LMFDB - Embedded newform 574.2.f.a.155.9

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			155.9
Root			$-1.93054i$ of defining polynomial
Character	$\chi$	$=$	574.155
Dual form			574.2.f.a.337.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000i q^{2} +(1.36510 - 1.36510i) q^{3} -1.00000 q^{4} -1.10200i q^{5} +(-1.36510 - 1.36510i) q^{6} +(0.707107 - 0.707107i) q^{7} +1.00000i q^{8} -0.726999i q^{9} +O(q^{10})$	\(q-1.00000i q^{2} +(1.36510 - 1.36510i) q^{3} -1.00000 q^{4} -1.10200i q^{5} +(-1.36510 - 1.36510i) q^{6} +(0.707107 - 0.707107i) q^{7} +1.00000i q^{8} -0.726999i q^{9} -1.10200 q^{10} +(3.14433 - 3.14433i) q^{11} +(-1.36510 + 1.36510i) q^{12} +(0.465387 - 0.465387i) q^{13} +(-0.707107 - 0.707107i) q^{14} +(-1.50433 - 1.50433i) q^{15} +1.00000 q^{16} +(-0.0491130 - 0.0491130i) q^{17} -0.726999 q^{18} +(-3.25974 - 3.25974i) q^{19} +1.10200i q^{20} -1.93054i q^{21} +(-3.14433 - 3.14433i) q^{22} -4.56114 q^{23} +(1.36510 + 1.36510i) q^{24} +3.78561 q^{25} +(-0.465387 - 0.465387i) q^{26} +(3.10287 + 3.10287i) q^{27} +(-0.707107 + 0.707107i) q^{28} +(-1.38814 + 1.38814i) q^{29} +(-1.50433 + 1.50433i) q^{30} -10.7831 q^{31} -1.00000i q^{32} -8.58465i q^{33} +(-0.0491130 + 0.0491130i) q^{34} +(-0.779228 - 0.779228i) q^{35} +0.726999i q^{36} +2.56208 q^{37} +(-3.25974 + 3.25974i) q^{38} -1.27060i q^{39} +1.10200 q^{40} +(2.07569 + 6.05735i) q^{41} -1.93054 q^{42} +0.265494i q^{43} +(-3.14433 + 3.14433i) q^{44} -0.801150 q^{45} +4.56114i q^{46} +(7.39861 + 7.39861i) q^{47} +(1.36510 - 1.36510i) q^{48} -1.00000i q^{49} -3.78561i q^{50} -0.134088 q^{51} +(-0.465387 + 0.465387i) q^{52} +(7.01374 - 7.01374i) q^{53} +(3.10287 - 3.10287i) q^{54} +(-3.46503 - 3.46503i) q^{55} +(0.707107 + 0.707107i) q^{56} -8.89974 q^{57} +(1.38814 + 1.38814i) q^{58} +5.52300 q^{59} +(1.50433 + 1.50433i) q^{60} +9.96496i q^{61} +10.7831i q^{62} +(-0.514066 - 0.514066i) q^{63} -1.00000 q^{64} +(-0.512855 - 0.512855i) q^{65} -8.58465 q^{66} +(-0.864013 - 0.864013i) q^{67} +(0.0491130 + 0.0491130i) q^{68} +(-6.22641 + 6.22641i) q^{69} +(-0.779228 + 0.779228i) q^{70} +(-5.54180 + 5.54180i) q^{71} +0.726999 q^{72} -11.2304i q^{73} -2.56208i q^{74} +(5.16773 - 5.16773i) q^{75} +(3.25974 + 3.25974i) q^{76} -4.44675i q^{77} -1.27060 q^{78} +(9.54867 - 9.54867i) q^{79} -1.10200i q^{80} +10.6525 q^{81} +(6.05735 - 2.07569i) q^{82} +2.94249 q^{83} +1.93054i q^{84} +(-0.0541222 + 0.0541222i) q^{85} +0.265494 q^{86} +3.78989i q^{87} +(3.14433 + 3.14433i) q^{88} +(-7.87950 + 7.87950i) q^{89} +0.801150i q^{90} -0.658157i q^{91} +4.56114 q^{92} +(-14.7201 + 14.7201i) q^{93} +(7.39861 - 7.39861i) q^{94} +(-3.59221 + 3.59221i) q^{95} +(-1.36510 - 1.36510i) q^{96} +(5.01092 + 5.01092i) q^{97} -1.00000 q^{98} +(-2.28592 - 2.28592i) 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 $\left(\mathbb{Z}/574\mathbb{Z}\right)^\times$.

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

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
$3$	1.36510	−	1.36510i	0.788141	−	0.788141i	−0.193048	−	0.981189i	$-0.561837\pi$
$3$	1.36510	−	1.36510i	0.788141	−	0.788141i	0.981189	+	0.193048i	$0.0618373\pi$
$4$	−1.00000			−0.500000
$5$		−	1.10200i		−	0.492827i	−0.969165	−	0.246414i	$-0.920748\pi$
$5$		−	1.10200i		−	0.492827i	0.969165	−	0.246414i	$-0.0792522\pi$
$6$	−1.36510	−	1.36510i	−0.557300	−	0.557300i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$			1.00000i			0.353553i
$9$		−	0.726999i		−	0.242333i
$10$	−1.10200			−0.348481
$11$	3.14433	−	3.14433i	0.948051	−	0.948051i	−0.0506649	−	0.998716i	$-0.516134\pi$
$11$	3.14433	−	3.14433i	0.948051	−	0.948051i	0.998716	+	0.0506649i	$0.0161340\pi$
$12$	−1.36510	+	1.36510i	−0.394071	+	0.394071i
$13$	0.465387	−	0.465387i	0.129075	−	0.129075i	−0.639618	−	0.768693i	$-0.720907\pi$
$13$	0.465387	−	0.465387i	0.129075	−	0.129075i	0.768693	+	0.639618i	$0.220907\pi$
$14$	−0.707107	−	0.707107i	−0.188982	−	0.188982i
$15$	−1.50433	−	1.50433i	−0.388417	−	0.388417i
$16$	1.00000			0.250000
$17$	−0.0491130	−	0.0491130i	−0.0119116	−	0.0119116i	0.701126	−	0.713038i	$-0.252681\pi$
$17$	−0.0491130	−	0.0491130i	−0.0119116	−	0.0119116i	−0.713038	+	0.701126i	$0.752681\pi$
$18$	−0.726999			−0.171355
$19$	−3.25974	−	3.25974i	−0.747835	−	0.747835i	0.226237	−	0.974072i	$-0.427358\pi$
$19$	−3.25974	−	3.25974i	−0.747835	−	0.747835i	−0.974072	+	0.226237i	$0.927358\pi$
$20$			1.10200i			0.246414i
$21$		−	1.93054i		−	0.421279i
$22$	−3.14433	−	3.14433i	−0.670373	−	0.670373i
$23$	−4.56114			−0.951063			−0.475532	−	0.879699i	$-0.657744\pi$
$23$	−4.56114			−0.951063			−0.475532	+	0.879699i	$0.657744\pi$
$24$	1.36510	+	1.36510i	0.278650	+	0.278650i
$25$	3.78561			0.757121
$26$	−0.465387	−	0.465387i	−0.0912700	−	0.0912700i
$27$	3.10287	+	3.10287i	0.597149	+	0.597149i
$28$	−0.707107	+	0.707107i	−0.133631	+	0.133631i
$29$	−1.38814	+	1.38814i	−0.257771	+	0.257771i	−0.824147	−	0.566376i	$-0.808345\pi$
$29$	−1.38814	+	1.38814i	−0.257771	+	0.257771i	0.566376	+	0.824147i	$0.308345\pi$
$30$	−1.50433	+	1.50433i	−0.274653	+	0.274653i
$31$	−10.7831			−1.93671			−0.968355	−	0.249576i	$-0.919709\pi$
$31$	−10.7831			−1.93671			−0.968355	+	0.249576i	$0.919709\pi$
$32$		−	1.00000i		−	0.176777i
$33$		−	8.58465i		−	1.49440i
$34$	−0.0491130	+	0.0491130i	−0.00842280	+	0.00842280i
$35$	−0.779228	−	0.779228i	−0.131714	−	0.131714i
$36$			0.726999i			0.121167i
$37$	2.56208			0.421204			0.210602	−	0.977572i	$-0.432458\pi$
$37$	2.56208			0.421204			0.210602	+	0.977572i	$0.432458\pi$
$38$	−3.25974	+	3.25974i	−0.528799	+	0.528799i
$39$		−	1.27060i		−	0.203459i
$40$	1.10200			0.174241
$41$	2.07569	+	6.05735i	0.324168	+	0.945999i
$41$	2.07569	+	6.05735i	0.324168	+	0.945999i
$42$	−1.93054			−0.297889
$43$			0.265494i			0.0404874i	0.999795	+	0.0202437i	$0.00644422\pi$
$43$			0.265494i			0.0404874i	−0.999795	+	0.0202437i	$0.993556\pi$
$44$	−3.14433	+	3.14433i	−0.474025	+	0.474025i
$45$	−0.801150			−0.119428
$46$			4.56114i			0.672503i
$47$	7.39861	+	7.39861i	1.07920	+	1.07920i	0.996581	+	0.0826175i	$0.0263280\pi$
$47$	7.39861	+	7.39861i	1.07920	+	1.07920i	0.0826175	+	0.996581i	$0.473672\pi$
$48$	1.36510	−	1.36510i	0.197035	−	0.197035i
$49$		−	1.00000i		−	0.142857i
$50$		−	3.78561i		−	0.535366i
$51$	−0.134088			−0.0187761
$52$	−0.465387	+	0.465387i	−0.0645376	+	0.0645376i
$53$	7.01374	−	7.01374i	0.963412	−	0.963412i	−0.0359419	−	0.999354i	$-0.511443\pi$
$53$	7.01374	−	7.01374i	0.963412	−	0.963412i	0.999354	+	0.0359419i	$0.0114431\pi$
$54$	3.10287	−	3.10287i	0.422248	−	0.422248i
$55$	−3.46503	−	3.46503i	−0.467225	−	0.467225i
$56$	0.707107	+	0.707107i	0.0944911	+	0.0944911i
$57$	−8.89974			−1.17880
$58$	1.38814	+	1.38814i	0.182271	+	0.182271i
$59$	5.52300			0.719034			0.359517	−	0.933139i	$-0.382942\pi$
$59$	5.52300			0.719034			0.359517	+	0.933139i	$0.382942\pi$
$60$	1.50433	+	1.50433i	0.194209	+	0.194209i
$61$			9.96496i			1.27588i	0.770085	+	0.637941i	$0.220214\pi$
$61$			9.96496i			1.27588i	−0.770085	+	0.637941i	$0.779786\pi$
$62$			10.7831i			1.36946i
$63$	−0.514066	−	0.514066i	−0.0647662	−	0.0647662i
$64$	−1.00000			−0.125000
$65$	−0.512855	−	0.512855i	−0.0636118	−	0.0636118i
$66$	−8.58465			−1.05670
$67$	−0.864013	−	0.864013i	−0.105556	−	0.105556i	0.652356	−	0.757912i	$-0.273781\pi$
$67$	−0.864013	−	0.864013i	−0.105556	−	0.105556i	−0.757912	+	0.652356i	$0.773781\pi$
$68$	0.0491130	+	0.0491130i	0.00595582	+	0.00595582i
$69$	−6.22641	+	6.22641i	−0.749572	+	0.749572i
$70$	−0.779228	+	0.779228i	−0.0931356	+	0.0931356i
$71$	−5.54180	+	5.54180i	−0.657690	+	0.657690i	−0.954833	−	0.297143i	$-0.903966\pi$
$71$	−5.54180	+	5.54180i	−0.657690	+	0.657690i	0.297143	+	0.954833i	$0.403966\pi$
$72$	0.726999			0.0856777
$73$		−	11.2304i		−	1.31441i	−0.753710	−	0.657207i	$-0.771738\pi$
$73$		−	11.2304i		−	1.31441i	0.753710	−	0.657207i	$-0.228262\pi$
$74$		−	2.56208i		−	0.297836i
$75$	5.16773	−	5.16773i	0.596719	−	0.596719i
$76$	3.25974	+	3.25974i	0.373917	+	0.373917i
$77$		−	4.44675i		−	0.506754i
$78$	−1.27060			−0.143867
$79$	9.54867	−	9.54867i	1.07431	−	1.07431i	0.0773010	−	0.997008i	$-0.475370\pi$
$79$	9.54867	−	9.54867i	1.07431	−	1.07431i	0.997008	−	0.0773010i	$-0.0246302\pi$
$80$		−	1.10200i		−	0.123207i
$81$	10.6525			1.18361
$82$	6.05735	−	2.07569i	0.668923	−	0.229222i
$83$	2.94249			0.322980			0.161490	−	0.986874i	$-0.448370\pi$
$83$	2.94249			0.322980			0.161490	+	0.986874i	$0.448370\pi$
$84$			1.93054i			0.210640i
$85$	−0.0541222	+	0.0541222i	−0.00587038	+	0.00587038i
$86$	0.265494			0.0286289
$87$			3.78989i			0.406319i
$88$	3.14433	+	3.14433i	0.335187	+	0.335187i
$89$	−7.87950	+	7.87950i	−0.835225	+	0.835225i	−0.988226	−	0.153001i	$-0.951106\pi$
$89$	−7.87950	+	7.87950i	−0.835225	+	0.835225i	0.153001	+	0.988226i	$0.451106\pi$
$90$			0.801150i			0.0844486i
$91$		−	0.658157i		−	0.0689936i
$92$	4.56114			0.475532
$93$	−14.7201	+	14.7201i	−1.52640	+	1.52640i
$94$	7.39861	−	7.39861i	0.763109	−	0.763109i
$95$	−3.59221	+	3.59221i	−0.368553	+	0.368553i
$96$	−1.36510	−	1.36510i	−0.139325	−	0.139325i
$97$	5.01092	+	5.01092i	0.508782	+	0.508782i	0.914152	−	0.405371i	$-0.132858\pi$
$97$	5.01092	+	5.01092i	0.508782	+	0.508782i	−0.405371	+	0.914152i	$0.632858\pi$
$98$	−1.00000			−0.101015
$99$	−2.28592	−	2.28592i	−0.229744	−	0.229744i
$100$	−3.78561			−0.378561
$101$	−1.70294	−	1.70294i	−0.169449	−	0.169449i	0.617288	−	0.786737i	$-0.288231\pi$
$101$	−1.70294	−	1.70294i	−0.169449	−	0.169449i	−0.786737	+	0.617288i	$0.788231\pi$
$102$			0.134088i			0.0132767i
$103$		−	8.44607i		−	0.832216i	−0.909315	−	0.416108i	$-0.863394\pi$
$103$		−	8.44607i		−	0.832216i	0.909315	−	0.416108i	$-0.136606\pi$
$104$	0.465387	+	0.465387i	0.0456350	+	0.0456350i
$105$	−2.12745			−0.207618
$106$	−7.01374	−	7.01374i	−0.681235	−	0.681235i
$107$	7.92678			0.766310			0.383155	−	0.923684i	$-0.374837\pi$
$107$	7.92678			0.766310			0.383155	+	0.923684i	$0.374837\pi$
$108$	−3.10287	−	3.10287i	−0.298574	−	0.298574i
$109$	6.68039	+	6.68039i	0.639865	+	0.639865i	0.950522	−	0.310657i	$-0.100549\pi$
$109$	6.68039	+	6.68039i	0.639865	+	0.639865i	−0.310657	+	0.950522i	$0.600549\pi$
$110$	−3.46503	+	3.46503i	−0.330378	+	0.330378i
$111$	3.49750	−	3.49750i	0.331968	−	0.331968i
$112$	0.707107	−	0.707107i	0.0668153	−	0.0668153i
$113$	−7.89831			−0.743010			−0.371505	−	0.928431i	$-0.621158\pi$
$113$	−7.89831			−0.743010			−0.371505	+	0.928431i	$0.621158\pi$
$114$			8.89974i			0.833537i
$115$			5.02635i			0.468710i
$116$	1.38814	−	1.38814i	0.128885	−	0.128885i
$117$	−0.338336	−	0.338336i	−0.0312792	−	0.0312792i
$118$		−	5.52300i		−	0.508434i
$119$	−0.0694562			−0.00636704
$120$	1.50433	−	1.50433i	0.137326	−	0.137326i
$121$		−	8.77361i		−	0.797601i
$122$	9.96496			0.902185
$123$	11.1024	+	5.43537i	1.00107	+	0.490091i
$124$	10.7831			0.968355
$125$		−	9.68170i		−	0.865957i
$126$	−0.514066	+	0.514066i	−0.0457967	+	0.0457967i
$127$	−8.04592			−0.713960			−0.356980	−	0.934112i	$-0.616194\pi$
$127$	−8.04592			−0.713960			−0.356980	+	0.934112i	$0.616194\pi$
$128$			1.00000i			0.0883883i
$129$	0.362426	+	0.362426i	0.0319098	+	0.0319098i
$130$	−0.512855	+	0.512855i	−0.0449803	+	0.0449803i
$131$		−	8.25232i		−	0.721008i	−0.932758	−	0.360504i	$-0.882605\pi$
$131$		−	8.25232i		−	0.721008i	0.932758	−	0.360504i	$-0.117395\pi$
$132$			8.58465i			0.747198i
$133$	−4.60996			−0.399735
$134$	−0.864013	+	0.864013i	−0.0746394	+	0.0746394i
$135$	3.41935	−	3.41935i	0.294291	−	0.294291i
$136$	0.0491130	−	0.0491130i	0.00421140	−	0.00421140i
$137$	14.7570	+	14.7570i	1.26078	+	1.26078i	0.950717	+	0.310059i	$0.100349\pi$
$137$	14.7570	+	14.7570i	1.26078	+	1.26078i	0.310059	+	0.950717i	$0.399651\pi$
$138$	6.22641	+	6.22641i	0.530028	+	0.530028i
$139$	0.663465			0.0562744			0.0281372	−	0.999604i	$-0.491042\pi$
$139$	0.663465			0.0562744			0.0281372	+	0.999604i	$0.491042\pi$
$140$	0.779228	+	0.779228i	0.0658568	+	0.0658568i
$141$	20.1997			1.70112
$142$	5.54180	+	5.54180i	0.465057	+	0.465057i
$143$		−	2.92666i		−	0.244740i
$144$		−	0.726999i		−	0.0605833i
$145$	1.52972	+	1.52972i	0.127036	+	0.127036i
$146$	−11.2304			−0.929431
$147$	−1.36510	−	1.36510i	−0.112592	−	0.112592i
$148$	−2.56208			−0.210602
$149$	11.2948	+	11.2948i	0.925309	+	0.925309i	0.997398	−	0.0720888i	$-0.0229665\pi$
$149$	11.2948	+	11.2948i	0.925309	+	0.925309i	−0.0720888	+	0.997398i	$0.522967\pi$
$150$	−5.16773	−	5.16773i	−0.421944	−	0.421944i
$151$	12.8072	−	12.8072i	1.04223	−	1.04223i	0.0431667	−	0.999068i	$-0.486255\pi$
$151$	12.8072	−	12.8072i	1.04223	−	1.04223i	0.999068	−	0.0431667i	$-0.0137446\pi$
$152$	3.25974	−	3.25974i	0.264400	−	0.264400i
$153$	−0.0357051	+	0.0357051i	−0.00288659	+	0.00288659i
$154$	−4.44675			−0.358330
$155$			11.8830i			0.954464i
$156$			1.27060i			0.101729i
$157$	−6.04281	+	6.04281i	−0.482269	+	0.482269i	−0.905856	−	0.423587i	$-0.860771\pi$
$157$	−6.04281	+	6.04281i	−0.482269	+	0.482269i	0.423587	+	0.905856i	$0.360771\pi$
$158$	−9.54867	−	9.54867i	−0.759651	−	0.759651i
$159$		−	19.1489i		−	1.51861i
$160$	−1.10200			−0.0871204
$161$	−3.22521	+	3.22521i	−0.254182	+	0.254182i
$162$		−	10.6525i		−	0.836937i
$163$	12.3376			0.966358			0.483179	−	0.875521i	$-0.339482\pi$
$163$	12.3376			0.966358			0.483179	+	0.875521i	$0.339482\pi$
$164$	−2.07569	−	6.05735i	−0.162084	−	0.473000i
$165$	−9.46024			−0.736479
$166$		−	2.94249i		−	0.228381i
$167$	−14.4137	+	14.4137i	−1.11536	+	1.11536i	−0.122952	+	0.992413i	$0.539236\pi$
$167$	−14.4137	+	14.4137i	−1.11536	+	1.11536i	−0.992413	+	0.122952i	$0.960764\pi$
$168$	1.93054			0.148945
$169$			12.5668i			0.966679i
$170$	0.0541222	+	0.0541222i	0.00415099	+	0.00415099i
$171$	−2.36983	+	2.36983i	−0.181225	+	0.181225i
$172$		−	0.265494i		−	0.0202437i
$173$			10.5955i			0.805565i	0.915296	+	0.402782i	$0.131957\pi$
$173$			10.5955i			0.805565i	−0.915296	+	0.402782i	$0.868043\pi$
$174$	3.78989			0.287311
$175$	2.67683	−	2.67683i	0.202349	−	0.202349i
$176$	3.14433	−	3.14433i	0.237013	−	0.237013i
$177$	7.53945	−	7.53945i	0.566700	−	0.566700i
$178$	7.87950	+	7.87950i	0.590593	+	0.590593i
$179$	1.43142	+	1.43142i	0.106989	+	0.106989i	0.758575	−	0.651586i	$-0.225896\pi$
$179$	1.43142	+	1.43142i	0.106989	+	0.106989i	−0.651586	+	0.758575i	$0.725896\pi$
$180$	0.801150			0.0597142
$181$	−10.0222	−	10.0222i	−0.744946	−	0.744946i	0.228579	−	0.973525i	$-0.426592\pi$
$181$	−10.0222	−	10.0222i	−0.744946	−	0.744946i	−0.973525	+	0.228579i	$0.926592\pi$
$182$	−0.658157			−0.0487858
$183$	13.6032	+	13.6032i	1.00558	+	1.00558i
$184$		−	4.56114i		−	0.336252i
$185$		−	2.82340i		−	0.207581i
$186$	14.7201	+	14.7201i	1.07933	+	1.07933i
$187$	−0.308855			−0.0225857
$188$	−7.39861	−	7.39861i	−0.539599	−	0.539599i
$189$	4.38813			0.319189
$190$	3.59221	+	3.59221i	0.260607	+	0.260607i
$191$	8.89884	+	8.89884i	0.643897	+	0.643897i	0.951511	−	0.307614i	$-0.0995305\pi$
$191$	8.89884	+	8.89884i	0.643897	+	0.643897i	−0.307614	+	0.951511i	$0.599531\pi$
$192$	−1.36510	+	1.36510i	−0.0985176	+	0.0985176i
$193$	1.80187	−	1.80187i	0.129701	−	0.129701i	−0.639276	−	0.768977i	$-0.720766\pi$
$193$	1.80187	−	1.80187i	0.129701	−	0.129701i	0.768977	+	0.639276i	$0.220766\pi$
$194$	5.01092	−	5.01092i	0.359763	−	0.359763i
$195$	−1.40020			−0.100270
$196$			1.00000i			0.0714286i
$197$			17.3369i			1.23521i	0.786490	+	0.617603i	$0.211896\pi$
$197$			17.3369i			1.23521i	−0.786490	+	0.617603i	$0.788104\pi$
$198$	−2.28592	+	2.28592i	−0.162454	+	0.162454i
$199$	−0.632062	−	0.632062i	−0.0448057	−	0.0448057i	0.684349	−	0.729155i	$-0.260087\pi$
$199$	−0.632062	−	0.632062i	−0.0448057	−	0.0448057i	−0.729155	+	0.684349i	$0.760087\pi$
$200$			3.78561i			0.267683i
$201$	−2.35893			−0.166386
$202$	−1.70294	+	1.70294i	−0.119818	+	0.119818i
$203$			1.96312i			0.137784i
$204$	0.134088			0.00938806
$205$	6.67517	−	2.28740i	0.466214	−	0.159759i
$206$	−8.44607			−0.588465
$207$			3.31595i			0.230474i
$208$	0.465387	−	0.465387i	0.0322688	−	0.0322688i
$209$	−20.4994			−1.41797
$210$			2.12745i			0.146808i
$211$	−5.55224	−	5.55224i	−0.382232	−	0.382232i	0.489674	−	0.871906i	$-0.337116\pi$
$211$	−5.55224	−	5.55224i	−0.382232	−	0.382232i	−0.871906	+	0.489674i	$0.837116\pi$
$212$	−7.01374	+	7.01374i	−0.481706	+	0.481706i
$213$			15.1302i			1.03671i
$214$		−	7.92678i		−	0.541863i
$215$	0.292573			0.0199533
$216$	−3.10287	+	3.10287i	−0.211124	+	0.211124i
$217$	−7.62484	+	7.62484i	−0.517608	+	0.517608i
$218$	6.68039	−	6.68039i	0.452453	−	0.452453i
$219$	−15.3306	−	15.3306i	−1.03594	−	1.03594i
$220$	3.46503	+	3.46503i	0.233613	+	0.233613i
$221$	−0.0457131			−0.00307500
$222$	−3.49750	−	3.49750i	−0.234737	−	0.234737i
$223$	−27.5489			−1.84481			−0.922406	−	0.386221i	$-0.873780\pi$
$223$	−27.5489			−1.84481			−0.922406	+	0.386221i	$0.873780\pi$
$224$	−0.707107	−	0.707107i	−0.0472456	−	0.0472456i
$225$		−	2.75213i		−	0.183476i
$226$			7.89831i			0.525388i
$227$	6.72572	+	6.72572i	0.446402	+	0.446402i	0.894156	−	0.447755i	$-0.147776\pi$
$227$	6.72572	+	6.72572i	0.446402	+	0.446402i	−0.447755	+	0.894156i	$0.647776\pi$
$228$	8.89974			0.589399
$229$	2.14501	+	2.14501i	0.141746	+	0.141746i	0.774419	−	0.632673i	$-0.218042\pi$
$229$	2.14501	+	2.14501i	0.141746	+	0.141746i	−0.632673	+	0.774419i	$0.718042\pi$
$230$	5.02635			0.331428
$231$	−6.07026	−	6.07026i	−0.399394	−	0.399394i
$232$	−1.38814	−	1.38814i	−0.0911357	−	0.0911357i
$233$	−20.0860	+	20.0860i	−1.31588	+	1.31588i	−0.398867	+	0.917009i	$0.630596\pi$
$233$	−20.0860	+	20.0860i	−1.31588	+	1.31588i	−0.917009	+	0.398867i	$0.869404\pi$
$234$	−0.338336	+	0.338336i	−0.0221177	+	0.0221177i
$235$	8.15324	−	8.15324i	0.531859	−	0.531859i
$236$	−5.52300			−0.359517
$237$		−	26.0698i		−	1.69341i
$238$			0.0694562i			0.00450218i
$239$	7.18197	−	7.18197i	0.464563	−	0.464563i	−0.435585	−	0.900148i	$-0.643458\pi$
$239$	7.18197	−	7.18197i	0.464563	−	0.464563i	0.900148	+	0.435585i	$0.143458\pi$
$240$	−1.50433	−	1.50433i	−0.0971044	−	0.0971044i
$241$		−	8.32804i		−	0.536456i	−0.963355	−	0.268228i	$-0.913562\pi$
$241$		−	8.32804i		−	0.536456i	0.963355	−	0.268228i	$-0.0864381\pi$
$242$	−8.77361			−0.563989
$243$	5.23307	−	5.23307i	0.335702	−	0.335702i
$244$		−	9.96496i		−	0.637941i
$245$	−1.10200			−0.0704039
$246$	5.43537	−	11.1024i	0.346546	−	0.707864i
$247$	−3.03408			−0.193054
$248$		−	10.7831i		−	0.684731i
$249$	4.01679	−	4.01679i	0.254554	−	0.254554i
$250$	−9.68170			−0.612324
$251$			7.71650i			0.487061i	0.969893	+	0.243531i	$0.0783056\pi$
$251$			7.71650i			0.487061i	−0.969893	+	0.243531i	$0.921694\pi$
$252$	0.514066	+	0.514066i	0.0323831	+	0.0323831i
$253$	−14.3417	+	14.3417i	−0.901656	+	0.901656i
$254$			8.04592i			0.504846i
$255$			0.147765i			0.00925338i
$256$	1.00000			0.0625000
$257$	6.29904	−	6.29904i	0.392924	−	0.392924i	−0.482805	−	0.875728i	$-0.660382\pi$
$257$	6.29904	−	6.29904i	0.392924	−	0.392924i	0.875728	+	0.482805i	$0.160382\pi$
$258$	0.362426	−	0.362426i	0.0225636	−	0.0225636i
$259$	1.81167	−	1.81167i	0.112571	−	0.112571i
$260$	0.512855	+	0.512855i	0.0318059	+	0.0318059i
$261$	1.00918	+	1.00918i	0.0624664	+	0.0624664i
$262$	−8.25232			−0.509830
$263$	−3.52198	−	3.52198i	−0.217174	−	0.217174i	0.590132	−	0.807307i	$-0.299076\pi$
$263$	−3.52198	−	3.52198i	−0.217174	−	0.217174i	−0.807307	+	0.590132i	$0.799076\pi$
$264$	8.58465			0.528349
$265$	−7.72911	−	7.72911i	−0.474796	−	0.474796i
$266$			4.60996i			0.282655i
$267$			21.5126i			1.31655i
$268$	0.864013	+	0.864013i	0.0527780	+	0.0527780i
$269$	−19.5527			−1.19215			−0.596073	−	0.802930i	$-0.703273\pi$
$269$	−19.5527			−1.19215			−0.596073	+	0.802930i	$0.703273\pi$
$270$	−3.41935	−	3.41935i	−0.208095	−	0.208095i
$271$	3.87526			0.235405			0.117703	−	0.993049i	$-0.462447\pi$
$271$	3.87526			0.235405			0.117703	+	0.993049i	$0.462447\pi$
$272$	−0.0491130	−	0.0491130i	−0.00297791	−	0.00297791i
$273$	−0.898451	−	0.898451i	−0.0543767	−	0.0543767i
$274$	14.7570	−	14.7570i	0.891503	−	0.891503i
$275$	11.9032	−	11.9032i	0.717790	−	0.717790i
$276$	6.22641	−	6.22641i	0.374786	−	0.374786i
$277$	−21.1197			−1.26896			−0.634479	−	0.772940i	$-0.718785\pi$
$277$	−21.1197			−1.26896			−0.634479	+	0.772940i	$0.718785\pi$
$278$		−	0.663465i		−	0.0397920i
$279$			7.83934i			0.469329i
$280$	0.779228	−	0.779228i	0.0465678	−	0.0465678i
$281$	−10.7472	−	10.7472i	−0.641125	−	0.641125i	0.309707	−	0.950832i	$-0.399769\pi$
$281$	−10.7472	−	10.7472i	−0.641125	−	0.641125i	−0.950832	+	0.309707i	$0.899769\pi$
$282$		−	20.1997i		−	1.20288i
$283$	−17.6179			−1.04727			−0.523637	−	0.851942i	$-0.675425\pi$
$283$	−17.6179			−1.04727			−0.523637	+	0.851942i	$0.675425\pi$
$284$	5.54180	−	5.54180i	0.328845	−	0.328845i
$285$			9.80747i			0.580944i
$286$	−2.92666			−0.173057
$287$	5.75093	+	2.81546i	0.339467	+	0.166191i
$288$	−0.726999			−0.0428388
$289$		−	16.9952i		−	0.999716i
$290$	1.52972	−	1.52972i	0.0898283	−	0.0898283i
$291$	13.6808			0.801984
$292$			11.2304i			0.657207i
$293$	−7.92227	−	7.92227i	−0.462824	−	0.462824i	0.436756	−	0.899580i	$-0.356127\pi$
$293$	−7.92227	−	7.92227i	−0.462824	−	0.462824i	−0.899580	+	0.436756i	$0.856127\pi$
$294$	−1.36510	+	1.36510i	−0.0796143	+	0.0796143i
$295$		−	6.08632i		−	0.354359i
$296$			2.56208i			0.148918i
$297$	19.5129			1.13225
$298$	11.2948	−	11.2948i	0.654293	−	0.654293i
$299$	−2.12270	+	2.12270i	−0.122759	+	0.122759i
$300$	−5.16773	+	5.16773i	−0.298359	+	0.298359i
$301$	0.187733	+	0.187733i	0.0108207	+	0.0108207i
$302$	−12.8072	−	12.8072i	−0.736971	−	0.736971i
$303$	−4.64937			−0.267099
$304$	−3.25974	−	3.25974i	−0.186959	−	0.186959i
$305$	10.9813			0.628789
$306$	0.0357051	+	0.0357051i	0.00204112	+	0.00204112i
$307$		−	18.6406i		−	1.06388i	−0.846783	−	0.531939i	$-0.821464\pi$
$307$		−	18.6406i		−	1.06388i	0.846783	−	0.531939i	$-0.178536\pi$
$308$			4.44675i			0.253377i
$309$	−11.5297	−	11.5297i	−0.655904	−	0.655904i
$310$	11.8830			0.674908
$311$	−18.3478	−	18.3478i	−1.04041	−	1.04041i	−0.999149	−	0.0412571i	$-0.986864\pi$
$311$	−18.3478	−	18.3478i	−1.04041	−	1.04041i	−0.0412571	−	0.999149i	$-0.513136\pi$
$312$	1.27060			0.0719336
$313$	−8.03245	−	8.03245i	−0.454021	−	0.454021i	0.442666	−	0.896687i	$-0.354033\pi$
$313$	−8.03245	−	8.03245i	−0.454021	−	0.454021i	−0.896687	+	0.442666i	$0.854033\pi$
$314$	6.04281	+	6.04281i	0.341016	+	0.341016i
$315$	−0.566498	+	0.566498i	−0.0319186	+	0.0319186i
$316$	−9.54867	+	9.54867i	−0.537154	+	0.537154i
$317$	−23.4141	+	23.4141i	−1.31507	+	1.31507i	−0.397437	+	0.917630i	$0.630100\pi$
$317$	−23.4141	+	23.4141i	−1.31507	+	1.31507i	−0.917630	+	0.397437i	$0.869900\pi$
$318$	−19.1489			−1.07382
$319$			8.72952i			0.488759i
$320$			1.10200i			0.0616034i
$321$	10.8208	−	10.8208i	0.603961	−	0.603961i
$322$	3.22521	+	3.22521i	0.179734	+	0.179734i
$323$			0.320191i			0.0178159i
$324$	−10.6525			−0.591804
$325$	1.76177	−	1.76177i	0.0977256	−	0.0977256i
$326$		−	12.3376i		−	0.683319i
$327$	18.2388			1.00861
$328$	−6.05735	+	2.07569i	−0.334461	+	0.114611i
$329$	10.4632			0.576856
$330$			9.46024i			0.520769i
$331$	22.7647	−	22.7647i	1.25126	−	1.25126i	0.296107	−	0.955155i	$-0.404312\pi$
$331$	22.7647	−	22.7647i	1.25126	−	1.25126i	0.955155	−	0.296107i	$-0.0956884\pi$
$332$	−2.94249			−0.161490
$333$		−	1.86263i		−	0.102072i
$334$	14.4137	+	14.4137i	0.788682	+	0.788682i
$335$	−0.952138	+	0.952138i	−0.0520209	+	0.0520209i
$336$		−	1.93054i		−	0.105320i
$337$			12.2735i			0.668578i	0.942471	+	0.334289i	$0.108496\pi$
$337$			12.2735i			0.668578i	−0.942471	+	0.334289i	$0.891504\pi$
$338$	12.5668			0.683545
$339$	−10.7820	+	10.7820i	−0.585597	+	0.585597i
$340$	0.0541222	−	0.0541222i	0.00293519	−	0.00293519i
$341$	−33.9058	+	33.9058i	−1.83610	+	1.83610i
$342$	2.36983	+	2.36983i	0.128146	+	0.128146i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	−0.265494			−0.0143145
$345$	6.86148	+	6.86148i	0.369410	+	0.369410i
$346$	10.5955			0.569620
$347$	−17.3914	−	17.3914i	−0.933620	−	0.933620i	0.0643103	−	0.997930i	$-0.479515\pi$
$347$	−17.3914	−	17.3914i	−0.933620	−	0.933620i	−0.997930	+	0.0643103i	$0.979515\pi$
$348$		−	3.78989i		−	0.203160i
$349$		−	7.16984i		−	0.383793i	−0.981415	−	0.191896i	$-0.938536\pi$
$349$		−	7.16984i		−	0.383793i	0.981415	−	0.191896i	$-0.0614637\pi$
$350$	−2.67683	−	2.67683i	−0.143082	−	0.143082i
$351$	2.88808			0.154154
$352$	−3.14433	−	3.14433i	−0.167593	−	0.167593i
$353$	−19.2027			−1.02206			−0.511029	−	0.859563i	$-0.670736\pi$
$353$	−19.2027			−1.02206			−0.511029	+	0.859563i	$0.670736\pi$
$354$	−7.53945	−	7.53945i	−0.400717	−	0.400717i
$355$	6.10703	+	6.10703i	0.324128	+	0.324128i
$356$	7.87950	−	7.87950i	0.417613	−	0.417613i
$357$	−0.0948147	+	0.0948147i	−0.00501813	+	0.00501813i
$358$	1.43142	−	1.43142i	0.0756528	−	0.0756528i
$359$	−10.9767			−0.579329			−0.289664	−	0.957128i	$-0.593544\pi$
$359$	−10.9767			−0.579329			−0.289664	+	0.957128i	$0.593544\pi$
$360$		−	0.801150i		−	0.0422243i
$361$			2.25177i			0.118514i
$362$	−10.0222	+	10.0222i	−0.526757	+	0.526757i
$363$	−11.9769	−	11.9769i	−0.628622	−	0.628622i
$364$			0.658157i			0.0344968i
$365$	−12.3758			−0.647779
$366$	13.6032	−	13.6032i	0.711049	−	0.711049i
$367$			31.6587i			1.65257i	0.563252	+	0.826285i	$0.309550\pi$
$367$			31.6587i			1.65257i	−0.563252	+	0.826285i	$0.690450\pi$
$368$	−4.56114			−0.237766
$369$	4.40369	−	1.50903i	0.229247	−	0.0785567i
$370$	−2.82340			−0.146782
$371$		−	9.91893i		−	0.514965i
$372$	14.7201	−	14.7201i	0.763201	−	0.763201i
$373$	5.34894			0.276957			0.138479	−	0.990365i	$-0.455779\pi$
$373$	5.34894			0.276957			0.138479	+	0.990365i	$0.455779\pi$
$374$			0.308855i			0.0159705i
$375$	−13.2165	−	13.2165i	−0.682497	−	0.682497i
$376$	−7.39861	+	7.39861i	−0.381554	+	0.381554i
$377$			1.29204i			0.0665436i
$378$		−	4.38813i		−	0.225701i
$379$	27.3151			1.40308			0.701540	−	0.712630i	$-0.252496\pi$
$379$	27.3151			1.40308			0.701540	+	0.712630i	$0.252496\pi$
$380$	3.59221	−	3.59221i	0.184277	−	0.184277i
$381$	−10.9835	+	10.9835i	−0.562701	+	0.562701i
$382$	8.89884	−	8.89884i	0.455304	−	0.455304i
$383$	0.586454	+	0.586454i	0.0299664	+	0.0299664i	0.721931	−	0.691965i	$-0.243255\pi$
$383$	0.586454	+	0.586454i	0.0299664	+	0.0299664i	−0.691965	+	0.721931i	$0.743255\pi$
$384$	1.36510	+	1.36510i	0.0696625	+	0.0696625i
$385$	−4.90030			−0.249742
$386$	−1.80187	−	1.80187i	−0.0917127	−	0.0917127i
$387$	0.193014			0.00981145
$388$	−5.01092	−	5.01092i	−0.254391	−	0.254391i
$389$			8.82079i			0.447232i	0.974677	+	0.223616i	$0.0717861\pi$
$389$			8.82079i			0.447232i	−0.974677	+	0.223616i	$0.928214\pi$
$390$			1.40020i			0.0709017i
$391$	0.224011	+	0.224011i	0.0113287	+	0.0113287i
$392$	1.00000			0.0505076
$393$	−11.2652	−	11.2652i	−0.568256	−	0.568256i
$394$	17.3369			0.873422
$395$	−10.5226	−	10.5226i	−0.529449	−	0.529449i
$396$	2.28592	+	2.28592i	0.114872	+	0.114872i
$397$	4.12183	−	4.12183i	0.206869	−	0.206869i	−0.596066	−	0.802935i	$-0.703270\pi$
$397$	4.12183	−	4.12183i	0.206869	−	0.206869i	0.802935	+	0.596066i	$0.203270\pi$
$398$	−0.632062	+	0.632062i	−0.0316824	+	0.0316824i
$399$	−6.29306	+	6.29306i	−0.315047	+	0.315047i
$400$	3.78561			0.189280
$401$		−	1.29717i		−	0.0647778i	−0.999475	−	0.0323889i	$-0.989688\pi$
$401$		−	1.29717i		−	0.0647778i	0.999475	−	0.0323889i	$-0.0103115\pi$
$402$			2.35893i			0.117653i
$403$	−5.01834	+	5.01834i	−0.249981	+	0.249981i
$404$	1.70294	+	1.70294i	0.0847244	+	0.0847244i
$405$		−	11.7390i		−	0.583314i
$406$	1.96312			0.0974282
$407$	8.05603	−	8.05603i	0.399323	−	0.399323i
$408$		−	0.134088i		−	0.00663836i
$409$	9.15651			0.452760			0.226380	−	0.974039i	$-0.427311\pi$
$409$	9.15651			0.452760			0.226380	+	0.974039i	$0.427311\pi$
$410$	−2.28740	−	6.67517i	−0.112967	−	0.329663i
$411$	40.2896			1.98734
$412$			8.44607i			0.416108i
$413$	3.90535	−	3.90535i	0.192170	−	0.192170i
$414$	3.31595			0.162970
$415$		−	3.24261i		−	0.159173i
$416$	−0.465387	−	0.465387i	−0.0228175	−	0.0228175i
$417$	0.905697	−	0.905697i	0.0443522	−	0.0443522i
$418$			20.4994i			1.00266i
$419$			28.1644i			1.37592i	0.725747	+	0.687961i	$0.241494\pi$
$419$			28.1644i			1.37592i	−0.725747	+	0.687961i	$0.758506\pi$
$420$	2.12745			0.103809
$421$	−13.8649	+	13.8649i	−0.675732	+	0.675732i	−0.959031	−	0.283300i	$-0.908571\pi$
$421$	−13.8649	+	13.8649i	−0.675732	+	0.675732i	0.283300	+	0.959031i	$0.408571\pi$
$422$	−5.55224	+	5.55224i	−0.270279	+	0.270279i
$423$	5.37879	−	5.37879i	0.261526	−	0.261526i
$424$	7.01374	+	7.01374i	0.340618	+	0.340618i
$425$	−0.185922	−	0.185922i	−0.00901856	−	0.00901856i
$426$	15.1302			0.733062
$427$	7.04629	+	7.04629i	0.340994	+	0.340994i
$428$	−7.92678			−0.383155
$429$	−3.99519	−	3.99519i	−0.192889	−	0.192889i
$430$		−	0.292573i		−	0.0141091i
$431$			28.0057i			1.34899i	0.738281	+	0.674494i	$0.235638\pi$
$431$			28.0057i			1.34899i	−0.738281	+	0.674494i	$0.764362\pi$
$432$	3.10287	+	3.10287i	0.149287	+	0.149287i
$433$	−16.9797			−0.815993			−0.407997	−	0.912983i	$-0.633772\pi$
$433$	−16.9797			−0.815993			−0.407997	+	0.912983i	$0.633772\pi$
$434$	7.62484	+	7.62484i	0.366004	+	0.366004i
$435$	4.17645			0.200245
$436$	−6.68039	−	6.68039i	−0.319933	−	0.319933i
$437$	14.8681	+	14.8681i	0.711238	+	0.711238i
$438$	−15.3306	+	15.3306i	−0.732523	+	0.732523i
$439$	10.1275	−	10.1275i	0.483359	−	0.483359i	−0.422844	−	0.906203i	$-0.638968\pi$
$439$	10.1275	−	10.1275i	0.483359	−	0.483359i	0.906203	+	0.422844i	$0.138968\pi$
$440$	3.46503	−	3.46503i	0.165189	−	0.165189i
$441$	−0.726999			−0.0346190
$442$			0.0457131i			0.00217435i
$443$		−	15.8026i		−	0.750806i	−0.926862	−	0.375403i	$-0.877504\pi$
$443$		−	15.8026i		−	0.750806i	0.926862	−	0.375403i	$-0.122496\pi$
$444$	−3.49750	+	3.49750i	−0.165984	+	0.165984i
$445$	8.68317	+	8.68317i	0.411622	+	0.411622i
$446$			27.5489i			1.30448i
$447$	30.8372			1.45855
$448$	−0.707107	+	0.707107i	−0.0334077	+	0.0334077i
$449$			2.78127i			0.131256i	0.997844	+	0.0656281i	$0.0209051\pi$
$449$			2.78127i			0.131256i	−0.997844	+	0.0656281i	$0.979095\pi$
$450$	−2.75213			−0.129737
$451$	25.5730	+	12.5197i	1.20418	+	0.589528i
$452$	7.89831			0.371505
$453$		−	34.9662i		−	1.64286i
$454$	6.72572	−	6.72572i	0.315654	−	0.315654i
$455$	−0.725286			−0.0340019
$456$		−	8.89974i		−	0.416768i
$457$	6.16597	+	6.16597i	0.288432	+	0.288432i	0.836460	−	0.548028i	$-0.184621\pi$
$457$	6.16597	+	6.16597i	0.288432	+	0.288432i	−0.548028	+	0.836460i	$0.684621\pi$
$458$	2.14501	−	2.14501i	0.100230	−	0.100230i
$459$		−	0.304783i		−	0.0142260i
$460$		−	5.02635i		−	0.234355i
$461$	−1.67237			−0.0778901			−0.0389450	−	0.999241i	$-0.512400\pi$
$461$	−1.67237			−0.0778901			−0.0389450	+	0.999241i	$0.512400\pi$
$462$	−6.07026	+	6.07026i	−0.282414	+	0.282414i
$463$	−7.51049	+	7.51049i	−0.349042	+	0.349042i	−0.859753	−	0.510711i	$-0.829382\pi$
$463$	−7.51049	+	7.51049i	−0.349042	+	0.349042i	0.510711	+	0.859753i	$0.329382\pi$
$464$	−1.38814	+	1.38814i	−0.0644427	+	0.0644427i
$465$	16.2215	+	16.2215i	0.752252	+	0.752252i
$466$	20.0860	+	20.0860i	0.930465	+	0.930465i
$467$	18.5583			0.858776			0.429388	−	0.903120i	$-0.358729\pi$
$467$	18.5583			0.858776			0.429388	+	0.903120i	$0.358729\pi$
$468$	0.338336	+	0.338336i	0.0156396	+	0.0156396i
$469$	−1.22190			−0.0564221
$470$	−8.15324	−	8.15324i	−0.376081	−	0.376081i
$471$			16.4981i			0.760192i
$472$			5.52300i			0.254217i
$473$	0.834800	+	0.834800i	0.0383841	+	0.0383841i
$474$	−26.0698			−1.19742
$475$	−12.3401	−	12.3401i	−0.566202	−	0.566202i
$476$	0.0694562			0.00318352
$477$	−5.09899	−	5.09899i	−0.233467	−	0.233467i
$478$	−7.18197	−	7.18197i	−0.328496	−	0.328496i
$479$	8.35146	−	8.35146i	0.381588	−	0.381588i	−0.490086	−	0.871674i	$-0.663035\pi$
$479$	8.35146	−	8.35146i	0.381588	−	0.381588i	0.871674	+	0.490086i	$0.163035\pi$
$480$	−1.50433	+	1.50433i	−0.0686631	+	0.0686631i
$481$	1.19236	−	1.19236i	0.0543670	−	0.0543670i
$482$	−8.32804			−0.379332
$483$			8.80548i			0.400663i
$484$			8.77361i			0.398800i
$485$	5.52201	−	5.52201i	0.250741	−	0.250741i
$486$	−5.23307	−	5.23307i	−0.237377	−	0.237377i
$487$		−	19.2797i		−	0.873648i	−0.899547	−	0.436824i	$-0.856103\pi$
$487$		−	19.2797i		−	0.873648i	0.899547	−	0.436824i	$-0.143897\pi$
$488$	−9.96496			−0.451092
$489$	16.8421	−	16.8421i	0.761627	−	0.761627i
$490$			1.10200i			0.0497831i
$491$	33.8815			1.52905			0.764526	−	0.644593i	$-0.222973\pi$
$491$	33.8815			1.52905			0.764526	+	0.644593i	$0.222973\pi$
$492$	−11.1024	−	5.43537i	−0.500536	−	0.245045i
$493$	0.136351			0.00614094
$494$			3.03408i			0.136510i
$495$	−2.51908	+	2.51908i	−0.113224	+	0.113224i
$496$	−10.7831			−0.484178
$497$			7.83729i			0.351550i
$498$	−4.01679	−	4.01679i	−0.179997	−	0.179997i
$499$	−23.2836	+	23.2836i	−1.04232	+	1.04232i	−0.0432545	+	0.999064i	$0.513773\pi$
$499$	−23.2836	+	23.2836i	−1.04232	+	1.04232i	−0.999064	+	0.0432545i	$0.986227\pi$
$500$			9.68170i			0.432979i
$501$			39.3523i			1.75813i
$502$	7.71650			0.344404
$503$	7.50994	−	7.50994i	0.334852	−	0.334852i	−0.519574	−	0.854426i	$-0.673909\pi$
$503$	7.50994	−	7.50994i	0.334852	−	0.334852i	0.854426	+	0.519574i	$0.173909\pi$
$504$	0.514066	−	0.514066i	0.0228983	−	0.0228983i
$505$	−1.87663	+	1.87663i	−0.0835090	+	0.0835090i
$506$	14.3417	+	14.3417i	0.637567	+	0.637567i
$507$	17.1550	+	17.1550i	0.761880	+	0.761880i
$508$	8.04592			0.356980
$509$	−17.1815	−	17.1815i	−0.761558	−	0.761558i	0.215046	−	0.976604i	$-0.431010\pi$
$509$	−17.1815	−	17.1815i	−0.761558	−	0.761558i	−0.976604	+	0.215046i	$0.931010\pi$
$510$	0.147765			0.00654313
$511$	−7.94106	−	7.94106i	−0.351292	−	0.351292i
$512$		−	1.00000i		−	0.0441942i
$513$		−	20.2291i		−	0.893137i
$514$	−6.29904	−	6.29904i	−0.277839	−	0.277839i
$515$	−9.30753			−0.410139
$516$	−0.362426	−	0.362426i	−0.0159549	−	0.0159549i
$517$	46.5274			2.04627
$518$	−1.81167	−	1.81167i	−0.0796001	−	0.0796001i
$519$	14.4640	+	14.4640i	0.634899	+	0.634899i
$520$	0.512855	−	0.512855i	0.0224902	−	0.0224902i
$521$	25.6029	−	25.6029i	1.12168	−	1.12168i	0.130196	−	0.991488i	$-0.458439\pi$
$521$	25.6029	−	25.6029i	1.12168	−	1.12168i	0.991488	−	0.130196i	$-0.0415606\pi$
$522$	1.00918	−	1.00918i	0.0441704	−	0.0441704i
$523$	−35.9558			−1.57224			−0.786119	−	0.618075i	$-0.787913\pi$
$523$	−35.9558			−1.57224			−0.786119	+	0.618075i	$0.787913\pi$
$524$			8.25232i			0.360504i
$525$		−	7.30828i		−	0.318959i
$526$	−3.52198	+	3.52198i	−0.153565	+	0.153565i
$527$	0.529592	+	0.529592i	0.0230694	+	0.0230694i
$528$		−	8.58465i		−	0.373599i
$529$	−2.19600			−0.0954784
$530$	−7.72911	+	7.72911i	−0.335731	+	0.335731i
$531$		−	4.01522i		−	0.174246i
$532$	4.60996			0.199867
$533$	3.78501	+	1.85301i	0.163947	+	0.0802630i
$534$	21.5126			0.930942
$535$		−	8.73527i		−	0.377659i
$536$	0.864013	−	0.864013i	0.0373197	−	0.0373197i
$537$	3.90806			0.168645
$538$			19.5527i			0.842975i
$539$	−3.14433	−	3.14433i	−0.135436	−	0.135436i
$540$	−3.41935	+	3.41935i	−0.147146	+	0.147146i
$541$		−	2.19333i		−	0.0942988i	−0.998888	−	0.0471494i	$-0.984986\pi$
$541$		−	2.19333i		−	0.0942988i	0.998888	−	0.0471494i	$-0.0150137\pi$
$542$		−	3.87526i		−	0.166457i
$543$	−27.3627			−1.17425
$544$	−0.0491130	+	0.0491130i	−0.00210570	+	0.00210570i
$545$	7.36176	−	7.36176i	0.315343	−	0.315343i
$546$	−0.898451	+	0.898451i	−0.0384501	+	0.0384501i
$547$	−0.296878	−	0.296878i	−0.0126936	−	0.0126936i	0.700732	−	0.713425i	$-0.252857\pi$
$547$	−0.296878	−	0.296878i	−0.0126936	−	0.0126936i	−0.713425	+	0.700732i	$0.752857\pi$
$548$	−14.7570	−	14.7570i	−0.630388	−	0.630388i
$549$	7.24452			0.309188
$550$	−11.9032	−	11.9032i	−0.507554	−	0.507554i
$551$	9.04993			0.385540
$552$	−6.22641	−	6.22641i	−0.265014	−	0.265014i
$553$		−	13.5039i		−	0.574242i
$554$			21.1197i			0.897289i
$555$	−3.85423	−	3.85423i	−0.163603	−	0.163603i
$556$	−0.663465			−0.0281372
$557$	8.54296	+	8.54296i	0.361977	+	0.361977i	0.864540	−	0.502563i	$-0.167610\pi$
$557$	8.54296	+	8.54296i	0.361977	+	0.361977i	−0.502563	+	0.864540i	$0.667610\pi$
$558$	7.83934			0.331866
$559$	0.123557	+	0.123557i	0.00522592	+	0.00522592i
$560$	−0.779228	−	0.779228i	−0.0329284	−	0.0329284i
$561$	−0.421618	+	0.421618i	−0.0178007	+	0.0178007i
$562$	−10.7472	+	10.7472i	−0.453344	+	0.453344i
$563$	−10.5874	+	10.5874i	−0.446206	+	0.446206i	−0.894091	−	0.447885i	$-0.852177\pi$
$563$	−10.5874	+	10.5874i	−0.446206	+	0.446206i	0.447885	+	0.894091i	$0.352177\pi$
$564$	−20.1997			−0.850561
$565$			8.70390i			0.366176i
$566$			17.6179i			0.740534i
$567$	7.53243	−	7.53243i	0.316332	−	0.316332i
$568$	−5.54180	−	5.54180i	−0.232529	−	0.232529i
$569$		−	39.6145i		−	1.66073i	−0.557223	−	0.830363i	$-0.688133\pi$
$569$		−	39.6145i		−	1.66073i	0.557223	−	0.830363i	$-0.311867\pi$
$570$	9.80747			0.410790
$571$	27.8001	−	27.8001i	1.16340	−	1.16340i	0.179669	−	0.983727i	$-0.442497\pi$
$571$	27.8001	−	27.8001i	1.16340	−	1.16340i	0.983727	−	0.179669i	$-0.0575027\pi$
$572$			2.92666i			0.122370i
$573$	24.2956			1.01496
$574$	2.81546	−	5.75093i	0.117515	−	0.240039i
$575$	−17.2667			−0.720070
$576$			0.726999i			0.0302916i
$577$	−11.3657	+	11.3657i	−0.473162	+	0.473162i	−0.902936	−	0.429774i	$-0.858593\pi$
$577$	−11.3657	+	11.3657i	−0.473162	+	0.473162i	0.429774	+	0.902936i	$0.358593\pi$
$578$	−16.9952			−0.706906
$579$		−	4.91946i		−	0.204446i
$580$	−1.52972	−	1.52972i	−0.0635182	−	0.0635182i
$581$	2.08065	−	2.08065i	0.0863200	−	0.0863200i
$582$		−	13.6808i		−	0.567088i
$583$		−	44.1070i		−	1.82673i
$584$	11.2304			0.464715
$585$	−0.372845	+	0.372845i	−0.0154152	+	0.0154152i
$586$	−7.92227	+	7.92227i	−0.327266	+	0.327266i
$587$	−14.3067	+	14.3067i	−0.590503	+	0.590503i	−0.937767	−	0.347265i	$-0.887111\pi$
$587$	−14.3067	+	14.3067i	−0.590503	+	0.590503i	0.347265	+	0.937767i	$0.387111\pi$
$588$	1.36510	+	1.36510i	0.0562958	+	0.0562958i
$589$	35.1502	+	35.1502i	1.44834	+	1.44834i
$590$	−6.08632			−0.250570
$591$	23.6667	+	23.6667i	0.973517	+	0.973517i
$592$	2.56208			0.105301
$593$	15.7316	+	15.7316i	0.646019	+	0.646019i	0.952029	−	0.306009i	$-0.0989939\pi$
$593$	15.7316	+	15.7316i	0.646019	+	0.646019i	−0.306009	+	0.952029i	$0.598994\pi$
$594$		−	19.5129i		−	0.800625i
$595$			0.0765404i			0.00313785i
$596$	−11.2948	−	11.2948i	−0.462655	−	0.462655i
$597$	−1.72566			−0.0706264
$598$	2.12270	+	2.12270i	0.0868035	+	0.0868035i
$599$	17.3836			0.710276			0.355138	−	0.934814i	$-0.384434\pi$
$599$	17.3836			0.710276			0.355138	+	0.934814i	$0.384434\pi$
$600$	5.16773	+	5.16773i	0.210972	+	0.210972i
$601$	4.72251	+	4.72251i	0.192635	+	0.192635i	0.796834	−	0.604199i	$-0.206507\pi$
$601$	4.72251	+	4.72251i	0.192635	+	0.192635i	−0.604199	+	0.796834i	$0.706507\pi$
$602$	0.187733	−	0.187733i	0.00765141	−	0.00765141i
$603$	−0.628137	+	0.628137i	−0.0255797	+	0.0255797i
$604$	−12.8072	+	12.8072i	−0.521117	+	0.521117i
$605$	−9.66847			−0.393079
$606$			4.64937i			0.188868i
$607$		−	21.2862i		−	0.863980i	−0.901878	−	0.431990i	$-0.857812\pi$
$607$		−	21.2862i		−	0.863980i	0.901878	−	0.431990i	$-0.142188\pi$
$608$	−3.25974	+	3.25974i	−0.132200	+	0.132200i
$609$	2.67986	+	2.67986i	0.108593	+	0.108593i
$610$		−	10.9813i		−	0.444621i
$611$	6.88644			0.278596
$612$	0.0357051	−	0.0357051i	0.00144329	−	0.00144329i
$613$			8.99338i			0.363239i	0.983369	+	0.181620i	$0.0581339\pi$
$613$			8.99338i			0.363239i	−0.983369	+	0.181620i	$0.941866\pi$
$614$	−18.6406			−0.752275
$615$	5.98975	−	12.2348i	0.241530	−	0.493355i
$616$	4.44675			0.179165
$617$		−	10.7712i		−	0.433632i	−0.976213	−	0.216816i	$-0.930433\pi$
$617$		−	10.7712i		−	0.433632i	0.976213	−	0.216816i	$-0.0695671\pi$
$618$	−11.5297	+	11.5297i	−0.463794	+	0.463794i
$619$	−10.4911			−0.421673			−0.210836	−	0.977521i	$-0.567619\pi$
$619$	−10.4911			−0.421673			−0.210836	+	0.977521i	$0.567619\pi$
$620$		−	11.8830i		−	0.477232i
$621$	−14.1526	−	14.1526i	−0.567926	−	0.567926i
$622$	−18.3478	+	18.3478i	−0.735678	+	0.735678i
$623$			11.1433i			0.446447i
$624$		−	1.27060i		−	0.0508647i
$625$	8.25885			0.330354
$626$	−8.03245	+	8.03245i	−0.321041	+	0.321041i
$627$	−27.9837	+	27.9837i	−1.11756	+	1.11756i
$628$	6.04281	−	6.04281i	0.241134	−	0.241134i
$629$	−0.125832	−	0.125832i	−0.00501723	−	0.00501723i
$630$	0.566498	+	0.566498i	0.0225698	+	0.0225698i
$631$	−46.9448			−1.86884			−0.934421	−	0.356171i	$-0.884082\pi$
$631$	−46.9448			−1.86884			−0.934421	+	0.356171i	$0.884082\pi$
$632$	9.54867	+	9.54867i	0.379826	+	0.379826i
$633$	−15.1587			−0.602505
$634$	23.4141	+	23.4141i	0.929892	+	0.929892i
$635$			8.86656i			0.351859i
$636$			19.1489i			0.759305i
$637$	−0.465387	−	0.465387i	−0.0184393	−	0.0184393i
$638$	8.72952			0.345605
$639$	4.02888	+	4.02888i	0.159380	+	0.159380i
$640$	1.10200			0.0435602
$641$	−9.89757	−	9.89757i	−0.390931	−	0.390931i	0.484088	−	0.875019i	$-0.339151\pi$
$641$	−9.89757	−	9.89757i	−0.390931	−	0.390931i	−0.875019	+	0.484088i	$0.839151\pi$
$642$	−10.8208	−	10.8208i	−0.427065	−	0.427065i
$643$	−15.9226	+	15.9226i	−0.627928	+	0.627928i	−0.947546	−	0.319619i	$-0.896445\pi$
$643$	−15.9226	+	15.9226i	−0.627928	+	0.627928i	0.319619	+	0.947546i	$0.396445\pi$
$644$	3.22521	−	3.22521i	0.127091	−	0.127091i
$645$	0.399392	−	0.399392i	0.0157260	−	0.0157260i
$646$	0.320191			0.0125977
$647$			4.31703i			0.169720i	0.996393	+	0.0848601i	$0.0270443\pi$
$647$			4.31703i			0.169720i	−0.996393	+	0.0848601i	$0.972956\pi$
$648$			10.6525i			0.418469i
$649$	17.3661	−	17.3661i	0.681680	−	0.681680i
$650$	−1.76177	−	1.76177i	−0.0691024	−	0.0691024i
$651$			20.8173i			0.815896i
$652$	−12.3376			−0.483179
$653$	5.11930	−	5.11930i	0.200334	−	0.200334i	−0.599809	−	0.800143i	$-0.704757\pi$
$653$	5.11930	−	5.11930i	0.200334	−	0.200334i	0.800143	+	0.599809i	$0.204757\pi$
$654$		−	18.2388i		−	0.713194i
$655$	−9.09401			−0.355333
$656$	2.07569	+	6.05735i	0.0810421	+	0.236500i
$657$	−8.16446			−0.318526
$658$		−	10.4632i		−	0.407899i
$659$	18.6365	−	18.6365i	0.725975	−	0.725975i	−0.243840	−	0.969815i	$-0.578407\pi$
$659$	18.6365	−	18.6365i	0.725975	−	0.725975i	0.969815	+	0.243840i	$0.0784073\pi$
$660$	9.46024			0.368239
$661$		−	31.8204i		−	1.23767i	−0.785521	−	0.618835i	$-0.787605\pi$
$661$		−	31.8204i		−	1.23767i	0.785521	−	0.618835i	$-0.212395\pi$
$662$	−22.7647	−	22.7647i	−0.884776	−	0.884776i
$663$	−0.0624030	+	0.0624030i	−0.00242353	+	0.00242353i
$664$			2.94249i			0.114191i
$665$			5.08016i			0.197000i
$666$	−1.86263			−0.0721756
$667$	6.33149	−	6.33149i	0.245156	−	0.245156i
$668$	14.4137	−	14.4137i	0.557682	−	0.557682i
$669$	−37.6071	+	37.6071i	−1.45397	+	1.45397i
$670$	0.952138	+	0.952138i	0.0367843	+	0.0367843i
$671$	31.3331	+	31.3331i	1.20960	+	1.20960i
$672$	−1.93054			−0.0744723
$673$	7.61339	+	7.61339i	0.293475	+	0.293475i	0.838451	−	0.544977i	$-0.183461\pi$
$673$	7.61339	+	7.61339i	0.293475	+	0.293475i	−0.544977	+	0.838451i	$0.683461\pi$
$674$	12.2735			0.472756
$675$	11.7463	+	11.7463i	0.452114	+	0.452114i
$676$		−	12.5668i		−	0.483340i
$677$			31.2129i			1.19961i	0.800146	+	0.599805i	$0.204755\pi$
$677$			31.2129i			1.19961i	−0.800146	+	0.599805i	$0.795245\pi$
$678$	10.7820	+	10.7820i	0.414080	+	0.414080i
$679$	7.08651			0.271955
$680$	−0.0541222	−	0.0541222i	−0.00207549	−	0.00207549i
$681$	18.3626			0.703655
$682$	33.9058	+	33.9058i	1.29832	+	1.29832i
$683$	−0.188686	−	0.188686i	−0.00721986	−	0.00721986i	0.703488	−	0.710707i	$-0.251625\pi$
$683$	−0.188686	−	0.188686i	−0.00721986	−	0.00721986i	−0.710707	+	0.703488i	$0.751625\pi$
$684$	2.36983	−	2.36983i	0.0906126	−	0.0906126i
$685$	16.2621	−	16.2621i	0.621345	−	0.621345i
$686$	−0.707107	+	0.707107i	−0.0269975	+	0.0269975i
$687$	5.85631			0.223432
$688$			0.265494i			0.0101219i
$689$		−	6.52822i		−	0.248705i
$690$	6.86148	−	6.86148i	0.261212	−	0.261212i
$691$	15.4803	+	15.4803i	0.588898	+	0.588898i	0.937333	−	0.348435i	$-0.113287\pi$
$691$	15.4803	+	15.4803i	0.588898	+	0.588898i	−0.348435	+	0.937333i	$0.613287\pi$
$692$		−	10.5955i		−	0.402782i
$693$	−3.23279			−0.122803
$694$	−17.3914	+	17.3914i	−0.660169	+	0.660169i
$695$		−	0.731135i		−	0.0277335i
$696$	−3.78989			−0.143656
$697$	0.195551	−	0.399438i	0.00740703	−	0.0151298i
$698$	−7.16984			−0.271382
$699$			54.8387i			2.07419i
$700$	−2.67683	+	2.67683i	−0.101175	+	0.101175i
$701$	29.2859			1.10611			0.553057	−	0.833143i	$-0.313461\pi$
$701$	29.2859			1.10611			0.553057	+	0.833143i	$0.313461\pi$
$702$		−	2.88808i		−	0.109003i
$703$	−8.35172	−	8.35172i	−0.314991	−	0.314991i
$704$	−3.14433	+	3.14433i	−0.118506	+	0.118506i
$705$		−	22.2600i		−	0.838359i
$706$			19.2027i			0.722705i
$707$	−2.40832			−0.0905742
$708$	−7.53945	+	7.53945i	−0.283350	+	0.283350i
$709$	−26.5520	+	26.5520i	−0.997182	+	0.997182i	−0.999996	−	0.00281399i	$-0.999104\pi$
$709$	−26.5520	+	26.5520i	−0.997182	+	0.997182i	0.00281399	+	0.999996i	$0.499104\pi$
$710$	6.10703	−	6.10703i	0.229193	−	0.229193i
$711$	−6.94187	−	6.94187i	−0.260341	−	0.260341i
$712$	−7.87950	−	7.87950i	−0.295297	−	0.295297i
$713$	49.1834			1.84193
$714$	0.0948147	+	0.0948147i	0.00354835	+	0.00354835i
$715$	−3.22517			−0.120614
$716$	−1.43142	−	1.43142i	−0.0534946	−	0.0534946i
$717$		−	19.6082i		−	0.732282i
$718$			10.9767i			0.409647i
$719$	−33.1823	−	33.1823i	−1.23749	−	1.23749i	−0.961023	−	0.276469i	$-0.910836\pi$
$719$	−33.1823	−	33.1823i	−1.23749	−	1.23749i	−0.276469	−	0.961023i	$-0.589164\pi$
$720$	−0.801150			−0.0298571
$721$	−5.97227	−	5.97227i	−0.222419	−	0.222419i
$722$	2.25177			0.0838020
$723$	−11.3686	−	11.3686i	−0.422803	−	0.422803i
$724$	10.0222	+	10.0222i	0.372473	+	0.372473i
$725$	−5.25494	+	5.25494i	−0.195164	+	0.195164i
$726$	−11.9769	+	11.9769i	−0.444503	+	0.444503i
$727$	5.80689	−	5.80689i	0.215366	−	0.215366i	−0.591176	−	0.806542i	$-0.701336\pi$
$727$	5.80689	−	5.80689i	0.215366	−	0.215366i	0.806542	+	0.591176i	$0.201336\pi$
$728$	0.658157			0.0243929
$729$			17.6701i			0.654447i
$730$			12.3758i			0.458049i
$731$	0.0130392	−	0.0130392i	0.000482272	−	0.000482272i
$732$	−13.6032	−	13.6032i	−0.502788	−	0.502788i
$733$		−	17.6993i		−	0.653740i	−0.945069	−	0.326870i	$-0.894006\pi$
$733$		−	17.6993i		−	0.653740i	0.945069	−	0.326870i	$-0.105994\pi$
$734$	31.6587			1.16854
$735$	−1.50433	+	1.50433i	−0.0554882	+	0.0554882i
$736$			4.56114i			0.168126i
$737$	−5.43348			−0.200145
$738$	−1.50903	−	4.40369i	−0.0555480	−	0.162102i
$739$	−24.0239			−0.883733			−0.441867	−	0.897081i	$-0.645684\pi$
$739$	−24.0239			−0.883733			−0.441867	+	0.897081i	$0.645684\pi$
$740$			2.82340i			0.103790i
$741$	−4.14182	+	4.14182i	−0.152154	+	0.152154i
$742$	−9.91893			−0.364135
$743$		−	19.1242i		−	0.701600i	−0.936450	−	0.350800i	$-0.885910\pi$
$743$		−	19.1242i		−	0.701600i	0.936450	−	0.350800i	$-0.114090\pi$
$744$	−14.7201	−	14.7201i	−0.539664	−	0.539664i
$745$	12.4469	−	12.4469i	0.456018	−	0.456018i
$746$		−	5.34894i		−	0.195839i
$747$		−	2.13919i		−	0.0782688i
$748$	0.308855			0.0112928
$749$	5.60508	−	5.60508i	0.204805	−	0.204805i
$750$	−13.2165	+	13.2165i	−0.482598	+	0.482598i
$751$	−28.7300	+	28.7300i	−1.04837	+	1.04837i	−0.0496040	+	0.998769i	$0.515796\pi$
$751$	−28.7300	+	28.7300i	−1.04837	+	1.04837i	−0.998769	+	0.0496040i	$0.984204\pi$
$752$	7.39861	+	7.39861i	0.269800	+	0.269800i
$753$	10.5338	+	10.5338i	0.383873	+	0.383873i
$754$	1.29204			0.0470534
$755$	−14.1135	−	14.1135i	−0.513642	−	0.513642i
$756$	−4.38813			−0.159595
$757$	−35.7965	−	35.7965i	−1.30105	−	1.30105i	−0.927687	−	0.373358i	$-0.878206\pi$
$757$	−35.7965	−	35.7965i	−1.30105	−	1.30105i	−0.373358	−	0.927687i	$-0.621794\pi$
$758$		−	27.3151i		−	0.992128i
$759$			39.1558i			1.42127i
$760$	−3.59221	−	3.59221i	−0.130303	−	0.130303i
$761$	34.5528			1.25254			0.626269	−	0.779607i	$-0.284581\pi$
$761$	34.5528			1.25254			0.626269	+	0.779607i	$0.284581\pi$
$762$	10.9835	+	10.9835i	0.397890	+	0.397890i
$763$	9.44750			0.342022
$764$	−8.89884	−	8.89884i	−0.321949	−	0.321949i
$765$	0.0393468	+	0.0393468i	0.00142259	+	0.00142259i
$766$	0.586454	−	0.586454i	0.0211894	−	0.0211894i
$767$	2.57034	−	2.57034i	0.0928094	−	0.0928094i
$768$	1.36510	−	1.36510i	0.0492588	−	0.0492588i
$769$	30.2025			1.08913			0.544566	−	0.838718i	$-0.316695\pi$
$769$	30.2025			1.08913			0.544566	+	0.838718i	$0.316695\pi$
$770$			4.90030i			0.176595i
$771$		−	17.1977i		−	0.619358i
$772$	−1.80187	+	1.80187i	−0.0648507	+	0.0648507i
$773$	−6.92770	−	6.92770i	−0.249172	−	0.249172i	0.571459	−	0.820631i	$-0.306378\pi$
$773$	−6.92770	−	6.92770i	−0.249172	−	0.249172i	−0.820631	+	0.571459i	$0.806378\pi$
$774$		−	0.193014i		−	0.00693774i
$775$	−40.8208			−1.46632
$776$	−5.01092	+	5.01092i	−0.179881	+	0.179881i
$777$		−	4.94621i		−	0.177444i
$778$	8.82079			0.316241
$779$	12.9792	−	26.5116i	0.465027	−	0.949876i
$780$	1.40020			0.0501351
$781$			34.8505i			1.24705i
$782$	0.224011	−	0.224011i	0.00801062	−	0.00801062i
$783$	−8.61443			−0.307855
$784$		−	1.00000i		−	0.0357143i
$785$	6.65915	+	6.65915i	0.237675	+	0.237675i
$786$	−11.2652	+	11.2652i	−0.401818	+	0.401818i
$787$			17.8230i			0.635322i	0.948204	+	0.317661i	$0.102897\pi$
$787$			17.8230i			0.635322i	−0.948204	+	0.317661i	$0.897103\pi$
$788$		−	17.3369i		−	0.617603i
$789$	−9.61570			−0.342328
$790$	−10.5226	+	10.5226i	−0.374377	+	0.374377i
$791$	−5.58495	+	5.58495i	−0.198578	+	0.198578i
$792$	2.28592	−	2.28592i	0.0812268	−	0.0812268i
$793$	4.63756	+	4.63756i	0.164685	+	0.164685i
$794$	−4.12183	−	4.12183i	−0.146278	−	0.146278i
$795$	−21.1020			−0.748412
$796$	0.632062	+	0.632062i	0.0224028	+	0.0224028i
$797$	34.9641			1.23849			0.619246	−	0.785197i	$-0.287438\pi$
$797$	34.9641			1.23849			0.619246	+	0.785197i	$0.287438\pi$
$798$	6.29306	+	6.29306i	0.222772	+	0.222772i
$799$		−	0.726736i		−	0.0257101i
$800$		−	3.78561i		−	0.133841i
$801$	5.72839	+	5.72839i	0.202403	+	0.202403i
$802$	−1.29717			−0.0458048
$803$	−35.3119	−	35.3119i	−1.24613	−	1.24613i
$804$	2.35893			0.0831930
$805$	3.55417	+	3.55417i	0.125268	+	0.125268i
$806$	5.01834	+	5.01834i	0.176764	+	0.176764i
$807$	−26.6913	+	26.6913i	−0.939580	+	0.939580i
$808$	1.70294	−	1.70294i	0.0599092	−	0.0599092i
$809$	15.8498	−	15.8498i	0.557248	−	0.557248i	−0.371275	−	0.928523i	$-0.621079\pi$
$809$	15.8498	−	15.8498i	0.557248	−	0.557248i	0.928523	+	0.371275i	$0.121079\pi$
$810$	−11.7390			−0.412465
$811$		−	13.7714i		−	0.483580i	−0.970329	−	0.241790i	$-0.922265\pi$
$811$		−	13.7714i		−	0.483580i	0.970329	−	0.241790i	$-0.0777346\pi$
$812$		−	1.96312i		−	0.0688921i
$813$	5.29012	−	5.29012i	0.185532	−	0.185532i
$814$	−8.05603	−	8.05603i	−0.282364	−	0.282364i
$815$		−	13.5960i		−	0.476248i
$816$	−0.134088			−0.00469403
$817$	0.865440	−	0.865440i	0.0302779	−	0.0302779i
$818$		−	9.15651i		−	0.320150i
$819$	−0.478480			−0.0167194
$820$	−6.67517	+	2.28740i	−0.233107	+	0.0798795i
$821$	−22.5579			−0.787276			−0.393638	−	0.919265i	$-0.628784\pi$
$821$	−22.5579			−0.787276			−0.393638	+	0.919265i	$0.628784\pi$
$822$		−	40.2896i		−	1.40526i
$823$	−0.947245	+	0.947245i	−0.0330189	+	0.0330189i	−0.723423	−	0.690405i	$-0.757433\pi$
$823$	−0.947245	+	0.947245i	−0.0330189	+	0.0330189i	0.690405	+	0.723423i	$0.257433\pi$
$824$	8.44607			0.294233
$825$		−	32.4981i		−	1.13144i
$826$	−3.90535	−	3.90535i	−0.135885	−	0.135885i
$827$	29.2128	−	29.2128i	1.01583	−	1.01583i	0.0159564	−	0.999873i	$-0.494921\pi$
$827$	29.2128	−	29.2128i	1.01583	−	1.01583i	0.999873	−	0.0159564i	$-0.00507930\pi$
$828$		−	3.31595i		−	0.115237i
$829$			1.17029i			0.0406458i	0.999793	+	0.0203229i	$0.00646942\pi$
$829$			1.17029i			0.0406458i	−0.999793	+	0.0203229i	$0.993531\pi$
$830$	−3.24261			−0.112553
$831$	−28.8305	+	28.8305i	−1.00012	+	1.00012i
$832$	−0.465387	+	0.465387i	−0.0161344	+	0.0161344i
$833$	−0.0491130	+	0.0491130i	−0.00170166	+	0.00170166i
$834$	−0.905697	−	0.905697i	−0.0313617	−	0.0313617i
$835$	15.8838	+	15.8838i	0.549682	+	0.549682i
$836$	20.4994			0.708985
$837$	−33.4588	−	33.4588i	−1.15650	−	1.15650i
$838$	28.1644			0.972924
$839$	27.2911	+	27.2911i	0.942192	+	0.942192i	0.998418	−	0.0562260i	$-0.0179067\pi$
$839$	27.2911	+	27.2911i	0.942192	+	0.942192i	−0.0562260	+	0.998418i	$0.517907\pi$
$840$		−	2.12745i		−	0.0734040i
$841$			25.1461i			0.867109i
$842$	13.8649	+	13.8649i	0.477815	+	0.477815i
$843$	−29.3420			−1.01059
$844$	5.55224	+	5.55224i	0.191116	+	0.191116i
$845$	13.8486			0.476406
$846$	−5.37879	−	5.37879i	−0.184927	−	0.184927i
$847$	−6.20388	−	6.20388i	−0.213168	−	0.213168i
$848$	7.01374	−	7.01374i	0.240853	−	0.240853i
$849$	−24.0502	+	24.0502i	−0.825400	+	0.825400i
$850$	−0.185922	+	0.185922i	−0.00637708	+	0.00637708i
$851$	−11.6860			−0.400592
$852$		−	15.1302i		−	0.518353i
$853$			5.97671i			0.204639i	0.994752	+	0.102319i	$0.0326264\pi$
$853$			5.97671i			0.204639i	−0.994752	+	0.102319i	$0.967374\pi$
$854$	7.04629	−	7.04629i	0.241119	−	0.241119i
$855$	2.61154	+	2.61154i	0.0893127	+	0.0893127i
$856$			7.92678i			0.270932i
$857$	26.5197			0.905894			0.452947	−	0.891537i	$-0.350373\pi$
$857$	26.5197			0.905894			0.452947	+	0.891537i	$0.350373\pi$
$858$	−3.99519	+	3.99519i	−0.136393	+	0.136393i
$859$		−	1.87534i		−	0.0639857i	−0.999488	−	0.0319929i	$-0.989815\pi$
$859$		−	1.87534i		−	0.0639857i	0.999488	−	0.0319929i	$-0.0101854\pi$
$860$	−0.292573			−0.00997666
$861$	11.6940	−	4.00721i	0.398530	−	0.136565i
$862$	28.0057			0.953878
$863$			32.8556i			1.11842i	0.829027	+	0.559209i	$0.188895\pi$
$863$			32.8556i			1.11842i	−0.829027	+	0.559209i	$0.811105\pi$
$864$	3.10287	−	3.10287i	0.105562	−	0.105562i
$865$	11.6762			0.397004
$866$			16.9797i			0.576994i
$867$	−23.2001	−	23.2001i	−0.787918	−	0.787918i
$868$	7.62484	−	7.62484i	0.258804	−	0.258804i
$869$		−	60.0483i		−	2.03700i
$870$		−	4.17645i		−	0.141595i
$871$	−0.804201			−0.0272493
$872$	−6.68039	+	6.68039i	−0.226227	+	0.226227i
$873$	3.64293	−	3.64293i	0.123295	−	0.123295i
$874$	14.8681	−	14.8681i	0.502921	−	0.502921i
$875$	−6.84599	−	6.84599i	−0.231437	−	0.231437i
$876$	15.3306	+	15.3306i	0.517972	+	0.517972i
$877$	−24.6201			−0.831362			−0.415681	−	0.909510i	$-0.636457\pi$
$877$	−24.6201			−0.831362			−0.415681	+	0.909510i	$0.636457\pi$
$878$	−10.1275	−	10.1275i	−0.341787	−	0.341787i
$879$	−21.6294			−0.729541
$880$	−3.46503	−	3.46503i	−0.116806	−	0.116806i
$881$		−	6.60127i		−	0.222403i	−0.993798	−	0.111201i	$-0.964530\pi$
$881$		−	6.60127i		−	0.222403i	0.993798	−	0.111201i	$-0.0354698\pi$
$882$			0.726999i			0.0244793i
$883$	−33.6965	−	33.6965i	−1.13398	−	1.13398i	−0.989509	−	0.144469i	$-0.953853\pi$
$883$	−33.6965	−	33.6965i	−1.13398	−	1.13398i	−0.144469	−	0.989509i	$-0.546147\pi$
$884$	0.0457131			0.00153750
$885$	−8.30844	−	8.30844i	−0.279285	−	0.279285i
$886$	−15.8026			−0.530900
$887$	−28.4971	−	28.4971i	−0.956838	−	0.956838i	0.0422686	−	0.999106i	$-0.486541\pi$
$887$	−28.4971	−	28.4971i	−0.956838	−	0.956838i	−0.999106	+	0.0422686i	$0.986541\pi$
$888$	3.49750	+	3.49750i	0.117368	+	0.117368i
$889$	−5.68932	+	5.68932i	−0.190814	+	0.190814i
$890$	8.68317	−	8.68317i	0.291061	−	0.291061i
$891$	33.4949	−	33.4949i	1.12212	−	1.12212i
$892$	27.5489			0.922406
$893$		−	48.2351i		−	1.61413i
$894$		−	30.8372i		−	1.03135i
$895$	1.57742	−	1.57742i	0.0527272	−	0.0527272i
$896$	0.707107	+	0.707107i	0.0236228	+	0.0236228i
$897$			5.79539i			0.193502i
$898$	2.78127			0.0928121
$899$	14.9685	−	14.9685i	0.499227	−	0.499227i
$900$			2.75213i			0.0917378i
$901$	−0.688932			−0.0229516
$902$	12.5197	−	25.5730i	0.416859	−	0.851486i
$903$	0.512548			0.0170565
$904$		−	7.89831i		−	0.262694i
$905$	−11.0444	+	11.0444i	−0.367130	+	0.367130i
$906$	−34.9662			−1.16167
$907$			20.0639i			0.666211i	0.942890	+	0.333105i	$0.108096\pi$
$907$			20.0639i			0.666211i	−0.942890	+	0.333105i	$0.891904\pi$
$908$	−6.72572	−	6.72572i	−0.223201	−	0.223201i
$909$	−1.23804	+	1.23804i	−0.0410631	+	0.0410631i
$910$			0.725286i			0.0240430i
$911$		−	21.3589i		−	0.707653i	−0.935311	−	0.353827i	$-0.884880\pi$
$911$		−	21.3589i		−	0.707653i	0.935311	−	0.353827i	$-0.115120\pi$
$912$	−8.89974			−0.294700
$913$	9.25215	−	9.25215i	0.306201	−	0.306201i
$914$	6.16597	−	6.16597i	0.203952	−	0.203952i
$915$	14.9906	−	14.9906i	0.495575	−	0.495575i
$916$	−2.14501	−	2.14501i	−0.0708732	−	0.0708732i
$917$	−5.83527	−	5.83527i	−0.192698	−	0.192698i
$918$	−0.304783			−0.0100593
$919$	−40.5026	−	40.5026i	−1.33606	−	1.33606i	−0.899842	−	0.436216i	$-0.856318\pi$
$919$	−40.5026	−	40.5026i	−1.33606	−	1.33606i	−0.436216	−	0.899842i	$-0.643682\pi$
$920$	−5.02635			−0.165714
$921$	−25.4464	−	25.4464i	−0.838486	−	0.838486i
$922$			1.67237i			0.0550766i
$923$			5.15817i			0.169783i
$924$	6.07026	+	6.07026i	0.199697	+	0.199697i
$925$	9.69904			0.318903
$926$	7.51049	+	7.51049i	0.246810	+	0.246810i
$927$	−6.14029			−0.201673
$928$	1.38814	+	1.38814i	0.0455678	+	0.0455678i
$929$	3.81824	+	3.81824i	0.125272	+	0.125272i	0.766963	−	0.641691i	$-0.221767\pi$
$929$	3.81824	+	3.81824i	0.125272	+	0.125272i	−0.641691	+	0.766963i	$0.721767\pi$
$930$	16.2215	−	16.2215i	0.531923	−	0.531923i
$931$	−3.25974	+	3.25974i	−0.106834	+	0.106834i
$932$	20.0860	−	20.0860i	0.657938	−	0.657938i
$933$	−50.0931			−1.63997
$934$		−	18.5583i		−	0.607246i
$935$			0.340356i			0.0111308i
$936$	0.338336	−	0.338336i	0.0110589	−	0.0110589i
$937$	−19.6676	−	19.6676i	−0.642514	−	0.642514i	0.308659	−	0.951173i	$-0.400120\pi$
$937$	−19.6676	−	19.6676i	−0.642514	−	0.642514i	−0.951173	+	0.308659i	$0.900120\pi$
$938$			1.22190i			0.0398964i
$939$	−21.9302			−0.715666
$940$	−8.15324	+	8.15324i	−0.265929	+	0.265929i
$941$		−	7.05660i		−	0.230039i	−0.993363	−	0.115019i	$-0.963307\pi$
$941$		−	7.05660i		−	0.230039i	0.993363	−	0.115019i	$-0.0366930\pi$
$942$	16.4981			0.537537
$943$	−9.46751	−	27.6284i	−0.308305	−	0.899705i
$944$	5.52300			0.179758
$945$		−	4.83569i		−	0.157305i
$946$	0.834800	−	0.834800i	0.0271417	−	0.0271417i
$947$	−38.0803			−1.23744			−0.618722	−	0.785610i	$-0.712349\pi$
$947$	−38.0803			−1.23744			−0.618722	+	0.785610i	$0.712349\pi$
$948$			26.0698i			0.846707i
$949$	−5.22647	−	5.22647i	−0.169658	−	0.169658i
$950$	−12.3401	+	12.3401i	−0.400365	+	0.400365i
$951$			63.9252i			2.07292i
$952$		−	0.0694562i		−	0.00225109i
$953$	−32.4323			−1.05059			−0.525293	−	0.850922i	$-0.676044\pi$
$953$	−32.4323			−1.05059			−0.525293	+	0.850922i	$0.676044\pi$
$954$	−5.09899	+	5.09899i	−0.165086	+	0.165086i
$955$	9.80647	−	9.80647i	0.317330	−	0.317330i
$956$	−7.18197	+	7.18197i	−0.232281	+	0.232281i
$957$	11.9167	+	11.9167i	0.385211	+	0.385211i
$958$	−8.35146	−	8.35146i	−0.269824	−	0.269824i
$959$	20.8696			0.673913
$960$	1.50433	+	1.50433i	0.0485522	+	0.0485522i
$961$	85.2763			2.75085
$962$	−1.19236	−	1.19236i	−0.0384433	−	0.0384433i
$963$		−	5.76276i		−	0.185702i
$964$			8.32804i			0.268228i
$965$	−1.98565	−	1.98565i	−0.0639204	−	0.0639204i
$966$	8.80548			0.283312
$967$	20.2978	+	20.2978i	0.652733	+	0.652733i	0.953650	−	0.300917i	$-0.0972928\pi$
$967$	20.2978	+	20.2978i	0.652733	+	0.652733i	−0.300917	+	0.953650i	$0.597293\pi$
$968$	8.77361			0.281994
$969$	0.437092	+	0.437092i	0.0140414	+	0.0140414i
$970$	−5.52201	−	5.52201i	−0.177301	−	0.177301i
$971$	−34.2101	+	34.2101i	−1.09785	+	1.09785i	−0.103192	+	0.994662i	$0.532905\pi$
$971$	−34.2101	+	34.2101i	−1.09785	+	1.09785i	−0.994662	+	0.103192i	$0.967095\pi$
$972$	−5.23307	+	5.23307i	−0.167851	+	0.167851i
$973$	0.469141	−	0.469141i	0.0150400	−	0.0150400i
$974$	−19.2797			−0.617763
$975$		−	4.81000i		−	0.154043i
$976$			9.96496i			0.318971i
$977$	−26.4866	+	26.4866i	−0.847381	+	0.847381i	−0.989806	−	0.142425i	$-0.954510\pi$
$977$	−26.4866	+	26.4866i	−0.847381	+	0.847381i	0.142425	+	0.989806i	$0.454510\pi$
$978$	−16.8421	−	16.8421i	−0.538552	−	0.538552i
$979$			49.5515i			1.58367i
$980$	1.10200			0.0352019
$981$	4.85664	−	4.85664i	0.155061	−	0.155061i
$982$		−	33.8815i		−	1.08120i
$983$	54.8251			1.74865			0.874324	−	0.485342i	$-0.161305\pi$
$983$	54.8251			1.74865			0.874324	+	0.485342i	$0.161305\pi$
$984$	−5.43537	+	11.1024i	−0.173273	+	0.353932i
$985$	19.1052			0.608743
$986$		−	0.136351i		−	0.00434230i
$987$	14.2833	−	14.2833i	0.454644	−	0.454644i
$988$	3.03408			0.0965269
$989$		−	1.21095i		−	0.0385061i
$990$	2.51908	+	2.51908i	0.0800616	+	0.0800616i
$991$	31.3036	−	31.3036i	0.994390	−	0.994390i	−0.00559418	−	0.999984i	$-0.501781\pi$
$991$	31.3036	−	31.3036i	0.994390	−	0.994390i	0.999984	+	0.00559418i	$0.00178069\pi$
$992$			10.7831i			0.342365i
$993$		−	62.1522i		−	1.97234i
$994$	7.83729			0.248584
$995$	−0.696529	+	0.696529i	−0.0220814	+	0.0220814i
$996$	−4.01679	+	4.01679i	−0.127277	+	0.127277i
$997$	−15.1624	+	15.1624i	−0.480197	+	0.480197i	−0.905194	−	0.424998i	$-0.860275\pi$
$997$	−15.1624	+	15.1624i	−0.480197	+	0.480197i	0.424998	+	0.905194i	$0.360275\pi$
$998$	23.2836	+	23.2836i	0.737031	+	0.737031i
$999$	7.94982	+	7.94982i	0.251521	+	0.251521i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	574.2.f.a.155.9	✓	20
41.9	even	4	inner	574.2.f.a.337.9	yes	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
574.2.f.a.155.9	✓	20	1.1	even	1	trivial
574.2.f.a.337.9	yes	20	41.9	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:	\( N \)	\(=\)	\( 574 = 2 \cdot 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	574.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(1.36510 - 1.36510i) q^{3} -1.00000 q^{4} -1.10200i q^{5} +(-1.36510 - 1.36510i) q^{6} +(0.707107 - 0.707107i) q^{7} +1.00000i q^{8} -0.726999i q^{9} +O(q^{10})\)	\(q-1.00000i q^{2} +(1.36510 - 1.36510i) q^{3} -1.00000 q^{4} -1.10200i q^{5} +(-1.36510 - 1.36510i) q^{6} +(0.707107 - 0.707107i) q^{7} +1.00000i q^{8} -0.726999i q^{9} -1.10200 q^{10} +(3.14433 - 3.14433i) q^{11} +(-1.36510 + 1.36510i) q^{12} +(0.465387 - 0.465387i) q^{13} +(-0.707107 - 0.707107i) q^{14} +(-1.50433 - 1.50433i) q^{15} +1.00000 q^{16} +(-0.0491130 - 0.0491130i) q^{17} -0.726999 q^{18} +(-3.25974 - 3.25974i) q^{19} +1.10200i q^{20} -1.93054i q^{21} +(-3.14433 - 3.14433i) q^{22} -4.56114 q^{23} +(1.36510 + 1.36510i) q^{24} +3.78561 q^{25} +(-0.465387 - 0.465387i) q^{26} +(3.10287 + 3.10287i) q^{27} +(-0.707107 + 0.707107i) q^{28} +(-1.38814 + 1.38814i) q^{29} +(-1.50433 + 1.50433i) q^{30} -10.7831 q^{31} -1.00000i q^{32} -8.58465i q^{33} +(-0.0491130 + 0.0491130i) q^{34} +(-0.779228 - 0.779228i) q^{35} +0.726999i q^{36} +2.56208 q^{37} +(-3.25974 + 3.25974i) q^{38} -1.27060i q^{39} +1.10200 q^{40} +(2.07569 + 6.05735i) q^{41} -1.93054 q^{42} +0.265494i q^{43} +(-3.14433 + 3.14433i) q^{44} -0.801150 q^{45} +4.56114i q^{46} +(7.39861 + 7.39861i) q^{47} +(1.36510 - 1.36510i) q^{48} -1.00000i q^{49} -3.78561i q^{50} -0.134088 q^{51} +(-0.465387 + 0.465387i) q^{52} +(7.01374 - 7.01374i) q^{53} +(3.10287 - 3.10287i) q^{54} +(-3.46503 - 3.46503i) q^{55} +(0.707107 + 0.707107i) q^{56} -8.89974 q^{57} +(1.38814 + 1.38814i) q^{58} +5.52300 q^{59} +(1.50433 + 1.50433i) q^{60} +9.96496i q^{61} +10.7831i q^{62} +(-0.514066 - 0.514066i) q^{63} -1.00000 q^{64} +(-0.512855 - 0.512855i) q^{65} -8.58465 q^{66} +(-0.864013 - 0.864013i) q^{67} +(0.0491130 + 0.0491130i) q^{68} +(-6.22641 + 6.22641i) q^{69} +(-0.779228 + 0.779228i) q^{70} +(-5.54180 + 5.54180i) q^{71} +0.726999 q^{72} -11.2304i q^{73} -2.56208i q^{74} +(5.16773 - 5.16773i) q^{75} +(3.25974 + 3.25974i) q^{76} -4.44675i q^{77} -1.27060 q^{78} +(9.54867 - 9.54867i) q^{79} -1.10200i q^{80} +10.6525 q^{81} +(6.05735 - 2.07569i) q^{82} +2.94249 q^{83} +1.93054i q^{84} +(-0.0541222 + 0.0541222i) q^{85} +0.265494 q^{86} +3.78989i q^{87} +(3.14433 + 3.14433i) q^{88} +(-7.87950 + 7.87950i) q^{89} +0.801150i q^{90} -0.658157i q^{91} +4.56114 q^{92} +(-14.7201 + 14.7201i) q^{93} +(7.39861 - 7.39861i) q^{94} +(-3.59221 + 3.59221i) q^{95} +(-1.36510 - 1.36510i) q^{96} +(5.01092 + 5.01092i) q^{97} -1.00000 q^{98} +(-2.28592 - 2.28592i) 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

Modular forms

Varieties

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Representations

Groups

Database

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