LMFDB - Embedded newform 574.2.f.a.337.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [574,2,Mod(155,574)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(574, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("574.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 574 = 2 \cdot 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	574.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:	$4.58341307602$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} + 40 x^{18} + 666 x^{16} + 6052 x^{14} + 33033 x^{12} + 112020 x^{10} + 235396 x^{8} + \cdots + 8464 $ x^20 + 40x^18 + 666x^16 + 6052x^14 + 33033x^12 + 112020x^10 + 235396x^8 + 296360x^6 + 208336x^4 + 71168*x^2 + 8464
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			337.4
Root			$-1.98313i$ of defining polynomial
Character	$\chi$	$=$	574.337
Dual form			574.2.f.a.155.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000i q^{2} +(-1.40228 - 1.40228i) q^{3} -1.00000 q^{4} -1.58615i q^{5} +(1.40228 - 1.40228i) q^{6} +(0.707107 + 0.707107i) q^{7} -1.00000i q^{8} +0.932805i q^{9} +O(q^{10})$	\(q+1.00000i q^{2} +(-1.40228 - 1.40228i) q^{3} -1.00000 q^{4} -1.58615i q^{5} +(1.40228 - 1.40228i) q^{6} +(0.707107 + 0.707107i) q^{7} -1.00000i q^{8} +0.932805i q^{9} +1.58615 q^{10} +(-1.52386 - 1.52386i) q^{11} +(1.40228 + 1.40228i) q^{12} +(-1.17480 - 1.17480i) q^{13} +(-0.707107 + 0.707107i) q^{14} +(-2.22424 + 2.22424i) q^{15} +1.00000 q^{16} +(-2.81650 + 2.81650i) q^{17} -0.932805 q^{18} +(-5.01036 + 5.01036i) q^{19} +1.58615i q^{20} -1.98313i q^{21} +(1.52386 - 1.52386i) q^{22} +6.10702 q^{23} +(-1.40228 + 1.40228i) q^{24} +2.48412 q^{25} +(1.17480 - 1.17480i) q^{26} +(-2.89880 + 2.89880i) q^{27} +(-0.707107 - 0.707107i) q^{28} +(-7.06728 - 7.06728i) q^{29} +(-2.22424 - 2.22424i) q^{30} -9.34523 q^{31} +1.00000i q^{32} +4.27378i q^{33} +(-2.81650 - 2.81650i) q^{34} +(1.12158 - 1.12158i) q^{35} -0.932805i q^{36} -2.74728 q^{37} +(-5.01036 - 5.01036i) q^{38} +3.29481i q^{39} -1.58615 q^{40} +(-4.76951 - 4.27221i) q^{41} +1.98313 q^{42} -7.14760i q^{43} +(1.52386 + 1.52386i) q^{44} +1.47957 q^{45} +6.10702i q^{46} +(-5.02180 + 5.02180i) q^{47} +(-1.40228 - 1.40228i) q^{48} +1.00000i q^{49} +2.48412i q^{50} +7.89906 q^{51} +(1.17480 + 1.17480i) q^{52} +(-7.43800 - 7.43800i) q^{53} +(-2.89880 - 2.89880i) q^{54} +(-2.41708 + 2.41708i) q^{55} +(0.707107 - 0.707107i) q^{56} +14.0519 q^{57} +(7.06728 - 7.06728i) q^{58} +10.7381 q^{59} +(2.22424 - 2.22424i) q^{60} +12.4049i q^{61} -9.34523i q^{62} +(-0.659593 + 0.659593i) q^{63} -1.00000 q^{64} +(-1.86341 + 1.86341i) q^{65} -4.27378 q^{66} +(-6.07639 + 6.07639i) q^{67} +(2.81650 - 2.81650i) q^{68} +(-8.56378 - 8.56378i) q^{69} +(1.12158 + 1.12158i) q^{70} +(6.10702 + 6.10702i) q^{71} +0.932805 q^{72} -16.1050i q^{73} -2.74728i q^{74} +(-3.48345 - 3.48345i) q^{75} +(5.01036 - 5.01036i) q^{76} -2.15507i q^{77} -3.29481 q^{78} +(2.49677 + 2.49677i) q^{79} -1.58615i q^{80} +10.9283 q^{81} +(4.27221 - 4.76951i) q^{82} -2.01947 q^{83} +1.98313i q^{84} +(4.46739 + 4.46739i) q^{85} +7.14760 q^{86} +19.8207i q^{87} +(-1.52386 + 1.52386i) q^{88} +(12.2966 + 12.2966i) q^{89} +1.47957i q^{90} -1.66142i q^{91} -6.10702 q^{92} +(13.1047 + 13.1047i) q^{93} +(-5.02180 - 5.02180i) q^{94} +(7.94719 + 7.94719i) q^{95} +(1.40228 - 1.40228i) q^{96} +(3.70310 - 3.70310i) q^{97} -1.00000 q^{98} +(1.42147 - 1.42147i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 4 q^{3} - 20 q^{4} + 4 q^{6}+O(q^{10}) $ 20 * q - 4 * q^3 - 20 * q^4 + 4 * q^6	$ 20 q - 4 q^{3} - 20 q^{4} + 4 q^{6} + 16 q^{11} + 4 q^{12} - 20 q^{13} + 4 q^{15} + 20 q^{16} - 4 q^{17} - 20 q^{18} + 12 q^{19} - 16 q^{22} + 8 q^{23} - 4 q^{24} - 20 q^{25} + 20 q^{26} - 16 q^{27} + 12 q^{29} + 4 q^{30} - 8 q^{31} - 4 q^{34} - 32 q^{37} + 12 q^{38} - 12 q^{41} - 16 q^{44} - 72 q^{45} + 12 q^{47} - 4 q^{48} + 80 q^{51} + 20 q^{52} - 16 q^{54} - 20 q^{55} + 48 q^{57} - 12 q^{58} - 8 q^{59} - 4 q^{60} + 16 q^{63} - 20 q^{64} + 20 q^{65} - 40 q^{66} - 4 q^{67} + 4 q^{68} - 8 q^{69} - 8 q^{71} + 20 q^{72} + 20 q^{75} - 12 q^{76} + 24 q^{78} + 24 q^{79} + 4 q^{81} + 12 q^{82} - 4 q^{85} + 8 q^{86} + 16 q^{88} - 48 q^{89} - 8 q^{92} - 8 q^{93} + 12 q^{94} + 28 q^{95} + 4 q^{96} + 16 q^{97} - 20 q^{98} - 8 q^{99}+O(q^{100}) $ 20 * q - 4 * q^3 - 20 * q^4 + 4 * q^6 + 16 * q^11 + 4 * q^12 - 20 * q^13 + 4 * q^15 + 20 * q^16 - 4 * q^17 - 20 * q^18 + 12 * q^19 - 16 * q^22 + 8 * q^23 - 4 * q^24 - 20 * q^25 + 20 * q^26 - 16 * q^27 + 12 * q^29 + 4 * q^30 - 8 * q^31 - 4 * q^34 - 32 * q^37 + 12 * q^38 - 12 * q^41 - 16 * q^44 - 72 * q^45 + 12 * q^47 - 4 * q^48 + 80 * q^51 + 20 * q^52 - 16 * q^54 - 20 * q^55 + 48 * q^57 - 12 * q^58 - 8 * q^59 - 4 * q^60 + 16 * q^63 - 20 * q^64 + 20 * q^65 - 40 * q^66 - 4 * q^67 + 4 * q^68 - 8 * q^69 - 8 * q^71 + 20 * q^72 + 20 * q^75 - 12 * q^76 + 24 * q^78 + 24 * q^79 + 4 * q^81 + 12 * q^82 - 4 * q^85 + 8 * q^86 + 16 * q^88 - 48 * q^89 - 8 * q^92 - 8 * q^93 + 12 * q^94 + 28 * q^95 + 4 * q^96 + 16 * q^97 - 20 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/574\mathbb{Z}\right)^\times$.

$n$	$211$	$493$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$			1.00000i			0.707107i
$2$			1.00000i			0.707107i
$3$	−1.40228	−	1.40228i	−0.809609	−	0.809609i	0.174965	−	0.984575i	$-0.444019\pi$
$3$	−1.40228	−	1.40228i	−0.809609	−	0.809609i	−0.984575	+	0.174965i	$0.944019\pi$
$4$	−1.00000			−0.500000
$5$		−	1.58615i		−	0.709348i	−0.934990	−	0.354674i	$-0.884592\pi$
$5$		−	1.58615i		−	0.709348i	0.934990	−	0.354674i	$-0.115408\pi$
$6$	1.40228	−	1.40228i	0.572480	−	0.572480i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$7$	0.707107	+	0.707107i	0.267261	+	0.267261i
$8$		−	1.00000i		−	0.353553i
$9$			0.932805i			0.310935i
$10$	1.58615			0.501585
$11$	−1.52386	−	1.52386i	−0.459462	−	0.459462i	0.439017	−	0.898479i	$-0.355327\pi$
$11$	−1.52386	−	1.52386i	−0.459462	−	0.459462i	−0.898479	+	0.439017i	$0.855327\pi$
$12$	1.40228	+	1.40228i	0.404805	+	0.404805i
$13$	−1.17480	−	1.17480i	−0.325831	−	0.325831i	0.525168	−	0.850999i	$-0.324003\pi$
$13$	−1.17480	−	1.17480i	−0.325831	−	0.325831i	−0.850999	+	0.525168i	$0.824003\pi$
$14$	−0.707107	+	0.707107i	−0.188982	+	0.188982i
$15$	−2.22424	+	2.22424i	−0.574295	+	0.574295i
$16$	1.00000			0.250000
$17$	−2.81650	+	2.81650i	−0.683101	+	0.683101i	−0.960698	−	0.277597i	$-0.910462\pi$
$17$	−2.81650	+	2.81650i	−0.683101	+	0.683101i	0.277597	+	0.960698i	$0.410462\pi$
$18$	−0.932805			−0.219864
$19$	−5.01036	+	5.01036i	−1.14946	+	1.14946i	−0.162795	+	0.986660i	$0.552051\pi$
$19$	−5.01036	+	5.01036i	−1.14946	+	1.14946i	−0.986660	+	0.162795i	$0.947949\pi$
$20$			1.58615i			0.354674i
$21$		−	1.98313i		−	0.432754i
$22$	1.52386	−	1.52386i	0.324889	−	0.324889i
$23$	6.10702			1.27340			0.636701	−	0.771111i	$-0.280299\pi$
$23$	6.10702			1.27340			0.636701	+	0.771111i	$0.280299\pi$
$24$	−1.40228	+	1.40228i	−0.286240	+	0.286240i
$25$	2.48412			0.496825
$26$	1.17480	−	1.17480i	0.230397	−	0.230397i
$27$	−2.89880	+	2.89880i	−0.557874	+	0.557874i
$28$	−0.707107	−	0.707107i	−0.133631	−	0.133631i
$29$	−7.06728	−	7.06728i	−1.31236	−	1.31236i	−0.919670	−	0.392691i	$-0.871544\pi$
$29$	−7.06728	−	7.06728i	−1.31236	−	1.31236i	−0.392691	−	0.919670i	$-0.628456\pi$
$30$	−2.22424	−	2.22424i	−0.406088	−	0.406088i
$31$	−9.34523			−1.67845			−0.839226	−	0.543782i	$-0.816992\pi$
$31$	−9.34523			−1.67845			−0.839226	+	0.543782i	$0.816992\pi$
$32$			1.00000i			0.176777i
$33$			4.27378i			0.743970i
$34$	−2.81650	−	2.81650i	−0.483025	−	0.483025i
$35$	1.12158	−	1.12158i	0.189581	−	0.189581i
$36$		−	0.932805i		−	0.155467i
$37$	−2.74728			−0.451650			−0.225825	−	0.974168i	$-0.572508\pi$
$37$	−2.74728			−0.451650			−0.225825	+	0.974168i	$0.572508\pi$
$38$	−5.01036	−	5.01036i	−0.812787	−	0.812787i
$39$			3.29481i			0.527592i
$40$	−1.58615			−0.250793
$41$	−4.76951	−	4.27221i	−0.744872	−	0.667207i
$41$	−4.76951	−	4.27221i	−0.744872	−	0.667207i
$42$	1.98313			0.306004
$43$		−	7.14760i		−	1.09000i	−0.838437	−	0.544999i	$-0.816530\pi$
$43$		−	7.14760i		−	1.09000i	0.838437	−	0.544999i	$-0.183470\pi$
$44$	1.52386	+	1.52386i	0.229731	+	0.229731i
$45$	1.47957			0.220561
$46$			6.10702i			0.900431i
$47$	−5.02180	+	5.02180i	−0.732504	+	0.732504i	−0.971115	−	0.238611i	$-0.923308\pi$
$47$	−5.02180	+	5.02180i	−0.732504	+	0.732504i	0.238611	+	0.971115i	$0.423308\pi$
$48$	−1.40228	−	1.40228i	−0.202402	−	0.202402i
$49$			1.00000i			0.142857i
$50$			2.48412i			0.351308i
$51$	7.89906			1.10609
$52$	1.17480	+	1.17480i	0.162916	+	0.162916i
$53$	−7.43800	−	7.43800i	−1.02169	−	1.02169i	−0.999760	−	0.0219276i	$-0.993020\pi$
$53$	−7.43800	−	7.43800i	−1.02169	−	1.02169i	−0.0219276	−	0.999760i	$-0.506980\pi$
$54$	−2.89880	−	2.89880i	−0.394476	−	0.394476i
$55$	−2.41708	+	2.41708i	−0.325919	+	0.325919i
$56$	0.707107	−	0.707107i	0.0944911	−	0.0944911i
$57$	14.0519			1.86122
$58$	7.06728	−	7.06728i	0.927980	−	0.927980i
$59$	10.7381			1.39798			0.698990	−	0.715131i	$-0.253633\pi$
$59$	10.7381			1.39798			0.698990	+	0.715131i	$0.253633\pi$
$60$	2.22424	−	2.22424i	0.287148	−	0.287148i
$61$			12.4049i			1.58829i	0.607731	+	0.794143i	$0.292080\pi$
$61$			12.4049i			1.58829i	−0.607731	+	0.794143i	$0.707920\pi$
$62$		−	9.34523i		−	1.18685i
$63$	−0.659593	+	0.659593i	−0.0831009	+	0.0831009i
$64$	−1.00000			−0.125000
$65$	−1.86341	+	1.86341i	−0.231128	+	0.231128i
$66$	−4.27378			−0.526066
$67$	−6.07639	+	6.07639i	−0.742349	+	0.742349i	−0.973030	−	0.230680i	$-0.925905\pi$
$67$	−6.07639	+	6.07639i	−0.742349	+	0.742349i	0.230680	+	0.973030i	$0.425905\pi$
$68$	2.81650	−	2.81650i	0.341551	−	0.341551i
$69$	−8.56378	−	8.56378i	−1.03096	−	1.03096i
$70$	1.12158	+	1.12158i	0.134054	+	0.134054i
$71$	6.10702	+	6.10702i	0.724770	+	0.724770i	0.969573	−	0.244803i	$-0.0787232\pi$
$71$	6.10702	+	6.10702i	0.724770	+	0.724770i	−0.244803	+	0.969573i	$0.578723\pi$
$72$	0.932805			0.109932
$73$		−	16.1050i		−	1.88495i	−0.334280	−	0.942474i	$-0.608493\pi$
$73$		−	16.1050i		−	1.88495i	0.334280	−	0.942474i	$-0.391507\pi$
$74$		−	2.74728i		−	0.319365i
$75$	−3.48345	−	3.48345i	−0.402234	−	0.402234i
$76$	5.01036	−	5.01036i	0.574728	−	0.574728i
$77$		−	2.15507i		−	0.245593i
$78$	−3.29481			−0.373064
$79$	2.49677	+	2.49677i	0.280908	+	0.280908i	0.833471	−	0.552563i	$-0.186350\pi$
$79$	2.49677	+	2.49677i	0.280908	+	0.280908i	−0.552563	+	0.833471i	$0.686350\pi$
$80$		−	1.58615i		−	0.177337i
$81$	10.9283			1.21425
$82$	4.27221	−	4.76951i	0.471787	−	0.526704i
$83$	−2.01947			−0.221666			−0.110833	−	0.993839i	$-0.535352\pi$
$83$	−2.01947			−0.221666			−0.110833	+	0.993839i	$0.535352\pi$
$84$			1.98313i			0.216377i
$85$	4.46739	+	4.46739i	0.484557	+	0.484557i
$86$	7.14760			0.770745
$87$			19.8207i			2.12500i
$88$	−1.52386	+	1.52386i	−0.162444	+	0.162444i
$89$	12.2966	+	12.2966i	1.30343	+	1.30343i	0.926061	+	0.377374i	$0.123173\pi$
$89$	12.2966	+	12.2966i	1.30343	+	1.30343i	0.377374	+	0.926061i	$0.376827\pi$
$90$			1.47957i			0.155960i
$91$		−	1.66142i		−	0.174164i
$92$	−6.10702			−0.636701
$93$	13.1047	+	13.1047i	1.35889	+	1.35889i
$94$	−5.02180	−	5.02180i	−0.517959	−	0.517959i
$95$	7.94719	+	7.94719i	0.815364	+	0.815364i
$96$	1.40228	−	1.40228i	0.143120	−	0.143120i
$97$	3.70310	−	3.70310i	0.375993	−	0.375993i	−0.493661	−	0.869654i	$-0.664342\pi$
$97$	3.70310	−	3.70310i	0.375993	−	0.375993i	0.869654	+	0.493661i	$0.164342\pi$
$98$	−1.00000			−0.101015
$99$	1.42147	−	1.42147i	0.142863	−	0.142863i
$100$	−2.48412			−0.248412
$101$	11.2599	−	11.2599i	1.12040	−	1.12040i	0.128724	−	0.991680i	$-0.458912\pi$
$101$	11.2599	−	11.2599i	1.12040	−	1.12040i	0.991680	−	0.128724i	$-0.0410881\pi$
$102$			7.89906i			0.782124i
$103$		−	3.35643i		−	0.330719i	−0.986233	−	0.165359i	$-0.947122\pi$
$103$		−	3.35643i		−	0.330719i	0.986233	−	0.165359i	$-0.0528784\pi$
$104$	−1.17480	+	1.17480i	−0.115199	+	0.115199i
$105$	−3.14554			−0.306974
$106$	7.43800	−	7.43800i	0.722442	−	0.722442i
$107$	1.29895			0.125574			0.0627872	−	0.998027i	$-0.480001\pi$
$107$	1.29895			0.125574			0.0627872	+	0.998027i	$0.480001\pi$
$108$	2.89880	−	2.89880i	0.278937	−	0.278937i
$109$	−4.52106	+	4.52106i	−0.433039	+	0.433039i	−0.889661	−	0.456622i	$-0.849059\pi$
$109$	−4.52106	+	4.52106i	−0.433039	+	0.433039i	0.456622	+	0.889661i	$0.349059\pi$
$110$	−2.41708	−	2.41708i	−0.230459	−	0.230459i
$111$	3.85247	+	3.85247i	0.365660	+	0.365660i
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	−10.6539			−1.00223			−0.501116	−	0.865380i	$-0.667077\pi$
$113$	−10.6539			−1.00223			−0.501116	+	0.865380i	$0.667077\pi$
$114$			14.0519i			1.31608i
$115$		−	9.68666i		−	0.903286i
$116$	7.06728	+	7.06728i	0.656181	+	0.656181i
$117$	1.09586	−	1.09586i	0.101312	−	0.101312i
$118$			10.7381i			0.988522i
$119$	−3.98313			−0.365133
$120$	2.22424	+	2.22424i	0.203044	+	0.203044i
$121$		−	6.35568i		−	0.577789i
$122$	−12.4049			−1.12309
$123$	0.697359	+	12.6791i	0.0628788	+	1.14323i
$124$	9.34523			0.839226
$125$		−	11.8710i		−	1.06177i
$126$	−0.659593	−	0.659593i	−0.0587612	−	0.0587612i
$127$	−4.16613			−0.369684			−0.184842	−	0.982768i	$-0.559177\pi$
$127$	−4.16613			−0.369684			−0.184842	+	0.982768i	$0.559177\pi$
$128$		−	1.00000i		−	0.0883883i
$129$	−10.0230	+	10.0230i	−0.882473	+	0.882473i
$130$	−1.86341	−	1.86341i	−0.163432	−	0.163432i
$131$		−	7.24503i		−	0.633002i	−0.948592	−	0.316501i	$-0.897492\pi$
$131$		−	7.24503i		−	0.633002i	0.948592	−	0.316501i	$-0.102508\pi$
$132$		−	4.27378i		−	0.371985i
$133$	−7.08572			−0.614410
$134$	−6.07639	−	6.07639i	−0.524920	−	0.524920i
$135$	4.59793	+	4.59793i	0.395727	+	0.395727i
$136$	2.81650	+	2.81650i	0.241513	+	0.241513i
$137$	4.97206	−	4.97206i	0.424792	−	0.424792i	−0.462058	−	0.886850i	$-0.652889\pi$
$137$	4.97206	−	4.97206i	0.424792	−	0.424792i	0.886850	+	0.462058i	$0.152889\pi$
$138$	8.56378	−	8.56378i	0.728997	−	0.728997i
$139$	−6.66802			−0.565574			−0.282787	−	0.959183i	$-0.591259\pi$
$139$	−6.66802			−0.565574			−0.282787	+	0.959183i	$0.591259\pi$
$140$	−1.12158	+	1.12158i	−0.0947907	+	0.0947907i
$141$	14.0840			1.18608
$142$	−6.10702	+	6.10702i	−0.512490	+	0.512490i
$143$			3.58047i			0.299414i
$144$			0.932805i			0.0777337i
$145$	−11.2098	+	11.2098i	−0.930922	+	0.930922i
$146$	16.1050			1.33286
$147$	1.40228	−	1.40228i	0.115658	−	0.115658i
$148$	2.74728			0.225825
$149$	15.2358	−	15.2358i	1.24817	−	1.24817i	0.291639	−	0.956528i	$-0.405799\pi$
$149$	15.2358	−	15.2358i	1.24817	−	1.24817i	0.956528	−	0.291639i	$-0.0942006\pi$
$150$	3.48345	−	3.48345i	0.284422	−	0.284422i
$151$	2.64895	+	2.64895i	0.215568	+	0.215568i	0.806628	−	0.591060i	$-0.201290\pi$
$151$	2.64895	+	2.64895i	0.215568	+	0.215568i	−0.591060	+	0.806628i	$0.701290\pi$
$152$	5.01036	+	5.01036i	0.406394	+	0.406394i
$153$	−2.62724	−	2.62724i	−0.212400	−	0.212400i
$154$	2.15507			0.173660
$155$			14.8229i			1.19061i
$156$		−	3.29481i		−	0.263796i
$157$	−13.4802	−	13.4802i	−1.07584	−	1.07584i	−0.996878	−	0.0789590i	$-0.974840\pi$
$157$	−13.4802	−	13.4802i	−1.07584	−	1.07584i	−0.0789590	−	0.996878i	$-0.525160\pi$
$158$	−2.49677	+	2.49677i	−0.198632	+	0.198632i
$159$			20.8604i			1.65434i
$160$	1.58615			0.125396
$161$	4.31832	+	4.31832i	0.340331	+	0.340331i
$162$			10.9283i			0.858608i
$163$	−17.2081			−1.34784			−0.673922	−	0.738802i	$-0.735392\pi$
$163$	−17.2081			−1.34784			−0.673922	+	0.738802i	$0.735392\pi$
$164$	4.76951	+	4.27221i	0.372436	+	0.333603i
$165$	6.77886			0.527734
$166$		−	2.01947i		−	0.156741i
$167$	−4.93231	−	4.93231i	−0.381673	−	0.381673i	0.490032	−	0.871705i	$-0.336985\pi$
$167$	−4.93231	−	4.93231i	−0.381673	−	0.381673i	−0.871705	+	0.490032i	$0.836985\pi$
$168$	−1.98313			−0.153002
$169$		−	10.2397i		−	0.787668i
$170$	−4.46739	+	4.46739i	−0.342633	+	0.342633i
$171$	−4.67369	−	4.67369i	−0.357406	−	0.357406i
$172$			7.14760i			0.544999i
$173$		−	0.436899i		−	0.0332168i	−0.999862	−	0.0166084i	$-0.994713\pi$
$173$		−	0.436899i		−	0.0332168i	0.999862	−	0.0166084i	$-0.00528686\pi$
$174$	−19.8207			−1.50260
$175$	1.75654	+	1.75654i	0.132782	+	0.132782i
$176$	−1.52386	−	1.52386i	−0.114865	−	0.114865i
$177$	−15.0579	−	15.0579i	−1.13182	−	1.13182i
$178$	−12.2966	+	12.2966i	−0.921668	+	0.921668i
$179$	−3.35925	+	3.35925i	−0.251082	+	0.251082i	−0.821414	−	0.570332i	$-0.806815\pi$
$179$	−3.35925	+	3.35925i	−0.251082	+	0.251082i	0.570332	+	0.821414i	$0.306815\pi$
$180$	−1.47957			−0.110281
$181$	−6.46558	+	6.46558i	−0.480583	+	0.480583i	−0.905318	−	0.424735i	$-0.860367\pi$
$181$	−6.46558	+	6.46558i	−0.480583	+	0.480583i	0.424735	+	0.905318i	$0.360367\pi$
$182$	1.66142			0.123153
$183$	17.3952	−	17.3952i	1.28589	−	1.28589i
$184$		−	6.10702i		−	0.450216i
$185$			4.35760i			0.320377i
$186$	−13.1047	+	13.1047i	−0.960881	+	0.960881i
$187$	8.58392			0.627718
$188$	5.02180	−	5.02180i	0.366252	−	0.366252i
$189$	−4.09952			−0.298196
$190$	−7.94719	+	7.94719i	−0.576549	+	0.576549i
$191$	15.5425	−	15.5425i	1.12462	−	1.12462i	0.133577	−	0.991038i	$-0.457354\pi$
$191$	15.5425	−	15.5425i	1.12462	−	1.12462i	0.991038	−	0.133577i	$-0.0426462\pi$
$192$	1.40228	+	1.40228i	0.101201	+	0.101201i
$193$	5.09221	+	5.09221i	0.366545	+	0.366545i	0.866216	−	0.499670i	$-0.166545\pi$
$193$	5.09221	+	5.09221i	0.366545	+	0.366545i	−0.499670	+	0.866216i	$0.666545\pi$
$194$	3.70310	+	3.70310i	0.265867	+	0.265867i
$195$	5.22607			0.374247
$196$		−	1.00000i		−	0.0714286i
$197$		−	5.17834i		−	0.368942i	−0.982838	−	0.184471i	$-0.940943\pi$
$197$		−	5.17834i		−	0.368942i	0.982838	−	0.184471i	$-0.0590571\pi$
$198$	1.42147	+	1.42147i	0.101019	+	0.101019i
$199$	4.18223	−	4.18223i	0.296470	−	0.296470i	−0.543159	−	0.839630i	$-0.682772\pi$
$199$	4.18223	−	4.18223i	0.296470	−	0.296470i	0.839630	+	0.543159i	$0.182772\pi$
$200$		−	2.48412i		−	0.175654i
$201$	17.0417			1.20203
$202$	11.2599	+	11.2599i	0.792245	+	0.792245i
$203$		−	9.99465i		−	0.701487i
$204$	−7.89906			−0.553045
$205$	−6.77637	+	7.56517i	−0.473282	+	0.528374i
$206$	3.35643			0.233853
$207$			5.69666i			0.395945i
$208$	−1.17480	−	1.17480i	−0.0814578	−	0.0814578i
$209$	15.2702			1.05626
$210$		−	3.14554i		−	0.217063i
$211$	−15.7282	+	15.7282i	−1.08277	+	1.08277i	−0.0865241	+	0.996250i	$0.527576\pi$
$211$	−15.7282	+	15.7282i	−1.08277	+	1.08277i	−0.996250	+	0.0865241i	$0.972424\pi$
$212$	7.43800	+	7.43800i	0.510844	+	0.510844i
$213$		−	17.1276i		−	1.17356i
$214$			1.29895i			0.0887945i
$215$	−11.3372			−0.773188
$216$	2.89880	+	2.89880i	0.197238	+	0.197238i
$217$	−6.60807	−	6.60807i	−0.448585	−	0.448585i
$218$	−4.52106	−	4.52106i	−0.306205	−	0.306205i
$219$	−22.5838	+	22.5838i	−1.52607	+	1.52607i
$220$	2.41708	−	2.41708i	0.162959	−	0.162959i
$221$	6.61765			0.445151
$222$	−3.85247	+	3.85247i	−0.258561	+	0.258561i
$223$	14.3426			0.960455			0.480227	−	0.877144i	$-0.340554\pi$
$223$	14.3426			0.960455			0.480227	+	0.877144i	$0.340554\pi$
$224$	−0.707107	+	0.707107i	−0.0472456	+	0.0472456i
$225$			2.31720i			0.154480i
$226$		−	10.6539i		−	0.708685i
$227$	12.3679	−	12.3679i	0.820889	−	0.820889i	−0.165347	−	0.986236i	$-0.552874\pi$
$227$	12.3679	−	12.3679i	0.820889	−	0.820889i	0.986236	+	0.165347i	$0.0528743\pi$
$228$	−14.0519			−0.930610
$229$	−3.41290	+	3.41290i	−0.225531	+	0.225531i	−0.810823	−	0.585292i	$-0.800980\pi$
$229$	−3.41290	+	3.41290i	−0.225531	+	0.225531i	0.585292	+	0.810823i	$0.300980\pi$
$230$	9.68666			0.638719
$231$	−3.02202	+	3.02202i	−0.198834	+	0.198834i
$232$	−7.06728	+	7.06728i	−0.463990	+	0.463990i
$233$	−7.39952	−	7.39952i	−0.484759	−	0.484759i	0.421889	−	0.906647i	$-0.361367\pi$
$233$	−7.39952	−	7.39952i	−0.484759	−	0.484759i	−0.906647	+	0.421889i	$0.861367\pi$
$234$	1.09586	+	1.09586i	0.0716386	+	0.0716386i
$235$	7.96533	+	7.96533i	0.519601	+	0.519601i
$236$	−10.7381			−0.698990
$237$		−	7.00235i		−	0.454852i
$238$		−	3.98313i		−	0.258188i
$239$	6.93393	+	6.93393i	0.448519	+	0.448519i	0.894862	−	0.446343i	$-0.147274\pi$
$239$	6.93393	+	6.93393i	0.448519	+	0.448519i	−0.446343	+	0.894862i	$0.647274\pi$
$240$	−2.22424	+	2.22424i	−0.143574	+	0.143574i
$241$			5.96031i			0.383938i	0.981401	+	0.191969i	$0.0614872\pi$
$241$			5.96031i			0.383938i	−0.981401	+	0.191969i	$0.938513\pi$
$242$	6.35568			0.408559
$243$	−6.62819	−	6.62819i	−0.425198	−	0.425198i
$244$		−	12.4049i		−	0.794143i
$245$	1.58615			0.101335
$246$	−12.6791	+	0.697359i	−0.808388	+	0.0444620i
$247$	11.7724			0.749057
$248$			9.34523i			0.593423i
$249$	2.83187	+	2.83187i	0.179462	+	0.179462i
$250$	11.8710			0.750785
$251$			7.29974i			0.460755i	0.973101	+	0.230378i	$0.0739962\pi$
$251$			7.29974i			0.460755i	−0.973101	+	0.230378i	$0.926004\pi$
$252$	0.659593	−	0.659593i	0.0415504	−	0.0415504i
$253$	−9.30626	−	9.30626i	−0.585080	−	0.585080i
$254$		−	4.16613i		−	0.261406i
$255$		−	12.5291i		−	0.784603i
$256$	1.00000			0.0625000
$257$	−17.0144	−	17.0144i	−1.06133	−	1.06133i	−0.997992	−	0.0633353i	$-0.979826\pi$
$257$	−17.0144	−	17.0144i	−1.06133	−	1.06133i	−0.0633353	−	0.997992i	$-0.520174\pi$
$258$	−10.0230	−	10.0230i	−0.624002	−	0.624002i
$259$	−1.94262	−	1.94262i	−0.120708	−	0.120708i
$260$	1.86341	−	1.86341i	0.115564	−	0.115564i
$261$	6.59240	−	6.59240i	0.408059	−	0.408059i
$262$	7.24503			0.447600
$263$	−10.1034	+	10.1034i	−0.623002	+	0.623002i	−0.946298	−	0.323296i	$-0.895209\pi$
$263$	−10.1034	+	10.1034i	−0.623002	+	0.623002i	0.323296	+	0.946298i	$0.395209\pi$
$264$	4.27378			0.263033
$265$	−11.7978	+	11.7978i	−0.724732	+	0.724732i
$266$		−	7.08572i		−	0.434453i
$267$		−	34.4866i		−	2.11055i
$268$	6.07639	−	6.07639i	0.371175	−	0.371175i
$269$	−7.51023			−0.457907			−0.228953	−	0.973437i	$-0.573530\pi$
$269$	−7.51023			−0.457907			−0.228953	+	0.973437i	$0.573530\pi$
$270$	−4.59793	+	4.59793i	−0.279821	+	0.279821i
$271$	−11.9601			−0.726522			−0.363261	−	0.931687i	$-0.618337\pi$
$271$	−11.9601			−0.726522			−0.363261	+	0.931687i	$0.618337\pi$
$272$	−2.81650	+	2.81650i	−0.170775	+	0.170775i
$273$	−2.32978	+	2.32978i	−0.141005	+	0.141005i
$274$	4.97206	+	4.97206i	0.300373	+	0.300373i
$275$	−3.78547	−	3.78547i	−0.228272	−	0.228272i
$276$	8.56378	+	8.56378i	0.515479	+	0.515479i
$277$	18.8642			1.13344			0.566721	−	0.823909i	$-0.308212\pi$
$277$	18.8642			1.13344			0.566721	+	0.823909i	$0.308212\pi$
$278$		−	6.66802i		−	0.399921i
$279$		−	8.71727i		−	0.521890i
$280$	−1.12158	−	1.12158i	−0.0670271	−	0.0670271i
$281$	18.3632	−	18.3632i	1.09546	−	1.09546i	0.100520	−	0.994935i	$-0.467949\pi$
$281$	18.3632	−	18.3632i	1.09546	−	1.09546i	0.994935	−	0.100520i	$-0.0320507\pi$
$282$			14.0840i			0.838688i
$283$	2.10610			0.125195			0.0625974	−	0.998039i	$-0.480062\pi$
$283$	2.10610			0.125195			0.0625974	+	0.998039i	$0.480062\pi$
$284$	−6.10702	−	6.10702i	−0.362385	−	0.362385i
$285$		−	22.2884i		−	1.32025i
$286$	−3.58047			−0.211718
$287$	−0.351646	−	6.39346i	−0.0207570	−	0.377394i
$288$	−0.932805			−0.0549661
$289$			1.13467i			0.0667456i
$290$	−11.2098	−	11.2098i	−0.658261	−	0.658261i
$291$	−10.3856			−0.608815
$292$			16.1050i			0.942474i
$293$	1.42089	−	1.42089i	0.0830090	−	0.0830090i	−0.664383	−	0.747392i	$-0.731306\pi$
$293$	1.42089	−	1.42089i	0.0830090	−	0.0830090i	0.747392	+	0.664383i	$0.231306\pi$
$294$	1.40228	+	1.40228i	0.0817829	+	0.0817829i
$295$		−	17.0322i		−	0.991655i
$296$			2.74728i			0.159682i
$297$	8.83474			0.512643
$298$	15.2358	+	15.2358i	0.882588	+	0.882588i
$299$	−7.17454	−	7.17454i	−0.414914	−	0.414914i
$300$	3.48345	+	3.48345i	0.201117	+	0.201117i
$301$	5.05411	−	5.05411i	0.291314	−	0.291314i
$302$	−2.64895	+	2.64895i	−0.152430	+	0.152430i
$303$	−31.5792			−1.81418
$304$	−5.01036	+	5.01036i	−0.287364	+	0.287364i
$305$	19.6761			1.12665
$306$	2.62724	−	2.62724i	0.150190	−	0.150190i
$307$		−	25.3910i		−	1.44914i	−0.689201	−	0.724570i	$-0.742038\pi$
$307$		−	25.3910i		−	1.44914i	0.689201	−	0.724570i	$-0.257962\pi$
$308$			2.15507i			0.122796i
$309$	−4.70667	+	4.70667i	−0.267753	+	0.267753i
$310$	−14.8229			−0.841887
$311$	4.91679	−	4.91679i	0.278805	−	0.278805i	−0.553827	−	0.832632i	$-0.686833\pi$
$311$	4.91679	−	4.91679i	0.278805	−	0.278805i	0.832632	+	0.553827i	$0.186833\pi$
$312$	3.29481			0.186532
$313$	−19.8081	+	19.8081i	−1.11962	+	1.11962i	−0.127822	+	0.991797i	$0.540799\pi$
$313$	−19.8081	+	19.8081i	−1.11962	+	1.11962i	−0.991797	+	0.127822i	$0.959201\pi$
$314$	13.4802	−	13.4802i	0.760732	−	0.760732i
$315$	1.04621	+	1.04621i	0.0589475	+	0.0589475i
$316$	−2.49677	−	2.49677i	−0.140454	−	0.140454i
$317$	5.92813	+	5.92813i	0.332957	+	0.332957i	0.853708	−	0.520751i	$-0.174348\pi$
$317$	5.92813	+	5.92813i	0.332957	+	0.332957i	−0.520751	+	0.853708i	$0.674348\pi$
$318$	−20.8604			−1.16979
$319$			21.5391i			1.20596i
$320$			1.58615i			0.0886685i
$321$	−1.82150	−	1.82150i	−0.101666	−	0.101666i
$322$	−4.31832	+	4.31832i	−0.240650	+	0.240650i
$323$		−	28.2233i		−	1.57039i
$324$	−10.9283			−0.607127
$325$	−2.91835	−	2.91835i	−0.161881	−	0.161881i
$326$		−	17.2081i		−	0.953070i
$327$	12.6796			0.701185
$328$	−4.27221	+	4.76951i	−0.235893	+	0.263352i
$329$	−7.10189			−0.391540
$330$			6.77886i			0.373164i
$331$	−0.234595	−	0.234595i	−0.0128945	−	0.0128945i	0.700630	−	0.713525i	$-0.252902\pi$
$331$	−0.234595	−	0.234595i	−0.0128945	−	0.0128945i	−0.713525	+	0.700630i	$0.752902\pi$
$332$	2.01947			0.110833
$333$		−	2.56267i		−	0.140434i
$334$	4.93231	−	4.93231i	0.269884	−	0.269884i
$335$	9.63807	+	9.63807i	0.526584	+	0.526584i
$336$		−	1.98313i		−	0.108189i
$337$			33.2342i			1.81038i	0.425004	+	0.905191i	$0.360273\pi$
$337$			33.2342i			1.81038i	−0.425004	+	0.905191i	$0.639727\pi$
$338$	10.2397			0.556965
$339$	14.9398	+	14.9398i	0.811417	+	0.811417i
$340$	−4.46739	−	4.46739i	−0.242278	−	0.242278i
$341$	14.2408	+	14.2408i	0.771185	+	0.771185i
$342$	4.67369	−	4.67369i	0.252724	−	0.252724i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−7.14760			−0.385373
$345$	−13.5835	+	13.5835i	−0.731308	+	0.731308i
$346$	0.436899			0.0234878
$347$	5.66767	−	5.66767i	0.304257	−	0.304257i	−0.538420	−	0.842677i	$-0.680979\pi$
$347$	5.66767	−	5.66767i	0.304257	−	0.304257i	0.842677	+	0.538420i	$0.180979\pi$
$348$		−	19.8207i		−	1.06250i
$349$		−	23.7758i		−	1.27269i	−0.771405	−	0.636344i	$-0.780446\pi$
$349$		−	23.7758i		−	1.27269i	0.771405	−	0.636344i	$-0.219554\pi$
$350$	−1.75654	+	1.75654i	−0.0938911	+	0.0938911i
$351$	6.81102			0.363545
$352$	1.52386	−	1.52386i	0.0812222	−	0.0812222i
$353$	4.33345			0.230646			0.115323	−	0.993328i	$-0.463210\pi$
$353$	4.33345			0.230646			0.115323	+	0.993328i	$0.463210\pi$
$354$	15.0579	−	15.0579i	0.800316	−	0.800316i
$355$	9.68666	−	9.68666i	0.514115	−	0.514115i
$356$	−12.2966	−	12.2966i	−0.651717	−	0.651717i
$357$	5.58548	+	5.58548i	0.295615	+	0.295615i
$358$	−3.35925	−	3.35925i	−0.177542	−	0.177542i
$359$	−30.4102			−1.60499			−0.802495	−	0.596659i	$-0.796495\pi$
$359$	−30.4102			−1.60499			−0.802495	+	0.596659i	$0.796495\pi$
$360$		−	1.47957i		−	0.0779802i
$361$		−	31.2074i		−	1.64249i
$362$	−6.46558	−	6.46558i	−0.339823	−	0.339823i
$363$	−8.91248	+	8.91248i	−0.467784	+	0.467784i
$364$			1.66142i			0.0870821i
$365$	−25.5450			−1.33708
$366$	17.3952	+	17.3952i	0.909262	+	0.909262i
$367$		−	6.73610i		−	0.351622i	−0.984424	−	0.175811i	$-0.943745\pi$
$367$		−	6.73610i		−	0.351622i	0.984424	−	0.175811i	$-0.0562547\pi$
$368$	6.10702			0.318350
$369$	3.98514	−	4.44902i	0.207458	−	0.231607i
$370$	−4.35760			−0.226541
$371$		−	10.5189i		−	0.546115i
$372$	−13.1047	−	13.1047i	−0.679445	−	0.679445i
$373$	−5.69811			−0.295037			−0.147518	−	0.989059i	$-0.547129\pi$
$373$	−5.69811			−0.295037			−0.147518	+	0.989059i	$0.547129\pi$
$374$			8.58392i			0.443864i
$375$	−16.6465	+	16.6465i	−0.859619	+	0.859619i
$376$	5.02180	+	5.02180i	0.258979	+	0.258979i
$377$			16.6053i			0.855217i
$378$		−	4.09952i		−	0.210856i
$379$	−9.74441			−0.500537			−0.250268	−	0.968177i	$-0.580519\pi$
$379$	−9.74441			−0.500537			−0.250268	+	0.968177i	$0.580519\pi$
$380$	−7.94719	−	7.94719i	−0.407682	−	0.407682i
$381$	5.84210	+	5.84210i	0.299300	+	0.299300i
$382$	15.5425	+	15.5425i	0.795223	+	0.795223i
$383$	−15.1746	+	15.1746i	−0.775388	+	0.775388i	−0.979043	−	0.203655i	$-0.934718\pi$
$383$	−15.1746	+	15.1746i	−0.775388	+	0.775388i	0.203655	+	0.979043i	$0.434718\pi$
$384$	−1.40228	+	1.40228i	−0.0715600	+	0.0715600i
$385$	−3.41826			−0.174211
$386$	−5.09221	+	5.09221i	−0.259187	+	0.259187i
$387$	6.66731			0.338919
$388$	−3.70310	+	3.70310i	−0.187997	+	0.187997i
$389$		−	13.9321i		−	0.706388i	−0.935550	−	0.353194i	$-0.885096\pi$
$389$		−	13.9321i		−	0.706388i	0.935550	−	0.353194i	$-0.114904\pi$
$390$			5.22607i			0.264632i
$391$	−17.2004	+	17.2004i	−0.869862	+	0.869862i
$392$	1.00000			0.0505076
$393$	−10.1596	+	10.1596i	−0.512484	+	0.512484i
$394$	5.17834			0.260881
$395$	3.96025	−	3.96025i	0.199262	−	0.199262i
$396$	−1.42147	+	1.42147i	−0.0714314	+	0.0714314i
$397$	−1.31578	−	1.31578i	−0.0660373	−	0.0660373i	0.673317	−	0.739354i	$-0.264869\pi$
$397$	−1.31578	−	1.31578i	−0.0660373	−	0.0660373i	−0.739354	+	0.673317i	$0.764869\pi$
$398$	4.18223	+	4.18223i	0.209636	+	0.209636i
$399$	9.93619	+	9.93619i	0.497432	+	0.497432i
$400$	2.48412			0.124206
$401$			30.3808i			1.51714i	0.651589	+	0.758572i	$0.274103\pi$
$401$			30.3808i			1.51714i	−0.651589	+	0.758572i	$0.725897\pi$
$402$			17.0417i			0.849961i
$403$	10.9788	+	10.9788i	0.546892	+	0.546892i
$404$	−11.2599	+	11.2599i	−0.560202	+	0.560202i
$405$		−	17.3339i		−	0.861329i
$406$	9.99465			0.496026
$407$	4.18647	+	4.18647i	0.207516	+	0.207516i
$408$		−	7.89906i		−	0.391062i
$409$	28.4107			1.40482			0.702409	−	0.711773i	$-0.252108\pi$
$409$	28.4107			1.40482			0.702409	+	0.711773i	$0.252108\pi$
$410$	−7.56517	−	6.77637i	−0.373617	−	0.334661i
$411$	−13.9445			−0.687831
$412$			3.35643i			0.165359i
$413$	7.59298	+	7.59298i	0.373626	+	0.373626i
$414$	−5.69666			−0.279975
$415$			3.20318i			0.157238i
$416$	1.17480	−	1.17480i	0.0575994	−	0.0575994i
$417$	9.35046	+	9.35046i	0.457894	+	0.457894i
$418$			15.2702i			0.746890i
$419$			35.4270i			1.73072i	0.501147	+	0.865362i	$0.332912\pi$
$419$			35.4270i			1.73072i	−0.501147	+	0.865362i	$0.667088\pi$
$420$	3.14554			0.153487
$421$	14.7557	+	14.7557i	0.719148	+	0.719148i	0.968431	−	0.249282i	$-0.0801948\pi$
$421$	14.7557	+	14.7557i	0.719148	+	0.719148i	−0.249282	+	0.968431i	$0.580195\pi$
$422$	−15.7282	−	15.7282i	−0.765637	−	0.765637i
$423$	−4.68435	−	4.68435i	−0.227761	−	0.227761i
$424$	−7.43800	+	7.43800i	−0.361221	+	0.361221i
$425$	−6.99653	+	6.99653i	−0.339382	+	0.339382i
$426$	17.1276			0.829833
$427$	−8.77159	+	8.77159i	−0.424487	+	0.424487i
$428$	−1.29895			−0.0627872
$429$	5.02084	−	5.02084i	0.242409	−	0.242409i
$430$		−	11.3372i		−	0.546727i
$431$		−	28.8932i		−	1.39173i	−0.718170	−	0.695867i	$-0.755020\pi$
$431$		−	28.8932i		−	1.39173i	0.718170	−	0.695867i	$-0.244980\pi$
$432$	−2.89880	+	2.89880i	−0.139468	+	0.139468i
$433$	−13.9634			−0.671039			−0.335520	−	0.942033i	$-0.608912\pi$
$433$	−13.9634			−0.671039			−0.335520	+	0.942033i	$0.608912\pi$
$434$	6.60807	−	6.60807i	0.317198	−	0.317198i
$435$	31.4386			1.50737
$436$	4.52106	−	4.52106i	0.216520	−	0.216520i
$437$	−30.5984	+	30.5984i	−1.46372	+	1.46372i
$438$	−22.5838	−	22.5838i	−1.07910	−	1.07910i
$439$	−5.52443	−	5.52443i	−0.263667	−	0.263667i	0.562875	−	0.826542i	$-0.309695\pi$
$439$	−5.52443	−	5.52443i	−0.263667	−	0.263667i	−0.826542	+	0.562875i	$0.809695\pi$
$440$	2.41708	+	2.41708i	0.115230	+	0.115230i
$441$	−0.932805			−0.0444193
$442$			6.61765i			0.314770i
$443$		−	25.7874i		−	1.22520i	−0.790394	−	0.612599i	$-0.790124\pi$
$443$		−	25.7874i		−	1.22520i	0.790394	−	0.612599i	$-0.209876\pi$
$444$	−3.85247	−	3.85247i	−0.182830	−	0.182830i
$445$	19.5042	−	19.5042i	0.924589	−	0.924589i
$446$			14.3426i			0.679144i
$447$	−42.7299			−2.02106
$448$	−0.707107	−	0.707107i	−0.0334077	−	0.0334077i
$449$			34.6856i			1.63691i	0.574567	+	0.818457i	$0.305170\pi$
$449$			34.6856i			1.63691i	−0.574567	+	0.818457i	$0.694830\pi$
$450$	−2.31720			−0.109234
$451$	0.757821	+	13.7783i	0.0356844	+	0.648797i
$452$	10.6539			0.501116
$453$		−	7.42916i		−	0.349052i
$454$	12.3679	+	12.3679i	0.580456	+	0.580456i
$455$	−2.63526			−0.123543
$456$		−	14.0519i		−	0.658040i
$457$	−21.6838	+	21.6838i	−1.01432	+	1.01432i	−0.0144284	+	0.999896i	$0.504593\pi$
$457$	−21.6838	+	21.6838i	−1.01432	+	1.01432i	−0.999896	+	0.0144284i	$0.995407\pi$
$458$	−3.41290	−	3.41290i	−0.159474	−	0.159474i
$459$		−	16.3289i		−	0.762168i
$460$			9.68666i			0.451643i
$461$	36.3096			1.69111			0.845554	−	0.533891i	$-0.179271\pi$
$461$	36.3096			1.69111			0.845554	+	0.533891i	$0.179271\pi$
$462$	−3.02202	−	3.02202i	−0.140597	−	0.140597i
$463$	−1.00359	−	1.00359i	−0.0466408	−	0.0466408i	0.683402	−	0.730043i	$-0.260500\pi$
$463$	−1.00359	−	1.00359i	−0.0466408	−	0.0466408i	−0.730043	+	0.683402i	$0.760500\pi$
$464$	−7.06728	−	7.06728i	−0.328090	−	0.328090i
$465$	20.7860	−	20.7860i	0.963927	−	0.963927i
$466$	7.39952	−	7.39952i	0.342776	−	0.342776i
$467$	18.2854			0.846146			0.423073	−	0.906096i	$-0.360951\pi$
$467$	18.2854			0.846146			0.423073	+	0.906096i	$0.360951\pi$
$468$	−1.09586	+	1.09586i	−0.0506562	+	0.0506562i
$469$	−8.59331			−0.396802
$470$	−7.96533	+	7.96533i	−0.367413	+	0.367413i
$471$			37.8061i			1.74202i
$472$		−	10.7381i		−	0.494261i
$473$	−10.8920	+	10.8920i	−0.500813	+	0.500813i
$474$	7.00235			0.321629
$475$	−12.4464	+	12.4464i	−0.571078	+	0.571078i
$476$	3.98313			0.182566
$477$	6.93820	−	6.93820i	0.317678	−	0.317678i
$478$	−6.93393	+	6.93393i	−0.317151	+	0.317151i
$479$	−20.1039	−	20.1039i	−0.918571	−	0.918571i	0.0783546	−	0.996926i	$-0.475033\pi$
$479$	−20.1039	−	20.1039i	−0.918571	−	0.918571i	−0.996926	+	0.0783546i	$0.975033\pi$
$480$	−2.22424	−	2.22424i	−0.101522	−	0.101522i
$481$	3.22751	+	3.22751i	0.147162	+	0.147162i
$482$	−5.96031			−0.271485
$483$		−	12.1110i		−	0.551070i
$484$			6.35568i			0.288895i
$485$	−5.87368	−	5.87368i	−0.266710	−	0.266710i
$486$	6.62819	−	6.62819i	0.300661	−	0.300661i
$487$			18.1781i			0.823730i	0.911245	+	0.411865i	$0.135122\pi$
$487$			18.1781i			0.823730i	−0.911245	+	0.411865i	$0.864878\pi$
$488$	12.4049			0.561544
$489$	24.1307	+	24.1307i	1.09123	+	1.09123i
$490$			1.58615i			0.0716550i
$491$	8.40653			0.379382			0.189691	−	0.981844i	$-0.439251\pi$
$491$	8.40653			0.379382			0.189691	+	0.981844i	$0.439251\pi$
$492$	−0.697359	−	12.6791i	−0.0314394	−	0.571616i
$493$	39.8100			1.79295
$494$			11.7724i			0.529663i
$495$	−2.25466	−	2.25466i	−0.101339	−	0.101339i
$496$	−9.34523			−0.419613
$497$			8.63663i			0.387406i
$498$	−2.83187	+	2.83187i	−0.126899	+	0.126899i
$499$	11.0199	+	11.0199i	0.493320	+	0.493320i	0.909351	−	0.416030i	$-0.136579\pi$
$499$	11.0199	+	11.0199i	0.493320	+	0.493320i	−0.416030	+	0.909351i	$0.636579\pi$
$500$			11.8710i			0.530885i
$501$			13.8330i			0.618013i
$502$	−7.29974			−0.325803
$503$	−13.8985	−	13.8985i	−0.619701	−	0.619701i	0.325753	−	0.945455i	$-0.394382\pi$
$503$	−13.8985	−	13.8985i	−0.619701	−	0.619701i	−0.945455	+	0.325753i	$0.894382\pi$
$504$	0.659593	+	0.659593i	0.0293806	+	0.0293806i
$505$	−17.8599	−	17.8599i	−0.794757	−	0.794757i
$506$	9.30626	−	9.30626i	0.413714	−	0.413714i
$507$	−14.3590	+	14.3590i	−0.637703	+	0.637703i
$508$	4.16613			0.184842
$509$	−2.42818	+	2.42818i	−0.107627	+	0.107627i	−0.758870	−	0.651243i	$-0.774248\pi$
$509$	−2.42818	+	2.42818i	−0.107627	+	0.107627i	0.651243	+	0.758870i	$0.274248\pi$
$510$	12.5291			0.554798
$511$	11.3880	−	11.3880i	0.503773	−	0.503773i
$512$			1.00000i			0.0441942i
$513$		−	29.0480i		−	1.28250i
$514$	17.0144	−	17.0144i	0.750472	−	0.750472i
$515$	−5.32380			−0.234595
$516$	10.0230	−	10.0230i	0.441236	−	0.441236i
$517$	15.3051			0.673116
$518$	1.94262	−	1.94262i	0.0853538	−	0.0853538i
$519$	−0.612656	+	0.612656i	−0.0268926	+	0.0268926i
$520$	1.86341	+	1.86341i	0.0817160	+	0.0817160i
$521$	−8.69534	−	8.69534i	−0.380950	−	0.380950i	0.490494	−	0.871444i	$-0.336816\pi$
$521$	−8.69534	−	8.69534i	−0.380950	−	0.380950i	−0.871444	+	0.490494i	$0.836816\pi$
$522$	6.59240	+	6.59240i	0.288541	+	0.288541i
$523$	−2.07808			−0.0908682			−0.0454341	−	0.998967i	$-0.514467\pi$
$523$	−2.07808			−0.0908682			−0.0454341	+	0.998967i	$0.514467\pi$
$524$			7.24503i			0.316501i
$525$		−	4.92634i		−	0.215003i
$526$	−10.1034	−	10.1034i	−0.440529	−	0.440529i
$527$	26.3208	−	26.3208i	1.14655	−	1.14655i
$528$			4.27378i			0.185992i
$529$	14.2957			0.621552
$530$	−11.7978	−	11.7978i	−0.512463	−	0.512463i
$531$			10.0165i			0.434681i
$532$	7.08572			0.307205
$533$	0.584231	+	10.6222i	0.0253059	+	0.460100i
$534$	34.4866			1.49238
$535$		−	2.06033i		−	0.0890760i
$536$	6.07639	+	6.07639i	0.262460	+	0.262460i
$537$	9.42125			0.406557
$538$		−	7.51023i		−	0.323789i
$539$	1.52386	−	1.52386i	0.0656374	−	0.0656374i
$540$	−4.59793	−	4.59793i	−0.197863	−	0.197863i
$541$			17.8201i			0.766148i	0.923718	+	0.383074i	$0.125134\pi$
$541$			17.8201i			0.766148i	−0.923718	+	0.383074i	$0.874866\pi$
$542$		−	11.9601i		−	0.513729i
$543$	18.1332			0.778169
$544$	−2.81650	−	2.81650i	−0.120756	−	0.120756i
$545$	7.17109	+	7.17109i	0.307176	+	0.307176i
$546$	−2.32978	−	2.32978i	−0.0997055	−	0.0997055i
$547$	10.5511	−	10.5511i	0.451131	−	0.451131i	−0.444599	−	0.895730i	$-0.646654\pi$
$547$	10.5511	−	10.5511i	0.451131	−	0.451131i	0.895730	+	0.444599i	$0.146654\pi$
$548$	−4.97206	+	4.97206i	−0.212396	+	0.212396i
$549$	−11.5714			−0.493853
$550$	3.78547	−	3.78547i	0.161413	−	0.161413i
$551$	70.8193			3.01700
$552$	−8.56378	+	8.56378i	−0.364499	+	0.364499i
$553$			3.53096i			0.150152i
$554$			18.8642i			0.801465i
$555$	6.11059	−	6.11059i	0.259380	−	0.259380i
$556$	6.66802			0.282787
$557$	4.79505	−	4.79505i	0.203173	−	0.203173i	−0.598185	−	0.801358i	$-0.704111\pi$
$557$	4.79505	−	4.79505i	0.203173	−	0.203173i	0.801358	+	0.598185i	$0.204111\pi$
$558$	8.71727			0.369032
$559$	−8.39700	+	8.39700i	−0.355155	+	0.355155i
$560$	1.12158	−	1.12158i	0.0473953	−	0.0473953i
$561$	−12.0371	−	12.0371i	−0.508206	−	0.508206i
$562$	18.3632	+	18.3632i	0.774604	+	0.774604i
$563$	9.34570	+	9.34570i	0.393875	+	0.393875i	0.876066	−	0.482191i	$-0.160159\pi$
$563$	9.34570	+	9.34570i	0.393875	+	0.393875i	−0.482191	+	0.876066i	$0.660159\pi$
$564$	−14.0840			−0.593042
$565$			16.8987i			0.710932i
$566$			2.10610i			0.0885260i
$567$	7.72747	+	7.72747i	0.324523	+	0.324523i
$568$	6.10702	−	6.10702i	0.256245	−	0.256245i
$569$			3.73057i			0.156394i	0.996938	+	0.0781968i	$0.0249162\pi$
$569$			3.73057i			0.156394i	−0.996938	+	0.0781968i	$0.975084\pi$
$570$	22.2884			0.933560
$571$	−12.1834	−	12.1834i	−0.509859	−	0.509859i	0.404624	−	0.914483i	$-0.367402\pi$
$571$	−12.1834	−	12.1834i	−0.509859	−	0.509859i	−0.914483	+	0.404624i	$0.867402\pi$
$572$		−	3.58047i		−	0.149707i
$573$	−43.5900			−1.82100
$574$	6.39346	−	0.351646i	0.266858	−	0.0146774i
$575$	15.1706			0.632658
$576$		−	0.932805i		−	0.0388669i
$577$	−17.0798	−	17.0798i	−0.711043	−	0.711043i	0.255710	−	0.966753i	$-0.417691\pi$
$577$	−17.0798	−	17.0798i	−0.711043	−	0.711043i	−0.966753	+	0.255710i	$0.917691\pi$
$578$	−1.13467			−0.0471963
$579$		−	14.2815i		−	0.593517i
$580$	11.2098	−	11.2098i	0.465461	−	0.465461i
$581$	−1.42798	−	1.42798i	−0.0592426	−	0.0592426i
$582$		−	10.3856i		−	0.430497i
$583$			22.6690i			0.938853i
$584$	−16.1050			−0.666430
$585$	−1.73820	−	1.73820i	−0.0718657	−	0.0718657i
$586$	1.42089	+	1.42089i	0.0586962	+	0.0586962i
$587$	−12.5201	−	12.5201i	−0.516759	−	0.516759i	0.399830	−	0.916589i	$-0.369069\pi$
$587$	−12.5201	−	12.5201i	−0.516759	−	0.516759i	−0.916589	+	0.399830i	$0.869069\pi$
$588$	−1.40228	+	1.40228i	−0.0578292	+	0.0578292i
$589$	46.8229	−	46.8229i	1.92931	−	1.92931i
$590$	17.0322			0.701206
$591$	−7.26151	+	7.26151i	−0.298699	+	0.298699i
$592$	−2.74728			−0.112912
$593$	24.6510	−	24.6510i	1.01230	−	1.01230i	0.0123729	−	0.999923i	$-0.496061\pi$
$593$	24.6510	−	24.6510i	1.01230	−	1.01230i	0.999923	−	0.0123729i	$-0.00393852\pi$
$594$			8.83474i			0.362494i
$595$			6.31785i			0.259006i
$596$	−15.2358	+	15.2358i	−0.624084	+	0.624084i
$597$	−11.7293			−0.480050
$598$	7.17454	−	7.17454i	0.293389	−	0.293389i
$599$	−14.9728			−0.611773			−0.305886	−	0.952068i	$-0.598953\pi$
$599$	−14.9728			−0.611773			−0.305886	+	0.952068i	$0.598953\pi$
$600$	−3.48345	+	3.48345i	−0.142211	+	0.142211i
$601$	4.64267	−	4.64267i	0.189379	−	0.189379i	−0.606049	−	0.795427i	$-0.707246\pi$
$601$	4.64267	−	4.64267i	0.189379	−	0.189379i	0.795427	+	0.606049i	$0.207246\pi$
$602$	5.05411	+	5.05411i	0.205990	+	0.205990i
$603$	−5.66809	−	5.66809i	−0.230822	−	0.230822i
$604$	−2.64895	−	2.64895i	−0.107784	−	0.107784i
$605$	−10.0811			−0.409854
$606$		−	31.5792i		−	1.28282i
$607$		−	30.9530i		−	1.25634i	−0.778075	−	0.628172i	$-0.783804\pi$
$607$		−	30.9530i		−	1.25634i	0.778075	−	0.628172i	$-0.216196\pi$
$608$	−5.01036	−	5.01036i	−0.203197	−	0.203197i
$609$	−14.0153	+	14.0153i	−0.567930	+	0.567930i
$610$			19.6761i			0.796660i
$611$	11.7992			0.477345
$612$	2.62724	+	2.62724i	0.106200	+	0.106200i
$613$			10.1505i			0.409974i	0.978765	+	0.204987i	$0.0657152\pi$
$613$			10.1505i			0.409974i	−0.978765	+	0.204987i	$0.934285\pi$
$614$	25.3910			1.02470
$615$	20.1109	−	1.10612i	0.810950	−	0.0446030i
$616$	−2.15507			−0.0868302
$617$			3.09595i			0.124638i	0.998056	+	0.0623191i	$0.0198496\pi$
$617$			3.09595i			0.124638i	−0.998056	+	0.0623191i	$0.980150\pi$
$618$	−4.70667	−	4.70667i	−0.189330	−	0.189330i
$619$	21.9289			0.881398			0.440699	−	0.897655i	$-0.354731\pi$
$619$	21.9289			0.881398			0.440699	+	0.897655i	$0.354731\pi$
$620$		−	14.8229i		−	0.595304i
$621$	−17.7030	+	17.7030i	−0.710397	+	0.710397i
$622$	4.91679	+	4.91679i	0.197145	+	0.197145i
$623$			17.3900i			0.696715i
$624$			3.29481i			0.131898i
$625$	−6.40850			−0.256340
$626$	−19.8081	−	19.8081i	−0.791690	−	0.791690i
$627$	−21.4132	−	21.4132i	−0.855160	−	0.855160i
$628$	13.4802	+	13.4802i	0.537918	+	0.537918i
$629$	7.73770	−	7.73770i	0.308522	−	0.308522i
$630$	−1.04621	+	1.04621i	−0.0416822	+	0.0416822i
$631$	27.7002			1.10273			0.551364	−	0.834265i	$-0.314108\pi$
$631$	27.7002			1.10273			0.551364	+	0.834265i	$0.314108\pi$
$632$	2.49677	−	2.49677i	0.0993160	−	0.0993160i
$633$	44.1108			1.75325
$634$	−5.92813	+	5.92813i	−0.235436	+	0.235436i
$635$			6.60811i			0.262235i
$636$		−	20.8604i		−	0.827168i
$637$	1.17480	−	1.17480i	0.0465473	−	0.0465473i
$638$	−21.5391			−0.852743
$639$	−5.69666	+	5.69666i	−0.225356	+	0.225356i
$640$	−1.58615			−0.0626981
$641$	−31.8489	+	31.8489i	−1.25795	+	1.25795i	−0.305887	+	0.952068i	$0.598953\pi$
$641$	−31.8489	+	31.8489i	−1.25795	+	1.25795i	−0.952068	+	0.305887i	$0.901047\pi$
$642$	1.82150	−	1.82150i	0.0718889	−	0.0718889i
$643$	17.3075	+	17.3075i	0.682540	+	0.682540i	0.960572	−	0.278032i	$-0.0896822\pi$
$643$	17.3075	+	17.3075i	0.682540	+	0.682540i	−0.278032	+	0.960572i	$0.589682\pi$
$644$	−4.31832	−	4.31832i	−0.170165	−	0.170165i
$645$	15.8979	+	15.8979i	0.625981	+	0.625981i
$646$	28.2233			1.11043
$647$			18.1376i			0.713062i	0.934283	+	0.356531i	$0.116041\pi$
$647$			18.1376i			0.713062i	−0.934283	+	0.356531i	$0.883959\pi$
$648$		−	10.9283i		−	0.429304i
$649$	−16.3634	−	16.3634i	−0.642319	−	0.642319i
$650$	2.91835	−	2.91835i	0.114467	−	0.114467i
$651$			18.5328i			0.726358i
$652$	17.2081			0.673922
$653$	13.1212	+	13.1212i	0.513474	+	0.513474i	0.915589	−	0.402115i	$-0.131725\pi$
$653$	13.1212	+	13.1212i	0.513474	+	0.513474i	−0.402115	+	0.915589i	$0.631725\pi$
$654$			12.6796i			0.495813i
$655$	−11.4917			−0.449019
$656$	−4.76951	−	4.27221i	−0.186218	−	0.166802i
$657$	15.0228			0.586096
$658$		−	7.10189i		−	0.276861i
$659$	−6.83367	−	6.83367i	−0.266202	−	0.266202i	0.561366	−	0.827568i	$-0.310276\pi$
$659$	−6.83367	−	6.83367i	−0.266202	−	0.266202i	−0.827568	+	0.561366i	$0.810276\pi$
$660$	−6.77886			−0.263867
$661$			10.3391i			0.402146i	0.979576	+	0.201073i	$0.0644429\pi$
$661$			10.3391i			0.402146i	−0.979576	+	0.201073i	$0.935557\pi$
$662$	0.234595	−	0.234595i	0.00911778	−	0.00911778i
$663$	−9.27983	−	9.27983i	−0.360399	−	0.360399i
$664$			2.01947i			0.0783706i
$665$			11.2390i			0.435830i
$666$	2.56267			0.0993016
$667$	−43.1600	−	43.1600i	−1.67116	−	1.67116i
$668$	4.93231	+	4.93231i	0.190837	+	0.190837i
$669$	−20.1125	−	20.1125i	−0.777593	−	0.777593i
$670$	−9.63807	+	9.63807i	−0.372351	+	0.372351i
$671$	18.9034	−	18.9034i	0.729757	−	0.729757i
$672$	1.98313			0.0765009
$673$	−20.8609	+	20.8609i	−0.804127	+	0.804127i	−0.983738	−	0.179610i	$-0.942516\pi$
$673$	−20.8609	+	20.8609i	−0.804127	+	0.804127i	0.179610	+	0.983738i	$0.442516\pi$
$674$	−33.2342			−1.28013
$675$	−7.20097	+	7.20097i	−0.277165	+	0.277165i
$676$			10.2397i			0.393834i
$677$		−	23.0766i		−	0.886906i	−0.896298	−	0.443453i	$-0.853753\pi$
$677$		−	23.0766i		−	0.886906i	0.896298	−	0.443453i	$-0.146247\pi$
$678$	−14.9398	+	14.9398i	−0.573758	+	0.573758i
$679$	5.23698			0.200977
$680$	4.46739	−	4.46739i	0.171317	−	0.171317i
$681$	−34.6867			−1.32920
$682$	−14.2408	+	14.2408i	−0.545310	+	0.545310i
$683$	−22.5184	+	22.5184i	−0.861644	+	0.861644i	−0.991529	−	0.129885i	$-0.958539\pi$
$683$	−22.5184	+	22.5184i	−0.861644	+	0.861644i	0.129885	+	0.991529i	$0.458539\pi$
$684$	4.67369	+	4.67369i	0.178703	+	0.178703i
$685$	−7.88644	−	7.88644i	−0.301326	−	0.301326i
$686$	−0.707107	−	0.707107i	−0.0269975	−	0.0269975i
$687$	9.57172			0.365184
$688$		−	7.14760i		−	0.272500i
$689$			17.4763i			0.665795i
$690$	−13.5835	−	13.5835i	−0.517113	−	0.517113i
$691$	−19.3661	+	19.3661i	−0.736720	+	0.736720i	−0.971942	−	0.235221i	$-0.924418\pi$
$691$	−19.3661	+	19.3661i	−0.736720	+	0.736720i	0.235221	+	0.971942i	$0.424418\pi$
$692$			0.436899i			0.0166084i
$693$	2.01026			0.0763634
$694$	5.66767	+	5.66767i	0.215142	+	0.215142i
$695$			10.5765i			0.401189i
$696$	19.8207			0.751301
$697$	25.4660	−	1.40065i	0.964593	−	0.0530534i
$698$	23.7758			0.899926
$699$			20.7525i			0.784930i
$700$	−1.75654	−	1.75654i	−0.0663910	−	0.0663910i
$701$	−14.9924			−0.566253			−0.283127	−	0.959083i	$-0.591372\pi$
$701$	−14.9924			−0.566253			−0.283127	+	0.959083i	$0.591372\pi$
$702$			6.81102i			0.257065i
$703$	13.7648	−	13.7648i	0.519151	−	0.519151i
$704$	1.52386	+	1.52386i	0.0574327	+	0.0574327i
$705$		−	22.3393i		−	0.841347i
$706$			4.33345i			0.163091i
$707$	15.9239			0.598881
$708$	15.0579	+	15.0579i	0.565909	+	0.565909i
$709$	34.3676	+	34.3676i	1.29070	+	1.29070i	0.934353	+	0.356350i	$0.115979\pi$
$709$	34.3676	+	34.3676i	1.29070	+	1.29070i	0.356350	+	0.934353i	$0.384021\pi$
$710$	9.68666	+	9.68666i	0.363534	+	0.363534i
$711$	−2.32899	+	2.32899i	−0.0873441	+	0.0873441i
$712$	12.2966	−	12.2966i	0.460834	−	0.460834i
$713$	−57.0715			−2.13734
$714$	−5.58548	+	5.58548i	−0.209031	+	0.209031i
$715$	5.67917			0.212389
$716$	3.35925	−	3.35925i	0.125541	−	0.125541i
$717$		−	19.4467i		−	0.726250i
$718$		−	30.4102i		−	1.13490i
$719$	−12.6627	+	12.6627i	−0.472239	+	0.472239i	−0.902638	−	0.430400i	$-0.858373\pi$
$719$	−12.6627	+	12.6627i	−0.472239	+	0.472239i	0.430400	+	0.902638i	$0.358373\pi$
$720$	1.47957			0.0551403
$721$	2.37335	−	2.37335i	0.0883883	−	0.0883883i
$722$	31.2074			1.16142
$723$	8.35806	−	8.35806i	0.310839	−	0.310839i
$724$	6.46558	−	6.46558i	0.240291	−	0.240291i
$725$	−17.5560	−	17.5560i	−0.652014	−	0.652014i
$726$	−8.91248	−	8.91248i	−0.330773	−	0.330773i
$727$	2.96258	+	2.96258i	0.109876	+	0.109876i	0.759907	−	0.650031i	$-0.225244\pi$
$727$	2.96258	+	2.96258i	0.109876	+	0.109876i	−0.650031	+	0.759907i	$0.725244\pi$
$728$	−1.66142			−0.0615763
$729$		−	14.1957i		−	0.525765i
$730$		−	25.5450i		−	0.945461i
$731$	20.1312	+	20.1312i	0.744579	+	0.744579i
$732$	−17.3952	+	17.3952i	−0.642945	+	0.642945i
$733$		−	11.1209i		−	0.410761i	−0.978682	−	0.205380i	$-0.934157\pi$
$733$		−	11.1209i		−	0.410761i	0.978682	−	0.205380i	$-0.0658431\pi$
$734$	6.73610			0.248634
$735$	−2.22424	−	2.22424i	−0.0820422	−	0.0820422i
$736$			6.10702i			0.225108i
$737$	18.5192			0.682163
$738$	4.44902	+	3.98514i	0.163771	+	0.146695i
$739$	−23.2928			−0.856838			−0.428419	−	0.903580i	$-0.640929\pi$
$739$	−23.2928			−0.856838			−0.428419	+	0.903580i	$0.640929\pi$
$740$		−	4.35760i		−	0.160188i
$741$	−16.5082	−	16.5082i	−0.606443	−	0.606443i
$742$	10.5189			0.386161
$743$			23.5886i			0.865383i	0.901542	+	0.432691i	$0.142436\pi$
$743$			23.5886i			0.865383i	−0.901542	+	0.432691i	$0.857564\pi$
$744$	13.1047	−	13.1047i	0.480441	−	0.480441i
$745$	−24.1663	−	24.1663i	−0.885386	−	0.885386i
$746$		−	5.69811i		−	0.208623i
$747$		−	1.88377i		−	0.0689236i
$748$	−8.58392			−0.313859
$749$	0.918498	+	0.918498i	0.0335612	+	0.0335612i
$750$	−16.6465	−	16.6465i	−0.607843	−	0.607843i
$751$	−1.98972	−	1.98972i	−0.0726058	−	0.0726058i	0.669871	−	0.742477i	$-0.266349\pi$
$751$	−1.98972	−	1.98972i	−0.0726058	−	0.0726058i	−0.742477	+	0.669871i	$0.766349\pi$
$752$	−5.02180	+	5.02180i	−0.183126	+	0.183126i
$753$	10.2363	−	10.2363i	0.373032	−	0.373032i
$754$	−16.6053			−0.604730
$755$	4.20163	−	4.20163i	0.152913	−	0.152913i
$756$	4.09952			0.149098
$757$	3.09270	−	3.09270i	0.112406	−	0.112406i	−0.648667	−	0.761073i	$-0.724673\pi$
$757$	3.09270	−	3.09270i	0.112406	−	0.112406i	0.761073	+	0.648667i	$0.224673\pi$
$758$		−	9.74441i		−	0.353933i
$759$			26.1001i			0.947372i
$760$	7.94719	−	7.94719i	0.288275	−	0.288275i
$761$	−23.7013			−0.859173			−0.429587	−	0.903026i	$-0.641341\pi$
$761$	−23.7013			−0.859173			−0.429587	+	0.903026i	$0.641341\pi$
$762$	−5.84210	+	5.84210i	−0.211637	+	0.211637i
$763$	−6.39375			−0.231469
$764$	−15.5425	+	15.5425i	−0.562308	+	0.562308i
$765$	−4.16721	+	4.16721i	−0.150666	+	0.150666i
$766$	−15.1746	−	15.1746i	−0.548282	−	0.548282i
$767$	−12.6151	−	12.6151i	−0.455506	−	0.455506i
$768$	−1.40228	−	1.40228i	−0.0506006	−	0.0506006i
$769$	−50.7910			−1.83157			−0.915785	−	0.401669i	$-0.868430\pi$
$769$	−50.7910			−1.83157			−0.915785	+	0.401669i	$0.868430\pi$
$770$		−	3.41826i		−	0.123186i
$771$			47.7180i			1.71852i
$772$	−5.09221	−	5.09221i	−0.183273	−	0.183273i
$773$	−22.9512	+	22.9512i	−0.825498	+	0.825498i	−0.986890	−	0.161392i	$-0.948401\pi$
$773$	−22.9512	+	22.9512i	−0.825498	+	0.825498i	0.161392	+	0.986890i	$0.448401\pi$
$774$			6.66731i			0.239652i
$775$	−23.2147			−0.833897
$776$	−3.70310	−	3.70310i	−0.132934	−	0.132934i
$777$			5.44821i			0.195453i
$778$	13.9321			0.499491
$779$	45.3023	−	2.49166i	1.62312	−	0.0892731i
$780$	−5.22607			−0.187123
$781$		−	18.6125i		−	0.666009i
$782$	−17.2004	−	17.2004i	−0.615086	−	0.615086i
$783$	40.9732			1.46426
$784$			1.00000i			0.0357143i
$785$	−21.3816	+	21.3816i	−0.763143	+	0.763143i
$786$	−10.1596	−	10.1596i	−0.362381	−	0.362381i
$787$		−	37.8952i		−	1.35082i	−0.737443	−	0.675409i	$-0.763967\pi$
$787$		−	37.8952i		−	1.35082i	0.737443	−	0.675409i	$-0.236033\pi$
$788$			5.17834i			0.184471i
$789$	28.3357			1.00878
$790$	3.96025	+	3.96025i	0.140899	+	0.140899i
$791$	−7.53343	−	7.53343i	−0.267858	−	0.267858i
$792$	−1.42147	−	1.42147i	−0.0505096	−	0.0505096i
$793$	14.5733	−	14.5733i	0.517513	−	0.517513i
$794$	1.31578	−	1.31578i	0.0466954	−	0.0466954i
$795$	33.0877			1.17350
$796$	−4.18223	+	4.18223i	−0.148235	+	0.148235i
$797$	−16.9168			−0.599223			−0.299612	−	0.954061i	$-0.596857\pi$
$797$	−16.9168			−0.599223			−0.299612	+	0.954061i	$0.596857\pi$
$798$	−9.93619	+	9.93619i	−0.351737	+	0.351737i
$799$		−	28.2878i		−	1.00075i
$800$			2.48412i			0.0878271i
$801$	−11.4703	+	11.4703i	−0.405283	+	0.405283i
$802$	−30.3808			−1.07278
$803$	−24.5418	+	24.5418i	−0.866062	+	0.866062i
$804$	−17.0417			−0.601013
$805$	6.84950	−	6.84950i	0.241413	−	0.241413i
$806$	−10.9788	+	10.9788i	−0.386711	+	0.386711i
$807$	10.5315	+	10.5315i	0.370726	+	0.370726i
$808$	−11.2599	−	11.2599i	−0.396123	−	0.396123i
$809$	−30.4167	−	30.4167i	−1.06939	−	1.06939i	−0.997405	−	0.0719882i	$-0.977066\pi$
$809$	−30.4167	−	30.4167i	−1.06939	−	1.06939i	−0.0719882	−	0.997405i	$-0.522934\pi$
$810$	17.3339			0.609052
$811$			35.2170i			1.23664i	0.785928	+	0.618318i	$0.212186\pi$
$811$			35.2170i			1.23664i	−0.785928	+	0.618318i	$0.787814\pi$
$812$			9.99465i			0.350743i
$813$	16.7714	+	16.7714i	0.588199	+	0.588199i
$814$	−4.18647	+	4.18647i	−0.146736	+	0.146736i
$815$			27.2947i			0.956091i
$816$	7.89906			0.276523
$817$	35.8120	+	35.8120i	1.25290	+	1.25290i
$818$			28.4107i			0.993357i
$819$	1.54978			0.0541537
$820$	6.77637	−	7.56517i	0.236641	−	0.264187i
$821$	−5.93171			−0.207018			−0.103509	−	0.994629i	$-0.533007\pi$
$821$	−5.93171			−0.207018			−0.103509	+	0.994629i	$0.533007\pi$
$822$		−	13.9445i		−	0.486370i
$823$	−22.6843	−	22.6843i	−0.790726	−	0.790726i	0.190886	−	0.981612i	$-0.438864\pi$
$823$	−22.6843	−	22.6843i	−0.790726	−	0.790726i	−0.981612	+	0.190886i	$0.938864\pi$
$824$	−3.35643			−0.116927
$825$			10.6166i			0.369623i
$826$	−7.59298	+	7.59298i	−0.264194	+	0.264194i
$827$	−15.1027	−	15.1027i	−0.525172	−	0.525172i	0.393957	−	0.919129i	$-0.371106\pi$
$827$	−15.1027	−	15.1027i	−0.525172	−	0.525172i	−0.919129	+	0.393957i	$0.871106\pi$
$828$		−	5.69666i		−	0.197973i
$829$			27.4318i			0.952745i	0.879243	+	0.476373i	$0.158049\pi$
$829$			27.4318i			0.952745i	−0.879243	+	0.476373i	$0.841951\pi$
$830$	−3.20318			−0.111184
$831$	−26.4530	−	26.4530i	−0.917646	−	0.917646i
$832$	1.17480	+	1.17480i	0.0407289	+	0.0407289i
$833$	−2.81650	−	2.81650i	−0.0975859	−	0.0975859i
$834$	−9.35046	+	9.35046i	−0.323780	+	0.323780i
$835$	−7.82338	+	7.82338i	−0.270739	+	0.270739i
$836$	−15.2702			−0.528131
$837$	27.0899	−	27.0899i	0.936364	−	0.936364i
$838$	−35.4270			−1.22381
$839$	10.1075	−	10.1075i	0.348951	−	0.348951i	−0.510768	−	0.859719i	$-0.670639\pi$
$839$	10.1075	−	10.1075i	0.348951	−	0.348951i	0.859719	+	0.510768i	$0.170639\pi$
$840$			3.14554i			0.108532i
$841$			70.8930i			2.44459i
$842$	−14.7557	+	14.7557i	−0.508515	+	0.508515i
$843$	−51.5008			−1.77378
$844$	15.7282	−	15.7282i	0.541387	−	0.541387i
$845$	−16.2417			−0.558731
$846$	4.68435	−	4.68435i	0.161051	−	0.161051i
$847$	4.49415	−	4.49415i	0.154421	−	0.154421i
$848$	−7.43800	−	7.43800i	−0.255422	−	0.255422i
$849$	−2.95335	−	2.95335i	−0.101359	−	0.101359i
$850$	−6.99653	−	6.99653i	−0.239979	−	0.239979i
$851$	−16.7777			−0.575132
$852$			17.1276i			0.586781i
$853$		−	30.5661i		−	1.04656i	−0.852160	−	0.523282i	$-0.824708\pi$
$853$		−	30.5661i		−	1.04656i	0.852160	−	0.523282i	$-0.175292\pi$
$854$	−8.77159	−	8.77159i	−0.300158	−	0.300158i
$855$	−7.41317	+	7.41317i	−0.253525	+	0.253525i
$856$		−	1.29895i		−	0.0443973i
$857$	−14.8307			−0.506607			−0.253304	−	0.967387i	$-0.581517\pi$
$857$	−14.8307			−0.506607			−0.253304	+	0.967387i	$0.581517\pi$
$858$	5.02084	+	5.02084i	0.171409	+	0.171409i
$859$			3.22363i			0.109989i	0.998487	+	0.0549943i	$0.0175141\pi$
$859$			3.22363i			0.109989i	−0.998487	+	0.0549943i	$0.982486\pi$
$860$	11.3372			0.386594
$861$	−8.47235	+	9.45856i	−0.288737	+	0.322347i
$862$	28.8932			0.984105
$863$		−	3.49816i		−	0.119079i	−0.998226	−	0.0595394i	$-0.981037\pi$
$863$		−	3.49816i		−	0.119079i	0.998226	−	0.0595394i	$-0.0189632\pi$
$864$	−2.89880	−	2.89880i	−0.0986190	−	0.0986190i
$865$	−0.692987			−0.0235623
$866$		−	13.9634i		−	0.474497i
$867$	1.59114	−	1.59114i	0.0540379	−	0.0540379i
$868$	6.60807	+	6.60807i	0.224293	+	0.224293i
$869$		−	7.60946i		−	0.258133i
$870$			31.4386i			1.06587i
$871$	14.2771			0.483761
$872$	4.52106	+	4.52106i	0.153102	+	0.153102i
$873$	3.45427	+	3.45427i	0.116909	+	0.116909i
$874$	−30.5984	−	30.5984i	−1.03501	−	1.03501i
$875$	8.39403	−	8.39403i	0.283770	−	0.283770i
$876$	22.5838	−	22.5838i	0.763036	−	0.763036i
$877$	−35.8719			−1.21131			−0.605654	−	0.795728i	$-0.707089\pi$
$877$	−35.8719			−1.21131			−0.605654	+	0.795728i	$0.707089\pi$
$878$	5.52443	−	5.52443i	0.186441	−	0.186441i
$879$	−3.98497			−0.134410
$880$	−2.41708	+	2.41708i	−0.0814797	+	0.0814797i
$881$			14.6893i			0.494896i	0.968901	+	0.247448i	$0.0795919\pi$
$881$			14.6893i			0.494896i	−0.968901	+	0.247448i	$0.920408\pi$
$882$		−	0.932805i		−	0.0314092i
$883$	29.1455	−	29.1455i	0.980824	−	0.980824i	−0.0189952	−	0.999820i	$-0.506047\pi$
$883$	29.1455	−	29.1455i	0.980824	−	0.980824i	0.999820	+	0.0189952i	$0.00604672\pi$
$884$	−6.61765			−0.222576
$885$	−23.8840	+	23.8840i	−0.802854	+	0.802854i
$886$	25.7874			0.866345
$887$	18.9492	−	18.9492i	0.636251	−	0.636251i	−0.313378	−	0.949629i	$-0.601461\pi$
$887$	18.9492	−	18.9492i	0.636251	−	0.636251i	0.949629	+	0.313378i	$0.101461\pi$
$888$	3.85247	−	3.85247i	0.129280	−	0.129280i
$889$	−2.94590	−	2.94590i	−0.0988023	−	0.0988023i
$890$	19.5042	+	19.5042i	0.653783	+	0.653783i
$891$	−16.6532	−	16.6532i	−0.557904	−	0.557904i
$892$	−14.3426			−0.480227
$893$		−	50.3220i		−	1.68396i
$894$		−	42.7299i		−	1.42910i
$895$	5.32828	+	5.32828i	0.178105	+	0.178105i
$896$	0.707107	−	0.707107i	0.0236228	−	0.0236228i
$897$			20.1215i			0.671837i
$898$	−34.6856			−1.15747
$899$	66.0454	+	66.0454i	2.20274	+	2.20274i
$900$		−	2.31720i		−	0.0772401i
$901$	41.8982			1.39583
$902$	−13.7783	+	0.757821i	−0.458769	+	0.0252327i
$903$	−14.1746			−0.471702
$904$			10.6539i			0.354343i
$905$	10.2554	+	10.2554i	0.340901	+	0.340901i
$906$	7.42916			0.246817
$907$			42.7081i			1.41810i	0.705159	+	0.709049i	$0.250875\pi$
$907$			42.7081i			1.41810i	−0.705159	+	0.709049i	$0.749125\pi$
$908$	−12.3679	+	12.3679i	−0.410444	+	0.410444i
$909$	10.5033	+	10.5033i	0.348373	+	0.348373i
$910$		−	2.63526i		−	0.0873581i
$911$		−	40.6781i		−	1.34773i	−0.738857	−	0.673863i	$-0.764634\pi$
$911$		−	40.6781i		−	1.34773i	0.738857	−	0.673863i	$-0.235366\pi$
$912$	14.0519			0.465305
$913$	3.07739	+	3.07739i	0.101847	+	0.101847i
$914$	−21.6838	−	21.6838i	−0.717236	−	0.717236i
$915$	−27.5914	−	27.5914i	−0.912145	−	0.912145i
$916$	3.41290	−	3.41290i	0.112765	−	0.112765i
$917$	5.12301	−	5.12301i	0.169177	−	0.169177i
$918$	16.3289			0.538934
$919$	40.2775	−	40.2775i	1.32863	−	1.32863i	0.422066	−	0.906565i	$-0.361305\pi$
$919$	40.2775	−	40.2775i	1.32863	−	1.32863i	0.906565	−	0.422066i	$-0.138695\pi$
$920$	−9.68666			−0.319360
$921$	−35.6054	+	35.6054i	−1.17324	+	1.17324i
$922$			36.3096i			1.19579i
$923$		−	14.3491i		−	0.472306i
$924$	3.02202	−	3.02202i	0.0994171	−	0.0994171i
$925$	−6.82458			−0.224391
$926$	1.00359	−	1.00359i	0.0329800	−	0.0329800i
$927$	3.13089			0.102832
$928$	7.06728	−	7.06728i	0.231995	−	0.231995i
$929$	14.1784	−	14.1784i	0.465177	−	0.465177i	−0.435171	−	0.900348i	$-0.643312\pi$
$929$	14.1784	−	14.1784i	0.465177	−	0.465177i	0.900348	+	0.435171i	$0.143312\pi$
$930$	20.7860	+	20.7860i	0.681599	+	0.681599i
$931$	−5.01036	−	5.01036i	−0.164208	−	0.164208i
$932$	7.39952	+	7.39952i	0.242379	+	0.242379i
$933$	−13.7895			−0.451447
$934$			18.2854i			0.598315i
$935$		−	13.6154i		−	0.445271i
$936$	−1.09586	−	1.09586i	−0.0358193	−	0.0358193i
$937$	−21.0233	+	21.0233i	−0.686800	+	0.686800i	−0.961523	−	0.274723i	$-0.911414\pi$
$937$	−21.0233	+	21.0233i	−0.686800	+	0.686800i	0.274723	+	0.961523i	$0.411414\pi$
$938$		−	8.59331i		−	0.280582i
$939$	55.5531			1.81291
$940$	−7.96533	−	7.96533i	−0.259800	−	0.259800i
$941$			5.03135i			0.164017i	0.996632	+	0.0820086i	$0.0261335\pi$
$941$			5.03135i			0.164017i	−0.996632	+	0.0820086i	$0.973867\pi$
$942$	−37.8061			−1.23179
$943$	−29.1275	−	26.0905i	−0.948522	−	0.849622i
$944$	10.7381			0.349495
$945$			6.50245i			0.211525i
$946$	−10.8920	−	10.8920i	−0.354128	−	0.354128i
$947$	−2.59221			−0.0842357			−0.0421178	−	0.999113i	$-0.513410\pi$
$947$	−2.59221			−0.0842357			−0.0421178	+	0.999113i	$0.513410\pi$
$948$			7.00235i			0.227426i
$949$	−18.9202	+	18.9202i	−0.614175	+	0.614175i
$950$	−12.4464	−	12.4464i	−0.403813	−	0.403813i
$951$		−	16.6259i		−	0.539131i
$952$			3.98313i			0.129094i
$953$	−3.81977			−0.123734			−0.0618672	−	0.998084i	$-0.519706\pi$
$953$	−3.81977			−0.123734			−0.0618672	+	0.998084i	$0.519706\pi$
$954$	6.93820	+	6.93820i	0.224632	+	0.224632i
$955$	−24.6527	−	24.6527i	−0.797744	−	0.797744i
$956$	−6.93393	−	6.93393i	−0.224259	−	0.224259i
$957$	30.2040	−	30.2040i	0.976357	−	0.976357i
$958$	20.1039	−	20.1039i	0.649528	−	0.649528i
$959$	7.03156			0.227061
$960$	2.22424	−	2.22424i	0.0717869	−	0.0717869i
$961$	56.3333			1.81720
$962$	−3.22751	+	3.22751i	−0.104059	+	0.104059i
$963$			1.21167i			0.0390455i
$964$		−	5.96031i		−	0.191969i
$965$	8.07702	−	8.07702i	0.260008	−	0.260008i
$966$	12.1110			0.389666
$967$	1.19772	−	1.19772i	0.0385162	−	0.0385162i	−0.687586	−	0.726103i	$-0.741330\pi$
$967$	1.19772	−	1.19772i	0.0385162	−	0.0385162i	0.726103	+	0.687586i	$0.241330\pi$
$968$	−6.35568			−0.204279
$969$	−39.5771	+	39.5771i	−1.27140	+	1.27140i
$970$	5.87368	−	5.87368i	0.188592	−	0.188592i
$971$	22.5633	+	22.5633i	0.724091	+	0.724091i	0.969436	−	0.245345i	$-0.0789011\pi$
$971$	22.5633	+	22.5633i	0.724091	+	0.724091i	−0.245345	+	0.969436i	$0.578901\pi$
$972$	6.62819	+	6.62819i	0.212599	+	0.212599i
$973$	−4.71500	−	4.71500i	−0.151156	−	0.151156i
$974$	−18.1781			−0.582465
$975$			8.18472i			0.262121i
$976$			12.4049i			0.397071i
$977$	11.0051	+	11.0051i	0.352085	+	0.352085i	0.860885	−	0.508800i	$-0.169911\pi$
$977$	11.0051	+	11.0051i	0.352085	+	0.352085i	−0.508800	+	0.860885i	$0.669911\pi$
$978$	−24.1307	+	24.1307i	−0.771615	+	0.771615i
$979$		−	37.4766i		−	1.19776i
$980$	−1.58615			−0.0506677
$981$	−4.21727	−	4.21727i	−0.134647	−	0.134647i
$982$			8.40653i			0.268263i
$983$	14.1424			0.451073			0.225537	−	0.974235i	$-0.427586\pi$
$983$	14.1424			0.451073			0.225537	+	0.974235i	$0.427586\pi$
$984$	12.6791	−	0.697359i	0.404194	−	0.0222310i
$985$	−8.21363			−0.261708
$986$			39.8100i			1.26781i
$987$	9.95887	+	9.95887i	0.316994	+	0.316994i
$988$	−11.7724			−0.374528
$989$		−	43.6505i		−	1.38801i
$990$	2.25466	−	2.25466i	0.0716578	−	0.0716578i
$991$	−27.7803	−	27.7803i	−0.882470	−	0.882470i	0.111315	−	0.993785i	$-0.464494\pi$
$991$	−27.7803	−	27.7803i	−0.882470	−	0.882470i	−0.993785	+	0.111315i	$0.964494\pi$
$992$		−	9.34523i		−	0.296711i
$993$			0.657937i			0.0208790i
$994$	−8.63663			−0.273937
$995$	−6.63364	−	6.63364i	−0.210301	−	0.210301i
$996$	−2.83187	−	2.83187i	−0.0897312	−	0.0897312i
$997$	5.77370	+	5.77370i	0.182855	+	0.182855i	0.792599	−	0.609744i	$-0.208728\pi$
$997$	5.77370	+	5.77370i	0.182855	+	0.182855i	−0.609744	+	0.792599i	$0.708728\pi$
$998$	−11.0199	+	11.0199i	−0.348830	+	0.348830i
$999$	7.96380	−	7.96380i	0.251963	−	0.251963i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.f.a.337.4	yes	20
41.32	even	4	inner	574.2.f.a.155.4	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.f.a.155.4	✓	20	41.32	even	4	inner
574.2.f.a.337.4	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000i q^{2} +(-1.40228 - 1.40228i) q^{3} -1.00000 q^{4} -1.58615i q^{5} +(1.40228 - 1.40228i) q^{6} +(0.707107 + 0.707107i) q^{7} -1.00000i q^{8} +0.932805i q^{9} +O(q^{10})\)	\(q+1.00000i q^{2} +(-1.40228 - 1.40228i) q^{3} -1.00000 q^{4} -1.58615i q^{5} +(1.40228 - 1.40228i) q^{6} +(0.707107 + 0.707107i) q^{7} -1.00000i q^{8} +0.932805i q^{9} +1.58615 q^{10} +(-1.52386 - 1.52386i) q^{11} +(1.40228 + 1.40228i) q^{12} +(-1.17480 - 1.17480i) q^{13} +(-0.707107 + 0.707107i) q^{14} +(-2.22424 + 2.22424i) q^{15} +1.00000 q^{16} +(-2.81650 + 2.81650i) q^{17} -0.932805 q^{18} +(-5.01036 + 5.01036i) q^{19} +1.58615i q^{20} -1.98313i q^{21} +(1.52386 - 1.52386i) q^{22} +6.10702 q^{23} +(-1.40228 + 1.40228i) q^{24} +2.48412 q^{25} +(1.17480 - 1.17480i) q^{26} +(-2.89880 + 2.89880i) q^{27} +(-0.707107 - 0.707107i) q^{28} +(-7.06728 - 7.06728i) q^{29} +(-2.22424 - 2.22424i) q^{30} -9.34523 q^{31} +1.00000i q^{32} +4.27378i q^{33} +(-2.81650 - 2.81650i) q^{34} +(1.12158 - 1.12158i) q^{35} -0.932805i q^{36} -2.74728 q^{37} +(-5.01036 - 5.01036i) q^{38} +3.29481i q^{39} -1.58615 q^{40} +(-4.76951 - 4.27221i) q^{41} +1.98313 q^{42} -7.14760i q^{43} +(1.52386 + 1.52386i) q^{44} +1.47957 q^{45} +6.10702i q^{46} +(-5.02180 + 5.02180i) q^{47} +(-1.40228 - 1.40228i) q^{48} +1.00000i q^{49} +2.48412i q^{50} +7.89906 q^{51} +(1.17480 + 1.17480i) q^{52} +(-7.43800 - 7.43800i) q^{53} +(-2.89880 - 2.89880i) q^{54} +(-2.41708 + 2.41708i) q^{55} +(0.707107 - 0.707107i) q^{56} +14.0519 q^{57} +(7.06728 - 7.06728i) q^{58} +10.7381 q^{59} +(2.22424 - 2.22424i) q^{60} +12.4049i q^{61} -9.34523i q^{62} +(-0.659593 + 0.659593i) q^{63} -1.00000 q^{64} +(-1.86341 + 1.86341i) q^{65} -4.27378 q^{66} +(-6.07639 + 6.07639i) q^{67} +(2.81650 - 2.81650i) q^{68} +(-8.56378 - 8.56378i) q^{69} +(1.12158 + 1.12158i) q^{70} +(6.10702 + 6.10702i) q^{71} +0.932805 q^{72} -16.1050i q^{73} -2.74728i q^{74} +(-3.48345 - 3.48345i) q^{75} +(5.01036 - 5.01036i) q^{76} -2.15507i q^{77} -3.29481 q^{78} +(2.49677 + 2.49677i) q^{79} -1.58615i q^{80} +10.9283 q^{81} +(4.27221 - 4.76951i) q^{82} -2.01947 q^{83} +1.98313i q^{84} +(4.46739 + 4.46739i) q^{85} +7.14760 q^{86} +19.8207i q^{87} +(-1.52386 + 1.52386i) q^{88} +(12.2966 + 12.2966i) q^{89} +1.47957i q^{90} -1.66142i q^{91} -6.10702 q^{92} +(13.1047 + 13.1047i) q^{93} +(-5.02180 - 5.02180i) q^{94} +(7.94719 + 7.94719i) q^{95} +(1.40228 - 1.40228i) q^{96} +(3.70310 - 3.70310i) q^{97} -1.00000 q^{98} +(1.42147 - 1.42147i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 4 q^{3} - 20 q^{4} + 4 q^{6}+O(q^{10}) \) 20 * q - 4 * q^3 - 20 * q^4 + 4 * q^6	\( 20 q - 4 q^{3} - 20 q^{4} + 4 q^{6} + 16 q^{11} + 4 q^{12} - 20 q^{13} + 4 q^{15} + 20 q^{16} - 4 q^{17} - 20 q^{18} + 12 q^{19} - 16 q^{22} + 8 q^{23} - 4 q^{24} - 20 q^{25} + 20 q^{26} - 16 q^{27} + 12 q^{29} + 4 q^{30} - 8 q^{31} - 4 q^{34} - 32 q^{37} + 12 q^{38} - 12 q^{41} - 16 q^{44} - 72 q^{45} + 12 q^{47} - 4 q^{48} + 80 q^{51} + 20 q^{52} - 16 q^{54} - 20 q^{55} + 48 q^{57} - 12 q^{58} - 8 q^{59} - 4 q^{60} + 16 q^{63} - 20 q^{64} + 20 q^{65} - 40 q^{66} - 4 q^{67} + 4 q^{68} - 8 q^{69} - 8 q^{71} + 20 q^{72} + 20 q^{75} - 12 q^{76} + 24 q^{78} + 24 q^{79} + 4 q^{81} + 12 q^{82} - 4 q^{85} + 8 q^{86} + 16 q^{88} - 48 q^{89} - 8 q^{92} - 8 q^{93} + 12 q^{94} + 28 q^{95} + 4 q^{96} + 16 q^{97} - 20 q^{98} - 8 q^{99}+O(q^{100}) \) 20 * q - 4 * q^3 - 20 * q^4 + 4 * q^6 + 16 * q^11 + 4 * q^12 - 20 * q^13 + 4 * q^15 + 20 * q^16 - 4 * q^17 - 20 * q^18 + 12 * q^19 - 16 * q^22 + 8 * q^23 - 4 * q^24 - 20 * q^25 + 20 * q^26 - 16 * q^27 + 12 * q^29 + 4 * q^30 - 8 * q^31 - 4 * q^34 - 32 * q^37 + 12 * q^38 - 12 * q^41 - 16 * q^44 - 72 * q^45 + 12 * q^47 - 4 * q^48 + 80 * q^51 + 20 * q^52 - 16 * q^54 - 20 * q^55 + 48 * q^57 - 12 * q^58 - 8 * q^59 - 4 * q^60 + 16 * q^63 - 20 * q^64 + 20 * q^65 - 40 * q^66 - 4 * q^67 + 4 * q^68 - 8 * q^69 - 8 * q^71 + 20 * q^72 + 20 * q^75 - 12 * q^76 + 24 * q^78 + 24 * q^79 + 4 * q^81 + 12 * q^82 - 4 * q^85 + 8 * q^86 + 16 * q^88 - 48 * q^89 - 8 * q^92 - 8 * q^93 + 12 * q^94 + 28 * q^95 + 4 * q^96 + 16 * q^97 - 20 * q^98 - 8 * q^99

Introduction

L-functions

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