LMFDB - Embedded newform 425.2.m.d.26.5

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			26.5
Character	$\chi$	$=$	425.26
Dual form			425.2.m.d.376.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.52941 - 1.52941i) q^{2} +(2.56367 + 1.06191i) q^{3} -2.67820i q^{4} +(5.54499 - 2.29681i) q^{6} +(-1.20249 - 2.90308i) q^{7} +(-1.03724 - 1.03724i) q^{8} +(3.32343 + 3.32343i) q^{9} +O(q^{10})$	\(q+(1.52941 - 1.52941i) q^{2} +(2.56367 + 1.06191i) q^{3} -2.67820i q^{4} +(5.54499 - 2.29681i) q^{6} +(-1.20249 - 2.90308i) q^{7} +(-1.03724 - 1.03724i) q^{8} +(3.32343 + 3.32343i) q^{9} +(-4.70589 + 1.94925i) q^{11} +(2.84399 - 6.86600i) q^{12} -1.39243i q^{13} +(-6.27910 - 2.60089i) q^{14} +2.18366 q^{16} +(1.88636 + 3.66628i) q^{17} +10.1658 q^{18} +(-3.63515 + 3.63515i) q^{19} -8.71946i q^{21} +(-4.21605 + 10.1784i) q^{22} +(-5.73163 + 2.37412i) q^{23} +(-1.55769 - 3.76059i) q^{24} +(-2.12960 - 2.12960i) q^{26} +(1.80528 + 4.35833i) q^{27} +(-7.77501 + 3.22051i) q^{28} +(2.65695 - 6.41445i) q^{29} +(2.33444 + 0.966958i) q^{31} +(5.41419 - 5.41419i) q^{32} -14.1343 q^{33} +(8.49228 + 2.72223i) q^{34} +(8.90079 - 8.90079i) q^{36} +(7.17082 + 2.97025i) q^{37} +11.1193i q^{38} +(1.47863 - 3.56974i) q^{39} +(-3.83241 - 9.25225i) q^{41} +(-13.3356 - 13.3356i) q^{42} +(2.08068 + 2.08068i) q^{43} +(5.22046 + 12.6033i) q^{44} +(-5.13501 + 12.3970i) q^{46} +5.08164i q^{47} +(5.59817 + 2.31884i) q^{48} +(-2.03211 + 2.03211i) q^{49} +(0.942759 + 11.4023i) q^{51} -3.72921 q^{52} +(-2.93446 + 2.93446i) q^{53} +(9.42669 + 3.90466i) q^{54} +(-1.76391 + 4.25846i) q^{56} +(-13.1795 + 5.45912i) q^{57} +(-5.74676 - 13.8739i) q^{58} +(-0.594603 - 0.594603i) q^{59} +(-2.29594 - 5.54290i) q^{61} +(5.04920 - 2.09145i) q^{62} +(5.65176 - 13.6446i) q^{63} -12.1937i q^{64} +(-21.6171 + 21.6171i) q^{66} -4.10703 q^{67} +(9.81903 - 5.05205i) q^{68} -17.2151 q^{69} +(-9.66181 - 4.00205i) q^{71} -6.89439i q^{72} +(0.227491 - 0.549213i) q^{73} +(15.5099 - 6.42439i) q^{74} +(9.73564 + 9.73564i) q^{76} +(11.3176 + 11.3176i) q^{77} +(-3.19816 - 7.72104i) q^{78} +(6.77961 - 2.80821i) q^{79} -1.00977i q^{81} +(-20.0118 - 8.28917i) q^{82} +(-3.35640 + 3.35640i) q^{83} -23.3524 q^{84} +6.36444 q^{86} +(13.6231 - 13.6231i) q^{87} +(6.90298 + 2.85931i) q^{88} +14.1707i q^{89} +(-4.04234 + 1.67439i) q^{91} +(6.35835 + 15.3504i) q^{92} +(4.95792 + 4.95792i) q^{93} +(7.77191 + 7.77191i) q^{94} +(19.6296 - 8.13083i) q^{96} +(-0.982991 + 2.37315i) q^{97} +6.21588i q^{98} +(-22.1179 - 9.16152i) 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 $\left(\mathbb{Z}/425\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.52941	−	1.52941i	1.08146	−	1.08146i	0.0850830	−	0.996374i	$-0.472884\pi$
$2$	1.52941	−	1.52941i	1.08146	−	1.08146i	0.996374	−	0.0850830i	$-0.0271155\pi$
$3$	2.56367	+	1.06191i	1.48013	+	0.613092i	0.969144	−	0.246495i	$-0.0792789\pi$
$3$	2.56367	+	1.06191i	1.48013	+	0.613092i	0.510990	+	0.859587i	$0.329279\pi$
$4$		−	2.67820i		−	1.33910i
$5$		0			0
$5$		0			0
$6$	5.54499	−	2.29681i	2.26373	−	0.937669i
$7$	−1.20249	−	2.90308i	−0.454500	−	1.09726i	−0.970593	−	0.240727i	$-0.922614\pi$
$7$	−1.20249	−	2.90308i	−0.454500	−	1.09726i	0.516093	−	0.856533i	$-0.327386\pi$
$8$	−1.03724	−	1.03724i	−0.366720	−	0.366720i
$9$	3.32343	+	3.32343i	1.10781	+	1.10781i
$10$		0			0
$11$	−4.70589	+	1.94925i	−1.41888	+	0.587720i	−0.954579	−	0.297958i	$-0.903695\pi$
$11$	−4.70589	+	1.94925i	−1.41888	+	0.587720i	−0.464301	+	0.885677i	$0.653695\pi$
$12$	2.84399	−	6.86600i	0.820990	−	1.98204i
$13$		−	1.39243i		−	0.386192i	−0.981180	−	0.193096i	$-0.938147\pi$
$13$		−	1.39243i		−	0.386192i	0.981180	−	0.193096i	$-0.0618529\pi$
$14$	−6.27910	−	2.60089i	−1.67816	−	0.695117i
$15$		0			0
$16$	2.18366			0.545915
$17$	1.88636	+	3.66628i	0.457510	+	0.889204i
$17$	1.88636	+	3.66628i	0.457510	+	0.889204i
$18$	10.1658			2.39610
$19$	−3.63515	+	3.63515i	−0.833960	+	0.833960i	−0.988056	−	0.154096i	$-0.950753\pi$
$19$	−3.63515	+	3.63515i	−0.833960	+	0.833960i	0.154096	+	0.988056i	$0.450753\pi$
$20$		0			0
$21$		−	8.71946i		−	1.90274i
$22$	−4.21605	+	10.1784i	−0.898865	+	2.17005i
$23$	−5.73163	+	2.37412i	−1.19513	+	0.495038i	−0.889421	−	0.457089i	$-0.848892\pi$
$23$	−5.73163	+	2.37412i	−1.19513	+	0.495038i	−0.305705	+	0.952126i	$0.598892\pi$
$24$	−1.55769	−	3.76059i	−0.317962	−	0.767628i
$25$		0			0
$26$	−2.12960	−	2.12960i	−0.417650	−	0.417650i
$27$	1.80528	+	4.35833i	0.347426	+	0.838761i
$28$	−7.77501	+	3.22051i	−1.46934	+	0.608620i
$29$	2.65695	−	6.41445i	0.493383	−	1.19113i	−0.459604	−	0.888124i	$-0.652009\pi$
$29$	2.65695	−	6.41445i	0.493383	−	1.19113i	0.952988	−	0.303009i	$-0.0979913\pi$
$30$		0			0
$31$	2.33444	+	0.966958i	0.419278	+	0.173671i	0.582340	−	0.812945i	$-0.302137\pi$
$31$	2.33444	+	0.966958i	0.419278	+	0.173671i	−0.163062	+	0.986616i	$0.552137\pi$
$32$	5.41419	−	5.41419i	0.957103	−	0.957103i
$33$	−14.1343			−2.46046
$34$	8.49228	+	2.72223i	1.45641	+	0.466859i
$35$		0			0
$36$	8.90079	−	8.90079i	1.48347	−	1.48347i
$37$	7.17082	+	2.97025i	1.17887	+	0.488306i	0.884117	−	0.467266i	$-0.154761\pi$
$37$	7.17082	+	2.97025i	1.17887	+	0.488306i	0.294758	+	0.955572i	$0.404761\pi$
$38$			11.1193i			1.80378i
$39$	1.47863	−	3.56974i	0.236771	−	0.571616i
$40$		0			0
$41$	−3.83241	−	9.25225i	−0.598522	−	1.44496i	−0.875088	−	0.483964i	$-0.839197\pi$
$41$	−3.83241	−	9.25225i	−0.598522	−	1.44496i	0.276566	−	0.960995i	$-0.410803\pi$
$42$	−13.3356	−	13.3356i	−2.05773	−	2.05773i
$43$	2.08068	+	2.08068i	0.317301	+	0.317301i	0.847730	−	0.530429i	$-0.177969\pi$
$43$	2.08068	+	2.08068i	0.317301	+	0.317301i	−0.530429	+	0.847730i	$0.677969\pi$
$44$	5.22046	+	12.6033i	0.787014	+	1.90002i
$45$		0			0
$46$	−5.13501	+	12.3970i	−0.757116	+	1.82784i
$47$			5.08164i			0.741233i	0.928786	+	0.370616i	$0.120854\pi$
$47$			5.08164i			0.741233i	−0.928786	+	0.370616i	$0.879146\pi$
$48$	5.59817	+	2.31884i	0.808027	+	0.334696i
$49$	−2.03211	+	2.03211i	−0.290302	+	0.290302i
$50$		0			0
$51$	0.942759	+	11.4023i	0.132013	+	1.59664i
$52$	−3.72921			−0.517149
$53$	−2.93446	+	2.93446i	−0.403079	+	0.403079i	−0.879317	−	0.476238i	$-0.842000\pi$
$53$	−2.93446	+	2.93446i	−0.403079	+	0.403079i	0.476238	+	0.879317i	$0.342000\pi$
$54$	9.42669	+	3.90466i	1.28281	+	0.531357i
$55$		0			0
$56$	−1.76391	+	4.25846i	−0.235713	+	0.569061i
$57$	−13.1795	+	5.45912i	−1.74567	+	0.723079i
$58$	−5.74676	−	13.8739i	−0.754586	−	1.82173i
$59$	−0.594603	−	0.594603i	−0.0774107	−	0.0774107i	0.667341	−	0.744752i	$-0.267432\pi$
$59$	−0.594603	−	0.594603i	−0.0774107	−	0.0774107i	−0.744752	+	0.667341i	$0.767432\pi$
$60$		0			0
$61$	−2.29594	−	5.54290i	−0.293965	−	0.709695i	−0.999999	−	0.00151663i	$-0.999517\pi$
$61$	−2.29594	−	5.54290i	−0.293965	−	0.709695i	0.706034	−	0.708178i	$-0.250483\pi$
$62$	5.04920	−	2.09145i	0.641249	−	0.265614i
$63$	5.65176	−	13.6446i	0.712055	−	1.71905i
$64$		−	12.1937i		−	1.52422i
$65$		0			0
$66$	−21.6171	+	21.6171i	−2.66088	+	2.66088i
$67$	−4.10703			−0.501754			−0.250877	−	0.968019i	$-0.580719\pi$
$67$	−4.10703			−0.501754			−0.250877	+	0.968019i	$0.580719\pi$
$68$	9.81903	−	5.05205i	1.19073	−	0.612651i
$69$	−17.2151			−2.07245
$70$		0			0
$71$	−9.66181	−	4.00205i	−1.14665	−	0.474956i	−0.273238	−	0.961946i	$-0.588095\pi$
$71$	−9.66181	−	4.00205i	−1.14665	−	0.474956i	−0.873407	+	0.486990i	$0.838095\pi$
$72$		−	6.89439i		−	0.812511i
$73$	0.227491	−	0.549213i	0.0266259	−	0.0642805i	−0.910007	−	0.414592i	$-0.863924\pi$
$73$	0.227491	−	0.549213i	0.0266259	−	0.0642805i	0.936633	+	0.350312i	$0.113924\pi$
$74$	15.5099	−	6.42439i	1.80298	−	0.746821i
$75$		0			0
$76$	9.73564	+	9.73564i	1.11675	+	1.11675i
$77$	11.3176	+	11.3176i	1.28976	+	1.28976i
$78$	−3.19816	−	7.72104i	−0.362120	−	0.874236i
$79$	6.77961	−	2.80821i	0.762765	−	0.315948i	0.0328274	−	0.999461i	$-0.489549\pi$
$79$	6.77961	−	2.80821i	0.762765	−	0.315948i	0.729938	+	0.683513i	$0.239549\pi$
$80$		0			0
$81$		−	1.00977i		−	0.112196i
$82$	−20.0118	−	8.28917i	−2.20994	−	0.915385i
$83$	−3.35640	+	3.35640i	−0.368413	+	0.368413i	−0.866898	−	0.498485i	$-0.833890\pi$
$83$	−3.35640	+	3.35640i	−0.368413	+	0.368413i	0.498485	+	0.866898i	$0.333890\pi$
$84$	−23.3524			−2.54796
$85$		0			0
$86$	6.36444			0.686295
$87$	13.6231	−	13.6231i	1.46055	−	1.46055i
$88$	6.90298	+	2.85931i	0.735860	+	0.304803i
$89$			14.1707i			1.50209i	0.660252	+	0.751044i	$0.270450\pi$
$89$			14.1707i			1.50209i	−0.660252	+	0.751044i	$0.729550\pi$
$90$		0			0
$91$	−4.04234	+	1.67439i	−0.423753	+	0.175524i
$92$	6.35835	+	15.3504i	0.662904	+	1.60039i
$93$	4.95792	+	4.95792i	0.514112	+	0.514112i
$94$	7.77191	+	7.77191i	0.801611	+	0.801611i
$95$		0			0
$96$	19.6296	−	8.13083i	2.00343	−	0.829849i
$97$	−0.982991	+	2.37315i	−0.0998076	+	0.240957i	−0.965894	−	0.258937i	$-0.916628\pi$
$97$	−0.982991	+	2.37315i	−0.0998076	+	0.240957i	0.866087	+	0.499894i	$0.166628\pi$
$98$			6.21588i			0.627898i
$99$	−22.1179	−	9.16152i	−2.22293	−	0.920768i
$100$		0			0
$101$	2.40549			0.239355			0.119678	−	0.992813i	$-0.461814\pi$
$101$	2.40549			0.239355			0.119678	+	0.992813i	$0.461814\pi$
$102$	18.8806	+	15.9969i	1.86946	+	1.58393i
$103$	4.86373			0.479237			0.239619	−	0.970867i	$-0.422978\pi$
$103$	4.86373			0.479237			0.239619	+	0.970867i	$0.422978\pi$
$104$	−1.44429	+	1.44429i	−0.141624	+	0.141624i
$105$		0			0
$106$			8.97598i			0.871824i
$107$	2.98115	−	7.19713i	0.288199	−	0.695773i	−0.711779	−	0.702403i	$-0.752110\pi$
$107$	2.98115	−	7.19713i	0.288199	−	0.695773i	0.999978	+	0.00662993i	$0.00211039\pi$
$108$	11.6725	−	4.83489i	1.12318	−	0.465238i
$109$	−6.45573	−	15.5855i	−0.618347	−	1.49282i	−0.853622	−	0.520893i	$-0.825599\pi$
$109$	−6.45573	−	15.5855i	−0.618347	−	1.49282i	0.235275	−	0.971929i	$-0.424401\pi$
$110$		0			0
$111$	15.2295	+	15.2295i	1.44552	+	1.44552i
$112$	−2.62584	−	6.33933i	−0.248118	−	0.599010i
$113$	9.68896	−	4.01330i	0.911460	−	0.377539i	0.122845	−	0.992426i	$-0.460798\pi$
$113$	9.68896	−	4.01330i	0.911460	−	0.377539i	0.788615	+	0.614887i	$0.210798\pi$
$114$	−11.8076	+	28.5061i	−1.10588	+	2.66984i
$115$		0			0
$116$	−17.1791	−	7.11584i	−1.59504	−	0.660689i
$117$	4.62766	−	4.62766i	0.427827	−	0.427827i
$118$	−1.81879			−0.167433
$119$	8.37516	−	9.88494i	0.767750	−	0.906151i
$120$		0			0
$121$	10.5677	−	10.5677i	0.960701	−	0.960701i
$122$	−11.9888	−	4.96593i	−1.08542	−	0.449594i
$123$		−	27.7894i		−	2.50568i
$124$	2.58970	−	6.25209i	0.232562	−	0.561455i
$125$		0			0
$126$	−12.2243	−	29.5120i	−1.08903	−	2.62914i
$127$	2.58600	+	2.58600i	0.229470	+	0.229470i	0.812471	−	0.583001i	$-0.198122\pi$
$127$	2.58600	+	2.58600i	0.229470	+	0.229470i	−0.583001	+	0.812471i	$0.698122\pi$
$128$	−7.82084	−	7.82084i	−0.691272	−	0.691272i
$129$	3.12469	+	7.54367i	0.275113	+	0.664183i
$130$		0			0
$131$	−3.31500	+	8.00312i	−0.289633	+	0.699236i	−0.999989	−	0.00460605i	$-0.998534\pi$
$131$	−3.31500	+	8.00312i	−0.289633	+	0.699236i	0.710356	+	0.703842i	$0.248534\pi$
$132$			37.8543i			3.29480i
$133$	14.9244	+	6.18187i	1.29411	+	0.536036i
$134$	−6.28134	+	6.28134i	−0.542625	+	0.542625i
$135$		0			0
$136$	1.84621	−	5.75943i	0.158311	−	0.493867i
$137$	−6.47788			−0.553442			−0.276721	−	0.960950i	$-0.589248\pi$
$137$	−6.47788			−0.553442			−0.276721	+	0.960950i	$0.589248\pi$
$138$	−26.3289	+	26.3289i	−2.24127	+	2.24127i
$139$	1.81492	+	0.751763i	0.153939	+	0.0637637i	0.458323	−	0.888786i	$-0.348450\pi$
$139$	1.81492	+	0.751763i	0.153939	+	0.0637637i	−0.304383	+	0.952550i	$0.598450\pi$
$140$		0			0
$141$	−5.39622	+	13.0276i	−0.454444	+	1.09712i
$142$	−20.8977	+	8.65609i	−1.75369	+	0.726403i
$143$	2.71420	+	6.55265i	0.226973	+	0.547960i
$144$	7.25723	+	7.25723i	0.604769	+	0.604769i
$145$		0			0
$146$	−0.492044	−	1.18790i	−0.0407219	−	0.0983113i
$147$	−7.36758	+	3.05175i	−0.607668	+	0.251704i
$148$	7.95491	−	19.2049i	0.653890	−	1.57863i
$149$			15.4657i			1.26700i	0.773743	+	0.633500i	$0.218382\pi$
$149$			15.4657i			1.26700i	−0.773743	+	0.633500i	$0.781618\pi$
$150$		0			0
$151$	8.89080	−	8.89080i	0.723523	−	0.723523i	−0.245798	−	0.969321i	$-0.579050\pi$
$151$	8.89080	−	8.89080i	0.723523	−	0.723523i	0.969321	+	0.245798i	$0.0790500\pi$
$152$	7.54104			0.611659
$153$	−5.91544	+	18.4538i	−0.478235	+	1.49190i
$154$	34.6186			2.78964
$155$		0			0
$156$	−9.56046	−	3.96007i	−0.765450	−	0.317060i
$157$		−	16.2713i		−	1.29859i	−0.760535	−	0.649296i	$-0.775063\pi$
$157$		−	16.2713i		−	1.29859i	0.760535	−	0.649296i	$-0.224937\pi$
$158$	6.07391	−	14.6637i	0.483214	−	1.16658i
$159$	−10.6391	+	4.40686i	−0.843735	+	0.349486i
$160$		0			0
$161$	13.7845	+	13.7845i	1.08637	+	1.08637i
$162$	−1.54435	−	1.54435i	−0.121335	−	0.121335i
$163$	2.84161	+	6.86024i	0.222572	+	0.537336i	0.995238	−	0.0974770i	$-0.0310772\pi$
$163$	2.84161	+	6.86024i	0.222572	+	0.537336i	−0.772666	+	0.634813i	$0.781077\pi$
$164$	−24.7793	+	10.2639i	−1.93494	+	0.801479i
$165$		0			0
$166$			10.2666i			0.796846i
$167$	11.3120	+	4.68558i	0.875348	+	0.362581i	0.774691	−	0.632340i	$-0.217906\pi$
$167$	11.3120	+	4.68558i	0.875348	+	0.362581i	0.100657	+	0.994921i	$0.467906\pi$
$168$	−9.04417	+	9.04417i	−0.697773	+	0.697773i
$169$	11.0611			0.850856
$170$		0			0
$171$	−24.1623			−1.84774
$172$	5.57247	−	5.57247i	0.424897	−	0.424897i
$173$	11.6362	+	4.81988i	0.884685	+	0.366449i	0.778312	−	0.627878i	$-0.216076\pi$
$173$	11.6362	+	4.81988i	0.884685	+	0.366449i	0.106373	+	0.994326i	$0.466076\pi$
$174$		−	41.6706i		−	3.15904i
$175$		0			0
$176$	−10.2761	+	4.25649i	−0.774588	+	0.320845i
$177$	−0.892952	−	2.15578i	−0.0671184	−	0.162038i
$178$	21.6728	+	21.6728i	1.62444	+	1.62444i
$179$	−1.22926	−	1.22926i	−0.0918790	−	0.0918790i	0.659673	−	0.751552i	$-0.270695\pi$
$179$	−1.22926	−	1.22926i	−0.0918790	−	0.0918790i	−0.751552	+	0.659673i	$0.770695\pi$
$180$		0			0
$181$	14.7396	−	6.10533i	1.09558	−	0.453805i	0.239633	−	0.970864i	$-0.422973\pi$
$181$	14.7396	−	6.10533i	1.09558	−	0.453805i	0.855950	+	0.517058i	$0.172973\pi$
$182$	−3.62157	+	8.74324i	−0.268449	+	0.648092i
$183$		−	16.6482i		−	1.23067i
$184$	8.40760	+	3.48254i	0.619817	+	0.256736i
$185$		0			0
$186$	15.1654			1.11198
$187$	−16.0235	−	13.5762i	−1.17176	−	0.992787i
$188$	13.6096			0.992583
$189$	10.4817	−	10.4817i	0.762433	−	0.762433i
$190$		0			0
$191$		−	0.0699121i		−	0.00505866i	−0.999997	−	0.00252933i	$-0.999195\pi$
$191$		−	0.0699121i		−	0.00505866i	0.999997	−	0.00252933i	$-0.000805112\pi$
$192$	12.9486	−	31.2607i	0.934484	−	2.25605i
$193$	−21.8532	+	9.05189i	−1.57303	+	0.651569i	−0.987290	−	0.158932i	$-0.949195\pi$
$193$	−21.8532	+	9.05189i	−1.57303	+	0.651569i	−0.585738	+	0.810501i	$0.699195\pi$
$194$	2.12612	+	5.13292i	0.152647	+	0.368522i
$195$		0			0
$196$	5.44240	+	5.44240i	0.388743	+	0.388743i
$197$	−3.31049	−	7.99222i	−0.235862	−	0.569422i	0.760985	−	0.648770i	$-0.224716\pi$
$197$	−3.31049	−	7.99222i	−0.235862	−	0.569422i	−0.996847	+	0.0793476i	$0.974716\pi$
$198$	−47.8391	+	19.8156i	−3.39977	+	1.40823i
$199$	−1.02504	+	2.47466i	−0.0726630	+	0.175424i	−0.956038	−	0.293243i	$-0.905266\pi$
$199$	−1.02504	+	2.47466i	−0.0726630	+	0.175424i	0.883375	+	0.468667i	$0.155266\pi$
$200$		0			0
$201$	−10.5291	−	4.36128i	−0.742663	−	0.307621i
$202$	3.67898	−	3.67898i	0.258852	−	0.258852i
$203$	−21.8166			−1.53123
$204$	30.5375	−	2.52489i	2.13805	−	0.176778i
$205$		0			0
$206$	7.43864	−	7.43864i	0.518275	−	0.518275i
$207$	−26.9388	−	11.1584i	−1.87238	−	0.775565i
$208$		−	3.04060i		−	0.210828i
$209$	10.0208	−	24.1924i	0.693155	−	1.67342i
$210$		0			0
$211$	−9.34054	−	22.5501i	−0.643029	−	1.55241i	−0.822573	−	0.568660i	$-0.807462\pi$
$211$	−9.34054	−	22.5501i	−0.643029	−	1.55241i	0.179544	−	0.983750i	$-0.442538\pi$
$212$	7.85905	+	7.85905i	0.539762	+	0.539762i
$213$	−20.5199	−	20.5199i	−1.40600	−	1.40600i
$214$	−6.44797	−	15.5668i	−0.440774	−	1.06412i
$215$		0			0
$216$	2.64813	−	6.39314i	0.180182	−	0.434998i
$217$		−	7.93983i		−	0.538990i
$218$	−33.7101	−	13.9632i	−2.28314	−	0.945707i
$219$	1.16642	−	1.16642i	0.0788197	−	0.0788197i
$220$		0			0
$221$	5.10506	−	2.62664i	0.343404	−	0.176687i
$222$	46.5842			3.12653
$223$	−5.31964	+	5.31964i	−0.356230	+	0.356230i	−0.862421	−	0.506191i	$-0.831053\pi$
$223$	−5.31964	+	5.31964i	−0.356230	+	0.356230i	0.506191	+	0.862421i	$0.331053\pi$
$224$	−22.2283	−	9.20728i	−1.48519	−	0.615187i
$225$		0			0
$226$	8.68041	−	20.9564i	0.577413	−	1.39400i
$227$	13.3546	−	5.53167i	0.886378	−	0.367150i	0.107411	−	0.994215i	$-0.465744\pi$
$227$	13.3546	−	5.53167i	0.886378	−	0.367150i	0.778967	+	0.627065i	$0.215744\pi$
$228$	14.6206	+	35.2973i	0.968273	+	2.33762i
$229$	1.93554	+	1.93554i	0.127904	+	0.127904i	0.768161	−	0.640257i	$-0.221172\pi$
$229$	1.93554	+	1.93554i	0.127904	+	0.127904i	−0.640257	+	0.768161i	$0.721172\pi$
$230$		0			0
$231$	16.9964	+	41.0329i	1.11828	+	2.69976i
$232$	−9.40922	+	3.89743i	−0.617746	+	0.255879i
$233$	−9.56695	+	23.0967i	−0.626752	+	1.51311i	0.216884	+	0.976197i	$0.430411\pi$
$233$	−9.56695	+	23.0967i	−0.626752	+	1.51311i	−0.843636	+	0.536915i	$0.819589\pi$
$234$		−	14.1552i		−	0.925353i
$235$		0			0
$236$	−1.59246	+	1.59246i	−0.103661	+	0.103661i
$237$	20.3627			1.32270
$238$	−2.30907	−	27.9272i	−0.149675	−	1.81025i
$239$	8.22192			0.531832			0.265916	−	0.963996i	$-0.414326\pi$
$239$	8.22192			0.531832			0.265916	+	0.963996i	$0.414326\pi$
$240$		0			0
$241$	−16.8277	−	6.97025i	−1.08397	−	0.448993i	−0.232067	−	0.972700i	$-0.574549\pi$
$241$	−16.8277	−	6.97025i	−1.08397	−	0.448993i	−0.851899	+	0.523706i	$0.824549\pi$
$242$		−	32.3247i		−	2.07791i
$243$	6.48811	−	15.6637i	0.416213	−	1.00483i
$244$	−14.8450	+	6.14898i	−0.950351	+	0.393648i
$245$		0			0
$246$	−42.5013	−	42.5013i	−2.70979	−	2.70979i
$247$	5.06170	+	5.06170i	0.322069	+	0.322069i
$248$	−1.41841	−	3.42435i	−0.0900691	−	0.217446i
$249$	−12.1689	+	5.04052i	−0.771172	+	0.319430i
$250$		0			0
$251$			13.5691i			0.856472i	0.903667	+	0.428236i	$0.140865\pi$
$251$			13.5691i			0.856472i	−0.903667	+	0.428236i	$0.859135\pi$
$252$	−36.5428	−	15.1365i	−2.30198	−	0.953512i
$253$	22.3447	−	22.3447i	1.40480	−	1.40480i
$254$	7.91010			0.496324
$255$		0			0
$256$	0.464893			0.0290558
$257$	5.68336	−	5.68336i	0.354519	−	0.354519i	−0.507269	−	0.861788i	$-0.669345\pi$
$257$	5.68336	−	5.68336i	0.354519	−	0.354519i	0.861788	+	0.507269i	$0.169345\pi$
$258$	16.3163	+	6.75843i	1.01581	+	0.420762i
$259$		−	24.3891i		−	1.51547i
$260$		0			0
$261$	30.1481	−	12.4878i	1.86612	−	0.772973i
$262$	7.17007	+	17.3101i	0.442968	+	1.06942i
$263$	1.69205	+	1.69205i	0.104336	+	0.104336i	0.757348	−	0.653012i	$-0.226495\pi$
$263$	1.69205	+	1.69205i	0.104336	+	0.104336i	−0.653012	+	0.757348i	$0.726495\pi$
$264$	14.6606	+	14.6606i	0.902299	+	0.902299i
$265$		0			0
$266$	32.2801	−	13.3708i	1.97922	−	0.819819i
$267$	−15.0479	+	36.3289i	−0.920918	+	2.22329i
$268$			10.9994i			0.671898i
$269$	−10.6989	−	4.43161i	−0.652321	−	0.270200i	0.0318823	−	0.999492i	$-0.489850\pi$
$269$	−10.6989	−	4.43161i	−0.652321	−	0.270200i	−0.684203	+	0.729291i	$0.739850\pi$
$270$		0			0
$271$	−23.6119			−1.43432			−0.717161	−	0.696908i	$-0.754559\pi$
$271$	−23.6119			−1.43432			−0.717161	+	0.696908i	$0.754559\pi$
$272$	4.11917	+	8.00591i	0.249761	+	0.485430i
$273$	−12.1413			−0.734824
$274$	−9.90733	+	9.90733i	−0.598524	+	0.598524i
$275$		0			0
$276$			46.1053i			2.77522i
$277$	−5.62393	+	13.5774i	−0.337909	+	0.815785i	0.660007	+	0.751260i	$0.270553\pi$
$277$	−5.62393	+	13.5774i	−0.337909	+	0.815785i	−0.997916	+	0.0645253i	$0.979447\pi$
$278$	3.92551	−	1.62600i	0.235436	−	0.0975209i
$279$	4.54474	+	10.9720i	0.272086	+	0.656874i
$280$		0			0
$281$	−12.7948	−	12.7948i	−0.763272	−	0.763272i	0.213640	−	0.976912i	$-0.431468\pi$
$281$	−12.7948	−	12.7948i	−0.763272	−	0.763272i	−0.976912	+	0.213640i	$0.931468\pi$
$282$	11.6716	+	28.1776i	0.695031	+	1.67795i
$283$	19.1354	−	7.92615i	1.13748	−	0.471161i	0.267165	−	0.963651i	$-0.413913\pi$
$283$	19.1354	−	7.92615i	1.13748	−	0.471161i	0.870318	+	0.492490i	$0.163913\pi$
$284$	−10.7183	+	25.8762i	−0.636013	+	1.53547i
$285$		0			0
$286$	14.1728	+	5.87057i	0.838056	+	0.347134i
$287$	−22.2515	+	22.2515i	−1.31347	+	1.31347i
$288$	35.9873			2.12057
$289$	−9.88327	+	13.8319i	−0.581369	+	0.813640i
$290$		0			0
$291$	−5.04012	+	5.04012i	−0.295457	+	0.295457i
$292$	−1.47090	−	0.609267i	−0.0860779	−	0.0356546i
$293$			21.3137i			1.24516i	0.782555	+	0.622581i	$0.213916\pi$
$293$			21.3137i			1.24516i	−0.782555	+	0.622581i	$0.786084\pi$
$294$	−6.60068	+	15.9354i	−0.384959	+	0.929374i
$295$		0			0
$296$	−4.35700	−	10.5187i	−0.253245	−	0.611388i
$297$	−16.9909	−	16.9909i	−0.985912	−	0.985912i
$298$	23.6534	+	23.6534i	1.37021	+	1.37021i
$299$	3.30580	+	7.98091i	0.191180	+	0.461548i
$300$		0			0
$301$	3.53837	−	8.54239i	0.203948	−	0.492375i
$302$		−	27.1954i		−	1.56492i
$303$	6.16687	+	2.55440i	0.354278	+	0.146747i
$304$	−7.93792	+	7.93792i	−0.455271	+	0.455271i
$305$		0			0
$306$	19.1763	+	37.2706i	1.09624	+	2.13062i
$307$	19.1510			1.09300			0.546501	−	0.837458i	$-0.315959\pi$
$307$	19.1510			1.09300			0.546501	+	0.837458i	$0.315959\pi$
$308$	30.3108	−	30.3108i	1.72712	−	1.72712i
$309$	12.4690	+	5.16482i	0.709336	+	0.293817i
$310$		0			0
$311$	−4.18606	+	10.1060i	−0.237370	+	0.573061i	−0.997009	−	0.0772831i	$-0.975375\pi$
$311$	−4.18606	+	10.1060i	−0.237370	+	0.573061i	0.759639	+	0.650345i	$0.225375\pi$
$312$	−5.23638	+	2.16898i	−0.296452	+	0.122794i
$313$	0.587959	+	1.41946i	0.0332334	+	0.0802325i	0.939625	−	0.342206i	$-0.111174\pi$
$313$	0.587959	+	1.41946i	0.0332334	+	0.0802325i	−0.906391	+	0.422439i	$0.861174\pi$
$314$	−24.8855	−	24.8855i	−1.40437	−	1.40437i
$315$		0			0
$316$	−7.52092	−	18.1571i	−0.423085	−	1.02142i
$317$	−18.0161	+	7.46250i	−1.01188	+	0.419136i	−0.826142	−	0.563462i	$-0.809469\pi$
$317$	−18.0161	+	7.46250i	−1.01188	+	0.419136i	−0.185742	+	0.982599i	$0.559469\pi$
$318$	−9.53165	+	23.0114i	−0.534508	+	1.29042i
$319$			35.3648i			1.98005i
$320$		0			0
$321$	15.2854	−	15.2854i	0.853146	−	0.853146i
$322$	42.1643			2.34972
$323$	−20.1847	−	6.47027i	−1.12311	−	0.360016i
$324$	−2.70435			−0.150242
$325$		0			0
$326$	14.8381	+	6.14615i	0.821807	+	0.340404i
$327$		−	46.8115i		−	2.58868i
$328$	−5.62168	+	13.5719i	−0.310405	+	0.749385i
$329$	14.7524	−	6.11064i	0.813325	−	0.336890i
$330$		0			0
$331$	−0.452451	−	0.452451i	−0.0248689	−	0.0248689i	0.694563	−	0.719432i	$-0.255598\pi$
$331$	−0.452451	−	0.452451i	−0.0248689	−	0.0248689i	−0.719432	+	0.694563i	$0.755598\pi$
$332$	8.98911	+	8.98911i	0.493342	+	0.493342i
$333$	13.9603	+	33.7031i	0.765019	+	1.84692i
$334$	24.4669	−	10.1345i	1.33877	−	0.554535i
$335$		0			0
$336$		−	19.0403i		−	1.03873i
$337$	−0.627042	−	0.259729i	−0.0341571	−	0.0141483i	0.365539	−	0.930796i	$-0.380885\pi$
$337$	−0.627042	−	0.259729i	−0.0341571	−	0.0141483i	−0.399697	+	0.916647i	$0.630885\pi$
$338$	16.9170	−	16.9170i	0.920164	−	0.920164i
$339$	29.1010			1.58055
$340$		0			0
$341$	−12.8705			−0.696975
$342$	−36.9541	+	36.9541i	−1.99825	+	1.99825i
$343$	−11.9785	−	4.96168i	−0.646781	−	0.267905i
$344$		−	4.31633i		−	0.232721i
$345$		0			0
$346$	25.1681	−	10.4250i	1.35305	−	0.560451i
$347$	5.47946	+	13.2286i	0.294153	+	0.710148i	0.999998	+	0.00178195i	$0.000567213\pi$
$347$	5.47946	+	13.2286i	0.294153	+	0.710148i	−0.705846	+	0.708366i	$0.749433\pi$
$348$	−36.4853	−	36.4853i	−1.95582	−	1.95582i
$349$	−13.8016	−	13.8016i	−0.738781	−	0.738781i	0.233561	−	0.972342i	$-0.424962\pi$
$349$	−13.8016	−	13.8016i	−0.738781	−	0.738781i	−0.972342	+	0.233561i	$0.924962\pi$
$350$		0			0
$351$	6.06869	−	2.51373i	0.323923	−	0.134173i
$352$	−14.9250	+	36.0322i	−0.795507	+	1.92052i
$353$		−	34.4925i		−	1.83585i	−0.396755	−	0.917924i	$-0.629864\pi$
$353$		−	34.4925i		−	1.83585i	0.396755	−	0.917924i	$-0.370136\pi$
$354$	−4.66276	−	1.93138i	−0.247823	−	0.102652i
$355$		0			0
$356$	37.9519			2.01144
$357$	31.9680	−	16.4481i	1.69193	−	0.870524i
$358$	−3.76008			−0.198726
$359$	−18.9573	+	18.9573i	−1.00053	+	1.00053i	−0.000526343		1.00000i	$0.500168\pi$
$359$	−18.9573	+	18.9573i	−1.00053	+	1.00053i	−1.00000		0.000526343i	$0.999832\pi$
$360$		0			0
$361$		−	7.42858i		−	0.390978i
$362$	13.2053	−	31.8804i	0.694055	−	1.67560i
$363$	38.3140	−	15.8702i	2.01096	−	0.832969i
$364$	4.48436	+	10.8262i	0.235044	+	0.567447i
$365$		0			0
$366$	−25.4620	−	25.4620i	−1.33092	−	1.33092i
$367$	8.27150	+	19.9692i	0.431769	+	1.04238i	0.978717	+	0.205216i	$0.0657896\pi$
$367$	8.27150	+	19.9692i	0.431769	+	1.04238i	−0.546948	+	0.837167i	$0.684210\pi$
$368$	−12.5159	+	5.18426i	−0.652437	+	0.270248i
$369$	18.0125	−	43.4859i	0.937691	−	2.26379i
$370$		0			0
$371$	12.0476	+	4.99029i	0.625481	+	0.259083i
$372$	13.2783	−	13.2783i	0.688446	−	0.688446i
$373$	−1.90459			−0.0986158			−0.0493079	−	0.998784i	$-0.515702\pi$
$373$	−1.90459			−0.0986158			−0.0493079	+	0.998784i	$0.515702\pi$
$374$	−45.2701	+	3.74300i	−2.34086	+	0.193546i
$375$		0			0
$376$	5.27088	−	5.27088i	0.271825	−	0.271825i
$377$	−8.93170	−	3.69963i	−0.460006	−	0.190541i
$378$		−	32.0617i		−	1.64908i
$379$	−9.35613	+	22.5877i	−0.480592	+	1.16025i	0.478736	+	0.877959i	$0.341095\pi$
$379$	−9.35613	+	22.5877i	−0.480592	+	1.16025i	−0.959328	+	0.282293i	$0.908905\pi$
$380$		0			0
$381$	3.88355	+	9.37572i	0.198960	+	0.480333i
$382$	−0.106924	−	0.106924i	−0.00547073	−	0.00547073i
$383$	24.2809	+	24.2809i	1.24069	+	1.24069i	0.959714	+	0.280980i	$0.0906595\pi$
$383$	24.2809	+	24.2809i	1.24069	+	1.24069i	0.280980	+	0.959714i	$0.409340\pi$
$384$	−11.7450	−	28.3550i	−0.599362	−	1.44699i
$385$		0			0
$386$	−19.5785	+	47.2666i	−0.996517	+	2.40580i
$387$			13.8300i			0.703018i
$388$	6.35576	+	2.63264i	0.322665	+	0.133652i
$389$	10.6102	−	10.6102i	0.537960	−	0.537960i	−0.384969	−	0.922929i	$-0.625788\pi$
$389$	10.6102	−	10.6102i	0.537960	−	0.537960i	0.922929	+	0.384969i	$0.125788\pi$
$390$		0			0
$391$	−19.5161	−	16.5353i	−0.986972	−	0.836227i
$392$	4.21558			0.212919
$393$	−16.9971	+	16.9971i	−0.857392	+	0.857392i
$394$	−17.2865	−	7.16030i	−0.870881	−	0.360731i
$395$		0			0
$396$	−24.5364	+	59.2360i	−1.23300	+	2.97672i
$397$	18.6295	−	7.71661i	0.934990	−	0.387285i	0.137420	−	0.990513i	$-0.456119\pi$
$397$	18.6295	−	7.71661i	0.934990	−	0.387285i	0.797569	+	0.603227i	$0.206119\pi$
$398$	2.21707	+	5.35248i	0.111132	+	0.268296i
$399$	31.6965	+	31.6965i	1.58681	+	1.58681i
$400$		0			0
$401$	5.77587	+	13.9442i	0.288433	+	0.696339i	0.999980	−	0.00629916i	$-0.00200510\pi$
$401$	5.77587	+	13.9442i	0.288433	+	0.696339i	−0.711547	+	0.702639i	$0.752005\pi$
$402$	−22.7735	+	9.43308i	−1.13584	+	0.470479i
$403$	1.34643	−	3.25056i	0.0670702	−	0.161922i
$404$		−	6.44237i		−	0.320520i
$405$		0			0
$406$	−33.3665	+	33.3665i	−1.65595	+	1.65595i
$407$	−39.5348			−1.95967
$408$	10.8490	−	12.8048i	0.537107	−	0.633930i
$409$	31.0341			1.53454			0.767269	−	0.641325i	$-0.221615\pi$
$409$	31.0341			1.53454			0.767269	+	0.641325i	$0.221615\pi$
$410$		0			0
$411$	−16.6071	−	6.87889i	−0.819169	−	0.339311i
$412$		−	13.0260i		−	0.641746i
$413$	−1.01117	+	2.44118i	−0.0497565	+	0.120123i
$414$	−58.2664	+	24.1347i	−2.86364	+	1.18616i
$415$		0			0
$416$	−7.53891	−	7.53891i	−0.369625	−	0.369625i
$417$	3.85454	+	3.85454i	0.188758	+	0.188758i
$418$	−21.6742	−	52.3261i	−1.06012	−	2.55935i
$419$	−8.81740	+	3.65228i	−0.430758	+	0.178426i	−0.587518	−	0.809211i	$-0.699895\pi$
$419$	−8.81740	+	3.65228i	−0.430758	+	0.178426i	0.156760	+	0.987637i	$0.449895\pi$
$420$		0			0
$421$			25.9719i			1.26579i	0.774236	+	0.632897i	$0.218134\pi$
$421$			25.9719i			1.26579i	−0.774236	+	0.632897i	$0.781866\pi$
$422$	−48.7738	−	20.2028i	−2.37427	−	0.983456i
$423$	−16.8885	+	16.8885i	−0.821145	+	0.821145i
$424$	6.08747			0.295634
$425$		0			0
$426$	−62.7666			−3.04105
$427$	−13.3306	+	13.3306i	−0.645113	+	0.645113i
$428$	−19.2753	−	7.98411i	−0.931709	−	0.385926i
$429$			19.6810i			0.950210i
$430$		0			0
$431$	−16.4907	+	6.83069i	−0.794331	+	0.329023i	−0.742683	−	0.669643i	$-0.766447\pi$
$431$	−16.4907	+	6.83069i	−0.794331	+	0.329023i	−0.0516475	+	0.998665i	$0.516447\pi$
$432$	3.94211	+	9.51710i	0.189665	+	0.457892i
$433$	−6.43699	−	6.43699i	−0.309342	−	0.309342i	0.535312	−	0.844654i	$-0.320194\pi$
$433$	−6.43699	−	6.43699i	−0.309342	−	0.309342i	−0.844654	+	0.535312i	$0.820194\pi$
$434$	−12.1433	−	12.1433i	−0.582895	−	0.582895i
$435$		0			0
$436$	−41.7411	+	17.2897i	−1.99903	+	0.828027i
$437$	12.2050	−	29.4656i	0.583846	−	1.40953i
$438$		−	3.56789i		−	0.170480i
$439$	14.3794	+	5.95614i	0.686291	+	0.284271i	0.698454	−	0.715655i	$-0.253872\pi$
$439$	14.3794	+	5.95614i	0.686291	+	0.284271i	−0.0121628	+	0.999926i	$0.503872\pi$
$440$		0			0
$441$	−13.5072			−0.643199
$442$	3.79053	−	11.8249i	0.180297	−	0.562455i
$443$	−11.7983			−0.560555			−0.280277	−	0.959919i	$-0.590426\pi$
$443$	−11.7983			−0.560555			−0.280277	+	0.959919i	$0.590426\pi$
$444$	40.7875	−	40.7875i	1.93569	−	1.93569i
$445$		0			0
$446$			16.2718i			0.770494i
$447$	−16.4231	+	39.6489i	−0.776787	+	1.87533i
$448$	−35.3993	+	14.6629i	−1.67246	+	0.692756i
$449$	2.00816	+	4.84812i	0.0947708	+	0.228797i	0.964155	−	0.265340i	$-0.0854842\pi$
$449$	2.00816	+	4.84812i	0.0947708	+	0.228797i	−0.869384	+	0.494137i	$0.835484\pi$
$450$		0			0
$451$	36.0698	+	36.0698i	1.69846	+	1.69846i
$452$	−10.7484	−	25.9489i	−0.505562	−	1.22053i
$453$	32.2342	−	13.3519i	1.51450	−	0.627325i
$454$	11.9645	−	28.8849i	0.561523	−	1.35564i
$455$		0			0
$456$	19.3327	+	8.00788i	0.905338	+	0.375003i
$457$	19.3101	−	19.3101i	0.903288	−	0.903288i	−0.0924309	−	0.995719i	$-0.529464\pi$
$457$	19.3101	−	19.3101i	0.903288	−	0.903288i	0.995719	+	0.0924309i	$0.0294637\pi$
$458$	5.92048			0.276646
$459$	−12.5735	+	14.8401i	−0.586879	+	0.692674i
$460$		0			0
$461$	17.4047	−	17.4047i	0.810617	−	0.810617i	−0.174110	−	0.984726i	$-0.555705\pi$
$461$	17.4047	−	17.4047i	0.810617	−	0.810617i	0.984726	+	0.174110i	$0.0557047\pi$
$462$	88.7505	+	36.7617i	4.12905	+	1.71031i
$463$			15.5098i			0.720804i	0.932797	+	0.360402i	$0.117360\pi$
$463$			15.5098i			0.720804i	−0.932797	+	0.360402i	$0.882640\pi$
$464$	5.80187	−	14.0070i	0.269345	−	0.650257i
$465$		0			0
$466$	20.6925	+	49.9561i	0.958561	+	2.31417i
$467$	2.04167	+	2.04167i	0.0944771	+	0.0944771i	0.752766	−	0.658289i	$-0.228719\pi$
$467$	2.04167	+	2.04167i	0.0944771	+	0.0944771i	−0.658289	+	0.752766i	$0.728719\pi$
$468$	−12.3938	−	12.3938i	−0.572902	−	0.572902i
$469$	4.93868	+	11.9230i	0.228047	+	0.550555i
$470$		0			0
$471$	17.2786	−	41.7143i	0.796157	−	1.92209i
$472$			1.23349i			0.0567761i
$473$	−13.8472	−	5.73571i	−0.636696	−	0.263728i
$474$	31.1430	−	31.1430i	1.43044	−	1.43044i
$475$		0			0
$476$	−26.4738	−	22.4303i	−1.21342	−	1.02809i
$477$	−19.5049			−0.893069
$478$	12.5747	−	12.5747i	0.575153	−	0.575153i
$479$	−12.1619	−	5.03763i	−0.555693	−	0.230175i	0.0871214	−	0.996198i	$-0.472233\pi$
$479$	−12.1619	−	5.03763i	−0.555693	−	0.230175i	−0.642814	+	0.766022i	$0.722233\pi$
$480$		0			0
$481$	4.13588	−	9.98489i	0.188580	−	0.455272i
$482$	−36.3968	+	15.0761i	−1.65783	+	0.686695i
$483$	20.7010	+	49.9767i	0.941929	+	2.27402i
$484$	−28.3024	−	28.3024i	−1.28647	−	1.28647i
$485$		0			0
$486$	−14.0332	−	33.8792i	−0.636560	−	1.53679i
$487$	−19.1451	+	7.93015i	−0.867546	+	0.359349i	−0.771654	−	0.636042i	$-0.780570\pi$
$487$	−19.1451	+	7.93015i	−0.867546	+	0.359349i	−0.0958919	+	0.995392i	$0.530570\pi$
$488$	−3.36787	+	8.13076i	−0.152456	+	0.368062i
$489$			20.6049i			0.931786i
$490$		0			0
$491$	4.49675	−	4.49675i	0.202935	−	0.202935i	−0.598321	−	0.801256i	$-0.704165\pi$
$491$	4.49675	−	4.49675i	0.202935	−	0.202935i	0.801256	+	0.598321i	$0.204165\pi$
$492$	−74.4253			−3.35535
$493$	28.5292	−	2.35884i	1.28489	−	0.106237i
$494$	15.4829			0.696607
$495$		0			0
$496$	5.09762	+	2.11151i	0.228890	+	0.0948094i
$497$			32.8614i			1.47404i
$498$	−10.9022	+	26.3203i	−0.488540	+	1.17944i
$499$	−11.3751	+	4.71171i	−0.509218	+	0.210925i	−0.622473	−	0.782641i	$-0.713872\pi$
$499$	−11.3751	+	4.71171i	−0.509218	+	0.210925i	0.113256	+	0.993566i	$0.463872\pi$
$500$		0			0
$501$	24.0245	+	24.0245i	1.07334	+	1.07334i
$502$	20.7527	+	20.7527i	0.926238	+	0.926238i
$503$	3.64281	+	8.79452i	0.162425	+	0.392128i	0.984048	−	0.177903i	$-0.0569312\pi$
$503$	3.64281	+	8.79452i	0.162425	+	0.392128i	−0.821623	+	0.570031i	$0.806931\pi$
$504$	−20.0149	+	8.29046i	−0.891536	+	0.369286i
$505$		0			0
$506$		−	68.3484i		−	3.03846i
$507$	28.3571	+	11.7459i	1.25938	+	0.521653i
$508$	6.92580	−	6.92580i	0.307283	−	0.307283i
$509$	−14.3580			−0.636406			−0.318203	−	0.948023i	$-0.603079\pi$
$509$	−14.3580			−0.636406			−0.318203	+	0.948023i	$0.603079\pi$
$510$		0			0
$511$	−1.86796			−0.0826339
$512$	16.3527	−	16.3527i	0.722694	−	0.722694i
$513$	−22.4056	−	9.28071i	−0.989232	−	0.409753i
$514$		−	17.3844i		−	0.766793i
$515$		0			0
$516$	20.2034	−	8.36853i	0.889406	−	0.368404i
$517$	−9.90536	−	23.9136i	−0.435637	−	1.05172i
$518$	−37.3010	−	37.3010i	−1.63891	−	1.63891i
$519$	24.7131	+	24.7131i	1.08479	+	1.08479i
$520$		0			0
$521$	−7.20077	+	2.98266i	−0.315472	+	0.130673i	−0.534800	−	0.844978i	$-0.679613\pi$
$521$	−7.20077	+	2.98266i	−0.315472	+	0.130673i	0.219329	+	0.975651i	$0.429613\pi$
$522$	27.0100	−	65.2078i	1.18219	−	2.85407i
$523$			31.3802i			1.37216i	0.727526	+	0.686080i	$0.240670\pi$
$523$			31.3802i			1.37216i	−0.727526	+	0.686080i	$0.759330\pi$
$524$	21.4339	+	8.87823i	0.936346	+	0.387847i
$525$		0			0
$526$	5.17568			0.225671
$527$	0.858464	+	10.3828i	0.0373953	+	0.452280i
$528$	−30.8644			−1.34320
$529$	10.9516	−	10.9516i	0.476158	−	0.476158i
$530$		0			0
$531$		−	3.95224i		−	0.171513i
$532$	16.5563	−	39.9703i	0.717805	−	1.73293i
$533$	−12.8832	+	5.33638i	−0.558031	+	0.231144i
$534$	32.5474	+	78.5763i	1.40846	+	3.40033i
$535$		0			0
$536$	4.25998	+	4.25998i	0.184003	+	0.184003i
$537$	−1.84605	−	4.45676i	−0.0796630	−	0.192324i
$538$	−23.1407	+	9.58519i	−0.997667	+	0.413247i
$539$	5.60183	−	13.5240i	0.241288	−	0.582520i
$540$		0			0
$541$	4.63851	+	1.92133i	0.199425	+	0.0826045i	0.480161	−	0.877181i	$-0.340578\pi$
$541$	4.63851	+	1.92133i	0.199425	+	0.0826045i	−0.280736	+	0.959785i	$0.590578\pi$
$542$	−36.1123	+	36.1123i	−1.55116	+	1.55116i
$543$	44.2706			1.89983
$544$	30.0631	+	9.63683i	1.28894	+	0.413176i
$545$		0			0
$546$	−18.5690	+	18.5690i	−0.794680	+	0.794680i
$547$	22.6980	+	9.40183i	0.970498	+	0.401993i	0.810897	−	0.585188i	$-0.198979\pi$
$547$	22.6980	+	9.40183i	0.970498	+	0.401993i	0.159600	+	0.987182i	$0.448979\pi$
$548$			17.3490i			0.741113i
$549$	10.7910	−	26.0518i	0.460549	−	1.11186i
$550$		0			0
$551$	13.6591	+	32.9759i	0.581895	+	1.40482i
$552$	17.8562	+	17.8562i	0.760009	+	0.760009i
$553$	−16.3049	−	16.3049i	−0.693354	−	0.693354i
$554$	12.1641	+	29.3667i	0.516802	+	1.24767i
$555$		0			0
$556$	2.01337	−	4.86070i	0.0853858	−	0.206140i
$557$			1.22515i			0.0519112i	0.999663	+	0.0259556i	$0.00826285\pi$
$557$			1.22515i			0.0519112i	−0.999663	+	0.0259556i	$0.991737\pi$
$558$	23.7314	+	9.82987i	1.00463	+	0.416132i
$559$	2.89721	−	2.89721i	0.122539	−	0.122539i
$560$		0			0
$561$	−26.6623	−	51.8202i	−1.12569	−	2.18785i
$562$	−39.1369			−1.65089
$563$	−1.54786	+	1.54786i	−0.0652345	+	0.0652345i	−0.738971	−	0.673737i	$-0.764688\pi$
$563$	−1.54786	+	1.54786i	−0.0652345	+	0.0652345i	0.673737	+	0.738971i	$0.264688\pi$
$564$	34.8905	+	14.4521i	1.46916	+	0.608545i
$565$		0			0
$566$	17.1436	−	41.3883i	0.720599	−	1.73968i
$567$	−2.93143	+	1.21424i	−0.123109	+	0.0509932i
$568$	5.87053	+	14.1727i	0.246322	+	0.594674i
$569$	−0.0566880	−	0.0566880i	−0.00237648	−	0.00237648i	0.705918	−	0.708294i	$-0.250535\pi$
$569$	−0.0566880	−	0.0566880i	−0.00237648	−	0.00237648i	−0.708294	+	0.705918i	$0.750535\pi$
$570$		0			0
$571$	−14.9414	−	36.0716i	−0.625276	−	1.50955i	−0.845431	−	0.534085i	$-0.820656\pi$
$571$	−14.9414	−	36.0716i	−0.625276	−	1.50955i	0.220155	−	0.975465i	$-0.429344\pi$
$572$	17.5493	−	7.26915i	0.733772	−	0.303938i
$573$	0.0742401	−	0.179231i	0.00310143	−	0.00748750i
$574$			68.0635i			2.84092i
$575$		0			0
$576$	40.5250	−	40.5250i	1.68854	−	1.68854i
$577$	−33.0033			−1.37395			−0.686974	−	0.726682i	$-0.741061\pi$
$577$	−33.0033			−1.37395			−0.686974	+	0.726682i	$0.741061\pi$
$578$	6.03905	+	36.2702i	0.251191	+	1.50864i
$579$	−65.6366			−2.72776
$580$		0			0
$581$	13.7800	+	5.70784i	0.571689	+	0.236801i
$582$			15.4168i			0.639049i
$583$	8.08927	−	19.5292i	0.335023	−	0.808818i
$584$	−0.805629	+	0.333702i	−0.0333372	+	0.0138087i
$585$		0			0
$586$	32.5975	+	32.5975i	1.34659	+	1.34659i
$587$	8.81184	+	8.81184i	0.363704	+	0.363704i	0.865175	−	0.501471i	$-0.167208\pi$
$587$	8.81184	+	8.81184i	0.363704	+	0.363704i	−0.501471	+	0.865175i	$0.667208\pi$
$588$	8.17319	+	19.7318i	0.337057	+	0.813727i
$589$	−12.0011	+	4.97101i	−0.494496	+	0.204827i
$590$		0			0
$591$		−	24.0048i		−	0.987427i
$592$	15.6586	+	6.48601i	0.643565	+	0.266573i
$593$	9.16755	−	9.16755i	0.376466	−	0.376466i	−0.493359	−	0.869826i	$-0.664231\pi$
$593$	9.16755	−	9.16755i	0.376466	−	0.376466i	0.869826	+	0.493359i	$0.164231\pi$
$594$	−51.9721			−2.13244
$595$		0			0
$596$	41.4202			1.69664
$597$	−5.25572	+	5.25572i	−0.215102	+	0.215102i
$598$	17.2620	+	7.15017i	0.705897	+	0.292392i
$599$		−	29.7824i		−	1.21688i	−0.793602	−	0.608438i	$-0.791796\pi$
$599$		−	29.7824i		−	1.21688i	0.793602	−	0.608438i	$-0.208204\pi$
$600$		0			0
$601$	−25.2558	+	10.4613i	−1.03021	+	0.426726i	−0.832787	−	0.553594i	$-0.813256\pi$
$601$	−25.2558	+	10.4613i	−1.03021	+	0.426726i	−0.197420	+	0.980319i	$0.563256\pi$
$602$	−7.65319	−	18.4764i	−0.311921	−	0.753044i
$603$	−13.6494	−	13.6494i	−0.555848	−	0.555848i
$604$	−23.8113	−	23.8113i	−0.968868	−	0.968868i
$605$		0			0
$606$	13.3384	−	5.52495i	0.541836	−	0.224436i
$607$	−5.52249	+	13.3325i	−0.224151	+	0.541148i	−0.995446	−	0.0953301i	$-0.969609\pi$
$607$	−5.52249	+	13.3325i	−0.224151	+	0.541148i	0.771295	+	0.636478i	$0.219609\pi$
$608$			39.3628i			1.59637i
$609$	−55.9305	−	23.1672i	−2.26642	−	0.938781i
$610$		0			0
$611$	7.07585			0.286258
$612$	49.4229	+	15.8427i	1.99780	+	0.640403i
$613$	32.6737			1.31968			0.659840	−	0.751406i	$-0.270624\pi$
$613$	32.6737			1.31968			0.659840	+	0.751406i	$0.270624\pi$
$614$	29.2897	−	29.2897i	1.18204	−	1.18204i
$615$		0			0
$616$		−	23.4782i		−	0.945963i
$617$	0.155258	−	0.374827i	0.00625046	−	0.0150900i	−0.920723	−	0.390216i	$-0.872400\pi$
$617$	0.155258	−	0.374827i	0.00625046	−	0.0150900i	0.926974	+	0.375126i	$0.122400\pi$
$618$	26.9693	−	11.1711i	1.08487	−	0.449366i
$619$	−9.57495	−	23.1160i	−0.384850	−	0.929109i	−0.991013	−	0.133769i	$-0.957292\pi$
$619$	−9.57495	−	23.1160i	−0.384850	−	0.929109i	0.606163	−	0.795340i	$-0.292708\pi$
$620$		0			0
$621$	−20.6944	−	20.6944i	−0.830436	−	0.830436i
$622$	9.05409	+	21.8585i	0.363036	+	0.876446i
$623$	41.1386	−	17.0402i	1.64818	−	0.682699i
$624$	3.22883	−	7.79509i	0.129257	−	0.312053i
$625$		0			0
$626$	3.07016	+	1.27170i	0.122708	+	0.0508275i
$627$	51.3801	−	51.3801i	2.05192	−	2.05192i
$628$	−43.5778			−1.73894
$629$	2.63698	+	31.8932i	0.105143	+	1.27167i
$630$		0			0
$631$	−15.0736	+	15.0736i	−0.600070	+	0.600070i	−0.940331	−	0.340261i	$-0.889485\pi$
$631$	−15.0736	+	15.0736i	−0.600070	+	0.600070i	0.340261	+	0.940331i	$0.389485\pi$
$632$	−9.94487	−	4.11930i	−0.395586	−	0.163857i
$633$		−	67.7296i		−	2.69201i
$634$	−16.1408	+	38.9672i	−0.641031	+	1.54759i
$635$		0			0
$636$	11.8024	+	28.4936i	0.467997	+	1.12984i
$637$	2.82959	+	2.82959i	0.112112	+	0.112112i
$638$	54.0873	+	54.0873i	2.14134	+	2.14134i
$639$	−18.8098	−	45.4108i	−0.744104	−	1.79643i
$640$		0			0
$641$	−17.3839	+	41.9684i	−0.686621	+	1.65765i	0.0648581	+	0.997894i	$0.479341\pi$
$641$	−17.3839	+	41.9684i	−0.686621	+	1.65765i	−0.751480	+	0.659756i	$0.770659\pi$
$642$		−	46.7552i		−	1.84528i
$643$	−39.1173	−	16.2029i	−1.54263	−	0.638980i	−0.560668	−	0.828040i	$-0.689456\pi$
$643$	−39.1173	−	16.2029i	−1.54263	−	0.638980i	−0.981965	+	0.189061i	$0.939456\pi$
$644$	36.9176	−	36.9176i	1.45476	−	1.45476i
$645$		0			0
$646$	−40.7664	+	20.9750i	−1.60393	+	0.825249i
$647$	31.4343			1.23581			0.617905	−	0.786253i	$-0.287982\pi$
$647$	31.4343			1.23581			0.617905	+	0.786253i	$0.287982\pi$
$648$	−1.04737	+	1.04737i	−0.0411446	+	0.0411446i
$649$	3.95717	+	1.63911i	0.155332	+	0.0643408i
$650$		0			0
$651$	8.43135	−	20.3551i	0.330451	−	0.797778i
$652$	18.3731	−	7.61038i	0.719545	−	0.298045i
$653$	−4.52807	−	10.9317i	−0.177197	−	0.427791i	0.810180	−	0.586182i	$-0.199370\pi$
$653$	−4.52807	−	10.9317i	−0.177197	−	0.427791i	−0.987377	+	0.158390i	$0.949370\pi$
$654$	−71.5940	−	71.5940i	−2.79955	−	2.79955i
$655$		0			0
$656$	−8.36867	−	20.2038i	−0.326742	−	0.788824i
$657$	2.58132	−	1.06922i	0.100707	−	0.0417142i
$658$	13.2168	−	31.9081i	0.515244	−	1.24391i
$659$		−	44.8149i		−	1.74574i	−0.487951	−	0.872871i	$-0.662255\pi$
$659$		−	44.8149i		−	1.74574i	0.487951	−	0.872871i	$-0.337745\pi$
$660$		0			0
$661$	0.787378	−	0.787378i	0.0306255	−	0.0306255i	−0.691628	−	0.722254i	$-0.743106\pi$
$661$	0.787378	−	0.787378i	0.0306255	−	0.0306255i	0.722254	+	0.691628i	$0.243106\pi$
$662$	−1.38397			−0.0537894
$663$	15.8769	−	1.31273i	0.616608	−	0.0509822i
$664$	6.96280			0.270209
$665$		0			0
$666$	72.8969	+	30.1949i	2.82470	+	1.17003i
$667$			43.0731i			1.66780i
$668$	12.5489	−	30.2957i	0.485531	−	1.17218i
$669$	−19.2868	+	7.98884i	−0.745669	+	0.308866i
$670$		0			0
$671$	21.6089	+	21.6089i	0.834203	+	0.834203i
$672$	−47.2088	−	47.2088i	−1.82112	−	1.82112i
$673$	12.0161	+	29.0095i	0.463188	+	1.11824i	0.967081	+	0.254469i	$0.0819008\pi$
$673$	12.0161	+	29.0095i	0.463188	+	1.11824i	−0.503892	+	0.863766i	$0.668099\pi$
$674$	−1.35624	+	0.561772i	−0.0522403	+	0.0216386i
$675$		0			0
$676$		−	29.6239i		−	1.13938i
$677$	−8.20680	−	3.39937i	−0.315413	−	0.130648i	0.219360	−	0.975644i	$-0.429603\pi$
$677$	−8.20680	−	3.39937i	−0.315413	−	0.130648i	−0.534773	+	0.844996i	$0.679603\pi$
$678$	44.5074	−	44.5074i	1.70930	−	1.70930i
$679$	8.07148			0.309755
$680$		0			0
$681$	40.1110			1.53706
$682$	−19.6842	+	19.6842i	−0.753749	+	0.753749i
$683$	−39.4375	−	16.3355i	−1.50903	−	0.625062i	−0.533675	−	0.845690i	$-0.679189\pi$
$683$	−39.4375	−	16.3355i	−1.50903	−	0.625062i	−0.975358	+	0.220628i	$0.929189\pi$
$684$			64.7114i			2.47430i
$685$		0			0
$686$	−25.9086	+	10.7317i	−0.989194	+	0.409737i
$687$	2.90672	+	7.01745i	0.110898	+	0.267733i
$688$	4.54350	+	4.54350i	0.173219	+	0.173219i
$689$	4.08604	+	4.08604i	0.155666	+	0.155666i
$690$		0			0
$691$	2.41767	−	1.00143i	0.0919724	−	0.0380962i	−0.336223	−	0.941782i	$-0.609150\pi$
$691$	2.41767	−	1.00143i	0.0919724	−	0.0380962i	0.428195	+	0.903686i	$0.359150\pi$
$692$	12.9086	−	31.1641i	0.490711	−	1.18468i
$693$			75.2266i			2.85762i
$694$	28.6123	+	11.8516i	1.08611	+	0.449881i
$695$		0			0
$696$	−28.2608			−1.07122
$697$	26.6921	−	31.5038i	1.01103	−	1.19329i
$698$	−42.2165			−1.59792
$699$	−49.0530	+	49.0530i	−1.85535	+	1.85535i
$700$		0			0
$701$		−	21.5744i		−	0.814855i	−0.913238	−	0.407427i	$-0.866426\pi$
$701$		−	21.5744i		−	0.814855i	0.913238	−	0.407427i	$-0.133574\pi$
$702$	5.43699	−	13.1260i	0.205206	−	0.495411i
$703$	−36.8643	+	15.2697i	−1.39036	+	0.575907i
$704$	23.7686	+	57.3824i	0.895812	+	2.16268i
$705$		0			0
$706$	−52.7532	−	52.7532i	−1.98539	−	1.98539i
$707$	−2.89259	−	6.98332i	−0.108787	−	0.262635i
$708$	−5.77359	+	2.39150i	−0.216985	+	0.0898781i
$709$	4.52774	−	10.9309i	0.170043	−	0.410519i	−0.815768	−	0.578379i	$-0.803686\pi$
$709$	4.52774	−	10.9309i	0.170043	−	0.410519i	0.985811	+	0.167860i	$0.0536855\pi$
$710$		0			0
$711$	31.8644	+	13.1987i	1.19501	+	0.494989i
$712$	14.6984	−	14.6984i	0.550846	−	0.550846i
$713$	−15.6758			−0.587064
$714$	23.7364	−	74.0481i	0.888312	−	2.77118i
$715$		0			0
$716$	−3.29219	+	3.29219i	−0.123035	+	0.123035i
$717$	21.0783	+	8.73090i	0.787182	+	0.326062i
$718$			57.9869i			2.16405i
$719$	3.57778	−	8.63753i	0.133429	−	0.322125i	−0.843018	−	0.537886i	$-0.819223\pi$
$719$	3.57778	−	8.63753i	0.133429	−	0.322125i	0.976446	+	0.215761i	$0.0692231\pi$
$720$		0			0
$721$	−5.84860	−	14.1198i	−0.217813	−	0.525848i
$722$	−11.3614	−	11.3614i	−0.422826	−	0.422826i
$723$	−35.7388	−	35.7388i	−1.32914	−	1.32914i
$724$	−16.3513	−	39.4754i	−0.607690	−	1.46709i
$725$		0			0
$726$	34.3258	−	82.8699i	1.27395	−	3.07559i
$727$		−	19.3245i		−	0.716705i	−0.933586	−	0.358353i	$-0.883339\pi$
$727$		−	19.3245i		−	0.716705i	0.933586	−	0.358353i	$-0.116661\pi$
$728$	5.92963	+	2.45613i	0.219767	+	0.0910304i
$729$	31.1247	−	31.1247i	1.15277	−	1.15277i
$730$		0			0
$731$	−3.70345	+	11.5533i	−0.136977	+	0.427314i
$732$	−44.5872			−1.64799
$733$	21.2713	−	21.2713i	0.785675	−	0.785675i	−0.195107	−	0.980782i	$-0.562505\pi$
$733$	21.2713	−	21.2713i	0.785675	−	0.785675i	0.980782	+	0.195107i	$0.0625054\pi$
$734$	43.1916	+	17.8905i	1.59423	+	0.660352i
$735$		0			0
$736$	−18.1782	+	43.8860i	−0.670057	+	1.61766i
$737$	19.3273	−	8.00562i	0.711929	−	0.294891i
$738$	−38.9594	−	94.0563i	−1.43412	−	3.46226i
$739$	25.8777	+	25.8777i	0.951925	+	0.951925i	0.998896	−	0.0469711i	$-0.0149569\pi$
$739$	25.8777	+	25.8777i	0.951925	+	0.951925i	−0.0469711	+	0.998896i	$0.514957\pi$
$740$		0			0
$741$	7.60147	+	18.3516i	0.279247	+	0.674162i
$742$	26.0580	−	10.7936i	0.956618	−	0.396244i
$743$	11.8189	−	28.5334i	0.433594	−	1.04679i	−0.544525	−	0.838744i	$-0.683290\pi$
$743$	11.8189	−	28.5334i	0.433594	−	1.04679i	0.978119	−	0.208044i	$-0.0667098\pi$
$744$		−	10.2851i		−	0.377070i
$745$		0			0
$746$	−2.91290	+	2.91290i	−0.106649	+	0.106649i
$747$	−22.3095			−0.816263
$748$	−36.3596	+	42.9141i	−1.32944	+	1.56909i
$749$	−24.4786			−0.894430
$750$		0			0
$751$	−23.8839	−	9.89302i	−0.871535	−	0.361001i	−0.0983268	−	0.995154i	$-0.531349\pi$
$751$	−23.8839	−	9.89302i	−0.871535	−	0.361001i	−0.773208	+	0.634153i	$0.781349\pi$
$752$			11.0966i			0.404650i
$753$	−14.4091	+	34.7866i	−0.525096	+	1.26769i
$754$	−19.3185	+	8.00198i	−0.703538	+	0.291415i
$755$		0			0
$756$	−28.0721	−	28.0721i	−1.02097	−	1.02097i
$757$	−36.5084	−	36.5084i	−1.32692	−	1.32692i	−0.908042	−	0.418879i	$-0.862423\pi$
$757$	−36.5084	−	36.5084i	−1.32692	−	1.32692i	−0.418879	−	0.908042i	$-0.637577\pi$
$758$	20.2365	+	48.8552i	0.735023	+	1.77450i
$759$	81.0123	−	33.5564i	2.94056	−	1.21802i
$760$		0			0
$761$			45.9470i			1.66558i	0.553590	+	0.832789i	$0.313258\pi$
$761$			45.9470i			1.66558i	−0.553590	+	0.832789i	$0.686742\pi$
$762$	20.2789	+	8.39978i	0.734626	+	0.304292i
$763$	−37.4830	+	37.4830i	−1.35697	+	1.35697i
$764$	−0.187238			−0.00677405
$765$		0			0
$766$	74.2708			2.68351
$767$	−0.827946	+	0.827946i	−0.0298954	+	0.0298954i
$768$	1.19183	+	0.493672i	0.0430065	+	0.0178139i
$769$			2.02033i			0.0728549i	0.999336	+	0.0364274i	$0.0115978\pi$
$769$			2.02033i			0.0728549i	−0.999336	+	0.0364274i	$0.988402\pi$
$770$		0			0
$771$	20.6055	−	8.53506i	0.742087	−	0.307383i
$772$	24.2427	+	58.5271i	0.872515	+	2.10644i
$773$	27.5831	+	27.5831i	0.992095	+	0.992095i	0.999969	−	0.00787410i	$-0.00250643\pi$
$773$	27.5831	+	27.5831i	0.992095	+	0.992095i	−0.00787410	+	0.999969i	$0.502506\pi$
$774$	21.1517	+	21.1517i	0.760284	+	0.760284i
$775$		0			0
$776$	3.48112	−	1.44193i	0.124965	−	0.0517622i
$777$	25.8990	−	62.5256i	0.929120	−	2.24309i
$778$		−	32.4548i		−	1.16356i
$779$	47.5647	+	19.7019i	1.70418	+	0.705895i
$780$		0			0
$781$	53.2684			1.90609
$782$	−55.1375	+	4.55885i	−1.97171	+	0.163024i
$783$	32.7528			1.17049
$784$	−4.43744	+	4.43744i	−0.158480	+	0.158480i
$785$		0			0
$786$			51.9912i			1.85446i
$787$	17.5711	−	42.4203i	0.626341	−	1.51212i	−0.217797	−	0.975994i	$-0.569887\pi$
$787$	17.5711	−	42.4203i	0.626341	−	1.51212i	0.844138	−	0.536127i	$-0.180113\pi$
$788$	−21.4047	+	8.86613i	−0.762512	+	0.315843i
$789$	2.54106	+	6.13466i	0.0904641	+	0.218400i
$790$		0			0
$791$	−23.3018	−	23.3018i	−0.828517	−	0.828517i
$792$	13.4389	+	32.4443i	0.477529	+	1.15286i
$793$	−7.71812	+	3.19695i	−0.274078	+	0.113527i
$794$	16.6904	−	40.2941i	0.592319	−	1.42998i
$795$		0			0
$796$	6.62763	+	2.74525i	0.234910	+	0.0973029i
$797$	−20.4263	+	20.4263i	−0.723536	+	0.723536i	−0.969324	−	0.245787i	$-0.920954\pi$
$797$	−20.4263	+	20.4263i	−0.723536	+	0.723536i	0.245787	+	0.969324i	$0.420954\pi$
$798$	96.9540			3.43213
$799$	−18.6307	+	9.58581i	−0.659108	+	0.339122i
$800$		0			0
$801$	−47.0952	+	47.0952i	−1.66403	+	1.66403i
$802$	30.1601	+	12.4927i	1.06499	+	0.441133i
$803$			3.02797i			0.106855i
$804$	−11.6804	+	28.1989i	−0.411935	+	0.994499i
$805$		0			0
$806$	−2.91220	−	7.03068i	−0.102578	−	0.247645i
$807$	−22.7224	−	22.7224i	−0.799865	−	0.799865i
$808$	−2.49507	−	2.49507i	−0.0877763	−	0.0877763i
$809$	11.8144	+	28.5224i	0.415370	+	1.00279i	0.983672	+	0.179972i	$0.0576008\pi$
$809$	11.8144	+	28.5224i	0.415370	+	1.00279i	−0.568301	+	0.822821i	$0.692399\pi$
$810$		0			0
$811$	12.6060	−	30.4337i	0.442658	−	1.06867i	−0.532355	−	0.846521i	$-0.678693\pi$
$811$	12.6060	−	30.4337i	0.442658	−	1.06867i	0.975013	−	0.222149i	$-0.0713072\pi$
$812$			58.4291i			2.05046i
$813$	−60.5331	−	25.0736i	−2.12299	−	0.879371i
$814$	−60.4650	+	60.4650i	−2.11930	+	2.11930i
$815$		0			0
$816$	2.05866	+	24.8987i	0.0720676	+	0.871628i
$817$	−15.1272			−0.529233
$818$	47.4639	−	47.4639i	1.65954	−	1.65954i
$819$	−18.9992	−	7.86971i	−0.663885	−	0.274990i
$820$		0			0
$821$	0.462837	−	1.11739i	0.0161531	−	0.0389971i	−0.915597	−	0.402097i	$-0.868282\pi$
$821$	0.462837	−	1.11739i	0.0161531	−	0.0389971i	0.931750	+	0.363100i	$0.118282\pi$
$822$	−35.9198	+	14.8785i	−1.25285	+	0.518946i
$823$	−3.91670	−	9.45575i	−0.136528	−	0.329607i	0.840798	−	0.541349i	$-0.182086\pi$
$823$	−3.91670	−	9.45575i	−0.136528	−	0.329607i	−0.977326	+	0.211742i	$0.932086\pi$
$824$	−5.04486	−	5.04486i	−0.175746	−	0.175746i
$825$		0			0
$826$	2.18708	+	5.28007i	0.0760982	+	0.183717i
$827$	−43.1593	+	17.8772i	−1.50080	+	0.621650i	−0.973634	−	0.228114i	$-0.926744\pi$
$827$	−43.1593	+	17.8772i	−1.50080	+	0.621650i	−0.527163	+	0.849764i	$0.676744\pi$
$828$	−29.8845	+	72.1475i	−1.03856	+	2.50730i
$829$		−	47.0678i		−	1.63473i	−0.576118	−	0.817366i	$-0.695433\pi$
$829$		−	47.0678i		−	1.63473i	0.576118	−	0.817366i	$-0.304567\pi$
$830$		0			0
$831$	−28.8358	+	28.8358i	−1.00030	+	1.00030i
$832$	−16.9790			−0.588640
$833$	−11.2836	−	3.61700i	−0.390954	−	0.125322i
$834$	11.7904			0.408267
$835$		0			0
$836$	−64.7920	−	26.8377i	−2.24088	−	0.928202i
$837$			11.9199i			0.412012i
$838$	−7.89958	+	19.0713i	−0.272886	+	0.658806i
$839$	34.1278	−	14.1362i	1.17822	−	0.488035i	0.294319	−	0.955707i	$-0.404907\pi$
$839$	34.1278	−	14.1362i	1.17822	−	0.488035i	0.883902	+	0.467672i	$0.154907\pi$
$840$		0			0
$841$	−13.5797	−	13.5797i	−0.468264	−	0.468264i
$842$	39.7217	+	39.7217i	1.36890	+	1.36890i
$843$	−19.2147	−	46.3884i	−0.661790	−	1.59770i
$844$	−60.3935	+	25.0158i	−2.07883	+	0.861079i
$845$		0			0
$846$			51.6588i			1.77607i
$847$	−43.3865	−	17.9713i	−1.49078	−	0.617500i
$848$	−6.40785	+	6.40785i	−0.220047	+	0.220047i
$849$	57.4737			1.97249
$850$		0			0
$851$	−48.1522			−1.65063
$852$	−54.9562	+	54.9562i	−1.88277	+	1.88277i
$853$	7.67139	+	3.17759i	0.262663	+	0.108799i	0.510129	−	0.860098i	$-0.329598\pi$
$853$	7.67139	+	3.17759i	0.262663	+	0.108799i	−0.247466	+	0.968897i	$0.579598\pi$
$854$			40.7759i			1.39532i
$855$		0			0
$856$	−10.5573	+	4.37299i	−0.360842	+	0.149466i
$857$	10.6533	+	25.7194i	0.363911	+	0.878559i	0.994720	+	0.102622i	$0.0327231\pi$
$857$	10.6533	+	25.7194i	0.363911	+	0.878559i	−0.630809	+	0.775938i	$0.717277\pi$
$858$	30.1004	+	30.1004i	1.02761	+	1.02761i
$859$	−34.0064	−	34.0064i	−1.16028	−	1.16028i	−0.984414	−	0.175869i	$-0.943726\pi$
$859$	−34.0064	−	34.0064i	−1.16028	−	1.16028i	−0.175869	−	0.984414i	$-0.556274\pi$
$860$		0			0
$861$	−80.6746	+	33.4165i	−2.74938	+	1.13883i
$862$	−14.7742	+	35.6680i	−0.503211	+	1.21486i
$863$		−	1.42615i		−	0.0485469i	−0.999705	−	0.0242734i	$-0.992273\pi$
$863$		−	1.42615i		−	0.0485469i	0.999705	−	0.0242734i	$-0.00772723\pi$
$864$	33.3710	+	13.8227i	1.13530	+	0.470258i
$865$		0			0
$866$	−19.6896			−0.669081
$867$	−40.0256	+	24.9652i	−1.35934	+	0.847864i
$868$	−21.2644			−0.721761
$869$	−26.4302	+	26.4302i	−0.896584	+	0.896584i
$870$		0			0
$871$			5.71878i			0.193773i
$872$	−9.46978	+	22.8621i	−0.320687	+	0.774208i
$873$	−11.1539	+	4.62009i	−0.377502	+	0.156366i
$874$	−26.3984	−	63.7315i	−0.892941	−	2.15575i
$875$		0			0
$876$	−3.12391	−	3.12391i	−0.105547	−	0.105547i
$877$	1.58263	+	3.82080i	0.0534415	+	0.129019i	0.948345	−	0.317240i	$-0.102756\pi$
$877$	1.58263	+	3.82080i	0.0534415	+	0.129019i	−0.894904	+	0.446259i	$0.852756\pi$
$878$	31.1014	−	12.8826i	1.04962	−	0.434767i
$879$	−22.6332	+	54.6414i	−0.763399	+	1.84301i
$880$		0			0
$881$	−6.15155	−	2.54806i	−0.207251	−	0.0858462i	0.276643	−	0.960973i	$-0.410778\pi$
$881$	−6.15155	−	2.54806i	−0.207251	−	0.0858462i	−0.483894	+	0.875127i	$0.660778\pi$
$882$	−20.6580	+	20.6580i	−0.695592	+	0.695592i
$883$	−56.3327			−1.89575			−0.947874	−	0.318646i	$-0.896772\pi$
$883$	−56.3327			−1.89575			−0.947874	+	0.318646i	$0.896772\pi$
$884$	−7.03465	−	13.6724i	−0.236601	−	0.459851i
$885$		0			0
$886$	−18.0445	+	18.0445i	−0.606216	+	0.606216i
$887$	−25.9241	−	10.7381i	−0.870445	−	0.360550i	−0.0976611	−	0.995220i	$-0.531136\pi$
$887$	−25.9241	−	10.7381i	−0.870445	−	0.360550i	−0.772783	+	0.634670i	$0.781136\pi$
$888$		−	31.5932i		−	1.06020i
$889$	4.39770	−	10.6170i	0.147494	−	0.356082i
$890$		0			0
$891$	1.96828	+	4.75186i	0.0659400	+	0.159193i
$892$	14.2470	+	14.2470i	0.477026	+	0.477026i
$893$	−18.4725	−	18.4725i	−0.618158	−	0.618158i
$894$	35.5218	+	85.7572i	1.18803	+	2.86815i
$895$		0			0
$896$	−13.3000	+	32.1090i	−0.444322	+	1.07269i
$897$			23.9709i			0.800364i
$898$	10.4861	+	4.34347i	0.349925	+	0.144944i
$899$	12.4050	−	12.4050i	0.413730	−	0.413730i
$900$		0			0
$901$	−16.2940	−	5.22310i	−0.542832	−	0.174007i
$902$	110.331			3.67363
$903$	18.1424	−	18.1424i	0.603742	−	0.603742i
$904$	−14.2125	−	5.88702i	−0.472702	−	0.195799i
$905$		0			0
$906$	28.8789	−	69.7199i	0.959438	−	2.31629i
$907$	22.5968	−	9.35991i	0.750315	−	0.310791i	0.0254448	−	0.999676i	$-0.491900\pi$
$907$	22.5968	−	9.35991i	0.750315	−	0.310791i	0.724870	+	0.688886i	$0.241900\pi$
$908$	−14.8149	−	35.7663i	−0.491650	−	1.18695i
$909$	7.99447	+	7.99447i	0.265160	+	0.265160i
$910$		0			0
$911$	7.56912	+	18.2735i	0.250776	+	0.605427i	0.998267	−	0.0588448i	$-0.0187417\pi$
$911$	7.56912	+	18.2735i	0.250776	+	0.605427i	−0.747491	+	0.664272i	$0.768742\pi$
$912$	−28.7795	+	11.9209i	−0.952985	+	0.394739i
$913$	9.25243	−	22.3373i	0.306211	−	0.739258i
$914$		−	59.0661i		−	1.95373i
$915$		0			0
$916$	5.18376	−	5.18376i	0.171276	−	0.171276i
$917$	27.2200			0.898882
$918$	3.46655	+	41.9265i	0.114413	+	1.38378i
$919$	−56.1931			−1.85364			−0.926820	−	0.375507i	$-0.877469\pi$
$919$	−56.1931			−1.85364			−0.926820	+	0.375507i	$0.877469\pi$
$920$		0			0
$921$	49.0967	+	20.3365i	1.61779	+	0.670111i
$922$		−	53.2378i		−	1.75329i
$923$	−5.57260	+	13.4534i	−0.183424	+	0.442825i
$924$	109.894	−	45.5196i	3.61525	−	1.49748i
$925$		0			0
$926$	23.7209	+	23.7209i	0.779518	+	0.779518i
$927$	16.1643	+	16.1643i	0.530904	+	0.530904i
$928$	−20.3438	−	49.1143i	−0.667818	−	1.61226i
$929$	−44.6817	+	18.5078i	−1.46596	+	0.607220i	−0.965933	−	0.258792i	$-0.916676\pi$
$929$	−44.6817	+	18.5078i	−1.46596	+	0.607220i	−0.500025	+	0.866011i	$0.666676\pi$
$930$		0			0
$931$		−	14.7741i		−	0.484201i
$932$	61.8574	+	25.6222i	2.02621	+	0.839282i
$933$	−21.4633	+	21.4633i	−0.702678	+	0.702678i
$934$	6.24510			0.204346
$935$		0			0
$936$	−9.59998			−0.313785
$937$	0.319776	−	0.319776i	0.0104466	−	0.0104466i	−0.701864	−	0.712311i	$-0.747649\pi$
$937$	0.319776	−	0.319776i	0.0104466	−	0.0104466i	0.712311	+	0.701864i	$0.247649\pi$
$938$	25.7885	+	10.6819i	0.842024	+	0.348778i
$939$			4.26337i			0.139130i
$940$		0			0
$941$	36.5967	−	15.1588i	1.19302	−	0.494164i	0.304281	−	0.952582i	$-0.401584\pi$
$941$	36.5967	−	15.1588i	1.19302	−	0.494164i	0.888736	+	0.458419i	$0.151584\pi$
$942$	−37.3722	−	90.2244i	−1.21765	−	2.93967i
$943$	43.9319	+	43.9319i	1.43062	+	1.43062i
$944$	−1.29841	−	1.29841i	−0.0422596	−	0.0422596i
$945$		0			0
$946$	−29.9504	+	12.4058i	−0.973770	+	0.403349i
$947$	6.26475	−	15.1244i	0.203577	−	0.491478i	−0.788810	−	0.614637i	$-0.789302\pi$
$947$	6.26475	−	15.1244i	0.203577	−	0.491478i	0.992387	+	0.123159i	$0.0393025\pi$
$948$		−	54.5353i		−	1.77123i
$949$	−0.764743	−	0.316767i	−0.0248246	−	0.0102827i
$950$		0			0
$951$	−54.1117			−1.75469
$952$	−18.9401	+	1.56600i	−0.613853	+	0.0507543i
$953$	20.6540			0.669047			0.334524	−	0.942387i	$-0.391425\pi$
$953$	20.6540			0.669047			0.334524	+	0.942387i	$0.391425\pi$
$954$	−29.8310	+	29.8310i	−0.965815	+	0.965815i
$955$		0			0
$956$		−	22.0199i		−	0.712175i
$957$	−37.5541	+	90.6635i	−1.21395	+	2.93073i
$958$	−26.3052	+	10.8960i	−0.849882	+	0.352033i
$959$	7.78960	+	18.8058i	0.251539	+	0.607270i
$960$		0			0
$961$	−17.4057	−	17.4057i	−0.561474	−	0.561474i
$962$	−8.94555	−	21.5965i	−0.288416	−	0.696298i
$963$	33.8268	−	14.0115i	1.09005	−	0.451515i
$964$	−18.6677	+	45.0678i	−0.601246	+	1.45154i
$965$		0			0
$966$	108.095	+	44.7745i	3.47791	+	1.44060i
$967$	14.4709	−	14.4709i	0.465354	−	0.465354i	−0.435052	−	0.900406i	$-0.643270\pi$
$967$	14.4709	−	14.4709i	0.465354	−	0.465354i	0.900406	+	0.435052i	$0.143270\pi$
$968$	−21.9225			−0.704616
$969$	−44.8760	−	38.0219i	−1.44162	−	1.22144i
$970$		0			0
$971$	−12.7203	+	12.7203i	−0.408213	+	0.408213i	−0.881115	−	0.472902i	$-0.843207\pi$
$971$	−12.7203	+	12.7203i	−0.408213	+	0.408213i	0.472902	+	0.881115i	$0.343207\pi$
$972$	−41.9504	−	17.3764i	−1.34556	−	0.557350i
$973$		−	6.17283i		−	0.197892i
$974$	−17.1522	+	41.4091i	−0.549593	+	1.32683i
$975$		0			0
$976$	−5.01355	−	12.1038i	−0.160480	−	0.387433i
$977$	21.4226	+	21.4226i	0.685370	+	0.685370i	0.961205	−	0.275835i	$-0.0889544\pi$
$977$	21.4226	+	21.4226i	0.685370	+	0.685370i	−0.275835	+	0.961205i	$0.588954\pi$
$978$	31.5134	+	31.5134i	1.00769	+	1.00769i
$979$	−27.6221	−	66.6857i	−0.882807	−	2.13128i
$980$		0			0
$981$	30.3422	−	73.2525i	0.968751	−	2.33877i
$982$		−	13.7548i		−	0.438932i
$983$	−30.8078	−	12.7610i	−0.982615	−	0.407013i	−0.167222	−	0.985919i	$-0.553480\pi$
$983$	−30.8078	−	12.7610i	−0.982615	−	0.407013i	−0.815394	+	0.578907i	$0.803480\pi$
$984$	−28.8242	+	28.8242i	−0.918883	+	0.918883i
$985$		0			0
$986$	40.0252	−	47.2404i	1.27466	−	1.50444i
$987$	44.3091			1.41037
$988$	13.5562	−	13.5562i	0.431281	−	0.431281i
$989$	−16.8655	−	6.98591i	−0.536291	−	0.222139i
$990$		0			0
$991$	−4.73199	+	11.4240i	−0.150317	+	0.362897i	−0.981045	−	0.193782i	$-0.937925\pi$
$991$	−4.73199	+	11.4240i	−0.150317	+	0.362897i	0.830728	+	0.556679i	$0.187925\pi$
$992$	17.8744	−	7.40382i	0.567513	−	0.235072i
$993$	−0.679473	−	1.64039i	−0.0215624	−	0.0520563i
$994$	50.2586	+	50.2586i	1.59411	+	1.59411i
$995$		0			0
$996$	13.4995	+	32.5907i	0.427748	+	1.03268i
$997$	18.9104	−	7.83294i	0.598898	−	0.248072i	−0.0625753	−	0.998040i	$-0.519931\pi$
$997$	18.9104	−	7.83294i	0.598898	−	0.248072i	0.661474	+	0.749968i	$0.269931\pi$
$998$	−10.1910	+	24.6033i	−0.322591	+	0.778803i
$999$			36.6149i			1.15844i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	425.2.m.d.26.5	yes	24
5.2	odd	4		425.2.n.e.349.5		24
5.3	odd	4		425.2.n.d.349.2		24
5.4	even	2		425.2.m.c.26.2	✓	24
17.2	even	8	inner	425.2.m.d.376.5	yes	24
17.6	odd	16		7225.2.a.cb.1.20		24
17.11	odd	16		7225.2.a.cb.1.19		24
85.2	odd	8		425.2.n.d.274.2		24
85.19	even	8		425.2.m.c.376.2	yes	24
85.53	odd	8		425.2.n.e.274.5		24
85.74	odd	16		7225.2.a.bx.1.5		24
85.79	odd	16		7225.2.a.bx.1.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
425.2.m.c.26.2	✓	24	5.4	even	2
425.2.m.c.376.2	yes	24	85.19	even	8
425.2.m.d.26.5	yes	24	1.1	even	1	trivial
425.2.m.d.376.5	yes	24	17.2	even	8	inner
425.2.n.d.274.2		24	85.2	odd	8
425.2.n.d.349.2		24	5.3	odd	4
425.2.n.e.274.5		24	85.53	odd	8
425.2.n.e.349.5		24	5.2	odd	4
7225.2.a.bx.1.5		24	85.74	odd	16
7225.2.a.bx.1.6		24	85.79	odd	16
7225.2.a.cb.1.19		24	17.11	odd	16
7225.2.a.cb.1.20		24	17.6	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)

\(f(q)\)	\(=\)	\(q+(1.52941 - 1.52941i) q^{2} +(2.56367 + 1.06191i) q^{3} -2.67820i q^{4} +(5.54499 - 2.29681i) q^{6} +(-1.20249 - 2.90308i) q^{7} +(-1.03724 - 1.03724i) q^{8} +(3.32343 + 3.32343i) q^{9} +O(q^{10})\)	\(q+(1.52941 - 1.52941i) q^{2} +(2.56367 + 1.06191i) q^{3} -2.67820i q^{4} +(5.54499 - 2.29681i) q^{6} +(-1.20249 - 2.90308i) q^{7} +(-1.03724 - 1.03724i) q^{8} +(3.32343 + 3.32343i) q^{9} +(-4.70589 + 1.94925i) q^{11} +(2.84399 - 6.86600i) q^{12} -1.39243i q^{13} +(-6.27910 - 2.60089i) q^{14} +2.18366 q^{16} +(1.88636 + 3.66628i) q^{17} +10.1658 q^{18} +(-3.63515 + 3.63515i) q^{19} -8.71946i q^{21} +(-4.21605 + 10.1784i) q^{22} +(-5.73163 + 2.37412i) q^{23} +(-1.55769 - 3.76059i) q^{24} +(-2.12960 - 2.12960i) q^{26} +(1.80528 + 4.35833i) q^{27} +(-7.77501 + 3.22051i) q^{28} +(2.65695 - 6.41445i) q^{29} +(2.33444 + 0.966958i) q^{31} +(5.41419 - 5.41419i) q^{32} -14.1343 q^{33} +(8.49228 + 2.72223i) q^{34} +(8.90079 - 8.90079i) q^{36} +(7.17082 + 2.97025i) q^{37} +11.1193i q^{38} +(1.47863 - 3.56974i) q^{39} +(-3.83241 - 9.25225i) q^{41} +(-13.3356 - 13.3356i) q^{42} +(2.08068 + 2.08068i) q^{43} +(5.22046 + 12.6033i) q^{44} +(-5.13501 + 12.3970i) q^{46} +5.08164i q^{47} +(5.59817 + 2.31884i) q^{48} +(-2.03211 + 2.03211i) q^{49} +(0.942759 + 11.4023i) q^{51} -3.72921 q^{52} +(-2.93446 + 2.93446i) q^{53} +(9.42669 + 3.90466i) q^{54} +(-1.76391 + 4.25846i) q^{56} +(-13.1795 + 5.45912i) q^{57} +(-5.74676 - 13.8739i) q^{58} +(-0.594603 - 0.594603i) q^{59} +(-2.29594 - 5.54290i) q^{61} +(5.04920 - 2.09145i) q^{62} +(5.65176 - 13.6446i) q^{63} -12.1937i q^{64} +(-21.6171 + 21.6171i) q^{66} -4.10703 q^{67} +(9.81903 - 5.05205i) q^{68} -17.2151 q^{69} +(-9.66181 - 4.00205i) q^{71} -6.89439i q^{72} +(0.227491 - 0.549213i) q^{73} +(15.5099 - 6.42439i) q^{74} +(9.73564 + 9.73564i) q^{76} +(11.3176 + 11.3176i) q^{77} +(-3.19816 - 7.72104i) q^{78} +(6.77961 - 2.80821i) q^{79} -1.00977i q^{81} +(-20.0118 - 8.28917i) q^{82} +(-3.35640 + 3.35640i) q^{83} -23.3524 q^{84} +6.36444 q^{86} +(13.6231 - 13.6231i) q^{87} +(6.90298 + 2.85931i) q^{88} +14.1707i q^{89} +(-4.04234 + 1.67439i) q^{91} +(6.35835 + 15.3504i) q^{92} +(4.95792 + 4.95792i) q^{93} +(7.77191 + 7.77191i) q^{94} +(19.6296 - 8.13083i) q^{96} +(-0.982991 + 2.37315i) q^{97} +6.21588i q^{98} +(-22.1179 - 9.16152i) 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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