LMFDB - Embedded newform 105.3.l.a.43.1

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			43.1
Character	$\chi$	$=$	105.43
Dual form			105.3.l.a.22.1

$q$-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 $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$

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	−0.489612	+	0.871941i	$0.662861\pi$
$2$	−2.72310	+	2.72310i	−1.36155	+	1.36155i	−0.871941	+	0.489612i	$0.837139\pi$
$3$	−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	0.943970	−	0.330031i	$-0.107059\pi$
$13$	7.98120	+	7.98120i	0.613939	+	0.613939i	−0.330031	+	0.943970i	$0.607059\pi$
$14$		−	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	−0.999690	−	0.0249097i	$-0.992070\pi$
$17$	−16.5713	+	16.5713i	−0.974780	+	0.974780i	0.0249097	+	0.999690i	$0.492070\pi$
$18$	−8.16931	−	8.16931i	−0.453851	−	0.453851i
$19$		−	1.38069i		−	0.0726681i	−0.999340	−	0.0363341i	$-0.988432\pi$
$19$		−	1.38069i		−	0.0726681i	0.999340	−	0.0363341i	$-0.0115680\pi$
$20$	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	0.986028	−	0.166581i	$-0.0532728\pi$
$23$	18.8473	+	18.8473i	0.819447	+	0.819447i	−0.166581	+	0.986028i	$0.553273\pi$
$24$		−	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	$0.289177\pi$
$29$			45.7370i			1.57714i	−0.614947	+	0.788568i	$0.710823\pi$
$30$	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	−0.676901	−	0.736074i	$-0.736677\pi$
$37$	2.18941	−	2.18941i	0.0591732	−	0.0591732i	0.736074	+	0.676901i	$0.236677\pi$
$38$	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	−0.999652	−	0.0263634i	$-0.991607\pi$
$43$	−44.1187	−	44.1187i	−1.02602	−	1.02602i	−0.0263634	−	0.999652i	$-0.508393\pi$
$44$		−	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	−0.539468	−	0.842006i	$-0.681375\pi$
$47$	14.2193	−	14.2193i	0.302538	−	0.302538i	0.842006	+	0.539468i	$0.181375\pi$
$48$	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	0.150237	−	0.988650i	$-0.451996\pi$
$53$	−44.4359	−	44.4359i	−0.838413	−	0.838413i	−0.988650	+	0.150237i	$0.951996\pi$
$54$			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	$-0.953183\pi$
$59$		−	17.2928i		−	0.293099i	0.989203	−	0.146549i	$-0.0468167\pi$
$60$	−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	−0.332135	−	0.943232i	$-0.607769\pi$
$67$	40.9435	−	40.9435i	0.611097	−	0.611097i	0.943232	+	0.332135i	$0.107769\pi$
$68$	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	0.996325	−	0.0856565i	$-0.0272988\pi$
$73$	66.4788	+	66.4788i	0.910668	+	0.910668i	−0.0856565	+	0.996325i	$0.527299\pi$
$74$			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	$0.0106969\pi$
$79$			5.30864i			0.0671980i	−0.999435	+	0.0335990i	$0.989303\pi$
$80$	−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	0.221209	−	0.975226i	$-0.429000\pi$
$83$	−62.5835	−	62.5835i	−0.754017	−	0.754017i	−0.975226	+	0.221209i	$0.929000\pi$
$84$		−	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	$-0.918985\pi$
$89$		−	44.8163i		−	0.503554i	0.967785	−	0.251777i	$-0.0810149\pi$
$90$	−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	−0.846702	−	0.532067i	$-0.821415\pi$
$97$	−30.5196	+	30.5196i	−0.314635	+	0.314635i	0.532067	+	0.846702i	$0.321415\pi$
$98$	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	0.504382	−	0.863480i	$-0.331720\pi$
$103$	−36.9871	−	36.9871i	−0.359098	−	0.359098i	−0.863480	+	0.504382i	$0.831720\pi$
$104$			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	−0.999944	−	0.0105734i	$-0.996634\pi$
$107$	−105.863	+	105.863i	−0.989371	+	0.989371i	0.0105734	+	0.999944i	$0.496634\pi$
$108$	−39.7942	−	39.7942i	−0.368464	−	0.368464i
$109$			41.7489i			0.383017i	0.981491	+	0.191509i	$0.0613380\pi$
$109$			41.7489i			0.383017i	−0.981491	+	0.191509i	$0.938662\pi$
$110$	−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	−0.858655	−	0.512554i	$-0.828700\pi$
$113$	−154.947	−	154.947i	−1.37121	−	1.37121i	−0.512554	−	0.858655i	$-0.671300\pi$
$114$		−	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	−0.290873	−	0.956762i	$-0.593946\pi$
$127$	84.5679	−	84.5679i	0.665889	−	0.665889i	0.956762	+	0.290873i	$0.0939456\pi$
$128$	−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	−0.711981	−	0.702199i	$-0.752202\pi$
$137$	−1.34004	+	1.34004i	−0.00978134	+	0.00978134i	0.702199	+	0.711981i	$0.252202\pi$
$138$	125.715	+	125.715i	0.910981	+	0.910981i
$139$		−	14.7459i		−	0.106086i	−0.998592	−	0.0530429i	$-0.983108\pi$
$139$		−	14.7459i		−	0.106086i	0.998592	−	0.0530429i	$-0.0168920\pi$
$140$	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	$0.0143436\pi$
$149$			13.4239i			0.0900930i	−0.998985	+	0.0450465i	$0.985656\pi$
$150$	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	−0.0761383	−	0.997097i	$-0.524259\pi$
$157$	144.591	−	144.591i	0.920959	−	0.920959i	0.997097	+	0.0761383i	$0.0242590\pi$
$158$	−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	0.992438	−	0.122746i	$-0.0391699\pi$
$163$	141.760	+	141.760i	0.869693	+	0.869693i	−0.122746	+	0.992438i	$0.539170\pi$
$164$		−	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	−0.252847	−	0.967506i	$-0.581367\pi$
$167$	119.348	−	119.348i	0.714660	−	0.714660i	0.967506	+	0.252847i	$0.0813668\pi$
$168$	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	0.724566	−	0.689206i	$-0.242040\pi$
$173$	6.11726	+	6.11726i	0.0353599	+	0.0353599i	−0.689206	+	0.724566i	$0.742040\pi$
$174$			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	$-0.772163\pi$
$179$		−	234.919i		−	1.31240i	0.754588	−	0.656199i	$-0.227837\pi$
$180$	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	0.946853	−	0.321666i	$-0.104243\pi$
$193$	120.661	+	120.661i	0.625187	+	0.625187i	−0.321666	+	0.946853i	$0.604243\pi$
$194$		−	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	−0.789987	−	0.613123i	$-0.789913\pi$
$197$	−34.8422	+	34.8422i	−0.176864	+	0.176864i	0.613123	+	0.789987i	$0.289913\pi$
$198$	−27.9525	−	27.9525i	−0.141174	−	0.141174i
$199$		−	22.8910i		−	0.115030i	−0.998345	−	0.0575151i	$-0.981682\pi$
$199$		−	22.8910i		−	0.115030i	0.998345	−	0.0575151i	$-0.0183177\pi$
$200$	−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	0.572637	−	0.819809i	$-0.305921\pi$
$223$	−55.1194	−	55.1194i	−0.247172	−	0.247172i	−0.819809	+	0.572637i	$0.805921\pi$
$224$			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	−0.246752	−	0.969079i	$-0.579363\pi$
$227$	163.968	−	163.968i	0.722327	−	0.722327i	0.969079	+	0.246752i	$0.0793633\pi$
$228$	18.3145	+	18.3145i	0.0803268	+	0.0803268i
$229$			161.221i			0.704022i	0.935996	+	0.352011i	$0.114502\pi$
$229$			161.221i			0.704022i	−0.935996	+	0.352011i	$0.885498\pi$
$230$	−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	0.724670	−	0.689096i	$-0.241992\pi$
$233$	8.28891	+	8.28891i	0.0355747	+	0.0355747i	−0.689096	+	0.724670i	$0.741992\pi$
$234$		−	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	$0.0444261\pi$
$239$			66.4975i			0.278232i	−0.990276	+	0.139116i	$0.955574\pi$
$240$	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	−0.593144	−	0.805097i	$-0.702113\pi$
$257$	54.4719	−	54.4719i	0.211953	−	0.211953i	0.805097	+	0.593144i	$0.202113\pi$
$258$	−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	0.409896	−	0.912132i	$-0.365565\pi$
$263$	−132.088	−	132.088i	−0.502236	−	0.502236i	−0.912132	+	0.409896i	$0.865565\pi$
$264$		−	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	$-0.878675\pi$
$269$		−	200.132i		−	0.743985i	0.928236	−	0.371993i	$-0.121325\pi$
$270$	−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	−0.239279	−	0.970951i	$-0.576911\pi$
$277$	202.673	−	202.673i	0.731672	−	0.731672i	0.970951	+	0.239279i	$0.0769110\pi$
$278$	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	0.740225	−	0.672359i	$-0.234719\pi$
$283$	19.2062	+	19.2062i	0.0678664	+	0.0678664i	−0.672359	+	0.740225i	$0.734719\pi$
$284$			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	0.998466	−	0.0553728i	$-0.0176347\pi$
$293$	276.326	+	276.326i	0.943093	+	0.943093i	−0.0553728	+	0.998466i	$0.517635\pi$
$294$		−	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	−0.556836	−	0.830623i	$-0.687985\pi$
$307$	84.0526	−	84.0526i	0.273787	−	0.273787i	0.830623	+	0.556836i	$0.187985\pi$
$308$	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	0.906985	+	0.421163i	$0.138378\pi$
$313$	415.710	+	415.710i	1.32815	+	1.32815i	0.421163	+	0.906985i	$0.361622\pi$
$314$			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	−0.920560	−	0.390600i	$-0.872267\pi$
$317$	−167.997	+	167.997i	−0.529960	+	0.529960i	0.390600	+	0.920560i	$0.372267\pi$
$318$	−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	−0.227730	−	0.973724i	$-0.573130\pi$
$337$	251.400	−	251.400i	0.745994	−	0.745994i	0.973724	+	0.227730i	$0.0731305\pi$
$338$	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	−0.282308	−	0.959324i	$-0.591100\pi$
$347$	234.925	−	234.925i	0.677016	−	0.677016i	0.959324	+	0.282308i	$0.0910999\pi$
$348$	−606.688	−	606.688i	−1.74336	−	1.74336i
$349$		−	497.584i		−	1.42574i	−0.701295	−	0.712871i	$-0.747395\pi$
$349$		−	497.584i		−	1.42574i	0.701295	−	0.712871i	$-0.252605\pi$
$350$	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	0.328394	−	0.944541i	$-0.393492\pi$
$353$	−217.500	−	217.500i	−0.616146	−	0.616146i	−0.944541	+	0.328394i	$0.893492\pi$
$354$		−	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	$0.265039\pi$
$359$			531.115i			1.47943i	−0.672921	+	0.739714i	$0.734961\pi$
$360$	−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	−0.917531	−	0.397664i	$-0.869821\pi$
$367$	−190.791	+	190.791i	−0.519867	+	0.519867i	0.397664	+	0.917531i	$0.369821\pi$
$368$	−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	0.426981	−	0.904260i	$-0.359577\pi$
$373$	−178.025	−	178.025i	−0.477279	−	0.477279i	−0.904260	+	0.426981i	$0.859577\pi$
$374$		−	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	$0.190632\pi$
$379$			427.303i			1.12745i	−0.825963	+	0.563725i	$0.809368\pi$
$380$	−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	−0.997603	−	0.0692020i	$-0.977955\pi$
$383$	−408.586	−	408.586i	−1.06680	−	1.06680i	−0.0692020	−	0.997603i	$-0.522045\pi$
$384$			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	$0.162636\pi$
$389$			380.438i			0.977990i	−0.872286	+	0.488995i	$0.837364\pi$
$390$	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	0.0590903	−	0.998253i	$-0.481180\pi$
$397$	419.765	−	419.765i	1.05734	−	1.05734i	0.998253	−	0.0590903i	$-0.0188200\pi$
$398$	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	$-0.785454\pi$
$409$		−	510.537i		−	1.24826i	0.781322	−	0.624129i	$-0.214546\pi$
$410$	−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	$0.167784\pi$
$419$			421.546i			1.00608i	−0.864265	+	0.503038i	$0.832216\pi$
$420$	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	0.957366	+	0.288879i	$0.0932824\pi$
$433$	539.624	+	539.624i	1.24624	+	1.24624i	0.288879	+	0.957366i	$0.406718\pi$
$434$		−	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	$0.0150508\pi$
$439$			41.4994i			0.0945318i	−0.998882	+	0.0472659i	$0.984949\pi$
$440$	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	0.925984	+	0.377563i	$0.123238\pi$
$443$	577.471	+	577.471i	1.30355	+	1.30355i	0.377563	+	0.925984i	$0.376762\pi$
$444$			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	$0.0841266\pi$
$449$			234.581i			0.522451i	−0.965278	+	0.261226i	$0.915873\pi$
$450$	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	−0.519305	−	0.854589i	$-0.673809\pi$
$457$	153.225	−	153.225i	0.335284	−	0.335284i	0.854589	+	0.519305i	$0.173809\pi$
$458$	−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	−0.909133	−	0.416506i	$-0.863255\pi$
$463$	−613.771	−	613.771i	−1.32564	−	1.32564i	−0.416506	−	0.909133i	$-0.636745\pi$
$464$		−	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	−0.998331	−	0.0577556i	$-0.981606\pi$
$467$	−439.249	+	439.249i	−0.940575	+	0.940575i	0.0577556	+	0.998331i	$0.481606\pi$
$468$	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	$0.00507549\pi$
$479$			15.2748i			0.0318889i	−0.999873	+	0.0159445i	$0.994925\pi$
$480$	−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	−0.860114	−	0.510101i	$-0.829608\pi$
$487$	−170.456	+	170.456i	−0.350013	+	0.350013i	0.510101	+	0.860114i	$0.329608\pi$
$488$	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	$-0.796916\pi$
$499$		−	594.406i		−	1.19119i	0.803284	−	0.595597i	$-0.203084\pi$
$500$	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	0.158855	−	0.987302i	$-0.449220\pi$
$503$	−416.709	−	416.709i	−0.828447	−	0.828447i	−0.987302	+	0.158855i	$0.949220\pi$
$504$		−	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	$-0.631766\pi$
$509$		−	932.017i		−	1.83107i	0.402234	−	0.915537i	$-0.368234\pi$
$510$	−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	0.836899	−	0.547357i	$-0.184366\pi$
$523$	151.430	+	151.430i	0.289542	+	0.289542i	−0.547357	+	0.836899i	$0.684366\pi$
$524$		−	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	−0.199699	−	0.979857i	$-0.563997\pi$
$547$	426.746	−	426.746i	0.780158	−	0.780158i	0.979857	+	0.199699i	$0.0639965\pi$
$548$	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	−0.504416	−	0.863461i	$-0.668292\pi$
$557$	199.988	−	199.988i	0.359045	−	0.359045i	0.863461	+	0.504416i	$0.168292\pi$
$558$	−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	0.627129	−	0.778916i	$-0.284230\pi$
$563$	−85.4562	−	85.4562i	−0.151787	−	0.151787i	−0.778916	+	0.627129i	$0.784230\pi$
$564$			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	$-0.663036\pi$
$569$		−	991.963i		−	1.74334i	0.490090	−	0.871672i	$-0.336964\pi$
$570$	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	0.113972	−	0.993484i	$-0.463643\pi$
$577$	639.002	−	639.002i	1.10746	−	1.10746i	0.993484	−	0.113972i	$-0.0363573\pi$
$578$	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	−0.947047	−	0.321094i	$-0.895949\pi$
$587$	−367.435	+	367.435i	−0.625953	+	0.625953i	0.321094	+	0.947047i	$0.395949\pi$
$588$	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	0.384278	−	0.923217i	$-0.374450\pi$
$593$	−319.591	−	319.591i	−0.538939	−	0.538939i	−0.923217	+	0.384278i	$0.874450\pi$
$594$			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	$0.0317797\pi$
$599$			119.408i			0.199346i	−0.995020	+	0.0996730i	$0.968220\pi$
$600$	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	−0.291360	+	0.956614i	$0.594108\pi$
$607$	−757.520	+	757.520i	−1.24797	+	1.24797i	−0.956614	+	0.291360i	$0.905892\pi$
$608$	−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	0.998955	−	0.0457151i	$-0.0145566\pi$
$613$	584.336	+	584.336i	0.953239	+	0.953239i	−0.0457151	+	0.998955i	$0.514557\pi$
$614$			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	−0.197070	−	0.980389i	$-0.563143\pi$
$617$	483.308	−	483.308i	0.783319	−	0.783319i	0.980389	+	0.197070i	$0.0631428\pi$
$618$	−246.712	−	246.712i	−0.399210	−	0.399210i
$619$			1053.61i			1.70211i	0.525074	+	0.851056i	$0.324038\pi$
$619$			1053.61i			1.70211i	−0.525074	+	0.851056i	$0.675962\pi$
$620$	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	0.740133	−	0.672461i	$-0.234763\pi$
$643$	43.5132	+	43.5132i	0.0676721	+	0.0676721i	−0.672461	+	0.740133i	$0.734763\pi$
$644$			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	−0.286045	−	0.958216i	$-0.592341\pi$
$647$	434.895	−	434.895i	0.672171	−	0.672171i	0.958216	+	0.286045i	$0.0923407\pi$
$648$	−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	0.976111	−	0.217272i	$-0.0697160\pi$
$653$	495.522	+	495.522i	0.758839	+	0.758839i	−0.217272	+	0.976111i	$0.569716\pi$
$654$			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	$-0.939134\pi$
$659$		−	250.489i		−	0.380104i	0.981774	−	0.190052i	$-0.0608657\pi$
$660$	−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	0.997317	−	0.0732040i	$-0.0233224\pi$
$673$	621.928	+	621.928i	0.924113	+	0.924113i	−0.0732040	+	0.997317i	$0.523322\pi$
$674$			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	−0.955388	−	0.295353i	$-0.904563\pi$
$677$	−446.844	+	446.844i	−0.660035	+	0.660035i	0.295353	+	0.955388i	$0.404563\pi$
$678$	−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	0.152238	−	0.988344i	$-0.451352\pi$
$683$	−571.060	−	571.060i	−0.836106	−	0.836106i	−0.988344	+	0.152238i	$0.951352\pi$
$684$		−	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	$-0.959080\pi$
$709$		−	181.787i		−	0.256400i	0.991748	−	0.128200i	$-0.0409199\pi$
$710$	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	$0.0639310\pi$
$719$			286.878i			0.398995i	−0.979898	+	0.199498i	$0.936069\pi$
$720$	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	−0.199521	+	0.979893i	$0.563939\pi$
$727$	−857.435	+	857.435i	−1.17941	+	1.17941i	−0.979893	+	0.199521i	$0.936061\pi$
$728$	−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	0.877595	−	0.479402i	$-0.159147\pi$
$733$	291.875	+	291.875i	0.398193	+	0.398193i	−0.479402	+	0.877595i	$0.659147\pi$
$734$		−	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	$0.260822\pi$
$739$			1080.02i			1.46147i	−0.682662	+	0.730734i	$0.739178\pi$
$740$	−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	−0.993638	−	0.112621i	$-0.964075\pi$
$743$	−821.950	−	821.950i	−1.10626	−	1.10626i	−0.112621	−	0.993638i	$-0.535925\pi$
$744$		−	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	−0.822672	−	0.568516i	$-0.807518\pi$
$757$	−192.396	+	192.396i	−0.254156	+	0.254156i	0.568516	+	0.822672i	$0.307518\pi$
$758$	−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	$0.0770977\pi$
$769$			368.887i			0.479697i	−0.970810	+	0.239848i	$0.922902\pi$
$770$	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	0.648390	−	0.761308i	$-0.275443\pi$
$773$	−87.2860	−	87.2860i	−0.112918	−	0.112918i	−0.761308	+	0.648390i	$0.775443\pi$
$774$			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	−0.294811	+	0.955556i	$0.595257\pi$
$787$	−984.039	+	984.039i	−1.25037	+	1.25037i	−0.955556	+	0.294811i	$0.904743\pi$
$788$	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	−0.784377	−	0.620285i	$-0.787017\pi$
$797$	−130.781	+	130.781i	−0.164092	+	0.164092i	0.620285	+	0.784377i	$0.287017\pi$
$798$	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	$-0.807788\pi$
$809$		−	918.729i		−	1.13564i	0.823154	−	0.567818i	$-0.192212\pi$
$810$	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	0.120347	−	0.992732i	$-0.461599\pi$
$823$	−717.973	−	717.973i	−0.872385	−	0.872385i	−0.992732	+	0.120347i	$0.961599\pi$
$824$		−	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	−0.935056	−	0.354499i	$-0.884651\pi$
$827$	−480.121	+	480.121i	−0.580557	+	0.580557i	0.354499	+	0.935056i	$0.384651\pi$
$828$	612.382	+	612.382i	0.739591	+	0.739591i
$829$		−	801.779i		−	0.967164i	−0.875299	−	0.483582i	$-0.839335\pi$
$829$		−	801.779i		−	0.967164i	0.875299	−	0.483582i	$-0.160665\pi$
$830$	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	$-0.672941\pi$
$839$		−	1436.37i		−	1.71200i	0.516974	−	0.856001i	$-0.327059\pi$
$840$	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	−0.999384	−	0.0350966i	$-0.988826\pi$
$853$	−882.412	−	882.412i	−1.03448	−	1.03448i	−0.0350966	−	0.999384i	$-0.511174\pi$
$854$		−	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	0.319917	−	0.947445i	$-0.396345\pi$
$857$	1086.13	−	1086.13i	1.26736	−	1.26736i	0.947445	−	0.319917i	$-0.103655\pi$
$858$	182.156	+	182.156i	0.212303	+	0.212303i
$859$		−	330.016i		−	0.384186i	−0.981377	−	0.192093i	$-0.938472\pi$
$859$		−	330.016i		−	0.384186i	0.981377	−	0.192093i	$-0.0615276\pi$
$860$	−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	0.688788	−	0.724962i	$-0.258143\pi$
$863$	−31.2182	−	31.2182i	−0.0361741	−	0.0361741i	−0.724962	+	0.688788i	$0.758143\pi$
$864$		−	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	−0.774016	−	0.633167i	$-0.781755\pi$
$877$	−123.525	+	123.525i	−0.140849	+	0.140849i	0.633167	+	0.774016i	$0.281755\pi$
$878$	−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	0.100676	−	0.994919i	$-0.467900\pi$
$883$	−789.617	−	789.617i	−0.894244	−	0.894244i	−0.994919	+	0.100676i	$0.967900\pi$
$884$			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	−0.330937	−	0.943653i	$-0.607365\pi$
$887$	543.479	−	543.479i	0.612716	−	0.612716i	0.943653	+	0.330937i	$0.107365\pi$
$888$	−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	−0.250806	−	0.968037i	$-0.580695\pi$
$907$	650.529	−	650.529i	0.717232	−	0.717232i	0.968037	+	0.250806i	$0.0806955\pi$
$908$	−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	$-0.903257\pi$
$919$		−	550.055i		−	0.598536i	0.954169	−	0.299268i	$-0.0967425\pi$
$920$	−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	$-0.911564\pi$
$929$		−	509.593i		−	0.548540i	0.961653	−	0.274270i	$-0.0884361\pi$
$930$	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	−0.440612	+	0.897698i	$0.645239\pi$
$937$	−1254.00	+	1254.00i	−1.33831	+	1.33831i	−0.897698	+	0.440612i	$0.854761\pi$
$938$	−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	−0.403514	−	0.914973i	$-0.632211\pi$
$947$	484.352	−	484.352i	0.511459	−	0.511459i	0.914973	+	0.403514i	$0.132211\pi$
$948$	−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	0.664256	−	0.747505i	$-0.268748\pi$
$953$	−79.3357	−	79.3357i	−0.0832483	−	0.0832483i	−0.747505	+	0.664256i	$0.768748\pi$
$954$			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	−0.217276	−	0.976110i	$-0.569717\pi$
$967$	733.793	−	733.793i	0.758835	−	0.758835i	0.976110	+	0.217276i	$0.0697171\pi$
$968$	−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	−0.955016	−	0.296555i	$-0.904162\pi$
$977$	−643.316	+	643.316i	−0.658460	+	0.658460i	0.296555	+	0.955016i	$0.404162\pi$
$978$	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	0.650829	−	0.759224i	$-0.274421\pi$
$983$	−106.552	−	106.552i	−0.108395	−	0.108395i	−0.759224	+	0.650829i	$0.774421\pi$
$984$		−	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	−0.703376	−	0.710818i	$-0.748325\pi$
$997$	7.41944	−	7.41944i	0.00744176	−	0.00744176i	0.710818	+	0.703376i	$0.248325\pi$
$998$	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.43.1	yes	24
3.2	odd	2		315.3.o.b.253.12		24
5.2	odd	4	inner	105.3.l.a.22.1	✓	24
5.3	odd	4		525.3.l.e.232.12		24
5.4	even	2		525.3.l.e.43.12		24
15.2	even	4		315.3.o.b.127.12		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.3.l.a.22.1	✓	24	5.2	odd	4	inner
105.3.l.a.43.1	yes	24	1.1	even	1	trivial
315.3.o.b.127.12		24	15.2	even	4
315.3.o.b.253.12		24	3.2	odd	2
525.3.l.e.43.12		24	5.4	even	2
525.3.l.e.232.12		24	5.3	odd	4

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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