LMFDB - Embedded newform 425.2.n.e.349.1

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			349.1
Character	$\chi$	$=$	425.349
Dual form			425.2.n.e.274.1

$q$-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 $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

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

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	−0.969206	−	0.246251i	$-0.920801\pi$
$2$	−1.71892	−	1.71892i	−1.21546	−	1.21546i	−0.246251	−	0.969206i	$-0.579199\pi$
$3$	0.281370	−	0.679288i	0.162449	−	0.392187i	−0.821605	−	0.570058i	$-0.806921\pi$
$3$	0.281370	−	0.679288i	0.162449	−	0.392187i	0.984054	+	0.177870i	$0.0569208\pi$
$4$			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	−0.481943	−	0.876203i	$-0.660069\pi$
$7$	−0.537508	+	0.222643i	−0.203159	+	0.0841511i	0.278784	+	0.960354i	$0.410069\pi$
$8$	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	−0.576318	−	0.817225i	$-0.695511\pi$
$11$	−1.34645	+	0.557719i	−0.405971	+	0.168159i	0.170347	+	0.985384i	$0.445511\pi$
$12$	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	−0.284365	−	0.958716i	$-0.591783\pi$
$19$	2.93943	−	2.93943i	0.674351	−	0.674351i	0.958716	+	0.284365i	$0.0917827\pi$
$20$		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	0.910021	+	0.414563i	$0.136066\pi$
$23$	2.68413	+	6.48006i	0.559679	+	1.35119i	−0.350341	+	0.936622i	$0.613934\pi$
$24$	−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	−0.187944	−	0.982180i	$-0.560182\pi$
$29$	3.44359	−	8.31356i	0.639458	−	1.54379i	0.827403	−	0.561609i	$-0.189818\pi$
$30$		0			0
$31$	7.14977	+	2.96153i	1.28414	+	0.531907i	0.917233	−	0.398352i	$-0.130418\pi$
$31$	7.14977	+	2.96153i	1.28414	+	0.531907i	0.366904	+	0.930259i	$0.380418\pi$
$32$	−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	−0.866166	−	0.499757i	$-0.833423\pi$
$37$	0.606375	−	1.46392i	0.0996874	−	0.240667i	0.965853	+	0.259090i	$0.0834227\pi$
$38$	−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	0.755124	−	0.655582i	$-0.227577\pi$
$41$	−1.55209	−	3.74708i	−0.242396	−	0.585195i	−0.997520	+	0.0703870i	$0.977577\pi$
$42$	0.735296	−	0.735296i	0.113459	−	0.113459i
$43$	−3.21091	+	3.21091i	−0.489659	+	0.489659i	−0.908199	−	0.418540i	$-0.862542\pi$
$43$	−3.21091	+	3.21091i	−0.489659	+	0.489659i	0.418540	+	0.908199i	$0.362542\pi$
$44$	−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	−0.999451	−	0.0331263i	$-0.989454\pi$
$53$	−7.51728	−	7.51728i	−1.03258	−	1.03258i	−0.0331263	−	0.999451i	$-0.510546\pi$
$54$	−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	0.751627	−	0.659588i	$-0.229269\pi$
$59$	0.706970	+	0.706970i	0.0920396	+	0.0920396i	−0.659588	+	0.751627i	$0.729269\pi$
$60$		0			0
$61$	−2.24969	−	5.43124i	−0.288044	−	0.695399i	0.711933	−	0.702247i	$-0.247820\pi$
$61$	−2.24969	−	5.43124i	−0.288044	−	0.695399i	−0.999977	+	0.00684869i	$0.997820\pi$
$62$	−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	$-0.975692\pi$
$67$		−	1.24894i		−	0.152582i	0.997086	−	0.0762909i	$-0.0243078\pi$
$68$	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	0.977672	−	0.210136i	$-0.0673907\pi$
$71$	12.8111	+	5.30655i	1.52040	+	0.629771i	0.542730	+	0.839907i	$0.317391\pi$
$72$	11.4152			1.34529
$73$	8.32740	+	3.44932i	0.974649	+	0.403713i	0.812441	−	0.583044i	$-0.198138\pi$
$73$	8.32740	+	3.44932i	0.974649	+	0.403713i	0.162208	+	0.986757i	$0.448138\pi$
$74$	−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	0.0432105	−	0.999066i	$-0.486241\pi$
$79$	6.93467	−	2.87243i	0.780211	−	0.323174i	0.737001	+	0.675892i	$0.236241\pi$
$80$		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	0.964835	+	0.262856i	$0.0846646\pi$
$83$	11.1848	+	11.1848i	1.22769	+	1.22769i	0.262856	+	0.964835i	$0.415335\pi$
$84$	−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	$-0.872317\pi$
$89$		−	7.36714i		−	0.780916i	0.920621	−	0.390458i	$-0.127683\pi$
$90$		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	0.899496	−	0.436929i	$-0.143934\pi$
$97$	12.0804	+	5.00387i	1.22658	+	0.508066i	0.327084	+	0.944995i	$0.393934\pi$
$98$	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	$-0.792172\pi$
$103$		−	12.3309i		−	1.21500i	0.794319	−	0.607501i	$-0.207828\pi$
$104$	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	0.666935	−	0.745116i	$-0.267606\pi$
$107$	6.32699	+	2.62073i	0.611653	+	0.253355i	−0.0552820	+	0.998471i	$0.517606\pi$
$108$	6.00519	+	14.4978i	0.577850	+	1.39505i
$109$	−3.44354	−	8.31343i	−0.329831	−	0.796282i	−0.998604	−	0.0528159i	$-0.983180\pi$
$109$	−3.44354	−	8.31343i	−0.329831	−	0.796282i	0.668773	−	0.743466i	$-0.266820\pi$
$110$		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	0.982086	−	0.188433i	$-0.0603407\pi$
$113$	1.64134	+	3.96255i	0.154404	+	0.372765i	−0.827682	+	0.561198i	$0.810341\pi$
$114$	−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	−0.0139969	+	0.999902i	$0.504455\pi$
$127$	−11.4261	+	11.4261i	−1.01390	+	1.01390i	−0.999902	+	0.0139969i	$0.995545\pi$
$128$	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	−0.698723	−	0.715392i	$-0.746248\pi$
$131$	3.44748	−	8.32295i	0.301208	−	0.727179i	0.999931	−	0.0117870i	$-0.00375201\pi$
$132$	−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	$0.0695594\pi$
$137$			5.07497i			0.433584i	−0.976218	+	0.216792i	$0.930441\pi$
$138$	−8.86455	−	8.86455i	−0.754601	−	0.754601i
$139$	−0.893998	−	0.370306i	−0.0758279	−	0.0314089i	0.344447	−	0.938806i	$-0.388066\pi$
$139$	−0.893998	−	0.370306i	−0.0758279	−	0.0314089i	−0.420275	+	0.907397i	$0.638066\pi$
$140$		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	$0.128222\pi$
$149$			9.57035i			0.784033i	−0.919958	+	0.392017i	$0.871778\pi$
$150$		0			0
$151$	−3.28367	+	3.28367i	−0.267221	+	0.267221i	−0.827979	−	0.560758i	$-0.810510\pi$
$151$	−3.28367	+	3.28367i	−0.267221	+	0.267221i	0.560758	+	0.827979i	$0.310510\pi$
$152$		−	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	−0.556550	−	0.830814i	$-0.687875\pi$
$163$	−4.62958	+	1.91763i	−0.362616	+	0.150201i	0.193934	+	0.981015i	$0.437875\pi$
$164$	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	−0.817831	−	0.575459i	$-0.804823\pi$
$167$	2.16295	−	5.22182i	0.167374	−	0.404077i	0.985205	+	0.171383i	$0.0548234\pi$
$168$	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	0.601097	+	0.799176i	$0.294730\pi$
$173$	−5.11709	+	12.3538i	−0.389045	+	0.939239i	−0.990143	+	0.140063i	$0.955270\pi$
$174$			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	−0.867746	−	0.497007i	$-0.834432\pi$
$179$	−18.2592	−	18.2592i	−1.36475	−	1.36475i	−0.497007	−	0.867746i	$-0.665568\pi$
$180$		0			0
$181$	−19.8785	+	8.23395i	−1.47756	+	0.612024i	−0.968568	−	0.248748i	$-0.919981\pi$
$181$	−19.8785	+	8.23395i	−1.47756	+	0.612024i	−0.508989	+	0.860773i	$0.669981\pi$
$182$	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	$-0.990092\pi$
$191$		−	0.860224i		−	0.0622437i	0.999516	−	0.0311218i	$-0.00990799\pi$
$192$	6.12916	+	2.53878i	0.442334	+	0.183221i
$193$	−9.11970	−	22.0169i	−0.656450	−	1.58481i	−0.803248	−	0.595644i	$-0.796897\pi$
$193$	−9.11970	−	22.0169i	−0.656450	−	1.58481i	0.146798	−	0.989166i	$-0.453103\pi$
$194$	−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	−0.320782	−	0.947153i	$-0.603946\pi$
$197$	1.71416	−	0.710026i	0.122128	−	0.0505873i	0.442911	+	0.896566i	$0.353946\pi$
$198$	3.33437	+	8.04989i	0.236964	+	0.572081i
$199$	−0.874896	+	2.11219i	−0.0620198	+	0.149729i	−0.951851	−	0.306560i	$-0.900822\pi$
$199$	−0.874896	+	2.11219i	−0.0620198	+	0.149729i	0.889831	+	0.456289i	$0.150822\pi$
$200$		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	0.906935	+	0.421270i	$0.138416\pi$
$211$	8.18558	+	19.7617i	0.563518	+	1.36045i	−0.343417	+	0.939183i	$0.611584\pi$
$212$	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	0.529156	−	0.848524i	$-0.322509\pi$
$223$	−4.76919	−	4.76919i	−0.319368	−	0.319368i	−0.848524	+	0.529156i	$0.822509\pi$
$224$	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	0.956005	+	0.293350i	$0.0947701\pi$
$227$	7.34398	+	17.7299i	0.487437	+	1.17678i	−0.468568	+	0.883427i	$0.655230\pi$
$228$	11.0391	−	4.57257i	0.731086	−	0.302826i
$229$	16.9779	+	16.9779i	1.12193	+	1.12193i	0.991451	+	0.130480i	$0.0416517\pi$
$229$	16.9779	+	16.9779i	1.12193	+	1.12193i	0.130480	+	0.991451i	$0.458348\pi$
$230$		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	0.487204	−	0.873288i	$-0.338017\pi$
$233$	3.26965	+	1.35433i	0.214202	+	0.0887253i	−0.273002	+	0.962013i	$0.588017\pi$
$234$		−	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	−0.220780	−	0.975324i	$-0.570860\pi$
$241$	−16.5574	−	6.85828i	−1.06655	−	0.441781i	−0.845773	+	0.533543i	$0.820860\pi$
$242$	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	$0.0238839\pi$
$251$			2.37527i			0.149926i	−0.997186	+	0.0749630i	$0.976116\pi$
$252$	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	0.439484	−	0.898250i	$-0.355161\pi$
$257$	−7.35458	−	7.35458i	−0.458766	−	0.458766i	−0.898250	+	0.439484i	$0.855161\pi$
$258$	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	−0.0309719	+	0.999520i	$0.509860\pi$
$263$	−16.7118	+	16.7118i	−1.03049	+	1.03049i	−0.999520	+	0.0309719i	$0.990140\pi$
$264$	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	−0.424180	−	0.905578i	$-0.639438\pi$
$269$	−22.3788	−	9.26961i	−1.36446	−	0.565178i	−0.940281	+	0.340399i	$0.889438\pi$
$270$		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	−0.0552152	−	0.998474i	$-0.517585\pi$
$277$	−13.3194	−	5.51708i	−0.800286	−	0.331489i	−0.745071	+	0.666985i	$0.767585\pi$
$278$	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	0.422513	−	0.906357i	$-0.361148\pi$
$281$	−8.11070	−	8.11070i	−0.483844	−	0.483844i	−0.906357	+	0.422513i	$0.861148\pi$
$282$	2.31995	−	0.960953i	0.138151	−	0.0572239i
$283$	−5.28429	−	12.7574i	−0.314119	−	0.758350i	−0.999544	−	0.0302064i	$-0.990384\pi$
$283$	−5.28429	−	12.7574i	−0.314119	−	0.758350i	0.685425	−	0.728143i	$-0.259616\pi$
$284$	−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	$-0.929993\pi$
$307$		−	7.64510i		−	0.436329i	0.975912	−	0.218164i	$-0.0700069\pi$
$308$	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	0.353372	+	0.935483i	$0.385035\pi$
$311$	−9.84019	+	23.7563i	−0.557986	+	1.34710i	−0.911358	+	0.411614i	$0.864965\pi$
$312$	−5.70095	−	13.7633i	−0.322752	−	0.779193i
$313$	29.0276	−	12.0236i	1.64074	−	0.679616i	0.644366	−	0.764717i	$-0.277121\pi$
$313$	29.0276	−	12.0236i	1.64074	−	0.679616i	0.996372	+	0.0851015i	$0.0271215\pi$
$314$	−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	0.887562	−	0.460689i	$-0.152398\pi$
$317$	−1.17145	−	2.82814i	−0.0657953	−	0.158844i	−0.953357	+	0.301845i	$0.902398\pi$
$318$	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	0.796924	−	0.604080i	$-0.206459\pi$
$331$	3.50849	+	3.50849i	0.192844	+	0.192844i	−0.604080	+	0.796924i	$0.706459\pi$
$332$	−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	−0.712392	−	0.701782i	$-0.752388\pi$
$337$	5.27926	−	12.7453i	0.287580	−	0.694279i	0.999972	+	0.00750257i	$0.00238816\pi$
$338$	−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	−0.824388	−	0.566025i	$-0.808481\pi$
$347$	−18.7598	+	7.77056i	−1.00708	+	0.417146i	−0.182691	+	0.983170i	$0.558481\pi$
$348$	18.2894	−	18.2894i	0.980413	−	0.980413i
$349$	10.7204	+	10.7204i	0.573849	+	0.573849i	0.933202	−	0.359353i	$-0.117003\pi$
$349$	10.7204	+	10.7204i	0.573849	+	0.573849i	−0.359353	+	0.933202i	$0.617003\pi$
$350$		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	−0.956112	−	0.293001i	$-0.905346\pi$
$359$	−12.5642	+	12.5642i	−0.663111	+	0.663111i	0.293001	+	0.956112i	$0.405346\pi$
$360$		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	−0.999364	−	0.0356729i	$-0.988643\pi$
$367$	−32.1994	+	13.3374i	−1.68080	+	0.696208i	−0.681432	+	0.731881i	$0.738643\pi$
$368$	−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	$0.0115695\pi$
$373$			1.40363i			0.0726771i	−0.999340	+	0.0363386i	$0.988431\pi$
$374$	−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	−0.0728466	−	0.997343i	$-0.523208\pi$
$379$	13.3140	−	32.1427i	0.683892	−	1.65106i	0.756738	−	0.653718i	$-0.226792\pi$
$380$		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	−0.849738	−	0.527206i	$-0.823240\pi$
$383$	−6.31207	+	6.31207i	−0.322531	+	0.322531i	0.527206	+	0.849738i	$0.323240\pi$
$384$	−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	−0.604008	−	0.796978i	$-0.706431\pi$
$389$	3.80596	−	3.80596i	0.192970	−	0.192970i	0.796978	+	0.604008i	$0.206431\pi$
$390$		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	−0.966303	−	0.257409i	$-0.917131\pi$
$397$	−9.26583	−	22.3697i	−0.465039	−	1.12270i	0.501264	−	0.865295i	$-0.332869\pi$
$398$	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	0.990150	−	0.140010i	$-0.0447135\pi$
$401$	3.82490	+	9.23412i	0.191006	+	0.461130i	−0.799144	+	0.601140i	$0.794713\pi$
$402$	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	0.259705	−	0.965688i	$-0.416375\pi$
$419$	23.0525	−	9.54866i	1.12619	−	0.466483i	0.866484	+	0.499205i	$0.166375\pi$
$420$		0			0
$421$		−	18.9333i		−	0.922750i	−0.887205	−	0.461375i	$-0.847356\pi$
$421$		−	18.9333i		−	0.922750i	0.887205	−	0.461375i	$-0.152644\pi$
$422$	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	−0.388962	−	0.921254i	$-0.627166\pi$
$431$	−0.261041	+	0.108127i	−0.0125739	+	0.00520828i	0.376388	+	0.926462i	$0.377166\pi$
$432$	−12.8472	+	5.32150i	−0.618112	+	0.256031i
$433$	−18.5844	+	18.5844i	−0.893109	+	0.893109i	−0.994815	−	0.101706i	$-0.967570\pi$
$433$	−18.5844	+	18.5844i	−0.893109	+	0.893109i	0.101706	+	0.994815i	$0.467570\pi$
$434$	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	−0.289743	−	0.957105i	$-0.593570\pi$
$439$	−24.5435	−	10.1662i	−1.17140	−	0.485208i	−0.881654	+	0.471896i	$0.843570\pi$
$440$		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	$0.0964767\pi$
$443$			12.5642i			0.596943i	−0.954419	+	0.298471i	$0.903523\pi$
$444$	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	0.998202	+	0.0599359i	$0.0190896\pi$
$449$	7.09318	+	17.1244i	0.334748	+	0.808153i	−0.663454	+	0.748217i	$0.730910\pi$
$450$		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	0.302726	−	0.953077i	$-0.402103\pi$
$457$	−13.9029	−	13.9029i	−0.650351	−	0.650351i	−0.953077	+	0.302726i	$0.902103\pi$
$458$		−	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	−0.300705	−	0.953717i	$-0.597222\pi$
$461$	14.0208	−	14.0208i	0.653012	−	0.653012i	0.953717	+	0.300705i	$0.0972220\pi$
$462$	−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	−0.647602	−	0.761979i	$-0.724228\pi$
$467$	2.47172	−	2.47172i	0.114377	−	0.114377i	0.761979	+	0.647602i	$0.224228\pi$
$468$	−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	0.249603	−	0.968348i	$-0.419700\pi$
$479$	−5.66030	−	2.34457i	−0.258626	−	0.107126i	−0.508229	+	0.861222i	$0.669700\pi$
$480$		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	0.973814	−	0.227348i	$-0.0730055\pi$
$487$	2.74668	+	6.63108i	0.124464	+	0.300483i	−0.849350	+	0.527831i	$0.823006\pi$
$488$	−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	−0.664231	−	0.747528i	$-0.731241\pi$
$491$	1.84574	−	1.84574i	0.0832970	−	0.0832970i	0.747528	+	0.664231i	$0.231241\pi$
$492$		−	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	−0.118857	−	0.992911i	$-0.537923\pi$
$499$	11.1511	−	4.61895i	0.499193	−	0.206773i	0.618050	+	0.786139i	$0.287923\pi$
$500$		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	−0.444802	−	0.895629i	$-0.646726\pi$
$503$	−2.82632	+	1.17070i	−0.126019	+	0.0521989i	0.318783	+	0.947828i	$0.396726\pi$
$504$	−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	0.0828724	−	0.996560i	$-0.473591\pi$
$521$	19.3137	−	7.99998i	0.846146	−	0.350485i	0.763274	+	0.646075i	$0.223591\pi$
$522$	−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	0.197954	−	0.980211i	$-0.436570\pi$
$541$	−8.26139	−	3.42198i	−0.355185	−	0.147122i	−0.553139	+	0.833089i	$0.686570\pi$
$542$	−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	−0.799562	−	0.600583i	$-0.794935\pi$
$547$	4.45519	−	10.7558i	0.190490	−	0.459884i	0.990052	+	0.140699i	$0.0449351\pi$
$548$	−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	0.666658	−	0.745364i	$-0.267724\pi$
$563$	−1.86751	−	1.86751i	−0.0787061	−	0.0787061i	−0.745364	+	0.666658i	$0.767724\pi$
$564$	−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	0.991922	+	0.126848i	$0.0404862\pi$
$569$	26.6868	+	26.6868i	1.11877	+	1.11877i	0.126848	+	0.991922i	$0.459514\pi$
$570$		0			0
$571$	13.1716	+	31.7991i	0.551215	+	1.33075i	0.916567	+	0.399882i	$0.130949\pi$
$571$	13.1716	+	31.7991i	0.551215	+	1.33075i	−0.365351	+	0.930870i	$0.619051\pi$
$572$	−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	$-0.989531\pi$
$577$		−	1.57974i		−	0.0657654i	0.999459	−	0.0328827i	$-0.0104688\pi$
$578$	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	−0.0224603	+	0.999748i	$0.507150\pi$
$587$	−24.7661	+	24.7661i	−1.02221	+	1.02221i	−0.999748	+	0.0224603i	$0.992850\pi$
$588$	−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	0.999952	−	0.00976794i	$-0.00310928\pi$
$593$	24.1126	+	24.1126i	0.990184	+	0.990184i	−0.00976794	+	0.999952i	$0.503109\pi$
$594$	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	$-0.961356\pi$
$599$		−	5.92805i		−	0.242213i	0.992639	−	0.121107i	$-0.0386443\pi$
$600$		0			0
$601$	−13.8906	+	5.75367i	−0.566609	+	0.234697i	−0.647552	−	0.762022i	$-0.724207\pi$
$601$	−13.8906	+	5.75367i	−0.566609	+	0.234697i	0.0809424	+	0.996719i	$0.474207\pi$
$602$	−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	0.130804	−	0.991408i	$-0.458244\pi$
$607$	−11.7701	−	4.87535i	−0.477735	−	0.197884i	−0.608539	+	0.793524i	$0.708244\pi$
$608$	−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	$-0.840250\pi$
$613$		−	23.8212i		−	0.962129i	0.876685	−	0.481064i	$-0.159750\pi$
$614$	−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	0.846526	−	0.532348i	$-0.178690\pi$
$617$	26.5455	+	10.9955i	1.06868	+	0.442663i	0.222157	+	0.975011i	$0.428690\pi$
$618$	8.43419	+	20.3619i	0.339273	+	0.819077i
$619$	−6.91812	−	16.7018i	−0.278063	−	0.671303i	0.721719	−	0.692186i	$-0.243352\pi$
$619$	−6.91812	−	16.7018i	−0.278063	−	0.671303i	−0.999782	+	0.0208833i	$0.993352\pi$
$620$		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	−0.320214	−	0.947345i	$-0.603755\pi$
$631$	15.7534	−	15.7534i	0.627132	−	0.627132i	0.947345	+	0.320214i	$0.103755\pi$
$632$	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	0.330453	+	0.943823i	$0.392799\pi$
$641$	−14.4463	+	34.8765i	−0.570596	+	1.37754i	−0.901049	+	0.433718i	$0.857201\pi$
$642$	−12.2402			−0.483084
$643$	17.2486	−	41.6419i	0.680219	−	1.64219i	−0.0833911	−	0.996517i	$-0.526575\pi$
$643$	17.2486	−	41.6419i	0.680219	−	1.64219i	0.763610	−	0.645677i	$-0.223425\pi$
$644$	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	$0.00266821\pi$
$647$			0.426429i			0.0167647i	−0.999965	+	0.00838233i	$0.997332\pi$
$648$	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	−0.132173	−	0.991227i	$-0.542196\pi$
$653$	12.1450	−	5.03061i	0.475269	−	0.196863i	0.607442	+	0.794364i	$0.292196\pi$
$654$	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	$-0.896923\pi$
$659$		−	16.3369i		−	0.636395i	0.948025	−	0.318197i	$-0.103077\pi$
$660$		0			0
$661$	−6.68312	+	6.68312i	−0.259943	+	0.259943i	−0.825031	−	0.565088i	$-0.808842\pi$
$661$	−6.68312	+	6.68312i	−0.259943	+	0.259943i	0.565088	+	0.825031i	$0.308842\pi$
$662$		−	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	0.167030	−	0.985952i	$-0.446582\pi$
$673$	25.4833	−	10.5555i	0.982311	−	0.406886i	0.815281	+	0.579066i	$0.196582\pi$
$674$	−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	−0.910211	−	0.414146i	$-0.864080\pi$
$677$	0.683020	−	1.64896i	0.0262506	−	0.0633745i	0.936461	+	0.350771i	$0.114080\pi$
$678$	−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	−0.971841	−	0.235636i	$-0.924283\pi$
$683$	−3.08452	+	7.44669i	−0.118026	+	0.284940i	0.853815	+	0.520576i	$0.174283\pi$
$684$			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	−0.999965	−	0.00836486i	$-0.997337\pi$
$691$	−44.7175	+	18.5226i	−1.70113	+	0.704632i	−0.701167	+	0.712997i	$0.747337\pi$
$692$	−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	$-0.835944\pi$
$701$		−	26.0994i		−	0.985761i	0.870097	−	0.492880i	$-0.164056\pi$
$702$	−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	−0.192946	−	0.981209i	$-0.561804\pi$
$709$	16.9696	−	40.9683i	0.637307	−	1.53860i	0.830253	−	0.557386i	$-0.188196\pi$
$710$		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	0.592286	+	0.805728i	$0.298225\pi$
$719$	−10.6254	+	25.6519i	−0.396259	+	0.956653i	−0.988545	+	0.150926i	$0.951775\pi$
$720$		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	0.528071	−	0.849200i	$-0.322915\pi$
$733$	−8.69424	−	8.69424i	−0.321129	−	0.321129i	−0.849200	+	0.528071i	$0.822915\pi$
$734$	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	0.998209	−	0.0598241i	$-0.0190540\pi$
$739$	25.5096	+	25.5096i	0.938385	+	0.938385i	−0.0598241	+	0.998209i	$0.519054\pi$
$740$		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	−0.243470	−	0.969908i	$-0.578286\pi$
$743$	−30.0236	−	12.4362i	−1.10146	−	0.456239i	−0.857988	+	0.513669i	$0.828286\pi$
$744$		−	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	−0.525715	−	0.850661i	$-0.676202\pi$
$751$	−41.0781	−	17.0151i	−1.49896	−	0.620890i	−0.973245	+	0.229771i	$0.926202\pi$
$752$	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	−0.201183	−	0.979554i	$-0.564479\pi$
$757$	21.4158	−	21.4158i	0.778370	−	0.778370i	0.979554	+	0.201183i	$0.0644787\pi$
$758$	−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	$0.0571433\pi$
$761$			9.85150i			0.357117i	−0.983929	+	0.178558i	$0.942857\pi$
$762$	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	$-0.779616\pi$
$769$		−	35.4042i		−	1.27671i	0.769743	−	0.638353i	$-0.220384\pi$
$770$		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	−0.877001	−	0.480488i	$-0.840459\pi$
$773$	−11.0242	+	11.0242i	−0.396513	+	0.396513i	0.480488	+	0.877001i	$0.340459\pi$
$774$	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	0.635354	−	0.772221i	$-0.280854\pi$
$787$	15.1089	+	6.25833i	0.538575	+	0.223085i	−0.0967790	+	0.995306i	$0.530854\pi$
$788$	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	0.601853	−	0.798607i	$-0.294429\pi$
$797$	−5.55459	−	5.55459i	−0.196754	−	0.196754i	−0.798607	+	0.601853i	$0.794429\pi$
$798$		−	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	−0.998113	−	0.0614049i	$-0.980442\pi$
$809$	−9.55001	−	23.0558i	−0.335760	−	0.810597i	0.662353	−	0.749192i	$-0.269558\pi$
$810$		0			0
$811$	−8.19051	+	19.7736i	−0.287608	+	0.694347i	−0.999972	−	0.00746314i	$-0.997624\pi$
$811$	−8.19051	+	19.7736i	−0.287608	+	0.694347i	0.712364	+	0.701810i	$0.247624\pi$
$812$	−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	0.351684	+	0.936119i	$0.385609\pi$
$821$	−16.0151	+	38.6638i	−0.558930	+	1.34938i	−0.910614	+	0.413258i	$0.864391\pi$
$822$	−3.47122	−	8.38026i	−0.121073	−	0.292295i
$823$	12.0322	−	4.98390i	0.419416	−	0.173728i	−0.162987	−	0.986628i	$-0.552113\pi$
$823$	12.0322	−	4.98390i	0.419416	−	0.173728i	0.582403	+	0.812900i	$0.302113\pi$
$824$	−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	0.856891	+	0.515497i	$0.172393\pi$
$827$	17.7000	+	42.7316i	0.615489	+	1.48592i	−0.241402	+	0.970425i	$0.577607\pi$
$828$	−62.3033	−	25.8069i	−2.16519	−	0.896851i
$829$			45.9531i			1.59602i	0.602646	+	0.798009i	$0.294113\pi$
$829$			45.9531i			1.59602i	−0.602646	+	0.798009i	$0.705887\pi$
$830$		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	−0.818288	−	0.574808i	$-0.805077\pi$
$839$	−28.6890	+	11.8834i	−0.990455	+	0.410260i	−0.172167	+	0.985068i	$0.555077\pi$
$840$		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	0.655747	+	0.754980i	$0.272354\pi$
$853$	−9.98231	+	24.0994i	−0.341788	+	0.825149i	−0.997535	+	0.0701683i	$0.977646\pi$
$854$		−	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	−0.167239	−	0.985916i	$-0.553485\pi$
$857$	12.0510	−	4.99167i	0.411653	−	0.170512i	0.578892	+	0.815404i	$0.303485\pi$
$858$	8.04054	−	8.04054i	0.274499	−	0.274499i
$859$	−32.4780	−	32.4780i	−1.10814	−	1.10814i	−0.993395	−	0.114741i	$-0.963396\pi$
$859$	−32.4780	−	32.4780i	−1.10814	−	1.10814i	−0.114741	−	0.993395i	$-0.536604\pi$
$860$		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	−0.724009	−	0.689790i	$-0.757703\pi$
$877$	−22.1575	+	9.17794i	−0.748206	+	0.309917i	−0.0241964	+	0.999707i	$0.507703\pi$
$878$	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	0.612196	−	0.790706i	$-0.290286\pi$
$881$	14.4244	+	5.97478i	0.485970	+	0.201295i	−0.126226	+	0.992002i	$0.540286\pi$
$882$	28.1615	+	28.1615i	0.948248	+	0.948248i
$883$			30.7396i			1.03447i	0.855844	+	0.517235i	$0.173039\pi$
$883$			30.7396i			1.03447i	−0.855844	+	0.517235i	$0.826961\pi$
$884$	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	−0.843530	−	0.537082i	$-0.819527\pi$
$887$	3.95243	−	9.54202i	0.132710	−	0.320390i	0.976240	+	0.216692i	$0.0695267\pi$
$888$	−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	−0.999794	−	0.0203010i	$-0.993538\pi$
$907$	−9.25140	−	22.3349i	−0.307188	−	0.741617i	0.692606	−	0.721316i	$-0.256462\pi$
$908$	−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	−0.998902	−	0.0468436i	$-0.985084\pi$
$911$	−9.83038	−	23.7326i	−0.325695	−	0.786298i	0.673207	−	0.739454i	$-0.264916\pi$
$912$	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	0.531375	−	0.847137i	$-0.321675\pi$
$929$	45.9061	−	19.0149i	1.50613	−	0.623860i	0.974755	+	0.223277i	$0.0716754\pi$
$930$		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	0.821321	−	0.570466i	$-0.193237\pi$
$937$	7.67880	+	7.67880i	0.250855	+	0.250855i	−0.570466	+	0.821321i	$0.693237\pi$
$938$	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	−0.00521060	−	0.999986i	$-0.501659\pi$
$941$	21.4179	−	8.87157i	0.698202	−	0.289205i	0.703413	+	0.710782i	$0.251659\pi$
$942$	−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	0.614955	−	0.788562i	$-0.289174\pi$
$947$	15.1465	+	6.27390i	0.492197	+	0.203874i	−0.122759	+	0.992437i	$0.539174\pi$
$948$	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	$-0.664480\pi$
$953$		−	53.6804i		−	1.73888i	0.494039	−	0.869440i	$-0.335520\pi$
$954$	−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	0.976015	−	0.217702i	$-0.0698560\pi$
$967$	23.5810	+	23.5810i	0.758314	+	0.758314i	−0.217702	+	0.976015i	$0.569856\pi$
$968$			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	−0.732259	−	0.681026i	$-0.761534\pi$
$971$	−1.59646	+	1.59646i	−0.0512330	+	0.0512330i	0.681026	+	0.732259i	$0.261534\pi$
$972$	−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	−0.889640	−	0.456663i	$-0.849045\pi$
$977$	−13.5336	+	13.5336i	−0.432978	+	0.432978i	0.456663	+	0.889640i	$0.349045\pi$
$978$	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	−0.316202	−	0.948692i	$-0.602408\pi$
$983$	18.1286	−	43.7663i	0.578213	−	1.39593i	0.894415	−	0.447238i	$-0.147592\pi$
$984$	−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	0.577248	+	0.816569i	$0.304127\pi$
$991$	−12.8543	+	31.0330i	−0.408330	+	0.985795i	−0.985577	+	0.169226i	$0.945873\pi$
$992$	−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	0.921293	−	0.388869i	$-0.127134\pi$
$997$	−0.162023	−	0.391159i	−0.00513133	−	0.0123881i	−0.926424	+	0.376481i	$0.877134\pi$
$998$	−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.349.1		24
5.2	odd	4		425.2.m.c.26.6	✓	24
5.3	odd	4		425.2.m.d.26.1	yes	24
5.4	even	2		425.2.n.d.349.6		24
17.2	even	8		425.2.n.d.274.6		24
85.2	odd	8		425.2.m.c.376.6	yes	24
85.19	even	8	inner	425.2.n.e.274.1		24
85.23	even	16		7225.2.a.cb.1.2		24
85.28	even	16		7225.2.a.cb.1.1		24
85.53	odd	8		425.2.m.d.376.1	yes	24
85.57	even	16		7225.2.a.bx.1.23		24
85.62	even	16		7225.2.a.bx.1.24		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.m.c.26.6	✓	24	5.2	odd	4
425.2.m.c.376.6	yes	24	85.2	odd	8
425.2.m.d.26.1	yes	24	5.3	odd	4
425.2.m.d.376.1	yes	24	85.53	odd	8
425.2.n.d.274.6		24	17.2	even	8
425.2.n.d.349.6		24	5.4	even	2
425.2.n.e.274.1		24	85.19	even	8	inner
425.2.n.e.349.1		24	1.1	even	1	trivial
7225.2.a.bx.1.23		24	85.57	even	16
7225.2.a.bx.1.24		24	85.62	even	16
7225.2.a.cb.1.1		24	85.28	even	16
7225.2.a.cb.1.2		24	85.23	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

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