LMFDB - Embedded newform 225.2.k.b.49.5

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			49.5
Root			$0.583700 - 2.17840i$ of defining polynomial
Character	$\chi$	$=$	225.49
Dual form			225.2.k.b.124.5

$q$-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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

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

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	0.301103	−	0.953592i	$-0.402645\pi$
$2$	1.80664	−	1.04307i	1.27749	−	0.737558i	0.976386	+	0.216033i	$0.0693120\pi$
$3$	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	−0.986436	−	0.164145i	$-0.947513\pi$
$7$	−3.53869	+	2.04307i	−1.33750	+	0.772206i	−0.351064	+	0.936351i	$0.614180\pi$
$8$		−	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	0.949754	−	0.312998i	$-0.101333\pi$
$11$	0.675970	+	1.17081i	0.203813	+	0.353014i	−0.745941	+	0.666012i	$0.768000\pi$
$12$	−0.498476	−	4.04307i	−0.143898	−	1.16713i
$13$	−0.561237	−	0.324030i	−0.155659	−	0.0898699i	0.420147	−	0.907456i	$-0.361978\pi$
$13$	−0.561237	−	0.324030i	−0.155659	−	0.0898699i	−0.575806	+	0.817586i	$0.695312\pi$
$14$	−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	$0.0524225\pi$
$17$			1.35194i			0.327893i	−0.986469	+	0.163947i	$0.947577\pi$
$18$	−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	0.000700856	−	1.00000i	$-0.499777\pi$
$23$	−4.14827	−	2.39500i	−0.864974	−	0.499393i	−0.865675	+	0.500607i	$0.833110\pi$
$24$	−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	0.987942	−	0.154823i	$-0.0494807\pi$
$29$	1.93807	+	3.35683i	0.359890	+	0.623349i	−0.628052	+	0.778172i	$0.716147\pi$
$30$		0			0
$31$	3.84823	−	6.66533i	0.691163	−	1.19713i	−0.280295	−	0.959914i	$-0.590432\pi$
$31$	3.84823	−	6.66533i	0.691163	−	1.19713i	0.971457	−	0.237215i	$-0.0762345\pi$
$32$	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	$-0.787747\pi$
$37$		−	7.52420i		−	1.23697i	0.785796	−	0.618485i	$-0.212253\pi$
$38$	−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	−0.858925	−	0.512102i	$-0.828867\pi$
$41$	0.0898394	−	0.155606i	0.0140306	−	0.0243016i	0.872955	+	0.487800i	$0.162200\pi$
$42$	1.80664	+	14.6534i	0.278771	+	2.26107i
$43$	−0.710419	+	0.410161i	−0.108338	+	0.0625489i	−0.553190	−	0.833055i	$-0.686590\pi$
$43$	−0.710419	+	0.410161i	−0.108338	+	0.0625489i	0.444852	+	0.895604i	$0.353256\pi$
$44$	3.17968			0.479355
$45$		0			0
$46$	−9.99258			−1.47333
$47$	−9.44526	+	5.45323i	−1.37773	+	0.795435i	−0.991886	−	0.127128i	$-0.959424\pi$
$47$	−9.44526	+	5.45323i	−1.37773	+	0.795435i	−0.385847	+	0.922563i	$0.626091\pi$
$48$	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	$0.0925091\pi$
$53$			4.17226i			0.573104i	−0.958065	+	0.286552i	$0.907491\pi$
$54$	−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	−0.697678	−	0.716411i	$-0.745784\pi$
$59$	2.08613	−	3.61328i	0.271591	−	0.470409i	0.969269	+	0.246002i	$0.0791169\pi$
$60$		0			0
$61$	1.91016	+	3.30850i	0.244571	+	0.423609i	0.962011	−	0.273011i	$-0.0880195\pi$
$61$	1.91016	+	3.30850i	0.244571	+	0.423609i	−0.717440	+	0.696620i	$0.754686\pi$
$62$		−	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	0.864492	−	0.502647i	$-0.167640\pi$
$67$	7.05113	+	4.07097i	0.861433	+	0.497349i	−0.00305885	+	0.999995i	$0.500974\pi$
$68$	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	$-0.743035\pi$
$73$		−	12.3445i		−	1.44482i	0.691467	−	0.722408i	$-0.256965\pi$
$74$	−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	0.995251	+	0.0973403i	$0.0310335\pi$
$79$	5.17226	+	8.95862i	0.581925	+	1.00792i	−0.413326	+	0.910583i	$0.635633\pi$
$80$		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	−0.952560	−	0.304350i	$-0.901561\pi$
$83$	−10.6161	+	6.12920i	−1.16527	+	0.672767i	−0.212706	+	0.977116i	$0.568228\pi$
$84$	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	0.234876	−	0.972025i	$-0.424532\pi$
$97$	11.7606	−	6.79001i	1.19411	−	0.689421i	0.959237	+	0.282605i	$0.0911984\pi$
$98$		−	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	0.900239	−	0.435397i	$-0.143392\pi$
$101$	0.734191	+	1.27166i	0.0730547	+	0.126535i	−0.827184	+	0.561931i	$0.810059\pi$
$102$	4.49756	+	1.90645i	0.445325	+	0.188767i
$103$	−6.51615	−	3.76210i	−0.642055	−	0.370691i	0.143351	−	0.989672i	$-0.454212\pi$
$103$	−6.51615	−	3.76210i	−0.642055	−	0.370691i	−0.785406	+	0.618981i	$0.787546\pi$
$104$	−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	$-0.981372\pi$
$107$		−	1.20999i		−	0.116974i	0.998288	−	0.0584871i	$-0.0186277\pi$
$108$	−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	0.899687	−	0.436537i	$-0.143795\pi$
$113$	10.3270	+	5.96227i	0.971478	+	0.560883i	0.0717915	+	0.997420i	$0.477128\pi$
$114$	−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	$0.101692\pi$
$127$			7.07871i			0.628134i	−0.949401	+	0.314067i	$0.898308\pi$
$128$	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	−0.704692	−	0.709514i	$-0.748915\pi$
$131$	3.00000	−	5.19615i	0.262111	−	0.453990i	0.966803	+	0.255524i	$0.0822479\pi$
$132$	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	−0.197581	−	0.980287i	$-0.563308\pi$
$137$	6.46781	−	3.73419i	0.552582	−	0.319033i	0.750163	+	0.661253i	$0.229975\pi$
$138$	−13.8173	+	10.4229i	−1.17621	+	0.887257i
$139$	4.00000	−	6.92820i	0.339276	−	0.587643i	−0.645021	−	0.764165i	$-0.723151\pi$
$139$	4.00000	−	6.92820i	0.339276	−	0.587643i	0.984297	+	0.176522i	$0.0564848\pi$
$140$		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	−0.997178	−	0.0750759i	$-0.976080\pi$
$149$	−5.29241	+	9.16673i	−0.433571	+	0.750968i	0.563607	+	0.826043i	$0.309413\pi$
$150$		0			0
$151$	−8.84823	−	15.3256i	−0.720059	−	1.24718i	−0.960976	−	0.276633i	$-0.910781\pi$
$151$	−8.84823	−	15.3256i	−0.720059	−	1.24718i	0.240917	−	0.970546i	$-0.422552\pi$
$152$			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	0.409954	−	0.912106i	$-0.365545\pi$
$157$	−2.19245	−	1.26581i	−0.174976	−	0.101023i	−0.584930	+	0.811084i	$0.698878\pi$
$158$	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	$0.107702\pi$
$163$			8.47580i			0.663876i	−0.943301	+	0.331938i	$0.892298\pi$
$164$	−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	0.861791	−	0.507264i	$-0.169343\pi$
$167$	11.0281	+	6.36710i	0.853383	+	0.492701i	−0.00840816	+	0.999965i	$0.502676\pi$
$168$	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	0.517782	−	0.855513i	$-0.326758\pi$
$173$	19.9605	−	11.5242i	1.51757	−	0.876169i	0.999787	−	0.0206561i	$-0.00657550\pi$
$174$	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	0.956102	+	0.293034i	$0.0946650\pi$
$191$	10.1140	+	17.5180i	0.731826	+	1.26756i	−0.224276	+	0.974526i	$0.572002\pi$
$192$	14.5524	−	10.9774i	1.05023	−	0.792227i
$193$	17.2593	+	9.96467i	1.24235	+	0.717273i	0.969573	−	0.244804i	$-0.0787235\pi$
$193$	17.2593	+	9.96467i	1.24235	+	0.717273i	0.272780	+	0.962076i	$0.412057\pi$
$194$	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	$0.187288\pi$
$197$			15.5800i			1.11003i	−0.831840	+	0.555015i	$0.812712\pi$
$198$	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	0.483760	+	0.875201i	$0.339271\pi$
$211$	−7.49629	+	12.9840i	−0.516066	+	0.893852i	−0.999826	+	0.0186518i	$0.994063\pi$
$212$	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	−0.558388	+	0.829580i	$0.688580\pi$
$223$	−23.2363	+	13.4155i	−1.55602	+	0.898368i	−0.997631	+	0.0687878i	$0.978087\pi$
$224$	−33.0410			−2.20764
$225$		0			0
$226$	24.8761			1.65474
$227$	−1.17081	+	0.675970i	−0.0777096	+	0.0448657i	−0.538351	−	0.842721i	$-0.680953\pi$
$227$	−1.17081	+	0.675970i	−0.0777096	+	0.0448657i	0.460642	+	0.887586i	$0.347619\pi$
$228$	0.323043	+	2.62015i	0.0213940	+	0.173524i
$229$	−4.11775	+	7.13215i	−0.272108	+	0.471306i	−0.969402	−	0.245480i	$-0.921054\pi$
$229$	−4.11775	+	7.13215i	−0.272108	+	0.471306i	0.697293	+	0.716786i	$0.254388\pi$
$230$		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	$0.0907626\pi$
$233$			8.58744i			0.562582i	−0.959623	+	0.281291i	$0.909237\pi$
$234$	−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	0.161706	+	0.986839i	$0.448300\pi$
$239$	−11.9623	+	20.7193i	−0.773775	+	1.34022i	−0.935480	+	0.353378i	$0.885033\pi$
$240$		0			0
$241$	3.12015	+	5.40426i	0.200987	+	0.348119i	0.948847	−	0.315737i	$-0.102252\pi$
$241$	3.12015	+	5.40426i	0.200987	+	0.348119i	−0.747860	+	0.663857i	$0.768919\pi$
$242$		−	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	−0.0724199	−	0.997374i	$-0.523072\pi$
$257$	−15.5885	−	9.00000i	−0.972381	−	0.561405i	−0.899961	+	0.435970i	$0.856405\pi$
$258$	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	0.757931	−	0.652335i	$-0.226211\pi$
$263$	27.5991	−	15.9344i	1.70183	−	0.982555i	0.943904	−	0.330220i	$-0.107123\pi$
$264$	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	−0.347611	−	0.937639i	$-0.613007\pi$
$277$	4.83660	−	2.79241i	0.290603	−	0.167780i	0.638214	+	0.769859i	$0.279674\pi$
$278$		−	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	0.961409	+	0.275124i	$0.0887188\pi$
$281$	12.0521	+	20.8749i	0.718969	+	1.24529i	−0.242440	+	0.970166i	$0.577948\pi$
$282$	4.82218	+	39.1120i	0.287157	+	2.32908i
$283$	9.12989	+	5.27114i	0.542715	+	0.313337i	0.746179	−	0.665746i	$-0.231886\pi$
$283$	9.12989	+	5.27114i	0.542715	+	0.313337i	−0.203463	+	0.979083i	$0.565220\pi$
$284$	−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	−0.0644541	−	0.997921i	$-0.520531\pi$
$293$	−16.4481	−	9.49629i	−0.960906	−	0.554779i	−0.896452	+	0.443141i	$0.853864\pi$
$294$	−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	$-0.681833\pi$
$307$		−	29.4791i		−	1.68246i	0.540679	−	0.841229i	$-0.318167\pi$
$308$	−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	−0.701183	−	0.712982i	$-0.747344\pi$
$311$	4.70628	−	8.15152i	0.266869	−	0.462230i	0.968052	+	0.250751i	$0.0806776\pi$
$312$	0.100842	+	0.817917i	0.00570908	+	0.0463055i
$313$	10.0641	−	5.81050i	0.568855	−	0.328429i	−0.187837	−	0.982200i	$-0.560148\pi$
$313$	10.0641	−	5.81050i	0.568855	−	0.328429i	0.756692	+	0.653771i	$0.226814\pi$
$314$	−5.28128			−0.298040
$315$		0			0
$316$	24.3297			1.36865
$317$	7.94984	−	4.58984i	0.446507	−	0.257791i	−0.259847	−	0.965650i	$-0.583672\pi$
$317$	7.94984	−	4.58984i	0.446507	−	0.257791i	0.706354	+	0.707859i	$0.250339\pi$
$318$	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	0.948023	−	0.318201i	$-0.103079\pi$
$331$	3.61033	+	6.25327i	0.198442	+	0.343711i	−0.749582	+	0.661912i	$0.769745\pi$
$332$			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	0.552904	−	0.833245i	$-0.313520\pi$
$337$	1.97791	+	1.14195i	0.107744	+	0.0622059i	−0.445160	+	0.895451i	$0.646853\pi$
$338$	−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	0.483436	−	0.875380i	$-0.339389\pi$
$347$	−0.613740	−	0.354343i	−0.0329473	−	0.0190221i	−0.516383	+	0.856358i	$0.672722\pi$
$348$	12.6058	−	9.50904i	0.675743	−	0.509738i
$349$	−10.6723	−	18.4849i	−0.571273	−	0.989474i	−0.996436	−	0.0843569i	$-0.973116\pi$
$349$	−10.6723	−	18.4849i	−0.571273	−	0.989474i	0.425163	−	0.905117i	$-0.360217\pi$
$350$		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	−0.714312	−	0.699827i	$-0.753260\pi$
$353$	−8.74408	+	5.04840i	−0.465401	+	0.268699i	0.248912	+	0.968526i	$0.419927\pi$
$354$	−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	−0.328860	−	0.944379i	$-0.606664\pi$
$367$	6.21778	−	3.58984i	0.324566	−	0.187388i	0.653426	+	0.756991i	$0.273331\pi$
$368$		−	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	0.903211	−	0.429197i	$-0.141204\pi$
$373$	18.9872	+	10.9623i	0.983120	+	0.567605i	0.0799096	+	0.996802i	$0.474537\pi$
$374$	−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	0.489436	−	0.872039i	$-0.337203\pi$
$383$	−0.412055	−	0.237900i	−0.0210550	−	0.0121561i	−0.510491	+	0.859883i	$0.670536\pi$
$384$	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	0.786470	−	0.617629i	$-0.211906\pi$
$389$	−2.79372	−	4.83886i	−0.141647	−	0.245340i	−0.928117	+	0.372289i	$0.878573\pi$
$390$		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	$-0.969983\pi$
$397$		−	3.75228i		−	0.188321i	0.995557	−	0.0941607i	$-0.0300168\pi$
$398$	−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	0.406048	+	0.913852i	$0.366906\pi$
$401$	−11.7826	+	20.4080i	−0.588394	+	1.01913i	−0.994443	+	0.105278i	$0.966427\pi$
$402$	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	−0.852774	−	0.522279i	$-0.825082\pi$
$409$	0.524200	−	0.907940i	0.0259200	−	0.0448948i	0.878694	+	0.477385i	$0.158415\pi$
$410$		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	0.353777	+	0.935330i	$0.384897\pi$
$419$	−12.9599	+	22.4471i	−0.633131	+	1.09661i	−0.986908	+	0.161285i	$0.948436\pi$
$420$		0			0
$421$	−3.82032	−	6.61699i	−0.186191	−	0.322492i	0.757786	−	0.652503i	$-0.226281\pi$
$421$	−3.82032	−	6.61699i	−0.186191	−	0.322492i	−0.943977	+	0.330011i	$0.892948\pi$
$422$			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	$-0.902799\pi$
$433$		−	12.5120i		−	0.601287i	0.953737	−	0.300644i	$-0.0972014\pi$
$434$	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	0.742295	−	0.670074i	$-0.233737\pi$
$439$	−4.38225	−	7.59028i	−0.209153	−	0.362264i	−0.951448	+	0.307809i	$0.900404\pi$
$440$		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	−0.422572	−	0.906329i	$-0.638873\pi$
$443$	3.17914	−	1.83548i	0.151046	−	0.0872062i	0.573618	+	0.819123i	$0.305539\pi$
$444$	−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	−0.997001	−	0.0773867i	$-0.975342\pi$
$457$	−30.5375	+	17.6308i	−1.42848	+	0.824735i	−0.431482	+	0.902122i	$0.642009\pi$
$458$			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	−0.914570	−	0.404428i	$-0.867470\pi$
$461$	−17.3384	−	30.0310i	−0.807530	−	1.39868i	0.107039	−	0.994255i	$-0.465863\pi$
$462$	−15.9352	+	12.0205i	−0.741371	+	0.559244i
$463$	−6.45080	−	3.72437i	−0.299794	−	0.173086i	0.342556	−	0.939497i	$-0.388707\pi$
$463$	−6.45080	−	3.72437i	−0.299794	−	0.173086i	−0.642350	+	0.766411i	$0.722041\pi$
$464$	−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	$-0.756148\pi$
$467$		−	29.9655i		−	1.38664i	0.720630	−	0.693319i	$-0.243852\pi$
$468$	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	0.760280	−	0.649595i	$-0.225062\pi$
$479$	−3.99258	−	6.91535i	−0.182426	−	0.315971i	−0.942706	+	0.333625i	$0.891728\pi$
$480$		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	$0.0872291\pi$
$487$			11.9442i			0.541243i	−0.962686	+	0.270621i	$0.912771\pi$
$488$	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	−0.743042	−	0.669244i	$-0.766618\pi$
$491$	4.61033	−	7.98533i	0.208061	−	0.360373i	0.951104	+	0.308872i	$0.0999513\pi$
$492$	−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	−0.301019	−	0.953618i	$-0.597327\pi$
$499$	15.0861	−	26.1299i	0.675348	−	1.16974i	0.976367	−	0.216119i	$-0.0693399\pi$
$500$		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	$-0.924074\pi$
$503$		−	10.5981i		−	0.472546i	0.971687	−	0.236273i	$-0.0759260\pi$
$504$	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	−0.348831	−	0.937186i	$-0.613421\pi$
$509$	14.3761	−	24.9002i	0.637211	−	1.10368i	0.986042	−	0.166496i	$-0.0532454\pi$
$510$		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	$0.0782412\pi$
$523$			11.1297i			0.486669i	−0.969942	+	0.243334i	$0.921759\pi$
$524$	−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	−0.448899	−	0.893582i	$-0.648184\pi$
$547$	2.35087	−	1.35727i	0.100516	−	0.0580328i	0.549415	+	0.835549i	$0.314851\pi$
$548$		−	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	$0.0606321\pi$
$557$			8.93676i			0.378663i	−0.981913	+	0.189331i	$0.939368\pi$
$558$	−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	0.661033	−	0.750357i	$-0.270118\pi$
$563$	8.10826	+	4.68130i	0.341722	+	0.197293i	−0.319311	+	0.947650i	$0.603451\pi$
$564$	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	0.946877	+	0.321595i	$0.104219\pi$
$569$	17.9368	+	31.0674i	0.751948	+	1.30241i	−0.194929	+	0.980817i	$0.562448\pi$
$570$		0			0
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	−0.995788	−	0.0916910i	$-0.970773\pi$
$571$	−10.0000	+	17.3205i	−0.418487	+	0.724841i	0.577301	+	0.816532i	$0.304106\pi$
$572$	−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	$-0.991009\pi$
$577$		−	1.35675i		−	0.0564821i	0.999601	−	0.0282411i	$-0.00899060\pi$
$578$	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	−0.916724	−	0.399521i	$-0.869176\pi$
$587$	−24.9329	+	14.3950i	−1.02909	+	0.594145i	−0.112366	+	0.993667i	$0.535843\pi$
$588$	−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	$0.218920\pi$
$593$			30.9171i			1.26961i	−0.772671	+	0.634807i	$0.781080\pi$
$594$	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	−0.851446	−	0.524442i	$-0.824274\pi$
$599$	0.696460	−	1.20630i	0.0284566	−	0.0492882i	0.879903	+	0.475153i	$0.157607\pi$
$600$		0			0
$601$	−4.41256	−	7.64279i	−0.179992	−	0.311756i	0.761885	−	0.647712i	$-0.224274\pi$
$601$	−4.41256	−	7.64279i	−0.179992	−	0.311756i	−0.941878	+	0.335956i	$0.890941\pi$
$602$		−	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	0.461614	−	0.887081i	$-0.347270\pi$
$607$	−1.86783	−	1.07839i	−0.0758129	−	0.0437706i	−0.537427	+	0.843310i	$0.680604\pi$
$608$	−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	$-0.938058\pi$
$613$		−	9.57521i		−	0.386739i	0.981126	−	0.193370i	$-0.0619416\pi$
$614$	−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	−0.330907	−	0.943663i	$-0.607355\pi$
$617$	−32.6291	−	18.8384i	−1.31360	−	0.758406i	−0.982690	+	0.185258i	$0.940688\pi$
$618$	−21.7044	+	16.3724i	−0.873078	+	0.658596i
$619$	8.55211	+	14.8127i	0.343738	+	0.595372i	0.985124	−	0.171847i	$-0.0549734\pi$
$619$	8.55211	+	14.8127i	0.343738	+	0.595372i	−0.641385	+	0.767219i	$0.721640\pi$
$620$		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	0.998814	−	0.0486939i	$-0.0155059\pi$
$641$	11.5763	+	20.0508i	0.457237	+	0.791957i	−0.541577	+	0.840651i	$0.682173\pi$
$642$	−4.02534	−	1.70628i	−0.158867	−	0.0673416i
$643$	−37.2944	−	21.5319i	−1.47075	−	0.849137i	−0.471287	−	0.881980i	$-0.656211\pi$
$643$	−37.2944	−	21.5319i	−1.47075	−	0.849137i	−0.999461	+	0.0328430i	$0.989544\pi$
$644$	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	$0.133006\pi$
$647$			20.6439i			0.811595i	−0.913963	+	0.405798i	$0.866994\pi$
$648$	−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	0.379686	−	0.925116i	$-0.376032\pi$
$653$	−5.91942	−	3.41758i	−0.231645	−	0.133740i	−0.611331	+	0.791375i	$0.709365\pi$
$654$	−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	−0.999636	−	0.0269806i	$-0.991411\pi$
$659$	−13.4307	−	23.2626i	−0.523184	−	0.906181i	0.476452	−	0.879200i	$-0.341923\pi$
$660$		0			0
$661$	1.06063	−	1.83706i	0.0412535	−	0.0714532i	−0.844661	−	0.535301i	$-0.820198\pi$
$661$	1.06063	−	1.83706i	0.0412535	−	0.0714532i	0.885915	+	0.463848i	$0.153532\pi$
$662$	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	0.210523	−	0.977589i	$-0.432483\pi$
$673$	30.1553	−	17.4102i	1.16240	−	0.671112i	0.951878	+	0.306477i	$0.0991501\pi$
$674$	4.76450			0.183522
$675$		0			0
$676$	−29.5874			−1.13798
$677$	21.3772	−	12.3421i	0.821592	−	0.474346i	−0.0293735	−	0.999569i	$-0.509351\pi$
$677$	21.3772	−	12.3421i	0.821592	−	0.474346i	0.850965	+	0.525222i	$0.176018\pi$
$678$	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	$-0.736790\pi$
$683$		−	38.4610i		−	1.47167i	0.677162	−	0.735834i	$-0.263210\pi$
$684$	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	0.861418	−	0.507896i	$-0.169577\pi$
$691$	−0.240304	−	0.416219i	−0.00914159	−	0.0158337i	−0.870560	+	0.492062i	$0.836243\pi$
$692$		−	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	0.925582	−	0.378548i	$-0.123577\pi$
$709$	3.59355	+	6.22421i	0.134959	+	0.233755i	−0.790623	+	0.612303i	$0.790243\pi$
$710$		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	−0.629174	−	0.777264i	$-0.716607\pi$
$727$	−7.29699	+	4.21292i	−0.270631	+	0.156249i	0.358544	+	0.933513i	$0.383273\pi$
$728$		−	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	0.808732	−	0.588177i	$-0.200154\pi$
$733$	19.0526	+	11.0000i	0.703722	+	0.406294i	−0.105010	+	0.994471i	$0.533487\pi$
$734$	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	0.144747	−	0.989469i	$-0.453763\pi$
$743$	−17.4393	−	10.0686i	−0.639785	−	0.369380i	−0.784532	+	0.620089i	$0.787097\pi$
$744$	−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	−0.955667	−	0.294449i	$-0.904864\pi$
$751$	−6.10662	+	10.5770i	−0.222834	+	0.385959i	0.732834	+	0.680408i	$0.238197\pi$
$752$	−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	$-0.587670\pi$
$757$		−	52.9533i		−	1.92462i	0.271955	−	0.962310i	$-0.412330\pi$
$758$	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	−0.648913	−	0.760863i	$-0.724776\pi$
$761$	9.22677	−	15.9812i	0.334470	−	0.579319i	0.983383	+	0.181543i	$0.0581093\pi$
$762$	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	−0.903379	−	0.428844i	$-0.858921\pi$
$769$	−2.22677	+	3.85688i	−0.0802995	+	0.139083i	0.823079	+	0.567927i	$0.192254\pi$
$770$		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	$0.246919\pi$
$773$			38.9368i			1.40046i	−0.713918	+	0.700229i	$0.753081\pi$
$774$	3.56999	+	3.68945i	0.128321	+	0.132614i
$775$		0			0
$776$	−4.98516	−	8.63456i	−0.178957	−	0.309962i
$777$	49.0288	+	20.7826i	1.75890	+	0.745571i
$778$	−10.0945	−	5.82806i	−0.361905	−	0.208946i
$779$	−0.0582214	+	0.100842i	−0.00208600	+	0.00361305i
$780$		0			0
$781$	−4.13453	−	7.16121i	−0.147945	−	0.256248i
$782$		−	13.5094i		−	0.483094i
$783$	12.6517	−	15.6715i	0.452134	−	0.560053i
$784$	30.7597			1.09856
$785$		0			0
$786$	−13.0558	−	17.3077i	−0.465686	−	0.617344i
$787$	29.6424	+	17.1140i	1.05664	+	0.610050i	0.924500	−	0.381182i	$-0.124483\pi$
$787$	29.6424	+	17.1140i	1.05664	+	0.610050i	0.132137	+	0.991231i	$0.457816\pi$
$788$	31.7340	+	18.3216i	1.13048	+	0.652681i
$789$	21.5423	−	50.8210i	0.766926	−	1.80928i
$790$		0			0
$791$	−48.7252			−1.73247
$792$	−0.723268	−	2.88857i	−0.0257002	−	0.102641i
$793$		−	2.47580i		−	0.0879183i
$794$	−3.91387	−	6.77902i	−0.138898	−	0.240578i
$795$		0			0
$796$	−4.21564	+	7.30171i	−0.149420	+	0.258802i
$797$	20.7547	+	11.9828i	0.735171	+	0.424451i	0.820311	−	0.571918i	$-0.193800\pi$
$797$	20.7547	+	11.9828i	0.735171	+	0.424451i	−0.0851400	+	0.996369i	$0.527134\pi$
$798$	−1.17081	−	9.49629i	−0.0414464	−	0.336165i
$799$	−7.37243	−	12.7694i	−0.260818	−	0.451750i
$800$		0			0
$801$	2.47209	−	8.65383i	0.0873470	−	0.305768i
$802$			49.1600i			1.73590i
$803$	14.4531	−	8.34452i	0.510040	−	0.294472i
$804$	12.9444	−	30.5375i	0.456513	−	1.07697i
$805$		0			0
$806$	−5.20257	+	9.01112i	−0.183253	+	0.317403i
$807$	43.5529	−	32.8536i	1.53313	−	1.15650i
$808$	0.933638	−	0.539036i	0.0328453	−	0.0189632i
$809$	0.283896			0.00998124			0.00499062	−	0.999988i	$-0.498411\pi$
$809$	0.283896			0.00998124			0.00499062	+	0.999988i	$0.498411\pi$
$810$		0			0
$811$	32.4413			1.13917			0.569584	−	0.821933i	$-0.307104\pi$
$811$	32.4413			1.13917			0.569584	+	0.821933i	$0.307104\pi$
$812$	−32.2603	+	18.6255i	−1.13211	+	0.653626i
$813$	−4.48055	+	3.37985i	−0.157140	+	0.118536i
$814$	10.6103	−	18.3776i	0.371892	−	0.644136i
$815$		0			0
$816$	−2.89903	+	6.83919i	−0.101486	+	0.239420i
$817$	0.460395	−	0.265809i	0.0161072	−	0.00929948i
$818$		−	2.18710i		−	0.0764701i
$819$	2.18208	−	7.63862i	0.0762481	−	0.266915i
$820$		0			0
$821$	−20.8347	−	36.0868i	−0.727136	−	1.25944i	−0.958089	−	0.286472i	$-0.907518\pi$
$821$	−20.8347	−	36.0868i	−0.727136	−	1.25944i	0.230953	−	0.972965i	$-0.425816\pi$
$822$	−3.30207	−	26.7826i	−0.115173	−	0.934150i
$823$	16.7685	+	9.68130i	0.584514	+	0.337469i	0.762925	−	0.646487i	$-0.223763\pi$
$823$	16.7685	+	9.68130i	0.584514	+	0.337469i	−0.178412	+	0.983956i	$0.557096\pi$
$824$	−2.76210	+	4.78410i	−0.0962223	+	0.166662i
$825$		0			0
$826$	17.7826	+	30.8003i	0.618735	+	1.07168i
$827$		−	18.8097i		−	0.654076i	−0.945011	−	0.327038i	$-0.893950\pi$
$827$		−	18.8097i		−	0.654076i	0.945011	−	0.327038i	$-0.106050\pi$
$828$	8.20910	+	32.7853i	0.285286	+	1.13937i
$829$	33.1016			1.14967			0.574833	−	0.818271i	$-0.305067\pi$
$829$	33.1016			1.14967			0.574833	+	0.818271i	$0.305067\pi$
$830$		0			0
$831$	3.77517	−	8.90611i	0.130959	−	0.308950i
$832$	−5.90657	−	3.41016i	−0.204774	−	0.118226i
$833$	11.3527	+	6.55451i	0.393349	+	0.227100i
$834$	−17.4078	−	23.0769i	−0.602781	−	0.799087i
$835$		0			0
$836$	−2.06063			−0.0712682
$837$	−39.5089	−	6.19692i	−1.36563	−	0.214197i
$838$			54.0719i			1.86788i
$839$	−19.8482	−	34.3781i	−0.685237	−	1.18687i	−0.973362	−	0.229273i	$-0.926365\pi$
$839$	−19.8482	−	34.3781i	−0.685237	−	1.18687i	0.288125	−	0.957593i	$-0.406968\pi$
$840$		0			0
$841$	6.98777	−	12.1032i	0.240958	−	0.417351i
$842$	−13.8039	−	7.96969i	−0.475714	−	0.274654i
$843$	38.4390	+	16.2937i	1.32391	+	0.561185i
$844$	17.6308	+	30.5375i	0.606878	+	1.05114i
$845$		0			0
$846$	47.4642	+	49.0525i	1.63185	+	1.68646i
$847$			37.4791i			1.28780i
$848$	−11.4623	+	6.61775i	−0.393616	+	0.227254i
$849$	18.1226	−	2.23436i	0.621965	−	0.0766831i
$850$		0			0
$851$	−18.0205	+	31.2124i	−0.617734	+	1.06995i
$852$	3.04890	+	24.7292i	0.104454	+	0.847208i
$853$	−3.56494	+	2.05822i	−0.122061	+	0.0704722i	−0.559788	−	0.828636i	$-0.689117\pi$
$853$	−3.56494	+	2.05822i	−0.122061	+	0.0704722i	0.437726	+	0.899108i	$0.355784\pi$
$854$	−32.5652			−1.11436
$855$		0			0
$856$	−0.888365			−0.0303637
$857$	−12.7694	+	7.37243i	−0.436195	+	0.251837i	−0.701982	−	0.712194i	$-0.747701\pi$
$857$	−12.7694	+	7.37243i	−0.436195	+	0.251837i	0.265787	+	0.964032i	$0.414368\pi$
$858$	−2.91469	−	1.23550i	−0.0995060	−	0.0421792i
$859$	−18.9269	+	32.7824i	−0.645779	+	1.11852i	0.338342	+	0.941023i	$0.390134\pi$
$859$	−18.9269	+	32.7824i	−0.645779	+	1.11852i	−0.984121	+	0.177499i	$0.943199\pi$
$860$		0			0
$861$	0.765809	+	1.01521i	0.0260987	+	0.0345982i
$862$	14.4263	−	8.32905i	0.491363	−	0.283688i
$863$			26.7704i			0.911274i	0.890166	+	0.455637i	$0.150588\pi$
$863$			26.7704i			0.911274i	−0.890166	+	0.455637i	$0.849412\pi$
$864$	6.51067	−	41.5093i	0.221497	−	1.41217i
$865$		0			0
$866$	−13.0508	−	22.6047i	−0.443484	−	0.768137i
$867$	20.9795	−	15.8257i	0.712503	−	0.537467i
$868$	64.0560	+	36.9828i	2.17420	+	1.25528i
$869$	−6.99258	+	12.1115i	−0.237207	+	0.410855i
$870$		0			0
$871$	−2.63824	−	4.56956i	−0.0893933	−	0.154834i
$872$			10.3552i			0.350671i
$873$	−9.89540	−	39.5200i	−0.334909	−	1.33755i
$874$	6.47580			0.219047
$875$		0			0
$876$	−49.9097	+	6.15345i	−1.68629	+	0.207906i
$877$	−40.6756	−	23.4841i	−1.37352	−	0.793001i	−0.382148	−	0.924101i	$-0.624816\pi$
$877$	−40.6756	−	23.4841i	−1.37352	−	0.793001i	−0.991369	+	0.131101i	$0.958149\pi$
$878$	−15.8343	−	9.14195i	−0.534382	−	0.308526i
$879$	−32.6489	+	4.02534i	−1.10122	+	0.135771i
$880$		0			0
$881$	−19.8055			−0.667264			−0.333632	−	0.942703i	$-0.608274\pi$
$881$	−19.8055			−0.667264			−0.333632	+	0.942703i	$0.608274\pi$
$882$	−58.3501	−	16.6686i	−1.96475	−	0.561259i
$883$		−	6.20257i		−	0.208733i	−0.994539	−	0.104367i	$-0.966718\pi$
$883$		−	6.20257i		−	0.208733i	0.994539	−	0.104367i	$-0.0332815\pi$
$884$	−1.03031	−	1.78455i	−0.0346532	−	0.0600210i
$885$		0			0
$886$	3.82905	−	6.63210i	0.128639	−	0.222810i
$887$	11.6285	+	6.71370i	0.390446	+	0.225424i	0.682353	−	0.731023i	$-0.260957\pi$
$887$	11.6285	+	6.71370i	0.390446	+	0.225424i	−0.291907	+	0.956447i	$0.594290\pi$
$888$	−7.63862	+	5.76210i	−0.256335	+	0.193363i
$889$	−14.4623	−	25.0494i	−0.485049	−	0.840129i
$890$		0			0
$891$	0.400338	−	12.1609i	0.0134118	−	0.407404i
$892$			63.1049i			2.11291i
$893$	6.12111	−	3.53402i	0.204835	−	0.118262i
$894$	23.0323	+	30.5331i	0.770314	+	1.02118i
$895$		0			0
$896$	−11.8142	+	20.4628i	−0.394685	+	0.683614i
$897$	4.95029	+	2.09836i	0.165285	+	0.0700621i
$898$	−50.8972	+	29.3855i	−1.69846	+	0.980607i
$899$	29.8325			0.994971
$900$		0			0
$901$	−5.64064			−0.187917
$902$	0.438860	−	0.253376i	0.0146124	−	0.00843650i
$903$	−0.710419	−	5.76210i	−0.0236413	−	0.191751i
$904$	4.37744	−	7.58196i	0.145592	−	0.252172i
$905$		0			0
$906$	−63.4618	+	7.82431i	−2.10838	+	0.259945i
$907$	−0.583325	+	0.336783i	−0.0193690	+	0.0111827i	−0.509653	−	0.860380i	$-0.670226\pi$
$907$	−0.583325	+	0.336783i	−0.0193690	+	0.0111827i	0.490284	+	0.871563i	$0.336893\pi$
$908$			3.17968i			0.105521i
$909$	4.27323	−	1.06997i	0.141734	−	0.0354887i
$910$		0			0
$911$	3.95485	+	6.85000i	0.131030	+	0.226951i	0.924074	−	0.382214i	$-0.124838\pi$
$911$	3.95485	+	6.85000i	0.131030	+	0.226951i	−0.793044	+	0.609165i	$0.791505\pi$
$912$	−3.27841	−	1.38967i	−0.108559	−	0.0460166i
$913$	−14.3523	−	8.28630i	−0.474992	−	0.274236i
$914$	−36.7802	+	63.7052i	−1.21658	+	2.10718i
$915$		0			0
$916$	9.68469	+	16.7744i	0.319991	+	0.554241i
$917$			24.5168i			0.809615i
$918$	9.20550	−	11.4027i	0.303827	−	0.376347i
$919$	8.58263			0.283115			0.141557	−	0.989930i	$-0.454789\pi$
$919$	8.58263			0.283115			0.141557	+	0.989930i	$0.454789\pi$
$920$		0			0
$921$	−30.7486	−	40.7623i	−1.01320	−	1.34316i
$922$	−62.6486	−	36.1702i	−2.06322	−	1.19120i
$923$	3.43277	+	1.98191i	0.112991	+	0.0652355i
$924$	−8.78259	+	20.7193i	−0.288926	+	0.681614i
$925$		0			0
$926$	−15.5390			−0.510644
$927$	−16.2217	+	15.6965i	−0.532790	+	0.515539i
$928$			31.3430i			1.02888i
$929$	14.8081	+	25.6484i	0.485838	+	0.841496i	0.999868	−	0.0162766i	$-0.00518122\pi$
$929$	14.8081	+	25.6484i	0.485838	+	0.841496i	−0.514030	+	0.857772i	$0.671848\pi$
$930$		0			0
$931$	−3.14195	+	5.44201i	−0.102973	+	0.178355i
$932$	17.4912	+	10.0986i	0.572944	+	0.330789i
$933$	−1.99492	−	16.1805i	−0.0653109	−	0.529727i
$934$	−31.2560	−	54.1370i	−1.02273	−	1.77142i
$935$		0			0
$936$	0.992582	+	1.02580i	0.0324435	+	0.0335292i
$937$			15.2058i			0.496753i	0.968664	+	0.248376i	$0.0798969\pi$
$937$			15.2058i			0.496753i	−0.968664	+	0.248376i	$0.920103\pi$
$938$	−60.1053	+	34.7018i	−1.96251	+	1.13305i
$939$	7.85544	−	18.5320i	0.256353	−	0.604769i
$940$		0			0
$941$	−2.82643	+	4.89553i	−0.0921391	+	0.159590i	−0.908411	−	0.418078i	$-0.862704\pi$
$941$	−2.82643	+	4.89553i	−0.0921391	+	0.159590i	0.816272	+	0.577668i	$0.196037\pi$
$942$	−7.30273	+	5.50872i	−0.237936	+	0.179484i
$943$	−0.745356	+	0.430332i	−0.0242721	+	0.0140135i
$944$	13.2355			0.430779
$945$		0			0
$946$	−2.31357			−0.0752206
$947$	34.9841	−	20.1981i	1.13683	−	0.656350i	0.191187	−	0.981554i	$-0.438766\pi$
$947$	34.9841	−	20.1981i	1.13683	−	0.656350i	0.945644	+	0.325204i	$0.105433\pi$
$948$	33.6420	−	25.3774i	1.09264	−	0.824221i
$949$	−4.00000	+	6.92820i	−0.129845	+	0.224899i
$950$		0			0
$951$	6.20518	−	14.6388i	0.201217	−	0.474696i
$952$	−3.51244	+	2.02791i	−0.113839	+	0.0657249i
$953$		−	22.9320i		−	0.742839i	−0.928465	−	0.371419i	$-0.878871\pi$
$953$		−	22.9320i		−	0.742839i	0.928465	−	0.371419i	$-0.121129\pi$
$954$	25.3297	−	6.34229i	0.820079	−	0.205339i
$955$		0			0
$956$	28.1345	+	48.7304i	0.909936	+	1.57605i
$957$	1.11064	+	9.00826i	0.0359020	+	0.291196i
$958$	−14.4263	−	8.32905i	−0.466094	−	0.269099i
$959$	−15.2584	+	26.4283i	−0.492719	+	0.853415i
$960$		0			0
$961$	−14.1177	−	24.4527i	−0.455411	−	0.788795i
$962$			10.1723i			0.327967i
$963$	−3.49035	−	0.997070i	−0.112475	−	0.0321301i
$964$	14.6768			0.472708
$965$		0			0
$966$	27.6005	−	65.1131i	0.888032	−	2.09498i
$967$	8.98071	+	5.18501i	0.288800	+	0.166739i	0.637401	−	0.770533i	$-0.280010\pi$
$967$	8.98071	+	5.18501i	0.288800	+	0.166739i	−0.348601	+	0.937271i	$0.613343\pi$
$968$	−5.83198	−	3.36710i	−0.187447	−	0.108223i
$969$	−0.913870	−	1.21149i	−0.0293577	−	0.0389186i
$970$		0			0
$971$	48.0410			1.54171			0.770854	−	0.637012i	$-0.219830\pi$
$971$	48.0410			1.54171			0.770854	+	0.637012i	$0.219830\pi$
$972$	−15.4115	+	33.2667i	−0.494323	+	1.06703i
$973$			32.6890i			1.04796i
$974$	12.4586	+	21.5789i	0.399198	+	0.691431i
$975$		0			0
$976$	−6.05953	+	10.4954i	−0.193961	+	0.335950i
$977$	23.4288	+	13.5266i	0.749553	+	0.432754i	0.825532	−	0.564355i	$-0.190875\pi$
$977$	23.4288	+	13.5266i	0.749553	+	0.432754i	−0.0759796	+	0.997109i	$0.524208\pi$
$978$	28.1969	+	11.9522i	0.901636	+	0.382190i
$979$	2.02791	+	3.51244i	0.0648122	+	0.112258i
$980$		0			0
$981$	−11.6223	+	40.6852i	−0.371072	+	1.29898i
$982$		−	19.2355i		−	0.613829i
$983$	−19.4697	+	11.2408i	−0.620987	+	0.358527i	−0.777253	−	0.629188i	$-0.783388\pi$
$983$	−19.4697	+	11.2408i	−0.620987	+	0.358527i	0.156266	+	0.987715i	$0.450054\pi$
$984$	−0.226773	+	0.0279592i	−0.00722925	+	0.000891306i
$985$		0			0
$986$	−5.46598	+	9.46735i	−0.174072	+	0.301502i
$987$	−9.44526	−	76.6091i	−0.300646	−	2.43849i
$988$	0.855437	−	0.493887i	0.0272151	−	0.0157126i
$989$	3.92935			0.124946
$990$		0			0
$991$	−26.5316			−0.842805			−0.421402	−	0.906874i	$-0.638462\pi$
$991$	−26.5316			−0.842805			−0.421402	+	0.906874i	$0.638462\pi$
$992$	53.8967	−	31.1173i	1.71122	−	0.987975i
$993$	11.5148	+	4.88095i	0.365410	+	0.154892i
$994$	26.0689	−	45.1526i	0.826855	−	1.43215i
$995$		0			0
$996$	30.0726	+	39.8662i	0.952887	+	1.26321i
$997$	24.5656	−	14.1829i	0.777999	−	0.449178i	−0.0577217	−	0.998333i	$-0.518384\pi$
$997$	24.5656	−	14.1829i	0.777999	−	0.449178i	0.835721	+	0.549155i	$0.185050\pi$
$998$		−	62.9433i		−	1.99243i
$999$	−36.4791	+	14.0658i	−1.15415	+	0.445021i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.k.b.49.5		12
3.2	odd	2		675.2.k.b.199.2		12
5.2	odd	4		45.2.e.b.31.3	yes	6
5.3	odd	4		225.2.e.b.76.1		6
5.4	even	2	inner	225.2.k.b.49.2		12
9.2	odd	6		675.2.k.b.424.5		12
9.4	even	3		2025.2.b.l.649.5		6
9.5	odd	6		2025.2.b.m.649.2		6
9.7	even	3	inner	225.2.k.b.124.2		12
15.2	even	4		135.2.e.b.91.1		6
15.8	even	4		675.2.e.b.226.3		6
15.14	odd	2		675.2.k.b.199.5		12
20.7	even	4		720.2.q.i.481.3		6
45.2	even	12		135.2.e.b.46.1		6
45.4	even	6		2025.2.b.l.649.2		6
45.7	odd	12		45.2.e.b.16.3	✓	6
45.13	odd	12		2025.2.a.n.1.3		3
45.14	odd	6		2025.2.b.m.649.5		6
45.22	odd	12		405.2.a.j.1.1		3
45.23	even	12		2025.2.a.o.1.1		3
45.29	odd	6		675.2.k.b.424.2		12
45.32	even	12		405.2.a.i.1.3		3
45.34	even	6	inner	225.2.k.b.124.5		12
45.38	even	12		675.2.e.b.451.3		6
45.43	odd	12		225.2.e.b.151.1		6
60.47	odd	4		2160.2.q.k.1441.3		6
180.7	even	12		720.2.q.i.241.3		6
180.47	odd	12		2160.2.q.k.721.3		6
180.67	even	12		6480.2.a.bv.1.1		3
180.167	odd	12		6480.2.a.bs.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.2.e.b.16.3	✓	6	45.7	odd	12
45.2.e.b.31.3	yes	6	5.2	odd	4
135.2.e.b.46.1		6	45.2	even	12
135.2.e.b.91.1		6	15.2	even	4
225.2.e.b.76.1		6	5.3	odd	4
225.2.e.b.151.1		6	45.43	odd	12
225.2.k.b.49.2		12	5.4	even	2	inner
225.2.k.b.49.5		12	1.1	even	1	trivial
225.2.k.b.124.2		12	9.7	even	3	inner
225.2.k.b.124.5		12	45.34	even	6	inner
405.2.a.i.1.3		3	45.32	even	12
405.2.a.j.1.1		3	45.22	odd	12
675.2.e.b.226.3		6	15.8	even	4
675.2.e.b.451.3		6	45.38	even	12
675.2.k.b.199.2		12	3.2	odd	2
675.2.k.b.199.5		12	15.14	odd	2
675.2.k.b.424.2		12	45.29	odd	6
675.2.k.b.424.5		12	9.2	odd	6
720.2.q.i.241.3		6	180.7	even	12
720.2.q.i.481.3		6	20.7	even	4
2025.2.a.n.1.3		3	45.13	odd	12
2025.2.a.o.1.1		3	45.23	even	12
2025.2.b.l.649.2		6	45.4	even	6
2025.2.b.l.649.5		6	9.4	even	3
2025.2.b.m.649.2		6	9.5	odd	6
2025.2.b.m.649.5		6	45.14	odd	6
2160.2.q.k.721.3		6	180.47	odd	12
2160.2.q.k.1441.3		6	60.47	odd	4
6480.2.a.bs.1.1		3	180.167	odd	12
6480.2.a.bv.1.1		3	180.67	even	12

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

Modular forms

Varieties

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Database

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