LMFDB - Embedded newform 225.4.e.b.151.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,4,Mod(76,225)]

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, 0]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("225.76");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	225.e (of order $3$, degree $2$, 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:	$13.2754297513$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-11})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 2x^{2} - 3x + 9 $ x^4 - x^3 - 2x^2 - 3x + 9
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 3 $
Twist minimal:	no (minimal twist has level 9)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			151.1
Root			$-1.18614 + 1.26217i$ of defining polynomial
Character	$\chi$	$=$	225.151
Dual form			225.4.e.b.76.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.686141 + 1.18843i) q^{2} +(5.05842 - 1.18843i) q^{3} +(3.05842 + 5.29734i) q^{4} +(-2.05842 + 6.82701i) q^{6} +(-2.55842 + 4.43132i) q^{7} -19.3723 q^{8} +(24.1753 - 12.0232i) q^{9} +O(q^{10})$	\(q+(-0.686141 + 1.18843i) q^{2} +(5.05842 - 1.18843i) q^{3} +(3.05842 + 5.29734i) q^{4} +(-2.05842 + 6.82701i) q^{6} +(-2.55842 + 4.43132i) q^{7} -19.3723 q^{8} +(24.1753 - 12.0232i) q^{9} +(-27.9891 + 48.4786i) q^{11} +(21.7663 + 23.1615i) q^{12} +(18.7921 + 32.5489i) q^{13} +(-3.51087 - 6.08101i) q^{14} +(-11.1753 + 19.3561i) q^{16} -23.6495 q^{17} +(-2.29894 + 36.9802i) q^{18} +39.0516 q^{19} +(-7.67527 + 25.4560i) q^{21} +(-38.4090 - 66.5263i) q^{22} +(35.5367 + 61.5513i) q^{23} +(-97.9932 + 23.0226i) q^{24} -51.5761 q^{26} +(108.000 - 89.5489i) q^{27} -31.2989 q^{28} +(14.1861 - 24.5711i) q^{29} +(-6.44158 - 11.1571i) q^{31} +(-92.8247 - 160.777i) q^{32} +(-83.9674 + 278.488i) q^{33} +(16.2269 - 28.1057i) q^{34} +(137.629 + 91.2927i) q^{36} +180.103 q^{37} +(-26.7949 + 46.4101i) q^{38} +(133.741 + 142.313i) q^{39} +(107.742 + 186.614i) q^{41} +(-24.9863 - 26.5879i) q^{42} +(30.6168 - 53.0299i) q^{43} -342.410 q^{44} -97.5326 q^{46} +(-30.9388 + 53.5876i) q^{47} +(-33.5258 + 111.192i) q^{48} +(158.409 + 274.372i) q^{49} +(-119.629 + 28.1057i) q^{51} +(-114.948 + 199.096i) q^{52} -492.310 q^{53} +(32.3194 + 189.794i) q^{54} +(49.5625 - 85.8447i) q^{56} +(197.539 - 46.4101i) q^{57} +(19.4674 + 33.7185i) q^{58} +(-394.815 - 683.840i) q^{59} +(-260.545 + 451.277i) q^{61} +17.6793 q^{62} +(-8.57207 + 137.889i) q^{63} +75.9590 q^{64} +(-273.351 - 290.872i) q^{66} +(152.215 + 263.644i) q^{67} +(-72.3301 - 125.279i) q^{68} +(252.909 + 269.120i) q^{69} +270.391 q^{71} +(-468.330 + 232.916i) q^{72} +925.464 q^{73} +(-123.576 + 214.040i) q^{74} +(119.436 + 206.870i) q^{76} +(-143.216 - 248.057i) q^{77} +(-260.894 + 61.2946i) q^{78} +(644.517 - 1116.34i) q^{79} +(439.887 - 581.326i) q^{81} -295.704 q^{82} +(356.917 - 618.198i) q^{83} +(-158.323 + 37.1966i) q^{84} +(42.0149 + 72.7720i) q^{86} +(42.5584 - 141.150i) q^{87} +(542.213 - 939.141i) q^{88} -404.804 q^{89} -192.313 q^{91} +(-217.372 + 376.500i) q^{92} +(-45.8437 - 48.7822i) q^{93} +(-42.4567 - 73.5372i) q^{94} +(-660.619 - 702.963i) q^{96} +(37.5137 - 64.9756i) q^{97} -434.763 q^{98} +(-93.7785 + 1508.50i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 3 q^{2} + 3 q^{3} - 5 q^{4} + 9 q^{6} + 7 q^{7} - 66 q^{8} + 45 q^{9}+O(q^{10}) $ 4 * q + 3 * q^2 + 3 * q^3 - 5 * q^4 + 9 * q^6 + 7 * q^7 - 66 * q^8 + 45 * q^9	$ 4 q + 3 q^{2} + 3 q^{3} - 5 q^{4} + 9 q^{6} + 7 q^{7} - 66 q^{8} + 45 q^{9} - 66 q^{11} + 156 q^{12} - 11 q^{13} - 60 q^{14} + 7 q^{16} - 198 q^{17} - 216 q^{18} - 154 q^{19} + 21 q^{21} - 33 q^{22} + 33 q^{23} - 99 q^{24} - 528 q^{26} + 432 q^{27} - 332 q^{28} + 51 q^{29} - 43 q^{31} - 423 q^{32} - 198 q^{33} - 297 q^{34} - 225 q^{36} + 100 q^{37} - 561 q^{38} + 759 q^{39} - 132 q^{41} + 486 q^{42} + 88 q^{43} - 462 q^{44} - 528 q^{46} + 399 q^{47} + 21 q^{48} + 513 q^{49} + 297 q^{51} - 770 q^{52} - 108 q^{53} + 1215 q^{54} - 66 q^{56} + 1221 q^{57} - 60 q^{58} - 798 q^{59} - 439 q^{61} - 228 q^{62} - 603 q^{63} - 1454 q^{64} - 990 q^{66} + 988 q^{67} + 693 q^{68} + 891 q^{69} + 2736 q^{71} - 891 q^{72} + 910 q^{73} - 816 q^{74} + 1529 q^{76} - 165 q^{77} + 990 q^{78} + 803 q^{79} - 567 q^{81} - 3630 q^{82} + 813 q^{83} + 642 q^{84} - 33 q^{86} + 153 q^{87} + 1221 q^{88} - 792 q^{89} - 1562 q^{91} - 858 q^{92} + 213 q^{93} - 2100 q^{94} + 1080 q^{96} + 736 q^{97} + 846 q^{98} + 297 q^{99}+O(q^{100}) $ 4 * q + 3 * q^2 + 3 * q^3 - 5 * q^4 + 9 * q^6 + 7 * q^7 - 66 * q^8 + 45 * q^9 - 66 * q^11 + 156 * q^12 - 11 * q^13 - 60 * q^14 + 7 * q^16 - 198 * q^17 - 216 * q^18 - 154 * q^19 + 21 * q^21 - 33 * q^22 + 33 * q^23 - 99 * q^24 - 528 * q^26 + 432 * q^27 - 332 * q^28 + 51 * q^29 - 43 * q^31 - 423 * q^32 - 198 * q^33 - 297 * q^34 - 225 * q^36 + 100 * q^37 - 561 * q^38 + 759 * q^39 - 132 * q^41 + 486 * q^42 + 88 * q^43 - 462 * q^44 - 528 * q^46 + 399 * q^47 + 21 * q^48 + 513 * q^49 + 297 * q^51 - 770 * q^52 - 108 * q^53 + 1215 * q^54 - 66 * q^56 + 1221 * q^57 - 60 * q^58 - 798 * q^59 - 439 * q^61 - 228 * q^62 - 603 * q^63 - 1454 * q^64 - 990 * q^66 + 988 * q^67 + 693 * q^68 + 891 * q^69 + 2736 * q^71 - 891 * q^72 + 910 * q^73 - 816 * q^74 + 1529 * q^76 - 165 * q^77 + 990 * q^78 + 803 * q^79 - 567 * q^81 - 3630 * q^82 + 813 * q^83 + 642 * q^84 - 33 * q^86 + 153 * q^87 + 1221 * q^88 - 792 * q^89 - 1562 * q^91 - 858 * q^92 + 213 * q^93 - 2100 * q^94 + 1080 * q^96 + 736 * q^97 + 846 * q^98 + 297 * 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 $

$2$	−0.686141	+	1.18843i	−0.242587	+	0.420174i	−0.961451	−	0.274978i	$-0.911329\pi$
$2$	−0.686141	+	1.18843i	−0.242587	+	0.420174i	0.718863	+	0.695152i	$0.244663\pi$
$3$	5.05842	−	1.18843i	0.973494	−	0.228714i
$3$	5.05842	−	1.18843i	0.973494	−	0.228714i
$4$	3.05842	+	5.29734i	0.382303	+	0.662168i
$5$		0			0
$5$		0			0
$6$	−2.05842	+	6.82701i	−0.140058	+	0.464519i
$7$	−2.55842	+	4.43132i	−0.138142	+	0.239269i	−0.926793	−	0.375572i	$-0.877446\pi$
$7$	−2.55842	+	4.43132i	−0.138142	+	0.239269i	0.788651	+	0.614841i	$0.210780\pi$
$8$	−19.3723			−0.856142
$9$	24.1753	−	12.0232i	0.895380	−	0.445302i
$10$		0			0
$11$	−27.9891	+	48.4786i	−0.767185	+	1.32880i	0.171898	+	0.985115i	$0.445010\pi$
$11$	−27.9891	+	48.4786i	−0.767185	+	1.32880i	−0.939083	+	0.343689i	$0.888323\pi$
$12$	21.7663	+	23.1615i	0.523616	+	0.557178i
$13$	18.7921	+	32.5489i	0.400923	+	0.694418i	0.993838	−	0.110847i	$-0.0353563\pi$
$13$	18.7921	+	32.5489i	0.400923	+	0.694418i	−0.592915	+	0.805265i	$0.702023\pi$
$14$	−3.51087	−	6.08101i	−0.0670229	−	0.116087i
$15$		0			0
$16$	−11.1753	+	19.3561i	−0.174614	+	0.302440i
$17$	−23.6495			−0.337402			−0.168701	−	0.985667i	$-0.553957\pi$
$17$	−23.6495			−0.337402			−0.168701	+	0.985667i	$0.553957\pi$
$18$	−2.29894	+	36.9802i	−0.0301036	+	0.484240i
$19$	39.0516			0.471529			0.235764	−	0.971810i	$-0.424241\pi$
$19$	39.0516			0.471529			0.235764	+	0.971810i	$0.424241\pi$
$20$		0			0
$21$	−7.67527	+	25.4560i	−0.0797562	+	0.264521i
$22$	−38.4090	−	66.5263i	−0.372219	−	0.644702i
$23$	35.5367	+	61.5513i	0.322170	+	0.558015i	0.980936	−	0.194334i	$-0.0622544\pi$
$23$	35.5367	+	61.5513i	0.322170	+	0.558015i	−0.658766	+	0.752348i	$0.728921\pi$
$24$	−97.9932	+	23.0226i	−0.833449	+	0.195811i
$25$		0			0
$26$	−51.5761			−0.389035
$27$	108.000	−	89.5489i	0.769800	−	0.638285i
$28$	−31.2989			−0.211248
$29$	14.1861	−	24.5711i	0.0908379	−	0.157336i	−0.817026	−	0.576601i	$-0.804379\pi$
$29$	14.1861	−	24.5711i	0.0908379	−	0.157336i	0.907864	+	0.419265i	$0.137712\pi$
$30$		0			0
$31$	−6.44158	−	11.1571i	−0.0373207	−	0.0646413i	0.846762	−	0.531972i	$-0.178549\pi$
$31$	−6.44158	−	11.1571i	−0.0373207	−	0.0646413i	−0.884082	+	0.467331i	$0.845216\pi$
$32$	−92.8247	−	160.777i	−0.512789	−	0.888177i
$33$	−83.9674	+	278.488i	−0.442935	+	1.46905i
$34$	16.2269	−	28.1057i	0.0818495	−	0.141768i
$35$		0			0
$36$	137.629	+	91.2927i	0.637171	+	0.422652i
$37$	180.103			0.800237			0.400119	−	0.916463i	$-0.368969\pi$
$37$	180.103			0.800237			0.400119	+	0.916463i	$0.368969\pi$
$38$	−26.7949	+	46.4101i	−0.114387	+	0.198124i
$39$	133.741	+	142.313i	0.549119	+	0.584315i
$40$		0			0
$41$	107.742	+	186.614i	0.410401	+	0.710835i	0.994934	−	0.100535i	$-0.0320554\pi$
$41$	107.742	+	186.614i	0.410401	+	0.710835i	−0.584533	+	0.811370i	$0.698722\pi$
$42$	−24.9863	−	26.5879i	−0.0917971	−	0.0976810i
$43$	30.6168	−	53.0299i	0.108582	−	0.188069i	−0.806614	−	0.591078i	$-0.798702\pi$
$43$	30.6168	−	53.0299i	0.108582	−	0.188069i	0.915196	+	0.403009i	$0.132036\pi$
$44$	−342.410			−1.17319
$45$		0			0
$46$	−97.5326			−0.312617
$47$	−30.9388	+	53.5876i	−0.0960189	+	0.166310i	−0.910033	−	0.414535i	$-0.863944\pi$
$47$	−30.9388	+	53.5876i	−0.0960189	+	0.166310i	0.814014	+	0.580845i	$0.197278\pi$
$48$	−33.5258	+	111.192i	−0.100813	+	0.334359i
$49$	158.409	+	274.372i	0.461834	+	0.799919i
$50$		0			0
$51$	−119.629	+	28.1057i	−0.328459	+	0.0771685i
$52$	−114.948	+	199.096i	−0.306548	+	0.530956i
$53$	−492.310			−1.27592			−0.637962	−	0.770068i	$-0.720222\pi$
$53$	−492.310			−1.27592			−0.637962	+	0.770068i	$0.720222\pi$
$54$	32.3194	+	189.794i	0.0814466	+	0.478290i
$55$		0			0
$56$	49.5625	−	85.8447i	0.118269	−	0.204848i
$57$	197.539	−	46.4101i	0.459031	−	0.107845i
$58$	19.4674	+	33.7185i	0.0440723	+	0.0763354i
$59$	−394.815	−	683.840i	−0.871196	−	1.50896i	−0.860761	−	0.509010i	$-0.830012\pi$
$59$	−394.815	−	683.840i	−0.871196	−	1.50896i	−0.0104351	−	0.999946i	$-0.503322\pi$
$60$		0			0
$61$	−260.545	+	451.277i	−0.546874	+	0.947214i	0.451612	+	0.892214i	$0.350849\pi$
$61$	−260.545	+	451.277i	−0.546874	+	0.947214i	−0.998486	+	0.0549998i	$0.982484\pi$
$62$	17.6793			0.0362141
$63$	−8.57207	+	137.889i	−0.0171425	+	0.275751i
$64$	75.9590			0.148358
$65$		0			0
$66$	−273.351	−	290.872i	−0.509805	−	0.542482i
$67$	152.215	+	263.644i	0.277552	+	0.480734i	0.970776	−	0.239988i	$-0.0771436\pi$
$67$	152.215	+	263.644i	0.277552	+	0.480734i	−0.693224	+	0.720722i	$0.743810\pi$
$68$	−72.3301	−	125.279i	−0.128990	−	0.223417i
$69$	252.909	+	269.120i	0.441256	+	0.469539i
$70$		0			0
$71$	270.391			0.451966			0.225983	−	0.974131i	$-0.427441\pi$
$71$	270.391			0.451966			0.225983	+	0.974131i	$0.427441\pi$
$72$	−468.330	+	232.916i	−0.766573	+	0.381242i
$73$	925.464			1.48380			0.741900	−	0.670510i	$-0.233925\pi$
$73$	925.464			1.48380			0.741900	+	0.670510i	$0.233925\pi$
$74$	−123.576	+	214.040i	−0.194127	+	0.336239i
$75$		0			0
$76$	119.436	+	206.870i	0.180267	+	0.312231i
$77$	−143.216	−	248.057i	−0.211961	−	0.367127i
$78$	−260.894	+	61.2946i	−0.378723	+	0.0889776i
$79$	644.517	−	1116.34i	0.917897	−	1.58984i	0.115294	−	0.993331i	$-0.463219\pi$
$79$	644.517	−	1116.34i	0.917897	−	1.58984i	0.802603	−	0.596513i	$-0.203448\pi$
$80$		0			0
$81$	439.887	−	581.326i	0.603411	−	0.797430i
$82$	−295.704			−0.398232
$83$	356.917	−	618.198i	0.472009	−	0.817543i	−0.527478	−	0.849569i	$-0.676862\pi$
$83$	356.917	−	618.198i	0.472009	−	0.817543i	0.999487	+	0.0320252i	$0.0101957\pi$
$84$	−158.323	+	37.1966i	−0.205649	+	0.0483153i
$85$		0			0
$86$	42.0149	+	72.7720i	0.0526812	+	0.0912466i
$87$	42.5584	−	141.150i	0.0524453	−	0.173941i
$88$	542.213	−	939.141i	0.656820	−	1.13764i
$89$	−404.804			−0.482125			−0.241063	−	0.970510i	$-0.577496\pi$
$89$	−404.804			−0.482125			−0.241063	+	0.970510i	$0.577496\pi$
$90$		0			0
$91$	−192.313			−0.221537
$92$	−217.372	+	376.500i	−0.246333	+	0.426661i
$93$	−45.8437	−	48.7822i	−0.0511158	−	0.0543922i
$94$	−42.4567	−	73.5372i	−0.0465859	−	0.0806892i
$95$		0			0
$96$	−660.619	−	702.963i	−0.702335	−	0.747353i
$97$	37.5137	−	64.9756i	0.0392674	−	0.0680131i	−0.845724	−	0.533621i	$-0.820831\pi$
$97$	37.5137	−	64.9756i	0.0392674	−	0.0680131i	0.884991	+	0.465608i	$0.154164\pi$
$98$	−434.763			−0.448140
$99$	−93.7785	+	1508.50i	−0.0952029	+	1.53141i
$100$		0			0
$101$	543.939	−	942.130i	0.535881	−	0.928172i	−0.463240	−	0.886233i	$-0.653313\pi$
$101$	543.939	−	942.130i	0.535881	−	0.928172i	0.999120	−	0.0419392i	$-0.0133536\pi$
$102$	48.6806	−	161.455i	0.0472558	−	0.156730i
$103$	−545.909	−	945.542i	−0.522233	−	0.904534i	−0.999665	−	0.0258657i	$-0.991766\pi$
$103$	−545.909	−	945.542i	−0.522233	−	0.904534i	0.477432	−	0.878669i	$-0.341568\pi$
$104$	−364.046	−	630.546i	−0.343247	−	0.594521i
$105$		0			0
$106$	337.794	−	585.076i	0.309523	−	0.536109i
$107$	1029.15			0.929833			0.464917	−	0.885354i	$-0.346084\pi$
$107$	1029.15			0.929833			0.464917	+	0.885354i	$0.346084\pi$
$108$	804.681	+	298.235i	0.716948	+	0.265719i
$109$	1776.52			1.56110			0.780548	−	0.625096i	$-0.214940\pi$
$109$	1776.52			1.56110			0.780548	+	0.625096i	$0.214940\pi$
$110$		0			0
$111$	911.038	−	214.040i	0.779026	−	0.183025i
$112$	−57.1821	−	99.0423i	−0.0482429	−	0.0835591i
$113$	−807.969	−	1399.44i	−0.672631	−	1.16503i	−0.977155	−	0.212526i	$-0.931831\pi$
$113$	−807.969	−	1399.44i	−0.672631	−	1.16503i	0.304524	−	0.952505i	$-0.401502\pi$
$114$	−80.3847	+	266.606i	−0.0660413	+	0.219034i
$115$		0			0
$116$	173.549			0.138910
$117$	845.645	+	560.937i	0.668204	+	0.443237i
$118$	1083.59			0.845364
$119$	60.5053	−	104.798i	0.0466094	−	0.0807298i
$120$		0			0
$121$	−901.282	−	1561.07i	−0.677147	−	1.17285i
$122$	−357.541	−	619.279i	−0.265330	−	0.459564i
$123$	766.781	+	815.930i	0.562100	+	0.598130i
$124$	39.4021	−	68.2465i	0.0285356	−	0.0494251i
$125$		0			0
$126$	−157.989	−	104.798i	−0.111705	−	0.0740966i
$127$	1206.10			0.842711			0.421356	−	0.906895i	$-0.361554\pi$
$127$	1206.10			0.842711			0.421356	+	0.906895i	$0.361554\pi$
$128$	690.479	−	1195.95i	0.476799	−	0.825841i
$129$	91.8505	−	304.634i	0.0626898	−	0.207919i
$130$		0			0
$131$	513.928	+	890.149i	0.342764	+	0.593684i	0.984945	−	0.172869i	$-0.0553036\pi$
$131$	513.928	+	890.149i	0.342764	+	0.593684i	−0.642181	+	0.766553i	$0.721970\pi$
$132$	−1732.06	+	406.931i	−1.14209	+	0.268324i
$133$	−99.9105	+	173.050i	−0.0651379	+	0.112822i
$134$	−417.763			−0.269322
$135$		0			0
$136$	458.144			0.288864
$137$	−630.454	+	1091.98i	−0.393163	+	0.680978i	−0.992865	−	0.119245i	$-0.961952\pi$
$137$	−630.454	+	1091.98i	−0.393163	+	0.680978i	0.599702	+	0.800223i	$0.295286\pi$
$138$	−493.361	+	115.911i	−0.304331	+	0.0714998i
$139$	−230.916	−	399.958i	−0.140907	−	0.244057i	0.786932	−	0.617040i	$-0.211668\pi$
$139$	−230.916	−	399.958i	−0.140907	−	0.244057i	−0.927838	+	0.372983i	$0.878335\pi$
$140$		0			0
$141$	−92.8164	+	307.837i	−0.0554365	+	0.183862i
$142$	−185.527	+	321.341i	−0.109641	+	0.189904i
$143$	−2103.90			−1.23033
$144$	−37.4431	+	602.302i	−0.0216685	+	0.348554i
$145$		0			0
$146$	−634.999	+	1099.85i	−0.359951	+	0.623454i
$147$	1127.37	+	1199.63i	0.632545	+	0.673089i
$148$	550.832	+	954.068i	0.305933	+	0.529891i
$149$	−729.661	−	1263.81i	−0.401182	−	0.694868i	0.592687	−	0.805433i	$-0.298067\pi$
$149$	−729.661	−	1263.81i	−0.401182	−	0.694868i	−0.993869	+	0.110565i	$0.964734\pi$
$150$		0			0
$151$	−770.659	+	1334.82i	−0.415333	+	0.719378i	−0.995463	−	0.0951456i	$-0.969668\pi$
$151$	−770.659	+	1334.82i	−0.415333	+	0.719378i	0.580130	+	0.814524i	$0.303002\pi$
$152$	−756.518			−0.403696
$153$	−571.732	+	284.341i	−0.302103	+	0.150246i
$154$	393.065			0.205676
$155$		0			0
$156$	−344.845	+	1143.72i	−0.176985	+	0.586994i
$157$	−1607.79	−	2784.77i	−0.817295	−	1.41560i	−0.907668	−	0.419688i	$-0.862139\pi$
$157$	−1607.79	−	2784.77i	−0.817295	−	1.41560i	0.0903734	−	0.995908i	$-0.471194\pi$
$158$	884.459	+	1531.93i	0.445341	+	0.771352i
$159$	−2490.31	+	585.076i	−1.24210	+	0.291821i
$160$		0			0
$161$	−363.671			−0.178021
$162$	389.042	+	921.647i	0.188679	+	0.446984i
$163$	−947.587			−0.455342			−0.227671	−	0.973738i	$-0.573111\pi$
$163$	−947.587			−0.455342			−0.227671	+	0.973738i	$0.573111\pi$
$164$	−659.040	+	1141.49i	−0.313795	+	0.543509i
$165$		0			0
$166$	489.791	+	848.342i	0.229007	+	0.396651i
$167$	342.980	+	594.058i	0.158926	+	0.275267i	0.934481	−	0.356012i	$-0.115864\pi$
$167$	342.980	+	594.058i	0.158926	+	0.275267i	−0.775556	+	0.631279i	$0.782530\pi$
$168$	148.687	−	493.140i	0.0682826	−	0.226468i
$169$	392.213	−	679.333i	0.178522	−	0.309209i
$170$		0			0
$171$	944.083	−	469.524i	0.422198	−	0.209973i
$172$	374.557			0.166045
$173$	−1106.41	+	1916.36i	−0.486237	+	0.842188i	−0.999875	−	0.0158193i	$-0.994964\pi$
$173$	−1106.41	+	1916.36i	−0.486237	+	0.842188i	0.513637	+	0.858007i	$0.328298\pi$
$174$	138.546	+	147.427i	0.0603630	+	0.0642321i
$175$		0			0
$176$	−625.572	−	1083.52i	−0.267922	−	0.464054i
$177$	−2809.84	−	2989.94i	−1.19322	−	1.26970i
$178$	277.753	−	481.082i	0.116958	−	0.202576i
$179$	3023.22			1.26238			0.631190	−	0.775629i	$-0.282567\pi$
$179$	3023.22			1.26238			0.631190	+	0.775629i	$0.282567\pi$
$180$		0			0
$181$	391.445			0.160751			0.0803753	−	0.996765i	$-0.474388\pi$
$181$	391.445			0.160751			0.0803753	+	0.996765i	$0.474388\pi$
$182$	131.953	−	228.550i	0.0537420	−	0.0930839i
$183$	−781.634	+	2592.39i	−0.315738	+	1.04718i
$184$	−688.426	−	1192.39i	−0.275823	−	0.477740i
$185$		0			0
$186$	89.4294	−	21.0106i	0.0352542	−	0.00828266i
$187$	661.928	−	1146.49i	0.258850	−	0.448341i
$188$	−378.496			−0.146833
$189$	120.510	+	707.686i	0.0463799	+	0.272363i
$190$		0			0
$191$	−1742.79	+	3018.61i	−0.660231	+	1.14355i	0.320324	+	0.947308i	$0.396208\pi$
$191$	−1742.79	+	3018.61i	−0.660231	+	1.14355i	−0.980555	+	0.196246i	$0.937125\pi$
$192$	384.233	−	90.2720i	0.144425	−	0.0339314i
$193$	1107.53	+	1918.31i	0.413068	+	0.715455i	0.995223	−	0.0976228i	$-0.0311239\pi$
$193$	1107.53	+	1918.31i	0.413068	+	0.715455i	−0.582156	+	0.813077i	$0.697791\pi$
$194$	51.4793	+	89.1647i	0.0190515	+	0.0329982i
$195$		0			0
$196$	−968.963	+	1678.29i	−0.353121	+	0.611623i
$197$	3975.11			1.43764			0.718820	−	0.695196i	$-0.244682\pi$
$197$	3975.11			1.43764			0.718820	+	0.695196i	$0.244682\pi$
$198$	−1728.40	−	1146.49i	−0.620365	−	0.411504i
$199$	−1555.34			−0.554046			−0.277023	−	0.960863i	$-0.589348\pi$
$199$	−1555.34			−0.554046			−0.277023	+	0.960863i	$0.589348\pi$
$200$		0			0
$201$	1083.29	+	1152.72i	0.380146	+	0.404512i
$202$	746.437	+	1292.87i	0.259996	+	0.450326i
$203$	72.5883	+	125.727i	0.0250970	+	0.0434693i
$204$	−514.762	−	547.756i	−0.176669	−	0.187993i
$205$		0			0
$206$	1498.28			0.506749
$207$	1599.15	+	1060.76i	0.536950	+	0.356172i
$208$	−840.027			−0.280026
$209$	−1093.02	+	1893.17i	−0.361750	+	0.626570i
$210$		0			0
$211$	−873.865	−	1513.58i	−0.285115	−	0.493834i	0.687522	−	0.726164i	$-0.258699\pi$
$211$	−873.865	−	1513.58i	−0.285115	−	0.493834i	−0.972637	+	0.232329i	$0.925365\pi$
$212$	−1505.69	−	2607.93i	−0.487789	−	0.844875i
$213$	1367.75	−	321.341i	0.439986	−	0.103371i
$214$	−706.145	+	1223.08i	−0.225566	+	0.390691i
$215$		0			0
$216$	−2092.21	+	1734.77i	−0.659058	+	0.546462i
$217$	65.9211			0.0206222
$218$	−1218.94	+	2111.27i	−0.378702	+	0.655931i
$219$	4681.39	−	1099.85i	1.44447	−	0.339365i
$220$		0			0
$221$	−444.423	−	769.764i	−0.135272	−	0.234298i
$222$	−370.728	+	1229.57i	−0.112080	+	0.371726i
$223$	−1270.97	+	2201.39i	−0.381662	+	0.661057i	−0.991300	−	0.131622i	$-0.957981\pi$
$223$	−1270.97	+	2201.39i	−0.381662	+	0.661057i	0.609638	+	0.792680i	$0.291315\pi$
$224$	949.939			0.283350
$225$		0			0
$226$	2217.52			0.652687
$227$	−1496.63	+	2592.24i	−0.437598	+	0.757943i	−0.997504	−	0.0706140i	$-0.977504\pi$
$227$	−1496.63	+	2592.24i	−0.437598	+	0.757943i	0.559905	+	0.828557i	$0.310837\pi$
$228$	850.009	+	904.492i	0.246900	+	0.262726i
$229$	2152.65	+	3728.50i	0.621185	+	1.07592i	0.989265	+	0.146130i	$0.0466816\pi$
$229$	2152.65	+	3728.50i	0.621185	+	1.07592i	−0.368081	+	0.929794i	$0.619985\pi$
$230$		0			0
$231$	−1019.25	−	1084.58i	−0.290309	−	0.308917i
$232$	−274.818	+	475.999i	−0.0777702	+	0.134702i
$233$	5581.34			1.56930			0.784648	−	0.619942i	$-0.212844\pi$
$233$	5581.34			1.56930			0.784648	+	0.619942i	$0.212844\pi$
$234$	−1246.87	+	620.108i	−0.348334	+	0.173238i
$235$		0			0
$236$	2415.02	−	4182.94i	0.666121	−	1.15376i
$237$	1933.55	−	6412.87i	0.529948	−	1.75764i
$238$	83.0303	+	143.813i	0.0226137	+	0.0391680i
$239$	−704.814	−	1220.77i	−0.190756	−	0.330399i	0.754745	−	0.656018i	$-0.227761\pi$
$239$	−704.814	−	1220.77i	−0.190756	−	0.330399i	−0.945501	+	0.325619i	$0.894427\pi$
$240$		0			0
$241$	−313.286	+	542.627i	−0.0837366	+	0.145036i	−0.904852	−	0.425726i	$-0.860019\pi$
$241$	−313.286	+	542.627i	−0.0837366	+	0.145036i	0.821116	+	0.570762i	$0.193352\pi$
$242$	2473.63			0.657069
$243$	1534.27	−	3463.37i	0.405034	−	0.914302i
$244$	−3187.42			−0.836286
$245$		0			0
$246$	−1495.80	+	351.424i	−0.387677	+	0.0910811i
$247$	733.862	+	1271.09i	0.189047	+	0.327438i
$248$	124.788	+	216.139i	0.0319518	+	0.0553422i
$249$	1070.75	−	3551.28i	0.272514	−	0.903828i
$250$		0			0
$251$	1705.53			0.428892			0.214446	−	0.976736i	$-0.431205\pi$
$251$	1705.53			0.428892			0.214446	+	0.976736i	$0.431205\pi$
$252$	−756.660	+	376.312i	−0.189147	+	0.0940692i
$253$	−3978.56			−0.988656
$254$	−827.556	+	1433.37i	−0.204431	+	0.354085i
$255$		0			0
$256$	1251.37	+	2167.43i	0.305510	+	0.529158i
$257$	−1798.69	−	3115.42i	−0.436573	−	0.756166i	0.560850	−	0.827918i	$-0.310475\pi$
$257$	−1798.69	−	3115.42i	−0.436573	−	0.756166i	−0.997423	+	0.0717513i	$0.977141\pi$
$258$	299.014	+	318.180i	0.0721542	+	0.0767791i
$259$	−460.780	+	798.094i	−0.110546	+	0.191472i
$260$		0			0
$261$	47.5311	−	764.576i	0.0112724	−	0.181326i
$262$	−1410.51			−0.332601
$263$	2068.75	−	3583.18i	0.485037	−	0.840108i	−0.514815	−	0.857301i	$-0.672140\pi$
$263$	2068.75	−	3583.18i	0.485037	−	0.840108i	0.999852	+	0.0171926i	$0.00547285\pi$
$264$	1626.64	−	5394.95i	0.379215	−	1.25771i
$265$		0			0
$266$	−137.105	−	237.473i	−0.0316032	−	0.0547384i
$267$	−2047.67	+	481.082i	−0.469346	+	0.110269i
$268$	−931.074	+	1612.67i	−0.212218	+	0.367572i
$269$	6090.99			1.38057			0.690287	−	0.723536i	$-0.257484\pi$
$269$	6090.99			1.38057			0.690287	+	0.723536i	$0.257484\pi$
$270$		0			0
$271$	−3196.62			−0.716534			−0.358267	−	0.933619i	$-0.616632\pi$
$271$	−3196.62			−0.716534			−0.358267	+	0.933619i	$0.616632\pi$
$272$	264.289	−	457.762i	0.0589150	−	0.102044i
$273$	−972.798	+	228.550i	−0.215665	+	0.0506684i
$274$	−865.160	−	1498.50i	−0.190753	−	0.330393i
$275$		0			0
$276$	−652.117	+	2162.83i	−0.142220	+	0.471692i
$277$	−1559.68	+	2701.45i	−0.338311	+	0.585972i	−0.984115	−	0.177531i	$-0.943189\pi$
$277$	−1559.68	+	2701.45i	−0.338311	+	0.585972i	0.645804	+	0.763503i	$0.276522\pi$
$278$	633.763			0.136729
$279$	−289.871	−	192.279i	−0.0622012	−	0.0412596i
$280$		0			0
$281$	−2474.17	+	4285.38i	−0.525254	+	0.909767i	0.474313	+	0.880356i	$0.342696\pi$
$281$	−2474.17	+	4285.38i	−0.525254	+	0.909767i	−0.999567	+	0.0294105i	$0.990637\pi$
$282$	−302.158	−	321.525i	−0.0638058	−	0.0678956i
$283$	−2272.47	−	3936.03i	−0.477329	−	0.826758i	0.522333	−	0.852741i	$-0.325062\pi$
$283$	−2272.47	−	3936.03i	−0.477329	−	0.826758i	−0.999662	+	0.0259834i	$0.991728\pi$
$284$	826.971	+	1432.36i	0.172788	+	0.299277i
$285$		0			0
$286$	1443.57	−	2500.34i	0.298462	−	0.516951i
$287$	−1102.60			−0.226774
$288$	−4177.11	−	2770.78i	−0.854648	−	0.566910i
$289$	−4353.70			−0.886160
$290$		0			0
$291$	112.541	−	373.256i	0.0226710	−	0.0751913i
$292$	2830.46	+	4902.50i	0.567261	+	0.982525i
$293$	3430.05	+	5941.03i	0.683911	+	1.18457i	0.973778	+	0.227501i	$0.0730555\pi$
$293$	3430.05	+	5941.03i	0.683911	+	1.18457i	−0.289867	+	0.957067i	$0.593611\pi$
$294$	−2199.22	+	516.686i	−0.436262	+	0.102496i
$295$		0			0
$296$	−3489.01			−0.685117
$297$	1318.38	+	7742.08i	0.257576	+	1.51260i
$298$	2002.60			0.389287
$299$	−1335.62	+	2313.36i	−0.258330	+	0.447441i
$300$		0			0
$301$	156.662	+	271.346i	0.0299994	+	0.0519605i
$302$	−1057.56	−	1831.75i	−0.201509	−	0.349024i
$303$	1631.82	−	5412.12i	0.309391	−	1.02613i
$304$	−436.412	+	755.888i	−0.0823353	+	0.142609i
$305$		0			0
$306$	54.3686	−	874.562i	0.0101570	−	0.163384i
$307$	−6332.25			−1.17720			−0.588600	−	0.808424i	$-0.700321\pi$
$307$	−6332.25			−1.17720			−0.588600	+	0.808424i	$0.700321\pi$
$308$	876.030	−	1517.33i	0.162066	−	0.280707i
$309$	−3885.15	−	4134.18i	−0.715270	−	0.761117i
$310$		0			0
$311$	−3538.84	−	6129.44i	−0.645238	−	1.11758i	−0.984247	−	0.176801i	$-0.943425\pi$
$311$	−3538.84	−	6129.44i	−0.645238	−	1.11758i	0.339009	−	0.940783i	$-0.389908\pi$
$312$	−2590.86	−	2756.93i	−0.470123	−	0.500257i
$313$	690.649	−	1196.24i	0.124721	−	0.216024i	−0.796903	−	0.604108i	$-0.793530\pi$
$313$	690.649	−	1196.24i	0.124721	−	0.216024i	0.921624	+	0.388084i	$0.126863\pi$
$314$	4412.67			0.793062
$315$		0			0
$316$	7884.83			1.40366
$317$	−4087.47	+	7079.70i	−0.724211	+	1.25437i	0.235086	+	0.971974i	$0.424463\pi$
$317$	−4087.47	+	7079.70i	−0.724211	+	1.25437i	−0.959298	+	0.282396i	$0.908871\pi$
$318$	1013.38	−	3361.00i	0.178703	−	0.592691i
$319$	794.115	+	1375.45i	0.139379	+	0.241412i
$320$		0			0
$321$	5205.90	−	1223.08i	0.905187	−	0.212665i
$322$	249.530	−	432.198i	0.0431855	−	0.0747995i
$323$	−923.549			−0.159095
$324$	4424.85	+	552.290i	0.758718	+	0.0947000i
$325$		0			0
$326$	650.178	−	1126.14i	0.110460	−	0.191323i
$327$	8986.37	−	2111.27i	1.51972	−	0.357044i
$328$	−2087.20	−	3615.14i	−0.351361	−	0.608576i
$329$	−158.309	−	274.199i	−0.0265284	−	0.0459486i
$330$		0			0
$331$	4830.64	−	8366.92i	0.802163	−	1.38939i	−0.116026	−	0.993246i	$-0.537016\pi$
$331$	4830.64	−	8366.92i	0.802163	−	1.38939i	0.918189	−	0.396142i	$-0.129651\pi$
$332$	4366.41			0.721801
$333$	4354.04	−	2165.41i	0.716517	−	0.356348i
$334$	−941.329			−0.154213
$335$		0			0
$336$	−406.956	−	433.041i	−0.0660752	−	0.0703104i
$337$	−2478.01	−	4292.04i	−0.400552	−	0.693776i	0.593241	−	0.805025i	$-0.297848\pi$
$337$	−2478.01	−	4292.04i	−0.400552	−	0.693776i	−0.993793	+	0.111249i	$0.964515\pi$
$338$	538.227	+	932.236i	0.0866144	+	0.150021i
$339$	−5750.19	−	6118.76i	−0.921260	−	0.980311i
$340$		0			0
$341$	721.177			0.114528
$342$	−89.7771	+	1444.14i	−0.0141947	+	0.228333i
$343$	−3376.19			−0.531478
$344$	−593.118	+	1027.31i	−0.0929616	+	0.161014i
$345$		0			0
$346$	−1518.31	−	2629.79i	−0.235910	−	0.408608i
$347$	−507.802	−	879.540i	−0.0785598	−	0.136070i	0.824069	−	0.566490i	$-0.191699\pi$
$347$	−507.802	−	879.540i	−0.0785598	−	0.136070i	−0.902629	+	0.430420i	$0.858365\pi$
$348$	877.883	−	206.251i	0.135228	−	0.0317707i
$349$	−6079.29	+	10529.6i	−0.932426	+	1.61501i	−0.153267	+	0.988185i	$0.548979\pi$
$349$	−6079.29	+	10529.6i	−0.932426	+	1.61501i	−0.779160	+	0.626825i	$0.784354\pi$
$350$		0			0
$351$	4944.26	+	1832.47i	0.751867	+	0.278661i
$352$	10392.3			1.57362
$353$	2118.04	−	3668.56i	0.319354	−	0.553138i	−0.660999	−	0.750387i	$-0.729867\pi$
$353$	2118.04	−	3668.56i	0.319354	−	0.553138i	0.980353	+	0.197249i	$0.0632007\pi$
$354$	5481.28	−	1287.78i	0.822957	−	0.193346i
$355$		0			0
$356$	−1238.06	−	2144.39i	−0.184318	−	0.319248i
$357$	181.516	−	602.020i	0.0269099	−	0.0892501i
$358$	−2074.35	+	3592.88i	−0.306237	+	0.530418i
$359$	−517.939			−0.0761443			−0.0380721	−	0.999275i	$-0.512122\pi$
$359$	−517.939			−0.0761443			−0.0380721	+	0.999275i	$0.512122\pi$
$360$		0			0
$361$	−5333.97			−0.777660
$362$	−268.586	+	465.205i	−0.0389961	+	0.0675432i
$363$	−6414.29	−	6825.42i	−0.927445	−	0.986892i
$364$	−588.173	−	1018.75i	−0.0846941	−	0.146694i
$365$		0			0
$366$	−2544.56	−	2707.66i	−0.363405	−	0.386699i
$367$	−2308.15	+	3997.83i	−0.328295	+	0.568624i	−0.982174	−	0.187976i	$-0.939807\pi$
$367$	−2308.15	+	3997.83i	−0.328295	+	0.568624i	0.653879	+	0.756600i	$0.273141\pi$
$368$	−1588.53			−0.225021
$369$	4848.38	+	3216.05i	0.684002	+	0.453715i
$370$		0			0
$371$	1259.54	−	2181.58i	0.176258	−	0.305288i
$372$	118.206	−	392.046i	0.0164750	−	0.0546415i
$373$	2382.71	+	4126.98i	0.330756	+	0.572887i	0.982660	−	0.185415i	$-0.0593629\pi$
$373$	2382.71	+	4126.98i	0.330756	+	0.572887i	−0.651904	+	0.758301i	$0.726030\pi$
$374$	908.351	+	1573.31i	0.125588	+	0.217524i
$375$		0			0
$376$	599.355	−	1038.11i	0.0822058	−	0.142385i
$377$	1066.35			0.145676
$378$	−923.722	−	342.355i	−0.125691	−	0.0465842i
$379$	−2000.33			−0.271108			−0.135554	−	0.990770i	$-0.543281\pi$
$379$	−2000.33			−0.271108			−0.135554	+	0.990770i	$0.543281\pi$
$380$		0			0
$381$	6100.98	−	1433.37i	0.820374	−	0.192740i
$382$	−2391.60	−	4142.38i	−0.320327	−	0.554823i
$383$	495.147	+	857.619i	0.0660596	+	0.114419i	0.897164	−	0.441699i	$-0.145624\pi$
$383$	495.147	+	857.619i	0.0660596	+	0.114419i	−0.831104	+	0.556117i	$0.812291\pi$
$384$	2071.44	−	6870.18i	0.275280	−	0.913001i
$385$		0			0
$386$	−3039.70			−0.400820
$387$	102.583	−	1650.12i	0.0134743	−	0.216746i
$388$	458.930			0.0600481
$389$	−202.205	+	350.230i	−0.0263553	+	0.0456487i	−0.878902	−	0.477002i	$-0.841723\pi$
$389$	−202.205	+	350.230i	−0.0263553	+	0.0456487i	0.852547	+	0.522651i	$0.175057\pi$
$390$		0			0
$391$	−840.423	−	1455.66i	−0.108701	−	0.188275i
$392$	−3068.74	−	5315.22i	−0.395395	−	0.684845i
$393$	3657.54	+	3891.98i	0.469462	+	0.499553i
$394$	−2727.49	+	4724.15i	−0.348753	+	0.604059i
$395$		0			0
$396$	−8277.86	+	4116.85i	−1.05045	+	0.522424i
$397$	−2919.61			−0.369096			−0.184548	−	0.982824i	$-0.559082\pi$
$397$	−2919.61			−0.369096			−0.184548	+	0.982824i	$0.559082\pi$
$398$	1067.18	−	1848.42i	0.134405	−	0.232796i
$399$	−299.731	+	994.097i	−0.0376074	+	0.124730i
$400$		0			0
$401$	5093.10	+	8821.52i	0.634258	+	1.09857i	0.986672	+	0.162723i	$0.0520277\pi$
$401$	5093.10	+	8821.52i	0.634258	+	1.09857i	−0.352414	+	0.935844i	$0.614639\pi$
$402$	−2113.22	+	496.482i	−0.262184	+	0.0615977i
$403$	242.102	−	419.332i	0.0299254	−	0.0518323i
$404$	6654.38			0.819474
$405$		0			0
$406$	−199.223			−0.0243529
$407$	−5040.93	+	8731.15i	−0.613930	+	1.06336i
$408$	2317.49	−	544.472i	0.281208	−	0.0660672i
$409$	−3457.12	−	5987.91i	−0.417955	−	0.723920i	0.577778	−	0.816194i	$-0.303920\pi$
$409$	−3457.12	−	5987.91i	−0.417955	−	0.723920i	−0.995734	+	0.0922740i	$0.970586\pi$
$410$		0			0
$411$	−1891.36	+	6272.94i	−0.226993	+	0.752850i
$412$	3339.24	−	5783.73i	0.399302	−	0.691612i
$413$	4040.41			0.481394
$414$	−2357.88	+	1172.65i	−0.279911	+	0.139209i
$415$		0			0
$416$	3488.75	−	6042.68i	0.411177	−	0.712180i
$417$	−1643.39	−	1748.73i	−0.192991	−	0.205361i
$418$	−1499.93	−	2597.96i	−0.175512	−	0.303996i
$419$	−2560.16	−	4434.32i	−0.298501	−	0.517019i	0.677292	−	0.735714i	$-0.263153\pi$
$419$	−2560.16	−	4434.32i	−0.298501	−	0.517019i	−0.975793	+	0.218695i	$0.929820\pi$
$420$		0			0
$421$	−933.246	+	1616.43i	−0.108037	+	0.187126i	−0.914975	−	0.403511i	$-0.867790\pi$
$421$	−933.246	+	1616.43i	−0.108037	+	0.187126i	0.806938	+	0.590636i	$0.201123\pi$
$422$	2398.38			0.276662
$423$	−103.661	+	1667.48i	−0.0119153	+	0.191668i
$424$	9537.16			1.09237
$425$		0			0
$426$	−556.580	+	1845.97i	−0.0633014	+	0.209947i
$427$	−1333.17	−	2309.11i	−0.151092	−	0.261700i
$428$	3147.59	+	5451.79i	0.355478	+	0.615706i
$429$	−10642.4	+	2500.34i	−1.19772	+	0.281393i
$430$		0			0
$431$	−4090.64			−0.457168			−0.228584	−	0.973524i	$-0.573410\pi$
$431$	−4090.64			−0.457168			−0.228584	+	0.973524i	$0.573410\pi$
$432$	526.391	+	3091.19i	0.0586250	+	0.344271i
$433$	−633.052			−0.0702599			−0.0351299	−	0.999383i	$-0.511185\pi$
$433$	−633.052			−0.0702599			−0.0351299	+	0.999383i	$0.511185\pi$
$434$	−45.2311	+	78.3426i	−0.00500268	+	0.00866490i
$435$		0			0
$436$	5433.34	+	9410.81i	0.596811	+	1.03371i
$437$	1387.76	+	2403.68i	0.151912	+	0.263120i
$438$	−1905.00	+	6318.16i	−0.207818	+	0.689254i
$439$	5653.26	−	9791.74i	0.614614	−	1.06454i	−0.375838	−	0.926685i	$-0.622645\pi$
$439$	5653.26	−	9791.74i	0.614614	−	1.06454i	0.990452	−	0.137857i	$-0.0440214\pi$
$440$		0			0
$441$	7128.40	+	4728.45i	0.769723	+	0.510576i
$442$	1219.75			0.131261
$443$	−4140.65	+	7171.82i	−0.444082	+	0.769172i	−0.997988	−	0.0634071i	$-0.979803\pi$
$443$	−4140.65	+	7171.82i	−0.444082	+	0.769172i	0.553906	+	0.832579i	$0.313137\pi$
$444$	3920.18	+	4171.45i	0.419017	+	0.445875i
$445$		0			0
$446$	−1744.13	−	3020.92i	−0.185173	−	0.320728i
$447$	−5192.88	−	5525.73i	−0.549474	−	0.584694i
$448$	−194.335	+	336.599i	−0.0204944	+	0.0354973i
$449$	6888.40			0.724017			0.362008	−	0.932175i	$-0.382091\pi$
$449$	6888.40			0.724017			0.362008	+	0.932175i	$0.382091\pi$
$450$		0			0
$451$	−12062.4			−1.25941
$452$	4942.22	−	8560.17i	0.514297	−	0.890789i
$453$	−2311.98	+	7667.96i	−0.239793	+	0.795302i
$454$	−2053.80	−	3557.28i	−0.212312	−	0.367735i
$455$		0			0
$456$	−3826.79	+	899.070i	−0.392995	+	0.0923307i
$457$	2141.80	−	3709.71i	0.219233	−	0.379722i	−0.735341	−	0.677697i	$-0.762978\pi$
$457$	2141.80	−	3709.71i	0.219233	−	0.379722i	0.954574	+	0.297975i	$0.0963113\pi$
$458$	−5908.09			−0.602766
$459$	−2554.14	+	2117.78i	−0.259732	+	0.215359i
$460$		0			0
$461$	−6889.16	+	11932.4i	−0.696009	+	1.20552i	0.273831	+	0.961778i	$0.411709\pi$
$461$	−6889.16	+	11932.4i	−0.696009	+	1.20552i	−0.969840	+	0.243744i	$0.921624\pi$
$462$	1988.29	−	467.131i	0.200224	−	0.0470409i
$463$	2867.27	+	4966.25i	0.287804	+	0.498491i	0.973285	−	0.229599i	$-0.0737415\pi$
$463$	2867.27	+	4966.25i	0.287804	+	0.498491i	−0.685481	+	0.728090i	$0.740408\pi$
$464$	317.068	+	549.178i	0.0317231	+	0.0549460i
$465$		0			0
$466$	−3829.59	+	6633.04i	−0.380691	+	0.659377i
$467$	8950.97			0.886941			0.443470	−	0.896289i	$-0.353747\pi$
$467$	8950.97			0.886941			0.443470	+	0.896289i	$0.353747\pi$
$468$	−385.138	+	6195.25i	−0.0380406	+	0.611914i
$469$	−1557.72			−0.153366
$470$		0			0
$471$	−11442.4	−	12175.8i	−1.11940	−	1.19115i
$472$	7648.47	+	13247.5i	0.745867	+	1.29188i
$473$	1713.88	+	2968.52i	0.166605	+	0.288568i
$474$	6294.56	+	6698.02i	0.609955	+	0.649051i
$475$		0			0
$476$	740.203			0.0712755
$477$	−11901.7	+	5919.12i	−1.14244	+	0.568172i
$478$	1934.41			0.185100
$479$	−4840.51	+	8384.00i	−0.461729	+	0.799739i	−0.999047	−	0.0436411i	$-0.986104\pi$
$479$	−4840.51	+	8384.00i	−0.461729	+	0.799739i	0.537318	+	0.843380i	$0.319438\pi$
$480$		0			0
$481$	3384.52	+	5862.16i	0.320833	+	0.555699i
$482$	−429.917	−	744.637i	−0.0406269	−	0.0703678i
$483$	−1839.60	+	432.198i	−0.173302	+	0.0407157i
$484$	5513.00	−	9548.80i	0.517750	−	0.896769i
$485$		0			0
$486$	3063.25	+	4199.73i	0.285909	+	0.391983i
$487$	−8704.66			−0.809950			−0.404975	−	0.914328i	$-0.632720\pi$
$487$	−8704.66			−0.809950			−0.404975	+	0.914328i	$0.632720\pi$
$488$	5047.35	−	8742.26i	0.468202	−	0.810950i
$489$	−4793.30	+	1126.14i	−0.443273	+	0.104143i
$490$		0			0
$491$	7797.85	+	13506.3i	0.716725	+	1.24140i	0.962290	+	0.272024i	$0.0876930\pi$
$491$	7797.85	+	13506.3i	0.716725	+	1.24140i	−0.245565	+	0.969380i	$0.578974\pi$
$492$	−1977.12	+	6557.36i	−0.181170	+	0.600871i
$493$	−335.495	+	581.094i	−0.0306489	+	0.0530855i
$494$	−2014.13			−0.183441
$495$		0			0
$496$	287.945			0.0260668
$497$	−691.776	+	1198.19i	−0.0624354	+	0.108141i
$498$	3485.76	+	3709.19i	0.313656	+	0.333761i
$499$	4848.14	+	8397.22i	0.434935	+	0.753329i	0.997290	−	0.0735663i	$-0.0234381\pi$
$499$	4848.14	+	8397.22i	0.434935	+	0.753329i	−0.562355	+	0.826896i	$0.690105\pi$
$500$		0			0
$501$	2440.93	+	2597.39i	0.217670	+	0.231622i
$502$	−1170.23	+	2026.90i	−0.104044	+	0.180209i
$503$	−20949.7			−1.85706			−0.928532	−	0.371253i	$-0.878928\pi$
$503$	−20949.7			−1.85706			−0.928532	+	0.371253i	$0.878928\pi$
$504$	166.061	−	2671.22i	0.0146764	−	0.236082i
$505$		0			0
$506$	2729.85	−	4728.24i	0.239835	−	0.415407i
$507$	1176.64	−	3902.47i	0.103070	−	0.341844i
$508$	3688.77	+	6389.14i	0.322171	+	0.558016i
$509$	−5637.37	−	9764.22i	−0.490908	−	0.850278i	0.509037	−	0.860745i	$-0.330002\pi$
$509$	−5637.37	−	9764.22i	−0.490908	−	0.850278i	−0.999945	+	0.0104668i	$0.996668\pi$
$510$		0			0
$511$	−2367.73	+	4101.03i	−0.204975	+	0.355027i
$512$	7613.21			0.657148
$513$	4217.57	−	3497.03i	0.362983	−	0.300970i
$514$	4936.62			0.423628
$515$		0			0
$516$	1894.67	−	445.135i	0.161644	−	0.0379767i
$517$	−1731.90	−	2999.74i	−0.147329	−	0.255181i
$518$	−632.320	−	1095.21i	−0.0536342	−	0.0928972i
$519$	−3319.24	+	11008.7i	−0.280729	+	0.931074i
$520$		0			0
$521$	8675.49			0.729520			0.364760	−	0.931102i	$-0.381151\pi$
$521$	8675.49			0.729520			0.364760	+	0.931102i	$0.381151\pi$
$522$	876.032	+	581.094i	0.0734538	+	0.0487237i
$523$	4226.14			0.353339			0.176670	−	0.984270i	$-0.443468\pi$
$523$	4226.14			0.353339			0.176670	+	0.984270i	$0.443468\pi$
$524$	−3143.62	+	5444.90i	−0.262079	+	0.453934i
$525$		0			0
$526$	2838.91	+	4917.14i	0.235328	+	0.407599i
$527$	152.340	+	263.860i	0.0125921	+	0.0218101i
$528$	−4452.10	−	4737.46i	−0.366956	−	0.390477i
$529$	3557.79	−	6162.27i	0.292413	−	0.506474i
$530$		0			0
$531$	−17766.7	−	11785.1i	−1.45199	−	0.963143i
$532$	−1222.27			−0.0996095
$533$	−4049.39	+	7013.75i	−0.329078	+	0.569980i
$534$	833.258	−	2763.60i	0.0675255	−	0.223957i
$535$		0			0
$536$	−2948.75	−	5107.38i	−0.237624	−	0.411577i
$537$	15292.7	−	3592.88i	1.22892	−	0.288723i
$538$	−4179.28	+	7238.72i	−0.334910	+	0.580081i
$539$	−17734.9			−1.41725
$540$		0			0
$541$	13357.8			1.06154			0.530771	−	0.847515i	$-0.321902\pi$
$541$	13357.8			1.06154			0.530771	+	0.847515i	$0.321902\pi$
$542$	2193.33	−	3798.96i	0.173822	−	0.301069i
$543$	1980.09	−	465.205i	0.156490	−	0.0367658i
$544$	2195.26	+	3802.29i	0.173016	+	0.299673i
$545$		0			0
$546$	395.860	−	1312.92i	0.0310280	−	0.102908i
$547$	10835.6	−	18767.7i	0.846974	−	1.46700i	−0.0369219	−	0.999318i	$-0.511755\pi$
$547$	10835.6	−	18767.7i	0.846974	−	1.46700i	0.883896	−	0.467684i	$-0.154911\pi$
$548$	−7712.78			−0.601229
$549$	−872.964	+	14042.3i	−0.0678637	+	1.09164i
$550$		0			0
$551$	553.991	−	959.541i	0.0428327	−	0.0741884i
$552$	−4899.42	−	5213.46i	−0.377778	−	0.401992i
$553$	3297.90	+	5712.12i	0.253600	+	0.439248i
$554$	−2140.32	−	3707.15i	−0.164140	−	0.284299i
$555$		0			0
$556$	1412.48	−	2446.48i	0.107738	−	0.186608i
$557$	−7477.63			−0.568828			−0.284414	−	0.958702i	$-0.591799\pi$
$557$	−7477.63			−0.568828			−0.284414	+	0.958702i	$0.591799\pi$
$558$	427.402	−	212.561i	0.0324254	−	0.0161262i
$559$	2301.42			0.174132
$560$		0			0
$561$	1985.78	−	6586.10i	0.149447	−	0.495660i
$562$	−3395.25	−	5880.75i	−0.254840	−	0.441396i
$563$	−11652.3	−	20182.4i	−0.872269	−	1.51082i	−0.859643	−	0.510895i	$-0.829314\pi$
$563$	−11652.3	−	20182.4i	−0.872269	−	1.51082i	−0.0126262	−	0.999920i	$-0.504019\pi$
$564$	−1914.59	+	449.816i	−0.142941	+	0.0335827i
$565$		0			0
$566$	6236.92			0.463176
$567$	1450.63	+	3436.56i	0.107444	+	0.254536i
$568$	−5238.10			−0.386947
$569$	7324.54	−	12686.5i	0.539650	−	0.934701i	−0.459273	−	0.888295i	$-0.651890\pi$
$569$	7324.54	−	12686.5i	0.539650	−	0.934701i	0.998923	−	0.0464057i	$-0.0147767\pi$
$570$		0			0
$571$	−11582.0	−	20060.6i	−0.848846	−	1.47025i	−0.882239	−	0.470803i	$-0.843964\pi$
$571$	−11582.0	−	20060.6i	−0.848846	−	1.47025i	0.0333922	−	0.999442i	$-0.489369\pi$
$572$	−6434.61	−	11145.1i	−0.470358	−	0.814683i
$573$	−5228.38	+	17340.6i	−0.381185	+	1.26425i
$574$	756.536	−	1310.36i	0.0550125	−	0.0952845i
$575$		0			0
$576$	1836.33	−	913.268i	0.132836	−	0.0660640i
$577$	−7865.97			−0.567529			−0.283765	−	0.958894i	$-0.591583\pi$
$577$	−7865.97			−0.567529			−0.283765	+	0.958894i	$0.591583\pi$
$578$	2987.25	−	5174.07i	0.214971	−	0.372341i
$579$	7882.15	+	8387.38i	0.565753	+	0.602016i
$580$		0			0
$581$	1826.29	+	3163.23i	0.130408	+	0.225874i
$582$	366.370	+	389.853i	0.0260937	+	0.0277662i
$583$	13779.3	−	23866.5i	0.978869	−	1.69545i
$584$	−17928.4			−1.27034
$585$		0			0
$586$	−9413.99			−0.663632
$587$	−478.091	+	828.078i	−0.0336166	+	0.0582256i	−0.882344	−	0.470605i	$-0.844036\pi$
$587$	−478.091	+	828.078i	−0.0336166	+	0.0582256i	0.848728	+	0.528830i	$0.177369\pi$
$588$	−2906.89	+	9641.06i	−0.203874	+	0.676174i
$589$	−251.554	−	435.704i	−0.0175978	−	0.0304803i
$590$		0			0
$591$	20107.8	−	4724.15i	1.39953	−	0.328808i
$592$	−2012.70	+	3486.10i	−0.139732	+	0.242023i
$593$	16966.0			1.17489			0.587444	−	0.809265i	$-0.300134\pi$
$593$	16966.0			1.17489			0.587444	+	0.809265i	$0.300134\pi$
$594$	−10105.5	−	3745.36i	−0.698038	−	0.258710i
$595$		0			0
$596$	4463.22	−	7730.53i	0.306746	−	0.531300i
$597$	−7867.57	+	1848.42i	−0.539361	+	0.126718i
$598$	−1832.84	−	3174.58i	−0.125335	−	0.217087i
$599$	3095.70	+	5361.92i	0.211164	+	0.365746i	0.952079	−	0.305852i	$-0.0989414\pi$
$599$	3095.70	+	5361.92i	0.211164	+	0.365746i	−0.740915	+	0.671598i	$0.765608\pi$
$600$		0			0
$601$	1359.27	−	2354.33i	0.0922559	−	0.159792i	−0.816204	−	0.577764i	$-0.803926\pi$
$601$	1359.27	−	2354.33i	0.0922559	−	0.159792i	0.908460	+	0.417972i	$0.137259\pi$
$602$	−429.968			−0.0291099
$603$	6849.66	+	4543.55i	0.462587	+	0.306845i
$604$	−9428.00			−0.635132
$605$		0			0
$606$	5312.28	+	5652.78i	0.356100	+	0.378925i
$607$	8412.49	+	14570.9i	0.562524	+	0.974321i	0.997275	+	0.0737701i	$0.0235031\pi$
$607$	8412.49	+	14570.9i	0.562524	+	0.974321i	−0.434751	+	0.900551i	$0.643164\pi$
$608$	−3624.95	−	6278.60i	−0.241795	−	0.418801i
$609$	516.599	+	549.712i	0.0343738	+	0.0365771i
$610$		0			0
$611$	−2325.62			−0.153985
$612$	−3254.85	−	2159.02i	−0.214983	−	0.142604i
$613$	20175.1			1.32930			0.664652	−	0.747153i	$-0.268580\pi$
$613$	20175.1			1.32930			0.664652	+	0.747153i	$0.268580\pi$
$614$	4344.81	−	7525.44i	0.285574	−	0.494629i
$615$		0			0
$616$	2774.42	+	4805.44i	0.181468	+	0.314313i
$617$	5655.31	+	9795.29i	0.369002	+	0.639130i	0.989410	−	0.145149i	$-0.0463662\pi$
$617$	5655.31	+	9795.29i	0.369002	+	0.639130i	−0.620408	+	0.784280i	$0.713033\pi$
$618$	7578.94	−	1780.60i	0.493317	−	0.115900i
$619$	8529.94	−	14774.3i	0.553873	−	0.959336i	−0.444117	−	0.895969i	$-0.646483\pi$
$619$	8529.94	−	14774.3i	0.553873	−	0.959336i	0.997990	−	0.0633676i	$-0.0201841\pi$
$620$		0			0
$621$	9349.81	+	3465.27i	0.604179	+	0.223924i
$622$	9712.56			0.626106
$623$	1035.66	−	1793.82i	0.0666017	−	0.115357i
$624$	−4249.21	+	998.314i	−0.272604	+	0.0640457i
$625$		0			0
$626$	947.764	+	1641.58i	0.0605116	+	0.104809i
$627$	−3279.06	+	10875.4i	−0.208857	+	0.692699i
$628$	9834.58	−	17034.0i	0.624908	−	1.08237i
$629$	−4259.34			−0.270002
$630$		0			0
$631$	−13186.3			−0.831916			−0.415958	−	0.909384i	$-0.636554\pi$
$631$	−13186.3			−0.831916			−0.415958	+	0.909384i	$0.636554\pi$
$632$	−12485.8	+	21626.0i	−0.785850	+	1.36113i
$633$	−6219.16	−	6617.79i	−0.390505	−	0.415535i
$634$	−5609.15	−	9715.34i	−0.351369	−	0.608589i
$635$		0			0
$636$	−10715.8	−	11402.6i	−0.668094	−	0.710917i
$637$	−5953.68	+	10312.1i	−0.370319	+	0.641412i
$638$	−2179.50			−0.135246
$639$	6536.79	−	3250.96i	0.404681	−	0.201261i
$640$		0			0
$641$	−8180.99	+	14169.9i	−0.504102	+	0.873131i	0.495886	+	0.868387i	$0.334843\pi$
$641$	−8180.99	+	14169.9i	−0.504102	+	0.873131i	−0.999989	+	0.00474343i	$0.998490\pi$
$642$	−2118.43	+	7026.05i	−0.130230	+	0.431926i
$643$	−14022.5	−	24287.6i	−0.860019	−	1.48960i	−0.871910	−	0.489667i	$-0.837118\pi$
$643$	−14022.5	−	24287.6i	−0.860019	−	1.48960i	0.0118907	−	0.999929i	$-0.496215\pi$
$644$	−1112.26	−	1926.49i	−0.0680577	−	0.117879i
$645$		0			0
$646$	633.685	−	1097.57i	0.0385944	−	0.0668475i
$647$	−21247.7			−1.29109			−0.645543	−	0.763724i	$-0.723369\pi$
$647$	−21247.7			−1.29109			−0.645543	+	0.763724i	$0.723369\pi$
$648$	−8521.61	+	11261.6i	−0.516606	+	0.682713i
$649$	44202.1			2.67347
$650$		0			0
$651$	333.457	−	78.3426i	0.0200756	−	0.00471657i
$652$	−2898.12	−	5019.69i	−0.174079	−	0.301513i
$653$	629.928	+	1091.07i	0.0377504	+	0.0653856i	0.884283	−	0.466951i	$-0.154647\pi$
$653$	629.928	+	1091.07i	0.0377504	+	0.0653856i	−0.846533	+	0.532336i	$0.821314\pi$
$654$	−3656.82	+	12128.3i	−0.218644	+	0.725159i
$655$		0			0
$656$	−4816.17			−0.286646
$657$	22373.3	−	11127.0i	1.32857	−	0.660740i
$658$	434.489			0.0257419
$659$	6023.35	−	10432.7i	0.356049	−	0.616695i	−0.631248	−	0.775581i	$-0.717457\pi$
$659$	6023.35	−	10432.7i	0.356049	−	0.616695i	0.987297	+	0.158886i	$0.0507902\pi$
$660$		0			0
$661$	−6554.04	−	11351.9i	−0.385662	−	0.667986i	0.606199	−	0.795313i	$-0.292693\pi$
$661$	−6554.04	−	11351.9i	−0.385662	−	0.667986i	−0.991861	+	0.127327i	$0.959360\pi$
$662$	6629.00	+	11481.8i	0.389189	+	0.674096i
$663$	−3162.89	−	3365.62i	−0.185274	−	0.197149i
$664$	−6914.30	+	11975.9i	−0.404107	+	0.699933i
$665$		0			0
$666$	−414.046	+	6660.25i	−0.0240900	+	0.387507i
$667$	2016.51			0.117061
$668$	−2097.95	+	3633.76i	−0.121515	+	0.210471i
$669$	−3812.91	+	12646.0i	−0.220352	+	0.730826i
$670$		0			0
$671$	−14584.8	−	25261.7i	−0.839108	−	1.45338i
$672$	4805.19	−	1128.94i	0.275840	−	0.0648061i
$673$	1371.82	−	2376.07i	0.0785734	−	0.136093i	−0.824061	−	0.566501i	$-0.808297\pi$
$673$	1371.82	−	2376.07i	0.0785734	−	0.136093i	0.902635	+	0.430408i	$0.141630\pi$
$674$	6801.06			0.388675
$675$		0			0
$676$	4798.21			0.272998
$677$	12502.0	−	21654.1i	0.709735	−	1.22930i	−0.255220	−	0.966883i	$-0.582148\pi$
$677$	12502.0	−	21654.1i	0.709735	−	1.22930i	0.964955	−	0.262415i	$-0.0845189\pi$
$678$	11217.2	−	2635.37i	0.635387	−	0.149278i
$679$	191.952	+	332.470i	0.0108489	+	0.0187909i
$680$		0			0
$681$	−4489.89	+	14891.3i	−0.252648	+	0.837937i
$682$	−494.829	+	857.068i	−0.0277829	+	0.0481215i
$683$	4846.23			0.271502			0.135751	−	0.990743i	$-0.456655\pi$
$683$	4846.23			0.271502			0.135751	+	0.990743i	$0.456655\pi$
$684$	5374.63	+	3565.13i	0.300445	+	0.199292i
$685$		0			0
$686$	2316.54	−	4012.36i	0.128930	−	0.223313i
$687$	15320.1	+	16302.1i	0.850798	+	0.905331i
$688$	684.303	+	1185.25i	0.0379198	+	0.0656790i
$689$	−9251.54	−	16024.1i	−0.511546	−	0.886024i
$690$		0			0
$691$	−1742.29	+	3017.73i	−0.0959187	+	0.166136i	−0.909992	−	0.414627i	$-0.863912\pi$
$691$	−1742.29	+	3017.73i	−0.0959187	+	0.166136i	0.814073	+	0.580763i	$0.197246\pi$
$692$	−13535.5			−0.743560
$693$	−6444.72	−	4274.94i	−0.353268	−	0.234331i
$694$	1393.70			0.0762305
$695$		0			0
$696$	−824.454	+	2734.40i	−0.0449006	+	0.148919i
$697$	−2548.04	−	4413.33i	−0.138470	−	0.239837i
$698$	−8342.49	−	14449.6i	−0.452390	−	0.783562i
$699$	28232.8	−	6633.04i	1.52770	−	0.358919i
$700$		0			0
$701$	15701.4			0.845981			0.422991	−	0.906134i	$-0.360980\pi$
$701$	15701.4			0.845981			0.422991	+	0.906134i	$0.360980\pi$
$702$	−5570.22	+	4618.58i	−0.299479	+	0.248315i
$703$	7033.32			0.377335
$704$	−2126.03	+	3682.39i	−0.113818	+	0.197138i
$705$		0			0
$706$	2906.55	+	5034.29i	0.154943	+	0.268368i
$707$	2783.25	+	4820.73i	0.148055	+	0.256439i
$708$	7245.07	−	24029.2i	0.384585	−	1.27552i
$709$	−7821.72	+	13547.6i	−0.414317	+	0.717618i	−0.995356	−	0.0962572i	$-0.969313\pi$
$709$	−7821.72	+	13547.6i	−0.414317	+	0.717618i	0.581039	+	0.813875i	$0.302646\pi$
$710$		0			0
$711$	2159.48	−	34736.9i	0.113905	−	1.83226i
$712$	7841.98			0.412768
$713$	457.824	−	792.975i	0.0240472	−	0.0416510i
$714$	590.914	+	628.790i	0.0309725	+	0.0329578i
$715$		0			0
$716$	9246.27	+	16015.0i	0.482611	+	0.835907i
$717$	−5016.05	−	5337.57i	−0.261266	−	0.278013i
$718$	355.379	−	615.535i	0.0184716	−	0.0319938i
$719$	−6964.13			−0.361222			−0.180611	−	0.983555i	$-0.557807\pi$
$719$	−6964.13			−0.361222			−0.180611	+	0.983555i	$0.557807\pi$
$720$		0			0
$721$	5586.66			0.288569
$722$	3659.86	−	6339.06i	0.188651	−	0.326752i
$723$	−939.858	+	3117.16i	−0.0483454	+	0.160343i
$724$	1197.20	+	2073.62i	0.0614554	+	0.106444i
$725$		0			0
$726$	12512.6	−	2939.73i	0.639652	−	0.150281i
$727$	−7103.61	+	12303.8i	−0.362391	+	0.627680i	−0.988354	−	0.152173i	$-0.951373\pi$
$727$	−7103.61	+	12303.8i	−0.362391	+	0.627680i	0.625963	+	0.779853i	$0.284706\pi$
$728$	3725.53			0.189667
$729$	3645.00	−	19342.6i	0.185185	−	0.982704i
$730$		0			0
$731$	−724.072	+	1254.13i	−0.0366358	+	0.0634551i
$732$	−16123.3	+	3788.03i	−0.814120	+	0.191270i
$733$	13265.3	+	22976.1i	0.668437	+	1.15777i	0.978341	+	0.206998i	$0.0663695\pi$
$733$	13265.3	+	22976.1i	0.668437	+	1.15777i	−0.309905	+	0.950768i	$0.600297\pi$
$734$	−3167.43	−	5486.15i	−0.159280	−	0.275882i
$735$		0			0
$736$	6597.36	−	11427.0i	0.330410	−	0.572288i
$737$	−17041.4			−0.851735
$738$	−7148.72	+	3555.30i	−0.356569	+	0.177334i
$739$	−5683.47			−0.282909			−0.141455	−	0.989945i	$-0.545178\pi$
$739$	−5683.47			−0.282909			−0.141455	+	0.989945i	$0.545178\pi$
$740$		0			0
$741$	5222.78	+	5557.55i	0.258925	+	0.275522i
$742$	1728.44	+	2993.74i	0.0855161	+	0.148118i
$743$	−7784.28	−	13482.8i	−0.384358	−	0.665727i	0.607322	−	0.794456i	$-0.292244\pi$
$743$	−7784.28	−	13482.8i	−0.384358	−	0.665727i	−0.991680	+	0.128729i	$0.958910\pi$
$744$	888.097	+	945.022i	0.0437624	+	0.0465674i
$745$		0			0
$746$	−6539.50			−0.320949
$747$	1195.86	−	19236.4i	0.0585734	−	0.942199i
$748$	8097.82			0.395836
$749$	−2633.01	+	4560.51i	−0.128449	+	0.222480i
$750$		0			0
$751$	4130.82	+	7154.79i	0.200713	+	0.347646i	0.948758	−	0.316002i	$-0.102341\pi$
$751$	4130.82	+	7154.79i	0.200713	+	0.347646i	−0.748045	+	0.663648i	$0.769007\pi$
$752$	−691.499	−	1197.71i	−0.0335324	−	0.0580798i
$753$	8627.27	−	2026.90i	0.417523	−	0.0980933i
$754$	−731.666	+	1267.28i	−0.0353391	+	0.0612092i
$755$		0			0
$756$	−3380.29	+	2802.78i	−0.162619	+	0.134836i
$757$	13381.5			0.642481			0.321240	−	0.946998i	$-0.395900\pi$
$757$	13381.5			0.642481			0.321240	+	0.946998i	$0.395900\pi$
$758$	1372.51	−	2377.25i	0.0657674	−	0.113913i
$759$	−20125.2	+	4728.24i	−0.962451	+	0.226119i
$760$		0			0
$761$	−2724.92	−	4719.70i	−0.129801	−	0.224821i	0.793799	−	0.608181i	$-0.208100\pi$
$761$	−2724.92	−	4719.70i	−0.129801	−	0.224821i	−0.923599	+	0.383359i	$0.874767\pi$
$762$	−2482.67	+	8234.08i	−0.118028	+	0.391456i
$763$	−4545.08	+	7872.31i	−0.215652	+	0.373521i
$764$	−21320.8			−1.00963
$765$		0			0
$766$	−1358.96			−0.0641009
$767$	14838.8	−	25701.6i	0.698564	−	1.20995i
$768$	8905.79	+	9476.63i	0.418438	+	0.445258i
$769$	9681.98	+	16769.7i	0.454020	+	0.786385i	0.998631	−	0.0523033i	$-0.0166563\pi$
$769$	9681.98	+	16769.7i	0.454020	+	0.786385i	−0.544612	+	0.838688i	$0.683323\pi$
$770$		0			0
$771$	−12801.0	−	13621.5i	−0.597946	−	0.636273i
$772$	−6774.62	+	11734.0i	−0.315834	+	0.547041i
$773$	1865.54			0.0868033			0.0434017	−	0.999058i	$-0.486180\pi$
$773$	1865.54			0.0868033			0.0434017	+	0.999058i	$0.486180\pi$
$774$	1890.67	+	1254.13i	0.0878020	+	0.0582413i
$775$		0			0
$776$	−726.725	+	1258.72i	−0.0336184	+	0.0582288i
$777$	−1382.34	+	4584.70i	−0.0638239	+	0.211680i
$778$	−277.483	−	480.614i	−0.0127869	−	0.0221476i
$779$	4207.49	+	7287.58i	0.193516	+	0.335179i
$780$		0			0
$781$	−7568.02	+	13108.2i	−0.346741	+	0.600574i
$782$	2306.59			0.105478
$783$	−668.212	−	3924.03i	−0.0304980	−	0.179098i
$784$	−7081.05			−0.322570
$785$		0			0
$786$	−7134.94	+	1676.29i	−0.323785	+	0.0760703i
$787$	−9603.65	−	16634.0i	−0.434985	−	0.753416i	0.562310	−	0.826927i	$-0.309913\pi$
$787$	−9603.65	−	16634.0i	−0.434985	−	0.753416i	−0.997294	+	0.0735110i	$0.976580\pi$
$788$	12157.6	+	21057.5i	0.549614	+	0.951959i
$789$	6206.25	−	20583.8i	0.280036	−	0.928775i
$790$		0			0
$791$	8268.50			0.371674
$792$	1816.70	−	29223.1i	0.0815072	−	1.31111i
$793$	−19584.7			−0.877017
$794$	2003.26	−	3469.76i	0.0895380	−	0.155084i
$795$		0			0
$796$	−4756.89	−	8239.18i	−0.211813	−	0.366872i
$797$	93.0372	+	161.145i	0.00413494	+	0.00716193i	0.868085	−	0.496415i	$-0.165350\pi$
$797$	93.0372	+	161.145i	0.00413494	+	0.00716193i	−0.863951	+	0.503577i	$0.832017\pi$
$798$	−975.757	−	1038.30i	−0.0432850	−	0.0460594i
$799$	731.686	−	1267.32i	0.0323970	−	0.0561132i
$800$		0			0
$801$	−9786.25	+	4867.03i	−0.431686	+	0.214692i
$802$	−13978.3			−0.615452
$803$	−25902.9	+	44865.2i	−1.13835	+	1.97168i
$804$	−2793.22	+	9264.07i	−0.122524	+	0.406366i
$805$		0			0
$806$	332.232	+	575.442i	0.0145191	+	0.0251477i
$807$	30810.8	−	7238.72i	1.34398	−	0.315756i
$808$	−10537.3	+	18251.2i	−0.458790	+	0.794647i
$809$	5903.09			0.256541			0.128270	−	0.991739i	$-0.459057\pi$
$809$	5903.09			0.256541			0.128270	+	0.991739i	$0.459057\pi$
$810$		0			0
$811$	23111.0			1.00066			0.500331	−	0.865834i	$-0.333212\pi$
$811$	23111.0			1.00066			0.500331	+	0.865834i	$0.333212\pi$
$812$	−444.011	+	769.050i	−0.0191893	+	0.0332369i
$813$	−16169.8	+	3798.96i	−0.697542	+	0.163881i
$814$	−6917.58	−	11981.6i	−0.297863	−	0.515915i
$815$		0			0
$816$	792.867	−	2629.64i	0.0340146	−	0.112814i
$817$	1195.64	−	2070.90i	0.0511995	−	0.0886802i
$818$	9488.29			0.405563
$819$	−4649.21	+	2312.21i	−0.198360	+	0.0986508i
$820$		0			0
$821$	4822.14	−	8352.20i	0.204987	−	0.355047i	−0.745142	−	0.666906i	$-0.767618\pi$
$821$	4822.14	−	8352.20i	0.204987	−	0.355047i	0.950128	+	0.311859i	$0.100952\pi$
$822$	−6157.21	−	6551.87i	−0.261262	−	0.278008i
$823$	−16786.7	−	29075.5i	−0.710994	−	1.23148i	−0.964484	−	0.264140i	$-0.914912\pi$
$823$	−16786.7	−	29075.5i	−0.710994	−	1.23148i	0.253490	−	0.967338i	$-0.418422\pi$
$824$	10575.5	+	18317.3i	0.447106	+	0.774410i
$825$		0			0
$826$	−2772.29	+	4801.75i	−0.116780	+	0.202269i
$827$	25916.1			1.08971			0.544855	−	0.838530i	$-0.316585\pi$
$827$	25916.1			1.08971			0.544855	+	0.838530i	$0.316585\pi$
$828$	−728.313	+	11715.5i	−0.0305684	+	0.491717i
$829$	−28650.6			−1.20033			−0.600166	−	0.799876i	$-0.704899\pi$
$829$	−28650.6			−1.20033			−0.600166	+	0.799876i	$0.704899\pi$
$830$		0			0
$831$	−4679.04	+	15518.6i	−0.195324	+	0.647816i
$832$	1427.43	+	2472.38i	0.0594799	+	0.103022i
$833$	−3746.29	−	6488.76i	−0.155824	−	0.269895i
$834$	3205.84	−	753.183i	0.133105	−	0.0312717i
$835$		0			0
$836$	−13371.7			−0.553192
$837$	−1694.80	−	628.135i	−0.0699891	−	0.0259397i
$838$	7026.51			0.289650
$839$	−356.480	+	617.441i	−0.0146687	+	0.0254070i	−0.873267	−	0.487243i	$-0.838003\pi$
$839$	−356.480	+	617.441i	−0.0146687	+	0.0254070i	0.858598	+	0.512650i	$0.171336\pi$
$840$		0			0
$841$	11792.0	+	20424.4i	0.483497	+	0.837441i
$842$	−1280.68	−	2218.20i	−0.0524169	−	0.0907887i
$843$	−7422.50	+	24617.6i	−0.303256	+	1.00578i
$844$	5345.30	−	9258.32i	0.218001	−	0.377588i
$845$		0			0
$846$	−1910.55	−	1267.32i	−0.0776432	−	0.0515027i
$847$	9223.44			0.374169
$848$	5501.69	−	9529.21i	0.222793	−	0.385890i
$849$	−16172.8	−	17209.4i	−0.653767	−	0.695672i
$850$		0			0
$851$	6400.27	+	11085.6i	0.257812	+	0.446544i
$852$	5885.43	+	6262.66i	0.236657	+	0.251826i
$853$	−15183.6	+	26298.8i	−0.609469	+	1.05563i	0.381859	+	0.924221i	$0.375284\pi$
$853$	−15183.6	+	26298.8i	−0.609469	+	1.05563i	−0.991328	+	0.131411i	$0.958049\pi$
$854$	3658.96			0.146612
$855$		0			0
$856$	−19937.1			−0.796069
$857$	4540.35	−	7864.12i	0.180975	−	0.313458i	−0.761238	−	0.648473i	$-0.775408\pi$
$857$	4540.35	−	7864.12i	0.180975	−	0.313458i	0.942213	+	0.335015i	$0.108741\pi$
$858$	4330.71	−	14363.3i	0.172317	−	0.571511i
$859$	−13080.1	−	22655.4i	−0.519543	−	0.899874i	−0.999742	−	0.0227150i	$-0.992769\pi$
$859$	−13080.1	−	22655.4i	−0.519543	−	0.899874i	0.480199	−	0.877159i	$-0.340564\pi$
$860$		0			0
$861$	−5577.39	+	1310.36i	−0.220763	+	0.0518663i
$862$	2806.76	−	4861.45i	0.110903	−	0.192090i
$863$	40102.0			1.58180			0.790898	−	0.611949i	$-0.209614\pi$
$863$	40102.0			1.58180			0.790898	+	0.611949i	$0.209614\pi$
$864$	−24422.5	−	9051.58i	−0.961655	−	0.356413i
$865$		0			0
$866$	434.362	−	752.338i	0.0170442	−	0.0295213i
$867$	−22022.9	+	5174.07i	−0.862671	+	0.202677i
$868$	201.615	+	349.207i	0.00788392	+	0.0136554i
$869$	36079.0	+	62490.6i	1.40839	+	2.43941i
$870$		0			0
$871$	−5720.87	+	9908.84i	−0.222554	+	0.385474i
$872$	−34415.2			−1.33652
$873$	125.691	−	2021.83i	0.00487284	−	0.0783834i
$874$	−3808.80			−0.147408
$875$		0			0
$876$	20143.9	+	21435.1i	0.776942	+	0.826741i
$877$	12626.1	+	21869.0i	0.486149	+	0.842036i	0.999873	−	0.0159201i	$-0.00506773\pi$
$877$	12626.1	+	21869.0i	0.486149	+	0.842036i	−0.513724	+	0.857956i	$0.671734\pi$
$878$	7757.86	+	13437.0i	0.298195	+	0.516489i
$879$	24411.1	+	25975.8i	0.936709	+	0.996750i
$880$		0			0
$881$	−2049.26			−0.0783670			−0.0391835	−	0.999232i	$-0.512476\pi$
$881$	−2049.26			−0.0783670			−0.0391835	+	0.999232i	$0.512476\pi$
$882$	−10510.5	+	5227.23i	−0.401256	+	0.199558i
$883$	−39413.4			−1.50211			−0.751057	−	0.660237i	$-0.770456\pi$
$883$	−39413.4			−1.50211			−0.751057	+	0.660237i	$0.770456\pi$
$884$	2718.47	−	4708.53i	0.103430	−	0.179146i
$885$		0			0
$886$	−5682.14	−	9841.75i	−0.215457	−	0.373183i
$887$	18484.2	+	32015.6i	0.699707	+	1.21193i	0.968568	+	0.248749i	$0.0800194\pi$
$887$	18484.2	+	32015.6i	0.699707	+	1.21193i	−0.268861	+	0.963179i	$0.586647\pi$
$888$	−17648.9	+	4146.45i	−0.666957	+	0.156695i
$889$	−3085.72	+	5344.63i	−0.116414	+	0.201634i
$890$		0			0
$891$	15869.8	+	37595.9i	0.596700	+	1.41359i
$892$	−15548.7			−0.583641
$893$	−1208.21	+	2092.68i	−0.0452757	+	0.0784198i
$894$	10130.0	−	2379.95i	0.378969	−	0.0890352i
$895$		0			0
$896$	3533.07	+	6119.46i	0.131732	+	0.228166i
$897$	−4006.85	+	13289.2i	−0.149147	+	0.494665i
$898$	−4726.41	+	8186.38i	−0.175637	+	0.304213i
$899$	−365.525			−0.0135605
$900$		0			0
$901$	11642.9			0.430499
$902$	8276.50	−	14335.3i	0.305518	−	0.529173i
$903$	1114.94	+	1186.40i	0.0410883	+	0.0437220i
$904$	15652.2	+	27110.4i	0.575868	+	0.997432i
$905$		0			0
$906$	−7526.49	−	8008.92i	−0.275994	−	0.293685i
$907$	1355.31	−	2347.47i	0.0496167	−	0.0859386i	−0.840150	−	0.542353i	$-0.817533\pi$
$907$	1355.31	−	2347.47i	0.0496167	−	0.0859386i	0.889767	+	0.456415i	$0.150867\pi$
$908$	−18309.3			−0.669180
$909$	1822.48	−	29316.1i	0.0664994	−	1.06970i
$910$		0			0
$911$	−11498.3	+	19915.6i	−0.418172	+	0.724296i	−0.995756	−	0.0920360i	$-0.970663\pi$
$911$	−11498.3	+	19915.6i	−0.418172	+	0.724296i	0.577583	+	0.816332i	$0.303996\pi$
$912$	−1309.24	+	4342.24i	−0.0475363	+	0.157660i
$913$	19979.6	+	34605.7i	0.724237	+	1.25441i
$914$	2939.15	+	5090.77i	0.106366	+	0.184231i
$915$		0			0
$916$	−13167.4	+	22806.7i	−0.474961	+	0.822657i
$917$	−5259.38			−0.189400
$918$	−764.337	−	4488.52i	−0.0274803	−	0.161376i
$919$	−39103.8			−1.40361			−0.701804	−	0.712370i	$-0.747622\pi$
$919$	−39103.8			−1.40361			−0.701804	+	0.712370i	$0.747622\pi$
$920$		0			0
$921$	−32031.2	+	7525.44i	−1.14600	+	0.269242i
$922$	−9453.86	−	16374.6i	−0.337686	−	0.584889i
$923$	5081.23	+	8800.94i	0.181203	+	0.313853i
$924$	2628.09	−	8716.39i	0.0935690	−	0.310333i
$925$		0			0
$926$	−7869.39			−0.279270
$927$	−24565.9	−	16295.2i	−0.870388	−	0.577350i
$928$	−5267.30			−0.186323
$929$	17977.3	−	31137.6i	0.634894	−	1.09967i	−0.351644	−	0.936134i	$-0.614377\pi$
$929$	17977.3	−	31137.6i	0.634894	−	1.09967i	0.986538	−	0.163534i	$-0.0522894\pi$
$930$		0			0
$931$	6186.12	+	10714.7i	0.217768	+	0.377185i
$932$	17070.1	+	29566.3i	0.599946	+	1.03914i
$933$	−25185.3	−	26799.6i	−0.883742	−	0.940387i
$934$	−6141.62	+	10637.6i	−0.215161	+	0.372669i
$935$		0			0
$936$	−16382.1	−	10866.6i	−0.572078	−	0.379473i
$937$	7263.94			0.253258			0.126629	−	0.991950i	$-0.459584\pi$
$937$	7263.94			0.253258			0.126629	+	0.991950i	$0.459584\pi$
$938$	1068.81	−	1851.24i	0.0372047	−	0.0644404i
$939$	2071.95	−	6871.87i	0.0720079	−	0.238823i
$940$		0			0
$941$	−3739.45	−	6476.92i	−0.129546	−	0.224380i	0.793955	−	0.607977i	$-0.208019\pi$
$941$	−3739.45	−	6476.92i	−0.129546	−	0.224380i	−0.923501	+	0.383597i	$0.874685\pi$
$942$	22321.1	−	5244.15i	0.772041	−	0.181384i
$943$	−7657.57	+	13263.3i	−0.264438	+	0.458020i
$944$	17648.7			0.608490
$945$		0			0
$946$	−4703.84			−0.161665
$947$	6745.68	−	11683.9i	0.231473	−	0.400923i	−0.726769	−	0.686882i	$-0.758979\pi$
$947$	6745.68	−	11683.9i	0.231473	−	0.400923i	0.958242	+	0.285959i	$0.0923121\pi$
$948$	39884.8	−	9370.57i	1.36645	−	0.321036i
$949$	17391.4	+	30122.8i	0.594889	+	1.03038i
$950$		0			0
$951$	−12262.4	+	40669.8i	−0.418124	+	1.38676i
$952$	−1172.13	+	2030.18i	−0.0399042	+	0.0691161i
$953$	13981.6			0.475246			0.237623	−	0.971357i	$-0.423632\pi$
$953$	13981.6			0.475246			0.237623	+	0.971357i	$0.423632\pi$
$954$	1131.79	−	18205.7i	0.0384099	−	0.617853i
$955$		0			0
$956$	4311.24	−	7467.29i	0.145853	−	0.252625i
$957$	5651.59	+	6013.85i	0.190899	+	0.203135i
$958$	−6642.54	−	11505.2i	−0.224019	−	0.388013i
$959$	−3225.93	−	5587.48i	−0.108624	−	0.188143i
$960$		0			0
$961$	14812.5	−	25656.0i	0.497214	−	0.861200i
$962$	−9289.02			−0.311320
$963$	24880.1	−	12373.7i	0.832554	−	0.414057i
$964$	−3832.64			−0.128051
$965$		0			0
$966$	748.589	−	2482.79i	0.0249332	−	0.0826940i
$967$	−4540.73	−	7864.78i	−0.151003	−	0.261545i	0.780593	−	0.625039i	$-0.214917\pi$
$967$	−4540.73	−	7864.78i	−0.151003	−	0.261545i	−0.931597	+	0.363494i	$0.881584\pi$
$968$	17459.9	+	30241.4i	0.579734	+	1.00413i
$969$	−4671.70	+	1097.57i	−0.154878	+	0.0363872i
$970$		0			0
$971$	−9709.13			−0.320887			−0.160443	−	0.987045i	$-0.551292\pi$
$971$	−9709.13			−0.320887			−0.160443	+	0.987045i	$0.551292\pi$
$972$	23039.1	−	2464.90i	0.760267	−	0.0813393i
$973$	2363.12			0.0778604
$974$	5972.62	−	10344.9i	0.196484	−	0.340320i
$975$		0			0
$976$	−5823.31	−	10086.3i	−0.190983	−	0.330793i
$977$	5427.45	+	9400.63i	0.177727	+	0.307833i	0.941102	−	0.338123i	$-0.109792\pi$
$977$	5427.45	+	9400.63i	0.177727	+	0.307833i	−0.763374	+	0.645956i	$0.776459\pi$
$978$	1950.53	−	6469.19i	0.0637742	−	0.211515i
$979$	11330.1	−	19624.3i	0.369880	−	0.640650i
$980$		0			0
$981$	42947.7	−	21359.3i	1.39777	−	0.695159i
$982$	−21401.7			−0.695474
$983$	−3755.05	+	6503.94i	−0.121839	+	0.211031i	−0.920493	−	0.390759i	$-0.872212\pi$
$983$	−3755.05	+	6503.94i	−0.121839	+	0.211031i	0.798654	+	0.601790i	$0.205546\pi$
$984$	−14854.3	−	15806.4i	−0.481238	−	0.512084i
$985$		0			0
$986$	−460.393	−	797.424i	−0.0148701	−	0.0257557i
$987$	−1126.66	−	1198.88i	−0.0363343	−	0.0386633i
$988$	−4488.92	+	7775.04i	−0.144546	+	0.250361i
$989$	4352.08			0.139927
$990$		0			0
$991$	46125.6			1.47854			0.739268	−	0.673412i	$-0.235172\pi$
$991$	46125.6			1.47854			0.739268	+	0.673412i	$0.235172\pi$
$992$	−1195.88	+	2071.32i	−0.0382753	+	0.0662947i
$993$	14491.9	−	48064.3i	0.463129	−	1.53603i
$994$	−949.311	−	1644.25i	−0.0302921	−	0.0524674i
$995$		0			0
$996$	22087.2	−	5189.18i	0.702669	−	0.165086i
$997$	22675.0	−	39274.3i	0.720287	−	1.24757i	−0.240598	−	0.970625i	$-0.577344\pi$
$997$	22675.0	−	39274.3i	0.720287	−	1.24757i	0.960885	−	0.276948i	$-0.0893231\pi$
$998$	−13306.0			−0.422039
$999$	19451.1	−	16128.0i	0.616023	−	0.510779i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.4.e.b.151.1		4
5.2	odd	4		225.4.k.b.124.2		8
5.3	odd	4		225.4.k.b.124.3		8
5.4	even	2		9.4.c.a.7.2	yes	4
9.2	odd	6		2025.4.a.n.1.1		2
9.4	even	3	inner	225.4.e.b.76.1		4
9.7	even	3		2025.4.a.g.1.2		2
15.14	odd	2		27.4.c.a.19.1		4
20.19	odd	2		144.4.i.c.97.2		4
45.4	even	6		9.4.c.a.4.2	✓	4
45.13	odd	12		225.4.k.b.49.2		8
45.14	odd	6		27.4.c.a.10.1		4
45.22	odd	12		225.4.k.b.49.3		8
45.29	odd	6		81.4.a.a.1.2		2
45.34	even	6		81.4.a.d.1.1		2
60.59	even	2		432.4.i.c.289.2		4
180.59	even	6		432.4.i.c.145.2		4
180.79	odd	6		1296.4.a.u.1.2		2
180.119	even	6		1296.4.a.i.1.1		2
180.139	odd	6		144.4.i.c.49.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
9.4.c.a.4.2	✓	4	45.4	even	6
9.4.c.a.7.2	yes	4	5.4	even	2
27.4.c.a.10.1		4	45.14	odd	6
27.4.c.a.19.1		4	15.14	odd	2
81.4.a.a.1.2		2	45.29	odd	6
81.4.a.d.1.1		2	45.34	even	6
144.4.i.c.49.2		4	180.139	odd	6
144.4.i.c.97.2		4	20.19	odd	2
225.4.e.b.76.1		4	9.4	even	3	inner
225.4.e.b.151.1		4	1.1	even	1	trivial
225.4.k.b.49.2		8	45.13	odd	12
225.4.k.b.49.3		8	45.22	odd	12
225.4.k.b.124.2		8	5.2	odd	4
225.4.k.b.124.3		8	5.3	odd	4
432.4.i.c.145.2		4	180.59	even	6
432.4.i.c.289.2		4	60.59	even	2
1296.4.a.i.1.1		2	180.119	even	6
1296.4.a.u.1.2		2	180.79	odd	6
2025.4.a.g.1.2		2	9.7	even	3
2025.4.a.n.1.1		2	9.2	odd	6

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	225.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.686141 + 1.18843i) q^{2} +(5.05842 - 1.18843i) q^{3} +(3.05842 + 5.29734i) q^{4} +(-2.05842 + 6.82701i) q^{6} +(-2.55842 + 4.43132i) q^{7} -19.3723 q^{8} +(24.1753 - 12.0232i) q^{9} +O(q^{10})\)	\(q+(-0.686141 + 1.18843i) q^{2} +(5.05842 - 1.18843i) q^{3} +(3.05842 + 5.29734i) q^{4} +(-2.05842 + 6.82701i) q^{6} +(-2.55842 + 4.43132i) q^{7} -19.3723 q^{8} +(24.1753 - 12.0232i) q^{9} +(-27.9891 + 48.4786i) q^{11} +(21.7663 + 23.1615i) q^{12} +(18.7921 + 32.5489i) q^{13} +(-3.51087 - 6.08101i) q^{14} +(-11.1753 + 19.3561i) q^{16} -23.6495 q^{17} +(-2.29894 + 36.9802i) q^{18} +39.0516 q^{19} +(-7.67527 + 25.4560i) q^{21} +(-38.4090 - 66.5263i) q^{22} +(35.5367 + 61.5513i) q^{23} +(-97.9932 + 23.0226i) q^{24} -51.5761 q^{26} +(108.000 - 89.5489i) q^{27} -31.2989 q^{28} +(14.1861 - 24.5711i) q^{29} +(-6.44158 - 11.1571i) q^{31} +(-92.8247 - 160.777i) q^{32} +(-83.9674 + 278.488i) q^{33} +(16.2269 - 28.1057i) q^{34} +(137.629 + 91.2927i) q^{36} +180.103 q^{37} +(-26.7949 + 46.4101i) q^{38} +(133.741 + 142.313i) q^{39} +(107.742 + 186.614i) q^{41} +(-24.9863 - 26.5879i) q^{42} +(30.6168 - 53.0299i) q^{43} -342.410 q^{44} -97.5326 q^{46} +(-30.9388 + 53.5876i) q^{47} +(-33.5258 + 111.192i) q^{48} +(158.409 + 274.372i) q^{49} +(-119.629 + 28.1057i) q^{51} +(-114.948 + 199.096i) q^{52} -492.310 q^{53} +(32.3194 + 189.794i) q^{54} +(49.5625 - 85.8447i) q^{56} +(197.539 - 46.4101i) q^{57} +(19.4674 + 33.7185i) q^{58} +(-394.815 - 683.840i) q^{59} +(-260.545 + 451.277i) q^{61} +17.6793 q^{62} +(-8.57207 + 137.889i) q^{63} +75.9590 q^{64} +(-273.351 - 290.872i) q^{66} +(152.215 + 263.644i) q^{67} +(-72.3301 - 125.279i) q^{68} +(252.909 + 269.120i) q^{69} +270.391 q^{71} +(-468.330 + 232.916i) q^{72} +925.464 q^{73} +(-123.576 + 214.040i) q^{74} +(119.436 + 206.870i) q^{76} +(-143.216 - 248.057i) q^{77} +(-260.894 + 61.2946i) q^{78} +(644.517 - 1116.34i) q^{79} +(439.887 - 581.326i) q^{81} -295.704 q^{82} +(356.917 - 618.198i) q^{83} +(-158.323 + 37.1966i) q^{84} +(42.0149 + 72.7720i) q^{86} +(42.5584 - 141.150i) q^{87} +(542.213 - 939.141i) q^{88} -404.804 q^{89} -192.313 q^{91} +(-217.372 + 376.500i) q^{92} +(-45.8437 - 48.7822i) q^{93} +(-42.4567 - 73.5372i) q^{94} +(-660.619 - 702.963i) q^{96} +(37.5137 - 64.9756i) q^{97} -434.763 q^{98} +(-93.7785 + 1508.50i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 3 q^{2} + 3 q^{3} - 5 q^{4} + 9 q^{6} + 7 q^{7} - 66 q^{8} + 45 q^{9}+O(q^{10}) \) 4 * q + 3 * q^2 + 3 * q^3 - 5 * q^4 + 9 * q^6 + 7 * q^7 - 66 * q^8 + 45 * q^9	\( 4 q + 3 q^{2} + 3 q^{3} - 5 q^{4} + 9 q^{6} + 7 q^{7} - 66 q^{8} + 45 q^{9} - 66 q^{11} + 156 q^{12} - 11 q^{13} - 60 q^{14} + 7 q^{16} - 198 q^{17} - 216 q^{18} - 154 q^{19} + 21 q^{21} - 33 q^{22} + 33 q^{23} - 99 q^{24} - 528 q^{26} + 432 q^{27} - 332 q^{28} + 51 q^{29} - 43 q^{31} - 423 q^{32} - 198 q^{33} - 297 q^{34} - 225 q^{36} + 100 q^{37} - 561 q^{38} + 759 q^{39} - 132 q^{41} + 486 q^{42} + 88 q^{43} - 462 q^{44} - 528 q^{46} + 399 q^{47} + 21 q^{48} + 513 q^{49} + 297 q^{51} - 770 q^{52} - 108 q^{53} + 1215 q^{54} - 66 q^{56} + 1221 q^{57} - 60 q^{58} - 798 q^{59} - 439 q^{61} - 228 q^{62} - 603 q^{63} - 1454 q^{64} - 990 q^{66} + 988 q^{67} + 693 q^{68} + 891 q^{69} + 2736 q^{71} - 891 q^{72} + 910 q^{73} - 816 q^{74} + 1529 q^{76} - 165 q^{77} + 990 q^{78} + 803 q^{79} - 567 q^{81} - 3630 q^{82} + 813 q^{83} + 642 q^{84} - 33 q^{86} + 153 q^{87} + 1221 q^{88} - 792 q^{89} - 1562 q^{91} - 858 q^{92} + 213 q^{93} - 2100 q^{94} + 1080 q^{96} + 736 q^{97} + 846 q^{98} + 297 q^{99}+O(q^{100}) \) 4 * q + 3 * q^2 + 3 * q^3 - 5 * q^4 + 9 * q^6 + 7 * q^7 - 66 * q^8 + 45 * q^9 - 66 * q^11 + 156 * q^12 - 11 * q^13 - 60 * q^14 + 7 * q^16 - 198 * q^17 - 216 * q^18 - 154 * q^19 + 21 * q^21 - 33 * q^22 + 33 * q^23 - 99 * q^24 - 528 * q^26 + 432 * q^27 - 332 * q^28 + 51 * q^29 - 43 * q^31 - 423 * q^32 - 198 * q^33 - 297 * q^34 - 225 * q^36 + 100 * q^37 - 561 * q^38 + 759 * q^39 - 132 * q^41 + 486 * q^42 + 88 * q^43 - 462 * q^44 - 528 * q^46 + 399 * q^47 + 21 * q^48 + 513 * q^49 + 297 * q^51 - 770 * q^52 - 108 * q^53 + 1215 * q^54 - 66 * q^56 + 1221 * q^57 - 60 * q^58 - 798 * q^59 - 439 * q^61 - 228 * q^62 - 603 * q^63 - 1454 * q^64 - 990 * q^66 + 988 * q^67 + 693 * q^68 + 891 * q^69 + 2736 * q^71 - 891 * q^72 + 910 * q^73 - 816 * q^74 + 1529 * q^76 - 165 * q^77 + 990 * q^78 + 803 * q^79 - 567 * q^81 - 3630 * q^82 + 813 * q^83 + 642 * q^84 - 33 * q^86 + 153 * q^87 + 1221 * q^88 - 792 * q^89 - 1562 * q^91 - 858 * q^92 + 213 * q^93 - 2100 * q^94 + 1080 * q^96 + 736 * q^97 + 846 * q^98 + 297 * q^99

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