LMFDB - Embedded newform 425.2.n.e.274.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(49,425)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(425, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 3]))

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

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

chi := DirichletCharacter("425.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.n (of order $8$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$3.39364208590$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{8})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			274.1
Character	$\chi$	$=$	425.274
Dual form			425.2.n.e.349.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.71892 + 1.71892i) q^{2} +(0.281370 + 0.679288i) q^{3} -3.90934i q^{4} +(-1.65129 - 0.683987i) q^{6} +(-0.537508 - 0.222643i) q^{7} +(3.28199 + 3.28199i) q^{8} +(1.73906 - 1.73906i) q^{9} +O(q^{10})$	\(q+(-1.71892 + 1.71892i) q^{2} +(0.281370 + 0.679288i) q^{3} -3.90934i q^{4} +(-1.65129 - 0.683987i) q^{6} +(-0.537508 - 0.222643i) q^{7} +(3.28199 + 3.28199i) q^{8} +(1.73906 - 1.73906i) q^{9} +(-1.34645 - 0.557719i) q^{11} +(2.65557 - 1.09997i) q^{12} +4.36532 q^{13} +(1.30663 - 0.541226i) q^{14} -3.46426 q^{16} +(-1.60415 + 3.79825i) q^{17} +5.97858i q^{18} +(2.93943 + 2.93943i) q^{19} -0.427768i q^{21} +(3.27311 - 1.35577i) q^{22} +(2.68413 - 6.48006i) q^{23} +(-1.30596 + 3.15288i) q^{24} +(-7.50361 + 7.50361i) q^{26} +(3.70851 + 1.53611i) q^{27} +(-0.870387 + 2.10130i) q^{28} +(3.44359 + 8.31356i) q^{29} +(7.14977 - 2.96153i) q^{31} +(-0.609218 + 0.609218i) q^{32} -1.07156i q^{33} +(-3.77147 - 9.28627i) q^{34} +(-6.79857 - 6.79857i) q^{36} +(0.606375 + 1.46392i) q^{37} -10.1053 q^{38} +(1.22827 + 2.96531i) q^{39} +(-1.55209 + 3.74708i) q^{41} +(0.735296 + 0.735296i) q^{42} +(-3.21091 - 3.21091i) q^{43} +(-2.18031 + 5.26375i) q^{44} +(6.52488 + 15.7525i) q^{46} -1.40493 q^{47} +(-0.974740 - 2.35323i) q^{48} +(-4.71040 - 4.71040i) q^{49} +(-3.03147 - 0.0209672i) q^{51} -17.0655i q^{52} +(-7.51728 + 7.51728i) q^{53} +(-9.01506 + 3.73416i) q^{54} +(-1.03338 - 2.49481i) q^{56} +(-1.16965 + 2.82379i) q^{57} +(-20.2095 - 8.37106i) q^{58} +(0.706970 - 0.706970i) q^{59} +(-2.24969 + 5.43124i) q^{61} +(-7.19923 + 17.3805i) q^{62} +(-1.32195 + 0.547568i) q^{63} -9.02291i q^{64} +(1.84191 + 1.84191i) q^{66} +1.24894i q^{67} +(14.8486 + 6.27118i) q^{68} +5.15706 q^{69} +(12.8111 - 5.30655i) q^{71} +11.4152 q^{72} +(8.32740 - 3.44932i) q^{73} +(-3.55866 - 1.47404i) q^{74} +(11.4912 - 11.4912i) q^{76} +(0.599557 + 0.599557i) q^{77} +(-7.20841 - 2.98582i) q^{78} +(6.93467 + 2.87243i) q^{79} -4.42683i q^{81} +(-3.77299 - 9.10882i) q^{82} +(11.1848 - 11.1848i) q^{83} -1.67229 q^{84} +11.0386 q^{86} +(-4.67838 + 4.67838i) q^{87} +(-2.58862 - 6.24949i) q^{88} +7.36714i q^{89} +(-2.34639 - 0.971907i) q^{91} +(-25.3327 - 10.4932i) q^{92} +(4.02347 + 4.02347i) q^{93} +(2.41495 - 2.41495i) q^{94} +(-0.585251 - 0.242419i) q^{96} +(12.0804 - 5.00387i) q^{97} +16.1936 q^{98} +(-3.31147 + 1.37165i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3} - 8 q^{6} - 12 q^{9}+O(q^{10}) $ 24 * q + 4 * q^3 - 8 * q^6 - 12 * q^9	$ 24 q + 4 q^{3} - 8 q^{6} - 12 q^{9} + 4 q^{11} - 20 q^{12} + 16 q^{13} + 24 q^{14} - 24 q^{16} + 20 q^{19} + 12 q^{22} + 8 q^{23} - 16 q^{24} + 16 q^{26} + 16 q^{27} + 20 q^{28} - 4 q^{29} + 24 q^{31} + 60 q^{32} - 16 q^{34} + 60 q^{36} - 16 q^{37} - 48 q^{38} - 8 q^{39} - 20 q^{41} + 12 q^{42} - 32 q^{43} - 64 q^{44} - 40 q^{46} - 88 q^{47} + 4 q^{48} - 24 q^{49} + 16 q^{51} - 12 q^{53} + 20 q^{54} - 32 q^{56} - 56 q^{57} - 28 q^{58} + 16 q^{59} - 64 q^{61} + 16 q^{62} - 40 q^{63} - 72 q^{66} + 48 q^{68} + 48 q^{69} - 24 q^{71} + 120 q^{72} + 20 q^{73} - 32 q^{74} + 52 q^{76} + 24 q^{77} - 100 q^{78} + 48 q^{79} + 8 q^{82} + 12 q^{83} + 40 q^{84} - 16 q^{86} - 24 q^{87} + 80 q^{88} + 24 q^{91} - 56 q^{92} + 32 q^{93} + 40 q^{94} + 132 q^{96} - 24 q^{97} + 48 q^{98} + 80 q^{99}+O(q^{100}) $ 24 * q + 4 * q^3 - 8 * q^6 - 12 * q^9 + 4 * q^11 - 20 * q^12 + 16 * q^13 + 24 * q^14 - 24 * q^16 + 20 * q^19 + 12 * q^22 + 8 * q^23 - 16 * q^24 + 16 * q^26 + 16 * q^27 + 20 * q^28 - 4 * q^29 + 24 * q^31 + 60 * q^32 - 16 * q^34 + 60 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 - 20 * q^41 + 12 * q^42 - 32 * q^43 - 64 * q^44 - 40 * q^46 - 88 * q^47 + 4 * q^48 - 24 * q^49 + 16 * q^51 - 12 * q^53 + 20 * q^54 - 32 * q^56 - 56 * q^57 - 28 * q^58 + 16 * q^59 - 64 * q^61 + 16 * q^62 - 40 * q^63 - 72 * q^66 + 48 * q^68 + 48 * q^69 - 24 * q^71 + 120 * q^72 + 20 * q^73 - 32 * q^74 + 52 * q^76 + 24 * q^77 - 100 * q^78 + 48 * q^79 + 8 * q^82 + 12 * q^83 + 40 * q^84 - 16 * q^86 - 24 * q^87 + 80 * q^88 + 24 * q^91 - 56 * q^92 + 32 * q^93 + 40 * q^94 + 132 * q^96 - 24 * q^97 + 48 * q^98 + 80 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

$n$	$52$	$326$
$\chi(n)$	$-1$	$e\left(\frac{7}{8}\right)$

Coefficient data

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

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

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

$2$	−1.71892	+	1.71892i	−1.21546	+	1.21546i	−0.246251	+	0.969206i	$0.579199\pi$
$2$	−1.71892	+	1.71892i	−1.21546	+	1.21546i	−0.969206	+	0.246251i	$0.920801\pi$
$3$	0.281370	+	0.679288i	0.162449	+	0.392187i	0.984054	−	0.177870i	$-0.0569208\pi$
$3$	0.281370	+	0.679288i	0.162449	+	0.392187i	−0.821605	+	0.570058i	$0.806921\pi$
$4$		−	3.90934i		−	1.95467i
$5$		0			0
$5$		0			0
$6$	−1.65129	−	0.683987i	−0.674137	−	0.279237i
$7$	−0.537508	−	0.222643i	−0.203159	−	0.0841511i	0.278784	−	0.960354i	$-0.410069\pi$
$7$	−0.537508	−	0.222643i	−0.203159	−	0.0841511i	−0.481943	+	0.876203i	$0.660069\pi$
$8$	3.28199	+	3.28199i	1.16036	+	1.16036i
$9$	1.73906	−	1.73906i	0.579686	−	0.579686i
$10$		0			0
$11$	−1.34645	−	0.557719i	−0.405971	−	0.168159i	0.170347	−	0.985384i	$-0.445511\pi$
$11$	−1.34645	−	0.557719i	−0.405971	−	0.168159i	−0.576318	+	0.817225i	$0.695511\pi$
$12$	2.65557	−	1.09997i	0.766597	−	0.317535i
$13$	4.36532			1.21072			0.605360	−	0.795952i	$-0.293029\pi$
$13$	4.36532			1.21072			0.605360	+	0.795952i	$0.293029\pi$
$14$	1.30663	−	0.541226i	0.349213	−	0.144649i
$15$		0			0
$16$	−3.46426			−0.866065
$17$	−1.60415	+	3.79825i	−0.389064	+	0.921211i
$17$	−1.60415	+	3.79825i	−0.389064	+	0.921211i
$18$			5.97858i			1.40917i
$19$	2.93943	+	2.93943i	0.674351	+	0.674351i	0.958716	−	0.284365i	$-0.0917827\pi$
$19$	2.93943	+	2.93943i	0.674351	+	0.674351i	−0.284365	+	0.958716i	$0.591783\pi$
$20$		0			0
$21$		−	0.427768i		−	0.0933466i
$22$	3.27311	−	1.35577i	0.697830	−	0.289051i
$23$	2.68413	−	6.48006i	0.559679	−	1.35119i	−0.350341	−	0.936622i	$-0.613934\pi$
$23$	2.68413	−	6.48006i	0.559679	−	1.35119i	0.910021	−	0.414563i	$-0.136066\pi$
$24$	−1.30596	+	3.15288i	−0.266579	+	0.643578i
$25$		0			0
$26$	−7.50361	+	7.50361i	−1.47158	+	1.47158i
$27$	3.70851	+	1.53611i	0.713702	+	0.295625i
$28$	−0.870387	+	2.10130i	−0.164488	+	0.397108i
$29$	3.44359	+	8.31356i	0.639458	+	1.54379i	0.827403	+	0.561609i	$0.189818\pi$
$29$	3.44359	+	8.31356i	0.639458	+	1.54379i	−0.187944	+	0.982180i	$0.560182\pi$
$30$		0			0
$31$	7.14977	−	2.96153i	1.28414	−	0.531907i	0.366904	−	0.930259i	$-0.380418\pi$
$31$	7.14977	−	2.96153i	1.28414	−	0.531907i	0.917233	+	0.398352i	$0.130418\pi$
$32$	−0.609218	+	0.609218i	−0.107696	+	0.107696i
$33$		−	1.07156i		−	0.186534i
$34$	−3.77147	−	9.28627i	−0.646801	−	1.59258i
$35$		0			0
$36$	−6.79857	−	6.79857i	−1.13309	−	1.13309i
$37$	0.606375	+	1.46392i	0.0996874	+	0.240667i	0.965853	−	0.259090i	$-0.0834227\pi$
$37$	0.606375	+	1.46392i	0.0996874	+	0.240667i	−0.866166	+	0.499757i	$0.833423\pi$
$38$	−10.1053			−1.63929
$39$	1.22827	+	2.96531i	0.196681	+	0.474829i
$40$		0			0
$41$	−1.55209	+	3.74708i	−0.242396	+	0.585195i	−0.997520	−	0.0703870i	$-0.977577\pi$
$41$	−1.55209	+	3.74708i	−0.242396	+	0.585195i	0.755124	+	0.655582i	$0.227577\pi$
$42$	0.735296	+	0.735296i	0.113459	+	0.113459i
$43$	−3.21091	−	3.21091i	−0.489659	−	0.489659i	0.418540	−	0.908199i	$-0.362542\pi$
$43$	−3.21091	−	3.21091i	−0.489659	−	0.489659i	−0.908199	+	0.418540i	$0.862542\pi$
$44$	−2.18031	+	5.26375i	−0.328695	+	0.793540i
$45$		0			0
$46$	6.52488	+	15.7525i	0.962041	+	2.32257i
$47$	−1.40493			−0.204930			−0.102465	−	0.994737i	$-0.532673\pi$
$47$	−1.40493			−0.204930			−0.102465	+	0.994737i	$0.532673\pi$
$48$	−0.974740	−	2.35323i	−0.140692	−	0.339660i
$49$	−4.71040	−	4.71040i	−0.672915	−	0.672915i
$50$		0			0
$51$	−3.03147	−	0.0209672i	−0.424490	−	0.00293599i
$52$		−	17.0655i		−	2.36656i
$53$	−7.51728	+	7.51728i	−1.03258	+	1.03258i	−0.0331263	+	0.999451i	$0.510546\pi$
$53$	−7.51728	+	7.51728i	−1.03258	+	1.03258i	−0.999451	+	0.0331263i	$0.989454\pi$
$54$	−9.01506	+	3.73416i	−1.22679	+	0.508155i
$55$		0			0
$56$	−1.03338	−	2.49481i	−0.138092	−	0.333383i
$57$	−1.16965	+	2.82379i	−0.154924	+	0.374020i
$58$	−20.2095	−	8.37106i	−2.65364	−	1.09917i
$59$	0.706970	−	0.706970i	0.0920396	−	0.0920396i	−0.659588	−	0.751627i	$-0.729269\pi$
$59$	0.706970	−	0.706970i	0.0920396	−	0.0920396i	0.751627	+	0.659588i	$0.229269\pi$
$60$		0			0
$61$	−2.24969	+	5.43124i	−0.288044	+	0.695399i	−0.999977	−	0.00684869i	$-0.997820\pi$
$61$	−2.24969	+	5.43124i	−0.288044	+	0.695399i	0.711933	+	0.702247i	$0.247820\pi$
$62$	−7.19923	+	17.3805i	−0.914303	+	2.20732i
$63$	−1.32195	+	0.547568i	−0.166549	+	0.0689870i
$64$		−	9.02291i		−	1.12786i
$65$		0			0
$66$	1.84191	+	1.84191i	0.226724	+	0.226724i
$67$			1.24894i			0.152582i	0.997086	+	0.0762909i	$0.0243078\pi$
$67$			1.24894i			0.152582i	−0.997086	+	0.0762909i	$0.975692\pi$
$68$	14.8486	+	6.27118i	1.80066	+	0.760492i
$69$	5.15706			0.620837
$70$		0			0
$71$	12.8111	−	5.30655i	1.52040	−	0.629771i	0.542730	−	0.839907i	$-0.317391\pi$
$71$	12.8111	−	5.30655i	1.52040	−	0.629771i	0.977672	+	0.210136i	$0.0673907\pi$
$72$	11.4152			1.34529
$73$	8.32740	−	3.44932i	0.974649	−	0.403713i	0.162208	−	0.986757i	$-0.448138\pi$
$73$	8.32740	−	3.44932i	0.974649	−	0.403713i	0.812441	+	0.583044i	$0.198138\pi$
$74$	−3.55866	−	1.47404i	−0.413686	−	0.171354i
$75$		0			0
$76$	11.4912	−	11.4912i	1.31813	−	1.31813i
$77$	0.599557	+	0.599557i	0.0683258	+	0.0683258i
$78$	−7.20841	−	2.98582i	−0.816191	−	0.338077i
$79$	6.93467	+	2.87243i	0.780211	+	0.323174i	0.737001	−	0.675892i	$-0.236241\pi$
$79$	6.93467	+	2.87243i	0.780211	+	0.323174i	0.0432105	+	0.999066i	$0.486241\pi$
$80$		0			0
$81$		−	4.42683i		−	0.491870i
$82$	−3.77299	−	9.10882i	−0.416658	−	1.00590i
$83$	11.1848	−	11.1848i	1.22769	−	1.22769i	0.262856	−	0.964835i	$-0.415335\pi$
$83$	11.1848	−	11.1848i	1.22769	−	1.22769i	0.964835	−	0.262856i	$-0.0846646\pi$
$84$	−1.67229			−0.182462
$85$		0			0
$86$	11.0386			1.19032
$87$	−4.67838	+	4.67838i	−0.501575	+	0.501575i
$88$	−2.58862	−	6.24949i	−0.275948	−	0.666197i
$89$			7.36714i			0.780916i	0.920621	+	0.390458i	$0.127683\pi$
$89$			7.36714i			0.780916i	−0.920621	+	0.390458i	$0.872317\pi$
$90$		0			0
$91$	−2.34639	−	0.971907i	−0.245968	−	0.101883i
$92$	−25.3327	−	10.4932i	−2.64112	−	1.09399i
$93$	4.02347	+	4.02347i	0.417214	+	0.417214i
$94$	2.41495	−	2.41495i	0.249083	−	0.249083i
$95$		0			0
$96$	−0.585251	−	0.242419i	−0.0597319	−	0.0247418i
$97$	12.0804	−	5.00387i	1.22658	−	0.508066i	0.327084	−	0.944995i	$-0.393934\pi$
$97$	12.0804	−	5.00387i	1.22658	−	0.508066i	0.899496	+	0.436929i	$0.143934\pi$
$98$	16.1936			1.63580
$99$	−3.31147	+	1.37165i	−0.332815	+	0.137856i
$100$		0			0
$101$	−10.3184			−1.02672			−0.513362	−	0.858172i	$-0.671600\pi$
$101$	−10.3184			−1.02672			−0.513362	+	0.858172i	$0.671600\pi$
$102$	5.24688	−	5.17479i	0.519518	−	0.512381i
$103$			12.3309i			1.21500i	0.794319	+	0.607501i	$0.207828\pi$
$103$			12.3309i			1.21500i	−0.794319	+	0.607501i	$0.792172\pi$
$104$	14.3269	+	14.3269i	1.40487	+	1.40487i
$105$		0			0
$106$		−	25.8431i		−	2.51011i
$107$	6.32699	−	2.62073i	0.611653	−	0.253355i	−0.0552820	−	0.998471i	$-0.517606\pi$
$107$	6.32699	−	2.62073i	0.611653	−	0.253355i	0.666935	+	0.745116i	$0.267606\pi$
$108$	6.00519	−	14.4978i	0.577850	−	1.39505i
$109$	−3.44354	+	8.31343i	−0.329831	+	0.796282i	0.668773	+	0.743466i	$0.266820\pi$
$109$	−3.44354	+	8.31343i	−0.329831	+	0.796282i	−0.998604	+	0.0528159i	$0.983180\pi$
$110$		0			0
$111$	−0.823806	+	0.823806i	−0.0781922	+	0.0781922i
$112$	1.86207	+	0.771293i	0.175949	+	0.0728803i
$113$	1.64134	−	3.96255i	0.154404	−	0.372765i	−0.827682	−	0.561198i	$-0.810341\pi$
$113$	1.64134	−	3.96255i	0.154404	−	0.372765i	0.982086	+	0.188433i	$0.0603407\pi$
$114$	−2.84332	−	6.86439i	−0.266301	−	0.642909i
$115$		0			0
$116$	32.5005	−	13.4622i	3.01760	−	1.24993i
$117$	7.59153	−	7.59153i	0.701837	−	0.701837i
$118$			2.43044i			0.223740i
$119$	1.70790	−	1.68443i	0.156563	−	0.154412i
$120$		0			0
$121$	−6.27629	−	6.27629i	−0.570572	−	0.570572i
$122$	−5.46881	−	13.2029i	−0.495123	−	1.19533i
$123$	−2.98206			−0.268883
$124$	−11.5776	−	27.9509i	−1.03970	−	2.51006i
$125$		0			0
$126$	1.33109	−	3.21353i	0.118583	−	0.286284i
$127$	−11.4261	−	11.4261i	−1.01390	−	1.01390i	−0.999902	−	0.0139969i	$-0.995545\pi$
$127$	−11.4261	−	11.4261i	−1.01390	−	1.01390i	−0.0139969	−	0.999902i	$-0.504455\pi$
$128$	14.2912	+	14.2912i	1.26317	+	1.26317i
$129$	1.27768	−	3.08459i	0.112493	−	0.271583i
$130$		0			0
$131$	3.44748	+	8.32295i	0.301208	+	0.727179i	0.999931	+	0.0117870i	$0.00375201\pi$
$131$	3.44748	+	8.32295i	0.301208	+	0.727179i	−0.698723	+	0.715392i	$0.746248\pi$
$132$	−4.18908			−0.364612
$133$	−0.925522	−	2.23441i	−0.0802530	−	0.193748i
$134$	−2.14681	−	2.14681i	−0.185456	−	0.185456i
$135$		0			0
$136$	−17.7307	+	7.20101i	−1.52039	+	0.617482i
$137$		−	5.07497i		−	0.433584i	−0.976218	−	0.216792i	$-0.930441\pi$
$137$		−	5.07497i		−	0.433584i	0.976218	−	0.216792i	$-0.0695594\pi$
$138$	−8.86455	+	8.86455i	−0.754601	+	0.754601i
$139$	−0.893998	+	0.370306i	−0.0758279	+	0.0314089i	−0.420275	−	0.907397i	$-0.638066\pi$
$139$	−0.893998	+	0.370306i	−0.0758279	+	0.0314089i	0.344447	+	0.938806i	$0.388066\pi$
$140$		0			0
$141$	−0.395305	−	0.954351i	−0.0332907	−	0.0803709i
$142$	−12.8998	+	31.1428i	−1.08252	+	2.61344i
$143$	−5.87770	−	2.43462i	−0.491518	−	0.203593i
$144$	−6.02455	+	6.02455i	−0.502046	+	0.502046i
$145$		0			0
$146$	−8.38501	+	20.2432i	−0.693948	+	1.67534i
$147$	1.87435	−	4.52509i	0.154594	−	0.373223i
$148$	5.72295	−	2.37052i	0.470424	−	0.194856i
$149$		−	9.57035i		−	0.784033i	−0.919958	−	0.392017i	$-0.871778\pi$
$149$		−	9.57035i		−	0.784033i	0.919958	−	0.392017i	$-0.128222\pi$
$150$		0			0
$151$	−3.28367	−	3.28367i	−0.267221	−	0.267221i	0.560758	−	0.827979i	$-0.310510\pi$
$151$	−3.28367	−	3.28367i	−0.267221	−	0.267221i	−0.827979	+	0.560758i	$0.810510\pi$
$152$			19.2944i			1.56498i
$153$	3.81566	+	9.39508i	0.308478	+	0.759548i
$154$	−2.06117			−0.166094
$155$		0			0
$156$	11.5924	−	4.80173i	0.928134	−	0.384446i
$157$	2.89768			0.231260			0.115630	−	0.993292i	$-0.463111\pi$
$157$	2.89768			0.231260			0.115630	+	0.993292i	$0.463111\pi$
$158$	−16.8576	+	6.98264i	−1.34112	+	0.555509i
$159$	−7.22154	−	2.99126i	−0.572705	−	0.237222i
$160$		0			0
$161$	−2.88548	+	2.88548i	−0.227407	+	0.227407i
$162$	7.60935	+	7.60935i	0.597847	+	0.597847i
$163$	−4.62958	−	1.91763i	−0.362616	−	0.150201i	0.193934	−	0.981015i	$-0.437875\pi$
$163$	−4.62958	−	1.91763i	−0.362616	−	0.150201i	−0.556550	+	0.830814i	$0.687875\pi$
$164$	14.6486	+	6.06765i	1.14386	+	0.473803i
$165$		0			0
$166$			38.4515i			2.98441i
$167$	2.16295	+	5.22182i	0.167374	+	0.404077i	0.985205	−	0.171383i	$-0.0548234\pi$
$167$	2.16295	+	5.22182i	0.167374	+	0.404077i	−0.817831	+	0.575459i	$0.804823\pi$
$168$	1.40393	−	1.40393i	0.108316	−	0.108316i
$169$	6.05598			0.465844
$170$		0			0
$171$	10.2237			0.781824
$172$	−12.5525	+	12.5525i	−0.957122	+	0.957122i
$173$	−5.11709	−	12.3538i	−0.389045	−	0.939239i	−0.990143	−	0.140063i	$-0.955270\pi$
$173$	−5.11709	−	12.3538i	−0.389045	−	0.939239i	0.601097	−	0.799176i	$-0.294730\pi$
$174$		−	16.0835i		−	1.21928i
$175$		0			0
$176$	4.66447	+	1.93209i	0.351597	+	0.145636i
$177$	0.679156	+	0.281316i	0.0510485	+	0.0211450i
$178$	−12.6635	−	12.6635i	−0.949169	−	0.949169i
$179$	−18.2592	+	18.2592i	−1.36475	+	1.36475i	−0.497007	+	0.867746i	$0.665568\pi$
$179$	−18.2592	+	18.2592i	−1.36475	+	1.36475i	−0.867746	+	0.497007i	$0.834432\pi$
$180$		0			0
$181$	−19.8785	−	8.23395i	−1.47756	−	0.612024i	−0.508989	−	0.860773i	$-0.669981\pi$
$181$	−19.8785	−	8.23395i	−1.47756	−	0.612024i	−0.968568	+	0.248748i	$0.919981\pi$
$182$	5.70387	−	2.36262i	0.422799	−	0.175129i
$183$	−4.32237			−0.319519
$184$	30.0768	−	12.4582i	2.21729	−	0.918432i
$185$		0			0
$186$	−13.8320			−1.01421
$187$	4.27827	−	4.21950i	0.312858	−	0.308560i
$188$			5.49234i			0.400570i
$189$	−1.65134	−	1.65134i	−0.120118	−	0.120118i
$190$		0			0
$191$			0.860224i			0.0622437i	0.999516	+	0.0311218i	$0.00990799\pi$
$191$			0.860224i			0.0622437i	−0.999516	+	0.0311218i	$0.990092\pi$
$192$	6.12916	−	2.53878i	0.442334	−	0.183221i
$193$	−9.11970	+	22.0169i	−0.656450	+	1.58481i	0.146798	+	0.989166i	$0.453103\pi$
$193$	−9.11970	+	22.0169i	−0.656450	+	1.58481i	−0.803248	+	0.595644i	$0.796897\pi$
$194$	−12.1640	+	29.3664i	−0.873322	+	2.10839i
$195$		0			0
$196$	−18.4146	+	18.4146i	−1.31533	+	1.31533i
$197$	1.71416	+	0.710026i	0.122128	+	0.0505873i	0.442911	−	0.896566i	$-0.353946\pi$
$197$	1.71416	+	0.710026i	0.122128	+	0.0505873i	−0.320782	+	0.947153i	$0.603946\pi$
$198$	3.33437	−	8.04989i	0.236964	−	0.572081i
$199$	−0.874896	−	2.11219i	−0.0620198	−	0.149729i	0.889831	−	0.456289i	$-0.150822\pi$
$199$	−0.874896	−	2.11219i	−0.0620198	−	0.149729i	−0.951851	+	0.306560i	$0.900822\pi$
$200$		0			0
$201$	−0.848387	+	0.351413i	−0.0598406	+	0.0247868i
$202$	17.7365	−	17.7365i	1.24794	−	1.24794i
$203$		−	5.23529i		−	0.367445i
$204$	−0.0819679	+	11.8510i	−0.00573890	+	0.829738i
$205$		0			0
$206$	−21.1958	−	21.1958i	−1.47678	−	1.47678i
$207$	−6.60134	−	15.9370i	−0.458825	−	1.10770i
$208$	−15.1226			−1.04856
$209$	−2.31843	−	5.59718i	−0.160369	−	0.387165i
$210$		0			0
$211$	8.18558	−	19.7617i	0.563518	−	1.36045i	−0.343417	−	0.939183i	$-0.611584\pi$
$211$	8.18558	−	19.7617i	0.563518	−	1.36045i	0.906935	−	0.421270i	$-0.138416\pi$
$212$	29.3876	+	29.3876i	2.01835	+	2.01835i
$213$	7.20935	+	7.20935i	0.493976	+	0.493976i
$214$	−6.37076	+	15.3804i	−0.435496	+	1.05138i
$215$		0			0
$216$	7.12978	+	17.2128i	0.485120	+	1.17118i
$217$	−4.50242			−0.305644
$218$	−8.37094	−	20.2092i	−0.566951	−	1.36874i
$219$	4.68617	+	4.68617i	0.316662	+	0.316662i
$220$		0			0
$221$	−7.00263	+	16.5806i	−0.471048	+	1.11533i
$222$		−	2.83211i		−	0.190079i
$223$	−4.76919	+	4.76919i	−0.319368	+	0.319368i	−0.848524	−	0.529156i	$-0.822509\pi$
$223$	−4.76919	+	4.76919i	−0.319368	+	0.319368i	0.529156	+	0.848524i	$0.322509\pi$
$224$	0.463098	−	0.191821i	0.0309420	−	0.0128166i
$225$		0			0
$226$	3.98996	+	9.63261i	0.265408	+	0.640752i
$227$	7.34398	−	17.7299i	0.487437	−	1.17678i	−0.468568	−	0.883427i	$-0.655230\pi$
$227$	7.34398	−	17.7299i	0.487437	−	1.17678i	0.956005	−	0.293350i	$-0.0947701\pi$
$228$	11.0391	+	4.57257i	0.731086	+	0.302826i
$229$	16.9779	−	16.9779i	1.12193	−	1.12193i	0.130480	−	0.991451i	$-0.458348\pi$
$229$	16.9779	−	16.9779i	1.12193	−	1.12193i	0.991451	−	0.130480i	$-0.0416517\pi$
$230$		0			0
$231$	−0.238574	+	0.575969i	−0.0156970	+	0.0378960i
$232$	−15.9832	+	38.5869i	−1.04935	+	2.53335i
$233$	3.26965	−	1.35433i	0.214202	−	0.0887253i	−0.273002	−	0.962013i	$-0.588017\pi$
$233$	3.26965	−	1.35433i	0.214202	−	0.0887253i	0.487204	+	0.873288i	$0.338017\pi$
$234$			26.0984i			1.70611i
$235$		0			0
$236$	−2.76378	−	2.76378i	−0.179907	−	0.179907i
$237$			5.51886i			0.358488i
$238$	−0.0403311	+	5.83113i	−0.00261428	+	0.377976i
$239$	−29.1160			−1.88336			−0.941680	−	0.336509i	$-0.890754\pi$
$239$	−29.1160			−1.88336			−0.941680	+	0.336509i	$0.890754\pi$
$240$		0			0
$241$	−16.5574	+	6.85828i	−1.06655	+	0.441781i	−0.845773	−	0.533543i	$-0.820860\pi$
$241$	−16.5574	+	6.85828i	−1.06655	+	0.441781i	−0.220780	+	0.975324i	$0.570860\pi$
$242$	21.5768			1.38701
$243$	14.1326	−	5.85392i	0.906607	−	0.375529i
$244$	21.2326	+	8.79481i	1.35928	+	0.563030i
$245$		0			0
$246$	5.12590	−	5.12590i	0.326816	−	0.326816i
$247$	12.8315	+	12.8315i	0.816451	+	0.816451i
$248$	33.1852	+	13.7458i	2.10727	+	0.872858i
$249$	10.7448	+	4.45063i	0.680923	+	0.282047i
$250$		0			0
$251$		−	2.37527i		−	0.149926i	−0.997186	−	0.0749630i	$-0.976116\pi$
$251$		−	2.37527i		−	0.149926i	0.997186	−	0.0749630i	$-0.0238839\pi$
$252$	2.14063	+	5.16793i	0.134847	+	0.325549i
$253$	−7.22811	+	7.22811i	−0.454427	+	0.454427i
$254$	39.2809			2.46470
$255$		0			0
$256$	−31.0848			−1.94280
$257$	−7.35458	+	7.35458i	−0.458766	+	0.458766i	−0.898250	−	0.439484i	$-0.855161\pi$
$257$	−7.35458	+	7.35458i	−0.458766	+	0.458766i	0.439484	+	0.898250i	$0.355161\pi$
$258$	3.10592	+	7.49836i	0.193366	+	0.466828i
$259$		−	0.921872i		−	0.0572823i
$260$		0			0
$261$	20.4463	+	8.46915i	1.26560	+	0.524227i
$262$	−20.2324	−	8.38052i	−1.24996	−	0.517750i
$263$	−16.7118	−	16.7118i	−1.03049	−	1.03049i	−0.999520	−	0.0309719i	$-0.990140\pi$
$263$	−16.7118	−	16.7118i	−1.03049	−	1.03049i	−0.0309719	−	0.999520i	$-0.509860\pi$
$264$	3.51684	−	3.51684i	0.216447	−	0.216447i
$265$		0			0
$266$	5.43165	+	2.24986i	0.333036	+	0.137948i
$267$	−5.00441	+	2.07290i	−0.306265	+	0.126859i
$268$	4.88251			0.298247
$269$	−22.3788	+	9.26961i	−1.36446	+	0.565178i	−0.940281	−	0.340399i	$-0.889438\pi$
$269$	−22.3788	+	9.26961i	−1.36446	+	0.565178i	−0.424180	+	0.905578i	$0.639438\pi$
$270$		0			0
$271$	7.98498			0.485053			0.242526	−	0.970145i	$-0.422024\pi$
$271$	7.98498			0.485053			0.242526	+	0.970145i	$0.422024\pi$
$272$	5.55720	−	13.1581i	0.336955	−	0.797828i
$273$		−	1.86734i		−	0.113017i
$274$	8.72345	+	8.72345i	0.527003	+	0.527003i
$275$		0			0
$276$		−	20.1607i		−	1.21353i
$277$	−13.3194	+	5.51708i	−0.800286	+	0.331489i	−0.745071	−	0.666985i	$-0.767585\pi$
$277$	−13.3194	+	5.51708i	−0.800286	+	0.331489i	−0.0552152	+	0.998474i	$0.517585\pi$
$278$	0.900182	−	2.17323i	0.0539893	−	0.130342i
$279$	7.28359	−	17.5841i	0.436057	−	1.05273i
$280$		0			0
$281$	−8.11070	+	8.11070i	−0.483844	+	0.483844i	−0.906357	−	0.422513i	$-0.861148\pi$
$281$	−8.11070	+	8.11070i	−0.483844	+	0.483844i	0.422513	+	0.906357i	$0.361148\pi$
$282$	2.31995	+	0.960953i	0.138151	+	0.0572239i
$283$	−5.28429	+	12.7574i	−0.314119	+	0.758350i	0.685425	+	0.728143i	$0.259616\pi$
$283$	−5.28429	+	12.7574i	−0.314119	+	0.758350i	−0.999544	+	0.0302064i	$0.990384\pi$
$284$	−20.7451	−	50.0831i	−1.23099	−	2.97188i
$285$		0			0
$286$	14.2882	−	5.91835i	0.844877	−	0.349960i
$287$	1.66852	−	1.66852i	0.0984896	−	0.0984896i
$288$			2.11893i			0.124859i
$289$	−11.8534	−	12.1859i	−0.697258	−	0.716820i
$290$		0			0
$291$	6.79814	+	6.79814i	0.398514	+	0.398514i
$292$	−13.4846	−	32.5546i	−0.789125	−	1.90512i
$293$	9.85034			0.575463			0.287731	−	0.957711i	$-0.407099\pi$
$293$	9.85034			0.575463			0.287731	+	0.957711i	$0.407099\pi$
$294$	4.55639	+	11.0001i	0.265734	+	0.641539i
$295$		0			0
$296$	−2.81445	+	6.79469i	−0.163587	+	0.394933i
$297$	−4.13661	−	4.13661i	−0.240031	−	0.240031i
$298$	16.4506	+	16.4506i	0.952959	+	0.952959i
$299$	11.7171	−	28.2875i	0.677615	−	1.63591i
$300$		0			0
$301$	1.01100	+	2.44077i	0.0582732	+	0.140684i
$302$	11.2887			0.649591
$303$	−2.90331	−	7.00920i	−0.166791	−	0.402668i
$304$	−10.1829	−	10.1829i	−0.584032	−	0.584032i
$305$		0			0
$306$	−22.7081	−	9.59056i	−1.29814	−	0.548256i
$307$			7.64510i			0.436329i	0.975912	+	0.218164i	$0.0700069\pi$
$307$			7.64510i			0.436329i	−0.975912	+	0.218164i	$0.929993\pi$
$308$	2.34387	−	2.34387i	0.133554	−	0.133554i
$309$	−8.37625	+	3.46956i	−0.476508	+	0.197376i
$310$		0			0
$311$	−9.84019	−	23.7563i	−0.557986	−	1.34710i	−0.911358	−	0.411614i	$-0.864965\pi$
$311$	−9.84019	−	23.7563i	−0.557986	−	1.34710i	0.353372	−	0.935483i	$-0.385035\pi$
$312$	−5.70095	+	13.7633i	−0.322752	+	0.779193i
$313$	29.0276	+	12.0236i	1.64074	+	0.679616i	0.996372	−	0.0851015i	$-0.0271215\pi$
$313$	29.0276	+	12.0236i	1.64074	+	0.679616i	0.644366	+	0.764717i	$0.277121\pi$
$314$	−4.98087	+	4.98087i	−0.281087	+	0.281087i
$315$		0			0
$316$	11.2293	−	27.1100i	0.631699	−	1.52506i
$317$	−1.17145	+	2.82814i	−0.0657953	+	0.158844i	−0.953357	−	0.301845i	$-0.902398\pi$
$317$	−1.17145	+	2.82814i	−0.0657953	+	0.158844i	0.887562	+	0.460689i	$0.152398\pi$
$318$	17.5549	−	7.27149i	0.984432	−	0.407765i
$319$		−	13.1144i		−	0.734264i
$320$		0			0
$321$	3.56046	+	3.56046i	0.198725	+	0.198725i
$322$		−	9.91978i		−	0.552808i
$323$	−15.8800	+	6.44939i	−0.883586	+	0.358854i
$324$	−17.3060			−0.961444
$325$		0			0
$326$	11.2541	−	4.66160i	0.623307	−	0.258182i
$327$	−6.61612			−0.365873
$328$	−17.3918	+	7.20393i	−0.960303	+	0.397771i
$329$	0.755159	+	0.312797i	0.0416333	+	0.0172451i
$330$		0			0
$331$	3.50849	−	3.50849i	0.192844	−	0.192844i	−0.604080	−	0.796924i	$-0.706459\pi$
$331$	3.50849	−	3.50849i	0.192844	−	0.192844i	0.796924	+	0.604080i	$0.206459\pi$
$332$	−43.7252	−	43.7252i	−2.39973	−	2.39973i
$333$	3.60036	+	1.49132i	0.197298	+	0.0817236i
$334$	−12.6938	−	5.25794i	−0.694573	−	0.287702i
$335$		0			0
$336$			1.48190i			0.0808442i
$337$	5.27926	+	12.7453i	0.287580	+	0.694279i	0.999972	−	0.00750257i	$-0.00238816\pi$
$337$	5.27926	+	12.7453i	0.287580	+	0.694279i	−0.712392	+	0.701782i	$0.752388\pi$
$338$	−10.4097	+	10.4097i	−0.566214	+	0.566214i
$339$	3.15354			0.171277
$340$		0			0
$341$	−11.2785			−0.610767
$342$	−17.5736	+	17.5736i	−0.950273	+	0.950273i
$343$	3.04164	+	7.34317i	0.164233	+	0.396494i
$344$		−	21.0764i		−	1.13636i
$345$		0			0
$346$	30.0309	+	12.4392i	1.61447	+	0.668736i
$347$	−18.7598	−	7.77056i	−1.00708	−	0.417146i	−0.182691	−	0.983170i	$-0.558481\pi$
$347$	−18.7598	−	7.77056i	−1.00708	−	0.417146i	−0.824388	+	0.566025i	$0.808481\pi$
$348$	18.2894	+	18.2894i	0.980413	+	0.980413i
$349$	10.7204	−	10.7204i	0.573849	−	0.573849i	−0.359353	−	0.933202i	$-0.617003\pi$
$349$	10.7204	−	10.7204i	0.573849	−	0.573849i	0.933202	+	0.359353i	$0.117003\pi$
$350$		0			0
$351$	16.1888	+	6.70562i	0.864094	+	0.357919i
$352$	1.16006	−	0.480511i	0.0618312	−	0.0256113i
$353$	−16.1876			−0.861579			−0.430789	−	0.902453i	$-0.641765\pi$
$353$	−16.1876			−0.861579			−0.430789	+	0.902453i	$0.641765\pi$
$354$	−1.65097	+	0.683854i	−0.0877481	+	0.0363465i
$355$		0			0
$356$	28.8007			1.52643
$357$	1.62477	+	0.686205i	0.0859919	+	0.0363178i
$358$		−	62.7719i		−	3.31760i
$359$	−12.5642	−	12.5642i	−0.663111	−	0.663111i	0.293001	−	0.956112i	$-0.405346\pi$
$359$	−12.5642	−	12.5642i	−0.663111	−	0.663111i	−0.956112	+	0.293001i	$0.905346\pi$
$360$		0			0
$361$		−	1.71951i		−	0.0905006i
$362$	48.3229	−	20.0160i	2.53980	−	1.05202i
$363$	2.49745	−	6.02937i	0.131082	−	0.316460i
$364$	−3.79951	+	9.17284i	−0.199149	+	0.480787i
$365$		0			0
$366$	7.42979	−	7.42979i	0.388362	−	0.388362i
$367$	−32.1994	−	13.3374i	−1.68080	−	0.696208i	−0.681432	−	0.731881i	$-0.738643\pi$
$367$	−32.1994	−	13.3374i	−1.68080	−	0.696208i	−0.999364	+	0.0356729i	$0.988643\pi$
$368$	−9.29852	+	22.4486i	−0.484719	+	1.17021i
$369$	3.81721	+	9.21555i	0.198716	+	0.479742i
$370$		0			0
$371$	5.71426	−	2.36692i	0.296670	−	0.122885i
$372$	15.7291	−	15.7291i	0.815516	−	0.815516i
$373$		−	1.40363i		−	0.0726771i	−0.999340	−	0.0363386i	$-0.988431\pi$
$373$		−	1.40363i		−	0.0726771i	0.999340	−	0.0363386i	$-0.0115695\pi$
$374$	−0.101029	+	14.6070i	−0.00522410	+	0.755308i
$375$		0			0
$376$	−4.61097	−	4.61097i	−0.237792	−	0.237792i
$377$	15.0323	+	36.2913i	0.774205	+	1.86910i
$378$	5.67704			0.291996
$379$	13.3140	+	32.1427i	0.683892	+	1.65106i	0.756738	+	0.653718i	$0.226792\pi$
$379$	13.3140	+	32.1427i	0.683892	+	1.65106i	−0.0728466	+	0.997343i	$0.523208\pi$
$380$		0			0
$381$	4.54663	−	10.9765i	0.232931	−	0.562345i
$382$	−1.47865	−	1.47865i	−0.0756545	−	0.0756545i
$383$	−6.31207	−	6.31207i	−0.322531	−	0.322531i	0.527206	−	0.849738i	$-0.323240\pi$
$383$	−6.31207	−	6.31207i	−0.322531	−	0.322531i	−0.849738	+	0.527206i	$0.823240\pi$
$384$	−5.68672	+	13.7289i	−0.290199	+	0.700602i
$385$		0			0
$386$	−22.1692	−	53.5212i	−1.12838	−	2.72416i
$387$	−11.1679			−0.567697
$388$	−19.5618	−	47.2264i	−0.993101	−	2.39756i
$389$	3.80596	+	3.80596i	0.192970	+	0.192970i	0.796978	−	0.604008i	$-0.206431\pi$
$389$	3.80596	+	3.80596i	0.192970	+	0.192970i	−0.604008	+	0.796978i	$0.706431\pi$
$390$		0			0
$391$	20.3071	+	20.5900i	1.02698	+	1.04128i
$392$		−	30.9190i		−	1.56165i
$393$	−4.68366	+	4.68366i	−0.236260	+	0.236260i
$394$	−4.16696	+	1.72601i	−0.209929	+	0.0869553i
$395$		0			0
$396$	5.36226	+	12.9456i	0.269464	+	0.650543i
$397$	−9.26583	+	22.3697i	−0.465039	+	1.12270i	0.501264	+	0.865295i	$0.332869\pi$
$397$	−9.26583	+	22.3697i	−0.465039	+	1.12270i	−0.966303	+	0.257409i	$0.917131\pi$
$398$	5.13454	+	2.12680i	0.257371	+	0.106607i
$399$	1.25739	−	1.25739i	0.0629484	−	0.0629484i
$400$		0			0
$401$	3.82490	−	9.23412i	0.191006	−	0.461130i	−0.799144	−	0.601140i	$-0.794713\pi$
$401$	3.82490	−	9.23412i	0.191006	−	0.461130i	0.990150	+	0.140010i	$0.0447135\pi$
$402$	0.854256	−	2.06236i	0.0426064	−	0.102861i
$403$	31.2110	−	12.9280i	1.55473	−	0.643991i
$404$			40.3383i			2.00691i
$405$		0			0
$406$	8.99902	+	8.99902i	0.446614	+	0.446614i
$407$		−	2.30928i		−	0.114467i
$408$	−9.88044	−	10.0181i	−0.489155	−	0.495968i
$409$	17.4563			0.863158			0.431579	−	0.902075i	$-0.357957\pi$
$409$	17.4563			0.863158			0.431579	+	0.902075i	$0.357957\pi$
$410$		0			0
$411$	3.44737	−	1.42795i	0.170046	−	0.0704355i
$412$	48.2058			2.37493
$413$	−0.537403	+	0.222600i	−0.0264439	+	0.0109534i
$414$	38.7416	+	16.0473i	1.90404	+	0.788681i
$415$		0			0
$416$	−2.65943	+	2.65943i	−0.130389	+	0.130389i
$417$	−0.503089	−	0.503089i	−0.0246364	−	0.0246364i
$418$	13.6063	+	5.63590i	0.665504	+	0.275661i
$419$	23.0525	+	9.54866i	1.12619	+	0.466483i	0.866484	−	0.499205i	$-0.166375\pi$
$419$	23.0525	+	9.54866i	1.12619	+	0.466483i	0.259705	+	0.965688i	$0.416375\pi$
$420$		0			0
$421$			18.9333i			0.922750i	0.887205	+	0.461375i	$0.152644\pi$
$421$			18.9333i			0.922750i	−0.887205	+	0.461375i	$0.847356\pi$
$422$	19.8984	+	48.0391i	0.968640	+	2.33850i
$423$	−2.44325	+	2.44325i	−0.118795	+	0.118795i
$424$	−49.3433			−2.39632
$425$		0			0
$426$	−24.7845			−1.20081
$427$	2.41845	−	2.41845i	0.117037	−	0.117037i
$428$	−10.2453	−	24.7344i	−0.495226	−	1.19558i
$429$		−	4.67768i		−	0.225841i
$430$		0			0
$431$	−0.261041	−	0.108127i	−0.0125739	−	0.00520828i	0.376388	−	0.926462i	$-0.377166\pi$
$431$	−0.261041	−	0.108127i	−0.0125739	−	0.00520828i	−0.388962	+	0.921254i	$0.627166\pi$
$432$	−12.8472	−	5.32150i	−0.618112	−	0.256031i
$433$	−18.5844	−	18.5844i	−0.893109	−	0.893109i	0.101706	−	0.994815i	$-0.467570\pi$
$433$	−18.5844	−	18.5844i	−0.893109	−	0.893109i	−0.994815	+	0.101706i	$0.967570\pi$
$434$	7.73928	−	7.73928i	0.371497	−	0.371497i
$435$		0			0
$436$	32.5000	+	13.4620i	1.55647	+	0.644711i
$437$	26.9375	−	11.1579i	1.28859	−	0.533753i
$438$	−16.1103			−0.769778
$439$	−24.5435	+	10.1662i	−1.17140	+	0.485208i	−0.881654	−	0.471896i	$-0.843570\pi$
$439$	−24.5435	+	10.1662i	−1.17140	+	0.485208i	−0.289743	+	0.957105i	$0.593570\pi$
$440$		0			0
$441$	−16.3833			−0.780158
$442$	−16.4636	−	40.5375i	−0.783095	−	1.92817i
$443$		−	12.5642i		−	0.596943i	−0.954419	−	0.298471i	$-0.903523\pi$
$443$		−	12.5642i		−	0.596943i	0.954419	−	0.298471i	$-0.0964767\pi$
$444$	3.22054	+	3.22054i	0.152840	+	0.152840i
$445$		0			0
$446$		−	16.3957i		−	0.776357i
$447$	6.50102	−	2.69281i	0.307488	−	0.127366i
$448$	−2.00889	+	4.84988i	−0.0949110	+	0.229135i
$449$	7.09318	−	17.1244i	0.334748	−	0.808153i	−0.663454	−	0.748217i	$-0.730910\pi$
$449$	7.09318	−	17.1244i	0.334748	−	0.808153i	0.998202	−	0.0599359i	$-0.0190896\pi$
$450$		0			0
$451$	4.17963	−	4.17963i	0.196811	−	0.196811i
$452$	−15.4909	−	6.41656i	−0.728633	−	0.301810i
$453$	1.30663	−	3.15448i	0.0613908	−	0.148211i
$454$	17.8526	+	43.0999i	0.837863	+	2.02278i
$455$		0			0
$456$	−13.1064	+	5.42887i	−0.613766	+	0.254230i
$457$	−13.9029	+	13.9029i	−0.650351	+	0.650351i	−0.953077	−	0.302726i	$-0.902103\pi$
$457$	−13.9029	+	13.9029i	−0.650351	+	0.650351i	0.302726	+	0.953077i	$0.402103\pi$
$458$			58.3671i			2.72732i
$459$	−11.7835	+	11.6217i	−0.550009	+	0.542453i
$460$		0			0
$461$	14.0208	+	14.0208i	0.653012	+	0.653012i	0.953717	−	0.300705i	$-0.0972220\pi$
$461$	14.0208	+	14.0208i	0.653012	+	0.653012i	−0.300705	+	0.953717i	$0.597222\pi$
$462$	−0.579954	−	1.40013i	−0.0269819	−	0.0651400i
$463$	−22.7218			−1.05597			−0.527985	−	0.849253i	$-0.677052\pi$
$463$	−22.7218			−1.05597			−0.527985	+	0.849253i	$0.677052\pi$
$464$	−11.9295	−	28.8003i	−0.553812	−	1.33702i
$465$		0			0
$466$	−3.29227	+	7.94823i	−0.152511	+	0.368195i
$467$	2.47172	+	2.47172i	0.114377	+	0.114377i	0.761979	−	0.647602i	$-0.224228\pi$
$467$	2.47172	+	2.47172i	0.114377	+	0.114377i	−0.647602	+	0.761979i	$0.724228\pi$
$468$	−29.6779	−	29.6779i	−1.37186	−	1.37186i
$469$	0.278067	−	0.671312i	0.0128399	−	0.0309983i
$470$		0			0
$471$	0.815322	+	1.96836i	0.0375680	+	0.0906973i
$472$	4.64054			0.213598
$473$	2.53255	+	6.11413i	0.116447	+	0.281128i
$474$	−9.48645	−	9.48645i	−0.435727	−	0.435727i
$475$		0			0
$476$	−6.58503	−	6.67675i	−0.301824	−	0.306028i
$477$			26.1459i			1.19714i
$478$	50.0480	−	50.0480i	2.28914	−	2.28914i
$479$	−5.66030	+	2.34457i	−0.258626	+	0.107126i	−0.508229	−	0.861222i	$-0.669700\pi$
$479$	−5.66030	+	2.34457i	−0.258626	+	0.107126i	0.249603	+	0.968348i	$0.419700\pi$
$480$		0			0
$481$	2.64702	+	6.39046i	0.120694	+	0.291380i
$482$	16.6719	−	40.2495i	0.759384	−	1.83331i
$483$	−2.77196	−	1.14818i	−0.126128	−	0.0522441i
$484$	−24.5361	+	24.5361i	−1.11528	+	1.11528i
$485$		0			0
$486$	−14.2304	+	34.3552i	−0.645503	+	1.55838i
$487$	2.74668	−	6.63108i	0.124464	−	0.300483i	−0.849350	−	0.527831i	$-0.823006\pi$
$487$	2.74668	−	6.63108i	0.124464	−	0.300483i	0.973814	+	0.227348i	$0.0730055\pi$
$488$	−25.2088	+	10.4418i	−1.14115	+	0.472679i
$489$		−	3.68438i		−	0.166614i
$490$		0			0
$491$	1.84574	+	1.84574i	0.0832970	+	0.0832970i	0.747528	−	0.664231i	$-0.231241\pi$
$491$	1.84574	+	1.84574i	0.0832970	+	0.0832970i	−0.664231	+	0.747528i	$0.731241\pi$
$492$			11.6579i			0.525577i
$493$	−37.1010	−	0.256610i	−1.67095	−	0.0115571i
$494$	−44.1126			−1.98472
$495$		0			0
$496$	−24.7687	+	10.2595i	−1.11215	+	0.460666i
$497$	−8.06755			−0.361879
$498$	−26.1196	+	10.8191i	−1.17045	+	0.484816i
$499$	11.1511	+	4.61895i	0.499193	+	0.206773i	0.618050	−	0.786139i	$-0.287923\pi$
$499$	11.1511	+	4.61895i	0.499193	+	0.206773i	−0.118857	+	0.992911i	$0.537923\pi$
$500$		0			0
$501$	−2.93853	+	2.93853i	−0.131284	+	0.131284i
$502$	4.08289	+	4.08289i	0.182229	+	0.182229i
$503$	−2.82632	−	1.17070i	−0.126019	−	0.0521989i	0.318783	−	0.947828i	$-0.396726\pi$
$503$	−2.82632	−	1.17070i	−0.126019	−	0.0521989i	−0.444802	+	0.895629i	$0.646726\pi$
$504$	−6.13573	−	2.54150i	−0.273307	−	0.113208i
$505$		0			0
$506$		−	24.8490i		−	1.10467i
$507$	1.70397	+	4.11376i	0.0756761	+	0.182698i
$508$	−44.6684	+	44.6684i	−1.98184	+	1.98184i
$509$	−11.2636			−0.499252			−0.249626	−	0.968342i	$-0.580308\pi$
$509$	−11.2636			−0.499252			−0.249626	+	0.968342i	$0.580308\pi$
$510$		0			0
$511$	−5.24401			−0.231981
$512$	24.8499	−	24.8499i	1.09822	−	1.09822i
$513$	6.38559	+	15.4162i	0.281931	+	0.680641i
$514$		−	25.2838i		−	1.11522i
$515$		0			0
$516$	−12.0587	−	4.99488i	−0.530855	−	0.219887i
$517$	1.89167	+	0.783556i	0.0831956	+	0.0344607i
$518$	1.58462	+	1.58462i	0.0696242	+	0.0696242i
$519$	6.95196	−	6.95196i	0.305157	−	0.305157i
$520$		0			0
$521$	19.3137	+	7.99998i	0.846146	+	0.350485i	0.763274	−	0.646075i	$-0.223591\pi$
$521$	19.3137	+	7.99998i	0.846146	+	0.350485i	0.0828724	+	0.996560i	$0.473591\pi$
$522$	−49.7033	+	20.5878i	−2.17545	+	0.901103i
$523$	7.12885			0.311723			0.155861	−	0.987779i	$-0.450185\pi$
$523$	7.12885			0.311723			0.155861	+	0.987779i	$0.450185\pi$
$524$	32.5372	−	13.4774i	1.42140	−	0.588761i
$525$		0			0
$526$	57.4523			2.50504
$527$	−0.220688	+	31.9074i	−0.00961331	+	1.38991i
$528$			3.71215i			0.161551i
$529$	−18.5231	−	18.5231i	−0.805354	−	0.805354i
$530$		0			0
$531$		−	2.45892i		−	0.106708i
$532$	−8.73506	+	3.61818i	−0.378713	+	0.156868i
$533$	−6.77536	+	16.3572i	−0.293473	+	0.708507i
$534$	5.03903	−	12.1653i	0.218060	−	0.526444i
$535$		0			0
$536$	−4.09900	+	4.09900i	−0.177050	+	0.177050i
$537$	−17.5408	−	7.26565i	−0.756942	−	0.313536i
$538$	22.5336	−	54.4010i	0.971494	−	2.34539i
$539$	3.71526	+	8.96942i	0.160027	+	0.386340i
$540$		0			0
$541$	−8.26139	+	3.42198i	−0.355185	+	0.147122i	−0.553139	−	0.833089i	$-0.686570\pi$
$541$	−8.26139	+	3.42198i	−0.355185	+	0.147122i	0.197954	+	0.980211i	$0.436570\pi$
$542$	−13.7255	+	13.7255i	−0.589561	+	0.589561i
$543$		−	15.8200i		−	0.678902i
$544$	−1.33668	−	3.29124i	−0.0573098	−	0.141111i
$545$		0			0
$546$	3.20980	+	3.20980i	0.137367	+	0.137367i
$547$	4.45519	+	10.7558i	0.190490	+	0.459884i	0.990052	−	0.140699i	$-0.0449351\pi$
$547$	4.45519	+	10.7558i	0.190490	+	0.459884i	−0.799562	+	0.600583i	$0.794935\pi$
$548$	−19.8398			−0.847514
$549$	5.53289	+	13.3576i	0.236138	+	0.570087i
$550$		0			0
$551$	−14.3149	+	34.5593i	−0.609837	+	1.47228i
$552$	16.9254	+	16.9254i	0.720395	+	0.720395i
$553$	−3.08791	−	3.08791i	−0.131311	−	0.131311i
$554$	13.4116	−	32.3784i	0.569802	−	1.37562i
$555$		0			0
$556$	1.44765	+	3.49494i	0.0613941	+	0.148218i
$557$	6.24826			0.264747			0.132374	−	0.991200i	$-0.457740\pi$
$557$	6.24826			0.264747			0.132374	+	0.991200i	$0.457740\pi$
$558$	17.7058	+	42.7455i	0.749545	+	1.80956i
$559$	−14.0166	−	14.0166i	−0.592840	−	0.592840i
$560$		0			0
$561$	4.07004	+	1.71894i	0.171837	+	0.0725737i
$562$		−	27.8832i		−	1.17618i
$563$	−1.86751	+	1.86751i	−0.0787061	+	0.0787061i	−0.745364	−	0.666658i	$-0.767724\pi$
$563$	−1.86751	+	1.86751i	−0.0787061	+	0.0787061i	0.666658	+	0.745364i	$0.267724\pi$
$564$	−3.73088	+	1.54538i	−0.157099	+	0.0650723i
$565$		0			0
$566$	−12.8457	−	31.0122i	−0.539943	−	1.30354i
$567$	−0.985603	+	2.37946i	−0.0413914	+	0.0999278i
$568$	59.4621	+	24.6300i	2.49498	+	1.03345i
$569$	26.6868	−	26.6868i	1.11877	−	1.11877i	0.126848	−	0.991922i	$-0.459514\pi$
$569$	26.6868	−	26.6868i	1.11877	−	1.11877i	0.991922	−	0.126848i	$-0.0404862\pi$
$570$		0			0
$571$	13.1716	−	31.7991i	0.551215	−	1.33075i	−0.365351	−	0.930870i	$-0.619051\pi$
$571$	13.1716	−	31.7991i	0.551215	−	1.33075i	0.916567	−	0.399882i	$-0.130949\pi$
$572$	−9.51776	+	22.9779i	−0.397958	+	0.960755i
$573$	−0.584340	+	0.242042i	−0.0244112	+	0.0101114i
$574$			5.73609i			0.239420i
$575$		0			0
$576$	−15.6914	−	15.6914i	−0.653806	−	0.653806i
$577$			1.57974i			0.0657654i	0.999459	+	0.0328827i	$0.0104688\pi$
$577$			1.57974i			0.0657654i	−0.999459	+	0.0328827i	$0.989531\pi$
$578$	41.3216	+	0.571630i	1.71875	+	0.0237767i
$579$	−17.5218			−0.728183
$580$		0			0
$581$	−8.50213	+	3.52170i	−0.352728	+	0.146105i
$582$	−23.3709			−0.968753
$583$	14.3142	−	5.92913i	0.592834	−	0.245560i
$584$	38.6511	+	16.0098i	1.59940	+	0.662491i
$585$		0			0
$586$	−16.9319	+	16.9319i	−0.699450	+	0.699450i
$587$	−24.7661	−	24.7661i	−1.02221	−	1.02221i	−0.999748	−	0.0224603i	$-0.992850\pi$
$587$	−24.7661	−	24.7661i	−1.02221	−	1.02221i	−0.0224603	−	0.999748i	$-0.507150\pi$
$588$	−17.6901	−	7.32749i	−0.729528	−	0.302180i
$589$	29.7215	+	12.3110i	1.22465	+	0.507267i
$590$		0			0
$591$			1.36419i			0.0561151i
$592$	−2.10064	−	5.07139i	−0.0863357	−	0.208433i
$593$	24.1126	−	24.1126i	0.990184	−	0.990184i	−0.00976794	−	0.999952i	$-0.503109\pi$
$593$	24.1126	−	24.1126i	0.990184	−	0.990184i	0.999952	+	0.00976794i	$0.00310928\pi$
$594$	14.2210			0.583493
$595$		0			0
$596$	−37.4137			−1.53253
$597$	1.18861	−	1.18861i	0.0486467	−	0.0486467i
$598$	28.4832	+	68.7644i	1.16476	+	2.81199i
$599$			5.92805i			0.242213i	0.992639	+	0.121107i	$0.0386443\pi$
$599$			5.92805i			0.242213i	−0.992639	+	0.121107i	$0.961356\pi$
$600$		0			0
$601$	−13.8906	−	5.75367i	−0.566609	−	0.234697i	0.0809424	−	0.996719i	$-0.474207\pi$
$601$	−13.8906	−	5.75367i	−0.566609	−	0.234697i	−0.647552	+	0.762022i	$0.724207\pi$
$602$	−5.93331	−	2.45766i	−0.241824	−	0.100167i
$603$	2.17197	+	2.17197i	0.0884494	+	0.0884494i
$604$	−12.8370	+	12.8370i	−0.522329	+	0.522329i
$605$		0			0
$606$	17.0388	+	7.05769i	0.692152	+	0.286699i
$607$	−11.7701	+	4.87535i	−0.477735	+	0.197884i	−0.608539	−	0.793524i	$-0.708244\pi$
$607$	−11.7701	+	4.87535i	−0.477735	+	0.197884i	0.130804	+	0.991408i	$0.458244\pi$
$608$	−3.58151			−0.145249
$609$	3.55627	−	1.47306i	0.144107	−	0.0596912i
$610$		0			0
$611$	−6.13295			−0.248113
$612$	36.7286	−	14.9167i	1.48466	−	0.602972i
$613$			23.8212i			0.962129i	0.876685	+	0.481064i	$0.159750\pi$
$613$			23.8212i			0.962129i	−0.876685	+	0.481064i	$0.840250\pi$
$614$	−13.1413	−	13.1413i	−0.530339	−	0.530339i
$615$		0			0
$616$			3.93548i			0.158565i
$617$	26.5455	−	10.9955i	1.06868	−	0.442663i	0.222157	−	0.975011i	$-0.428690\pi$
$617$	26.5455	−	10.9955i	1.06868	−	0.442663i	0.846526	+	0.532348i	$0.178690\pi$
$618$	8.43419	−	20.3619i	0.339273	−	0.819077i
$619$	−6.91812	+	16.7018i	−0.278063	+	0.671303i	−0.999782	−	0.0208833i	$-0.993352\pi$
$619$	−6.91812	+	16.7018i	−0.278063	+	0.671303i	0.721719	+	0.692186i	$0.243352\pi$
$620$		0			0
$621$	19.9082	−	19.9082i	0.798889	−	0.798889i
$622$	57.7496	+	23.9207i	2.31555	+	0.959131i
$623$	1.64024	−	3.95990i	0.0657149	−	0.158650i
$624$	−4.25505	−	10.2726i	−0.170338	−	0.411233i
$625$		0			0
$626$	−70.5636	+	29.2284i	−2.82029	+	1.16820i
$627$	3.14976	−	3.14976i	0.125789	−	0.125789i
$628$		−	11.3280i		−	0.452037i
$629$	−6.53304	−	0.0451859i	−0.260489	−	0.00180168i
$630$		0			0
$631$	15.7534	+	15.7534i	0.627132	+	0.627132i	0.947345	−	0.320214i	$-0.103755\pi$
$631$	15.7534	+	15.7534i	0.627132	+	0.627132i	−0.320214	+	0.947345i	$0.603755\pi$
$632$	13.3322	+	32.1869i	0.530328	+	1.28032i
$633$	15.7271			0.625096
$634$	−2.84770	−	6.87496i	−0.113097	−	0.273039i
$635$		0			0
$636$	−11.6938	+	28.2314i	−0.463691	+	1.11945i
$637$	−20.5624	−	20.5624i	−0.814712	−	0.814712i
$638$	22.5425	+	22.5425i	0.892466	+	0.892466i
$639$	13.0509	−	31.5077i	0.516286	−	1.24642i
$640$		0			0
$641$	−14.4463	−	34.8765i	−0.570596	−	1.37754i	−0.901049	−	0.433718i	$-0.857201\pi$
$641$	−14.4463	−	34.8765i	−0.570596	−	1.37754i	0.330453	−	0.943823i	$-0.392799\pi$
$642$	−12.2402			−0.483084
$643$	17.2486	+	41.6419i	0.680219	+	1.64219i	0.763610	+	0.645677i	$0.223425\pi$
$643$	17.2486	+	41.6419i	0.680219	+	1.64219i	−0.0833911	+	0.996517i	$0.526575\pi$
$644$	11.2803	+	11.2803i	0.444507	+	0.444507i
$645$		0			0
$646$	16.2104	−	38.3823i	0.637789	−	1.51013i
$647$		−	0.426429i		−	0.0167647i	−0.999965	−	0.00838233i	$-0.997332\pi$
$647$		−	0.426429i		−	0.0167647i	0.999965	−	0.00838233i	$-0.00266821\pi$
$648$	14.5288	−	14.5288i	0.570747	−	0.570747i
$649$	−1.34619	+	0.557611i	−0.0528427	+	0.0218882i
$650$		0			0
$651$	−1.26685	−	3.05844i	−0.0496517	−	0.119870i
$652$	−7.49668	+	18.0986i	−0.293593	+	0.708795i
$653$	12.1450	+	5.03061i	0.475269	+	0.196863i	0.607442	−	0.794364i	$-0.292196\pi$
$653$	12.1450	+	5.03061i	0.475269	+	0.196863i	−0.132173	+	0.991227i	$0.542196\pi$
$654$	11.3726	−	11.3726i	0.444702	−	0.444702i
$655$		0			0
$656$	5.37684	−	12.9808i	0.209930	−	0.506817i
$657$	8.48326	−	20.4804i	0.330963	−	0.799016i
$658$	−1.83573	+	0.760383i	−0.0715641	+	0.0296428i
$659$			16.3369i			0.636395i	0.948025	+	0.318197i	$0.103077\pi$
$659$			16.3369i			0.636395i	−0.948025	+	0.318197i	$0.896923\pi$
$660$		0			0
$661$	−6.68312	−	6.68312i	−0.259943	−	0.259943i	0.565088	−	0.825031i	$-0.308842\pi$
$661$	−6.68312	−	6.68312i	−0.259943	−	0.259943i	−0.825031	+	0.565088i	$0.808842\pi$
$662$			12.0616i			0.468788i
$663$	−13.2333	−	0.0915284i	−0.513939	−	0.00355467i
$664$	73.4169			2.84913
$665$		0			0
$666$	−8.75216	+	3.62526i	−0.339139	+	0.140476i
$667$	63.1154			2.44384
$668$	20.4139	−	8.45570i	0.789836	−	0.327161i
$669$	−4.58156	−	1.89774i	−0.177133	−	0.0733710i
$670$		0			0
$671$	6.05821	−	6.05821i	0.233875	−	0.233875i
$672$	0.260604	+	0.260604i	0.0100530	+	0.0100530i
$673$	25.4833	+	10.5555i	0.982311	+	0.406886i	0.815281	−	0.579066i	$-0.196582\pi$
$673$	25.4833	+	10.5555i	0.982311	+	0.406886i	0.167030	+	0.985952i	$0.446582\pi$
$674$	−30.9827	−	12.8334i	−1.19341	−	0.494325i
$675$		0			0
$676$		−	23.6749i		−	0.910572i
$677$	0.683020	+	1.64896i	0.0262506	+	0.0633745i	0.936461	−	0.350771i	$-0.114080\pi$
$677$	0.683020	+	1.64896i	0.0262506	+	0.0633745i	−0.910211	+	0.414146i	$0.864080\pi$
$678$	−5.42066	+	5.42066i	−0.208179	+	0.208179i
$679$	−7.60739			−0.291945
$680$		0			0
$681$	14.1101			0.540701
$682$	19.3869	−	19.3869i	0.742361	−	0.742361i
$683$	−3.08452	−	7.44669i	−0.118026	−	0.284940i	0.853815	−	0.520576i	$-0.174283\pi$
$683$	−3.08452	−	7.44669i	−0.118026	−	0.284940i	−0.971841	+	0.235636i	$0.924283\pi$
$684$		−	39.9678i		−	1.52821i
$685$		0			0
$686$	−17.8506	−	7.39396i	−0.681539	−	0.282303i
$687$	16.3100	+	6.75581i	0.622264	+	0.257750i
$688$	11.1234	+	11.1234i	0.424076	+	0.424076i
$689$	−32.8153	+	32.8153i	−1.25016	+	1.25016i
$690$		0			0
$691$	−44.7175	−	18.5226i	−1.70113	−	0.704632i	−0.701167	−	0.712997i	$-0.747337\pi$
$691$	−44.7175	−	18.5226i	−1.70113	−	0.704632i	−0.999965	+	0.00836486i	$0.997337\pi$
$692$	−48.2950	+	20.0045i	−1.83590	+	0.760456i
$693$	2.08533			0.0792150
$694$	45.6035	−	18.8896i	1.73108	−	0.717038i
$695$		0			0
$696$	−30.7088			−1.16401
$697$	−11.7425	−	11.9061i	−0.444780	−	0.450976i
$698$			36.8548i			1.39498i
$699$	1.83996	+	1.83996i	0.0695939	+	0.0695939i
$700$		0			0
$701$			26.0994i			0.985761i	0.870097	+	0.492880i	$0.164056\pi$
$701$			26.0994i			0.985761i	−0.870097	+	0.492880i	$0.835944\pi$
$702$	−39.3536	+	16.3008i	−1.48530	+	0.615233i
$703$	−2.52069	+	6.08548i	−0.0950695	+	0.229518i
$704$	−5.03225	+	12.1489i	−0.189660	+	0.457880i
$705$		0			0
$706$	27.8251	−	27.8251i	1.04721	−	1.04721i
$707$	5.54624	+	2.29733i	0.208588	+	0.0864000i
$708$	1.09976	−	2.65505i	0.0413315	−	0.0997830i
$709$	16.9696	+	40.9683i	0.637307	+	1.53860i	0.830253	+	0.557386i	$0.188196\pi$
$709$	16.9696	+	40.9683i	0.637307	+	1.53860i	−0.192946	+	0.981209i	$0.561804\pi$
$710$		0			0
$711$	17.0551	−	7.06446i	0.639617	−	0.264938i
$712$	−24.1789	+	24.1789i	−0.906143	+	0.906143i
$713$		−	54.2801i		−	2.03280i
$714$	−3.97237	+	1.61331i	−0.148662	+	0.0603767i
$715$		0			0
$716$	71.3813	+	71.3813i	2.66764	+	2.66764i
$717$	−8.19239	−	19.7782i	−0.305951	−	0.738630i
$718$	43.1935			1.61197
$719$	−10.6254	−	25.6519i	−0.396259	−	0.956653i	−0.988545	−	0.150926i	$-0.951775\pi$
$719$	−10.6254	−	25.6519i	−0.396259	−	0.956653i	0.592286	−	0.805728i	$-0.298225\pi$
$720$		0			0
$721$	2.74539	−	6.62796i	0.102244	−	0.246838i
$722$	2.95569	+	2.95569i	0.110000	+	0.110000i
$723$	−9.31750	−	9.31750i	−0.346522	−	0.346522i
$724$	−32.1893	+	77.7118i	−1.19631	+	2.88814i
$725$		0			0
$726$	6.07108	+	14.6569i	0.225319	+	0.543968i
$727$	−38.4267			−1.42517			−0.712584	−	0.701586i	$-0.752475\pi$
$727$	−38.4267			−1.42517			−0.712584	+	0.701586i	$0.752475\pi$
$728$	−4.51105	−	10.8906i	−0.167191	−	0.403634i
$729$	−1.43773	−	1.43773i	−0.0532494	−	0.0532494i
$730$		0			0
$731$	17.3466	−	7.04504i	0.641588	−	0.260570i
$732$			16.8976i			0.624554i
$733$	−8.69424	+	8.69424i	−0.321129	+	0.321129i	−0.849200	−	0.528071i	$-0.822915\pi$
$733$	−8.69424	+	8.69424i	−0.321129	+	0.321129i	0.528071	+	0.849200i	$0.322915\pi$
$734$	78.2740	−	32.4221i	2.88915	−	1.19672i
$735$		0			0
$736$	2.31255	+	5.58299i	0.0852417	+	0.205792i
$737$	0.696555	−	1.68163i	0.0256579	−	0.0619438i
$738$	−22.4022	−	9.27930i	−0.824637	−	0.341576i
$739$	25.5096	−	25.5096i	0.938385	−	0.938385i	−0.0598241	−	0.998209i	$-0.519054\pi$
$739$	25.5096	−	25.5096i	0.938385	−	0.938385i	0.998209	+	0.0598241i	$0.0190540\pi$
$740$		0			0
$741$	−5.10590	+	12.3267i	−0.187570	+	0.452834i
$742$	−5.75379	+	13.8909i	−0.211228	+	0.509950i
$743$	−30.0236	+	12.4362i	−1.10146	+	0.456239i	−0.857988	−	0.513669i	$-0.828286\pi$
$743$	−30.0236	+	12.4362i	−1.10146	+	0.456239i	−0.243470	+	0.969908i	$0.578286\pi$
$744$			26.4100i			0.968238i
$745$		0			0
$746$	2.41272	+	2.41272i	0.0883359	+	0.0883359i
$747$		−	38.9020i		−	1.42335i
$748$	−16.4955	−	16.7252i	−0.603134	−	0.611535i
$749$	−3.98429			−0.145583
$750$		0			0
$751$	−41.0781	+	17.0151i	−1.49896	+	0.620890i	−0.973245	−	0.229771i	$-0.926202\pi$
$751$	−41.0781	+	17.0151i	−1.49896	+	0.620890i	−0.525715	+	0.850661i	$0.676202\pi$
$752$	4.86704			0.177483
$753$	1.61350	−	0.668332i	0.0587991	−	0.0243554i
$754$	−88.2210	−	36.5423i	−3.21282	−	1.33079i
$755$		0			0
$756$	−6.45567	+	6.45567i	−0.234790	+	0.234790i
$757$	21.4158	+	21.4158i	0.778370	+	0.778370i	0.979554	−	0.201183i	$-0.0644787\pi$
$757$	21.4158	+	21.4158i	0.778370	+	0.778370i	−0.201183	+	0.979554i	$0.564479\pi$
$758$	−78.1362	−	32.3651i	−2.83803	−	1.17555i
$759$	−6.94374	−	2.87619i	−0.252042	−	0.104399i
$760$		0			0
$761$		−	9.85150i		−	0.357117i	−0.983929	−	0.178558i	$-0.942857\pi$
$761$		−	9.85150i		−	0.357117i	0.983929	−	0.178558i	$-0.0571433\pi$
$762$	11.0525	+	26.6830i	0.400389	+	0.966624i
$763$	3.70185	−	3.70185i	0.134016	−	0.134016i
$764$	3.36291			0.121666
$765$		0			0
$766$	21.6998			0.784046
$767$	3.08615	−	3.08615i	0.111434	−	0.111434i
$768$	−8.74636	−	21.1156i	−0.315607	−	0.761943i
$769$			35.4042i			1.27671i	0.769743	+	0.638353i	$0.220384\pi$
$769$			35.4042i			1.27671i	−0.769743	+	0.638353i	$0.779616\pi$
$770$		0			0
$771$	−7.06524	−	2.92652i	−0.254448	−	0.105396i
$772$	86.0715	+	35.6520i	3.09778	+	1.28314i
$773$	−11.0242	−	11.0242i	−0.396513	−	0.396513i	0.480488	−	0.877001i	$-0.340459\pi$
$773$	−11.0242	−	11.0242i	−0.396513	−	0.396513i	−0.877001	+	0.480488i	$0.840459\pi$
$774$	19.1967	−	19.1967i	0.690011	−	0.690011i
$775$		0			0
$776$	56.0705	+	23.2252i	2.01281	+	0.833735i
$777$	0.626217	−	0.259387i	0.0224654	−	0.00930547i
$778$	−13.0842			−0.469093
$779$	−15.5765	+	6.45201i	−0.558087	+	0.231167i
$780$		0			0
$781$	−20.2092			−0.723141
$782$	−70.2987	−	0.486222i	−2.51387	−	0.0173873i
$783$			36.1206i			1.29085i
$784$	16.3181	+	16.3181i	0.582788	+	0.582788i
$785$		0			0
$786$		−	16.1016i		−	0.574326i
$787$	15.1089	−	6.25833i	0.538575	−	0.223085i	−0.0967790	−	0.995306i	$-0.530854\pi$
$787$	15.1089	−	6.25833i	0.538575	−	0.223085i	0.635354	+	0.772221i	$0.280854\pi$
$788$	2.77573	−	6.70122i	0.0988814	−	0.238721i
$789$	6.64991	−	16.0543i	0.236743	−	0.571549i
$790$		0			0
$791$	−1.76447	+	1.76447i	−0.0627372	+	0.0627372i
$792$	−15.3700	−	6.36645i	−0.546148	−	0.226222i
$793$	−9.82062	+	23.7091i	−0.348740	+	0.841934i
$794$	−22.5244	−	54.3788i	−0.799363	−	1.92983i
$795$		0			0
$796$	−8.25725	+	3.42027i	−0.292671	+	0.121228i
$797$	−5.55459	+	5.55459i	−0.196754	+	0.196754i	−0.798607	−	0.601853i	$-0.794429\pi$
$797$	−5.55459	+	5.55459i	−0.196754	+	0.196754i	0.601853	+	0.798607i	$0.294429\pi$
$798$			4.32270i			0.153022i
$799$	2.25372	−	5.33627i	0.0797308	−	0.188784i
$800$		0			0
$801$	12.8119	+	12.8119i	0.452686	+	0.452686i
$802$	9.29799	+	22.4473i	0.328323	+	0.792643i
$803$	−13.1362			−0.463567
$804$	1.37379	+	3.31663i	0.0484500	+	0.116969i
$805$		0			0
$806$	−31.4269	+	75.8713i	−1.10697	+	2.67245i
$807$	−12.5935	−	12.5935i	−0.443312	−	0.443312i
$808$	−33.8651	−	33.8651i	−1.19137	−	1.19137i
$809$	−9.55001	+	23.0558i	−0.335760	+	0.810597i	0.662353	+	0.749192i	$0.269558\pi$
$809$	−9.55001	+	23.0558i	−0.335760	+	0.810597i	−0.998113	+	0.0614049i	$0.980442\pi$
$810$		0			0
$811$	−8.19051	−	19.7736i	−0.287608	−	0.694347i	0.712364	−	0.701810i	$-0.247624\pi$
$811$	−8.19051	−	19.7736i	−0.287608	−	0.694347i	−0.999972	+	0.00746314i	$0.997624\pi$
$812$	−20.4665			−0.718234
$813$	2.24674	+	5.42410i	0.0787965	+	0.190232i
$814$	3.96946	+	3.96946i	0.139130	+	0.139130i
$815$		0			0
$816$	10.5018	+	0.0726358i	0.367636	+	0.00254276i
$817$		−	18.8765i		−	0.660404i
$818$	−30.0059	+	30.0059i	−1.04913	+	1.04913i
$819$	−5.77071	+	2.39031i	−0.201645	+	0.0835240i
$820$		0			0
$821$	−16.0151	−	38.6638i	−0.558930	−	1.34938i	−0.910614	−	0.413258i	$-0.864391\pi$
$821$	−16.0151	−	38.6638i	−0.558930	−	1.34938i	0.351684	−	0.936119i	$-0.385609\pi$
$822$	−3.47122	+	8.38026i	−0.121073	+	0.292295i
$823$	12.0322	+	4.98390i	0.419416	+	0.173728i	0.582403	−	0.812900i	$-0.302113\pi$
$823$	12.0322	+	4.98390i	0.419416	+	0.173728i	−0.162987	+	0.986628i	$0.552113\pi$
$824$	−40.4700	+	40.4700i	−1.40984	+	1.40984i
$825$		0			0
$826$	0.541121	−	1.30638i	0.0188280	−	0.0454548i
$827$	17.7000	−	42.7316i	0.615489	−	1.48592i	−0.241402	−	0.970425i	$-0.577607\pi$
$827$	17.7000	−	42.7316i	0.615489	−	1.48592i	0.856891	−	0.515497i	$-0.172393\pi$
$828$	−62.3033	+	25.8069i	−2.16519	+	0.896851i
$829$		−	45.9531i		−	1.59602i	−0.602646	−	0.798009i	$-0.705887\pi$
$829$		−	45.9531i		−	1.59602i	0.602646	−	0.798009i	$-0.294113\pi$
$830$		0			0
$831$	−7.49538	−	7.49538i	−0.260012	−	0.260012i
$832$		−	39.3878i		−	1.36553i
$833$	25.4475	−	10.3351i	0.881703	−	0.358089i
$834$	1.72953			0.0598889
$835$		0			0
$836$	−21.8813	+	9.06353i	−0.756780	+	0.313469i
$837$	31.0642			1.07374
$838$	−56.0386	+	23.2120i	−1.93582	+	0.801844i
$839$	−28.6890	−	11.8834i	−0.990455	−	0.410260i	−0.172167	−	0.985068i	$-0.555077\pi$
$839$	−28.6890	−	11.8834i	−0.990455	−	0.410260i	−0.818288	+	0.574808i	$0.805077\pi$
$840$		0			0
$841$	−36.7508	+	36.7508i	−1.26727	+	1.26727i
$842$	−32.5447	−	32.5447i	−1.12156	−	1.12156i
$843$	−7.79161	−	3.22739i	−0.268357	−	0.111157i
$844$	−77.2553	−	32.0002i	−2.65924	−	1.10149i
$845$		0			0
$846$		−	8.39948i		−	0.288780i
$847$	1.97618	+	4.77092i	0.0679024	+	0.163931i
$848$	26.0418	−	26.0418i	0.894279	−	0.894279i
$849$	−10.1528			−0.348443
$850$		0			0
$851$	11.1139			0.380978
$852$	28.1838	−	28.1838i	0.965561	−	0.965561i
$853$	−9.98231	−	24.0994i	−0.341788	−	0.825149i	−0.997535	−	0.0701683i	$-0.977646\pi$
$853$	−9.98231	−	24.0994i	−0.341788	−	0.825149i	0.655747	−	0.754980i	$-0.272354\pi$
$854$			8.31423i			0.284507i
$855$		0			0
$856$	29.3663	+	12.1639i	1.00372	+	0.415755i
$857$	12.0510	+	4.99167i	0.411653	+	0.170512i	0.578892	−	0.815404i	$-0.303485\pi$
$857$	12.0510	+	4.99167i	0.411653	+	0.170512i	−0.167239	+	0.985916i	$0.553485\pi$
$858$	8.04054	+	8.04054i	0.274499	+	0.274499i
$859$	−32.4780	+	32.4780i	−1.10814	+	1.10814i	−0.114741	+	0.993395i	$0.536604\pi$
$859$	−32.4780	+	32.4780i	−1.10814	+	1.10814i	−0.993395	+	0.114741i	$0.963396\pi$
$860$		0			0
$861$	1.60288	+	0.663934i	0.0546259	+	0.0226268i
$862$	0.634568	−	0.262847i	0.0216135	−	0.00895259i
$863$	22.8031			0.776228			0.388114	−	0.921611i	$-0.373127\pi$
$863$	22.8031			0.776228			0.388114	+	0.921611i	$0.373127\pi$
$864$	−3.19512	+	1.32346i	−0.108700	+	0.0450251i
$865$		0			0
$866$	63.8900			2.17107
$867$	4.94257	−	11.4806i	0.167859	−	0.389903i
$868$			17.6015i			0.597434i
$869$	−7.73520	−	7.73520i	−0.262399	−	0.262399i
$870$		0			0
$871$			5.45200i			0.184734i
$872$	−38.5863	+	15.9830i	−1.30670	+	0.541252i
$873$	12.3065	−	29.7105i	0.416512	−	1.00555i
$874$	−27.1238	+	65.4827i	−0.917476	+	2.21498i
$875$		0			0
$876$	18.3198	−	18.3198i	0.618970	−	0.618970i
$877$	−22.1575	−	9.17794i	−0.748206	−	0.309917i	−0.0241964	−	0.999707i	$-0.507703\pi$
$877$	−22.1575	−	9.17794i	−0.748206	−	0.309917i	−0.724009	+	0.689790i	$0.757703\pi$
$878$	24.7133	−	59.6631i	0.834032	−	2.01353i
$879$	2.77159	+	6.69122i	0.0934835	+	0.225689i
$880$		0			0
$881$	14.4244	−	5.97478i	0.485970	−	0.201295i	−0.126226	−	0.992002i	$-0.540286\pi$
$881$	14.4244	−	5.97478i	0.485970	−	0.201295i	0.612196	+	0.790706i	$0.290286\pi$
$882$	28.1615	−	28.1615i	0.948248	−	0.948248i
$883$		−	30.7396i		−	1.03447i	−0.855844	−	0.517235i	$-0.826961\pi$
$883$		−	30.7396i		−	1.03447i	0.855844	−	0.517235i	$-0.173039\pi$
$884$	64.8190	+	27.3757i	2.18010	+	0.920743i
$885$		0			0
$886$	21.5968	+	21.5968i	0.725558	+	0.725558i
$887$	3.95243	+	9.54202i	0.132710	+	0.320390i	0.976240	−	0.216692i	$-0.0695267\pi$
$887$	3.95243	+	9.54202i	0.132710	+	0.320390i	−0.843530	+	0.537082i	$0.819527\pi$
$888$	−5.40746			−0.181462
$889$	3.59766	+	8.68552i	0.120662	+	0.291303i
$890$		0			0
$891$	−2.46893	+	5.96053i	−0.0827123	+	0.199685i
$892$	18.6444	+	18.6444i	0.624260	+	0.624260i
$893$	−4.12969	−	4.12969i	−0.138195	−	0.138195i
$894$	−6.54599	+	15.8034i	−0.218931	+	0.528546i
$895$		0			0
$896$	−4.49979	−	10.8634i	−0.150327	−	0.362922i
$897$	22.5122			0.751660
$898$	17.2429	+	41.6280i	0.575403	+	1.38915i
$899$	49.2417	+	49.2417i	1.64230	+	1.64230i
$900$		0			0
$901$	−16.4936	−	40.6113i	−0.549482	−	1.35296i
$902$			14.3689i			0.478431i
$903$	−1.37352	+	1.37352i	−0.0457080	+	0.0457080i
$904$	18.3919	−	7.61818i	0.611706	−	0.253377i
$905$		0			0
$906$	3.17630	+	7.66828i	0.105526	+	0.254761i
$907$	−9.25140	+	22.3349i	−0.307188	+	0.741617i	0.692606	+	0.721316i	$0.256462\pi$
$907$	−9.25140	+	22.3349i	−0.307188	+	0.741617i	−0.999794	+	0.0203010i	$0.993538\pi$
$908$	−69.3124	−	28.7101i	−2.30021	−	0.952779i
$909$	−17.9444	+	17.9444i	−0.595177	+	0.595177i
$910$		0			0
$911$	−9.83038	+	23.7326i	−0.325695	+	0.786298i	0.673207	+	0.739454i	$0.264916\pi$
$911$	−9.83038	+	23.7326i	−0.325695	+	0.786298i	−0.998902	+	0.0468436i	$0.985084\pi$
$912$	4.05198	−	9.78234i	0.134174	−	0.323926i
$913$	−21.2978	+	8.82184i	−0.704854	+	0.291960i
$914$		−	47.7959i		−	1.58095i
$915$		0			0
$916$	−66.3724	−	66.3724i	−2.19300	−	2.19300i
$917$		−	5.24120i		−	0.173080i
$918$	0.278262	−	40.2316i	0.00918403	−	1.32784i
$919$	44.4217			1.46534			0.732669	−	0.680585i	$-0.238274\pi$
$919$	44.4217			1.46534			0.732669	+	0.680585i	$0.238274\pi$
$920$		0			0
$921$	−5.19323	+	2.15110i	−0.171123	+	0.0708813i
$922$	−48.2010			−1.58742
$923$	55.9246	−	23.1647i	1.84078	−	0.762477i
$924$	2.25166	+	0.932668i	0.0740742	+	0.0306825i
$925$		0			0
$926$	39.0568	−	39.0568i	1.28349	−	1.28349i
$927$	21.4442	+	21.4442i	0.704319	+	0.704319i
$928$	−7.16267	−	2.96687i	−0.235126	−	0.0973924i
$929$	45.9061	+	19.0149i	1.50613	+	0.623860i	0.974755	−	0.223277i	$-0.0716754\pi$
$929$	45.9061	+	19.0149i	1.50613	+	0.623860i	0.531375	+	0.847137i	$0.321675\pi$
$930$		0			0
$931$		−	27.6918i		−	0.907562i
$932$	−5.29455	−	12.7822i	−0.173429	−	0.418694i
$933$	13.3687	−	13.3687i	0.437670	−	0.437670i
$934$	−8.49735			−0.278042
$935$		0			0
$936$	49.8307			1.62877
$937$	7.67880	−	7.67880i	0.250855	−	0.250855i	−0.570466	−	0.821321i	$-0.693237\pi$
$937$	7.67880	−	7.67880i	0.250855	−	0.250855i	0.821321	+	0.570466i	$0.193237\pi$
$938$	0.675956	+	1.63190i	0.0220707	+	0.0532835i
$939$			23.1012i			0.753880i
$940$		0			0
$941$	21.4179	+	8.87157i	0.698202	+	0.289205i	0.703413	−	0.710782i	$-0.251659\pi$
$941$	21.4179	+	8.87157i	0.698202	+	0.289205i	−0.00521060	+	0.999986i	$0.501659\pi$
$942$	−4.78491	−	1.98198i	−0.155901	−	0.0645763i
$943$	20.1153	+	20.1153i	0.655043	+	0.655043i
$944$	−2.44913	+	2.44913i	−0.0797123	+	0.0797123i
$945$		0			0
$946$	−14.8629	−	6.15642i	−0.483235	−	0.200162i
$947$	15.1465	−	6.27390i	0.492197	−	0.203874i	−0.122759	−	0.992437i	$-0.539174\pi$
$947$	15.1465	−	6.27390i	0.492197	−	0.203874i	0.614955	+	0.788562i	$0.289174\pi$
$948$	21.5751			0.700726
$949$	36.3517	−	15.0574i	1.18003	−	0.488783i
$950$		0			0
$951$	−2.25073			−0.0729850
$952$	11.1336	+	0.0770058i	0.360842	+	0.00249577i
$953$			53.6804i			1.73888i	0.494039	+	0.869440i	$0.335520\pi$
$953$			53.6804i			1.73888i	−0.494039	+	0.869440i	$0.664480\pi$
$954$	−44.9427	−	44.9427i	−1.45507	−	1.45507i
$955$		0			0
$956$			113.825i			3.68135i
$957$	8.90844	−	3.69000i	0.287969	−	0.119281i
$958$	5.69946	−	13.7597i	0.184141	−	0.444556i
$959$	−1.12991	+	2.72784i	−0.0364866	+	0.0880864i
$960$		0			0
$961$	20.4283	−	20.4283i	0.658976	−	0.658976i
$962$	−15.5347	−	6.43467i	−0.500858	−	0.207462i
$963$	6.44541	−	15.5606i	0.207700	−	0.501433i
$964$	26.8114	+	64.7284i	0.863536	+	2.08476i
$965$		0			0
$966$	6.73839	−	2.79113i	0.216804	−	0.0898032i
$967$	23.5810	−	23.5810i	0.758314	−	0.758314i	−0.217702	−	0.976015i	$-0.569856\pi$
$967$	23.5810	−	23.5810i	0.758314	−	0.758314i	0.976015	+	0.217702i	$0.0698560\pi$
$968$		−	41.1975i		−	1.32414i
$969$	−8.84915	−	8.97241i	−0.284276	−	0.288235i
$970$		0			0
$971$	−1.59646	−	1.59646i	−0.0512330	−	0.0512330i	0.681026	−	0.732259i	$-0.261534\pi$
$971$	−1.59646	−	1.59646i	−0.0512330	−	0.0512330i	−0.732259	+	0.681026i	$0.761534\pi$
$972$	−22.8850	−	55.2492i	−0.734036	−	1.77212i
$973$	0.562976			0.0180482
$974$	6.67695	+	16.1196i	0.213943	+	0.516504i
$975$		0			0
$976$	7.79352	−	18.8152i	0.249464	−	0.602261i
$977$	−13.5336	−	13.5336i	−0.432978	−	0.432978i	0.456663	−	0.889640i	$-0.349045\pi$
$977$	−13.5336	−	13.5336i	−0.432978	−	0.432978i	−0.889640	+	0.456663i	$0.849045\pi$
$978$	6.33314	+	6.33314i	0.202512	+	0.202512i
$979$	4.10880	−	9.91952i	0.131318	−	0.317029i
$980$		0			0
$981$	8.46902	+	20.4460i	0.270395	+	0.652792i
$982$	−6.34534			−0.202488
$983$	18.1286	+	43.7663i	0.578213	+	1.39593i	0.894415	+	0.447238i	$0.147592\pi$
$983$	18.1286	+	43.7663i	0.578213	+	1.39593i	−0.316202	+	0.948692i	$0.602408\pi$
$984$	−9.78709	−	9.78709i	−0.312001	−	0.312001i
$985$		0			0
$986$	64.2146	−	63.3324i	2.04501	−	2.01691i
$987$			0.600983i			0.0191295i
$988$	50.1628	−	50.1628i	1.59589	−	1.59589i
$989$	−29.4254	+	12.1884i	−0.935672	+	0.387568i
$990$		0			0
$991$	−12.8543	−	31.0330i	−0.408330	−	0.985795i	−0.985577	−	0.169226i	$-0.945873\pi$
$991$	−12.8543	−	31.0330i	−0.408330	−	0.985795i	0.577248	−	0.816569i	$-0.304127\pi$
$992$	−2.55155	+	6.15999i	−0.0810119	+	0.195580i
$993$	3.37046	+	1.39609i	0.106958	+	0.0443036i
$994$	13.8674	−	13.8674i	0.439848	−	0.439848i
$995$		0			0
$996$	17.3990	−	42.0050i	0.551310	−	1.33098i
$997$	−0.162023	+	0.391159i	−0.00513133	+	0.0123881i	−0.926424	−	0.376481i	$-0.877134\pi$
$997$	−0.162023	+	0.391159i	−0.00513133	+	0.0123881i	0.921293	+	0.388869i	$0.127134\pi$
$998$	−27.1074	+	11.2283i	−0.858071	+	0.355425i
$999$			6.36041i			0.201234i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.n.e.274.1		24
5.2	odd	4		425.2.m.d.376.1	yes	24
5.3	odd	4		425.2.m.c.376.6	yes	24
5.4	even	2		425.2.n.d.274.6		24
17.9	even	8		425.2.n.d.349.6		24
85.3	even	16		7225.2.a.bx.1.23		24
85.9	even	8	inner	425.2.n.e.349.1		24
85.37	even	16		7225.2.a.cb.1.2		24
85.43	odd	8		425.2.m.c.26.6	✓	24
85.48	even	16		7225.2.a.bx.1.24		24
85.77	odd	8		425.2.m.d.26.1	yes	24
85.82	even	16		7225.2.a.cb.1.1		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.m.c.26.6	✓	24	85.43	odd	8
425.2.m.c.376.6	yes	24	5.3	odd	4
425.2.m.d.26.1	yes	24	85.77	odd	8
425.2.m.d.376.1	yes	24	5.2	odd	4
425.2.n.d.274.6		24	5.4	even	2
425.2.n.d.349.6		24	17.9	even	8
425.2.n.e.274.1		24	1.1	even	1	trivial
425.2.n.e.349.1		24	85.9	even	8	inner
7225.2.a.bx.1.23		24	85.3	even	16
7225.2.a.bx.1.24		24	85.48	even	16
7225.2.a.cb.1.1		24	85.82	even	16
7225.2.a.cb.1.2		24	85.37	even	16

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:	\( N \)	\(=\)	\( 425 = 5^{2} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	425.n (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.71892 + 1.71892i) q^{2} +(0.281370 + 0.679288i) q^{3} -3.90934i q^{4} +(-1.65129 - 0.683987i) q^{6} +(-0.537508 - 0.222643i) q^{7} +(3.28199 + 3.28199i) q^{8} +(1.73906 - 1.73906i) q^{9} +O(q^{10})\)	\(q+(-1.71892 + 1.71892i) q^{2} +(0.281370 + 0.679288i) q^{3} -3.90934i q^{4} +(-1.65129 - 0.683987i) q^{6} +(-0.537508 - 0.222643i) q^{7} +(3.28199 + 3.28199i) q^{8} +(1.73906 - 1.73906i) q^{9} +(-1.34645 - 0.557719i) q^{11} +(2.65557 - 1.09997i) q^{12} +4.36532 q^{13} +(1.30663 - 0.541226i) q^{14} -3.46426 q^{16} +(-1.60415 + 3.79825i) q^{17} +5.97858i q^{18} +(2.93943 + 2.93943i) q^{19} -0.427768i q^{21} +(3.27311 - 1.35577i) q^{22} +(2.68413 - 6.48006i) q^{23} +(-1.30596 + 3.15288i) q^{24} +(-7.50361 + 7.50361i) q^{26} +(3.70851 + 1.53611i) q^{27} +(-0.870387 + 2.10130i) q^{28} +(3.44359 + 8.31356i) q^{29} +(7.14977 - 2.96153i) q^{31} +(-0.609218 + 0.609218i) q^{32} -1.07156i q^{33} +(-3.77147 - 9.28627i) q^{34} +(-6.79857 - 6.79857i) q^{36} +(0.606375 + 1.46392i) q^{37} -10.1053 q^{38} +(1.22827 + 2.96531i) q^{39} +(-1.55209 + 3.74708i) q^{41} +(0.735296 + 0.735296i) q^{42} +(-3.21091 - 3.21091i) q^{43} +(-2.18031 + 5.26375i) q^{44} +(6.52488 + 15.7525i) q^{46} -1.40493 q^{47} +(-0.974740 - 2.35323i) q^{48} +(-4.71040 - 4.71040i) q^{49} +(-3.03147 - 0.0209672i) q^{51} -17.0655i q^{52} +(-7.51728 + 7.51728i) q^{53} +(-9.01506 + 3.73416i) q^{54} +(-1.03338 - 2.49481i) q^{56} +(-1.16965 + 2.82379i) q^{57} +(-20.2095 - 8.37106i) q^{58} +(0.706970 - 0.706970i) q^{59} +(-2.24969 + 5.43124i) q^{61} +(-7.19923 + 17.3805i) q^{62} +(-1.32195 + 0.547568i) q^{63} -9.02291i q^{64} +(1.84191 + 1.84191i) q^{66} +1.24894i q^{67} +(14.8486 + 6.27118i) q^{68} +5.15706 q^{69} +(12.8111 - 5.30655i) q^{71} +11.4152 q^{72} +(8.32740 - 3.44932i) q^{73} +(-3.55866 - 1.47404i) q^{74} +(11.4912 - 11.4912i) q^{76} +(0.599557 + 0.599557i) q^{77} +(-7.20841 - 2.98582i) q^{78} +(6.93467 + 2.87243i) q^{79} -4.42683i q^{81} +(-3.77299 - 9.10882i) q^{82} +(11.1848 - 11.1848i) q^{83} -1.67229 q^{84} +11.0386 q^{86} +(-4.67838 + 4.67838i) q^{87} +(-2.58862 - 6.24949i) q^{88} +7.36714i q^{89} +(-2.34639 - 0.971907i) q^{91} +(-25.3327 - 10.4932i) q^{92} +(4.02347 + 4.02347i) q^{93} +(2.41495 - 2.41495i) q^{94} +(-0.585251 - 0.242419i) q^{96} +(12.0804 - 5.00387i) q^{97} +16.1936 q^{98} +(-3.31147 + 1.37165i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3} - 8 q^{6} - 12 q^{9}+O(q^{10}) \) 24 * q + 4 * q^3 - 8 * q^6 - 12 * q^9	\( 24 q + 4 q^{3} - 8 q^{6} - 12 q^{9} + 4 q^{11} - 20 q^{12} + 16 q^{13} + 24 q^{14} - 24 q^{16} + 20 q^{19} + 12 q^{22} + 8 q^{23} - 16 q^{24} + 16 q^{26} + 16 q^{27} + 20 q^{28} - 4 q^{29} + 24 q^{31} + 60 q^{32} - 16 q^{34} + 60 q^{36} - 16 q^{37} - 48 q^{38} - 8 q^{39} - 20 q^{41} + 12 q^{42} - 32 q^{43} - 64 q^{44} - 40 q^{46} - 88 q^{47} + 4 q^{48} - 24 q^{49} + 16 q^{51} - 12 q^{53} + 20 q^{54} - 32 q^{56} - 56 q^{57} - 28 q^{58} + 16 q^{59} - 64 q^{61} + 16 q^{62} - 40 q^{63} - 72 q^{66} + 48 q^{68} + 48 q^{69} - 24 q^{71} + 120 q^{72} + 20 q^{73} - 32 q^{74} + 52 q^{76} + 24 q^{77} - 100 q^{78} + 48 q^{79} + 8 q^{82} + 12 q^{83} + 40 q^{84} - 16 q^{86} - 24 q^{87} + 80 q^{88} + 24 q^{91} - 56 q^{92} + 32 q^{93} + 40 q^{94} + 132 q^{96} - 24 q^{97} + 48 q^{98} + 80 q^{99}+O(q^{100}) \) 24 * q + 4 * q^3 - 8 * q^6 - 12 * q^9 + 4 * q^11 - 20 * q^12 + 16 * q^13 + 24 * q^14 - 24 * q^16 + 20 * q^19 + 12 * q^22 + 8 * q^23 - 16 * q^24 + 16 * q^26 + 16 * q^27 + 20 * q^28 - 4 * q^29 + 24 * q^31 + 60 * q^32 - 16 * q^34 + 60 * q^36 - 16 * q^37 - 48 * q^38 - 8 * q^39 - 20 * q^41 + 12 * q^42 - 32 * q^43 - 64 * q^44 - 40 * q^46 - 88 * q^47 + 4 * q^48 - 24 * q^49 + 16 * q^51 - 12 * q^53 + 20 * q^54 - 32 * q^56 - 56 * q^57 - 28 * q^58 + 16 * q^59 - 64 * q^61 + 16 * q^62 - 40 * q^63 - 72 * q^66 + 48 * q^68 + 48 * q^69 - 24 * q^71 + 120 * q^72 + 20 * q^73 - 32 * q^74 + 52 * q^76 + 24 * q^77 - 100 * q^78 + 48 * q^79 + 8 * q^82 + 12 * q^83 + 40 * q^84 - 16 * q^86 - 24 * q^87 + 80 * q^88 + 24 * q^91 - 56 * q^92 + 32 * q^93 + 40 * q^94 + 132 * q^96 - 24 * q^97 + 48 * q^98 + 80 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more