LMFDB - Embedded newform 287.2.f.a.50.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(50,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 3]))

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

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

chi := DirichletCharacter("287.50");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.f (of order $4$, 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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			50.19
Character	$\chi$	$=$	287.50
Dual form			287.2.f.a.155.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.69233i q^{2} +(-2.23891 - 2.23891i) q^{3} -5.24863 q^{4} -1.01652i q^{5} +(6.02789 - 6.02789i) q^{6} +(0.707107 + 0.707107i) q^{7} -8.74637i q^{8} +7.02546i q^{9} +O(q^{10})$	\(q+2.69233i q^{2} +(-2.23891 - 2.23891i) q^{3} -5.24863 q^{4} -1.01652i q^{5} +(6.02789 - 6.02789i) q^{6} +(0.707107 + 0.707107i) q^{7} -8.74637i q^{8} +7.02546i q^{9} +2.73681 q^{10} +(2.78912 + 2.78912i) q^{11} +(11.7512 + 11.7512i) q^{12} +(1.55052 + 1.55052i) q^{13} +(-1.90376 + 1.90376i) q^{14} +(-2.27590 + 2.27590i) q^{15} +13.0508 q^{16} +(4.43119 - 4.43119i) q^{17} -18.9148 q^{18} +(2.80812 - 2.80812i) q^{19} +5.33534i q^{20} -3.16630i q^{21} +(-7.50924 + 7.50924i) q^{22} -1.96635 q^{23} +(-19.5824 + 19.5824i) q^{24} +3.96668 q^{25} +(-4.17451 + 4.17451i) q^{26} +(9.01266 - 9.01266i) q^{27} +(-3.71134 - 3.71134i) q^{28} +(0.381133 + 0.381133i) q^{29} +(-6.12748 - 6.12748i) q^{30} -3.57507 q^{31} +17.6444i q^{32} -12.4892i q^{33} +(11.9302 + 11.9302i) q^{34} +(0.718789 - 0.718789i) q^{35} -36.8740i q^{36} +6.35360 q^{37} +(7.56039 + 7.56039i) q^{38} -6.94296i q^{39} -8.89087 q^{40} +(0.932741 + 6.33482i) q^{41} +8.52472 q^{42} -9.44202i q^{43} +(-14.6391 - 14.6391i) q^{44} +7.14154 q^{45} -5.29405i q^{46} +(-6.13875 + 6.13875i) q^{47} +(-29.2197 - 29.2197i) q^{48} +1.00000i q^{49} +10.6796i q^{50} -19.8421 q^{51} +(-8.13810 - 8.13810i) q^{52} +(7.68459 + 7.68459i) q^{53} +(24.2650 + 24.2650i) q^{54} +(2.83520 - 2.83520i) q^{55} +(6.18462 - 6.18462i) q^{56} -12.5743 q^{57} +(-1.02613 + 1.02613i) q^{58} +2.14451 q^{59} +(11.9454 - 11.9454i) q^{60} +0.630004i q^{61} -9.62525i q^{62} +(-4.96775 + 4.96775i) q^{63} -21.4028 q^{64} +(1.57614 - 1.57614i) q^{65} +33.6251 q^{66} +(2.57310 - 2.57310i) q^{67} +(-23.2577 + 23.2577i) q^{68} +(4.40248 + 4.40248i) q^{69} +(1.93522 + 1.93522i) q^{70} +(3.62299 + 3.62299i) q^{71} +61.4473 q^{72} +6.20833i q^{73} +17.1060i q^{74} +(-8.88106 - 8.88106i) q^{75} +(-14.7388 + 14.7388i) q^{76} +3.94442i q^{77} +18.6927 q^{78} +(-7.63214 - 7.63214i) q^{79} -13.2665i q^{80} -19.2807 q^{81} +(-17.0554 + 2.51125i) q^{82} +6.18759 q^{83} +16.6187i q^{84} +(-4.50440 - 4.50440i) q^{85} +25.4210 q^{86} -1.70665i q^{87} +(24.3947 - 24.3947i) q^{88} +(-4.79453 - 4.79453i) q^{89} +19.2274i q^{90} +2.19277i q^{91} +10.3206 q^{92} +(8.00426 + 8.00426i) q^{93} +(-16.5275 - 16.5275i) q^{94} +(-2.85452 - 2.85452i) q^{95} +(39.5042 - 39.5042i) q^{96} +(9.70603 - 9.70603i) q^{97} -2.69233 q^{98} +(-19.5949 + 19.5949i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6}+O(q^{10}) $ 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6	$ 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6} - 32 q^{10} - 8 q^{11} + 16 q^{12} + 16 q^{13} - 8 q^{15} + 28 q^{16} + 20 q^{17} - 12 q^{18} - 20 q^{19} + 4 q^{22} + 16 q^{23} - 12 q^{24} - 40 q^{25} - 20 q^{26} - 20 q^{27} - 12 q^{29} + 4 q^{30} + 32 q^{34} + 4 q^{35} - 16 q^{38} + 64 q^{40} + 16 q^{41} + 32 q^{42} + 8 q^{44} + 72 q^{45} - 24 q^{47} - 40 q^{48} - 64 q^{51} - 96 q^{52} + 8 q^{53} + 52 q^{54} - 8 q^{55} - 88 q^{57} - 36 q^{58} + 48 q^{59} + 52 q^{60} - 8 q^{63} - 84 q^{64} - 44 q^{65} + 56 q^{66} + 40 q^{67} - 60 q^{68} + 28 q^{69} - 8 q^{70} + 20 q^{71} + 80 q^{72} - 20 q^{75} - 4 q^{76} + 12 q^{78} - 12 q^{79} + 16 q^{81} - 52 q^{82} + 40 q^{83} + 8 q^{85} + 80 q^{86} + 96 q^{88} - 8 q^{89} - 20 q^{92} - 64 q^{93} + 52 q^{94} + 68 q^{96} - 60 q^{97} - 4 q^{98} - 36 q^{99}+O(q^{100}) $ 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6 - 32 * q^10 - 8 * q^11 + 16 * q^12 + 16 * q^13 - 8 * q^15 + 28 * q^16 + 20 * q^17 - 12 * q^18 - 20 * q^19 + 4 * q^22 + 16 * q^23 - 12 * q^24 - 40 * q^25 - 20 * q^26 - 20 * q^27 - 12 * q^29 + 4 * q^30 + 32 * q^34 + 4 * q^35 - 16 * q^38 + 64 * q^40 + 16 * q^41 + 32 * q^42 + 8 * q^44 + 72 * q^45 - 24 * q^47 - 40 * q^48 - 64 * q^51 - 96 * q^52 + 8 * q^53 + 52 * q^54 - 8 * q^55 - 88 * q^57 - 36 * q^58 + 48 * q^59 + 52 * q^60 - 8 * q^63 - 84 * q^64 - 44 * q^65 + 56 * q^66 + 40 * q^67 - 60 * q^68 + 28 * q^69 - 8 * q^70 + 20 * q^71 + 80 * q^72 - 20 * q^75 - 4 * q^76 + 12 * q^78 - 12 * q^79 + 16 * q^81 - 52 * q^82 + 40 * q^83 + 8 * q^85 + 80 * q^86 + 96 * q^88 - 8 * q^89 - 20 * q^92 - 64 * q^93 + 52 * q^94 + 68 * q^96 - 60 * q^97 - 4 * q^98 - 36 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$

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 $

$2$			2.69233i			1.90376i	0.306466	+	0.951882i	$0.400853\pi$
$2$			2.69233i			1.90376i	−0.306466	+	0.951882i	$0.599147\pi$
$3$	−2.23891	−	2.23891i	−1.29264	−	1.29264i	−0.933150	−	0.359487i	$-0.882952\pi$
$3$	−2.23891	−	2.23891i	−1.29264	−	1.29264i	−0.359487	−	0.933150i	$-0.617048\pi$
$4$	−5.24863			−2.62431
$5$		−	1.01652i		−	0.454602i	−0.973825	−	0.227301i	$-0.927010\pi$
$5$		−	1.01652i		−	0.454602i	0.973825	−	0.227301i	$-0.0729902\pi$
$6$	6.02789	−	6.02789i	2.46087	−	2.46087i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		−	8.74637i		−	3.09231i
$9$			7.02546i			2.34182i
$10$	2.73681			0.865455
$11$	2.78912	+	2.78912i	0.840953	+	0.840953i	0.988983	−	0.148030i	$-0.0472933\pi$
$11$	2.78912	+	2.78912i	0.840953	+	0.840953i	−0.148030	+	0.988983i	$0.547293\pi$
$12$	11.7512	+	11.7512i	3.39229	+	3.39229i
$13$	1.55052	+	1.55052i	0.430037	+	0.430037i	0.888641	−	0.458604i	$-0.151650\pi$
$13$	1.55052	+	1.55052i	0.430037	+	0.430037i	−0.458604	+	0.888641i	$0.651650\pi$
$14$	−1.90376	+	1.90376i	−0.508802	+	0.508802i
$15$	−2.27590	+	2.27590i	−0.587636	+	0.587636i
$16$	13.0508			3.26271
$17$	4.43119	−	4.43119i	1.07472	−	1.07472i	0.0777478	−	0.996973i	$-0.475227\pi$
$17$	4.43119	−	4.43119i	1.07472	−	1.07472i	0.996973	−	0.0777478i	$-0.0247729\pi$
$18$	−18.9148			−4.45827
$19$	2.80812	−	2.80812i	0.644228	−	0.644228i	−0.307364	−	0.951592i	$-0.599447\pi$
$19$	2.80812	−	2.80812i	0.644228	−	0.644228i	0.951592	+	0.307364i	$0.0994470\pi$
$20$			5.33534i			1.19302i
$21$		−	3.16630i		−	0.690944i
$22$	−7.50924	+	7.50924i	−1.60097	+	1.60097i
$23$	−1.96635			−0.410011			−0.205006	−	0.978761i	$-0.565721\pi$
$23$	−1.96635			−0.410011			−0.205006	+	0.978761i	$0.565721\pi$
$24$	−19.5824	+	19.5824i	−3.99723	+	3.99723i
$25$	3.96668			0.793337
$26$	−4.17451	+	4.17451i	−0.818688	+	0.818688i
$27$	9.01266	−	9.01266i	1.73449	−	1.73449i
$28$	−3.71134	−	3.71134i	−0.701377	−	0.701377i
$29$	0.381133	+	0.381133i	0.0707745	+	0.0707745i	0.741608	−	0.670833i	$-0.234063\pi$
$29$	0.381133	+	0.381133i	0.0707745	+	0.0707745i	−0.670833	+	0.741608i	$0.734063\pi$
$30$	−6.12748	−	6.12748i	−1.11872	−	1.11872i
$31$	−3.57507			−0.642101			−0.321050	−	0.947062i	$-0.604036\pi$
$31$	−3.57507			−0.642101			−0.321050	+	0.947062i	$0.604036\pi$
$32$			17.6444i			3.11912i
$33$		−	12.4892i		−	2.17409i
$34$	11.9302	+	11.9302i	2.04601	+	2.04601i
$35$	0.718789	−	0.718789i	0.121498	−	0.121498i
$36$		−	36.8740i		−	6.14567i
$37$	6.35360			1.04453			0.522263	−	0.852785i	$-0.325088\pi$
$37$	6.35360			1.04453			0.522263	+	0.852785i	$0.325088\pi$
$38$	7.56039	+	7.56039i	1.22646	+	1.22646i
$39$		−	6.94296i		−	1.11176i
$40$	−8.89087			−1.40577
$41$	0.932741	+	6.33482i	0.145670	+	0.989333i
$41$	0.932741	+	6.33482i	0.145670	+	0.989333i
$42$	8.52472			1.31539
$43$		−	9.44202i		−	1.43989i	−0.694029	−	0.719947i	$-0.744166\pi$
$43$		−	9.44202i		−	1.43989i	0.694029	−	0.719947i	$-0.255834\pi$
$44$	−14.6391	−	14.6391i	−2.20692	−	2.20692i
$45$	7.14154			1.06460
$46$		−	5.29405i		−	0.780565i
$47$	−6.13875	+	6.13875i	−0.895429	+	0.895429i	−0.995028	−	0.0995987i	$-0.968244\pi$
$47$	−6.13875	+	6.13875i	−0.895429	+	0.895429i	0.0995987	+	0.995028i	$0.468244\pi$
$48$	−29.2197	−	29.2197i	−4.21750	−	4.21750i
$49$			1.00000i			0.142857i
$50$			10.6796i			1.51033i
$51$	−19.8421			−2.77845
$52$	−8.13810	−	8.13810i	−1.12855	−	1.12855i
$53$	7.68459	+	7.68459i	1.05556	+	1.05556i	0.998363	+	0.0571971i	$0.0182164\pi$
$53$	7.68459	+	7.68459i	1.05556	+	1.05556i	0.0571971	+	0.998363i	$0.481784\pi$
$54$	24.2650	+	24.2650i	3.30205	+	3.30205i
$55$	2.83520	−	2.83520i	0.382299	−	0.382299i
$56$	6.18462	−	6.18462i	0.826454	−	0.826454i
$57$	−12.5743			−1.66551
$58$	−1.02613	+	1.02613i	−0.134738	+	0.134738i
$59$	2.14451			0.279191			0.139595	−	0.990209i	$-0.455420\pi$
$59$	2.14451			0.279191			0.139595	+	0.990209i	$0.455420\pi$
$60$	11.9454	−	11.9454i	1.54214	−	1.54214i
$61$			0.630004i			0.0806638i	0.999186	+	0.0403319i	$0.0128415\pi$
$61$			0.630004i			0.0806638i	−0.999186	+	0.0403319i	$0.987158\pi$
$62$		−	9.62525i		−	1.22241i
$63$	−4.96775	+	4.96775i	−0.625878	+	0.625878i
$64$	−21.4028			−2.67535
$65$	1.57614	−	1.57614i	0.195496	−	0.195496i
$66$	33.6251			4.13896
$67$	2.57310	−	2.57310i	0.314354	−	0.314354i	−0.532240	−	0.846594i	$-0.678649\pi$
$67$	2.57310	−	2.57310i	0.314354	−	0.314354i	0.846594	+	0.532240i	$0.178649\pi$
$68$	−23.2577	+	23.2577i	−2.82040	+	2.82040i
$69$	4.40248	+	4.40248i	0.529996	+	0.529996i
$70$	1.93522	+	1.93522i	0.231303	+	0.231303i
$71$	3.62299	+	3.62299i	0.429970	+	0.429970i	0.888618	−	0.458648i	$-0.151666\pi$
$71$	3.62299	+	3.62299i	0.429970	+	0.429970i	−0.458648	+	0.888618i	$0.651666\pi$
$72$	61.4473			7.24163
$73$			6.20833i			0.726630i	0.931666	+	0.363315i	$0.118355\pi$
$73$			6.20833i			0.726630i	−0.931666	+	0.363315i	$0.881645\pi$
$74$			17.1060i			1.98853i
$75$	−8.88106	−	8.88106i	−1.02550	−	1.02550i
$76$	−14.7388	+	14.7388i	−1.69066	+	1.69066i
$77$			3.94442i			0.449508i
$78$	18.6927			2.11653
$79$	−7.63214	−	7.63214i	−0.858683	−	0.858683i	0.132500	−	0.991183i	$-0.457700\pi$
$79$	−7.63214	−	7.63214i	−0.858683	−	0.858683i	−0.991183	+	0.132500i	$0.957700\pi$
$80$		−	13.2665i		−	1.48323i
$81$	−19.2807			−2.14230
$82$	−17.0554	+	2.51125i	−1.88346	+	0.277321i
$83$	6.18759			0.679176			0.339588	−	0.940574i	$-0.389712\pi$
$83$	6.18759			0.679176			0.339588	+	0.940574i	$0.389712\pi$
$84$			16.6187i			1.81325i
$85$	−4.50440	−	4.50440i	−0.488571	−	0.488571i
$86$	25.4210			2.74122
$87$		−	1.70665i		−	0.182972i
$88$	24.3947	−	24.3947i	2.60048	−	2.60048i
$89$	−4.79453	−	4.79453i	−0.508219	−	0.508219i	0.405761	−	0.913979i	$-0.367007\pi$
$89$	−4.79453	−	4.79453i	−0.508219	−	0.508219i	−0.913979	+	0.405761i	$0.867007\pi$
$90$			19.2274i			2.02674i
$91$			2.19277i			0.229864i
$92$	10.3206			1.07600
$93$	8.00426	+	8.00426i	0.830003	+	0.830003i
$94$	−16.5275	−	16.5275i	−1.70468	−	1.70468i
$95$	−2.85452	−	2.85452i	−0.292867	−	0.292867i
$96$	39.5042	−	39.5042i	4.03189	−	4.03189i
$97$	9.70603	−	9.70603i	0.985498	−	0.985498i	−0.0143984	−	0.999896i	$-0.504583\pi$
$97$	9.70603	−	9.70603i	0.985498	−	0.985498i	0.999896	+	0.0143984i	$0.00458330\pi$
$98$	−2.69233			−0.271966
$99$	−19.5949	+	19.5949i	−1.96936	+	1.96936i
$100$	−20.8196			−2.08196
$101$	0.462646	−	0.462646i	0.0460350	−	0.0460350i	−0.683715	−	0.729750i	$-0.739637\pi$
$101$	0.462646	−	0.462646i	0.0460350	−	0.0460350i	0.729750	+	0.683715i	$0.239637\pi$
$102$		−	53.4214i		−	5.28951i
$103$		−	9.02454i		−	0.889214i	−0.895726	−	0.444607i	$-0.853343\pi$
$103$		−	9.02454i		−	0.889214i	0.895726	−	0.444607i	$-0.146657\pi$
$104$	13.5614	−	13.5614i	1.32981	−	1.32981i
$105$	−3.21861			−0.314105
$106$	−20.6894	+	20.6894i	−2.00954	+	2.00954i
$107$	7.54460			0.729364			0.364682	−	0.931132i	$-0.381178\pi$
$107$	7.54460			0.729364			0.364682	+	0.931132i	$0.381178\pi$
$108$	−47.3041	+	47.3041i	−4.55184	+	4.55184i
$109$	−6.23392	+	6.23392i	−0.597101	+	0.597101i	−0.939540	−	0.342439i	$-0.888747\pi$
$109$	−6.23392	+	6.23392i	−0.597101	+	0.597101i	0.342439	+	0.939540i	$0.388747\pi$
$110$	7.63330	+	7.63330i	0.727807	+	0.727807i
$111$	−14.2252	−	14.2252i	−1.35019	−	1.35019i
$112$	9.22833	+	9.22833i	0.871996	+	0.871996i
$113$	4.58647			0.431459			0.215730	−	0.976453i	$-0.430787\pi$
$113$	4.58647			0.431459			0.215730	+	0.976453i	$0.430787\pi$
$114$		−	33.8541i		−	3.17073i
$115$			1.99883i			0.186392i
$116$	−2.00042	−	2.00042i	−0.185735	−	0.185735i
$117$	−10.8931	+	10.8931i	−1.00707	+	1.00707i
$118$			5.77371i			0.531513i
$119$	6.26665			0.574462
$120$	19.9059	+	19.9059i	1.81715	+	1.81715i
$121$			4.55843i			0.414402i
$122$	−1.69618			−0.153565
$123$	12.0948	−	16.2714i	1.09055	−	1.46715i
$124$	18.7642			1.68507
$125$		−	9.11483i		−	0.815255i
$126$	−13.3748	−	13.3748i	−1.19152	−	1.19152i
$127$	2.99213			0.265508			0.132754	−	0.991149i	$-0.457618\pi$
$127$	2.99213			0.265508			0.132754	+	0.991149i	$0.457618\pi$
$128$		−	22.3346i		−	1.97411i
$129$	−21.1399	+	21.1399i	−1.86126	+	1.86126i
$130$	4.24348	+	4.24348i	0.372178	+	0.372178i
$131$			3.82111i			0.333852i	0.985969	+	0.166926i	$0.0533841\pi$
$131$			3.82111i			0.333852i	−0.985969	+	0.166926i	$0.946616\pi$
$132$			65.5512i			5.70550i
$133$	3.97129			0.344354
$134$	6.92763	+	6.92763i	0.598456	+	0.598456i
$135$	−9.16157	−	9.16157i	−0.788502	−	0.788502i
$136$	−38.7568	−	38.7568i	−3.32337	−	3.32337i
$137$	−14.3622	+	14.3622i	−1.22705	+	1.22705i	−0.261973	+	0.965075i	$0.584373\pi$
$137$	−14.3622	+	14.3622i	−1.22705	+	1.22705i	−0.965075	+	0.261973i	$0.915627\pi$
$138$	−11.8529	+	11.8529i	−1.00899	+	1.00899i
$139$	−3.08487			−0.261656			−0.130828	−	0.991405i	$-0.541763\pi$
$139$	−3.08487			−0.261656			−0.130828	+	0.991405i	$0.541763\pi$
$140$	−3.77266	+	3.77266i	−0.318848	+	0.318848i
$141$	27.4883			2.31493
$142$	−9.75427	+	9.75427i	−0.818560	+	0.818560i
$143$			8.64919i			0.723281i
$144$			91.6882i			7.64068i
$145$	0.387429	−	0.387429i	0.0321743	−	0.0321743i
$146$	−16.7149			−1.38333
$147$	2.23891	−	2.23891i	0.184662	−	0.184662i
$148$	−33.3477			−2.74116
$149$	−0.713811	+	0.713811i	−0.0584777	+	0.0584777i	−0.735741	−	0.677263i	$-0.763166\pi$
$149$	−0.713811	+	0.713811i	−0.0584777	+	0.0584777i	0.677263	+	0.735741i	$0.263166\pi$
$150$	23.9107	−	23.9107i	1.95230	−	1.95230i
$151$	−4.28311	−	4.28311i	−0.348555	−	0.348555i	0.511016	−	0.859571i	$-0.329269\pi$
$151$	−4.28311	−	4.28311i	−0.348555	−	0.348555i	−0.859571	+	0.511016i	$0.829269\pi$
$152$	−24.5609	−	24.5609i	−1.99215	−	1.99215i
$153$	31.1311	+	31.1311i	2.51680	+	2.51680i
$154$	−10.6197			−0.855757
$155$			3.63413i			0.291901i
$156$			36.4410i			2.91762i
$157$	8.49402	+	8.49402i	0.677897	+	0.677897i	0.959524	−	0.281627i	$-0.0908741\pi$
$157$	8.49402	+	8.49402i	0.677897	+	0.677897i	−0.281627	+	0.959524i	$0.590874\pi$
$158$	20.5482	−	20.5482i	1.63473	−	1.63473i
$159$		−	34.4103i		−	2.72891i
$160$	17.9359			1.41796
$161$	−1.39042	−	1.39042i	−0.109580	−	0.109580i
$162$		−	51.9101i		−	4.07844i
$163$	5.18965			0.406485			0.203242	−	0.979128i	$-0.434852\pi$
$163$	5.18965			0.406485			0.203242	+	0.979128i	$0.434852\pi$
$164$	−4.89561	−	33.2491i	−0.382283	−	2.59632i
$165$	−12.6956			−0.988348
$166$			16.6590i			1.29299i
$167$	−12.6424	−	12.6424i	−0.978300	−	0.978300i	0.0214691	−	0.999770i	$-0.493166\pi$
$167$	−12.6424	−	12.6424i	−0.978300	−	0.978300i	−0.999770	+	0.0214691i	$0.993166\pi$
$168$	−27.6936			−2.13661
$169$		−	8.19178i		−	0.630137i
$170$	12.1273	−	12.1273i	0.930123	−	0.930123i
$171$	19.7284	+	19.7284i	1.50867	+	1.50867i
$172$			49.5577i			3.77874i
$173$		−	7.48801i		−	0.569303i	−0.958631	−	0.284651i	$-0.908122\pi$
$173$		−	7.48801i		−	0.569303i	0.958631	−	0.284651i	$-0.0918779\pi$
$174$	4.59485			0.348335
$175$	2.80487	+	2.80487i	0.212028	+	0.212028i
$176$	36.4004	+	36.4004i	2.74378	+	2.74378i
$177$	−4.80136	−	4.80136i	−0.360893	−	0.360893i
$178$	12.9084	−	12.9084i	0.967528	−	0.967528i
$179$	−12.2275	+	12.2275i	−0.913923	+	0.913923i	−0.996578	−	0.0826556i	$-0.973660\pi$
$179$	−12.2275	+	12.2275i	−0.913923	+	0.913923i	0.0826556	+	0.996578i	$0.473660\pi$
$180$	−37.4833			−2.79384
$181$	−5.18811	+	5.18811i	−0.385629	+	0.385629i	−0.873125	−	0.487496i	$-0.837910\pi$
$181$	−5.18811	+	5.18811i	−0.385629	+	0.385629i	0.487496	+	0.873125i	$0.337910\pi$
$182$	−5.90365			−0.437607
$183$	1.41053	−	1.41053i	0.104269	−	0.104269i
$184$			17.1984i			1.26788i
$185$		−	6.45857i		−	0.474844i
$186$	−21.5501	+	21.5501i	−1.58013	+	1.58013i
$187$	24.7183			1.80758
$188$	32.2200	−	32.2200i	2.34989	−	2.34989i
$189$	12.7458			0.927123
$190$	7.68530	−	7.68530i	0.557550	−	0.557550i
$191$	−17.4996	+	17.4996i	−1.26623	+	1.26623i	−0.318207	+	0.948021i	$0.603081\pi$
$191$	−17.4996	+	17.4996i	−1.26623	+	1.26623i	−0.948021	+	0.318207i	$0.896919\pi$
$192$	47.9190	+	47.9190i	3.45826	+	3.45826i
$193$	−14.3631	−	14.3631i	−1.03388	−	1.03388i	−0.999406	−	0.0344759i	$-0.989024\pi$
$193$	−14.3631	−	14.3631i	−1.03388	−	1.03388i	−0.0344759	−	0.999406i	$-0.510976\pi$
$194$	26.1318	+	26.1318i	1.87615	+	1.87615i
$195$	−7.05767			−0.505410
$196$		−	5.24863i		−	0.374902i
$197$		−	10.7034i		−	0.762584i	−0.924455	−	0.381292i	$-0.875479\pi$
$197$		−	10.7034i		−	0.762584i	0.924455	−	0.381292i	$-0.124521\pi$
$198$	−52.7559	−	52.7559i	−3.74920	−	3.74920i
$199$	11.4240	−	11.4240i	0.809826	−	0.809826i	−0.174781	−	0.984607i	$-0.555922\pi$
$199$	11.4240	−	11.4240i	0.809826	−	0.809826i	0.984607	+	0.174781i	$0.0559219\pi$
$200$		−	34.6941i		−	2.45324i
$201$	−11.5219			−0.812692
$202$	1.24559	+	1.24559i	0.0876396	+	0.0876396i
$203$			0.539003i			0.0378306i
$204$	104.144			7.29152
$205$	6.43949	−	0.948152i	0.449753	−	0.0662218i
$206$	24.2970			1.69285
$207$		−	13.8145i		−	0.960173i
$208$	20.2356	+	20.2356i	1.40309	+	1.40309i
$209$	15.6644			1.08353
$210$		−	8.66556i		−	0.597981i
$211$	−11.3322	+	11.3322i	−0.780138	+	0.780138i	−0.979854	−	0.199715i	$-0.935998\pi$
$211$	−11.3322	+	11.3322i	−0.780138	+	0.780138i	0.199715	+	0.979854i	$0.435998\pi$
$212$	−40.3336	−	40.3336i	−2.77012	−	2.77012i
$213$		−	16.2231i		−	1.11159i
$214$			20.3125i			1.38854i
$215$	−9.59802			−0.654579
$216$	−78.8281	−	78.8281i	−5.36357	−	5.36357i
$217$	−2.52795	−	2.52795i	−0.171609	−	0.171609i
$218$	−16.7838	−	16.7838i	−1.13674	−	1.13674i
$219$	13.8999	−	13.8999i	0.939269	−	0.939269i
$220$	−14.8809	+	14.8809i	−1.00327	+	1.00327i
$221$	13.7413			0.924339
$222$	38.2988	−	38.2988i	2.57045	−	2.57045i
$223$	−11.2677			−0.754541			−0.377271	−	0.926103i	$-0.623137\pi$
$223$	−11.2677			−0.754541			−0.377271	+	0.926103i	$0.623137\pi$
$224$	−12.4765	+	12.4765i	−0.833619	+	0.833619i
$225$			27.8678i			1.85785i
$226$			12.3483i			0.821396i
$227$	8.59572	−	8.59572i	0.570518	−	0.570518i	−0.361755	−	0.932273i	$-0.617822\pi$
$227$	8.59572	−	8.59572i	0.570518	−	0.570518i	0.932273	+	0.361755i	$0.117822\pi$
$228$	65.9978			4.37081
$229$	7.61989	−	7.61989i	0.503536	−	0.503536i	−0.408999	−	0.912535i	$-0.634122\pi$
$229$	7.61989	−	7.61989i	0.503536	−	0.503536i	0.912535	+	0.408999i	$0.134122\pi$
$230$	−5.38151			−0.354846
$231$	8.83121	−	8.83121i	0.581051	−	0.581051i
$232$	3.33353	−	3.33353i	0.218857	−	0.218857i
$233$	11.7676	+	11.7676i	0.770918	+	0.770918i	0.978267	−	0.207349i	$-0.0664836\pi$
$233$	11.7676	+	11.7676i	0.770918	+	0.770918i	−0.207349	+	0.978267i	$0.566484\pi$
$234$	−29.3278	−	29.3278i	−1.91722	−	1.91722i
$235$	6.24017	+	6.24017i	0.407064	+	0.407064i
$236$	−11.2557			−0.732685
$237$			34.1754i			2.21993i
$238$			16.8719i			1.09364i
$239$	19.7945	+	19.7945i	1.28040	+	1.28040i	0.940442	+	0.339955i	$0.110412\pi$
$239$	19.7945	+	19.7945i	1.28040	+	1.28040i	0.339955	+	0.940442i	$0.389588\pi$
$240$	−29.7024	+	29.7024i	−1.91728	+	1.91728i
$241$			14.9523i			0.963159i	0.876402	+	0.481580i	$0.159937\pi$
$241$			14.9523i			0.963159i	−0.876402	+	0.481580i	$0.840063\pi$
$242$	−12.2728			−0.788924
$243$	16.1299	+	16.1299i	1.03473	+	1.03473i
$244$		−	3.30666i		−	0.211687i
$245$	1.01652			0.0649432
$246$	43.8081	+	32.5631i	2.79310	+	2.07615i
$247$	8.70810			0.554083
$248$			31.2689i			1.98557i
$249$	−13.8535	−	13.8535i	−0.877928	−	0.877928i
$250$	24.5401			1.55205
$251$			20.1867i			1.27417i	0.770794	+	0.637085i	$0.219860\pi$
$251$			20.1867i			1.27417i	−0.770794	+	0.637085i	$0.780140\pi$
$252$	26.0739	−	26.0739i	1.64250	−	1.64250i
$253$	−5.48438	−	5.48438i	−0.344800	−	0.344800i
$254$			8.05579i			0.505465i
$255$			20.1699i			1.26309i
$256$	17.3264			1.08290
$257$	−5.44906	−	5.44906i	−0.339903	−	0.339903i	0.516428	−	0.856331i	$-0.327261\pi$
$257$	−5.44906	−	5.44906i	−0.339903	−	0.339903i	−0.856331	+	0.516428i	$0.827261\pi$
$258$	−56.9154	−	56.9154i	−3.54340	−	3.54340i
$259$	4.49267	+	4.49267i	0.279161	+	0.279161i
$260$	−8.27256	+	8.27256i	−0.513042	+	0.513042i
$261$	−2.67763	+	2.67763i	−0.165741	+	0.165741i
$262$	−10.2877			−0.635575
$263$	−10.4559	+	10.4559i	−0.644737	+	0.644737i	−0.951716	−	0.306979i	$-0.900682\pi$
$263$	−10.4559	+	10.4559i	−0.644737	+	0.644737i	0.306979	+	0.951716i	$0.400682\pi$
$264$	−109.235			−6.72297
$265$	7.81155	−	7.81155i	0.479860	−	0.479860i
$266$			10.6920i			0.655569i
$267$			21.4691i			1.31389i
$268$	−13.5052	+	13.5052i	−0.824964	+	0.824964i
$269$	−15.8085			−0.963859			−0.481930	−	0.876210i	$-0.660064\pi$
$269$	−15.8085			−0.963859			−0.481930	+	0.876210i	$0.660064\pi$
$270$	24.6659	−	24.6659i	1.50112	−	1.50112i
$271$	−24.7062			−1.50079			−0.750396	−	0.660988i	$-0.770137\pi$
$271$	−24.7062			−1.50079			−0.750396	+	0.660988i	$0.770137\pi$
$272$	57.8307	−	57.8307i	3.50650	−	3.50650i
$273$	4.90941	−	4.90941i	0.297131	−	0.297131i
$274$	−38.6678	−	38.6678i	−2.33601	−	2.33601i
$275$	11.0636	+	11.0636i	0.667159	+	0.667159i
$276$	−23.1070	−	23.1070i	−1.39088	−	1.39088i
$277$	26.6313			1.60012			0.800059	−	0.599921i	$-0.204801\pi$
$277$	26.6313			1.60012			0.800059	+	0.599921i	$0.204801\pi$
$278$		−	8.30549i		−	0.498130i
$279$		−	25.1165i		−	1.50369i
$280$	−6.28680	−	6.28680i	−0.375708	−	0.375708i
$281$	18.8891	−	18.8891i	1.12683	−	1.12683i	0.136142	−	0.990689i	$-0.456530\pi$
$281$	18.8891	−	18.8891i	1.12683	−	1.12683i	0.990689	−	0.136142i	$-0.0434704\pi$
$282$			74.0074i			4.40708i
$283$	18.3227			1.08917			0.544587	−	0.838705i	$-0.316687\pi$
$283$	18.3227			1.08917			0.544587	+	0.838705i	$0.316687\pi$
$284$	−19.0157	−	19.0157i	−1.12838	−	1.12838i
$285$			12.7820i			0.757143i
$286$	−23.2864			−1.37696
$287$	−3.81985	+	5.13894i	−0.225479	+	0.303342i
$288$	−123.960			−7.30441
$289$		−	22.2708i		−	1.31005i
$290$	1.04309	+	1.04309i	0.0612522	+	0.0612522i
$291$	−43.4619			−2.54778
$292$		−	32.5852i		−	1.90691i
$293$	−14.3442	+	14.3442i	−0.837997	+	0.837997i	−0.988595	−	0.150598i	$-0.951880\pi$
$293$	−14.3442	+	14.3442i	−0.837997	+	0.837997i	0.150598	+	0.988595i	$0.451880\pi$
$294$	6.02789	+	6.02789i	0.351554	+	0.351554i
$295$		−	2.17994i		−	0.126921i
$296$		−	55.5709i		−	3.22999i
$297$	50.2749			2.91724
$298$	−1.92181	−	1.92181i	−0.111328	−	0.111328i
$299$	−3.04886	−	3.04886i	−0.176320	−	0.176320i
$300$	46.6134	+	46.6134i	2.69122	+	2.69122i
$301$	6.67652	−	6.67652i	0.384828	−	0.384828i
$302$	11.5315	−	11.5315i	0.663565	−	0.663565i
$303$	−2.07165			−0.119013
$304$	36.6484	−	36.6484i	2.10193	−	2.10193i
$305$	0.640413			0.0366700
$306$	−83.8152	+	83.8152i	−4.79140	+	4.79140i
$307$		−	2.93586i		−	0.167558i	−0.996484	−	0.0837791i	$-0.973301\pi$
$307$		−	2.93586i		−	0.167558i	0.996484	−	0.0837791i	$-0.0266990\pi$
$308$		−	20.7028i		−	1.17965i
$309$	−20.2051	+	20.2051i	−1.14943	+	1.14943i
$310$	−9.78427			−0.555709
$311$	−7.91164	+	7.91164i	−0.448628	+	0.448628i	−0.894898	−	0.446270i	$-0.852752\pi$
$311$	−7.91164	+	7.91164i	−0.448628	+	0.448628i	0.446270	+	0.894898i	$0.352752\pi$
$312$	−60.7257			−3.43791
$313$	9.61467	−	9.61467i	0.543453	−	0.543453i	−0.381086	−	0.924540i	$-0.624450\pi$
$313$	9.61467	−	9.61467i	0.543453	−	0.543453i	0.924540	+	0.381086i	$0.124450\pi$
$314$	−22.8687	+	22.8687i	−1.29056	+	1.29056i
$315$	5.04983	+	5.04983i	0.284526	+	0.284526i
$316$	40.0583	+	40.0583i	2.25345	+	2.25345i
$317$	−2.95221	−	2.95221i	−0.165812	−	0.165812i	0.619323	−	0.785136i	$-0.287407\pi$
$317$	−2.95221	−	2.95221i	−0.165812	−	0.165812i	−0.785136	+	0.619323i	$0.787407\pi$
$318$	92.6437			5.19520
$319$			2.12605i			0.119036i
$320$			21.7564i			1.21622i
$321$	−16.8917	−	16.8917i	−0.942802	−	0.942802i
$322$	3.74346	−	3.74346i	0.208615	−	0.208615i
$323$		−	24.8866i		−	1.38473i
$324$	101.197			5.62208
$325$	6.15042	+	6.15042i	0.341164	+	0.341164i
$326$			13.9722i			0.773851i
$327$	27.9144			1.54367
$328$	55.4067	−	8.15810i	3.05932	−	0.450456i
$329$	−8.68151			−0.478627
$330$		−	34.1806i		−	1.88158i
$331$	−6.86341	−	6.86341i	−0.377247	−	0.377247i	0.492861	−	0.870108i	$-0.335951\pi$
$331$	−6.86341	−	6.86341i	−0.377247	−	0.377247i	−0.870108	+	0.492861i	$0.835951\pi$
$332$	−32.4763			−1.78237
$333$			44.6370i			2.44609i
$334$	34.0376	−	34.0376i	1.86245	−	1.86245i
$335$	−2.61561	−	2.61561i	−0.142906	−	0.142906i
$336$		−	41.3229i		−	2.25435i
$337$		−	2.93409i		−	0.159830i	−0.996802	−	0.0799150i	$-0.974535\pi$
$337$		−	2.93409i		−	0.159830i	0.996802	−	0.0799150i	$-0.0254649\pi$
$338$	22.0549			1.19963
$339$	−10.2687	−	10.2687i	−0.557720	−	0.557720i
$340$	23.6419	+	23.6419i	1.28216	+	1.28216i
$341$	−9.97130	−	9.97130i	−0.539976	−	0.539976i
$342$	−53.1152	+	53.1152i	−2.87214	+	2.87214i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−82.5834			−4.45260
$345$	4.47521	−	4.47521i	0.240937	−	0.240937i
$346$	20.1602			1.08382
$347$	12.0780	−	12.0780i	0.648382	−	0.648382i	−0.304220	−	0.952602i	$-0.598396\pi$
$347$	12.0780	−	12.0780i	0.648382	−	0.648382i	0.952602	+	0.304220i	$0.0983959\pi$
$348$			8.95754i			0.480175i
$349$		−	11.9602i		−	0.640217i	−0.947381	−	0.320109i	$-0.896281\pi$
$349$		−	11.9602i		−	0.640217i	0.947381	−	0.320109i	$-0.103719\pi$
$350$	−7.55163	+	7.55163i	−0.403651	+	0.403651i
$351$	27.9486			1.49179
$352$	−49.2124	+	49.2124i	−2.62303	+	2.62303i
$353$	−25.8611			−1.37645			−0.688225	−	0.725498i	$-0.741610\pi$
$353$	−25.8611			−1.37645			−0.688225	+	0.725498i	$0.741610\pi$
$354$	12.9268	−	12.9268i	0.687054	−	0.687054i
$355$	3.68285	−	3.68285i	0.195465	−	0.195465i
$356$	25.1647	+	25.1647i	1.33373	+	1.33373i
$357$	−14.0305	−	14.0305i	−0.742571	−	0.742571i
$358$	−32.9203	−	32.9203i	−1.73989	−	1.73989i
$359$	−12.5945			−0.664711			−0.332355	−	0.943154i	$-0.607843\pi$
$359$	−12.5945			−0.664711			−0.332355	+	0.943154i	$0.607843\pi$
$360$		−	62.4625i		−	3.29206i
$361$			3.22888i			0.169941i
$362$	−13.9681	−	13.9681i	−0.734147	−	0.734147i
$363$	10.2059	−	10.2059i	0.535672	−	0.535672i
$364$		−	11.5090i		−	0.603236i
$365$	6.31090			0.330328
$366$	3.79760	+	3.79760i	0.198504	+	0.198504i
$367$		−	6.86951i		−	0.358585i	−0.983796	−	0.179293i	$-0.942619\pi$
$367$		−	6.86951i		−	0.358585i	0.983796	−	0.179293i	$-0.0573809\pi$
$368$	−25.6625			−1.33775
$369$	−44.5051	+	6.55294i	−2.31684	+	0.341132i
$370$	17.3886			0.903990
$371$			10.8677i			0.564221i
$372$	−42.0114	−	42.0114i	−2.17819	−	2.17819i
$373$	−6.61957			−0.342748			−0.171374	−	0.985206i	$-0.554821\pi$
$373$	−6.61957			−0.342748			−0.171374	+	0.985206i	$0.554821\pi$
$374$			66.5497i			3.44120i
$375$	−20.4073	+	20.4073i	−1.05383	+	1.05383i
$376$	53.6918	+	53.6918i	2.76894	+	2.76894i
$377$			1.18191i			0.0608713i
$378$			34.3159i			1.76502i
$379$	15.3080			0.786319			0.393160	−	0.919470i	$-0.371382\pi$
$379$	15.3080			0.786319			0.393160	+	0.919470i	$0.371382\pi$
$380$	14.9823	+	14.9823i	0.768576	+	0.768576i
$381$	−6.69911	−	6.69911i	−0.343206	−	0.343206i
$382$	−47.1147	−	47.1147i	−2.41060	−	2.41060i
$383$	−12.5601	+	12.5601i	−0.641791	+	0.641791i	−0.950995	−	0.309205i	$-0.899937\pi$
$383$	−12.5601	+	12.5601i	−0.641791	+	0.641791i	0.309205	+	0.950995i	$0.399937\pi$
$384$	−50.0051	+	50.0051i	−2.55181	+	2.55181i
$385$	4.00959			0.204347
$386$	38.6703	−	38.6703i	1.96827	−	1.96827i
$387$	66.3346			3.37198
$388$	−50.9433	+	50.9433i	−2.58626	+	2.58626i
$389$			19.0858i			0.967689i	0.875154	+	0.483845i	$0.160760\pi$
$389$			19.0858i			0.967689i	−0.875154	+	0.483845i	$0.839240\pi$
$390$		−	19.0016i		−	0.962181i
$391$	−8.71325	+	8.71325i	−0.440648	+	0.440648i
$392$	8.74637			0.441758
$393$	8.55514	−	8.55514i	0.431550	−	0.431550i
$394$	28.8170			1.45178
$395$	−7.75824	+	7.75824i	−0.390359	+	0.390359i
$396$	102.846	−	102.846i	5.16822	−	5.16822i
$397$	−17.4302	−	17.4302i	−0.874798	−	0.874798i	0.118193	−	0.992991i	$-0.462290\pi$
$397$	−17.4302	−	17.4302i	−0.874798	−	0.874798i	−0.992991	+	0.118193i	$0.962290\pi$
$398$	30.7571	+	30.7571i	1.54172	+	1.54172i
$399$	−8.89137	−	8.89137i	−0.445125	−	0.445125i
$400$	51.7685			2.58843
$401$		−	8.75452i		−	0.437180i	−0.975817	−	0.218590i	$-0.929854\pi$
$401$		−	8.75452i		−	0.437180i	0.975817	−	0.218590i	$-0.0701457\pi$
$402$		−	31.0207i		−	1.54717i
$403$	−5.54321	−	5.54321i	−0.276127	−	0.276127i
$404$	−2.42825	+	2.42825i	−0.120810	+	0.120810i
$405$			19.5993i			0.973897i
$406$	−1.45117			−0.0720205
$407$	17.7210	+	17.7210i	0.878396	+	0.878396i
$408$			173.546i			8.59182i
$409$	−37.1176			−1.83534			−0.917672	−	0.397338i	$-0.869934\pi$
$409$	−37.1176			−1.83534			−0.917672	+	0.397338i	$0.869934\pi$
$410$	2.55273	+	17.3372i	0.126071	+	0.856223i
$411$	64.3116			3.17226
$412$			47.3664i			2.33358i
$413$	1.51640	+	1.51640i	0.0746169	+	0.0746169i
$414$	37.1931			1.82794
$415$		−	6.28981i		−	0.308755i
$416$	−27.3580	+	27.3580i	−1.34133	+	1.34133i
$417$	6.90676	+	6.90676i	0.338226	+	0.338226i
$418$			42.1737i			2.06278i
$419$		−	8.16398i		−	0.398836i	−0.979914	−	0.199418i	$-0.936095\pi$
$419$		−	8.16398i		−	0.398836i	0.979914	−	0.199418i	$-0.0639052\pi$
$420$	16.8933			0.824309
$421$	−10.0831	−	10.0831i	−0.491419	−	0.491419i	0.417334	−	0.908753i	$-0.362965\pi$
$421$	−10.0831	−	10.0831i	−0.491419	−	0.491419i	−0.908753	+	0.417334i	$0.862965\pi$
$422$	−30.5099	−	30.5099i	−1.48520	−	1.48520i
$423$	−43.1276	−	43.1276i	−2.09693	−	2.09693i
$424$	67.2123	−	67.2123i	3.26412	−	3.26412i
$425$	17.5771	−	17.5771i	0.852616	−	0.852616i
$426$	43.6779			2.11620
$427$	−0.445480	+	0.445480i	−0.0215583	+	0.0215583i
$428$	−39.5988			−1.91408
$429$	19.3648	−	19.3648i	0.934940	−	0.934940i
$430$		−	25.8410i		−	1.24616i
$431$		−	28.6671i		−	1.38085i	−0.723406	−	0.690423i	$-0.757425\pi$
$431$		−	28.6671i		−	1.38085i	0.723406	−	0.690423i	$-0.242575\pi$
$432$	117.623	−	117.623i	5.65913	−	5.65913i
$433$	−7.13095			−0.342692			−0.171346	−	0.985211i	$-0.554812\pi$
$433$	−7.13095			−0.342692			−0.171346	+	0.985211i	$0.554812\pi$
$434$	6.80608	−	6.80608i	0.326702	−	0.326702i
$435$	−1.73484			−0.0831793
$436$	32.7195	−	32.7195i	1.56698	−	1.56698i
$437$	−5.52174	+	5.52174i	−0.264141	+	0.264141i
$438$	37.4231	+	37.4231i	1.78815	+	1.78815i
$439$	6.94092	+	6.94092i	0.331272	+	0.331272i	0.853069	−	0.521797i	$-0.174738\pi$
$439$	6.94092	+	6.94092i	0.331272	+	0.331272i	−0.521797	+	0.853069i	$0.674738\pi$
$440$	−24.7977	−	24.7977i	−1.18219	−	1.18219i
$441$	−7.02546			−0.334546
$442$			36.9961i			1.75972i
$443$		−	16.7018i		−	0.793527i	−0.917921	−	0.396763i	$-0.870133\pi$
$443$		−	16.7018i		−	0.793527i	0.917921	−	0.396763i	$-0.129867\pi$
$444$	74.6625	+	74.6625i	3.54333	+	3.54333i
$445$	−4.87374	+	4.87374i	−0.231037	+	0.231037i
$446$		−	30.3363i		−	1.43647i
$447$	3.19632			0.151181
$448$	−15.1341	−	15.1341i	−0.715017	−	0.715017i
$449$		−	17.9810i		−	0.848576i	−0.905527	−	0.424288i	$-0.860524\pi$
$449$		−	17.9810i		−	0.848576i	0.905527	−	0.424288i	$-0.139476\pi$
$450$	−75.0292			−3.53691
$451$	−15.0671	+	20.2701i	−0.709481	+	0.954484i
$452$	−24.0727			−1.13228
$453$			19.1790i			0.901109i
$454$	23.1425	+	23.1425i	1.08613	+	1.08613i
$455$	2.22899			0.104497
$456$			109.979i			5.15026i
$457$	−13.8232	+	13.8232i	−0.646623	+	0.646623i	−0.952175	−	0.305552i	$-0.901159\pi$
$457$	−13.8232	+	13.8232i	−0.646623	+	0.646623i	0.305552	+	0.952175i	$0.401159\pi$
$458$	20.5152	+	20.5152i	0.958614	+	0.958614i
$459$		−	79.8736i		−	3.72818i
$460$		−	10.4911i		−	0.489151i
$461$	2.31221			0.107691			0.0538453	−	0.998549i	$-0.482852\pi$
$461$	2.31221			0.107691			0.0538453	+	0.998549i	$0.482852\pi$
$462$	23.7765	+	23.7765i	1.10618	+	1.10618i
$463$	2.27339	+	2.27339i	0.105653	+	0.105653i	0.757957	−	0.652304i	$-0.226197\pi$
$463$	2.27339	+	2.27339i	0.105653	+	0.105653i	−0.652304	+	0.757957i	$0.726197\pi$
$464$	4.97410	+	4.97410i	0.230917	+	0.230917i
$465$	8.13651	−	8.13651i	0.377321	−	0.377321i
$466$	−31.6821	+	31.6821i	−1.46765	+	1.46765i
$467$	31.2538			1.44625			0.723127	−	0.690715i	$-0.242704\pi$
$467$	31.2538			1.44625			0.723127	+	0.690715i	$0.242704\pi$
$468$	57.1739	−	57.1739i	2.64287	−	2.64287i
$469$	3.63891			0.168029
$470$	−16.8006	+	16.8006i	−0.774954	+	0.774954i
$471$		−	38.0348i		−	1.75255i
$472$		−	18.7566i		−	0.863345i
$473$	26.3350	−	26.3350i	1.21088	−	1.21088i
$474$	−92.0114			−4.22622
$475$	11.1389	−	11.1389i	0.511090	−	0.511090i
$476$	−32.8913			−1.50757
$477$	−53.9878	+	53.9878i	−2.47193	+	2.47193i
$478$	−53.2932	+	53.2932i	−2.43757	+	2.43757i
$479$	16.5281	+	16.5281i	0.755189	+	0.755189i	0.975443	−	0.220254i	$-0.0706885\pi$
$479$	16.5281	+	16.5281i	0.755189	+	0.755189i	−0.220254	+	0.975443i	$0.570688\pi$
$480$	−40.1569	−	40.1569i	−1.83290	−	1.83290i
$481$	9.85138	+	9.85138i	0.449184	+	0.449184i
$482$	−40.2564			−1.83363
$483$			6.22604i			0.283295i
$484$		−	23.9255i		−	1.08752i
$485$	−9.86639	−	9.86639i	−0.448010	−	0.448010i
$486$	−43.4270	+	43.4270i	−1.96989	+	1.96989i
$487$		−	7.66021i		−	0.347117i	−0.984824	−	0.173559i	$-0.944473\pi$
$487$		−	7.66021i		−	0.347117i	0.984824	−	0.173559i	$-0.0555266\pi$
$488$	5.51025			0.249437
$489$	−11.6192	−	11.6192i	−0.525437	−	0.525437i
$490$			2.73681i			0.123636i
$491$	−38.0052			−1.71515			−0.857574	−	0.514360i	$-0.828030\pi$
$491$	−38.0052			−1.71515			−0.857574	+	0.514360i	$0.828030\pi$
$492$	−63.4811	+	85.4028i	−2.86195	+	3.85025i
$493$	3.37774			0.152126
$494$			23.4451i			1.05484i
$495$	19.9186	+	19.9186i	0.895276	+	0.895276i
$496$	−46.6576			−2.09499
$497$			5.12368i			0.229828i
$498$	37.2981	−	37.2981i	1.67137	−	1.67137i
$499$	25.2471	+	25.2471i	1.13021	+	1.13021i	0.990141	+	0.140072i	$0.0447335\pi$
$499$	25.2471	+	25.2471i	1.13021	+	1.13021i	0.140072	+	0.990141i	$0.455267\pi$
$500$			47.8403i			2.13948i
$501$			56.6106i			2.52917i
$502$	−54.3491			−2.42572
$503$	−15.4355	−	15.4355i	−0.688237	−	0.688237i	0.273605	−	0.961842i	$-0.411784\pi$
$503$	−15.4355	−	15.4355i	−0.688237	−	0.688237i	−0.961842	+	0.273605i	$0.911784\pi$
$504$	43.4498	+	43.4498i	1.93541	+	1.93541i
$505$	−0.470289	−	0.470289i	−0.0209276	−	0.0209276i
$506$	14.7658	−	14.7658i	0.656418	−	0.656418i
$507$	−18.3407	+	18.3407i	−0.814538	+	0.814538i
$508$	−15.7046			−0.696777
$509$	6.38995	−	6.38995i	0.283229	−	0.283229i	−0.551166	−	0.834396i	$-0.685817\pi$
$509$	6.38995	−	6.38995i	0.283229	−	0.283229i	0.834396	+	0.551166i	$0.185817\pi$
$510$	−54.3040			−2.40462
$511$	−4.38995	+	4.38995i	−0.194200	+	0.194200i
$512$			1.97912i			0.0874654i
$513$		−	50.6173i		−	2.23481i
$514$	14.6706	−	14.6706i	0.647095	−	0.647095i
$515$	−9.17364			−0.404239
$516$	110.955	−	110.955i	4.88453	−	4.88453i
$517$	−34.2435			−1.50603
$518$	−12.0957	+	12.0957i	−0.531457	+	0.531457i
$519$	−16.7650	+	16.7650i	−0.735902	+	0.735902i
$520$	−13.7855	−	13.7855i	−0.604533	−	0.604533i
$521$	12.2603	+	12.2603i	0.537133	+	0.537133i	0.922686	−	0.385553i	$-0.125989\pi$
$521$	12.2603	+	12.2603i	0.537133	+	0.537133i	−0.385553	+	0.922686i	$0.625989\pi$
$522$	−7.20906	−	7.20906i	−0.315532	−	0.315532i
$523$	−34.1912			−1.49508			−0.747538	−	0.664219i	$-0.768764\pi$
$523$	−34.1912			−1.49508			−0.747538	+	0.664219i	$0.768764\pi$
$524$		−	20.0556i		−	0.876133i
$525$		−	12.5597i		−	0.548151i
$526$	−28.1506	−	28.1506i	−1.22743	−	1.22743i
$527$	−15.8418	+	15.8418i	−0.690079	+	0.690079i
$528$		−	162.995i		−	7.09343i
$529$	−19.1335			−0.831891
$530$	21.0313	+	21.0313i	0.913540	+	0.913540i
$531$			15.0662i			0.653815i
$532$	−20.8438			−0.903693
$533$	−8.37604	+	11.2685i	−0.362806	+	0.488093i
$534$	−57.8017			−2.50133
$535$		−	7.66924i		−	0.331570i
$536$	−22.5053	−	22.5053i	−0.972080	−	0.972080i
$537$	54.7524			2.36274
$538$		−	42.5616i		−	1.83496i
$539$	−2.78912	+	2.78912i	−0.120136	+	0.120136i
$540$	48.0856	+	48.0856i	2.06928	+	2.06928i
$541$		−	0.264263i		−	0.0113616i	−0.999984	−	0.00568079i	$-0.998192\pi$
$541$		−	0.264263i		−	0.0113616i	0.999984	−	0.00568079i	$-0.00180826\pi$
$542$		−	66.5171i		−	2.85715i
$543$	23.2315			0.996958
$544$	78.1856	+	78.1856i	3.35218	+	3.35218i
$545$	6.33691	+	6.33691i	0.271444	+	0.271444i
$546$	13.2177	+	13.2177i	0.565667	+	0.565667i
$547$	−15.0527	+	15.0527i	−0.643605	+	0.643605i	−0.951440	−	0.307835i	$-0.900396\pi$
$547$	−15.0527	+	15.0527i	−0.643605	+	0.643605i	0.307835	+	0.951440i	$0.400396\pi$
$548$	75.3820	−	75.3820i	3.22016	−	3.22016i
$549$	−4.42607			−0.188900
$550$	−29.7868	+	29.7868i	−1.27011	+	1.27011i
$551$	2.14053			0.0911898
$552$	38.5057	−	38.5057i	1.63891	−	1.63891i
$553$		−	10.7935i		−	0.458985i
$554$			71.7001i			3.04625i
$555$	−14.4602	+	14.4602i	−0.613800	+	0.613800i
$556$	16.1913			0.686666
$557$	−17.2011	+	17.2011i	−0.728836	+	0.728836i	−0.970388	−	0.241552i	$-0.922343\pi$
$557$	−17.2011	+	17.2011i	−0.728836	+	0.728836i	0.241552	+	0.970388i	$0.422343\pi$
$558$	67.6218			2.86266
$559$	14.6400	−	14.6400i	0.619208	−	0.619208i
$560$	9.38080	−	9.38080i	0.396411	−	0.396411i
$561$	−55.3420	−	55.3420i	−2.33654	−	2.33654i
$562$	50.8557	+	50.8557i	2.14522	+	2.14522i
$563$	−17.9514	−	17.9514i	−0.756560	−	0.756560i	0.219135	−	0.975695i	$-0.429677\pi$
$563$	−17.9514	−	17.9514i	−0.756560	−	0.756560i	−0.975695	+	0.219135i	$0.929677\pi$
$564$	−144.276			−6.07510
$565$		−	4.66225i		−	0.196142i
$566$			49.3308i			2.07353i
$567$	−13.6335	−	13.6335i	−0.572555	−	0.572555i
$568$	31.6880	−	31.6880i	1.32960	−	1.32960i
$569$			8.00394i			0.335543i	0.985826	+	0.167771i	$0.0536571\pi$
$569$			8.00394i			0.335543i	−0.985826	+	0.167771i	$0.946343\pi$
$570$	−34.4134			−1.44142
$571$	32.0491	+	32.0491i	1.34121	+	1.34121i	0.894856	+	0.446355i	$0.147278\pi$
$571$	32.0491	+	32.0491i	1.34121	+	1.34121i	0.446355	+	0.894856i	$0.352722\pi$
$572$		−	45.3964i		−	1.89812i
$573$	78.3603			3.27355
$574$	−13.8357	−	10.2843i	−0.577492	−	0.429258i
$575$	−7.79987			−0.325277
$576$		−	150.365i		−	6.26519i
$577$	15.0182	+	15.0182i	0.625215	+	0.625215i	0.946860	−	0.321646i	$-0.104236\pi$
$577$	15.0182	+	15.0182i	0.625215	+	0.625215i	−0.321646	+	0.946860i	$0.604236\pi$
$578$	59.9604			2.49402
$579$			64.3156i			2.67287i
$580$	−2.03347	+	2.03347i	−0.0844354	+	0.0844354i
$581$	4.37528	+	4.37528i	0.181517	+	0.181517i
$582$		−	117.014i		−	4.85037i
$583$			42.8666i			1.77535i
$584$	54.3003			2.24696
$585$	11.0731	+	11.0731i	0.457816	+	0.457816i
$586$	−38.6193	−	38.6193i	−1.59535	−	1.59535i
$587$	12.3957	+	12.3957i	0.511626	+	0.511626i	0.915024	−	0.403398i	$-0.132171\pi$
$587$	12.3957	+	12.3957i	0.511626	+	0.511626i	−0.403398	+	0.915024i	$0.632171\pi$
$588$	−11.7512	+	11.7512i	−0.484612	+	0.484612i
$589$	−10.0392	+	10.0392i	−0.413659	+	0.413659i
$590$	5.86911			0.241627
$591$	−23.9639	+	23.9639i	−0.985744	+	0.985744i
$592$	82.9198			3.40798
$593$	−27.6396	+	27.6396i	−1.13502	+	1.13502i	−0.145695	+	0.989330i	$0.546542\pi$
$593$	−27.6396	+	27.6396i	−1.13502	+	1.13502i	−0.989330	+	0.145695i	$0.953458\pi$
$594$			135.356i			5.55374i
$595$		−	6.37018i		−	0.261152i
$596$	3.74653	−	3.74653i	0.153464	−	0.153464i
$597$	−51.1547			−2.09362
$598$	8.20853	−	8.20853i	0.335672	−	0.335672i
$599$	32.0430			1.30924			0.654622	−	0.755957i	$-0.272828\pi$
$599$	32.0430			1.30924			0.654622	+	0.755957i	$0.272828\pi$
$600$	−77.6770	+	77.6770i	−3.17115	+	3.17115i
$601$	1.95235	−	1.95235i	0.0796379	−	0.0796379i	−0.666166	−	0.745804i	$-0.732066\pi$
$601$	1.95235	−	1.95235i	0.0796379	−	0.0796379i	0.745804	+	0.666166i	$0.232066\pi$
$602$	17.9754	+	17.9754i	0.732621	+	0.732621i
$603$	18.0772	+	18.0772i	0.736162	+	0.736162i
$604$	22.4804	+	22.4804i	0.914717	+	0.914717i
$605$	4.63374			0.188388
$606$		−	5.57755i		−	0.226572i
$607$		−	33.4167i		−	1.35634i	−0.734905	−	0.678170i	$-0.762773\pi$
$607$		−	33.4167i		−	1.35634i	0.734905	−	0.678170i	$-0.237227\pi$
$608$	49.5476	+	49.5476i	2.00942	+	2.00942i
$609$	1.20678	−	1.20678i	0.0489012	−	0.0489012i
$610$			1.72420i			0.0698109i
$611$	−19.0365			−0.770135
$612$	−163.396	−	163.396i	−6.60488	−	6.60488i
$613$		−	36.7049i		−	1.48250i	−0.671231	−	0.741249i	$-0.734234\pi$
$613$		−	36.7049i		−	1.48250i	0.671231	−	0.741249i	$-0.265766\pi$
$614$	7.90429			0.318991
$615$	−16.5403	−	12.2946i	−0.666968	−	0.495767i
$616$	34.4993			1.39002
$617$		−	12.4425i		−	0.500917i	−0.968127	−	0.250459i	$-0.919419\pi$
$617$		−	12.4425i		−	0.500917i	0.968127	−	0.250459i	$-0.0805814\pi$
$618$	−54.3989	−	54.3989i	−2.18824	−	2.18824i
$619$	−19.7926			−0.795533			−0.397767	−	0.917487i	$-0.630215\pi$
$619$	−19.7926			−0.795533			−0.397767	+	0.917487i	$0.630215\pi$
$620$		−	19.0742i		−	0.766039i
$621$	−17.7220	+	17.7220i	−0.711160	+	0.711160i
$622$	−21.3007	−	21.3007i	−0.854081	−	0.854081i
$623$		−	6.78049i		−	0.271654i
$624$		−	90.6114i		−	3.62736i
$625$	10.5680			0.422720
$626$	25.8859	+	25.8859i	1.03461	+	1.03461i
$627$	−35.0713	−	35.0713i	−1.40061	−	1.40061i
$628$	−44.5820	−	44.5820i	−1.77901	−	1.77901i
$629$	28.1540	−	28.1540i	1.12257	−	1.12257i
$630$	−13.5958	+	13.5958i	−0.541669	+	0.541669i
$631$	24.3578			0.969670			0.484835	−	0.874606i	$-0.338880\pi$
$631$	24.3578			0.969670			0.484835	+	0.874606i	$0.338880\pi$
$632$	−66.7535	+	66.7535i	−2.65531	+	2.65531i
$633$	50.7435			2.01687
$634$	7.94831	−	7.94831i	0.315668	−	0.315668i
$635$		−	3.04156i		−	0.120701i
$636$			180.607i			7.16152i
$637$	−1.55052	+	1.55052i	−0.0614338	+	0.0614338i
$638$	−5.72403			−0.226616
$639$	−25.4532	+	25.4532i	−1.00691	+	1.00691i
$640$	−22.7036			−0.897437
$641$	2.81444	−	2.81444i	0.111164	−	0.111164i	−0.649337	−	0.760501i	$-0.724954\pi$
$641$	2.81444	−	2.81444i	0.111164	−	0.111164i	0.760501	+	0.649337i	$0.224954\pi$
$642$	45.4780	−	45.4780i	1.79487	−	1.79487i
$643$	0.541371	+	0.541371i	0.0213496	+	0.0213496i	0.717701	−	0.696351i	$-0.245194\pi$
$643$	0.541371	+	0.541371i	0.0213496	+	0.0213496i	−0.696351	+	0.717701i	$0.745194\pi$
$644$	7.29778	+	7.29778i	0.287573	+	0.287573i
$645$	21.4891	+	21.4891i	0.846134	+	0.846134i
$646$	67.0030			2.63620
$647$			19.8068i			0.778686i	0.921093	+	0.389343i	$0.127298\pi$
$647$			19.8068i			0.778686i	−0.921093	+	0.389343i	$0.872702\pi$
$648$			168.637i			6.62467i
$649$	5.98130	+	5.98130i	0.234786	+	0.234786i
$650$	−16.5590	+	16.5590i	−0.649496	+	0.649496i
$651$			11.3197i			0.443655i
$652$	−27.2386			−1.06674
$653$	−4.85404	−	4.85404i	−0.189953	−	0.189953i	0.605723	−	0.795676i	$-0.292884\pi$
$653$	−4.85404	−	4.85404i	−0.189953	−	0.189953i	−0.795676	+	0.605723i	$0.792884\pi$
$654$			75.1547i			2.93878i
$655$	3.88424			0.151770
$656$	12.1731	+	82.6747i	0.475278	+	3.22791i
$657$	−43.6164			−1.70164
$658$		−	23.3735i		−	0.911192i
$659$	−10.4059	−	10.4059i	−0.405357	−	0.405357i	0.474759	−	0.880116i	$-0.342535\pi$
$659$	−10.4059	−	10.4059i	−0.405357	−	0.405357i	−0.880116	+	0.474759i	$0.842535\pi$
$660$	66.6342			2.59373
$661$		−	23.0822i		−	0.897792i	−0.893584	−	0.448896i	$-0.851817\pi$
$661$		−	23.0822i		−	0.897792i	0.893584	−	0.448896i	$-0.148183\pi$
$662$	18.4786	−	18.4786i	0.718190	−	0.718190i
$663$	−30.7656	−	30.7656i	−1.19484	−	1.19484i
$664$		−	54.1189i		−	2.10022i
$665$		−	4.03690i		−	0.156544i
$666$	−120.177			−4.65678
$667$	−0.749438	−	0.749438i	−0.0290184	−	0.0290184i
$668$	66.3554	+	66.3554i	2.56737	+	2.56737i
$669$	25.2274	+	25.2274i	0.975348	+	0.975348i
$670$	7.04209	−	7.04209i	0.272060	−	0.272060i
$671$	−1.75716	+	1.75716i	−0.0678344	+	0.0678344i
$672$	55.8674			2.15513
$673$	−10.6938	+	10.6938i	−0.412215	+	0.412215i	−0.882509	−	0.470295i	$-0.844148\pi$
$673$	−10.6938	+	10.6938i	−0.412215	+	0.412215i	0.470295	+	0.882509i	$0.344148\pi$
$674$	7.89953			0.304279
$675$	35.7504	−	35.7504i	1.37603	−	1.37603i
$676$			42.9956i			1.65368i
$677$			20.2794i			0.779401i	0.920942	+	0.389700i	$0.127421\pi$
$677$			20.2794i			0.779401i	−0.920942	+	0.389700i	$0.872579\pi$
$678$	27.6467	−	27.6467i	1.06177	−	1.06177i
$679$	13.7264			0.526771
$680$	−39.3971	+	39.3971i	−1.51081	+	1.51081i
$681$	−38.4901			−1.47495
$682$	26.8460	−	26.8460i	1.02799	−	1.02799i
$683$	−0.0651579	+	0.0651579i	−0.00249320	+	0.00249320i	−0.708352	−	0.705859i	$-0.750561\pi$
$683$	−0.0651579	+	0.0651579i	−0.00249320	+	0.00249320i	0.705859	+	0.708352i	$0.250561\pi$
$684$	−103.547	−	103.547i	−3.95921	−	3.95921i
$685$	14.5995	+	14.5995i	0.557819	+	0.557819i
$686$	−1.90376	−	1.90376i	−0.0726860	−	0.0726860i
$687$	−34.1205			−1.30178
$688$		−	123.226i		−	4.69796i
$689$			23.8302i			0.907859i
$690$	12.0487	+	12.0487i	0.458688	+	0.458688i
$691$	−1.94480	+	1.94480i	−0.0739835	+	0.0739835i	−0.743130	−	0.669147i	$-0.766660\pi$
$691$	−1.94480	+	1.94480i	−0.0739835	+	0.0739835i	0.669147	+	0.743130i	$0.266660\pi$
$692$			39.3018i			1.49403i
$693$	−27.7114			−1.05267
$694$	32.5180	+	32.5180i	1.23436	+	1.23436i
$695$			3.13584i			0.118949i
$696$	−14.9269			−0.565805
$697$	32.2039	+	23.9376i	1.21981	+	0.906703i
$698$	32.2009			1.21882
$699$		−	52.6931i		−	1.99303i
$700$	−14.7217	−	14.7217i	−0.556428	−	0.556428i
$701$	31.0050			1.17104			0.585521	−	0.810657i	$-0.300890\pi$
$701$	31.0050			1.17104			0.585521	+	0.810657i	$0.300890\pi$
$702$			75.2469i			2.84001i
$703$	17.8417	−	17.8417i	0.672912	−	0.672912i
$704$	−59.6950	−	59.6950i	−2.24984	−	2.24984i
$705$		−	27.9424i		−	1.05237i
$706$		−	69.6267i		−	2.62043i
$707$	0.654280			0.0246067
$708$	25.2006	+	25.2006i	0.947095	+	0.947095i
$709$	−21.5066	−	21.5066i	−0.807696	−	0.807696i	0.176588	−	0.984285i	$-0.443494\pi$
$709$	−21.5066	−	21.5066i	−0.807696	−	0.807696i	−0.984285	+	0.176588i	$0.943494\pi$
$710$	9.91543	+	9.91543i	0.372119	+	0.372119i
$711$	53.6193	−	53.6193i	2.01088	−	2.01088i
$712$	−41.9347	+	41.9347i	−1.57157	+	1.57157i
$713$	7.02982			0.263269
$714$	37.7746	−	37.7746i	1.41368	−	1.41368i
$715$	8.79208			0.328805
$716$	64.1773	−	64.1773i	2.39842	−	2.39842i
$717$		−	88.6361i		−	3.31018i
$718$		−	33.9084i		−	1.26545i
$719$	−24.0517	+	24.0517i	−0.896977	+	0.896977i	−0.995168	−	0.0981905i	$-0.968695\pi$
$719$	−24.0517	+	24.0517i	−0.896977	+	0.896977i	0.0981905	+	0.995168i	$0.468695\pi$
$720$	93.2030			3.47347
$721$	6.38131	−	6.38131i	0.237652	−	0.237652i
$722$	−8.69321			−0.323528
$723$	33.4768	−	33.4768i	1.24502	−	1.24502i
$724$	27.2305	−	27.2305i	1.01201	−	1.01201i
$725$	1.51183	+	1.51183i	0.0561480	+	0.0561480i
$726$	27.4777	+	27.4777i	1.01979	+	1.01979i
$727$	24.9094	+	24.9094i	0.923840	+	0.923840i	0.997298	−	0.0734582i	$-0.0234035\pi$
$727$	24.9094	+	24.9094i	0.923840	+	0.923840i	−0.0734582	+	0.997298i	$0.523404\pi$
$728$	19.1787			0.710812
$729$		−	14.3848i		−	0.532769i
$730$			16.9910i			0.628866i
$731$	−41.8394	−	41.8394i	−1.54748	−	1.54748i
$732$	−7.40332	+	7.40332i	−0.273635	+	0.273635i
$733$		−	4.76588i		−	0.176032i	−0.996119	−	0.0880159i	$-0.971947\pi$
$733$		−	4.76588i		−	0.176032i	0.996119	−	0.0880159i	$-0.0280526\pi$
$734$	18.4950			0.682661
$735$	−2.27590	−	2.27590i	−0.0839480	−	0.0839480i
$736$		−	34.6950i		−	1.27887i
$737$	14.3534			0.528714
$738$	−17.6427	−	119.822i	−0.649435	−	4.41072i
$739$	−1.01930			−0.0374957			−0.0187478	−	0.999824i	$-0.505968\pi$
$739$	−1.01930			−0.0374957			−0.0187478	+	0.999824i	$0.505968\pi$
$740$			33.8986i			1.24614i
$741$	−19.4967	−	19.4967i	−0.716229	−	0.716229i
$742$	−29.2593			−1.07414
$743$		−	9.00230i		−	0.330262i	−0.986272	−	0.165131i	$-0.947195\pi$
$743$		−	9.00230i		−	0.330262i	0.986272	−	0.165131i	$-0.0528048\pi$
$744$	70.0082	−	70.0082i	2.56663	−	2.56663i
$745$	0.725604	+	0.725604i	0.0265841	+	0.0265841i
$746$		−	17.8220i		−	0.652511i
$747$			43.4707i			1.59051i
$748$	−129.737			−4.74365
$749$	5.33483	+	5.33483i	0.194931	+	0.194931i
$750$	−54.9432	−	54.9432i	−2.00624	−	2.00624i
$751$	12.4682	+	12.4682i	0.454972	+	0.454972i	0.897001	−	0.442029i	$-0.145741\pi$
$751$	12.4682	+	12.4682i	0.454972	+	0.454972i	−0.442029	+	0.897001i	$0.645741\pi$
$752$	−80.1158	+	80.1158i	−2.92152	+	2.92152i
$753$	45.1962	−	45.1962i	1.64704	−	1.64704i
$754$	−3.18208			−0.115885
$755$	−4.35387	+	4.35387i	−0.158454	+	0.158454i
$756$	−66.8981			−2.43306
$757$	−16.4486	+	16.4486i	−0.597836	+	0.597836i	−0.939736	−	0.341900i	$-0.888930\pi$
$757$	−16.4486	+	16.4486i	−0.597836	+	0.597836i	0.341900	+	0.939736i	$0.388930\pi$
$758$			41.2142i			1.49697i
$759$			24.5581i			0.891403i
$760$	−24.9667	+	24.9667i	−0.905636	+	0.905636i
$761$	0.169966			0.00616125			0.00308063	−	0.999995i	$-0.499019\pi$
$761$	0.169966			0.00616125			0.00308063	+	0.999995i	$0.499019\pi$
$762$	18.0362	−	18.0362i	0.653383	−	0.653383i
$763$	−8.81609			−0.319164
$764$	91.8490	−	91.8490i	3.32298	−	3.32298i
$765$	31.6455	−	31.6455i	1.14414	−	1.14414i
$766$	−33.8159	−	33.8159i	−1.22182	−	1.22182i
$767$	3.32510	+	3.32510i	0.120062	+	0.120062i
$768$	−38.7922	−	38.7922i	−1.39979	−	1.39979i
$769$	46.2561			1.66804			0.834020	−	0.551735i	$-0.186034\pi$
$769$	46.2561			1.66804			0.834020	+	0.551735i	$0.186034\pi$
$770$			10.7951i			0.389029i
$771$			24.3999i			0.878742i
$772$	75.3868	+	75.3868i	2.71323	+	2.71323i
$773$	6.90168	−	6.90168i	0.248236	−	0.248236i	−0.572010	−	0.820246i	$-0.693836\pi$
$773$	6.90168	−	6.90168i	0.248236	−	0.248236i	0.820246	+	0.572010i	$0.193836\pi$
$774$			178.594i			6.41944i
$775$	−14.1812			−0.509402
$776$	−84.8925	−	84.8925i	−3.04746	−	3.04746i
$777$		−	20.1174i		−	0.721708i
$778$	−51.3853			−1.84225
$779$	20.4082	+	15.1697i	0.731200	+	0.543511i
$780$	37.0431			1.32635
$781$			20.2099i			0.723168i
$782$	−23.4589	−	23.4589i	−0.838889	−	0.838889i
$783$	6.87004			0.245515
$784$			13.0508i			0.466101i
$785$	8.63436	−	8.63436i	0.308173	−	0.308173i
$786$	23.0332	+	23.0332i	0.821568	+	0.821568i
$787$		−	15.6573i		−	0.558124i	−0.960273	−	0.279062i	$-0.909977\pi$
$787$		−	15.6573i		−	0.558124i	0.960273	−	0.279062i	$-0.0900235\pi$
$788$			56.1780i			2.00126i
$789$	46.8196			1.66682
$790$	−20.8877	−	20.8877i	−0.743152	−	0.743152i
$791$	3.24313	+	3.24313i	0.115312	+	0.115312i
$792$	171.384	+	171.384i	6.08987	+	6.08987i
$793$	−0.976834	+	0.976834i	−0.0346884	+	0.0346884i
$794$	46.9279	−	46.9279i	1.66541	−	1.66541i
$795$	−34.9788			−1.24057
$796$	−59.9603	+	59.9603i	−2.12524	+	2.12524i
$797$	10.3584			0.366912			0.183456	−	0.983028i	$-0.441271\pi$
$797$	10.3584			0.366912			0.183456	+	0.983028i	$0.441271\pi$
$798$	23.9385	−	23.9385i	0.847413	−	0.847413i
$799$			54.4039i			1.92467i
$800$			69.9897i			2.47451i
$801$	33.6838	−	33.6838i	1.19016	−	1.19016i
$802$	23.5700			0.832287
$803$	−17.3158	+	17.3158i	−0.611061	+	0.611061i
$804$	60.4742			2.13276
$805$	−1.41339	+	1.41339i	−0.0498154	+	0.0498154i
$806$	14.9241	−	14.9241i	0.525681	−	0.525681i
$807$	35.3938	+	35.3938i	1.24592	+	1.24592i
$808$	−4.04647	−	4.04647i	−0.142354	−	0.142354i
$809$	−15.6547	−	15.6547i	−0.550388	−	0.550388i	0.376165	−	0.926553i	$-0.377243\pi$
$809$	−15.6547	−	15.6547i	−0.550388	−	0.550388i	−0.926553	+	0.376165i	$0.877243\pi$
$810$	−52.7677			−1.85407
$811$		−	28.5632i		−	1.00299i	−0.865161	−	0.501495i	$-0.832784\pi$
$811$		−	28.5632i		−	1.00299i	0.865161	−	0.501495i	$-0.167216\pi$
$812$		−	2.82902i		−	0.0992793i
$813$	55.3150	+	55.3150i	1.93998	+	1.93998i
$814$	−47.7107	+	47.7107i	−1.67226	+	1.67226i
$815$		−	5.27539i		−	0.184789i
$816$	−258.956			−9.06527
$817$	−26.5144	−	26.5144i	−0.927620	−	0.927620i
$818$		−	99.9326i		−	3.49406i
$819$	−15.4052			−0.538301
$820$	−33.7985	+	4.97650i	−1.18029	+	0.173787i
$821$	4.23904			0.147943			0.0739717	−	0.997260i	$-0.476433\pi$
$821$	4.23904			0.147943			0.0739717	+	0.997260i	$0.476433\pi$
$822$			173.148i			6.03922i
$823$	−8.18760	−	8.18760i	−0.285402	−	0.285402i	0.549857	−	0.835259i	$-0.314682\pi$
$823$	−8.18760	−	8.18760i	−0.285402	−	0.285402i	−0.835259	+	0.549857i	$0.814682\pi$
$824$	−78.9319			−2.74972
$825$		−	49.5408i		−	1.72479i
$826$	−4.08263	+	4.08263i	−0.142053	+	0.142053i
$827$	−39.0555	−	39.0555i	−1.35809	−	1.35809i	−0.876269	−	0.481822i	$-0.839975\pi$
$827$	−39.0555	−	39.0555i	−1.35809	−	1.35809i	−0.481822	−	0.876269i	$-0.660025\pi$
$828$			72.5071i			2.51980i
$829$			43.2304i			1.50145i	0.660613	+	0.750727i	$0.270297\pi$
$829$			43.2304i			1.50145i	−0.660613	+	0.750727i	$0.729703\pi$
$830$	16.9342			0.587796
$831$	−59.6251	−	59.6251i	−2.06837	−	2.06837i
$832$	−33.1855	−	33.1855i	−1.15050	−	1.15050i
$833$	4.43119	+	4.43119i	0.153532	+	0.153532i
$834$	−18.5953	+	18.5953i	−0.643901	+	0.643901i
$835$	−12.8513	+	12.8513i	−0.444738	+	0.444738i
$836$	−82.2167			−2.84352
$837$	−32.2209	+	32.2209i	−1.11372	+	1.11372i
$838$	21.9801			0.759290
$839$	−19.5721	+	19.5721i	−0.675705	+	0.675705i	−0.959025	−	0.283320i	$-0.908564\pi$
$839$	−19.5721	+	19.5721i	−0.675705	+	0.675705i	0.283320	+	0.959025i	$0.408564\pi$
$840$			28.1512i			0.971308i
$841$		−	28.7095i		−	0.989982i
$842$	27.1470	−	27.1470i	0.935546	−	0.935546i
$843$	−84.5823			−2.91317
$844$	59.4783	−	59.4783i	2.04733	−	2.04733i
$845$	−8.32712			−0.286462
$846$	116.114	−	116.114i	3.99207	−	3.99207i
$847$	−3.22329	+	3.22329i	−0.110754	+	0.110754i
$848$	100.290	+	100.290i	3.44399	+	3.44399i
$849$	−41.0230	−	41.0230i	−1.40791	−	1.40791i
$850$	47.3234	+	47.3234i	1.62318	+	1.62318i
$851$	−12.4934			−0.428267
$852$			85.1491i			2.91716i
$853$		−	5.76193i		−	0.197285i	−0.995123	−	0.0986424i	$-0.968550\pi$
$853$		−	5.76193i		−	0.197285i	0.995123	−	0.0986424i	$-0.0314500\pi$
$854$	−1.19938	−	1.19938i	−0.0410419	−	0.0410419i
$855$	20.0543	−	20.0543i	0.685843	−	0.685843i
$856$		−	65.9878i		−	2.25542i
$857$	4.78071			0.163306			0.0816530	−	0.996661i	$-0.473980\pi$
$857$	4.78071			0.163306			0.0816530	+	0.996661i	$0.473980\pi$
$858$	52.1363	+	52.1363i	1.77990	+	1.77990i
$859$			17.9989i			0.614115i	0.951691	+	0.307058i	$0.0993445\pi$
$859$			17.9989i			0.614115i	−0.951691	+	0.307058i	$0.900656\pi$
$860$	50.3764			1.71782
$861$	20.0580	−	2.95334i	0.683573	−	0.100650i
$862$	77.1812			2.62880
$863$			41.3724i			1.40833i	0.710035	+	0.704166i	$0.248679\pi$
$863$			41.3724i			1.40833i	−0.710035	+	0.704166i	$0.751321\pi$
$864$	159.023	+	159.023i	5.41007	+	5.41007i
$865$	−7.61173			−0.258806
$866$		−	19.1989i		−	0.652404i
$867$	−49.8625	+	49.8625i	−1.69342	+	1.69342i
$868$	13.2683	+	13.2683i	0.450355	+	0.450355i
$869$		−	42.5740i		−	1.44422i
$870$		−	4.67076i		−	0.158354i
$871$	7.97929			0.270368
$872$	54.5242	+	54.5242i	1.84642	+	1.84642i
$873$	68.1894	+	68.1894i	2.30786	+	2.30786i
$874$	−14.8663	−	14.8663i	−0.502861	−	0.502861i
$875$	6.44516	−	6.44516i	0.217886	−	0.217886i
$876$	−72.9555	+	72.9555i	−2.46494	+	2.46494i
$877$	−53.6189			−1.81058			−0.905291	−	0.424793i	$-0.860347\pi$
$877$	−53.6189			−1.81058			−0.905291	+	0.424793i	$0.860347\pi$
$878$	−18.6872	+	18.6872i	−0.630664	+	0.630664i
$879$	64.2309			2.16645
$880$	37.0018	−	37.0018i	1.24733	−	1.24733i
$881$		−	11.6336i		−	0.391946i	−0.980609	−	0.195973i	$-0.937214\pi$
$881$		−	11.6336i		−	0.391946i	0.980609	−	0.195973i	$-0.0627865\pi$
$882$		−	18.9148i		−	0.636896i
$883$	27.1252	−	27.1252i	0.912835	−	0.912835i	−0.0836598	−	0.996494i	$-0.526661\pi$
$883$	27.1252	−	27.1252i	0.912835	−	0.912835i	0.996494	+	0.0836598i	$0.0266609\pi$
$884$	−72.1229			−2.42576
$885$	−4.88069	+	4.88069i	−0.164063	+	0.164063i
$886$	44.9667			1.51069
$887$	−33.0700	+	33.0700i	−1.11038	+	1.11038i	−0.117284	+	0.993098i	$0.537419\pi$
$887$	−33.0700	+	33.0700i	−1.11038	+	1.11038i	−0.993098	+	0.117284i	$0.962581\pi$
$888$	−124.418	+	124.418i	−4.17521	+	4.17521i
$889$	2.11575	+	2.11575i	0.0709601	+	0.0709601i
$890$	−13.1217	−	13.1217i	−0.439841	−	0.439841i
$891$	−53.7764	−	53.7764i	−1.80158	−	1.80158i
$892$	59.1400			1.98015
$893$			34.4768i			1.15372i
$894$			8.60554i			0.287812i
$895$	12.4295	+	12.4295i	0.415471	+	0.415471i
$896$	15.7929	−	15.7929i	0.527604	−	0.527604i
$897$			13.6523i			0.455836i
$898$	48.4108			1.61549
$899$	−1.36257	−	1.36257i	−0.0454444	−	0.0454444i
$900$		−	146.268i		−	4.87559i
$901$	68.1037			2.26886
$902$	−54.5739	−	40.5655i	−1.81711	−	1.35068i
$903$	−29.8963			−0.994886
$904$		−	40.1150i		−	1.33420i
$905$	5.27383	+	5.27383i	0.175308	+	0.175308i
$906$	−51.6362			−1.71550
$907$			3.86908i			0.128471i	0.997935	+	0.0642354i	$0.0204609\pi$
$907$			3.86908i			0.128471i	−0.997935	+	0.0642354i	$0.979539\pi$
$908$	−45.1157	+	45.1157i	−1.49722	+	1.49722i
$909$	3.25030	+	3.25030i	0.107806	+	0.107806i
$910$			6.00118i			0.198937i
$911$		−	25.7684i		−	0.853744i	−0.904312	−	0.426872i	$-0.859616\pi$
$911$		−	25.7684i		−	0.853744i	0.904312	−	0.426872i	$-0.140384\pi$
$912$	−164.105			−5.43406
$913$	17.2579	+	17.2579i	0.571155	+	0.571155i
$914$	−37.2167	−	37.2167i	−1.23102	−	1.23102i
$915$	−1.43383	−	1.43383i	−0.0474009	−	0.0474009i
$916$	−39.9940	+	39.9940i	−1.32144	+	1.32144i
$917$	−2.70193	+	2.70193i	−0.0892258	+	0.0892258i
$918$	215.046			7.09757
$919$	12.3867	−	12.3867i	0.408598	−	0.408598i	−0.472651	−	0.881250i	$-0.656703\pi$
$919$	12.3867	−	12.3867i	0.408598	−	0.408598i	0.881250	+	0.472651i	$0.156703\pi$
$920$	17.4825			0.576382
$921$	−6.57313	+	6.57313i	−0.216592	+	0.216592i
$922$			6.22524i			0.205017i
$923$			11.2350i			0.369806i
$924$	−46.3517	+	46.3517i	−1.52486	+	1.52486i
$925$	25.2027			0.828660
$926$	−6.12071	+	6.12071i	−0.201139	+	0.201139i
$927$	63.4015			2.08238
$928$	−6.72485	+	6.72485i	−0.220754	+	0.220754i
$929$	7.02695	−	7.02695i	0.230547	−	0.230547i	−0.582374	−	0.812921i	$-0.697876\pi$
$929$	7.02695	−	7.02695i	0.230547	−	0.230547i	0.812921	+	0.582374i	$0.197876\pi$
$930$	21.9061	+	21.9061i	0.718331	+	0.718331i
$931$	2.80812	+	2.80812i	0.0920325	+	0.0920325i
$932$	−61.7635	−	61.7635i	−2.02313	−	2.02313i
$933$	35.4270			1.15983
$934$			84.1455i			2.75333i
$935$		−	25.1266i		−	0.821729i
$936$	95.2753	+	95.2753i	3.11417	+	3.11417i
$937$	−15.5961	+	15.5961i	−0.509501	+	0.509501i	−0.914373	−	0.404872i	$-0.867316\pi$
$937$	−15.5961	+	15.5961i	−0.509501	+	0.509501i	0.404872	+	0.914373i	$0.367316\pi$
$938$			9.79715i			0.319888i
$939$	−43.0528			−1.40498
$940$	−32.7523	−	32.7523i	−1.06826	−	1.06826i
$941$		−	1.44201i		−	0.0470081i	−0.999724	−	0.0235040i	$-0.992518\pi$
$941$		−	1.44201i		−	0.0470081i	0.999724	−	0.0235040i	$-0.00748225\pi$
$942$	102.402			3.33644
$943$	−1.83409	−	12.4565i	−0.0597263	−	0.405638i
$944$	27.9876			0.910919
$945$		−	12.9564i		−	0.421472i
$946$	70.9024	+	70.9024i	2.30523	+	2.30523i
$947$	27.9097			0.906942			0.453471	−	0.891271i	$-0.350186\pi$
$947$	27.9097			0.906942			0.453471	+	0.891271i	$0.350186\pi$
$948$		−	179.374i		−	5.82580i
$949$	−9.62614	+	9.62614i	−0.312478	+	0.312478i
$950$	29.9897	+	29.9897i	0.972993	+	0.972993i
$951$			13.2195i			0.428671i
$952$		−	54.8104i		−	1.77642i
$953$	11.2914			0.365765			0.182883	−	0.983135i	$-0.441457\pi$
$953$	11.2914			0.365765			0.182883	+	0.983135i	$0.441457\pi$
$954$	−145.353	−	145.353i	−4.70597	−	4.70597i
$955$	17.7887	+	17.7887i	0.575630	+	0.575630i
$956$	−103.894	−	103.894i	−3.36016	−	3.36016i
$957$	4.76005	−	4.76005i	0.153870	−	0.153870i
$958$	−44.4991	+	44.4991i	−1.43770	+	1.43770i
$959$	−20.3113			−0.655885
$960$	48.7107	−	48.7107i	1.57213	−	1.57213i
$961$	−18.2189			−0.587706
$962$	−26.5231	+	26.5231i	−0.855141	+	0.855141i
$963$			53.0043i			1.70804i
$964$		−	78.4788i		−	2.52763i
$965$	−14.6004	+	14.6004i	−0.470005	+	0.470005i
$966$	−16.7625			−0.539326
$967$	−23.6426	+	23.6426i	−0.760294	+	0.760294i	−0.976375	−	0.216081i	$-0.930672\pi$
$967$	−23.6426	+	23.6426i	−0.760294	+	0.760294i	0.216081	+	0.976375i	$0.430672\pi$
$968$	39.8697			1.28146
$969$	−55.7190	+	55.7190i	−1.78995	+	1.78995i
$970$	26.5635	−	26.5635i	0.852904	−	0.852904i
$971$	16.8886	+	16.8886i	0.541983	+	0.541983i	0.924110	−	0.382127i	$-0.124808\pi$
$971$	16.8886	+	16.8886i	0.541983	+	0.541983i	−0.382127	+	0.924110i	$0.624808\pi$
$972$	−84.6600	−	84.6600i	−2.71547	−	2.71547i
$973$	−2.18133	−	2.18133i	−0.0699304	−	0.0699304i
$974$	20.6238			0.660829
$975$		−	27.5405i		−	0.882003i
$976$			8.22208i			0.263183i
$977$	−10.7005	−	10.7005i	−0.342338	−	0.342338i	0.514908	−	0.857246i	$-0.327826\pi$
$977$	−10.7005	−	10.7005i	−0.342338	−	0.342338i	−0.857246	+	0.514908i	$0.827826\pi$
$978$	31.2826	−	31.2826i	1.00031	−	1.00031i
$979$		−	26.7451i		−	0.854776i
$980$	−5.33534			−0.170431
$981$	−43.7962	−	43.7962i	−1.39830	−	1.39830i
$982$		−	102.322i		−	3.26524i
$983$	6.90070			0.220098			0.110049	−	0.993926i	$-0.464899\pi$
$983$	6.90070			0.220098			0.110049	+	0.993926i	$0.464899\pi$
$984$	−142.316	−	105.786i	−4.53687	−	3.37232i
$985$	−10.8802			−0.346672
$986$			9.09398i			0.289611i
$987$	19.4371	+	19.4371i	0.618691	+	0.618691i
$988$	−45.7056			−1.45409
$989$			18.5663i			0.590373i
$990$	−53.6275	+	53.6275i	−1.70439	+	1.70439i
$991$	33.6028	+	33.6028i	1.06743	+	1.06743i	0.997556	+	0.0698728i	$0.0222593\pi$
$991$	33.6028	+	33.6028i	1.06743	+	1.06743i	0.0698728	+	0.997556i	$0.477741\pi$
$992$		−	63.0799i		−	2.00279i
$993$			30.7332i			0.975288i
$994$	−13.7946			−0.437539
$995$	−11.6127	−	11.6127i	−0.368149	−	0.368149i
$996$	72.7117	+	72.7117i	2.30396	+	2.30396i
$997$	4.72300	+	4.72300i	0.149579	+	0.149579i	0.777930	−	0.628351i	$-0.216270\pi$
$997$	4.72300	+	4.72300i	0.149579	+	0.149579i	−0.628351	+	0.777930i	$0.716270\pi$
$998$	−67.9734	+	67.9734i	−2.15166	+	2.15166i
$999$	57.2628	−	57.2628i	1.81172	−	1.81172i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.f.a.50.19	✓	40
41.32	even	4	inner	287.2.f.a.155.2	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.f.a.50.19	✓	40	1.1	even	1	trivial
287.2.f.a.155.2	yes	40	41.32	even	4	inner

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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.69233i q^{2} +(-2.23891 - 2.23891i) q^{3} -5.24863 q^{4} -1.01652i q^{5} +(6.02789 - 6.02789i) q^{6} +(0.707107 + 0.707107i) q^{7} -8.74637i q^{8} +7.02546i q^{9} +O(q^{10})\)	\(q+2.69233i q^{2} +(-2.23891 - 2.23891i) q^{3} -5.24863 q^{4} -1.01652i q^{5} +(6.02789 - 6.02789i) q^{6} +(0.707107 + 0.707107i) q^{7} -8.74637i q^{8} +7.02546i q^{9} +2.73681 q^{10} +(2.78912 + 2.78912i) q^{11} +(11.7512 + 11.7512i) q^{12} +(1.55052 + 1.55052i) q^{13} +(-1.90376 + 1.90376i) q^{14} +(-2.27590 + 2.27590i) q^{15} +13.0508 q^{16} +(4.43119 - 4.43119i) q^{17} -18.9148 q^{18} +(2.80812 - 2.80812i) q^{19} +5.33534i q^{20} -3.16630i q^{21} +(-7.50924 + 7.50924i) q^{22} -1.96635 q^{23} +(-19.5824 + 19.5824i) q^{24} +3.96668 q^{25} +(-4.17451 + 4.17451i) q^{26} +(9.01266 - 9.01266i) q^{27} +(-3.71134 - 3.71134i) q^{28} +(0.381133 + 0.381133i) q^{29} +(-6.12748 - 6.12748i) q^{30} -3.57507 q^{31} +17.6444i q^{32} -12.4892i q^{33} +(11.9302 + 11.9302i) q^{34} +(0.718789 - 0.718789i) q^{35} -36.8740i q^{36} +6.35360 q^{37} +(7.56039 + 7.56039i) q^{38} -6.94296i q^{39} -8.89087 q^{40} +(0.932741 + 6.33482i) q^{41} +8.52472 q^{42} -9.44202i q^{43} +(-14.6391 - 14.6391i) q^{44} +7.14154 q^{45} -5.29405i q^{46} +(-6.13875 + 6.13875i) q^{47} +(-29.2197 - 29.2197i) q^{48} +1.00000i q^{49} +10.6796i q^{50} -19.8421 q^{51} +(-8.13810 - 8.13810i) q^{52} +(7.68459 + 7.68459i) q^{53} +(24.2650 + 24.2650i) q^{54} +(2.83520 - 2.83520i) q^{55} +(6.18462 - 6.18462i) q^{56} -12.5743 q^{57} +(-1.02613 + 1.02613i) q^{58} +2.14451 q^{59} +(11.9454 - 11.9454i) q^{60} +0.630004i q^{61} -9.62525i q^{62} +(-4.96775 + 4.96775i) q^{63} -21.4028 q^{64} +(1.57614 - 1.57614i) q^{65} +33.6251 q^{66} +(2.57310 - 2.57310i) q^{67} +(-23.2577 + 23.2577i) q^{68} +(4.40248 + 4.40248i) q^{69} +(1.93522 + 1.93522i) q^{70} +(3.62299 + 3.62299i) q^{71} +61.4473 q^{72} +6.20833i q^{73} +17.1060i q^{74} +(-8.88106 - 8.88106i) q^{75} +(-14.7388 + 14.7388i) q^{76} +3.94442i q^{77} +18.6927 q^{78} +(-7.63214 - 7.63214i) q^{79} -13.2665i q^{80} -19.2807 q^{81} +(-17.0554 + 2.51125i) q^{82} +6.18759 q^{83} +16.6187i q^{84} +(-4.50440 - 4.50440i) q^{85} +25.4210 q^{86} -1.70665i q^{87} +(24.3947 - 24.3947i) q^{88} +(-4.79453 - 4.79453i) q^{89} +19.2274i q^{90} +2.19277i q^{91} +10.3206 q^{92} +(8.00426 + 8.00426i) q^{93} +(-16.5275 - 16.5275i) q^{94} +(-2.85452 - 2.85452i) q^{95} +(39.5042 - 39.5042i) q^{96} +(9.70603 - 9.70603i) q^{97} -2.69233 q^{98} +(-19.5949 + 19.5949i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6}+O(q^{10}) \) 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6	\( 40 q + 4 q^{3} - 36 q^{4} + 8 q^{6} - 32 q^{10} - 8 q^{11} + 16 q^{12} + 16 q^{13} - 8 q^{15} + 28 q^{16} + 20 q^{17} - 12 q^{18} - 20 q^{19} + 4 q^{22} + 16 q^{23} - 12 q^{24} - 40 q^{25} - 20 q^{26} - 20 q^{27} - 12 q^{29} + 4 q^{30} + 32 q^{34} + 4 q^{35} - 16 q^{38} + 64 q^{40} + 16 q^{41} + 32 q^{42} + 8 q^{44} + 72 q^{45} - 24 q^{47} - 40 q^{48} - 64 q^{51} - 96 q^{52} + 8 q^{53} + 52 q^{54} - 8 q^{55} - 88 q^{57} - 36 q^{58} + 48 q^{59} + 52 q^{60} - 8 q^{63} - 84 q^{64} - 44 q^{65} + 56 q^{66} + 40 q^{67} - 60 q^{68} + 28 q^{69} - 8 q^{70} + 20 q^{71} + 80 q^{72} - 20 q^{75} - 4 q^{76} + 12 q^{78} - 12 q^{79} + 16 q^{81} - 52 q^{82} + 40 q^{83} + 8 q^{85} + 80 q^{86} + 96 q^{88} - 8 q^{89} - 20 q^{92} - 64 q^{93} + 52 q^{94} + 68 q^{96} - 60 q^{97} - 4 q^{98} - 36 q^{99}+O(q^{100}) \) 40 * q + 4 * q^3 - 36 * q^4 + 8 * q^6 - 32 * q^10 - 8 * q^11 + 16 * q^12 + 16 * q^13 - 8 * q^15 + 28 * q^16 + 20 * q^17 - 12 * q^18 - 20 * q^19 + 4 * q^22 + 16 * q^23 - 12 * q^24 - 40 * q^25 - 20 * q^26 - 20 * q^27 - 12 * q^29 + 4 * q^30 + 32 * q^34 + 4 * q^35 - 16 * q^38 + 64 * q^40 + 16 * q^41 + 32 * q^42 + 8 * q^44 + 72 * q^45 - 24 * q^47 - 40 * q^48 - 64 * q^51 - 96 * q^52 + 8 * q^53 + 52 * q^54 - 8 * q^55 - 88 * q^57 - 36 * q^58 + 48 * q^59 + 52 * q^60 - 8 * q^63 - 84 * q^64 - 44 * q^65 + 56 * q^66 + 40 * q^67 - 60 * q^68 + 28 * q^69 - 8 * q^70 + 20 * q^71 + 80 * q^72 - 20 * q^75 - 4 * q^76 + 12 * q^78 - 12 * q^79 + 16 * q^81 - 52 * q^82 + 40 * q^83 + 8 * q^85 + 80 * q^86 + 96 * q^88 - 8 * q^89 - 20 * q^92 - 64 * q^93 + 52 * q^94 + 68 * q^96 - 60 * q^97 - 4 * q^98 - 36 * q^99

Introduction

L-functions

Modular forms

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