4.90645i	0.583660	−	0.336976i
$213$	−8.45755	−	6.37985i	−0.579502	−	0.437140i
$214$	−1.26210	+	2.18602i	−0.0862754	+	0.149433i
$215$		0			0
$216$	−3.55953	−	1.37250i	−0.242195	−	0.0933867i
$217$		−	31.4487i		−	2.13488i
$218$	−25.4813	−	14.7116i	−1.72581	−	0.996396i
$219$	−12.8761	+	17.0695i	−0.870089	+	1.15345i
$220$		0			0
$221$	0.438069	+	0.758758i	0.0294677	+	0.0510396i
$222$	−25.0311	+	10.6103i	−1.67998	+	0.712119i
$223$	−23.2363	−	13.4155i	−1.55602	−	0.898368i	−0.997631	−	0.0687878i	$-0.978087\pi$
$223$	−23.2363	−	13.4155i	−1.55602	−	0.898368i	−0.558388	−	0.829580i	$-0.688580\pi$
$224$	−33.0410			−2.20764
$225$		0			0
$226$	24.8761			1.65474
$227$	−1.17081	−	0.675970i	−0.0777096	−	0.0448657i	0.460642	−	0.887586i	$-0.347619\pi$
$227$	−1.17081	−	0.675970i	−0.0777096	−	0.0448657i	−0.538351	+	0.842721i	$0.680953\pi$
$228$	0.323043	−	2.62015i	0.0213940	−	0.173524i
$229$	−4.11775	−	7.13215i	−0.272108	−	0.471306i	0.697293	−	0.716786i	$-0.254388\pi$
$229$	−4.11775	−	7.13215i	−0.272108	−	0.471306i	−0.969402	+	0.245480i	$0.921054\pi$
$230$		0			0
$231$	−9.49629	−	1.17081i	−0.624810	−	0.0770339i
$232$	2.46456	+	1.42291i	0.161806	+	0.0934188i
$233$		−	8.58744i		−	0.562582i	−0.959623	−	0.281291i	$-0.909237\pi$
$233$		−	8.58744i		−	0.562582i	0.959623	−	0.281291i	$-0.0907626\pi$
$234$	−1.11404	−	3.89982i	−0.0728270	−	0.254939i
$235$		0			0
$236$	−4.90645	+	8.49822i	−0.319383	+	0.553187i
$237$	16.4964	−	6.99258i	1.07156	−	0.454217i
$238$	−9.98025	+	5.76210i	−0.646923	+	0.373501i
$239$	−11.9623	−	20.7193i	−0.773775	−	1.34022i	−0.935480	−	0.353378i	$-0.885033\pi$
$239$	−11.9623	−	20.7193i	−0.773775	−	1.34022i	0.161706	−	0.986839i	$-0.448300\pi$
$240$		0			0
$241$	3.12015	−	5.40426i	0.200987	−	0.348119i	−0.747860	−	0.663857i	$-0.768919\pi$
$241$	3.12015	−	5.40426i	0.200987	−	0.348119i	0.948847	+	0.315737i	$0.102252\pi$
$242$			19.1345i			1.23001i
$243$	−15.5257	−	1.39741i	−0.995974	−	0.0896438i
$244$	8.98516			0.575216
$245$		0			0
$246$	−0.390976	+	0.518303i	−0.0249277	+	0.0330458i
$247$	0.363716	−	0.209991i	0.0231427	−	0.0133614i
$248$	−4.89363	+	2.82534i	−0.310746	+	0.179409i
$249$	−8.28630	−	19.5484i	−0.525123	−	1.23883i
$250$		0			0
$251$	−28.5726			−1.80349			−0.901743	−	0.432272i	$-0.857712\pi$
$251$	−28.5726			−1.80349			−0.901743	+	0.432272i	$0.857712\pi$
$252$	27.7221	−	7.91920i	1.74633	−	0.498863i
$253$			6.47580i			0.407130i
$254$	7.38356	−	12.7887i	0.463286	−	0.802434i
$255$		0			0
$256$	−4.49258	−	7.78138i	−0.280786	−	0.486336i
$257$	−15.5885	+	9.00000i	−0.972381	+	0.561405i	−0.899961	−	0.435970i	$-0.856405\pi$
$257$	−15.5885	+	9.00000i	−0.972381	+	0.561405i	−0.0724199	+	0.997374i	$0.523072\pi$
$258$	0.362697	−	2.94178i	0.0225805	−	0.183147i
$259$	15.3724	−	26.6258i	0.955196	−	1.65445i
$260$		0			0
$261$	11.2802	+	2.82444i	0.698226	+	0.174828i
$262$			12.5168i			0.773289i
$263$	27.5991	+	15.9344i	1.70183	+	0.982555i	0.943904	+	0.330220i	$0.107123\pi$
$263$	27.5991	+	15.9344i	1.70183	+	0.982555i	0.757931	+	0.652335i	$0.226211\pi$
$264$	0.670955	+	1.58287i	0.0412944	+	0.0974188i
$265$		0			0
$266$	2.76210	+	4.78410i	0.169355	+	0.293332i
$267$	4.14827	+	3.12920i	0.253870	+	0.191504i
$268$	16.5838	+	9.57468i	1.01302	+	0.584867i
$269$	31.4971			1.92041			0.960207	−	0.279289i	$-0.0900987\pi$
$269$	31.4971			1.92041			0.960207	+	0.279289i	$0.0900987\pi$
$270$		0			0
$271$	−3.24030			−0.196834			−0.0984172	−	0.995145i	$-0.531378\pi$
$271$	−3.24030			−0.196834			−0.0984172	+	0.995145i	$0.531378\pi$
$272$	−3.71413	−	2.14435i	−0.225202	−	0.130020i
$273$	3.66162	+	2.76210i	0.221612	+	0.167170i
$274$	7.79001	+	13.4927i	0.470612	+	0.815123i
$275$		0			0
$276$	−7.61534	−	17.9656i	−0.458390	−	1.08140i
$277$	4.83660	+	2.79241i	0.290603	+	0.167780i	0.638214	−	0.769859i	$-0.279674\pi$
$277$	4.83660	+	2.79241i	0.290603	+	0.167780i	−0.347611	+	0.937639i	$0.613007\pi$
$278$			16.6890i			1.00094i
$279$	−16.0558	+	16.5931i	−0.961237	+	0.993402i
$280$		0			0
$281$	12.0521	−	20.8749i	0.718969	−	1.24529i	−0.242440	−	0.970166i	$-0.577948\pi$
$281$	12.0521	−	20.8749i	0.718969	−	1.24529i	0.961409	−	0.275124i	$-0.0887188\pi$
$282$	4.82218	−	39.1120i	0.287157	−	2.32908i
$283$	9.12989	−	5.27114i	0.542715	−	0.313337i	−0.203463	−	0.979083i	$-0.565220\pi$
$283$	9.12989	−	5.27114i	0.542715	−	0.313337i	0.746179	+	0.665746i	$0.231886\pi$
$284$	−7.19275	−	12.4582i	−0.426811	−	0.739259i
$285$		0			0
$286$	−0.913870	+	1.58287i	−0.0540383	+	0.0935970i
$287$		−	0.734191i		−	0.0433379i
$288$	17.4332	+	16.8687i	1.02726	+	0.993999i
$289$	15.1723			0.892486
$290$		0			0
$291$	9.17968	+	21.6560i	0.538122	+	1.26950i
$292$	−25.1438	+	14.5168i	−1.47143	+	0.849530i
$293$	−16.4481	+	9.49629i	−0.960906	+	0.554779i	−0.896452	−	0.443141i	$-0.853864\pi$
$293$	−16.4481	+	9.49629i	−0.960906	+	0.554779i	−0.0644541	+	0.997921i	$0.520531\pi$
$294$	−21.0992	+	27.9705i	−1.23053	+	1.63127i
$295$		0			0
$296$	−5.52420			−0.321088
$297$	4.41271	+	5.46598i	0.256052	+	0.317168i
$298$		−	22.0813i		−	1.27914i
$299$	1.55211	−	2.68833i	0.0897607	−	0.155470i
$300$		0			0
$301$	1.67597	+	2.90286i	0.0966013	+	0.167318i
$302$	−31.9712	+	18.4586i	−1.83973	+	1.06217i
$303$	2.34163	−	0.992582i	0.134523	−	0.0570223i
$304$	−1.02791	+	1.78039i	−0.0589546	+	0.102112i
$305$		0			0
$306$	8.20759	+	2.05509i	0.469197	+	0.117482i
$307$			29.4791i			1.68246i	0.540679	+	0.841229i	$0.318167\pi$
$307$			29.4791i			1.68246i	−0.540679	+	0.841229i	$0.681833\pi$
$308$	−11.2519	−	6.49629i	−0.641137	−	0.370161i
$309$	−12.9344	−	1.59470i	−0.735810	−	0.0907193i
$310$		0			0
$311$	4.70628	+	8.15152i	0.266869	+	0.462230i	0.968052	−	0.250751i	$-0.0806776\pi$
$311$	4.70628	+	8.15152i	0.266869	+	0.462230i	−0.701183	+	0.712982i	$0.747344\pi$
$312$	0.100842	−	0.817917i	0.00570908	−	0.0463055i
$313$	10.0641	+	5.81050i	0.568855	+	0.328429i	0.756692	−	0.653771i	$-0.226814\pi$
$313$	10.0641	+	5.81050i	0.568855	+	0.328429i	−0.187837	+	0.982200i	$0.560148\pi$
$314$	−5.28128			−0.298040
$315$		0			0
$316$	24.3297			1.36865
$317$	7.94984	+	4.58984i	0.446507	+	0.257791i	0.706354	−	0.707859i	$-0.250339\pi$
$317$	7.94984	+	4.58984i	0.446507	+	0.257791i	−0.259847	+	0.965650i	$0.583672\pi$
$318$	13.8801	−	5.88356i	0.778355	−	0.329934i
$319$	−2.62015	−	4.53824i	−0.146700	−	0.254092i
$320$		0			0
$321$	−1.26210	+	1.67312i	−0.0704435	+	0.0933846i
$322$	35.3607	+	20.4155i	1.97057	+	1.13771i
$323$			0.876139i			0.0487497i
$324$	−18.6699	−	9.97484i	−1.03721	−	0.554158i
$325$		0			0
$326$	8.84081	−	15.3127i	0.489647	−	0.848094i
$327$	−19.5027	−	14.7116i	−1.07850	−	0.813554i
$328$	−0.114245	+	0.0659593i	−0.00630812	+	0.00364199i
$329$	22.2826	+	38.5946i	1.22848	+	2.12779i
$330$		0			0
$331$	3.61033	−	6.25327i	0.198442	−	0.343711i	−0.749582	−	0.661912i	$-0.769745\pi$
$331$	3.61033	−	6.25327i	0.198442	−	0.343711i	0.948023	+	0.318201i	$0.103079\pi$
$332$		−	28.8310i		−	1.58231i
$333$	−21.7044	+	6.20017i	−1.18939	+	0.339767i
$334$	26.5652			1.45358
$335$		0			0
$336$	−22.2826	−	2.74726i	−1.21561	−	0.149875i
$337$	1.97791	−	1.14195i	0.107744	−	0.0622059i	−0.445160	−	0.895451i	$-0.646853\pi$
$337$	1.97791	−	1.14195i	0.107744	−	0.0622059i	0.552904	+	0.833245i	$0.313520\pi$
$338$	−22.7276	+	13.1218i	−1.23622	+	0.713731i
$339$	20.4987	+	2.52732i	1.11334	+	0.137265i
$340$		0			0
$341$	10.4051			0.563470
$342$	0.985122	−	3.93436i	0.0532693	−	0.212746i
$343$		−	11.0181i		−	0.594921i
$344$	0.301136	−	0.521583i	0.0162362	−	0.0281219i
$345$		0			0
$346$	24.0410	+	41.6402i	1.29245	+	2.23859i
$347$	−0.613740	+	0.354343i	−0.0329473	+	0.0190221i	−0.516383	−	0.856358i	$-0.672722\pi$
$347$	−0.613740	+	0.354343i	−0.0329473	+	0.0190221i	0.483436	+	0.875380i	$0.339389\pi$
$348$	12.6058	+	9.50904i	0.675743	+	0.509738i
$349$	−10.6723	+	18.4849i	−0.571273	+	0.989474i	0.425163	+	0.905117i	$0.360217\pi$
$349$	−10.6723	+	18.4849i	−0.571273	+	0.989474i	−0.996436	+	0.0843569i	$0.973116\pi$
$350$		0			0
$351$	−0.521796	−	3.32675i	−0.0278514	−	0.177569i
$352$		−	10.9320i		−	0.582675i
$353$	−8.74408	−	5.04840i	−0.465401	−	0.268699i	0.248912	−	0.968526i	$-0.419927\pi$
$353$	−8.74408	−	5.04840i	−0.465401	−	0.268699i	−0.714312	+	0.699827i	$0.753260\pi$
$354$	−9.07871	+	12.0353i	−0.482528	+	0.639671i
$355$		0			0
$356$	3.52791	+	6.11052i	0.186979	+	0.323857i
$357$	−8.80944	+	3.73419i	−0.466245	+	0.197634i
$358$	−4.02534	−	2.32403i	−0.212746	−	0.122829i
$359$	−30.5578			−1.61278			−0.806388	−	0.591386i	$-0.798581\pi$
$359$	−30.5578			−1.61278			−0.806388	+	0.591386i	$0.798581\pi$
$360$		0			0
$361$	−18.5800			−0.977896
$362$	0.846198	+	0.488553i	0.0444752	+	0.0256778i
$363$	−1.94399	+	15.7674i	−0.102033	+	0.827576i
$364$	3.11404	+	5.39367i	0.163220	+	0.282705i
$365$		0			0
$366$	13.7002	+	1.68912i	0.716119	+	0.0882916i
$367$	6.21778	+	3.58984i	0.324566	+	0.187388i	0.653426	−	0.756991i	$-0.273331\pi$
$367$	6.21778	+	3.58984i	0.324566	+	0.187388i	−0.328860	+	0.944379i	$0.606664\pi$
$368$			15.1952i			0.792102i
$369$	−0.374833	+	0.387376i	−0.0195130	+	0.0201660i
$370$		0			0
$371$	−8.52420	+	14.7643i	−0.442554	+	0.766527i
$372$	−28.8666	+	12.2361i	−1.49666	+	0.634414i
$373$	18.9872	−	10.9623i	0.983120	−	0.567605i	0.0799096	−	0.996802i	$-0.474537\pi$
$373$	18.9872	−	10.9623i	0.983120	−	0.567605i	0.903211	+	0.429197i	$0.141204\pi$
$374$	−1.90645	−	3.30207i	−0.0985803	−	0.170746i
$375$		0			0
$376$	4.00371	−	6.93463i	0.206476	−	0.357626i
$377$			2.51197i			0.129373i
$378$	43.7581	−	6.86339i	2.25067	−	0.353014i
$379$	17.3929			0.893414			0.446707	−	0.894680i	$-0.352597\pi$
$379$	17.3929			0.893414			0.446707	+	0.894680i	$0.352597\pi$
$380$		0			0
$381$	7.38356	−	9.78813i	0.378271	−	0.501461i
$382$	36.5449	−	21.0992i	1.86980	−	1.07953i
$383$	−0.412055	+	0.237900i	−0.0210550	+	0.0121561i	−0.510491	−	0.859883i	$-0.670536\pi$
$383$	−0.412055	+	0.237900i	−0.0210550	+	0.0121561i	0.489436	+	0.872039i	$0.337203\pi$
$384$	3.90886	+	9.22149i	0.199473	+	0.470582i
$385$		0			0
$386$	41.5752			2.11612
$387$	0.597746	−	2.38727i	0.0303852	−	0.121352i
$388$			31.9394i			1.62148i
$389$	−2.79372	+	4.83886i	−0.141647	+	0.245340i	−0.928117	−	0.372289i	$-0.878573\pi$
$389$	−2.79372	+	4.83886i	−0.141647	+	0.245340i	0.786470	+	0.617629i	$0.211906\pi$
$390$		0			0
$391$	3.23790	+	5.60821i	0.163748	+	0.283619i
$392$	−6.16528	+	3.55953i	−0.311394	+	0.179783i
$393$	−1.27166	+	10.3142i	−0.0641466	+	0.520283i
$394$	16.2510	−	28.1475i	0.818712	−	1.41805i
$395$		0			0
$396$	2.62015	+	9.17213i	0.131668	+	0.460917i
$397$			3.75228i			0.188321i	0.995557	+	0.0941607i	$0.0300168\pi$
$397$			3.75228i			0.188321i	−0.995557	+	0.0941607i	$0.969983\pi$
$398$	−6.47649	−	3.73921i	−0.324637	−	0.187429i
$399$	1.79001	+	4.22286i	0.0896125	+	0.211407i
$400$		0			0
$401$	−11.7826	−	20.4080i	−0.588394	−	1.01913i	−0.994443	−	0.105278i	$-0.966427\pi$
$401$	−11.7826	−	20.4080i	−0.588394	−	1.01913i	0.406048	−	0.913852i	$-0.366906\pi$
$402$	23.4863	+	17.7166i	1.17139	+	0.883625i
$403$	−4.31954	−	2.49389i	−0.215172	−	0.124229i
$404$	3.45355			0.171820
$405$		0			0
$406$	−33.0410			−1.63980
$407$	8.80944	+	5.08613i	0.436668	+	0.252110i
$408$	1.37250	+	1.03533i	0.0679488	+	0.0512563i
$409$	0.524200	+	0.907940i	0.0259200	+	0.0448948i	0.878694	−	0.477385i	$-0.158415\pi$
$409$	0.524200	+	0.907940i	0.0259200	+	0.0448948i	−0.852774	+	0.522279i	$0.825082\pi$
$410$		0			0
$411$	5.04840	+	11.9098i	0.249019	+	0.587468i
$412$	−15.3256	−	8.84823i	−0.755037	−	0.435921i
$413$		−	17.0484i		−	0.838897i
$414$	−8.23419	−	28.8247i	−0.404688	−	1.41666i
$415$		0			0
$416$	−2.62015	+	4.53824i	−0.128464	+	0.222505i
$417$	−1.69554	+	13.7523i	−0.0830310	+	0.673452i
$418$	−1.58287	+	0.913870i	−0.0774207	+	0.0446988i
$419$	−12.9599	−	22.4471i	−0.633131	−	1.09661i	−0.986908	−	0.161285i	$-0.948436\pi$
$419$	−12.9599	−	22.4471i	−0.633131	−	1.09661i	0.353777	−	0.935330i	$-0.384897\pi$
$420$		0			0
$421$	−3.82032	+	6.61699i	−0.186191	+	0.322492i	−0.943977	−	0.330011i	$-0.892948\pi$
$421$	−3.82032	+	6.61699i	−0.186191	+	0.322492i	0.757786	+	0.652503i	$0.226281\pi$
$422$		−	31.2765i		−	1.52252i
$423$	7.94724	−	31.7395i	0.386408	−	1.54323i
$424$	3.06324			0.148764
$425$		0			0
$426$	−8.62517	−	20.3479i	−0.417891	−	0.985858i
$427$	−13.5189	+	7.80516i	−0.654227	+	0.377718i
$428$	−2.46456	+	1.42291i	−0.119129	+	0.0687791i
$429$	−0.913870	+	1.21149i	−0.0441220	+	0.0584911i
$430$		0			0
$431$	7.98516			0.384632			0.192316	−	0.981333i	$-0.438400\pi$
$431$	7.98516			0.384632			0.192316	+	0.981333i	$0.438400\pi$
$432$	10.3542	+	12.8257i	0.498168	+	0.617075i
$433$			12.5120i			0.601287i	0.953737	+	0.300644i	$0.0972014\pi$
$433$			12.5120i			0.601287i	−0.953737	+	0.300644i	$0.902799\pi$
$434$	32.8031	−	56.8166i	1.57460	−	2.72728i
$435$		0			0
$436$	−16.5861	−	28.7280i	−0.794332	−	1.37582i
$437$	2.68833	−	1.55211i	0.128600	−	0.0742474i
$438$	−41.0671	+	17.4078i	−1.96226	+	0.831775i
$439$	−4.38225	+	7.59028i	−0.209153	+	0.362264i	−0.951448	−	0.307809i	$-0.900404\pi$
$439$	−4.38225	+	7.59028i	−0.209153	+	0.362264i	0.742295	+	0.670074i	$0.233737\pi$
$440$		0			0
$441$	−20.2281	+	20.9049i	−0.963242	+	0.995474i
$442$			1.82774i			0.0869367i
$443$	3.17914	+	1.83548i	0.151046	+	0.0872062i	0.573618	−	0.819123i	$-0.305539\pi$
$443$	3.17914	+	1.83548i	0.151046	+	0.0872062i	−0.422572	+	0.906329i	$0.638873\pi$
$444$	−30.4208	−	3.75064i	−1.44371	−	0.177997i
$445$		0			0
$446$	−27.9865	−	48.4740i	−1.32520	−	2.29531i
$447$	2.24338	−	18.1957i	0.106108	−	0.860626i
$448$	−37.2419	−	21.5016i	−1.75951	−	1.01586i
$449$	−28.1723			−1.32953			−0.664766	−	0.747052i	$-0.731469\pi$
$449$	−28.1723			−1.32953			−0.664766	+	0.747052i	$0.731469\pi$
$450$		0			0
$451$	0.242915			0.0114384
$452$	24.2884	+	14.0229i	1.14243	+	0.659581i
$453$	−28.2205	+	11.9623i	−1.32592	+	0.562036i
$454$	−1.41016	−	2.44247i	−0.0661821	−	0.114631i
$455$		0			0
$456$	0.496291	−	0.657916i	0.0232409	−	0.0308097i
$457$	−30.5375	−	17.6308i	−1.42848	−	0.824735i	−0.431482	−	0.902122i	$-0.642009\pi$
$457$	−30.5375	−	17.6308i	−1.42848	−	0.824735i	−0.997001	+	0.0773867i	$0.975342\pi$
$458$		−	17.1803i		−	0.802784i
$459$	6.55451	+	2.52732i	0.305938	+	0.117965i
$460$		0			0
$461$	−17.3384	+	30.0310i	−0.807530	+	1.39868i	0.107039	+	0.994255i	$0.465863\pi$
$461$	−17.3384	+	30.0310i	−0.807530	+	1.39868i	−0.914570	+	0.404428i	$0.867470\pi$
$462$	−15.9352	−	12.0205i	−0.741371	−	0.559244i
$463$	−6.45080	+	3.72437i	−0.299794	+	0.173086i	−0.642350	−	0.766411i	$-0.722041\pi$
$463$	−6.45080	+	3.72437i	−0.299794	+	0.173086i	0.342556	+	0.939497i	$0.388707\pi$
$464$	−6.14806	−	10.6488i	−0.285417	−	0.494356i
$465$		0			0
$466$	8.95725	−	15.5144i	0.414937	−	0.718692i
$467$			29.9655i			1.38664i	0.720630	+	0.693319i	$0.243852\pi$
$467$			29.9655i			1.38664i	−0.720630	+	0.693319i	$0.756148\pi$
$468$	1.11064	−	4.43567i	0.0513395	−	0.205039i
$469$	−33.2691			−1.53622
$470$		0			0
$471$	−4.35194	−	0.536558i	−0.200527	−	0.0247233i
$472$	−2.65284	+	1.53162i	−0.122107	+	0.0704984i
$473$	−0.960443	+	0.554512i	−0.0441612	+	0.0254965i
$474$	37.0968	+	4.57373i	1.70391	+	0.210078i
$475$		0			0
$476$	−12.9926			−0.595514
$477$	12.0353	−	3.43807i	0.551061	−	0.157418i
$478$		−	49.9097i		−	2.28282i
$479$	−3.99258	+	6.91535i	−0.182426	+	0.315971i	−0.942706	−	0.333625i	$-0.891728\pi$
$479$	−3.99258	+	6.91535i	−0.182426	+	0.315971i	0.760280	+	0.649595i	$0.225062\pi$
$480$		0			0
$481$	−2.43807	−	4.22286i	−0.111166	−	0.192546i
$482$	11.2740	−	6.50904i	0.513516	−	0.296479i
$483$	27.0641	+	20.4155i	1.23146	+	0.928937i
$484$	−10.7863	+	18.6824i	−0.490286	+	0.849201i
$485$		0			0
$486$	−26.5918	−	18.7189i	−1.20623	−	0.849108i
$487$		−	11.9442i		−	0.541243i	−0.962686	−	0.270621i	$-0.912771\pi$
$487$		−	11.9442i		−	0.541243i	0.962686	−	0.270621i	$-0.0872291\pi$
$488$	2.42907	+	1.40242i	0.109959	+	0.0634847i
$489$	8.84081	−	11.7200i	0.399795	−	0.529995i
$490$		0			0
$491$	4.61033	+	7.98533i	0.208061	+	0.360373i	0.951104	−	0.308872i	$-0.0999513\pi$
$491$	4.61033	+	7.98533i	0.208061	+	0.360373i	−0.743042	+	0.669244i	$0.766618\pi$
$492$	−0.673910	+	0.285660i	−0.0303822	+	0.0128786i
$493$	−4.53824	−	2.62015i	−0.204392	−	0.118006i
$494$	0.876139			0.0394193
$495$		0			0
$496$	24.4152			1.09627
$497$	21.6442	+	12.4963i	0.970876	+	0.560535i
$498$	5.41993	−	43.9602i	0.242873	−	1.96990i
$499$	15.0861	+	26.1299i	0.675348	+	1.16974i	0.976367	+	0.216119i	$0.0693399\pi$
$499$	15.0861	+	26.1299i	0.675348	+	1.16974i	−0.301019	+	0.953618i	$0.597327\pi$
$500$		0			0
$501$	21.8905	+	2.69892i	0.977996	+	0.120579i
$502$	−51.6204	−	29.8031i	−2.30393	−	1.33018i
$503$			10.5981i			0.472546i	0.971687	+	0.236273i	$0.0759260\pi$
$503$			10.5981i			0.472546i	−0.971687	+	0.236273i	$0.924074\pi$
$504$	8.73048	+	2.18602i	0.388887	+	0.0973731i
$505$		0			0
$506$	−6.75468	+	11.6995i	−0.300282	+	0.520104i
$507$	−20.0613	+	8.50371i	−0.890955	+	0.377663i
$508$	14.4182	−	8.32435i	0.639704	−	0.369333i
$509$	14.3761	+	24.9002i	0.637211	+	1.10368i	0.986042	+	0.166496i	$0.0532454\pi$
$509$	14.3761	+	24.9002i	0.637211	+	1.10368i	−0.348831	+	0.937186i	$0.613421\pi$
$510$		0			0
$511$	25.2207	−	43.6835i	1.11570	−	1.93244i
$512$		−	30.3094i		−	1.33950i
$513$	1.21149	−	3.14195i	0.0534884	−	0.138720i
$514$	−37.5503			−1.65627
$515$		0			0
$516$	2.01243	−	2.66781i	0.0885924	−	0.117444i
$517$	−12.7694	+	7.37243i	−0.561599	+	0.324239i
$518$	55.5449	−	32.0689i	2.44050	−	1.40903i
$519$	15.5800	+	36.7553i	0.683887	+	1.61338i
$520$		0			0
$521$	−36.0942			−1.58132			−0.790658	−	0.612259i	$-0.790261\pi$
$521$	−36.0942			−1.58132			−0.790658	+	0.612259i	$0.790261\pi$
$522$	17.4332	+	16.8687i	0.763030	+	0.738324i
$523$		−	11.1297i		−	0.486669i	−0.969942	−	0.243334i	$-0.921759\pi$
$523$		−	11.1297i		−	0.486669i	0.969942	−	0.243334i	$-0.0782412\pi$
$524$	−7.05582	+	12.2210i	−0.308235	+	0.533878i
$525$		0			0
$526$	33.2411	+	57.5754i	1.44938	+	2.51041i
$527$	9.01112	−	5.20257i	0.392531	−	0.226628i
$528$	0.908959	−	7.37243i	0.0395574	−	0.320844i
$529$	−0.0279088	+	0.0483395i	−0.00121343	+	0.00210172i
$530$		0			0
$531$	−8.70388	+	8.99513i	−0.377716	+	0.390355i
$532$			6.22808i			0.270021i
$533$	−0.100842	−	0.0582214i	−0.00436797	−	0.00252185i
$534$	4.23048	+	9.98025i	0.183071	+	0.431888i
$535$		0			0
$536$	2.98887	+	5.17688i	0.129100	+	0.223607i
$537$	−3.08089	−	2.32403i	−0.132950	−	0.100289i
$538$	56.9040	+	32.8536i	2.45331	+	1.41642i
$539$	13.1090			0.564646
$540$		0			0
$541$	−34.7374			−1.49348			−0.746740	−	0.665116i	$-0.768382\pi$
$541$	−34.7374			−1.49348			−0.746740	+	0.665116i	$0.768382\pi$
$542$	−5.85407	−	3.37985i	−0.251454	−	0.145177i
$543$	0.647658	+	0.488553i	0.0277937	+	0.0209658i
$544$	−5.46598	−	9.46735i	−0.234352	−	0.405909i
$545$		0			0
$546$	3.73419	+	8.80944i	0.159809	+	0.377009i
$547$	2.35087	+	1.35727i	0.100516	+	0.0580328i	0.549415	−	0.835549i	$-0.314851\pi$
$547$	2.35087	+	1.35727i	0.100516	+	0.0580328i	−0.448899	+	0.893582i	$0.648184\pi$
$548$			17.5652i			0.750347i
$549$	11.1177	+	2.78377i	0.474494	+	0.118808i
$550$		0			0
$551$	−1.25599	+	2.17543i	−0.0535068	+	0.0926766i
$552$	0.745356	−	6.04547i	0.0317245	−	0.257312i
$553$	−36.6061	+	21.1345i	−1.55665	+	0.898732i
$554$	5.82534	+	10.0898i	0.247495	+	0.428674i
$555$		0			0
$556$	−9.40776	+	16.2947i	−0.398978	+	0.691050i
$557$		−	8.93676i		−	0.378663i	−0.981913	−	0.189331i	$-0.939368\pi$
$557$		−	8.93676i		−	0.378663i	0.981913	−	0.189331i	$-0.0606321\pi$
$558$	−46.3148	+	13.2305i	−1.96066	+	0.560091i
$559$	0.531618			0.0224850
$560$		0			0
$561$	−1.23550	−	2.91469i	−0.0521627	−	0.123059i
$562$	43.5477	−	25.1423i	1.83695	−	1.06056i
$563$	8.10826	−	4.68130i	0.341722	−	0.197293i	−0.319311	−	0.947650i	$-0.603451\pi$
$563$	8.10826	−	4.68130i	0.341722	−	0.197293i	0.661033	+	0.750357i	$0.270118\pi$
$564$	26.7560	−	35.4695i	1.12663	−	1.49354i
$565$		0			0
$566$	21.9926			0.924417
$567$	36.7553	−	1.20999i	1.54358	−	0.0508149i
$568$		−	4.49064i		−	0.188423i
$569$	17.9368	−	31.0674i	0.751948	−	1.30241i	−0.194929	−	0.980817i	$-0.562448\pi$
$569$	17.9368	−	31.0674i	0.751948	−	1.30241i	0.946877	−	0.321595i	$-0.104219\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	−1.78455	+	1.03031i	−0.0746159	+	0.0430795i
$573$	32.2577	−	13.6736i	1.34758	−	0.571221i
$574$	0.765809	−	1.32642i	0.0319643	−	0.0553637i
$575$		0			0
$576$	8.67226	+	30.3582i	0.361344	+	1.26493i
$577$			1.35675i			0.0564821i	0.999601	+	0.0282411i	$0.00899060\pi$
$577$			1.35675i			0.0564821i	−0.999601	+	0.0282411i	$0.991009\pi$
$578$	27.4108	+	15.8257i	1.14014	+	0.658260i
$579$	34.2592	+	4.22388i	1.42377	+	0.175538i
$580$		0			0
$581$	25.0447	+	43.3787i	1.03903	+	1.79965i
$582$	−6.00427	+	48.6997i	−0.248885	+	2.01867i
$583$	−4.88494	−	2.82032i	−0.202314	−	0.116806i
$584$	−9.06324			−0.375039
$585$		0			0
$586$	−39.6210			−1.63673
$587$	−24.9329	−	14.3950i	−1.02909	−	0.594145i	−0.112366	−	0.993667i	$-0.535843\pi$
$587$	−24.9329	−	14.3950i	−1.02909	−	0.594145i	−0.916724	+	0.399521i	$0.869176\pi$
$588$	−36.3679	+	15.4158i	−1.49979	+	0.635737i
$589$	−2.49389	−	4.31954i	−0.102759	−	0.177984i
$590$		0			0
$591$	16.2510	−	21.5434i	0.668476	−	0.886176i
$592$	20.6709	+	11.9344i	0.849570	+	0.490499i
$593$		−	30.9171i		−	1.26961i	−0.772671	−	0.634807i	$-0.781080\pi$
$593$		−	30.9171i		−	1.26961i	0.772671	−	0.634807i	$-0.218920\pi$
$594$	2.27082	+	14.4778i	0.0931730	+	0.594032i
$595$		0			0
$596$	12.4474	−	21.5596i	0.509867	−	0.883115i
$597$	−4.95694	−	3.73921i	−0.202874	−	0.153035i
$598$	5.60821	−	3.23790i	0.229337	−	0.132408i
$599$	0.696460	+	1.20630i	0.0284566	+	0.0492882i	0.879903	−	0.475153i	$-0.157607\pi$
$599$	0.696460	+	1.20630i	0.0284566	+	0.0492882i	−0.851446	+	0.524442i	$0.824274\pi$
$600$		0			0
$601$	−4.41256	+	7.64279i	−0.179992	+	0.311756i	−0.941878	−	0.335956i	$-0.890941\pi$
$601$	−4.41256	+	7.64279i	−0.179992	+	0.311756i	0.761885	+	0.647712i	$0.224274\pi$
$602$			6.99258i			0.284996i
$603$	17.5535	+	16.9852i	0.714835	+	0.691689i
$604$	−41.6210			−1.69353
$605$		0			0
$606$	5.26581	+	0.649230i	0.213909	+	0.0263732i
$607$	−1.86783	+	1.07839i	−0.0758129	+	0.0437706i	−0.537427	−	0.843310i	$-0.680604\pi$
$607$	−1.86783	+	1.07839i	−0.0758129	+	0.0437706i	0.461614	+	0.887081i	$0.347270\pi$
$608$	−4.53824	+	2.62015i	−0.184050	+	0.106261i
$609$	−27.2268	−	3.35683i	−1.10328	−	0.136026i
$610$		0			0
$611$	7.06804			0.285942
$612$	6.85518	+	6.63322i	0.277104	+	0.268132i
$613$			9.57521i			0.386739i	0.981126	+	0.193370i	$0.0619416\pi$
$613$			9.57521i			0.386739i	−0.981126	+	0.193370i	$0.938058\pi$
$614$	−30.7486	+	53.2581i	−1.24091	+	2.14932i
$615$		0			0
$616$	−2.02791	−	3.51244i	−0.0817068	−	0.141520i
$617$	−32.6291	+	18.8384i	−1.31360	+	0.758406i	−0.982690	−	0.185258i	$-0.940688\pi$
$617$	−32.6291	+	18.8384i	−1.31360	+	0.758406i	−0.330907	+	0.943663i	$0.607355\pi$
$618$	−21.7044	−	16.3724i	−0.873078	−	0.658596i
$619$	8.55211	−	14.8127i	0.343738	−	0.595372i	−0.641385	−	0.767219i	$-0.721640\pi$
$619$	8.55211	−	14.8127i	0.343738	−	0.595372i	0.985124	+	0.171847i	$0.0549734\pi$
$620$		0			0
$621$	−3.85675	−	24.5890i	−0.154766	−	0.986722i
$622$			19.6358i			0.787325i
$623$	−10.6161	−	6.12920i	−0.425324	−	0.245561i
$624$	−2.14435	+	2.84269i	−0.0858428	+	0.113799i
$625$		0			0
$626$	12.1215	+	20.9950i	0.484471	+	0.839128i
$627$	−1.39718	+	0.592243i	−0.0557979	+	0.0236519i
$628$	−5.15650	−	2.97711i	−0.205767	−	0.118799i
$629$	10.1723			0.405595
$630$		0			0
$631$	33.1090			1.31805			0.659025	−	0.752121i	$-0.270969\pi$
$631$	33.1090			1.31805			0.659025	+	0.752121i	$0.270969\pi$
$632$	6.57734	+	3.79743i	0.261632	+	0.151054i
$633$	3.17757	−	25.7728i	0.126297	−	1.02438i
$634$	9.57500	+	16.5844i	0.380272	+	0.658650i
$635$		0			0
$636$	16.8687	+	2.07977i	0.668888	+	0.0824684i
$637$	−5.44201	−	3.14195i	−0.215620	−	0.124489i
$638$		−	10.9320i		−	0.432800i
$639$	−5.04013	−	17.6436i	−0.199385	−	0.697968i
$640$		0			0
$641$	11.5763	−	20.0508i	0.457237	−	0.791957i	−0.541577	−	0.840651i	$-0.682173\pi$
$641$	11.5763	−	20.0508i	0.457237	−	0.791957i	0.998814	+	0.0486939i	$0.0155059\pi$
$642$	−4.02534	+	1.70628i	−0.158867	+	0.0673416i
$643$	−37.2944	+	21.5319i	−1.47075	+	0.849137i	−0.999461	−	0.0328430i	$-0.989544\pi$
$643$	−37.2944	+	21.5319i	−1.47075	+	0.849137i	−0.471287	+	0.881980i	$0.656211\pi$
$644$	23.0168	+	39.8662i	0.906988	+	1.57095i
$645$		0			0
$646$	−0.913870	+	1.58287i	−0.0359557	+	0.0622771i
$647$		−	20.6439i		−	0.811595i	−0.913963	−	0.405798i	$-0.866994\pi$
$647$		−	20.6439i		−	0.811595i	0.913963	−	0.405798i	$-0.133006\pi$
$648$	−3.49035	−	5.61065i	−0.137114	−	0.220407i
$649$	5.64064			0.221415
$650$		0			0
$651$	32.8031	−	43.4859i	1.28565	−	1.70435i
$652$	17.2638	−	9.96728i	0.676104	−	0.390349i
$653$	−5.91942	+	3.41758i	−0.231645	+	0.133740i	−0.611331	−	0.791375i	$-0.709365\pi$
$653$	−5.91942	+	3.41758i	−0.231645	+	0.133740i	0.379686	+	0.925116i	$0.376032\pi$
$654$	−19.8892	−	46.9212i	−0.777730	−	1.83476i
$655$		0			0
$656$	0.569988			0.0222543
$657$	−35.6091	+	10.1723i	−1.38924	+	0.396858i
$658$			92.9688i			3.62430i
$659$	−13.4307	+	23.2626i	−0.523184	+	0.906181i	0.476452	+	0.879200i	$0.341923\pi$
$659$	−13.4307	+	23.2626i	−0.523184	+	0.906181i	−0.999636	+	0.0269806i	$0.991411\pi$
$660$		0			0
$661$	1.06063	+	1.83706i	0.0412535	+	0.0714532i	0.885915	−	0.463848i	$-0.153532\pi$
$661$	1.06063	+	1.83706i	0.0412535	+	0.0714532i	−0.844661	+	0.535301i	$0.820198\pi$
$662$	13.0451	−	7.53162i	0.507014	−	0.292725i
$663$	−0.185691	+	1.50611i	−0.00721165	+	0.0584926i
$664$	4.50000	−	7.79423i	0.174634	−	0.302475i
$665$		0			0
$666$	−45.6792	−	11.4376i	−1.77003	−	0.443198i
$667$			18.5667i			0.718907i
$668$	25.9375	+	14.9750i	1.00355	+	0.579401i
$669$	−18.1369	−	42.7874i	−0.701214	−	1.65425i
$670$		0			0
$671$	−2.58242	−	4.47288i	−0.0996933	−	0.172674i
$672$	−45.6876	−	34.4639i	−1.76244	−	1.32947i
$673$	30.1553	+	17.4102i	1.16240	+	0.671112i	0.951878	−	0.306477i	$-0.0991501\pi$
$673$	30.1553	+	17.4102i	1.16240	+	0.671112i	0.210523	+	0.977589i	$0.432483\pi$
$674$	4.76450			0.183522
$675$		0			0
$676$	−29.5874			−1.13798
$677$	21.3772	+	12.3421i	0.821592	+	0.474346i	0.850965	−	0.525222i	$-0.176018\pi$
$677$	21.3772	+	12.3421i	0.821592	+	0.474346i	−0.0293735	+	0.999569i	$0.509351\pi$
$678$	34.3976	+	25.9474i	1.32103	+	0.996505i
$679$	−27.7449	−	48.0555i	−1.06475	−	1.84420i
$680$		0			0
$681$	−0.913870	−	2.15594i	−0.0350196	−	0.0826157i
$682$	18.7984	+	10.8532i	0.719827	+	0.415592i
$683$			38.4610i			1.47167i	0.677162	+	0.735834i	$0.263210\pi$
$683$			38.4610i			1.47167i	−0.677162	+	0.735834i	$0.736790\pi$
$684$	3.17968	−	3.28608i	0.121578	−	0.125646i
$685$		0			0
$686$	11.4926	−	19.9057i	0.438789	−	0.760005i
$687$	1.74545	−	14.1571i	0.0665932	−	0.540127i
$688$	−2.25363	+	1.30114i	−0.0859190	+	0.0496054i
$689$	1.35194	+	2.34163i	0.0515048	+	0.0892089i
$690$		0			0
$691$	−0.240304	+	0.416219i	−0.00914159	+	0.0158337i	−0.870560	−	0.492062i	$-0.836243\pi$
$691$	−0.240304	+	0.416219i	−0.00914159	+	0.0158337i	0.861418	+	0.507896i	$0.169577\pi$
$692$			54.2084i			2.06070i
$693$	−11.9098	−	11.5242i	−0.452417	−	0.437768i
$694$	−1.47841			−0.0561197
$695$		0			0
$696$	1.92369	+	4.53824i	0.0729174	+	0.172021i
$697$	0.210370	−	0.121457i	0.00796835	−	0.00460053i
$698$	−38.5619	+	22.2637i	−1.45959	+	0.842694i
$699$	8.95725	−	11.8743i	0.338794	−	0.449128i
$700$		0			0
$701$	−18.1797			−0.686637			−0.343318	−	0.939219i	$-0.611551\pi$
$701$	−18.1797			−0.686637			−0.343318	+	0.939219i	$0.611551\pi$
$702$	2.52732	−	6.55451i	0.0953875	−	0.247384i
$703$		−	4.87614i		−	0.183907i
$704$	7.11404	−	12.3219i	0.268120	−	0.464398i
$705$		0			0
$706$	−10.5316	−	18.2413i	−0.396363	−	0.686520i
$707$	−5.19615	+	3.00000i	−0.195421	+	0.112827i
$708$	−15.6486	+	6.63322i	−0.588111	+	0.249292i
$709$	3.59355	−	6.22421i	0.134959	−	0.233755i	−0.790623	−	0.612303i	$-0.790243\pi$
$709$	3.59355	−	6.22421i	0.134959	−	0.233755i	0.925582	+	0.378548i	$0.123577\pi$
$710$		0			0
$711$	30.1042	+	7.53778i	1.12900	+	0.282689i
$712$			2.20257i			0.0825449i
$713$	−31.9270	−	18.4331i	−1.19568	−	0.690323i
$714$	−19.8105	−	2.44247i	−0.741389	−	0.0914071i
$715$		0			0
$716$	−2.62015	−	4.53824i	−0.0979197	−	0.169602i
$717$	5.07063	−	41.1271i	0.189366	−	1.53592i
$718$	−55.2069	−	31.8737i	−2.06030	−	1.18952i
$719$	−12.5168			−0.466797			−0.233399	−	0.972381i	$-0.574985\pi$
$719$	−12.5168			−0.466797			−0.233399	+	0.972381i	$0.574985\pi$
$720$		0			0
$721$	30.7449			1.14500
$722$	−33.5674	−	19.3802i	−1.24925	−	0.721255i
$723$	9.95141	−	4.21826i	0.370097	−	0.156879i
$724$	0.550803	+	0.954019i	0.0204704	+	0.0354558i
$725$		0			0
$726$	−19.9586	+	26.4584i	−0.740732	+	0.981963i
$727$	−7.29699	−	4.21292i	−0.270631	−	0.156249i	0.358544	−	0.933513i	$-0.383273\pi$
$727$	−7.29699	−	4.21292i	−0.270631	−	0.156249i	−0.629174	+	0.777264i	$0.716607\pi$
$728$			1.94418i			0.0720562i
$729$	−20.0107	−	18.1266i	−0.741136	−	0.671355i
$730$		0			0
$731$	−0.554512	+	0.960443i	−0.0205094	+	0.0355233i
$732$	12.4243	+	9.37211i	0.459215	+	0.346403i
$733$	19.0526	−	11.0000i	0.703722	−	0.406294i	−0.105010	−	0.994471i	$-0.533487\pi$
$733$	19.0526	−	11.0000i	0.703722	−	0.406294i	0.808732	+	0.588177i	$0.200154\pi$
$734$	7.48887	+	12.9711i	0.276419	+	0.478772i
$735$		0			0
$736$	−19.3663	+	33.5434i	−0.713852	+	1.23643i
$737$		−	11.0074i		−	0.405463i
$738$	−1.08125	+	0.308874i	−0.0398013	+	0.0113698i
$739$	1.81290			0.0666887			0.0333444	−	0.999444i	$-0.489384\pi$
$739$	1.81290			0.0666887			0.0333444	+	0.999444i	$0.489384\pi$
$740$		0			0
$741$	0.721965	+	0.0890123i	0.0265220	+	0.00326995i
$742$	−30.8003	+	17.7826i	−1.13072	+	0.652819i
$743$	−17.4393	+	10.0686i	−0.639785	+	0.369380i	−0.784532	−	0.620089i	$-0.787097\pi$
$743$	−17.4393	+	10.0686i	−0.639785	+	0.369380i	0.144747	+	0.989469i	$0.453763\pi$
$744$	−9.71370	−	1.19762i	−0.356122	−	0.0439068i
$745$		0			0
$746$	45.7374			1.67457
$747$	8.93237	−	35.6739i	0.326818	−	1.30524i
$748$		−	4.29873i		−	0.157177i
$749$	2.47209	−	4.28179i	0.0903282	−	0.156453i
$750$		0			0
$751$	−6.10662	−	10.5770i	−0.222834	−	0.385959i	0.732834	−	0.680408i	$-0.238197\pi$
$751$	−6.10662	−	10.5770i	−0.222834	−	0.385959i	−0.955667	+	0.294449i	$0.904864\pi$
$752$	−29.9628	+	17.2991i	−1.09263	+	0.630832i
$753$	−39.5089	−	29.8031i	−1.43979	−	1.08608i
$754$	−2.62015	+	4.53824i	−0.0954203	+	0.165273i
$755$		0			0
$756$	46.5931	+	17.9656i	1.69457	+	0.653402i
$757$			52.9533i			1.92462i	0.271955	+	0.962310i	$0.412330\pi$
$757$			52.9533i			1.92462i	−0.271955	+	0.962310i	$0.587670\pi$
$758$	31.4228	+	18.1419i	1.14133	+	0.658945i
$759$	−6.75468	+	8.95445i	−0.245179	+	0.325026i
$760$		0			0
$761$	9.22677	+	15.9812i	0.334470	+	0.579319i	0.983383	−	0.181543i	$-0.0581093\pi$
$761$	9.22677	+	15.9812i	0.334470	+	0.579319i	−0.648913	+	0.760863i	$0.724776\pi$
$762$	23.5491	−	9.98212i	0.853094	−	0.361614i
$763$	49.9105	+	28.8158i	1.80688	+	1.04320i
$764$	47.5752			1.72121
$765$		0			0
$766$	−0.992582			−0.0358634
$767$	−2.34163	−	1.35194i	−0.0845513	−	0.0488157i
$768$	1.90434	−	15.4458i	0.0687169	−	0.557353i
$769$	−2.22677	−	3.85688i	−0.0802995	−	0.139083i	0.823079	−	0.567927i	$-0.192254\pi$
$769$	−2.22677	−	3.85688i	−0.0802995	−	0.139083i	−0.903379	+	0.428844i	$0.858921\pi$
$770$		0			0
$771$	−30.9426	−	3.81497i	−1.11437	−	0.137393i
$772$	40.5929	+	23.4363i	1.46097	+	0.843491i
$773$		−	38.9368i		−	1.40046i	−0.713918	−	0.700229i	$-0.753081\pi$
$773$		−	38.9368i		−	1.40046i	0.713918	−	0.700229i	$-0.246919\pi$
$774$	3.56999	−	3.68945i	0.128321	−	0.132614i
$775$		0			0
$776$	−4.98516	+	8.63456i	−0.178957

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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.k (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.80664 + 1.04307i) q^{2} +(1.38276 + 1.04307i) q^{3} +(1.17597 + 2.03684i) q^{4} +(1.41016 + 3.32675i) q^{6} +(-3.53869 - 2.04307i) q^{7} +0.734191i q^{8} +(0.824030 + 2.88461i) q^{9} +O(q^{10})\)	\(q+(1.80664 + 1.04307i) q^{2} +(1.38276 + 1.04307i) q^{3} +(1.17597 + 2.03684i) q^{4} +(1.41016 + 3.32675i) q^{6} +(-3.53869 - 2.04307i) q^{7} +0.734191i q^{8} +(0.824030 + 2.88461i) q^{9} +(0.675970 - 1.17081i) q^{11} +(-0.498476 + 4.04307i) q^{12} +(-0.561237 + 0.324030i) q^{13} +(-4.26210 - 7.38217i) q^{14} +(1.58613 - 2.74726i) q^{16} -1.35194i q^{17} +(-1.52011 + 6.07097i) q^{18} -0.648061 q^{19} +(-2.76210 - 6.51615i) q^{21} +(2.44247 - 1.41016i) q^{22} +(-4.14827 + 2.39500i) q^{23} +(-0.765809 + 1.01521i) q^{24} -1.35194 q^{26} +(-1.86940 + 4.84823i) q^{27} -9.61033i q^{28} +(1.93807 - 3.35683i) q^{29} +(3.84823 + 6.66533i) q^{31} +(7.00279 - 4.04307i) q^{32} +(2.15594 - 0.913870i) q^{33} +(1.41016 - 2.44247i) q^{34} +(-4.90645 + 5.07063i) q^{36} +7.52420i q^{37} +(-1.17081 - 0.675970i) q^{38} +(-1.11404 - 0.137352i) q^{39} +(0.0898394 + 0.155606i) q^{41} +(1.80664 - 14.6534i) q^{42} +(-0.710419 - 0.410161i) q^{43} +3.17968 q^{44} -9.99258 q^{46} +(-9.44526 - 5.45323i) q^{47} +(5.05880 - 2.14435i) q^{48} +(4.84823 + 8.39738i) q^{49} +(1.41016 - 1.86940i) q^{51} +(-1.32000 - 0.762100i) q^{52} -4.17226i q^{53} +(-8.43436 + 6.80911i) q^{54} +(1.50000 - 2.59808i) q^{56} +(-0.896110 - 0.675970i) q^{57} +(7.00279 - 4.04307i) q^{58} +(2.08613 + 3.61328i) q^{59} +(1.91016 - 3.30850i) q^{61} +16.0558i q^{62} +(2.97746 - 11.8913i) q^{63} +10.5242 q^{64} +(4.84823 + 0.597746i) q^{66} +(7.05113 - 4.07097i) q^{67} +(2.75368 - 1.58984i) q^{68} +(-8.23419 - 1.01521i) q^{69} -6.11644 q^{71} +(-2.11785 + 0.604996i) q^{72} +12.3445i q^{73} +(-7.84823 + 13.5935i) q^{74} +(-0.762100 - 1.32000i) q^{76} +(-4.78410 + 2.76210i) q^{77} +(-1.86940 - 1.41016i) q^{78} +(5.17226 - 8.95862i) q^{79} +(-7.64195 + 4.75401i) q^{81} +0.374833i q^{82} +(-10.6161 - 6.12920i) q^{83} +(10.0242 - 13.2887i) q^{84} +(-0.855648 - 1.48203i) q^{86} +(6.18127 - 2.62015i) q^{87} +(0.859601 + 0.496291i) q^{88} +3.00000 q^{89} +2.64806 q^{91} +(-9.75648 - 5.63290i) q^{92} +(-1.63121 + 13.2305i) q^{93} +(-11.3761 - 19.7041i) q^{94} +(13.9003 + 1.71380i) q^{96} +(11.7606 + 6.79001i) q^{97} +20.2281i q^{98} +(3.93436 + 0.985122i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 10 q^{4} - 8 q^{6} + 14 q^{9}+O(q^{10}) \) 12 * q + 10 * q^4 - 8 * q^6 + 14 * q^9	\( 12 q + 10 q^{4} - 8 q^{6} + 14 q^{9} + 4 q^{11} - 18 q^{14} - 10 q^{16} - 16 q^{19} - 30 q^{24} - 8 q^{26} - 14 q^{29} - 16 q^{31} - 8 q^{34} + 20 q^{36} + 28 q^{39} + 26 q^{41} + 88 q^{44} - 12 q^{46} - 4 q^{49} - 8 q^{51} - 10 q^{54} + 18 q^{56} - 4 q^{59} - 2 q^{61} + 60 q^{64} - 4 q^{66} - 78 q^{69} - 40 q^{71} - 32 q^{74} + 24 q^{76} + 4 q^{79} - 38 q^{81} + 54 q^{84} - 56 q^{86} + 36 q^{89} + 40 q^{91} - 62 q^{94} + 26 q^{96} - 44 q^{99}+O(q^{100}) \) 12 * q + 10 * q^4 - 8 * q^6 + 14 * q^9 + 4 * q^11 - 18 * q^14 - 10 * q^16 - 16 * q^19 - 30 * q^24 - 8 * q^26 - 14 * q^29 - 16 * q^31 - 8 * q^34 + 20 * q^36 + 28 * q^39 + 26 * q^41 + 88 * q^44 - 12 * q^46 - 4 * q^49 - 8 * q^51 - 10 * q^54 + 18 * q^56 - 4 * q^59 - 2 * q^61 + 60 * q^64 - 4 * q^66 - 78 * q^69 - 40 * q^71 - 32 * q^74 + 24 * q^76 + 4 * q^79 - 38 * q^81 + 54 * q^84 - 56 * q^86 + 36 * q^89 + 40 * q^91 - 62 * q^94 + 26 * q^96 - 44 * q^99

Introduction

L-functions

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