LMFDB - Embedded newform 105.3.l.a.22.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,3,Mod(22,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("105.22");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	105.l (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.86104277578$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			22.1
Character	$\chi$	$=$	105.22
Dual form			105.3.l.a.43.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.72310 - 2.72310i) q^{2} +(-1.22474 + 1.22474i) q^{3} +10.8306i q^{4} +(4.39513 - 2.38387i) q^{5} +6.67022 q^{6} +(-1.87083 - 1.87083i) q^{7} +(18.6004 - 18.6004i) q^{8} -3.00000i q^{9} +O(q^{10})$	\(q+(-2.72310 - 2.72310i) q^{2} +(-1.22474 + 1.22474i) q^{3} +10.8306i q^{4} +(4.39513 - 2.38387i) q^{5} +6.67022 q^{6} +(-1.87083 - 1.87083i) q^{7} +(18.6004 - 18.6004i) q^{8} -3.00000i q^{9} +(-18.4599 - 5.47689i) q^{10} +3.42164 q^{11} +(-13.2647 - 13.2647i) q^{12} +(7.98120 - 7.98120i) q^{13} +10.1889i q^{14} +(-2.46329 + 8.30254i) q^{15} -57.9794 q^{16} +(-16.5713 - 16.5713i) q^{17} +(-8.16931 + 8.16931i) q^{18} +1.38069i q^{19} +(25.8187 + 47.6019i) q^{20} +4.58258 q^{21} +(-9.31750 - 9.31750i) q^{22} +(18.8473 - 18.8473i) q^{23} +45.5616i q^{24} +(13.6344 - 20.9548i) q^{25} -43.4673 q^{26} +(3.67423 + 3.67423i) q^{27} +(20.2622 - 20.2622i) q^{28} -45.7370i q^{29} +(29.3165 - 15.9009i) q^{30} +43.2632 q^{31} +(83.4823 + 83.4823i) q^{32} +(-4.19064 + 4.19064i) q^{33} +90.2505i q^{34} +(-12.6823 - 3.76274i) q^{35} +32.4918 q^{36} +(2.18941 + 2.18941i) q^{37} +(3.75977 - 3.75977i) q^{38} +19.5499i q^{39} +(37.4104 - 126.092i) q^{40} +6.61005 q^{41} +(-12.4788 - 12.4788i) q^{42} +(-44.1187 + 44.1187i) q^{43} +37.0585i q^{44} +(-7.15160 - 13.1854i) q^{45} -102.646 q^{46} +(14.2193 + 14.2193i) q^{47} +(71.0100 - 71.0100i) q^{48} +7.00000i q^{49} +(-94.1899 + 19.9343i) q^{50} +40.5911 q^{51} +(86.4412 + 86.4412i) q^{52} +(-44.4359 + 44.4359i) q^{53} -20.0106i q^{54} +(15.0386 - 8.15674i) q^{55} -69.5964 q^{56} +(-1.69100 - 1.69100i) q^{57} +(-124.547 + 124.547i) q^{58} +17.2928i q^{59} +(-89.9215 - 26.6789i) q^{60} +48.0848 q^{61} +(-117.810 - 117.810i) q^{62} +(-5.61249 + 5.61249i) q^{63} -222.745i q^{64} +(16.0523 - 54.1046i) q^{65} +22.8231 q^{66} +(40.9435 + 40.9435i) q^{67} +(179.477 - 179.477i) q^{68} +46.1662i q^{69} +(24.2890 + 44.7817i) q^{70} -38.7743 q^{71} +(-55.8013 - 55.8013i) q^{72} +(66.4788 - 66.4788i) q^{73} -11.9240i q^{74} +(8.96566 + 42.3629i) q^{75} -14.9537 q^{76} +(-6.40131 - 6.40131i) q^{77} +(53.2363 - 53.2363i) q^{78} -5.30864i q^{79} +(-254.827 + 138.215i) q^{80} -9.00000 q^{81} +(-17.9999 - 17.9999i) q^{82} +(-62.5835 + 62.5835i) q^{83} +49.6320i q^{84} +(-112.337 - 33.3292i) q^{85} +240.280 q^{86} +(56.0161 + 56.0161i) q^{87} +(63.6441 - 63.6441i) q^{88} +44.8163i q^{89} +(-16.4307 + 55.3798i) q^{90} -29.8629 q^{91} +(204.127 + 204.127i) q^{92} +(-52.9864 + 52.9864i) q^{93} -77.4411i q^{94} +(3.29139 + 6.06833i) q^{95} -204.489 q^{96} +(-30.5196 - 30.5196i) q^{97} +(19.0617 - 19.0617i) q^{98} -10.2649i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8}+O(q^{10}) $ 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8	$ 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8} - 40 q^{10} - 48 q^{12} + 64 q^{13} - 184 q^{16} + 24 q^{17} + 24 q^{18} + 72 q^{20} + 8 q^{22} + 8 q^{23} - 136 q^{25} - 80 q^{26} + 96 q^{30} + 96 q^{31} + 56 q^{32} - 72 q^{33} + 168 q^{36} + 8 q^{37} + 56 q^{38} + 232 q^{40} + 320 q^{41} - 112 q^{43} - 72 q^{45} + 320 q^{46} + 64 q^{47} + 192 q^{48} - 256 q^{50} - 192 q^{51} + 96 q^{52} - 72 q^{53} - 80 q^{55} - 336 q^{56} + 48 q^{57} - 512 q^{58} - 192 q^{60} - 496 q^{61} - 776 q^{62} + 312 q^{65} - 192 q^{66} - 192 q^{67} + 568 q^{68} + 112 q^{70} - 144 q^{71} + 144 q^{72} + 224 q^{73} + 144 q^{75} + 416 q^{76} + 112 q^{77} - 216 q^{78} - 528 q^{80} - 216 q^{81} + 352 q^{82} - 32 q^{83} + 24 q^{85} + 240 q^{86} + 384 q^{87} + 216 q^{88} - 24 q^{90} + 1304 q^{92} + 376 q^{95} + 168 q^{96} - 816 q^{97} - 56 q^{98}+O(q^{100}) $ 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8 - 40 * q^10 - 48 * q^12 + 64 * q^13 - 184 * q^16 + 24 * q^17 + 24 * q^18 + 72 * q^20 + 8 * q^22 + 8 * q^23 - 136 * q^25 - 80 * q^26 + 96 * q^30 + 96 * q^31 + 56 * q^32 - 72 * q^33 + 168 * q^36 + 8 * q^37 + 56 * q^38 + 232 * q^40 + 320 * q^41 - 112 * q^43 - 72 * q^45 + 320 * q^46 + 64 * q^47 + 192 * q^48 - 256 * q^50 - 192 * q^51 + 96 * q^52 - 72 * q^53 - 80 * q^55 - 336 * q^56 + 48 * q^57 - 512 * q^58 - 192 * q^60 - 496 * q^61 - 776 * q^62 + 312 * q^65 - 192 * q^66 - 192 * q^67 + 568 * q^68 + 112 * q^70 - 144 * q^71 + 144 * q^72 + 224 * q^73 + 144 * q^75 + 416 * q^76 + 112 * q^77 - 216 * q^78 - 528 * q^80 - 216 * q^81 + 352 * q^82 - 32 * q^83 + 24 * q^85 + 240 * q^86 + 384 * q^87 + 216 * q^88 - 24 * q^90 + 1304 * q^92 + 376 * q^95 + 168 * q^96 - 816 * q^97 - 56 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$	−2.72310	−	2.72310i	−1.36155	−	1.36155i	−0.871941	−	0.489612i	$-0.837139\pi$
$2$	−2.72310	−	2.72310i	−1.36155	−	1.36155i	−0.489612	−	0.871941i	$-0.662861\pi$
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$3$	−1.22474	+	1.22474i	−0.408248	+	0.408248i
$4$			10.8306i			2.70765i
$5$	4.39513	−	2.38387i	0.879026	−	0.476773i
$5$	4.39513	−	2.38387i	0.879026	−	0.476773i
$6$	6.67022			1.11170
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$7$	−1.87083	−	1.87083i	−0.267261	−	0.267261i
$8$	18.6004	−	18.6004i	2.32505	−	2.32505i
$9$		−	3.00000i		−	0.333333i
$10$	−18.4599	−	5.47689i	−1.84599	−	0.547689i
$11$	3.42164			0.311059			0.155529	−	0.987831i	$-0.450292\pi$
$11$	3.42164			0.311059			0.155529	+	0.987831i	$0.450292\pi$
$12$	−13.2647	−	13.2647i	−1.10539	−	1.10539i
$13$	7.98120	−	7.98120i	0.613939	−	0.613939i	−0.330031	−	0.943970i	$-0.607059\pi$
$13$	7.98120	−	7.98120i	0.613939	−	0.613939i	0.943970	+	0.330031i	$0.107059\pi$
$14$			10.1889i			0.727780i
$15$	−2.46329	+	8.30254i	−0.164219	+	0.553503i
$16$	−57.9794			−3.62371
$17$	−16.5713	−	16.5713i	−0.974780	−	0.974780i	0.0249097	−	0.999690i	$-0.492070\pi$
$17$	−16.5713	−	16.5713i	−0.974780	−	0.974780i	−0.999690	+	0.0249097i	$0.992070\pi$
$18$	−8.16931	+	8.16931i	−0.453851	+	0.453851i
$19$			1.38069i			0.0726681i	0.999340	+	0.0363341i	$0.0115680\pi$
$19$			1.38069i			0.0726681i	−0.999340	+	0.0363341i	$0.988432\pi$
$20$	25.8187	+	47.6019i	1.29093	+	2.38010i
$21$	4.58258			0.218218
$22$	−9.31750	−	9.31750i	−0.423523	−	0.423523i
$23$	18.8473	−	18.8473i	0.819447	−	0.819447i	−0.166581	−	0.986028i	$-0.553273\pi$
$23$	18.8473	−	18.8473i	0.819447	−	0.819447i	0.986028	+	0.166581i	$0.0532728\pi$
$24$			45.5616i			1.89840i
$25$	13.6344	−	20.9548i	0.545375	−	0.838192i
$26$	−43.4673			−1.67182
$27$	3.67423	+	3.67423i	0.136083	+	0.136083i
$28$	20.2622	−	20.2622i	0.723650	−	0.723650i
$29$		−	45.7370i		−	1.57714i	−0.614947	−	0.788568i	$-0.710823\pi$
$29$		−	45.7370i		−	1.57714i	0.614947	−	0.788568i	$-0.289177\pi$
$30$	29.3165	−	15.9009i	0.977216	−	0.530030i
$31$	43.2632			1.39559			0.697793	−	0.716299i	$-0.254165\pi$
$31$	43.2632			1.39559			0.697793	+	0.716299i	$0.254165\pi$
$32$	83.4823	+	83.4823i	2.60882	+	2.60882i
$33$	−4.19064	+	4.19064i	−0.126989	+	0.126989i
$34$			90.2505i			2.65443i
$35$	−12.6823	−	3.76274i	−0.362353	−	0.107507i
$36$	32.4918			0.902550
$37$	2.18941	+	2.18941i	0.0591732	+	0.0591732i	0.736074	−	0.676901i	$-0.236677\pi$
$37$	2.18941	+	2.18941i	0.0591732	+	0.0591732i	−0.676901	+	0.736074i	$0.736677\pi$
$38$	3.75977	−	3.75977i	0.0989414	−	0.0989414i
$39$			19.5499i			0.501279i
$40$	37.4104	−	126.092i	0.935260	−	3.15231i
$41$	6.61005			0.161221			0.0806104	−	0.996746i	$-0.474313\pi$
$41$	6.61005			0.161221			0.0806104	+	0.996746i	$0.474313\pi$
$42$	−12.4788	−	12.4788i	−0.297115	−	0.297115i
$43$	−44.1187	+	44.1187i	−1.02602	+	1.02602i	−0.0263634	+	0.999652i	$0.508393\pi$
$43$	−44.1187	+	44.1187i	−1.02602	+	1.02602i	−0.999652	+	0.0263634i	$0.991607\pi$
$44$			37.0585i			0.842238i
$45$	−7.15160	−	13.1854i	−0.158924	−	0.293009i
$46$	−102.646			−2.23144
$47$	14.2193	+	14.2193i	0.302538	+	0.302538i	0.842006	−	0.539468i	$-0.181375\pi$
$47$	14.2193	+	14.2193i	0.302538	+	0.302538i	−0.539468	+	0.842006i	$0.681375\pi$
$48$	71.0100	−	71.0100i	1.47938	−	1.47938i
$49$			7.00000i			0.142857i
$50$	−94.1899	+	19.9343i	−1.88380	+	0.398686i
$51$	40.5911			0.795905
$52$	86.4412	+	86.4412i	1.66233	+	1.66233i
$53$	−44.4359	+	44.4359i	−0.838413	+	0.838413i	−0.988650	−	0.150237i	$-0.951996\pi$
$53$	−44.4359	+	44.4359i	−0.838413	+	0.838413i	0.150237	+	0.988650i	$0.451996\pi$
$54$		−	20.0106i		−	0.370568i
$55$	15.0386	−	8.15674i	0.273429	−	0.148304i
$56$	−69.5964			−1.24279
$57$	−1.69100	−	1.69100i	−0.0296666	−	0.0296666i
$58$	−124.547	+	124.547i	−2.14735	+	2.14735i
$59$			17.2928i			0.293099i	0.989203	+	0.146549i	$0.0468167\pi$
$59$			17.2928i			0.293099i	−0.989203	+	0.146549i	$0.953183\pi$
$60$	−89.9215	−	26.6789i	−1.49869	−	0.444648i
$61$	48.0848			0.788276			0.394138	−	0.919051i	$-0.371043\pi$
$61$	48.0848			0.788276			0.394138	+	0.919051i	$0.371043\pi$
$62$	−117.810	−	117.810i	−1.90016	−	1.90016i
$63$	−5.61249	+	5.61249i	−0.0890871	+	0.0890871i
$64$		−	222.745i		−	3.48038i
$65$	16.0523	−	54.1046i	0.246959	−	0.832378i
$66$	22.8231			0.345805
$67$	40.9435	+	40.9435i	0.611097	+	0.611097i	0.943232	−	0.332135i	$-0.107769\pi$
$67$	40.9435	+	40.9435i	0.611097	+	0.611097i	−0.332135	+	0.943232i	$0.607769\pi$
$68$	179.477	−	179.477i	2.63936	−	2.63936i
$69$			46.1662i			0.669075i
$70$	24.2890	+	44.7817i	0.346986	+	0.639738i
$71$	−38.7743			−0.546118			−0.273059	−	0.961997i	$-0.588035\pi$
$71$	−38.7743			−0.546118			−0.273059	+	0.961997i	$0.588035\pi$
$72$	−55.8013	−	55.8013i	−0.775018	−	0.775018i
$73$	66.4788	−	66.4788i	0.910668	−	0.910668i	−0.0856565	−	0.996325i	$-0.527299\pi$
$73$	66.4788	−	66.4788i	0.910668	−	0.910668i	0.996325	+	0.0856565i	$0.0272988\pi$
$74$		−	11.9240i		−	0.161135i
$75$	8.96566	+	42.3629i	0.119542	+	0.564839i
$76$	−14.9537			−0.196760
$77$	−6.40131	−	6.40131i	−0.0831339	−	0.0831339i
$78$	53.2363	−	53.2363i	0.682517	−	0.682517i
$79$		−	5.30864i		−	0.0671980i	−0.999435	−	0.0335990i	$-0.989303\pi$
$79$		−	5.30864i		−	0.0671980i	0.999435	−	0.0335990i	$-0.0106969\pi$
$80$	−254.827	+	138.215i	−3.18534	+	1.72769i
$81$	−9.00000			−0.111111
$82$	−17.9999	−	17.9999i	−0.219511	−	0.219511i
$83$	−62.5835	+	62.5835i	−0.754017	+	0.754017i	−0.975226	−	0.221209i	$-0.929000\pi$
$83$	−62.5835	+	62.5835i	−0.754017	+	0.754017i	0.221209	+	0.975226i	$0.429000\pi$
$84$			49.6320i			0.590857i
$85$	−112.337	−	33.3292i	−1.32161	−	0.392109i
$86$	240.280			2.79395
$87$	56.0161	+	56.0161i	0.643863	+	0.643863i
$88$	63.6441	−	63.6441i	0.723228	−	0.723228i
$89$			44.8163i			0.503554i	0.967785	+	0.251777i	$0.0810149\pi$
$89$			44.8163i			0.503554i	−0.967785	+	0.251777i	$0.918985\pi$
$90$	−16.4307	+	55.3798i	−0.182563	+	0.615331i
$91$	−29.8629			−0.328164
$92$	204.127	+	204.127i	2.21877	+	2.21877i
$93$	−52.9864	+	52.9864i	−0.569746	+	0.569746i
$94$		−	77.4411i		−	0.823842i
$95$	3.29139	+	6.06833i	0.0346462	+	0.0638772i
$96$	−204.489			−2.13010
$97$	−30.5196	−	30.5196i	−0.314635	−	0.314635i	0.532067	−	0.846702i	$-0.321415\pi$
$97$	−30.5196	−	30.5196i	−0.314635	−	0.314635i	−0.846702	+	0.532067i	$0.821415\pi$
$98$	19.0617	−	19.0617i	0.194507	−	0.194507i
$99$		−	10.2649i		−	0.103686i
$100$	226.953	+	147.668i	2.26953	+	1.47668i
$101$	115.859			1.14712			0.573561	−	0.819163i	$-0.305561\pi$
$101$	115.859			1.14712			0.573561	+	0.819163i	$0.305561\pi$
$102$	−110.534	−	110.534i	−1.08367	−	1.08367i
$103$	−36.9871	+	36.9871i	−0.359098	+	0.359098i	−0.863480	−	0.504382i	$-0.831720\pi$
$103$	−36.9871	+	36.9871i	−0.359098	+	0.359098i	0.504382	+	0.863480i	$0.331720\pi$
$104$		−	296.908i		−	2.85488i
$105$	20.1410	−	10.9242i	0.191819	−	0.104040i
$106$	242.007			2.28309
$107$	−105.863	−	105.863i	−0.989371	−	0.989371i	0.0105734	−	0.999944i	$-0.496634\pi$
$107$	−105.863	−	105.863i	−0.989371	−	0.989371i	−0.999944	+	0.0105734i	$0.996634\pi$
$108$	−39.7942	+	39.7942i	−0.368464	+	0.368464i
$109$		−	41.7489i		−	0.383017i	−0.981491	−	0.191509i	$-0.938662\pi$
$109$		−	41.7489i		−	0.383017i	0.981491	−	0.191509i	$-0.0613380\pi$
$110$	−63.1633	−	18.7400i	−0.574212	−	0.170363i
$111$	−5.36293			−0.0483147
$112$	108.470	+	108.470i	0.968478	+	0.968478i
$113$	−154.947	+	154.947i	−1.37121	+	1.37121i	−0.512554	+	0.858655i	$0.671300\pi$
$113$	−154.947	+	154.947i	−1.37121	+	1.37121i	−0.858655	+	0.512554i	$0.828700\pi$
$114$			9.20953i			0.0807853i
$115$	37.9069	−	127.766i	0.329625	−	1.11101i
$116$	495.358			4.27033
$117$	−23.9436	−	23.9436i	−0.204646	−	0.204646i
$118$	47.0902	−	47.0902i	0.399069	−	0.399069i
$119$			62.0040i			0.521042i
$120$	108.613	+	200.249i	0.905105	+	1.66874i
$121$	−109.292			−0.903243
$122$	−130.940	−	130.940i	−1.07328	−	1.07328i
$123$	−8.09563	+	8.09563i	−0.0658181	+	0.0658181i
$124$			468.566i			3.77876i
$125$	9.97143	−	124.602i	0.0797714	−	0.996813i
$126$	30.5668			0.242593
$127$	84.5679	+	84.5679i	0.665889	+	0.665889i	0.956762	−	0.290873i	$-0.0939456\pi$
$127$	84.5679	+	84.5679i	0.665889	+	0.665889i	−0.290873	+	0.956762i	$0.593946\pi$
$128$	−272.627	+	272.627i	−2.12990	+	2.12990i
$129$		−	108.068i		−	0.837738i
$130$	−191.045	+	103.620i	−1.46957	+	0.797078i
$131$	75.1775			0.573874			0.286937	−	0.957949i	$-0.407363\pi$
$131$	75.1775			0.573874			0.286937	+	0.957949i	$0.407363\pi$
$132$	−45.3872	−	45.3872i	−0.343842	−	0.343842i
$133$	2.58304	−	2.58304i	0.0194214	−	0.0194214i
$134$		−	222.987i		−	1.66408i
$135$	24.9076	+	7.38987i	0.184501	+	0.0547397i
$136$	−616.465			−4.53283
$137$	−1.34004	−	1.34004i	−0.00978134	−	0.00978134i	0.702199	−	0.711981i	$-0.252202\pi$
$137$	−1.34004	−	1.34004i	−0.00978134	−	0.00978134i	−0.711981	+	0.702199i	$0.752202\pi$
$138$	125.715	−	125.715i	0.910981	−	0.910981i
$139$			14.7459i			0.106086i	0.998592	+	0.0530429i	$0.0168920\pi$
$139$			14.7459i			0.106086i	−0.998592	+	0.0530429i	$0.983108\pi$
$140$	40.7527	−	137.357i	0.291090	−	0.981124i
$141$	−34.8300			−0.247021
$142$	105.587	+	105.587i	0.743568	+	0.743568i
$143$	27.3088	−	27.3088i	0.190971	−	0.190971i
$144$			173.938i			1.20790i
$145$	−109.031	−	201.020i	−0.751936	−	1.38634i
$146$	−362.057			−2.47984
$147$	−8.57321	−	8.57321i	−0.0583212	−	0.0583212i
$148$	−23.7126	+	23.7126i	−0.160220	+	0.160220i
$149$		−	13.4239i		−	0.0900930i	−0.998985	−	0.0450465i	$-0.985656\pi$
$149$		−	13.4239i		−	0.0900930i	0.998985	−	0.0450465i	$-0.0143436\pi$
$150$	90.9442	−	139.773i	0.606295	−	0.931821i
$151$	−133.609			−0.884826			−0.442413	−	0.896811i	$-0.645877\pi$
$151$	−133.609			−0.884826			−0.442413	+	0.896811i	$0.645877\pi$
$152$	25.6815	+	25.6815i	0.168957	+	0.168957i
$153$	−49.7138	+	49.7138i	−0.324927	+	0.324927i
$154$			34.8629i			0.226382i
$155$	190.147	−	103.134i	1.22676	−	0.665378i
$156$	−211.737			−1.35729
$157$	144.591	+	144.591i	0.920959	+	0.920959i	0.997097	−	0.0761383i	$-0.0242590\pi$
$157$	144.591	+	144.591i	0.920959	+	0.920959i	−0.0761383	+	0.997097i	$0.524259\pi$
$158$	−14.4560	+	14.4560i	−0.0914936	+	0.0914936i
$159$		−	108.845i		−	0.684561i
$160$	565.927	+	167.905i	3.53704	+	1.04941i
$161$	−70.5200			−0.438013
$162$	24.5079	+	24.5079i	0.151284	+	0.151284i
$163$	141.760	−	141.760i	0.869693	−	0.869693i	−0.122746	−	0.992438i	$-0.539170\pi$
$163$	141.760	−	141.760i	0.869693	−	0.869693i	0.992438	+	0.122746i	$0.0391699\pi$
$164$			71.5908i			0.436529i
$165$	−8.42850	+	28.4084i	−0.0510818	+	0.172172i
$166$	340.843			2.05327
$167$	119.348	+	119.348i	0.714660	+	0.714660i	0.967506	−	0.252847i	$-0.0813668\pi$
$167$	119.348	+	119.348i	0.714660	+	0.714660i	−0.252847	+	0.967506i	$0.581367\pi$
$168$	85.2379	−	85.2379i	0.507368	−	0.507368i
$169$			41.6008i			0.246159i
$170$	215.145	+	396.663i	1.26556	+	2.33331i
$171$	4.14208			0.0242227
$172$	−477.832	−	477.832i	−2.77809	−	2.77809i
$173$	6.11726	−	6.11726i	0.0353599	−	0.0353599i	−0.689206	−	0.724566i	$-0.742040\pi$
$173$	6.11726	−	6.11726i	0.0353599	−	0.0353599i	0.724566	+	0.689206i	$0.242040\pi$
$174$		−	305.075i		−	1.75331i
$175$	−64.7104	+	13.6953i	−0.369774	+	0.0782587i
$176$	−198.385			−1.12719
$177$	−21.1793	−	21.1793i	−0.119657	−	0.119657i
$178$	122.039	−	122.039i	0.685615	−	0.685615i
$179$			234.919i			1.31240i	0.754588	+	0.656199i	$0.227837\pi$
$179$			234.919i			1.31240i	−0.754588	+	0.656199i	$0.772163\pi$
$180$	142.806	−	77.4561i	0.793365	−	0.430311i
$181$	128.874			0.712013			0.356007	−	0.934483i	$-0.384138\pi$
$181$	128.874			0.712013			0.356007	+	0.934483i	$0.384138\pi$
$182$	81.3199	+	81.3199i	0.446812	+	0.446812i
$183$	−58.8917	+	58.8917i	−0.321812	+	0.321812i
$184$		−	701.135i		−	3.81051i
$185$	14.8420	+	4.40348i	0.0802270	+	0.0238026i
$186$	288.575			1.55148
$187$	−56.7010	−	56.7010i	−0.303214	−	0.303214i
$188$	−154.003	+	154.003i	−0.819166	+	0.819166i
$189$		−	13.7477i		−	0.0727393i
$190$	7.56191	−	25.4875i	0.0397995	−	0.134145i
$191$	73.4776			0.384699			0.192350	−	0.981326i	$-0.438389\pi$
$191$	73.4776			0.384699			0.192350	+	0.981326i	$0.438389\pi$
$192$	272.805	+	272.805i	1.42086	+	1.42086i
$193$	120.661	−	120.661i	0.625187	−	0.625187i	−0.321666	−	0.946853i	$-0.604243\pi$
$193$	120.661	−	120.661i	0.625187	−	0.625187i	0.946853	+	0.321666i	$0.104243\pi$
$194$			166.216i			0.856783i
$195$	46.6043	+	85.9243i	0.238996	+	0.440637i
$196$	−75.8142			−0.386807
$197$	−34.8422	−	34.8422i	−0.176864	−	0.176864i	0.613123	−	0.789987i	$-0.289913\pi$
$197$	−34.8422	−	34.8422i	−0.176864	−	0.176864i	−0.789987	+	0.613123i	$0.789913\pi$
$198$	−27.9525	+	27.9525i	−0.141174	+	0.141174i
$199$			22.8910i			0.115030i	0.998345	+	0.0575151i	$0.0183177\pi$
$199$			22.8910i			0.115030i	−0.998345	+	0.0575151i	$0.981682\pi$
$200$	−136.163	−	643.373i	−0.680816	−	3.21687i
$201$	−100.291			−0.498959
$202$	−315.497	−	315.497i	−1.56187	−	1.56187i
$203$	−85.5660	+	85.5660i	−0.421507	+	0.421507i
$204$			439.626i			2.15503i
$205$	29.0521	−	15.7575i	0.141717	−	0.0768657i
$206$	201.439			0.977861
$207$	−56.5418	−	56.5418i	−0.273149	−	0.273149i
$208$	−462.746	+	462.746i	−2.22474	+	2.22474i
$209$			4.72425i			0.0226040i
$210$	−84.5940	−	25.0983i	−0.402828	−	0.119516i
$211$	−216.288			−1.02506			−0.512531	−	0.858668i	$-0.671292\pi$
$211$	−216.288			−1.02506			−0.512531	+	0.858668i	$0.671292\pi$
$212$	−481.267	−	481.267i	−2.27013	−	2.27013i
$213$	47.4887	−	47.4887i	0.222952	−	0.222952i
$214$			576.550i			2.69416i
$215$	−88.7344	+	299.080i	−0.412718	+	1.39107i
$216$	136.685			0.632799
$217$	−80.9380	−	80.9380i	−0.372986	−	0.372986i
$218$	−113.687	+	113.687i	−0.521498	+	0.521498i
$219$			162.839i			0.743557i
$220$	88.3424	+	162.877i	0.401556	+	0.740349i
$221$	−264.517			−1.19691
$222$	14.6038	+	14.6038i	0.0657830	+	0.0657830i
$223$	−55.1194	+	55.1194i	−0.247172	+	0.247172i	−0.819809	−	0.572637i	$-0.805921\pi$
$223$	−55.1194	+	55.1194i	−0.247172	+	0.247172i	0.572637	+	0.819809i	$0.305921\pi$
$224$		−	312.362i		−	1.39447i
$225$	−62.8644	−	40.9031i	−0.279397	−	0.181792i
$226$	843.872			3.73395
$227$	163.968	+	163.968i	0.722327	+	0.722327i	0.969079	−	0.246752i	$-0.0793633\pi$
$227$	163.968	+	163.968i	0.722327	+	0.722327i	−0.246752	+	0.969079i	$0.579363\pi$
$228$	18.3145	−	18.3145i	0.0803268	−	0.0803268i
$229$		−	161.221i		−	0.704022i	−0.935996	−	0.352011i	$-0.885498\pi$
$229$		−	161.221i		−	0.704022i	0.935996	−	0.352011i	$-0.114502\pi$
$230$	−451.143	+	244.695i	−1.96149	+	1.06389i
$231$	15.6799			0.0678786
$232$	−850.727	−	850.727i	−3.66693	−	3.66693i
$233$	8.28891	−	8.28891i	0.0355747	−	0.0355747i	−0.689096	−	0.724670i	$-0.741992\pi$
$233$	8.28891	−	8.28891i	0.0355747	−	0.0355747i	0.724670	+	0.689096i	$0.241992\pi$
$234$			130.402i			0.557273i
$235$	96.3924	+	28.5987i	0.410180	+	0.121697i
$236$	−187.292			−0.793608
$237$	6.50173	+	6.50173i	0.0274335	+	0.0274335i
$238$	168.843	−	168.843i	0.709426	−	0.709426i
$239$		−	66.4975i		−	0.278232i	−0.990276	−	0.139116i	$-0.955574\pi$
$239$		−	66.4975i		−	0.278232i	0.990276	−	0.139116i	$-0.0444261\pi$
$240$	142.820	−	481.377i	0.595084	−	2.00574i
$241$	−152.923			−0.634535			−0.317267	−	0.948336i	$-0.602765\pi$
$241$	−152.923			−0.634535			−0.317267	+	0.948336i	$0.602765\pi$
$242$	297.614	+	297.614i	1.22981	+	1.22981i
$243$	11.0227	−	11.0227i	0.0453609	−	0.0453609i
$244$			520.788i			2.13438i
$245$	16.6871	+	30.7659i	0.0681104	+	0.125575i
$246$	44.0905			0.179230
$247$	11.0196	+	11.0196i	0.0446138	+	0.0446138i
$248$	804.714	−	804.714i	3.24481	−	3.24481i
$249$		−	153.298i		−	0.615653i
$250$	−366.457	+	312.150i	−1.46583	+	1.24860i
$251$	462.911			1.84427			0.922134	−	0.386871i	$-0.126444\pi$
$251$	462.911			1.84427			0.922134	+	0.386871i	$0.126444\pi$
$252$	−60.7866	−	60.7866i	−0.241217	−	0.241217i
$253$	64.4887	−	64.4887i	0.254896	−	0.254896i
$254$		−	460.575i		−	1.81329i
$255$	178.403	−	96.7638i	0.699621	−	0.379466i
$256$	593.807			2.31956
$257$	54.4719	+	54.4719i	0.211953	+	0.211953i	0.805097	−	0.593144i	$-0.202113\pi$
$257$	54.4719	+	54.4719i	0.211953	+	0.211953i	−0.593144	+	0.805097i	$0.702113\pi$
$258$	−294.281	+	294.281i	−1.14062	+	1.14062i
$259$		−	8.19201i		−	0.0316294i
$260$	585.985	+	173.856i	2.25379	+	0.668678i
$261$	−137.211			−0.525712
$262$	−204.716	−	204.716i	−0.781360	−	0.781360i
$263$	−132.088	+	132.088i	−0.502236	+	0.502236i	−0.912132	−	0.409896i	$-0.865565\pi$
$263$	−132.088	+	132.088i	−0.502236	+	0.502236i	0.409896	+	0.912132i	$0.365565\pi$
$264$			155.895i			0.590513i
$265$	−89.3724	+	301.231i	−0.337254	+	1.13672i
$266$	−14.0678			−0.0528864
$267$	−54.8885	−	54.8885i	−0.205575	−	0.205575i
$268$	−443.443	+	443.443i	−1.65464	+	1.65464i
$269$			200.132i			0.743985i	0.928236	+	0.371993i	$0.121325\pi$
$269$			200.132i			0.743985i	−0.928236	+	0.371993i	$0.878675\pi$
$270$	−47.7027	−	87.9494i	−0.176677	−	0.325739i
$271$	−119.987			−0.442758			−0.221379	−	0.975188i	$-0.571056\pi$
$271$	−119.987			−0.442758			−0.221379	+	0.975188i	$0.571056\pi$
$272$	960.792	+	960.792i	3.53232	+	3.53232i
$273$	36.5745	−	36.5745i	0.133972	−	0.133972i
$274$			7.29816i			0.0266356i
$275$	46.6520	−	71.6999i	0.169644	−	0.260727i
$276$	−500.007			−1.81162
$277$	202.673	+	202.673i	0.731672	+	0.731672i	0.970951	−	0.239279i	$-0.0769110\pi$
$277$	202.673	+	202.673i	0.731672	+	0.731672i	−0.239279	+	0.970951i	$0.576911\pi$
$278$	40.1547	−	40.1547i	0.144441	−	0.144441i
$279$		−	129.790i		−	0.465196i
$280$	−305.885	+	165.909i	−1.09245	+	0.592530i
$281$	−283.806			−1.00999			−0.504994	−	0.863123i	$-0.668505\pi$
$281$	−283.806			−1.00999			−0.504994	+	0.863123i	$0.668505\pi$
$282$	94.8456	+	94.8456i	0.336332	+	0.336332i
$283$	19.2062	−	19.2062i	0.0678664	−	0.0678664i	−0.672359	−	0.740225i	$-0.734719\pi$
$283$	19.2062	−	19.2062i	0.0678664	−	0.0678664i	0.740225	+	0.672359i	$0.234719\pi$
$284$		−	419.949i		−	1.47869i
$285$	−11.4633	−	3.40105i	−0.0402220	−	0.0119335i
$286$	−148.730			−0.520034
$287$	−12.3663	−	12.3663i	−0.0430881	−	0.0430881i
$288$	250.447	−	250.447i	0.869608	−	0.869608i
$289$			260.213i			0.900392i
$290$	−250.496	+	844.300i	−0.863780	+	2.91138i
$291$	74.7573			0.256898
$292$	720.005	+	720.005i	2.46577	+	2.46577i
$293$	276.326	−	276.326i	0.943093	−	0.943093i	−0.0553728	−	0.998466i	$-0.517635\pi$
$293$	276.326	−	276.326i	0.943093	−	0.943093i	0.998466	+	0.0553728i	$0.0176347\pi$
$294$			46.6915i			0.158815i
$295$	41.2237	+	76.0042i	0.139742	+	0.257641i
$296$	81.4478			0.275162
$297$	12.5719	+	12.5719i	0.0423297	+	0.0423297i
$298$	−36.5546	+	36.5546i	−0.122666	+	0.122666i
$299$		−	300.848i		−	1.00618i
$300$	−458.816	+	97.1035i	−1.52939	+	0.323678i
$301$	165.077			0.548429
$302$	363.830	+	363.830i	1.20474	+	1.20474i
$303$	−141.898	+	141.898i	−0.468311	+	0.468311i
$304$		−	80.0519i		−	0.263328i
$305$	211.339	−	114.628i	0.692916	−	0.375829i
$306$	270.752			0.884809
$307$	84.0526	+	84.0526i	0.273787	+	0.273787i	0.830623	−	0.556836i	$-0.187985\pi$
$307$	84.0526	+	84.0526i	0.273787	+	0.273787i	−0.556836	+	0.830623i	$0.687985\pi$
$308$	69.3300	−	69.3300i	0.225097	−	0.225097i
$309$		−	90.5995i		−	0.293202i
$310$	−798.635	−	236.948i	−2.57624	−	0.764347i
$311$	−228.140			−0.733569			−0.366785	−	0.930306i	$-0.619541\pi$
$311$	−228.140			−0.733569			−0.366785	+	0.930306i	$0.619541\pi$
$312$	363.636	+	363.636i	1.16550	+	1.16550i
$313$	415.710	−	415.710i	1.32815	−	1.32815i	0.421163	−	0.906985i	$-0.361622\pi$
$313$	415.710	−	415.710i	1.32815	−	1.32815i	0.906985	−	0.421163i	$-0.138378\pi$
$314$		−	787.470i		−	2.50787i
$315$	−11.2882	+	38.0470i	−0.0358356	+	0.120784i
$316$	57.4958			0.181949
$317$	−167.997	−	167.997i	−0.529960	−	0.529960i	0.390600	−	0.920560i	$-0.372267\pi$
$317$	−167.997	−	167.997i	−0.529960	−	0.529960i	−0.920560	+	0.390600i	$0.872267\pi$
$318$	−296.397	+	296.397i	−0.932066	+	0.932066i
$319$		−	156.496i		−	0.490582i
$320$	−530.993	−	978.992i	−1.65935	−	3.05935i
$321$	259.310			0.807818
$322$	192.033	+	192.033i	0.596377	+	0.596377i
$323$	22.8798	−	22.8798i	0.0708354	−	0.0708354i
$324$		−	97.4754i		−	0.300850i
$325$	−58.4259	−	276.063i	−0.179772	−	0.849425i
$326$	−772.054			−2.36826
$327$	51.1317	+	51.1317i	0.156366	+	0.156366i
$328$	122.950	−	122.950i	0.374847	−	0.374847i
$329$		−	53.2036i		−	0.161713i
$330$	100.311	−	54.4072i	0.303971	−	0.164870i
$331$	−379.871			−1.14765			−0.573823	−	0.818979i	$-0.694540\pi$
$331$	−379.871			−1.14765			−0.573823	+	0.818979i	$0.694540\pi$
$332$	−677.816	−	677.816i	−2.04161	−	2.04161i
$333$	6.56822	−	6.56822i	0.0197244	−	0.0197244i
$334$		−	649.995i		−	1.94609i
$335$	277.556	+	82.3483i	0.828525	+	0.245816i
$336$	−265.695			−0.790759
$337$	251.400	+	251.400i	0.745994	+	0.745994i	0.973724	−	0.227730i	$-0.0731305\pi$
$337$	251.400	+	251.400i	0.745994	+	0.745994i	−0.227730	+	0.973724i	$0.573130\pi$
$338$	113.283	−	113.283i	0.335158	−	0.335158i
$339$		−	379.540i		−	1.11959i
$340$	360.975	−	1216.67i	1.06169	−	3.57845i
$341$	148.031			0.434109
$342$	−11.2793	−	11.2793i	−0.0329805	−	0.0329805i
$343$	13.0958	−	13.0958i	0.0381802	−	0.0381802i
$344$			1641.25i			4.77108i
$345$	110.054	+	202.907i	0.318997	+	0.588135i
$346$	−33.3159			−0.0962886
$347$	234.925	+	234.925i	0.677016	+	0.677016i	0.959324	−	0.282308i	$-0.0910999\pi$
$347$	234.925	+	234.925i	0.677016	+	0.677016i	−0.282308	+	0.959324i	$0.591100\pi$
$348$	−606.688	+	606.688i	−1.74336	+	1.74336i
$349$			497.584i			1.42574i	0.701295	+	0.712871i	$0.252605\pi$
$349$			497.584i			1.42574i	−0.701295	+	0.712871i	$0.747395\pi$
$350$	213.507	+	138.920i	0.610020	+	0.396913i
$351$	58.6496			0.167093
$352$	285.647	+	285.647i	0.811497	+	0.811497i
$353$	−217.500	+	217.500i	−0.616146	+	0.616146i	−0.944541	−	0.328394i	$-0.893492\pi$
$353$	−217.500	+	217.500i	−0.616146	+	0.616146i	0.328394	+	0.944541i	$0.393492\pi$
$354$			115.347i			0.325839i
$355$	−170.418	+	92.4328i	−0.480052	+	0.260374i
$356$	−485.387			−1.36345
$357$	−75.9391	−	75.9391i	−0.212714	−	0.212714i
$358$	639.709	−	639.709i	1.78690	−	1.78690i
$359$		−	531.115i		−	1.47943i	−0.672921	−	0.739714i	$-0.734961\pi$
$359$		−	531.115i		−	1.47943i	0.672921	−	0.739714i	$-0.265039\pi$
$360$	−378.277	−	112.231i	−1.05077	−	0.311753i
$361$	359.094			0.994719
$362$	−350.938	−	350.938i	−0.969443	−	0.969443i
$363$	133.855	−	133.855i	0.368747	−	0.368747i
$364$		−	323.433i		−	0.888553i
$365$	133.707	−	450.659i	0.366319	−	1.23468i
$366$	320.736			0.876329
$367$	−190.791	−	190.791i	−0.519867	−	0.519867i	0.397664	−	0.917531i	$-0.369821\pi$
$367$	−190.791	−	190.791i	−0.519867	−	0.519867i	−0.917531	+	0.397664i	$0.869821\pi$
$368$	−1092.75	+	1092.75i	−2.96944	+	2.96944i
$369$		−	19.8302i		−	0.0537403i
$370$	−28.4251	−	52.4074i	−0.0768247	−	0.141642i
$371$	166.264			0.448151
$372$	−573.874	−	573.874i	−1.54267	−	1.54267i
$373$	−178.025	+	178.025i	−0.477279	+	0.477279i	−0.904260	−	0.426981i	$-0.859577\pi$
$373$	−178.025	+	178.025i	−0.477279	+	0.477279i	0.426981	+	0.904260i	$0.359577\pi$
$374$			308.805i			0.825683i
$375$	140.393	+	164.818i	0.374381	+	0.439514i
$376$	528.969			1.40683
$377$	−365.036	−	365.036i	−0.968265	−	0.968265i
$378$	−37.4365	+	37.4365i	−0.0990384	+	0.0990384i
$379$		−	427.303i		−	1.12745i	−0.825963	−	0.563725i	$-0.809368\pi$
$379$		−	427.303i		−	1.12745i	0.825963	−	0.563725i	$-0.190632\pi$
$380$	−65.7237	+	35.6477i	−0.172957	+	0.0938098i
$381$	−207.148			−0.543696
$382$	−200.087	−	200.087i	−0.523788	−	0.523788i
$383$	−408.586	+	408.586i	−1.06680	+	1.06680i	−0.0692020	+	0.997603i	$0.522045\pi$
$383$	−408.586	+	408.586i	−1.06680	+	1.06680i	−0.997603	+	0.0692020i	$0.977955\pi$
$384$		−	667.798i		−	1.73906i
$385$	−43.3945	−	12.8747i	−0.112713	−	0.0334409i
$386$	−657.146			−1.70245
$387$	132.356	+	132.356i	0.342005	+	0.342005i
$388$	330.545	−	330.545i	0.851920	−	0.851920i
$389$		−	380.438i		−	0.977990i	−0.872286	−	0.488995i	$-0.837364\pi$
$389$		−	380.438i		−	0.977990i	0.872286	−	0.488995i	$-0.162636\pi$
$390$	107.072	−	360.889i	0.274545	−	0.925357i
$391$	−624.646			−1.59756
$392$	130.203	+	130.203i	0.332150	+	0.332150i
$393$	−92.0733	+	92.0733i	−0.234283	+	0.234283i
$394$			189.758i			0.481619i
$395$	−12.6551	−	23.3322i	−0.0320382	−	0.0590688i
$396$	111.175			0.280746
$397$	419.765	+	419.765i	1.05734	+	1.05734i	0.998253	+	0.0590903i	$0.0188200\pi$
$397$	419.765	+	419.765i	1.05734	+	1.05734i	0.0590903	+	0.998253i	$0.481180\pi$
$398$	62.3346	−	62.3346i	0.156620	−	0.156620i
$399$			6.32714i			0.0158575i
$400$	−790.513	+	1214.95i	−1.97628	+	3.03737i
$401$	−116.260			−0.289926			−0.144963	−	0.989437i	$-0.546306\pi$
$401$	−116.260			−0.289926			−0.144963	+	0.989437i	$0.546306\pi$
$402$	273.102	+	273.102i	0.679359	+	0.679359i
$403$	345.292	−	345.292i	0.856805	−	0.856805i
$404$			1254.83i			3.10600i
$405$	−39.5562	+	21.4548i	−0.0976696	+	0.0529748i
$406$	466.010			1.14781
$407$	7.49137	+	7.49137i	0.0184063	+	0.0184063i
$408$	755.012	−	755.012i	1.85052	−	1.85052i
$409$			510.537i			1.24826i	0.781322	+	0.624129i	$0.214546\pi$
$409$			510.537i			1.24826i	−0.781322	+	0.624129i	$0.785454\pi$
$410$	−122.021	−	36.2025i	−0.297612	−	0.0882988i
$411$	3.28242			0.00798643
$412$	−400.592	−	400.592i	−0.972311	−	0.972311i
$413$	32.3519	−	32.3519i	0.0783339	−	0.0783339i
$414$			307.939i			0.743813i
$415$	−125.872	+	424.253i	−0.303306	+	1.02230i
$416$	1332.58			3.20331
$417$	−18.0600	−	18.0600i	−0.0433093	−	0.0433093i
$418$	12.8646	−	12.8646i	0.0307766	−	0.0307766i
$419$		−	421.546i		−	1.00608i	−0.864265	−	0.503038i	$-0.832216\pi$
$419$		−	421.546i		−	1.00608i	0.864265	−	0.503038i	$-0.167784\pi$
$420$	118.316	+	218.139i	0.281705	+	0.519379i
$421$	−617.382			−1.46646			−0.733232	−	0.679978i	$-0.761989\pi$
$421$	−617.382			−1.46646			−0.733232	+	0.679978i	$0.761989\pi$
$422$	588.976	+	588.976i	1.39568	+	1.39568i
$423$	42.6578	−	42.6578i	0.100846	−	0.100846i
$424$			1653.05i			3.89871i
$425$	−573.186	+	121.309i	−1.34867	+	0.285433i
$426$	−258.633			−0.607120
$427$	−89.9585	−	89.9585i	−0.210676	−	0.210676i
$428$	1146.56	−	1146.56i	2.67887	−	2.67887i
$429$			66.8927i			0.155927i
$430$	1056.06	−	572.794i	2.45595	−	1.33208i
$431$	−13.8516			−0.0321382			−0.0160691	−	0.999871i	$-0.505115\pi$
$431$	−13.8516			−0.0321382			−0.0160691	+	0.999871i	$0.505115\pi$
$432$	−213.030	−	213.030i	−0.493125	−	0.493125i
$433$	539.624	−	539.624i	1.24624	−	1.24624i	0.288879	−	0.957366i	$-0.406718\pi$
$433$	539.624	−	539.624i	1.24624	−	1.24624i	0.957366	−	0.288879i	$-0.0932824\pi$
$434$			440.805i			1.01568i
$435$	379.733	+	112.663i	0.872949	+	0.258996i
$436$	452.165			1.03708
$437$	26.0223	+	26.0223i	0.0595476	+	0.0595476i
$438$	443.428	−	443.428i	1.01239	−	1.01239i
$439$		−	41.4994i		−	0.0945318i	−0.998882	−	0.0472659i	$-0.984949\pi$
$439$		−	41.4994i		−	0.0945318i	0.998882	−	0.0472659i	$-0.0150508\pi$
$440$	128.005	−	431.443i	0.290921	−	0.980552i
$441$	21.0000			0.0476190
$442$	720.308	+	720.308i	1.62966	+	1.62966i
$443$	577.471	−	577.471i	1.30355	−	1.30355i	0.377563	−	0.925984i	$-0.376762\pi$
$443$	577.471	−	577.471i	1.30355	−	1.30355i	0.925984	−	0.377563i	$-0.123238\pi$
$444$		−	58.0837i		−	0.130819i
$445$	106.836	+	196.973i	0.240081	+	0.442637i
$446$	300.192			0.673076
$447$	16.4408	+	16.4408i	0.0367803	+	0.0367803i
$448$	−416.717	+	416.717i	−0.930172	+	0.930172i
$449$		−	234.581i		−	0.522451i	−0.965278	−	0.261226i	$-0.915873\pi$
$449$		−	234.581i		−	0.522451i	0.965278	−	0.261226i	$-0.0841266\pi$
$450$	59.8029	+	282.570i	0.132895	+	0.627933i
$451$	22.6173			0.0501491
$452$	−1678.16	−	1678.16i	−3.71275	−	3.71275i
$453$	163.637	−	163.637i	0.361229	−	0.361229i
$454$		−	893.005i		−	1.96697i
$455$	−131.252	+	71.1892i	−0.288465	+	0.156460i
$456$	−62.9066			−0.137953
$457$	153.225	+	153.225i	0.335284	+	0.335284i	0.854589	−	0.519305i	$-0.173809\pi$
$457$	153.225	+	153.225i	0.335284	+	0.335284i	−0.519305	+	0.854589i	$0.673809\pi$
$458$	−439.022	+	439.022i	−0.958562	+	0.958562i
$459$		−	121.773i		−	0.265302i
$460$	1383.78	+	410.554i	3.00821	+	0.892509i
$461$	623.452			1.35239			0.676195	−	0.736723i	$-0.263628\pi$
$461$	623.452			1.35239			0.676195	+	0.736723i	$0.263628\pi$
$462$	−42.6981	−	42.6981i	−0.0924202	−	0.0924202i
$463$	−613.771	+	613.771i	−1.32564	+	1.32564i	−0.416506	+	0.909133i	$0.636745\pi$
$463$	−613.771	+	613.771i	−1.32564	+	1.32564i	−0.909133	+	0.416506i	$0.863255\pi$
$464$			2651.80i			5.71509i
$465$	−106.570	+	359.194i	−0.229182	+	0.772461i
$466$	−45.1431			−0.0968737
$467$	−439.249	−	439.249i	−0.940575	−	0.940575i	0.0577556	−	0.998331i	$-0.481606\pi$
$467$	−439.249	−	439.249i	−0.940575	−	0.940575i	−0.998331	+	0.0577556i	$0.981606\pi$
$468$	259.324	−	259.324i	0.554110	−	0.554110i
$469$		−	153.197i		−	0.326645i
$470$	−184.609	−	340.364i	−0.392786	−	0.724179i
$471$	−354.173			−0.751960
$472$	321.654	+	321.654i	0.681470	+	0.681470i
$473$	−150.958	+	150.958i	−0.319151	+	0.319151i
$474$		−	35.4098i		−	0.0747042i
$475$	28.9322	+	18.8249i	0.0609099	+	0.0396314i
$476$	−671.540			−1.41080
$477$	133.308	+	133.308i	0.279471	+	0.279471i
$478$	−181.080	+	181.080i	−0.378828	+	0.378828i
$479$		−	15.2748i		−	0.0318889i	−0.999873	−	0.0159445i	$-0.994925\pi$
$479$		−	15.2748i		−	0.0318889i	0.999873	−	0.0159445i	$-0.00507549\pi$
$480$	−898.757	+	487.475i	−1.87241	+	1.01557i
$481$	34.9482			0.0726574
$482$	416.425	+	416.425i	0.863952	+	0.863952i
$483$	86.3690	−	86.3690i	0.178818	−	0.178818i
$484$		−	1183.70i		−	2.44566i
$485$	−206.892	−	61.3830i	−0.426581	−	0.126563i
$486$	−60.0319			−0.123523
$487$	−170.456	−	170.456i	−0.350013	−	0.350013i	0.510101	−	0.860114i	$-0.329608\pi$
$487$	−170.456	−	170.456i	−0.350013	−	0.350013i	−0.860114	+	0.510101i	$0.829608\pi$
$488$	894.399	−	894.399i	1.83278	−	1.83278i
$489$			347.239i			0.710101i
$490$	38.3382	−	129.219i	0.0782413	−	0.263713i
$491$	539.988			1.09977			0.549886	−	0.835239i	$-0.314671\pi$
$491$	539.988			1.09977			0.549886	+	0.835239i	$0.314671\pi$
$492$	−87.6805	−	87.6805i	−0.178212	−	0.178212i
$493$	−757.919	+	757.919i	−1.53736	+	1.53736i
$494$		−	60.0150i		−	0.121488i
$495$	−24.4702	−	45.1157i	−0.0494348	−	0.0911429i
$496$	−2508.38			−5.05721
$497$	72.5402	+	72.5402i	0.145956	+	0.145956i
$498$	−417.445	+	417.445i	−0.838243	+	0.838243i
$499$			594.406i			1.19119i	0.803284	+	0.595597i	$0.203084\pi$
$499$			594.406i			1.19119i	−0.803284	+	0.595597i	$0.796916\pi$
$500$	1349.51	+	107.996i	2.69902	+	0.215993i
$501$	−292.342			−0.583517
$502$	−1260.56	−	1260.56i	−2.51107	−	2.51107i
$503$	−416.709	+	416.709i	−0.828447	+	0.828447i	−0.987302	−	0.158855i	$-0.949220\pi$
$503$	−416.709	+	416.709i	−0.828447	+	0.828447i	0.158855	+	0.987302i	$0.449220\pi$
$504$			208.789i			0.414264i
$505$	509.217	−	276.193i	1.00835	−	0.546917i
$506$	−351.219			−0.694108
$507$	−50.9504	−	50.9504i	−0.100494	−	0.100494i
$508$	−915.921	+	915.921i	−1.80299	+	1.80299i
$509$			932.017i			1.83107i	0.402234	+	0.915537i	$0.368234\pi$
$509$			932.017i			1.83107i	−0.402234	+	0.915537i	$0.631766\pi$
$510$	−749.309	−	222.313i	−1.46923	−	0.435908i
$511$	−248.741			−0.486773
$512$	−526.490	−	526.490i	−1.02830	−	1.02830i
$513$	−5.07299	+	5.07299i	−0.00988888	+	0.00988888i
$514$		−	296.665i		−	0.577170i
$515$	−74.3909	+	250.735i	−0.144448	+	0.486865i
$516$	1170.44			2.26830
$517$	48.6533	+	48.6533i	0.0941069	+	0.0941069i
$518$	−22.3077	+	22.3077i	−0.0430651	+	0.0430651i
$519$			14.9842i			0.0288712i
$520$	−707.788	−	1304.95i	−1.36113	−	2.50952i
$521$	−536.572			−1.02989			−0.514945	−	0.857223i	$-0.672188\pi$
$521$	−536.572			−1.02989			−0.514945	+	0.857223i	$0.672188\pi$
$522$	373.640	+	373.640i	0.715785	+	0.715785i
$523$	151.430	−	151.430i	0.289542	−	0.289542i	−0.547357	−	0.836899i	$-0.684366\pi$
$523$	151.430	−	151.430i	0.289542	−	0.289542i	0.836899	+	0.547357i	$0.184366\pi$
$524$			814.217i			1.55385i
$525$	62.4805	−	96.0270i	0.119011	−	0.182909i
$526$	719.379			1.36764
$527$	−716.926	−	716.926i	−1.36039	−	1.36039i
$528$	242.971	−	242.971i	0.460172	−	0.460172i
$529$		−	181.439i		−	0.342985i
$530$	1063.65	−	576.912i	2.00689	−	1.08851i
$531$	51.8785			0.0976995
$532$	27.9759	+	27.9759i	0.0525863	+	0.0525863i
$533$	52.7562	−	52.7562i	0.0989797	−	0.0989797i
$534$			298.934i			0.559802i
$535$	−717.643	−	212.918i	−1.34139	−	0.397978i
$536$	1523.13			2.84167
$537$	−287.716	−	287.716i	−0.535784	−	0.535784i
$538$	544.981	−	544.981i	1.01298	−	1.01298i
$539$			23.9515i			0.0444369i
$540$	−80.0367	+	269.764i	−0.148216	+	0.499564i
$541$	363.668			0.672215			0.336107	−	0.941824i	$-0.390890\pi$
$541$	363.668			0.672215			0.336107	+	0.941824i	$0.390890\pi$
$542$	326.738	+	326.738i	0.602838	+	0.602838i
$543$	−157.838	+	157.838i	−0.290678	+	0.290678i
$544$		−	2766.82i		−	5.08606i
$545$	−99.5237	−	183.492i	−0.182612	−	0.336682i
$546$	−199.192			−0.364821
$547$	426.746	+	426.746i	0.780158	+	0.780158i	0.979857	−	0.199699i	$-0.0639965\pi$
$547$	426.746	+	426.746i	0.780158	+	0.780158i	−0.199699	+	0.979857i	$0.563997\pi$
$548$	14.5135	−	14.5135i	0.0264844	−	0.0264844i
$549$		−	144.255i		−	0.262759i
$550$	−322.285	+	68.2081i	−0.585972	+	0.124015i
$551$	63.1487			0.114608
$552$	858.711	+	858.711i	1.55564	+	1.55564i
$553$	−9.93156	+	9.93156i	−0.0179594	+	0.0179594i
$554$		−	1103.80i		−	1.99242i
$555$	−23.5708	+	12.7845i	−0.0424699	+	0.0230351i
$556$	−159.707			−0.287243
$557$	199.988	+	199.988i	0.359045	+	0.359045i	0.863461	−	0.504416i	$-0.168292\pi$
$557$	199.988	+	199.988i	0.359045	+	0.359045i	−0.504416	+	0.863461i	$0.668292\pi$
$558$	−353.431	+	353.431i	−0.633388	+	0.633388i
$559$			704.240i			1.25982i
$560$	735.315	+	218.161i	1.31306	+	0.389574i
$561$	138.888			0.247573
$562$	772.835	+	772.835i	1.37515	+	1.37515i
$563$	−85.4562	+	85.4562i	−0.151787	+	0.151787i	−0.778916	−	0.627129i	$-0.784230\pi$
$563$	−85.4562	+	85.4562i	−0.151787	+	0.151787i	0.627129	+	0.778916i	$0.284230\pi$
$564$		−	377.229i		−	0.668846i
$565$	−311.639	+	1050.38i	−0.551573	+	1.85908i
$566$	−104.601			−0.184807
$567$	16.8375	+	16.8375i	0.0296957	+	0.0296957i
$568$	−721.219	+	721.219i	−1.26975	+	1.26975i
$569$			991.963i			1.74334i	0.490090	+	0.871672i	$0.336964\pi$
$569$			991.963i			1.74334i	−0.490090	+	0.871672i	$0.663036\pi$
$570$	21.9543	+	40.4771i	0.0385163	+	0.0710125i
$571$	273.348			0.478719			0.239359	−	0.970931i	$-0.423063\pi$
$571$	273.348			0.478719			0.239359	+	0.970931i	$0.423063\pi$
$572$	295.771	+	295.771i	0.517082	+	0.517082i
$573$	−89.9913	+	89.9913i	−0.157053	+	0.157053i
$574$			67.3493i			0.117333i
$575$	−137.970	−	651.912i	−0.239948	−	1.13376i
$576$	−668.234			−1.16013
$577$	639.002	+	639.002i	1.10746	+	1.10746i	0.993484	+	0.113972i	$0.0363573\pi$
$577$	639.002	+	639.002i	1.10746	+	1.10746i	0.113972	+	0.993484i	$0.463643\pi$
$578$	708.588	−	708.588i	1.22593	−	1.22593i
$579$			295.558i			0.510463i
$580$	2177.17	−	1180.87i	3.75373	−	2.03598i
$581$	234.166			0.403039
$582$	−203.572	−	203.572i	−0.349780	−	0.349780i
$583$	−152.044	+	152.044i	−0.260796	+	0.260796i
$584$		−	2473.07i		−	4.23470i
$585$	−162.314	−	48.1570i	−0.277459	−	0.0823196i
$586$	−1504.93			−2.56814
$587$	−367.435	−	367.435i	−0.625953	−	0.625953i	0.321094	−	0.947047i	$-0.395949\pi$
$587$	−367.435	−	367.435i	−0.625953	−	0.625953i	−0.947047	+	0.321094i	$0.895949\pi$
$588$	92.8530	−	92.8530i	0.157913	−	0.157913i
$589$			59.7332i			0.101415i
$590$	94.7108	−	319.224i	0.160527	−	0.541058i
$591$	85.3456			0.144409
$592$	−126.941	−	126.941i	−0.214427	−	0.214427i
$593$	−319.591	+	319.591i	−0.538939	+	0.538939i	−0.923217	−	0.384278i	$-0.874450\pi$
$593$	−319.591	+	319.591i	−0.538939	+	0.538939i	0.384278	+	0.923217i	$0.374450\pi$
$594$		−	68.4693i		−	0.115268i
$595$	147.809	+	272.516i	0.248419	+	0.458010i
$596$	145.388			0.243940
$597$	−28.0356	−	28.0356i	−0.0469608	−	0.0469608i
$598$	−819.240	+	819.240i	−1.36997	+	1.36997i
$599$		−	119.408i		−	0.199346i	−0.995020	−	0.0996730i	$-0.968220\pi$
$599$		−	119.408i		−	0.199346i	0.995020	−	0.0996730i	$-0.0317797\pi$
$600$	954.734	+	621.203i	1.59122	+	1.03534i
$601$	183.966			0.306100			0.153050	−	0.988218i	$-0.451090\pi$
$601$	183.966			0.306100			0.153050	+	0.988218i	$0.451090\pi$
$602$	−449.522	−	449.522i	−0.746714	−	0.746714i
$603$	122.831	−	122.831i	0.203699	−	0.203699i
$604$		−	1447.06i		−	2.39580i
$605$	−480.354	+	260.538i	−0.793974	+	0.430642i
$606$	772.807			1.27526
$607$	−757.520	−	757.520i	−1.24797	−	1.24797i	−0.956614	−	0.291360i	$-0.905892\pi$
$607$	−757.520	−	757.520i	−1.24797	−	1.24797i	−0.291360	−	0.956614i	$-0.594108\pi$
$608$	−115.264	+	115.264i	−0.189578	+	0.189578i
$609$		−	209.593i		−	0.344159i
$610$	−887.642	−	263.355i	−1.45515	−	0.431730i
$611$	226.974			0.371479
$612$	−538.430	−	538.430i	−0.879787	−	0.879787i
$613$	584.336	−	584.336i	0.953239	−	0.953239i	−0.0457151	−	0.998955i	$-0.514557\pi$
$613$	584.336	−	584.336i	0.953239	−	0.953239i	0.998955	+	0.0457151i	$0.0145566\pi$
$614$		−	457.768i		−	0.745550i
$615$	−16.2825	+	54.8802i	−0.0264756	+	0.0892362i
$616$	−238.134			−0.386582
$617$	483.308	+	483.308i	0.783319	+	0.783319i	0.980389	−	0.197070i	$-0.0631428\pi$
$617$	483.308	+	483.308i	0.783319	+	0.783319i	−0.197070	+	0.980389i	$0.563143\pi$
$618$	−246.712	+	246.712i	−0.399210	+	0.399210i
$619$		−	1053.61i		−	1.70211i	−0.525074	−	0.851056i	$-0.675962\pi$
$619$		−	1053.61i		−	1.70211i	0.525074	−	0.851056i	$-0.324038\pi$
$620$	1117.00	+	2059.41i	1.80161	+	3.32163i
$621$	138.499			0.223025
$622$	621.249	+	621.249i	0.998793	+	0.998793i
$623$	83.8436	−	83.8436i	0.134580	−	0.134580i
$624$		−	1133.49i		−	1.81649i
$625$	−253.208	−	571.411i	−0.405133	−	0.914258i
$626$	−2264.05			−3.61669
$627$	−5.78599	−	5.78599i	−0.00922806	−	0.00922806i
$628$	−1566.00	+	1566.00i	−2.49363	+	2.49363i
$629$		−	72.5625i		−	0.115362i
$630$	134.345	−	72.8671i	0.213246	−	0.115662i
$631$	−127.766			−0.202481			−0.101241	−	0.994862i	$-0.532281\pi$
$631$	−127.766			−0.202481			−0.101241	+	0.994862i	$0.532281\pi$
$632$	−98.7430	−	98.7430i	−0.156239	−	0.156239i
$633$	264.898	−	264.898i	0.418480	−	0.418480i
$634$			914.949i			1.44314i
$635$	573.286	+	170.089i	0.902812	+	0.267856i
$636$	1178.86			1.85355
$637$	55.8684	+	55.8684i	0.0877055	+	0.0877055i
$638$	−426.154	+	426.154i	−0.667953	+	0.667953i
$639$			116.323i			0.182039i
$640$	−548.326	+	1848.14i	−0.856760	+	2.88772i
$641$	745.868			1.16360			0.581801	−	0.813331i	$-0.302348\pi$
$641$	745.868			1.16360			0.581801	+	0.813331i	$0.302348\pi$
$642$	−706.127	−	706.127i	−1.09989	−	1.09989i
$643$	43.5132	−	43.5132i	0.0676721	−	0.0676721i	−0.672461	−	0.740133i	$-0.734763\pi$
$643$	43.5132	−	43.5132i	0.0676721	−	0.0676721i	0.740133	+	0.672461i	$0.234763\pi$
$644$		−	763.774i		−	1.18598i
$645$	−257.620	−	474.974i	−0.399411	−	0.736394i
$646$	−124.608			−0.192892
$647$	434.895	+	434.895i	0.672171	+	0.672171i	0.958216	−	0.286045i	$-0.0923407\pi$
$647$	434.895	+	434.895i	0.672171	+	0.672171i	−0.286045	+	0.958216i	$0.592341\pi$
$648$	−167.404	+	167.404i	−0.258339	+	0.258339i
$649$			59.1699i			0.0911708i
$650$	−592.649	+	910.849i	−0.911768	+	1.40131i
$651$	198.257			0.304542
$652$	1535.34	+	1535.34i	2.35482	+	2.35482i
$653$	495.522	−	495.522i	0.758839	−	0.758839i	−0.217272	−	0.976111i	$-0.569716\pi$
$653$	495.522	−	495.522i	0.758839	−	0.758839i	0.976111	+	0.217272i	$0.0697160\pi$
$654$		−	278.474i		−	0.425801i
$655$	330.415	−	179.213i	0.504450	−	0.273608i
$656$	−383.247			−0.584218
$657$	−199.436	−	199.436i	−0.303556	−	0.303556i
$658$	−144.879	+	144.879i	−0.220181	+	0.220181i
$659$			250.489i			0.380104i	0.981774	+	0.190052i	$0.0608657\pi$
$659$			250.489i			0.380104i	−0.981774	+	0.190052i	$0.939134\pi$
$660$	−307.679	−	91.2857i	−0.466181	−	0.138312i
$661$	48.3637			0.0731674			0.0365837	−	0.999331i	$-0.488352\pi$
$661$	48.3637			0.0731674			0.0365837	+	0.999331i	$0.488352\pi$
$662$	1034.43	+	1034.43i	1.56258	+	1.56258i
$663$	323.966	−	323.966i	0.488637	−	0.488637i
$664$			2328.16i			3.50626i
$665$	5.19519	−	17.5104i	0.00781231	−	0.0263315i
$666$	−35.7719			−0.0537116
$667$	−862.017	−	862.017i	−1.29238	−	1.29238i
$668$	−1292.61	+	1292.61i	−1.93505	+	1.93505i
$669$		−	135.014i		−	0.201815i
$670$	−531.571	−	980.057i	−0.793389	−	1.46277i
$671$	164.529			0.245200
$672$	382.564	+	382.564i	0.569292	+	0.569292i
$673$	621.928	−	621.928i	0.924113	−	0.924113i	−0.0732040	−	0.997317i	$-0.523322\pi$
$673$	621.928	−	621.928i	0.924113	−	0.924113i	0.997317	+	0.0732040i	$0.0233224\pi$
$674$		−	1369.18i		−	2.03142i
$675$	127.089	−	26.8970i	0.188280	−	0.0398474i
$676$	−450.562			−0.666511
$677$	−446.844	−	446.844i	−0.660035	−	0.660035i	0.295353	−	0.955388i	$-0.404563\pi$
$677$	−446.844	−	446.844i	−0.660035	−	0.660035i	−0.955388	+	0.295353i	$0.904563\pi$
$678$	−1033.53	+	1033.53i	−1.52438	+	1.52438i
$679$			114.194i			0.168179i
$680$	−2709.45	+	1469.57i	−3.98448	+	2.16113i
$681$	−401.638			−0.589777
$682$	−403.105	−	403.105i	−0.591062	−	0.591062i
$683$	−571.060	+	571.060i	−0.836106	+	0.836106i	−0.988344	−	0.152238i	$-0.951352\pi$
$683$	−571.060	+	571.060i	−0.836106	+	0.836106i	0.152238	+	0.988344i	$0.451352\pi$
$684$			44.8612i			0.0655866i
$685$	−9.08415	−	2.69518i	−0.0132615	−	0.00393458i
$686$	−71.3225			−0.103969
$687$	197.455	+	197.455i	0.287416	+	0.287416i
$688$	2557.98	−	2557.98i	3.71799	−	3.71799i
$689$			709.304i			1.02947i
$690$	252.847	−	852.224i	0.366445	−	1.23511i
$691$	988.525			1.43057			0.715286	−	0.698832i	$-0.246296\pi$
$691$	988.525			1.43057			0.715286	+	0.698832i	$0.246296\pi$
$692$	66.2535	+	66.2535i	0.0957421	+	0.0957421i
$693$	−19.2039	+	19.2039i	−0.0277113	+	0.0277113i
$694$		−	1279.45i		−	1.84359i
$695$	35.1523	+	64.8103i	0.0505788	+	0.0932522i
$696$	2083.85			2.99403
$697$	−109.537	−	109.537i	−0.157155	−	0.157155i
$698$	1354.97	−	1354.97i	1.94122	−	1.94122i
$699$			20.3036i			0.0290466i
$700$	−148.328	−	700.853i	−0.211897	−	1.00122i
$701$	271.597			0.387443			0.193721	−	0.981057i	$-0.437944\pi$
$701$	271.597			0.387443			0.193721	+	0.981057i	$0.437944\pi$
$702$	−159.709	−	159.709i	−0.227506	−	0.227506i
$703$	−3.02290	+	3.02290i	−0.00430000	+	0.00430000i
$704$		−	762.153i		−	1.08260i
$705$	−153.082	+	83.0299i	−0.217138	+	0.117773i
$706$	1184.55			1.67783
$707$	−216.753	−	216.753i	−0.306581	−	0.306581i
$708$	229.384	−	229.384i	0.323989	−	0.323989i
$709$			181.787i			0.256400i	0.991748	+	0.128200i	$0.0409199\pi$
$709$			181.787i			0.256400i	−0.991748	+	0.128200i	$0.959080\pi$
$710$	715.771	+	212.363i	1.00813	+	0.299103i
$711$	−15.9259			−0.0223993
$712$	833.602	+	833.602i	1.17079	+	1.17079i
$713$	815.393	−	815.393i	1.14361	−	1.14361i
$714$			413.580i			0.579244i
$715$	54.9254	−	185.127i	0.0768187	−	0.258918i
$716$	−2544.31			−3.55351
$717$	81.4424	+	81.4424i	0.113588	+	0.113588i
$718$	−1446.28	+	1446.28i	−2.01432	+	2.01432i
$719$		−	286.878i		−	0.398995i	−0.979898	−	0.199498i	$-0.936069\pi$
$719$		−	286.878i		−	0.398995i	0.979898	−	0.199498i	$-0.0639310\pi$
$720$	414.645	+	764.482i	0.575896	+	1.06178i
$721$	138.393			0.191946
$722$	−977.850	−	977.850i	−1.35436	−	1.35436i
$723$	187.291	−	187.291i	0.259048	−	0.259048i
$724$			1395.79i			1.92788i
$725$	−958.409	−	623.595i	−1.32194	−	0.860131i
$726$	−729.004			−1.00414
$727$	−857.435	−	857.435i	−1.17941	−	1.17941i	−0.979893	−	0.199521i	$-0.936061\pi$
$727$	−857.435	−	857.435i	−1.17941	−	1.17941i	−0.199521	−	0.979893i	$-0.563939\pi$
$728$	−555.463	+	555.463i	−0.762999	+	0.762999i
$729$			27.0000i			0.0370370i
$730$	−1591.29	+	863.096i	−2.17985	+	1.18232i
$731$	1462.20			2.00028
$732$	−637.832	−	637.832i	−0.871355	−	0.871355i
$733$	291.875	−	291.875i	0.398193	−	0.398193i	−0.479402	−	0.877595i	$-0.659147\pi$
$733$	291.875	−	291.875i	0.398193	−	0.398193i	0.877595	+	0.479402i	$0.159147\pi$
$734$			1039.09i			1.41565i
$735$	−58.1178	−	17.2430i	−0.0790718	−	0.0234599i
$736$	3146.83			4.27558
$737$	140.094	+	140.094i	0.190087	+	0.190087i
$738$	−53.9996	+	53.9996i	−0.0731702	+	0.0731702i
$739$		−	1080.02i		−	1.46147i	−0.682662	−	0.730734i	$-0.739178\pi$
$739$		−	1080.02i		−	1.46147i	0.682662	−	0.730734i	$-0.260822\pi$
$740$	−47.6923	+	160.748i	−0.0644491	+	0.217226i
$741$	−26.9924			−0.0364270
$742$	−452.754	−	452.754i	−0.610181	−	0.610181i
$743$	−821.950	+	821.950i	−1.10626	+	1.10626i	−0.112621	+	0.993638i	$0.535925\pi$
$743$	−821.950	+	821.950i	−1.10626	+	1.10626i	−0.993638	+	0.112621i	$0.964075\pi$
$744$			1971.14i			2.64938i
$745$	−32.0007	−	58.9996i	−0.0429539	−	0.0791942i
$746$	969.562			1.29968
$747$	187.750	+	187.750i	0.251339	+	0.251339i
$748$	614.105	−	614.105i	0.820996	−	0.820996i
$749$			396.102i			0.528841i
$750$	66.5116	−	831.120i	0.0886821	−	1.10816i
$751$	834.946			1.11178			0.555889	−	0.831256i	$-0.312378\pi$
$751$	834.946			1.11178			0.555889	+	0.831256i	$0.312378\pi$
$752$	−824.425	−	824.425i	−1.09631	−	1.09631i
$753$	−566.948	+	566.948i	−0.752919	+	0.752919i
$754$			1988.06i			2.63669i
$755$	−587.228	+	318.505i	−0.777785	+	0.421861i
$756$	148.896			0.196952
$757$	−192.396	−	192.396i	−0.254156	−	0.254156i	0.568516	−	0.822672i	$-0.307518\pi$
$757$	−192.396	−	192.396i	−0.254156	−	0.254156i	−0.822672	+	0.568516i	$0.807518\pi$
$758$	−1163.59	+	1163.59i	−1.53508	+	1.53508i
$759$			157.964i			0.208122i
$760$	174.095	+	51.6523i	0.229072	+	0.0679636i
$761$	95.1019			0.124970			0.0624848	−	0.998046i	$-0.480097\pi$
$761$	95.1019			0.124970			0.0624848	+	0.998046i	$0.480097\pi$
$762$	564.086	+	564.086i	0.740271	+	0.740271i
$763$	−78.1050	+	78.1050i	−0.102366	+	0.102366i
$764$			795.806i			1.04163i
$765$	−99.9877	+	337.010i	−0.130703	+	0.440535i
$766$	2225.25			2.90502
$767$	138.017	+	138.017i	0.179945	+	0.179945i
$768$	−727.262	+	727.262i	−0.946956	+	0.946956i
$769$		−	368.887i		−	0.479697i	−0.970810	−	0.239848i	$-0.922902\pi$
$769$		−	368.887i		−	0.479697i	0.970810	−	0.239848i	$-0.0770977\pi$
$770$	83.1084	+	153.227i	0.107933	+	0.198996i
$771$	−133.428			−0.173059
$772$	1306.83	+	1306.83i	1.69279	+	1.69279i
$773$	−87.2860	+	87.2860i	−0.112918	+	0.112918i	−0.761308	−	0.648390i	$-0.775443\pi$
$773$	−87.2860	+	87.2860i	−0.112918	+	0.112918i	0.648390	+	0.761308i	$0.275443\pi$
$774$		−	720.839i		−	0.931316i
$775$	589.866	−	906.572i	0.761118	−	1.16977i
$776$	−1135.35			−1.46308
$777$	10.0331	+	10.0331i	0.0129126	+	0.0129126i
$778$	−1035.97	+	1035.97i	−1.33158	+	1.33158i
$779$			9.12646i			0.0117156i
$780$	−930.611	+	504.752i	−1.19309	+	0.647118i
$781$	−132.672			−0.169875
$782$	1700.98	+	1700.98i	2.17516	+	2.17516i
$783$	168.048	−	168.048i	0.214621	−	0.214621i
$784$		−	405.856i		−	0.517673i
$785$	980.179	+	290.810i	1.24864	+	0.370459i
$786$	501.450			0.637977
$787$	−984.039	−	984.039i	−1.25037	−	1.25037i	−0.955556	−	0.294811i	$-0.904743\pi$
$787$	−984.039	−	984.039i	−1.25037	−	1.25037i	−0.294811	−	0.955556i	$-0.595257\pi$
$788$	377.362	−	377.362i	0.478886	−	0.478886i
$789$		−	323.548i		−	0.410074i
$790$	−29.0748	+	97.9971i	−0.0368036	+	0.124047i
$791$	579.757			0.732942
$792$	−190.932	−	190.932i	−0.241076	−	0.241076i
$793$	383.775	−	383.775i	0.483953	−	0.483953i
$794$		−	2286.13i		−	2.87926i
$795$	−259.472	−	478.389i	−0.326380	−	0.601748i
$796$	−247.923			−0.311461
$797$	−130.781	−	130.781i	−0.164092	−	0.164092i	0.620285	−	0.784377i	$-0.287017\pi$
$797$	−130.781	−	130.781i	−0.164092	−	0.164092i	−0.784377	+	0.620285i	$0.787017\pi$
$798$	17.2295	−	17.2295i	0.0215908	−	0.0215908i
$799$		−	471.262i		−	0.589815i
$800$	2887.59	−	611.127i	3.60948	−	0.763909i
$801$	134.449			0.167851
$802$	316.589	+	316.589i	0.394749	+	0.394749i
$803$	227.467	−	227.467i	0.283271	−	0.283271i
$804$		−	1086.21i		−	1.35101i
$805$	−309.945	+	168.110i	−0.385025	+	0.208833i
$806$	−1880.53			−2.33317
$807$	−245.111	−	245.111i	−0.303731	−	0.303731i
$808$	2155.03	−	2155.03i	2.66712	−	2.66712i
$809$			918.729i			1.13564i	0.823154	+	0.567818i	$0.192212\pi$
$809$			918.729i			1.13564i	−0.823154	+	0.567818i	$0.807788\pi$
$810$	166.139	+	49.2920i	0.205110	+	0.0608543i
$811$	−70.2534			−0.0866256			−0.0433128	−	0.999062i	$-0.513791\pi$
$811$	−70.2534			−0.0866256			−0.0433128	+	0.999062i	$0.513791\pi$
$812$	−926.731	−	926.731i	−1.14129	−	1.14129i
$813$	146.954	−	146.954i	0.180755	−	0.180755i
$814$		−	40.7996i		−	0.0501223i
$815$	285.117	−	960.990i	0.349837	−	1.17913i
$816$	−2353.45			−2.88413
$817$	−60.9144	−	60.9144i	−0.0745586	−	0.0745586i
$818$	1390.25	−	1390.25i	1.69957	−	1.69957i
$819$			89.5888i			0.109388i
$820$	170.663	+	314.651i	0.208125	+	0.383721i
$821$	346.864			0.422489			0.211245	−	0.977433i	$-0.432248\pi$
$821$	346.864			0.422489			0.211245	+	0.977433i	$0.432248\pi$
$822$	−8.93838	−	8.93838i	−0.0108739	−	0.0108739i
$823$	−717.973	+	717.973i	−0.872385	+	0.872385i	−0.992732	−	0.120347i	$-0.961599\pi$
$823$	−717.973	+	717.973i	−0.872385	+	0.872385i	0.120347	+	0.992732i	$0.461599\pi$
$824$			1375.95i			1.66984i
$825$	30.6773	+	144.951i	0.0371846	+	0.175698i
$826$	−176.195			−0.213311
$827$	−480.121	−	480.121i	−0.580557	−	0.580557i	0.354499	−	0.935056i	$-0.384651\pi$
$827$	−480.121	−	480.121i	−0.580557	−	0.580557i	−0.935056	+	0.354499i	$0.884651\pi$
$828$	612.382	−	612.382i	0.739591	−	0.739591i
$829$			801.779i			0.967164i	0.875299	+	0.483582i	$0.160665\pi$
$829$			801.779i			0.967164i	−0.875299	+	0.483582i	$0.839335\pi$
$830$	1498.05	−	812.523i	1.80488	−	0.978943i
$831$	−496.446			−0.597408
$832$	−1777.77	−	1777.77i	−2.13674	−	2.13674i
$833$	115.999	−	115.999i	0.139254	−	0.139254i
$834$			98.3585i			0.117936i
$835$	809.061	+	240.041i	0.968935	+	0.287474i
$836$	−51.1664			−0.0612038
$837$	158.959	+	158.959i	0.189915	+	0.189915i
$838$	−1147.91	+	1147.91i	−1.36982	+	1.36982i
$839$			1436.37i			1.71200i	0.516974	+	0.856001i	$0.327059\pi$
$839$			1436.37i			1.71200i	−0.516974	+	0.856001i	$0.672941\pi$
$840$	171.436	−	577.827i	0.204091	−	0.687890i
$841$	−1250.87			−1.48736
$842$	1681.19	+	1681.19i	1.99667	+	1.99667i
$843$	347.590	−	347.590i	0.412326	−	0.412326i
$844$		−	2342.53i		−	2.77551i
$845$	99.1707	+	182.841i	0.117362	+	0.216380i
$846$	−232.323			−0.274614
$847$	204.467	+	204.467i	0.241402	+	0.241402i
$848$	2576.37	−	2576.37i	3.03817	−	3.03817i
$849$			47.0454i			0.0554127i
$850$	1891.18	+	1230.51i	2.22492	+	1.44766i
$851$	82.5287			0.0969785
$852$	514.331	+	514.331i	0.603675	+	0.603675i
$853$	−882.412	+	882.412i	−1.03448	+	1.03448i	−0.0350966	+	0.999384i	$0.511174\pi$
$853$	−882.412	+	882.412i	−1.03448	+	1.03448i	−0.999384	+	0.0350966i	$0.988826\pi$
$854$			489.933i			0.573692i
$855$	18.2050	−	9.87417i	0.0212924	−	0.0115487i
$856$	−3938.18			−4.60068
$857$	1086.13	+	1086.13i	1.26736	+	1.26736i	0.947445	+	0.319917i	$0.103655\pi$
$857$	1086.13	+	1086.13i	1.26736	+	1.26736i	0.319917	+	0.947445i	$0.396345\pi$
$858$	182.156	−	182.156i	0.212303	−	0.212303i
$859$			330.016i			0.384186i	0.981377	+	0.192093i	$0.0615276\pi$
$859$			330.016i			0.384186i	−0.981377	+	0.192093i	$0.938472\pi$
$860$	−3239.22	−	961.047i	−3.76653	−	1.11750i
$861$	30.2911			0.0351813
$862$	37.7193	+	37.7193i	0.0437578	+	0.0437578i
$863$	−31.2182	+	31.2182i	−0.0361741	+	0.0361741i	−0.724962	−	0.688788i	$-0.758143\pi$
$863$	−31.2182	+	31.2182i	−0.0361741	+	0.0361741i	0.688788	+	0.724962i	$0.258143\pi$
$864$			613.467i			0.710032i
$865$	12.3034	−	41.4689i	0.0142236	−	0.0479409i
$866$	−2938.90			−3.39365
$867$	−318.695	−	318.695i	−0.367584	−	0.367584i
$868$	876.607	−	876.607i	1.00992	−	1.00992i
$869$		−	18.1643i		−	0.0209025i
$870$	−727.259	−	1340.85i	−0.835929	−	1.54120i
$871$	653.557			0.750353
$872$	−776.547	−	776.547i	−0.890535	−	0.890535i
$873$	−91.5587	+	91.5587i	−0.104878	+	0.104878i
$874$		−	141.723i		−	0.162154i
$875$	−251.763	+	214.454i	−0.287729	+	0.245090i
$876$	−1763.64			−2.01329
$877$	−123.525	−	123.525i	−0.140849	−	0.140849i	0.633167	−	0.774016i	$-0.281755\pi$
$877$	−123.525	−	123.525i	−0.140849	−	0.140849i	−0.774016	+	0.633167i	$0.781755\pi$
$878$	−113.007	+	113.007i	−0.128710	+	0.128710i
$879$			676.858i			0.770032i
$880$	−871.928	+	472.923i	−0.990828	+	0.537413i
$881$	−1251.95			−1.42106			−0.710530	−	0.703667i	$-0.751545\pi$
$881$	−1251.95			−1.42106			−0.710530	+	0.703667i	$0.751545\pi$
$882$	−57.1852	−	57.1852i	−0.0648358	−	0.0648358i
$883$	−789.617	+	789.617i	−0.894244	+	0.894244i	−0.994919	−	0.100676i	$-0.967900\pi$
$883$	−789.617	+	789.617i	−0.894244	+	0.894244i	0.100676	+	0.994919i	$0.467900\pi$
$884$		−	2864.88i		−	3.24081i
$885$	−143.574	−	42.5972i	−0.162231	−	0.0481324i
$886$	−3145.03			−3.54969
$887$	543.479	+	543.479i	0.612716	+	0.612716i	0.943653	−	0.330937i	$-0.107365\pi$
$887$	543.479	+	543.479i	0.612716	+	0.612716i	−0.330937	+	0.943653i	$0.607365\pi$
$888$	−99.7528	+	99.7528i	−0.112334	+	0.112334i
$889$		−	316.424i		−	0.355933i
$890$	245.454	−	827.305i	0.275791	−	0.929556i
$891$	−30.7948			−0.0345621
$892$	−596.976	−	596.976i	−0.669256	−	0.669256i
$893$	−19.6325	+	19.6325i	−0.0219848	+	0.0219848i
$894$		−	89.5401i		−	0.100157i
$895$	560.016	+	1032.50i	0.625716	+	1.15363i
$896$	1020.08			1.13848
$897$	368.462	+	368.462i	0.410771	+	0.410771i
$898$	−638.787	+	638.787i	−0.711344	+	0.711344i
$899$		−	1978.73i		−	2.20103i
$900$	443.005	−	680.859i	0.492228	−	0.756510i
$901$	1472.72			1.63454
$902$	−61.5891	−	61.5891i	−0.0682806	−	0.0682806i
$903$	−202.177	+	202.177i	−0.223895	+	0.223895i
$904$			5764.15i			6.37627i
$905$	566.420	−	307.219i	0.625878	−	0.339469i
$906$	−891.199			−0.983663
$907$	650.529	+	650.529i	0.717232	+	0.717232i	0.968037	−	0.250806i	$-0.0806955\pi$
$907$	650.529	+	650.529i	0.717232	+	0.717232i	−0.250806	+	0.968037i	$0.580695\pi$
$908$	−1775.87	+	1775.87i	−1.95581	+	1.95581i
$909$		−	347.578i		−	0.382374i
$910$	551.267	+	163.556i	0.605788	+	0.179732i
$911$	−64.0563			−0.0703143			−0.0351572	−	0.999382i	$-0.511193\pi$
$911$	−64.0563			−0.0703143			−0.0351572	+	0.999382i	$0.511193\pi$
$912$	98.0431	+	98.0431i	0.107503	+	0.107503i
$913$	−214.138	+	214.138i	−0.234544	+	0.234544i
$914$		−	834.494i		−	0.913013i
$915$	−118.447	+	399.226i	−0.129450	+	0.436313i
$916$	1746.12			1.90624
$917$	−140.644	−	140.644i	−0.153374	−	0.153374i
$918$	−331.602	+	331.602i	−0.361222	+	0.361222i
$919$			550.055i			0.598536i	0.954169	+	0.299268i	$0.0967425\pi$
$919$			550.055i			0.598536i	−0.954169	+	0.299268i	$0.903257\pi$
$920$	−1671.41	−	3081.58i	−1.81675	−	3.34954i
$921$	−205.886			−0.223546
$922$	−1697.72	−	1697.72i	−1.84135	−	1.84135i
$923$	−309.466	+	309.466i	−0.335283	+	0.335283i
$924$			169.823i			0.183791i
$925$	75.7298	−	16.0274i	0.0818701	−	0.0173269i
$926$	3342.72			3.60985
$927$	110.961	+	110.961i	0.119699	+	0.119699i
$928$	3818.23	−	3818.23i	4.11447	−	4.11447i
$929$			509.593i			0.548540i	0.961653	+	0.274270i	$0.0884361\pi$
$929$			509.593i			0.548540i	−0.961653	+	0.274270i	$0.911564\pi$
$930$	1268.32	−	687.924i	1.36379	−	0.739703i
$931$	−9.66486			−0.0103812
$932$	89.7738	+	89.7738i	0.0963239	+	0.0963239i
$933$	279.413	−	279.413i	0.299478	−	0.299478i
$934$			2392.24i			2.56128i
$935$	−384.376	−	114.041i	−0.411097	−	0.121969i
$936$	−890.723			−0.951627
$937$	−1254.00	−	1254.00i	−1.33831	−	1.33831i	−0.897698	−	0.440612i	$-0.854761\pi$
$937$	−1254.00	−	1254.00i	−1.33831	−	1.33831i	−0.440612	−	0.897698i	$-0.645239\pi$
$938$	−417.170	+	417.170i	−0.444745	+	0.444745i
$939$			1018.28i			1.08443i
$940$	−309.741	+	1043.99i	−0.329512	+	1.11062i
$941$	−1596.36			−1.69645			−0.848223	−	0.529639i	$-0.822327\pi$
$941$	−1596.36			−1.69645			−0.848223	+	0.529639i	$0.822327\pi$
$942$	964.450	+	964.450i	1.02383	+	1.02383i
$943$	124.581	−	124.581i	0.132112	−	0.132112i
$944$		−	1002.63i		−	1.06211i
$945$	−32.7727	−	60.4231i	−0.0346801	−	0.0639398i
$946$	822.151			0.869082
$947$	484.352	+	484.352i	0.511459	+	0.511459i	0.914973	−	0.403514i	$-0.132211\pi$
$947$	484.352	+	484.352i	0.511459	+	0.511459i	−0.403514	+	0.914973i	$0.632211\pi$
$948$	−70.4176	+	70.4176i	−0.0742802	+	0.0742802i
$949$		−	1061.16i		−	1.11819i
$950$	−27.5232	−	130.048i	−0.0289718	−	0.136892i
$951$	411.508			0.432711
$952$	1153.30	+	1153.30i	1.21145	+	1.21145i
$953$	−79.3357	+	79.3357i	−0.0832483	+	0.0832483i	−0.747505	−	0.664256i	$-0.768748\pi$
$953$	−79.3357	+	79.3357i	−0.0832483	+	0.0832483i	0.664256	+	0.747505i	$0.268748\pi$
$954$		−	726.021i		−	0.761029i
$955$	322.944	−	175.161i	0.338161	−	0.183414i
$956$	720.207			0.753355
$957$	191.667	+	191.667i	0.200279	+	0.200279i
$958$	−41.5948	+	41.5948i	−0.0434184	+	0.0434184i
$959$			5.01398i			0.00522835i
$960$	1849.35	+	548.684i	1.92640	+	0.571546i
$961$	910.704			0.947663
$962$	−95.1676	−	95.1676i	−0.0989268	−	0.0989268i
$963$	−317.588	+	317.588i	−0.329790	+	0.329790i
$964$		−	1656.25i		−	1.71810i
$965$	242.682	−	817.962i	0.251484	−	0.847629i
$966$	−470.384			−0.486940
$967$	733.793	+	733.793i	0.758835	+	0.758835i	0.976110	−	0.217276i	$-0.0697171\pi$
$967$	733.793	+	733.793i	0.758835	+	0.758835i	−0.217276	+	0.976110i	$0.569717\pi$
$968$	−2032.88	+	2032.88i	−2.10009	+	2.10009i
$969$			56.0439i			0.0578369i
$970$	396.236	+	730.541i	0.408491	+	0.753135i
$971$	907.453			0.934556			0.467278	−	0.884111i	$-0.345235\pi$
$971$	907.453			0.934556			0.467278	+	0.884111i	$0.345235\pi$
$972$	119.382	+	119.382i	0.122821	+	0.122821i
$973$	27.5871	−	27.5871i	0.0283526	−	0.0283526i
$974$			928.341i			0.953123i
$975$	409.664	+	266.550i	0.420168	+	0.273385i
$976$	−2787.93			−2.85649
$977$	−643.316	−	643.316i	−0.658460	−	0.658460i	0.296555	−	0.955016i	$-0.404162\pi$
$977$	−643.316	−	643.316i	−0.658460	−	0.658460i	−0.955016	+	0.296555i	$0.904162\pi$
$978$	945.569	−	945.569i	0.966840	−	0.966840i
$979$			153.345i			0.156635i
$980$	−333.213	+	180.731i	−0.340014	+	0.184419i
$981$	−125.247			−0.127672
$982$	−1470.44	−	1470.44i	−1.49740	−	1.49740i
$983$	−106.552	+	106.552i	−0.108395	+	0.108395i	−0.759224	−	0.650829i	$-0.774421\pi$
$983$	−106.552	+	106.552i	−0.108395	+	0.108395i	0.650829	+	0.759224i	$0.274421\pi$
$984$			301.164i			0.306061i
$985$	−236.195	−	70.0770i	−0.239792	−	0.0711441i
$986$	4127.79			4.18639
$987$	65.1609	+	65.1609i	0.0660191	+	0.0660191i
$988$	−119.349	+	119.349i	−0.120798	+	0.120798i
$989$			1663.03i			1.68153i
$990$	−56.2199	+	189.490i	−0.0567878	+	0.191404i
$991$	−1218.66			−1.22972			−0.614862	−	0.788634i	$-0.710788\pi$
$991$	−1218.66			−1.22972			−0.614862	+	0.788634i	$0.710788\pi$
$992$	3611.71	+	3611.71i	3.64084	+	3.64084i
$993$	465.245	−	465.245i	0.468525	−	0.468525i
$994$		−	395.069i		−	0.397454i
$995$	54.5690	+	100.609i	0.0548433	+	0.101115i
$996$	1660.30			1.66697
$997$	7.41944	+	7.41944i	0.00744176	+	0.00744176i	0.710818	−	0.703376i	$-0.248325\pi$
$997$	7.41944	+	7.41944i	0.00744176	+	0.00744176i	−0.703376	+	0.710818i	$0.748325\pi$
$998$	1618.63	−	1618.63i	1.62187	−	1.62187i
$999$			16.0888i			0.0161049i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.3.l.a.22.1	✓	24
3.2	odd	2		315.3.o.b.127.12		24
5.2	odd	4		525.3.l.e.43.12		24
5.3	odd	4	inner	105.3.l.a.43.1	yes	24
5.4	even	2		525.3.l.e.232.12		24
15.8	even	4		315.3.o.b.253.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.1	✓	24	1.1	even	1	trivial
105.3.l.a.43.1	yes	24	5.3	odd	4	inner
315.3.o.b.127.12		24	3.2	odd	2
315.3.o.b.253.12		24	15.8	even	4
525.3.l.e.43.12		24	5.2	odd	4
525.3.l.e.232.12		24	5.4	even	2

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	105.l (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.72310 - 2.72310i) q^{2} +(-1.22474 + 1.22474i) q^{3} +10.8306i q^{4} +(4.39513 - 2.38387i) q^{5} +6.67022 q^{6} +(-1.87083 - 1.87083i) q^{7} +(18.6004 - 18.6004i) q^{8} -3.00000i q^{9} +O(q^{10})\)	\(q+(-2.72310 - 2.72310i) q^{2} +(-1.22474 + 1.22474i) q^{3} +10.8306i q^{4} +(4.39513 - 2.38387i) q^{5} +6.67022 q^{6} +(-1.87083 - 1.87083i) q^{7} +(18.6004 - 18.6004i) q^{8} -3.00000i q^{9} +(-18.4599 - 5.47689i) q^{10} +3.42164 q^{11} +(-13.2647 - 13.2647i) q^{12} +(7.98120 - 7.98120i) q^{13} +10.1889i q^{14} +(-2.46329 + 8.30254i) q^{15} -57.9794 q^{16} +(-16.5713 - 16.5713i) q^{17} +(-8.16931 + 8.16931i) q^{18} +1.38069i q^{19} +(25.8187 + 47.6019i) q^{20} +4.58258 q^{21} +(-9.31750 - 9.31750i) q^{22} +(18.8473 - 18.8473i) q^{23} +45.5616i q^{24} +(13.6344 - 20.9548i) q^{25} -43.4673 q^{26} +(3.67423 + 3.67423i) q^{27} +(20.2622 - 20.2622i) q^{28} -45.7370i q^{29} +(29.3165 - 15.9009i) q^{30} +43.2632 q^{31} +(83.4823 + 83.4823i) q^{32} +(-4.19064 + 4.19064i) q^{33} +90.2505i q^{34} +(-12.6823 - 3.76274i) q^{35} +32.4918 q^{36} +(2.18941 + 2.18941i) q^{37} +(3.75977 - 3.75977i) q^{38} +19.5499i q^{39} +(37.4104 - 126.092i) q^{40} +6.61005 q^{41} +(-12.4788 - 12.4788i) q^{42} +(-44.1187 + 44.1187i) q^{43} +37.0585i q^{44} +(-7.15160 - 13.1854i) q^{45} -102.646 q^{46} +(14.2193 + 14.2193i) q^{47} +(71.0100 - 71.0100i) q^{48} +7.00000i q^{49} +(-94.1899 + 19.9343i) q^{50} +40.5911 q^{51} +(86.4412 + 86.4412i) q^{52} +(-44.4359 + 44.4359i) q^{53} -20.0106i q^{54} +(15.0386 - 8.15674i) q^{55} -69.5964 q^{56} +(-1.69100 - 1.69100i) q^{57} +(-124.547 + 124.547i) q^{58} +17.2928i q^{59} +(-89.9215 - 26.6789i) q^{60} +48.0848 q^{61} +(-117.810 - 117.810i) q^{62} +(-5.61249 + 5.61249i) q^{63} -222.745i q^{64} +(16.0523 - 54.1046i) q^{65} +22.8231 q^{66} +(40.9435 + 40.9435i) q^{67} +(179.477 - 179.477i) q^{68} +46.1662i q^{69} +(24.2890 + 44.7817i) q^{70} -38.7743 q^{71} +(-55.8013 - 55.8013i) q^{72} +(66.4788 - 66.4788i) q^{73} -11.9240i q^{74} +(8.96566 + 42.3629i) q^{75} -14.9537 q^{76} +(-6.40131 - 6.40131i) q^{77} +(53.2363 - 53.2363i) q^{78} -5.30864i q^{79} +(-254.827 + 138.215i) q^{80} -9.00000 q^{81} +(-17.9999 - 17.9999i) q^{82} +(-62.5835 + 62.5835i) q^{83} +49.6320i q^{84} +(-112.337 - 33.3292i) q^{85} +240.280 q^{86} +(56.0161 + 56.0161i) q^{87} +(63.6441 - 63.6441i) q^{88} +44.8163i q^{89} +(-16.4307 + 55.3798i) q^{90} -29.8629 q^{91} +(204.127 + 204.127i) q^{92} +(-52.9864 + 52.9864i) q^{93} -77.4411i q^{94} +(3.29139 + 6.06833i) q^{95} -204.489 q^{96} +(-30.5196 - 30.5196i) q^{97} +(19.0617 - 19.0617i) q^{98} -10.2649i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8}+O(q^{10}) \) 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8	\( 24 q + 8 q^{2} + 16 q^{5} + 24 q^{6} - 48 q^{8} - 40 q^{10} - 48 q^{12} + 64 q^{13} - 184 q^{16} + 24 q^{17} + 24 q^{18} + 72 q^{20} + 8 q^{22} + 8 q^{23} - 136 q^{25} - 80 q^{26} + 96 q^{30} + 96 q^{31} + 56 q^{32} - 72 q^{33} + 168 q^{36} + 8 q^{37} + 56 q^{38} + 232 q^{40} + 320 q^{41} - 112 q^{43} - 72 q^{45} + 320 q^{46} + 64 q^{47} + 192 q^{48} - 256 q^{50} - 192 q^{51} + 96 q^{52} - 72 q^{53} - 80 q^{55} - 336 q^{56} + 48 q^{57} - 512 q^{58} - 192 q^{60} - 496 q^{61} - 776 q^{62} + 312 q^{65} - 192 q^{66} - 192 q^{67} + 568 q^{68} + 112 q^{70} - 144 q^{71} + 144 q^{72} + 224 q^{73} + 144 q^{75} + 416 q^{76} + 112 q^{77} - 216 q^{78} - 528 q^{80} - 216 q^{81} + 352 q^{82} - 32 q^{83} + 24 q^{85} + 240 q^{86} + 384 q^{87} + 216 q^{88} - 24 q^{90} + 1304 q^{92} + 376 q^{95} + 168 q^{96} - 816 q^{97} - 56 q^{98}+O(q^{100}) \) 24 * q + 8 * q^2 + 16 * q^5 + 24 * q^6 - 48 * q^8 - 40 * q^10 - 48 * q^12 + 64 * q^13 - 184 * q^16 + 24 * q^17 + 24 * q^18 + 72 * q^20 + 8 * q^22 + 8 * q^23 - 136 * q^25 - 80 * q^26 + 96 * q^30 + 96 * q^31 + 56 * q^32 - 72 * q^33 + 168 * q^36 + 8 * q^37 + 56 * q^38 + 232 * q^40 + 320 * q^41 - 112 * q^43 - 72 * q^45 + 320 * q^46 + 64 * q^47 + 192 * q^48 - 256 * q^50 - 192 * q^51 + 96 * q^52 - 72 * q^53 - 80 * q^55 - 336 * q^56 + 48 * q^57 - 512 * q^58 - 192 * q^60 - 496 * q^61 - 776 * q^62 + 312 * q^65 - 192 * q^66 - 192 * q^67 + 568 * q^68 + 112 * q^70 - 144 * q^71 + 144 * q^72 + 224 * q^73 + 144 * q^75 + 416 * q^76 + 112 * q^77 - 216 * q^78 - 528 * q^80 - 216 * q^81 + 352 * q^82 - 32 * q^83 + 24 * q^85 + 240 * q^86 + 384 * q^87 + 216 * q^88 - 24 * q^90 + 1304 * q^92 + 376 * q^95 + 168 * q^96 - 816 * q^97 - 56 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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