LMFDB - Embedded newform 425.2.m.d.151.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [425,2,Mod(26,425)]

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([0, 1]))

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

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

chi := DirichletCharacter("425.26");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 425 = 5^{2} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	425.m (of order $8$, degree $4$, 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			151.3
Character	$\chi$	$=$	425.151
Dual form			425.2.m.d.76.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.639117 - 0.639117i) q^{2} +(-1.10274 - 2.66226i) q^{3} -1.18306i q^{4} +(-0.996713 + 2.40628i) q^{6} +(-0.671652 - 0.278207i) q^{7} +(-2.03435 + 2.03435i) q^{8} +(-3.75027 + 3.75027i) q^{9} +O(q^{10})$	\(q+(-0.639117 - 0.639117i) q^{2} +(-1.10274 - 2.66226i) q^{3} -1.18306i q^{4} +(-0.996713 + 2.40628i) q^{6} +(-0.671652 - 0.278207i) q^{7} +(-2.03435 + 2.03435i) q^{8} +(-3.75027 + 3.75027i) q^{9} +(-0.958080 + 2.31301i) q^{11} +(-3.14961 + 1.30461i) q^{12} -6.29663i q^{13} +(0.251457 + 0.607071i) q^{14} +0.234252 q^{16} +(-2.08128 + 3.55925i) q^{17} +4.79372 q^{18} +(-0.143443 - 0.143443i) q^{19} +2.09490i q^{21} +(2.09061 - 0.865959i) q^{22} +(0.255217 - 0.616148i) q^{23} +(7.65933 + 3.17260i) q^{24} +(-4.02428 + 4.02428i) q^{26} +(6.13299 + 2.54037i) q^{27} +(-0.329136 + 0.794604i) q^{28} +(7.33161 - 3.03685i) q^{29} +(-2.12864 - 5.13900i) q^{31} +(3.91898 + 3.91898i) q^{32} +7.21436 q^{33} +(3.60496 - 0.944595i) q^{34} +(4.43679 + 4.43679i) q^{36} +(3.04037 + 7.34010i) q^{37} +0.183354i q^{38} +(-16.7633 + 6.94358i) q^{39} +(-4.73632 - 1.96185i) q^{41} +(1.33889 - 1.33889i) q^{42} +(-8.45426 + 8.45426i) q^{43} +(2.73643 + 1.13347i) q^{44} +(-0.556904 + 0.230677i) q^{46} -10.9207i q^{47} +(-0.258320 - 0.623640i) q^{48} +(-4.57603 - 4.57603i) q^{49} +(11.7708 + 1.61597i) q^{51} -7.44929 q^{52} +(2.74061 + 2.74061i) q^{53} +(-2.29611 - 5.54329i) q^{54} +(1.93234 - 0.800403i) q^{56} +(-0.223702 + 0.540065i) q^{57} +(-6.62666 - 2.74485i) q^{58} +(-2.38470 + 2.38470i) q^{59} +(-1.04828 - 0.434212i) q^{61} +(-1.92397 + 4.64487i) q^{62} +(3.56223 - 1.47552i) q^{63} -5.47788i q^{64} +(-4.61082 - 4.61082i) q^{66} -5.61946 q^{67} +(4.21081 + 2.46228i) q^{68} -1.92179 q^{69} +(-1.51683 - 3.66196i) q^{71} -15.2587i q^{72} +(-4.79409 + 1.98578i) q^{73} +(2.74803 - 6.63433i) q^{74} +(-0.169702 + 0.169702i) q^{76} +(1.28699 - 1.28699i) q^{77} +(15.1514 + 6.27594i) q^{78} +(5.37312 - 12.9718i) q^{79} -3.21797i q^{81} +(1.77321 + 4.28091i) q^{82} +(-8.73235 - 8.73235i) q^{83} +2.47840 q^{84} +10.8065 q^{86} +(-16.1698 - 16.1698i) q^{87} +(-2.75640 - 6.65453i) q^{88} +13.0419i q^{89} +(-1.75177 + 4.22914i) q^{91} +(-0.728940 - 0.301937i) q^{92} +(-11.3340 + 11.3340i) q^{93} +(-6.97959 + 6.97959i) q^{94} +(6.11171 - 14.7550i) q^{96} +(11.0168 - 4.56330i) q^{97} +5.84924i q^{98} +(-5.08135 - 12.2675i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 8 q^{6} + 12 q^{9}+O(q^{10}) $ 24 * q - 8 * q^6 + 12 * q^9	$ 24 q - 8 q^{6} + 12 q^{9} + 4 q^{11} + 12 q^{12} - 24 q^{14} - 24 q^{16} - 4 q^{17} + 40 q^{18} - 20 q^{19} - 16 q^{22} - 8 q^{23} + 16 q^{24} + 16 q^{26} + 12 q^{27} - 48 q^{28} + 4 q^{29} + 24 q^{31} + 60 q^{32} - 48 q^{33} + 16 q^{34} + 60 q^{36} + 12 q^{37} + 8 q^{39} - 20 q^{41} - 12 q^{42} - 32 q^{43} + 64 q^{44} - 40 q^{46} + 40 q^{48} + 24 q^{49} + 16 q^{51} + 48 q^{52} + 12 q^{53} - 20 q^{54} - 32 q^{56} - 68 q^{57} + 16 q^{58} - 16 q^{59} - 64 q^{61} - 100 q^{62} + 44 q^{63} - 72 q^{66} - 40 q^{67} - 20 q^{68} - 48 q^{69} - 24 q^{71} + 32 q^{74} + 52 q^{76} - 24 q^{77} + 16 q^{78} - 48 q^{79} - 100 q^{82} - 12 q^{83} - 40 q^{84} - 16 q^{86} - 24 q^{87} - 4 q^{88} + 24 q^{91} + 88 q^{92} + 32 q^{93} - 40 q^{94} + 132 q^{96} + 88 q^{97} - 80 q^{99}+O(q^{100}) $ 24 * q - 8 * q^6 + 12 * q^9 + 4 * q^11 + 12 * q^12 - 24 * q^14 - 24 * q^16 - 4 * q^17 + 40 * q^18 - 20 * q^19 - 16 * q^22 - 8 * q^23 + 16 * q^24 + 16 * q^26 + 12 * q^27 - 48 * q^28 + 4 * q^29 + 24 * q^31 + 60 * q^32 - 48 * q^33 + 16 * q^34 + 60 * q^36 + 12 * q^37 + 8 * q^39 - 20 * q^41 - 12 * q^42 - 32 * q^43 + 64 * q^44 - 40 * q^46 + 40 * q^48 + 24 * q^49 + 16 * q^51 + 48 * q^52 + 12 * q^53 - 20 * q^54 - 32 * q^56 - 68 * q^57 + 16 * q^58 - 16 * q^59 - 64 * q^61 - 100 * q^62 + 44 * q^63 - 72 * q^66 - 40 * q^67 - 20 * q^68 - 48 * q^69 - 24 * q^71 + 32 * q^74 + 52 * q^76 - 24 * q^77 + 16 * q^78 - 48 * q^79 - 100 * q^82 - 12 * q^83 - 40 * q^84 - 16 * q^86 - 24 * q^87 - 4 * q^88 + 24 * q^91 + 88 * q^92 + 32 * q^93 - 40 * q^94 + 132 * q^96 + 88 * q^97 - 80 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$52$	$326$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

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 $

$2$	−0.639117	−	0.639117i	−0.451924	−	0.451924i	0.444069	−	0.895993i	$-0.353535\pi$
$2$	−0.639117	−	0.639117i	−0.451924	−	0.451924i	−0.895993	+	0.444069i	$0.853535\pi$
$3$	−1.10274	−	2.66226i	−0.636670	−	1.53706i	−0.831090	−	0.556139i	$-0.812282\pi$
$3$	−1.10274	−	2.66226i	−0.636670	−	1.53706i	0.194420	−	0.980918i	$-0.437718\pi$
$4$		−	1.18306i		−	0.591530i
$5$		0			0
$5$		0			0
$6$	−0.996713	+	2.40628i	−0.406906	+	0.982359i
$7$	−0.671652	−	0.278207i	−0.253861	−	0.105152i	0.252124	−	0.967695i	$-0.418871\pi$
$7$	−0.671652	−	0.278207i	−0.253861	−	0.105152i	−0.505985	+	0.862542i	$0.668871\pi$
$8$	−2.03435	+	2.03435i	−0.719250	+	0.719250i
$9$	−3.75027	+	3.75027i	−1.25009	+	1.25009i
$10$		0			0
$11$	−0.958080	+	2.31301i	−0.288872	+	0.697399i	−0.999984	−	0.00567999i	$-0.998192\pi$
$11$	−0.958080	+	2.31301i	−0.288872	+	0.697399i	0.711112	+	0.703079i	$0.248192\pi$
$12$	−3.14961	+	1.30461i	−0.909215	+	0.376609i
$13$		−	6.29663i		−	1.74637i	−0.487388	−	0.873186i	$-0.662050\pi$
$13$		−	6.29663i		−	1.74637i	0.487388	−	0.873186i	$-0.337950\pi$
$14$	0.251457	+	0.607071i	0.0672047	+	0.162247i
$15$		0			0
$16$	0.234252			0.0585630
$17$	−2.08128	+	3.55925i	−0.504785	+	0.863245i
$17$	−2.08128	+	3.55925i	−0.504785	+	0.863245i
$18$	4.79372			1.12989
$19$	−0.143443	−	0.143443i	−0.0329081	−	0.0329081i	0.690461	−	0.723369i	$-0.257408\pi$
$19$	−0.143443	−	0.143443i	−0.0329081	−	0.0329081i	−0.723369	+	0.690461i	$0.757408\pi$
$20$		0			0
$21$			2.09490i			0.457146i
$22$	2.09061	−	0.865959i	0.445719	−	0.184623i
$23$	0.255217	−	0.616148i	0.0532164	−	0.128476i	−0.895035	−	0.445995i	$-0.852850\pi$
$23$	0.255217	−	0.616148i	0.0532164	−	0.128476i	0.948252	+	0.317519i	$0.102850\pi$
$24$	7.65933	+	3.17260i	1.56345	+	0.647604i
$25$		0			0
$26$	−4.02428	+	4.02428i	−0.789227	+	0.789227i
$27$	6.13299	+	2.54037i	1.18030	+	0.488894i
$28$	−0.329136	+	0.794604i	−0.0622008	+	0.150166i
$29$	7.33161	−	3.03685i	1.36145	−	0.563929i	0.421990	−	0.906600i	$-0.361332\pi$
$29$	7.33161	−	3.03685i	1.36145	−	0.563929i	0.939455	+	0.342671i	$0.111332\pi$
$30$		0			0
$31$	−2.12864	−	5.13900i	−0.382315	−	0.922991i	−0.991517	−	0.129976i	$-0.958510\pi$
$31$	−2.12864	−	5.13900i	−0.382315	−	0.922991i	0.609202	−	0.793015i	$-0.291490\pi$
$32$	3.91898	+	3.91898i	0.692784	+	0.692784i
$33$	7.21436			1.25586
$34$	3.60496	−	0.944595i	0.618245	−	0.161997i
$35$		0			0
$36$	4.43679	+	4.43679i	0.739465	+	0.739465i
$37$	3.04037	+	7.34010i	0.499834	+	1.20670i	0.949573	+	0.313545i	$0.101517\pi$
$37$	3.04037	+	7.34010i	0.499834	+	1.20670i	−0.449740	+	0.893160i	$0.648483\pi$
$38$			0.183354i			0.0297439i
$39$	−16.7633	+	6.94358i	−2.68427	+	1.11186i
$40$		0			0
$41$	−4.73632	−	1.96185i	−0.739688	−	0.306389i	−0.0191619	−	0.999816i	$-0.506100\pi$
$41$	−4.73632	−	1.96185i	−0.739688	−	0.306389i	−0.720526	+	0.693427i	$0.756100\pi$
$42$	1.33889	−	1.33889i	0.206595	−	0.206595i
$43$	−8.45426	+	8.45426i	−1.28926	+	1.28926i	−0.354028	+	0.935235i	$0.615188\pi$
$43$	−8.45426	+	8.45426i	−1.28926	+	1.28926i	−0.935235	+	0.354028i	$0.884812\pi$
$44$	2.73643	+	1.13347i	0.412532	+	0.170876i
$45$		0			0
$46$	−0.556904	+	0.230677i	−0.0821110	+	0.0340115i
$47$		−	10.9207i		−	1.59294i	−0.604675	−	0.796472i	$-0.706697\pi$
$47$		−	10.9207i		−	1.59294i	0.604675	−	0.796472i	$-0.293303\pi$
$48$	−0.258320	−	0.623640i	−0.0372853	−	0.0900147i
$49$	−4.57603	−	4.57603i	−0.653719	−	0.653719i
$50$		0			0
$51$	11.7708	+	1.61597i	1.64824	+	0.226281i
$52$	−7.44929			−1.03303
$53$	2.74061	+	2.74061i	0.376451	+	0.376451i	0.869820	−	0.493369i	$-0.164235\pi$
$53$	2.74061	+	2.74061i	0.376451	+	0.376451i	−0.493369	+	0.869820i	$0.664235\pi$
$54$	−2.29611	−	5.54329i	−0.312461	−	0.754347i
$55$		0			0
$56$	1.93234	−	0.800403i	0.258220	−	0.106958i
$57$	−0.223702	+	0.540065i	−0.0296301	+	0.0715333i
$58$	−6.62666	−	2.74485i	−0.870123	−	0.360417i
$59$	−2.38470	+	2.38470i	−0.310462	+	0.310462i	−0.845088	−	0.534626i	$-0.820452\pi$
$59$	−2.38470	+	2.38470i	−0.310462	+	0.310462i	0.534626	+	0.845088i	$0.320452\pi$
$60$		0			0
$61$	−1.04828	−	0.434212i	−0.134219	−	0.0555952i	0.314563	−	0.949237i	$-0.398142\pi$
$61$	−1.04828	−	0.434212i	−0.134219	−	0.0555952i	−0.448782	+	0.893641i	$0.648142\pi$
$62$	−1.92397	+	4.64487i	−0.244344	+	0.589899i
$63$	3.56223	−	1.47552i	0.448798	−	0.185898i
$64$		−	5.47788i		−	0.684734i
$65$		0			0
$66$	−4.61082	−	4.61082i	−0.567552	−	0.567552i
$67$	−5.61946			−0.686526			−0.343263	−	0.939239i	$-0.611532\pi$
$67$	−5.61946			−0.686526			−0.343263	+	0.939239i	$0.611532\pi$
$68$	4.21081	+	2.46228i	0.510635	+	0.298595i
$69$	−1.92179			−0.231356
$70$		0			0
$71$	−1.51683	−	3.66196i	−0.180015	−	0.434595i	0.807954	−	0.589245i	$-0.200575\pi$
$71$	−1.51683	−	3.66196i	−0.180015	−	0.434595i	−0.987969	+	0.154650i	$0.950575\pi$
$72$		−	15.2587i		−	1.79825i
$73$	−4.79409	+	1.98578i	−0.561105	+	0.232417i	−0.645165	−	0.764043i	$-0.723211\pi$
$73$	−4.79409	+	1.98578i	−0.561105	+	0.232417i	0.0840596	+	0.996461i	$0.473211\pi$
$74$	2.74803	−	6.63433i	0.319452	−	0.771225i
$75$		0			0
$76$	−0.169702	+	0.169702i	−0.0194661	+	0.0194661i
$77$	1.28699	−	1.28699i	0.146666	−	0.146666i
$78$	15.1514	+	6.27594i	1.71556	+	0.710610i
$79$	5.37312	−	12.9718i	0.604523	−	1.45945i	−0.264358	−	0.964425i	$-0.585160\pi$
$79$	5.37312	−	12.9718i	0.604523	−	1.45945i	0.868880	−	0.495022i	$-0.164840\pi$
$80$		0			0
$81$		−	3.21797i		−	0.357552i
$82$	1.77321	+	4.28091i	0.195818	+	0.472747i
$83$	−8.73235	−	8.73235i	−0.958500	−	0.958500i	0.0406730	−	0.999173i	$-0.487050\pi$
$83$	−8.73235	−	8.73235i	−0.958500	−	0.958500i	−0.999173	+	0.0406730i	$0.987050\pi$
$84$	2.47840			0.270415
$85$		0			0
$86$	10.8065			1.16530
$87$	−16.1698	−	16.1698i	−1.73358	−	1.73358i
$88$	−2.75640	−	6.65453i	−0.293833	−	0.709376i
$89$			13.0419i			1.38244i	0.722644	+	0.691221i	$0.242927\pi$
$89$			13.0419i			1.38244i	−0.722644	+	0.691221i	$0.757073\pi$
$90$		0			0
$91$	−1.75177	+	4.22914i	−0.183635	+	0.443335i
$92$	−0.728940	−	0.301937i	−0.0759972	−	0.0314791i
$93$	−11.3340	+	11.3340i	−1.17528	+	1.17528i
$94$	−6.97959	+	6.97959i	−0.719890	+	0.719890i
$95$		0			0
$96$	6.11171	−	14.7550i	0.623774	−	1.50592i
$97$	11.0168	−	4.56330i	1.11858	−	0.463333i	0.254699	−	0.967020i	$-0.418024\pi$
$97$	11.0168	−	4.56330i	1.11858	−	0.463333i	0.863886	+	0.503688i	$0.168024\pi$
$98$			5.84924i			0.590862i
$99$	−5.08135	−	12.2675i	−0.510695	−	1.23293i
$100$		0			0
$101$	−10.0642			−1.00143			−0.500713	−	0.865613i	$-0.666929\pi$
$101$	−10.0642			−1.00143			−0.500713	+	0.865613i	$0.666929\pi$
$102$	−6.49011	−	8.55569i	−0.642617	−	0.847140i
$103$	−9.80719			−0.966331			−0.483166	−	0.875529i	$-0.660513\pi$
$103$	−9.80719			−0.966331			−0.483166	+	0.875529i	$0.660513\pi$
$104$	12.8095	+	12.8095i	1.25608	+	1.25608i
$105$		0			0
$106$		−	3.50314i		−	0.340255i
$107$	3.52458	−	1.45993i	0.340734	−	0.141137i	−0.205754	−	0.978604i	$-0.565965\pi$
$107$	3.52458	−	1.45993i	0.340734	−	0.141137i	0.546488	+	0.837467i	$0.315965\pi$
$108$	3.00541	−	7.25570i	0.289195	−	0.698180i
$109$	−2.96319	−	1.22739i	−0.283822	−	0.117563i	0.236231	−	0.971697i	$-0.424088\pi$
$109$	−2.96319	−	1.22739i	−0.283822	−	0.117563i	−0.520053	+	0.854134i	$0.674088\pi$
$110$		0			0
$111$	16.1885	−	16.1885i	1.53655	−	1.53655i
$112$	−0.157336	−	0.0651706i	−0.0148668	−	0.00615805i
$113$	0.154329	−	0.372584i	0.0145181	−	0.0350498i	−0.916454	−	0.400139i	$-0.868962\pi$
$113$	0.154329	−	0.372584i	0.0145181	−	0.0350498i	0.930972	+	0.365090i	$0.118962\pi$
$114$	0.488136	−	0.202193i	0.0457181	−	0.0189371i
$115$		0			0
$116$	−3.59278	−	8.67373i	−0.333581	−	0.805335i
$117$	23.6141	+	23.6141i	2.18312	+	2.18312i
$118$	3.04821			0.280610
$119$	2.38811	−	1.81155i	0.218917	−	0.166065i
$120$		0			0
$121$	3.34607	+	3.34607i	0.304188	+	0.304188i
$122$	0.392462	+	0.947487i	0.0355318	+	0.0857814i
$123$			14.7727i			1.33201i
$124$	−6.07974	+	2.51831i	−0.545976	+	0.226151i
$125$		0			0
$126$	−3.21971	−	1.33365i	−0.286835	−	0.118811i
$127$	−1.52815	+	1.52815i	−0.135601	+	0.135601i	−0.771649	−	0.636048i	$-0.780568\pi$
$127$	−1.52815	+	1.52815i	−0.135601	+	0.135601i	0.636048	+	0.771649i	$0.280568\pi$
$128$	4.33696	−	4.33696i	0.383336	−	0.383336i
$129$	31.8303	+	13.1846i	2.80251	+	1.16084i
$130$		0			0
$131$	−7.43241	+	3.07860i	−0.649372	+	0.268979i	−0.682959	−	0.730457i	$-0.739307\pi$
$131$	−7.43241	+	3.07860i	−0.649372	+	0.268979i	0.0335863	+	0.999436i	$0.489307\pi$
$132$		−	8.53501i		−	0.742877i
$133$	0.0564370	+	0.136251i	0.00489371	+	0.0118144i
$134$	3.59149	+	3.59149i	0.310258	+	0.310258i
$135$		0			0
$136$	−3.00670	−	11.4748i	−0.257823	−	0.983956i
$137$	7.87082			0.672450			0.336225	−	0.941782i	$-0.390850\pi$
$137$	7.87082			0.672450			0.336225	+	0.941782i	$0.390850\pi$
$138$	1.22825	+	1.22825i	0.104555	+	0.104555i
$139$	−6.68268	−	16.1334i	−0.566818	−	1.36842i	−0.904223	−	0.427060i	$-0.859549\pi$
$139$	−6.68268	−	16.1334i	−0.566818	−	1.36842i	0.337405	−	0.941359i	$-0.390451\pi$
$140$		0			0
$141$	−29.0737	+	12.0427i	−2.44845	+	1.01418i
$142$	−1.37099	+	3.30986i	−0.115051	+	0.277757i
$143$	14.5642	+	6.03268i	1.21792	+	0.504478i
$144$	−0.878508	+	0.878508i	−0.0732090	+	0.0732090i
$145$		0			0
$146$	4.33312	+	1.79484i	0.358612	+	0.148542i
$147$	−7.13639	+	17.2288i	−0.588600	+	1.42101i
$148$	8.68377	−	3.59694i	0.713802	−	0.295666i
$149$		−	7.42906i		−	0.608613i	−0.952574	−	0.304306i	$-0.901575\pi$
$149$		−	7.42906i		−	0.608613i	0.952574	−	0.304306i	$-0.0984246\pi$
$150$		0			0
$151$	−9.55527	−	9.55527i	−0.777597	−	0.777597i	0.201825	−	0.979422i	$-0.435313\pi$
$151$	−9.55527	−	9.55527i	−0.777597	−	0.777597i	−0.979422	+	0.201825i	$0.935313\pi$
$152$	0.583627			0.0473384
$153$	−5.54278	−	21.1535i	−0.448107	−	1.71016i
$154$	−1.64508			−0.132564
$155$		0			0
$156$	8.21466	+	19.8320i	0.657699	+	1.58783i
$157$		−	2.75786i		−	0.220101i	−0.993926	−	0.110051i	$-0.964899\pi$
$157$		−	2.75786i		−	0.220101i	0.993926	−	0.110051i	$-0.0351013\pi$
$158$	−11.7246	+	4.85648i	−0.932757	+	0.386361i
$159$	4.27402	−	10.3184i	0.338952	−	0.818303i
$160$		0			0
$161$	−0.342834	+	0.342834i	−0.0270191	+	0.0270191i
$162$	−2.05666	+	2.05666i	−0.161586	+	0.161586i
$163$	1.27839	+	0.529525i	0.100131	+	0.0414756i	0.432187	−	0.901784i	$-0.357742\pi$
$163$	1.27839	+	0.529525i	0.100131	+	0.0414756i	−0.332056	+	0.943260i	$0.607742\pi$
$164$	−2.32098	+	5.60334i	−0.181238	+	0.437548i
$165$		0			0
$166$			11.1620i			0.866338i
$167$	−5.61942	−	13.5665i	−0.434844	−	1.04981i	−0.977705	−	0.209983i	$-0.932659\pi$
$167$	−5.61942	−	13.5665i	−0.434844	−	1.04981i	0.542861	−	0.839822i	$-0.317341\pi$
$168$	−4.26176	−	4.26176i	−0.328802	−	0.328802i
$169$	−26.6476			−2.04981
$170$		0			0
$171$	1.07590			0.0822762
$172$	10.0019	+	10.0019i	0.762637	+	0.762637i
$173$	5.64428	+	13.6265i	0.429127	+	1.03600i	0.979565	+	0.201127i	$0.0644605\pi$
$173$	5.64428	+	13.6265i	0.429127	+	1.03600i	−0.550439	+	0.834876i	$0.685539\pi$
$174$			20.6688i			1.56689i
$175$		0			0
$176$	−0.224432	+	0.541828i	−0.0169172	+	0.0408418i
$177$	8.97842	+	3.71899i	0.674860	+	0.279536i
$178$	8.33531	−	8.33531i	0.624758	−	0.624758i
$179$	−10.0949	+	10.0949i	−0.754531	+	0.754531i	−0.975321	−	0.220790i	$-0.929136\pi$
$179$	−10.0949	+	10.0949i	−0.754531	+	0.754531i	0.220790	+	0.975321i	$0.429136\pi$
$180$		0			0
$181$	2.30531	−	5.56552i	0.171353	−	0.413682i	−0.814752	−	0.579810i	$-0.803127\pi$
$181$	2.30531	−	5.56552i	0.171353	−	0.413682i	0.986104	+	0.166129i	$0.0531267\pi$
$182$	3.82250	−	1.58333i	0.283343	−	0.117364i
$183$			3.26962i			0.241698i
$184$	0.734259	+	1.77266i	0.0541303	+	0.130682i
$185$		0			0
$186$	14.4875			1.06227
$187$	−6.23855	−	8.22408i	−0.456208	−	0.601404i
$188$	−12.9198			−0.942274
$189$	−3.41249	−	3.41249i	−0.248222	−	0.248222i
$190$		0			0
$191$			14.1379i			1.02298i	0.859288	+	0.511492i	$0.170907\pi$
$191$			14.1379i			1.02298i	−0.859288	+	0.511492i	$0.829093\pi$
$192$	−14.5835	+	6.04070i	−1.05248	+	0.435950i
$193$	8.90773	−	21.5052i	0.641192	−	1.54797i	−0.183881	−	0.982949i	$-0.558866\pi$
$193$	8.90773	−	21.5052i	0.641192	−	1.54797i	0.825073	−	0.565026i	$-0.191134\pi$
$194$	−9.95749	−	4.12453i	−0.714906	−	0.296124i
$195$		0			0
$196$	−5.41372	+	5.41372i	−0.386694	+	0.386694i
$197$	−8.59019	−	3.55817i	−0.612026	−	0.253509i	0.0550686	−	0.998483i	$-0.482462\pi$
$197$	−8.59019	−	3.55817i	−0.612026	−	0.253509i	−0.667094	+	0.744973i	$0.732462\pi$
$198$	−4.59277	+	11.0879i	−0.326394	+	0.787984i
$199$	6.98662	−	2.89395i	0.495268	−	0.205147i	−0.121046	−	0.992647i	$-0.538625\pi$
$199$	6.98662	−	2.89395i	0.495268	−	0.205147i	0.616315	+	0.787500i	$0.288625\pi$
$200$		0			0
$201$	6.19683	+	14.9605i	0.437090	+	1.05523i
$202$	6.43221	+	6.43221i	0.452569	+	0.452569i
$203$	−5.76916			−0.404916
$204$	1.91179	−	13.9255i	0.133852	−	0.974982i
$205$		0			0
$206$	6.26794	+	6.26794i	0.436708	+	0.436708i
$207$	1.35359	+	3.26785i	0.0940809	+	0.227131i
$208$		−	1.47500i		−	0.102273i
$209$	0.469216	−	0.194356i	0.0324563	−	0.0134439i
$210$		0			0
$211$	23.0644	+	9.55359i	1.58782	+	0.657697i	0.989628	−	0.143656i	$-0.0458859\pi$
$211$	23.0644	+	9.55359i	1.58782	+	0.657697i	0.598192	+	0.801353i	$0.295886\pi$
$212$	3.24230	−	3.24230i	0.222682	−	0.222682i
$213$	−8.07642	+	8.07642i	−0.553387	+	0.553387i
$214$	−3.18568	−	1.31955i	−0.217769	−	0.0902028i
$215$		0			0
$216$	−17.6446	+	7.30864i	−1.20056	+	0.497290i
$217$			4.04382i			0.274512i
$218$	1.10938	+	2.67827i	0.0751364	+	0.181395i
$219$	10.5733	+	10.5733i	0.714478	+	0.714478i
$220$		0			0
$221$	22.4113	+	13.1051i	1.50755	+	0.881542i
$222$	−20.6927			−1.38880
$223$	−8.60440	−	8.60440i	−0.576193	−	0.576193i	0.357659	−	0.933852i	$-0.383575\pi$
$223$	−8.60440	−	8.60440i	−0.576193	−	0.576193i	−0.933852	+	0.357659i	$0.883575\pi$
$224$	−1.54190	−	3.72248i	−0.103023	−	0.248719i
$225$		0			0
$226$	−0.336759	+	0.139490i	−0.0224009	+	0.00927876i
$227$	0.760206	−	1.83530i	0.0504566	−	0.121813i	−0.896641	−	0.442757i	$-0.854000\pi$
$227$	0.760206	−	1.83530i	0.0504566	−	0.121813i	0.947098	+	0.320944i	$0.104000\pi$
$228$	0.638928	+	0.264653i	0.0423141	+	0.0175271i
$229$	1.62070	−	1.62070i	0.107099	−	0.107099i	−0.651527	−	0.758626i	$-0.725871\pi$
$229$	1.62070	−	1.62070i	0.107099	−	0.107099i	0.758626	+	0.651527i	$0.225871\pi$
$230$		0			0
$231$	−4.84554	−	2.00709i	−0.318813	−	0.132057i
$232$	−8.73703	+	21.0930i	−0.573614	+	1.38483i
$233$	20.9749	−	8.68807i	1.37411	−	0.569174i	0.431209	−	0.902252i	$-0.358087\pi$
$233$	20.9749	−	8.68807i	1.37411	−	0.569174i	0.942899	+	0.333078i	$0.108087\pi$
$234$		−	30.1843i		−	1.97321i
$235$		0			0
$236$	2.82125	+	2.82125i	0.183647	+	0.183647i
$237$	−40.4596			−2.62813
$238$	−2.68407	−	0.368487i	−0.173982	−	0.0238854i
$239$	13.2285			0.855683			0.427841	−	0.903854i	$-0.359274\pi$
$239$	13.2285			0.855683			0.427841	+	0.903854i	$0.359274\pi$
$240$		0			0
$241$	1.10950	+	2.67856i	0.0714689	+	0.172541i	0.955577	−	0.294741i	$-0.0952333\pi$
$241$	1.10950	+	2.67856i	0.0714689	+	0.172541i	−0.884108	+	0.467282i	$0.845233\pi$
$242$		−	4.27706i		−	0.274940i
$243$	9.83190	−	4.07251i	0.630717	−	0.261251i
$244$	−0.513699	+	1.24018i	−0.0328862	+	0.0793943i
$245$		0			0
$246$	9.44150	−	9.44150i	0.601968	−	0.601968i
$247$	−0.903209	+	0.903209i	−0.0574698	+	0.0574698i
$248$	14.7849	+	6.12410i	0.938842	+	0.388881i
$249$	−13.6182	+	32.8773i	−0.863021	+	2.08352i
$250$		0			0
$251$		−	9.85445i		−	0.622008i	−0.950409	−	0.311004i	$-0.899335\pi$
$251$		−	9.85445i		−	0.622008i	0.950409	−	0.311004i	$-0.100665\pi$
$252$	−1.74563	−	4.21432i	−0.109964	−	0.265477i
$253$	1.18064	+	1.18064i	0.0742261	+	0.0742261i
$254$	1.95333			0.122563
$255$		0			0
$256$	−16.4994			−1.03121
$257$	3.74014	+	3.74014i	0.233303	+	0.233303i	0.814070	−	0.580767i	$-0.197247\pi$
$257$	3.74014	+	3.74014i	0.233303	+	0.233303i	−0.580767	+	0.814070i	$0.697247\pi$
$258$	−11.9168	−	28.7698i	−0.741910	−	1.79113i
$259$		−	5.77584i		−	0.358893i
$260$		0			0
$261$	−16.1065	+	38.8845i	−0.996967	+	2.40689i
$262$	6.71776	+	2.78259i	0.415025	+	0.171909i
$263$	8.89552	−	8.89552i	0.548521	−	0.548521i	−0.377492	−	0.926013i	$-0.623213\pi$
$263$	8.89552	−	8.89552i	0.548521	−	0.548521i	0.926013	+	0.377492i	$0.123213\pi$
$264$	−14.6765	+	14.6765i	−0.903276	+	0.903276i
$265$		0			0
$266$	0.0510104	−	0.123150i	0.00312765	−	0.00755081i
$267$	34.7210	−	14.3819i	2.12489	−	0.880159i
$268$			6.64815i			0.406101i
$269$	3.52167	+	8.50207i	0.214720	+	0.518380i	0.994137	−	0.108125i	$-0.0344847\pi$
$269$	3.52167	+	8.50207i	0.214720	+	0.518380i	−0.779417	+	0.626505i	$0.784485\pi$
$270$		0			0
$271$	−14.6023			−0.887028			−0.443514	−	0.896267i	$-0.646268\pi$
$271$	−14.6023			−0.887028			−0.443514	+	0.896267i	$0.646268\pi$
$272$	−0.487545	+	0.833762i	−0.0295617	+	0.0505543i
$273$	13.1908			0.798346
$274$	−5.03038	−	5.03038i	−0.303896	−	0.303896i
$275$		0			0
$276$			2.27359i			0.136854i
$277$	12.0713	−	5.00008i	0.725291	−	0.300425i	0.0106758	−	0.999943i	$-0.496602\pi$
$277$	12.0713	−	5.00008i	0.725291	−	0.300425i	0.714615	+	0.699518i	$0.246602\pi$
$278$	−6.04013	+	14.5822i	−0.362263	+	0.874580i
$279$	27.2556	+	11.2896i	1.63175	+	0.675892i
$280$		0			0
$281$	5.34654	−	5.34654i	0.318948	−	0.318948i	−0.529415	−	0.848363i	$-0.677589\pi$
$281$	5.34654	−	5.34654i	0.318948	−	0.318948i	0.848363	+	0.529415i	$0.177589\pi$
$282$	26.2782	+	10.8848i	1.56484	+	0.648179i
$283$	1.57590	−	3.80456i	0.0936775	−	0.226157i	−0.870095	−	0.492885i	$-0.835942\pi$
$283$	1.57590	−	3.80456i	0.0936775	−	0.226157i	0.963772	+	0.266727i	$0.0859424\pi$
$284$	−4.33232	+	1.79450i	−0.257076	+	0.106484i
$285$		0			0
$286$	−5.45262	−	13.1638i	−0.322420	−	0.778392i
$287$	2.63536	+	2.63536i	0.155560	+	0.155560i
$288$	−29.3944			−1.73208
$289$	−8.33654	−	14.8156i	−0.490385	−	0.871506i
$290$		0			0
$291$	−24.2974	−	24.2974i	−1.42434	−	1.42434i
$292$	2.34929	+	5.67169i	0.137482	+	0.331911i
$293$		−	18.5803i		−	1.08547i	−0.839903	−	0.542736i	$-0.817388\pi$
$293$		−	18.5803i		−	1.08547i	0.839903	−	0.542736i	$-0.182612\pi$
$294$	15.5722	−	6.45021i	0.908189	−	0.376184i
$295$		0			0
$296$	−21.1175	−	8.74714i	−1.22743	−	0.508417i
$297$	−11.7518	+	11.7518i	−0.681909	+	0.681909i
$298$	−4.74804	+	4.74804i	−0.275047	+	0.275047i
$299$	−3.87966	−	1.60701i	−0.224366	−	0.0929356i
$300$		0			0
$301$	8.03036	−	3.32628i	0.462862	−	0.191724i
$302$			12.2139i			0.702829i
$303$	11.0983	+	26.7936i	0.637578	+	1.53925i
$304$	−0.0336019	−	0.0336019i	−0.00192720	−	0.00192720i
$305$		0			0
$306$	−9.97708	+	17.0620i	−0.570351	+	0.975372i
$307$	9.82624			0.560813			0.280407	−	0.959881i	$-0.409531\pi$
$307$	9.82624			0.560813			0.280407	+	0.959881i	$0.409531\pi$
$308$	−1.52259	−	1.52259i	−0.0867576	−	0.0867576i
$309$	10.8148	+	26.1093i	0.615234	+	1.48531i
$310$		0			0
$311$	26.5045	−	10.9785i	1.50293	−	0.622536i	0.528849	−	0.848716i	$-0.322624\pi$
$311$	26.5045	−	10.9785i	1.50293	−	0.622536i	0.974086	+	0.226180i	$0.0726237\pi$
$312$	19.9767	−	48.2280i	1.13096	−	2.73037i
$313$	−0.894911	−	0.370684i	−0.0505834	−	0.0209523i	0.357248	−	0.934009i	$-0.383715\pi$
$313$	−0.894911	−	0.370684i	−0.0505834	−	0.0209523i	−0.407832	+	0.913057i	$0.633715\pi$
$314$	−1.76259	+	1.76259i	−0.0994689	+	0.0994689i
$315$		0			0
$316$	−15.3465	−	6.35671i	−0.863306	−	0.357593i
$317$	−10.1506	+	24.5058i	−0.570116	+	1.37638i	0.331341	+	0.943511i	$0.392499\pi$
$317$	−10.1506	+	24.5058i	−0.570116	+	1.37638i	−0.901456	+	0.432870i	$0.857501\pi$
$318$	−9.32626	+	3.86307i	−0.522991	+	0.216630i
$319$			19.8676i			1.11237i
$320$		0			0
$321$	−7.77342	−	7.77342i	−0.433870	−	0.433870i
$322$	0.438222			0.0244211
$323$	0.809096	−	0.212005i	0.0450193	−	0.0117963i
$324$	−3.80705			−0.211503
$325$		0			0
$326$	−0.478610	−	1.15547i	−0.0265077	−	0.0639953i
$327$			9.24228i			0.511099i
$328$	13.6264	−	5.64423i	0.752391	−	0.311651i
$329$	−3.03821	+	7.33489i	−0.167502	+	0.404386i
$330$		0			0
$331$	4.33174	−	4.33174i	0.238094	−	0.238094i	−0.577967	−	0.816060i	$-0.696154\pi$
$331$	4.33174	−	4.33174i	0.238094	−	0.238094i	0.816060	+	0.577967i	$0.196154\pi$
$332$	−10.3309	+	10.3309i	−0.566981	+	0.566981i
$333$	−38.9295	−	16.1251i	−2.13333	−	0.883652i
$334$	−5.07910	+	12.2620i	−0.277916	+	0.670949i
$335$		0			0
$336$			0.490736i			0.0267718i
$337$	−6.07517	−	14.6668i	−0.330936	−	0.798950i	−0.998518	−	0.0544140i	$-0.982671\pi$
$337$	−6.07517	−	14.6668i	−0.330936	−	0.798950i	0.667583	−	0.744536i	$-0.267329\pi$
$338$	17.0309	+	17.0309i	0.926360	+	0.926360i
$339$	−1.16210			−0.0631167
$340$		0			0
$341$	13.9260			0.754133
$342$	−0.687626	−	0.687626i	−0.0371826	−	0.0371826i
$343$	3.74787	+	9.04815i	0.202366	+	0.488554i
$344$		−	34.3978i		−	1.85461i
$345$		0			0
$346$	5.10157	−	12.3163i	0.274262	−	0.662127i
$347$	−1.57373	−	0.651859i	−0.0844821	−	0.0349936i	0.340042	−	0.940410i	$-0.389559\pi$
$347$	−1.57373	−	0.651859i	−0.0844821	−	0.0349936i	−0.424524	+	0.905417i	$0.639559\pi$
$348$	−19.1298	+	19.1298i	−1.02547	+	1.02547i
$349$	24.9284	−	24.9284i	1.33439	−	1.33439i	0.432985	−	0.901401i	$-0.357460\pi$
$349$	24.9284	−	24.9284i	1.33439	−	1.33439i	0.901401	−	0.432985i	$-0.142540\pi$
$350$		0			0
$351$	15.9958	−	38.6172i	0.853791	−	2.06123i
$352$	−12.8193	+	5.30994i	−0.683273	+	0.283021i
$353$		−	22.4928i		−	1.19717i	−0.801059	−	0.598586i	$-0.795730\pi$
$353$		−	22.4928i		−	1.19717i	0.801059	−	0.598586i	$-0.204270\pi$
$354$	−3.36140	−	8.11513i	−0.178656	−	0.431314i
$355$		0			0
$356$	15.4294			0.817755
$357$	−7.45629	−	4.36008i	−0.394629	−	0.230760i
$358$	12.9037			0.681981
$359$	−12.7307	−	12.7307i	−0.671898	−	0.671898i	0.286255	−	0.958153i	$-0.407590\pi$
$359$	−12.7307	−	12.7307i	−0.671898	−	0.671898i	−0.958153	+	0.286255i	$0.907590\pi$
$360$		0			0
$361$		−	18.9588i		−	0.997834i
$362$	−5.03038	+	2.08365i	−0.264391	+	0.109514i
$363$	5.21826	−	12.5980i	0.273887	−	0.661223i
$364$	5.00333	+	2.07245i	0.262246	+	0.108626i
$365$		0			0
$366$	2.08967	−	2.08967i	0.109229	−	0.109229i
$367$	28.9008	+	11.9711i	1.50861	+	0.624887i	0.975271	−	0.221015i	$-0.0709368\pi$
$367$	28.9008	+	11.9711i	1.50861	+	0.624887i	0.533340	+	0.845901i	$0.320937\pi$
$368$	0.0597851	−	0.144334i	0.00311651	−	0.00752393i
$369$	25.1199	−	10.4050i	1.30769	−	0.541663i
$370$		0			0
$371$	−1.07828	−	2.60319i	−0.0559814	−	0.135151i
$372$	13.4088	+	13.4088i	0.695213	+	0.695213i
$373$	24.3521			1.26091			0.630453	−	0.776228i	$-0.282869\pi$
$373$	24.3521			1.26091			0.630453	+	0.776228i	$0.282869\pi$
$374$	−1.26898	+	9.24331i	−0.0656175	+	0.477960i
$375$		0			0
$376$	22.2164	+	22.2164i	1.14573	+	1.14573i
$377$	−19.1219	−	46.1644i	−0.984830	−	2.37759i
$378$			4.36196i			0.224355i
$379$	6.04944	−	2.50576i	0.310739	−	0.128712i	−0.221864	−	0.975078i	$-0.571214\pi$
$379$	6.04944	−	2.50576i	0.310739	−	0.128712i	0.532603	+	0.846365i	$0.321214\pi$
$380$		0			0
$381$	5.75348	+	2.38317i	0.294760	+	0.122093i
$382$	9.03578	−	9.03578i	0.462311	−	0.462311i
$383$	−13.0036	+	13.0036i	−0.664451	+	0.664451i	−0.956426	−	0.291975i	$-0.905688\pi$
$383$	−13.0036	+	13.0036i	−0.664451	+	0.664451i	0.291975	+	0.956426i	$0.405688\pi$
$384$	−16.3287	−	6.76355i	−0.833269	−	0.345151i
$385$		0			0
$386$	−19.4374	+	8.05123i	−0.989337	+	0.409797i
$387$		−	63.4115i		−	3.22339i
$388$	−5.39865	−	13.0335i	−0.274075	−	0.661676i
$389$	1.52050	+	1.52050i	0.0770922	+	0.0770922i	0.744602	−	0.667509i	$-0.232640\pi$
$389$	1.52050	+	1.52050i	0.0770922	+	0.0770922i	−0.667509	+	0.744602i	$0.732640\pi$
$390$		0			0
$391$	1.66185	+	2.19076i	0.0840433	+	0.110791i
$392$	18.6185			0.940375
$393$	16.3921	+	16.3921i	0.826872	+	0.826872i
$394$	3.21605	+	7.76423i	0.162022	+	0.391156i
$395$		0			0
$396$	−14.5131	+	6.01154i	−0.729313	+	0.302091i
$397$	−0.148348	+	0.358143i	−0.00744535	+	0.0179747i	−0.927558	−	0.373678i	$-0.878097\pi$
$397$	−0.148348	+	0.358143i	−0.00744535	+	0.0179747i	0.920113	+	0.391653i	$0.128097\pi$
$398$	−6.31484	−	2.61569i	−0.316534	−	0.131113i
$399$	0.300500	−	0.300500i	0.0150438	−	0.0150438i
$400$		0			0
$401$	−15.4465	−	6.39816i	−0.771362	−	0.319509i	−0.0379382	−	0.999280i	$-0.512079\pi$
$401$	−15.4465	−	6.39816i	−0.771362	−	0.319509i	−0.733424	+	0.679771i	$0.762079\pi$
$402$	5.60099	−	13.5220i	0.279352	−	0.674415i
$403$	−32.3584	+	13.4033i	−1.61188	+	0.667665i
$404$			11.9066i			0.592374i
$405$		0			0
$406$	3.68717	+	3.68717i	0.182991	+	0.182991i
$407$	−19.8906			−0.985943
$408$	−27.2333	+	20.6584i	−1.34825	+	1.02274i
$409$	−15.7306			−0.777828			−0.388914	−	0.921274i	$-0.627150\pi$
$409$	−15.7306			−0.777828			−0.388914	+	0.921274i	$0.627150\pi$
$410$		0			0
$411$	−8.67951	−	20.9542i	−0.428129	−	1.03359i
$412$			11.6025i			0.571613i
$413$	2.26513	−	0.938249i	0.111460	−	0.0461682i
$414$	1.22344	−	2.95364i	0.0601287	−	0.145164i
$415$		0			0
$416$	24.6764	−	24.6764i	1.20986	−	1.20986i
$417$	−35.5821	+	35.5821i	−1.74246	+	1.74246i
$418$	−0.424100	−	0.175668i	−0.0207434	−	0.00859220i
$419$	−4.06462	+	9.81286i	−0.198570	+	0.479390i	−0.991529	−	0.129885i	$-0.958539\pi$
$419$	−4.06462	+	9.81286i	−0.198570	+	0.479390i	0.792959	+	0.609274i	$0.208539\pi$
$420$		0			0
$421$			17.0231i			0.829656i	0.909900	+	0.414828i	$0.136158\pi$
$421$			17.0231i			0.829656i	−0.909900	+	0.414828i	$0.863842\pi$
$422$	−8.63499	−	20.8467i	−0.420345	−	1.01480i
$423$	40.9555	+	40.9555i	1.99132	+	1.99132i
$424$	−11.1507			−0.541526
$425$		0			0
$426$	10.3235			0.500178
$427$	0.583279	+	0.583279i	0.0282269	+	0.0282269i
$428$	−1.72718	−	4.16979i	−0.0834865	−	0.201554i
$429$		−	45.4261i		−	2.19320i
$430$		0			0
$431$	−7.53530	+	18.1918i	−0.362963	+	0.876270i	0.631901	+	0.775049i	$0.282275\pi$
$431$	−7.53530	+	18.1918i	−0.362963	+	0.876270i	−0.994864	+	0.101221i	$0.967725\pi$
$432$	1.43667	+	0.595087i	0.0691217	+	0.0286311i
$433$	15.5266	−	15.5266i	0.746159	−	0.746159i	−0.227597	−	0.973755i	$-0.573087\pi$
$433$	15.5266	−	15.5266i	0.746159	−	0.746159i	0.973755	+	0.227597i	$0.0730868\pi$
$434$	2.58447	−	2.58447i	0.124059	−	0.124059i
$435$		0			0
$436$	−1.45208	+	3.50563i	−0.0695419	+	0.167889i
$437$	−0.124991	+	0.0517732i	−0.00597915	+	0.00247665i
$438$		−	13.5152i		−	0.645779i
$439$	−3.25235	−	7.85186i	−0.155226	−	0.374749i	0.827066	−	0.562105i	$-0.190008\pi$
$439$	−3.25235	−	7.85186i	−0.155226	−	0.374749i	−0.982292	+	0.187356i	$0.940008\pi$
$440$		0			0
$441$	34.3227			1.63441
$442$	−5.94777	−	22.6991i	−0.282907	−	1.07969i
$443$	−4.70952			−0.223756			−0.111878	−	0.993722i	$-0.535687\pi$
$443$	−4.70952			−0.223756			−0.111878	+	0.993722i	$0.535687\pi$
$444$	−19.1520	−	19.1520i	−0.908912	−	0.908912i
$445$		0			0
$446$			10.9984i			0.520791i
$447$	−19.7781	+	8.19236i	−0.935472	+	0.387485i
$448$	−1.52398	+	3.67923i	−0.0720015	+	0.173827i
$449$	−24.2399	−	10.0405i	−1.14395	−	0.473839i	−0.271449	−	0.962453i	$-0.587503\pi$
$449$	−24.2399	−	10.0405i	−1.14395	−	0.473839i	−0.872500	+	0.488613i	$0.837503\pi$
$450$		0			0
$451$	9.07554	−	9.07554i	0.427351	−	0.427351i
$452$	−0.440789	−	0.182581i	−0.0207330	−	0.00858788i
$453$	−14.9016	+	35.9756i	−0.700138	+	1.69028i
$454$	−1.65883	+	0.687110i	−0.0778528	+	0.0322477i
$455$		0			0
$456$	−0.643591	−	1.55377i	−0.0301389	−	0.0727618i
$457$	−14.6247	−	14.6247i	−0.684115	−	0.684115i	0.276810	−	0.960925i	$-0.410723\pi$
$457$	−14.6247	−	14.6247i	−0.684115	−	0.684115i	−0.960925	+	0.276810i	$0.910723\pi$
$458$	−2.07163			−0.0968009
$459$	−21.8063	+	16.5416i	−1.01783	+	0.772098i
$460$		0			0
$461$	−1.37250	−	1.37250i	−0.0639239	−	0.0639239i	0.674422	−	0.738346i	$-0.264393\pi$
$461$	−1.37250	−	1.37250i	−0.0639239	−	0.0639239i	−0.738346	+	0.674422i	$0.764393\pi$
$462$	1.81410	+	4.37963i	0.0843996	+	0.203759i
$463$			10.6872i			0.496676i	0.968673	+	0.248338i	$0.0798844\pi$
$463$			10.6872i			0.496676i	−0.968673	+	0.248338i	$0.920116\pi$
$464$	1.71744	−	0.711389i	0.0797304	−	0.0330254i
$465$		0			0
$466$	−18.9581	−	7.85269i	−0.878216	−	0.363769i
$467$	−3.43207	+	3.43207i	−0.158817	+	0.158817i	−0.782042	−	0.623225i	$-0.785822\pi$
$467$	−3.43207	+	3.43207i	−0.158817	+	0.158817i	0.623225	+	0.782042i	$0.285822\pi$
$468$	27.9368	−	27.9368i	1.29138	−	1.29138i
$469$	3.77432	+	1.56337i	0.174282	+	0.0721899i
$470$		0			0
$471$	−7.34214	+	3.04121i	−0.338308	+	0.140132i
$472$		−	9.70263i		−	0.446600i
$473$	−11.4549	−	27.6547i	−0.526699	−	1.27156i
$474$	25.8584	+	25.8584i	1.18772	+	1.18772i
$475$		0			0
$476$	−2.14317	−	2.82527i	−0.0982321	−	0.129496i
$477$	−20.5560			−0.941196
$478$	−8.45458	−	8.45458i	−0.386703	−	0.386703i
$479$	2.91185	+	7.02983i	0.133046	+	0.321201i	0.976337	−	0.216256i	$-0.0693847\pi$
$479$	2.91185	+	7.02983i	0.133046	+	0.321201i	−0.843291	+	0.537458i	$0.819385\pi$
$480$		0			0
$481$	46.2179	−	19.1441i	2.10736	−	0.872895i
$482$	1.00282	−	2.42101i	0.0456770	−	0.110274i
$483$	1.29077	+	0.534655i	0.0587321	+	0.0243276i
$484$	3.95860	−	3.95860i	0.179937	−	0.179937i
$485$		0			0
$486$	−8.88654	−	3.68093i	−0.403102	−	0.166970i
$487$	0.162865	−	0.393190i	0.00738010	−	0.0178171i	−0.920147	−	0.391574i	$-0.871931\pi$
$487$	0.162865	−	0.393190i	0.00738010	−	0.0178171i	0.927527	+	0.373757i	$0.121931\pi$
$488$	3.01591	−	1.24923i	0.136524	−	0.0565500i
$489$		−	3.98733i		−	0.180313i
$490$		0			0
$491$	0.197439	+	0.197439i	0.00891028	+	0.00891028i	0.711548	−	0.702638i	$-0.247994\pi$
$491$	0.197439	+	0.197439i	0.00891028	+	0.00891028i	−0.702638	+	0.711548i	$0.747994\pi$
$492$	17.4770			0.787924
$493$	−4.45022	+	32.4156i	−0.200428	+	1.45992i
$494$	1.15451			0.0519440
$495$		0			0
$496$	−0.498639	−	1.20382i	−0.0223895	−	0.0540531i
$497$			2.88156i			0.129256i
$498$	29.7161	−	12.3088i	1.33161	−	0.551571i
$499$	7.08936	−	17.1152i	0.317363	−	0.766183i	−0.682029	−	0.731325i	$-0.738902\pi$
$499$	7.08936	−	17.1152i	0.317363	−	0.766183i	0.999392	−	0.0348579i	$-0.0110979\pi$
$500$		0			0
$501$	−29.9207	+	29.9207i	−1.33676	+	1.33676i
$502$	−6.29815	+	6.29815i	−0.281100	+	0.281100i
$503$	7.50624	+	3.10919i	0.334687	+	0.138632i	0.543697	−	0.839282i	$-0.317024\pi$
$503$	7.50624	+	3.10919i	0.334687	+	0.138632i	−0.209010	+	0.977913i	$0.567024\pi$
$504$	−4.24508	+	10.2485i	−0.189091	+	0.456506i
$505$		0			0
$506$		−	1.50913i		−	0.0670891i
$507$	29.3855	+	70.9428i	1.30505	+	3.15068i
$508$	1.80789	+	1.80789i	0.0802120	+	0.0802120i
$509$	15.1877			0.673181			0.336590	−	0.941651i	$-0.390726\pi$
$509$	15.1877			0.673181			0.336590	+	0.941651i	$0.390726\pi$
$510$		0			0
$511$	3.77241			0.166882
$512$	1.87113	+	1.87113i	0.0826930	+	0.0826930i
$513$	−0.515338	−	1.24414i	−0.0227527	−	0.0549299i
$514$		−	4.78077i		−	0.210871i
$515$		0			0
$516$	15.5981	−	37.6572i	0.686669	−	1.65777i
$517$	25.2596	+	10.4629i	1.11092	+	0.460157i
$518$	−3.69144	+	3.69144i	−0.162193	+	0.162193i
$519$	30.0531	−	30.0531i	1.31918	−	1.31918i
$520$		0			0
$521$	−14.2931	+	34.5065i	−0.626190	+	1.51176i	0.218131	+	0.975919i	$0.430004\pi$
$521$	−14.2931	+	34.5065i	−0.626190	+	1.51176i	−0.844321	+	0.535837i	$0.819996\pi$
$522$	35.1457	−	14.5578i	1.53828	−	0.637178i
$523$			8.03541i			0.351364i	0.984447	+	0.175682i	$0.0562130\pi$
$523$			8.03541i			0.351364i	−0.984447	+	0.175682i	$0.943787\pi$
$524$	3.64217	+	8.79298i	0.159109	+	0.384123i
$525$		0			0
$526$	−11.3706			−0.495780
$527$	22.7213	+	3.11932i	0.989754	+	0.135880i
$528$	1.68998			0.0735469
$529$	15.9490	+	15.9490i	0.693433	+	0.693433i
$530$		0			0
$531$		−	17.8866i		−	0.776210i
$532$	0.161193	−	0.0667683i	0.00698860	−	0.00289477i
$533$	−12.3530	+	29.8228i	−0.535069	+	1.29177i
$534$	−31.3825	−	12.9991i	−1.35805	−	0.562524i
$535$		0			0
$536$	11.4319	−	11.4319i	0.493784	−	0.493784i
$537$	38.0075	+	15.7432i	1.64014	+	0.679370i
$538$	3.18306	−	7.68457i	0.137231	−	0.331306i
$539$	14.9686	−	6.20020i	0.644744	−	0.267062i
$540$		0			0
$541$	6.24786	+	15.0837i	0.268616	+	0.648498i	0.999419	−	0.0340917i	$-0.0108538\pi$
$541$	6.24786	+	15.0837i	0.268616	+	0.648498i	−0.730802	+	0.682589i	$0.760854\pi$
$542$	9.33259	+	9.33259i	0.400869	+	0.400869i
$543$	−17.3590			−0.744947
$544$	−22.1051	+	5.79213i	−0.947750	+	0.248336i
$545$		0			0
$546$	−8.43049	−	8.43049i	−0.360792	−	0.360792i
$547$	−11.0229	−	26.6116i	−0.471304	−	1.13783i	−0.963587	−	0.267394i	$-0.913838\pi$
$547$	−11.0229	−	26.6116i	−0.471304	−	1.13783i	0.492283	−	0.870435i	$-0.336162\pi$
$548$		−	9.31165i		−	0.397774i
$549$	5.55975	−	2.30292i	0.237284	−	0.0982864i
$550$		0			0
$551$	−1.48729	−	0.616054i	−0.0633605	−	0.0262448i
$552$	3.90958	−	3.90958i	0.166403	−	0.166403i
$553$	−7.21773	+	7.21773i	−0.306929	+	0.306929i
$554$	−10.9106	−	4.51931i	−0.463546	−	0.192007i
$555$		0			0
$556$	−19.0868	+	7.90601i	−0.809461	+	0.335290i
$557$			7.64838i			0.324072i	0.986785	+	0.162036i	$0.0518061\pi$
$557$			7.64838i			0.324072i	−0.986785	+	0.162036i	$0.948194\pi$
$558$	−10.2041	−	24.6349i	−0.431974	−	1.04288i
$559$	53.2334	+	53.2334i	2.25153	+	2.25153i
$560$		0			0
$561$	−15.0151	+	25.6777i	−0.633938	+	1.08411i
$562$	−6.83413			−0.288280
$563$	−29.9736	−	29.9736i	−1.26324	−	1.26324i	−0.949514	−	0.313724i	$-0.898423\pi$
$563$	−29.9736	−	29.9736i	−1.26324	−	1.26324i	−0.313724	−	0.949514i	$-0.601577\pi$
$564$	14.2472	+	34.3959i	0.599917	+	1.44833i
$565$		0			0
$566$	−3.43874	+	1.42437i	−0.144541	+	0.0598709i
$567$	−0.895263	+	2.16136i	−0.0375975	+	0.0907684i
$568$	10.5355	+	4.36393i	0.442058	+	0.183107i
$569$	−21.7924	+	21.7924i	−0.913584	+	0.913584i	−0.996552	−	0.0829686i	$-0.973560\pi$
$569$	−21.7924	+	21.7924i	−0.913584	+	0.913584i	0.0829686	+	0.996552i	$0.473560\pi$
$570$		0			0
$571$	−20.3678	−	8.43662i	−0.852366	−	0.353062i	−0.0866487	−	0.996239i	$-0.527616\pi$
$571$	−20.3678	−	8.43662i	−0.852366	−	0.353062i	−0.765717	+	0.643177i	$0.777616\pi$
$572$	7.13702	−	17.2303i	0.298414	−	0.720434i
$573$	37.6388	−	15.5905i	1.57238	−	0.651303i
$574$		−	3.36860i		−	0.140603i
$575$		0			0
$576$	20.5435	+	20.5435i	0.855979	+	0.855979i
$577$	20.2437			0.842755			0.421378	−	0.906885i	$-0.361547\pi$
$577$	20.2437			0.842755			0.421378	+	0.906885i	$0.361547\pi$
$578$	−4.14088	+	14.7969i	−0.172238	+	0.615471i
$579$	−67.0753			−2.78755
$580$		0			0
$581$	3.43569	+	8.29450i	0.142537	+	0.344114i
$582$			31.0577i			1.28738i
$583$	−8.96478	+	3.71333i	−0.371283	+	0.153791i
$584$	5.71308	−	13.7926i	0.236409	−	0.570742i
$585$		0			0
$586$	−11.8750	+	11.8750i	−0.490551	+	0.490551i
$587$	−9.02526	+	9.02526i	−0.372513	+	0.372513i	−0.868392	−	0.495879i	$-0.834846\pi$
$587$	−9.02526	+	9.02526i	−0.372513	+	0.372513i	0.495879	+	0.868392i	$0.334846\pi$
$588$	20.3827	+	8.44278i	0.840567	+	0.348174i
$589$	−0.431815	+	1.04249i	−0.0177926	+	0.0429552i
$590$		0			0
$591$			26.7931i			1.10212i
$592$	0.712213	+	1.71943i	0.0292718	+	0.0706683i
$593$	2.03582	+	2.03582i	0.0836009	+	0.0836009i	0.747671	−	0.664070i	$-0.231172\pi$
$593$	2.03582	+	2.03582i	0.0836009	+	0.0836009i	−0.664070	+	0.747671i	$0.731172\pi$
$594$	15.0216			0.616342
$595$		0			0
$596$	−8.78902			−0.360012
$597$	−15.4089	−	15.4089i	−0.630645	−	0.630645i
$598$	1.45249	+	3.50662i	0.0593967	+	0.143396i
$599$		−	12.6720i		−	0.517762i	−0.965909	−	0.258881i	$-0.916646\pi$
$599$		−	12.6720i		−	0.517762i	0.965909	−	0.258881i	$-0.0833538\pi$
$600$		0			0
$601$	−5.25226	+	12.6801i	−0.214244	+	0.517231i	−0.994067	−	0.108769i	$-0.965309\pi$
$601$	−5.25226	+	12.6801i	−0.214244	+	0.517231i	0.779823	+	0.626000i	$0.215309\pi$
$602$	−7.25822	−	3.00645i	−0.295823	−	0.122534i
$603$	21.0745	−	21.0745i	0.858219	−	0.858219i
$604$	−11.3045	+	11.3045i	−0.459972	+	0.459972i
$605$		0			0
$606$	10.0311	−	24.2173i	0.407487	−	0.983760i
$607$	−7.20998	+	2.98647i	−0.292644	+	0.121217i	−0.524175	−	0.851610i	$-0.675626\pi$
$607$	−7.20998	+	2.98647i	−0.292644	+	0.121217i	0.231531	+	0.972827i	$0.425626\pi$
$608$		−	1.12430i		−	0.0455965i
$609$	6.36191	+	15.3590i	0.257798	+	0.622379i
$610$		0			0
$611$	−68.7635			−2.78187
$612$	−25.0258	+	6.55744i	−1.01161	+	0.265069i
$613$	−44.7999			−1.80945			−0.904726	−	0.425994i	$-0.859924\pi$
$613$	−44.7999			−1.80945			−0.904726	+	0.425994i	$0.859924\pi$
$614$	−6.28011	−	6.28011i	−0.253445	−	0.253445i
$615$		0			0
$616$			5.23638i			0.210980i
$617$	−19.9388	+	8.25893i	−0.802707	+	0.332492i	−0.746040	−	0.665901i	$-0.768047\pi$
$617$	−19.9388	+	8.25893i	−0.802707	+	0.332492i	−0.0566667	+	0.998393i	$0.518047\pi$
$618$	9.77495	−	23.5988i	0.393206	−	0.949284i
$619$	35.6401	+	14.7626i	1.43250	+	0.593360i	0.957967	−	0.286879i	$-0.0926179\pi$
$619$	35.6401	+	14.7626i	1.43250	+	0.593360i	0.474530	+	0.880239i	$0.342618\pi$
$620$		0			0
$621$	3.13049	−	3.13049i	0.125622	−	0.125622i
$622$	−23.9561	−	9.92293i	−0.960551	−	0.397873i
$623$	3.62836	−	8.75963i	0.145367	−	0.350947i
$624$	−3.92683	+	1.62655i	−0.157199	+	0.0651140i
$625$		0			0
$626$	0.335042	+	0.808864i	0.0133910	+	0.0323287i
$627$	−1.03485	−	1.03485i	−0.0413280	−	0.0413280i
$628$	−3.26271			−0.130196
$629$	−32.4531	−	4.45538i	−1.29399	−	0.177647i
$630$		0			0
$631$	17.1283	+	17.1283i	0.681866	+	0.681866i	0.960420	−	0.278555i	$-0.0898553\pi$
$631$	17.1283	+	17.1283i	0.681866	+	0.681866i	−0.278555	+	0.960420i	$0.589855\pi$
$632$	15.4585	+	37.3200i	0.614904	+	1.48451i
$633$		−	71.9387i		−	2.85931i
$634$	22.1495	−	9.17461i	0.879668	−	0.364370i
$635$		0			0
$636$	−12.2073	−	5.05642i	−0.484050	−	0.200500i
$637$	−28.8136	+	28.8136i	−1.14164	+	1.14164i
$638$	12.6977	−	12.6977i	0.502708	−	0.502708i
$639$	19.4219	+	8.04480i	0.768317	+	0.318247i
$640$		0			0
$641$	40.1257	−	16.6206i	1.58487	−	0.656475i	0.595694	−	0.803211i	$-0.296877\pi$
$641$	40.1257	−	16.6206i	1.58487	−	0.656475i	0.989176	+	0.146737i	$0.0468770\pi$
$642$			9.93625i			0.392152i
$643$	13.5786	+	32.7815i	0.535486	+	1.29278i	0.927845	+	0.372965i	$0.121659\pi$
$643$	13.5786	+	32.7815i	0.535486	+	1.29278i	−0.392359	+	0.919812i	$0.628341\pi$
$644$	0.405593	+	0.405593i	0.0159826	+	0.0159826i
$645$		0			0
$646$	−0.652603	−	0.381611i	−0.0256763	−	0.0150143i
$647$	−28.2269			−1.10971			−0.554857	−	0.831946i	$-0.687227\pi$
$647$	−28.2269			−1.10971			−0.554857	+	0.831946i	$0.687227\pi$
$648$	6.54647	+	6.54647i	0.257170	+	0.257170i
$649$	−3.23111	−	7.80059i	−0.126832	−	0.306200i
$650$		0			0
$651$	10.7657	−	4.45930i	0.421941	−	0.174774i
$652$	0.626459	−	1.51241i	0.0245340	−	0.0592304i
$653$	3.44513	+	1.42702i	0.134818	+	0.0558436i	0.449073	−	0.893495i	$-0.351754\pi$
$653$	3.44513	+	1.42702i	0.134818	+	0.0558436i	−0.314254	+	0.949339i	$0.601754\pi$
$654$	5.90689	−	5.90689i	0.230978	−	0.230978i
$655$		0			0
$656$	−1.10949	−	0.459567i	−0.0433184	−	0.0179431i
$657$	10.5319	−	25.4263i	0.410889	−	0.991974i
$658$	6.62962	−	2.74608i	0.258450	−	0.107053i
$659$			16.0238i			0.624200i	0.950049	+	0.312100i	$0.101032\pi$
$659$			16.0238i			0.624200i	−0.950049	+	0.312100i	$0.898968\pi$
$660$		0			0
$661$	−19.4741	−	19.4741i	−0.757454	−	0.757454i	0.218404	−	0.975858i	$-0.429915\pi$
$661$	−19.4741	−	19.4741i	−0.757454	−	0.757454i	−0.975858	+	0.218404i	$0.929915\pi$
$662$	−5.53698			−0.215201
$663$	10.1752	−	74.1162i	0.395171	−	2.87844i
$664$	35.5292			1.37880
$665$		0			0
$666$	14.5747	+	35.1864i	0.564757	+	1.36344i
$667$		−	5.29241i		−	0.204923i
$668$	−16.0500	+	6.64811i	−0.620991	+	0.257223i
$669$	−13.4187	+	32.3956i	−0.518797	+	1.25249i
$670$		0			0
$671$	2.00868	−	2.00868i	0.0775441	−	0.0775441i
$672$	−8.20989	+	8.20989i	−0.316703	+	0.316703i
$673$	−17.4988	−	7.24825i	−0.674530	−	0.279400i	0.0190080	−	0.999819i	$-0.493949\pi$
$673$	−17.4988	−	7.24825i	−0.674530	−	0.279400i	−0.693538	+	0.720420i	$0.743949\pi$
$674$	−5.49103	+	13.2565i	−0.211507	+	0.510622i
$675$		0			0
$676$			31.5257i			1.21253i
$677$	−4.05297	−	9.78472i	−0.155768	−	0.376058i	0.826659	−	0.562703i	$-0.190238\pi$
$677$	−4.05297	−	9.78472i	−0.155768	−	0.376058i	−0.982427	+	0.186645i	$0.940238\pi$
$678$	0.742719	+	0.742719i	0.0285240	+	0.0285240i
$679$	−8.66898			−0.332685
$680$		0			0
$681$	−5.72436			−0.219358
$682$	−8.90032	−	8.90032i	−0.340811	−	0.340811i
$683$	17.2457	+	41.6347i	0.659887	+	1.59311i	0.797977	+	0.602688i	$0.205904\pi$
$683$	17.2457	+	41.6347i	0.659887	+	1.59311i	−0.138090	+	0.990420i	$0.544096\pi$
$684$		−	1.27285i		−	0.0486688i
$685$		0			0
$686$	3.38750	−	8.17815i	0.129335	−	0.312243i
$687$	−6.10193	−	2.52750i	−0.232803	−	0.0964303i
$688$	−1.98043	+	1.98043i	−0.0755031	+	0.0755031i
$689$	17.2566	−	17.2566i	0.657424	−	0.657424i
$690$		0			0
$691$	−4.99288	+	12.0539i	−0.189938	+	0.458551i	−0.989947	−	0.141437i	$-0.954828\pi$
$691$	−4.99288	+	12.0539i	−0.189938	+	0.458551i	0.800009	+	0.599988i	$0.204828\pi$
$692$	16.1209	−	6.67752i	0.612827	−	0.253841i
$693$			9.65314i			0.366692i
$694$	0.589181	+	1.42241i	0.0223650	+	0.0539939i
$695$		0			0
$696$	65.7899			2.49376
$697$	16.8403	−	12.7746i	0.637872	−	0.483872i
$698$	−31.8643			−1.20608
$699$	−46.2598	−	46.2598i	−1.74971	−	1.74971i
$700$		0			0
$701$			4.42228i			0.167027i	0.996507	+	0.0835136i	$0.0266142\pi$
$701$			4.42228i			0.167027i	−0.996507	+	0.0835136i	$0.973386\pi$
$702$	−34.9041	+	14.4577i	−1.31737	+	0.545672i
$703$	0.616767	−	1.48901i	0.0232618	−	0.0561590i
$704$	12.6704	+	5.24825i	0.477533	+	0.197801i
$705$		0			0
$706$	−14.3755	+	14.3755i	−0.541030	+	0.541030i
$707$	6.75965	+	2.79994i	0.254223	+	0.105302i
$708$	4.39978	−	10.6220i	0.165354	−	0.399200i
$709$	−29.6088	+	12.2644i	−1.11198	+	0.460597i	−0.861619	−	0.507555i	$-0.830549\pi$
$709$	−29.6088	+	12.2644i	−1.11198	+	0.460597i	−0.250361	+	0.968152i	$0.580549\pi$
$710$		0			0
$711$	28.4973	+	68.7985i	1.06873	+	2.58015i
$712$	−26.5318	−	26.5318i	−0.994321	−	0.994321i
$713$	−3.70965			−0.138927
$714$	1.97884	+	7.55204i	0.0740561	+	0.282628i
$715$		0			0
$716$	11.9429	+	11.9429i	0.446327	+	0.446327i
$717$	−14.5877	−	35.2178i	−0.544787	−	1.31523i
$718$			16.2728i			0.607294i
$719$	25.6163	−	10.6106i	0.955329	−	0.395710i	0.150098	−	0.988671i	$-0.452041\pi$
$719$	25.6163	−	10.6106i	0.955329	−	0.395710i	0.805231	+	0.592961i	$0.202041\pi$
$720$		0			0
$721$	6.58702	+	2.72843i	0.245313	+	0.101612i
$722$	−12.1169	+	12.1169i	−0.450945	+	0.450945i
$723$	5.90754	−	5.90754i	0.219704	−	0.219704i
$724$	−6.58434	−	2.72732i	−0.244705	−	0.101360i
$725$		0			0
$726$	−11.3867	+	4.71651i	−0.422599	+	0.175046i
$727$			10.5407i			0.390934i	0.980710	+	0.195467i	$0.0626222\pi$
$727$			10.5407i			0.390934i	−0.980710	+	0.195467i	$0.937378\pi$
$728$	−5.03984	−	12.1673i	−0.186789	−	0.450948i
$729$	−28.5105	−	28.5105i	−1.05594	−	1.05594i
$730$		0			0
$731$	−12.4951	−	47.6865i	−0.462150	−	1.76375i
$732$	3.86816			0.142971
$733$	−11.6126	−	11.6126i	−0.428920	−	0.428920i	0.459340	−	0.888260i	$-0.348086\pi$
$733$	−11.6126	−	11.6126i	−0.428920	−	0.428920i	−0.888260	+	0.459340i	$0.848086\pi$
$734$	−10.8201	−	26.1219i	−0.399376	−	0.964178i
$735$		0			0
$736$	3.41486	−	1.41448i	0.125873	−	0.0521385i
$737$	5.38389	−	12.9979i	0.198318	−	0.478783i
$738$	−22.7046	−	9.40454i	−0.835767	−	0.346186i
$739$	1.27919	−	1.27919i	0.0470556	−	0.0470556i	−0.683187	−	0.730243i	$-0.739407\pi$
$739$	1.27919	−	1.27919i	0.0470556	−	0.0470556i	0.730243	+	0.683187i	$0.239407\pi$
$740$		0			0
$741$	3.40059	+	1.40857i	0.124924	+	0.0517451i
$742$	−0.974598	+	2.35289i	−0.0357786	+	0.0863773i
$743$	−39.8234	+	16.4954i	−1.46098	+	0.605157i	−0.964782	−	0.263052i	$-0.915271\pi$
$743$	−39.8234	+	16.4954i	−1.46098	+	0.605157i	−0.496198	+	0.868210i	$0.665271\pi$
$744$		−	46.1146i		−	1.69064i
$745$		0			0
$746$	−15.5639	−	15.5639i	−0.569833	−	0.569833i
$747$	65.4973			2.39642
$748$	−9.72957	+	7.38058i	−0.355748	+	0.269861i
$749$	−2.77345			−0.101340
$750$		0			0
$751$	−11.2128	−	27.0700i	−0.409160	−	0.987799i	−0.985359	−	0.170490i	$-0.945465\pi$
$751$	−11.2128	−	27.0700i	−0.409160	−	0.987799i	0.576199	−	0.817309i	$-0.304535\pi$
$752$		−	2.55819i		−	0.0932876i
$753$	−26.2351	+	10.8669i	−0.956061	+	0.396013i
$754$	−17.2833	+	41.7256i	−0.629421	+	1.51956i
$755$		0			0
$756$	−4.03717	+	4.03717i	−0.146831	+	0.146831i
$757$	7.31966	−	7.31966i	0.266038	−	0.266038i	−0.561464	−	0.827501i	$-0.689762\pi$
$757$	7.31966	−	7.31966i	0.266038	−	0.266038i	0.827501	+	0.561464i	$0.189762\pi$
$758$	−5.46777	−	2.26483i	−0.198598	−	0.0822622i
$759$	1.84123	−	4.44511i	0.0668323	−	0.161347i
$760$		0			0
$761$			40.0677i			1.45245i	0.687455	+	0.726227i	$0.258728\pi$
$761$			40.0677i			1.45245i	−0.687455	+	0.726227i	$0.741272\pi$
$762$	−2.15402	−	5.20027i	−0.0780319	−	0.188386i
$763$	1.64876	+	1.64876i	0.0596891	+	0.0596891i
$764$	16.7260			0.605125
$765$		0			0
$766$	16.6216			0.600562
$767$	15.0156	+	15.0156i	0.542182	+	0.542182i
$768$	18.1946	+	43.9257i	0.656542	+	1.58503i
$769$			40.8532i			1.47320i	0.676327	+	0.736602i	$0.263571\pi$
$769$			40.8532i			1.47320i	−0.676327	+	0.736602i	$0.736429\pi$
$770$		0			0
$771$	5.83281	−	14.0816i	0.210063	−	0.507138i
$772$	−25.4419	−	10.5384i	−0.915673	−	0.379284i
$773$	12.0994	−	12.0994i	0.435183	−	0.435183i	−0.455204	−	0.890387i	$-0.650434\pi$
$773$	12.0994	−	12.0994i	0.435183	−	0.435183i	0.890387	+	0.455204i	$0.150434\pi$
$774$	−40.5273	+	40.5273i	−1.45673	+	1.45673i
$775$		0			0
$776$	−13.1286	+	31.6953i	−0.471290	+	1.13779i
$777$	−15.3768	+	6.36928i	−0.551640	+	0.228497i
$778$		−	1.94355i		−	0.0696796i
$779$	0.397979	+	0.960806i	0.0142591	+	0.0344245i
$780$		0			0
$781$	9.92341			0.355087
$782$	0.338036	−	2.46227i	0.0120881	−	0.0880504i
$783$	52.6794			1.88261
$784$	−1.07194	−	1.07194i	−0.0382837	−	0.0382837i
$785$		0			0
$786$		−	20.9529i		−	0.747366i
$787$	17.0188	−	7.04943i	0.606655	−	0.251285i	−0.0581423	−	0.998308i	$-0.518518\pi$
$787$	17.0188	−	7.04943i	0.606655	−	0.251285i	0.664798	+	0.747023i	$0.268518\pi$
$788$	−4.20953	+	10.1627i	−0.149958	+	0.362031i
$789$	−33.4917	−	13.8727i	−1.19234	−	0.493882i
$790$		0			0
$791$	−0.207311	+	0.207311i	−0.00737114	+	0.00737114i
$792$	35.2935	+	14.6191i	1.25410	+	0.519465i
$793$	−2.73408	+	6.60064i	−0.0970899	+	0.234396i
$794$	0.323707	−	0.134084i	0.0114879	−	0.00475845i
$795$		0			0
$796$	−3.42372	−	8.26559i	−0.121350	−	0.292966i
$797$	20.2228	+	20.2228i	0.716328	+	0.716328i	0.967851	−	0.251523i	$-0.0809314\pi$
$797$	20.2228	+	20.2228i	0.716328	+	0.716328i	−0.251523	+	0.967851i	$0.580931\pi$
$798$	−0.384109			−0.0135973
$799$	38.8694	+	22.7290i	1.37510	+	0.804094i
$800$		0			0
$801$	−48.9107	−	48.9107i	−1.72817	−	1.72817i
$802$	5.78296	+	13.9613i	0.204203	+	0.492991i
$803$		−	12.9913i		−	0.458453i
$804$	17.6991	−	7.33121i	0.624200	−	0.258552i
$805$		0			0
$806$	29.2470	+	12.1145i	1.03018	+	0.426716i
$807$	18.7512	−	18.7512i	0.660074	−	0.660074i
$808$	20.4741	−	20.4741i	0.720276	−	0.720276i
$809$	−25.1095	−	10.4007i	−0.882801	−	0.365668i	−0.105219	−	0.994449i	$-0.533554\pi$
$809$	−25.1095	−	10.4007i	−0.882801	−	0.365668i	−0.777583	+	0.628781i	$0.783554\pi$
$810$		0			0
$811$	17.5782	−	7.28112i	0.617254	−	0.255675i	−0.0520727	−	0.998643i	$-0.516583\pi$
$811$	17.5782	−	7.28112i	0.617254	−	0.255675i	0.669326	+	0.742968i	$0.266583\pi$
$812$			6.82526i			0.239520i
$813$	16.1026	+	38.8752i	0.564744	+	1.36341i
$814$	12.7124	+	12.7124i	0.445571	+	0.445571i
$815$		0			0
$816$	2.75733	+	0.378544i	0.0965258	+	0.0132517i
$817$	2.42541			0.0848545
$818$	10.0537	+	10.0537i	0.351519	+	0.351519i
$819$	−9.29082	−	22.4300i	−0.324648	−	0.783768i
$820$		0			0
$821$	−26.6213	+	11.0269i	−0.929089	+	0.384841i	−0.795333	−	0.606173i	$-0.792704\pi$
$821$	−26.6213	+	11.0269i	−0.929089	+	0.384841i	−0.133756	+	0.991014i	$0.542704\pi$
$822$	−7.84495	+	18.9394i	−0.273624	+	0.660587i
$823$	38.5431	+	15.9651i	1.34353	+	0.556507i	0.934483	−	0.356007i	$-0.115862\pi$
$823$	38.5431	+	15.9651i	1.34353	+	0.556507i	0.409044	+	0.912514i	$0.365862\pi$
$824$	19.9512	−	19.9512i	0.695034	−	0.695034i
$825$		0			0
$826$	−2.04734	−	0.848034i	−0.0712359	−	0.0295069i
$827$	−10.3591	+	25.0091i	−0.360221	+	0.869650i	0.635046	+	0.772474i	$0.280981\pi$
$827$	−10.3591	+	25.0091i	−0.360221	+	0.869650i	−0.995267	+	0.0971760i	$0.969019\pi$
$828$	3.86606	−	1.60138i	0.134355	−	0.0556516i
$829$		−	21.8341i		−	0.758331i	−0.925329	−	0.379165i	$-0.876211\pi$
$829$		−	21.8341i		−	0.758331i	0.925329	−	0.379165i	$-0.123789\pi$
$830$		0			0
$831$	−26.6230	−	26.6230i	−0.923542	−	0.923542i
$832$	−34.4922			−1.19580
$833$	25.8112	−	6.76324i	0.894307	−	0.234332i
$834$	45.4822			1.57492
$835$		0			0
$836$	−0.229934	−	0.555110i	−0.00795244	−	0.0191989i
$837$		−	36.9250i		−	1.27631i
$838$	8.86933	−	3.67380i	0.306386	−	0.126909i
$839$	17.4844	−	42.2111i	0.603629	−	1.45729i	−0.266191	−	0.963920i	$-0.585765\pi$
$839$	17.4844	−	42.2111i	0.603629	−	1.45729i	0.869820	−	0.493369i	$-0.164235\pi$
$840$		0			0
$841$	24.0239	−	24.0239i	0.828411	−	0.828411i
$842$	10.8798	−	10.8798i	0.374942	−	0.374942i
$843$	−20.1298	−	8.33802i	−0.693305	−	0.287177i
$844$	11.3025	−	27.2866i	0.389047	−	0.939243i
$845$		0			0
$846$		−	52.3506i		−	1.79985i
$847$	−1.31649	−	3.17830i	−0.0452353	−	0.109208i
$848$	0.641993	+	0.641993i	0.0220461	+	0.0220461i
$849$	−11.8665			−0.407259
$850$		0			0
$851$	5.29854			0.181632
$852$	9.55488	+	9.55488i	0.327345	+	0.327345i
$853$	−0.0371375	−	0.0896578i	−0.00127156	−	0.00306983i	0.923242	−	0.384218i	$-0.125529\pi$
$853$	−0.0371375	−	0.0896578i	−0.00127156	−	0.00306983i	−0.924514	+	0.381148i	$0.875529\pi$
$854$		−	0.745567i		−	0.0255128i
$855$		0			0
$856$	−4.20022	+	10.1402i	−0.143560	+	0.346585i
$857$	43.2082	+	17.8974i	1.47596	+	0.611364i	0.968210	−	0.250139i	$-0.0804762\pi$
$857$	43.2082	+	17.8974i	1.47596	+	0.611364i	0.507753	+	0.861503i	$0.330476\pi$
$858$	−29.0326	+	29.0326i	−0.991157	+	0.991157i
$859$	−18.6065	+	18.6065i	−0.634845	+	0.634845i	−0.949279	−	0.314434i	$-0.898185\pi$
$859$	−18.6065	+	18.6065i	−0.634845	+	0.634845i	0.314434	+	0.949279i	$0.398185\pi$
$860$		0			0
$861$	4.10988	−	9.92213i	0.140064	−	0.338145i
$862$	16.4426	−	6.81077i	0.560039	−	0.231976i
$863$		−	33.5202i		−	1.14104i	−0.821284	−	0.570520i	$-0.806742\pi$
$863$		−	33.5202i		−	1.14104i	0.821284	−	0.570520i	$-0.193258\pi$
$864$	14.0794	+	33.9907i	0.478992	+	1.15639i
$865$		0			0
$866$	−19.8466			−0.674414
$867$	−30.2499	+	38.5319i	−1.02734	+	1.30861i
$868$	4.78408			0.162382
$869$	24.8561	+	24.8561i	0.843187	+	0.843187i
$870$		0			0
$871$			35.3837i			1.19893i
$872$	8.52509	−	3.53121i	0.288696	−	0.119582i
$873$	−24.2023	+	58.4295i	−0.819123	+	1.97754i
$874$	0.112973	+	0.0467950i	0.00382138	+	0.00158287i
$875$		0			0
$876$	12.5088	−	12.5088i	0.422635	−	0.422635i
$877$	−3.66588	−	1.51846i	−0.123788	−	0.0512747i	0.319930	−	0.947441i	$-0.396341\pi$
$877$	−3.66588	−	1.51846i	−0.123788	−	0.0512747i	−0.443718	+	0.896167i	$0.646341\pi$
$878$	−2.93963	+	7.09689i	−0.0992076	+	0.239508i
$879$	−49.4656	+	20.4893i	−1.66843	+	0.691088i
$880$		0			0
$881$	−17.1301	−	41.3558i	−0.577129	−	1.39331i	−0.895378	−	0.445306i	$-0.853095\pi$
$881$	−17.1301	−	41.3558i	−0.577129	−	1.39331i	0.318249	−	0.948007i	$-0.396905\pi$
$882$	−21.9362	−	21.9362i	−0.738630	−	0.738630i
$883$	6.22372			0.209445			0.104722	−	0.994501i	$-0.466605\pi$
$883$	6.22372			0.209445			0.104722	+	0.994501i	$0.466605\pi$
$884$	15.5041	−	26.5139i	0.521458	−	0.891759i
$885$		0			0
$886$	3.00993	+	3.00993i	0.101121	+	0.101121i
$887$	6.44546	+	15.5607i	0.216417	+	0.522478i	0.994385	−	0.105827i	$-0.0337491\pi$
$887$	6.44546	+	15.5607i	0.216417	+	0.522478i	−0.777967	+	0.628305i	$0.783749\pi$
$888$			65.8661i			2.21032i
$889$	1.45152	−	0.601240i	0.0486825	−	0.0201650i
$890$		0			0
$891$	7.44320	+	3.08308i	0.249357	+	0.103287i
$892$	−10.1795	+	10.1795i	−0.340835	+	0.340835i
$893$	−1.56650	+	1.56650i	−0.0524208	+	0.0524208i
$894$	17.8764	+	7.40465i	0.597876	+	0.247648i
$895$		0			0
$896$	−4.11950	+	1.70635i	−0.137623	+	0.0570052i
$897$			12.1008i			0.404033i
$898$	9.07506	+	21.9091i	0.302839	+	0.731118i
$899$	−31.2127	−	31.2127i	−1.04100	−	1.04100i
$900$		0			0
$901$	−15.4585	+	4.05054i	−0.514997	+	0.134943i
$902$	−11.6007			−0.386260
$903$	−17.7109	−	17.7109i	−0.589381	−	0.589381i
$904$	0.444006	+	1.07193i	0.0147674	+	0.0356517i
$905$		0			0
$906$	32.5165	−	13.4688i	1.08029	−	0.447470i
$907$	11.0738	−	26.7345i	0.367699	−	0.887705i	−0.626427	−	0.779480i	$-0.715483\pi$
$907$	11.0738	−	26.7345i	0.367699	−	0.887705i	0.994126	−	0.108225i	$-0.0345167\pi$
$908$	−2.17127	−	0.899369i	−0.0720561	−	0.0298466i
$909$	37.7435	−	37.7435i	1.25187	−	1.25187i
$910$		0			0
$911$	14.2044	+	5.88367i	0.470614	+	0.194935i	0.605370	−	0.795944i	$-0.293025\pi$
$911$	14.2044	+	5.88367i	0.470614	+	0.194935i	−0.134756	+	0.990879i	$0.543025\pi$
$912$	−0.0524027	+	0.126511i	−0.00173523	+	0.00418921i
$913$	28.5643	−	11.8317i	0.945340	−	0.391573i
$914$			18.6938i			0.618336i
$915$		0			0
$916$	−1.91738	−	1.91738i	−0.0633521	−	0.0633521i
$917$	5.84848			0.193134
$918$	24.5088	+	3.36473i	0.808911	+	0.111053i
$919$	9.89298			0.326339			0.163170	−	0.986598i	$-0.447828\pi$
$919$	9.89298			0.326339			0.163170	+	0.986598i	$0.447828\pi$
$920$		0			0
$921$	−10.8358	−	26.1600i	−0.357053	−	0.862002i
$922$			1.75438i			0.0577774i
$923$	−23.0580	+	9.55095i	−0.758964	+	0.314373i
$924$	−2.37450	+	5.73256i	−0.0781154	+	0.188587i
$925$		0			0
$926$	6.83036	−	6.83036i	0.224460	−	0.224460i
$927$	36.7796	−	36.7796i	1.20800	−	1.20800i
$928$	40.6338	+	16.8311i	1.33387	+	0.552507i
$929$	−2.76136	+	6.66651i	−0.0905973	+	0.218721i	−0.962683	−	0.270632i	$-0.912767\pi$
$929$	−2.76136	+	6.66651i	−0.0905973	+	0.218721i	0.872085	+	0.489354i	$0.162767\pi$
$930$		0			0
$931$			1.31280i			0.0430253i
$932$	−10.2785	−	24.8145i	−0.336684	−	0.812826i
$933$	−58.4555	−	58.4555i	−1.91375	−	1.91375i
$934$	4.38699			0.143547
$935$		0			0
$936$	−96.0783			−3.14042
$937$	3.46962	+	3.46962i	0.113348	+	0.113348i	0.761506	−	0.648158i	$-0.224460\pi$
$937$	3.46962	+	3.46962i	0.113348	+	0.113348i	−0.648158	+	0.761506i	$0.724460\pi$
$938$	−1.41305	−	3.41141i	−0.0461378	−	0.111386i
$939$			2.79126i			0.0910892i
$940$		0			0
$941$	10.0630	−	24.2941i	0.328043	−	0.791966i	−0.670695	−	0.741734i	$-0.734004\pi$
$941$	10.0630	−	24.2941i	0.328043	−	0.791966i	0.998738	−	0.0502322i	$-0.0159961\pi$
$942$	6.63617	+	2.74879i	0.216218	+	0.0895605i
$943$	−2.41758	+	2.41758i	−0.0787271	+	0.0787271i
$944$	−0.558622	+	0.558622i	−0.0181816	+	0.0181816i
$945$		0			0
$946$	−10.3535	+	24.9956i	−0.336622	+	0.812677i
$947$	30.5201	−	12.6418i	0.991770	−	0.410804i	0.172997	−	0.984922i	$-0.444655\pi$
$947$	30.5201	−	12.6418i	0.991770	−	0.410804i	0.818773	+	0.574118i	$0.194655\pi$
$948$			47.8661i			1.55462i
$949$	12.5037	+	30.1866i	0.405887	+	0.979899i
$950$		0			0
$951$	76.4343			2.47855
$952$	−1.17292	+	8.54356i	−0.0380144	+	0.276898i
$953$	51.4399			1.66630			0.833151	−	0.553046i	$-0.186535\pi$
$953$	51.4399			1.66630			0.833151	+	0.553046i	$0.186535\pi$
$954$	13.1377	+	13.1377i	0.425349	+	0.425349i
$955$		0			0
$956$		−	15.6501i		−	0.506162i
$957$	52.8928	−	21.9089i	1.70978	−	0.708215i
$958$	2.63187	−	6.35390i	0.0850319	−	0.205285i
$959$	−5.28645	−	2.18972i	−0.170708	−	0.0707098i
$960$		0			0
$961$	0.0421545	−	0.0421545i	0.00135982	−	0.00135982i
$962$	−41.7739	−	17.3033i	−1.34685	−	0.557882i
$963$	−7.74299	+	18.6932i	−0.249514	+	0.602381i
$964$	3.16890	−	1.31260i	0.102063	−	0.0422760i
$965$		0			0
$966$	−0.483247	−	1.16666i	−0.0155482	−	0.0375367i
$967$	−21.4243	−	21.4243i	−0.688960	−	0.688960i	0.273042	−	0.962002i	$-0.411970\pi$
$967$	−21.4243	−	21.4243i	−0.688960	−	0.688960i	−0.962002	+	0.273042i	$0.911970\pi$
$968$	−13.6141			−0.437575
$969$	−1.45664	−	1.92024i	−0.0467940	−	0.0616869i
$970$		0			0
$971$	−24.6251	−	24.6251i	−0.790256	−	0.790256i	0.191279	−	0.981536i	$-0.438736\pi$
$971$	−24.6251	−	24.6251i	−0.790256	−	0.790256i	−0.981536	+	0.191279i	$0.938736\pi$
$972$	−4.81802	−	11.6317i	−0.154538	−	0.373088i
$973$			12.6952i			0.406990i
$974$	−0.355384	+	0.147205i	−0.0113872	+	0.00471675i
$975$		0			0
$976$	−0.245562	−	0.101715i	−0.00786025	−	0.00325582i
$977$	14.6363	−	14.6363i	0.468257	−	0.468257i	−0.433092	−	0.901349i	$-0.642578\pi$
$977$	14.6363	−	14.6363i	0.468257	−	0.468257i	0.901349	+	0.433092i	$0.142578\pi$
$978$	−2.54837	+	2.54837i	−0.0814878	+	0.0814878i
$979$	−30.1661	−	12.4952i	−0.964113	−	0.399349i
$980$		0			0
$981$	15.7158	−	6.50969i	0.501767	−	0.207839i
$982$		−	0.252373i		−	0.00805354i
$983$	−16.9619	−	40.9497i	−0.541002	−	1.30609i	−0.924017	−	0.382352i	$-0.875114\pi$
$983$	−16.9619	−	40.9497i	−0.541002	−	1.30609i	0.383015	−	0.923742i	$-0.374886\pi$
$984$	−30.0528	−	30.0528i	−0.958050	−	0.958050i
$985$		0			0
$986$	23.5616	−	17.8731i	0.750353	−	0.569196i
$987$	22.8778			0.728207
$988$	1.06855	+	1.06855i	0.0339951	+	0.0339951i
$989$	3.05141	+	7.36675i	0.0970291	+	0.234249i
$990$		0			0
$991$	24.1426	−	10.0002i	0.766915	−	0.317667i	0.0352929	−	0.999377i	$-0.488764\pi$
$991$	24.1426	−	10.0002i	0.766915	−	0.317667i	0.731622	+	0.681710i	$0.238764\pi$
$992$	11.7975	−	28.4817i	0.374571	−	0.904295i
$993$	−16.3090	−	6.75542i	−0.517551	−	0.214377i
$994$	1.84165	−	1.84165i	0.0584137	−	0.0584137i
$995$		0			0
$996$	38.8958	+	16.1112i	1.23246	+	0.510502i
$997$	−10.0553	+	24.2756i	−0.318454	+	0.768816i	0.680882	+	0.732393i	$0.261596\pi$
$997$	−10.0553	+	24.2756i	−0.318454	+	0.768816i	−0.999336	+	0.0364232i	$0.988404\pi$
$998$	−15.4696	+	6.40770i	−0.489681	+	0.202832i
$999$			52.7404i			1.66863i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.d.151.3	yes	24
5.2	odd	4		425.2.n.d.49.4		24
5.3	odd	4		425.2.n.e.49.3		24
5.4	even	2		425.2.m.c.151.4	yes	24
17.5	odd	16		7225.2.a.cb.1.14		24
17.8	even	8	inner	425.2.m.d.76.3	yes	24
17.12	odd	16		7225.2.a.cb.1.13		24
85.8	odd	8		425.2.n.d.399.4		24
85.29	odd	16		7225.2.a.bx.1.12		24
85.39	odd	16		7225.2.a.bx.1.11		24
85.42	odd	8		425.2.n.e.399.3		24
85.59	even	8		425.2.m.c.76.4	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.m.c.76.4	✓	24	85.59	even	8
425.2.m.c.151.4	yes	24	5.4	even	2
425.2.m.d.76.3	yes	24	17.8	even	8	inner
425.2.m.d.151.3	yes	24	1.1	even	1	trivial
425.2.n.d.49.4		24	5.2	odd	4
425.2.n.d.399.4		24	85.8	odd	8
425.2.n.e.49.3		24	5.3	odd	4
425.2.n.e.399.3		24	85.42	odd	8
7225.2.a.bx.1.11		24	85.39	odd	16
7225.2.a.bx.1.12		24	85.29	odd	16
7225.2.a.cb.1.13		24	17.12	odd	16
7225.2.a.cb.1.14		24	17.5	odd	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.m (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.639117 - 0.639117i) q^{2} +(-1.10274 - 2.66226i) q^{3} -1.18306i q^{4} +(-0.996713 + 2.40628i) q^{6} +(-0.671652 - 0.278207i) q^{7} +(-2.03435 + 2.03435i) q^{8} +(-3.75027 + 3.75027i) q^{9} +O(q^{10})\)	\(q+(-0.639117 - 0.639117i) q^{2} +(-1.10274 - 2.66226i) q^{3} -1.18306i q^{4} +(-0.996713 + 2.40628i) q^{6} +(-0.671652 - 0.278207i) q^{7} +(-2.03435 + 2.03435i) q^{8} +(-3.75027 + 3.75027i) q^{9} +(-0.958080 + 2.31301i) q^{11} +(-3.14961 + 1.30461i) q^{12} -6.29663i q^{13} +(0.251457 + 0.607071i) q^{14} +0.234252 q^{16} +(-2.08128 + 3.55925i) q^{17} +4.79372 q^{18} +(-0.143443 - 0.143443i) q^{19} +2.09490i q^{21} +(2.09061 - 0.865959i) q^{22} +(0.255217 - 0.616148i) q^{23} +(7.65933 + 3.17260i) q^{24} +(-4.02428 + 4.02428i) q^{26} +(6.13299 + 2.54037i) q^{27} +(-0.329136 + 0.794604i) q^{28} +(7.33161 - 3.03685i) q^{29} +(-2.12864 - 5.13900i) q^{31} +(3.91898 + 3.91898i) q^{32} +7.21436 q^{33} +(3.60496 - 0.944595i) q^{34} +(4.43679 + 4.43679i) q^{36} +(3.04037 + 7.34010i) q^{37} +0.183354i q^{38} +(-16.7633 + 6.94358i) q^{39} +(-4.73632 - 1.96185i) q^{41} +(1.33889 - 1.33889i) q^{42} +(-8.45426 + 8.45426i) q^{43} +(2.73643 + 1.13347i) q^{44} +(-0.556904 + 0.230677i) q^{46} -10.9207i q^{47} +(-0.258320 - 0.623640i) q^{48} +(-4.57603 - 4.57603i) q^{49} +(11.7708 + 1.61597i) q^{51} -7.44929 q^{52} +(2.74061 + 2.74061i) q^{53} +(-2.29611 - 5.54329i) q^{54} +(1.93234 - 0.800403i) q^{56} +(-0.223702 + 0.540065i) q^{57} +(-6.62666 - 2.74485i) q^{58} +(-2.38470 + 2.38470i) q^{59} +(-1.04828 - 0.434212i) q^{61} +(-1.92397 + 4.64487i) q^{62} +(3.56223 - 1.47552i) q^{63} -5.47788i q^{64} +(-4.61082 - 4.61082i) q^{66} -5.61946 q^{67} +(4.21081 + 2.46228i) q^{68} -1.92179 q^{69} +(-1.51683 - 3.66196i) q^{71} -15.2587i q^{72} +(-4.79409 + 1.98578i) q^{73} +(2.74803 - 6.63433i) q^{74} +(-0.169702 + 0.169702i) q^{76} +(1.28699 - 1.28699i) q^{77} +(15.1514 + 6.27594i) q^{78} +(5.37312 - 12.9718i) q^{79} -3.21797i q^{81} +(1.77321 + 4.28091i) q^{82} +(-8.73235 - 8.73235i) q^{83} +2.47840 q^{84} +10.8065 q^{86} +(-16.1698 - 16.1698i) q^{87} +(-2.75640 - 6.65453i) q^{88} +13.0419i q^{89} +(-1.75177 + 4.22914i) q^{91} +(-0.728940 - 0.301937i) q^{92} +(-11.3340 + 11.3340i) q^{93} +(-6.97959 + 6.97959i) q^{94} +(6.11171 - 14.7550i) q^{96} +(11.0168 - 4.56330i) q^{97} +5.84924i q^{98} +(-5.08135 - 12.2675i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 8 q^{6} + 12 q^{9}+O(q^{10}) \) 24 * q - 8 * q^6 + 12 * q^9	\( 24 q - 8 q^{6} + 12 q^{9} + 4 q^{11} + 12 q^{12} - 24 q^{14} - 24 q^{16} - 4 q^{17} + 40 q^{18} - 20 q^{19} - 16 q^{22} - 8 q^{23} + 16 q^{24} + 16 q^{26} + 12 q^{27} - 48 q^{28} + 4 q^{29} + 24 q^{31} + 60 q^{32} - 48 q^{33} + 16 q^{34} + 60 q^{36} + 12 q^{37} + 8 q^{39} - 20 q^{41} - 12 q^{42} - 32 q^{43} + 64 q^{44} - 40 q^{46} + 40 q^{48} + 24 q^{49} + 16 q^{51} + 48 q^{52} + 12 q^{53} - 20 q^{54} - 32 q^{56} - 68 q^{57} + 16 q^{58} - 16 q^{59} - 64 q^{61} - 100 q^{62} + 44 q^{63} - 72 q^{66} - 40 q^{67} - 20 q^{68} - 48 q^{69} - 24 q^{71} + 32 q^{74} + 52 q^{76} - 24 q^{77} + 16 q^{78} - 48 q^{79} - 100 q^{82} - 12 q^{83} - 40 q^{84} - 16 q^{86} - 24 q^{87} - 4 q^{88} + 24 q^{91} + 88 q^{92} + 32 q^{93} - 40 q^{94} + 132 q^{96} + 88 q^{97} - 80 q^{99}+O(q^{100}) \) 24 * q - 8 * q^6 + 12 * q^9 + 4 * q^11 + 12 * q^12 - 24 * q^14 - 24 * q^16 - 4 * q^17 + 40 * q^18 - 20 * q^19 - 16 * q^22 - 8 * q^23 + 16 * q^24 + 16 * q^26 + 12 * q^27 - 48 * q^28 + 4 * q^29 + 24 * q^31 + 60 * q^32 - 48 * q^33 + 16 * q^34 + 60 * q^36 + 12 * q^37 + 8 * q^39 - 20 * q^41 - 12 * q^42 - 32 * q^43 + 64 * q^44 - 40 * q^46 + 40 * q^48 + 24 * q^49 + 16 * q^51 + 48 * q^52 + 12 * q^53 - 20 * q^54 - 32 * q^56 - 68 * q^57 + 16 * q^58 - 16 * q^59 - 64 * q^61 - 100 * q^62 + 44 * q^63 - 72 * q^66 - 40 * q^67 - 20 * q^68 - 48 * q^69 - 24 * q^71 + 32 * q^74 + 52 * q^76 - 24 * q^77 + 16 * q^78 - 48 * q^79 - 100 * q^82 - 12 * q^83 - 40 * q^84 - 16 * q^86 - 24 * q^87 - 4 * q^88 + 24 * q^91 + 88 * q^92 + 32 * q^93 - 40 * q^94 + 132 * q^96 + 88 * q^97 - 80 * q^99

Introduction

L-functions

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