LMFDB - Embedded newform 1218.2.m.a.307.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1218,2,Mod(307,1218)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1218.307"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1218, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([0, 2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1218 = 2 \cdot 3 \cdot 7 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1218.m (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,0,0,0,-40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(6)] == traces)

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

Self dual:	no
Analytic conductor:	$9.72577896619$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			307.9
Character	$\chi$	$=$	1218.307
Dual form			1218.2.m.a.853.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +1.75408 q^{5} -1.00000 q^{6} +(-1.92667 - 1.81327i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-1.24032 + 1.24032i) q^{10} +(-0.974388 + 0.974388i) q^{11} +(0.707107 - 0.707107i) q^{12} +2.81222 q^{13} +(2.64454 - 0.0801852i) q^{14} +(1.24032 + 1.24032i) q^{15} -1.00000 q^{16} +(0.797609 + 0.797609i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(-1.41596 - 1.41596i) q^{19} -1.75408i q^{20} +(-0.0801852 - 2.64454i) q^{21} -1.37799i q^{22} +8.03078 q^{23} +1.00000i q^{24} -1.92322 q^{25} +(-1.98854 + 1.98854i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.81327 + 1.92667i) q^{28} +(1.61984 + 5.13577i) q^{29} -1.75408 q^{30} +(7.15468 + 7.15468i) q^{31} +(0.707107 - 0.707107i) q^{32} -1.37799 q^{33} -1.12799 q^{34} +(-3.37952 - 3.18061i) q^{35} +1.00000 q^{36} +(-0.0852589 - 0.0852589i) q^{37} +2.00246 q^{38} +(1.98854 + 1.98854i) q^{39} +(1.24032 + 1.24032i) q^{40} +(-2.43786 + 2.43786i) q^{41} +(1.92667 + 1.81327i) q^{42} +(6.66860 - 6.66860i) q^{43} +(0.974388 + 0.974388i) q^{44} +1.75408i q^{45} +(-5.67862 + 5.67862i) q^{46} +(7.23024 - 7.23024i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(0.424105 + 6.98714i) q^{49} +(1.35992 - 1.35992i) q^{50} +1.12799i q^{51} -2.81222i q^{52} +11.0778 q^{53} -1.00000i q^{54} +(-1.70915 + 1.70915i) q^{55} +(-0.0801852 - 2.64454i) q^{56} -2.00246i q^{57} +(-4.77694 - 2.48613i) q^{58} -2.61946i q^{59} +(1.24032 - 1.24032i) q^{60} +(5.33534 + 5.33534i) q^{61} -10.1182 q^{62} +(1.81327 - 1.92667i) q^{63} +1.00000i q^{64} +4.93286 q^{65} +(0.974388 - 0.974388i) q^{66} -6.79023i q^{67} +(0.797609 - 0.797609i) q^{68} +(5.67862 + 5.67862i) q^{69} +(4.63872 - 0.140651i) q^{70} -14.6504i q^{71} +(-0.707107 + 0.707107i) q^{72} +(-8.50374 + 8.50374i) q^{73} +0.120574 q^{74} +(-1.35992 - 1.35992i) q^{75} +(-1.41596 + 1.41596i) q^{76} +(3.64415 - 0.110495i) q^{77} -2.81222 q^{78} +(-0.362059 + 0.362059i) q^{79} -1.75408 q^{80} -1.00000 q^{81} -3.44766i q^{82} +14.4683i q^{83} +(-2.64454 + 0.0801852i) q^{84} +(1.39907 + 1.39907i) q^{85} +9.43083i q^{86} +(-2.48613 + 4.77694i) q^{87} -1.37799 q^{88} +(-6.61641 - 6.61641i) q^{89} +(-1.24032 - 1.24032i) q^{90} +(-5.41823 - 5.09932i) q^{91} -8.03078i q^{92} +10.1182i q^{93} +10.2251i q^{94} +(-2.48369 - 2.48369i) q^{95} +1.00000 q^{96} +(-6.73439 + 6.73439i) q^{97} +(-5.24054 - 4.64077i) q^{98} +(-0.974388 - 0.974388i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 40 q^{6} + 4 q^{10} + 4 q^{14} - 4 q^{15} - 40 q^{16} + 8 q^{19} - 4 q^{21} + 24 q^{25} - 12 q^{28} + 8 q^{29} - 24 q^{31} - 12 q^{35} + 40 q^{36} - 16 q^{37} - 4 q^{40} + 16 q^{41} - 20 q^{43} + 4 q^{46}+ \cdots - 8 q^{98}+O(q^{100}) $ 40 * q - 40 * q^6 + 4 * q^10 + 4 * q^14 - 4 * q^15 - 40 * q^16 + 8 * q^19 - 4 * q^21 + 24 * q^25 - 12 * q^28 + 8 * q^29 - 24 * q^31 - 12 * q^35 + 40 * q^36 - 16 * q^37 - 4 * q^40 + 16 * q^41 - 20 * q^43 + 4 * q^46 - 16 * q^47 + 28 * q^49 + 32 * q^50 + 16 * q^53 - 24 * q^55 - 4 * q^56 - 20 * q^58 - 4 * q^60 - 44 * q^61 + 12 * q^63 - 4 * q^69 - 28 * q^70 - 52 * q^73 - 32 * q^75 + 8 * q^76 + 44 * q^77 + 4 * q^79 - 40 * q^81 - 4 * q^84 - 24 * q^85 - 12 * q^87 + 24 * q^89 + 4 * q^90 - 16 * q^95 + 40 * q^96 - 68 * q^97 - 8 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1218\mathbb{Z}\right)^\times$.

$n$	$379$	$407$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$-1$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$3$	0.707107	+	0.707107i	0.408248	+	0.408248i
$4$		−	1.00000i		−	0.500000i
$5$	1.75408			0.784447			0.392223	−	0.919870i	$-0.371706\pi$
$5$	1.75408			0.784447			0.392223	+	0.919870i	$0.371706\pi$
$6$	−1.00000			−0.408248
$7$	−1.92667	−	1.81327i	−0.728212	−	0.685352i
$7$	−1.92667	−	1.81327i	−0.728212	−	0.685352i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$			1.00000i			0.333333i
$10$	−1.24032	+	1.24032i	−0.392223	+	0.392223i
$11$	−0.974388	+	0.974388i	−0.293789	+	0.293789i	−0.838575	−	0.544786i	$-0.816611\pi$
$11$	−0.974388	+	0.974388i	−0.293789	+	0.293789i	0.544786	+	0.838575i	$0.316611\pi$
$12$	0.707107	−	0.707107i	0.204124	−	0.204124i
$13$	2.81222			0.779971			0.389985	−	0.920821i	$-0.372480\pi$
$13$	2.81222			0.779971			0.389985	+	0.920821i	$0.372480\pi$
$14$	2.64454	−	0.0801852i	0.706782	−	0.0214304i
$15$	1.24032	+	1.24032i	0.320249	+	0.320249i
$16$	−1.00000			−0.250000
$17$	0.797609	+	0.797609i	0.193449	+	0.193449i	0.797184	−	0.603736i	$-0.206322\pi$
$17$	0.797609	+	0.797609i	0.193449	+	0.193449i	−0.603736	+	0.797184i	$0.706322\pi$
$18$	−0.707107	−	0.707107i	−0.166667	−	0.166667i
$19$	−1.41596	−	1.41596i	−0.324842	−	0.324842i	0.525779	−	0.850621i	$-0.323774\pi$
$19$	−1.41596	−	1.41596i	−0.324842	−	0.324842i	−0.850621	+	0.525779i	$0.823774\pi$
$20$		−	1.75408i		−	0.392223i
$21$	−0.0801852	−	2.64454i	−0.0174978	−	0.577085i
$22$		−	1.37799i		−	0.293789i
$23$	8.03078			1.67453			0.837267	−	0.546795i	$-0.184152\pi$
$23$	8.03078			1.67453			0.837267	+	0.546795i	$0.184152\pi$
$24$			1.00000i			0.204124i
$25$	−1.92322			−0.384643
$26$	−1.98854	+	1.98854i	−0.389985	+	0.389985i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	−1.81327	+	1.92667i	−0.342676	+	0.364106i
$29$	1.61984	+	5.13577i	0.300797	+	0.953688i
$29$	1.61984	+	5.13577i	0.300797	+	0.953688i
$30$	−1.75408			−0.320249
$31$	7.15468	+	7.15468i	1.28502	+	1.28502i	0.937775	+	0.347243i	$0.112882\pi$
$31$	7.15468	+	7.15468i	1.28502	+	1.28502i	0.347243	+	0.937775i	$0.387118\pi$
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−1.37799			−0.239878
$34$	−1.12799			−0.193449
$35$	−3.37952	−	3.18061i	−0.571244	−	0.537622i
$36$	1.00000			0.166667
$37$	−0.0852589	−	0.0852589i	−0.0140165	−	0.0140165i	0.700064	−	0.714080i	$-0.253155\pi$
$37$	−0.0852589	−	0.0852589i	−0.0140165	−	0.0140165i	−0.714080	+	0.700064i	$0.753155\pi$
$38$	2.00246			0.324842
$39$	1.98854	+	1.98854i	0.318422	+	0.318422i
$40$	1.24032	+	1.24032i	0.196112	+	0.196112i
$41$	−2.43786	+	2.43786i	−0.380730	+	0.380730i	−0.871365	−	0.490635i	$-0.836765\pi$
$41$	−2.43786	+	2.43786i	−0.380730	+	0.380730i	0.490635	+	0.871365i	$0.336765\pi$
$42$	1.92667	+	1.81327i	0.297291	+	0.279794i
$43$	6.66860	−	6.66860i	1.01695	−	1.01695i	0.0170987	−	0.999854i	$-0.494557\pi$
$43$	6.66860	−	6.66860i	1.01695	−	1.01695i	0.999854	−	0.0170987i	$-0.00544295\pi$
$44$	0.974388	+	0.974388i	0.146895	+	0.146895i
$45$			1.75408i			0.261482i
$46$	−5.67862	+	5.67862i	−0.837267	+	0.837267i
$47$	7.23024	−	7.23024i	1.05464	−	1.05464i	0.0562211	−	0.998418i	$-0.482095\pi$
$47$	7.23024	−	7.23024i	1.05464	−	1.05464i	0.998418	−	0.0562211i	$-0.0179052\pi$
$48$	−0.707107	−	0.707107i	−0.102062	−	0.102062i
$49$	0.424105	+	6.98714i	0.0605865	+	0.998163i
$50$	1.35992	−	1.35992i	0.192322	−	0.192322i
$51$			1.12799i			0.157950i
$52$		−	2.81222i		−	0.389985i
$53$	11.0778			1.52165			0.760825	−	0.648957i	$-0.224794\pi$
$53$	11.0778			1.52165			0.760825	+	0.648957i	$0.224794\pi$
$54$		−	1.00000i		−	0.136083i
$55$	−1.70915	+	1.70915i	−0.230462	+	0.230462i
$56$	−0.0801852	−	2.64454i	−0.0107152	−	0.353391i
$57$		−	2.00246i		−	0.265233i
$58$	−4.77694	−	2.48613i	−0.627243	−	0.326445i
$59$		−	2.61946i		−	0.341024i	−0.985356	−	0.170512i	$-0.945458\pi$
$59$		−	2.61946i		−	0.341024i	0.985356	−	0.170512i	$-0.0545422\pi$
$60$	1.24032	−	1.24032i	0.160125	−	0.160125i
$61$	5.33534	+	5.33534i	0.683120	+	0.683120i	0.960702	−	0.277582i	$-0.0895331\pi$
$61$	5.33534	+	5.33534i	0.683120	+	0.683120i	−0.277582	+	0.960702i	$0.589533\pi$
$62$	−10.1182			−1.28502
$63$	1.81327	−	1.92667i	0.228451	−	0.242737i
$64$			1.00000i			0.125000i
$65$	4.93286			0.611846
$66$	0.974388	−	0.974388i	0.119939	−	0.119939i
$67$		−	6.79023i		−	0.829559i	−0.909922	−	0.414779i	$-0.863859\pi$
$67$		−	6.79023i		−	0.829559i	0.909922	−	0.414779i	$-0.136141\pi$
$68$	0.797609	−	0.797609i	0.0967243	−	0.0967243i
$69$	5.67862	+	5.67862i	0.683625	+	0.683625i
$70$	4.63872	−	0.140651i	0.554433	−	0.0168110i
$71$		−	14.6504i		−	1.73868i	−0.494215	−	0.869340i	$-0.664544\pi$
$71$		−	14.6504i		−	1.73868i	0.494215	−	0.869340i	$-0.335456\pi$
$72$	−0.707107	+	0.707107i	−0.0833333	+	0.0833333i
$73$	−8.50374	+	8.50374i	−0.995288	+	0.995288i	−0.999989	−	0.00470093i	$-0.998504\pi$
$73$	−8.50374	+	8.50374i	−0.995288	+	0.995288i	0.00470093	+	0.999989i	$0.498504\pi$
$74$	0.120574			0.0140165
$75$	−1.35992	−	1.35992i	−0.157030	−	0.157030i
$76$	−1.41596	+	1.41596i	−0.162421	+	0.162421i
$77$	3.64415	−	0.110495i	0.415290	−	0.0125920i
$78$	−2.81222			−0.318422
$79$	−0.362059	+	0.362059i	−0.0407349	+	0.0407349i	−0.727181	−	0.686446i	$-0.759170\pi$
$79$	−0.362059	+	0.362059i	−0.0407349	+	0.0407349i	0.686446	+	0.727181i	$0.259170\pi$
$80$	−1.75408			−0.196112
$81$	−1.00000			−0.111111
$82$		−	3.44766i		−	0.380730i
$83$			14.4683i			1.58811i	0.607848	+	0.794053i	$0.292033\pi$
$83$			14.4683i			1.58811i	−0.607848	+	0.794053i	$0.707967\pi$
$84$	−2.64454	+	0.0801852i	−0.288543	+	0.00874892i
$85$	1.39907	+	1.39907i	0.151750	+	0.151750i
$86$			9.43083i			1.01695i
$87$	−2.48613	+	4.77694i	−0.266541	+	0.512142i
$88$	−1.37799			−0.146895
$89$	−6.61641	−	6.61641i	−0.701338	−	0.701338i	0.263359	−	0.964698i	$-0.415169\pi$
$89$	−6.61641	−	6.61641i	−0.701338	−	0.701338i	−0.964698	+	0.263359i	$0.915169\pi$
$90$	−1.24032	−	1.24032i	−0.130741	−	0.130741i
$91$	−5.41823	−	5.09932i	−0.567984	−	0.534554i
$92$		−	8.03078i		−	0.837267i
$93$			10.1182i			1.04921i
$94$			10.2251i			1.05464i
$95$	−2.48369	−	2.48369i	−0.254822	−	0.254822i
$96$	1.00000			0.102062
$97$	−6.73439	+	6.73439i	−0.683774	+	0.683774i	−0.960848	−	0.277074i	$-0.910635\pi$
$97$	−6.73439	+	6.73439i	−0.683774	+	0.683774i	0.277074	+	0.960848i	$0.410635\pi$
$98$	−5.24054	−	4.64077i	−0.529375	−	0.468788i
$99$	−0.974388	−	0.974388i	−0.0979297	−	0.0979297i
$100$			1.92322i			0.192322i
$101$	−2.18785	−	2.18785i	−0.217699	−	0.217699i	0.589829	−	0.807528i	$-0.299195\pi$
$101$	−2.18785	−	2.18785i	−0.217699	−	0.217699i	−0.807528	+	0.589829i	$0.799195\pi$
$102$	−0.797609	−	0.797609i	−0.0789750	−	0.0789750i
$103$		−	0.531996i		−	0.0524191i	−0.999656	−	0.0262095i	$-0.991656\pi$
$103$		−	0.531996i		−	0.0524191i	0.999656	−	0.0262095i	$-0.00834371\pi$
$104$	1.98854	+	1.98854i	0.194993	+	0.194993i
$105$	−0.140651	−	4.63872i	−0.0137261	−	0.452693i
$106$	−7.83318	+	7.83318i	−0.760825	+	0.760825i
$107$	−4.67199			−0.451658			−0.225829	−	0.974167i	$-0.572509\pi$
$107$	−4.67199			−0.451658			−0.225829	+	0.974167i	$0.572509\pi$
$108$	0.707107	+	0.707107i	0.0680414	+	0.0680414i
$109$		−	7.44268i		−	0.712880i	−0.934318	−	0.356440i	$-0.883990\pi$
$109$		−	7.44268i		−	0.712880i	0.934318	−	0.356440i	$-0.116010\pi$
$110$		−	2.41711i		−	0.230462i
$111$		−	0.120574i		−	0.0114444i
$112$	1.92667	+	1.81327i	0.182053	+	0.171338i
$113$	12.7560	+	12.7560i	1.19998	+	1.19998i	0.974172	+	0.225807i	$0.0725019\pi$
$113$	12.7560	+	12.7560i	1.19998	+	1.19998i	0.225807	+	0.974172i	$0.427498\pi$
$114$	1.41596	+	1.41596i	0.132616	+	0.132616i
$115$	14.0866			1.31358
$116$	5.13577	−	1.61984i	0.476844	−	0.150399i
$117$			2.81222i			0.259990i
$118$	1.85223	+	1.85223i	0.170512	+	0.170512i
$119$	−0.0904480	−	2.98301i	−0.00829136	−	0.273452i
$120$			1.75408i			0.160125i
$121$			9.10113i			0.827376i
$122$	−7.54530			−0.683120
$123$	−3.44766			−0.310865
$124$	7.15468	−	7.15468i	0.642509	−	0.642509i
$125$	−12.1438			−1.08618
$126$	0.0801852	+	2.64454i	0.00714347	+	0.235594i
$127$	−9.17944	+	9.17944i	−0.814543	+	0.814543i	−0.985311	−	0.170768i	$-0.945375\pi$
$127$	−9.17944	+	9.17944i	−0.814543	+	0.814543i	0.170768	+	0.985311i	$0.445375\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	9.43083			0.830338
$130$	−3.48806	+	3.48806i	−0.305923	+	0.305923i
$131$	10.7880	−	10.7880i	0.942550	−	0.942550i	−0.0558868	−	0.998437i	$-0.517799\pi$
$131$	10.7880	−	10.7880i	0.942550	−	0.942550i	0.998437	+	0.0558868i	$0.0177986\pi$
$132$			1.37799i			0.119939i
$133$	0.160568	+	5.29559i	0.0139230	+	0.459185i
$134$	4.80142	+	4.80142i	0.414779	+	0.414779i
$135$	−1.24032	+	1.24032i	−0.106750	+	0.106750i
$136$			1.12799i			0.0967243i
$137$	9.82765	−	9.82765i	0.839633	−	0.839633i	−0.149178	−	0.988810i	$-0.547663\pi$
$137$	9.82765	−	9.82765i	0.839633	−	0.839633i	0.988810	+	0.149178i	$0.0476626\pi$
$138$	−8.03078			−0.683625
$139$		−	0.140812i		−	0.0119435i	−0.999982	−	0.00597174i	$-0.998099\pi$
$139$		−	0.140812i		−	0.0119435i	0.999982	−	0.00597174i	$-0.00190088\pi$
$140$	−3.18061	+	3.37952i	−0.268811	+	0.285622i
$141$	10.2251			0.861109
$142$	10.3594	+	10.3594i	0.869340	+	0.869340i
$143$	−2.74020	+	2.74020i	−0.229147	+	0.229147i
$144$		−	1.00000i		−	0.0833333i
$145$	2.84133	+	9.00853i	0.235960	+	0.748118i
$146$		−	12.0261i		−	0.995288i
$147$	−4.64077	+	5.24054i	−0.382764	+	0.432233i
$148$	−0.0852589	+	0.0852589i	−0.00700824	+	0.00700824i
$149$		−	19.3666i		−	1.58657i	−0.608850	−	0.793285i	$-0.708369\pi$
$149$		−	19.3666i		−	1.58657i	0.608850	−	0.793285i	$-0.291631\pi$
$150$	1.92322			0.157030
$151$			16.9550i			1.37978i	0.723917	+	0.689888i	$0.242340\pi$
$151$			16.9550i			1.37978i	−0.723917	+	0.689888i	$0.757660\pi$
$152$		−	2.00246i		−	0.162421i
$153$	−0.797609	+	0.797609i	−0.0644828	+	0.0644828i
$154$	−2.49867	+	2.65494i	−0.201349	+	0.213941i
$155$	12.5498	+	12.5498i	1.00803	+	1.00803i
$156$	1.98854	−	1.98854i	0.159211	−	0.159211i
$157$	−15.8986	+	15.8986i	−1.26885	+	1.26885i	−0.322165	+	0.946684i	$0.604411\pi$
$157$	−15.8986	+	15.8986i	−1.26885	+	1.26885i	−0.946684	+	0.322165i	$0.895589\pi$
$158$		−	0.512029i		−	0.0407349i
$159$	7.83318	+	7.83318i	0.621211	+	0.621211i
$160$	1.24032	−	1.24032i	0.0980558	−	0.0980558i
$161$	−15.4727	−	14.5620i	−1.21942	−	1.14764i
$162$	0.707107	−	0.707107i	0.0555556	−	0.0555556i
$163$	3.57404	+	3.57404i	0.279941	+	0.279941i	0.833085	−	0.553145i	$-0.186572\pi$
$163$	3.57404	+	3.57404i	0.279941	+	0.279941i	−0.553145	+	0.833085i	$0.686572\pi$
$164$	2.43786	+	2.43786i	0.190365	+	0.190365i
$165$	−2.41711			−0.188171
$166$	−10.2307	−	10.2307i	−0.794053	−	0.794053i
$167$	−11.0130			−0.852213			−0.426107	−	0.904673i	$-0.640115\pi$
$167$	−11.0130			−0.852213			−0.426107	+	0.904673i	$0.640115\pi$
$168$	1.81327	−	1.92667i	0.139897	−	0.148646i
$169$	−5.09139			−0.391646
$170$	−1.97858			−0.151750
$171$	1.41596	−	1.41596i	0.108281	−	0.108281i
$172$	−6.66860	−	6.66860i	−0.508476	−	0.508476i
$173$	−8.86813			−0.674232			−0.337116	−	0.941463i	$-0.609451\pi$
$173$	−8.86813			−0.674232			−0.337116	+	0.941463i	$0.609451\pi$
$174$	−1.61984	−	5.13577i	−0.122800	−	0.389342i
$175$	3.70540	+	3.48731i	0.280102	+	0.263616i
$176$	0.974388	−	0.974388i	0.0734473	−	0.0734473i
$177$	1.85223	−	1.85223i	0.139222	−	0.139222i
$178$	9.35702			0.701338
$179$		−	0.00698063i		−	0.000521757i	−1.00000		0.000260878i	$-0.999917\pi$
$179$		−	0.00698063i		−	0.000521757i	1.00000		0.000260878i	$-8.30402e-5\pi$
$180$	1.75408			0.130741
$181$			10.6830i			0.794059i	0.917806	+	0.397030i	$0.129959\pi$
$181$			10.6830i			0.794059i	−0.917806	+	0.397030i	$0.870041\pi$
$182$	7.43703	−	0.225499i	0.551269	−	0.0167151i
$183$			7.54530i			0.557765i
$184$	5.67862	+	5.67862i	0.418633	+	0.418633i
$185$	−0.149551	−	0.149551i	−0.0109952	−	0.0109952i
$186$	−7.15468	−	7.15468i	−0.524606	−	0.524606i
$187$	−1.55436			−0.113666
$188$	−7.23024	−	7.23024i	−0.527320	−	0.527320i
$189$	2.64454	−	0.0801852i	0.192362	−	0.00583262i
$190$	3.51247			0.254822
$191$	2.81779	−	2.81779i	0.203888	−	0.203888i	−0.597776	−	0.801664i	$-0.703949\pi$
$191$	2.81779	−	2.81779i	0.203888	−	0.203888i	0.801664	+	0.597776i	$0.203949\pi$
$192$	−0.707107	+	0.707107i	−0.0510310	+	0.0510310i
$193$	4.23504	−	4.23504i	0.304845	−	0.304845i	−0.538061	−	0.842906i	$-0.680843\pi$
$193$	4.23504	−	4.23504i	0.304845	−	0.304845i	0.842906	+	0.538061i	$0.180843\pi$
$194$		−	9.52387i		−	0.683774i
$195$	3.48806	+	3.48806i	0.249785	+	0.249785i
$196$	6.98714	−	0.424105i	0.499081	−	0.0302932i
$197$	−25.1299			−1.79043			−0.895215	−	0.445635i	$-0.852978\pi$
$197$	−25.1299			−1.79043			−0.895215	+	0.445635i	$0.852978\pi$
$198$	1.37799			0.0979297
$199$		−	17.3537i		−	1.23017i	−0.788461	−	0.615085i	$-0.789122\pi$
$199$		−	17.3537i		−	1.23017i	0.788461	−	0.615085i	$-0.210878\pi$
$200$	−1.35992	−	1.35992i	−0.0961608	−	0.0961608i
$201$	4.80142	−	4.80142i	0.338666	−	0.338666i
$202$	3.09409			0.217699
$203$	6.19163	−	12.8321i	0.434567	−	0.900639i
$204$	1.12799			0.0789750
$205$	−4.27619	+	4.27619i	−0.298662	+	0.298662i
$206$	0.376178	+	0.376178i	0.0262095	+	0.0262095i
$207$			8.03078i			0.558178i
$208$	−2.81222			−0.194993
$209$	2.75938			0.190870
$210$	3.37952	+	3.18061i	0.233209	+	0.219483i
$211$	−17.2024	−	17.2024i	−1.18426	−	1.18426i	−0.978629	−	0.205632i	$-0.934075\pi$
$211$	−17.2024	−	17.2024i	−1.18426	−	1.18426i	−0.205632	−	0.978629i	$-0.565925\pi$
$212$		−	11.0778i		−	0.760825i
$213$	10.3594	−	10.3594i	0.709813	−	0.709813i
$214$	3.30359	−	3.30359i	0.225829	−	0.225829i
$215$	11.6972	−	11.6972i	0.797745	−	0.797745i
$216$	−1.00000			−0.0680414
$217$	−0.811333	−	26.7581i	−0.0550769	−	1.81646i
$218$	5.26277	+	5.26277i	0.356440	+	0.356440i
$219$	−12.0261			−0.812649
$220$	1.70915	+	1.70915i	0.115231	+	0.115231i
$221$	2.24305	+	2.24305i	0.150884	+	0.150884i
$222$	0.0852589	+	0.0852589i	0.00572220	+	0.00572220i
$223$		−	20.3314i		−	1.36149i	−0.732520	−	0.680746i	$-0.761656\pi$
$223$		−	20.3314i		−	1.36149i	0.732520	−	0.680746i	$-0.238344\pi$
$224$	−2.64454	+	0.0801852i	−0.176695	+	0.00535760i
$225$		−	1.92322i		−	0.128214i
$226$	−18.0396			−1.19998
$227$			11.5582i			0.767143i	0.923511	+	0.383571i	$0.125306\pi$
$227$			11.5582i			0.767143i	−0.923511	+	0.383571i	$0.874694\pi$
$228$	−2.00246			−0.132616
$229$	−4.13109	+	4.13109i	−0.272990	+	0.272990i	−0.830303	−	0.557313i	$-0.811832\pi$
$229$	−4.13109	+	4.13109i	−0.272990	+	0.272990i	0.557313	+	0.830303i	$0.311832\pi$
$230$	−9.96073	+	9.96073i	−0.656791	+	0.656791i
$231$	2.65494	+	2.49867i	0.174682	+	0.164401i
$232$	−2.48613	+	4.77694i	−0.163223	+	0.313621i
$233$	18.9572			1.24193			0.620965	−	0.783838i	$-0.286741\pi$
$233$	18.9572			1.24193			0.620965	+	0.783838i	$0.286741\pi$
$234$	−1.98854	−	1.98854i	−0.129995	−	0.129995i
$235$	12.6824	−	12.6824i	0.827308	−	0.827308i
$236$	−2.61946			−0.170512
$237$	−0.512029			−0.0332599
$238$	2.17326	+	2.04535i	0.140872	+	0.132580i
$239$	0.644234			0.0416720			0.0208360	−	0.999783i	$-0.493367\pi$
$239$	0.644234			0.0416720			0.0208360	+	0.999783i	$0.493367\pi$
$240$	−1.24032	−	1.24032i	−0.0800623	−	0.0800623i
$241$	−1.19558			−0.0770140			−0.0385070	−	0.999258i	$-0.512260\pi$
$241$	−1.19558			−0.0770140			−0.0385070	+	0.999258i	$0.512260\pi$
$242$	−6.43547	−	6.43547i	−0.413688	−	0.413688i
$243$	−0.707107	−	0.707107i	−0.0453609	−	0.0453609i
$244$	5.33534	−	5.33534i	0.341560	−	0.341560i
$245$	0.743913	+	12.2560i	0.0475269	+	0.783006i
$246$	2.43786	−	2.43786i	0.155432	−	0.155432i
$247$	−3.98198	−	3.98198i	−0.253368	−	0.253368i
$248$			10.1182i			0.642509i
$249$	−10.2307	+	10.2307i	−0.648342	+	0.648342i
$250$	8.58700	−	8.58700i	0.543089	−	0.543089i
$251$	2.41274	+	2.41274i	0.152291	+	0.152291i	0.779140	−	0.626849i	$-0.215656\pi$
$251$	2.41274	+	2.41274i	0.152291	+	0.152291i	−0.626849	+	0.779140i	$0.715656\pi$
$252$	−1.92667	−	1.81327i	−0.121369	−	0.114225i
$253$	−7.82510	+	7.82510i	−0.491960	+	0.491960i
$254$		−	12.9817i		−	0.814543i
$255$			1.97858i			0.123903i
$256$	1.00000			0.0625000
$257$		−	17.4543i		−	1.08877i	−0.838836	−	0.544385i	$-0.816763\pi$
$257$		−	17.4543i		−	1.08877i	0.838836	−	0.544385i	$-0.183237\pi$
$258$	−6.66860	+	6.66860i	−0.415169	+	0.415169i
$259$	0.00966827	+	0.318863i	0.000600757	+	0.0198132i
$260$		−	4.93286i		−	0.305923i
$261$	−5.13577	+	1.61984i	−0.317896	+	0.100266i
$262$			15.2565i			0.942550i
$263$	−12.2849	+	12.2849i	−0.757520	+	0.757520i	−0.975870	−	0.218351i	$-0.929932\pi$
$263$	−12.2849	+	12.2849i	−0.757520	+	0.757520i	0.218351	+	0.975870i	$0.429932\pi$
$264$	−0.974388	−	0.974388i	−0.0599695	−	0.0599695i
$265$	19.4313			1.19365
$266$	−3.85808	−	3.63101i	−0.236554	−	0.222631i
$267$		−	9.35702i		−	0.572640i
$268$	−6.79023			−0.414779
$269$	−3.54778	+	3.54778i	−0.216312	+	0.216312i	−0.806942	−	0.590630i	$-0.798879\pi$
$269$	−3.54778	+	3.54778i	−0.216312	+	0.216312i	0.590630	+	0.806942i	$0.298879\pi$
$270$		−	1.75408i		−	0.106750i
$271$	20.9376	−	20.9376i	1.27187	−	1.27187i	0.326766	−	0.945105i	$-0.394041\pi$
$271$	20.9376	−	20.9376i	1.27187	−	1.27187i	0.945105	−	0.326766i	$-0.105959\pi$
$272$	−0.797609	−	0.797609i	−0.0483621	−	0.0483621i
$273$	−0.225499	−	7.43703i	−0.0136478	−	0.450109i
$274$			13.8984i			0.839633i
$275$	1.87396	−	1.87396i	0.113004	−	0.113004i
$276$	5.67862	−	5.67862i	0.341813	−	0.341813i
$277$	−9.79679			−0.588632			−0.294316	−	0.955708i	$-0.595092\pi$
$277$	−9.79679			−0.588632			−0.294316	+	0.955708i	$0.595092\pi$
$278$	0.0995688	+	0.0995688i	0.00597174	+	0.00597174i
$279$	−7.15468	+	7.15468i	−0.428339	+	0.428339i
$280$	−0.140651	−	4.63872i	−0.00840550	−	0.277216i
$281$	2.35918			0.140737			0.0703684	−	0.997521i	$-0.477583\pi$
$281$	2.35918			0.140737			0.0703684	+	0.997521i	$0.477583\pi$
$282$	−7.23024	+	7.23024i	−0.430555	+	0.430555i
$283$	−30.8600			−1.83444			−0.917219	−	0.398383i	$-0.869571\pi$
$283$	−30.8600			−1.83444			−0.917219	+	0.398383i	$0.869571\pi$
$284$	−14.6504			−0.869340
$285$		−	3.51247i		−	0.208061i
$286$		−	3.87523i		−	0.229147i
$287$	9.11745	−	0.276451i	0.538186	−	0.0163184i
$288$	0.707107	+	0.707107i	0.0416667	+	0.0416667i
$289$		−	15.7276i		−	0.925155i
$290$	−8.37911	−	4.36087i	−0.492039	−	0.256079i
$291$	−9.52387			−0.558299
$292$	8.50374	+	8.50374i	0.497644	+	0.497644i
$293$	11.8321	+	11.8321i	0.691241	+	0.691241i	0.962505	−	0.271264i	$-0.0874416\pi$
$293$	11.8321	+	11.8321i	0.691241	+	0.691241i	−0.271264	+	0.962505i	$0.587442\pi$
$294$	−0.424105	−	6.98714i	−0.0247343	−	0.407498i
$295$		−	4.59472i		−	0.267515i
$296$		−	0.120574i		−	0.00700824i
$297$		−	1.37799i		−	0.0799593i
$298$	13.6942	+	13.6942i	0.793285	+	0.793285i
$299$	22.5844			1.30609
$300$	−1.35992	+	1.35992i	−0.0785150	+	0.0785150i
$301$	−24.9402	+	0.756213i	−1.43753	+	0.0435874i
$302$	−11.9890	−	11.9890i	−0.689888	−	0.689888i
$303$		−	3.09409i		−	0.177751i
$304$	1.41596	+	1.41596i	0.0812106	+	0.0812106i
$305$	9.35859	+	9.35859i	0.535871	+	0.535871i
$306$		−	1.12799i		−	0.0644828i
$307$	14.2537	+	14.2537i	0.813501	+	0.813501i	0.985157	−	0.171656i	$-0.0549117\pi$
$307$	14.2537	+	14.2537i	0.813501	+	0.813501i	−0.171656	+	0.985157i	$0.554912\pi$
$308$	−0.110495	−	3.64415i	−0.00629602	−	0.207645i
$309$	0.376178	−	0.376178i	0.0214000	−	0.0214000i
$310$	−17.7482			−1.00803
$311$	8.29685	+	8.29685i	0.470471	+	0.470471i	0.902067	−	0.431596i	$-0.142049\pi$
$311$	8.29685	+	8.29685i	0.470471	+	0.470471i	−0.431596	+	0.902067i	$0.642049\pi$
$312$			2.81222i			0.159211i
$313$		−	32.7075i		−	1.84874i	−0.381499	−	0.924369i	$-0.624592\pi$
$313$		−	32.7075i		−	1.84874i	0.381499	−	0.924369i	$-0.375408\pi$
$314$		−	22.4841i		−	1.26885i
$315$	3.18061	−	3.37952i	0.179207	−	0.190415i
$316$	0.362059	+	0.362059i	0.0203674	+	0.0203674i
$317$	−15.3036	−	15.3036i	−0.859539	−	0.859539i	0.131745	−	0.991284i	$-0.457942\pi$
$317$	−15.3036	−	15.3036i	−0.859539	−	0.859539i	−0.991284	+	0.131745i	$0.957942\pi$
$318$	−11.0778			−0.621211
$319$	−6.58259	−	3.42587i	−0.368554	−	0.191812i
$320$			1.75408i			0.0980558i
$321$	−3.30359	−	3.30359i	−0.184389	−	0.184389i
$322$	21.2377	−	0.643950i	1.18353	−	0.0358859i
$323$		−	2.25876i		−	0.125681i
$324$			1.00000i			0.0555556i
$325$	−5.40852			−0.300010
$326$	−5.05446			−0.279941
$327$	5.26277	−	5.26277i	0.291032	−	0.291032i
$328$	−3.44766			−0.190365
$329$	−27.0407	+	0.819902i	−1.49080	+	0.0452027i
$330$	1.70915	−	1.70915i	0.0940857	−	0.0940857i
$331$	−19.8350	−	19.8350i	−1.09023	−	1.09023i	−0.995504	−	0.0947245i	$-0.969803\pi$
$331$	−19.8350	−	19.8350i	−1.09023	−	1.09023i	−0.0947245	−	0.995504i	$-0.530197\pi$
$332$	14.4683			0.794053
$333$	0.0852589	−	0.0852589i	0.00467216	−	0.00467216i
$334$	7.78738	−	7.78738i	0.426107	−	0.426107i
$335$		−	11.9106i		−	0.650745i
$336$	0.0801852	+	2.64454i	0.00437446	+	0.144271i
$337$	−0.424044	−	0.424044i	−0.0230991	−	0.0230991i	0.695463	−	0.718562i	$-0.255199\pi$
$337$	−0.424044	−	0.424044i	−0.0230991	−	0.0230991i	−0.718562	+	0.695463i	$0.755199\pi$
$338$	3.60016	−	3.60016i	0.195823	−	0.195823i
$339$			18.0396i			0.979779i
$340$	1.39907	−	1.39907i	0.0758750	−	0.0758750i
$341$	−13.9429			−0.755049
$342$			2.00246i			0.108281i
$343$	11.8525	−	14.2309i	0.639973	−	0.768398i
$344$	9.43083			0.508476
$345$	9.96073	+	9.96073i	0.536268	+	0.536268i
$346$	6.27072	−	6.27072i	0.337116	−	0.337116i
$347$		−	10.5269i		−	0.565111i	−0.959251	−	0.282556i	$-0.908818\pi$
$347$		−	10.5269i		−	0.565111i	0.959251	−	0.282556i	$-0.0911821\pi$
$348$	4.77694	+	2.48613i	0.256071	+	0.133271i
$349$		−	8.52015i		−	0.456073i	−0.973653	−	0.228036i	$-0.926769\pi$
$349$		−	8.52015i		−	0.456073i	0.973653	−	0.228036i	$-0.0732305\pi$
$350$	−5.08601	+	0.154213i	−0.271859	+	0.00824306i
$351$	−1.98854	+	1.98854i	−0.106141	+	0.106141i
$352$			1.37799i			0.0734473i
$353$	11.8004			0.628075			0.314037	−	0.949411i	$-0.398318\pi$
$353$	11.8004			0.628075			0.314037	+	0.949411i	$0.398318\pi$
$354$			2.61946i			0.139222i
$355$		−	25.6979i		−	1.36390i
$356$	−6.61641	+	6.61641i	−0.350669	+	0.350669i
$357$	2.04535	−	2.17326i	0.108251	−	0.115021i
$358$	0.00493605	+	0.00493605i	0.000260878	+	0.000260878i
$359$	11.5953	−	11.5953i	0.611975	−	0.611975i	−0.331485	−	0.943460i	$-0.607550\pi$
$359$	11.5953	−	11.5953i	0.611975	−	0.611975i	0.943460	+	0.331485i	$0.107550\pi$
$360$	−1.24032	+	1.24032i	−0.0653706	+	0.0653706i
$361$		−	14.9901i		−	0.788955i
$362$	−7.55400	−	7.55400i	−0.397030	−	0.397030i
$363$	−6.43547	+	6.43547i	−0.337775	+	0.337775i
$364$	−5.09932	+	5.41823i	−0.267277	+	0.283992i
$365$	−14.9162	+	14.9162i	−0.780750	+	0.780750i
$366$	−5.33534	−	5.33534i	−0.278882	−	0.278882i
$367$	−4.64135	−	4.64135i	−0.242277	−	0.242277i	0.575515	−	0.817791i	$-0.304802\pi$
$367$	−4.64135	−	4.64135i	−0.242277	−	0.242277i	−0.817791	+	0.575515i	$0.804802\pi$
$368$	−8.03078			−0.418633
$369$	−2.43786	−	2.43786i	−0.126910	−	0.126910i
$370$	0.211496			0.0109952
$371$	−21.3432	−	20.0870i	−1.10808	−	1.04287i
$372$	10.1182			0.524606
$373$	5.39543			0.279365			0.139682	−	0.990196i	$-0.455392\pi$
$373$	5.39543			0.279365			0.139682	+	0.990196i	$0.455392\pi$
$374$	1.09910	−	1.09910i	0.0568331	−	0.0568331i
$375$	−8.58700	−	8.58700i	−0.443431	−	0.443431i
$376$	10.2251			0.527320
$377$	4.55537	+	14.4429i	0.234613	+	0.743849i
$378$	−1.81327	+	1.92667i	−0.0932645	+	0.0990971i
$379$	−4.96063	+	4.96063i	−0.254811	+	0.254811i	−0.822940	−	0.568129i	$-0.807667\pi$
$379$	−4.96063	+	4.96063i	−0.254811	+	0.254811i	0.568129	+	0.822940i	$0.307667\pi$
$380$	−2.48369	+	2.48369i	−0.127411	+	0.127411i
$381$	−12.9817			−0.665072
$382$			3.98495i			0.203888i
$383$	−25.5817			−1.30717			−0.653583	−	0.756855i	$-0.726735\pi$
$383$	−25.5817			−1.30717			−0.653583	+	0.756855i	$0.726735\pi$
$384$		−	1.00000i		−	0.0510310i
$385$	6.39212	−	0.193816i	0.325773	−	0.00987778i
$386$			5.98925i			0.304845i
$387$	6.66860	+	6.66860i	0.338984	+	0.338984i
$388$	6.73439	+	6.73439i	0.341887	+	0.341887i
$389$	21.1746	+	21.1746i	1.07360	+	1.07360i	0.997067	+	0.0765299i	$0.0243841\pi$
$389$	21.1746	+	21.1746i	1.07360	+	1.07360i	0.0765299	+	0.997067i	$0.475616\pi$
$390$	−4.93286			−0.249785
$391$	6.40542	+	6.40542i	0.323936	+	0.323936i
$392$	−4.64077	+	5.24054i	−0.234394	+	0.264687i
$393$	15.2565			0.769589
$394$	17.7695	−	17.7695i	0.895215	−	0.895215i
$395$	−0.635080	+	0.635080i	−0.0319543	+	0.0319543i
$396$	−0.974388	+	0.974388i	−0.0489649	+	0.0489649i
$397$		−	11.8569i		−	0.595082i	−0.954709	−	0.297541i	$-0.903834\pi$
$397$		−	11.8569i		−	0.595082i	0.954709	−	0.297541i	$-0.0961664\pi$
$398$	12.2709	+	12.2709i	0.615085	+	0.615085i
$399$	−3.63101	+	3.85808i	−0.181778	+	0.193146i
$400$	1.92322			0.0961608
$401$	30.3495			1.51558			0.757791	−	0.652497i	$-0.226279\pi$
$401$	30.3495			1.51558			0.757791	+	0.652497i	$0.226279\pi$
$402$			6.79023i			0.338666i
$403$	20.1206	+	20.1206i	1.00228	+	1.00228i
$404$	−2.18785	+	2.18785i	−0.108850	+	0.108850i
$405$	−1.75408			−0.0871608
$406$	4.69555	+	13.4518i	0.233036	+	0.667603i
$407$	0.166151			0.00823578
$408$	−0.797609	+	0.797609i	−0.0394875	+	0.0394875i
$409$	18.7328	+	18.7328i	0.926278	+	0.926278i	0.997463	−	0.0711847i	$-0.0226780\pi$
$409$	18.7328	+	18.7328i	0.926278	+	0.926278i	−0.0711847	+	0.997463i	$0.522678\pi$
$410$		−	6.04745i		−	0.298662i
$411$	13.8984			0.685557
$412$	−0.531996			−0.0262095
$413$	−4.74978	+	5.04682i	−0.233721	+	0.248338i
$414$	−5.67862	−	5.67862i	−0.279089	−	0.279089i
$415$			25.3786i			1.24579i
$416$	1.98854	−	1.98854i	0.0974963	−	0.0974963i
$417$	0.0995688	−	0.0995688i	0.00487591	−	0.00487591i
$418$	−1.95118	+	1.95118i	−0.0954352	+	0.0954352i
$419$	20.5940			1.00608			0.503041	−	0.864263i	$-0.332215\pi$
$419$	20.5940			1.00608			0.503041	+	0.864263i	$0.332215\pi$
$420$	−4.63872	+	0.140651i	−0.226346	+	0.00686306i
$421$	−8.18215	−	8.18215i	−0.398774	−	0.398774i	0.479027	−	0.877800i	$-0.340990\pi$
$421$	−8.18215	−	8.18215i	−0.398774	−	0.398774i	−0.877800	+	0.479027i	$0.840990\pi$
$422$	24.3279			1.18426
$423$	7.23024	+	7.23024i	0.351546	+	0.351546i
$424$	7.83318	+	7.83318i	0.380413	+	0.380413i
$425$	−1.53397	−	1.53397i	−0.0744087	−	0.0744087i
$426$			14.6504i			0.709813i
$427$	−0.605022	−	19.9538i	−0.0292791	−	0.965634i
$428$			4.67199i			0.225829i
$429$	−3.87523			−0.187098
$430$			16.5424i			0.797745i
$431$	−19.8698			−0.957094			−0.478547	−	0.878062i	$-0.658836\pi$
$431$	−19.8698			−0.957094			−0.478547	+	0.878062i	$0.658836\pi$
$432$	0.707107	−	0.707107i	0.0340207	−	0.0340207i
$433$	−22.7897	+	22.7897i	−1.09520	+	1.09520i	−0.100239	+	0.994963i	$0.531961\pi$
$433$	−22.7897	+	22.7897i	−1.09520	+	1.09520i	−0.994963	+	0.100239i	$0.968039\pi$
$434$	19.4945	+	18.3471i	0.935766	+	0.880689i
$435$	−4.36087	+	8.37911i	−0.209088	+	0.401748i
$436$	−7.44268			−0.356440
$437$	−11.3712	−	11.3712i	−0.543959	−	0.543959i
$438$	8.50374	−	8.50374i	0.406325	−	0.406325i
$439$	−14.5826			−0.695990			−0.347995	−	0.937496i	$-0.613137\pi$
$439$	−14.5826			−0.695990			−0.347995	+	0.937496i	$0.613137\pi$
$440$	−2.41711			−0.115231
$441$	−6.98714	+	0.424105i	−0.332721	+	0.0201955i
$442$	−3.17216			−0.150884
$443$	−15.5422	−	15.5422i	−0.738434	−	0.738434i	0.233841	−	0.972275i	$-0.424871\pi$
$443$	−15.5422	−	15.5422i	−0.738434	−	0.738434i	−0.972275	+	0.233841i	$0.924871\pi$
$444$	−0.120574			−0.00572220
$445$	−11.6057	−	11.6057i	−0.550163	−	0.550163i
$446$	14.3765	+	14.3765i	0.680746	+	0.680746i
$447$	13.6942	−	13.6942i	0.647715	−	0.647715i
$448$	1.81327	−	1.92667i	0.0856689	−	0.0910265i
$449$	2.40542	−	2.40542i	0.113519	−	0.113519i	−0.648066	−	0.761584i	$-0.724422\pi$
$449$	2.40542	−	2.40542i	0.113519	−	0.113519i	0.761584	+	0.648066i	$0.224422\pi$
$450$	1.35992	+	1.35992i	0.0641072	+	0.0641072i
$451$		−	4.75085i		−	0.223709i
$452$	12.7560	−	12.7560i	0.599990	−	0.599990i
$453$	−11.9890	+	11.9890i	−0.563291	+	0.563291i
$454$	−8.17286	−	8.17286i	−0.383571	−	0.383571i
$455$	−9.50398	−	8.94460i	−0.445554	−	0.419329i
$456$	1.41596	−	1.41596i	0.0663082	−	0.0663082i
$457$		−	0.681948i		−	0.0319002i	−0.999873	−	0.0159501i	$-0.994923\pi$
$457$		−	0.681948i		−	0.0319002i	0.999873	−	0.0159501i	$-0.00507729\pi$
$458$		−	5.84224i		−	0.272990i
$459$	−1.12799			−0.0526500
$460$		−	14.0866i		−	0.656791i
$461$	2.19456	−	2.19456i	0.102211	−	0.102211i	−0.654152	−	0.756363i	$-0.726974\pi$
$461$	2.19456	−	2.19456i	0.102211	−	0.102211i	0.756363	+	0.654152i	$0.226974\pi$
$462$	−3.64415	+	0.110495i	−0.169541	+	0.00514068i
$463$		−	13.3416i		−	0.620036i	−0.950731	−	0.310018i	$-0.899665\pi$
$463$		−	13.3416i		−	0.620036i	0.950731	−	0.310018i	$-0.100335\pi$
$464$	−1.61984	−	5.13577i	−0.0751994	−	0.238422i
$465$			17.7482i			0.823052i
$466$	−13.4048	+	13.4048i	−0.620965	+	0.620965i
$467$	14.7760	+	14.7760i	0.683750	+	0.683750i	0.960843	−	0.277093i	$-0.0893710\pi$
$467$	14.7760	+	14.7760i	0.683750	+	0.683750i	−0.277093	+	0.960843i	$0.589371\pi$
$468$	2.81222			0.129995
$469$	−12.3125	+	13.0825i	−0.568539	+	0.604095i
$470$			17.9356i			0.827308i
$471$	−22.4841			−1.03601
$472$	1.85223	−	1.85223i	0.0852560	−	0.0852560i
$473$			12.9956i			0.597539i
$474$	0.362059	−	0.362059i	0.0166299	−	0.0166299i
$475$	2.72319	+	2.72319i	0.124948	+	0.124948i
$476$	−2.98301	+	0.0904480i	−0.136726	+	0.00414568i
$477$			11.0778i			0.507217i
$478$	−0.455542	+	0.455542i	−0.0208360	+	0.0208360i
$479$	−16.2787	+	16.2787i	−0.743791	+	0.743791i	−0.973305	−	0.229514i	$-0.926286\pi$
$479$	−16.2787	+	16.2787i	−0.743791	+	0.743791i	0.229514	+	0.973305i	$0.426286\pi$
$480$	1.75408			0.0800623
$481$	−0.239767	−	0.239767i	−0.0109324	−	0.0109324i
$482$	0.845402	−	0.845402i	0.0385070	−	0.0385070i
$483$	−0.643950	−	21.2377i	−0.0293007	−	0.966348i
$484$	9.10113			0.413688
$485$	−11.8126	+	11.8126i	−0.536384	+	0.536384i
$486$	1.00000			0.0453609
$487$	−9.83563			−0.445695			−0.222848	−	0.974853i	$-0.571535\pi$
$487$	−9.83563			−0.445695			−0.222848	+	0.974853i	$0.571535\pi$
$488$			7.54530i			0.341560i
$489$			5.05446i			0.228570i
$490$	−9.19231	−	8.14026i	−0.415266	−	0.367739i
$491$	1.57380	+	1.57380i	0.0710244	+	0.0710244i	0.741727	−	0.670702i	$-0.234007\pi$
$491$	1.57380	+	1.57380i	0.0710244	+	0.0710244i	−0.670702	+	0.741727i	$0.734007\pi$
$492$			3.44766i			0.155432i
$493$	−2.80433	+	5.38833i	−0.126301	+	0.242678i
$494$	5.63138			0.253368
$495$	−1.70915	−	1.70915i	−0.0768207	−	0.0768207i
$496$	−7.15468	−	7.15468i	−0.321254	−	0.321254i
$497$	−26.5651	+	28.2264i	−1.19161	+	1.26613i
$498$		−	14.4683i		−	0.648342i
$499$		−	1.95275i		−	0.0874172i	−0.999044	−	0.0437086i	$-0.986083\pi$
$499$		−	1.95275i		−	0.0874172i	0.999044	−	0.0437086i	$-0.0139173\pi$
$500$			12.1438i			0.543089i
$501$	−7.78738	−	7.78738i	−0.347915	−	0.347915i
$502$	−3.41213			−0.152291
$503$	−3.73717	+	3.73717i	−0.166632	+	0.166632i	−0.785497	−	0.618865i	$-0.787593\pi$
$503$	−3.73717	+	3.73717i	−0.166632	+	0.166632i	0.618865	+	0.785497i	$0.287593\pi$
$504$	2.64454	−	0.0801852i	0.117797	−	0.00357173i
$505$	−3.83766	−	3.83766i	−0.170774	−	0.170774i
$506$		−	11.0664i		−	0.491960i
$507$	−3.60016	−	3.60016i	−0.159889	−	0.159889i
$508$	9.17944	+	9.17944i	0.407272	+	0.407272i
$509$		−	7.59158i		−	0.336491i	−0.985745	−	0.168245i	$-0.946190\pi$
$509$		−	7.59158i		−	0.336491i	0.985745	−	0.168245i	$-0.0538101\pi$
$510$	−1.39907	−	1.39907i	−0.0619517	−	0.0619517i
$511$	31.8035	−	0.964316i	1.40690	−	0.0426588i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	2.00246			0.0884109
$514$	12.3421	+	12.3421i	0.544385	+	0.544385i
$515$		−	0.933161i		−	0.0411200i
$516$		−	9.43083i		−	0.415169i
$517$			14.0901i			0.619683i
$518$	−0.232307	−	0.218634i	−0.0102070	−	0.00960621i
$519$	−6.27072	−	6.27072i	−0.275254	−	0.275254i
$520$	3.48806	+	3.48806i	0.152961	+	0.152961i
$521$	−29.0264			−1.27167			−0.635835	−	0.771825i	$-0.719344\pi$
$521$	−29.0264			−1.27167			−0.635835	+	0.771825i	$0.719344\pi$
$522$	2.48613	−	4.77694i	0.108815	−	0.209081i
$523$			21.0093i			0.918674i	0.888262	+	0.459337i	$0.151913\pi$
$523$			21.0093i			0.918674i	−0.888262	+	0.459337i	$0.848087\pi$
$524$	−10.7880	−	10.7880i	−0.471275	−	0.471275i
$525$	0.154213	+	5.08601i	0.00673043	+	0.221972i
$526$		−	17.3735i		−	0.757520i
$527$			11.4133i			0.497170i
$528$	1.37799			0.0599695
$529$	41.4934			1.80406
$530$	−13.7400	+	13.7400i	−0.596827	+	0.596827i
$531$	2.61946			0.113675
$532$	5.29559	−	0.160568i	0.229593	−	0.00696150i
$533$	−6.85581	+	6.85581i	−0.296958	+	0.296958i
$534$	6.61641	+	6.61641i	0.286320	+	0.286320i
$535$	−8.19502			−0.354302
$536$	4.80142	−	4.80142i	0.207390	−	0.207390i
$537$	0.00493605	−	0.00493605i	0.000213006	−	0.000213006i
$538$		−	5.01732i		−	0.216312i
$539$	−7.22143	−	6.39495i	−0.311049	−	0.275450i
$540$	1.24032	+	1.24032i	0.0533748	+	0.0533748i
$541$	12.4891	−	12.4891i	0.536949	−	0.536949i	−0.385682	−	0.922632i	$-0.626034\pi$
$541$	12.4891	−	12.4891i	0.536949	−	0.536949i	0.922632	+	0.385682i	$0.126034\pi$
$542$			29.6103i			1.27187i
$543$	−7.55400	+	7.55400i	−0.324173	+	0.324173i
$544$	1.12799			0.0483621
$545$		−	13.0550i		−	0.559216i
$546$	5.41823	+	5.09932i	0.231879	+	0.218231i
$547$	36.6230			1.56589			0.782943	−	0.622093i	$-0.213718\pi$
$547$	36.6230			1.56589			0.782943	+	0.622093i	$0.213718\pi$
$548$	−9.82765	−	9.82765i	−0.419816	−	0.419816i
$549$	−5.33534	+	5.33534i	−0.227707	+	0.227707i
$550$			2.65018i			0.113004i
$551$	4.97839	−	9.56564i	0.212087	−	0.407510i
$552$			8.03078i			0.341813i
$553$	1.35408	−	0.0410572i	0.0575813	−	0.00174593i
$554$	6.92738	−	6.92738i	0.294316	−	0.294316i
$555$		−	0.211496i		−	0.00897753i
$556$	−0.140812			−0.00597174
$557$			26.9864i			1.14345i	0.820446	+	0.571724i	$0.193725\pi$
$557$			26.9864i			1.14345i	−0.820446	+	0.571724i	$0.806275\pi$
$558$		−	10.1182i		−	0.428339i
$559$	18.7536	−	18.7536i	0.793193	−	0.793193i
$560$	3.37952	+	3.18061i	0.142811	+	0.134405i
$561$	−1.09910	−	1.09910i	−0.0464040	−	0.0464040i
$562$	−1.66819	+	1.66819i	−0.0703684	+	0.0703684i
$563$	8.54805	−	8.54805i	0.360257	−	0.360257i	−0.503650	−	0.863908i	$-0.668010\pi$
$563$	8.54805	−	8.54805i	0.360257	−	0.360257i	0.863908	+	0.503650i	$0.168010\pi$
$564$		−	10.2251i		−	0.430555i
$565$	22.3749	+	22.3749i	0.941320	+	0.941320i
$566$	21.8213	−	21.8213i	0.917219	−	0.917219i
$567$	1.92667	+	1.81327i	0.0809125	+	0.0761502i
$568$	10.3594	−	10.3594i	0.434670	−	0.434670i
$569$	9.68554	+	9.68554i	0.406039	+	0.406039i	0.880355	−	0.474316i	$-0.157305\pi$
$569$	9.68554	+	9.68554i	0.406039	+	0.406039i	−0.474316	+	0.880355i	$0.657305\pi$
$570$	2.48369	+	2.48369i	0.104030	+	0.104030i
$571$	−15.6336			−0.654246			−0.327123	−	0.944982i	$-0.606079\pi$
$571$	−15.6336			−0.654246			−0.327123	+	0.944982i	$0.606079\pi$
$572$	2.74020	+	2.74020i	0.114573	+	0.114573i
$573$	3.98495			0.166474
$574$	−6.25153	+	6.64249i	−0.260934	+	0.277252i
$575$	−15.4449			−0.644098
$576$	−1.00000			−0.0416667
$577$	−30.2982	+	30.2982i	−1.26133	+	1.26133i	−0.310880	+	0.950449i	$0.600624\pi$
$577$	−30.2982	+	30.2982i	−1.26133	+	1.26133i	−0.950449	+	0.310880i	$0.899376\pi$
$578$	11.1211	+	11.1211i	0.462578	+	0.462578i
$579$	5.98925			0.248905
$580$	9.00853	−	2.84133i	0.374059	−	0.117980i
$581$	26.2350	−	27.8757i	1.08841	−	1.15648i
$582$	6.73439	−	6.73439i	0.279150	−	0.279150i
$583$	−10.7941	+	10.7941i	−0.447044	+	0.447044i
$584$	−12.0261			−0.497644
$585$			4.93286i			0.203949i
$586$	−16.7332			−0.691241
$587$			43.6940i			1.80344i	0.432316	+	0.901722i	$0.357697\pi$
$587$			43.6940i			1.80344i	−0.432316	+	0.901722i	$0.642303\pi$
$588$	5.24054	+	4.64077i	0.216116	+	0.191382i
$589$		−	20.2614i		−	0.834857i
$590$	3.24896	+	3.24896i	0.133758	+	0.133758i
$591$	−17.7695	−	17.7695i	−0.730940	−	0.730940i
$592$	0.0852589	+	0.0852589i	0.00350412	+	0.00350412i
$593$	0.850948			0.0349442			0.0174721	−	0.999847i	$-0.494438\pi$
$593$	0.850948			0.0349442			0.0174721	+	0.999847i	$0.494438\pi$
$594$	0.974388	+	0.974388i	0.0399796	+	0.0399796i
$595$	−0.158653	−	5.23242i	−0.00650413	−	0.214508i
$596$	−19.3666			−0.793285
$597$	12.2709	−	12.2709i	0.502215	−	0.502215i
$598$	−15.9696	+	15.9696i	−0.653043	+	0.653043i
$599$	−1.77481	+	1.77481i	−0.0725166	+	0.0725166i	−0.742435	−	0.669918i	$-0.766329\pi$
$599$	−1.77481	+	1.77481i	−0.0725166	+	0.0725166i	0.669918	+	0.742435i	$0.266329\pi$
$600$		−	1.92322i		−	0.0785150i
$601$	−7.09714	−	7.09714i	−0.289498	−	0.289498i	0.547384	−	0.836882i	$-0.315624\pi$
$601$	−7.09714	−	7.09714i	−0.289498	−	0.289498i	−0.836882	+	0.547384i	$0.815624\pi$
$602$	17.1006	−	18.1701i	0.696970	−	0.740557i
$603$	6.79023			0.276520
$604$	16.9550			0.689888
$605$			15.9641i			0.649032i
$606$	2.18785	+	2.18785i	0.0888754	+	0.0888754i
$607$	−19.8800	+	19.8800i	−0.806906	+	0.806906i	−0.984164	−	0.177259i	$-0.943277\pi$
$607$	−19.8800	+	19.8800i	−0.806906	+	0.806906i	0.177259	+	0.984164i	$0.443277\pi$
$608$	−2.00246			−0.0812106
$609$	13.4518	−	4.69555i	0.545096	−	0.190273i
$610$	−13.2350			−0.535871
$611$	20.3331	−	20.3331i	0.822588	−	0.822588i
$612$	0.797609	+	0.797609i	0.0322414	+	0.0322414i
$613$			1.15003i			0.0464494i	0.999730	+	0.0232247i	$0.00739332\pi$
$613$			1.15003i			0.0464494i	−0.999730	+	0.0232247i	$0.992607\pi$
$614$	−20.1578			−0.813501
$615$	−6.04745			−0.243857
$616$	2.65494	+	2.49867i	0.106970	+	0.100674i
$617$	6.24774	+	6.24774i	0.251525	+	0.251525i	0.821596	−	0.570071i	$-0.193084\pi$
$617$	6.24774	+	6.24774i	0.251525	+	0.251525i	−0.570071	+	0.821596i	$0.693084\pi$
$618$			0.531996i			0.0214000i
$619$	−16.9109	+	16.9109i	−0.679707	+	0.679707i	−0.959934	−	0.280227i	$-0.909590\pi$
$619$	−16.9109	+	16.9109i	−0.679707	+	0.679707i	0.280227	+	0.959934i	$0.409590\pi$
$620$	12.5498	−	12.5498i	0.504014	−	0.504014i
$621$	−5.67862	+	5.67862i	−0.227875	+	0.227875i
$622$	−11.7335			−0.470471
$623$	0.750295	+	24.7450i	0.0300599	+	0.991387i
$624$	−1.98854	−	1.98854i	−0.0796054	−	0.0796054i
$625$	−11.6852			−0.467406
$626$	23.1277	+	23.1277i	0.924369	+	0.924369i
$627$	1.95118	+	1.95118i	0.0779225	+	0.0779225i
$628$	15.8986	+	15.8986i	0.634424	+	0.634424i
$629$		−	0.136006i		−	0.00542293i
$630$	0.140651	+	4.63872i	0.00560367	+	0.184811i
$631$		−	28.9630i		−	1.15300i	−0.817098	−	0.576499i	$-0.804419\pi$
$631$		−	28.9630i		−	1.15300i	0.817098	−	0.576499i	$-0.195581\pi$
$632$	−0.512029			−0.0203674
$633$		−	24.3279i		−	0.966945i
$634$	21.6426			0.859539
$635$	−16.1014	+	16.1014i	−0.638966	+	0.638966i
$636$	7.83318	−	7.83318i	0.310606	−	0.310606i
$637$	1.19268	+	19.6494i	0.0472557	+	0.778538i
$638$	7.07705	−	2.23213i	0.280183	−	0.0883710i
$639$	14.6504			0.579560
$640$	−1.24032	−	1.24032i	−0.0490279	−	0.0490279i
$641$	10.7959	−	10.7959i	0.426411	−	0.426411i	−0.460993	−	0.887404i	$-0.652507\pi$
$641$	10.7959	−	10.7959i	0.426411	−	0.426411i	0.887404	+	0.460993i	$0.152507\pi$
$642$	4.67199			0.184389
$643$	−29.7180			−1.17196			−0.585982	−	0.810324i	$-0.699291\pi$
$643$	−29.7180			−1.17196			−0.585982	+	0.810324i	$0.699291\pi$
$644$	−14.5620	+	15.4727i	−0.573822	+	0.609708i
$645$	16.5424			0.651356
$646$	1.59718	+	1.59718i	0.0628403	+	0.0628403i
$647$	−5.96838			−0.234641			−0.117321	−	0.993094i	$-0.537431\pi$
$647$	−5.96838			−0.234641			−0.117321	+	0.993094i	$0.537431\pi$
$648$	−0.707107	−	0.707107i	−0.0277778	−	0.0277778i
$649$	2.55237	+	2.55237i	0.100189	+	0.100189i
$650$	3.82440	−	3.82440i	0.150005	−	0.150005i
$651$	18.3471	−	19.4945i	0.719080	−	0.764050i
$652$	3.57404	−	3.57404i	0.139970	−	0.139970i
$653$	18.5939	+	18.5939i	0.727637	+	0.727637i	0.970148	−	0.242512i	$-0.0779713\pi$
$653$	18.5939	+	18.5939i	0.727637	+	0.727637i	−0.242512	+	0.970148i	$0.577971\pi$
$654$			7.44268i			0.291032i
$655$	18.9229	−	18.9229i	0.739381	−	0.739381i
$656$	2.43786	−	2.43786i	0.0951825	−	0.0951825i
$657$	−8.50374	−	8.50374i	−0.331763	−	0.331763i
$658$	18.5409	−	19.7004i	0.722799	−	0.768001i
$659$	−14.2598	+	14.2598i	−0.555482	+	0.555482i	−0.928018	−	0.372536i	$-0.878488\pi$
$659$	−14.2598	+	14.2598i	−0.555482	+	0.555482i	0.372536	+	0.928018i	$0.378488\pi$
$660$			2.41711i			0.0940857i
$661$		−	7.46111i		−	0.290204i	−0.989417	−	0.145102i	$-0.953649\pi$
$661$		−	7.46111i		−	0.290204i	0.989417	−	0.145102i	$-0.0463510\pi$
$662$	28.0509			1.09023
$663$			3.17216i			0.123196i
$664$	−10.2307	+	10.2307i	−0.397027	+	0.397027i
$665$	0.281648	+	9.28886i	0.0109219	+	0.360207i
$666$			0.120574i			0.00467216i
$667$	13.0086	+	41.2442i	0.503695	+	1.59698i
$668$			11.0130i			0.426107i
$669$	14.3765	−	14.3765i	0.555827	−	0.555827i
$670$	8.42205	+	8.42205i	0.325372	+	0.325372i
$671$	−10.3974			−0.401386
$672$	−1.92667	−	1.81327i	−0.0743229	−	0.0699484i
$673$			11.2747i			0.434609i	0.976104	+	0.217304i	$0.0697264\pi$
$673$			11.2747i			0.434609i	−0.976104	+	0.217304i	$0.930274\pi$
$674$	0.599688			0.0230991
$675$	1.35992	−	1.35992i	0.0523433	−	0.0523433i
$676$			5.09139i			0.195823i
$677$	20.3459	−	20.3459i	0.781957	−	0.781957i	−0.198204	−	0.980161i	$-0.563511\pi$
$677$	20.3459	−	20.3459i	0.781957	−	0.781957i	0.980161	+	0.198204i	$0.0635108\pi$
$678$	−12.7560	−	12.7560i	−0.489889	−	0.489889i
$679$	25.1862	−	0.763674i	0.966558	−	0.0293071i
$680$			1.97858i			0.0758750i
$681$	−8.17286	+	8.17286i	−0.313185	+	0.313185i
$682$	9.85910	−	9.85910i	0.377524	−	0.377524i
$683$	−29.8656			−1.14277			−0.571387	−	0.820680i	$-0.693595\pi$
$683$	−29.8656			−1.14277			−0.571387	+	0.820680i	$0.693595\pi$
$684$	−1.41596	−	1.41596i	−0.0541404	−	0.0541404i
$685$	17.2384	−	17.2384i	0.658647	−	0.658647i
$686$	1.68183	+	18.4437i	0.0642125	+	0.704185i
$687$	−5.84224			−0.222895
$688$	−6.66860	+	6.66860i	−0.254238	+	0.254238i
$689$	31.1532			1.18684
$690$	−14.0866			−0.536268
$691$		−	15.0394i		−	0.572126i	−0.958211	−	0.286063i	$-0.907653\pi$
$691$		−	15.0394i		−	0.572126i	0.958211	−	0.286063i	$-0.0923467\pi$
$692$			8.86813i			0.337116i
$693$	0.110495	+	3.64415i	0.00419735	+	0.138430i
$694$	7.44361	+	7.44361i	0.282556	+	0.282556i
$695$		−	0.246994i		−	0.00936903i
$696$	−5.13577	+	1.61984i	−0.194671	+	0.0614000i
$697$	−3.88892			−0.147303
$698$	6.02465	+	6.02465i	0.228036	+	0.228036i
$699$	13.4048	+	13.4048i	0.507016	+	0.507016i
$700$	3.48731	−	3.70540i	0.131808	−	0.140051i
$701$			27.2445i			1.02901i	0.857487	+	0.514505i	$0.172024\pi$
$701$			27.2445i			1.02901i	−0.857487	+	0.514505i	$0.827976\pi$
$702$		−	2.81222i		−	0.106141i
$703$			0.241446i			0.00910629i
$704$	−0.974388	−	0.974388i	−0.0367236	−	0.0367236i
$705$	17.9356			0.675495
$706$	−8.34418	+	8.34418i	−0.314037	+	0.314037i
$707$	0.248100	+	8.18243i	0.00933076	+	0.307732i
$708$	−1.85223	−	1.85223i	−0.0696112	−	0.0696112i
$709$			45.8587i			1.72226i	0.508384	+	0.861130i	$0.330243\pi$
$709$			45.8587i			1.72226i	−0.508384	+	0.861130i	$0.669757\pi$
$710$	18.1711	+	18.1711i	0.681951	+	0.681951i
$711$	−0.362059	−	0.362059i	−0.0135783	−	0.0135783i
$712$		−	9.35702i		−	0.350669i
$713$	57.4576	+	57.4576i	2.15181	+	2.15181i
$714$	0.0904480	+	2.98301i	0.00338493	+	0.111636i
$715$	−4.80652	+	4.80652i	−0.179754	+	0.179754i
$716$	−0.00698063			−0.000260878
$717$	0.455542	+	0.455542i	0.0170125	+	0.0170125i
$718$			16.3982i			0.611975i
$719$			1.27022i			0.0473713i	0.999719	+	0.0236857i	$0.00754009\pi$
$719$			1.27022i			0.0473713i	−0.999719	+	0.0236857i	$0.992460\pi$
$720$		−	1.75408i		−	0.0653706i
$721$	−0.964651	+	1.02498i	−0.0359255	+	0.0381722i
$722$	10.5996	+	10.5996i	0.394477	+	0.394477i
$723$	−0.845402	−	0.845402i	−0.0314408	−	0.0314408i
$724$	10.6830			0.397030
$725$	−3.11531	−	9.87719i	−0.115700	−	0.366830i
$726$		−	9.10113i		−	0.337775i
$727$	9.96164	+	9.96164i	0.369457	+	0.369457i	0.867279	−	0.497822i	$-0.165867\pi$
$727$	9.96164	+	9.96164i	0.369457	+	0.369457i	−0.497822	+	0.867279i	$0.665867\pi$
$728$	−0.225499	−	7.43703i	−0.00835754	−	0.275635i
$729$		−	1.00000i		−	0.0370370i
$730$		−	21.0947i		−	0.780750i
$731$	10.6379			0.393456
$732$	7.54530			0.278882
$733$	−16.3802	+	16.3802i	−0.605016	+	0.605016i	−0.941639	−	0.336623i	$-0.890715\pi$
$733$	−16.3802	+	16.3802i	−0.605016	+	0.605016i	0.336623	+	0.941639i	$0.390715\pi$
$734$	6.56386			0.242277
$735$	−8.14026	+	9.19231i	−0.300258	+	0.339064i
$736$	5.67862	−	5.67862i	0.209317	−	0.209317i
$737$	6.61632	+	6.61632i	0.243715	+	0.243715i
$738$	3.44766			0.126910
$739$	37.0687	−	37.0687i	1.36359	−	1.36359i	0.494303	−	0.869290i	$-0.335423\pi$
$739$	37.0687	−	37.0687i	1.36359	−	1.36359i	0.869290	−	0.494303i	$-0.164577\pi$
$740$	−0.149551	+	0.149551i	−0.00549759	+	0.00549759i
$741$		−	5.63138i		−	0.206874i
$742$	29.2956	−	0.888274i	1.07548	−	0.0326096i
$743$	−10.8389	−	10.8389i	−0.397641	−	0.397641i	0.479759	−	0.877400i	$-0.340724\pi$
$743$	−10.8389	−	10.8389i	−0.397641	−	0.397641i	−0.877400	+	0.479759i	$0.840724\pi$
$744$	−7.15468	+	7.15468i	−0.262303	+	0.262303i
$745$		−	33.9704i		−	1.24458i
$746$	−3.81515	+	3.81515i	−0.139682	+	0.139682i
$747$	−14.4683			−0.529369
$748$			1.55436i			0.0568331i
$749$	9.00137	+	8.47158i	0.328903	+	0.309545i
$750$	12.1438			0.443431
$751$	−16.3442	−	16.3442i	−0.596407	−	0.596407i	0.342948	−	0.939354i	$-0.388575\pi$
$751$	−16.3442	−	16.3442i	−0.596407	−	0.596407i	−0.939354	+	0.342948i	$0.888575\pi$
$752$	−7.23024	+	7.23024i	−0.263660	+	0.263660i
$753$			3.41213i			0.124345i
$754$	−13.4338	−	6.99156i	−0.489231	−	0.254618i
$755$			29.7403i			1.08236i
$756$	−0.0801852	−	2.64454i	−0.00291631	−	0.0961808i
$757$	11.3964	−	11.3964i	0.414210	−	0.414210i	−0.468992	−	0.883202i	$-0.655383\pi$
$757$	11.3964	−	11.3964i	0.414210	−	0.414210i	0.883202	+	0.468992i	$0.155383\pi$
$758$		−	7.01540i		−	0.254811i
$759$	−11.0664			−0.401683
$760$		−	3.51247i		−	0.127411i
$761$			20.8510i			0.755848i	0.925837	+	0.377924i	$0.123362\pi$
$761$			20.8510i			0.755848i	−0.925837	+	0.377924i	$0.876638\pi$
$762$	9.17944	−	9.17944i	0.332536	−	0.332536i
$763$	−13.4956	+	14.3396i	−0.488573	+	0.519128i
$764$	−2.81779	−	2.81779i	−0.101944	−	0.101944i
$765$	−1.39907	+	1.39907i	−0.0505834	+	0.0505834i
$766$	18.0890	−	18.0890i	0.653583	−	0.653583i
$767$		−	7.36650i		−	0.265989i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	−22.2038	+	22.2038i	−0.800691	+	0.800691i	−0.983203	−	0.182513i	$-0.941577\pi$
$769$	−22.2038	+	22.2038i	−0.800691	+	0.800691i	0.182513	+	0.983203i	$0.441577\pi$
$770$	−4.38286	+	4.65696i	−0.157947	+	0.167825i
$771$	12.3421	−	12.3421i	0.444488	−	0.444488i
$772$	−4.23504	−	4.23504i	−0.152423	−	0.152423i
$773$	18.2554	+	18.2554i	0.656600	+	0.656600i	0.954574	−	0.297974i	$-0.0963110\pi$
$773$	18.2554	+	18.2554i	0.656600	+	0.656600i	−0.297974	+	0.954574i	$0.596311\pi$
$774$	−9.43083			−0.338984
$775$	−13.7600	−	13.7600i	−0.494273	−	0.494273i
$776$	−9.52387			−0.341887
$777$	−0.218634	+	0.232307i	−0.00784344	+	0.00833396i
$778$	−29.9455			−1.07360
$779$	6.90380			0.247354
$780$	3.48806	−	3.48806i	0.124892	−	0.124892i
$781$	14.2752	+	14.2752i	0.510805	+	0.510805i
$782$	−9.05863			−0.323936
$783$	−4.77694	−	2.48613i	−0.170714	−	0.0888471i
$784$	−0.424105	−	6.98714i	−0.0151466	−	0.249541i
$785$	−27.8874	+	27.8874i	−0.995344	+	0.995344i
$786$	−10.7880	+	10.7880i	−0.384795	+	0.384795i
$787$	−4.85460			−0.173048			−0.0865240	−	0.996250i	$-0.527576\pi$
$787$	−4.85460			−0.173048			−0.0865240	+	0.996250i	$0.527576\pi$
$788$			25.1299i			0.895215i
$789$	−17.3735			−0.618512
$790$		−	0.898139i		−	0.0319543i
$791$	−1.44651	−	47.7065i	−0.0514321	−	1.69625i
$792$		−	1.37799i		−	0.0489649i
$793$	15.0042	+	15.0042i	0.532813	+	0.532813i
$794$	8.38411	+	8.38411i	0.297541	+	0.297541i
$795$	13.7400	+	13.7400i	0.487307	+	0.487307i
$796$	−17.3537			−0.615085
$797$	21.8979	+	21.8979i	0.775664	+	0.775664i	0.979090	−	0.203427i	$-0.0652078\pi$
$797$	21.8979	+	21.8979i	0.775664	+	0.775664i	−0.203427	+	0.979090i	$0.565208\pi$
$798$	−0.160568	−	5.29559i	−0.00568404	−	0.187462i
$799$	11.5338			0.408037
$800$	−1.35992	+	1.35992i	−0.0480804	+	0.0480804i
$801$	6.61641	−	6.61641i	0.233779	−	0.233779i
$802$	−21.4603	+	21.4603i	−0.757791	+	0.757791i
$803$		−	16.5719i		−	0.584810i
$804$	−4.80142	−	4.80142i	−0.169333	−	0.169333i
$805$	−27.1402	−	25.5428i	−0.956567	−	0.900266i
$806$	−28.4548			−1.00228
$807$	−5.01732			−0.176618
$808$		−	3.09409i		−	0.108850i
$809$	−38.1732	−	38.1732i	−1.34210	−	1.34210i	−0.893970	−	0.448126i	$-0.852092\pi$
$809$	−38.1732	−	38.1732i	−1.34210	−	1.34210i	−0.448126	−	0.893970i	$-0.647908\pi$
$810$	1.24032	−	1.24032i	0.0435804	−	0.0435804i
$811$	22.3267			0.783996			0.391998	−	0.919966i	$-0.371784\pi$
$811$	22.3267			0.783996			0.391998	+	0.919966i	$0.371784\pi$
$812$	−12.8321	−	6.19163i	−0.450320	−	0.217284i
$813$	29.6103			1.03848
$814$	−0.117486	+	0.117486i	−0.00411789	+	0.00411789i
$815$	6.26914	+	6.26914i	0.219598	+	0.219598i
$816$		−	1.12799i		−	0.0394875i
$817$	−18.8849			−0.660699
$818$	−26.4922			−0.926278
$819$	5.09932	−	5.41823i	0.178185	−	0.189328i
$820$	4.27619	+	4.27619i	0.149331	+	0.149331i
$821$		−	38.8842i		−	1.35707i	−0.734569	−	0.678534i	$-0.762616\pi$
$821$		−	38.8842i		−	1.35707i	0.734569	−	0.678534i	$-0.237384\pi$
$822$	−9.82765	+	9.82765i	−0.342779	+	0.342779i
$823$	17.1334	−	17.1334i	0.597232	−	0.597232i	−0.342343	−	0.939575i	$-0.611220\pi$
$823$	17.1334	−	17.1334i	0.597232	−	0.597232i	0.939575	+	0.342343i	$0.111220\pi$
$824$	0.376178	−	0.376178i	0.0131048	−	0.0131048i
$825$	2.65018			0.0922674
$826$	−0.210042	−	6.92724i	−0.00730828	−	0.241030i
$827$	−27.1714	−	27.1714i	−0.944843	−	0.944843i	0.0537133	−	0.998556i	$-0.482894\pi$
$827$	−27.1714	−	27.1714i	−0.944843	−	0.944843i	−0.998556	+	0.0537133i	$0.982894\pi$
$828$	8.03078			0.279089
$829$	12.2851	+	12.2851i	0.426681	+	0.426681i	0.887496	−	0.460815i	$-0.152443\pi$
$829$	12.2851	+	12.2851i	0.426681	+	0.426681i	−0.460815	+	0.887496i	$0.652443\pi$
$830$	−17.9454	−	17.9454i	−0.622893	−	0.622893i
$831$	−6.92738	−	6.92738i	−0.240308	−	0.240308i
$832$			2.81222i			0.0974963i
$833$	−5.23473	+	5.91127i	−0.181373	+	0.204814i
$834$			0.140812i			0.00487591i
$835$	−19.3177			−0.668516
$836$		−	2.75938i		−	0.0954352i
$837$	−10.1182			−0.349738
$838$	−14.5621	+	14.5621i	−0.503041	+	0.503041i
$839$	10.4253	−	10.4253i	0.359920	−	0.359920i	−0.503863	−	0.863783i	$-0.668088\pi$
$839$	10.4253	−	10.4253i	0.359920	−	0.359920i	0.863783	+	0.503863i	$0.168088\pi$
$840$	3.18061	−	3.37952i	0.109742	−	0.116605i
$841$	−23.7522	+	16.6383i	−0.819042	+	0.573734i
$842$	11.5713			0.398774
$843$	1.66819	+	1.66819i	0.0574556	+	0.0574556i
$844$	−17.2024	+	17.2024i	−0.592131	+	0.592131i
$845$	−8.93069			−0.307225
$846$	−10.2251			−0.351546
$847$	16.5028	−	17.5349i	0.567043	−	0.602505i
$848$	−11.0778			−0.380413
$849$	−21.8213	−	21.8213i	−0.748906	−	0.748906i
$850$	2.16937			0.0744087
$851$	−0.684695	−	0.684695i	−0.0234711	−	0.0234711i
$852$	−10.3594	−	10.3594i	−0.354907	−	0.354907i
$853$	−9.04834	+	9.04834i	−0.309809	+	0.309809i	−0.844835	−	0.535026i	$-0.820302\pi$
$853$	−9.04834	+	9.04834i	−0.309809	+	0.309809i	0.535026	+	0.844835i	$0.320302\pi$
$854$	14.5373	+	13.6817i	0.497456	+	0.468177i
$855$	2.48369	−	2.48369i	0.0849405	−	0.0849405i
$856$	−3.30359	−	3.30359i	−0.112915	−	0.112915i
$857$		−	40.0792i		−	1.36908i	−0.728976	−	0.684539i	$-0.760003\pi$
$857$		−	40.0792i		−	1.36908i	0.728976	−	0.684539i	$-0.239997\pi$
$858$	2.74020	−	2.74020i	0.0935489	−	0.0935489i
$859$	26.1486	−	26.1486i	0.892179	−	0.892179i	−0.102549	−	0.994728i	$-0.532700\pi$
$859$	26.1486	−	26.1486i	0.892179	−	0.892179i	0.994728	+	0.102549i	$0.0326998\pi$
$860$	−11.6972	−	11.6972i	−0.398873	−	0.398873i
$861$	6.64249	+	6.25153i	0.226376	+	0.213052i
$862$	14.0501	−	14.0501i	0.478547	−	0.478547i
$863$			32.1806i			1.09544i	0.836661	+	0.547721i	$0.184504\pi$
$863$			32.1806i			1.09544i	−0.836661	+	0.547721i	$0.815496\pi$
$864$			1.00000i			0.0340207i
$865$	−15.5554			−0.528899
$866$		−	32.2295i		−	1.09520i
$867$	11.1211	−	11.1211i	0.377693	−	0.377693i
$868$	−26.7581	+	0.811333i	−0.908228	+	0.0275384i
$869$		−	0.705573i		−	0.0239349i
$870$	−2.84133	−	9.00853i	−0.0963301	−	0.305418i
$871$		−	19.0957i		−	0.647031i
$872$	5.26277	−	5.26277i	0.178220	−	0.178220i
$873$	−6.73439	−	6.73439i	−0.227925	−	0.227925i
$874$	16.0813			0.543959
$875$	23.3972	+	22.0201i	0.790969	+	0.744414i
$876$			12.0261i			0.406325i
$877$	−31.6495			−1.06873			−0.534364	−	0.845254i	$-0.679449\pi$
$877$	−31.6495			−1.06873			−0.534364	+	0.845254i	$0.679449\pi$
$878$	10.3115	−	10.3115i	0.347995	−	0.347995i
$879$			16.7332i			0.564396i
$880$	1.70915	−	1.70915i	0.0576155	−	0.0576155i
$881$	−22.1844	−	22.1844i	−0.747412	−	0.747412i	0.226580	−	0.973993i	$-0.427246\pi$
$881$	−22.1844	−	22.1844i	−0.747412	−	0.747412i	−0.973993	+	0.226580i	$0.927246\pi$
$882$	4.64077	−	5.24054i	0.156263	−	0.176458i
$883$		−	44.6781i		−	1.50354i	−0.659427	−	0.751769i	$-0.729201\pi$
$883$		−	44.6781i		−	1.50354i	0.659427	−	0.751769i	$-0.270799\pi$
$884$	2.24305	−	2.24305i	0.0754421	−	0.0754421i
$885$	3.24896	−	3.24896i	0.109213	−	0.109213i
$886$	21.9801			0.738434
$887$	−4.69607	−	4.69607i	−0.157678	−	0.157678i	0.623859	−	0.781537i	$-0.285564\pi$
$887$	−4.69607	−	4.69607i	−0.157678	−	0.157678i	−0.781537	+	0.623859i	$0.785564\pi$
$888$	0.0852589	−	0.0852589i	0.00286110	−	0.00286110i
$889$	34.3305	−	1.04094i	1.15141	−	0.0349120i
$890$	16.4129			0.550163
$891$	0.974388	−	0.974388i	0.0326432	−	0.0326432i
$892$	−20.3314			−0.680746
$893$	−20.4754			−0.685183
$894$			19.3666i			0.647715i
$895$		−	0.0122446i		−	0.000409290i
$896$	0.0801852	+	2.64454i	0.00267880	+	0.0883477i
$897$	15.9696	+	15.9696i	0.533208	+	0.533208i
$898$			3.40178i			0.113519i
$899$	−25.1553	+	48.3342i	−0.838976	+	1.61204i
$900$	−1.92322			−0.0641072
$901$	8.83574	+	8.83574i	0.294361	+	0.294361i
$902$	3.35936	+	3.35936i	0.111854	+	0.111854i
$903$	−18.1701	−	17.1006i	−0.604663	−	0.569074i
$904$			18.0396i			0.599990i
$905$			18.7388i			0.622897i
$906$		−	16.9550i		−	0.563291i
$907$	−5.89049	−	5.89049i	−0.195590	−	0.195590i	0.602516	−	0.798107i	$-0.294165\pi$
$907$	−5.89049	−	5.89049i	−0.195590	−	0.195590i	−0.798107	+	0.602516i	$0.794165\pi$
$908$	11.5582			0.383571
$909$	2.18785	−	2.18785i	0.0725664	−	0.0725664i
$910$	13.0451	−	0.395542i	0.432441	−	0.0131121i
$911$	13.5248	+	13.5248i	0.448097	+	0.448097i	0.894721	−	0.446625i	$-0.147374\pi$
$911$	13.5248	+	13.5248i	0.448097	+	0.448097i	−0.446625	+	0.894721i	$0.647374\pi$
$912$			2.00246i			0.0663082i
$913$	−14.0978	−	14.0978i	−0.466569	−	0.466569i
$914$	0.482210	+	0.482210i	0.0159501	+	0.0159501i
$915$			13.2350i			0.437537i
$916$	4.13109	+	4.13109i	0.136495	+	0.136495i
$917$	−40.3464	+	1.22335i	−1.33236	+	0.0403985i
$918$	0.797609	−	0.797609i	0.0263250	−	0.0263250i
$919$	−49.7198			−1.64010			−0.820052	−	0.572289i	$-0.806056\pi$
$919$	−49.7198			−1.64010			−0.820052	+	0.572289i	$0.806056\pi$
$920$	9.96073	+	9.96073i	0.328396	+	0.328396i
$921$			20.1578i			0.664221i
$922$			3.10357i			0.102211i
$923$		−	41.2002i		−	1.35612i
$924$	2.49867	−	2.65494i	0.0822003	−	0.0873410i
$925$	0.163971	+	0.163971i	0.00539134	+	0.00539134i
$926$	9.43393	+	9.43393i	0.310018	+	0.310018i
$927$	0.531996			0.0174730
$928$	4.77694	+	2.48613i	0.156811	+	0.0816113i
$929$			11.2264i			0.368325i	0.982896	+	0.184163i	$0.0589573\pi$
$929$			11.2264i			0.368325i	−0.982896	+	0.184163i	$0.941043\pi$
$930$	−12.5498	−	12.5498i	−0.411526	−	0.411526i
$931$	9.29296	−	10.4940i	0.304565	−	0.343927i
$932$		−	18.9572i		−	0.620965i
$933$			11.7335i			0.384138i
$934$	−20.8964			−0.683750
$935$	−2.72647			−0.0891651
$936$	−1.98854	+	1.98854i	−0.0649976	+	0.0649976i
$937$	1.32768			0.0433733			0.0216866	−	0.999765i	$-0.493096\pi$
$937$	1.32768			0.0433733			0.0216866	+	0.999765i	$0.493096\pi$
$938$	−0.544476	−	17.9570i	−0.0177778	−	0.586317i
$939$	23.1277	−	23.1277i	0.754744	−	0.754744i
$940$	−12.6824	−	12.6824i	−0.413654	−	0.413654i
$941$	−38.4127			−1.25222			−0.626109	−	0.779736i	$-0.715353\pi$
$941$	−38.4127			−1.25222			−0.626109	+	0.779736i	$0.715353\pi$
$942$	15.8986	−	15.8986i	0.518005	−	0.518005i
$943$	−19.5779	+	19.5779i	−0.637545	+	0.637545i
$944$			2.61946i			0.0852560i
$945$	4.63872	−	0.140651i	0.150898	−	0.00457538i
$946$	−9.18929	−	9.18929i	−0.298770	−	0.298770i
$947$	28.6572	−	28.6572i	0.931235	−	0.931235i	−0.0665485	−	0.997783i	$-0.521199\pi$
$947$	28.6572	−	28.6572i	0.931235	−	0.931235i	0.997783	+	0.0665485i	$0.0211987\pi$
$948$			0.512029i			0.0166299i
$949$	−23.9144	+	23.9144i	−0.776296	+	0.776296i
$950$	−3.85117			−0.124948
$951$		−	21.6426i		−	0.701810i
$952$	2.04535	−	2.17326i	0.0662901	−	0.0704358i
$953$	−6.91902			−0.224129			−0.112065	−	0.993701i	$-0.535746\pi$
$953$	−6.91902			−0.224129			−0.112065	+	0.993701i	$0.535746\pi$
$954$	−7.83318	−	7.83318i	−0.253608	−	0.253608i
$955$	4.94262	−	4.94262i	0.159939	−	0.159939i
$956$		−	0.644234i		−	0.0208360i
$957$	−2.23213	−	7.07705i	−0.0721547	−	0.228769i
$958$		−	23.0215i		−	0.743791i
$959$	−36.7548	+	1.11445i	−1.18687	+	0.0359873i
$960$	−1.24032	+	1.24032i	−0.0400311	+	0.0400311i
$961$			71.3788i			2.30254i
$962$	0.339082			0.0109324
$963$		−	4.67199i		−	0.150553i
$964$			1.19558i			0.0385070i
$965$	7.42859	−	7.42859i	0.239135	−	0.239135i
$966$	15.4727	+	14.5620i	0.497824	+	0.468524i
$967$	−34.5265	−	34.5265i	−1.11030	−	1.11030i	−0.993110	−	0.117188i	$-0.962612\pi$
$967$	−34.5265	−	34.5265i	−1.11030	−	1.11030i	−0.117188	−	0.993110i	$-0.537388\pi$
$968$	−6.43547	+	6.43547i	−0.206844	+	0.206844i
$969$	1.59718	−	1.59718i	0.0513089	−	0.0513089i
$970$		−	16.7056i		−	0.536384i
$971$	27.8144	+	27.8144i	0.892607	+	0.892607i	0.994768	−	0.102161i	$-0.0325757\pi$
$971$	27.8144	+	27.8144i	0.892607	+	0.892607i	−0.102161	+	0.994768i	$0.532576\pi$
$972$	−0.707107	+	0.707107i	−0.0226805	+	0.0226805i
$973$	−0.255329	+	0.271297i	−0.00818549	+	0.00869739i
$974$	6.95484	−	6.95484i	0.222848	−	0.222848i
$975$	−3.82440	−	3.82440i	−0.122479	−	0.122479i
$976$	−5.33534	−	5.33534i	−0.170780	−	0.170780i
$977$	15.4743			0.495066			0.247533	−	0.968879i	$-0.420380\pi$
$977$	15.4743			0.495066			0.247533	+	0.968879i	$0.420380\pi$
$978$	−3.57404	−	3.57404i	−0.114285	−	0.114285i
$979$	12.8939			0.412091
$980$	12.2560	−	0.743913i	0.391503	−	0.0237634i
$981$	7.44268			0.237627
$982$	−2.22568			−0.0710244
$983$	−6.29237	+	6.29237i	−0.200695	+	0.200695i	−0.800298	−	0.599602i	$-0.795325\pi$
$983$	−6.29237	+	6.29237i	−0.200695	+	0.200695i	0.599602	+	0.800298i	$0.295325\pi$
$984$	−2.43786	−	2.43786i	−0.0777162	−	0.0777162i
$985$	−44.0797			−1.40450
$986$	−1.82717	−	5.79309i	−0.0581888	−	0.184490i
$987$	−19.7004	−	18.5409i	−0.627071	−	0.590163i
$988$	−3.98198	+	3.98198i	−0.126684	+	0.126684i
$989$	53.5541	−	53.5541i	1.70292	−	1.70292i
$990$	2.41711			0.0768207
$991$			12.8569i			0.408412i	0.978928	+	0.204206i	$0.0654613\pi$
$991$			12.8569i			0.408412i	−0.978928	+	0.204206i	$0.934539\pi$
$992$	10.1182			0.321254
$993$		−	28.0509i		−	0.890167i
$994$	−1.17474	−	38.7435i	−0.0372606	−	1.22887i
$995$		−	30.4397i		−	0.965003i
$996$	10.2307	+	10.2307i	0.324171	+	0.324171i
$997$	23.0928	+	23.0928i	0.731357	+	0.731357i	0.970889	−	0.239531i	$-0.0769938\pi$
$997$	23.0928	+	23.0928i	0.731357	+	0.731357i	−0.239531	+	0.970889i	$0.576994\pi$
$998$	1.38080	+	1.38080i	0.0437086	+	0.0437086i
$999$	0.120574			0.00381480

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1218.2.m.a.307.9	✓	40
7.6	odd	2		1218.2.m.b.307.9	yes	40
29.12	odd	4		1218.2.m.b.853.9	yes	40
203.41	even	4	inner	1218.2.m.a.853.9	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1218.2.m.a.307.9	✓	40	1.1	even	1	trivial
1218.2.m.a.853.9	yes	40	203.41	even	4	inner
1218.2.m.b.307.9	yes	40	7.6	odd	2
1218.2.m.b.853.9	yes	40	29.12	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1218 = 2 \cdot 3 \cdot 7 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1218.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(0.707107 + 0.707107i) q^{3} -1.00000i q^{4} +1.75408 q^{5} -1.00000 q^{6} +(-1.92667 - 1.81327i) q^{7} +(0.707107 + 0.707107i) q^{8} +1.00000i q^{9} +(-1.24032 + 1.24032i) q^{10} +(-0.974388 + 0.974388i) q^{11} +(0.707107 - 0.707107i) q^{12} +2.81222 q^{13} +(2.64454 - 0.0801852i) q^{14} +(1.24032 + 1.24032i) q^{15} -1.00000 q^{16} +(0.797609 + 0.797609i) q^{17} +(-0.707107 - 0.707107i) q^{18} +(-1.41596 - 1.41596i) q^{19} -1.75408i q^{20} +(-0.0801852 - 2.64454i) q^{21} -1.37799i q^{22} +8.03078 q^{23} +1.00000i q^{24} -1.92322 q^{25} +(-1.98854 + 1.98854i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(-1.81327 + 1.92667i) q^{28} +(1.61984 + 5.13577i) q^{29} -1.75408 q^{30} +(7.15468 + 7.15468i) q^{31} +(0.707107 - 0.707107i) q^{32} -1.37799 q^{33} -1.12799 q^{34} +(-3.37952 - 3.18061i) q^{35} +1.00000 q^{36} +(-0.0852589 - 0.0852589i) q^{37} +2.00246 q^{38} +(1.98854 + 1.98854i) q^{39} +(1.24032 + 1.24032i) q^{40} +(-2.43786 + 2.43786i) q^{41} +(1.92667 + 1.81327i) q^{42} +(6.66860 - 6.66860i) q^{43} +(0.974388 + 0.974388i) q^{44} +1.75408i q^{45} +(-5.67862 + 5.67862i) q^{46} +(7.23024 - 7.23024i) q^{47} +(-0.707107 - 0.707107i) q^{48} +(0.424105 + 6.98714i) q^{49} +(1.35992 - 1.35992i) q^{50} +1.12799i q^{51} -2.81222i q^{52} +11.0778 q^{53} -1.00000i q^{54} +(-1.70915 + 1.70915i) q^{55} +(-0.0801852 - 2.64454i) q^{56} -2.00246i q^{57} +(-4.77694 - 2.48613i) q^{58} -2.61946i q^{59} +(1.24032 - 1.24032i) q^{60} +(5.33534 + 5.33534i) q^{61} -10.1182 q^{62} +(1.81327 - 1.92667i) q^{63} +1.00000i q^{64} +4.93286 q^{65} +(0.974388 - 0.974388i) q^{66} -6.79023i q^{67} +(0.797609 - 0.797609i) q^{68} +(5.67862 + 5.67862i) q^{69} +(4.63872 - 0.140651i) q^{70} -14.6504i q^{71} +(-0.707107 + 0.707107i) q^{72} +(-8.50374 + 8.50374i) q^{73} +0.120574 q^{74} +(-1.35992 - 1.35992i) q^{75} +(-1.41596 + 1.41596i) q^{76} +(3.64415 - 0.110495i) q^{77} -2.81222 q^{78} +(-0.362059 + 0.362059i) q^{79} -1.75408 q^{80} -1.00000 q^{81} -3.44766i q^{82} +14.4683i q^{83} +(-2.64454 + 0.0801852i) q^{84} +(1.39907 + 1.39907i) q^{85} +9.43083i q^{86} +(-2.48613 + 4.77694i) q^{87} -1.37799 q^{88} +(-6.61641 - 6.61641i) q^{89} +(-1.24032 - 1.24032i) q^{90} +(-5.41823 - 5.09932i) q^{91} -8.03078i q^{92} +10.1182i q^{93} +10.2251i q^{94} +(-2.48369 - 2.48369i) q^{95} +1.00000 q^{96} +(-6.73439 + 6.73439i) q^{97} +(-5.24054 - 4.64077i) q^{98} +(-0.974388 - 0.974388i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 40 q^{6} + 4 q^{10} + 4 q^{14} - 4 q^{15} - 40 q^{16} + 8 q^{19} - 4 q^{21} + 24 q^{25} - 12 q^{28} + 8 q^{29} - 24 q^{31} - 12 q^{35} + 40 q^{36} - 16 q^{37} - 4 q^{40} + 16 q^{41} - 20 q^{43} + 4 q^{46}+ \cdots - 8 q^{98}+O(q^{100}) \) 40 * q - 40 * q^6 + 4 * q^10 + 4 * q^14 - 4 * q^15 - 40 * q^16 + 8 * q^19 - 4 * q^21 + 24 * q^25 - 12 * q^28 + 8 * q^29 - 24 * q^31 - 12 * q^35 + 40 * q^36 - 16 * q^37 - 4 * q^40 + 16 * q^41 - 20 * q^43 + 4 * q^46 - 16 * q^47 + 28 * q^49 + 32 * q^50 + 16 * q^53 - 24 * q^55 - 4 * q^56 - 20 * q^58 - 4 * q^60 - 44 * q^61 + 12 * q^63 - 4 * q^69 - 28 * q^70 - 52 * q^73 - 32 * q^75 + 8 * q^76 + 44 * q^77 + 4 * q^79 - 40 * q^81 - 4 * q^84 - 24 * q^85 - 12 * q^87 + 24 * q^89 + 4 * q^90 - 16 * q^95 + 40 * q^96 - 68 * q^97 - 8 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

Groups

Database

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